LMFDB - Embedded newform 100.9.d.c.99.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(99,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.99"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,104] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.8
Character	$\chi$	$=$	100.99
Dual form			100.9.d.c.99.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-11.2775 + 11.3498i) q^{2} -137.297 q^{3} +(-1.63618 - 255.995i) q^{4} +(1548.37 - 1558.29i) q^{6} +3940.57 q^{7} +(2923.94 + 2868.41i) q^{8} +12289.4 q^{9} -17097.0i q^{11} +(224.642 + 35147.3i) q^{12} -10938.7i q^{13} +(-44439.8 + 44724.8i) q^{14} +(-65530.6 + 837.705i) q^{16} +101666. i q^{17} +(-138594. + 139483. i) q^{18} -93432.1i q^{19} -541029. q^{21} +(194047. + 192811. i) q^{22} +147346. q^{23} +(-401448. - 393824. i) q^{24} +(124152. + 123361. i) q^{26} -786497. q^{27} +(-6447.48 - 1.00877e6i) q^{28} -41637.4 q^{29} -138577. i q^{31} +(729514. - 753207. i) q^{32} +2.34736e6i q^{33} +(-1.15389e6 - 1.14653e6i) q^{34} +(-20107.7 - 3.14603e6i) q^{36} +1.14978e6i q^{37} +(1.06044e6 + 1.05368e6i) q^{38} +1.50185e6i q^{39} +3.83906e6 q^{41} +(6.10145e6 - 6.14057e6i) q^{42} -3.18959e6 q^{43} +(-4.37673e6 + 27973.6i) q^{44} +(-1.66170e6 + 1.67235e6i) q^{46} -3.51218e6 q^{47} +(8.99715e6 - 115014. i) q^{48} +9.76332e6 q^{49} -1.39584e7i q^{51} +(-2.80024e6 + 17897.6i) q^{52} -5.66612e6i q^{53} +(8.86971e6 - 8.92658e6i) q^{54} +(1.15220e7 + 1.13032e7i) q^{56} +1.28279e7i q^{57} +(469565. - 472576. i) q^{58} +1.69068e7i q^{59} -5.16010e6 q^{61} +(1.57282e6 + 1.56280e6i) q^{62} +4.84274e7 q^{63} +(321668. + 1.67741e7i) q^{64} +(-2.66421e7 - 2.64723e7i) q^{66} +1.05358e7 q^{67} +(2.60259e7 - 166343. i) q^{68} -2.02302e7 q^{69} -1.85971e7i q^{71} +(3.59336e7 + 3.52511e7i) q^{72} -2.38535e6i q^{73} +(-1.30498e7 - 1.29666e7i) q^{74} +(-2.39181e7 + 152871. i) q^{76} -6.73718e7i q^{77} +(-1.70457e7 - 1.69371e7i) q^{78} -4.42560e7i q^{79} +2.73525e7 q^{81} +(-4.32950e7 + 4.35726e7i) q^{82} -1.51824e7 q^{83} +(885218. + 1.38500e8i) q^{84} +(3.59706e7 - 3.62013e7i) q^{86} +5.71668e6 q^{87} +(4.90411e7 - 4.99905e7i) q^{88} +5.42739e7 q^{89} -4.31047e7i q^{91} +(-241085. - 3.77199e7i) q^{92} +1.90261e7i q^{93} +(3.96086e7 - 3.98625e7i) q^{94} +(-1.00160e8 + 1.03413e8i) q^{96} -1.24798e8i q^{97} +(-1.10106e8 + 1.10812e8i) q^{98} -2.10112e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 104 q^{4} + 8736 q^{6} + 77600 q^{9} - 136944 q^{14} - 162848 q^{16} + 828992 q^{21} - 327584 q^{24} + 2074248 q^{26} - 5529792 q^{29} - 7587928 q^{34} - 10937832 q^{36} - 17152896 q^{41} - 33842400 q^{44}+ \cdots - 906779904 q^{96}+O(q^{100}) $ 32 * q + 104 * q^4 + 8736 * q^6 + 77600 * q^9 - 136944 * q^14 - 162848 * q^16 + 828992 * q^21 - 327584 * q^24 + 2074248 * q^26 - 5529792 * q^29 - 7587928 * q^34 - 10937832 * q^36 - 17152896 * q^41 - 33842400 * q^44 - 15948304 * q^46 + 65607200 * q^49 - 17797408 * q^54 + 68269536 * q^56 + 16743424 * q^61 + 95087744 * q^64 + 38716000 * q^66 - 15054528 * q^69 + 276421752 * q^74 + 5140800 * q^76 + 281173344 * q^81 - 139523648 * q^84 - 203449344 * q^86 - 213294912 * q^89 - 110529264 * q^94 - 906779904 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−11.2775	+	11.3498i	−0.704843	+	0.709363i
$2$	−11.2775	+	11.3498i	−0.704843	+	0.709363i
$3$	−137.297			−1.69502			−0.847512	−	0.530777i	$-0.821900\pi$
$3$	−137.297			−1.69502			−0.847512	+	0.530777i	$0.821900\pi$
$4$	−1.63618	−	255.995i	−0.00639132	−	0.999980i
$5$		0			0
$5$		0			0
$6$	1548.37	−	1558.29i	1.19473	−	1.20239i
$7$	3940.57			1.64122			0.820611	−	0.571487i	$-0.193633\pi$
$7$	3940.57			1.64122			0.820611	+	0.571487i	$0.193633\pi$
$8$	2923.94	+	2868.41i	0.713853	+	0.700295i
$9$	12289.4			1.87310
$10$		0			0
$11$		−	17097.0i		−	1.16775i	−0.811845	−	0.583873i	$-0.801537\pi$
$11$		−	17097.0i		−	1.16775i	0.811845	−	0.583873i	$-0.198463\pi$
$12$	224.642	+	35147.3i	0.0108334	+	1.69499i
$13$		−	10938.7i		−	0.382994i	−0.981493	−	0.191497i	$-0.938666\pi$
$13$		−	10938.7i		−	0.382994i	0.981493	−	0.191497i	$-0.0613341\pi$
$14$	−44439.8	+	44724.8i	−1.15680	+	1.16422i
$15$		0			0
$16$	−65530.6	+	837.705i	−0.999918	+	0.0127824i
$17$			101666.i			1.21725i	0.793459	+	0.608624i	$0.208278\pi$
$17$			101666.i			1.21725i	−0.793459	+	0.608624i	$0.791722\pi$
$18$	−138594.	+	139483.i	−1.32025	+	1.32871i
$19$		−	93432.1i		−	0.716938i	−0.933542	−	0.358469i	$-0.883299\pi$
$19$		−	93432.1i		−	0.716938i	0.933542	−	0.358469i	$-0.116701\pi$
$20$		0			0
$21$	−541029.			−2.78191
$22$	194047.	+	192811.i	0.828355	+	0.823078i
$23$	147346.			0.526536			0.263268	−	0.964723i	$-0.415200\pi$
$23$	147346.			0.526536			0.263268	+	0.964723i	$0.415200\pi$
$24$	−401448.	−	393824.i	−1.21000	−	1.18702i
$25$		0			0
$26$	124152.	+	123361.i	0.271681	+	0.269951i
$27$	−786497.			−1.47993
$28$	−6447.48	−	1.00877e6i	−0.0104896	−	1.64119i
$29$	−41637.4			−0.0588696			−0.0294348	−	0.999567i	$-0.509371\pi$
$29$	−41637.4			−0.0588696			−0.0294348	+	0.999567i	$0.509371\pi$
$30$		0			0
$31$		−	138577.i		−	0.150052i	−0.997182	−	0.0750262i	$-0.976096\pi$
$31$		−	138577.i		−	0.150052i	0.997182	−	0.0750262i	$-0.0239040\pi$
$32$	729514.	−	753207.i	0.695719	−	0.718314i
$33$			2.34736e6i			1.97936i
$34$	−1.15389e6	−	1.14653e6i	−0.863470	−	0.857969i
$35$		0			0
$36$	−20107.7	−	3.14603e6i	−0.0119716	−	1.87307i
$37$			1.14978e6i			0.613489i	0.951792	+	0.306745i	$0.0992397\pi$
$37$			1.14978e6i			0.613489i	−0.951792	+	0.306745i	$0.900760\pi$
$38$	1.06044e6	+	1.05368e6i	0.508569	+	0.505329i
$39$			1.50185e6i			0.649183i
$40$		0			0
$41$	3.83906e6			1.35859			0.679297	−	0.733864i	$-0.262285\pi$
$41$	3.83906e6			1.35859			0.679297	+	0.733864i	$0.262285\pi$
$42$	6.10145e6	−	6.14057e6i	1.96081	−	1.97338i
$43$	−3.18959e6			−0.932956			−0.466478	−	0.884533i	$-0.654477\pi$
$43$	−3.18959e6			−0.932956			−0.466478	+	0.884533i	$0.654477\pi$
$44$	−4.37673e6	+	27973.6i	−1.16772	+	0.00746343i
$45$		0			0
$46$	−1.66170e6	+	1.67235e6i	−0.371125	+	0.373505i
$47$	−3.51218e6			−0.719756			−0.359878	−	0.932999i	$-0.617182\pi$
$47$	−3.51218e6			−0.719756			−0.359878	+	0.932999i	$0.617182\pi$
$48$	8.99715e6	−	115014.i	1.69488	−	0.0216664i
$49$	9.76332e6			1.69361
$50$		0			0
$51$		−	1.39584e7i		−	2.06326i
$52$	−2.80024e6	+	17897.6i	−0.382986	+	0.00244783i
$53$		−	5.66612e6i		−	0.718096i	−0.933319	−	0.359048i	$-0.883101\pi$
$53$		−	5.66612e6i		−	0.718096i	0.933319	−	0.359048i	$-0.116899\pi$
$54$	8.86971e6	−	8.92658e6i	1.04312	−	1.04981i
$55$		0			0
$56$	1.15220e7	+	1.13032e7i	1.17159	+	1.14934i
$57$			1.28279e7i			1.21523i
$58$	469565.	−	472576.i	0.0414939	−	0.0417599i
$59$			1.69068e7i			1.39525i	0.716461	+	0.697627i	$0.245761\pi$
$59$			1.69068e7i			1.39525i	−0.716461	+	0.697627i	$0.754239\pi$
$60$		0			0
$61$	−5.16010e6			−0.372682			−0.186341	−	0.982485i	$-0.559663\pi$
$61$	−5.16010e6			−0.372682			−0.186341	+	0.982485i	$0.559663\pi$
$62$	1.57282e6	+	1.56280e6i	0.106442	+	0.105763i
$63$	4.84274e7			3.07418
$64$	321668.	+	1.67741e7i	0.0191729	+	0.999816i
$65$		0			0
$66$	−2.66421e7	−	2.64723e7i	−1.40408	−	1.39514i
$67$	1.05358e7			0.522838			0.261419	−	0.965225i	$-0.415810\pi$
$67$	1.05358e7			0.522838			0.261419	+	0.965225i	$0.415810\pi$
$68$	2.60259e7	−	166343.i	1.21722	−	0.00777981i
$69$	−2.02302e7			−0.892490
$70$		0			0
$71$		−	1.85971e7i		−	0.731833i	−0.930648	−	0.365916i	$-0.880756\pi$
$71$		−	1.85971e7i		−	0.731833i	0.930648	−	0.365916i	$-0.119244\pi$
$72$	3.59336e7	+	3.52511e7i	1.33712	+	1.31173i
$73$		−	2.38535e6i		−	0.0839964i	−0.999118	−	0.0419982i	$-0.986628\pi$
