LMFDB - Embedded newform 490.5.d.a.489.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,5,Mod(489,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("490.489");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	490.d (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:	$50.6512819111$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			489.18
Character	$\chi$	$=$	490.489
Dual form			490.5.d.a.489.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843i q^{2} -12.5406 q^{3} -8.00000 q^{4} +(-14.7215 + 20.2059i) q^{5} -35.4702i q^{6} -22.6274i q^{8} +76.2668 q^{9} +O(q^{10})$	\(q+2.82843i q^{2} -12.5406 q^{3} -8.00000 q^{4} +(-14.7215 + 20.2059i) q^{5} -35.4702i q^{6} -22.6274i q^{8} +76.2668 q^{9} +(-57.1508 - 41.6387i) q^{10} -7.20277 q^{11} +100.325 q^{12} -292.752 q^{13} +(184.617 - 253.394i) q^{15} +64.0000 q^{16} +122.942 q^{17} +215.715i q^{18} -87.5492i q^{19} +(117.772 - 161.647i) q^{20} -20.3725i q^{22} -514.307i q^{23} +283.762i q^{24} +(-191.554 - 594.922i) q^{25} -828.029i q^{26} +59.3570 q^{27} +931.646 q^{29} +(716.706 + 522.175i) q^{30} +14.4094i q^{31} +181.019i q^{32} +90.3271 q^{33} +347.732i q^{34} -610.135 q^{36} -1728.56i q^{37} +247.627 q^{38} +3671.29 q^{39} +(457.207 + 333.110i) q^{40} -2540.41i q^{41} +410.931i q^{43} +57.6222 q^{44} +(-1122.76 + 1541.04i) q^{45} +1454.68 q^{46} -3038.83 q^{47} -802.599 q^{48} +(1682.69 - 541.798i) q^{50} -1541.76 q^{51} +2342.02 q^{52} -1988.31i q^{53} +167.887i q^{54} +(106.036 - 145.538i) q^{55} +1097.92i q^{57} +2635.09i q^{58} +3913.59i q^{59} +(-1476.93 + 2027.15i) q^{60} +4770.08i q^{61} -40.7560 q^{62} -512.000 q^{64} +(4309.76 - 5915.32i) q^{65} +255.484i q^{66} +7649.97i q^{67} -983.534 q^{68} +6449.73i q^{69} +1844.25 q^{71} -1725.72i q^{72} -10598.6 q^{73} +4889.10 q^{74} +(2402.21 + 7460.68i) q^{75} +700.394i q^{76} +10384.0i q^{78} -3780.52 q^{79} +(-942.177 + 1293.18i) q^{80} -6921.99 q^{81} +7185.36 q^{82} -3661.83 q^{83} +(-1809.89 + 2484.15i) q^{85} -1162.29 q^{86} -11683.4 q^{87} +162.980i q^{88} +149.690i q^{89} +(-4358.71 - 3175.65i) q^{90} +4114.46i q^{92} -180.703i q^{93} -8595.11i q^{94} +(1769.01 + 1288.86i) q^{95} -2270.09i q^{96} +12754.1 q^{97} -549.333 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 256 q^{4} + 1032 q^{9}+O(q^{10}) $ 32 * q - 256 * q^4 + 1032 * q^9	$ 32 q - 256 q^{4} + 1032 q^{9} + 288 q^{11} - 76 q^{15} + 2048 q^{16} - 588 q^{25} + 912 q^{29} - 1216 q^{30} - 8256 q^{36} + 4848 q^{39} - 2304 q^{44} - 3328 q^{46} + 15744 q^{50} - 5416 q^{51} + 608 q^{60} - 16384 q^{64} - 1872 q^{65} - 53808 q^{71} + 12672 q^{74} + 48152 q^{79} - 35360 q^{81} + 8324 q^{85} - 13248 q^{86} - 85980 q^{95} + 101048 q^{99}+O(q^{100}) $ 32 * q - 256 * q^4 + 1032 * q^9 + 288 * q^11 - 76 * q^15 + 2048 * q^16 - 588 * q^25 + 912 * q^29 - 1216 * q^30 - 8256 * q^36 + 4848 * q^39 - 2304 * q^44 - 3328 * q^46 + 15744 * q^50 - 5416 * q^51 + 608 * q^60 - 16384 * q^64 - 1872 * q^65 - 53808 * q^71 + 12672 * q^74 + 48152 * q^79 - 35360 * q^81 + 8324 * q^85 - 13248 * q^86 - 85980 * q^95 + 101048 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$-1$	$-1$

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 $

$2$			2.82843i			0.707107i
$2$			2.82843i			0.707107i
$3$	−12.5406			−1.39340			−0.696700	−	0.717362i	$-0.745349\pi$
$3$	−12.5406			−1.39340			−0.696700	+	0.717362i	$0.745349\pi$
$4$	−8.00000			−0.500000
$5$	−14.7215	+	20.2059i	−0.588860	+	0.808235i
$5$	−14.7215	+	20.2059i	−0.588860	+	0.808235i
$6$		−	35.4702i		−	0.985283i
$7$		0			0
$7$		0			0
$8$		−	22.6274i		−	0.353553i
$9$	76.2668			0.941566
$10$	−57.1508	−	41.6387i	−0.571508	−	0.416387i
$11$	−7.20277			−0.0595270			−0.0297635	−	0.999557i	$-0.509475\pi$
$11$	−7.20277			−0.0595270			−0.0297635	+	0.999557i	$0.509475\pi$
$12$	100.325			0.696700
$13$	−292.752			−1.73226			−0.866131	−	0.499816i	$-0.833401\pi$
$13$	−292.752			−1.73226			−0.866131	+	0.499816i	$0.833401\pi$
$14$		0			0
$15$	184.617	−	253.394i	0.820518	−	1.12619i
$16$	64.0000			0.250000
$17$	122.942			0.425404			0.212702	−	0.977117i	$-0.431774\pi$
$17$	122.942			0.425404			0.212702	+	0.977117i	$0.431774\pi$
$18$			215.715i			0.665787i
$19$		−	87.5492i		−	0.242519i	−0.992621	−	0.121259i	$-0.961307\pi$
$19$		−	87.5492i		−	0.242519i	0.992621	−	0.121259i	$-0.0386933\pi$
$20$	117.772	−	161.647i	0.294430	−	0.404117i
$21$		0			0
$22$		−	20.3725i		−	0.0420920i
$23$		−	514.307i		−	0.972226i	−0.873896	−	0.486113i	$-0.838414\pi$
$23$		−	514.307i		−	0.972226i	0.873896	−	0.486113i	$-0.161586\pi$
$24$			283.762i			0.492642i
$25$	−191.554	−	594.922i	−0.306487	−	0.951875i
$26$		−	828.029i		−	1.22489i
$27$	59.3570			0.0814225
$28$		0			0
$29$	931.646			1.10778			0.553892	−	0.832589i	$-0.313142\pi$
$29$	931.646			1.10778			0.553892	+	0.832589i	$0.313142\pi$
$30$	716.706	+	522.175i	0.796340	+	0.580194i
$31$			14.4094i			0.0149942i	0.999972	+	0.00749711i	$0.00238643\pi$
$31$			14.4094i			0.0149942i	−0.999972	+	0.00749711i	$0.997614\pi$
$32$			181.019i			0.176777i
$33$	90.3271			0.0829450
$34$			347.732i			0.300806i
$35$		0			0
$36$	−610.135			−0.470783
$37$		−	1728.56i		−	1.26264i	−0.775521	−	0.631322i	$-0.782513\pi$
$37$		−	1728.56i		−	1.26264i	0.775521	−	0.631322i	$-0.217487\pi$
$38$	247.627			0.171487
$39$	3671.29			2.41374
$40$	457.207	+	333.110i	0.285754	+	0.208194i
$41$		−	2540.41i		−	1.51125i	−0.655005	−	0.755625i	$-0.727333\pi$
$41$		−	2540.41i		−	1.51125i	0.655005	−	0.755625i	$-0.272667\pi$
$42$		0			0
$43$			410.931i			0.222245i	0.993807	+	0.111122i	$0.0354446\pi$
$43$			410.931i			0.222245i	−0.993807	+	0.111122i	$0.964555\pi$
$44$	57.6222			0.0297635
$45$	−1122.76	+	1541.04i	−0.554451	+	0.761006i
$46$	1454.68			0.687467
$47$	−3038.83			−1.37566			−0.687829	−	0.725873i	$-0.741436\pi$
$47$	−3038.83			−1.37566			−0.687829	+	0.725873i	$0.741436\pi$
$48$	−802.599			−0.348350
$49$		0			0
$50$	1682.69	−	541.798i	0.673077	−	0.216719i
$51$	−1541.76			−0.592759
$52$	2342.02			0.866131
$53$		−	1988.31i		−	0.707836i	−0.935276	−	0.353918i	$-0.884849\pi$
$53$		−	1988.31i		−	0.707836i	0.935276	−	0.353918i	$-0.115151\pi$
$54$			167.887i			0.0575744i
$55$	106.036	−	145.538i	0.0350531	−	0.0481118i
$56$		0			0
$57$			1097.92i			0.337926i
$58$			2635.09i			0.783322i
$59$			3913.59i			1.12427i	0.827045	+	0.562136i	$0.190020\pi$
$59$			3913.59i			1.12427i	−0.827045	+	0.562136i	$0.809980\pi$
$60$	−1476.93	+	2027.15i	−0.410259	+	0.563097i
$61$			4770.08i			1.28194i	0.767568	+	0.640968i	$0.221467\pi$
$61$			4770.08i			1.28194i	−0.767568	+	0.640968i	$0.778533\pi$
$62$	−40.7560			−0.0106025
$63$		0			0
$64$	−512.000			−0.125000
$65$	4309.76	−	5915.32i	1.02006	−	1.40008i
$66$			255.484i			0.0586510i
