LMFDB - Embedded newform 42.12.f.a.5.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,12,Mod(5,42)] 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("42.5"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	42.f (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:	$32.2704135835$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.27
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(27.7128 + 16.0000i) q^{2} +(320.393 + 272.938i) q^{3} +(512.000 + 886.810i) q^{4} +(4602.68 - 7972.08i) q^{5} +(4512.00 + 12690.2i) q^{6} +(-26134.7 - 35976.5i) q^{7} +32768.0i q^{8} +(28156.9 + 174895. i) q^{9} +(255107. - 147286. i) q^{10} +(727772. - 420179. i) q^{11} +(-78002.6 + 423872. i) q^{12} -1.15435e6i q^{13} +(-148642. - 1.41516e6i) q^{14} +(3.65055e6 - 1.29796e6i) q^{15} +(-524288. + 908093. i) q^{16} +(-5.51557e6 - 9.55325e6i) q^{17} +(-2.01801e6 + 5.29734e6i) q^{18} +(2.84416e6 + 1.64208e6i) q^{19} +9.42630e6 q^{20} +(1.44595e6 - 1.86598e7i) q^{21} +2.68915e7 q^{22} +(3.04590e7 + 1.75855e7i) q^{23} +(-8.94363e6 + 1.04987e7i) q^{24} +(-1.79553e7 - 3.10996e7i) q^{25} +(1.84695e7 - 3.19901e7i) q^{26} +(-3.87142e7 + 6.37203e7i) q^{27} +(1.85233e7 - 4.15964e7i) q^{28} +8.82728e7i q^{29} +(1.21934e8 + 2.24388e7i) q^{30} +(-2.70586e7 + 1.56223e7i) q^{31} +(-2.90590e7 + 1.67772e7i) q^{32} +(3.47856e8 + 6.40138e7i) q^{33} -3.52997e8i q^{34} +(-4.07097e8 + 4.27596e7i) q^{35} +(-1.40682e8 + 1.14516e8i) q^{36} +(2.80276e8 - 4.85453e8i) q^{37} +(5.25465e7 + 9.10131e7i) q^{38} +(3.15064e8 - 3.69845e8i) q^{39} +(2.61229e8 + 1.50821e8i) q^{40} -6.02276e7 q^{41} +(3.38628e8 - 4.93979e8i) q^{42} +7.98515e8 q^{43} +(7.45238e8 + 4.30263e8i) q^{44} +(1.52387e9 + 5.80517e8i) q^{45} +(5.62737e8 + 9.74689e8i) q^{46} +(-1.32750e9 + 2.29930e9i) q^{47} +(-4.15831e8 + 1.47849e8i) q^{48} +(-6.11284e8 + 1.88047e9i) q^{49} -1.14914e9i q^{50} +(8.40291e8 - 4.56621e9i) q^{51} +(1.02368e9 - 5.91025e8i) q^{52} +(3.07329e9 - 1.77436e9i) q^{53} +(-2.09240e9 + 1.14644e9i) q^{54} -7.73581e9i q^{55} +(1.17888e9 - 8.56381e8i) q^{56} +(4.63066e8 + 1.30239e9i) q^{57} +(-1.41237e9 + 2.44629e9i) q^{58} +(2.88094e9 + 4.98993e9i) q^{59} +(3.02012e9 + 2.57279e9i) q^{60} +(1.76873e8 + 1.02118e8i) q^{61} -9.99828e8 q^{62} +(5.55623e9 - 5.58381e9i) q^{63} -1.07374e9 q^{64} +(-9.20253e9 - 5.31309e9i) q^{65} +(8.61585e9 + 7.33970e9i) q^{66} +(4.17296e9 + 7.22778e9i) q^{67} +(5.64795e9 - 9.78253e9i) q^{68} +(4.95912e9 + 1.39477e10i) q^{69} +(-1.19660e10 - 5.32856e9i) q^{70} +5.34061e9i q^{71} +(-5.73096e9 + 9.22645e8i) q^{72} +(-1.30790e10 + 7.55117e9i) q^{73} +(1.55345e10 - 8.96884e9i) q^{74} +(2.73547e9 - 1.48648e10i) q^{75} +3.36297e9i q^{76} +(-3.41366e10 - 1.52014e10i) q^{77} +(1.46488e10 - 5.20840e9i) q^{78} +(1.53802e10 - 2.66394e10i) q^{79} +(4.82626e9 + 8.35933e9i) q^{80} +(-2.97954e10 + 9.84900e9i) q^{81} +(-1.66908e9 - 9.63641e8i) q^{82} -5.81737e10 q^{83} +(1.72880e10 - 8.27151e9i) q^{84} -1.01546e11 q^{85} +(2.21291e10 + 1.27762e10i) q^{86} +(-2.40930e10 + 2.82820e10i) q^{87} +(1.37684e10 + 2.38476e10i) q^{88} +(-4.18851e9 + 7.25471e9i) q^{89} +(3.29426e10 + 4.04698e10i) q^{90} +(-4.15292e10 + 3.01684e10i) q^{91} +3.60152e10i q^{92} +(-1.29333e10 - 2.38004e9i) q^{93} +(-7.35775e10 + 4.24800e10i) q^{94} +(2.61815e10 - 1.51159e10i) q^{95} +(-1.38894e10 - 2.55599e9i) q^{96} +1.54517e10i q^{97} +(-4.70278e10 + 4.23325e10i) q^{98} +(9.39790e10 + 1.15453e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30720 q^{4} - 95298 q^{7} - 91434 q^{9} + 245184 q^{10} - 8480820 q^{15} - 31457280 q^{16} + 12170496 q^{18} + 1649724 q^{19} + 43254216 q^{21} + 20705664 q^{22} + 4521984 q^{24} - 336132444 q^{25}+ \cdots + 288758042496 q^{99}+O(q^{100}) $ 60 * q + 30720 * q^4 - 95298 * q^7 - 91434 * q^9 + 245184 * q^10 - 8480820 * q^15 - 31457280 * q^16 + 12170496 * q^18 + 1649724 * q^19 + 43254216 * q^21 + 20705664 * q^22 + 4521984 * q^24 - 336132444 * q^25 + 28121088 * q^28 - 77109120 * q^30 - 275992974 * q^31 + 1056712914 * q^33 - 187256832 * q^36 + 555437556 * q^37 - 563926680 * q^39 + 251068416 * q^40 + 1167043776 * q^42 + 2546594304 * q^43 + 544480776 * q^45 - 452472192 * q^46 - 1309143414 * q^49 + 2007979044 * q^51 + 3219419136 * q^52 - 9840998592 * q^54 + 17053196256 * q^57 + 12235419456 * q^58 - 4342179840 * q^60 - 3056592000 * q^61 - 42499692960 * q^63 - 64424509440 * q^64 + 48796070400 * q^66 + 27979853436 * q^67 - 4966503360 * q^70 - 12462587904 * q^72 - 105678747168 * q^73 + 173211633504 * q^75 - 16600538880 * q^78 - 27787555926 * q^79 - 71399556486 * q^81 + 31231064832 * q^82 - 25272410112 * q^84 + 12868048152 * q^85 + 137017459998 * q^87 + 10601299968 * q^88 + 333571182180 * q^91 - 14607989424 * q^93 - 430917051648 * q^94 + 4630511616 * q^96 + 288758042496 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	27.7128	+	16.0000i	0.612372	+	0.353553i
$2$	27.7128	+	16.0000i	0.612372	+	0.353553i
$3$	320.393	+	272.938i	0.761231	+	0.648480i
$3$	320.393	+	272.938i	0.761231	+	0.648480i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	4602.68	−	7972.08i	0.658683	−	1.14087i	−0.322274	−	0.946646i	$-0.604447\pi$
$5$	4602.68	−	7972.08i	0.658683	−	1.14087i	0.980957	−	0.194225i	$-0.0622193\pi$
$6$	4512.00	+	12690.2i	0.236885	+	0.666247i
