LMFDB - Embedded newform 240.9.c.e.209.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [240,9,Mod(209,240)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("240.209"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(240, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1, 1])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	240.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,21928] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$97.7708664147$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11030 x^{14} + 49274731 x^{12} + 114127354194 x^{10} + 145952808215673 x^{8} + \cdots + 37\!\cdots\!00 $ x^16 + 11030x^14 + 49274731x^12 + 114127354194x^10 + 145952808215673x^8 + 102178334474381688x^6 + 37133934963356085616x^4 + 6178447219085671000280*x^2 + 379932896280343584768100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{44}\cdot 3^{20}\cdot 5^{10} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.8
Root			$-1.41421 + 12.8953i$ of defining polynomial
Character	$\chi$	$=$	240.209
Dual form			240.9.c.e.209.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-38.6282 + 71.1959i) q^{3} +(447.247 - 436.572i) q^{5} -730.421i q^{7} +(-3576.72 - 5500.34i) q^{9} -2177.02i q^{11} -20679.8i q^{13} +(13805.8 + 48706.2i) q^{15} -87242.2 q^{17} -218350. q^{19} +(52003.0 + 28214.9i) q^{21} -74313.2 q^{23} +(9434.46 - 390511. i) q^{25} +(529764. - 42179.6i) q^{27} +564034. i q^{29} -194831. q^{31} +(154995. + 84094.2i) q^{33} +(-318882. - 326679. i) q^{35} +2.88646e6i q^{37} +(1.47232e6 + 798825. i) q^{39} +3.26199e6i q^{41} -5.76157e6i q^{43} +(-4.00097e6 - 898514. i) q^{45} +5.22994e6 q^{47} +5.23129e6 q^{49} +(3.37001e6 - 6.21129e6i) q^{51} -23530.8 q^{53} +(-950424. - 973663. i) q^{55} +(8.43445e6 - 1.55456e7i) q^{57} +1.90089e7i q^{59} +2.23567e7 q^{61} +(-4.01757e6 + 2.61251e6i) q^{63} +(-9.02824e6 - 9.24899e6i) q^{65} +1.36408e7i q^{67} +(2.87059e6 - 5.29080e6i) q^{69} -1.49189e7i q^{71} +9.97784e6i q^{73} +(2.74384e7 + 1.57564e7i) q^{75} -1.59014e6 q^{77} +1.79651e7 q^{79} +(-1.74608e7 + 3.93464e7i) q^{81} -1.52131e7 q^{83} +(-3.90188e7 + 3.80875e7i) q^{85} +(-4.01570e7 - 2.17876e7i) q^{87} -7.04410e7i q^{89} -1.51050e7 q^{91} +(7.52597e6 - 1.38712e7i) q^{93} +(-9.76561e7 + 9.53253e7i) q^{95} +3.77001e7i q^{97} +(-1.19743e7 + 7.78658e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 21928 q^{9} + 62920 q^{15} - 96048 q^{19} + 667112 q^{21} + 1292160 q^{25} + 5127152 q^{31} + 5420160 q^{39} - 8741480 q^{45} - 21439680 q^{49} - 3556688 q^{51} - 27329120 q^{55} + 67157264 q^{61}+ \cdots - 754526432 q^{99}+O(q^{100}) $ 16 * q + 21928 * q^9 + 62920 * q^15 - 96048 * q^19 + 667112 * q^21 + 1292160 * q^25 + 5127152 * q^31 + 5420160 * q^39 - 8741480 * q^45 - 21439680 * q^49 - 3556688 * q^51 - 27329120 * q^55 + 67157264 * q^61 + 97106152 * q^69 - 17107360 * q^75 + 296926128 * q^79 - 214283008 * q^81 + 190319120 * q^85 - 143834880 * q^91 - 754526432 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−38.6282	+	71.1959i	−0.476892	+	0.878962i
$3$	−38.6282	+	71.1959i	−0.476892	+	0.878962i
$4$		0			0
$5$	447.247	−	436.572i	0.715595	−	0.698515i
$5$	447.247	−	436.572i	0.715595	−	0.698515i
$6$		0			0
$7$		−	730.421i		−	0.304215i	−0.988364	−	0.152108i	$-0.951394\pi$
$7$		−	730.421i		−	0.304215i	0.988364	−	0.152108i	$-0.0486061\pi$
$8$		0			0
$9$	−3576.72	−	5500.34i	−0.545149	−	0.838339i
$10$		0			0
$11$		−	2177.02i		−	0.148693i	−0.997232	−	0.0743465i	$-0.976313\pi$
$11$		−	2177.02i		−	0.148693i	0.997232	−	0.0743465i	$-0.0236871\pi$
$12$		0			0
$13$		−	20679.8i		−	0.724058i	−0.932167	−	0.362029i	$-0.882084\pi$
$13$		−	20679.8i		−	0.724058i	0.932167	−	0.362029i	$-0.117916\pi$
$14$		0			0
$15$	13805.8	+	48706.2i	0.272707	+	0.962097i
$16$		0			0
$17$	−87242.2			−1.04455			−0.522277	−	0.852776i	$-0.674917\pi$
$17$	−87242.2			−1.04455			−0.522277	+	0.852776i	$0.674917\pi$
$18$		0			0
$19$	−218350.			−1.67547			−0.837737	−	0.546074i	$-0.816122\pi$
$19$	−218350.			−1.67547			−0.837737	+	0.546074i	$0.816122\pi$
$20$		0			0
$21$	52003.0	+	28214.9i	0.267394	+	0.145078i
$22$		0			0
$23$	−74313.2			−0.265555			−0.132778	−	0.991146i	$-0.542390\pi$
$23$	−74313.2			−0.265555			−0.132778	+	0.991146i	$0.542390\pi$
$24$		0			0
$25$	9434.46	−	390511.i	0.0241522	−	0.999708i
$26$		0			0
$27$	529764.	−	42179.6i	0.996845	−	0.0793683i
$28$		0			0
$29$			564034.i			0.797469i	0.917067	+	0.398734i	$0.130550\pi$
$29$			564034.i			0.797469i	−0.917067	+	0.398734i	$0.869450\pi$
$30$		0			0
$31$	−194831.			−0.210965			−0.105483	−	0.994421i	$-0.533639\pi$
$31$	−194831.			−0.210965			−0.105483	+	0.994421i	$0.533639\pi$
$32$		0			0
$33$	154995.	+	84094.2i	0.130696	+	0.0709105i
$34$		0			0
$35$	−318882.	−	326679.i	−0.212499	−	0.217695i
$36$		0			0
$37$			2.88646e6i			1.54013i	0.637964	+	0.770066i	$0.279777\pi$
$37$			2.88646e6i			1.54013i	−0.637964	+	0.770066i	$0.720223\pi$
$38$		0			0
$39$	1.47232e6	+	798825.i	0.636420	+	0.345297i
$40$		0			0
$41$			3.26199e6i			1.15438i	0.816611	+	0.577188i	$0.195850\pi$
$41$			3.26199e6i			1.15438i	−0.816611	+	0.577188i	$0.804150\pi$
$42$		0			0
$43$		−	5.76157e6i		−	1.68526i	−0.538492	−	0.842630i	$-0.681006\pi$
$43$		−	5.76157e6i		−	1.68526i	0.538492	−	0.842630i	$-0.318994\pi$
$44$		0			0
$45$	−4.00097e6	−	898514.i	−0.975699	−	0.219116i
$46$		0			0
$47$	5.22994e6			1.07178			0.535889	−	0.844288i	$-0.319976\pi$
$47$	5.22994e6			1.07178			0.535889	+	0.844288i	$0.319976\pi$
$48$		0			0
$49$	5.23129e6			0.907453
$50$		0			0
$51$	3.37001e6	−	6.21129e6i	0.498139	−	0.918124i
$52$		0			0
$53$	−23530.8			−0.00298218			−0.00149109	−	0.999999i	$-0.500475\pi$
$53$	−23530.8			−0.00298218			−0.00149109	+	0.999999i	$0.500475\pi$
$54$		0			0
$55$	−950424.	−	973663.i	−0.103864	−	0.106404i
$56$		0			0
$57$	8.43445e6	−	1.55456e7i	0.799020	−	1.47268i
$58$		0			0
$59$			1.90089e7i			1.56874i	0.620296	+	0.784368i	$0.287012\pi$
$59$			1.90089e7i			1.56874i	−0.620296	+	0.784368i	$0.712988\pi$
$60$		0			0
$61$	2.23567e7			1.61469			0.807343	−	0.590083i	$-0.200905\pi$
$61$	2.23567e7			1.61469			0.807343	+	0.590083i	$0.200905\pi$
$62$		0			0
$63$	−4.01757e6	+	2.61251e6i	−0.255036	+	0.165843i
$64$		0			0
$65$	−9.02824e6	−	9.24899e6i	−0.505766	−	0.518132i
$66$		0			0
$67$			1.36408e7i			0.676924i	0.940980	+	0.338462i	$0.109907\pi$