$67$			7649.97i			1.70416i	0.523412	+	0.852080i	$0.324659\pi$
$67$			7649.97i			1.70416i	−0.523412	+	0.852080i	$0.675341\pi$
$68$	−983.534			−0.212702
$69$			6449.73i			1.35470i
$70$		0			0
$71$	1844.25			0.365849			0.182925	−	0.983127i	$-0.441444\pi$
$71$	1844.25			0.365849			0.182925	+	0.983127i	$0.441444\pi$
$72$		−	1725.72i		−	0.332894i
$73$	−10598.6			−1.98885			−0.994426	−	0.105438i	$-0.966376\pi$
$73$	−10598.6			−1.98885			−0.994426	+	0.105438i	$0.966376\pi$
$74$	4889.10			0.892824
$75$	2402.21	+	7460.68i	0.427059	+	1.32634i
$76$			700.394i			0.121259i
$77$		0			0
$78$			10384.0i			1.70677i
$79$	−3780.52			−0.605756			−0.302878	−	0.953029i	$-0.597947\pi$
$79$	−3780.52			−0.605756			−0.302878	+	0.953029i	$0.597947\pi$
$80$	−942.177	+	1293.18i	−0.147215	+	0.202059i
$81$	−6921.99			−1.05502
$82$	7185.36			1.06861
$83$	−3661.83			−0.531547			−0.265774	−	0.964035i	$-0.585627\pi$
$83$	−3661.83			−0.531547			−0.265774	+	0.964035i	$0.585627\pi$
$84$		0			0
$85$	−1809.89	+	2484.15i	−0.250504	+	0.343826i
$86$	−1162.29			−0.157151
$87$	−11683.4			−1.54359
$88$			162.980i			0.0210460i
$89$			149.690i			0.0188978i	0.999955	+	0.00944892i	$0.00300773\pi$
$89$			149.690i			0.0188978i	−0.999955	+	0.00944892i	$0.996992\pi$
$90$	−4358.71	−	3175.65i	−0.538113	−	0.392056i
$91$		0			0
$92$			4114.46i			0.486113i
$93$		−	180.703i		−	0.0208929i
$94$		−	8595.11i		−	0.972737i
$95$	1769.01	+	1288.86i	0.196012	+	0.142810i
$96$		−	2270.09i		−	0.246321i
$97$	12754.1			1.35552			0.677759	−	0.735284i	$-0.262951\pi$
$97$	12754.1			1.35552			0.677759	+	0.735284i	$0.262951\pi$
$98$		0			0
$99$	−549.333			−0.0560486
$100$	1532.43	+	4759.37i	0.153243	+	0.475937i
$101$			11501.7i			1.12751i	0.825942	+	0.563755i	$0.190644\pi$
$101$			11501.7i			1.12751i	−0.825942	+	0.563755i	$0.809356\pi$
$102$		−	4360.77i		−	0.419144i
$103$	7573.12			0.713839			0.356919	−	0.934135i	$-0.383827\pi$
$103$	7573.12			0.713839			0.356919	+	0.934135i	$0.383827\pi$
$104$			6624.23i			0.612447i
$105$		0			0
$106$	5623.80			0.500516
$107$		−	6319.95i		−	0.552008i	−0.961156	−	0.276004i	$-0.910990\pi$
$107$		−	6319.95i		−	0.552008i	0.961156	−	0.276004i	$-0.0890104\pi$
$108$	−474.856			−0.0407113
$109$	19611.6			1.65067			0.825335	−	0.564644i	$-0.190986\pi$
$109$	19611.6			1.65067			0.825335	+	0.564644i	$0.190986\pi$
$110$	411.644	+	299.914i	0.0340202	+	0.0247863i
$111$			21677.2i			1.75937i
$112$		0			0
$113$			15860.1i			1.24208i	0.783780	+	0.621039i	$0.213289\pi$
$113$			15860.1i			1.24208i	−0.783780	+	0.621039i	$0.786711\pi$
$114$	−3105.39			−0.238949
$115$	10392.0	+	7571.38i	0.785787	+	0.572505i
$116$	−7453.17			−0.553892
$117$	−22327.3			−1.63104
$118$	−11069.3			−0.794981
$119$		0			0
$120$	−5733.65	−	4177.40i	−0.398170	−	0.290097i
$121$	−14589.1			−0.996457
$122$	−13491.8			−0.906465
$123$			31858.3i			2.10578i
$124$		−	115.276i		−	0.00749711i
$125$	14840.9	+	4887.62i	0.949816	+	0.312808i
$126$		0			0
$127$		−	3905.57i		−	0.242146i	−0.992644	−	0.121073i	$-0.961367\pi$
$127$		−	3905.57i		−	0.242146i	0.992644	−	0.121073i	$-0.0386335\pi$
$128$		−	1448.15i		−	0.0883883i
$129$		−	5153.32i		−	0.309676i
$130$	16731.0	+	12189.8i	0.990003	+	0.721292i
$131$		−	32819.0i		−	1.91242i	−0.292688	−	0.956208i	$-0.594550\pi$
$131$		−	32819.0i		−	1.91242i	0.292688	−	0.956208i	$-0.405450\pi$
$132$	−722.617			−0.0414725
$133$		0			0
$134$	−21637.4			−1.20502
$135$	−873.825	+	1199.36i	−0.0479465	+	0.0658085i
$136$		−	2781.86i		−	0.150403i
$137$			14483.7i			0.771683i	0.922565	+	0.385842i	$0.126089\pi$
$137$			14483.7i			0.771683i	−0.922565	+	0.385842i	$0.873911\pi$
$138$	−18242.6			−0.957918
$139$		−	20012.6i		−	1.03580i	−0.855442	−	0.517899i	$-0.826714\pi$
$139$		−	20012.6i		−	1.03580i	0.855442	−	0.517899i	$-0.173286\pi$
$140$		0			0
$141$	38108.8			1.91684
$142$			5216.31i			0.258694i
$143$	2108.63			0.103116
$144$	4881.08			0.235391
$145$	−13715.2	+	18824.7i	−0.652330	+	0.895350i
$146$		−	29977.3i		−	1.40633i
$147$		0			0
$148$			13828.5i			0.631322i
$149$	18060.1			0.813482			0.406741	−	0.913543i	$-0.366665\pi$
$149$	18060.1			0.813482			0.406741	+	0.913543i	$0.366665\pi$
$150$	−21102.0	+	6794.47i	−0.937866	+	0.301976i
$151$	−17960.8			−0.787720			−0.393860	−	0.919170i	$-0.628861\pi$
$151$	−17960.8			−0.787720			−0.393860	+	0.919170i	$0.628861\pi$
$152$	−1981.01			−0.0857433
$153$	9376.38			0.400546
$154$		0			0
$155$	−291.155	−	212.129i	−0.0121188	−	0.00882950i
$156$	−29370.3			−1.20687
$157$	−14703.5			−0.596516			−0.298258	−	0.954485i	$-0.596406\pi$
$157$	−14703.5			−0.596516			−0.298258	+	0.954485i	$0.596406\pi$
$158$		−	10692.9i		−	0.428334i
$159$			24934.6i			0.986299i
$160$	−3657.65	−	2664.88i	−0.142877	−	0.104097i
$161$		0			0
$162$		−	19578.3i		−	0.746012i
$163$			14083.8i			0.530085i	0.964237	+	0.265043i	$0.0853861\pi$
$163$			14083.8i			0.530085i	−0.964237	+	0.265043i	$0.914614\pi$
$164$			20323.3i			0.755625i
$165$	−1329.75	+	1825.14i	−0.0488430	+	0.0670391i
$166$		−	10357.2i		−	0.375860i
$167$	−43007.4			−1.54209			−0.771045	−	0.636781i	$-0.780266\pi$
$167$	−43007.4			−1.54209			−0.771045	+	0.636781i	$0.780266\pi$
$168$		0			0
$169$	57143.0			2.00073
$170$	−7026.23	−	5119.14i	−0.243122	−	0.177133i
$171$		−	6677.10i		−	0.228347i
$172$		−	3287.44i		−	0.111122i
$173$	22797.5			0.761721			0.380860	−	0.924633i	$-0.375628\pi$
$173$	22797.5			0.761721			0.380860	+	0.924633i	$0.375628\pi$
$174$		−	33045.7i		−	1.09148i
$175$		0			0
$176$	−460.977			−0.0148818
$177$		−	49078.8i		−	1.56656i
$178$	−423.387			−0.0133628
$179$	−12330.7			−0.384842			−0.192421	−	0.981313i	$-0.561634\pi$
$179$	−12330.7			−0.384842			−0.192421	+	0.981313i	$0.561634\pi$
$180$	8982.10	−	12328.3i	0.277225	−	0.380503i
$181$		−	35555.8i		−	1.08531i	−0.839956	−	0.542655i	$-0.817419\pi$
$181$		−	35555.8i		−	1.08531i	0.839956	−	0.542655i	$-0.182581\pi$
$182$		0			0
$183$		−	59819.7i		−	1.78625i
$184$	−11637.4			−0.343734
$185$	34927.0	+	25447.0i	1.02051	+	0.743521i
$186$	511.106			0.0147735
$187$	−885.522			−0.0253231
$188$	24310.6			0.687829
$189$		0			0
$190$	−3645.44	+	5003.51i	−0.100982	+	0.138601i
$191$	−53945.6			−1.47873			−0.739366	−	0.673304i	$-0.764874\pi$
$191$	−53945.6			−1.47873			−0.739366	+	0.673304i	$0.764874\pi$
$192$	6420.79			0.174175
$193$		−	2415.08i		−	0.0648361i	−0.999474	−	0.0324181i	$-0.989679\pi$
$193$		−	2415.08i		−	0.0648361i	0.999474	−	0.0324181i	$-0.0103208\pi$
$194$			36073.9i			0.958496i
$195$	−54047.0	+	74181.7i	−1.42135	+	1.95087i
$196$		0			0
$197$			26051.4i			0.671272i	0.941992	+	0.335636i	$0.108951\pi$
$197$			26051.4i			0.671272i	−0.941992	+	0.335636i	$0.891049\pi$
$198$		−	1553.75i		−	0.0396324i
$199$		−	1320.85i		−	0.0333540i	−0.999861	−	0.0166770i	$-0.994691\pi$
