LMFDB - Embedded newform 9.15.d.a.5.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9,15,Mod(2,9)] 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("9.2"); S:= CuspForms(chi, 15); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 15, names="a")

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	9.d (of order $6$, degree $2$, 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:	$11.1896071337$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.12
Character	$\chi$	$=$	9.5
Dual form			9.15.d.a.2.12

$q$-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} +(840.821 - 2018.91i) q^{3} +(17237.5 - 29856.3i) q^{4} +(103308. + 59645.1i) q^{5} +(-63434.5 - 489115. i) q^{6} +(163246. + 282751. i) q^{7} -4.07989e6i q^{8} +(-3.36901e6 - 3.39508e6i) q^{9} +2.69023e7 q^{10} +(-2.55183e7 + 1.47330e7i) q^{11} +(-4.57834e7 - 5.99048e7i) q^{12} +(-3.84596e7 + 6.66141e7i) q^{13} +(6.37658e7 + 3.68152e7i) q^{14} +(2.07282e8 - 1.58419e8i) q^{15} +(-1.77628e8 - 3.07661e8i) q^{16} -3.47954e8i q^{17} +(-1.04082e9 - 2.83190e8i) q^{18} +1.79868e7 q^{19} +(3.56156e9 - 2.05627e9i) q^{20} +(7.08108e8 - 9.18363e7i) q^{21} +(-3.32258e9 + 5.75488e9i) q^{22} +(1.21799e9 + 7.03208e8i) q^{23} +(-8.23693e9 - 3.43046e9i) q^{24} +(4.06332e9 + 7.03788e9i) q^{25} +1.73468e10i q^{26} +(-9.68709e9 + 3.94707e9i) q^{27} +1.12558e10 q^{28} +(8.71076e9 - 5.02916e9i) q^{29} +(2.26200e10 - 5.43132e10i) q^{30} +(6.77264e9 - 1.17306e10i) q^{31} +(-1.14941e10 - 6.63613e9i) q^{32} +(8.28825e9 + 6.39069e10i) q^{33} +(-3.92352e10 - 6.79574e10i) q^{34} +3.89473e10i q^{35} +(-1.59438e11 + 4.20633e10i) q^{36} +4.16724e10 q^{37} +(3.51292e9 - 2.02818e9i) q^{38} +(1.02150e11 + 1.33657e11i) q^{39} +(2.43346e11 - 4.21487e11i) q^{40} +(-2.44149e11 - 1.40960e11i) q^{41} +(1.27942e11 - 9.77823e10i) q^{42} +(1.29317e9 + 2.23983e9i) q^{43} +1.01584e12i q^{44} +(-1.45547e11 - 5.51685e11i) q^{45} +3.17174e11 q^{46} +(-3.91113e11 + 2.25809e11i) q^{47} +(-7.70493e11 + 9.99271e10i) q^{48} +(2.85813e11 - 4.95043e11i) q^{49} +(1.58718e12 + 9.16358e11i) q^{50} +(-7.02487e11 - 2.92567e11i) q^{51} +(1.32590e12 + 2.29653e12i) q^{52} -1.74490e12i q^{53} +(-1.44687e12 + 1.86320e12i) q^{54} -3.51500e12 q^{55} +(1.15359e12 - 6.66027e11i) q^{56} +(1.51237e10 - 3.63136e10i) q^{57} +(1.13417e12 - 1.96445e12i) q^{58} +(3.57141e12 + 2.06195e12i) q^{59} +(-1.15678e12 - 8.91943e12i) q^{60} +(-8.17270e11 - 1.41555e12i) q^{61} -3.05473e12i q^{62} +(4.09983e11 - 1.50682e12i) q^{63} +2.82736e12 q^{64} +(-7.94640e12 + 4.58786e12i) q^{65} +(8.82487e12 + 1.15468e13i) q^{66} +(1.15275e12 - 1.99661e12i) q^{67} +(-1.03886e13 - 5.99787e12i) q^{68} +(2.44382e12 - 1.86774e12i) q^{69} +(4.39169e12 + 7.60663e12i) q^{70} +8.75750e12i q^{71} +(-1.38516e13 + 1.37452e13i) q^{72} -1.12442e13 q^{73} +(8.13885e12 - 4.69897e12i) q^{74} +(1.76253e13 - 2.28588e12i) q^{75} +(3.10048e11 - 5.37019e11i) q^{76} +(-8.33152e12 - 4.81021e12i) q^{77} +(3.50216e13 + 1.45856e13i) q^{78} +(-5.16374e11 - 8.94386e11i) q^{79} -4.23786e13i q^{80} +(-1.76341e11 + 2.28761e13i) q^{81} -6.35783e13 q^{82} +(8.74183e12 - 5.04710e12i) q^{83} +(9.46415e12 - 2.27245e13i) q^{84} +(2.07538e13 - 3.59466e13i) q^{85} +(5.05125e11 + 2.91634e11i) q^{86} +(-2.82922e12 - 2.18148e13i) q^{87} +(6.01091e13 + 1.04112e14i) q^{88} +5.62078e13i q^{89} +(-9.06340e13 - 9.13354e13i) q^{90} -2.51135e13 q^{91} +(4.19904e13 - 2.42432e13i) q^{92} +(-1.79883e13 - 2.35366e13i) q^{93} +(-5.09245e13 + 8.82037e13i) q^{94} +(1.85818e12 + 1.07282e12i) q^{95} +(-2.30622e13 + 1.76258e13i) q^{96} +(-5.37337e13 - 9.30695e13i) q^{97} -1.28913e14i q^{98} +(1.35991e14 + 3.70010e13i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 3 q^{2} - 2199 q^{3} + 98303 q^{4} - 107994 q^{5} + 24957 q^{6} - 146330 q^{7} - 5316525 q^{9} - 32772 q^{10} - 15978711 q^{11} - 53795046 q^{12} - 23281436 q^{13} - 349442850 q^{14} + 207365400 q^{15}+ \cdots - 195117933369168 q^{99}+O(q^{100}) $ 26 * q - 3 * q^2 - 2199 * q^3 + 98303 * q^4 - 107994 * q^5 + 24957 * q^6 - 146330 * q^7 - 5316525 * q^9 - 32772 * q^10 - 15978711 * q^11 - 53795046 * q^12 - 23281436 * q^13 - 349442850 * q^14 + 207365400 * q^15 - 671072257 * q^16 - 2272246668 * q^18 + 195706222 * q^19 + 2822935854 * q^20 + 1958992050 * q^21 - 204235521 * q^22 - 6101133672 * q^23 + 10931998527 * q^24 + 14614789727 * q^25 - 34016586282 * q^27 - 9052979204 * q^28 + 85191770166 * q^29 + 91857763818 * q^30 + 15357554728 * q^31 - 237242922057 * q^32 + 76352726421 * q^33 - 16566014943 * q^34 - 570464313633 * q^36 - 77721425444 * q^37 + 476314869819 * q^38 + 353897273784 * q^39 - 88855733850 * q^40 - 938882938233 * q^41 + 700091392140 * q^42 - 29709800063 * q^43 - 84148700094 * q^45 + 1553142786144 * q^46 - 1272741434580 * q^47 + 803069876301 * q^48 - 945184029255 * q^49 + 3573994524699 * q^50 - 1993755292875 * q^51 + 1825489374856 * q^52 + 6488294941323 * q^54 - 3772940931372 * q^55 - 7790759725422 * q^56 - 10739943123909 * q^57 + 3747043240302 * q^58 + 5874788534451 * q^59 + 1848130753878 * q^60 - 4867968901544 * q^61 + 5766639947244 * q^63 + 1211169309434 * q^64 - 22156719464856 * q^65 - 6375059860230 * q^66 - 8251061484125 * q^67 + 30687017243265 * q^68 + 23068377735552 * q^69 + 6871822387932 * q^70 - 46243200240621 * q^72 + 16120119648922 * q^73 + 8549243621166 * q^74 + 1090840096221 * q^75 + 14422972781521 * q^76 + 13919363311398 * q^77 + 109811947190436 * q^78 - 10740904544582 * q^79 - 140975607018501 * q^81 - 67076318933382 * q^82 - 11295125984532 * q^83 + 30827942753826 * q^84 + 10590724937466 * q^85 + 97019495740221 * q^86 + 151937485500582 * q^87 - 26136212294541 * q^88 - 392755154255226 * q^90 + 70870424994080 * q^91 - 474274297000284 * q^92 - 124466752375728 * q^93 - 46678164316620 * q^94 + 440317551118746 * q^95 + 823174447870656 * q^96 + 7621755375583 * q^97 - 195117933369168 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

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

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	$-0.323581\pi$
$2$	195.306	−	112.760i	1.52583	−	0.880936i	0.999531	−	0.0306339i	$-0.00975259\pi$
$3$	840.821	−	2018.91i	0.384463	−	0.923140i
$3$	840.821	−	2018.91i	0.384463	−	0.923140i
$4$	17237.5	−	29856.3i	1.05210	−	1.82228i
$5$	103308.	+	59645.1i	1.32235	+	0.763457i	0.984103	−	0.177601i	$-0.0568336\pi$
$5$	103308.	+	59645.1i	1.32235	+	0.763457i	0.338244	+	0.941058i	$0.390167\pi$
$6$	−63434.5	−	489115.i	−0.226604	−	1.74724i
$7$	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
$9$	−3.36901e6	−	3.39508e6i	−0.704376	−	0.709827i
$10$	2.69023e7			2.69023
$11$	−2.55183e7	+	1.47330e7i	−1.30949	+	0.756036i	−0.982011	−	0.188822i	$-0.939533\pi$
$11$	−2.55183e7	+	1.47330e7i	−1.30949	+	0.756036i	−0.327481	+	0.944858i	$0.606200\pi$
$12$	−4.57834e7	−	5.99048e7i	−1.27773	−	1.67183i
$13$	−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
$15$	2.07282e8	−	1.58419e8i	1.21317	−	0.927191i
$16$	−1.77628e8	−	3.07661e8i	−0.661716	−	1.14613i
$17$		−	3.47954e8i		−	0.847968i	−0.905670	−	0.423984i	$-0.860631\pi$
$17$		−	3.47954e8i		−	0.847968i	0.905670	−	0.423984i	$-0.139369\pi$
$18$	−1.04082e9	−	2.83190e8i	−1.70007	−	0.462562i
$19$	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
$21$	7.08108e8	−	9.18363e7i	0.393156	−	0.0509893i
$22$	−3.32258e9	+	5.75488e9i	−1.33204	+	2.30716i
$23$	1.21799e9	+	7.03208e8i	0.357725	+	0.206533i	0.668082	−	0.744087i	$-0.267115\pi$
$23$	1.21799e9	+	7.03208e8i	0.357725	+	0.206533i	−0.310357	+	0.950620i	$0.600449\pi$
$24$	−8.23693e9	−	3.43046e9i	−1.79592	−	0.747952i
$25$	4.06332e9	+	7.03788e9i	0.665734	+	1.15309i
$26$			1.73468e10i			2.15976i
$27$	−9.68709e9	+	3.94707e9i	−0.926076	+	0.377336i
$28$	1.12558e10			0.834203
$29$	8.71076e9	−	5.02916e9i	0.504975	−	0.291548i	−0.225791	−	0.974176i	$-0.572497\pi$
$29$	8.71076e9	−	5.02916e9i	0.504975	−	0.291548i	0.730766	+	0.682628i	$0.239163\pi$
$30$	2.26200e10	−	5.43132e10i	1.03429	−	2.48346i
$31$	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
$33$	8.28825e9	+	6.39069e10i	0.194476	+	1.49951i
$34$	−3.92352e10	−	6.79574e10i	−0.747006	−	1.29385i
$35$			3.89473e10i			0.605343i
$36$	−1.59438e11	+	4.20633e10i	−2.03458	+	0.536767i
$37$	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
$39$	1.02150e11	+	1.33657e11i	0.744365	+	0.973956i
$40$	2.43346e11	−	4.21487e11i	1.48526	−	2.57255i
$41$	−2.44149e11	−	1.40960e11i	−1.25363	−	0.723782i	−0.281799	−	0.959474i	$-0.590931\pi$
