LMFDB - Embedded newform 875.2.bb.c.332.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			332.1
Character	$\chi$	$=$	875.332
Dual form			875.2.bb.c.593.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.03043 + 1.64421i) q^{2} +(-1.62597 - 2.50378i) q^{3} +(1.00339 - 4.72059i) q^{4} +(7.41816 + 2.41031i) q^{6} +(2.37291 + 1.17017i) q^{7} +(3.35206 + 6.57879i) q^{8} +(-2.40492 + 5.40154i) q^{9} +(-0.0967529 + 0.0430772i) q^{11} +(-13.4508 + 5.16329i) q^{12} +(1.56081 + 0.247208i) q^{13} +(-6.74202 + 1.52562i) q^{14} +(-8.80536 - 3.92040i) q^{16} +(-4.61951 - 0.242098i) q^{17} +(-3.99823 - 14.9216i) q^{18} +(1.21152 - 0.257516i) q^{19} +(-0.928454 - 7.84391i) q^{21} +(0.125622 - 0.246547i) q^{22} +(-0.0975052 - 0.120409i) q^{23} +(11.0215 - 19.0898i) q^{24} +(-3.57557 + 2.06436i) q^{26} +(8.58862 - 1.36030i) q^{27} +(7.90484 - 10.0274i) q^{28} +(-4.84593 + 1.57454i) q^{29} +(-2.18491 + 1.96730i) q^{31} +(10.0607 - 2.69575i) q^{32} +(0.265174 + 0.172206i) q^{33} +(9.77764 - 7.10387i) q^{34} +(23.0854 + 16.7725i) q^{36} +(-0.184837 - 0.481518i) q^{37} +(-2.03649 + 2.51485i) q^{38} +(-1.91888 - 4.30988i) q^{39} +(-2.31834 - 3.19093i) q^{41} +(14.7822 + 14.3999i) q^{42} +(-4.39882 + 4.39882i) q^{43} +(0.106269 + 0.499954i) q^{44} +(0.395954 + 0.0841627i) q^{46} +(-0.264637 - 5.04958i) q^{47} +(4.50147 + 28.4212i) q^{48} +(4.26142 + 5.55340i) q^{49} +(6.90505 + 11.9599i) q^{51} +(2.73307 - 7.11989i) q^{52} +(-10.6348 + 6.90633i) q^{53} +(-15.2019 + 16.8835i) q^{54} +(0.255867 + 19.5333i) q^{56} +(-2.61466 - 2.61466i) q^{57} +(7.25044 - 11.1647i) q^{58} +(1.30205 + 12.3882i) q^{59} +(-8.51001 - 0.894439i) q^{61} +(1.20165 - 7.58691i) q^{62} +(-12.0274 + 10.0032i) q^{63} +(-4.66418 + 6.41969i) q^{64} +(-0.821558 + 0.0863492i) q^{66} +(0.111213 - 2.12208i) q^{67} +(-5.77803 + 21.5639i) q^{68} +(-0.142937 + 0.439913i) q^{69} +(2.43082 + 7.48129i) q^{71} +(-43.5970 + 2.28482i) q^{72} +(12.7590 + 4.89772i) q^{73} +(1.16701 + 0.673776i) q^{74} -5.97747i q^{76} +(-0.279994 - 0.0109987i) q^{77} +(10.9825 + 5.59585i) q^{78} +(-4.59640 - 4.13862i) q^{79} +(-5.50165 - 6.11020i) q^{81} +(9.95377 + 2.66710i) q^{82} +(-7.96975 + 4.06079i) q^{83} +(-37.9595 - 3.48767i) q^{84} +(1.69891 - 16.1641i) q^{86} +(11.8217 + 9.57299i) q^{87} +(-0.607717 - 0.492120i) q^{88} +(1.42130 - 13.5228i) q^{89} +(3.41439 + 2.41301i) q^{91} +(-0.666237 + 0.339465i) q^{92} +(8.47830 + 2.27175i) q^{93} +(8.83988 + 9.81768i) q^{94} +(-23.1080 - 20.8065i) q^{96} +(9.63928 + 4.91146i) q^{97} +(-17.7835 - 4.26912i) q^{98} -0.626212i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.03043	+	1.64421i	−1.43573	+	1.16263i	−0.476790	+	0.879017i	$0.658200\pi$
$2$	−2.03043	+	1.64421i	−1.43573	+	1.16263i	−0.958939	+	0.283613i	$0.908467\pi$
$3$	−1.62597	−	2.50378i	−0.938757	−	1.44556i	−0.894770	−	0.446527i	$-0.852661\pi$
$3$	−1.62597	−	2.50378i	−0.938757	−	1.44556i	−0.0439870	−	0.999032i	$-0.514006\pi$
$4$	1.00339	−	4.72059i	0.501696	−	2.36030i
$5$		0			0
$5$		0			0
$6$	7.41816	+	2.41031i	3.02845	+	0.984003i
$7$	2.37291	+	1.17017i	0.896876	+	0.442281i
$7$	2.37291	+	1.17017i	0.896876	+	0.442281i
$8$	3.35206	+	6.57879i	1.18513	+	2.32595i
$9$	−2.40492	+	5.40154i	−0.801640	+	1.80051i
$10$		0			0
$11$	−0.0967529	+	0.0430772i	−0.0291721	+	0.0129883i	−0.421271	−	0.906935i	$-0.638416\pi$
$11$	−0.0967529	+	0.0430772i	−0.0291721	+	0.0129883i	0.392099	+	0.919923i	$0.371749\pi$
$12$	−13.4508	+	5.16329i	−3.88292	+	1.49051i
$13$	1.56081	+	0.247208i	0.432890	+	0.0685631i	0.369077	−	0.929399i	$-0.379674\pi$
$13$	1.56081	+	0.247208i	0.432890	+	0.0685631i	0.0638133	+	0.997962i	$0.479674\pi$
$14$	−6.74202	+	1.52562i	−1.80188	+	0.407740i
$15$		0			0
$16$	−8.80536	−	3.92040i	−2.20134	−	0.980100i
$17$	−4.61951	−	0.242098i	−1.12040	−	0.0587175i	−0.516872	−	0.856063i	$-0.672904\pi$
$17$	−4.61951	−	0.242098i	−1.12040	−	0.0587175i	−0.603524	+	0.797345i	$0.706237\pi$
$18$	−3.99823	−	14.9216i	−0.942393	−	3.51706i
$19$	1.21152	−	0.257516i	0.277941	−	0.0590782i	−0.0668320	−	0.997764i	$-0.521289\pi$
$19$	1.21152	−	0.257516i	0.277941	−	0.0590782i	0.344773	+	0.938686i	$0.387956\pi$
$20$		0			0
$21$	−0.928454	−	7.84391i	−0.202605	−	1.71168i
$22$	0.125622	−	0.246547i	0.0267827	−	0.0525640i
$23$	−0.0975052	−	0.120409i	−0.0203312	−	0.0251070i	0.766879	−	0.641792i	$-0.221809\pi$
$23$	−0.0975052	−	0.120409i	−0.0203312	−	0.0251070i	−0.787210	+	0.616685i	$0.788475\pi$
$24$	11.0215	−	19.0898i	2.24975	−	3.89668i
$25$		0			0
$26$	−3.57557	+	2.06436i	−0.701227	+	0.404853i
$27$	8.58862	−	1.36030i	1.65288	−	0.261791i
$28$	7.90484	−	10.0274i	1.49387	−	1.89500i
$29$	−4.84593	+	1.57454i	−0.899866	+	0.292384i	−0.722182	−	0.691703i	$-0.756861\pi$
$29$	−4.84593	+	1.57454i	−0.899866	+	0.292384i	−0.177684	+	0.984088i	$0.556861\pi$
$30$		0			0
$31$	−2.18491	+	1.96730i	−0.392421	+	0.353338i	−0.841597	−	0.540106i	$-0.818384\pi$
$31$	−2.18491	+	1.96730i	−0.392421	+	0.353338i	0.449176	+	0.893443i	$0.351718\pi$
$32$	10.0607	−	2.69575i	1.77850	−	0.476546i
$33$	0.265174	+	0.172206i	0.0461608	+	0.0299772i
$34$	9.77764	−	7.10387i	1.67685	−	1.21830i
$35$		0			0
$36$	23.0854	+	16.7725i	3.84756	+	2.79542i
$37$	−0.184837	−	0.481518i	−0.0303871	−	0.0791610i	0.917547	−	0.397626i	$-0.130166\pi$
$37$	−0.184837	−	0.481518i	−0.0303871	−	0.0791610i	−0.947935	+	0.318465i	$0.896833\pi$
$38$	−2.03649	+	2.51485i	−0.330362	+	0.407963i
$39$	−1.91888	−	4.30988i	−0.307267	−	0.690133i
$40$		0			0
$41$	−2.31834	−	3.19093i	−0.362064	−	0.498339i	0.588658	−	0.808382i	$-0.299656\pi$
$41$	−2.31834	−	3.19093i	−0.362064	−	0.498339i	−0.950722	+	0.310043i	$0.899656\pi$
$42$	14.7822	+	14.3999i	2.28094	+	2.22196i
$43$	−4.39882	+	4.39882i	−0.670814	+	0.670814i	−0.957904	−	0.287090i	$-0.907312\pi$
$43$	−4.39882	+	4.39882i	−0.670814	+	0.670814i	0.287090	+	0.957904i	$0.407312\pi$
$44$	0.106269	+	0.499954i	0.0160206	+	0.0753709i
$45$		0			0
$46$	0.395954	+	0.0841627i	0.0583803	+	0.0124091i
$47$	−0.264637	−	5.04958i	−0.0386013	−	0.736557i	−0.947542	−	0.319631i	$-0.896441\pi$
$47$	−0.264637	−	5.04958i	−0.0386013	−	0.736557i	0.908941	−	0.416925i	$-0.136892\pi$
$48$	4.50147	+	28.4212i	0.649732	+	4.10224i
$49$	4.26142	+	5.55340i	0.608775	+	0.793343i
$50$		0			0
$51$	6.90505	+	11.9599i	0.966900	+	1.67472i
$52$	2.73307	−	7.11989i	0.379009	−	0.987351i
$53$	−10.6348	+	6.90633i	−1.46080	+	0.948657i	−0.462738	+	0.886495i	$0.653133\pi$
$53$	−10.6348	+	6.90633i	−1.46080	+	0.948657i	−0.998066	+	0.0621626i	$0.980200\pi$
$54$	−15.2019	+	16.8835i	−2.06872	+	2.29755i
$55$		0			0
$56$	0.255867	+	19.5333i	0.0341917	+	2.61025i
$57$	−2.61466	−	2.61466i	−0.346320	−	0.346320i
$58$	7.25044	−	11.1647i	0.952029	−	1.46600i
$59$	1.30205	+	12.3882i	0.169512	+	1.61280i	0.666814	+	0.745224i	$0.267657\pi$
$59$	1.30205	+	12.3882i	0.169512	+	1.61280i	−0.497302	+	0.867577i	$0.665676\pi$
$60$		0			0
$61$	−8.51001	−	0.894439i	−1.08960	−	0.114521i	−0.457348	−	0.889288i	$-0.651201\pi$
$61$	−8.51001	−	0.894439i	−1.08960	−	0.114521i	−0.632247	+	0.774767i	$0.717867\pi$
$62$	1.20165	−	7.58691i	0.152609	−	0.963538i
$63$	−12.0274	+	10.0032i	−1.51530	+	1.26029i
$64$	−4.66418	+	6.41969i	−0.583022	+	0.802461i
$65$		0			0
$66$	−0.821558	+	0.0863492i	−0.101127	+	0.0106289i
$67$	0.111213	−	2.12208i	0.0135869	−	0.259253i	−0.983387	−	0.181520i	$-0.941898\pi$
$67$	0.111213	−	2.12208i	0.0135869	−	0.259253i	0.996974	−	0.0777332i	$-0.0247682\pi$
$68$	−5.77803	+	21.5639i	−0.700689	+	2.61501i
$69$	−0.142937	+	0.439913i	−0.0172075	+	0.0529594i
$70$		0			0
$71$	2.43082	+	7.48129i	0.288485	+	0.887866i	0.985332	+	0.170646i	$0.0545856\pi$
$71$	2.43082	+	7.48129i	0.288485	+	0.887866i	−0.696847	+	0.717220i	$0.745414\pi$
$72$	−43.5970	+	2.28482i	−5.13795	+	0.269269i
$73$	12.7590	+	4.89772i	1.49333	+	0.573235i	0.961787	−	0.273798i	$-0.0882799\pi$
$73$	12.7590	+	4.89772i	1.49333	+	0.573235i	0.531541	+	0.847033i	$0.321613\pi$
$74$	1.16701	+	0.673776i	0.135663	+	0.0783249i
$75$		0			0
$76$		−	5.97747i		−	0.685663i
$77$	−0.279994	−	0.0109987i	−0.0319082	−	0.00125341i
$78$	10.9825	+	5.59585i	1.24352	+	0.633606i
$79$	−4.59640	−	4.13862i	−0.517136	−	0.465631i	0.368754	−	0.929527i	$-0.379784\pi$
$79$	−4.59640	−	4.13862i	−0.517136	−	0.465631i	−0.885890	+	0.463896i	$0.846451\pi$
$80$		0			0
$81$	−5.50165	−	6.11020i	−0.611294	−	0.678911i
$82$	9.95377	+	2.66710i	1.09921	+	0.294532i
