LMFDB - Embedded newform 735.2.s.l.656.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(521,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("735.521"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,3,-2,3,4,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			656.1
Root			$-2.06288i$ of defining polynomial
Character	$\chi$	$=$	735.656
Dual form			735.2.s.l.521.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.78651 - 1.03144i) q^{2} +(-1.08415 - 1.35078i) q^{3} +(1.12774 + 1.95330i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.543588 + 3.53142i) q^{6} -0.527019i q^{8} +(-0.649237 + 2.92891i) q^{9} +(-1.78651 + 1.03144i) q^{10} +(4.06348 - 2.34605i) q^{11} +(1.41585 - 3.64100i) q^{12} +0.638688i q^{13} +(-1.71189 + 0.263509i) q^{15} +(1.71189 - 2.96508i) q^{16} +(-2.07462 - 3.59334i) q^{17} +(4.18086 - 4.56286i) q^{18} +(0.776975 + 0.448587i) q^{19} +2.25548 q^{20} -9.67925 q^{22} +(-5.89275 - 3.40218i) q^{23} +(-0.711889 + 0.571367i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.658769 - 1.14102i) q^{26} +(4.66019 - 2.29839i) q^{27} -2.14740i q^{29} +(3.33010 + 1.29495i) q^{30} +(2.02453 - 1.16886i) q^{31} +(-7.02943 + 4.05844i) q^{32} +(-7.57444 - 2.94542i) q^{33} +8.55938i q^{34} +(-6.45320 + 2.03489i) q^{36} +(5.69122 - 9.85748i) q^{37} +(-0.925382 - 1.60281i) q^{38} +(0.862730 - 0.692434i) q^{39} +(-0.456412 - 0.263509i) q^{40} -4.10624 q^{41} +3.14924 q^{43} +(9.16509 + 5.29147i) q^{44} +(2.21189 + 2.02671i) q^{45} +(7.01829 + 12.1560i) q^{46} +(-3.40471 + 5.89714i) q^{47} +(-5.86113 + 0.902197i) q^{48} +2.06288i q^{50} +(-2.60464 + 6.69809i) q^{51} +(-1.24755 + 0.720273i) q^{52} +(-1.96187 + 1.13269i) q^{53} +(-10.6961 - 0.700610i) q^{54} -4.69211i q^{55} +(-0.236414 - 1.53586i) q^{57} +(-2.21492 + 3.83635i) q^{58} +(-0.254055 - 0.440035i) q^{59} +(-2.44528 - 3.04666i) q^{60} +(-4.48946 - 2.59199i) q^{61} -4.82244 q^{62} +9.89660 q^{64} +(0.553120 + 0.319344i) q^{65} +(10.4938 + 13.0746i) q^{66} +(-2.41425 - 4.18160i) q^{67} +(4.67925 - 8.10471i) q^{68} +(1.79301 + 11.6483i) q^{69} +1.22800i q^{71} +(1.54359 + 0.342160i) q^{72} +(-12.5197 + 7.22826i) q^{73} +(-20.3348 + 11.7403i) q^{74} +(-0.627739 + 1.61429i) q^{75} +2.02356i q^{76} +(-2.25548 + 0.347183i) q^{78} +(-4.54056 + 7.86448i) q^{79} +(-1.71189 - 2.96508i) q^{80} +(-8.15698 - 3.80311i) q^{81} +(7.33583 + 4.23534i) q^{82} +2.76359 q^{83} -4.14924 q^{85} +(-5.62613 - 3.24825i) q^{86} +(-2.90067 + 2.32810i) q^{87} +(-1.23641 - 2.14153i) q^{88} +(-6.90067 + 11.9523i) q^{89} +(-1.86113 - 5.90216i) q^{90} -15.3471i q^{92} +(-3.77377 - 1.46748i) q^{93} +(12.1651 - 7.02352i) q^{94} +(0.776975 - 0.448587i) q^{95} +(13.1030 + 5.09528i) q^{96} -12.9085i q^{97} +(4.23321 + 13.4247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 2 q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{9} + 3 q^{10} + 18 q^{12} - q^{15} + q^{16} - 12 q^{17} + 26 q^{18} - 9 q^{19} + 6 q^{20} - 40 q^{22} - 27 q^{23} + 7 q^{24} - 4 q^{25} - 6 q^{26}+ \cdots - 34 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^9 + 3 * q^10 + 18 * q^12 - q^15 + q^16 - 12 * q^17 + 26 * q^18 - 9 * q^19 + 6 * q^20 - 40 * q^22 - 27 * q^23 + 7 * q^24 - 4 * q^25 - 6 * q^26 + 4 * q^27 + 10 * q^30 + 21 * q^31 - 21 * q^32 - 4 * q^33 + 9 * q^36 + 7 * q^37 - 12 * q^38 + 15 * q^39 - 3 * q^40 - 30 * q^41 + 16 * q^43 + 5 * q^45 - 7 * q^46 - 6 * q^47 - 25 * q^48 + 12 * q^51 - 30 * q^52 - 24 * q^53 - 7 * q^54 + 6 * q^57 - 13 * q^58 - 12 * q^59 + 9 * q^60 - 15 * q^61 + 24 * q^62 + 38 * q^64 + 3 * q^65 + 16 * q^66 + 4 * q^67 - 13 * q^69 + 13 * q^72 - 15 * q^73 - 54 * q^74 + q^75 - 6 * q^78 - 29 * q^79 - q^80 + 28 * q^81 - 27 * q^82 + 30 * q^83 - 24 * q^85 - 9 * q^86 + 29 * q^87 - 2 * q^88 - 3 * q^89 + 7 * q^90 + 45 * q^93 + 24 * q^94 - 9 * q^95 + 42 * q^96 - 34 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.78651	−	1.03144i	−1.26325	−	0.729338i	−0.289549	−	0.957163i	$-0.593505\pi$
$2$	−1.78651	−	1.03144i	−1.26325	−	0.729338i	−0.973702	+	0.227825i	$0.926839\pi$
$3$	−1.08415	−	1.35078i	−0.625934	−	0.779876i
$3$	−1.08415	−	1.35078i	−0.625934	−	0.779876i
$4$	1.12774	+	1.95330i	0.563869	+	0.976650i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.543588	+	3.53142i	0.221919	+	1.44170i
$7$		0			0
$7$		0			0
$8$		−	0.527019i		−	0.186329i
$9$	−0.649237	+	2.92891i	−0.216412	+	0.976302i
$10$	−1.78651	+	1.03144i	−0.564943	+	0.326170i
$11$	4.06348	−	2.34605i	1.22519	−	0.707362i	0.259167	−	0.965833i	$-0.416552\pi$
$11$	4.06348	−	2.34605i	1.22519	−	0.707362i	0.966019	+	0.258471i	$0.0832186\pi$
$12$	1.41585	−	3.64100i	0.408721	−	1.05107i
$13$			0.638688i			0.177140i	0.996070	+	0.0885701i	$0.0282297\pi$
$13$			0.638688i			0.177140i	−0.996070	+	0.0885701i	$0.971770\pi$
$14$		0			0
$15$	−1.71189	+	0.263509i	−0.442008	+	0.0680378i
$16$	1.71189	−	2.96508i	0.427972	−	0.741270i
$17$	−2.07462	−	3.59334i	−0.503169	−	0.871514i	−0.999993	−	0.00366299i	$-0.998834\pi$
$17$	−2.07462	−	3.59334i	−0.503169	−	0.871514i	0.496824	−	0.867851i	$-0.334499\pi$
$18$	4.18086	−	4.56286i	0.985438	−	1.07548i
$19$	0.776975	+	0.448587i	0.178250	+	0.102913i	0.586470	−	0.809971i	$-0.300517\pi$
$19$	0.776975	+	0.448587i	0.178250	+	0.102913i	−0.408220	+	0.912884i	$0.633850\pi$
$20$	2.25548			0.504340
$21$		0			0
$22$	−9.67925			−2.06362
$23$	−5.89275	−	3.40218i	−1.22872	−	0.709403i	−0.261960	−	0.965079i	$-0.584369\pi$
$23$	−5.89275	−	3.40218i	−1.22872	−	0.709403i	−0.966763	+	0.255675i	$0.917702\pi$
$24$	−0.711889	+	0.571367i	−0.145314	+	0.116630i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.658769	−	1.14102i	0.129195	−	0.223773i
$27$	4.66019	−	2.29839i	0.896854	−	0.442326i
$28$		0			0
$29$		−	2.14740i		−	0.398762i	−0.979922	−	0.199381i	$-0.936107\pi$
$29$		−	2.14740i		−	0.398762i	0.979922	−	0.199381i	$-0.0638932\pi$
$30$	3.33010	+	1.29495i	0.607989	+	0.236424i
$31$	2.02453	−	1.16886i	0.363615	−	0.209933i	−0.307050	−	0.951693i	$-0.599342\pi$
$31$	2.02453	−	1.16886i	0.363615	−	0.209933i	0.670666	+	0.741760i	$0.266009\pi$
$32$	−7.02943	+	4.05844i	−1.24264	+	0.717438i
$33$	−7.57444	−	2.94542i	−1.31854	−	0.512731i
$34$			8.55938i			1.46792i
$35$		0			0
$36$	−6.45320	+	2.03489i	−1.07553	+	0.339148i
$37$	5.69122	−	9.85748i	0.935631	−	1.62056i	0.162126	−	0.986770i	$-0.448165\pi$
$37$	5.69122	−	9.85748i	0.935631	−	1.62056i	0.773505	−	0.633790i	$-0.218502\pi$
$38$	−0.925382	−	1.60281i	−0.150117	−	0.260010i
$39$	0.862730	−	0.692434i	0.138147	−	0.110878i
$40$	−0.456412	−	0.263509i	−0.0721650	−	0.0416645i
$41$	−4.10624			−0.641287			−0.320643	−	0.947200i	$-0.603899\pi$
$41$	−4.10624			−0.641287			−0.320643	+	0.947200i	$0.603899\pi$
$42$		0			0
$43$	3.14924			0.480254			0.240127	−	0.970741i	$-0.422811\pi$
$43$	3.14924			0.480254			0.240127	+	0.970741i	$0.422811\pi$
$44$	9.16509	+	5.29147i	1.38169	+	0.797719i
$45$	2.21189	+	2.02671i	0.329729	+	0.302124i
$46$	7.01829	+	12.1560i	1.03479	+	1.79231i
$47$	−3.40471	+	5.89714i	−0.496629	+	0.860186i	−0.999992	−	0.00388861i	$-0.998762\pi$
$47$	−3.40471	+	5.89714i	−0.496629	+	0.860186i	0.503364	+	0.864075i	$0.332096\pi$
$48$	−5.86113	+	0.902197i	−0.845981	+	0.130221i
$49$		0			0
$50$			2.06288i			0.291735i
$51$	−2.60464	+	6.69809i	−0.364722	+	0.937920i
$52$	−1.24755	+	0.720273i	−0.173004	+	0.0998839i
$53$	−1.96187	+	1.13269i	−0.269484	+	0.155587i	−0.628653	−	0.777686i	$-0.716393\pi$
$53$	−1.96187	+	1.13269i	−0.269484	+	0.155587i	0.359169	+	0.933272i	$0.383060\pi$
$54$	−10.6961	−	0.700610i	−1.45556	−	0.0953410i
$55$		−	4.69211i		−	0.632683i
$56$		0			0
$57$	−0.236414	−	1.53586i	−0.0313138	−	0.203430i
$58$	−2.21492	+	3.83635i	−0.290833	+	0.503737i
$59$	−0.254055	−	0.440035i	−0.0330751	−	0.0572877i	0.849014	−	0.528370i	$-0.177197\pi$
$59$	−0.254055	−	0.440035i	−0.0330751	−	0.0572877i	−0.882089	+	0.471083i	$0.843863\pi$
$60$	−2.44528	−	3.04666i	−0.315684	−	0.393323i
$61$	−4.48946	−	2.59199i	−0.574816	−	0.331870i	0.184255	−	0.982879i	$-0.441013\pi$
$61$	−4.48946	−	2.59199i	−0.574816	−	0.331870i	−0.759070	+	0.651008i	$0.774346\pi$
$62$	−4.82244			−0.612450
$63$		0			0
$64$	9.89660			1.23708
$65$	0.553120	+	0.319344i	0.0686061	+	0.0396097i
$66$	10.4938	+	13.0746i	1.29169	+	1.60937i
$67$	−2.41425	−	4.18160i	−0.294947	−	0.510863i	0.680026	−	0.733188i	$-0.261969\pi$
$67$	−2.41425	−	4.18160i	−0.294947	−	0.510863i	−0.974973	+	0.222325i	$0.928635\pi$
$68$	4.67925	−	8.10471i	0.567443	−	0.982840i