$67$			1.36408e7i			0.676924i	−0.940980	+	0.338462i	$0.890093\pi$
$68$		0			0
$69$	2.87059e6	−	5.29080e6i	0.126641	−	0.233413i
$70$		0			0
$71$		−	1.49189e7i		−	0.587090i	−0.955945	−	0.293545i	$-0.905165\pi$
$71$		−	1.49189e7i		−	0.587090i	0.955945	−	0.293545i	$-0.0948351\pi$
$72$		0			0
$73$			9.97784e6i			0.351354i	0.984448	+	0.175677i	$0.0562115\pi$
$73$			9.97784e6i			0.351354i	−0.984448	+	0.175677i	$0.943789\pi$
$74$		0			0
$75$	2.74384e7	+	1.57564e7i	0.867188	+	0.497981i
$76$		0			0
$77$	−1.59014e6			−0.0452347
$78$		0			0
$79$	1.79651e7			0.461234			0.230617	−	0.973045i	$-0.425926\pi$
$79$	1.79651e7			0.461234			0.230617	+	0.973045i	$0.425926\pi$
$80$		0			0
$81$	−1.74608e7	+	3.93464e7i	−0.405625	+	0.914039i
$82$		0			0
$83$	−1.52131e7			−0.320558			−0.160279	−	0.987072i	$-0.551239\pi$
$83$	−1.52131e7			−0.320558			−0.160279	+	0.987072i	$0.551239\pi$
$84$		0			0
$85$	−3.90188e7	+	3.80875e7i	−0.747478	+	0.729637i
$86$		0			0
$87$	−4.01570e7	−	2.17876e7i	−0.700945	−	0.380306i
$88$		0			0
$89$		−	7.04410e7i		−	1.12270i	−0.827577	−	0.561352i	$-0.810281\pi$
$89$		−	7.04410e7i		−	1.12270i	0.827577	−	0.561352i	$-0.189719\pi$
$90$		0			0
$91$	−1.51050e7			−0.220270
$92$		0			0
$93$	7.52597e6	−	1.38712e7i	0.100608	−	0.185430i
$94$		0			0
$95$	−9.76561e7	+	9.53253e7i	−1.19896	+	1.17034i
$96$		0			0
$97$			3.77001e7i			0.425849i	0.977069	+	0.212925i	$0.0682989\pi$
$97$			3.77001e7i			0.425849i	−0.977069	+	0.212925i	$0.931701\pi$
$98$		0			0
$99$	−1.19743e7	+	7.78658e6i	−0.124655	+	0.0810599i
$100$		0			0
$101$			2.01688e8i			1.93818i	0.246703	+	0.969091i	$0.420653\pi$
$101$			2.01688e8i			1.93818i	−0.246703	+	0.969091i	$0.579347\pi$
$102$		0			0
$103$			1.46669e8i			1.30313i	0.758593	+	0.651565i	$0.225887\pi$
$103$			1.46669e8i			1.30313i	−0.758593	+	0.651565i	$0.774113\pi$
$104$		0			0
$105$	3.55760e7	−	1.00841e7i	0.292685	−	0.0829618i
$106$		0			0
$107$	1.16566e8			0.889275			0.444637	−	0.895711i	$-0.353333\pi$
$107$	1.16566e8			0.889275			0.444637	+	0.895711i	$0.353333\pi$
$108$		0			0
$109$	−1.52027e8			−1.07700			−0.538498	−	0.842627i	$-0.681008\pi$
$109$	−1.52027e8			−1.07700			−0.538498	+	0.842627i	$0.681008\pi$
$110$		0			0
$111$	−2.05504e8	−	1.11499e8i	−1.35372	−	0.734476i
$112$		0			0
$113$	−2.57848e8			−1.58143			−0.790714	−	0.612185i	$-0.790291\pi$
$113$	−2.57848e8			−1.58143			−0.790714	+	0.612185i	$0.790291\pi$
$114$		0			0
$115$	−3.32364e7	+	3.24431e7i	−0.190030	+	0.185494i
$116$		0			0
$117$	−1.13746e8	+	7.39660e7i	−0.607007	+	0.394720i
$118$		0			0
$119$			6.37236e7i			0.317770i
$120$		0			0
$121$	2.09619e8			0.977890
$122$		0			0
$123$	−2.32240e8	−	1.26005e8i	−1.01465	−	0.550512i
$124$		0			0
$125$	−1.66267e8	−	1.78774e8i	−0.681029	−	0.732257i
$126$		0			0
$127$			3.38411e8i			1.30086i	0.759568	+	0.650428i	$0.225410\pi$
$127$			3.38411e8i			1.30086i	−0.759568	+	0.650428i	$0.774590\pi$
$128$		0			0
$129$	4.10200e8	+	2.22559e8i	1.48128	+	0.803687i
$130$		0			0
$131$			2.54469e8i			0.864070i	0.901857	+	0.432035i	$0.142204\pi$
$131$			2.54469e8i			0.864070i	−0.901857	+	0.432035i	$0.857796\pi$
$132$		0			0
$133$			1.59487e8i			0.509705i
$134$		0			0
$135$	2.18521e8	−	2.50145e8i	0.657898	−	0.753107i
$136$		0			0
$137$	−1.70222e8			−0.483206			−0.241603	−	0.970375i	$-0.577673\pi$
$137$	−1.70222e8			−0.483206			−0.241603	+	0.970375i	$0.577673\pi$
$138$		0			0
$139$	6.16232e8			1.65076			0.825382	−	0.564574i	$-0.190960\pi$
$139$	6.16232e8			1.65076			0.825382	+	0.564574i	$0.190960\pi$
$140$		0			0
$141$	−2.02023e8	+	3.72350e8i	−0.511122	+	0.942053i
$142$		0			0
$143$	−4.50203e7			−0.107662
$144$		0			0
$145$	2.46242e8	+	2.52263e8i	0.557044	+	0.570664i
$146$		0			0
$147$	−2.02075e8	+	3.72446e8i	−0.432757	+	0.797617i
$148$		0			0
$149$			4.28239e8i			0.868842i	0.900710	+	0.434421i	$0.143047\pi$
$149$			4.28239e8i			0.868842i	−0.900710	+	0.434421i	$0.856953\pi$
$150$		0			0
$151$	1.22999e8			0.236589			0.118294	−	0.992979i	$-0.462257\pi$
$151$	1.22999e8			0.236589			0.118294	+	0.992979i	$0.462257\pi$
$152$		0			0
$153$	3.12041e8	+	4.79862e8i	0.569438	+	0.875691i
$154$		0			0
$155$	−8.71375e7	+	8.50577e7i	−0.150966	+	0.147363i
$156$		0			0
$157$		−	5.76997e8i		−	0.949675i	−0.880074	−	0.474837i	$-0.842507\pi$
$157$		−	5.76997e8i		−	0.949675i	0.880074	−	0.474837i	$-0.157493\pi$
$158$		0			0
$159$	908954.	−	1.67530e6i	0.00142218	−	0.00262122i
$160$		0			0
$161$			5.42800e7i			0.0807860i
$162$		0			0
$163$		−	1.02316e9i		−	1.44941i	−0.689059	−	0.724705i	$-0.741976\pi$
$163$		−	1.02316e9i		−	1.44941i	0.689059	−	0.724705i	$-0.258024\pi$
$164$		0			0
$165$	1.06034e8	−	3.00555e7i	0.143057	−	0.0405497i
$166$		0			0
$167$	−6.13627e8			−0.788930			−0.394465	−	0.918911i	$-0.629070\pi$
$167$	−6.13627e8			−0.788930			−0.394465	+	0.918911i	$0.629070\pi$
$168$		0			0
$169$	3.88075e8			0.475740
$170$		0			0
$171$	7.80975e8	+	1.20100e9i	0.913383	+	1.40462i
$172$		0			0
$173$	−2.25079e8			−0.251276			−0.125638	−	0.992076i	$-0.540098\pi$
$173$	−2.25079e8			−0.251276			−0.125638	+	0.992076i	$0.540098\pi$
$174$		0			0
$175$	−2.85238e8	−	6.89113e6i	−0.304127	−	0.00734748i
$176$		0			0
$177$	−1.35336e9	−	7.34281e8i	−1.37886	−	0.748117i
$178$		0			0
$179$			7.28271e8i			0.709383i	0.934983	+	0.354691i	$0.115414\pi$
$179$			7.28271e8i			0.709383i	−0.934983	+	0.354691i	$0.884586\pi$
$180$		0			0
$181$	9.56534e7			0.0891223			0.0445611	−	0.999007i	$-0.485811\pi$
$181$	9.56534e7			0.0891223			0.0445611	+	0.999007i	$0.485811\pi$
$182$		0			0
$183$	−8.63599e8	+	1.59170e9i	−0.770030	+	1.41925i
$184$		0			0
$185$	1.26015e9	+	1.29096e9i	1.07581	+	1.10211i
$186$		0			0
$187$			1.89928e8i			0.155318i
$188$		0			0
$189$	−3.08089e7	−	3.86951e8i	−0.0241451	−	0.303256i
$190$		0			0
$191$			2.55333e9i			1.91855i	0.282467	+	0.959277i	$0.408847\pi$
$191$			2.55333e9i			1.91855i	−0.282467	+	0.959277i	$0.591153\pi$
$192$		0			0
$193$		−	3.11662e8i		−	0.224623i	−0.993673	−	0.112312i	$-0.964174\pi$
$193$		−	3.11662e8i		−	0.224623i	0.993673	−	0.112312i	$-0.0358255\pi$
$194$		0			0
$195$	1.00724e9	−	2.85502e8i	0.696614	−	0.197456i
$196$		0			0
$197$	−1.07737e9			−0.715322			−0.357661	−	0.933852i	$-0.616426\pi$
$197$	−1.07737e9			−0.715322			−0.357661	+	0.933852i	$0.616426\pi$
$198$		0			0
$199$	−9.36166e8			−0.596954			−0.298477	−	0.954417i	$-0.596479\pi$