$73$		−	2.38535e6i		−	0.0839964i	0.999118	−	0.0419982i	$-0.0133724\pi$
$74$	−1.30498e7	−	1.29666e7i	−0.435186	−	0.432414i
$75$		0			0
$76$	−2.39181e7	+	152871.i	−0.716923	+	0.00458218i
$77$		−	6.73718e7i		−	1.91653i
$78$	−1.70457e7	−	1.69371e7i	−0.460506	−	0.457572i
$79$		−	4.42560e7i		−	1.13622i	−0.822951	−	0.568112i	$-0.807674\pi$
$79$		−	4.42560e7i		−	1.13622i	0.822951	−	0.568112i	$-0.192326\pi$
$80$		0			0
$81$	2.73525e7			0.635415
$82$	−4.32950e7	+	4.35726e7i	−0.957596	+	0.963736i
$83$	−1.51824e7			−0.319910			−0.159955	−	0.987124i	$-0.551135\pi$
$83$	−1.51824e7			−0.319910			−0.159955	+	0.987124i	$0.551135\pi$
$84$	885218.	+	1.38500e8i	0.0177801	+	2.78185i
$85$		0			0
$86$	3.59706e7	−	3.62013e7i	0.657588	−	0.661805i
$87$	5.71668e6			0.0997854
$88$	4.90411e7	−	4.99905e7i	0.817766	−	0.833599i
$89$	5.42739e7			0.865030			0.432515	−	0.901627i	$-0.357626\pi$
$89$	5.42739e7			0.865030			0.432515	+	0.901627i	$0.357626\pi$
$90$		0			0
$91$		−	4.31047e7i		−	0.628577i
$92$	−241085.	−	3.77199e7i	−0.00336526	−	0.526525i
$93$			1.90261e7i			0.254342i
$94$	3.96086e7	−	3.98625e7i	0.507315	−	0.510568i
$95$		0			0
$96$	−1.00160e8	+	1.03413e8i	−1.17926	+	1.21756i
$97$		−	1.24798e8i		−	1.40968i	−0.709365	−	0.704841i	$-0.751018\pi$
$97$		−	1.24798e8i		−	1.40968i	0.709365	−	0.704841i	$-0.248982\pi$
$98$	−1.10106e8	+	1.10812e8i	−1.19373	+	1.20138i
$99$		−	2.10112e8i		−	2.18731i
$100$		0			0
$101$	1.96354e8			1.88693			0.943463	−	0.331478i	$-0.107547\pi$
$101$	1.96354e8			1.88693			0.943463	+	0.331478i	$0.107547\pi$
$102$	1.58425e8	+	1.57416e8i	1.46360	+	1.45428i
$103$	1.08404e8			0.963152			0.481576	−	0.876404i	$-0.340065\pi$
$103$	1.08404e8			0.963152			0.481576	+	0.876404i	$0.340065\pi$
$104$	3.13766e7	−	3.19841e7i	0.268209	−	0.273401i
$105$		0			0
$106$	6.43094e7	+	6.38996e7i	0.509390	+	0.506145i
$107$	−5.19293e7			−0.396166			−0.198083	−	0.980185i	$-0.563472\pi$
$107$	−5.19293e7			−0.396166			−0.198083	+	0.980185i	$0.563472\pi$
$108$	1.28685e6	+	2.01339e8i	0.00945871	+	1.47990i
$109$	−2.01131e8			−1.42486			−0.712432	−	0.701741i	$-0.752406\pi$
$109$	−2.01131e8			−1.42486			−0.712432	+	0.701741i	$0.752406\pi$
$110$		0			0
$111$		−	1.57861e8i		−	1.03988i
$112$	−2.58228e8	+	3.30104e6i	−1.64109	+	0.0209787i
$113$			6.82663e7i			0.418690i	0.977842	+	0.209345i	$0.0671332\pi$
$113$			6.82663e7i			0.418690i	−0.977842	+	0.209345i	$0.932867\pi$
$114$	−1.45595e8	−	1.44667e8i	−0.862037	−	0.856544i
$115$		0			0
$116$	68126.1	+	1.06590e7i	0.000376254	+	0.0588684i
$117$		−	1.34430e8i		−	0.717387i
$118$	−1.91889e8	−	1.90666e8i	−0.989741	−	0.983435i
$119$			4.00621e8i			1.99777i
$120$		0			0
$121$	−7.79470e7			−0.363629
$122$	5.81930e7	−	5.85661e7i	0.262683	−	0.264367i
$123$	−5.27091e8			−2.30285
$124$	−3.54749e7	+	226736.i	−0.150049	+	0.000959032i
$125$		0			0
$126$	−5.46140e8	+	5.49642e8i	−2.16682	+	2.18071i
$127$	−3.48984e8			−1.34150			−0.670751	−	0.741683i	$-0.734028\pi$
$127$	−3.48984e8			−1.34150			−0.670751	+	0.741683i	$0.734028\pi$
$128$	−1.94011e8	−	1.85519e8i	−0.722746	−	0.691113i
$129$	4.37921e8			1.58138
$130$		0			0
$131$		−	1.49192e8i		−	0.506596i	−0.967388	−	0.253298i	$-0.918485\pi$
$131$		−	1.49192e8i		−	0.506596i	0.967388	−	0.253298i	$-0.0815153\pi$
$132$	6.00912e8	−	3.84069e6i	1.97931	−	0.0126507i
$133$		−	3.68176e8i		−	1.17665i
$134$	−1.18817e8	+	1.19579e8i	−0.368519	+	0.370882i
$135$		0			0
$136$	−2.91619e8	+	2.97265e8i	−0.852433	+	0.868936i
$137$			6.05661e8i			1.71928i	0.510897	+	0.859642i	$0.329313\pi$
$137$			6.05661e8i			1.71928i	−0.510897	+	0.859642i	$0.670687\pi$
$138$	2.28146e8	−	2.29609e8i	0.629066	−	0.633099i
$139$		−	5.19290e8i		−	1.39107i	−0.718490	−	0.695537i	$-0.755166\pi$
$139$		−	5.19290e8i		−	1.39107i	0.718490	−	0.695537i	$-0.244834\pi$
$140$		0			0
$141$	4.82211e8			1.22000
$142$	2.11074e8	+	2.09729e8i	0.519135	+	0.515828i
$143$	−1.87018e8			−0.447239
$144$	−8.05335e8	+	1.02949e7i	−1.87295	+	0.0239427i
$145$		0			0
$146$	2.70732e7	+	2.69008e7i	0.0595839	+	0.0592043i
$147$	−1.34047e9			−2.87071
$148$	2.94337e8	−	1.88124e6i	0.613477	−	0.00392100i
$149$	6.13964e8			1.24565			0.622827	−	0.782359i	$-0.285984\pi$
$149$	6.13964e8			1.24565			0.622827	+	0.782359i	$0.285984\pi$
$150$		0			0
$151$			5.41162e8i			1.04093i	0.853884	+	0.520463i	$0.174241\pi$
$151$			5.41162e8i			1.04093i	−0.853884	+	0.520463i	$0.825759\pi$
$152$	2.68001e8	−	2.73190e8i	0.502068	−	0.511788i
$153$			1.24941e9i			2.28003i
$154$	7.64657e8	+	7.59785e8i	1.35951	+	1.35085i
$155$		0			0
$156$	3.84465e8	−	2.45729e6i	0.649170	−	0.00414913i
$157$		−	6.43982e8i		−	1.05993i	−0.848021	−	0.529963i	$-0.822206\pi$
$157$		−	6.43982e8i		−	1.05993i	0.848021	−	0.529963i	$-0.177794\pi$
$158$	5.02297e8	+	4.99097e8i	0.805995	+	0.800860i
$159$			7.77941e8i			1.21719i
$160$		0			0
$161$	5.80629e8			0.864162
$162$	−3.08468e8	+	3.10446e8i	−0.447868	+	0.450740i
$163$	6.74607e8			0.955653			0.477826	−	0.878454i	$-0.341425\pi$
$163$	6.74607e8			0.955653			0.477826	+	0.878454i	$0.341425\pi$
$164$	−6.28138e6	−	9.82780e8i	−0.00868320	−	1.35857i
$165$		0			0
$166$	1.71219e8	−	1.72317e8i	0.225486	−	0.226932i
$167$	4.55554e8			0.585699			0.292849	−	0.956159i	$-0.405397\pi$
$167$	4.55554e8			0.585699			0.292849	+	0.956159i	$0.405397\pi$
$168$	−1.58194e9	−	1.55189e9i	−1.98588	−	1.94816i
$169$	6.96076e8			0.853316
$170$		0			0
$171$		−	1.14823e9i		−	1.34290i
$172$	5.21874e6	+	8.16519e8i	0.00596282	+	0.932937i
$173$		−	9.64344e8i		−	1.07658i	−0.842759	−	0.538292i	$-0.819070\pi$
$173$		−	9.64344e8i		−	1.07658i	0.842759	−	0.538292i	$-0.180930\pi$
$174$	−6.44699e7	+	6.48832e7i	−0.0703331	+	0.0707841i
$175$		0			0
$176$	1.43222e7	+	1.12037e9i	0.0149265	+	1.16765i
$177$		−	2.32125e9i		−	2.36499i
$178$	−6.12074e8	+	6.15998e8i	−0.609711	+	0.613620i
$179$		−	1.01365e9i		−	0.987363i	−0.869643	−	0.493682i	$-0.835651\pi$
$179$		−	1.01365e9i		−	0.987363i	0.869643	−	0.493682i	$-0.164349\pi$
$180$		0			0
$181$	1.51507e8			0.141162			0.0705812	−	0.997506i	$-0.477515\pi$
$181$	1.51507e8			0.141162			0.0705812	+	0.997506i	$0.477515\pi$
$182$	4.89230e8	+	4.86113e8i	0.445889	+	0.443049i
$183$	7.08465e8			0.631705
$184$	4.30832e8	+	4.22649e8i	0.375869	+	0.368730i
$185$		0			0
$186$	−2.15943e8	−	2.14567e8i	−0.180421	−	0.179272i
$187$	1.73817e9			1.42143
$188$	5.74654e6	+	8.99099e8i	0.00460019	+	0.719741i
$189$	−3.09925e9			−2.42890
$190$		0			0
$191$		−	5.46186e8i		−	0.410399i	−0.978720	−	0.205200i	$-0.934216\pi$
$191$		−	5.46186e8i		−	0.410399i	0.978720	−	0.205200i	$-0.0657844\pi$
$192$	−4.41640e7	−	2.30304e9i	−0.0324985	−	1.69471i
$193$		−	1.52005e9i		−	1.09554i	−0.836628	−	0.547771i	$-0.815477\pi$
$193$		−	1.52005e9i		−	1.09554i	0.836628	−	0.547771i	$-0.184523\pi$
$194$	1.41643e9	+	1.40741e9i	0.999976	+	0.993605i
$195$		0			0
$196$	−1.59745e7	−	2.49936e9i	−0.0108244	−	1.69358i
$197$			1.98770e9i			1.31974i	0.751382	+	0.659868i	$0.229388\pi$
$197$			1.98770e9i			1.31974i	−0.751382	+	0.659868i	$0.770612\pi$
$198$	2.38473e9	+	2.36954e9i	1.55160	+	1.54171i
$199$		−	1.68735e9i		−	1.07595i	−0.842960	−	0.537976i	$-0.819189\pi$
$199$		−	1.68735e9i		−	1.07595i	0.842960	−	0.537976i	$-0.180811\pi$
$200$		0			0
$201$	−1.44653e9			−0.886222
$202$	−2.21438e9	+	2.22858e9i	−1.32999	+	1.33852i
$203$	−1.64075e8			−0.0966182
$204$	−3.57327e9	+	2.28384e7i	−2.06322	+	0.0131870i
$205$		0			0
$206$	−1.22252e9	+	1.23036e9i	−0.678872	+	0.683224i
$207$	1.81080e9			0.986256
$208$	9.16339e6	+	7.16819e8i	0.00489556	+	0.382962i
$209$	−1.59740e9			−0.837201
$210$		0			0
$211$		−	3.55239e9i		−	1.79222i	−0.443834	−	0.896109i	$-0.646382\pi$
