LMFDB - Embedded newform 490.4.c.f.99.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(99,490)]

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, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("490.99");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.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:	$28.9109359028$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 185x^{10} + 12748x^{8} + 405460x^{6} + 5908496x^{4} + 33016000x^{2} + 60840000 $ x^12 + 185x^10 + 12748x^8 + 405460x^6 + 5908496x^4 + 33016000*x^2 + 60840000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.6
Root			$8.18765i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.4.c.f.99.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +9.18765i q^{3} -4.00000 q^{4} +(8.58556 - 7.16157i) q^{5} +18.3753 q^{6} +8.00000i q^{8} -57.4130 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +9.18765i q^{3} -4.00000 q^{4} +(8.58556 - 7.16157i) q^{5} +18.3753 q^{6} +8.00000i q^{8} -57.4130 q^{9} +(-14.3231 - 17.1711i) q^{10} +35.4764 q^{11} -36.7506i q^{12} -45.5531i q^{13} +(65.7981 + 78.8812i) q^{15} +16.0000 q^{16} -93.7447i q^{17} +114.826i q^{18} -44.8775 q^{19} +(-34.3422 + 28.6463i) q^{20} -70.9527i q^{22} -122.473i q^{23} -73.5012 q^{24} +(22.4238 - 122.972i) q^{25} -91.1063 q^{26} -279.424i q^{27} +17.8390 q^{29} +(157.762 - 131.596i) q^{30} +27.1587 q^{31} -32.0000i q^{32} +325.945i q^{33} -187.489 q^{34} +229.652 q^{36} +78.0182i q^{37} +89.7550i q^{38} +418.526 q^{39} +(57.2926 + 68.6845i) q^{40} -21.0352 q^{41} +467.300i q^{43} -141.905 q^{44} +(-492.923 + 411.167i) q^{45} -244.946 q^{46} -578.861i q^{47} +147.002i q^{48} +(-245.945 - 44.8475i) q^{50} +861.294 q^{51} +182.213i q^{52} -161.262i q^{53} -558.848 q^{54} +(304.584 - 254.067i) q^{55} -412.319i q^{57} -35.6781i q^{58} +559.436 q^{59} +(-263.192 - 315.525i) q^{60} -108.776 q^{61} -54.3174i q^{62} -64.0000 q^{64} +(-326.232 - 391.099i) q^{65} +651.889 q^{66} -407.643i q^{67} +374.979i q^{68} +1125.24 q^{69} +1159.37 q^{71} -459.304i q^{72} +256.677i q^{73} +156.036 q^{74} +(1129.83 + 206.022i) q^{75} +179.510 q^{76} -837.053i q^{78} +853.583 q^{79} +(137.369 - 114.585i) q^{80} +1017.10 q^{81} +42.0703i q^{82} -828.152i q^{83} +(-671.359 - 804.851i) q^{85} +934.599 q^{86} +163.899i q^{87} +283.811i q^{88} -164.983 q^{89} +(822.335 + 985.846i) q^{90} +489.892i q^{92} +249.525i q^{93} -1157.72 q^{94} +(-385.299 + 321.394i) q^{95} +294.005 q^{96} -38.6575i q^{97} -2036.80 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 48 q^{4} + 8 q^{5} + 28 q^{6} - 62 q^{9}+O(q^{10}) $ 12 * q - 48 * q^4 + 8 * q^5 + 28 * q^6 - 62 * q^9	$ 12 q - 48 q^{4} + 8 q^{5} + 28 q^{6} - 62 q^{9} - 12 q^{10} + 62 q^{11} + 86 q^{15} + 192 q^{16} - 186 q^{19} - 32 q^{20} - 112 q^{24} - 126 q^{25} + 236 q^{26} - 338 q^{29} - 28 q^{30} + 652 q^{31} - 272 q^{34} + 248 q^{36} + 868 q^{39} + 48 q^{40} + 396 q^{41} - 248 q^{44} - 664 q^{45} - 376 q^{46} + 160 q^{50} + 1448 q^{51} - 1540 q^{54} + 298 q^{55} - 1336 q^{59} - 344 q^{60} + 314 q^{61} - 768 q^{64} - 1862 q^{65} + 1600 q^{66} + 90 q^{69} + 2216 q^{71} + 1012 q^{74} + 4550 q^{75} + 744 q^{76} + 1772 q^{79} + 128 q^{80} - 1228 q^{81} + 2282 q^{85} - 396 q^{86} - 6094 q^{89} + 100 q^{90} - 3604 q^{94} - 1166 q^{95} + 448 q^{96} - 8546 q^{99}+O(q^{100}) $ 12 * q - 48 * q^4 + 8 * q^5 + 28 * q^6 - 62 * q^9 - 12 * q^10 + 62 * q^11 + 86 * q^15 + 192 * q^16 - 186 * q^19 - 32 * q^20 - 112 * q^24 - 126 * q^25 + 236 * q^26 - 338 * q^29 - 28 * q^30 + 652 * q^31 - 272 * q^34 + 248 * q^36 + 868 * q^39 + 48 * q^40 + 396 * q^41 - 248 * q^44 - 664 * q^45 - 376 * q^46 + 160 * q^50 + 1448 * q^51 - 1540 * q^54 + 298 * q^55 - 1336 * q^59 - 344 * q^60 + 314 * q^61 - 768 * q^64 - 1862 * q^65 + 1600 * q^66 + 90 * q^69 + 2216 * q^71 + 1012 * q^74 + 4550 * q^75 + 744 * q^76 + 1772 * q^79 + 128 * q^80 - 1228 * q^81 + 2282 * q^85 - 396 * q^86 - 6094 * q^89 + 100 * q^90 - 3604 * q^94 - 1166 * q^95 + 448 * q^96 - 8546 * 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 $

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$			9.18765i			1.76816i	0.467331	+	0.884082i	$0.345216\pi$
$3$			9.18765i			1.76816i	−0.467331	+	0.884082i	$0.654784\pi$
$4$	−4.00000			−0.500000
$5$	8.58556	−	7.16157i	0.767916	−	0.640551i
$5$	8.58556	−	7.16157i	0.767916	−	0.640551i
$6$	18.3753			1.25028
$7$		0			0
$7$		0			0
$8$			8.00000i			0.353553i
$9$	−57.4130			−2.12641
$10$	−14.3231	−	17.1711i	−0.452938	−	0.542999i
$11$	35.4764			0.972411			0.486206	−	0.873844i	$-0.338381\pi$
$11$	35.4764			0.972411			0.486206	+	0.873844i	$0.338381\pi$
$12$		−	36.7506i		−	0.884082i
$13$		−	45.5531i		−	0.971859i	−0.873998	−	0.485930i	$-0.838481\pi$
$13$		−	45.5531i		−	0.971859i	0.873998	−	0.485930i	$-0.161519\pi$
$14$		0			0
$15$	65.7981	+	78.8812i	1.13260	+	1.35780i
$16$	16.0000			0.250000
$17$		−	93.7447i		−	1.33744i	−0.743516	−	0.668718i	$-0.766843\pi$
$17$		−	93.7447i		−	1.33744i	0.743516	−	0.668718i	$-0.233157\pi$
$18$			114.826i			1.50360i
$19$	−44.8775			−0.541874			−0.270937	−	0.962597i	$-0.587334\pi$
$19$	−44.8775			−0.541874			−0.270937	+	0.962597i	$0.587334\pi$
$20$	−34.3422	+	28.6463i	−0.383958	+	0.320275i
$21$		0			0
$22$		−	70.9527i		−	0.687599i
$23$		−	122.473i		−	1.11032i	−0.831743	−	0.555161i	$-0.812657\pi$
$23$		−	122.473i		−	1.11032i	0.831743	−	0.555161i	$-0.187343\pi$
$24$	−73.5012			−0.625141
$25$	22.4238	−	122.972i	0.179390	−	0.983778i
$26$	−91.1063			−0.687208
$27$		−	279.424i		−	1.99167i
$28$		0			0
$29$	17.8390			0.114228			0.0571142	−	0.998368i	$-0.481810\pi$
$29$	17.8390			0.114228			0.0571142	+	0.998368i	$0.481810\pi$
$30$	157.762	−	131.596i	0.960111	−	0.800868i
$31$	27.1587			0.157350			0.0786749	−	0.996900i	$-0.474931\pi$
$31$	27.1587			0.157350			0.0786749	+	0.996900i	$0.474931\pi$
$32$		−	32.0000i		−	0.176777i
$33$			325.945i			1.71938i
$34$	−187.489			−0.945711
$35$		0			0
$36$	229.652			1.06320
$37$			78.0182i			0.346652i	0.984865	+	0.173326i	$0.0554514\pi$
$37$			78.0182i			0.346652i	−0.984865	+	0.173326i	$0.944549\pi$
$38$			89.7550i			0.383163i
$39$	418.526			1.71841
$40$	57.2926	+	68.6845i	0.226469	+	0.271499i
$41$	−21.0352			−0.0801254			−0.0400627	−	0.999197i	$-0.512756\pi$
$41$	−21.0352			−0.0801254			−0.0400627	+	0.999197i	$0.512756\pi$
$42$		0			0
$43$			467.300i			1.65727i	0.559791	+	0.828634i	$0.310882\pi$
$43$			467.300i			1.65727i	−0.559791	+	0.828634i	$0.689118\pi$
$44$	−141.905			−0.486206
$45$	−492.923	+	411.167i	−1.63290	+	1.36207i
$46$	−244.946			−0.785116
$47$		−	578.861i		−	1.79650i	−0.439484	−	0.898250i	$-0.644839\pi$
$47$		−	578.861i		−	1.79650i	0.439484	−	0.898250i	$-0.355161\pi$
$48$			147.002i			0.442041i
$49$		0			0
$50$	−245.945	−	44.8475i	−0.695636	−	0.126848i
$51$	861.294			2.36481
$52$			182.213i			0.485930i
$53$		−	161.262i		−	0.417944i	−0.977922	−	0.208972i	$-0.932988\pi$
