LMFDB - Embedded newform 351.2.l.b.199.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(127,351)] 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("351.127"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Character	$\chi$	$=$	351.199
Dual form			351.2.l.b.127.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.65149i q^{2} -5.03038 q^{4} +(-2.43120 - 1.40366i) q^{5} +(0.226187 + 0.130589i) q^{7} +8.03502i q^{8} +(-3.72178 + 6.44631i) q^{10} +1.55873i q^{11} +(-2.26304 + 2.80689i) q^{13} +(0.346256 - 0.599733i) q^{14} +11.2440 q^{16} +(-3.65449 - 6.32976i) q^{17} +(0.447398 - 0.258305i) q^{19} +(12.2299 + 7.06093i) q^{20} +4.13296 q^{22} +(1.37475 + 2.38113i) q^{23} +(1.44050 + 2.49502i) q^{25} +(7.44243 + 6.00043i) q^{26} +(-1.13781 - 0.656914i) q^{28} -3.56626 q^{29} +(-3.17297 - 1.83191i) q^{31} -13.7433i q^{32} +(-16.7833 + 9.68983i) q^{34} +(-0.366605 - 0.634978i) q^{35} +(1.90801 + 1.10159i) q^{37} +(-0.684893 - 1.18627i) q^{38} +(11.2784 - 19.5348i) q^{40} +(-6.42975 + 3.71222i) q^{41} +(1.74859 - 3.02865i) q^{43} -7.84102i q^{44} +(6.31353 - 3.64512i) q^{46} +(-7.10819 + 4.10392i) q^{47} +(-3.46589 - 6.00310i) q^{49} +(6.61553 - 3.81948i) q^{50} +(11.3840 - 14.1197i) q^{52} -4.68042 q^{53} +(2.18792 - 3.78960i) q^{55} +(-1.04929 + 1.81742i) q^{56} +9.45590i q^{58} -11.1417i q^{59} +(1.80731 - 3.13036i) q^{61} +(-4.85729 + 8.41308i) q^{62} -13.9521 q^{64} +(9.44183 - 3.64759i) q^{65} +(-7.11290 + 4.10664i) q^{67} +(18.3835 + 31.8411i) q^{68} +(-1.68364 + 0.972048i) q^{70} +(5.40445 - 3.12026i) q^{71} -3.76021i q^{73} +(2.92085 - 5.05907i) q^{74} +(-2.25058 + 1.29937i) q^{76} +(-0.203554 + 0.352565i) q^{77} +(-1.36567 - 2.36542i) q^{79} +(-27.3365 - 15.7827i) q^{80} +(9.84289 + 17.0484i) q^{82} +(-7.18029 + 4.14554i) q^{83} +20.5186i q^{85} +(-8.03044 - 4.63638i) q^{86} -12.5244 q^{88} +(1.18531 + 0.684339i) q^{89} +(-0.878421 + 0.339353i) q^{91} +(-6.91550 - 11.9780i) q^{92} +(10.8815 + 18.8473i) q^{94} -1.45029 q^{95} +(-11.7284 - 6.77137i) q^{97} +(-15.9171 + 9.18977i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 20 q^{4} + 3 q^{5} - 6 q^{7} - 7 q^{10} + 9 q^{14} + 24 q^{16} - 9 q^{17} - 6 q^{19} + 24 q^{20} + 26 q^{22} - 6 q^{23} + 4 q^{25} + 12 q^{26} + 3 q^{28} - 48 q^{29} - 27 q^{31} + 15 q^{34} + 27 q^{35}+ \cdots - 117 q^{98}+O(q^{100}) $ 22 * q - 20 * q^4 + 3 * q^5 - 6 * q^7 - 7 * q^10 + 9 * q^14 + 24 * q^16 - 9 * q^17 - 6 * q^19 + 24 * q^20 + 26 * q^22 - 6 * q^23 + 4 * q^25 + 12 * q^26 + 3 * q^28 - 48 * q^29 - 27 * q^31 + 15 * q^34 + 27 * q^35 + 6 * q^37 - 21 * q^38 + 13 * q^40 - 6 * q^41 - 4 * q^43 - 15 * q^46 + 6 * q^47 + 7 * q^49 - 18 * q^50 - 22 * q^52 + 24 * q^53 - 13 * q^55 + 9 * q^56 + 3 * q^61 - 24 * q^64 + 57 * q^65 - 45 * q^67 + 69 * q^68 - 24 * q^70 - 9 * q^71 + 6 * q^74 + 18 * q^76 - 42 * q^77 - 6 * q^79 - 105 * q^80 - 16 * q^82 - 42 * q^83 - 45 * q^86 + 22 * q^88 + 30 * q^89 + 15 * q^91 + 3 * q^92 + 44 * q^94 - 6 * q^95 - 27 * q^97 - 117 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	2.65149i		−	1.87488i	−0.348141	−	0.937442i	$-0.613187\pi$
$2$		−	2.65149i		−	1.87488i	0.348141	−	0.937442i	$-0.386813\pi$
$3$		0			0
$3$		0			0
$4$	−5.03038			−2.51519
$5$	−2.43120	−	1.40366i	−1.08727	−	0.627734i	−0.154420	−	0.988005i	$-0.549351\pi$
$5$	−2.43120	−	1.40366i	−1.08727	−	0.627734i	−0.932848	+	0.360271i	$0.882684\pi$
$6$		0			0
$7$	0.226187	+	0.130589i	0.0854907	+	0.0493581i	0.542136	−	0.840291i	$-0.317616\pi$
$7$	0.226187	+	0.130589i	0.0854907	+	0.0493581i	−0.456645	+	0.889649i	$0.650949\pi$
$8$			8.03502i			2.84081i
$9$		0			0
$10$	−3.72178	+	6.44631i	−1.17693	+	2.03850i
$11$			1.55873i			0.469975i	0.971998	+	0.234988i	$0.0755050\pi$
$11$			1.55873i			0.469975i	−0.971998	+	0.234988i	$0.924495\pi$
$12$		0			0
$13$	−2.26304	+	2.80689i	−0.627656	+	0.778491i
$13$	−2.26304	+	2.80689i	−0.627656	+	0.778491i
$14$	0.346256	−	0.599733i	0.0925407	−	0.160285i
$15$		0			0
$16$	11.2440			2.81100
$17$	−3.65449	−	6.32976i	−0.886344	−	1.53519i	−0.844166	−	0.536082i	$-0.819904\pi$
$17$	−3.65449	−	6.32976i	−0.886344	−	1.53519i	−0.0421777	−	0.999110i	$-0.513430\pi$
$18$		0			0
$19$	0.447398	−	0.258305i	0.102640	−	0.0592593i	−0.447801	−	0.894133i	$-0.647793\pi$
$19$	0.447398	−	0.258305i	0.102640	−	0.0592593i	0.550441	+	0.834874i	$0.314459\pi$
$20$	12.2299	+	7.06093i	2.73469	+	1.57887i
$21$		0			0
$22$	4.13296			0.881150
$23$	1.37475	+	2.38113i	0.286654	+	0.496500i	0.973009	−	0.230767i	$-0.0741236\pi$
$23$	1.37475	+	2.38113i	0.286654	+	0.496500i	−0.686355	+	0.727267i	$0.740790\pi$
$24$		0			0
$25$	1.44050	+	2.49502i	0.288101	+	0.499005i
$26$	7.44243	+	6.00043i	1.45958	+	1.17678i
$27$		0			0
$28$	−1.13781	−	0.656914i	−0.215026	−	0.124145i
$29$	−3.56626			−0.662238			−0.331119	−	0.943589i	$-0.607426\pi$
$29$	−3.56626			−0.662238			−0.331119	+	0.943589i	$0.607426\pi$
$30$		0			0
$31$	−3.17297	−	1.83191i	−0.569882	−	0.329021i	0.187221	−	0.982318i	$-0.440052\pi$
$31$	−3.17297	−	1.83191i	−0.569882	−	0.329021i	−0.757102	+	0.653297i	$0.773385\pi$
$32$		−	13.7433i		−	2.42949i
$33$		0			0
$34$	−16.7833	+	9.68983i	−2.87831	+	1.66179i
$35$	−0.366605	−	0.634978i	−0.0619675	−	0.107331i
$36$		0			0
$37$	1.90801	+	1.10159i	0.313675	+	0.181100i	0.648570	−	0.761155i	$-0.275367\pi$
$37$	1.90801	+	1.10159i	0.313675	+	0.181100i	−0.334895	+	0.942256i	$0.608701\pi$
$38$	−0.684893	−	1.18627i	−0.111104	−	0.192438i
$39$		0			0
$40$	11.2784	−	19.5348i	1.78327	−	3.08872i
$41$	−6.42975	+	3.71222i	−1.00416	+	0.579751i	−0.909476	−	0.415757i	$-0.863517\pi$
$41$	−6.42975	+	3.71222i	−1.00416	+	0.579751i	−0.0946819	+	0.995508i	$0.530183\pi$
$42$		0			0
$43$	1.74859	−	3.02865i	0.266658	−	0.461865i	−0.701339	−	0.712828i	$-0.747414\pi$
$43$	1.74859	−	3.02865i	0.266658	−	0.461865i	0.967997	+	0.250963i	$0.0807472\pi$
$44$		−	7.84102i		−	1.18208i
$45$		0			0
$46$	6.31353	−	3.64512i	0.930880	−	0.537444i
$47$	−7.10819	+	4.10392i	−1.03684	+	0.598618i	−0.918936	−	0.394407i	$-0.870950\pi$
$47$	−7.10819	+	4.10392i	−1.03684	+	0.598618i	−0.117901	+	0.993025i	$0.537617\pi$
$48$		0			0
$49$	−3.46589	−	6.00310i	−0.495128	−	0.857586i
$50$	6.61553	−	3.81948i	0.935577	−	0.540155i
$51$		0			0
$52$	11.3840	−	14.1197i	1.57867	−	1.95805i
$53$	−4.68042			−0.642905			−0.321452	−	0.946926i	$-0.604171\pi$
$53$	−4.68042			−0.642905			−0.321452	+	0.946926i	$0.604171\pi$
$54$		0			0
$55$	2.18792	−	3.78960i	0.295020	−	0.510989i
$56$	−1.04929	+	1.81742i	−0.140217	+	0.242863i
$57$		0			0
$58$			9.45590i			1.24162i
$59$		−	11.1417i		−	1.45053i	−0.688469	−	0.725265i	$-0.741717\pi$
$59$		−	11.1417i		−	1.45053i	0.688469	−	0.725265i	$-0.258283\pi$
$60$		0			0
$61$	1.80731	−	3.13036i	0.231403	−	0.400801i	−0.726818	−	0.686830i	$-0.759002\pi$
$61$	1.80731	−	3.13036i	0.231403	−	0.400801i	0.958221	+	0.286028i	$0.0923352\pi$
$62$	−4.85729	+	8.41308i	−0.616877	+	1.06846i
$63$		0			0
$64$	−13.9521			−1.74401
$65$	9.44183	−	3.64759i	1.17112	−	0.452427i
$66$		0			0
$67$	−7.11290	+	4.10664i	−0.868979	+	0.501706i	−0.867009	−	0.498293i	$-0.833961\pi$
$67$	−7.11290	+	4.10664i	−0.868979	+	0.501706i	−0.00197050	+	0.999998i	$0.500627\pi$
$68$	18.3835	+	31.8411i	2.22932	+	3.86130i
$69$		0			0
$70$	−1.68364	+	0.972048i	−0.201233	+	0.116182i
