LMFDB - Embedded newform 490.4.c.e.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			$7.00242i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.4.c.e.99.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +6.00242i q^{3} -4.00000 q^{4} +(-3.14360 - 10.7293i) q^{5} +12.0048 q^{6} +8.00000i q^{8} -9.02909 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +6.00242i q^{3} -4.00000 q^{4} +(-3.14360 - 10.7293i) q^{5} +12.0048 q^{6} +8.00000i q^{8} -9.02909 q^{9} +(-21.4586 + 6.28719i) q^{10} +9.14868 q^{11} -24.0097i q^{12} -32.7036i q^{13} +(64.4018 - 18.8692i) q^{15} +16.0000 q^{16} +109.798i q^{17} +18.0582i q^{18} -22.2644 q^{19} +(12.5744 + 42.9172i) q^{20} -18.2974i q^{22} -191.279i q^{23} -48.0194 q^{24} +(-105.236 + 67.4571i) q^{25} -65.4072 q^{26} +107.869i q^{27} -190.986 q^{29} +(-37.7384 - 128.804i) q^{30} -35.6111 q^{31} -32.0000i q^{32} +54.9143i q^{33} +219.595 q^{34} +36.1164 q^{36} -57.7420i q^{37} +44.5287i q^{38} +196.301 q^{39} +(85.8344 - 25.1488i) q^{40} -39.7463 q^{41} -323.003i q^{43} -36.5947 q^{44} +(28.3838 + 96.8758i) q^{45} -382.557 q^{46} +57.1037i q^{47} +96.0388i q^{48} +(134.914 + 210.471i) q^{50} -659.052 q^{51} +130.814i q^{52} -529.738i q^{53} +215.738 q^{54} +(-28.7597 - 98.1589i) q^{55} -133.640i q^{57} +381.973i q^{58} -766.697 q^{59} +(-257.607 + 75.4768i) q^{60} -524.009 q^{61} +71.2221i q^{62} -64.0000 q^{64} +(-350.887 + 102.807i) q^{65} +109.829 q^{66} -370.893i q^{67} -439.191i q^{68} +1148.14 q^{69} -722.165 q^{71} -72.2327i q^{72} -829.047i q^{73} -115.484 q^{74} +(-404.906 - 631.669i) q^{75} +89.0575 q^{76} -392.602i q^{78} -494.621 q^{79} +(-50.2975 - 171.669i) q^{80} -891.261 q^{81} +79.4926i q^{82} -1241.34i q^{83} +(1178.05 - 345.159i) q^{85} -646.005 q^{86} -1146.38i q^{87} +73.1895i q^{88} +20.7580 q^{89} +(193.752 - 56.7676i) q^{90} +765.115i q^{92} -213.753i q^{93} +114.207 q^{94} +(69.9902 + 238.881i) q^{95} +192.078 q^{96} +1010.36i q^{97} -82.6042 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$			6.00242i			1.15517i	0.816332	+	0.577583i	$0.196004\pi$
$3$			6.00242i			1.15517i	−0.816332	+	0.577583i	$0.803996\pi$
$4$	−4.00000			−0.500000
$5$	−3.14360	−	10.7293i	−0.281172	−	0.959657i
$5$	−3.14360	−	10.7293i	−0.281172	−	0.959657i
$6$	12.0048			0.816826
$7$		0			0
$7$		0			0
$8$			8.00000i			0.353553i
$9$	−9.02909			−0.334411
$10$	−21.4586	+	6.28719i	−0.678580	+	0.198818i
$11$	9.14868			0.250766			0.125383	−	0.992108i	$-0.459984\pi$
$11$	9.14868			0.250766			0.125383	+	0.992108i	$0.459984\pi$
$12$		−	24.0097i		−	0.577583i
$13$		−	32.7036i		−	0.697719i	−0.937175	−	0.348859i	$-0.886569\pi$
$13$		−	32.7036i		−	0.697719i	0.937175	−	0.348859i	$-0.113431\pi$
$14$		0			0
$15$	64.4018	−	18.8692i	1.10856	−	0.324800i
$16$	16.0000			0.250000
$17$			109.798i			1.56646i	0.621731	+	0.783231i	$0.286430\pi$
$17$			109.798i			1.56646i	−0.621731	+	0.783231i	$0.713570\pi$
$18$			18.0582i			0.236464i
$19$	−22.2644			−0.268831			−0.134416	−	0.990925i	$-0.542916\pi$
$19$	−22.2644			−0.268831			−0.134416	+	0.990925i	$0.542916\pi$
$20$	12.5744	+	42.9172i	0.140586	+	0.479829i
$21$		0			0
$22$		−	18.2974i		−	0.177319i
$23$		−	191.279i		−	1.73410i	−0.498219	−	0.867051i	$-0.666012\pi$
$23$		−	191.279i		−	1.73410i	0.498219	−	0.867051i	$-0.333988\pi$
$24$	−48.0194			−0.408413
$25$	−105.236	+	67.4571i	−0.841885	+	0.539657i
$26$	−65.4072			−0.493362
$27$			107.869i			0.768867i
$28$		0			0
$29$	−190.986			−1.22294			−0.611470	−	0.791267i	$-0.709422\pi$
$29$	−190.986			−1.22294			−0.611470	+	0.791267i	$0.709422\pi$
$30$	−37.7384	−	128.804i	−0.229668	−	0.783874i
$31$	−35.6111			−0.206320			−0.103160	−	0.994665i	$-0.532895\pi$
$31$	−35.6111			−0.206320			−0.103160	+	0.994665i	$0.532895\pi$
$32$		−	32.0000i		−	0.176777i
$33$			54.9143i			0.289677i
$34$	219.595			1.10766
$35$		0			0
$36$	36.1164			0.167205
$37$		−	57.7420i		−	0.256560i	−0.991738	−	0.128280i	$-0.959054\pi$
$37$		−	57.7420i		−	0.256560i	0.991738	−	0.128280i	$-0.0409457\pi$
$38$			44.5287i			0.190092i
$39$	196.301			0.805982
$40$	85.8344	−	25.1488i	0.339290	−	0.0994092i
$41$	−39.7463			−0.151398			−0.0756991	−	0.997131i	$-0.524119\pi$
$41$	−39.7463			−0.151398			−0.0756991	+	0.997131i	$0.524119\pi$
$42$		0			0
$43$		−	323.003i		−	1.14552i	−0.819722	−	0.572761i	$-0.805872\pi$
$43$		−	323.003i		−	1.14552i	0.819722	−	0.572761i	$-0.194128\pi$
$44$	−36.5947			−0.125383
$45$	28.3838	+	96.8758i	0.0940268	+	0.320920i
$46$	−382.557			−1.22620
$47$			57.1037i			0.177222i	0.996066	+	0.0886110i	$0.0282428\pi$
$47$			57.1037i			0.177222i	−0.996066	+	0.0886110i	$0.971757\pi$
$48$			96.0388i			0.288792i
$49$		0			0
$50$	134.914	+	210.471i	0.381595	+	0.595303i
$51$	−659.052			−1.80952
$52$			130.814i			0.348859i
$53$		−	529.738i		−	1.37293i	−0.727165	−	0.686463i	$-0.759162\pi$
$53$		−	529.738i		−	1.37293i	0.727165	−	0.686463i	$-0.240838\pi$
$54$	215.738			0.543671
$55$	−28.7597	−	98.1589i	−0.0705084	−	0.240650i
$56$		0			0
$57$		−	133.640i		−	0.310545i
$58$			381.973i			0.864750i
$59$	−766.697			−1.69179			−0.845894	−	0.533352i	$-0.820932\pi$
$59$	−766.697			−1.69179			−0.845894	+	0.533352i	$0.820932\pi$
$60$	−257.607	+	75.4768i	−0.554282	+	0.162400i
$61$	−524.009			−1.09988			−0.549939	−	0.835205i	$-0.685349\pi$
$61$	−524.009			−1.09988			−0.549939	+	0.835205i	$0.685349\pi$
$62$			71.2221i			0.145891i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−350.887	+	102.807i	−0.669571	+	0.196179i
$66$	109.829			0.204833
$67$		−	370.893i		−	0.676295i	−0.941093	−	0.338148i	$-0.890200\pi$
$67$		−	370.893i		−	0.676295i	0.941093	−	0.338148i	$-0.109800\pi$
$68$		−	439.191i		−	0.783231i
$69$	1148.14			2.00318
$70$		0			0
$71$	−722.165			−1.20712			−0.603558	−	0.797319i	$-0.706251\pi$
$71$	−722.165			−1.20712			−0.603558	+	0.797319i	$0.706251\pi$
$72$		−	72.2327i		−	0.118232i
$73$		−	829.047i		−	1.32921i	−0.747193	−	0.664607i	$-0.768599\pi$
$73$		−	829.047i		−	1.32921i	0.747193	−	0.664607i	$-0.231401\pi$
$74$	−115.484			−0.181416
$75$	−404.906	−	631.669i	−0.623394	−	0.972518i
$76$	89.0575			0.134416
$77$		0			0
$78$		−	392.602i		−	0.569915i
$79$	−494.621			−0.704421			−0.352210	−	0.935921i	$-0.614570\pi$
$79$	−494.621			−0.704421			−0.352210	+	0.935921i	$0.614570\pi$
$80$	−50.2975	−	171.669i	−0.0702929	−	0.239914i
$81$	−891.261			−1.22258
$82$			79.4926i			0.107055i
$83$		−	1241.34i		−	1.64162i	−0.571201	−	0.820810i	$-0.693522\pi$
$83$		−	1241.34i		−	1.64162i	0.571201	−	0.820810i	$-0.306478\pi$
