LMFDB - Embedded newform 147.6.c.c.146.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(146,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("147.146");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.c (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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + \cdots + 90230547456 $ x^16 - 171x^14 + 21495x^12 - 1128902x^10 + 42970860x^8 - 655075344x^6 + 7244325760x^4 - 29387167488*x^2 + 90230547456
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{8}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.8
Root			$-1.84692 + 1.06632i$ of defining polynomial
Character	$\chi$	$=$	147.146
Dual form			147.6.c.c.146.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.13264i q^{2} +(9.16236 - 12.6115i) q^{3} +27.4518 q^{4} +95.0525 q^{5} +(-26.8959 - 19.5400i) q^{6} -126.790i q^{8} +(-75.1022 - 231.103i) q^{9} +O(q^{10})$	\(q-2.13264i q^{2} +(9.16236 - 12.6115i) q^{3} +27.4518 q^{4} +95.0525 q^{5} +(-26.8959 - 19.5400i) q^{6} -126.790i q^{8} +(-75.1022 - 231.103i) q^{9} -202.713i q^{10} -130.679i q^{11} +(251.524 - 346.210i) q^{12} +14.6710i q^{13} +(870.905 - 1198.76i) q^{15} +608.062 q^{16} -640.492 q^{17} +(-492.860 + 160.166i) q^{18} +542.677i q^{19} +2609.37 q^{20} -278.692 q^{22} +4094.31i q^{23} +(-1599.01 - 1161.69i) q^{24} +5909.98 q^{25} +31.2880 q^{26} +(-3602.68 - 1170.29i) q^{27} +3594.70i q^{29} +(-2556.52 - 1857.33i) q^{30} -2900.94i q^{31} -5354.04i q^{32} +(-1648.06 - 1197.33i) q^{33} +1365.94i q^{34} +(-2061.69 - 6344.20i) q^{36} -4342.05 q^{37} +1157.34 q^{38} +(185.024 + 134.421i) q^{39} -12051.7i q^{40} -10945.3 q^{41} +20541.6 q^{43} -3587.38i q^{44} +(-7138.66 - 21966.9i) q^{45} +8731.70 q^{46} -8816.03 q^{47} +(5571.28 - 7668.60i) q^{48} -12603.9i q^{50} +(-5868.42 + 8077.60i) q^{51} +402.745i q^{52} -6977.45i q^{53} +(-2495.82 + 7683.23i) q^{54} -12421.4i q^{55} +(6844.00 + 4972.20i) q^{57} +7666.22 q^{58} -40020.1 q^{59} +(23908.0 - 32908.1i) q^{60} +33210.2i q^{61} -6186.66 q^{62} +8039.72 q^{64} +1394.51i q^{65} +(-2553.47 + 3514.73i) q^{66} +6436.18 q^{67} -17582.7 q^{68} +(51635.6 + 37513.6i) q^{69} -32493.9i q^{71} +(-29301.5 + 9522.18i) q^{72} -12737.8i q^{73} +9260.03i q^{74} +(54149.3 - 74533.9i) q^{75} +14897.5i q^{76} +(286.672 - 394.590i) q^{78} +8597.89 q^{79} +57797.8 q^{80} +(-47768.3 + 34712.7i) q^{81} +23342.3i q^{82} -31669.6 q^{83} -60880.4 q^{85} -43807.8i q^{86} +(45334.8 + 32936.0i) q^{87} -16568.7 q^{88} +31945.9 q^{89} +(-46847.6 + 15224.2i) q^{90} +112396. i q^{92} +(-36585.3 - 26579.4i) q^{93} +18801.4i q^{94} +51582.8i q^{95} +(-67522.8 - 49055.7i) q^{96} -143107. i q^{97} +(-30200.3 + 9814.28i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 172 q^{4} + 1212 q^{9}+O(q^{10}) $ 16 * q - 172 * q^4 + 1212 * q^9	$ 16 q - 172 q^{4} + 1212 q^{9} + 1188 q^{15} + 5716 q^{16} + 876 q^{18} - 21900 q^{22} + 13156 q^{25} - 900 q^{30} - 15132 q^{36} + 20932 q^{37} + 34836 q^{39} + 111052 q^{43} - 163392 q^{46} - 63192 q^{51} - 31368 q^{57} + 83412 q^{58} - 120132 q^{60} - 158884 q^{64} + 204404 q^{67} - 661728 q^{72} - 277512 q^{78} + 502616 q^{79} - 358524 q^{81} + 205152 q^{85} + 719028 q^{88} - 35352 q^{93} + 215472 q^{99}+O(q^{100}) $ 16 * q - 172 * q^4 + 1212 * q^9 + 1188 * q^15 + 5716 * q^16 + 876 * q^18 - 21900 * q^22 + 13156 * q^25 - 900 * q^30 - 15132 * q^36 + 20932 * q^37 + 34836 * q^39 + 111052 * q^43 - 163392 * q^46 - 63192 * q^51 - 31368 * q^57 + 83412 * q^58 - 120132 * q^60 - 158884 * q^64 + 204404 * q^67 - 661728 * q^72 - 277512 * q^78 + 502616 * q^79 - 358524 * q^81 + 205152 * q^85 + 719028 * q^88 - 35352 * q^93 + 215472 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	2.13264i		−	0.377001i	−0.982073	−	0.188501i	$-0.939637\pi$
$2$		−	2.13264i		−	0.377001i	0.982073	−	0.188501i	$-0.0603628\pi$
$3$	9.16236	−	12.6115i	0.587766	−	0.809031i
$3$	9.16236	−	12.6115i	0.587766	−	0.809031i
$4$	27.4518			0.857870
$5$	95.0525			1.70035			0.850175	−	0.526500i	$-0.176496\pi$
$5$	95.0525			1.70035			0.850175	+	0.526500i	$0.176496\pi$
$6$	−26.8959	−	19.5400i	−0.305006	−	0.221589i
$7$		0			0
$7$		0			0
$8$		−	126.790i		−	0.700420i
$9$	−75.1022	−	231.103i	−0.309063	−	0.951042i
$10$		−	202.713i		−	0.641035i
$11$		−	130.679i		−	0.325630i	−0.986657	−	0.162815i	$-0.947943\pi$
$11$		−	130.679i		−	0.325630i	0.986657	−	0.162815i	$-0.0520573\pi$
$12$	251.524	−	346.210i	0.504227	−	0.694043i
$13$			14.6710i			0.0240769i	0.999928	+	0.0120385i	$0.00383205\pi$
$13$			14.6710i			0.0240769i	−0.999928	+	0.0120385i	$0.996168\pi$
$14$		0			0
$15$	870.905	−	1198.76i	0.999408	−	1.37564i
$16$	608.062			0.593811
$17$	−640.492			−0.537516			−0.268758	−	0.963208i	$-0.586613\pi$
$17$	−640.492			−0.537516			−0.268758	+	0.963208i	$0.586613\pi$
$18$	−492.860	+	160.166i	−0.358544	+	0.116517i
$19$			542.677i			0.344872i	0.985021	+	0.172436i	$0.0551637\pi$
$19$			542.677i			0.344872i	−0.985021	+	0.172436i	$0.944836\pi$
$20$	2609.37			1.45868
$21$		0			0
$22$	−278.692			−0.122763
$23$			4094.31i			1.61384i	0.590659	+	0.806922i	$0.298868\pi$
$23$			4094.31i			1.61384i	−0.590659	+	0.806922i	$0.701132\pi$
$24$	−1599.01	−	1161.69i	−0.566661	−	0.411683i
$25$	5909.98			1.89119
$26$	31.2880			0.00907703
$27$	−3602.68	−	1170.29i	−0.951079	−	0.308948i
$28$		0			0
$29$			3594.70i			0.793721i	0.917879	+	0.396861i	$0.129900\pi$
$29$			3594.70i			0.793721i	−0.917879	+	0.396861i	$0.870100\pi$
$30$	−2556.52	−	1857.33i	−0.518617	−	0.376778i
$31$		−	2900.94i		−	0.542168i	−0.962556	−	0.271084i	$-0.912618\pi$
$31$		−	2900.94i		−	0.542168i	0.962556	−	0.271084i	$-0.0873821\pi$
$32$		−	5354.04i		−	0.924287i
$33$	−1648.06	−	1197.33i	−0.263445	−	0.191394i
$34$			1365.94i			0.202644i
$35$		0			0
$36$	−2061.69	−	6344.20i	−0.265136	−	0.815870i
$37$	−4342.05			−0.521423			−0.260712	−	0.965417i	$-0.583957\pi$
$37$	−4342.05			−0.521423			−0.260712	+	0.965417i	$0.583957\pi$
$38$	1157.34			0.130017
$39$	185.024	+	134.421i	0.0194790	+	0.0141516i
$40$		−	12051.7i		−	1.19096i
$41$	−10945.3			−1.01687			−0.508436	−	0.861100i	$-0.669776\pi$
$41$	−10945.3			−1.01687			−0.508436	+	0.861100i	$0.669776\pi$
$42$		0			0
$43$	20541.6			1.69419			0.847096	−	0.531440i	$-0.178349\pi$
$43$	20541.6			1.69419			0.847096	+	0.531440i	$0.178349\pi$
$44$		−	3587.38i		−	0.279348i
$45$	−7138.66	−	21966.9i	−0.525515	−	1.61710i
$46$	8731.70			0.608421
$47$	−8816.03			−0.582141			−0.291071	−	0.956702i	$-0.594011\pi$
$47$	−8816.03			−0.582141			−0.291071	+	0.956702i	$0.594011\pi$
$48$	5571.28	−	7668.60i	0.349022	−	0.480411i
$49$		0			0
$50$		−	12603.9i		−	0.712982i
$51$	−5868.42	+	8077.60i	−0.315934	+	0.434867i
$52$			402.745i			0.0206549i
$53$		−	6977.45i		−	0.341198i	−0.985341	−	0.170599i	$-0.945430\pi$
$53$		−	6977.45i		−	0.341198i	0.985341	−	0.170599i	$-0.0545703\pi$
$54$	−2495.82	+	7683.23i	−0.116474	+	0.358558i
$55$		−	12421.4i		−	0.553685i
$56$		0			0
$57$	6844.00	+	4972.20i	0.279012	+	0.202704i
$58$	7666.22			0.299234
$59$	−40020.1			−1.49675			−0.748373	−	0.663278i	$-0.769165\pi$
$59$	−40020.1			−1.49675			−0.748373	+	0.663278i	$0.769165\pi$
$60$	23908.0	−	32908.1i	0.857362	−	1.18012i
$61$			33210.2i			1.14274i	0.820693	+	0.571370i	$0.193588\pi$
