LMFDB - Embedded newform 27.15.d.a.17.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,15,Mod(8,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("27.8"); S:= CuspForms(chi, 15); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 15, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	27.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$33.5688214010$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	27.17
Dual form			27.15.d.a.8.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-195.306 + 112.760i) q^{2} +(17237.5 - 29856.3i) q^{4} +(-103308. - 59645.1i) q^{5} +(163246. + 282751. i) q^{7} +4.07989e6i q^{8} +2.69023e7 q^{10} +(2.55183e7 - 1.47330e7i) q^{11} +(-3.84596e7 + 6.66141e7i) q^{13} +(-6.37658e7 - 3.68152e7i) q^{14} +(-1.77628e8 - 3.07661e8i) q^{16} +3.47954e8i q^{17} +1.79868e7 q^{19} +(-3.56156e9 + 2.05627e9i) q^{20} +(-3.32258e9 + 5.75488e9i) q^{22} +(-1.21799e9 - 7.03208e8i) q^{23} +(4.06332e9 + 7.03788e9i) q^{25} -1.73468e10i q^{26} +1.12558e10 q^{28} +(-8.71076e9 + 5.02916e9i) q^{29} +(6.77264e9 - 1.17306e10i) q^{31} +(1.14941e10 + 6.63613e9i) q^{32} +(-3.92352e10 - 6.79574e10i) q^{34} -3.89473e10i q^{35} +4.16724e10 q^{37} +(-3.51292e9 + 2.02818e9i) q^{38} +(2.43346e11 - 4.21487e11i) q^{40} +(2.44149e11 + 1.40960e11i) q^{41} +(1.29317e9 + 2.23983e9i) q^{43} -1.01584e12i q^{44} +3.17174e11 q^{46} +(3.91113e11 - 2.25809e11i) q^{47} +(2.85813e11 - 4.95043e11i) q^{49} +(-1.58718e12 - 9.16358e11i) q^{50} +(1.32590e12 + 2.29653e12i) q^{52} +1.74490e12i q^{53} -3.51500e12 q^{55} +(-1.15359e12 + 6.66027e11i) q^{56} +(1.13417e12 - 1.96445e12i) q^{58} +(-3.57141e12 - 2.06195e12i) q^{59} +(-8.17270e11 - 1.41555e12i) q^{61} +3.05473e12i q^{62} +2.82736e12 q^{64} +(7.94640e12 - 4.58786e12i) q^{65} +(1.15275e12 - 1.99661e12i) q^{67} +(1.03886e13 + 5.99787e12i) q^{68} +(4.39169e12 + 7.60663e12i) q^{70} -8.75750e12i q^{71} -1.12442e13 q^{73} +(-8.13885e12 + 4.69897e12i) q^{74} +(3.10048e11 - 5.37019e11i) q^{76} +(8.33152e12 + 4.81021e12i) q^{77} +(-5.16374e11 - 8.94386e11i) q^{79} +4.23786e13i q^{80} -6.35783e13 q^{82} +(-8.74183e12 + 5.04710e12i) q^{83} +(2.07538e13 - 3.59466e13i) q^{85} +(-5.05125e11 - 2.91634e11i) q^{86} +(6.01091e13 + 1.04112e14i) q^{88} -5.62078e13i q^{89} -2.51135e13 q^{91} +(-4.19904e13 + 2.42432e13i) q^{92} +(-5.09245e13 + 8.82037e13i) q^{94} +(-1.85818e12 - 1.07282e12i) q^{95} +(-5.37337e13 - 9.30695e13i) q^{97} +1.28913e14i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 3 q^{2} + 98303 q^{4} + 107994 q^{5} - 146330 q^{7} - 32772 q^{10} + 15978711 q^{11} - 23281436 q^{13} + 349442850 q^{14} - 671072257 q^{16} + 195706222 q^{19} - 2822935854 q^{20} - 204235521 q^{22}+ \cdots + 7621755375583 q^{97}+O(q^{100}) $ 26 * q + 3 * q^2 + 98303 * q^4 + 107994 * q^5 - 146330 * q^7 - 32772 * q^10 + 15978711 * q^11 - 23281436 * q^13 + 349442850 * q^14 - 671072257 * q^16 + 195706222 * q^19 - 2822935854 * q^20 - 204235521 * q^22 + 6101133672 * q^23 + 14614789727 * q^25 - 9052979204 * q^28 - 85191770166 * q^29 + 15357554728 * q^31 + 237242922057 * q^32 - 16566014943 * q^34 - 77721425444 * q^37 - 476314869819 * q^38 - 88855733850 * q^40 + 938882938233 * q^41 - 29709800063 * q^43 + 1553142786144 * q^46 + 1272741434580 * q^47 - 945184029255 * q^49 - 3573994524699 * q^50 + 1825489374856 * q^52 - 3772940931372 * q^55 + 7790759725422 * q^56 + 3747043240302 * q^58 - 5874788534451 * q^59 - 4867968901544 * q^61 + 1211169309434 * q^64 + 22156719464856 * q^65 - 8251061484125 * q^67 - 30687017243265 * q^68 + 6871822387932 * q^70 + 16120119648922 * q^73 - 8549243621166 * q^74 + 14422972781521 * q^76 - 13919363311398 * q^77 - 10740904544582 * q^79 - 67076318933382 * q^82 + 11295125984532 * q^83 + 10590724937466 * q^85 - 97019495740221 * q^86 - 26136212294541 * q^88 + 70870424994080 * q^91 + 474274297000284 * q^92 - 46678164316620 * q^94 - 440317551118746 * q^95 + 7621755375583 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−195.306	+	112.760i	−1.52583	+	0.880936i	−0.526295	+	0.850302i	$0.676419\pi$
$2$	−195.306	+	112.760i	−1.52583	+	0.880936i	−0.999531	+	0.0306339i	$0.990247\pi$
$3$		0			0
$3$		0			0
$4$	17237.5	−	29856.3i	1.05210	−	1.82228i
$5$	−103308.	−	59645.1i	−1.32235	−	0.763457i	−0.338244	−	0.941058i	$-0.609833\pi$
$5$	−103308.	−	59645.1i	−1.32235	−	0.763457i	−0.984103	+	0.177601i	$0.943166\pi$
$6$		0			0
$7$	163246.	+	282751.i	0.198224	+	0.343334i	0.947953	−	0.318411i	$-0.103149\pi$
$7$	163246.	+	282751.i	0.198224	+	0.343334i	−0.749729	+	0.661746i	$0.769816\pi$
$8$			4.07989e6i			1.94545i
$9$		0			0
$10$	2.69023e7			2.69023
$11$	2.55183e7	−	1.47330e7i	1.30949	−	0.756036i	0.327481	−	0.944858i	$-0.393800\pi$
$11$	2.55183e7	−	1.47330e7i	1.30949	−	0.756036i	0.982011	+	0.188822i	$0.0604670\pi$
$12$		0			0
$13$	−3.84596e7	+	6.66141e7i	−0.612917	+	1.06160i	0.377829	+	0.925875i	$0.376671\pi$
$13$	−3.84596e7	+	6.66141e7i	−0.612917	+	1.06160i	−0.990746	+	0.135728i	$0.956663\pi$
$14$	−6.37658e7	−	3.68152e7i	−0.604911	−	0.349246i
$15$		0			0
$16$	−1.77628e8	−	3.07661e8i	−0.661716	−	1.14613i
$17$			3.47954e8i			0.847968i	0.905670	+	0.423984i	$0.139369\pi$
$17$			3.47954e8i			0.847968i	−0.905670	+	0.423984i	$0.860631\pi$
$18$		0			0
$19$	1.79868e7			0.0201223			0.0100612	−	0.999949i	$-0.496797\pi$
$19$	1.79868e7			0.0201223			0.0100612	+	0.999949i	$0.496797\pi$
$20$	−3.56156e9	+	2.05627e9i	−2.78247	+	1.60646i
$21$		0			0
$22$	−3.32258e9	+	5.75488e9i	−1.33204	+	2.30716i
$23$	−1.21799e9	−	7.03208e8i	−0.357725	−	0.206533i	0.310357	−	0.950620i	$-0.399551\pi$
$23$	−1.21799e9	−	7.03208e8i	−0.357725	−	0.206533i	−0.668082	+	0.744087i	$0.732885\pi$
$24$		0			0
$25$	4.06332e9	+	7.03788e9i	0.665734	+	1.15309i
$26$		−	1.73468e10i		−	2.15976i
$27$		0			0
$28$	1.12558e10			0.834203
$29$	−8.71076e9	+	5.02916e9i	−0.504975	+	0.291548i	−0.730766	−	0.682628i	$-0.760837\pi$
$29$	−8.71076e9	+	5.02916e9i	−0.504975	+	0.291548i	0.225791	+	0.974176i	$0.427503\pi$
$30$		0			0
$31$	6.77264e9	−	1.17306e10i	0.246165	−	0.426370i	−0.716294	−	0.697799i	$-0.754163\pi$
$31$	6.77264e9	−	1.17306e10i	0.246165	−	0.426370i	0.962459	+	0.271429i	$0.0874962\pi$
$32$	1.14941e10	+	6.63613e9i	0.334523	+	0.193137i
$33$		0			0
$34$	−3.92352e10	−	6.79574e10i	−0.747006	−	1.29385i
$35$		−	3.89473e10i		−	0.605343i
$36$		0			0
$37$	4.16724e10			0.438971			0.219486	−	0.975616i	$-0.429562\pi$
$37$	4.16724e10			0.438971			0.219486	+	0.975616i	$0.429562\pi$
$38$	−3.51292e9	+	2.02818e9i	−0.0307032	+	0.0177265i
$39$		0			0
$40$	2.43346e11	−	4.21487e11i	1.48526	−	2.57255i
$41$	2.44149e11	+	1.40960e11i	1.25363	+	0.723782i	0.971828	−	0.235692i	$-0.0757357\pi$
$41$	2.44149e11	+	1.40960e11i	1.25363	+	0.723782i	0.281799	+	0.959474i	$0.409069\pi$
$42$		0			0
$43$	1.29317e9	+	2.23983e9i	0.00475746	+	0.00824016i	0.868394	−	0.495874i	$-0.165152\pi$
$43$	1.29317e9	+	2.23983e9i	0.00475746	+	0.00824016i	−0.863637	+	0.504114i	$0.831819\pi$
$44$		−	1.01584e12i		−	3.18169i
$45$		0			0
$46$	3.17174e11			0.727768
$47$	3.91113e11	−	2.25809e11i	0.772001	−	0.445715i	−0.0615871	−	0.998102i	$-0.519616\pi$
$47$	3.91113e11	−	2.25809e11i	0.772001	−	0.445715i	0.833588	+	0.552387i	$0.186283\pi$
$48$		0			0
$49$	2.85813e11	−	4.95043e11i	0.421414	−	0.729911i
$50$	−1.58718e12	−	9.16358e11i	−2.03159	−	1.17294i
$51$		0			0
$52$	1.32590e12	+	2.29653e12i	1.28970	+	2.23382i
$53$			1.74490e12i			1.48538i	0.669633	+	0.742692i	$0.266451\pi$
$53$			1.74490e12i			1.48538i	−0.669633	+	0.742692i	$0.733549\pi$
$54$		0			0
$55$	−3.51500e12			−2.30880
$56$	−1.15359e12	+	6.66027e11i	−0.667938	+	0.385634i
$57$		0			0
$58$	1.13417e12	−	1.96445e12i	0.513669	−	0.889702i
$59$	−3.57141e12	−	2.06195e12i	−1.43508	−	0.828542i	−0.437575	−	0.899182i	$-0.644163\pi$
$59$	−3.57141e12	−	2.06195e12i	−1.43508	−	0.828542i	−0.997502	+	0.0706396i	$0.977496\pi$
$60$		0			0