$71$	5.40445	−	3.12026i	0.641390	−	0.370307i	−0.143760	−	0.989613i	$-0.545919\pi$
$71$	5.40445	−	3.12026i	0.641390	−	0.370307i	0.785150	+	0.619306i	$0.212586\pi$
$72$		0			0
$73$		−	3.76021i		−	0.440099i	−0.975489	−	0.220050i	$-0.929378\pi$
$73$		−	3.76021i		−	0.440099i	0.975489	−	0.220050i	$-0.0706220\pi$
$74$	2.92085	−	5.05907i	0.339542	−	0.588105i
$75$		0			0
$76$	−2.25058	+	1.29937i	−0.258159	+	0.149048i
$77$	−0.203554	+	0.352565i	−0.0231971	+	0.0401785i
$78$		0			0
$79$	−1.36567	−	2.36542i	−0.153650	−	0.266130i	0.778916	−	0.627128i	$-0.215770\pi$
$79$	−1.36567	−	2.36542i	−0.153650	−	0.266130i	−0.932567	+	0.360998i	$0.882436\pi$
$80$	−27.3365	−	15.7827i	−3.05631	−	1.76456i
$81$		0			0
$82$	9.84289	+	17.0484i	1.08697	+	1.88268i
$83$	−7.18029	+	4.14554i	−0.788139	+	0.455032i	−0.839307	−	0.543658i	$-0.817039\pi$
$83$	−7.18029	+	4.14554i	−0.788139	+	0.455032i	0.0511680	+	0.998690i	$0.483706\pi$
$84$		0			0
$85$			20.5186i			2.22555i
$86$	−8.03044	−	4.63638i	−0.865944	−	0.499953i
$87$		0			0
$88$	−12.5244			−1.33511
$89$	1.18531	+	0.684339i	0.125643	+	0.0725398i	0.561504	−	0.827474i	$-0.310223\pi$
$89$	1.18531	+	0.684339i	0.125643	+	0.0725398i	−0.435861	+	0.900014i	$0.643556\pi$
$90$		0			0
$91$	−0.878421	+	0.339353i	−0.0920836	+	0.0355739i
$92$	−6.91550	−	11.9780i	−0.720990	−	1.24879i
$93$		0			0
$94$	10.8815	+	18.8473i	1.12234	+	1.94395i
$95$	−1.45029			−0.148796
$96$		0			0
$97$	−11.7284	−	6.77137i	−1.19083	−	0.687528i	−0.232338	−	0.972635i	$-0.574638\pi$
$97$	−11.7284	−	6.77137i	−1.19083	−	0.687528i	−0.958496	+	0.285107i	$0.907971\pi$
$98$	−15.9171	+	9.18977i	−1.60787	+	0.928307i
$99$		0			0
$100$	−7.24628	−	12.5509i	−0.724628	−	1.25509i
$101$	15.4095			1.53331			0.766653	−	0.642061i	$-0.221921\pi$
$101$	15.4095			1.53331			0.766653	+	0.642061i	$0.221921\pi$
$102$		0			0
$103$	5.49573	−	9.51889i	0.541510	−	0.937924i	−0.457307	−	0.889309i	$-0.651186\pi$
$103$	5.49573	−	9.51889i	0.541510	−	0.937924i	0.998818	−	0.0486148i	$-0.0154807\pi$
$104$	−22.5534	−	18.1836i	−2.21155	−	1.78305i
$105$		0			0
$106$			12.4101i			1.20537i
$107$	0.595733	−	1.03184i	0.0575917	−	0.0997518i	−0.835792	−	0.549046i	$-0.814991\pi$
$107$	0.595733	−	1.03184i	0.0575917	−	0.0997518i	0.893384	+	0.449294i	$0.148325\pi$
$108$		0			0
$109$		−	1.56215i		−	0.149627i	−0.997198	−	0.0748135i	$-0.976164\pi$
$109$		−	1.56215i		−	0.149627i	0.997198	−	0.0748135i	$-0.0238362\pi$
$110$	−10.0481	−	5.80125i	−0.958045	−	0.553128i
$111$		0			0
$112$	2.54325	+	1.46835i	0.240314	+	0.138746i
$113$	4.59209			0.431988			0.215994	−	0.976395i	$-0.430701\pi$
$113$	4.59209			0.431988			0.215994	+	0.976395i	$0.430701\pi$
$114$		0			0
$115$		−	7.71868i		−	0.719771i
$116$	17.9397			1.66566
$117$		0			0
$118$	−29.5422			−2.71958
$119$		−	1.90895i		−	0.174993i
$120$		0			0
$121$	8.57035			0.779123
$122$	−8.30010	−	4.79207i	−0.751456	−	0.433853i
$123$		0			0
$124$	15.9612	+	9.21522i	1.43336	+	0.827552i
$125$			5.94868i			0.532066i
$126$		0			0
$127$	5.62331	−	9.73987i	0.498988	−	0.864273i	−0.501011	−	0.865441i	$-0.667038\pi$
$127$	5.62331	−	9.73987i	0.498988	−	0.864273i	0.999999	+	0.00116769i	$0.000371687\pi$
$128$			9.50727i			0.840332i
$129$		0			0
$130$	−9.67153	−	25.0349i	−0.848249	−	2.19571i
$131$	1.93018	−	3.34317i	0.168640	−	0.292094i	−0.769302	−	0.638886i	$-0.779396\pi$
$131$	1.93018	−	3.34317i	0.168640	−	0.292094i	0.937942	+	0.346792i	$0.112729\pi$
$132$		0			0
$133$	0.134928			0.0116997
$134$	10.8887	+	18.8598i	0.940640	+	1.62924i
$135$		0			0
$136$	50.8598	−	29.3639i	4.36119	−	2.51793i
$137$	1.93203	+	1.11546i	0.165065	+	0.0953002i	0.580257	−	0.814434i	$-0.302952\pi$
$137$	1.93203	+	1.11546i	0.165065	+	0.0953002i	−0.415192	+	0.909734i	$0.636286\pi$
$138$		0			0
$139$	16.2457			1.37795			0.688973	−	0.724787i	$-0.258062\pi$
$139$	16.2457			1.37795			0.688973	+	0.724787i	$0.258062\pi$
$140$	1.84416	+	3.19419i	0.155860	+	0.269958i
$141$		0			0
$142$	−8.27333	−	14.3298i	−0.694282	−	1.20253i
$143$	−4.37519	−	3.52748i	−0.365872	−	0.294983i
$144$		0			0
$145$	8.67031	+	5.00581i	0.720030	+	0.415710i
$146$	−9.97015			−0.825136
$147$		0			0
$148$	−9.59803	−	5.54143i	−0.788953	−	0.455502i
$149$			7.63642i			0.625600i	0.949819	+	0.312800i	$0.101267\pi$
$149$			7.63642i			0.625600i	−0.949819	+	0.312800i	$0.898733\pi$
$150$		0			0
$151$	−10.8516	+	6.26520i	−0.883095	+	0.509855i	−0.871677	−	0.490080i	$-0.836968\pi$
$151$	−10.8516	+	6.26520i	−0.883095	+	0.509855i	−0.0114171	+	0.999935i	$0.503634\pi$
$152$	2.07549	+	3.59485i	0.168344	+	0.291581i
$153$		0			0
$154$	0.934822	+	0.539720i	0.0753301	+	0.0434919i
$155$	5.14275	+	8.90751i	0.413076	+	0.715468i
$156$		0			0
$157$	−5.04228	+	8.73349i	−0.402418	+	0.697009i	−0.994017	−	0.109224i	$-0.965164\pi$
$157$	−5.04228	+	8.73349i	−0.402418	+	0.697009i	0.591599	+	0.806232i	$0.298497\pi$
$158$	−6.27187	+	3.62107i	−0.498964	+	0.288077i
$159$		0			0
$160$	−19.2908	+	33.4127i	−1.52507	+	2.64150i
$161$			0.718108i			0.0565948i
$162$		0			0
$163$	−10.8176	+	6.24553i	−0.847297	+	0.489187i	−0.859738	−	0.510735i	$-0.829373\pi$
$163$	−10.8176	+	6.24553i	−0.847297	+	0.489187i	0.0124407	+	0.999923i	$0.496040\pi$
$164$	32.3441	−	18.6739i	2.52565	−	1.45818i
$165$		0			0
$166$	10.9918	+	19.0384i	0.853133	+	1.47767i
$167$	21.0667	−	12.1628i	1.63019	−	0.941189i	0.646152	−	0.763209i	$-0.276377\pi$
$167$	21.0667	−	12.1628i	1.63019	−	0.941189i	0.984034	−	0.177980i	$-0.0569562\pi$
$168$		0			0
$169$	−2.75726	−	12.7042i	−0.212097	−	0.977249i
$170$	54.4048			4.17265
$171$		0			0
$172$	−8.79610	+	15.2353i	−0.670696	+	1.16168i
$173$	−5.27316	+	9.13338i	−0.400911	+	0.694398i	−0.993836	−	0.110860i	$-0.964640\pi$
$173$	−5.27316	+	9.13338i	−0.400911	+	0.694398i	0.592925	+	0.805258i	$0.297973\pi$
$174$		0			0
$175$			0.752457i			0.0568804i
$176$			17.5264i			1.32110i
$177$		0			0
$178$	1.81452	−	3.14283i	0.136004	−	0.235565i
$179$	−3.54457	+	6.13938i	−0.264934	+	0.458879i	−0.967546	−	0.252694i	$-0.918683\pi$
$179$	−3.54457	+	6.13938i	−0.264934	+	0.458879i	0.702612	+	0.711573i	$0.252017\pi$
$180$		0			0
$181$	15.7315			1.16931			0.584656	−	0.811281i	$-0.301230\pi$
$181$	15.7315			1.16931			0.584656	+	0.811281i	$0.301230\pi$
$182$	0.899791	+	2.32912i	0.0666970	+	0.172646i
$183$		0			0
$184$	−19.1324	+	11.0461i	−1.41046	+	0.814330i
$185$	−3.09251	−	5.35639i	−0.227366	−	0.393809i
$186$		0			0
$187$	9.86640	−	5.69637i	0.721502	−	0.416560i
$188$	35.7569	−	20.6443i	2.60784	−	1.50564i
$189$		0			0
$190$			3.84542i			0.278976i
$191$	4.06091	−	7.03371i	0.293837	−	0.508941i	−0.680876	−	0.732398i	$-0.738401\pi$
$191$	4.06091	−	7.03371i	0.293837	−	0.508941i	0.974714	+	0.223457i	$0.0717342\pi$
$192$		0			0
$193$	−6.67526	+	3.85396i	−0.480495	+	0.277414i	−0.720623	−	0.693327i	$-0.756144\pi$
$193$	−6.67526	+	3.85396i	−0.480495	+	0.277414i	0.240127	+	0.970741i	$0.422811\pi$
$194$	−17.9542	+	31.0976i	−1.28904	+	2.23268i
$195$		0			0
$196$	17.4348	+	30.1979i	1.24534	+	2.15699i
$197$	3.46949	+	2.00311i	0.247191	+	0.142716i	0.618477	−	0.785803i	$-0.287750\pi$
$197$	3.46949	+	2.00311i	0.247191	+	0.142716i	−0.371287	+	0.928518i	$0.621083\pi$
$198$		0			0
$199$	−6.44292	−	11.1595i	−0.456726	−	0.791073i	0.542059	−	0.840340i	$-0.317645\pi$
