LMFDB - Embedded newform 63.10.e.b.46.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,10,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$32.4472576783$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 430 x^{8} + 61 x^{7} + 146753 x^{6} + 23608 x^{5} + 16136944 x^{4} + 30575648 x^{3} + \cdots + 761760000 $ x^10 - x^9 + 430x^8 + 61x^7 + 146753x^6 + 23608x^5 + 16136944x^4 + 30575648x^3 + 1399072384x^2 + 1034227200x + 761760000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.4
Root			$-5.11725 - 8.86334i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.10.e.b.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.2345 + 21.1908i) q^{2} +(-43.3662 + 75.1124i) q^{4} +(-1014.15 - 1756.56i) q^{5} +(-4235.51 + 4734.35i) q^{7} +10405.9 q^{8} +O(q^{10})$	\(q+(12.2345 + 21.1908i) q^{2} +(-43.3662 + 75.1124i) q^{4} +(-1014.15 - 1756.56i) q^{5} +(-4235.51 + 4734.35i) q^{7} +10405.9 q^{8} +(24815.2 - 42981.2i) q^{10} +(4289.29 - 7429.26i) q^{11} -38438.1 q^{13} +(-152144. - 31831.3i) q^{14} +(149514. + 258966. i) q^{16} +(-150942. + 261439. i) q^{17} +(458143. + 793527. i) q^{19} +175919. q^{20} +209909. q^{22} +(966607. + 1.67421e6i) q^{23} +(-1.08043e6 + 1.87136e6i) q^{25} +(-470272. - 814534. i) q^{26} +(-171931. - 523450. i) q^{28} -4.52529e6 q^{29} +(-147255. + 255054. i) q^{31} +(-994560. + 1.72263e6i) q^{32} -7.38680e6 q^{34} +(1.26116e7 + 2.63858e6i) q^{35} +(8.05632e6 + 1.39540e7i) q^{37} +(-1.12103e7 + 1.94168e7i) q^{38} +(-1.05531e7 - 1.82785e7i) q^{40} -1.28783e7 q^{41} +1.15410e7 q^{43} +(372020. + 644357. i) q^{44} +(-2.36519e7 + 4.09663e7i) q^{46} +(-1.39268e7 - 2.41219e7i) q^{47} +(-4.47455e6 - 4.01048e7i) q^{49} -5.28742e7 q^{50} +(1.66692e6 - 2.88718e6i) q^{52} +(-2.11827e7 + 3.66896e7i) q^{53} -1.73999e7 q^{55} +(-4.40742e7 + 4.92651e7i) q^{56} +(-5.53647e7 - 9.58945e7i) q^{58} +(1.17321e6 - 2.03205e6i) q^{59} +(4.34201e6 + 7.52057e6i) q^{61} -7.20638e6 q^{62} +1.04431e8 q^{64} +(3.89820e7 + 6.75188e7i) q^{65} +(-1.26144e8 + 2.18488e8i) q^{67} +(-1.30915e7 - 2.26752e7i) q^{68} +(9.83831e7 + 2.99531e8i) q^{70} +2.50094e8 q^{71} +(-2.32270e7 + 4.02303e7i) q^{73} +(-1.97130e8 + 3.41439e8i) q^{74} -7.94716e7 q^{76} +(1.70054e7 + 5.17737e7i) q^{77} +(-5.53584e7 - 9.58836e7i) q^{79} +(3.03259e8 - 5.25261e8i) q^{80} +(-1.57560e8 - 2.72902e8i) q^{82} -2.81805e8 q^{83} +6.12310e8 q^{85} +(1.41198e8 + 2.44562e8i) q^{86} +(4.46338e7 - 7.73080e7i) q^{88} +(-1.45677e8 - 2.52321e8i) q^{89} +(1.62805e8 - 1.81980e8i) q^{91} -1.67672e8 q^{92} +(3.40774e8 - 5.90238e8i) q^{94} +(9.29250e8 - 1.60951e9i) q^{95} +1.01107e8 q^{97} +(7.95107e8 - 5.85481e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 18 q^{2} - 940 q^{4} - 1533 q^{5} - 1036 q^{7} - 34272 q^{8}+O(q^{10}) $ 10 * q + 18 * q^2 - 940 * q^4 - 1533 * q^5 - 1036 * q^7 - 34272 * q^8	\( 10 q + 18 q^{2} - 940 q^{4} - 1533 q^{5} - 1036 q^{7} - 34272 q^{8} + 4298 q^{10} - 42213 q^{11} - 319676 q^{13} + 39522 q^{14} + 322064 q^{16} - 324681 q^{17} - 16121 q^{19} + 350616 q^{20} - 62692 q^{22} - 2638863 q^{23} - 1304092 q^{25} - 4179252 q^{26} - 22156316 q^{28} - 15292500 q^{29} + 19179237 q^{31} + 6263520 q^{32} - 62909700 q^{34} + 43746759 q^{35} + 39566985 q^{37} - 67365270 q^{38} + 5721744 q^{40} + 53436852 q^{41} + 101835992 q^{43} - 99704916 q^{44} - 14489202 q^{46} - 32509659 q^{47} - 49024598 q^{49} - 3328464 q^{50} + 103893272 q^{52} + 25714707 q^{53} - 144695222 q^{55} - 115352832 q^{56} - 46645516 q^{58} - 46776513 q^{59} - 113075039 q^{61} - 467465628 q^{62} - 192008960 q^{64} + 338113566 q^{65} - 126707879 q^{67} - 32262636 q^{68} + 697712470 q^{70} + 1188736032 q^{71} - 859257651 q^{73} - 591757530 q^{74} + 1101475592 q^{76} - 1911891891 q^{77} - 527065417 q^{79} + 1257352656 q^{80} - 1341703076 q^{82} + 144863208 q^{83} - 1197360222 q^{85} + 678648216 q^{86} + 903700608 q^{88} - 1661554797 q^{89} + 726641384 q^{91} + 1301840952 q^{92} - 272580882 q^{94} + 1197123495 q^{95} + 869770188 q^{97} + 2404833858 q^{98}+O(q^{100}) \) 10 * q + 18 * q^2 - 940 * q^4 - 1533 * q^5 - 1036 * q^7 - 34272 * q^8 + 4298 * q^10 - 42213 * q^11 - 319676 * q^13 + 39522 * q^14 + 322064 * q^16 - 324681 * q^17 - 16121 * q^19 + 350616 * q^20 - 62692 * q^22 - 2638863 * q^23 - 1304092 * q^25 - 4179252 * q^26 - 22156316 * q^28 - 15292500 * q^29 + 19179237 * q^31 + 6263520 * q^32 - 62909700 * q^34 + 43746759 * q^35 + 39566985 * q^37 - 67365270 * q^38 + 5721744 * q^40 + 53436852 * q^41 + 101835992 * q^43 - 99704916 * q^44 - 14489202 * q^46 - 32509659 * q^47 - 49024598 * q^49 - 3328464 * q^50 + 103893272 * q^52 + 25714707 * q^53 - 144695222 * q^55 - 115352832 * q^56 - 46645516 * q^58 - 46776513 * q^59 - 113075039 * q^61 - 467465628 * q^62 - 192008960 * q^64 + 338113566 * q^65 - 126707879 * q^67 - 32262636 * q^68 + 697712470 * q^70 + 1188736032 * q^71 - 859257651 * q^73 - 591757530 * q^74 + 1101475592 * q^76 - 1911891891 * q^77 - 527065417 * q^79 + 1257352656 * q^80 - 1341703076 * q^82 + 144863208 * q^83 - 1197360222 * q^85 + 678648216 * q^86 + 903700608 * q^88 - 1661554797 * q^89 + 726641384 * q^91 + 1301840952 * q^92 - 272580882 * q^94 + 1197123495 * q^95 + 869770188 * q^97 + 2404833858 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	12.2345	+	21.1908i	0.540694	+	0.936509i	0.998864	+	0.0476448i	$0.0151716\pi$
$2$	12.2345	+	21.1908i	0.540694	+	0.936509i	−0.458171	+	0.888864i	$0.651495\pi$
$3$		0			0
$3$		0			0
$4$	−43.3662	+	75.1124i	−0.0846995	+	0.146704i
$5$	−1014.15	−	1756.56i	−0.725666	−	1.25689i	−0.958699	−	0.284421i	$-0.908199\pi$
$5$	−1014.15	−	1756.56i	−0.725666	−	1.25689i	0.233034	−	0.972469i	$-0.425135\pi$
$6$		0			0
$7$	−4235.51	+	4734.35i	−0.666752	+	0.745280i
$7$	−4235.51	+	4734.35i	−0.666752	+	0.745280i
$8$	10405.9			0.898201
$9$		0			0
$10$	24815.2	−	42981.2i	0.784726	−	1.35919i
$11$	4289.29	−	7429.26i	0.0883320	−	0.152996i	−0.818474	−	0.574543i	$-0.805180\pi$
$11$	4289.29	−	7429.26i	0.0883320	−	0.152996i	0.906806	+	0.421548i	$0.138513\pi$
$12$		0			0
$13$	−38438.1			−0.373265			−0.186633	−	0.982430i	$-0.559757\pi$
$13$	−38438.1			−0.373265			−0.186633	+	0.982430i	$0.559757\pi$
$14$	−152144.	−	31831.3i	−1.05847	−	0.221451i
$15$		0			0
$16$	149514.	+	258966.i	0.570352	+	0.987878i
$17$	−150942.	+	261439.i	−0.438318	+	0.759190i	−0.997560	−	0.0698150i	$-0.977759\pi$
$17$	−150942.	+	261439.i	−0.438318	+	0.759190i	0.559242	+	0.829005i	$0.311092\pi$
$18$		0			0
$19$	458143.	+	793527.i	0.806510	+	1.39692i	0.915267	+	0.402848i	$0.131980\pi$
$19$	458143.	+	793527.i	0.806510	+	1.39692i	−0.108757	+	0.994068i	$0.534687\pi$
$20$	175919.			0.245854
$21$		0			0
$22$	209909.			0.191042
$23$	966607.	+	1.67421e6i	0.720236	+	1.24749i	0.960905	+	0.276878i	$0.0892999\pi$
$23$	966607.	+	1.67421e6i	0.720236	+	1.24749i	−0.240669	+	0.970607i	$0.577367\pi$
$24$		0			0
$25$	−1.08043e6	+	1.87136e6i	−0.553182	+	0.958139i
$26$	−470272.	−	814534.i	−0.201822	−	0.349566i
$27$		0			0
$28$	−171931.	−	523450.i	−0.0528619	−	0.160940i
$29$	−4.52529e6			−1.18811			−0.594054	−	0.804425i	$-0.702473\pi$
$29$	−4.52529e6			−1.18811			−0.594054	+	0.804425i	$0.702473\pi$
$30$		0			0
$31$	−147255.	+	255054.i	−0.0286380	+	0.0496025i	−0.879989	−	0.474994i	$-0.842450\pi$
$31$	−147255.	+	255054.i	−0.0286380	+	0.0496025i	0.851351	+	0.524596i	$0.175784\pi$
$32$	−994560.	+	1.72263e6i	−0.167670	+	0.290413i
$33$		0			0
$34$	−7.38680e6			−0.947984
$35$	1.26116e7	+	2.63858e6i	1.42057	+	0.297210i
$36$		0			0
$37$	8.05632e6	+	1.39540e7i	0.706690	+	1.22402i	0.966078	+	0.258250i	$0.0831458\pi$
$37$	8.05632e6	+	1.39540e7i	0.706690	+	1.22402i	−0.259388	+	0.965773i	$0.583521\pi$
$38$	−1.12103e7	+	1.94168e7i	−0.872150	+	1.51061i
$39$		0			0
$40$	−1.05531e7	−	1.82785e7i	−0.651794	−	1.12894i
$41$	−1.28783e7			−0.711757			−0.355878	−	0.934532i	$-0.615818\pi$
$41$	−1.28783e7			−0.711757			−0.355878	+	0.934532i	$0.615818\pi$
$42$		0			0
$43$	1.15410e7			0.514795			0.257398	−	0.966306i	$-0.417135\pi$
$43$	1.15410e7			0.514795			0.257398	+	0.966306i	$0.417135\pi$
$44$	372020.	+	644357.i	0.0149634	+	0.0259173i
$45$		0			0
$46$	−2.36519e7	+	4.09663e7i	−0.778854	+	1.34902i
$47$	−1.39268e7	−	2.41219e7i	−0.416304	−	0.721059i	0.579261	−	0.815142i	$-0.303341\pi$