$7$	−26134.7	−	35976.5i	−0.587730	−	0.809057i
$7$	−26134.7	−	35976.5i	−0.587730	−	0.809057i
$8$			32768.0i			0.353553i
$9$	28156.9	+	174895.i	0.158946	+	0.987287i
$10$	255107.	−	147286.i	0.806718	−	0.465759i
$11$	727772.	−	420179.i	1.36250	−	0.786638i	0.372541	−	0.928016i	$-0.378487\pi$
$11$	727772.	−	420179.i	1.36250	−	0.786638i	0.989956	+	0.141378i	$0.0451533\pi$
$12$	−78002.6	+	423872.i	−0.0904924	+	0.491743i
$13$		−	1.15435e6i		−	0.862278i	−0.902286	−	0.431139i	$-0.858112\pi$
$13$		−	1.15435e6i		−	0.862278i	0.902286	−	0.431139i	$-0.141888\pi$
$14$	−148642.	−	1.41516e6i	−0.0738649	−	0.703238i
$15$	3.65055e6	−	1.29796e6i	1.24124	−	0.441325i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	−5.51557e6	−	9.55325e6i	−0.942153	−	1.63186i	−0.761353	−	0.648338i	$-0.775464\pi$
$17$	−5.51557e6	−	9.55325e6i	−0.942153	−	1.63186i	−0.180801	−	0.983520i	$-0.557869\pi$
$18$	−2.01801e6	+	5.29734e6i	−0.251724	+	0.660784i
$19$	2.84416e6	+	1.64208e6i	0.263517	+	0.152142i	0.625938	−	0.779873i	$-0.284716\pi$
$19$	2.84416e6	+	1.64208e6i	0.263517	+	0.152142i	−0.362421	+	0.932015i	$0.618050\pi$
$20$	9.42630e6			0.658683
$21$	1.44595e6	−	1.86598e7i	0.0772589	−	0.997011i
$22$	2.68915e7			1.11247
$23$	3.04590e7	+	1.75855e7i	0.986764	+	0.569708i	0.904305	−	0.426886i	$-0.140390\pi$
$23$	3.04590e7	+	1.75855e7i	0.986764	+	0.569708i	0.0824583	+	0.996595i	$0.473723\pi$
$24$	−8.94363e6	+	1.04987e7i	−0.229272	+	0.269136i
$25$	−1.79553e7	−	3.10996e7i	−0.367725	−	0.636919i
$26$	1.84695e7	−	3.19901e7i	0.304861	−	0.528035i
$27$	−3.87142e7	+	6.37203e7i	−0.519241	+	0.854628i
$28$	1.85233e7	−	4.15964e7i	0.203399	−	0.456759i
$29$			8.82728e7i			0.799168i	0.916697	+	0.399584i	$0.130845\pi$
$29$			8.82728e7i			0.799168i	−0.916697	+	0.399584i	$0.869155\pi$
$30$	1.21934e8	+	2.24388e7i	0.916135	+	0.168591i
$31$	−2.70586e7	+	1.56223e7i	−0.169753	+	0.0980068i	−0.582469	−	0.812853i	$-0.697913\pi$
$31$	−2.70586e7	+	1.56223e7i	−0.169753	+	0.0980068i	0.412717	+	0.910860i	$0.364580\pi$
$32$	−2.90590e7	+	1.67772e7i	−0.153093	+	0.0883883i
$33$	3.47856e8	+	6.40138e7i	1.54729	+	0.284739i
$34$		−	3.52997e8i		−	1.33241i
$35$	−4.07097e8	+	4.27596e7i	−1.31016	+	0.137613i
$36$	−1.40682e8	+	1.14516e8i	−0.387771	+	0.315648i
$37$	2.80276e8	−	4.85453e8i	0.664472	−	1.15090i	−0.314956	−	0.949106i	$-0.601990\pi$
$37$	2.80276e8	−	4.85453e8i	0.664472	−	1.15090i	0.979428	−	0.201793i	$-0.0646768\pi$
$38$	5.25465e7	+	9.10131e7i	0.107581	+	0.186335i
$39$	3.15064e8	−	3.69845e8i	0.559170	−	0.656393i
$40$	2.61229e8	+	1.50821e8i	0.403359	+	0.232879i
$41$	−6.02276e7			−0.0811866			−0.0405933	−	0.999176i	$-0.512925\pi$
$41$	−6.02276e7			−0.0811866			−0.0405933	+	0.999176i	$0.512925\pi$
$42$	3.38628e8	−	4.93979e8i	0.399808	−	0.583227i
$43$	7.98515e8			0.828336			0.414168	−	0.910201i	$-0.364073\pi$
$43$	7.98515e8			0.828336			0.414168	+	0.910201i	$0.364073\pi$
$44$	7.45238e8	+	4.30263e8i	0.681248	+	0.393319i
$45$	1.52387e9	+	5.80517e8i	1.23106	+	0.468971i
$46$	5.62737e8	+	9.74689e8i	0.402845	+	0.697747i
$47$	−1.32750e9	+	2.29930e9i	−0.844299	+	1.46237i	0.0419305	+	0.999121i	$0.486649\pi$
$47$	−1.32750e9	+	2.29930e9i	−0.844299	+	1.46237i	−0.886229	+	0.463247i	$0.846684\pi$
$48$	−4.15831e8	+	1.47849e8i	−0.235554	+	0.0837514i
$49$	−6.11284e8	+	1.88047e9i	−0.309146	+	0.951014i
$50$		−	1.14914e9i		−	0.520042i
$51$	8.40291e8	−	4.56621e9i	0.341031	−	1.85319i
$52$	1.02368e9	−	5.91025e8i	0.373377	−	0.215569i
$53$	3.07329e9	−	1.77436e9i	1.00945	−	0.582808i	0.0984216	−	0.995145i	$-0.468621\pi$
$53$	3.07329e9	−	1.77436e9i	1.00945	−	0.582808i	0.911031	+	0.412337i	$0.135287\pi$
$54$	−2.09240e9	+	1.14644e9i	−0.620126	+	0.339771i
$55$		−	7.73581e9i		−	2.07258i
$56$	1.17888e9	−	8.56381e8i	0.286045	−	0.207794i
$57$	4.63066e8	+	1.30239e9i	0.101937	+	0.286701i
$58$	−1.41237e9	+	2.44629e9i	−0.282549	+	0.489389i
$59$	2.88094e9	+	4.98993e9i	0.524624	+	0.908675i	0.999589	+	0.0286703i	$0.00912728\pi$
$59$	2.88094e9	+	4.98993e9i	0.524624	+	0.908675i	−0.474965	+	0.880005i	$0.657539\pi$
$60$	3.02012e9	+	2.57279e9i	0.501410	+	0.427143i
$61$	1.76873e8	+	1.02118e8i	0.0268131	+	0.0154806i	0.513347	−	0.858181i	$-0.328406\pi$
$61$	1.76873e8	+	1.02118e8i	0.0268131	+	0.0154806i	−0.486534	+	0.873662i	$0.661739\pi$
$62$	−9.99828e8			−0.138602
$63$	5.55623e9	−	5.58381e9i	0.705354	−	0.708855i
$64$	−1.07374e9			−0.125000
$65$	−9.20253e9	−	5.31309e9i	−0.983748	−	0.567967i
$66$	8.61585e9	+	7.33970e9i	0.846850	+	0.721417i
$67$	4.17296e9	+	7.22778e9i	0.377601	+	0.654024i	0.990713	−	0.135972i	$-0.0434158\pi$
$67$	4.17296e9	+	7.22778e9i	0.377601	+	0.654024i	−0.613112	+	0.789996i	$0.710082\pi$
$68$	5.64795e9	−	9.78253e9i	0.471077	−	0.815929i
$69$	4.95912e9	+	1.39477e10i	0.381711	+	1.07358i
$70$	−1.19660e10	−	5.32856e9i	−0.850958	−	0.378940i
$71$			5.34061e9i			0.351294i	0.984453	+	0.175647i	$0.0562017\pi$
$71$			5.34061e9i			0.351294i	−0.984453	+	0.175647i	$0.943798\pi$
$72$	−5.73096e9	+	9.22645e8i	−0.349059	+	0.0561961i
$73$	−1.30790e10	+	7.55117e9i	−0.738413	+	0.426323i	−0.821492	−	0.570220i	$-0.806858\pi$
$73$	−1.30790e10	+	7.55117e9i	−0.738413	+	0.426323i	0.0830793	+	0.996543i	$0.473525\pi$
$74$	1.55345e10	−	8.96884e9i	0.813809	−	0.469853i
$75$	2.73547e9	−	1.48648e10i	0.133105	−	0.723305i
$76$			3.36297e9i			0.152142i
