LMFDB - Embedded newform 117.14.b.c.64.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,14,Mod(64,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 14, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.64"); S:= CuspForms(chi, 14); N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	117.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,-49154] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$125.460186874$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 81921 x^{12} + 2522899104 x^{10} + 37246030694192 x^{8} + \cdots + 56\!\cdots\!64 $ x^14 + 81921x^12 + 2522899104x^10 + 37246030694192x^8 + 270611051280428544x^6 + 843436691228915970048x^4 + 602910050859212473368576x^2 + 56765934420683632215588864
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{8}\cdot 13^{6} $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.5
Root			$-87.5010i$ of defining polynomial
Character	$\chi$	$=$	117.64
Dual form			117.14.b.c.64.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-87.5010i q^{2} +535.569 q^{4} -31938.7i q^{5} -191671. i q^{7} -763671. i q^{8} -2.79467e6 q^{10} +9.74341e6i q^{11} +(-633744. + 1.73918e7i) q^{13} -1.67714e7 q^{14} -6.24346e7 q^{16} +6.29773e7 q^{17} -3.67427e7i q^{19} -1.71054e7i q^{20} +8.52559e8 q^{22} +6.82777e8 q^{23} +2.00624e8 q^{25} +(1.52180e9 + 5.54533e7i) q^{26} -1.02653e8i q^{28} +4.28310e9 q^{29} -1.74048e8i q^{31} -7.92899e8i q^{32} -5.51058e9i q^{34} -6.12171e9 q^{35} +2.72739e7i q^{37} -3.21503e9 q^{38} -2.43906e10 q^{40} +2.25984e10i q^{41} +3.58063e10 q^{43} +5.21827e9i q^{44} -5.97437e10i q^{46} +5.55708e10i q^{47} +6.01513e10 q^{49} -1.75548e10i q^{50} +(-3.39414e8 + 9.31449e9i) q^{52} +4.92496e10 q^{53} +3.11192e11 q^{55} -1.46374e11 q^{56} -3.74776e11i q^{58} +3.00035e11i q^{59} -8.99954e10 q^{61} -1.52294e10 q^{62} -5.80844e11 q^{64} +(5.55470e11 + 2.02410e10i) q^{65} -1.13281e12i q^{67} +3.37287e10 q^{68} +5.35656e11i q^{70} +8.22933e11i q^{71} +9.13149e11i q^{73} +2.38649e9 q^{74} -1.96783e10i q^{76} +1.86753e12 q^{77} +1.70734e12 q^{79} +1.99408e12i q^{80} +1.97738e12 q^{82} -3.23695e12i q^{83} -2.01141e12i q^{85} -3.13309e12i q^{86} +7.44077e12 q^{88} -1.90362e12i q^{89} +(3.33349e12 + 1.21470e11i) q^{91} +3.65674e11 q^{92} +4.86250e12 q^{94} -1.17351e12 q^{95} +8.72249e12i q^{97} -5.26330e12i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 49154 q^{4} - 3968358 q^{10} - 14362478 q^{13} - 72843942 q^{14} + 243447170 q^{16} + 178512492 q^{17} + 1330288056 q^{22} + 1641693744 q^{23} + 1601386654 q^{25} - 138020766 q^{26} + 10348326348 q^{29}+ \cdots - 11940434574336 q^{95}+O(q^{100}) $ 14 * q - 49154 * q^4 - 3968358 * q^10 - 14362478 * q^13 - 72843942 * q^14 + 243447170 * q^16 + 178512492 * q^17 + 1330288056 * q^22 + 1641693744 * q^23 + 1601386654 * q^25 - 138020766 * q^26 + 10348326348 * q^29 - 20242816056 * q^35 + 72234754500 * q^38 - 50528567766 * q^40 - 42288191696 * q^43 + 202681235282 * q^49 + 605927200580 * q^52 + 541269433788 * q^53 + 294791560608 * q^55 + 1027260370698 * q^56 + 1693279412900 * q^61 - 1808450592168 * q^62 - 4815047793506 * q^64 - 534977124552 * q^65 - 65016763122 * q^68 - 7595100503238 * q^74 + 1391939668824 * q^77 - 5060278211056 * q^79 + 507818992992 * q^82 + 2586979258080 * q^88 + 3450737986176 * q^91 - 7241299383420 * q^92 + 11219792119974 * q^94 - 11940434574336 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	87.5010i		−	0.966759i	−0.875411	−	0.483379i	$-0.839409\pi$
$2$		−	87.5010i		−	0.966759i	0.875411	−	0.483379i	$-0.160591\pi$
$3$		0			0
$3$		0			0
$4$	535.569			0.0653771
$5$		−	31938.7i		−	0.914138i	−0.889431	−	0.457069i	$-0.848899\pi$
$5$		−	31938.7i		−	0.914138i	0.889431	−	0.457069i	$-0.151101\pi$
$6$		0			0
$7$		−	191671.i		−	0.615770i	−0.951424	−	0.307885i	$-0.900379\pi$
$7$		−	191671.i		−	0.615770i	0.951424	−	0.307885i	$-0.0996213\pi$
$8$		−	763671.i		−	1.02996i
$9$		0			0
$10$	−2.79467e6			−0.883751
$11$			9.74341e6i			1.65828i	0.559039	+	0.829142i	$0.311170\pi$
$11$			9.74341e6i			1.65828i	−0.559039	+	0.829142i	$0.688830\pi$
$12$		0			0
$13$	−633744.	+	1.73918e7i	−0.0364152	+	0.999337i
$13$	−633744.	+	1.73918e7i	−0.0364152	+	0.999337i
$14$	−1.67714e7			−0.595302
$15$		0			0
$16$	−6.24346e7			−0.930349
$17$	6.29773e7			0.632800			0.316400	−	0.948626i	$-0.397526\pi$
$17$	6.29773e7			0.632800			0.316400	+	0.948626i	$0.397526\pi$
$18$		0			0
$19$		−	3.67427e7i		−	0.179173i	−0.995979	−	0.0895866i	$-0.971445\pi$
$19$		−	3.67427e7i		−	0.179173i	0.995979	−	0.0895866i	$-0.0285546\pi$
$20$		−	1.71054e7i		−	0.0597637i
$21$		0			0
$22$	8.52559e8			1.60316
$23$	6.82777e8			0.961718			0.480859	−	0.876798i	$-0.340325\pi$
$23$	6.82777e8			0.961718			0.480859	+	0.876798i	$0.340325\pi$
$24$		0			0
$25$	2.00624e8			0.164351
$26$	1.52180e9	+	5.54533e7i	0.966118	+	0.0352047i
$27$		0			0
$28$		−	1.02653e8i		−	0.0402573i
$29$	4.28310e9			1.33712			0.668562	−	0.743656i	$-0.266910\pi$
$29$	4.28310e9			1.33712			0.668562	+	0.743656i	$0.266910\pi$
$30$		0			0
$31$		−	1.74048e8i		−	0.0352223i	−0.999845	−	0.0176111i	$-0.994394\pi$
$31$		−	1.74048e8i		−	0.0352223i	0.999845	−	0.0176111i	$-0.00560609\pi$
$32$		−	7.92899e8i		−	0.130540i
$33$		0			0
$34$		−	5.51058e9i		−	0.611765i
$35$	−6.12171e9			−0.562899
$36$		0			0
$37$			2.72739e7i			0.00174757i	1.00000		0.000873787i	$0.000278135\pi$
$37$			2.72739e7i			0.00174757i	−1.00000		0.000873787i	$0.999722\pi$
$38$	−3.21503e9			−0.173217
$39$		0			0
$40$	−2.43906e10			−0.941528
$41$			2.25984e10i			0.742990i	0.928435	+	0.371495i	$0.121155\pi$
$41$			2.25984e10i			0.742990i	−0.928435	+	0.371495i	$0.878845\pi$
$42$		0			0
$43$	3.58063e10			0.863804			0.431902	−	0.901921i	$-0.357843\pi$
$43$	3.58063e10			0.863804			0.431902	+	0.901921i	$0.357843\pi$
$44$			5.21827e9i			0.108414i
$45$		0			0
$46$		−	5.97437e10i		−	0.929750i
$47$			5.55708e10i			0.751987i	0.926622	+	0.375993i	$0.122698\pi$
$47$			5.55708e10i			0.751987i	−0.926622	+	0.375993i	$0.877302\pi$
$48$		0			0
$49$	6.01513e10			0.620827
$50$		−	1.75548e10i		−	0.158888i
$51$		0			0
$52$	−3.39414e8	+	9.31449e9i	−0.00238072	+	0.0653337i
$53$	4.92496e10			0.305217			0.152609	−	0.988287i	$-0.451233\pi$
$53$	4.92496e10			0.305217			0.152609	+	0.988287i	$0.451233\pi$
$54$		0			0
$55$	3.11192e11			1.51590
$56$	−1.46374e11			−0.634221
