LMFDB - Embedded newform 126.12.g.b.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,12,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	126.g (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:	$96.8112407505$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 1516x^{4} + 1461x^{3} + 2295252x^{2} - 40905x + 729 $ x^6 - x^5 + 1516x^4 + 1461x^3 + 2295252x^2 - 40905x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$19.7087 + 34.1365i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.12.g.b.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(16.0000 - 27.7128i) q^{2} +(-512.000 - 886.810i) q^{4} +(-2025.94 + 3509.03i) q^{5} +(-41231.5 + 16652.0i) q^{7} -32768.0 q^{8} +(64830.0 + 112289. i) q^{10} +(-52646.6 - 91186.6i) q^{11} +144812. q^{13} +(-198230. + 1.40907e6i) q^{14} +(-524288. + 908093. i) q^{16} +(3.54738e6 + 6.14424e6i) q^{17} +(2.86658e6 - 4.96507e6i) q^{19} +4.14912e6 q^{20} -3.36938e6 q^{22} +(-1.91165e7 + 3.31108e7i) q^{23} +(1.62052e7 + 2.80683e7i) q^{25} +(2.31699e6 - 4.01315e6i) q^{26} +(3.58777e7 + 2.80387e7i) q^{28} -1.21081e7 q^{29} +(-5.57549e7 - 9.65703e7i) q^{31} +(1.67772e7 + 2.90590e7i) q^{32} +2.27032e8 q^{34} +(2.51001e7 - 1.78418e8i) q^{35} +(1.38165e8 - 2.39309e8i) q^{37} +(-9.17307e7 - 1.58882e8i) q^{38} +(6.63859e7 - 1.14984e8i) q^{40} -1.41611e9 q^{41} +1.35192e9 q^{43} +(-5.39101e7 + 9.33751e7i) q^{44} +(6.11728e8 + 1.05954e9i) q^{46} +(3.25084e7 - 5.63062e7i) q^{47} +(1.42275e9 - 1.37317e9i) q^{49} +1.03713e9 q^{50} +(-7.41438e7 - 1.28421e8i) q^{52} +(-2.08376e9 - 3.60918e9i) q^{53} +4.26635e8 q^{55} +(1.35107e9 - 5.45653e8i) q^{56} +(-1.93729e8 + 3.35548e8i) q^{58} +(4.30251e8 + 7.45216e8i) q^{59} +(-2.59606e8 + 4.49651e8i) q^{61} -3.56831e9 q^{62} +1.07374e9 q^{64} +(-2.93380e8 + 5.08150e8i) q^{65} +(-7.81246e9 - 1.35316e10i) q^{67} +(3.63251e9 - 6.29170e9i) q^{68} +(-4.54287e9 - 3.55029e9i) q^{70} +6.55768e9 q^{71} +(-4.05303e9 - 7.02006e9i) q^{73} +(-4.42128e9 - 7.65788e9i) q^{74} -5.87076e9 q^{76} +(3.68914e9 + 2.88309e9i) q^{77} +(1.72527e10 - 2.98826e10i) q^{79} +(-2.12435e9 - 3.67948e9i) q^{80} +(-2.26577e10 + 3.92443e10i) q^{82} +1.62544e10 q^{83} -2.87471e10 q^{85} +(2.16306e10 - 3.74654e10i) q^{86} +(1.72512e9 + 2.98800e9i) q^{88} +(1.95499e10 - 3.38615e10i) q^{89} +(-5.97082e9 + 2.41141e9i) q^{91} +3.91506e10 q^{92} +(-1.04027e9 - 1.80180e9i) q^{94} +(1.16150e10 + 2.01178e10i) q^{95} -1.29214e10 q^{97} +(-1.52906e10 - 6.13991e10i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 96 q^{2} - 3072 q^{4} - 1045 q^{5} + 45731 q^{7} - 196608 q^{8} + 33440 q^{10} - 181565 q^{11} + 1186364 q^{13} + 703808 q^{14} - 3145728 q^{16} + 701848 q^{17} - 7893102 q^{19} + 2140160 q^{20} - 11620160 q^{22}+ \cdots - 30564771552 q^{98}+O(q^{100}) $ 6 * q + 96 * q^2 - 3072 * q^4 - 1045 * q^5 + 45731 * q^7 - 196608 * q^8 + 33440 * q^10 - 181565 * q^11 + 1186364 * q^13 + 703808 * q^14 - 3145728 * q^16 + 701848 * q^17 - 7893102 * q^19 + 2140160 * q^20 - 11620160 * q^22 - 59247728 * q^23 + 124585550 * q^25 + 18981824 * q^26 - 24306688 * q^28 + 30040070 * q^29 - 299540305 * q^31 + 100663296 * q^32 + 44918272 * q^34 + 181163920 * q^35 - 352325094 * q^37 + 252579264 * q^38 + 34242560 * q^40 - 1199954472 * q^41 - 4298844576 * q^43 - 185922560 * q^44 + 1895927296 * q^46 + 1179123942 * q^47 + 3621837009 * q^49 + 7973475200 * q^50 - 607418368 * q^52 + 67875849 * q^53 + 1874846050 * q^55 - 1498513408 * q^56 + 480641120 * q^58 + 2911039823 * q^59 - 10148733466 * q^61 - 19170579520 * q^62 + 6442450944 * q^64 + 2404013040 * q^65 - 5535975380 * q^67 + 718692352 * q^68 - 11741350880 * q^70 + 20558197876 * q^71 + 29230853572 * q^73 + 11274403008 * q^74 + 16165072896 * q^76 - 34001756425 * q^77 + 58886709107 * q^79 - 1095761920 * q^80 - 19199271552 * q^82 - 26001713726 * q^83 - 93104330000 * q^85 - 68781513216 * q^86 + 5949521920 * q^88 + 32237877702 * q^89 + 67979059274 * q^91 + 121339346944 * q^92 - 37731966144 * q^94 + 37720110280 * q^95 + 175446876934 * q^97 - 30564771552 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	16.0000	−	27.7128i	0.353553	−	0.612372i
$2$	16.0000	−	27.7128i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−512.000	−	886.810i	−0.250000	−	0.433013i
$5$	−2025.94	+	3509.03i	−0.289929	+	0.502171i	−0.973792	−	0.227439i	$-0.926965\pi$
$5$	−2025.94	+	3509.03i	−0.289929	+	0.502171i	0.683864	+	0.729610i	$0.260298\pi$
$6$		0			0
$7$	−41231.5	+	16652.0i	−0.927235	+	0.374479i
$7$	−41231.5	+	16652.0i	−0.927235	+	0.374479i
$8$	−32768.0			−0.353553
$9$		0			0
$10$	64830.0	+	112289.i	0.205011	+	0.355089i
$11$	−52646.6	−	91186.6i	−0.0985623	−	0.170715i	0.812527	−	0.582923i	$-0.198091\pi$
$11$	−52646.6	−	91186.6i	−0.0985623	−	0.170715i	−0.911090	+	0.412208i	$0.864758\pi$
$12$		0			0
$13$	144812.			0.108172			0.0540862	−	0.998536i	$-0.482775\pi$
$13$	144812.			0.108172			0.0540862	+	0.998536i	$0.482775\pi$
$14$	−198230.	+	1.40907e6i	−0.0985067	+	0.700212i
$15$		0			0
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	3.54738e6	+	6.14424e6i	0.605952	+	1.04954i	0.991900	+	0.127019i	$0.0405410\pi$
$17$	3.54738e6	+	6.14424e6i	0.605952	+	1.04954i	−0.385948	+	0.922520i	$0.626126\pi$
$18$		0			0
$19$	2.86658e6	−	4.96507e6i	0.265595	−	0.460024i	−0.702124	−	0.712054i	$-0.747765\pi$
$19$	2.86658e6	−	4.96507e6i	0.265595	−	0.460024i	0.967719	+	0.252030i	$0.0810983\pi$
$20$	4.14912e6			0.289929
$21$		0			0
$22$	−3.36938e6			−0.139388
$23$	−1.91165e7	+	3.31108e7i	−0.619306	+	1.07267i	0.370307	+	0.928910i	$0.379253\pi$
$23$	−1.91165e7	+	3.31108e7i	−0.619306	+	1.07267i	−0.989613	+	0.143760i	$0.954081\pi$
$24$		0			0
$25$	1.62052e7	+	2.80683e7i	0.331883	+	0.574838i
$26$	2.31699e6	−	4.01315e6i	0.0382447	−	0.0662418i
$27$		0			0
$28$	3.58777e7	+	2.80387e7i	0.393963	+	0.307885i
$29$	−1.21081e7			−0.109619			−0.0548095	−	0.998497i	$-0.517455\pi$
$29$	−1.21081e7			−0.109619			−0.0548095	+	0.998497i	$0.517455\pi$
$30$		0			0
$31$	−5.57549e7	−	9.65703e7i	−0.349779	−	0.605835i	0.636431	−	0.771334i	$-0.280410\pi$
$31$	−5.57549e7	−	9.65703e7i	−0.349779	−	0.605835i	−0.986210	+	0.165499i	$0.947077\pi$
$32$	1.67772e7	+	2.90590e7i	0.0883883	+	0.153093i
$33$		0			0
$34$	2.27032e8			0.856946
$35$	2.51001e7	−	1.78418e8i	0.0807796	−	0.574203i
$36$		0			0
$37$	1.38165e8	−	2.39309e8i	0.327558	−	0.567347i	−0.654469	−	0.756089i	$-0.727108\pi$
$37$	1.38165e8	−	2.39309e8i	0.327558	−	0.567347i	0.982027	+	0.188742i	$0.0604409\pi$
$38$	−9.17307e7	−	1.58882e8i	−0.187804	−	0.325286i
$39$		0			0
$40$	6.63859e7	−	1.14984e8i	0.102505	−	0.177544i
$41$	−1.41611e9			−1.90891			−0.954453	−	0.298363i	$-0.903559\pi$
$41$	−1.41611e9			−1.90891			−0.954453	+	0.298363i	$0.903559\pi$
$42$		0			0
$43$	1.35192e9			1.40240			0.701202	−	0.712963i	$-0.252647\pi$
$43$	1.35192e9			1.40240			0.701202	+	0.712963i	$0.252647\pi$
$44$	−5.39101e7	+	9.33751e7i	−0.0492811	+	0.0853574i
$45$		0			0
$46$	6.11728e8	+	1.05954e9i	0.437916	+	0.758492i
$47$	3.25084e7	−	5.63062e7i	0.0206756	−	0.0358111i	−0.855502	−	0.517799i	$-0.826752\pi$
$47$	3.25084e7	−	5.63062e7i	0.0206756	−	0.0358111i	0.876178	+	0.481988i	$0.160085\pi$
$48$		0			0
$49$	1.42275e9	−	1.37317e9i	0.719531	−	0.694460i
$50$	1.03713e9			0.469353
$51$		0			0
$52$	−7.41438e7	−	1.28421e8i	−0.0270431	−	0.0468400i
$53$	−2.08376e9	−	3.60918e9i	−0.684432	−	1.18547i	−0.973615	−	0.228197i	$-0.926717\pi$
$53$	−2.08376e9	−	3.60918e9i	−0.684432	−	1.18547i	0.289183	−	0.957274i	$-0.406616\pi$
$54$		0			0
$55$	4.26635e8			0.114304
$56$	1.35107e9	−	5.45653e8i	0.327827	−	0.132398i
$57$		0			0
$58$	−1.93729e8	+	3.35548e8i	−0.0387562	+	0.0671276i
$59$	4.30251e8	+	7.45216e8i	0.0783494	+	0.135705i	0.902538	−	0.430610i	$-0.141702\pi$
$59$	4.30251e8	+	7.45216e8i	0.0783494	+	0.135705i	−0.824189	+	0.566316i	$0.808368\pi$
$60$		0			0
$61$	−2.59606e8	+	4.49651e8i	−0.0393551	+	0.0681650i	−0.885032	−	0.465530i	$-0.845864\pi$