$61$			33210.2i			1.14274i	−0.820693	+	0.571370i	$0.806412\pi$
$62$	−6186.66			−0.204398
$63$		0			0
$64$	8039.72			0.245353
$65$			1394.51i			0.0409392i
$66$	−2553.47	+	3514.73i	−0.0721558	+	0.0993190i
$67$	6436.18			0.175163			0.0875813	−	0.996157i	$-0.472086\pi$
$67$	6436.18			0.175163			0.0875813	+	0.996157i	$0.472086\pi$
$68$	−17582.7			−0.461119
$69$	51635.6	+	37513.6i	1.30565	+	0.948562i
$70$		0			0
$71$		−	32493.9i		−	0.764990i	−0.923958	−	0.382495i	$-0.875065\pi$
$71$		−	32493.9i		−	0.764990i	0.923958	−	0.382495i	$-0.124935\pi$
$72$	−29301.5	+	9522.18i	−0.666128	+	0.216474i
$73$		−	12737.8i		−	0.279761i	−0.990168	−	0.139880i	$-0.955328\pi$
$73$		−	12737.8i		−	0.279761i	0.990168	−	0.139880i	$-0.0446718\pi$
$74$			9260.03i			0.196577i
$75$	54149.3	−	74533.9i	1.11158	−	1.53003i
$76$			14897.5i			0.295855i
$77$		0			0
$78$	286.672	−	394.590i	0.00533517	−	0.00734360i
$79$	8597.89			0.154997			0.0774986	−	0.996992i	$-0.475307\pi$
$79$	8597.89			0.154997			0.0774986	+	0.996992i	$0.475307\pi$
$80$	57797.8			1.00969
$81$	−47768.3	+	34712.7i	−0.808960	+	0.587863i
$82$			23342.3i			0.383362i
$83$	−31669.6			−0.504601			−0.252300	−	0.967649i	$-0.581187\pi$
$83$	−31669.6			−0.504601			−0.252300	+	0.967649i	$0.581187\pi$
$84$		0			0
$85$	−60880.4			−0.913966
$86$		−	43807.8i		−	0.638713i
$87$	45334.8	+	32936.0i	0.642145	+	0.466522i
$88$	−16568.7			−0.228077
$89$	31945.9			0.427504			0.213752	−	0.976888i	$-0.431432\pi$
$89$	31945.9			0.427504			0.213752	+	0.976888i	$0.431432\pi$
$90$	−46847.6	+	15224.2i	−0.609651	+	0.198120i
$91$		0			0
$92$			112396.i			1.38447i
$93$	−36585.3	−	26579.4i	−0.438631	−	0.318668i
$94$			18801.4i			0.219468i
$95$			51582.8i			0.586403i
$96$	−67522.8	−	49055.7i	−0.747777	−	0.543264i
$97$		−	143107.i		−	1.54430i	−0.635441	−	0.772149i	$-0.719182\pi$
$97$		−	143107.i		−	1.54430i	0.635441	−	0.772149i	$-0.280818\pi$
$98$		0			0
$99$	−30200.3	+	9814.28i	−0.309687	+	0.100640i
$100$	162240.			1.62240
$101$	53587.7			0.522711			0.261355	−	0.965243i	$-0.415831\pi$
$101$	53587.7			0.522711			0.261355	+	0.965243i	$0.415831\pi$
$102$	17226.6	+	12515.2i	0.163946	+	0.119107i
$103$			153816.i			1.42860i	0.699842	+	0.714298i	$0.253254\pi$
$103$			153816.i			1.42860i	−0.699842	+	0.714298i	$0.746746\pi$
$104$	1860.13			0.0168639
$105$		0			0
$106$	−14880.4			−0.128632
$107$			153413.i			1.29540i	0.761897	+	0.647698i	$0.224268\pi$
$107$			153413.i			1.29540i	−0.761897	+	0.647698i	$0.775732\pi$
$108$	−98900.2	−	32126.7i	−0.815902	−	0.265038i
$109$	−127739.			−1.02981			−0.514907	−	0.857246i	$-0.672174\pi$
$109$	−127739.			−1.02981			−0.514907	+	0.857246i	$0.672174\pi$
$110$	−26490.3			−0.208740
$111$	−39783.4	+	54759.9i	−0.306475	+	0.421847i
$112$		0			0
$113$			90418.2i			0.666131i	0.942904	+	0.333066i	$0.108083\pi$
$113$			90418.2i			0.666131i	−0.942904	+	0.333066i	$0.891917\pi$
$114$	10603.9	−	14595.8i	0.0764196	−	0.105188i
$115$			389175.i			2.74410i
$116$			98681.2i			0.680910i
$117$	3390.51	−	1101.82i	0.0228981	−	0.00744128i
$118$			85348.6i			0.564276i
$119$		0			0
$120$	−151990.	−	110422.i	−0.963523	−	0.700005i
$121$	143974.			0.893965
$122$	70825.5			0.430814
$123$	−100284.	+	138037.i	−0.597683	+	0.822681i
$124$		−	79636.0i		−	0.465110i
$125$	264719.			1.51534
$126$		0			0
$127$	132321.			0.727982			0.363991	−	0.931402i	$-0.381414\pi$
$127$	132321.			0.727982			0.363991	+	0.931402i	$0.381414\pi$
$128$		−	188475.i		−	1.01679i
$129$	188209.	−	259061.i	0.995788	−	1.37065i
$130$	2974.00			0.0154341
$131$	147778.			0.752368			0.376184	−	0.926545i	$-0.377236\pi$
$131$	147778.			0.752368			0.376184	+	0.926545i	$0.377236\pi$
$132$	−45242.4	−	32868.8i	−0.226001	−	0.164191i
$133$		0			0
$134$		−	13726.1i		−	0.0660366i
$135$	−342444.	−	111239.i	−1.61717	−	0.525321i
$136$			81207.7i			0.376487i
$137$		−	226682.i		−	1.03185i	−0.856634	−	0.515925i	$-0.827448\pi$
$137$		−	226682.i		−	1.03185i	0.856634	−	0.515925i	$-0.172552\pi$
$138$	80003.0	−	110120.i	0.357609	−	0.492232i
$139$			230678.i			1.01267i	0.862335	+	0.506337i	$0.169001\pi$
$139$			230678.i			1.01267i	−0.862335	+	0.506337i	$0.830999\pi$
$140$		0			0
$141$	−80775.7	+	111184.i	−0.342163	+	0.470971i
$142$	−69297.8			−0.288402
$143$	1917.19			0.00784016
$144$	−45666.8	−	140525.i	−0.183525	−	0.564739i
$145$			341685.i			1.34960i
$146$	−27165.1			−0.105470
$147$		0			0
$148$	−119197.			−0.447313
$149$		−	9357.83i		−	0.0345310i	−0.999851	−	0.0172655i	$-0.994504\pi$
$149$		−	9357.83i		−	0.0345310i	0.999851	−	0.0172655i	$-0.00549605\pi$
$150$	−158954.	−	115481.i	−0.576825	−	0.419067i
$151$	138457.			0.494166			0.247083	−	0.968994i	$-0.420528\pi$
$151$	138457.			0.494166			0.247083	+	0.968994i	$0.420528\pi$
$152$	68805.8			0.241555
$153$	48102.4	+	148020.i	0.166126	+	0.511200i
$154$		0			0
$155$		−	275741.i		−	0.921876i
$156$	5079.24	+	3690.10i	0.0167104	+	0.0121402i
$157$		−	15464.9i		−	0.0500724i	−0.999687	−	0.0250362i	$-0.992030\pi$
$157$		−	15464.9i		−	0.0500724i	0.999687	−	0.0250362i	$-0.00797010\pi$
$158$		−	18336.2i		−	0.0584342i
$159$	−87996.4	−	63929.9i	−0.276040	−	0.200545i
$160$		−	508915.i		−	1.57161i
$161$		0			0
$162$	74029.8	+	101873.i	0.221625	+	0.304979i
$163$	289645.			0.853880			0.426940	−	0.904280i	$-0.359592\pi$
$163$	289645.			0.853880			0.426940	+	0.904280i	$0.359592\pi$
$164$	−300467.			−0.872344
$165$	−156653.	−	113809.i	−0.447948	−	0.325437i
$166$			67540.0i			0.190235i
$167$	−347837.			−0.965128			−0.482564	−	0.875861i	$-0.660294\pi$
$167$	−347837.			−0.965128			−0.482564	+	0.875861i	$0.660294\pi$
$168$		0			0
$169$	371078.			0.999420
$170$			129836.i			0.344567i
$171$	125414.	−	40756.3i	0.327987	−	0.106587i
$172$	563904.			1.45340
$173$	−508138.			−1.29082			−0.645411	−	0.763836i	$-0.723314\pi$
$173$	−508138.			−1.29082			−0.645411	+	0.763836i	$0.723314\pi$
$174$	70240.7	−	96682.9i	0.175880	−	0.242090i
$175$		0			0
$176$		−	79460.9i		−	0.193362i
$177$	−366679.	+	504716.i	−0.879736	+	1.21091i
$178$		−	68129.1i		−	0.161169i
$179$			400409.i			0.934053i	0.884243	+	0.467026i	$0.154675\pi$
$179$			400409.i			0.934053i	−0.884243	+	0.467026i	$0.845325\pi$
$180$	−195969.	−	603032.i	−0.450824	−	1.38727i
$181$		−	10694.7i		−	0.0242646i	−0.999926	−	0.0121323i	$-0.996138\pi$
$181$		−	10694.7i		−	0.0242646i	0.999926	−	0.0121323i	$-0.00386192\pi$
$182$		0			0
$183$	418832.	+	304284.i	0.924511	+	0.671663i
$184$	519116.			1.13037
$185$	−412722.			−0.886602
$186$	−56684.4	+	78023.3i	−0.120138	+	0.165364i
$187$			83698.9i			0.175031i
$188$	−242016.			−0.499402
$189$		0			0
$190$	110008.			0.221075
$191$		−	197252.i		−	0.391236i	−0.980680	−	0.195618i	$-0.937329\pi$
$191$		−	197252.i		−	0.391236i	0.980680	−	0.195618i	$-0.0626712\pi$
$192$	73662.9	−	101393.i	0.144210	−	0.198498i
$193$	−125511.			−0.242542			−0.121271	−	0.992619i	$-0.538697\pi$
$193$	−125511.			−0.242542			−0.121271	+	0.992619i	$0.538697\pi$
$194$	−305196.			−0.582203
$195$	17587.0	+	12777.0i	0.0331211	+	0.0240627i
$196$		0			0
$197$		−	631690.i		−	1.15968i	−0.814730	−	0.579841i	$-0.803115\pi$
$197$		−	631690.i		−	1.15968i	0.814730	−	0.579841i	$-0.196885\pi$
$198$	20930.4	+	64406.5i	0.0379414	+	0.116753i
$199$		−	622380.i		−	1.11410i	−0.830480	−	0.557049i	$-0.811934\pi$