$199$		−	1320.85i		−	0.0333540i	0.999861	−	0.0166770i	$-0.00530871\pi$
$200$	−13461.5	+	4334.38i	−0.336539	+	0.108360i
$201$		−	95935.3i		−	2.37458i
$202$	−32531.8			−0.797270
$203$		0			0
$204$	12334.1			0.296379
$205$	51331.2	+	37398.7i	1.22144	+	0.889915i
$206$			21420.0i			0.504760i
$207$		−	39224.6i		−	0.915414i
$208$	−18736.2			−0.433066
$209$			630.597i			0.0144364i
$210$		0			0
$211$	−5370.71			−0.120633			−0.0603166	−	0.998179i	$-0.519211\pi$
$211$	−5370.71			−0.120633			−0.0603166	+	0.998179i	$0.519211\pi$
$212$			15906.5i			0.353918i
$213$	−23128.0			−0.509774
$214$	17875.5			0.390329
$215$	−8303.21	−	6049.52i	−0.179626	−	0.130871i
$216$		−	1343.10i		−	0.0287872i
$217$		0			0
$218$			55470.0i			1.16720i
$219$	132913.			2.77127
$220$	−848.285	+	1164.31i	−0.0175266	+	0.0240559i
$221$	−35991.5			−0.736912
$222$	−61312.3			−1.24406
$223$	63898.3			1.28493			0.642465	−	0.766315i	$-0.277912\pi$
$223$	63898.3			1.28493			0.642465	+	0.766315i	$0.277912\pi$
$224$		0			0
$225$	−14609.2	−	45372.8i	−0.288578	−	0.896253i
$226$	−44859.1			−0.878282
$227$	24691.8			0.479182			0.239591	−	0.970874i	$-0.422987\pi$
$227$	24691.8			0.479182			0.239591	+	0.970874i	$0.422987\pi$
$228$		−	8783.36i		−	0.168963i
$229$			33600.9i			0.640737i	0.947293	+	0.320368i	$0.103807\pi$
$229$			33600.9i			0.640737i	−0.947293	+	0.320368i	$0.896193\pi$
$230$	−21415.1	+	29393.1i	−0.404822	+	0.555635i
$231$		0			0
$232$		−	21080.8i		−	0.391661i
$233$			25805.6i			0.475338i	0.971346	+	0.237669i	$0.0763833\pi$
$233$			25805.6i			0.475338i	−0.971346	+	0.237669i	$0.923617\pi$
$234$		−	63151.1i		−	1.15332i
$235$	44736.2	−	61402.2i	0.810071	−	1.11186i
$236$		−	31308.7i		−	0.562136i
$237$	47410.1			0.844061
$238$		0			0
$239$	−31292.6			−0.547830			−0.273915	−	0.961754i	$-0.588319\pi$
$239$	−31292.6			−0.547830			−0.273915	+	0.961754i	$0.588319\pi$
$240$	11815.5	−	16217.2i	0.205130	−	0.281549i
$241$		−	36495.5i		−	0.628356i	−0.949364	−	0.314178i	$-0.898271\pi$
$241$		−	36495.5i		−	0.628356i	0.949364	−	0.314178i	$-0.101729\pi$
$242$		−	41264.3i		−	0.704601i
$243$	81998.0			1.38864
$244$		−	38160.6i		−	0.640968i
$245$		0			0
$246$	−90108.8			−1.48901
$247$			25630.2i			0.420106i
$248$	326.048			0.00530125
$249$	45921.5			0.740658
$250$	−13824.3	+	41976.4i	−0.221189	+	0.671622i
$251$			69357.1i			1.10089i	0.834872	+	0.550444i	$0.185542\pi$
$251$			69357.1i			1.10089i	−0.834872	+	0.550444i	$0.814458\pi$
$252$		0			0
$253$			3704.44i			0.0578737i
$254$	11046.6			0.171223
$255$	22697.1	−	31152.7i	0.349052	−	0.479088i
$256$	4096.00			0.0625000
$257$	110087.			1.66674			0.833371	−	0.552715i	$-0.186408\pi$
$257$	110087.			1.66674			0.833371	+	0.552715i	$0.186408\pi$
$258$	14575.8			0.218974
$259$		0			0
$260$	−34478.1	+	47322.5i	−0.510030	+	0.700038i
$261$	71053.7			1.04305
$262$	92826.1			1.35228
$263$			569.380i			0.00823172i	0.999992	+	0.00411586i	$0.00131012\pi$
$263$			569.380i			0.00823172i	−0.999992	+	0.00411586i	$0.998690\pi$
$264$		−	2043.87i		−	0.0293255i
$265$	40175.6	+	29270.9i	0.572098	+	0.416817i
$266$		0			0
$267$		−	1877.20i		−	0.0263323i
$268$		−	61199.8i		−	0.852080i
$269$		−	57201.4i		−	0.790500i	−0.918574	−	0.395250i	$-0.870658\pi$
$269$		−	57201.4i		−	0.790500i	0.918574	−	0.395250i	$-0.129342\pi$
$270$	−3392.30	−	2471.55i	−0.0465337	−	0.0339033i
$271$			83963.1i			1.14327i	0.820507	+	0.571637i	$0.193691\pi$
$271$			83963.1i			1.14327i	−0.820507	+	0.571637i	$0.806309\pi$
$272$	7868.28			0.106351
$273$		0			0
$274$	−40966.2			−0.545663
$275$	1379.72	+	4285.09i	0.0182443	+	0.0566623i
$276$		−	51597.8i		−	0.677350i
$277$			58362.2i			0.760628i	0.924857	+	0.380314i	$0.124184\pi$
$277$			58362.2i			0.760628i	−0.924857	+	0.380314i	$0.875816\pi$
$278$	56604.3			0.732419
$279$			1098.96i			0.0141180i
$280$		0			0
$281$	29284.0			0.370867			0.185434	−	0.982657i	$-0.440631\pi$
$281$	29284.0			0.370867			0.185434	+	0.982657i	$0.440631\pi$
$282$			107788.i			1.35541i
$283$	128556.			1.60516			0.802581	−	0.596544i	$-0.203460\pi$
$283$	128556.			1.60516			0.802581	+	0.596544i	$0.203460\pi$
$284$	−14754.0			−0.182925
$285$	−22184.4	−	16163.0i	−0.273123	−	0.198991i
$286$			5964.10i			0.0729144i
$287$		0			0
$288$			13805.8i			0.166447i
$289$	−68406.3			−0.819031
$290$	−53244.4	−	38792.6i	−0.633108	−	0.461267i
$291$	−159944.			−1.88878
$292$	84788.7			0.994426
$293$	127398.			1.48398			0.741990	−	0.670411i	$-0.233882\pi$
$293$	127398.			1.48398			0.741990	+	0.670411i	$0.233882\pi$
$294$		0			0
$295$	−79077.6	−	57614.0i	−0.908676	−	0.662040i
$296$	−39112.8			−0.446412
$297$	−427.535			−0.00484684
$298$			51081.7i			0.575219i
$299$			150565.i			1.68415i
$300$	−19217.7	−	59685.4i	−0.213530	−	0.663172i
$301$		0			0
$302$		−	50800.8i		−	0.557002i
$303$		−	144239.i		−	1.57107i
$304$		−	5603.15i		−	0.0606296i
$305$	−96383.6	−	70222.8i	−1.03610	−	0.754881i
$306$			26520.4i			0.283229i
$307$	63793.8			0.676865			0.338432	−	0.940991i	$-0.390103\pi$
$307$	63793.8			0.676865			0.338432	+	0.940991i	$0.390103\pi$
$308$		0			0
$309$	−94971.5			−0.994664
$310$	599.990	−	823.511i	0.00624340	−	0.00856932i
$311$			20322.5i			0.210114i	0.994466	+	0.105057i	$0.0335026\pi$
$311$			20322.5i			0.210114i	−0.994466	+	0.105057i	$0.966497\pi$
$312$		−	83071.9i		−	0.853385i
$313$	97038.1			0.990498			0.495249	−	0.868751i	$-0.335077\pi$
$313$	97038.1			0.990498			0.495249	+	0.868751i	$0.335077\pi$
$314$		−	41587.8i		−	0.421800i
$315$		0			0
$316$	30244.2			0.302878
$317$		−	21346.8i		−	0.212429i	−0.994343	−	0.106215i	$-0.966127\pi$
$317$		−	21346.8i		−	0.212429i	0.994343	−	0.106215i	$-0.0338731\pi$
$318$	−70525.8			−0.697419
$319$	−6710.44			−0.0659431
$320$	7537.41	−	10345.4i	0.0736075	−	0.101029i
$321$			79255.9i			0.769169i
$322$		0			0
$323$		−	10763.5i		−	0.103168i
$324$	55375.9			0.527510
$325$	56078.0	+	174165.i	0.530916	+	1.64890i
$326$	−39835.1			−0.374827
$327$	−245941.			−2.30004
$328$	−57482.9			−0.534307
$329$		0			0
$330$	−5162.27	−	3761.11i	−0.0474038	−	0.0345372i
$331$	58020.8			0.529575			0.264788	−	0.964307i	$-0.414698\pi$
$331$	58020.8			0.529575			0.264788	+	0.964307i	$0.414698\pi$
$332$	29294.6			0.265774
$333$		−	131832.i		−	1.18886i
$334$		−	121643.i		−	1.09042i
$335$	−154574.	−	112619.i	−1.37736	−	1.00351i
$336$		0			0
$337$		−	98548.0i		−	0.867737i	−0.900976	−	0.433869i	$-0.857148\pi$
$337$		−	98548.0i		−	0.867737i	0.900976	−	0.433869i	$-0.142852\pi$
$338$			161625.i			1.41473i
$339$		−	198895.i		−	1.73071i
$340$	14479.1	−	19873.2i	0.125252	−	0.171913i
$341$		−	103.788i		−	0.000892561i
$342$	18885.7			0.161466
$343$		0			0
$344$	9298.30			0.0785754
$345$	−130322.	−	94949.7i	−1.09492	−	0.797729i