$77$	−3.41366e10	−	1.52014e10i	−1.43722	−	0.640007i
$78$	1.46488e10	−	5.20840e9i	0.574490	−	0.204260i
$79$	1.53802e10	−	2.66394e10i	0.562360	−	0.974036i	−0.434930	−	0.900464i	$-0.643227\pi$
$79$	1.53802e10	−	2.66394e10i	0.562360	−	0.974036i	0.997290	−	0.0735715i	$-0.0234397\pi$
$80$	4.82626e9	+	8.35933e9i	0.164671	+	0.285218i
$81$	−2.97954e10	+	9.84900e9i	−0.949472	+	0.313852i
$82$	−1.66908e9	−	9.63641e8i	−0.0497164	−	0.0287038i
$83$	−5.81737e10			−1.62105			−0.810526	−	0.585703i	$-0.800819\pi$
$83$	−5.81737e10			−1.62105			−0.810526	+	0.585703i	$0.800819\pi$
$84$	1.72880e10	−	8.27151e9i	0.451033	−	0.215799i
$85$	−1.01546e11			−2.48232
$86$	2.21291e10	+	1.27762e10i	0.507250	+	0.292861i
$87$	−2.40930e10	+	2.82820e10i	−0.518245	+	0.608352i
$88$	1.37684e10	+	2.38476e10i	0.278118	+	0.481715i
$89$	−4.18851e9	+	7.25471e9i	−0.0795086	+	0.137713i	−0.903038	−	0.429561i	$-0.858668\pi$
$89$	−4.18851e9	+	7.25471e9i	−0.0795086	+	0.137713i	0.823529	+	0.567274i	$0.192002\pi$
$90$	3.29426e10	+	4.04698e10i	0.588063	+	0.722432i
$91$	−4.15292e10	+	3.01684e10i	−0.697632	+	0.506787i
$92$			3.60152e10i			0.569708i
$93$	−1.29333e10	−	2.38004e9i	−0.192777	−	0.0354755i
$94$	−7.35775e10	+	4.24800e10i	−1.03405	+	0.597009i
$95$	2.61815e10	−	1.51159e10i	0.347149	−	0.200426i
$96$	−1.38894e10	−	2.55599e9i	−0.173857	−	0.0319939i
$97$			1.54517e10i			0.182698i	0.995819	+	0.0913489i	$0.0291178\pi$
$97$			1.54517e10i			0.182698i	−0.995819	+	0.0913489i	$0.970882\pi$
$98$	−4.70278e10	+	4.23325e10i	−0.525547	+	0.473075i
$99$	9.39790e10	+	1.15453e11i	0.993201	+	1.22014i
$100$	1.83863e10	−	3.18459e10i	0.183863	−	0.318459i
$101$	−6.47712e10	−	1.12187e11i	−0.613217	−	1.06212i	−0.990694	−	0.136105i	$-0.956542\pi$
$101$	−6.47712e10	−	1.12187e11i	−0.613217	−	1.06212i	0.377477	−	0.926019i	$-0.376792\pi$
$102$	9.63462e10	−	1.13098e11i	0.864039	−	1.01427i
$103$	3.00806e10	+	1.73671e10i	0.255672	+	0.147612i	0.622358	−	0.782732i	$-0.286175\pi$
$103$	3.00806e10	+	1.73671e10i	0.255672	+	0.147612i	−0.366687	+	0.930344i	$0.619508\pi$
$104$	3.78256e10			0.304861
$105$	−1.42102e11	−	9.74123e10i	−1.08657	−	0.744856i
$106$	1.13559e11			0.824215
$107$	−1.91254e11	−	1.10421e11i	−1.31826	−	0.761097i	−0.334811	−	0.942285i	$-0.608672\pi$
$107$	−1.91254e11	−	1.10421e11i	−1.31826	−	0.761097i	−0.983448	+	0.181188i	$0.942006\pi$
$108$	−7.63294e10	−	1.70733e9i	−0.499875	−	0.0111812i
$109$	7.33696e10	+	1.27080e11i	0.456742	+	0.791100i	0.998786	−	0.0492499i	$-0.0156831\pi$
$109$	7.33696e10	+	1.27080e11i	0.456742	+	0.791100i	−0.542045	+	0.840350i	$0.682350\pi$
$110$	1.23773e11	−	2.14381e11i	0.732767	−	1.26919i
$111$	2.22297e11	−	7.90378e10i	1.25215	−	0.445204i
$112$	4.63721e10	−	4.87071e9i	0.248632	−	0.0261152i
$113$		−	1.75457e11i		−	0.895856i	−0.894070	−	0.447928i	$-0.852162\pi$
$113$		−	1.75457e11i		−	0.895856i	0.894070	−	0.447928i	$-0.147838\pi$
$114$	−8.00539e9	+	4.35019e10i	−0.0389409	+	0.211608i
$115$	2.80387e11	−	1.61881e11i	1.29993	−	0.750514i
$116$	−7.82812e10	+	4.51957e10i	−0.346050	+	0.199792i
$117$	2.01889e11	−	3.25028e10i	0.851316	−	0.137056i
$118$			1.84380e11i			0.741930i
$119$	−1.99544e11	+	4.48102e11i	−0.766534	+	1.72135i
$120$	4.25314e10	+	1.19621e11i	0.156032	+	0.438846i
$121$	2.10445e11	−	3.64502e11i	0.737598	−	1.27756i
$122$	3.26777e9	+	5.65994e9i	0.0109464	+	0.0189598i
$123$	−1.92965e10	−	1.64384e10i	−0.0618018	−	0.0526479i
$124$	−2.77080e10	−	1.59972e10i	−0.0848763	−	0.0490034i
$125$	1.18910e11			0.348508
$126$	2.43320e11	−	6.58434e10i	0.682558	−	0.184703i
$127$	3.72428e9			0.0100028			0.00500141	−	0.999987i	$-0.498408\pi$
$127$	3.72428e9			0.0100028			0.00500141	+	0.999987i	$0.498408\pi$
$128$	−2.97564e10	−	1.71799e10i	−0.0765466	−	0.0441942i
$129$	2.55839e11	+	2.17945e11i	0.630555	+	0.537159i
$130$	−1.70019e11	−	2.94481e11i	−0.401614	−	0.695615i
$131$	2.95885e10	−	5.12489e10i	0.0670087	−	0.116063i	−0.830575	−	0.556907i	$-0.811988\pi$
$131$	2.95885e10	−	5.12489e10i	0.0670087	−	0.116063i	0.897583	+	0.440845i	$0.145321\pi$
$132$	1.21334e11	+	3.41257e11i	0.263528	+	0.741183i
$133$	−1.52551e10	−	1.45238e11i	−0.0317857	−	0.302619i
$134$			2.67070e11i			0.534009i
$135$	3.29794e11	+	6.01917e11i	0.633005	+	1.15532i
$136$	3.13041e11	−	1.80734e11i	0.576949	−	0.333102i
$137$	−3.65425e11	+	2.10978e11i	−0.646898	+	0.373487i	−0.787267	−	0.616613i	$-0.788504\pi$
$137$	−3.65425e11	+	2.10978e11i	−0.646898	+	0.373487i	0.140369	+	0.990099i	$0.455171\pi$
$138$	−8.57323e10	+	4.65876e11i	−0.145817	+	0.792384i
$139$		−	6.86390e11i		−	1.12199i	−0.827819	−	0.560996i	$-0.810418\pi$
$139$		−	6.86390e11i		−	1.12199i	0.827819	−	0.560996i	$-0.189582\pi$
$140$	−2.46353e11	−	3.39125e11i	−0.387128	−	0.532912i
$141$	−1.05289e12	+	3.74355e11i	−1.59102	+	0.565689i
$142$	−8.54498e10	+	1.48003e11i	−0.124201	+	0.215122i
$143$	−4.85032e11	−	8.40100e11i	−0.678300	−	1.17485i
$144$	−1.73583e11	−	6.61262e10i	−0.233622	−	0.0889980i
$145$	7.03718e11	+	4.06292e11i	0.911748	+	0.526398i
$146$	−4.83275e11			−0.602911
$147$	−7.09102e11	+	4.35647e11i	−0.852046	+	0.523467i
$148$	5.74006e11			0.664472
$149$	−2.06360e11	−	1.19142e11i	−0.230198	−	0.132905i	0.380465	−	0.924795i	$-0.375764\pi$
$149$	−2.06360e11	−	1.19142e11i	−0.230198	−	0.132905i	−0.610663	+	0.791890i	$0.709097\pi$