$69$	1.79301	+	11.6483i	0.215853	+	1.40229i
$70$		0			0
$71$			1.22800i			0.145737i	0.997342	+	0.0728686i	$0.0232154\pi$
$71$			1.22800i			0.145737i	−0.997342	+	0.0728686i	$0.976785\pi$
$72$	1.54359	+	0.342160i	0.181914	+	0.0403239i
$73$	−12.5197	+	7.22826i	−1.46532	+	0.846004i	−0.999249	−	0.0387429i	$-0.987665\pi$
$73$	−12.5197	+	7.22826i	−1.46532	+	0.846004i	−0.466072	+	0.884747i	$0.654331\pi$
$74$	−20.3348	+	11.7403i	−2.36387	+	1.36478i
$75$	−0.627739	+	1.61429i	−0.0724850	+	0.186403i
$76$			2.02356i			0.232118i
$77$		0			0
$78$	−2.25548	+	0.347183i	−0.255382	+	0.0393108i
$79$	−4.54056	+	7.86448i	−0.510853	+	0.884824i	0.489068	+	0.872246i	$0.337337\pi$
$79$	−4.54056	+	7.86448i	−0.510853	+	0.884824i	−0.999921	+	0.0125778i	$0.995996\pi$
$80$	−1.71189	−	2.96508i	−0.191395	−	0.331506i
$81$	−8.15698	−	3.80311i	−0.906331	−	0.422568i
$82$	7.33583	+	4.23534i	0.810107	+	0.467715i
$83$	2.76359			0.303343			0.151671	−	0.988431i	$-0.451534\pi$
$83$	2.76359			0.303343			0.151671	+	0.988431i	$0.451534\pi$
$84$		0			0
$85$	−4.14924			−0.450048
$86$	−5.62613	−	3.24825i	−0.606682	−	0.350268i
$87$	−2.90067	+	2.32810i	−0.310985	+	0.249599i
$88$	−1.23641	−	2.14153i	−0.131802	−	0.228288i
$89$	−6.90067	+	11.9523i	−0.731470	+	1.26694i	0.224785	+	0.974408i	$0.427832\pi$
$89$	−6.90067	+	11.9523i	−0.731470	+	1.26694i	−0.956255	+	0.292535i	$0.905501\pi$
$90$	−1.86113	−	5.90216i	−0.196180	−	0.622142i
$91$		0			0
$92$		−	15.3471i		−	1.60004i
$93$	−3.77377	−	1.46748i	−0.391321	−	0.152170i
$94$	12.1651	−	7.02352i	1.25473	−	0.724421i
$95$	0.776975	−	0.448587i	0.0797160	−	0.0460241i
$96$	13.1030	+	5.09528i	1.33732	+	0.520035i
$97$		−	12.9085i		−	1.31066i	−0.755344	−	0.655329i	$-0.772530\pi$
$97$		−	12.9085i		−	1.31066i	0.755344	−	0.655329i	$-0.227470\pi$
$98$		0			0
$99$	4.23321	+	13.4247i	0.425453	+	1.34923i
$100$	1.12774	−	1.95330i	0.112774	−	0.195330i
$101$	−4.51989	−	7.82869i	−0.449746	−	0.778983i	0.548623	−	0.836070i	$-0.315152\pi$
$101$	−4.51989	−	7.82869i	−0.449746	−	0.778983i	−0.998369	+	0.0570865i	$0.981819\pi$
$102$	11.5619	−	9.27965i	1.14480	−	0.918823i
$103$	13.4412	+	7.76030i	1.32440	+	0.764645i	0.984428	−	0.175789i	$-0.0562476\pi$
$103$	13.4412	+	7.76030i	1.32440	+	0.764645i	0.339976	+	0.940434i	$0.389581\pi$
$104$	0.336601			0.0330064
$105$		0			0
$106$	4.67320			0.453901
$107$	4.64012	+	2.67897i	0.448577	+	0.258986i	0.707229	−	0.706985i	$-0.249945\pi$
$107$	4.64012	+	2.67897i	0.448577	+	0.258986i	−0.258652	+	0.965971i	$0.583278\pi$
$108$	9.74493	+	6.51076i	0.937707	+	0.626499i
$109$	−0.679436	−	1.17682i	−0.0650782	−	0.112719i	0.831650	−	0.555299i	$-0.187396\pi$
$109$	−0.679436	−	1.17682i	−0.0650782	−	0.112719i	−0.896729	+	0.442581i	$0.854063\pi$
$110$	−4.83963	+	8.38248i	−0.461440	+	0.799238i
$111$	−19.4855	+	2.99938i	−1.84948	+	0.284689i
$112$		0			0
$113$		−	11.9390i		−	1.12312i	−0.827435	−	0.561562i	$-0.810201\pi$
$113$		−	11.9390i		−	1.12312i	0.827435	−	0.561562i	$-0.189799\pi$
$114$	−1.16180	+	2.98768i	−0.108812	+	0.279821i
$115$	−5.89275	+	3.40218i	−0.549502	+	0.317255i
$116$	4.19452	−	2.42171i	0.389451	−	0.224850i
$117$	−1.87066	−	0.414660i	−0.172942	−	0.0383353i
$118$			1.04817i			0.0964917i
$119$		0			0
$120$	0.138874	+	0.902197i	0.0126774	+	0.0823590i
$121$	5.50793	−	9.54001i	0.500721	−	0.867274i
$122$	5.34696	+	9.26121i	0.484091	+	0.838471i
$123$	4.45178	+	5.54665i	0.401404	+	0.500124i
$124$	4.56627	+	2.63634i	0.410063	+	0.236750i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−16.8492			−1.49513			−0.747563	−	0.664191i	$-0.768776\pi$
$127$	−16.8492			−1.49513			−0.747563	+	0.664191i	$0.768776\pi$
$128$	−3.62150	−	2.09088i	−0.320099	−	0.184809i
$129$	−3.41425	−	4.25394i	−0.300608	−	0.374539i
$130$	−0.658769	−	1.14102i	−0.0577778	−	0.100074i
$131$	6.93473	−	12.0113i	0.605890	−	1.04943i	−0.386020	−	0.922490i	$-0.626150\pi$
$131$	6.93473	−	12.0113i	0.605890	−	1.04943i	0.991910	−	0.126942i	$-0.0405163\pi$
$132$	−2.78870	−	18.1168i	−0.242725	−	1.57687i
$133$		0			0
$134$			9.96060i			0.860465i
$135$	0.339627	−	5.18504i	0.0292305	−	0.446257i
$136$	−1.89376	+	1.09336i	−0.162389	+	0.0937551i
$137$	3.75708	−	2.16915i	0.320989	−	0.185323i	−0.330844	−	0.943685i	$-0.607333\pi$
$137$	3.75708	−	2.16915i	0.320989	−	0.185323i	0.651833	+	0.758362i	$0.274000\pi$
$138$	8.81130	−	22.6592i	0.750068	−	1.92888i
$139$		−	10.9631i		−	0.929881i	−0.885342	−	0.464941i	$-0.846076\pi$
$139$		−	10.9631i		−	0.929881i	0.885342	−	0.464941i	$-0.153924\pi$
$140$		0			0
$141$	11.6570	−	1.79435i	0.981695	−	0.151111i
$142$	1.26661	−	2.19384i	0.106292	−	0.184103i
$143$	1.49840	+	2.59530i	0.125302	+	0.217030i
$144$	7.57301	+	6.93900i	0.631085	+	0.578250i
$145$	−1.85970	−	1.07370i	−0.154440	−	0.0891659i
$146$	29.8221			2.46809
$147$		0			0
$148$	25.6728			2.11029
$149$	−7.50546	−	4.33328i	−0.614871	−	0.354996i	0.159998	−	0.987117i	$-0.448851\pi$
$149$	−7.50546	−	4.33328i	−0.614871	−	0.354996i	−0.774870	+	0.632121i	$0.782184\pi$
$150$	2.78651	−	2.23647i	0.227517	−	0.182607i
$151$	−6.73018	−	11.6570i	−0.547694	−	0.948634i	−0.998432	−	0.0559778i	$-0.982172\pi$
$151$	−6.73018	−	11.6570i	−0.547694	−	0.948634i	0.450738	−	0.892656i	$-0.351161\pi$
$152$	0.236414	−	0.409481i	0.0191757	−	0.0332133i
$153$	11.8715	−	3.74343i	0.959753	−	0.302638i
$154$		0			0
$155$		−	2.33772i		−	0.187770i
$156$	2.32546	+	0.904286i	0.186186	+	0.0724009i
$157$	6.76643	−	3.90660i	0.540020	−	0.311781i	−0.205067	−	0.978748i	$-0.565741\pi$
$157$	6.76643	−	3.90660i	0.540020	−	0.311781i	0.745087	+	0.666967i	$0.232408\pi$
$158$	16.2235	−	9.36664i	1.29067	−	0.745170i
$159$	3.65698	+	1.42206i	0.290018	+	0.112777i
$160$			8.11688i			0.641696i
$161$		0			0
$162$	10.6498	+	15.2077i	0.836730	+	1.19483i
$163$	−8.33945	+	14.4443i	−0.653196	+	1.13137i	0.329147	+	0.944279i	$0.393239\pi$
$163$	−8.33945	+	14.4443i	−0.653196	+	1.13137i	−0.982343	+	0.187090i	$0.940095\pi$
$164$	−4.63077	−	8.02072i	−0.361602	−	0.626313i
$165$	−6.33802	+	5.08695i	−0.493414	+	0.396018i
$166$	−4.93717	−	2.85047i	−0.383198	−	0.221240i
$167$	0.465112			0.0359915			0.0179957	−	0.999838i	$-0.494271\pi$
$167$	0.465112			0.0359915			0.0179957	+	0.999838i	$0.494271\pi$
$168$		0			0
$169$	12.5921			0.968621
$170$	7.41264	+	4.27969i	0.568524	+	0.328237i
$171$	−1.81831	+	1.98445i	−0.139050	+	0.151755i
$172$	3.55152	+	6.15141i	0.270801	+	0.469040i
$173$	5.59208	−	9.68576i	0.425158	−	0.736395i	−0.571277	−	0.820757i	$-0.693552\pi$
$173$	5.59208	−	9.68576i	0.425158	−	0.736395i	0.996435	+	0.0843622i	$0.0268853\pi$
$174$	7.58338	−	1.16730i	0.574894	−	0.0884929i
$175$		0			0
$176$		−	16.0647i		−	1.21092i
$177$	−0.318960	+	0.820237i	−0.0239745	+	0.0616528i
$178$	24.6562	−	14.2353i	1.84806	−	1.06698i
$179$	0.214505	−	0.123845i	0.0160329	−	0.00925660i	−0.491962	−	0.870617i	$-0.663720\pi$
$179$	0.214505	−	0.123845i	0.0160329	−	0.00925660i	0.507995	+	0.861360i	$0.330387\pi$
$180$	−1.46434	+	6.60608i	−0.109145	+	0.492388i
$181$		−	14.3385i		−	1.06578i	−0.846186	−	0.532888i	$-0.821107\pi$
$181$		−	14.3385i		−	1.06578i	0.846186	−	0.532888i	$-0.178893\pi$
$182$		0			0
$183$	1.36603	+	8.87439i	0.100980	+	0.656014i
$184$	−1.79301	+	3.10559i	−0.132183	+	0.228947i
$185$	−5.69122	−	9.85748i	−0.418427	−	0.724737i
$186$	5.22825	+	6.51407i	0.383354	+	0.477635i
$187$	−16.8604	−	9.73433i	−1.23295	−	0.711845i
$188$	−15.3585			−1.12013
$189$		0			0
$190$	−1.85076			−0.134268
$191$	−14.7572	−	8.52006i	−1.06779	−	0.616490i	−0.140214	−	0.990121i	$-0.544779\pi$
$191$	−14.7572	−	8.52006i	−1.06779	−	0.616490i	−0.927577	+	0.373632i	$0.878112\pi$
$192$	−10.7294	−	13.3682i	−0.774328	−	0.964765i
$193$	−1.41181	−	2.44533i	−0.101624	−	0.176019i	0.810730	−	0.585421i	$-0.199071\pi$
$193$	−1.41181	−	2.44533i	−0.101624	−	0.176019i	−0.912354	+	0.409402i	$0.865737\pi$
$194$	−13.3143	+	23.0611i	−0.955913	+	1.65569i
$195$	−0.168300	−	1.09336i	−0.0120522	−	0.0782973i
$196$		0			0
$197$			9.59675i			0.683740i	0.939747	+	0.341870i	$0.111060\pi$
$197$			9.59675i			0.683740i	−0.939747	+	0.341870i	$0.888940\pi$
$198$	6.28413	−	28.3496i	0.446594	−	2.01472i
$199$	−10.5777	+	6.10706i	−0.749836	+	0.432918i	−0.825635	−	0.564205i	$-0.809183\pi$
$199$	−10.5777	+	6.10706i	−0.749836	+	0.432918i	0.0757989	+	0.997123i	$0.475849\pi$
$200$	−0.456412	+	0.263509i	−0.0322732	+	0.0186329i
$201$	−3.03103	+	7.79460i	−0.213792	+	0.549789i
$202$			18.6480i			1.31207i
$203$		0			0
$204$	−16.0207	+	2.46605i	−1.12168	+	0.172658i