$53$		−	161.262i		−	0.417944i	0.977922	−	0.208972i	$-0.0670118\pi$
$54$	−558.848			−1.40833
$55$	304.584	−	254.067i	0.746730	−	0.622879i
$56$		0			0
$57$		−	412.319i		−	0.958123i
$58$		−	35.6781i		−	0.0807717i
$59$	559.436			1.23445			0.617223	−	0.786788i	$-0.288258\pi$
$59$	559.436			1.23445			0.617223	+	0.786788i	$0.288258\pi$
$60$	−263.192	−	315.525i	−0.566299	−	0.678901i
$61$	−108.776			−0.228318			−0.114159	−	0.993463i	$-0.536417\pi$
$61$	−108.776			−0.228318			−0.114159	+	0.993463i	$0.536417\pi$
$62$		−	54.3174i		−	0.111263i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−326.232	−	391.099i	−0.622525	−	0.746306i
$66$	651.889			1.21579
$67$		−	407.643i		−	0.743307i	−0.928372	−	0.371653i	$-0.878791\pi$
$67$		−	407.643i		−	0.743307i	0.928372	−	0.371653i	$-0.121209\pi$
$68$			374.979i			0.668718i
$69$	1125.24			1.96323
$70$		0			0
$71$	1159.37			1.93791			0.968954	−	0.247243i	$-0.0795245\pi$
$71$	1159.37			1.93791			0.968954	+	0.247243i	$0.0795245\pi$
$72$		−	459.304i		−	0.751798i
$73$			256.677i			0.411531i	0.978601	+	0.205766i	$0.0659685\pi$
$73$			256.677i			0.411531i	−0.978601	+	0.205766i	$0.934032\pi$
$74$	156.036			0.245120
$75$	1129.83	+	206.022i	1.73948	+	0.317191i
$76$	179.510			0.270937
$77$		0			0
$78$		−	837.053i		−	1.21510i
$79$	853.583			1.21564			0.607820	−	0.794075i	$-0.292044\pi$
$79$	853.583			1.21564			0.607820	+	0.794075i	$0.292044\pi$
$80$	137.369	−	114.585i	0.191979	−	0.160138i
$81$	1017.10			1.39520
$82$			42.0703i			0.0566572i
$83$		−	828.152i		−	1.09520i	−0.836741	−	0.547599i	$-0.815542\pi$
$83$		−	828.152i		−	1.09520i	0.836741	−	0.547599i	$-0.184458\pi$
$84$		0			0
$85$	−671.359	−	804.851i	−0.856696	−	1.02704i
$86$	934.599			1.17187
$87$			163.899i			0.201975i
$88$			283.811i			0.343799i
$89$	−164.983			−0.196497			−0.0982483	−	0.995162i	$-0.531324\pi$
$89$	−164.983			−0.196497			−0.0982483	+	0.995162i	$0.531324\pi$
$90$	822.335	+	985.846i	0.963130	+	1.15464i
$91$		0			0
$92$			489.892i			0.555161i
$93$			249.525i			0.278220i
$94$	−1157.72			−1.27032
$95$	−385.299	+	321.394i	−0.416114	+	0.347098i
$96$	294.005			0.312570
$97$		−	38.6575i		−	0.0404647i	−0.999795	−	0.0202324i	$-0.993559\pi$
$97$		−	38.6575i		−	0.0404647i	0.999795	−	0.0202324i	$-0.00644060\pi$
$98$		0			0
$99$	−2036.80			−2.06774
$100$	−89.6950	+	491.889i	−0.0896950	+	0.491889i
$101$	766.628			0.755270			0.377635	−	0.925954i	$-0.376737\pi$
$101$	766.628			0.755270			0.377635	+	0.925954i	$0.376737\pi$
$102$		−	1722.59i		−	1.67217i
$103$			529.223i			0.506271i	0.967431	+	0.253136i	$0.0814619\pi$
$103$			529.223i			0.506271i	−0.967431	+	0.253136i	$0.918538\pi$
$104$	364.425			0.343604
$105$		0			0
$106$	−322.524			−0.295531
$107$		−	713.613i		−	0.644743i	−0.946613	−	0.322372i	$-0.895520\pi$
$107$		−	713.613i		−	0.644743i	0.946613	−	0.322372i	$-0.104480\pi$
$108$			1117.70i			0.995837i
$109$	318.229			0.279640			0.139820	−	0.990177i	$-0.455348\pi$
$109$	318.229			0.279640			0.139820	+	0.990177i	$0.455348\pi$
$110$	−508.133	−	609.169i	−0.440442	−	0.528018i
$111$	−716.804			−0.612937
$112$		0			0
$113$		−	506.300i		−	0.421493i	−0.977541	−	0.210747i	$-0.932411\pi$
$113$		−	506.300i		−	0.421493i	0.977541	−	0.210747i	$-0.0675895\pi$
$114$	−824.638			−0.677495
$115$	−877.099	−	1051.50i	−0.711217	−	0.852633i
$116$	−71.3561			−0.0571142
$117$			2615.34i			2.06657i
$118$		−	1118.87i		−	0.872885i
$119$		0			0
$120$	−631.049	+	526.384i	−0.480056	+	0.400434i
$121$	−72.4280			−0.0544163
$122$			217.552i			0.161445i
$123$		−	193.264i		−	0.141675i
$124$	−108.635			−0.0786749
$125$	−688.154	−	1216.38i	−0.492403	−	0.870367i
$126$		0			0
$127$			2225.10i			1.55469i	0.629074	+	0.777345i	$0.283434\pi$
$127$			2225.10i			1.55469i	−0.629074	+	0.777345i	$0.716566\pi$
$128$			128.000i			0.0883883i
$129$	−4293.39			−2.93032
$130$	−782.199	+	652.464i	−0.527718	+	0.440192i
$131$	−1809.22			−1.20666			−0.603330	−	0.797492i	$-0.706160\pi$
$131$	−1809.22			−1.20666			−0.603330	+	0.797492i	$0.706160\pi$
$132$		−	1303.78i		−	0.859692i
$133$		0			0
$134$	−815.287			−0.525597
$135$	−2001.12	−	2399.01i	−1.27577	−	1.52944i
$136$	749.958			0.472855
$137$			2323.86i			1.44920i	0.689170	+	0.724600i	$0.257975\pi$
$137$			2323.86i			1.44920i	−0.689170	+	0.724600i	$0.742025\pi$
$138$		−	2250.48i		−	1.38821i
$139$	−1939.15			−1.18328			−0.591642	−	0.806200i	$-0.701520\pi$
$139$	−1939.15			−1.18328			−0.591642	+	0.806200i	$0.701520\pi$
$140$		0			0
$141$	5318.37			3.17651
$142$		−	2318.73i		−	1.37031i
$143$		−	1616.06i		−	0.945047i
$144$	−918.608			−0.531602
$145$	153.158	−	127.755i	0.0877178	−	0.0731691i
$146$	513.354			0.290997
$147$		0			0
$148$		−	312.073i		−	0.173326i
$149$	360.298			0.198099			0.0990497	−	0.995082i	$-0.468420\pi$
$149$	360.298			0.198099			0.0990497	+	0.995082i	$0.468420\pi$
$150$	412.043	−	2259.65i	0.224288	−	1.23000i
$151$	353.760			0.190653			0.0953263	−	0.995446i	$-0.469611\pi$
$151$	353.760			0.190653			0.0953263	+	0.995446i	$0.469611\pi$
$152$		−	359.020i		−	0.191581i
$153$			5382.16i			2.84394i
$154$		0			0
$155$	233.173	−	194.499i	0.120831	−	0.100791i
$156$	−1674.11			−0.859204
$157$		−	1406.80i		−	0.715127i	−0.933889	−	0.357563i	$-0.883608\pi$
$157$		−	1406.80i		−	0.715127i	0.933889	−	0.357563i	$-0.116392\pi$
$158$		−	1707.17i		−	0.859587i
$159$	1481.62			0.738994
$160$	−229.170	−	274.738i	−0.113234	−	0.135750i
$161$		0			0
$162$		−	2034.20i		−	0.986555i
$163$		−	269.618i		−	0.129559i	−0.997900	−	0.0647794i	$-0.979366\pi$
$163$		−	269.618i		−	0.129559i	0.997900	−	0.0647794i	$-0.0206344\pi$
$164$	84.1406			0.0400627
$165$	2334.28	+	2798.42i	1.10135	+	1.32034i
$166$	−1656.30			−0.774422
$167$		−	248.313i		−	0.115060i	−0.998344	−	0.0575300i	$-0.981678\pi$
$167$		−	248.313i		−	0.115060i	0.998344	−	0.0575300i	$-0.0183225\pi$
$168$		0			0
$169$	121.912			0.0554900
$170$	−1609.70	+	1342.72i	−0.726226	+	0.605775i
$171$	2576.55			1.15224
$172$		−	1869.20i		−	0.828634i
$173$			113.927i			0.0500679i	0.999687	+	0.0250339i	$0.00796938\pi$
$173$			113.927i			0.0500679i	−0.999687	+	0.0250339i	$0.992031\pi$
$174$	327.798			0.142818
$175$		0			0
$176$	567.622			0.243103
$177$			5139.90i			2.18270i
$178$			329.967i			0.138944i
$179$	−1564.68			−0.653349			−0.326674	−	0.945137i	$-0.605928\pi$
$179$	−1564.68			−0.653349			−0.326674	+	0.945137i	$0.605928\pi$
$180$	1971.69	−	1644.67i	0.816451	−	0.681036i
$181$	−4811.12			−1.97573			−0.987867	−	0.155300i	$-0.950366\pi$
$181$	−4811.12			−1.97573			−0.987867	+	0.155300i	$0.950366\pi$
$182$		0			0
$183$		−	999.398i		−	0.403703i
$184$	979.784			0.392558
$185$	558.733	+	669.830i	0.222048	+	0.266199i
$186$	499.049			0.196732
$187$		−	3325.72i		−	1.30054i
$188$			2315.44i			0.898250i
$189$		0			0
$190$	642.787	+	770.597i	0.245435	+	0.294237i
$191$	2465.11			0.933871			0.466935	−	0.884291i	$-0.345358\pi$