$84$		0			0
$85$	1178.05	−	345.159i	1.50327	−	0.440445i
$86$	−646.005			−0.810007
$87$		−	1146.38i		−	1.41270i
$88$			73.1895i			0.0886593i
$89$	20.7580			0.0247229			0.0123615	−	0.999924i	$-0.496065\pi$
$89$	20.7580			0.0247229			0.0123615	+	0.999924i	$0.496065\pi$
$90$	193.752	−	56.7676i	0.226924	−	0.0664870i
$91$		0			0
$92$			765.115i			0.867051i
$93$		−	213.753i		−	0.238335i
$94$	114.207			0.125315
$95$	69.9902	+	238.881i	0.0755878	+	0.257986i
$96$	192.078			0.204207
$97$			1010.36i			1.05759i	0.848748	+	0.528797i	$0.177357\pi$
$97$			1010.36i			1.05759i	−0.848748	+	0.528797i	$0.822643\pi$
$98$		0			0
$99$	−82.6042			−0.0838590
$100$	420.942	−	269.829i	0.420942	−	0.269829i
$101$	1286.97			1.26790			0.633950	−	0.773374i	$-0.281433\pi$
$101$	1286.97			1.26790			0.633950	+	0.773374i	$0.281433\pi$
$102$			1318.10i			1.27953i
$103$			1648.16i			1.57668i	0.615242	+	0.788338i	$0.289058\pi$
$103$			1648.16i			1.57668i	−0.615242	+	0.788338i	$0.710942\pi$
$104$	261.629			0.246681
$105$		0			0
$106$	−1059.48			−0.970805
$107$		−	68.3883i		−	0.0617883i	−0.999523	−	0.0308941i	$-0.990165\pi$
$107$		−	68.3883i		−	0.0617883i	0.999523	−	0.0308941i	$-0.00983548\pi$
$108$		−	431.476i		−	0.384433i
$109$	−187.622			−0.164871			−0.0824353	−	0.996596i	$-0.526270\pi$
$109$	−187.622			−0.164871			−0.0824353	+	0.996596i	$0.526270\pi$
$110$	−196.318	+	57.5195i	−0.170165	+	0.0498570i
$111$	346.592			0.296370
$112$		0			0
$113$			979.328i			0.815287i	0.913141	+	0.407643i	$0.133649\pi$
$113$			979.328i			0.815287i	−0.913141	+	0.407643i	$0.866351\pi$
$114$	−267.280			−0.219589
$115$	−2052.29	+	601.303i	−1.66414	+	0.487580i
$116$	763.946			0.611470
$117$			295.284i			0.233325i
$118$			1533.39i			1.19627i
$119$		0			0
$120$	150.954	+	515.214i	0.114834	+	0.391937i
$121$	−1247.30			−0.937116
$122$			1048.02i			0.777731i
$123$		−	238.574i		−	0.174890i
$124$	142.444			0.103160
$125$	1054.59	+	917.046i	0.754600	+	0.656185i
$126$		0			0
$127$			58.6732i			0.0409953i	0.999790	+	0.0204977i	$0.00652507\pi$
$127$			58.6732i			0.0409953i	−0.999790	+	0.0204977i	$0.993475\pi$
$128$			128.000i			0.0883883i
$129$	1938.80			1.32327
$130$	205.614	+	701.773i	0.138719	+	0.473458i
$131$	−1530.15			−1.02053			−0.510265	−	0.860017i	$-0.670453\pi$
$131$	−1530.15			−1.02053			−0.510265	+	0.860017i	$0.670453\pi$
$132$		−	219.657i		−	0.144839i
$133$		0			0
$134$	−741.786			−0.478213
$135$	1157.36	−	339.097i	0.737849	−	0.216184i
$136$	−878.381			−0.553828
$137$		−	3042.88i		−	1.89760i	−0.315882	−	0.948798i	$-0.602301\pi$
$137$		−	3042.88i		−	1.89760i	0.315882	−	0.948798i	$-0.397699\pi$
$138$		−	2296.27i		−	1.41646i
$139$	−1793.28			−1.09427			−0.547136	−	0.837044i	$-0.684282\pi$
$139$	−1793.28			−1.09427			−0.547136	+	0.837044i	$0.684282\pi$
$140$		0			0
$141$	−342.761			−0.204721
$142$			1444.33i			0.853559i
$143$		−	299.195i		−	0.174964i
$144$	−144.465			−0.0836027
$145$	600.384	+	2049.15i	0.343856	+	1.17360i
$146$	−1658.09			−0.939897
$147$		0			0
$148$			230.968i			0.128280i
$149$	2008.16			1.10413			0.552064	−	0.833802i	$-0.313841\pi$
$149$	2008.16			1.10413			0.552064	+	0.833802i	$0.313841\pi$
$150$	−1263.34	+	809.813i	−0.687674	+	0.440806i
$151$	−59.1933			−0.0319012			−0.0159506	−	0.999873i	$-0.505077\pi$
$151$	−59.1933			−0.0319012			−0.0159506	+	0.999873i	$0.505077\pi$
$152$		−	178.115i		−	0.0950462i
$153$		−	991.373i		−	0.523841i
$154$		0			0
$155$	111.947	+	382.082i	0.0580115	+	0.197997i
$156$	−785.203			−0.402991
$157$			2671.04i			1.35778i	0.734238	+	0.678892i	$0.237540\pi$
$157$			2671.04i			1.35778i	−0.734238	+	0.678892i	$0.762460\pi$
$158$			989.242i			0.498101i
$159$	3179.71			1.58596
$160$	−343.337	+	100.595i	−0.169645	+	0.0497046i
$161$		0			0
$162$			1782.52i			0.864495i
$163$			2767.06i			1.32965i	0.747000	+	0.664824i	$0.231493\pi$
$163$			2767.06i			1.32965i	−0.747000	+	0.664824i	$0.768507\pi$
$164$	158.985			0.0756991
$165$	589.191	−	172.628i	0.277991	−	0.0814490i
$166$	−2482.68			−1.16080
$167$			1603.11i			0.742828i	0.928467	+	0.371414i	$0.121127\pi$
$167$			1603.11i			0.742828i	−0.928467	+	0.371414i	$0.878873\pi$
$168$		0			0
$169$	1127.48			0.513189
$170$	−690.319	−	2356.10i	−0.311441	−	1.06297i
$171$	201.027			0.0899001
$172$			1292.01i			0.572761i
$173$		−	592.913i		−	0.260568i	−0.991477	−	0.130284i	$-0.958411\pi$
$173$		−	592.913i		−	0.260568i	0.991477	−	0.130284i	$-0.0415890\pi$
$174$	−2292.76			−0.998930
$175$		0			0
$176$	146.379			0.0626916
$177$		−	4602.04i		−	1.95430i
$178$		−	41.5159i		−	0.0174817i
$179$	499.392			0.208527			0.104263	−	0.994550i	$-0.466751\pi$
$179$	499.392			0.208527			0.104263	+	0.994550i	$0.466751\pi$
$180$	−113.535	−	387.503i	−0.0470134	−	0.160460i
$181$	1133.42			0.465450			0.232725	−	0.972543i	$-0.425236\pi$
$181$	1133.42			0.465450			0.232725	+	0.972543i	$0.425236\pi$
$182$		0			0
$183$		−	3145.33i		−	1.27054i
$184$	1530.23			0.613098
$185$	−619.531	+	181.518i	−0.246210	+	0.0721375i
$186$	−427.505			−0.168528
$187$			1004.50i			0.392816i
$188$		−	228.415i		−	0.0886110i
$189$		0			0
$190$	477.762	−	139.980i	0.182424	−	0.0534486i
$191$	2389.57			0.905251			0.452625	−	0.891701i	$-0.350487\pi$
$191$	2389.57			0.905251			0.452625	+	0.891701i	$0.350487\pi$
$192$		−	384.155i		−	0.144396i
$193$			608.230i			0.226846i	0.993547	+	0.113423i	$0.0361816\pi$
$193$			608.230i			0.226846i	−0.993547	+	0.113423i	$0.963818\pi$
$194$	2020.72			0.747832
$195$	−617.090	−	2106.17i	−0.226619	−	0.773466i
$196$		0			0
$197$		−	2976.07i		−	1.07633i	−0.842841	−	0.538163i	$-0.819118\pi$
$197$		−	2976.07i		−	1.07633i	0.842841	−	0.538163i	$-0.180882\pi$
$198$			165.208i			0.0592973i
$199$	1731.83			0.616916			0.308458	−	0.951238i	$-0.400187\pi$
$199$	1731.83			0.616916			0.308458	+	0.951238i	$0.400187\pi$
$200$	−539.657	−	841.885i	−0.190798	−	0.297651i
$201$	2226.26			0.781234
$202$		−	2573.93i		−	0.896540i
$203$		0			0
$204$	2636.21			0.904762
$205$	124.946	+	426.450i	0.0425689	+	0.145291i
$206$	3296.31			1.11488
$207$			1727.07i			0.579902i
$208$		−	523.257i		−	0.174430i
$209$	−203.690			−0.0674139
$210$		0			0
$211$	−785.955			−0.256433			−0.128217	−	0.991746i	$-0.540925\pi$
$211$	−785.955			−0.256433			−0.128217	+	0.991746i	$0.540925\pi$
$212$			2118.95i			0.686463i
$213$		−	4334.74i		−	1.39442i
$214$	−136.777			−0.0436909
$215$	−3465.59	+	1015.39i	−1.09931	+	0.322088i
$216$	−862.952			−0.271835
$217$		0			0
$218$			375.243i			0.116581i
$219$	4976.29			1.53546
$220$	115.039	+	392.636i	0.0352542	+	0.120325i