$205$	−2.05312	+	3.55611i	−0.143396	+	0.248369i
$206$	−16.0086	−	27.7277i	−1.11537	−	1.93188i
$207$	13.7905	−	15.0505i	0.958503	−	1.04608i
$208$	1.89376	+	1.09336i	0.131309	+	0.0758111i
$209$	4.20964			0.291187
$210$		0			0
$211$	5.64113			0.388351			0.194176	−	0.980967i	$-0.437797\pi$
$211$	5.64113			0.388351			0.194176	+	0.980967i	$0.437797\pi$
$212$	−4.42496	−	2.55475i	−0.303908	−	0.175461i
$213$	1.65877	−	1.33134i	0.113657	−	0.0912220i
$214$	−5.52640	−	9.57200i	−0.377777	−	0.654329i
$215$	1.57462	−	2.72732i	0.107388	−	0.186002i
$216$	−1.21130	−	2.45601i	−0.0824183	−	0.167110i
$217$		0			0
$218$			2.80319i			0.189856i
$219$	23.3371	+	9.07491i	1.57697	+	0.613226i
$220$	9.16509	−	5.29147i	0.617910	−	0.356751i
$221$	2.29503	−	1.32503i	0.154380	−	0.0891314i
$222$	37.9046	+	14.7397i	2.54399	+	0.989263i
$223$		−	0.392378i		−	0.0262755i	−0.999914	−	0.0131378i	$-0.995818\pi$
$223$		−	0.392378i		−	0.0262755i	0.999914	−	0.0131378i	$-0.00418200\pi$
$224$		0			0
$225$	2.86113	−	0.902197i	0.190742	−	0.0601465i
$226$	−12.3143	+	21.3290i	−0.819137	+	1.41879i
$227$	11.7125	+	20.2867i	0.777388	+	1.34648i	0.933442	+	0.358728i	$0.116789\pi$
$227$	11.7125	+	20.2867i	0.777388	+	1.34648i	−0.156054	+	0.987749i	$0.549877\pi$
$228$	2.73339	−	2.19384i	0.181023	−	0.145290i
$229$	−6.69286	−	3.86412i	−0.442276	−	0.255348i	0.262286	−	0.964990i	$-0.415523\pi$
$229$	−6.69286	−	3.86412i	−0.442276	−	0.255348i	−0.704563	+	0.709642i	$0.748857\pi$
$230$	14.0366			0.925545
$231$		0			0
$232$	−1.13172			−0.0743011
$233$	−3.53323	−	2.03991i	−0.231469	−	0.133639i	0.379780	−	0.925077i	$-0.376000\pi$
$233$	−3.53323	−	2.03991i	−0.231469	−	0.133639i	−0.611250	+	0.791438i	$0.709333\pi$
$234$	2.91425	+	2.67026i	0.190510	+	0.174561i
$235$	3.40471	+	5.89714i	0.222099	+	0.384687i
$236$	0.573014	−	0.992490i	0.0373001	−	0.0646056i
$237$	15.5459	−	2.39296i	1.00981	−	0.155440i
$238$		0			0
$239$			5.76281i			0.372765i	0.982477	+	0.186383i	$0.0596764\pi$
$239$			5.76281i			0.372765i	−0.982477	+	0.186383i	$0.940324\pi$
$240$	−2.14924	+	5.52698i	−0.138733	+	0.356765i
$241$	17.6840	−	10.2098i	1.13912	−	0.657674i	0.192911	−	0.981216i	$-0.438207\pi$
$241$	17.6840	−	10.2098i	1.13912	−	0.657674i	0.946214	+	0.323542i	$0.104874\pi$
$242$	−19.6799	+	11.3622i	−1.26507	+	0.730390i
$243$	3.70621	+	15.1415i	0.237754	+	0.971325i
$244$		−	11.6923i		−	0.748525i
$245$		0			0
$246$	−2.23210	−	14.5009i	−0.142314	−	0.924542i
$247$	−0.286507	+	0.496245i	−0.0182300	+	0.0315753i
$248$	−0.616011	−	1.06696i	−0.0391167	−	0.0677522i
$249$	−2.99614	−	3.73301i	−0.189873	−	0.236570i
$250$	1.78651	+	1.03144i	0.112989	+	0.0652340i
$251$	4.42544			0.279331			0.139666	−	0.990199i	$-0.455397\pi$
$251$	4.42544			0.279331			0.139666	+	0.990199i	$0.455397\pi$
$252$		0			0
$253$	−31.9268			−2.00722
$254$	30.1012	+	17.3790i	1.88872	+	1.09045i
$255$	4.49840	+	5.60472i	0.281700	+	0.350981i
$256$	−5.58338	−	9.67069i	−0.348961	−	0.604418i
$257$	12.7539	−	22.0904i	0.795565	−	1.37796i	−0.126915	−	0.991914i	$-0.540508\pi$
$257$	12.7539	−	22.0904i	0.795565	−	1.37796i	0.922480	−	0.386045i	$-0.126159\pi$
$258$	1.71189	+	11.1213i	0.106578	+	0.692381i
$259$		0			0
$260$			1.44055i			0.0893389i
$261$	6.28953	+	1.39417i	0.389312	+	0.0862971i
$262$	−24.7779	+	14.3055i	−1.53078	+	0.883798i
$263$	−0.310020	+	0.178990i	−0.0191166	+	0.0110370i	−0.509528	−	0.860454i	$-0.670180\pi$
$263$	−0.310020	+	0.178990i	−0.0191166	+	0.0110370i	0.490411	+	0.871491i	$0.336847\pi$
$264$	−1.55229	+	3.99187i	−0.0955368	+	0.245683i
$265$			2.26538i			0.139161i
$266$		0			0
$267$	23.6264	−	3.63678i	1.44591	−	0.222568i
$268$	5.44528	−	9.43149i	0.332623	−	0.576120i
$269$	4.26905	+	7.39421i	0.260288	+	0.450833i	0.966319	−	0.257349i	$-0.0828490\pi$
$269$	4.26905	+	7.39421i	0.260288	+	0.450833i	−0.706030	+	0.708182i	$0.749516\pi$
$270$	−5.95481	+	8.91281i	−0.362398	+	0.542416i
$271$	7.30474	+	4.21739i	0.443731	+	0.256188i	0.705179	−	0.709029i	$-0.250867\pi$
$271$	7.30474	+	4.21739i	0.443731	+	0.256188i	−0.261448	+	0.965218i	$0.584200\pi$
$272$	−14.2061			−0.861369
$273$		0			0
$274$	−8.94940			−0.540653
$275$	−4.06348	−	2.34605i	−0.245037	−	0.141472i
$276$	−20.7306	+	16.6385i	−1.24783	+	1.00152i
$277$	−5.05294	−	8.75195i	−0.303602	−	0.525853i	0.673347	−	0.739326i	$-0.264856\pi$
$277$	−5.05294	−	8.75195i	−0.303602	−	0.525853i	−0.976949	+	0.213473i	$0.931523\pi$
$278$	−11.3078	+	19.5857i	−0.678198	+	1.17467i
$279$	2.10909	+	6.68851i	0.126268	+	0.400431i
$280$		0			0
$281$			15.1554i			0.904094i	0.891994	+	0.452047i	$0.149306\pi$
$281$			15.1554i			0.904094i	−0.891994	+	0.452047i	$0.850694\pi$
$282$	−22.6760	−	8.81787i	−1.35034	−	0.525096i
$283$	−20.7322	+	11.9697i	−1.23240	+	0.711527i	−0.967530	−	0.252757i	$-0.918663\pi$
$283$	−20.7322	+	11.9697i	−1.23240	+	0.711527i	−0.264871	+	0.964284i	$0.585329\pi$
$284$	−2.39866	+	1.38487i	−0.142334	+	0.0821768i
$285$	−1.44830	−	0.563191i	−0.0857900	−	0.0333605i
$286$		−	6.18202i		−	0.365551i
$287$		0			0
$288$	−7.32303	−	23.2234i	−0.431514	−	1.36845i
$289$	−0.108084	+	0.187206i	−0.00635786	+	0.0110121i
$290$	2.21492	+	3.83635i	0.130064	+	0.225278i
$291$	−17.4366	+	13.9947i	−1.02215	+	0.820386i
$292$	−28.2379	−	16.3032i	−1.65250	−	0.954071i
$293$	−21.2223			−1.23982			−0.619909	−	0.784673i	$-0.712831\pi$
$293$	−21.2223			−1.23982			−0.619909	+	0.784673i	$0.712831\pi$
$294$		0			0
$295$	−0.508109			−0.0295833
$296$	−5.19508	−	2.99938i	−0.301958	−	0.174335i
$297$	13.5444	−	20.2725i	0.785929	−	1.17633i
$298$	8.93904	+	15.4829i	0.517825	+	0.896899i
$299$	2.17293	−	3.76363i	0.125664	−	0.217656i
$300$	−3.86113	+	0.594339i	−0.222922	+	0.0343142i
$301$		0			0
$302$			27.7671i			1.59782i
$303$	−5.67462	+	14.5929i	−0.325999	+	0.838339i
$304$	2.66019	−	1.53586i	0.152572	−	0.0880877i
$305$	−4.48946	+	2.59199i	−0.257065	+	0.148417i
$306$	−25.0696	−	5.55707i	−1.43314	−	0.317676i
$307$			24.2817i			1.38583i	0.721019	+	0.692916i	$0.243674\pi$
$307$			24.2817i			1.38583i	−0.721019	+	0.692916i	$0.756326\pi$
$308$		0			0
$309$	−4.08982	−	26.5695i	−0.232662	−	1.51149i
$310$	−2.41122	+	4.17635i	−0.136948	+	0.237201i
$311$	3.55858	+	6.16364i	0.201789	+	0.349508i	0.949105	−	0.314960i	$-0.101991\pi$
$311$	3.55858	+	6.16364i	0.201789	+	0.349508i	−0.747316	+	0.664469i	$0.768658\pi$
$312$	−0.364926	−	0.454675i	−0.0206598	−	0.0257409i
$313$	−3.07200	−	1.77362i	−0.173640	−	0.100251i	0.410661	−	0.911788i	$-0.365298\pi$
$313$	−3.07200	−	1.77362i	−0.173640	−	0.100251i	−0.584301	+	0.811537i	$0.698631\pi$
$314$	−16.1177			−0.909575
$315$		0			0
$316$	−20.4823			−1.15222
$317$	18.2527	+	10.5382i	1.02517	+	0.591885i	0.915599	−	0.402093i	$-0.131717\pi$
$317$	18.2527	+	10.5382i	1.02517	+	0.591885i	0.109576	+	0.993978i	$0.465051\pi$
$318$	−5.06645	−	6.31249i	−0.284112	−	0.353987i
$319$	−5.03791	−	8.72592i	−0.282069	−	0.488558i
$320$	4.94830	−	8.57071i	0.276619	−	0.479117i
$321$	−1.41187	−	9.17220i	−0.0788028	−	0.511942i
$322$		0			0
$323$		−	3.72259i		−	0.207130i
$324$	−1.77033	−	20.2219i	−0.0983517	−	1.12344i
$325$	0.553120	−	0.319344i	0.0306816	−	0.0177140i
$326$	29.7970	−	17.2033i	1.65030	−	0.952802i
$327$	−0.853016	+	2.19362i	−0.0471719	+	0.121307i
$328$			2.16407i			0.119491i
$329$		0			0
$330$	16.5698	−	2.55057i	0.912138	−	0.140404i
$331$	7.40412	−	12.8243i	0.406967	−	0.704888i	−0.587581	−	0.809165i	$-0.699920\pi$
$331$	7.40412	−	12.8243i	0.406967	−	0.704888i	0.994548	+	0.104277i	$0.0332529\pi$
$332$	3.11660	+	5.39811i	0.171046	+	0.296260i
$333$	25.1767	+	23.0689i	1.37967	+	1.26417i
$334$	−0.830926	−	0.479736i	−0.0454663	−	0.0262500i
$335$	−4.82849			−0.263809
$336$		0			0
$337$	20.5062			1.11704			0.558522	−	0.829490i	$-0.311369\pi$
$337$	20.5062			1.11704			0.558522	+	0.829490i	$0.311369\pi$
$338$	−22.4958	−	12.9880i	−1.22361	−	0.706453i
$339$	−16.1270	+	12.9436i	−0.875897	+	0.703001i
$340$	−4.67925	−	8.10471i	−0.253768	−	0.439539i
$341$	5.48442	−	9.49929i	0.296998	−	0.514415i
$342$	5.29527	−	1.66975i	0.286335	−	0.0902899i
$343$		0			0
$344$		−	1.65971i		−	0.0894854i
$345$	10.9842	+	4.27136i	0.591371	+	0.229962i
$346$	−19.9806	+	11.5358i	−1.07416	+	0.620168i
$347$	−13.7103	+	7.91567i	−0.736010	+	0.424935i	−0.820617	−	0.571479i	$-0.806370\pi$
$347$	−13.7103	+	7.91567i	−0.736010	+	0.424935i	0.0846070	+	0.996414i	$0.473037\pi$
$348$	−7.81869	−	3.04040i	−0.419126	−	0.162982i
$349$		−	8.96019i		−	0.479628i	−0.970819	−	0.239814i	$-0.922914\pi$
