LMFDB - Embedded newform 54.14.c.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,14,Mod(19,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("54.19");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	54.c (of order $3$, degree $2$, not 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:	$57.9047016340$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 344289641 x^{10} - 1721448150 x^{9} + \cdots + 46\!\cdots\!81 $ x^12 - 6x^11 + 344289641x^10 - 1721448150x^9 + 44498590579746150x^8 - 177994351990295766x^7 + 2696841810892288778677841x^6 - 8090524809696641600080506x^5 + 78572845327087816276031567845630x^4 - 157145677169967824051067681339210x^3 + 1037322927871683662837271494543288573121x^2 - 1037322849298846426274131419391565968746*x + 4698777961808815750710889000554461462406934581
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{45} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			19.4
Root			$0.500000 - 3035.92i$ of defining polynomial
Character	$\chi$	$=$	54.19
Dual form			54.14.c.a.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-32.0000 + 55.4256i) q^{2} +(-2048.00 - 3547.24i) q^{4} +(10927.3 + 18926.7i) q^{5} +(-146006. + 252890. i) q^{7} +262144. q^{8} +O(q^{10})$	\(q+(-32.0000 + 55.4256i) q^{2} +(-2048.00 - 3547.24i) q^{4} +(10927.3 + 18926.7i) q^{5} +(-146006. + 252890. i) q^{7} +262144. q^{8} -1.39870e6 q^{10} +(-1.12078e6 + 1.94125e6i) q^{11} +(8.69332e6 + 1.50573e7i) q^{13} +(-9.34440e6 - 1.61850e7i) q^{14} +(-8.38861e6 + 1.45295e7i) q^{16} -1.02646e8 q^{17} +2.84600e8 q^{19} +(4.47583e7 - 7.75236e7i) q^{20} +(-7.17298e7 - 1.24240e8i) q^{22} +(1.29161e8 + 2.23713e8i) q^{23} +(3.71539e8 - 6.43525e8i) q^{25} -1.11274e9 q^{26} +1.19608e9 q^{28} +(-1.74217e9 + 3.01753e9i) q^{29} +(4.05701e9 + 7.02694e9i) q^{31} +(-5.36871e8 - 9.29888e8i) q^{32} +(3.28468e9 - 5.68923e9i) q^{34} -6.38182e9 q^{35} -1.28194e10 q^{37} +(-9.10720e9 + 1.57741e10i) q^{38} +(2.86453e9 + 4.96151e9i) q^{40} +(-2.35711e9 - 4.08263e9i) q^{41} +(-1.66397e10 + 2.88208e10i) q^{43} +9.18142e9 q^{44} -1.65326e10 q^{46} +(-1.52063e9 + 2.63380e9i) q^{47} +(5.80889e9 + 1.00613e10i) q^{49} +(2.37785e10 + 4.11856e10i) q^{50} +(3.56078e10 - 6.16746e10i) q^{52} +5.94638e10 q^{53} -4.89884e10 q^{55} +(-3.82746e10 + 6.62936e10i) q^{56} +(-1.11499e11 - 1.93122e11i) q^{58} +(-2.89332e11 - 5.01138e11i) q^{59} +(1.43544e11 - 2.48625e11i) q^{61} -5.19297e11 q^{62} +6.87195e10 q^{64} +(-1.89989e11 + 3.29071e11i) q^{65} +(-4.37420e11 - 7.57634e11i) q^{67} +(2.10219e11 + 3.64110e11i) q^{68} +(2.04218e11 - 3.53716e11i) q^{70} -1.64422e12 q^{71} -1.62988e12 q^{73} +(4.10222e11 - 7.10525e11i) q^{74} +(-5.82861e11 - 1.00954e12i) q^{76} +(-3.27281e11 - 5.66868e11i) q^{77} +(1.51346e12 - 2.62139e12i) q^{79} -3.66660e11 q^{80} +3.01710e11 q^{82} +(4.62483e11 - 8.01045e11i) q^{83} +(-1.12165e12 - 1.94275e12i) q^{85} +(-1.06494e12 - 1.84453e12i) q^{86} +(-2.93805e11 + 5.08886e11i) q^{88} -6.03750e12 q^{89} -5.07711e12 q^{91} +(5.29042e11 - 9.16328e11i) q^{92} +(-9.73201e10 - 1.68563e11i) q^{94} +(3.10991e12 + 5.38653e12i) q^{95} +(-5.99631e11 + 1.03859e12i) q^{97} -7.43538e11 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 384 q^{2} - 24576 q^{4} + 36504 q^{5} + 153942 q^{7} + 3145728 q^{8}+O(q^{10}) $ 12 * q - 384 * q^2 - 24576 * q^4 + 36504 * q^5 + 153942 * q^7 + 3145728 * q^8	\( 12 q - 384 q^{2} - 24576 q^{4} + 36504 q^{5} + 153942 q^{7} + 3145728 q^{8} - 4672512 q^{10} + 1456506 q^{11} + 24033660 q^{13} + 9852288 q^{14} - 100663296 q^{16} + 1079532 q^{17} + 337140888 q^{19} + 149520384 q^{20} + 93216384 q^{22} - 445386186 q^{23} - 2193691326 q^{25} - 3076308480 q^{26} - 1261092864 q^{28} + 9171393012 q^{29} + 4264851066 q^{31} - 6442450944 q^{32} - 34545024 q^{34} - 5180969412 q^{35} - 49108850688 q^{37} - 10788508416 q^{38} + 9569304576 q^{40} + 15964345782 q^{41} + 78379952838 q^{43} - 11931697152 q^{44} + 57009431808 q^{46} - 94117799358 q^{47} - 15284873538 q^{49} - 140396244864 q^{50} + 98441871360 q^{52} + 592790415264 q^{53} - 1108282558212 q^{55} + 40354971648 q^{56} + 586969152768 q^{58} - 46698155010 q^{59} + 928192122600 q^{61} - 545900936448 q^{62} + 824633720832 q^{64} + 1327744890468 q^{65} + 2282039666898 q^{67} - 2210881536 q^{68} + 165791021184 q^{70} - 2360122970688 q^{71} + 1355834901228 q^{73} + 1571483222016 q^{74} - 690464538624 q^{76} + 3622976109756 q^{77} + 2457538059750 q^{79} - 1224870985728 q^{80} - 2043436260096 q^{82} + 9950916891942 q^{83} - 576987174720 q^{85} + 5016316981632 q^{86} + 381814308864 q^{88} - 22604686696296 q^{89} + 14791528659540 q^{91} - 1824301817856 q^{92} - 6023539158912 q^{94} + 7488669126384 q^{95} + 1124429902242 q^{97} + 1956463812864 q^{98}+O(q^{100}) \) 12 * q - 384 * q^2 - 24576 * q^4 + 36504 * q^5 + 153942 * q^7 + 3145728 * q^8 - 4672512 * q^10 + 1456506 * q^11 + 24033660 * q^13 + 9852288 * q^14 - 100663296 * q^16 + 1079532 * q^17 + 337140888 * q^19 + 149520384 * q^20 + 93216384 * q^22 - 445386186 * q^23 - 2193691326 * q^25 - 3076308480 * q^26 - 1261092864 * q^28 + 9171393012 * q^29 + 4264851066 * q^31 - 6442450944 * q^32 - 34545024 * q^34 - 5180969412 * q^35 - 49108850688 * q^37 - 10788508416 * q^38 + 9569304576 * q^40 + 15964345782 * q^41 + 78379952838 * q^43 - 11931697152 * q^44 + 57009431808 * q^46 - 94117799358 * q^47 - 15284873538 * q^49 - 140396244864 * q^50 + 98441871360 * q^52 + 592790415264 * q^53 - 1108282558212 * q^55 + 40354971648 * q^56 + 586969152768 * q^58 - 46698155010 * q^59 + 928192122600 * q^61 - 545900936448 * q^62 + 824633720832 * q^64 + 1327744890468 * q^65 + 2282039666898 * q^67 - 2210881536 * q^68 + 165791021184 * q^70 - 2360122970688 * q^71 + 1355834901228 * q^73 + 1571483222016 * q^74 - 690464538624 * q^76 + 3622976109756 * q^77 + 2457538059750 * q^79 - 1224870985728 * q^80 - 2043436260096 * q^82 + 9950916891942 * q^83 - 576987174720 * q^85 + 5016316981632 * q^86 + 381814308864 * q^88 - 22604686696296 * q^89 + 14791528659540 * q^91 - 1824301817856 * q^92 - 6023539158912 * q^94 + 7488669126384 * q^95 + 1124429902242 * q^97 + 1956463812864 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

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

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 $

$2$	−32.0000	+	55.4256i	−0.353553	+	0.612372i
$2$	−32.0000	+	55.4256i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−2048.00	−	3547.24i	−0.250000	−	0.433013i
$5$	10927.3	+	18926.7i	0.312758	+	0.541713i	0.978958	−	0.204060i	$-0.0654138\pi$
$5$	10927.3	+	18926.7i	0.312758	+	0.541713i	−0.666200	+	0.745773i	$0.732080\pi$
$6$		0			0
$7$	−146006.	+	252890.i	−0.469066	+	0.812446i	−0.999375	−	0.0353584i	$-0.988743\pi$
$7$	−146006.	+	252890.i	−0.469066	+	0.812446i	0.530309	+	0.847805i	$0.322076\pi$
$8$	262144.			0.353553
$9$		0			0
$10$	−1.39870e6			−0.442307
$11$	−1.12078e6	+	1.94125e6i	−0.190751	+	0.330391i	−0.945499	−	0.325624i	$-0.894426\pi$
$11$	−1.12078e6	+	1.94125e6i	−0.190751	+	0.330391i	0.754748	+	0.656015i	$0.227759\pi$
$12$		0			0
$13$	8.69332e6	+	1.50573e7i	0.499521	+	0.865196i	1.00000		0.000553009i	$-0.000176028\pi$
$13$	8.69332e6	+	1.50573e7i	0.499521	+	0.865196i	−0.500479	+	0.865749i	$0.666843\pi$
$14$	−9.34440e6	−	1.61850e7i	−0.331680	−	0.574486i
$15$		0			0
$16$	−8.38861e6	+	1.45295e7i	−0.125000	+	0.216506i
$17$	−1.02646e8			−1.03139			−0.515697	−	0.856771i	$-0.672467\pi$
$17$	−1.02646e8			−1.03139			−0.515697	+	0.856771i	$0.672467\pi$
$18$		0			0
$19$	2.84600e8			1.38783			0.693915	−	0.720057i	$-0.255884\pi$
$19$	2.84600e8			1.38783			0.693915	+	0.720057i	$0.255884\pi$
$20$	4.47583e7	−	7.75236e7i	0.156379	−	0.270856i
$21$		0			0
$22$	−7.17298e7	−	1.24240e8i	−0.134882	−	0.233622i
$23$	1.29161e8	+	2.23713e8i	0.181928	+	0.315108i	0.942537	−	0.334102i	$-0.108433\pi$
$23$	1.29161e8	+	2.23713e8i	0.181928	+	0.315108i	−0.760609	+	0.649210i	$0.775100\pi$
$24$		0			0
$25$	3.71539e8	−	6.43525e8i	0.304365	−	0.527175i
$26$	−1.11274e9			−0.706429
$27$		0			0
$28$	1.19608e9			0.469066
$29$	−1.74217e9	+	3.01753e9i	−0.543881	+	0.942030i	0.454795	+	0.890596i	$0.349713\pi$
$29$	−1.74217e9	+	3.01753e9i	−0.543881	+	0.942030i	−0.998676	+	0.0514340i	$0.983621\pi$
$30$		0			0
$31$	4.05701e9	+	7.02694e9i	0.821022	+	1.42205i	0.904922	+	0.425578i	$0.139929\pi$