$221$	3590.78			1.09295
$222$		−	693.184i		−	0.209565i
$223$		−	6112.17i		−	1.83543i	−0.397237	−	0.917716i	$-0.630031\pi$
$223$		−	6112.17i		−	1.83543i	0.397237	−	0.917716i	$-0.369969\pi$
$224$		0			0
$225$	950.182	−	609.076i	0.281535	−	0.180467i
$226$	1958.66			0.576495
$227$		−	2133.14i		−	0.623706i	−0.950130	−	0.311853i	$-0.899050\pi$
$227$		−	2133.14i		−	0.623706i	0.950130	−	0.311853i	$-0.100950\pi$
$228$			534.561i			0.155273i
$229$	2452.04			0.707578			0.353789	−	0.935325i	$-0.384893\pi$
$229$	2452.04			0.707578			0.353789	+	0.935325i	$0.384893\pi$
$230$	1202.61	+	4104.57i	0.344771	+	1.17673i
$231$		0			0
$232$		−	1527.89i		−	0.432375i
$233$			4067.42i			1.14363i	0.820383	+	0.571814i	$0.193760\pi$
$233$			4067.42i			1.14363i	−0.820383	+	0.571814i	$0.806240\pi$
$234$	590.567			0.164985
$235$	612.683	−	179.511i	0.170072	−	0.0498298i
$236$	3066.79			0.845894
$237$		−	2968.93i		−	0.813723i
$238$		0			0
$239$	−860.208			−0.232813			−0.116406	−	0.993202i	$-0.537137\pi$
$239$	−860.208			−0.232813			−0.116406	+	0.993202i	$0.537137\pi$
$240$	1030.43	−	301.907i	0.277141	−	0.0812001i
$241$	−60.9641			−0.0162948			−0.00814739	−	0.999967i	$-0.502593\pi$
$241$	−60.9641			−0.0162948			−0.00814739	+	0.999967i	$0.502593\pi$
$242$			2494.60i			0.662641i
$243$		−	2437.26i		−	0.643417i
$244$	2096.04			0.549939
$245$		0			0
$246$	−477.148			−0.123666
$247$			728.125i			0.187569i
$248$		−	284.888i		−	0.0729453i
$249$	7451.03			1.89635
$250$	1834.09	−	2109.17i	0.463993	−	0.533583i
$251$	−4683.77			−1.17784			−0.588919	−	0.808192i	$-0.700446\pi$
$251$	−4683.77			−1.17784			−0.588919	+	0.808192i	$0.700446\pi$
$252$		0			0
$253$		−	1749.95i		−	0.434855i
$254$	117.346			0.0289881
$255$	2071.79	+	7071.17i	0.508787	+	1.73652i
$256$	256.000			0.0625000
$257$		−	930.412i		−	0.225827i	−0.993605	−	0.112913i	$-0.963982\pi$
$257$		−	930.412i		−	0.225827i	0.993605	−	0.112913i	$-0.0360183\pi$
$258$		−	3877.60i		−	0.935693i
$259$		0			0
$260$	1403.55	−	411.227i	0.334785	−	0.0980894i
$261$	1724.43			0.408964
$262$			3060.29i			0.721624i
$263$		−	5682.86i		−	1.33240i	−0.745775	−	0.666198i	$-0.767921\pi$
$263$		−	5682.86i		−	1.33240i	0.745775	−	0.666198i	$-0.232079\pi$
$264$	−439.314			−0.102416
$265$	−5683.71	+	1665.28i	−1.31754	+	0.386028i
$266$		0			0
$267$			124.598i			0.0285591i
$268$			1483.57i			0.338148i
$269$	2418.73			0.548224			0.274112	−	0.961698i	$-0.411616\pi$
$269$	2418.73			0.548224			0.274112	+	0.961698i	$0.411616\pi$
$270$	−678.193	−	2314.72i	−0.152865	−	0.521738i
$271$	−327.762			−0.0734692			−0.0367346	−	0.999325i	$-0.511696\pi$
$271$	−327.762			−0.0734692			−0.0367346	+	0.999325i	$0.511696\pi$
$272$			1756.76i			0.391615i
$273$		0			0
$274$	−6085.76			−1.34180
$275$	−962.767	+	617.144i	−0.211117	+	0.135328i
$276$	−4592.54			−1.00159
$277$		−	1530.62i		−	0.332008i	−0.986125	−	0.166004i	$-0.946914\pi$
$277$		−	1530.62i		−	0.332008i	0.986125	−	0.166004i	$-0.0530864\pi$
$278$			3586.55i			0.773767i
$279$	321.535			0.0689958
$280$		0			0
$281$	9173.67			1.94753			0.973764	−	0.227561i	$-0.0730751\pi$
$281$	9173.67			1.94753			0.973764	+	0.227561i	$0.0730751\pi$
$282$			685.522i			0.144760i
$283$		−	3450.42i		−	0.724756i	−0.932031	−	0.362378i	$-0.881965\pi$
$283$		−	3450.42i		−	0.724756i	0.932031	−	0.362378i	$-0.118035\pi$
$284$	2888.66			0.603558
$285$	−1433.87	+	420.111i	−0.298017	+	0.0873165i
$286$	−598.389			−0.123719
$287$		0			0
$288$			288.931i			0.0591160i
$289$	−7142.53			−1.45380
$290$	4098.30	−	1200.77i	0.829864	−	0.243143i
$291$	−6064.62			−1.22170
$292$			3316.19i			0.664607i
$293$			5618.66i			1.12029i	0.828394	+	0.560146i	$0.189255\pi$
$293$			5618.66i			1.12029i	−0.828394	+	0.560146i	$0.810745\pi$
$294$		0			0
$295$	2410.18	+	8226.12i	0.475683	+	1.62354i
$296$	461.936			0.0907078
$297$			986.859i			0.192806i
$298$		−	4016.32i		−	0.780736i
$299$	−6255.50			−1.20992
$300$	1619.63	+	2526.68i	0.311697	+	0.486259i
$301$		0			0
$302$			118.387i			0.0225576i
$303$			7724.91i			1.46464i
$304$	−356.230			−0.0672078
$305$	1647.27	+	5622.25i	0.309254	+	1.05551i
$306$	−1982.75			−0.370412
$307$			3600.31i			0.669317i	0.942339	+	0.334658i	$0.108621\pi$
$307$			3600.31i			0.669317i	−0.942339	+	0.334658i	$0.891379\pi$
$308$		0			0
$309$	−9892.94			−1.82132
$310$	764.163	−	223.894i	0.140005	−	0.0410203i
$311$	−4567.54			−0.832803			−0.416401	−	0.909181i	$-0.636709\pi$
$311$	−4567.54			−0.832803			−0.416401	+	0.909181i	$0.636709\pi$
$312$			1570.41i			0.284958i
$313$		−	2299.84i		−	0.415318i	−0.978201	−	0.207659i	$-0.933416\pi$
$313$		−	2299.84i		−	0.415318i	0.978201	−	0.207659i	$-0.0665844\pi$
$314$	5342.08			0.960099
$315$		0			0
$316$	1978.48			0.352210
$317$		−	10423.8i		−	1.84688i	−0.383743	−	0.923440i	$-0.625365\pi$
$317$		−	10423.8i		−	1.84688i	0.383743	−	0.923440i	$-0.374635\pi$
$318$		−	6359.42i		−	1.12144i
$319$	−1747.27			−0.306673
$320$	201.190	+	686.675i	0.0351465	+	0.119957i
$321$	410.496			0.0713758
$322$		0			0
$323$		−	2444.58i		−	0.421114i
$324$	3565.04			0.611290
$325$	2206.09	+	3441.58i	0.376529	+	0.587399i
$326$	5534.11			0.940203
$327$		−	1126.18i		−	0.190453i
$328$		−	317.970i		−	0.0535274i
$329$		0			0
$330$	−345.256	−	1178.38i	−0.0575931	−	0.196569i
$331$	6217.79			1.03251			0.516255	−	0.856435i	$-0.327326\pi$
$331$	6217.79			1.03251			0.516255	+	0.856435i	$0.327326\pi$
$332$			4965.35i			0.820810i
$333$			521.358i			0.0857965i
$334$	3206.22			0.525259
$335$	−3979.42	+	1165.94i	−0.649012	+	0.190155i
$336$		0			0
$337$			11329.0i			1.83125i	0.402034	+	0.915625i	$0.368303\pi$
$337$			11329.0i			1.83125i	−0.402034	+	0.915625i	$0.631697\pi$
$338$		−	2254.95i		−	0.362879i
$339$	−5878.34			−0.941792
$340$	−4712.21	+	1380.64i	−0.751633	+	0.220222i
$341$	−325.794			−0.0517383
$342$		−	402.054i		−	0.0635690i
$343$		0			0
$344$	2584.02			0.405003
$345$	−3609.27	−	12318.7i	−0.563237	−	1.92236i
$346$	−1185.83			−0.184250
$347$			10969.1i			1.69698i	0.529211	+	0.848490i	$0.322488\pi$
$347$			10969.1i			1.69698i	−0.529211	+	0.848490i	$0.677512\pi$
$348$			4585.53i			0.706350i
$349$	−3925.09			−0.602021			−0.301010	−	0.953621i	$-0.597324\pi$
$349$	−3925.09			−0.602021			−0.301010	+	0.953621i	$0.597324\pi$
$350$		0			0
$351$	3527.70			0.536453
$352$		−	292.758i		−	0.0443297i
$353$		−	8409.37i		−	1.26795i	−0.773354	−	0.633974i	$-0.781422\pi$
$353$		−	8409.37i		−	1.26795i	0.773354	−	0.633974i	$-0.218578\pi$
$354$	−9204.08			−1.38190
$355$	2270.19	+	7748.32i	0.339407	+	1.15842i