$346$			64481.2i			0.538618i
$347$			45911.0i			0.381292i	0.981659	+	0.190646i	$0.0610583\pi$
$347$			45911.0i			0.381292i	−0.981659	+	0.190646i	$0.938942\pi$
$348$	93467.3			0.771794
$349$		−	14058.4i		−	0.115421i	−0.998333	−	0.0577104i	$-0.981620\pi$
$349$		−	14058.4i		−	0.115421i	0.998333	−	0.0577104i	$-0.0183800\pi$
$350$		0			0
$351$	−17376.9			−0.141045
$352$		−	1303.84i		−	0.0105230i
$353$	−13423.8			−0.107727			−0.0538635	−	0.998548i	$-0.517154\pi$
$353$	−13423.8			−0.107727			−0.0538635	+	0.998548i	$0.517154\pi$
$354$	138816.			1.10773
$355$	−27150.1	+	37264.6i	−0.215434	+	0.295692i
$356$		−	1197.52i		−	0.00944892i
$357$		0			0
$358$		−	34876.5i		−	0.272124i
$359$	−97101.0			−0.753416			−0.376708	−	0.926332i	$-0.622944\pi$
$359$	−97101.0			−0.753416			−0.376708	+	0.926332i	$0.622944\pi$
$360$	34869.7	+	25405.2i	0.269056	+	0.196028i
$361$	122656.			0.941185
$362$	100567.			0.767430
$363$	182956.			1.38846
$364$		0			0
$365$	156027.	−	214154.i	1.17116	−	1.60746i
$366$	169196.			1.26307
$367$	−11672.2			−0.0866601			−0.0433301	−	0.999061i	$-0.513797\pi$
$367$	−11672.2			−0.0866601			−0.0433301	+	0.999061i	$0.513797\pi$
$368$		−	32915.7i		−	0.243056i
$369$		−	193749.i		−	1.42294i
$370$	−71975.0	+	98788.6i	−0.525749	+	0.721611i
$371$		0			0
$372$			1445.62i			0.0104465i
$373$			197752.i			1.42136i	0.703517	+	0.710678i	$0.251612\pi$
$373$			197752.i			1.42136i	−0.703517	+	0.710678i	$0.748388\pi$
$374$		−	2504.63i		−	0.0179061i
$375$	−186114.	−	61293.8i	−1.32347	−	0.435867i
$376$			68760.9i			0.486369i
$377$	−272742.			−1.91897
$378$		0			0
$379$	−8503.45			−0.0591993			−0.0295997	−	0.999562i	$-0.509423\pi$
$379$	−8503.45			−0.0591993			−0.0295997	+	0.999562i	$0.509423\pi$
$380$	−14152.1	−	10310.9i	−0.0980060	−	0.0714048i
$381$			48978.2i			0.337406i
$382$		−	152581.i		−	1.04562i
$383$	−230180.			−1.56917			−0.784584	−	0.620022i	$-0.787124\pi$
$383$	−230180.			−1.56917			−0.784584	+	0.620022i	$0.787124\pi$
$384$			18160.7i			0.123160i
$385$		0			0
$386$	6830.88			0.0458461
$387$			31340.4i			0.209258i
$388$	−102033.			−0.677759
$389$	80008.2			0.528731			0.264366	−	0.964423i	$-0.414837\pi$
$389$	80008.2			0.528731			0.264366	+	0.964423i	$0.414837\pi$
$390$	−209817.	−	152868.i	−1.37947	−	1.00505i
$391$		−	63229.9i		−	0.413589i
$392$		0			0
$393$			411570.i			2.66476i
$394$	−73684.5			−0.474661
$395$	55655.0	−	76388.8i	0.356706	−	0.489593i
$396$	4394.66			0.0280243
$397$	47711.1			0.302718			0.151359	−	0.988479i	$-0.451635\pi$
$397$	47711.1			0.302718			0.151359	+	0.988479i	$0.451635\pi$
$398$	3735.94			0.0235849
$399$		0			0
$400$	−12259.5	−	38075.0i	−0.0766217	−	0.237969i
$401$	54109.8			0.336501			0.168251	−	0.985744i	$-0.446188\pi$
$401$	54109.8			0.336501			0.168251	+	0.985744i	$0.446188\pi$
$402$	271346.			1.67908
$403$		−	4218.40i		−	0.0259739i
$404$		−	92013.9i		−	0.563755i
$405$	101902.	−	139865.i	0.621259	−	0.852704i
$406$		0			0
$407$			12450.4i			0.0751615i
$408$			34886.2i			0.209572i
$409$			182282.i			1.08968i	0.838541	+	0.544838i	$0.183409\pi$
$409$			182282.i			1.08968i	−0.838541	+	0.544838i	$0.816591\pi$
$410$	−105779.	+	145187.i	−0.629265	+	0.863691i
$411$		−	181635.i		−	1.07526i
$412$	−60584.9			−0.356919
$413$		0			0
$414$	110944.			0.647296
$415$	53907.6	−	73990.4i	0.313007	−	0.429615i
$416$		−	52993.8i		−	0.306224i
$417$			250971.i			1.44328i
$418$	−1783.60			−0.0102081
$419$			50823.7i			0.289493i	0.989469	+	0.144746i	$0.0462366\pi$
$419$			50823.7i			0.289493i	−0.989469	+	0.144746i	$0.953763\pi$
$420$		0			0
$421$	10731.4			0.0605471			0.0302735	−	0.999542i	$-0.490362\pi$
$421$	10731.4			0.0605471			0.0302735	+	0.999542i	$0.490362\pi$
$422$		−	15190.7i		−	0.0853006i
$423$	−231762.			−1.29527
$424$	−44990.4			−0.250258
$425$	−23550.0	−	73140.8i	−0.130381	−	0.404932i
$426$		−	65415.7i		−	0.360465i
$427$		0			0
$428$			50559.6i			0.276004i
$429$	−26443.5			−0.143683
$430$	17110.6	−	23485.0i	0.0925399	−	0.127015i
$431$	83963.7			0.451999			0.225999	−	0.974127i	$-0.427435\pi$
$431$	83963.7			0.451999			0.225999	+	0.974127i	$0.427435\pi$
$432$	3798.85			0.0203556
$433$	−7149.73			−0.0381342			−0.0190671	−	0.999818i	$-0.506070\pi$
$433$	−7149.73			−0.0381342			−0.0190671	+	0.999818i	$0.506070\pi$
$434$		0			0
$435$	171997.	−	236073.i	0.908957	−	1.24758i
$436$	−156893.			−0.825335
$437$	−45027.2			−0.235783
$438$			375934.i			1.95958i
$439$		−	253551.i		−	1.31564i	−0.753176	−	0.657819i	$-0.771479\pi$
$439$		−	253551.i		−	1.31564i	0.753176	−	0.657819i	$-0.228521\pi$
$440$	−3293.16	−	2399.31i	−0.0170101	−	0.0123931i
$441$		0			0
$442$		−	101799.i		−	0.521075i
$443$			71406.3i			0.363856i	0.983312	+	0.181928i	$0.0582337\pi$
$443$			71406.3i			0.363856i	−0.983312	+	0.181928i	$0.941766\pi$
$444$		−	173417.i		−	0.879684i
$445$	−3024.61	−	2203.66i	−0.0152739	−	0.0111282i
$446$			180732.i			0.908582i
$447$	−226485.			−1.13351
$448$		0			0
$449$	315051.			1.56275			0.781373	−	0.624064i	$-0.214520\pi$
$449$	315051.			1.56275			0.781373	+	0.624064i	$0.214520\pi$
$450$	128334.	−	41321.2i	0.633746	−	0.204055i
$451$			18298.0i			0.0899602i
$452$		−	126881.i		−	0.621039i
$453$	225239.			1.09761
$454$			69838.9i			0.338833i
$455$		0			0
$456$	24843.1			0.119475
$457$		−	69407.3i		−	0.332332i	−0.986098	−	0.166166i	$-0.946861\pi$
$457$		−	69407.3i		−	0.332332i	0.986098	−	0.166166i	$-0.0531388\pi$
$458$	−95037.7			−0.453069
$459$	7297.46			0.0346375
$460$	−83136.2	−	60571.0i	−0.392893	−	0.286253i
$461$		−	166851.i		−	0.785104i	−0.919730	−	0.392552i	$-0.871592\pi$
$461$		−	166851.i		−	0.785104i	0.919730	−	0.392552i	$-0.128408\pi$
$462$		0			0
$463$			166871.i			0.778429i	0.921147	+	0.389214i	$0.127253\pi$
$463$			166871.i			0.778429i	−0.921147	+	0.389214i	$0.872747\pi$
$464$	59625.4			0.276946
$465$	3651.26	+	2660.22i	0.0168864	+	0.0123030i
$466$	−72989.3			−0.336115
$467$	−182547.			−0.837028			−0.418514	−	0.908210i	$-0.637449\pi$
$467$	−182547.			−0.837028			−0.418514	+	0.908210i	$0.637449\pi$
$468$	178618.			0.815520
$469$		0			0
$470$	173672.	+	126533.i	0.786200	+	0.572807i
$471$	184391.			0.831186
$472$	88554.5			0.397490
$473$		−	2959.84i		−	0.0132296i
$474$			134096.i			0.596841i
$475$	−52084.9	+	16770.4i	−0.230847	+	0.0743288i
$476$		0			0
$477$		−	151642.i		−	0.666474i
$478$		−	88508.9i		−	0.387374i
$479$		−	72068.0i		−	0.314103i	−0.987590	−	0.157051i	$-0.949801\pi$
$479$		−	72068.0i		−	0.314103i	0.987590	−	0.157051i	$-0.0501988\pi$
$480$	45869.2	+	33419.2i	0.199085	+	0.145049i
$481$			506040.i			2.18723i
$482$	103225.			0.444315
$483$		0			0
$484$	116713.			0.498228
$485$	−187759.	+	257707.i	−0.798211	+	1.09558i
$486$			231925.i			0.981919i