$61$	−2.59606e8	+	4.49651e8i	−0.0393551	+	0.0681650i	0.845677	+	0.533695i	$0.179197\pi$
$62$	−3.56831e9			−0.494662
$63$		0			0
$64$	1.07374e9			0.125000
$65$	−2.93380e8	+	5.08150e8i	−0.0313623	+	0.0543211i
$66$		0			0
$67$	−7.81246e9	−	1.35316e10i	−0.706930	−	1.22444i	−0.965990	−	0.258578i	$-0.916746\pi$
$67$	−7.81246e9	−	1.35316e10i	−0.706930	−	1.22444i	0.259060	−	0.965861i	$-0.416587\pi$
$68$	3.63251e9	−	6.29170e9i	0.302976	−	0.524770i
$69$		0			0
$70$	−4.54287e9	−	3.55029e9i	−0.323066	−	0.252479i
$71$	6.55768e9			0.431350			0.215675	−	0.976465i	$-0.430805\pi$
$71$	6.55768e9			0.431350			0.215675	+	0.976465i	$0.430805\pi$
$72$		0			0
$73$	−4.05303e9	−	7.02006e9i	−0.228826	−	0.396338i	0.728635	−	0.684902i	$-0.240155\pi$
$73$	−4.05303e9	−	7.02006e9i	−0.228826	−	0.396338i	−0.957460	+	0.288565i	$0.906822\pi$
$74$	−4.42128e9	−	7.65788e9i	−0.231619	−	0.401175i
$75$		0			0
$76$	−5.87076e9			−0.265595
$77$	3.68914e9	+	2.88309e9i	0.155320	+	0.121383i
$78$		0			0
$79$	1.72527e10	−	2.98826e10i	0.630824	−	1.09262i	−0.356559	−	0.934273i	$-0.616050\pi$
$79$	1.72527e10	−	2.98826e10i	0.630824	−	1.09262i	0.987383	−	0.158347i	$-0.0506165\pi$
$80$	−2.12435e9	−	3.67948e9i	−0.0724822	−	0.125543i
$81$		0			0
$82$	−2.26577e10	+	3.92443e10i	−0.674900	+	1.16896i
$83$	1.62544e10			0.452941			0.226471	−	0.974018i	$-0.427281\pi$
$83$	1.62544e10			0.452941			0.226471	+	0.974018i	$0.427281\pi$
$84$		0			0
$85$	−2.87471e10			−0.702731
$86$	2.16306e10	−	3.74654e10i	0.495825	−	0.858793i
$87$		0			0
$88$	1.72512e9	+	2.98800e9i	0.0348470	+	0.0603568i
$89$	1.95499e10	−	3.38615e10i	0.371108	−	0.642778i	−0.618628	−	0.785684i	$-0.712311\pi$
$89$	1.95499e10	−	3.38615e10i	0.371108	−	0.642778i	0.989736	+	0.142906i	$0.0456447\pi$
$90$		0			0
$91$	−5.97082e9	+	2.41141e9i	−0.100301	+	0.0405083i
$92$	3.91506e10			0.619306
$93$		0			0
$94$	−1.04027e9	−	1.80180e9i	−0.0146198	−	0.0253223i
$95$	1.16150e10	+	2.01178e10i	0.154007	+	0.266748i
$96$		0			0
$97$	−1.29214e10			−0.152780			−0.0763898	−	0.997078i	$-0.524339\pi$
$97$	−1.29214e10			−0.152780			−0.0763898	+	0.997078i	$0.524339\pi$
$98$	−1.52906e10	−	6.13991e10i	−0.170876	−	0.686150i
$99$		0			0
$100$	1.65941e10	−	2.87419e10i	0.165941	−	0.287419i
$101$	−1.96967e10	−	3.41157e10i	−0.186477	−	0.322988i	0.757596	−	0.652724i	$-0.226374\pi$
$101$	−1.96967e10	−	3.41157e10i	−0.186477	−	0.322988i	−0.944073	+	0.329736i	$0.893040\pi$
$102$		0			0
$103$	4.63576e10	−	8.02938e10i	0.394018	−	0.682460i	−0.598957	−	0.800781i	$-0.704418\pi$
$103$	4.63576e10	−	8.02938e10i	0.394018	−	0.682460i	0.992975	+	0.118321i	$0.0377513\pi$
$104$	−4.74521e9			−0.0382447
$105$		0			0
$106$	−1.33361e11			−0.967933
$107$	−9.80632e10	+	1.69850e11i	−0.675920	+	1.17073i	0.300279	+	0.953851i	$0.402920\pi$
$107$	−9.80632e10	+	1.69850e11i	−0.675920	+	1.17073i	−0.976199	+	0.216876i	$0.930413\pi$
$108$		0			0
$109$	−9.82277e10	−	1.70135e11i	−0.611488	−	1.05913i	−0.990990	−	0.133938i	$-0.957238\pi$
$109$	−9.82277e10	−	1.70135e11i	−0.611488	−	1.05913i	0.379501	−	0.925191i	$-0.376096\pi$
$110$	6.82616e9	−	1.18233e10i	0.0404126	−	0.0699967i
$111$		0			0
$112$	6.49561e9	−	4.61725e10i	0.0348274	−	0.247562i
$113$	−2.08490e9			−0.0106452			−0.00532260	−	0.999986i	$-0.501694\pi$
$113$	−2.08490e9			−0.0106452			−0.00532260	+	0.999986i	$0.501694\pi$
$114$		0			0
$115$	−7.74577e10	−	1.34161e11i	−0.359109	−	0.621995i
$116$	6.19933e9	+	1.07376e10i	0.0274047	+	0.0474664i
$117$		0			0
$118$	2.75360e10			0.110803
$119$	−2.48578e11	−	1.94265e11i	−0.954891	−	0.746254i
$120$		0			0
$121$	1.37113e11	−	2.37486e11i	0.480571	−	0.832373i
$122$	8.30739e9	+	1.43888e10i	0.0278282	+	0.0481999i
$123$		0			0
$124$	−5.70930e10	+	9.88880e10i	−0.174889	+	0.302917i
$125$	−3.29169e11			−0.964747
$126$		0			0
$127$	8.43468e10			0.226542			0.113271	−	0.993564i	$-0.463867\pi$
$127$	8.43468e10			0.226542			0.113271	+	0.993564i	$0.463867\pi$
$128$	1.71799e10	−	2.97564e10i	0.0441942	−	0.0765466i
$129$		0			0
$130$	9.38818e9	+	1.62608e10i	0.0221765	+	0.0384108i
$131$	−2.21933e11	+	3.84399e11i	−0.502608	+	0.870542i	0.497388	+	0.867528i	$0.334293\pi$
$131$	−2.21933e11	+	3.84399e11i	−0.502608	+	0.870542i	−0.999995	+	0.00301363i	$0.999041\pi$
$132$		0			0
$133$	−3.55152e10	+	2.52452e11i	−0.0739998	+	0.526010i
$134$	−4.99998e11			−0.999750
$135$		0			0
$136$	−1.16240e11	−	2.01334e11i	−0.214236	−	0.371068i
$137$	−1.23849e11	−	2.14513e11i	−0.219245	−	0.379743i	0.735332	−	0.677707i	$-0.237026\pi$
$137$	−1.23849e11	−	2.14513e11i	−0.219245	−	0.379743i	−0.954577	+	0.297963i	$0.903693\pi$
$138$		0			0
$139$	−6.84023e11			−1.11812			−0.559061	−	0.829127i	$-0.688838\pi$
$139$	−6.84023e11			−1.11812			−0.559061	+	0.829127i	$0.688838\pi$
$140$	−1.71075e11	+	6.90912e10i	−0.268832	+	0.108572i
$141$		0			0
$142$	1.04923e11	−	1.81732e11i	0.152505	−	0.264147i
$143$	−7.62387e9	−	1.32049e10i	−0.0106617	−	0.0184666i
$144$		0			0
$145$	2.45302e10	−	4.24875e10i	0.0317817	−	0.0550475i
$146$	−2.59394e11			−0.323608
$147$		0			0
$148$	−2.82962e11			−0.327558
$149$	1.46183e11	−	2.53196e11i	0.163069	−	0.282444i	−0.772899	−	0.634529i	$-0.781194\pi$
$149$	1.46183e11	−	2.53196e11i	0.163069	−	0.282444i	0.935968	+	0.352085i	$0.114527\pi$
$150$		0			0
$151$	−1.55769e11	−	2.69800e11i	−0.161476	−	0.279685i	0.773922	−	0.633281i	$-0.218292\pi$
$151$	−1.55769e11	−	2.69800e11i	−0.161476	−	0.279685i	−0.935398	+	0.353596i	$0.884959\pi$
$152$	−9.39322e10	+	1.62695e11i	−0.0939020	+	0.162643i
$153$		0			0
$154$	1.38925e11	−	5.61070e10i	0.129246	−	0.0521979i
$155$	4.51824e11			0.405644
$156$		0			0
$157$	−7.11430e11	−	1.23223e12i	−0.595229	−	1.03097i	−0.993514	−	0.113706i	$-0.963728\pi$
$157$	−7.11430e11	−	1.23223e12i	−0.595229	−	1.03097i	0.398285	−	0.917262i	$-0.369605\pi$
$158$	−5.52087e11	−	9.56243e11i	−0.446060	−	0.772599i
$159$		0			0
$160$	−1.35958e11			−0.102505
$161$	2.36842e11	−	1.68353e12i	0.172550	−	1.22653i
$162$		0			0
$163$	6.15917e11	−	1.06680e12i	0.419267	−	0.726191i	−0.576599	−	0.817027i	$-0.695621\pi$
$163$	6.15917e11	−	1.06680e12i	0.419267	−	0.726191i	0.995866	+	0.0908359i	$0.0289539\pi$
$164$	7.25046e11	+	1.25582e12i	0.477226	+	0.826580i
$165$		0			0
$166$	2.60071e11	−	4.50456e11i	0.160139	−	0.277369i
$167$	3.18702e12			1.89864			0.949322	−	0.314305i	$-0.101771\pi$
$167$	3.18702e12			1.89864			0.949322	+	0.314305i	$0.101771\pi$
$168$		0			0
$169$	−1.77119e12			−0.988299
$170$	−4.59953e11	+	7.96662e11i	−0.248453	+	0.430333i
$171$		0			0
$172$	−6.92181e11	−	1.19889e12i	−0.350601	−	0.607259i
$173$	9.21668e11	−	1.59638e12i	0.452190	−	0.783216i	−0.546332	−	0.837569i	$-0.683976\pi$
$173$	9.21668e11	−	1.59638e12i	0.452190	−	0.783216i	0.998522	+	0.0543531i	$0.0173096\pi$
$174$		0			0
$175$	−1.13556e12	−	8.87447e11i	−0.522998	−	0.408727i
$176$	1.10408e11			0.0492811
$177$		0			0
$178$	−6.25598e11	−	1.08357e12i	−0.262413	−	0.454512i
$179$	−1.28675e12	−	2.22871e12i	−0.523360	−	0.906487i	−0.999630	−	0.0271876i	$-0.991345\pi$
$179$	−1.28675e12	−	2.22871e12i	−0.523360	−	0.906487i	0.476270	−	0.879299i	$-0.341988\pi$
$180$		0			0
$181$	−2.56519e12			−0.981495			−0.490747	−	0.871302i	$-0.663276\pi$
$181$	−2.56519e12			−0.981495			−0.490747	+	0.871302i	$0.663276\pi$
$182$	−2.87062e10	+	2.04051e11i	−0.0106557	+	0.0757436i
$183$		0			0
$184$	6.26410e11	−	1.08497e12i	0.218958	−	0.379246i
$185$	5.59827e11	+	9.69649e11i	0.189937	+	0.328980i
$186$		0			0
$187$	3.73515e11	−	6.46947e11i	0.119448	−	0.206890i
$188$	−6.65772e10			−0.0206756
$189$		0			0
$190$	7.43363e11			0.217799
$191$	1.67834e12	−	2.90697e12i	0.477745	−	0.827478i	−0.521930	−	0.852989i	$-0.674788\pi$
$191$	1.67834e12	−	2.90697e12i	0.477745	−	0.827478i	0.999675	+	0.0255101i	$0.00812099\pi$
$192$		0			0
$193$	3.22781e12	+	5.59073e12i	0.867647	+	1.50281i	0.864395	+	0.502814i	$0.167702\pi$
$193$	3.22781e12	+	5.59073e12i	0.867647	+	1.50281i	0.00325223	+	0.999995i	$0.498965\pi$
$194$	−2.06743e11	+	3.58089e11i	−0.0540158	+	0.0935580i
$195$		0			0
$196$	−1.94619e12	−	5.58642e11i	−0.480593	−	0.137951i