$211$		−	3.55239e9i		−	1.79222i	0.443834	−	0.896109i	$-0.353618\pi$
$212$	−1.45050e9	+	9.27077e6i	−0.718081	+	0.00458958i
$213$			2.55332e9i			1.24047i
$214$	5.85632e8	−	5.89387e8i	0.279235	−	0.281025i
$215$		0			0
$216$	−2.29967e9	−	2.25599e9i	−1.05645	−	1.03639i
$217$		−	5.46071e8i		−	0.246269i
$218$	2.26826e9	−	2.28280e9i	1.00431	−	1.01075i
$219$			3.27501e8i			0.142376i
$220$		0			0
$221$	1.11209e9			0.466198
$222$	1.79169e9	+	1.78028e9i	0.737651	+	0.732952i
$223$	1.41187e9			0.570920			0.285460	−	0.958391i	$-0.407854\pi$
$223$	1.41187e9			0.570920			0.285460	+	0.958391i	$0.407854\pi$
$224$	2.87470e9	−	2.96807e9i	1.14183	−	1.17891i
$225$		0			0
$226$	−7.74809e8	−	7.69873e8i	−0.297003	−	0.295111i
$227$	1.08981e9			0.410438			0.205219	−	0.978716i	$-0.434209\pi$
$227$	1.08981e9			0.410438			0.205219	+	0.978716i	$0.434209\pi$
$228$	3.28388e9	−	2.09888e7i	1.21520	−	0.00776690i
$229$	2.25807e9			0.821097			0.410549	−	0.911839i	$-0.365337\pi$
$229$	2.25807e9			0.821097			0.410549	+	0.911839i	$0.365337\pi$
$230$		0			0
$231$			9.24994e9i			3.24856i
$232$	−1.21745e8	−	1.19433e8i	−0.0420243	−	0.0412261i
$233$		−	6.52483e8i		−	0.221384i	−0.993855	−	0.110692i	$-0.964693\pi$
$233$		−	6.52483e8i		−	0.221384i	0.993855	−	0.110692i	$-0.0353067\pi$
$234$	1.52576e9	+	1.51604e9i	0.508888	+	0.505645i
$235$		0			0
$236$	4.32805e9	−	2.76625e7i	1.39522	−	0.00891750i
$237$			6.07622e9i			1.92593i
$238$	−4.54697e9	−	4.51800e9i	−1.41715	−	1.40812i
$239$			4.79300e9i			1.46898i	0.678619	+	0.734490i	$0.262579\pi$
$239$			4.79300e9i			1.46898i	−0.678619	+	0.734490i	$0.737421\pi$
$240$		0			0
$241$	−5.18381e9			−1.53667			−0.768335	−	0.640048i	$-0.778915\pi$
$241$	−5.18381e9			−1.53667			−0.768335	+	0.640048i	$0.778915\pi$
$242$	8.79047e8	−	8.84683e8i	0.256301	−	0.257945i
$243$	1.40479e9			0.402889
$244$	8.44283e6	+	1.32096e9i	0.00238193	+	0.372675i
$245$		0			0
$246$	5.94427e9	−	5.98238e9i	1.62315	−	1.63355i
$247$	−1.02202e9			−0.274583
$248$	3.97494e8	−	4.05190e8i	0.105081	−	0.107115i
$249$	2.08449e9			0.542255
$250$		0			0
$251$		−	2.41878e9i		−	0.609398i	−0.952449	−	0.304699i	$-0.901444\pi$
$251$		−	2.41878e9i		−	0.609398i	0.952449	−	0.304699i	$-0.0985558\pi$
$252$	−7.92358e7	−	1.23972e10i	−0.0196481	−	3.07412i
$253$		−	2.51917e9i		−	0.614859i
$254$	3.93567e9	−	3.96090e9i	0.945548	−	0.951611i
$255$		0			0
$256$	4.29356e9	−	1.09791e8i	0.999673	−	0.0255627i
$257$		−	5.25554e9i		−	1.20472i	−0.798226	−	0.602358i	$-0.794228\pi$
$257$		−	5.25554e9i		−	1.20472i	0.798226	−	0.602358i	$-0.205772\pi$
$258$	−4.93865e9	+	4.97032e9i	−1.11463	+	1.12177i
$259$			4.53078e9i			1.00687i
$260$		0			0
$261$	−5.11700e8			−0.110269
$262$	1.69331e9	+	1.68252e9i	0.359360	+	0.357071i
$263$	−1.24951e9			−0.261165			−0.130583	−	0.991437i	$-0.541685\pi$
$263$	−1.24951e9			−0.261165			−0.130583	+	0.991437i	$0.541685\pi$
$264$	−6.73319e9	+	6.86354e9i	−1.38613	+	1.41297i
$265$		0			0
$266$	4.17873e9	+	4.15210e9i	0.834675	+	0.829357i
$267$	−7.45164e9			−1.46625
$268$	−1.72384e7	−	2.69710e9i	−0.00334162	−	0.522827i
$269$	5.36357e9			1.02434			0.512171	−	0.858884i	$-0.328841\pi$
$269$	5.36357e9			1.02434			0.512171	+	0.858884i	$0.328841\pi$
$270$		0			0
$271$			6.72329e8i			0.124654i	0.998056	+	0.0623268i	$0.0198521\pi$
$271$			6.72329e8i			0.124654i	−0.998056	+	0.0623268i	$0.980148\pi$
$272$	−8.51659e7	−	6.66222e9i	−0.0155593	−	1.21715i
$273$			5.91814e9i			1.06545i
$274$	−6.87414e9	−	6.83034e9i	−1.21960	−	1.21183i
$275$		0			0
$276$	3.31002e7	+	5.17882e9i	0.00570419	+	0.892472i
$277$			8.55117e9i			1.45247i	0.687448	+	0.726234i	$0.258731\pi$
$277$			8.55117e9i			1.45247i	−0.687448	+	0.726234i	$0.741269\pi$
$278$	5.89384e9	+	5.85629e9i	0.986777	+	0.980490i
$279$		−	1.70303e9i		−	0.281064i
$280$		0			0
$281$	−8.47677e8			−0.135958			−0.0679791	−	0.997687i	$-0.521655\pi$
$281$	−8.47677e8			−0.135958			−0.0679791	+	0.997687i	$0.521655\pi$
$282$	−5.43813e9	+	5.47300e9i	−0.859911	+	0.865425i
$283$	−2.59848e9			−0.405111			−0.202555	−	0.979271i	$-0.564925\pi$
$283$	−2.59848e9			−0.405111			−0.202555	+	0.979271i	$0.564925\pi$
$284$	−4.76076e9	+	3.04282e7i	−0.731818	+	0.00467738i
$285$		0			0
$286$	2.10910e9	−	2.12262e9i	0.315233	−	0.317255i
$287$	1.51281e10			2.22975
$288$	8.96531e9	−	9.25649e9i	1.30315	−	1.34548i
$289$	−3.36016e9			−0.481691
$290$		0			0
$291$			1.71344e10i			2.38944i
$292$	−6.10637e8	+	3.90285e6i	−0.0839946	+	0.000536847i
$293$		−	1.18893e10i		−	1.61319i	−0.591107	−	0.806594i	$-0.701309\pi$
$293$		−	1.18893e10i		−	1.61319i	0.591107	−	0.806594i	$-0.298691\pi$
$294$	1.51172e10	−	1.52141e10i	2.02340	−	2.03637i
$295$		0			0
$296$	−3.29803e9	+	3.36188e9i	−0.429624	+	0.437941i
$297$			1.34467e10i			1.72818i
$298$	−6.92397e9	+	6.96837e9i	−0.877992	+	0.883621i
$299$		−	1.61177e9i		−	0.201660i
$300$		0			0
$301$	−1.25688e10			−1.53119
$302$	−6.14209e9	−	6.10296e9i	−0.738394	−	0.733690i
$303$	−2.69588e10			−3.19838
$304$	7.82685e7	+	6.12266e9i	0.00916417	+	0.716879i
$305$		0			0
$306$	−1.41806e10	−	1.40903e10i	−1.61737	−	1.60706i
$307$	−1.74109e10			−1.96005			−0.980026	−	0.198868i	$-0.936273\pi$
$307$	−1.74109e10			−1.96005			−0.980026	+	0.198868i	$0.936273\pi$
$308$	−1.72468e10	+	1.10232e8i	−1.91649	+	0.0122491i
$309$	−1.48835e10			−1.63257
$310$		0			0
$311$			8.61717e9i			0.921135i	0.887625	+	0.460567i	$0.152354\pi$
$311$			8.61717e9i			0.921135i	−0.887625	+	0.460567i	$0.847646\pi$
$312$	−4.30791e9	+	4.39131e9i	−0.454620	+	0.463421i
$313$			9.76978e9i			1.01791i	0.860794	+	0.508953i	$0.169967\pi$
$313$			9.76978e9i			1.01791i	−0.860794	+	0.508953i	$0.830033\pi$
$314$	7.30907e9	+	7.26250e9i	0.751871	+	0.747081i
$315$		0			0
$316$	−1.13293e10	+	7.24107e7i	−1.13620	+	0.00726197i
$317$		−	6.57561e9i		−	0.651177i	−0.945512	−	0.325589i	$-0.894438\pi$
$317$		−	6.57561e9i		−	0.651177i	0.945512	−	0.325589i	$-0.105562\pi$
$318$	−8.82948e9	−	8.77322e9i	−0.863429	−	0.857928i
$319$			7.11872e8i			0.0687447i
$320$		0			0
$321$	7.12973e9			0.671510
$322$	−6.54804e9	+	6.59002e9i	−0.609099	+	0.613004i
$323$	9.49884e9			0.872691
$324$	−4.47536e7	−	7.00211e9i	−0.00406114	−	0.635402i
$325$		0			0
$326$	−7.60787e9	+	7.65665e9i	−0.673586	+	0.677905i
$327$	2.76147e10			2.41518
$328$	1.12252e10	+	1.10120e10i	0.969837	+	0.951417i
$329$	−1.38400e10			−1.18128
$330$		0			0
$331$		−	2.32794e10i		−	1.93936i	−0.244370	−	0.969682i	$-0.578581\pi$
$331$		−	2.32794e10i		−	1.93936i	0.244370	−	0.969682i	$-0.421419\pi$
$332$	2.48411e7	+	3.88661e9i	0.00204464	+	0.319903i
$333$			1.41301e10i			1.14913i
$334$	−5.13751e9	+	5.17045e9i	−0.412826	+	0.415473i
$335$		0			0
$336$	3.54540e10	−	4.53223e8i	2.78168	−	0.0355594i
$337$		−	1.99301e9i		−	0.154522i	−0.997011	−	0.0772610i	$-0.975383\pi$
$337$		−	1.99301e9i		−	0.154522i	0.997011	−	0.0772610i	$-0.0246175\pi$
$338$	−7.84999e9	+	7.90033e9i	−0.601454	+	0.605311i
$339$		−	9.37275e9i		−	0.709690i
$340$		0			0
$341$	−2.36924e9			−0.175223
$342$	1.30322e10	+	1.29491e10i	0.952603	+	0.946534i
$343$	1.57565e10			1.13837
$344$	−9.32619e9	−	9.14906e9i	−0.665994	−	0.653345i
$345$		0			0
$346$	1.09451e10	+	1.08754e10i	0.763688	+	0.758823i
$347$	6.31855e9			0.435813			0.217906	−	0.975970i	$-0.430077\pi$
$347$	6.31855e9			0.435813			0.217906	+	0.975970i	$0.430077\pi$
$348$	−9.35350e6	−	1.46344e9i	−0.000637760	−	0.0997834i
$349$	1.87010e9			0.126056			0.0630279	−	0.998012i	$-0.479924\pi$
$349$	1.87010e9			0.126056			0.0630279	+	0.998012i	$0.479924\pi$
$350$		0			0
$351$			8.60323e9i			0.566804i
$352$	−1.28776e10	−	1.24725e10i	−0.838808	−	0.812422i