$83$	−7.96975	+	4.06079i	−0.874794	+	0.445730i	−0.832920	−	0.553393i	$-0.813333\pi$
$83$	−7.96975	+	4.06079i	−0.874794	+	0.445730i	−0.0418738	+	0.999123i	$0.513333\pi$
$84$	−37.9595	−	3.48767i	−4.14172	−	0.380536i
$85$		0			0
$86$	1.69891	−	16.1641i	0.183198	−	1.74301i
$87$	11.8217	+	9.57299i	1.26741	+	1.02633i
$88$	−0.607717	−	0.492120i	−0.0647829	−	0.0524601i
$89$	1.42130	−	13.5228i	0.150658	−	1.43341i	−0.614167	−	0.789176i	$-0.710508\pi$
$89$	1.42130	−	13.5228i	0.150658	−	1.43341i	0.764825	−	0.644238i	$-0.222825\pi$
$90$		0			0
$91$	3.41439	+	2.41301i	0.357925	+	0.252952i
$92$	−0.666237	+	0.339465i	−0.0694600	+	0.0353916i
$93$	8.47830	+	2.27175i	0.879159	+	0.235570i
$94$	8.83988	+	9.81768i	0.911764	+	1.01262i
$95$		0			0
$96$	−23.1080	−	20.8065i	−2.35845	−	2.12356i
$97$	9.63928	+	4.91146i	0.978721	+	0.498683i	0.868750	−	0.495252i	$-0.164924\pi$
$97$	9.63928	+	4.91146i	0.978721	+	0.498683i	0.109971	+	0.993935i	$0.464924\pi$
$98$	−17.7835	−	4.26912i	−1.79640	−	0.431246i
$99$		−	0.626212i		−	0.0629366i
$100$		0			0
$101$	8.01192	+	4.62568i	0.797216	+	0.460273i	0.842497	−	0.538701i	$-0.181085\pi$
$101$	8.01192	+	4.62568i	0.797216	+	0.460273i	−0.0452808	+	0.998974i	$0.514418\pi$
$102$	−33.6847	−	12.9304i	−3.33529	−	1.28030i
$103$	6.66815	−	0.349463i	0.657033	−	0.0344336i	0.279093	−	0.960264i	$-0.409966\pi$
$103$	6.66815	−	0.349463i	0.657033	−	0.0344336i	0.377939	+	0.925830i	$0.376633\pi$
$104$	3.60560	+	11.0969i	0.353558	+	1.08814i
$105$		0			0
$106$	10.2378	−	31.5086i	0.994381	−	3.06039i
$107$	−3.32004	+	12.3906i	−0.320960	+	1.19784i	0.597350	+	0.801980i	$0.296220\pi$
$107$	−3.32004	+	12.3906i	−0.320960	+	1.19784i	−0.918311	+	0.395860i	$0.870447\pi$
$108$	2.19632	−	41.9083i	0.211341	−	4.03263i
$109$	−11.1859	+	1.17568i	−1.07141	+	0.112610i	−0.623774	−	0.781605i	$-0.714401\pi$
$109$	−11.1859	+	1.17568i	−1.07141	+	0.112610i	−0.447638	+	0.894215i	$0.647735\pi$
$110$		0			0
$111$	−0.905075	+	1.24573i	−0.0859059	+	0.118239i
$112$	−16.3068	−	19.6065i	−1.54085	−	1.85264i
$113$	0.610226	−	3.85282i	0.0574053	−	0.362443i	−0.942218	−	0.335000i	$-0.891264\pi$
$113$	0.610226	−	3.85282i	0.0574053	−	0.362443i	0.999623	−	0.0274425i	$-0.00873632\pi$
$114$	9.60792	+	1.00983i	0.899864	+	0.0945796i
$115$		0			0
$116$	2.57038	+	24.4555i	0.238654	+	2.27064i
$117$	−5.08892	+	7.83625i	−0.470471	+	0.724462i
$118$	−23.0124	−	23.0124i	−2.11846	−	2.11846i
$119$	−10.6784	−	5.98007i	−0.978887	−	0.548192i
$120$		0			0
$121$	−7.35293	+	8.16626i	−0.668448	+	0.742387i
$122$	18.7496	−	12.1761i	1.69751	−	1.10238i
$123$	−4.21981	+	10.9930i	−0.380488	+	0.991204i
$124$	7.09450	+	12.2880i	0.637105	+	1.10350i
$125$		0			0
$126$	7.97331	−	40.0863i	0.710319	−	3.57117i
$127$	1.52389	+	9.62146i	0.135223	+	0.853767i	0.958285	+	0.285815i	$0.0922642\pi$
$127$	1.52389	+	9.62146i	0.135223	+	0.853767i	−0.823062	+	0.567952i	$0.807736\pi$
$128$	0.00519057	+	0.0990419i	0.000458786	+	0.00875415i
$129$	18.1661	+	3.86131i	1.59943	+	0.339970i
$130$		0			0
$131$	1.71127	+	8.05088i	0.149514	+	0.703409i	0.987487	+	0.157697i	$0.0504071\pi$
$131$	1.71127	+	8.05088i	0.149514	+	0.703409i	−0.837973	+	0.545711i	$0.816260\pi$
$132$	1.07899	−	1.07899i	0.0939137	−	0.0939137i
$133$	3.17616	+	0.806614i	0.275408	+	0.0699423i
$134$	3.26332	+	4.49158i	0.281908	+	0.388013i
$135$		0			0
$136$	−13.8922	−	31.2023i	−1.19124	−	2.67558i
$137$	8.29301	−	10.2410i	0.708520	−	0.874949i	−0.288058	−	0.957613i	$-0.593009\pi$
$137$	8.29301	−	10.2410i	0.708520	−	0.874949i	0.996577	+	0.0826639i	$0.0263428\pi$
$138$	−0.433087	−	1.12823i	−0.0368668	−	0.0960413i
$139$	−3.54704	−	2.57708i	−0.300856	−	0.218585i	0.427107	−	0.904201i	$-0.359533\pi$
$139$	−3.54704	−	2.57708i	−0.300856	−	0.218585i	−0.727963	+	0.685616i	$0.759533\pi$
$140$		0			0
$141$	−12.2128	+	8.87308i	−1.02850	+	0.747248i
$142$	−17.2364	−	11.1934i	−1.44645	−	0.939333i
$143$	−0.161662	+	0.0433172i	−0.0135188	+	0.00362236i
$144$	42.3524	−	38.1343i	3.52936	−	3.17785i
$145$		0			0
$146$	−33.9591	+	11.0340i	−2.81047	+	0.913178i
$147$	6.97554	−	19.6994i	0.575333	−	1.62478i
$148$	−2.45851	+	0.389390i	−0.202089	+	0.0320077i
$149$	1.49934	−	0.865642i	0.122830	−	0.0709162i	−0.437326	−	0.899303i	$-0.644074\pi$
$149$	1.49934	−	0.865642i	0.122830	−	0.0709162i	0.560156	+	0.828387i	$0.310741\pi$
$150$		0			0
$151$	−2.72492	+	4.71971i	−0.221751	+	0.384084i	−0.955340	−	0.295510i	$-0.904511\pi$
$151$	−2.72492	+	4.71971i	−0.221751	+	0.384084i	0.733589	+	0.679594i	$0.237844\pi$
$152$	5.75522	+	7.10710i	0.466810	+	0.576462i
$153$	12.4173	−	24.3702i	1.00388	−	1.97022i
$154$	0.586591	−	0.438036i	0.0472688	−	0.0352979i
$155$		0			0
$156$	−22.2706	+	4.73375i	−1.78307	+	0.379004i
$157$	−1.97748	−	7.38005i	−0.157820	−	0.588992i	−0.998847	−	0.0479996i	$-0.984715\pi$
$157$	−1.97748	−	7.38005i	−0.157820	−	0.588992i	0.841027	−	0.540993i	$-0.181951\pi$
$158$	16.1374	+	0.845726i	1.28382	+	0.0672823i
$159$	34.5839	+	15.3977i	2.74268	+	1.22112i
$160$		0			0
$161$	−0.0904728	−	0.399817i	−0.00713026	−	0.0315100i
$162$	21.2171	+	3.36046i	1.66698	+	0.264023i
$163$	−19.2184	+	7.37725i	−1.50530	+	0.577831i	−0.964677	−	0.263434i	$-0.915145\pi$
$163$	−19.2184	+	7.37725i	−1.50530	+	0.577831i	−0.540623	+	0.841265i	$0.681811\pi$
$164$	−17.3893	+	7.74220i	−1.35787	+	0.604564i
$165$		0			0
$166$	9.50522	−	21.3491i	0.737748	−	1.65701i
$167$	3.69194	+	7.24584i	0.285691	+	0.560700i	0.988597	−	0.150582i	$-0.0481148\pi$
$167$	3.69194	+	7.24584i	0.285691	+	0.560700i	−0.702907	+	0.711282i	$0.748115\pi$
$168$	48.4912	−	32.4014i	3.74118	−	2.49982i
$169$	−9.98872	−	3.24553i	−0.768363	−	0.249656i
$170$		0			0
$171$	−1.52262	+	7.16336i	−0.116438	+	0.547796i
$172$	16.3513	+	25.1788i	1.24677	+	1.91986i
$173$	−9.34882	+	7.57052i	−0.710777	+	0.575576i	−0.915051	−	0.403338i	$-0.867850\pi$
$173$	−9.34882	+	7.57052i	−0.710777	+	0.575576i	0.204274	+	0.978914i	$0.434517\pi$
$174$	−39.7430			−3.01291
$175$		0			0
$176$	1.02082			0.0769475
$177$	28.9002	−	23.4029i	2.17227	−	1.75907i
$178$	19.3484	+	29.7940i	1.45023	+	2.23315i
$179$	−3.42929	+	16.1335i	−0.256317	+	1.20588i	0.642061	+	0.766653i	$0.278079\pi$
$179$	−3.42929	+	16.1335i	−0.256317	+	1.20588i	−0.898378	+	0.439223i	$0.855254\pi$
$180$		0			0
$181$	17.4861	+	5.68158i	1.29973	+	0.422308i	0.875488	−	0.483240i	$-0.160540\pi$
$181$	17.4861	+	5.68158i	1.29973	+	0.422308i	0.424244	+	0.905548i	$0.360540\pi$
$182$	−10.9001	+	0.714524i	−0.807973	+	0.0529641i
$183$	11.5976	+	22.7616i	0.857319	+	1.68258i
$184$	0.465301	−	1.04508i	0.0343024	−	0.0770446i
$185$		0			0
$186$	−20.9498	+	9.32746i	−1.53611	+	0.683922i
$187$	0.457380	−	0.175572i	0.0334469	−	0.0128391i
$188$	−24.1025	−	3.81747i	−1.75786	−	0.278417i
$189$	21.9718	+	6.82223i	1.59822	+	0.496245i
$190$		0			0
$191$	23.4078	+	10.4218i	1.69373	+	0.754097i	0.999407	+	0.0344325i	$0.0109624\pi$
$191$	23.4078	+	10.4218i	1.69373	+	0.754097i	0.694322	+	0.719664i	$0.255704\pi$
$192$	23.6573	+	1.23983i	1.70732	+	0.0894769i
$193$	0.143491	+	0.535514i	0.0103287	+	0.0385472i	0.970898	−	0.239494i	$-0.0769815\pi$
$193$	0.143491	+	0.535514i	0.0103287	+	0.0385472i	−0.960569	+	0.278041i	$0.910315\pi$
$194$	−27.6473	+	5.87662i	−1.98496	+	0.421917i
$195$		0			0
$196$	30.4912	−	14.5442i	2.17794	−	1.03887i
$197$	−1.61473	+	3.16908i	−0.115045	+	0.225788i	−0.941348	−	0.337438i	$-0.890440\pi$
$197$	−1.61473	+	3.16908i	−0.115045	+	0.225788i	0.826303	+	0.563226i	$0.190440\pi$
$198$	1.02962	+	1.27148i	0.0731720	+	0.0903599i
$199$	1.30189	−	2.25493i	0.0922882	−	0.159848i	−0.816185	−	0.577790i	$-0.803915\pi$
$199$	1.30189	−	2.25493i	0.0922882	−	0.159848i	0.908474	+	0.417942i	$0.137249\pi$
$200$		0			0
$201$	−5.49404	+	3.17199i	−0.387520	+	0.223735i
$202$	−23.8732	+	3.78114i	−1.67971	+	0.266040i
$203$	−13.3414	−	1.93430i	−0.936385	−	0.135761i
$204$	63.3862	−	20.5954i	4.43792	−	1.44197i
$205$		0			0
$206$	−12.9646	+	11.6734i	−0.903287	+	0.813323i
$207$	0.884885	−	0.237104i	0.0615038	−	0.0164799i
$208$	−12.7743	−	8.29575i	−0.885741	−	0.575207i
$209$	−0.106125	+	0.0771042i	−0.00734081	+	0.00533341i
$210$		0			0
$211$	2.95158	+	2.14445i	0.203195	+	0.147630i	0.684729	−	0.728797i	$-0.259920\pi$
$211$	2.95158	+	2.14445i	0.203195	+	0.147630i	−0.481534	+	0.876427i	$0.659920\pi$
$212$	21.9311	+	57.1324i	1.50623	+	3.92387i
$213$	14.7791	−	18.2506i	1.01265	−	1.25051i
$214$	−13.6315	−	30.6170i	−0.931833	−	2.09293i
$215$		0			0
$216$	37.7387	+	51.9429i	2.56779	+	3.53427i