$199$	−6.44292	−	11.1595i	−0.456726	−	0.791073i	−0.998786	+	0.0492670i	$0.984311\pi$
$200$	−20.0476	+	11.5745i	−1.41758	+	0.818439i
$201$		0			0
$202$		−	40.8582i		−	2.87477i
$203$	−0.806643	−	0.465716i	−0.0566152	−	0.0326868i
$204$		0			0
$205$	20.8427			1.45572
$206$	−25.2392	−	14.5719i	−1.75850	−	1.01527i
$207$		0			0
$208$	−25.4457	+	31.5607i	−1.76434	+	2.18834i
$209$	0.402628	+	0.697373i	0.0278504	+	0.0482383i
$210$		0			0
$211$	−8.60754	−	14.9087i	−0.592567	−	1.02636i	−0.993885	−	0.110418i	$-0.964781\pi$
$211$	−8.60754	−	14.9087i	−0.592567	−	1.02636i	0.401318	−	0.915939i	$-0.368552\pi$
$212$	23.5443			1.61703
$213$		0			0
$214$	−2.73591	−	1.57958i	−0.187023	−	0.107978i
$215$	−8.50238	+	4.90885i	−0.579858	+	0.334781i
$216$		0			0
$217$	−0.478456	−	0.828711i	−0.0324797	−	0.0562565i
$218$	−4.14203			−0.280534
$219$		0			0
$220$	−11.0061	+	19.0631i	−0.742031	+	1.28524i
$221$	26.0372	+	4.06678i	1.75145	+	0.273561i
$222$		0			0
$223$			9.43422i			0.631762i	0.948799	+	0.315881i	$0.102300\pi$
$223$			9.43422i			0.631762i	−0.948799	+	0.315881i	$0.897700\pi$
$224$	1.79472	−	3.10855i	0.119915	−	0.207699i
$225$		0			0
$226$		−	12.1759i		−	0.809927i
$227$	−15.8982	−	9.17883i	−1.05520	−	0.609220i	−0.131100	−	0.991369i	$-0.541851\pi$
$227$	−15.8982	−	9.17883i	−1.05520	−	0.609220i	−0.924101	+	0.382149i	$0.875184\pi$
$228$		0			0
$229$	11.3476	+	6.55153i	0.749870	+	0.432937i	0.825647	−	0.564187i	$-0.190810\pi$
$229$	11.3476	+	6.55153i	0.749870	+	0.432937i	−0.0757771	+	0.997125i	$0.524144\pi$
$230$	−20.4660			−1.34949
$231$		0			0
$232$		−	28.6550i		−	1.88129i
$233$	−4.84195			−0.317207			−0.158603	−	0.987342i	$-0.550699\pi$
$233$	−4.84195			−0.317207			−0.158603	+	0.987342i	$0.550699\pi$
$234$		0			0
$235$	23.0420			1.50309
$236$			56.0472i			3.64836i
$237$		0			0
$238$	−5.06155			−0.328092
$239$	13.6653	+	7.88968i	0.883936	+	0.510341i	0.871954	−	0.489587i	$-0.162853\pi$
$239$	13.6653	+	7.88968i	0.883936	+	0.510341i	0.0119822	+	0.999928i	$0.496186\pi$
$240$		0			0
$241$	−14.1046	−	8.14332i	−0.908560	−	0.524557i	−0.0285922	−	0.999591i	$-0.509102\pi$
$241$	−14.1046	−	8.14332i	−0.908560	−	0.524557i	−0.879967	+	0.475034i	$0.842436\pi$
$242$		−	22.7242i		−	1.46077i
$243$		0			0
$244$	−9.09147	+	15.7469i	−0.582022	+	1.00809i
$245$			19.4597i			1.24323i
$246$		0			0
$247$	−0.287446	+	1.84035i	−0.0182898	+	0.117099i
$248$	14.7195	−	25.4949i	0.934687	−	1.61893i
$249$		0			0
$250$	15.7728			0.997562
$251$	−13.7361	−	23.7917i	−0.867017	−	1.50172i	−0.865030	−	0.501719i	$-0.832701\pi$
$251$	−13.7361	−	23.7917i	−0.867017	−	1.50172i	−0.00198652	−	0.999998i	$-0.500632\pi$
$252$		0			0
$253$	−3.71154	+	2.14286i	−0.233343	+	0.134720i
$254$	−25.8251	−	14.9101i	−1.62041	−	0.935546i
$255$		0			0
$256$	−2.69579			−0.168487
$257$	−4.89985	−	8.48679i	−0.305644	−	0.529392i	0.671760	−	0.740769i	$-0.265539\pi$
$257$	−4.89985	−	8.48679i	−0.305644	−	0.529392i	−0.977405	+	0.211377i	$0.932205\pi$
$258$		0			0
$259$	0.287712	+	0.498332i	0.0178775	+	0.0309648i
$260$	−47.4960	+	18.3488i	−2.94558	+	1.13794i
$261$		0			0
$262$	−8.86436	−	5.11784i	−0.547642	−	0.316181i
$263$	−23.0973			−1.42424			−0.712119	−	0.702059i	$-0.752264\pi$
$263$	−23.0973			−1.42424			−0.712119	+	0.702059i	$0.752264\pi$
$264$		0			0
$265$	11.3790	+	6.56970i	0.699009	+	0.403573i
$266$		−	0.357759i		−	0.0219356i
$267$		0			0
$268$	35.7806	−	20.6580i	2.18565	−	1.26189i
$269$	10.8197	+	18.7403i	0.659688	+	1.14261i	0.980696	+	0.195537i	$0.0626450\pi$
$269$	10.8197	+	18.7403i	0.659688	+	1.14261i	−0.321008	+	0.947076i	$0.604022\pi$
$270$		0			0
$271$	−23.0990	−	13.3362i	−1.40316	−	0.810116i	−0.408447	−	0.912782i	$-0.633929\pi$
$271$	−23.0990	−	13.3362i	−1.40316	−	0.810116i	−0.994716	+	0.102666i	$0.967263\pi$
$272$	−41.0911	−	71.1718i	−2.49151	−	4.31542i
$273$		0			0
$274$	2.95763	−	5.12276i	0.178677	−	0.309478i
$275$	−3.88907	+	2.24536i	−0.234520	+	0.135400i
$276$		0			0
$277$	−3.22139	+	5.57961i	−0.193554	+	0.335246i	−0.946426	−	0.322922i	$-0.895335\pi$
$277$	−3.22139	+	5.57961i	−0.193554	+	0.335246i	0.752871	+	0.658168i	$0.228668\pi$
$278$		−	43.0754i		−	2.58349i
$279$		0			0
$280$	5.10207	−	2.94568i	0.304907	−	0.176038i
$281$	−1.22438	+	0.706894i	−0.0730402	+	0.0421698i	−0.536075	−	0.844170i	$-0.680094\pi$
$281$	−1.22438	+	0.706894i	−0.0730402	+	0.0421698i	0.463035	+	0.886340i	$0.346760\pi$
$282$		0			0
$283$	−9.98988	−	17.3030i	−0.593837	−	1.02856i	−0.993710	−	0.111985i	$-0.964279\pi$
$283$	−9.98988	−	17.3030i	−0.593837	−	1.02856i	0.399873	−	0.916571i	$-0.369054\pi$
$284$	−27.1864	+	15.6961i	−1.61322	+	0.931392i
$285$		0			0
$286$	−9.35307	+	11.6008i	−0.553058	+	0.685967i
$287$	−1.93910			−0.114462
$288$		0			0
$289$	−18.2106	+	31.5416i	−1.07121	+	1.85539i
$290$	13.2728	−	22.9892i	0.779408	−	1.34997i
$291$		0			0
$292$			18.9153i			1.10693i
$293$		−	3.37211i		−	0.197001i	−0.995137	−	0.0985005i	$-0.968595\pi$
$293$		−	3.37211i		−	0.197001i	0.995137	−	0.0985005i	$-0.0314046\pi$
$294$		0			0
$295$	−15.6392	+	27.0878i	−0.910548	+	1.57712i
$296$	−8.85131	+	15.3309i	−0.514472	+	0.891092i
$297$		0			0
$298$	20.2479			1.17293
$299$	−9.79468	−	1.52984i	−0.566441	−	0.0884730i
$300$		0			0
$301$	0.791019	−	0.456695i	0.0455936	−	0.0263235i
$302$	16.6121	+	28.7730i	0.955919	+	1.65570i
$303$		0			0
$304$	5.03054	−	2.90438i	0.288521	−	0.166578i
$305$	−8.78789	+	5.07369i	−0.503193	+	0.290519i
$306$		0			0
$307$			20.7017i			1.18151i	0.806851	+	0.590756i	$0.201170\pi$
$307$			20.7017i			1.18151i	−0.806851	+	0.590756i	$0.798830\pi$
$308$	1.02395	−	1.77354i	0.0583451	−	0.101057i
$309$		0			0
$310$	23.6181	−	13.6359i	1.34142	−	0.774469i
$311$	−4.13884	+	7.16868i	−0.234692	+	0.406499i	−0.959183	−	0.282786i	$-0.908742\pi$
$311$	−4.13884	+	7.16868i	−0.234692	+	0.406499i	0.724491	+	0.689284i	$0.242075\pi$
$312$		0			0
$313$	6.19041	+	10.7221i	0.349902	+	0.606049i	0.986232	−	0.165369i	$-0.0528814\pi$
$313$	6.19041	+	10.7221i	0.349902	+	0.606049i	−0.636329	+	0.771417i	$0.719548\pi$
$314$	23.1567	+	13.3696i	1.30681	+	0.754488i
$315$		0			0
$316$	6.86987	+	11.8990i	0.386460	+	0.669369i
$317$	28.4498	−	16.4255i	1.59790	−	0.922547i	0.606006	−	0.795460i	$-0.292771\pi$
$317$	28.4498	−	16.4255i	1.59790	−	0.922547i	0.991892	−	0.127087i	$-0.0405628\pi$
$318$		0			0
$319$		−	5.55885i		−	0.311236i
$320$	33.9204	+	19.5839i	1.89621	+	1.09478i
$321$		0			0
$322$	1.90405			0.106109
$323$	−3.27002	−	1.88795i	−0.181949	−	0.105048i
$324$		0			0
$325$	−10.2632	−	1.60302i	−0.569299	−	0.0889194i
$326$	16.5599	+	28.6826i	0.917170	+	1.58858i
$327$		0			0
$328$	−29.8277	−	51.6632i	−1.64696	−	2.85262i
$329$	−2.14371			−0.118187
$330$		0			0
$331$	12.0206	+	6.94008i	0.660710	+	0.381461i	0.792547	−	0.609810i	$-0.208754\pi$
$331$	12.0206	+	6.94008i	0.660710	+	0.381461i	−0.131837	+	0.991271i	$0.542088\pi$
$332$	36.1196	−	20.8537i	1.98232	−	1.14449i
$333$		0			0
$334$	−32.2496	−	55.8580i	−1.76462	−	3.05641i
$335$	23.0572			1.25975
$336$		0			0
$337$	−12.3880	+	21.4566i	−0.674816	+	1.16882i	0.301706	+	0.953401i	$0.402444\pi$
$337$	−12.3880	+	21.4566i	−0.674816	+	1.16882i	−0.976522	+	0.215415i	$0.930889\pi$
$338$	−33.6851	+	7.31085i	−1.83223	+	0.397658i
$339$		0			0