$41$	−2.44149e11	−	1.40960e11i	−1.25363	−	0.723782i	−0.971828	+	0.235692i	$0.924264\pi$
$42$	1.27942e11	−	9.77823e10i	0.554969	−	0.424146i
$43$	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
$45$	−1.45547e11	−	5.51685e11i	−0.389507	−	1.47640i
$46$	3.17174e11			0.727768
$47$	−3.91113e11	+	2.25809e11i	−0.772001	+	0.445715i	−0.833588	−	0.552387i	$-0.813717\pi$
$47$	−3.91113e11	+	2.25809e11i	−0.772001	+	0.445715i	0.0615871	+	0.998102i	$0.480384\pi$
$48$	−7.70493e11	+	9.99271e10i	−1.31244	+	0.170214i
$49$	2.85813e11	−	4.95043e11i	0.421414	−	0.729911i
$50$	1.58718e12	+	9.16358e11i	2.03159	+	1.17294i
$51$	−7.02487e11	−	2.92567e11i	−0.782794	−	0.326013i
$52$	1.32590e12	+	2.29653e12i	1.28970	+	2.23382i
$53$		−	1.74490e12i		−	1.48538i	−0.669633	−	0.742692i	$-0.733549\pi$
$53$		−	1.74490e12i		−	1.48538i	0.669633	−	0.742692i	$-0.266451\pi$
$54$	−1.44687e12	+	1.86320e12i	−1.08062	+	1.39156i
$55$	−3.51500e12			−2.30880
$56$	1.15359e12	−	6.66027e11i	0.667938	−	0.385634i
$57$	1.51237e10	−	3.63136e10i	0.00773629	−	0.0185757i
$58$	1.13417e12	−	1.96445e12i	0.513669	−	0.889702i
$59$	3.57141e12	+	2.06195e12i	1.43508	+	0.828542i	0.997502	−	0.0706396i	$-0.0225040\pi$
$59$	3.57141e12	+	2.06195e12i	1.43508	+	0.828542i	0.437575	+	0.899182i	$0.355837\pi$
$60$	−1.15678e12	−	8.91943e12i	−0.413231	−	3.18624i
$61$	−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
$63$	4.09983e11	−	1.50682e12i	0.104084	−	0.382541i
$64$	2.82736e12			0.642868
$65$	−7.94640e12	+	4.58786e12i	−1.62098	+	0.935872i
$66$	8.82487e12	+	1.15468e13i	1.61771	+	2.11667i
$67$	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
$69$	2.44382e12	−	1.86774e12i	0.328191	−	0.250826i
$70$	4.39169e12	+	7.60663e12i	0.533268	+	0.923647i
$71$			8.75750e12i			0.962879i	0.876479	+	0.481440i	$0.159886\pi$
$71$			8.75750e12i			0.962879i	−0.876479	+	0.481440i	$0.840114\pi$
$72$	−1.38516e13	+	1.37452e13i	−1.38093	+	1.37033i
$73$	−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
$75$	1.76253e13	−	2.28588e12i	1.32041	−	0.171247i
$76$	3.10048e11	−	5.37019e11i	0.0211706	−	0.0366686i
$77$	−8.33152e12	−	4.81021e12i	−0.519146	−	0.299729i
$78$	3.50216e13	+	1.45856e13i	1.99376	+	0.830349i
$79$	−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
$81$	−1.76341e11	+	2.28761e13i	−0.00770828	+	0.999970i
$82$	−6.35783e13			−2.55042
$83$	8.74183e12	−	5.04710e12i	0.322148	−	0.185992i	−0.330201	−	0.943910i	$-0.607117\pi$
$83$	8.74183e12	−	5.04710e12i	0.322148	−	0.185992i	0.652350	+	0.757918i	$0.273783\pi$
$84$	9.46415e12	−	2.27245e13i	0.320720	−	0.770087i
$85$	2.07538e13	−	3.59466e13i	0.647388	−	1.12131i
$86$	5.05125e11	+	2.91634e11i	0.0145181	+	0.00838203i
$87$	−2.82922e12	−	2.18148e13i	−0.0749950	−	0.578252i
$88$	6.01091e13	+	1.04112e14i	1.47083	+	2.54754i
$89$			5.62078e13i			1.27077i	0.772196	+	0.635384i	$0.219158\pi$
$89$			5.62078e13i			1.27077i	−0.772196	+	0.635384i	$0.780842\pi$
$90$	−9.06340e13	−	9.13354e13i	−1.89493	−	1.90960i
$91$	−2.51135e13			−0.485980
$92$	4.19904e13	−	2.42432e13i	0.752722	−	0.434585i
$93$	−1.79883e13	−	2.35366e13i	−0.298958	−	0.391169i
$94$	−5.09245e13	+	8.82037e13i	−0.785292	+	1.36017i
$95$	1.85818e12	+	1.07282e12i	0.0266087	+	0.0153625i
$96$	−2.30622e13	+	1.76258e13i	−0.306904	+	0.234557i
$97$	−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
$99$	1.35991e14	+	3.70010e13i	1.45903	+	0.396979i
$100$	2.80167e14			2.80167
$101$	−4.76606e13	+	2.75169e13i	−0.444539	+	0.256655i	−0.705521	−	0.708689i	$-0.749287\pi$
$101$	−4.76606e13	+	2.75169e13i	−0.444539	+	0.256655i	0.260982	+	0.965344i	$0.415954\pi$
$102$	−1.70190e14	+	2.20723e13i	−1.48160	+	0.192153i
$103$	−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
$105$	7.86311e13	+	3.27477e13i	0.558816	+	0.232732i
$106$	−1.96754e14	−	3.40788e14i	−1.30853	−	2.26644i
$107$			1.14144e14i			0.710832i	0.934708	+	0.355416i	$0.115661\pi$
$107$			1.14144e14i			0.710832i	−0.934708	+	0.355416i	$0.884339\pi$
$108$	−4.91368e13	+	3.57258e14i	−0.286708	+	2.08457i
$109$	−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
$111$	3.50390e13	−	8.41327e13i	0.168768	−	0.405232i
$112$	5.79942e13	−	1.00449e14i	0.262336	−	0.454380i
$113$	1.83781e14	+	1.06106e14i	0.781179	+	0.451014i	0.836848	−	0.547435i	$-0.184396\pi$
$113$	1.83781e14	+	1.06106e14i	0.781179	+	0.451014i	−0.0556691	+	0.998449i	$0.517729\pi$
$114$	−1.14098e12	−	8.79760e12i	−0.00455979	−	0.0351585i
$115$	8.38858e13	+	1.45294e14i	0.315358	+	0.546216i
$116$		−	3.46761e14i		−	1.22694i
$117$	3.55731e14	−	9.38498e13i	1.18528	−	0.312703i
$118$	9.30021e14			2.91957
$119$	9.83842e13	−	5.68022e13i	0.291137	−	0.168088i
$120$	−6.46334e14	−	8.45688e14i	−1.80380	−	2.36016i
$121$	2.44247e14	−	4.23049e14i	0.643180	−	1.11402i
$122$	−3.19235e14	−	1.84310e14i	−0.793581	−	0.458174i
$123$	−4.89870e14	+	3.74393e14i	−1.15013	+	0.879006i
$124$	−2.33487e14	−	4.04412e14i	−0.517978	−	0.897165i
$125$			2.41339e14i			0.506124i
$126$	−8.98370e13	−	3.40521e14i	−0.178181	−	0.675382i
$127$	−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
$129$	5.60933e12	−	7.27488e11i	0.00943589	−	0.00122376i
$130$	−1.03465e15	+	1.79207e15i	−1.64889	+	2.85596i
$131$	5.75621e14	+	3.32335e14i	0.869436	+	0.501969i	0.867161	−	0.498028i	$-0.165942\pi$
$131$	5.75621e14	+	3.32335e14i	0.869436	+	0.501969i	0.00227534	+	0.999997i	$0.499276\pi$
$132$	2.05089e15	+	8.54142e14i	2.93715	+	1.22324i
$133$	2.93627e12	+	5.08577e12i	0.00398873	+	0.00690868i
$134$		−	5.19933e14i		−	0.670215i
$135$	−1.23618e15	−	1.70022e14i	−1.51267	−	0.208051i
$136$	−1.41962e15			−1.64968
$137$	3.95132e13	−	2.28130e13i	0.0436213	−	0.0251848i	−0.478031	−	0.878343i	$-0.658649\pi$
$137$	3.95132e13	−	2.28130e13i	0.0436213	−	0.0251848i	0.521652	+	0.853158i	$0.325316\pi$
$138$	2.66687e14	−	6.40346e14i	0.279800	−	0.671832i
$139$	−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
$141$	1.27032e14	+	9.79487e14i	0.114652	+	0.884026i
$142$	9.87494e14	+	1.71039e15i	0.848235	+	1.46919i
$143$		−	2.26650e15i		−	1.85355i
$144$	−4.46103e14	+	1.63957e15i	−0.347454	+	1.27701i
$145$	1.19986e15			0.890337
$146$	−2.19606e15	+	1.26789e15i	−1.55301	+	0.896630i
$147$	−7.59128e14	−	9.93272e14i	−0.511792	−	0.669649i
$148$	7.18329e14	−	1.24418e15i	0.461840	−	0.799930i
$149$	−2.39632e15	−	1.38351e15i	−1.46974	−	0.848555i	−0.470317	−	0.882498i	$-0.655860\pi$
$149$	−2.39632e15	−	1.38351e15i	−1.46974	−	0.848555i	−0.999424	+	0.0339428i	$0.989194\pi$
$150$	3.18458e15	−	2.43387e15i	1.86386	−	1.42449i
$151$	−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
$153$	−1.18133e15	+	1.17226e15i	−0.601911	+	0.597289i
$154$	−2.16959e15			−1.05617
$155$	1.39934e15	−	8.07910e14i	0.651031	−	0.375873i
$156$	5.75132e15	−	7.45903e14i	2.55797	−	0.331749i
$157$	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
$159$	−3.52279e15	−	1.46715e15i	−1.37122	−	0.571075i
$160$	−7.91625e14	−	1.37113e15i	−0.294903	−	0.510788i
$161$			4.59184e14i			0.163759i
$162$	2.54507e15	+	4.48772e15i	0.869148	+	1.53257i
$163$	−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
$165$	−2.95549e15	+	7.09647e15i	−0.887650	+	2.13135i
$166$	1.13822e15	−	1.97145e15i	0.327695	−	0.567584i
$167$	4.80709e15	+	2.77538e15i	1.32699	+	0.766137i	0.984833	−	0.173506i	$-0.0555098\pi$
$167$	4.80709e15	+	2.77538e15i	1.32699	+	0.766137i	0.342155	+	0.939643i	$0.388843\pi$
$168$	−3.74682e14	−	2.88901e15i	−0.0991969	−	0.764863i
$169$	−9.89600e14	−	1.71404e15i	−0.251335	−	0.435325i
$170$		−	9.36076e15i		−	2.28123i
$171$	−6.05976e13	−	6.10665e13i	−0.0141737	−	0.0142834i
$172$	8.91640e13			0.0200212
$173$	6.42000e15	−	3.70659e15i	1.38424	−	0.799193i	0.391585	−	0.920142i	$-0.371927\pi$
$173$	6.42000e15	−	3.70659e15i	1.38424	−	0.799193i	0.992659	+	0.120949i	$0.0385937\pi$
$174$	−3.01240e15	−	3.94154e15i	−0.623832	−	0.816246i
$175$	−1.32664e15	+	2.29781e15i	−0.263929	+	0.457139i
$176$	9.06553e15	+	5.23399e15i	1.73302	+	1.00056i
$177$	7.16581e15	−	5.47661e15i	1.31660	−	1.00623i
$178$	6.33798e15	+	1.09777e16i	1.11947	+	1.93897i
$179$			6.42965e15i			1.09198i	0.837791	+	0.545992i	$0.183847\pi$
$179$			6.42965e15i			1.09198i	−0.837791	+	0.545992i	$0.816153\pi$
$180$	−1.89801e16	−	5.16420e15i	−3.10022	−	0.843520i
$181$	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
$183$	−3.54505e15	+	4.59766e14i	−0.515780	+	0.0668928i
$184$	2.86901e15	−	4.96928e15i	0.401798	−	0.695935i
$185$	4.30510e15	+	2.48555e15i	0.580472	+	0.335136i
$186$	−6.16721e15	−	2.56848e15i	−0.800753	−	0.333492i
$187$	5.12641e15	+	8.87920e15i	0.641094	+	1.11041i