$353$		−	3.02132e10i		−	1.94580i	−0.231225	−	0.972900i	$-0.574273\pi$
$353$		−	3.02132e10i		−	1.94580i	0.231225	−	0.972900i	$-0.425727\pi$
$354$	2.63457e10	+	2.61779e10i	1.67763	+	1.66695i
$355$		0			0
$356$	−8.88017e7	−	1.38938e10i	−0.00552868	−	0.865012i
$357$		−	5.50041e10i		−	3.38627i
$358$	1.15048e10	+	1.14315e10i	0.700399	+	0.695937i
$359$		−	1.82078e10i		−	1.09618i	−0.836421	−	0.548088i	$-0.815356\pi$
$359$		−	1.82078e10i		−	1.09618i	0.836421	−	0.548088i	$-0.184644\pi$
$360$		0			0
$361$	8.25401e9			0.486000
$362$	−1.70862e9	+	1.71958e9i	−0.0994974	+	0.100135i
$363$	1.07019e10			0.616359
$364$	−1.10346e10	+	7.05269e7i	−0.628565	+	0.00401744i
$365$		0			0
$366$	−7.98972e9	+	8.04094e9i	−0.445253	+	0.448108i
$367$	−1.46648e10			−0.808372			−0.404186	−	0.914677i	$-0.632445\pi$
$367$	−1.46648e10			−0.808372			−0.404186	+	0.914677i	$0.632445\pi$
$368$	−9.65570e9	+	1.23433e8i	−0.526493	+	0.00673037i
$369$	4.71799e10			2.54479
$370$		0			0
$371$		−	2.23278e10i		−	1.17855i
$372$	4.87059e9	−	3.11301e7i	0.254337	−	0.00162558i
$373$		−	1.41277e10i		−	0.729857i	−0.931036	−	0.364928i	$-0.881094\pi$
$373$		−	1.41277e10i		−	0.729857i	0.931036	−	0.364928i	$-0.118906\pi$
$374$	−1.96022e10	+	1.97279e10i	−1.00189	+	1.00831i
$375$		0			0
$376$	−1.02694e10	−	1.00744e10i	−0.513800	−	0.504042i
$377$			4.55458e8i			0.0225467i
$378$	3.49518e10	−	3.51759e10i	1.71199	−	1.72297i
$379$		−	3.94069e9i		−	0.190992i	−0.995430	−	0.0954960i	$-0.969556\pi$
$379$		−	3.94069e9i		−	0.190992i	0.995430	−	0.0954960i	$-0.0304437\pi$
$380$		0			0
$381$	4.79145e10			2.27388
$382$	6.19910e9	+	6.15961e9i	0.291122	+	0.289267i
$383$	3.43063e10			1.59433			0.797166	−	0.603760i	$-0.206332\pi$
$383$	3.43063e10			1.59433			0.797166	+	0.603760i	$0.206332\pi$
$384$	2.66371e10	+	2.54712e10i	1.22507	+	1.17145i
$385$		0			0
$386$	1.72523e10	+	1.71424e10i	0.777137	+	0.772185i
$387$	−3.91983e10			−1.74752
$388$	−3.19477e10	+	2.04192e8i	−1.40965	+	0.00900972i
$389$	−4.14309e8			−0.0180936			−0.00904681	−	0.999959i	$-0.502880\pi$
$389$	−4.14309e8			−0.0180936			−0.00904681	+	0.999959i	$0.502880\pi$
$390$		0			0
$391$			1.49801e10i			0.640924i
$392$	2.85474e10	+	2.80052e10i	1.20899	+	1.18603i
$393$			2.04837e10i			0.858692i
$394$	−2.25601e10	−	2.24163e10i	−0.936171	−	0.930207i
$395$		0			0
$396$	−5.37876e10	+	3.43780e8i	−2.18726	+	0.0139798i
$397$			2.25453e10i			0.907598i	0.891104	+	0.453799i	$0.149932\pi$
$397$			2.25453e10i			0.907598i	−0.891104	+	0.453799i	$0.850068\pi$
$398$	1.91511e10	+	1.90291e10i	0.763240	+	0.758377i
$399$			5.05494e10i			1.99446i
$400$		0			0
$401$	−2.53666e10			−0.981037			−0.490519	−	0.871431i	$-0.663193\pi$
$401$	−2.53666e10			−0.981037			−0.490519	+	0.871431i	$0.663193\pi$
$402$	1.63132e10	−	1.64178e10i	0.624648	−	0.628653i
$403$	−1.51584e9			−0.0574691
$404$	−3.21270e8	−	5.02657e10i	−0.0120599	−	1.88689i
$405$		0			0
$406$	1.85036e9	−	1.86222e9i	0.0681007	−	0.0685373i
$407$	1.96577e10			0.716399
$408$	4.00384e10	−	4.08135e10i	1.44489	−	1.47287i
$409$	−1.47057e10			−0.525523			−0.262761	−	0.964861i	$-0.584633\pi$
$409$	−1.47057e10			−0.525523			−0.262761	+	0.964861i	$0.584633\pi$
$410$		0			0
$411$		−	8.31554e10i		−	2.91423i
$412$	−1.77367e8	−	2.77508e10i	−0.00615581	−	0.963132i
$413$			6.66225e10i			2.28992i
$414$	−2.04213e10	+	2.05523e10i	−0.695156	+	0.699613i
$415$		0			0
$416$	−8.23909e9	−	7.97992e9i	−0.275110	−	0.266456i
$417$			7.12968e10i			2.35790i
$418$	1.80147e10	−	1.81302e10i	0.590095	−	0.593879i
$419$			7.30915e9i			0.237143i	0.992946	+	0.118572i	$0.0378315\pi$
$419$			7.30915e9i			0.237143i	−0.992946	+	0.118572i	$0.962168\pi$
$420$		0			0
$421$	−4.09140e10			−1.30240			−0.651199	−	0.758907i	$-0.725734\pi$
$421$	−4.09140e10			−1.30240			−0.651199	+	0.758907i	$0.725734\pi$
$422$	4.03189e10	+	4.00621e10i	1.27133	+	1.26323i
$423$	−4.31627e10			−1.34818
$424$	1.62528e10	−	1.65674e10i	0.502879	−	0.512615i
$425$		0			0
$426$	−2.89797e10	−	2.87951e10i	−0.879946	−	0.874340i
$427$	−2.03337e10			−0.611654
$428$	8.49655e7	+	1.32936e10i	0.00253202	+	0.396158i
$429$	2.56770e10			0.758080
$430$		0			0
$431$			3.95128e9i			0.114506i	0.998360	+	0.0572531i	$0.0182342\pi$
$431$			3.95128e9i			0.114506i	−0.998360	+	0.0572531i	$0.981766\pi$
$432$	5.15396e10	−	6.58852e8i	1.47981	−	0.0189170i
$433$		−	2.88725e10i		−	0.821358i	−0.911780	−	0.410679i	$-0.865292\pi$
$433$		−	2.88725e10i		−	0.821358i	0.911780	−	0.410679i	$-0.134708\pi$
$434$	6.19780e9	+	6.15831e9i	0.174694	+	0.173581i
$435$		0			0
$436$	3.29086e8	+	5.14885e10i	0.00910676	+	1.42484i
$437$		−	1.37669e10i		−	0.377493i
$438$	−3.71707e9	−	3.69339e9i	−0.100996	−	0.100353i
$439$			1.66340e10i			0.447857i	0.974606	+	0.223929i	$0.0718883\pi$
$439$			1.66340e10i			0.447857i	−0.974606	+	0.223929i	$0.928112\pi$
$440$		0			0
$441$	1.19986e11			3.17231
$442$	−1.25416e10	+	1.26220e10i	−0.328596	+	0.330703i
$443$	1.61256e10			0.418699			0.209350	−	0.977841i	$-0.432865\pi$
$443$	1.61256e10			0.418699			0.209350	+	0.977841i	$0.432865\pi$
$444$	−4.04116e10	+	2.58288e8i	−1.03986	+	0.00664619i
$445$		0			0
$446$	−1.59224e10	+	1.60245e10i	−0.402410	+	0.404990i
$447$	−8.42953e10			−2.11141
$448$	1.26756e9	+	6.60997e10i	0.0314670	+	1.64092i
$449$	−1.31471e10			−0.323478			−0.161739	−	0.986834i	$-0.551710\pi$
$449$	−1.31471e10			−0.323478			−0.161739	+	0.986834i	$0.551710\pi$
$450$		0			0
$451$		−	6.56363e10i		−	1.58649i
$452$	1.74758e10	−	1.11696e8i	0.418682	−	0.00267598i
$453$		−	7.42999e10i		−	1.76439i
$454$	−1.22903e10	+	1.23691e10i	−0.289294	+	0.291149i
$455$		0			0
$456$	−3.67958e10	+	3.75081e10i	−0.851017	+	0.867493i
$457$		−	6.79985e10i		−	1.55896i	−0.626427	−	0.779480i	$-0.715484\pi$
$457$		−	6.79985e10i		−	1.55896i	0.626427	−	0.779480i	$-0.284516\pi$
$458$	−2.54653e10	+	2.56286e10i	−0.578745	+	0.582456i
$459$		−	7.99597e10i		−	1.80144i
$460$		0			0
$461$	−2.86783e10			−0.634966			−0.317483	−	0.948264i	$-0.602838\pi$
$461$	−2.86783e10			−0.634966			−0.317483	+	0.948264i	$0.602838\pi$
$462$	−1.04985e11	−	1.04316e11i	−2.30441	−	2.28973i
$463$	4.22729e9			0.0919894			0.0459947	−	0.998942i	$-0.485354\pi$
$463$	4.22729e9			0.0919894			0.0459947	+	0.998942i	$0.485354\pi$
$464$	2.72852e9	−	3.48799e7i	0.0588648	−	0.000752494i
$465$		0			0
$466$	7.40556e9	+	7.35838e9i	0.157041	+	0.156041i
$467$	4.27269e10			0.898325			0.449163	−	0.893450i	$-0.351722\pi$
$467$	4.27269e10			0.898325			0.449163	+	0.893450i	$0.351722\pi$
$468$	−3.44134e10	+	2.19952e8i	−0.717372	+	0.00458505i
$469$	4.15170e10			0.858093
$470$		0			0
$471$			8.84167e10i			1.79660i
$472$	−4.84956e10	+	4.94345e10i	−0.977089	+	0.996006i
$473$			5.45323e10i			1.08946i
$474$	−6.89639e10	−	6.85245e10i	−1.36618	−	1.35748i
$475$		0			0
$476$	1.02557e11	−	6.55487e8i	1.99773	−	0.0127684i
$477$		−	6.96334e10i		−	1.34507i
$478$	−5.43996e10	−	5.40531e10i	−1.04204	−	1.03540i
$479$		−	6.73017e10i		−	1.27845i	−0.769020	−	0.639225i	$-0.779255\pi$
$479$		−	6.73017e10i		−	1.27845i	0.769020	−	0.639225i	$-0.220745\pi$
$480$		0			0
$481$	1.25770e10			0.234962
$482$	5.84604e10	−	5.88352e10i	1.08311	−	1.09006i
$483$	−7.97185e10			−1.46477
$484$	1.27535e8	+	1.99540e10i	0.00232406	+	0.363621i
$485$		0			0
$486$	−1.58425e10	+	1.59440e10i	−0.283973	+	0.285794i
$487$	9.69928e10			1.72434			0.862172	−	0.506616i	$-0.169104\pi$
$487$	9.69928e10			1.72434			0.862172	+	0.506616i	$0.169104\pi$
$488$	−1.50878e10	−	1.48013e10i	−0.266040	−	0.260988i
$489$	−9.26214e10			−1.61985
$490$		0			0
$491$			1.73575e10i			0.298648i	0.988788	+	0.149324i	$0.0477098\pi$
$491$			1.73575e10i			0.298648i	−0.988788	+	0.149324i	$0.952290\pi$