$356$	−83.0319			−0.0123615
$357$		0			0
$358$		−	998.784i		−	0.147451i
$359$	−5024.14			−0.738618			−0.369309	−	0.929307i	$-0.620406\pi$
$359$	−5024.14			−0.738618			−0.369309	+	0.929307i	$0.620406\pi$
$360$	−775.006	+	227.070i	−0.113462	+	0.0332435i
$361$	−6363.30			−0.927730
$362$		−	2266.84i		−	0.329123i
$363$		−	7486.83i		−	1.08253i
$364$		0			0
$365$	−8895.10	+	2606.19i	−1.27559	+	0.373738i
$366$	−6290.65			−0.898409
$367$			2700.78i			0.384140i	0.981381	+	0.192070i	$0.0615201\pi$
$367$			2700.78i			0.384140i	−0.981381	+	0.192070i	$0.938480\pi$
$368$		−	3060.46i		−	0.433526i
$369$	358.873			0.0506292
$370$	363.035	+	1239.06i	0.0510089	+	0.174097i
$371$		0			0
$372$			855.011i			0.119167i
$373$			7738.90i			1.07428i	0.843494	+	0.537138i	$0.180495\pi$
$373$			7738.90i			1.07428i	−0.843494	+	0.537138i	$0.819505\pi$
$374$	2009.01			0.277763
$375$	−5504.50	+	6330.07i	−0.758003	+	0.871689i
$376$	−456.830			−0.0626574
$377$			6245.94i			0.853269i
$378$		0			0
$379$	−5512.60			−0.747132			−0.373566	−	0.927604i	$-0.621865\pi$
$379$	−5512.60			−0.747132			−0.373566	+	0.927604i	$0.621865\pi$
$380$	−279.961	−	955.524i	−0.0377939	−	0.128993i
$381$	−352.182			−0.0473565
$382$		−	4779.13i		−	0.640109i
$383$		−	921.050i		−	0.122881i	−0.998111	−	0.0614405i	$-0.980431\pi$
$383$		−	921.050i		−	0.122881i	0.998111	−	0.0614405i	$-0.0195695\pi$
$384$	−768.310			−0.102103
$385$		0			0
$386$	1216.46			0.160405
$387$			2916.42i			0.383075i
$388$		−	4041.45i		−	0.528797i
$389$	−734.690			−0.0957590			−0.0478795	−	0.998853i	$-0.515246\pi$
$389$	−734.690			−0.0957590			−0.0478795	+	0.998853i	$0.515246\pi$
$390$	−4212.34	+	1234.18i	−0.546923	+	0.160244i
$391$	21002.0			2.71640
$392$		0			0
$393$		−	9184.58i		−	1.17888i
$394$	−5952.14			−0.761078
$395$	1554.89	+	5306.94i	0.198063	+	0.676002i
$396$	330.417			0.0419295
$397$		−	6234.68i		−	0.788185i	−0.919071	−	0.394093i	$-0.871059\pi$
$397$		−	6234.68i		−	0.788185i	0.919071	−	0.394093i	$-0.128941\pi$
$398$		−	3463.67i		−	0.436226i
$399$		0			0
$400$	−1683.77	+	1079.31i	−0.210471	+	0.134914i
$401$	1147.33			0.142880			0.0714399	−	0.997445i	$-0.477241\pi$
$401$	1147.33			0.142880			0.0714399	+	0.997445i	$0.477241\pi$
$402$		−	4452.51i		−	0.552416i
$403$			1164.61i			0.143954i
$404$	−5147.86			−0.633950
$405$	2801.76	+	9562.60i	0.343755	+	1.17326i
$406$		0			0
$407$		−	528.263i		−	0.0643367i
$408$		−	5272.42i		−	0.639764i
$409$	−5333.98			−0.644862			−0.322431	−	0.946593i	$-0.604500\pi$
$409$	−5333.98			−0.644862			−0.322431	+	0.946593i	$0.604500\pi$
$410$	852.900	−	249.893i	0.102736	−	0.0301008i
$411$	18264.7			2.19204
$412$		−	6592.63i		−	0.788338i
$413$		0			0
$414$	3454.14			0.410053
$415$	−13318.7	+	3902.26i	−1.57539	+	0.461577i
$416$	−1046.51			−0.123340
$417$		−	10764.0i		−	1.26407i
$418$			407.379i			0.0476688i
$419$	11602.6			1.35280			0.676401	−	0.736533i	$-0.263538\pi$
$419$	11602.6			1.35280			0.676401	+	0.736533i	$0.263538\pi$
$420$		0			0
$421$	−5948.07			−0.688578			−0.344289	−	0.938864i	$-0.611880\pi$
$421$	−5948.07			−0.688578			−0.344289	+	0.938864i	$0.611880\pi$
$422$			1571.91i			0.181326i
$423$		−	515.595i		−	0.0592649i
$424$	4237.90			0.485403
$425$	−7406.64	−	11554.6i	−0.845352	−	1.31878i
$426$	−8669.48			−0.986004
$427$		0			0
$428$			273.553i			0.0308941i
$429$	1795.89			0.202113
$430$	2030.78	+	6931.18i	0.227751	+	0.777329i
$431$	3708.25			0.414432			0.207216	−	0.978295i	$-0.433560\pi$
$431$	3708.25			0.414432			0.207216	+	0.978295i	$0.433560\pi$
$432$			1725.90i			0.192217i
$433$		−	4775.00i		−	0.529958i	−0.964254	−	0.264979i	$-0.914635\pi$
$433$		−	4775.00i		−	0.529958i	0.964254	−	0.264979i	$-0.0853651\pi$
$434$		0			0
$435$	−12299.9	+	3603.76i	−1.35571	+	0.397211i
$436$	750.487			0.0824353
$437$			4258.70i			0.466181i
$438$		−	9952.59i		−	1.08574i
$439$	−3933.57			−0.427652			−0.213826	−	0.976872i	$-0.568593\pi$
$439$	−3933.57			−0.427652			−0.213826	+	0.976872i	$0.568593\pi$
$440$	785.271	−	230.078i	0.0850826	−	0.0249285i
$441$		0			0
$442$		−	7181.56i		−	0.772832i
$443$			8730.40i			0.936329i	0.883641	+	0.468165i	$0.155085\pi$
$443$			8730.40i			0.936329i	−0.883641	+	0.468165i	$0.844915\pi$
$444$	−1386.37			−0.148185
$445$	−65.2547	−	222.718i	−0.00695139	−	0.0237255i
$446$	−12224.3			−1.29785
$447$			12053.8i			1.27545i
$448$		0			0
$449$	18724.5			1.96807			0.984035	−	0.177977i	$-0.0569553\pi$
$449$	18724.5			1.96807			0.984035	+	0.177977i	$0.0569553\pi$
$450$	−1218.15	−	1900.36i	−0.127609	−	0.199076i
$451$	−363.626			−0.0379656
$452$		−	3917.31i		−	0.407643i
$453$		−	355.303i		−	0.0368512i
$454$	−4266.28			−0.441027
$455$		0			0
$456$	1069.12			0.109794
$457$		−	4384.10i		−	0.448752i	−0.974503	−	0.224376i	$-0.927966\pi$
$457$		−	4384.10i		−	0.448752i	0.974503	−	0.224376i	$-0.0720343\pi$
$458$		−	4904.08i		−	0.500333i
$459$	−11843.8			−1.20440
$460$	8209.14	−	2405.21i	0.832072	−	0.243790i
$461$	12719.7			1.28507			0.642533	−	0.766258i	$-0.277883\pi$
$461$	12719.7			1.28507			0.642533	+	0.766258i	$0.277883\pi$
$462$		0			0
$463$			4806.34i			0.482440i	0.970470	+	0.241220i	$0.0775476\pi$
$463$			4806.34i			0.482440i	−0.970470	+	0.241220i	$0.922452\pi$
$464$	−3055.78			−0.305735
$465$	−2293.42	+	671.952i	−0.228720	+	0.0670129i
$466$	8134.83			0.808667
$467$			1985.62i			0.196753i	0.995149	+	0.0983763i	$0.0313649\pi$
$467$			1985.62i			0.196753i	−0.995149	+	0.0983763i	$0.968635\pi$
$468$		−	1181.13i		−	0.116662i
$469$		0			0
$470$	−359.022	−	1225.37i	−0.0352350	−	0.120259i
$471$	−16032.7			−1.56847
$472$		−	6133.58i		−	0.598137i
$473$		−	2955.05i		−	0.287259i
$474$	−5937.85			−0.575389
$475$	2343.00	−	1501.89i	0.226325	−	0.145077i
$476$		0			0
$477$			4783.05i			0.459121i
$478$			1720.42i			0.164623i
$479$	6897.05			0.657900			0.328950	−	0.944347i	$-0.393305\pi$
$479$	6897.05			0.657900			0.328950	+	0.944347i	$0.393305\pi$
$480$	−603.814	−	2060.86i	−0.0574171	−	0.195968i
$481$	−1888.37			−0.179007
$482$			121.928i			0.0115222i
$483$		0			0
$484$	4989.21			0.468558
$485$	10840.5	−	3176.17i	1.01493	−	0.297366i
$486$	−4874.52			−0.454965
$487$			11260.0i			1.04772i	0.851805	+	0.523859i	$0.175508\pi$
$487$			11260.0i			1.04772i	−0.851805	+	0.523859i	$0.824492\pi$
$488$		−	4192.07i		−	0.388865i
$489$	−16609.0			−1.53596
$490$		0			0
$491$	13161.5			1.20972			0.604858	−	0.796333i	$-0.293230\pi$
$491$	13161.5			1.20972			0.604858	+	0.796333i	$0.293230\pi$
$492$			954.297i			0.0874452i
$493$		−	20969.9i		−	1.91569i