$31$	4.05701e9	+	7.02694e9i	0.821022	+	1.42205i	−0.0838996	+	0.996474i	$0.526738\pi$
$32$	−5.36871e8	−	9.29888e8i	−0.0883883	−	0.153093i
$33$		0			0
$34$	3.28468e9	−	5.68923e9i	0.364653	−	0.631597i
$35$	−6.38182e9			−0.586817
$36$		0			0
$37$	−1.28194e10			−0.821405			−0.410703	−	0.911769i	$-0.634717\pi$
$37$	−1.28194e10			−0.821405			−0.410703	+	0.911769i	$0.634717\pi$
$38$	−9.10720e9	+	1.57741e10i	−0.490672	+	0.849869i
$39$		0			0
$40$	2.86453e9	+	4.96151e9i	0.110577	+	0.191524i
$41$	−2.35711e9	−	4.08263e9i	−0.0774970	−	0.134229i	0.824672	−	0.565611i	$-0.191359\pi$
$41$	−2.35711e9	−	4.08263e9i	−0.0774970	−	0.134229i	−0.902169	+	0.431382i	$0.858026\pi$
$42$		0			0
$43$	−1.66397e10	+	2.88208e10i	−0.401422	+	0.695283i	−0.993898	−	0.110305i	$-0.964817\pi$
$43$	−1.66397e10	+	2.88208e10i	−0.401422	+	0.695283i	0.592476	+	0.805588i	$0.298151\pi$
$44$	9.18142e9			0.190751
$45$		0			0
$46$	−1.65326e10			−0.257285
$47$	−1.52063e9	+	2.63380e9i	−0.0205772	+	0.0356408i	−0.876131	−	0.482074i	$-0.839884\pi$
$47$	−1.52063e9	+	2.63380e9i	−0.0205772	+	0.0356408i	0.855553	+	0.517715i	$0.173217\pi$
$48$		0			0
$49$	5.80889e9	+	1.00613e10i	0.0599541	+	0.103843i
$50$	2.37785e10	+	4.11856e10i	0.215218	+	0.372769i
$51$		0			0
$52$	3.56078e10	−	6.16746e10i	0.249761	−	0.432598i
$53$	5.94638e10			0.368519			0.184259	−	0.982878i	$-0.441011\pi$
$53$	5.94638e10			0.368519			0.184259	+	0.982878i	$0.441011\pi$
$54$		0			0
$55$	−4.89884e10			−0.238636
$56$	−3.82746e10	+	6.62936e10i	−0.165840	+	0.287243i
$57$		0			0
$58$	−1.11499e11	−	1.93122e11i	−0.384582	−	0.666116i
$59$	−2.89332e11	−	5.01138e11i	−0.893015	−	1.54675i	−0.836242	−	0.548361i	$-0.815252\pi$
$59$	−2.89332e11	−	5.01138e11i	−0.893015	−	1.54675i	−0.0567738	−	0.998387i	$-0.518081\pi$
$60$		0			0
$61$	1.43544e11	−	2.48625e11i	0.356731	−	0.617876i	−0.630682	−	0.776041i	$-0.717225\pi$
$61$	1.43544e11	−	2.48625e11i	0.356731	−	0.617876i	0.987413	+	0.158166i	$0.0505581\pi$
$62$	−5.19297e11			−1.16110
$63$		0			0
$64$	6.87195e10			0.125000
$65$	−1.89989e11	+	3.29071e11i	−0.312458	+	0.541194i
$66$		0			0
$67$	−4.37420e11	−	7.57634e11i	−0.590762	−	1.02323i	−0.994130	−	0.108192i	$-0.965494\pi$
$67$	−4.37420e11	−	7.57634e11i	−0.590762	−	1.02323i	0.403368	−	0.915038i	$-0.367839\pi$
$68$	2.10219e11	+	3.64110e11i	0.257849	+	0.446607i
$69$		0			0
$70$	2.04218e11	−	3.53716e11i	0.207471	−	0.359350i
$71$	−1.64422e12			−1.52329			−0.761644	−	0.647996i	$-0.775607\pi$
$71$	−1.64422e12			−1.52329			−0.761644	+	0.647996i	$0.775607\pi$
$72$		0			0
$73$	−1.62988e12			−1.26054			−0.630270	−	0.776376i	$-0.717056\pi$
$73$	−1.62988e12			−1.26054			−0.630270	+	0.776376i	$0.717056\pi$
$74$	4.10222e11	−	7.10525e11i	0.290411	−	0.503006i
$75$		0			0
$76$	−5.82861e11	−	1.00954e12i	−0.346958	−	0.600948i
$77$	−3.27281e11	−	5.66868e11i	−0.178950	−	0.309950i
$78$		0			0
$79$	1.51346e12	−	2.62139e12i	0.700478	−	1.21326i	−0.267821	−	0.963469i	$-0.586304\pi$
$79$	1.51346e12	−	2.62139e12i	0.700478	−	1.21326i	0.968299	−	0.249795i	$-0.0803632\pi$
$80$	−3.66660e11			−0.156379
$81$		0			0
$82$	3.01710e11			0.109597
$83$	4.62483e11	−	8.01045e11i	0.155270	−	0.268936i	−0.777887	−	0.628404i	$-0.783708\pi$
$83$	4.62483e11	−	8.01045e11i	0.155270	−	0.268936i	0.933157	+	0.359468i	$0.117042\pi$
$84$		0			0
$85$	−1.12165e12	−	1.94275e12i	−0.322577	−	0.558719i
$86$	−1.06494e12	−	1.84453e12i	−0.283848	−	0.491639i
$87$		0			0
$88$	−2.93805e11	+	5.08886e11i	−0.0674408	+	0.116811i
$89$	−6.03750e12			−1.28772			−0.643861	−	0.765143i	$-0.722668\pi$
$89$	−6.03750e12			−1.28772			−0.643861	+	0.765143i	$0.722668\pi$
$90$		0			0
$91$	−5.07711e12			−0.937233
$92$	5.29042e11	−	9.16328e11i	0.0909640	−	0.157554i
$93$		0			0
$94$	−9.73201e10	−	1.68563e11i	−0.0145503	−	0.0252018i
$95$	3.10991e12	+	5.38653e12i	0.434055	+	0.751805i
$96$		0			0
$97$	−5.99631e11	+	1.03859e12i	−0.0730916	+	0.126598i	−0.900255	−	0.435363i	$-0.856620\pi$
$97$	−5.99631e11	+	1.03859e12i	−0.0730916	+	0.126598i	0.827163	+	0.561962i	$0.189953\pi$
$98$	−7.43538e11			−0.0847878
$99$		0			0
$100$	−3.04365e12			−0.304365
$101$	−6.16075e12	+	1.06707e13i	−0.577490	+	1.00024i	0.418276	+	0.908320i	$0.362634\pi$
$101$	−6.16075e12	+	1.06707e13i	−0.577490	+	1.00024i	−0.995766	+	0.0919222i	$0.970699\pi$
$102$		0			0
$103$	−1.90932e12	−	3.30704e12i	−0.157557	−	0.272897i	0.776430	−	0.630203i	$-0.217028\pi$
$103$	−1.90932e12	−	3.30704e12i	−0.157557	−	0.272897i	−0.933987	+	0.357307i	$0.883695\pi$
$104$	2.27890e12	+	3.94717e12i	0.176607	+	0.305893i
$105$		0			0
$106$	−1.90284e12	+	3.29582e12i	−0.130291	+	0.225671i
$107$	−2.89672e13			−1.86600			−0.933002	−	0.359872i	$-0.882821\pi$
$107$	−2.89672e13			−1.86600			−0.933002	+	0.359872i	$0.882821\pi$
$108$		0			0
$109$	2.01531e13			1.15099			0.575494	−	0.817806i	$-0.304810\pi$
$109$	2.01531e13			1.15099			0.575494	+	0.817806i	$0.304810\pi$
$110$	1.56763e12	−	2.71521e12i	0.0843705	−	0.146134i
$111$		0			0
$112$	−2.44958e12	−	4.24279e12i	−0.117267	−	0.203112i
$113$	−7.37102e12	−	1.27670e13i	−0.333056	−	0.576870i	0.650053	−	0.759889i	$-0.274747\pi$
$113$	−7.37102e12	−	1.27670e13i	−0.333056	−	0.576870i	−0.983110	+	0.183018i	$0.941413\pi$
$114$		0			0
$115$	−2.82276e12	+	4.88916e12i	−0.113799	+	0.197105i
$116$	1.42719e13			0.543881
$117$		0			0
$118$	3.70345e13			1.26291
$119$	1.49870e13	−	2.59582e13i	0.483792	−	0.837952i
$120$		0			0
$121$	1.47491e13	+	2.55461e13i	0.427228	+	0.739980i
$122$	9.18680e12	+	1.59120e13i	0.252247	+	0.436904i
$123$		0			0
$124$	1.66175e13	−	2.87824e13i	0.410511	−	0.711026i
$125$	4.29177e13			1.00629
$126$		0			0
$127$	−6.27677e13			−1.32743			−0.663715	−	0.747985i	$-0.731021\pi$
$127$	−6.27677e13			−1.32743			−0.663715	+	0.747985i	$0.731021\pi$
$128$	−2.19902e12	+	3.80882e12i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.21593e13	−	2.10605e13i	−0.220941	−	0.382682i
$131$	2.97023e13	+	5.14459e13i	0.513484	+	0.889380i	0.999878	+	0.0156407i	$0.00497878\pi$
$131$	2.97023e13	+	5.14459e13i	0.513484	+	0.889380i	−0.486394	+	0.873740i	$0.661688\pi$
$132$		0			0
$133$	−4.15533e13	+	7.19725e13i	−0.650984	+	1.12754i
$134$	5.59898e13			0.835463
$135$		0			0
$136$	−2.69081e13			−0.364653
$137$	6.70609e13	−	1.16153e14i	0.866535	−	1.50088i	0.00101949	−	0.999999i	$-0.499675\pi$
$137$	6.70609e13	−	1.16153e14i	0.866535	−	1.50088i	0.865515	−	0.500883i	$-0.166991\pi$
$138$		0			0
$139$	7.44053e13	+	1.28874e14i	0.874999	+	1.51554i	0.856764	+	0.515709i	$0.172472\pi$
$139$	7.44053e13	+	1.28874e14i	0.874999	+	1.51554i	0.0182356	+	0.999834i	$0.494195\pi$
$140$	1.30700e13	+	2.26379e13i	0.146704	+	0.254099i
$141$		0			0
$142$	5.26152e13	−	9.11322e13i	0.538563	−	0.932819i
$143$	−3.89731e13			−0.381137
$144$		0			0
$145$	−7.61491e13			−0.680413
$146$	5.21561e13	−	9.03370e13i	0.445668	−	0.771920i
$147$		0			0
$148$	2.62542e13	+	4.54736e13i	0.205351	+	0.355679i
$149$	1.10148e13	+	1.90782e13i	0.0824645	+	0.142833i	0.904308	−	0.426881i	$-0.140388\pi$
$149$	1.10148e13	+	1.90782e13i	0.0824645	+	0.142833i	−0.821843	+	0.569713i	$0.807054\pi$
$150$		0			0
$151$	−2.09503e13	+	3.62870e13i	−0.143827	+	0.249116i	−0.928935	−	0.370244i	$-0.879274\pi$
$151$	−2.09503e13	+	3.62870e13i	−0.143827	+	0.249116i	0.785108	+	0.619359i	$0.212608\pi$
$152$	7.46062e13			0.490672
$153$		0			0
$154$	4.18920e13			0.253073
$155$	−8.86644e13	+	1.53571e14i	−0.513562	+	0.889516i
$156$		0			0
$157$	6.74371e13	+	1.16805e14i	0.359378	+	0.622461i	0.987857	−	0.155366i	$-0.0496556\pi$
$157$	6.74371e13	+	1.16805e14i	0.359378	+	0.622461i	−0.628479	+	0.777826i	$0.716322\pi$
$158$	9.68614e13	+	1.67769e14i	0.495313	+	0.857907i
$159$		0			0
$160$	1.17331e13	−	2.03224e13i	0.0552883	−	0.0957622i
$161$	−7.54330e13			−0.341345
$162$		0			0
$163$	1.65656e14			0.691813			0.345907	−	0.938269i	$-0.387571\pi$
$163$	1.65656e14			0.691813			0.345907	+	0.938269i	$0.387571\pi$
$164$	−9.65472e12	+	1.67225e13i	−0.0387485	+	0.0671143i
$165$		0			0
$166$	2.95989e13	+	5.12669e13i	0.109793	+	0.190167i
$167$	−8.10102e13	−	1.40314e14i	−0.288990	−	0.500545i	0.684579	−	0.728939i	$-0.259986\pi$
$167$	−8.10102e13	−	1.40314e14i	−0.288990	−	0.500545i	−0.973569	+	0.228393i	$0.926653\pi$
$168$		0			0
$169$	2.90013e11	−	5.02318e11i	0.000957534	−	0.00165850i
$170$	1.43571e14			0.456192
$171$		0			0
$172$	1.36313e14			0.401422
$173$	−1.33981e14	+	2.32062e14i	−0.379964	+	0.658118i	−0.991057	−	0.133442i	$-0.957397\pi$