$197$	−1.83594e12			−0.440852			−0.220426	−	0.975404i	$-0.570745\pi$
$197$	−1.83594e12			−0.440852			−0.220426	+	0.975404i	$0.570745\pi$
$198$		0			0
$199$	2.33660e12	+	4.04710e12i	0.530752	+	0.919290i	0.999356	+	0.0358815i	$0.0114239\pi$
$199$	2.33660e12	+	4.04710e12i	0.530752	+	0.919290i	−0.468604	+	0.883408i	$0.655243\pi$
$200$	−5.31012e11	−	9.19741e11i	−0.117338	−	0.203236i
$201$		0			0
$202$	−1.26059e12			−0.263719
$203$	4.99234e11	−	2.01624e11i	0.101643	−	0.0410500i
$204$		0			0
$205$	2.86894e12	−	4.96915e12i	0.553446	−	0.958597i
$206$	−1.48344e12	−	2.56940e12i	−0.278613	−	0.482572i
$207$		0			0
$208$	−7.59233e10	+	1.31503e11i	−0.0135216	+	0.0234200i
$209$	−6.03664e11			−0.104711
$210$		0			0
$211$	−3.79876e12			−0.625300			−0.312650	−	0.949868i	$-0.601217\pi$
$211$	−3.79876e12			−0.625300			−0.312650	+	0.949868i	$0.601217\pi$
$212$	−2.13377e12	+	3.69580e12i	−0.342216	+	0.592735i
$213$		0			0
$214$	3.13802e12	+	5.43521e12i	0.477948	+	0.827830i
$215$	−2.73890e12	+	4.74391e12i	−0.406597	+	0.704247i
$216$		0			0
$217$	3.90695e12	+	3.05331e12i	0.551200	+	0.430767i
$218$	−6.28657e12			−0.864775
$219$		0			0
$220$	−2.18437e11	−	3.78344e11i	−0.0285760	−	0.0494951i
$221$	5.13703e11	+	8.89760e11i	0.0655473	+	0.113531i
$222$		0			0
$223$	8.19004e12			0.994511			0.497255	−	0.867604i	$-0.334341\pi$
$223$	8.19004e12			0.994511			0.497255	+	0.867604i	$0.334341\pi$
$224$	−1.17564e12	−	9.18772e11i	−0.139287	−	0.108854i
$225$		0			0
$226$	−3.33584e10	+	5.77784e10i	−0.00376364	+	0.00651882i
$227$	5.11838e12	+	8.86530e12i	0.563625	+	0.976228i	0.997176	+	0.0750987i	$0.0239272\pi$
$227$	5.11838e12	+	8.86530e12i	0.563625	+	0.976228i	−0.433551	+	0.901129i	$0.642739\pi$
$228$		0			0
$229$	7.22941e12	−	1.25217e13i	0.758592	−	1.31392i	−0.184977	−	0.982743i	$-0.559221\pi$
$229$	7.22941e12	−	1.25217e13i	0.758592	−	1.31392i	0.943569	−	0.331176i	$-0.107445\pi$
$230$	−4.95729e12			−0.507857
$231$		0			0
$232$	3.96757e11			0.0387562
$233$	1.25785e12	−	2.17866e12i	0.119997	−	0.207841i	−0.799769	−	0.600308i	$-0.795045\pi$
$233$	1.25785e12	−	2.17866e12i	0.119997	−	0.207841i	0.919766	+	0.392467i	$0.128378\pi$
$234$		0			0
$235$	1.31720e11	+	2.28146e11i	0.0119889	+	0.0207653i
$236$	4.40577e11	−	7.63101e11i	0.0391747	−	0.0678525i
$237$		0			0
$238$	−9.36088e12	+	3.78054e12i	−0.794590	+	0.320908i
$239$	1.73543e13			1.43952			0.719762	−	0.694221i	$-0.244251\pi$
$239$	1.73543e13			1.43952			0.719762	+	0.694221i	$0.244251\pi$
$240$		0			0
$241$	1.01743e13	+	1.76225e13i	0.806144	+	1.39628i	0.915516	+	0.402282i	$0.131783\pi$
$241$	1.01743e13	+	1.76225e13i	0.806144	+	1.39628i	−0.109371	+	0.994001i	$0.534884\pi$
$242$	−4.38760e12	−	7.59955e12i	−0.339815	−	0.588577i
$243$		0			0
$244$	5.31673e11			0.0393551
$245$	1.93611e12	+	7.77443e12i	0.140125	+	0.562672i
$246$		0			0
$247$	4.15116e11	−	7.19002e11i	0.0287301	−	0.0497619i
$248$	1.82698e12	+	3.16442e12i	0.123666	+	0.214195i
$249$		0			0
$250$	−5.26670e12	+	9.12219e12i	−0.341089	+	0.590784i
$251$	7.04025e12			0.446049			0.223024	−	0.974813i	$-0.428407\pi$
$251$	7.04025e12			0.446049			0.223024	+	0.974813i	$0.428407\pi$
$252$		0			0
$253$	4.02568e12			0.244161
$254$	1.34955e12	−	2.33749e12i	0.0800946	−	0.138728i
$255$		0			0
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	−1.42096e13	+	2.46117e13i	−0.790587	+	1.36934i	0.135017	+	0.990843i	$0.456891\pi$
$257$	−1.42096e13	+	2.46117e13i	−0.790587	+	1.36934i	−0.925604	+	0.378493i	$0.876442\pi$
$258$		0			0
$259$	−1.71178e12	+	1.21678e13i	−0.0912639	+	0.648728i
$260$	6.00843e11			0.0313623
$261$		0			0
$262$	7.10184e12	+	1.23008e13i	0.355397	+	0.615566i
$263$	−5.01802e12	−	8.69147e12i	−0.245910	−	0.425929i	0.716477	−	0.697611i	$-0.245753\pi$
$263$	−5.01802e12	−	8.69147e12i	−0.245910	−	0.425929i	−0.962387	+	0.271682i	$0.912420\pi$
$264$		0			0
$265$	1.68863e13			0.793745
$266$	6.42790e12	+	5.02345e12i	0.295951	+	0.231288i
$267$		0			0
$268$	−7.99996e12	+	1.38563e13i	−0.353465	+	0.612220i
$269$	1.63911e13	+	2.83902e13i	0.709530	+	1.22894i	0.965032	+	0.262133i	$0.0844260\pi$
$269$	1.63911e13	+	2.83902e13i	0.709530	+	1.22894i	−0.255502	+	0.966809i	$0.582241\pi$
$270$		0			0
$271$	−3.21299e12	+	5.56506e12i	−0.133530	+	0.231280i	−0.925035	−	0.379882i	$-0.875965\pi$
$271$	−3.21299e12	+	5.56506e12i	−0.133530	+	0.231280i	0.791505	+	0.611163i	$0.209298\pi$
$272$	−7.43939e12			−0.302976
$273$		0			0
$274$	−7.92634e12			−0.310059
$275$	1.70630e12	−	2.95540e12i	0.0654223	−	0.113315i
$276$		0			0
$277$	1.69865e13	+	2.94214e13i	0.625842	+	1.08399i	0.988377	+	0.152020i	$0.0485778\pi$
$277$	1.69865e13	+	2.94214e13i	0.625842	+	1.08399i	−0.362536	+	0.931970i	$0.618089\pi$
$278$	−1.09444e13	+	1.89562e13i	−0.395316	+	0.684707i
$279$		0			0
$280$	−8.22481e11	+	5.84642e12i	−0.0285599	+	0.203011i
$281$	3.07171e13			1.04591			0.522956	−	0.852360i	$-0.324829\pi$
$281$	3.07171e13			1.04591			0.522956	+	0.852360i	$0.324829\pi$
$282$		0			0
$283$	−1.22425e13	−	2.12046e13i	−0.400907	−	0.694391i	0.592929	−	0.805255i	$-0.297972\pi$
$283$	−1.22425e13	−	2.12046e13i	−0.400907	−	0.694391i	−0.993836	+	0.110864i	$0.964638\pi$
$284$	−3.35753e12	−	5.81542e12i	−0.107837	−	0.186780i
$285$		0			0
$286$	−4.87928e11			−0.0150780
$287$	5.83882e13	−	2.35810e13i	1.77000	−	0.714845i
$288$		0			0
$289$	−8.03181e12	+	1.39115e13i	−0.234356	+	0.405916i
$290$	−7.84966e11	−	1.35960e12i	−0.0224730	−	0.0389244i
$291$		0			0
$292$	−4.15031e12	+	7.18854e12i	−0.114413	+	0.198169i
$293$	−3.60691e13			−0.975806			−0.487903	−	0.872898i	$-0.662238\pi$
$293$	−3.60691e13			−0.975806			−0.487903	+	0.872898i	$0.662238\pi$
$294$		0			0
$295$	−3.48664e12			−0.0908629
$296$	−4.52739e12	+	7.84167e12i	−0.115809	+	0.200588i
$297$		0			0
$298$	−4.67785e12	−	8.10227e12i	−0.115307	−	0.199718i
$299$	−2.76830e12	+	4.79484e12i	−0.0669918	+	0.116033i
$300$		0			0
$301$	−5.57415e13	+	2.25121e13i	−1.30036	+	0.525170i
$302$	−9.96923e12			−0.228362
$303$		0			0
$304$	3.00583e12	+	5.20625e12i	0.0663987	+	0.115006i
$305$	−1.05189e12	−	1.82193e12i	−0.0228203	−	0.0395260i
$306$		0			0
$307$	3.34874e13			0.700842			0.350421	−	0.936592i	$-0.386039\pi$
$307$	3.34874e13			0.700842			0.350421	+	0.936592i	$0.386039\pi$
$308$	6.67914e11	−	4.74771e12i	0.0137307	−	0.0976012i
$309$		0			0
$310$	7.22918e12	−	1.25213e13i	0.143417	−	0.248405i
$311$	1.18427e12	+	2.05121e12i	0.0230817	+	0.0399787i	0.877336	−	0.479877i	$-0.159319\pi$
$311$	1.18427e12	+	2.05121e12i	0.0230817	+	0.0399787i	−0.854254	+	0.519856i	$0.825986\pi$
$312$		0			0
$313$	3.86507e13	−	6.69450e13i	0.727216	−	1.25958i	−0.230839	−	0.972992i	$-0.574147\pi$
$313$	3.86507e13	−	6.69450e13i	0.727216	−	1.25958i	0.958055	−	0.286584i	$-0.0925196\pi$
$314$	−4.55315e13			−0.841781
$315$		0			0
$316$	−3.53336e13			−0.630824
$317$	2.39639e13	−	4.15068e13i	0.420467	−	0.728271i	−0.575518	−	0.817789i	$-0.695199\pi$
$317$	2.39639e13	−	4.15068e13i	0.420467	−	0.728271i	0.995985	+	0.0895184i	$0.0285328\pi$
$318$		0			0
$319$	6.37449e11	+	1.10409e12i	0.0108043	+	0.0187136i
$320$	−2.17533e12	+	3.76779e12i	−0.0362411	+	0.0627714i
$321$		0			0
$322$	−4.28660e13	−	3.35001e13i	−0.690090	−	0.539310i
$323$	4.06754e13			0.643751
$324$		0			0
$325$	2.34671e12	+	4.06462e12i	0.0359006	+	0.0621816i
$326$	−1.97093e13	−	3.41376e13i	−0.296466	−	0.513495i
$327$		0			0
$328$	4.64029e13			0.674900
$329$	−4.02759e11	+	2.86292e12i	−0.00576061	+	0.0409479i
$330$		0			0
$331$	3.32211e13	−	5.75407e13i	0.459579	−	0.796015i	−0.539359	−	0.842076i	$-0.681334\pi$
$331$	3.32211e13	−	5.75407e13i	0.459579	−	0.796015i	0.998939	+	0.0460610i	$0.0146669\pi$
$332$	−8.32226e12	−	1.44146e13i	−0.113235	−	0.196129i
$333$		0			0
$334$	5.09922e13	−	8.83212e13i	0.671272	−	1.16268i
$335$	6.33103e13			0.819837
$336$		0			0
$337$	8.31081e13			1.04155			0.520773	−	0.853695i	$-0.325644\pi$
$337$	8.31081e13			1.04155			0.520773	+	0.853695i	$0.325644\pi$
$338$	−2.83390e13	+	4.90847e13i	−0.349416	+	0.605207i