$494$	1456.25			0.132631
$495$	259.674	+	886.285i	0.0235788	+	0.0804759i
$496$	−569.777			−0.0515801
$497$		0			0
$498$		−	14902.1i		−	1.34092i
$499$	−12404.0			−1.11278			−0.556392	−	0.830920i	$-0.687815\pi$
$499$	−12404.0			−1.11278			−0.556392	+	0.830920i	$0.687815\pi$
$500$	−4218.34	−	3668.19i	−0.377300	−	0.328092i
$501$	−9622.54			−0.858091
$502$			9367.55i			0.832857i
$503$		−	10548.2i		−	0.935027i	−0.883986	−	0.467514i	$-0.845150\pi$
$503$		−	10548.2i		−	0.935027i	0.883986	−	0.467514i	$-0.154850\pi$
$504$		0			0
$505$	−4045.70	−	13808.2i	−0.356497	−	1.21675i
$506$	−3499.89			−0.307489
$507$			6767.58i			0.592818i
$508$		−	234.693i		−	0.0204977i
$509$	−10749.6			−0.936088			−0.468044	−	0.883705i	$-0.655041\pi$
$509$	−10749.6			−0.936088			−0.468044	+	0.883705i	$0.655041\pi$
$510$	14142.3	−	4143.59i	1.22791	−	0.359767i
$511$		0			0
$512$		−	512.000i		−	0.0441942i
$513$		−	2401.64i		−	0.206696i
$514$	−1860.82			−0.159684
$515$	17683.6	−	5181.14i	1.51307	−	0.443317i
$516$	−7755.20			−0.661635
$517$			522.424i			0.0444413i
$518$		0			0
$519$	3558.91			0.301000
$520$	−822.455	−	2807.09i	−0.0693597	−	0.236729i
$521$	−13734.3			−1.15492			−0.577459	−	0.816420i	$-0.695956\pi$
$521$	−13734.3			−1.15492			−0.577459	+	0.816420i	$0.695956\pi$
$522$		−	3448.87i		−	0.289182i
$523$		−	13966.9i		−	1.16775i	−0.811845	−	0.583873i	$-0.801537\pi$
$523$		−	13966.9i		−	1.16775i	0.811845	−	0.583873i	$-0.198463\pi$
$524$	6120.58			0.510265
$525$		0			0
$526$	−11365.7			−0.942146
$527$		−	3910.01i		−	0.323193i
$528$			878.628i			0.0724193i
$529$	−24420.5			−2.00711
$530$	3330.56	+	11367.4i	0.272963	+	0.931641i
$531$	6922.57			0.565752
$532$		0			0
$533$			1299.85i			0.105633i
$534$	249.196			0.0201943
$535$	−733.759	+	214.985i	−0.0592956	+	0.0173731i
$536$	2967.14			0.239106
$537$			2997.56i			0.240883i
$538$		−	4837.45i		−	0.387653i
$539$		0			0
$540$	−4629.44	+	1356.39i	−0.368924	+	0.108092i
$541$	19473.7			1.54758			0.773790	−	0.633443i	$-0.218359\pi$
$541$	19473.7			1.54758			0.773790	+	0.633443i	$0.218359\pi$
$542$			655.525i			0.0519505i
$543$			6803.27i			0.537672i
$544$	3513.53			0.276914
$545$	589.806	+	2013.05i	0.0463569	+	0.158219i
$546$		0			0
$547$		−	14279.9i		−	1.11620i	−0.829773	−	0.558101i	$-0.811530\pi$
$547$		−	14279.9i		−	1.11620i	0.829773	−	0.558101i	$-0.188470\pi$
$548$			12171.5i			0.948798i
$549$	4731.33			0.367811
$550$	1234.29	+	1925.53i	0.0956913	+	0.149282i
$551$	4252.19			0.328765
$552$			9185.08i			0.708230i
$553$		0			0
$554$	−3061.24			−0.234765
$555$	−1089.55	−	3718.69i	−0.0833308	−	0.284414i
$556$	7173.11			0.547136
$557$		−	8.99517i		−	0.000684269i	−1.00000		0.000342134i	$-0.999891\pi$
$557$		−	8.99517i		−	0.000684269i	1.00000		0.000342134i	$-0.000108905\pi$
$558$		−	643.071i		−	0.0487874i
$559$	−10563.3			−0.799252
$560$		0			0
$561$	−6029.46			−0.453768
$562$		−	18347.3i		−	1.37711i
$563$			14998.9i			1.12279i	0.827548	+	0.561394i	$0.189735\pi$
$563$			14998.9i			1.12279i	−0.827548	+	0.561394i	$0.810265\pi$
$564$	1371.04			0.102361
$565$	10507.5	−	3078.61i	0.782396	−	0.229236i
$566$	−6900.83			−0.512480
$567$		0			0
$568$		−	5777.32i		−	0.426780i
$569$	−995.051			−0.0733123			−0.0366561	−	0.999328i	$-0.511671\pi$
$569$	−995.051			−0.0733123			−0.0366561	+	0.999328i	$0.511671\pi$
$570$	840.221	+	2867.73i	0.0617421	+	0.210730i
$571$	−10830.2			−0.793750			−0.396875	−	0.917873i	$-0.629905\pi$
$571$	−10830.2			−0.793750			−0.396875	+	0.917873i	$0.629905\pi$
$572$			1196.78i			0.0874822i
$573$			14343.2i			1.04572i
$574$		0			0
$575$	12903.1	+	20129.3i	0.935821	+	1.45991i
$576$	577.862			0.0418013
$577$			7969.91i			0.575029i	0.957776	+	0.287515i	$0.0928290\pi$
$577$			7969.91i			0.575029i	−0.957776	+	0.287515i	$0.907171\pi$
$578$			14285.1i			1.02799i
$579$	−3650.86			−0.262046
$580$	−2401.54	−	8196.60i	−0.171928	−	0.586802i
$581$		0			0
$582$			12129.2i			0.863871i
$583$		−	4846.40i		−	0.344284i
$584$	6632.38			0.469948
$585$	3168.19	−	928.252i	0.223912	−	0.0656043i
$586$	11237.3			0.792166
$587$		−	17898.0i		−	1.25849i	−0.777209	−	0.629243i	$-0.783365\pi$
$587$		−	17898.0i		−	1.25849i	0.777209	−	0.629243i	$-0.216635\pi$
$588$		0			0
$589$	792.858			0.0554654
$590$	16452.2	−	4820.37i	1.14801	−	0.336358i
$591$	17863.6			1.24334
$592$		−	923.872i		−	0.0641401i
$593$		−	10769.4i		−	0.745781i	−0.927875	−	0.372890i	$-0.878367\pi$
$593$		−	10769.4i		−	0.745781i	0.927875	−	0.372890i	$-0.121633\pi$
$594$	1973.72			0.136334
$595$		0			0
$596$	−8032.65			−0.552064
$597$			10395.2i			0.712642i
$598$			12511.0i			0.855540i
$599$	17177.4			1.17170			0.585852	−	0.810418i	$-0.300760\pi$
$599$	17177.4			1.17170			0.585852	+	0.810418i	$0.300760\pi$
$600$	5053.35	−	3239.25i	0.343837	−	0.220403i
$601$	−13125.5			−0.890849			−0.445424	−	0.895320i	$-0.646947\pi$
$601$	−13125.5			−0.890849			−0.445424	+	0.895320i	$0.646947\pi$
$602$		0			0
$603$			3348.82i			0.226160i
$604$	236.773			0.0159506
$605$	3921.01	+	13382.7i	0.263491	+	0.899311i
$606$	15449.8			1.03565
$607$			5942.07i			0.397333i	0.980067	+	0.198667i	$0.0636611\pi$
$607$			5942.07i			0.397333i	−0.980067	+	0.198667i	$0.936339\pi$
$608$			712.460i			0.0475231i
$609$		0			0
$610$	11244.5	−	3294.55i	0.746355	−	0.218676i
$611$	1867.50			0.123651
$612$			3965.49i			0.261921i
$613$		−	4731.24i		−	0.311734i	−0.987778	−	0.155867i	$-0.950183\pi$
$613$		−	4731.24i		−	0.311734i	0.987778	−	0.155867i	$-0.0498172\pi$
$614$	7200.61			0.473279
$615$	−2559.73	+	749.981i	−0.167835	+	0.0491742i
$616$		0			0
$617$			4234.66i			0.276306i	0.990411	+	0.138153i	$0.0441166\pi$
$617$			4234.66i			0.276306i	−0.990411	+	0.138153i	$0.955883\pi$
$618$			19785.9i			1.28787i
$619$	−23698.8			−1.53883			−0.769414	−	0.638751i	$-0.779452\pi$
$619$	−23698.8			−1.53883			−0.769414	+	0.638751i	$0.779452\pi$
$620$	−447.787	−	1528.33i	−0.0290057	−	0.0989985i
$621$	20633.0			1.33329
$622$			9135.09i			0.588880i
$623$		0			0
$624$	3140.81			0.201495
$625$	6524.07	−	14197.8i	0.417541	−	0.908658i
$626$	−4599.67			−0.293674
$627$		−	1222.63i		−	0.0778743i
$628$		−	10684.2i		−	0.678892i
$629$	6339.94			0.401892
$630$		0			0
$631$	−21626.1			−1.36438			−0.682188	−	0.731177i	$-0.738971\pi$
$631$	−21626.1			−1.36438			−0.682188	+	0.731177i	$0.738971\pi$
$632$		−	3956.97i		−	0.249050i
$633$		−	4717.64i		−	0.296223i
$634$	−20847.7			−1.30594
$635$	629.523	−	184.445i	0.0393415	−	0.0115267i
$636$	−12718.8			−0.792979
$637$		0			0
$638$			3494.55i			0.216850i