$492$	8.62414e8	+	1.34933e11i	0.0147182	+	2.30280i
$493$		−	4.23309e9i		−	0.0716589i
$494$	1.15259e10	−	1.15998e10i	0.193538	−	0.194779i
$495$		0			0
$496$	1.16086e8	+	9.08101e9i	0.00191803	+	0.150040i
$497$		−	7.32833e10i		−	1.20110i
$498$	−2.35079e10	+	2.36586e10i	−0.382205	+	0.384655i
$499$			1.42959e10i			0.230573i	0.993332	+	0.115287i	$0.0367787\pi$
$499$			1.42959e10i			0.230573i	−0.993332	+	0.115287i	$0.963221\pi$
$500$		0			0
$501$	−6.25462e10			−0.992773
$502$	2.74526e10	+	2.72777e10i	0.432284	+	0.429530i
$503$	6.90584e10			1.07881			0.539404	−	0.842047i	$-0.318649\pi$
$503$	6.90584e10			1.07881			0.539404	+	0.842047i	$0.318649\pi$
$504$	1.41599e11	+	1.38910e11i	2.19451	+	2.15283i
$505$		0			0
$506$	2.85921e10	+	2.84100e10i	0.436158	+	0.433380i
$507$	−9.55691e10			−1.44639
$508$	5.71000e8	+	8.93382e10i	0.00857396	+	1.34147i
$509$	5.98939e10			0.892302			0.446151	−	0.894958i	$-0.352794\pi$
$509$	5.98939e10			0.892302			0.446151	+	0.894958i	$0.352794\pi$
$510$		0			0
$511$		−	9.39964e9i		−	0.137857i
$512$	−4.71745e10	+	4.99693e10i	−0.686480	+	0.727149i
$513$			7.34840e10i			1.06102i
$514$	5.96493e10	+	5.92693e10i	0.854581	+	0.849136i
$515$		0			0
$516$	−7.16516e8	−	1.12106e11i	−0.0101071	−	1.58135i
$517$			6.00476e10i			0.840491i
$518$	−5.14235e10	−	5.10959e10i	−0.714238	−	0.709687i
$519$			1.32401e11i			1.82483i
$520$		0			0
$521$	2.97388e10			0.403620			0.201810	−	0.979425i	$-0.435318\pi$
$521$	2.97388e10			0.403620			0.201810	+	0.979425i	$0.435318\pi$
$522$	5.77069e9	−	5.80770e9i	0.0777224	−	0.0782207i
$523$	−3.20935e10			−0.428954			−0.214477	−	0.976729i	$-0.568805\pi$
$523$	−3.20935e10			−0.428954			−0.214477	+	0.976729i	$0.568805\pi$
$524$	−3.81925e10	+	2.44105e8i	−0.506586	+	0.00323781i
$525$		0			0
$526$	1.40913e10	−	1.41817e10i	0.184081	−	0.185261i
$527$	1.40885e10			0.182651
$528$	−1.96640e9	−	1.53824e11i	−0.0253008	−	1.97919i
$529$	−5.66001e10			−0.722760
$530$		0			0
$531$			2.07775e11i			2.61345i
$532$	−9.42511e10	+	6.02401e8i	−1.17663	+	0.00752037i
$533$		−	4.19943e10i		−	0.520333i
$534$	8.40358e10	−	8.45746e10i	1.03347	−	1.04010i
$535$		0			0
$536$	3.08060e10	+	3.02209e10i	0.373229	+	0.366141i
$537$			1.39171e11i			1.67360i
$538$	−6.04876e10	+	6.08755e10i	−0.722000	+	0.726630i
$539$		−	1.66923e11i		−	1.97770i
$540$		0			0
$541$	3.92268e10			0.457924			0.228962	−	0.973435i	$-0.426467\pi$
$541$	3.92268e10			0.457924			0.228962	+	0.973435i	$0.426467\pi$
$542$	−7.63081e9	−	7.58219e9i	−0.0884247	−	0.0878613i
$543$	−2.08015e10			−0.239274
$544$	7.65753e10	+	7.41665e10i	0.874366	+	0.846861i
$545$		0			0
$546$	−6.71697e10	−	6.67418e10i	−0.755793	−	0.750978i
$547$	9.39638e10			1.04957			0.524785	−	0.851235i	$-0.324146\pi$
$547$	9.39638e10			1.04957			0.524785	+	0.851235i	$0.324146\pi$
$548$	1.55046e11	−	9.90969e8i	1.71925	−	0.0109885i
$549$	−6.34147e10			−0.698073
$550$		0			0
$551$			3.89027e9i			0.0422059i
$552$	−5.91519e10	−	5.80285e10i	−0.637107	−	0.625007i
$553$		−	1.74394e11i		−	1.86480i
$554$	−9.70541e10	−	9.64358e10i	−1.03033	−	1.02376i
$555$		0			0
$556$	−1.32935e11	+	8.49650e8i	−1.39105	+	0.00889080i
$557$			8.98122e10i			0.933071i	0.884503	+	0.466535i	$0.154498\pi$
$557$			8.98122e10i			0.933071i	−0.884503	+	0.466535i	$0.845502\pi$
$558$	1.93290e10	+	1.92059e10i	0.199376	+	0.198106i
$559$			3.48899e10i			0.357316i
$560$		0			0
$561$	−2.38646e11			−2.40936
$562$	9.55967e9	−	9.62097e9i	0.0958292	−	0.0964436i
$563$	−1.80533e10			−0.179689			−0.0898446	−	0.995956i	$-0.528637\pi$
$563$	−1.80533e10			−0.179689			−0.0898446	+	0.995956i	$0.528637\pi$
$564$	−7.88983e8	−	1.23444e11i	−0.00779742	−	1.21998i
$565$		0			0
$566$	2.93043e10	−	2.94922e10i	0.285540	−	0.287370i
$567$	1.07785e11			1.04286
$568$	5.33441e10	−	5.43769e10i	0.512499	−	0.522421i
$569$	6.90947e10			0.659167			0.329584	−	0.944126i	$-0.393092\pi$
$569$	6.90947e10			0.659167			0.329584	+	0.944126i	$0.393092\pi$
$570$		0			0
$571$			7.86073e10i			0.739467i	0.929138	+	0.369733i	$0.120551\pi$
$571$			7.86073e10i			0.739467i	−0.929138	+	0.369733i	$0.879449\pi$
$572$	3.05995e8	+	4.78757e10i	0.00285844	+	0.447230i
$573$			7.49896e10i			0.695637i
$574$	−1.70607e11	+	1.71701e11i	−1.57163	+	1.58170i
$575$		0			0
$576$	3.95312e9	+	2.06145e11i	0.0359128	+	1.87276i
$577$		−	1.80277e11i		−	1.62643i	−0.581962	−	0.813216i	$-0.697715\pi$
$577$		−	1.80277e11i		−	1.62643i	0.581962	−	0.813216i	$-0.302285\pi$
$578$	3.78942e10	−	3.81371e10i	0.339517	−	0.341693i
$579$			2.08698e11i			1.85697i
$580$		0			0
$581$	−5.98273e10			−0.525043
$582$	−1.94472e11	−	1.93233e11i	−1.69498	−	1.68418i
$583$	−9.68734e10			−0.838553
$584$	6.84216e9	−	6.97462e9i	0.0588223	−	0.0599611i
$585$		0			0
$586$	1.34941e11	+	1.34081e11i	1.14433	+	1.13704i
$587$	3.62809e9			0.0305581			0.0152790	−	0.999883i	$-0.495136\pi$
$587$	3.62809e9			0.0305581			0.0152790	+	0.999883i	$0.495136\pi$
$588$	2.19325e9	+	3.43154e11i	0.0183476	+	2.87065i
$589$	−1.29475e10			−0.107578
$590$		0			0
$591$		−	2.72906e11i		−	2.23698i
$592$	−9.63175e8	−	7.53457e10i	−0.00784185	−	0.613439i
$593$		−	8.72511e10i		−	0.705589i	−0.935701	−	0.352795i	$-0.885231\pi$
$593$		−	8.72511e10i		−	0.705589i	0.935701	−	0.352795i	$-0.114769\pi$
$594$	−1.52617e11	−	1.51645e11i	−1.22591	−	1.21810i
$595$		0			0
$596$	−1.00455e9	−	1.57172e11i	−0.00796137	−	1.24563i
$597$			2.31668e11i			1.82376i
$598$	1.82933e10	+	1.81768e10i	0.143050	+	0.142139i
$599$			1.90496e10i			0.147972i	0.997259	+	0.0739858i	$0.0235720\pi$
$599$			1.90496e10i			0.147972i	−0.997259	+	0.0739858i	$0.976428\pi$
$600$		0			0
$601$	1.75085e11			1.34200			0.670998	−	0.741459i	$-0.265866\pi$
$601$	1.75085e11			1.34200			0.670998	+	0.741459i	$0.265866\pi$
$602$	1.41745e11	−	1.42654e11i	1.07925	−	1.08617i
$603$	1.29479e11			0.979329
$604$	1.38535e11	−	8.85437e8i	1.04090	−	0.00665289i
$605$		0			0
$606$	3.04028e11	−	3.05977e11i	2.25436	−	2.26881i
$607$	−1.75308e11			−1.29136			−0.645680	−	0.763608i	$-0.723426\pi$
$607$	−1.75308e11			−1.29136			−0.645680	+	0.763608i	$0.723426\pi$
$608$	−7.03737e10	−	6.81600e10i	−0.514987	−	0.498787i
$609$	2.25270e10			0.163770
$610$		0			0
$611$			3.84186e10i			0.275662i
$612$	3.19843e11	−	2.04426e9i	2.27998	−	0.0145724i
$613$		−	1.26999e10i		−	0.0899412i	−0.998988	−	0.0449706i	$-0.985681\pi$
$613$		−	1.26999e10i		−	0.0899412i	0.998988	−	0.0449706i	$-0.0143194\pi$
$614$	1.96351e11	−	1.97610e11i	1.38153	−	1.39039i
$615$		0			0
$616$	1.93250e11	−	1.96991e11i	1.34214	−	1.36812i
$617$			2.29769e11i			1.58544i	0.609586	+	0.792720i	$0.291336\pi$
$617$			2.29769e11i			1.58544i	−0.609586	+	0.792720i	$0.708664\pi$
$618$	1.67848e11	−	1.68925e11i	1.15070	−	1.15808i
$619$			1.67400e11i			1.14023i	0.821564	+	0.570116i	$0.193102\pi$
$619$			1.67400e11i			1.14023i	−0.821564	+	0.570116i	$0.806898\pi$
$620$		0			0
$621$	−1.15887e11			−0.779237
$622$	−9.78032e10	−	9.71801e10i	−0.653419	−	0.649256i
$623$	2.13870e11			1.41971
$624$	−1.25810e9	−	9.84170e10i	−0.00829810	−	0.649130i
$625$		0			0
$626$	−1.10885e11	−	1.10179e11i	−0.722065	−	0.717464i
$627$	2.19319e11			1.41907
$628$	−1.64856e11	+	1.05367e9i	−1.05990	+	0.00677432i
$629$	−1.16893e11			−0.746768
$630$		0			0
$631$			2.92637e9i			0.0184591i	0.999957	+	0.00922957i	$0.00293791\pi$
$631$			2.92637e9i			0.0184591i	−0.999957	+	0.00922957i	$0.997062\pi$
$632$	1.26944e11	−	1.29402e11i	0.795693	−	0.811098i
$633$			4.87732e11i			3.03785i
$634$	7.46319e10	+	7.41564e10i	0.461921	+	0.458978i
$635$		0			0
$636$	1.99149e11	−	1.27285e9i	1.21716	−	0.00777944i
$637$		−	1.06798e11i		−	0.648642i