$199$		−	622380.i		−	1.11410i	0.830480	−	0.557049i	$-0.188066\pi$
$200$		−	749323.i		−	1.32463i
$201$	58970.6	−	81170.2i	0.102955	−	0.141712i
$202$		−	114283.i		−	0.197063i
$203$		0			0
$204$	−161099.	+	221745.i	−0.271030	+	0.373060i
$205$	−1.04037e6			−1.72904
$206$	328035.			0.538583
$207$	946208.	−	307492.i	1.53483	−	0.498779i
$208$			8920.87i			0.0142971i
$209$	70916.5			0.112300
$210$		0			0
$211$	−271742.			−0.420195			−0.210098	−	0.977680i	$-0.567378\pi$
$211$	−271742.			−0.420195			−0.210098	+	0.977680i	$0.567378\pi$
$212$		−	191544.i		−	0.292704i
$213$	−409798.	−	297721.i	−0.618900	−	0.449635i
$214$	327175.			0.488366
$215$	1.95253e6			2.88072
$216$	−148381.	+	456782.i	−0.216394	+	0.666154i
$217$		0			0
$218$			272423.i			0.388241i
$219$	−160643.	−	116708.i	−0.226335	−	0.164434i
$220$		−	340989.i		−	0.474989i
$221$		−	9396.65i		−	0.0129417i
$222$	116783.	+	84843.8i	0.159037	+	0.115541i
$223$		−	256397.i		−	0.345264i	−0.984986	−	0.172632i	$-0.944773\pi$
$223$		−	256397.i		−	0.345264i	0.984986	−	0.172632i	$-0.0552271\pi$
$224$		0			0
$225$	−443852.	−	1.36581e6i	−0.584497	−	1.79860i
$226$	192830.			0.251133
$227$	117895.			0.151856			0.0759278	−	0.997113i	$-0.475808\pi$
$227$	117895.			0.151856			0.0759278	+	0.997113i	$0.475808\pi$
$228$	187880.	+	136496.i	0.239356	+	0.173893i
$229$		−	373781.i		−	0.471008i	−0.971873	−	0.235504i	$-0.924326\pi$
$229$		−	373781.i		−	0.471008i	0.971873	−	0.235504i	$-0.0756741\pi$
$230$	829970.			1.03453
$231$		0			0
$232$	455771.			0.555938
$233$			1.26480e6i			1.52627i	0.646240	+	0.763134i	$0.276340\pi$
$233$			1.26480e6i			1.52627i	−0.646240	+	0.763134i	$0.723660\pi$
$234$	−2349.80	−	7230.74i	−0.00280537	−	0.00863264i
$235$	−837986.			−0.989845
$236$	−1.09863e6			−1.28401
$237$	78776.9	−	108433.i	0.0911021	−	0.125398i
$238$		0			0
$239$			520817.i			0.589780i	0.955531	+	0.294890i	$0.0952830\pi$
$239$			520817.i			0.589780i	−0.955531	+	0.294890i	$0.904717\pi$
$240$	529564.	−	728920.i	0.593459	−	0.816868i
$241$			954289.i			1.05837i	0.848507	+	0.529185i	$0.177502\pi$
$241$			954289.i			1.05837i	−0.848507	+	0.529185i	$0.822498\pi$
$242$		−	307045.i		−	0.337026i
$243$	110.689	+	920483.i	0.000120251	+	1.00000i
$244$			911681.i			0.980321i
$245$		0			0
$246$	294383.	+	213871.i	0.310152	+	0.225327i
$247$	−7961.60			−0.00830344
$248$	−367808.			−0.379745
$249$	−290169.	+	399403.i	−0.296587	+	0.408238i
$250$		−	564551.i		−	0.571285i
$251$	789792.			0.791277			0.395638	−	0.918406i	$-0.370523\pi$
$251$	789792.			0.791277			0.395638	+	0.918406i	$0.370523\pi$
$252$		0			0
$253$	535040.			0.525515
$254$		−	282194.i		−	0.274450i
$255$	−557808.	+	767796.i	−0.537198	+	0.739427i
$256$	−144679.			−0.137977
$257$	−1.10769e6			−1.04613			−0.523064	−	0.852293i	$-0.675211\pi$
$257$	−1.10769e6			−1.04613			−0.523064	+	0.852293i	$0.675211\pi$
$258$	−552485.	−	401383.i	−0.516739	−	0.375414i
$259$		0			0
$260$			38281.9i			0.0351205i
$261$	830747.	−	269970.i	0.754862	−	0.245310i
$262$		−	315157.i		−	0.283644i
$263$			1.05399e6i			0.939608i	0.882771	+	0.469804i	$0.155675\pi$
$263$			1.05399e6i			0.939608i	−0.882771	+	0.469804i	$0.844325\pi$
$264$	−151809.	+	208957.i	−0.134056	+	0.184522i
$265$		−	663224.i		−	0.580157i
$266$		0			0
$267$	292700.	−	402887.i	0.251272	−	0.345864i
$268$	176685.			0.150267
$269$	459896.			0.387507			0.193753	−	0.981050i	$-0.437934\pi$
$269$	459896.			0.387507			0.193753	+	0.981050i	$0.437934\pi$
$270$	−237234.	+	730310.i	−0.198047	+	0.609675i
$271$			885691.i			0.732586i	0.930499	+	0.366293i	$0.119373\pi$
$271$			885691.i			0.732586i	−0.930499	+	0.366293i	$0.880627\pi$
$272$	−389459.			−0.319183
$273$		0			0
$274$	−483433.			−0.389009
$275$		−	772310.i		−	0.615828i
$276$	1.41749e6	+	1.02982e6i	1.12008	+	0.813743i
$277$	−770456.			−0.603321			−0.301660	−	0.953415i	$-0.597541\pi$
$277$	−770456.			−0.603321			−0.301660	+	0.953415i	$0.597541\pi$
$278$	491955.			0.381780
$279$	−670415.	+	217867.i	−0.515624	+	0.167564i
$280$		0			0
$281$			2.25084e6i			1.70051i	0.526374	+	0.850253i	$0.323551\pi$
$281$			2.25084e6i			1.70051i	−0.526374	+	0.850253i	$0.676449\pi$
$282$	237115.	+	172266.i	0.177557	+	0.128996i
$283$			5068.25i			0.00376177i	0.999998	+	0.00188088i	$0.000598704\pi$
$283$			5068.25i			0.00376177i	−0.999998	+	0.00188088i	$0.999401\pi$
$284$		−	892016.i		−	0.656262i
$285$	650539.	+	472620.i	0.474418	+	0.344667i
$286$		−	4088.68i		−	0.00295575i
$287$		0			0
$288$	−1.23734e6	+	402101.i	−0.879036	+	0.285663i
$289$	−1.00963e6			−0.711076
$290$	728693.			0.508803
$291$	−1.80480e6	−	1.31120e6i	−1.24939	−	0.907686i
$292$		−	349675.i		−	0.239998i
$293$	−2.51767e6			−1.71329			−0.856643	−	0.515909i	$-0.827454\pi$
$293$	−2.51767e6			−1.71329			−0.856643	+	0.515909i	$0.827454\pi$
$294$		0			0
$295$	−3.80401e6			−2.54499
$296$			550526.i			0.365215i
$297$	−152933.	+	470795.i	−0.100603	+	0.309699i
$298$	−19956.9			−0.0130182
$299$	−60067.6			−0.0388564
$300$	1.48650e6	−	2.04609e6i	0.953589	−	1.31257i
$301$		0			0
$302$		−	295280.i		−	0.186301i
$303$	490989.	−	675823.i	0.307231	−	0.422889i
$304$			329981.i			0.204788i
$305$			3.15671e6i			1.94306i
$306$	315673.	−	102585.i	0.192723	−	0.0626299i
$307$			2.31011e6i			1.39890i	0.714681	+	0.699451i	$0.246572\pi$
$307$			2.31011e6i			1.39890i	−0.714681	+	0.699451i	$0.753428\pi$
$308$		0			0
$309$	1.93986e6	+	1.40932e6i	1.15578	+	0.839680i
$310$	−588057.			−0.347549
$311$	2.35286e6			1.37941			0.689707	−	0.724089i	$-0.257739\pi$
$311$	2.35286e6			1.37941			0.689707	+	0.724089i	$0.257739\pi$
$312$	17043.2	−	23459.1i	0.00991205	−	0.0136435i
$313$		−	1.99117e6i		−	1.14881i	−0.818572	−	0.574404i	$-0.805234\pi$
$313$		−	1.99117e6i		−	1.14881i	0.818572	−	0.574404i	$-0.194766\pi$
$314$	−32981.1			−0.0188774
$315$		0			0
$316$	236028.			0.132967
$317$		−	2.09384e6i		−	1.17029i	−0.810927	−	0.585147i	$-0.801037\pi$
$317$		−	2.09384e6i		−	1.17029i	0.810927	−	0.585147i	$-0.198963\pi$
$318$	−136340.	+	187665.i	−0.0756056	+	0.104068i
$319$	469752.			0.258459
$320$	764196.			0.417186
$321$	1.93478e6	+	1.40563e6i	1.04802	+	0.761390i
$322$		0			0
$323$		−	347581.i		−	0.185374i
$324$	−1.31133e6	+	952928.i	−0.693983	+	0.504310i
$325$			86705.1i			0.0455341i
$326$		−	617709.i		−	0.321914i
$327$	−1.17040e6	+	1.61099e6i	−0.605289	+	0.833152i
$328$			1.38774e6i			0.712237i
$329$		0			0
$330$	−242714.	+	334084.i	−0.122690	+	0.168877i
$331$	275243.			0.138085			0.0690426	−	0.997614i	$-0.478006\pi$
$331$	275243.			0.138085			0.0690426	+	0.997614i	$0.478006\pi$
$332$	−869390.			−0.432882
$333$	326097.	+	1.00346e6i	0.161152	+	0.495895i
$334$			741812.i			0.363855i
$335$	611775.			0.297838
$336$		0			0
$337$	455651.			0.218553			0.109277	−	0.994011i	$-0.465147\pi$
$337$	455651.			0.218553			0.109277	+	0.994011i	$0.465147\pi$
$338$		−	791376.i		−	0.376783i
$339$	1.14031e6	+	828445.i	0.538921	+	0.391529i
$340$	−1.67128e6			−0.784064
$341$	−379091.			−0.176546
$342$	−86918.5	−	267464.i	−0.0401834	−	0.123652i
$343$		0			0
$344$		−	2.60446e6i		−	1.18665i
$345$	4.90809e6	+	3.56576e6i	2.22006	+	1.61289i
$346$			1.08368e6i			0.486642i
$347$		−	1.71199e6i		−	0.763271i	−0.924313	−	0.381636i	$-0.875361\pi$
$347$		−	1.71199e6i		−	0.763271i	0.924313	−	0.381636i	$-0.124639\pi$