$487$		−	85511.1i		−	0.360549i	−0.983616	−	0.180275i	$-0.942301\pi$
$487$		−	85511.1i		−	0.360549i	0.983616	−	0.180275i	$-0.0576986\pi$
$488$	107935.			0.453232
$489$		−	176620.i		−	0.738621i
$490$		0			0
$491$	−360859.			−1.49684			−0.748418	−	0.663227i	$-0.769186\pi$
$491$	−360859.			−1.49684			−0.748418	+	0.663227i	$0.769186\pi$
$492$		−	254866.i		−	1.05289i
$493$	114538.			0.471256
$494$	−72493.3			−0.297060
$495$	8087.00	−	11099.7i	0.0330048	−	0.0453004i
$496$			922.204i			0.00374855i
$497$		0			0
$498$			129886.i			0.523724i
$499$	−386496.			−1.55219			−0.776094	−	0.630617i	$-0.782802\pi$
$499$	−386496.			−1.55219			−0.776094	+	0.630617i	$0.782802\pi$
$500$	−118727.	−	39101.0i	−0.474908	−	0.156404i
$501$	539338.			2.14875
$502$	−196171.			−0.778446
$503$	−125251.			−0.495044			−0.247522	−	0.968882i	$-0.579616\pi$
$503$	−125251.			−0.495044			−0.247522	+	0.968882i	$0.579616\pi$
$504$		0			0
$505$	−232403.	−	169323.i	−0.911293	−	0.663946i
$506$	−10477.7			−0.0409229
$507$	−716608.			−2.78783
$508$			31244.5i			0.121073i
$509$			346375.i			1.33694i	0.743741	+	0.668468i	$0.233050\pi$
$509$			346375.i			1.33694i	−0.743741	+	0.668468i	$0.766950\pi$
$510$	88113.1	+	64197.1i	0.338766	+	0.246817i
$511$		0			0
$512$			11585.2i			0.0441942i
$513$		−	5196.66i		−	0.0197465i
$514$			311372.i			1.17856i
$515$	−111488.	+	153021.i	−0.420351	+	0.576950i
$516$			41226.6i			0.154838i
$517$	21888.0			0.0818889
$518$		0			0
$519$	−285895.			−1.06138
$520$	−133848.	−	97518.7i	−0.495001	−	0.360646i
$521$		−	21462.8i		−	0.0790697i	−0.999218	−	0.0395349i	$-0.987412\pi$
$521$		−	21462.8i		−	0.0790697i	0.999218	−	0.0395349i	$-0.0125876\pi$
$522$			200970.i			0.737549i
$523$	354870.			1.29738			0.648689	−	0.761054i	$-0.275318\pi$
$523$	354870.			1.29738			0.648689	+	0.761054i	$0.275318\pi$
$524$			262552.i			0.956208i
$525$		0			0
$526$	−1610.45			−0.00582070
$527$			1771.52i			0.00637860i
$528$	5780.94			0.0207363
$529$	15328.9			0.0547772
$530$	−82790.7	+	113634.i	−0.294734	+	0.404534i
$531$			298477.i			1.05858i
$532$		0			0
$533$			743711.i			2.61788i
$534$	5309.52			0.0186197
$535$	127700.	+	93039.1i	0.446152	+	0.325056i
$536$	173099.			0.602511
$537$	154635.			0.536239
$538$	161790.			0.558968
$539$		0			0
$540$	6990.60	−	9594.88i	0.0239733	−	0.0329043i
$541$	55590.3			0.189935			0.0949675	−	0.995480i	$-0.469725\pi$
$541$	55590.3			0.189935			0.0949675	+	0.995480i	$0.469725\pi$
$542$	−237484.			−0.808416
$543$			445892.i			1.51227i
$544$			22254.8i			0.0752015i
$545$	−288712.	+	396270.i	−0.972014	+	1.33413i
$546$		0			0
$547$			486947.i			1.62745i	0.581251	+	0.813725i	$0.302564\pi$
$547$			486947.i			1.62745i	−0.581251	+	0.813725i	$0.697436\pi$
$548$		−	115870.i		−	0.385842i
$549$			363799.i			1.20703i
$550$	−12120.1	+	3902.44i	−0.0400663	+	0.0129006i
$551$		−	81564.9i		−	0.268658i
$552$	145941.			0.478959
$553$		0			0
$554$	−165073.			−0.537845
$555$	−438006.	−	319121.i	−1.42198	−	1.03602i
$556$			160101.i			0.517899i
$557$			130911.i			0.421956i	0.977491	+	0.210978i	$0.0676648\pi$
$557$			130911.i			0.421956i	−0.977491	+	0.210978i	$0.932335\pi$
$558$	−3108.33			−0.00998296
$559$		−	120301.i		−	0.384986i
$560$		0			0
$561$	11105.0			0.0352852
$562$			82827.8i			0.262243i
$563$	−492483.			−1.55373			−0.776863	−	0.629670i	$-0.783190\pi$
$563$	−492483.			−1.55373			−0.776863	+	0.629670i	$0.783190\pi$
$564$	−304870.			−0.958422
$565$	−320467.	−	233485.i	−1.00389	−	0.731410i
$566$			363611.i			1.13502i
$567$		0			0
$568$		−	41730.5i		−	0.129347i
$569$	86080.9			0.265878			0.132939	−	0.991124i	$-0.457559\pi$
$569$	86080.9			0.265878			0.132939	+	0.991124i	$0.457559\pi$
$570$	45716.0	−	62747.1i	0.140708	−	0.193127i
$571$	27624.9			0.0847283			0.0423642	−	0.999102i	$-0.486511\pi$
$571$	27624.9			0.0847283			0.0423642	+	0.999102i	$0.486511\pi$
$572$	−16869.0			−0.0515582
$573$	676510.			2.06047
$574$		0			0
$575$	−305973.	+	98517.8i	−0.925437	+	0.297975i
$576$	−39048.6			−0.117696
$577$	301458.			0.905473			0.452736	−	0.891644i	$-0.350448\pi$
$577$	301458.			0.905473			0.452736	+	0.891644i	$0.350448\pi$
$578$		−	193482.i		−	0.579143i
$579$			30286.6i			0.0903427i
$580$	109722.	−	150598.i	0.326165	−	0.447675i
$581$		0			0
$582$		−	452389.i		−	1.33557i
$583$			14321.4i			0.0421354i
$584$			239819.i			0.703165i
$585$	328691.	−	451142.i	0.960454	−	1.31826i
$586$			360337.i			1.04933i
$587$	155451.			0.451147			0.225574	−	0.974226i	$-0.427574\pi$
$587$	155451.			0.451147			0.225574	+	0.974226i	$0.427574\pi$
$588$		0			0
$589$	1261.53			0.00363638
$590$	162957.	−	223665.i	0.468133	−	0.642531i
$591$		−	326700.i		−	0.935351i
$592$		−	110628.i		−	0.315661i
$593$	90729.5			0.258012			0.129006	−	0.991644i	$-0.458821\pi$
$593$	90729.5			0.258012			0.129006	+	0.991644i	$0.458821\pi$
$594$		−	1209.25i		−	0.00342724i
$595$		0			0
$596$	−144481.			−0.406741
$597$			16564.3i			0.0464755i
$598$	−425861.			−1.19087
$599$	−132600.			−0.369563			−0.184782	−	0.982780i	$-0.559158\pi$
$599$	−132600.			−0.369563			−0.184782	+	0.982780i	$0.559158\pi$
$600$	168816.	−	54355.8i	0.468933	−	0.150988i
$601$			247185.i			0.684343i	0.939638	+	0.342171i	$0.111162\pi$
$601$			247185.i			0.684343i	−0.939638	+	0.342171i	$0.888838\pi$
$602$		0			0
$603$			583439.i			1.60458i
$604$	143686.			0.393860
$605$	214774.	−	294786.i	0.586774	−	0.805371i
$606$	407969.			1.11092
$607$	96948.7			0.263126			0.131563	−	0.991308i	$-0.458000\pi$
$607$	96948.7			0.263126			0.131563	+	0.991308i	$0.458000\pi$
$608$	15848.1			0.0428716
$609$		0			0
$610$	198620.	−	272614.i	0.533781	−	0.732637i
$611$	889625.			2.38300
$612$	−75011.0			−0.200273
$613$		−	220111.i		−	0.585761i	−0.956149	−	0.292880i	$-0.905386\pi$
$613$		−	220111.i		−	0.585761i	0.956149	−	0.292880i	$-0.0946137\pi$
$614$			180436.i			0.478615i
$615$	−643724.	−	469002.i	−1.70196	−	1.24001i
$616$		0			0
$617$			219063.i			0.575438i	0.957715	+	0.287719i	$0.0928970\pi$
$617$			219063.i			0.575438i	−0.957715	+	0.287719i	$0.907103\pi$
$618$		−	268620.i		−	0.703333i
$619$			17582.3i			0.0458875i	0.999737	+	0.0229438i	$0.00730387\pi$
$619$			17582.3i			0.0458875i	−0.999737	+	0.0229438i	$0.992696\pi$
$620$	2329.24	+	1697.03i	0.00605942	+	0.00441475i
$621$		−	30527.8i		−	0.0791611i
$622$	−57480.6			−0.148573
$623$		0			0
$624$	234963.			0.603434
$625$	−317239.	+	227920.i	−0.812131	+	0.583475i
$626$			274465.i			0.700388i
$627$		−	7908.07i		−	0.0201157i
$628$	117628.			0.298258
$629$		−	212512.i		−	0.537134i
$630$		0			0
$631$	541622.			1.36031			0.680154	−	0.733069i	$-0.261913\pi$
$631$	541622.			1.36031			0.680154	+	0.733069i	$0.261913\pi$
$632$			85543.5i			0.214167i
$633$	67352.0			0.168090
$634$	60377.9			0.150210