$638$	−8.07961e9	−	8.02814e9i	−0.0487650	−	0.0484543i
$639$		−	2.28548e11i		−	1.37080i
$640$		0			0
$641$	−1.15318e11			−0.683071			−0.341535	−	0.939869i	$-0.610947\pi$
$641$	−1.15318e11			−0.683071			−0.341535	+	0.939869i	$0.610947\pi$
$642$	−8.04055e10	+	8.09210e10i	−0.473310	+	0.476345i
$643$	−4.99010e10			−0.291921			−0.145961	−	0.989290i	$-0.546627\pi$
$643$	−4.99010e10			−0.291921			−0.145961	+	0.989290i	$0.546627\pi$
$644$	−9.50011e8	−	1.48638e11i	−0.00552313	−	0.864144i
$645$		0			0
$646$	−1.07123e11	+	1.07810e11i	−0.615110	+	0.619054i
$647$	−5.43112e10			−0.309936			−0.154968	−	0.987919i	$-0.549527\pi$
$647$	−5.43112e10			−0.309936			−0.154968	+	0.987919i	$0.549527\pi$
$648$	7.99773e10	+	7.84583e10i	0.453593	+	0.444978i
$649$	2.89055e11			1.62930
$650$		0			0
$651$			7.49739e10i			0.417432i
$652$	−1.10378e9	−	1.72696e11i	−0.00610788	−	0.955633i
$653$		−	1.40265e11i		−	0.771433i	−0.922617	−	0.385716i	$-0.873954\pi$
$653$		−	1.40265e11i		−	0.771433i	0.922617	−	0.385716i	$-0.126046\pi$
$654$	−3.11425e11	+	3.13421e11i	−1.70232	+	1.71324i
$655$		0			0
$656$	−2.51576e11	+	3.21600e9i	−1.35848	+	0.0173660i
$657$		−	2.93146e10i		−	0.157334i
$658$	1.56081e11	−	1.57081e11i	0.832617	−	0.837955i
$659$			2.51334e11i			1.33263i	0.745670	+	0.666315i	$0.232129\pi$
$659$			2.51334e11i			1.33263i	−0.745670	+	0.666315i	$0.767871\pi$
$660$		0			0
$661$	1.18006e10			0.0618155			0.0309077	−	0.999522i	$-0.490160\pi$
$661$	1.18006e10			0.0618155			0.0309077	+	0.999522i	$0.490160\pi$
$662$	2.64216e11	+	2.62533e11i	1.37571	+	1.36695i
$663$	−1.52686e11			−0.790216
$664$	−4.43924e10	−	4.35493e10i	−0.228369	−	0.224031i
$665$		0			0
$666$	−1.60374e11	−	1.59352e11i	−0.815150	−	0.809956i
$667$	−6.13511e9			−0.0309970
$668$	−7.45368e8	−	1.16620e11i	−0.00374339	−	0.585687i
$669$	−1.93846e11			−0.967724
$670$		0			0
$671$			8.82220e10i			0.435198i
$672$	−3.94688e11	+	4.07507e11i	−1.93543	+	1.99829i
$673$			3.32886e11i			1.62269i	0.584567	+	0.811345i	$0.301264\pi$
$673$			3.32886e11i			1.62269i	−0.584567	+	0.811345i	$0.698736\pi$
$674$	2.26203e10	+	2.24762e10i	0.109612	+	0.108914i
$675$		0			0
$676$	−1.13890e9	−	1.78192e11i	−0.00545381	−	0.853299i
$677$		−	1.55980e11i		−	0.742530i	−0.928527	−	0.371265i	$-0.878924\pi$
$677$		−	1.55980e11i		−	0.742530i	0.928527	−	0.371265i	$-0.121076\pi$
$678$	1.06379e11	+	1.05701e11i	0.503427	+	0.500220i
$679$		−	4.91776e11i		−	2.31360i
$680$		0			0
$681$	−1.49627e11			−0.695701
$682$	2.67191e10	−	2.68904e10i	0.123505	−	0.124297i
$683$	−2.38756e10			−0.109716			−0.0548581	−	0.998494i	$-0.517471\pi$
$683$	−2.38756e10			−0.109716			−0.0548581	+	0.998494i	$0.517471\pi$
$684$	−2.93940e11	+	1.87870e9i	−1.34287	+	0.00858289i
$685$		0			0
$686$	−1.77694e11	+	1.78833e11i	−0.802371	+	0.807516i
$687$	−3.10025e11			−1.39178
$688$	2.09016e11	−	2.67194e9i	0.932880	−	0.0119254i
$689$	−6.19799e10			−0.275026
$690$		0			0
$691$			3.49556e11i			1.53322i	0.642113	+	0.766610i	$0.278058\pi$
$691$			3.49556e11i			1.53322i	−0.642113	+	0.766610i	$0.721942\pi$
$692$	−2.46867e11	+	1.57784e9i	−1.07656	+	0.00688078i
$693$		−	8.27962e11i		−	3.58986i
$694$	−7.12574e10	+	7.17143e10i	−0.307180	+	0.309149i
$695$		0			0
$696$	1.67153e10	+	1.63978e10i	0.0712322	+	0.0698793i
$697$			3.90301e11i			1.65374i
$698$	−2.10900e10	+	2.12253e10i	−0.0888496	+	0.0894193i
$699$			8.95839e10i			0.375250i
$700$		0			0
$701$	−2.57887e10			−0.106796			−0.0533982	−	0.998573i	$-0.517005\pi$
$701$	−2.57887e10			−0.106796			−0.0533982	+	0.998573i	$0.517005\pi$
$702$	−9.76450e10	−	9.70229e10i	−0.402070	−	0.399508i
$703$	1.07426e11			0.439834
$704$	2.86787e11	−	5.49954e9i	1.16753	−	0.0223891i
$705$		0			0
$706$	3.42914e11	+	3.40730e11i	1.38028	+	1.37148i
$707$	7.73749e11			3.09686
$708$	−5.94228e11	+	3.79797e9i	−2.36494	+	0.0151154i
$709$	1.18322e11			0.468251			0.234126	−	0.972206i	$-0.424777\pi$
$709$	1.18322e11			0.468251			0.234126	+	0.972206i	$0.424777\pi$
$710$		0			0
$711$		−	5.43882e11i		−	2.12827i
$712$	1.58694e11	+	1.55680e11i	0.617504	+	0.605776i
$713$		−	2.04187e10i		−	0.0790079i
$714$	6.24285e11	+	6.20308e11i	2.40210	+	2.38679i
$715$		0			0
$716$	−2.59490e11	+	1.65851e9i	−0.987343	+	0.00631055i
$717$		−	6.58064e11i		−	2.48996i
$718$	2.06655e11	+	2.05339e11i	0.777587	+	0.772632i
$719$		−	1.28179e11i		−	0.479624i	−0.970819	−	0.239812i	$-0.922914\pi$
$719$		−	1.28179e11i		−	0.479624i	0.970819	−	0.239812i	$-0.0770858\pi$
$720$		0			0
$721$	4.27173e11			1.58075
$722$	−9.30846e10	+	9.36814e10i	−0.342554	+	0.344750i
$723$	7.11721e11			2.60469
$724$	−2.47893e8	−	3.87850e10i	−0.000902213	−	0.141159i
$725$		0			0
$726$	−1.20690e11	+	1.21464e11i	−0.434437	+	0.437222i
$727$	−2.11824e11			−0.758295			−0.379148	−	0.925336i	$-0.623783\pi$
$727$	−2.11824e11			−0.758295			−0.379148	+	0.925336i	$0.623783\pi$
$728$	1.23642e11	−	1.26036e11i	0.440190	−	0.448712i
$729$	−3.72333e11			−1.31832
$730$		0			0
$731$		−	3.24272e11i		−	1.13564i
$732$	−1.15917e9	−	1.81363e11i	−0.00403743	−	0.631692i
$733$		−	2.18401e11i		−	0.756552i	−0.925693	−	0.378276i	$-0.876517\pi$
$733$		−	2.18401e11i		−	0.756552i	0.925693	−	0.378276i	$-0.123483\pi$
$734$	1.65382e11	−	1.66442e11i	0.569776	−	0.573429i
$735$		0			0
$736$	1.07491e11	−	1.10982e11i	0.366321	−	0.378218i
$737$		−	1.80129e11i		−	0.610541i
$738$	−5.32071e11	+	5.35483e11i	−1.79368	+	1.80518i
$739$			1.87281e11i			0.627936i	0.949433	+	0.313968i	$0.101659\pi$
$739$			1.87281e11i			0.627936i	−0.949433	+	0.313968i	$0.898341\pi$
$740$		0			0
$741$	1.40321e11			0.465424
$742$	2.53416e11	+	2.51801e11i	0.836023	+	0.830696i
$743$	−4.43366e11			−1.45481			−0.727406	−	0.686207i	$-0.759274\pi$
$743$	−4.43366e11			−1.45481			−0.727406	+	0.686207i	$0.759274\pi$
$744$	−5.45747e10	+	5.56313e10i	−0.178115	+	0.181563i
$745$		0			0
$746$	1.60347e11	+	1.59326e11i	0.517733	+	0.514435i
$747$	−1.86583e11			−0.599224
$748$	−2.84396e9	−	4.44963e11i	−0.00908484	−	1.42141i
$749$	−2.04631e11			−0.650196
$750$		0			0
$751$		−	1.63129e11i		−	0.512827i	−0.966567	−	0.256414i	$-0.917459\pi$
$751$		−	1.63129e11i		−	0.512827i	0.966567	−	0.256414i	$-0.0825409\pi$
$752$	2.30155e11	−	2.94217e9i	0.719697	−	0.00920018i
$753$			3.32090e11i			1.03294i
$754$	−5.16936e9	−	5.13643e9i	−0.0159938	−	0.0158919i
$755$		0			0
$756$	5.07092e9	+	7.93391e11i	0.0155238	+	2.42885i
$757$			8.66867e10i			0.263979i	0.991251	+	0.131989i	$0.0421365\pi$
$757$			8.66867e10i			0.263979i	−0.991251	+	0.131989i	$0.957864\pi$
$758$	4.47260e10	+	4.44411e10i	0.135483	+	0.134619i
$759$			3.45875e11i			1.04220i
$760$		0			0
$761$	3.59912e11			1.07314			0.536571	−	0.843855i	$-0.319719\pi$
$761$	3.59912e11			1.07314			0.536571	+	0.843855i	$0.319719\pi$
$762$	−5.40355e11	+	5.43820e11i	−1.60273	+	1.61300i
$763$	−7.92573e11			−2.33852
$764$	−1.39821e11	+	8.93656e8i	−0.410391	+	0.00262299i
$765$		0			0
$766$	−3.86889e11	+	3.89370e11i	−1.12375	+	1.13096i
$767$	1.84938e11			0.534373
$768$	−5.89493e11	+	1.50739e10i	−1.69447	+	0.0433293i
$769$	6.61724e11			1.89222			0.946110	−	0.323845i	$-0.104976\pi$
$769$	6.61724e11			1.89222			0.946110	+	0.323845i	$0.104976\pi$
$770$		0			0
$771$			7.21569e11i			2.04202i
$772$	−3.89125e11	+	2.48707e9i	−1.09552	+	0.00700195i
$773$			2.24564e11i			0.628958i	0.949264	+	0.314479i	$0.101830\pi$
$773$			2.24564e11i			0.628958i	−0.949264	+	0.314479i	$0.898170\pi$
$774$	4.42059e11	−	4.44893e11i	1.23173	−	1.23963i
$775$		0			0
$776$	3.57972e11	−	3.64903e11i	0.987194	−	1.00631i
$777$		−	6.22063e11i		−	1.70667i
$778$	4.67236e9	−	4.70232e9i	0.0127532	−	0.0128349i
$779$		−	3.58691e11i		−	0.974027i
$780$		0			0