$199$	−9.36166e8			−0.596954			−0.298477	+	0.954417i	$0.596479\pi$
$200$		0			0
$201$	−9.71167e8	−	5.26919e8i	−0.594990	−	0.322819i
$202$		0			0
$203$	4.11983e8			0.242602
$204$		0			0
$205$	1.42409e9	+	1.45891e9i	0.806349	+	0.826065i
$206$		0			0
$207$	2.65798e8	+	4.08748e8i	0.144767	+	0.222625i
$208$		0			0
$209$			4.75350e8i			0.249131i
$210$		0			0
$211$	−1.43472e6			−0.000723833			−0.000361916	−	1.00000i	$-0.500115\pi$
$211$	−1.43472e6			−0.000723833			−0.000361916		1.00000i	$0.500115\pi$
$212$		0			0
$213$	1.06217e9	+	5.76292e8i	0.516030	+	0.279978i
$214$		0			0
$215$	−2.51534e9	−	2.57684e9i	−1.17718	−	1.20596i
$216$		0			0
$217$			1.42309e8i			0.0641789i
$218$		0			0
$219$	−7.10382e8	−	3.85426e8i	−0.308827	−	0.167558i
$220$		0			0
$221$			1.80415e9i			0.756318i
$222$		0			0
$223$			1.56417e8i			0.0632508i	0.999500	+	0.0316254i	$0.0100683\pi$
$223$			1.56417e8i			0.0632508i	−0.999500	+	0.0316254i	$0.989932\pi$
$224$		0			0
$225$	−2.18169e9	+	1.34486e9i	−0.851261	+	0.524742i
$226$		0			0
$227$	3.69707e8			0.139237			0.0696185	−	0.997574i	$-0.477822\pi$
$227$	3.69707e8			0.139237			0.0696185	+	0.997574i	$0.477822\pi$
$228$		0			0
$229$	5.62664e8			0.204601			0.102300	−	0.994754i	$-0.467380\pi$
$229$	5.62664e8			0.204601			0.102300	+	0.994754i	$0.467380\pi$
$230$		0			0
$231$	6.14242e7	−	1.13211e8i	0.0215721	−	0.0397596i
$232$		0			0
$233$	−3.58929e9			−1.21782			−0.608912	−	0.793238i	$-0.708394\pi$
$233$	−3.58929e9			−1.21782			−0.608912	+	0.793238i	$0.708394\pi$
$234$		0			0
$235$	2.33907e9	−	2.28325e9i	0.766959	−	0.748654i
$236$		0			0
$237$	−6.93960e8	+	1.27904e9i	−0.219959	+	0.405407i
$238$		0			0
$239$		−	3.91899e9i		−	1.20111i	−0.799584	−	0.600554i	$-0.794947\pi$
$239$		−	3.91899e9i		−	1.20111i	0.799584	−	0.600554i	$-0.205053\pi$
$240$		0			0
$241$	−4.89507e9			−1.45108			−0.725539	−	0.688181i	$-0.758410\pi$
$241$	−4.89507e9			−1.45108			−0.725539	+	0.688181i	$0.758410\pi$
$242$		0			0
$243$	−2.12682e9	−	2.76302e9i	−0.609967	−	0.792427i
$244$		0			0
$245$	2.33968e9	−	2.28383e9i	0.649369	−	0.633870i
$246$		0			0
$247$			4.51543e9i			1.21314i
$248$		0			0
$249$	5.87657e8	−	1.08311e9i	0.152871	−	0.281758i
$250$		0			0
$251$			1.48997e9i			0.375389i	0.982227	+	0.187695i	$0.0601015\pi$
$251$			1.48997e9i			0.375389i	−0.982227	+	0.187695i	$0.939898\pi$
$252$		0			0
$253$			1.61781e8i			0.0394862i
$254$		0			0
$255$	−1.20445e9	−	4.24923e9i	−0.284858	−	1.00496i
$256$		0			0
$257$	4.87455e9			1.11738			0.558692	−	0.829375i	$-0.311303\pi$
$257$	4.87455e9			1.11738			0.558692	+	0.829375i	$0.311303\pi$
$258$		0			0
$259$	2.10833e9			0.468532
$260$		0			0
$261$	3.10238e9	−	2.01739e9i	0.668549	−	0.434739i
$262$		0			0
$263$	4.82355e9			1.00819			0.504097	−	0.863647i	$-0.331826\pi$
$263$	4.82355e9			1.00819			0.504097	+	0.863647i	$0.331826\pi$
$264$		0			0
$265$	−1.05241e7	+	1.02729e7i	−0.00213403	+	0.00208310i
$266$		0			0
$267$	5.01511e9	+	2.72101e9i	0.986815	+	0.535408i
$268$		0			0
$269$		−	2.31084e9i		−	0.441328i	−0.975350	−	0.220664i	$-0.929178\pi$
$269$		−	2.31084e9i		−	0.441328i	0.975350	−	0.220664i	$-0.0708224\pi$
$270$		0			0
$271$	−9.26866e9			−1.71846			−0.859230	−	0.511589i	$-0.829057\pi$
$271$	−9.26866e9			−1.71846			−0.859230	+	0.511589i	$0.829057\pi$
$272$		0			0
$273$	5.83479e8	−	1.07541e9i	0.105045	−	0.193609i
$274$		0			0
$275$	−8.50149e8	−	2.05390e7i	−0.148650	−	0.00359127i
$276$		0			0
$277$		−	5.73091e9i		−	0.973429i	−0.873561	−	0.486714i	$-0.838195\pi$
$277$		−	5.73091e9i		−	0.973429i	0.873561	−	0.486714i	$-0.161805\pi$
$278$		0			0
$279$	6.96856e8	+	1.07164e9i	0.115007	+	0.176860i
$280$		0			0
$281$			9.07009e9i			1.45474i	0.686244	+	0.727371i	$0.259258\pi$
$281$			9.07009e9i			1.45474i	−0.686244	+	0.727371i	$0.740742\pi$
$282$		0			0
$283$			9.68545e8i			0.150999i	0.997146	+	0.0754995i	$0.0240551\pi$
$283$			9.68545e8i			0.150999i	−0.997146	+	0.0754995i	$0.975945\pi$
$284$		0			0
$285$	−3.01449e9	−	1.06350e10i	−0.456914	−	1.61197i
$286$		0			0
$287$	2.38263e9			0.351179
$288$		0			0
$289$	6.35450e8			0.0910940
$290$		0			0
$291$	−2.68410e9	−	1.45629e9i	−0.374305	−	0.203084i
$292$		0			0
$293$	7.35704e9			0.998234			0.499117	−	0.866535i	$-0.333658\pi$
$293$	7.35704e9			0.998234			0.499117	+	0.866535i	$0.333658\pi$
$294$		0			0
$295$	8.29877e9	+	8.50169e9i	1.09579	+	1.12258i
$296$		0			0
$297$	−9.18256e7	−	1.15331e9i	−0.0118015	−	0.148224i
$298$		0			0
$299$			1.53678e9i			0.192277i
$300$		0			0
$301$	−4.20837e9			−0.512682
$302$		0			0
$303$	−1.43594e10	−	7.79085e9i	−1.70359	−	0.924303i
$304$		0			0
$305$	9.99895e9	−	9.76030e9i	1.15546	−	1.12788i
$306$		0			0
$307$		−	1.23892e10i		−	1.39472i	−0.716719	−	0.697362i	$-0.754357\pi$
$307$		−	1.23892e10i		−	1.39472i	0.716719	−	0.697362i	$-0.245643\pi$
$308$		0			0
$309$	−1.04422e10	−	5.66554e9i	−1.14540	−	0.621452i
$310$		0			0
$311$		−	2.27468e9i		−	0.243153i	−0.992582	−	0.121576i	$-0.961205\pi$
$311$		−	2.27468e9i		−	0.243153i	0.992582	−	0.121576i	$-0.0387949\pi$
$312$		0			0
$313$		−	1.95006e8i		−	0.0203175i	−0.999948	−	0.0101588i	$-0.996766\pi$
$313$		−	1.95006e8i		−	0.0203175i	0.999948	−	0.0101588i	$-0.00323369\pi$
$314$		0			0
$315$	−6.56294e8	+	2.92240e9i	−0.0666586	+	0.296823i
$316$		0			0
$317$	1.09690e10			1.08625			0.543125	−	0.839652i	$-0.317241\pi$
$317$	1.09690e10			1.08625			0.543125	+	0.839652i	$0.317241\pi$
$318$		0			0
$319$	1.22791e9			0.118578
$320$		0			0
$321$	−4.50273e9	+	8.29901e9i	−0.424088	+	0.781639i
$322$		0			0
$323$	1.90493e10			1.75012
$324$		0			0
$325$	−8.07570e9	−	1.95103e8i	−0.723847	−	0.0174876i
$326$		0			0
$327$	5.87252e9	−	1.08237e10i	0.513610	−	0.946638i
$328$		0			0
$329$		−	3.82006e9i		−	0.326052i
$330$		0			0
$331$	−5.50117e9			−0.458293			−0.229147	−	0.973392i	$-0.573593\pi$
$331$	−5.50117e9			−0.458293			−0.229147	+	0.973392i	$0.573593\pi$
$332$		0			0
$333$	1.58765e10	−	1.03240e10i	1.29115	−	0.839601i
$334$		0			0
$335$	5.95518e9	+	6.10079e9i	0.472842	+	0.484403i
$336$		0			0
$337$			6.52223e9i			0.505681i	0.967508	+	0.252840i	$0.0813647\pi$
$337$			6.52223e9i			0.505681i	−0.967508	+	0.252840i	$0.918635\pi$
$338$		0			0
$339$	9.96020e9	−	1.83577e10i	0.754170	−	1.39002i
$340$		0			0
$341$			4.24150e8i			0.0313691i
$342$		0			0
$343$		−	8.03178e9i		−	0.580277i
$344$		0			0
$345$	−1.02595e9	−	3.61951e9i	−0.0724189	−	0.255490i