$217$	−7.48667	+	2.11153i	−0.508228	+	0.143340i
$218$	20.7790	−	20.7790i	1.40733	−	1.40733i
$219$	−8.48299	−	39.9093i	−0.573227	−	2.69682i
$220$		0			0
$221$	−7.15032	−	1.51985i	−0.480983	−	0.102236i
$222$	−0.210548	−	4.01749i	−0.0141310	−	0.269636i
$223$	−0.124073	−	0.783365i	−0.00830853	−	0.0524580i	0.983186	−	0.182608i	$-0.0584540\pi$
$223$	−0.124073	−	0.783365i	−0.00830853	−	0.0524580i	−0.991494	+	0.130150i	$0.958454\pi$
$224$	27.0276	+	5.37589i	1.80586	+	0.359192i
$225$		0			0
$226$	5.09581	+	8.82620i	0.338968	+	0.587110i
$227$	−2.83390	+	7.38256i	−0.188092	+	0.489998i	−0.994906	−	0.100809i	$-0.967857\pi$
$227$	−2.83390	+	7.38256i	−0.188092	+	0.489998i	0.806813	+	0.590806i	$0.201190\pi$
$228$	−14.9663	+	9.71921i	−0.991166	+	0.643671i
$229$	14.0477	−	15.6016i	0.928299	−	1.03098i	−0.0711395	−	0.997466i	$-0.522664\pi$
$229$	14.0477	−	15.6016i	0.928299	−	1.03098i	0.999438	−	0.0335139i	$-0.0106698\pi$
$230$		0			0
$231$	0.427724	+	0.718927i	0.0281422	+	0.0473019i
$232$	−26.6024	−	26.6024i	−1.74653	−	1.74653i
$233$	9.44187	−	14.5392i	0.618558	−	0.952495i	−0.381052	−	0.924554i	$-0.624438\pi$
$233$	9.44187	−	14.5392i	0.618558	−	0.952495i	0.999610	−	0.0279415i	$-0.00889523\pi$
$234$	−2.55174	−	24.2782i	−0.166812	−	1.58711i
$235$		0			0
$236$	59.7859	+	6.28375i	3.89173	+	0.409037i
$237$	−2.88856	+	18.2377i	−0.187632	+	1.18466i
$238$	31.5142	−	5.41540i	2.04276	−	0.351028i
$239$	−6.02822	+	8.29714i	−0.389933	+	0.536697i	−0.958182	−	0.286160i	$-0.907621\pi$
$239$	−6.02822	+	8.29714i	−0.389933	+	0.536697i	0.568249	+	0.822857i	$0.307621\pi$
$240$		0			0
$241$	−27.4420	+	2.88427i	−1.76769	+	0.185792i	−0.931769	−	0.363051i	$-0.881735\pi$
$241$	−27.4420	+	2.88427i	−1.76769	+	0.185792i	−0.835925	+	0.548843i	$0.815068\pi$
$242$	1.50257	−	28.6707i	0.0965888	−	1.84302i
$243$	0.398760	−	1.48819i	0.0255804	−	0.0954675i
$244$	−12.7612	+	39.2748i	−0.816950	+	2.51431i
$245$		0			0
$246$	−9.50673	−	29.2587i	−0.606127	−	1.86547i
$247$	1.95461	−	0.102437i	0.124369	−	0.00651788i
$248$	−20.2664	−	7.77954i	−1.28692	−	0.494002i
$249$	23.1260	+	13.3518i	1.46555	+	0.846134i
$250$		0			0
$251$		−	0.542621i		−	0.0342499i	−0.999853	−	0.0171250i	$-0.994549\pi$
$251$		−	0.542621i		−	0.0342499i	0.999853	−	0.0171250i	$-0.00545131\pi$
$252$	35.1529	+	66.8134i	2.21443	+	4.20885i
$253$	0.0146208	+	0.00744966i	0.000919201	+	0.000468356i
$254$	−18.9138	−	17.0301i	−1.18676	−	1.06856i
$255$		0			0
$256$	−10.7927	−	11.9865i	−0.674545	−	0.749158i
$257$	16.6152	+	4.45204i	1.03643	+	0.277711i	0.736633	−	0.676293i	$-0.236414\pi$
$257$	16.6152	+	4.45204i	1.03643	+	0.277711i	0.299797	+	0.954003i	$0.403081\pi$
$258$	−43.2337	+	22.0286i	−2.69161	+	1.37144i
$259$	0.124853	−	1.35889i	0.00775799	−	0.0844373i
$260$		0			0
$261$	3.14914	−	29.9621i	0.194927	−	1.85461i
$262$	−16.7119	−	13.5330i	−1.03247	−	0.836074i
$263$	−15.6543	−	12.6766i	−0.965286	−	0.781673i	0.0106024	−	0.999944i	$-0.496625\pi$
$263$	−15.6543	−	12.6766i	−0.965286	−	0.781673i	−0.975888	+	0.218271i	$0.929958\pi$
$264$	−0.244027	+	2.32177i	−0.0150188	+	0.142895i
$265$		0			0
$266$	−7.77520	+	3.58450i	−0.476728	+	0.219780i
$267$	−36.1692	+	18.4291i	−2.21352	+	1.12784i
$268$	−9.90586	−	2.65427i	−0.605097	−	0.162135i
$269$	−1.65919	−	1.84272i	−0.101163	−	0.112353i	0.690437	−	0.723392i	$-0.257418\pi$
$269$	−1.65919	−	1.84272i	−0.101163	−	0.112353i	−0.791600	+	0.611040i	$0.790752\pi$
$270$		0			0
$271$	6.12866	+	5.51827i	0.372290	+	0.335211i	0.833944	−	0.551849i	$-0.186077\pi$
$271$	6.12866	+	5.51827i	0.372290	+	0.335211i	−0.461655	+	0.887060i	$0.652744\pi$
$272$	39.7274	+	20.2421i	2.40882	+	1.22736i
$273$	0.489937	−	12.4724i	0.0296524	−	0.754862i
$274$			34.4291i			2.07994i
$275$		0			0
$276$	1.93323	+	1.11615i	0.116367	+	0.0671844i
$277$	−11.9863	−	4.60110i	−0.720185	−	0.276453i	−0.0294552	−	0.999566i	$-0.509377\pi$
$277$	−11.9863	−	4.60110i	−0.720185	−	0.276453i	−0.690730	+	0.723113i	$0.742711\pi$
$278$	11.4393	−	0.599506i	0.686081	−	0.0359560i
$279$	−5.37192	−	16.5331i	−0.321609	−	0.989809i
$280$		0			0
$281$	8.46995	−	26.0678i	0.505275	−	1.55508i	−0.295033	−	0.955487i	$-0.595331\pi$
$281$	8.46995	−	26.0678i	0.505275	−	1.55508i	0.800308	−	0.599589i	$-0.204669\pi$
$282$	10.2079	−	38.0964i	0.607872	−	2.26861i
$283$	0.833086	−	15.8962i	0.0495218	−	0.944933i	−0.855033	−	0.518574i	$-0.826463\pi$
$283$	0.833086	−	15.8962i	0.0495218	−	0.944933i	0.904554	−	0.426358i	$-0.140204\pi$
$284$	37.7552	−	3.96823i	2.24036	−	0.235471i
$285$		0			0
$286$	0.257020	−	0.353758i	0.0151979	−	0.0209181i
$287$	−1.76731	−	10.2846i	−0.104321	−	0.607083i
$288$	−9.63393	+	60.8263i	−0.567685	+	3.58422i
$289$	4.37440	+	0.459768i	0.257317	+	0.0270451i
$290$		0			0
$291$	−3.37601	−	32.1206i	−0.197905	−	1.88294i
$292$	35.9224	−	55.3157i	2.10220	−	3.23711i
$293$	16.2607	+	16.2607i	0.949961	+	0.949961i	0.998806	−	0.0488456i	$-0.0155542\pi$
$293$	16.2607	+	16.2607i	0.949961	+	0.949961i	−0.0488456	+	0.998806i	$0.515554\pi$
$294$	18.2265	+	51.4674i	1.06299	+	3.00164i
$295$		0			0
$296$	2.54822	−	2.83008i	0.148112	−	0.164495i
$297$	−0.772376	+	0.501587i	−0.0448178	+	0.0291050i
$298$	−1.62100	+	4.22284i	−0.0939019	+	0.244623i
$299$	−0.122421	−	0.212039i	−0.00707978	−	0.0122625i
$300$		0			0
$301$	−15.5854	+	5.29066i	−0.898325	+	0.304949i
$302$	−2.22742	−	14.0634i	−0.128173	−	0.809255i
$303$	−1.44548	−	27.5813i	−0.0830405	−	1.58451i
$304$	−11.6774	−	2.48211i	−0.669746	−	0.142359i
$305$		0			0
$306$	14.8574	+	69.8985i	0.849340	+	3.99583i
$307$	−7.08123	+	7.08123i	−0.404147	+	0.404147i	−0.879692	−	0.475544i	$-0.842251\pi$
$307$	−7.08123	+	7.08123i	−0.404147	+	0.404147i	0.475544	+	0.879692i	$0.342251\pi$
$308$	−0.332864	+	1.31070i	−0.0189667	+	0.0746840i
$309$	−11.7172	−	16.1274i	−0.666570	−	0.917455i
$310$		0			0
$311$	2.77144	+	6.22474i	0.157154	+	0.352973i	0.974913	−	0.222588i	$-0.0714505\pi$
$311$	2.77144	+	6.22474i	0.157154	+	0.352973i	−0.817759	+	0.575561i	$0.804784\pi$
$312$	21.9216	−	27.0709i	1.24106	−	1.53259i
$313$	3.32236	+	8.65505i	0.187791	+	0.489212i	0.994862	−	0.101243i	$-0.0322818\pi$
$313$	3.32236	+	8.65505i	0.187791	+	0.489212i	−0.807071	+	0.590455i	$0.798948\pi$
$314$	16.1495	+	11.7333i	0.911367	+	0.662147i
$315$		0			0
$316$	−24.1487	+	17.5451i	−1.35847	+	0.986987i
$317$	−15.0451	−	9.77042i	−0.845019	−	0.548762i	0.0479656	−	0.998849i	$-0.484726\pi$
$317$	−15.0451	−	9.77042i	−0.845019	−	0.548762i	−0.892985	+	0.450087i	$0.851393\pi$
$318$	−95.5371	+	25.5991i	−5.35746	+	1.43553i
$319$	0.401031	−	0.361090i	0.0224534	−	0.0202172i
$320$		0			0
$321$	36.4216	−	11.8341i	2.03285	−	0.660514i
$322$	0.841080	+	0.663043i	0.0468716	+	0.0369499i
$323$	−5.65896	+	0.896291i	−0.314873	+	0.0498710i
$324$	−34.3641	+	19.8401i	−1.90911	+	1.10223i
$325$		0			0
$326$	26.8918	−	46.5780i	1.48940	−	2.57972i
$327$	21.1316	+	26.0953i	1.16858	+	1.44308i
$328$	13.2212	−	25.9481i	0.730018	−	1.43274i
$329$	5.28089	−	12.2919i	0.291145	−	0.677673i
$330$		0			0
$331$	20.8396	−	4.42959i	1.14545	−	0.243472i	0.404178	−	0.914680i	$-0.367558\pi$
$331$	20.8396	−	4.42959i	1.14545	−	0.243472i	0.741269	+	0.671208i	$0.234224\pi$
$332$	11.1725	+	41.6965i	0.613173	+	2.28839i
$333$	3.04546	+	0.159606i	0.166890	+	0.00874633i
$334$	−19.4099	−	8.64184i	−1.06206	−	0.472860i
$335$		0			0
$336$	−22.5759	+	72.7084i	−1.23162	+	3.96657i
$337$	1.92468	+	0.304839i	0.104844	+	0.0166057i	0.208636	−	0.977993i	$-0.433098\pi$
$337$	1.92468	+	0.304839i	0.104844	+	0.0166057i	−0.103792	+	0.994599i	$0.533098\pi$
$338$	25.6177	−	9.83371i	1.39342	−	0.534884i
$339$	−10.6388	+	4.73671i	−0.577822	+	0.257263i
$340$		0			0
$341$	0.126651	−	0.284462i	0.00685852	−	0.0154045i
$342$	−8.68648	−	17.0482i	−0.469711	−	0.921860i
$343$	3.61357	+	18.1643i	0.195115	+	0.980780i
$344$	−43.6840	−	14.1938i	−2.35528	−	0.765278i
$345$		0			0
$346$	6.53458	−	30.7428i	0.351301	−	1.65274i
$347$	−15.8909	−	24.4698i	−0.853067	−	1.31361i	−0.948048	−	0.318128i	$-0.896946\pi$
$347$	−15.8909	−	24.4698i	−0.853067	−	1.31361i	0.0949811	−	0.995479i	$-0.469721\pi$
$348$	57.0519	−	46.1997i	3.05830	−	2.47657i
$349$	−6.38042			−0.341536			−0.170768	−	0.985311i	$-0.554625\pi$
$349$	−6.38042			−0.341536			−0.170768	+	0.985311i	$0.554625\pi$
$350$		0			0
$351$	13.7415			0.733466
$352$	−0.857276	+	0.694208i	−0.0456929	+	0.0370014i
$353$	−3.45275	−	5.31678i	−0.183772	−	0.282983i	0.734763	−	0.678324i	$-0.237293\pi$
