LMFDB - Embedded newform 9.19.d.a.2.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9,19,Mod(2,9)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 19, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9.2"); S:= CuspForms(chi, 19); N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 19 $
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:	$18.4847523939$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2.3
Character	$\chi$	$=$	9.2
Dual form			9.19.d.a.5.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-645.469 - 372.662i) q^{2} +(-1755.59 + 19604.6i) q^{3} +(146682. + 254060. i) q^{4} +(690555. - 398692. i) q^{5} +(8.43904e6 - 1.19999e7i) q^{6} +(1.15930e7 - 2.00797e7i) q^{7} -2.32684e7i q^{8} +(-3.81256e8 - 6.88350e7i) q^{9} -5.94309e8 q^{10} +(-1.51520e9 - 8.74799e8i) q^{11} +(-5.23824e9 + 2.42960e9i) q^{12} +(-1.24028e9 - 2.14822e9i) q^{13} +(-1.49659e10 + 8.64057e9i) q^{14} +(6.60385e9 + 1.42380e10i) q^{15} +(2.97805e10 - 5.15813e10i) q^{16} -1.51023e9i q^{17} +(2.20437e11 + 1.86511e11i) q^{18} +5.30794e11 q^{19} +(2.02583e11 + 1.16962e11i) q^{20} +(3.73302e11 + 2.62528e11i) q^{21} +(6.52008e11 + 1.12931e12i) q^{22} +(-9.81493e11 + 5.66665e11i) q^{23} +(4.56167e11 + 4.08498e10i) q^{24} +(-1.58944e12 + 2.75299e12i) q^{25} +1.84882e12i q^{26} +(2.01881e12 - 7.35351e12i) q^{27} +6.80195e12 q^{28} +(7.09811e12 + 4.09810e12i) q^{29} +(1.04336e12 - 1.16512e13i) q^{30} +(2.24111e13 + 3.88172e13i) q^{31} +(-4.37272e13 + 2.52459e13i) q^{32} +(1.98101e13 - 2.81689e13i) q^{33} +(-5.62806e11 + 9.74809e11i) q^{34} -1.84882e13i q^{35} +(-3.84351e13 - 1.06959e14i) q^{36} +1.43753e14 q^{37} +(-3.42611e14 - 1.97807e14i) q^{38} +(4.42924e13 - 2.05437e13i) q^{39} +(-9.27694e12 - 1.60681e13i) q^{40} +(-5.46553e14 + 3.15553e14i) q^{41} +(-1.43121e14 - 3.08569e14i) q^{42} +(-1.65386e14 + 2.86458e14i) q^{43} -5.13267e14i q^{44} +(-2.90722e14 + 1.04469e14i) q^{45} +8.44698e14 q^{46} +(1.71622e15 + 9.90862e14i) q^{47} +(9.58945e14 + 6.74388e14i) q^{48} +(5.45409e14 + 9.44677e14i) q^{49} +(2.05187e15 - 1.18465e15i) q^{50} +(2.96075e13 + 2.65135e12i) q^{51} +(3.63852e14 - 6.30210e14i) q^{52} -1.72957e15i q^{53} +(-4.04345e15 + 3.99413e15i) q^{54} -1.39510e15 q^{55} +(-4.67224e14 - 2.69752e14i) q^{56} +(-9.31856e14 + 1.04060e16i) q^{57} +(-3.05441e15 - 5.29039e15i) q^{58} +(-4.81326e14 + 2.77893e14i) q^{59} +(-2.64863e15 + 3.76622e15i) q^{60} +(4.02790e15 - 6.97652e15i) q^{61} -3.34071e16i q^{62} +(-5.80211e15 + 6.85752e15i) q^{63} +2.20192e16 q^{64} +(-1.71296e15 - 9.88977e14i) q^{65} +(-2.32843e16 + 1.07997e16i) q^{66} +(5.87079e15 + 1.01685e16i) q^{67} +(3.83690e14 - 2.21524e14i) q^{68} +(-9.38612e15 - 2.02366e16i) q^{69} +(-6.88985e15 + 1.19336e16i) q^{70} -1.13705e16i q^{71} +(-1.60168e15 + 8.87124e15i) q^{72} +5.61405e16 q^{73} +(-9.27878e16 - 5.35711e16i) q^{74} +(-5.11807e16 - 3.59933e16i) q^{75} +(7.78577e16 + 1.34854e17i) q^{76} +(-3.51315e16 + 2.02832e16i) q^{77} +(-3.62452e16 - 3.24576e15i) q^{78} +(-2.73765e16 + 4.74175e16i) q^{79} -4.74929e16i q^{80} +(1.40618e17 + 5.24876e16i) q^{81} +4.70378e17 q^{82} +(-1.38796e17 - 8.01338e16i) q^{83} +(-1.19414e16 + 1.33349e17i) q^{84} +(-6.02118e14 - 1.04290e15i) q^{85} +(2.13504e17 - 1.23266e17i) q^{86} +(-9.28027e16 + 1.31961e17i) q^{87} +(-2.03552e16 + 3.52562e16i) q^{88} +2.64257e17i q^{89} +(2.26584e17 + 4.09093e16i) q^{90} -5.75144e16 q^{91} +(-2.87934e17 - 1.66239e17i) q^{92} +(-8.00338e17 + 3.71213e17i) q^{93} +(-7.38513e17 - 1.27914e18i) q^{94} +(3.66542e17 - 2.11623e17i) q^{95} +(-4.18168e17 - 9.01574e17i) q^{96} +(-4.66141e17 + 8.07380e17i) q^{97} -8.13013e17i q^{98} +(5.17461e17 + 4.37821e17i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 3 q^{2} + 3804 q^{3} + 2097151 q^{4} + 2192181 q^{5} + 3257181 q^{6} + 4302359 q^{7} + 397977264 q^{9} - 524292 q^{10} + 1022992575 q^{11} + 32417762010 q^{12} + 3839449319 q^{13} + 129938709678 q^{14}+ \cdots - 52\!\cdots\!15 q^{99}+O(q^{100}) $ 34 * q - 3 * q^2 + 3804 * q^3 + 2097151 * q^4 + 2192181 * q^5 + 3257181 * q^6 + 4302359 * q^7 + 397977264 * q^9 - 524292 * q^10 + 1022992575 * q^11 + 32417762010 * q^12 + 3839449319 * q^13 + 129938709678 * q^14 - 124119415395 * q^15 - 240517906433 * q^16 - 285581999484 * q^18 - 608222566264 * q^19 + 1471193748174 * q^20 - 1381493495229 * q^21 + 851254438911 * q^22 + 375441179325 * q^23 + 305135298351 * q^24 + 12156817117552 * q^25 + 11936276558406 * q^27 + 4648789868540 * q^28 - 31101186224271 * q^29 + 62775784981818 * q^30 - 20376334153801 * q^31 - 113411230023465 * q^32 - 20701744605945 * q^33 - 99737362554111 * q^34 - 472069890962721 * q^36 + 56970364072604 * q^37 + 1244853240655323 * q^38 + 277868300554299 * q^39 + 236076863983350 * q^40 - 1178988706876521 * q^41 + 1034549802657900 * q^42 - 230641688892691 * q^43 - 5286549794938479 * q^45 + 131852496280800 * q^46 + 3640523435126673 * q^47 + 11085451646520237 * q^48 - 4168576830678822 * q^49 - 18078797603969781 * q^50 + 7526452896180882 * q^51 + 1286623499256920 * q^52 - 26455557995217045 * q^54 - 1446925762710942 * q^55 + 59834487378592914 * q^56 + 23867830767470574 * q^57 + 8463343484826222 * q^58 - 29968086845368137 * q^59 + 17080074037610118 * q^60 - 6976259792083513 * q^61 - 73583064644919705 * q^63 - 120930519493421318 * q^64 + 47229492730318989 * q^65 + 58361174960027994 * q^66 - 20333770074023707 * q^67 - 116938167206248431 * q^68 + 99272218824151677 * q^69 - 18312927374667108 * q^70 + 186892024430477907 * q^72 + 209341663176867296 * q^73 - 88916838511745634 * q^74 - 103202922056583144 * q^75 - 180442619960522287 * q^76 + 384727796507616477 * q^77 - 113580855335113884 * q^78 + 126425698081194923 * q^79 + 749177961563573568 * q^81 - 856725985700547270 * q^82 - 819712186371296103 * q^83 - 1069135371708878382 * q^84 + 372804006624771096 * q^85 + 1989011602082127453 * q^86 - 689457779704913391 * q^87 - 648793548761104653 * q^88 + 2069849112225424614 * q^90 - 29982940436364482 * q^91 - 2013198581519506428 * q^92 - 2088815715502953 * q^93 - 769920889934866620 * q^94 + 167036756670646446 * q^95 + 338414304229215984 * q^96 + 1172101248161568089 * q^97 - 529477370297396415 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−645.469	−	372.662i	−1.26068	−	0.727855i	−0.287475	−	0.957788i	$-0.592816\pi$
$2$	−645.469	−	372.662i	−1.26068	−	0.727855i	−0.973206	+	0.229933i	$0.926149\pi$
$3$	−1755.59	+	19604.6i	−0.0891931	+	0.996014i
$3$	−1755.59	+	19604.6i	−0.0891931	+	0.996014i
$4$	146682.	+	254060.i	0.559546	+	0.969162i
$5$	690555.	−	398692.i	0.353564	−	0.204130i	−0.312690	−	0.949855i	$-0.601230\pi$
$5$	690555.	−	398692.i	0.353564	−	0.204130i	0.666254	+	0.745725i	$0.267897\pi$
$6$	8.43904e6	−	1.19999e7i	0.837398	−	1.19074i
$7$	1.15930e7	−	2.00797e7i	0.287286	−	0.497595i	−0.685875	−	0.727720i	$-0.740580\pi$
$7$	1.15930e7	−	2.00797e7i	0.287286	−	0.497595i	0.973161	+	0.230125i	$0.0739135\pi$
$8$		−	2.32684e7i		−	0.173363i
$9$	−3.81256e8	−	6.88350e7i	−0.984089	−	0.177675i
$10$	−5.94309e8			−0.594309
$11$	−1.51520e9	−	8.74799e8i	−0.642591	−	0.371000i	0.143021	−	0.989720i	$-0.454318\pi$
$11$	−1.51520e9	−	8.74799e8i	−0.642591	−	0.371000i	−0.785612	+	0.618720i	$0.787652\pi$
$12$	−5.23824e9	+	2.42960e9i	−1.01521	+	0.470873i
$13$	−1.24028e9	−	2.14822e9i	−0.116958	−	0.202577i	0.801603	−	0.597857i	$-0.203981\pi$
$13$	−1.24028e9	−	2.14822e9i	−0.116958	−	0.202577i	−0.918561	+	0.395280i	$0.870648\pi$
$14$	−1.49659e10	+	8.64057e9i	−0.724354	+	0.418206i
$15$	6.60385e9	+	1.42380e10i	0.171781	+	0.370362i
$16$	2.97805e10	−	5.15813e10i	0.433363	−	0.750606i
$17$		−	1.51023e9i		−	0.0127351i	−0.999980	−	0.00636757i	$-0.997973\pi$
$17$		−	1.51023e9i		−	0.0127351i	0.999980	−	0.00636757i	$-0.00202687\pi$
$18$	2.20437e11	+	1.86511e11i	1.11130	+	0.940266i
$19$	5.30794e11			1.64492			0.822458	−	0.568826i	$-0.192602\pi$
$19$	5.30794e11			1.64492			0.822458	+	0.568826i	$0.192602\pi$
$20$	2.02583e11	+	1.16962e11i	0.395671	+	0.228441i
$21$	3.73302e11	+	2.62528e11i	0.469987	+	0.330523i
$22$	6.52008e11	+	1.12931e12i	0.540068	+	0.935426i
$23$	−9.81493e11	+	5.66665e11i	−0.544925	+	0.314612i	−0.747072	−	0.664743i	$-0.768541\pi$
$23$	−9.81493e11	+	5.66665e11i	−0.544925	+	0.314612i	0.202148	+	0.979355i	$0.435208\pi$
$24$	4.56167e11	+	4.08498e10i	0.172672	+	0.0154628i
$25$	−1.58944e12	+	2.75299e12i	−0.416662	+	0.721679i
$26$			1.84882e12i			0.340513i
$27$	2.01881e12	−	7.35351e12i	0.264741	−	0.964320i
$28$	6.80195e12			0.643000
$29$	7.09811e12	+	4.09810e12i	0.489284	+	0.282488i	0.724277	−	0.689509i	$-0.242174\pi$
$29$	7.09811e12	+	4.09810e12i	0.489284	+	0.282488i	−0.234994	+	0.971997i	$0.575507\pi$
$30$	1.04336e12	−	1.16512e13i	0.0530083	−	0.591940i
$31$	2.24111e13	+	3.88172e13i	0.847634	+	1.46815i	0.883314	+	0.468782i	$0.155307\pi$
$31$	2.24111e13	+	3.88172e13i	0.847634	+	1.46815i	−0.0356800	+	0.999363i	$0.511360\pi$
$32$	−4.37272e13	+	2.52459e13i	−1.24280	+	0.717532i
$33$	1.98101e13	−	2.81689e13i	0.426836	−	0.606939i
$34$	−5.62806e11	+	9.74809e11i	−0.00926934	+	0.0160550i
$35$		−	1.84882e13i		−	0.234575i
$36$	−3.84351e13	−	1.06959e14i	−0.378447	−	1.05316i
$37$	1.43753e14			1.10611			0.553057	−	0.833143i	$-0.313461\pi$
$37$	1.43753e14			1.10611			0.553057	+	0.833143i	$0.313461\pi$
$38$	−3.42611e14	−	1.97807e14i	−2.07372	−	1.19726i
$39$	4.42924e13	−	2.05437e13i	0.212201	−	0.0984231i
$40$	−9.27694e12	−	1.60681e13i	−0.0353887	−	0.0612950i
$41$	−5.46553e14	+	3.15553e14i	−1.66947	+	0.963867i	−0.701542	+	0.712628i	$0.747505\pi$
$41$	−5.46553e14	+	3.15553e14i	−1.66947	+	0.963867i	−0.967925	+	0.251240i	$0.919162\pi$
$42$	−1.43121e14	−	3.08569e14i	−0.351932	−	0.758768i
$43$	−1.65386e14	+	2.86458e14i	−0.329067	+	0.569960i	−0.982327	−	0.187173i	$-0.940067\pi$
$43$	−1.65386e14	+	2.86458e14i	−0.329067	+	0.569960i	0.653260	+	0.757133i	$0.273401\pi$
$44$		−	5.13267e14i		−	0.830366i
$45$	−2.90722e14	+	1.04469e14i	−0.384207	+	0.138063i
$46$	8.44698e14			0.915969
$47$	1.71622e15	+	9.90862e14i	1.53353	+	0.885386i	0.999195	+	0.0401149i	$0.0127724\pi$
$47$	1.71622e15	+	9.90862e14i	1.53353	+	0.885386i	0.534338	+	0.845271i	$0.320561\pi$
$48$	9.58945e14	+	6.74388e14i	0.708961	+	0.498584i