$340$		−	103.216i		−	5.59769i
$341$	2.85546	−	4.94580i	0.154632	−	0.267830i
$342$		0			0
$343$		−	3.63868i		−	0.196470i
$344$	24.3353	+	14.0500i	1.31207	+	0.757525i
$345$		0			0
$346$	24.2170	+	13.9817i	1.30192	+	0.751662i
$347$	−19.0566			−1.02301			−0.511506	−	0.859280i	$-0.670912\pi$
$347$	−19.0566			−1.02301			−0.511506	+	0.859280i	$0.670912\pi$
$348$		0			0
$349$			23.7393i			1.27073i	0.772210	+	0.635367i	$0.219151\pi$
$349$			23.7393i			1.27073i	−0.772210	+	0.635367i	$0.780849\pi$
$350$	1.99513			0.106644
$351$		0			0
$352$	21.4221			1.14180
$353$			2.19138i			0.116635i	0.998298	+	0.0583176i	$0.0185736\pi$
$353$			2.19138i			0.116635i	−0.998298	+	0.0583176i	$0.981426\pi$
$354$		0			0
$355$	−17.5191			−0.929816
$356$	−5.96256	−	3.44249i	−0.316015	−	0.182452i
$357$		0			0
$358$	16.2785	+	9.39839i	0.860345	+	0.496721i
$359$			5.58420i			0.294723i	0.989083	+	0.147361i	$0.0470780\pi$
$359$			5.58420i			0.294723i	−0.989083	+	0.147361i	$0.952922\pi$
$360$		0			0
$361$	−9.36656	+	16.2234i	−0.492977	+	0.853861i
$362$		−	41.7118i		−	2.19232i
$363$		0			0
$364$	4.41880	−	1.70708i	0.231608	−	0.0894752i
$365$	−5.27805	+	9.14184i	−0.276266	+	0.478506i
$366$		0			0
$367$	−13.3773			−0.698292			−0.349146	−	0.937068i	$-0.613528\pi$
$367$	−13.3773			−0.698292			−0.349146	+	0.937068i	$0.613528\pi$
$368$	15.4576	+	26.7734i	0.805785	+	1.39566i
$369$		0			0
$370$	−14.2024	+	8.19975i	−0.738347	+	0.426285i
$371$	−1.05865	−	0.611212i	−0.0549624	−	0.0317326i
$372$		0			0
$373$	7.81997			0.404903			0.202451	−	0.979292i	$-0.435109\pi$
$373$	7.81997			0.404903			0.202451	+	0.979292i	$0.435109\pi$
$374$	−15.1038	−	26.1606i	−0.781001	−	1.35273i
$375$		0			0
$376$	−32.9751	−	57.1145i	−1.70056	−	2.94546i
$377$	8.07061	−	10.0101i	0.415658	−	0.515547i
$378$		0			0
$379$	32.9974	+	19.0510i	1.69496	+	0.978586i	0.950399	+	0.311032i	$0.100675\pi$
$379$	32.9974	+	19.0510i	1.69496	+	0.978586i	0.744561	+	0.667554i	$0.232659\pi$
$380$	7.29550			0.374251
$381$		0			0
$382$	−18.6498	−	10.7675i	−0.954206	−	0.550911i
$383$		−	17.7970i		−	0.909382i	−0.890649	−	0.454691i	$-0.849750\pi$
$383$		−	17.7970i		−	0.909382i	0.890649	−	0.454691i	$-0.150250\pi$
$384$		0			0
$385$	0.989761	−	0.571439i	0.0504429	−	0.0291232i
$386$	10.2187	+	17.6994i	0.520120	+	0.900873i
$387$		0			0
$388$	58.9981	+	34.0626i	2.99518	+	1.72927i
$389$	17.2599	+	29.8950i	0.875112	+	1.51574i	0.856644	+	0.515909i	$0.172546\pi$
$389$	17.2599	+	29.8950i	0.875112	+	1.51574i	0.0184682	+	0.999829i	$0.494121\pi$
$390$		0			0
$391$	10.0480	−	17.4036i	0.508148	−	0.880139i
$392$	48.2351	−	27.8485i	2.43624	−	1.40656i
$393$		0			0
$394$	5.31122	−	9.19930i	0.267575	−	0.463454i
$395$			7.66775i			0.385806i
$396$		0			0
$397$	−7.59209	+	4.38329i	−0.381036	+	0.219991i	−0.678269	−	0.734814i	$-0.737270\pi$
$397$	−7.59209	+	4.38329i	−0.381036	+	0.219991i	0.297233	+	0.954805i	$0.403936\pi$
$398$	−29.5892	+	17.0833i	−1.48317	+	0.856309i
$399$		0			0
$400$	16.1970	+	28.0540i	0.809851	+	1.40270i
$401$	−18.6147	+	10.7472i	−0.929574	+	0.536690i	−0.886677	−	0.462390i	$-0.846992\pi$
$401$	−18.6147	+	10.7472i	−0.929574	+	0.536690i	−0.0428973	+	0.999079i	$0.513659\pi$
$402$		0			0
$403$	12.3225	−	4.76047i	0.613829	−	0.237136i
$404$	−77.5159			−3.85656
$405$		0			0
$406$	−1.23484	+	2.13880i	−0.0612840	+	0.106147i
$407$	−1.71708	+	2.97408i	−0.0851127	+	0.147420i
$408$		0			0
$409$		−	35.4841i		−	1.75457i	−0.479966	−	0.877287i	$-0.659351\pi$
$409$		−	35.4841i		−	1.75457i	0.479966	−	0.877287i	$-0.340649\pi$
$410$		−	55.2642i		−	2.72930i
$411$		0			0
$412$	−27.6456	+	47.8837i	−1.36200	+	2.35906i
$413$	1.45499	−	2.52012i	0.0715954	−	0.124007i
$414$		0			0
$415$	23.2757			1.14256
$416$	38.5758	+	31.1016i	1.89134	+	1.52488i
$417$		0			0
$418$	1.84908	−	1.06756i	0.0904412	−	0.0522163i
$419$	−10.0143	−	17.3453i	−0.489232	−	0.847375i	0.510691	−	0.859764i	$-0.329390\pi$
$419$	−10.0143	−	17.3453i	−0.489232	−	0.847375i	−0.999923	+	0.0123892i	$0.996056\pi$
$420$		0			0
$421$	−15.3946	+	8.88807i	−0.750286	+	0.433178i	−0.825797	−	0.563967i	$-0.809275\pi$
$421$	−15.3946	+	8.88807i	−0.750286	+	0.433178i	0.0755111	+	0.997145i	$0.475941\pi$
$422$	−39.5302	+	22.8228i	−1.92430	+	1.11100i
$423$		0			0
$424$		−	37.6073i		−	1.82637i
$425$	10.5286	−	18.2361i	0.510712	−	0.884580i
$426$		0			0
$427$	0.817582	−	0.472031i	0.0395656	−	0.0228432i
$428$	−2.99677	+	5.19055i	−0.144854	+	0.250895i
$429$		0			0
$430$	13.0158	+	22.5440i	0.627676	+	1.08717i
$431$	1.72978	+	0.998690i	0.0833206	+	0.0481052i	0.541081	−	0.840970i	$-0.318015\pi$
$431$	1.72978	+	0.998690i	0.0833206	+	0.0481052i	−0.457761	+	0.889075i	$0.651348\pi$
$432$		0			0
$433$	−12.2465	−	21.2116i	−0.588532	−	1.01937i	−0.994425	−	0.105446i	$-0.966373\pi$
$433$	−12.2465	−	21.2116i	−0.588532	−	1.01937i	0.405893	−	0.913920i	$-0.366960\pi$
$434$	−2.19732	+	1.26862i	−0.105475	+	0.0608957i
$435$		0			0
$436$			7.85823i			0.376341i
$437$	1.23012	+	0.710208i	0.0588444	+	0.0339738i
$438$		0			0
$439$	15.3304			0.731678			0.365839	−	0.930678i	$-0.380782\pi$
$439$	15.3304			0.731678			0.365839	+	0.930678i	$0.380782\pi$
$440$	30.4495	+	17.5800i	1.45162	+	0.838095i
$441$		0			0
$442$	10.7830	−	69.0373i	0.512895	−	3.28377i
$443$	−4.73265	−	8.19718i	−0.224855	−	0.389460i	0.731421	−	0.681926i	$-0.238857\pi$
$443$	−4.73265	−	8.19718i	−0.224855	−	0.389460i	−0.956276	+	0.292466i	$0.905524\pi$
$444$		0			0
$445$	−1.92115	−	3.32754i	−0.0910714	−	0.157740i
$446$	25.0147			1.18448
$447$		0			0
$448$	−3.15579	−	1.82199i	−0.149097	−	0.0860811i
$449$	14.1283	−	8.15697i	0.666755	−	0.384951i	−0.128091	−	0.991762i	$-0.540885\pi$
$449$	14.1283	−	8.15697i	0.666755	−	0.384951i	0.794846	+	0.606811i	$0.207552\pi$
$450$		0			0
$451$	−5.78635	−	10.0223i	−0.272469	−	0.471929i
$452$	−23.1000			−1.08653
$453$		0			0
$454$	−24.3376	+	42.1539i	−1.14222	+	1.97838i
$455$	2.61196	+	0.407964i	0.122450	+	0.0191257i
$456$		0			0
$457$		−	2.16145i		−	0.101109i	−0.998721	−	0.0505543i	$-0.983901\pi$
$457$		−	2.16145i		−	0.101109i	0.998721	−	0.0505543i	$-0.0160988\pi$
$458$	17.3713	−	30.0880i	0.811708	−	1.40592i
$459$		0			0
$460$			38.8279i			1.81036i
$461$	−2.65520	−	1.53298i	−0.123665	−	0.0713980i	0.436891	−	0.899514i	$-0.356079\pi$
$461$	−2.65520	−	1.53298i	−0.123665	−	0.0713980i	−0.560556	+	0.828116i	$0.689413\pi$
$462$		0			0
$463$	−13.8184	−	7.97807i	−0.642197	−	0.370772i	0.143264	−	0.989685i	$-0.454240\pi$
$463$	−13.8184	−	7.97807i	−0.642197	−	0.370772i	−0.785460	+	0.618912i	$0.787574\pi$
$464$	−40.0990			−1.86155
$465$		0			0
$466$			12.8384i			0.594726i
$467$	−3.15406			−0.145952			−0.0729762	−	0.997334i	$-0.523250\pi$
$467$	−3.15406			−0.145952			−0.0729762	+	0.997334i	$0.523250\pi$
$468$		0			0
$469$	−2.14513			−0.0990529
$470$		−	61.0955i		−	2.81812i
$471$		0			0
$472$	89.5241			4.12068
$473$	4.72086	+	2.72559i	0.217065	+	0.125323i
$474$		0			0
$475$	1.28896	+	0.744179i	0.0591413	+	0.0341453i
$476$			9.60274i			0.440141i
$477$		0			0
$478$	20.9194	−	36.2334i	0.956830	−	1.65728i
$479$			9.93675i			0.454022i	0.973892	+	0.227011i	$0.0728953\pi$
$479$			9.93675i			0.454022i	−0.973892	+	0.227011i	$0.927105\pi$
$480$		0			0
$481$	−7.40996	+	2.86263i	−0.337865	+	0.130525i