$339$		0			0
$340$	1.47185e13	+	2.54932e13i	0.175683	+	0.304292i
$341$	−5.87061e12	+	1.01682e13i	−0.0689500	+	0.119425i
$342$		0			0
$343$	−3.57960e13	+	8.03097e13i	−0.407114	+	0.913377i
$344$	−4.42996e13			−0.495825
$345$		0			0
$346$	−2.94934e13	−	5.10840e13i	−0.319746	−	0.553817i
$347$	−5.80583e13	−	1.00560e14i	−0.619516	−	1.07303i	−0.989574	−	0.144024i	$-0.953996\pi$
$347$	−5.80583e13	−	1.00560e14i	−0.619516	−	1.07303i	0.370059	−	0.929008i	$-0.379338\pi$
$348$		0			0
$349$	8.26069e13			0.854037			0.427018	−	0.904243i	$-0.359564\pi$
$349$	8.26069e13			0.854037			0.427018	+	0.904243i	$0.359564\pi$
$350$	−4.27626e13	+	1.72704e13i	−0.435201	+	0.175763i
$351$		0			0
$352$	1.76653e12	−	3.05972e12i	0.0174235	−	0.0301784i
$353$	−8.51580e13	−	1.47498e14i	−0.826922	−	1.43227i	−0.900441	−	0.434978i	$-0.856756\pi$
$353$	−8.51580e13	−	1.47498e14i	−0.826922	−	1.43227i	0.0735190	−	0.997294i	$-0.476577\pi$
$354$		0			0
$355$	−1.32855e13	+	2.30111e13i	−0.125061	+	0.216611i
$356$	−4.00383e13			−0.371108
$357$		0			0
$358$	−8.23517e13			−0.740143
$359$	4.99740e13	−	8.65575e13i	0.442308	−	0.766099i	−0.555553	−	0.831481i	$-0.687493\pi$
$359$	4.99740e13	−	8.65575e13i	0.442308	−	0.766099i	0.997860	+	0.0653820i	$0.0208266\pi$
$360$		0			0
$361$	4.18105e13	+	7.24179e13i	0.358919	+	0.621665i
$362$	−4.10431e13	+	7.10887e13i	−0.347011	+	0.601040i
$363$		0			0
$364$	5.19553e12	+	4.06034e12i	0.0426159	+	0.0333047i
$365$	3.28448e13			0.265372
$366$		0			0
$367$	−8.57782e13	−	1.48572e14i	−0.672533	−	1.16486i	−0.977183	−	0.212397i	$-0.931873\pi$
$367$	−8.57782e13	−	1.48572e14i	−0.672533	−	1.16486i	0.304651	−	0.952464i	$-0.401460\pi$
$368$	−2.00451e13	−	3.47191e13i	−0.154827	−	0.268167i
$369$		0			0
$370$	3.58289e13			0.268611
$371$	1.46017e14	+	1.14113e14i	1.07856	+	0.842905i
$372$		0			0
$373$	3.03239e13	−	5.25225e13i	0.217463	−	0.376658i	−0.736568	−	0.676363i	$-0.763555\pi$
$373$	3.03239e13	−	5.25225e13i	0.217463	−	0.376658i	0.954032	+	0.299705i	$0.0968884\pi$
$374$	−1.19525e13	−	2.07023e13i	−0.0844625	−	0.146293i
$375$		0			0
$376$	−1.06524e12	+	1.84504e12i	−0.00730992	+	0.0126611i
$377$	−1.75339e12			−0.0118578
$378$		0			0
$379$	−2.96338e14			−1.94658			−0.973289	−	0.229584i	$-0.926263\pi$
$379$	−2.96338e14			−1.94658			−0.973289	+	0.229584i	$0.926263\pi$
$380$	1.18938e13	−	2.06007e13i	0.0770036	−	0.133374i
$381$		0			0
$382$	−5.37068e13	−	9.30230e13i	−0.337817	−	0.585116i
$383$	−6.42064e13	+	1.11209e14i	−0.398093	+	0.689518i	−0.993491	−	0.113913i	$-0.963661\pi$
$383$	−6.42064e13	+	1.11209e14i	−0.398093	+	0.689518i	0.595397	+	0.803431i	$0.296995\pi$
$384$		0			0
$385$	−1.75908e13	+	7.10433e12i	−0.105987	+	0.0428045i
$386$	2.06580e14			1.22704
$387$		0			0
$388$	6.61576e12	+	1.14588e13i	0.0381949	+	0.0661555i
$389$	−1.45561e14	−	2.52119e14i	−0.828556	−	1.43510i	−0.899171	−	0.437598i	$-0.855829\pi$
$389$	−1.45561e14	−	2.52119e14i	−0.828556	−	1.43510i	0.0706147	−	0.997504i	$-0.477504\pi$
$390$		0			0
$391$	−2.71254e14			−1.50108
$392$	−4.66206e13	+	4.49962e13i	−0.254393	+	0.245529i
$393$		0			0
$394$	−2.93750e13	+	5.08789e13i	−0.155865	+	0.269966i
$395$	6.99059e13	+	1.21081e14i	0.365788	+	0.633564i
$396$		0			0
$397$	1.47254e14	−	2.55052e14i	0.749411	−	1.29802i	−0.198694	−	0.980062i	$-0.563670\pi$
$397$	1.47254e14	−	2.55052e14i	0.749411	−	1.29802i	0.948105	−	0.317956i	$-0.102997\pi$
$398$	1.49542e14			0.750597
$399$		0			0
$400$	−3.39848e13			−0.165941
$401$	−9.46182e13	+	1.63884e14i	−0.455702	+	0.789298i	−0.998728	−	0.0504171i	$-0.983945\pi$
$401$	−9.46182e13	+	1.63884e14i	−0.455702	+	0.789298i	0.543027	+	0.839715i	$0.317278\pi$
$402$		0			0
$403$	−8.07399e12	−	1.39846e13i	−0.0378364	−	0.0655347i
$404$	−2.01694e13	+	3.49344e13i	−0.0932386	+	0.161494i
$405$		0			0
$406$	2.40018e12	−	1.70611e13i	0.0107982	−	0.0767565i
$407$	−2.90957e13			−0.129140
$408$		0			0
$409$	−1.66115e14	−	2.87719e14i	−0.717679	−	1.24306i	−0.961917	−	0.273342i	$-0.911871\pi$
$409$	−1.66115e14	−	2.87719e14i	−0.717679	−	1.24306i	0.244238	−	0.969715i	$-0.421462\pi$
$410$	−9.18061e13	−	1.59013e14i	−0.391346	−	0.677830i
$411$		0			0
$412$	−9.49404e13			−0.394018
$413$	−3.01492e13	−	2.35618e13i	−0.123467	−	0.0964904i
$414$		0			0
$415$	−3.29304e13	+	5.70372e13i	−0.131321	+	0.227454i
$416$	2.42955e12	+	4.20810e12i	0.00956118	+	0.0165605i
$417$		0			0
$418$	−9.65862e12	+	1.67292e13i	−0.0370208	+	0.0641219i
$419$	1.68918e14			0.638997			0.319498	−	0.947587i	$-0.396486\pi$
$419$	1.68918e14			0.638997			0.319498	+	0.947587i	$0.396486\pi$
$420$		0			0
$421$	−3.02870e14			−1.11610			−0.558052	−	0.829806i	$-0.688451\pi$
$421$	−3.02870e14			−1.11610			−0.558052	+	0.829806i	$0.688451\pi$
$422$	−6.07802e13	+	1.05274e14i	−0.221077	+	0.382916i
$423$		0			0
$424$	6.82806e13	+	1.18265e14i	0.241983	+	0.419127i
$425$	−1.14972e14	+	1.99137e14i	−0.402210	+	0.696648i
$426$		0			0
$427$	3.21636e12	−	2.28627e13i	0.0109651	−	0.0779426i
$428$	2.00833e14			0.675920
$429$		0			0
$430$	8.76447e13	+	1.51805e14i	0.287507	+	0.497978i
$431$	−9.44616e13	−	1.63612e14i	−0.305936	−	0.529897i	0.671533	−	0.740974i	$-0.265636\pi$
$431$	−9.44616e13	−	1.63612e14i	−0.305936	−	0.529897i	−0.977469	+	0.211078i	$0.932303\pi$
$432$		0			0
$433$	1.47708e14			0.466359			0.233180	−	0.972434i	$-0.425087\pi$
$433$	1.47708e14			0.466359			0.233180	+	0.972434i	$0.425087\pi$
$434$	1.47127e14	−	5.94196e13i	0.458668	−	0.185241i
$435$		0			0
$436$	−1.00585e14	+	1.74219e14i	−0.305744	+	0.529564i
$437$	1.09598e14	+	1.89830e14i	0.328969	+	0.569791i
$438$		0			0
$439$	−1.48497e14	+	2.57205e14i	−0.434674	+	0.752877i	−0.997269	−	0.0738555i	$-0.976470\pi$
$439$	−1.48497e14	+	2.57205e14i	−0.434674	+	0.752877i	0.562595	+	0.826732i	$0.309803\pi$
$440$	−1.39800e13			−0.0404126
$441$		0			0
$442$	3.28770e13			0.0926979
$443$	−2.93183e13	+	5.07807e13i	−0.0816428	+	0.141409i	−0.903956	−	0.427626i	$-0.859350\pi$
$443$	−2.93183e13	+	5.07807e13i	−0.0816428	+	0.141409i	0.822313	+	0.569036i	$0.192683\pi$
$444$		0			0
$445$	7.92139e13	+	1.37202e14i	0.215190	+	0.372719i
$446$	1.31041e14	−	2.26969e14i	0.351613	−	0.609011i
$447$		0			0
$448$	−4.42720e13	+	1.78800e13i	−0.115904	+	0.0468099i
$449$	−6.20981e14			−1.60592			−0.802959	−	0.596035i	$-0.796742\pi$
$449$	−6.20981e14			−1.60592			−0.802959	+	0.596035i	$0.796742\pi$
$450$		0			0
$451$	7.45532e13	+	1.29130e14i	0.188146	+	0.325879i
$452$	1.06747e12	+	1.84891e12i	0.00266130	+	0.00460950i
$453$		0			0
$454$	3.27577e14			0.797087
$455$	3.63481e12	−	2.58372e13i	0.00873813	−	0.0621129i
$456$		0			0
$457$	2.59807e14	−	4.49998e14i	0.609693	−	1.05602i	−0.381598	−	0.924328i	$-0.624626\pi$
$457$	2.59807e14	−	4.49998e14i	0.609693	−	1.05602i	0.991291	−	0.131691i	$-0.0420406\pi$
$458$	−2.31341e14	−	4.00695e14i	−0.536405	−	0.929081i
$459$		0			0
$460$	−7.93167e13	+	1.37381e14i	−0.179555	+	0.310998i
$461$	−1.08562e14			−0.242841			−0.121421	−	0.992601i	$-0.538745\pi$
$461$	−1.08562e14			−0.242841			−0.121421	+	0.992601i	$0.538745\pi$
$462$		0			0
$463$	6.91128e14			1.50960			0.754802	−	0.655953i	$-0.227733\pi$
$463$	6.91128e14			1.50960			0.754802	+	0.655953i	$0.227733\pi$
$464$	6.34811e12	−	1.09953e13i	0.0137024	−	0.0237332i
$465$		0			0
$466$	−4.02511e13	−	6.97170e13i	−0.0848507	−	0.146966i
$467$	−8.50470e13	+	1.47306e14i	−0.177181	+	0.306886i	−0.940914	−	0.338646i	$-0.890031\pi$
$467$	−8.50470e13	+	1.47306e14i	−0.177181	+	0.306886i	0.763733	+	0.645532i	$0.223364\pi$
$468$		0			0
$469$	5.47448e14	+	4.27834e14i	1.11402	+	0.870613i
$470$	8.43008e12			0.0169548
$471$		0			0
$472$	−1.40985e13	−	2.44192e13i	−0.0277007	−	0.0479790i
$473$	−7.11738e13	−	1.23277e14i	−0.138224	−	0.239411i
$474$		0			0
$475$	1.85814e14			0.352586
$476$	−4.50046e13	+	3.19905e14i	−0.0844149	+	0.600043i
$477$		0			0
$478$	2.77669e14	−	4.80937e14i	0.508948	−	0.881524i
$479$	3.00492e14	+	5.20467e14i	0.544487	+	0.943079i	0.998639	+	0.0521549i	$0.0166090\pi$