$49$	5.45409e14	+	9.44677e14i	0.334933	+	0.580121i
$50$	2.05187e15	−	1.18465e15i	1.05056	−	0.606539i
$51$	2.96075e13	+	2.65135e12i	0.0126844	+	0.00113589i
$52$	3.63852e14	−	6.30210e14i	0.130886	−	0.226702i
$53$		−	1.72957e15i		−	0.524150i	−0.965048	−	0.262075i	$-0.915593\pi$
$53$		−	1.72957e15i		−	0.524150i	0.965048	−	0.262075i	$-0.0844067\pi$
$54$	−4.04345e15	+	3.99413e15i	−1.03564	+	1.02301i
$55$	−1.39510e15			−0.302929
$56$	−4.67224e14	−	2.69752e14i	−0.0862647	−	0.0498049i
$57$	−9.31856e14	+	1.04060e16i	−0.146715	+	1.63836i
$58$	−3.05441e15	−	5.29039e15i	−0.411221	−	0.712255i
$59$	−4.81326e14	+	2.77893e14i	−0.0555611	+	0.0320782i	−0.527523	−	0.849541i	$-0.676879\pi$
$59$	−4.81326e14	+	2.77893e14i	−0.0555611	+	0.0320782i	0.471962	+	0.881619i	$0.343546\pi$
$60$	−2.64863e15	+	3.76622e15i	−0.262821	+	0.373718i
$61$	4.02790e15	−	6.97652e15i	0.344437	−	0.596583i	−0.640814	−	0.767696i	$-0.721403\pi$
$61$	4.02790e15	−	6.97652e15i	0.344437	−	0.596583i	0.985251	+	0.171113i	$0.0547364\pi$
$62$		−	3.34071e16i		−	2.46782i
$63$	−5.80211e15	+	6.85752e15i	−0.371126	+	0.438634i
$64$	2.20192e16			1.22231
$65$	−1.71296e15	−	9.88977e14i	−0.0827041	−	0.0477492i
$66$	−2.32843e16	+	1.07997e16i	−0.979868	+	0.454482i
$67$	5.87079e15	+	1.01685e16i	0.215786	+	0.373752i	0.953515	−	0.301344i	$-0.0974353\pi$
$67$	5.87079e15	+	1.01685e16i	0.215786	+	0.373752i	−0.737729	+	0.675097i	$0.764102\pi$
$68$	3.83690e14	−	2.21524e14i	0.0123424	−	0.00712590i
$69$	−9.38612e15	−	2.02366e16i	−0.264755	−	0.570814i
$70$	−6.88985e15	+	1.19336e16i	−0.170737	+	0.295725i
$71$		−	1.13705e16i		−	0.248002i	−0.992282	−	0.124001i	$-0.960427\pi$
$71$		−	1.13705e16i		−	0.248002i	0.992282	−	0.124001i	$-0.0395725\pi$
$72$	−1.60168e15	+	8.87124e15i	−0.0308024	+	0.170605i
$73$	5.61405e16			0.953610			0.476805	−	0.879009i	$-0.341795\pi$
$73$	5.61405e16			0.953610			0.476805	+	0.879009i	$0.341795\pi$
$74$	−9.27878e16	−	5.35711e16i	−1.39446	−	0.805091i
$75$	−5.11807e16	−	3.59933e16i	−0.681639	−	0.479370i
$76$	7.78577e16	+	1.34854e17i	0.920406	+	1.59419i
$77$	−3.51315e16	+	2.02832e16i	−0.369215	+	0.213167i
$78$	−3.62452e16	−	3.24576e15i	−0.339156	−	0.0303714i
$79$	−2.73765e16	+	4.74175e16i	−0.228420	+	0.395635i	−0.957340	−	0.288964i	$-0.906689\pi$
$79$	−2.73765e16	+	4.74175e16i	−0.228420	+	0.395635i	0.728920	+	0.684599i	$0.240023\pi$
$80$		−	4.74929e16i		−	0.353850i
$81$	1.40618e17	+	5.24876e16i	0.936863	+	0.349697i
$82$	4.70378e17			2.80622
$83$	−1.38796e17	−	8.01338e16i	−0.742461	−	0.428660i	0.0805027	−	0.996754i	$-0.474347\pi$
$83$	−1.38796e17	−	8.01338e16i	−0.742461	−	0.428660i	−0.822963	+	0.568095i	$0.807681\pi$
$84$	−1.19414e16	+	1.33349e17i	−0.0573512	+	0.640437i
$85$	−6.02118e14	−	1.04290e15i	−0.00259963	−	0.00450269i
$86$	2.13504e17	−	1.23266e17i	0.829696	−	0.479025i
$87$	−9.28027e16	+	1.31961e17i	−0.325003	+	0.462138i
$88$	−2.03552e16	+	3.52562e16i	−0.0643178	+	0.111402i
$89$			2.64257e17i			0.754252i	0.926162	+	0.377126i	$0.123088\pi$
$89$			2.64257e17i			0.754252i	−0.926162	+	0.377126i	$0.876912\pi$
$90$	2.26584e17	+	4.09093e16i	0.584853	+	0.105594i
$91$	−5.75144e16			−0.134401
$92$	−2.87934e17	−	1.66239e17i	−0.609821	−	0.352080i
$93$	−8.00338e17	+	3.71213e17i	−1.53790	+	0.713307i
$94$	−7.38513e17	−	1.27914e18i	−1.28887	−	2.23238i
$95$	3.66542e17	−	2.11623e17i	0.581583	−	0.335777i
$96$	−4.18168e17	−	9.01574e17i	−0.603823	−	1.30185i
$97$	−4.66141e17	+	8.07380e17i	−0.613157	+	1.06202i	0.377548	+	0.925990i	$0.376767\pi$
$97$	−4.66141e17	+	8.07380e17i	−0.613157	+	1.06202i	−0.990705	+	0.136029i	$0.956566\pi$
$98$		−	8.13013e17i		−	0.975131i
$99$	5.17461e17	+	4.37821e17i	0.566449	+	0.479270i
$100$	−9.32565e17			−0.932565
$101$	1.70701e18	+	9.85542e17i	1.56079	+	0.901120i	0.997178	+	0.0750781i	$0.0239206\pi$
$101$	1.70701e18	+	9.85542e17i	1.56079	+	0.901120i	0.563608	+	0.826042i	$0.309413\pi$
$102$	−1.81226e16	−	1.27449e16i	−0.0151642	−	0.0106644i
$103$	−7.17649e17	−	1.24301e18i	−0.550018	−	0.952660i	−0.998273	−	0.0587537i	$-0.981287\pi$
$103$	−7.17649e17	−	1.24301e18i	−0.550018	−	0.952660i	0.448254	−	0.893906i	$-0.352046\pi$
$104$	−4.99858e16	+	2.88593e16i	−0.0351194	+	0.0202762i
$105$	3.62453e17	+	3.24577e16i	0.233640	+	0.0209225i
$106$	−6.44545e17	+	1.11638e18i	−0.381505	+	0.660786i
$107$			1.92539e18i			1.04729i	0.851938	+	0.523643i	$0.175428\pi$
$107$			1.92539e18i			1.04729i	−0.851938	+	0.523643i	$0.824572\pi$
$108$	2.16436e18	−	5.65727e17i	1.08272	−	0.283004i
$109$	2.82156e18			1.29912			0.649561	−	0.760309i	$-0.274953\pi$
$109$	2.82156e18			1.29912			0.649561	+	0.760309i	$0.274953\pi$
$110$	9.00494e17	+	5.19901e17i	0.381898	+	0.220489i
$111$	−2.52370e17	+	2.81820e18i	−0.0986578	+	1.10171i
$112$	−6.90492e17	−	1.19597e18i	−0.248998	−	0.431278i
$113$	−2.75489e18	+	1.59053e18i	−0.917060	+	0.529465i	−0.882696	−	0.469945i	$-0.844274\pi$
$113$	−2.75489e18	+	1.59053e18i	−0.917060	+	0.529465i	−0.0343638	+	0.999409i	$0.510940\pi$
$114$	4.47939e18	−	6.36947e18i	1.37745	−	1.95866i
$115$	−4.51850e17	+	7.82626e17i	−0.128444	+	0.222471i
$116$			2.40446e18i			0.632260i
$117$	3.24991e17	+	9.04398e17i	0.0791039	+	0.220134i
$118$	4.14241e17			0.0933932
$119$	−3.03251e16	−	1.75082e16i	−0.00633694	−	0.00365863i
$120$	3.31295e17	−	1.53661e17i	0.0642072	−	0.0297806i
$121$	−1.24941e18	−	2.16405e18i	−0.224718	−	0.389223i
$122$	−5.19977e18	+	3.00209e18i	−0.868451	+	0.501401i
$123$	−5.22675e18	−	1.12689e19i	−0.811121	−	1.74878i
$124$	−6.57460e18	+	1.13875e19i	−0.948580	+	1.64299i
$125$			5.57656e18i			0.748474i
$126$	6.30062e18	−	2.26409e18i	0.787133	−	0.282852i
$127$	3.39033e16			0.00394465			0.00197232	−	0.999998i	$-0.499372\pi$
$127$	3.39033e16			0.00394465			0.00197232	+	0.999998i	$0.499372\pi$
$128$	−2.74990e18	−	1.58766e18i	−0.298145	−	0.172134i
$129$	−5.32552e18	−	3.74523e18i	−0.538338	−	0.378591i
$130$	7.37108e17	+	1.27671e18i	0.0695090	+	0.120393i
$131$	9.60199e18	−	5.54371e18i	0.845122	−	0.487932i	−0.0138799	−	0.999904i	$-0.504418\pi$
$131$	9.60199e18	−	5.54371e18i	0.845122	−	0.487932i	0.859002	+	0.511972i	$0.171085\pi$
$132$	1.00624e19	+	9.01086e17i	0.827057	+	0.0740629i
$133$	6.15352e18	−	1.06582e19i	0.472562	−	0.818501i
$134$		−	8.75128e18i		−	0.628244i
$135$	−1.53769e18	−	5.88289e18i	−0.103244	−	0.394990i
$136$	−3.51408e16			−0.00220781
$137$	2.82820e18	+	1.63286e18i	0.166351	+	0.0960428i	0.580864	−	0.814001i	$-0.302715\pi$
$137$	2.82820e18	+	1.63286e18i	0.166351	+	0.0960428i	−0.414513	+	0.910043i	$0.636048\pi$
$138$	−1.48294e18	+	1.65599e19i	−0.0816981	+	0.912318i
$139$	−1.56514e19	−	2.71090e19i	−0.808015	−	1.39952i	−0.914237	−	0.405180i	$-0.867209\pi$
$139$	−1.56514e19	−	2.71090e19i	−0.808015	−	1.39952i	0.106222	−	0.994342i	$-0.466125\pi$
$140$	4.69712e18	−	2.71188e18i	0.227342	−	0.131256i
$141$	−2.24384e19	+	3.19062e19i	−1.01864	+	1.44845i
$142$	−4.23735e18	+	7.33931e18i	−0.180509	+	0.312651i
$143$			4.33997e18i			0.173565i
$144$	−1.49046e19	+	1.76157e19i	−0.559832	+	0.661665i
$145$	6.53551e18			0.230657
$146$	−3.62370e19	−	2.09214e19i	−1.20220	−	0.694090i
$147$	−1.94775e19	+	9.03404e18i	−0.607683	+	0.281855i
$148$	2.10859e19	+	3.65218e19i	0.618922	+	1.07200i
$149$	5.14911e19	−	2.97284e19i	1.42251	−	0.821287i	0.425997	−	0.904724i	$-0.359923\pi$
$149$	5.14911e19	−	2.97284e19i	1.42251	−	0.821287i	0.996513	+	0.0834376i	$0.0265899\pi$
$150$	1.96222e19	+	4.23057e19i	0.510419	+	1.10047i
$151$	2.90898e19	−	5.03849e19i	0.712767	−	1.23455i	−0.251047	−	0.967975i	$-0.580775\pi$
$151$	2.90898e19	−	5.03849e19i	0.712767	−	1.23455i	0.963814	−	0.266574i	$-0.0858917\pi$
$152$		−	1.23507e19i		−	0.285168i
$153$	−1.03957e17	+	5.75786e17i	−0.00226272	+	0.0125325i
$154$	3.02350e19			0.620617
$155$	3.09522e19	+	1.78703e19i	0.599386	+	0.346056i
$156$	1.17162e19	+	8.23954e18i	0.214124	+	0.150585i
$157$	3.14388e19	+	5.44536e19i	0.542462	+	0.939572i	0.998762	+	0.0497457i	$0.0158411\pi$
$157$	3.14388e19	+	5.44536e19i	0.542462	+	0.939572i	−0.456300	+	0.889826i	$0.650826\pi$
$158$	3.53413e19	−	2.04043e19i	0.575929	−	0.332513i
$159$	3.39074e19	+	3.03641e18i	0.522061	+	0.0467505i
$160$	−2.01307e19	+	3.48674e19i	−0.292940	+	0.507387i
$161$			2.62775e19i			0.361536i
$162$	−7.12045e19	−	8.62821e19i	−0.926558	−	1.12276i
$163$	−1.61354e19			−0.198651			−0.0993255	−	0.995055i	$-0.531669\pi$
$163$	−1.61354e19			−0.198651			−0.0993255	+	0.995055i	$0.531669\pi$
$164$	−1.60339e20	−	9.25716e19i	−1.86829	−	1.07866i
$165$	2.44922e18	−	2.73503e19i	0.0270192	−	0.301722i
$166$	5.97256e19	+	1.03448e20i	0.624004	+	1.08081i
$167$	−6.82271e19	+	3.93909e19i	−0.675318	+	0.389895i	−0.798089	−	0.602540i	$-0.794155\pi$
$167$	−6.82271e19	+	3.93909e19i	−0.675318	+	0.389895i	0.122770	+	0.992435i	$0.460822\pi$
$168$	6.10862e18	−	8.68614e18i	0.0573006	−	0.0814786i
$169$	5.31511e19	−	9.20605e19i	0.472642	−	0.818640i
$170$			8.97545e17i			0.00756861i
$171$	−2.02369e20	−	3.65372e19i	−1.61874	−	0.292261i
$172$	−9.70366e19			−0.736511
$173$	−7.73314e19	−	4.46473e19i	−0.557110	−	0.321647i	0.194875	−	0.980828i	$-0.437570\pi$
$173$	−7.73314e19	−	4.46473e19i	−0.557110	−	0.321647i	−0.751985	+	0.659181i	$0.770903\pi$
$174$	1.09078e20	−	5.05925e19i	0.746094	−	0.346053i
$175$	3.68529e19	+	6.38310e19i	0.239402	+	0.414657i
$176$	−9.02464e19	+	5.21038e19i	−0.556950	+	0.321555i
$177$	−4.60297e18	−	9.92404e18i	−0.0269947	−	0.0582008i
$178$	9.84785e19	−	1.70570e20i	0.548986	−	0.950872i
$179$		−	3.90626e19i		−	0.207054i	−0.994627	−	0.103527i	$-0.966987\pi$
$179$		−	3.90626e19i		−	0.207054i	0.994627	−	0.103527i	$-0.0330129\pi$
$180$	−6.91851e19	−	5.85372e19i	−0.348787	−	0.295107i
$181$	−8.65404e19			−0.415061			−0.207530	−	0.978229i	$-0.566543\pi$
$181$	−8.65404e19			−0.415061			−0.207530	+	0.978229i	$0.566543\pi$
$182$	3.71238e19	+	2.14334e19i	0.169437	+	0.0978248i
$183$	1.29700e20	+	9.12130e19i	0.563483	+	0.396275i
$184$	1.31854e19	+	2.28378e19i	0.0545423	+	0.0944700i
$185$	9.92690e19	−	5.73130e19i	0.391082	−	0.225791i
$186$	6.54931e20	+	5.86491e19i	2.45798	+	0.220112i
$187$	−1.32115e18	+	2.28830e18i	−0.00472474	+	0.00818349i
$188$			5.81365e20i			1.98166i
$189$	−1.24252e20	−	1.25787e20i	−0.403784	−	0.408770i
$190$	−3.15456e20			−0.977588