$482$	−21.5919	+	37.3983i	−0.983484	+	1.70344i
$483$		0			0
$484$	−43.1122			−1.95964
$485$	19.0093	+	32.9251i	0.863170	+	1.49505i
$486$		0			0
$487$	−20.0246	+	11.5612i	−0.907402	+	0.523889i	−0.879594	−	0.475725i	$-0.842186\pi$
$487$	−20.0246	+	11.5612i	−0.907402	+	0.523889i	−0.0278074	+	0.999613i	$0.508853\pi$
$488$	25.1525	+	14.5218i	1.13860	+	0.657371i
$489$		0			0
$490$	51.5971			2.33092
$491$	14.8527	+	25.7257i	0.670295	+	1.16098i	0.977820	+	0.209445i	$0.0671657\pi$
$491$	14.8527	+	25.7257i	0.670295	+	1.16098i	−0.307526	+	0.951540i	$0.599501\pi$
$492$		0			0
$493$	13.0329	+	22.5736i	0.586971	+	1.01666i
$494$	4.87967	+	0.762161i	0.219547	+	0.0342912i
$495$		0			0
$496$	−35.6768	−	20.5980i	−1.60194	−	0.924878i
$497$	1.62989			0.0731105
$498$		0			0
$499$	32.4943	+	18.7606i	1.45465	+	0.839841i	0.998740	−	0.0501867i	$-0.0159817\pi$
$499$	32.4943	+	18.7606i	1.45465	+	0.839841i	0.455907	+	0.890027i	$0.349315\pi$
$500$		−	29.9241i		−	1.33825i
$501$		0			0
$502$	−63.0833	+	36.4212i	−2.81555	+	1.62556i
$503$	−14.5097	−	25.1315i	−0.646956	−	1.12056i	−0.983846	−	0.179016i	$-0.942709\pi$
$503$	−14.5097	−	25.1315i	−0.646956	−	1.12056i	0.336891	−	0.941544i	$-0.390625\pi$
$504$		0			0
$505$	−37.4637	−	21.6297i	−1.66711	−	0.962509i
$506$	5.68176	+	9.84110i	0.252585	+	0.437490i
$507$		0			0
$508$	−28.2874	+	48.9953i	−1.25505	+	2.17381i
$509$	−7.13709	+	4.12060i	−0.316346	+	0.182643i	−0.649763	−	0.760137i	$-0.725132\pi$
$509$	−7.13709	+	4.12060i	−0.316346	+	0.182643i	0.333417	+	0.942780i	$0.391798\pi$
$510$		0			0
$511$	0.491043	−	0.850512i	0.0217225	−	0.0376244i
$512$			26.1624i			1.15622i
$513$		0			0
$514$	−22.5026	+	12.9919i	−0.992548	+	0.573048i
$515$	−26.7225	+	15.4282i	−1.17753	+	0.679849i
$516$		0			0
$517$	−6.39691	−	11.0798i	−0.281336	−	0.487288i
$518$	1.32132	−	0.762864i	0.0580555	−	0.0335183i
$519$		0			0
$520$	29.3084	+	75.8654i	1.28526	+	3.32692i
$521$	−37.2716			−1.63290			−0.816449	−	0.577418i	$-0.804060\pi$
$521$	−37.2716			−1.63290			−0.816449	+	0.577418i	$0.804060\pi$
$522$		0			0
$523$	−1.53435	+	2.65756i	−0.0670922	+	0.116207i	−0.897620	−	0.440770i	$-0.854706\pi$
$523$	−1.53435	+	2.65756i	−0.0670922	+	0.116207i	0.830528	+	0.556977i	$0.188039\pi$
$524$	−9.70954	+	16.8174i	−0.424163	+	0.734672i
$525$		0			0
$526$			61.2421i			2.67028i
$527$			26.7788i			1.16650i
$528$		0			0
$529$	7.72015	−	13.3717i	0.335659	−	0.581378i
$530$	17.4195	−	30.1714i	0.756653	−	1.31056i
$531$		0			0
$532$	−0.678737			−0.0294270
$533$	4.13102	−	26.4485i	0.178934	−	1.14561i
$534$		0			0
$535$	−2.89670	+	1.67241i	−0.125235	+	0.0723046i
$536$	−32.9969	−	57.1524i	−1.42525	−	2.46861i
$537$		0			0
$538$	49.6896	−	28.6883i	2.14227	−	1.23684i
$539$	9.35723	−	5.40240i	0.403044	−	0.232698i
$540$		0			0
$541$			7.25981i			0.312124i	0.987747	+	0.156062i	$0.0498799\pi$
$541$			7.25981i			0.312124i	−0.987747	+	0.156062i	$0.950120\pi$
$542$	−35.3608	+	61.2466i	−1.51887	+	2.63077i
$543$		0			0
$544$	−86.9915	+	50.2246i	−3.72973	+	2.15336i
$545$	−2.19273	+	3.79791i	−0.0939261	+	0.162685i
$546$		0			0
$547$	−12.8226	−	22.2094i	−0.548256	−	0.949607i	−0.998394	−	0.0566482i	$-0.981959\pi$
$547$	−12.8226	−	22.2094i	−0.548256	−	0.949607i	0.450138	−	0.892959i	$-0.351375\pi$
$548$	−9.71888	−	5.61120i	−0.415170	−	0.239698i
$549$		0			0
$550$	5.95354	+	10.3118i	0.253860	+	0.439698i
$551$	−1.59554	+	0.921184i	−0.0679722	+	0.0392438i
$552$		0			0
$553$		−	0.713370i		−	0.0303356i
$554$	14.7943	+	8.54147i	0.628548	+	0.362892i
$555$		0			0
$556$	−81.7223			−3.46580
$557$	7.49468	+	4.32706i	0.317560	+	0.183343i	0.650304	−	0.759674i	$-0.274641\pi$
$557$	7.49468	+	4.32706i	0.317560	+	0.183343i	−0.332744	+	0.943017i	$0.607975\pi$
$558$		0			0
$559$	4.54395	+	11.7621i	0.192189	+	0.497483i
$560$	−4.12210	−	7.13969i	−0.174191	−	0.301707i
$561$		0			0
$562$	1.87432	+	3.24642i	0.0790634	+	0.136942i
$563$	46.1111			1.94335			0.971677	−	0.236315i	$-0.0759396\pi$
$563$	46.1111			1.94335			0.971677	+	0.236315i	$0.0759396\pi$
$564$		0			0
$565$	−11.1643	−	6.44572i	−0.469686	−	0.271173i
$566$	−45.8786	+	26.4880i	−1.92842	+	1.11338i
$567$		0			0
$568$	25.0714	+	43.4249i	1.05197	+	1.82207i
$569$	−17.2315			−0.722382			−0.361191	−	0.932492i	$-0.617630\pi$
$569$	−17.2315			−0.722382			−0.361191	+	0.932492i	$0.617630\pi$
$570$		0			0
$571$	10.7707	−	18.6554i	0.450741	−	0.780706i	−0.547692	−	0.836680i	$-0.684493\pi$
$571$	10.7707	−	18.6554i	0.450741	−	0.780706i	0.998432	+	0.0559746i	$0.0178266\pi$
$572$	22.0089	+	17.7446i	0.920238	+	0.741938i
$573$		0			0
$574$			5.14150i			0.214602i
$575$	−3.96065	+	6.86005i	−0.165171	+	0.286084i
$576$		0			0
$577$		−	19.9386i		−	0.830056i	−0.909809	−	0.415028i	$-0.863772\pi$
$577$		−	19.9386i		−	0.830056i	0.909809	−	0.415028i	$-0.136228\pi$
$578$	83.6322	+	48.2851i	3.47864	+	2.00839i
$579$		0			0
$580$	−43.6150	−	25.1811i	−1.81101	−	1.04559i
$581$	−2.16545			−0.0898381
$582$		0			0
$583$		−	7.29552i		−	0.302149i
$584$	30.2134			1.25024
$585$		0			0
$586$	−8.94111			−0.369354
$587$			16.5883i			0.684674i	0.939577	+	0.342337i	$0.111218\pi$
$587$			16.5883i			0.684674i	−0.939577	+	0.342337i	$0.888782\pi$
$588$		0			0
$589$	−1.89277			−0.0779902
$590$	71.8231	+	41.4671i	2.95691	+	1.70717i
$591$		0			0
$592$	21.4537	+	12.3863i	0.881741	+	0.509073i
$593$			15.4909i			0.636137i	0.948068	+	0.318068i	$0.103034\pi$
$593$			15.4909i			0.636137i	−0.948068	+	0.318068i	$0.896966\pi$
$594$		0			0
$595$	−2.67951	+	4.64104i	−0.109849	+	0.190264i
$596$		−	38.4142i		−	1.57350i
$597$		0			0
$598$	−4.05635	+	25.9705i	−0.165877	+	1.06201i
$599$	17.4824	−	30.2804i	0.714312	−	1.23722i	−0.248913	−	0.968526i	$-0.580073\pi$
$599$	17.4824	−	30.2804i	0.714312	−	1.23722i	0.963224	−	0.268698i	$-0.0865934\pi$
$600$		0			0
$601$	28.6673			1.16936			0.584682	−	0.811262i	$-0.301219\pi$
$601$	28.6673			1.16936			0.584682	+	0.811262i	$0.301219\pi$
$602$	−1.21092	−	2.09738i	−0.0493535	−	0.0854827i
$603$		0			0
$604$	54.5880	−	31.5164i	2.22115	−	1.28238i
$605$	−20.8363	−	12.0298i	−0.847115	−	0.489082i
$606$		0			0
$607$	16.2734			0.660518			0.330259	−	0.943890i	$-0.392864\pi$
$607$	16.2734			0.660518			0.330259	+	0.943890i	$0.392864\pi$
$608$	−3.54996	−	6.14870i	−0.143970	−	0.249363i
$609$		0			0
$610$	13.4528	+	23.3010i	0.544689	+	0.943429i
$611$	4.56691	−	29.2393i	0.184757	−	1.18289i
$612$		0			0
$613$	−18.0575	−	10.4255i	−0.729336	−	0.421082i	0.0888435	−	0.996046i	$-0.471683\pi$
$613$	−18.0575	−	10.4255i	−0.729336	−	0.421082i	−0.818179	+	0.574964i	$0.805016\pi$
$614$	54.8904			2.21520
$615$		0			0
$616$	−2.83287	−	1.63556i	−0.114140	−	0.0658985i
$617$		−	17.9721i		−	0.723530i	−0.932269	−	0.361765i	$-0.882174\pi$
$617$		−	17.9721i		−	0.723530i	0.932269	−	0.361765i	$-0.117826\pi$
$618$		0			0
$619$	6.56515	−	3.79039i	0.263876	−	0.152349i	−0.362226	−	0.932090i	$-0.617983\pi$
$619$	6.56515	−	3.79039i	0.263876	−	0.152349i	0.626101	+	0.779742i	$0.284650\pi$
$620$	−25.8700	−	44.8082i	−1.03897	−	1.79954i
$621$		0			0
$622$	19.0077	+	10.9741i	0.762138	+	0.440021i
$623$	0.178735	+	0.309578i	0.00716085	+	0.0124030i
$624$		0			0
$625$	15.5524	−	26.9376i	0.622097	−	1.07750i
$626$	28.4295	−	16.4138i	1.13627	−	0.656027i
$627$		0			0
$628$	25.3646	−	43.9328i	1.01216	−	1.75311i