$479$	3.00492e14	+	5.20467e14i	0.544487	+	0.943079i	−0.454152	+	0.890924i	$0.650058\pi$
$480$		0			0
$481$	2.00080e13	−	3.46548e13i	0.0354328	−	0.0613714i
$482$	6.51158e14			1.14006
$483$		0			0
$484$	−2.80806e14			−0.480571
$485$	2.61780e13	−	4.53416e13i	0.0442952	−	0.0767215i
$486$		0			0
$487$	−4.94440e13	−	8.56394e13i	−0.0817907	−	0.141666i	0.822228	−	0.569158i	$-0.192731\pi$
$487$	−4.94440e13	−	8.56394e13i	−0.0817907	−	0.141666i	−0.904019	+	0.427492i	$0.859397\pi$
$488$	8.50677e12	−	1.47342e13i	0.0139141	−	0.0241000i
$489$		0			0
$490$	2.46429e14	+	7.07359e13i	0.394106	+	0.113126i
$491$	−9.24926e14			−1.46271			−0.731356	−	0.681996i	$-0.761112\pi$
$491$	−9.24926e14			−1.46271			−0.731356	+	0.681996i	$0.761112\pi$
$492$		0			0
$493$	−4.29519e13	−	7.43948e13i	−0.0664238	−	0.115049i
$494$	−1.32837e13	−	2.30081e13i	−0.0203152	−	0.0351870i
$495$		0			0
$496$	1.16926e14			0.174889
$497$	−2.70383e14	+	1.09199e14i	−0.399963	+	0.161531i
$498$		0			0
$499$	−3.80904e14	+	6.59746e14i	−0.551141	+	0.954604i	0.447051	+	0.894508i	$0.352474\pi$
$499$	−3.80904e14	+	6.59746e14i	−0.551141	+	0.954604i	−0.998193	+	0.0600962i	$0.980859\pi$
$500$	1.68534e14	+	2.91910e14i	0.241187	+	0.417748i
$501$		0			0
$502$	1.12644e14	−	1.95105e14i	0.157702	−	0.273148i
$503$	9.31585e14			1.29003			0.645013	−	0.764172i	$-0.276852\pi$
$503$	9.31585e14			1.29003			0.645013	+	0.764172i	$0.276852\pi$
$504$		0			0
$505$	1.59617e14			0.216260
$506$	6.44108e13	−	1.11563e14i	0.0863239	−	0.149517i
$507$		0			0
$508$	−4.31856e13	−	7.47996e13i	−0.0566354	−	0.0980954i
$509$	3.94996e13	−	6.84153e13i	0.0512442	−	0.0887575i	−0.839265	−	0.543722i	$-0.817015\pi$
$509$	3.94996e13	−	6.84153e13i	0.0512442	−	0.0887575i	0.890510	+	0.454964i	$0.150348\pi$
$510$		0			0
$511$	2.84011e14	+	2.21957e14i	0.360595	+	0.281808i
$512$	−3.51844e13			−0.0441942
$513$		0			0
$514$	4.54707e14	+	7.87576e14i	0.559029	+	0.968267i
$515$	1.87835e14	+	3.25340e14i	0.228474	+	0.395729i
$516$		0			0
$517$	−6.84583e12			−0.00815132
$518$	3.09815e14	+	2.42123e14i	0.364997	+	0.285248i
$519$		0			0
$520$	9.61349e12	−	1.66511e13i	0.0110882	−	0.0192054i
$521$	−3.72402e14	−	6.45019e14i	−0.425015	−	0.736147i	0.571407	−	0.820667i	$-0.306398\pi$
$521$	−3.72402e14	−	6.45019e14i	−0.425015	−	0.736147i	−0.996422	+	0.0845194i	$0.973064\pi$
$522$		0			0
$523$	−5.72376e14	+	9.91385e14i	−0.639620	+	1.10786i	0.345896	+	0.938273i	$0.387575\pi$
$523$	−5.72376e14	+	9.91385e14i	−0.639620	+	1.10786i	−0.985516	+	0.169582i	$0.945758\pi$
$524$	4.54518e14			0.502608
$525$		0			0
$526$	−3.21154e14			−0.347769
$527$	3.95567e14	−	6.85143e14i	0.423899	−	0.734214i
$528$		0			0
$529$	−2.54476e14	−	4.40766e14i	−0.267080	−	0.462596i
$530$	2.70180e14	−	4.67966e14i	0.280631	−	0.486068i
$531$		0			0
$532$	2.42060e14	−	9.77600e13i	0.246269	−	0.0994597i
$533$	−2.05069e14			−0.206491
$534$		0			0
$535$	−3.97340e14	−	6.88213e14i	−0.391937	−	0.678855i
$536$	2.55999e14	+	4.43403e14i	0.249938	+	0.432905i
$537$		0			0
$538$	1.04903e15			1.00343
$539$	−2.00118e14	−	5.74426e13i	−0.189473	−	0.0543871i
$540$		0			0
$541$	−8.16840e14	+	1.41481e15i	−0.757795	+	1.31254i	0.186178	+	0.982516i	$0.440390\pi$
$541$	−8.16840e14	+	1.41481e15i	−0.757795	+	1.31254i	−0.943973	+	0.330024i	$0.892943\pi$
$542$	1.02816e14	+	1.78082e14i	0.0944198	+	0.163540i
$543$		0			0
$544$	−1.19030e14	+	2.06166e14i	−0.107118	+	0.185534i
$545$	7.96013e14			0.709152
$546$		0			0
$547$	−4.36207e14			−0.380857			−0.190429	−	0.981701i	$-0.560988\pi$
$547$	−4.36207e14			−0.380857			−0.190429	+	0.981701i	$0.560988\pi$
$548$	−1.26821e14	+	2.19661e14i	−0.109622	+	0.189872i
$549$		0			0
$550$	−5.46016e13	−	9.45727e13i	−0.0462605	−	0.0801256i
$551$	−3.47088e13	+	6.01174e13i	−0.0291142	+	0.0504274i
$552$		0			0
$553$	−2.13751e14	+	1.51940e15i	−0.175760	+	1.24935i
$554$	1.08713e15			0.885074
$555$		0			0
$556$	3.50220e14	+	6.06598e14i	0.279530	+	0.484161i
$557$	5.72978e14	+	9.92427e14i	0.452829	+	0.784323i	0.998561	−	0.0536370i	$-0.0170814\pi$
$557$	5.72978e14	+	9.92427e14i	0.452829	+	0.784323i	−0.545731	+	0.837960i	$0.683748\pi$
$558$		0			0
$559$	1.95774e14			0.151701
$560$	1.48861e14	+	1.16336e14i	0.114221	+	0.0892647i
$561$		0			0
$562$	4.91473e14	−	8.51257e14i	0.369786	−	0.640488i
$563$	−2.36853e14	−	4.10241e14i	−0.176475	−	0.305663i	0.764196	−	0.644984i	$-0.223136\pi$
$563$	−2.36853e14	−	4.10241e14i	−0.176475	−	0.305663i	−0.940671	+	0.339321i	$0.889803\pi$
$564$		0			0
$565$	4.22388e12	−	7.31597e12i	0.00308635	−	0.00534571i
$566$	−7.83518e14			−0.566968
$567$		0			0
$568$	−2.14882e14			−0.152505
$569$	8.50002e14	−	1.47225e15i	0.597451	−	1.03482i	−0.395745	−	0.918360i	$-0.629514\pi$
$569$	8.50002e14	−	1.47225e15i	0.597451	−	1.03482i	0.993196	−	0.116455i	$-0.0371531\pi$
$570$		0			0
$571$	−1.04664e15	−	1.81284e15i	−0.721604	−	1.24986i	−0.960356	−	0.278775i	$-0.910072\pi$
$571$	−1.04664e15	−	1.81284e15i	−0.721604	−	1.24986i	0.238752	−	0.971081i	$-0.423262\pi$
$572$	−7.80685e12	+	1.35219e13i	−0.00533086	+	0.00923332i
$573$		0			0
$574$	2.80715e14	−	1.99540e15i	0.188040	−	1.33664i
$575$	−1.23915e15			−0.822148
$576$		0			0
$577$	1.03914e15	+	1.79985e15i	0.676408	+	1.17157i	0.976055	+	0.217522i	$0.0697975\pi$
$577$	1.03914e15	+	1.79985e15i	0.676408	+	1.17157i	−0.299648	+	0.954050i	$0.596869\pi$
$578$	2.57018e14	+	4.45168e14i	0.165714	+	0.287026i
$579$		0			0
$580$	−5.02378e13			−0.0317817
$581$	−6.70194e14	+	2.70669e14i	−0.419983	+	0.169617i
$582$		0			0
$583$	−2.19406e14	+	3.80022e14i	−0.134918	+	0.233685i
$584$	1.32810e14	+	2.30033e14i	0.0809021	+	0.140126i
$585$		0			0
$586$	−5.77106e14	+	9.99576e14i	−0.344999	+	0.597557i
$587$	−8.10690e14			−0.480115			−0.240057	−	0.970759i	$-0.577166\pi$
$587$	−8.10690e14			−0.480115			−0.240057	+	0.970759i	$0.577166\pi$
$588$		0			0
$589$	−6.39304e14			−0.371598
$590$	−5.57863e13	+	9.66247e13i	−0.0321249	+	0.0556419i
$591$		0			0
$592$	1.44876e14	+	2.50933e14i	0.0818895	+	0.141837i
$593$	−6.65707e14	+	1.15304e15i	−0.372805	+	0.645718i	−0.989996	−	0.141096i	$-0.954937\pi$
$593$	−6.65707e14	+	1.15304e15i	−0.372805	+	0.645718i	0.617191	+	0.786814i	$0.288271\pi$
$594$		0			0
$595$	1.18528e15	−	4.78696e14i	0.651597	−	0.263158i
$596$	−2.99382e14			−0.163069
$597$		0			0
$598$	8.85857e13	+	1.53435e14i	0.0473704	+	0.0820479i
$599$	−2.64501e14	−	4.58130e14i	−0.140146	−	0.242740i	0.787406	−	0.616435i	$-0.211424\pi$
$599$	−2.64501e14	−	4.58130e14i	−0.140146	−	0.242740i	−0.927551	+	0.373696i	$0.878090\pi$
$600$		0			0
$601$	−1.87111e15			−0.973399			−0.486699	−	0.873570i	$-0.661799\pi$
$601$	−1.87111e15			−0.973399			−0.486699	+	0.873570i	$0.661799\pi$
$602$	−2.67991e14	+	1.90495e15i	−0.138146	+	0.981979i
$603$		0			0
$604$	−1.59508e14	+	2.76275e14i	−0.0807381	+	0.139842i
$605$	5.55563e14	+	9.62263e14i	0.278663	+	0.482658i
$606$		0			0
$607$	1.42289e15	−	2.46452e15i	0.700864	−	1.21393i	−0.267300	−	0.963613i	$-0.586131\pi$
$607$	1.42289e15	−	2.46452e15i	0.700864	−	1.21393i	0.968164	−	0.250318i	$-0.0805352\pi$
$608$	1.92373e14			0.0939020
$609$		0			0
$610$	−6.73210e13			−0.0322728
$611$	4.70761e12	−	8.15382e12i	0.00223653	−	0.00387378i
$612$		0			0
$613$	−1.52101e15	−	2.63446e15i	−0.709739	−	1.22930i	−0.964954	−	0.262420i	$-0.915479\pi$
$613$	−1.52101e15	−	2.63446e15i	−0.709739	−	1.22930i	0.255214	−	0.966885i	$-0.417854\pi$
$614$	5.35798e14	−	9.28029e14i	0.247785	−	0.429176i
$615$		0			0
$616$	−1.20886e14	−	9.44731e13i	−0.0549138	−	0.0429155i
$617$	−3.00980e15			−1.35509			−0.677546	−	0.735481i	$-0.736956\pi$
$617$	−3.00980e15			−1.35509			−0.677546	+	0.735481i	$0.736956\pi$
$618$		0			0
$619$	1.77621e15	+	3.07648e15i	0.785589	+	1.36068i	0.928646	+	0.370966i	$0.120973\pi$
$619$	1.77621e15	+	3.07648e15i	0.785589	+	1.36068i	−0.143057	+	0.989714i	$0.545693\pi$
$620$	−2.31334e14	−	4.00682e14i	−0.101411	−	0.175649i
$621$		0			0
$622$	7.57932e13			0.0326425
$623$	−2.42212e14	+	1.72171e15i	−0.103398	+	0.734978i
$624$		0			0
