LMFDB - Embedded newform 555.2.g.a.184.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(184,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("555.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			184.17
Character	$\chi$	$=$	555.184
Dual form			555.2.g.a.184.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.414618 q^{2} -1.00000i q^{3} -1.82809 q^{4} +(1.55319 - 1.60860i) q^{5} +0.414618i q^{6} -0.262182i q^{7} +1.58720 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.414618 q^{2} -1.00000i q^{3} -1.82809 q^{4} +(1.55319 - 1.60860i) q^{5} +0.414618i q^{6} -0.262182i q^{7} +1.58720 q^{8} -1.00000 q^{9} +(-0.643980 + 0.666956i) q^{10} +5.76010 q^{11} +1.82809i q^{12} -2.13826 q^{13} +0.108705i q^{14} +(-1.60860 - 1.55319i) q^{15} +2.99810 q^{16} -0.318926 q^{17} +0.414618 q^{18} -6.26778i q^{19} +(-2.83937 + 2.94068i) q^{20} -0.262182 q^{21} -2.38824 q^{22} -8.22627 q^{23} -1.58720i q^{24} +(-0.175212 - 4.99693i) q^{25} +0.886562 q^{26} +1.00000i q^{27} +0.479292i q^{28} -5.91180i q^{29} +(0.666956 + 0.643980i) q^{30} -1.32410i q^{31} -4.41746 q^{32} -5.76010i q^{33} +0.132233 q^{34} +(-0.421746 - 0.407217i) q^{35} +1.82809 q^{36} +(2.74005 + 5.43067i) q^{37} +2.59874i q^{38} +2.13826i q^{39} +(2.46522 - 2.55317i) q^{40} -5.96208 q^{41} +0.108705 q^{42} +0.0737737 q^{43} -10.5300 q^{44} +(-1.55319 + 1.60860i) q^{45} +3.41076 q^{46} -8.04534i q^{47} -2.99810i q^{48} +6.93126 q^{49} +(0.0726462 + 2.07182i) q^{50} +0.318926i q^{51} +3.90894 q^{52} -5.23540i q^{53} -0.414618i q^{54} +(8.94652 - 9.26572i) q^{55} -0.416134i q^{56} -6.26778 q^{57} +2.45114i q^{58} +7.31368i q^{59} +(2.94068 + 2.83937i) q^{60} -2.66859i q^{61} +0.548995i q^{62} +0.262182i q^{63} -4.16465 q^{64} +(-3.32112 + 3.43962i) q^{65} +2.38824i q^{66} +3.69751i q^{67} +0.583026 q^{68} +8.22627i q^{69} +(0.174864 + 0.168840i) q^{70} +7.33380 q^{71} -1.58720 q^{72} -2.43334i q^{73} +(-1.13607 - 2.25165i) q^{74} +(-4.99693 + 0.175212i) q^{75} +11.4581i q^{76} -1.51019i q^{77} -0.886562i q^{78} -10.9171i q^{79} +(4.65662 - 4.82276i) q^{80} +1.00000 q^{81} +2.47199 q^{82} +13.2259i q^{83} +0.479292 q^{84} +(-0.495352 + 0.513026i) q^{85} -0.0305879 q^{86} -5.91180 q^{87} +9.14242 q^{88} +9.15126i q^{89} +(0.643980 - 0.666956i) q^{90} +0.560613i q^{91} +15.0384 q^{92} -1.32410 q^{93} +3.33574i q^{94} +(-10.0824 - 9.73504i) q^{95} +4.41746i q^{96} +1.87245 q^{97} -2.87383 q^{98} -5.76010 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) $ 40 * q + 44 * q^4 - 40 * q^9	$ 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) $ 40 * q + 44 * q^4 - 40 * q^9 + 4 * q^10 + 8 * q^11 + 52 * q^16 - 16 * q^21 + 8 * q^25 - 16 * q^26 + 16 * q^30 - 32 * q^34 - 44 * q^36 - 28 * q^40 + 8 * q^41 + 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 - 48 * q^65 - 56 * q^70 + 24 * q^71 - 68 * q^74 + 8 * q^75 + 40 * q^81 - 16 * q^84 - 64 * q^85 + 80 * q^86 - 4 * q^90 + 32 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−0.414618			−0.293179			−0.146590	−	0.989197i	$-0.546830\pi$
$2$	−0.414618			−0.293179			−0.146590	+	0.989197i	$0.546830\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.82809			−0.914046
$5$	1.55319	−	1.60860i	0.694607	−	0.719389i
$5$	1.55319	−	1.60860i	0.694607	−	0.719389i
$6$			0.414618i			0.169267i
$7$		−	0.262182i		−	0.0990954i	−0.998772	−	0.0495477i	$-0.984222\pi$
$7$		−	0.262182i		−	0.0990954i	0.998772	−	0.0495477i	$-0.0157780\pi$
$8$	1.58720			0.561159
$9$	−1.00000			−0.333333
$10$	−0.643980	+	0.666956i	−0.203644	+	0.210910i
$11$	5.76010			1.73674			0.868368	−	0.495920i	$-0.165169\pi$
$11$	5.76010			1.73674			0.868368	+	0.495920i	$0.165169\pi$
$12$			1.82809i			0.527725i
$13$	−2.13826			−0.593047			−0.296524	−	0.955026i	$-0.595827\pi$
$13$	−2.13826			−0.593047			−0.296524	+	0.955026i	$0.595827\pi$
$14$			0.108705i			0.0290527i
$15$	−1.60860	−	1.55319i	−0.415340	−	0.401031i
$16$	2.99810			0.749526
$17$	−0.318926			−0.0773510			−0.0386755	−	0.999252i	$-0.512314\pi$
$17$	−0.318926			−0.0773510			−0.0386755	+	0.999252i	$0.512314\pi$
$18$	0.414618			0.0977265
$19$		−	6.26778i		−	1.43793i	−0.695048	−	0.718964i	$-0.744617\pi$
$19$		−	6.26778i		−	1.43793i	0.695048	−	0.718964i	$-0.255383\pi$
$20$	−2.83937	+	2.94068i	−0.634903	+	0.657555i
$21$	−0.262182			−0.0572127
$22$	−2.38824			−0.509175
$23$	−8.22627			−1.71529			−0.857647	−	0.514238i	$-0.828075\pi$
$23$	−8.22627			−1.71529			−0.857647	+	0.514238i	$0.828075\pi$
$24$		−	1.58720i		−	0.323985i
$25$	−0.175212	−	4.99693i	−0.0350424	−	0.999386i
$26$	0.886562			0.173869
$27$			1.00000i			0.192450i
$28$			0.479292i			0.0905777i
$29$		−	5.91180i		−	1.09779i	−0.835890	−	0.548896i	$-0.815048\pi$
$29$		−	5.91180i		−	1.09779i	0.835890	−	0.548896i	$-0.184952\pi$
$30$	0.666956	+	0.643980i	0.121769	+	0.117574i
$31$		−	1.32410i		−	0.237815i	−0.992905	−	0.118908i	$-0.962061\pi$
$31$		−	1.32410i		−	0.237815i	0.992905	−	0.118908i	$-0.0379392\pi$
$32$	−4.41746			−0.780904
$33$		−	5.76010i		−	1.00271i
$34$	0.132233			0.0226777
$35$	−0.421746	−	0.407217i	−0.0712882	−	0.0688323i
$36$	1.82809			0.304682
$37$	2.74005	+	5.43067i	0.450461	+	0.892796i
$37$	2.74005	+	5.43067i	0.450461	+	0.892796i
$38$			2.59874i			0.421571i
$39$			2.13826i			0.342396i
$40$	2.46522	−	2.55317i	0.389785	−	0.403692i
$41$	−5.96208			−0.931121			−0.465560	−	0.885016i	$-0.654147\pi$
$41$	−5.96208			−0.931121			−0.465560	+	0.885016i	$0.654147\pi$
$42$	0.108705			0.0167736
$43$	0.0737737			0.0112504			0.00562519	−	0.999984i	$-0.498209\pi$
$43$	0.0737737			0.0112504			0.00562519	+	0.999984i	$0.498209\pi$
$44$	−10.5300			−1.58746
$45$	−1.55319	+	1.60860i	−0.231536	+	0.239796i
$46$	3.41076			0.502889
$47$		−	8.04534i		−	1.17353i	−0.809756	−	0.586766i	$-0.800401\pi$
$47$		−	8.04534i		−	1.17353i	0.809756	−	0.586766i	$-0.199599\pi$
$48$		−	2.99810i		−	0.432739i
$49$	6.93126			0.990180
$50$	0.0726462	+	2.07182i	0.0102737	+	0.292999i
$51$			0.318926i			0.0446586i
$52$	3.90894			0.542072
$53$		−	5.23540i		−	0.719138i	−0.933119	−	0.359569i	$-0.882924\pi$
$53$		−	5.23540i		−	0.719138i	0.933119	−	0.359569i	$-0.117076\pi$
$54$		−	0.414618i		−	0.0564224i
$55$	8.94652	−	9.26572i	1.20635	−	1.24939i
$56$		−	0.416134i		−	0.0556082i
$57$	−6.26778			−0.830188
$58$			2.45114i			0.321850i
$59$			7.31368i			0.952160i	0.879402	+	0.476080i	$0.157943\pi$
$59$			7.31368i			0.952160i	−0.879402	+	0.476080i	$0.842057\pi$
$60$	2.94068	+	2.83937i	0.379640	+	0.366561i
$61$		−	2.66859i		−	0.341677i	−0.985299	−	0.170839i	$-0.945352\pi$
$61$		−	2.66859i		−	0.341677i	0.985299	−	0.170839i	$-0.0546477\pi$
$62$			0.548995i			0.0697225i
$63$			0.262182i			0.0330318i
$64$	−4.16465			−0.520581
$65$	−3.32112	+	3.43962i	−0.411935	+	0.426632i
$66$			2.38824i			0.293972i
$67$			3.69751i			0.451722i	0.974160	+	0.225861i	$0.0725195\pi$
$67$			3.69751i			0.451722i	−0.974160	+	0.225861i	$0.927480\pi$
$68$	0.583026			0.0707023
$69$			8.22627i			0.990326i
$70$	0.174864	+	0.168840i	0.0209002	+	0.0201802i
$71$	7.33380			0.870362			0.435181	−	0.900343i	$-0.356684\pi$
$71$	7.33380			0.870362			0.435181	+	0.900343i	$0.356684\pi$
