LMFDB - Embedded newform 728.2.z.a.99.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [728,2,Mod(99,728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 1]))

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

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

chi := DirichletCharacter("728.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.z (of order $4$, 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:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			99.18
Character	$\chi$	$=$	728.99
Dual form			728.2.z.a.603.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.17472 + 0.787426i) q^{2} +2.30698 q^{3} +(0.759920 - 1.85001i) q^{4} +(-0.308723 + 0.308723i) q^{5} +(-2.71005 + 1.81658i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.564051 + 2.77161i) q^{8} +2.32216 q^{9} +(0.119566 - 0.605758i) q^{10} +(3.25457 - 3.25457i) q^{11} +(1.75312 - 4.26793i) q^{12} +(1.82077 - 3.11204i) q^{13} +(-1.38744 - 0.273856i) q^{14} +(-0.712217 + 0.712217i) q^{15} +(-2.84504 - 2.81171i) q^{16} -7.35952i q^{17} +(-2.72788 + 1.82853i) q^{18} +(2.66450 + 2.66450i) q^{19} +(0.336534 + 0.805744i) q^{20} +(1.63128 + 1.63128i) q^{21} +(-1.26046 + 6.38593i) q^{22} -3.21182 q^{23} +(1.30126 + 6.39406i) q^{24} +4.80938i q^{25} +(0.311607 + 5.08949i) q^{26} -1.56377 q^{27} +(1.84550 - 0.770807i) q^{28} +2.81223i q^{29} +(0.275835 - 1.39747i) q^{30} +(0.400087 - 0.400087i) q^{31} +(5.55614 + 1.06271i) q^{32} +(7.50822 - 7.50822i) q^{33} +(5.79508 + 8.64536i) q^{34} -0.436600 q^{35} +(1.76465 - 4.29600i) q^{36} +(0.845714 + 0.845714i) q^{37} +(-5.22812 - 1.03193i) q^{38} +(4.20049 - 7.17941i) q^{39} +(-1.02980 - 0.681525i) q^{40} +(3.82324 + 3.82324i) q^{41} +(-3.20081 - 0.631780i) q^{42} +6.36630i q^{43} +(-3.54776 - 8.49418i) q^{44} +(-0.716903 + 0.716903i) q^{45} +(3.77298 - 2.52907i) q^{46} +(2.19728 + 2.19728i) q^{47} +(-6.56346 - 6.48657i) q^{48} +1.00000i q^{49} +(-3.78703 - 5.64966i) q^{50} -16.9783i q^{51} +(-4.37365 - 5.73334i) q^{52} -13.2075i q^{53} +(1.83699 - 1.23135i) q^{54} +2.00952i q^{55} +(-1.56098 + 2.35867i) q^{56} +(6.14694 + 6.14694i) q^{57} +(-2.21443 - 3.30358i) q^{58} +(1.36248 - 1.36248i) q^{59} +(0.776378 + 1.85883i) q^{60} +4.63407i q^{61} +(-0.154950 + 0.785027i) q^{62} +(1.64201 + 1.64201i) q^{63} +(-7.36369 + 3.12667i) q^{64} +(0.398643 + 1.52287i) q^{65} +(-2.90787 + 14.7322i) q^{66} +(8.05913 + 8.05913i) q^{67} +(-13.6152 - 5.59265i) q^{68} -7.40961 q^{69} +(0.512881 - 0.343790i) q^{70} +(-0.561120 + 0.561120i) q^{71} +(1.30982 + 6.43612i) q^{72} +(-1.08699 + 1.08699i) q^{73} +(-1.65941 - 0.327537i) q^{74} +11.0951i q^{75} +(6.95413 - 2.90453i) q^{76} +4.60265 q^{77} +(0.718871 + 11.7414i) q^{78} -8.61872i q^{79} +(1.74637 - 0.0102893i) q^{80} -10.5741 q^{81} +(-7.50173 - 1.48070i) q^{82} +(-3.51763 - 3.51763i) q^{83} +(4.25752 - 1.77824i) q^{84} +(2.27205 + 2.27205i) q^{85} +(-5.01299 - 7.47860i) q^{86} +6.48776i q^{87} +(10.8561 + 7.18466i) q^{88} +(-0.134118 + 0.134118i) q^{89} +(0.277650 - 1.40667i) q^{90} +(3.48802 - 0.913062i) q^{91} +(-2.44073 + 5.94189i) q^{92} +(0.922992 - 0.922992i) q^{93} +(-4.31138 - 0.850988i) q^{94} -1.64518 q^{95} +(12.8179 + 2.45165i) q^{96} +(2.97399 + 2.97399i) q^{97} +(-0.787426 - 1.17472i) q^{98} +(7.55761 - 7.55761i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 12 q^{6} - 12 q^{8} + 168 q^{9} - 16 q^{16} + 12 q^{18} - 20 q^{20} + 24 q^{22} - 32 q^{24} + 44 q^{26} - 20 q^{34} - 16 q^{40} - 8 q^{41} - 52 q^{44} - 32 q^{46} - 64 q^{48} + 72 q^{50} - 56 q^{52}+ \cdots - 128 q^{99}+O(q^{100}) $ 168 * q - 12 * q^6 - 12 * q^8 + 168 * q^9 - 16 * q^16 + 12 * q^18 - 20 * q^20 + 24 * q^22 - 32 * q^24 + 44 * q^26 - 20 * q^34 - 16 * q^40 - 8 * q^41 - 52 * q^44 - 32 * q^46 - 64 * q^48 + 72 * q^50 - 56 * q^52 - 56 * q^54 - 44 * q^58 - 48 * q^59 + 76 * q^60 + 8 * q^65 - 120 * q^66 + 128 * q^68 - 24 * q^70 + 44 * q^72 - 40 * q^73 - 32 * q^74 - 44 * q^76 - 52 * q^78 + 168 * q^81 - 80 * q^83 + 28 * q^84 - 20 * q^86 + 40 * q^89 + 24 * q^92 + 128 * q^94 + 72 * q^96 - 8 * q^97 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.17472	+	0.787426i	−0.830650	+	0.556794i
$2$	−1.17472	+	0.787426i	−0.830650	+	0.556794i
$3$	2.30698			1.33194			0.665968	−	0.745981i	$-0.268019\pi$
$3$	2.30698			1.33194			0.665968	+	0.745981i	$0.268019\pi$
$4$	0.759920	−	1.85001i	0.379960	−	0.925003i
$5$	−0.308723	+	0.308723i	−0.138065	+	0.138065i	−0.772762	−	0.634697i	$-0.781125\pi$
$5$	−0.308723	+	0.308723i	−0.138065	+	0.138065i	0.634697	+	0.772762i	$0.281125\pi$
$6$	−2.71005	+	1.81658i	−1.10637	+	0.741614i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	0.564051	+	2.77161i	0.199422	+	0.979914i
$9$	2.32216			0.774052
$10$	0.119566	−	0.605758i	0.0378099	−	0.191558i
$11$	3.25457	−	3.25457i	0.981289	−	0.981289i	−0.0185393	−	0.999828i	$-0.505902\pi$
$11$	3.25457	−	3.25457i	0.981289	−	0.981289i	0.999828	+	0.0185393i	$0.00590158\pi$
$12$	1.75312	−	4.26793i	0.506082	−	1.23204i
$13$	1.82077	−	3.11204i	0.504992	−	0.863124i
$13$	1.82077	−	3.11204i	0.504992	−	0.863124i
$14$	−1.38744	−	0.273856i	−0.370810	−	0.0731911i
$15$	−0.712217	+	0.712217i	−0.183894	+	0.183894i
$16$	−2.84504	−	2.81171i	−0.711261	−	0.702928i
$17$		−	7.35952i		−	1.78495i	−0.451101	−	0.892473i	$-0.648968\pi$
$17$		−	7.35952i		−	1.78495i	0.451101	−	0.892473i	$-0.351032\pi$
$18$	−2.72788	+	1.82853i	−0.642967	+	0.430988i
$19$	2.66450	+	2.66450i	0.611277	+	0.611277i	0.943279	−	0.332002i	$-0.107724\pi$
$19$	2.66450	+	2.66450i	0.611277	+	0.611277i	−0.332002	+	0.943279i	$0.607724\pi$
$20$	0.336534	+	0.805744i	0.0752513	+	0.180170i
$21$	1.63128	+	1.63128i	0.355975	+	0.355975i
$22$	−1.26046	+	6.38593i	−0.268732	+	1.36148i
$23$	−3.21182			−0.669712			−0.334856	−	0.942269i	$-0.608688\pi$
$23$	−3.21182			−0.669712			−0.334856	+	0.942269i	$0.608688\pi$
$24$	1.30126	+	6.39406i	0.265618	+	1.30518i
$25$			4.80938i			0.961876i
$26$	0.311607	+	5.08949i	0.0611112	+	0.998131i
$27$	−1.56377			−0.300948
$28$	1.84550	−	0.770807i	0.348766	−	0.145669i
$29$			2.81223i			0.522219i	0.965309	+	0.261109i	$0.0840883\pi$
$29$			2.81223i			0.522219i	−0.965309	+	0.261109i	$0.915912\pi$
$30$	0.275835	−	1.39747i	0.0503604	−	0.255142i
$31$	0.400087	−	0.400087i	0.0718577	−	0.0718577i	−0.670265	−	0.742122i	$-0.733819\pi$
$31$	0.400087	−	0.400087i	0.0718577	−	0.0718577i	0.742122	+	0.670265i	$0.233819\pi$
$32$	5.55614	+	1.06271i	0.982195	+	0.187862i
$33$	7.50822	−	7.50822i	1.30701	−	1.30701i
$34$	5.79508	+	8.64536i	0.993848	+	1.48267i
$35$	−0.436600			−0.0737989
$36$	1.76465	−	4.29600i	0.294109	−	0.716001i
$37$	0.845714	+	0.845714i	0.139035	+	0.139035i	0.773199	−	0.634164i	$-0.218656\pi$
$37$	0.845714	+	0.845714i	0.139035	+	0.139035i	−0.634164	+	0.773199i	$0.718656\pi$
$38$	−5.22812	−	1.03193i	−0.848113	−	0.167402i
$39$	4.20049	−	7.17941i	0.672616	−	1.14963i
$40$	−1.02980	−	0.681525i	−0.162825	−	0.107759i
$41$	3.82324	+	3.82324i	0.597089	+	0.597089i	0.939537	−	0.342448i	$-0.111256\pi$
$41$	3.82324	+	3.82324i	0.597089	+	0.597089i	−0.342448	+	0.939537i	$0.611256\pi$
$42$	−3.20081	−	0.631780i	−0.493895	−	0.0974858i
$43$			6.36630i			0.970852i	0.874278	+	0.485426i	$0.161335\pi$
$43$			6.36630i			0.970852i	−0.874278	+	0.485426i	$0.838665\pi$
$44$	−3.54776	−	8.49418i	−0.534844	−	1.28055i
$45$	−0.716903	+	0.716903i	−0.106870	+	0.106870i
$46$	3.77298	−	2.52907i	0.556296	−	0.372892i
$47$	2.19728	+	2.19728i	0.320507	+	0.320507i	0.848961	−	0.528455i	$-0.177228\pi$
$47$	2.19728	+	2.19728i	0.320507	+	0.320507i	−0.528455	+	0.848961i	$0.677228\pi$
$48$	−6.56346	−	6.48657i	−0.947353	−	0.936255i
$49$			1.00000i			0.142857i
$50$	−3.78703	−	5.64966i	−0.535567	−	0.798983i
$51$		−	16.9783i		−	2.37743i
$52$	−4.37365	−	5.73334i	−0.606516	−	0.795072i
$53$		−	13.2075i		−	1.81419i	−0.420923	−	0.907096i	$-0.638294\pi$
$53$		−	13.2075i		−	1.81419i	0.420923	−	0.907096i	$-0.361706\pi$
$54$	1.83699	−	1.23135i	0.249982	−	0.167566i
$55$			2.00952i			0.270963i
$56$	−1.56098	+	2.35867i	−0.208595	+	0.315191i
$57$	6.14694	+	6.14694i	0.814182	+	0.814182i
$58$	−2.21443	−	3.30358i	−0.290768	−	0.433781i
$59$	1.36248	−	1.36248i	0.177379	−	0.177379i	−0.612833	−	0.790212i	$-0.709970\pi$
$59$	1.36248	−	1.36248i	0.177379	−	0.177379i	0.790212	+	0.612833i	$0.209970\pi$
$60$	0.776378	+	1.85883i	0.100230	+	0.239974i
$61$			4.63407i			0.593332i	0.954981	+	0.296666i	$0.0958749\pi$
$61$			4.63407i			0.593332i	−0.954981	+	0.296666i	$0.904125\pi$
$62$	−0.154950	+	0.785027i	−0.0196787	+	0.0996985i
$63$	1.64201	+	1.64201i	0.206874	+	0.206874i
$64$	−7.36369	+	3.12667i	−0.920461	+	0.390833i
$65$	0.398643	+	1.52287i	0.0494456	+	0.188889i
$66$	−2.90787	+	14.7322i	−0.357934	+	1.81341i
$67$	8.05913	+	8.05913i	0.984580	+	0.984580i	0.999883	−	0.0153034i	$-0.00487141\pi$