$348$	1.24452e6	+	904153.i	0.550877	+	0.400215i
$349$		−	1.94736e6i		−	0.855822i	−0.903821	−	0.427911i	$-0.859250\pi$
$349$		−	1.94736e6i		−	0.855822i	0.903821	−	0.427911i	$-0.140750\pi$
$350$		0			0
$351$	17169.4	−	52854.9i	0.00743852	−	0.0228990i
$352$	−699661.			−0.300975
$353$	−3.59350e6			−1.53490			−0.767452	−	0.641106i	$-0.778476\pi$
$353$	−3.59350e6			−1.53490			−0.767452	+	0.641106i	$0.778476\pi$
$354$	1.07638e6	+	781995.i	0.456517	+	0.331662i
$355$		−	3.08862e6i		−	1.30075i
$356$	876973.			0.366742
$357$		0			0
$358$	853930.			0.352139
$359$			2.58351e6i			1.05797i	0.848630	+	0.528987i	$0.177428\pi$
$359$			2.58351e6i			1.05797i	−0.848630	+	0.528987i	$0.822572\pi$
$360$	−2.78518e6	+	905107.i	−1.13265	+	0.368081i
$361$	2.18160e6			0.881064
$362$	−22808.0			−0.00914779
$363$	1.31914e6	−	1.81574e6i	0.525442	−	0.723246i
$364$		0			0
$365$		−	1.21076e6i		−	0.475691i
$366$	648929.	−	893219.i	0.253218	−	0.348542i
$367$		−	3.76563e6i		−	1.45939i	−0.683772	−	0.729696i	$-0.739662\pi$
$367$		−	3.76563e6i		−	1.45939i	0.683772	−	0.729696i	$-0.260338\pi$
$368$			2.48960e6i			0.958317i
$369$	822014.	+	2.52948e6i	0.314277	+	0.967088i
$370$			880189.i			0.334250i
$371$		0			0
$372$	−1.00433e6	−	729654.i	−0.376288	−	0.273376i
$373$	−1.93722e6			−0.720952			−0.360476	−	0.932768i	$-0.617386\pi$
$373$	−1.93722e6			−0.720952			−0.360476	+	0.932768i	$0.617386\pi$
$374$	178500.			0.0659870
$375$	2.42545e6	−	3.33852e6i	0.890665	−	1.22596i
$376$			1.11778e6i			0.407743i
$377$	−52737.8			−0.0191104
$378$		0			0
$379$	2.04113e6			0.729917			0.364959	−	0.931024i	$-0.381083\pi$
$379$	2.04113e6			0.729917			0.364959	+	0.931024i	$0.381083\pi$
$380$			1.41604e6i			0.503057i
$381$	1.21238e6	−	1.66878e6i	0.427883	−	0.588960i
$382$	−420668.			−0.147496
$383$	470701.			0.163964			0.0819819	−	0.996634i	$-0.473875\pi$
$383$	470701.			0.163964			0.0819819	+	0.996634i	$0.473875\pi$
$384$	−2.37696e6	−	1.72688e6i	−0.822611	−	0.597632i
$385$		0			0
$386$			267670.i			0.0914388i
$387$	−1.54272e6	−	4.74722e6i	−0.523612	−	1.61125i
$388$		−	3.92855e6i		−	1.32481i
$389$		−	4.59134e6i		−	1.53839i	−0.639017	−	0.769193i	$-0.720659\pi$
$389$		−	4.59134e6i		−	1.53839i	0.639017	−	0.769193i	$-0.279341\pi$
$390$	27248.8	−	37506.7i	0.00907166	−	0.0124867i
$391$		−	2.62238e6i		−	0.867467i
$392$		0			0
$393$	1.35399e6	−	1.86371e6i	0.442216	−	0.608690i
$394$	−1.34717e6			−0.437202
$395$	817250.			0.263550
$396$	−829054.	+	269420.i	−0.265671	+	0.0863360i
$397$		−	4.55566e6i		−	1.45069i	−0.688384	−	0.725346i	$-0.741680\pi$
$397$		−	4.55566e6i		−	1.45069i	0.688384	−	0.725346i	$-0.258320\pi$
$398$	−1.32731e6			−0.420016
$399$		0			0
$400$	3.59363e6			1.12301
$401$		−	2.41750e6i		−	0.750766i	−0.926870	−	0.375383i	$-0.877511\pi$
$401$		−	2.41750e6i		−	0.750766i	0.926870	−	0.375383i	$-0.122489\pi$
$402$	−173107.	−	125763.i	−0.0534256	−	0.0388140i
$403$	42559.6			0.0130537
$404$	1.47108e6			0.448418
$405$	−4.54050e6	+	3.29953e6i	−1.37552	+	0.999573i
$406$		0			0
$407$			567414.i			0.169791i
$408$	1.02415e6	+	744054.i	0.304590	+	0.221286i
$409$			64985.1i			0.0192090i	0.999954	+	0.00960452i	$0.00305726\pi$
$409$			64985.1i			0.0192090i	−0.999954	+	0.00960452i	$0.996943\pi$
$410$			2.21875e6i			0.651851i
$411$	−2.85882e6	−	2.07695e6i	−0.834798	−	0.606486i
$412$			4.22254e6i			1.22555i
$413$		0			0
$414$	−655771.	−	2.01792e6i	−0.188040	−	0.578634i
$415$	−3.01028e6			−0.857998
$416$	78549.1			0.0222540
$417$	2.90921e6	+	2.11356e6i	0.819285	+	0.595216i
$418$		−	151239.i		−	0.0423374i
$419$	4.52870e6			1.26020			0.630098	−	0.776515i	$-0.283015\pi$
$419$	4.52870e6			1.26020			0.630098	+	0.776515i	$0.283015\pi$
$420$		0			0
$421$	−3.77935e6			−1.03923			−0.519615	−	0.854401i	$-0.673925\pi$
$421$	−3.77935e6			−1.03923			−0.519615	+	0.854401i	$0.673925\pi$
$422$			579529.i			0.158414i
$423$	662104.	+	2.03741e6i	0.179918	+	0.553641i
$424$	−884667.			−0.238982
$425$	−3.78529e6			−1.01655
$426$	−634932.	+	873953.i	−0.169513	+	0.233326i
$427$		0			0
$428$			4.21147e6i			1.11128i
$429$	17566.0	−	24178.7i	0.00460818	−	0.00634293i
$430$		−	4.16404e6i		−	1.08604i
$431$		−	6.61895e6i		−	1.71631i	−0.513391	−	0.858155i	$-0.671611\pi$
$431$		−	6.61895e6i		−	1.71631i	0.513391	−	0.858155i	$-0.328389\pi$
$432$	−2.19065e6	−	711612.i	−0.564761	−	0.183457i
$433$		−	5.25855e6i		−	1.34786i	−0.738794	−	0.673932i	$-0.764604\pi$
$433$		−	5.25855e6i		−	1.34786i	0.738794	−	0.673932i	$-0.235396\pi$
$434$		0			0
$435$	4.30918e6	+	3.13065e6i	1.09187	+	0.793251i
$436$	−3.50668e6			−0.883446
$437$	−2.22189e6			−0.556569
$438$	−248897.	+	342594.i	−0.0619917	+	0.0853286i
$439$			416451.i			0.103134i	0.998670	+	0.0515671i	$0.0164216\pi$
$439$			416451.i			0.103134i	−0.998670	+	0.0515671i	$0.983578\pi$
$440$	−1.57490e6			−0.387812
$441$		0			0
$442$	−20039.7			−0.00487905
$443$			7.00727e6i			1.69644i	0.529641	+	0.848222i	$0.322327\pi$
$443$			7.00727e6i			1.69644i	−0.529641	+	0.848222i	$0.677673\pi$
$444$	−1.09213e6	+	1.50326e6i	−0.262915	+	0.361890i
$445$	3.03653e6			0.726906
$446$	−546803.			−0.130165
$447$	−118017.	−	85739.8i	−0.0279367	−	0.0202961i
$448$		0			0
$449$		−	1.63032e6i		−	0.381643i	−0.981625	−	0.190822i	$-0.938885\pi$
$449$		−	1.63032e6i		−	0.381643i	0.981625	−	0.190822i	$-0.0611152\pi$
$450$	−2.91279e6	+	946579.i	−0.678076	+	0.220356i
$451$			1.43032e6i			0.331124i
$452$			2.48215e6i			0.571454i
$453$	1.26860e6	−	1.74616e6i	0.290454	−	0.399796i
$454$		−	251428.i		−	0.0572498i
$455$		0			0
$456$	630423.	−	867747.i	0.141978	−	0.195425i
$457$	8.38895e6			1.87896			0.939479	−	0.342606i	$-0.111310\pi$
$457$	8.38895e6			1.87896			0.939479	+	0.342606i	$0.111310\pi$
$458$	−797141.			−0.177571
$459$	2.30749e6	+	749565.i	0.511220	+	0.166065i
$460$			1.06836e7i			2.35408i
$461$	186426.			0.0408560			0.0204280	−	0.999791i	$-0.493497\pi$
$461$	186426.			0.0408560			0.0204280	+	0.999791i	$0.493497\pi$
$462$		0			0
$463$	−5.23908e6			−1.13580			−0.567901	−	0.823097i	$-0.692244\pi$
$463$	−5.23908e6			−1.13580			−0.567901	+	0.823097i	$0.692244\pi$
$464$			2.18580e6i			0.471320i
$465$	−3.47752e6	−	2.52644e6i	−0.745826	−	0.541847i
$466$	2.69736e6			0.575405
$467$	−564223.			−0.119718			−0.0598589	−	0.998207i	$-0.519065\pi$
$467$	−564223.			−0.119718			−0.0598589	+	0.998207i	$0.519065\pi$
$468$	93075.7	−	30247.1i	0.0196436	−	0.00638365i
$469$		0			0
$470$			1.78712e6i			0.373173i
$471$	−195036.	−	141695.i	−0.0405101	−	0.0294308i
$472$			5.07413e6i			1.04835i
$473$		−	2.68435e6i		−	0.551679i
$474$	−231248.	−	168003.i	−0.0472751	−	0.0343456i
$475$			3.20721e6i			0.652219i
$476$		0			0
$477$	−1.61251e6	+	524022.i	−0.324494	+	0.105452i
$478$	1.11072e6			0.222348
$479$	−2.69727e6			−0.537137			−0.268568	−	0.963261i	$-0.586551\pi$
$479$	−2.69727e6			−0.537137			−0.268568	+	0.963261i	$0.586551\pi$
$480$	−6.41821e6	−	4.66286e6i	−1.27148	−	0.923740i
$481$		−	63702.1i		−	0.0125543i
$482$	2.03516e6			0.399007
$483$		0			0
$484$	3.95235e6			0.766906
$485$		−	1.36027e7i		−	2.62585i
$486$	1.96306e6	−	236.061i	0.377001	−	4.53350e-5i
$487$	−2.84365e6			−0.543317			−0.271658	−	0.962394i	$-0.587572\pi$
$487$	−2.84365e6			−0.543317			−0.271658	+	0.962394i	$0.587572\pi$
$488$	4.21071e6			0.800397