$150$	3.13644e11	−	3.68177e11i	0.337237	−	0.395872i
$151$	7.83165e11	+	1.35648e12i	0.811858	+	1.40618i	0.911562	+	0.411162i	$0.134877\pi$
$151$	7.83165e11	+	1.35648e12i	0.811858	+	1.40618i	−0.0997041	+	0.995017i	$0.531790\pi$
$152$	−5.38076e10	+	9.31975e10i	−0.0537903	+	0.0931675i
$153$	1.51551e12	−	1.23364e12i	1.46136	−	1.18955i
$154$	−7.02800e11	−	9.67460e11i	−0.653834	−	0.900055i
$155$			2.87618e11i			0.258221i
$156$	4.89295e11	+	9.00419e10i	0.424019	+	0.0780296i
$157$	−1.82145e12	+	1.05161e12i	−1.52394	+	0.879849i	−0.524344	+	0.851506i	$0.675689\pi$
$157$	−1.82145e12	+	1.05161e12i	−1.52394	+	0.879849i	−0.999598	+	0.0283422i	$0.990977\pi$
$158$	8.52460e11	−	4.92168e11i	0.688747	−	0.397648i
$159$	1.46895e12	+	2.70322e11i	1.14637	+	0.210959i
$160$			3.08881e11i			0.232879i
$161$	−1.63372e11	−	1.55540e12i	−0.119024	−	1.13318i
$162$	−9.83299e11	−	2.03784e11i	−0.692394	−	0.143495i
$163$	−3.68204e11	+	6.37748e11i	−0.250643	+	0.434127i	−0.963703	−	0.266976i	$-0.913976\pi$
$163$	−3.68204e11	+	6.37748e11i	−0.250643	+	0.434127i	0.713060	+	0.701103i	$0.247309\pi$
$164$	−3.08365e10	−	5.34104e10i	−0.0202966	−	0.0351548i
$165$	2.11139e12	−	2.47850e12i	1.34403	−	1.57771i
$166$	−1.61216e12	−	9.30779e11i	−0.992687	−	0.573128i
$167$	−4.42690e11			−0.263730			−0.131865	−	0.991268i	$-0.542096\pi$
$167$	−4.42690e11			−0.263730			−0.131865	+	0.991268i	$0.542096\pi$
$168$	6.11443e11	+	4.73810e10i	0.352497	+	0.0273151i
$169$	4.59648e11			0.256477
$170$	−2.81412e12	−	1.62473e12i	−1.52010	−	0.877633i
$171$	−2.07108e11	+	5.43665e11i	−0.108323	+	0.284350i
$172$	4.08840e11	+	7.08131e11i	0.207084	+	0.358680i
$173$	−1.54860e12	+	2.68225e12i	−0.759776	+	1.31597i	0.183189	+	0.983078i	$0.441358\pi$
$173$	−1.54860e12	+	2.68225e12i	−0.759776	+	1.31597i	−0.942965	+	0.332893i	$0.891975\pi$
$174$	−1.12020e12	+	3.98287e11i	−0.532444	+	0.189311i
$175$	−6.49595e11	+	1.45875e12i	−0.299180	+	0.671847i
$176$			8.81180e11i			0.393319i
$177$	−4.38907e11	+	2.38506e12i	−0.189898	+	1.03192i
$178$	−2.32151e11	+	1.34032e11i	−0.0973778	+	0.0562211i
$179$	2.83357e12	−	1.63596e12i	1.15250	−	0.665398i	0.203007	−	0.979177i	$-0.434929\pi$
$179$	2.83357e12	−	1.63596e12i	1.15250	−	0.665398i	0.949496	+	0.313779i	$0.101595\pi$
$180$	2.65415e11	+	1.64861e12i	0.104695	+	0.650309i
$181$			2.29724e12i			0.878971i	0.898250	+	0.439486i	$0.144839\pi$
$181$			2.29724e12i			0.878971i	−0.898250	+	0.439486i	$0.855161\pi$
$182$	−1.63359e12	+	1.71585e11i	−0.606387	+	0.0636921i
$183$	2.87972e10	+	8.09932e10i	0.0103722	+	0.0291721i
$184$	−5.76243e11	+	9.98082e11i	−0.201422	+	0.348874i
$185$	−2.58005e12	−	4.46877e12i	−0.875352	−	1.51615i
$186$	−3.20338e11	−	2.72891e11i	−0.105509	−	0.0898810i
$187$	−8.02816e12	−	4.63506e12i	−2.56736	−	1.48227i
$188$	−2.71872e12			−0.844299
$189$	3.30421e12	−	2.72511e11i	0.996616	−	0.0821947i
$190$	9.67419e11			0.283446
$191$	4.49491e12	+	2.59514e12i	1.27949	+	0.738715i	0.976755	−	0.214359i	$-0.0687663\pi$
$191$	4.49491e12	+	2.59514e12i	1.27949	+	0.738715i	0.302737	+	0.953074i	$0.402100\pi$
$192$	−3.44020e11	−	2.93065e11i	−0.0951539	−	0.0810600i
$193$	1.25368e12	+	2.17144e12i	0.336993	+	0.583689i	0.983866	−	0.178909i	$-0.0572568\pi$
$193$	1.25368e12	+	2.17144e12i	0.336993	+	0.583689i	−0.646873	+	0.762598i	$0.723923\pi$
$194$	−2.47228e11	+	4.28211e11i	−0.0645934	+	0.111879i
$195$	−1.49829e12	−	4.21400e12i	−0.380544	−	1.07030i
$196$	−1.98059e12	+	4.20706e11i	−0.489088	+	0.103889i
$197$			4.51891e12i			1.08510i	0.840024	+	0.542549i	$0.182541\pi$
$197$			4.51891e12i			1.08510i	−0.840024	+	0.542549i	$0.817459\pi$
$198$	7.57180e11	+	4.70318e12i	0.176824	+	1.09833i
$199$	5.11327e12	−	2.95215e12i	1.16147	−	0.670574i	0.209812	−	0.977742i	$-0.432715\pi$
$199$	5.11327e12	−	2.95215e12i	1.16147	−	0.670574i	0.951655	+	0.307168i	$0.0993813\pi$
$200$	1.01907e12	−	5.88361e11i	0.225185	−	0.130011i
$201$	−6.35746e11	+	3.45469e12i	−0.136680	+	0.742731i
$202$		−	4.14536e12i		−	0.867220i
$203$	3.17574e12	−	2.30698e12i	0.646573	−	0.469695i
$204$	4.47959e12	−	1.59272e12i	0.887712	−	0.315627i
$205$	−2.77209e11	+	4.80139e11i	−0.0534762	+	0.0926235i
$206$	5.55746e11	+	9.62581e11i	0.104377	+	0.180787i
$207$	−2.21799e12	+	5.82229e12i	−0.405623	+	1.06477i
$208$	1.04825e12	+	6.05209e11i	0.186689	+	0.107785i
$209$	2.75987e12			0.478722
$210$	−2.37945e12	−	4.97320e12i	−0.402041	−	0.840291i
$211$	6.63643e12			1.09240			0.546199	−	0.837656i	$-0.316074\pi$
$211$	6.63643e12			1.09240			0.546199	+	0.837656i	$0.316074\pi$
$212$	3.14705e12	+	1.81695e12i	0.504727	+	0.291404i
$213$	−1.45766e12	+	1.71110e12i	−0.227807	+	0.267416i
$214$	−3.53347e12	−	6.12014e12i	−0.538177	−	0.932150i
$215$	3.67531e12	−	6.36583e12i	0.545610	−	0.945025i
$216$	−2.08799e12	−	1.26859e12i	−0.302157	−	0.183580i
$217$	1.26920e12	+	5.65190e11i	0.179062	+	0.0797381i
$218$			4.69566e12i			0.645930i
$219$	−6.25143e12	−	1.15041e12i	−0.838565	−	0.154316i
$220$	6.86019e12	−	3.96073e12i	0.897453	−	0.518145i
$221$	−1.10278e13	+	6.36688e12i	−1.40711	+	0.812398i
$222$	7.42508e12	+	1.36639e12i	0.924187	+	0.170072i
$223$		−	4.72774e12i		−	0.574086i	−0.957918	−	0.287043i	$-0.907328\pi$
$223$		−	4.72774e12i		−	0.574086i	0.957918	−	0.287043i	$-0.0926723\pi$
$224$	1.36303e12	+	6.06972e11i	0.161489	+	0.0719126i