$57$		0			0
$58$		−	3.74776e11i		−	1.29268i
$59$			3.00035e11i			0.926050i	0.886345	+	0.463025i	$0.153236\pi$
$59$			3.00035e11i			0.926050i	−0.886345	+	0.463025i	$0.846764\pi$
$60$		0			0
$61$	−8.99954e10			−0.223654			−0.111827	−	0.993728i	$-0.535670\pi$
$61$	−8.99954e10			−0.223654			−0.111827	+	0.993728i	$0.535670\pi$
$62$	−1.52294e10			−0.0340515
$63$		0			0
$64$	−5.80844e11			−1.05655
$65$	5.55470e11	+	2.02410e10i	0.913532	+	0.0332885i
$66$		0			0
$67$		−	1.13281e12i		−	1.52992i	−0.644077	−	0.764960i	$-0.722759\pi$
$67$		−	1.13281e12i		−	1.52992i	0.644077	−	0.764960i	$-0.277241\pi$
$68$	3.37287e10			0.0413706
$69$		0			0
$70$			5.35656e11i			0.544188i
$71$			8.22933e11i			0.762404i	0.924492	+	0.381202i	$0.124490\pi$
$71$			8.22933e11i			0.762404i	−0.924492	+	0.381202i	$0.875510\pi$
$72$		0			0
$73$			9.13149e11i			0.706225i	0.935581	+	0.353113i	$0.114877\pi$
$73$			9.13149e11i			0.706225i	−0.935581	+	0.353113i	$0.885123\pi$
$74$	2.38649e9			0.00168948
$75$		0			0
$76$		−	1.96783e10i		−	0.0117138i
$77$	1.86753e12			1.02112
$78$		0			0
$79$	1.70734e12			0.790211			0.395106	−	0.918636i	$-0.370708\pi$
$79$	1.70734e12			0.790211			0.395106	+	0.918636i	$0.370708\pi$
$80$			1.99408e12i			0.850467i
$81$		0			0
$82$	1.97738e12			0.718292
$83$		−	3.23695e12i		−	1.08675i	−0.839491	−	0.543374i	$-0.817147\pi$
$83$		−	3.23695e12i		−	1.08675i	0.839491	−	0.543374i	$-0.182853\pi$
$84$		0			0
$85$		−	2.01141e12i		−	0.578466i
$86$		−	3.13309e12i		−	0.835090i
$87$		0			0
$88$	7.44077e12			1.70797
$89$		−	1.90362e12i		−	0.406018i	−0.979177	−	0.203009i	$-0.934928\pi$
$89$		−	1.90362e12i		−	0.406018i	0.979177	−	0.203009i	$-0.0650722\pi$
$90$		0			0
$91$	3.33349e12	+	1.21470e11i	0.615362	+	0.0224234i
$92$	3.65674e11			0.0628743
$93$		0			0
$94$	4.86250e12			0.726990
$95$	−1.17351e12			−0.163789
$96$		0			0
$97$			8.72249e12i			1.06322i	0.846988	+	0.531612i	$0.178413\pi$
$97$			8.72249e12i			1.06322i	−0.846988	+	0.531612i	$0.821587\pi$
$98$		−	5.26330e12i		−	0.600190i
$99$		0			0
$100$	1.07448e11			0.0107448
$101$	9.35975e12			0.877355			0.438677	−	0.898645i	$-0.355447\pi$
$101$	9.35975e12			0.877355			0.438677	+	0.898645i	$0.355447\pi$
$102$		0			0
$103$	−4.32981e12			−0.357295			−0.178648	−	0.983913i	$-0.557172\pi$
$103$	−4.32981e12			−0.357295			−0.178648	+	0.983913i	$0.557172\pi$
$104$	1.32816e13	+	4.83972e11i	1.02928	+	0.0375063i
$105$		0			0
$106$		−	4.30939e12i		−	0.295072i
$107$	−2.03267e13			−1.30940			−0.654700	−	0.755889i	$-0.727205\pi$
$107$	−2.03267e13			−1.30940			−0.654700	+	0.755889i	$0.727205\pi$
$108$		0			0
$109$			8.76206e12i			0.500419i	0.968192	+	0.250210i	$0.0804996\pi$
$109$			8.76206e12i			0.500419i	−0.968192	+	0.250210i	$0.919500\pi$
$110$		−	2.72296e13i		−	1.46551i
$111$		0			0
$112$			1.19669e13i			0.572881i
$113$	−8.52942e12			−0.385398			−0.192699	−	0.981258i	$-0.561724\pi$
$113$	−8.52942e12			−0.385398			−0.192699	+	0.981258i	$0.561724\pi$
$114$		0			0
$115$		−	2.18070e13i		−	0.879143i
$116$	2.29390e12			0.0874172
$117$		0			0
$118$	2.62534e13			0.895267
$119$		−	1.20709e13i		−	0.389659i
$120$		0			0
$121$	−6.04114e13			−1.74990
$122$			7.87469e12i			0.216219i
$123$		0			0
$124$		−	9.32146e10i		−	0.00230273i
$125$		−	4.53953e13i		−	1.06438i
$126$		0			0
$127$	−3.34991e13			−0.708449			−0.354224	−	0.935160i	$-0.615255\pi$
$127$	−3.34991e13			−0.708449			−0.354224	+	0.935160i	$0.615255\pi$
$128$			4.43290e13i			0.890889i
$129$		0			0
$130$	1.77110e12	−	4.86042e13i	0.0321819	−	0.883165i
$131$	1.10053e14			1.90256			0.951280	−	0.308329i	$-0.0997696\pi$
$131$	1.10053e14			1.90256			0.951280	+	0.308329i	$0.0997696\pi$
$132$		0			0
$133$	−7.04251e12			−0.110330
$134$	−9.91216e13			−1.47906
$135$		0			0
$136$		−	4.80940e13i		−	0.651760i
$137$		−	1.09480e14i		−	1.41466i	−0.706883	−	0.707330i	$-0.749899\pi$
$137$		−	1.09480e14i		−	1.41466i	0.706883	−	0.707330i	$-0.250101\pi$
$138$		0			0
$139$	−1.77596e13			−0.208851			−0.104425	−	0.994533i	$-0.533300\pi$
$139$	−1.77596e13			−0.208851			−0.104425	+	0.994533i	$0.533300\pi$
$140$	−3.27860e12			−0.0368007
$141$		0			0
$142$	7.20075e13			0.737061
$143$	−1.69455e14	−	6.17483e12i	−1.65718	−	0.0603867i
$144$		0			0
$145$		−	1.36797e14i		−	1.22232i
$146$	7.99015e13			0.682750
$147$		0			0
$148$			1.46070e10i			0.000114251i
$149$			1.57109e14i			1.17622i	0.808780	+	0.588111i	$0.200128\pi$
$149$			1.57109e14i			1.17622i	−0.808780	+	0.588111i	$0.799872\pi$
$150$		0			0
$151$			7.81355e13i			0.536412i	0.963362	+	0.268206i	$0.0864307\pi$
$151$			7.81355e13i			0.536412i	−0.963362	+	0.268206i	$0.913569\pi$
$152$	−2.80594e13			−0.184542
$153$		0			0
$154$		−	1.63411e14i		−	0.987179i
$155$	−5.55886e12			−0.0321980
$156$		0			0
$157$	5.69426e12			0.0303451			0.0151726	−	0.999885i	$-0.495170\pi$
$157$	5.69426e12			0.0303451			0.0151726	+	0.999885i	$0.495170\pi$
$158$		−	1.49394e14i		−	0.763944i
$159$		0			0
$160$	−2.53241e13			−0.119331
$161$		−	1.30868e14i		−	0.592198i
$162$		0			0
$163$		−	1.35936e14i		−	0.567693i	−0.958870	−	0.283847i	$-0.908389\pi$
$163$		−	1.35936e14i		−	0.567693i	0.958870	−	0.283847i	$-0.0916106\pi$
$164$			1.21030e13i			0.0485745i
$165$		0			0
$166$	−2.83237e14			−1.05062
$167$		−	4.92949e14i		−	1.75851i	−0.476351	−	0.879255i	$-0.658041\pi$
$167$		−	4.92949e14i		−	1.75851i	0.476351	−	0.879255i	$-0.341959\pi$
$168$		0			0
$169$	−3.02072e14	−	2.20439e13i	−0.997348	−	0.0727820i
$170$	−1.76001e14			−0.559237
$171$		0			0
$172$	1.91768e13			0.0564729
$173$	3.51977e14			0.998194			0.499097	−	0.866546i	$-0.333665\pi$
$173$	3.51977e14			0.998194			0.499097	+	0.866546i	$0.333665\pi$
$174$		0			0
$175$		−	3.84538e13i		−	0.101203i
$176$		−	6.08327e14i		−	1.54278i
$177$		0			0
$178$	−1.66569e14			−0.392522
$179$	−5.79869e14			−1.31760			−0.658802	−	0.752316i	$-0.728937\pi$
$179$	−5.79869e14			−1.31760			−0.658802	+	0.752316i	$0.728937\pi$
$180$		0			0
$181$	−1.86793e14			−0.394867			−0.197433	−	0.980316i	$-0.563261\pi$
$181$	−1.86793e14			−0.394867			−0.197433	+	0.980316i	$0.563261\pi$
$182$	1.06288e13	−	2.91684e14i	0.0216780	−	0.594907i
$183$		0			0
$184$		−	5.21417e14i		−	0.990534i
$185$	8.71091e11			0.00159752
$186$		0			0
$187$			6.13614e14i			1.04936i
$188$			2.97620e13i			0.0491627i
$189$		0			0
$190$			1.02684e14i			0.158345i