$346$		0			0
$347$	−4.65773e8			−0.0321260			−0.0160630	−	0.999871i	$-0.505113\pi$
$347$	−4.65773e8			−0.0321260			−0.0160630	+	0.999871i	$0.505113\pi$
$348$		0			0
$349$	4.05878e9			0.273586			0.136793	−	0.990600i	$-0.456320\pi$
$349$	4.05878e9			0.273586			0.136793	+	0.990600i	$0.456320\pi$
$350$		0			0
$351$	−8.72266e8	−	1.09554e10i	−0.0574673	−	0.721774i
$352$		0			0
$353$	−2.43727e10			−1.56966			−0.784828	−	0.619713i	$-0.787249\pi$
$353$	−2.43727e10			−1.56966			−0.784828	+	0.619713i	$0.787249\pi$
$354$		0			0
$355$	−6.51320e9	−	6.67245e9i	−0.410092	−	0.420119i
$356$		0			0
$357$	−4.53686e9	−	2.46153e9i	−0.279307	−	0.151542i
$358$		0			0
$359$			5.90288e9i			0.355375i	0.984087	+	0.177687i	$0.0568616\pi$
$359$			5.90288e9i			0.355375i	−0.984087	+	0.177687i	$0.943138\pi$
$360$		0			0
$361$	3.06929e10			1.80721
$362$		0			0
$363$	−8.09723e9	+	1.49241e10i	−0.466348	+	0.859529i
$364$		0			0
$365$	4.35605e9	+	4.46256e9i	0.245426	+	0.251427i
$366$		0			0
$367$		−	1.56819e9i		−	0.0864438i	−0.999065	−	0.0432219i	$-0.986238\pi$
$367$		−	1.56819e9i		−	0.0864438i	0.999065	−	0.0432219i	$-0.0137622\pi$
$368$		0			0
$369$	1.79421e10	−	1.16672e10i	0.967759	−	0.629307i
$370$		0			0
$371$			1.71874e7i			0.000907225i
$372$		0			0
$373$		−	1.22323e10i		−	0.631936i	−0.948770	−	0.315968i	$-0.897671\pi$
$373$		−	1.22323e10i		−	0.631936i	0.948770	−	0.315968i	$-0.102329\pi$
$374$		0			0
$375$	1.91505e10	−	4.93181e9i	0.968403	−	0.249391i
$376$		0			0
$377$	1.16641e10			0.577414
$378$		0			0
$379$	−2.39355e10			−1.16007			−0.580037	−	0.814590i	$-0.696962\pi$
$379$	−2.39355e10			−1.16007			−0.580037	+	0.814590i	$0.696962\pi$
$380$		0			0
$381$	−2.40935e10	−	1.30722e10i	−1.14340	−	0.620367i
$382$		0			0
$383$	2.90510e10			1.35010			0.675049	−	0.737773i	$-0.264122\pi$
$383$	2.90510e10			1.35010			0.675049	+	0.737773i	$0.264122\pi$
$384$		0			0
$385$	−7.11184e8	+	6.94210e8i	−0.0323697	+	0.0315972i
$386$		0			0
$387$	−3.16906e10	+	2.06075e10i	−1.41282	+	0.918718i
$388$		0			0
$389$		−	6.21492e9i		−	0.271417i	−0.990749	−	0.135709i	$-0.956669\pi$
$389$		−	6.21492e9i		−	0.271417i	0.990749	−	0.135709i	$-0.0433311\pi$
$390$		0			0
$391$	6.48325e9			0.277387
$392$		0			0
$393$	−1.81171e10	−	9.82967e9i	−0.759485	−	0.412068i
$394$		0			0
$395$	8.03483e9	−	7.84306e9i	0.330057	−	0.322179i
$396$		0			0
$397$			2.28461e10i			0.919709i	0.887994	+	0.459855i	$0.152099\pi$
$397$			2.28461e10i			0.919709i	−0.887994	+	0.459855i	$0.847901\pi$
$398$		0			0
$399$	−1.13548e10	−	6.16070e9i	−0.448012	−	0.243074i
$400$		0			0
$401$			2.23687e9i			0.0865093i	0.999064	+	0.0432546i	$0.0137727\pi$
$401$			2.23687e9i			0.0865093i	−0.999064	+	0.0432546i	$0.986227\pi$
$402$		0			0
$403$			4.02907e9i			0.152751i
$404$		0			0
$405$	9.36824e9	+	2.52205e10i	0.348207	+	0.937418i
$406$		0			0
$407$	6.28386e9			0.229007
$408$		0			0
$409$	−2.59818e10			−0.928486			−0.464243	−	0.885708i	$-0.653674\pi$
$409$	−2.59818e10			−0.928486			−0.464243	+	0.885708i	$0.653674\pi$
$410$		0			0
$411$	6.57536e9	−	1.21191e10i	0.230437	−	0.424720i
$412$		0			0
$413$	1.38845e10			0.477234
$414$		0			0
$415$	−6.80403e9	+	6.64164e9i	−0.229390	+	0.223915i
$416$		0			0
$417$	−2.38039e10	+	4.38732e10i	−0.787236	+	1.45096i
$418$		0			0
$419$			1.01456e10i			0.329172i	0.986363	+	0.164586i	$0.0526288\pi$
$419$			1.01456e10i			0.329172i	−0.986363	+	0.164586i	$0.947371\pi$
$420$		0			0
$421$	−2.70663e10			−0.861590			−0.430795	−	0.902450i	$-0.641767\pi$
$421$	−2.70663e10			−0.861590			−0.430795	+	0.902450i	$0.641767\pi$
$422$		0			0
$423$	−1.87060e10	−	2.87665e10i	−0.584279	−	0.898514i
$424$		0			0
$425$	−8.23083e8	+	3.40691e10i	−0.0252283	+	1.04425i
$426$		0			0
$427$		−	1.63298e10i		−	0.491212i
$428$		0			0
$429$	1.73905e9	−	3.20526e9i	0.0513433	−	0.0946312i
$430$		0			0
$431$			4.84284e10i			1.40343i	0.712458	+	0.701715i	$0.247582\pi$
$431$			4.84284e10i			1.40343i	−0.712458	+	0.701715i	$0.752418\pi$
$432$		0			0
$433$		−	6.72992e9i		−	0.191451i	−0.995408	−	0.0957257i	$-0.969483\pi$
$433$		−	6.72992e9i		−	0.191451i	0.995408	−	0.0957257i	$-0.0305172\pi$
$434$		0			0
$435$	−2.74719e10	+	7.78695e9i	−0.767242	+	0.217476i
$436$		0			0
$437$	1.62263e10			0.444931
$438$		0			0
$439$	4.12187e10			1.10978			0.554889	−	0.831924i	$-0.312761\pi$
$439$	4.12187e10			1.10978			0.554889	+	0.831924i	$0.312761\pi$
$440$		0			0
$441$	−1.87109e10	−	2.87739e10i	−0.494697	−	0.760753i
$442$		0			0
$443$	−4.80890e10			−1.24862			−0.624311	−	0.781176i	$-0.714620\pi$
$443$	−4.80890e10			−1.24862			−0.624311	+	0.781176i	$0.714620\pi$
$444$		0			0
$445$	−3.07526e10	−	3.15045e10i	−0.784227	−	0.803402i
$446$		0			0
$447$	−3.04888e10	−	1.65421e10i	−0.763679	−	0.414343i
$448$		0			0
$449$			7.27138e10i			1.78909i	0.446981	+	0.894543i	$0.352499\pi$
$449$			7.27138e10i			1.78909i	−0.446981	+	0.894543i	$0.647501\pi$
$450$		0			0
$451$	7.10140e9			0.171648
$452$		0			0
$453$	−4.75124e9	+	8.75704e9i	−0.112827	+	0.207953i
$454$		0			0
$455$	−6.75566e9	+	6.59442e9i	−0.157624	+	0.153862i
$456$		0			0
$457$		−	1.44181e10i		−	0.330556i	−0.986247	−	0.165278i	$-0.947148\pi$
$457$		−	1.44181e10i		−	0.330556i	0.986247	−	0.165278i	$-0.0528521\pi$
$458$		0			0
$459$	−4.62178e10	+	3.67984e9i	−1.04126	+	0.0829045i
$460$		0			0
$461$		−	4.70966e10i		−	1.04276i	−0.853324	−	0.521382i	$-0.825417\pi$
$461$		−	4.70966e10i		−	1.04276i	0.853324	−	0.521382i	$-0.174583\pi$
$462$		0			0
$463$			1.72398e10i			0.375153i	0.982250	+	0.187576i	$0.0600632\pi$
$463$			1.72398e10i			0.375153i	−0.982250	+	0.187576i	$0.939937\pi$
$464$		0			0
$465$	−2.68980e9	−	9.48946e9i	−0.0575318	−	0.202969i
$466$		0			0
$467$	2.51932e10			0.529682			0.264841	−	0.964292i	$-0.414680\pi$
$467$	2.51932e10			0.529682			0.264841	+	0.964292i	$0.414680\pi$
$468$		0			0
$469$	9.96351e9			0.205931
$470$		0			0
$471$	4.10798e10	+	2.22884e10i	0.834728	+	0.452892i
$472$		0			0
$473$	−1.25430e10			−0.250587
$474$		0			0
$475$	−2.06001e9	+	8.52679e10i	−0.0404664	+	1.67499i
$476$		0			0
$477$	8.41632e7	+	1.29428e8i	0.00162573	+	0.00250008i
$478$		0			0
$479$			5.83204e10i			1.10784i	0.832569	+	0.553921i	$0.186869\pi$
$479$			5.83204e10i			1.10784i	−0.832569	+	0.553921i	$0.813131\pi$
$480$		0			0
$481$	5.96914e10			1.11515
$482$		0			0
$483$	−3.86451e9	−	2.09674e9i	−0.0710078	−	0.0385261i
$484$		0			0