$173$	−1.33981e14	+	2.32062e14i	−0.379964	+	0.658118i	0.611092	+	0.791559i	$0.290730\pi$
$174$		0			0
$175$	1.08494e14	+	1.87917e14i	0.285534	+	0.494560i
$176$	−1.88035e13	−	3.25687e13i	−0.0476878	−	0.0825977i
$177$		0			0
$178$	1.93200e14	−	3.34632e14i	0.455278	−	0.788565i
$179$	−8.14358e14			−1.85042			−0.925211	−	0.379454i	$-0.876112\pi$
$179$	−8.14358e14			−1.85042			−0.925211	+	0.379454i	$0.876112\pi$
$180$		0			0
$181$	−6.82572e14			−1.44291			−0.721453	−	0.692464i	$-0.756525\pi$
$181$	−6.82572e14			−1.44291			−0.721453	+	0.692464i	$0.756525\pi$
$182$	1.62468e14	−	2.81402e14i	0.331362	−	0.573936i
$183$		0			0
$184$	3.38587e13	+	5.86450e13i	0.0643212	+	0.111408i
$185$	−1.40082e14	−	2.42629e14i	−0.256901	−	0.444966i
$186$		0			0
$187$	1.15044e14	−	1.99261e14i	0.196740	−	0.340763i
$188$	1.24570e13			0.0205772
$189$		0			0
$190$	−3.98069e14			−0.613846
$191$	−2.97121e14	+	5.14629e14i	−0.442809	+	0.766968i	−0.997897	−	0.0648238i	$-0.979351\pi$
$191$	−2.97121e14	+	5.14629e14i	−0.442809	+	0.766968i	0.555087	+	0.831792i	$0.312685\pi$
$192$		0			0
$193$	−4.17764e14	−	7.23589e14i	−0.581847	−	1.00779i	−0.995260	−	0.0972448i	$-0.968997\pi$
$193$	−4.17764e14	−	7.23589e14i	−0.581847	−	1.00779i	0.413414	−	0.910543i	$-0.364336\pi$
$194$	−3.83764e13	−	6.64698e13i	−0.0516836	−	0.0895186i
$195$		0			0
$196$	2.37932e13	−	4.12111e13i	0.0299770	−	0.0519217i
$197$	9.13748e14			1.11377			0.556886	−	0.830589i	$-0.311996\pi$
$197$	9.13748e14			1.11377			0.556886	+	0.830589i	$0.311996\pi$
$198$		0			0
$199$	−5.29824e14			−0.604765			−0.302382	−	0.953187i	$-0.597782\pi$
$199$	−5.29824e14			−0.604765			−0.302382	+	0.953187i	$0.597782\pi$
$200$	9.73968e13	−	1.68696e14i	0.107609	−	0.186385i
$201$		0			0
$202$	−3.94288e14	−	6.82927e14i	−0.408347	−	0.707278i
$203$	−5.08736e14	−	8.81157e14i	−0.510233	−	0.883749i
$204$		0			0
$205$	5.15138e13	−	8.92244e13i	0.0484756	−	0.0839622i
$206$	2.44393e14			0.222819
$207$		0			0
$208$	−2.91699e14			−0.249761
$209$	−3.18974e14	+	5.52478e14i	−0.264730	+	0.458526i
$210$		0			0
$211$	1.98238e13	+	3.43358e13i	0.0154650	+	0.0267862i	0.873654	−	0.486547i	$-0.161744\pi$
$211$	1.98238e13	+	3.43358e13i	0.0154650	+	0.0267862i	−0.858189	+	0.513333i	$0.828410\pi$
$212$	−1.21782e14	−	2.10932e14i	−0.0921297	−	0.159573i
$213$		0			0
$214$	9.26952e14	−	1.60553e15i	0.659732	−	1.14269i
$215$	−7.27310e14			−0.502192
$216$		0			0
$217$	−2.36939e15			−1.54045
$218$	−6.44901e14	+	1.11700e15i	−0.406936	+	0.704833i
$219$		0			0
$220$	1.00328e14	+	1.73774e14i	0.0596590	+	0.103332i
$221$	−8.92335e14	−	1.54557e15i	−0.515203	−	0.892358i
$222$		0			0
$223$	1.67180e15	−	2.89564e15i	0.910337	−	1.57675i	0.0967496	−	0.995309i	$-0.469155\pi$
$223$	1.67180e15	−	2.89564e15i	0.910337	−	1.57675i	0.813588	−	0.581442i	$-0.197511\pi$
$224$	3.13546e14			0.165840
$225$		0			0
$226$	9.43490e14			0.471013
$227$	7.83386e14	−	1.35686e15i	0.380021	−	0.658216i	−0.611044	−	0.791597i	$-0.709250\pi$
$227$	7.83386e14	−	1.35686e15i	0.380021	−	0.658216i	0.991065	+	0.133381i	$0.0425835\pi$
$228$		0			0
$229$	1.93486e15	+	3.35128e15i	0.886582	+	1.53561i	0.843890	+	0.536517i	$0.180260\pi$
$229$	1.93486e15	+	3.35128e15i	0.886582	+	1.53561i	0.0426925	+	0.999088i	$0.486406\pi$
$230$	−1.80657e14	−	3.12906e14i	−0.0804679	−	0.139375i
$231$		0			0
$232$	−4.56700e14	+	7.91028e14i	−0.192291	+	0.333058i
$233$	−5.09381e14			−0.208559			−0.104280	−	0.994548i	$-0.533254\pi$
$233$	−5.09381e14			−0.208559			−0.104280	+	0.994548i	$0.533254\pi$
$234$		0			0
$235$	−6.64655e13			−0.0257428
$236$	−1.18511e15	+	2.05266e15i	−0.446508	+	0.773374i
$237$		0			0
$238$	9.59166e14	+	1.66132e15i	0.342093	+	0.592522i
$239$	7.94675e14	+	1.37642e15i	0.275806	+	0.477709i	0.970338	−	0.241752i	$-0.0777220\pi$
$239$	7.94675e14	+	1.37642e15i	0.275806	+	0.477709i	−0.694532	+	0.719461i	$0.744389\pi$
$240$		0			0
$241$	1.97767e14	−	3.42542e14i	0.0650193	−	0.112617i	−0.831683	−	0.555250i	$-0.812622\pi$
$241$	1.97767e14	−	3.42542e14i	0.0650193	−	0.112617i	0.896703	+	0.442634i	$0.145956\pi$
$242$	−1.88788e15			−0.604191
$243$		0			0
$244$	−1.17591e15			−0.356731
$245$	−1.26951e14	+	2.19886e14i	−0.0375022	+	0.0649558i
$246$		0			0
$247$	2.47412e15	+	4.28530e15i	0.693250	+	1.20074i
$248$	1.06352e15	+	1.84207e15i	0.290275	+	0.502771i
$249$		0			0
$250$	−1.37337e15	+	2.37874e15i	−0.355776	+	0.616222i
$251$	2.94268e15			0.742786			0.371393	−	0.928476i	$-0.378880\pi$
$251$	2.94268e15			0.742786			0.371393	+	0.928476i	$0.378880\pi$
$252$		0			0
$253$	−5.79042e14			−0.138812
$254$	2.00857e15	−	3.47894e15i	0.469318	−	0.812882i
$255$		0			0
$256$	−1.40737e14	−	2.43764e14i	−0.0312500	−	0.0541266i
$257$	4.25116e15	+	7.36322e15i	0.920326	+	1.59405i	0.798910	+	0.601450i	$0.205410\pi$
$257$	4.25116e15	+	7.36322e15i	0.920326	+	1.59405i	0.121416	+	0.992602i	$0.461257\pi$
$258$		0			0
$259$	1.87172e15	−	3.24191e15i	0.385293	−	0.667348i
$260$	1.55639e15			0.312458
$261$		0			0
$262$	−3.80190e15			−0.726176
$263$	4.13547e14	−	7.16284e14i	0.0770570	−	0.133467i	−0.824922	−	0.565247i	$-0.808781\pi$
$263$	4.13547e14	−	7.16284e14i	0.0770570	−	0.133467i	0.901979	+	0.431780i	$0.142114\pi$
$264$		0			0
$265$	6.49780e14	+	1.12545e15i	0.115257	+	0.199631i
$266$	−2.65941e15	−	4.60624e15i	−0.460315	−	0.797289i
$267$		0			0
$268$	−1.79167e15	+	3.10327e15i	−0.295381	+	0.511615i
$269$	1.21446e16			1.95431			0.977156	−	0.212521i	$-0.0681674\pi$
$269$	1.21446e16			1.95431			0.977156	+	0.212521i	$0.0681674\pi$
$270$		0			0
$271$	−8.66147e14			−0.132828			−0.0664142	−	0.997792i	$-0.521156\pi$
$271$	−8.66147e14			−0.132828			−0.0664142	+	0.997792i	$0.521156\pi$
$272$	8.61058e14	−	1.49140e15i	0.128924	−	0.223303i
$273$		0			0
$274$	4.29190e15	+	7.43379e15i	0.612733	+	1.06128i
$275$	8.32826e14	+	1.44250e15i	0.116116	+	0.201119i
$276$		0			0
$277$	1.11698e15	−	1.93467e15i	0.148569	−	0.257329i	−0.782130	−	0.623116i	$-0.785867\pi$
$277$	1.11698e15	−	1.93467e15i	0.148569	−	0.257329i	0.930699	+	0.365787i	$0.119200\pi$
$278$	−9.52388e15			−1.23744
$279$		0			0
$280$	−1.67296e15			−0.207471
$281$	2.37385e15	−	4.11163e15i	0.287649	−	0.498222i	−0.685599	−	0.727979i	$-0.740460\pi$
$281$	2.37385e15	−	4.11163e15i	0.287649	−	0.498222i	0.973248	+	0.229757i	$0.0737931\pi$
$282$		0			0
$283$	3.28026e15	+	5.68158e15i	0.379574	+	0.657442i	0.991000	−	0.133860i	$-0.0427371\pi$
$283$	3.28026e15	+	5.68158e15i	0.379574	+	0.657442i	−0.611426	+	0.791302i	$0.709404\pi$
$284$	3.36737e15	+	5.83246e15i	0.380822	+	0.659603i
$285$		0			0
$286$	1.24714e15	−	2.16011e15i	0.134752	−	0.233398i
$287$	1.37661e15			0.145405
$288$		0			0
$289$	6.31651e14			0.0637736
$290$	2.43677e15	−	4.22061e15i	0.240562	−	0.416666i
$291$		0			0
$292$	3.33799e15	+	5.78157e15i	0.315135	+	0.545830i
$293$	−5.53057e15	−	9.57923e15i	−0.510658	−	0.884486i	−0.999924	−	0.0123510i	$-0.996068\pi$
$293$	−5.53057e15	−	9.57923e15i	−0.510658	−	0.884486i	0.489266	−	0.872135i	$-0.337265\pi$
$294$		0			0
$295$	6.32325e15	−	1.09522e16i	0.558595	−	0.967516i
$296$	−3.36054e15			−0.290411
$297$		0			0
$298$	−1.40990e15			−0.116622
$299$	−2.24567e15	+	3.88961e15i	−0.181754	+	0.314807i
$300$		0			0
$301$	−4.85900e15	−	8.41604e15i	−0.376587	−	0.652267i
$302$	−1.34082e15	−	2.32237e15i	−0.101701	−	0.176151i
$303$		0			0
$304$	−2.38740e15	+	4.13509e15i	−0.173479	+	0.300474i
$305$	6.27419e15			0.446281
$306$		0			0
$307$	−4.85853e15			−0.331211			−0.165606	−	0.986192i	$-0.552958\pi$
$307$	−4.85853e15			−0.331211			−0.165606	+	0.986192i	$0.552958\pi$
$308$	−1.34054e15	+	2.32189e15i	−0.0894749	+	0.154975i
$309$		0			0
$310$	−5.67452e15	−	9.82856e15i	−0.363144	−	0.628983i
$311$	3.88280e15	+	6.72520e15i	0.243334	+	0.421466i	0.961662	−	0.274238i	$-0.0884256\pi$
$311$	3.88280e15	+	6.72520e15i	0.243334	+	0.421466i	−0.718328	+	0.695704i	$0.755092\pi$
$312$		0			0
$313$	1.24807e16	−	2.16172e16i	0.750241	−	1.29945i	−0.197465	−	0.980310i	$-0.563271\pi$
$313$	1.24807e16	−	2.16172e16i	0.750241	−	1.29945i	0.947706	−	0.319145i	$-0.103396\pi$
$314$	−8.63195e15			−0.508237
$315$		0			0
$316$	−1.23983e16			−0.700478
$317$	5.36996e14	−	9.30105e14i	0.0297226	−	0.0514810i	−0.850782	−	0.525520i	$-0.823871\pi$
$317$	5.36996e14	−	9.30105e14i	0.0297226	−	0.0514810i	0.880504	+	0.474039i	$0.157204\pi$
$318$		0			0
$319$	−3.90518e15	−	6.76397e15i	−0.207492	−	0.359387i