$629$		−	16.1030i		−	0.642069i
$630$		0			0
$631$	11.9576	−	6.90373i	0.476025	−	0.274833i	−0.242734	−	0.970093i	$-0.578044\pi$
$631$	11.9576	−	6.90373i	0.476025	−	0.274833i	0.718758	+	0.695260i	$0.244711\pi$
$632$	19.0062	−	10.9732i	0.756026	−	0.436492i
$633$		0			0
$634$	−43.5519	−	75.4342i	−1.72967	−	2.99587i
$635$	−27.3428	+	15.7864i	−1.08507	+	0.626464i
$636$		0			0
$637$	24.6935	+	3.85691i	0.978393	+	0.152816i
$638$	−14.7392			−0.583531
$639$		0			0
$640$	13.3449	−	23.1141i	0.527505	−	0.913665i
$641$	17.2674	−	29.9080i	0.682022	−	1.18130i	−0.292341	−	0.956314i	$-0.594434\pi$
$641$	17.2674	−	29.9080i	0.682022	−	1.18130i	0.974363	−	0.224982i	$-0.0722324\pi$
$642$		0			0
$643$			9.01569i			0.355544i	0.984072	+	0.177772i	$0.0568890\pi$
$643$			9.01569i			0.355544i	−0.984072	+	0.177772i	$0.943111\pi$
$644$		−	3.61236i		−	0.142347i
$645$		0			0
$646$	−5.00587	+	8.67041i	−0.196953	+	0.341133i
$647$	−2.14777	+	3.72004i	−0.0844374	+	0.146250i	−0.905151	−	0.425089i	$-0.860243\pi$
$647$	−2.14777	+	3.72004i	−0.0844374	+	0.146250i	0.820714	+	0.571339i	$0.193576\pi$
$648$		0			0
$649$	17.3670			0.681714
$650$	−4.25038	+	27.2127i	−0.166714	+	1.06737i
$651$		0			0
$652$	54.4165	−	31.4174i	2.13112	−	1.23040i
$653$	−18.5812	−	32.1836i	−0.727138	−	1.25944i	−0.958088	−	0.286474i	$-0.907517\pi$
$653$	−18.5812	−	32.1836i	−0.727138	−	1.25944i	0.230950	−	0.972966i	$-0.425817\pi$
$654$		0			0
$655$	−9.38531	+	5.41861i	−0.366715	+	0.211723i
$656$	−72.2960	+	41.7401i	−2.82269	+	1.62968i
$657$		0			0
$658$			5.68402i			0.221586i
$659$	0.658878	−	1.14121i	0.0256663	−	0.0444553i	−0.852907	−	0.522063i	$-0.825163\pi$
$659$	0.658878	−	1.14121i	0.0256663	−	0.0444553i	0.878573	+	0.477608i	$0.158496\pi$
$660$		0			0
$661$	−29.0245	+	16.7573i	−1.12892	+	0.651783i	−0.943664	−	0.330906i	$-0.892646\pi$
$661$	−29.0245	+	16.7573i	−1.12892	+	0.651783i	−0.185258	+	0.982690i	$0.559312\pi$
$662$	18.4015	−	31.8724i	0.715196	−	1.23875i
$663$		0			0
$664$	−33.3095	−	57.6938i	−1.29266	−	2.23895i
$665$	−0.328036	−	0.189392i	−0.0127207	−	0.00734430i
$666$		0			0
$667$	−4.90270	−	8.49173i	−0.189833	−	0.328801i
$668$	−105.973	+	61.1837i	−4.10023	+	2.36727i
$669$		0			0
$670$		−	61.1359i		−	2.36189i
$671$	4.87939	+	2.81712i	0.188367	+	0.108754i
$672$		0			0
$673$	23.1500			0.892367			0.446184	−	0.894941i	$-0.352783\pi$
$673$	23.1500			0.892367			0.446184	+	0.894941i	$0.352783\pi$
$674$	56.8919	+	32.8466i	2.19140	+	1.26520i
$675$		0			0
$676$	13.8701	+	63.9072i	0.533465	+	2.45797i
$677$	8.44612	+	14.6291i	0.324611	+	0.562243i	0.981434	−	0.191803i	$-0.0614333\pi$
$677$	8.44612	+	14.6291i	0.324611	+	0.562243i	−0.656823	+	0.754045i	$0.728100\pi$
$678$		0			0
$679$	−1.76854	−	3.06319i	−0.0678702	−	0.117555i
$680$	−164.867			−6.32237
$681$		0			0
$682$	−13.1137	−	7.57122i	−0.502151	−	0.289917i
$683$	19.4097	−	11.2062i	0.742692	−	0.428793i	−0.0803552	−	0.996766i	$-0.525605\pi$
$683$	19.4097	−	11.2062i	0.742692	−	0.428793i	0.823047	+	0.567973i	$0.192272\pi$
$684$		0			0
$685$	−3.13145	−	5.42383i	−0.119646	−	0.207234i
$686$	−9.64792			−0.368359
$687$		0			0
$688$	19.6612	−	34.0542i	0.749576	−	1.29830i
$689$	10.5920	−	13.1374i	0.403523	−	0.500496i
$690$		0			0
$691$		−	26.2186i		−	0.997404i	−0.866774	−	0.498702i	$-0.833810\pi$
$691$		−	26.2186i		−	0.997404i	0.866774	−	0.498702i	$-0.166190\pi$
$692$	26.5260	−	45.9444i	1.00837	−	1.74654i
$693$		0			0
$694$			50.5283i			1.91803i
$695$	−39.4967	−	22.8034i	−1.49820	−	0.864984i
$696$		0			0
$697$	46.9949	+	27.1325i	1.78006	+	1.02772i
$698$	62.9444			2.38248
$699$		0			0
$700$		−	3.78515i		−	0.143065i
$701$	49.5379			1.87102			0.935510	−	0.353300i	$-0.114941\pi$
$701$	49.5379			1.87102			0.935510	+	0.353300i	$0.114941\pi$
$702$		0			0
$703$	1.13819			0.0429275
$704$		−	21.7476i		−	0.819642i
$705$		0			0
$706$	5.81041			0.218678
$707$	3.48544	+	2.01232i	0.131084	+	0.0756811i
$708$		0			0
$709$	−25.0446	−	14.4595i	−0.940569	−	0.543038i	−0.0504304	−	0.998728i	$-0.516059\pi$
$709$	−25.0446	−	14.4595i	−0.940569	−	0.543038i	−0.890139	+	0.455690i	$0.849393\pi$
$710$			46.4516i			1.74330i
$711$		0			0
$712$	−5.49868	+	9.52399i	−0.206072	+	0.356927i
$713$		−	10.0737i		−	0.377261i
$714$		0			0
$715$	5.68561	+	14.7173i	0.212630	+	0.550395i
$716$	17.8306	−	30.8835i	0.666360	−	1.15417i
$717$		0			0
$718$	14.8064			0.552571
$719$	5.28737	+	9.15800i	0.197186	+	0.341536i	0.947615	−	0.319415i	$-0.103486\pi$
$719$	5.28737	+	9.15800i	0.197186	+	0.341536i	−0.750429	+	0.660951i	$0.770153\pi$
$720$		0			0
$721$	2.48613	−	1.43537i	0.0925883	−	0.0534559i
$722$	43.0160	+	24.8353i	1.60089	+	0.924274i
$723$		0			0
$724$	−79.1354			−2.94104
$725$	−5.13721	−	8.89791i	−0.190791	−	0.330460i
$726$		0			0
$727$	−4.91833	−	8.51880i	−0.182411	−	0.315945i	0.760290	−	0.649584i	$-0.225057\pi$
$727$	−4.91833	−	8.51880i	−0.182411	−	0.315945i	−0.942701	+	0.333639i	$0.891723\pi$
$728$	−2.72671	−	7.05814i	−0.101059	−	0.261592i
$729$		0			0
$730$	24.2395	+	13.9947i	0.897143	+	0.517966i
$731$	−25.5609			−0.945403
$732$		0			0
$733$	−42.6470	−	24.6222i	−1.57520	−	0.909443i	−0.995515	−	0.0946033i	$-0.969842\pi$
$733$	−42.6470	−	24.6222i	−1.57520	−	0.909443i	−0.579686	−	0.814840i	$-0.696825\pi$
$734$			35.4699i			1.30922i
$735$		0			0
$736$	32.7245	−	18.8935i	1.20624	−	0.696423i
$737$	−6.40115	−	11.0871i	−0.235789	−	0.408399i
$738$		0			0
$739$	7.35764	+	4.24793i	0.270655	+	0.156263i	0.629185	−	0.777255i	$-0.283389\pi$
$739$	7.35764	+	4.24793i	0.270655	+	0.156263i	−0.358530	+	0.933518i	$0.616722\pi$
$740$	15.5565	+	26.9447i	0.571869	+	0.990506i
$741$		0			0
$742$	−1.62062	+	2.80700i	−0.0594949	+	0.103048i
$743$	−23.6772	+	13.6701i	−0.868634	+	0.501506i	−0.866894	−	0.498493i	$-0.833887\pi$
$743$	−23.6772	+	13.6701i	−0.868634	+	0.501506i	−0.00173965	+	0.999998i	$0.500554\pi$
$744$		0			0
$745$	10.7189	−	18.5657i	0.392711	−	0.680195i
$746$		−	20.7346i		−	0.759146i
$747$		0			0
$748$	−49.6318	+	28.6549i	−1.81472	+	1.04773i
$749$	0.269494	−	0.155593i	0.00984711	−	0.00568523i
$750$		0			0
$751$	16.2482	+	28.1427i	0.592906	+	1.02694i	0.993839	+	0.110835i	$0.0353526\pi$
$751$	16.2482	+	28.1427i	0.592906	+	1.02694i	−0.400933	+	0.916107i	$0.631314\pi$
$752$	−79.9245	+	46.1444i	−2.91455	+	1.68271i
$753$		0			0
$754$	−26.5417	−	21.3991i	−0.966591	−	0.779310i
$755$	35.1768			1.28021
$756$		0			0
$757$	18.7348	−	32.4496i	0.680928	−	1.17940i	−0.293770	−	0.955876i	$-0.594910\pi$
$757$	18.7348	−	32.4496i	0.680928	−	1.17940i	0.974698	−	0.223525i	$-0.0717566\pi$
$758$	50.5136	−	87.4921i	1.83474	−	3.17786i
$759$		0			0
$760$		−	11.6531i		−	0.422702i
$761$			18.6887i			0.677465i	0.940883	+	0.338732i	$0.109998\pi$
$761$			18.6887i			0.677465i	−0.940883	+	0.338732i	$0.890002\pi$
$762$		0			0
$763$	0.204000	−	0.353339i	0.00738531	−	0.0127917i
$764$	−20.4280	+	35.3823i	−0.739058	+	1.28009i
$765$		0			0
$766$	−47.1884			−1.70499
$767$	31.2736	+	25.2142i	1.12923	+	0.910434i
$768$		0			0
$769$	38.8944	−	22.4557i	1.40257	−	0.809773i	0.407912	−	0.913021i	$-0.366257\pi$
$769$	38.8944	−	22.4557i	1.40257	−	0.809773i	0.994656	+	0.103248i	$0.0329237\pi$
$770$	−1.51516	−	2.62434i	−0.0546027	−	0.0945746i
$771$		0			0
$772$	33.5791	−	19.3869i	1.20854	−	0.697750i