$61$	−8.17270e11	−	1.41555e12i	−0.260050	−	0.450420i	0.706205	−	0.708007i	$-0.250406\pi$
$61$	−8.17270e11	−	1.41555e12i	−0.260050	−	0.450420i	−0.966255	+	0.257588i	$0.917072\pi$
$62$			3.05473e12i			0.867422i
$63$		0			0
$64$	2.82736e12			0.642868
$65$	7.94640e12	−	4.58786e12i	1.62098	−	0.935872i
$66$		0			0
$67$	1.15275e12	−	1.99661e12i	0.190200	−	0.329436i	−0.755117	−	0.655591i	$-0.772420\pi$
$67$	1.15275e12	−	1.99661e12i	0.190200	−	0.329436i	0.945316	+	0.326155i	$0.105753\pi$
$68$	1.03886e13	+	5.99787e12i	1.54524	+	0.892144i
$69$		0			0
$70$	4.39169e12	+	7.60663e12i	0.533268	+	0.923647i
$71$		−	8.75750e12i		−	0.962879i	−0.876479	−	0.481440i	$-0.840114\pi$
$71$		−	8.75750e12i		−	0.962879i	0.876479	−	0.481440i	$-0.159886\pi$
$72$		0			0
$73$	−1.12442e13			−1.01782			−0.508908	−	0.860821i	$-0.669951\pi$
$73$	−1.12442e13			−1.01782			−0.508908	+	0.860821i	$0.669951\pi$
$74$	−8.13885e12	+	4.69897e12i	−0.669794	+	0.386705i
$75$		0			0
$76$	3.10048e11	−	5.37019e11i	0.0211706	−	0.0366686i
$77$	8.33152e12	+	4.81021e12i	0.519146	+	0.299729i
$78$		0			0
$79$	−5.16374e11	−	8.94386e11i	−0.0268890	−	0.0465731i	0.852268	−	0.523106i	$-0.175227\pi$
$79$	−5.16374e11	−	8.94386e11i	−0.0268890	−	0.0465731i	−0.879157	+	0.476533i	$0.841893\pi$
$80$			4.23786e13i			2.02077i
$81$		0			0
$82$	−6.35783e13			−2.55042
$83$	−8.74183e12	+	5.04710e12i	−0.322148	+	0.185992i	−0.652350	−	0.757918i	$-0.726217\pi$
$83$	−8.74183e12	+	5.04710e12i	−0.322148	+	0.185992i	0.330201	+	0.943910i	$0.392883\pi$
$84$		0			0
$85$	2.07538e13	−	3.59466e13i	0.647388	−	1.12131i
$86$	−5.05125e11	−	2.91634e11i	−0.0145181	−	0.00838203i
$87$		0			0
$88$	6.01091e13	+	1.04112e14i	1.47083	+	2.54754i
$89$		−	5.62078e13i		−	1.27077i	−0.772196	−	0.635384i	$-0.780842\pi$
$89$		−	5.62078e13i		−	1.27077i	0.772196	−	0.635384i	$-0.219158\pi$
$90$		0			0
$91$	−2.51135e13			−0.485980
$92$	−4.19904e13	+	2.42432e13i	−0.752722	+	0.434585i
$93$		0			0
$94$	−5.09245e13	+	8.82037e13i	−0.785292	+	1.36017i
$95$	−1.85818e12	−	1.07282e12i	−0.0266087	−	0.0153625i
$96$		0			0
$97$	−5.37337e13	−	9.30695e13i	−0.665035	−	1.15187i	−0.979276	−	0.202531i	$-0.935083\pi$
$97$	−5.37337e13	−	9.30695e13i	−0.665035	−	1.15187i	0.314241	−	0.949343i	$-0.398250\pi$
$98$			1.28913e14i			1.48496i
$99$		0			0
$100$	2.80167e14			2.80167
$101$	4.76606e13	−	2.75169e13i	0.444539	−	0.256655i	−0.260982	−	0.965344i	$-0.584046\pi$
$101$	4.76606e13	−	2.75169e13i	0.444539	−	0.256655i	0.705521	+	0.708689i	$0.250713\pi$
$102$		0			0
$103$	−7.88824e12	+	1.36628e13i	−0.0641386	+	0.111091i	−0.896312	−	0.443425i	$-0.853763\pi$
$103$	−7.88824e12	+	1.36628e13i	−0.0641386	+	0.111091i	0.832173	+	0.554516i	$0.187097\pi$
$104$	−2.71778e14	−	1.56911e14i	−2.06529	−	1.19240i
$105$		0			0
$106$	−1.96754e14	−	3.40788e14i	−1.30853	−	2.26644i
$107$		−	1.14144e14i		−	0.710832i	−0.934708	−	0.355416i	$-0.884339\pi$
$107$		−	1.14144e14i		−	0.710832i	0.934708	−	0.355416i	$-0.115661\pi$
$108$		0			0
$109$	−9.59637e13			−0.524954			−0.262477	−	0.964938i	$-0.584539\pi$
$109$	−9.59637e13			−0.524954			−0.262477	+	0.964938i	$0.584539\pi$
$110$	6.86500e14	−	3.96351e14i	3.52283	−	2.03391i
$111$		0			0
$112$	5.79942e13	−	1.00449e14i	0.262336	−	0.454380i
$113$	−1.83781e14	−	1.06106e14i	−0.781179	−	0.451014i	0.0556691	−	0.998449i	$-0.482271\pi$
$113$	−1.83781e14	−	1.06106e14i	−0.781179	−	0.451014i	−0.836848	+	0.547435i	$0.815604\pi$
$114$		0			0
$115$	8.38858e13	+	1.45294e14i	0.315358	+	0.546216i
$116$			3.46761e14i			1.22694i
$117$		0			0
$118$	9.30021e14			2.91957
$119$	−9.83842e13	+	5.68022e13i	−0.291137	+	0.168088i
$120$		0			0
$121$	2.44247e14	−	4.23049e14i	0.643180	−	1.11402i
$122$	3.19235e14	+	1.84310e14i	0.793581	+	0.458174i
$123$		0			0
$124$	−2.33487e14	−	4.04412e14i	−0.517978	−	0.897165i
$125$		−	2.41339e14i		−	0.506124i
$126$		0			0
$127$	−4.79615e14			−0.900050			−0.450025	−	0.893016i	$-0.648585\pi$
$127$	−4.79615e14			−0.900050			−0.450025	+	0.893016i	$0.648585\pi$
$128$	−7.40520e14	+	4.27539e14i	−1.31543	+	0.759462i
$129$		0			0
$130$	−1.03465e15	+	1.79207e15i	−1.64889	+	2.85596i
$131$	−5.75621e14	−	3.32335e14i	−0.869436	−	0.501969i	−0.00227534	−	0.999997i	$-0.500724\pi$
$131$	−5.75621e14	−	3.32335e14i	−0.869436	−	0.501969i	−0.867161	+	0.498028i	$0.834058\pi$
$132$		0			0
$133$	2.93627e12	+	5.08577e12i	0.00398873	+	0.00690868i
$134$			5.19933e14i			0.670215i
$135$		0			0
$136$	−1.41962e15			−1.64968
$137$	−3.95132e13	+	2.28130e13i	−0.0436213	+	0.0251848i	−0.521652	−	0.853158i	$-0.674684\pi$
$137$	−3.95132e13	+	2.28130e13i	−0.0436213	+	0.0251848i	0.478031	+	0.878343i	$0.341351\pi$
$138$		0			0
$139$	−2.16373e14	+	3.74770e14i	−0.215824	+	0.373818i	−0.953527	−	0.301307i	$-0.902577\pi$
$139$	−2.16373e14	+	3.74770e14i	−0.215824	+	0.373818i	0.737703	+	0.675125i	$0.235910\pi$
$140$	−1.16282e15	−	6.71356e14i	−1.10311	−	0.636879i
$141$		0			0
$142$	9.87494e14	+	1.71039e15i	0.848235	+	1.46919i
$143$			2.26650e15i			1.85355i
$144$		0			0
$145$	1.19986e15			0.890337
$146$	2.19606e15	−	1.26789e15i	1.55301	−	0.896630i
$147$		0			0
$148$	7.18329e14	−	1.24418e15i	0.461840	−	0.799930i
$149$	2.39632e15	+	1.38351e15i	1.46974	+	0.848555i	0.999424	−	0.0339428i	$-0.0108064\pi$
$149$	2.39632e15	+	1.38351e15i	1.46974	+	0.848555i	0.470317	+	0.882498i	$0.344140\pi$
$150$		0			0
$151$	−5.90234e13	−	1.02232e14i	−0.0329751	−	0.0571145i	0.849067	−	0.528285i	$-0.177165\pi$
$151$	−5.90234e13	−	1.02232e14i	−0.0329751	−	0.0571145i	−0.882042	+	0.471171i	$0.843832\pi$
$152$			7.33841e13i			0.0391469i
$153$		0			0
$154$	−2.16959e15			−1.05617
$155$	−1.39934e15	+	8.07910e14i	−0.651031	+	0.375873i
$156$		0			0
$157$	1.45515e15	−	2.52039e15i	0.618884	−	1.07194i	−0.370805	−	0.928711i	$-0.620918\pi$
$157$	1.45515e15	−	2.52039e15i	0.618884	−	1.07194i	0.989690	−	0.143228i	$-0.0457483\pi$
$158$	2.01701e14	+	1.16452e14i	0.0820558	+	0.0473750i
$159$		0			0
$160$	−7.91625e14	−	1.37113e15i	−0.294903	−	0.510788i
$161$		−	4.59184e14i		−	0.163759i
$162$		0			0
$163$	−1.66748e15			−0.545441			−0.272720	−	0.962093i	$-0.587923\pi$
$163$	−1.66748e15			−0.545441			−0.272720	+	0.962093i	$0.587923\pi$
$164$	8.41706e15	−	4.85959e15i	2.63787	−	1.52298i
$165$		0			0
$166$	1.13822e15	−	1.97145e15i	0.327695	−	0.567584i
$167$	−4.80709e15	−	2.77538e15i	−1.32699	−	0.766137i	−0.342155	−	0.939643i	$-0.611157\pi$
$167$	−4.80709e15	−	2.77538e15i	−1.32699	−	0.766137i	−0.984833	+	0.173506i	$0.944490\pi$
$168$		0			0
$169$	−9.89600e14	−	1.71404e15i	−0.251335	−	0.435325i
$170$			9.36076e15i			2.28123i
$171$		0			0
$172$	8.91640e13			0.0200212
$173$	−6.42000e15	+	3.70659e15i	−1.38424	+	0.799193i	−0.992659	−	0.120949i	$-0.961406\pi$
$173$	−6.42000e15	+	3.70659e15i	−1.38424	+	0.799193i	−0.391585	+	0.920142i	$0.628073\pi$
$174$		0			0
$175$	−1.32664e15	+	2.29781e15i	−0.263929	+	0.457139i
$176$	−9.06553e15	−	5.23399e15i	−1.73302	−	1.00056i
$177$		0			0
$178$	6.33798e15	+	1.09777e16i	1.11947	+	1.93897i
$179$		−	6.42965e15i		−	1.09198i	−0.837791	−	0.545992i	$-0.816153\pi$
$179$		−	6.42965e15i		−	1.09198i	0.837791	−	0.545992i	$-0.183847\pi$
$180$		0			0
$181$	2.89701e15			0.455198			0.227599	−	0.973755i	$-0.426912\pi$
$181$	2.89701e15			0.455198			0.227599	+	0.973755i	$0.426912\pi$
$182$	4.90482e15	−	2.83180e15i	0.741521	−	0.428117i
$183$		0			0
$184$	2.86901e15	−	4.96928e15i	0.401798	−	0.695935i
$185$	−4.30510e15	−	2.48555e15i	−0.580472	−	0.335136i
$186$		0			0
$187$	5.12641e15	+	8.87920e15i	0.641094	+	1.11041i
$188$		−	1.55696e16i		−	1.87574i
$189$		0			0
$190$	4.83885e14			0.0541336
$191$	1.13009e15	−	6.52459e14i	0.121865	−	0.0703589i	−0.437828	−	0.899059i	$-0.644252\pi$
$191$	1.13009e15	−	6.52459e14i	0.121865	−	0.0703589i	0.559694	+	0.828700i	$0.310919\pi$
$192$		0			0
$193$	2.74464e15	−	4.75385e15i	0.275159	−	0.476590i	−0.695016	−	0.718994i	$-0.744603\pi$
$193$	2.74464e15	−	4.75385e15i	0.275159	−	0.476590i	0.970175	+	0.242404i	$0.0779361\pi$