$191$	4.25888e20	+	2.45886e20i	1.25891	+	0.726832i	0.972863	−	0.231383i	$-0.0743250\pi$
$191$	4.25888e20	+	2.45886e20i	1.25891	+	0.726832i	0.286048	+	0.958215i	$0.407658\pi$
$192$	−3.86567e19	+	4.31677e20i	−0.109022	+	1.21744i
$193$	−3.11532e19	−	5.39589e19i	−0.0838468	−	0.145227i	0.821052	−	0.570853i	$-0.193387\pi$
$193$	−3.11532e19	−	5.39589e19i	−0.0838468	−	0.145227i	−0.904899	+	0.425626i	$0.860054\pi$
$194$	6.01759e20	−	3.47426e20i	1.54599	−	0.892579i
$195$	2.23957e19	−	3.18456e19i	0.0549355	−	0.0781155i
$196$	−1.60003e20	+	2.77133e20i	−0.374821	+	0.649209i
$197$			4.63415e19i			0.103699i	0.998655	+	0.0518495i	$0.0165116\pi$
$197$			4.63415e19i			0.103699i	−0.998655	+	0.0518495i	$0.983488\pi$
$198$	−1.70846e20	−	4.75438e20i	−0.365273	−	1.01650i
$199$	−4.21171e20			−0.860560			−0.430280	−	0.902696i	$-0.641585\pi$
$199$	−4.21171e20			−0.860560			−0.430280	+	0.902696i	$0.641585\pi$
$200$	6.40577e19	+	3.69837e19i	0.125113	+	0.0722338i
$201$	−2.09656e20	+	9.72425e19i	−0.391509	+	0.181590i
$202$	−7.34548e20	−	1.27227e21i	−1.31177	−	2.27205i
$203$	1.64577e20	−	9.50188e19i	0.281129	−	0.162310i
$204$	3.66927e18	+	7.91097e18i	0.00599664	+	0.0129288i
$205$	−2.51617e20	+	4.35813e20i	−0.393509	+	0.681578i
$206$			1.06976e21i			1.60133i
$207$	4.13207e20	−	1.48484e20i	0.592153	−	0.212787i
$208$	−1.47744e20			−0.202740
$209$	−8.04257e20	−	4.64338e20i	−1.05701	−	0.610264i
$210$	−2.21857e20	−	1.56023e20i	−0.279318	−	0.196433i
$211$	3.45235e20	+	5.97964e20i	0.416459	+	0.721328i	0.995580	−	0.0939133i	$-0.0299376\pi$
$211$	3.45235e20	+	5.97964e20i	0.416459	+	0.721328i	−0.579121	+	0.815241i	$0.696604\pi$
$212$	4.39415e20	−	2.53696e20i	0.507986	−	0.293286i
$213$	2.22914e20	+	1.99619e19i	0.247013	+	0.0221200i
$214$	7.17521e20	−	1.24278e21i	0.762273	−	1.32030i
$215$			2.63753e20i			0.268690i
$216$	−1.71105e20	−	4.69745e19i	−0.167178	−	0.0458964i
$217$	1.03925e21			0.974055
$218$	−1.82123e21	−	1.05149e21i	−1.63778	−	0.945573i
$219$	−9.85597e19	+	1.10061e21i	−0.0850555	+	0.949809i
$220$	−2.04636e20	−	3.54439e20i	−0.169503	−	0.293588i
$221$	−3.24432e18	+	1.87311e18i	−0.00257984	+	0.00148947i
$222$	1.21313e21	−	1.72501e21i	0.926258	−	1.31709i
$223$	−1.30998e21	+	2.26896e21i	−0.960554	+	1.66373i	−0.239442	+	0.970911i	$0.576964\pi$
$223$	−1.30998e21	+	2.26896e21i	−0.960554	+	1.66373i	−0.721112	+	0.692818i	$0.756369\pi$
$224$			1.17071e21i			0.824549i
$225$	7.95485e20	−	9.40185e20i	0.538257	−	0.636166i
$226$	2.37092e21			1.54149
$227$	−1.77007e21	−	1.02195e21i	−1.10601	−	0.638553i	−0.168214	−	0.985751i	$-0.553800\pi$
$227$	−1.77007e21	−	1.02195e21i	−1.10601	−	0.638553i	−0.937792	+	0.347198i	$0.887133\pi$
$228$	−2.78043e21	+	1.28962e21i	−1.66993	+	0.774547i
$229$	8.10589e20	+	1.40398e21i	0.468038	+	0.810666i	0.999333	−	0.0365212i	$-0.0116277\pi$
$229$	8.10589e20	+	1.40398e21i	0.468038	+	0.810666i	−0.531295	+	0.847187i	$0.678294\pi$
$230$	5.83310e20	−	3.36774e20i	0.323854	−	0.186977i
$231$	−3.35966e20	−	7.24345e20i	−0.179385	−	0.386757i
$232$	9.53562e19	−	1.65162e20i	0.0489731	−	0.0848238i
$233$		−	6.77409e20i		−	0.334694i	−0.985898	−	0.167347i	$-0.946480\pi$
$233$		−	6.77409e20i		−	0.334694i	0.985898	−	0.167347i	$-0.0535200\pi$
$234$	1.27263e20	−	7.04873e20i	0.0605007	−	0.335095i
$235$	1.58020e21			0.722936
$236$	−1.41203e20	−	8.15237e19i	−0.0621780	−	0.0358985i
$237$	−8.81536e20	−	6.19949e20i	−0.373684	−	0.262797i
$238$	1.30493e19	+	2.26020e19i	0.00532591	+	0.00922475i
$239$	2.01548e21	−	1.16364e21i	0.792130	−	0.457336i	−0.0485819	−	0.998819i	$-0.515470\pi$
$239$	2.01548e21	−	1.16364e21i	0.792130	−	0.457336i	0.840712	+	0.541483i	$0.182137\pi$
$240$	9.31077e20	+	8.33780e19i	0.352439	+	0.0315610i
$241$	−1.63983e21	+	2.84026e21i	−0.597922	+	1.03563i	0.395205	+	0.918593i	$0.370673\pi$
$241$	−1.63983e21	+	2.84026e21i	−0.597922	+	1.03563i	−0.993127	+	0.117038i	$0.962660\pi$
$242$			1.86243e21i			0.654249i
$243$	−1.27586e21	+	2.66461e21i	−0.431864	+	0.901939i
$244$	2.36327e21			0.770914
$245$	7.53270e20	+	4.34901e20i	0.236841	+	0.136740i
$246$	−8.25790e20	+	9.22155e21i	−0.250296	+	2.79504i
$247$	−6.58332e20	−	1.14026e21i	−0.192386	−	0.333222i
$248$	9.03215e20	−	5.21472e20i	0.254523	−	0.146949i
$249$	1.81465e21	−	2.58035e21i	0.493174	−	0.701268i
$250$	2.07817e21	−	3.59950e21i	0.544780	−	0.943587i
$251$		−	5.75986e21i		−	1.45663i	−0.685244	−	0.728313i	$-0.740304\pi$
$251$		−	5.75986e21i		−	1.45663i	0.685244	−	0.728313i	$-0.259696\pi$
$252$	−2.59328e21	−	4.68212e20i	−0.632769	−	0.114245i
$253$	1.98287e21			0.466885
$254$	−2.18835e19	−	1.26345e19i	−0.00497294	−	0.00287113i
$255$	2.15026e19	−	9.97335e18i	0.00471661	−	0.00218766i
$256$	−1.70279e21	−	2.94931e21i	−0.360579	−	0.624541i
$257$	4.21545e21	−	2.43379e21i	0.861878	−	0.497606i	−0.00276268	−	0.999996i	$-0.500879\pi$
$257$	4.21545e21	−	2.43379e21i	0.861878	−	0.497606i	0.864641	+	0.502391i	$0.167546\pi$
$258$	2.04176e21	+	4.40205e21i	0.403113	+	0.869115i
$259$	1.66653e21	−	2.88651e21i	0.317772	−	0.550397i
$260$		−	5.80259e20i		−	0.106872i
$261$	−2.42411e21	−	2.05102e21i	−0.431308	−	0.364927i
$262$	−8.26372e21			−1.42057
$263$	−2.89335e21	−	1.67048e21i	−0.480618	−	0.277485i	0.240056	−	0.970759i	$-0.422834\pi$
$263$	−2.89335e21	−	1.67048e21i	−0.480618	−	0.277485i	−0.720674	+	0.693274i	$0.756168\pi$
$264$	−6.55447e20	−	4.60950e20i	−0.105221	−	0.0739977i
$265$	−6.89566e20	−	1.19436e21i	−0.106995	−	0.185320i
$266$	−7.94381e21	+	4.58636e21i	−1.19150	+	0.687913i
$267$	−5.18064e21	−	4.63926e20i	−0.751246	−	0.0672741i
$268$	−1.72227e21	+	2.98307e21i	−0.241484	+	0.418263i
$269$		−	3.82333e21i		−	0.518407i	−0.965823	−	0.259203i	$-0.916540\pi$
$269$		−	3.82333e21i		−	0.518407i	0.965823	−	0.259203i	$-0.0834600\pi$
$270$	−1.19980e21	+	4.37026e21i	−0.157338	+	0.573104i
$271$	−6.62934e21			−0.840905			−0.420452	−	0.907315i	$-0.638129\pi$
$271$	−6.62934e21			−0.840905			−0.420452	+	0.907315i	$0.638129\pi$
$272$	−7.78997e19	−	4.49754e19i	−0.00955908	−	0.00551894i
$273$	1.00972e20	−	1.12754e21i	0.0119877	−	0.133866i
$274$	−1.21701e21	−	2.10793e21i	−0.139811	−	0.242159i
$275$	4.81662e21	−	2.78088e21i	0.535486	−	0.309163i
$276$	3.76453e21	−	5.35297e21i	0.405069	−	0.575987i
$277$	−1.00810e21	+	1.74608e21i	−0.104999	+	0.181864i	−0.913738	−	0.406304i	$-0.866817\pi$
$277$	−1.00810e21	+	1.74608e21i	−0.104999	+	0.181864i	0.808739	+	0.588168i	$0.200151\pi$
$278$			2.33307e22i			2.35247i
$279$	−5.87240e21	−	1.63420e22i	−0.573294	−	1.59539i
$280$	−4.30192e20			−0.0406668
$281$	7.82095e21	+	4.51543e21i	0.715983	+	0.413373i	0.813272	−	0.581883i	$-0.197684\pi$
$281$	7.82095e21	+	4.51543e21i	0.715983	+	0.413373i	−0.0972894	+	0.995256i	$0.531017\pi$
$282$	2.63735e22	−	1.22326e22i	2.33844	−	1.08462i
$283$	6.87418e21	+	1.19064e22i	0.590396	+	1.02260i	0.994179	+	0.107741i	$0.0343617\pi$
$283$	6.87418e21	+	1.19064e22i	0.590396	+	1.02260i	−0.403783	+	0.914855i	$0.632305\pi$
$284$	2.88879e21	−	1.66784e21i	0.240354	−	0.138768i
$285$	3.50528e21	+	7.55742e21i	0.282566	+	0.609214i
$286$	1.61734e21	−	2.80132e21i	0.126330	−	0.218811i
$287$			1.46329e22i			1.10762i
$288$	1.84091e22	−	6.61520e21i	1.35052	−	0.485300i
$289$	1.40608e22			0.999838
$290$	−4.21847e21	−	2.43553e21i	−0.290786	−	0.167885i
$291$	−1.50100e22	−	1.05559e22i	−1.00310	−	0.705438i
$292$	8.23479e21	+	1.42631e22i	0.533589	+	0.924203i
$293$	−2.03968e21	+	1.17761e21i	−0.128160	+	0.0739934i	−0.562710	−	0.826655i	$-0.690241\pi$
$293$	−2.03968e21	+	1.17761e21i	−0.128160	+	0.0739934i	0.434549	+	0.900648i	$0.356908\pi$
$294$	1.59388e22	+	1.42732e21i	0.971244	+	0.0869749i
$295$	−2.21588e20	+	3.83801e20i	−0.0130963	+	0.0226834i
$296$		−	3.34490e21i		−	0.191760i
$297$	−9.49173e21	+	9.37596e21i	−0.527883	+	0.521444i
$298$	−4.43145e22			−2.39111
$299$	2.43465e21	+	1.40564e21i	0.127466	+	0.0735927i
$300$	1.63720e21	−	1.82825e22i	0.0831784	−	0.928849i
$301$	3.83466e21	+	6.64183e21i	0.189073	+	0.327484i
$302$	−3.75531e22	+	2.16813e22i	−1.79715	+	1.03758i
$303$	−2.23179e22	+	3.17349e22i	−1.03674	+	1.47419i
$304$	1.58073e22	−	2.73790e22i	0.712845	−	1.23468i
$305$		−	6.42356e21i		−	0.281240i
$306$	2.81675e20	−	3.32911e20i	0.0119744	−	0.0141526i
$307$	−7.18865e21			−0.296758			−0.148379	−	0.988931i	$-0.547406\pi$
$307$	−7.18865e21			−0.296758			−0.148379	+	0.988931i	$0.547406\pi$
$308$	−1.03063e22	−	5.95033e21i	−0.413186	−	0.238553i
$309$	2.56285e22	−	1.18870e22i	0.997921	−	0.462856i
$310$	−1.33191e22	−	2.30694e22i	−0.503757	−	0.872532i
$311$	1.39418e22	−	8.04927e21i	0.512240	−	0.295742i	−0.221514	−	0.975157i	$-0.571100\pi$
$311$	1.39418e22	−	8.04927e21i	0.512240	−	0.295742i	0.733754	+	0.679415i	$0.237766\pi$
$312$	−4.78019e20	−	1.03061e21i	−0.0170630	−	0.0367879i
$313$	3.10923e19	−	5.38535e19i	0.00107834	−	0.00186773i	−0.865486	−	0.500934i	$-0.832990\pi$
$313$	3.10923e19	−	5.38535e19i	0.00107834	−	0.00186773i	0.866564	+	0.499066i	$0.166323\pi$
$314$		−	4.68642e22i		−	1.57933i
$315$	−1.27264e21	+	7.04875e21i	−0.0416782	+	0.230843i
$316$	−1.60625e22			−0.511246
$317$	4.94428e22	+	2.85458e22i	1.52957	+	0.883098i	0.999380	+	0.0352194i	$0.0112130\pi$
$317$	4.94428e22	+	2.85458e22i	1.52957	+	0.883098i	0.530191	+	0.847878i	$0.322120\pi$
$318$	−2.07547e22	−	1.45959e22i	−0.624125	−	0.438922i
$319$	−7.17002e21	−	1.24188e22i	−0.209606	−	0.363048i
$320$	1.52055e22	−	8.77888e21i	0.432165	−	0.249511i
$321$	−3.77465e22	−	3.38020e21i	−1.04311	−	0.0934107i
$322$	9.79262e21	−	1.69613e22i	0.263145	−	0.455781i
$323$		−	8.01623e20i		−	0.0209482i
$324$	7.29110e21	+	4.34244e22i	0.185305	+	1.10364i
$325$	7.88538e21			0.194927
$326$	1.04149e22	+	6.01304e21i	0.250436	+	0.144589i
$327$	−4.95349e21	+	5.53153e22i	−0.115873	+	1.29394i
$328$	7.34242e21	+	1.27174e22i	0.167099	+	0.289424i
$329$	3.97925e22	−	2.29742e22i	0.881127	−	0.508719i
$330$	−1.17733e22	+	1.67411e22i	−0.253672	+	0.360709i
$331$	−2.93924e22	+	5.09092e22i	−0.616288	+	1.06744i	0.373869	+	0.927482i	$0.378031\pi$
$331$	−2.93924e22	+	5.09092e22i	−0.616288	+	1.06744i	−0.990157	+	0.139961i	$0.955302\pi$
$332$		−	4.70166e22i		−	0.959420i
$333$	−5.48066e22	−	9.89521e21i	−1.08851	−	0.196529i
$334$	5.87180e22			1.13515
$335$	8.10820e21	+	4.68127e21i	0.152588	+	0.0880969i
$336$	2.46586e22	−	1.14372e22i	0.451768	−	0.209539i