$635$	78915.4	+	57495.9i	0.195711	+	0.142590i
$636$		−	199477.i		−	0.493150i
$637$		0			0
$638$		−	18980.0i		−	0.0466288i
$639$	140655.			0.344471
$640$	29261.2	+	21319.0i	0.0714385	+	0.0520484i
$641$	380770.			0.926717			0.463358	−	0.886171i	$-0.346644\pi$
$641$	380770.			0.926717			0.463358	+	0.886171i	$0.346644\pi$
$642$	−224170.			−0.543885
$643$	209750.			0.507319			0.253659	−	0.967294i	$-0.418366\pi$
$643$	209750.			0.507319			0.253659	+	0.967294i	$0.418366\pi$
$644$		0			0
$645$	104127.	+	75864.6i	0.250291	+	0.182356i
$646$	30443.7			0.0729511
$647$	424586.			1.01428			0.507139	−	0.861864i	$-0.330703\pi$
$647$	424586.			1.01428			0.507139	+	0.861864i	$0.330703\pi$
$648$			156627.i			0.373006i
$649$		−	28188.7i		−	0.0669246i
$650$	−492612.	+	158613.i	−1.16595	+	0.375414i
$651$		0			0
$652$		−	112671.i		−	0.265043i
$653$			356215.i			0.835383i	0.908589	+	0.417691i	$0.137161\pi$
$653$			356215.i			0.835383i	−0.908589	+	0.417691i	$0.862839\pi$
$654$		−	695627.i		−	1.62638i
$655$	663136.	+	483145.i	1.54568	+	1.12615i
$656$		−	162586.i		−	0.377812i
$657$	−808321.			−1.87263
$658$		0			0
$659$	252669.			0.581810			0.290905	−	0.956752i	$-0.406044\pi$
$659$	252669.			0.581810			0.290905	+	0.956752i	$0.406044\pi$
$660$	10638.0	−	14601.1i	0.0244215	−	0.0335195i
$661$		−	283526.i		−	0.648919i	−0.945900	−	0.324459i	$-0.894818\pi$
$661$		−	283526.i		−	0.648919i	0.945900	−	0.324459i	$-0.105182\pi$
$662$			164108.i			0.374466i
$663$	451355.			1.02681
$664$			82857.7i			0.187930i
$665$		0			0
$666$	372876.			0.840652
$667$		−	479153.i		−	1.07702i
$668$	344059.			0.771045
$669$	−801323.			−1.79042
$670$	318535.	−	437202.i	0.709590	−	0.973941i
$671$		−	34357.8i		−	0.0763098i
$672$		0			0
$673$		−	859774.i		−	1.89825i	−0.314896	−	0.949126i	$-0.601970\pi$
$673$		−	859774.i		−	1.89825i	0.314896	−	0.949126i	$-0.398030\pi$
$674$	278736.			0.613583
$675$	−11370.1	−	35312.8i	−0.0249549	−	0.0775041i
$676$	−457144.			−1.00037
$677$	−770343.			−1.68076			−0.840382	−	0.541995i	$-0.817669\pi$
$677$	−770343.			−1.68076			−0.840382	+	0.541995i	$0.817669\pi$
$678$	562561.			1.22380
$679$		0			0
$680$	56209.8	+	40953.1i	0.121561	+	0.0885664i
$681$	−309650.			−0.667693
$682$	293.557			0.000631136
$683$			902432.i			1.93452i	0.253789	+	0.967260i	$0.418323\pi$
$683$			902432.i			1.93452i	−0.253789	+	0.967260i	$0.581677\pi$
$684$			53416.8i			0.114174i
$685$	−292656.	−	213222.i	−0.623701	−	0.454414i
$686$		0			0
$687$		−	421375.i		−	0.892803i
$688$			26299.6i			0.0555612i
$689$			582083.i			1.22616i
$690$	268558.	−	368607.i	0.564080	−	0.774222i
$691$		−	230372.i		−	0.482474i	−0.970466	−	0.241237i	$-0.922447\pi$
$691$		−	230372.i		−	0.482474i	0.970466	−	0.241237i	$-0.0775532\pi$
$692$	−182380.			−0.380860
$693$		0			0
$694$	−129856.			−0.269614
$695$	404373.	+	294616.i	0.837167	+	0.609940i
$696$			264365.i			0.545740i
$697$		−	312323.i		−	0.642892i
$698$	39763.0			0.0816148
$699$		−	323618.i		−	0.662336i
$700$		0			0
$701$	236661.			0.481604			0.240802	−	0.970574i	$-0.422590\pi$
$701$	236661.			0.481604			0.240802	+	0.970574i	$0.422590\pi$
$702$		−	49149.3i		−	0.0997340i
$703$	−151334.			−0.306215
$704$	3687.82			0.00744088
$705$	−561019.	+	770021.i	−1.12875	+	1.54926i
$706$		−	37968.1i		−	0.0761746i
$707$		0			0
$708$			392631.i			0.783281i
$709$	−62819.6			−0.124969			−0.0624845	−	0.998046i	$-0.519902\pi$
$709$	−62819.6			−0.124969			−0.0624845	+	0.998046i	$0.519902\pi$
$710$	−105400.	−	76792.0i	−0.209086	−	0.152335i
$711$	−288328.			−0.570359
$712$	3387.09			0.00668139
$713$	7410.88			0.0145778
$714$		0			0
$715$	−31042.2	+	42606.7i	−0.0607212	+	0.0833423i
$716$	98645.7			0.192421
$717$	392428.			0.763347
$718$		−	274643.i		−	0.532745i
$719$		−	513270.i		−	0.992861i	−0.868076	−	0.496431i	$-0.834644\pi$
$719$		−	513270.i		−	0.992861i	0.868076	−	0.496431i	$-0.165356\pi$
$720$	−71856.8	+	98626.4i	−0.138613	+	0.190252i
$721$		0			0
$722$			346924.i			0.665518i
$723$			457676.i			0.875551i
$724$			284447.i			0.542655i
$725$	−178461.	−	554257.i	−0.339521	−	1.05447i
$726$			517479.i			0.981792i
$727$	724922.			1.37158			0.685792	−	0.727797i	$-0.259456\pi$
$727$	724922.			1.37158			0.685792	+	0.727797i	$0.259456\pi$
$728$		0			0
$729$	−467624.			−0.879916
$730$	605718.	+	441312.i	1.13665	+	0.828132i
$731$			50520.6i			0.0945439i
$732$			478558.i			0.893125i
$733$	331377.			0.616758			0.308379	−	0.951264i	$-0.400214\pi$
$733$	331377.			0.616758			0.308379	+	0.951264i	$0.400214\pi$
$734$		−	33013.9i		−	0.0612780i
$735$		0			0
$736$	93099.6			0.171867
$737$		−	55101.0i		−	0.101444i
$738$	548005.			1.00617
$739$	264589.			0.484489			0.242244	−	0.970215i	$-0.422116\pi$
$739$	264589.			0.484489			0.242244	+	0.970215i	$0.422116\pi$
$740$	−279416.	−	203576.i	−0.510256	−	0.371760i
$741$		−	321419.i		−	0.585376i
$742$		0			0
$743$			105627.i			0.191337i	0.995413	+	0.0956683i	$0.0304988\pi$
$743$			105627.i			0.191337i	−0.995413	+	0.0956683i	$0.969501\pi$
$744$	−4088.84			−0.00738677
$745$	−265872.	+	364920.i	−0.479027	+	0.657485i
$746$	−559327.			−1.00505
$747$	−279276.			−0.500486
$748$	7084.18			0.0126615
$749$		0			0
$750$	173365.	−	526409.i	0.308204	−	0.935838i
$751$	−955586.			−1.69430			−0.847149	−	0.531355i	$-0.821683\pi$
$751$	−955586.			−1.69430			−0.847149	+	0.531355i	$0.821683\pi$
$752$	−194485.			−0.343915
$753$		−	869780.i		−	1.53398i
$754$		−	771430.i		−	1.35692i
$755$	264410.	−	362914.i	0.463857	−	0.636663i
$756$		0			0
$757$		−	1.03602e6i		−	1.80791i	−0.427624	−	0.903957i	$-0.640649\pi$
$757$		−	1.03602e6i		−	1.80791i	0.427624	−	0.903957i	$-0.359351\pi$
$758$		−	24051.4i		−	0.0418602i
$759$		−	46455.9i		−	0.0806413i
$760$	29163.5	−	40028.1i	0.0504908	−	0.0693007i
$761$		−	1.09775e6i		−	1.89554i	−0.318957	−	0.947769i	$-0.603332\pi$
$761$		−	1.09775e6i		−	1.89554i	0.318957	−	0.947769i	$-0.396668\pi$
$762$	−138531.			−0.238582
$763$		0			0
$764$	431565.			0.739366
$765$	−138034.	+	189458.i	−0.235866	+	0.323735i
$766$		−	651047.i		−	1.10957i
$767$		−	1.14571e6i		−	1.94754i
$768$	−51366.3			−0.0870875
$769$			610743.i			1.03278i	0.856355	+	0.516388i	$0.172724\pi$
$769$			610743.i			1.03278i	−0.856355	+	0.516388i	$0.827276\pi$
$770$		0			0
$771$	−1.38055e6			−2.32244
$772$			19320.6i			0.0324181i
$773$	−110846.			−0.185507			−0.0927536	−	0.995689i	$-0.529567\pi$
$773$	−110846.			−0.185507			−0.0927536	+	0.995689i	$0.529567\pi$
$774$	−88643.9			−0.147968
$775$	8572.49	−	2760.19i	0.0142726	−	0.00459553i
$776$		−	288592.i		−	0.479248i
$777$		0			0
$778$			226297.i			0.373870i
$779$	−222411.			−0.366506
$780$	432376.	−	593453.i	0.710677	−	0.975433i
$781$	−13283.7			−0.0217779
$782$	178841.			0.292451
$783$	55299.8			0.0901986