$47$	−1.39268e7	−	2.41219e7i	−0.416304	−	0.721059i	−0.995564	+	0.0940834i	$0.970008\pi$
$48$		0			0
$49$	−4.47455e6	−	4.01048e7i	−0.110884	−	0.993833i
$50$	−5.28742e7			−1.19641
$51$		0			0
$52$	1.66692e6	−	2.88718e6i	0.0316154	−	0.0547594i
$53$	−2.11827e7	+	3.66896e7i	−0.368757	+	0.638706i	−0.989372	−	0.145410i	$-0.953550\pi$
$53$	−2.11827e7	+	3.66896e7i	−0.368757	+	0.638706i	0.620614	+	0.784116i	$0.286883\pi$
$54$		0			0
$55$	−1.73999e7			−0.256398
$56$	−4.40742e7	+	4.92651e7i	−0.598878	+	0.669411i
$57$		0			0
$58$	−5.53647e7	−	9.58945e7i	−0.642402	−	1.11267i
$59$	1.17321e6	−	2.03205e6i	0.0126049	−	0.0218324i	−0.859654	−	0.510876i	$-0.829321\pi$
$59$	1.17321e6	−	2.03205e6i	0.0126049	−	0.0218324i	0.872259	+	0.489044i	$0.162654\pi$
$60$		0			0
$61$	4.34201e6	+	7.52057e6i	0.0401519	+	0.0695451i	0.885403	−	0.464824i	$-0.153882\pi$
$61$	4.34201e6	+	7.52057e6i	0.0401519	+	0.0695451i	−0.845251	+	0.534369i	$0.820549\pi$
$62$	−7.20638e6			−0.0619376
$63$		0			0
$64$	1.04431e8			0.778070
$65$	3.89820e7	+	6.75188e7i	0.270866	+	0.469153i
$66$		0			0
$67$	−1.26144e8	+	2.18488e8i	−0.764771	+	1.32462i	0.175597	+	0.984462i	$0.443814\pi$
$67$	−1.26144e8	+	2.18488e8i	−0.764771	+	1.32462i	−0.940368	+	0.340159i	$0.889519\pi$
$68$	−1.30915e7	−	2.26752e7i	−0.0742507	−	0.128606i
$69$		0			0
$70$	9.83831e7	+	2.99531e8i	0.489755	+	1.49108i
$71$	2.50094e8			1.16799			0.583997	−	0.811756i	$-0.301488\pi$
$71$	2.50094e8			1.16799			0.583997	+	0.811756i	$0.301488\pi$
$72$		0			0
$73$	−2.32270e7	+	4.02303e7i	−0.0957282	+	0.165806i	−0.909912	−	0.414801i	$-0.863851\pi$
$73$	−2.32270e7	+	4.02303e7i	−0.0957282	+	0.165806i	0.814184	+	0.580607i	$0.197185\pi$
$74$	−1.97130e8	+	3.41439e8i	−0.764206	+	1.32364i
$75$		0			0
$76$	−7.94716e7			−0.273244
$77$	1.70054e7	+	5.17737e7i	0.0551289	+	0.167842i
$78$		0			0
$79$	−5.53584e7	−	9.58836e7i	−0.159905	−	0.276963i	0.774929	−	0.632048i	$-0.217785\pi$
$79$	−5.53584e7	−	9.58836e7i	−0.159905	−	0.276963i	−0.934834	+	0.355084i	$0.884452\pi$
$80$	3.03259e8	−	5.25261e8i	0.827769	−	1.43374i
$81$		0			0
$82$	−1.57560e8	−	2.72902e8i	−0.384843	−	0.666567i
$83$	−2.81805e8			−0.651774			−0.325887	−	0.945409i	$-0.605663\pi$
$83$	−2.81805e8			−0.651774			−0.325887	+	0.945409i	$0.605663\pi$
$84$		0			0
$85$	6.12310e8			1.27229
$86$	1.41198e8	+	2.44562e8i	0.278347	+	0.482111i
$87$		0			0
$88$	4.46338e7	−	7.73080e7i	0.0793399	−	0.137421i
$89$	−1.45677e8	−	2.52321e8i	−0.246115	−	0.426283i	0.716330	−	0.697762i	$-0.245821\pi$
$89$	−1.45677e8	−	2.52321e8i	−0.246115	−	0.426283i	−0.962444	+	0.271479i	$0.912487\pi$
$90$		0			0
$91$	1.62805e8	−	1.81980e8i	0.248875	−	0.278187i
$92$	−1.67672e8			−0.244015
$93$		0			0
$94$	3.40774e8	−	5.90238e8i	0.450185	−	0.779744i
$95$	9.29250e8	−	1.60951e9i	1.17051	−	2.02739i
$96$		0			0
$97$	1.01107e8			0.115960			0.0579798	−	0.998318i	$-0.481534\pi$
$97$	1.01107e8			0.115960			0.0579798	+	0.998318i	$0.481534\pi$
$98$	7.95107e8	−	5.85481e8i	0.870780	−	0.641203i
$99$		0			0
$100$	−9.37085e7	−	1.62308e8i	−0.0937085	−	0.162308i
$101$	−5.29724e8	+	9.17509e8i	−0.506528	+	0.877332i	0.493443	+	0.869778i	$0.335738\pi$
$101$	−5.29724e8	+	9.17509e8i	−0.506528	+	0.877332i	−0.999971	+	0.00755447i	$0.997595\pi$
$102$		0			0
$103$	2.52542e8	+	4.37415e8i	0.221088	+	0.382936i	0.955139	−	0.296159i	$-0.0957058\pi$
$103$	2.52542e8	+	4.37415e8i	0.221088	+	0.382936i	−0.734050	+	0.679095i	$0.762372\pi$
$104$	−3.99983e8			−0.335267
$105$		0			0
$106$	−1.03664e9			−0.797539
$107$	−943656.	−	1.63446e6i	−0.000695964	−	0.00120544i	0.865677	−	0.500603i	$-0.166888\pi$
$107$	−943656.	−	1.63446e6i	−0.000695964	−	0.00120544i	−0.866373	+	0.499397i	$0.833555\pi$
$108$		0			0
$109$	5.32240e7	−	9.21867e7i	0.0361151	−	0.0625531i	−0.847403	−	0.530950i	$-0.821835\pi$
$109$	5.32240e7	−	9.21867e7i	0.0361151	−	0.0625531i	0.883518	+	0.468397i	$0.155168\pi$
$110$	−2.12879e8	−	3.68717e8i	−0.138633	−	0.240119i
$111$		0			0
$112$	−1.85931e9	−	3.89001e8i	−1.11653	−	0.233598i
$113$	2.40785e9			1.38924			0.694620	−	0.719377i	$-0.255573\pi$
$113$	2.40785e9			1.38924			0.694620	+	0.719377i	$0.255573\pi$
$114$		0			0
$115$	1.96057e9	−	3.39580e9i	1.04530	−	1.81051i
$116$	1.96245e8	−	3.39906e8i	0.100632	−	0.174300i
$117$		0			0
$118$	5.74144e7			0.0272616
$119$	−5.98429e8	−	1.82194e9i	−0.273559	−	0.832861i
$120$		0			0
$121$	1.14218e9	+	1.97831e9i	0.484395	+	0.838997i
$122$	−1.06245e8	+	1.84021e8i	−0.0434198	+	0.0752052i
$123$		0			0
$124$	−1.27718e7	−	2.21214e7i	−0.00485126	−	0.00840262i
$125$	4.21360e8			0.154368
$126$		0			0
$127$	1.51077e9			0.515326			0.257663	−	0.966235i	$-0.417048\pi$
$127$	1.51077e9			0.515326			0.257663	+	0.966235i	$0.417048\pi$
$128$	1.78687e9	+	3.09496e9i	0.588368	+	1.01908i
$129$		0			0
$130$	−9.53851e8	+	1.65212e9i	−0.292911	+	0.507336i
$131$	−1.02677e8	−	1.77843e8i	−0.0304617	−	0.0527612i	0.850393	−	0.526149i	$-0.176364\pi$
$131$	−1.02677e8	−	1.77843e8i	−0.0304617	−	0.0527612i	−0.880854	+	0.473387i	$0.843031\pi$
$132$		0			0
$133$	−5.69730e9	−	1.19198e9i	−1.57884	−	0.330321i
$134$	−6.17325e9			−1.65403
$135$		0			0
$136$	−1.57068e9	+	2.72050e9i	−0.393698	+	0.681905i
$137$	−2.94515e9	+	5.10114e9i	−0.714273	+	1.23716i	0.248966	+	0.968512i	$0.419909\pi$
$137$	−2.94515e9	+	5.10114e9i	−0.714273	+	1.23716i	−0.963239	+	0.268645i	$0.913424\pi$
$138$		0			0
$139$	1.53632e9			0.349073			0.174537	−	0.984651i	$-0.444157\pi$
$139$	1.53632e9			0.349073			0.174537	+	0.984651i	$0.444157\pi$
$140$	−7.45106e8	+	8.32862e8i	−0.163924	+	0.183230i
$141$		0			0
$142$	3.05977e9	+	5.29968e9i	0.631527	+	1.09384i
$143$	−1.64872e8	+	2.85567e8i	−0.0329712	+	0.0571079i
$144$		0			0
$145$	4.58932e9	+	7.94893e9i	0.862169	+	1.49332i
$146$	−1.13668e9			−0.207038
$147$		0			0
$148$	−1.39749e9			−0.239425
$149$	−3.06047e8	−	5.30089e8i	−0.0508686	−	0.0881070i	0.839470	−	0.543406i	$-0.182866\pi$
$149$	−3.06047e8	−	5.30089e8i	−0.0508686	−	0.0881070i	−0.890338	+	0.455299i	$0.849532\pi$
$150$		0			0
$151$	−5.27233e8	+	9.13194e8i	−0.0825289	+	0.142944i	−0.904336	−	0.426822i	$-0.859633\pi$
$151$	−5.27233e8	+	9.13194e8i	−0.0825289	+	0.142944i	0.821807	+	0.569766i	$0.192966\pi$
$152$	4.76738e9	+	8.25734e9i	0.724408	+	1.25471i
$153$		0			0
$154$	−8.89072e8	+	9.93784e8i	−0.127378	+	0.142380i
$155$	5.97355e8			0.0831266
$156$		0			0
$157$	1.84813e9	−	3.20105e9i	0.242764	−	0.420479i	−0.718737	−	0.695282i	$-0.755279\pi$
$157$	1.84813e9	−	3.20105e9i	0.242764	−	0.420479i	0.961500	+	0.274803i	$0.0886128\pi$
$158$	1.35457e9	−	2.34618e9i	0.172919	−	0.299505i
$159$		0			0
$160$	4.03453e9			0.486690
$161$	−1.20204e10	−	2.51488e9i	−1.40994	−	0.294986i
$162$		0			0
$163$	−6.57764e9	−	1.13928e10i	−0.729837	−	1.26412i	−0.956952	−	0.290247i	$-0.906262\pi$
$163$	−6.57764e9	−	1.13928e10i	−0.729837	−	1.26412i	0.227114	−	0.973868i	$-0.427071\pi$
$164$	5.58483e8	−	9.67321e8i	0.0602855	−	0.104418i
$165$		0			0
$166$	−3.44774e9	−	5.97167e9i	−0.352410	−	0.610393i
$167$	−6.15786e9			−0.612641			−0.306320	−	0.951928i	$-0.599098\pi$
$167$	−6.15786e9			−0.612641			−0.306320	+	0.951928i	$0.599098\pi$
$168$		0			0
$169$	−9.12701e9			−0.860673
$170$	7.49131e9	+	1.29753e10i	0.687920	+	1.19151i
$171$		0			0
$172$	−5.00488e8	+	8.66871e8i	−0.0436029	+	0.0755225i
$173$	−7.73798e9	−	1.34026e10i	−0.656780	−	1.13758i	−0.981444	−	0.191747i	$-0.938585\pi$
$173$	−7.73798e9	−	1.34026e10i	−0.656780	−	1.13758i	0.324664	−	0.945829i	$-0.394749\pi$
$174$		0			0
$175$	−4.28351e9	−	1.30413e10i	−0.345246	−	1.05112i
$176$	2.56524e9			0.201521
$177$		0			0
$178$	3.56458e9	−	6.17404e9i	0.266145	−	0.460977i
$179$	−1.98868e9	+	3.44450e9i	−0.144786	+	0.250777i	−0.929293	−	0.369343i	$-0.879583\pi$
$179$	−1.98868e9	+	3.44450e9i	−0.144786	+	0.250777i	0.784507	+	0.620120i	$0.212916\pi$
$180$		0			0
$181$	−2.68948e10			−1.86258			−0.931288	−	0.364283i	$-0.881314\pi$
$181$	−2.68948e10			−1.86258			−0.931288	+	0.364283i	$0.881314\pi$
$182$	5.84813e9	+	1.22354e9i	0.395090	+	0.0826600i
$183$		0			0
$184$	1.00584e10	+	1.74217e10i	0.646917	+	1.12049i
$185$	1.63406e10	−	2.83028e10i	1.02564	−	1.77646i
$186$		0			0
$187$	1.29487e9	+	2.24277e9i	0.0774351	+	0.134121i
$188$	2.41580e9			0.141043
$189$		0			0
$190$	4.54756e10			2.53156