$485$	1.64588e10	+	1.68613e10i	0.297462	+	0.304736i
$486$		0			0
$487$			5.49773e9i			0.0977389i	0.998805	+	0.0488694i	$0.0155618\pi$
$487$			5.49773e9i			0.0977389i	−0.998805	+	0.0488694i	$0.984438\pi$
$488$		0			0
$489$	7.28446e10	+	3.95227e10i	1.27398	+	0.691212i
$490$		0			0
$491$			4.11937e10i			0.708769i	0.935100	+	0.354384i	$0.115310\pi$
$491$			4.11937e10i			0.708769i	−0.935100	+	0.354384i	$0.884690\pi$
$492$		0			0
$493$		−	4.92076e10i		−	0.832999i
$494$		0			0
$495$	−1.95608e9	+	8.71018e9i	−0.0325811	+	0.145080i
$496$		0			0
$497$	−1.08971e10			−0.178602
$498$		0			0
$499$	7.74223e10			1.24872			0.624358	−	0.781138i	$-0.285361\pi$
$499$	7.74223e10			1.24872			0.624358	+	0.781138i	$0.285361\pi$
$500$		0			0
$501$	2.37033e10	−	4.36877e10i	0.376234	−	0.693440i
$502$		0			0
$503$	−2.52285e10			−0.394112			−0.197056	−	0.980392i	$-0.563138\pi$
$503$	−2.52285e10			−0.394112			−0.197056	+	0.980392i	$0.563138\pi$
$504$		0			0
$505$	8.80514e10	+	9.02043e10i	1.35385	+	1.38695i
$506$		0			0
$507$	−1.49907e10	+	2.76294e10i	−0.226876	+	0.418157i
$508$		0			0
$509$			4.44215e10i			0.661793i	0.943667	+	0.330896i	$0.107351\pi$
$509$			4.44215e10i			0.661793i	−0.943667	+	0.330896i	$0.892649\pi$
$510$		0			0
$511$	7.28803e9			0.106887
$512$		0			0
$513$	−1.15674e11	+	9.20989e9i	−1.67019	+	0.132980i
$514$		0			0
$515$	6.40314e10	+	6.55970e10i	0.910257	+	0.932514i
$516$		0			0
$517$		−	1.13857e10i		−	0.159366i
$518$		0			0
$519$	8.69440e9	−	1.60247e10i	0.119831	−	0.220862i
$520$		0			0
$521$			1.17782e11i			1.59855i	0.600964	+	0.799276i	$0.294784\pi$
$521$			1.17782e11i			1.59855i	−0.600964	+	0.799276i	$0.705216\pi$
$522$		0			0
$523$		−	1.43437e11i		−	1.91714i	−0.284858	−	0.958570i	$-0.591946\pi$
$523$		−	1.43437e11i		−	1.91714i	0.284858	−	0.958570i	$-0.408054\pi$
$524$		0			0
$525$	1.15088e10	−	2.00416e10i	0.151494	−	0.263812i
$526$		0			0
$527$	1.69975e10			0.220365
$528$		0			0
$529$	−7.27885e10			−0.929480
$530$		0			0
$531$	1.04556e11	−	6.79897e10i	1.31513	−	0.855194i
$532$		0			0
$533$	6.74574e10			0.835835
$534$		0			0
$535$	5.21337e10	−	5.08894e10i	0.636360	−	0.621172i
$536$		0			0
$537$	−5.18499e10	−	2.81318e10i	−0.623521	−	0.338299i
$538$		0			0
$539$		−	1.13886e10i		−	0.134932i
$540$		0			0
$541$	1.24963e11			1.45879			0.729395	−	0.684092i	$-0.239802\pi$
$541$	1.24963e11			1.45879			0.729395	+	0.684092i	$0.239802\pi$
$542$		0			0
$543$	−3.69492e9	+	6.81013e9i	−0.0425017	+	0.0783351i
$544$		0			0
$545$	−6.79934e10	+	6.63706e10i	−0.770692	+	0.752298i
$546$		0			0
$547$			9.81775e10i			1.09664i	0.836270	+	0.548318i	$0.184732\pi$
$547$			9.81775e10i			1.09664i	−0.836270	+	0.548318i	$0.815268\pi$
$548$		0			0
$549$	−7.99636e10	−	1.22969e11i	−0.880244	−	1.35365i
$550$		0			0
$551$		−	1.23157e11i		−	1.33614i
$552$		0			0
$553$		−	1.31221e10i		−	0.140314i
$554$		0			0
$555$	−1.40588e11	+	3.98499e10i	−1.48176	+	0.420006i
$556$		0			0
$557$	1.37299e11			1.42642			0.713209	−	0.700951i	$-0.247241\pi$
$557$	1.37299e11			1.42642			0.713209	+	0.700951i	$0.247241\pi$
$558$		0			0
$559$	−1.19148e11			−1.22023
$560$		0			0
$561$	−1.35221e10	−	7.33657e9i	−0.136519	−	0.0740699i
$562$		0			0
$563$	−1.43382e11			−1.42712			−0.713560	−	0.700594i	$-0.752918\pi$
$563$	−1.43382e11			−1.42712			−0.713560	+	0.700594i	$0.752918\pi$
$564$		0			0
$565$	−1.15322e11	+	1.12569e11i	−1.13166	+	1.10465i
$566$		0			0
$567$	2.87394e10	+	1.27538e10i	0.278065	+	0.123398i
$568$		0			0
$569$			1.19680e11i			1.14175i	0.821037	+	0.570875i	$0.193396\pi$
$569$			1.19680e11i			1.14175i	−0.821037	+	0.570875i	$0.806604\pi$
$570$		0			0
$571$	−1.15478e11			−1.08631			−0.543155	−	0.839633i	$-0.682770\pi$
$571$	−1.15478e11			−1.08631			−0.543155	+	0.839633i	$0.682770\pi$
$572$		0			0
$573$	−1.81787e11	−	9.86307e10i	−1.68634	−	0.914942i
$574$		0			0
$575$	−7.01105e8	+	2.90201e10i	−0.00641375	+	0.265478i
$576$		0			0
$577$			2.12014e11i			1.91277i	0.292115	+	0.956383i	$0.405641\pi$
$577$			2.12014e11i			1.91277i	−0.292115	+	0.956383i	$0.594359\pi$
$578$		0			0
$579$	2.21891e10	+	1.20390e10i	0.197436	+	0.107121i
$580$		0			0
$581$			1.11120e10i			0.0975187i
$582$		0			0
$583$			5.12270e7i			0.000443429i
$584$		0			0
$585$	−1.85811e10	+	8.27395e10i	−0.158653	+	0.706463i
$586$		0			0
$587$	1.33379e11			1.12340			0.561700	−	0.827341i	$-0.310147\pi$
$587$	1.33379e11			1.12340			0.561700	+	0.827341i	$0.310147\pi$
$588$		0			0
$589$	4.25412e10			0.353467
$590$		0			0
$591$	4.16170e10	−	7.67046e10i	0.341131	−	0.628741i
$592$		0			0
$593$	−3.04033e10			−0.245868			−0.122934	−	0.992415i	$-0.539230\pi$
$593$	−3.04033e10			−0.245868			−0.122934	+	0.992415i	$0.539230\pi$
$594$		0			0
$595$	2.78199e10	+	2.85002e10i	0.221967	+	0.227394i
$596$		0			0
$597$	3.61624e10	−	6.66512e10i	0.284682	−	0.524700i
$598$		0			0
$599$			1.35292e11i			1.05091i	0.850821	+	0.525456i	$0.176105\pi$
$599$			1.35292e11i			1.05091i	−0.850821	+	0.525456i	$0.823895\pi$
$600$		0			0
$601$	7.80555e10			0.598282			0.299141	−	0.954209i	$-0.403300\pi$
$601$	7.80555e10			0.598282			0.299141	+	0.954209i	$0.403300\pi$
$602$		0			0
$603$	7.50289e10	−	4.87892e10i	0.567492	−	0.369024i
$604$		0			0
$605$	9.37517e10	−	9.15140e10i	0.699773	−	0.683072i
$606$		0			0
$607$			1.85685e11i			1.36780i	0.729577	+	0.683899i	$0.239717\pi$
$607$			1.85685e11i			1.36780i	−0.729577	+	0.683899i	$0.760283\pi$
$608$		0			0
$609$	−1.59142e10	+	2.93315e10i	−0.115695	+	0.213238i
$610$		0			0
$611$		−	1.08154e11i		−	0.776030i
$612$		0			0
$613$		−	1.15663e11i		−	0.819126i	−0.912282	−	0.409563i	$-0.865681\pi$
$613$		−	1.15663e11i		−	0.819126i	0.912282	−	0.409563i	$-0.134319\pi$
$614$		0			0
$615$	−1.58879e11	+	4.50344e10i	−1.11062	+	0.314807i
$616$		0			0
$617$	−2.17291e11			−1.49934			−0.749671	−	0.661811i	$-0.769788\pi$
$617$	−2.17291e11			−1.49934			−0.749671	+	0.661811i	$0.769788\pi$
$618$		0			0
$619$	3.38274e10			0.230412			0.115206	−	0.993342i	$-0.463247\pi$
$619$	3.38274e10			0.230412			0.115206	+	0.993342i	$0.463247\pi$
$620$		0			0
$621$	−3.93685e10	+	3.13450e9i	−0.264717	+	0.0210767i
$622$		0			0
$623$	−5.14516e10			−0.341544
$624$		0			0
$625$	−1.52410e11	−	7.36852e9i	−0.998833	−	0.0482903i
$626$		0			0
$627$	−3.38430e10	−	1.83619e10i	−0.218977	−	0.118809i
$628$		0			0
$629$		−	2.51821e11i		−	1.60875i
$630$		0			0