$639$	6520.49			0.403672
$640$	1373.35	−	402.380i	0.0848225	−	0.0248523i
$641$	334.627			0.0206193			0.0103096	−	0.999947i	$-0.496718\pi$
$641$	334.627			0.0206193			0.0103096	+	0.999947i	$0.496718\pi$
$642$		−	820.991i		−	0.0504703i
$643$		−	9514.06i		−	0.583512i	−0.956493	−	0.291756i	$-0.905761\pi$
$643$		−	9514.06i		−	0.583512i	0.956493	−	0.291756i	$-0.0942395\pi$
$644$		0			0
$645$	−6094.80	−	20802.0i	−0.372066	−	1.26989i
$646$	−4889.15			−0.297773
$647$			3009.69i			0.182880i	0.995811	+	0.0914398i	$0.0291469\pi$
$647$			3009.69i			0.182880i	−0.995811	+	0.0914398i	$0.970853\pi$
$648$		−	7130.09i		−	0.432247i
$649$	−7014.27			−0.424244
$650$	6883.16	−	4412.18i	0.415354	−	0.266246i
$651$		0			0
$652$		−	11068.2i		−	0.664824i
$653$		−	24188.9i		−	1.44960i	−0.688962	−	0.724798i	$-0.741933\pi$
$653$		−	24188.9i		−	1.44960i	0.688962	−	0.724798i	$-0.258067\pi$
$654$	−2252.37			−0.134671
$655$	4810.16	+	16417.4i	0.286944	+	0.979359i
$656$	−635.941			−0.0378496
$657$			7485.54i			0.444504i
$658$		0			0
$659$	9983.62			0.590147			0.295073	−	0.955475i	$-0.404656\pi$
$659$	9983.62			0.590147			0.295073	+	0.955475i	$0.404656\pi$
$660$	−2356.77	+	690.513i	−0.138995	+	0.0407245i
$661$	20564.0			1.21006			0.605028	−	0.796204i	$-0.293162\pi$
$661$	20564.0			1.21006			0.605028	+	0.796204i	$0.293162\pi$
$662$		−	12435.6i		−	0.730095i
$663$			21553.4i			1.26254i
$664$	9930.70			0.580401
$665$		0			0
$666$	1042.72			0.0606673
$667$			36531.6i			2.12070i
$668$		−	6412.44i		−	0.371414i
$669$	36687.9			2.12023
$670$	2331.87	+	7958.84i	0.134460	+	0.458921i
$671$	−4793.99			−0.275812
$672$		0			0
$673$			28158.5i			1.61282i	0.591355	+	0.806411i	$0.298593\pi$
$673$			28158.5i			1.61282i	−0.591355	+	0.806411i	$0.701407\pi$
$674$	22658.0			1.29489
$675$	−7276.53	−	11351.7i	−0.414924	−	0.647297i
$676$	−4509.90			−0.256594
$677$		−	4810.13i		−	0.273070i	−0.990635	−	0.136535i	$-0.956403\pi$
$677$		−	4810.13i		−	0.273070i	0.990635	−	0.136535i	$-0.0435966\pi$
$678$			11756.7i			0.665948i
$679$		0			0
$680$	2761.28	+	9424.42i	0.155721	+	0.531485i
$681$	12804.0			0.720485
$682$			651.589i			0.0365845i
$683$			22559.8i			1.26387i	0.775019	+	0.631937i	$0.217740\pi$
$683$			22559.8i			1.26387i	−0.775019	+	0.631937i	$0.782260\pi$
$684$	−804.108			−0.0449500
$685$	−32648.0	+	9565.58i	−1.82104	+	0.533550i
$686$		0			0
$687$			14718.2i			0.817370i
$688$		−	5168.04i		−	0.286381i
$689$	−17324.3			−0.957916
$690$	−24637.4	+	7218.55i	−1.35932	+	0.398269i
$691$	−22147.2			−1.21928			−0.609638	−	0.792680i	$-0.708685\pi$
$691$	−22147.2			−1.21928			−0.609638	+	0.792680i	$0.708685\pi$
$692$			2371.65i			0.130284i
$693$		0			0
$694$	21938.2			1.19995
$695$	5637.34	+	19240.6i	0.307678	+	1.05013i
$696$	9171.05			0.499465
$697$		−	4364.05i		−	0.237160i
$698$			7850.18i			0.425693i
$699$	−24414.4			−1.32108
$700$		0			0
$701$	−3360.84			−0.181080			−0.0905400	−	0.995893i	$-0.528859\pi$
$701$	−3360.84			−0.181080			−0.0905400	+	0.995893i	$0.528859\pi$
$702$		−	7055.41i		−	0.379329i
$703$			1285.59i			0.0689715i
$704$	−585.516			−0.0313458
$705$	1077.50	+	3677.58i	0.0575618	+	0.196462i
$706$	−16818.7			−0.896575
$707$		0			0
$708$			18408.2i			0.977148i
$709$	15432.0			0.817437			0.408718	−	0.912661i	$-0.365976\pi$
$709$	15432.0			0.817437			0.408718	+	0.912661i	$0.365976\pi$
$710$	15496.6	−	4540.39i	0.819125	−	0.239997i
$711$	4465.98			0.235566
$712$			166.064i			0.00874087i
$713$			6811.64i			0.357781i
$714$		0			0
$715$	−3210.15	+	940.547i	−0.167906	+	0.0491951i
$716$	−1997.57			−0.104263
$717$		−	5163.33i		−	0.268937i
$718$			10048.3i			0.522282i
$719$	−11650.6			−0.604301			−0.302151	−	0.953260i	$-0.597705\pi$
$719$	−11650.6			−0.604301			−0.302151	+	0.953260i	$0.597705\pi$
$720$	454.141	+	1550.01i	0.0235067	+	0.0802299i
$721$		0			0
$722$			12726.6i			0.656004i
$723$		−	365.932i		−	0.0188232i
$724$	−4533.68			−0.232725
$725$	20098.6	−	12883.4i	1.02958	−	0.659969i
$726$	−14973.7			−0.765461
$727$		−	6809.99i		−	0.347412i	−0.984798	−	0.173706i	$-0.944426\pi$
$727$		−	6809.99i		−	0.347412i	0.984798	−	0.173706i	$-0.0555743\pi$
$728$		0			0
$729$	−9434.57			−0.479326
$730$	5212.38	+	17790.2i	0.264272	+	0.901979i
$731$	35465.0			1.79442
$732$			12581.3i			0.635271i
$733$			31889.5i			1.60691i	0.595365	+	0.803456i	$0.297008\pi$
$733$			31889.5i			1.60691i	−0.595365	+	0.803456i	$0.702992\pi$
$734$	5401.55			0.271628
$735$		0			0
$736$	−6120.92			−0.306549
$737$		−	3393.18i		−	0.169592i
$738$		−	717.746i		−	0.0358003i
$739$	20503.7			1.02062			0.510312	−	0.859989i	$-0.329530\pi$
$739$	20503.7			1.02062			0.510312	+	0.859989i	$0.329530\pi$
$740$	2478.13	−	726.070i	0.123105	−	0.0360687i
$741$	−4370.51			−0.216673
$742$		0			0
$743$		−	27013.1i		−	1.33380i	−0.745146	−	0.666902i	$-0.767620\pi$
$743$		−	27013.1i		−	1.33380i	0.745146	−	0.666902i	$-0.232380\pi$
$744$	1710.02			0.0842640
$745$	−6312.85	−	21546.2i	−0.310449	−	1.05958i
$746$	15477.8			0.759628
$747$			11208.1i			0.548975i
$748$		−	4018.02i		−	0.196408i
$749$		0			0
$750$	12660.1	+	11009.0i	0.616377	+	0.535989i
$751$	−2926.38			−0.142191			−0.0710953	−	0.997470i	$-0.522649\pi$
$751$	−2926.38			−0.142191			−0.0710953	+	0.997470i	$0.522649\pi$
$752$			913.660i			0.0443055i
$753$		−	28114.0i		−	1.36060i
$754$	12491.9			0.603352
$755$	186.080	+	635.102i	0.00896972	+	0.0306142i
$756$		0			0
$757$		−	8929.57i		−	0.428733i	−0.976753	−	0.214366i	$-0.931231\pi$
$757$		−	8929.57i		−	0.428733i	0.976753	−	0.214366i	$-0.0687687\pi$
$758$			11025.2i			0.528302i
$759$	10503.9			0.502330
$760$	−1911.05	+	559.921i	−0.0912118	+	0.0267243i
$761$	−12222.6			−0.582218			−0.291109	−	0.956690i	$-0.594024\pi$
$761$	−12222.6			−0.582218			−0.291109	+	0.956690i	$0.594024\pi$
$762$			704.363i			0.0334861i
$763$		0			0
$764$	−9558.26			−0.452625
$765$	−10636.7	+	3116.47i	−0.502708	+	0.147289i
$766$	−1842.10			−0.0868900
$767$			25073.7i			1.18039i
$768$			1536.62i			0.0721979i
$769$	19856.8			0.931148			0.465574	−	0.885009i	$-0.345848\pi$
$769$	19856.8			0.931148			0.465574	+	0.885009i	$0.345848\pi$
$770$		0			0
$771$	5584.72			0.260868
$772$		−	2432.92i		−	0.113423i
$773$		−	23058.2i		−	1.07289i	−0.843934	−	0.536447i	$-0.819766\pi$
$773$		−	23058.2i		−	1.07289i	0.843934	−	0.536447i	$-0.180234\pi$
$774$	5832.84			0.270875
$775$	3747.55	−	2402.22i	0.173698	−	0.111342i
$776$	−8082.89			−0.373916
$777$		0			0
$778$			1469.38i			0.0677119i
$779$	884.926			0.0407006
$780$	2468.36	+	8424.68i	0.113310	+	0.386733i