$353$	−3.45275	−	5.31678i	−0.183772	−	0.282983i	−0.918535	+	0.395340i	$0.870627\pi$
$354$	−20.2005	+	95.0357i	−1.07364	+	5.05109i
$355$		0			0
$356$	−62.4095	−	20.2781i	−3.30770	−	1.07474i
$357$	2.39001	+	36.4598i	0.126493	+	1.92966i
$358$	−19.5639	−	38.3964i	−1.03399	−	2.02931i
$359$	−5.34738	+	12.0104i	−0.282224	+	0.633886i	−0.997916	−	0.0645307i	$-0.979445\pi$
$359$	−5.34738	+	12.0104i	−0.282224	+	0.633886i	0.715692	+	0.698416i	$0.246112\pi$
$360$		0			0
$361$	−15.9559	+	7.10403i	−0.839784	+	0.373896i
$362$	−44.8459	+	17.2147i	−2.35705	+	0.904787i
$363$	32.4022	+	5.13201i	1.70067	+	0.269360i
$364$	14.8168	−	13.6967i	0.776611	−	0.717904i
$365$		0			0
$366$	−60.9728	−	27.1468i	−3.18710	−	1.41899i
$367$	−8.06232	−	0.422528i	−0.420850	−	0.0220558i	−0.159264	−	0.987236i	$-0.550912\pi$
$367$	−8.06232	−	0.422528i	−0.420850	−	0.0220558i	−0.261586	+	0.965180i	$0.584245\pi$
$368$	0.386518	+	1.44250i	0.0201486	+	0.0751957i
$369$	22.8113	−	4.84870i	1.18751	−	0.252413i
$370$		0			0
$371$	−33.3170	+	3.94361i	−1.72973	+	0.204742i
$372$	19.2311	−	37.7431i	0.997086	−	1.95689i
$373$	6.63765	+	8.19682i	0.343685	+	0.424415i	0.919454	−	0.393197i	$-0.128631\pi$
$373$	6.63765	+	8.19682i	0.343685	+	0.424415i	−0.575770	+	0.817612i	$0.695298\pi$
$374$	−0.640001	+	1.10851i	−0.0330936	+	0.0573199i
$375$		0			0
$376$	32.3330	−	18.6675i	1.66745	−	0.962702i
$377$	−7.95280	+	1.25960i	−0.409590	+	0.0648727i
$378$	−55.8294	+	22.2742i	−2.87155	+	1.14566i
$379$	−29.5616	+	9.60515i	−1.51848	+	0.493384i	−0.945343	−	0.326077i	$-0.894273\pi$
$379$	−29.5616	+	9.60515i	−1.51848	+	0.493384i	−0.573135	+	0.819461i	$0.694273\pi$
$380$		0			0
$381$	21.6122	−	19.4597i	1.10723	−	0.996953i
$382$	−64.6635	+	17.3265i	−3.30847	+	0.886502i
$383$	−10.9091	−	7.08447i	−0.557430	−	0.361999i	0.234969	−	0.972003i	$-0.424501\pi$
$383$	−10.9091	−	7.08447i	−0.557430	−	0.361999i	−0.792399	+	0.610004i	$0.791168\pi$
$384$	0.239540	−	0.174036i	0.0122240	−	0.00888122i
$385$		0			0
$386$	−1.17184	−	0.851394i	−0.0596453	−	0.0433348i
$387$	−13.1816	−	34.3392i	−0.670057	−	1.74556i
$388$	32.8570	−	40.5750i	1.66806	−	2.05988i
$389$	−3.28318	−	7.37415i	−0.166464	−	0.373884i	0.810982	−	0.585072i	$-0.198934\pi$
$389$	−3.28318	−	7.37415i	−0.166464	−	0.373884i	−0.977446	+	0.211188i	$0.932267\pi$
$390$		0			0
$391$	0.421275	+	0.579836i	0.0213048	+	0.0293236i
$392$	−22.2501	+	46.6503i	−1.12380	+	2.35620i
$393$	17.3752	−	17.3752i	0.876461	−	0.876461i
$394$	−1.93204	−	9.08954i	−0.0973348	−	0.457924i
$395$		0			0
$396$	−2.95609	−	0.628336i	−0.148549	−	0.0315751i
$397$	1.06447	+	20.3112i	0.0534241	+	1.01939i	0.885473	+	0.464690i	$0.153834\pi$
$397$	1.06447	+	20.3112i	0.0534241	+	1.01939i	−0.832049	+	0.554702i	$0.812832\pi$
$398$	1.06419	+	6.71904i	0.0533431	+	0.336795i
$399$	−3.14477	−	9.26395i	−0.157436	−	0.463777i
$400$		0			0
$401$	−14.0818	−	24.3904i	−0.703213	−	1.21800i	−0.967333	−	0.253511i	$-0.918415\pi$
$401$	−14.0818	−	24.3904i	−0.703213	−	1.21800i	0.264119	−	0.964490i	$-0.414919\pi$
$402$	5.93985	−	15.4738i	0.296253	−	0.771765i
$403$	−3.89656	+	2.53046i	−0.194101	+	0.126051i
$404$	29.8751	−	33.1796i	1.48634	−	1.65075i
$405$		0			0
$406$	30.2692	−	18.0086i	1.50223	−	0.893753i
$407$	0.0386260	+	0.0386260i	0.00191462	+	0.00191462i
$408$	−55.5355	+	85.5171i	−2.74941	+	4.23373i
$409$	−0.404006	−	3.84386i	−0.0199768	−	0.190067i	0.979983	−	0.199083i	$-0.0637965\pi$
$409$	−0.404006	−	3.84386i	−0.0199768	−	0.190067i	−0.999959	+	0.00901688i	$0.997130\pi$
$410$		0			0
$411$	−39.1255	−	4.11226i	−1.92992	−	0.202843i
$412$	5.04110	−	31.8283i	0.248357	−	1.56807i
$413$	−11.4066	+	30.9196i	−0.561280	+	1.52146i
$414$	−1.40685	+	1.93636i	−0.0691427	+	0.0951668i
$415$		0			0
$416$	16.3692	−	1.72047i	0.802567	−	0.0843532i
$417$	−0.685036	+	13.0713i	−0.0335464	+	0.640103i
$418$	0.0887034	−	0.331046i	0.00433862	−	0.0161920i
$419$	−2.14134	+	6.59038i	−0.104612	+	0.321961i	−0.989639	−	0.143577i	$-0.954139\pi$
$419$	−2.14134	+	6.59038i	−0.104612	+	0.321961i	0.885028	+	0.465539i	$0.154139\pi$
$420$		0			0
$421$	7.05679	+	21.7186i	0.343927	+	1.05850i	0.962156	+	0.272500i	$0.0878504\pi$
$421$	7.05679	+	21.7186i	0.343927	+	1.05850i	−0.618229	+	0.785998i	$0.712150\pi$
$422$	−9.51888	+	0.498863i	−0.463372	+	0.0242843i
$423$	27.9119	+	10.7144i	1.35712	+	0.520951i
$424$	−81.0838	−	46.8138i	−3.93778	−	2.27348i
$425$		0			0
$426$			61.3564i			2.97273i
$427$	−19.1469	−	12.0806i	−0.926582	−	0.584619i
$428$	55.1595	+	28.1051i	2.66623	+	1.35851i
$429$	0.371315	+	0.334333i	0.0179272	+	0.0161418i
$430$		0			0
$431$	3.70416	+	4.11389i	0.178423	+	0.198159i	0.825722	−	0.564077i	$-0.190768\pi$
$431$	3.70416	+	4.11389i	0.178423	+	0.198159i	−0.647299	+	0.762236i	$0.724101\pi$
$432$	−80.9589	−	21.6929i	−3.89514	−	1.04370i
$433$	−26.6331	+	13.5702i	−1.27990	+	0.652143i	−0.955839	−	0.293892i	$-0.905049\pi$
$433$	−26.6331	+	13.5702i	−1.27990	+	0.652143i	−0.324064	+	0.946035i	$0.605049\pi$
$434$	11.7293	−	16.5969i	0.563027	−	0.796678i
$435$		0			0
$436$	−5.67390	+	53.9836i	−0.271731	+	2.58534i
$437$	−0.149136	−	0.120768i	−0.00713416	−	0.00577713i
$438$	82.8433	+	67.0852i	3.95841	+	3.20545i
$439$	−0.771106	+	7.33659i	−0.0368029	+	0.350156i	0.960589	+	0.277974i	$0.0896629\pi$
$439$	−0.771106	+	7.33659i	−0.0368029	+	0.350156i	−0.997391	+	0.0721821i	$0.977004\pi$
$440$		0			0
$441$	−40.2453	+	9.66274i	−1.91644	+	0.460131i
$442$	17.0172	−	8.67067i	0.809424	−	0.412422i
$443$	8.73088	+	2.33943i	0.414817	+	0.111150i	0.460190	−	0.887820i	$-0.347781\pi$
$443$	8.73088	+	2.33943i	0.414817	+	0.111150i	−0.0453736	+	0.998970i	$0.514448\pi$
$444$	4.97243	+	5.52244i	0.235981	+	0.262083i
$445$		0			0
$446$	1.53994	+	1.38656i	0.0729180	+	0.0656557i
$447$	−4.60526	−	2.34650i	−0.217821	−	0.110986i
$448$	−18.5798	+	9.77550i	−0.877813	+	0.461849i
$449$		−	1.97023i		−	0.0929809i	−0.998919	−	0.0464905i	$-0.985196\pi$
$449$		−	1.97023i		−	0.0929809i	0.998919	−	0.0464905i	$-0.0148037\pi$
$450$		0			0
$451$	0.361763	+	0.208864i	0.0170347	+	0.00983501i
$452$	−17.5753	−	6.74652i	−0.826671	−	0.317329i
$453$	16.2478	−	0.851510i	0.763387	−	0.0400074i
$454$	−6.38443	−	19.6493i	−0.299636	−	0.922186i
$455$		0			0
$456$	8.43680	−	25.9658i	0.395089	−	1.21596i
$457$	0.527159	−	1.96739i	0.0246595	−	0.0920304i	−0.952499	−	0.304540i	$-0.901497\pi$
$457$	0.527159	−	1.96739i	0.0246595	−	0.0920304i	0.977159	+	0.212510i	$0.0681638\pi$
$458$	−2.87065	+	54.7752i	−0.134136	+	2.55948i
$459$	−40.0046	+	4.20465i	−1.86725	+	0.196256i
$460$		0			0
$461$	15.8458	−	21.8099i	0.738014	−	1.01579i	−0.260716	−	0.965415i	$-0.583959\pi$
$461$	15.8458	−	21.8099i	0.738014	−	1.01579i	0.998730	−	0.0503737i	$-0.0160412\pi$
$462$	−2.05053	−	0.756460i	−0.0953992	−	0.0351937i
$463$	−0.995965	+	6.28827i	−0.0462864	+	0.292241i	−0.999963	−	0.00859262i	$-0.997265\pi$
$463$	−0.995965	+	6.28827i	−0.0462864	+	0.292241i	0.953677	+	0.300834i	$0.0972649\pi$
$464$	48.8430	+	5.13360i	2.26748	+	0.238322i
$465$		0			0
$466$	4.73444	+	45.0452i	0.219319	+	2.08668i
$467$	13.0573	−	20.1065i	0.604221	−	0.930418i	−0.395707	−	0.918377i	$-0.629500\pi$
$467$	13.0573	−	20.1065i	0.604221	−	0.930418i	0.999928	−	0.0120413i	$-0.00383297\pi$
$468$	31.8855	+	31.8855i	1.47391	+	1.47391i
$469$	2.74708	−	4.90536i	0.126848	−	0.226509i
$470$		0			0
$471$	−15.2627	+	16.9510i	−0.703268	+	0.781059i
$472$	−77.1345	+	50.0917i	−3.55040	+	2.30566i
$473$	0.236110	−	0.615087i	0.0108563	−	0.0282818i
$474$	−24.1215	−	41.7797i	−1.10794	−	1.91900i
$475$		0			0
$476$	−38.9441	+	44.4080i	−1.78500	+	2.03544i
$477$	−11.7289	−	74.0535i	−0.537031	−	3.39068i
$478$	−1.40235	−	26.7584i	−0.0641419	−	1.22390i
$479$	1.63940	+	0.348466i	0.0749063	+	0.0159218i	0.245212	−	0.969469i	$-0.421142\pi$
$479$	1.63940	+	0.348466i	0.0749063	+	0.0159218i	−0.170306	+	0.985391i	$0.554476\pi$
$480$		0			0
$481$	−0.169461	−	0.797250i	−0.00772675	−	0.0363515i
$482$	50.9766	−	50.9766i	2.32192	−	2.32192i
$483$	−0.853948	+	0.876616i	−0.0388560	+	0.0398874i
$484$	31.1717	+	42.9041i	1.41689	+	1.95019i
$485$		0			0
$486$	1.63724	+	3.67731i	0.0742668	+	0.166806i
$487$	−19.4054	+	23.9636i	−0.879341	+	1.08590i	0.116354	+	0.993208i	$0.462879\pi$
$487$	−19.4054	+	23.9636i	−0.879341	+	1.08590i	−0.995695	+	0.0926877i	$0.970454\pi$
$488$	−22.6417	−	58.9838i	−1.02494	−	2.67007i
$489$	49.7196	+	36.1234i	2.24840	+	1.63356i
$490$		0			0