$781$	−3.17954e11			−0.854594
$782$	−1.70021e11	−	1.68938e11i	−0.454648	−	0.451751i
$783$	3.27477e10			0.0871231
$784$	−6.39797e11	+	8.17879e9i	−1.69347	+	0.0216483i
$785$		0			0
$786$	−2.32486e11	−	2.31004e11i	−0.609124	−	0.605243i
$787$	−6.78642e11			−1.76906			−0.884528	−	0.466486i	$-0.845520\pi$
$787$	−6.78642e11			−1.76906			−0.884528	+	0.466486i	$0.845520\pi$
$788$	5.08842e11	−	3.25224e9i	1.31971	−	0.00843485i
$789$	1.71553e11			0.442682
$790$		0			0
$791$			2.69008e11i			0.687163i
$792$	6.02687e11	−	6.14355e11i	1.53176	−	1.56142i
$793$			5.64447e10i			0.142735i
$794$	−2.55884e11	−	2.54254e11i	−0.643816	−	0.639714i
$795$		0			0
$796$	−4.31952e11	+	2.76080e9i	−1.07593	+	0.00687674i
$797$			2.55700e11i			0.633720i	0.948472	+	0.316860i	$0.102628\pi$
$797$			2.55700e11i			0.633720i	−0.948472	+	0.316860i	$0.897372\pi$
$798$	−5.73726e11	−	5.70071e11i	−1.41479	−	1.40578i
$799$		−	3.57068e11i		−	0.876121i
$800$		0			0
$801$	6.66996e11			1.62029
$802$	2.86072e11	−	2.87906e11i	0.691478	−	0.695911i
$803$	−4.07822e10			−0.0980863
$804$	2.36677e9	+	3.70303e11i	0.00566412	+	0.886204i
$805$		0			0
$806$	1.70949e10	−	1.72045e10i	0.0405067	−	0.0407664i
$807$	−7.36401e11			−1.73628
$808$	5.74129e11	+	5.63224e11i	1.34699	+	1.32141i
$809$	−4.12911e10			−0.0963968			−0.0481984	−	0.998838i	$-0.515348\pi$
$809$	−4.12911e10			−0.0963968			−0.0481984	+	0.998838i	$0.515348\pi$
$810$		0			0
$811$		−	2.06089e11i		−	0.476399i	−0.971216	−	0.238200i	$-0.923443\pi$
$811$		−	2.06089e11i		−	0.476399i	0.971216	−	0.238200i	$-0.0765573\pi$
$812$	2.68456e8	+	4.20024e10i	0.000617517	+	0.0966162i
$813$		−	9.23087e10i		−	0.211291i
$814$	−2.21690e11	+	2.23111e11i	−0.504949	+	0.508187i
$815$		0			0
$816$	1.16930e10	+	9.14702e11i	0.0263734	+	2.06309i
$817$			2.98010e11i			0.668872i
$818$	1.65843e11	−	1.66907e11i	0.370411	−	0.372786i
$819$		−	5.29732e11i		−	1.17739i
$820$		0			0
$821$	8.40243e11			1.84941			0.924703	−	0.380688i	$-0.124313\pi$
$821$	8.40243e11			1.84941			0.924703	+	0.380688i	$0.124313\pi$
$822$	9.43798e11	+	9.37785e11i	2.06724	+	2.05407i
$823$	−3.94949e11			−0.860878			−0.430439	−	0.902620i	$-0.641641\pi$
$823$	−3.94949e11			−0.860878			−0.430439	+	0.902620i	$0.641641\pi$
$824$	3.16966e11	+	3.10946e11i	0.687549	+	0.674491i
$825$		0			0
$826$	−7.56152e11	−	7.51334e11i	−1.62438	−	1.61404i
$827$	−3.63473e11			−0.777051			−0.388526	−	0.921438i	$-0.627016\pi$
$827$	−3.63473e11			−0.777051			−0.388526	+	0.921438i	$0.627016\pi$
$828$	−2.96279e9	−	4.63556e11i	−0.00630347	−	0.986236i
$829$	4.62310e11			0.978847			0.489424	−	0.872046i	$-0.337207\pi$
$829$	4.62310e11			0.978847			0.489424	+	0.872046i	$0.337207\pi$
$830$		0			0
$831$		−	1.17405e12i		−	2.46197i
$832$	1.83487e11	−	3.51862e9i	0.382923	−	0.00734310i
$833$			9.92595e11i			2.06154i
$834$	−8.09205e11	−	8.04050e11i	−1.67261	−	1.66195i
$835$		0			0
$836$	2.61364e9	+	4.08927e11i	0.00535081	+	0.837184i
$837$			1.08990e11i			0.222067i
$838$	−8.29574e10	−	8.24289e10i	−0.168221	−	0.167149i
$839$		−	1.39033e11i		−	0.280588i	−0.990110	−	0.140294i	$-0.955195\pi$
$839$		−	1.39033e11i		−	0.280588i	0.990110	−	0.140294i	$-0.0448049\pi$
$840$		0			0
$841$	−4.98513e11			−0.996534
$842$	4.61407e11	−	4.64366e11i	0.917986	−	0.923872i
$843$	1.16383e11			0.230452
$844$	−9.09393e11	+	5.81234e9i	−1.79218	+	0.0114546i
$845$		0			0
$846$	4.86767e11	−	4.89888e11i	0.950254	−	0.956347i
$847$	−3.07156e11			−0.596795
$848$	4.74654e9	+	3.71305e11i	0.00917896	+	0.718037i
$849$	3.56763e11			0.686672
$850$		0			0
$851$			1.69415e11i			0.323024i
$852$	6.53638e11	−	4.17769e9i	1.24045	−	0.00792826i
$853$			2.95120e11i			0.557446i	0.960372	+	0.278723i	$0.0899111\pi$
$853$			2.95120e11i			0.557446i	−0.960372	+	0.278723i	$0.910089\pi$
$854$	2.29314e11	−	2.30784e11i	0.431120	−	0.433885i
$855$		0			0
$856$	−1.51838e11	−	1.48954e11i	−0.282804	−	0.277433i
$857$			2.93094e11i			0.543355i	0.962388	+	0.271678i	$0.0875784\pi$
$857$			2.93094e11i			0.543355i	−0.962388	+	0.271678i	$0.912422\pi$
$858$	−2.89572e11	+	2.91429e11i	−0.534328	+	0.537754i
$859$			5.58133e11i			1.02510i	0.858658	+	0.512549i	$0.171299\pi$
$859$			5.58133e11i			1.02510i	−0.858658	+	0.512549i	$0.828701\pi$
$860$		0			0
$861$	−2.07704e12			−3.77949
$862$	−4.48463e10	−	4.45605e10i	−0.0812264	−	0.0807089i
$863$	3.25698e11			0.587181			0.293590	−	0.955931i	$-0.405150\pi$
$863$	3.25698e11			0.587181			0.293590	+	0.955931i	$0.405150\pi$
$864$	−5.73760e11	+	5.92395e11i	−1.02962	+	1.06306i
$865$		0			0
$866$	3.27697e11	+	3.25609e11i	0.582641	+	0.578929i
$867$	4.61339e11			0.816477
$868$	−1.39791e11	+	8.93469e8i	−0.246264	+	0.00157398i
$869$	−7.56643e11			−1.32682
$870$		0			0
$871$		−	1.15247e11i		−	0.200243i
$872$	−5.88096e11	−	5.76927e11i	−1.01714	−	0.997826i
$873$		−	1.53370e12i		−	2.64048i
$874$	1.56251e11	+	1.55256e11i	0.267780	+	0.266074i
$875$		0			0
$876$	8.38385e10	−	5.35849e8i	0.142373	−	0.000909969i
$877$		−	2.02891e11i		−	0.342976i	−0.985186	−	0.171488i	$-0.945143\pi$
$877$		−	2.02891e11i		−	0.342976i	0.985186	−	0.171488i	$-0.0548575\pi$
$878$	−1.88793e11	−	1.87590e11i	−0.317693	−	0.315669i
$879$			1.63236e12i			2.73439i
$880$		0			0
$881$	−6.22197e10			−0.103282			−0.0516409	−	0.998666i	$-0.516445\pi$
$881$	−6.22197e10			−0.103282			−0.0516409	+	0.998666i	$0.516445\pi$
$882$	−1.35314e12	+	1.36181e12i	−2.23598	+	2.25032i
$883$	7.69290e10			0.126546			0.0632729	−	0.997996i	$-0.479846\pi$
$883$	7.69290e10			0.126546			0.0632729	+	0.997996i	$0.479846\pi$
$884$	−1.81957e9	−	2.84689e11i	−0.00297962	−	0.466188i
$885$		0			0
$886$	−1.81857e11	+	1.83023e11i	−0.295117	+	0.297010i
$887$	7.30650e10			0.118036			0.0590180	−	0.998257i	$-0.481203\pi$
$887$	7.30650e10			0.118036			0.0590180	+	0.998257i	$0.481203\pi$
$888$	4.52810e11	−	4.61576e11i	0.728222	−	0.742321i
$889$	−1.37520e12			−2.20170
$890$		0			0
$891$		−	4.67645e11i		−	0.742003i
$892$	−2.31007e9	−	3.61432e11i	−0.00364893	−	0.570909i
$893$			3.28150e11i			0.516020i
$894$	9.50640e11	−	9.56736e11i	1.48822	−	1.49776i
$895$		0			0
$896$	−7.64514e11	−	7.31053e11i	−1.18619	−	1.13427i
$897$			2.21291e11i			0.341818i
$898$	1.48266e11	−	1.49217e11i	0.228001	−	0.229463i
$899$			5.76996e9i			0.00883353i
$900$		0			0
$901$	5.76050e11			0.874100
$902$	7.44959e11	+	7.40213e11i	1.12540	+	1.11823i
$903$	1.72566e12			2.59540
$904$	−1.95816e11	+	1.99607e11i	−0.293207	+	0.298883i
$905$		0			0
$906$	8.43290e11	+	8.37917e11i	1.25160	+	1.24362i
$907$	7.63733e11			1.12853			0.564264	−	0.825594i	$-0.309160\pi$
$907$	7.63733e11			1.12853			0.564264	+	0.825594i	$0.309160\pi$
$908$	−1.78312e9	−	2.78985e11i	−0.00262324	−	0.410429i
$909$	2.41308e12			3.53441
$910$		0			0
$911$			6.04985e11i			0.878357i	0.898400	+	0.439178i	$0.144730\pi$
$911$			6.04985e11i			0.878357i	−0.898400	+	0.439178i	$0.855270\pi$
$912$	−1.07460e10	−	8.40623e11i	−0.0155335	−	1.21513i
$913$			2.59573e11i			0.373573i
$914$	7.71770e11	+	7.66853e11i	1.10587	+	1.09882i
$915$		0			0
$916$	−3.69459e9	−	5.78053e11i	−0.00524789	−	0.821080i
$917$		−	5.87904e11i		−	0.831436i
$918$	9.07527e11	+	9.01745e11i	1.27788	+	1.26974i
$919$		−	1.09773e12i		−	1.53898i	−0.638657	−	0.769492i	$-0.720510\pi$
$919$		−	1.09773e12i		−	1.53898i	0.638657	−	0.769492i	$-0.279490\pi$
$920$		0			0
$921$	2.39046e12			3.32233
$922$	3.23420e11	−	3.25493e11i	0.447551	−	0.450421i
$923$	−2.03428e11			−0.280287
$924$	2.36794e12	−	1.51345e10i	3.24850	−	0.0207626i
$925$		0			0
$926$	−4.76732e10	+	4.79789e10i	−0.0648381	+	0.0652539i
$927$	1.33222e12			1.80408
$928$	−3.03750e10	+	3.13616e10i	−0.0409567	+	0.0422869i