$784$		0			0
$785$	216458.	−	297097.i	0.351264	−	0.482125i
$786$	−1.16410e6			−1.88427
$787$	27520.1			0.0444325			0.0222163	−	0.999753i	$-0.492928\pi$
$787$	27520.1			0.0444325			0.0222163	+	0.999753i	$0.492928\pi$
$788$		−	208411.i		−	0.335636i
$789$		−	7140.37i		−	0.0114701i
$790$	216060.	+	157416.i	0.346195	+	0.252229i
$791$		0			0
$792$			12430.0i			0.0198162i
$793$		−	1.39645e6i		−	2.22065i
$794$			134947.i			0.214054i
$795$	−503826.	−	367075.i	−0.797162	−	0.580793i
$796$			10566.8i			0.0166770i
$797$	−793651.			−1.24943			−0.624717	−	0.780852i	$-0.714786\pi$
$797$	−793651.			−1.24943			−0.624717	+	0.780852i	$0.714786\pi$
$798$		0			0
$799$	−373599.			−0.585211
$800$	107692.	−	34675.0i	0.168269	−	0.0541798i
$801$			11416.4i			0.0177936i
$802$			153046.i			0.237942i
$803$	76339.2			0.118390
$804$			767482.i			1.18729i
$805$		0			0
$806$	11931.4			0.0183663
$807$			717340.i			1.10148i
$808$	260255.			0.398635
$809$	134444.			0.205421			0.102710	−	0.994711i	$-0.467249\pi$
$809$	134444.			0.205421			0.102710	+	0.994711i	$0.467249\pi$
$810$	395597.	+	288223.i	0.602953	+	0.439297i
$811$		−	1.12692e6i		−	1.71337i	−0.515838	−	0.856686i	$-0.672519\pi$
$811$		−	1.12692e6i		−	1.71337i	0.515838	−	0.856686i	$-0.327481\pi$
$812$		0			0
$813$		−	1.05295e6i		−	1.59304i
$814$	−35215.1			−0.0531472
$815$	−284576.	−	207335.i	−0.428433	−	0.312146i
$816$	−98673.0			−0.148190
$817$	35976.6			0.0538985
$818$	−515571.			−0.770517
$819$		0			0
$820$	−410650.	−	299189.i	−0.610722	−	0.444957i
$821$	357314.			0.530108			0.265054	−	0.964234i	$-0.414610\pi$
$821$	357314.			0.530108			0.265054	+	0.964234i	$0.414610\pi$
$822$	513741.			0.760327
$823$			572975.i			0.845933i	0.906145	+	0.422967i	$0.139011\pi$
$823$			572975.i			0.845933i	−0.906145	+	0.422967i	$0.860989\pi$
$824$		−	171360.i		−	0.252380i
$825$	−17302.6	−	53737.6i	−0.0254216	−	0.0789533i
$826$		0			0
$827$			985411.i			1.44081i	0.693554	+	0.720405i	$0.256044\pi$
$827$			985411.i			1.44081i	−0.693554	+	0.720405i	$0.743956\pi$
$828$			313797.i			0.457707i
$829$		−	114256.i		−	0.166253i	−0.996539	−	0.0831267i	$-0.973509\pi$
$829$		−	114256.i		−	0.166253i	0.996539	−	0.0831267i	$-0.0264906\pi$
$830$	209276.	+	152474.i	0.303784	+	0.221329i
$831$		−	731898.i		−	1.05986i
$832$	149889.			0.216533
$833$		0			0
$834$	−709852.			−1.02055
$835$	633133.	−	869001.i	0.908076	−	1.24637i
$836$		−	5044.78i		−	0.00721821i
$837$			855.301i			0.00122087i
$838$	−143751.			−0.204702
$839$			808131.i			1.14804i	0.818841	+	0.574021i	$0.194617\pi$
$839$			808131.i			1.14804i	−0.818841	+	0.574021i	$0.805383\pi$
$840$		0			0
$841$	160684.			0.227185
$842$			30353.0i			0.0428132i
$843$	−367240.			−0.516766
$844$	42965.7			0.0603166
$845$	−841231.	+	1.15462e6i	−1.17815	+	1.61706i
$846$		−	655522.i		−	0.915896i
$847$		0			0
$848$		−	127252.i		−	0.176959i
$849$	−1.61217e6			−2.23663
$850$	206873.	−	66609.6i	0.286330	−	0.0921932i
$851$	−889011.			−1.22757
$852$	185024.			0.254887
$853$	1.24179e6			1.70668			0.853338	−	0.521358i	$-0.174574\pi$
$853$	1.24179e6			1.70668			0.853338	+	0.521358i	$0.174574\pi$
$854$		0			0
$855$	134917.	+	98297.0i	0.184558	+	0.134465i
$856$	−143004.			−0.195164
$857$	42353.6			0.0576672			0.0288336	−	0.999584i	$-0.490821\pi$
$857$	42353.6			0.0576672			0.0288336	+	0.999584i	$0.490821\pi$
$858$		−	74793.5i		−	0.101599i
$859$			873616.i			1.18395i	0.805956	+	0.591976i	$0.201652\pi$
$859$			873616.i			1.18395i	−0.805956	+	0.591976i	$0.798348\pi$
$860$	66425.7	+	48396.1i	0.0898130	+	0.0654356i
$861$		0			0
$862$			237485.i			0.319611i
$863$			1.18302e6i			1.58844i	0.607631	+	0.794219i	$0.292120\pi$
$863$			1.18302e6i			1.58844i	−0.607631	+	0.794219i	$0.707880\pi$
$864$			10744.8i			0.0143936i
$865$	−335614.	+	460644.i	−0.448547	+	0.615649i
$866$		−	20222.5i		−	0.0269649i
$867$	857857.			1.14124
$868$		0			0
$869$	27230.3			0.0360589
$870$	667717.	+	486482.i	0.882173	+	0.642730i
$871$		−	2.23955e6i		−	2.95205i
$872$		−	443760.i		−	0.583600i
$873$	972712.			1.27631
$874$		−	127356.i		−	0.166724i
$875$		0			0
$876$	−1.06330e6			−1.38563
$877$			17710.5i			0.0230268i	0.999934	+	0.0115134i	$0.00366490\pi$
$877$			17710.5i			0.0230268i	−0.999934	+	0.0115134i	$0.996335\pi$
$878$	717150.			0.930296
$879$	−1.59765e6			−2.06778
$880$	6786.28	−	9314.45i	0.00876328	−	0.0120280i
$881$			761550.i			0.981175i	0.871392	+	0.490588i	$0.163218\pi$
$881$			761550.i			0.981175i	−0.871392	+	0.490588i	$0.836782\pi$
$882$		0			0
$883$			1.12110e6i			1.43789i	0.695069	+	0.718943i	$0.255374\pi$
$883$			1.12110e6i			1.43789i	−0.695069	+	0.718943i	$0.744626\pi$
$884$	287932.			0.368456
$885$	991680.	+	722514.i	1.26615	+	0.922486i
$886$	−201968.			−0.257285
$887$	494682.			0.628751			0.314376	−	0.949299i	$-0.398205\pi$
$887$	494682.			0.628751			0.314376	+	0.949299i	$0.398205\pi$
$888$	490499.			0.622031
$889$		0			0
$890$	6232.89	−	8554.89i	0.00786881	−	0.0108003i
$891$	49857.5			0.0628022
$892$	−511186.			−0.642465
$893$			266047.i			0.333623i
$894$		−	640596.i		−	0.801510i
$895$	181527.	−	249153.i	0.226618	−	0.311042i
$896$		0			0
$897$		−	1.88817e6i		−	2.34670i
$898$			891099.i			1.10503i
$899$			13424.5i			0.0166103i
$900$	116874.	+	362982.i	0.144289	+	0.448126i
$901$		−	244447.i		−	0.301116i
$902$	−51754.5			−0.0636115
$903$		0			0
$904$	358873.			0.439141
$905$	718437.	+	523436.i	0.877185	+	0.639096i
$906$			637073.i			0.776127i
$907$			124964.i			0.151905i	0.997111	+	0.0759525i	$0.0241997\pi$
$907$			124964.i			0.151905i	−0.997111	+	0.0759525i	$0.975800\pi$
$908$	−197534.			−0.239591
$909$			877201.i			1.06163i
$910$		0			0
$911$	1.43305e6			1.72673			0.863366	−	0.504578i	$-0.168352\pi$
$911$	1.43305e6			1.72673			0.863366	+	0.504578i	$0.168352\pi$
$912$			70266.9i			0.0844814i
$913$	26375.3			0.0316414
$914$	196313.			0.234994
$915$	1.20871e6	+	880636.i	1.44371	+	1.05185i
$916$		−	268807.i		−	0.320368i
$917$		0			0
$918$			20640.3i			0.0244924i
$919$	1.44340e6			1.70905			0.854527	−	0.519408i	$-0.173847\pi$
$919$	1.44340e6			1.70905			0.854527	+	0.519408i	$0.173847\pi$
$920$	171321.	−	235145.i	0.202411	−	0.277818i
$921$	−800013.			−0.943144
$922$	471926.			0.555152
$923$	−539907.			−0.633747
$924$		0			0
$925$	−1.02836e6	+	331113.i	−1.20188	+	0.386984i
$926$	−471982.			−0.550432
$927$	577578.			0.672126
$928$			168646.i			0.195830i
$929$			527717.i			0.611463i	0.952118	+	0.305731i	$0.0989009\pi$
$929$			527717.i			0.611463i	−0.952118	+	0.305731i	$0.901099\pi$
$930$	−7524.24	+	10327.3i	−0.00869955	+	0.0119405i
$931$		0			0
$932$		−	206445.i		−	0.237669i
$933$		−	254856.i		−	0.292773i
$934$		−	516320.i		−	0.591868i
$935$	13036.2	−	17892.7i	0.0149117	−	0.0204670i