$489$	2.65383e6	−	3.65287e6i	0.501881	−	0.690815i
$490$		0			0
$491$		−	7.38962e6i		−	1.38331i	−0.722229	−	0.691654i	$-0.756882\pi$
$491$		−	7.38962e6i		−	1.38331i	0.722229	−	0.691654i	$-0.243118\pi$
$492$	−2.75299e6	+	3.78936e6i	−0.512734	+	0.705754i
$493$		−	2.30238e6i		−	0.426638i
$494$			16979.3i			0.00313041i
$495$	−2.87062e6	+	932872.i	−0.526577	+	0.171123i
$496$		−	1.76395e6i		−	0.321945i
$497$		0			0
$498$	851784.	+	618826.i	0.153906	+	0.111814i
$499$	2.13675e6			0.384152			0.192076	−	0.981380i	$-0.438478\pi$
$499$	2.13675e6			0.384152			0.192076	+	0.981380i	$0.438478\pi$
$500$	7.26702e6			1.29996
$501$	−3.18701e6	+	4.38677e6i	−0.567269	+	0.780818i
$502$		−	1.68434e6i		−	0.298313i
$503$	−2.60933e6			−0.459842			−0.229921	−	0.973209i	$-0.573847\pi$
$503$	−2.60933e6			−0.459842			−0.229921	+	0.973209i	$0.573847\pi$
$504$		0			0
$505$	5.09364e6			0.888791
$506$		−	1.14105e6i		−	0.198120i
$507$	3.39995e6	−	4.67986e6i	0.587425	−	0.808562i
$508$	3.63246e6			0.624514
$509$	5.78866e6			0.990338			0.495169	−	0.868797i	$-0.335106\pi$
$509$	5.78866e6			0.990338			0.495169	+	0.868797i	$0.335106\pi$
$510$	1.63743e6	+	1.18961e6i	0.278765	+	0.202524i
$511$		0			0
$512$		−	5.72266e6i		−	0.964768i
$513$	635092.	−	1.95509e6i	0.106548	−	0.328000i
$514$			2.36231e6i			0.394392i
$515$			1.46206e7i			2.42911i
$516$	5.16669e6	−	7.11170e6i	0.854257	−	1.17584i
$517$			1.15207e6i			0.189563i
$518$		0			0
$519$	−4.65574e6	+	6.40840e6i	−0.758701	+	1.04431i
$520$	176810.			0.0286746
$521$	306226.			0.0494250			0.0247125	−	0.999695i	$-0.492133\pi$
$521$	306226.			0.0494250			0.0247125	+	0.999695i	$0.492133\pi$
$522$	−575750.	−	1.77169e6i	−0.0924821	−	0.284584i
$523$		−	7.18513e6i		−	1.14863i	−0.818634	−	0.574315i	$-0.805268\pi$
$523$		−	7.18513e6i		−	1.14863i	0.818634	−	0.574315i	$-0.194732\pi$
$524$	4.05677e6			0.645434
$525$		0			0
$526$	2.24778e6			0.354234
$527$			1.85803e6i			0.291424i
$528$	−1.00213e6	−	728050.i	−0.156436	−	0.113652i
$529$	−1.03270e7			−1.60449
$530$	−1.41442e6			−0.218720
$531$	3.00560e6	+	9.24877e6i	0.462589	+	1.42347i
$532$		0			0
$533$		−	160578.i		−	0.0244831i
$534$	−859214.	−	624224.i	−0.130391	−	0.0947299i
$535$			1.45823e7i			2.20263i
$536$		−	816040.i		−	0.122687i
$537$	5.04978e6	+	3.66869e6i	0.755678	+	0.549004i
$538$		−	980795.i		−	0.146091i
$539$		0			0
$540$	−9.40071e6	−	3.05373e6i	−1.38732	−	0.450657i
$541$	7.76483e6			1.14061			0.570307	−	0.821431i	$-0.306824\pi$
$541$	7.76483e6			1.14061			0.570307	+	0.821431i	$0.306824\pi$
$542$	1.88886e6			0.276186
$543$	−134877.	−	97988.9i	−0.0196308	−	0.0142619i
$544$			3.42922e6i			0.496819i
$545$	−1.21420e7			−1.75104
$546$		0			0
$547$	−7.87821e6			−1.12580			−0.562898	−	0.826527i	$-0.690313\pi$
$547$	−7.87821e6			−1.12580			−0.562898	+	0.826527i	$0.690313\pi$
$548$		−	6.22285e6i		−	0.885193i
$549$	7.67498e6	−	2.49416e6i	1.08679	−	0.353178i
$550$	−1.64706e6			−0.232168
$551$	−1.95076e6			−0.273732
$552$	4.75633e6	−	6.54685e6i	0.664391	−	0.914503i
$553$		0			0
$554$			1.64311e6i			0.227453i
$555$	−3.78151e6	+	5.20507e6i	−0.521114	+	0.717289i
$556$			6.33255e6i			0.868743i
$557$		−	4.59766e6i		−	0.627913i	−0.949437	−	0.313956i	$-0.898345\pi$
$557$		−	4.59766e6i		−	0.627913i	0.949437	−	0.313956i	$-0.101655\pi$
$558$	464632.	+	1.42976e6i	0.0631719	+	0.194391i
$559$			301365.i			0.0407909i
$560$		0			0
$561$	1.05557e6	+	766879.i	0.141606	+	0.102877i
$562$	4.80023e6			0.641094
$563$	−2.72419e6			−0.362215			−0.181107	−	0.983463i	$-0.557968\pi$
$563$	−2.72419e6			−0.362215			−0.181107	+	0.983463i	$0.557968\pi$
$564$	−2.21744e6	+	3.05220e6i	−0.293531	+	0.404031i
$565$			8.59448e6i			1.13266i
$566$	10808.8			0.00141819
$567$		0			0
$568$	−4.11988e6			−0.535814
$569$			8.67813e6i			1.12369i	0.827243	+	0.561844i	$0.189908\pi$
$569$			8.67813e6i			1.12369i	−0.827243	+	0.561844i	$0.810092\pi$
$570$	1.00793e6	−	1.38737e6i	0.129940	−	0.178856i
$571$	1.07384e7			1.37832			0.689161	−	0.724608i	$-0.257979\pi$
$571$	1.07384e7			1.37832			0.689161	+	0.724608i	$0.257979\pi$
$572$	52630.3			0.00672583
$573$	−2.48765e6	−	1.80730e6i	−0.316522	−	0.229955i
$574$		0			0
$575$			2.41973e7i			3.05209i
$576$	−603801.	−	1.85801e6i	−0.0758294	−	0.233341i
$577$			7.06870e6i			0.883894i	0.897041	+	0.441947i	$0.145712\pi$
$577$			7.06870e6i			0.883894i	−0.897041	+	0.441947i	$0.854288\pi$
$578$			2.15317e6i			0.268077i
$579$	−1.14997e6	+	1.58288e6i	−0.142558	+	0.196224i
$580$			9.37989e6i			1.15779i
$581$		0			0
$582$	−2.79631e6	+	3.84899e6i	−0.342199	+	0.471020i
$583$	−911805.			−0.111104
$584$	−1.61502e6			−0.195950
$585$	322276.	−	104731.i	0.0389349	−	0.0126528i
$586$			5.36929e6i			0.645911i
$587$	3.96818e6			0.475331			0.237666	−	0.971347i	$-0.423618\pi$
$587$	3.96818e6			0.475331			0.237666	+	0.971347i	$0.423618\pi$
$588$		0			0
$589$	1.57427e6			0.186978
$590$			8.11260e6i			0.959467i
$591$	−7.96659e6	−	5.78777e6i	−0.938218	−	0.681621i
$592$	−2.64023e6			−0.309626
$593$	−1.67421e7			−1.95512			−0.977562	−	0.210649i	$-0.932442\pi$
$593$	−1.67421e7			−1.95512			−0.977562	+	0.210649i	$0.932442\pi$
$594$	1.00404e6	+	326151.i	0.116757	+	0.0379274i
$595$		0			0
$596$		−	256889.i		−	0.0296231i
$597$	−7.84918e6	−	5.70247e6i	−0.901339	−	0.654828i
$598$			128103.i			0.0146489i
$599$			1.08814e7i			1.23913i	0.784944	+	0.619567i	$0.212692\pi$
$599$			1.08814e7i			1.23913i	−0.784944	+	0.619567i	$0.787308\pi$
$600$	−9.45012e6	−	6.86557e6i	−1.07167	−	0.778571i
$601$		−	1.72048e7i		−	1.94296i	−0.237128	−	0.971478i	$-0.576206\pi$
$601$		−	1.72048e7i		−	1.94296i	0.237128	−	0.971478i	$-0.423794\pi$
$602$		0			0
$603$	−483372.	−	1.48742e6i	−0.0541362	−	0.166587i
$604$	3.80090e6			0.423930
$605$	1.36851e7			1.52005
$606$	−1.44129e6	−	1.04711e6i	−0.159430	−	0.115827i
$607$			5.56535e6i			0.613085i	0.951857	+	0.306543i	$0.0991722\pi$
$607$			5.56535e6i			0.613085i	−0.951857	+	0.306543i	$0.900828\pi$
$608$	2.90552e6			0.318760
$609$		0			0
$610$	6.73214e6			0.732535
$611$		−	129340.i		−	0.0140162i
$612$	1.32050e6	+	4.06341e6i	0.142515	+	0.438543i
$613$	−1.18075e7			−1.26914			−0.634568	−	0.772867i	$-0.718822\pi$
$613$	−1.18075e7			−1.26914			−0.634568	+	0.772867i	$0.718822\pi$
$614$	4.92664e6			0.527388
$615$	−9.53229e6	+	1.31207e7i	−1.01627	+	1.39885i
$616$		0			0
$617$		−	5.91582e6i		−	0.625608i	−0.949818	−	0.312804i	$-0.898732\pi$
$617$		−	5.91582e6i		−	0.625608i	0.949818	−	0.312804i	$-0.101268\pi$
$618$	3.00558e6	−	4.13703e6i	0.316560	−	0.435730i
$619$			2.82876e6i			0.296736i	0.988932	+	0.148368i	$0.0474020\pi$
$619$			2.82876e6i			0.296736i	−0.988932	+	0.148368i	$0.952598\pi$
$620$		−	7.56960e6i		−	0.790849i
$621$	4.79155e6	−	1.47505e7i	0.498594	−	1.53489i
$622$		−	5.01780e6i		−	0.520041i
$623$		0			0
$624$	112506.	+	81736.2i	0.0115668	+	0.00840336i
$625$	6.69352e6			0.685416
$626$	−4.24646e6			−0.433103
$627$	649762.	−	894366.i	0.0660063	−	0.0908545i
$628$		−	424540.i		−	0.0429556i
$629$	2.78105e6			0.280273
$630$		0			0
$631$	−9.60301e6			−0.960139			−0.480069	−	0.877231i	$-0.659389\pi$
$631$	−9.60301e6			−0.960139			−0.480069	+	0.877231i	$0.659389\pi$
$632$		−	1.09012e6i		−	0.108563i
$633$	−2.48980e6	+	3.42709e6i	−0.246976	+	0.339951i
$634$	−4.46541e6			−0.441203
$635$	1.25775e7			1.23782