$337$	−4.40234e21	−	7.62508e21i	−0.0785262	−	0.136011i	0.824088	−	0.566462i	$-0.191688\pi$
$337$	−4.40234e21	−	7.62508e21i	−0.0785262	−	0.136011i	−0.902614	+	0.430450i	$0.858355\pi$
$338$	−6.86148e22	+	3.96148e22i	−1.19170	+	0.688029i
$339$	−2.63453e22	−	5.68006e22i	−0.445559	−	0.960629i
$340$	1.76639e20	−	3.05948e20i	0.00290922	−	0.00503892i
$341$		−	7.84209e22i		−	1.25789i
$342$	1.17007e23	+	9.89987e22i	1.82800	+	1.54666i
$343$	6.30484e22			0.959460
$344$	6.66542e21	+	3.84828e21i	0.0988101	+	0.0570481i
$345$	−1.45498e22	−	1.02323e22i	−0.210128	−	0.147775i
$346$	3.32767e22	+	5.76369e22i	0.468225	+	0.810990i
$347$	−1.00383e23	+	5.79559e22i	−1.37624	+	0.794571i	−0.991704	−	0.128541i	$-0.958971\pi$
$347$	−1.00383e23	+	5.79559e22i	−1.37624	+	0.794571i	−0.384533	+	0.923111i	$0.625637\pi$
$348$	−4.71384e22	−	4.22124e21i	−0.629740	−	0.0563932i
$349$	8.90449e21	−	1.54230e22i	0.115926	−	0.200789i	−0.802224	−	0.597024i	$-0.796350\pi$
$349$	8.90449e21	−	1.54230e22i	0.115926	−	0.200789i	0.918149	+	0.396234i	$0.129683\pi$
$350$		−	5.49346e22i		−	0.697001i
$351$	−1.83009e22	+	4.78354e21i	−0.226312	+	0.0591542i
$352$	8.83404e22			1.06482
$353$	−4.36106e22	−	2.51786e22i	−0.512412	−	0.295841i	0.221412	−	0.975180i	$-0.428933\pi$
$353$	−4.36106e22	−	2.51786e22i	−0.512412	−	0.295841i	−0.733825	+	0.679339i	$0.762267\pi$
$354$	−7.27237e20	+	8.12101e21i	−0.00833003	+	0.0930209i
$355$	−4.53333e21	−	7.85195e21i	−0.0506246	−	0.0876845i
$356$	−6.71371e22	+	3.87617e22i	−0.730992	+	0.422039i
$357$	3.96479e20	−	5.63773e20i	0.00420926	−	0.00598536i
$358$	−1.45571e22	+	2.52137e22i	−0.150705	+	0.261030i
$359$		−	1.74830e22i		−	0.176509i	−0.996098	−	0.0882545i	$-0.971871\pi$
$359$		−	1.74830e22i		−	0.176509i	0.996098	−	0.0882545i	$-0.0281289\pi$
$360$	2.43084e21	+	6.76465e21i	0.0239350	+	0.0666075i
$361$	1.77615e23			1.70575
$362$	5.58592e22	+	3.22503e22i	0.523260	+	0.302104i
$363$	4.46186e22	−	2.06950e22i	0.407715	−	0.189106i
$364$	−8.43630e21	−	1.46121e22i	−0.0752038	−	0.130257i
$365$	3.87681e22	−	2.23828e22i	0.337162	−	0.194661i
$366$	−4.97259e22	−	1.07210e23i	−0.421942	−	0.909712i
$367$	−9.61070e22	+	1.66462e23i	−0.795721	+	1.37823i	0.126660	+	0.991946i	$0.459574\pi$
$367$	−9.61070e22	+	1.66462e23i	−0.795721	+	1.37823i	−0.922381	+	0.386282i	$0.873759\pi$
$368$			6.75022e22i			0.545365i
$369$	2.30098e23	−	8.26845e22i	1.81416	−	0.651908i
$370$	−8.54334e22			−0.657374
$371$	−3.47293e22	−	2.00510e22i	−0.260814	−	0.150581i
$372$	−2.11705e23	−	1.48884e23i	−1.55183	−	1.09134i
$373$	−3.18881e22	−	5.52318e22i	−0.228165	−	0.395193i	0.729099	−	0.684408i	$-0.239939\pi$
$373$	−3.18881e22	−	5.52318e22i	−0.228165	−	0.395193i	−0.957264	+	0.289215i	$0.906606\pi$
$374$	1.70552e21	−	9.84684e20i	0.0119128	−	0.00687785i
$375$	−1.09326e23	−	9.79015e21i	−0.745490	−	0.0667587i
$376$	2.30558e22	−	3.99338e22i	0.153493	−	0.265858i
$377$		−	2.03311e22i		−	0.132157i
$378$	3.33252e22	+	1.27496e23i	0.211518	+	0.809225i
$379$	−2.20529e23			−1.36682			−0.683411	−	0.730034i	$-0.739504\pi$
$379$	−2.20529e23			−1.36682			−0.683411	+	0.730034i	$0.739504\pi$
$380$	1.07530e23	+	6.20825e22i	0.650845	+	0.375765i
$381$	−5.95202e19	+	6.64658e20i	−0.000351835	+	0.00392892i
$382$	−1.83265e23	−	3.17424e23i	−1.05806	−	1.83261i
$383$	−1.75631e22	+	1.01401e22i	−0.0990404	+	0.0571810i	−0.548702	−	0.836018i	$-0.684878\pi$
$383$	−1.75631e22	+	1.01401e22i	−0.0990404	+	0.0571810i	0.449662	+	0.893199i	$0.351545\pi$
$384$	3.59530e22	−	5.11233e22i	0.198040	−	0.281603i
$385$	−1.61735e22	+	2.80133e22i	−0.0870275	+	0.150736i
$386$			4.64384e22i			0.244113i
$387$	8.27729e22	−	9.78294e22i	0.425099	−	0.502424i
$388$	−2.73497e23			−1.37236
$389$	2.98295e22	+	1.72221e22i	0.146251	+	0.0844382i	0.571340	−	0.820713i	$-0.306424\pi$
$389$	2.98295e22	+	1.72221e22i	0.146251	+	0.0844382i	−0.425089	+	0.905152i	$0.639757\pi$
$390$	−2.63234e22	+	1.22093e22i	−0.126113	+	0.0584937i
$391$	8.55797e20	+	1.48228e21i	0.00400663	+	0.00693970i
$392$	2.19811e22	−	1.26908e22i	0.100572	−	0.0580651i
$393$	9.18248e22	+	1.97975e23i	0.410608	+	0.885274i
$394$	1.72697e22	−	2.99120e22i	0.0754778	−	0.130731i
$395$			4.36591e22i			0.186510i
$396$	−3.53308e22	+	1.95686e23i	−0.147536	+	0.817154i
$397$	1.58393e23			0.646577			0.323289	−	0.946300i	$-0.395212\pi$
$397$	1.58393e23			0.646577			0.323289	+	0.946300i	$0.395212\pi$
$398$	2.71853e23	+	1.56954e23i	1.08489	+	0.626363i
$399$	1.98146e23	+	1.39348e23i	0.773090	+	0.543683i
$400$	9.46684e22	+	1.63970e23i	0.361131	+	0.625498i
$401$	2.56854e23	−	1.48295e23i	0.958048	−	0.553129i	0.0624764	−	0.998046i	$-0.480100\pi$
$401$	2.56854e23	−	1.48295e23i	0.958048	−	0.553129i	0.895572	+	0.444917i	$0.146767\pi$
$402$	1.71565e23	+	1.53636e22i	0.625740	+	0.0560350i
$403$	5.55920e22	−	9.62882e22i	0.198275	−	0.343422i
$404$			5.78244e23i			2.01687i
$405$	1.18031e23	−	1.98178e22i	0.402625	−	0.0676020i
$406$	−1.41639e23			−0.472552
$407$	−2.17813e23	−	1.25755e23i	−0.710779	−	0.410368i
$408$	6.16927e19	−	6.88919e20i	0.000196921	−	0.00219901i
$409$	−1.51953e23	−	2.63191e23i	−0.474460	−	0.821790i	0.525112	−	0.851033i	$-0.324023\pi$
$409$	−1.51953e23	−	2.63191e23i	−0.474460	−	0.821790i	−0.999572	+	0.0292436i	$0.990690\pi$
$410$	3.24822e23	−	1.87536e23i	0.992179	−	0.572835i
$411$	−3.69767e22	+	5.25790e22i	−0.110497	+	0.157122i
$412$	2.10532e23	−	3.64652e23i	0.615521	−	1.06611i
$413$			1.28865e22i			0.0368625i
$414$	−3.22046e23	−	5.81448e22i	−0.901395	−	0.162745i
$415$	−1.27795e23			−0.350010
$416$	1.08468e23	+	6.26239e22i	0.290710	+	0.167842i
$417$	5.58937e23	−	2.59246e23i	1.46601	−	0.679967i
$418$	3.46082e23	+	5.99432e23i	0.888367	+	1.53870i
$419$	−4.79370e23	+	2.76764e23i	−1.20433	+	0.695318i	−0.961514	−	0.274755i	$-0.911403\pi$
$419$	−4.79370e23	+	2.76764e23i	−1.20433	+	0.695318i	−0.242812	+	0.970073i	$0.578070\pi$
$420$	4.49190e22	+	9.68458e22i	0.110455	+	0.238143i
$421$	−2.36804e23	+	4.10156e23i	−0.569967	+	0.987212i	0.426601	+	0.904440i	$0.359711\pi$
$421$	−2.36804e23	+	4.10156e23i	−0.569967	+	0.987212i	−0.996568	+	0.0827722i	$0.973623\pi$
$422$		−	5.14623e23i		−	1.21249i
$423$	−5.86115e23	−	4.95909e23i	−1.35182	−	1.14377i
$424$	−4.02444e22			−0.0908683
$425$	4.15765e21	+	2.40042e21i	0.00919069	+	0.00530625i
$426$	−1.36445e23	−	9.59562e22i	−0.295305	−	0.207676i
$427$	−9.33912e22	−	1.61758e23i	−0.197904	−	0.342780i
$428$	−4.89166e23	+	2.82420e23i	−1.01499	+	0.586005i
$429$	−8.50832e22	−	7.61920e21i	−0.172873	−	0.0154808i
$430$	9.82906e22	−	1.70244e23i	0.195567	−	0.338732i
$431$		−	2.08841e23i		−	0.406931i	−0.979082	−	0.203466i	$-0.934779\pi$
$431$		−	2.08841e23i		−	0.406931i	0.979082	−	0.203466i	$-0.0652205\pi$
$432$	−3.19182e23	−	3.23124e23i	−0.609095	−	0.616616i
$433$	−4.47033e22			−0.0835504			−0.0417752	−	0.999127i	$-0.513301\pi$
$433$	−4.47033e22			−0.0835504			−0.0417752	+	0.999127i	$0.513301\pi$
$434$	−6.70805e23	−	3.87290e23i	−1.22797	−	0.708971i
$435$	−1.14737e22	+	1.28126e23i	−0.0205731	+	0.229738i
$436$	4.13870e23	+	7.16845e23i	0.726919	+	1.25906i
$437$	−5.20970e23	+	3.00782e23i	−0.896355	+	0.517511i
$438$	4.73773e23	−	6.73680e23i	0.798551	−	1.13550i
$439$	−3.53428e22	+	6.12155e22i	−0.0583607	+	0.101084i	−0.893730	−	0.448606i	$-0.851921\pi$
$439$	−3.53428e22	+	6.12155e22i	−0.0583607	+	0.101084i	0.835369	+	0.549690i	$0.185254\pi$
$440$			3.24618e22i			0.0525168i
$441$	−1.42914e23	−	3.97707e23i	−0.226531	−	0.630400i
$442$	2.79214e21			0.00433648
$443$	−4.61385e23	−	2.66381e23i	−0.702150	−	0.405387i	0.105998	−	0.994366i	$-0.466196\pi$
$443$	−4.61385e23	−	2.66381e23i	−0.702150	−	0.405387i	−0.808148	+	0.588980i	$0.799530\pi$
$444$	−7.53011e23	+	3.49261e23i	−1.12293	+	0.520840i
$445$	1.05357e23	+	1.82484e23i	0.153966	+	0.266676i
$446$	1.69111e24	−	9.76361e23i	2.42191	−	1.39829i
$447$	4.92414e23	+	1.06165e24i	0.691135	+	1.49009i
$448$	2.55270e23	−	4.42140e23i	0.351154	−	0.608216i
$449$			4.48388e23i			0.604556i	0.953220	+	0.302278i	$0.0977471\pi$
$449$			4.48388e23i			0.604556i	−0.953220	+	0.302278i	$0.902253\pi$
$450$	−8.63832e23	+	3.10413e23i	−1.14161	+	0.410230i
$451$	1.10418e24			1.43038
$452$	−8.08182e23	−	4.66604e23i	−1.02627	−	0.592520i
$453$	9.36705e23	+	6.58747e23i	1.16605	+	0.820040i
$454$	7.61683e23	+	1.31927e24i	0.929547	+	1.61002i
$455$	−3.97168e22	+	2.29305e22i	−0.0475195	+	0.0274354i
$456$	2.42131e23	+	2.16828e22i	0.284031	+	0.0254350i
$457$	8.15264e23	−	1.41208e24i	0.937675	−	1.62410i	0.167882	−	0.985807i	$-0.446307\pi$
$457$	8.15264e23	−	1.41208e24i	0.937675	−	1.62410i	0.769793	−	0.638294i	$-0.220360\pi$
$458$		−	1.20830e24i		−	1.36266i
$459$	−1.11055e22	−	3.04887e21i	−0.0122807	−	0.00337152i
$460$	−2.65112e23			−0.287481
$461$	8.99579e23	+	5.19372e23i	0.956601	+	0.552294i	0.895125	−	0.445815i	$-0.147086\pi$
$461$	8.99579e23	+	5.19372e23i	0.956601	+	0.552294i	0.0614757	+	0.998109i	$0.480419\pi$
$462$	−5.30803e22	+	5.92744e23i	−0.0553548	+	0.618144i
$463$	−8.62105e23	−	1.49321e24i	−0.881721	−	1.52719i	−0.849427	−	0.527707i	$-0.823052\pi$
$463$	−8.62105e23	−	1.49321e24i	−0.881721	−	1.52719i	−0.0322941	−	0.999478i	$-0.510281\pi$
$464$	4.22770e23	−	2.44086e23i	0.424074	−	0.244839i
$465$	−4.04678e23	+	5.75431e23i	−0.398137	+	0.566131i
$466$	−2.52445e23	+	4.37247e23i	−0.243609	+	0.421943i
$467$			1.89554e24i			1.79424i	0.441783	+	0.897122i	$0.354346\pi$
$467$			1.89554e24i			1.79424i	−0.441783	+	0.897122i	$0.645654\pi$
$468$	−1.82101e23	+	2.15226e23i	−0.169083	+	0.199840i
$469$	2.72241e23			0.247970
$470$	−1.01997e24	−	5.88878e23i	−0.911393	−	0.526193i
$471$	−1.12273e24	+	5.20746e23i	−0.984211	+	0.456497i
$472$	6.46614e21	+	1.11997e22i	0.00556119	+	0.00963226i
$473$	5.01185e23	−	2.89360e23i	0.422910	−	0.244167i
$474$	3.37973e23	+	7.28673e23i	0.279819	+	0.603292i
$475$	−8.43664e23	+	1.46127e24i	−0.685373	+	1.18710i
$476$		−	1.02725e22i		−	0.00818870i
$477$	−1.19055e23	+	6.59410e23i	−0.0931284	+	0.515810i
$478$	−1.73457e24			−1.33150
$479$	3.48558e23	+	2.01240e23i	0.262576	+	0.151599i	0.625509	−	0.780217i	$-0.284891\pi$
$479$	3.48558e23	+	2.01240e23i	0.262576	+	0.151599i	−0.362933	+	0.931815i	$0.618225\pi$
$480$	−6.48218e23	−	4.55866e23i	−0.479236	−	0.337028i
$481$	−1.78293e23	−	3.08813e23i	−0.129369	−	0.224073i