$625$	−1.24395e14	+	2.15459e14i	−0.0521751	+	0.0903700i
$626$	−1.23682e15	−	2.14224e15i	−0.514220	−	0.890654i
$627$		0			0
$628$	−7.28505e14	+	1.26181e15i	−0.297615	+	0.515484i
$629$	1.96049e15			0.793938
$630$		0			0
$631$	4.61646e15			1.83716			0.918582	−	0.395230i	$-0.129335\pi$
$631$	4.61646e15			1.83716			0.918582	+	0.395230i	$0.129335\pi$
$632$	−5.65337e14	+	9.79193e14i	−0.223030	+	0.386300i
$633$		0			0
$634$	−7.66846e14	−	1.32822e15i	−0.297315	−	0.514965i
$635$	−1.70881e14	+	2.95975e14i	−0.0656809	+	0.113763i
$636$		0			0
$637$	2.06031e14	−	1.98852e14i	0.0778334	−	0.0751215i
$638$	4.07967e13			0.0152796
$639$		0			0
$640$	6.96107e13	+	1.20569e14i	0.0256263	+	0.0443861i
$641$	5.94333e14	+	1.02942e15i	0.216926	+	0.375726i	0.953867	−	0.300231i	$-0.0970638\pi$
$641$	5.94333e14	+	1.02942e15i	0.216926	+	0.375726i	−0.736941	+	0.675957i	$0.763730\pi$
$642$		0			0
$643$	−1.96941e15			−0.706604			−0.353302	−	0.935509i	$-0.614941\pi$
$643$	−1.96941e15			−0.706604			−0.353302	+	0.935509i	$0.614941\pi$
$644$	−1.61424e15	+	6.51936e14i	−0.574243	+	0.231917i
$645$		0			0
$646$	6.50807e14	−	1.12723e15i	0.227600	−	0.394216i
$647$	8.58806e13	+	1.48750e14i	0.0297798	+	0.0515801i	0.880531	−	0.473988i	$-0.157186\pi$
$647$	8.58806e13	+	1.48750e14i	0.0297798	+	0.0515801i	−0.850751	+	0.525568i	$0.823853\pi$
$648$		0			0
$649$	4.53025e13	−	7.84662e13i	0.0154446	−	0.0267508i
$650$	1.50190e14			0.0507711
$651$		0			0
$652$	−1.26140e15			−0.419267
$653$	7.20449e14	−	1.24785e15i	0.237455	−	0.411283i	−0.722529	−	0.691341i	$-0.757020\pi$
$653$	7.20449e14	−	1.24785e15i	0.237455	−	0.411283i	0.959983	+	0.280058i	$0.0903536\pi$
$654$		0			0
$655$	−8.99244e14	−	1.55754e15i	−0.291441	−	0.504790i
$656$	7.42447e14	−	1.28596e15i	0.238613	−	0.413290i
$657$		0			0
$658$	7.28954e13	+	5.69683e13i	0.0230387	+	0.0180049i
$659$	−5.36683e15			−1.68208			−0.841042	−	0.540969i	$-0.818058\pi$
$659$	−5.36683e15			−1.68208			−0.841042	+	0.540969i	$0.818058\pi$
$660$		0			0
$661$	−2.14926e15	−	3.72263e15i	−0.662492	−	1.14747i	−0.979959	−	0.199201i	$-0.936165\pi$
$661$	−2.14926e15	−	3.72263e15i	−0.662492	−	1.14747i	0.317467	−	0.948269i	$-0.397168\pi$
$662$	−1.06308e15	−	1.84130e15i	−0.324972	−	0.562867i
$663$		0			0
$664$	−5.32625e14			−0.160139
$665$	−8.13908e14	−	6.36075e14i	−0.242693	−	0.189666i
$666$		0			0
$667$	2.31464e14	−	4.00907e14i	0.0678877	−	0.117585i
$668$	−1.63175e15	−	2.82628e15i	−0.474661	−	0.822137i
$669$		0			0
$670$	1.01296e15	−	1.75451e15i	0.289856	−	0.502046i
$671$	5.46695e13			0.0155157
$672$		0			0
$673$	−1.97865e15			−0.552441			−0.276221	−	0.961094i	$-0.589082\pi$
$673$	−1.97865e15			−0.552441			−0.276221	+	0.961094i	$0.589082\pi$
$674$	1.32973e15	−	2.30316e15i	0.368242	−	0.637815i
$675$		0			0
$676$	9.06849e14	+	1.57071e15i	0.247075	+	0.427946i
$677$	2.74962e15	−	4.76248e15i	0.743079	−	1.28705i	−0.208008	−	0.978127i	$-0.566698\pi$
$677$	2.74962e15	−	4.76248e15i	0.743079	−	1.28705i	0.951087	−	0.308923i	$-0.0999686\pi$
$678$		0			0
$679$	5.32769e14	−	2.15167e14i	0.141663	−	0.0572127i
$680$	9.41984e14			0.248453
$681$		0			0
$682$	1.87860e14	+	3.25382e14i	0.0487550	+	0.0844462i
$683$	−2.76887e14	−	4.79582e14i	−0.0712834	−	0.123466i	0.828181	−	0.560461i	$-0.189376\pi$
$683$	−2.76887e14	−	4.79582e14i	−0.0712834	−	0.123466i	−0.899464	+	0.436995i	$0.856043\pi$
$684$		0			0
$685$	1.00364e15			0.254261
$686$	1.65287e15	+	2.27696e15i	0.415390	+	0.572233i
$687$		0			0
$688$	−7.08793e14	+	1.22767e15i	−0.175300	+	0.303629i
$689$	−3.01754e14	−	5.22653e14i	−0.0740367	−	0.128235i
$690$		0			0
$691$	2.90759e15	−	5.03610e15i	0.702108	−	1.21609i	−0.265617	−	0.964079i	$-0.585576\pi$
$691$	2.90759e15	−	5.03610e15i	0.702108	−	1.21609i	0.967725	−	0.252009i	$-0.0810911\pi$
$692$	−1.88758e15			−0.452190
$693$		0			0
$694$	−3.71573e15			−0.876127
$695$	1.38579e15	−	2.40025e15i	0.324175	−	0.561488i
$696$		0			0
$697$	−5.02346e15	−	8.70089e15i	−1.15670	−	2.00347i
$698$	1.32171e15	−	2.28927e15i	0.301948	−	0.522989i
$699$		0			0
$700$	−2.05591e14	+	1.46140e15i	−0.0462344	+	0.328647i
$701$	5.79768e13			0.0129362			0.00646808	−	0.999979i	$-0.497941\pi$
$701$	5.79768e13			0.0129362			0.00646808	+	0.999979i	$0.497941\pi$
$702$		0			0
$703$	−7.92123e14	−	1.37200e15i	−0.173996	−	0.301369i
$704$	−5.65289e13	−	9.79109e13i	−0.0123203	−	0.0213394i
$705$		0			0
$706$	−5.45011e15			−1.16944
$707$	1.38022e15	+	1.07865e15i	0.293860	+	0.229654i
$708$		0			0
$709$	−1.37829e15	+	2.38727e15i	−0.288926	+	0.500435i	−0.973554	−	0.228458i	$-0.926632\pi$
$709$	−1.37829e15	+	2.38727e15i	−0.288926	+	0.500435i	0.684627	+	0.728893i	$0.259965\pi$
$710$	4.25135e14	+	7.36355e14i	0.0884312	+	0.153167i
$711$		0			0
$712$	−6.40612e14	+	1.10957e15i	−0.131206	+	0.227256i
$713$	4.26335e15			0.866481
$714$		0			0
$715$	6.17820e13			0.0123646
$716$	−1.31763e15	+	2.28220e15i	−0.261680	+	0.453243i
$717$		0			0
$718$	−1.59917e15	−	2.76984e15i	−0.312759	−	0.541714i
$719$	1.42291e15	−	2.46456e15i	0.276165	−	0.478333i	−0.694263	−	0.719721i	$-0.744270\pi$
$719$	1.42291e15	−	2.46456e15i	0.276165	−	0.478333i	0.970429	+	0.241389i	$0.0776029\pi$
$720$		0			0
$721$	−5.74343e14	+	4.08258e15i	−0.109781	+	0.780353i
$722$	2.67587e15			0.507588
$723$		0			0
$724$	1.31338e15	+	2.27484e15i	0.245374	+	0.425000i
$725$	−1.96214e14	−	3.39852e14i	−0.0363806	−	0.0630131i
$726$		0			0
$727$	−4.90303e15			−0.895417			−0.447708	−	0.894180i	$-0.647760\pi$
$727$	−4.90303e15			−0.895417			−0.447708	+	0.894180i	$0.647760\pi$
$728$	1.95652e14	−	7.90172e13i	0.0354619	−	0.0143218i
$729$		0			0
$730$	5.25517e14	−	9.10221e14i	0.0938233	−	0.162507i
$731$	4.79575e15	+	8.30649e15i	0.849789	+	1.47188i
$732$		0			0
$733$	1.74781e15	−	3.02729e15i	0.305085	−	0.528423i	−0.672195	−	0.740374i	$-0.734648\pi$
$733$	1.74781e15	−	3.02729e15i	0.305085	−	0.528423i	0.977280	+	0.211951i	$0.0679817\pi$
$734$	−5.48980e15			−0.951105
$735$		0			0
$736$	−1.28289e15			−0.218958
$737$	−8.22600e14	+	1.42478e15i	−0.139353	+	0.241367i
$738$		0			0
$739$	3.86353e15	+	6.69184e15i	0.644823	+	1.11687i	0.984342	+	0.176267i	$0.0564022\pi$
$739$	3.86353e15	+	6.69184e15i	0.644823	+	1.11687i	−0.339520	+	0.940599i	$0.610264\pi$
$740$	5.73263e14	−	9.92921e14i	0.0949685	−	0.164490i
$741$		0			0
$742$	5.49866e15	−	2.22072e15i	0.897502	−	0.362470i
$743$	7.17014e15			1.16169			0.580843	−	0.814015i	$-0.302723\pi$
$743$	7.17014e15			1.16169			0.580843	+	0.814015i	$0.302723\pi$
$744$		0			0
$745$	5.92314e14	+	1.02592e15i	0.0945568	+	0.163777i
$746$	−9.70364e14	−	1.68072e15i	−0.153770	−	0.266337i
$747$		0			0
$748$	−7.64958e14			−0.119448
$749$	1.21494e15	−	8.63614e15i	0.188324	−	1.33866i
$750$		0			0
$751$	−1.30924e15	+	2.26768e15i	−0.199987	+	0.346387i	−0.948524	−	0.316706i	$-0.897423\pi$
$751$	−1.30924e15	+	2.26768e15i	−0.199987	+	0.346387i	0.748537	+	0.663093i	$0.230757\pi$
$752$	3.40875e13	+	5.90413e13i	0.00516889	+	0.00895278i
$753$		0			0
$754$	−2.80543e13	+	4.85915e13i	−0.00419235	+	0.00726136i
$755$	1.26231e15			0.187266
$756$		0			0
$757$	2.41716e15			0.353409			0.176705	−	0.984264i	$-0.443456\pi$
$757$	2.41716e15			0.353409			0.176705	+	0.984264i	$0.443456\pi$
$758$	−4.74141e15	+	8.21236e15i	−0.688219	+	1.19203i
$759$		0			0
$760$	−3.80602e14	−	6.59222e14i	−0.0544498	−	0.0943098i
$761$	2.84142e15	−	4.92148e15i	0.403571	−	0.699005i	−0.590583	−	0.806977i	$-0.701102\pi$
$761$	2.84142e15	−	4.92148e15i	0.403571	−	0.699005i	0.994154	+	0.107972i	$0.0344356\pi$
$762$		0			0
$763$	6.88317e15	+	5.37925e15i	0.963615	+	0.753072i
$764$	−3.43724e15			−0.477745
$765$		0			0
$766$	2.05460e15	+	3.55868e15i	0.281495	+	0.487563i
$767$	6.23055e13	+	1.07916e14i	0.00847524	+	0.0146796i
$768$		0			0
$769$	1.24672e15			0.167176			0.0835880	−	0.996500i	$-0.473362\pi$
$769$	1.24672e15			0.167176			0.0835880	+	0.996500i	$0.473362\pi$
$770$	−8.45720e13	+	6.01160e14i	−0.0112597	+	0.0800371i
$771$		0			0
$772$	3.30528e15	−	5.72491e15i	0.433823	−	0.751404i