$191$	−7.07758e13			−0.105480			−0.0527398	−	0.998608i	$-0.516795\pi$
$191$	−7.07758e13			−0.105480			−0.0527398	+	0.998608i	$0.516795\pi$
$192$		0			0
$193$			4.06497e14i			0.566155i	0.959097	+	0.283077i	$0.0913553\pi$
$193$			4.06497e14i			0.566155i	−0.959097	+	0.283077i	$0.908645\pi$
$194$	7.63227e14			1.02788
$195$		0			0
$196$	3.22152e13			0.0405878
$197$		−	1.43964e15i		−	1.75479i	−0.479770	−	0.877394i	$-0.659280\pi$
$197$		−	1.43964e15i		−	1.75479i	0.479770	−	0.877394i	$-0.340720\pi$
$198$		0			0
$199$	1.38293e15			1.57854			0.789269	−	0.614048i	$-0.210460\pi$
$199$	1.38293e15			1.57854			0.789269	+	0.614048i	$0.210460\pi$
$200$		−	1.53211e14i		−	0.169276i
$201$		0			0
$202$		−	8.18988e14i		−	0.848191i
$203$		−	8.20946e14i		−	0.823361i
$204$		0			0
$205$	7.21763e14			0.679195
$206$			3.78863e14i			0.345418i
$207$		0			0
$208$	3.95676e13	−	1.08585e15i	0.0338788	−	0.929732i
$209$	3.58000e14			0.297120
$210$		0			0
$211$	1.51265e15			1.18006			0.590029	−	0.807382i	$-0.299116\pi$
$211$	1.51265e15			1.18006			0.590029	+	0.807382i	$0.299116\pi$
$212$	2.63765e13			0.0199542
$213$		0			0
$214$			1.77861e15i			1.26587i
$215$		−	1.14361e15i		−	0.789636i
$216$		0			0
$217$	−3.33599e13			−0.0216888
$218$	7.66690e14			0.483785
$219$		0			0
$220$	1.66665e14			0.0991051
$221$	−3.99115e13	+	1.09529e15i	−0.0230435	+	0.632380i
$222$		0			0
$223$		−	2.47515e15i		−	1.34778i	−0.738831	−	0.673891i	$-0.764622\pi$
$223$		−	2.47515e15i		−	1.34778i	0.738831	−	0.673891i	$-0.235378\pi$
$224$	−1.51976e14			−0.0803826
$225$		0			0
$226$			7.46333e14i			0.372587i
$227$		−	1.78560e15i		−	0.866195i	−0.901347	−	0.433097i	$-0.857421\pi$
$227$		−	1.78560e15i		−	0.866195i	0.901347	−	0.433097i	$-0.142579\pi$
$228$		0			0
$229$			1.48202e15i			0.679084i	0.940591	+	0.339542i	$0.110272\pi$
$229$			1.48202e15i			0.679084i	−0.940591	+	0.339542i	$0.889728\pi$
$230$	−1.90813e15			−0.849920
$231$		0			0
$232$		−	3.27088e15i		−	1.37719i
$233$	1.08461e15			0.444079			0.222039	−	0.975038i	$-0.428729\pi$
$233$	1.08461e15			0.444079			0.222039	+	0.975038i	$0.428729\pi$
$234$		0			0
$235$	1.77486e15			0.687420
$236$			1.60690e14i			0.0605424i
$237$		0			0
$238$	−1.05622e15			−0.376707
$239$			2.75278e15i			0.955401i	0.878523	+	0.477700i	$0.158530\pi$
$239$			2.75278e15i			0.955401i	−0.878523	+	0.477700i	$0.841470\pi$
$240$		0			0
$241$		−	2.34617e15i		−	0.771345i	−0.922636	−	0.385672i	$-0.873969\pi$
$241$		−	2.34617e15i		−	0.771345i	0.922636	−	0.385672i	$-0.126031\pi$
$242$			5.28606e15i			1.69173i
$243$		0			0
$244$	−4.81988e13			−0.0146218
$245$		−	1.92115e15i		−	0.567521i
$246$		0			0
$247$	6.39021e14	+	2.32855e13i	0.179054	+	0.00652462i
$248$	−1.32915e14			−0.0362776
$249$		0			0
$250$	−3.97214e15			−1.02900
$251$	5.69252e15			1.43690			0.718448	−	0.695581i	$-0.244853\pi$
$251$	5.69252e15			1.43690			0.718448	+	0.695581i	$0.244853\pi$
$252$		0			0
$253$			6.65258e15i			1.59480i
$254$			2.93120e15i			0.684899i
$255$		0			0
$256$	−8.79439e14			−0.195275
$257$	1.80324e15			0.390381			0.195190	−	0.980765i	$-0.437468\pi$
$257$	1.80324e15			0.390381			0.195190	+	0.980765i	$0.437468\pi$
$258$		0			0
$259$	5.22760e12			0.00107610
$260$	2.97492e14	+	1.08404e13i	0.0597240	+	0.00217630i
$261$		0			0
$262$		−	9.62975e15i		−	1.83932i
$263$	−4.61101e15			−0.859178			−0.429589	−	0.903024i	$-0.641342\pi$
$263$	−4.61101e15			−0.859178			−0.429589	+	0.903024i	$0.641342\pi$
$264$		0			0
$265$		−	1.57297e15i		−	0.279011i
$266$			6.16227e14i			0.106662i
$267$		0			0
$268$		−	6.06695e14i		−	0.100022i
$269$	−6.36121e15			−1.02365			−0.511823	−	0.859091i	$-0.671030\pi$
$269$	−6.36121e15			−1.02365			−0.511823	+	0.859091i	$0.671030\pi$
$270$		0			0
$271$			9.80335e15i			1.50340i	0.659506	+	0.751700i	$0.270766\pi$
$271$			9.80335e15i			1.50340i	−0.659506	+	0.751700i	$0.729234\pi$
$272$	−3.93197e15			−0.588724
$273$		0			0
$274$	−9.57964e15			−1.36764
$275$			1.95477e15i			0.272541i
$276$		0			0
$277$	7.93739e14			0.105574			0.0527872	−	0.998606i	$-0.483189\pi$
$277$	7.93739e14			0.105574			0.0527872	+	0.998606i	$0.483189\pi$
$278$			1.55398e15i			0.201909i
$279$		0			0
$280$			4.67498e15i			0.579765i
$281$			4.13004e15i			0.500452i	0.968187	+	0.250226i	$0.0805050\pi$
$281$			4.13004e15i			0.500452i	−0.968187	+	0.250226i	$0.919495\pi$
$282$		0			0
$283$	−4.88199e15			−0.564917			−0.282459	−	0.959280i	$-0.591150\pi$
$283$	−4.88199e15			−0.564917			−0.282459	+	0.959280i	$0.591150\pi$
$284$			4.40738e14i			0.0498438i
$285$		0			0
$286$	−5.40304e14	+	1.48275e16i	−0.0583793	+	1.60210i
$287$	4.33146e15			0.457511
$288$		0			0
$289$	−5.93844e15			−0.599565
$290$	−1.19698e16			−1.18168
$291$		0			0
$292$			4.89054e14i			0.0461709i
$293$		−	7.21337e15i		−	0.666037i	−0.942920	−	0.333019i	$-0.891933\pi$
$293$		−	7.21337e15i		−	0.666037i	0.942920	−	0.333019i	$-0.108067\pi$
$294$		0			0
$295$	9.58273e15			0.846537
$296$	2.08283e13			0.00179994
$297$		0			0
$298$	1.37472e16			1.13712
$299$	−4.32706e14	+	1.18747e16i	−0.0350211	+	0.961080i
$300$		0			0
$301$		−	6.86303e15i		−	0.531905i
$302$	6.83694e15			0.518581
$303$		0			0
$304$			2.29402e15i			0.166694i
$305$			2.87433e15i			0.204451i
$306$		0			0
$307$			6.03857e15i			0.411656i	0.978588	+	0.205828i	$0.0659887\pi$
$307$			6.03857e15i			0.411656i	−0.978588	+	0.205828i	$0.934011\pi$
$308$	1.00019e15			0.0667579
$309$		0			0
$310$			4.86406e14i			0.0311277i
$311$	1.68566e16			1.05640			0.528200	−	0.849120i	$-0.322867\pi$
$311$	1.68566e16			1.05640			0.528200	+	0.849120i	$0.322867\pi$
$312$		0			0
$313$	2.02486e15			0.121718			0.0608592	−	0.998146i	$-0.480616\pi$
$313$	2.02486e15			0.121718			0.0608592	+	0.998146i	$0.480616\pi$
$314$		−	4.98253e14i		−	0.0293364i
$315$		0			0
$316$	9.14397e14			0.0516617
$317$			1.40459e16i			0.777438i	0.921356	+	0.388719i	$0.127082\pi$
$317$			1.40459e16i			0.777438i	−0.921356	+	0.388719i	$0.872918\pi$
$318$		0			0
$319$			4.17321e16i			2.21733i
$320$			1.85514e16i			0.965832i
$321$		0			0
$322$	−1.14511e16			−0.572512
$323$		−	2.31396e15i		−	0.113381i
$324$		0			0
$325$	−1.27144e14	+	3.48921e15i	−0.00598488	+	0.164242i
$326$	−1.18945e16			−0.548822
$327$		0			0
$328$	1.72578e16			0.765252
$329$	1.06513e16			0.463051
$330$		0			0
$331$		−	1.06454e16i		−	0.444917i	−0.974942	−	0.222458i	$-0.928592\pi$