$482$	2.11691e24	−	1.22220e24i	1.50758	−	0.870401i
$483$	−5.15158e23	−	4.61324e22i	−0.360095	−	0.0322465i
$484$	3.66532e23	−	6.34852e23i	0.251480	−	0.435576i
$485$			7.43387e23i			0.500656i
$486$	1.81653e24	−	1.24446e24i	1.20092	−	0.822723i
$487$	−8.49131e23			−0.551079			−0.275540	−	0.961290i	$-0.588856\pi$
$487$	−8.49131e23			−0.551079			−0.275540	+	0.961290i	$0.588856\pi$
$488$	−1.62333e23	−	9.37229e22i	−0.103426	−	0.0597128i
$489$	2.83271e22	−	3.16327e23i	0.0177183	−	0.197859i
$490$	−3.24142e23	−	5.61430e23i	−0.199054	−	0.344771i
$491$	1.41731e24	−	8.18283e23i	0.854536	−	0.493367i	−0.00764245	−	0.999971i	$-0.502433\pi$
$491$	1.41731e24	−	8.18283e23i	0.854536	−	0.493367i	0.862179	+	0.506604i	$0.169099\pi$
$492$	2.09631e24	−	2.98085e24i	1.24100	−	1.76463i
$493$	6.18908e21	−	1.07198e22i	0.00359753	−	0.00623110i
$494$			9.81341e23i			0.560115i
$495$	5.31891e23	+	9.60318e22i	0.298109	+	0.0538230i
$496$	2.66965e24			1.46933
$497$	−2.28317e23	−	1.31819e23i	−0.123404	−	0.0712475i
$498$	−2.13290e24	+	9.89282e23i	−1.13216	+	0.525117i
$499$	−1.15695e24	−	2.00389e24i	−0.603127	−	1.04465i	−0.992344	−	0.123501i	$-0.960588\pi$
$499$	−1.15695e24	−	2.00389e24i	−0.603127	−	1.04465i	0.389217	−	0.921146i	$-0.372746\pi$
$500$	−1.41678e24	+	8.17979e23i	−0.725392	+	0.418805i
$501$	−6.52463e23	−	1.40672e24i	−0.328108	−	0.707403i
$502$	−2.14648e24	+	3.71781e24i	−1.06021	+	1.83634i
$503$			7.66061e23i			0.371665i	0.982581	+	0.185832i	$0.0594982\pi$
$503$			7.66061e23i			0.371665i	−0.982581	+	0.185832i	$0.940502\pi$
$504$	1.59564e23	+	1.35006e23i	0.0760430	+	0.0643396i
$505$	1.57171e24			0.735784
$506$	−1.27988e24	−	7.38940e23i	−0.588593	−	0.339825i
$507$	1.71149e24	+	1.20362e24i	0.773220	+	0.543775i
$508$	4.97299e21	+	8.61347e21i	0.00220721	+	0.00382300i
$509$	−3.73659e24	+	2.15732e24i	−1.62935	+	0.940708i	−0.645068	+	0.764125i	$0.723171\pi$
$509$	−3.73659e24	+	2.15732e24i	−1.62935	+	0.940708i	−0.984286	+	0.176583i	$0.943495\pi$
$510$	−1.75960e22	−	1.57572e21i	−0.00753845	−	0.000675068i
$511$	6.50840e23	−	1.12729e24i	0.273959	−	0.474511i
$512$			3.37064e24i			1.39406i
$513$	1.07157e24	−	3.90320e24i	0.435477	−	1.58622i
$514$	−3.62792e24			−1.44874
$515$	−9.91152e23	−	5.72242e23i	−0.388933	−	0.224551i
$516$	1.70356e23	−	1.90236e24i	0.0656917	−	0.733576i
$517$	−1.73361e24	−	3.00270e24i	−0.656956	−	1.13788i
$518$	−2.15139e24	+	1.24210e24i	−0.801218	+	0.462583i
$519$	1.01105e24	−	1.43766e24i	0.370056	−	0.526201i
$520$	−2.30120e22	+	3.98579e22i	−0.00827796	+	0.0143378i
$521$		−	3.40963e24i		−	1.20550i	−0.797930	−	0.602751i	$-0.794071\pi$
$521$		−	3.40963e24i		−	1.20550i	0.797930	−	0.602751i	$-0.205929\pi$
$522$	8.00348e23	+	2.22724e24i	0.278128	+	0.773986i
$523$	3.13396e24			1.07048			0.535240	−	0.844700i	$-0.320221\pi$
$523$	3.13396e24			1.07048			0.535240	+	0.844700i	$0.320221\pi$
$524$	2.81687e24	+	1.62632e24i	0.945769	+	0.546040i
$525$	−1.31608e24	+	6.10423e23i	−0.434358	+	0.201464i
$526$	1.24505e24	+	2.15649e24i	0.403938	+	0.699640i
$527$	5.86230e22	−	3.38460e22i	0.0186970	−	0.0107947i
$528$	−8.63036e23	−	1.86071e24i	−0.270597	−	0.583410i
$529$	−9.79857e23	+	1.69716e24i	−0.302038	+	0.523145i
$530$			1.02790e24i			0.311507i
$531$	2.02637e23	−	7.28166e22i	0.0603766	−	0.0216960i
$532$	3.61043e24			1.05768
$533$	1.35576e24	+	7.82746e23i	0.390514	+	0.225463i
$534$	3.17106e24	+	2.23008e24i	0.898116	+	0.631609i
$535$	7.67639e23	+	1.32959e24i	0.213783	+	0.370283i
$536$	2.36605e23	−	1.36604e23i	0.0647949	−	0.0374094i
$537$	7.65805e23	+	6.85779e22i	0.206229	+	0.0184678i
$538$	−1.42481e24	+	2.46784e24i	−0.377325	+	0.653546i
$539$		−	1.90849e24i		−	0.497041i
$540$	1.26906e24	−	1.25358e24i	0.325040	−	0.321075i
$541$	−2.80191e24			−0.705796			−0.352898	−	0.935662i	$-0.614804\pi$
$541$	−2.80191e24			−0.705796			−0.352898	+	0.935662i	$0.614804\pi$
$542$	4.27904e24	+	2.47050e24i	1.06011	+	0.612057i
$543$	1.51929e23	−	1.69659e24i	0.0370206	−	0.413407i
$544$	3.81272e22	+	6.60383e22i	0.00913787	+	0.0158273i
$545$	1.94844e24	−	1.12493e24i	0.459323	−	0.265190i
$546$	−4.85366e23	+	6.90166e23i	−0.112548	+	0.160037i
$547$	−1.76776e23	+	3.06186e23i	−0.0403217	+	0.0698392i	−0.885482	−	0.464674i	$-0.846172\pi$
$547$	−1.76776e23	+	3.06186e23i	−0.0403217	+	0.0698392i	0.845160	+	0.534513i	$0.179505\pi$
$548$			9.58045e23i			0.214962i
$549$	−2.01589e24	+	2.38258e24i	−0.444955	+	0.525893i
$550$	−4.14531e24			−0.900103
$551$	3.76763e24	+	2.17524e24i	0.804830	+	0.464669i
$552$	−4.70873e23	+	2.18400e23i	−0.0989582	+	0.0458988i
$553$	6.34753e23	+	1.09943e24i	0.131244	+	0.227321i
$554$	1.30139e24	−	7.51360e23i	0.264741	−	0.152848i
$555$	9.49320e23	+	2.04674e24i	0.190010	+	0.409662i
$556$	4.59154e24	−	7.95278e24i	0.904243	−	1.56619i
$557$		−	5.15005e24i		−	0.997963i	−0.866612	−	0.498982i	$-0.833707\pi$
$557$		−	5.15005e24i		−	0.997963i	0.866612	−	0.498982i	$-0.166293\pi$
$558$	−2.29958e24	+	1.27367e25i	−0.438470	+	2.42855i
$559$	8.20500e23			0.153947
$560$	−9.53645e23	−	5.50587e23i	−0.176074	−	0.101656i
$561$	−4.25417e22	−	2.99179e22i	−0.00772946	−	0.00543582i
$562$	−3.36546e24	−	5.82914e24i	−0.601751	−	1.04226i
$563$	−7.65356e23	+	4.41878e23i	−0.134675	+	0.0777548i	−0.565824	−	0.824526i	$-0.691442\pi$
$563$	−7.65356e23	+	4.41878e23i	−0.134675	+	0.0777548i	0.431149	+	0.902281i	$0.358108\pi$
$564$	−1.13974e25	−	1.02064e24i	−1.97376	−	0.176750i
$565$	−1.26827e24	+	2.19670e24i	−0.216160	+	0.374399i
$566$		−	1.02470e25i		−	1.71889i
$567$	2.68413e24	−	2.21508e24i	0.443155	−	0.365715i
$568$	−2.64574e23			−0.0429944
$569$	−3.65540e24	−	2.11045e24i	−0.584688	−	0.337570i	0.178306	−	0.983975i	$-0.442938\pi$
$569$	−3.65540e24	−	2.11045e24i	−0.584688	−	0.337570i	−0.762994	+	0.646405i	$0.776272\pi$
$570$	5.53810e23	−	6.18437e24i	0.0871941	−	0.973692i
$571$	7.00346e23	+	1.21304e24i	0.108540	+	0.187996i	0.915179	−	0.403048i	$-0.132049\pi$
$571$	7.00346e23	+	1.21304e24i	0.108540	+	0.187996i	−0.806639	+	0.591044i	$0.798716\pi$
$572$	−1.10261e24	+	6.36594e23i	−0.168213	+	0.0971177i
$573$	−5.56818e24	+	7.91766e24i	−0.836222	+	1.18906i
$574$	5.45311e24	−	9.44506e24i	0.806190	−	1.39636i
$575$		−	3.60272e24i		−	0.524348i
$576$	−8.39496e24	−	1.51569e24i	−1.20286	−	0.217175i
$577$	−2.32175e24			−0.327517			−0.163758	−	0.986500i	$-0.552362\pi$
$577$	−2.32175e24			−0.327517			−0.163758	+	0.986500i	$0.552362\pi$
$578$	−9.07581e24	−	5.23992e24i	−1.26048	−	0.727737i
$579$	1.11253e24	−	5.16014e23i	0.152127	−	0.0705594i
$580$	9.58639e23	+	1.66041e24i	0.129063	+	0.223544i
$581$	−3.21813e24	+	1.85799e24i	−0.426598	+	0.246296i
$582$	5.75469e24	+	1.24072e25i	0.751129	+	1.61944i
$583$	−1.51303e24	+	2.62064e24i	−0.194460	+	0.336814i
$584$		−	1.30630e24i		−	0.165321i
$585$	5.85000e23	+	4.94965e23i	0.0729043	+	0.0616839i
$586$	1.75540e24			0.215426
$587$	−3.93340e24	−	2.27095e24i	−0.475363	−	0.274451i	0.243119	−	0.969996i	$-0.421829\pi$
$587$	−3.93340e24	−	2.27095e24i	−0.475363	−	0.274451i	−0.718482	+	0.695546i	$0.755163\pi$
$588$	−5.15218e24	−	3.62332e24i	−0.613190	−	0.431232i
$589$	1.18957e25	+	2.06039e25i	1.39429	+	2.41497i
$590$	2.86056e23	−	1.65155e23i	0.0330205	−	0.0190644i
$591$	−9.08505e23	−	8.13566e22i	−0.103286	−	0.00924923i
$592$	4.28101e24	−	7.41494e24i	0.479348	−	0.830256i
$593$			7.26561e24i			0.801272i	0.916237	+	0.400636i	$0.131211\pi$
$593$			7.26561e24i			0.801272i	−0.916237	+	0.400636i	$0.868789\pi$
$594$	9.62068e24	−	2.51469e24i	1.04503	−	0.273153i
$595$	−2.79215e22			−0.00298735
$596$	1.51056e25	+	8.72121e24i	1.59192	+	0.919095i
$597$	7.39403e23	−	8.25687e24i	0.0767560	−	0.857130i
$598$	−1.04766e24	−	1.81460e24i	−0.107130	−	0.185554i
$599$	5.29599e24	−	3.05764e24i	0.533465	−	0.307996i	−0.208962	−	0.977924i	$-0.567008\pi$
$599$	5.29599e24	−	3.05764e24i	0.533465	−	0.307996i	0.742426	+	0.669928i	$0.233675\pi$
$600$	−8.37508e23	+	1.19089e24i	−0.0831051	+	0.118171i
$601$	−2.32166e24	+	4.02123e24i	−0.226949	+	0.393087i	−0.956902	−	0.290410i	$-0.906208\pi$
$601$	−2.32166e24	+	4.02123e24i	−0.226949	+	0.393087i	0.729953	+	0.683497i	$0.239542\pi$
$602$		−	5.71613e24i		−	0.550470i
$603$	−1.53833e24	−	4.28092e24i	−0.145946	−	0.406145i
$604$	1.70677e25			1.59530
$605$	−1.72558e24	−	9.96262e23i	−0.158904	−	0.0917435i
$606$	2.62319e25	−	1.21669e25i	2.38000	−	1.10389i
$607$	9.34913e24	+	1.61932e25i	0.835744	+	1.44755i	0.893424	+	0.449215i	$0.148296\pi$
$607$	9.34913e24	+	1.61932e25i	0.835744	+	1.44755i	−0.0576800	+	0.998335i	$0.518370\pi$
$608$	−2.32101e25	+	1.34004e25i	−2.04430	+	1.18028i
$609$	1.57387e24	+	3.39328e24i	0.136588	+	0.294486i
$610$	−2.39382e24	+	4.14621e24i	−0.204702	+	0.354554i
$611$		−	4.91578e24i		−	0.414211i
$612$	−1.61533e23	+	5.80459e22i	−0.0134121	+	0.00481958i
$613$	−1.83336e25			−1.50005			−0.750023	−	0.661412i	$-0.769957\pi$
$613$	−1.83336e25			−1.50005			−0.750023	+	0.661412i	$0.769957\pi$
$614$	4.64005e24	+	2.67894e24i	0.374117	+	0.215997i
$615$	−8.10218e24	−	5.69794e24i	−0.643763	−	0.452733i
$616$	4.71957e23	+	8.17454e23i	0.0369553	+	0.0640084i
$617$	1.69943e24	−	9.81164e23i	0.131140	−	0.0757138i	−0.432995	−	0.901396i	$-0.642543\pi$
$617$	1.69943e24	−	9.81164e23i	0.131140	−	0.0757138i	0.564135	+	0.825683i	$0.309210\pi$
$618$	−2.09722e25	−	1.87806e24i	−1.59495	−	0.142828i
$619$	5.08828e24	−	8.81316e24i	0.381378	−	0.660566i	−0.609882	−	0.792492i	$-0.708783\pi$
$619$	5.08828e24	−	8.81316e24i	0.381378	−	0.660566i	0.991259	+	0.131927i	$0.0421164\pi$
$620$			1.04850e25i			0.774536i
$621$	2.18553e24	+	8.36141e24i	0.159123	+	0.608772i
$622$	−1.19986e25			−0.861030
$623$	5.30621e24	+	3.06354e24i	0.375312	+	0.216686i
$624$	2.59378e23	−	2.89646e24i	0.0180830	−	0.201932i
$625$	−3.83989e24	−	6.65089e24i	−0.263876	−	0.457046i
$626$	−4.01383e22	+	2.31739e22i	−0.00271888	+	0.00156975i
$627$	1.05151e25	−	1.49519e25i	0.702109	−	0.998364i
$628$	−9.22299e24	+	1.59747e25i	−0.607065	+	1.05147i
$629$		−	2.17100e23i		−	0.0140865i
$630$	3.44825e24	−	4.07549e24i	0.220563	−	0.260684i
$631$	7.07325e24			0.446021			0.223010	−	0.974816i	$-0.428412\pi$
$631$	7.07325e24			0.446021			0.223010	+	0.974816i	$0.428412\pi$
$632$	1.10333e24	+	6.37008e23i	0.0685885	+	0.0395996i
$633$	−1.23289e25	+	5.71839e24i	−0.755598	+	0.350462i