$72$	−1.58720			−0.187053
$73$		−	2.43334i		−	0.284801i	−0.989809	−	0.142400i	$-0.954518\pi$
$73$		−	2.43334i		−	0.284801i	0.989809	−	0.142400i	$-0.0454821\pi$
$74$	−1.13607	−	2.25165i	−0.132066	−	0.261749i
$75$	−4.99693	+	0.175212i	−0.576996	+	0.0202318i
$76$			11.4581i			1.31433i
$77$		−	1.51019i		−	0.172103i
$78$		−	0.886562i		−	0.100383i
$79$		−	10.9171i		−	1.22827i	−0.789201	−	0.614135i	$-0.789505\pi$
$79$		−	10.9171i		−	1.22827i	0.789201	−	0.614135i	$-0.210495\pi$
$80$	4.65662	−	4.82276i	0.520626	−	0.539201i
$81$	1.00000			0.111111
$82$	2.47199			0.272985
$83$			13.2259i			1.45173i	0.687839	+	0.725863i	$0.258559\pi$
$83$			13.2259i			1.45173i	−0.687839	+	0.725863i	$0.741441\pi$
$84$	0.479292			0.0522951
$85$	−0.495352	+	0.513026i	−0.0537285	+	0.0556455i
$86$	−0.0305879			−0.00329838
$87$	−5.91180			−0.633811
$88$	9.14242			0.974585
$89$			9.15126i			0.970032i	0.874505	+	0.485016i	$0.161186\pi$
$89$			9.15126i			0.970032i	−0.874505	+	0.485016i	$0.838814\pi$
$90$	0.643980	−	0.666956i	0.0678815	−	0.0703034i
$91$			0.560613i			0.0587682i
$92$	15.0384			1.56786
$93$	−1.32410			−0.137303
$94$			3.33574i			0.344056i
$95$	−10.0824	−	9.73504i	−1.03443	−	0.998794i
$96$			4.41746i			0.450855i
$97$	1.87245			0.190118			0.0950591	−	0.995472i	$-0.469696\pi$
$97$	1.87245			0.190118			0.0950591	+	0.995472i	$0.469696\pi$
$98$	−2.87383			−0.290300
$99$	−5.76010			−0.578912
$100$	0.320304	+	9.13484i	0.0320304	+	0.913484i
$101$	5.97477			0.594512			0.297256	−	0.954798i	$-0.403929\pi$
$101$	5.97477			0.594512			0.297256	+	0.954798i	$0.403929\pi$
$102$		−	0.132233i		−	0.0130930i
$103$	17.2219			1.69692			0.848461	−	0.529258i	$-0.177530\pi$
$103$	17.2219			1.69692			0.848461	+	0.529258i	$0.177530\pi$
$104$	−3.39384			−0.332794
$105$	−0.407217	+	0.421746i	−0.0397404	+	0.0411582i
$106$			2.17069i			0.210836i
$107$			6.85177i			0.662386i	0.943563	+	0.331193i	$0.107451\pi$
$107$			6.85177i			0.662386i	−0.943563	+	0.331193i	$0.892549\pi$
$108$		−	1.82809i		−	0.175908i
$109$		−	10.2808i		−	0.984720i	−0.870392	−	0.492360i	$-0.836134\pi$
$109$		−	10.2808i		−	0.984720i	0.870392	−	0.492360i	$-0.163866\pi$
$110$	−3.70939	+	3.84174i	−0.353677	+	0.366295i
$111$	5.43067	−	2.74005i	0.515456	−	0.260074i
$112$		−	0.786048i		−	0.0742745i
$113$	−11.8584			−1.11555			−0.557774	−	0.829993i	$-0.688344\pi$
$113$	−11.8584			−1.11555			−0.557774	+	0.829993i	$0.688344\pi$
$114$	2.59874			0.243394
$115$	−12.7769	+	13.2328i	−1.19146	+	1.23397i
$116$			10.8073i			1.00343i
$117$	2.13826			0.197682
$118$		−	3.03239i		−	0.279154i
$119$			0.0836166i			0.00766512i
$120$	−2.55317	−	2.46522i	−0.233072	−	0.225042i
$121$	22.1788			2.01625
$122$			1.10644i			0.100173i
$123$			5.96208i			0.537583i
$124$			2.42057i			0.217374i
$125$	−8.31022	−	7.47932i	−0.743288	−	0.668971i
$126$		−	0.108705i		−	0.00968424i
$127$			17.9887i			1.59624i	0.602498	+	0.798120i	$0.294172\pi$
$127$			17.9887i			1.59624i	−0.602498	+	0.798120i	$0.705828\pi$
$128$	10.5617			0.933528
$129$		−	0.0737737i		−	0.00649541i
$130$	1.37700	−	1.42613i	0.120771	−	0.125080i
$131$			17.7072i			1.54708i	0.633746	+	0.773541i	$0.281516\pi$
$131$			17.7072i			1.54708i	−0.633746	+	0.773541i	$0.718484\pi$
$132$			10.5300i			0.916519i
$133$	−1.64330			−0.142492
$134$		−	1.53305i		−	0.132436i
$135$	1.60860	+	1.55319i	0.138447	+	0.133677i
$136$	−0.506199			−0.0434062
$137$		−	17.2127i		−	1.47058i	−0.677751	−	0.735292i	$-0.737045\pi$
$137$		−	17.2127i		−	1.47058i	0.677751	−	0.735292i	$-0.262955\pi$
$138$		−	3.41076i		−	0.290343i
$139$	9.54110			0.809265			0.404633	−	0.914479i	$-0.367399\pi$
$139$	9.54110			0.809265			0.404633	+	0.914479i	$0.367399\pi$
$140$	0.770991	+	0.744431i	0.0651606	+	0.0629159i
$141$	−8.04534			−0.677539
$142$	−3.04073			−0.255172
$143$	−12.3166			−1.02997
$144$	−2.99810			−0.249842
$145$	−9.50974	−	9.18213i	−0.789741	−	0.762535i
$146$			1.00891i			0.0834977i
$147$		−	6.93126i		−	0.571681i
$148$	−5.00905	−	9.92776i	−0.411742	−	0.816057i
$149$	2.86180			0.234448			0.117224	−	0.993106i	$-0.462601\pi$
$149$	2.86180			0.234448			0.117224	+	0.993106i	$0.462601\pi$
$150$	2.07182	−	0.0726462i	0.169163	−	0.00593153i
$151$	6.98060			0.568073			0.284036	−	0.958813i	$-0.408326\pi$
$151$	6.98060			0.568073			0.284036	+	0.958813i	$0.408326\pi$
$152$		−	9.94820i		−	0.806905i
$153$	0.318926			0.0257837
$154$			0.626154i			0.0504569i
$155$	−2.12995	−	2.05657i	−0.171082	−	0.165188i
$156$		−	3.90894i		−	0.312966i
$157$		−	5.46733i		−	0.436341i	−0.975911	−	0.218170i	$-0.929991\pi$
$157$		−	5.46733i		−	0.436341i	0.975911	−	0.218170i	$-0.0700088\pi$
$158$			4.52643i			0.360104i
$159$	−5.23540			−0.415194
$160$	−6.86115	+	7.10594i	−0.542421	+	0.561774i
$161$			2.15678i			0.169978i
$162$	−0.414618			−0.0325755
$163$	9.17810			0.718884			0.359442	−	0.933167i	$-0.382967\pi$
$163$	9.17810			0.718884			0.359442	+	0.933167i	$0.382967\pi$
$164$	10.8992			0.851087
$165$	−9.26572	−	8.94652i	−0.721336	−	0.696486i
$166$		−	5.48368i		−	0.425616i
$167$	6.61145			0.511610			0.255805	−	0.966728i	$-0.417660\pi$
$167$	6.61145			0.511610			0.255805	+	0.966728i	$0.417660\pi$
$168$	−0.416134			−0.0321054
$169$	−8.42784			−0.648295
$170$	0.205382	−	0.212710i	0.0157521	−	0.0163141i
$171$			6.26778i			0.479309i
$172$	−0.134865			−0.0102834
$173$			12.9620i			0.985484i	0.870175	+	0.492742i	$0.164005\pi$
$173$			12.9620i			0.985484i	−0.870175	+	0.492742i	$0.835995\pi$
$174$	2.45114			0.185820
$175$	−1.31010	+	0.0459374i	−0.0990345	+	0.00347254i
$176$	17.2694			1.30173
$177$	7.31368			0.549730
$178$		−	3.79428i		−	0.284393i
$179$			25.2410i			1.88660i	0.331943	+	0.943300i	$0.392296\pi$
$179$			25.2410i			1.88660i	−0.331943	+	0.943300i	$0.607704\pi$
$180$	2.83937	−	2.94068i	0.211634	−	0.219185i
$181$	−3.59537			−0.267242			−0.133621	−	0.991033i	$-0.542660\pi$
$181$	−3.59537			−0.267242			−0.133621	+	0.991033i	$0.542660\pi$
$182$		−	0.232440i		−	0.0172296i
$183$	−2.66859			−0.197268
$184$	−13.0567			−0.962553
$185$	12.9916	+	4.02720i	0.955161	+	0.296086i
$186$	0.548995			0.0402543
$187$	−1.83705			−0.134338
$188$			14.7076i			1.07266i
$189$	0.262182			0.0190709
$190$	4.18034	+	4.03633i	0.303273	+	0.292826i
$191$			3.51942i			0.254656i	0.991861	+	0.127328i	$0.0406402\pi$
$191$			3.51942i			0.254656i	−0.991861	+	0.127328i	$0.959360\pi$
$192$			4.16465i			0.300557i
$193$	5.90729			0.425216			0.212608	−	0.977138i	$-0.431804\pi$
$193$	5.90729			0.425216			0.212608	+	0.977138i	$0.431804\pi$
$194$	−0.776351			−0.0557387
$195$	3.43962	+	3.32112i	0.246316	+	0.237831i
$196$	−12.6710			−0.905070
$197$		−	19.9230i		−	1.41945i	−0.704477	−	0.709727i	$-0.748818\pi$
$197$		−	19.9230i		−	1.41945i	0.704477	−	0.709727i	$-0.251182\pi$
$198$	2.38824			0.169725
$199$			22.7262i			1.61102i	0.592583	+	0.805510i	$0.298108\pi$
$199$			22.7262i			1.61102i	−0.592583	+	0.805510i	$0.701892\pi$
$200$	−0.278096	−	7.93111i	−0.0196644	−	0.560814i
$201$	3.69751			0.260802
$202$	−2.47725			−0.174299
$203$	−1.54996			−0.108786
$204$		−	0.583026i		−	0.0408200i
$205$	−9.26024	+	9.59063i	−0.646763	+	0.669839i