$491$	−5.12812	+	3.72580i	−0.231429	+	0.168143i	−0.697456	−	0.716627i	$-0.745685\pi$
$491$	−5.12812	+	3.72580i	−0.231429	+	0.168143i	0.466027	+	0.884770i	$0.345685\pi$
$492$	47.6593	+	30.9503i	2.14865	+	1.39535i
$493$	22.7670	−	6.10040i	1.02537	−	0.274748i
$494$	−3.80026	+	3.42177i	−0.170982	+	0.153953i
$495$		0			0
$496$	26.9515	−	8.75709i	1.21016	−	0.393205i
$497$	−2.98624	+	20.5969i	−0.133951	+	0.923898i
$498$	−68.9087	+	10.9141i	−3.08787	+	0.489071i
$499$	36.2714	−	20.9413i	1.62373	−	0.937462i	0.637821	−	0.770184i	$-0.279836\pi$
$499$	36.2714	−	20.9413i	1.62373	−	0.937462i	0.985910	−	0.167277i	$-0.0534975\pi$
$500$		0			0
$501$	12.1390	−	21.0254i	0.542331	−	0.939344i
$502$	0.892181	+	1.10175i	0.0398200	+	0.0491736i
$503$	−16.7270	+	32.8287i	−0.745822	+	1.46376i	0.135268	+	0.990809i	$0.456811\pi$
$503$	−16.7270	+	32.8287i	−0.745822	+	1.46376i	−0.881090	+	0.472949i	$0.843189\pi$
$504$	−106.125	−	45.5940i	−4.72720	−	2.03092i
$505$		0			0
$506$	−0.0419352	+	0.00891361i	−0.00186425	+	0.000396258i
$507$	8.11531	+	30.2867i	0.360413	+	1.34508i
$508$	46.9481	+	2.46044i	2.08298	+	0.109165i
$509$	−36.9024	−	16.4300i	−1.63567	−	0.728246i	−0.636591	−	0.771202i	$-0.719656\pi$
$509$	−36.9024	−	16.4300i	−1.63567	−	0.728246i	−0.999077	+	0.0429553i	$0.986323\pi$
$510$		0			0
$511$	24.5448	+	26.5520i	1.08580	+	1.17459i
$512$	41.4263	+	6.56128i	1.83080	+	0.289970i
$513$	10.0550	−	3.85974i	0.443938	−	0.170412i
$514$	−41.0561	+	18.2794i	−1.81091	+	0.806268i
$515$		0			0
$516$	36.4554	−	81.8801i	1.60486	−	3.60457i
$517$	0.243126	+	0.477162i	0.0106927	+	0.0209855i
$518$	1.98079	+	2.96441i	0.0870310	+	0.130249i
$519$	34.1559	+	11.0979i	1.49928	+	0.487145i
$520$		0			0
$521$	−3.31243	+	15.5838i	−0.145120	+	0.682737i	0.844086	+	0.536208i	$0.180144\pi$
$521$	−3.31243	+	15.5838i	−0.145120	+	0.682737i	−0.989206	+	0.146529i	$0.953190\pi$
$522$	42.8698	+	66.0137i	1.87636	+	2.88934i
$523$	−10.3099	+	8.34883i	−0.450822	+	0.365069i	−0.827678	−	0.561203i	$-0.810339\pi$
$523$	−10.3099	+	8.34883i	−0.450822	+	0.365069i	0.376856	+	0.926272i	$0.377005\pi$
$524$	39.7220			1.73526
$525$		0			0
$526$	52.6279			2.29469
$527$	10.5695	−	8.55901i	0.460414	−	0.372836i
$528$	−1.65984	−	2.55592i	−0.0722351	−	0.111232i
$529$	4.77698	−	22.4739i	0.207695	−	0.977127i
$530$		0			0
$531$	−70.0464	−	22.7595i	−3.03976	−	0.987677i
$532$	6.99463	−	14.1840i	0.303256	−	0.614955i
$533$	−2.82967	−	5.55354i	−0.122567	−	0.240550i
$534$	43.1376	−	96.8886i	1.86674	−	4.19278i
$535$		0			0
$536$	14.3335	−	6.38167i	0.619112	−	0.275646i
$537$	45.9708	−	17.6465i	1.98378	−	0.761503i
$538$	6.39869	+	1.01345i	0.275867	+	0.0436931i
$539$	−0.651530	−	0.353738i	−0.0280634	−	0.0152366i
$540$		0			0
$541$	29.3706	+	13.0766i	1.26274	+	0.562209i	0.925335	−	0.379150i	$-0.123784\pi$
$541$	29.3706	+	13.0766i	1.26274	+	0.562209i	0.337407	+	0.941359i	$0.390450\pi$
$542$	−21.5170	−	1.12766i	−0.924234	−	0.0484370i
$543$	−14.2065	−	53.0195i	−0.609661	−	2.27528i
$544$	−47.1281	+	10.0174i	−2.02060	+	0.429492i
$545$		0			0
$546$	19.5124	+	26.1298i	0.835053	+	1.11825i
$547$	−0.393959	+	0.773188i	−0.0168445	+	0.0330591i	−0.899275	−	0.437383i	$-0.855905\pi$
$547$	−0.393959	+	0.773188i	−0.0168445	+	0.0330591i	0.882431	+	0.470442i	$0.155905\pi$
$548$	−40.0225	−	49.4237i	−1.70968	−	2.11128i
$549$	25.2972	−	43.8161i	1.07966	−	1.87003i
$550$		0			0
$551$	−5.46546	+	3.15548i	−0.232836	+	0.134428i
$552$	−3.37323	+	0.534267i	−0.143574	+	0.0227399i
$553$	−6.06398	−	15.1991i	−0.257867	−	0.646333i
$554$	31.9024	−	10.3657i	1.35540	−	0.440397i
$555$		0			0
$556$	−15.7244	+	14.1583i	−0.666863	+	0.600446i
$557$	31.3762	−	8.40723i	1.32945	−	0.356226i	0.476941	−	0.878935i	$-0.341745\pi$
$557$	31.3762	−	8.40723i	1.32945	−	0.356226i	0.852511	+	0.522709i	$0.175079\pi$
$558$	38.0911	+	24.7366i	1.61252	+	1.04719i
$559$	−7.95314	+	5.77829i	−0.336382	+	0.244396i
$560$		0			0
$561$	−1.18328	−	0.859705i	−0.0499582	−	0.0362968i
$562$	25.6633	+	66.8552i	1.08254	+	2.82012i
$563$	−9.24684	+	11.4189i	−0.389708	+	0.481249i	−0.933810	−	0.357770i	$-0.883537\pi$
$563$	−9.24684	+	11.4189i	−0.389708	+	0.481249i	0.544102	+	0.839019i	$0.316870\pi$
$564$	29.6320	+	66.5546i	1.24773	+	2.80245i
$565$		0			0
$566$	24.4452	+	33.6459i	1.02751	+	1.41424i
$567$	−5.90498	−	20.9368i	−0.247986	−	0.879263i
$568$	−41.0696	+	41.0696i	−1.72324	+	1.72324i
$569$	8.77121	+	41.2653i	0.367708	+	1.72993i	0.640589	+	0.767884i	$0.278690\pi$
$569$	8.77121	+	41.2653i	0.367708	+	1.72993i	−0.272881	+	0.962048i	$0.587977\pi$
$570$		0			0
$571$	22.1173	+	4.70117i	0.925579	+	0.196738i	0.645958	−	0.763373i	$-0.276458\pi$
$571$	22.1173	+	4.70117i	0.925579	+	0.196738i	0.279620	+	0.960111i	$0.409791\pi$
$572$	0.0422723	+	0.806603i	0.00176749	+	0.0337258i
$573$	−11.9665	−	75.5537i	−0.499909	−	3.15630i
$574$	20.4985	+	17.9764i	0.855589	+	0.750319i
$575$		0			0
$576$	−23.4592	−	40.6326i	−0.977468	−	1.69302i
$577$	9.20378	−	23.9767i	0.383158	−	0.998162i	−0.597402	−	0.801942i	$-0.703800\pi$
$577$	9.20378	−	23.9767i	0.383158	−	0.998162i	0.980560	−	0.196220i	$-0.0628665\pi$
$578$	−9.63784	+	6.25889i	−0.400881	+	0.260335i
$579$	1.10750	−	1.23000i	0.0460261	−	0.0511171i
$580$		0			0
$581$	−23.6633	+	0.309966i	−0.981720	+	0.0128596i
$582$	59.6676	+	59.6676i	2.47330	+	2.47330i
$583$	0.731444	−	1.12633i	0.0302933	−	0.0466476i
$584$	10.5479	+	100.356i	0.436474	+	4.15277i
$585$		0			0
$586$	−59.7522	−	6.28020i	−2.46834	−	0.259433i
$587$	5.73052	−	36.1811i	0.236524	−	1.49335i	−0.528269	−	0.849077i	$-0.677159\pi$
$587$	5.73052	−	36.1811i	0.236524	−	1.49335i	0.764793	−	0.644276i	$-0.222841\pi$
$588$	−85.9934	−	52.6949i	−3.54631	−	2.17310i
$589$	−2.14044	+	2.94607i	−0.0881955	+	0.121391i
$590$		0			0
$591$	10.5602	−	1.10992i	0.434389	−	0.0456561i
$592$	−0.260182	+	4.96458i	−0.0106934	+	0.204043i
$593$	−4.31960	+	16.1210i	−0.177385	+	0.662009i	0.818748	+	0.574152i	$0.194668\pi$
$593$	−4.31960	+	16.1210i	−0.177385	+	0.662009i	−0.996133	+	0.0878564i	$0.971998\pi$
$594$	0.743541	−	2.28838i	0.0305078	−	0.0938935i
$595$		0			0
$596$	−2.58192	−	7.94633i	−0.105760	−	0.325494i
$597$	−7.76269	+	0.406825i	−0.317706	+	0.0166503i
$598$	0.597203	+	0.229245i	0.0244215	+	0.00937452i
$599$	−17.1188	−	9.88355i	−0.699455	−	0.403831i	0.107689	−	0.994185i	$-0.465655\pi$
$599$	−17.1188	−	9.88355i	−0.699455	−	0.403831i	−0.807145	+	0.590354i	$0.798988\pi$
$600$		0			0
$601$		−	23.8371i		−	0.972336i	−0.873865	−	0.486168i	$-0.838394\pi$
$601$		−	23.8371i		−	0.972336i	0.873865	−	0.486168i	$-0.161606\pi$
$602$	22.9460	−	36.3679i	0.935209	−	1.48224i
$603$	11.1950	+	5.70414i	0.455896	+	0.232291i
$604$	19.5456	+	17.5990i	0.795301	+	0.716092i
$605$		0			0
$606$	48.2844	+	53.6252i	1.96142	+	2.17838i
$607$	−4.47778	−	1.19982i	−0.181747	−	0.0486991i	0.166797	−	0.985991i	$-0.446657\pi$
$607$	−4.47778	−	1.19982i	−0.181747	−	0.0486991i	−0.348545	+	0.937292i	$0.613324\pi$
$608$	11.4945	−	5.85674i	0.466164	−	0.237522i
$609$	16.8498	+	36.5492i	0.682787	+	1.48105i
$610$		0			0
$611$	0.835247	−	7.94685i	0.0337905	−	0.321495i
$612$	−102.583	−	83.0697i	−4.14665	−	3.35789i
$613$	−22.6821	−	18.3676i	−0.916121	−	0.741860i	0.0503244	−	0.998733i	$-0.483974\pi$
$613$	−22.6821	−	18.3676i	−0.916121	−	0.741860i	−0.966445	+	0.256873i	$0.917308\pi$
$614$	2.73491	−	26.0209i	0.110372	−	1.05012i
$615$		0			0
$616$	−0.866197	−	1.87889i	−0.0349001	−	0.0757025i
$617$	15.1045	−	7.69612i	0.608084	−	0.309834i	−0.122699	−	0.992444i	$-0.539155\pi$
$617$	15.1045	−	7.69612i	0.608084	−	0.309834i	0.730783	+	0.682610i	$0.239155\pi$
$618$	50.3077	+	13.4799i	2.02367	+	0.542242i
$619$	−1.23720	−	1.37405i	−0.0497273	−	0.0552278i	0.717768	−	0.696282i	$-0.245164\pi$
$619$	−1.23720	−	1.37405i	−0.0497273	−	0.0552278i	−0.767495	+	0.641055i	$0.778497\pi$
$620$		0			0
$621$	−1.00123	−	0.901510i	−0.0401779	−	0.0361763i
$622$	−15.8620	−	8.08208i	−0.636007	−	0.324062i
$623$	19.1966	−	30.4253i	0.769094	−	1.21896i
$624$			45.4728i			1.82037i
$625$		0			0
$626$	−20.9765	−	12.1108i	−0.838390	−	0.484044i
$627$	0.365608	+	0.140344i	0.0146010	+	0.00560479i
$628$	−36.8224	+	1.92978i	−1.46937	+	0.0770066i
$629$	0.737284	+	2.26913i	0.0293974	+	0.0904760i
$630$		0			0
$631$	−14.8852	+	45.8121i	−0.592572	+	1.82375i	−0.0261130	+	0.999659i	$0.508313\pi$
$631$	−14.8852	+	45.8121i	−0.592572	+	1.82375i	−0.566459	+	0.824090i	$0.691687\pi$
$632$	11.8197	−	44.1116i	0.470161	−	1.75467i