$225$	4.93359e12	−	4.01597e12i	0.570373	−	0.464287i
$226$	2.80730e12	−	4.86239e12i	0.316733	−	0.548597i
$227$	−3.33701e12	−	5.77986e12i	−0.367464	−	0.636466i	0.621704	−	0.783252i	$-0.286441\pi$
$227$	−3.33701e12	−	5.77986e12i	−0.367464	−	0.636466i	−0.989168	+	0.146786i	$0.953107\pi$
$228$	−9.17883e11	+	1.07747e12i	−0.0986610	+	0.115815i
$229$	2.47842e12	+	1.43092e12i	0.260064	+	0.150148i	0.624364	−	0.781134i	$-0.285358\pi$
$229$	2.47842e12	+	1.43092e12i	0.260064	+	0.150148i	−0.364300	+	0.931282i	$0.618692\pi$
$230$	1.03604e13			1.06139
$231$	−6.78812e12	−	1.41876e13i	−0.679022	−	1.41920i
$232$	−2.89252e12			−0.282549
$233$	3.91014e12	+	2.25752e12i	0.373022	+	0.215364i	0.674778	−	0.738021i	$-0.264239\pi$
$233$	3.91014e12	+	2.25752e12i	0.373022	+	0.215364i	−0.301756	+	0.953385i	$0.597573\pi$
$234$	6.11496e12	+	2.32948e12i	0.569779	+	0.217056i
$235$	1.22201e13	+	2.11659e13i	1.11225	+	1.92647i
$236$	−2.95008e12	+	5.10969e12i	−0.262312	+	0.454337i
$237$	1.21986e13	−	4.33723e12i	1.05973	−	0.376787i
$238$	−1.26996e13	+	9.22546e12i	−1.07799	+	0.783095i
$239$			4.58710e12i			0.380496i	0.981736	+	0.190248i	$0.0609292\pi$
$239$			4.58710e12i			0.380496i	−0.981736	+	0.190248i	$0.939071\pi$
$240$	−7.35275e11	+	3.99555e12i	−0.0596057	+	0.323902i
$241$	−5.81657e12	+	3.35820e12i	−0.460865	+	0.266080i	−0.712408	−	0.701766i	$-0.752395\pi$
$241$	−5.81657e12	+	3.35820e12i	−0.460865	+	0.266080i	0.251543	+	0.967846i	$0.419062\pi$
$242$	1.16641e13	−	6.73425e12i	0.903369	−	0.521560i
$243$	−1.22344e13	−	4.97675e12i	−0.926295	−	0.376800i
$244$			2.09137e11i			0.0154806i
$245$	1.21777e13	+	1.35284e13i	0.881356	+	0.979113i
$246$	−2.71747e11	−	7.64298e11i	−0.0192319	−	0.0540903i
$247$	1.89552e12	−	3.28314e12i	0.131189	−	0.227225i
$248$	−5.11912e11	−	8.86657e11i	−0.0346506	−	0.0600166i
$249$	−1.86385e13	−	1.58778e13i	−1.23400	−	1.05122i
$250$	3.29533e12	+	1.90256e12i	0.213417	+	0.123216i
$251$	−4.09853e12			−0.259671			−0.129835	−	0.991536i	$-0.541445\pi$
$251$	−4.09853e12			−0.259671			−0.129835	+	0.991536i	$0.541445\pi$
$252$	7.79657e12	+	2.06841e12i	0.483282	+	0.128213i
$253$	2.95563e13			1.79262
$254$	1.03210e11	+	5.95885e10i	0.00612545	+	0.00353653i
$255$	−3.25346e13	−	2.77157e13i	−1.88962	−	1.60974i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	−6.55417e11	+	1.13522e12i	−0.0364658	+	0.0631606i	−0.883682	−	0.468087i	$-0.844943\pi$
$257$	−6.55417e11	+	1.13522e12i	−0.0364658	+	0.0631606i	0.847217	+	0.531248i	$0.178277\pi$
$258$	3.60290e12	+	1.01333e13i	0.196220	+	0.551877i
$259$	−2.47898e13	+	2.60381e12i	−1.32167	+	0.138823i
$260$		−	1.08812e13i		−	0.567967i
$261$	−1.54385e13	+	2.48549e12i	−0.789008	+	0.127025i
$262$	1.63996e12	−	9.46833e11i	0.0820686	−	0.0473823i
$263$	−6.96817e12	+	4.02308e12i	−0.341478	+	0.197152i	−0.660925	−	0.750452i	$-0.729836\pi$
$263$	−6.96817e12	+	4.02308e12i	−0.341478	+	0.197152i	0.319448	+	0.947604i	$0.396503\pi$
$264$	−2.09760e12	+	1.13985e13i	−0.100670	+	0.547051i
$265$		−	3.26674e13i		−	1.53554i
$266$	1.90104e12	−	4.26904e12i	0.0875273	−	0.196553i
$267$	−3.32206e12	+	1.18116e12i	−0.149829	+	0.0532717i
$268$	−4.27311e12	+	7.40125e12i	−0.188801	+	0.327012i
$269$	1.87377e13	+	3.24547e13i	0.811108	+	1.40488i	0.912089	+	0.409993i	$0.134469\pi$
$269$	1.87377e13	+	3.24547e13i	0.811108	+	1.40488i	−0.100980	+	0.994888i	$0.532198\pi$
$270$	−4.91143e11	+	2.19575e13i	−0.0208309	+	0.931285i
$271$	1.82872e13	+	1.05581e13i	0.760006	+	0.438790i	0.829298	−	0.558807i	$-0.188741\pi$
$271$	1.82872e13	+	1.05581e13i	0.760006	+	0.438790i	−0.0692916	+	0.997596i	$0.522074\pi$
$272$	1.15670e13			0.471077
$273$	−2.15398e13	−	1.66913e12i	−0.859701	−	0.0666186i
$274$	−1.35026e13			−0.528190
$275$	−2.61348e13	−	1.50889e13i	−1.00205	−	0.578533i
$276$	−9.82990e12	+	1.15390e13i	−0.369445	+	0.433680i
$277$	−2.43548e12	−	4.21838e12i	−0.0897319	−	0.155420i	0.817666	−	0.575693i	$-0.195268\pi$
$277$	−2.43548e12	−	4.21838e12i	−0.0897319	−	0.155420i	−0.907398	+	0.420273i	$0.861934\pi$
$278$	1.09822e13	−	1.90218e13i	0.396684	−	0.687077i
$279$	−3.49415e12	−	4.29254e12i	−0.123742	−	0.152017i
$280$	−1.40115e12	−	1.33398e13i	−0.0486535	−	0.463211i
$281$		−	2.51624e12i		−	0.0856776i	−0.999082	−	0.0428388i	$-0.986360\pi$
$281$		−	2.51624e12i		−	0.0856776i	0.999082	−	0.0428388i	$-0.0136402\pi$
$282$	−3.51681e13	−	6.47177e12i	−1.17430	−	0.216099i
$283$	−3.54151e13	+	2.04469e13i	−1.15975	+	0.669579i	−0.951243	−	0.308443i	$-0.900192\pi$
$283$	−3.54151e13	+	2.04469e13i	−1.15975	+	0.669579i	−0.208502	+	0.978022i	$0.566859\pi$
$284$	−4.73611e12	+	2.73439e12i	−0.152115	+	0.0878234i
$285$	1.25141e13	+	2.30289e12i	0.394233	+	0.0725482i
$286$		−	3.10420e13i		−	0.959261i
$287$	1.57403e12	+	2.16677e12i	0.0477158	+	0.0656846i
$288$	−3.75246e12	−	4.60988e12i	−0.111598	−	0.137098i
$289$	−4.37072e13	+	7.57030e13i	−1.27531	+	2.20890i
$290$	1.30013e13	+	2.25190e13i	0.372220	+	0.644703i
$291$	−4.21737e12	+	4.95064e12i	−0.118476	+	0.139075i
$292$	−1.33929e13	−	7.73240e12i	−0.369206	−	0.213161i
$293$	1.68636e13			0.456224			0.228112	−	0.973635i	$-0.426745\pi$
$293$	1.68636e13			0.456224			0.228112	+	0.973635i	$0.426745\pi$
$294$	−2.66215e13	+	7.27368e11i	−0.706843	+	0.0193127i
$295$	5.30402e13			1.38224
$296$	1.59073e13	+	9.18409e12i	0.406904	+	0.234926i