$331$		−	1.06454e16i		−	0.444917i	0.974942	−	0.222458i	$-0.0714081\pi$
$332$		−	1.73361e15i		−	0.0710484i
$333$		0			0
$334$	−4.31335e16			−1.70006
$335$	−3.61803e16			−1.39856
$336$		0			0
$337$	−3.10858e16			−1.15603			−0.578014	−	0.816027i	$-0.696172\pi$
$337$	−3.10858e16			−1.15603			−0.578014	+	0.816027i	$0.696172\pi$
$338$	−1.92886e15	+	2.64316e16i	−0.0703627	+	0.964195i
$339$		0			0
$340$		−	1.07725e15i		−	0.0378184i
$341$	1.69582e15			0.0584085
$342$		0			0
$343$		−	3.01000e16i		−	0.998057i
$344$		−	2.73443e16i		−	0.889686i
$345$		0			0
$346$		−	3.07984e16i		−	0.965013i
$347$	4.50444e16			1.38516			0.692579	−	0.721342i	$-0.256474\pi$
$347$	4.50444e16			1.38516			0.692579	+	0.721342i	$0.256474\pi$
$348$		0			0
$349$		−	1.59465e16i		−	0.472391i	−0.971706	−	0.236195i	$-0.924099\pi$
$349$		−	1.59465e16i		−	0.472391i	0.971706	−	0.236195i	$-0.0759005\pi$
$350$	−3.36475e15			−0.0978387
$351$		0			0
$352$	7.72554e15			0.216472
$353$			2.81276e16i			0.773744i	0.922133	+	0.386872i	$0.126444\pi$
$353$			2.81276e16i			0.773744i	−0.922133	+	0.386872i	$0.873556\pi$
$354$		0			0
$355$	2.62834e16			0.696943
$356$		−	1.01952e15i		−	0.0265443i
$357$		0			0
$358$			5.07391e16i			1.27381i
$359$			1.42870e16i			0.352231i	0.984369	+	0.176116i	$0.0563533\pi$
$359$			1.42870e16i			0.352231i	−0.984369	+	0.176116i	$0.943647\pi$
$360$		0			0
$361$	4.07030e16			0.967897
$362$			1.63446e16i			0.381741i
$363$		0			0
$364$	1.78532e15	+	6.50557e13i	0.0402306	+	0.00146597i
$365$	2.91648e16			0.645587
$366$		0			0
$367$	5.30985e16			1.13437			0.567183	−	0.823592i	$-0.308033\pi$
$367$	5.30985e16			1.13437			0.567183	+	0.823592i	$0.308033\pi$
$368$	−4.26289e16			−0.894733
$369$		0			0
$370$		−	7.62213e13i		−	0.00154442i
$371$		−	9.43970e15i		−	0.187944i
$372$		0			0
$373$	8.49419e16			1.63311			0.816553	−	0.577270i	$-0.195882\pi$
$373$	8.49419e16			1.63311			0.816553	+	0.577270i	$0.195882\pi$
$374$	5.36919e16			1.01448
$375$		0			0
$376$	4.24378e16			0.774518
$377$	−2.71439e15	+	7.44907e16i	−0.0486916	+	1.33624i
$378$		0			0
$379$		−	7.54106e16i		−	1.30701i	−0.756924	−	0.653503i	$-0.773299\pi$
$379$		−	7.54106e16i		−	1.30701i	0.756924	−	0.653503i	$-0.226701\pi$
$380$	−6.28498e14			−0.0107081
$381$		0			0
$382$			6.19296e15i			0.101973i
$383$		−	3.22518e15i		−	0.0522110i	−0.999659	−	0.0261055i	$-0.991689\pi$
$383$		−	3.22518e15i		−	0.0522110i	0.999659	−	0.0261055i	$-0.00831058\pi$
$384$		0			0
$385$		−	5.96464e16i		−	0.933446i
$386$	3.55689e16			0.547335
$387$		0			0
$388$			4.67150e15i			0.0695104i
$389$	−6.43418e16			−0.941500			−0.470750	−	0.882267i	$-0.656017\pi$
$389$	−6.43418e16			−0.941500			−0.470750	+	0.882267i	$0.656017\pi$
$390$		0			0
$391$	4.29994e16			0.608575
$392$		−	4.59358e16i		−	0.639429i
$393$		0			0
$394$	−1.25970e17			−1.69646
$395$		−	5.45301e16i		−	0.722362i
$396$		0			0
$397$			8.57754e16i			1.09957i	0.835305	+	0.549787i	$0.185291\pi$
$397$			8.57754e16i			1.09957i	−0.835305	+	0.549787i	$0.814709\pi$
$398$		−	1.21008e17i		−	1.52607i
$399$		0			0
$400$	−1.25259e16			−0.152904
$401$		−	8.64300e16i		−	1.03807i	−0.854753	−	0.519034i	$-0.826292\pi$
$401$		−	8.64300e16i		−	1.03807i	0.854753	−	0.519034i	$-0.173708\pi$
$402$		0			0
$403$	3.02700e15	+	1.10302e14i	0.0351989	+	0.00128263i
$404$	5.01279e15			0.0573589
$405$		0			0
$406$	−7.18336e16			−0.795992
$407$	−2.65740e14			−0.00289797
$408$		0			0
$409$		−	8.84315e16i		−	0.934126i	−0.884224	−	0.467063i	$-0.845312\pi$
$409$		−	8.84315e16i		−	0.934126i	0.884224	−	0.467063i	$-0.154688\pi$
$410$		−	6.31550e16i		−	0.656618i
$411$		0			0
$412$	−2.31891e15			−0.0233589
$413$	5.75080e16			0.570234
$414$		0			0
$415$	−1.03384e17			−0.993437
$416$	1.37899e16	+	5.02495e14i	0.130453	+	0.00475363i
$417$		0			0
$418$		−	3.13253e16i		−	0.287243i
$419$	−7.71802e16			−0.696811			−0.348405	−	0.937344i	$-0.613277\pi$
$419$	−7.71802e16			−0.696811			−0.348405	+	0.937344i	$0.613277\pi$
$420$		0			0
$421$			1.56354e17i			1.36859i	0.729204	+	0.684297i	$0.239891\pi$
$421$			1.56354e17i			1.36859i	−0.729204	+	0.684297i	$0.760109\pi$
$422$		−	1.32359e17i		−	1.14083i
$423$		0			0
$424$		−	3.76105e16i		−	0.314363i
$425$	1.26348e16			0.104001
$426$		0			0
$427$			1.72495e16i			0.137719i
$428$	−1.08863e16			−0.0856047
$429$		0			0
$430$	−1.00067e17			−0.763387
$431$			1.47738e17i			1.11017i	0.831794	+	0.555085i	$0.187314\pi$
$431$			1.47738e17i			1.11017i	−0.831794	+	0.555085i	$0.812686\pi$
$432$		0			0
$433$	9.85012e16			0.718241			0.359120	−	0.933291i	$-0.383077\pi$
$433$	9.85012e16			0.718241			0.359120	+	0.933291i	$0.383077\pi$
$434$			2.91903e15i			0.0209679i
$435$		0			0
$436$			4.69269e15i			0.0327160i
$437$		−	2.50871e16i		−	0.172314i
$438$		0			0
$439$	2.62228e16			0.174848			0.0874239	−	0.996171i	$-0.472137\pi$
$439$	2.62228e16			0.174848			0.0874239	+	0.996171i	$0.472137\pi$
$440$		−	2.37648e17i		−	1.56132i
$441$		0			0
$442$	9.58387e16	+	3.49230e15i	0.611359	+	0.0222775i
$443$	6.03593e16			0.379420			0.189710	−	0.981840i	$-0.439245\pi$
$443$	6.03593e16			0.379420			0.189710	+	0.981840i	$0.439245\pi$
$444$		0			0
$445$	−6.07992e16			−0.371157
$446$	−2.16578e17			−1.30298
$447$		0			0
$448$			1.11331e17i			0.650592i
$449$		−	1.69726e17i		−	0.977569i	−0.872405	−	0.488785i	$-0.837440\pi$
$449$		−	1.69726e17i		−	0.977569i	0.872405	−	0.488785i	$-0.162560\pi$
$450$		0			0
$451$	−2.20186e17			−1.23209
$452$	−4.56809e15			−0.0251962
$453$		0			0
$454$	−1.56242e17			−0.837401
$455$	3.87960e15	−	1.06467e17i	0.0204981	−	0.562526i
$456$		0			0
$457$		−	1.32615e17i		−	0.680986i	−0.940247	−	0.340493i	$-0.889406\pi$
$457$		−	1.32615e17i		−	0.680986i	0.940247	−	0.340493i	$-0.110594\pi$
$458$	1.29678e17			0.656510
$459$		0			0
$460$		−	1.16791e16i		−	0.0574758i
$461$			6.00255e15i			0.0291259i	0.999894	+	0.0145630i	$0.00463570\pi$
$461$			6.00255e15i			0.0291259i	−0.999894	+	0.0145630i	$0.995364\pi$
$462$		0			0
$463$		−	3.23963e17i		−	1.52834i	−0.645016	−	0.764169i	$-0.723149\pi$
$463$		−	3.23963e17i		−	1.52834i	0.645016	−	0.764169i	$-0.276851\pi$
$464$	−2.67414e17			−1.24399
$465$		0			0
$466$		−	9.49045e16i		−	0.429317i
$467$	−1.53186e17			−0.683373			−0.341687	−	0.939814i	$-0.610998\pi$
$467$	−1.53186e17			−0.683373			−0.341687	+	0.939814i	$0.610998\pi$
$468$		0			0
$469$	−2.17126e17			−0.942080
$470$		−	1.55302e17i		−	0.664569i