$191$	2465.11			0.933871			0.466935	+	0.884291i	$0.345358\pi$
$192$		−	588.010i		−	0.221021i
$193$		−	2353.62i		−	0.877811i	−0.898533	−	0.438905i	$-0.855366\pi$
$193$		−	2353.62i		−	0.877811i	0.898533	−	0.438905i	$-0.144634\pi$
$194$	−77.3151			−0.0286129
$195$	3593.29	−	2997.31i	1.31959	−	1.10073i
$196$		0			0
$197$			1552.27i			0.561393i	0.959797	+	0.280697i	$0.0905655\pi$
$197$			1552.27i			0.561393i	−0.959797	+	0.280697i	$0.909435\pi$
$198$			4073.61i			1.46211i
$199$	760.404			0.270872			0.135436	−	0.990786i	$-0.456756\pi$
$199$	760.404			0.270872			0.135436	+	0.990786i	$0.456756\pi$
$200$	983.778	+	179.390i	0.347818	+	0.0634240i
$201$	3745.29			1.31429
$202$		−	1533.26i		−	0.534057i
$203$		0			0
$204$	−3445.18			−1.18240
$205$	−180.599	+	150.645i	−0.0615296	+	0.0513243i
$206$	1058.45			0.357988
$207$			7031.54i			2.36099i
$208$		−	728.850i		−	0.242965i
$209$	−1592.09			−0.526924
$210$		0			0
$211$	−2942.38			−0.960008			−0.480004	−	0.877266i	$-0.659365\pi$
$211$	−2942.38			−0.960008			−0.480004	+	0.877266i	$0.659365\pi$
$212$			645.048i			0.208972i
$213$			10651.9i			3.42654i
$214$	−1427.23			−0.455902
$215$	3346.60	+	4012.03i	1.06156	+	1.27264i
$216$	2235.39			0.704163
$217$		0			0
$218$		−	636.458i		−	0.197736i
$219$	−2358.26			−0.727655
$220$	−1218.34	+	1016.27i	−0.373365	+	0.311439i
$221$	−4270.37			−1.29980
$222$			1433.61i			0.433412i
$223$		−	1219.27i		−	0.366136i	−0.983100	−	0.183068i	$-0.941397\pi$
$223$		−	1219.27i		−	0.366136i	0.983100	−	0.183068i	$-0.0586028\pi$
$224$		0			0
$225$	−1287.41	+	7060.20i	−0.381456	+	2.09191i
$226$	−1012.60			−0.298041
$227$		−	4573.67i		−	1.33729i	−0.743581	−	0.668646i	$-0.766874\pi$
$227$		−	4573.67i		−	1.33729i	0.743581	−	0.668646i	$-0.233126\pi$
$228$			1649.28i			0.479061i
$229$	−3084.27			−0.890020			−0.445010	−	0.895526i	$-0.646800\pi$
$229$	−3084.27			−0.890020			−0.445010	+	0.895526i	$0.646800\pi$
$230$	−2103.00	+	1754.20i	−0.602903	+	0.502906i
$231$		0			0
$232$			142.712i			0.0403858i
$233$			5932.87i			1.66813i	0.551663	+	0.834067i	$0.313994\pi$
$233$			5932.87i			1.66813i	−0.551663	+	0.834067i	$0.686006\pi$
$234$	5230.68			1.46128
$235$	−4145.55	−	4969.85i	−1.15075	−	1.37956i
$236$	−2237.74			−0.617223
$237$			7842.42i			2.14945i
$238$		0			0
$239$	807.121			0.218445			0.109222	−	0.994017i	$-0.465164\pi$
$239$	807.121			0.218445			0.109222	+	0.994017i	$0.465164\pi$
$240$	1052.77	+	1262.10i	0.283150	+	0.339451i
$241$	4261.56			1.13905			0.569526	−	0.821974i	$-0.307127\pi$
$241$	4261.56			1.13905			0.569526	+	0.821974i	$0.307127\pi$
$242$			144.856i			0.0384781i
$243$			1800.32i			0.475270i
$244$	435.105			0.114159
$245$		0			0
$246$	−386.528			−0.100179
$247$			2044.31i			0.526625i
$248$			217.270i			0.0556316i
$249$	7608.77			1.93649
$250$	−2432.75	+	1376.31i	−0.615443	+	0.348182i
$251$	2962.48			0.744980			0.372490	−	0.928036i	$-0.378504\pi$
$251$	2962.48			0.744980			0.372490	+	0.928036i	$0.378504\pi$
$252$		0			0
$253$		−	4344.90i		−	1.07969i
$254$	4450.20			1.09933
$255$	7394.69	−	6168.22i	1.81597	−	1.51478i
$256$	256.000			0.0625000
$257$		−	6170.94i		−	1.49779i	−0.662687	−	0.748896i	$-0.730584\pi$
$257$		−	6170.94i		−	1.49779i	0.662687	−	0.748896i	$-0.269416\pi$
$258$			8586.78i			2.07205i
$259$		0			0
$260$	1304.93	+	1564.40i	0.311262	+	0.373153i
$261$	−1024.19			−0.242896
$262$			3618.44i			0.853237i
$263$			129.912i			0.0304589i	0.999884	+	0.0152294i	$0.00484787\pi$
$263$			129.912i			0.0304589i	−0.999884	+	0.0152294i	$0.995152\pi$
$264$	−2607.56			−0.607894
$265$	−1154.89	−	1384.53i	−0.267714	−	0.320946i
$266$		0			0
$267$		−	1515.81i		−	0.347438i
$268$			1630.57i			0.371653i
$269$	−2473.67			−0.560678			−0.280339	−	0.959901i	$-0.590447\pi$
$269$	−2473.67			−0.560678			−0.280339	+	0.959901i	$0.590447\pi$
$270$	−4798.02	+	4002.23i	−1.08148	+	0.902104i
$271$	2878.92			0.645321			0.322660	−	0.946515i	$-0.395423\pi$
$271$	2878.92			0.645321			0.322660	+	0.946515i	$0.395423\pi$
$272$		−	1499.92i		−	0.334359i
$273$		0			0
$274$	4647.71			1.02474
$275$	795.513	−	4362.61i	0.174441	−	0.956637i
$276$	−4500.96			−0.981615
$277$		−	544.478i		−	0.118103i	−0.998255	−	0.0590514i	$-0.981192\pi$
$277$		−	544.478i		−	0.118103i	0.998255	−	0.0590514i	$-0.0188076\pi$
$278$			3878.30i			0.836709i
$279$	−1559.26			−0.334590
$280$		0			0
$281$	−97.2982			−0.0206560			−0.0103280	−	0.999947i	$-0.503288\pi$
$281$	−97.2982			−0.0206560			−0.0103280	+	0.999947i	$0.503288\pi$
$282$		−	10636.7i		−	2.24613i
$283$			5087.62i			1.06865i	0.845279	+	0.534325i	$0.179434\pi$
$283$			5087.62i			1.06865i	−0.845279	+	0.534325i	$0.820566\pi$
$284$	−4637.46			−0.968954
$285$	−2952.85	−	3539.99i	−0.613726	−	0.735758i
$286$	−3232.12			−0.668249
$287$		0			0
$288$			1837.22i			0.375899i
$289$	−3875.07			−0.788738
$290$	−255.511	−	306.316i	−0.0517384	−	0.0620259i
$291$	355.172			0.0715483
$292$		−	1026.71i		−	0.205766i
$293$		−	4413.85i		−	0.880068i	−0.897981	−	0.440034i	$-0.854966\pi$
$293$		−	4413.85i		−	0.880068i	0.897981	−	0.440034i	$-0.145034\pi$
$294$		0			0
$295$	4803.07	−	4006.44i	0.947951	−	0.790725i
$296$	−624.145			−0.122560
$297$		−	9912.95i		−	1.93673i
$298$		−	720.597i		−	0.140077i
$299$	−5579.03			−1.07908
$300$	−4519.31	−	824.087i	−0.869741	−	0.158596i
$301$		0			0
$302$		−	707.519i		−	0.134812i
$303$			7043.51i			1.33544i
$304$	−718.040			−0.135469
$305$	−933.905	+	779.009i	−0.175329	+	0.146249i
$306$	10764.3			2.01097
$307$		−	1193.21i		−	0.221824i	−0.993830	−	0.110912i	$-0.964623\pi$
$307$		−	1193.21i		−	0.221824i	0.993830	−	0.110912i	$-0.0353772\pi$
$308$		0			0
$309$	−4862.32			−0.895171
$310$	−388.998	−	466.345i	−0.0712697	−	0.0854408i
$311$	−9729.55			−1.77399			−0.886997	−	0.461775i	$-0.847213\pi$
$311$	−9729.55			−1.77399			−0.886997	+	0.461775i	$0.847213\pi$
$312$			3348.21i			0.607549i
$313$		−	2794.49i		−	0.504646i	−0.967643	−	0.252323i	$-0.918805\pi$
$313$		−	2794.49i		−	0.504646i	0.967643	−	0.252323i	$-0.0811945\pi$
$314$	−2813.60			−0.505671
$315$		0			0
$316$	−3414.33			−0.607820
$317$			6231.90i			1.10416i	0.833792	+	0.552079i	$0.186165\pi$
$317$			6231.90i			1.10416i	−0.833792	+	0.552079i	$0.813835\pi$
$318$		−	2963.24i		−	0.522548i
$319$	632.864			0.111077
$320$	−549.476	+	458.341i	−0.0959895	+	0.0800688i
$321$	6556.43			1.14001
$322$		0			0
$323$			4207.03i			0.724722i
$324$	−4068.40			−0.697600
$325$	−5601.77	−	1021.47i	−0.956094	−	0.174342i
$326$	−539.235			−0.0916119
$327$			2923.78i			0.494450i
$328$		−	168.281i		−	0.0283286i
$329$		0			0
$330$	5596.83	−	4668.55i	0.933623	−	0.778773i
$331$	−10892.5			−1.80878			−0.904391	−	0.426704i	$-0.859675\pi$
$331$	−10892.5			−1.80878			−0.904391	+	0.426704i	$0.859675\pi$
$332$			3312.61i			0.547599i
$333$		−	4479.26i		−	0.737122i
$334$	−496.625			−0.0813597
$335$	−2919.37	−	3499.85i	−0.476126	−	0.570797i
$336$		0			0
$337$			413.950i			0.0669119i	0.999440	+	0.0334560i	$0.0106513\pi$