$194$	2.09890e16	+	1.21180e16i	2.02945	+	1.17171i
$195$		0			0
$196$	−9.85343e15	−	1.70666e16i	−0.886737	−	1.53587i
$197$			6.69322e14i			0.0581261i	0.999578	+	0.0290631i	$0.00925236\pi$
$197$			6.69322e14i			0.0581261i	−0.999578	+	0.0290631i	$0.990748\pi$
$198$		0			0
$199$	−1.20978e16			−0.978893			−0.489447	−	0.872033i	$-0.662801\pi$
$199$	−1.20978e16			−0.978893			−0.489447	+	0.872033i	$0.662801\pi$
$200$	−2.87138e16	+	1.65779e16i	−2.24326	+	1.29515i
$201$		0			0
$202$	−6.20559e15	+	1.07484e16i	−0.452193	+	0.783221i
$203$	−2.84400e15	−	1.64198e15i	−0.200197	−	0.115584i
$204$		0			0
$205$	−1.68151e16	−	2.91246e16i	−1.10515	−	1.91418i
$206$		−	3.55790e15i		−	0.226008i
$207$		0			0
$208$	2.73261e16			1.62231
$209$	4.58992e14	−	2.64999e14i	0.0263500	−	0.0152132i
$210$		0			0
$211$	1.83193e16	−	3.17300e16i	0.983857	−	1.70409i	0.336948	−	0.941523i	$-0.390605\pi$
$211$	1.83193e16	−	3.17300e16i	0.983857	−	1.70409i	0.646909	−	0.762567i	$-0.276061\pi$
$212$	5.20962e16	+	3.00777e16i	2.70679	+	1.56277i
$213$		0			0
$214$	1.28709e16	+	2.22930e16i	0.626198	+	1.08461i
$215$		−	3.08524e14i		−	0.0145285i
$216$		0			0
$217$	4.42243e15			0.195183
$218$	1.87422e16	−	1.08208e16i	0.800988	−	0.462451i
$219$		0			0
$220$	−6.05900e16	+	1.04945e17i	−2.42908	+	4.20730i
$221$	−2.31786e16	−	1.33822e16i	−0.900206	−	0.519734i
$222$		0			0
$223$	−1.16994e16	−	2.02639e16i	−0.426608	−	0.738906i	0.569961	−	0.821671i	$-0.306958\pi$
$223$	−1.16994e16	−	2.02639e16i	−0.426608	−	0.738906i	−0.996569	+	0.0827653i	$0.973625\pi$
$224$			4.33329e15i			0.153137i
$225$		0			0
$226$	4.78579e16			1.58926
$227$	4.30758e16	−	2.48698e16i	1.38692	−	0.800740i	0.393955	−	0.919130i	$-0.371107\pi$
$227$	4.30758e16	−	2.48698e16i	1.38692	−	0.800740i	0.992967	+	0.118390i	$0.0377733\pi$
$228$		0			0
$229$	−9.31885e15	+	1.61407e16i	−0.282172	+	0.488736i	−0.971919	−	0.235314i	$-0.924388\pi$
$229$	−9.31885e15	+	1.61407e16i	−0.282172	+	0.488736i	0.689747	+	0.724050i	$0.257722\pi$
$230$	−3.27668e16	−	1.89179e16i	−0.962362	−	0.555620i
$231$		0			0
$232$	−2.05184e16	−	3.55390e16i	−0.567190	−	0.982402i
$233$		−	1.10854e16i		−	0.297345i	−0.988886	−	0.148672i	$-0.952500\pi$
$233$		−	1.10854e16i		−	0.297345i	0.988886	−	0.148672i	$-0.0475000\pi$
$234$		0			0
$235$	−5.38737e16			−1.36114
$236$	−1.23125e17	+	7.10860e16i	−3.01968	+	1.74341i
$237$		0			0
$238$	1.28100e16	−	2.21876e16i	0.296149	−	0.512945i
$239$	1.63305e16	+	9.42841e15i	0.366618	+	0.211667i	0.671980	−	0.740569i	$-0.265444\pi$
$239$	1.63305e16	+	9.42841e15i	0.366618	+	0.211667i	−0.305362	+	0.952236i	$0.598777\pi$
$240$		0			0
$241$	3.48644e16	+	6.03870e16i	0.738352	+	1.27886i	0.953237	+	0.302224i	$0.0977290\pi$
$241$	3.48644e16	+	6.03870e16i	0.738352	+	1.27886i	−0.214885	+	0.976639i	$0.568938\pi$
$242$			1.10165e17i			2.26640i
$243$		0			0
$244$	−5.63509e16			−1.09439
$245$	−5.90537e16	+	3.40947e16i	−1.11451	+	0.643464i
$246$		0			0
$247$	−6.91765e14	+	1.19817e15i	−0.0123333	+	0.0213619i
$248$	4.78594e16	+	2.76317e16i	0.829480	+	0.478901i
$249$		0			0
$250$	2.72133e16	+	4.71348e16i	0.445863	+	0.772257i
$251$		−	6.39458e16i		−	1.01882i	−0.860525	−	0.509408i	$-0.829864\pi$
$251$		−	6.39458e16i		−	1.01882i	0.860525	−	0.509408i	$-0.170136\pi$
$252$		0			0
$253$	−4.14414e16			−0.624584
$254$	9.36715e16	−	5.40813e16i	1.37332	−	0.792886i
$255$		0			0
$256$	7.32567e16	−	1.26884e17i	1.01664	−	1.76087i
$257$	−1.93005e16	−	1.11431e16i	−0.260637	−	0.150479i	0.363988	−	0.931404i	$-0.381415\pi$
$257$	−1.93005e16	−	1.11431e16i	−0.260637	−	0.150479i	−0.624625	+	0.780925i	$0.714748\pi$
$258$		0			0
$259$	6.80285e15	+	1.17829e16i	0.0870147	+	0.150714i
$260$		−	3.16334e17i		−	3.93851i
$261$		0			0
$262$	1.49896e17			1.76881
$263$	3.33508e16	−	1.92551e16i	0.383191	−	0.221236i	−0.296015	−	0.955183i	$-0.595658\pi$
$263$	3.33508e16	−	1.92551e16i	0.383191	−	0.221236i	0.679206	+	0.733948i	$0.262324\pi$
$264$		0			0
$265$	1.04075e17	−	1.80262e17i	1.13403	−	1.96419i
$266$	−1.14694e15	−	6.62187e14i	−0.0121722	−	0.00702763i
$267$		0			0
$268$	−3.97410e16	−	6.88334e16i	−0.400217	−	0.693196i
$269$			7.62726e16i			0.748347i	0.927359	+	0.374173i	$0.122073\pi$
$269$			7.62726e16i			0.748347i	−0.927359	+	0.374173i	$0.877927\pi$
$270$		0			0
$271$	−1.49067e17			−1.38866			−0.694330	−	0.719657i	$-0.744299\pi$
$271$	−1.49067e17			−1.38866			−0.694330	+	0.719657i	$0.744299\pi$
$272$	1.07052e17	−	6.18064e16i	0.971879	−	0.561114i
$273$		0			0
$274$	5.14477e15	−	8.91101e15i	0.0443723	−	0.0768551i
$275$	2.07378e17	+	1.19730e17i	1.74355	+	1.00664i
$276$		0			0
$277$	1.21604e17	+	2.10624e17i	0.971827	+	1.68325i	0.690031	+	0.723780i	$0.257597\pi$
$277$	1.21604e17	+	2.10624e17i	0.971827	+	1.68325i	0.281796	+	0.959474i	$0.409070\pi$
$278$		−	9.75928e16i		−	0.760509i
$279$		0			0
$280$	1.58901e17			1.17766
$281$	−1.72947e17	+	9.98511e16i	−1.25017	+	0.721786i	−0.971143	−	0.238497i	$-0.923345\pi$
$281$	−1.72947e17	+	9.98511e16i	−1.25017	+	0.721786i	−0.279027	+	0.960283i	$0.590012\pi$
$282$		0			0
$283$	−7.68288e15	+	1.33071e16i	−0.0528469	+	0.0915335i	−0.891239	−	0.453535i	$-0.850163\pi$
$283$	−7.68288e15	+	1.33071e16i	−0.0528469	+	0.0915335i	0.838392	+	0.545068i	$0.183496\pi$
$284$	−2.61467e17	−	1.50958e17i	−1.75464	−	1.01304i
$285$		0			0
$286$	−2.55570e17	−	4.42661e17i	−1.63286	−	2.82819i
$287$			9.20444e16i			0.573884i
$288$		0			0
$289$	4.73057e16			0.280950
$290$	−2.34339e17	+	1.35296e17i	−1.35850	+	0.784329i
$291$		0			0
$292$	−1.93823e17	+	3.35710e17i	−1.07084	+	1.85475i
$293$	6.23149e16	+	3.59775e16i	0.336139	+	0.194070i	0.658563	−	0.752525i	$-0.271165\pi$
$293$	6.23149e16	+	3.59775e16i	0.336139	+	0.194070i	−0.322425	+	0.946595i	$0.604498\pi$
$294$		0			0
$295$	2.45971e17	+	4.26034e17i	1.26511	+	2.19124i
$296$			1.70019e17i			0.853994i
$297$		0			0
$298$	−6.24019e17			−2.99009
$299$	9.36871e16	−	5.40902e16i	0.438512	−	0.253175i
$300$		0			0
$301$	−4.22208e14	+	7.31286e14i	−0.00188609	+	0.00326680i
$302$	2.30552e16	+	1.33109e16i	0.100628	+	0.0580978i
$303$		0			0
$304$	−3.19496e15	−	5.53383e15i	−0.0133153	−	0.0230627i
$305$			1.94985e17i			0.794148i
$306$		0			0
$307$	4.06801e17			1.58275			0.791376	−	0.611329i	$-0.209365\pi$
$307$	4.06801e17			1.58275			0.791376	+	0.611329i	$0.209365\pi$
$308$	2.87230e17	−	1.65832e17i	1.09238	−	0.630687i
$309$		0			0
$310$	1.82200e17	−	3.15579e17i	0.662240	−	1.14703i
$311$	−3.50740e17	−	2.02500e17i	−1.24641	−	0.719618i	−0.276022	−	0.961151i	$-0.589016\pi$
$311$	−3.50740e17	−	2.02500e17i	−1.24641	−	0.719618i	−0.970393	+	0.241533i	$0.922350\pi$
$312$		0			0
$313$	1.13584e17	+	1.96734e17i	0.385929	+	0.668449i	0.991898	−	0.127040i	$-0.0405476\pi$
$313$	1.13584e17	+	1.96734e17i	0.385929	+	0.668449i	−0.605968	+	0.795489i	$0.707214\pi$
$314$			6.56328e17i			2.18079i
$315$		0			0
$316$	−3.56041e16			−0.113159
$317$	3.51492e17	−	2.02934e17i	1.09270	−	0.630869i	0.158404	−	0.987374i	$-0.449365\pi$
$317$	3.51492e17	−	2.02934e17i	1.09270	−	0.630869i	0.934293	+	0.356505i	$0.116032\pi$
$318$		0			0
$319$	−1.48189e17	+	2.56671e17i	−0.440841	+	0.763558i
$320$	−2.92090e17	−	1.68638e17i	−0.850095	−	0.490802i
$321$		0			0
$322$	5.17775e16	+	8.96812e16i	0.144261	+	0.249868i
$323$			6.25857e15i			0.0170631i
$324$		0			0
$325$	−6.25095e17			−1.63216
$326$	3.25668e17	−	1.88025e17i	0.832247	−	0.480498i
$327$		0			0
$328$	−5.75100e17	+	9.96102e17i	−1.40808	+	2.43886i
$329$	1.27695e17	+	7.37250e16i	0.306058	+	0.176703i
$330$		0			0
$331$	−4.07010e17	−	7.04962e17i	−0.934995	−	1.61946i	−0.774643	−	0.632399i	$-0.782070\pi$
$331$	−4.07010e17	−	7.04962e17i	−0.934995	−	1.61946i	−0.160352	−	0.987060i	$-0.551263\pi$
$332$			3.47998e17i			0.782727i
$333$		0			0
$334$	1.25180e18			2.69967
$335$	−2.38177e17	+	1.37511e17i	−0.503020	+	0.290419i
$336$		0			0
$337$	1.41935e17	−	2.45839e17i	0.287529	−	0.498015i	−0.685690	−	0.727893i	$-0.740500\pi$