$67$	8.05913	+	8.05913i	0.984580	+	0.984580i	−0.0153034	+	0.999883i	$0.504871\pi$
$68$	−13.6152	−	5.59265i	−1.65108	−	0.678208i
$69$	−7.40961			−0.892013
$70$	0.512881	−	0.343790i	0.0613010	−	0.0410908i
$71$	−0.561120	+	0.561120i	−0.0665927	+	0.0665927i	−0.739619	−	0.673026i	$-0.764994\pi$
$71$	−0.561120	+	0.561120i	−0.0665927	+	0.0665927i	0.673026	+	0.739619i	$0.264994\pi$
$72$	1.30982	+	6.43612i	0.154363	+	0.758504i
$73$	−1.08699	+	1.08699i	−0.127223	+	0.127223i	−0.767851	−	0.640628i	$-0.778674\pi$
$73$	−1.08699	+	1.08699i	−0.127223	+	0.127223i	0.640628	+	0.767851i	$0.278674\pi$
$74$	−1.65941	−	0.327537i	−0.192903	−	0.0380754i
$75$			11.0951i			1.28116i
$76$	6.95413	−	2.90453i	0.797694	−	0.333172i
$77$	4.60265			0.524521
$78$	0.718871	+	11.7414i	0.0813961	+	1.32945i
$79$		−	8.61872i		−	0.969682i	−0.874602	−	0.484841i	$-0.838877\pi$
$79$		−	8.61872i		−	0.969682i	0.874602	−	0.484841i	$-0.161123\pi$
$80$	1.74637	−	0.0102893i	0.195250	−	0.00115038i
$81$	−10.5741			−1.17490
$82$	−7.50173	−	1.48070i	−0.828428	−	0.163516i
$83$	−3.51763	−	3.51763i	−0.386110	−	0.386110i	0.487188	−	0.873297i	$-0.338023\pi$
$83$	−3.51763	−	3.51763i	−0.386110	−	0.386110i	−0.873297	+	0.487188i	$0.838023\pi$
$84$	4.25752	−	1.77824i	0.464534	−	0.194021i
$85$	2.27205	+	2.27205i	0.246439	+	0.246439i
$86$	−5.01299	−	7.47860i	−0.540565	−	0.806438i
$87$			6.48776i			0.695561i
$88$	10.8561	+	7.18466i	1.15727	+	0.765887i
$89$	−0.134118	+	0.134118i	−0.0142165	+	0.0142165i	−0.714179	−	0.699963i	$-0.753200\pi$
$89$	−0.134118	+	0.134118i	−0.0142165	+	0.0142165i	0.699963	+	0.714179i	$0.253200\pi$
$90$	0.277650	−	1.40667i	0.0292669	−	0.148276i
$91$	3.48802	−	0.913062i	0.365644	−	0.0957150i
$92$	−2.44073	+	5.94189i	−0.254464	+	0.619485i
$93$	0.922992	−	0.922992i	0.0957098	−	0.0957098i
$94$	−4.31138	−	0.850988i	−0.444685	−	0.0877727i
$95$	−1.64518			−0.168792
$96$	12.8179	+	2.45165i	1.30822	+	0.250220i
$97$	2.97399	+	2.97399i	0.301963	+	0.301963i	0.841781	−	0.539819i	$-0.181507\pi$
$97$	2.97399	+	2.97399i	0.301963	+	0.301963i	−0.539819	+	0.841781i	$0.681507\pi$
$98$	−0.787426	−	1.17472i	−0.0795420	−	0.118664i
$99$	7.55761	−	7.55761i	0.759569	−	0.759569i
$100$	8.89738	+	3.65475i	0.889738	+	0.365475i
$101$	−3.97265			−0.395293			−0.197647	−	0.980273i	$-0.563330\pi$
$101$	−3.97265			−0.395293			−0.197647	+	0.980273i	$0.563330\pi$
$102$	13.3691	+	19.9447i	1.32374	+	1.97482i
$103$	7.85013			0.773496			0.386748	−	0.922185i	$-0.373598\pi$
$103$	7.85013			0.773496			0.386748	+	0.922185i	$0.373598\pi$
$104$	9.65238	+	3.29113i	0.946494	+	0.322722i
$105$	−1.00723			−0.0982953
$106$	10.3999	+	15.5151i	1.01013	+	1.50696i
$107$	−6.33622			−0.612545			−0.306273	−	0.951944i	$-0.599082\pi$
$107$	−6.33622			−0.612545			−0.306273	+	0.951944i	$0.599082\pi$
$108$	−1.18834	+	2.89298i	−0.114348	+	0.278378i
$109$	−13.4537	+	13.4537i	−1.28863	+	1.28863i	−0.353009	+	0.935620i	$0.614842\pi$
$109$	−13.4537	+	13.4537i	−1.28863	+	1.28863i	−0.935620	+	0.353009i	$0.885158\pi$
$110$	−1.58235	−	2.36061i	−0.150871	−	0.225076i
$111$	1.95105	+	1.95105i	0.185185	+	0.185185i
$112$	−0.0235668	−	3.99993i	−0.00222686	−	0.377958i
$113$	3.45377			0.324903			0.162452	−	0.986717i	$-0.448060\pi$
$113$	3.45377			0.324903			0.162452	+	0.986717i	$0.448060\pi$
$114$	−12.0612	−	2.38065i	−1.12963	−	0.222969i
$115$	0.991563	−	0.991563i	0.0924637	−	0.0924637i
$116$	5.20265	+	2.13707i	0.483054	+	0.198422i
$117$	4.22812	−	7.22664i	0.390890	−	0.668103i
$118$	−0.527675	+	2.67338i	−0.0485764	+	0.246104i
$119$	5.20397	−	5.20397i	0.477047	−	0.477047i
$120$	−2.37572	−	1.57226i	−0.216872	−	0.143527i
$121$		−	10.1844i		−	0.925856i
$122$	−3.64899	−	5.44373i	−0.330364	−	0.492852i
$123$	8.82013	+	8.82013i	0.795284	+	0.795284i
$124$	−0.436129	−	1.04420i	−0.0391655	−	0.0937716i
$125$	−3.02838	−	3.02838i	−0.270866	−	0.270866i
$126$	−3.22186	−	0.635937i	−0.287026	−	0.0566537i
$127$	17.6002			1.56176			0.780881	−	0.624680i	$-0.214770\pi$
$127$	17.6002			1.56176			0.780881	+	0.624680i	$0.214770\pi$
$128$	6.18824	−	9.47131i	0.546968	−	0.837154i
$129$			14.6869i			1.29311i
$130$	−1.66744	−	1.47504i	−0.146244	−	0.129370i
$131$	−15.8191			−1.38213			−0.691063	−	0.722795i	$-0.742857\pi$
$131$	−15.8191			−1.38213			−0.691063	+	0.722795i	$0.742857\pi$
$132$	−8.18460	−	19.5959i	−0.712378	−	1.70560i
$133$			3.76817i			0.326741i
$134$	−15.8132	−	3.12123i	−1.36605	−	0.269633i
$135$	0.482772	−	0.482772i	0.0415504	−	0.0415504i
$136$	20.3978	−	4.15115i	1.74909	−	0.355958i
$137$	−12.2517	+	12.2517i	−1.04674	+	1.04674i	−0.0478835	+	0.998853i	$0.515248\pi$
$137$	−12.2517	+	12.2517i	−1.04674	+	1.04674i	−0.998853	+	0.0478835i	$0.984752\pi$
$138$	8.70420	−	5.83452i	0.740951	−	0.496668i
$139$	−20.0418			−1.69993			−0.849963	−	0.526843i	$-0.823376\pi$
$139$	−20.0418			−1.69993			−0.849963	+	0.526843i	$0.823376\pi$
$140$	−0.331781	+	0.807712i	−0.0280406	+	0.0682641i
$141$	5.06909	+	5.06909i	0.426894	+	0.426894i
$142$	0.217317	−	1.10100i	0.0182368	−	0.0923937i
$143$	−4.20251	−	16.0542i	−0.351431	−	1.34252i
$144$	−6.60663	−	6.52924i	−0.550553	−	0.544103i
$145$	−0.868200	−	0.868200i	−0.0721001	−	0.0721001i
$146$	0.420982	−	2.13283i	0.0348407	−	0.176515i
$147$			2.30698i			0.190277i
$148$	2.20725	−	0.921900i	0.181435	−	0.0757797i
$149$	−11.6375	+	11.6375i	−0.953377	+	0.953377i	−0.998961	−	0.0455831i	$-0.985485\pi$
$149$	−11.6375	+	11.6375i	−0.953377	+	0.953377i	0.0455831	+	0.998961i	$0.485485\pi$
$150$	−8.73661	−	13.0337i	−0.713341	−	1.06419i
$151$	−13.2541	−	13.2541i	−1.07860	−	1.07860i	−0.996635	−	0.0819648i	$-0.973880\pi$
$151$	−13.2541	−	13.2541i	−1.07860	−	1.07860i	−0.0819648	−	0.996635i	$-0.526120\pi$
$152$	−5.88204	+	8.88786i	−0.477096	+	0.720901i
$153$		−	17.0900i		−	1.38164i
$154$	−5.40681	+	3.62425i	−0.435694	+	0.292050i
$155$			0.247032i			0.0198421i
$156$	−10.0899	−	13.2267i	−0.807840	−	1.05898i
$157$			21.0225i			1.67778i	0.544301	+	0.838890i	$0.316795\pi$
$157$			21.0225i			1.67778i	−0.544301	+	0.838890i	$0.683205\pi$
$158$	6.78661	+	10.1246i	0.539913	+	0.805467i
$159$		−	30.4695i		−	2.41639i
$160$	−2.04339	+	1.38722i	−0.161544	+	0.109670i
$161$	−2.27110	−	2.27110i	−0.178988	−	0.178988i
$162$	12.4215	−	8.32629i	0.975927	−	0.654175i
$163$	10.0319	−	10.0319i	0.785763	−	0.785763i	−0.195034	−	0.980796i	$-0.562482\pi$
$163$	10.0319	−	10.0319i	0.785763	−	0.785763i	0.980796	+	0.195034i	$0.0624817\pi$
$164$	9.97836	−	4.16765i	0.779179	−	0.325439i
$165$			4.63592i			0.360906i
$166$	6.90209	+	1.36235i	0.535706	+	0.105739i
$167$	−9.80242	−	9.80242i	−0.758534	−	0.758534i	0.217521	−	0.976056i	$-0.430203\pi$
$167$	−9.80242	−	9.80242i	−0.758534	−	0.758534i	−0.976056	+	0.217521i	$0.930203\pi$
$168$	−3.60116	+	5.44141i	−0.277835	+	0.419814i
$169$	−6.36957	−	11.3326i	−0.489967	−	0.871741i
$170$	−4.45809	−	0.879945i	−0.341920	−	0.0674887i
$171$	6.18738	+	6.18738i	0.473160	+	0.473160i
$172$	11.7777	+	4.83788i	0.898041	+	0.368885i
$173$	4.71685			0.358616			0.179308	−	0.983793i	$-0.442614\pi$
$173$	4.71685			0.358616			0.179308	+	0.983793i	$0.442614\pi$
$174$	−5.10864	−	7.62129i	−0.387285	−	0.577768i
$175$	−3.40075	+	3.40075i	−0.257072	+	0.257072i
$176$	−18.4103	+	0.108470i	−1.38773	+	0.00817623i
$177$	3.14321	−	3.14321i	0.236258	−	0.236258i
$178$	0.0519426	−	0.263158i	0.00389326	−	0.0197246i
$179$		−	0.161126i		−	0.0120431i	−0.999982	−	0.00602155i	$-0.998083\pi$
$179$		−	0.161126i		−	0.0120431i	0.999982	−	0.00602155i	$-0.00191673\pi$
$180$	0.781485	+	1.87106i	0.0582485	+	0.139461i
$181$	−18.7784			−1.39579			−0.697893	−	0.716202i	$-0.745879\pi$
$181$	−18.7784			−1.39579			−0.697893	+	0.716202i	$0.745879\pi$
$182$	−3.37847	+	3.81915i	−0.250429	+	0.283094i
$183$			10.6907i			0.790280i
$184$	−1.81163	−	8.90194i	−0.133555	−	0.656260i
$185$	−0.522182			−0.0383916
$186$	−0.357466	+	1.81104i	−0.0262107	+	0.132792i
$187$	−23.9521	−	23.9521i	−1.75155	−	1.75155i
$188$	5.73474	−	2.39523i	0.418249	−	0.174690i
$189$	−1.10575	−	1.10575i	−0.0804317	−	0.0804317i
$190$	1.93262	−	1.29546i	0.140207	−	0.0939824i
$191$			7.71346i			0.558127i	0.960273	+	0.279063i	$0.0900239\pi$
$191$			7.71346i			0.558127i	−0.960273	+	0.279063i	$0.909976\pi$
$192$	−16.9879	+	7.21316i	−1.22600	+	0.520565i
$193$	−2.63668	+	2.63668i	−0.189792	+	0.189792i	−0.795606	−	0.605814i	$-0.792848\pi$
$193$	−2.63668	+	2.63668i	−0.189792	+	0.189792i	0.605814	+	0.795606i	$0.292848\pi$
$194$	−5.83539	−	1.15180i	−0.418957	−	0.0826944i
$195$	0.919661	+	3.51323i	0.0658583	+	0.251588i
$196$	1.85001	+	0.759920i	0.132143	+	0.0542800i
$197$	−15.2705	+	15.2705i	−1.08798	+	1.08798i	−0.0922447	+	0.995736i	$0.529404\pi$
$197$	−15.2705	+	15.2705i	−1.08798	+	1.08798i	−0.995736	+	0.0922447i	$0.970596\pi$
$198$	−2.92700	+	14.8291i	−0.208013	+	1.05386i
$199$	13.9152			0.986425			0.493213	−	0.869909i	$-0.335822\pi$