$349$		−	8.96019i		−	0.479628i	0.970819	−	0.239814i	$-0.0770865\pi$
$350$		0			0
$351$	1.46796	+	2.97641i	0.0783538	+	0.158869i
$352$	−19.0426	+	32.9828i	−1.01498	+	1.75799i
$353$	6.72876	+	11.6545i	0.358136	+	0.620309i	0.987649	−	0.156680i	$-0.0500792\pi$
$353$	6.72876	+	11.6545i	0.358136	+	0.620309i	−0.629514	+	0.776989i	$0.716746\pi$
$354$	1.41585	−	1.13637i	0.0752516	−	0.0603975i
$355$	1.06348	+	0.614002i	0.0564438	+	0.0325878i
$356$	−31.1286			−1.64981
$357$		0			0
$358$	−0.510954			−0.0270048
$359$	4.85824	+	2.80491i	0.256408	+	0.148037i	0.622695	−	0.782465i	$-0.286038\pi$
$359$	4.85824	+	2.80491i	0.256408	+	0.148037i	−0.366287	+	0.930502i	$0.619371\pi$
$360$	1.06811	−	1.16571i	0.0562945	−	0.0614381i
$361$	−9.09754	−	15.7574i	−0.478818	−	0.829337i
$362$	−14.7894	+	25.6159i	−0.777311	+	1.34634i
$363$	−18.8579	+	2.90278i	−0.989784	+	0.152356i
$364$		0			0
$365$			14.4565i			0.756689i
$366$	6.71299	−	17.2631i	0.350894	−	0.902359i
$367$	1.71154	−	0.988156i	0.0893415	−	0.0515813i	−0.454664	−	0.890663i	$-0.650241\pi$
$367$	1.71154	−	0.988156i	0.0893415	−	0.0515813i	0.544005	+	0.839082i	$0.316907\pi$
$368$	−20.1755	+	11.6483i	−1.05172	+	0.607210i
$369$	2.66592	−	12.0268i	0.138782	−	0.626090i
$370$			23.4806i			1.22070i
$371$		0			0
$372$	−1.38940	−	9.02623i	−0.0720370	−	0.467988i
$373$	11.5467	−	19.9995i	0.597866	−	1.03553i	−0.395270	−	0.918565i	$-0.629349\pi$
$373$	11.5467	−	19.9995i	0.597866	−	1.03553i	0.993136	−	0.116969i	$-0.0373177\pi$
$374$	20.0808	+	34.7809i	1.03835	+	1.79848i
$375$	1.08415	+	1.35078i	0.0559853	+	0.0697542i
$376$	3.10790	+	1.79435i	0.160278	+	0.0925364i
$377$	1.37152			0.0706368
$378$		0			0
$379$	−17.0645			−0.876547			−0.438273	−	0.898842i	$-0.644410\pi$
$379$	−17.0645			−0.876547			−0.438273	+	0.898842i	$0.644410\pi$
$380$	1.75245	+	1.01178i	0.0898988	+	0.0519031i
$381$	18.2671	+	22.7597i	0.935851	+	1.16601i
$382$	17.5759	+	30.4423i	0.899259	+	1.55756i
$383$	13.3056	−	23.0460i	0.679886	−	1.17760i	−0.295129	−	0.955457i	$-0.595363\pi$
$383$	13.3056	−	23.0460i	0.679886	−	1.17760i	0.975015	−	0.222139i	$-0.0713040\pi$
$384$	1.10193	+	7.15869i	0.0562327	+	0.365316i
$385$		0			0
$386$			5.82479i			0.296474i
$387$	−2.04460	+	9.22382i	−0.103933	+	0.468873i
$388$	25.2141	−	14.5574i	1.28005	−	0.739040i
$389$	−8.20951	+	4.73976i	−0.416239	+	0.240316i	−0.693467	−	0.720489i	$-0.743918\pi$
$389$	−8.20951	+	4.73976i	−0.416239	+	0.240316i	0.277228	+	0.960804i	$0.410584\pi$
$390$	−0.827069	+	2.12689i	−0.0418803	+	0.107699i
$391$			28.2329i			1.42780i
$392$		0			0
$393$	−23.7430	+	3.65473i	−1.19767	+	0.184357i
$394$	9.89848	−	17.1447i	0.498678	−	0.863736i
$395$	4.54056	+	7.86448i	0.228460	+	0.395705i
$396$	−21.4485	+	23.4083i	−1.07783	+	1.17631i
$397$	−10.7042	−	6.18009i	−0.537230	−	0.310170i	0.206726	−	0.978399i	$-0.433719\pi$
$397$	−10.7042	−	6.18009i	−0.537230	−	0.310170i	−0.743956	+	0.668229i	$0.767053\pi$
$398$	25.1963			1.26297
$399$		0			0
$400$	−3.42378			−0.171189
$401$	−7.11494	−	4.10781i	−0.355303	−	0.205134i	0.311715	−	0.950176i	$-0.399096\pi$
$401$	−7.11494	−	4.10781i	−0.355303	−	0.205134i	−0.667019	+	0.745041i	$0.732430\pi$
$402$	13.4546	−	10.7988i	0.671056	−	0.538595i
$403$	0.746537	+	1.29304i	0.0371877	+	0.0644109i
$404$	10.1945	−	17.6574i	0.507196	−	0.878490i
$405$	−7.37208	+	5.16260i	−0.366322	+	0.256532i
$406$		0			0
$407$		−	53.4076i		−	2.64732i
$408$	3.53002	+	1.37269i	0.174762	+	0.0679584i
$409$	17.9575	−	10.3678i	0.887942	−	0.512653i	0.0146731	−	0.999892i	$-0.495329\pi$
$409$	17.9575	−	10.3678i	0.887942	−	0.512653i	0.873269	+	0.487239i	$0.161996\pi$
$410$	7.33583	−	4.23534i	0.362291	−	0.209169i
$411$	−7.00330	−	2.72332i	−0.345447	−	0.134331i
$412$			35.0064i			1.72464i
$413$		0			0
$414$	−40.1604	+	12.6638i	−1.97378	+	0.622390i
$415$	1.38179	−	2.39334i	0.0678296	−	0.117484i
$416$	−2.59208	−	4.48961i	−0.127087	−	0.220121i
$417$	−14.8088	+	11.8857i	−0.725192	+	0.582045i
$418$	−7.52054	−	4.34199i	−0.367842	−	0.212374i
$419$	6.93924			0.339004			0.169502	−	0.985530i	$-0.445784\pi$
$419$	6.93924			0.339004			0.169502	+	0.985530i	$0.445784\pi$
$420$		0			0
$421$	−15.2162			−0.741594			−0.370797	−	0.928714i	$-0.620915\pi$
$421$	−15.2162			−0.741594			−0.370797	+	0.928714i	$0.620915\pi$
$422$	−10.0779	−	5.81849i	−0.490585	−	0.283240i
$423$	−15.0617	−	13.8007i	−0.732325	−	0.671014i
$424$	0.596948	+	1.03394i	0.0289904	+	0.0502128i
$425$	−2.07462	+	3.59334i	−0.100634	+	0.174303i
$426$	−4.33660	+	0.667529i	−0.210109	+	0.0323419i
$427$		0			0
$428$			12.0847i			0.584137i
$429$	1.88120	−	4.83770i	0.0908253	−	0.233566i
$430$	−5.62613	+	3.24825i	−0.271316	+	0.156645i
$431$	26.9043	−	15.5332i	1.29594	−	0.748209i	0.316236	−	0.948681i	$-0.397581\pi$
$431$	26.9043	−	15.5332i	1.29594	−	0.748209i	0.979699	+	0.200472i	$0.0642475\pi$
$432$	1.16281	−	17.7524i	0.0559456	−	0.854114i
$433$		−	22.3083i		−	1.07207i	−0.844196	−	0.536034i	$-0.819922\pi$
$433$		−	22.3083i		−	1.07207i	0.844196	−	0.536034i	$-0.180078\pi$
$434$		0			0
$435$	0.565860	+	3.67611i	0.0271309	+	0.176256i
$436$	1.53245	−	2.65429i	0.0733912	−	0.127117i
$437$	−3.05235	−	5.28682i	−0.146014	−	0.252903i
$438$	−32.3316	−	40.2832i	−1.54486	−	1.92481i
$439$	22.4126	+	12.9399i	1.06970	+	0.617590i	0.928099	−	0.372334i	$-0.121443\pi$
$439$	22.4126	+	12.9399i	1.06970	+	0.617590i	0.141598	+	0.989924i	$0.454776\pi$
$440$	−2.47283			−0.117887
$441$		0			0
$442$	−5.46677			−0.260028
$443$	26.8166	+	15.4826i	1.27409	+	0.735599i	0.975756	−	0.218862i	$-0.0702343\pi$
$443$	26.8166	+	15.4826i	1.27409	+	0.735599i	0.298338	+	0.954460i	$0.403568\pi$
$444$	−27.8332	−	34.6785i	−1.32091	−	1.64577i
$445$	6.90067	+	11.9523i	0.327123	+	0.566594i
$446$	−0.404714	+	0.700985i	−0.0191638	+	0.0331926i
$447$	2.28372	+	14.8362i	0.108016	+	0.701728i
$448$		0			0
$449$		−	24.2032i		−	1.14222i	−0.820874	−	0.571110i	$-0.806513\pi$
$449$		−	24.2032i		−	1.14222i	0.820874	−	0.571110i	$-0.193487\pi$
$450$	−6.04198	−	1.33930i	−0.284822	−	0.0631351i
$451$	−16.6856	+	9.63346i	−0.785696	+	0.453622i
$452$	23.3204	−	13.4640i	1.09690	−	0.633295i
$453$	−8.44959	+	21.7290i	−0.396996	+	1.02092i
$454$		−	48.3231i		−	2.26792i
$455$		0			0
$456$	−0.809428	+	0.124594i	−0.0379049	+	0.00583467i
$457$	1.20726	−	2.09103i	0.0564731	−	0.0978143i	−0.836407	−	0.548109i	$-0.815348\pi$
$457$	1.20726	−	2.09103i	0.0564731	−	0.0978143i	0.892880	+	0.450295i	$0.148681\pi$
$458$	7.97122	+	13.8066i	0.372471	+	0.645138i
$459$	−17.9270	−	11.9774i	−0.836763	−	0.559056i
$460$	−13.2910	−	7.67354i	−0.619694	−	0.357781i
$461$	7.45376			0.347156			0.173578	−	0.984820i	$-0.444467\pi$
$461$	7.45376			0.347156			0.173578	+	0.984820i	$0.444467\pi$
$462$		0			0
$463$	13.8862			0.645345			0.322672	−	0.946511i	$-0.395419\pi$
$463$	13.8862			0.645345			0.322672	+	0.946511i	$0.395419\pi$
$464$	−6.36721	−	3.67611i	−0.295590	−	0.170659i
$465$	−3.15776	+	2.53444i	−0.146437	+	0.117532i
$466$	4.20809	+	7.28862i	0.194936	+	0.337639i
$467$	−10.0692	+	17.4404i	−0.465948	+	0.807045i	−0.999244	−	0.0388836i	$-0.987620\pi$
$467$	−10.0692	+	17.4404i	−0.465948	+	0.807045i	0.533296	+	0.845929i	$0.320953\pi$
$468$	−1.29966	−	4.12158i	−0.0600767	−	0.190520i
$469$		0			0
$470$		−	14.0470i		−	0.647942i
$471$	−12.6128	−	4.90465i	−0.581167	−	0.225994i
$472$	−0.231907	+	0.133892i	−0.0106744	+	0.00616286i
$473$	12.7969	−	7.38828i	0.588401	−	0.339713i
$474$	−30.2410	−	11.7596i	−1.38902	−	0.540136i
$475$		−	0.897174i		−	0.0411652i
$476$		0			0
$477$	−2.04382	−	6.48153i	−0.0935799	−	0.296769i
$478$	5.94399	−	10.2953i	0.271872	−	0.470896i
$479$	−16.6189	−	28.7847i	−0.759335	−	1.31521i	−0.943190	−	0.332253i	$-0.892191\pi$
$479$	−16.6189	−	28.7847i	−0.759335	−	1.31521i	0.183855	−	0.982953i	$-0.441142\pi$
$480$	10.9642	−	8.79992i	0.500443	−	0.401659i
$481$	6.29586	+	3.63491i	0.287066	+	0.165738i
$482$	−42.1234			−1.91867
$483$		0			0
$484$	24.8460			1.12936
$485$	−11.1791	−	6.45424i	−0.507616	−	0.293072i
$486$	8.99634	−	30.8731i	0.408082	−	1.40043i
$487$	16.1039	+	27.8927i	0.729736	+	1.26394i	0.956995	+	0.290105i	$0.0936902\pi$
$487$	16.1039	+	27.8927i	0.729736	+	1.26394i	−0.227259	+	0.973834i	$0.572976\pi$
$488$	−1.36603	+	2.36603i	−0.0618371	+	0.107105i
$489$	28.5524	−	4.39504i	1.29118	−	0.198751i
$490$		0			0
$491$			22.5003i			1.01542i	0.861527	+	0.507712i	$0.169509\pi$
$491$			22.5003i			1.01542i	−0.861527	+	0.507712i	$0.830491\pi$
$492$	−5.81382	+	14.9508i	−0.262107	+	0.674036i
$493$	−7.71635	+	4.45504i	−0.347527	+	0.200645i