$320$	7.50919e14	+	1.30063e15i	0.0390947	+	0.0677141i
$321$		0			0
$322$	2.41386e15	−	4.18092e15i	0.120684	−	0.209030i
$323$	−2.92131e16			−1.43140
$324$		0			0
$325$	1.29196e16			0.608147
$326$	−5.30101e15	+	9.18161e15i	−0.244593	+	0.423648i
$327$		0			0
$328$	−6.17902e14	−	1.07024e15i	−0.0273993	−	0.0474570i
$329$	−4.44042e14	−	7.69103e14i	−0.0193041	−	0.0334358i
$330$		0			0
$331$	−1.86953e16	+	3.23811e16i	−0.781357	+	1.35335i	0.149795	+	0.988717i	$0.452139\pi$
$331$	−1.86953e16	+	3.23811e16i	−0.781357	+	1.35335i	−0.931152	+	0.364632i	$0.881195\pi$
$332$	−3.78866e15			−0.155270
$333$		0			0
$334$	1.03693e16			0.408693
$335$	9.55965e15	−	1.65578e16i	0.369531	−	0.640046i
$336$		0			0
$337$	−4.45382e15	−	7.71424e15i	−0.165630	−	0.286879i	0.771249	−	0.636533i	$-0.219632\pi$
$337$	−4.45382e15	−	7.71424e15i	−0.165630	−	0.286879i	−0.936879	+	0.349655i	$0.886299\pi$
$338$	1.85608e13	+	3.21483e13i	0.000677079	+	0.00117274i
$339$		0			0
$340$	−4.59426e15	+	7.95750e15i	−0.161288	+	0.279360i
$341$	−1.81880e16			−0.626444
$342$		0			0
$343$	−3.16853e16			−1.05062
$344$	−4.36200e15	+	7.55521e15i	−0.141924	+	0.245820i
$345$		0			0
$346$	−8.57477e15	−	1.48519e16i	−0.268675	−	0.465359i
$347$	−8.89968e15	−	1.54147e16i	−0.273674	−	0.474017i	0.696126	−	0.717920i	$-0.254905\pi$
$347$	−8.89968e15	−	1.54147e16i	−0.273674	−	0.474017i	−0.969800	+	0.243903i	$0.921572\pi$
$348$		0			0
$349$	−2.02979e16	+	3.51571e16i	−0.601294	+	1.04147i	0.391332	+	0.920250i	$0.372014\pi$
$349$	−2.02979e16	+	3.51571e16i	−0.601294	+	1.04147i	−0.992625	+	0.121222i	$0.961319\pi$
$350$	−1.38872e16			−0.403807
$351$		0			0
$352$	2.40685e15			0.0674408
$353$	−2.52713e16	+	4.37711e16i	−0.695170	+	1.20407i	0.274953	+	0.961458i	$0.411338\pi$
$353$	−2.52713e16	+	4.37711e16i	−0.695170	+	1.20407i	−0.970123	+	0.242613i	$0.921996\pi$
$354$		0			0
$355$	−1.79670e16	−	3.11197e16i	−0.476420	−	0.825184i
$356$	1.23648e16	+	2.14165e16i	0.321930	+	0.557600i
$357$		0			0
$358$	2.60595e16	−	4.51363e16i	0.654223	−	1.13315i
$359$	4.12005e16			1.01575			0.507877	−	0.861430i	$-0.330430\pi$
$359$	4.12005e16			1.01575			0.507877	+	0.861430i	$0.330430\pi$
$360$		0			0
$361$	3.89441e16			0.926073
$362$	2.18423e16	−	3.78320e16i	0.510144	−	0.883595i
$363$		0			0
$364$	1.03979e16	+	1.80097e16i	0.234308	+	0.405834i
$365$	−1.78102e16	−	3.08481e16i	−0.394244	−	0.682850i
$366$		0			0
$367$	1.92069e16	−	3.32673e16i	0.410325	−	0.710703i	−0.584600	−	0.811321i	$-0.698749\pi$
$367$	1.92069e16	−	3.32673e16i	0.410325	−	0.710703i	0.994925	+	0.100618i	$0.0320820\pi$
$368$	−4.33391e15			−0.0909640
$369$		0			0
$370$	1.79305e16			0.363313
$371$	−8.68209e15	+	1.50378e16i	−0.172860	+	0.299402i
$372$		0			0
$373$	2.62379e16	+	4.54454e16i	0.504455	+	0.873741i	0.999987	+	0.00515150i	$0.00163978\pi$
$373$	2.62379e16	+	4.54454e16i	0.504455	+	0.873741i	−0.495532	+	0.868590i	$0.665027\pi$
$374$	7.36279e15	+	1.27527e16i	0.139116	+	0.240956i
$375$		0			0
$376$	−3.98623e14	+	6.90436e14i	−0.00727514	+	0.0126009i
$377$	−6.05810e16			−1.08672
$378$		0			0
$379$	−3.80121e16			−0.658820			−0.329410	−	0.944187i	$-0.606850\pi$
$379$	−3.80121e16			−0.658820			−0.329410	+	0.944187i	$0.606850\pi$
$380$	1.27382e16	−	2.20632e16i	0.217027	−	0.375903i
$381$		0			0
$382$	−1.90158e16	−	3.29363e16i	−0.313113	−	0.542328i
$383$	−9.58764e15	−	1.66063e16i	−0.155210	−	0.268832i	0.777926	−	0.628357i	$-0.216272\pi$
$383$	−9.58764e15	−	1.66063e16i	−0.155210	−	0.268832i	−0.933135	+	0.359525i	$0.882939\pi$
$384$		0			0
$385$	7.15261e15	−	1.23887e16i	0.111936	−	0.193879i
$386$	5.34738e16			0.822856
$387$		0			0
$388$	4.91218e15			0.0730916
$389$	−3.75175e16	+	6.49823e16i	−0.548987	+	0.950873i	0.449358	+	0.893352i	$0.351653\pi$
$389$	−3.75175e16	+	6.49823e16i	−0.548987	+	0.950873i	−0.998344	+	0.0575208i	$0.981680\pi$
$390$		0			0
$391$	−1.32578e16	−	2.29633e16i	−0.187639	−	0.325001i
$392$	1.52277e15	+	2.63751e15i	0.0211970	+	0.0367142i
$393$		0			0
$394$	−2.92399e16	+	5.06451e16i	−0.393778	+	0.682043i
$395$	6.61522e16			0.876320
$396$		0			0
$397$	6.62792e16			0.849647			0.424824	−	0.905276i	$-0.360336\pi$
$397$	6.62792e16			0.849647			0.424824	+	0.905276i	$0.360336\pi$
$398$	1.69544e16	−	2.93658e16i	0.213817	−	0.370341i
$399$		0			0
$400$	6.23339e15	+	1.07966e16i	0.0760912	+	0.131794i
$401$	−4.76233e15	−	8.24860e15i	−0.0571980	−	0.0990699i	0.836009	−	0.548716i	$-0.184883\pi$
$401$	−4.76233e15	−	8.24860e15i	−0.0571980	−	0.0990699i	−0.893207	+	0.449646i	$0.851550\pi$
$402$		0			0
$403$	−7.05377e16	+	1.22175e17i	−0.820236	+	1.42069i
$404$	5.04688e16			0.577490
$405$		0			0
$406$	6.51182e16			0.721578
$407$	1.43677e16	−	2.48857e16i	0.156684	−	0.271385i
$408$		0			0
$409$	−8.61134e15	−	1.49153e16i	−0.0909639	−	0.157554i	0.816953	−	0.576704i	$-0.195661\pi$
$409$	−8.61134e15	−	1.49153e16i	−0.0909639	−	0.157554i	−0.907917	+	0.419150i	$0.862328\pi$
$410$	3.29688e15	+	5.71036e15i	0.0342774	+	0.0593702i
$411$		0			0
$412$	−7.82059e15	+	1.35457e16i	−0.0787784	+	0.136448i
$413$	1.68977e17			1.67553
$414$		0			0
$415$	2.02148e16			0.194248
$416$	9.33438e15	−	1.61676e16i	0.0883037	−	0.152946i
$417$		0			0
$418$	−2.04143e16	−	3.53586e16i	−0.187193	−	0.324227i
$419$	−7.14576e16	−	1.23768e17i	−0.645145	−	1.11742i	−0.984268	−	0.176682i	$-0.943463\pi$
$419$	−7.14576e16	−	1.23768e17i	−0.645145	−	1.11742i	0.339123	−	0.940742i	$-0.389870\pi$
$420$		0			0
$421$	−5.30966e16	+	9.19660e16i	−0.464765	+	0.804996i	−0.999191	−	0.0402192i	$-0.987194\pi$
$421$	−5.30966e16	+	9.19660e16i	−0.464765	+	0.804996i	0.534426	+	0.845215i	$0.320528\pi$
$422$	−2.53744e15			−0.0218708
$423$		0			0
$424$	1.55881e16			0.130291
$425$	−3.81371e16	+	6.60553e16i	−0.313920	+	0.543726i
$426$		0			0
$427$	4.19166e16	+	7.26016e16i	0.334660	+	0.579649i
$428$	5.93249e16	+	1.02754e17i	0.466501	+	0.808003i
$429$		0			0
$430$	2.32739e16	−	4.03116e16i	0.177552	−	0.307528i
$431$	9.79018e16			0.735679			0.367840	−	0.929889i	$-0.380098\pi$
$431$	9.79018e16			0.735679			0.367840	+	0.929889i	$0.380098\pi$
$432$		0			0
$433$	1.01860e17			0.742736			0.371368	−	0.928486i	$-0.378889\pi$
$433$	1.01860e17			0.742736			0.371368	+	0.928486i	$0.378889\pi$
$434$	7.58206e16	−	1.31325e17i	0.544633	−	0.943332i
$435$		0			0
$436$	−4.12736e16	−	7.14880e16i	−0.287747	−	0.498392i
$437$	3.67591e16	+	6.36687e16i	0.252485	+	0.437317i
$438$		0			0
$439$	−7.75733e16	+	1.34361e17i	−0.517241	+	0.895887i	0.482559	+	0.875864i	$0.339707\pi$
$439$	−7.75733e16	+	1.34361e17i	−0.517241	+	0.895887i	−0.999800	+	0.0200235i	$0.993626\pi$
$440$	−1.28420e16			−0.0843705
$441$		0			0
$442$	1.14219e17			0.728607
$443$	−4.10565e15	+	7.11119e15i	−0.0258082	+	0.0447011i	−0.878641	−	0.477483i	$-0.841549\pi$
$443$	−4.10565e15	+	7.11119e15i	−0.0258082	+	0.0447011i	0.852833	+	0.522184i	$0.174883\pi$
$444$		0			0
$445$	−6.59736e16	−	1.14270e17i	−0.402745	−	0.697575i
$446$	1.06995e17	+	1.85321e17i	0.643706	+	1.11493i
$447$		0			0
$448$	−1.00335e16	+	1.73785e16i	−0.0586333	+	0.101556i
$449$	2.94000e16			0.169335			0.0846675	−	0.996409i	$-0.473017\pi$
$449$	2.94000e16			0.169335			0.0846675	+	0.996409i	$0.473017\pi$
$450$		0			0
$451$	1.05672e16			0.0591306
$452$	−3.01917e16	+	5.22935e16i	−0.166528	+	0.288435i
$453$		0			0
$454$	5.01367e16	+	8.68393e16i	0.268715	+	0.465429i
$455$	−5.54792e16	−	9.60928e16i	−0.293127	−	0.507711i
$456$		0			0
$457$	−1.27616e17	+	2.21038e17i	−0.655316	+	1.13504i	0.326499	+	0.945198i	$0.394131\pi$
$457$	−1.27616e17	+	2.21038e17i	−0.655316	+	1.13504i	−0.981815	+	0.189842i	$0.939202\pi$
$458$	−2.47662e17			−1.25382
$459$		0			0
$460$	2.31240e16			0.113799
$461$	−6.15012e16	+	1.06523e17i	−0.298420	+	0.516878i	−0.975775	−	0.218778i	$-0.929793\pi$
$461$	−6.15012e16	+	1.06523e17i	−0.298420	+	0.516878i	0.677355	+	0.735656i	$0.263126\pi$
$462$		0			0
$463$	2.63262e16	+	4.55984e16i	0.124197	+	0.215116i	0.921419	−	0.388571i	$-0.127031\pi$
$463$	2.63262e16	+	4.55984e16i	0.124197	+	0.215116i	−0.797222	+	0.603687i	$0.793698\pi$
$464$	−2.92288e16	−	5.06258e16i	−0.135970	−	0.235508i
$465$		0			0
$466$	1.63002e16	−	2.82328e16i	0.0737368	−	0.127716i
$467$	−3.35303e17			−1.49581			−0.747907	−	0.663803i	$-0.768941\pi$
$467$	−3.35303e17			−1.49581			−0.747907	+	0.663803i	$0.768941\pi$
$468$		0			0
$469$	2.55464e17			1.10843
$470$	2.12690e15	−	3.68389e15i	0.00910144	−	0.0157642i
$471$		0			0