$631$	−1.52115e11			−0.959518			−0.479759	−	0.877400i	$-0.659276\pi$
$631$	−1.52115e11			−0.959518			−0.479759	+	0.877400i	$0.659276\pi$
$632$		0			0
$633$	5.54208e7	−	1.02146e8i	0.000345190	−	0.000636222i
$634$		0			0
$635$	1.47741e11	+	1.51353e11i	0.908668	+	0.930886i
$636$		0			0
$637$		−	1.08182e11i		−	0.657049i
$638$		0			0
$639$	−8.20593e10	+	5.33609e10i	−0.492181	+	0.320052i
$640$		0			0
$641$		−	4.57219e10i		−	0.270827i	−0.990789	−	0.135414i	$-0.956764\pi$
$641$		−	4.57219e10i		−	0.270827i	0.990789	−	0.135414i	$-0.0432363\pi$
$642$		0			0
$643$		−	1.00594e11i		−	0.588478i	−0.955732	−	0.294239i	$-0.904934\pi$
$643$		−	1.00594e11i		−	0.588478i	0.955732	−	0.294239i	$-0.0950661\pi$
$644$		0			0
$645$	2.80624e11	−	7.95432e10i	1.62138	−	0.459583i
$646$		0			0
$647$	−3.59986e10			−0.205432			−0.102716	−	0.994711i	$-0.532753\pi$
$647$	−3.59986e10			−0.205432			−0.102716	+	0.994711i	$0.532753\pi$
$648$		0			0
$649$	4.13827e10			0.233260
$650$		0			0
$651$	−1.01318e10	−	5.49713e9i	−0.0564108	−	0.0306064i
$652$		0			0
$653$	2.65780e11			1.46174			0.730868	−	0.682518i	$-0.239115\pi$
$653$	2.65780e11			1.46174			0.730868	+	0.682518i	$0.239115\pi$
$654$		0			0
$655$	1.11094e11	+	1.13810e11i	0.603567	+	0.618324i
$656$		0			0
$657$	5.48816e10	−	3.56880e10i	0.294554	−	0.191540i
$658$		0			0
$659$			2.80479e10i			0.148716i	0.997232	+	0.0743582i	$0.0236908\pi$
$659$			2.80479e10i			0.148716i	−0.997232	+	0.0743582i	$0.976309\pi$
$660$		0			0
$661$	−1.78499e11			−0.935041			−0.467520	−	0.883982i	$-0.654853\pi$
$661$	−1.78499e11			−0.935041			−0.467520	+	0.883982i	$0.654853\pi$
$662$		0			0
$663$	−1.28448e11	−	6.96913e10i	−0.664775	−	0.360682i
$664$		0			0
$665$	6.96276e10	+	7.13301e10i	0.356037	+	0.364742i
$666$		0			0
$667$		−	4.19152e10i		−	0.211772i
$668$		0			0
$669$	−1.11363e10	−	6.04213e9i	−0.0555950	−	0.0301638i
$670$		0			0
$671$		−	4.86708e10i		−	0.240093i
$672$		0			0
$673$		−	1.05186e11i		−	0.512740i	−0.966579	−	0.256370i	$-0.917473\pi$
$673$		−	1.05186e11i		−	0.512740i	0.966579	−	0.256370i	$-0.0825266\pi$
$674$		0			0
$675$	−1.14735e10	−	2.07277e11i	−0.0552691	−	0.998471i
$676$		0			0
$677$	−8.52625e10			−0.405885			−0.202943	−	0.979191i	$-0.565050\pi$
$677$	−8.52625e10			−0.405885			−0.202943	+	0.979191i	$0.565050\pi$
$678$		0			0
$679$	2.75370e10			0.129550
$680$		0			0
$681$	−1.42811e10	+	2.63217e10i	−0.0664010	+	0.122384i
$682$		0			0
$683$	−4.98208e9			−0.0228943			−0.0114472	−	0.999934i	$-0.503644\pi$
$683$	−4.98208e9			−0.0228943			−0.0114472	+	0.999934i	$0.503644\pi$
$684$		0			0
$685$	−7.61311e10	+	7.43140e10i	−0.345780	+	0.337527i
$686$		0			0
$687$	−2.17347e10	+	4.00594e10i	−0.0975723	+	0.179836i
$688$		0			0
$689$			4.86613e8i			0.00215927i
$690$		0			0
$691$	2.04194e11			0.895635			0.447818	−	0.894125i	$-0.352201\pi$
$691$	2.04194e11			0.895635			0.447818	+	0.894125i	$0.352201\pi$
$692$		0			0
$693$	5.68748e9	+	8.74631e9i	0.0246597	+	0.0379221i
$694$		0			0
$695$	2.75608e11	−	2.69030e11i	1.18128	−	1.15308i
$696$		0			0
$697$		−	2.84583e11i		−	1.20581i
$698$		0			0
$699$	1.38648e11	−	2.55543e11i	0.580770	−	1.07042i
$700$		0			0
$701$		−	2.11340e11i		−	0.875205i	−0.899169	−	0.437602i	$-0.855828\pi$
$701$		−	2.11340e11i		−	0.875205i	0.899169	−	0.437602i	$-0.144172\pi$
$702$		0			0
$703$		−	6.30256e11i		−	2.58045i
$704$		0			0
$705$	7.22036e10	+	2.54730e11i	0.292282	+	1.03115i
$706$		0			0
$707$	1.47317e11			0.589625
$708$		0			0
$709$	−1.90004e11			−0.751929			−0.375964	−	0.926634i	$-0.622688\pi$
$709$	−1.90004e11			−0.751929			−0.375964	+	0.926634i	$0.622688\pi$
$710$		0			0
$711$	−6.42561e10	−	9.88142e10i	−0.251441	−	0.386670i
$712$		0			0
$713$	1.44785e10			0.0560229
$714$		0			0
$715$	−2.01352e10	+	1.96546e10i	−0.0770427	+	0.0752039i
$716$		0			0
$717$	2.79016e11	+	1.51383e11i	1.05573	+	0.572798i
$718$		0			0
$719$		−	2.56685e11i		−	0.960474i	−0.877139	−	0.480237i	$-0.840551\pi$
$719$		−	2.56685e11i		−	0.960474i	0.877139	−	0.480237i	$-0.159449\pi$
$720$		0			0
$721$	1.07130e11			0.396432
$722$		0			0
$723$	1.89088e11	−	3.48509e11i	0.692007	−	1.27544i
$724$		0			0
$725$	2.20262e11	+	5.32136e9i	0.797236	+	0.0192606i
$726$		0			0
$727$			1.56910e11i			0.561712i	0.959750	+	0.280856i	$0.0906183\pi$
$727$			1.56910e11i			0.561712i	−0.959750	+	0.280856i	$0.909382\pi$
$728$		0			0
$729$	2.78871e11	−	4.46905e10i	0.987401	−	0.158236i
$730$		0			0
$731$			5.02652e11i			1.76035i
$732$		0			0
$733$		−	4.26702e11i		−	1.47812i	−0.673642	−	0.739058i	$-0.735271\pi$
$733$		−	4.26702e11i		−	1.47812i	0.673642	−	0.739058i	$-0.264729\pi$
$734$		0			0
$735$	7.22222e10	+	2.54796e11i	0.247469	+	0.873058i
$736$		0			0
$737$	2.96962e10			0.100654
$738$		0			0
$739$	−3.08781e10			−0.103532			−0.0517658	−	0.998659i	$-0.516485\pi$
$739$	−3.08781e10			−0.103532			−0.0517658	+	0.998659i	$0.516485\pi$
$740$		0			0
$741$	−3.21480e11	−	1.74423e11i	−1.06631	−	0.578537i
$742$		0			0
$743$	−9.68533e10			−0.317804			−0.158902	−	0.987294i	$-0.550795\pi$
$743$	−9.68533e10			−0.317804			−0.158902	+	0.987294i	$0.550795\pi$
$744$		0			0
$745$	1.86957e11	+	1.91528e11i	0.606899	+	0.621739i
$746$		0			0
$747$	5.44132e10	+	8.36775e10i	0.174752	+	0.268736i
$748$		0			0
$749$		−	8.51421e10i		−	0.270531i
$750$		0			0
$751$	−4.26875e10			−0.134196			−0.0670982	−	0.997746i	$-0.521374\pi$
$751$	−4.26875e10			−0.134196			−0.0670982	+	0.997746i	$0.521374\pi$
$752$		0			0
$753$	−1.06080e11	−	5.75548e10i	−0.329953	−	0.179020i
$754$		0			0
$755$	5.50110e10	−	5.36980e10i	0.169302	−	0.165261i
$756$		0			0
$757$		−	9.28927e10i		−	0.282877i	−0.989947	−	0.141439i	$-0.954827\pi$
$757$		−	9.28927e10i		−	0.282877i	0.989947	−	0.141439i	$-0.0451728\pi$
$758$		0			0
$759$	−1.15182e10	−	6.24931e9i	−0.0347069	−	0.0188306i
$760$		0			0
$761$			1.68912e11i			0.503643i	0.967774	+	0.251821i	$0.0810295\pi$
$761$			1.68912e11i			0.503643i	−0.967774	+	0.251821i	$0.918970\pi$
$762$		0			0
$763$			1.11043e11i			0.327639i
$764$		0			0
$765$	3.49054e11	+	7.83884e10i	1.01917	+	0.228879i
$766$		0			0
$767$	3.93102e11			1.13586
$768$		0			0
$769$	2.66965e11			0.763394			0.381697	−	0.924288i	$-0.375340\pi$
$769$	2.66965e11			0.763394			0.381697	+	0.924288i	$0.375340\pi$
$770$		0			0
$771$	−1.88295e11	+	3.47048e11i	−0.532871	+	0.982138i
$772$		0			0
$773$	−5.94080e11			−1.66390			−0.831950	−	0.554851i	$-0.812775\pi$