$191$	8.68177e8	+	1.50373e9i	0.0472018	+	0.0817559i	0.888661	−	0.458565i	$-0.151636\pi$
$191$	8.68177e8	+	1.50373e9i	0.0472018	+	0.0817559i	−0.841459	+	0.540321i	$0.818303\pi$
$192$		0			0
$193$	−7.30896e9	+	1.26595e10i	−0.379182	+	0.656763i	−0.990943	−	0.134280i	$-0.957128\pi$
$193$	−7.30896e9	+	1.26595e10i	−0.379182	+	0.656763i	0.611761	+	0.791042i	$0.290461\pi$
$194$	1.23699e9	+	2.14253e9i	0.0626986	+	0.108597i
$195$		0			0
$196$	3.20641e9	+	1.40310e9i	0.155191	+	0.0679102i
$197$	4.40160e9			0.208215			0.104108	−	0.994566i	$-0.466801\pi$
$197$	4.40160e9			0.208215			0.104108	+	0.994566i	$0.466801\pi$
$198$		0			0
$199$	1.76429e10	−	3.05585e10i	0.797502	−	1.38131i	−0.123736	−	0.992315i	$-0.539488\pi$
$199$	1.76429e10	−	3.05585e10i	0.797502	−	1.38131i	0.921238	−	0.388999i	$-0.127179\pi$
$200$	−1.12429e10	+	1.94732e10i	−0.496869	+	0.860602i
$201$		0			0
$202$	−2.59236e10			−1.09551
$203$	1.91669e10	−	2.14243e10i	0.792173	−	0.885472i
$204$		0			0
$205$	1.30605e10	+	2.26215e10i	0.516498	+	0.894600i
$206$	−6.17945e9	+	1.07031e10i	−0.239082	+	0.414102i
$207$		0			0
$208$	−5.74705e9	−	9.95418e9i	−0.212892	−	0.368740i
$209$	7.86042e9			0.284962
$210$		0			0
$211$	1.08123e10			0.375533			0.187766	−	0.982214i	$-0.439875\pi$
$211$	1.08123e10			0.375533			0.187766	+	0.982214i	$0.439875\pi$
$212$	−1.83723e9	−	3.18217e9i	−0.0624671	−	0.108196i
$213$		0			0
$214$	2.30903e7	−	3.99936e7i	0.000752607	−	0.00130355i
$215$	−1.17043e10	−	2.02724e10i	−0.373569	−	0.647041i
$216$		0			0
$217$	−5.83812e8	−	1.77744e9i	−0.0178733	−	0.0544159i
$218$	2.60468e9			0.0781088
$219$		0			0
$220$	7.54567e8	−	1.30695e9i	0.0217168	−	0.0376146i
$221$	5.80193e9	−	1.00492e10i	0.163609	−	0.283379i
$222$		0			0
$223$	3.21844e10			0.871512			0.435756	−	0.900065i	$-0.356481\pi$
$223$	3.21844e10			0.871512			0.435756	+	0.900065i	$0.356481\pi$
$224$	−3.94306e9	−	1.20048e10i	−0.104645	−	0.318595i
$225$		0			0
$226$	2.94589e10	+	5.10243e10i	0.751153	+	1.30104i
$227$	−4.50385e9	+	7.80090e9i	−0.112582	+	0.194997i	−0.916810	−	0.399323i	$-0.869245\pi$
$227$	−4.50385e9	+	7.80090e9i	−0.112582	+	0.194997i	0.804229	+	0.594320i	$0.202579\pi$
$228$		0			0
$229$	−2.31909e10	−	4.01679e10i	−0.557261	−	0.965204i	−0.997724	−	0.0674334i	$-0.978519\pi$
$229$	−2.31909e10	−	4.01679e10i	−0.557261	−	0.965204i	0.440463	−	0.897771i	$-0.354814\pi$
$230$	9.59463e10			2.26075
$231$		0			0
$232$	−4.70896e10			−1.06716
$233$	−2.17672e10	−	3.77018e10i	−0.483838	−	0.838032i	0.515990	−	0.856595i	$-0.327424\pi$
$233$	−2.17672e10	−	3.77018e10i	−0.483838	−	0.838032i	−0.999828	+	0.0185626i	$0.994091\pi$
$234$		0			0
$235$	−2.82476e10	+	4.89263e10i	−0.604194	+	1.04650i
$236$	1.01755e8	+	1.76245e8i	0.00213526	+	0.00369838i
$237$		0			0
$238$	3.12868e10	−	3.49717e10i	0.632070	−	0.706513i
$239$	2.74289e10			0.543773			0.271887	−	0.962329i	$-0.412352\pi$
$239$	2.74289e10			0.543773			0.271887	+	0.962329i	$0.412352\pi$
$240$		0			0
$241$	5.75409e9	−	9.96638e9i	0.109875	−	0.190310i	−0.805844	−	0.592128i	$-0.798288\pi$
$241$	5.75409e9	−	9.96638e9i	0.109875	−	0.190310i	0.915720	+	0.401818i	$0.131622\pi$
$242$	−2.79480e10	+	4.84073e10i	−0.523819	+	0.907281i
$243$		0			0
$244$	−7.53185e8			−0.0136034
$245$	−6.59084e10	+	4.85320e10i	−1.16867	+	0.860559i
$246$		0			0
$247$	−1.76102e10	−	3.05017e10i	−0.301042	−	0.521420i
$248$	−1.53232e9	+	2.65406e9i	−0.0257227	+	0.0445531i
$249$		0			0
$250$	5.15513e9	+	8.92894e9i	0.0834659	+	0.144567i
$251$	2.69146e10			0.428012			0.214006	−	0.976832i	$-0.431349\pi$
$251$	2.69146e10			0.428012			0.214006	+	0.976832i	$0.431349\pi$
$252$		0			0
$253$	1.65842e10			0.254480
$254$	1.84835e10	+	3.20144e10i	0.278634	+	0.482607i
$255$		0			0
$256$	−1.69887e10	+	2.94254e10i	−0.247219	+	0.428195i
$257$	−1.78979e10	−	3.10001e10i	−0.255919	−	0.443265i	0.709225	−	0.704982i	$-0.249045\pi$
$257$	−1.78979e10	−	3.10001e10i	−0.255919	−	0.443265i	−0.965145	+	0.261716i	$0.915711\pi$
$258$		0			0
$259$	−1.00186e11	−	2.09606e10i	−1.38343	−	0.289438i
$260$	−6.76200e9			−0.0917688
$261$		0			0
$262$	2.51242e9	−	4.35163e9i	0.0329409	−	0.0570554i
$263$	−6.63817e10	+	1.14976e11i	−0.855554	+	1.48186i	0.0205759	+	0.999788i	$0.493450\pi$
$263$	−6.63817e10	+	1.14976e11i	−0.855554	+	1.48186i	−0.876130	+	0.482075i	$0.839883\pi$
$264$		0			0
$265$	8.59298e10			1.07038
$266$	−4.44447e10	−	1.35314e11i	−0.544318	−	1.65720i
$267$		0			0
$268$	−1.09408e10	−	1.89500e10i	−0.129551	−	0.224390i
$269$	3.64397e10	−	6.31154e10i	0.424316	−	0.734937i	−0.572040	−	0.820226i	$-0.693848\pi$
$269$	3.64397e10	−	6.31154e10i	0.424316	−	0.734937i	0.996356	+	0.0852884i	$0.0271812\pi$
$270$		0			0
$271$	−2.06838e10	−	3.58253e10i	−0.232953	−	0.403486i	0.725723	−	0.687987i	$-0.241505\pi$
$271$	−2.06838e10	−	3.58253e10i	−0.232953	−	0.403486i	−0.958676	+	0.284501i	$0.908172\pi$
$272$	−9.02719e10			−0.999982
$273$		0			0
$274$	−1.44130e11			−1.54481
$275$	9.26857e9	+	1.60536e10i	0.0977273	+	0.169269i
$276$		0			0
$277$	8.09314e10	−	1.40177e11i	0.825958	−	1.43060i	−0.0752266	−	0.997166i	$-0.523968\pi$
$277$	8.09314e10	−	1.40177e11i	0.825958	−	1.43060i	0.901185	−	0.433435i	$-0.142699\pi$
$278$	1.87962e10	+	3.25559e10i	0.188742	+	0.326910i
$279$		0			0
$280$	1.31235e11	+	2.74567e10i	1.27596	+	0.266954i
$281$	−1.39939e11			−1.33894			−0.669471	−	0.742838i	$-0.733479\pi$
$281$	−1.39939e11			−1.33894			−0.669471	+	0.742838i	$0.733479\pi$
$282$		0			0
$283$	−8.86550e10	+	1.53555e11i	−0.821607	+	1.42306i	0.0828783	+	0.996560i	$0.473589\pi$
$283$	−8.86550e10	+	1.53555e11i	−0.821607	+	1.42306i	−0.904485	+	0.426505i	$0.859745\pi$
$284$	−1.08456e10	+	1.87851e10i	−0.0989285	+	0.171349i
$285$		0			0
$286$	−8.06852e9			−0.0713094
$287$	5.45462e10	−	6.09705e10i	0.474565	−	0.530458i
$288$		0			0
$289$	1.37270e10	+	2.37759e10i	0.115754	+	0.200492i
$290$	−1.12296e11	+	1.94503e11i	−0.932338	+	1.61486i
$291$		0			0
$292$	−2.01453e9	−	3.48927e9i	−0.0162163	−	0.0280874i
$293$	1.65710e11			1.31355			0.656773	−	0.754088i	$-0.271921\pi$
$293$	1.65710e11			1.31355			0.656773	+	0.754088i	$0.271921\pi$
$294$		0			0
$295$	−4.75922e9			−0.0365879
$296$	8.38331e10	+	1.45203e11i	0.634750	+	1.09942i
$297$		0			0
$298$	7.48866e9	−	1.29707e10i	0.0550087	−	0.0952778i
$299$	−3.71546e10	−	6.43536e10i	−0.268839	−	0.465643i
$300$		0			0
$301$	−4.88819e10	+	5.46391e10i	−0.343241	+	0.383667i
$302$	−2.58017e10			−0.178491
$303$		0			0
$304$	−1.36998e11	+	2.37287e11i	−0.919988	+	1.59347i
$305$	8.80688e9	−	1.52540e10i	0.0582737	−	0.100933i
$306$		0			0
$307$	2.12825e11			1.36741			0.683706	−	0.729757i	$-0.260367\pi$
$307$	2.12825e11			1.36741			0.683706	+	0.729757i	$0.260367\pi$
$308$	−4.62631e9	−	9.67908e8i	−0.0292925	−	0.00612852i
$309$		0			0
$310$	7.30834e9	+	1.26584e10i	0.0449460	+	0.0778488i
$311$	−7.94338e10	+	1.37583e11i	−0.481486	+	0.833959i	−0.999774	−	0.0212476i	$-0.993236\pi$
$311$	−7.94338e10	+	1.37583e11i	−0.481486	+	0.833959i	0.518288	+	0.855206i	$0.326570\pi$
$312$		0			0
$313$	1.48658e11	+	2.57484e11i	0.875468	+	1.51635i	0.856264	+	0.516539i	$0.172780\pi$
$313$	1.48658e11	+	2.57484e11i	0.875468	+	1.51635i	0.0192038	+	0.999816i	$0.493887\pi$
$314$	9.04437e10			0.525043
$315$		0			0
$316$	9.60273e9			0.0541755
$317$	7.66580e10	+	1.32776e11i	0.426374	+	0.738502i	0.996548	−	0.0830226i	$-0.0264574\pi$
$317$	7.66580e10	+	1.32776e11i	0.426374	+	0.738502i	−0.570174	+	0.821524i	$0.693124\pi$
$318$		0			0
$319$	−1.94103e10	+	3.36196e10i	−0.104948	+	0.181775i
$320$	−1.05908e11	−	1.83439e11i	−0.564619	−	0.977948i
$321$		0			0
$322$	−9.37711e10	−	2.85490e11i	−0.486091	−	1.47992i
$323$	−2.76612e11			−1.41403
$324$		0			0
$325$	4.15298e10	−	7.19318e10i	0.206483	−	0.357640i
$326$	1.60948e11	−	2.78771e11i	0.789237	−	1.36700i
$327$		0			0
$328$	−1.34010e11			−0.639301
$329$	1.73188e11	+	3.62342e10i	0.814962	+	0.170505i
$330$		0			0
$331$	−1.22438e11	−	2.12070e11i	−0.560650	−	0.971074i	−0.997440	−	0.0715104i	$-0.977218\pi$
$331$	−1.22438e11	−	2.12070e11i	−0.560650	−	0.971074i	0.436790	−	0.899563i	$-0.356115\pi$
$332$	1.22208e10	−	2.11671e10i	0.0552050	−	0.0956179i
$333$		0			0
$334$	−7.53384e10	−	1.30490e11i	−0.331251	−	0.573744i
$335$	5.11716e11			2.21987
$336$		0			0
$337$	−4.96265e10			−0.209594			−0.104797	−	0.994494i	$-0.533419\pi$