$337$	1.41935e17	−	2.45839e17i	0.287529	−	0.498015i	0.973219	+	0.229879i	$0.0738330\pi$
$338$	3.86549e17	+	2.23174e17i	0.766987	+	0.442820i
$339$		0			0
$340$	−7.15488e17	−	1.23926e18i	−1.36223	−	2.35945i
$341$		−	3.99125e17i		−	0.744438i
$342$		0			0
$343$	4.08066e17			0.730586
$344$	−9.13826e15	+	5.27598e15i	−0.0160308	+	0.00925537i
$345$		0			0
$346$	8.35909e17	−	1.44784e18i	1.40808	−	2.43886i
$347$	6.01786e17	+	3.47441e17i	0.993426	+	0.573555i	0.906297	−	0.422642i	$-0.138897\pi$
$347$	6.01786e17	+	3.47441e17i	0.993426	+	0.573555i	0.0871295	+	0.996197i	$0.472231\pi$
$348$		0			0
$349$	6.07877e16	+	1.05287e17i	0.0963912	+	0.166955i	0.910188	−	0.414195i	$-0.135937\pi$
$349$	6.07877e16	+	1.05287e17i	0.0963912	+	0.166955i	−0.813797	+	0.581149i	$0.802603\pi$
$350$		−	5.98368e17i		−	0.930019i
$351$		0			0
$352$	3.91080e17			0.584073
$353$	4.47436e17	−	2.58327e17i	0.655100	−	0.378222i	−0.135307	−	0.990804i	$-0.543202\pi$
$353$	4.47436e17	−	2.58327e17i	0.655100	−	0.378222i	0.790407	+	0.612581i	$0.209869\pi$
$354$		0			0
$355$	−5.22342e17	+	9.04723e17i	−0.735117	+	1.27326i
$356$	−1.67816e18	−	9.68884e17i	−2.31570	−	1.33697i
$357$		0			0
$358$	7.25006e17	+	1.25575e18i	0.961967	+	1.66618i
$359$		−	5.70293e17i		−	0.742057i	−0.928622	−	0.371028i	$-0.879005\pi$
$359$		−	5.70293e17i		−	0.742057i	0.928622	−	0.371028i	$-0.120995\pi$
$360$		0			0
$361$	−7.98683e17			−0.999595
$362$	−5.65803e17	+	3.26667e17i	−0.694553	+	0.401001i
$363$		0			0
$364$	−4.32896e17	+	7.49798e17i	−0.511298	+	0.885593i
$365$	1.16162e18	+	6.70662e17i	1.34590	+	0.777058i
$366$		0			0
$367$	−2.36841e17	−	4.10220e17i	−0.264115	−	0.457461i	0.703216	−	0.710976i	$-0.251747\pi$
$367$	−2.36841e17	−	4.10220e17i	−0.264115	−	0.457461i	−0.967331	+	0.253515i	$0.918413\pi$
$368$			4.99638e17i			0.546664i
$369$		0			0
$370$	1.12108e18			1.18093
$371$	−4.93371e17	+	2.84848e17i	−0.509983	+	0.294439i
$372$		0			0
$373$	5.72914e17	−	9.92316e17i	0.570332	−	0.987843i	−0.426200	−	0.904629i	$-0.640148\pi$
$373$	5.72914e17	−	9.92316e17i	0.570332	−	0.987843i	0.996532	−	0.0832143i	$-0.0265186\pi$
$374$	−2.00243e18	−	1.15611e18i	−1.95640	−	1.12953i
$375$		0			0
$376$	9.21279e17	+	1.59570e18i	0.867114	+	1.50189i
$377$		−	7.73679e17i		−	0.714778i
$378$		0			0
$379$	−9.57846e16			−0.0852749			−0.0426374	−	0.999091i	$-0.513576\pi$
$379$	−9.57846e16			−0.0852749			−0.0426374	+	0.999091i	$0.513576\pi$
$380$	−6.40611e16	+	3.69857e16i	−0.0559898	+	0.0323257i
$381$		0			0
$382$	−1.47142e17	+	2.54858e17i	−0.123963	+	0.214711i
$383$	−7.70880e17	−	4.45068e17i	−0.637669	−	0.368158i	0.146047	−	0.989278i	$-0.453345\pi$
$383$	−7.70880e17	−	4.45068e17i	−0.637669	−	0.368158i	−0.783716	+	0.621119i	$0.786678\pi$
$384$		0			0
$385$	−5.73811e17	−	9.93869e17i	−0.457661	−	0.792691i
$386$			1.23794e18i			0.969591i
$387$		0			0
$388$	−3.70495e18			−2.79872
$389$	−6.37685e17	+	3.68167e17i	−0.473106	+	0.273148i	−0.717539	−	0.696518i	$-0.754732\pi$
$389$	−6.37685e17	+	3.68167e17i	−0.473106	+	0.273148i	0.244433	+	0.969666i	$0.421398\pi$
$390$		0			0
$391$	2.44684e17	−	4.23805e17i	0.175133	−	0.303340i
$392$	2.01972e18	+	1.16609e18i	1.42000	+	0.819839i
$393$		0			0
$394$	−7.54726e16	−	1.30722e17i	−0.0512054	−	0.0886903i
$395$			1.23197e17i			0.0821144i
$396$		0			0
$397$	6.60321e17			0.424836			0.212418	−	0.977179i	$-0.431866\pi$
$397$	6.60321e17			0.424836			0.212418	+	0.977179i	$0.431866\pi$
$398$	2.36277e18	−	1.36415e18i	1.49362	−	0.862342i
$399$		0			0
$400$	1.44352e18	−	2.50025e18i	0.881054	−	1.52603i
$401$	−8.78035e17	−	5.06934e17i	−0.526625	−	0.304047i	0.213016	−	0.977049i	$-0.431671\pi$
$401$	−8.78035e17	−	5.06934e17i	−0.526625	−	0.304047i	−0.739641	+	0.673002i	$0.765005\pi$
$402$		0			0
$403$	5.20947e17	+	9.02306e17i	0.301758	+	0.522659i
$404$		−	1.89729e18i		−	1.08010i
$405$		0			0
$406$	7.40598e17			0.407287
$407$	1.06341e18	−	6.13959e17i	0.574829	−	0.331878i
$408$		0			0
$409$	3.56261e17	−	6.17062e17i	0.186082	−	0.322304i	−0.757858	−	0.652419i	$-0.773754\pi$
$409$	3.56261e17	−	6.17062e17i	0.186082	−	0.322304i	0.943941	+	0.330115i	$0.107088\pi$
$410$	6.56817e18	+	3.79213e18i	3.37254	+	1.94714i
$411$		0			0
$412$	2.71948e17	+	4.71027e17i	0.134960	+	0.233757i
$413$		−	1.34642e18i		−	0.656948i
$414$		0			0
$415$	1.20414e18			0.567989
$416$	−8.84119e17	+	5.10446e17i	−0.410069	+	0.236754i
$417$		0			0
$418$	−5.97625e16	+	1.03512e17i	−0.0268037	+	0.0464254i
$419$	−1.65428e18	−	9.55098e17i	−0.729643	−	0.421260i	0.0886486	−	0.996063i	$-0.471745\pi$
$419$	−1.65428e18	−	9.55098e17i	−0.729643	−	0.421260i	−0.818292	+	0.574803i	$0.805079\pi$
$420$		0			0
$421$	1.81139e18	+	3.13741e18i	0.772745	+	1.33843i	0.936053	+	0.351858i	$0.114450\pi$
$421$	1.81139e18	+	3.13741e18i	0.772745	+	1.33843i	−0.163308	+	0.986575i	$0.552217\pi$
$422$			8.26273e18i			3.46686i
$423$		0			0
$424$	−7.11900e18			−2.88973
$425$	−2.44886e18	+	1.41385e18i	−0.977780	+	0.564521i
$426$		0			0
$427$	2.66832e17	−	4.62167e17i	0.103096	−	0.178568i
$428$	−3.40792e18	−	1.96756e18i	−1.29534	−	0.747864i
$429$		0			0
$430$	3.47891e16	+	6.02565e16i	0.0127986	+	0.0221679i
$431$			3.56102e18i			1.28894i	0.764628	+	0.644472i	$0.222923\pi$
$431$			3.56102e18i			1.28894i	−0.764628	+	0.644472i	$0.777077\pi$
$432$		0			0
$433$	−3.99698e18			−1.40061			−0.700304	−	0.713845i	$-0.746952\pi$
$433$	−3.99698e18			−1.40061			−0.700304	+	0.713845i	$0.746952\pi$
$434$	−8.63726e17	+	4.98672e17i	−0.297816	+	0.171944i
$435$		0			0
$436$	−1.65418e18	+	2.86512e18i	−0.552302	+	0.956615i
$437$	−2.19077e16	−	1.26484e16i	−0.00719826	−	0.00415592i
$438$		0			0
$439$	−2.79452e18	−	4.84025e18i	−0.889314	−	1.54034i	−0.840687	−	0.541521i	$-0.817849\pi$
$439$	−2.79452e18	−	4.84025e18i	−0.889314	−	1.54034i	−0.0486271	−	0.998817i	$-0.515485\pi$
$440$		−	1.43408e19i		−	4.49165i
$441$		0			0
$442$	6.03589e18			1.83141
$443$	−4.01235e18	+	2.31653e18i	−1.19832	+	0.691850i	−0.960180	−	0.279380i	$-0.909871\pi$
$443$	−4.01235e18	+	2.31653e18i	−1.19832	+	0.691850i	−0.238140	+	0.971231i	$0.576538\pi$
$444$		0			0
$445$	−3.35252e18	+	5.80673e18i	−0.970177	+	1.68040i
$446$	4.56991e18	+	2.63844e18i	1.30186	+	0.751628i
$447$		0			0
$448$	4.61556e17	+	7.99439e17i	0.127432	+	0.220719i
$449$		−	2.27057e18i		−	0.617177i	−0.951196	−	0.308588i	$-0.900143\pi$
$449$		−	2.27057e18i		−	0.617177i	0.951196	−	0.308588i	$-0.0998566\pi$
$450$		0			0
$451$	8.30703e18			2.18882
$452$	−6.33585e18	+	3.65800e18i	−1.64375	+	0.949020i
$453$		0			0
$454$	−5.60863e18	+	9.71443e18i	−1.41080	+	2.44358i
$455$	2.59444e18	+	1.49790e18i	0.642634	+	0.371025i
$456$		0			0
$457$	−1.85245e18	−	3.20854e18i	−0.444973	−	0.770716i	0.553078	−	0.833130i	$-0.313453\pi$
$457$	−1.85245e18	−	3.20854e18i	−0.444973	−	0.770716i	−0.998050	+	0.0624143i	$0.980120\pi$
$458$		−	4.20317e18i		−	0.994302i
$459$		0			0
$460$	5.78394e18			1.32715
$461$	−3.22510e18	+	1.86201e18i	−0.728848	+	0.420801i	−0.818001	−	0.575217i	$-0.804917\pi$
$461$	−3.22510e18	+	1.86201e18i	−0.728848	+	0.420801i	0.0891526	+	0.996018i	$0.471584\pi$
$462$		0			0
$463$	3.25940e18	−	5.64545e18i	0.714614	−	1.23775i	−0.248495	−	0.968633i	$-0.579936\pi$
$463$	3.25940e18	−	5.64545e18i	0.714614	−	1.23775i	0.963108	−	0.269114i	$-0.0867308\pi$
$464$	3.09455e18	+	1.78664e18i	0.668301	+	0.385844i
$465$		0			0
$466$	1.24999e18	+	2.16504e18i	0.261942	+	0.453697i
$467$		−	4.68367e18i		−	0.966869i	−0.875380	−	0.483435i	$-0.839389\pi$
$467$		−	4.68367e18i		−	0.966869i	0.875380	−	0.483435i	$-0.160611\pi$
$468$		0			0
$469$	7.52725e17			0.150809
$470$	1.05218e19	−	6.07479e18i	2.07686	−	1.19907i
$471$		0			0
$472$	8.41255e18	−	1.45710e19i	1.61188	−	2.79186i
$473$	6.59987e16	+	3.81044e16i	0.0124597	+	0.00719361i
$474$		0			0
$475$	7.30860e16	+	1.26589e17i	0.0133961	+	0.0232028i
$476$			3.91652e18i			0.707378i
$477$		0			0
$478$	−4.25258e18			−0.745860
$479$	2.56355e18	−	1.48007e18i	0.443092	−	0.255819i	−0.261817	−	0.965118i	$-0.584322\pi$