$472$	−7.58468e16	−	1.31370e17i	−0.315729	−	0.546858i
$473$	−3.72989e16	−	6.46036e16i	−0.153143	−	0.265252i
$474$		0			0
$475$	1.05740e17	−	1.83147e17i	0.422407	−	0.731630i
$476$	−1.22773e17			−0.483792
$477$		0			0
$478$	−1.01718e17			−0.390048
$479$	−1.28704e17	+	2.22922e17i	−0.486869	+	0.843282i	−0.999886	−	0.0150967i	$-0.995194\pi$
$479$	−1.28704e17	+	2.22922e17i	−0.486869	+	0.843282i	0.513017	+	0.858378i	$0.328528\pi$
$480$		0			0
$481$	−1.11443e17	−	1.93026e17i	−0.410309	−	0.710676i
$482$	1.26571e16	+	2.19227e16i	0.0459756	+	0.0796321i
$483$		0			0
$484$	6.04122e16	−	1.04637e17i	0.213614	−	0.369990i
$485$	−2.62094e16			−0.0914400
$486$		0			0
$487$	−1.57963e17			−0.536560			−0.268280	−	0.963341i	$-0.586455\pi$
$487$	−1.57963e17			−0.536560			−0.268280	+	0.963341i	$0.586455\pi$
$488$	3.76291e16	−	6.51756e16i	0.126123	−	0.218452i
$489$		0			0
$490$	−8.12487e15	−	1.40727e16i	−0.0265181	−	0.0459307i
$491$	−9.68006e16	−	1.67664e17i	−0.311780	−	0.540019i	0.666968	−	0.745087i	$-0.267592\pi$
$491$	−9.68006e16	−	1.67664e17i	−0.311780	−	0.540019i	−0.978748	+	0.205068i	$0.934259\pi$
$492$		0			0
$493$	1.78827e17	−	3.09738e17i	0.560956	−	0.971604i
$494$	−3.16687e17			−0.980404
$495$		0			0
$496$	−1.36131e17			−0.410511
$497$	2.40067e17	−	4.15808e17i	0.714522	−	1.23759i
$498$		0			0
$499$	−2.03789e17	−	3.52972e17i	−0.590917	−	1.02350i	−0.994109	−	0.108383i	$-0.965433\pi$
$499$	−2.03789e17	−	3.52972e17i	−0.590917	−	1.02350i	0.403192	−	0.915115i	$-0.367901\pi$
$500$	−8.78955e16	−	1.52239e17i	−0.251572	−	0.435735i
$501$		0			0
$502$	−9.41657e16	+	1.63100e17i	−0.262615	+	0.454862i
$503$	3.41866e17			0.941162			0.470581	−	0.882357i	$-0.344044\pi$
$503$	3.41866e17			0.941162			0.470581	+	0.882357i	$0.344044\pi$
$504$		0			0
$505$	−2.69282e17			−0.722458
$506$	1.85294e16	−	3.20938e16i	0.0490774	−	0.0850046i
$507$		0			0
$508$	1.28548e17	+	2.22652e17i	0.331858	+	0.574794i
$509$	3.30769e17	+	5.72909e17i	0.843062	+	1.46023i	0.887294	+	0.461205i	$0.152583\pi$
$509$	3.30769e17	+	5.72909e17i	0.843062	+	1.46023i	−0.0442315	+	0.999021i	$0.514084\pi$
$510$		0			0
$511$	2.37972e17	−	4.12180e17i	0.591276	−	1.02412i
$512$	1.80144e16			0.0441942
$513$		0			0
$514$	−5.44148e17			−1.30154
$515$	4.17275e16	−	7.22742e16i	0.0985543	−	0.170701i
$516$		0			0
$517$	−3.40857e15	−	5.90382e15i	−0.00785026	−	0.0135970i
$518$	1.19790e17	+	2.07482e17i	0.272444	+	0.471886i
$519$		0			0
$520$	−4.98045e16	+	8.62640e16i	−0.110471	+	0.191341i
$521$	−1.27627e17			−0.279575			−0.139787	−	0.990182i	$-0.544642\pi$
$521$	−1.27627e17			−0.279575			−0.139787	+	0.990182i	$0.544642\pi$
$522$		0			0
$523$	−1.90574e17			−0.407196			−0.203598	−	0.979055i	$-0.565264\pi$
$523$	−1.90574e17			−0.407196			−0.203598	+	0.979055i	$0.565264\pi$
$524$	1.21661e17	−	2.10723e17i	0.256742	−	0.444690i
$525$		0			0
$526$	2.64670e16	+	4.58422e16i	0.0544875	+	0.0943752i
$527$	−4.16436e17	−	7.21289e17i	−0.846797	−	1.46670i
$528$		0			0
$529$	2.18653e17	−	3.78718e17i	0.433804	−	0.751371i
$530$	−8.31718e16			−0.162998
$531$		0			0
$532$	3.40405e17			0.650984
$533$	4.09822e16	−	7.09833e16i	0.0774227	−	0.134100i
$534$		0			0
$535$	−3.16534e17	−	5.48253e17i	−0.583608	−	1.01084i
$536$	−1.14667e17	−	1.98609e17i	−0.208866	−	0.361766i
$537$		0			0
$538$	−3.88628e17	+	6.73123e17i	−0.690954	+	1.19677i
$539$	−2.60419e16			−0.0457453
$540$		0			0
$541$	6.46355e17			1.10838			0.554191	−	0.832390i	$-0.313028\pi$
$541$	6.46355e17			1.10838			0.554191	+	0.832390i	$0.313028\pi$
$542$	2.77167e16	−	4.80067e16i	0.0469619	−	0.0813405i
$543$		0			0
$544$	5.51077e16	+	9.54494e16i	0.0911632	+	0.157899i
$545$	2.20220e17	+	3.81432e17i	0.359981	+	0.623505i
$546$		0			0
$547$	−1.79901e17	+	3.11598e17i	−0.287155	+	0.497367i	−0.973129	−	0.230259i	$-0.926043\pi$
$547$	−1.79901e17	+	3.11598e17i	−0.287155	+	0.497367i	0.685975	+	0.727625i	$0.259376\pi$
$548$	−5.49363e17			−0.866535
$549$		0			0
$550$	−1.06602e17			−0.164213
$551$	−4.95822e17	+	8.58789e17i	−0.754815	+	1.30738i
$552$		0			0
$553$	4.41949e17	+	7.65478e17i	0.657141	+	1.13820i
$554$	7.14869e16	+	1.23819e17i	0.105054	+	0.181959i
$555$		0			0
$556$	3.04764e17	−	5.27867e17i	0.437500	−	0.757772i
$557$	1.20436e18			1.70883			0.854413	−	0.519595i	$-0.173917\pi$
$557$	1.20436e18			1.70883			0.854413	+	0.519595i	$0.173917\pi$
$558$		0			0
$559$	−5.78617e17			−0.802075
$560$	5.35346e16	−	9.27247e16i	0.0733521	−	0.127050i
$561$		0			0
$562$	1.51926e17	+	2.63144e17i	0.203398	+	0.352296i
$563$	7.49238e15	+	1.29772e16i	0.00991551	+	0.0171742i	0.870941	−	0.491388i	$-0.163510\pi$
$563$	7.49238e15	+	1.29772e16i	0.00991551	+	0.0171742i	−0.861025	+	0.508563i	$0.830177\pi$
$564$		0			0
$565$	1.61091e17	−	2.79018e17i	0.208332	−	0.360842i
$566$	−4.19874e17			−0.536799
$567$		0			0
$568$	−4.31024e17			−0.538563
$569$	−3.97144e17	+	6.87874e17i	−0.490590	+	0.849727i	−0.999941	−	0.0108318i	$-0.996552\pi$
$569$	−3.97144e17	+	6.87874e17i	−0.490590	+	0.849727i	0.509351	+	0.860559i	$0.329885\pi$
$570$		0			0
$571$	4.75009e17	+	8.22740e17i	0.573545	+	0.993408i	0.996198	+	0.0871169i	$0.0277654\pi$
$571$	4.75009e17	+	8.22740e17i	0.573545	+	0.993408i	−0.422654	+	0.906291i	$0.638901\pi$
$572$	7.98170e16	+	1.38247e17i	0.0952843	+	0.165037i
$573$		0			0
$574$	−4.40515e16	+	7.62995e16i	−0.0514084	+	0.0890419i
$575$	1.91953e17			0.221490
$576$		0			0
$577$	2.58846e17			0.292011			0.146005	−	0.989284i	$-0.453358\pi$
$577$	2.58846e17			0.292011			0.146005	+	0.989284i	$0.453358\pi$
$578$	−2.02128e16	+	3.50097e16i	−0.0225474	+	0.0390532i
$579$		0			0
$580$	1.55953e17	+	2.70119e17i	0.170103	+	0.294627i
$581$	1.35051e17	+	2.33915e17i	0.145664	+	0.252298i
$582$		0			0
$583$	−6.66458e16	+	1.15434e17i	−0.0702954	+	0.121755i
$584$	−4.27263e17			−0.445668
$585$		0			0
$586$	7.07913e17			0.722180
$587$	6.50180e17	−	1.12614e18i	0.655973	−	1.13618i	−0.325676	−	0.945481i	$-0.605592\pi$
$587$	6.50180e17	−	1.12614e18i	0.655973	−	1.13618i	0.981649	−	0.190697i	$-0.0610747\pi$
$588$		0			0
$589$	1.15462e18	+	1.99987e18i	1.13944	+	1.97357i
$590$	4.04688e17	+	7.00940e17i	0.394987	+	0.684137i
$591$		0			0
$592$	1.07537e17	−	1.86260e17i	0.102676	−	0.177839i
$593$	1.53388e18			1.44855			0.724277	−	0.689509i	$-0.242174\pi$
$593$	1.53388e18			1.44855			0.724277	+	0.689509i	$0.242174\pi$
$594$		0			0
$595$	6.55069e17			0.605239
$596$	4.51167e16	−	7.81445e16i	0.0412322	−	0.0714163i
$597$		0			0
$598$	−1.43723e17	−	2.48935e17i	−0.128519	−	0.222602i
$599$	−4.15847e17	−	7.20268e17i	−0.367840	−	0.637118i	0.621388	−	0.783503i	$-0.286569\pi$
$599$	−4.15847e17	−	7.20268e17i	−0.367840	−	0.637118i	−0.989228	+	0.146386i	$0.953236\pi$
$600$		0			0
$601$	3.69383e17	−	6.39790e17i	0.319737	−	0.553800i	−0.660696	−	0.750653i	$-0.729739\pi$
$601$	3.69383e17	−	6.39790e17i	0.319737	−	0.553800i	0.980433	+	0.196853i	$0.0630722\pi$
$602$	6.21953e17			0.532574
$603$		0			0
$604$	1.71625e17			0.143827
$605$	−3.22335e17	+	5.58301e17i	−0.267238	+	0.462870i
$606$		0			0
$607$	9.65998e16	+	1.67316e17i	0.0783880	+	0.135772i	0.902555	−	0.430575i	$-0.141689\pi$
$607$	9.65998e16	+	1.67316e17i	0.0783880	+	0.135772i	−0.824167	+	0.566347i	$0.808356\pi$
$608$	−1.52793e17	−	2.64646e17i	−0.122668	−	0.212467i
$609$		0			0
$610$	−2.00774e17	+	3.47751e17i	−0.157784	+	0.273290i
$611$	−5.28772e16			−0.0411150
$612$		0			0
$613$	−1.81666e18			−1.38286			−0.691432	−	0.722441i	$-0.743020\pi$
$613$	−1.81666e18			−1.38286			−0.691432	+	0.722441i	$0.743020\pi$
$614$	1.55473e17	−	2.69287e17i	0.117101	−	0.202825i
$615$		0			0
$616$	−8.57948e16	−	1.48601e17i	−0.0632683	−	0.109584i
$617$	−1.96368e17	−	3.40119e17i	−0.143290	−	0.248186i	0.785443	−	0.618934i	$-0.212435\pi$
$617$	−1.96368e17	−	3.40119e17i	−0.143290	−	0.248186i	−0.928734	+	0.370747i	$0.879102\pi$
$618$		0			0
$619$	−1.15858e17	+	2.00672e17i	−0.0827822	+	0.143383i	−0.904444	−	0.426592i	$-0.859714\pi$
$619$	−1.15858e17	+	2.00672e17i	−0.0827822	+	0.143383i	0.821662	+	0.569975i	$0.193047\pi$
$620$	7.26339e17			0.513562
$621$		0			0
$622$	−4.96998e17			−0.344126
$623$	8.81512e17	−	1.52682e18i	0.604026	−	1.04620i
$624$		0			0
$625$	1.54363e16	+	2.67365e16i	0.0103591	+	0.0179426i
$626$	7.98764e17	+	1.38350e18i	0.530500	+	0.918853i
$627$		0			0
$628$	2.76222e17	−	4.78431e17i	0.179689	−	0.311230i
$629$	1.31586e18			0.847193
$630$		0			0