$188$			1.55696e16i			1.87574i
$189$	−2.69741e15	−	2.09469e15i	−0.313123	−	0.243157i
$190$	4.83885e14			0.0541336
$191$	−1.13009e15	+	6.52459e14i	−0.121865	+	0.0703589i	−0.559694	−	0.828700i	$-0.689081\pi$
$191$	−1.13009e15	+	6.52459e14i	−0.121865	+	0.0703589i	0.437828	+	0.899059i	$0.355748\pi$
$192$	2.37731e15	−	5.70819e15i	0.247159	−	0.593458i
$193$	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
$195$	2.58096e15	+	1.99006e16i	0.240735	+	1.85620i
$196$	−9.85343e15	−	1.70666e16i	−0.886737	−	1.53587i
$197$		−	6.69322e14i		−	0.0581261i	−0.999578	−	0.0290631i	$-0.990748\pi$
$197$		−	6.69322e14i		−	0.0581261i	0.999578	−	0.0290631i	$-0.00925236\pi$
$198$	3.07321e16	−	8.10781e15i	2.57594	−	0.679590i
$199$	−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
$201$	−3.06173e15	−	4.00608e15i	−0.230991	−	0.302237i
$202$	−6.20559e15	+	1.07484e16i	−0.452193	+	0.783221i
$203$	2.84400e15	+	1.64198e15i	0.200197	+	0.115584i
$204$	−2.08441e16	+	1.59305e16i	−1.41766	+	1.08348i
$205$	−1.68151e16	−	2.91246e16i	−1.10515	−	1.91418i
$206$			3.55790e15i			0.226008i
$207$	−1.71598e15	−	6.50429e15i	−0.105371	−	0.399400i
$208$	2.73261e16			1.62231
$209$	−4.58992e14	+	2.64999e14i	−0.0263500	+	0.0152132i
$210$	1.90497e16	−	2.47061e15i	1.05768	−	0.137173i
$211$	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
$213$	1.76806e16	+	7.36349e15i	0.888872	+	0.370191i
$214$	1.28709e16	+	2.22930e16i	0.626198	+	1.08461i
$215$			3.08524e14i			0.0145285i
$216$	1.61036e16	+	3.95223e16i	0.734086	+	1.80163i
$217$	4.42243e15			0.195183
$218$	−1.87422e16	+	1.08208e16i	−0.800988	+	0.462451i
$219$	−9.45437e15	+	2.27010e16i	−0.391312	+	0.939586i
$220$	−6.05900e16	+	1.04945e17i	−2.42908	+	4.20730i
$221$	2.31786e16	+	1.33822e16i	0.900206	+	0.519734i
$222$	−2.64347e15	−	2.03826e16i	−0.0994725	−	0.766987i
$223$	−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
$225$	1.02048e16	−	3.75060e16i	0.349564	−	1.28476i
$226$	4.78579e16			1.58926
$227$	−4.30758e16	+	2.48698e16i	−1.38692	+	0.800740i	−0.992967	−	0.118390i	$-0.962227\pi$
$227$	−4.30758e16	+	2.48698e16i	−1.38692	+	0.800740i	−0.393955	+	0.919130i	$0.628893\pi$
$228$	−8.23496e14	−	1.07749e15i	−0.0257109	−	0.0336412i
$229$	−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
$231$	−1.67167e16	+	1.27761e16i	−0.476284	+	0.364010i
$232$	−2.05184e16	−	3.55390e16i	−0.567190	−	0.982402i
$233$			1.10854e16i			0.297345i	0.988886	+	0.148672i	$0.0475000\pi$
$233$			1.10854e16i			0.297345i	−0.988886	+	0.148672i	$0.952500\pi$
$234$	5.88938e16	−	5.84416e16i	1.53306	−	1.52129i
$235$	−5.38737e16			−1.36114
$236$	1.23125e17	−	7.10860e16i	3.01968	−	1.74341i
$237$	−2.23986e15	+	2.90493e14i	−0.0533313	+	0.00691667i
$238$	1.28100e16	−	2.21876e16i	0.296149	−	0.512945i
$239$	−1.63305e16	−	9.42841e15i	−0.366618	−	0.211667i	0.305362	−	0.952236i	$-0.401223\pi$
$239$	−1.63305e16	−	9.42841e15i	−0.366618	−	0.211667i	−0.671980	+	0.740569i	$0.734556\pi$
$240$	−8.55585e16	−	3.56328e16i	−1.86545	−	0.776911i
$241$	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
$243$	4.60365e16	+	1.95907e16i	0.920149	+	0.391568i
$244$	−5.63509e16			−1.09439
$245$	5.90537e16	−	3.40947e16i	1.11451	−	0.643464i
$246$	−5.34579e16	+	1.28359e17i	−0.980543	+	2.35440i
$247$	−6.91765e14	+	1.19817e15i	−0.0123333	+	0.0213619i
$248$	−4.78594e16	−	2.76317e16i	−0.829480	−	0.478901i
$249$	−2.83931e15	−	2.18927e16i	−0.0478430	−	0.368895i
$250$	2.72133e16	+	4.71348e16i	0.445863	+	0.772257i
$251$			6.39458e16i			1.01882i	0.860525	+	0.509408i	$0.170136\pi$
$251$			6.39458e16i			1.01882i	−0.860525	+	0.509408i	$0.829864\pi$
$252$	−3.79211e16	−	3.82145e16i	−0.587593	−	0.592140i
$253$	−4.14414e16			−0.624584
$254$	−9.36715e16	+	5.40813e16i	−1.37332	+	0.792886i
$255$	−5.51226e16	−	7.21246e16i	−0.786228	−	1.02873i
$256$	7.32567e16	−	1.26884e17i	1.01664	−	1.76087i
$257$	1.93005e16	+	1.11431e16i	0.260637	+	0.150479i	0.624625	−	0.780925i	$-0.285252\pi$
$257$	1.93005e16	+	1.11431e16i	0.260637	+	0.150479i	−0.363988	+	0.931404i	$0.618585\pi$
$258$	1.01350e15	−	7.74589e14i	0.0133195	−	0.0101797i
$259$	6.80285e15	+	1.17829e16i	0.0870147	+	0.150714i
$260$			3.16334e17i			3.93851i
$261$	−4.64210e16	−	1.26304e16i	−0.562641	−	0.153086i
$262$	1.49896e17			1.76881
$263$	−3.33508e16	+	1.92551e16i	−0.383191	+	0.221236i	−0.679206	−	0.733948i	$-0.737676\pi$
$263$	−3.33508e16	+	1.92551e16i	−0.383191	+	0.221236i	0.296015	+	0.955183i	$0.404342\pi$
$264$	2.60733e17	−	3.38152e16i	2.91722	−	0.378342i
$265$	1.04075e17	−	1.80262e17i	1.13403	−	1.96419i
$266$	1.14694e15	+	6.62187e14i	0.0121722	+	0.00702763i
$267$	1.13478e17	+	4.72607e16i	1.17310	+	0.488563i
$268$	−3.97410e16	−	6.88334e16i	−0.400217	−	0.693196i
$269$		−	7.62726e16i		−	0.748347i	−0.927359	−	0.374173i	$-0.877927\pi$
$269$		−	7.62726e16i		−	0.748347i	0.927359	−	0.374173i	$-0.122073\pi$
$270$	−2.60605e17	+	1.06185e17i	−2.49136	+	1.01512i
$271$	−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
$273$	−2.11160e16	+	5.07019e16i	−0.186841	+	0.448628i
$274$	5.14477e15	−	8.91101e15i	0.0443723	−	0.0768551i
$275$	−2.07378e17	−	1.19730e17i	−1.74355	−	1.00664i
$276$	−1.36383e16	−	1.05159e17i	−0.111788	−	0.861950i
$277$	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
$279$	−6.26433e16	+	1.65267e16i	−0.476042	+	0.125591i
$280$	1.58901e17			1.17766
$281$	1.72947e17	−	9.98511e16i	1.25017	−	0.721786i	0.279027	−	0.960283i	$-0.409988\pi$
$281$	1.72947e17	−	9.98511e16i	1.25017	−	0.721786i	0.971143	+	0.238497i	$0.0766547\pi$
$282$	1.35257e17	+	1.76975e17i	0.953708	+	1.24787i
$283$	−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
$285$	3.72833e15	−	2.84945e15i	0.0244118	−	0.0186572i
$286$	−2.55570e17	−	4.42661e17i	−1.63286	−	2.82819i
$287$		−	9.20444e16i		−	0.573884i
$288$	1.61936e16	+	6.13806e16i	0.0985362	+	0.373494i
$289$	4.73057e16			0.280950
$290$	2.34339e17	−	1.35296e17i	1.35850	−	0.784329i
$291$	−2.33079e17	+	3.02286e16i	−1.31902	+	0.171067i
$292$	−1.93823e17	+	3.35710e17i	−1.07084	+	1.85475i
$293$	−6.23149e16	−	3.59775e16i	−0.336139	−	0.194070i	0.322425	−	0.946595i	$-0.395502\pi$
$293$	−6.23149e16	−	3.59775e16i	−0.336139	−	0.194070i	−0.658563	+	0.752525i	$0.728835\pi$
$294$	−2.60263e17	−	1.08393e17i	−1.37082	−	0.570911i
$295$	2.45971e17	+	4.26034e17i	1.26511	+	2.19124i
$296$		−	1.70019e17i		−	0.853994i
$297$	1.89046e17	−	2.43442e17i	0.927410	−	1.19427i
$298$	−6.24019e17			−2.99009
$299$	−9.36871e16	+	5.40902e16i	−0.438512	+	0.253175i
$300$	2.35570e17	−	5.65630e17i	1.07714	−	2.58633i
$301$	−4.22208e14	+	7.31286e14i	−0.00188609	+	0.00326680i
$302$	−2.30552e16	−	1.33109e16i	−0.100628	−	0.0580978i
$303$	1.54800e16	+	1.19359e17i	0.0660195	+	0.509046i
$304$	−3.19496e15	−	5.53383e15i	−0.0133153	−	0.0230627i
$305$		−	1.94985e17i		−	0.794148i
$306$	−9.85370e16	+	3.62156e17i	−0.392238	+	1.44160i
$307$	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
$309$	2.09514e16	+	2.74136e16i	0.0778939	+	0.101919i
$310$	1.82200e17	−	3.15579e17i	0.662240	−	1.14703i
$311$	3.50740e17	+	2.02500e17i	1.24641	+	0.719618i	0.970393	−	0.241533i	$-0.0776503\pi$
$311$	3.50740e17	+	2.02500e17i	1.24641	+	0.719618i	0.276022	+	0.961151i	$0.410984\pi$
$312$	5.45306e17	−	4.16761e17i	1.89478	−	1.44812i
$313$	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
$315$	1.32229e17	−	1.31214e17i	0.429688	−	0.426389i
$316$	−3.56041e16			−0.113159
$317$	−3.51492e17	+	2.02934e17i	−1.09270	+	0.630869i	−0.934293	−	0.356505i	$-0.883968\pi$
$317$	−3.51492e17	+	2.02934e17i	−1.09270	+	0.630869i	−0.158404	+	0.987374i	$0.550635\pi$
$318$	−8.53456e17	+	1.10687e17i	−2.59532	+	0.336594i
$319$	−1.48189e17	+	2.56671e17i	−0.440841	+	0.763558i
$320$	2.92090e17	+	1.68638e17i	0.850095	+	0.490802i
$321$	2.30446e17	+	9.59747e16i	0.656198	+	0.273289i
$322$	5.17775e16	+	8.96812e16i	0.144261	+	0.249868i
$323$		−	6.25857e15i		−	0.0170631i
$324$	6.79956e17	+	3.99593e17i	1.81412	+	1.06611i
$325$	−6.25095e17			−1.63216
$326$	−3.25668e17	+	1.88025e17i	−0.832247	+	0.480498i
$327$	−8.06882e16	+	1.93742e17i	−0.201825	+	0.484606i
$328$	−5.75100e17	+	9.96102e17i	−1.40808	+	2.43886i
$329$	−1.27695e17	−	7.37250e16i	−0.306058	−	0.176703i
$330$	2.22973e17	+	1.71924e18i	0.523184	+	4.03403i
$331$	−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
$333$	−1.40395e17	−	1.41481e17i	−0.309201	−	0.311594i
$334$	1.25180e18			2.69967
$335$	2.38177e17	−	1.37511e17i	0.503020	−	0.290419i
$336$	−1.54034e17	−	2.01544e17i	−0.318598	−	0.416865i
$337$	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