$471$		0			0
$472$	2.29128e17			0.953797
$473$			3.48876e17i			1.43243i
$474$		0			0
$475$		−	7.37149e15i		−	0.0294474i
$476$		−	6.46481e15i		−	0.0254748i
$477$		0			0
$478$	2.40871e17			0.923642
$479$		−	2.82516e16i		−	0.106872i	−0.998571	−	0.0534358i	$-0.982983\pi$
$479$		−	2.82516e16i		−	0.106872i	0.998571	−	0.0534358i	$-0.0170173\pi$
$480$		0			0
$481$	−4.74341e14	−	1.72847e13i	−0.00174641	−	6.36382e-5i
$482$	−2.05292e17			−0.745705
$483$		0			0
$484$	−3.23545e16			−0.114404
$485$	2.78585e17			0.971933
$486$		0			0
$487$			1.42186e17i			0.482968i	0.970405	+	0.241484i	$0.0776341\pi$
$487$			1.42186e17i			0.482968i	−0.970405	+	0.241484i	$0.922366\pi$
$488$			6.87269e16i			0.230355i
$489$		0			0
$490$	−1.68103e17			−0.548656
$491$	−1.85733e17			−0.598218			−0.299109	−	0.954219i	$-0.596689\pi$
$491$	−1.85733e17			−0.598218			−0.299109	+	0.954219i	$0.596689\pi$
$492$		0			0
$493$	2.69738e17			0.846131
$494$	2.03751e15	−	5.59150e16i	0.00630774	−	0.173102i
$495$		0			0
$496$			1.08666e16i			0.0327690i
$497$	1.57732e17			0.469466
$498$		0			0
$499$			4.33272e17i			1.25634i	0.778076	+	0.628170i	$0.216196\pi$
$499$			4.33272e17i			1.25634i	−0.778076	+	0.628170i	$0.783804\pi$
$500$		−	2.43123e16i		−	0.0695859i
$501$		0			0
$502$		−	4.98101e17i		−	1.38913i
$503$	3.06362e17			0.843419			0.421709	−	0.906731i	$-0.361430\pi$
$503$	3.06362e17			0.843419			0.421709	+	0.906731i	$0.361430\pi$
$504$		0			0
$505$		−	2.98938e17i		−	0.802024i
$506$	5.82107e17			1.54179
$507$		0			0
$508$	−1.79411e16			−0.0463163
$509$			2.56714e17i			0.654311i	0.944971	+	0.327155i	$0.106090\pi$
$509$			2.56714e17i			0.654311i	−0.944971	+	0.327155i	$0.893910\pi$
$510$		0			0
$511$	1.75024e17			0.434873
$512$			4.40095e17i			1.07967i
$513$		0			0
$514$		−	1.57785e17i		−	0.377404i
$515$			1.38288e17i			0.326617i
$516$		0			0
$517$	−5.41449e17			−1.24701
$518$		−	4.57421e14i		−	0.00104033i
$519$		0			0
$520$	1.54574e16	−	4.24196e17i	0.0342859	−	0.940904i
$521$	2.71617e17			0.594993			0.297496	−	0.954723i	$-0.403848\pi$
$521$	2.71617e17			0.594993			0.297496	+	0.954723i	$0.403848\pi$
$522$		0			0
$523$	7.18991e17			1.53625			0.768127	−	0.640298i	$-0.221189\pi$
$523$	7.18991e17			1.53625			0.768127	+	0.640298i	$0.221189\pi$
$524$	5.89409e16			0.124384
$525$		0			0
$526$			4.03468e17i			0.830618i
$527$		−	1.09611e16i		−	0.0222886i
$528$		0			0
$529$	−3.78523e16			−0.0750984
$530$	−1.37636e17			−0.269736
$531$		0			0
$532$	−3.77175e15			−0.00721302
$533$	−3.93026e17	−	1.43216e16i	−0.742497	−	0.0270561i
$534$		0			0
$535$			6.49207e17i			1.19697i
$536$	−8.65091e17			−1.57576
$537$		0			0
$538$			5.56612e17i			0.989619i
$539$			5.86079e17i			1.02951i
$540$		0			0
$541$			5.41301e16i			0.0928232i	0.998922	+	0.0464116i	$0.0147786\pi$
$541$			5.41301e16i			0.0928232i	−0.998922	+	0.0464116i	$0.985221\pi$
$542$	8.57804e17			1.45342
$543$		0			0
$544$		−	4.99346e16i		−	0.0826055i
$545$	2.79849e17			0.457453
$546$		0			0
$547$	1.79153e17			0.285961			0.142980	−	0.989726i	$-0.454331\pi$
$547$	1.79153e17			0.285961			0.142980	+	0.989726i	$0.454331\pi$
$548$		−	5.86342e16i		−	0.0924864i
$549$		0			0
$550$	1.71044e17			0.263482
$551$		−	1.57373e17i		−	0.239577i
$552$		0			0
$553$		−	3.27247e17i		−	0.486589i
$554$		−	6.94529e16i		−	0.102065i
$555$		0			0
$556$	−9.51148e15			−0.0136541
$557$		−	7.43876e16i		−	0.105546i	−0.998607	−	0.0527730i	$-0.983194\pi$
$557$		−	7.43876e16i		−	0.105546i	0.998607	−	0.0527730i	$-0.0168060\pi$
$558$		0			0
$559$	−2.26921e16	+	6.22735e17i	−0.0314555	+	0.863231i
$560$	3.82207e17			0.523693
$561$		0			0
$562$	3.61382e17			0.483817
$563$	−5.58736e17			−0.739438			−0.369719	−	0.929144i	$-0.620546\pi$
$563$	−5.58736e17			−0.739438			−0.369719	+	0.929144i	$0.620546\pi$
$564$		0			0
$565$			2.72418e17i			0.352307i
$566$			4.27179e17i			0.546139i
$567$		0			0
$568$	6.28451e17			0.785248
$569$	−6.17454e17			−0.762737			−0.381368	−	0.924423i	$-0.624547\pi$
$569$	−6.17454e17			−0.762737			−0.381368	+	0.924423i	$0.624547\pi$
$570$		0			0
$571$	4.66410e17			0.563162			0.281581	−	0.959537i	$-0.409141\pi$
$571$	4.66410e17			0.563162			0.281581	+	0.959537i	$0.409141\pi$
$572$	−9.07549e16	−	3.30705e15i	−0.108342	−	0.00394790i
$573$		0			0
$574$		−	3.79007e17i		−	0.442303i
$575$	1.36982e17			0.158060
$576$		0			0
$577$			1.40520e18i			1.58524i	0.609713	+	0.792622i	$0.291285\pi$
$577$			1.40520e18i			1.58524i	−0.609713	+	0.792622i	$0.708715\pi$
$578$			5.19619e17i			0.579635i
$579$		0			0
$580$		−	7.32640e16i		−	0.0799114i
$581$	−6.20429e17			−0.669187
$582$		0			0
$583$			4.79859e17i			0.506137i
$584$	6.97346e17			0.727386
$585$		0			0
$586$	−6.31177e17			−0.643897
$587$			3.58281e17i			0.361473i	0.983532	+	0.180737i	$0.0578482\pi$
$587$			3.58281e17i			0.361473i	−0.983532	+	0.180737i	$0.942152\pi$
$588$		0			0
$589$	−6.39499e15			−0.00631089
$590$		−	8.38499e17i		−	0.818398i
$591$		0			0
$592$		−	1.70283e15i		−	0.00162585i
$593$		−	2.27371e17i		−	0.214724i	−0.994220	−	0.107362i	$-0.965760\pi$
$593$		−	2.27371e17i		−	0.214724i	0.994220	−	0.107362i	$-0.0342403\pi$
$594$		0			0
$595$	−3.85529e17			−0.356202
$596$			8.41426e16i			0.0768980i
$597$		0			0
$598$	1.03905e18	+	3.78622e16i	0.929133	+	0.0338570i
$599$	1.22701e18			1.08536			0.542681	−	0.839939i	$-0.317409\pi$
$599$	1.22701e18			1.08536			0.542681	+	0.839939i	$0.317409\pi$
$600$		0			0
$601$	−1.49251e18			−1.29191			−0.645957	−	0.763374i	$-0.723541\pi$
$601$	−1.49251e18			−1.29191			−0.645957	+	0.763374i	$0.723541\pi$
$602$	−6.00522e17			−0.514224
$603$		0			0
$604$			4.18470e16i			0.0350690i
$605$			1.92946e18i			1.59965i
$606$		0			0
$607$	−1.66922e18			−1.35452			−0.677262	−	0.735742i	$-0.736834\pi$
$607$	−1.66922e18			−1.35452			−0.677262	+	0.735742i	$0.736834\pi$
$608$	−2.91333e16			−0.0233892
$609$		0			0
$610$	2.51507e17			0.197654
$611$	−9.66474e17	−	3.52177e16i	−0.751488	−	0.0273837i
$612$		0			0
$613$			9.85345e17i			0.750059i	0.927013	+	0.375029i	$0.122367\pi$
$613$			9.85345e17i			0.750059i	−0.927013	+	0.375029i	$0.877633\pi$
$614$	5.28381e17			0.397972
$615$		0			0
$616$		−	1.42618e18i		−	1.05172i
$617$			1.96101e18i			1.43096i	0.698636	+	0.715478i	$0.253791\pi$
$617$			1.96101e18i			1.43096i	−0.698636	+	0.715478i	$0.746209\pi$
$618$		0			0
$619$			1.98675e18i			1.41956i	0.704424	+	0.709780i	$0.251206\pi$