$337$	−4.96265e10			−0.209594			−0.104797	+	0.994494i	$0.533419\pi$
$338$	−1.11664e11	−	1.93408e11i	−0.465361	−	0.806028i
$339$		0			0
$340$	−2.65535e10	+	4.59921e10i	−0.107762	+	0.186650i
$341$	1.26324e9	+	2.18800e9i	0.00505931	+	0.00876298i
$342$		0			0
$343$	2.08822e11	+	1.48680e11i	0.814616	+	0.580001i
$344$	1.20094e11			0.462390
$345$		0			0
$346$	1.89341e11	−	3.27948e11i	0.710234	−	1.23016i
$347$	−1.52077e11	+	2.63405e11i	−0.563094	+	0.975308i	0.434130	+	0.900850i	$0.357056\pi$
$347$	−1.52077e11	+	2.63405e11i	−0.563094	+	0.975308i	−0.997224	+	0.0744576i	$0.976277\pi$
$348$		0			0
$349$	4.96999e11			1.79325			0.896626	−	0.442788i	$-0.146011\pi$
$349$	4.96999e11			1.79325			0.896626	+	0.442788i	$0.146011\pi$
$350$	2.23949e11	−	2.50325e11i	0.797707	−	0.891658i
$351$		0			0
$352$	8.53191e9	+	1.47777e10i	0.0296213	+	0.0513056i
$353$	8.82246e10	−	1.52809e11i	0.302415	−	0.523798i	−0.674267	−	0.738487i	$-0.735540\pi$
$353$	8.82246e10	−	1.52809e11i	0.302415	−	0.523798i	0.976682	+	0.214689i	$0.0688738\pi$
$354$		0			0
$355$	−2.53632e11	−	4.39304e11i	−0.847573	−	1.46804i
$356$	2.52699e10			0.0833832
$357$		0			0
$358$	−9.73223e10			−0.313140
$359$	−8.72570e10	−	1.51134e11i	−0.277253	−	0.480215i	0.693448	−	0.720506i	$-0.256091\pi$
$359$	−8.72570e10	−	1.51134e11i	−0.277253	−	0.480215i	−0.970701	+	0.240291i	$0.922757\pi$
$360$		0			0
$361$	−2.58446e11	+	4.47641e11i	−0.800916	+	1.38723i
$362$	−3.29044e11	−	5.69921e11i	−1.00708	−	1.74432i
$363$		0			0
$364$	6.60870e9	+	2.01204e10i	0.0197315	+	0.0600733i
$365$	9.42224e10			0.277867
$366$		0			0
$367$	−1.94008e11	+	3.36032e11i	−0.558243	+	0.966905i	0.439401	+	0.898291i	$0.355191\pi$
$367$	−1.94008e11	+	3.36032e11i	−0.558243	+	0.966905i	−0.997643	+	0.0686134i	$0.978143\pi$
$368$	−2.89043e11	+	5.00637e11i	−0.821575	+	1.42301i
$369$		0			0
$370$	7.99677e11			2.21823
$371$	−8.39817e10	−	2.55685e11i	−0.230145	−	0.700686i
$372$		0			0
$373$	−3.02948e11	−	5.24721e11i	−0.810360	−	1.40359i	−0.912612	−	0.408827i	$-0.865938\pi$
$373$	−3.02948e11	−	5.24721e11i	−0.810360	−	1.40359i	0.102251	−	0.994759i	$-0.467395\pi$
$374$	−3.16841e10	+	5.48785e10i	−0.0837373	+	0.145037i
$375$		0			0
$376$	−1.44920e11	−	2.51009e11i	−0.373924	−	0.647656i
$377$	1.73944e11			0.443479
$378$		0			0
$379$	5.34706e11			1.33119			0.665593	−	0.746315i	$-0.268179\pi$
$379$	5.34706e11			1.33119			0.665593	+	0.746315i	$0.268179\pi$
$380$	8.05960e10	+	1.39596e11i	0.198284	+	0.343438i
$381$		0			0
$382$	−2.12434e10	+	3.67947e10i	−0.0510434	+	0.0884098i
$383$	1.26206e11	+	2.18595e11i	0.299699	+	0.519094i	0.976067	−	0.217470i	$-0.0697804\pi$
$383$	1.26206e11	+	2.18595e11i	0.299699	+	0.519094i	−0.676368	+	0.736564i	$0.736447\pi$
$384$		0			0
$385$	7.36974e10	−	8.23772e10i	0.170954	−	0.191088i
$386$	−3.57686e11			−0.820086
$387$		0			0
$388$	−4.38461e9	+	7.59436e9i	−0.00982172	+	0.0170117i
$389$	4.16836e10	−	7.21981e10i	0.0922979	−	0.159865i	−0.816180	−	0.577798i	$-0.803912\pi$
$389$	4.16836e10	−	7.21981e10i	0.0922979	−	0.159865i	0.908478	+	0.417933i	$0.137245\pi$
$390$		0			0
$391$	−5.83606e11			−1.26277
$392$	−4.65616e10	−	4.17325e11i	−0.0995958	−	0.892663i
$393$		0			0
$394$	5.38514e10	+	9.32733e10i	0.112581	+	0.194995i
$395$	−1.12283e11	+	1.94480e11i	−0.232075	+	0.401966i
$396$		0			0
$397$	−5.67001e10	−	9.82075e10i	−0.114558	−	0.198421i	0.803045	−	0.595919i	$-0.203212\pi$
$397$	−5.67001e10	−	9.82075e10i	−0.114558	−	0.198421i	−0.917603	+	0.397498i	$0.869879\pi$
$398$	8.63410e11			1.72482
$399$		0			0
$400$	−6.46160e11			−1.26203
$401$	2.56734e11	+	4.44676e11i	0.495831	+	0.858805i	0.999988	−	0.00480724i	$-0.00153020\pi$
$401$	2.56734e11	+	4.44676e11i	0.495831	+	0.858805i	−0.504157	+	0.863612i	$0.668197\pi$
$402$		0			0
$403$	5.66022e9	−	9.80379e9i	0.0106896	−	0.0185149i
$404$	−4.59442e10	−	7.95777e10i	−0.0858054	−	0.148619i
$405$		0			0
$406$	6.88496e11	+	1.44046e11i	1.25758	+	0.263108i
$407$	1.38223e11			0.249693
$408$		0			0
$409$	−3.87550e11	+	6.71256e11i	−0.684814	+	1.18613i	0.288681	+	0.957425i	$0.406783\pi$
$409$	−3.87550e11	+	6.71256e11i	−0.684814	+	1.18613i	−0.973495	+	0.228708i	$0.926550\pi$
$410$	−3.19578e11	+	5.53526e11i	−0.558534	+	0.967409i
$411$		0			0
$412$	−4.38071e10			−0.0749043
$413$	4.65133e9	+	1.41611e10i	0.00786686	+	0.0239510i
$414$		0			0
$415$	2.85792e11	+	4.95007e11i	0.472970	+	0.819209i
$416$	3.82290e10	−	6.62146e10i	0.0625855	−	0.108401i
$417$		0			0
$418$	9.61684e10	+	1.66569e11i	0.154077	+	0.266870i
$419$	−9.73463e11			−1.54297			−0.771483	−	0.636250i	$-0.780485\pi$
$419$	−9.73463e11			−1.54297			−0.771483	+	0.636250i	$0.780485\pi$
$420$		0			0
$421$	−8.24555e11			−1.27924			−0.639618	−	0.768693i	$-0.720907\pi$
$421$	−8.24555e11			−1.27924			−0.639618	+	0.768693i	$0.720907\pi$
$422$	1.32283e11	+	2.29121e11i	0.203048	+	0.351690i
$423$		0			0
$424$	−2.20425e11	+	3.81787e11i	−0.331218	+	0.573687i
$425$	−3.26165e11	−	5.64935e11i	−0.484939	−	0.839940i
$426$		0			0
$427$	−5.39956e10	−	1.12969e10i	−0.0786019	−	0.0164450i
$428$	1.63691e8			0.000235791
$429$		0			0
$430$	2.86392e11	−	4.96045e11i	0.403973	−	0.699702i
$431$	−2.22097e11	+	3.84683e11i	−0.310024	+	0.536977i	−0.978367	−	0.206876i	$-0.933670\pi$
$431$	−2.22097e11	+	3.84683e11i	−0.310024	+	0.536977i	0.668343	+	0.743853i	$0.267004\pi$
$432$		0			0
$433$	7.57077e11			1.03501			0.517505	−	0.855680i	$-0.326861\pi$
$433$	7.57077e11			1.03501			0.517505	+	0.855680i	$0.326861\pi$
$434$	3.05227e10	−	3.41175e10i	0.0412970	−	0.0461609i
$435$		0			0
$436$	4.61624e9	+	7.99557e9i	0.00611786	+	0.0105964i
$437$	−8.85688e11	+	1.53406e12i	−1.16175	+	2.01222i
$438$		0			0
$439$	−5.04945e10	−	8.74591e10i	−0.0648865	−	0.112387i	0.831757	−	0.555140i	$-0.187335\pi$
$439$	−5.04945e10	−	8.74591e10i	−0.0648865	−	0.112387i	−0.896644	+	0.442753i	$0.854002\pi$
$440$	−1.81061e11			−0.230297
$441$		0			0
$442$	2.83935e11			0.353849
$443$	3.63399e11	+	6.29425e11i	0.448298	+	0.776475i	0.998275	−	0.0587046i	$-0.0186970\pi$
$443$	3.63399e11	+	6.29425e11i	0.448298	+	0.776475i	−0.549977	+	0.835180i	$0.685364\pi$
$444$		0			0
$445$	−2.95477e11	+	5.11781e11i	−0.357194	+	0.618678i
$446$	3.93760e11	+	6.82012e11i	0.471221	+	0.816179i
$447$		0			0
$448$	−4.42317e11	+	4.94412e11i	−0.518780	+	0.579880i
$449$	1.85410e11			0.215291			0.107645	−	0.994189i	$-0.465669\pi$
$449$	1.85410e11			0.215291			0.107645	+	0.994189i	$0.465669\pi$
$450$		0			0
$451$	−5.52388e10	+	9.56764e10i	−0.0628709	+	0.108896i
$452$	−1.04419e11	+	1.80860e11i	−0.117668	+	0.203807i
$453$		0			0
$454$	−2.20410e11			−0.243489
$455$	−4.84766e11	−	1.01422e11i	−0.530250	−	0.110938i
$456$		0			0
$457$	4.49165e11	+	7.77977e11i	0.481707	+	0.834341i	0.999780	−	0.0209954i	$-0.00668354\pi$
$457$	4.49165e11	+	7.77977e11i	0.481707	+	0.834341i	−0.518072	+	0.855337i	$0.673350\pi$
$458$	5.67459e11	−	9.82868e11i	0.602615	−	1.04376i
$459$		0			0
$460$	1.70045e11	+	2.94526e11i	0.177073	+	0.306700i
$461$	6.56915e11			0.677416			0.338708	−	0.940892i	$-0.390010\pi$
$461$	6.56915e11			0.677416			0.338708	+	0.940892i	$0.390010\pi$
$462$		0			0
$463$	7.36860e11			0.745196			0.372598	−	0.927993i	$-0.378467\pi$
$463$	7.36860e11			0.745196			0.372598	+	0.927993i	$0.378467\pi$
$464$	−6.76596e11	−	1.17190e12i	−0.677639	−	1.17370i
$465$		0			0
$466$	5.32621e11	−	9.22526e11i	0.523217	−	0.906238i
$467$	−3.97280e11	−	6.88109e11i	−0.386519	−	0.669470i	0.605460	−	0.795876i	$-0.292989\pi$
$467$	−3.97280e11	−	6.88109e11i	−0.386519	−	0.669470i	−0.991979	+	0.126406i	$0.959656\pi$
$468$		0			0
$469$	−5.00115e11	−	1.52262e12i	−0.477301	−	1.45316i
$470$	−1.38238e12			−1.30674
$471$		0			0
$472$	1.22082e10	−	2.11453e10i	0.0113218	−	0.0196099i
$473$	4.95026e10	−	8.57410e10i	0.0454729	−	0.0787614i
$474$		0			0
$475$	−1.97997e12			−1.78459
$476$	1.62802e11	+	3.40611e10i	0.145354	+	0.0304108i
$477$		0			0
$478$	3.35579e11	+	5.81240e11i	0.294015	+	0.509248i
$479$	5.76669e11	−	9.98820e11i	0.500515	−	0.866917i	−0.499485	−	0.866322i	$-0.666478\pi$
$479$	5.76669e11	−	9.98820e11i	0.500515	−	0.866917i	1.00000		0.000594242i	$-0.000189153\pi$
$480$		0			0
$481$	−3.09670e11	−	5.36364e11i	−0.263783	−	0.456885i
$482$	2.81594e11			0.237636
$483$		0			0
$484$	−1.98128e11			−0.164112