$206$	−7.14050			−0.497502
$207$	8.22627			0.571765
$208$	−6.41073			−0.444504
$209$		−	36.1031i		−	2.49730i
$210$	0.168840	−	0.174864i	0.0116511	−	0.0120667i
$211$	−9.92676			−0.683386			−0.341693	−	0.939812i	$-0.611000\pi$
$211$	−9.92676			−0.683386			−0.341693	+	0.939812i	$0.611000\pi$
$212$			9.57079i			0.657325i
$213$		−	7.33380i		−	0.502504i
$214$		−	2.84087i		−	0.194198i
$215$	0.114584	−	0.118673i	0.00781459	−	0.00809341i
$216$			1.58720i			0.107995i
$217$	−0.347154			−0.0235664
$218$			4.26260i			0.288700i
$219$	−2.43334			−0.164430
$220$	−16.3551	+	16.9386i	−1.10266	+	1.14200i
$221$	0.681948			0.0458728
$222$	−2.25165	+	1.13607i	−0.151121	+	0.0762482i
$223$		−	19.4009i		−	1.29918i	−0.760285	−	0.649589i	$-0.774941\pi$
$223$		−	19.4009i		−	1.29918i	0.760285	−	0.649589i	$-0.225059\pi$
$224$			1.15818i			0.0773840i
$225$	0.175212	+	4.99693i	0.0116808	+	0.333129i
$226$	4.91672			0.327055
$227$	26.6876			1.77132			0.885658	−	0.464339i	$-0.153708\pi$
$227$	26.6876			1.77132			0.885658	+	0.464339i	$0.153708\pi$
$228$	11.4581			0.758830
$229$	12.3672			0.817249			0.408625	−	0.912703i	$-0.366009\pi$
$229$	12.3672			0.817249			0.408625	+	0.912703i	$0.366009\pi$
$230$	5.29755	−	5.48656i	0.349310	−	0.361773i
$231$	−1.51019			−0.0993634
$232$		−	9.38318i		−	0.616036i
$233$			17.2351i			1.12911i	0.825396	+	0.564554i	$0.190952\pi$
$233$			17.2351i			1.12911i	−0.825396	+	0.564554i	$0.809048\pi$
$234$	−0.886562			−0.0579564
$235$	−12.9418	−	12.4959i	−0.844227	−	0.815144i
$236$		−	13.3701i		−	0.870318i
$237$	−10.9171			−0.709142
$238$		−	0.0346690i		−	0.00224726i
$239$		−	1.88181i		−	0.121724i	−0.998146	−	0.0608621i	$-0.980615\pi$
$239$		−	1.88181i		−	0.121724i	0.998146	−	0.0608621i	$-0.0193850\pi$
$240$	−4.82276	−	4.65662i	−0.311308	−	0.300583i
$241$		−	12.4854i		−	0.804254i	−0.915584	−	0.402127i	$-0.868271\pi$
$241$		−	12.4854i		−	0.804254i	0.915584	−	0.402127i	$-0.131729\pi$
$242$	−9.19573			−0.591124
$243$		−	1.00000i		−	0.0641500i
$244$			4.87842i			0.312309i
$245$	10.7656	−	11.1497i	0.687786	−	0.712325i
$246$		−	2.47199i		−	0.157608i
$247$			13.4022i			0.852759i
$248$		−	2.10160i		−	0.133452i
$249$	13.2259			0.838155
$250$	3.44557	+	3.10106i	0.217917	+	0.196129i
$251$		−	11.0417i		−	0.696948i	−0.937318	−	0.348474i	$-0.886700\pi$
$251$		−	11.0417i		−	0.696948i	0.937318	−	0.348474i	$-0.113300\pi$
$252$		−	0.479292i		−	0.0301926i
$253$	−47.3841			−2.97902
$254$		−	7.45845i		−	0.467985i
$255$	0.513026	+	0.495352i	0.0321269	+	0.0310202i
$256$	3.95023			0.246890
$257$	−23.2765			−1.45195			−0.725974	−	0.687722i	$-0.758611\pi$
$257$	−23.2765			−1.45195			−0.725974	+	0.687722i	$0.758611\pi$
$258$			0.0305879i			0.00190432i
$259$	1.42382	−	0.718390i	0.0884720	−	0.0446386i
$260$	6.07132	−	6.28793i	0.376527	−	0.389961i
$261$			5.91180i			0.365931i
$262$		−	7.34171i		−	0.453573i
$263$			11.7240i			0.722935i	0.932385	+	0.361467i	$0.117724\pi$
$263$			11.7240i			0.722935i	−0.932385	+	0.361467i	$0.882276\pi$
$264$		−	9.14242i		−	0.562677i
$265$	−8.42169	−	8.13156i	−0.517340	−	0.499518i
$266$	0.681341			0.0417757
$267$	9.15126			0.560048
$268$		−	6.75938i		−	0.412895i
$269$	3.14696			0.191874			0.0959368	−	0.995387i	$-0.469415\pi$
$269$	3.14696			0.191874			0.0959368	+	0.995387i	$0.469415\pi$
$270$	−0.666956	−	0.643980i	−0.0405897	−	0.0391914i
$271$	9.98429			0.606503			0.303251	−	0.952911i	$-0.401928\pi$
$271$	9.98429			0.606503			0.303251	+	0.952911i	$0.401928\pi$
$272$	−0.956174			−0.0579765
$273$	0.560613			0.0339298
$274$			7.13671i			0.431145i
$275$	−1.00924	−	28.7828i	−0.0608595	−	1.73567i
$276$		−	15.0384i		−	0.905203i
$277$	−9.73495			−0.584917			−0.292458	−	0.956278i	$-0.594473\pi$
$277$	−9.73495			−0.584917			−0.292458	+	0.956278i	$0.594473\pi$
$278$	−3.95591			−0.237260
$279$			1.32410i			0.0792717i
$280$	−0.669394	−	0.646334i	−0.0400040	−	0.0386259i
$281$		−	10.1462i		−	0.605271i	−0.953106	−	0.302636i	$-0.902133\pi$
$281$		−	10.1462i		−	0.605271i	0.953106	−	0.302636i	$-0.0978665\pi$
$282$	3.33574			0.198641
$283$	24.9586			1.48363			0.741817	−	0.670603i	$-0.233964\pi$
$283$	24.9586			1.48363			0.741817	+	0.670603i	$0.233964\pi$
$284$	−13.4069			−0.795551
$285$	−9.73504	+	10.0824i	−0.576654	+	0.597228i
$286$	5.10669			0.301965
$287$			1.56315i			0.0922698i
$288$	4.41746			0.260301
$289$	−16.8983			−0.994017
$290$	3.94291	+	3.80708i	0.231536	+	0.223559i
$291$		−	1.87245i		−	0.109765i
$292$			4.44837i			0.260321i
$293$		−	2.46417i		−	0.143958i	−0.997406	−	0.0719791i	$-0.977069\pi$
$293$		−	2.46417i		−	0.143958i	0.997406	−	0.0719791i	$-0.0229315\pi$
$294$			2.87383i			0.167605i
$295$	11.7648	+	11.3595i	0.684974	+	0.661377i
$296$	4.34899	+	8.61954i	0.252780	+	0.501000i
$297$			5.76010i			0.334235i
$298$	−1.18655			−0.0687352
$299$	17.5899			1.01725
$300$	9.13484	−	0.320304i	0.527401	−	0.0184928i
$301$		−	0.0193421i		−	0.00111486i
$302$	−2.89428			−0.166547
$303$		−	5.97477i		−	0.343242i
$304$		−	18.7914i		−	1.07776i
$305$	−4.29270	−	4.14482i	−0.245799	−	0.237331i
$306$	−0.132233			−0.00755924
$307$		−	26.7108i		−	1.52447i	−0.647302	−	0.762234i	$-0.724103\pi$
$307$		−	26.7108i		−	1.52447i	0.647302	−	0.762234i	$-0.275897\pi$
$308$			2.76077i			0.157310i
$309$		−	17.2219i		−	0.979718i
$310$	0.883116	+	0.852693i	0.0501576	+	0.0484297i
$311$		−	17.9298i		−	1.01671i	−0.861149	−	0.508353i	$-0.830254\pi$
$311$		−	17.9298i		−	1.01671i	0.861149	−	0.508353i	$-0.169746\pi$
$312$			3.39384i			0.192138i
$313$	17.2439			0.974685			0.487342	−	0.873211i	$-0.337966\pi$
$313$	17.2439			0.974685			0.487342	+	0.873211i	$0.337966\pi$
$314$			2.26686i			0.127926i
$315$	0.421746	+	0.407217i	0.0237627	+	0.0229441i
$316$			19.9575i			1.12270i
$317$		−	1.81182i		−	0.101762i	−0.998705	−	0.0508811i	$-0.983797\pi$
$317$		−	1.81182i		−	0.101762i	0.998705	−	0.0508811i	$-0.0162030\pi$
$318$	2.17069			0.121726
$319$		−	34.0526i		−	1.90658i
$320$	−6.46848	+	6.69926i	−0.361599	+	0.374500i
$321$	6.85177			0.382428
$322$		−	0.894239i		−	0.0498340i
$323$			1.99896i			0.111225i
$324$	−1.82809			−0.101561
$325$	0.374650	+	10.6847i	0.0207818	+	0.592683i
$326$	−3.80541			−0.210762
$327$	−10.2808			−0.568529
$328$	−9.46300			−0.522507
$329$	−2.10934			−0.116292
$330$	3.84174	+	3.70939i	0.211481	+	0.204195i
$331$			29.6303i			1.62863i	0.580423	+	0.814315i	$0.302887\pi$
$331$			29.6303i			1.62863i	−0.580423	+	0.814315i	$0.697113\pi$
$332$		−	24.1781i		−	1.32694i
$333$	−2.74005	−	5.43067i	−0.150154	−	0.297599i
$334$	−2.74123			−0.149993
$335$	5.94782	+	5.74292i	0.324964	+	0.313769i
$336$	−0.786048			−0.0428824
$337$		−	20.2688i		−	1.10411i	−0.833807	−	0.552056i	$-0.813843\pi$
$337$		−	20.2688i		−	1.10411i	0.833807	−	0.552056i	$-0.186157\pi$
$338$	3.49433			0.190067
$339$			11.8584i			0.644061i
$340$	0.905550	−	0.937858i	0.0491103	−	0.0508625i
$341$		−	7.62694i		−	0.413022i
$342$		−	2.59874i		−	0.140524i
$343$		−	3.65252i		−	0.197218i
$344$	0.117093			0.00631325
$345$	13.2328	+	12.7769i	0.712430	+	0.687887i
$346$		−	5.37429i		−	0.288924i
$347$	−27.3184			−1.46653			−0.733265	−	0.679943i	$-0.762005\pi$