$199$	13.9152			0.986425			0.493213	+	0.869909i	$0.335822\pi$
$200$	−13.3297	+	2.71274i	−0.942556	+	0.191820i
$201$	18.5923	+	18.5923i	1.31140	+	1.31140i
$202$	4.66674	−	3.12817i	0.328350	−	0.220097i
$203$	−1.98855	+	1.98855i	−0.139569	+	0.139569i
$204$	−31.4099	−	12.9021i	−2.19913	−	0.903330i
$205$	−2.36064			−0.164874
$206$	−9.22168	+	6.18140i	−0.642505	+	0.430678i
$207$	−7.45836			−0.518392
$208$	−13.9303	+	3.73439i	−0.965895	+	0.258933i
$209$	17.3436			1.19968
$210$	1.18321	−	0.793117i	0.0816490	−	0.0547303i
$211$	1.65051			0.113626			0.0568130	−	0.998385i	$-0.481906\pi$
$211$	1.65051			0.113626			0.0568130	+	0.998385i	$0.481906\pi$
$212$	−24.4340	−	10.0367i	−1.67813	−	0.689321i
$213$	−1.29449	+	1.29449i	−0.0886972	+	0.0886972i
$214$	7.44326	−	4.98930i	0.508811	−	0.341062i
$215$	−1.96542	−	1.96542i	−0.134041	−	0.134041i
$216$	−0.882047	−	4.33417i	−0.0600157	−	0.294903i
$217$	0.565808			0.0384095
$218$	5.21049	−	26.3980i	0.352899	−	1.78790i
$219$	−2.50767	+	2.50767i	−0.169452	+	0.169452i
$220$	3.71762	+	1.52707i	0.250642	+	0.102955i
$221$	−22.9031	−	13.4000i	−1.54063	−	0.901383i
$222$	−3.82823	−	0.755622i	−0.256934	−	0.0507140i
$223$	18.7648	−	18.7648i	1.25658	−	1.25658i	0.303871	−	0.952713i	$-0.401721\pi$
$223$	18.7648	−	18.7648i	1.25658	−	1.25658i	0.952713	−	0.303871i	$-0.0982792\pi$
$224$	3.17733	+	4.68023i	0.212295	+	0.312711i
$225$			11.1681i			0.744542i
$226$	−4.05720	+	2.71959i	−0.269881	+	0.180904i
$227$	15.4040	+	15.4040i	1.02240	+	1.02240i	0.999743	+	0.0226589i	$0.00721317\pi$
$227$	15.4040	+	15.4040i	1.02240	+	1.02240i	0.0226589	+	0.999743i	$0.492787\pi$
$228$	16.0431	−	6.70069i	1.06248	−	0.443764i
$229$	−10.4687	−	10.4687i	−0.691794	−	0.691794i	0.270833	−	0.962626i	$-0.412701\pi$
$229$	−10.4687	−	10.4687i	−0.691794	−	0.691794i	−0.962626	+	0.270833i	$0.912701\pi$
$230$	−0.384023	+	1.94559i	−0.0253218	+	0.128288i
$231$	10.6182			0.698628
$232$	−7.79442	+	1.58624i	−0.511729	+	0.104142i
$233$		−	12.2653i		−	0.803525i	−0.915744	−	0.401762i	$-0.868398\pi$
$233$		−	12.2653i		−	0.803525i	0.915744	−	0.401762i	$-0.131602\pi$
$234$	0.723600	+	11.8186i	0.0473032	+	0.772606i
$235$	−1.35670			−0.0885015
$236$	−1.48522	−	3.55597i	−0.0966794	−	0.231474i
$237$		−	19.8832i		−	1.29155i
$238$	−2.01545	+	10.2109i	−0.130642	+	0.661876i
$239$	−2.97528	+	2.97528i	−0.192455	+	0.192455i	−0.796756	−	0.604301i	$-0.793452\pi$
$239$	−2.97528	+	2.97528i	−0.192455	+	0.192455i	0.604301	+	0.796756i	$0.293452\pi$
$240$	4.02884	−	0.0237371i	0.260060	−	0.00153223i
$241$	−12.2286	+	12.2286i	−0.787716	+	0.787716i	−0.981119	−	0.193403i	$-0.938047\pi$
$241$	−12.2286	+	12.2286i	−0.787716	+	0.787716i	0.193403	+	0.981119i	$0.438047\pi$
$242$	8.01947	+	11.9638i	0.515511	+	0.769062i
$243$	−19.7028			−1.26394
$244$	8.57306	+	3.52153i	0.548834	+	0.225443i
$245$	−0.308723	−	0.308723i	−0.0197236	−	0.0197236i
$246$	−17.3064	−	3.41596i	−1.10341	−	0.217793i
$247$	13.1435	−	3.44057i	0.836298	−	0.218918i
$248$	1.33456	+	0.883216i	0.0847443	+	0.0560843i
$249$	−8.11510	−	8.11510i	−0.514273	−	0.514273i
$250$	5.94211	+	1.17286i	0.375812	+	0.0741784i
$251$		−	18.9930i		−	1.19883i	−0.800439	−	0.599415i	$-0.795400\pi$
$251$		−	18.9930i		−	1.19883i	0.800439	−	0.599415i	$-0.204600\pi$
$252$	4.28553	−	1.78993i	0.269963	−	0.112755i
$253$	−10.4531	+	10.4531i	−0.657181	+	0.657181i
$254$	−20.6752	+	13.8588i	−1.29728	+	0.869580i
$255$	5.24158	+	5.24158i	0.328240	+	0.328240i
$256$	0.188531	+	15.9989i	0.0117832	+	0.999931i
$257$			14.7617i			0.920811i	0.887709	+	0.460406i	$0.152296\pi$
$257$			14.7617i			0.920811i	−0.887709	+	0.460406i	$0.847704\pi$
$258$	−11.5649	−	17.2530i	−0.719997	−	1.07412i
$259$			1.19602i			0.0743171i
$260$	3.12026	+	0.419769i	0.193510	+	0.0260330i
$261$			6.53045i			0.404224i
$262$	18.5830	−	12.4564i	1.14806	−	0.769559i
$263$		−	21.2125i		−	1.30802i	−0.756486	−	0.654010i	$-0.773085\pi$
$263$		−	21.2125i		−	1.30802i	0.756486	−	0.654010i	$-0.226915\pi$
$264$	25.0449	+	16.5749i	1.54141	+	1.02011i
$265$	4.07746	+	4.07746i	0.250477	+	0.250477i
$266$	−2.96715	−	4.42653i	−0.181928	−	0.271408i
$267$	−0.309407	+	0.309407i	−0.0189354	+	0.0189354i
$268$	21.0337	−	8.78514i	1.28484	−	0.536638i
$269$		−	5.87515i		−	0.358214i	−0.983830	−	0.179107i	$-0.942679\pi$
$269$		−	5.87515i		−	0.358214i	0.983830	−	0.179107i	$-0.0573209\pi$
$270$	−0.186973	+	0.947267i	−0.0113788	+	0.0576488i
$271$	21.5454	+	21.5454i	1.30879	+	1.30879i	0.922291	+	0.386497i	$0.126315\pi$
$271$	21.5454	+	21.5454i	1.30879	+	1.30879i	0.386497	+	0.922291i	$0.373685\pi$
$272$	−20.6929	+	20.9382i	−1.25469	+	1.26956i
$273$	8.04680	−	2.10642i	0.487015	−	0.127486i
$274$	4.74499	−	24.0397i	0.286655	−	1.45229i
$275$	15.6525	+	15.6525i	0.943878	+	0.943878i
$276$	−5.63072	+	13.7078i	−0.338929	+	0.825114i
$277$	−7.55761			−0.454092			−0.227046	−	0.973884i	$-0.572907\pi$
$277$	−7.55761			−0.454092			−0.227046	+	0.973884i	$0.572907\pi$
$278$	23.5435	−	15.7815i	1.41204	−	0.946509i
$279$	0.929064	−	0.929064i	0.0556216	−	0.0556216i
$280$	−0.246265	−	1.21009i	−0.0147171	−	0.0723165i
$281$	16.6452	−	16.6452i	0.992969	−	0.992969i	−0.00700631	−	0.999975i	$-0.502230\pi$
$281$	16.6452	−	16.6452i	0.992969	−	0.992969i	0.999975	+	0.00700631i	$0.00223020\pi$
$282$	−9.94627	−	1.96321i	−0.592292	−	0.116908i
$283$		−	4.26888i		−	0.253759i	−0.991918	−	0.126879i	$-0.959504\pi$
$283$		−	4.26888i		−	0.253759i	0.991918	−	0.126879i	$-0.0404961\pi$
$284$	0.611669	+	1.46448i	0.0362959	+	0.0869010i
$285$	−3.79540			−0.224820
$286$	17.5782	+	15.5499i	1.03942	+	0.919487i
$287$			5.40687i			0.319158i
$288$	12.9022	+	2.46777i	0.760271	+	0.145415i
$289$	−37.1626			−2.18603
$290$	1.70353	+	0.336246i	0.100035	+	0.0197451i
$291$	6.86093	+	6.86093i	0.402195	+	0.402195i
$292$	1.18491	+	2.83697i	0.0693418	+	0.166021i
$293$	20.7876	+	20.7876i	1.21442	+	1.21442i	0.969557	+	0.244867i	$0.0787442\pi$
$293$	20.7876	+	20.7876i	1.21442	+	1.21442i	0.244867	+	0.969557i	$0.421256\pi$
$294$	−1.81658	−	2.71005i	−0.105945	−	0.158053i
$295$			0.841256i			0.0489798i
$296$	−1.86697	+	2.82102i	−0.108515	+	0.163968i
$297$	−5.08940	+	5.08940i	−0.295317	+	0.295317i
$298$	4.50708	−	22.8344i	0.261088	−	1.32276i
$299$	−5.84800	+	9.99532i	−0.338199	+	0.578044i
$300$	20.5261	+	8.43143i	1.18507	+	0.486789i
$301$	−4.50165	+	4.50165i	−0.259471	+	0.259471i
$302$	26.0064	+	5.13318i	1.49650	+	0.295381i
$303$	−9.16482			−0.526505
$304$	−0.0888037	−	15.0724i	−0.00509324	−	0.864461i
$305$	−1.43064	−	1.43064i	−0.0819184	−	0.0819184i
$306$	13.4571	+	20.0759i	0.769290	+	1.14766i
$307$	−13.7067	+	13.7067i	−0.782282	+	0.782282i	−0.980215	−	0.197933i	$-0.936577\pi$
$307$	−13.7067	+	13.7067i	−0.782282	+	0.782282i	0.197933	+	0.980215i	$0.436577\pi$
$308$	3.49765	−	8.51493i	0.199297	−	0.485183i
$309$	18.1101			1.03025
$310$	−0.194519	−	0.290192i	−0.0110479	−	0.0164818i
$311$	11.5656			0.655824			0.327912	−	0.944708i	$-0.393655\pi$
$311$	11.5656			0.655824			0.327912	+	0.944708i	$0.393655\pi$
$312$	22.2678	+	7.59257i	1.26067	+	0.429845i
$313$	24.8146			1.40260			0.701302	−	0.712865i	$-0.252603\pi$
$313$	24.8146			1.40260			0.701302	+	0.712865i	$0.252603\pi$
$314$	−16.5537	−	24.6955i	−0.934178	−	1.39365i
$315$	−1.01385			−0.0571242
$316$	−15.9447	−	6.54954i	−0.896959	−	0.368441i
$317$	1.66646	−	1.66646i	0.0935974	−	0.0935974i	−0.658758	−	0.752355i	$-0.728918\pi$
$317$	1.66646	−	1.66646i	0.0935974	−	0.0935974i	0.752355	+	0.658758i	$0.228918\pi$
$318$	23.9925	+	35.7930i	1.34543	+	2.00717i
$319$	9.15260	+	9.15260i	0.512447	+	0.512447i
$320$	1.30807	−	3.23861i	0.0731231	−	0.181044i
$321$	−14.6175			−0.815871
$322$	4.45623	+	0.879578i	0.248336	+	0.0490169i
$323$	19.6094	−	19.6094i	1.09110	−	1.09110i
$324$	−8.03544	+	19.5621i	−0.446413	+	1.08678i
$325$	14.9670	+	8.75679i	0.830219	+	0.485739i
$326$	−3.88528	+	19.6841i	−0.215186	+	1.09020i
$327$	−31.0374	+	31.0374i	−1.71637	+	1.71637i
$328$	−8.44003	+	12.7530i	−0.466023	+	0.704169i
$329$			3.10743i			0.171318i
$330$	−3.65044	−	5.44589i	−0.200950	−	0.299786i
$331$	−5.45988	−	5.45988i	−0.300102	−	0.300102i	0.540952	−	0.841054i	$-0.318064\pi$
$331$	−5.45988	−	5.45988i	−0.300102	−	0.300102i	−0.841054	+	0.540952i	$0.818064\pi$
$332$	−9.18075	+	3.83452i	−0.503859	+	0.210446i
$333$	1.96388	+	1.96388i	0.107620	+	0.107620i
$334$	19.2338	+	3.79639i	1.05242	+	0.207729i
$335$	−4.97607			−0.271872
$336$	−0.0543682	−	9.22776i	−0.00296603	−	0.503416i
$337$		−	9.11530i		−	0.496542i	−0.968691	−	0.248271i	$-0.920138\pi$
$337$		−	9.11530i		−	0.496542i	0.968691	−	0.248271i	$-0.0798624\pi$
$338$	16.4061	+	8.29707i	0.892372	+	0.451301i
$339$	7.96778			0.432750
$340$	5.92989	−	2.47673i	0.321593	−	0.134320i
$341$		−	2.60422i		−	0.141026i
$342$	−12.1405	−	2.39631i	−0.656484	−	0.129578i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−17.6449	+	3.59092i	−0.951351	+	0.193609i