$297$	−1.40114e12	+	6.26407e13i	−0.0351821	+	1.57288i
$298$	−3.81255e12	−	6.60353e12i	−0.0939780	−	0.162775i
$299$	2.02998e13	−	3.51602e13i	0.491247	−	0.850864i
$300$	1.45828e13	−	5.18492e12i	0.346477	−	0.123190i
$301$	−2.08689e13	−	2.87277e13i	−0.486838	−	0.670171i
$302$			5.01226e13i			1.14814i
$303$	9.86781e12	−	5.36225e13i	0.221966	−	1.20618i
$304$	−2.98232e12	+	1.72184e12i	−0.0658794	+	0.0380355i
$305$	1.62818e12	−	9.40032e11i	0.0353227	−	0.0203936i
$306$	6.17373e13	−	9.93929e12i	1.31547	−	0.211781i
$307$		−	3.53956e13i		−	0.740779i	−0.928877	−	0.370390i	$-0.879224\pi$
$307$		−	3.53956e13i		−	0.740779i	0.928877	−	0.370390i	$-0.120776\pi$
$308$	−3.99721e12	−	3.80558e13i	−0.0821728	−	0.782334i
$309$	4.89751e12	+	1.37744e13i	0.0989017	+	0.278165i
$310$	−4.60189e12	+	7.97071e12i	−0.0912950	+	0.158128i
$311$	2.45767e13	+	4.25681e13i	0.479006	+	0.829663i	0.999710	−	0.0240743i	$-0.00766383\pi$
$311$	2.45767e13	+	4.25681e13i	0.479006	+	0.829663i	−0.520704	+	0.853737i	$0.674330\pi$
$312$	1.21191e13	+	1.03240e13i	0.232070	+	0.197697i
$313$	2.54623e13	+	1.47006e13i	0.479074	+	0.276594i	0.720031	−	0.693942i	$-0.244128\pi$
$313$	2.54623e13	+	1.47006e13i	0.479074	+	0.276594i	−0.240956	+	0.970536i	$0.577461\pi$
$314$	−6.73032e13			−1.24429
$315$	−1.89410e13	−	6.99952e13i	−0.344109	−	1.27163i
$316$	3.14987e13			0.562360
$317$	−7.06341e13	−	4.07806e13i	−1.23933	−	0.715530i	−0.270376	−	0.962755i	$-0.587148\pi$
$317$	−7.06341e13	−	4.07806e13i	−1.23933	−	0.715530i	−0.968958	+	0.247225i	$0.920481\pi$
$318$	3.63837e13	+	3.09946e13i	0.627418	+	0.534487i
$319$	3.70904e13	+	6.42425e13i	0.628656	+	1.08886i
$320$	−4.94209e12	+	8.55996e12i	−0.0823353	+	0.142609i
$321$	−3.11387e13	−	8.75787e13i	−0.509944	−	1.43424i
$322$	2.03589e13	−	4.57185e13i	0.327753	−	0.736011i
$323$		−	3.62280e13i		−	0.573364i
$324$	−2.39895e13	−	2.13802e13i	−0.373270	−	0.332671i
$325$	−3.58996e13	+	2.07267e13i	−0.549201	+	0.317081i
$326$	−2.04079e13	+	1.17825e13i	−0.306974	+	0.177232i
$327$	−1.11778e13	+	6.07409e13i	−0.165327	+	0.898398i
$328$		−	1.97354e12i		−	0.0287038i
$329$	1.17414e14	−	1.23327e13i	1.67936	−	0.176392i
$330$	9.81687e13	−	3.49040e13i	1.38085	−	0.490962i
$331$	−8.99651e12	+	1.55824e13i	−0.124457	+	0.215566i	−0.921521	−	0.388329i	$-0.873052\pi$
$331$	−8.99651e12	+	1.55824e13i	−0.124457	+	0.215566i	0.797063	+	0.603896i	$0.206386\pi$
$332$	−2.97849e13	−	5.15890e13i	−0.405263	−	0.701936i
$333$	9.27949e13	+	3.53501e13i	1.24188	+	0.473093i
$334$	−1.22682e13	−	7.08303e12i	−0.161501	−	0.0932425i
$335$	7.68273e13			0.994877
$336$	1.61867e13	+	1.10962e13i	0.206202	+	0.141353i
$337$	6.30532e13			0.790211			0.395105	−	0.918636i	$-0.370708\pi$
$337$	6.30532e13			0.790211			0.395105	+	0.918636i	$0.370708\pi$
$338$	1.27381e13	+	7.35437e12i	0.157059	+	0.0906783i
$339$	4.78887e13	−	5.62151e13i	0.580945	−	0.681953i
$340$	−5.19914e13	−	9.00518e13i	−0.620580	−	1.07488i
$341$	−1.31283e13	+	2.27390e13i	−0.154192	+	0.267068i
$342$	−1.44382e13	+	1.17528e13i	−0.166867	+	0.135830i
$343$	8.36282e13	−	2.71536e13i	0.951120	−	0.308823i
$344$			2.61657e13i			0.292861i
$345$	1.34018e14	+	2.46624e13i	1.47624	+	0.271663i
$346$	−8.58321e13	+	4.95552e13i	−0.930532	+	0.537243i
$347$	−2.47703e13	+	1.43011e13i	−0.264313	+	0.152601i	−0.626301	−	0.779582i	$-0.715432\pi$
$347$	−2.47703e13	+	1.43011e13i	−0.264313	+	0.152601i	0.361987	+	0.932183i	$0.382098\pi$
$348$	−3.74164e13	−	6.88551e12i	−0.392985	−	0.0723186i
$349$			4.06262e11i			0.00420016i	0.999998	+	0.00210008i	$0.000668477\pi$
$349$			4.06262e11i			0.00420016i	−0.999998	+	0.00210008i	$0.999332\pi$
$350$	−4.13420e13	+	3.00325e13i	−0.420744	+	0.305644i
$351$	7.35552e13	+	4.46895e13i	0.736927	+	0.447730i
$352$	−1.40989e13	+	2.44200e13i	−0.139059	+	0.240858i
$353$	1.93426e13	+	3.35024e13i	0.187825	+	0.325323i	0.944525	−	0.328440i	$-0.106523\pi$
$353$	1.93426e13	+	3.35024e13i	0.187825	+	0.325323i	−0.756700	+	0.653763i	$0.773189\pi$
$354$	−5.03243e13	+	5.90742e13i	−0.481127	+	0.564780i
$355$	4.25758e13	+	2.45812e13i	0.400781	+	0.231391i
$356$	−8.57807e12			−0.0795086
$357$	−1.86237e14	+	8.91057e13i	−1.69977	+	0.813262i
$358$	1.04702e14			0.941015
$359$	−1.53290e14	−	8.85022e13i	−1.35674	−	0.783312i	−0.367554	−	0.930002i	$-0.619805\pi$
$359$	−1.53290e14	−	8.85022e13i	−1.35674	−	0.783312i	−0.989182	+	0.146690i	$0.953138\pi$
$360$	−1.90224e13	+	4.99343e13i	−0.165806	+	0.435247i
$361$	−5.28523e13	−	9.15429e13i	−0.453706	−	0.785841i
$362$	−3.67559e13	+	6.36630e13i	−0.310763	+	0.538258i
$363$	1.66912e14	−	5.93455e13i	1.38995	−	0.494199i
$364$	−4.80166e13	−	2.13823e13i	−0.393853	−	0.175387i
$365$			1.39023e14i			1.12325i
$366$	−4.97840e11	+	2.70531e12i	−0.00396227	+	0.0215313i
$367$	1.30031e14	−	7.50736e13i	1.01949	−	0.588605i	0.105536	−	0.994415i	$-0.466344\pi$
$367$	1.30031e14	−	7.50736e13i	1.01949	−	0.588605i	0.913957	+	0.405811i	$0.133011\pi$
$368$	−3.19386e13	+	1.84398e13i	−0.246691	+	0.142427i
$369$	−1.69582e12	−	1.05335e13i	−0.0129043	−	0.0801545i
$370$		−	1.65123e14i		−	1.23793i
$371$	−1.44155e14	−	6.41936e13i	−1.06481	−	0.474171i
$372$	−4.51122e12	−	1.26880e13i	−0.0328328	−	0.0923435i
$373$	−1.17474e14	+	2.03470e14i	−0.842446	+	1.45916i	0.0453752	+	0.998970i	$0.485552\pi$
$373$	−1.17474e14	+	2.03470e14i	−0.842446	+	1.45916i	−0.887821	+	0.460189i	$0.847782\pi$