$479$	2.56355e18	−	1.48007e18i	0.443092	−	0.255819i	0.704908	+	0.709299i	$0.250988\pi$
$480$		0			0
$481$	−1.60270e18	+	2.77596e18i	−0.269053	+	0.466013i
$482$	−1.36184e19	−	7.86262e18i	−2.25319	−	1.30088i
$483$		0			0
$484$	−8.42045e18	−	1.45846e19i	−1.35337	−	2.34411i
$485$			1.28198e19i			2.03090i
$486$		0			0
$487$	6.20013e18			0.954330			0.477165	−	0.878814i	$-0.341664\pi$
$487$	6.20013e18			0.954330			0.477165	+	0.878814i	$0.341664\pi$
$488$	5.77530e18	−	3.33437e18i	0.876266	−	0.505913i
$489$		0			0
$490$	7.68902e18	−	1.33178e19i	1.13370	−	1.96363i
$491$	6.04995e18	+	3.49294e18i	0.879389	+	0.507716i	0.870457	−	0.492244i	$-0.163823\pi$
$491$	6.04995e18	+	3.49294e18i	0.879389	+	0.507716i	0.00893228	+	0.999960i	$0.497157\pi$
$492$		0			0
$493$	−1.74992e18	−	3.03095e18i	−0.247223	−	0.428203i
$494$		−	3.12013e17i		−	0.0434594i
$495$		0			0
$496$	−4.81205e18			−0.651566
$497$	2.47619e18	−	1.42963e18i	0.330589	−	0.190866i
$498$		0			0
$499$	−6.57061e18	+	1.13806e19i	−0.852907	+	1.47728i	0.0256658	+	0.999671i	$0.491829\pi$
$499$	−6.57061e18	+	1.13806e19i	−0.852907	+	1.47728i	−0.878573	+	0.477608i	$0.841504\pi$
$500$	−7.20548e18	−	4.16009e18i	−0.922302	−	0.532491i
$501$		0			0
$502$	7.21051e18	+	1.24890e19i	0.897512	+	1.55454i
$503$		−	1.30311e19i		−	1.59958i	−0.600279	−	0.799791i	$-0.704944\pi$
$503$		−	1.30311e19i		−	1.59958i	0.600279	−	0.799791i	$-0.295056\pi$
$504$		0			0
$505$	−6.56499e18			−0.783780
$506$	8.09375e18	−	4.67293e18i	0.953007	−	0.550219i
$507$		0			0
$508$	−8.26738e18	+	1.43195e19i	−0.946939	+	1.64015i
$509$	−3.96383e18	−	2.28852e18i	−0.447807	−	0.258541i	0.259097	−	0.965851i	$-0.416575\pi$
$509$	−3.96383e18	−	2.28852e18i	−0.447807	−	0.258541i	−0.706903	+	0.707310i	$0.749908\pi$
$510$		0			0
$511$	−1.83557e18	−	3.17931e18i	−0.201756	−	0.349451i
$512$			1.90320e19i			2.06346i
$513$		0			0
$514$	5.02599e18			0.530249
$515$	1.62984e18	−	9.40990e17i	0.169627	−	0.0979342i
$516$		0			0
$517$	6.65370e18	−	1.15245e19i	0.673953	−	1.16732i
$518$	−2.65727e18	−	1.53418e18i	−0.265539	−	0.153309i
$519$		0			0
$520$	1.87180e19	+	3.24205e19i	1.82069	+	3.15352i
$521$		−	1.78294e19i		−	1.71109i	−0.517728	−	0.855545i	$-0.673222\pi$
$521$		−	1.78294e19i		−	1.71109i	0.517728	−	0.855545i	$-0.326778\pi$
$522$		0			0
$523$	−1.62151e18			−0.151498			−0.0757492	−	0.997127i	$-0.524135\pi$
$523$	−1.62151e18			−0.151498			−0.0757492	+	0.997127i	$0.524135\pi$
$524$	−1.98446e19	+	1.14573e19i	−1.82946	+	1.05624i
$525$		0			0
$526$	−4.34240e18	+	7.52125e18i	−0.389789	+	0.675134i
$527$	4.08170e18	+	2.35657e18i	0.361548	+	0.208740i
$528$		0			0
$529$	−4.80742e18	−	8.32669e18i	−0.414688	−	0.718262i
$530$			4.69417e19i			3.99602i
$531$		0			0
$532$	2.02456e17			0.0167861
$533$	−1.87798e19	+	1.08425e19i	−1.53674	+	0.887236i
$534$		0			0
$535$	−6.80814e18	+	1.17920e19i	−0.542690	+	0.939967i
$536$	8.14597e18	+	4.70308e18i	0.640899	+	0.370023i
$537$		0			0
$538$	−8.60049e18	−	1.48965e19i	−0.659245	−	1.14185i
$539$		−	1.68435e19i		−	1.27442i
$540$		0			0
$541$	−3.01853e18			−0.222543			−0.111272	−	0.993790i	$-0.535492\pi$
$541$	−3.01853e18			−0.222543			−0.111272	+	0.993790i	$0.535492\pi$
$542$	2.91136e19	−	1.68087e19i	2.11885	−	1.22332i
$543$		0			0
$544$	−2.30907e18	+	3.99942e18i	−0.163774	+	0.283665i
$545$	9.91385e18	+	5.72376e18i	0.694171	+	0.400780i
$546$		0			0
$547$	−5.68792e18	−	9.85176e18i	−0.388188	−	0.672361i	0.604018	−	0.796971i	$-0.293566\pi$
$547$	−5.68792e18	−	9.85176e18i	−0.388188	−	0.672361i	−0.992206	+	0.124609i	$0.960232\pi$
$548$			1.57296e18i			0.105987i
$549$		0			0
$550$	−5.40028e19			−3.54713
$551$	−1.56678e17	+	9.04584e16i	−0.0101613	+	0.00586661i
$552$		0			0
$553$	1.68592e17	−	2.92010e17i	0.0106601	−	0.0184638i
$554$	−4.74999e19	−	2.74241e19i	−2.96568	−	1.71223i
$555$		0			0
$556$	7.45949e18	+	1.29202e19i	0.454136	+	0.786586i
$557$			2.05977e19i			1.23832i	0.785265	+	0.619160i	$0.212527\pi$
$557$			2.05977e19i			1.23832i	−0.785265	+	0.619160i	$0.787473\pi$
$558$		0			0
$559$	−1.98939e17			−0.0116637
$560$	−1.19826e19	+	6.91814e18i	−0.693799	+	0.400565i
$561$		0			0
$562$	2.25184e19	−	3.90030e19i	1.27169	−	2.20264i
$563$	1.44839e19	+	8.36228e18i	0.807842	+	0.466408i	0.846206	−	0.532856i	$-0.178881\pi$
$563$	1.44839e19	+	8.36228e18i	0.807842	+	0.466408i	−0.0383639	+	0.999264i	$0.512215\pi$
$564$		0			0
$565$	1.26574e19	+	2.19232e19i	0.688660	+	1.19279i
$566$		−	3.46528e18i		−	0.186219i
$567$		0			0
$568$	3.57297e19			1.87323
$569$	2.80623e19	−	1.62018e19i	1.45324	−	0.839028i	0.454575	−	0.890708i	$-0.349791\pi$
$569$	2.80623e19	−	1.62018e19i	1.45324	−	0.839028i	0.998664	+	0.0516804i	$0.0164577\pi$
$570$		0			0
$571$	3.58807e18	−	6.21472e18i	0.181304	−	0.314028i	−0.761021	−	0.648728i	$-0.775301\pi$
$571$	3.58807e18	−	6.21472e18i	0.181304	−	0.314028i	0.942325	+	0.334699i	$0.108635\pi$
$572$	6.76694e19	+	3.90689e19i	3.37769	+	1.95011i
$573$		0			0
$574$	−1.03789e19	−	1.79768e19i	−0.505555	−	0.875647i
$575$		−	1.14294e19i		−	0.549984i
$576$		0			0
$577$	1.53662e19			0.721667			0.360834	−	0.932630i	$-0.382492\pi$
$577$	1.53662e19			0.721667			0.360834	+	0.932630i	$0.382492\pi$
$578$	−9.23908e18	+	5.33418e18i	−0.428681	+	0.247499i
$579$		0			0
$580$	2.06826e19	−	3.58233e19i	0.936720	−	1.62245i
$581$	−2.85414e18	−	1.64784e18i	−0.127715	−	0.0737364i
$582$		0			0
$583$	2.57076e19	+	4.45268e19i	1.12300	+	1.94510i
$584$		−	4.58752e19i		−	1.98010i
$585$		0			0
$586$	−1.62273e19			−0.683852
$587$	8.23102e18	−	4.75218e18i	0.342757	−	0.197891i	−0.318733	−	0.947844i	$-0.603257\pi$
$587$	8.23102e18	−	4.75218e18i	0.342757	−	0.197891i	0.661491	+	0.749953i	$0.269924\pi$
$588$		0			0
$589$	1.21818e17	−	2.10995e17i	0.00495341	−	0.00857956i
$590$	−9.60790e19	−	5.54712e19i	−3.86068	−	2.22897i
$591$		0			0
$592$	−7.40218e18	−	1.28210e19i	−0.290474	−	0.503116i
$593$		−	4.81259e17i		−	0.0186636i	−0.999956	−	0.00933182i	$-0.997030\pi$
$593$		−	4.81259e17i		−	0.0186636i	0.999956	−	0.00933182i	$-0.00297045\pi$
$594$		0			0
$595$	1.35519e19			0.513311
$596$	8.26133e19	−	4.76968e19i	3.09262	−	1.78552i
$597$		0			0
$598$	−1.21984e19	+	2.11283e19i	−0.446062	+	0.772602i
$599$	−4.07021e17	−	2.34994e17i	−0.0147106	−	0.00849315i	0.492627	−	0.870241i	$-0.336037\pi$
$599$	−4.07021e17	−	2.34994e17i	−0.0147106	−	0.00849315i	−0.507337	+	0.861748i	$0.669370\pi$
$600$		0			0
$601$	−1.96883e19	−	3.41012e19i	−0.695164	−	1.20406i	−0.970125	−	0.242604i	$-0.921998\pi$
$601$	−1.96883e19	−	3.41012e19i	−0.695164	−	1.20406i	0.274961	−	0.961455i	$-0.411335\pi$
$602$		−	1.90433e17i		−	0.00664608i
$603$		0			0
$604$	−4.06967e18			−0.138772
$605$	−5.04656e19	+	2.91363e19i	−1.70101	+	0.982081i
$606$		0			0
$607$	−1.77833e19	+	3.08016e19i	−0.585722	+	1.01450i	0.409063	+	0.912506i	$0.365856\pi$
$607$	−1.77833e19	+	3.08016e19i	−0.585722	+	1.01450i	−0.994785	+	0.101994i	$0.967478\pi$
$608$	2.06742e17	+	1.19363e17i	0.00673137	+	0.00388636i
$609$		0			0
$610$	−2.19864e19	−	3.80816e19i	−0.699593	−	1.21173i
$611$			3.47382e19i			1.09275i
$612$		0			0
$613$	−1.21958e19			−0.374962			−0.187481	−	0.982268i	$-0.560032\pi$
$613$	−1.21958e19			−0.374962			−0.187481	+	0.982268i	$0.560032\pi$
$614$	−7.94505e19	+	4.58708e19i	−2.41501	+	1.39430i
$615$		0			0
$616$	−1.96251e19	+	3.39917e19i	−0.583106	+	1.00997i
$617$	4.58698e18	+	2.64829e18i	0.134751	+	0.0777983i	0.565860	−	0.824501i	$-0.308544\pi$
$617$	4.58698e18	+	2.64829e18i	0.134751	+	0.0777983i	−0.431109	+	0.902300i	$0.641878\pi$
$618$		0			0
$619$	1.50766e19	+	2.61134e19i	0.432980	+	0.749944i	0.997128	−	0.0757298i	$-0.0241286\pi$
$619$	1.50766e19	+	2.61134e19i	0.432980	+	0.749944i	−0.564148	+	0.825674i	$0.690795\pi$
$620$			5.57055e19i			1.58182i
$621$		0			0
$622$	9.13354e19			2.53575
$623$	1.58928e19	−	9.17570e18i	0.436298	−	0.251897i
$624$		0			0
$625$	1.04059e19	−	1.80235e19i	0.279330	−	0.483814i