$339$	3.68744e17	−	2.81820e17i	0.716683	−	0.547740i
$340$	−7.15488e17	−	1.23926e18i	−1.36223	−	2.35945i
$341$			3.99125e17i			0.744438i
$342$	−1.87209e16	−	5.09367e15i	−0.0342093	−	0.00930782i
$343$	4.08066e17			0.730586
$344$	9.13826e15	−	5.27598e15i	0.0160308	−	0.00925537i
$345$	3.63869e17	−	4.71911e16i	0.625477	−	0.0811197i
$346$	8.35909e17	−	1.44784e18i	1.40808	−	2.43886i
$347$	−6.01786e17	−	3.47441e17i	−0.993426	−	0.573555i	−0.0871295	−	0.996197i	$-0.527769\pi$
$347$	−6.01786e17	−	3.47441e17i	−0.993426	−	0.573555i	−0.906297	+	0.422642i	$0.861103\pi$
$348$	−7.00079e17	−	2.91564e17i	−1.13264	−	0.471715i
$349$	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
$351$	1.09632e17	−	7.97099e17i	0.167027	−	1.21440i
$352$	3.91080e17			0.584073
$353$	−4.47436e17	+	2.58327e17i	−0.655100	+	0.378222i	−0.790407	−	0.612581i	$-0.790131\pi$
$353$	−4.47436e17	+	2.58327e17i	−0.655100	+	0.378222i	0.135307	+	0.990804i	$0.456798\pi$
$354$	7.81981e17	−	1.87763e18i	1.12247	−	2.69517i
$355$	−5.22342e17	+	9.04723e17i	−0.735117	+	1.27326i
$356$	1.67816e18	+	9.68884e17i	2.31570	+	1.33697i
$357$	−3.19548e16	−	2.46389e17i	−0.0432373	−	0.333383i
$358$	7.25006e17	+	1.25575e18i	0.961967	+	1.66618i
$359$			5.70293e17i			0.742057i	0.928622	+	0.371028i	$0.120995\pi$
$359$			5.70293e17i			0.742057i	−0.928622	+	0.371028i	$0.879005\pi$
$360$	−2.25082e18	+	5.93816e17i	−2.87225	+	0.757765i
$361$	−7.98683e17			−0.999595
$362$	5.65803e17	−	3.26667e17i	0.694553	−	0.401001i
$363$	−6.48728e17	−	8.48821e17i	−0.781118	−	1.02204i
$364$	−4.32896e17	+	7.49798e17i	−0.511298	+	0.885593i
$365$	−1.16162e18	−	6.70662e17i	−1.34590	−	0.777058i
$366$	−6.40525e17	+	4.89534e17i	−0.728062	+	0.556436i
$367$	−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
$369$	3.43972e17	+	1.30380e18i	0.369265	+	1.39967i
$370$	1.12108e18			1.18093
$371$	4.93371e17	−	2.84848e17i	0.509983	−	0.294439i
$372$	−1.01279e18	+	1.31352e17i	−1.02735	+	0.133240i
$373$	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
$375$	4.87241e17	+	2.02923e17i	0.467224	+	0.194586i
$376$	9.21279e17	+	1.59570e18i	0.867114	+	1.50189i
$377$			7.73679e17i			0.714778i
$378$	−7.63017e17	−	1.04944e17i	−0.691977	−	0.0951734i
$379$	−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
$381$	−4.03270e17	+	9.68298e17i	−0.346036	+	0.830872i
$382$	−1.47142e17	+	2.54858e17i	−0.123963	+	0.214711i
$383$	7.70880e17	+	4.45068e17i	0.637669	+	0.368158i	0.783716	−	0.621119i	$-0.213322\pi$
$383$	7.70880e17	+	4.45068e17i	0.637669	+	0.368158i	−0.146047	+	0.989278i	$0.546655\pi$
$384$	−2.40518e17	−	1.85453e18i	−0.195357	−	1.50631i
$385$	−5.73811e17	−	9.93869e17i	−0.457661	−	0.792691i
$386$		−	1.23794e18i		−	0.969591i
$387$	3.24771e15	−	1.19364e16i	0.00249804	−	0.00918114i
$388$	−3.70495e18			−2.79872
$389$	6.37685e17	−	3.68167e17i	0.473106	−	0.273148i	−0.244433	−	0.969666i	$-0.578602\pi$
$389$	6.37685e17	−	3.68167e17i	0.473106	−	0.273148i	0.717539	+	0.696518i	$0.245268\pi$
$390$	2.74807e18	+	3.59568e18i	2.00251	+	2.62016i
$391$	2.44684e17	−	4.23805e17i	0.175133	−	0.303340i
$392$	−2.01972e18	−	1.16609e18i	−1.42000	−	0.819839i
$393$	1.15495e18	−	8.82692e17i	0.797654	−	0.609623i
$394$	−7.54726e16	−	1.30722e17i	−0.0512054	−	0.0886903i
$395$		−	1.23197e17i		−	0.0821144i
$396$	3.44887e18	−	3.42238e18i	2.25845	−	2.24111i
$397$	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
$399$	1.27366e16	−	1.65184e15i	0.00791120	−	0.00102602i
$400$	1.44352e18	−	2.50025e18i	0.881054	−	1.52603i
$401$	8.78035e17	+	5.06934e17i	0.526625	+	0.304047i	0.739641	−	0.673002i	$-0.234995\pi$
$401$	8.78035e17	+	5.06934e17i	0.526625	+	0.304047i	−0.213016	+	0.977049i	$0.568329\pi$
$402$	−1.04970e18	−	4.37171e17i	−0.618703	−	0.257673i
$403$	5.20947e17	+	9.02306e17i	0.301758	+	0.522659i
$404$			1.89729e18i			1.08010i
$405$	−1.38267e18	+	2.35278e18i	−0.773628	+	1.31642i
$406$	7.40598e17			0.407287
$407$	−1.06341e18	+	6.13959e17i	−0.574829	+	0.331878i
$408$	−1.19364e18	+	2.86607e18i	−0.634239	+	1.52288i
$409$	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
$411$	−1.28337e16	−	9.89552e16i	−0.00647830	−	0.0499512i
$412$	2.71948e17	+	4.71027e17i	0.134960	+	0.233757i
$413$			1.34642e18i			0.656948i
$414$	−1.06856e18	−	1.07683e18i	−0.512623	−	0.516589i
$415$	1.20414e18			0.567989
$416$	8.84119e17	−	5.10446e17i	0.410069	−	0.236754i
$417$	5.74694e17	+	7.51952e17i	0.262110	+	0.342955i
$418$	−5.97625e16	+	1.03512e17i	−0.0268037	+	0.0464254i
$419$	1.65428e18	+	9.55098e17i	0.729643	+	0.421260i	0.818292	−	0.574803i	$-0.194921\pi$
$419$	1.65428e18	+	9.55098e17i	0.729643	+	0.421260i	−0.0886486	+	0.996063i	$0.528255\pi$
$420$	2.33313e18	−	1.78314e18i	1.01203	−	0.773466i
$421$	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
$423$	2.08431e18	+	5.67107e17i	0.860159	+	0.234036i
$424$	−7.11900e18			−2.88973
$425$	2.44886e18	−	1.41385e18i	0.977780	−	0.564521i
$426$	4.28342e18	−	5.55528e17i	1.68238	−	0.218192i
$427$	2.66832e17	−	4.62167e17i	0.103096	−	0.178568i
$428$	3.40792e18	+	1.96756e18i	1.29534	+	0.747864i
$429$	−4.57586e18	−	1.90572e18i	−1.71109	−	0.712621i
$430$	3.47891e16	+	6.02565e16i	0.0127986	+	0.0221679i
$431$		−	3.56102e18i		−	1.28894i	−0.764628	−	0.644472i	$-0.777077\pi$
$431$		−	3.56102e18i		−	1.28894i	0.764628	−	0.644472i	$-0.222923\pi$
$432$	2.93506e18	+	2.27923e18i	1.04527	+	0.811711i
$433$	−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
$435$	1.00887e18	−	2.42240e18i	0.342302	−	0.821906i
$436$	−1.65418e18	+	2.86512e18i	−0.552302	+	0.956615i
$437$	2.19077e16	+	1.26484e16i	0.00719826	+	0.00415592i
$438$	7.13271e17	+	5.49971e18i	0.230641	+	1.77837i
$439$	−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
$441$	−2.64362e18	+	6.97445e17i	−0.814945	+	0.215001i
$442$	6.03589e18			1.83141
$443$	4.01235e18	−	2.31653e18i	1.19832	−	0.691850i	0.238140	−	0.971231i	$-0.423462\pi$
$443$	4.01235e18	−	2.31653e18i	1.19832	−	0.691850i	0.960180	+	0.279380i	$0.0901291\pi$
$444$	−1.90790e18	−	2.49637e18i	−0.560887	−	0.733887i
$445$	−3.35252e18	+	5.80673e18i	−0.970177	+	1.68040i
$446$	−4.56991e18	−	2.63844e18i	−1.30186	−	0.751628i
$447$	−4.80806e18	+	3.67466e18i	−1.34840	+	1.03054i
$448$	4.61556e17	+	7.99439e17i	0.127432	+	0.220719i
$449$			2.27057e18i			0.617177i	0.951196	+	0.308588i	$0.0998566\pi$
$449$			2.27057e18i			0.617177i	−0.951196	+	0.308588i	$0.900143\pi$
$450$	−2.23611e18	−	8.47582e18i	−0.598420	−	2.26827i
$451$	8.30703e18			2.18882
$452$	6.33585e18	−	3.65800e18i	1.64375	−	0.949020i
$453$	−2.56024e17	+	3.32044e16i	−0.0654024	+	0.00848220i
$454$	−5.60863e18	+	9.71443e18i	−1.41080	+	2.44358i
$455$	−2.59444e18	−	1.49790e18i	−0.642634	−	0.371025i
$456$	−1.48156e17	−	6.17029e16i	−0.0361381	−	0.0150505i
$457$	−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
$459$	1.37340e18	+	3.37066e18i	0.319969	+	0.785283i
$460$	5.78394e18			1.32715
$461$	3.22510e18	−	1.86201e18i	0.728848	−	0.420801i	−0.0891526	−	0.996018i	$-0.528416\pi$
$461$	3.22510e18	−	1.86201e18i	0.728848	−	0.420801i	0.818001	+	0.575217i	$0.195083\pi$
$462$	−1.82424e18	+	4.38021e18i	−0.406058	+	0.974991i
$463$	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
$465$	−4.54501e17	−	3.50445e18i	−0.0966861	−	0.745502i
$466$	1.24999e18	+	2.16504e18i	0.261942	+	0.453697i
$467$			4.68367e18i			0.966869i	0.875380	+	0.483435i	$0.160611\pi$
$467$			4.68367e18i			0.966869i	−0.875380	+	0.483435i	$0.839389\pi$
$468$	3.32992e18	−	1.22386e19i	0.677193	−	2.48891i
$469$	7.52725e17			0.150809
$470$	−1.05218e19	+	6.07479e18i	−2.07686	+	1.19907i
$471$	−3.86492e18	−	5.05700e18i	−0.751612	−	0.983438i
$472$	8.41255e18	−	1.45710e19i	1.61188	−	2.79186i
$473$	−6.59987e16	−	3.81044e16i	−0.0124597	−	0.00719361i
$474$	−4.04702e17	+	3.09301e17i	−0.0752812	+	0.0575351i
$475$	7.30860e16	+	1.26589e17i	0.0133961	+	0.0232028i
$476$		−	3.91652e18i		−	0.707378i
$477$	−5.92407e18	+	5.87858e18i	−1.05437	+	1.04627i
$478$	−4.25258e18			−0.745860
$479$	−2.56355e18	+	1.48007e18i	−0.443092	+	0.255819i	−0.704908	−	0.709299i	$-0.749012\pi$
$479$	−2.56355e18	+	1.48007e18i	−0.443092	+	0.255819i	0.261817	+	0.965118i	$0.415678\pi$
$480$	−3.43381e18	+	4.45339e17i	−0.584908	+	0.0758582i
$481$	−1.60270e18	+	2.77596e18i	−0.269053	+	0.466013i
$482$	1.36184e19	+	7.86262e18i	2.25319	+	1.30088i
$483$	9.27050e17	+	3.86091e17i	0.151173	+	0.0629593i
$484$	−8.42045e18	−	1.45846e19i	−1.35337	−	2.34411i
$485$		−	1.28198e19i		−	2.03090i
$486$	1.12002e19	−	1.36488e18i	1.74893	−	0.213129i