$347$	−27.3184			−1.46653			−0.733265	+	0.679943i	$0.762005\pi$
$348$	10.8073			0.579332
$349$	10.2089			0.546471			0.273236	−	0.961947i	$-0.411906\pi$
$349$	10.2089			0.546471			0.273236	+	0.961947i	$0.411906\pi$
$350$	0.543193	−	0.0190465i	0.0290349	−	0.00101808i
$351$		−	2.13826i		−	0.114132i
$352$	−25.4450			−1.35622
$353$	2.13989			0.113895			0.0569475	−	0.998377i	$-0.481863\pi$
$353$	2.13989			0.113895			0.0569475	+	0.998377i	$0.481863\pi$
$354$	−3.03239			−0.161170
$355$	11.3908	−	11.7972i	0.604559	−	0.626129i
$356$		−	16.7293i		−	0.886653i
$357$	0.0836166			0.00442546
$358$		−	10.4654i		−	0.553112i
$359$	−24.1396			−1.27404			−0.637021	−	0.770847i	$-0.719833\pi$
$359$	−24.1396			−1.27404			−0.637021	+	0.770847i	$0.719833\pi$
$360$	−2.46522	+	2.55317i	−0.129928	+	0.134564i
$361$	−20.2851			−1.06763
$362$	1.49071			0.0783498
$363$		−	22.1788i		−	1.16408i
$364$		−	1.02485i		−	0.0537169i
$365$	−3.91428	−	3.77943i	−0.204883	−	0.197825i
$366$	1.10644			0.0578348
$367$			11.7602i			0.613878i	0.951729	+	0.306939i	$0.0993048\pi$
$367$			11.7602i			0.613878i	−0.951729	+	0.306939i	$0.900695\pi$
$368$	−24.6632			−1.28566
$369$	5.96208			0.310374
$370$	−5.38655	−	1.66975i	−0.280034	−	0.0868062i
$371$	−1.37263			−0.0712632
$372$	2.42057			0.125501
$373$			12.1124i			0.627155i	0.949563	+	0.313578i	$0.101528\pi$
$373$			12.1124i			0.627155i	−0.949563	+	0.313578i	$0.898472\pi$
$374$	0.761674			0.0393852
$375$	−7.47932	+	8.31022i	−0.386231	+	0.429138i
$376$		−	12.7695i		−	0.658538i
$377$			12.6410i			0.651043i
$378$	−0.108705			−0.00559120
$379$	8.11802			0.416995			0.208497	−	0.978023i	$-0.433143\pi$
$379$	8.11802			0.416995			0.208497	+	0.978023i	$0.433143\pi$
$380$	18.4315	+	17.7965i	0.945516	+	0.912944i
$381$	17.9887			0.921590
$382$		−	1.45922i		−	0.0746600i
$383$	14.9304			0.762905			0.381453	−	0.924388i	$-0.375424\pi$
$383$	14.9304			0.762905			0.381453	+	0.924388i	$0.375424\pi$
$384$		−	10.5617i		−	0.538972i
$385$	−2.42930	−	2.34561i	−0.123809	−	0.119544i
$386$	−2.44927			−0.124665
$387$	−0.0737737			−0.00375013
$388$	−3.42301			−0.173777
$389$		−	0.640059i		−	0.0324523i	−0.999868	−	0.0162261i	$-0.994835\pi$
$389$		−	0.640059i		−	0.0324523i	0.999868	−	0.0162261i	$-0.00516516\pi$
$390$	−1.42613	−	1.37700i	−0.0722148	−	0.0697270i
$391$	2.62357			0.132680
$392$	11.0013			0.555648
$393$	17.7072			0.893208
$394$			8.26043i			0.416155i
$395$	−17.5613	−	16.9563i	−0.883605	−	0.853165i
$396$	10.5300			0.529152
$397$			15.4326i			0.774538i	0.921967	+	0.387269i	$0.126581\pi$
$397$			15.4326i			0.774538i	−0.921967	+	0.387269i	$0.873419\pi$
$398$		−	9.42271i		−	0.472318i
$399$			1.64330i			0.0822677i
$400$	−0.525304	−	14.9813i	−0.0262652	−	0.749065i
$401$			29.0147i			1.44892i	0.689315	+	0.724462i	$0.257912\pi$
$401$			29.0147i			1.44892i	−0.689315	+	0.724462i	$0.742088\pi$
$402$	−1.53305			−0.0764617
$403$			2.83127i			0.141036i
$404$	−10.9224			−0.543411
$405$	1.55319	−	1.60860i	0.0771785	−	0.0799322i
$406$	0.642644			0.0318939
$407$	15.7829	+	31.2812i	0.782332	+	1.55055i
$408$			0.506199i			0.0250606i
$409$			31.1142i			1.53850i	0.638949	+	0.769249i	$0.279370\pi$
$409$			31.1142i			1.53850i	−0.638949	+	0.769249i	$0.720630\pi$
$410$	3.83946	−	3.97645i	0.189618	−	0.196383i
$411$	−17.2127			−0.849042
$412$	−31.4832			−1.55106
$413$	1.91751			0.0943547
$414$	−3.41076			−0.167630
$415$	21.2752	+	20.5422i	1.04436	+	1.00838i
$416$	9.44569			0.463113
$417$		−	9.54110i		−	0.467229i
$418$			14.9690i			0.732157i
$419$	2.82253			0.137889			0.0689447	−	0.997620i	$-0.478037\pi$
$419$	2.82253			0.137889			0.0689447	+	0.997620i	$0.478037\pi$
$420$	0.744431	−	0.770991i	0.0363245	−	0.0376205i
$421$			19.3935i			0.945180i	0.881282	+	0.472590i	$0.156681\pi$
$421$			19.3935i			0.945180i	−0.881282	+	0.472590i	$0.843319\pi$
$422$	4.11582			0.200355
$423$			8.04534i			0.391178i
$424$		−	8.30961i		−	0.403550i
$425$	0.0558798	+	1.59365i	0.00271057	+	0.0773035i
$426$			3.04073i			0.147324i
$427$	−0.699654			−0.0338586
$428$		−	12.5257i		−	0.605451i
$429$			12.3166i			0.594652i
$430$	−0.0475088	+	0.0492038i	−0.00229108	+	0.00237282i
$431$		−	3.37756i		−	0.162691i	−0.996686	−	0.0813456i	$-0.974078\pi$
$431$		−	3.37756i		−	0.162691i	0.996686	−	0.0813456i	$-0.0259217\pi$
$432$			2.99810i			0.144246i
$433$			16.7643i			0.805643i	0.915279	+	0.402821i	$0.131970\pi$
$433$			16.7643i			0.805643i	−0.915279	+	0.402821i	$0.868030\pi$
$434$	0.143936			0.00690917
$435$	−9.18213	+	9.50974i	−0.440250	+	0.455957i
$436$			18.7942i			0.900080i
$437$			51.5604i			2.46647i
$438$	1.00891			0.0482074
$439$			19.6474i			0.937721i	0.883272	+	0.468860i	$0.155335\pi$
$439$			19.6474i			0.937721i	−0.883272	+	0.468860i	$0.844665\pi$
$440$	14.1999	−	14.7065i	0.676953	−	0.701106i
$441$	−6.93126			−0.330060
$442$	−0.282748			−0.0134490
$443$			35.7080i			1.69654i	0.529567	+	0.848268i	$0.322354\pi$
$443$			35.7080i			1.69654i	−0.529567	+	0.848268i	$0.677646\pi$
$444$	−9.92776	+	5.00905i	−0.471151	+	0.237719i
$445$	14.7208	+	14.2136i	0.697831	+	0.673791i
$446$			8.04396i			0.380892i
$447$		−	2.86180i		−	0.135358i
$448$			1.09189i			0.0515871i
$449$			21.4279i			1.01124i	0.862755	+	0.505622i	$0.168737\pi$
$449$			21.4279i			1.01124i	−0.862755	+	0.505622i	$0.831263\pi$
$450$	−0.0726462	−	2.07182i	−0.00342457	−	0.0976664i
$451$	−34.3422			−1.61711
$452$	21.6783			1.01966
$453$		−	6.98060i		−	0.327977i
$454$	−11.0651			−0.519313
$455$	0.901804	+	0.870738i	0.0422772	+	0.0408208i
$456$	−9.94820			−0.465867
$457$	37.7170			1.76433			0.882164	−	0.470942i	$-0.156086\pi$
$457$	37.7170			1.76433			0.882164	+	0.470942i	$0.156086\pi$
$458$	−5.12768			−0.239601
$459$		−	0.318926i		−	0.0148862i
$460$	23.3574	−	24.1908i	1.08905	−	1.12790i
$461$		−	19.5399i		−	0.910065i	−0.890475	−	0.455033i	$-0.849628\pi$
$461$		−	19.5399i		−	0.910065i	0.890475	−	0.455033i	$-0.150372\pi$
$462$	0.626154			0.0291313
$463$	−25.4885			−1.18455			−0.592277	−	0.805735i	$-0.701771\pi$
$463$	−25.4885			−1.18455			−0.592277	+	0.805735i	$0.701771\pi$
$464$		−	17.7242i		−	0.822824i
$465$	−2.05657	+	2.12995i	−0.0953713	+	0.0987740i
$466$		−	7.14598i		−	0.331031i
$467$	22.8861			1.05904			0.529522	−	0.848296i	$-0.322371\pi$
$467$	22.8861			1.05904			0.529522	+	0.848296i	$0.322371\pi$
$468$	−3.90894			−0.180691
$469$	0.969418			0.0447636
$470$	5.36589	+	5.18104i	0.247510	+	0.238983i
$471$	−5.46733			−0.251921
$472$			11.6083i			0.534313i
$473$	0.424944			0.0195389
$474$	4.52643			0.207906
$475$	−31.3196	+	1.09819i	−1.43704	+	0.0503885i
$476$		−	0.152859i		−	0.00700627i
$477$			5.23540i			0.239713i
$478$			0.780233i			0.0356870i
$479$			22.1945i			1.01409i	0.861918	+	0.507047i	$0.169263\pi$
$479$			22.1945i			1.01409i	−0.861918	+	0.507047i	$0.830737\pi$
$480$	7.10594	+	6.86115i	0.324341	+	0.313167i
$481$	−5.85894	−	11.6122i	−0.267144	−	0.529470i
$482$			5.17666i			0.235791i
$483$	2.15678			0.0981367
$484$	−40.5449			−1.84295
$485$	2.90826	−	3.01203i	0.132057	−	0.136769i
$486$			0.414618i			0.0188075i
$487$	16.8598			0.763992			0.381996	−	0.924164i	$-0.375237\pi$