$634$	−2.12759e25	−	3.68509e25i	−1.28553	−	2.22661i
$635$	2.34121e22	−	1.35170e22i	0.00139469	−	0.000805222i
$636$	4.20217e24	+	9.05991e24i	0.246808	+	0.532120i
$637$	1.35292e24	−	2.34332e24i	0.0783460	−	0.135699i
$638$			1.06880e25i			0.610251i
$639$	−7.82689e23	+	4.33508e24i	−0.0440637	+	0.244056i
$640$	−2.53194e24			−0.140551
$641$	1.22775e25	+	7.08840e24i	0.672027	+	0.387995i	0.796844	−	0.604185i	$-0.206501\pi$
$641$	1.22775e25	+	7.08840e24i	0.672027	+	0.387995i	−0.124818	+	0.992180i	$0.539835\pi$
$642$	2.31045e25	+	1.62485e25i	1.24704	+	0.876996i
$643$	−6.88531e24	−	1.19257e25i	−0.366459	−	0.634725i	0.622550	−	0.782580i	$-0.286097\pi$
$643$	−6.88531e24	−	1.19257e25i	−0.366459	−	0.634725i	−0.989009	+	0.147855i	$0.952763\pi$
$644$	−6.67606e24	+	3.85442e24i	−0.350387	+	0.202296i
$645$	−5.17076e24	−	4.63041e23i	−0.267619	−	0.0239653i
$646$	−2.98734e23	+	5.17423e23i	−0.0152473	+	0.0264091i
$647$		−	3.66744e25i		−	1.84597i	−0.384836	−	0.922985i	$-0.625742\pi$
$647$		−	3.66744e25i		−	1.84597i	0.384836	−	0.922985i	$-0.374258\pi$
$648$	1.22130e24	−	3.27196e24i	0.0606246	−	0.162418i
$649$	9.72403e23			0.0476041
$650$	−5.08977e24	−	2.93858e24i	−0.245741	−	0.141879i
$651$	−1.82450e24	+	2.03741e25i	−0.0868790	+	0.970173i
$652$	−2.36676e24	−	4.09935e24i	−0.111154	−	0.192525i
$653$	−5.39534e23	+	3.11500e23i	−0.0249920	+	0.0144291i	−0.512444	−	0.858721i	$-0.671260\pi$
$653$	−5.39534e23	+	3.11500e23i	−0.0249920	+	0.0144291i	0.487452	+	0.873150i	$0.337926\pi$
$654$	2.38112e25	−	3.38584e25i	1.08788	−	1.54691i
$655$	4.42047e24	−	7.65647e24i	0.199203	−	0.345030i
$656$			3.75892e25i			1.67082i
$657$	−2.14039e25	−	3.86444e24i	−0.938437	−	0.169433i
$658$	−3.42465e25			−1.48109
$659$	2.53715e25	+	1.46482e25i	1.08237	+	0.624908i	0.931535	−	0.363650i	$-0.118470\pi$
$659$	2.53715e25	+	1.46482e25i	1.08237	+	0.624908i	0.150837	+	0.988559i	$0.451803\pi$
$660$	7.30788e24	−	3.38954e24i	0.307536	−	0.142641i
$661$	−9.58637e24	−	1.66041e25i	−0.397961	−	0.689289i	0.595513	−	0.803346i	$-0.296949\pi$
$661$	−9.58637e24	−	1.66041e25i	−0.397961	−	0.689289i	−0.993474	+	0.114056i	$0.963616\pi$
$662$	3.79438e25	−	2.19069e25i	1.55389	−	0.897137i
$663$	−3.10258e22	−	6.68918e22i	−0.00125343	−	0.00270241i
$664$	−1.86459e24	+	3.22956e24i	−0.0743139	+	0.128715i
$665$		−	9.81343e24i		−	0.385857i
$666$	3.16884e25	+	2.68114e25i	1.22923	+	1.04004i
$667$	−9.28899e24			−0.355497
$668$	−2.00153e25	−	1.15559e25i	−0.755743	−	0.436329i
$669$	−4.21821e25	−	2.96650e25i	−1.57142	−	1.10512i
$670$	−3.48906e24	−	6.04323e24i	−0.128244	−	0.222124i
$671$	−1.22061e25	+	7.04720e24i	−0.442664	+	0.255572i
$672$	−2.29512e25	−	2.05528e24i	−0.821262	−	0.0735441i
$673$	−9.46897e24	+	1.64007e25i	−0.334324	+	0.579065i	−0.983355	−	0.181696i	$-0.941841\pi$
$673$	−9.46897e24	+	1.64007e25i	−0.334324	+	0.579065i	0.649031	+	0.760762i	$0.275175\pi$
$674$			6.56234e24i			0.228623i
$675$	1.70354e25	+	1.72457e25i	0.585622	+	0.592853i
$676$	3.11852e25			1.05786
$677$	3.26750e25	+	1.88649e25i	1.09375	+	0.631477i	0.934572	−	0.355773i	$-0.115782\pi$
$677$	3.26750e25	+	1.88649e25i	1.09375	+	0.631477i	0.159177	+	0.987250i	$0.449116\pi$
$678$	−4.16237e24	+	4.64809e25i	−0.137491	+	1.53535i
$679$	1.08080e25	+	1.87200e25i	0.352303	+	0.610207i
$680$	−2.42666e22	+	1.40103e22i	−0.000780601	+	0.000450680i
$681$	2.31424e25	−	3.29073e25i	0.734656	−	1.04464i
$682$	−2.92245e25	+	5.06183e25i	−0.915561	+	1.58580i
$683$			3.74558e25i			1.15806i	0.815305	+	0.579032i	$0.196569\pi$
$683$			3.74558e25i			1.15806i	−0.815305	+	0.579032i	$0.803431\pi$
$684$	−2.04011e25	−	5.67731e25i	−0.622513	−	1.73236i
$685$	2.60404e24			0.0784210
$686$	−4.06958e25	−	2.34957e25i	−1.20957	−	0.698348i
$687$	−2.89475e25	+	1.34264e25i	−0.849181	+	0.393867i
$688$	9.85056e24	+	1.70617e25i	0.285210	+	0.493999i
$689$	−3.71550e24	+	2.14515e24i	−0.106180	+	0.0613033i
$690$	5.57825e24	+	1.20268e25i	0.157346	+	0.339240i
$691$	1.77444e25	−	3.07342e25i	0.494037	−	0.855697i	−0.505940	−	0.862569i	$-0.668854\pi$
$691$	1.77444e25	−	3.07342e25i	0.494037	−	0.855697i	0.999976	+	0.00687225i	$0.00218752\pi$
$692$		−	2.61957e25i		−	0.719906i
$693$	1.47903e25	−	5.31481e24i	0.401215	−	0.144174i
$694$	8.63918e25			2.31333
$695$	−2.16163e25	−	1.24802e25i	−0.571370	−	0.329881i
$696$	3.07052e24	+	2.15937e24i	0.0801177	+	0.0563436i
$697$	4.76558e23	+	8.25423e23i	0.0122750	+	0.0212609i
$698$	−1.14951e25	+	6.63673e24i	−0.292291	+	0.168754i
$699$	1.32803e25	+	1.18925e24i	0.333360	+	0.0298524i
$700$	−1.08113e25	+	1.87257e25i	−0.267913	+	0.464040i
$701$			6.71832e24i			0.164361i	0.996617	+	0.0821804i	$0.0261884\pi$
$701$			6.71832e24i			0.164361i	−0.996617	+	0.0821804i	$0.973812\pi$
$702$	1.35953e25	+	3.73241e24i	0.328363	+	0.0901478i
$703$	7.63030e25			1.81946
$704$	−3.33634e25	−	1.92624e25i	−0.785446	−	0.453478i
$705$	−2.77417e24	+	3.09790e25i	−0.0644809	+	0.720055i
$706$	1.87662e25	+	3.25040e25i	0.430659	+	0.745924i
$707$	3.95789e25	−	2.28509e25i	0.896785	−	0.517759i
$708$	1.84613e24	−	2.62510e24i	0.0413012	−	0.0587283i
$709$	2.46314e25	−	4.26628e25i	0.544093	−	0.942396i	−0.454571	−	0.890711i	$-0.650207\pi$
$709$	2.46314e25	−	4.26628e25i	0.544093	−	0.942396i	0.998663	−	0.0516856i	$-0.0164594\pi$
$710$			6.75759e24i			0.147390i
$711$	1.37014e25	−	1.61937e25i	0.295080	−	0.348755i
$712$	6.14885e24			0.130760
$713$	−4.39927e25	−	2.53992e25i	−0.923793	−	0.533352i
$714$	−4.66011e23	+	2.16145e23i	−0.00966302	+	0.00448190i
$715$	1.73031e24	+	2.99699e24i	0.0354299	+	0.0613664i
$716$	9.92425e24	−	5.72977e24i	0.200669	−	0.115856i
$717$	1.92742e25	+	4.15554e25i	0.384861	+	0.829764i
$718$	−6.51526e24	+	1.12848e25i	−0.128473	+	0.222522i
$719$			1.43829e25i			0.280084i	0.990146	+	0.140042i	$0.0447237\pi$
$719$			1.43829e25i			0.280084i	−0.990146	+	0.140042i	$0.955276\pi$
$720$	−3.26917e24	+	1.81070e25i	−0.0628703	+	0.348220i
$721$	−3.32790e25			−0.632051
$722$	−1.14645e26	−	6.61903e25i	−2.15041	−	1.24154i
$723$	−5.28032e25	−	3.71344e25i	−0.978173	−	0.687910i
$724$	−1.26939e25	−	2.19865e25i	−0.232246	−	0.402261i
$725$	−2.25640e25	+	1.30273e25i	−0.407731	+	0.235404i
$726$	−3.65122e25	−	3.26967e24i	−0.651641	−	0.0583545i
$727$	−1.98839e25	+	3.44399e25i	−0.350503	+	0.607089i	−0.986338	−	0.164736i	$-0.947323\pi$
$727$	−1.98839e25	+	3.44399e25i	−0.350503	+	0.607089i	0.635835	+	0.771825i	$0.280656\pi$
$728$			1.33827e24i			0.0233003i
$729$	−4.99986e25	−	2.96907e25i	−0.859824	−	0.510590i
$730$	−3.33648e25			−0.566739
$731$	4.32618e23	+	2.49772e23i	0.00725852	+	0.00419071i
$732$	−4.14894e24	+	4.63309e25i	−0.0687602	+	0.767841i
$733$	6.67894e24	+	1.15683e25i	0.109338	+	0.189379i	0.915502	−	0.402313i	$-0.131794\pi$
$733$	6.67894e24	+	1.15683e25i	0.109338	+	0.189379i	−0.806164	+	0.591692i	$0.798460\pi$
$734$	1.24068e26	−	7.16308e25i	2.00630	−	1.15834i
$735$	−9.84846e24	+	1.40040e25i	−0.157319	+	0.223700i
$736$	2.86120e25	−	4.95574e25i	0.451489	−	0.782002i
$737$		−	2.05430e25i		−	0.320226i
$738$	−1.79335e26	−	3.23785e25i	−2.76157	−	0.498596i
$739$	−9.06442e25			−1.37892			−0.689462	−	0.724322i	$-0.742153\pi$
$739$	−9.06442e25			−1.37892			−0.689462	+	0.724322i	$0.742153\pi$
$740$	2.91219e25	+	1.68135e25i	0.437657	+	0.252681i
$741$	2.35101e25	−	1.09045e25i	0.349053	−	0.161898i
$742$	1.49445e25	+	2.58846e25i	0.219202	+	0.379670i
$743$	−3.05226e25	+	1.76222e25i	−0.442305	+	0.255365i	−0.704575	−	0.709630i	$-0.748862\pi$
$743$	−3.05226e25	+	1.76222e25i	−0.442305	+	0.255365i	0.262270	+	0.964995i	$0.415529\pi$
$744$	8.63754e24	+	1.86226e25i	0.123661	+	0.266615i
$745$	2.37049e25	−	4.10581e25i	0.335299	−	0.580755i
$746$			4.75339e25i			0.664284i
$747$	4.74008e25	+	4.01055e25i	0.654485	+	0.553756i
$748$	−7.75154e23			−0.0105748
$749$	3.86614e25	+	2.23212e25i	0.521124	+	0.300871i
$750$	6.69182e25	+	4.70609e25i	0.891236	+	0.626770i
$751$	−4.25821e25	−	7.37544e25i	−0.560361	−	0.970574i	−0.997465	−	0.0711627i	$-0.977329\pi$
$751$	−4.25821e25	−	7.37544e25i	−0.560361	−	0.970574i	0.437104	−	0.899411i	$-0.356004\pi$
$752$	1.02220e26	−	5.90166e25i	1.32915	−	0.767386i
$753$	1.12919e26	+	1.01119e25i	1.45082	+	0.129921i
$754$	−7.57663e24	+	1.31231e25i	−0.0961908	+	0.166607i
$755$		−	4.63914e25i		−	0.581989i
$756$	1.37318e25	−	5.00182e25i	0.170228	−	0.620057i
$757$	−5.32244e25			−0.652001			−0.326000	−	0.945370i	$-0.605701\pi$
$757$	−5.32244e25			−0.652001			−0.326000	+	0.945370i	$0.605701\pi$
$758$	1.42344e26	+	8.21826e25i	1.72313	+	0.994849i
$759$	−3.48110e24	+	3.88733e25i	−0.0416429	+	0.465024i
$760$	−4.92414e24	−	8.52886e24i	−0.0582114	−	0.100825i
$761$	2.12078e24	−	1.22443e24i	0.0247762	−	0.0143045i	−0.487561	−	0.873089i	$-0.662113\pi$
$761$	2.12078e24	−	1.22443e24i	0.0247762	−	0.0143045i	0.512337	+	0.858785i	$0.328780\pi$
$762$	2.86111e23	−	4.06836e23i	0.00330324	−	0.00469704i
$763$	3.27104e25	−	5.66561e25i	0.373220	−	0.646437i
$764$			1.44268e26i			1.62678i
$765$	1.57773e23	+	4.39059e23i	0.00175825	+	0.00489294i
$766$	1.51153e25			0.166478
$767$	1.19395e24	+	6.89330e23i	0.0129966	+	0.00750359i
$768$	6.08093e25	−	2.82046e25i	0.654213	−	0.303437i
$769$	7.54142e25	+	1.30621e26i	0.801892	+	1.38892i	0.918369	+	0.395724i	$0.129506\pi$
$769$	7.54142e25	+	1.30621e26i	0.801892	+	1.38892i	−0.116478	+	0.993193i	$0.537160\pi$
$770$	2.08789e25	−	1.20545e25i	0.219428	−	0.126687i
$771$	4.03128e25	+	8.69147e25i	0.418749	+	0.902826i
$772$	9.13920e24	−	1.58296e25i	0.0938323	−	0.162522i
$773$		−	8.21015e25i		−	0.833174i	−0.909096	−	0.416587i	$-0.863226\pi$
$773$		−	8.21015e25i		−	0.833174i	0.909096	−	0.416587i	$-0.136774\pi$
$774$	−8.98847e25	+	3.22996e25i	−0.901606	+	0.323987i
$775$	−1.42484e26			−1.41271
$776$	1.87865e25	+	1.08464e25i	0.184115	+	0.106299i
$777$	5.36631e25	+	3.77391e25i	0.519860	+	0.365597i
$778$	−1.28360e25	−	2.22326e25i	−0.122918	−	0.212899i
$779$	−2.90107e26	+	1.67494e26i	−2.74613	+	1.58548i
$780$	1.13757e25	+	1.01870e24i	0.106446	+	0.00953220i
$781$	−9.94690e24	+	1.72285e25i	−0.0920086	+	0.159364i
$782$		−	1.27569e24i		−	0.0116650i
$783$	4.44651e25	−	4.39228e25i	0.401942	−	0.397040i
$784$	6.49702e25			0.580590
$785$	4.34204e25	+	2.50688e25i	0.383590	+	0.221466i
$786$	1.45077e25	−	1.62006e26i	0.126705	−	1.41491i