$773$	−5.94080e11			−1.66390			−0.831950	+	0.554851i	$0.812775\pi$
$774$		0			0
$775$	−1.83812e9	+	7.60836e10i	−0.00509528	+	0.210904i
$776$		0			0
$777$	−8.14410e10	+	1.50104e11i	−0.223439	+	0.411822i
$778$		0			0
$779$		−	7.12254e11i		−	1.93413i
$780$		0			0
$781$	−3.24788e10			−0.0872962
$782$		0			0
$783$	2.37907e10	+	2.98805e11i	0.0632937	+	0.794953i
$784$		0			0
$785$	−2.51901e11	−	2.58060e11i	−0.663363	−	0.679583i
$786$		0			0
$787$		−	2.88926e11i		−	0.753162i	−0.926384	−	0.376581i	$-0.877100\pi$
$787$		−	2.88926e11i		−	0.753162i	0.926384	−	0.376581i	$-0.122900\pi$
$788$		0			0
$789$	−1.86325e11	+	3.43417e11i	−0.480799	+	0.886164i
$790$		0			0
$791$			1.88337e11i			0.481095i
$792$		0			0
$793$		−	4.62332e11i		−	1.16913i
$794$		0			0
$795$	−3.24862e8	−	1.14610e9i	−0.000813262	−	0.00286914i
$796$		0			0
$797$	6.62883e11			1.64287			0.821436	−	0.570300i	$-0.193173\pi$
$797$	6.62883e11			1.64287			0.821436	+	0.570300i	$0.193173\pi$
$798$		0			0
$799$	−4.56271e11			−1.11953
$800$		0			0
$801$	−3.87450e11	+	2.51948e11i	−0.941207	+	0.612041i
$802$		0			0
$803$	2.17219e10			0.0522439
$804$		0			0
$805$	2.36971e10	+	2.42765e10i	0.0564303	+	0.0578100i
$806$		0			0
$807$	1.64523e11	+	8.92637e10i	0.387910	+	0.210465i
$808$		0			0
$809$		−	1.18255e10i		−	0.0276073i	−0.999905	−	0.0138037i	$-0.995606\pi$
$809$		−	1.18255e10i		−	0.0276073i	0.999905	−	0.0138037i	$-0.00439398\pi$
$810$		0			0
$811$	−3.61021e11			−0.834543			−0.417272	−	0.908782i	$-0.637014\pi$
$811$	−3.61021e11			−0.834543			−0.417272	+	0.908782i	$0.637014\pi$
$812$		0			0
$813$	3.58032e11	−	6.59891e11i	0.819520	−	1.51046i
$814$		0			0
$815$	−4.46682e11	−	4.57603e11i	−1.01244	−	1.03719i
$816$		0			0
$817$			1.25804e12i			2.82361i
$818$		0			0
$819$	5.40263e10	+	8.30826e10i	0.120080	+	0.184661i
$820$		0			0
$821$		−	5.25498e11i		−	1.15664i	−0.815810	−	0.578321i	$-0.803708\pi$
$821$		−	5.25498e11i		−	1.15664i	0.815810	−	0.578321i	$-0.196292\pi$
$822$		0			0
$823$		−	4.67936e11i		−	1.01997i	−0.860183	−	0.509985i	$-0.829651\pi$
$823$		−	4.67936e11i		−	1.01997i	0.860183	−	0.509985i	$-0.170349\pi$
$824$		0			0
$825$	3.43020e10	−	5.97337e10i	0.0740464	−	0.128945i
$826$		0			0
$827$	−7.96968e10			−0.170380			−0.0851900	−	0.996365i	$-0.527150\pi$
$827$	−7.96968e10			−0.170380			−0.0851900	+	0.996365i	$0.527150\pi$
$828$		0			0
$829$	−6.02617e11			−1.27592			−0.637960	−	0.770070i	$-0.720221\pi$
$829$	−6.02617e11			−1.27592			−0.637960	+	0.770070i	$0.720221\pi$
$830$		0			0
$831$	4.08017e11	+	2.21375e11i	0.855607	+	0.464220i
$832$		0			0
$833$	−4.56389e11			−0.947884
$834$		0			0
$835$	−2.74443e11	+	2.67892e11i	−0.564554	+	0.551080i
$836$		0			0
$837$	−1.03214e11	+	8.21788e9i	−0.210300	+	0.0167440i
$838$		0			0
$839$			6.85128e11i			1.38269i	0.722526	+	0.691344i	$0.242981\pi$
$839$			6.85128e11i			1.38269i	−0.722526	+	0.691344i	$0.757019\pi$
$840$		0			0
$841$	1.82112e11			0.364044
$842$		0			0
$843$	−6.45753e11	−	3.50361e11i	−1.27866	−	0.693755i
$844$		0			0
$845$	1.73565e11	−	1.69423e11i	0.340437	−	0.332311i
$846$		0			0
$847$		−	1.53111e11i		−	0.297489i
$848$		0			0
$849$	−6.89565e10	−	3.74132e10i	−0.132722	−	0.0720101i
$850$		0			0
$851$		−	2.14502e11i		−	0.408990i
$852$		0			0
$853$			1.32424e11i			0.250133i	0.992148	+	0.125066i	$0.0399144\pi$
$853$			1.32424e11i			0.250133i	−0.992148	+	0.125066i	$0.960086\pi$
$854$		0			0
$855$	8.73611e11	+	1.96190e11i	1.63476	+	0.367124i
$856$		0			0
$857$	1.29958e11			0.240924			0.120462	−	0.992718i	$-0.461562\pi$
$857$	1.29958e11			0.240924			0.120462	+	0.992718i	$0.461562\pi$
$858$		0			0
$859$	7.50473e11			1.37836			0.689180	−	0.724590i	$-0.257971\pi$
$859$	7.50473e11			1.37836			0.689180	+	0.724590i	$0.257971\pi$
$860$		0			0
$861$	−9.20366e10	+	1.69633e11i	−0.167474	+	0.308673i
$862$		0			0
$863$	−6.04327e11			−1.08950			−0.544752	−	0.838597i	$-0.683376\pi$
$863$	−6.04327e11			−1.08950			−0.544752	+	0.838597i	$0.683376\pi$
$864$		0			0
$865$	−1.00666e11	+	9.82633e10i	−0.179812	+	0.175520i
$866$		0			0
$867$	−2.45463e10	+	4.52414e10i	−0.0434420	+	0.0800682i
$868$		0			0
$869$		−	3.91103e10i		−	0.0685823i
$870$		0			0
$871$	2.82089e11			0.490132
$872$		0			0
$873$	2.07364e11	−	1.34843e11i	0.357006	−	0.232151i
$874$		0			0
$875$	−1.30580e11	+	1.21445e11i	−0.222764	+	0.207179i
$876$		0			0
$877$			3.31935e11i			0.561118i	0.959837	+	0.280559i	$0.0905198\pi$
$877$			3.31935e11i			0.561118i	−0.959837	+	0.280559i	$0.909480\pi$
$878$		0			0
$879$	−2.84189e11	+	5.23791e11i	−0.476049	+	0.877410i
$880$		0			0
$881$			6.49478e11i			1.07810i	0.842272	+	0.539052i	$0.181217\pi$
$881$			6.49478e11i			1.07810i	−0.842272	+	0.539052i	$0.818783\pi$
$882$		0			0
$883$			5.92973e11i			0.975421i	0.873005	+	0.487710i	$0.162168\pi$
$883$			5.92973e11i			0.975421i	−0.873005	+	0.487710i	$0.837832\pi$
$884$		0			0
$885$	−9.25852e11	+	2.62434e11i	−1.50928	+	0.427806i
$886$		0			0
$887$	−1.10066e12			−1.77811			−0.889055	−	0.457801i	$-0.848637\pi$
$887$	−1.10066e12			−1.77811			−0.889055	+	0.457801i	$0.848637\pi$
$888$		0			0
$889$	2.47182e11			0.395740
$890$		0			0
$891$	8.56577e10	+	3.80125e10i	0.135911	+	0.0603137i
$892$		0			0
$893$	−1.14195e12			−1.79574
$894$		0			0
$895$	3.17943e11	+	3.25717e11i	0.495515	+	0.507631i
$896$		0			0
$897$	−1.09413e11	−	5.93633e10i	−0.169005	−	0.0916955i
$898$		0			0
$899$		−	1.09891e11i		−	0.168238i
$900$		0			0
$901$	2.05288e9			0.00311505
$902$		0			0
$903$	1.62562e11	−	2.99619e11i	0.244494	−	0.450628i
$904$		0			0
$905$	4.27807e10	−	4.17596e10i	0.0637754	−	0.0622533i
$906$		0			0
$907$			9.58927e11i			1.41696i	0.705733	+	0.708478i	$0.250618\pi$
$907$			9.58927e11i			1.41696i	−0.705733	+	0.708478i	$0.749382\pi$
$908$		0			0
$909$	1.10935e12	−	7.21382e11i	1.62485	−	1.05660i
$910$		0			0
$911$		−	6.47922e11i		−	0.940696i	−0.882481	−	0.470348i	$-0.844128\pi$
$911$		−	6.47922e11i		−	0.940696i	0.882481	−	0.470348i	$-0.155872\pi$
$912$		0			0
$913$			3.31192e10i			0.0476648i
$914$		0			0
$915$	3.08652e11	+	1.08891e12i	0.440337	+	1.55348i
$916$		0			0
$917$	1.85869e11			0.262864
$918$		0			0
$919$	1.94228e11			0.272302			0.136151	−	0.990688i	$-0.456527\pi$
$919$	1.94228e11			0.272302			0.136151	+	0.990688i	$0.456527\pi$
$920$		0			0
$921$	8.82058e11	+	4.78571e11i	1.22591	+	0.665132i
$922$		0			0
$923$	−3.08521e11			−0.425088