$494$	1.02369	−	0.591030i	0.0460582	−	0.0265917i
$495$	13.7427	+	3.04629i	0.617690	+	0.136920i
$496$		−	8.00383i		−	0.359383i
$497$		0			0
$498$	1.50225	+	9.75939i	0.0673176	+	0.437329i
$499$	−3.20702	+	5.55472i	−0.143566	+	0.248663i	−0.928837	−	0.370489i	$-0.879190\pi$
$499$	−3.20702	+	5.55472i	−0.143566	+	0.248663i	0.785271	+	0.619152i	$0.212524\pi$
$500$	−1.12774	−	1.95330i	−0.0504340	−	0.0873543i
$501$	−0.504252	−	0.628266i	−0.0225283	−	0.0280689i
$502$	−7.90608	−	4.56458i	−0.352866	−	0.203727i
$503$	38.0103			1.69479			0.847397	−	0.530960i	$-0.178169\pi$
$503$	38.0103			1.69479			0.847397	+	0.530960i	$0.178169\pi$
$504$		0			0
$505$	−9.03979			−0.402265
$506$	57.0374	+	32.9306i	2.53562	+	1.46394i
$507$	−13.6517	−	17.0092i	−0.606293	−	0.755404i
$508$	−19.0015	−	32.9116i	−0.843056	−	1.46022i
$509$	−6.34981	+	10.9982i	−0.281450	+	0.487486i	−0.971742	−	0.236045i	$-0.924149\pi$
$509$	−6.34981	+	10.9982i	−0.281450	+	0.487486i	0.690292	+	0.723531i	$0.257482\pi$
$510$	−2.25548	−	14.6527i	−0.0998742	−	0.648833i
$511$		0			0
$512$			31.3992i			1.38766i
$513$	4.65188	+	0.304705i	0.205386	+	0.0134530i
$514$	−45.5698	+	26.3097i	−2.01000	+	1.16047i
$515$	13.4412	−	7.76030i	0.592292	−	0.341960i
$516$	4.45885	−	11.4664i	0.196290	−	0.504779i
$517$			31.9506i			1.40518i
$518$		0			0
$519$	−19.1460	+	2.94713i	−0.840417	+	0.129365i
$520$	0.168300	−	0.291505i	0.00738046	−	0.0127833i
$521$	18.0970	+	31.3449i	0.792843	+	1.37324i	0.924200	+	0.381909i	$0.124733\pi$
$521$	18.0970	+	31.3449i	0.792843	+	1.37324i	−0.131357	+	0.991335i	$0.541933\pi$
$522$	−9.79829	−	8.97798i	−0.428860	−	0.392955i
$523$	4.27382	+	2.46749i	0.186881	+	0.107896i	0.590522	−	0.807022i	$-0.298922\pi$
$523$	4.27382	+	2.46749i	0.186881	+	0.107896i	−0.403640	+	0.914918i	$0.632255\pi$
$524$	31.2823			1.36657
$525$		0			0
$526$	0.738470			0.0321988
$527$	−8.40023	−	4.84988i	−0.365920	−	0.211264i
$528$	−21.7000	+	17.4166i	−0.944370	+	0.757959i
$529$	11.6496	+	20.1778i	0.506506	+	0.877295i
$530$	2.33660	−	4.04711i	0.101495	−	0.175795i
$531$	1.45376	−	0.458415i	0.0630880	−	0.0198935i
$532$		0			0
$533$		−	2.62261i		−	0.113598i
$534$	−45.9598	−	17.8721i	−1.98888	−	0.773399i
$535$	4.64012	−	2.67897i	0.200610	−	0.115822i
$536$	−2.20378	+	1.27235i	−0.0951888	+	0.0549573i
$537$	−0.399844	−	0.155484i	−0.0172545	−	0.00670964i
$538$		−	17.6131i		−	0.759354i
$539$		0			0
$540$	10.5110	−	5.18398i	0.452319	−	0.223083i
$541$	−8.32849	+	14.4254i	−0.358070	+	0.620195i	−0.987638	−	0.156750i	$-0.949898\pi$
$541$	−8.32849	+	14.4254i	−0.358070	+	0.620195i	0.629569	+	0.776945i	$0.283232\pi$
$542$	−8.69998	−	15.0688i	−0.373696	−	0.647261i
$543$	−19.3683	+	15.5451i	−0.831172	+	0.667106i
$544$	29.1668	+	16.8394i	1.25051	+	0.721985i
$545$	−1.35887			−0.0582077
$546$		0			0
$547$	21.2868			0.910159			0.455079	−	0.890451i	$-0.349611\pi$
$547$	21.2868			0.910159			0.455079	+	0.890451i	$0.349611\pi$
$548$	8.47401	+	4.89247i	0.361992	+	0.208996i
$549$	10.5064	−	11.4664i	0.448403	−	0.489373i
$550$	4.83963	+	8.38248i	0.206362	+	0.357430i
$551$	0.963296	−	1.66848i	0.0410378	−	0.0710795i
$552$	6.13887	−	0.944951i	0.261288	−	0.0402198i
$553$		0			0
$554$			20.8472i			0.885713i
$555$	−7.14520	+	18.3746i	−0.303297	+	0.779959i
$556$	21.4143	−	12.3636i	0.908169	−	0.524331i
$557$	16.5937	−	9.58040i	0.703099	−	0.405935i	−0.105401	−	0.994430i	$-0.533613\pi$
$557$	16.5937	−	9.58040i	0.703099	−	0.405935i	0.808501	+	0.588495i	$0.200279\pi$
$558$	3.13091	−	14.1245i	0.132542	−	0.597936i
$559$			2.01138i			0.0850723i
$560$		0			0
$561$	5.13017	+	33.3282i	0.216596	+	1.40712i
$562$	15.6319	−	27.0752i	0.659390	−	1.14210i
$563$	−13.6243	−	23.5981i	−0.574198	−	0.994540i	−0.996128	−	0.0879116i	$-0.971981\pi$
$563$	−13.6243	−	23.5981i	−0.574198	−	0.994540i	0.421930	−	0.906628i	$-0.361353\pi$
$564$	16.6509	+	20.7460i	0.701131	+	0.873566i
$565$	−10.3394	−	5.96948i	−0.434984	−	0.251138i
$566$	49.3843			2.07578
$567$		0			0
$568$	0.647181			0.0271551
$569$	−22.7124	−	13.1130i	−0.952153	−	0.549726i	−0.0584038	−	0.998293i	$-0.518601\pi$
$569$	−22.7124	−	13.1130i	−0.952153	−	0.549726i	−0.893749	+	0.448567i	$0.851934\pi$
$570$	2.00650	+	2.49998i	0.0840432	+	0.104713i
$571$	13.4388	+	23.2767i	0.562397	+	0.974101i	0.997287	+	0.0736170i	$0.0234542\pi$
$571$	13.4388	+	23.2767i	0.562397	+	0.974101i	−0.434889	+	0.900484i	$0.643212\pi$
$572$	−3.37960	+	5.85363i	−0.141308	+	0.244753i
$573$	4.49023	+	29.1708i	0.187582	+	1.21863i
$574$		0			0
$575$			6.80436i			0.283761i
$576$	−6.42524	+	28.9862i	−0.267718	+	1.20776i
$577$	8.93069	−	5.15614i	0.371790	−	0.214653i	−0.302450	−	0.953165i	$-0.597805\pi$
$577$	8.93069	−	5.15614i	0.371790	−	0.214653i	0.674240	+	0.738512i	$0.264471\pi$
$578$	0.386185	−	0.222964i	0.0160632	−	0.00927407i
$579$	−1.77250	+	4.55815i	−0.0736624	+	0.189430i
$580$		−	4.84341i		−	0.201112i
$581$		0			0
$582$	45.5853	−	7.01690i	1.88957	−	0.290860i
$583$	−5.31469	+	9.20532i	−0.220112	+	0.381245i
$584$	3.80943	+	6.59812i	0.157635	+	0.273032i
$585$	−1.29443	+	1.41271i	−0.0535183	+	0.0584082i
$586$	37.9138	+	21.8895i	1.56620	+	0.904248i
$587$	22.1492			0.914197			0.457098	−	0.889416i	$-0.348889\pi$
$587$	22.1492			0.914197			0.457098	+	0.889416i	$0.348889\pi$
$588$		0			0
$589$	2.09734			0.0864195
$590$	0.907741	+	0.524084i	0.0373711	+	0.0215762i
$591$	12.9631	−	10.4043i	0.533233	−	0.427977i
$592$	−19.4855	−	33.7498i	−0.800848	−	1.38711i
$593$	1.45861	−	2.52638i	0.0598978	−	0.103746i	−0.834522	−	0.550975i	$-0.814256\pi$
$593$	1.45861	−	2.52638i	0.0598978	−	0.103746i	0.894419	+	0.447229i	$0.147589\pi$
$594$	−45.1072	+	22.2467i	−1.85077	+	0.912795i
$595$		0			0
$596$		−	19.5472i		−	0.800686i
$597$	19.7172	+	7.66727i	0.806970	+	0.313800i
$598$	−7.76391	+	4.48250i	−0.317490	+	0.183303i
$599$	31.4551	−	18.1606i	1.28522	−	0.742023i	0.307424	−	0.951573i	$-0.400533\pi$
$599$	31.4551	−	18.1606i	1.28522	−	0.742023i	0.977798	+	0.209550i	$0.0671998\pi$
$600$	0.850763	+	0.330830i	0.0347323	+	0.0135061i
$601$			7.15198i			0.291735i	0.989304	+	0.145868i	$0.0465974\pi$
$601$			7.15198i			0.291735i	−0.989304	+	0.145868i	$0.953403\pi$
$602$		0			0
$603$	13.8149	−	4.35625i	0.562587	−	0.177400i
$604$	15.1798	−	26.2921i	0.617656	−	1.06981i
$605$	−5.50793	−	9.54001i	−0.223929	−	0.387857i
$606$	25.1894	−	20.2172i	1.02325	−	0.821269i
$607$	37.8248	+	21.8382i	1.53526	+	0.886384i	0.999106	+	0.0422651i	$0.0134574\pi$
$607$	37.8248	+	21.8382i	1.53526	+	0.886384i	0.536156	+	0.844119i	$0.319876\pi$
$608$	−7.28226			−0.295334
$609$		0			0
$610$	10.6939			0.432984
$611$	−3.76643	−	2.17455i	−0.152373	−	0.0879729i
$612$	20.7000	+	18.9670i	0.836747	+	0.766694i
$613$	7.27926	+	12.6080i	0.294007	+	0.509234i	0.974753	−	0.223285i	$-0.0716779\pi$
$613$	7.27926	+	12.6080i	0.294007	+	0.509234i	−0.680747	+	0.732519i	$0.738345\pi$
$614$	25.0452	−	43.3795i	1.01074	−	1.75065i
$615$	7.02943	−	1.08203i	0.283454	−	0.0436318i
$616$		0			0
$617$		−	4.68442i		−	0.188588i	−0.995544	−	0.0942938i	$-0.969941\pi$
$617$		−	4.68442i		−	0.188588i	0.995544	−	0.0942938i	$-0.0300593\pi$
$618$	−20.0984	+	51.6851i	−0.808476	+	2.07908i
$619$	33.0429	−	19.0773i	1.32810	−	0.766782i	0.343098	−	0.939299i	$-0.388524\pi$
$619$	33.0429	−	19.0773i	1.32810	−	0.766782i	0.985006	+	0.172518i	$0.0551902\pi$
$620$	4.56627	−	2.63634i	0.183386	−	0.105878i
$621$	−35.2809	−	2.31095i	−1.41577	−	0.0927350i
$622$		−	14.6819i		−	0.588689i
$623$		0			0
$624$	−0.576223	−	3.74343i	−0.0230674	−	0.149857i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	3.65877	+	6.33717i	0.146234	+	0.253284i
$627$	−4.56388	−	5.68631i	−0.182264	−	0.227089i
$628$	15.2615	+	8.81125i	0.609001	+	0.351607i
$629$	−47.2285			−1.88312
$630$		0			0
$631$	23.9959			0.955264			0.477632	−	0.878560i	$-0.341495\pi$
$631$	23.9959			0.955264			0.477632	+	0.878560i	$0.341495\pi$
$632$	4.14473	+	2.39296i	0.164869	+	0.0951869i
$633$	−6.11583	−	7.61995i	−0.243082	−	0.302866i
$634$	−21.7391	−	37.6532i	−0.863369	−	1.49540i
$635$	−8.42461	+	14.5918i	−0.334320	+	0.579060i
$636$	1.34640	+	8.74690i	0.0533883	+	0.346837i
$637$		0			0
$638$			20.7852i			0.822895i
$639$	−3.59671	−	0.797266i	−0.142284	−	0.0315393i
$640$	−3.62150	+	2.09088i	−0.143152	+	0.0826491i
$641$	−20.0037	+	11.5491i	−0.790099	+	0.456164i	−0.839997	−	0.542590i	$-0.817444\pi$
$641$	−20.0037	+	11.5491i	−0.790099	+	0.456164i	0.0498985	+	0.998754i	$0.484110\pi$
$642$	−6.93827	+	17.8425i	−0.273832	+	0.704186i