$487$	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
$489$	−1.40205e18	+	3.36649e18i	−0.209702	+	0.503518i
$490$	7.68902e18	−	1.33178e19i	1.13370	−	1.96363i
$491$	−6.04995e18	−	3.49294e18i	−0.879389	−	0.507716i	−0.00893228	−	0.999960i	$-0.502843\pi$
$491$	−6.04995e18	−	3.49294e18i	−0.879389	−	0.507716i	−0.870457	+	0.492244i	$0.836177\pi$
$492$	2.73383e18	+	2.10793e19i	0.391756	+	3.02065i
$493$	−1.74992e18	−	3.03095e18i	−0.247223	−	0.428203i
$494$			3.12013e17i			0.0434594i
$495$	1.18421e19	+	1.19337e19i	1.62627	+	1.63885i
$496$	−4.81205e18			−0.651566
$497$	−2.47619e18	+	1.42963e18i	−0.330589	+	0.190866i
$498$	−3.02315e18	−	3.95560e18i	−0.397973	−	0.520723i
$499$	−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
$501$	9.64513e18	−	7.37148e18i	1.21743	−	0.930445i
$502$	7.21051e18	+	1.24890e19i	0.897512	+	1.55454i
$503$			1.30311e19i			1.59958i	0.600279	+	0.799791i	$0.295056\pi$
$503$			1.30311e19i			1.59958i	−0.600279	+	0.799791i	$0.704944\pi$
$504$	−6.14768e18	−	1.67269e18i	−0.744213	−	0.202489i
$505$	−6.56499e18			−0.783780
$506$	−8.09375e18	+	4.67293e18i	−0.953007	+	0.550219i
$507$	−4.29256e18	+	5.56713e17i	−0.498495	+	0.0646511i
$508$	−8.26738e18	+	1.43195e19i	−0.946939	+	1.64015i
$509$	3.96383e18	+	2.28852e18i	0.447807	+	0.258541i	0.706903	−	0.707310i	$-0.250092\pi$
$509$	3.96383e18	+	2.28852e18i	0.447807	+	0.258541i	−0.259097	+	0.965851i	$0.583425\pi$
$510$	−1.88985e19	−	7.87072e18i	−2.10589	−	0.877048i
$511$	−1.83557e18	−	3.17931e18i	−0.201756	−	0.349451i
$512$		−	1.90320e19i		−	2.06346i
$513$	−1.74239e17	+	7.09950e16i	−0.0186348	+	0.00759287i
$514$	5.02599e18			0.530249
$515$	−1.62984e18	+	9.40990e17i	−0.169627	+	0.0979342i
$516$	7.49709e16	−	1.80014e17i	0.00769741	−	0.0184824i
$517$	6.65370e18	−	1.15245e19i	0.673953	−	1.16732i
$518$	2.65727e18	+	1.53418e18i	0.265539	+	0.153309i
$519$	−2.08519e18	−	1.60780e19i	−0.205577	−	1.58511i
$520$	1.87180e19	+	3.24205e19i	1.82069	+	3.15352i
$521$			1.78294e19i			1.71109i	0.517728	+	0.855545i	$0.326778\pi$
$521$			1.78294e19i			1.71109i	−0.517728	+	0.855545i	$0.673222\pi$
$522$	−1.04905e19	+	2.76763e18i	−0.993351	+	0.262068i
$523$	−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
$525$	3.52360e18	+	4.61042e18i	0.320532	+	0.419397i
$526$	−4.34240e18	+	7.52125e18i	−0.389789	+	0.675134i
$527$	−4.08170e18	−	2.35657e18i	−0.361548	−	0.208740i
$528$	1.81894e19	−	1.39016e19i	1.58994	−	1.21515i
$529$	−4.80742e18	−	8.32669e18i	−0.414688	−	0.718262i
$530$		−	4.69417e19i		−	3.99602i
$531$	−5.03161e18	−	1.90720e19i	−0.422713	−	1.60226i
$532$	2.02456e17			0.0167861
$533$	1.87798e19	−	1.08425e19i	1.53674	−	0.887236i
$534$	2.74921e19	−	3.56551e18i	2.22033	−	0.287961i
$535$	−6.80814e18	+	1.17920e19i	−0.542690	+	0.939967i
$536$	−8.14597e18	−	4.70308e18i	−0.640899	−	0.370023i
$537$	1.29809e19	+	5.40618e18i	1.00805	+	0.419827i
$538$	−8.60049e18	−	1.48965e19i	−0.659245	−	1.14185i
$539$			1.68435e19i			1.27442i
$540$	−2.63849e19	+	3.39770e19i	−1.97061	+	2.53763i
$541$	−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
$543$	2.43587e18	−	5.84881e18i	0.175007	−	0.420212i
$544$	−2.30907e18	+	3.99942e18i	−0.163774	+	0.283665i
$545$	−9.91385e18	−	5.72376e18i	−0.694171	−	0.400780i
$546$	1.59307e18	+	1.22834e19i	0.110125	+	0.849123i
$547$	−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
$549$	−2.05252e18	+	7.54371e18i	−0.136547	+	0.501855i
$550$	−5.40028e19			−3.54713
$551$	1.56678e17	−	9.04584e16i	0.0101613	−	0.00586661i
$552$	−7.62019e18	−	9.97055e18i	−0.487969	−	0.638477i
$553$	1.68592e17	−	2.92010e17i	0.0106601	−	0.0184638i
$554$	4.74999e19	+	2.74241e19i	2.96568	+	1.71223i
$555$	8.63792e18	−	6.60170e18i	0.532548	−	0.407010i
$556$	7.45949e18	+	1.29202e19i	0.454136	+	0.786586i
$557$		−	2.05977e19i		−	1.23832i	−0.785265	−	0.619160i	$-0.787473\pi$
$557$		−	2.05977e19i		−	1.23832i	0.785265	−	0.619160i	$-0.212527\pi$
$558$	−1.03710e19	+	1.02914e19i	−0.615720	+	0.610992i
$559$	−1.98939e17			−0.0116637
$560$	1.19826e19	−	6.91814e18i	0.693799	−	0.400565i
$561$	2.22367e19	−	2.88393e18i	1.27154	−	0.164909i
$562$	2.25184e19	−	3.90030e19i	1.27169	−	2.20264i
$563$	−1.44839e19	−	8.36228e18i	−0.807842	−	0.466408i	0.0383639	−	0.999264i	$-0.487785\pi$
$563$	−1.44839e19	−	8.36228e18i	−0.807842	−	0.466408i	−0.846206	+	0.532856i	$0.821119\pi$
$564$	3.14336e19	+	1.30912e19i	1.73157	+	0.721153i
$565$	1.26574e19	+	2.19232e19i	0.688660	+	1.19279i
$566$			3.46528e18i			0.186219i
$567$	−6.49702e18	+	3.68458e18i	−0.344852	+	0.195572i
$568$	3.57297e19			1.87323
$569$	−2.80623e19	+	1.62018e19i	−1.45324	+	0.839028i	−0.998664	−	0.0516804i	$-0.983542\pi$
$569$	−2.80623e19	+	1.62018e19i	−1.45324	+	0.839028i	−0.454575	+	0.890708i	$0.650209\pi$
$570$	4.06861e17	−	9.76920e17i	0.0208124	−	0.0499729i
$571$	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
$573$	3.67049e17	+	2.83015e18i	0.0180985	+	0.139549i
$574$	−1.03789e19	−	1.79768e19i	−0.505555	−	0.875647i
$575$			1.14294e19i			0.549984i
$576$	−9.52542e18	−	9.59913e18i	−0.452821	−	0.456325i
$577$	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
$579$	−7.28984e18	−	9.53831e18i	−0.334171	−	0.437242i
$580$	2.06826e19	−	3.58233e19i	0.936720	−	1.62245i
$581$	2.85414e18	+	1.64784e18i	0.127715	+	0.0737364i
$582$	−4.21131e19	+	3.21858e19i	−1.86190	+	1.42299i
$583$	2.57076e19	+	4.45268e19i	1.12300	+	1.94510i
$584$			4.58752e19i			1.98010i
$585$	4.23477e19	+	1.15221e19i	1.80609	+	0.491408i
$586$	−1.62273e19			−0.683852
$587$	−8.23102e18	+	4.75218e18i	−0.342757	+	0.197891i	−0.661491	−	0.749953i	$-0.730076\pi$
$587$	−8.23102e18	+	4.75218e18i	−0.342757	+	0.197891i	0.318733	+	0.947844i	$0.396743\pi$
$588$	−4.27409e19	+	5.54318e18i	−1.75874	+	0.228096i
$589$	1.21818e17	−	2.10995e17i	0.00495341	−	0.00857956i
$590$	9.60790e19	+	5.54712e19i	3.86068	+	2.22897i
$591$	−1.35130e18	−	5.62780e17i	−0.0536586	−	0.0223473i
$592$	−7.40218e18	−	1.28210e19i	−0.290474	−	0.503116i
$593$			4.81259e17i			0.0186636i	0.999956	+	0.00933182i	$0.00297045\pi$
$593$			4.81259e17i			0.0186636i	−0.999956	+	0.00933182i	$0.997030\pi$
$594$	9.47124e18	−	6.88624e19i	0.362996	−	2.63923i
$595$	1.35519e19			0.513311
$596$	−8.26133e19	+	4.76968e19i	−3.09262	+	1.78552i
$597$	−1.01721e19	+	2.44244e19i	−0.376348	+	0.903656i
$598$	−1.21984e19	+	2.11283e19i	−0.446062	+	0.772602i
$599$	4.07021e17	+	2.34994e17i	0.0147106	+	0.00849315i	0.507337	−	0.861748i	$-0.330630\pi$
$599$	4.07021e17	+	2.34994e17i	0.0147106	+	0.00849315i	−0.492627	+	0.870241i	$0.663963\pi$
$600$	−9.32613e18	−	7.19095e19i	−0.333152	−	2.56879i
$601$	−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
$603$	−1.06623e19	+	2.81295e18i	−0.367814	+	0.0970377i
$604$	−4.06967e18			−0.138772
$605$	5.04656e19	−	2.91363e19i	1.70101	−	0.982081i
$606$	1.64822e19	+	2.15660e19i	0.549172	+	0.718557i
$607$	−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
$609$	5.70630e18	−	4.36115e18i	0.183668	−	0.140372i
$610$	−2.19864e19	−	3.80816e19i	−0.699593	−	1.21173i
$611$		−	3.47382e19i		−	1.09275i
$612$	1.46361e19	+	5.54771e19i	0.455162	+	1.72526i
$613$	−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
$615$	−7.29384e19	+	9.45956e18i	−2.19195	+	0.284279i
$616$	−1.96251e19	+	3.39917e19i	−0.583106	+	1.00997i
$617$	−4.58698e18	−	2.64829e18i	−0.134751	−	0.0777983i	0.431109	−	0.902300i	$-0.358122\pi$
$617$	−4.58698e18	−	2.64829e18i	−0.134751	−	0.0777983i	−0.565860	+	0.824501i	$0.691456\pi$
$618$	7.18308e18	+	2.99156e18i	0.208637	+	0.0868917i
$619$	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
$621$	−1.45744e19	−	2.00454e18i	−0.409213	−	0.0562826i
$622$	9.13354e19			2.53575
$623$	−1.58928e19	+	9.17570e18i	−0.436298	+	0.251897i
$624$	2.29763e19	−	5.51688e19i	0.623718	−	1.49762i
$625$	1.04059e19	−	1.80235e19i	0.279330	−	0.483814i
$626$	4.43673e19	+	2.56155e19i	1.17772	+	0.679958i
$627$	1.49079e17	+	1.14948e18i	0.00391330	+	0.0301737i
$628$	−5.01663e19	−	8.68906e19i	−1.30225	−	2.25557i
$629$		−	1.45001e19i		−	0.372234i
$630$	1.10295e19	−	4.05370e19i	0.280008	−	1.02912i
$631$	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
$633$	−4.86566e19	−	6.36642e19i	−1.19486	−	1.56340i
$634$	−4.57655e19	+	7.92682e19i	−1.11151	+	1.92519i
$635$	−4.95482e19	−	2.86067e19i	−1.19018	−	0.687150i
$636$	−1.04528e20	+	7.98874e19i	−2.48332	+	1.89792i
$637$	2.19845e19	+	3.80783e19i	0.516584	+	0.894750i
$638$			6.68391e19i			1.55341i
$639$	2.97324e19	−	2.95041e19i	0.683477	−	0.678229i
$640$	1.02003e20			2.31927
$641$	5.21564e19	−	3.01125e19i	1.17301	−	0.677237i	0.218622	−	0.975810i	$-0.429844\pi$