$345$	2.28752	−	2.28752i	0.123156	−	0.123156i
$346$	−5.54097	+	3.71417i	−0.297884	+	0.199675i
$347$	−25.5760			−1.37299			−0.686496	−	0.727134i	$-0.740852\pi$
$347$	−25.5760			−1.37299			−0.686496	+	0.727134i	$0.740852\pi$
$348$	12.0024	+	4.93018i	0.643396	+	0.264286i
$349$	18.6586	+	18.6586i	0.998772	+	0.998772i	0.999999	−	0.00122768i	$-0.000390781\pi$
$349$	18.6586	+	18.6586i	0.998772	+	0.998772i	−0.00122768	+	0.999999i	$0.500391\pi$
$350$	1.31708	−	6.67275i	0.0704008	−	0.356673i
$351$	−2.84727	+	4.86651i	−0.151976	+	0.259755i
$352$	21.5415	−	14.6242i	1.14816	−	0.779471i
$353$	−21.4724	−	21.4724i	−1.14286	−	1.14286i	−0.987925	−	0.154934i	$-0.950484\pi$
$353$	−21.4724	−	21.4724i	−1.14286	−	1.14286i	−0.154934	−	0.987925i	$-0.549516\pi$
$354$	−1.21734	+	6.16742i	−0.0647007	+	0.327795i
$355$		−	0.346461i		−	0.0183882i
$356$	0.146200	+	0.350038i	0.00774858	+	0.0185520i
$357$	12.0054	−	12.0054i	0.635396	−	0.635396i
$358$	0.126875	+	0.189277i	0.00670553	+	0.0100036i
$359$	−6.38497	−	6.38497i	−0.336986	−	0.336986i	0.518246	−	0.855232i	$-0.326585\pi$
$359$	−6.38497	−	6.38497i	−0.336986	−	0.336986i	−0.855232	+	0.518246i	$0.826585\pi$
$360$	−2.39135	−	1.58261i	−0.126035	−	0.0834107i
$361$		−	4.80093i		−	0.252681i
$362$	22.0593	−	14.7866i	1.15941	−	0.777166i
$363$		−	23.4952i		−	1.23318i
$364$	0.961450	−	7.14672i	0.0503937	−	0.374590i
$365$		−	0.671158i		−	0.0351300i
$366$	−8.41815	−	12.5586i	−0.440024	−	0.656447i
$367$		−	7.32743i		−	0.382489i	−0.981542	−	0.191244i	$-0.938748\pi$
$367$		−	7.32743i		−	0.382489i	0.981542	−	0.191244i	$-0.0612523\pi$
$368$	9.13778	+	9.03073i	0.476339	+	0.470759i
$369$	8.87815	+	8.87815i	0.462178	+	0.462178i
$370$	0.613416	−	0.411180i	0.0318900	−	0.0213762i
$371$	9.33913	−	9.33913i	0.484863	−	0.484863i
$372$	−1.00614	−	2.40894i	−0.0521659	−	0.124898i
$373$			20.8485i			1.07950i	0.841827	+	0.539748i	$0.181480\pi$
$373$			20.8485i			1.07950i	−0.841827	+	0.539748i	$0.818520\pi$
$374$	46.9974	+	9.27641i	2.43018	+	0.479672i
$375$	−6.98641	−	6.98641i	−0.360777	−	0.360777i
$376$	−4.85064	+	7.32940i	−0.250153	+	0.377985i
$377$	8.75178	+	5.12044i	0.450739	+	0.263716i
$378$	2.16965	+	0.428248i	0.111595	+	0.0220267i
$379$	−14.8530	−	14.8530i	−0.762949	−	0.762949i	0.213905	−	0.976854i	$-0.431382\pi$
$379$	−14.8530	−	14.8530i	−0.762949	−	0.762949i	−0.976854	+	0.213905i	$0.931382\pi$
$380$	−1.25021	+	3.04359i	−0.0641342	+	0.156133i
$381$	40.6032			2.08017
$382$	−6.07378	−	9.06114i	−0.310762	−	0.463608i
$383$	−0.695732	+	0.695732i	−0.0355503	+	0.0355503i	−0.724658	−	0.689108i	$-0.758002\pi$
$383$	−0.695732	+	0.695732i	−0.0355503	+	0.0355503i	0.689108	+	0.724658i	$0.258002\pi$
$384$	14.2761	−	21.8501i	0.728526	−	1.11503i
$385$	−1.42094	+	1.42094i	−0.0724180	+	0.0724180i
$386$	1.02116	−	5.17354i	0.0519758	−	0.263326i
$387$			14.7835i			0.751490i
$388$	7.76189	−	3.24190i	0.394050	−	0.164583i
$389$	34.6577			1.75722			0.878608	−	0.477543i	$-0.158473\pi$
$389$	34.6577			1.75722			0.878608	+	0.477543i	$0.158473\pi$
$390$	−3.84675	−	3.40289i	−0.194788	−	0.172312i
$391$			23.6375i			1.19540i
$392$	−2.77161	+	0.564051i	−0.139988	+	0.0284889i
$393$	−36.4945			−1.84090
$394$	5.91414	−	29.9630i	0.297950	−	1.50951i
$395$	2.66080	+	2.66080i	0.133879	+	0.133879i
$396$	−8.23845	−	19.7248i	−0.413997	−	0.991209i
$397$	15.8377	+	15.8377i	0.794871	+	0.794871i	0.982282	−	0.187411i	$-0.0600095\pi$
$397$	15.8377	+	15.8377i	0.794871	+	0.794871i	−0.187411	+	0.982282i	$0.560009\pi$
$398$	−16.3465	+	10.9572i	−0.819375	+	0.549236i
$399$			8.69308i			0.435198i
$400$	13.5226	−	13.6829i	0.676130	−	0.684145i
$401$	4.26188	−	4.26188i	0.212828	−	0.212828i	−0.592640	−	0.805468i	$-0.701914\pi$
$401$	4.26188	−	4.26188i	0.212828	−	0.212828i	0.805468	+	0.592640i	$0.201914\pi$
$402$	−36.4807	−	7.20061i	−1.81949	−	0.359134i
$403$	−0.516618	−	1.97355i	−0.0257346	−	0.0983096i
$404$	−3.01890	+	7.34942i	−0.150196	+	0.365647i
$405$	3.26445	−	3.26445i	0.162212	−	0.162212i
$406$	0.770147	−	3.90182i	0.0382218	−	0.193644i
$407$	5.50486			0.272866
$408$	47.0572	−	9.57662i	2.32968	−	0.474113i
$409$	4.64032	+	4.64032i	0.229449	+	0.229449i	0.812463	−	0.583013i	$-0.198126\pi$
$409$	4.64032	+	4.64032i	0.229449	+	0.229449i	−0.583013	+	0.812463i	$0.698126\pi$
$410$	2.77308	−	1.85883i	0.136953	−	0.0918010i
$411$	−28.2645	+	28.2645i	−1.39419	+	1.39419i
$412$	5.96547	−	14.5228i	0.293898	−	0.715486i
$413$	1.92683			0.0948133
$414$	8.76146	−	5.87291i	0.430602	−	0.288638i
$415$	2.17194			0.106617
$416$	13.4237	−	15.3560i	0.658149	−	0.752888i
$417$	−46.2361			−2.26419
$418$	−20.3738	+	13.6568i	−0.996514	+	0.667974i
$419$	10.1698			0.496830			0.248415	−	0.968654i	$-0.420090\pi$
$419$	10.1698			0.496830			0.248415	+	0.968654i	$0.420090\pi$
$420$	−0.765412	+	1.86338i	−0.0373483	+	0.0909234i
$421$	11.3830	−	11.3830i	0.554774	−	0.554774i	−0.373041	−	0.927815i	$-0.621685\pi$
$421$	11.3830	−	11.3830i	0.554774	−	0.554774i	0.927815	+	0.373041i	$0.121685\pi$
$422$	−1.93889	+	1.29966i	−0.0943835	+	0.0632663i
$423$	5.10243	+	5.10243i	0.248089	+	0.248089i
$424$	36.6062	−	7.44972i	1.77775	−	0.361790i
$425$	35.3947			1.71690
$426$	0.501345	−	2.53998i	0.0242903	−	0.123062i
$427$	−3.27679	+	3.27679i	−0.158575	+	0.158575i
$428$	−4.81502	+	11.7220i	−0.232743	+	0.566606i
$429$	−9.69511	−	37.0366i	−0.468084	−	1.78815i
$430$	3.85644	+	0.761190i	0.185974	+	0.0367078i
$431$	−10.0473	+	10.0473i	−0.483959	+	0.483959i	−0.906393	−	0.422434i	$-0.861176\pi$
$431$	−10.0473	+	10.0473i	−0.483959	+	0.483959i	0.422434	+	0.906393i	$0.361176\pi$
$432$	4.44899	+	4.39688i	0.214052	+	0.211545i
$433$		−	15.3538i		−	0.737856i	−0.929458	−	0.368928i	$-0.879725\pi$
$433$		−	15.3538i		−	0.737856i	0.929458	−	0.368928i	$-0.120275\pi$
$434$	−0.664664	+	0.445532i	−0.0319049	+	0.0213862i
$435$	−2.00292	−	2.00292i	−0.0960327	−	0.0960327i
$436$	14.6657	+	35.1131i	0.702358	+	1.68161i
$437$	−8.55789	−	8.55789i	−0.409379	−	0.409379i
$438$	0.971197	−	4.92040i	0.0464056	−	0.235106i
$439$	−3.80035			−0.181381			−0.0906905	−	0.995879i	$-0.528907\pi$
$439$	−3.80035			−0.181381			−0.0906905	+	0.995879i	$0.528907\pi$
$440$	−5.56961	+	1.13347i	−0.265521	+	0.0540361i
$441$			2.32216i			0.110579i
$442$	37.4562	−	2.29328i	1.78161	−	0.109080i
$443$	4.80162			0.228132			0.114066	−	0.993473i	$-0.463612\pi$
$443$	4.80162			0.228132			0.114066	+	0.993473i	$0.463612\pi$
$444$	5.09208	−	2.12681i	0.241660	−	0.100934i
$445$		−	0.0828104i		−	0.00392559i
$446$	−7.26744	+	36.8192i	−0.344123	+	1.74344i
$447$	−26.8474	+	26.8474i	−1.26984	+	1.26984i
$448$	−7.41780	−	2.99603i	−0.350458	−	0.141549i
$449$	−28.3112	+	28.3112i	−1.33609	+	1.33609i	−0.436271	+	0.899815i	$0.643701\pi$
$449$	−28.3112	+	28.3112i	−1.33609	+	1.33609i	−0.899815	+	0.436271i	$0.856299\pi$
$450$	−8.79408	−	13.1194i	−0.414557	−	0.618454i
$451$	24.8859			1.17183
$452$	2.62459	−	6.38949i	0.123450	−	0.300536i
$453$	−30.5768	−	30.5768i	−1.43663	−	1.43663i
$454$	−30.2249	−	5.96585i	−1.41853	−	0.279991i
$455$	−0.794949	+	1.35872i	−0.0372678	+	0.0636976i
$456$	−13.5697	+	20.5041i	−0.635462	+	0.960194i
$457$	−1.37861	−	1.37861i	−0.0644889	−	0.0644889i	0.674127	−	0.738616i	$-0.264520\pi$
$457$	−1.37861	−	1.37861i	−0.0644889	−	0.0644889i	−0.738616	+	0.674127i	$0.764520\pi$
$458$	20.5412	+	4.05445i	0.959825	+	0.189452i
$459$			11.5086i			0.537176i
$460$	−1.08089	−	2.58791i	−0.0503967	−	0.120662i
$461$	−14.0302	+	14.0302i	−0.653452	+	0.653452i	−0.953823	−	0.300371i	$-0.902890\pi$
$461$	−14.0302	+	14.0302i	−0.653452	+	0.653452i	0.300371	+	0.953823i	$0.402890\pi$
$462$	−12.4734	+	8.36107i	−0.580316	+	0.388992i
$463$	−17.3484	−	17.3484i	−0.806249	−	0.806249i	0.177815	−	0.984064i	$-0.443097\pi$
$463$	−17.3484	−	17.3484i	−0.806249	−	0.806249i	−0.984064	+	0.177815i	$0.943097\pi$
$464$	7.90719	−	8.00092i	0.367082	−	0.371433i
$465$			0.569897i			0.0264283i
$466$	9.65800	+	14.4082i	0.447398	+	0.667448i
$467$		−	4.11535i		−	0.190436i	−0.995456	−	0.0952178i	$-0.969645\pi$
$467$		−	4.11535i		−	0.190436i	0.995456	−	0.0952178i	$-0.0303547\pi$
$468$	−10.1563	−	13.3137i	−0.469475	−	0.615427i
$469$			11.3973i			0.526280i
$470$	1.59374	−	1.06830i	0.0735138	−	0.0492771i
$471$			48.4985i			2.23469i
$472$	4.54477	+	3.00775i	0.209190	+	0.138443i
$473$	20.7195	+	20.7195i	0.952686	+	0.952686i
$474$	15.6566	+	23.3572i	0.719130	+	1.07283i
$475$	−12.8146	+	12.8146i	−0.587973	+	0.587973i
$476$	−5.67277	−	13.5820i	−0.260011	−	0.622529i
$477$		−	30.6699i		−	1.40428i
$478$	1.15230	−	5.83792i	0.0527048	−	0.267020i
$479$	1.20602	+	1.20602i	0.0551044	+	0.0551044i	0.734122	−	0.679018i	$-0.237594\pi$
$479$	1.20602	+	1.20602i	0.0551044	+	0.0551044i	−0.679018	+	0.734122i	$0.737594\pi$
$480$	−4.71405	+	3.20030i	−0.215166	+	0.146073i
$481$	4.17175	−	1.09204i	0.190215	−	0.0497928i
$482$	4.73604	−	23.9943i	0.215721	−	1.09291i