$643$		−	22.7592i		−	0.897536i	−0.893648	−	0.448768i	$-0.851863\pi$
$643$		−	22.7592i		−	0.897536i	0.893648	−	0.448768i	$-0.148137\pi$
$644$		0			0
$645$	−5.39114	+	0.829853i	−0.212276	+	0.0326754i
$646$	−3.83963	+	6.65043i	−0.151068	+	0.261658i
$647$	1.21349	+	2.10183i	0.0477073	+	0.0826315i	0.888893	−	0.458115i	$-0.151475\pi$
$647$	1.21349	+	2.10183i	0.0477073	+	0.0826315i	−0.841186	+	0.540746i	$0.818142\pi$
$648$	−2.00431	+	4.29888i	−0.0787367	+	0.168876i
$649$	−2.06469	−	1.19205i	−0.0810463	−	0.0467921i
$650$	−1.31754			−0.0516781
$651$		0			0
$652$	−37.6189			−1.47327
$653$	34.7760	+	20.0779i	1.36089	+	0.785709i	0.989742	−	0.142865i	$-0.0456315\pi$
$653$	34.7760	+	20.0779i	1.36089	+	0.785709i	0.371146	+	0.928574i	$0.378965\pi$
$654$	3.78651	−	3.03908i	0.148064	−	0.118837i
$655$	−6.93473	−	12.0113i	−0.270962	−	0.469321i
$656$	−7.02943	+	12.1753i	−0.274453	+	0.475366i
$657$	−13.0426	−	41.3619i	−0.508842	−	1.61368i
$658$		0			0
$659$		−	0.627454i		−	0.0244421i	−0.999925	−	0.0122211i	$-0.996110\pi$
$659$		−	0.627454i		−	0.0244421i	0.999925	−	0.0122211i	$-0.00389018\pi$
$660$	−17.0840	−	6.64332i	−0.664993	−	0.258591i
$661$	28.5745	−	16.4975i	1.11142	−	0.641678i	0.172222	−	0.985058i	$-0.444905\pi$
$661$	28.5745	−	16.4975i	1.11142	−	0.641678i	0.939197	+	0.343380i	$0.111572\pi$
$662$	−26.4550	+	15.2738i	−1.02820	+	0.593634i
$663$	−4.27799	−	1.66355i	−0.166143	−	0.0646069i
$664$		−	1.45646i		−	0.0565217i
$665$		0			0
$666$	−21.1842	−	67.1810i	−0.820869	−	2.60321i
$667$	−7.30584	+	12.6541i	−0.282883	+	0.489968i
$668$	0.524525	+	0.908504i	0.0202945	+	0.0351511i
$669$	−0.530017	+	0.425396i	−0.0204917	+	0.0164468i
$670$	8.62613	+	4.98030i	0.333257	+	0.192406i
$671$	−24.3238			−0.939009
$672$		0			0
$673$	1.14437			0.0441121			0.0220560	−	0.999757i	$-0.492979\pi$
$673$	1.14437			0.0441121			0.0220560	+	0.999757i	$0.492979\pi$
$674$	−36.6345	−	21.1509i	−1.41111	−	0.814703i
$675$	−4.32056	−	2.88665i	−0.166299	−	0.111107i
$676$	14.2006	+	24.5961i	0.546176	+	0.946004i
$677$	7.98910	−	13.8375i	0.307046	−	0.531820i	−0.670669	−	0.741757i	$-0.733993\pi$
$677$	7.98910	−	13.8375i	0.307046	−	0.531820i	0.977715	+	0.209938i	$0.0673261\pi$
$678$	42.1615	−	6.48988i	1.61920	−	0.249242i
$679$		0			0
$680$			2.18673i			0.0838571i
$681$	14.7048	−	37.8150i	0.563490	−	1.44907i
$682$	−19.5959	+	11.3137i	−0.750366	+	0.433224i
$683$	1.96122	−	1.13231i	0.0750442	−	0.0433268i	−0.462008	−	0.886876i	$-0.652871\pi$
$683$	1.96122	−	1.13231i	0.0750442	−	0.0433268i	0.537053	+	0.843549i	$0.319538\pi$
$684$	−5.92680	−	1.31377i	−0.226617	−	0.0502331i
$685$		−	4.33830i		−	0.165758i
$686$		0			0
$687$	2.03646	+	13.2299i	0.0776960	+	0.504752i
$688$	5.39114	−	9.33773i	0.205535	−	0.355998i
$689$	−0.723434	−	1.25303i	−0.0275607	−	0.0477365i
$690$	−15.2178	−	18.9604i	−0.579330	−	0.721810i
$691$	2.40044	+	1.38589i	0.0913169	+	0.0527218i	0.544963	−	0.838460i	$-0.316544\pi$
$691$	2.40044	+	1.38589i	0.0913169	+	0.0527218i	−0.453646	+	0.891182i	$0.649877\pi$
$692$	25.2256			0.958934
$693$		0			0
$694$	32.6582			1.23969
$695$	−9.49436	−	5.48157i	−0.360141	−	0.207928i
$696$	1.22695	+	1.52871i	0.0465076	+	0.0579456i
$697$	8.51888	+	14.7551i	0.322676	+	0.558891i
$698$	−9.24191	+	16.0075i	−0.349811	+	0.605891i
$699$	1.07507	+	6.98419i	0.0406629	+	0.264166i
$700$		0			0
$701$			23.1184i			0.873169i	0.899663	+	0.436585i	$0.143812\pi$
$701$			23.1184i			0.873169i	−0.899663	+	0.436585i	$0.856188\pi$
$702$	0.447471	−	6.83148i	0.0168887	−	0.257838i
$703$	8.84388	−	5.10602i	0.333553	−	0.192577i
$704$	40.2147	−	23.2180i	1.51565	−	0.875060i
$705$	4.27454	−	10.9924i	0.160989	−	0.413998i
$706$		−	27.7612i		−	1.04481i
$707$		0			0
$708$	−1.96187	+	0.301989i	−0.0737317	+	0.0113495i
$709$	18.0134	−	31.2002i	0.676508	−	1.17175i	−0.299517	−	0.954091i	$-0.596826\pi$
$709$	18.0134	−	31.2002i	0.676508	−	1.17175i	0.976026	−	0.217656i	$-0.0698410\pi$
$710$	−1.26661	−	2.19384i	−0.0475351	−	0.0823333i
$711$	−20.0864	−	18.4048i	−0.753300	−	0.690234i
$712$	6.29910	+	3.63678i	0.236069	+	0.136294i
$713$	−15.9067			−0.595710
$714$		0			0
$715$	2.99679			0.112074
$716$	0.483812	+	0.279329i	0.0180809	+	0.0104390i
$717$	7.78431	−	6.24775i	0.290710	−	0.233326i
$718$	−5.78619	−	10.0220i	−0.215939	−	0.374017i
$719$	8.57099	−	14.8454i	0.319644	−	0.553640i	−0.660770	−	0.750589i	$-0.729770\pi$
$719$	8.57099	−	14.8454i	0.319644	−	0.553640i	0.980414	+	0.196949i	$0.0631034\pi$
$720$	9.79586	−	3.08892i	0.365070	−	0.115117i
$721$		0			0
$722$			37.5343i			1.39688i
$723$	−32.9634	−	12.8182i	−1.22592	−	0.476715i
$724$	28.0075	−	16.1701i	1.04089	−	0.600958i
$725$	−1.85970	+	1.07370i	−0.0690676	+	0.0398762i
$726$	36.6838	+	14.2650i	1.36147	+	0.529423i
$727$		−	16.6832i		−	0.618747i	−0.950941	−	0.309374i	$-0.899881\pi$
$727$		−	16.6832i		−	0.618747i	0.950941	−	0.309374i	$-0.100119\pi$
$728$		0			0
$729$	16.4348	−	21.4219i	0.608695	−	0.793404i
$730$	14.9110	−	25.8267i	0.551882	−	0.955888i
$731$	−6.53347	−	11.3163i	−0.241649	−	0.418548i
$732$	−15.7938	+	12.6763i	−0.583757	+	0.468528i
$733$	−32.9814	−	19.0418i	−1.21820	−	0.703326i	−0.253664	−	0.967292i	$-0.581636\pi$
$733$	−32.9814	−	19.0418i	−1.21820	−	0.703326i	−0.964532	+	0.263967i	$0.914969\pi$
$734$	−4.07690			−0.150481
$735$		0			0
$736$	55.2302			2.03581
$737$	−19.6205	−	11.3279i	−0.722730	−	0.417268i
$738$	−17.1676	+	18.7362i	−0.631948	+	0.689689i
$739$	11.2186	+	19.4312i	0.412684	+	0.714790i	0.995182	−	0.0980422i	$-0.0312580\pi$
$739$	11.2186	+	19.4312i	0.412684	+	0.714790i	−0.582498	+	0.812832i	$0.697925\pi$
$740$	12.8364	−	22.2333i	0.471876	−	0.817313i
$741$	0.980937	−	0.150995i	0.0360356	−	0.00554693i
$742$		0			0
$743$		−	6.39189i		−	0.234496i	−0.993103	−	0.117248i	$-0.962593\pi$
$743$		−	6.39189i		−	0.234496i	0.993103	−	0.117248i	$-0.0374072\pi$
$744$	−0.773388	+	1.98885i	−0.0283538	+	0.0729146i
$745$	−7.50546	+	4.33328i	−0.274979	+	0.158759i
$746$	−41.2565	+	23.8195i	−1.51051	+	0.872093i
$747$	−1.79422	+	8.09428i	−0.0656472	+	0.296154i
$748$		−	43.9111i		−	1.60555i
$749$		0			0
$750$	−0.543588	−	3.53142i	−0.0198490	−	0.128949i
$751$	5.49944	−	9.52531i	0.200677	−	0.347583i	−0.748069	−	0.663620i	$-0.769019\pi$
$751$	5.49944	−	9.52531i	0.200677	−	0.347583i	0.948747	+	0.316037i	$0.102352\pi$
$752$	11.6570	+	20.1905i	0.425086	+	0.736271i
$753$	−4.79784	−	5.97781i	−0.174843	−	0.217844i
$754$	−2.45023	−	1.41464i	−0.0892320	−	0.0515181i
$755$	−13.4604			−0.489873
$756$		0			0
$757$	−27.8216			−1.01119			−0.505597	−	0.862770i	$-0.668728\pi$
$757$	−27.8216			−1.01119			−0.505597	+	0.862770i	$0.668728\pi$
$758$	30.4859	+	17.6011i	1.10730	+	0.639299i
$759$	34.6134	+	43.1262i	1.25639	+	1.56538i
$760$	−0.236414	−	0.409481i	−0.00857563	−	0.0148534i
$761$	−6.54766	+	11.3409i	−0.237352	+	0.411106i	−0.959954	−	0.280159i	$-0.909613\pi$
$761$	−6.54766	+	11.3409i	−0.237352	+	0.411106i	0.722601	+	0.691265i	$0.242946\pi$
$762$	−9.15904	−	59.5017i	−0.331797	−	2.15552i
$763$		0			0
$764$		−	38.4336i		−	1.39048i
$765$	2.69384	−	12.1527i	0.0973959	−	0.439383i
$766$	−47.5412	+	27.4479i	−1.71773	+	0.991734i
$767$	0.281045	−	0.162262i	0.0101480	−	0.00585893i
$768$	−7.00980	+	18.0264i	−0.252944	+	0.650472i
$769$		−	7.74247i		−	0.279201i	−0.990208	−	0.139600i	$-0.955418\pi$
$769$		−	7.74247i		−	0.279201i	0.990208	−	0.139600i	$-0.0445818\pi$
$770$		0			0
$771$	−43.6664	+	6.72153i	−1.57261	+	0.242070i
$772$	3.18431	−	5.51538i	0.114606	−	0.198503i
$773$	19.1733	+	33.2091i	0.689614	+	1.19445i	0.971963	+	0.235135i	$0.0755532\pi$
$773$	19.1733	+	33.2091i	0.689614	+	1.19445i	−0.282349	+	0.959312i	$0.591113\pi$
$774$	13.1665	−	14.3695i	0.473261	−	0.516502i
$775$	−2.02453	−	1.16886i	−0.0727231	−	0.0419867i
$776$	−6.80301			−0.244214
$777$		0			0
$778$	19.5551			0.701086
$779$	−3.19045	−	1.84201i	−0.114310	−	0.0659967i
$780$	1.94587	−	1.56177i	0.0696732	−	0.0559203i
$781$	2.88096	+	4.98997i	0.103089	+	0.178555i
$782$	29.1205	−	50.4383i	1.04135	−	1.80367i
$783$	−4.93557	−	10.0073i	−0.176383	−	0.357632i
$784$		0			0
$785$		−	7.81320i		−	0.278865i
$786$	46.1866	+	17.9603i	1.64742	+	0.640621i
$787$	21.6178	−	12.4811i	0.770592	−	0.444901i	−0.0624938	−	0.998045i	$-0.519905\pi$
$787$	21.6178	−	12.4811i	0.770592	−	0.444901i	0.833086	+	0.553144i	$0.186572\pi$
$788$	−18.7453	+	10.8226i	−0.667775	+	0.385540i
$789$	0.577885	+	0.224718i	0.0205732	+	0.00800016i
$790$		−	18.7333i		−	0.666500i
$791$		0			0