$641$	5.21564e19	−	3.01125e19i	1.17301	−	0.677237i	0.954387	+	0.298573i	$0.0965105\pi$
$642$	5.58296e19	−	7.24068e18i	1.24199	−	0.161077i
$643$	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
$645$	6.22881e17	+	2.59413e17i	0.0134118	+	0.00558566i
$646$	−7.05715e17	−	1.22233e18i	−0.0150315	−	0.0260353i
$647$			4.01993e19i			0.847010i	0.905894	+	0.423505i	$0.139200\pi$
$647$			4.01993e19i			0.847010i	−0.905894	+	0.423505i	$0.860800\pi$
$648$	9.33321e19	+	7.19452e17i	1.94539	+	0.0149960i
$649$	−1.21515e20			−2.50563
$650$	−1.22085e20	+	7.04856e19i	−2.49039	+	1.43783i
$651$	3.71847e18	−	8.92848e18i	0.0750408	−	0.180182i
$652$	−2.87433e19	+	4.97848e19i	−0.573856	+	0.993948i
$653$	−7.34748e19	−	4.24207e19i	−1.45126	−	0.837887i	−0.452709	−	0.891658i	$-0.649542\pi$
$653$	−7.34748e19	−	4.24207e19i	−1.45126	−	0.837887i	−0.998553	+	0.0537713i	$0.982876\pi$
$654$	6.08741e18	+	4.69373e19i	0.118957	+	0.917220i
$655$	3.96443e19	+	6.86660e19i	0.766464	+	1.32755i
$656$			1.00154e20i			1.91575i
$657$	3.78819e19	+	3.81750e19i	0.716925	+	0.722473i
$658$	−3.32529e19			−0.622656
$659$	−2.98496e19	+	1.72337e19i	−0.553020	+	0.319286i	−0.750339	−	0.661053i	$-0.770110\pi$
$659$	−2.98496e19	+	1.72337e19i	−0.553020	+	0.319286i	0.197319	+	0.980339i	$0.436776\pi$
$660$	1.60929e20	+	2.10566e20i	2.95003	+	3.85994i
$661$	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
$663$	4.65065e19	−	3.55435e19i	0.825884	−	0.631198i
$664$	−2.05916e19	−	3.56657e19i	−0.361838	−	0.626722i
$665$			7.00537e17i			0.0121809i
$666$	−4.33732e19	−	1.18012e19i	−0.746281	−	0.203051i
$667$	1.41462e19			0.240856
$668$	1.65725e20	−	9.56813e19i	2.79224	−	1.61210i
$669$	−5.07481e19	+	6.58164e18i	−0.846129	+	0.109737i
$670$	3.10115e19	−	5.37135e19i	0.511681	−	0.886257i
$671$	4.17107e19	+	2.40817e19i	0.681066	+	0.393214i
$672$	−8.74851e18	−	3.64352e18i	−0.141367	−	0.0588757i
$673$	−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
$675$	−6.71407e19	−	5.21383e19i	−1.05162	−	0.816640i
$676$	−6.82331e19			−1.05771
$677$	7.21965e19	−	4.16826e19i	1.10763	−	0.639491i	0.169416	−	0.985545i	$-0.445812\pi$
$677$	7.21965e19	−	4.16826e19i	1.10763	−	0.639491i	0.938215	+	0.346053i	$0.112478\pi$
$678$	4.02399e19	−	9.66206e19i	0.611011	−	1.46711i
$679$	1.75436e19	−	3.03865e19i	0.263652	−	0.456659i
$680$	−1.46658e20	−	8.46732e19i	−2.18144	−	1.25946i
$681$	1.39908e19	+	1.07877e20i	0.205975	+	1.58818i
$682$	4.50053e19	+	7.79514e19i	0.655802	+	1.13588i
$683$			1.24590e20i			1.79696i	0.439016	+	0.898479i	$0.355327\pi$
$683$			1.24590e20i			1.79696i	−0.439016	+	0.898479i	$0.644673\pi$
$684$	−2.86777e18	+	7.56584e17i	−0.0409404	+	0.0108010i
$685$	5.44273e18			0.0769100
$686$	7.96976e19	−	4.60134e19i	1.11475	−	0.643600i
$687$	2.47512e19	+	3.23854e19i	0.342688	+	0.448386i
$688$	4.59405e17	−	7.95713e17i	0.00629617	−	0.0109053i
$689$	1.16235e20	+	6.71081e19i	1.57689	+	0.910418i
$690$	6.57445e19	−	5.02465e19i	0.882908	−	0.674780i
$691$	−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
$693$	1.17379e19	+	4.44918e19i	0.152918	+	0.579626i
$694$	−1.56710e20			−2.02106
$695$	−4.47063e19	+	2.58112e19i	−0.570789	+	0.329545i
$696$	−8.90023e19	+	1.15429e19i	−1.12496	+	0.145899i
$697$	−4.90475e19	+	8.49527e19i	−0.613744	+	1.06304i
$698$	2.37444e19	+	1.37088e19i	0.294152	+	0.169829i
$699$	2.23804e19	+	9.32085e18i	0.274491	+	0.114318i
$700$	4.57361e19	+	7.92172e19i	0.555358	+	0.961908i
$701$		−	5.95665e19i		−	0.716103i	−0.933702	−	0.358052i	$-0.883441\pi$
$701$		−	5.95665e19i		−	0.716103i	0.933702	−	0.358052i	$-0.116559\pi$
$702$	−6.84690e19	−	1.68040e20i	−0.814956	−	2.00011i
$703$	7.49551e17			0.00883312
$704$	−7.21495e19	+	4.16555e19i	−0.841831	+	0.486031i
$705$	−4.52981e19	+	1.08766e20i	−0.523307	+	1.25652i
$706$	−5.82578e19	+	1.00905e20i	−0.666379	+	1.15420i
$707$	−1.55608e19	−	8.98404e18i	−0.176237	−	0.101750i
$708$	−3.99904e19	−	3.08348e20i	−0.448459	−	3.45786i
$709$	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
$711$	−1.29684e18	+	4.76632e18i	−0.0141189	+	0.0518915i
$712$	2.29322e20			2.47221
$713$	1.64980e19	−	9.52515e18i	0.176119	−	0.101682i
$714$	−3.40237e19	−	4.45180e19i	−0.359662	−	0.470596i
$715$	1.35186e20	−	2.34149e20i	1.41511	−	2.45103i
$716$	1.91965e20	+	1.10831e20i	1.98990	+	1.14887i
$717$	−3.27661e19	+	2.50421e19i	−0.336349	+	0.257062i
$718$	6.43062e19	+	1.11382e20i	0.653704	+	1.13225i
$719$		−	1.59134e19i		−	0.160199i	−0.996787	−	0.0800994i	$-0.974476\pi$
$719$		−	1.59134e19i		−	0.160199i	0.996787	−	0.0800994i	$-0.0255238\pi$
$720$	−1.43879e20	+	1.42774e20i	−1.43440	+	1.42338i
$721$	−5.15090e18			−0.0508553
$722$	−1.55987e20	+	9.00593e19i	−1.52521	+	0.880579i
$723$	1.51231e20	−	1.96135e19i	1.46444	−	0.189927i
$724$	4.99374e19	−	8.64941e19i	0.478912	−	0.829501i
$725$	7.07892e19	+	4.08702e19i	0.672359	+	0.388186i
$726$	−2.22413e20	−	9.26291e19i	−2.09221	−	0.871347i
$727$	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
$729$	7.82603e19	−	7.64712e19i	0.715235	−	0.698884i
$730$	−3.02495e20			−2.73815
$731$	7.79357e17	−	4.49962e17i	0.00698739	−	0.00403417i
$732$	−4.73810e19	+	1.13767e20i	−0.420752	+	1.01028i
$733$	−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
$735$	−1.91804e19	−	1.47892e20i	−0.165519	−	1.27624i
$736$	−9.33315e18	−	1.61655e19i	−0.0797781	−	0.138180i
$737$			6.79336e19i			0.575191i
$738$	2.14196e20	+	2.15853e20i	1.79646	+	1.81036i
$739$	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
$741$	1.83735e18	+	2.40406e18i	0.0149784	+	0.0195983i
$742$	6.42387e19	−	1.11265e20i	0.518764	−	0.898525i
$743$	5.27339e19	+	3.04459e19i	0.421860	+	0.243561i	0.695873	−	0.718165i	$-0.255018\pi$
$743$	5.27339e19	+	3.04459e19i	0.421860	+	0.243561i	−0.274013	+	0.961726i	$0.588351\pi$
$744$	−9.60270e19	+	7.33905e19i	−0.760997	+	0.581607i
$745$	−1.65040e20	−	2.85857e20i	−1.29567	−	2.24417i
$746$		−	2.58407e20i		−	2.00970i
$747$	−4.65866e19	−	1.26755e19i	−0.358936	−	0.0976609i
$748$	3.53467e20			2.69797
$749$	−3.22743e19	+	1.86336e19i	−0.244053	+	0.140904i
$750$	1.18042e20	−	1.53092e19i	0.884320	−	0.114690i
$751$	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
$753$	1.29101e20	+	5.37669e19i	0.940510	+	0.391697i
$754$	8.72399e19	+	1.51104e20i	0.629674	+	1.09063i
$755$		−	1.40818e19i		−	0.100700i
$756$	−1.09036e20	+	4.44276e19i	−0.772536	+	0.314775i
$757$	−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
$759$	−3.48448e19	+	8.36664e19i	−0.240130	+	0.576579i
$760$	4.37700e18	−	7.58119e18i	0.0298870	−	0.0517657i
$761$	−3.15134e19	−	1.81943e19i	−0.213208	−	0.123096i	0.389594	−	0.920987i	$-0.372616\pi$
$761$	−3.15134e19	−	1.81943e19i	−0.213208	−	0.123096i	−0.602801	+	0.797891i	$0.705949\pi$
$762$	3.04241e19	+	2.34587e20i	0.203955	+	1.57260i
$763$	−1.56657e19	−	2.71338e19i	−0.104059	−	0.180235i
$764$			4.49871e19i			0.296098i
$765$	−1.91961e20	+	5.06437e19i	−1.25194	+	0.330290i
$766$	2.00743e20			1.29730
$767$	−2.74710e20	+	1.58604e20i	−1.75917	+	1.01566i
$768$	−1.94572e20	−	2.54586e20i	−1.23467	−	1.61549i
$769$	−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
$771$	3.87252e19	−	2.95965e19i	0.239119	−	0.182751i
$772$	−9.46217e19	−	1.63890e20i	−0.578988	−	1.00284i
$773$			6.97639e19i			0.423033i	0.977374	+	0.211516i	$0.0678402\pi$
$773$			6.97639e19i			0.423033i	−0.977374	+	0.211516i	$0.932160\pi$
$774$	−7.11650e17	−	2.69746e18i	−0.00427641	−	0.0162094i
$775$	1.10078e20			0.655522
$776$	−3.79714e20	+	2.19228e20i	−2.24091	+	1.29379i
$777$	2.95085e19	−	3.82704e18i	0.172584	−	0.0223828i
$778$	8.30290e19	−	1.43810e20i	0.481252	−	0.833553i
$779$	−4.39145e18	−	2.53541e18i	−0.0252259	−	0.0145642i
$780$	6.38649e20	+	2.65980e20i	3.63580	+	1.51421i
$781$	−1.29024e20	−	2.23476e20i	−0.727971	−	1.26088i
$782$		−	1.10362e20i		−	0.617124i
$783$	−6.45315e19	+	8.30999e19i	−0.357634	+	0.460541i
$784$	−2.03074e20			−1.11543
$785$	3.00658e20	−	1.73585e20i	1.63676	−	0.944983i
$786$	1.26036e20	−	3.02626e20i	0.680043	−	1.63286i
$787$	−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
$789$	1.08322e19	+	8.35222e19i	0.0569086	+	0.438796i
$790$	−1.38916e19	−	2.40610e19i	−0.0723375	−	0.125292i
$791$			6.92854e19i			0.357607i
$792$	1.50960e20	−	5.54829e20i	0.772301	−	2.83846i
$793$	1.25728e20			0.637556
$794$	1.28964e20	−	7.44577e19i	0.648226	−	0.374253i
$795$	−2.76425e20	−	3.61685e20i	−1.37723	−	1.80203i
$796$	−2.08537e20	+	3.61196e20i	−1.02989	+	1.78382i
$797$	3.90330e19	+	2.25357e19i	0.191084	+	0.110322i	0.592490	−	0.805578i	$-0.298145\pi$