$337$			413.950i			0.0669119i	−0.999440	+	0.0334560i	$0.989349\pi$
$338$		−	243.823i		−	0.0392374i
$339$	4651.71			0.745270
$340$	2685.44	+	3219.40i	0.428348	+	0.513520i
$341$	963.492			0.153009
$342$		−	5153.10i		−	0.814760i
$343$		0			0
$344$	−3738.40			−0.585933
$345$	9660.82	−	8058.49i	1.50760	−	1.25755i
$346$	227.855			0.0354033
$347$			1709.53i			0.264474i	0.991218	+	0.132237i	$0.0422161\pi$
$347$			1709.53i			0.264474i	−0.991218	+	0.132237i	$0.957784\pi$
$348$		−	655.595i		−	0.100987i
$349$	6269.06			0.961534			0.480767	−	0.876848i	$-0.340358\pi$
$349$	6269.06			0.961534			0.480767	+	0.876848i	$0.340358\pi$
$350$		0			0
$351$	−12728.6			−1.93563
$352$		−	1135.24i		−	0.171900i
$353$		−	6723.74i		−	1.01379i	−0.862007	−	0.506896i	$-0.830793\pi$
$353$		−	6723.74i		−	1.01379i	0.862007	−	0.506896i	$-0.169207\pi$
$354$	10279.8			1.54340
$355$	9953.81	−	8302.88i	1.48815	−	1.24133i
$356$	659.933			0.0982483
$357$		0			0
$358$			3129.35i			0.461988i
$359$	−1762.95			−0.259178			−0.129589	−	0.991568i	$-0.541366\pi$
$359$	−1762.95			−0.259178			−0.129589	+	0.991568i	$0.541366\pi$
$360$	−3289.34	−	3943.38i	−0.481565	−	0.577318i
$361$	−4845.01			−0.706373
$362$			9622.25i			1.39706i
$363$		−	665.444i		−	0.0962169i
$364$		0			0
$365$	1838.21	+	2203.72i	0.263607	+	0.316021i
$366$	−1998.80			−0.285461
$367$			6177.31i			0.878618i	0.898336	+	0.439309i	$0.144777\pi$
$367$			6177.31i			0.878618i	−0.898336	+	0.439309i	$0.855223\pi$
$368$		−	1959.57i		−	0.277580i
$369$	1207.69			0.170379
$370$	1339.66	−	1117.47i	0.188231	−	0.157012i
$371$		0			0
$372$		−	998.099i		−	0.139110i
$373$		−	8193.45i		−	1.13738i	−0.822554	−	0.568688i	$-0.807451\pi$
$373$		−	8193.45i		−	1.13738i	0.822554	−	0.568688i	$-0.192549\pi$
$374$	−6651.44			−0.919620
$375$	11175.6	−	6322.52i	1.53895	−	0.870650i
$376$	4630.89			0.635159
$377$		−	812.624i		−	0.111014i
$378$		0			0
$379$	10828.4			1.46760			0.733799	−	0.679367i	$-0.237745\pi$
$379$	10828.4			1.46760			0.733799	+	0.679367i	$0.237745\pi$
$380$	1541.19	−	1285.57i	0.208057	−	0.173549i
$381$	−20443.4			−2.74895
$382$		−	4930.23i		−	0.660346i
$383$			7453.03i			0.994339i	0.867653	+	0.497170i	$0.165627\pi$
$383$			7453.03i			0.994339i	−0.867653	+	0.497170i	$0.834373\pi$
$384$	−1176.02			−0.156285
$385$		0			0
$386$	−4707.25			−0.620706
$387$		−	26829.1i		−	3.52403i
$388$			154.630i			0.0202324i
$389$	4059.01			0.529049			0.264524	−	0.964379i	$-0.414785\pi$
$389$	4059.01			0.529049			0.264524	+	0.964379i	$0.414785\pi$
$390$	−5994.62	−	7186.57i	−0.778331	−	0.933093i
$391$	−11481.2			−1.48498
$392$		0			0
$393$		−	16622.5i		−	2.13357i
$394$	3104.54			0.396965
$395$	7328.49	−	6112.99i	0.933509	−	0.778679i
$396$	8147.21			1.03387
$397$			10247.9i			1.29554i	0.761837	+	0.647769i	$0.224298\pi$
$397$			10247.9i			1.29554i	−0.761837	+	0.647769i	$0.775702\pi$
$398$		−	1520.81i		−	0.191536i
$399$		0			0
$400$	358.780	−	1967.56i	0.0448475	−	0.245945i
$401$	2745.99			0.341965			0.170983	−	0.985274i	$-0.445306\pi$
$401$	2745.99			0.341965			0.170983	+	0.985274i	$0.445306\pi$
$402$		−	7490.57i		−	0.929343i
$403$		−	1237.16i		−	0.152922i
$404$	−3066.51			−0.377635
$405$	8732.38	−	7284.04i	1.07140	−	0.893696i
$406$		0			0
$407$			2767.80i			0.337088i
$408$			6890.35i			0.836086i
$409$	10406.5			1.25812			0.629059	−	0.777357i	$-0.283440\pi$
$409$	10406.5			1.25812			0.629059	+	0.777357i	$0.283440\pi$
$410$	301.290	+	361.197i	0.0362918	+	0.0435080i
$411$	−21350.8			−2.56242
$412$		−	2116.89i		−	0.253136i
$413$		0			0
$414$	14063.1			1.66948
$415$	−5930.87	−	7110.15i	−0.701530	−	0.841020i
$416$	−1457.70			−0.171802
$417$		−	17816.2i		−	2.09224i
$418$			3184.18i			0.372592i
$419$	3901.99			0.454951			0.227476	−	0.973784i	$-0.426953\pi$
$419$	3901.99			0.454951			0.227476	+	0.973784i	$0.426953\pi$
$420$		0			0
$421$	−7780.63			−0.900724			−0.450362	−	0.892846i	$-0.648705\pi$
$421$	−7780.63			−0.900724			−0.450362	+	0.892846i	$0.648705\pi$
$422$			5884.76i			0.678828i
$423$			33234.1i			3.82009i
$424$	1290.10			0.147766
$425$	−11528.0	−	2102.11i	−1.31574	−	0.239923i
$426$	21303.7			2.42293
$427$		0			0
$428$			2854.45i			0.322372i
$429$	14847.8			1.67100
$430$	8024.06	−	6693.20i	0.899894	−	0.750639i
$431$	−13353.0			−1.49232			−0.746161	−	0.665766i	$-0.768105\pi$
$431$	−13353.0			−1.49232			−0.746161	+	0.665766i	$0.768105\pi$
$432$		−	4470.78i		−	0.497918i
$433$			12859.5i			1.42723i	0.700540	+	0.713613i	$0.252942\pi$
$433$			12859.5i			1.42723i	−0.700540	+	0.713613i	$0.747058\pi$
$434$		0			0
$435$	1173.77	+	1407.16i	0.129375	+	0.155100i
$436$	−1272.92			−0.139820
$437$			5496.28i			0.601654i
$438$			4716.52i			0.514530i
$439$	12233.5			1.33001			0.665006	−	0.746838i	$-0.268429\pi$
$439$	12233.5			1.33001			0.665006	+	0.746838i	$0.268429\pi$
$440$	2032.53	+	2436.68i	0.220221	+	0.264009i
$441$		0			0
$442$			8540.73i			0.919098i
$443$			8620.21i			0.924511i	0.886747	+	0.462255i	$0.152960\pi$
$443$			8620.21i			0.924511i	−0.886747	+	0.462255i	$0.847040\pi$
$444$	2867.22			0.306469
$445$	−1416.47	+	1181.54i	−0.150893	+	0.125866i
$446$	−2438.54			−0.258897
$447$			3310.30i			0.350272i
$448$		0			0
$449$	−53.3141			−0.00560367			−0.00280183	−	0.999996i	$-0.500892\pi$
$449$	−53.3141			−0.00560367			−0.00280183	+	0.999996i	$0.500892\pi$
$450$	14120.4	+	2574.83i	1.47921	+	0.269730i
$451$	−746.251			−0.0779148
$452$			2025.20i			0.210747i
$453$			3250.22i			0.337105i
$454$	−9147.35			−0.945608
$455$		0			0
$456$	3298.55			0.338747
$457$			6421.65i			0.657313i	0.944450	+	0.328656i	$0.106596\pi$
$457$			6421.65i			0.657313i	−0.944450	+	0.328656i	$0.893404\pi$
$458$			6168.55i			0.629339i
$459$	−26194.5			−2.66374
$460$	3508.40	+	4206.00i	0.355608	+	0.426317i
$461$	13775.0			1.39168			0.695840	−	0.718197i	$-0.255032\pi$
$461$	13775.0			1.39168			0.695840	+	0.718197i	$0.255032\pi$
$462$		0			0
$463$		−	6286.78i		−	0.631040i	−0.948919	−	0.315520i	$-0.897821\pi$
$463$		−	6286.78i		−	0.631040i	0.948919	−	0.315520i	$-0.102179\pi$
$464$	285.424			0.0285571
$465$	1786.99	+	2142.31i	0.178214	+	0.213650i
$466$	11865.7			1.17955
$467$		−	6945.27i		−	0.688198i	−0.938933	−	0.344099i	$-0.888184\pi$
$467$		−	6945.27i		−	0.688198i	0.938933	−	0.344099i	$-0.111816\pi$
$468$		−	10461.4i		−	1.03328i
$469$		0			0
$470$	−9939.69	+	8291.11i	−0.975497	+	0.813703i
$471$	12925.2			1.26446
$472$			4475.48i			0.436443i
$473$			16578.1i			1.61155i
$474$	15684.8			1.51989
$475$	−1006.32	+	5518.69i	−0.0972068	+	0.533084i
$476$		0			0
$477$			9258.54i			0.888720i
$478$		−	1614.24i		−	0.154464i
$479$	7228.76			0.689542			0.344771	−	0.938687i	$-0.387957\pi$
$479$	7228.76			0.689542			0.344771	+	0.938687i	$0.387957\pi$
$480$	2524.20	−	2105.54i	0.240028	−	0.200217i
$481$	3553.97			0.336897
$482$		−	8523.12i		−	0.805431i
$483$		0			0
$484$	289.712			0.0272081
$485$	−276.849	−	331.897i	−0.0259197	−	0.0310735i