$792$	7.07507	−	2.23098i	0.251402	−	0.0792744i
$793$	1.65547	−	2.86736i	0.0587875	−	0.101823i
$794$	12.7488	+	22.0816i	0.452438	+	0.783645i
$795$	3.06003	−	2.45601i	0.108528	−	0.0871056i
$796$	−23.8578	−	13.7743i	−0.845619	−	0.488218i
$797$	5.81191			0.205868			0.102934	−	0.994688i	$-0.467177\pi$
$797$	5.81191			0.205868			0.102934	+	0.994688i	$0.467177\pi$
$798$		0			0
$799$	28.2539			0.999552
$800$	7.02943	+	4.05844i	0.248528	+	0.143488i
$801$	−30.5270	−	27.9713i	−1.07862	−	0.988318i
$802$	8.47393	+	14.6773i	0.299225	+	0.518273i
$803$	−33.9158	+	58.7438i	−1.19686	+	2.07302i
$804$	−18.6434	+	2.86976i	−0.657502	+	0.101209i
$805$		0			0
$806$		−	3.08003i		−	0.108490i
$807$	5.35969	−	13.7830i	0.188670	−	0.485184i
$808$	−4.12586	+	2.38207i	−0.145147	+	0.0838009i
$809$	−1.51563	+	0.875048i	−0.0532866	+	0.0307650i	−0.526407	−	0.850233i	$-0.676461\pi$
$809$	−1.51563	+	0.875048i	−0.0532866	+	0.0307650i	0.473120	+	0.880998i	$0.343128\pi$
$810$	18.4952	−	1.61916i	0.649855	−	0.0568915i
$811$			28.4479i			0.998940i	0.866331	+	0.499470i	$0.166472\pi$
$811$			28.4479i			0.998940i	−0.866331	+	0.499470i	$0.833528\pi$
$812$		0			0
$813$	−2.22265	−	14.4394i	−0.0779516	−	0.506412i
$814$	−55.0868	+	95.4131i	−1.93079	+	3.34423i
$815$	8.33945	+	14.4443i	0.292118	+	0.505963i
$816$	15.4015	+	19.1893i	0.539161	+	0.671761i
$817$	2.44688	+	1.41271i	0.0856055	+	0.0494244i
$818$	−42.7750			−1.49559
$819$		0			0
$820$	−9.26153			−0.323427
$821$	−25.9378	−	14.9752i	−0.905236	−	0.522638i	−0.0263407	−	0.999653i	$-0.508385\pi$
$821$	−25.9378	−	14.9752i	−0.905236	−	0.522638i	−0.878895	+	0.477015i	$0.841719\pi$
$822$	9.70250	+	12.0887i	0.338413	+	0.421642i
$823$	−8.06283	−	13.9652i	−0.281053	−	0.486798i	0.690592	−	0.723245i	$-0.257350\pi$
$823$	−8.06283	−	13.9652i	−0.281053	−	0.486798i	−0.971644	+	0.236447i	$0.924017\pi$
$824$	4.08982	−	7.08378i	0.142476	−	0.246775i
$825$	1.23641	+	8.03236i	0.0430464	+	0.279651i
$826$		0			0
$827$		−	15.9844i		−	0.555831i	−0.960605	−	0.277916i	$-0.910356\pi$
$827$		−	15.9844i		−	0.555831i	0.960605	−	0.277916i	$-0.0896436\pi$
$828$	44.9501	+	9.96389i	1.56213	+	0.346269i
$829$	−18.0763	+	10.4363i	−0.627815	+	0.362469i	−0.779905	−	0.625898i	$-0.784733\pi$
$829$	−18.0763	+	10.4363i	−0.627815	+	0.362469i	0.152091	+	0.988367i	$0.451399\pi$
$830$	−4.93717	+	2.85047i	−0.171372	+	0.0989414i
$831$	−6.34385	+	16.3139i	−0.220066	+	0.565921i
$832$			6.32084i			0.219136i
$833$		0			0
$834$	38.7155	−	5.95943i	1.34061	−	0.206358i
$835$	0.232556	−	0.402799i	0.00804794	−	0.0139394i
$836$	4.74737	+	8.22268i	0.164191	+	0.284387i
$837$	6.74817	−	10.1003i	0.233251	−	0.349116i
$838$	−12.3970	−	7.15741i	−0.428247	−	0.247249i
$839$	−14.2504			−0.491977			−0.245989	−	0.969273i	$-0.579113\pi$
$839$	−14.2504			−0.491977			−0.245989	+	0.969273i	$0.579113\pi$
$840$		0			0
$841$	24.3887			0.840989
$842$	27.1839	+	15.6946i	0.936819	+	0.540873i
$843$	20.4716	−	16.4307i	0.705081	−	0.565903i
$844$	6.36172	+	11.0188i	0.218979	+	0.379283i
$845$	6.29604	−	10.9051i	0.216590	−	0.375145i
$846$	12.6732	+	40.1903i	0.435714	+	1.38177i
$847$		0			0
$848$			7.75614i			0.266347i
$849$	38.6453	+	15.0277i	1.32630	+	0.515750i
$850$	7.41264	−	4.27969i	0.254252	−	0.146792i
$851$	−67.0739	+	38.7251i	−2.29926	+	1.32748i
$852$	4.47117	+	1.73867i	0.153180	+	0.0595658i
$853$			49.6034i			1.69839i	0.528081	+	0.849194i	$0.322912\pi$
$853$			49.6034i			1.69839i	−0.528081	+	0.849194i	$0.677088\pi$
$854$		0			0
$855$	0.809428	+	2.56693i	0.0276819	+	0.0877871i
$856$	1.41187	−	2.44543i	0.0482567	−	0.0835830i
$857$	2.62252	+	4.54233i	0.0895834	+	0.155163i	0.907335	−	0.420408i	$-0.138113\pi$
$857$	2.62252	+	4.54233i	0.0895834	+	0.155163i	−0.817752	+	0.575571i	$0.804780\pi$
$858$	−8.35058	+	6.70224i	−0.285084	+	0.228811i
$859$	10.1722	+	5.87292i	0.347071	+	0.200382i	0.663394	−	0.748270i	$-0.269115\pi$
$859$	10.1722	+	5.87292i	0.347071	+	0.200382i	−0.316323	+	0.948651i	$0.602448\pi$
$860$	7.10303			0.242211
$861$		0			0
$862$	−64.0863			−2.18279
$863$	−30.3896	−	17.5454i	−1.03447	−	0.597254i	−0.116211	−	0.993225i	$-0.537075\pi$
$863$	−30.3896	−	17.5454i	−1.03447	−	0.597254i	−0.918263	+	0.395971i	$0.870408\pi$
$864$	−23.4306	+	35.0695i	−0.797124	+	1.19309i
$865$	−5.59208	−	9.68576i	−0.190136	−	0.329326i
$866$	−23.0097	+	39.8539i	−0.781901	+	1.35429i
$867$	0.370054	−	0.0569621i	0.0125677	−	0.00193454i
$868$		0			0
$869$			42.6096i			1.44543i
$870$	2.78078	−	7.15105i	0.0942771	−	0.242443i
$871$	2.67074	−	1.54195i	0.0904944	−	0.0522470i
$872$	−0.620205	+	0.358076i	−0.0210028	+	0.0121260i
$873$	37.8077	+	8.38066i	1.27960	+	0.283642i
$874$			12.5933i			0.425973i
$875$		0			0
$876$	8.59208	+	55.8184i	0.290299	+	1.88593i
$877$	8.42662	−	14.5953i	0.284547	−	0.492850i	−0.687952	−	0.725756i	$-0.741490\pi$
$877$	8.42662	−	14.5953i	0.284547	−	0.492850i	0.972499	+	0.232906i	$0.0748235\pi$
$878$	−26.6936	−	46.2346i	−0.900864	−	1.56034i
$879$	23.0081	+	28.6667i	0.776045	+	0.966905i
$880$	−13.9125	−	8.03236i	−0.468989	−	0.270771i
$881$	−51.9437			−1.75003			−0.875015	−	0.484096i	$-0.839148\pi$
$881$	−51.9437			−1.75003			−0.875015	+	0.484096i	$0.839148\pi$
$882$		0			0
$883$	14.9096			0.501748			0.250874	−	0.968020i	$-0.419282\pi$
$883$	14.9096			0.501748			0.250874	+	0.968020i	$0.419282\pi$
$884$	5.17638	+	2.98858i	0.174100	+	0.100517i
$885$	0.550867	+	0.686346i	0.0185172	+	0.0230713i
$886$	−31.9387	−	55.3194i	−1.07300	−	1.85849i
$887$	−6.59427	+	11.4216i	−0.221414	+	0.383500i	−0.955238	−	0.295840i	$-0.904401\pi$
$887$	−6.59427	+	11.4216i	−0.221414	+	0.383500i	0.733824	+	0.679340i	$0.237734\pi$
$888$	1.58073	+	10.2692i	0.0530458	+	0.344612i
$889$		0			0
$890$		−	28.4705i		−	0.954335i
$891$	−42.0681	+	3.68285i	−1.40933	+	0.123380i
$892$	0.766431	−	0.442499i	0.0256620	−	0.0148160i
$893$	−5.29076	+	3.05462i	−0.177048	+	0.102219i
$894$	11.2228	−	28.8605i	0.375345	−	0.965239i
$895$		−	0.247690i		−	0.00827935i
$896$		0			0
$897$	−7.43963	+	1.14518i	−0.248402	+	0.0382363i
$898$	−24.9642	+	43.2392i	−0.833065	+	1.44291i
$899$	−2.51001	−	4.34747i	−0.0837135	−	0.144996i
$900$	4.98886	+	4.57120i	0.166295	+	0.152373i
$901$	8.14028	+	4.69979i	0.271192	+	0.156573i
$902$	39.7453			1.32338
$903$		0			0
$904$	−6.29206			−0.209271
$905$	−12.4175	−	7.16927i	−0.412773	−	0.238315i
$906$	37.5074	−	30.1037i	1.24610	−	1.00013i
$907$	−23.4709	−	40.6527i	−0.779337	−	1.34985i	−0.932324	−	0.361623i	$-0.882223\pi$
$907$	−23.4709	−	40.6527i	−0.779337	−	1.34985i	0.152987	−	0.988228i	$-0.451111\pi$
$908$	−26.4174	+	45.7562i	−0.876691	+	1.51847i
$909$	25.8640	−	8.15567i	0.857854	−	0.270507i
$910$		0			0
$911$		−	45.2977i		−	1.50078i	−0.660996	−	0.750389i	$-0.729866\pi$
$911$		−	45.2977i		−	1.50078i	0.660996	−	0.750389i	$-0.270134\pi$
$912$	−4.95867	−	1.92824i	−0.164198	−	0.0638504i
$913$	11.2298	−	6.48352i	0.371652	−	0.214573i
$914$	−4.31355	+	2.49043i	−0.142680	+	0.0823761i
$915$	8.36846	+	3.25418i	0.276653	+	0.107580i
$916$		−	17.4309i		−	0.575932i
$917$		0			0
$918$	19.6728	+	39.8884i	0.649300	+	1.31651i
$919$	−21.5911	+	37.3969i	−0.712225	+	1.23361i	0.251795	+	0.967781i	$0.418979\pi$
$919$	−21.5911	+	37.3969i	−0.712225	+	1.23361i	−0.964020	+	0.265830i	$0.914354\pi$
$920$	1.79301	+	3.10559i	0.0591139	+	0.102388i
$921$	32.7994	−	26.3250i	1.08078	−	0.867440i
$922$	−13.3162	−	7.68811i	−0.438546	−	0.253195i
$923$	−0.784311			−0.0258159
$924$		0			0
$925$	−11.3824			−0.374252
$926$	−24.8077	−	14.3227i	−0.815232	−	0.470675i
$927$	−31.4557	+	34.3298i	−1.03314	+	1.12754i
$928$	8.71510	+	15.0950i	0.286087	+	0.495517i
$929$	−4.50570	+	7.80410i	−0.147827	+	0.256044i	−0.930424	−	0.366484i	$-0.880561\pi$
$929$	−4.50570	+	7.80410i	−0.147827	+	0.256044i	0.782597	+	0.622529i	$0.213895\pi$
$930$	8.25548	−	1.27076i	0.270708	−	0.0416698i
$931$		0			0
$932$		−	9.20194i		−	0.301419i
$933$	4.46772	−	11.4892i	0.146267	−	0.376139i
$934$	35.9774	−	20.7716i	1.17722	−	0.679667i
$935$	−16.8604	+	9.73433i	−0.551392	+	0.318347i
$936$	−0.218534	+	0.985871i	−0.00714299	+	0.0322242i
$937$			21.9677i			0.717654i	0.933404	+	0.358827i	$0.116823\pi$
$937$			21.9677i			0.717654i	−0.933404	+	0.358827i	$0.883177\pi$
$938$		0			0
$939$	0.934731	+	6.07248i	0.0305038	+	0.198168i
$940$	−7.67925	+	13.3009i	−0.250470	+	0.433826i
$941$	0.823861	+	1.42697i	0.0268571	+	0.0465178i	0.879142	−	0.476561i	$-0.158117\pi$
$941$	0.823861	+	1.42697i	0.0268571	+	0.0465178i	−0.852284	+	0.523079i	$0.824783\pi$