$781$	−6606.86			−0.302704
$782$		−	42003.9i		−	1.92079i
$783$		−	20601.5i		−	0.940279i
$784$		0			0
$785$	28658.4	−	8396.67i	1.30301	−	0.381771i
$786$	−18369.2			−0.833596
$787$		−	12766.9i		−	0.578260i	−0.957290	−	0.289130i	$-0.906634\pi$
$787$		−	12766.9i		−	0.578260i	0.957290	−	0.289130i	$-0.0933660\pi$
$788$			11904.3i			0.538163i
$789$	34110.9			1.53914
$790$	10613.9	−	3109.78i	0.478006	−	0.140052i
$791$		0			0
$792$		−	660.834i		−	0.0296486i
$793$			17137.0i			0.767405i
$794$	−12469.4			−0.557331
$795$	−9995.72	−	34116.1i	−0.445927	−	1.52198i
$796$	−6927.33			−0.308458
$797$		−	23674.8i		−	1.05220i	−0.850423	−	0.526100i	$-0.823654\pi$
$797$		−	23674.8i		−	1.05220i	0.850423	−	0.526100i	$-0.176346\pi$
$798$		0			0
$799$	−6269.86			−0.277611
$800$	2158.63	+	3367.54i	0.0953988	+	0.148826i
$801$	−187.426			−0.00826761
$802$		−	2294.66i		−	0.101031i
$803$		−	7584.69i		−	0.333322i
$804$	−8905.02			−0.390617
$805$		0			0
$806$	2329.22			0.101791
$807$			14518.2i			0.633291i
$808$			10295.7i			0.448270i
$809$	18134.3			0.788093			0.394046	−	0.919091i	$-0.371075\pi$
$809$	18134.3			0.788093			0.394046	+	0.919091i	$0.371075\pi$
$810$	19125.2	−	5603.53i	0.829619	−	0.243071i
$811$	1527.66			0.0661449			0.0330724	−	0.999453i	$-0.489471\pi$
$811$	1527.66			0.0661449			0.0330724	+	0.999453i	$0.489471\pi$
$812$		0			0
$813$		−	1967.37i		−	0.0848691i
$814$	−1056.53			−0.0454929
$815$	29688.6	−	8698.50i	1.27601	−	0.373859i
$816$	−10544.8			−0.452381
$817$			7191.45i			0.307952i
$818$			10668.0i			0.455986i
$819$		0			0
$820$	−499.785	−	1705.80i	−0.0212845	−	0.0726453i
$821$	−734.066			−0.0312047			−0.0156024	−	0.999878i	$-0.504967\pi$
$821$	−734.066			−0.0312047			−0.0156024	+	0.999878i	$0.504967\pi$
$822$		−	36529.3i		−	1.55001i
$823$		−	20888.0i		−	0.884700i	−0.896842	−	0.442350i	$-0.854145\pi$
$823$		−	20888.0i		−	0.884700i	0.896842	−	0.442350i	$-0.145855\pi$
$824$	−13185.3			−0.557439
$825$	−3704.36	−	5778.94i	−0.156326	−	0.243875i
$826$		0			0
$827$			3587.86i			0.150861i	0.997151	+	0.0754305i	$0.0240331\pi$
$827$			3587.86i			0.150861i	−0.997151	+	0.0754305i	$0.975967\pi$
$828$		−	6908.29i		−	0.289951i
$829$	16536.6			0.692812			0.346406	−	0.938085i	$-0.387402\pi$
$829$	16536.6			0.692812			0.346406	+	0.938085i	$0.387402\pi$
$830$	7804.53	+	26637.4i	0.326384	+	1.11397i
$831$	9187.44			0.383524
$832$			2093.03i			0.0872148i
$833$		0			0
$834$	−21528.0			−0.893830
$835$	17200.2	−	5039.53i	0.712861	−	0.208862i
$836$	814.758			0.0337069
$837$		−	3841.33i		−	0.158633i
$838$		−	23205.2i		−	0.956576i
$839$	6813.22			0.280356			0.140178	−	0.990126i	$-0.455233\pi$
$839$	6813.22			0.280356			0.140178	+	0.990126i	$0.455233\pi$
$840$		0			0
$841$	12086.8			0.495584
$842$			11896.1i			0.486898i
$843$			55064.3i			2.24972i
$844$	3143.82			0.128217
$845$	−3544.33	−	12097.0i	−0.144294	−	0.492485i
$846$	−1031.19			−0.0419066
$847$		0			0
$848$		−	8475.81i		−	0.343232i
$849$	20710.9			0.837214
$850$	−23109.3	+	14813.3i	−0.932519	+	0.597754i
$851$	−11044.8			−0.444902
$852$			17339.0i			0.697210i
$853$			13905.1i			0.558149i	0.960269	+	0.279074i	$0.0900276\pi$
$853$			13905.1i			0.558149i	−0.960269	+	0.279074i	$0.909972\pi$
$854$		0			0
$855$	−631.947	−	2156.88i	−0.0252774	−	0.0862733i
$856$	547.107			0.0218455
$857$		−	10419.5i		−	0.415311i	−0.978202	−	0.207656i	$-0.933417\pi$
$857$		−	10419.5i		−	0.415311i	0.978202	−	0.207656i	$-0.0665833\pi$
$858$		−	3591.79i		−	0.142916i
$859$	8686.75			0.345039			0.172519	−	0.985006i	$-0.444809\pi$
$859$	8686.75			0.345039			0.172519	+	0.985006i	$0.444809\pi$
$860$	13862.4	−	4061.56i	0.549654	−	0.161044i
$861$		0			0
$862$		−	7416.51i		−	0.293048i
$863$			1991.10i			0.0785376i	0.999229	+	0.0392688i	$0.0125029\pi$
$863$			1991.10i			0.0785376i	−0.999229	+	0.0392688i	$0.987497\pi$
$864$	3451.81			0.135918
$865$	−6361.54	+	1863.88i	−0.250056	+	0.0732644i
$866$	−9550.00			−0.374737
$867$		−	42872.5i		−	1.67938i
$868$		0			0
$869$	−4525.13			−0.176645
$870$	7207.52	+	24599.7i	0.280871	+	0.958631i
$871$	−12129.5			−0.471864
$872$		−	1500.97i		−	0.0582906i
$873$		−	9122.64i		−	0.353671i
$874$	8517.40			0.329640
$875$		0			0
$876$	−19905.2			−0.767732
$877$		−	23847.3i		−	0.918205i	−0.888383	−	0.459102i	$-0.848171\pi$
$877$		−	23847.3i		−	0.918205i	0.888383	−	0.459102i	$-0.151829\pi$
$878$			7867.15i			0.302396i
$879$	−33725.6			−1.29412
$880$	−460.156	−	1570.54i	−0.0176271	−	0.0601625i
$881$	18359.1			0.702082			0.351041	−	0.936360i	$-0.385828\pi$
$881$	18359.1			0.702082			0.351041	+	0.936360i	$0.385828\pi$
$882$		0			0
$883$		−	32592.8i		−	1.24217i	−0.783743	−	0.621085i	$-0.786692\pi$
$883$		−	32592.8i		−	1.24217i	0.783743	−	0.621085i	$-0.213308\pi$
$884$	−14363.1			−0.546475
$885$	−49376.7	+	14467.0i	−1.87546	+	0.549493i
$886$	17460.8			0.662085
$887$			3241.53i			0.122706i	0.998116	+	0.0613528i	$0.0195415\pi$
$887$			3241.53i			0.122706i	−0.998116	+	0.0613528i	$0.980459\pi$
$888$			2772.74i			0.104783i
$889$		0			0
$890$	−445.437	+	130.509i	−0.0167765	+	0.00491537i
$891$	−8153.86			−0.306582
$892$			24448.7i			0.917716i
$893$		−	1271.38i		−	0.0476428i
$894$	24107.7			0.901880
$895$	−1569.89	−	5358.13i	−0.0586319	−	0.200114i
$896$		0			0
$897$		−	37548.1i		−	1.39765i
$898$		−	37449.0i		−	1.39164i
$899$	6801.23			0.252318
$900$	−3800.73	+	2436.31i	−0.140768	+	0.0902335i
$901$	58164.0			2.15064
$902$			727.253i			0.0268457i
$903$		0			0
$904$	−7834.62			−0.288247
$905$	−3563.01	−	12160.8i	−0.130871	−	0.446673i
$906$	−710.606			−0.0260577
$907$		−	25884.4i		−	0.947606i	−0.880631	−	0.473803i	$-0.842881\pi$
$907$		−	25884.4i		−	0.947606i	0.880631	−	0.473803i	$-0.157119\pi$
$908$			8532.55i			0.311853i
$909$	−11620.1			−0.423999
$910$		0			0
$911$	1292.86			0.0470189			0.0235095	−	0.999724i	$-0.492516\pi$
$911$	1292.86			0.0470189			0.0235095	+	0.999724i	$0.492516\pi$
$912$		−	2138.24i		−	0.0776363i
$913$		−	11356.6i		−	0.411663i
$914$	−8768.20			−0.317315
$915$	−33747.1	+	9887.63i	−1.21928	+	0.357240i
$916$	−9808.16			−0.353789
$917$		0			0
$918$			23687.5i			0.851640i
$919$	−20310.5			−0.729032			−0.364516	−	0.931197i	$-0.618765\pi$
$919$	−20310.5			−0.729032			−0.364516	+	0.931197i	$0.618765\pi$
$920$	−4810.42	−	16418.3i	−0.172386	−	0.588364i
$921$	−21610.6			−0.773173
$922$		−	25439.4i		−	0.908679i
$923$			23617.4i			0.842227i
$924$		0			0
$925$	3895.11	+	6076.52i	0.138455	+	0.215994i
$926$	9612.69			0.341137
$927$		−	14881.4i		−	0.527258i