$487$	16.8598			0.763992			0.381996	+	0.924164i	$0.375237\pi$
$488$		−	4.23557i		−	0.191735i
$489$		−	9.17810i		−	0.415048i
$490$	−4.46359	+	4.62285i	−0.201645	+	0.208839i
$491$	−30.3511			−1.36973			−0.684864	−	0.728671i	$-0.740138\pi$
$491$	−30.3511			−1.36973			−0.684864	+	0.728671i	$0.740138\pi$
$492$		−	10.8992i		−	0.491375i
$493$			1.88543i			0.0849154i
$494$		−	5.55678i		−	0.250011i
$495$	−8.94652	+	9.26572i	−0.402116	+	0.416463i
$496$		−	3.96978i		−	0.178248i
$497$		−	1.92279i		−	0.0862488i
$498$	−5.48368			−0.245730
$499$			14.4064i			0.644921i	0.946583	+	0.322460i	$0.104510\pi$
$499$			14.4064i			0.644921i	−0.946583	+	0.322460i	$0.895490\pi$
$500$	15.1918	+	13.6729i	0.679400	+	0.611470i
$501$		−	6.61145i		−	0.295378i
$502$			4.57810i			0.204331i
$503$	3.54217			0.157937			0.0789687	−	0.996877i	$-0.474837\pi$
$503$	3.54217			0.157937			0.0789687	+	0.996877i	$0.474837\pi$
$504$			0.416134i			0.0185361i
$505$	9.27995	−	9.61104i	0.412952	−	0.427686i
$506$	19.6463			0.873386
$507$			8.42784i			0.374293i
$508$		−	32.8850i		−	1.45904i
$509$	3.67428			0.162859			0.0814297	−	0.996679i	$-0.474051\pi$
$509$	3.67428			0.162859			0.0814297	+	0.996679i	$0.474051\pi$
$510$	−0.212710	−	0.205382i	−0.00941895	−	0.00909448i
$511$	−0.637977			−0.0282224
$512$	−22.7612			−1.00591
$513$	6.26778			0.276729
$514$	9.65086			0.425681
$515$	26.7488	−	27.7032i	1.17869	−	1.22075i
$516$			0.134865i			0.00593710i
$517$		−	46.3420i		−	2.03812i
$518$	−0.590342	+	0.297857i	−0.0259382	+	0.0130871i
$519$	12.9620			0.568970
$520$	−5.27128	+	5.45935i	−0.231161	+	0.239408i
$521$	−20.1638			−0.883393			−0.441696	−	0.897165i	$-0.645623\pi$
$521$	−20.1638			−0.883393			−0.441696	+	0.897165i	$0.645623\pi$
$522$		−	2.45114i		−	0.107283i
$523$	35.6588			1.55925			0.779625	−	0.626246i	$-0.215410\pi$
$523$	35.6588			1.55925			0.779625	+	0.626246i	$0.215410\pi$
$524$		−	32.3703i		−	1.41410i
$525$	0.0459374	+	1.31010i	0.00200487	+	0.0571776i
$526$		−	4.86100i		−	0.211949i
$527$			0.422290i			0.0183952i
$528$		−	17.2694i		−	0.751553i
$529$	44.6714			1.94224
$530$	3.49178	+	3.37149i	0.151673	+	0.146448i
$531$		−	7.31368i		−	0.317387i
$532$	3.00410			0.130244
$533$	12.7485			0.552199
$534$	−3.79428			−0.164195
$535$	11.0218	+	10.6421i	0.476513	+	0.460098i
$536$			5.86867i			0.253488i
$537$	25.2410			1.08923
$538$	−1.30479			−0.0562534
$539$	39.9248			1.71968
$540$	−2.94068	−	2.83937i	−0.126547	−	0.122187i
$541$		−	34.4594i		−	1.48152i	−0.671767	−	0.740762i	$-0.734465\pi$
$541$		−	34.4594i		−	1.48152i	0.671767	−	0.740762i	$-0.265535\pi$
$542$	−4.13967			−0.177814
$543$			3.59537i			0.154292i
$544$	1.40884			0.0604037
$545$	−16.5377	−	15.9680i	−0.708397	−	0.683994i
$546$	−0.232440			−0.00994753
$547$	3.31887			0.141905			0.0709524	−	0.997480i	$-0.477396\pi$
$547$	3.31887			0.141905			0.0709524	+	0.997480i	$0.477396\pi$
$548$			31.4665i			1.34418i
$549$			2.66859i			0.113892i
$550$	0.418449	+	11.9339i	0.0178427	+	0.508863i
$551$	−37.0538			−1.57855
$552$			13.0567i			0.555730i
$553$	−2.86227			−0.121716
$554$	4.03629			0.171486
$555$	4.02720	−	12.9916i	0.170945	−	0.551463i
$556$	−17.4420			−0.739705
$557$	−24.6624			−1.04498			−0.522490	−	0.852646i	$-0.674997\pi$
$557$	−24.6624			−1.04498			−0.522490	+	0.852646i	$0.674997\pi$
$558$		−	0.548995i		−	0.0232408i
$559$	−0.157747			−0.00667201
$560$	−1.26444	−	1.22088i	−0.0534323	−	0.0515916i
$561$			1.83705i			0.0775602i
$562$			4.20680i			0.177453i
$563$	1.04569			0.0440708			0.0220354	−	0.999757i	$-0.492985\pi$
$563$	1.04569			0.0440708			0.0220354	+	0.999757i	$0.492985\pi$
$564$	14.7076			0.619302
$565$	−18.4184	+	19.0755i	−0.774867	+	0.802513i
$566$	−10.3483			−0.434971
$567$		−	0.262182i		−	0.0110106i
$568$	11.6402			0.488411
$569$			25.2686i			1.05931i	0.848212	+	0.529657i	$0.177679\pi$
$569$			25.2686i			1.05931i	−0.848212	+	0.529657i	$0.822321\pi$
$570$	4.03633	−	4.18034i	0.169063	−	0.175095i
$571$	−30.6450			−1.28245			−0.641226	−	0.767352i	$-0.721574\pi$
$571$	−30.6450			−1.28245			−0.641226	+	0.767352i	$0.721574\pi$
$572$	22.5159			0.941437
$573$	3.51942			0.147026
$574$		−	0.648110i		−	0.0270516i
$575$	1.44134	+	41.1061i	0.0601081	+	1.71424i
$576$	4.16465			0.173527
$577$	−29.5154			−1.22874			−0.614372	−	0.789017i	$-0.710591\pi$
$577$	−29.5154			−1.22874			−0.614372	+	0.789017i	$0.710591\pi$
$578$	7.00634			0.291425
$579$		−	5.90729i		−	0.245499i
$580$	17.3847	+	16.7858i	0.721859	+	0.696992i
$581$	3.46758			0.143859
$582$			0.776351i			0.0321808i
$583$		−	30.1565i		−	1.24895i
$584$		−	3.86219i		−	0.159818i
$585$	3.32112	−	3.43962i	0.137312	−	0.142211i
$586$			1.02169i			0.0422056i
$587$	−20.5402			−0.847785			−0.423892	−	0.905713i	$-0.639336\pi$
$587$	−20.5402			−0.847785			−0.423892	+	0.905713i	$0.639336\pi$
$588$			12.6710i			0.522542i
$589$	−8.29915			−0.341961
$590$	−4.87791	−	4.70987i	−0.200820	−	0.193902i
$591$	−19.9230			−0.819522
$592$	8.21494	+	16.2817i	0.337632	+	0.669174i
$593$		−	43.1573i		−	1.77226i	−0.463438	−	0.886129i	$-0.653384\pi$
$593$		−	43.1573i		−	1.77226i	0.463438	−	0.886129i	$-0.346616\pi$
$594$		−	2.38824i		−	0.0979908i
$595$	0.134506	+	0.129872i	0.00551421	+	0.00532425i
$596$	−5.23163			−0.214296
$597$	22.7262			0.930122
$598$	−7.29310			−0.298237
$599$	20.8680			0.852642			0.426321	−	0.904572i	$-0.359809\pi$
$599$	20.8680			0.852642			0.426321	+	0.904572i	$0.359809\pi$
$600$	−7.93111	+	0.278096i	−0.323786	+	0.0113532i
$601$	−0.343724			−0.0140208			−0.00701039	−	0.999975i	$-0.502231\pi$
$601$	−0.343724			−0.0140208			−0.00701039	+	0.999975i	$0.502231\pi$
$602$			0.00801959i			0.000326854i
$603$		−	3.69751i		−	0.150574i
$604$	−12.7612			−0.519245
$605$	34.4478	−	35.6769i	1.40050	−	1.45047i
$606$			2.47725i			0.100631i
$607$	42.2030			1.71297			0.856483	−	0.516175i	$-0.172644\pi$
$607$	42.2030			1.71297			0.856483	+	0.516175i	$0.172644\pi$
$608$			27.6877i			1.12288i
$609$			1.54996i			0.0628077i
$610$	1.77983	+	1.71852i	0.0720632	+	0.0695807i
$611$			17.2030i			0.695960i
$612$	−0.583026			−0.0235674
$613$			17.0103i			0.687041i	0.939145	+	0.343520i	$0.111619\pi$
$613$			17.0103i			0.687041i	−0.939145	+	0.343520i	$0.888381\pi$
$614$			11.0748i			0.446942i
$615$	9.59063	+	9.26024i	0.386731	+	0.373409i
$616$		−	2.39697i		−	0.0965768i
$617$		−	10.2068i		−	0.410912i	−0.978666	−	0.205456i	$-0.934132\pi$
$617$		−	10.2068i		−	0.410912i	0.978666	−	0.205456i	$-0.0658677\pi$
$618$			7.14050i			0.287233i
$619$	23.0364			0.925912			0.462956	−	0.886381i	$-0.346789\pi$
$619$	23.0364			0.925912			0.462956	+	0.886381i	$0.346789\pi$
$620$	3.89374	+	3.75961i	0.156376	+	0.150989i
$621$		−	8.22627i		−	0.330109i
$622$			7.43403i			0.298077i
$623$	2.39929			0.0961256
$624$			6.41073i			0.256635i
$625$	−24.9386	+	1.75105i	−0.997544	+	0.0700418i
$626$	−7.14965			−0.285757
$627$	−36.1031			−1.44182
$628$			9.99479i			0.398835i
$629$	−0.873872	−	1.73198i	−0.0348436	−	0.0690587i
$630$	−0.174864	−	0.168840i	−0.00696674	−	0.00672674i
$631$		−	24.1719i		−	0.962267i	−0.876647	−	0.481134i	$-0.840225\pi$
$631$		−	24.1719i		−	0.962267i	0.876647	−	0.481134i	$-0.159775\pi$