$483$	−5.23939	−	5.23939i	−0.238400	−	0.238400i
$484$	−18.8412	−	7.73934i	−0.856419	−	0.351788i
$485$	−1.83628			−0.0833810
$486$	23.1452	−	15.5145i	1.04989	−	0.703753i
$487$	6.22727	−	6.22727i	0.282185	−	0.282185i	−0.551795	−	0.833980i	$-0.686057\pi$
$487$	6.22727	−	6.22727i	0.282185	−	0.282185i	0.833980	+	0.551795i	$0.186057\pi$
$488$	−12.8439	+	2.61386i	−0.581414	+	0.118324i
$489$	23.1435	−	23.1435i	1.04659	−	1.04659i
$490$	0.605758	+	0.119566i	0.0273654	+	0.00540142i
$491$			6.88539i			0.310733i	0.987857	+	0.155367i	$0.0496559\pi$
$491$			6.88539i			0.310733i	−0.987857	+	0.155367i	$0.950344\pi$
$492$	23.0199	−	9.61469i	1.03782	−	0.433464i
$493$	20.6967			0.932132
$494$	−12.7306	+	14.3912i	−0.572779	+	0.647490i
$495$			4.66642i			0.209740i
$496$	−2.26319	+	0.0133343i	−0.101620	+	0.000598727i
$497$	−0.793544			−0.0355953
$498$	15.9230	+	3.14290i	0.713526	+	0.140837i
$499$	−10.0565	−	10.0565i	−0.450192	−	0.450192i	0.445226	−	0.895418i	$-0.353123\pi$
$499$	−10.0565	−	10.0565i	−0.450192	−	0.450192i	−0.895418	+	0.445226i	$0.853123\pi$
$500$	−7.90384	+	3.30119i	−0.353471	+	0.147634i
$501$	−22.6140	−	22.6140i	−1.01032	−	1.01032i
$502$	14.9556	+	22.3114i	0.667501	+	0.995808i
$503$			30.2262i			1.34772i	0.738858	+	0.673861i	$0.235365\pi$
$503$			30.2262i			1.34772i	−0.738858	+	0.673861i	$0.764635\pi$
$504$	−3.62485	+	5.47721i	−0.161464	+	0.243974i
$505$	1.22645	−	1.22645i	0.0545762	−	0.0545762i
$506$	4.04839	−	20.5105i	0.179973	−	0.911802i
$507$	−14.6945	−	26.1442i	−0.652604	−	1.16110i
$508$	13.3747	−	32.5604i	0.593407	−	1.44463i
$509$	7.53053	−	7.53053i	0.333785	−	0.333785i	−0.520237	−	0.854022i	$-0.674156\pi$
$509$	7.53053	−	7.53053i	0.333785	−	0.333785i	0.854022	+	0.520237i	$0.174156\pi$
$510$	−10.2847	−	2.03002i	−0.455415	−	0.0898906i
$511$	−1.53724			−0.0680034
$512$	−12.8194	−	18.6457i	−0.566543	−	0.824032i
$513$	−4.16666	−	4.16666i	−0.183962	−	0.183962i
$514$	−11.6238	−	17.3409i	−0.512702	−	0.764872i
$515$	−2.42351	+	2.42351i	−0.106793	+	0.106793i
$516$	27.1709	+	11.1609i	1.19613	+	0.491331i
$517$	14.3024			0.629019
$518$	−0.941777	−	1.40499i	−0.0413793	−	0.0617315i
$519$	10.8817			0.477653
$520$	−3.99596	+	1.96386i	−0.175234	+	0.0861211i
$521$	−19.1146			−0.837426			−0.418713	−	0.908119i	$-0.637519\pi$
$521$	−19.1146			−0.837426			−0.418713	+	0.908119i	$0.637519\pi$
$522$	−5.14224	−	7.67143i	−0.225070	−	0.335769i
$523$	−33.5877			−1.46869			−0.734344	−	0.678778i	$-0.762510\pi$
$523$	−33.5877			−1.46869			−0.734344	+	0.678778i	$0.762510\pi$
$524$	−12.0213	+	29.2655i	−0.525152	+	1.27847i
$525$	−7.84545	+	7.84545i	−0.342404	+	0.342404i
$526$	16.7033	+	24.9187i	0.728298	+	1.08651i
$527$	−2.94445	−	2.94445i	−0.128262	−	0.128262i
$528$	−42.4722	+	0.250238i	−1.84836	+	0.0108902i
$529$	−12.6842			−0.551486
$530$	−8.00057	−	1.57916i	−0.347522	−	0.0685945i
$531$	3.16389	−	3.16389i	0.137301	−	0.137301i
$532$	6.97113	+	2.86351i	0.302237	+	0.124149i
$533$	18.8593	−	4.93681i	0.816887	−	0.213837i
$534$	0.119831	−	0.607101i	0.00518558	−	0.0262718i
$535$	1.95614	−	1.95614i	0.0845711	−	0.0845711i
$536$	−17.7910	+	26.8826i	−0.768456	+	1.16115i
$537$		−	0.371714i		−	0.0160406i
$538$	4.62625	+	6.90164i	0.199452	+	0.297551i
$539$	3.25457	+	3.25457i	0.140184	+	0.140184i
$540$	−0.526262	−	1.26000i	−0.0226467	−	0.0542217i
$541$	−25.7532	−	25.7532i	−1.10722	−	1.10722i	−0.993515	−	0.113701i	$-0.963730\pi$
$541$	−25.7532	−	25.7532i	−1.10722	−	1.10722i	−0.113701	−	0.993515i	$-0.536270\pi$
$542$	−42.2751	−	8.34433i	−1.81587	−	0.358419i
$543$	−43.3214			−1.85910
$544$	7.82102	−	40.8905i	0.335323	−	1.75317i
$545$		−	8.30692i		−	0.355829i
$546$	−7.79407	+	8.81071i	−0.333555	+	0.377063i
$547$	45.4367			1.94273			0.971366	−	0.237589i	$-0.0763570\pi$
$547$	45.4367			1.94273			0.971366	+	0.237589i	$0.0763570\pi$
$548$	13.3554	+	31.9761i	0.570516	+	1.36595i
$549$			10.7610i			0.459270i
$550$	−30.7123	−	6.06205i	−1.30958	−	0.258487i
$551$	−7.49318	+	7.49318i	−0.319220	+	0.319220i
$552$	−4.17940	−	20.5366i	−0.177887	−	0.874095i
$553$	6.09436	−	6.09436i	0.259158	−	0.259158i
$554$	8.87805	−	5.95106i	0.377192	−	0.252836i
$555$	−1.20466			−0.0511351
$556$	−15.2302	+	37.0775i	−0.645904	+	1.57244i
$557$	−16.3395	−	16.3395i	−0.692326	−	0.692326i	0.270418	−	0.962743i	$-0.412838\pi$
$557$	−16.3395	−	16.3395i	−0.692326	−	0.692326i	−0.962743	+	0.270418i	$0.912838\pi$
$558$	−0.359818	+	1.82296i	−0.0152323	+	0.0771719i
$559$	19.8122	+	11.5916i	0.837966	+	0.490272i
$560$	1.24215	+	1.22759i	0.0524902	+	0.0518753i
$561$	−55.2569	−	55.2569i	−2.33295	−	2.33295i
$562$	−6.44653	+	32.6603i	−0.271931	+	1.37769i
$563$			0.0579692i			0.00244311i	0.999999	+	0.00122156i	$0.000388833\pi$
$563$			0.0579692i			0.00244311i	−0.999999	+	0.00122156i	$0.999611\pi$
$564$	13.2299	−	5.52574i	0.557081	−	0.232676i
$565$	−1.06626	+	1.06626i	−0.0448578	+	0.0448578i
$566$	3.36143	+	5.01473i	0.141291	+	0.210785i
$567$	−7.47699	−	7.47699i	−0.314004	−	0.314004i
$568$	−1.87171	−	1.23871i	−0.0785352	−	0.0519750i
$569$			17.8855i			0.749801i	0.927065	+	0.374900i	$0.122323\pi$
$569$			17.8855i			0.749801i	−0.927065	+	0.374900i	$0.877677\pi$
$570$	4.45852	−	2.98860i	0.186747	−	0.125179i
$571$		−	27.9419i		−	1.16933i	−0.811275	−	0.584665i	$-0.801226\pi$
$571$		−	27.9419i		−	1.16933i	0.811275	−	0.584665i	$-0.198774\pi$
$572$	−32.8939	−	4.42522i	−1.37536	−	0.185028i
$573$			17.7948i			0.743389i
$574$	−4.25751	−	6.35154i	−0.177705	−	0.265108i
$575$		−	15.4469i		−	0.644180i
$576$	−17.0996	+	7.26061i	−0.712485	+	0.302525i
$577$	23.2682	+	23.2682i	0.968670	+	0.968670i	0.999524	−	0.0308540i	$-0.00982270\pi$
$577$	23.2682	+	23.2682i	0.968670	+	0.968670i	−0.0308540	+	0.999524i	$0.509823\pi$
$578$	43.6555	−	29.2628i	1.81583	−	1.21717i
$579$	−6.08277	+	6.08277i	−0.252791	+	0.252791i
$580$	−2.26594	+	0.946412i	−0.0940880	+	0.0392976i
$581$		−	4.97468i		−	0.206384i
$582$	−13.4621	−	2.65718i	−0.558024	−	0.110144i
$583$	−42.9848	−	42.9848i	−1.78025	−	1.78025i
$584$	−3.62584	−	2.39960i	−0.150038	−	0.0992962i
$585$	0.925712	+	3.53635i	0.0382735	+	0.146210i
$586$	−40.7882	−	8.05084i	−1.68495	−	0.332577i
$587$	25.0160	+	25.0160i	1.03252	+	1.03252i	0.999453	+	0.0330681i	$0.0105278\pi$
$587$	25.0160	+	25.0160i	1.03252	+	1.03252i	0.0330681	+	0.999453i	$0.489472\pi$
$588$	4.26793	+	1.75312i	0.176006	+	0.0722975i
$589$	2.13206			0.0878499
$590$	−0.662427	−	0.988237i	−0.0272717	−	0.0406851i
$591$	−35.2288	+	35.2288i	−1.44912	+	1.44912i
$592$	−0.0281864	−	4.78400i	−0.00115845	−	0.196621i
$593$	32.7412	−	32.7412i	1.34452	−	1.34452i	0.453021	−	0.891500i	$-0.350346\pi$
$593$	32.7412	−	32.7412i	1.34452	−	1.34452i	0.891500	−	0.453021i	$-0.149654\pi$
$594$	1.97108	−	9.98612i	0.0808743	−	0.409736i
$595$			3.21317i			0.131727i
$596$	12.6858	+	30.3729i	0.519631	+	1.24412i
$597$	32.1022			1.31386
$598$	−1.00083	−	16.3465i	−0.0409269	−	0.668460i
$599$		−	4.75407i		−	0.194246i	−0.995272	−	0.0971230i	$-0.969036\pi$
$599$		−	4.75407i		−	0.194246i	0.995272	−	0.0971230i	$-0.0309640\pi$
$600$	−30.7515	+	6.25823i	−1.25542	+	0.255491i
$601$	19.9892			0.815377			0.407688	−	0.913121i	$-0.366335\pi$
$601$	19.9892			0.815377			0.407688	+	0.913121i	$0.366335\pi$
$602$	1.74345	−	8.83289i	0.0710577	−	0.360002i
$603$	18.7146	+	18.7146i	0.762116	+	0.762116i
$604$	−34.5921	+	14.4481i	−1.40753	+	0.587883i
$605$	3.14416	+	3.14416i	0.127828	+	0.127828i
$606$	10.7661	−	7.21662i	0.437342	−	0.293155i
$607$			2.88939i			0.117277i	0.998279	+	0.0586384i	$0.0186759\pi$
$607$			2.88939i			0.117277i	−0.998279	+	0.0586384i	$0.981324\pi$
$608$	11.9727	+	17.6359i	0.485558	+	0.715229i
$609$	−4.58754	+	4.58754i	−0.185897	+	0.185897i
$610$	2.80713	+	0.554076i	0.113657	+	0.0224339i
$611$	10.8388	−	2.83727i	0.438490	−	0.114784i
$612$	−31.6165	−	12.9870i	−1.27802	−	0.524969i
$613$	−8.92779	+	8.92779i	−0.360590	+	0.360590i	−0.864030	−	0.503440i	$-0.832068\pi$
$613$	−8.92779	+	8.92779i	−0.360590	+	0.360590i	0.503440	+	0.864030i	$0.332068\pi$
$614$	5.30848	−	26.8945i	0.214233	−	1.08537i
$615$	−5.44595			−0.219602
$616$	2.59613	+	12.7568i	0.104601	+	0.513985i
$617$	2.43211	+	2.43211i	0.0979131	+	0.0979131i	0.754367	−	0.656453i	$-0.227944\pi$
$617$	2.43211	+	2.43211i	0.0979131	+	0.0979131i	−0.656453	+	0.754367i	$0.727944\pi$
$618$	−21.2742	+	14.2604i	−0.855775	+	0.573636i
$619$	−20.5450	+	20.5450i	−0.825774	+	0.825774i	−0.986929	−	0.161155i	$-0.948478\pi$
$619$	−20.5450	+	20.5450i	−0.825774	+	0.825774i	0.161155	+	0.986929i	$0.448478\pi$
$620$	0.457010	+	0.187724i	0.0183540	+	0.00753919i
$621$	5.02256			0.201548
$622$	−13.5863	+	9.10704i	−0.544760	+	0.365159i
$623$	−0.189671			−0.00759902
$624$	−32.1370	+	8.61516i	−1.28651	+	0.344882i
$625$	−22.1770			−0.887082
$626$	−29.1501	+	19.5397i	−1.16507	+	0.780961i
$627$	40.0112			1.59789