$374$	−1.48322e14	−	2.56901e14i	−1.04812	−	1.81540i
$375$	3.80979e13	+	3.24550e13i	0.265295	+	0.226001i
$376$	−7.53433e13	−	4.34995e13i	−0.517025	−	0.298505i
$377$	1.01897e14			0.689105
$378$	9.59292e13	+	4.53154e13i	0.639361	+	0.302023i
$379$	−2.39971e13			−0.157632			−0.0788159	−	0.996889i	$-0.525114\pi$
$379$	−2.39971e13			−0.157632			−0.0788159	+	0.996889i	$0.525114\pi$
$380$	2.68099e13	+	1.54787e13i	0.173574	+	0.100213i
$381$	1.19324e12	+	1.01650e12i	0.00761446	+	0.00648663i
$382$	8.30444e13	+	1.43837e14i	0.522350	+	0.904737i
$383$	−1.58093e13	+	2.73824e13i	−0.0980208	+	0.169777i	−0.910865	−	0.412704i	$-0.864584\pi$
$383$	−1.58093e13	+	2.73824e13i	−0.0980208	+	0.169777i	0.812845	+	0.582481i	$0.197918\pi$
$384$	−4.84472e12	−	1.36260e13i	−0.0296106	−	0.0832809i
$385$	−2.78307e14	+	2.02173e14i	−1.67683	+	1.21812i
$386$			8.02354e13i			0.476580i
$387$	2.24837e13	+	1.39656e14i	0.131661	+	0.817805i
$388$	−1.37028e13	+	7.91130e12i	−0.0791104	+	0.0456744i
$389$	−1.31115e14	+	7.56991e13i	−0.746326	+	0.430892i	−0.824365	−	0.566059i	$-0.808468\pi$
$389$	−1.31115e14	+	7.56991e13i	−0.746326	+	0.430892i	0.0780387	+	0.996950i	$0.475134\pi$
$390$	2.59021e13	−	1.40754e14i	0.145372	−	0.789963i
$391$		−	3.87977e14i		−	2.14701i
$392$	−6.16191e13	−	2.00305e13i	−0.336234	−	0.109300i
$393$	2.34677e13	−	8.34397e12i	0.126273	−	0.0448966i
$394$	−7.23025e13	+	1.25232e14i	−0.383640	+	0.664484i
$395$	−1.41581e14	−	2.45225e14i	−0.740833	−	1.28316i
$396$	−5.42673e13	+	1.42453e14i	−0.280037	+	0.735104i
$397$	3.57883e13	+	2.06624e13i	0.182135	+	0.105156i	0.588295	−	0.808646i	$-0.299799\pi$
$397$	3.57883e13	+	2.06624e13i	0.182135	+	0.105156i	−0.406160	+	0.913802i	$0.633133\pi$
$398$	1.88938e14			0.948334
$399$	3.47533e13	−	5.06970e13i	0.172046	−	0.250975i
$400$	3.76551e13			0.183863
$401$	1.88222e14	+	1.08670e14i	0.906515	+	0.523377i	0.879308	−	0.476253i	$-0.158005\pi$
$401$	1.88222e14	+	1.08670e14i	0.906515	+	0.523377i	0.0272071	+	0.999630i	$0.491339\pi$
$402$	−7.28934e13	+	8.55674e13i	−0.346294	+	0.406504i
$403$	1.80335e13	+	3.12350e13i	0.0845090	+	0.146374i
$404$	6.63257e13	−	1.14880e14i	0.306609	−	0.531062i
$405$	−5.86220e13	+	2.82864e14i	−0.267336	+	1.28995i
$406$	1.24921e14	−	1.31211e13i	0.562006	−	0.0590305i
$407$		−	4.71065e14i		−	2.09079i
$408$	1.49626e14	+	2.75346e13i	0.655201	+	0.120573i
$409$	1.87158e14	−	1.08056e14i	0.808595	−	0.466842i	−0.0378728	−	0.999283i	$-0.512058\pi$
$409$	1.87158e14	−	1.08056e14i	0.808595	−	0.466842i	0.846468	+	0.532440i	$0.178725\pi$
$410$	−1.53645e13	+	8.87067e12i	−0.0654947	+	0.0378134i
$411$	−1.74664e14	−	3.21423e13i	−0.734638	−	0.135191i
$412$			3.55678e13i			0.147612i
$413$	1.04228e14	−	2.34056e14i	0.426833	−	0.958506i
$414$	−1.54623e14	+	1.25864e14i	−0.624846	+	0.508628i
$415$	−2.67755e14	+	4.63765e14i	−1.06776	+	1.84941i
$416$	1.93667e13	+	3.35441e13i	0.0762153	+	0.132009i
$417$	1.87342e14	−	2.19915e14i	0.727590	−	0.854095i
$418$	7.64837e13	+	4.41579e13i	0.293156	+	0.169254i
$419$	−4.42084e14			−1.67235			−0.836175	−	0.548462i	$-0.815214\pi$
$419$	−4.42084e14			−1.67235			−0.836175	+	0.548462i	$0.815214\pi$
$420$	1.36300e13	−	1.75892e14i	0.0508891	−	0.656714i
$421$	2.21406e14			0.815903			0.407951	−	0.913004i	$-0.366243\pi$
$421$	2.21406e14			0.815903			0.407951	+	0.913004i	$0.366243\pi$
$422$	1.83914e14	+	1.06183e14i	0.668954	+	0.386221i
$423$	−4.39514e14	−	1.67432e14i	−1.57798	−	0.601127i
$424$	5.81424e13	+	1.00706e14i	0.206054	+	0.356896i
$425$	−1.98068e14	+	3.43064e14i	−0.692907	+	1.20015i
$426$	−6.77733e13	+	2.40968e13i	−0.234048	+	0.0832161i
$427$	−9.48689e11	−	9.03208e12i	−0.00323423	−	0.0307918i
$428$		−	2.26142e14i		−	0.761097i
$429$	7.38940e13	−	4.01546e14i	0.245524	−	1.33420i
$430$	2.03706e14	−	1.17610e14i	0.668233	−	0.385805i
$431$	−6.86139e13	+	3.96143e13i	−0.222222	+	0.128300i	−0.606979	−	0.794718i	$-0.707619\pi$
$431$	−6.86139e13	+	3.96143e13i	−0.222222	+	0.128300i	0.384757	+	0.923018i	$0.374285\pi$
$432$	−3.75666e13	−	6.85639e13i	−0.120127	−	0.219247i
$433$			1.70820e12i			0.00539331i	0.999996	+	0.00269666i	$0.000858373\pi$
$433$			1.70820e12i			0.00539331i	−0.999996	+	0.00269666i	$0.999142\pi$
$434$	2.61302e13	+	3.59703e13i	0.0814609	+	0.112137i
$435$	1.14574e14	+	3.22245e14i	0.352693	+	0.991962i
$436$	−7.51305e13	+	1.30130e14i	−0.228371	+	0.395550i
$437$	5.77536e13	+	1.00032e14i	0.173353	+	0.300256i
$438$	−1.54838e14	−	1.31904e14i	−0.458955	−	0.390976i
$439$	−2.73935e14	−	1.58156e14i	−0.801848	−	0.462947i	0.0422689	−	0.999106i	$-0.486541\pi$
$439$	−2.73935e14	−	1.58156e14i	−0.801848	−	0.462947i	−0.844117	+	0.536159i	$0.819875\pi$
$440$	2.53487e14			0.732767
$441$	−3.46096e14	−	5.39623e13i	−0.988062	−	0.154056i
$442$	−4.07480e14			−1.14890
$443$	−2.43370e14	−	1.40510e14i	−0.677714	−	0.391278i	0.121279	−	0.992618i	$-0.461300\pi$
$443$	−2.43370e14	−	1.40510e14i	−0.677714	−	0.391278i	−0.798993	+	0.601340i	$0.794634\pi$
$444$	1.83908e14	+	1.56668e14i	0.505817	+	0.430897i
$445$	3.85568e13	+	6.67823e13i	0.104742	+	0.181418i
$446$	7.56439e13	−	1.31019e14i	0.202970	−	0.351555i
$447$	−3.35981e13	−	9.44959e13i	−0.0890478	−	0.250450i
$448$	2.80619e13	+	3.86294e13i	0.0734663	+	0.101132i
$449$			5.09422e14i			1.31742i	0.752399	+	0.658708i	$0.228897\pi$