$632$		−	17.3276i		−	0.689255i
$633$			9.92676i			0.394553i
$634$			0.751215i			0.0298346i
$635$	28.9367	+	27.9399i	1.14832	+	1.10876i
$636$	9.57079			0.379507
$637$	−14.8209			−0.587224
$638$			14.1188i			0.558969i
$639$	−7.33380			−0.290121
$640$	16.4042	−	16.9895i	0.648435	−	0.671570i
$641$	−18.2250			−0.719844			−0.359922	−	0.932982i	$-0.617197\pi$
$641$	−18.2250			−0.719844			−0.359922	+	0.932982i	$0.617197\pi$
$642$	−2.84087			−0.112120
$643$	−19.4225			−0.765950			−0.382975	−	0.923759i	$-0.625101\pi$
$643$	−19.4225			−0.765950			−0.382975	+	0.923759i	$0.625101\pi$
$644$		−	3.94278i		−	0.155367i
$645$	−0.118673	−	0.114584i	−0.00467273	−	0.00451176i
$646$		−	0.828805i		−	0.0326089i
$647$	−1.85853			−0.0730662			−0.0365331	−	0.999332i	$-0.511631\pi$
$647$	−1.85853			−0.0730662			−0.0365331	+	0.999332i	$0.511631\pi$
$648$	1.58720			0.0623510
$649$			42.1276i			1.65365i
$650$	−0.155337	−	4.43009i	−0.00609280	−	0.173762i
$651$			0.347154i			0.0136060i
$652$	−16.7784			−0.657093
$653$	2.35920			0.0923226			0.0461613	−	0.998934i	$-0.485301\pi$
$653$	2.35920			0.0923226			0.0461613	+	0.998934i	$0.485301\pi$
$654$	4.26260			0.166681
$655$	28.4838	+	27.5026i	1.11295	+	1.07461i
$656$	−17.8749			−0.697899
$657$			2.43334i			0.0949336i
$658$	0.874571			0.0340943
$659$	24.7589			0.964468			0.482234	−	0.876042i	$-0.339825\pi$
$659$	24.7589			0.964468			0.482234	+	0.876042i	$0.339825\pi$
$660$	16.9386	+	16.3551i	0.659334	+	0.636620i
$661$			26.9924i			1.04988i	0.851139	+	0.524941i	$0.175913\pi$
$661$			26.9924i			1.04988i	−0.851139	+	0.524941i	$0.824087\pi$
$662$		−	12.2853i		−	0.477481i
$663$		−	0.681948i		−	0.0264847i
$664$			20.9920i			0.814649i
$665$	−2.55235	+	2.64341i	−0.0989759	+	0.102507i
$666$	1.13607	+	2.25165i	0.0440219	+	0.0872498i
$667$			48.6320i			1.88304i
$668$	−12.0863			−0.467635
$669$	−19.4009			−0.750081
$670$	−2.46608	−	2.38112i	−0.0952728	−	0.0919907i
$671$		−	15.3713i		−	0.593404i
$672$	1.15818			0.0446777
$673$		−	32.5168i		−	1.25343i	−0.779249	−	0.626715i	$-0.784399\pi$
$673$		−	32.5168i		−	1.25343i	0.779249	−	0.626715i	$-0.215601\pi$
$674$			8.40382i			0.323703i
$675$	4.99693	−	0.175212i	0.192332	−	0.00674392i
$676$	15.4069			0.592571
$677$		−	6.77173i		−	0.260259i	−0.991497	−	0.130129i	$-0.958461\pi$
$677$		−	6.77173i		−	0.260259i	0.991497	−	0.130129i	$-0.0415393\pi$
$678$		−	4.91672i		−	0.188826i
$679$		−	0.490921i		−	0.0188398i
$680$	−0.786222	+	0.814273i	−0.0301502	+	0.0312259i
$681$		−	26.6876i		−	1.02267i
$682$			3.16227i			0.121090i
$683$	−46.5562			−1.78143			−0.890713	−	0.454567i	$-0.849794\pi$
$683$	−46.5562			−1.78143			−0.890713	+	0.454567i	$0.849794\pi$
$684$		−	11.4581i		−	0.438110i
$685$	−27.6885	−	26.7346i	−1.05792	−	1.02148i
$686$			1.51440i			0.0578201i
$687$		−	12.3672i		−	0.471839i
$688$	0.221181			0.00843245
$689$			11.1947i			0.426483i
$690$	−5.48656	−	5.29755i	−0.208870	−	0.201674i
$691$	−43.9079			−1.67033			−0.835167	−	0.549997i	$-0.814629\pi$
$691$	−43.9079			−1.67033			−0.835167	+	0.549997i	$0.814629\pi$
$692$		−	23.6958i		−	0.900778i
$693$			1.51019i			0.0573675i
$694$	11.3267			0.429956
$695$	14.8191	−	15.3478i	0.562121	−	0.582177i
$696$	−9.38318			−0.355669
$697$	1.90146			0.0720231
$698$	−4.23280			−0.160214
$699$	17.2351			0.651891
$700$	2.39499	−	0.0839778i	0.0905221	−	0.00317406i
$701$		−	2.69143i		−	0.101654i	−0.998707	−	0.0508270i	$-0.983814\pi$
$701$		−	2.69143i		−	0.101654i	0.998707	−	0.0508270i	$-0.0161857\pi$
$702$			0.886562i			0.0334611i
$703$	34.0382	−	17.1740i	1.28378	−	0.647730i
$704$	−23.9888			−0.904111
$705$	−12.4959	+	12.9418i	−0.470624	+	0.487415i
$706$	−0.887238			−0.0333917
$707$		−	1.56648i		−	0.0589134i
$708$	−13.3701			−0.502479
$709$		−	27.7618i		−	1.04262i	−0.853368	−	0.521308i	$-0.825444\pi$
$709$		−	27.7618i		−	1.04262i	0.853368	−	0.521308i	$-0.174556\pi$
$710$	−4.72282	+	4.89133i	−0.177244	+	0.183568i
$711$			10.9171i			0.409424i
$712$			14.5249i			0.544342i
$713$			10.8924i			0.407923i
$714$	−0.0346690			−0.00129745
$715$	−19.1300	+	19.8125i	−0.715422	+	0.740947i
$716$		−	46.1428i		−	1.72444i
$717$	−1.88181			−0.0702775
$718$	10.0087			0.373523
$719$	−16.1159			−0.601020			−0.300510	−	0.953779i	$-0.597157\pi$
$719$	−16.1159			−0.601020			−0.300510	+	0.953779i	$0.597157\pi$
$720$	−4.65662	+	4.82276i	−0.173542	+	0.179734i
$721$		−	4.51526i		−	0.168157i
$722$	8.41055			0.313008
$723$	−12.4854			−0.464336
$724$	6.57267			0.244271
$725$	−29.5408	+	1.03582i	−1.09712	+	0.0384693i
$726$			9.19573i			0.341285i
$727$	20.2735			0.751902			0.375951	−	0.926640i	$-0.377316\pi$
$727$	20.2735			0.751902			0.375951	+	0.926640i	$0.377316\pi$
$728$			0.889803i			0.0329783i
$729$	−1.00000			−0.0370370
$730$	1.62293	+	1.56702i	0.0600674	+	0.0579981i
$731$	−0.0235284			−0.000870228
$732$	4.87842			0.180312
$733$		−	41.3055i		−	1.52565i	−0.646604	−	0.762826i	$-0.723811\pi$
$733$		−	41.3055i		−	1.52565i	0.646604	−	0.762826i	$-0.276189\pi$
$734$		−	4.87600i		−	0.179976i
$735$	−11.1497	−	10.7656i	−0.411261	−	0.397093i
$736$	36.3392			1.33948
$737$			21.2980i			0.784522i
$738$	−2.47199			−0.0909951
$739$	20.7459			0.763149			0.381575	−	0.924338i	$-0.375382\pi$
$739$	20.7459			0.763149			0.381575	+	0.924338i	$0.375382\pi$
$740$	−23.7498	−	7.36209i	−0.873061	−	0.270636i
$741$	13.4022			0.492340
$742$	0.569116			0.0208929
$743$			22.5669i			0.827899i	0.910300	+	0.413950i	$0.135851\pi$
$743$			22.5669i			0.827899i	−0.910300	+	0.413950i	$0.864149\pi$
$744$	−2.10160			−0.0770485
$745$	4.44491	−	4.60350i	0.162849	−	0.168659i
$746$		−	5.02201i		−	0.183869i
$747$		−	13.2259i		−	0.483909i
$748$	3.35829			0.122791
$749$	1.79641			0.0656393
$750$	3.10106	−	3.44557i	0.113235	−	0.125814i
$751$	−44.0977			−1.60915			−0.804574	−	0.593852i	$-0.797606\pi$
$751$	−44.0977			−1.60915			−0.804574	+	0.593852i	$0.797606\pi$
$752$		−	24.1207i		−	0.879593i
$753$	−11.0417			−0.402383
$754$		−	5.24118i		−	0.190872i
$755$	10.8422	−	11.2290i	0.394587	−	0.408666i
$756$	−0.479292			−0.0174317
$757$	−2.09968			−0.0763143			−0.0381572	−	0.999272i	$-0.512149\pi$
$757$	−2.09968			−0.0763143			−0.0381572	+	0.999272i	$0.512149\pi$
$758$	−3.36588			−0.122254
$759$			47.3841i			1.71994i
$760$	−16.0027	−	15.4514i	−0.580479	−	0.560482i
$761$	18.0396			0.653936			0.326968	−	0.945035i	$-0.393973\pi$
$761$	18.0396			0.653936			0.326968	+	0.945035i	$0.393973\pi$
$762$	−7.45845			−0.270191
$763$	−2.69543			−0.0975812
$764$		−	6.43383i		−	0.232768i
$765$	0.495352	−	0.513026i	0.0179095	−	0.0185485i
$766$	−6.19040			−0.223668
$767$		−	15.6386i		−	0.564676i
$768$		−	3.95023i		−	0.142542i
$769$		−	7.75505i		−	0.279654i	−0.990176	−	0.139827i	$-0.955345\pi$
$769$		−	7.75505i		−	0.279654i	0.990176	−	0.139827i	$-0.0446547\pi$
$770$	1.00723	+	0.972535i	0.0362982	+	0.0350477i
$771$			23.2765i			0.838283i
$772$	−10.7991			−0.388667
$773$		−	2.35359i		−	0.0846526i	−0.999104	−	0.0423263i	$-0.986523\pi$
$773$		−	2.35359i		−	0.0846526i	0.999104	−	0.0423263i	$-0.0134769\pi$
$774$	0.0305879			0.00109946
$775$	−6.61642	+	0.231998i	−0.237669	+	0.00833362i