$628$	38.8918	+	15.9754i	1.55195	+	0.637490i
$629$	6.22405	−	6.22405i	0.248169	−	0.248169i
$630$	1.19099	−	0.798335i	0.0474502	−	0.0318064i
$631$	18.4822	+	18.4822i	0.735766	+	0.735766i	0.971756	−	0.235989i	$-0.0758330\pi$
$631$	18.4822	+	18.4822i	0.735766	+	0.735766i	−0.235989	+	0.971756i	$0.575833\pi$
$632$	23.8878	−	4.86140i	0.950205	−	0.193376i
$633$	3.80770			0.151343
$634$	−0.645403	+	3.26982i	−0.0256322	+	0.129861i
$635$	−5.43357	+	5.43357i	−0.215625	+	0.215625i
$636$	−56.3687	−	23.1544i	−2.23517	−	0.918131i
$637$	3.11204	+	1.82077i	0.123303	+	0.0721417i
$638$	−17.9587	−	3.54472i	−0.710992	−	0.140337i
$639$	−1.30301	+	1.30301i	−0.0515462	+	0.0515462i
$640$	1.01356	+	4.83446i	0.0400645	+	0.191099i
$641$			47.8020i			1.88807i	0.329851	+	0.944033i	$0.393001\pi$
$641$			47.8020i			1.88807i	−0.329851	+	0.944033i	$0.606999\pi$
$642$	17.1715	−	11.5102i	0.677704	−	0.454272i
$643$	17.7744	+	17.7744i	0.700955	+	0.700955i	0.964616	−	0.263660i	$-0.0849298\pi$
$643$	17.7744	+	17.7744i	0.700955	+	0.700955i	−0.263660	+	0.964616i	$0.584930\pi$
$644$	−5.92741	+	2.47570i	−0.233573	+	0.0975561i
$645$	−4.53419	−	4.53419i	−0.178534	−	0.178534i
$646$	−7.59455	+	38.4765i	−0.298803	+	1.51384i
$647$	37.3312			1.46764			0.733820	−	0.679344i	$-0.237736\pi$
$647$	37.3312			1.46764			0.733820	+	0.679344i	$0.237736\pi$
$648$	−5.96431	−	29.3072i	−0.234300	−	1.15130i
$649$		−	8.86855i		−	0.348121i
$650$	−24.4773	+	1.49864i	−0.960078	+	0.0587814i
$651$	1.30531			0.0511590
$652$	−10.9357	−	26.1826i	−0.428274	−	1.02539i
$653$		−	44.9715i		−	1.75987i	−0.475093	−	0.879936i	$-0.657586\pi$
$653$		−	44.9715i		−	1.75987i	0.475093	−	0.879936i	$-0.342414\pi$
$654$	12.0205	−	60.8998i	0.470039	−	2.38137i
$655$	4.88373	−	4.88373i	0.190823	−	0.190823i
$656$	−0.127423	−	21.6271i	−0.00497502	−	0.844397i
$657$	−2.52416	+	2.52416i	−0.0984771	+	0.0984771i
$658$	−2.44687	−	3.65035i	−0.0953889	−	0.142305i
$659$	10.4352			0.406496			0.203248	−	0.979127i	$-0.434850\pi$
$659$	10.4352			0.406496			0.203248	+	0.979127i	$0.434850\pi$
$660$	8.57647	+	3.52293i	0.333839	+	0.137130i
$661$	−4.79732	−	4.79732i	−0.186594	−	0.186594i	0.607628	−	0.794222i	$-0.292121\pi$
$661$	−4.79732	−	4.79732i	−0.186594	−	0.186594i	−0.794222	+	0.607628i	$0.792121\pi$
$662$	10.7131	+	2.11456i	0.416375	+	0.0821848i
$663$	−52.8370	−	30.9136i	−2.05202	−	1.20058i
$664$	7.76539	−	11.7336i	0.301355	−	0.455353i
$665$	−1.16332	−	1.16332i	−0.0451115	−	0.0451115i
$666$	−3.85341	−	0.760593i	−0.149317	−	0.0294724i
$667$		−	9.03240i		−	0.349736i
$668$	−25.5836	+	10.6855i	−0.989859	+	0.413433i
$669$	43.2900	−	43.2900i	1.67369	−	1.67369i
$670$	5.84548	−	3.91829i	0.225831	−	0.151377i
$671$	15.0819	+	15.0819i	0.582230	+	0.582230i
$672$	7.33005	+	10.7972i	0.282763	+	0.416511i
$673$			7.35473i			0.283504i	0.989902	+	0.141752i	$0.0452735\pi$
$673$			7.35473i			0.283504i	−0.989902	+	0.141752i	$0.954726\pi$
$674$	7.17763	+	10.7079i	0.276472	+	0.412453i
$675$		−	7.52077i		−	0.289474i
$676$	−25.8058	+	3.17184i	−0.992531	+	0.121994i
$677$		−	17.2816i		−	0.664185i	−0.943247	−	0.332093i	$-0.892245\pi$
$677$		−	17.2816i		−	0.664185i	0.943247	−	0.332093i	$-0.107755\pi$
$678$	−9.35988	+	6.27403i	−0.359464	+	0.240953i
$679$			4.20586i			0.161406i
$680$	−5.01570	+	7.57881i	−0.192343	+	0.290634i
$681$	35.5368	+	35.5368i	1.36177	+	1.36177i
$682$	2.05063	+	3.05922i	0.0785226	+	0.117144i
$683$	17.4628	−	17.4628i	0.668195	−	0.668195i	−0.289103	−	0.957298i	$-0.593357\pi$
$683$	17.4628	−	17.4628i	0.668195	−	0.668195i	0.957298	+	0.289103i	$0.0933569\pi$
$684$	16.1486	−	6.74477i	0.617457	−	0.257893i
$685$		−	7.56478i		−	0.289035i
$686$	0.273856	−	1.38744i	0.0104559	−	0.0529729i
$687$	−24.1512	−	24.1512i	−0.921424	−	0.921424i
$688$	17.9002	−	18.1124i	0.682439	−	0.690529i
$689$	−41.1023	−	24.0479i	−1.56587	−	0.916152i
$690$	−0.885934	+	4.48843i	−0.0337269	+	0.170872i
$691$	13.0662	+	13.0662i	0.497061	+	0.497061i	0.910522	−	0.413461i	$-0.135680\pi$
$691$	13.0662	+	13.0662i	0.497061	+	0.497061i	−0.413461	+	0.910522i	$0.635680\pi$
$692$	3.58443	−	8.72620i	0.136260	−	0.331720i
$693$	10.6881			0.406007
$694$	30.0446	−	20.1392i	1.14048	−	0.764474i
$695$	6.18737	−	6.18737i	0.234700	−	0.234700i
$696$	−17.9816	+	3.65943i	−0.681590	+	0.138710i
$697$	28.1372	−	28.1372i	1.06577	−	1.06577i
$698$	−36.6108	−	7.22630i	−1.38574	−	0.273520i
$699$		−	28.2957i		−	1.07024i
$700$	3.70710	+	8.87569i	0.140115	+	0.335470i
$701$	−14.6400			−0.552944			−0.276472	−	0.961022i	$-0.589165\pi$
$701$	−14.6400			−0.552944			−0.276472	+	0.961022i	$0.589165\pi$
$702$	−0.487282	−	7.95879i	−0.0183913	−	0.300385i
$703$			4.50680i			0.169977i
$704$	−13.7897	+	34.1416i	−0.519718	+	1.28676i
$705$	−3.12988			−0.117878
$706$	42.1318	+	8.31605i	1.58565	+	0.312979i
$707$	−2.80909	−	2.80909i	−0.105647	−	0.105647i
$708$	−3.42637	−	8.20354i	−0.128771	−	0.308308i
$709$	7.27499	+	7.27499i	0.273218	+	0.273218i	0.830394	−	0.557176i	$-0.188115\pi$
$709$	7.27499	+	7.27499i	0.273218	+	0.273218i	−0.557176	+	0.830394i	$0.688115\pi$
$710$	0.272813	+	0.406994i	0.0102385	+	0.0152742i
$711$		−	20.0140i		−	0.750585i
$712$	−0.447372	−	0.296073i	−0.0167660	−	0.0110958i
$713$	−1.28501	+	1.28501i	−0.0481239	+	0.0481239i
$714$	−4.64960	+	23.5564i	−0.174007	+	0.881577i
$715$	6.25370	+	3.65888i	0.233875	+	0.136834i
$716$	−0.298084	−	0.122443i	−0.0111399	−	0.00457590i
$717$	−6.86390	+	6.86390i	−0.256337	+	0.256337i
$718$	12.5282	+	2.47284i	0.467549	+	0.0922856i
$719$	22.3752			0.834454			0.417227	−	0.908802i	$-0.363002\pi$
$719$	22.3752			0.834454			0.417227	+	0.908802i	$0.363002\pi$
$720$	4.05534	−	0.0238933i	0.151134	−	0.000890451i
$721$	5.55088	+	5.55088i	0.206726	+	0.206726i
$722$	3.78038	+	5.63974i	0.140691	+	0.209889i
$723$	−28.2112	+	28.2112i	−1.04919	+	1.04919i
$724$	−14.2701	+	34.7401i	−0.530343	+	1.29111i
$725$	−13.5251			−0.502310
$726$	18.5008	+	27.6003i	0.686628	+	1.02434i
$727$	26.5309			0.983976			0.491988	−	0.870602i	$-0.336270\pi$
$727$	26.5309			0.983976			0.491988	+	0.870602i	$0.336270\pi$
$728$	4.49808	+	9.15245i	0.166710	+	0.339212i
$729$	−13.7319			−0.508587
$730$	0.528487	+	0.788421i	0.0195602	+	0.0291808i
$731$	46.8529			1.73292
$732$	19.7779	+	8.12409i	0.731012	+	0.300275i
$733$	−1.27103	+	1.27103i	−0.0469465	+	0.0469465i	−0.730190	−	0.683244i	$-0.760569\pi$
$733$	−1.27103	+	1.27103i	−0.0469465	+	0.0469465i	0.683244	+	0.730190i	$0.260569\pi$
$734$	5.76981	+	8.60766i	0.212968	+	0.317714i
$735$	−0.712217	−	0.712217i	−0.0262705	−	0.0262705i
$736$	−17.8453	−	3.41323i	−0.657788	−	0.125813i
$737$	52.4580			1.93231
$738$	−17.4202	−	3.43843i	−0.641247	−	0.126570i
$739$	3.88679	−	3.88679i	0.142978	−	0.142978i	−0.631995	−	0.774973i	$-0.717764\pi$
$739$	3.88679	−	3.88679i	0.142978	−	0.142978i	0.774973	+	0.631995i	$0.217764\pi$
$740$	−0.396817	+	0.966040i	−0.0145873	+	0.0355123i
$741$	30.3217	−	7.93733i	1.11389	−	0.291585i
$742$	−3.61696	+	18.3247i	−0.132783	+	0.672721i
$743$	−18.7330	+	18.7330i	−0.687245	+	0.687245i	−0.961622	−	0.274377i	$-0.911528\pi$
$743$	−18.7330	+	18.7330i	−0.687245	+	0.687245i	0.274377	+	0.961622i	$0.411528\pi$
$744$	3.07879	+	2.03756i	0.112874	+	0.0747007i
$745$		−	7.18549i		−	0.263256i
$746$	−16.4167	−	24.4911i	−0.601057	−	0.896683i
$747$	−8.16848	−	8.16848i	−0.298869	−	0.298869i
$748$	−62.5131	+	26.1098i	−2.28571	+	0.954668i
$749$	−4.48038	−	4.48038i	−0.163710	−	0.163710i
$750$	13.7083	+	2.70577i	0.500558	+	0.0988009i
$751$	−27.1095			−0.989241			−0.494621	−	0.869109i	$-0.664693\pi$
$751$	−27.1095			−0.989241			−0.494621	+	0.869109i	$0.664693\pi$
$752$	−0.0732322	−	12.4295i	−0.00267050	−	0.453257i
$753$		−	43.8165i		−	1.59676i
$754$	−14.3128	+	0.876311i	−0.521242	+	0.0319134i
$755$	8.18366			0.297834
$756$	−2.88593	+	1.20536i	−0.104960	+	0.0438387i
$757$		−	4.80139i		−	0.174509i	−0.996186	−	0.0872547i	$-0.972191\pi$
$757$		−	4.80139i		−	0.174509i	0.996186	−	0.0872547i	$-0.0278094\pi$
$758$	29.1438	+	5.75245i	1.05855	+	0.208938i
$759$	−24.1151	+	24.1151i	−0.875322	+	0.875322i
$760$	−0.927966	−	4.55981i	−0.0336609	−	0.165402i
$761$	8.24646	−	8.24646i	0.298934	−	0.298934i	−0.541662	−	0.840596i	$-0.682205\pi$
$761$	8.24646	−	8.24646i	0.298934	−	0.298934i	0.840596	+	0.541662i	$0.182205\pi$
$762$	−47.6973	+	31.9720i	−1.72789	+	1.15823i
$763$	−19.0264			−0.688801
$764$	14.2700	+	5.86162i	0.516269	+	0.212066i
$765$	5.27606	+	5.27606i	0.190756	+	0.190756i
$766$	0.269451	−	1.36513i	0.00973565	−	0.0493240i
$767$	−1.75932	−	6.72084i	−0.0635254	−	0.242676i
$768$	0.434938	+	36.9091i	0.0156945	+	1.33184i
$769$	24.0851	+	24.0851i	0.868530	+	0.868530i	0.992310	−	0.123780i	$-0.0395017\pi$
$769$	24.0851	+	24.0851i	0.868530	+	0.868530i	−0.123780	+	0.992310i	$0.539502\pi$
$770$	0.550319	−	2.78809i	0.0198321	−	0.100476i
$771$			34.0550i			1.22646i
$772$	2.87421	+	6.88154i	0.103445	+	0.247672i