$636$	−2.41566e6	−	1.75499e6i	−0.236806	−	0.172041i
$637$		0			0
$638$		−	1.00181e6i		−	0.0974395i
$639$	−7.50943e6	+	2.44036e6i	−0.727537	+	0.236430i
$640$		−	1.79150e7i		−	1.72889i
$641$		−	9.00157e6i		−	0.865312i	−0.901559	−	0.432656i	$-0.857576\pi$
$641$		−	9.00157e6i		−	0.865312i	0.901559	−	0.432656i	$-0.142424\pi$
$642$	2.99770e6	−	4.12618e6i	0.287045	−	0.395104i
$643$			6.92082e6i			0.660131i	0.943958	+	0.330065i	$0.107071\pi$
$643$			6.92082e6i			0.660131i	−0.943958	+	0.330065i	$0.892929\pi$
$644$		0			0
$645$	1.78898e7	−	2.46244e7i	1.69319	−	2.33059i
$646$	−741265.			−0.0698863
$647$	1.66850e6			0.156699			0.0783495	−	0.996926i	$-0.475035\pi$
$647$	1.66850e6			0.156699			0.0783495	+	0.996926i	$0.475035\pi$
$648$	4.40121e6	+	6.05652e6i	0.411751	+	0.566612i
$649$			5.22979e6i			0.487385i
$650$	184911.			0.0171664
$651$		0			0
$652$	7.95128e6			0.732518
$653$		−	1.81810e7i		−	1.66853i	−0.551364	−	0.834265i	$-0.685892\pi$
$653$		−	1.81810e7i		−	1.66853i	0.551364	−	0.834265i	$-0.314108\pi$
$654$	3.43567e6	+	2.49603e6i	0.314099	+	0.228195i
$655$	1.40466e7			1.27929
$656$	−6.65540e6			−0.603830
$657$	−2.94374e6	+	956635.i	−0.266064	+	0.0864635i
$658$		0			0
$659$		−	5.58660e6i		−	0.501111i	−0.968102	−	0.250556i	$-0.919387\pi$
$659$		−	5.58660e6i		−	0.501111i	0.968102	−	0.250556i	$-0.0806133\pi$
$660$	−4.30040e6	−	3.12427e6i	−0.384281	−	0.279182i
$661$		−	1.30855e7i		−	1.16489i	−0.812870	−	0.582445i	$-0.802096\pi$
$661$		−	1.30855e7i		−	1.16489i	0.812870	−	0.582445i	$-0.197904\pi$
$662$		−	586996.i		−	0.0520583i
$663$	−118506.	−	86095.5i	−0.0104703	−	0.00760671i
$664$			4.01538e6i			0.353432i
$665$		0			0
$666$	2.14002e6	−	695449.i	0.186953	−	0.0607547i
$667$	−1.47178e7			−1.28094
$668$	−9.54877e6			−0.827954
$669$	−3.23356e6	−	2.34920e6i	−0.279329	−	0.202934i
$670$		−	1.30470e6i		−	0.112285i
$671$	4.33988e6			0.372110
$672$		0			0
$673$	9.79316e6			0.833461			0.416730	−	0.909030i	$-0.363176\pi$
$673$	9.79316e6			0.833461			0.416730	+	0.909030i	$0.363176\pi$
$674$		−	971740.i		−	0.0823949i
$675$	−2.12918e7	−	6.91642e6i	−1.79867	−	0.584281i
$676$	1.01868e7			0.857373
$677$	8.00917e6			0.671608			0.335804	−	0.941932i	$-0.390992\pi$
$677$	8.00917e6			0.671608			0.335804	+	0.941932i	$0.390992\pi$
$678$	1.76678e6	−	2.43188e6i	0.147607	−	0.203174i
$679$		0			0
$680$			7.71900e6i			0.640160i
$681$	1.08020e6	−	1.48684e6i	0.0892555	−	0.122856i
$682$			808466.i			0.0665581i
$683$		−	2.00990e7i		−	1.64863i	−0.566133	−	0.824314i	$-0.691561\pi$
$683$		−	2.00990e7i		−	1.64863i	0.566133	−	0.824314i	$-0.308439\pi$
$684$	3.44285e6	−	1.11883e6i	0.281370	−	0.0914377i
$685$		−	2.15467e7i		−	1.75451i
$686$		0			0
$687$	−4.71395e6	−	3.42471e6i	−0.381060	−	0.276842i
$688$	1.24906e7			1.00603
$689$	102366.			0.00821500
$690$	7.60449e6	−	1.04672e7i	0.608061	−	0.836967i
$691$			7.78435e6i			0.620193i	0.950705	+	0.310097i	$0.100361\pi$
$691$			7.78435e6i			0.620193i	−0.950705	+	0.310097i	$0.899639\pi$
$692$	−1.39493e7			−1.10736
$693$		0			0
$694$	−3.65107e6			−0.287754
$695$			2.19266e7i			1.72190i
$696$	4.17594e6	−	5.74797e6i	0.326761	−	0.449771i
$697$	7.01036e6			0.546586
$698$	−4.15303e6			−0.322646
$699$	1.59510e7	+	1.15885e7i	1.23480	+	0.897088i
$700$		0			0
$701$		−	1.12400e7i		−	0.863912i	−0.901895	−	0.431956i	$-0.857824\pi$
$701$		−	1.12400e7i		−	0.863912i	0.901895	−	0.431956i	$-0.142176\pi$
$702$	−112721.	−	36616.1i	−0.00863297	−	0.00280433i
$703$		−	2.35633e6i		−	0.179824i
$704$		−	1.05062e6i		−	0.0798942i
$705$	−7.67793e6	+	1.05683e7i	−0.581797	+	0.800815i
$706$			7.66366e6i			0.578661i
$707$		0			0
$708$	−1.00660e7	+	1.38554e7i	−0.754699	+	1.03881i
$709$	−1.15696e7			−0.864376			−0.432188	−	0.901783i	$-0.642258\pi$
$709$	−1.15696e7			−0.864376			−0.432188	+	0.901783i	$0.642258\pi$
$710$	−6.58693e6			−0.490385
$711$	−645721.	−	1.98700e6i	−0.0479039	−	0.147409i
$712$		−	4.05040e6i		−	0.299432i
$713$	1.18773e7			0.874974
$714$		0			0
$715$	182234.			0.0133310
$716$			1.09920e7i			0.801296i
$717$	6.56830e6	+	4.77191e6i	0.477150	+	0.346653i
$718$	5.50971e6			0.398857
$719$	−461291.			−0.0332777			−0.0166388	−	0.999862i	$-0.505297\pi$
$719$	−461291.			−0.0332777			−0.0166388	+	0.999862i	$0.505297\pi$
$720$	−4.34075e6	−	1.33573e7i	−0.312056	−	0.960254i
$721$		0			0
$722$		−	4.65257e6i		−	0.332162i
$723$	1.20351e7	+	8.74354e6i	0.856254	+	0.622073i
$724$		−	293590.i		−	0.0208159i
$725$			2.12446e7i			1.50108i
$726$	−3.87231e6	−	2.81326e6i	−0.272665	−	0.198093i
$727$			2.83046e6i			0.198619i	0.995057	+	0.0993096i	$0.0316634\pi$
$727$			2.83046e6i			0.198619i	−0.995057	+	0.0993096i	$0.968337\pi$
$728$		0			0
$729$	1.16097e7	+	8.43240e6i	0.809102	+	0.587669i
$730$	−2.58211e6			−0.179336
$731$	−1.31567e7			−0.910656
$732$	1.14977e7	+	8.35315e6i	0.793111	+	0.576199i
$733$		−	2.05309e7i		−	1.41140i	−0.708513	−	0.705698i	$-0.750634\pi$
$733$		−	2.05309e7i		−	1.41140i	0.708513	−	0.705698i	$-0.249366\pi$
$734$	−8.03073e6			−0.550193
$735$		0			0
$736$	2.19211e7			1.49165
$737$		−	841074.i		−	0.0570381i
$738$	5.39448e6	−	1.75306e6i	0.364594	−	0.118483i
$739$	−1.51479e7			−1.02033			−0.510167	−	0.860075i	$-0.670416\pi$
$739$	−1.51479e7			−1.02033			−0.510167	+	0.860075i	$0.670416\pi$
$740$	−1.13300e7			−0.760589
$741$	−72947.1	+	100408.i	−0.00488048	+	0.00671774i
$742$		0			0
$743$		−	3.14063e6i		−	0.208711i	−0.994540	−	0.104355i	$-0.966722\pi$
$743$		−	3.14063e6i		−	0.208711i	0.994540	−	0.104355i	$-0.0332779\pi$
$744$	−3.36999e6	+	4.63863e6i	−0.223201	+	0.307226i
$745$		−	889485.i		−	0.0587148i
$746$			4.13140e6i			0.271800i
$747$	2.37846e6	+	7.31895e6i	0.155953	+	0.479896i
$748$			2.29769e6i			0.150154i
$749$		0			0
$750$	−7.11986e6	−	5.17262e6i	−0.462188	−	0.335782i
$751$	−1.43376e6			−0.0927634			−0.0463817	−	0.998924i	$-0.514769\pi$
$751$	−1.43376e6			−0.0927634			−0.0463817	+	0.998924i	$0.514769\pi$
$752$	−5.36069e6			−0.345682
$753$	7.23636e6	−	9.96050e6i	0.465085	−	0.640168i
$754$			112471.i			0.00720463i
$755$	1.31607e7			0.840256
$756$		0			0
$757$	−6.81110e6			−0.431994			−0.215997	−	0.976394i	$-0.569300\pi$
$757$	−6.81110e6			−0.431994			−0.215997	+	0.976394i	$0.569300\pi$
$758$		−	4.35301e6i		−	0.275180i
$759$	4.90223e6	−	6.74769e6i	0.308880	−	0.425158i
$760$	6.54016e6			0.410728
$761$	−110270.			−0.00690235			−0.00345117	−	0.999994i	$-0.501099\pi$
$761$	−110270.			−0.00690235			−0.00345117	+	0.999994i	$0.501099\pi$
$762$	−3.55890e6	−	2.58557e6i	−0.222039	−	0.161313i
$763$		0			0
$764$		−	5.41493e6i		−	0.335629i
$765$	4.57225e6	+	1.40696e7i	0.282473	+	0.869220i
$766$		−	1.00384e6i		−	0.0618146i
$767$		−	587134.i		−	0.0360370i
$768$	−1.32560e6	+	1.82463e6i	−0.0810980	+	0.111628i
$769$			1.61688e7i			0.985968i	0.870038	+	0.492984i	$0.164094\pi$
$769$			1.61688e7i			0.985968i	−0.870038	+	0.492984i	$0.835906\pi$
$770$		0			0
$771$	−1.01491e7	+	1.39697e7i	−0.614879	+	0.846351i
$772$	−3.44550e6			−0.208070
$773$	1.67611e7			1.00892			0.504458	−	0.863436i	$-0.331692\pi$
$773$	1.67611e7			1.00892			0.504458	+	0.863436i	$0.331692\pi$
$774$	−1.01241e7	+	3.29007e6i	−0.607443	+	0.197402i
$775$		−	1.71445e7i		−	1.02534i
$776$	−1.81445e7			−1.08166
$777$		0			0
$778$	−9.79168e6			−0.579974
$779$		−	5.93974e6i		−	0.350690i