$626$	−4.43673e19	−	2.56155e19i	−1.17772	−	0.679958i
$627$		0			0
$628$	−5.01663e19	−	8.68906e19i	−1.30225	−	2.25557i
$629$			1.45001e19i			0.372234i
$630$		0			0
$631$	4.08708e18			0.102614			0.0513071	−	0.998683i	$-0.483661\pi$
$631$	4.08708e18			0.102614			0.0513071	+	0.998683i	$0.483661\pi$
$632$	3.64900e18	−	2.10675e18i	0.0906054	−	0.0523111i
$633$		0			0
$634$	−4.57655e19	+	7.92682e19i	−1.11151	+	1.92519i
$635$	4.95482e19	+	2.86067e19i	1.19018	+	0.687150i
$636$		0			0
$637$	2.19845e19	+	3.80783e19i	0.516584	+	0.894750i
$638$		−	6.68391e19i		−	1.55341i
$639$		0			0
$640$	1.02003e20			2.31927
$641$	−5.21564e19	+	3.01125e19i	−1.17301	+	0.677237i	−0.954387	−	0.298573i	$-0.903490\pi$
$641$	−5.21564e19	+	3.01125e19i	−1.17301	+	0.677237i	−0.218622	+	0.975810i	$0.570156\pi$
$642$		0			0
$643$	1.27078e19	−	2.20105e19i	0.279636	−	0.484344i	−0.691658	−	0.722225i	$-0.743119\pi$
$643$	1.27078e19	−	2.20105e19i	0.279636	−	0.484344i	0.971294	+	0.237881i	$0.0764528\pi$
$644$	−1.37095e19	−	7.91520e18i	−0.298416	−	0.172290i
$645$		0			0
$646$	−7.05715e17	−	1.22233e18i	−0.0150315	−	0.0260353i
$647$		−	4.01993e19i		−	0.847010i	−0.905894	−	0.423505i	$-0.860800\pi$
$647$		−	4.01993e19i		−	0.847010i	0.905894	−	0.423505i	$-0.139200\pi$
$648$		0			0
$649$	−1.21515e20			−2.50563
$650$	1.22085e20	−	7.04856e19i	2.49039	−	1.43783i
$651$		0			0
$652$	−2.87433e19	+	4.97848e19i	−0.573856	+	0.993948i
$653$	7.34748e19	+	4.24207e19i	1.45126	+	0.837887i	0.998553	−	0.0537713i	$-0.0171242\pi$
$653$	7.34748e19	+	4.24207e19i	1.45126	+	0.837887i	0.452709	+	0.891658i	$0.350458\pi$
$654$		0			0
$655$	3.96443e19	+	6.86660e19i	0.766464	+	1.32755i
$656$		−	1.00154e20i		−	1.91575i
$657$		0			0
$658$	−3.32529e19			−0.622656
$659$	2.98496e19	−	1.72337e19i	0.553020	−	0.319286i	−0.197319	−	0.980339i	$-0.563224\pi$
$659$	2.98496e19	−	1.72337e19i	0.553020	−	0.319286i	0.750339	+	0.661053i	$0.229890\pi$
$660$		0			0
$661$	3.66421e19	−	6.34659e19i	0.664614	−	1.15115i	−0.314775	−	0.949166i	$-0.601929\pi$
$661$	3.66421e19	−	6.34659e19i	0.664614	−	1.15115i	0.979390	−	0.201980i	$-0.0647375\pi$
$662$	1.58983e20	+	9.17888e19i	2.85328	+	1.64734i
$663$		0			0
$664$	−2.05916e19	−	3.56657e19i	−0.361838	−	0.626722i
$665$		−	7.00537e17i		−	0.0121809i
$666$		0			0
$667$	1.41462e19			0.240856
$668$	−1.65725e20	+	9.56813e19i	−2.79224	+	1.61210i
$669$		0			0
$670$	3.10115e19	−	5.37135e19i	0.511681	−	0.886257i
$671$	−4.17107e19	−	2.40817e19i	−0.681066	−	0.393214i
$672$		0			0
$673$	−3.55039e19	−	6.14945e19i	−0.567767	−	0.983402i	−0.996786	−	0.0801066i	$-0.974474\pi$
$673$	−3.55039e19	−	6.14945e19i	−0.567767	−	0.983402i	0.429019	−	0.903296i	$-0.358859\pi$
$674$			6.40184e19i			1.01318i
$675$		0			0
$676$	−6.82331e19			−1.05771
$677$	−7.21965e19	+	4.16826e19i	−1.10763	+	0.639491i	−0.938215	−	0.346053i	$-0.887522\pi$
$677$	−7.21965e19	+	4.16826e19i	−1.10763	+	0.639491i	−0.169416	+	0.985545i	$0.554188\pi$
$678$		0			0
$679$	1.75436e19	−	3.03865e19i	0.263652	−	0.456659i
$680$	1.46658e20	+	8.46732e19i	2.18144	+	1.25946i
$681$		0			0
$682$	4.50053e19	+	7.79514e19i	0.655802	+	1.13588i
$683$		−	1.24590e20i		−	1.79696i	−0.439016	−	0.898479i	$-0.644673\pi$
$683$		−	1.24590e20i		−	1.79696i	0.439016	−	0.898479i	$-0.355327\pi$
$684$		0			0
$685$	5.44273e18			0.0769100
$686$	−7.96976e19	+	4.60134e19i	−1.11475	+	0.643600i
$687$		0			0
$688$	4.59405e17	−	7.95713e17i	0.00629617	−	0.0109053i
$689$	−1.16235e20	−	6.71081e19i	−1.57689	−	0.910418i
$690$		0			0
$691$	−3.10500e19	−	5.37802e19i	−0.412777	−	0.714950i	0.582416	−	0.812891i	$-0.302108\pi$
$691$	−3.10500e19	−	5.37802e19i	−0.412777	−	0.714950i	−0.995192	+	0.0979410i	$0.968774\pi$
$692$			2.55570e20i			3.36331i
$693$		0			0
$694$	−1.56710e20			−2.02106
$695$	4.47063e19	−	2.58112e19i	0.570789	−	0.329545i
$696$		0			0
$697$	−4.90475e19	+	8.49527e19i	−0.613744	+	1.06304i
$698$	−2.37444e19	−	1.37088e19i	−0.294152	−	0.169829i
$699$		0			0
$700$	4.57361e19	+	7.92172e19i	0.555358	+	0.961908i
$701$			5.95665e19i			0.716103i	0.933702	+	0.358052i	$0.116559\pi$
$701$			5.95665e19i			0.716103i	−0.933702	+	0.358052i	$0.883441\pi$
$702$		0			0
$703$	7.49551e17			0.00883312
$704$	7.21495e19	−	4.16555e19i	0.841831	−	0.486031i
$705$		0			0
$706$	−5.82578e19	+	1.00905e20i	−0.666379	+	1.15420i
$707$	1.55608e19	+	8.98404e18i	0.176237	+	0.101750i
$708$		0			0
$709$	4.42928e19	+	7.67173e19i	0.491823	+	0.851863i	0.999956	−	0.00941592i	$-0.00299723\pi$
$709$	4.42928e19	+	7.67173e19i	0.491823	+	0.851863i	−0.508132	+	0.861279i	$0.669664\pi$
$710$		−	2.35597e20i		−	2.59036i
$711$		0			0
$712$	2.29322e20			2.47221
$713$	−1.64980e19	+	9.52515e18i	−0.176119	+	0.101682i
$714$		0			0
$715$	1.35186e20	−	2.34149e20i	1.41511	−	2.45103i
$716$	−1.91965e20	−	1.10831e20i	−1.98990	−	1.14887i
$717$		0			0
$718$	6.43062e19	+	1.11382e20i	0.653704	+	1.13225i
$719$			1.59134e19i			0.160199i	0.996787	+	0.0800994i	$0.0255238\pi$
$719$			1.59134e19i			0.160199i	−0.996787	+	0.0800994i	$0.974476\pi$
$720$		0			0
$721$	−5.15090e18			−0.0508553
$722$	1.55987e20	−	9.00593e19i	1.52521	−	0.880579i
$723$		0			0
$724$	4.99374e19	−	8.64941e19i	0.478912	−	0.829501i
$725$	−7.07892e19	−	4.08702e19i	−0.672359	−	0.388186i
$726$		0			0
$727$	2.49392e19	+	4.31960e19i	0.232350	+	0.402441i	0.958499	−	0.285095i	$-0.0920253\pi$
$727$	2.49392e19	+	4.31960e19i	0.232350	+	0.402441i	−0.726149	+	0.687537i	$0.758692\pi$
$728$		−	1.02461e20i		−	0.945447i
$729$		0			0
$730$	−3.02495e20			−2.73815
$731$	−7.79357e17	+	4.49962e17i	−0.00698739	+	0.00403417i
$732$		0			0
$733$	−9.33104e19	+	1.61618e20i	−0.820733	+	1.42155i	0.0844038	+	0.996432i	$0.473101\pi$
$733$	−9.33104e19	+	1.61618e20i	−0.820733	+	1.42155i	−0.905137	+	0.425120i	$0.860232\pi$
$734$	9.25126e19	+	5.34122e19i	0.805988	+	0.465337i
$735$		0			0
$736$	−9.33315e18	−	1.61655e19i	−0.0797781	−	0.138180i
$737$		−	6.79336e19i		−	0.575191i
$738$		0			0
$739$	2.24865e18			0.0186815			0.00934073	−	0.999956i	$-0.497027\pi$
$739$	2.24865e18			0.0186815			0.00934073	+	0.999956i	$0.497027\pi$
$740$	−1.48419e20	+	8.56896e19i	−1.22143	+	0.705190i
$741$		0			0
$742$	6.42387e19	−	1.11265e20i	0.518764	−	0.898525i
$743$	−5.27339e19	−	3.04459e19i	−0.421860	−	0.243561i	0.274013	−	0.961726i	$-0.411649\pi$
$743$	−5.27339e19	−	3.04459e19i	−0.421860	−	0.243561i	−0.695873	+	0.718165i	$0.744982\pi$
$744$		0			0
$745$	−1.65040e20	−	2.85857e20i	−1.29567	−	2.24417i
$746$			2.58407e20i			2.00970i
$747$		0			0
$748$	3.53467e20			2.69797
$749$	3.22743e19	−	1.86336e19i	0.244053	−	0.140904i
$750$		0			0
$751$	9.22296e19	−	1.59746e20i	0.684527	−	1.18564i	−0.289058	−	0.957312i	$-0.593342\pi$
$751$	9.22296e19	−	1.59746e20i	0.684527	−	1.18564i	0.973585	−	0.228324i	$-0.0733245\pi$
$752$	−1.38945e20	−	8.02202e19i	−1.02169	−	0.589874i
$753$		0			0
$754$	8.72399e19	+	1.51104e20i	0.629674	+	1.09063i
$755$			1.40818e19i			0.100700i
$756$		0			0
$757$	−1.79301e20			−1.25867			−0.629336	−	0.777133i	$-0.716673\pi$
$757$	−1.79301e20			−1.25867			−0.629336	+	0.777133i	$0.716673\pi$
$758$	1.87073e19	−	1.08006e19i	0.130115	−	0.0751217i
$759$		0			0
$760$	4.37700e18	−	7.58119e18i	0.0298870	−	0.0517657i
$761$	3.15134e19	+	1.81943e19i	0.213208	+	0.123096i	0.602801	−	0.797891i	$-0.294051\pi$
$761$	3.15134e19	+	1.81943e19i	0.213208	+	0.123096i	−0.389594	+	0.920987i	$0.627384\pi$
$762$		0			0
$763$	−1.56657e19	−	2.71338e19i	−0.104059	−	0.180235i
$764$		−	4.49871e19i		−	0.296098i
$765$		0			0
$766$	2.00743e20			1.29730
$767$	2.74710e20	−	1.58604e20i	1.75917	−	1.01566i
$768$		0			0
$769$	−5.77176e19	+	9.99698e19i	−0.362931	+	0.628614i	−0.988442	−	0.151601i	$-0.951557\pi$
$769$	−5.77176e19	+	9.99698e19i	−0.362931	+	0.628614i	0.625511	+	0.780215i	$0.284891\pi$
$770$	2.24137e20	+	1.29406e20i	1.39662	+	0.806339i
$771$		0			0
$772$	−9.46217e19	−	1.63890e20i	−0.578988	−	1.00284i