$633$	0.570035	−	10.8769i	0.0226569	−	0.432319i
$634$	46.6127	−	4.89919i	1.85122	−	0.194572i
$635$		0			0
$636$	107.388	−	147.806i	4.25820	−	5.86091i
$637$	5.27842	+	9.72126i	0.209139	+	0.385170i
$638$	−0.220557	+	1.39255i	−0.00873195	+	0.0551314i
$639$	−46.2564	−	4.86174i	−1.82988	−	0.192328i
$640$		0			0
$641$	−3.17123	−	30.1722i	−0.125256	−	1.19173i	−0.858880	−	0.512176i	$-0.828839\pi$
$641$	−3.17123	−	30.1722i	−0.125256	−	1.19173i	0.733624	−	0.679555i	$-0.237827\pi$
$642$	−54.4936	+	83.9128i	−2.15069	+	3.31178i
$643$	15.1791	+	15.1791i	0.598605	+	0.598605i	0.939941	−	0.341336i	$-0.110879\pi$
$643$	15.1791	+	15.1791i	0.598605	+	0.598605i	−0.341336	+	0.939941i	$0.610879\pi$
$644$	−1.97815	+	0.0259118i	−0.0779501	+	0.00102107i
$645$		0			0
$646$	10.0164	−	11.1244i	0.394091	−	0.437682i
$647$	−16.7535	+	10.8798i	−0.658648	+	0.427731i	−0.830216	−	0.557441i	$-0.811783\pi$
$647$	−16.7535	+	10.8798i	−0.658648	+	0.427731i	0.171568	+	0.985172i	$0.445117\pi$
$648$	21.7558	−	56.6759i	0.854650	−	2.22644i
$649$	−0.659624	−	1.14250i	−0.0258925	−	0.0448471i
$650$		0			0
$651$	17.4599	+	15.3117i	0.684309	+	0.600113i
$652$	15.5414	+	98.1244i	0.608647	+	3.84285i
$653$	2.31269	+	44.1288i	0.0905026	+	1.72689i	0.546970	+	0.837152i	$0.315781\pi$
$653$	2.31269	+	44.1288i	0.0905026	+	1.72689i	−0.456467	+	0.889740i	$0.650885\pi$
$654$	−85.8123	−	18.2400i	−3.35553	−	0.713239i
$655$		0			0
$656$	7.90415	+	37.1861i	0.308605	+	1.45187i
$657$	−57.1396	+	57.1396i	−2.22923	+	2.22923i
$658$	9.48794	+	33.6406i	0.369878	+	1.31145i
$659$	−20.2475	−	27.8683i	−0.788730	−	1.08559i	−0.994265	−	0.106944i	$-0.965893\pi$
$659$	−20.2475	−	27.8683i	−0.788730	−	1.08559i	0.205535	−	0.978650i	$-0.434107\pi$
$660$		0			0
$661$	−10.5407	−	23.6749i	−0.409987	−	0.920845i	−0.994028	−	0.109121i	$-0.965196\pi$
$661$	−10.5407	−	23.6749i	−0.409987	−	0.920845i	0.584042	−	0.811724i	$-0.301470\pi$
$662$	−35.0301	+	43.2586i	−1.36148	+	1.68129i
$663$	7.82088	+	20.3741i	0.303738	+	0.791264i
$664$	−53.4302	−	38.8193i	−2.07349	−	1.50648i
$665$		0			0
$666$	−6.44600	+	4.68329i	−0.249777	+	0.181474i
$667$	0.662091	+	0.429967i	0.0256363	+	0.0166484i
$668$	37.9091	−	10.1577i	1.46675	−	0.393014i
$669$	−1.75964	+	1.58438i	−0.0680314	+	0.0612558i
$670$		0			0
$671$	0.861899	−	0.280048i	0.0332732	−	0.0108111i
$672$	−30.4862	−	76.4123i	−1.17603	−	2.94767i
$673$	−48.8149	+	7.73152i	−1.88168	+	0.298028i	−0.988446	−	0.151572i	$-0.951566\pi$
$673$	−48.8149	+	7.73152i	−1.88168	+	0.298028i	−0.893230	+	0.449600i	$0.851566\pi$
$674$	−4.40914	+	2.54562i	−0.169834	+	0.0980536i
$675$		0			0
$676$	−25.3434	+	43.8961i	−0.974748	+	1.68831i
$677$	−17.1183	−	21.1393i	−0.657910	−	0.812451i	0.333568	−	0.942726i	$-0.391747\pi$
$677$	−17.1183	−	21.1393i	−0.657910	−	0.812451i	−0.991478	+	0.130275i	$0.958414\pi$
$678$	13.8132	−	27.1100i	0.530494	−	1.04115i
$679$	17.1259	+	22.9340i	0.657233	+	0.880127i
$680$		0			0
$681$	23.0922	−	4.90839i	0.884894	−	0.188090i
$682$	0.210560	+	0.785819i	0.00806274	+	0.0300906i
$683$	18.3535	+	0.961868i	0.702278	+	0.0368049i	0.400133	−	0.916457i	$-0.368964\pi$
$683$	18.3535	+	0.961868i	0.702278	+	0.0368049i	0.302145	+	0.953262i	$0.402297\pi$
$684$	32.2875	+	14.3753i	1.23454	+	0.549654i
$685$		0			0
$686$	−37.2030	−	30.9398i	−1.42042	−	1.18129i
$687$	−61.9041	−	9.80465i	−2.36179	−	0.374071i
$688$	55.9783	−	21.4881i	2.13415	−	0.819225i
$689$	−18.3062	+	8.15045i	−0.697411	+	0.310507i
$690$		0			0
$691$	−9.92070	+	22.2823i	−0.377401	+	0.847657i	0.620580	+	0.784143i	$0.286897\pi$
$691$	−9.92070	+	22.2823i	−0.377401	+	0.847657i	−0.997981	+	0.0635139i	$0.979769\pi$
$692$	26.3568	+	51.7281i	1.00194	+	1.96641i
$693$	0.732772	−	1.48595i	0.0278357	−	0.0564464i
$694$	72.4987	+	23.5562i	2.75201	+	0.894183i
$695$		0			0
$696$	−23.3518	+	109.861i	−0.885146	+	4.16428i
$697$	9.93709	+	15.3018i	0.376394	+	0.579596i
$698$	12.9550	−	10.4907i	0.490353	−	0.397080i
$699$	−51.7553			−1.95756
$700$		0			0
$701$	−8.02401			−0.303063			−0.151531	−	0.988452i	$-0.548420\pi$
$701$	−8.02401			−0.303063			−0.151531	+	0.988452i	$0.548420\pi$
$702$	−27.9011	+	22.5938i	−1.05306	+	0.852749i
$703$	−0.347932	−	0.535769i	−0.0131225	−	0.0202069i
$704$	0.174731	−	0.822044i	0.00658541	−	0.0309819i
$705$		0			0
$706$	15.7524	+	5.11828i	0.592851	+	0.192629i
$707$	13.5988	+	20.3516i	0.511434	+	0.765401i
$708$	−81.4772	−	159.908i	−3.06210	−	6.00971i
$709$	−1.02292	+	2.29751i	−0.0384165	+	0.0862848i	−0.931734	−	0.363140i	$-0.881705\pi$
$709$	−1.02292	+	2.29751i	−0.0384165	+	0.0862848i	0.893318	+	0.449425i	$0.148371\pi$
$710$		0			0
$711$	33.4089	−	14.8746i	1.25293	−	0.557841i
$712$	93.7279	−	35.9788i	3.51260	−	1.34836i
$713$	0.449921	+	0.0712604i	0.0168497	+	0.00266872i
$714$	−64.8002	−	70.0993i	−2.42509	−	2.62340i
$715$		0			0
$716$	72.7188	+	32.3765i	2.71763	+	1.20997i
$717$	30.5760	+	1.60242i	1.14188	+	0.0598434i
$718$	−8.89015	−	33.1785i	−0.331777	−	1.23821i
$719$	38.5150	−	8.18661i	1.43637	−	0.305309i	0.577032	−	0.816722i	$-0.304211\pi$
$719$	38.5150	−	8.18661i	1.43637	−	0.305309i	0.859335	+	0.511413i	$0.170878\pi$
$720$		0			0
$721$	16.2319	+	6.97360i	0.604506	+	0.259710i
$722$	20.7168	−	40.6590i	0.771000	−	1.51317i
$723$	51.8416	+	64.0190i	1.92801	+	2.38089i
$724$	44.3658	−	76.8439i	1.64884	−	2.85588i
$725$		0			0
$726$	−74.2284	+	42.8558i	−2.75487	+	1.59053i
$727$	28.5317	−	4.51898i	1.05818	−	0.167600i	0.396995	−	0.917821i	$-0.370053\pi$
$727$	28.5317	−	4.51898i	1.05818	−	0.167600i	0.661187	+	0.750221i	$0.270053\pi$
$728$	−4.42944	+	30.5511i	−0.164166	+	1.13230i
$729$	−27.8335	+	9.04365i	−1.03087	+	0.334950i
$730$		0			0
$731$	21.3853	−	19.2554i	0.790965	−	0.712188i
$732$	119.085	−	31.9087i	4.40151	−	1.17938i
$733$	7.86575	+	5.10808i	0.290528	+	0.188671i	0.681671	−	0.731659i	$-0.261254\pi$
$733$	7.86575	+	5.10808i	0.290528	+	0.188671i	−0.391143	+	0.920330i	$0.627920\pi$
$734$	17.0647	−	12.3982i	0.629869	−	0.457626i
$735$		0			0
$736$	−1.30556	−	0.948546i	−0.0481236	−	0.0349639i
$737$	0.0806528	+	0.210108i	0.00297089	+	0.00773942i
$738$	−38.3445	+	47.3515i	−1.41148	+	1.74303i
$739$	2.94919	+	6.62398i	0.108488	+	0.243667i	0.959629	−	0.281270i	$-0.0907556\pi$
$739$	2.94919	+	6.62398i	0.108488	+	0.243667i	−0.851141	+	0.524937i	$0.824089\pi$
$740$		0			0
$741$	−3.43462	−	4.72735i	−0.126174	−	0.173664i
$742$	61.1637	−	62.7873i	2.24539	−	2.30500i
$743$	−3.41793	+	3.41793i	−0.125392	+	0.125392i	−0.767018	−	0.641626i	$-0.778260\pi$
$743$	−3.41793	+	3.41793i	−0.125392	+	0.125392i	0.641626	+	0.767018i	$0.278260\pi$
$744$	13.4744	+	63.3920i	0.493995	+	2.32406i
$745$		0			0
$746$	−26.9545	−	5.72936i	−0.986876	−	0.209767i
$747$	−2.76791	−	52.8148i	−0.101272	−	1.93239i
$748$	−0.369871	−	2.33527i	−0.0135238	−	0.0853860i
$749$	−22.3772	+	25.5167i	−0.817644	+	0.932360i
$750$		0			0
$751$	−5.61814	−	9.73090i	−0.205009	−	0.355086i	0.745127	−	0.666923i	$-0.232389\pi$
$751$	−5.61814	−	9.73090i	−0.205009	−	0.355086i	−0.950136	+	0.311837i	$0.899056\pi$
$752$	−17.4661	+	45.5009i	−0.636925	+	1.65925i
$753$	−1.35860	+	0.882288i	−0.0495103	+	0.0321524i
$754$	14.0765	−	15.6336i	0.512637	−	0.569342i
$755$		0			0
$756$	54.2513	−	96.8746i	1.97310	−	3.52330i
$757$	−4.30306	−	4.30306i	−0.156397	−	0.156397i	0.624571	−	0.780968i	$-0.285274\pi$
$757$	−4.30306	−	4.30306i	−0.156397	−	0.156397i	−0.780968	+	0.624571i	$0.785274\pi$
$758$	44.2298	−	68.1080i	1.60650	−	2.47379i
$759$	−0.00512070	−	0.0487202i	−0.000185870	−	0.00176843i
$760$		0			0
$761$	−7.04163	−	0.740105i	−0.255259	−	0.0268288i	−0.0239652	−	0.999713i	$-0.507629\pi$
$761$	−7.04163	−	0.740105i	−0.255259	−	0.0268288i	−0.231293	+	0.972884i	$0.574296\pi$
$762$	−11.8862	+	75.0466i	−0.430592	+	2.71865i
$763$	−27.9188	−	10.2995i	−1.01073	−	0.372868i
$764$	72.6844	−	100.041i	2.62963	−	3.61937i
$765$		0			0
$766$	33.7985	−	3.55237i	1.22119	−	0.128352i
$767$	−1.03020	+	19.6574i	−0.0371984	+	0.709789i
$768$	−12.4630	+	46.5124i	−0.449719	+	1.67837i
$769$	−5.23318	+	16.1061i	−0.188713	+	0.580800i	−0.999993	−	0.00385911i	$-0.998772\pi$
$769$	−5.23318	+	16.1061i	−0.188713	+	0.580800i	0.811279	+	0.584659i	$0.198772\pi$
$770$		0			0
$771$	−15.8690	−	48.8398i	−0.571509	−	1.75892i
$772$	2.67192	−	0.140029i	0.0961645	−	0.00503977i
$773$	−10.5330	−	4.04324i	−0.378846	−	0.145425i	0.161491	−	0.986874i	$-0.448370\pi$
$773$	−10.5330	−	4.04324i	−0.378846	−	0.145425i	−0.540337	+	0.841449i	$0.681703\pi$