$928$			6111.56i			0.216187i
$929$	−49155.2			−1.73599			−0.867993	−	0.496577i	$-0.834590\pi$
$929$	−49155.2			−1.73599			−0.867993	+	0.496577i	$0.834590\pi$
$930$	1343.90	+	4586.83i	0.0473853	+	0.161729i
$931$		0			0
$932$		−	16269.7i		−	0.571814i
$933$		−	27416.3i		−	0.962026i
$934$	3971.24			0.139125
$935$	10777.6	−	3157.75i	0.376969	−	0.110449i
$936$	−2362.27			−0.0824927
$937$			16877.6i			0.588440i	0.955738	+	0.294220i	$0.0950599\pi$
$937$			16877.6i			0.588440i	−0.955738	+	0.294220i	$0.904940\pi$
$938$		0			0
$939$	13804.6			0.479761
$940$	−2450.73	+	718.044i	−0.0850362	+	0.0249149i
$941$	−782.274			−0.0271003			−0.0135502	−	0.999908i	$-0.504313\pi$
$941$	−782.274			−0.0271003			−0.0135502	+	0.999908i	$0.504313\pi$
$942$			32065.4i			1.10907i
$943$			7602.62i			0.262540i
$944$	−12267.2			−0.422947
$945$		0			0
$946$	−5910.10			−0.203122
$947$		−	10355.1i		−	0.355329i	−0.984091	−	0.177664i	$-0.943146\pi$
$947$		−	10355.1i		−	0.355329i	0.984091	−	0.177664i	$-0.0568541\pi$
$948$			11875.7i			0.406862i
$949$	−27112.8			−0.927418
$950$	−3003.78	−	4686.01i	−0.102585	−	0.160036i
$951$	62568.3			2.13345
$952$		0			0
$953$			21907.4i			0.744647i	0.928103	+	0.372324i	$0.121439\pi$
$953$			21907.4i			0.744647i	−0.928103	+	0.372324i	$0.878561\pi$
$954$	9566.10			0.324648
$955$	−7511.83	−	25638.4i	−0.254531	−	0.868731i
$956$	3440.83			0.116406
$957$		−	10487.9i		−	0.354258i
$958$		−	13794.1i		−	0.465206i
$959$		0			0
$960$	−4121.71	+	1207.63i	−0.138571	+	0.0406000i
$961$	−28522.9			−0.957432
$962$			3776.74i			0.126577i
$963$			617.484i			0.0206627i
$964$	243.856			0.00814739
$965$	6525.88	−	1912.03i	0.217695	−	0.0637828i
$966$		0			0
$967$			41853.5i			1.39185i	0.718116	+	0.695924i	$0.245005\pi$
$967$			41853.5i			1.39185i	−0.718116	+	0.695924i	$0.754995\pi$
$968$		−	9978.41i		−	0.331321i
$969$	14673.4			0.486457
$970$	−6352.34	−	21680.9i	−0.210269	−	0.717663i
$971$	−853.827			−0.0282190			−0.0141095	−	0.999900i	$-0.504491\pi$
$971$	−853.827			−0.0282190			−0.0141095	+	0.999900i	$0.504491\pi$
$972$			9749.05i			0.321709i
$973$		0			0
$974$	22520.0			0.740849
$975$	−20657.8	+	13241.9i	−0.678544	+	0.434954i
$976$	−8384.15			−0.274969
$977$			20962.6i			0.686443i	0.939255	+	0.343221i	$0.111518\pi$
$977$			20962.6i			0.686443i	−0.939255	+	0.343221i	$0.888482\pi$
$978$			33218.1i			1.08609i
$979$	189.908			0.00619968
$980$		0			0
$981$	1694.05			0.0551345
$982$		−	26323.0i		−	0.855398i
$983$			46290.9i			1.50198i	0.660311	+	0.750992i	$0.270424\pi$
$983$			46290.9i			1.50198i	−0.660311	+	0.750992i	$0.729576\pi$
$984$	1908.59			0.0618331
$985$	−31931.2	+	9355.57i	−1.03291	+	0.302633i
$986$	−41939.7			−1.35460
$987$		0			0
$988$		−	2912.50i		−	0.0937843i
$989$	−61783.5			−1.98645
$990$	1772.57	−	519.349i	0.0569051	−	0.0166727i
$991$	−29867.9			−0.957402			−0.478701	−	0.877978i	$-0.658892\pi$
$991$	−29867.9			−0.957402			−0.478701	+	0.877978i	$0.658892\pi$
$992$			1139.55i			0.0364727i
$993$			37321.8i			1.19272i
$994$		0			0
$995$	−5444.18	−	18581.3i	−0.173459	−	0.592029i
$996$	−29804.1			−0.948173
$997$			21989.4i			0.698506i	0.937029	+	0.349253i	$0.113565\pi$
$997$			21989.4i			0.698506i	−0.937029	+	0.349253i	$0.886435\pi$
$998$			24808.0i			0.786857i
$999$	6228.58			0.197261

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.c.e.99.6		12
5.2	odd	4		2450.4.a.cx.1.6		6
5.3	odd	4		2450.4.a.cw.1.1		6
5.4	even	2	inner	490.4.c.e.99.7		12
7.3	odd	6		70.4.i.a.9.7	yes	24
7.5	odd	6		70.4.i.a.39.6	yes	24
7.6	odd	2		490.4.c.f.99.1		12
35.3	even	12		350.4.e.o.51.1		12
35.12	even	12		350.4.e.n.151.6		12
35.13	even	4		2450.4.a.cv.1.6		6
35.17	even	12		350.4.e.n.51.6		12
35.19	odd	6		70.4.i.a.39.7	yes	24
35.24	odd	6		70.4.i.a.9.6	✓	24
35.27	even	4		2450.4.a.cy.1.1		6
35.33	even	12		350.4.e.o.151.1		12
35.34	odd	2		490.4.c.f.99.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.i.a.9.6	✓	24	35.24	odd	6
70.4.i.a.9.7	yes	24	7.3	odd	6
70.4.i.a.39.6	yes	24	7.5	odd	6
70.4.i.a.39.7	yes	24	35.19	odd	6
350.4.e.n.51.6		12	35.17	even	12
350.4.e.n.151.6		12	35.12	even	12
350.4.e.o.51.1		12	35.3	even	12
350.4.e.o.151.1		12	35.33	even	12
490.4.c.e.99.6		12	1.1	even	1	trivial
490.4.c.e.99.7		12	5.4	even	2	inner
490.4.c.f.99.1		12	7.6	odd	2
490.4.c.f.99.12		12	35.34	odd	2
2450.4.a.cv.1.6		6	35.13	even	4
2450.4.a.cw.1.1		6	5.3	odd	4
2450.4.a.cx.1.6		6	5.2	odd	4
2450.4.a.cy.1.1		6	35.27	even	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)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +6.00242i q^{3} -4.00000 q^{4} +(-3.14360 - 10.7293i) q^{5} +12.0048 q^{6} +8.00000i q^{8} -9.02909 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +6.00242i q^{3} -4.00000 q^{4} +(-3.14360 - 10.7293i) q^{5} +12.0048 q^{6} +8.00000i q^{8} -9.02909 q^{9} +(-21.4586 + 6.28719i) q^{10} +9.14868 q^{11} -24.0097i q^{12} -32.7036i q^{13} +(64.4018 - 18.8692i) q^{15} +16.0000 q^{16} +109.798i q^{17} +18.0582i q^{18} -22.2644 q^{19} +(12.5744 + 42.9172i) q^{20} -18.2974i q^{22} -191.279i q^{23} -48.0194 q^{24} +(-105.236 + 67.4571i) q^{25} -65.4072 q^{26} +107.869i q^{27} -190.986 q^{29} +(-37.7384 - 128.804i) q^{30} -35.6111 q^{31} -32.0000i q^{32} +54.9143i q^{33} +219.595 q^{34} +36.1164 q^{36} -57.7420i q^{37} +44.5287i q^{38} +196.301 q^{39} +(85.8344 - 25.1488i) q^{40} -39.7463 q^{41} -323.003i q^{43} -36.5947 q^{44} +(28.3838 + 96.8758i) q^{45} -382.557 q^{46} +57.1037i q^{47} +96.0388i q^{48} +(134.914 + 210.471i) q^{50} -659.052 q^{51} +130.814i q^{52} -529.738i q^{53} +215.738 q^{54} +(-28.7597 - 98.1589i) q^{55} -133.640i q^{57} +381.973i q^{58} -766.697 q^{59} +(-257.607 + 75.4768i) q^{60} -524.009 q^{61} +71.2221i q^{62} -64.0000 q^{64} +(-350.887 + 102.807i) q^{65} +109.829 q^{66} -370.893i q^{67} -439.191i q^{68} +1148.14 q^{69} -722.165 q^{71} -72.2327i q^{72} -829.047i q^{73} -115.484 q^{74} +(-404.906 - 631.669i) q^{75} +89.0575 q^{76} -392.602i q^{78} -494.621 q^{79} +(-50.2975 - 171.669i) q^{80} -891.261 q^{81} +79.4926i q^{82} -1241.34i q^{83} +(1178.05 - 345.159i) q^{85} -646.005 q^{86} -1146.38i q^{87} +73.1895i q^{88} +20.7580 q^{89} +(193.752 - 56.7676i) q^{90} +765.115i q^{92} -213.753i q^{93} +114.207 q^{94} +(69.9902 + 238.881i) q^{95} +192.078 q^{96} +1010.36i q^{97} -82.6042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 48 q^{4} - 8 q^{5} - 28 q^{6} - 62 q^{9}+O(q^{10}) \) 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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