$773$		−	6.97639e19i		−	0.423033i	−0.977374	−	0.211516i	$-0.932160\pi$
$773$		−	6.97639e19i		−	0.423033i	0.977374	−	0.211516i	$-0.0678402\pi$
$774$		0			0
$775$	1.10078e20			0.655522
$776$	3.79714e20	−	2.19228e20i	2.24091	−	1.29379i
$777$		0			0
$778$	8.30290e19	−	1.43810e20i	0.481252	−	0.833553i
$779$	4.39145e18	+	2.53541e18i	0.0252259	+	0.0145642i
$780$		0			0
$781$	−1.29024e20	−	2.23476e20i	−0.727971	−	1.26088i
$782$			1.10362e20i			0.617124i
$783$		0			0
$784$	−2.03074e20			−1.11543
$785$	−3.00658e20	+	1.73585e20i	−1.63676	+	0.944983i
$786$		0			0
$787$	−9.28671e19	+	1.60851e20i	−0.496637	+	0.860200i	−0.999992	−	0.00387937i	$-0.998765\pi$
$787$	−9.28671e19	+	1.60851e20i	−0.496637	+	0.860200i	0.503356	+	0.864079i	$0.332098\pi$
$788$	1.99835e19	+	1.15375e19i	0.105922	+	0.0611543i
$789$		0			0
$790$	−1.38916e19	−	2.40610e19i	−0.0723375	−	0.125292i
$791$		−	6.92854e19i		−	0.357607i
$792$		0			0
$793$	1.25728e20			0.637556
$794$	−1.28964e20	+	7.44577e19i	−0.648226	+	0.374253i
$795$		0			0
$796$	−2.08537e20	+	3.61196e20i	−1.02989	+	1.78382i
$797$	−3.90330e19	−	2.25357e19i	−0.191084	−	0.110322i	0.401406	−	0.915900i	$-0.368522\pi$
$797$	−3.90330e19	−	2.25357e19i	−0.191084	−	0.110322i	−0.592490	+	0.805578i	$0.701855\pi$
$798$		0			0
$799$	7.85713e19	+	1.36090e20i	0.377952	+	0.654632i
$800$			1.07859e20i			0.514311i
$801$		0			0
$802$	2.28647e20			1.07138
$803$	−2.86933e20	+	1.65661e20i	−1.33282	+	0.769505i
$804$		0			0
$805$	−2.73881e19	+	4.74375e19i	−0.125023	+	0.216546i
$806$	−2.03488e20	−	1.17484e20i	−0.920859	−	0.531658i
$807$		0			0
$808$	1.12266e20	+	1.94450e20i	0.499308	+	0.864827i
$809$			1.85225e20i			0.816695i	0.912827	+	0.408347i	$0.133895\pi$
$809$			1.85225e20i			0.816695i	−0.912827	+	0.408347i	$0.866105\pi$
$810$		0			0
$811$	2.56899e20			1.11331			0.556656	−	0.830743i	$-0.312084\pi$
$811$	2.56899e20			1.11331			0.556656	+	0.830743i	$0.312084\pi$
$812$	−9.80470e19	+	5.66074e19i	−0.421252	+	0.243210i
$813$		0			0
$814$	−1.38460e20	+	2.39819e20i	−0.584726	+	1.01278i
$815$	1.72265e20	+	9.94570e19i	0.721262	+	0.416421i
$816$		0			0
$817$	2.32599e16	+	4.02873e16i	9.57311e−5	+	0.000165811i
$818$			1.60688e20i			0.655707i
$819$		0			0
$820$	−1.15940e21			−4.65091
$821$	9.58723e19	−	5.53519e19i	0.381321	−	0.220156i	−0.297072	−	0.954855i	$-0.596010\pi$
$821$	9.58723e19	−	5.53519e19i	0.381321	−	0.220156i	0.678393	+	0.734699i	$0.262677\pi$
$822$		0			0
$823$	−6.70496e19	+	1.16133e20i	−0.262179	+	0.454107i	−0.966821	−	0.255456i	$-0.917774\pi$
$823$	−6.70496e19	+	1.16133e20i	−0.262179	+	0.454107i	0.704642	+	0.709563i	$0.251108\pi$
$824$	−5.57429e19	−	3.21832e19i	−0.216122	−	0.124778i
$825$		0			0
$826$	1.51822e20	+	2.62964e20i	0.578729	+	1.00239i
$827$			9.74201e19i			0.368222i	0.982905	+	0.184111i	$0.0589406\pi$
$827$			9.74201e19i			0.368222i	−0.982905	+	0.184111i	$0.941059\pi$
$828$		0			0
$829$	−2.13764e20			−0.794426			−0.397213	−	0.917726i	$-0.630023\pi$
$829$	−2.13764e20			−0.794426			−0.397213	+	0.917726i	$0.630023\pi$
$830$	−2.35175e20	+	1.35778e20i	−0.866652	+	0.500362i
$831$		0			0
$832$	−1.08739e20	+	1.88342e20i	−0.394025	+	0.682471i
$833$	1.72252e20	+	9.94498e19i	0.618941	+	0.357346i
$834$		0			0
$835$	3.31075e20	+	5.73439e20i	1.16983	+	2.02620i
$836$		−	1.82717e19i		−	0.0640230i
$837$		0			0
$838$	4.30787e20			1.48441
$839$	5.36477e19	−	3.09735e19i	0.183323	−	0.105842i	−0.405530	−	0.914082i	$-0.632913\pi$
$839$	5.36477e19	−	3.09735e19i	0.183323	−	0.105842i	0.588853	+	0.808240i	$0.299580\pi$
$840$		0			0
$841$	−9.81942e19	+	1.70077e20i	−0.330000	+	0.571577i
$842$	−7.07548e20	−	4.08503e20i	−2.35815	−	1.36148i
$843$		0			0
$844$	−6.31560e20	−	1.09389e21i	−2.07022	−	3.58573i
$845$			2.36099e20i			0.767534i
$846$		0			0
$847$	1.59490e20			0.509975
$848$	5.36837e20	−	3.09943e20i	1.70244	−	0.982903i
$849$		0			0
$850$	3.18851e20	−	5.52265e20i	0.994614	−	1.72272i
$851$	−5.07566e19	−	2.93043e19i	−0.157031	−	0.0906619i
$852$		0			0
$853$	−1.15430e20	−	1.99930e20i	−0.351297	−	0.608464i	0.635180	−	0.772364i	$-0.280926\pi$
$853$	−1.15430e20	−	1.99930e20i	−0.351297	−	0.608464i	−0.986477	+	0.163900i	$0.947593\pi$
$854$			1.20352e20i			0.363285i
$855$		0			0
$856$	4.65696e20			1.38288
$857$	4.98714e20	−	2.87933e20i	1.46888	−	0.848058i	0.469488	−	0.882939i	$-0.344439\pi$
$857$	4.98714e20	−	2.87933e20i	1.46888	−	0.848058i	0.999391	+	0.0348813i	$0.0111053\pi$
$858$		0			0
$859$	1.49999e20	−	2.59806e20i	0.434646	−	0.752829i	−0.562621	−	0.826715i	$-0.690207\pi$
$859$	1.49999e20	−	2.59806e20i	0.434646	−	0.752829i	0.997267	+	0.0738862i	$0.0235401\pi$
$860$	−9.21138e18	−	5.31819e18i	−0.0264750	−	0.0152853i
$861$		0			0
$862$	−4.01540e20	−	6.95488e20i	−1.13548	−	1.96670i
$863$			9.77909e19i			0.274298i	0.990550	+	0.137149i	$0.0437939\pi$
$863$			9.77909e19i			0.274298i	−0.990550	+	0.137149i	$0.956206\pi$
$864$		0			0
$865$	8.84320e20			2.44060
$866$	7.80633e20	−	4.50698e20i	2.13708	−	1.23385i
$867$		0			0
$868$	7.62318e19	−	1.32037e20i	0.205352	−	0.355680i
$869$	−2.63540e19	−	1.52155e19i	−0.0704219	−	0.0406581i
$870$		0			0
$871$	8.86684e19	+	1.53578e20i	0.233153	+	0.403833i
$872$		−	3.91522e20i		−	1.02127i
$873$		0			0
$874$	5.70494e18			0.0146444
$875$	6.82387e19	−	3.93976e19i	0.173770	−	0.100326i
$876$		0			0
$877$	6.00678e19	−	1.04041e20i	0.150538	−	0.260739i	−0.780888	−	0.624671i	$-0.785233\pi$
$877$	6.00678e19	−	1.04041e20i	0.150538	−	0.260739i	0.931425	+	0.363933i	$0.118566\pi$
$878$	1.09157e21	+	6.30219e20i	2.71388	+	1.56686i
$879$		0			0
$880$	6.24364e20	+	1.08143e21i	1.52777	+	2.64618i
$881$			7.52553e20i			1.82686i	0.406993	+	0.913431i	$0.366577\pi$
$881$			7.52553e20i			1.82686i	−0.406993	+	0.913431i	$0.633423\pi$
$882$		0			0
$883$	−4.53963e20			−1.08466			−0.542332	−	0.840164i	$-0.682459\pi$
$883$	−4.53963e20			−1.08466			−0.542332	+	0.840164i	$0.682459\pi$
$884$	−7.99086e20	+	4.61352e20i	−1.89421	+	1.09362i
$885$		0			0
$886$	5.22423e20	−	9.04864e20i	1.21895	−	2.11129i
$887$	−6.11609e20	−	3.53113e20i	−1.41582	−	0.817425i	−0.419893	−	0.907573i	$-0.637933\pi$
$887$	−6.11609e20	−	3.53113e20i	−1.41582	−	0.817425i	−0.995928	+	0.0901484i	$0.971266\pi$
$888$		0			0
$889$	−7.82953e19	−	1.35611e20i	−0.178412	−	0.309018i
$890$		−	1.51212e21i		−	3.41866i
$891$		0			0
$892$	−8.06674e20			−1.79533
$893$	7.03487e18	−	4.06158e18i	0.0155344	−	0.00896882i
$894$		0			0
$895$	−3.83497e20	+	6.64236e20i	−0.833682	+	1.44398i
$896$	−2.41774e20	−	1.39588e20i	−0.521499	−	0.301088i
$897$		0			0
$898$	2.56028e20	+	4.43454e20i	0.543693	+	0.941704i
$899$			1.36243e20i			0.287075i
$900$		0			0
$901$	−6.07144e20			−1.25956
$902$	−1.62241e21	+	9.36698e20i	−3.33976	+	1.92821i
$903$		0			0
$904$	4.32900e20	−	7.49805e20i	0.877423	−	1.51974i
$905$	−2.99286e20	−	1.72793e20i	−0.601930	−	0.347525i
$906$		0			0
$907$	−1.15570e20	−	2.00174e20i	−0.228873	−	0.396420i	0.728601	−	0.684938i	$-0.240171\pi$
$907$	−1.15570e20	−	2.00174e20i	−0.228873	−	0.396420i	−0.957474	+	0.288518i	$0.906837\pi$
$908$		−	1.71478e21i		−	3.36982i
$909$		0			0
$910$	−6.75612e20			−1.30740
$911$	5.84807e20	−	3.37639e20i	1.12301	−	0.648371i	0.180844	−	0.983512i	$-0.442117\pi$
$911$	5.84807e20	−	3.37639e20i	1.12301	−	0.648371i	0.942168	+	0.335141i	$0.108784\pi$
$912$		0			0
$913$	−1.48718e20	+	2.57587e20i	−0.281234	+	0.487111i
$914$	7.23589e20	+	4.17764e20i	1.35790	+	0.783985i
$915$		0			0
$916$	3.21268e20	+	5.56453e20i	0.593744	+	1.02840i
$917$		−	2.17010e20i		−	0.398010i
$918$		0			0
$919$	7.49953e20			1.35464			0.677322	−	0.735687i	$-0.263140\pi$
$919$	7.49953e20			1.35464			0.677322	+	0.735687i	$0.263140\pi$
$920$	−5.92786e20	+	3.42245e20i	−1.06263	+	0.613511i
$921$		0			0
$922$	4.19920e20	−	7.27324e20i	0.741397	−	1.28414i
$923$	5.83373e20	+	3.36810e20i	1.02220	+	0.590165i
$924$		0			0
$925$	1.69328e20	+	2.93285e20i	0.292238	+	0.506171i
$926$			1.47012e21i			2.51812i
$927$		0			0