$797$	3.90330e19	+	2.25357e19i	0.191084	+	0.110322i	−0.401406	+	0.915900i	$0.631478\pi$
$798$	2.30127e18	−	1.75879e18i	0.0111673	−	0.00853480i
$799$	7.85713e19	+	1.36090e20i	0.377952	+	0.654632i
$800$		−	1.07859e20i		−	0.514311i
$801$	1.90830e20	−	1.89364e20i	0.902025	−	0.895099i
$802$	2.28647e20			1.07138
$803$	2.86933e20	−	1.65661e20i	1.33282	−	0.769505i
$804$	−1.72383e20	+	2.23568e19i	−0.793786	+	0.102948i
$805$	−2.73881e19	+	4.74375e19i	−0.125023	+	0.216546i
$806$	2.03488e20	+	1.17484e20i	0.920859	+	0.531658i
$807$	−1.53987e20	−	6.41316e19i	−0.690829	−	0.287712i
$808$	1.12266e20	+	1.94450e20i	0.499308	+	0.864827i
$809$		−	1.85225e20i		−	0.816695i	−0.912827	−	0.408347i	$-0.866105\pi$
$809$		−	1.85225e20i		−	0.816695i	0.912827	−	0.408347i	$-0.133895\pi$
$810$	−4.74397e18	+	6.15420e20i	−0.0207370	+	2.69015i
$811$	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
$813$	−1.25338e20	+	3.00952e20i	−0.533889	+	1.28193i
$814$	−1.38460e20	+	2.39819e20i	−0.584726	+	1.01278i
$815$	−1.72265e20	−	9.94570e19i	−0.721262	−	0.416421i
$816$	3.47701e19	+	2.68096e20i	0.144336	+	1.11291i
$817$	2.32599e16	+	4.02873e16i	9.57311e−5	+	0.000165811i
$818$		−	1.60688e20i		−	0.655707i
$819$	8.46078e19	+	8.52625e19i	0.342313	+	0.344962i
$820$	−1.15940e21			−4.65091
$821$	−9.58723e19	+	5.53519e19i	−0.381321	+	0.220156i	−0.678393	−	0.734699i	$-0.737323\pi$
$821$	−9.58723e19	+	5.53519e19i	−0.381321	+	0.220156i	0.297072	+	0.954855i	$0.403990\pi$
$822$	−1.36647e19	−	1.78794e19i	−0.0538885	−	0.0705099i
$823$	−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
$825$	−4.16091e20	+	3.18006e20i	−1.59960	+	1.22252i
$826$	1.51822e20	+	2.62964e20i	0.578729	+	1.00239i
$827$		−	9.74201e19i		−	0.368222i	−0.982905	−	0.184111i	$-0.941059\pi$
$827$		−	9.74201e19i		−	0.368222i	0.982905	−	0.184111i	$-0.0589406\pi$
$828$	−2.23773e20	−	6.08852e19i	−0.838680	−	0.228192i
$829$	−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
$831$	5.27478e20	−	6.84099e19i	1.92751	−	0.249984i
$832$	−1.08739e20	+	1.88342e20i	−0.394025	+	0.682471i
$833$	−1.72252e20	−	9.94498e19i	−0.618941	−	0.357346i
$834$	1.97031e20	+	8.20581e19i	0.702057	+	0.292388i
$835$	3.31075e20	+	5.73439e20i	1.16983	+	2.02620i
$836$			1.82717e19i			0.0640230i
$837$	−1.93059e19	+	1.40367e20i	−0.0670828	+	0.487738i
$838$	4.30787e20			1.48441
$839$	−5.36477e19	+	3.09735e19i	−0.183323	+	0.105842i	−0.588853	−	0.808240i	$-0.700420\pi$
$839$	−5.36477e19	+	3.09735e19i	−0.183323	+	0.105842i	0.405530	+	0.914082i	$0.367087\pi$
$840$	1.33607e20	−	3.20806e20i	0.452767	−	1.08715i
$841$	−9.81942e19	+	1.70077e20i	−0.330000	+	0.571577i
$842$	7.07548e20	+	4.08503e20i	2.35815	+	1.36148i
$843$	−5.61726e19	−	4.33121e20i	−0.185666	−	1.43158i
$844$	−6.31560e20	−	1.09389e21i	−2.07022	−	3.58573i
$845$		−	2.36099e20i		−	0.767534i
$846$	4.71024e20	−	1.24267e20i	1.51862	−	0.400647i
$847$	1.59490e20			0.509975
$848$	−5.36837e20	+	3.09943e20i	−1.70244	+	0.982903i
$849$	2.04060e19	+	2.67000e19i	0.0641806	+	0.0839763i
$850$	3.18851e20	−	5.52265e20i	0.994614	−	1.72272i
$851$	5.07566e19	+	2.93043e19i	0.157031	+	0.0906619i
$852$	5.24616e20	−	4.00948e20i	1.60977	−	1.23030i
$853$	−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
$855$	−2.61792e18	−	9.92303e18i	−0.00783779	−	0.0297086i
$856$	4.65696e20			1.38288
$857$	−4.98714e20	+	2.87933e20i	−1.46888	+	0.848058i	−0.999391	−	0.0348813i	$-0.988895\pi$
$857$	−4.98714e20	+	2.87933e20i	−1.46888	+	0.848058i	−0.469488	+	0.882939i	$0.655561\pi$
$858$	−1.10858e21	+	1.43775e20i	−3.23859	+	0.420021i
$859$	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
$861$	−1.85829e20	−	7.73928e19i	−0.529775	−	0.220637i
$862$	−4.01540e20	−	6.95488e20i	−1.13548	−	1.96670i
$863$		−	9.77909e19i		−	0.274298i	−0.990550	−	0.137149i	$-0.956206\pi$
$863$		−	9.77909e19i		−	0.274298i	0.990550	−	0.137149i	$-0.0437939\pi$
$864$	1.37538e20	+	1.89167e19i	0.382671	+	0.0526320i
$865$	8.84320e20			2.44060
$866$	−7.80633e20	+	4.50698e20i	−2.13708	+	1.23385i
$867$	3.97756e19	−	9.55059e19i	0.108015	−	0.259356i
$868$	7.62318e19	−	1.32037e20i	0.205352	−	0.355680i
$869$	2.63540e19	+	1.52155e19i	0.0704219	+	0.0406581i
$870$	−7.61125e19	−	5.86869e20i	−0.201754	−	1.55563i
$871$	8.86684e19	+	1.53578e20i	0.233153	+	0.403833i
$872$			3.91522e20i			1.02127i
$873$	−1.34949e20	+	4.95982e20i	−0.349197	+	1.28341i
$874$	5.70494e18			0.0146444
$875$	−6.82387e19	+	3.93976e19i	−0.173770	+	0.100326i
$876$	5.14799e20	+	6.73582e20i	1.30049	+	1.70162i
$877$	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
$879$	−1.25031e20	+	9.55574e19i	−0.308387	+	0.235691i
$880$	6.24364e20	+	1.08143e21i	1.52777	+	2.64618i
$881$		−	7.52553e20i		−	1.82686i	−0.406993	−	0.913431i	$-0.633423\pi$
$881$		−	7.52553e20i		−	1.82686i	0.406993	−	0.913431i	$-0.366577\pi$
$882$	−4.37669e20	+	4.34309e20i	−1.05406	+	1.04597i
$883$	−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
$885$	1.06694e21	−	1.38374e20i	2.50921	−	0.325426i
$886$	5.22423e20	−	9.04864e20i	1.21895	−	2.11129i
$887$	6.11609e20	+	3.53113e20i	1.41582	+	0.817425i	0.995928	−	0.0901484i	$-0.0287341\pi$
$887$	6.11609e20	+	3.53113e20i	1.41582	+	0.817425i	0.419893	+	0.907573i	$0.362067\pi$
$888$	−3.43252e20	−	1.42955e20i	−0.788357	−	0.328329i
$889$	−7.82953e19	−	1.35611e20i	−0.178412	−	0.309018i
$890$			1.51212e21i			3.41866i
$891$	−3.32534e20	−	5.86357e20i	−0.745919	−	1.31528i
$892$	−8.06674e20			−1.79533
$893$	−7.03487e18	+	4.06158e18i	−0.0155344	+	0.00896882i
$894$	−5.24689e20	+	1.25984e21i	−1.14958	+	2.76027i
$895$	−3.83497e20	+	6.64236e20i	−0.833682	+	1.44398i
$896$	2.41774e20	+	1.39588e20i	0.521499	+	0.301088i
$897$	3.04292e19	+	2.34626e20i	0.0651244	+	0.502144i
$898$	2.56028e20	+	4.43454e20i	0.543693	+	0.941704i
$899$		−	1.36243e20i		−	0.287075i
$900$	−9.43884e20	−	9.51188e20i	−1.97343	−	1.98870i
$901$	−6.07144e20			−1.25956
$902$	1.62241e21	−	9.36698e20i	3.33976	−	1.92821i
$903$	1.12140e18	+	1.46728e18i	0.00229058	+	0.00299708i
$904$	4.32900e20	−	7.49805e20i	0.877423	−	1.51974i
$905$	2.99286e20	+	1.72793e20i	0.601930	+	0.347525i
$906$	−4.62589e19	+	3.53542e19i	−0.0923204	+	0.0705577i
$907$	−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
$909$	2.53991e20	+	6.91070e19i	0.495303	+	0.134764i
$910$	−6.75612e20			−1.30740
$911$	−5.84807e20	+	3.37639e20i	−1.12301	+	0.648371i	−0.942168	−	0.335141i	$-0.891216\pi$
$911$	−5.84807e20	+	3.37639e20i	−1.12301	+	0.648371i	−0.180844	+	0.983512i	$0.557883\pi$
$912$	−1.38587e19	+	1.79737e18i	−0.0264094	+	0.00342510i
$913$	−1.48718e20	+	2.57587e20i	−0.281234	+	0.487111i
$914$	−7.23589e20	−	4.17764e20i	−1.35790	−	0.783985i
$915$	−3.93656e20	−	1.63947e20i	−0.733110	−	0.305321i
$916$	3.21268e20	+	5.56453e20i	0.593744	+	1.02840i
$917$			2.17010e20i			0.398010i
$918$	6.48308e20	+	5.03445e20i	1.18000	+	0.916334i
$919$	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
$921$	3.42047e20	−	8.21293e20i	0.608510	−	1.46110i
$922$	4.19920e20	−	7.27324e20i	0.741397	−	1.28414i
$923$	−5.83373e20	−	3.36810e20i	−1.02220	−	0.590165i
$924$	9.32912e19	+	7.19326e20i	0.162232	+	1.25090i
$925$	1.69328e20	+	2.93285e20i	0.292238	+	0.506171i
$926$		−	1.47012e21i		−	2.51812i
$927$	7.29619e19	−	1.92490e19i	0.124033	−	0.0327228i
$928$	−1.33497e20			−0.225234
$929$	3.51076e20	−	2.02694e20i	0.587884	−	0.339415i	−0.176377	−	0.984323i	$-0.556438\pi$
$929$	3.51076e20	−	2.02694e20i	0.587884	−	0.339415i	0.764260	+	0.644908i	$0.223104\pi$
$930$	−4.83927e20	−	6.33189e20i	−0.804266	−	1.05233i
$931$	5.14085e18	−	8.90422e18i	0.00847984	−	0.0146875i
$932$	3.30969e20	+	1.91085e20i	0.541847	+	0.312835i
$933$	7.03738e20	−	5.37846e20i	1.14351	−	0.873949i
$934$	5.28129e20	+	9.14747e20i	0.851750	+	1.47527i
$935$			1.22306e21i			1.95779i
$936$	−3.82897e20	−	1.45134e21i	−0.608347	−	2.30590i
$937$	−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
$939$	4.92691e20	−	6.38983e19i	0.765448	−	0.0992728i
$940$	−9.28650e20	+	1.60847e21i	−1.43205	+	2.48038i
$941$	−1.69522e20	−	9.78738e19i	−0.259477	−	0.149809i	0.364619	−	0.931157i	$-0.381199\pi$
$941$	−1.69522e20	−	9.78738e19i	−0.259477	−	0.149809i	−0.624096	+	0.781348i	$0.714533\pi$
$942$	−1.32507e21	−	5.51855e20i	−2.01317	−	0.838433i
$943$	−1.98248e20	−	3.43375e20i	−0.298969	−	0.517830i
$944$		−	1.46504e21i		−	2.19304i
$945$	−1.53728e20	−	3.77286e20i	−0.228418	−	0.560594i
$946$	−1.71866e19			−0.0253484
$947$	−4.18348e20	+	2.41533e20i	−0.612474	+	0.353612i	−0.773933	−	0.633268i	$-0.781713\pi$