$929$	−5.68272e11			−0.762945			−0.381473	−	0.924380i	$-0.624583\pi$
$929$	−5.68272e11			−0.762945			−0.381473	+	0.924380i	$0.624583\pi$
$930$		0			0
$931$		−	9.12208e11i		−	1.21421i
$932$	−1.67032e11	+	1.06758e9i	−0.221379	+	0.00141493i
$933$		−	1.18311e12i		−	1.56135i
$934$	−4.81852e11	+	4.84942e11i	−0.633179	+	0.637238i
$935$		0			0
$936$	3.85601e11	−	3.93066e11i	0.502383	−	0.512109i
$937$			1.49600e11i			0.194076i	0.995281	+	0.0970382i	$0.0309369\pi$
$937$			1.49600e11i			0.194076i	−0.995281	+	0.0970382i	$0.969063\pi$
$938$	−4.68207e11	+	4.71209e11i	−0.604821	+	0.608699i
$939$		−	1.34136e12i		−	1.72537i
$940$		0			0
$941$	−5.28765e11			−0.674379			−0.337190	−	0.941437i	$-0.609476\pi$
$941$	−5.28765e11			−0.674379			−0.337190	+	0.941437i	$0.609476\pi$
$942$	−1.00351e12	−	9.97119e11i	−1.27444	−	1.26632i
$943$	5.65671e11			0.715348
$944$	−1.41629e10	−	1.10791e12i	−0.0178346	−	1.39514i
$945$		0			0
$946$	−6.18931e11	−	6.14988e11i	−0.772819	−	0.767896i
$947$	−9.04370e11			−1.12447			−0.562233	−	0.826979i	$-0.690057\pi$
$947$	−9.04370e11			−1.12447			−0.562233	+	0.826979i	$0.690057\pi$
$948$	1.55548e12	−	9.94176e9i	1.92589	−	0.0123092i
$949$	−2.60926e10			−0.0321701
$950$		0			0
$951$			9.02811e11i			1.10376i
$952$	−1.14915e12	+	1.17139e12i	−1.39903	+	1.42612i
$953$			5.71895e11i			0.693337i	0.937988	+	0.346669i	$0.112687\pi$
$953$			5.71895e11i			0.693337i	−0.937988	+	0.346669i	$0.887313\pi$
$954$	7.90326e11	+	7.85291e11i	0.954141	+	0.948062i
$955$		0			0
$956$	1.22698e12	−	7.84220e9i	1.46895	−	0.00938872i
$957$		−	9.77379e10i		−	0.116524i
$958$	7.63861e11	+	7.58994e11i	0.906885	+	0.901107i
$959$			2.38665e12i			2.82173i
$960$		0			0
$961$	8.33688e11			0.977484
$962$	−1.41838e11	+	1.42747e11i	−0.165612	+	0.166674i
$963$	−6.38181e11			−0.742060
$964$	8.48163e9	+	1.32703e12i	0.00982135	+	1.53664i
$965$		0			0
$966$	8.99025e11	−	9.04790e11i	1.03244	−	1.03906i
$967$	9.92056e11			1.13457			0.567284	−	0.823522i	$-0.307994\pi$
$967$	9.92056e11			1.13457			0.567284	+	0.823522i	$0.307994\pi$
$968$	−2.27913e11	−	2.23584e11i	−0.259577	−	0.254647i
$969$	−1.30416e12			−1.47923
$970$		0			0
$971$			4.62553e11i			0.520336i	0.965563	+	0.260168i	$0.0837780\pi$
$971$			4.62553e11i			0.520336i	−0.965563	+	0.260168i	$0.916222\pi$
$972$	−2.29848e9	−	3.59618e11i	−0.00257499	−	0.402880i
$973$		−	2.04630e12i		−	2.28306i
$974$	−1.09384e12	+	1.10085e12i	−1.21539	+	1.22319i
$975$		0			0
$976$	3.38145e11	−	4.32264e9i	0.372652	−	0.00476376i
$977$			1.35557e11i			0.148780i	0.997229	+	0.0743899i	$0.0237009\pi$
$977$			1.35557e11i			0.148780i	−0.997229	+	0.0743899i	$0.976299\pi$
$978$	1.04454e12	−	1.05123e12i	1.14174	−	1.14906i
$979$		−	9.27919e11i		−	1.01013i
$980$		0			0
$981$	−2.47179e12			−2.66892
$982$	−1.97004e11	−	1.95749e11i	−0.211850	−	0.210500i
$983$	−1.95656e10			−0.0209546			−0.0104773	−	0.999945i	$-0.503335\pi$
$983$	−1.95656e10			−0.0209546			−0.0104773	+	0.999945i	$0.503335\pi$
$984$	−1.54118e12	−	1.51191e12i	−1.64390	−	1.61267i
$985$		0			0
$986$	4.80448e10	+	4.77387e10i	0.0508322	+	0.0505083i
$987$	1.90019e12			2.00230
$988$	1.67221e9	+	2.61633e11i	0.00175494	+	0.274577i
$989$	−4.69975e11			−0.491235
$990$		0			0
$991$			4.63152e11i			0.480208i	0.970747	+	0.240104i	$0.0771815\pi$
$991$			4.63152e11i			0.480208i	−0.970747	+	0.240104i	$0.922818\pi$
$992$	−1.04377e11	−	1.01093e11i	−0.107785	−	0.104394i
$993$			3.19619e12i			3.28727i
$994$	8.31751e11	+	8.26452e11i	0.852016	+	0.846588i
$995$		0			0
$996$	−3.41060e9	−	5.33620e11i	−0.00346572	−	0.542244i
$997$		−	5.69988e11i		−	0.576879i	−0.957498	−	0.288439i	$-0.906864\pi$
$997$		−	5.69988e11i		−	0.576879i	0.957498	−	0.288439i	$-0.0931364\pi$
$998$	−1.62256e11	−	1.61222e11i	−0.163560	−	0.162518i
$999$		−	9.04296e11i		−	0.907922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.d.c.99.8		32
4.3	odd	2	inner	100.9.d.c.99.26		32
5.2	odd	4		100.9.b.d.51.5		16
5.3	odd	4		20.9.b.a.11.12	yes	16
5.4	even	2	inner	100.9.d.c.99.25		32
15.8	even	4		180.9.c.a.91.5		16
20.3	even	4		20.9.b.a.11.11	✓	16
20.7	even	4		100.9.b.d.51.6		16
20.19	odd	2	inner	100.9.d.c.99.7		32
40.3	even	4		320.9.b.d.191.2		16
40.13	odd	4		320.9.b.d.191.15		16
60.23	odd	4		180.9.c.a.91.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.11	✓	16	20.3	even	4
20.9.b.a.11.12	yes	16	5.3	odd	4
100.9.b.d.51.5		16	5.2	odd	4
100.9.b.d.51.6		16	20.7	even	4
100.9.d.c.99.7		32	20.19	odd	2	inner
100.9.d.c.99.8		32	1.1	even	1	trivial
100.9.d.c.99.25		32	5.4	even	2	inner
100.9.d.c.99.26		32	4.3	odd	2	inner
180.9.c.a.91.5		16	15.8	even	4
180.9.c.a.91.6		16	60.23	odd	4
320.9.b.d.191.2		16	40.3	even	4
320.9.b.d.191.15		16	40.13	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-11.2775 + 11.3498i) q^{2} -137.297 q^{3} +(-1.63618 - 255.995i) q^{4} +(1548.37 - 1558.29i) q^{6} +3940.57 q^{7} +(2923.94 + 2868.41i) q^{8} +12289.4 q^{9} -17097.0i q^{11} +(224.642 + 35147.3i) q^{12} -10938.7i q^{13} +(-44439.8 + 44724.8i) q^{14} +(-65530.6 + 837.705i) q^{16} +101666. i q^{17} +(-138594. + 139483. i) q^{18} -93432.1i q^{19} -541029. q^{21} +(194047. + 192811. i) q^{22} +147346. q^{23} +(-401448. - 393824. i) q^{24} +(124152. + 123361. i) q^{26} -786497. q^{27} +(-6447.48 - 1.00877e6i) q^{28} -41637.4 q^{29} -138577. i q^{31} +(729514. - 753207. i) q^{32} +2.34736e6i q^{33} +(-1.15389e6 - 1.14653e6i) q^{34} +(-20107.7 - 3.14603e6i) q^{36} +1.14978e6i q^{37} +(1.06044e6 + 1.05368e6i) q^{38} +1.50185e6i q^{39} +3.83906e6 q^{41} +(6.10145e6 - 6.14057e6i) q^{42} -3.18959e6 q^{43} +(-4.37673e6 + 27973.6i) q^{44} +(-1.66170e6 + 1.67235e6i) q^{46} -3.51218e6 q^{47} +(8.99715e6 - 115014. i) q^{48} +9.76332e6 q^{49} -1.39584e7i q^{51} +(-2.80024e6 + 17897.6i) q^{52} -5.66612e6i q^{53} +(8.86971e6 - 8.92658e6i) q^{54} +(1.15220e7 + 1.13032e7i) q^{56} +1.28279e7i q^{57} +(469565. - 472576. i) q^{58} +1.69068e7i q^{59} -5.16010e6 q^{61} +(1.57282e6 + 1.56280e6i) q^{62} +4.84274e7 q^{63} +(321668. + 1.67741e7i) q^{64} +(-2.66421e7 - 2.64723e7i) q^{66} +1.05358e7 q^{67} +(2.60259e7 - 166343. i) q^{68} -2.02302e7 q^{69} -1.85971e7i q^{71} +(3.59336e7 + 3.52511e7i) q^{72} -2.38535e6i q^{73} +(-1.30498e7 - 1.29666e7i) q^{74} +(-2.39181e7 + 152871. i) q^{76} -6.73718e7i q^{77} +(-1.70457e7 - 1.69371e7i) q^{78} -4.42560e7i q^{79} +2.73525e7 q^{81} +(-4.32950e7 + 4.35726e7i) q^{82} -1.51824e7 q^{83} +(885218. + 1.38500e8i) q^{84} +(3.59706e7 - 3.62013e7i) q^{86} +5.71668e6 q^{87} +(4.90411e7 - 4.99905e7i) q^{88} +5.42739e7 q^{89} -4.31047e7i q^{91} +(-241085. - 3.77199e7i) q^{92} +1.90261e7i q^{93} +(3.96086e7 - 3.98625e7i) q^{94} +(-1.00160e8 + 1.03413e8i) q^{96} -1.24798e8i q^{97} +(-1.10106e8 + 1.10812e8i) q^{98} -2.10112e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 104 q^{4} + 8736 q^{6} + 77600 q^{9} - 136944 q^{14} - 162848 q^{16} + 828992 q^{21} - 327584 q^{24} + 2074248 q^{26} - 5529792 q^{29} - 7587928 q^{34} - 10937832 q^{36} - 17152896 q^{41} - 33842400 q^{44}+ \cdots - 906779904 q^{96}+O(q^{100}) \) 32 * q + 104 * q^4 + 8736 * q^6 + 77600 * q^9 - 136944 * q^14 - 162848 * q^16 + 828992 * q^21 - 327584 * q^24 + 2074248 * q^26 - 5529792 * q^29 - 7587928 * q^34 - 10937832 * q^36 - 17152896 * q^41 - 33842400 * q^44 - 15948304 * q^46 + 65607200 * q^49 - 17797408 * q^54 + 68269536 * q^56 + 16743424 * q^61 + 95087744 * q^64 + 38716000 * q^66 - 15054528 * q^69 + 276421752 * q^74 + 5140800 * q^76 + 281173344 * q^81 - 139523648 * q^84 - 203449344 * q^86 - 213294912 * q^89 - 110529264 * q^94 - 906779904 * q^96

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