$928$	−1.33497e20			−0.225234
$929$	−3.51076e20	+	2.02694e20i	−0.587884	+	0.339415i	−0.764260	−	0.644908i	$-0.776896\pi$
$929$	−3.51076e20	+	2.02694e20i	−0.587884	+	0.339415i	0.176377	+	0.984323i	$0.443562\pi$
$930$		0			0
$931$	5.14085e18	−	8.90422e18i	0.00847984	−	0.0146875i
$932$	−3.30969e20	−	1.91085e20i	−0.541847	−	0.312835i
$933$		0			0
$934$	5.28129e20	+	9.14747e20i	0.851750	+	1.47527i
$935$		−	1.22306e21i		−	1.95779i
$936$		0			0
$937$	−5.19955e20			−0.819952			−0.409976	−	0.912096i	$-0.634463\pi$
$937$	−5.19955e20			−0.819952			−0.409976	+	0.912096i	$0.634463\pi$
$938$	−1.47011e20	+	8.48771e19i	−0.230108	+	0.132853i
$939$		0			0
$940$	−9.28650e20	+	1.60847e21i	−1.43205	+	2.48038i
$941$	1.69522e20	+	9.78738e19i	0.259477	+	0.149809i	0.624096	−	0.781348i	$-0.285467\pi$
$941$	1.69522e20	+	9.78738e19i	0.259477	+	0.149809i	−0.364619	+	0.931157i	$0.618801\pi$
$942$		0			0
$943$	−1.98248e20	−	3.43375e20i	−0.298969	−	0.517830i
$944$			1.46504e21i			2.19304i
$945$		0			0
$946$	−1.71866e19			−0.0253484
$947$	4.18348e20	−	2.41533e20i	0.612474	−	0.353612i	−0.161459	−	0.986879i	$-0.551620\pi$
$947$	4.18348e20	−	2.41533e20i	0.612474	−	0.353612i	0.773933	+	0.633268i	$0.218287\pi$
$948$		0			0
$949$	4.32448e20	−	7.49022e20i	0.623836	−	1.08052i
$950$	−2.85482e19	−	1.64823e19i	−0.0408803	−	0.0236022i
$951$		0			0
$952$	−2.31747e20	−	4.01397e20i	−0.327006	−	0.566390i
$953$		−	5.49731e20i		−	0.770016i	−0.922913	−	0.385008i	$-0.874199\pi$
$953$		−	5.49731e20i		−	0.770016i	0.922913	−	0.385008i	$-0.125801\pi$
$954$		0			0
$955$	−1.55664e20			−0.214864
$956$	5.62995e20	−	3.25045e20i	0.771434	−	0.445388i
$957$		0			0
$958$	−3.33784e20	+	5.78131e20i	−0.450720	+	0.780671i
$959$	−1.29008e19	−	7.44826e18i	−0.0172936	−	0.00998446i
$960$		0			0
$961$	2.86735e20	+	4.96639e20i	0.378806	+	0.656111i
$962$		−	7.22882e20i		−	0.948074i
$963$		0			0
$964$	2.40391e21			3.10727
$965$	−5.67088e20	+	3.27409e20i	−0.727712	+	0.420145i
$966$		0			0
$967$	−4.30134e20	+	7.45014e20i	−0.544025	+	0.942278i	0.454643	+	0.890674i	$0.349767\pi$
$967$	−4.30134e20	+	7.45014e20i	−0.544025	+	0.942278i	−0.998668	+	0.0516046i	$0.983566\pi$
$968$	1.72599e21	+	9.96503e20i	2.16726	+	1.25127i
$969$		0			0
$970$	−1.44556e21	−	2.50378e21i	−1.78910	−	3.09880i
$971$			9.81266e20i			1.20574i	0.797841	+	0.602868i	$0.205975\pi$
$971$			9.81266e20i			1.20574i	−0.797841	+	0.602868i	$0.794025\pi$
$972$		0			0
$973$	−1.41288e20			−0.171126
$974$	−1.21092e21	+	6.99126e20i	−1.45614	+	0.840703i
$975$		0			0
$976$	−2.90340e20	+	5.02884e20i	−0.344158	+	0.596100i
$977$	−6.49778e20	−	3.75150e20i	−0.764721	−	0.441512i	0.0662671	−	0.997802i	$-0.478891\pi$
$977$	−6.49778e20	−	3.75150e20i	−0.764721	−	0.441512i	−0.830988	+	0.556290i	$0.812224\pi$
$978$		0			0
$979$	−8.28109e20	−	1.43433e21i	−0.960746	−	1.66406i
$980$			2.35083e21i			2.70794i
$981$		0			0
$982$	−1.57545e21			−1.78906
$983$	1.41689e21	−	8.18042e20i	1.59758	−	0.922361i	0.605623	−	0.795752i	$-0.292924\pi$
$983$	1.41689e21	−	8.18042e20i	1.59758	−	0.922361i	0.991953	−	0.126609i	$-0.0404094\pi$
$984$		0			0
$985$	3.99218e19	−	6.91465e19i	0.0443768	−	0.0768629i
$986$	6.83537e20	+	3.94641e20i	0.754439	+	0.435575i
$987$		0			0
$988$	2.38487e19	+	4.13071e19i	0.0259517	+	0.0449496i
$989$		−	3.63746e18i		−	0.00393028i
$990$		0			0
$991$	5.66881e20			0.603916			0.301958	−	0.953321i	$-0.402360\pi$
$991$	5.66881e20			0.603916			0.301958	+	0.953321i	$0.402360\pi$
$992$	1.55691e20	−	8.98883e19i	0.164696	−	0.0950870i
$993$		0			0
$994$	−3.22409e20	+	5.58429e20i	−0.336281	+	0.582456i
$995$	1.24980e21	+	7.21575e20i	1.29444	+	0.747343i
$996$		0			0
$997$	−4.39881e20	−	7.61896e20i	−0.449230	−	0.778090i	0.549106	−	0.835753i	$-0.314968\pi$
$997$	−4.39881e20	−	7.61896e20i	−0.449230	−	0.778090i	−0.998336	+	0.0576630i	$0.981635\pi$
$998$		−	2.96360e21i		−	3.00543i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.15.d.a.17.2		26
3.2	odd	2		9.15.d.a.5.12	yes	26
9.2	odd	6	inner	27.15.d.a.8.2		26
9.4	even	3		81.15.b.a.80.2		26
9.5	odd	6		81.15.b.a.80.25		26
9.7	even	3		9.15.d.a.2.12	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.15.d.a.2.12	✓	26	9.7	even	3
9.15.d.a.5.12	yes	26	3.2	odd	2
27.15.d.a.8.2		26	9.2	odd	6	inner
27.15.d.a.17.2		26	1.1	even	1	trivial
81.15.b.a.80.2		26	9.4	even	3
81.15.b.a.80.25		26	9.5	odd	6

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-195.306 + 112.760i) q^{2} +(17237.5 - 29856.3i) q^{4} +(-103308. - 59645.1i) q^{5} +(163246. + 282751. i) q^{7} +4.07989e6i q^{8} +2.69023e7 q^{10} +(2.55183e7 - 1.47330e7i) q^{11} +(-3.84596e7 + 6.66141e7i) q^{13} +(-6.37658e7 - 3.68152e7i) q^{14} +(-1.77628e8 - 3.07661e8i) q^{16} +3.47954e8i q^{17} +1.79868e7 q^{19} +(-3.56156e9 + 2.05627e9i) q^{20} +(-3.32258e9 + 5.75488e9i) q^{22} +(-1.21799e9 - 7.03208e8i) q^{23} +(4.06332e9 + 7.03788e9i) q^{25} -1.73468e10i q^{26} +1.12558e10 q^{28} +(-8.71076e9 + 5.02916e9i) q^{29} +(6.77264e9 - 1.17306e10i) q^{31} +(1.14941e10 + 6.63613e9i) q^{32} +(-3.92352e10 - 6.79574e10i) q^{34} -3.89473e10i q^{35} +4.16724e10 q^{37} +(-3.51292e9 + 2.02818e9i) q^{38} +(2.43346e11 - 4.21487e11i) q^{40} +(2.44149e11 + 1.40960e11i) q^{41} +(1.29317e9 + 2.23983e9i) q^{43} -1.01584e12i q^{44} +3.17174e11 q^{46} +(3.91113e11 - 2.25809e11i) q^{47} +(2.85813e11 - 4.95043e11i) q^{49} +(-1.58718e12 - 9.16358e11i) q^{50} +(1.32590e12 + 2.29653e12i) q^{52} +1.74490e12i q^{53} -3.51500e12 q^{55} +(-1.15359e12 + 6.66027e11i) q^{56} +(1.13417e12 - 1.96445e12i) q^{58} +(-3.57141e12 - 2.06195e12i) q^{59} +(-8.17270e11 - 1.41555e12i) q^{61} +3.05473e12i q^{62} +2.82736e12 q^{64} +(7.94640e12 - 4.58786e12i) q^{65} +(1.15275e12 - 1.99661e12i) q^{67} +(1.03886e13 + 5.99787e12i) q^{68} +(4.39169e12 + 7.60663e12i) q^{70} -8.75750e12i q^{71} -1.12442e13 q^{73} +(-8.13885e12 + 4.69897e12i) q^{74} +(3.10048e11 - 5.37019e11i) q^{76} +(8.33152e12 + 4.81021e12i) q^{77} +(-5.16374e11 - 8.94386e11i) q^{79} +4.23786e13i q^{80} -6.35783e13 q^{82} +(-8.74183e12 + 5.04710e12i) q^{83} +(2.07538e13 - 3.59466e13i) q^{85} +(-5.05125e11 - 2.91634e11i) q^{86} +(6.01091e13 + 1.04112e14i) q^{88} -5.62078e13i q^{89} -2.51135e13 q^{91} +(-4.19904e13 + 2.42432e13i) q^{92} +(-5.09245e13 + 8.82037e13i) q^{94} +(-1.85818e12 - 1.07282e12i) q^{95} +(-5.37337e13 - 9.30695e13i) q^{97} +1.28913e14i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 3 q^{2} + 98303 q^{4} + 107994 q^{5} - 146330 q^{7} - 32772 q^{10} + 15978711 q^{11} - 23281436 q^{13} + 349442850 q^{14} - 671072257 q^{16} + 195706222 q^{19} - 2822935854 q^{20} - 204235521 q^{22}+ \cdots + 7621755375583 q^{97}+O(q^{100}) \) 26 * q + 3 * q^2 + 98303 * q^4 + 107994 * q^5 - 146330 * q^7 - 32772 * q^10 + 15978711 * q^11 - 23281436 * q^13 + 349442850 * q^14 - 671072257 * q^16 + 195706222 * q^19 - 2822935854 * q^20 - 204235521 * q^22 + 6101133672 * q^23 + 14614789727 * q^25 - 9052979204 * q^28 - 85191770166 * q^29 + 15357554728 * q^31 + 237242922057 * q^32 - 16566014943 * q^34 - 77721425444 * q^37 - 476314869819 * q^38 - 88855733850 * q^40 + 938882938233 * q^41 - 29709800063 * q^43 + 1553142786144 * q^46 + 1272741434580 * q^47 - 945184029255 * q^49 - 3573994524699 * q^50 + 1825489374856 * q^52 - 3772940931372 * q^55 + 7790759725422 * q^56 + 3747043240302 * q^58 - 5874788534451 * q^59 - 4867968901544 * q^61 + 1211169309434 * q^64 + 22156719464856 * q^65 - 8251061484125 * q^67 - 30687017243265 * q^68 + 6871822387932 * q^70 + 16120119648922 * q^73 - 8549243621166 * q^74 + 14422972781521 * q^76 - 13919363311398 * q^77 - 10740904544582 * q^79 - 67076318933382 * q^82 + 11295125984532 * q^83 + 10590724937466 * q^85 - 97019495740221 * q^86 - 26136212294541 * q^88 + 70870424994080 * q^91 + 474274297000284 * q^92 - 46678164316620 * q^94 - 440317551118746 * q^95 + 7621755375583 * q^97

Introduction

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