$631$	−3.03856e18			−1.91636			−0.958180	−	0.286165i	$-0.907620\pi$
$631$	−3.03856e18			−1.91636			−0.958180	+	0.286165i	$0.907620\pi$
$632$	3.96744e17	−	6.87181e17i	0.247656	−	0.428953i
$633$		0			0
$634$	3.43678e16	+	5.95267e16i	0.0210170	+	0.0364026i
$635$	−6.85882e17	−	1.18798e18i	−0.415165	−	0.719086i
$636$		0			0
$637$	−1.00997e17	+	1.74932e17i	−0.0598966	+	0.103744i
$638$	4.99863e17			0.293438
$639$		0			0
$640$	−9.61177e16			−0.0552883
$641$	−1.47678e18	+	2.55785e18i	−0.840887	+	1.45646i	0.0482578	+	0.998835i	$0.484633\pi$
$641$	−1.47678e18	+	2.55785e18i	−0.840887	+	1.45646i	−0.889145	+	0.457625i	$0.848700\pi$
$642$		0			0
$643$	−5.96115e17	−	1.03250e18i	−0.332628	−	0.576129i	0.650398	−	0.759593i	$-0.274602\pi$
$643$	−5.96115e17	−	1.03250e18i	−0.332628	−	0.576129i	−0.983026	+	0.183465i	$0.941269\pi$
$644$	1.54487e17	+	2.67579e17i	0.0853362	+	0.147807i
$645$		0			0
$646$	9.34819e17	−	1.61915e18i	0.506076	−	0.876550i
$647$	−2.23653e18			−1.19866			−0.599331	−	0.800502i	$-0.704567\pi$
$647$	−2.23653e18			−1.19866			−0.599331	+	0.800502i	$0.704567\pi$
$648$		0			0
$649$	1.29711e18			0.681375
$650$	−4.13428e17	+	7.16079e17i	−0.215012	+	0.372412i
$651$		0			0
$652$	−3.39264e17	−	5.87623e17i	−0.172953	−	0.299564i
$653$	−2.19229e17	−	3.79715e17i	−0.110653	−	0.191656i	0.805381	−	0.592758i	$-0.201961\pi$
$653$	−2.19229e17	−	3.79715e17i	−0.110653	−	0.191656i	−0.916034	+	0.401102i	$0.868627\pi$
$654$		0			0
$655$	−6.49133e17	+	1.12433e18i	−0.321192	+	0.556322i
$656$	7.90915e16			0.0387485
$657$		0			0
$658$	5.68374e16			0.0273002
$659$	6.64942e17	−	1.15171e18i	0.316248	−	0.547758i	−0.663454	−	0.748217i	$-0.730910\pi$
$659$	6.64942e17	−	1.15171e18i	0.316248	−	0.547758i	0.979702	+	0.200459i	$0.0642434\pi$
$660$		0			0
$661$	−2.57315e17	−	4.45682e17i	−0.119993	−	0.207834i	0.799772	−	0.600304i	$-0.204954\pi$
$661$	−2.57315e17	−	4.45682e17i	−0.119993	−	0.207834i	−0.919765	+	0.392471i	$0.871620\pi$
$662$	−1.19650e18	−	2.07239e18i	−0.552503	−	0.956963i
$663$		0			0
$664$	1.21237e17	−	2.09989e17i	0.0548964	−	0.0950833i
$665$	−1.81627e18			−0.814402
$666$		0			0
$667$	−9.00081e17			−0.395789
$668$	−3.31818e17	+	5.74725e17i	−0.144495	+	0.250273i
$669$		0			0
$670$	6.11818e17	+	1.05970e18i	0.261298	+	0.452581i
$671$	3.21762e17	+	5.57307e17i	0.136094	+	0.235721i
$672$		0			0
$673$	1.89072e18	−	3.27482e18i	0.784384	−	1.35859i	−0.144982	−	0.989434i	$-0.546312\pi$
$673$	1.89072e18	−	3.27482e18i	0.784384	−	1.35859i	0.929366	−	0.369159i	$-0.120354\pi$
$674$	5.70089e17			0.234236
$675$		0			0
$676$	−2.37579e15			−0.000957534
$677$	−8.47886e17	+	1.46858e18i	−0.338463	+	0.586235i	−0.984144	−	0.177372i	$-0.943240\pi$
$677$	−8.47886e17	+	1.46858e18i	−0.338463	+	0.586235i	0.645681	+	0.763607i	$0.276574\pi$
$678$		0			0
$679$	−1.75100e17	−	3.03282e17i	−0.0685696	−	0.118766i
$680$	−2.94033e17	−	5.09280e17i	−0.114048	−	0.197537i
$681$		0			0
$682$	5.82017e17	−	1.00808e18i	0.221481	−	0.383617i
$683$	−3.06899e18			−1.15681			−0.578404	−	0.815750i	$-0.696324\pi$
$683$	−3.06899e18			−1.15681			−0.578404	+	0.815750i	$0.696324\pi$
$684$		0			0
$685$	2.93118e18			1.08406
$686$	1.01393e18	−	1.75618e18i	0.371451	−	0.643372i
$687$		0			0
$688$	−2.79168e17	−	4.83533e17i	−0.100355	−	0.173821i
$689$	5.16938e17	+	8.95363e17i	0.184083	+	0.318841i
$690$		0			0
$691$	2.86999e17	−	4.97097e17i	0.100294	−	0.173714i	−0.811512	−	0.584336i	$-0.801355\pi$
$691$	2.86999e17	−	4.97097e17i	0.100294	−	0.173714i	0.911806	+	0.410622i	$0.134688\pi$
$692$	1.09757e18			0.379964
$693$		0			0
$694$	1.13916e18			0.387033
$695$	−1.62610e18	+	2.81649e18i	−0.547326	+	0.947996i
$696$		0			0
$697$	2.41948e17	+	4.19067e17i	0.0799299	+	0.138443i
$698$	−1.29907e18	−	2.25005e18i	−0.425179	−	0.736431i
$699$		0			0
$700$	4.44392e17	−	7.69709e17i	0.142767	−	0.247280i
$701$	−5.78307e18			−1.84073			−0.920367	−	0.391056i	$-0.872110\pi$
$701$	−5.78307e18			−1.84073			−0.920367	+	0.391056i	$0.872110\pi$
$702$		0			0
$703$	−3.64841e18			−1.13997
$704$	−7.70193e16	+	1.33401e17i	−0.0238439	+	0.0412989i
$705$		0			0
$706$	−1.61736e18	−	2.80135e18i	−0.491560	−	0.851406i
$707$	−1.79901e18	−	3.11598e18i	−0.541762	−	0.938359i
$708$		0			0
$709$	−1.04576e18	+	1.81130e18i	−0.309193	+	0.535538i	−0.978186	−	0.207731i	$-0.933392\pi$
$709$	−1.04576e18	+	1.81130e18i	−0.309193	+	0.535538i	0.668993	+	0.743269i	$0.266726\pi$
$710$	2.29977e18			0.673760
$711$		0			0
$712$	−1.58269e18			−0.455278
$713$	−1.04801e18	+	1.81521e18i	−0.298734	+	0.517422i
$714$		0			0
$715$	−4.25872e17	−	7.37632e17i	−0.119204	−	0.206467i
$716$	1.66781e18	+	2.88872e18i	0.462605	+	0.801256i
$717$		0			0
$718$	−1.31842e18	+	2.28356e18i	−0.359123	+	0.622020i
$719$	2.54253e18			0.686321			0.343161	−	0.939277i	$-0.388502\pi$
$719$	2.54253e18			0.686321			0.343161	+	0.939277i	$0.388502\pi$
$720$		0			0
$721$	1.11509e18			0.295618
$722$	−1.24621e18	+	2.15850e18i	−0.327416	+	0.567101i
$723$		0			0
$724$	1.39791e18	+	2.42125e18i	0.360726	+	0.624796i
$725$	1.29457e18	+	2.24226e18i	0.331077	+	0.573442i
$726$		0			0
$727$	−2.67471e18	+	4.63273e18i	−0.671897	+	1.16376i	0.305469	+	0.952202i	$0.401187\pi$
$727$	−2.67471e18	+	4.63273e18i	−0.671897	+	1.16376i	−0.977366	+	0.211557i	$0.932147\pi$
$728$	−1.33093e18			−0.331362
$729$		0			0
$730$	2.27970e18			0.557545
$731$	1.70800e18	−	2.95835e18i	0.414024	−	0.717111i
$732$		0			0
$733$	5.07526e17	+	8.79060e17i	0.120860	+	0.209335i	0.920107	−	0.391667i	$-0.128101\pi$
$733$	5.07526e17	+	8.79060e17i	0.120860	+	0.209335i	−0.799247	+	0.601003i	$0.794768\pi$
$734$	1.22924e18	+	2.12911e18i	0.290143	+	0.502543i
$735$		0			0
$736$	1.38685e17	−	2.40210e17i	0.0321606	−	0.0557038i
$737$	1.96100e18			0.450754
$738$		0			0
$739$	−4.21697e18			−0.952384			−0.476192	−	0.879341i	$-0.657983\pi$
$739$	−4.21697e18			−0.952384			−0.476192	+	0.879341i	$0.657983\pi$
$740$	−5.73776e17	+	9.93809e17i	−0.128451	+	0.222483i
$741$		0			0
$742$	−5.55654e17	−	9.62420e17i	−0.122230	−	0.211709i
$743$	6.27655e17	+	1.08713e18i	0.136865	+	0.237058i	0.926309	−	0.376766i	$-0.122964\pi$
$743$	6.27655e17	+	1.08713e18i	0.136865	+	0.237058i	−0.789443	+	0.613824i	$0.789631\pi$
$744$		0			0
$745$	−2.40725e17	+	4.16948e17i	−0.0515829	+	0.0893441i
$746$	−3.35846e18			−0.713407
$747$		0			0
$748$	−9.42437e17			−0.196740
$749$	4.22940e18	−	7.32553e18i	0.875279	−	1.51603i
$750$		0			0
$751$	−4.76700e18	−	8.25669e18i	−0.969584	−	1.67937i	−0.696759	−	0.717306i	$-0.745375\pi$
$751$	−4.76700e18	−	8.25669e18i	−0.969584	−	1.67937i	−0.272826	−	0.962064i	$-0.587958\pi$
$752$	−2.55119e16	−	4.41879e16i	−0.00514430	−	0.00891020i
$753$		0			0
$754$	1.93859e18	−	3.35774e18i	0.384214	−	0.665478i
$755$	−9.15722e17			−0.179932
$756$		0			0
$757$	8.60869e18			1.66270			0.831350	−	0.555749i	$-0.187569\pi$
$757$	8.60869e18			1.66270			0.831350	+	0.555749i	$0.187569\pi$
$758$	1.21639e18	−	2.10684e18i	0.232928	−	0.403443i
$759$		0			0
$760$	8.15245e17	+	1.41205e18i	0.153462	+	0.265803i
$761$	2.59150e18	+	4.48862e18i	0.483673	+	0.837746i	0.999824	−	0.0187517i	$-0.00596919\pi$
$761$	2.59150e18	+	4.48862e18i	0.483673	+	0.837746i	−0.516151	+	0.856497i	$0.672636\pi$
$762$		0			0
$763$	−2.94248e18	+	5.09653e18i	−0.539889	+	0.935116i
$764$	2.43402e18			0.442809
$765$		0			0
$766$	1.22722e18			0.219500
$767$	5.03052e18	−	8.71311e18i	0.892160	−	1.54527i
$768$		0			0
$769$	2.02951e18	+	3.51522e18i	0.353892	+	0.612959i	0.986928	−	0.161164i	$-0.0515247\pi$
$769$	2.02951e18	+	3.51522e18i	0.353892	+	0.612959i	−0.633036	+	0.774123i	$0.718191\pi$
$770$	4.57767e17	+	7.92876e17i	0.0791507	+	0.137093i
$771$		0			0
$772$	−1.71116e18	+	2.96382e18i	−0.290923	+	0.503894i
$773$	−1.51385e18			−0.255221			−0.127610	−	0.991824i	$-0.540731\pi$
$773$	−1.51385e18			−0.255221			−0.127610	+	0.991824i	$0.540731\pi$
$774$		0			0
$775$	6.02935e18			0.999561
$776$	−1.57190e17	+	2.72260e17i	−0.0258418	+	0.0447593i
$777$		0			0
$778$	−2.40112e18	−	4.15886e18i	−0.388192	−	0.672369i
$779$	−6.70833e17	−	1.16192e18i	−0.107553	−	0.186287i
$780$		0			0
$781$	1.84281e18	−	3.19184e18i	0.290569	−	0.503280i
$782$	1.69700e18			0.265362
$783$		0			0
$784$	−1.94914e17			−0.0299770
$785$	−1.47381e18	+	2.55272e18i	−0.224797	+	0.389359i
$786$		0			0
$787$	2.55698e18	+	4.42882e18i	0.383612	+	0.664435i	0.991576	−	0.129530i	$-0.0413467\pi$
$787$	2.55698e18	+	4.42882e18i	0.383612	+	0.664435i	−0.607964	+	0.793965i	$0.708013\pi$