$773$	3.01957e15	+	5.23005e15i	0.393512	+	0.681583i	0.992910	−	0.118869i	$-0.0379267\pi$
$773$	3.01957e15	+	5.23005e15i	0.393512	+	0.681583i	−0.599398	+	0.800451i	$0.704593\pi$
$774$		0			0
$775$	1.80704e15	−	3.12989e15i	0.232171	−	0.402132i
$776$	4.23409e14			0.0540158
$777$		0			0
$778$	−9.31590e15			−1.17176
$779$	−4.05938e15	+	7.03106e15i	−0.506996	+	0.878142i
$780$		0			0
$781$	−3.45240e14	−	5.97973e14i	−0.0425148	−	0.0736378i
$782$	−4.34006e15	+	7.51720e15i	−0.530712	+	0.919219i
$783$		0			0
$784$	5.01041e14	+	2.01193e15i	0.0604136	+	0.242591i
$785$	5.76525e15			0.690296
$786$		0			0
$787$	3.02878e15	+	5.24601e15i	0.357608	+	0.619395i	0.987561	−	0.157238i	$-0.0502591\pi$
$787$	3.02878e15	+	5.24601e15i	0.357608	+	0.619395i	−0.629953	+	0.776633i	$0.716926\pi$
$788$	9.39999e14	+	1.62813e15i	0.110213	+	0.190895i
$789$		0			0
$790$	4.47398e15			0.517303
$791$	8.59635e13	−	3.47177e13i	0.00987060	−	0.00398640i
$792$		0			0
$793$	−3.75941e13	+	6.51149e13i	−0.00425713	+	0.00737357i
$794$	−4.71214e15	−	8.16166e15i	−0.529914	−	0.917837i
$795$		0			0
$796$	2.39268e15	−	4.14424e15i	0.265376	−	0.459645i
$797$	−1.24702e16			−1.37357			−0.686786	−	0.726860i	$-0.740979\pi$
$797$	−1.24702e16			−1.37357			−0.686786	+	0.726860i	$0.740979\pi$
$798$		0			0
$799$	4.61278e14			0.0501136
$800$	−5.43757e14	+	9.41814e14i	−0.0586691	+	0.101618i
$801$		0			0
$802$	3.02778e15	+	5.24427e15i	0.322230	+	0.558118i
$803$	−4.26757e14	+	7.39165e14i	−0.0451071	+	0.0781279i
$804$		0			0
$805$	5.42774e15	+	4.24182e15i	0.565903	+	0.442257i
$806$	−5.16735e14			−0.0535088
$807$		0			0
$808$	6.45421e14	+	1.11790e15i	0.0659296	+	0.114194i
$809$	−6.47498e15	−	1.12150e16i	−0.656934	−	1.13784i	−0.981405	−	0.191948i	$-0.938520\pi$
$809$	−6.47498e15	−	1.12150e16i	−0.656934	−	1.13784i	0.324471	−	0.945896i	$-0.394814\pi$
$810$		0			0
$811$	7.45614e15			0.746276			0.373138	−	0.927776i	$-0.378282\pi$
$811$	7.45614e15			0.746276			0.373138	+	0.927776i	$0.378282\pi$
$812$	−4.34409e14	−	3.39494e14i	−0.0431858	−	0.0337500i
$813$		0			0
$814$	−4.65531e14	+	8.06323e14i	−0.0456577	+	0.0790815i
$815$	2.49562e15	+	4.32254e15i	0.243115	+	0.421087i
$816$		0			0
$817$	3.87538e15	−	6.71235e15i	0.372471	−	0.645139i
$818$	−1.06314e16			−1.01495
$819$		0			0
$820$	−5.87559e15			−0.553446
$821$	1.13256e15	−	1.96165e15i	0.105968	−	0.183542i	−0.808165	−	0.588956i	$-0.799539\pi$
$821$	1.13256e15	−	1.96165e15i	0.105968	−	0.183542i	0.914133	+	0.405414i	$0.132873\pi$
$822$		0			0
$823$	9.14381e15	+	1.58375e16i	0.844166	+	1.46214i	0.886343	+	0.463029i	$0.153237\pi$
$823$	9.14381e15	+	1.58375e16i	0.844166	+	1.46214i	−0.0421768	+	0.999110i	$0.513429\pi$
$824$	−1.51905e15	+	2.63107e15i	−0.139307	+	0.241286i
$825$		0			0
$826$	−1.13535e15	+	4.58530e14i	−0.102740	+	0.0414933i
$827$	−1.05801e16			−0.951064			−0.475532	−	0.879698i	$-0.657744\pi$
$827$	−1.05801e16			−0.951064			−0.475532	+	0.879698i	$0.657744\pi$
$828$		0			0
$829$	4.72854e15	+	8.19007e15i	0.419447	+	0.726503i	0.995884	−	0.0906382i	$-0.0288907\pi$
$829$	4.72854e15	+	8.19007e15i	0.419447	+	0.726503i	−0.576437	+	0.817142i	$0.695557\pi$
$830$	1.05377e15	+	1.82519e15i	0.0928577	+	0.160834i
$831$		0			0
$832$	1.55491e14			0.0135216
$833$	1.34841e16	+	3.87053e15i	1.16486	+	0.334367i
$834$		0			0
$835$	−6.45670e15	+	1.11833e16i	−0.550471	+	0.953444i
$836$	3.09076e14	+	5.35335e14i	0.0261776	+	0.0453410i
$837$		0			0
$838$	2.70269e15	−	4.68119e15i	0.225920	−	0.391304i
$839$	1.26662e16			1.05186			0.525928	−	0.850529i	$-0.323718\pi$
$839$	1.26662e16			1.05186			0.525928	+	0.850529i	$0.323718\pi$
$840$		0			0
$841$	−1.20539e16			−0.987984
$842$	−4.84592e15	+	8.39338e15i	−0.394602	+	0.683471i
$843$		0			0
$844$	1.94497e15	+	3.36878e15i	0.156325	+	0.270763i
$845$	3.58832e15	−	6.21515e15i	0.286536	−	0.496295i
$846$		0			0
$847$	−1.69874e15	+	1.20751e16i	−0.133896	+	0.951770i
$848$	4.36996e15			0.342216
$849$		0			0
$850$	3.67910e15	+	6.37239e15i	0.284405	+	0.492605i
$851$	5.28246e15	+	9.14949e15i	0.405717	+	0.702723i
$852$		0			0
$853$	−3.71945e15			−0.282007			−0.141003	−	0.990009i	$-0.545033\pi$
$853$	−3.71945e15			−0.282007			−0.141003	+	0.990009i	$0.545033\pi$
$854$	−5.82129e14	−	4.54938e14i	−0.0438532	−	0.0342716i
$855$		0			0
$856$	3.21333e15	−	5.56566e15i	0.238974	−	0.413915i
$857$	9.04452e15	+	1.56656e16i	0.668330	+	1.15758i	0.978371	+	0.206858i	$0.0663238\pi$
$857$	9.04452e15	+	1.56656e16i	0.668330	+	1.15758i	−0.310041	+	0.950723i	$0.600343\pi$
$858$		0			0
$859$	5.65368e15	−	9.79246e15i	0.412448	−	0.714380i	−0.582709	−	0.812681i	$-0.698007\pi$
$859$	5.65368e15	−	9.79246e15i	0.412448	−	0.714380i	0.995157	+	0.0983005i	$0.0313406\pi$
$860$	5.60926e15			0.406597
$861$		0			0
$862$	−6.04554e15			−0.432659
$863$	−1.11368e16	+	1.92895e16i	−0.791956	+	1.37171i	0.132798	+	0.991143i	$0.457604\pi$
$863$	−1.11368e16	+	1.92895e16i	−0.791956	+	1.37171i	−0.924754	+	0.380565i	$0.875729\pi$
$864$		0			0
$865$	3.73448e15	+	6.46831e15i	0.262206	+	0.454153i
$866$	2.36333e15	−	4.09340e15i	0.164883	−	0.285585i
$867$		0			0
$868$	7.07348e14	−	5.02801e15i	0.0487275	−	0.346368i
$869$	−3.63319e15			−0.248702
$870$		0			0
$871$	−1.13134e15	−	1.95954e15i	−0.0764704	−	0.132451i
$872$	3.21872e15	+	5.57499e15i	0.216194	+	0.374459i
$873$		0			0
$874$	7.01428e15			0.465233
$875$	1.35721e16	−	5.48132e15i	0.894547	−	0.361277i
$876$		0			0
$877$	−2.64901e15	+	4.58823e15i	−0.172420	+	0.298639i	−0.939265	−	0.343192i	$-0.888492\pi$
$877$	−2.64901e15	+	4.58823e15i	−0.172420	+	0.298639i	0.766846	+	0.641831i	$0.221825\pi$
$878$	4.75191e15	+	8.23055e15i	0.307361	+	0.532364i
$879$		0			0
$880$	−2.23680e14	+	3.87425e14i	−0.0142880	+	0.0247476i
$881$	−2.81571e16			−1.78740			−0.893698	−	0.448668i	$-0.851898\pi$
$881$	−2.81571e16			−1.78740			−0.893698	+	0.448668i	$0.851898\pi$
$882$		0			0
$883$	−2.33232e16			−1.46219			−0.731096	−	0.682274i	$-0.760991\pi$
$883$	−2.33232e16			−1.46219			−0.731096	+	0.682274i	$0.760991\pi$
$884$	5.26032e14	−	9.11114e14i	0.0327737	−	0.0567656i
$885$		0			0
$886$	9.38184e14	+	1.62498e15i	0.0577301	+	0.0999916i
$887$	−2.78023e15	+	4.81550e15i	−0.170020	+	0.294484i	−0.938427	−	0.345478i	$-0.887717\pi$
$887$	−2.78023e15	+	4.81550e15i	−0.170020	+	0.294484i	0.768406	+	0.639962i	$0.221050\pi$
$888$		0			0
$889$	−3.47775e15	+	1.40454e15i	−0.210057	+	0.0848351i
$890$	5.06969e15			0.304324
$891$		0			0
$892$	−4.19330e15	−	7.26301e15i	−0.248628	−	0.430636i
$893$	−1.86376e14	−	3.22813e14i	−0.0109827	−	0.0190225i
$894$		0			0
$895$	1.04275e16			0.606949
$896$	−2.12848e14	+	1.51298e15i	−0.0123133	+	0.0875265i
$897$		0			0
$898$	−9.93569e15	+	1.72091e16i	−0.567778	+	0.983420i
$899$	6.75084e14	+	1.16928e15i	0.0383424	+	0.0664110i
$900$		0			0
$901$	1.47838e16	−	2.56062e16i	0.829466	−	1.43668i
$902$	4.77140e15			0.266079
$903$		0			0
$904$	6.83180e13			0.00376364
$905$	5.19692e15	−	9.00133e15i	0.284563	−	0.492878i
$906$		0			0
$907$	3.25330e15	+	5.63487e15i	0.175988	+	0.304820i	0.940503	−	0.339786i	$-0.110355\pi$
$907$	3.25330e15	+	5.63487e15i	0.175988	+	0.304820i	−0.764515	+	0.644606i	$0.777021\pi$
$908$	5.24122e15	−	9.07807e15i	0.281813	−	0.488114i
$909$		0			0
$910$	−6.57864e14	−	5.14125e14i	−0.0349469	−	0.0273112i
$911$	2.29311e16			1.21080			0.605402	−	0.795920i	$-0.293013\pi$
$911$	2.29311e16			1.21080			0.605402	+	0.795920i	$0.293013\pi$
$912$		0			0
$913$	−8.55740e14	−	1.48219e15i	−0.0446429	−	0.0773238i
$914$	−8.31381e15	−	1.43999e16i	−0.431118	−	0.746718i
$915$		0			0
$916$	−1.48058e16			−0.758592
$917$	2.74961e15	−	1.95450e16i	0.140036	−	0.995413i
$918$		0			0
$919$	−5.78274e15	+	1.00160e16i	−0.291003	+	0.504033i	−0.974047	−	0.226345i	$-0.927322\pi$
$919$	−5.78274e15	+	1.00160e16i	−0.291003	+	0.504033i	0.683044	+	0.730377i	$0.260656\pi$
$920$	2.53813e15	+	4.39618e15i	0.126964	+	0.219909i
$921$		0			0
$922$	−1.73699e15	+	3.00856e15i	−0.0858574	+	0.148709i
$923$	9.49633e14			0.0466602
$924$		0			0