$773$	−2.77119	+	1.59995i	−0.0996728	+	0.0575461i	−0.549008	−	0.835817i	$-0.684994\pi$
$773$	−2.77119	+	1.59995i	−0.0996728	+	0.0575461i	0.449335	+	0.893363i	$0.351661\pi$
$774$		0			0
$775$		−	10.5555i		−	0.379165i
$776$	54.4081	−	94.2376i	1.95314	−	3.38293i
$777$		0			0
$778$	79.2663	−	45.7644i	2.84183	−	1.64073i
$779$	−1.91777	+	3.32167i	−0.0687112	+	0.119011i
$780$		0			0
$781$	4.86365	+	8.42408i	0.174035	+	0.301437i
$782$	−46.1455	−	26.6421i	−1.65016	−	0.952719i
$783$		0			0
$784$	−38.9705	−	67.4989i	−1.39180	−	2.41067i
$785$	24.5176	−	14.1553i	0.875072	−	0.505223i
$786$		0			0
$787$			30.2482i			1.07823i	0.842232	+	0.539115i	$0.181241\pi$
$787$			30.2482i			1.07823i	−0.842232	+	0.539115i	$0.818759\pi$
$788$	−17.4528	−	10.0764i	−0.621732	−	0.358957i
$789$		0			0
$790$	20.3309			0.723343
$791$	1.03867	+	0.599678i	0.0369309	+	0.0213221i
$792$		0			0
$793$	4.69654	+	12.1571i	0.166779	+	0.431710i
$794$	11.6223	+	20.1303i	0.412458	+	0.714399i
$795$		0			0
$796$	32.4103	+	56.1364i	1.14875	+	1.98970i
$797$	−32.9516			−1.16720			−0.583602	−	0.812040i	$-0.698357\pi$
$797$	−32.9516			−1.16720			−0.583602	+	0.812040i	$0.698357\pi$
$798$		0			0
$799$	51.9536	+	29.9954i	1.83799	+	1.06116i
$800$	34.2898	−	19.7972i	1.21233	−	0.699937i
$801$		0			0
$802$	28.4961	+	49.3567i	1.00623	+	1.74284i
$803$	5.86116			0.206836
$804$		0			0
$805$	1.00798	−	1.74587i	0.0355265	−	0.0615337i
$806$	−12.6223	−	32.6731i	−0.444602	−	1.15086i
$807$		0			0
$808$			123.816i			4.35583i
$809$	−25.6465	+	44.4211i	−0.901684	+	1.56176i	−0.0763761	+	0.997079i	$0.524335\pi$
$809$	−25.6465	+	44.4211i	−0.901684	+	1.56176i	−0.825308	+	0.564683i	$0.808998\pi$
$810$		0			0
$811$		−	51.3422i		−	1.80287i	−0.432915	−	0.901435i	$-0.642515\pi$
$811$		−	51.3422i		−	1.80287i	0.432915	−	0.901435i	$-0.357485\pi$
$812$	4.05772	+	2.34273i	0.142398	+	0.0822136i
$813$		0			0
$814$	7.88573	+	4.55283i	0.276395	+	0.159577i
$815$	35.0663			1.22832
$816$		0			0
$817$		−	1.80668i		−	0.0632079i
$818$	−94.0856			−3.28962
$819$		0			0
$820$	−104.847			−3.66141
$821$			3.85541i			0.134555i	0.997734	+	0.0672774i	$0.0214313\pi$
$821$			3.85541i			0.134555i	−0.997734	+	0.0672774i	$0.978569\pi$
$822$		0			0
$823$	−41.8727			−1.45959			−0.729796	−	0.683665i	$-0.760385\pi$
$823$	−41.8727			−1.45959			−0.729796	+	0.683665i	$0.760385\pi$
$824$	76.4845	+	44.1583i	2.66446	+	1.53833i
$825$		0			0
$826$	−6.68206	−	3.85789i	−0.232499	−	0.134233i
$827$		−	33.2317i		−	1.15558i	−0.816185	−	0.577790i	$-0.803915\pi$
$827$		−	33.2317i		−	1.15558i	0.816185	−	0.577790i	$-0.196085\pi$
$828$		0			0
$829$	−23.8687	+	41.3417i	−0.828993	+	1.43586i	0.0698363	+	0.997558i	$0.477752\pi$
$829$	−23.8687	+	41.3417i	−0.828993	+	1.43586i	−0.898829	+	0.438299i	$0.855581\pi$
$830$		−	61.7151i		−	2.14216i
$831$		0			0
$832$	31.5742	−	39.1620i	1.09464	−	1.35770i
$833$	−25.3321	+	43.8765i	−0.877706	+	1.52023i
$834$		0			0
$835$	−68.2898			−2.36327
$836$	−2.02538	−	3.50805i	−0.0700491	−	0.121329i
$837$		0			0
$838$	−45.9909	+	26.5529i	−1.58873	+	0.917254i
$839$	13.7524	+	7.93993i	0.474784	+	0.274117i	0.718240	−	0.695795i	$-0.244948\pi$
$839$	13.7524	+	7.93993i	0.474784	+	0.274117i	−0.243456	+	0.969912i	$0.578281\pi$
$840$		0			0
$841$	−16.2818			−0.561440
$842$	23.5666	+	40.8185i	0.812159	+	1.40670i
$843$		0			0
$844$	43.2992	+	74.9965i	1.49042	+	2.58148i
$845$	−11.1289	+	34.7568i	−0.382846	+	1.19567i
$846$		0			0
$847$	1.93850	+	1.11920i	0.0666078	+	0.0384560i
$848$	−52.6266			−1.80720
$849$		0			0
$850$	−48.3527	−	27.9165i	−1.65848	−	0.957527i
$851$			6.05763i			0.207653i
$852$		0			0
$853$	−35.9630	+	20.7633i	−1.23135	+	0.710921i	−0.967312	−	0.253591i	$-0.918388\pi$
$853$	−35.9630	+	20.7633i	−1.23135	+	0.710921i	−0.264040	+	0.964512i	$0.585055\pi$
$854$	−1.25158	−	2.16781i	−0.0428283	−	0.0741809i
$855$		0			0
$856$	8.29086	+	4.78673i	0.283376	+	0.163607i
$857$	−20.4844	−	35.4799i	−0.699732	−	1.21197i	−0.968559	−	0.248783i	$-0.919969\pi$
$857$	−20.4844	−	35.4799i	−0.699732	−	1.21197i	0.268827	−	0.963188i	$-0.413364\pi$
$858$		0			0
$859$	−14.2210	+	24.6315i	−0.485215	+	0.840417i	−0.999856	−	0.0169889i	$-0.994592\pi$
$859$	−14.2210	+	24.6315i	−0.485215	+	0.840417i	0.514641	+	0.857406i	$0.327925\pi$
$860$	42.7702	−	24.6934i	1.45845	−	0.842038i
$861$		0			0
$862$	2.64801	−	4.58649i	0.0901917	−	0.156217i
$863$			24.5762i			0.836584i	0.908313	+	0.418292i	$0.137371\pi$
$863$			24.5762i			0.836584i	−0.908313	+	0.418292i	$0.862629\pi$
$864$		0			0
$865$	25.6403	−	14.8034i	0.871795	−	0.503331i
$866$	−56.2424	+	32.4716i	−1.91119	+	1.10343i
$867$		0			0
$868$	2.40682	+	4.16873i	0.0816928	+	0.141496i
$869$	3.68705	−	2.12872i	0.125075	−	0.0722119i
$870$		0			0
$871$	4.56994	−	29.2586i	0.154846	−	0.991391i
$872$	12.5519			0.425062
$873$		0			0
$874$	1.88311	−	3.26164i	0.0636970	−	0.110326i
$875$	−0.776834	+	1.34552i	−0.0262618	+	0.0454867i
$876$		0			0
$877$		−	14.6119i		−	0.493410i	−0.969091	−	0.246705i	$-0.920652\pi$
$877$		−	14.6119i		−	0.493410i	0.969091	−	0.246705i	$-0.0793478\pi$
$878$		−	40.6483i		−	1.37181i
$879$		0			0
$880$	24.6010	−	42.6102i	0.829300	−	1.43639i
$881$	−1.19861	+	2.07605i	−0.0403820	+	0.0699438i	−0.885510	−	0.464620i	$-0.846191\pi$
$881$	−1.19861	+	2.07605i	−0.0403820	+	0.0699438i	0.845128	+	0.534564i	$0.179524\pi$
$882$		0			0
$883$	−5.90861			−0.198840			−0.0994202	−	0.995046i	$-0.531699\pi$
$883$	−5.90861			−0.198840			−0.0994202	+	0.995046i	$0.531699\pi$
$884$	−130.977	−	20.4575i	−4.40524	−	0.688059i
$885$		0			0
$886$	−21.7347	+	12.5485i	−0.730192	+	0.421577i
$887$	−13.6302	−	23.6081i	−0.457656	−	0.792683i	0.541181	−	0.840906i	$-0.317978\pi$
$887$	−13.6302	−	23.6081i	−0.457656	−	0.792683i	−0.998837	+	0.0482229i	$0.984644\pi$
$888$		0			0
$889$	2.54384	−	1.46869i	0.0853178	−	0.0492582i
$890$	−8.82292	+	5.09391i	−0.295745	+	0.170748i
$891$		0			0
$892$		−	47.4578i		−	1.58900i
$893$	−2.12013	+	3.67217i	−0.0709473	+	0.122884i
$894$		0			0
$895$	17.2352	−	9.95073i	0.576108	−	0.332616i
$896$	−1.24155	+	2.15042i	−0.0414772	+	0.0718406i
$897$		0			0
$898$	−21.6281	−	37.4610i	−0.721739	−	1.25009i
$899$	11.3156	+	6.53308i	0.377397	+	0.217890i
$900$		0			0
$901$	17.1045	+	29.6259i	0.569834	+	0.986982i
$902$	−26.5739	+	15.3424i	−0.884813	+	0.510847i
$903$		0			0
$904$			36.8976i			1.22719i
$905$	−38.2464	−	22.0816i	−1.27135	−	0.734017i
$906$		0			0
$907$	44.2501			1.46930			0.734651	−	0.678445i	$-0.237346\pi$
$907$	44.2501			1.46930			0.734651	+	0.678445i	$0.237346\pi$
$908$	79.9741	+	46.1730i	2.65403	+	1.53231i
$909$		0			0
$910$	1.08171	−	6.92557i	0.0358584	−	0.229580i
$911$	6.61845	+	11.4635i	0.219279	+	0.379802i	0.954588	−	0.297930i	$-0.0962962\pi$
$911$	6.61845	+	11.4635i	0.219279	+	0.379802i	−0.735309	+	0.677732i	$0.762963\pi$
$912$		0			0
$913$	−6.46179	−	11.1921i	−0.213854	−	0.370406i
$914$	−5.73107			−0.189567
$915$		0			0
$916$	−57.0827	−	32.9567i	−1.88607	−	1.08892i
$917$	0.873163	−	0.504121i	0.0288344	−	0.0166475i
$918$		0			0
$919$	−21.5036	−	37.2452i	−0.709337	−	1.22861i	−0.965103	−	0.261869i	$-0.915661\pi$
$919$	−21.5036	−	37.2452i	−0.709337	−	1.22861i	0.255767	−	0.966739i	$-0.417672\pi$
$920$	62.0198			2.04473
$921$		0			0