$788$	−1.87136e18	−	3.24128e18i	−0.278443	−	0.482277i
$789$		0			0
$790$	−2.11687e18	+	3.66652e18i	−0.309826	+	0.536634i
$791$	4.30486e18			0.624902
$792$		0			0
$793$	4.99149e18			0.712778
$794$	−2.12093e18	+	3.67356e18i	−0.300396	+	0.520301i
$795$		0			0
$796$	1.08508e18	+	1.87941e18i	0.151191	+	0.261871i
$797$	5.54336e18	+	9.60138e18i	0.766115	+	1.32695i	0.939655	+	0.342123i	$0.111146\pi$
$797$	5.54336e18	+	9.60138e18i	0.766115	+	1.32695i	−0.173540	+	0.984827i	$0.555521\pi$
$798$		0			0
$799$	1.56086e17	−	2.70350e17i	0.0212232	−	0.0367597i
$800$	−7.97874e17			−0.107609
$801$		0			0
$802$	6.09578e17			0.0808902
$803$	1.82673e18	−	3.16399e18i	0.240449	−	0.416471i
$804$		0			0
$805$	−8.24281e17	−	1.42770e18i	−0.106758	−	0.184911i
$806$	−4.51441e18	−	7.81919e18i	−0.579994	−	1.00458i
$807$		0			0
$808$	−1.61500e18	+	2.79727e18i	−0.204174	+	0.353639i
$809$	1.01551e19			1.27356			0.636778	−	0.771047i	$-0.280267\pi$
$809$	1.01551e19			1.27356			0.636778	+	0.771047i	$0.280267\pi$
$810$		0			0
$811$	8.70589e18			1.07443			0.537214	−	0.843446i	$-0.319477\pi$
$811$	8.70589e18			1.07443			0.537214	+	0.843446i	$0.319477\pi$
$812$	−2.08378e18	+	3.60922e18i	−0.255116	+	0.441874i
$813$		0			0
$814$	9.19536e17	+	1.59268e18i	0.110792	+	0.191898i
$815$	1.81018e18	+	3.13532e18i	0.216370	+	0.374764i
$816$		0			0
$817$	−4.73566e18	+	8.20241e18i	−0.557105	+	0.964935i
$818$	1.10225e18			0.128642
$819$		0			0
$820$	−4.22001e17			−0.0484756
$821$	3.57522e17	−	6.19247e17i	0.0407448	−	0.0705721i	−0.844934	−	0.534871i	$-0.820360\pi$
$821$	3.57522e17	−	6.19247e17i	0.0407448	−	0.0705721i	0.885679	+	0.464299i	$0.153694\pi$
$822$		0			0
$823$	−6.22452e18	−	1.07812e19i	−0.698244	−	1.20939i	−0.969075	−	0.246767i	$-0.920632\pi$
$823$	−6.22452e18	−	1.07812e19i	−0.698244	−	1.20939i	0.270831	−	0.962627i	$-0.412701\pi$
$824$	−5.00517e17	−	8.66922e17i	−0.0557048	−	0.0964835i
$825$		0			0
$826$	−5.40727e18	+	9.36567e18i	−0.592390	+	1.02605i
$827$	−4.42505e18			−0.480986			−0.240493	−	0.970651i	$-0.577309\pi$
$827$	−4.42505e18			−0.480986			−0.240493	+	0.970651i	$0.577309\pi$
$828$		0			0
$829$	1.96050e18			0.209779			0.104890	−	0.994484i	$-0.466551\pi$
$829$	1.96050e18			0.209779			0.104890	+	0.994484i	$0.466551\pi$
$830$	−6.46874e17	+	1.12042e18i	−0.0686771	+	0.118952i
$831$		0			0
$832$	5.97400e17	+	1.03473e18i	0.0624401	+	0.108149i
$833$	−5.96260e17	−	1.03275e18i	−0.0618363	−	0.107104i
$834$		0			0
$835$	1.77045e18	−	3.06651e18i	0.180768	−	0.313099i
$836$	2.61303e18			0.264730
$837$		0			0
$838$	9.14658e18			0.912373
$839$	−4.88000e18	+	8.45241e18i	−0.483022	+	0.836619i	−0.999810	−	0.0194945i	$-0.993794\pi$
$839$	−4.88000e18	+	8.45241e18i	−0.483022	+	0.836619i	0.516788	+	0.856114i	$0.327128\pi$
$840$		0			0
$841$	−9.40017e17	−	1.62816e18i	−0.0916139	−	0.158680i
$842$	−3.39818e18	−	5.88582e18i	−0.328638	−	0.569218i
$843$		0			0
$844$	8.11981e16	−	1.40639e17i	0.00773250	−	0.0133931i
$845$	1.26763e16			0.00119791
$846$		0			0
$847$	−8.61382e18			−0.801592
$848$	−4.98819e17	+	8.63980e17i	−0.0460649	+	0.0797867i
$849$		0			0
$850$	−2.44077e18	−	4.22754e18i	−0.221975	−	0.384472i
$851$	−1.65577e18	−	2.86787e18i	−0.149437	−	0.258832i
$852$		0			0
$853$	1.17246e18	−	2.03076e18i	0.104215	−	0.180506i	−0.809202	−	0.587530i	$-0.800100\pi$
$853$	1.17246e18	−	2.03076e18i	0.104215	−	0.180506i	0.913417	+	0.407025i	$0.133434\pi$
$854$	−5.36532e18			−0.473281
$855$		0			0
$856$	−7.59359e18			−0.659732
$857$	5.33861e18	−	9.24675e18i	0.460313	−	0.797285i	−0.538664	−	0.842521i	$-0.681071\pi$
$857$	5.33861e18	−	9.24675e18i	0.460313	−	0.797285i	0.998976	+	0.0452360i	$0.0144040\pi$
$858$		0			0
$859$	8.60207e18	+	1.48992e19i	0.730546	+	1.26534i	0.956650	+	0.291239i	$0.0940675\pi$
$859$	8.60207e18	+	1.48992e19i	0.730546	+	1.26534i	−0.226105	+	0.974103i	$0.572599\pi$
$860$	1.48953e18	+	2.57994e18i	0.125548	+	0.217455i
$861$		0			0
$862$	−3.13286e18	+	5.42627e18i	−0.260102	+	0.450510i
$863$	1.42851e18			0.117710			0.0588548	−	0.998267i	$-0.481255\pi$
$863$	1.42851e18			0.117710			0.0588548	+	0.998267i	$0.481255\pi$
$864$		0			0
$865$	−5.85620e18			−0.475348
$866$	−3.25953e18	+	5.64568e18i	−0.262597	+	0.454831i
$867$		0			0
$868$	4.85252e18	+	8.40481e18i	0.385114	+	0.667036i
$869$	3.39250e18	+	5.87599e18i	0.267234	+	0.462863i
$870$		0			0
$871$	7.60526e18	−	1.31727e19i	0.590196	−	1.02225i
$872$	5.28303e18			0.406936
$873$		0			0
$874$	−4.70517e18			−0.357068
$875$	−6.26625e18	+	1.08535e19i	−0.472015	+	0.817553i
$876$		0			0
$877$	−6.22801e18	−	1.07872e19i	−0.462223	−	0.800594i	0.536848	−	0.843679i	$-0.319615\pi$
$877$	−6.22801e18	−	1.07872e19i	−0.462223	−	0.800594i	−0.999071	+	0.0430847i	$0.986281\pi$
$878$	−4.96469e18	−	8.59909e18i	−0.365744	−	0.633488i
$879$		0			0
$880$	4.10945e17	−	7.11777e17i	0.0298295	−	0.0516662i
$881$	3.63494e18			0.261911			0.130956	−	0.991388i	$-0.458195\pi$
$881$	3.63494e18			0.261911			0.130956	+	0.991388i	$0.458195\pi$
$882$		0			0
$883$	−1.55878e18			−0.110673			−0.0553364	−	0.998468i	$-0.517623\pi$
$883$	−1.55878e18			−0.110673			−0.0553364	+	0.998468i	$0.517623\pi$
$884$	−3.65501e18	+	6.33066e18i	−0.257601	+	0.446179i
$885$		0			0
$886$	−2.62762e17	−	4.55116e17i	−0.0182491	−	0.0316085i
$887$	4.28354e18	+	7.41931e18i	0.295325	+	0.511517i	0.975060	−	0.221940i	$-0.0712389\pi$
$887$	4.28354e18	+	7.41931e18i	0.295325	+	0.511517i	−0.679736	+	0.733457i	$0.737906\pi$
$888$		0			0
$889$	9.16447e18	−	1.58733e19i	0.622653	−	1.07847i
$890$	8.44462e18			0.569568
$891$		0			0
$892$	−1.36954e19			−0.910337
$893$	−4.32770e17	+	7.49580e17i	−0.0285577	+	0.0494634i
$894$		0			0
$895$	−8.89875e18	−	1.54131e19i	−0.578734	−	1.00240i
$896$	−6.42142e17	−	1.11222e18i	−0.0414600	−	0.0718108i
$897$		0			0
$898$	−9.40801e17	+	1.62952e18i	−0.0598690	+	0.103696i
$899$	−2.82720e19			−1.78615
$900$		0			0
$901$	−6.10373e18			−0.380088
$902$	−3.38150e17	+	5.85693e17i	−0.0209058	+	0.0362099i
$903$		0			0
$904$	−1.93227e18	−	3.34679e18i	−0.117753	−	0.203954i
$905$	−7.45868e18	−	1.29188e19i	−0.451280	−	0.781640i
$906$		0			0
$907$	−3.41915e18	+	5.92214e18i	−0.203925	+	0.353209i	−0.949790	−	0.312889i	$-0.898703\pi$
$907$	−3.41915e18	+	5.92214e18i	−0.203925	+	0.353209i	0.745865	+	0.666098i	$0.232037\pi$
$908$	−6.41749e18			−0.380021
$909$		0			0
$910$	7.10134e18			0.414545
$911$	2.67920e18	−	4.64050e18i	0.155287	−	0.268965i	−0.777876	−	0.628417i	$-0.783703\pi$
$911$	2.67920e18	−	4.64050e18i	0.155287	−	0.268965i	0.933163	+	0.359452i	$0.117036\pi$
$912$		0			0
$913$	1.03668e18	+	1.79559e18i	0.0592360	+	0.102600i
$914$	−8.16744e18	−	1.41464e19i	−0.463378	−	0.802594i
$915$		0			0
$916$	7.92519e18	−	1.37268e19i	0.443291	−	0.767803i
$917$	−1.73469e19			−0.963432
$918$		0			0
$919$	2.65287e19			1.45266			0.726332	−	0.687344i	$-0.241224\pi$
$919$	2.65287e19			1.45266			0.726332	+	0.687344i	$0.241224\pi$
$920$	−7.39969e17	+	1.28166e18i	−0.0402340	+	0.0696873i
$921$		0			0
$922$	−3.93608e18	−	6.81748e18i	−0.211015	−	0.365488i
$923$	−1.42938e19	−	2.47575e19i	−0.760914	−	1.31794i
$924$		0			0
$925$	−4.76292e18	+	8.24962e18i	−0.250007	+	0.433025i
$926$	−3.36976e18			−0.175642
$927$		0			0
$928$	3.74129e18			0.192291
$929$	1.11800e18	−	1.93644e18i	0.0570613	−	0.0988330i	−0.836084	−	0.548602i	$-0.815160\pi$
$929$	1.11800e18	−	1.93644e18i	0.0570613	−	0.0988330i	0.893145	+	0.449769i	$0.148494\pi$
$930$		0			0
$931$	1.65321e18	+	2.86344e18i	0.0832061	+	0.144117i
$932$	1.04321e18	+	1.80690e18i	0.0521398	+	0.0903087i
$933$		0			0
$934$	1.07297e19	−	1.85844e19i	0.528850	−	0.915996i
$935$	5.02847e18			0.246128
$936$		0			0
$937$	−9.93409e18			−0.479536			−0.239768	−	0.970830i	$-0.577071\pi$
$937$	−9.93409e18			−0.479536			−0.239768	+	0.970830i	$0.577071\pi$
$938$	−8.17485e18	+	1.41593e19i	−0.391888	+	0.678769i
$939$		0			0
$940$	1.36121e17	+	2.35769e17i	0.00643569	+	0.0111469i
$941$	1.37093e18	+	2.37453e18i	0.0643700	+	0.111492i	0.896414	−	0.443217i	$-0.146163\pi$
$941$	1.37093e18	+	2.37453e18i	0.0643700	+	0.111492i	−0.832044	+	0.554709i	$0.812830\pi$
$942$		0			0
$943$	6.08892e17	−	1.05463e18i	0.0281977	−	0.0488399i
$944$	9.70838e18			0.446508
$945$		0			0
$946$	4.77426e18			0.216578
$947$	6.52057e18	−	1.12940e19i	0.293772	−	0.508828i	−0.680926	−	0.732352i	$-0.738423\pi$