$619$			1.98675e18i			1.41956i	−0.704424	+	0.709780i	$0.748794\pi$
$620$	−2.97715e15			−0.00210501
$621$		0			0
$622$		−	1.47497e18i		−	1.02128i
$623$	−3.64869e17			−0.250014
$624$		0			0
$625$	−1.20496e18			−0.808637
$626$		−	1.77177e17i		−	0.117672i
$627$		0			0
$628$	3.04967e15			0.00198388
$629$			1.71763e15i			0.00110586i
$630$		0			0
$631$		−	6.31756e17i		−	0.398436i	−0.979955	−	0.199218i	$-0.936160\pi$
$631$		−	6.31756e17i		−	0.398436i	0.979955	−	0.199218i	$-0.0638402\pi$
$632$		−	1.30384e18i		−	0.813888i
$633$		0			0
$634$	1.22903e18			0.751595
$635$			1.06992e18i			0.647620i
$636$		0			0
$637$	−3.81205e16	+	1.04614e18i	−0.0226075	+	0.620415i
$638$	3.65160e18			2.14362
$639$		0			0
$640$	1.41581e18			0.814395
$641$	−2.69186e18			−1.53276			−0.766381	−	0.642386i	$-0.777944\pi$
$641$	−2.69186e18			−1.53276			−0.766381	+	0.642386i	$0.777944\pi$
$642$		0			0
$643$		−	1.54575e18i		−	0.862517i	−0.902228	−	0.431259i	$-0.858070\pi$
$643$		−	1.54575e18i		−	0.862517i	0.902228	−	0.431259i	$-0.141930\pi$
$644$		−	7.00891e16i		−	0.0387161i
$645$		0			0
$646$	−2.02474e17			−0.109612
$647$	2.64371e18			1.41689			0.708444	−	0.705767i	$-0.249398\pi$
$647$	2.64371e18			1.41689			0.708444	+	0.705767i	$0.249398\pi$
$648$		0			0
$649$	−2.92337e18			−1.53565
$650$	3.05309e17	+	1.11253e16i	0.158783	+	0.00578594i
$651$		0			0
$652$		−	7.28029e16i		−	0.0371141i
$653$	−3.47578e18			−1.75435			−0.877175	−	0.480170i	$-0.840575\pi$
$653$	−3.47578e18			−1.75435			−0.877175	+	0.480170i	$0.840575\pi$
$654$		0			0
$655$		−	3.51495e18i		−	1.73920i
$656$		−	1.41092e18i		−	0.691239i
$657$		0			0
$658$		−	9.31999e17i		−	0.447659i
$659$	6.64948e17			0.316251			0.158126	−	0.987419i	$-0.449455\pi$
$659$	6.64948e17			0.316251			0.158126	+	0.987419i	$0.449455\pi$
$660$		0			0
$661$		−	1.05716e18i		−	0.492981i	−0.969145	−	0.246491i	$-0.920723\pi$
$661$		−	1.05716e18i		−	0.492981i	0.969145	−	0.246491i	$-0.0792774\pi$
$662$	−9.31481e17			−0.430127
$663$		0			0
$664$	−2.47197e18			−1.11931
$665$			2.24929e17i			0.100856i
$666$		0			0
$667$	2.92440e18			1.28594
$668$		−	2.64008e17i		−	0.114966i
$669$		0			0
$670$			3.16581e18i			1.35207i
$671$		−	8.76863e17i		−	0.370882i
$672$		0			0
$673$	9.84944e17			0.408614			0.204307	−	0.978907i	$-0.434506\pi$
$673$	9.84944e17			0.408614			0.204307	+	0.978907i	$0.434506\pi$
$674$			2.72004e18i			1.11760i
$675$		0			0
$676$	−1.61780e17	−	1.18060e16i	−0.0652037	−	0.00475828i
$677$	−2.66054e18			−1.06205			−0.531023	−	0.847357i	$-0.678192\pi$
$677$	−2.66054e18			−1.06205			−0.531023	+	0.847357i	$0.678192\pi$
$678$		0			0
$679$	1.67185e18			0.654701
$680$	−1.53606e18			−0.595799
$681$		0			0
$682$		−	1.48386e17i		−	0.0564670i
$683$		−	5.21508e17i		−	0.196574i	−0.995158	−	0.0982871i	$-0.968664\pi$
$683$		−	5.21508e17i		−	0.196574i	0.995158	−	0.0982871i	$-0.0313364\pi$
$684$		0			0
$685$	−3.49666e18			−1.29320
$686$	−2.63379e18			−0.964881
$687$		0			0
$688$	−2.23556e18			−0.803639
$689$	−3.12116e16	+	8.56537e17i	−0.0111145	+	0.305015i
$690$		0			0
$691$			3.35433e18i			1.17219i	0.810242	+	0.586096i	$0.199336\pi$
$691$			3.35433e18i			1.17219i	−0.810242	+	0.586096i	$0.800664\pi$
$692$	1.88508e17			0.0652590
$693$		0			0
$694$		−	3.94144e18i		−	1.33911i
$695$			5.67217e17i			0.190919i
$696$		0			0
$697$			1.42319e18i			0.470163i
$698$	−1.39534e18			−0.456688
$699$		0			0
$700$		−	2.05947e16i		−	0.00661634i
$701$	2.15474e18			0.685848			0.342924	−	0.939363i	$-0.388583\pi$
$701$	2.15474e18			0.685848			0.342924	+	0.939363i	$0.388583\pi$
$702$		0			0
$703$	1.00212e15			0.000313118
$704$		−	5.65940e18i		−	1.75206i
$705$		0			0
$706$	2.46120e18			0.748024
$707$		−	1.79399e18i		−	0.540249i
$708$		0			0
$709$		−	6.64329e18i		−	1.96419i	−0.188393	−	0.982094i	$-0.560328\pi$
$709$		−	6.64329e18i		−	1.96419i	0.188393	−	0.982094i	$-0.439672\pi$
$710$		−	2.29982e18i		−	0.673776i
$711$		0			0
$712$	−1.45374e18			−0.418184
$713$		−	1.18836e17i		−	0.0338739i
$714$		0			0
$715$	−1.97216e17	+	5.41217e18i	−0.0552017	+	1.51489i
$716$	−3.10560e17			−0.0861411
$717$		0			0
$718$	1.25013e18			0.340523
$719$	5.03748e18			1.35980			0.679901	−	0.733304i	$-0.262023\pi$
$719$	5.03748e18			1.35980			0.679901	+	0.733304i	$0.262023\pi$
$720$		0			0
$721$			8.29899e17i			0.220012i
$722$		−	3.56155e18i		−	0.935723i
$723$		0			0
$724$	−1.00041e17			−0.0258152
$725$	8.59295e17			0.219758
$726$		0			0
$727$	2.44730e18			0.614770			0.307385	−	0.951585i	$-0.400546\pi$
$727$	2.44730e18			0.614770			0.307385	+	0.951585i	$0.400546\pi$
$728$	9.27634e16	−	2.54569e18i	0.0230953	−	0.633800i
$729$		0			0
$730$		−	2.55195e18i		−	0.624127i
$731$	2.25499e18			0.546614
$732$		0			0
$733$		−	4.52485e18i		−	1.07753i	−0.842457	−	0.538763i	$-0.818892\pi$
$733$		−	4.52485e18i		−	1.07753i	0.842457	−	0.538763i	$-0.181108\pi$
$734$		−	4.64618e18i		−	1.09666i
$735$		0			0
$736$		−	5.41373e17i		−	0.125543i
$737$	1.10374e19			2.53704
$738$		0			0
$739$			5.57733e18i			1.25962i	0.776751	+	0.629808i	$0.216866\pi$
$739$			5.57733e18i			1.25962i	−0.776751	+	0.629808i	$0.783134\pi$
$740$	4.66529e14			0.000104441
$741$		0			0
$742$	−8.25984e17			−0.181696
$743$		−	1.21489e18i		−	0.264916i	−0.991189	−	0.132458i	$-0.957713\pi$
$743$		−	1.21489e18i		−	0.264916i	0.991189	−	0.132458i	$-0.0422870\pi$
$744$		0			0
$745$	5.01784e18			1.07523
$746$		−	7.43251e18i		−	1.57882i
$747$		0			0
$748$			3.28633e17i			0.0686041i
$749$			3.89603e18i			0.806289i
$750$		0			0
$751$	2.90122e18			0.590093			0.295047	−	0.955483i	$-0.404665\pi$
$751$	2.90122e18			0.590093			0.295047	+	0.955483i	$0.404665\pi$
$752$		−	3.46954e18i		−	0.699610i
$753$		0			0
$754$	6.51802e18	+	2.37512e17i	1.29182	+	0.0470730i
$755$	2.49554e18			0.490354
$756$		0			0
$757$	7.74004e18			1.49493			0.747463	−	0.664303i	$-0.231272\pi$
$757$	7.74004e18			1.49493			0.747463	+	0.664303i	$0.231272\pi$
$758$	−6.59851e18			−1.26356
$759$		0			0
$760$			8.96179e17i			0.168697i
$761$			3.77780e18i			0.705081i	0.935796	+	0.352541i	$0.114682\pi$
$761$			3.77780e18i			0.705081i	−0.935796	+	0.352541i	$0.885318\pi$
$762$		0			0
$763$	1.67943e18			0.308144
$764$	−3.79053e16			−0.00689594
$765$		0			0
$766$	−2.82207e17			−0.0504755
$767$	−5.21814e18	−	1.90146e17i	−0.925435	−	0.0337223i
$768$		0			0