$486$	3600.64			0.336067
$487$		−	1423.58i		−	0.132461i	−0.997804	−	0.0662306i	$-0.978903\pi$
$487$		−	1423.58i		−	0.132461i	0.997804	−	0.0662306i	$-0.0210973\pi$
$488$		−	870.210i		−	0.0807224i
$489$	2477.15			0.229081
$490$		0			0
$491$	−7574.62			−0.696207			−0.348104	−	0.937456i	$-0.613174\pi$
$491$	−7574.62			−0.696207			−0.348104	+	0.937456i	$0.613174\pi$
$492$			773.055i			0.0708374i
$493$		−	1672.31i		−	0.152773i
$494$	4088.62			0.372380
$495$	−17487.1	+	14586.7i	−1.58785	+	1.32449i
$496$	434.539			0.0393375
$497$		0			0
$498$		−	15217.5i		−	1.36931i
$499$	13841.1			1.24171			0.620854	−	0.783926i	$-0.286786\pi$
$499$	13841.1			1.24171			0.620854	+	0.783926i	$0.286786\pi$
$500$	2752.62	+	4865.50i	0.246202	+	0.435184i
$501$	2281.41			0.203445
$502$		−	5924.96i		−	0.526780i
$503$			10917.4i			0.967763i	0.875134	+	0.483882i	$0.160773\pi$
$503$			10917.4i			0.967763i	−0.875134	+	0.483882i	$0.839227\pi$
$504$		0			0
$505$	6581.93	−	5490.26i	0.579984	−	0.483789i
$506$	−8689.79			−0.763455
$507$			1120.08i			0.0981155i
$508$		−	8900.40i		−	0.777345i
$509$	−8831.06			−0.769018			−0.384509	−	0.923121i	$-0.625629\pi$
$509$	−8831.06			−0.769018			−0.384509	+	0.923121i	$0.625629\pi$
$510$	−12336.4	−	14789.4i	−1.07111	−	1.28409i
$511$		0			0
$512$		−	512.000i		−	0.0441942i
$513$			12539.9i			1.07924i
$514$	−12341.9			−1.05910
$515$	3790.07	+	4543.68i	0.324292	+	0.388774i
$516$	17173.6			1.46516
$517$		−	20535.9i		−	1.74694i
$518$		0			0
$519$	−1046.73			−0.0885283
$520$	3128.79	−	2609.86i	0.263859	−	0.220096i
$521$	20972.0			1.76353			0.881767	−	0.471684i	$-0.156354\pi$
$521$	20972.0			1.76353			0.881767	+	0.471684i	$0.156354\pi$
$522$			2048.38i			0.171754i
$523$		−	536.004i		−	0.0448142i	−0.999749	−	0.0224071i	$-0.992867\pi$
$523$		−	536.004i		−	0.0448142i	0.999749	−	0.0224071i	$-0.00713299\pi$
$524$	7236.89			0.603330
$525$		0			0
$526$	259.823			0.0215377
$527$		−	2545.98i		−	0.210446i
$528$			5215.11i			0.429846i
$529$	−2832.64			−0.232813
$530$	−2769.05	+	2309.78i	−0.226943	+	0.189303i
$531$	−32118.9			−2.62493
$532$		0			0
$533$			958.218i			0.0778706i
$534$	−3031.62			−0.245676
$535$	−5110.59	−	6126.77i	−0.412991	−	0.495109i
$536$	3261.15			0.262799
$537$		−	14375.7i		−	1.15523i
$538$			4947.34i			0.396459i
$539$		0			0
$540$	8004.46	+	9596.05i	0.637884	+	0.764719i
$541$	8203.34			0.651921			0.325960	−	0.945383i	$-0.394312\pi$
$541$	8203.34			0.651921			0.325960	+	0.945383i	$0.394312\pi$
$542$		−	5757.84i		−	0.456311i
$543$		−	44202.9i		−	3.49342i
$544$	−2999.83			−0.236428
$545$	2732.17	−	2279.02i	0.214740	−	0.179124i
$546$		0			0
$547$		−	23851.1i		−	1.86435i	−0.362013	−	0.932173i	$-0.617910\pi$
$547$		−	23851.1i		−	1.86435i	0.362013	−	0.932173i	$-0.382090\pi$
$548$		−	9295.42i		−	0.724600i
$549$	6245.17			0.485496
$550$	−8725.22	−	1591.03i	−0.676444	−	0.123348i
$551$	−800.571			−0.0618974
$552$			9001.92i			0.694107i
$553$		0			0
$554$	−1088.96			−0.0835114
$555$	−6154.17	+	5133.44i	−0.470684	+	0.392617i
$556$	7756.60			0.591642
$557$			25438.3i			1.93511i	0.252660	+	0.967555i	$0.418695\pi$
$557$			25438.3i			1.93511i	−0.252660	+	0.967555i	$0.581305\pi$
$558$			3118.52i			0.236591i
$559$	21287.0			1.61063
$560$		0			0
$561$	30555.6			2.29957
$562$			194.596i			0.0146060i
$563$			7219.84i			0.540462i	0.962796	+	0.270231i	$0.0871000\pi$
$563$			7219.84i			0.540462i	−0.962796	+	0.270231i	$0.912900\pi$
$564$	−21273.5			−1.58825
$565$	−3625.91	−	4346.87i	−0.269988	−	0.323671i
$566$	10175.2			0.755649
$567$		0			0
$568$			9274.93i			0.685154i
$569$	6801.74			0.501131			0.250566	−	0.968100i	$-0.419383\pi$
$569$	6801.74			0.501131			0.250566	+	0.968100i	$0.419383\pi$
$570$	−7079.98	+	5905.70i	−0.520259	+	0.433970i
$571$	17178.3			1.25900			0.629502	−	0.776999i	$-0.283259\pi$
$571$	17178.3			1.25900			0.629502	+	0.776999i	$0.283259\pi$
$572$			6464.24i			0.472523i
$573$			22648.6i			1.65124i
$574$		0			0
$575$	−15060.8	−	2746.31i	−1.09231	−	0.199181i
$576$	3674.43			0.265801
$577$		−	17496.5i		−	1.26237i	−0.775631	−	0.631187i	$-0.782568\pi$
$577$		−	17496.5i		−	1.26237i	0.775631	−	0.631187i	$-0.217432\pi$
$578$			7750.14i			0.557722i
$579$	21624.3			1.55211
$580$	−612.632	+	511.022i	−0.0438589	+	0.0365845i
$581$		0			0
$582$		−	710.344i		−	0.0505923i
$583$		−	5720.99i		−	0.406414i
$584$	−2053.42			−0.145498
$585$	18730.0	+	22454.2i	1.32374	+	1.58695i
$586$	−8827.70			−0.622302
$587$		−	9824.21i		−	0.690781i	−0.938459	−	0.345390i	$-0.887746\pi$
$587$		−	9824.21i		−	0.690781i	0.938459	−	0.345390i	$-0.112254\pi$
$588$		0			0
$589$	−1218.81			−0.0852638
$590$	−8012.88	−	9606.14i	−0.559127	−	0.670302i
$591$	−14261.7			−0.992636
$592$			1248.29i			0.0866629i
$593$		−	3309.32i		−	0.229170i	−0.993413	−	0.114585i	$-0.963446\pi$
$593$		−	3309.32i		−	0.229170i	0.993413	−	0.114585i	$-0.0365538\pi$
$594$	−19825.9			−1.36947
$595$		0			0
$596$	−1441.19			−0.0990497
$597$			6986.33i			0.478947i
$598$			11158.1i			0.763022i
$599$	10718.0			0.731096			0.365548	−	0.930792i	$-0.380882\pi$
$599$	10718.0			0.731096			0.365548	+	0.930792i	$0.380882\pi$
$600$	−1648.17	+	9038.61i	−0.112144	+	0.615000i
$601$	−8655.81			−0.587484			−0.293742	−	0.955885i	$-0.594901\pi$
$601$	−8655.81			−0.587484			−0.293742	+	0.955885i	$0.594901\pi$
$602$		0			0
$603$			23404.0i			1.58057i
$604$	−1415.04			−0.0953263
$605$	−621.835	+	518.699i	−0.0417871	+	0.0348564i
$606$	14087.0			0.944300
$607$		−	16498.6i		−	1.10322i	−0.834101	−	0.551611i	$-0.814013\pi$
$607$		−	16498.6i		−	1.10322i	0.834101	−	0.551611i	$-0.185987\pi$
$608$			1436.08i			0.0957907i
$609$		0			0
$610$	1558.02	+	1867.81i	0.103414	+	0.123976i
$611$	−26368.9			−1.74595
$612$		−	21528.7i		−	1.42197i
$613$		−	17687.2i		−	1.16538i	−0.812693	−	0.582692i	$-0.801999\pi$
$613$		−	17687.2i		−	1.16538i	0.812693	−	0.582692i	$-0.198001\pi$
$614$	−2386.42			−0.156853
$615$	−1384.07	−	1659.28i	−0.0907499	−	0.108794i
$616$		0			0
$617$			19665.9i			1.28318i	0.767049	+	0.641589i	$0.221724\pi$
$617$			19665.9i			1.28318i	−0.767049	+	0.641589i	$0.778276\pi$
$618$			9724.64i			0.632981i
$619$	−19963.6			−1.29629			−0.648147	−	0.761516i	$-0.724456\pi$
$619$	−19963.6			−1.29629			−0.648147	+	0.761516i	$0.724456\pi$
$620$	−932.691	+	777.996i	−0.0604157	+	0.0503953i
$621$	−34221.9			−2.21140
$622$			19459.1i			1.25440i
$623$		0			0
$624$	6696.42			0.429602
$625$	−14619.4	−	5515.00i	−0.935638	−	0.352960i
$626$	−5588.99			−0.356839
$627$		−	14627.6i		−	0.931689i
$628$			5627.20i			0.357563i
$629$	7313.79			0.463625
$630$		0			0
$631$	16085.0			1.01479			0.507395	−	0.861713i	$-0.330608\pi$
$631$	16085.0			1.01479			0.507395	+	0.861713i	$0.330608\pi$
$632$			6828.66i			0.429794i
$633$		−	27033.5i		−	1.69745i
$634$	12463.8			0.780758
$635$	15935.2	+	19103.7i	0.995858	+	1.19387i
$636$	−5926.48			−0.369497
$637$		0			0
$638$		−	1265.73i		−	0.0785433i