$942$	17.4740	+	21.7715i	0.569334	+	0.709355i
$943$	24.1970	+	13.9702i	0.787964	+	0.454931i
$944$	−1.73965			−0.0566209
$945$		0			0
$946$	−30.4823			−0.991064
$947$	23.6645	+	13.6627i	0.768994	+	0.443979i	0.832516	−	0.554002i	$-0.186900\pi$
$947$	23.6645	+	13.6627i	0.768994	+	0.443979i	−0.0635217	+	0.997980i	$0.520233\pi$
$948$	22.2059	+	27.6671i	0.721213	+	0.898586i
$949$	−4.61660	−	7.99619i	−0.149861	−	0.259567i
$950$	−0.925382	+	1.60281i	−0.0300233	+	0.0520020i
$951$	−5.55384	−	36.0805i	−0.180095	−	1.16999i
$952$		0			0
$953$			55.2380i			1.78933i	0.446734	+	0.894667i	$0.352587\pi$
$953$			55.2380i			1.78933i	−0.446734	+	0.894667i	$0.647413\pi$
$954$	−3.03401	+	13.6874i	−0.0982299	+	0.443145i
$955$	−14.7572	+	8.52006i	−0.477531	+	0.275703i
$956$	−11.2565	+	6.49894i	−0.364061	+	0.210191i
$957$	−6.32499	+	16.2653i	−0.204458	+	0.525784i
$958$			68.5654i			2.21525i
$959$		0			0
$960$	−16.9419	+	2.60785i	−0.546797	+	0.0841679i
$961$	−12.7675	+	22.1140i	−0.411856	+	0.713355i
$962$	−7.49840	−	12.9876i	−0.241758	−	0.418737i
$963$	−10.8590	+	11.8512i	−0.349926	+	0.381899i
$964$	39.8858	+	23.0281i	1.28464	+	0.741684i
$965$	−2.82362			−0.0908956
$966$		0			0
$967$	−34.5930			−1.11244			−0.556218	−	0.831036i	$-0.687748\pi$
$967$	−34.5930			−1.11244			−0.556218	+	0.831036i	$0.687748\pi$
$968$	−5.02776	−	2.90278i	−0.161598	−	0.0932989i
$969$	−5.02841	+	4.03584i	−0.161536	+	0.129650i
$970$	13.3143	+	23.0611i	0.427497	+	0.740447i
$971$	2.12246	−	3.67621i	0.0681129	−	0.117975i	−0.829958	−	0.557826i	$-0.811636\pi$
$971$	2.12246	−	3.67621i	0.0681129	−	0.117975i	0.898071	+	0.439851i	$0.144969\pi$
$972$	−25.3962	+	24.3150i	−0.814583	+	0.779903i
$973$		0			0
$974$		−	66.4407i		−	2.12890i
$975$	−1.03103	−	0.400929i	−0.0330194	−	0.0128400i
$976$	−15.3709	+	8.87439i	−0.492010	+	0.284062i
$977$	33.6806	−	19.4455i	1.07754	−	0.622118i	0.147308	−	0.989091i	$-0.452939\pi$
$977$	33.6806	−	19.4455i	1.07754	−	0.622118i	0.930232	+	0.366973i	$0.119606\pi$
$978$	−55.5423	−	21.5983i	−1.77605	−	0.690638i
$979$			64.7574i			2.06966i
$980$		0			0
$981$	3.88790	−	1.22597i	0.124131	−	0.0391422i
$982$	23.2077	−	40.1970i	0.740588	−	1.28274i
$983$	−13.1884	−	22.8429i	−0.420644	−	0.728577i	0.575359	−	0.817901i	$-0.304862\pi$
$983$	−13.1884	−	22.8429i	−0.420644	−	0.728577i	−0.996003	+	0.0893246i	$0.971529\pi$
$984$	2.92319	−	2.34617i	0.0931878	−	0.0747932i
$985$	8.31103	+	4.79838i	0.264812	+	0.152889i
$986$	18.3804			0.585352
$987$		0			0
$988$	−1.29242			−0.0411174
$989$	−18.5577	−	10.7143i	−0.590099	−	0.340694i
$990$	−21.4094	−	19.6170i	−0.680436	−	0.623470i
$991$	6.90833	+	11.9656i	0.219450	+	0.380099i	0.954640	−	0.297762i	$-0.0962403\pi$
$991$	6.90833	+	11.9656i	0.219450	+	0.380099i	−0.735190	+	0.677861i	$0.762907\pi$
$992$	−9.48750	+	16.4328i	−0.301228	+	0.521743i
$993$	−25.3501	+	3.90211i	−0.804460	+	0.123830i
$994$		0			0
$995$			12.2141i			0.387213i
$996$	3.91282	−	10.0622i	0.123983	−	0.318834i
$997$	−53.1001	+	30.6574i	−1.68170	+	0.970929i	−0.721165	+	0.692763i	$0.756393\pi$
$997$	−53.1001	+	30.6574i	−1.68170	+	0.970929i	−0.960533	+	0.278166i	$0.910274\pi$
$998$	11.4587	−	6.61570i	0.362720	−	0.209416i
$999$	3.86579	−	59.0184i	0.122308	−	1.86726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.s.l.656.1		8
3.2	odd	2		735.2.s.k.656.4		8
7.2	even	3		735.2.b.d.146.7		8
7.3	odd	6		735.2.s.k.521.4		8
7.4	even	3		105.2.s.c.101.4	yes	8
7.5	odd	6		735.2.b.c.146.7		8
7.6	odd	2		105.2.s.d.26.1	yes	8
21.2	odd	6		735.2.b.c.146.2		8
21.5	even	6		735.2.b.d.146.2		8
21.11	odd	6		105.2.s.d.101.1	yes	8
21.17	even	6	inner	735.2.s.l.521.1		8
21.20	even	2		105.2.s.c.26.4	✓	8
35.4	even	6		525.2.t.g.101.1		8
35.13	even	4		525.2.q.e.299.2		16
35.18	odd	12		525.2.q.f.374.2		16
35.27	even	4		525.2.q.e.299.7		16
35.32	odd	12		525.2.q.f.374.7		16
35.34	odd	2		525.2.t.f.26.4		8
105.32	even	12		525.2.q.e.374.2		16
105.53	even	12		525.2.q.e.374.7		16
105.62	odd	4		525.2.q.f.299.2		16
105.74	odd	6		525.2.t.f.101.4		8
105.83	odd	4		525.2.q.f.299.7		16
105.104	even	2		525.2.t.g.26.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.4	✓	8	21.20	even	2
105.2.s.c.101.4	yes	8	7.4	even	3
105.2.s.d.26.1	yes	8	7.6	odd	2
105.2.s.d.101.1	yes	8	21.11	odd	6
525.2.q.e.299.2		16	35.13	even	4
525.2.q.e.299.7		16	35.27	even	4
525.2.q.e.374.2		16	105.32	even	12
525.2.q.e.374.7		16	105.53	even	12
525.2.q.f.299.2		16	105.62	odd	4
525.2.q.f.299.7		16	105.83	odd	4
525.2.q.f.374.2		16	35.18	odd	12
525.2.q.f.374.7		16	35.32	odd	12
525.2.t.f.26.4		8	35.34	odd	2
525.2.t.f.101.4		8	105.74	odd	6
525.2.t.g.26.1		8	105.104	even	2
525.2.t.g.101.1		8	35.4	even	6
735.2.b.c.146.2		8	21.2	odd	6
735.2.b.c.146.7		8	7.5	odd	6
735.2.b.d.146.2		8	21.5	even	6
735.2.b.d.146.7		8	7.2	even	3
735.2.s.k.521.4		8	7.3	odd	6
735.2.s.k.656.4		8	3.2	odd	2
735.2.s.l.521.1		8	21.17	even	6	inner
735.2.s.l.656.1		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.78651 - 1.03144i) q^{2} +(-1.08415 - 1.35078i) q^{3} +(1.12774 + 1.95330i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.543588 + 3.53142i) q^{6} -0.527019i q^{8} +(-0.649237 + 2.92891i) q^{9} +(-1.78651 + 1.03144i) q^{10} +(4.06348 - 2.34605i) q^{11} +(1.41585 - 3.64100i) q^{12} +0.638688i q^{13} +(-1.71189 + 0.263509i) q^{15} +(1.71189 - 2.96508i) q^{16} +(-2.07462 - 3.59334i) q^{17} +(4.18086 - 4.56286i) q^{18} +(0.776975 + 0.448587i) q^{19} +2.25548 q^{20} -9.67925 q^{22} +(-5.89275 - 3.40218i) q^{23} +(-0.711889 + 0.571367i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.658769 - 1.14102i) q^{26} +(4.66019 - 2.29839i) q^{27} -2.14740i q^{29} +(3.33010 + 1.29495i) q^{30} +(2.02453 - 1.16886i) q^{31} +(-7.02943 + 4.05844i) q^{32} +(-7.57444 - 2.94542i) q^{33} +8.55938i q^{34} +(-6.45320 + 2.03489i) q^{36} +(5.69122 - 9.85748i) q^{37} +(-0.925382 - 1.60281i) q^{38} +(0.862730 - 0.692434i) q^{39} +(-0.456412 - 0.263509i) q^{40} -4.10624 q^{41} +3.14924 q^{43} +(9.16509 + 5.29147i) q^{44} +(2.21189 + 2.02671i) q^{45} +(7.01829 + 12.1560i) q^{46} +(-3.40471 + 5.89714i) q^{47} +(-5.86113 + 0.902197i) q^{48} +2.06288i q^{50} +(-2.60464 + 6.69809i) q^{51} +(-1.24755 + 0.720273i) q^{52} +(-1.96187 + 1.13269i) q^{53} +(-10.6961 - 0.700610i) q^{54} -4.69211i q^{55} +(-0.236414 - 1.53586i) q^{57} +(-2.21492 + 3.83635i) q^{58} +(-0.254055 - 0.440035i) q^{59} +(-2.44528 - 3.04666i) q^{60} +(-4.48946 - 2.59199i) q^{61} -4.82244 q^{62} +9.89660 q^{64} +(0.553120 + 0.319344i) q^{65} +(10.4938 + 13.0746i) q^{66} +(-2.41425 - 4.18160i) q^{67} +(4.67925 - 8.10471i) q^{68} +(1.79301 + 11.6483i) q^{69} +1.22800i q^{71} +(1.54359 + 0.342160i) q^{72} +(-12.5197 + 7.22826i) q^{73} +(-20.3348 + 11.7403i) q^{74} +(-0.627739 + 1.61429i) q^{75} +2.02356i q^{76} +(-2.25548 + 0.347183i) q^{78} +(-4.54056 + 7.86448i) q^{79} +(-1.71189 - 2.96508i) q^{80} +(-8.15698 - 3.80311i) q^{81} +(7.33583 + 4.23534i) q^{82} +2.76359 q^{83} -4.14924 q^{85} +(-5.62613 - 3.24825i) q^{86} +(-2.90067 + 2.32810i) q^{87} +(-1.23641 - 2.14153i) q^{88} +(-6.90067 + 11.9523i) q^{89} +(-1.86113 - 5.90216i) q^{90} -15.3471i q^{92} +(-3.77377 - 1.46748i) q^{93} +(12.1651 - 7.02352i) q^{94} +(0.776975 - 0.448587i) q^{95} +(13.1030 + 5.09528i) q^{96} -12.9085i q^{97} +(4.23321 + 13.4247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 2 q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{9} + 3 q^{10} + 18 q^{12} - q^{15} + q^{16} - 12 q^{17} + 26 q^{18} - 9 q^{19} + 6 q^{20} - 40 q^{22} - 27 q^{23} + 7 q^{24} - 4 q^{25} - 6 q^{26}+ \cdots - 34 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^9 + 3 * q^10 + 18 * q^12 - q^15 + q^16 - 12 * q^17 + 26 * q^18 - 9 * q^19 + 6 * q^20 - 40 * q^22 - 27 * q^23 + 7 * q^24 - 4 * q^25 - 6 * q^26 + 4 * q^27 + 10 * q^30 + 21 * q^31 - 21 * q^32 - 4 * q^33 + 9 * q^36 + 7 * q^37 - 12 * q^38 + 15 * q^39 - 3 * q^40 - 30 * q^41 + 16 * q^43 + 5 * q^45 - 7 * q^46 - 6 * q^47 - 25 * q^48 + 12 * q^51 - 30 * q^52 - 24 * q^53 - 7 * q^54 + 6 * q^57 - 13 * q^58 - 12 * q^59 + 9 * q^60 - 15 * q^61 + 24 * q^62 + 38 * q^64 + 3 * q^65 + 16 * q^66 + 4 * q^67 - 13 * q^69 + 13 * q^72 - 15 * q^73 - 54 * q^74 + q^75 - 6 * q^78 - 29 * q^79 - q^80 + 28 * q^81 - 27 * q^82 + 30 * q^83 - 24 * q^85 - 9 * q^86 + 29 * q^87 - 2 * q^88 - 3 * q^89 + 7 * q^90 + 45 * q^93 + 24 * q^94 - 9 * q^95 + 42 * q^96 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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