$936$			505209.i			0.576659i
$937$	37174.4			0.0423413			0.0211707	−	0.999776i	$-0.493261\pi$
$937$	37174.4			0.0423413			0.0211707	+	0.999776i	$0.493261\pi$
$938$		0			0
$939$	−1.21692e6			−1.38016
$940$	−357889.	+	491218.i	−0.405035	+	0.555928i
$941$		−	776066.i		−	0.876434i	−0.898869	−	0.438217i	$-0.855610\pi$
$941$		−	776066.i		−	0.876434i	0.898869	−	0.438217i	$-0.144390\pi$
$942$			521537.i			0.587737i
$943$	−1.30655e6			−1.46928
$944$			250470.i			0.281068i
$945$		0			0
$946$	8371.69			0.00935472
$947$			248082.i			0.276628i	0.990388	+	0.138314i	$0.0441683\pi$
$947$			248082.i			0.276628i	−0.990388	+	0.138314i	$0.955832\pi$
$948$	−379280.			−0.422030
$949$	3.10276e6			3.44521
$950$	−47433.9	−	147318.i	−0.0525584	−	0.163234i
$951$			267702.i			0.295999i
$952$		0			0
$953$			899097.i			0.989968i	0.868902	+	0.494984i	$0.164826\pi$
$953$			899097.i			0.989968i	−0.868902	+	0.494984i	$0.835174\pi$
$954$	428909.			0.471268
$955$	794160.	−	1.09002e6i	0.870766	−	1.19516i
$956$	250341.			0.273915
$957$	84153.0			0.0918852
$958$	203839.			0.222104
$959$		0			0
$960$	−94523.7	+	129738.i	−0.102565	+	0.140774i
$961$	923313.			0.999775
$962$	−1.43130e6			−1.54661
$963$		−	482002.i		−	0.519752i
$964$			291964.i			0.314178i
$965$	48798.8	+	35553.6i	0.0524028	+	0.0381794i
$966$		0			0
$967$		−	603847.i		−	0.645764i	−0.946439	−	0.322882i	$-0.895348\pi$
$967$		−	603847.i		−	0.645764i	0.946439	−	0.322882i	$-0.104652\pi$
$968$			330114.i			0.352301i
$969$			134980.i			0.143755i
$970$	−728905.	−	531063.i	−0.774690	−	0.564420i
$971$		−	1.17983e6i		−	1.25136i	−0.780080	−	0.625679i	$-0.784822\pi$
$971$		−	1.17983e6i		−	1.25136i	0.780080	−	0.625679i	$-0.215178\pi$
$972$	−655984.			−0.694321
$973$		0			0
$974$	241862.			0.254947
$975$	−703252.	−	2.18413e6i	−0.739779	−	2.29757i
$976$			305285.i			0.320484i
$977$		−	1.33150e6i		−	1.39493i	−0.716621	−	0.697463i	$-0.754312\pi$
$977$		−	1.33150e6i		−	1.39493i	0.716621	−	0.697463i	$-0.245688\pi$
$978$	499557.			0.522284
$979$		−	1078.18i		−	0.00112493i
$980$		0			0
$981$	1.49571e6			1.55421
$982$		−	1.02066e6i		−	1.05842i
$983$	−454887.			−0.470757			−0.235378	−	0.971904i	$-0.575633\pi$
$983$	−454887.			−0.470757			−0.235378	+	0.971904i	$0.575633\pi$
$984$	720871.			0.744504
$985$	−526391.	−	383516.i	−0.542546	−	0.395286i
$986$			323963.i			0.333228i
$987$		0			0
$988$		−	205042.i		−	0.210053i
$989$	211345.			0.216072
$990$	31394.8	+	22873.5i	0.0320323	+	0.0233379i
$991$	−1.26573e6			−1.28883			−0.644415	−	0.764676i	$-0.722899\pi$
$991$	−1.26573e6			−1.28883			−0.644415	+	0.764676i	$0.722899\pi$
$992$	−2608.39			−0.00265063
$993$	−727616.			−0.737911
$994$		0			0
$995$	26689.0	+	19445.0i	0.0269579	+	0.0196409i
$996$	−367372.			−0.370329
$997$	1.44225e6			1.45094			0.725472	−	0.688252i	$-0.241621\pi$
$997$	1.44225e6			1.45094			0.725472	+	0.688252i	$0.241621\pi$
$998$		−	1.09318e6i		−	1.09756i
$999$		−	102602.i		−	0.102808i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.5.d.a.489.18		32
5.4	even	2	inner	490.5.d.a.489.19		32
7.2	even	3		70.5.h.a.59.15	yes	32
7.3	odd	6		70.5.h.a.19.2	✓	32
7.6	odd	2	inner	490.5.d.a.489.20		32
35.2	odd	12		350.5.k.e.101.16		32
35.3	even	12		350.5.k.e.201.1		32
35.9	even	6		70.5.h.a.59.2	yes	32
35.17	even	12		350.5.k.e.201.16		32
35.23	odd	12		350.5.k.e.101.1		32
35.24	odd	6		70.5.h.a.19.15	yes	32
35.34	odd	2	inner	490.5.d.a.489.17		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.5.h.a.19.2	✓	32	7.3	odd	6
70.5.h.a.19.15	yes	32	35.24	odd	6
70.5.h.a.59.2	yes	32	35.9	even	6
70.5.h.a.59.15	yes	32	7.2	even	3
350.5.k.e.101.1		32	35.23	odd	12
350.5.k.e.101.16		32	35.2	odd	12
350.5.k.e.201.1		32	35.3	even	12
350.5.k.e.201.16		32	35.17	even	12
490.5.d.a.489.17		32	35.34	odd	2	inner
490.5.d.a.489.18		32	1.1	even	1	trivial
490.5.d.a.489.19		32	5.4	even	2	inner
490.5.d.a.489.20		32	7.6	odd	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	490.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843i q^{2} -12.5406 q^{3} -8.00000 q^{4} +(-14.7215 + 20.2059i) q^{5} -35.4702i q^{6} -22.6274i q^{8} +76.2668 q^{9} +O(q^{10})\)	\(q+2.82843i q^{2} -12.5406 q^{3} -8.00000 q^{4} +(-14.7215 + 20.2059i) q^{5} -35.4702i q^{6} -22.6274i q^{8} +76.2668 q^{9} +(-57.1508 - 41.6387i) q^{10} -7.20277 q^{11} +100.325 q^{12} -292.752 q^{13} +(184.617 - 253.394i) q^{15} +64.0000 q^{16} +122.942 q^{17} +215.715i q^{18} -87.5492i q^{19} +(117.772 - 161.647i) q^{20} -20.3725i q^{22} -514.307i q^{23} +283.762i q^{24} +(-191.554 - 594.922i) q^{25} -828.029i q^{26} +59.3570 q^{27} +931.646 q^{29} +(716.706 + 522.175i) q^{30} +14.4094i q^{31} +181.019i q^{32} +90.3271 q^{33} +347.732i q^{34} -610.135 q^{36} -1728.56i q^{37} +247.627 q^{38} +3671.29 q^{39} +(457.207 + 333.110i) q^{40} -2540.41i q^{41} +410.931i q^{43} +57.6222 q^{44} +(-1122.76 + 1541.04i) q^{45} +1454.68 q^{46} -3038.83 q^{47} -802.599 q^{48} +(1682.69 - 541.798i) q^{50} -1541.76 q^{51} +2342.02 q^{52} -1988.31i q^{53} +167.887i q^{54} +(106.036 - 145.538i) q^{55} +1097.92i q^{57} +2635.09i q^{58} +3913.59i q^{59} +(-1476.93 + 2027.15i) q^{60} +4770.08i q^{61} -40.7560 q^{62} -512.000 q^{64} +(4309.76 - 5915.32i) q^{65} +255.484i q^{66} +7649.97i q^{67} -983.534 q^{68} +6449.73i q^{69} +1844.25 q^{71} -1725.72i q^{72} -10598.6 q^{73} +4889.10 q^{74} +(2402.21 + 7460.68i) q^{75} +700.394i q^{76} +10384.0i q^{78} -3780.52 q^{79} +(-942.177 + 1293.18i) q^{80} -6921.99 q^{81} +7185.36 q^{82} -3661.83 q^{83} +(-1809.89 + 2484.15i) q^{85} -1162.29 q^{86} -11683.4 q^{87} +162.980i q^{88} +149.690i q^{89} +(-4358.71 - 3175.65i) q^{90} +4114.46i q^{92} -180.703i q^{93} -8595.11i q^{94} +(1769.01 + 1288.86i) q^{95} -2270.09i q^{96} +12754.1 q^{97} -549.333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 256 q^{4} + 1032 q^{9}+O(q^{10}) \) 32 * q - 256 * q^4 + 1032 * q^9	\( 32 q - 256 q^{4} + 1032 q^{9} + 288 q^{11} - 76 q^{15} + 2048 q^{16} - 588 q^{25} + 912 q^{29} - 1216 q^{30} - 8256 q^{36} + 4848 q^{39} - 2304 q^{44} - 3328 q^{46} + 15744 q^{50} - 5416 q^{51} + 608 q^{60} - 16384 q^{64} - 1872 q^{65} - 53808 q^{71} + 12672 q^{74} + 48152 q^{79} - 35360 q^{81} + 8324 q^{85} - 13248 q^{86} - 85980 q^{95} + 101048 q^{99}+O(q^{100}) \) 32 * q - 256 * q^4 + 1032 * q^9 + 288 * q^11 - 76 * q^15 + 2048 * q^16 - 588 * q^25 + 912 * q^29 - 1216 * q^30 - 8256 * q^36 + 4848 * q^39 - 2304 * q^44 - 3328 * q^46 + 15744 * q^50 - 5416 * q^51 + 608 * q^60 - 16384 * q^64 - 1872 * q^65 - 53808 * q^71 + 12672 * q^74 + 48152 * q^79 - 35360 * q^81 + 8324 * q^85 - 13248 * q^86 - 85980 * q^95 + 101048 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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