$769$		−	5.74448e17i		−	0.100168i	−0.998745	−	0.0500841i	$-0.984051\pi$
$769$		−	5.74448e17i		−	0.100168i	0.998745	−	0.0500841i	$-0.0159489\pi$
$770$	−5.21912e18			−0.902418
$771$		0			0
$772$			2.17707e17i			0.0370135i
$773$			2.70309e18i			0.455715i	0.973694	+	0.227858i	$0.0731721\pi$
$773$			2.70309e18i			0.455715i	−0.973694	+	0.227858i	$0.926828\pi$
$774$		0			0
$775$		−	3.49182e16i		−	0.00578883i
$776$	6.66112e18			1.09508
$777$		0			0
$778$			5.62997e18i			0.910204i
$779$	8.30327e17			0.133124
$780$		0			0
$781$	−8.01818e18			−1.26428
$782$		−	3.76250e18i		−	0.588345i
$783$		0			0
$784$	−3.75552e18			−0.577585
$785$		−	1.81867e17i		−	0.0277397i
$786$		0			0
$787$		−	1.21559e19i		−	1.82369i	−0.410539	−	0.911843i	$-0.634659\pi$
$787$		−	1.21559e19i		−	1.82369i	0.410539	−	0.911843i	$-0.365341\pi$
$788$		−	7.71029e17i		−	0.114723i
$789$		0			0
$790$	−4.77144e18			−0.698350
$791$			1.63484e18i			0.237317i
$792$		0			0
$793$	5.70341e16	−	1.56518e18i	0.00814439	−	0.223506i
$794$	7.50544e18			1.06302
$795$		0			0
$796$	7.40654e17			0.103200
$797$	−1.19259e19			−1.64821			−0.824103	−	0.566440i	$-0.808320\pi$
$797$	−1.19259e19			−1.64821			−0.824103	+	0.566440i	$0.808320\pi$
$798$		0			0
$799$			3.49970e18i			0.475857i
$800$		−	1.59075e17i		−	0.0214544i
$801$		0			0
$802$	−7.56271e18			−1.00356
$803$	−8.89719e18			−1.17112
$804$		0			0
$805$	−4.17976e18			−0.541350
$806$	9.65152e15	−	2.64865e17i	0.00123999	−	0.0340289i
$807$		0			0
$808$		−	7.14777e18i		−	0.903643i
$809$	2.02703e18			0.254211			0.127106	−	0.991889i	$-0.459431\pi$
$809$	2.02703e18			0.254211			0.127106	+	0.991889i	$0.459431\pi$
$810$		0			0
$811$			5.40615e18i			0.667195i	0.942716	+	0.333597i	$0.108263\pi$
$811$			5.40615e18i			0.667195i	−0.942716	+	0.333597i	$0.891737\pi$
$812$		−	4.39673e17i		−	0.0538290i
$813$		0			0
$814$			2.32526e16i			0.00280164i
$815$	−4.34160e18			−0.518950
$816$		0			0
$817$		−	1.31562e18i		−	0.154770i
$818$	−7.73785e18			−0.903075
$819$		0			0
$820$	3.86554e17			0.0444038
$821$			1.19996e19i			1.36753i	0.729704	+	0.683763i	$0.239658\pi$
$821$			1.19996e19i			1.36753i	−0.729704	+	0.683763i	$0.760342\pi$
$822$		0			0
$823$	−7.49361e17			−0.0840605			−0.0420303	−	0.999116i	$-0.513383\pi$
$823$	−7.49361e17			−0.0840605			−0.0420303	+	0.999116i	$0.513383\pi$
$824$			3.30655e18i			0.368001i
$825$		0			0
$826$		−	5.03201e18i		−	0.551279i
$827$			9.04543e18i			0.983204i	0.870820	+	0.491602i	$0.163588\pi$
$827$			9.04543e18i			0.983204i	−0.870820	+	0.491602i	$0.836412\pi$
$828$		0			0
$829$	5.57893e18			0.596962			0.298481	−	0.954416i	$-0.403520\pi$
$829$	5.57893e18			0.596962			0.298481	+	0.954416i	$0.403520\pi$
$830$			9.04620e18i			0.960414i
$831$		0			0
$832$	3.68107e17	−	1.01019e19i	0.0384744	−	1.05585i
$833$	3.78817e18			0.392859
$834$		0			0
$835$	−1.57441e19			−1.60752
$836$	1.91734e17			0.0194248
$837$		0			0
$838$			6.75335e18i			0.673648i
$839$		−	1.48570e19i		−	1.47054i	−0.677774	−	0.735271i	$-0.737055\pi$
$839$		−	1.48570e19i		−	1.47054i	0.677774	−	0.735271i	$-0.262945\pi$
$840$		0			0
$841$	8.08435e18			0.787900
$842$	1.36811e19			1.32310
$843$		0			0
$844$	8.10130e17			0.0771488
$845$	−7.04052e17	+	9.64777e18i	−0.0665328	+	0.911714i
$846$		0			0
$847$			1.15791e19i			1.07754i
$848$	−3.07488e18			−0.283959
$849$		0			0
$850$		−	1.10556e18i		−	0.100544i
$851$			1.86220e16i			0.00168067i
$852$		0			0
$853$		−	1.30706e19i		−	1.16179i	−0.813978	−	0.580895i	$-0.802703\pi$
$853$		−	1.30706e19i		−	1.16179i	0.813978	−	0.580895i	$-0.197297\pi$
$854$	1.50935e18			0.133142
$855$		0			0
$856$			1.55229e19i			1.34863i
$857$	1.17760e19			1.01536			0.507682	−	0.861544i	$-0.330502\pi$
$857$	1.17760e19			1.01536			0.507682	+	0.861544i	$0.330502\pi$
$858$		0			0
$859$	−1.70251e19			−1.44588			−0.722942	−	0.690909i	$-0.757210\pi$
$859$	−1.70251e19			−1.44588			−0.722942	+	0.690909i	$0.757210\pi$
$860$		−	6.12480e17i		−	0.0516241i
$861$		0			0
$862$	1.29272e19			1.07327
$863$			1.24318e19i			1.02439i	0.858870	+	0.512194i	$0.171167\pi$
$863$			1.24318e19i			1.02439i	−0.858870	+	0.512194i	$0.828833\pi$
$864$		0			0
$865$		−	1.12417e19i		−	0.912487i
$866$		−	8.61895e18i		−	0.694366i
$867$		0			0
$868$	−1.78665e16			−0.00141795
$869$			1.66353e19i			1.31039i
$870$		0			0
$871$	1.97015e19	+	7.17909e17i	1.52891	+	0.0557123i
$872$	6.69134e18			0.515413
$873$		0			0
$874$	−2.19515e18			−0.166586
$875$	−8.70096e18			−0.655413
$876$		0			0
$877$			2.36133e19i			1.75251i	0.481850	+	0.876254i	$0.339965\pi$
$877$			2.36133e19i			1.75251i	−0.481850	+	0.876254i	$0.660035\pi$
$878$		−	2.29452e18i		−	0.169036i
$879$		0			0
$880$	−1.94291e19			−1.41032
$881$	5.00094e17			0.0360336			0.0180168	−	0.999838i	$-0.494265\pi$
$881$	5.00094e17			0.0360336			0.0180168	+	0.999838i	$0.494265\pi$
$882$		0			0
$883$	−4.54937e18			−0.323003			−0.161501	−	0.986872i	$-0.551634\pi$
$883$	−4.54937e18			−0.323003			−0.161501	+	0.986872i	$0.551634\pi$
$884$	−2.13754e16	+	5.86602e17i	−0.00150652	+	0.0413431i
$885$		0			0
$886$		−	5.28150e18i		−	0.366807i
$887$	−1.04938e19			−0.723484			−0.361742	−	0.932278i	$-0.617818\pi$
$887$	−1.04938e19			−0.723484			−0.361742	+	0.932278i	$0.617818\pi$
$888$		0			0
$889$			6.42079e18i			0.436242i
$890$			5.31999e18i			0.358819i
$891$		0			0
$892$		−	1.32561e18i		−	0.0881140i
$893$	2.04182e18			0.134736
$894$		0			0
$895$			1.85202e19i			1.20447i
$896$	8.49658e18			0.548583
$897$		0			0
$898$	−1.48512e19			−0.945074
$899$		−	7.45465e17i		−	0.0470966i
$900$		0			0
$901$	3.10160e18			0.193141
$902$			1.92665e19i			1.19113i
$903$		0			0
$904$			6.51368e18i			0.396946i
$905$			5.96593e18i			0.360963i
$906$		0			0
$907$	−8.50215e18			−0.507086			−0.253543	−	0.967324i	$-0.581596\pi$
$907$	−8.50215e18			−0.507086			−0.253543	+	0.967324i	$0.581596\pi$
$908$		−	9.56310e17i		−	0.0566293i
$909$		0			0
$910$	−9.31601e18	−	3.39469e17i	−0.543827	−	0.0198167i
$911$	6.48478e18			0.375859			0.187930	−	0.982182i	$-0.439822\pi$
$911$	6.48478e18			0.375859			0.187930	+	0.982182i	$0.439822\pi$
$912$		0			0
$913$	3.15390e19			1.80213
$914$	−1.16040e19			−0.658349
$915$		0			0
$916$			7.93724e17i			0.0443965i
$917$		−	2.10939e19i		−	1.17154i
$918$		0			0
$919$	−1.40012e19			−0.766682			−0.383341	−	0.923607i	$-0.625227\pi$
$919$	−1.40012e19			−0.766682			−0.383341	+	0.923607i	$0.625227\pi$