$922$	−4.06468	+	7.04023i	−0.133863	+	0.231858i
$923$	−3.47228	+	22.2310i	−0.114291	+	0.731741i
$924$		0			0
$925$			6.34738i			0.208701i
$926$	−21.1538	+	36.6394i	−0.695156	+	1.20404i
$927$		0			0
$928$			49.0121i			1.60890i
$929$	−5.52988	−	3.19267i	−0.181429	−	0.104748i	0.406535	−	0.913635i	$-0.366737\pi$
$929$	−5.52988	−	3.19267i	−0.181429	−	0.104748i	−0.587964	+	0.808887i	$0.700070\pi$
$930$		0			0
$931$	−3.10126	−	1.79052i	−0.101640	−	0.0586818i
$932$	24.3569			0.797837
$933$		0			0
$934$			8.36295i			0.273644i
$935$	−31.9830			−1.04596
$936$		0			0
$937$	58.7846			1.92041			0.960204	−	0.279298i	$-0.0901018\pi$
$937$	58.7846			1.92041			0.960204	+	0.279298i	$0.0901018\pi$
$938$			5.68779i			0.185713i
$939$		0			0
$940$	−115.910			−3.78057
$941$	−46.2325	−	26.6923i	−1.50714	−	0.870145i	−0.999966	−	0.00829925i	$-0.997358\pi$
$941$	−46.2325	−	26.6923i	−1.50714	−	0.870145i	−0.507170	−	0.861846i	$-0.669308\pi$
$942$		0			0
$943$	−17.6785	−	10.2067i	−0.575692	−	0.332376i
$944$		−	125.278i		−	4.07744i
$945$		0			0
$946$	7.22687	−	12.5173i	0.234966	−	0.406973i
$947$		−	3.74167i		−	0.121588i	−0.998150	−	0.0607940i	$-0.980637\pi$
$947$		−	3.74167i		−	0.121588i	0.998150	−	0.0607940i	$-0.0193633\pi$
$948$		0			0
$949$	10.5545	+	8.50952i	0.342614	+	0.276231i
$950$	1.97318	−	3.41765i	0.0640184	−	0.110883i
$951$		0			0
$952$	15.3384			0.497122
$953$	−11.2711	−	19.5221i	−0.365107	−	0.632384i	0.623686	−	0.781675i	$-0.285634\pi$
$953$	−11.2711	−	19.5221i	−0.365107	−	0.632384i	−0.988793	+	0.149291i	$0.952301\pi$
$954$		0			0
$955$	−19.7458	+	11.4003i	−0.638960	+	0.368904i
$956$	−68.7418	−	39.6881i	−2.22327	−	1.28361i
$957$		0			0
$958$	26.3472			0.851238
$959$	0.291334	+	0.504606i	0.00940768	+	0.0162946i
$960$		0			0
$961$	−8.78819	−	15.2216i	−0.283490	−	0.491019i
$962$	7.59023	+	19.6474i	0.244719	+	0.633458i
$963$		0			0
$964$	70.9518	+	40.9640i	2.28520	+	1.31936i
$965$	21.6385			0.696570
$966$		0			0
$967$	−1.37859	−	0.795929i	−0.0443325	−	0.0255954i	0.477670	−	0.878539i	$-0.341481\pi$
$967$	−1.37859	−	0.795929i	−0.0443325	−	0.0255954i	−0.522002	+	0.852944i	$0.674815\pi$
$968$			68.8630i			2.21334i
$969$		0			0
$970$	87.3006	−	50.4030i	2.80305	−	1.61834i
$971$	2.45081	+	4.24492i	0.0786501	+	0.136226i	0.902668	−	0.430338i	$-0.141606\pi$
$971$	2.45081	+	4.24492i	0.0786501	+	0.136226i	−0.824018	+	0.566564i	$0.808272\pi$
$972$		0			0
$973$	3.67458	+	2.12152i	0.117802	+	0.0680128i
$974$	30.6544	+	53.0950i	0.982231	+	1.70127i
$975$		0			0
$976$	20.3214	−	35.1977i	0.650473	−	1.12665i
$977$	3.34922	−	1.93367i	0.107151	−	0.0618637i	−0.445467	−	0.895298i	$-0.646962\pi$
$977$	3.34922	−	1.93367i	0.107151	−	0.0618637i	0.552618	+	0.833435i	$0.313629\pi$
$978$		0			0
$979$	−1.06670	+	1.84758i	−0.0340919	+	0.0590489i
$980$		−	97.8897i		−	3.12697i
$981$		0			0
$982$	68.2114	−	39.3819i	2.17671	−	1.25673i
$983$	45.0382	−	26.0028i	1.43650	−	0.829361i	0.438891	−	0.898540i	$-0.355371\pi$
$983$	45.0382	−	26.0028i	1.43650	−	0.829361i	0.997604	+	0.0691791i	$0.0220380\pi$
$984$		0			0
$985$	−5.62335	−	9.73993i	−0.179175	−	0.310340i
$986$	59.8536	−	34.5565i	1.90613	−	1.10050i
$987$		0			0
$988$	1.44597	−	9.25768i	0.0460023	−	0.294526i
$989$	9.61549			0.305755
$990$		0			0
$991$	4.08818	−	7.08094i	0.129865	−	0.224933i	−0.793759	−	0.608233i	$-0.791879\pi$
$991$	4.08818	−	7.08094i	0.129865	−	0.224933i	0.923624	+	0.383299i	$0.125212\pi$
$992$	−25.1765	+	43.6069i	−0.799353	+	1.38452i
$993$		0			0
$994$		−	4.32163i		−	0.137074i
$995$			36.1746i			1.14681i
$996$		0			0
$997$	−15.2339	+	26.3859i	−0.482463	+	0.835650i	−0.999797	−	0.0201329i	$-0.993591\pi$
$997$	−15.2339	+	26.3859i	−0.482463	+	0.835650i	0.517334	+	0.855783i	$0.326924\pi$
$998$	49.7435	−	86.1583i	1.57460	−	2.72729i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.l.b.199.1		22
3.2	odd	2		117.2.l.b.4.11	✓	22
9.2	odd	6		117.2.r.b.43.11	yes	22
9.7	even	3		351.2.r.b.316.1		22
13.10	even	6		351.2.r.b.10.1		22
39.23	odd	6		117.2.r.b.49.11	yes	22
117.88	even	6	inner	351.2.l.b.127.11		22
117.101	odd	6		117.2.l.b.88.1	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.11	✓	22	3.2	odd	2
117.2.l.b.88.1	yes	22	117.101	odd	6
117.2.r.b.43.11	yes	22	9.2	odd	6
117.2.r.b.49.11	yes	22	39.23	odd	6
351.2.l.b.127.11		22	117.88	even	6	inner
351.2.l.b.199.1		22	1.1	even	1	trivial
351.2.r.b.10.1		22	13.10	even	6
351.2.r.b.316.1		22	9.7	even	3

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.65149i q^{2} -5.03038 q^{4} +(-2.43120 - 1.40366i) q^{5} +(0.226187 + 0.130589i) q^{7} +8.03502i q^{8} +(-3.72178 + 6.44631i) q^{10} +1.55873i q^{11} +(-2.26304 + 2.80689i) q^{13} +(0.346256 - 0.599733i) q^{14} +11.2440 q^{16} +(-3.65449 - 6.32976i) q^{17} +(0.447398 - 0.258305i) q^{19} +(12.2299 + 7.06093i) q^{20} +4.13296 q^{22} +(1.37475 + 2.38113i) q^{23} +(1.44050 + 2.49502i) q^{25} +(7.44243 + 6.00043i) q^{26} +(-1.13781 - 0.656914i) q^{28} -3.56626 q^{29} +(-3.17297 - 1.83191i) q^{31} -13.7433i q^{32} +(-16.7833 + 9.68983i) q^{34} +(-0.366605 - 0.634978i) q^{35} +(1.90801 + 1.10159i) q^{37} +(-0.684893 - 1.18627i) q^{38} +(11.2784 - 19.5348i) q^{40} +(-6.42975 + 3.71222i) q^{41} +(1.74859 - 3.02865i) q^{43} -7.84102i q^{44} +(6.31353 - 3.64512i) q^{46} +(-7.10819 + 4.10392i) q^{47} +(-3.46589 - 6.00310i) q^{49} +(6.61553 - 3.81948i) q^{50} +(11.3840 - 14.1197i) q^{52} -4.68042 q^{53} +(2.18792 - 3.78960i) q^{55} +(-1.04929 + 1.81742i) q^{56} +9.45590i q^{58} -11.1417i q^{59} +(1.80731 - 3.13036i) q^{61} +(-4.85729 + 8.41308i) q^{62} -13.9521 q^{64} +(9.44183 - 3.64759i) q^{65} +(-7.11290 + 4.10664i) q^{67} +(18.3835 + 31.8411i) q^{68} +(-1.68364 + 0.972048i) q^{70} +(5.40445 - 3.12026i) q^{71} -3.76021i q^{73} +(2.92085 - 5.05907i) q^{74} +(-2.25058 + 1.29937i) q^{76} +(-0.203554 + 0.352565i) q^{77} +(-1.36567 - 2.36542i) q^{79} +(-27.3365 - 15.7827i) q^{80} +(9.84289 + 17.0484i) q^{82} +(-7.18029 + 4.14554i) q^{83} +20.5186i q^{85} +(-8.03044 - 4.63638i) q^{86} -12.5244 q^{88} +(1.18531 + 0.684339i) q^{89} +(-0.878421 + 0.339353i) q^{91} +(-6.91550 - 11.9780i) q^{92} +(10.8815 + 18.8473i) q^{94} -1.45029 q^{95} +(-11.7284 - 6.77137i) q^{97} +(-15.9171 + 9.18977i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 20 q^{4} + 3 q^{5} - 6 q^{7} - 7 q^{10} + 9 q^{14} + 24 q^{16} - 9 q^{17} - 6 q^{19} + 24 q^{20} + 26 q^{22} - 6 q^{23} + 4 q^{25} + 12 q^{26} + 3 q^{28} - 48 q^{29} - 27 q^{31} + 15 q^{34} + 27 q^{35}+ \cdots - 117 q^{98}+O(q^{100}) \) 22 * q - 20 * q^4 + 3 * q^5 - 6 * q^7 - 7 * q^10 + 9 * q^14 + 24 * q^16 - 9 * q^17 - 6 * q^19 + 24 * q^20 + 26 * q^22 - 6 * q^23 + 4 * q^25 + 12 * q^26 + 3 * q^28 - 48 * q^29 - 27 * q^31 + 15 * q^34 + 27 * q^35 + 6 * q^37 - 21 * q^38 + 13 * q^40 - 6 * q^41 - 4 * q^43 - 15 * q^46 + 6 * q^47 + 7 * q^49 - 18 * q^50 - 22 * q^52 + 24 * q^53 - 13 * q^55 + 9 * q^56 + 3 * q^61 - 24 * q^64 + 57 * q^65 - 45 * q^67 + 69 * q^68 - 24 * q^70 - 9 * q^71 + 6 * q^74 + 18 * q^76 - 42 * q^77 - 6 * q^79 - 105 * q^80 - 16 * q^82 - 42 * q^83 - 45 * q^86 + 22 * q^88 + 30 * q^89 + 15 * q^91 + 3 * q^92 + 44 * q^94 - 6 * q^95 - 27 * q^97 - 117 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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