$780$	482795.	+	350753.i	0.0284136	+	0.0206426i
$781$	−4.24627e6			−0.249103
$782$	−5.59259e6			−0.327036
$783$	4.20686e6	−	1.29506e7i	0.245219	−	0.754891i
$784$		0			0
$785$		−	1.46998e6i		−	0.0851406i
$786$	−3.97462e6	−	2.88758e6i	−0.229477	−	0.166716i
$787$			2.06482e7i			1.18836i	0.804334	+	0.594178i	$0.202522\pi$
$787$			2.06482e7i			1.18836i	−0.804334	+	0.594178i	$0.797478\pi$
$788$		−	1.73411e7i		−	0.994856i
$789$	1.32924e7	+	9.65703e6i	0.760172	+	0.552270i
$790$		−	1.74290e6i		−	0.0993586i
$791$		0			0
$792$	1.24435e6	+	3.82908e6i	0.0704902	+	0.216911i
$793$	−487226.			−0.0275136
$794$	−9.71560e6			−0.546913
$795$	−8.36428e6	−	6.07670e6i	−0.469365	−	0.340996i
$796$		−	1.70855e7i		−	0.955751i
$797$	−2.91426e7			−1.62511			−0.812556	−	0.582884i	$-0.801924\pi$
$797$	−2.91426e7			−1.62511			−0.812556	+	0.582884i	$0.801924\pi$
$798$		0			0
$799$	5.64660e6			0.312911
$800$		−	3.16423e7i		−	1.74800i
$801$	−2.39921e6	−	7.38279e6i	−0.132125	−	0.406574i
$802$	−5.15565e6			−0.283040
$803$	−1.66456e6			−0.0910983
$804$	1.61885e6	−	2.22827e6i	0.0883216	−	0.121570i
$805$		0			0
$806$		−	90764.4i		−	0.00492128i
$807$	4.21374e6	−	5.80000e6i	0.227763	−	0.313505i
$808$		−	6.79435e6i		−	0.366117i
$809$			2.18383e7i			1.17313i	0.809901	+	0.586567i	$0.199521\pi$
$809$			2.18383e7i			1.17313i	−0.809901	+	0.586567i	$0.800479\pi$
$810$	7.03672e6	+	9.68326e6i	0.376841	+	0.518572i
$811$		−	2.56638e6i		−	0.137015i	−0.997651	−	0.0685077i	$-0.978176\pi$
$811$		−	2.56638e6i		−	0.137015i	0.997651	−	0.0685077i	$-0.0218238\pi$
$812$		0			0
$813$	1.11699e7	+	8.11502e6i	0.592685	+	0.430589i
$814$	1.21009e6			0.0640114
$815$	2.75315e7			1.45190
$816$	−3.56837e6	+	4.91168e6i	−0.187605	+	0.258229i
$817$			1.11474e7i			0.584279i
$818$	138590.			0.00724184
$819$		0			0
$820$	−2.85602e7			−1.48329
$821$		−	965227.i		−	0.0499771i	−0.999688	−	0.0249886i	$-0.992045\pi$
$821$		−	965227.i		−	0.0499771i	0.999688	−	0.0249886i	$-0.00795494\pi$
$822$	−4.42938e6	+	6.09683e6i	−0.228646	+	0.314720i
$823$	2.07808e7			1.06945			0.534726	−	0.845025i	$-0.320415\pi$
$823$	2.07808e7			1.06945			0.534726	+	0.845025i	$0.320415\pi$
$824$	1.95023e7			1.00062
$825$	−9.74002e6	−	7.07618e6i	−0.498224	−	0.361963i
$826$		0			0
$827$			5.06026e6i			0.257282i	0.991691	+	0.128641i	$0.0410615\pi$
$827$			5.06026e6i			0.257282i	−0.991691	+	0.128641i	$0.958939\pi$
$828$	2.59752e7	−	8.44122e6i	1.31669	−	0.427887i
$829$		−	1.66931e7i		−	0.843627i	−0.906683	−	0.421814i	$-0.861394\pi$
$829$		−	1.66931e7i		−	0.843627i	0.906683	−	0.421814i	$-0.138606\pi$
$830$			6.41985e6i			0.323467i
$831$	−7.05919e6	+	9.71664e6i	−0.354611	+	0.488105i
$832$			117951.i			0.00590734i
$833$		0			0
$834$	4.50747e6	−	6.20431e6i	0.224397	−	0.308872i
$835$	−3.30628e7			−1.64106
$836$	1.94679e6			0.0963392
$837$	−3.39495e6	+	1.04511e7i	−0.167502	+	0.515644i
$838$		−	9.65809e6i		−	0.475096i
$839$	1.76055e7			0.863461			0.431731	−	0.902003i	$-0.357903\pi$
$839$	1.76055e7			0.863461			0.431731	+	0.902003i	$0.357903\pi$
$840$		0			0
$841$	7.58926e6			0.370007
$842$			8.06000e6i			0.391791i
$843$	2.83865e7	+	2.06230e7i	1.37576	+	0.999500i
$844$	−7.45982e6			−0.360473
$845$	3.52719e7			1.69936
$846$	4.34507e6	−	1.41203e6i	0.208723	−	0.0678294i
$847$		0			0
$848$		−	4.24272e6i		−	0.202607i
$849$	63918.5	+	46437.1i	0.00304339	+	0.00221104i
$850$			8.07268e6i			0.383240i
$851$		−	1.77777e7i		−	0.841495i
$852$	−1.12497e7	−	8.17298e6i	−0.530936	−	0.385728i
$853$			5.38585e6i			0.253444i	0.991938	+	0.126722i	$0.0404456\pi$
$853$			5.38585e6i			0.253444i	−0.991938	+	0.126722i	$0.959554\pi$
$854$		0			0
$855$	1.19209e7	−	3.87398e6i	0.557693	−	0.181235i
$856$	1.94512e7			0.907321
$857$	−2.24902e7			−1.04602			−0.523011	−	0.852326i	$-0.675191\pi$
$857$	−2.24902e7			−1.04602			−0.523011	+	0.852326i	$0.675191\pi$
$858$	−51564.6	−	37461.9i	−0.00239129	−	0.00173729i
$859$			3.12962e7i			1.44713i	0.690255	+	0.723566i	$0.257498\pi$
$859$			3.12962e7i			1.44713i	−0.690255	+	0.723566i	$0.742502\pi$
$860$	5.36005e7			2.47128
$861$		0			0
$862$	−1.41158e7			−0.647051
$863$			1.79759e7i			0.821604i	0.911725	+	0.410802i	$0.134751\pi$
$863$			1.79759e7i			0.821604i	−0.911725	+	0.410802i	$0.865249\pi$
$864$	−6.26581e6	+	1.92889e7i	−0.285557	+	0.879070i
$865$	−4.82998e7			−2.19485
$866$	−1.12146e7			−0.508146
$867$	−9.25056e6	+	1.27330e7i	−0.417946	+	0.575283i
$868$		0			0
$869$		−	1.12356e6i		−	0.0504717i
$870$	6.67655e6	−	9.18995e6i	0.299057	−	0.411637i
$871$			94425.1i			0.00421737i
$872$			1.61960e7i			0.721302i
$873$	−3.30724e7	+	1.07476e7i	−1.46869	+	0.477285i
$874$			4.73850e6i			0.209827i
$875$		0			0
$876$	−4.40995e6	−	3.20385e6i	−0.194166	−	0.141063i
$877$	2.11950e7			0.930540			0.465270	−	0.885169i	$-0.345957\pi$
$877$	2.11950e7			0.930540			0.465270	+	0.885169i	$0.345957\pi$
$878$	888141.			0.0388817
$879$	−2.30678e7	+	3.17517e7i	−1.00701	+	1.38610i
$880$		−	7.55296e6i		−	0.328784i
$881$	6.16325e6			0.267529			0.133764	−	0.991013i	$-0.457293\pi$
$881$	6.16325e6			0.267529			0.133764	+	0.991013i	$0.457293\pi$
$882$		0			0
$883$	−1.51180e7			−0.652519			−0.326260	−	0.945280i	$-0.605788\pi$
$883$	−1.51180e7			−0.652519			−0.326260	+	0.945280i	$0.605788\pi$
$884$		−	257955.i		−	0.0111023i
$885$	−3.48537e7	+	4.79745e7i	−1.49586	+	2.05898i
$886$	1.49440e7			0.639562
$887$	−2.42779e7			−1.03610			−0.518051	−	0.855350i	$-0.673342\pi$
$887$	−2.42779e7			−1.03610			−0.518051	+	0.855350i	$0.673342\pi$
$888$	6.94298e6	+	5.04412e6i	0.295470	+	0.214661i
$889$		0			0
$890$		−	6.47584e6i		−	0.274045i
$891$	4.53622e6	+	6.24231e6i	0.191426	+	0.263422i
$892$		−	7.03857e6i		−	0.296191i
$893$		−	4.78426e6i		−	0.200764i
$894$	−182852.	+	251687.i	−0.00765168	+	0.0105322i
$895$			3.80599e7i			1.58822i
$896$		0			0
$897$	−550361.	+	757545.i	−0.0228384	+	0.0314360i
$898$	−3.47689e6			−0.143880
$899$	1.04280e7			0.430330
$900$	−1.21846e7	−	3.74941e7i	−0.501422	−	1.54297i
$901$			4.46900e6i			0.183400i
$902$	3.05035e6			0.124834
$903$		0			0
$904$	1.14641e7			0.466572
$905$		−	1.01656e6i		−	0.0412583i
$906$	−3.72393e6	−	2.70546e6i	−0.150724	−	0.109502i
$907$	−2.06772e7			−0.834591			−0.417295	−	0.908771i	$-0.637022\pi$
$907$	−2.06772e7			−0.834591			−0.417295	+	0.908771i	$0.637022\pi$
$908$	3.23643e6			0.130272
$909$	−4.02455e6	−	1.23843e7i	−0.161550	−	0.497120i
$910$		0			0
$911$			4.74564e7i			1.89452i	0.320466	+	0.947260i	$0.396161\pi$
$911$			4.74564e7i			1.89452i	−0.320466	+	0.947260i	$0.603839\pi$
$912$	4.16157e6	+	3.02341e6i	0.165680	+	0.120368i
$913$			4.13856e6i			0.164313i
$914$		−	1.78906e7i		−	0.708370i
$915$	3.98110e7	+	2.89230e7i	1.57199	+	1.14206i
$916$		−	1.02610e7i		−	0.404063i
$917$		0			0
$918$	1.59855e6	−	4.92105e6i	0.0626067	−	0.192731i
$919$	−4.98420e7			−1.94674			−0.973368	−	0.229249i	$-0.926373\pi$
$919$	−4.98420e7			−1.94674			−0.973368	+	0.229249i	$0.926373\pi$
$920$	4.93433e7			1.92202
$921$	2.91341e7	+	2.11661e7i	1.13176	+	0.822227i
$922$		−	397581.i		−	0.0154028i
$923$	476717.			0.0184186
$924$		0			0
$925$	−2.56614e7			−0.986111
$926$			1.11731e7i			0.428199i
$927$	3.55474e7	−	1.15519e7i	1.35865	−	0.441526i
$928$	1.92462e7			0.733626
$929$	−98732.8			−0.00375338			−0.00187669	−	0.999998i	$-0.500597\pi$