$776$	2.97194			0.106686
$777$	−0.718390	−	1.42382i	−0.0257721	−	0.0510793i
$778$			0.265380i			0.00951433i
$779$			37.3690i			1.33888i
$780$	−6.28793	−	6.07132i	−0.225144	−	0.217388i
$781$	42.2434			1.51159
$782$	−1.08778			−0.0388990
$783$	5.91180			0.211270
$784$	20.7806			0.742165
$785$	−8.79477	−	8.49180i	−0.313899	−	0.303085i
$786$	−7.34171			−0.261870
$787$		−	26.3936i		−	0.940831i	−0.882445	−	0.470415i	$-0.844104\pi$
$787$		−	26.3936i		−	0.940831i	0.882445	−	0.470415i	$-0.155896\pi$
$788$			36.4210i			1.29745i
$789$	11.7240			0.417386
$790$	7.28124	+	7.03040i	0.259055	+	0.250130i
$791$			3.10906i			0.110546i
$792$	−9.14242			−0.324862
$793$			5.70614i			0.202631i
$794$		−	6.39862i		−	0.227078i
$795$	−8.13156	+	8.42169i	−0.288397	+	0.298686i
$796$		−	41.5456i		−	1.47255i
$797$	−21.5767			−0.764285			−0.382143	−	0.924103i	$-0.624814\pi$
$797$	−21.5767			−0.764285			−0.382143	+	0.924103i	$0.624814\pi$
$798$		−	0.681341i		−	0.0241192i
$799$			2.56587i			0.0907739i
$800$	0.773993	+	22.0737i	0.0273648	+	0.780425i
$801$		−	9.15126i		−	0.323344i
$802$		−	12.0300i		−	0.424795i
$803$		−	14.0163i		−	0.494624i
$804$	−6.75938			−0.238385
$805$	3.46940	+	3.34988i	0.122280	+	0.118068i
$806$		−	1.17390i		−	0.0413487i
$807$		−	3.14696i		−	0.110778i
$808$	9.48314			0.333616
$809$		−	0.272002i		−	0.00956308i	−0.999989	−	0.00478154i	$-0.998478\pi$
$809$		−	0.272002i		−	0.00956308i	0.999989	−	0.00478154i	$-0.00152202\pi$
$810$	−0.643980	+	0.666956i	−0.0226272	+	0.0234345i
$811$	45.3237			1.59153			0.795765	−	0.605605i	$-0.207069\pi$
$811$	45.3237			1.59153			0.795765	+	0.605605i	$0.207069\pi$
$812$	2.83348			0.0994356
$813$		−	9.98429i		−	0.350164i
$814$	−6.54390	−	12.9698i	−0.229363	−	0.454590i
$815$	14.2553	−	14.7639i	0.499342	−	0.517158i
$816$			0.956174i			0.0334728i
$817$		−	0.462397i		−	0.0161772i
$818$		−	12.9005i		−	0.451056i
$819$		−	0.560613i		−	0.0195894i
$820$	16.9286	−	17.5325i	0.591171	−	0.612263i
$821$	34.8523			1.21635			0.608177	−	0.793802i	$-0.291901\pi$
$821$	34.8523			1.21635			0.608177	+	0.793802i	$0.291901\pi$
$822$	7.13671			0.248921
$823$			16.2163i			0.565265i	0.959228	+	0.282633i	$0.0912077\pi$
$823$			16.2163i			0.565265i	−0.959228	+	0.282633i	$0.908792\pi$
$824$	27.3345			0.952243
$825$	−28.7828	+	1.00924i	−1.00209	+	0.0351372i
$826$	−0.795036			−0.0276628
$827$	−29.2841			−1.01831			−0.509154	−	0.860675i	$-0.670042\pi$
$827$	−29.2841			−1.01831			−0.509154	+	0.860675i	$0.670042\pi$
$828$	−15.0384			−0.522619
$829$		−	42.9452i		−	1.49155i	−0.666200	−	0.745773i	$-0.732080\pi$
$829$		−	42.9452i		−	1.49155i	0.666200	−	0.745773i	$-0.267920\pi$
$830$	−8.82107	−	8.51719i	−0.306184	−	0.295636i
$831$			9.73495i			0.337702i
$832$	8.90510			0.308729
$833$	−2.21056			−0.0765914
$834$			3.95591i			0.136982i
$835$	10.2688	−	10.6352i	0.355368	−	0.368047i
$836$			65.9997i			2.28265i
$837$	1.32410			0.0457675
$838$	−1.17027			−0.0404263
$839$	−33.9666			−1.17266			−0.586329	−	0.810073i	$-0.699427\pi$
$839$	−33.9666			−1.17266			−0.586329	+	0.810073i	$0.699427\pi$
$840$	−0.646334	+	0.669394i	−0.0223006	+	0.0230963i
$841$	−5.94933			−0.205149
$842$		−	8.04088i		−	0.277107i
$843$	−10.1462			−0.349454
$844$	18.1470			0.624646
$845$	−13.0900	+	13.5570i	−0.450310	+	0.466377i
$846$		−	3.33574i		−	0.114685i
$847$		−	5.81487i		−	0.199801i
$848$		−	15.6963i		−	0.539012i
$849$		−	24.9586i		−	0.856576i
$850$	−0.0231688	−	0.660757i	−0.000794682	−	0.0226638i
$851$	−22.5403	−	44.6741i	−0.772673	−	1.53141i
$852$			13.4069i			0.459311i
$853$	−29.1098			−0.996699			−0.498349	−	0.866976i	$-0.666060\pi$
$853$	−29.1098			−0.996699			−0.498349	+	0.866976i	$0.666060\pi$
$854$	0.290089			0.00992666
$855$	10.0824	+	9.73504i	0.344810	+	0.332931i
$856$			10.8751i			0.371703i
$857$	33.4568			1.14286			0.571431	−	0.820650i	$-0.306388\pi$
$857$	33.4568			1.14286			0.571431	+	0.820650i	$0.306388\pi$
$858$		−	5.10669i		−	0.174340i
$859$		−	28.5018i		−	0.972470i	−0.873828	−	0.486235i	$-0.838370\pi$
$859$		−	28.5018i		−	0.972470i	0.873828	−	0.486235i	$-0.161630\pi$
$860$	−0.209471	+	0.216944i	−0.00714290	+	0.00739774i
$861$	1.56315			0.0532720
$862$			1.40040i			0.0476977i
$863$		−	27.3062i		−	0.929516i	−0.885438	−	0.464758i	$-0.846141\pi$
$863$		−	27.3062i		−	0.929516i	0.885438	−	0.464758i	$-0.153859\pi$
$864$		−	4.41746i		−	0.150285i
$865$	20.8508	+	20.1325i	0.708947	+	0.684524i
$866$		−	6.95080i		−	0.236198i
$867$			16.8983i			0.573896i
$868$	0.634630			0.0215407
$869$		−	62.8837i		−	2.13318i
$870$	3.80708	−	3.94291i	0.129072	−	0.133677i
$871$		−	7.90624i		−	0.267893i
$872$		−	16.3176i		−	0.552584i
$873$	−1.87245			−0.0633727
$874$		−	21.3779i		−	0.723118i
$875$	−1.96094	+	2.17879i	−0.0662919	+	0.0736564i
$876$	4.44837			0.150296
$877$		−	41.3152i		−	1.39511i	−0.716529	−	0.697557i	$-0.754270\pi$
$877$		−	41.3152i		−	1.39511i	0.716529	−	0.697557i	$-0.245730\pi$
$878$		−	8.14618i		−	0.274920i
$879$	−2.46417			−0.0831143
$880$	26.8226	−	27.7796i	0.904190	−	0.936450i
$881$	19.9059			0.670648			0.335324	−	0.942103i	$-0.391154\pi$
$881$	19.9059			0.670648			0.335324	+	0.942103i	$0.391154\pi$
$882$	2.87383			0.0967668
$883$	9.77509			0.328958			0.164479	−	0.986381i	$-0.447406\pi$
$883$	9.77509			0.328958			0.164479	+	0.986381i	$0.447406\pi$
$884$	−1.24666			−0.0419298
$885$	11.3595	−	11.7648i	0.381846	−	0.395470i
$886$		−	14.8052i		−	0.497389i
$887$			8.64433i			0.290248i	0.989413	+	0.145124i	$0.0463582\pi$
$887$			8.64433i			0.290248i	−0.989413	+	0.145124i	$0.953642\pi$
$888$	8.61954	−	4.34899i	0.289253	−	0.145943i
$889$	4.71631			0.158180
$890$	−6.10349	−	5.89323i	−0.204590	−	0.197542i
$891$	5.76010			0.192971
$892$			35.4666i			1.18751i
$893$	−50.4264			−1.68745
$894$			1.18655i			0.0396843i
$895$	40.6027	+	39.2040i	1.35720	+	1.31044i
$896$		−	2.76907i		−	0.0925083i
$897$		−	17.5899i		−	0.587310i
$898$		−	8.88439i		−	0.296476i
$899$	−7.82780			−0.261072
$900$	−0.320304	−	9.13484i	−0.0106768	−	0.304495i
$901$			1.66971i			0.0556260i
$902$	14.2389			0.474104
$903$	−0.0193421			−0.000643665
$904$	−18.8217			−0.625999
$905$	−5.58429	+	5.78353i	−0.185628	+	0.192251i
$906$			2.89428i			0.0961561i
$907$	−28.7329			−0.954060			−0.477030	−	0.878887i	$-0.658287\pi$
$907$	−28.7329			−0.954060			−0.477030	+	0.878887i	$0.658287\pi$
$908$	−48.7873			−1.61906
$909$	−5.97477			−0.198171
$910$	−0.373905	−	0.361024i	−0.0123948	−	0.0119678i
$911$			5.99532i			0.198634i	0.995056	+	0.0993169i	$0.0316657\pi$
$911$			5.99532i			0.198634i	−0.995056	+	0.0993169i	$0.968334\pi$
$912$	−18.7914			−0.622247
$913$			76.1823i			2.52127i
$914$	−15.6382			−0.517265
$915$	−4.14482	+	4.29270i	−0.137023	+	0.141912i
$916$	−22.6084			−0.747003
$917$	4.64249			0.153309
$918$			0.132233i			0.00436433i
$919$		−	39.2031i		−	1.29319i	−0.762834	−	0.646595i	$-0.776192\pi$
$919$		−	39.2031i		−	1.29319i	0.762834	−	0.646595i	$-0.223808\pi$
$920$	−20.2795	+	21.0031i	−0.668596	+	0.692450i
$921$	−26.7108			−0.880152
$922$			8.10161i			0.266812i
$923$	−15.6816			−0.516166
$924$	2.76077			0.0908227
$925$	26.6566	−	14.6433i	0.876463	−	0.481470i