$485$	−1.02537e11	−	1.77599e11i	−0.0841479	−	0.145748i
$486$		0			0
$487$	9.72094e11	−	1.68372e12i	0.783120	−	1.35640i	−0.146996	−	0.989137i	$-0.546961\pi$
$487$	9.72094e11	−	1.68372e12i	0.783120	−	1.35640i	0.930116	−	0.367266i	$-0.119706\pi$
$488$	4.51824e10	+	7.82582e10i	0.0360645	+	0.0624655i
$489$		0			0
$490$	−1.83479e12	−	8.02887e11i	−1.43782	−	0.629176i
$491$	7.04431e9			0.00546980			0.00273490	−	0.999996i	$-0.499129\pi$
$491$	7.04431e9			0.00546980			0.00273490	+	0.999996i	$0.499129\pi$
$492$		0			0
$493$	6.83056e11	−	1.18309e12i	0.520769	−	0.901999i
$494$	4.30903e11	−	7.46346e11i	0.325543	−	0.563857i
$495$		0			0
$496$	−8.80670e10			−0.0653350
$497$	−1.05927e12	+	1.18403e12i	−0.778762	+	0.870481i
$498$		0			0
$499$	−3.49974e10	−	6.06172e10i	−0.0252687	−	0.0437667i	0.853115	−	0.521724i	$-0.174711\pi$
$499$	−3.49974e10	−	6.06172e10i	−0.0252687	−	0.0437667i	−0.878383	+	0.477957i	$0.841377\pi$
$500$	−1.82727e10	+	3.16493e10i	−0.0130749	+	0.0226464i
$501$		0			0
$502$	3.29286e11	+	5.70340e11i	0.231423	+	0.400837i
$503$	2.76650e12			1.92697			0.963484	−	0.267766i	$-0.0862855\pi$
$503$	2.76650e12			1.92697			0.963484	+	0.267766i	$0.0862855\pi$
$504$		0			0
$505$	2.14888e12			1.47028
$506$	2.02900e11	+	3.51433e11i	0.137596	+	0.238322i
$507$		0			0
$508$	−6.55164e10	+	1.13478e11i	−0.0436479	+	0.0756003i
$509$	4.88478e11	+	8.46068e11i	0.322563	+	0.558696i	0.981016	−	0.193926i	$-0.0621222\pi$
$509$	4.88478e11	+	8.46068e11i	0.322563	+	0.558696i	−0.658453	+	0.752622i	$0.728789\pi$
$510$		0			0
$511$	−9.20863e10	−	2.80360e11i	−0.0597449	−	0.181896i
$512$	9.98363e11			0.642057
$513$		0			0
$514$	4.37944e11	−	7.58541e11i	0.276748	−	0.479342i
$515$	5.12230e11	−	8.87208e11i	0.320872	−	0.555767i
$516$		0			0
$517$	−2.38944e11			−0.147092
$518$	−7.81548e11	−	2.37945e12i	−0.476949	−	1.45209i
$519$		0			0
$520$	4.05642e11	+	7.02592e11i	0.243292	+	0.421394i
$521$	5.65660e11	−	9.79751e11i	0.336345	−	0.582567i	−0.647397	−	0.762153i	$-0.724142\pi$
$521$	5.65660e11	−	9.79751e11i	0.336345	−	0.582567i	0.983742	+	0.179586i	$0.0574757\pi$
$522$		0			0
$523$	1.54001e12	+	2.66738e12i	0.900050	+	1.55893i	0.827428	+	0.561572i	$0.189803\pi$
$523$	1.54001e12	+	2.66738e12i	0.900050	+	1.55893i	0.0726222	+	0.997360i	$0.476863\pi$
$524$	1.78109e10			0.0103204
$525$		0			0
$526$	−3.24859e12			−1.85037
$527$	−4.44540e10	−	7.69966e10i	−0.0251052	−	0.0434834i
$528$		0			0
$529$	−9.68084e11	+	1.67677e12i	−0.537480	+	0.930943i
$530$	1.05131e12	+	1.82092e12i	0.578747	+	1.00242i
$531$		0			0
$532$	3.36603e11	−	3.76246e11i	0.182186	−	0.203643i
$533$	4.95019e11			0.265674
$534$		0			0
$535$	−1.91401e9	+	3.31517e9i	−0.00101007	+	0.00174950i
$536$	−1.31264e12	+	2.27356e12i	−0.686918	+	1.18978i
$537$		0			0
$538$	1.78329e12			0.917701
$539$	−3.17141e11	−	1.38778e11i	−0.161847	−	0.0708226i
$540$		0			0
$541$	1.39651e12	+	2.41883e12i	0.700901	+	1.21400i	0.968151	+	0.250369i	$0.0805518\pi$
$541$	1.39651e12	+	2.41883e12i	0.700901	+	1.21400i	−0.267250	+	0.963627i	$0.586115\pi$
$542$	5.06111e11	−	8.76611e11i	0.251912	−	0.436325i
$543$		0			0
$544$	−3.00242e11	−	5.20034e11i	−0.146986	−	0.254587i
$545$	−2.15908e11			−0.104830
$546$		0			0
$547$	1.47553e12			0.704700			0.352350	−	0.935868i	$-0.385383\pi$
$547$	1.47553e12			0.704700			0.352350	+	0.935868i	$0.385383\pi$
$548$	−2.55439e11	−	4.42434e11i	−0.120997	−	0.209573i
$549$		0			0
$550$	−2.26793e11	+	3.92817e11i	−0.105681	+	0.183045i
$551$	−2.07323e12	−	3.59094e12i	−0.958220	−	1.65969i
$552$		0			0
$553$	6.88418e11	+	1.44030e11i	0.313032	+	0.0654920i
$554$	3.96062e12			1.78636
$555$		0			0
$556$	−6.66245e10	+	1.15397e11i	−0.0295663	+	0.0512104i
$557$	1.10846e12	−	1.91990e12i	0.487944	−	0.845144i	−0.511960	−	0.859010i	$-0.671080\pi$
$557$	1.10846e12	−	1.91990e12i	0.487944	−	0.845144i	0.999904	+	0.0138652i	$0.00441356\pi$
$558$		0			0
$559$	−4.43614e11			−0.192155
$560$	1.20231e12	+	3.66048e12i	0.516619	+	1.57287i
$561$		0			0
$562$	−1.71209e12	−	2.96543e12i	−0.723957	−	1.25393i
$563$	3.26827e11	−	5.66082e11i	0.137098	−	0.237460i	−0.789299	−	0.614009i	$-0.789556\pi$
$563$	3.26827e11	−	5.66082e11i	0.137098	−	0.237460i	0.926397	+	0.376549i	$0.122889\pi$
$564$		0			0
$565$	−2.44192e12	−	4.22953e12i	−1.00812	−	1.74612i
$566$	−4.33860e12			−1.77695
$567$		0			0
$568$	2.60244e12			1.04909
$569$	1.29888e12	+	2.24973e12i	0.519474	+	0.899756i	0.999744	+	0.0226349i	$0.00720553\pi$
$569$	1.29888e12	+	2.24973e12i	0.519474	+	0.899756i	−0.480269	+	0.877121i	$0.659461\pi$
$570$		0			0
$571$	5.19555e11	−	8.99896e11i	0.204536	−	0.354266i	−0.745449	−	0.666563i	$-0.767765\pi$
$571$	5.19555e11	−	8.99896e11i	0.204536	−	0.354266i	0.949985	+	0.312296i	$0.101098\pi$
$572$	−1.42998e10	−	2.47679e10i	−0.00558530	−	0.00967402i
$573$		0			0
$574$	1.95936e12	+	4.09933e11i	0.753373	+	0.157619i
$575$	−4.17742e12			−1.59369
$576$		0			0
$577$	−2.33010e11	+	4.03585e11i	−0.0875152	+	0.151581i	−0.906460	−	0.422291i	$-0.861226\pi$
$577$	−2.33010e11	+	4.03585e11i	−0.0875152	+	0.151581i	0.818945	+	0.573872i	$0.194559\pi$
$578$	−3.35887e11	+	5.81773e11i	−0.125175	+	0.216809i
$579$		0			0
$580$	−7.96085e11			−0.292101
$581$	1.19359e12	−	1.33416e12i	0.434572	−	0.485754i
$582$		0			0
$583$	1.81718e11	+	3.14744e11i	0.0651461	+	0.112836i
$584$	−2.41697e11	+	4.18631e11i	−0.0859832	+	0.148927i
$585$		0			0
$586$	2.02738e12	+	3.51153e12i	0.710226	+	1.23015i
$587$	−5.17776e12			−1.79999			−0.899996	−	0.435897i	$-0.856431\pi$
$587$	−5.17776e12			−1.79999			−0.899996	+	0.435897i	$0.856431\pi$
$588$		0			0
$589$	−2.69856e11			−0.0923874
$590$	−5.82267e10	−	1.00852e11i	−0.0197828	−	0.0342649i
$591$		0			0
$592$	−2.40907e12	+	4.17263e12i	−0.806123	+	1.39625i
$593$	1.94396e12	+	3.36705e12i	0.645568	+	1.11816i	0.984170	+	0.177227i	$0.0567128\pi$
$593$	1.94396e12	+	3.36705e12i	0.645568	+	1.11816i	−0.338601	+	0.940930i	$0.609954\pi$
$594$		0			0
$595$	−2.59344e12	+	2.89889e12i	−0.848302	+	0.948212i
$596$	5.30883e10			0.0172342
$597$		0			0
$598$	9.09136e11	−	1.57467e12i	0.290719	−	0.503540i
$599$	3.53757e11	−	6.12726e11i	0.112275	−	0.194467i	−0.804412	−	0.594072i	$-0.797519\pi$
$599$	3.53757e11	−	6.12726e11i	0.112275	−	0.194467i	0.916687	+	0.399605i	$0.130853\pi$
$600$		0			0
$601$	−3.16274e12			−0.988845			−0.494422	−	0.869222i	$-0.664620\pi$
$601$	−3.16274e12			−0.988845			−0.494422	+	0.869222i	$0.664620\pi$
$602$	−1.75589e12	−	3.67364e11i	−0.544895	−	0.114002i
$603$		0			0
$604$	−4.57281e10	−	7.92034e10i	−0.0139803	−	0.0242146i
$605$	2.31668e12	−	4.01260e12i	0.703018	−	1.21766i
$606$		0			0
$607$	−1.94652e12	−	3.37148e12i	−0.581983	−	1.00802i	−0.995244	−	0.0974119i	$-0.968944\pi$
$607$	−1.94652e12	−	3.37148e12i	−0.581983	−	1.00802i	0.413261	−	0.910613i	$-0.364390\pi$
$608$	−1.82260e12			−0.540911
$609$		0			0
$610$	4.30991e11			0.126033
$611$	5.35319e11	+	9.27200e11i	0.155392	+	0.269146i
$612$		0			0
$613$	3.04157e12	−	5.26815e12i	0.870012	−	1.50691i	0.00802931	−	0.999968i	$-0.497444\pi$
$613$	3.04157e12	−	5.26815e12i	0.870012	−	1.50691i	0.861983	−	0.506937i	$-0.169223\pi$
$614$	2.60381e12	+	4.50992e12i	0.739351	+	1.28059i
$615$		0			0
$616$	1.76956e11	+	5.38751e11i	0.0495169	+	0.150756i
$617$	5.40996e12			1.50283			0.751416	−	0.659829i	$-0.229371\pi$
$617$	5.40996e12			1.50283			0.751416	+	0.659829i	$0.229371\pi$
$618$		0			0
$619$	6.49701e11	−	1.12531e12i	0.177871	−	0.308082i	−0.763280	−	0.646068i	$-0.776412\pi$
$619$	6.49701e11	−	1.12531e12i	0.177871	−	0.308082i	0.941151	+	0.337986i	$0.109746\pi$
$620$	−2.59050e10	+	4.48688e10i	−0.00704078	+	0.0121950i
$621$		0			0
$622$	−3.88733e12			−1.04135
$623$	1.81159e12	+	3.79018e11i	0.481797	+	0.100801i
$624$		0			0
$625$	1.68290e12	+	2.91487e12i	0.441162	+	0.764115i
$626$	−3.63752e12	+	6.30038e12i	−0.946720	+	1.63977i
$627$		0			0
$628$	1.60292e11	+	2.77635e11i	0.0411239	+	0.0712287i
$629$	−4.86415e12			−1.23902
$630$		0			0
$631$	−3.33319e12			−0.837004			−0.418502	−	0.908216i	$-0.637445\pi$
$631$	−3.33319e12			−0.837004			−0.418502	+	0.908216i	$0.637445\pi$
$632$	−5.76053e11	−	9.97753e11i	−0.143627	−	0.248769i
$633$		0			0
$634$	−1.87575e12	+	3.24889e12i	−0.461076	+	0.798607i
$635$	−1.53215e12	−	2.65376e12i	−0.373954	−	0.647708i
$636$		0			0
$637$	1.71993e11	+	1.54155e12i	0.0413890	+	0.370963i