$639$	−66562.7			−4.12078
$640$	916.681	+	1098.95i	0.0566172	+	0.0678748i
$641$	−23172.5			−1.42786			−0.713931	−	0.700216i	$-0.753087\pi$
$641$	−23172.5			−1.42786			−0.713931	+	0.700216i	$0.753087\pi$
$642$		−	13112.9i		−	0.806111i
$643$		−	12677.6i		−	0.777535i	−0.921336	−	0.388768i	$-0.872901\pi$
$643$		−	12677.6i		−	0.777535i	0.921336	−	0.388768i	$-0.127099\pi$
$644$		0			0
$645$	−36861.2	+	30747.4i	−2.25024	+	1.87702i
$646$	8414.06			0.512456
$647$			3398.92i			0.206530i	0.994654	+	0.103265i	$0.0329290\pi$
$647$			3398.92i			0.206530i	−0.994654	+	0.103265i	$0.967071\pi$
$648$			8136.80i			0.493278i
$649$	19846.7			1.20039
$650$	−2042.95	+	11203.5i	−0.123278	+	0.676060i
$651$		0			0
$652$			1078.47i			0.0647794i
$653$		−	13753.6i		−	0.824224i	−0.911133	−	0.412112i	$-0.864791\pi$
$653$		−	13753.6i		−	0.824224i	0.911133	−	0.412112i	$-0.135209\pi$
$654$	5847.56			0.349629
$655$	−15533.2	+	12956.9i	−0.926613	+	0.772926i
$656$	−336.563			−0.0200313
$657$		−	14736.6i		−	0.875083i
$658$		0			0
$659$	−3871.62			−0.228857			−0.114429	−	0.993431i	$-0.536504\pi$
$659$	−3871.62			−0.228857			−0.114429	+	0.993431i	$0.536504\pi$
$660$	−9337.10	−	11193.7i	−0.550676	−	0.660171i
$661$	8392.02			0.493815			0.246908	−	0.969039i	$-0.420586\pi$
$661$	8392.02			0.493815			0.246908	+	0.969039i	$0.420586\pi$
$662$			21785.0i			1.27900i
$663$		−	39234.6i		−	2.29826i
$664$	6625.21			0.387211
$665$		0			0
$666$	−8958.51			−0.521224
$667$		−	2184.80i		−	0.126830i
$668$			993.251i			0.0575300i
$669$	11202.2			0.647388
$670$	−6999.69	+	5838.73i	−0.403615	+	0.336672i
$671$	−3858.98			−0.222019
$672$		0			0
$673$		−	18527.8i		−	1.06121i	−0.847620	−	0.530604i	$-0.821965\pi$
$673$		−	18527.8i		−	1.06121i	0.847620	−	0.530604i	$-0.178035\pi$
$674$	827.901			0.0473139
$675$	−34361.4	−	6265.74i	−1.95936	−	0.357286i
$676$	−487.646			−0.0277450
$677$			19787.2i			1.12332i	0.827369	+	0.561659i	$0.189837\pi$
$677$			19787.2i			1.12332i	−0.827369	+	0.561659i	$0.810163\pi$
$678$		−	9303.43i		−	0.526985i
$679$		0			0
$680$	6438.81	−	5370.88i	0.363113	−	0.302888i
$681$	42021.3			2.36455
$682$		−	1926.98i		−	0.108194i
$683$			27984.2i			1.56777i	0.620908	+	0.783883i	$0.286764\pi$
$683$			27984.2i			1.56777i	−0.620908	+	0.783883i	$0.713236\pi$
$684$	−10306.2			−0.576122
$685$	16642.5	+	19951.6i	0.928286	+	1.11286i
$686$		0			0
$687$		−	28337.2i		−	1.57370i
$688$			7476.80i			0.414317i
$689$	−7345.99			−0.406183
$690$	−16117.0	−	19321.6i	−0.889221	−	1.06603i
$691$	10860.2			0.597891			0.298946	−	0.954270i	$-0.403365\pi$
$691$	10860.2			0.597891			0.298946	+	0.954270i	$0.403365\pi$
$692$		−	455.710i		−	0.0250339i
$693$		0			0
$694$	3419.07			0.187012
$695$	−16648.7	+	13887.4i	−0.908663	+	0.757954i
$696$	−1311.19			−0.0714088
$697$			1971.93i			0.107163i
$698$		−	12538.1i		−	0.679907i
$699$	−54509.2			−2.94954
$700$		0			0
$701$	−5808.02			−0.312933			−0.156466	−	0.987683i	$-0.550010\pi$
$701$	−5808.02			−0.312933			−0.156466	+	0.987683i	$0.550010\pi$
$702$			25457.3i			1.36869i
$703$		−	3501.26i		−	0.187842i
$704$	−2270.49			−0.121551
$705$	45661.2	−	38087.9i	2.43929	−	2.03471i
$706$	−13447.5			−0.716859
$707$		0			0
$708$		−	20559.6i		−	1.09135i
$709$	−7207.83			−0.381800			−0.190900	−	0.981610i	$-0.561141\pi$
$709$	−7207.83			−0.381800			−0.190900	+	0.981610i	$0.561141\pi$
$710$	−16605.8	−	19907.6i	−0.877751	−	1.05228i
$711$	−49006.7			−2.58494
$712$		−	1319.87i		−	0.0694720i
$713$		−	3326.21i		−	0.174709i
$714$		0			0
$715$	−11573.5	−	13874.8i	−0.605350	−	0.725717i
$716$	6258.71			0.326674
$717$			7415.55i			0.386247i
$718$			3525.90i			0.183266i
$719$	−4956.92			−0.257110			−0.128555	−	0.991702i	$-0.541034\pi$
$719$	−4956.92			−0.257110			−0.128555	+	0.991702i	$0.541034\pi$
$720$	−7886.76	+	6578.68i	−0.408226	+	0.340518i
$721$		0			0
$722$			9690.02i			0.499481i
$723$			39153.8i			2.01403i
$724$	19244.5			0.987867
$725$	400.018	−	2193.71i	0.0204914	−	0.112375i
$726$	−1330.89			−0.0680356
$727$			3302.14i			0.168459i	0.996446	+	0.0842295i	$0.0268429\pi$
$727$			3302.14i			0.168459i	−0.996446	+	0.0842295i	$0.973157\pi$
$728$		0			0
$729$	10921.0			0.554844
$730$	4407.43	−	3676.42i	0.223461	−	0.186398i
$731$	43806.9			2.21649
$732$			3997.59i			0.201852i
$733$			28053.6i			1.41362i	0.707405	+	0.706809i	$0.249866\pi$
$733$			28053.6i			1.41362i	−0.707405	+	0.706809i	$0.750134\pi$
$734$	12354.6			0.621277
$735$		0			0
$736$	−3919.14			−0.196279
$737$		−	14461.7i		−	0.722800i
$738$		−	2415.38i		−	0.120476i
$739$	20132.1			1.00213			0.501064	−	0.865410i	$-0.332942\pi$
$739$	20132.1			1.00213			0.501064	+	0.865410i	$0.332942\pi$
$740$	−2234.93	−	2679.32i	−0.111024	−	0.133100i
$741$	−18782.4			−0.931160
$742$		0			0
$743$			4320.73i			0.213341i	0.994294	+	0.106670i	$0.0340190\pi$
$743$			4320.73i			0.213341i	−0.994294	+	0.106670i	$0.965981\pi$
$744$	−1996.20			−0.0983658
$745$	3093.36	−	2580.30i	0.152124	−	0.126893i
$746$	−16386.9			−0.804246
$747$			47546.7i			2.32884i
$748$			13302.9i			0.650269i
$749$		0			0
$750$	−12645.0	−	22351.3i	−0.615642	−	1.08820i
$751$	−5222.83			−0.253773			−0.126887	−	0.991917i	$-0.540498\pi$
$751$	−5222.83			−0.253773			−0.126887	+	0.991917i	$0.540498\pi$
$752$		−	9261.77i		−	0.449125i
$753$			27218.2i			1.31725i
$754$	−1625.25			−0.0784987
$755$	3037.23	−	2533.48i	0.146405	−	0.122123i
$756$		0			0
$757$			16291.5i			0.782198i	0.920349	+	0.391099i	$0.127905\pi$
$757$			16291.5i			0.782198i	−0.920349	+	0.391099i	$0.872095\pi$
$758$		−	21656.9i		−	1.03775i
$759$	39919.4			1.90907
$760$	−2571.15	−	3082.39i	−0.122718	−	0.147118i
$761$	−727.281			−0.0346438			−0.0173219	−	0.999850i	$-0.505514\pi$
$761$	−727.281			−0.0346438			−0.0173219	+	0.999850i	$0.505514\pi$
$762$			40886.9i			1.94380i
$763$		0			0
$764$	−9860.45			−0.466935
$765$	38544.8	+	46208.9i	1.82168	+	2.18390i
$766$	14906.1			0.703104
$767$		−	25484.0i		−	1.19971i
$768$			2352.04i			0.110510i
$769$	31107.7			1.45874			0.729371	−	0.684118i	$-0.239813\pi$
$769$	31107.7			1.45874			0.729371	+	0.684118i	$0.239813\pi$
$770$		0			0
$771$	56696.5			2.64834
$772$			9414.49i			0.438905i
$773$		−	30354.3i		−	1.41238i	−0.708023	−	0.706189i	$-0.750413\pi$
$773$		−	30354.3i		−	1.41238i	0.708023	−	0.706189i	$-0.249587\pi$
$774$	−53658.1			−2.49186
$775$	609.000	−	3339.77i	0.0282270	−	0.154797i
$776$	309.260			0.0143064
$777$		0			0
$778$		−	8118.02i		−	0.374094i
$779$	944.006			0.0434179
$780$	−14373.1	+	11989.2i	−0.659796	+	0.550363i
$781$	41130.1			1.88444
$782$			22962.4i			1.05004i
$783$		−	4984.65i		−	0.227506i
$784$		0			0
$785$	−10074.9	−	12078.2i	−0.458075	−	0.549157i
$786$	−33245.0			−1.50866
$787$			30312.8i			1.37298i	0.727139	+	0.686491i	$0.240850\pi$
$787$			30312.8i			1.37298i	−0.727139	+	0.686491i	$0.759150\pi$
$788$		−	6209.07i		−	0.280697i
$789$	−1193.58			−0.0538563