$787$	3.67590e25	+	6.36685e25i	0.317389	+	0.549733i	0.979942	−	0.199281i	$-0.0638607\pi$
$787$	3.67590e25	+	6.36685e25i	0.317389	+	0.549733i	−0.662554	+	0.749014i	$0.730527\pi$
$788$	−1.17735e25	+	6.79745e24i	−0.100501	+	0.0580243i
$789$	3.78285e25	−	5.37902e25i	0.319247	−	0.453953i
$790$	1.62701e25	−	2.81806e25i	0.135752	−	0.235129i
$791$			7.37565e25i			0.608432i
$792$	1.01874e25	−	1.20405e25i	0.0830878	−	0.0982015i
$793$	−1.99828e25			−0.161138
$794$	−1.02238e26	−	5.90269e25i	−0.815128	−	0.470614i
$795$	2.46255e25	−	1.14218e25i	0.194125	−	0.0900391i
$796$	−6.17781e25	−	1.07003e26i	−0.481523	−	0.834022i
$797$	5.12679e25	−	2.95995e25i	0.395112	−	0.228118i	−0.289261	−	0.957250i	$-0.593409\pi$
$797$	5.12679e25	−	2.95995e25i	0.395112	−	0.228118i	0.684373	+	0.729132i	$0.260076\pi$
$798$	−7.59675e25	−	1.63787e26i	−0.578898	−	1.24811i
$799$	1.49643e24	−	2.59190e24i	0.0112755	−	0.0195298i
$800$		−	1.60507e26i		−	1.19587i
$801$	1.81901e25	−	1.00750e26i	0.134012	−	0.742251i
$802$	−2.21055e26			−1.61039
$803$	−8.50639e25	−	4.91117e25i	−0.612781	−	0.353789i
$804$	−5.54581e25	−	3.90014e25i	−0.395057	−	0.277828i
$805$	1.04766e25	+	1.81460e25i	0.0738004	+	0.127826i
$806$	−7.17659e25	+	4.14341e25i	−0.499922	+	0.288630i
$807$	7.49546e25	+	6.71218e24i	0.516341	+	0.0462383i
$808$	2.29320e25	−	3.97194e25i	0.156221	−	0.270583i
$809$			2.71764e26i			1.83086i	0.402478	+	0.915430i	$0.368149\pi$
$809$			2.71764e26i			1.83086i	−0.402478	+	0.915430i	$0.631851\pi$
$810$	−8.35706e25	−	3.11938e25i	−0.556786	−	0.207828i
$811$	1.13546e26			0.748142			0.374071	−	0.927400i	$-0.377962\pi$
$811$	1.13546e26			0.748142			0.374071	+	0.927400i	$0.377962\pi$
$812$	4.82810e25	+	2.78750e25i	0.314609	+	0.181640i
$813$	1.16384e25	−	1.29965e26i	0.0750029	−	0.837553i
$814$	9.37278e25	+	1.62341e26i	0.597377	+	1.03469i
$815$	−1.11424e25	+	6.43305e24i	−0.0702358	+	0.0405507i
$816$	1.01848e24	−	1.44823e24i	0.00634954	−	0.00902873i
$817$	−8.77861e25	+	1.52050e26i	−0.541287	+	0.937536i
$818$			2.26509e26i			1.38135i
$819$	2.19277e25	+	3.95900e24i	0.132263	+	0.0238798i
$820$	−1.47630e26			−0.880746
$821$	3.06818e25	+	1.77142e25i	0.181048	+	0.104528i	0.587785	−	0.809017i	$-0.300000\pi$
$821$	3.06818e25	+	1.77142e25i	0.181048	+	0.104528i	−0.406737	+	0.913545i	$0.633334\pi$
$822$	4.34615e25	−	2.01583e25i	0.253664	−	0.117654i
$823$	−6.69907e25	−	1.16031e26i	−0.386737	−	0.669848i	0.605271	−	0.796019i	$-0.293065\pi$
$823$	−6.69907e25	−	1.16031e26i	−0.386737	−	0.669848i	−0.992009	+	0.126171i	$0.959731\pi$
$824$	−2.89228e25	+	1.66986e25i	−0.165156	+	0.0953530i
$825$	4.60618e25	+	9.93097e25i	0.260169	+	0.560927i
$826$	4.80232e24	−	8.31785e24i	0.0268306	−	0.0464719i
$827$		−	3.20897e26i		−	1.77344i	−0.462308	−	0.886720i	$-0.652978\pi$
$827$		−	3.20897e26i		−	1.77344i	0.462308	−	0.886720i	$-0.347022\pi$
$828$	9.83336e25	+	8.31995e25i	0.537562	+	0.454828i
$829$	2.27624e26			1.23091			0.615456	−	0.788171i	$-0.288972\pi$
$829$	2.27624e26			1.23091			0.615456	+	0.788171i	$0.288972\pi$
$830$	8.24876e25	+	4.76242e25i	0.441251	+	0.254756i
$831$	−3.24613e25	−	2.28287e25i	−0.171774	−	0.120802i
$832$	−2.73099e25	−	4.73022e25i	−0.142959	−	0.247612i
$833$	1.42668e24	−	8.23696e23i	0.00738792	−	0.00426542i
$834$	−4.57388e26	−	4.09591e25i	−2.34309	−	0.209824i
$835$	−3.14097e25	+	5.44032e25i	−0.159179	+	0.275706i
$836$		−	2.72439e26i		−	1.36588i
$837$	3.30687e26	−	8.64360e25i	1.64016	−	0.428712i
$838$	4.12558e26			2.02436
$839$	7.79027e25	+	4.49772e25i	0.378177	+	0.218341i	0.677025	−	0.735960i	$-0.263269\pi$
$839$	7.79027e25	+	4.49772e25i	0.378177	+	0.218341i	−0.298848	+	0.954301i	$0.596602\pi$
$840$	7.55239e23	−	8.43371e24i	0.00362720	−	0.0405047i
$841$	−7.16399e25	−	1.24084e26i	−0.340401	−	0.589592i
$842$	3.05699e26	−	1.76495e26i	1.43709	−	0.829707i
$843$	−1.02253e26	+	1.45399e26i	−0.475586	+	0.676259i
$844$	−1.01279e26	+	1.75421e26i	−0.466056	+	0.807232i
$845$		−	8.47637e25i		−	0.385922i
$846$	1.93513e26	+	5.38517e26i	0.871720	+	2.42586i
$847$	−5.79380e25			−0.258234
$848$	−8.92134e25	−	5.15074e25i	−0.393430	−	0.227147i
$849$	−2.45489e26	+	1.13862e26i	−1.07118	+	0.496834i
$850$	−1.78909e24	−	3.09880e24i	−0.00772436	−	0.0133790i
$851$	−1.41092e26	+	8.14595e25i	−0.602749	+	0.347997i
$852$	2.76258e25	+	5.95615e25i	0.116777	+	0.251773i
$853$	1.28989e26	−	2.23415e26i	0.539523	−	0.934482i	−0.459406	−	0.888226i	$-0.651938\pi$
$853$	1.28989e26	−	2.23415e26i	0.539523	−	0.934482i	0.998930	−	0.0462556i	$-0.0147289\pi$
$854$			1.39213e26i			0.576182i
$855$	−1.54314e26	+	5.54518e25i	−0.631989	+	0.227102i
$856$	4.48009e25			0.181561
$857$	−2.53418e25	−	1.46311e25i	−0.101627	−	0.0586744i	0.448325	−	0.893871i	$-0.352021\pi$
$857$	−2.53418e25	−	1.46311e25i	−0.101627	−	0.0586744i	−0.549952	+	0.835196i	$0.685354\pi$
$858$	5.20792e25	+	3.66252e25i	0.206671	+	0.145343i
$859$	−1.85440e26	−	3.21191e26i	−0.728223	−	1.26132i	−0.957633	−	0.287990i	$-0.907013\pi$
$859$	−1.85440e26	−	3.21191e26i	−0.728223	−	1.26132i	0.229410	−	0.973330i	$-0.426320\pi$
$860$	−6.70091e25	+	3.86877e25i	−0.260404	+	0.150344i
$861$	−2.86871e26	−	2.56893e25i	−1.10321	−	0.0987924i
$862$	−7.78272e25	+	1.34801e26i	−0.296187	+	0.513011i
$863$		−	2.57206e26i		−	0.968689i	−0.874877	−	0.484345i	$-0.839058\pi$
$863$		−	2.57206e26i		−	0.968689i	0.874877	−	0.484345i	$-0.160942\pi$
$864$	9.73693e25	+	3.72515e26i	0.362909	+	1.38842i
$865$	−7.12021e25			−0.262632
$866$	2.88546e25	+	1.66592e25i	0.105331	+	0.0608126i
$867$	−2.46850e25	+	2.75656e26i	−0.0891786	+	0.995853i
$868$	1.52439e26	+	2.64033e26i	0.545029	+	0.944017i
$869$	8.29614e25	−	4.78978e25i	0.293561	−	0.169487i
$870$	5.51535e25	−	7.84254e25i	0.193152	−	0.274652i
$871$	1.45628e25	−	2.52235e25i	0.0504757	−	0.0874264i
$872$		−	6.56532e25i		−	0.225220i
$873$	2.33295e26	−	2.75732e26i	0.792096	−	0.936179i
$874$	4.48360e26			1.50669
$875$	1.11976e26	+	6.46493e25i	0.372436	+	0.215026i
$876$	−2.94078e26	+	1.36399e26i	−0.968112	+	0.449030i
$877$	−1.45634e26	−	2.52245e26i	−0.474532	−	0.821913i	0.525043	−	0.851076i	$-0.324049\pi$
$877$	−1.45634e26	−	2.52245e26i	−0.474532	−	0.821913i	−0.999575	+	0.0291625i	$0.990716\pi$
$878$	4.56254e25	−	2.63418e25i	0.147148	−	0.0849562i
$879$	−1.95057e25	−	4.20544e25i	−0.0622674	−	0.134249i
$880$	−4.15467e25	+	7.19610e25i	−0.131278	+	0.227381i
$881$		−	5.28020e26i		−	1.65146i	−0.564068	−	0.825728i	$-0.690765\pi$
$881$		−	5.28020e26i		−	1.65146i	0.564068	−	0.825728i	$-0.309235\pi$
$882$	−5.59638e25	+	3.09966e26i	−0.173257	+	0.959616i
$883$	5.01880e26			1.53799			0.768995	−	0.639255i	$-0.220757\pi$
$883$	5.01880e26			1.53799			0.768995	+	0.639255i	$0.220757\pi$
$884$	−9.51764e23	−	5.49501e23i	−0.00288708	−	0.00166686i
$885$	−7.13523e24	−	5.01793e24i	−0.0214249	−	0.0150673i
$886$	1.98540e26	+	3.43881e26i	0.590125	+	1.02213i
$887$	−2.82317e26	+	1.62996e26i	−0.830662	+	0.479583i	−0.854079	−	0.520143i	$-0.825879\pi$
$887$	−2.82317e26	+	1.62996e26i	−0.830662	+	0.479583i	0.0234174	+	0.999726i	$0.492545\pi$
$888$	6.55752e25	+	5.87226e24i	0.190995	+	0.0171036i
$889$	3.93042e23	−	6.80769e23i	0.00113324	−	0.00196284i
$890$		−	1.57050e26i		−	0.448259i
$891$	−1.67148e26	−	2.02541e26i	−0.472282	−	0.572288i
$892$	−7.68602e26			−2.14990
$893$	9.10961e26	+	5.25944e26i	2.52253	+	1.45638i
$894$	7.77980e25	−	8.68766e26i	0.213271	−	2.38158i
$895$	−1.55740e25	−	2.69749e25i	−0.0422660	−	0.0732069i
$896$	−6.37594e25	+	3.68115e25i	−0.171306	+	0.0989035i
$897$	−3.18313e25	+	4.52624e25i	−0.0846685	+	0.120394i
$898$	1.67097e26	−	2.89420e26i	0.440029	−	0.762153i
$899$			3.67372e26i			0.957786i
$900$	3.55546e26	+	6.41932e25i	0.917728	+	0.165694i
$901$	−2.61206e24			−0.00667512
$902$	−7.12714e26	−	4.11486e26i	−1.80325	−	1.04111i
$903$	−1.36942e26	+	6.35165e25i	−0.343042	+	0.159110i
$904$	3.70092e25	+	6.41019e25i	0.0917897	+	0.158984i
$905$	−5.97609e25	+	3.45030e25i	−0.146751	+	0.0847265i
$906$	−3.59124e26	−	7.74275e26i	−0.873154	−	1.88253i
$907$	−2.16740e26	+	3.75404e26i	−0.521763	+	0.903719i	0.477917	+	0.878405i	$0.341392\pi$
$907$	−2.16740e26	+	3.75404e26i	−0.521763	+	0.903719i	−0.999680	+	0.0253143i	$0.991941\pi$
$908$		−	5.99605e26i		−	1.42920i
$909$	−5.82968e26	−	4.93246e26i	−1.37585	−	1.16410i
$910$	3.41813e25			0.0798760
$911$	−3.65906e26	−	2.11256e26i	−0.846652	−	0.488814i	0.0128681	−	0.999917i	$-0.495904\pi$
$911$	−3.65906e26	−	2.11256e26i	−0.846652	−	0.488814i	−0.859520	+	0.511103i	$0.829237\pi$
$912$	5.09002e26	+	3.57961e26i	1.16618	+	0.820129i
$913$	1.40202e26	+	2.42837e26i	0.318066	+	0.550906i
$914$	−1.05246e27	+	6.07635e26i	−2.36422	+	1.36498i
$915$	1.25931e26	+	1.12771e25i	0.280119	+	0.0250847i
$916$	−2.37797e26	+	4.11876e26i	−0.523778	+	0.907210i
$917$		−	2.57074e26i		−	0.560704i
$918$	6.03207e24	+	6.10656e24i	0.0130281	+	0.0131890i
$919$	5.05196e26			1.08049			0.540244	−	0.841508i	$-0.318332\pi$
$919$	5.05196e26			1.08049			0.540244	+	0.841508i	$0.318332\pi$
$920$	1.82105e25	+	1.05138e25i	0.0385684	+	0.0222675i
$921$	1.26203e25	−	1.40930e26i	0.0264688	−	0.295575i
$922$	−3.87100e26	−	6.70477e26i	−0.803980	−	1.39253i
$923$	−2.44264e25	+	1.41026e25i	−0.0502393	+	0.0290057i
$924$	1.34747e26	−	1.91604e26i	0.274455	−	0.390262i
$925$	−2.28486e26	+	3.95749e26i	−0.460875	+	0.798260i
$926$			1.28509e27i			2.56706i
$927$	1.88046e26	+	5.23303e26i	0.372003	+	1.03523i
$928$	−4.13841e26			−0.810777
$929$	3.19777e26	+	1.84623e26i	0.620449	+	0.358216i	0.777044	−	0.629447i	$-0.216718\pi$
$929$	3.19777e26	+	1.84623e26i	0.620449	+	0.358216i	−0.156595	+	0.987663i	$0.550052\pi$
$930$	4.75648e26	−	2.20615e26i	0.913986	−	0.423925i
$931$	2.89500e26	+	5.01429e26i	0.550937	+	0.954250i
$932$	1.72103e26	−	9.93635e25i	0.324373	−	0.187277i
$933$	1.33326e26	+	2.87453e26i	0.248875	+	0.536577i
$934$	7.06396e26	−	1.22351e27i	1.30595	−	2.26197i
$935$			2.10693e24i			0.00385785i
$936$	2.10439e25	−	7.56202e24i	0.0381632	−	0.0137137i
$937$	−5.18228e26			−0.930817			−0.465408	−	0.885096i	$-0.654093\pi$
$937$	−5.18228e26			−0.930817			−0.465408	+	0.885096i	$0.654093\pi$
$938$	−1.75723e26	−	1.01454e26i	−0.312611	−	0.180486i
$939$	1.00119e24	+	7.04096e23i	0.00176411	+	0.00124063i
$940$	2.31786e26	+	4.01464e26i	0.404516	+	0.700642i