$947$	−4.18348e20	+	2.41533e20i	−0.612474	+	0.353612i	0.161459	+	0.986879i	$0.448380\pi$
$948$	−2.99366e19	+	7.18813e19i	−0.0435055	+	0.104462i
$949$	4.32448e20	−	7.49022e20i	0.623836	−	1.08052i
$950$	2.85482e19	+	1.64823e19i	0.0408803	+	0.0236022i
$951$	1.14163e20	+	8.80260e20i	0.162279	+	1.25126i
$952$	−2.31747e20	−	4.01397e20i	−0.327006	−	0.566390i
$953$			5.49731e20i			0.770016i	0.922913	+	0.385008i	$0.125801\pi$
$953$			5.49731e20i			0.770016i	−0.922913	+	0.385008i	$0.874199\pi$
$954$	−4.94137e20	+	1.81612e21i	−0.687082	+	2.52525i
$955$	−1.55664e20			−0.214864
$956$	−5.62995e20	+	3.25045e20i	−0.771434	+	0.445388i
$957$	3.93595e20	+	5.14995e20i	0.535385	+	0.700518i
$958$	−3.33784e20	+	5.78131e20i	−0.450720	+	0.780671i
$959$	1.29008e19	+	7.44826e18i	0.0172936	+	0.00998446i
$960$	5.86061e20	−	4.47909e20i	0.779910	−	0.596061i
$961$	2.86735e20	+	4.96639e20i	0.378806	+	0.656111i
$962$			7.22882e20i			0.948074i
$963$	3.87528e20	−	3.84553e20i	0.504568	−	0.500693i
$964$	2.40391e21			3.10727
$965$	5.67088e20	−	3.27409e20i	0.727712	−	0.420145i
$966$	2.24594e20	−	2.91281e19i	0.286126	−	0.0371084i
$967$	−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
$969$	−1.26355e19	−	5.26234e18i	−0.0157516	−	0.00656013i
$970$	−1.44556e21	−	2.50378e21i	−1.78910	−	3.09880i
$971$		−	9.81266e20i		−	1.20574i	−0.797841	−	0.602868i	$-0.794025\pi$
$971$		−	9.81266e20i		−	1.20574i	0.797841	−	0.602868i	$-0.205975\pi$
$972$	1.37846e21	−	1.03678e21i	1.68163	−	1.26481i
$973$	−1.41288e20			−0.171126
$974$	1.21092e21	−	6.99126e20i	1.45614	−	0.840703i
$975$	−5.25593e20	+	1.26201e21i	−0.627505	+	1.50671i
$976$	−2.90340e20	+	5.02884e20i	−0.344158	+	0.596100i
$977$	6.49778e20	+	3.75150e20i	0.764721	+	0.441512i	0.830988	−	0.556290i	$-0.187776\pi$
$977$	6.49778e20	+	3.75150e20i	0.764721	+	0.441512i	−0.0662671	+	0.997802i	$0.521109\pi$
$978$	1.05776e20	+	8.15590e20i	0.123599	+	0.953015i
$979$	−8.28109e20	−	1.43433e21i	−0.960746	−	1.66406i
$980$		−	2.35083e21i		−	2.70794i
$981$	3.23302e20	+	3.25804e20i	0.369765	+	0.372626i
$982$	−1.57545e21			−1.78906
$983$	−1.41689e21	+	8.18042e20i	−1.59758	+	0.922361i	−0.605623	+	0.795752i	$0.707076\pi$
$983$	−1.41689e21	+	8.18042e20i	−1.59758	+	0.922361i	−0.991953	+	0.126609i	$0.959591\pi$
$984$	1.52748e21	+	1.99862e21i	1.71006	+	2.23751i
$985$	3.99218e19	−	6.91465e19i	0.0443768	−	0.0768629i
$986$	−6.83537e20	−	3.94641e20i	−0.754439	−	0.435575i
$987$	−2.56213e20	+	1.95816e20i	−0.280790	+	0.214599i
$988$	2.38487e19	+	4.13071e19i	0.0259517	+	0.0449496i
$989$			3.63746e18i			0.00393028i
$990$	3.65847e21	+	9.95413e20i	3.92512	+	1.06796i
$991$	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
$993$	−1.76548e21	+	2.28969e20i	−1.85446	+	0.240509i
$994$	−3.22409e20	+	5.58429e20i	−0.336281	+	0.582456i
$995$	−1.24980e21	−	7.21575e20i	−1.29444	−	0.747343i
$996$	−7.02577e20	−	2.92604e20i	−0.722567	−	0.300930i
$997$	−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
$999$	−4.03684e20	+	1.64484e20i	−0.406521	+	0.165640i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(195.306 - 112.760i) q^{2} +(840.821 - 2018.91i) q^{3} +(17237.5 - 29856.3i) q^{4} +(103308. + 59645.1i) q^{5} +(-63434.5 - 489115. i) q^{6} +(163246. + 282751. i) q^{7} -4.07989e6i q^{8} +(-3.36901e6 - 3.39508e6i) q^{9} +2.69023e7 q^{10} +(-2.55183e7 + 1.47330e7i) q^{11} +(-4.57834e7 - 5.99048e7i) q^{12} +(-3.84596e7 + 6.66141e7i) q^{13} +(6.37658e7 + 3.68152e7i) q^{14} +(2.07282e8 - 1.58419e8i) q^{15} +(-1.77628e8 - 3.07661e8i) q^{16} -3.47954e8i q^{17} +(-1.04082e9 - 2.83190e8i) q^{18} +1.79868e7 q^{19} +(3.56156e9 - 2.05627e9i) q^{20} +(7.08108e8 - 9.18363e7i) q^{21} +(-3.32258e9 + 5.75488e9i) q^{22} +(1.21799e9 + 7.03208e8i) q^{23} +(-8.23693e9 - 3.43046e9i) q^{24} +(4.06332e9 + 7.03788e9i) q^{25} +1.73468e10i q^{26} +(-9.68709e9 + 3.94707e9i) q^{27} +1.12558e10 q^{28} +(8.71076e9 - 5.02916e9i) q^{29} +(2.26200e10 - 5.43132e10i) q^{30} +(6.77264e9 - 1.17306e10i) q^{31} +(-1.14941e10 - 6.63613e9i) q^{32} +(8.28825e9 + 6.39069e10i) q^{33} +(-3.92352e10 - 6.79574e10i) q^{34} +3.89473e10i q^{35} +(-1.59438e11 + 4.20633e10i) q^{36} +4.16724e10 q^{37} +(3.51292e9 - 2.02818e9i) q^{38} +(1.02150e11 + 1.33657e11i) q^{39} +(2.43346e11 - 4.21487e11i) q^{40} +(-2.44149e11 - 1.40960e11i) q^{41} +(1.27942e11 - 9.77823e10i) q^{42} +(1.29317e9 + 2.23983e9i) q^{43} +1.01584e12i q^{44} +(-1.45547e11 - 5.51685e11i) q^{45} +3.17174e11 q^{46} +(-3.91113e11 + 2.25809e11i) q^{47} +(-7.70493e11 + 9.99271e10i) q^{48} +(2.85813e11 - 4.95043e11i) q^{49} +(1.58718e12 + 9.16358e11i) q^{50} +(-7.02487e11 - 2.92567e11i) q^{51} +(1.32590e12 + 2.29653e12i) q^{52} -1.74490e12i q^{53} +(-1.44687e12 + 1.86320e12i) q^{54} -3.51500e12 q^{55} +(1.15359e12 - 6.66027e11i) q^{56} +(1.51237e10 - 3.63136e10i) q^{57} +(1.13417e12 - 1.96445e12i) q^{58} +(3.57141e12 + 2.06195e12i) q^{59} +(-1.15678e12 - 8.91943e12i) q^{60} +(-8.17270e11 - 1.41555e12i) q^{61} -3.05473e12i q^{62} +(4.09983e11 - 1.50682e12i) q^{63} +2.82736e12 q^{64} +(-7.94640e12 + 4.58786e12i) q^{65} +(8.82487e12 + 1.15468e13i) q^{66} +(1.15275e12 - 1.99661e12i) q^{67} +(-1.03886e13 - 5.99787e12i) q^{68} +(2.44382e12 - 1.86774e12i) q^{69} +(4.39169e12 + 7.60663e12i) q^{70} +8.75750e12i q^{71} +(-1.38516e13 + 1.37452e13i) q^{72} -1.12442e13 q^{73} +(8.13885e12 - 4.69897e12i) q^{74} +(1.76253e13 - 2.28588e12i) q^{75} +(3.10048e11 - 5.37019e11i) q^{76} +(-8.33152e12 - 4.81021e12i) q^{77} +(3.50216e13 + 1.45856e13i) q^{78} +(-5.16374e11 - 8.94386e11i) q^{79} -4.23786e13i q^{80} +(-1.76341e11 + 2.28761e13i) q^{81} -6.35783e13 q^{82} +(8.74183e12 - 5.04710e12i) q^{83} +(9.46415e12 - 2.27245e13i) q^{84} +(2.07538e13 - 3.59466e13i) q^{85} +(5.05125e11 + 2.91634e11i) q^{86} +(-2.82922e12 - 2.18148e13i) q^{87} +(6.01091e13 + 1.04112e14i) q^{88} +5.62078e13i q^{89} +(-9.06340e13 - 9.13354e13i) q^{90} -2.51135e13 q^{91} +(4.19904e13 - 2.42432e13i) q^{92} +(-1.79883e13 - 2.35366e13i) q^{93} +(-5.09245e13 + 8.82037e13i) q^{94} +(1.85818e12 + 1.07282e12i) q^{95} +(-2.30622e13 + 1.76258e13i) q^{96} +(-5.37337e13 - 9.30695e13i) q^{97} -1.28913e14i q^{98} +(1.35991e14 + 3.70010e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 3 q^{2} - 2199 q^{3} + 98303 q^{4} - 107994 q^{5} + 24957 q^{6} - 146330 q^{7} - 5316525 q^{9} - 32772 q^{10} - 15978711 q^{11} - 53795046 q^{12} - 23281436 q^{13} - 349442850 q^{14} + 207365400 q^{15}+ \cdots - 195117933369168 q^{99}+O(q^{100}) \) 26 * q - 3 * q^2 - 2199 * q^3 + 98303 * q^4 - 107994 * q^5 + 24957 * q^6 - 146330 * q^7 - 5316525 * q^9 - 32772 * q^10 - 15978711 * q^11 - 53795046 * q^12 - 23281436 * q^13 - 349442850 * q^14 + 207365400 * q^15 - 671072257 * q^16 - 2272246668 * q^18 + 195706222 * q^19 + 2822935854 * q^20 + 1958992050 * q^21 - 204235521 * q^22 - 6101133672 * q^23 + 10931998527 * q^24 + 14614789727 * q^25 - 34016586282 * q^27 - 9052979204 * q^28 + 85191770166 * q^29 + 91857763818 * q^30 + 15357554728 * q^31 - 237242922057 * q^32 + 76352726421 * q^33 - 16566014943 * q^34 - 570464313633 * q^36 - 77721425444 * q^37 + 476314869819 * q^38 + 353897273784 * q^39 - 88855733850 * q^40 - 938882938233 * q^41 + 700091392140 * q^42 - 29709800063 * q^43 - 84148700094 * q^45 + 1553142786144 * q^46 - 1272741434580 * q^47 + 803069876301 * q^48 - 945184029255 * q^49 + 3573994524699 * q^50 - 1993755292875 * q^51 + 1825489374856 * q^52 + 6488294941323 * q^54 - 3772940931372 * q^55 - 7790759725422 * q^56 - 10739943123909 * q^57 + 3747043240302 * q^58 + 5874788534451 * q^59 + 1848130753878 * q^60 - 4867968901544 * q^61 + 5766639947244 * q^63 + 1211169309434 * q^64 - 22156719464856 * q^65 - 6375059860230 * q^66 - 8251061484125 * q^67 + 30687017243265 * q^68 + 23068377735552 * q^69 + 6871822387932 * q^70 - 46243200240621 * q^72 + 16120119648922 * q^73 + 8549243621166 * q^74 + 1090840096221 * q^75 + 14422972781521 * q^76 + 13919363311398 * q^77 + 109811947190436 * q^78 - 10740904544582 * q^79 - 140975607018501 * q^81 - 67076318933382 * q^82 - 11295125984532 * q^83 + 30827942753826 * q^84 + 10590724937466 * q^85 + 97019495740221 * q^86 + 151937485500582 * q^87 - 26136212294541 * q^88 - 392755154255226 * q^90 + 70870424994080 * q^91 - 474274297000284 * q^92 - 124466752375728 * q^93 - 46678164316620 * q^94 + 440317551118746 * q^95 + 823174447870656 * q^96 + 7621755375583 * q^97 - 195117933369168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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