$773$	33.3001	−	33.3001i	1.19772	−	1.19772i	0.222874	−	0.974847i	$-0.428456\pi$
$773$	33.3001	−	33.3001i	1.19772	−	1.19772i	0.974847	−	0.222874i	$-0.0715440\pi$
$774$	−11.6410	−	17.3665i	−0.418425	−	0.624225i
$775$	1.92417	+	1.92417i	0.0691182	+	0.0691182i
$776$	−6.56527	+	9.92024i	−0.235679	+	0.356116i
$777$			2.75919i			0.0989855i
$778$	−40.7130	+	27.2904i	−1.45963	+	0.978408i
$779$			20.3740i			0.729974i
$780$	7.19837	+	0.968399i	0.257743	+	0.0346742i
$781$			3.65241i			0.130693i
$782$	−18.6128	−	27.7674i	−0.665592	−	0.992959i
$783$		−	4.39769i		−	0.157160i
$784$	2.81171	−	2.84504i	0.100418	−	0.101609i
$785$	−6.49013	−	6.49013i	−0.231643	−	0.231643i
$786$	42.8707	−	28.7367i	1.52915	−	1.02500i
$787$	15.9271	−	15.9271i	0.567741	−	0.567741i	−0.363754	−	0.931495i	$-0.618505\pi$
$787$	15.9271	−	15.9271i	0.567741	−	0.567741i	0.931495	+	0.363754i	$0.118505\pi$
$788$	16.6462	+	39.8550i	0.592996	+	1.41978i
$789$		−	48.9369i		−	1.74220i
$790$	−5.22086	−	1.03050i	−0.185750	−	0.0366636i
$791$	2.44218	+	2.44218i	0.0868340	+	0.0868340i
$792$	25.2097	+	16.6839i	0.895787	+	0.592837i
$793$	14.4214	+	8.43760i	0.512120	+	0.299628i
$794$	−31.0758	−	6.13380i	−1.10284	−	0.217680i
$795$	9.40662	+	9.40662i	0.333619	+	0.333619i
$796$	10.5745	−	25.7433i	0.374802	−	0.912446i
$797$	28.8545			1.02208			0.511040	−	0.859557i	$-0.329260\pi$
$797$	28.8545			1.02208			0.511040	+	0.859557i	$0.329260\pi$
$798$	−6.84516	−	10.2119i	−0.242316	−	0.361498i
$799$	16.1709	−	16.1709i	0.572087	−	0.572087i
$800$	−5.11097	+	26.7216i	−0.180700	+	0.944750i
$801$	−0.311443	+	0.311443i	−0.0110043	+	0.0110043i
$802$	−1.65059	+	8.36241i	−0.0582842	+	0.295287i
$803$			7.07537i			0.249685i
$804$	48.5244	−	20.2671i	1.71132	−	0.714767i
$805$	1.40228			0.0494240
$806$	2.16091	+	1.91157i	0.0761147	+	0.0673321i
$807$		−	13.5539i		−	0.477118i
$808$	−2.24078	−	11.0106i	−0.0788303	−	0.387353i
$809$	19.3562			0.680527			0.340264	−	0.940330i	$-0.389484\pi$
$809$	19.3562			0.680527			0.340264	+	0.940330i	$0.389484\pi$
$810$	−1.26429	+	6.40532i	−0.0444227	+	0.225060i
$811$	−14.8791	−	14.8791i	−0.522475	−	0.522475i	0.395843	−	0.918318i	$-0.370452\pi$
$811$	−14.8791	−	14.8791i	−0.522475	−	0.522475i	−0.918318	+	0.395843i	$0.870452\pi$
$812$	2.16769	+	5.18997i	0.0760709	+	0.182132i
$813$	49.7047	+	49.7047i	1.74322	+	1.74322i
$814$	−6.46666	+	4.33467i	−0.226656	+	0.151930i
$815$			6.19418i			0.216973i
$816$	−47.7380	+	48.3039i	−1.67117	+	1.69097i
$817$	−16.9630	+	16.9630i	−0.593459	+	0.593459i
$818$	−9.10498	−	1.79715i	−0.318348	−	0.0628360i
$819$	8.09974	−	2.12027i	0.283028	−	0.0740884i
$820$	−1.79390	+	4.36720i	−0.0626456	+	0.152509i
$821$	−26.3748	+	26.3748i	−0.920488	+	0.920488i	−0.997064	−	0.0765758i	$-0.975601\pi$
$821$	−26.3748	+	26.3748i	−0.920488	+	0.920488i	0.0765758	+	0.997064i	$0.475601\pi$
$822$	10.9466	−	55.4590i	0.381806	−	1.93436i
$823$	−41.5439			−1.44813			−0.724065	−	0.689731i	$-0.757729\pi$
$823$	−41.5439			−1.44813			−0.724065	+	0.689731i	$0.757729\pi$
$824$	4.42788	+	21.7575i	0.154252	+	0.757960i
$825$	36.1099	+	36.1099i	1.25719	+	1.25719i
$826$	−2.26348	+	1.51724i	−0.0787567	+	0.0527915i
$827$	−3.33553	+	3.33553i	−0.115988	+	0.115988i	−0.762718	−	0.646731i	$-0.776136\pi$
$827$	−3.33553	+	3.33553i	−0.115988	+	0.115988i	0.646731	+	0.762718i	$0.276136\pi$
$828$	−5.66776	+	13.7980i	−0.196968	+	0.479514i
$829$	−50.8931			−1.76759			−0.883796	−	0.467873i	$-0.845020\pi$
$829$	−50.8931			−1.76759			−0.883796	+	0.467873i	$0.845020\pi$
$830$	−2.55142	+	1.71025i	−0.0885611	+	0.0593635i
$831$	−17.4352			−0.604822
$832$	−3.67731	+	28.6090i	−0.127488	+	0.991840i
$833$	7.35952			0.254992
$834$	54.3143	−	36.4075i	1.88075	−	1.26069i
$835$	6.05246			0.209454
$836$	13.1797	−	32.0857i	0.455830	−	1.10971i
$837$	−0.625644	+	0.625644i	−0.0216254	+	0.0216254i
$838$	−11.9467	+	8.00800i	−0.412692	+	0.276632i
$839$	22.3335	+	22.3335i	0.771037	+	0.771037i	0.978288	−	0.207251i	$-0.0664516\pi$
$839$	22.3335	+	22.3335i	0.771037	+	0.771037i	−0.207251	+	0.978288i	$0.566452\pi$
$840$	−0.568128	−	2.79165i	−0.0196023	−	0.0963209i
$841$	21.0913			0.727288
$842$	−4.40854	+	22.3351i	−0.151928	+	0.769719i
$843$	38.4001	−	38.4001i	1.32257	−	1.32257i
$844$	1.25426	−	3.05346i	0.0431734	−	0.105104i
$845$	5.46507	+	1.53221i	0.188004	+	0.0527097i
$846$	−10.0117	−	1.97613i	−0.344210	−	0.0679406i
$847$	7.20147	−	7.20147i	0.247445	−	0.247445i
$848$	−37.1358	+	37.5760i	−1.27525	+	1.29036i
$849$		−	9.84823i		−	0.337990i
$850$	−41.5788	+	27.8707i	−1.42614	+	0.955959i
$851$	−2.71628	−	2.71628i	−0.0931130	−	0.0931130i
$852$	1.41111	+	3.37853i	0.0483438	+	0.115747i
$853$	10.7946	+	10.7946i	0.369600	+	0.369600i	0.867331	−	0.497732i	$-0.165834\pi$
$853$	10.7946	+	10.7946i	0.369600	+	0.369600i	−0.497732	+	0.867331i	$0.665834\pi$
$854$	1.26907	−	6.42952i	0.0434267	−	0.220014i
$855$	−3.82037			−0.130654
$856$	−3.57395	−	17.5616i	−0.122155	−	0.600242i
$857$		−	24.6513i		−	0.842073i	−0.907044	−	0.421036i	$-0.861666\pi$
$857$		−	24.6513i		−	0.842073i	0.907044	−	0.421036i	$-0.138334\pi$
$858$	40.5526	+	35.8734i	1.38444	+	1.22470i
$859$	50.1054			1.70958			0.854788	−	0.518978i	$-0.173687\pi$
$859$	50.1054			1.70958			0.854788	+	0.518978i	$0.173687\pi$
$860$	−5.12961	+	2.14248i	−0.174918	+	0.0730579i
$861$			12.4735i			0.425097i
$862$	3.89121	−	19.7141i	0.132535	−	0.671466i
$863$	−1.51329	+	1.51329i	−0.0515128	+	0.0515128i	−0.732394	−	0.680881i	$-0.761597\pi$
$863$	−1.51329	+	1.51329i	−0.0515128	+	0.0515128i	0.680881	+	0.732394i	$0.261597\pi$
$864$	−8.68852	−	1.66183i	−0.295590	−	0.0565366i
$865$	−1.45620	+	1.45620i	−0.0495123	+	0.0495123i
$866$	12.0900	+	18.0364i	0.410834	+	0.612901i
$867$	−85.7333			−2.91166
$868$	0.429969	−	1.04675i	0.0145941	−	0.0355289i
$869$	−28.0502	−	28.0502i	−0.951538	−	0.951538i
$870$	3.93002	+	0.775713i	0.133240	+	0.0262991i
$871$	39.7542	−	10.4065i	1.34702	−	0.352610i
$872$	−44.8770	−	29.6998i	−1.51973	−	1.00576i
$873$	6.90607	+	6.90607i	0.233735	+	0.233735i
$874$	16.7918	+	3.31439i	0.567991	+	0.112111i
$875$		−	4.28277i		−	0.144784i
$876$	2.73357	+	6.54483i	0.0923588	+	0.221129i
$877$	−15.4722	+	15.4722i	−0.522459	+	0.522459i	−0.918313	−	0.395855i	$-0.870448\pi$
$877$	−15.4722	+	15.4722i	−0.522459	+	0.522459i	0.395855	+	0.918313i	$0.370448\pi$
$878$	4.46434	−	2.99250i	0.150664	−	0.100992i
$879$	47.9565	+	47.9565i	1.61753	+	1.61753i
$880$	5.65019	−	5.71716i	0.190468	−	0.192726i
$881$		−	15.9804i		−	0.538393i	−0.963085	−	0.269196i	$-0.913242\pi$
$881$		−	15.9804i		−	0.538393i	0.963085	−	0.269196i	$-0.0867581\pi$
$882$	−1.82853	−	2.72788i	−0.0615697	−	0.0918524i
$883$		−	46.3824i		−	1.56089i	−0.625222	−	0.780447i	$-0.714992\pi$
$883$		−	46.3824i		−	1.56089i	0.625222	−	0.780447i	$-0.285008\pi$
$884$	−42.1947	+	32.1879i	−1.41916	+	1.08260i
$885$			1.94076i			0.0652379i
$886$	−5.64055	+	3.78092i	−0.189498	+	0.127023i
$887$		−	38.8388i		−	1.30408i	−0.758186	−	0.652039i	$-0.773914\pi$
$887$		−	38.8388i		−	1.30408i	0.758186	−	0.652039i	$-0.226086\pi$
$888$	−4.30705	+	6.50803i	−0.144535	+	0.218395i
$889$	12.4452	+	12.4452i	0.417399	+	0.417399i
$890$	0.0652071	+	0.0972788i	0.00218575	+	0.00326079i
$891$	−34.4140	+	34.4140i	−1.15291	+	1.15291i
$892$	−20.4552	−	48.9747i	−0.684892	−	1.63980i
$893$			11.7093i			0.391837i
$894$	10.3977	−	52.6784i	0.347753	−	1.76183i
$895$	0.0497432	+	0.0497432i	0.00166273	+	0.00166273i
$896$	11.0730	−	2.32148i	0.369922	−	0.0775554i
$897$	−13.4912	+	23.0590i	−0.450459	+	0.769918i
$898$	10.9647	−	55.5506i	0.365895	−	1.85375i
$899$	1.12514	+	1.12514i	0.0375254	+	0.0375254i
$900$	20.6611	+	8.48689i	0.688704	+	0.282896i
$901$	−97.2010			−3.23824
$902$	−29.2339	+	19.5958i	−0.973384	+	0.652470i
$903$	−10.3852	+	10.3852i	−0.345599	+	0.345599i
$904$	1.94810	+	9.57252i	0.0647930	+	0.318377i
$905$	5.79732	−	5.79732i	0.192709	−	0.192709i
$906$	59.9962	+	11.8421i	1.99324	+	0.393429i
$907$			47.0520i			1.56234i	0.624320	+	0.781168i	$0.285376\pi$
$907$			47.0520i			1.56234i	−0.624320	+	0.781168i	$0.714624\pi$
$908$	40.2034	−	16.7917i	1.33420	−	0.557253i
$909$	−9.22511			−0.305978
$910$	−0.136048	−	2.22207i	−0.00450993	−	0.0736609i
$911$		−	3.60690i		−	0.119502i	−0.998213	−	0.0597509i	$-0.980969\pi$
$911$		−	3.60690i		−	0.119502i	0.998213	−	0.0597509i	$-0.0190306\pi$
$912$	−0.204868	−	34.7717i	−0.00678387	−	1.15141i
$913$	−22.8967			−0.757771
$914$	2.70504	+	0.533925i	0.0894747	+	0.0176607i
$915$	−3.30047	−	3.30047i	−0.109110	−	0.109110i
$916$	−27.3226	+	11.4118i	−0.902765	+	0.377057i
$917$	−11.1858	−	11.1858i	−0.369388	−	0.369388i
$918$	−9.06217	−	13.5194i	−0.299096	−	0.446205i
$919$		−	48.6029i		−	1.60326i	−0.597819	−	0.801631i	$-0.703966\pi$
$919$		−	48.6029i		−	1.60326i	0.597819	−	0.801631i	$-0.296034\pi$
$920$	3.30752	+	2.18894i	0.109046	+	0.0721672i