$925$	8.95597e15			0.434844
$926$	1.10580e16	−	1.91531e16i	0.533725	−	0.924440i
$927$		0			0
$928$	−2.03140e14	−	3.51848e14i	−0.00968904	−	0.0167819i
$929$	4.44320e15	−	7.69584e15i	0.210673	−	0.364897i	−0.741252	−	0.671227i	$-0.765768\pi$
$929$	4.44320e15	−	7.69584e15i	0.210673	−	0.364897i	0.951925	+	0.306330i	$0.0991011\pi$
$930$		0			0
$931$	−2.73948e15	−	1.10004e16i	−0.128364	−	0.515447i
$932$	−2.57607e15			−0.119997
$933$		0			0
$934$	2.72150e15	+	4.71378e15i	0.125286	+	0.217001i
$935$	1.51344e15	+	2.62135e15i	0.0692628	+	0.119967i
$936$		0			0
$937$	−3.18066e16			−1.43863			−0.719317	−	0.694682i	$-0.755545\pi$
$937$	−3.18066e16			−1.43863			−0.719317	+	0.694682i	$0.755545\pi$
$938$	2.06157e16	−	8.32596e15i	0.927004	−	0.374385i
$939$		0			0
$940$	1.34881e14	−	2.33621e14i	0.00599444	−	0.0103827i
$941$	−3.87623e15	−	6.71383e15i	−0.171264	−	0.296638i	0.767598	−	0.640932i	$-0.221452\pi$
$941$	−3.87623e15	−	6.71383e15i	−0.171264	−	0.296638i	−0.938862	+	0.344293i	$0.888119\pi$
$942$		0			0
$943$	2.70710e16	−	4.68883e16i	1.18220	−	2.04762i
$944$	−9.02301e14			−0.0391747
$945$		0			0
$946$	−4.55512e15			−0.195478
$947$	2.01214e16	−	3.48513e16i	0.858487	−	1.48694i	−0.0148841	−	0.999889i	$-0.504738\pi$
$947$	2.01214e16	−	3.48513e16i	0.858487	−	1.48694i	0.873372	−	0.487055i	$-0.161929\pi$
$948$		0			0
$949$	−5.86929e14	−	1.01659e15i	−0.0247526	−	0.0428728i
$950$	2.97303e15	−	5.14944e15i	0.124658	−	0.215914i
$951$		0			0
$952$	8.14539e15	+	6.36568e15i	0.337605	+	0.263841i
$953$	−3.88317e16			−1.60020			−0.800102	−	0.599864i	$-0.795222\pi$
$953$	−3.88317e16			−1.60020			−0.800102	+	0.599864i	$0.795222\pi$
$954$		0			0
$955$	6.80042e15	+	1.17787e16i	0.277024	+	0.479819i
$956$	−8.88540e15	−	1.53900e16i	−0.359881	−	0.623332i
$957$		0			0
$958$	1.92315e16			0.770021
$959$	8.67855e15	+	6.78235e15i	0.345497	+	0.270009i
$960$		0			0
$961$	6.48702e15	−	1.12359e16i	0.255309	−	0.442209i
$962$	−6.40255e14	−	1.10895e15i	−0.0250547	−	0.0433961i
$963$		0			0
$964$	1.04185e16	−	1.80454e16i	0.403072	−	0.698142i
$965$	−2.61574e16			−1.00622
$966$		0			0
$967$	−4.65408e16			−1.77006			−0.885031	−	0.465533i	$-0.845863\pi$
$967$	−4.65408e16			−1.77006			−0.885031	+	0.465533i	$0.845863\pi$
$968$	−4.49290e15	+	7.78194e15i	−0.169907	+	0.294288i
$969$		0			0
$970$	−8.37695e14	−	1.45093e15i	−0.0313214	−	0.0542503i
$971$	−8.37772e15	+	1.45106e16i	−0.311473	+	0.539486i	−0.978681	−	0.205384i	$-0.934156\pi$
$971$	−8.37772e15	+	1.45106e16i	−0.311473	+	0.539486i	0.667209	+	0.744871i	$0.267489\pi$
$972$		0			0
$973$	2.82033e16	−	1.13903e16i	1.03676	−	0.418713i
$974$	−3.16441e15			−0.115670
$975$		0			0
$976$	−2.72217e14	−	4.71493e14i	−0.00983877	−	0.0170412i
$977$	−1.41296e16	−	2.44733e16i	−0.507822	−	0.879573i	−0.999959	−	0.00905544i	$-0.997118\pi$
$977$	−1.41296e16	−	2.44733e16i	−0.507822	−	0.879573i	0.492137	−	0.870518i	$-0.336216\pi$
$978$		0			0
$979$	−4.11695e15			−0.146309
$980$	5.90315e15	−	5.69747e15i	0.208613	−	0.201344i
$981$		0			0
$982$	−1.47988e16	+	2.56323e16i	−0.517147	+	0.895724i
$983$	1.66234e16	+	2.87926e16i	0.577665	+	1.00054i	0.995747	+	0.0921351i	$0.0293692\pi$
$983$	1.66234e16	+	2.87926e16i	0.577665	+	1.00054i	−0.418082	+	0.908409i	$0.637297\pi$
$984$		0			0
$985$	3.71949e15	−	6.44235e15i	0.127816	−	0.221383i
$986$	−2.74892e15			−0.0939375
$987$		0			0
$988$	−8.50158e14			−0.0287301
$989$	−2.58439e16	+	4.47629e16i	−0.868517	+	1.50432i
$990$		0			0
$991$	−2.98994e16	−	5.17873e16i	−0.993706	−	1.72115i	−0.593866	−	0.804564i	$-0.702399\pi$
$991$	−2.98994e16	−	5.17873e16i	−0.993706	−	1.72115i	−0.399840	−	0.916585i	$-0.630934\pi$
$992$	1.87082e15	−	3.24036e15i	0.0618328	−	0.107098i
$993$		0			0
$994$	−1.29993e15	+	9.24026e15i	−0.0424909	+	0.302036i
$995$	−1.89352e16			−0.615521
$996$		0			0
$997$	4.47658e14	+	7.75367e14i	0.0143921	+	0.0249278i	0.873132	−	0.487484i	$-0.162085\pi$
$997$	4.47658e14	+	7.75367e14i	0.0143921	+	0.0249278i	−0.858740	+	0.512412i	$0.828752\pi$
$998$	1.21889e16	+	2.11119e16i	0.389716	+	0.675007i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.12.g.b.37.1		6
3.2	odd	2		42.12.e.a.37.3	yes	6
7.4	even	3	inner	126.12.g.b.109.1		6
21.11	odd	6		42.12.e.a.25.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.e.a.25.3	✓	6	21.11	odd	6
42.12.e.a.37.3	yes	6	3.2	odd	2
126.12.g.b.37.1		6	1.1	even	1	trivial
126.12.g.b.109.1		6	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(16.0000 - 27.7128i) q^{2} +(-512.000 - 886.810i) q^{4} +(-2025.94 + 3509.03i) q^{5} +(-41231.5 + 16652.0i) q^{7} -32768.0 q^{8} +(64830.0 + 112289. i) q^{10} +(-52646.6 - 91186.6i) q^{11} +144812. q^{13} +(-198230. + 1.40907e6i) q^{14} +(-524288. + 908093. i) q^{16} +(3.54738e6 + 6.14424e6i) q^{17} +(2.86658e6 - 4.96507e6i) q^{19} +4.14912e6 q^{20} -3.36938e6 q^{22} +(-1.91165e7 + 3.31108e7i) q^{23} +(1.62052e7 + 2.80683e7i) q^{25} +(2.31699e6 - 4.01315e6i) q^{26} +(3.58777e7 + 2.80387e7i) q^{28} -1.21081e7 q^{29} +(-5.57549e7 - 9.65703e7i) q^{31} +(1.67772e7 + 2.90590e7i) q^{32} +2.27032e8 q^{34} +(2.51001e7 - 1.78418e8i) q^{35} +(1.38165e8 - 2.39309e8i) q^{37} +(-9.17307e7 - 1.58882e8i) q^{38} +(6.63859e7 - 1.14984e8i) q^{40} -1.41611e9 q^{41} +1.35192e9 q^{43} +(-5.39101e7 + 9.33751e7i) q^{44} +(6.11728e8 + 1.05954e9i) q^{46} +(3.25084e7 - 5.63062e7i) q^{47} +(1.42275e9 - 1.37317e9i) q^{49} +1.03713e9 q^{50} +(-7.41438e7 - 1.28421e8i) q^{52} +(-2.08376e9 - 3.60918e9i) q^{53} +4.26635e8 q^{55} +(1.35107e9 - 5.45653e8i) q^{56} +(-1.93729e8 + 3.35548e8i) q^{58} +(4.30251e8 + 7.45216e8i) q^{59} +(-2.59606e8 + 4.49651e8i) q^{61} -3.56831e9 q^{62} +1.07374e9 q^{64} +(-2.93380e8 + 5.08150e8i) q^{65} +(-7.81246e9 - 1.35316e10i) q^{67} +(3.63251e9 - 6.29170e9i) q^{68} +(-4.54287e9 - 3.55029e9i) q^{70} +6.55768e9 q^{71} +(-4.05303e9 - 7.02006e9i) q^{73} +(-4.42128e9 - 7.65788e9i) q^{74} -5.87076e9 q^{76} +(3.68914e9 + 2.88309e9i) q^{77} +(1.72527e10 - 2.98826e10i) q^{79} +(-2.12435e9 - 3.67948e9i) q^{80} +(-2.26577e10 + 3.92443e10i) q^{82} +1.62544e10 q^{83} -2.87471e10 q^{85} +(2.16306e10 - 3.74654e10i) q^{86} +(1.72512e9 + 2.98800e9i) q^{88} +(1.95499e10 - 3.38615e10i) q^{89} +(-5.97082e9 + 2.41141e9i) q^{91} +3.91506e10 q^{92} +(-1.04027e9 - 1.80180e9i) q^{94} +(1.16150e10 + 2.01178e10i) q^{95} -1.29214e10 q^{97} +(-1.52906e10 - 6.13991e10i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 96 q^{2} - 3072 q^{4} - 1045 q^{5} + 45731 q^{7} - 196608 q^{8} + 33440 q^{10} - 181565 q^{11} + 1186364 q^{13} + 703808 q^{14} - 3145728 q^{16} + 701848 q^{17} - 7893102 q^{19} + 2140160 q^{20} - 11620160 q^{22}+ \cdots - 30564771552 q^{98}+O(q^{100}) \) 6 * q + 96 * q^2 - 3072 * q^4 - 1045 * q^5 + 45731 * q^7 - 196608 * q^8 + 33440 * q^10 - 181565 * q^11 + 1186364 * q^13 + 703808 * q^14 - 3145728 * q^16 + 701848 * q^17 - 7893102 * q^19 + 2140160 * q^20 - 11620160 * q^22 - 59247728 * q^23 + 124585550 * q^25 + 18981824 * q^26 - 24306688 * q^28 + 30040070 * q^29 - 299540305 * q^31 + 100663296 * q^32 + 44918272 * q^34 + 181163920 * q^35 - 352325094 * q^37 + 252579264 * q^38 + 34242560 * q^40 - 1199954472 * q^41 - 4298844576 * q^43 - 185922560 * q^44 + 1895927296 * q^46 + 1179123942 * q^47 + 3621837009 * q^49 + 7973475200 * q^50 - 607418368 * q^52 + 67875849 * q^53 + 1874846050 * q^55 - 1498513408 * q^56 + 480641120 * q^58 + 2911039823 * q^59 - 10148733466 * q^61 - 19170579520 * q^62 + 6442450944 * q^64 + 2404013040 * q^65 - 5535975380 * q^67 + 718692352 * q^68 - 11741350880 * q^70 + 20558197876 * q^71 + 29230853572 * q^73 + 11274403008 * q^74 + 16165072896 * q^76 - 34001756425 * q^77 + 58886709107 * q^79 - 1095761920 * q^80 - 19199271552 * q^82 - 26001713726 * q^83 - 93104330000 * q^85 - 68781513216 * q^86 + 5949521920 * q^88 + 32237877702 * q^89 + 67979059274 * q^91 + 121339346944 * q^92 - 37731966144 * q^94 + 37720110280 * q^95 + 175446876934 * q^97 - 30564771552 * q^98

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