$929$	−98732.8			−0.00375338			−0.00187669	+	0.999998i	$0.500597\pi$
$930$	−5.38799e6	+	7.41631e6i	−0.204277	+	0.281178i
$931$		0			0
$932$			3.47210e7i			1.30934i
$933$	2.15577e7	−	2.96732e7i	0.810772	−	1.11599i
$934$			1.20329e6i			0.0451338i
$935$			7.95579e6i			0.297615i
$936$	−139700.	−	429881.i	−0.00521202	−	0.0160383i
$937$		−	2.17619e7i		−	0.809743i	−0.914373	−	0.404872i	$-0.867316\pi$
$937$		−	2.17619e7i		−	0.809743i	0.914373	−	0.404872i	$-0.132684\pi$
$938$		0			0
$939$	−2.51118e7	−	1.82438e7i	−0.929422	−	0.675231i
$940$	−2.30042e7			−0.849158
$941$	−2.89614e7			−1.06622			−0.533109	−	0.846046i	$-0.678977\pi$
$941$	−2.89614e7			−1.06622			−0.533109	+	0.846046i	$0.678977\pi$
$942$	−302185.	+	415943.i	−0.0110955	+	0.0152724i
$943$		−	4.48133e7i		−	1.64107i
$944$	−2.43347e7			−0.888784
$945$		0			0
$946$	−5.72476e6			−0.207984
$947$		−	3.11506e7i		−	1.12873i	−0.825524	−	0.564367i	$-0.809120\pi$
$947$		−	3.11506e7i		−	1.12873i	0.825524	−	0.564367i	$-0.190880\pi$
$948$	2.16257e6	−	2.97667e6i	0.0781537	−	0.107575i
$949$	186876.			0.00673577
$950$	6.83983e6			0.245887
$951$	−2.64065e7	−	1.91845e7i	−0.946804	−	0.687859i
$952$		0			0
$953$		−	6.07840e6i		−	0.216799i	−0.994107	−	0.108399i	$-0.965427\pi$
$953$		−	6.07840e6i		−	0.216799i	0.994107	−	0.108399i	$-0.0345725\pi$
$954$	1.11755e6	+	3.43891e6i	0.0397554	+	0.122335i
$955$		−	1.87493e7i		−	0.665238i
$956$			1.42974e7i			0.505955i
$957$	4.30404e6	−	5.92430e6i	0.151913	−	0.209102i
$958$			5.75230e6i			0.202501i
$959$		0			0
$960$	7.00184e6	−	9.63769e6i	0.245208	−	0.337516i
$961$	2.02137e7			0.706054
$962$	−135854.			−0.00473297
$963$	3.54542e7	−	1.15217e7i	1.23198	−	0.400359i
$964$			2.61970e7i			0.907943i
$965$	−1.19301e7			−0.412407
$966$		0			0
$967$	412575.			0.0141885			0.00709426	−	0.999975i	$-0.497742\pi$
$967$	412575.			0.0141885			0.00709426	+	0.999975i	$0.497742\pi$
$968$		−	1.82544e7i		−	0.626151i
$969$	−4.38353e6	−	3.18466e6i	−0.149973	−	0.108957i
$970$	−2.90096e7			−0.989949
$971$	2.34602e7			0.798516			0.399258	−	0.916839i	$-0.369268\pi$
$971$	2.34602e7			0.798516			0.399258	+	0.916839i	$0.369268\pi$
$972$	3038.63	+	2.52689e7i	0.000103160	+	0.857870i
$973$		0			0
$974$			6.06448e6i			0.204831i
$975$	1.09349e6	+	794424.i	0.0368385	+	0.0267634i
$976$			2.01939e7i			0.678571i
$977$			1.56531e7i			0.524643i	0.964981	+	0.262322i	$0.0844881\pi$
$977$			1.56531e7i			0.524643i	−0.964981	+	0.262322i	$0.915512\pi$
$978$	−7.79026e6	−	5.65967e6i	−0.260438	−	0.189210i
$979$		−	4.17465e6i		−	0.139208i
$980$		0			0
$981$	9.59352e6	+	2.95210e7i	0.318277	+	0.979396i
$982$	−1.57594e7			−0.521509
$983$	6.11410e6			0.201813			0.100906	−	0.994896i	$-0.467826\pi$
$983$	6.11410e6			0.201813			0.100906	+	0.994896i	$0.467826\pi$
$984$	1.75016e7	+	1.27150e7i	0.576222	+	0.418629i
$985$		−	6.00437e7i		−	1.97186i
$986$	−4.91015e6			−0.160843
$987$		0			0
$988$	−218561.			−0.00712327
$989$			8.41036e7i			2.73416i
$990$	1.98948e6	+	6.12200e6i	0.0645137	+	0.198520i
$991$	−3.56283e7			−1.15242			−0.576211	−	0.817301i	$-0.695469\pi$
$991$	−3.56283e7			−1.15242			−0.576211	+	0.817301i	$0.695469\pi$
$992$	−1.55317e7			−0.501119
$993$	2.52188e6	−	3.47125e6i	0.0811617	−	0.111715i
$994$		0			0
$995$		−	5.91588e7i		−	1.89436i
$996$	−7.96567e6	+	1.09644e7i	−0.254433	+	0.350215i
$997$		−	5.76360e7i		−	1.83635i	−0.396171	−	0.918177i	$-0.629661\pi$
$997$		−	5.76360e7i		−	1.83635i	0.396171	−	0.918177i	$-0.370339\pi$
$998$		−	4.55693e6i		−	0.144826i
$999$	1.56430e7	+	5.08148e6i	0.495914	+	0.161093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.c.c.146.8		16
3.2	odd	2	inner	147.6.c.c.146.9		16
7.4	even	3		21.6.g.c.5.5	yes	16
7.5	odd	6		21.6.g.c.17.4	yes	16
7.6	odd	2	inner	147.6.c.c.146.7		16
21.5	even	6		21.6.g.c.17.5	yes	16
21.11	odd	6		21.6.g.c.5.4	✓	16
21.20	even	2	inner	147.6.c.c.146.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.g.c.5.4	✓	16	21.11	odd	6
21.6.g.c.5.5	yes	16	7.4	even	3
21.6.g.c.17.4	yes	16	7.5	odd	6
21.6.g.c.17.5	yes	16	21.5	even	6
147.6.c.c.146.7		16	7.6	odd	2	inner
147.6.c.c.146.8		16	1.1	even	1	trivial
147.6.c.c.146.9		16	3.2	odd	2	inner
147.6.c.c.146.10		16	21.20	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.13264i q^{2} +(9.16236 - 12.6115i) q^{3} +27.4518 q^{4} +95.0525 q^{5} +(-26.8959 - 19.5400i) q^{6} -126.790i q^{8} +(-75.1022 - 231.103i) q^{9} +O(q^{10})\)	\(q-2.13264i q^{2} +(9.16236 - 12.6115i) q^{3} +27.4518 q^{4} +95.0525 q^{5} +(-26.8959 - 19.5400i) q^{6} -126.790i q^{8} +(-75.1022 - 231.103i) q^{9} -202.713i q^{10} -130.679i q^{11} +(251.524 - 346.210i) q^{12} +14.6710i q^{13} +(870.905 - 1198.76i) q^{15} +608.062 q^{16} -640.492 q^{17} +(-492.860 + 160.166i) q^{18} +542.677i q^{19} +2609.37 q^{20} -278.692 q^{22} +4094.31i q^{23} +(-1599.01 - 1161.69i) q^{24} +5909.98 q^{25} +31.2880 q^{26} +(-3602.68 - 1170.29i) q^{27} +3594.70i q^{29} +(-2556.52 - 1857.33i) q^{30} -2900.94i q^{31} -5354.04i q^{32} +(-1648.06 - 1197.33i) q^{33} +1365.94i q^{34} +(-2061.69 - 6344.20i) q^{36} -4342.05 q^{37} +1157.34 q^{38} +(185.024 + 134.421i) q^{39} -12051.7i q^{40} -10945.3 q^{41} +20541.6 q^{43} -3587.38i q^{44} +(-7138.66 - 21966.9i) q^{45} +8731.70 q^{46} -8816.03 q^{47} +(5571.28 - 7668.60i) q^{48} -12603.9i q^{50} +(-5868.42 + 8077.60i) q^{51} +402.745i q^{52} -6977.45i q^{53} +(-2495.82 + 7683.23i) q^{54} -12421.4i q^{55} +(6844.00 + 4972.20i) q^{57} +7666.22 q^{58} -40020.1 q^{59} +(23908.0 - 32908.1i) q^{60} +33210.2i q^{61} -6186.66 q^{62} +8039.72 q^{64} +1394.51i q^{65} +(-2553.47 + 3514.73i) q^{66} +6436.18 q^{67} -17582.7 q^{68} +(51635.6 + 37513.6i) q^{69} -32493.9i q^{71} +(-29301.5 + 9522.18i) q^{72} -12737.8i q^{73} +9260.03i q^{74} +(54149.3 - 74533.9i) q^{75} +14897.5i q^{76} +(286.672 - 394.590i) q^{78} +8597.89 q^{79} +57797.8 q^{80} +(-47768.3 + 34712.7i) q^{81} +23342.3i q^{82} -31669.6 q^{83} -60880.4 q^{85} -43807.8i q^{86} +(45334.8 + 32936.0i) q^{87} -16568.7 q^{88} +31945.9 q^{89} +(-46847.6 + 15224.2i) q^{90} +112396. i q^{92} +(-36585.3 - 26579.4i) q^{93} +18801.4i q^{94} +51582.8i q^{95} +(-67522.8 - 49055.7i) q^{96} -143107. i q^{97} +(-30200.3 + 9814.28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 172 q^{4} + 1212 q^{9}+O(q^{10}) \) 16 * q - 172 * q^4 + 1212 * q^9	\( 16 q - 172 q^{4} + 1212 q^{9} + 1188 q^{15} + 5716 q^{16} + 876 q^{18} - 21900 q^{22} + 13156 q^{25} - 900 q^{30} - 15132 q^{36} + 20932 q^{37} + 34836 q^{39} + 111052 q^{43} - 163392 q^{46} - 63192 q^{51} - 31368 q^{57} + 83412 q^{58} - 120132 q^{60} - 158884 q^{64} + 204404 q^{67} - 661728 q^{72} - 277512 q^{78} + 502616 q^{79} - 358524 q^{81} + 205152 q^{85} + 719028 q^{88} - 35352 q^{93} + 215472 q^{99}+O(q^{100}) \) 16 * q - 172 * q^4 + 1212 * q^9 + 1188 * q^15 + 5716 * q^16 + 876 * q^18 - 21900 * q^22 + 13156 * q^25 - 900 * q^30 - 15132 * q^36 + 20932 * q^37 + 34836 * q^39 + 111052 * q^43 - 163392 * q^46 - 63192 * q^51 - 31368 * q^57 + 83412 * q^58 - 120132 * q^60 - 158884 * q^64 + 204404 * q^67 - 661728 * q^72 - 277512 * q^78 + 502616 * q^79 - 358524 * q^81 + 205152 * q^85 + 719028 * q^88 - 35352 * q^93 + 215472 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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