$774$	83.2250	+	48.0500i	2.99146	+	1.72712i
$775$		0			0
$776$			79.8783i			2.86746i
$777$	−3.60537	+	1.89692i	−0.129342	+	0.0680515i
$778$	18.7909	+	9.57443i	0.673686	+	0.343260i
$779$	−3.63043	−	3.26885i	−0.130074	−	0.117119i
$780$		0			0
$781$	−0.557462	−	0.619124i	−0.0199476	−	0.0221540i
$782$	−1.80874	−	0.484650i	−0.0646804	−	0.0173311i
$783$	−39.4780	+	20.1150i	−1.41083	+	0.718853i
$784$	−15.7518	−	65.6062i	−0.562565	−	2.34308i
$785$		0			0
$786$	−6.71063	+	63.8474i	−0.239360	+	2.27736i
$787$	5.20240	+	4.21282i	0.185446	+	0.150171i	0.717548	−	0.696509i	$-0.245264\pi$
$787$	5.20240	+	4.21282i	0.185446	+	0.150171i	−0.532102	+	0.846680i	$0.678598\pi$
$788$	13.3397	+	10.8023i	0.475208	+	0.384816i
$789$	−6.28595	+	59.8068i	−0.223786	+	2.12918i
$790$		0			0
$791$	5.95645	−	8.42833i	0.211787	−	0.299677i
$792$	4.11971	−	2.09910i	0.146388	−	0.0745882i
$793$	−13.0614	−	3.49979i	−0.463824	−	0.124281i
$794$	−35.5572	−	39.4903i	−1.26188	−	1.40146i
$795$		0			0
$796$	−9.33831	−	8.40825i	−0.330988	−	0.298023i
$797$	−7.70734	−	3.92708i	−0.273008	−	0.139104i	0.312127	−	0.950040i	$-0.398958\pi$
$797$	−7.70734	−	3.92708i	−0.273008	−	0.139104i	−0.585135	+	0.810936i	$0.698958\pi$
$798$	21.6171	+	13.6391i	0.765236	+	0.482819i
$799$			23.3907i			0.827502i
$800$		0			0
$801$	69.6258	+	40.1985i	2.46011	+	1.42034i
$802$	68.6951	+	26.3696i	2.42571	+	0.931142i
$803$	−1.44545	+	0.0757529i	−0.0510088	+	0.00267326i
$804$	9.46097	+	29.1179i	0.333663	+	1.02691i
$805$		0			0
$806$	3.75109	−	11.5447i	0.132126	−	0.406643i
$807$	−1.91597	+	7.15048i	−0.0674452	+	0.251709i
$808$	−3.57496	+	68.2143i	−0.125767	+	2.39977i
$809$	−9.86480	+	1.03683i	−0.346828	+	0.0364531i	−0.276341	−	0.961060i	$-0.589122\pi$
$809$	−9.86480	+	1.03683i	−0.346828	+	0.0364531i	−0.0704869	+	0.997513i	$0.522455\pi$
$810$		0			0
$811$	6.48171	−	8.92131i	0.227604	−	0.313270i	−0.679907	−	0.733298i	$-0.737980\pi$
$811$	6.48171	−	8.92131i	0.227604	−	0.313270i	0.907511	+	0.420029i	$0.137980\pi$
$812$	−22.5177	+	61.0386i	−0.790218	+	2.14203i
$813$	3.85150	−	24.3174i	0.135078	−	0.852849i
$814$	−0.141936	−	0.0149181i	−0.00497487	−	0.000522880i
$815$		0			0
$816$	−13.9139	−	132.382i	−0.487083	−	4.63429i
$817$	−4.19648	+	6.46201i	−0.146816	+	0.226077i
$818$	7.14040	+	7.14040i	0.249658	+	0.249658i
$819$	−21.2453	+	12.6399i	−0.742370	+	0.441672i
$820$		0			0
$821$	−4.00225	+	4.44495i	−0.139679	+	0.155130i	−0.808926	−	0.587911i	$-0.799950\pi$
$821$	−4.00225	+	4.44495i	−0.139679	+	0.155130i	0.669246	+	0.743041i	$0.266617\pi$
$822$	86.2029	−	55.9808i	3.00667	−	1.95255i
$823$	14.4864	−	37.7383i	0.504963	−	1.31547i	−0.410055	−	0.912061i	$-0.634491\pi$
$823$	14.4864	−	37.7383i	0.504963	−	1.31547i	0.915018	−	0.403413i	$-0.132176\pi$
$824$	24.6511	+	42.6969i	0.858761	+	1.48742i
$825$		0			0
$826$	−27.6781	−	81.5348i	−0.963044	−	2.83696i
$827$	2.34114	+	14.7814i	0.0814094	+	0.513999i	0.994371	+	0.105954i	$0.0337895\pi$
$827$	2.34114	+	14.7814i	0.0814094	+	0.513999i	−0.912962	+	0.408045i	$0.866211\pi$
$828$	−0.231385	−	4.41509i	−0.00804118	−	0.153435i
$829$	−12.2556	−	2.60501i	−0.425654	−	0.0904756i	−0.00989649	−	0.999951i	$-0.503150\pi$
$829$	−12.2556	−	2.60501i	−0.425654	−	0.0904756i	−0.415758	+	0.909475i	$0.636484\pi$
$830$		0			0
$831$	7.96923	+	37.4923i	0.276449	+	1.30059i
$832$	−8.86689	+	8.86689i	−0.307404	+	0.307404i
$833$	−18.3412	−	26.6857i	−0.635485	−	0.924604i
$834$	−20.1010	−	27.6666i	−0.696040	−	0.958016i
$835$		0			0
$836$	0.257492	+	0.578337i	0.00890556	+	0.0200022i
$837$	−16.0892	+	19.8686i	−0.556125	+	0.686758i
$838$	−6.48811	−	16.9021i	−0.224128	−	0.583873i
$839$	28.6107	+	20.7869i	0.987750	+	0.717643i	0.959427	−	0.281956i	$-0.0909833\pi$
$839$	28.6107	+	20.7869i	0.987750	+	0.717643i	0.0283231	+	0.999599i	$0.490983\pi$
$840$		0			0
$841$	−2.45765	+	1.78558i	−0.0847464	+	0.0615719i
$842$	−50.0381	−	32.4951i	−1.72443	−	1.11986i
$843$	−79.0401	+	21.1787i	−2.72228	+	0.729434i
$844$	13.0846	−	11.7815i	0.450392	−	0.405535i
$845$		0			0
$846$	−74.2898	+	24.1382i	−2.55414	+	0.829889i
$847$	−27.0037	+	10.7737i	−0.927859	+	0.370187i
$848$	120.719	−	19.1200i	4.14551	−	0.656584i
$849$	−41.1553	+	23.7610i	−1.41244	+	0.815475i
$850$		0			0
$851$	−0.0399564	+	0.0692065i	−0.00136969	+	0.00237237i
$852$	−71.3246	−	88.0785i	−2.44354	−	3.01752i
$853$	12.7236	−	24.9715i	0.435648	−	0.855007i	−0.563927	−	0.825825i	$-0.690710\pi$
$853$	12.7236	−	24.9715i	0.435648	−	0.855007i	0.999574	−	0.0291816i	$-0.00929012\pi$
$854$	58.7393	−	6.95274i	2.01002	−	0.237918i
$855$		0			0
$856$	−92.6438	+	19.6920i	−3.16650	+	0.673060i
$857$	−6.76369	−	25.2424i	−0.231043	−	0.862265i	−0.979893	−	0.199525i	$-0.936060\pi$
$857$	−6.76369	−	25.2424i	−0.231043	−	0.862265i	0.748850	−	0.662740i	$-0.230606\pi$
$858$	−1.30364	−	0.0683209i	−0.0445056	−	0.00233244i
$859$	−22.9720	−	10.2278i	−0.783796	−	0.348968i	−0.0244881	−	0.999700i	$-0.507796\pi$
$859$	−22.9720	−	10.2278i	−0.783796	−	0.348968i	−0.759308	+	0.650732i	$0.774462\pi$
$860$		0			0
$861$	−22.8769	+	21.1475i	−0.779642	+	0.720705i
$862$	−14.2851	−	2.26254i	−0.486553	−	0.0770625i
$863$	29.2115	−	11.2133i	0.994373	−	0.381704i	0.193866	−	0.981028i	$-0.437897\pi$
$863$	29.2115	−	11.2133i	0.994373	−	0.381704i	0.800506	+	0.599324i	$0.204564\pi$
$864$	82.7404	−	36.8384i	2.81489	−	1.25327i
$865$		0			0
$866$	31.7642	−	71.3436i	1.07939	−	2.42435i
$867$	−5.96150	−	11.7001i	−0.202463	−	0.397356i
$868$	2.45558	+	37.4602i	0.0833479	+	1.27148i
$869$	0.622995	+	0.202423i	0.0211337	+	0.00686674i
$870$		0			0
$871$	0.698176	−	3.28466i	0.0236568	−	0.111297i
$872$	−45.2302	−	69.6485i	−1.53169	−	2.35859i
$873$	−49.7111	+	40.2553i	−1.68247	+	1.36243i
$874$	0.501379			0.0169594
$875$		0			0
$876$	−196.907			−6.65288
$877$	−10.7177	+	8.67899i	−0.361910	+	0.293069i	−0.792978	−	0.609251i	$-0.791470\pi$
$877$	−10.7177	+	8.67899i	−0.361910	+	0.293069i	0.431068	+	0.902319i	$0.358137\pi$
$878$	−10.4972	−	16.1643i	−0.354263	−	0.545517i
$879$	14.2738	−	67.1528i	0.481442	−	2.26501i
$880$		0			0
$881$	3.33473	+	1.08352i	0.112350	+	0.0365047i	0.364652	−	0.931144i	$-0.381188\pi$
$881$	3.33473	+	1.08352i	0.112350	+	0.0365047i	−0.252302	+	0.967648i	$0.581188\pi$
$882$	65.8276	−	85.7911i	2.21653	−	2.88874i
$883$	16.0761	+	31.5512i	0.541005	+	1.06178i	0.986077	+	0.166288i	$0.0531781\pi$
$883$	16.0761	+	31.5512i	0.541005	+	1.06178i	−0.445072	+	0.895495i	$0.646822\pi$
$884$	−14.3492	+	32.2287i	−0.482615	+	1.08397i
$885$		0			0
$886$	−21.5739	+	9.60533i	−0.724790	+	0.322697i
$887$	0.401690	−	0.154194i	0.0134874	−	0.00517734i	−0.351615	−	0.936145i	$-0.614367\pi$
$887$	0.401690	−	0.154194i	0.0134874	−	0.00517734i	0.365102	+	0.930967i	$0.381034\pi$
$888$	−11.2292	−	1.77854i	−0.376829	−	0.0596838i
$889$	−7.64265	+	24.6141i	−0.256326	+	0.825530i
$890$		0			0
$891$	0.795511	+	0.354184i	0.0266506	+	0.0118656i
$892$	−3.82244	−	0.200326i	−0.127985	−	0.00670740i
$893$	−1.62096	−	6.04950i	−0.0542433	−	0.202439i
$894$	13.2088	−	2.80761i	0.441768	−	0.0939006i
$895$		0			0
$896$	−0.103579	+	0.241092i	−0.00346032	+	0.00805430i
$897$	−0.331847	+	0.651286i	−0.0110800	+	0.0217458i
$898$	3.23947	+	4.00041i	0.108102	+	0.133495i
$899$	7.49033	−	12.9736i	0.249816	−	0.432695i
$900$		0			0
$901$	50.7997	−	29.3292i	1.69238	−	0.977097i
$902$	−1.07795	+	0.170730i	−0.0358917	+	0.00568469i
$903$	38.5881	+	30.4199i	1.28413	+	1.01231i
$904$	27.3924	−	8.90032i	0.911057	−	0.296020i
$905$		0			0
$906$	−31.5899	+	28.4436i	−1.04950	+	0.944977i
$907$	12.2853	−	3.29185i	0.407928	−	0.109304i	−0.0490192	−	0.998798i	$-0.515610\pi$
$907$	12.2853	−	3.29185i	0.407928	−	0.109304i	0.456947	+	0.889494i	$0.348943\pi$
$908$	32.0065	+	20.7853i	1.06217	+	0.689784i
$909$	−44.2538	+	32.1523i	−1.46781	+	1.06642i
$910$		0			0
$911$	5.78586	+	4.20367i	0.191694	+	0.139274i	0.679493	−	0.733682i	$-0.262200\pi$
$911$	5.78586	+	4.20367i	0.191694	+	0.139274i	−0.487799	+	0.872956i	$0.662200\pi$
$912$	12.7725	+	33.2736i	0.422940	+	1.10180i
$913$	0.596169	−	0.736208i	0.0197303	−	0.0243649i
$914$	2.16443	+	4.86139i	0.0715930	+	0.160801i
$915$		0			0
$916$	−59.5532	−	81.9680i	−1.96769	−	2.70830i
$917$	−5.36018	+	21.1065i	−0.177009	+	0.696998i
$918$	74.3130	−	74.3130i	2.45270	−	2.45270i
$919$	−10.7899	−	50.7623i	−0.355925	−	1.67449i	−0.683720	−	0.729745i	$-0.739639\pi$
$919$	−10.7899	−	50.7623i	−0.355925	−	1.67449i	0.327795	−	0.944749i	$-0.393694\pi$