$638$	−9.49900e11			−0.226979
$639$		0			0
$640$	3.62431e12	−	6.27749e12i	0.853917	−	1.47903i
$641$	9.73337e11	−	1.68587e12i	0.227721	−	0.394424i	−0.729412	−	0.684075i	$-0.760206\pi$
$641$	9.73337e11	−	1.68587e12i	0.227721	−	0.394424i	0.957132	+	0.289651i	$0.0935394\pi$
$642$		0			0
$643$	−1.31531e12			−0.303443			−0.151722	−	0.988423i	$-0.548482\pi$
$643$	−1.31531e12			−0.303443			−0.151722	+	0.988423i	$0.548482\pi$
$644$	7.10177e11	−	7.93819e11i	0.162697	−	0.181859i
$645$		0			0
$646$	−3.38421e12	−	5.86162e12i	−0.764558	−	1.32425i
$647$	−3.35402e12	+	5.80933e12i	−0.752483	+	1.30334i	0.194134	+	0.980975i	$0.437810\pi$
$647$	−3.35402e12	+	5.80933e12i	−0.752483	+	1.30334i	−0.946616	+	0.322363i	$0.895523\pi$
$648$		0			0
$649$	−1.00644e10	−	1.74321e10i	−0.00222684	−	0.00385699i
$650$	2.03239e12			0.446577
$651$		0			0
$652$	1.14099e12			0.247268
$653$	−3.93686e12	−	6.81883e12i	−0.847306	−	1.46758i	−0.883604	−	0.468236i	$-0.844890\pi$
$653$	−3.93686e12	−	6.81883e12i	−0.847306	−	1.46758i	0.0362978	−	0.999341i	$-0.488444\pi$
$654$		0			0
$655$	−2.08261e11	+	3.60718e11i	−0.0442101	+	0.0765741i
$656$	−1.92549e12	−	3.33505e12i	−0.405952	−	0.703129i
$657$		0			0
$658$	1.35104e12	+	4.11330e12i	0.280965	+	0.855410i
$659$	−8.22995e12			−1.69986			−0.849929	−	0.526897i	$-0.823356\pi$
$659$	−8.22995e12			−1.69986			−0.849929	+	0.526897i	$0.823356\pi$
$660$		0			0
$661$	−2.84912e12	+	4.93481e12i	−0.580502	+	1.00546i	0.414918	+	0.909859i	$0.363810\pi$
$661$	−2.84912e12	+	4.93481e12i	−0.580502	+	1.00546i	−0.995420	+	0.0955999i	$0.969523\pi$
$662$	2.99595e12	−	5.18913e12i	0.606280	−	1.05011i
$663$		0			0
$664$	−2.93243e12			−0.585425
$665$	3.68413e12	+	1.12165e13i	0.730529	+	2.22412i
$666$		0			0
$667$	−4.37418e12	−	7.57630e12i	−0.855718	−	1.48215i
$668$	2.67043e11	−	4.62532e11i	0.0518904	−	0.0898768i
$669$		0			0
$670$	6.26060e12	+	1.08437e13i	1.20027	+	2.07893i
$671$	7.44964e10			0.0141868
$672$		0			0
$673$	9.28143e12			1.74400			0.872002	−	0.489503i	$-0.162822\pi$
$673$	9.28143e12			1.74400			0.872002	+	0.489503i	$0.162822\pi$
$674$	−6.07156e11	−	1.05162e12i	−0.113326	−	0.196287i
$675$		0			0
$676$	3.95803e11	−	6.85552e11i	0.0728986	−	0.126264i
$677$	6.45102e11	+	1.11735e12i	0.118026	+	0.204428i	0.918986	−	0.394291i	$-0.129010\pi$
$677$	6.45102e11	+	1.11735e12i	0.118026	+	0.204428i	−0.800959	+	0.598719i	$0.795677\pi$
$678$		0			0
$679$	−4.28238e11	+	4.78674e11i	−0.0773163	+	0.0864223i
$680$	6.37162e12			1.14277
$681$		0			0
$682$	−3.09102e10	+	5.35381e10i	−0.00547107	+	0.00947618i
$683$	1.27194e11	−	2.20307e11i	0.0223653	−	0.0387379i	−0.854626	−	0.519244i	$-0.826214\pi$
$683$	1.27194e11	−	2.20307e11i	0.0223653	−	0.0387379i	0.876991	+	0.480506i	$0.159547\pi$
$684$		0			0
$685$	1.19473e13			2.07329
$686$	−5.95811e11	+	6.24413e12i	−0.102719	+	1.07650i
$687$		0			0
$688$	1.72554e12	+	2.98872e12i	0.293614	+	0.508555i
$689$	8.14225e11	−	1.41028e12i	0.137644	−	0.238407i
$690$		0			0
$691$	7.84952e11	+	1.35958e12i	0.130976	+	0.226857i	0.924053	−	0.382264i	$-0.124856\pi$
$691$	7.84952e11	+	1.35958e12i	0.130976	+	0.226857i	−0.793077	+	0.609121i	$0.791522\pi$
$692$	1.34227e12			0.222516
$693$		0			0
$694$	−7.44235e12			−1.21785
$695$	−1.55806e12	−	2.69864e12i	−0.253310	−	0.438746i
$696$		0			0
$697$	1.94388e12	−	3.36689e12i	0.311976	−	0.540359i
$698$	6.08054e12	+	1.05318e13i	0.969600	+	1.67940i
$699$		0			0
$700$	1.16533e12	+	2.43807e11i	0.183445	+	0.0383800i
$701$	8.33084e12			1.30304			0.651520	−	0.758632i	$-0.274132\pi$
$701$	8.33084e12			1.30304			0.651520	+	0.758632i	$0.274132\pi$
$702$		0			0
$703$	−7.38189e12	+	1.27858e13i	−1.13990	+	1.97437i
$704$	4.47934e11	−	7.75844e11i	0.0687285	−	0.119041i
$705$		0			0
$706$	4.31753e12			0.654056
$707$	−2.10016e12	−	6.39402e12i	−0.316129	−	0.962468i
$708$		0			0
$709$	−1.16510e12	−	2.01801e12i	−0.173163	−	0.299926i	0.766361	−	0.642410i	$-0.222065\pi$
$709$	−1.16510e12	−	2.01801e12i	−0.173163	−	0.299926i	−0.939524	+	0.342483i	$0.888732\pi$
$710$	6.20613e12	−	1.07493e13i	0.916554	−	1.58752i
$711$		0			0
$712$	−1.51590e12	−	2.62562e12i	−0.221060	−	0.382888i
$713$	−5.69352e11			−0.0825046
$714$		0			0
$715$	6.68820e11			0.0957044
$716$	−1.72483e11	−	2.98750e11i	−0.0245267	−	0.0424814i
$717$		0			0
$718$	2.13509e12	−	3.69809e12i	0.299817	−	0.519299i
$719$	−7.83347e11	−	1.35680e12i	−0.109314	−	0.189337i	0.806179	−	0.591672i	$-0.201532\pi$
$719$	−7.83347e11	−	1.35680e12i	−0.109314	−	0.189337i	−0.915492	+	0.402335i	$0.868199\pi$
$720$		0			0
$721$	−3.14052e12	−	6.57054e11i	−0.432806	−	0.0905508i
$722$	−1.26478e13			−1.73220
$723$		0			0
$724$	1.16632e12	−	2.02013e12i	0.157759	−	0.273247i
$725$	4.88927e12	−	8.46847e12i	0.657239	−	1.13837i
$726$		0			0
$727$	2.09663e11			0.0278367			0.0139183	−	0.999903i	$-0.495570\pi$
$727$	2.09663e11			0.0278367			0.0139183	+	0.999903i	$0.495570\pi$
$728$	1.69413e12	−	1.89366e12i	0.223540	−	0.249868i
$729$		0			0
$730$	1.15276e12	+	1.99665e12i	0.150241	+	0.260225i
$731$	−1.74202e12	+	3.01726e12i	−0.225644	+	0.390827i
$732$		0			0
$733$	−4.07588e12	−	7.05962e12i	−0.521498	−	0.903262i	−0.999687	−	0.0250047i	$-0.992040\pi$
$733$	−4.07588e12	−	7.05962e12i	−0.521498	−	0.903262i	0.478189	−	0.878257i	$-0.341293\pi$
$734$	−9.49438e12			−1.20735
$735$		0			0
$736$	−3.84540e12			−0.483049
$737$	1.08214e12	+	1.87432e12i	0.135107	+	0.234013i
$738$		0			0
$739$	3.82789e12	−	6.63011e12i	0.472128	−	0.817750i	−0.527363	−	0.849640i	$-0.676819\pi$
$739$	3.82789e12	−	6.63011e12i	0.472128	−	0.817750i	0.999491	+	0.0318898i	$0.0101526\pi$
$740$	1.41726e12	+	2.45477e12i	0.173743	+	0.300931i
$741$		0			0
$742$	4.39070e12	−	4.90782e12i	0.531761	−	0.594390i
$743$	7.82269e12			0.941686			0.470843	−	0.882217i	$-0.343950\pi$
$743$	7.82269e12			0.941686			0.470843	+	0.882217i	$0.343950\pi$
$744$		0			0
$745$	−6.20754e11	+	1.07518e12i	−0.0738272	+	0.127872i
$746$	7.41284e12	−	1.28394e13i	0.876314	−	1.51782i
$747$		0			0
$748$	−2.24614e11			−0.0262349
$749$	1.17350e10	+	2.45517e9i	0.00136243	+	0.000285045i
$750$		0			0
$751$	−5.68288e12	−	9.84304e12i	−0.651912	−	1.12914i	−0.982658	−	0.185425i	$-0.940634\pi$
$751$	−5.68288e12	−	9.84304e12i	−0.651912	−	1.12914i	0.330747	−	0.943720i	$-0.392699\pi$
$752$	4.16450e12	−	7.21313e12i	0.474879	−	0.822514i
$753$		0			0
$754$	2.12812e12	+	3.68601e12i	0.239786	+	0.415322i
$755$	2.13877e12			0.239554
$756$		0			0
$757$	−1.15682e13			−1.28037			−0.640184	−	0.768222i	$-0.721142\pi$
$757$	−1.15682e13			−1.28037			−0.640184	+	0.768222i	$0.721142\pi$
$758$	6.54187e12	+	1.13308e13i	0.719764	+	1.24667i
$759$		0			0
$760$	9.66966e12	−	1.67483e13i	1.05136	−	1.82100i
$761$	1.05812e12	+	1.83272e12i	0.114368	+	0.198091i	0.917527	−	0.397674i	$-0.130182\pi$
$761$	1.05812e12	+	1.83272e12i	0.114368	+	0.198091i	−0.803159	+	0.595765i	$0.796849\pi$
$762$		0			0
$763$	2.11013e11	+	6.42439e11i	0.0225398	+	0.0686233i
$764$	−1.50598e11			−0.0159919
$765$		0			0
$766$	−3.08813e12	+	5.34880e12i	−0.324091	+	0.561342i
$767$	−4.50959e10	+	7.81083e10i	−0.00470498	+	0.00814926i
$768$		0			0
$769$	2.61186e12			0.269328			0.134664	−	0.990891i	$-0.457005\pi$
$769$	2.61186e12			0.269328			0.134664	+	0.990891i	$0.457005\pi$
$770$	2.64729e12	+	5.53861e11i	0.271390	+	0.0567797i
$771$		0			0
$772$	−6.33923e11	−	1.09799e12i	−0.0642331	−	0.111255i
$773$	−4.15174e12	+	7.19102e12i	−0.418237	+	0.724407i	−0.995762	−	0.0919653i	$-0.970685\pi$
$773$	−4.15174e12	+	7.19102e12i	−0.418237	+	0.724407i	0.577525	+	0.816373i	$0.304018\pi$
$774$		0			0
$775$	−3.18199e11	−	5.51137e11i	−0.0316841	−	0.0548784i
$776$	1.05210e12			0.104155
$777$		0			0
$778$	2.03991e12			0.199620
$779$	−5.90011e12	−	1.02193e13i	−0.574039	−	0.994265i
$780$		0			0
$781$	1.07272e12	−	1.85801e12i	0.103171	−	0.178698i
$782$	−7.14013e12	−	1.23671e13i	−0.682772	−	1.18260i
$783$		0			0
$784$	9.71677e12	−	7.15499e12i	0.918543	−	0.676374i
$785$	−7.49710e12			−0.704661
$786$		0			0
$787$	−4.23933e12	+	7.34274e12i	−0.393923	+	0.682295i	−0.992963	−	0.118424i	$-0.962216\pi$
$787$	−4.23933e12	+	7.34274e12i	−0.393923	+	0.682295i	0.599040	+	0.800719i	$0.295549\pi$
$788$	−1.90881e11	+	3.30615e11i	−0.0176357	+	0.0305460i
$789$		0			0
$790$	−5.49492e12			−0.501926