$941$	4.68738e25	−	2.70626e25i	0.0810258	−	0.0467803i	−0.458940	−	0.888467i	$-0.651771\pi$
$941$	4.68738e25	−	2.70626e25i	0.0810258	−	0.0467803i	0.539966	+	0.841687i	$0.318437\pi$
$942$	9.18751e26	+	8.22742e25i	1.57304	+	0.140866i
$943$	3.57625e26	−	6.19425e26i	0.606489	−	1.05047i
$944$			3.31032e25i			0.0556060i
$945$	−1.35953e26	−	3.73242e25i	−0.226206	−	0.0621017i
$946$	−4.31333e26			−0.710874
$947$	5.60194e26	+	3.23428e26i	0.914511	+	0.527993i	0.881880	−	0.471474i	$-0.156278\pi$
$947$	5.60194e26	+	3.23428e26i	0.914511	+	0.527993i	0.0326313	+	0.999467i	$0.489611\pi$
$948$	2.81991e25	−	3.14898e26i	0.0455996	−	0.509208i
$949$	−6.96299e25	−	1.20602e26i	−0.111532	−	0.193179i
$950$	1.08912e27	−	6.28803e26i	1.72808	−	0.997705i
$951$	−6.46429e26	+	9.19189e26i	−1.01601	+	1.44471i
$952$	−4.07388e23	+	7.05618e23i	−0.000634273	+	0.00109859i
$953$			9.24992e26i			1.42660i	0.700860	+	0.713299i	$0.252800\pi$
$953$			9.24992e26i			1.42660i	−0.700860	+	0.713299i	$0.747200\pi$
$954$	3.22583e26	−	3.81261e26i	0.492840	−	0.582488i
$955$	3.92132e26			0.593474
$956$	5.91266e26	+	3.41368e26i	0.886466	+	0.511801i
$957$	2.56053e26	−	1.18763e26i	0.380297	−	0.176389i
$958$	−1.49989e26	−	2.59789e26i	−0.220684	−	0.382235i
$959$	6.55750e25	−	3.78597e25i	0.0955808	−	0.0551836i
$960$	1.45412e26	+	3.13509e26i	0.209970	+	0.452698i
$961$	−6.54990e26	+	1.13448e27i	−0.936967	+	1.62287i
$962$			2.65772e26i			0.376646i
$963$	1.32535e26	−	7.34068e26i	0.186077	−	1.03062i
$964$	−9.62129e26			−1.33826
$965$	−4.30259e25	−	2.48410e25i	−0.0592904	−	0.0342313i
$966$	3.15327e26	+	2.21757e26i	0.430494	+	0.302749i
$967$	−1.05210e26	−	1.82229e26i	−0.142304	−	0.246478i	0.786060	−	0.618151i	$-0.212118\pi$
$967$	−1.05210e26	−	1.82229e26i	−0.142304	−	0.246478i	−0.928364	+	0.371672i	$0.878784\pi$
$968$	−5.03540e25	+	2.90719e25i	−0.0674770	+	0.0389579i
$969$	1.57155e25	+	1.40732e24i	0.0208647	+	0.00186844i
$970$	2.77032e26	−	4.79833e26i	0.364405	−	0.631167i
$971$		−	4.31727e26i		−	0.562648i	−0.959613	−	0.281324i	$-0.909227\pi$
$971$		−	4.31727e26i		−	0.562648i	0.959613	−	0.281324i	$-0.0907735\pi$
$972$	−8.64116e26	+	6.67034e25i	−1.11577	+	0.0861294i
$973$	−7.25788e26			−0.928527
$974$	5.48088e26	+	3.16439e26i	0.694735	+	0.401106i
$975$	−1.38435e25	+	1.54589e26i	−0.0173862	+	0.194150i
$976$	−2.39905e26	−	4.15528e26i	−0.298532	−	0.517073i
$977$	1.04988e27	−	6.06151e26i	1.29447	−	0.747360i	0.315023	−	0.949084i	$-0.397988\pi$
$977$	1.04988e27	−	6.06151e26i	1.29447	−	0.747360i	0.979442	+	0.201724i	$0.0646545\pi$
$978$	−1.36167e26	+	1.93623e26i	−0.166350	+	0.236541i
$979$	2.31172e26	−	4.00401e26i	0.279828	−	0.484675i
$980$			2.55168e26i			0.306049i
$981$	−1.07574e27	−	1.94222e26i	−1.27845	−	0.230822i
$982$	−1.21977e27			−1.43640
$983$	−9.35414e26	−	5.40061e26i	−1.09150	−	0.630175i	−0.157522	−	0.987516i	$-0.550350\pi$
$983$	−9.35414e26	−	5.40061e26i	−1.09150	−	0.630175i	−0.933974	+	0.357340i	$0.883684\pi$
$984$	−2.62210e26	+	1.21618e26i	−0.303175	+	0.140619i
$985$	1.84760e25	+	3.20014e25i	0.0211681	+	0.0366642i
$986$	−7.98972e24	+	4.61287e24i	−0.00907067	+	0.00523695i
$987$	3.80540e26	+	8.20448e26i	0.428101	+	0.922989i
$988$	1.93130e26	−	3.34512e26i	0.215297	−	0.372906i
$989$		−	3.74875e26i		−	0.414114i
$990$	−3.07532e26	−	2.60201e26i	−0.336646	−	0.284834i
$991$	−3.32780e26			−0.360989			−0.180495	−	0.983576i	$-0.557770\pi$
$991$	−3.32780e26			−0.360989			−0.180495	+	0.983576i	$0.557770\pi$
$992$	−1.95995e27	−	1.13158e27i	−2.10688	−	1.21641i
$993$	−9.46451e26	−	6.65601e26i	−1.00822	−	0.709040i
$994$	9.82476e25	+	1.70170e26i	0.103716	+	0.179641i
$995$	−2.90842e26	+	1.67918e26i	−0.304263	+	0.175666i
$996$	9.21739e26	+	8.25418e25i	0.955596	+	0.0855736i
$997$	−2.22642e26	+	3.85628e26i	−0.228745	+	0.396198i	−0.957436	−	0.288644i	$-0.906796\pi$
$997$	−2.22642e26	+	3.85628e26i	−0.228745	+	0.396198i	0.728691	+	0.684842i	$0.240129\pi$
$998$			1.72460e27i			1.75596i
$999$	2.90209e26	−	1.05709e27i	0.292834	−	1.06665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.19.d.a.2.3	✓	34
3.2	odd	2		27.19.d.a.8.15		34
9.2	odd	6		81.19.b.a.80.6		34
9.4	even	3		27.19.d.a.17.15		34
9.5	odd	6	inner	9.19.d.a.5.3	yes	34
9.7	even	3		81.19.b.a.80.29		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.19.d.a.2.3	✓	34	1.1	even	1	trivial
9.19.d.a.5.3	yes	34	9.5	odd	6	inner
27.19.d.a.8.15		34	3.2	odd	2
27.19.d.a.17.15		34	9.4	even	3
81.19.b.a.80.6		34	9.2	odd	6
81.19.b.a.80.29		34	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-645.469 - 372.662i) q^{2} +(-1755.59 + 19604.6i) q^{3} +(146682. + 254060. i) q^{4} +(690555. - 398692. i) q^{5} +(8.43904e6 - 1.19999e7i) q^{6} +(1.15930e7 - 2.00797e7i) q^{7} -2.32684e7i q^{8} +(-3.81256e8 - 6.88350e7i) q^{9} -5.94309e8 q^{10} +(-1.51520e9 - 8.74799e8i) q^{11} +(-5.23824e9 + 2.42960e9i) q^{12} +(-1.24028e9 - 2.14822e9i) q^{13} +(-1.49659e10 + 8.64057e9i) q^{14} +(6.60385e9 + 1.42380e10i) q^{15} +(2.97805e10 - 5.15813e10i) q^{16} -1.51023e9i q^{17} +(2.20437e11 + 1.86511e11i) q^{18} +5.30794e11 q^{19} +(2.02583e11 + 1.16962e11i) q^{20} +(3.73302e11 + 2.62528e11i) q^{21} +(6.52008e11 + 1.12931e12i) q^{22} +(-9.81493e11 + 5.66665e11i) q^{23} +(4.56167e11 + 4.08498e10i) q^{24} +(-1.58944e12 + 2.75299e12i) q^{25} +1.84882e12i q^{26} +(2.01881e12 - 7.35351e12i) q^{27} +6.80195e12 q^{28} +(7.09811e12 + 4.09810e12i) q^{29} +(1.04336e12 - 1.16512e13i) q^{30} +(2.24111e13 + 3.88172e13i) q^{31} +(-4.37272e13 + 2.52459e13i) q^{32} +(1.98101e13 - 2.81689e13i) q^{33} +(-5.62806e11 + 9.74809e11i) q^{34} -1.84882e13i q^{35} +(-3.84351e13 - 1.06959e14i) q^{36} +1.43753e14 q^{37} +(-3.42611e14 - 1.97807e14i) q^{38} +(4.42924e13 - 2.05437e13i) q^{39} +(-9.27694e12 - 1.60681e13i) q^{40} +(-5.46553e14 + 3.15553e14i) q^{41} +(-1.43121e14 - 3.08569e14i) q^{42} +(-1.65386e14 + 2.86458e14i) q^{43} -5.13267e14i q^{44} +(-2.90722e14 + 1.04469e14i) q^{45} +8.44698e14 q^{46} +(1.71622e15 + 9.90862e14i) q^{47} +(9.58945e14 + 6.74388e14i) q^{48} +(5.45409e14 + 9.44677e14i) q^{49} +(2.05187e15 - 1.18465e15i) q^{50} +(2.96075e13 + 2.65135e12i) q^{51} +(3.63852e14 - 6.30210e14i) q^{52} -1.72957e15i q^{53} +(-4.04345e15 + 3.99413e15i) q^{54} -1.39510e15 q^{55} +(-4.67224e14 - 2.69752e14i) q^{56} +(-9.31856e14 + 1.04060e16i) q^{57} +(-3.05441e15 - 5.29039e15i) q^{58} +(-4.81326e14 + 2.77893e14i) q^{59} +(-2.64863e15 + 3.76622e15i) q^{60} +(4.02790e15 - 6.97652e15i) q^{61} -3.34071e16i q^{62} +(-5.80211e15 + 6.85752e15i) q^{63} +2.20192e16 q^{64} +(-1.71296e15 - 9.88977e14i) q^{65} +(-2.32843e16 + 1.07997e16i) q^{66} +(5.87079e15 + 1.01685e16i) q^{67} +(3.83690e14 - 2.21524e14i) q^{68} +(-9.38612e15 - 2.02366e16i) q^{69} +(-6.88985e15 + 1.19336e16i) q^{70} -1.13705e16i q^{71} +(-1.60168e15 + 8.87124e15i) q^{72} +5.61405e16 q^{73} +(-9.27878e16 - 5.35711e16i) q^{74} +(-5.11807e16 - 3.59933e16i) q^{75} +(7.78577e16 + 1.34854e17i) q^{76} +(-3.51315e16 + 2.02832e16i) q^{77} +(-3.62452e16 - 3.24576e15i) q^{78} +(-2.73765e16 + 4.74175e16i) q^{79} -4.74929e16i q^{80} +(1.40618e17 + 5.24876e16i) q^{81} +4.70378e17 q^{82} +(-1.38796e17 - 8.01338e16i) q^{83} +(-1.19414e16 + 1.33349e17i) q^{84} +(-6.02118e14 - 1.04290e15i) q^{85} +(2.13504e17 - 1.23266e17i) q^{86} +(-9.28027e16 + 1.31961e17i) q^{87} +(-2.03552e16 + 3.52562e16i) q^{88} +2.64257e17i q^{89} +(2.26584e17 + 4.09093e16i) q^{90} -5.75144e16 q^{91} +(-2.87934e17 - 1.66239e17i) q^{92} +(-8.00338e17 + 3.71213e17i) q^{93} +(-7.38513e17 - 1.27914e18i) q^{94} +(3.66542e17 - 2.11623e17i) q^{95} +(-4.18168e17 - 9.01574e17i) q^{96} +(-4.66141e17 + 8.07380e17i) q^{97} -8.13013e17i q^{98} +(5.17461e17 + 4.37821e17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} + 3804 q^{3} + 2097151 q^{4} + 2192181 q^{5} + 3257181 q^{6} + 4302359 q^{7} + 397977264 q^{9} - 524292 q^{10} + 1022992575 q^{11} + 32417762010 q^{12} + 3839449319 q^{13} + 129938709678 q^{14}+ \cdots - 52\!\cdots\!15 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 + 3804 * q^3 + 2097151 * q^4 + 2192181 * q^5 + 3257181 * q^6 + 4302359 * q^7 + 397977264 * q^9 - 524292 * q^10 + 1022992575 * q^11 + 32417762010 * q^12 + 3839449319 * q^13 + 129938709678 * q^14 - 124119415395 * q^15 - 240517906433 * q^16 - 285581999484 * q^18 - 608222566264 * q^19 + 1471193748174 * q^20 - 1381493495229 * q^21 + 851254438911 * q^22 + 375441179325 * q^23 + 305135298351 * q^24 + 12156817117552 * q^25 + 11936276558406 * q^27 + 4648789868540 * q^28 - 31101186224271 * q^29 + 62775784981818 * q^30 - 20376334153801 * q^31 - 113411230023465 * q^32 - 20701744605945 * q^33 - 99737362554111 * q^34 - 472069890962721 * q^36 + 56970364072604 * q^37 + 1244853240655323 * q^38 + 277868300554299 * q^39 + 236076863983350 * q^40 - 1178988706876521 * q^41 + 1034549802657900 * q^42 - 230641688892691 * q^43 - 5286549794938479 * q^45 + 131852496280800 * q^46 + 3640523435126673 * q^47 + 11085451646520237 * q^48 - 4168576830678822 * q^49 - 18078797603969781 * q^50 + 7526452896180882 * q^51 + 1286623499256920 * q^52 - 26455557995217045 * q^54 - 1446925762710942 * q^55 + 59834487378592914 * q^56 + 23867830767470574 * q^57 + 8463343484826222 * q^58 - 29968086845368137 * q^59 + 17080074037610118 * q^60 - 6976259792083513 * q^61 - 73583064644919705 * q^63 - 120930519493421318 * q^64 + 47229492730318989 * q^65 + 58361174960027994 * q^66 - 20333770074023707 * q^67 - 116938167206248431 * q^68 + 99272218824151677 * q^69 - 18312927374667108 * q^70 + 186892024430477907 * q^72 + 209341663176867296 * q^73 - 88916838511745634 * q^74 - 103202922056583144 * q^75 - 180442619960522287 * q^76 + 384727796507616477 * q^77 - 113580855335113884 * q^78 + 126425698081194923 * q^79 + 749177961563573568 * q^81 - 856725985700547270 * q^82 - 819712186371296103 * q^83 - 1069135371708878382 * q^84 + 372804006624771096 * q^85 + 1989011602082127453 * q^86 - 689457779704913391 * q^87 - 648793548761104653 * q^88 + 2069849112225424614 * q^90 - 29982940436364482 * q^91 - 2013198581519506428 * q^92 - 2088815715502953 * q^93 - 769920889934866620 * q^94 + 167036756670646446 * q^95 + 338414304229215984 * q^96 + 1172101248161568089 * q^97 - 529477370297396415 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more