$920$		0			0
$921$	29.2438	+	6.21595i	0.963615	+	0.204823i
$922$	3.68622	+	70.3373i	0.121399	+	2.31643i
$923$	1.94461	+	12.2778i	0.0640076	+	0.404128i
$924$	3.82293	−	1.29775i	0.125765	−	0.0426927i
$925$		0			0
$926$	−8.31699	−	14.4055i	−0.273313	−	0.473393i
$927$	−14.1487	+	36.8587i	−0.464705	+	1.21060i
$928$	−44.5088	+	28.9044i	−1.46107	+	0.948832i
$929$	−12.6656	+	14.0666i	−0.415546	+	0.461510i	−0.914184	−	0.405300i	$-0.867167\pi$
$929$	−12.6656	+	14.0666i	−0.415546	+	0.461510i	0.498638	+	0.866810i	$0.333834\pi$
$930$		0			0
$931$	6.59288	+	5.63066i	0.216073	+	0.184537i
$932$	−59.1597	−	59.1597i	−1.93784	−	1.93784i
$933$	11.0791	−	17.0603i	0.362714	−	0.558531i
$934$	6.54734	+	62.2937i	0.214235	+	2.03831i
$935$		0			0
$936$	−68.6114	−	7.21135i	−2.24263	−	0.235710i
$937$	3.85562	−	24.3434i	0.125958	−	0.795266i	−0.841132	−	0.540830i	$-0.818110\pi$
$937$	3.85562	−	24.3434i	0.125958	−	0.795266i	0.967090	−	0.254436i	$-0.0818897\pi$
$938$	2.48768	+	14.4767i	0.0812257	+	0.472683i
$939$	16.2683	−	22.3914i	0.530895	−	0.730714i
$940$		0			0
$941$	41.5233	−	4.36427i	1.35362	−	0.142271i	0.600221	−	0.799834i	$-0.295079\pi$
$941$	41.5233	−	4.36427i	1.35362	−	0.142271i	0.753400	+	0.657563i	$0.228413\pi$
$942$	3.11893	−	59.5127i	0.101620	−	1.93903i
$943$	−0.158165	+	0.590281i	−0.00515057	+	0.0192222i
$944$	37.1015	−	114.187i	1.20755	−	3.71646i
$945$		0			0
$946$	0.531927	+	1.63710i	0.0172944	+	0.0532268i
$947$	34.0499	−	1.78448i	1.10647	−	0.0579878i	0.509666	−	0.860372i	$-0.329769\pi$
$947$	34.0499	−	1.78448i	1.10647	−	0.0579878i	0.596808	+	0.802384i	$0.296436\pi$
$948$	83.1942	+	31.9353i	2.70202	+	1.03721i
$949$	18.7036	+	10.7985i	0.607145	+	0.350535i
$950$		0			0
$951$			53.5562i			1.73668i
$952$	3.54701	−	90.2964i	0.114959	−	2.92652i
$953$	−3.18846	−	1.62460i	−0.103284	−	0.0526261i	0.401585	−	0.915822i	$-0.368459\pi$
$953$	−3.18846	−	1.62460i	−0.103284	−	0.0526261i	−0.504870	+	0.863196i	$0.668459\pi$
$954$	145.574	+	131.075i	4.71313	+	4.24373i
$955$		0			0
$956$	33.1187	+	36.7821i	1.07114	+	1.18962i
$957$	−1.55616	−	0.416971i	−0.0503034	−	0.0134788i
$958$	−3.90164	+	1.98798i	−0.126056	+	0.0642289i
$959$	31.6623	−	14.5968i	1.02243	−	0.471356i
$960$		0			0
$961$	−2.33683	+	22.2334i	−0.0753815	+	0.717207i
$962$	1.65492	+	1.34013i	0.0533569	+	0.0432075i
$963$	−58.9436	−	47.7316i	−1.89943	−	1.53813i
$964$	−13.9196	+	132.437i	−0.448321	+	4.26549i
$965$		0			0
$966$	0.292539	−	3.18397i	0.00941230	−	0.102443i
$967$	19.1875	−	9.77652i	0.617028	−	0.314392i	−0.117393	−	0.993086i	$-0.537454\pi$
$967$	19.1875	−	9.77652i	0.617028	−	0.314392i	0.734421	+	0.678694i	$0.237454\pi$
$968$	−78.3715	−	20.9996i	−2.51896	−	0.674952i
$969$	11.4454	+	12.7115i	0.367681	+	0.408351i
$970$		0			0
$971$	−40.5671	−	36.5268i	−1.30186	−	1.17220i	−0.973765	−	0.227557i	$-0.926926\pi$
$971$	−40.5671	−	36.5268i	−1.30186	−	1.17220i	−0.328096	−	0.944644i	$-0.606407\pi$
$972$	−6.62503	−	3.37562i	−0.212498	−	0.108273i
$973$	−5.40121	−	10.2658i	−0.173155	−	0.329106i
$974$		−	80.5628i		−	2.58140i
$975$		0			0
$976$	71.4272	+	41.2385i	2.28633	+	1.32001i
$977$	12.0845	+	4.63881i	0.386618	+	0.148409i	0.543910	−	0.839143i	$-0.316943\pi$
$977$	12.0845	+	4.63881i	0.386618	+	0.148409i	−0.157292	+	0.987552i	$0.550277\pi$
$978$	−160.346	+	8.40340i	−5.12732	+	0.268711i
$979$	0.445009	+	1.36960i	0.0142225	+	0.0437725i
$980$		0			0
$981$	20.5506	−	63.2483i	0.656131	−	2.01936i
$982$	4.28629	−	15.9967i	0.136781	−	0.510474i
$983$	0.408216	−	7.78922i	0.0130201	−	0.248438i	−0.984364	−	0.176148i	$-0.943636\pi$
$983$	0.408216	−	7.78922i	0.0130201	−	0.248438i	0.997384	−	0.0722893i	$-0.0230305\pi$
$984$	−86.4656	+	9.08790i	−2.75642	+	0.289712i
$985$		0			0
$986$	−36.1964	+	49.8201i	−1.15273	+	1.58660i
$987$	−39.3628	+	6.76410i	−1.25293	+	0.215304i
$988$	1.47768	−	9.32968i	0.0470112	−	0.296817i
$989$	0.958565	+	0.100749i	0.0304806	+	0.00320364i
$990$		0			0
$991$	−2.39825	−	22.8178i	−0.0761830	−	0.724833i	−0.964228	−	0.265076i	$-0.914603\pi$
$991$	−2.39825	−	22.8178i	−0.0761830	−	0.724833i	0.888045	−	0.459757i	$-0.152064\pi$
$992$	−16.6783	+	25.6824i	−0.529538	+	0.815417i
$993$	−44.9754	−	44.9754i	−1.42725	−	1.42725i
$994$	−27.8023	−	46.7305i	−0.881834	−	1.48220i
$995$		0			0
$996$	86.2327	−	95.7711i	2.73239	−	3.03462i
$997$	9.51219	−	6.17729i	0.301254	−	0.195637i	−0.385156	−	0.922852i	$-0.625852\pi$
$997$	9.51219	−	6.17729i	0.301254	−	0.195637i	0.686410	+	0.727215i	$0.259186\pi$
$998$	−39.2146	+	102.158i	−1.24132	+	3.23374i
$999$	−2.24251	−	3.88414i	−0.0709499	−	0.122889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.c.332.1		288
5.2	odd	4		875.2.bb.b.668.1		288
5.3	odd	4		875.2.bb.a.668.18		288
5.4	even	2		175.2.x.a.87.18	yes	288
7.5	odd	6	inner	875.2.bb.c.82.18		288
25.2	odd	20		175.2.x.a.73.1	yes	288
25.11	even	5		875.2.bb.a.157.18		288
25.14	even	10		875.2.bb.b.157.1		288
25.23	odd	20	inner	875.2.bb.c.843.18		288
35.12	even	12		875.2.bb.b.418.1		288
35.19	odd	6		175.2.x.a.12.1	✓	288
35.33	even	12		875.2.bb.a.418.18		288
175.61	odd	30		875.2.bb.a.782.18		288
175.89	odd	30		875.2.bb.b.782.1		288
175.152	even	60		175.2.x.a.173.18	yes	288
175.173	even	60	inner	875.2.bb.c.593.1		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.12.1	✓	288	35.19	odd	6
175.2.x.a.73.1	yes	288	25.2	odd	20
175.2.x.a.87.18	yes	288	5.4	even	2
175.2.x.a.173.18	yes	288	175.152	even	60
875.2.bb.a.157.18		288	25.11	even	5
875.2.bb.a.418.18		288	35.33	even	12
875.2.bb.a.668.18		288	5.3	odd	4
875.2.bb.a.782.18		288	175.61	odd	30
875.2.bb.b.157.1		288	25.14	even	10
875.2.bb.b.418.1		288	35.12	even	12
875.2.bb.b.668.1		288	5.2	odd	4
875.2.bb.b.782.1		288	175.89	odd	30
875.2.bb.c.82.18		288	7.5	odd	6	inner
875.2.bb.c.332.1		288	1.1	even	1	trivial
875.2.bb.c.593.1		288	175.173	even	60	inner
875.2.bb.c.843.18		288	25.23	odd	20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.03043 + 1.64421i) q^{2} +(-1.62597 - 2.50378i) q^{3} +(1.00339 - 4.72059i) q^{4} +(7.41816 + 2.41031i) q^{6} +(2.37291 + 1.17017i) q^{7} +(3.35206 + 6.57879i) q^{8} +(-2.40492 + 5.40154i) q^{9} +(-0.0967529 + 0.0430772i) q^{11} +(-13.4508 + 5.16329i) q^{12} +(1.56081 + 0.247208i) q^{13} +(-6.74202 + 1.52562i) q^{14} +(-8.80536 - 3.92040i) q^{16} +(-4.61951 - 0.242098i) q^{17} +(-3.99823 - 14.9216i) q^{18} +(1.21152 - 0.257516i) q^{19} +(-0.928454 - 7.84391i) q^{21} +(0.125622 - 0.246547i) q^{22} +(-0.0975052 - 0.120409i) q^{23} +(11.0215 - 19.0898i) q^{24} +(-3.57557 + 2.06436i) q^{26} +(8.58862 - 1.36030i) q^{27} +(7.90484 - 10.0274i) q^{28} +(-4.84593 + 1.57454i) q^{29} +(-2.18491 + 1.96730i) q^{31} +(10.0607 - 2.69575i) q^{32} +(0.265174 + 0.172206i) q^{33} +(9.77764 - 7.10387i) q^{34} +(23.0854 + 16.7725i) q^{36} +(-0.184837 - 0.481518i) q^{37} +(-2.03649 + 2.51485i) q^{38} +(-1.91888 - 4.30988i) q^{39} +(-2.31834 - 3.19093i) q^{41} +(14.7822 + 14.3999i) q^{42} +(-4.39882 + 4.39882i) q^{43} +(0.106269 + 0.499954i) q^{44} +(0.395954 + 0.0841627i) q^{46} +(-0.264637 - 5.04958i) q^{47} +(4.50147 + 28.4212i) q^{48} +(4.26142 + 5.55340i) q^{49} +(6.90505 + 11.9599i) q^{51} +(2.73307 - 7.11989i) q^{52} +(-10.6348 + 6.90633i) q^{53} +(-15.2019 + 16.8835i) q^{54} +(0.255867 + 19.5333i) q^{56} +(-2.61466 - 2.61466i) q^{57} +(7.25044 - 11.1647i) q^{58} +(1.30205 + 12.3882i) q^{59} +(-8.51001 - 0.894439i) q^{61} +(1.20165 - 7.58691i) q^{62} +(-12.0274 + 10.0032i) q^{63} +(-4.66418 + 6.41969i) q^{64} +(-0.821558 + 0.0863492i) q^{66} +(0.111213 - 2.12208i) q^{67} +(-5.77803 + 21.5639i) q^{68} +(-0.142937 + 0.439913i) q^{69} +(2.43082 + 7.48129i) q^{71} +(-43.5970 + 2.28482i) q^{72} +(12.7590 + 4.89772i) q^{73} +(1.16701 + 0.673776i) q^{74} -5.97747i q^{76} +(-0.279994 - 0.0109987i) q^{77} +(10.9825 + 5.59585i) q^{78} +(-4.59640 - 4.13862i) q^{79} +(-5.50165 - 6.11020i) q^{81} +(9.95377 + 2.66710i) q^{82} +(-7.96975 + 4.06079i) q^{83} +(-37.9595 - 3.48767i) q^{84} +(1.69891 - 16.1641i) q^{86} +(11.8217 + 9.57299i) q^{87} +(-0.607717 - 0.492120i) q^{88} +(1.42130 - 13.5228i) q^{89} +(3.41439 + 2.41301i) q^{91} +(-0.666237 + 0.339465i) q^{92} +(8.47830 + 2.27175i) q^{93} +(8.83988 + 9.81768i) q^{94} +(-23.1080 - 20.8065i) q^{96} +(9.63928 + 4.91146i) q^{97} +(-17.7835 - 4.26912i) q^{98} -0.626212i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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