$924$		0			0
$925$	1.12719e12	+	2.72322e10i	1.53968	+	0.0371976i
$926$		0			0
$927$	8.06727e11	−	5.24592e11i	1.09247	−	0.710400i
$928$		0			0
$929$		−	5.12221e11i		−	0.687693i	−0.939026	−	0.343847i	$-0.888270\pi$
$929$		−	5.12221e11i		−	0.687693i	0.939026	−	0.343847i	$-0.111730\pi$
$930$		0			0
$931$	−1.14225e12			−1.52041
$932$		0			0
$933$	1.61948e11	+	8.78668e10i	0.213722	+	0.115957i
$934$		0			0
$935$	8.29171e10	+	8.49446e10i	0.108492	+	0.111145i
$936$		0			0
$937$		−	8.32141e11i		−	1.07954i	−0.841813	−	0.539770i	$-0.818511\pi$
$937$		−	8.32141e11i		−	1.07954i	0.841813	−	0.539770i	$-0.181489\pi$
$938$		0			0
$939$	1.38837e10	+	7.53274e9i	0.0178584	+	0.00968927i
$940$		0			0
$941$			1.31067e12i			1.67162i	0.549022	+	0.835808i	$0.315000\pi$
$941$			1.31067e12i			1.67162i	−0.549022	+	0.835808i	$0.685000\pi$
$942$		0			0
$943$		−	2.42409e11i		−	0.306550i
$944$		0			0
$945$	−1.82711e11	−	1.59612e11i	−0.229107	−	0.200143i
$946$		0			0
$947$	−9.13380e11			−1.13567			−0.567834	−	0.823143i	$-0.692219\pi$
$947$	−9.13380e11			−1.13567			−0.567834	+	0.823143i	$0.692219\pi$
$948$		0			0
$949$	2.06340e11			0.254401
$950$		0			0
$951$	−4.23712e11	+	7.80947e11i	−0.518023	+	0.954772i
$952$		0			0
$953$	−9.07769e11			−1.10053			−0.550267	−	0.834989i	$-0.685474\pi$
$953$	−9.07769e11			−1.10053			−0.550267	+	0.834989i	$0.685474\pi$
$954$		0			0
$955$	1.11471e12	+	1.14197e12i	1.34014	+	1.37291i
$956$		0			0
$957$	−4.74320e10	+	8.74223e10i	−0.0565489	+	0.104226i
$958$		0			0
$959$			1.24333e11i			0.146999i
$960$		0			0
$961$	−8.14932e11			−0.955494
$962$		0			0
$963$	−4.16923e11	−	6.41152e11i	−0.484787	−	0.745514i
$964$		0			0
$965$	−1.36063e11	−	1.39390e11i	−0.156903	−	0.160739i
$966$		0			0
$967$		−	2.24389e11i		−	0.256624i	−0.991734	−	0.128312i	$-0.959044\pi$
$967$		−	2.24389e11i		−	0.256624i	0.991734	−	0.128312i	$-0.0409558\pi$
$968$		0			0
$969$	−7.35840e11	+	1.35623e12i	−0.834620	+	1.53829i
$970$		0			0
$971$		−	4.09704e10i		−	0.0460885i	−0.999734	−	0.0230443i	$-0.992664\pi$
$971$		−	4.09704e10i		−	0.0460885i	0.999734	−	0.0230443i	$-0.00733587\pi$
$972$		0			0
$973$		−	4.50109e11i		−	0.502188i
$974$		0			0
$975$	3.25841e11	−	5.67421e11i	0.360568	−	0.627895i
$976$		0			0
$977$	−7.04262e11			−0.772958			−0.386479	−	0.922298i	$-0.626309\pi$
$977$	−7.04262e11			−0.772958			−0.386479	+	0.922298i	$0.626309\pi$
$978$		0			0
$979$	−1.53351e11			−0.166938
$980$		0			0
$981$	5.43757e11	+	8.36199e11i	0.587123	+	0.902887i
$982$		0			0
$983$	2.23345e11			0.239200			0.119600	−	0.992822i	$-0.461839\pi$
$983$	2.23345e11			0.239200			0.119600	+	0.992822i	$0.461839\pi$
$984$		0			0
$985$	−4.81852e11	+	4.70351e11i	−0.511881	+	0.499663i
$986$		0			0
$987$	2.71973e11	+	1.47562e11i	0.286587	+	0.155491i
$988$		0			0
$989$			4.28161e11i			0.447530i
$990$		0			0
$991$	9.74500e11			1.01039			0.505193	−	0.863007i	$-0.331421\pi$
$991$	9.74500e11			1.01039			0.505193	+	0.863007i	$0.331421\pi$
$992$		0			0
$993$	2.12500e11	−	3.91661e11i	0.218556	−	0.402822i
$994$		0			0
$995$	−4.18697e11	+	4.08704e11i	−0.427177	+	0.416981i
$996$		0			0
$997$			1.22811e12i			1.24295i	0.783432	+	0.621477i	$0.213467\pi$
$997$			1.22811e12i			1.24295i	−0.783432	+	0.621477i	$0.786533\pi$
$998$		0			0
$999$	1.21749e11	+	1.52914e12i	0.122238	+	1.53527i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.9.c.e.209.8		16
3.2	odd	2	inner	240.9.c.e.209.10		16
4.3	odd	2		30.9.b.a.29.13	yes	16
5.4	even	2	inner	240.9.c.e.209.9		16
12.11	even	2		30.9.b.a.29.3	✓	16
15.14	odd	2	inner	240.9.c.e.209.7		16
20.3	even	4		150.9.d.e.101.8		16
20.7	even	4		150.9.d.e.101.9		16
20.19	odd	2		30.9.b.a.29.4	yes	16
60.23	odd	4		150.9.d.e.101.16		16
60.47	odd	4		150.9.d.e.101.1		16
60.59	even	2		30.9.b.a.29.14	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.9.b.a.29.3	✓	16	12.11	even	2
30.9.b.a.29.4	yes	16	20.19	odd	2
30.9.b.a.29.13	yes	16	4.3	odd	2
30.9.b.a.29.14	yes	16	60.59	even	2
150.9.d.e.101.1		16	60.47	odd	4
150.9.d.e.101.8		16	20.3	even	4
150.9.d.e.101.9		16	20.7	even	4
150.9.d.e.101.16		16	60.23	odd	4
240.9.c.e.209.7		16	15.14	odd	2	inner
240.9.c.e.209.8		16	1.1	even	1	trivial
240.9.c.e.209.9		16	5.4	even	2	inner
240.9.c.e.209.10		16	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	240.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-38.6282 + 71.1959i) q^{3} +(447.247 - 436.572i) q^{5} -730.421i q^{7} +(-3576.72 - 5500.34i) q^{9} -2177.02i q^{11} -20679.8i q^{13} +(13805.8 + 48706.2i) q^{15} -87242.2 q^{17} -218350. q^{19} +(52003.0 + 28214.9i) q^{21} -74313.2 q^{23} +(9434.46 - 390511. i) q^{25} +(529764. - 42179.6i) q^{27} +564034. i q^{29} -194831. q^{31} +(154995. + 84094.2i) q^{33} +(-318882. - 326679. i) q^{35} +2.88646e6i q^{37} +(1.47232e6 + 798825. i) q^{39} +3.26199e6i q^{41} -5.76157e6i q^{43} +(-4.00097e6 - 898514. i) q^{45} +5.22994e6 q^{47} +5.23129e6 q^{49} +(3.37001e6 - 6.21129e6i) q^{51} -23530.8 q^{53} +(-950424. - 973663. i) q^{55} +(8.43445e6 - 1.55456e7i) q^{57} +1.90089e7i q^{59} +2.23567e7 q^{61} +(-4.01757e6 + 2.61251e6i) q^{63} +(-9.02824e6 - 9.24899e6i) q^{65} +1.36408e7i q^{67} +(2.87059e6 - 5.29080e6i) q^{69} -1.49189e7i q^{71} +9.97784e6i q^{73} +(2.74384e7 + 1.57564e7i) q^{75} -1.59014e6 q^{77} +1.79651e7 q^{79} +(-1.74608e7 + 3.93464e7i) q^{81} -1.52131e7 q^{83} +(-3.90188e7 + 3.80875e7i) q^{85} +(-4.01570e7 - 2.17876e7i) q^{87} -7.04410e7i q^{89} -1.51050e7 q^{91} +(7.52597e6 - 1.38712e7i) q^{93} +(-9.76561e7 + 9.53253e7i) q^{95} +3.77001e7i q^{97} +(-1.19743e7 + 7.78658e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 21928 q^{9} + 62920 q^{15} - 96048 q^{19} + 667112 q^{21} + 1292160 q^{25} + 5127152 q^{31} + 5420160 q^{39} - 8741480 q^{45} - 21439680 q^{49} - 3556688 q^{51} - 27329120 q^{55} + 67157264 q^{61}+ \cdots - 754526432 q^{99}+O(q^{100}) \) 16 * q + 21928 * q^9 + 62920 * q^15 - 96048 * q^19 + 667112 * q^21 + 1292160 * q^25 + 5127152 * q^31 + 5420160 * q^39 - 8741480 * q^45 - 21439680 * q^49 - 3556688 * q^51 - 27329120 * q^55 + 67157264 * q^61 + 97106152 * q^69 - 17107360 * q^75 + 296926128 * q^79 - 214283008 * q^81 + 190319120 * q^85 - 143834880 * q^91 - 754526432 * q^99

Introduction

L-functions

Modular forms

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Database

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