$791$	−1.01985e13	+	1.13996e13i	−0.926278	+	1.03537i
$792$		0			0
$793$	−1.66899e11	−	2.89077e11i	−0.0149873	−	0.0259588i
$794$	1.38740e12	−	2.40304e12i	0.123882	−	0.214570i
$795$		0			0
$796$	1.53021e12	+	2.65041e12i	0.135096	+	0.233993i
$797$	8.15126e12			0.715587			0.357794	−	0.933801i	$-0.383529\pi$
$797$	8.15126e12			0.715587			0.357794	+	0.933801i	$0.383529\pi$
$798$		0			0
$799$	8.40853e12			0.729894
$800$	−2.14911e12	−	3.72237e12i	−0.185504	−	0.321303i
$801$		0			0
$802$	−6.28203e12	+	1.08808e13i	−0.536186	+	0.928701i
$803$	1.99254e11	+	3.45119e11i	0.0169117	+	0.0292920i
$804$		0			0
$805$	7.77292e12	+	2.36650e13i	0.652383	+	1.98621i
$806$	2.77000e11			0.0231192
$807$		0			0
$808$	−5.51224e12	+	9.54749e12i	−0.454964	+	0.788021i
$809$	−1.95100e12	+	3.37922e12i	−0.160136	+	0.277363i	−0.934917	−	0.354866i	$-0.884526\pi$
$809$	−1.95100e12	+	3.37922e12i	−0.160136	+	0.277363i	0.774782	+	0.632229i	$0.217860\pi$
$810$		0			0
$811$	−1.54921e13			−1.25752			−0.628761	−	0.777598i	$-0.716438\pi$
$811$	−1.54921e13			−1.25752			−0.628761	+	0.777598i	$0.716438\pi$
$812$	7.78037e11	+	2.36876e12i	0.0628055	+	0.191214i
$813$		0			0
$814$	1.69110e12	+	2.92906e12i	0.135008	+	0.233840i
$815$	−1.33414e13	+	2.31080e13i	−1.05924	+	1.83465i
$816$		0			0
$817$	5.28742e12	+	9.15808e12i	0.415188	+	0.719126i
$818$	−1.89659e13			−1.48110
$819$		0			0
$820$	−2.26554e12			−0.174988
$821$	−3.37626e12	−	5.84785e12i	−0.259353	−	0.449213i	0.706716	−	0.707498i	$-0.250176\pi$
$821$	−3.37626e12	−	5.84785e12i	−0.259353	−	0.449213i	−0.966069	+	0.258285i	$0.916843\pi$
$822$		0			0
$823$	−9.11164e11	+	1.57818e12i	−0.0692305	+	0.119911i	−0.898563	−	0.438845i	$-0.855388\pi$
$823$	−9.11164e11	+	1.57818e12i	−0.0692305	+	0.119911i	0.829332	+	0.558756i	$0.188721\pi$
$824$	2.62792e12	+	4.55169e12i	0.198582	+	0.343954i
$825$		0			0
$826$	−2.43179e11	+	2.71820e11i	−0.0181767	+	0.0203175i
$827$	2.37120e13			1.76276			0.881382	−	0.472404i	$-0.156614\pi$
$827$	2.37120e13			1.76276			0.881382	+	0.472404i	$0.156614\pi$
$828$		0			0
$829$	9.38126e12	−	1.62488e13i	0.689868	−	1.19489i	−0.282013	−	0.959411i	$-0.591002\pi$
$829$	9.38126e12	−	1.62488e13i	0.689868	−	1.19489i	0.971880	−	0.235475i	$-0.0756646\pi$
$830$	−6.99305e12	+	1.21123e13i	−0.511464	+	0.885882i
$831$		0			0
$832$	−4.01412e12			−0.290426
$833$	1.11603e13	+	4.88367e12i	0.803110	+	0.351434i
$834$		0			0
$835$	6.24499e12	+	1.08166e13i	0.444573	+	0.770022i
$836$	−3.40876e11	+	5.90415e11i	−0.0241362	+	0.0418051i
$837$		0			0
$838$	−1.19098e13	−	2.06284e13i	−0.834272	−	1.44500i
$839$	5.63044e12			0.392296			0.196148	−	0.980574i	$-0.437157\pi$
$839$	5.63044e12			0.392296			0.196148	+	0.980574i	$0.437157\pi$
$840$		0			0
$841$	5.97112e12			0.411599
$842$	−1.00880e13	−	1.74730e13i	−0.691675	−	1.19802i
$843$		0			0
$844$	−4.68889e11	+	8.12139e11i	−0.0318074	+	0.0550921i
$845$	9.25614e12	+	1.60321e13i	0.624561	+	1.08177i
$846$		0			0
$847$	−1.42037e13	−	2.97168e12i	−0.948258	−	0.198393i
$848$	−1.26685e13			−0.841285
$849$		0			0
$850$	7.98094e12	−	1.38234e13i	0.524407	−	0.908300i
$851$	−1.55746e13	+	2.69760e13i	−1.01797	+	1.76317i
$852$		0			0
$853$	2.09580e13			1.35544			0.677719	−	0.735321i	$-0.262968\pi$
$853$	2.09580e13			1.35544			0.677719	+	0.735321i	$0.262968\pi$
$854$	−4.21220e11	−	1.28242e12i	−0.0270987	−	0.0825031i
$855$		0			0
$856$	−9.81957e9	−	1.70080e10i	−0.000625116	−	0.00108273i
$857$	5.40299e12	−	9.35825e12i	0.342153	−	0.592626i	−0.642679	−	0.766135i	$-0.722177\pi$
$857$	5.40299e12	−	9.35825e12i	0.342153	−	0.592626i	0.984832	+	0.173509i	$0.0555106\pi$
$858$		0			0
$859$	4.86016e12	+	8.41804e12i	0.304566	+	0.527524i	0.977165	−	0.212484i	$-0.0681553\pi$
$859$	4.86016e12	+	8.41804e12i	0.304566	+	0.527524i	−0.672599	+	0.740007i	$0.734822\pi$
$860$	2.03028e12			0.126565
$861$		0			0
$862$	−1.08690e13			−0.670512
$863$	−8.16020e12	−	1.41339e13i	−0.500786	−	0.867387i	−1.00000		0.000907842i	$-0.999711\pi$
$863$	−8.16020e12	−	1.41339e13i	−0.500786	−	0.867387i	0.499214	−	0.866479i	$-0.333622\pi$
$864$		0			0
$865$	−1.56949e13	+	2.71844e13i	−0.953206	+	1.65100i
$866$	9.26246e12	+	1.60431e13i	0.559623	+	0.969296i
$867$		0			0
$868$	1.58826e11	+	3.32292e10i	0.00949689	+	0.00198692i
$869$	−9.49793e11			−0.0564989
$870$		0			0
$871$	4.84875e12	−	8.39829e12i	0.285462	−	0.494435i
$872$	5.53843e11	−	9.59284e11i	0.0324386	−	0.0561853i
$873$		0			0
$874$	−4.33438e13			−2.51261
$875$	−1.78467e12	+	1.99486e12i	−0.102925	+	0.115047i
$876$		0			0
$877$	1.01234e13	+	1.75342e13i	0.577867	+	1.00089i	0.995724	+	0.0923817i	$0.0294480\pi$
$877$	1.01234e13	+	1.75342e13i	0.577867	+	1.00089i	−0.417857	+	0.908513i	$0.637219\pi$
$878$	1.23555e12	−	2.14004e12i	0.0701674	−	0.121534i
$879$		0			0
$880$	−2.60153e12	−	4.50599e12i	−0.146237	−	0.253290i
$881$	1.15345e13			0.645072			0.322536	−	0.946557i	$-0.395465\pi$
$881$	1.15345e13			0.645072			0.322536	+	0.946557i	$0.395465\pi$
$882$		0			0
$883$	1.65115e13			0.914035			0.457017	−	0.889458i	$-0.348918\pi$
$883$	1.65115e13			0.914035			0.457017	+	0.889458i	$0.348918\pi$
$884$	5.03215e11	+	8.71593e11i	0.0277152	+	0.0480041i
$885$		0			0
$886$	−8.89201e12	+	1.54014e13i	−0.484784	+	0.839670i
$887$	−9.41136e12	−	1.63010e13i	−0.510500	−	0.884213i	−0.999926	−	0.0121677i	$-0.996127\pi$
$887$	−9.41136e12	−	1.63010e13i	−0.510500	−	0.884213i	0.489425	−	0.872045i	$-0.337207\pi$
$888$		0			0
$889$	−6.39888e12	+	7.15252e12i	−0.343595	+	0.384062i
$890$	−1.44601e13			−0.772530
$891$		0			0
$892$	−1.39571e12	+	2.41745e12i	−0.0738167	+	0.127854i
$893$	1.27609e13	−	2.21025e13i	0.671506	−	1.16308i
$894$		0			0
$895$	8.06729e12			0.420266
$896$	−2.22209e13	−	4.64902e12i	−1.15180	−	0.240977i
$897$		0			0
$898$	2.26840e12	+	3.92899e12i	0.116406	+	0.201622i
$899$	6.66373e11	−	1.15419e12i	0.0340251	−	0.0589331i
$900$		0			0
$901$	−6.39472e12	−	1.10760e13i	−0.323266	−	0.559913i
$902$	−2.70328e12			−0.135976
$903$		0			0
$904$	2.50558e13			1.24782
$905$	2.72753e13	+	4.72422e13i	1.35161	+	2.34105i
$906$		0			0
$907$	1.05352e13	−	1.82476e13i	0.516906	−	0.895308i	−0.482901	−	0.875675i	$-0.660417\pi$
$907$	1.05352e13	−	1.82476e13i	0.516906	−	0.895308i	0.999807	−	0.0196327i	$-0.00624968\pi$
$908$	−3.90630e11	−	6.76590e11i	−0.0190712	−	0.0330323i
$909$		0			0
$910$	−3.78166e12	−	1.15134e13i	−0.182809	−	0.556568i
$911$	1.97328e13			0.949198			0.474599	−	0.880202i	$-0.342593\pi$
$911$	1.97328e13			0.949198			0.474599	+	0.880202i	$0.342593\pi$
$912$		0			0
$913$	−1.20874e12	+	2.09360e12i	−0.0575725	+	0.0997186i
$914$	−1.09906e13	+	1.90363e13i	−0.520912	+	0.902246i
$915$		0			0
$916$	4.02281e12			0.188799
$917$	1.27686e12	+	2.67143e11i	0.0596323	+	0.0124762i
$918$		0			0
$919$	−1.24173e13	−	2.15074e13i	−0.574259	−	0.994645i	−0.996122	−	0.0879858i	$-0.971957\pi$
$919$	−1.24173e13	−	2.15074e13i	−0.574259	−	0.994645i	0.421863	−	0.906660i	$-0.361376\pi$
$920$	2.04014e13	−	3.53363e13i	0.938891	−	1.62621i
$921$		0			0
$922$	8.03703e12	+	1.39205e13i	0.366274	+	0.634406i
$923$	−9.61314e12			−0.435971
$924$		0			0
$925$	−3.48172e13			−1.56371
$926$	9.01512e12	+	1.56146e13i	0.402923	+	0.697883i
$927$		0			0
$928$	4.50067e12	−	7.79540e12i	0.199210	−	0.345042i
$929$	−1.81790e13	−	3.14869e13i	−0.800754	−	1.38695i	−0.919121	−	0.393976i	$-0.871099\pi$
$929$	−1.81790e13	−	3.14869e13i	−0.800754	−	1.38695i	0.118367	−	0.992970i	$-0.462234\pi$
$930$		0			0
$931$	2.97742e13	−	2.19244e13i	1.29887	−	0.956431i
$932$	3.77583e12			0.163923
$933$		0			0
$934$	9.72105e12	−	1.68373e13i	0.417977	−	0.723957i
$935$	2.62637e12	−	4.54901e12i	0.112384	−	0.194655i
$936$		0			0
$937$	9.42112e12			0.399277			0.199639	−	0.979870i	$-0.436023\pi$
$937$	9.42112e12			0.399277			0.199639	+	0.979870i	$0.436023\pi$
$938$	2.61469e13	−	2.92263e13i	1.10283	−	1.23271i
$939$		0			0
$940$	−2.44998e12	−	4.24350e12i	−0.102350	−	0.177275i
$941$	−1.16425e13	+	2.01654e13i	−0.484054	+	0.838406i	−0.999832	−	0.0183158i	$-0.994170\pi$
$941$	−1.16425e13	+	2.01654e13i	−0.484054	+	0.838406i	0.515778	+	0.856722i	$0.327503\pi$
$942$		0			0
$943$	−1.24483e13	−	2.15610e13i	−0.512633	−	0.887906i
$944$	7.01644e11			0.0287570
$945$		0			0
$946$	2.42256e12			0.0983477
$947$	−1.01843e13	−	1.76397e13i	−0.411488	−	0.712717i	0.583565	−	0.812066i	$-0.301657\pi$