$926$	10.5680			0.347287
$927$	−17.2219			−0.565641
$928$			26.1151i			0.857271i
$929$	56.4611			1.85243			0.926215	−	0.376996i	$-0.123043\pi$
$929$	56.4611			1.85243			0.926215	+	0.376996i	$0.123043\pi$
$930$	0.852693	−	0.883116i	0.0279609	−	0.0289585i
$931$		−	43.4436i		−	1.42381i
$932$		−	31.5073i		−	1.03206i
$933$	−17.9298			−0.586996
$934$	−9.48900			−0.310490
$935$	−2.85328	+	2.95508i	−0.0933123	+	0.0966415i
$936$	3.39384			0.110931
$937$			3.19227i			0.104287i	0.998640	+	0.0521435i	$0.0166053\pi$
$937$			3.19227i			0.104287i	−0.998640	+	0.0521435i	$0.983395\pi$
$938$	−0.401938			−0.0131238
$939$		−	17.2439i		−	0.562734i
$940$	23.6587	+	22.8437i	0.771662	+	0.745079i
$941$	−1.72920			−0.0563703			−0.0281852	−	0.999603i	$-0.508973\pi$
$941$	−1.72920			−0.0563703			−0.0281852	+	0.999603i	$0.508973\pi$
$942$	2.26686			0.0738582
$943$	49.0457			1.59715
$944$			21.9272i			0.713669i
$945$	0.407217	−	0.421746i	0.0132468	−	0.0137194i
$946$	−0.176190			−0.00572842
$947$	−4.93951			−0.160513			−0.0802563	−	0.996774i	$-0.525574\pi$
$947$	−4.93951			−0.160513			−0.0802563	+	0.996774i	$0.525574\pi$
$948$	19.9575			0.648189
$949$			5.20312i			0.168900i
$950$	12.9857	−	0.455330i	0.421312	−	0.0147729i
$951$	−1.81182			−0.0587524
$952$			0.132716i			0.00430135i
$953$		−	24.9850i		−	0.809342i	−0.914462	−	0.404671i	$-0.867386\pi$
$953$		−	24.9850i		−	0.809342i	0.914462	−	0.404671i	$-0.132614\pi$
$954$		−	2.17069i		−	0.0702788i
$955$	5.66136	+	5.46633i	0.183197	+	0.176886i
$956$			3.44012i			0.111261i
$957$	−34.0526			−1.10076
$958$		−	9.20226i		−	0.297311i
$959$	−4.51286			−0.145728
$960$	6.69926	+	6.46848i	0.216218	+	0.208769i
$961$	29.2468			0.943444
$962$	2.42922	+	4.81463i	0.0783212	+	0.155230i
$963$		−	6.85177i		−	0.220795i
$964$			22.8244i			0.735125i
$965$	9.17513	−	9.50249i	0.295358	−	0.305896i
$966$	−0.894239			−0.0287717
$967$	−36.2075			−1.16435			−0.582177	−	0.813062i	$-0.697799\pi$
$967$	−36.2075			−1.16435			−0.582177	+	0.813062i	$0.697799\pi$
$968$	35.2021			1.13144
$969$	1.99896			0.0642158
$970$	−1.20582	+	1.24884i	−0.0387165	+	0.0400979i
$971$	−57.8143			−1.85535			−0.927675	−	0.373390i	$-0.878195\pi$
$971$	−57.8143			−1.85535			−0.927675	+	0.373390i	$0.878195\pi$
$972$			1.82809i			0.0586361i
$973$		−	2.50150i		−	0.0801944i
$974$	−6.99039			−0.223987
$975$	10.6847	−	0.374650i	0.342186	−	0.0119984i
$976$		−	8.00069i		−	0.256096i
$977$	43.8532			1.40299			0.701493	−	0.712676i	$-0.252517\pi$
$977$	43.8532			1.40299			0.701493	+	0.712676i	$0.252517\pi$
$978$			3.80541i			0.121684i
$979$			52.7122i			1.68469i
$980$	−19.6804	+	20.3826i	−0.628668	+	0.651098i
$981$			10.2808i			0.328240i
$982$	12.5841			0.401576
$983$			50.9930i			1.62642i	0.581968	+	0.813212i	$0.302283\pi$
$983$			50.9930i			1.62642i	−0.581968	+	0.813212i	$0.697717\pi$
$984$			9.46300i			0.301669i
$985$	−32.0482	−	30.9441i	−1.02114	−	0.985963i
$986$		−	0.781732i		−	0.0248954i
$987$			2.10934i			0.0671410i
$988$		−	24.5004i		−	0.779461i
$989$	−0.606882			−0.0192977
$990$	3.70939	−	3.84174i	0.117892	−	0.122098i
$991$		−	59.6919i		−	1.89617i	−0.318010	−	0.948087i	$-0.603015\pi$
$991$		−	59.6919i		−	1.89617i	0.318010	−	0.948087i	$-0.396985\pi$
$992$			5.84915i			0.185711i
$993$	29.6303			0.940290
$994$			0.797223i			0.0252864i
$995$	36.5575	+	35.2981i	1.15895	+	1.11902i
$996$	−24.1781			−0.766112
$997$	42.3485			1.34119			0.670594	−	0.741824i	$-0.266039\pi$
$997$	42.3485			1.34119			0.670594	+	0.741824i	$0.266039\pi$
$998$		−	5.97317i		−	0.189077i
$999$	−5.43067	+	2.74005i	−0.171819	+	0.0866912i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.g.a.184.17	✓	40
3.2	odd	2		1665.2.g.e.739.23		40
5.4	even	2	inner	555.2.g.a.184.24	yes	40
15.14	odd	2		1665.2.g.e.739.18		40
37.36	even	2	inner	555.2.g.a.184.23	yes	40
111.110	odd	2		1665.2.g.e.739.17		40
185.184	even	2	inner	555.2.g.a.184.18	yes	40
555.554	odd	2		1665.2.g.e.739.24		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.g.a.184.17	✓	40	1.1	even	1	trivial
555.2.g.a.184.18	yes	40	185.184	even	2	inner
555.2.g.a.184.23	yes	40	37.36	even	2	inner
555.2.g.a.184.24	yes	40	5.4	even	2	inner
1665.2.g.e.739.17		40	111.110	odd	2
1665.2.g.e.739.18		40	15.14	odd	2
1665.2.g.e.739.23		40	3.2	odd	2
1665.2.g.e.739.24		40	555.554	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.414618 q^{2} -1.00000i q^{3} -1.82809 q^{4} +(1.55319 - 1.60860i) q^{5} +0.414618i q^{6} -0.262182i q^{7} +1.58720 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.414618 q^{2} -1.00000i q^{3} -1.82809 q^{4} +(1.55319 - 1.60860i) q^{5} +0.414618i q^{6} -0.262182i q^{7} +1.58720 q^{8} -1.00000 q^{9} +(-0.643980 + 0.666956i) q^{10} +5.76010 q^{11} +1.82809i q^{12} -2.13826 q^{13} +0.108705i q^{14} +(-1.60860 - 1.55319i) q^{15} +2.99810 q^{16} -0.318926 q^{17} +0.414618 q^{18} -6.26778i q^{19} +(-2.83937 + 2.94068i) q^{20} -0.262182 q^{21} -2.38824 q^{22} -8.22627 q^{23} -1.58720i q^{24} +(-0.175212 - 4.99693i) q^{25} +0.886562 q^{26} +1.00000i q^{27} +0.479292i q^{28} -5.91180i q^{29} +(0.666956 + 0.643980i) q^{30} -1.32410i q^{31} -4.41746 q^{32} -5.76010i q^{33} +0.132233 q^{34} +(-0.421746 - 0.407217i) q^{35} +1.82809 q^{36} +(2.74005 + 5.43067i) q^{37} +2.59874i q^{38} +2.13826i q^{39} +(2.46522 - 2.55317i) q^{40} -5.96208 q^{41} +0.108705 q^{42} +0.0737737 q^{43} -10.5300 q^{44} +(-1.55319 + 1.60860i) q^{45} +3.41076 q^{46} -8.04534i q^{47} -2.99810i q^{48} +6.93126 q^{49} +(0.0726462 + 2.07182i) q^{50} +0.318926i q^{51} +3.90894 q^{52} -5.23540i q^{53} -0.414618i q^{54} +(8.94652 - 9.26572i) q^{55} -0.416134i q^{56} -6.26778 q^{57} +2.45114i q^{58} +7.31368i q^{59} +(2.94068 + 2.83937i) q^{60} -2.66859i q^{61} +0.548995i q^{62} +0.262182i q^{63} -4.16465 q^{64} +(-3.32112 + 3.43962i) q^{65} +2.38824i q^{66} +3.69751i q^{67} +0.583026 q^{68} +8.22627i q^{69} +(0.174864 + 0.168840i) q^{70} +7.33380 q^{71} -1.58720 q^{72} -2.43334i q^{73} +(-1.13607 - 2.25165i) q^{74} +(-4.99693 + 0.175212i) q^{75} +11.4581i q^{76} -1.51019i q^{77} -0.886562i q^{78} -10.9171i q^{79} +(4.65662 - 4.82276i) q^{80} +1.00000 q^{81} +2.47199 q^{82} +13.2259i q^{83} +0.479292 q^{84} +(-0.495352 + 0.513026i) q^{85} -0.0305879 q^{86} -5.91180 q^{87} +9.14242 q^{88} +9.15126i q^{89} +(0.643980 - 0.666956i) q^{90} +0.560613i q^{91} +15.0384 q^{92} -1.32410 q^{93} +3.33574i q^{94} +(-10.0824 - 9.73504i) q^{95} +4.41746i q^{96} +1.87245 q^{97} -2.87383 q^{98} -5.76010 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) \) 40 * q + 44 * q^4 - 40 * q^9	\( 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 40 * q^9 + 4 * q^10 + 8 * q^11 + 52 * q^16 - 16 * q^21 + 8 * q^25 - 16 * q^26 + 16 * q^30 - 32 * q^34 - 44 * q^36 - 28 * q^40 + 8 * q^41 + 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 - 48 * q^65 - 56 * q^70 + 24 * q^71 - 68 * q^74 + 8 * q^75 + 40 * q^81 - 16 * q^84 - 64 * q^85 + 80 * q^86 - 4 * q^90 + 32 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

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Database

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