$921$	−31.6211	+	31.6211i	−1.04195	+	1.04195i
$922$	5.43377	−	27.5293i	0.178952	−	0.906629i
$923$	0.724555	+	2.76790i	0.0238490	+	0.0911066i
$924$	8.06901	−	19.6438i	0.265451	−	0.646233i
$925$	−4.06736	+	4.06736i	−0.133734	+	0.133734i
$926$	34.0400	+	6.71888i	1.11863	+	0.220796i
$927$	18.2292			0.598727
$928$	−2.98858	+	15.6251i	−0.0981050	+	0.512921i
$929$	−3.49837	−	3.49837i	−0.114778	−	0.114778i	0.647385	−	0.762163i	$-0.275863\pi$
$929$	−3.49837	−	3.49837i	−0.114778	−	0.114778i	−0.762163	+	0.647385i	$0.775863\pi$
$930$	−0.448752	−	0.669468i	−0.0147152	−	0.0219527i
$931$	−2.66450	+	2.66450i	−0.0873253	+	0.0873253i
$932$	−22.6908	−	9.32063i	−0.743263	−	0.305307i
$933$	26.6816			0.873515
$934$	3.24053	+	4.83437i	0.106033	+	0.158185i
$935$	14.7891			0.483655
$936$	22.4143	+	7.64252i	0.732636	+	0.249804i
$937$	−20.1024			−0.656716			−0.328358	−	0.944553i	$-0.606495\pi$
$937$	−20.1024			−0.656716			−0.328358	+	0.944553i	$0.606495\pi$
$938$	−8.97456	−	13.3886i	−0.293030	−	0.437155i
$939$	57.2467			1.86818
$940$	−1.03099	+	2.50991i	−0.0336270	+	0.0818641i
$941$	−22.5373	+	22.5373i	−0.734694	+	0.734694i	−0.971546	−	0.236852i	$-0.923884\pi$
$941$	−22.5373	+	22.5373i	−0.734694	+	0.734694i	0.236852	+	0.971546i	$0.423884\pi$
$942$	−38.1890	−	56.9721i	−1.24427	−	1.85625i
$943$	−12.2796	−	12.2796i	−0.399877	−	0.399877i
$944$	−7.70720	+	0.0454094i	−0.250848	+	0.00147795i
$945$	0.682742			0.0222096
$946$	−40.6547	−	8.02449i	−1.32180	−	0.260899i
$947$	5.29700	−	5.29700i	0.172129	−	0.172129i	−0.615785	−	0.787914i	$-0.711161\pi$
$947$	5.29700	−	5.29700i	0.172129	−	0.172129i	0.787914	+	0.615785i	$0.211161\pi$
$948$	−36.7841	−	15.1097i	−1.19469	−	0.490739i
$949$	1.40359	+	5.36193i	0.0455626	+	0.174055i
$950$	4.96297	−	25.1440i	0.161020	−	0.815780i
$951$	3.84448	−	3.84448i	0.124666	−	0.124666i
$952$	17.3587	+	11.4881i	0.562599	+	0.372331i
$953$			47.5513i			1.54034i	0.637839	+	0.770170i	$0.279828\pi$
$953$			47.5513i			1.54034i	−0.637839	+	0.770170i	$0.720172\pi$
$954$	24.1503	+	36.0285i	0.781895	+	1.16647i
$955$	−2.38132	−	2.38132i	−0.0770578	−	0.0770578i
$956$	3.24330	+	7.76525i	0.104896	+	0.251146i
$957$	21.1149	+	21.1149i	0.682547	+	0.682547i
$958$	−2.36638	−	0.467080i	−0.0764543	−	0.0150907i
$959$	−17.3266			−0.559504
$960$	3.01768	−	7.47141i	0.0973953	−	0.241139i
$961$			30.6799i			0.989673i
$962$	−4.04072	+	4.56778i	−0.130278	+	0.147271i
$963$	−14.7137			−0.474142
$964$	13.3303	+	31.9158i	0.429339	+	1.02794i
$965$		−	1.62801i		−	0.0524074i
$966$	10.2804	+	2.02917i	0.330767	+	0.0652874i
$967$	20.3534	−	20.3534i	0.654521	−	0.654521i	−0.299557	−	0.954078i	$-0.596839\pi$
$967$	20.3534	−	20.3534i	0.654521	−	0.654521i	0.954078	+	0.299557i	$0.0968389\pi$
$968$	28.2273	−	5.74453i	0.907258	−	0.184636i
$969$	45.2385	−	45.2385i	1.45327	−	1.45327i
$970$	2.15711	−	1.44593i	0.0692605	−	0.0464261i
$971$	−22.5065			−0.722269			−0.361135	−	0.932514i	$-0.617610\pi$
$971$	−22.5065			−0.722269			−0.361135	+	0.932514i	$0.617610\pi$
$972$	−14.9726	+	36.4503i	−0.480246	+	1.16915i
$973$	−14.1717	−	14.1717i	−0.454324	−	0.454324i
$974$	−2.41177	+	12.2188i	−0.0772780	+	0.391516i
$975$	34.5285	+	20.2017i	1.10580	+	0.646974i
$976$	13.0297	−	13.1841i	0.417070	−	0.422014i
$977$	7.84442	+	7.84442i	0.250965	+	0.250965i	0.821366	−	0.570401i	$-0.193212\pi$
$977$	7.84442	+	7.84442i	0.250965	+	0.250965i	−0.570401	+	0.821366i	$0.693212\pi$
$978$	−8.96327	+	45.4109i	−0.286614	+	1.45208i
$979$			0.872991i			0.0279009i
$980$	−0.805744	+	0.336534i	−0.0257385	+	0.0107502i
$981$	−31.2416	+	31.2416i	−0.997466	+	0.997466i
$982$	−5.42173	−	8.08838i	−0.173014	−	0.258111i
$983$	−28.9316	−	28.9316i	−0.922773	−	0.922773i	0.0744513	−	0.997225i	$-0.476279\pi$
$983$	−28.9316	−	28.9316i	−0.922773	−	0.922773i	−0.997225	+	0.0744513i	$0.976279\pi$
$984$	−19.4710	+	29.4210i	−0.620712	+	0.937907i
$985$		−	9.42873i		−	0.300424i
$986$	−24.3128	+	16.2971i	−0.774276	+	0.519006i
$987$			7.16877i			0.228184i
$988$	3.62290	−	26.9300i	0.115260	−	0.856758i
$989$		−	20.4474i		−	0.650191i
$990$	−3.67446	−	5.48172i	−0.116782	−	0.174220i
$991$		−	25.5515i		−	0.811672i	−0.913946	−	0.405836i	$-0.866980\pi$
$991$		−	25.5515i		−	0.811672i	0.913946	−	0.405836i	$-0.133020\pi$
$992$	2.64811	−	1.79776i	0.0840776	−	0.0570790i
$993$	−12.5958	−	12.5958i	−0.399717	−	0.399717i
$994$	0.932189	−	0.624857i	0.0295673	−	0.0198193i
$995$	−4.29595	+	4.29595i	−0.136191	+	0.136191i
$996$	−21.1798	+	8.84615i	−0.671108	+	0.280301i
$997$			18.0376i			0.571256i	0.958341	+	0.285628i	$0.0922022\pi$
$997$			18.0376i			0.571256i	−0.958341	+	0.285628i	$0.907798\pi$
$998$	19.7324	+	3.89480i	0.624617	+	0.123288i
$999$	−1.32250	−	1.32250i	−0.0418421	−	0.0418421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.z.a.99.18	✓	168
8.3	odd	2	inner	728.2.z.a.99.59	yes	168
13.5	odd	4	inner	728.2.z.a.603.59	yes	168
104.83	even	4	inner	728.2.z.a.603.18	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.z.a.99.18	✓	168	1.1	even	1	trivial
728.2.z.a.99.59	yes	168	8.3	odd	2	inner
728.2.z.a.603.18	yes	168	104.83	even	4	inner
728.2.z.a.603.59	yes	168	13.5	odd	4	inner

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.z (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17472 + 0.787426i) q^{2} +2.30698 q^{3} +(0.759920 - 1.85001i) q^{4} +(-0.308723 + 0.308723i) q^{5} +(-2.71005 + 1.81658i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.564051 + 2.77161i) q^{8} +2.32216 q^{9} +(0.119566 - 0.605758i) q^{10} +(3.25457 - 3.25457i) q^{11} +(1.75312 - 4.26793i) q^{12} +(1.82077 - 3.11204i) q^{13} +(-1.38744 - 0.273856i) q^{14} +(-0.712217 + 0.712217i) q^{15} +(-2.84504 - 2.81171i) q^{16} -7.35952i q^{17} +(-2.72788 + 1.82853i) q^{18} +(2.66450 + 2.66450i) q^{19} +(0.336534 + 0.805744i) q^{20} +(1.63128 + 1.63128i) q^{21} +(-1.26046 + 6.38593i) q^{22} -3.21182 q^{23} +(1.30126 + 6.39406i) q^{24} +4.80938i q^{25} +(0.311607 + 5.08949i) q^{26} -1.56377 q^{27} +(1.84550 - 0.770807i) q^{28} +2.81223i q^{29} +(0.275835 - 1.39747i) q^{30} +(0.400087 - 0.400087i) q^{31} +(5.55614 + 1.06271i) q^{32} +(7.50822 - 7.50822i) q^{33} +(5.79508 + 8.64536i) q^{34} -0.436600 q^{35} +(1.76465 - 4.29600i) q^{36} +(0.845714 + 0.845714i) q^{37} +(-5.22812 - 1.03193i) q^{38} +(4.20049 - 7.17941i) q^{39} +(-1.02980 - 0.681525i) q^{40} +(3.82324 + 3.82324i) q^{41} +(-3.20081 - 0.631780i) q^{42} +6.36630i q^{43} +(-3.54776 - 8.49418i) q^{44} +(-0.716903 + 0.716903i) q^{45} +(3.77298 - 2.52907i) q^{46} +(2.19728 + 2.19728i) q^{47} +(-6.56346 - 6.48657i) q^{48} +1.00000i q^{49} +(-3.78703 - 5.64966i) q^{50} -16.9783i q^{51} +(-4.37365 - 5.73334i) q^{52} -13.2075i q^{53} +(1.83699 - 1.23135i) q^{54} +2.00952i q^{55} +(-1.56098 + 2.35867i) q^{56} +(6.14694 + 6.14694i) q^{57} +(-2.21443 - 3.30358i) q^{58} +(1.36248 - 1.36248i) q^{59} +(0.776378 + 1.85883i) q^{60} +4.63407i q^{61} +(-0.154950 + 0.785027i) q^{62} +(1.64201 + 1.64201i) q^{63} +(-7.36369 + 3.12667i) q^{64} +(0.398643 + 1.52287i) q^{65} +(-2.90787 + 14.7322i) q^{66} +(8.05913 + 8.05913i) q^{67} +(-13.6152 - 5.59265i) q^{68} -7.40961 q^{69} +(0.512881 - 0.343790i) q^{70} +(-0.561120 + 0.561120i) q^{71} +(1.30982 + 6.43612i) q^{72} +(-1.08699 + 1.08699i) q^{73} +(-1.65941 - 0.327537i) q^{74} +11.0951i q^{75} +(6.95413 - 2.90453i) q^{76} +4.60265 q^{77} +(0.718871 + 11.7414i) q^{78} -8.61872i q^{79} +(1.74637 - 0.0102893i) q^{80} -10.5741 q^{81} +(-7.50173 - 1.48070i) q^{82} +(-3.51763 - 3.51763i) q^{83} +(4.25752 - 1.77824i) q^{84} +(2.27205 + 2.27205i) q^{85} +(-5.01299 - 7.47860i) q^{86} +6.48776i q^{87} +(10.8561 + 7.18466i) q^{88} +(-0.134118 + 0.134118i) q^{89} +(0.277650 - 1.40667i) q^{90} +(3.48802 - 0.913062i) q^{91} +(-2.44073 + 5.94189i) q^{92} +(0.922992 - 0.922992i) q^{93} +(-4.31138 - 0.850988i) q^{94} -1.64518 q^{95} +(12.8179 + 2.45165i) q^{96} +(2.97399 + 2.97399i) q^{97} +(-0.787426 - 1.17472i) q^{98} +(7.55761 - 7.55761i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 12 q^{6} - 12 q^{8} + 168 q^{9} - 16 q^{16} + 12 q^{18} - 20 q^{20} + 24 q^{22} - 32 q^{24} + 44 q^{26} - 20 q^{34} - 16 q^{40} - 8 q^{41} - 52 q^{44} - 32 q^{46} - 64 q^{48} + 72 q^{50} - 56 q^{52}+ \cdots - 128 q^{99}+O(q^{100}) \) 168 * q - 12 * q^6 - 12 * q^8 + 168 * q^9 - 16 * q^16 + 12 * q^18 - 20 * q^20 + 24 * q^22 - 32 * q^24 + 44 * q^26 - 20 * q^34 - 16 * q^40 - 8 * q^41 - 52 * q^44 - 32 * q^46 - 64 * q^48 + 72 * q^50 - 56 * q^52 - 56 * q^54 - 44 * q^58 - 48 * q^59 + 76 * q^60 + 8 * q^65 - 120 * q^66 + 128 * q^68 - 24 * q^70 + 44 * q^72 - 40 * q^73 - 32 * q^74 - 44 * q^76 - 52 * q^78 + 168 * q^81 - 80 * q^83 + 28 * q^84 - 20 * q^86 + 40 * q^89 + 24 * q^92 + 128 * q^94 + 72 * q^96 - 8 * q^97 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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