$947$	−1.01843e13	−	1.76397e13i	−0.411488	−	0.712717i	−0.995053	+	0.0993491i	$0.968324\pi$
$948$		0			0
$949$	8.92802e11	−	1.54638e12i	0.0357320	−	0.0618896i
$950$	−2.42239e13	−	4.19571e13i	−0.964914	−	1.67128i
$951$		0			0
$952$	−6.22717e12	−	1.89589e13i	−0.245711	−	0.748077i
$953$	−2.26713e13			−0.890344			−0.445172	−	0.895445i	$-0.646857\pi$
$953$	−2.26713e13			−0.890344			−0.445172	+	0.895445i	$0.646857\pi$
$954$		0			0
$955$	1.76092e12	−	3.05001e12i	0.0685054	−	0.118655i
$956$	−1.18949e12	+	2.06025e12i	−0.0460573	+	0.0797736i
$957$		0			0
$958$	2.82210e13			1.08250
$959$	−1.16764e13	−	3.55493e13i	−0.445785	−	1.35721i
$960$		0			0
$961$	1.31764e13	+	2.28223e13i	0.498360	+	0.863184i
$962$	7.57732e12	−	1.31243e13i	0.285251	−	0.494070i
$963$		0			0
$964$	4.99066e11	+	8.64408e11i	0.0186128	+	0.0322383i
$965$	2.96495e13			1.10064
$966$		0			0
$967$	4.32858e12			0.159194			0.0795969	−	0.996827i	$-0.474637\pi$
$967$	4.32858e12			0.159194			0.0795969	+	0.996827i	$0.474637\pi$
$968$	1.18854e13	+	2.05861e13i	0.435084	+	0.753588i
$969$		0			0
$970$	2.50898e12	−	4.34568e12i	0.0909965	−	0.157611i
$971$	1.63561e13	+	2.83297e13i	0.590465	+	1.02272i	0.994170	+	0.107826i	$0.0343890\pi$
$971$	1.63561e13	+	2.83297e13i	0.590465	+	1.02272i	−0.403705	+	0.914889i	$0.632278\pi$
$972$		0			0
$973$	−6.50712e12	+	7.27350e12i	−0.232745	+	0.260157i
$974$	4.75724e13			1.69371
$975$		0			0
$976$	−1.29838e12	+	2.24887e12i	−0.0458014	+	0.0793304i
$977$	−3.14481e12	+	5.44698e12i	−0.110426	+	0.191263i	−0.915942	−	0.401311i	$-0.868555\pi$
$977$	−3.14481e12	+	5.44698e12i	−0.110426	+	0.191263i	0.805516	+	0.592573i	$0.201888\pi$
$978$		0			0
$979$	−2.49941e12			−0.0869591
$980$	−7.87158e11	−	7.05519e12i	−0.0272612	−	0.244338i
$981$		0			0
$982$	8.61836e10	+	1.49274e11i	0.00295749	+	0.00512252i
$983$	5.33975e12	−	9.24871e12i	0.182402	−	0.315930i	−0.760296	−	0.649577i	$-0.774946\pi$
$983$	5.33975e12	−	9.24871e12i	0.182402	−	0.315930i	0.942698	+	0.333647i	$0.108279\pi$
$984$		0			0
$985$	−4.46388e12	−	7.73166e12i	−0.151095	−	0.261704i
$986$	3.34274e13			1.12631
$987$		0			0
$988$	3.05474e12			0.101992
$989$	1.11556e13	+	1.93221e13i	0.370774	+	0.642200i
$990$		0			0
$991$	−2.84247e13	+	4.92330e13i	−0.936191	+	1.62153i	−0.163695	+	0.986511i	$0.552341\pi$
$991$	−2.84247e13	+	4.92330e13i	−0.936191	+	1.62153i	−0.772496	+	0.635019i	$0.780992\pi$
$992$	−2.92908e11	−	5.07332e11i	−0.00960350	−	0.0166337i
$993$		0			0
$994$	−3.80502e13	−	7.96081e12i	−1.23629	−	0.258653i
$995$	−7.15702e13			−2.31488
$996$		0			0
$997$	8.88145e12	−	1.53831e13i	0.284679	−	0.493079i	−0.687852	−	0.725851i	$-0.741446\pi$
$997$	8.88145e12	−	1.53831e13i	0.284679	−	0.493079i	0.972531	+	0.232772i	$0.0747796\pi$
$998$	8.56351e11	−	1.48324e12i	0.0273253	−	0.0473288i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.10.e.b.46.4		10
3.2	odd	2		7.10.c.a.4.2	yes	10
7.2	even	3	inner	63.10.e.b.37.4		10
12.11	even	2		112.10.i.c.81.5		10
21.2	odd	6		7.10.c.a.2.2	✓	10
21.5	even	6		49.10.c.g.30.2		10
21.11	odd	6		49.10.a.e.1.4		5
21.17	even	6		49.10.a.f.1.4		5
21.20	even	2		49.10.c.g.18.2		10
84.23	even	6		112.10.i.c.65.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.c.a.2.2	✓	10	21.2	odd	6
7.10.c.a.4.2	yes	10	3.2	odd	2
49.10.a.e.1.4		5	21.11	odd	6
49.10.a.f.1.4		5	21.17	even	6
49.10.c.g.18.2		10	21.20	even	2
49.10.c.g.30.2		10	21.5	even	6
63.10.e.b.37.4		10	7.2	even	3	inner
63.10.e.b.46.4		10	1.1	even	1	trivial
112.10.i.c.65.5		10	84.23	even	6
112.10.i.c.81.5		10	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(12.2345 + 21.1908i) q^{2} +(-43.3662 + 75.1124i) q^{4} +(-1014.15 - 1756.56i) q^{5} +(-4235.51 + 4734.35i) q^{7} +10405.9 q^{8} +O(q^{10})\)	\(q+(12.2345 + 21.1908i) q^{2} +(-43.3662 + 75.1124i) q^{4} +(-1014.15 - 1756.56i) q^{5} +(-4235.51 + 4734.35i) q^{7} +10405.9 q^{8} +(24815.2 - 42981.2i) q^{10} +(4289.29 - 7429.26i) q^{11} -38438.1 q^{13} +(-152144. - 31831.3i) q^{14} +(149514. + 258966. i) q^{16} +(-150942. + 261439. i) q^{17} +(458143. + 793527. i) q^{19} +175919. q^{20} +209909. q^{22} +(966607. + 1.67421e6i) q^{23} +(-1.08043e6 + 1.87136e6i) q^{25} +(-470272. - 814534. i) q^{26} +(-171931. - 523450. i) q^{28} -4.52529e6 q^{29} +(-147255. + 255054. i) q^{31} +(-994560. + 1.72263e6i) q^{32} -7.38680e6 q^{34} +(1.26116e7 + 2.63858e6i) q^{35} +(8.05632e6 + 1.39540e7i) q^{37} +(-1.12103e7 + 1.94168e7i) q^{38} +(-1.05531e7 - 1.82785e7i) q^{40} -1.28783e7 q^{41} +1.15410e7 q^{43} +(372020. + 644357. i) q^{44} +(-2.36519e7 + 4.09663e7i) q^{46} +(-1.39268e7 - 2.41219e7i) q^{47} +(-4.47455e6 - 4.01048e7i) q^{49} -5.28742e7 q^{50} +(1.66692e6 - 2.88718e6i) q^{52} +(-2.11827e7 + 3.66896e7i) q^{53} -1.73999e7 q^{55} +(-4.40742e7 + 4.92651e7i) q^{56} +(-5.53647e7 - 9.58945e7i) q^{58} +(1.17321e6 - 2.03205e6i) q^{59} +(4.34201e6 + 7.52057e6i) q^{61} -7.20638e6 q^{62} +1.04431e8 q^{64} +(3.89820e7 + 6.75188e7i) q^{65} +(-1.26144e8 + 2.18488e8i) q^{67} +(-1.30915e7 - 2.26752e7i) q^{68} +(9.83831e7 + 2.99531e8i) q^{70} +2.50094e8 q^{71} +(-2.32270e7 + 4.02303e7i) q^{73} +(-1.97130e8 + 3.41439e8i) q^{74} -7.94716e7 q^{76} +(1.70054e7 + 5.17737e7i) q^{77} +(-5.53584e7 - 9.58836e7i) q^{79} +(3.03259e8 - 5.25261e8i) q^{80} +(-1.57560e8 - 2.72902e8i) q^{82} -2.81805e8 q^{83} +6.12310e8 q^{85} +(1.41198e8 + 2.44562e8i) q^{86} +(4.46338e7 - 7.73080e7i) q^{88} +(-1.45677e8 - 2.52321e8i) q^{89} +(1.62805e8 - 1.81980e8i) q^{91} -1.67672e8 q^{92} +(3.40774e8 - 5.90238e8i) q^{94} +(9.29250e8 - 1.60951e9i) q^{95} +1.01107e8 q^{97} +(7.95107e8 - 5.85481e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 18 q^{2} - 940 q^{4} - 1533 q^{5} - 1036 q^{7} - 34272 q^{8}+O(q^{10}) \) 10 * q + 18 * q^2 - 940 * q^4 - 1533 * q^5 - 1036 * q^7 - 34272 * q^8	\( 10 q + 18 q^{2} - 940 q^{4} - 1533 q^{5} - 1036 q^{7} - 34272 q^{8} + 4298 q^{10} - 42213 q^{11} - 319676 q^{13} + 39522 q^{14} + 322064 q^{16} - 324681 q^{17} - 16121 q^{19} + 350616 q^{20} - 62692 q^{22} - 2638863 q^{23} - 1304092 q^{25} - 4179252 q^{26} - 22156316 q^{28} - 15292500 q^{29} + 19179237 q^{31} + 6263520 q^{32} - 62909700 q^{34} + 43746759 q^{35} + 39566985 q^{37} - 67365270 q^{38} + 5721744 q^{40} + 53436852 q^{41} + 101835992 q^{43} - 99704916 q^{44} - 14489202 q^{46} - 32509659 q^{47} - 49024598 q^{49} - 3328464 q^{50} + 103893272 q^{52} + 25714707 q^{53} - 144695222 q^{55} - 115352832 q^{56} - 46645516 q^{58} - 46776513 q^{59} - 113075039 q^{61} - 467465628 q^{62} - 192008960 q^{64} + 338113566 q^{65} - 126707879 q^{67} - 32262636 q^{68} + 697712470 q^{70} + 1188736032 q^{71} - 859257651 q^{73} - 591757530 q^{74} + 1101475592 q^{76} - 1911891891 q^{77} - 527065417 q^{79} + 1257352656 q^{80} - 1341703076 q^{82} + 144863208 q^{83} - 1197360222 q^{85} + 678648216 q^{86} + 903700608 q^{88} - 1661554797 q^{89} + 726641384 q^{91} + 1301840952 q^{92} - 272580882 q^{94} + 1197123495 q^{95} + 869770188 q^{97} + 2404833858 q^{98}+O(q^{100}) \) 10 * q + 18 * q^2 - 940 * q^4 - 1533 * q^5 - 1036 * q^7 - 34272 * q^8 + 4298 * q^10 - 42213 * q^11 - 319676 * q^13 + 39522 * q^14 + 322064 * q^16 - 324681 * q^17 - 16121 * q^19 + 350616 * q^20 - 62692 * q^22 - 2638863 * q^23 - 1304092 * q^25 - 4179252 * q^26 - 22156316 * q^28 - 15292500 * q^29 + 19179237 * q^31 + 6263520 * q^32 - 62909700 * q^34 + 43746759 * q^35 + 39566985 * q^37 - 67365270 * q^38 + 5721744 * q^40 + 53436852 * q^41 + 101835992 * q^43 - 99704916 * q^44 - 14489202 * q^46 - 32509659 * q^47 - 49024598 * q^49 - 3328464 * q^50 + 103893272 * q^52 + 25714707 * q^53 - 144695222 * q^55 - 115352832 * q^56 - 46645516 * q^58 - 46776513 * q^59 - 113075039 * q^61 - 467465628 * q^62 - 192008960 * q^64 + 338113566 * q^65 - 126707879 * q^67 - 32262636 * q^68 + 697712470 * q^70 + 1188736032 * q^71 - 859257651 * q^73 - 591757530 * q^74 + 1101475592 * q^76 - 1911891891 * q^77 - 527065417 * q^79 + 1257352656 * q^80 - 1341703076 * q^82 + 144863208 * q^83 - 1197360222 * q^85 + 678648216 * q^86 + 903700608 * q^88 - 1661554797 * q^89 + 726641384 * q^91 + 1301840952 * q^92 - 272580882 * q^94 + 1197123495 * q^95 + 869770188 * q^97 + 2404833858 * q^98

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