$947$	6.52057e18	−	1.12940e19i	0.293772	−	0.508828i	0.974698	+	0.223524i	$0.0717560\pi$
$948$		0			0
$949$	−1.41690e19	−	2.45415e19i	−0.629666	−	1.09061i
$950$	6.76736e18	+	1.17214e19i	0.298687	+	0.517341i
$951$		0			0
$952$	3.92874e18	−	6.80479e18i	0.171046	−	0.296261i
$953$	−1.23319e19			−0.533243			−0.266621	−	0.963801i	$-0.585907\pi$
$953$	−1.23319e19			−0.533243			−0.266621	+	0.963801i	$0.585907\pi$
$954$		0			0
$955$	−1.29869e19			−0.553969
$956$	3.25499e18	−	5.63781e18i	0.137903	−	0.238855i
$957$		0			0
$958$	−8.23707e18	−	1.42670e19i	−0.344268	−	0.596290i
$959$	1.95826e19	+	3.39181e19i	0.812924	+	1.40803i
$960$		0			0
$961$	−2.07099e19	+	3.58705e19i	−0.848155	+	1.46905i
$962$	1.42648e19			0.580265
$963$		0			0
$964$	−1.62010e18			−0.0650193
$965$	9.13008e18	−	1.58138e19i	0.363954	−	0.630388i
$966$		0			0
$967$	1.53868e19	+	2.66507e19i	0.605167	+	1.04818i	0.992025	+	0.126041i	$0.0402270\pi$
$967$	1.53868e19	+	2.66507e19i	0.605167	+	1.04818i	−0.386858	+	0.922139i	$0.626440\pi$
$968$	3.86638e18	+	6.69677e18i	0.151048	+	0.261623i
$969$		0			0
$970$	8.38702e17	−	1.45267e18i	0.0323289	−	0.0559953i
$971$	2.27430e19			0.870809			0.435404	−	0.900235i	$-0.356605\pi$
$971$	2.27430e19			0.870809			0.435404	+	0.900235i	$0.356605\pi$
$972$		0			0
$973$	−4.34545e19			−1.64173
$974$	5.05483e18	−	8.75521e18i	0.189702	−	0.328574i
$975$		0			0
$976$	2.40826e18	+	4.17124e18i	0.0891827	+	0.154469i
$977$	−1.35929e18	−	2.35436e18i	−0.0500033	−	0.0866082i	0.839940	−	0.542679i	$-0.182590\pi$
$977$	−1.35929e18	−	2.35436e18i	−0.0500033	−	0.0866082i	−0.889944	+	0.456070i	$0.849257\pi$
$978$		0			0
$979$	6.76670e18	−	1.17203e19i	0.245634	−	0.425451i
$980$	1.03998e18			0.0375022
$981$		0			0
$982$	1.23905e19			0.440924
$983$	−1.05770e19	+	1.83199e19i	−0.373908	+	0.647627i	−0.990163	−	0.139920i	$-0.955316\pi$
$983$	−1.05770e19	+	1.83199e19i	−0.373908	+	0.647627i	0.616255	+	0.787546i	$0.288649\pi$
$984$		0			0
$985$	9.98481e18	+	1.72942e19i	0.348341	+	0.603344i
$986$	1.14449e19	+	1.98232e19i	0.396656	+	0.687028i
$987$		0			0
$988$	1.01340e19	−	1.75526e19i	0.346625	−	0.600372i
$989$	−8.59679e18			−0.292119
$990$		0			0
$991$	−2.51495e19			−0.843434			−0.421717	−	0.906727i	$-0.638572\pi$
$991$	−2.51495e19			−0.843434			−0.421717	+	0.906727i	$0.638572\pi$
$992$	4.35618e18	−	7.54512e18i	0.145138	−	0.251386i
$993$		0			0
$994$	1.53643e19	+	2.66117e19i	0.505244	+	0.875108i
$995$	−5.78955e18	−	1.00278e19i	−0.189145	−	0.327609i
$996$		0			0
$997$	2.35308e18	−	4.07565e18i	0.0758783	−	0.131425i	−0.825590	−	0.564271i	$-0.809157\pi$
$997$	2.35308e18	−	4.07565e18i	0.0758783	−	0.131425i	0.901468	+	0.432846i	$0.142491\pi$
$998$	2.60849e19			0.835683
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.14.c.a.19.4		12
3.2	odd	2		18.14.c.a.7.1	✓	12
9.2	odd	6		162.14.a.e.1.4		6
9.4	even	3	inner	54.14.c.a.37.4		12
9.5	odd	6		18.14.c.a.13.1	yes	12
9.7	even	3		162.14.a.h.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.14.c.a.7.1	✓	12	3.2	odd	2
18.14.c.a.13.1	yes	12	9.5	odd	6
54.14.c.a.19.4		12	1.1	even	1	trivial
54.14.c.a.37.4		12	9.4	even	3	inner
162.14.a.e.1.4		6	9.2	odd	6
162.14.a.h.1.3		6	9.7	even	3

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	54.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-32.0000 + 55.4256i) q^{2} +(-2048.00 - 3547.24i) q^{4} +(10927.3 + 18926.7i) q^{5} +(-146006. + 252890. i) q^{7} +262144. q^{8} +O(q^{10})\)	\(q+(-32.0000 + 55.4256i) q^{2} +(-2048.00 - 3547.24i) q^{4} +(10927.3 + 18926.7i) q^{5} +(-146006. + 252890. i) q^{7} +262144. q^{8} -1.39870e6 q^{10} +(-1.12078e6 + 1.94125e6i) q^{11} +(8.69332e6 + 1.50573e7i) q^{13} +(-9.34440e6 - 1.61850e7i) q^{14} +(-8.38861e6 + 1.45295e7i) q^{16} -1.02646e8 q^{17} +2.84600e8 q^{19} +(4.47583e7 - 7.75236e7i) q^{20} +(-7.17298e7 - 1.24240e8i) q^{22} +(1.29161e8 + 2.23713e8i) q^{23} +(3.71539e8 - 6.43525e8i) q^{25} -1.11274e9 q^{26} +1.19608e9 q^{28} +(-1.74217e9 + 3.01753e9i) q^{29} +(4.05701e9 + 7.02694e9i) q^{31} +(-5.36871e8 - 9.29888e8i) q^{32} +(3.28468e9 - 5.68923e9i) q^{34} -6.38182e9 q^{35} -1.28194e10 q^{37} +(-9.10720e9 + 1.57741e10i) q^{38} +(2.86453e9 + 4.96151e9i) q^{40} +(-2.35711e9 - 4.08263e9i) q^{41} +(-1.66397e10 + 2.88208e10i) q^{43} +9.18142e9 q^{44} -1.65326e10 q^{46} +(-1.52063e9 + 2.63380e9i) q^{47} +(5.80889e9 + 1.00613e10i) q^{49} +(2.37785e10 + 4.11856e10i) q^{50} +(3.56078e10 - 6.16746e10i) q^{52} +5.94638e10 q^{53} -4.89884e10 q^{55} +(-3.82746e10 + 6.62936e10i) q^{56} +(-1.11499e11 - 1.93122e11i) q^{58} +(-2.89332e11 - 5.01138e11i) q^{59} +(1.43544e11 - 2.48625e11i) q^{61} -5.19297e11 q^{62} +6.87195e10 q^{64} +(-1.89989e11 + 3.29071e11i) q^{65} +(-4.37420e11 - 7.57634e11i) q^{67} +(2.10219e11 + 3.64110e11i) q^{68} +(2.04218e11 - 3.53716e11i) q^{70} -1.64422e12 q^{71} -1.62988e12 q^{73} +(4.10222e11 - 7.10525e11i) q^{74} +(-5.82861e11 - 1.00954e12i) q^{76} +(-3.27281e11 - 5.66868e11i) q^{77} +(1.51346e12 - 2.62139e12i) q^{79} -3.66660e11 q^{80} +3.01710e11 q^{82} +(4.62483e11 - 8.01045e11i) q^{83} +(-1.12165e12 - 1.94275e12i) q^{85} +(-1.06494e12 - 1.84453e12i) q^{86} +(-2.93805e11 + 5.08886e11i) q^{88} -6.03750e12 q^{89} -5.07711e12 q^{91} +(5.29042e11 - 9.16328e11i) q^{92} +(-9.73201e10 - 1.68563e11i) q^{94} +(3.10991e12 + 5.38653e12i) q^{95} +(-5.99631e11 + 1.03859e12i) q^{97} -7.43538e11 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 384 q^{2} - 24576 q^{4} + 36504 q^{5} + 153942 q^{7} + 3145728 q^{8}+O(q^{10}) \) 12 * q - 384 * q^2 - 24576 * q^4 + 36504 * q^5 + 153942 * q^7 + 3145728 * q^8	\( 12 q - 384 q^{2} - 24576 q^{4} + 36504 q^{5} + 153942 q^{7} + 3145728 q^{8} - 4672512 q^{10} + 1456506 q^{11} + 24033660 q^{13} + 9852288 q^{14} - 100663296 q^{16} + 1079532 q^{17} + 337140888 q^{19} + 149520384 q^{20} + 93216384 q^{22} - 445386186 q^{23} - 2193691326 q^{25} - 3076308480 q^{26} - 1261092864 q^{28} + 9171393012 q^{29} + 4264851066 q^{31} - 6442450944 q^{32} - 34545024 q^{34} - 5180969412 q^{35} - 49108850688 q^{37} - 10788508416 q^{38} + 9569304576 q^{40} + 15964345782 q^{41} + 78379952838 q^{43} - 11931697152 q^{44} + 57009431808 q^{46} - 94117799358 q^{47} - 15284873538 q^{49} - 140396244864 q^{50} + 98441871360 q^{52} + 592790415264 q^{53} - 1108282558212 q^{55} + 40354971648 q^{56} + 586969152768 q^{58} - 46698155010 q^{59} + 928192122600 q^{61} - 545900936448 q^{62} + 824633720832 q^{64} + 1327744890468 q^{65} + 2282039666898 q^{67} - 2210881536 q^{68} + 165791021184 q^{70} - 2360122970688 q^{71} + 1355834901228 q^{73} + 1571483222016 q^{74} - 690464538624 q^{76} + 3622976109756 q^{77} + 2457538059750 q^{79} - 1224870985728 q^{80} - 2043436260096 q^{82} + 9950916891942 q^{83} - 576987174720 q^{85} + 5016316981632 q^{86} + 381814308864 q^{88} - 22604686696296 q^{89} + 14791528659540 q^{91} - 1824301817856 q^{92} - 6023539158912 q^{94} + 7488669126384 q^{95} + 1124429902242 q^{97} + 1956463812864 q^{98}+O(q^{100}) \) 12 * q - 384 * q^2 - 24576 * q^4 + 36504 * q^5 + 153942 * q^7 + 3145728 * q^8 - 4672512 * q^10 + 1456506 * q^11 + 24033660 * q^13 + 9852288 * q^14 - 100663296 * q^16 + 1079532 * q^17 + 337140888 * q^19 + 149520384 * q^20 + 93216384 * q^22 - 445386186 * q^23 - 2193691326 * q^25 - 3076308480 * q^26 - 1261092864 * q^28 + 9171393012 * q^29 + 4264851066 * q^31 - 6442450944 * q^32 - 34545024 * q^34 - 5180969412 * q^35 - 49108850688 * q^37 - 10788508416 * q^38 + 9569304576 * q^40 + 15964345782 * q^41 + 78379952838 * q^43 - 11931697152 * q^44 + 57009431808 * q^46 - 94117799358 * q^47 - 15284873538 * q^49 - 140396244864 * q^50 + 98441871360 * q^52 + 592790415264 * q^53 - 1108282558212 * q^55 + 40354971648 * q^56 + 586969152768 * q^58 - 46698155010 * q^59 + 928192122600 * q^61 - 545900936448 * q^62 + 824633720832 * q^64 + 1327744890468 * q^65 + 2282039666898 * q^67 - 2210881536 * q^68 + 165791021184 * q^70 - 2360122970688 * q^71 + 1355834901228 * q^73 + 1571483222016 * q^74 - 690464538624 * q^76 + 3622976109756 * q^77 + 2457538059750 * q^79 - 1224870985728 * q^80 - 2043436260096 * q^82 + 9950916891942 * q^83 - 576987174720 * q^85 + 5016316981632 * q^86 + 381814308864 * q^88 - 22604686696296 * q^89 + 14791528659540 * q^91 - 1824301817856 * q^92 - 6023539158912 * q^94 + 7488669126384 * q^95 + 1124429902242 * q^97 + 1956463812864 * q^98

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