$790$	−12226.0	−	14657.0i	−0.550609	−	0.660091i
$791$		0			0
$792$		−	16294.4i		−	0.731057i
$793$			4955.10i			0.221892i
$794$	20495.9			0.916084
$795$	12720.5	−	10610.7i	0.567486	−	0.473363i
$796$	−3041.62			−0.135436
$797$			34499.2i			1.53328i	0.642078	+	0.766639i	$0.278073\pi$
$797$			34499.2i			1.53328i	−0.642078	+	0.766639i	$0.721927\pi$
$798$		0			0
$799$	−54265.1			−2.40271
$800$	−3935.11	−	717.560i	−0.173909	−	0.0317120i
$801$	9472.18			0.417832
$802$		−	5491.98i		−	0.241806i
$803$			9105.97i			0.400178i
$804$	−14981.1			−0.657144
$805$		0			0
$806$	−2474.33			−0.108132
$807$		−	22727.2i		−	0.991371i
$808$			6133.02i			0.267028i
$809$	−22849.8			−0.993025			−0.496513	−	0.868029i	$-0.665386\pi$
$809$	−22849.8			−0.993025			−0.496513	+	0.868029i	$0.665386\pi$
$810$	−14568.1	−	17464.8i	−0.631938	−	0.757592i
$811$	5593.76			0.242199			0.121100	−	0.992640i	$-0.461358\pi$
$811$	5593.76			0.242199			0.121100	+	0.992640i	$0.461358\pi$
$812$		0			0
$813$			26450.5i			1.14103i
$814$	5535.60			0.238357
$815$	−1930.89	−	2314.82i	−0.0829890	−	0.0994903i
$816$	13780.7			0.591202
$817$		−	20971.2i		−	0.898031i
$818$		−	20813.1i		−	0.889624i
$819$		0			0
$820$	722.395	−	602.579i	0.0307648	−	0.0256622i
$821$	34682.4			1.47433			0.737164	−	0.675714i	$-0.236165\pi$
$821$	34682.4			1.47433			0.737164	+	0.675714i	$0.236165\pi$
$822$			42701.6i			1.81191i
$823$			22182.3i			0.939522i	0.882794	+	0.469761i	$0.155660\pi$
$823$			22182.3i			0.939522i	−0.882794	+	0.469761i	$0.844340\pi$
$824$	−4233.79			−0.178994
$825$	40082.1	+	7308.90i	1.69149	+	0.308440i
$826$		0			0
$827$			42247.1i			1.77639i	0.459463	+	0.888197i	$0.348042\pi$
$827$			42247.1i			1.77639i	−0.459463	+	0.888197i	$0.651958\pi$
$828$		−	28126.2i		−	1.18050i
$829$	−44662.3			−1.87115			−0.935577	−	0.353122i	$-0.885120\pi$
$829$	−44662.3			−1.87115			−0.935577	+	0.353122i	$0.885120\pi$
$830$	−14220.3	+	11861.7i	−0.594691	+	0.496056i
$831$	5002.47			0.208825
$832$			2915.40i			0.121482i
$833$		0			0
$834$	−35632.5			−1.47944
$835$	−1778.31	−	2131.90i	−0.0737017	−	0.0883564i
$836$	6368.36			0.263462
$837$		−	7588.79i		−	0.313390i
$838$		−	7803.97i		−	0.321699i
$839$	31559.5			1.29863			0.649317	−	0.760518i	$-0.275055\pi$
$839$	31559.5			1.29863			0.649317	+	0.760518i	$0.275055\pi$
$840$		0			0
$841$	−24070.8			−0.986952
$842$			15561.3i			0.636908i
$843$		−	893.942i		−	0.0365231i
$844$	11769.5			0.480004
$845$	1046.68	−	873.078i	0.0426117	−	0.0355442i
$846$	66468.3			2.70121
$847$		0			0
$848$		−	2580.19i		−	0.104486i
$849$	−46743.3			−1.88955
$850$	−4204.22	+	23056.0i	−0.169651	+	0.930369i
$851$	9555.12			0.384895
$852$		−	42607.4i		−	1.71327i
$853$			39859.6i			1.59996i	0.600027	+	0.799980i	$0.295156\pi$
$853$			39859.6i			1.59996i	−0.600027	+	0.799980i	$0.704844\pi$
$854$		0			0
$855$	22121.1	−	18452.2i	0.884827	−	0.738071i
$856$	5708.90			0.227951
$857$			22061.1i			0.879339i	0.898160	+	0.439669i	$0.144904\pi$
$857$			22061.1i			0.879339i	−0.898160	+	0.439669i	$0.855096\pi$
$858$		−	29695.6i		−	1.18157i
$859$	−17384.6			−0.690518			−0.345259	−	0.938508i	$-0.612209\pi$
$859$	−17384.6			−0.690518			−0.345259	+	0.938508i	$0.612209\pi$
$860$	−13386.4	−	16048.1i	−0.530782	−	0.636321i
$861$		0			0
$862$			26706.0i			1.05523i
$863$			38430.3i			1.51586i	0.652339	+	0.757928i	$0.273788\pi$
$863$			38430.3i			1.51586i	−0.652339	+	0.757928i	$0.726212\pi$
$864$	−8941.57			−0.352081
$865$	815.900	+	978.131i	0.0320710	+	0.0384479i
$866$	25719.0			1.00920
$867$		−	35602.8i		−	1.39462i
$868$		0			0
$869$	30282.0			1.18210
$870$	2814.33	−	2347.55i	0.109672	−	0.0914819i
$871$	−18569.4			−0.722389
$872$			2545.83i			0.0988678i
$873$			2219.44i			0.0860445i
$874$	10992.6			0.425434
$875$		0			0
$876$	9433.04			0.363828
$877$		−	4326.65i		−	0.166591i	−0.996525	−	0.0832956i	$-0.973455\pi$
$877$		−	4326.65i		−	0.166591i	0.996525	−	0.0832956i	$-0.0265446\pi$
$878$		−	24467.1i		−	0.940460i
$879$	40552.9			1.55610
$880$	4873.35	−	4065.06i	0.186683	−	0.155720i
$881$	−28322.7			−1.08310			−0.541552	−	0.840667i	$-0.682163\pi$
$881$	−28322.7			−1.08310			−0.541552	+	0.840667i	$0.682163\pi$
$882$		0			0
$883$			47353.8i			1.80474i	0.430964	+	0.902369i	$0.358173\pi$
$883$			47353.8i			1.80474i	−0.430964	+	0.902369i	$0.641827\pi$
$884$	17081.5			0.649900
$885$	36809.8	+	44128.9i	1.39813	+	1.67613i
$886$	17240.4			0.653728
$887$			38608.5i			1.46150i	0.682648	+	0.730748i	$0.260828\pi$
$887$			38608.5i			1.46150i	−0.682648	+	0.730748i	$0.739172\pi$
$888$		−	5734.43i		−	0.216706i
$889$		0			0
$890$	2363.08	+	2832.95i	0.0890007	+	0.106697i
$891$	36083.0			1.35671
$892$			4877.07i			0.183068i
$893$			25977.8i			0.973477i
$894$	6620.60			0.247680
$895$	−13433.6	+	11205.5i	−0.501717	+	0.418503i
$896$		0			0
$897$		−	51258.2i		−	1.90798i
$898$			106.628i			0.00396239i
$899$	484.485			0.0179738
$900$	5149.66	−	28240.8i	0.190728	−	1.04596i
$901$	−15117.5			−0.558974
$902$			1492.50i			0.0550941i
$903$		0			0
$904$	4050.40			0.149020
$905$	−41306.2	+	34455.2i	−1.51720	+	1.26556i
$906$	6500.44			0.238369
$907$		−	5590.57i		−	0.204666i	−0.994750	−	0.102333i	$-0.967369\pi$
$907$		−	5590.57i		−	0.204666i	0.994750	−	0.102333i	$-0.0326307\pi$
$908$			18294.7i			0.668646i
$909$	−44014.4			−1.60601
$910$		0			0
$911$	27415.0			0.997035			0.498517	−	0.866880i	$-0.333878\pi$
$911$	27415.0			0.997035			0.498517	+	0.866880i	$0.333878\pi$
$912$		−	6597.10i		−	0.239531i
$913$		−	29379.8i		−	1.06498i
$914$	12843.3			0.464790
$915$	−7157.26	−	8580.40i	−0.258592	−	0.310010i
$916$	12337.1			0.445010
$917$		0			0
$918$			52389.0i			1.88355i
$919$	42634.8			1.53035			0.765176	−	0.643821i	$-0.222652\pi$
$919$	42634.8			1.53035			0.765176	+	0.643821i	$0.222652\pi$
$920$	8412.00	−	7016.79i	0.301451	−	0.251453i
$921$	10962.8			0.392222
$922$		−	27549.9i		−	0.984066i
$923$		−	52812.8i		−	1.88337i
$924$		0			0
$925$	9594.07	+	1749.46i	0.341028	+	0.0621859i
$926$	−12573.6			−0.446212
$927$		−	30384.3i		−	1.07654i
$928$		−	570.849i		−	0.0201929i
$929$	16027.2			0.566021			0.283011	−	0.959117i	$-0.408667\pi$
$929$	16027.2			0.566021			0.283011	+	0.959117i	$0.408667\pi$
$930$	4284.62	−	3573.98i	0.151073	−	0.126017i
$931$		0			0
$932$		−	23731.5i		−	0.834067i
$933$		−	89391.8i		−	3.13671i
$934$	−13890.5			−0.486630
$935$	−23817.4	−	28553.2i	−0.833061	−	0.998705i
$936$	−20922.7			−0.730642
$937$			20639.6i			0.719601i	0.933029	+	0.359800i	$0.117155\pi$
$937$			20639.6i			0.719601i	−0.933029	+	0.359800i	$0.882845\pi$
$938$		0			0
$939$	25674.8			0.892297
$940$	16582.2	+	19879.4i	0.575375	+	0.689781i
$941$	−32957.5			−1.14175			−0.570873	−	0.821038i	$-0.693395\pi$
$941$	−32957.5			−1.14175			−0.570873	+	0.821038i	$0.693395\pi$
$942$		−	25850.4i		−	0.894109i
$943$			2576.24i			0.0889649i
$944$	8950.97			0.308611
$945$		0			0
$946$	33156.2			1.13954
$947$		−	29530.6i		−	1.01332i	−0.862146	−	0.506660i	$-0.830880\pi$