$920$	−1.66534e19			−0.905485
$921$		0			0
$922$	5.25229e17			0.0281577
$923$	−1.43123e19	−	5.21529e17i	−0.761899	−	0.0277631i
$924$		0			0
$925$			5.47180e15i			0.000287216i
$926$	−2.83471e19			−1.47753
$927$		0			0
$928$		−	3.39607e18i		−	0.174548i
$929$			3.60756e18i			0.184124i	0.995753	+	0.0920621i	$0.0293458\pi$
$929$			3.60756e18i			0.184124i	−0.995753	+	0.0920621i	$0.970654\pi$
$930$		0			0
$931$		−	2.21012e18i		−	0.111236i
$932$	5.80884e17			0.0290326
$933$		0			0
$934$			1.34039e19i			0.660657i
$935$	1.95980e19			0.959261
$936$		0			0
$937$	3.43026e19			1.65585			0.827923	−	0.560841i	$-0.189522\pi$
$937$	3.43026e19			1.65585			0.827923	+	0.560841i	$0.189522\pi$
$938$			1.89987e19i			0.910764i
$939$		0			0
$940$	9.50558e17			0.0449415
$941$		−	1.71617e19i		−	0.805802i	−0.915244	−	0.402901i	$-0.868002\pi$
$941$		−	1.71617e19i		−	0.805802i	0.915244	−	0.402901i	$-0.131998\pi$
$942$		0			0
$943$			1.54297e19i			0.714547i
$944$		−	1.87326e19i		−	0.861549i
$945$		0			0
$946$	3.05270e19			1.38482
$947$		−	9.83424e18i		−	0.443063i	−0.975153	−	0.221532i	$-0.928894\pi$
$947$		−	9.83424e18i		−	0.443063i	0.975153	−	0.221532i	$-0.0711056\pi$
$948$		0			0
$949$	−1.58813e19	−	5.78703e17i	−0.705757	−	0.0257173i
$950$	−6.45013e17			−0.0284685
$951$		0			0
$952$	−9.21821e18			−0.401335
$953$	3.20088e19			1.38409			0.692047	−	0.721852i	$-0.256709\pi$
$953$	3.20088e19			1.38409			0.692047	+	0.721852i	$0.256709\pi$
$954$		0			0
$955$			2.26049e18i			0.0964229i
$956$			1.47431e18i			0.0624613i
$957$		0			0
$958$	−2.47205e18			−0.103319
$959$	−2.09842e19			−0.871106
$960$		0			0
$961$	2.43873e19			0.998759
$962$	−1.51242e15	+	4.15053e16i	−6.15228e−5	+	0.00168836i
$963$		0			0
$964$		−	1.25654e18i		−	0.0504283i
$965$	1.29830e19			0.517544
$966$		0			0
$967$			7.50976e18i			0.295362i	0.989035	+	0.147681i	$0.0471808\pi$
$967$			7.50976e18i			0.295362i	−0.989035	+	0.147681i	$0.952819\pi$
$968$			4.61345e19i			1.80234i
$969$		0			0
$970$		−	2.43765e19i		−	0.939625i
$971$	2.99621e19			1.14722			0.573611	−	0.819128i	$-0.305542\pi$
$971$	2.99621e19			1.14722			0.573611	+	0.819128i	$0.305542\pi$
$972$		0			0
$973$			3.40399e18i			0.128604i
$974$	1.24414e19			0.466913
$975$		0			0
$976$	5.61883e18			0.208076
$977$			3.69718e19i			1.36005i	0.733188	+	0.680026i	$0.238032\pi$
$977$			3.69718e19i			1.36005i	−0.733188	+	0.680026i	$0.761968\pi$
$978$		0			0
$979$	1.85478e19			0.673294
$980$		−	1.02891e18i		−	0.0371029i
$981$		0			0
$982$			1.62518e19i			0.578333i
$983$		−	4.64432e18i		−	0.164181i	−0.996625	−	0.0820907i	$-0.973840\pi$
$983$		−	4.64432e18i		−	0.164181i	0.996625	−	0.0820907i	$-0.0261597\pi$
$984$		0			0
$985$	−4.59803e19			−1.60412
$986$		−	2.36024e19i		−	0.818005i
$987$		0			0
$988$	3.42240e17	+	1.24710e16i	0.0117061	+	0.000426561i
$989$	2.44477e19			0.830735
$990$		0			0
$991$	1.34705e19			0.451758			0.225879	−	0.974155i	$-0.427475\pi$
$991$	1.34705e19			0.451758			0.225879	+	0.974155i	$0.427475\pi$
$992$	−1.38002e17			−0.00459791
$993$		0			0
$994$		−	1.38017e19i		−	0.453861i
$995$		−	4.41689e19i		−	1.44300i
$996$		0			0
$997$	2.44003e19			0.786823			0.393412	−	0.919362i	$-0.371295\pi$
$997$	2.44003e19			0.786823			0.393412	+	0.919362i	$0.371295\pi$
$998$	3.79117e19			1.21458
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.14.b.c.64.5		14
3.2	odd	2		13.14.b.a.12.10	yes	14
13.12	even	2	inner	117.14.b.c.64.10		14
39.5	even	4		169.14.a.d.1.10		14
39.8	even	4		169.14.a.d.1.5		14
39.38	odd	2		13.14.b.a.12.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.14.b.a.12.5	✓	14	39.38	odd	2
13.14.b.a.12.10	yes	14	3.2	odd	2
117.14.b.c.64.5		14	1.1	even	1	trivial
117.14.b.c.64.10		14	13.12	even	2	inner
169.14.a.d.1.5		14	39.8	even	4
169.14.a.d.1.10		14	39.5	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	117.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-87.5010i q^{2} +535.569 q^{4} -31938.7i q^{5} -191671. i q^{7} -763671. i q^{8} -2.79467e6 q^{10} +9.74341e6i q^{11} +(-633744. + 1.73918e7i) q^{13} -1.67714e7 q^{14} -6.24346e7 q^{16} +6.29773e7 q^{17} -3.67427e7i q^{19} -1.71054e7i q^{20} +8.52559e8 q^{22} +6.82777e8 q^{23} +2.00624e8 q^{25} +(1.52180e9 + 5.54533e7i) q^{26} -1.02653e8i q^{28} +4.28310e9 q^{29} -1.74048e8i q^{31} -7.92899e8i q^{32} -5.51058e9i q^{34} -6.12171e9 q^{35} +2.72739e7i q^{37} -3.21503e9 q^{38} -2.43906e10 q^{40} +2.25984e10i q^{41} +3.58063e10 q^{43} +5.21827e9i q^{44} -5.97437e10i q^{46} +5.55708e10i q^{47} +6.01513e10 q^{49} -1.75548e10i q^{50} +(-3.39414e8 + 9.31449e9i) q^{52} +4.92496e10 q^{53} +3.11192e11 q^{55} -1.46374e11 q^{56} -3.74776e11i q^{58} +3.00035e11i q^{59} -8.99954e10 q^{61} -1.52294e10 q^{62} -5.80844e11 q^{64} +(5.55470e11 + 2.02410e10i) q^{65} -1.13281e12i q^{67} +3.37287e10 q^{68} +5.35656e11i q^{70} +8.22933e11i q^{71} +9.13149e11i q^{73} +2.38649e9 q^{74} -1.96783e10i q^{76} +1.86753e12 q^{77} +1.70734e12 q^{79} +1.99408e12i q^{80} +1.97738e12 q^{82} -3.23695e12i q^{83} -2.01141e12i q^{85} -3.13309e12i q^{86} +7.44077e12 q^{88} -1.90362e12i q^{89} +(3.33349e12 + 1.21470e11i) q^{91} +3.65674e11 q^{92} +4.86250e12 q^{94} -1.17351e12 q^{95} +8.72249e12i q^{97} -5.26330e12i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 49154 q^{4} - 3968358 q^{10} - 14362478 q^{13} - 72843942 q^{14} + 243447170 q^{16} + 178512492 q^{17} + 1330288056 q^{22} + 1641693744 q^{23} + 1601386654 q^{25} - 138020766 q^{26} + 10348326348 q^{29}+ \cdots - 11940434574336 q^{95}+O(q^{100}) \) 14 * q - 49154 * q^4 - 3968358 * q^10 - 14362478 * q^13 - 72843942 * q^14 + 243447170 * q^16 + 178512492 * q^17 + 1330288056 * q^22 + 1641693744 * q^23 + 1601386654 * q^25 - 138020766 * q^26 + 10348326348 * q^29 - 20242816056 * q^35 + 72234754500 * q^38 - 50528567766 * q^40 - 42288191696 * q^43 + 202681235282 * q^49 + 605927200580 * q^52 + 541269433788 * q^53 + 294791560608 * q^55 + 1027260370698 * q^56 + 1693279412900 * q^61 - 1808450592168 * q^62 - 4815047793506 * q^64 - 534977124552 * q^65 - 65016763122 * q^68 - 7595100503238 * q^74 + 1391939668824 * q^77 - 5060278211056 * q^79 + 507818992992 * q^82 + 2586979258080 * q^88 + 3450737986176 * q^91 - 7241299383420 * q^92 + 11219792119974 * q^94 - 11940434574336 * q^95

Introduction

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