$947$		−	29530.6i		−	1.01332i	0.862146	−	0.506660i	$-0.169120\pi$
$948$		−	31369.7i		−	1.07473i
$949$	11692.4			0.399950
$950$	11037.4	+	2012.64i	0.376947	+	0.0687356i
$951$	−57256.5			−1.95233
$952$		0			0
$953$		−	41951.6i		−	1.42596i	−0.701182	−	0.712982i	$-0.747344\pi$
$953$		−	41951.6i		−	1.42596i	0.701182	−	0.712982i	$-0.252656\pi$
$954$	18517.1			0.628420
$955$	21164.4	−	17654.1i	0.717134	−	0.598191i
$956$	−3228.49			−0.109222
$957$			5814.53i			0.196402i
$958$		−	14457.5i		−	0.487580i
$959$		0			0
$960$	−4211.08	−	5048.40i	−0.141575	−	0.169725i
$961$	−29053.4			−0.975241
$962$		−	7107.95i		−	0.238222i
$963$			40970.6i			1.37099i
$964$	−17046.2			−0.569526
$965$	−16855.6	−	20207.2i	−0.562282	−	0.674085i
$966$		0			0
$967$		−	24197.6i		−	0.804699i	−0.915486	−	0.402349i	$-0.868194\pi$
$967$		−	24197.6i		−	0.804699i	0.915486	−	0.402349i	$-0.131806\pi$
$968$		−	579.424i		−	0.0192391i
$969$	−38652.7			−1.28143
$970$	−663.793	+	553.697i	−0.0219723	+	0.0183280i
$971$	−9056.44			−0.299315			−0.149657	−	0.988738i	$-0.547817\pi$
$971$	−9056.44			−0.299315			−0.149657	+	0.988738i	$0.547817\pi$
$972$		−	7201.28i		−	0.237635i
$973$		0			0
$974$	−2847.16			−0.0936642
$975$	9384.94	−	51467.1i	0.308265	−	1.69053i
$976$	−1740.42			−0.0570794
$977$			22533.8i			0.737891i	0.929451	+	0.368946i	$0.120281\pi$
$977$			22533.8i			0.737891i	−0.929451	+	0.368946i	$0.879719\pi$
$978$		−	4954.31i		−	0.161985i
$979$	−5853.01			−0.191075
$980$		0			0
$981$	−18270.5			−0.594629
$982$			15149.2i			0.492293i
$983$			26648.2i			0.864645i	0.901719	+	0.432322i	$0.142306\pi$
$983$			26648.2i			0.864645i	−0.901719	+	0.432322i	$0.857694\pi$
$984$	1546.11			0.0500896
$985$	11116.7	+	13327.1i	0.359601	+	0.431103i
$986$	−3344.63			−0.108027
$987$		0			0
$988$		−	8177.25i		−	0.263313i
$989$	57231.6			1.84010
$990$	29173.4	+	34974.2i	0.936558	+	1.12278i
$991$	−35170.4			−1.12737			−0.563686	−	0.825989i	$-0.690617\pi$
$991$	−35170.4			−1.12737			−0.563686	+	0.825989i	$0.690617\pi$
$992$		−	869.078i		−	0.0278158i
$993$		−	100077.i		−	3.19823i
$994$		0			0
$995$	6528.50	−	5445.69i	0.208007	−	0.173508i
$996$	−30435.1			−0.968245
$997$			3808.67i			0.120985i	0.998169	+	0.0604923i	$0.0192671\pi$
$997$			3808.67i			0.120985i	−0.998169	+	0.0604923i	$0.980733\pi$
$998$		−	27682.2i		−	0.878020i
$999$	21800.2			0.690417

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.c.f.99.6		12
5.2	odd	4		2450.4.a.cy.1.6		6
5.3	odd	4		2450.4.a.cv.1.1		6
5.4	even	2	inner	490.4.c.f.99.7		12
7.2	even	3		70.4.i.a.39.1	yes	24
7.4	even	3		70.4.i.a.9.12	yes	24
7.6	odd	2		490.4.c.e.99.1		12
35.2	odd	12		350.4.e.n.151.1		12
35.4	even	6		70.4.i.a.9.1	✓	24
35.9	even	6		70.4.i.a.39.12	yes	24
35.13	even	4		2450.4.a.cw.1.6		6
35.18	odd	12		350.4.e.o.51.6		12
35.23	odd	12		350.4.e.o.151.6		12
35.27	even	4		2450.4.a.cx.1.1		6
35.32	odd	12		350.4.e.n.51.1		12
35.34	odd	2		490.4.c.e.99.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.i.a.9.1	✓	24	35.4	even	6
70.4.i.a.9.12	yes	24	7.4	even	3
70.4.i.a.39.1	yes	24	7.2	even	3
70.4.i.a.39.12	yes	24	35.9	even	6
350.4.e.n.51.1		12	35.32	odd	12
350.4.e.n.151.1		12	35.2	odd	12
350.4.e.o.51.6		12	35.18	odd	12
350.4.e.o.151.6		12	35.23	odd	12
490.4.c.e.99.1		12	7.6	odd	2
490.4.c.e.99.12		12	35.34	odd	2
490.4.c.f.99.6		12	1.1	even	1	trivial
490.4.c.f.99.7		12	5.4	even	2	inner
2450.4.a.cv.1.1		6	5.3	odd	4
2450.4.a.cw.1.6		6	35.13	even	4
2450.4.a.cx.1.1		6	35.27	even	4
2450.4.a.cy.1.6		6	5.2	odd	4

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +9.18765i q^{3} -4.00000 q^{4} +(8.58556 - 7.16157i) q^{5} +18.3753 q^{6} +8.00000i q^{8} -57.4130 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +9.18765i q^{3} -4.00000 q^{4} +(8.58556 - 7.16157i) q^{5} +18.3753 q^{6} +8.00000i q^{8} -57.4130 q^{9} +(-14.3231 - 17.1711i) q^{10} +35.4764 q^{11} -36.7506i q^{12} -45.5531i q^{13} +(65.7981 + 78.8812i) q^{15} +16.0000 q^{16} -93.7447i q^{17} +114.826i q^{18} -44.8775 q^{19} +(-34.3422 + 28.6463i) q^{20} -70.9527i q^{22} -122.473i q^{23} -73.5012 q^{24} +(22.4238 - 122.972i) q^{25} -91.1063 q^{26} -279.424i q^{27} +17.8390 q^{29} +(157.762 - 131.596i) q^{30} +27.1587 q^{31} -32.0000i q^{32} +325.945i q^{33} -187.489 q^{34} +229.652 q^{36} +78.0182i q^{37} +89.7550i q^{38} +418.526 q^{39} +(57.2926 + 68.6845i) q^{40} -21.0352 q^{41} +467.300i q^{43} -141.905 q^{44} +(-492.923 + 411.167i) q^{45} -244.946 q^{46} -578.861i q^{47} +147.002i q^{48} +(-245.945 - 44.8475i) q^{50} +861.294 q^{51} +182.213i q^{52} -161.262i q^{53} -558.848 q^{54} +(304.584 - 254.067i) q^{55} -412.319i q^{57} -35.6781i q^{58} +559.436 q^{59} +(-263.192 - 315.525i) q^{60} -108.776 q^{61} -54.3174i q^{62} -64.0000 q^{64} +(-326.232 - 391.099i) q^{65} +651.889 q^{66} -407.643i q^{67} +374.979i q^{68} +1125.24 q^{69} +1159.37 q^{71} -459.304i q^{72} +256.677i q^{73} +156.036 q^{74} +(1129.83 + 206.022i) q^{75} +179.510 q^{76} -837.053i q^{78} +853.583 q^{79} +(137.369 - 114.585i) q^{80} +1017.10 q^{81} +42.0703i q^{82} -828.152i q^{83} +(-671.359 - 804.851i) q^{85} +934.599 q^{86} +163.899i q^{87} +283.811i q^{88} -164.983 q^{89} +(822.335 + 985.846i) q^{90} +489.892i q^{92} +249.525i q^{93} -1157.72 q^{94} +(-385.299 + 321.394i) q^{95} +294.005 q^{96} -38.6575i q^{97} -2036.80 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 48 q^{4} + 8 q^{5} + 28 q^{6} - 62 q^{9}+O(q^{10}) \) 12 * q - 48 * q^4 + 8 * q^5 + 28 * q^6 - 62 * q^9	\( 12 q - 48 q^{4} + 8 q^{5} + 28 q^{6} - 62 q^{9} - 12 q^{10} + 62 q^{11} + 86 q^{15} + 192 q^{16} - 186 q^{19} - 32 q^{20} - 112 q^{24} - 126 q^{25} + 236 q^{26} - 338 q^{29} - 28 q^{30} + 652 q^{31} - 272 q^{34} + 248 q^{36} + 868 q^{39} + 48 q^{40} + 396 q^{41} - 248 q^{44} - 664 q^{45} - 376 q^{46} + 160 q^{50} + 1448 q^{51} - 1540 q^{54} + 298 q^{55} - 1336 q^{59} - 344 q^{60} + 314 q^{61} - 768 q^{64} - 1862 q^{65} + 1600 q^{66} + 90 q^{69} + 2216 q^{71} + 1012 q^{74} + 4550 q^{75} + 744 q^{76} + 1772 q^{79} + 128 q^{80} - 1228 q^{81} + 2282 q^{85} - 396 q^{86} - 6094 q^{89} + 100 q^{90} - 3604 q^{94} - 1166 q^{95} + 448 q^{96} - 8546 q^{99}+O(q^{100}) \) 12 * q - 48 * q^4 + 8 * q^5 + 28 * q^6 - 62 * q^9 - 12 * q^10 + 62 * q^11 + 86 * q^15 + 192 * q^16 - 186 * q^19 - 32 * q^20 - 112 * q^24 - 126 * q^25 + 236 * q^26 - 338 * q^29 - 28 * q^30 + 652 * q^31 - 272 * q^34 + 248 * q^36 + 868 * q^39 + 48 * q^40 + 396 * q^41 - 248 * q^44 - 664 * q^45 - 376 * q^46 + 160 * q^50 + 1448 * q^51 - 1540 * q^54 + 298 * q^55 - 1336 * q^59 - 344 * q^60 + 314 * q^61 - 768 * q^64 - 1862 * q^65 + 1600 * q^66 + 90 * q^69 + 2216 * q^71 + 1012 * q^74 + 4550 * q^75 + 744 * q^76 + 1772 * q^79 + 128 * q^80 - 1228 * q^81 + 2282 * q^85 - 396 * q^86 - 6094 * q^89 + 100 * q^90 - 3604 * q^94 - 1166 * q^95 + 448 * q^96 - 8546 * q^99

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