$449$			5.09422e14i			1.31742i	−0.752399	+	0.658708i	$0.771103\pi$
$450$	2.00979e14	−	3.23563e13i	0.513431	−	0.0826589i
$451$	−4.38319e13	+	2.53064e13i	−0.110616	+	0.0638644i
$452$	1.55597e14	−	8.98337e13i	0.387917	−	0.223964i
$453$	−1.19314e14	+	6.48363e14i	−0.293868	+	1.59690i
$454$		−	2.13568e14i		−	0.519673i
$455$	4.93593e13	+	4.69930e14i	0.118661	+	1.12972i
$456$	−4.26767e13	+	1.51737e13i	−0.101364	+	0.0360401i
$457$	2.57547e14	−	4.46085e14i	0.604391	−	1.04684i	−0.387756	−	0.921762i	$-0.626750\pi$
$457$	2.57547e14	−	4.46085e14i	0.604391	−	1.04684i	0.992147	−	0.125074i	$-0.0399169\pi$
$458$	4.57894e13	+	7.93096e13i	0.106171	+	0.183893i
$459$	8.22267e14	+	1.83924e13i	1.88384	+	0.0421374i
$460$	2.87116e14	+	1.65766e14i	0.649964	+	0.375257i
$461$	9.30351e13			0.208109			0.104055	−	0.994572i	$-0.466818\pi$
$461$	9.30351e13			0.208109			0.104055	+	0.994572i	$0.466818\pi$
$462$	3.88838e13	−	5.01788e14i	0.0859485	−	1.10915i
$463$	4.74353e14			1.03611			0.518055	−	0.855347i	$-0.326656\pi$
$463$	4.74353e14			1.03611			0.518055	+	0.855347i	$0.326656\pi$
$464$	−8.01600e13	−	4.62804e13i	−0.173025	−	0.0998960i
$465$	−7.85019e13	+	9.21510e13i	−0.167451	+	0.196566i
$466$	7.22406e13	+	1.25124e14i	0.152286	+	0.263766i
$467$	−8.21526e13	+	1.42292e14i	−0.171151	+	0.296442i	−0.938822	−	0.344402i	$-0.888082\pi$
$467$	−8.21526e13	+	1.42292e14i	−0.171151	+	0.296442i	0.767672	+	0.640843i	$0.221415\pi$
$468$	1.32191e14	+	1.62396e14i	0.272176	+	0.334367i
$469$	1.50971e14	−	3.39024e14i	0.307215	−	0.689891i
$470$			7.82088e14i			1.57296i
$471$	−8.70605e14	−	1.60212e14i	−1.73064	−	0.318478i
$472$	−1.63510e14	+	9.44026e13i	−0.321265	+	0.185482i
$473$	5.81136e14	−	3.35519e14i	1.12860	−	0.651600i
$474$	4.07454e14	+	7.49812e13i	0.782163	+	0.143937i
$475$		−	1.17936e14i		−	0.223786i
$476$	−4.99548e14	+	5.24703e13i	−0.936999	+	0.0984181i
$477$	3.96862e14	+	4.87542e14i	0.735848	+	0.903985i
$478$	−7.33937e13	+	1.27122e14i	−0.134526	+	0.233005i
$479$	8.55545e13	+	1.48185e14i	0.155024	+	0.268509i	0.933068	−	0.359701i	$-0.117121\pi$
$479$	8.55545e13	+	1.48185e14i	0.155024	+	0.268509i	−0.778044	+	0.628210i	$0.783788\pi$
$480$	−8.43053e13	+	9.89634e13i	−0.151018	+	0.177275i
$481$	−5.60380e14	−	3.23535e14i	−0.992395	−	0.572959i
$482$	−2.14925e14			−0.376295
$483$	3.72184e14	−	5.42931e14i	0.644242	−	0.939799i
$484$	4.30992e14			0.737598
$485$	1.23183e14	+	7.11195e13i	0.208435	+	0.120340i
$486$	−2.59422e14	−	3.33671e14i	−0.434018	−	0.558237i
$487$	−3.76710e14	−	6.52481e14i	−0.623158	−	1.07934i	−0.988894	−	0.148622i	$-0.952516\pi$
$487$	−3.76710e14	−	6.52481e14i	−0.623158	−	1.07934i	0.365736	−	0.930719i	$-0.380817\pi$
$488$	−3.34619e12	+	5.79578e12i	−0.00547321	+	0.00947988i
$489$	−2.92035e14	+	1.03833e14i	−0.472321	+	0.167934i
$490$	1.21024e14	+	5.69753e14i	0.193549	+	0.911188i
$491$		−	8.25959e14i		−	1.30620i	−0.757271	−	0.653101i	$-0.773468\pi$
$491$		−	8.25959e14i		−	1.30620i	0.757271	−	0.653101i	$-0.226532\pi$
$492$	4.69791e12	−	2.55288e13i	0.00734677	−	0.0399229i
$493$	8.43293e14	−	4.86875e14i	1.30413	−	0.752939i
$494$	1.05061e14	−	6.06568e13i	0.160673	−	0.0927643i
$495$	1.35295e15	−	2.17816e14i	2.04623	−	0.329429i
$496$		−	3.27624e13i		−	0.0490034i
$497$	1.92136e14	−	1.39575e14i	0.284217	−	0.206466i
$498$	−2.62479e14	−	7.38234e14i	−0.384002	−	1.08002i
$499$	4.91981e14	−	8.52136e14i	0.711862	−	1.23298i	−0.252296	−	0.967650i	$-0.581186\pi$
$499$	4.91981e14	−	8.52136e14i	0.711862	−	1.23298i	0.964158	−	0.265330i	$-0.0854810\pi$
$500$	6.08818e13	+	1.05450e14i	0.0871270	+	0.150908i
$501$	−1.41835e14	−	1.20827e14i	−0.200759	−	0.171023i
$502$	−1.13582e14	−	6.55765e13i	−0.159015	−	0.0918074i
$503$	6.87652e14			0.952236			0.476118	−	0.879381i	$-0.342044\pi$
$503$	6.87652e14			0.952236			0.476118	+	0.879381i	$0.342044\pi$
$504$	1.82970e14	+	1.82067e14i	0.250618	+	0.249380i
$505$	−1.19249e15			−1.61566
$506$	8.19088e14	+	4.72901e14i	1.09775	+	0.633785i
$507$	1.47268e14	+	1.25455e14i	0.195238	+	0.166320i
$508$	1.90683e12	+	3.30273e12i	0.00250070	+	0.00433135i
$509$	8.97516e13	−	1.55454e14i	0.116438	−	0.201676i	−0.801916	−	0.597437i	$-0.796186\pi$
$509$	8.97516e13	−	1.55454e14i	0.116438	−	0.201676i	0.918354	+	0.395761i	$0.129519\pi$
$510$	−4.58174e14	−	1.28863e15i	−0.588024	−	1.65384i
$511$	6.13480e14	+	2.73189e14i	0.778907	+	0.346855i
$512$		−	3.51844e13i		−	0.0441942i
$513$	−2.14743e14	+	1.17659e14i	−0.266854	+	0.146211i
$514$	−3.63269e13	+	2.09733e13i	−0.0446613	+	0.0257852i
$515$	2.76903e14	−	1.59870e14i	0.336813	−	0.194459i
$516$	−6.22862e13	+	3.38468e14i	−0.0749581	+	0.407328i
$517$			2.23115e15i			2.65663i
$518$	−7.28656e14	−	3.24478e14i	−0.858437	−	0.382271i
$519$	−1.22825e15	+	4.36705e14i	−1.43175	+	0.509058i
$520$	1.74099e14	−	3.01549e14i	0.200807	−	0.347808i
$521$	1.71293e14	+	2.96687e14i	0.195493	+	0.338604i	0.947062	−	0.321051i	$-0.104036\pi$
$521$	1.71293e14	+	2.96687e14i	0.195493	+	0.338604i	−0.751569	+	0.659654i	$0.770703\pi$
$522$	−4.67611e14	−	1.78136e14i	−0.528077	−	0.201170i
$523$	−1.17891e15	−	6.80646e14i	−1.31742	−	0.760610i	−0.334104	−	0.942536i	$-0.608434\pi$
$523$	−1.17891e15	−	6.80646e14i	−1.31742	−	0.760610i	−0.983312	+	0.181926i	$0.941767\pi$
$524$	6.05973e13			0.0670087
$525$	−6.06273e14	+	2.90074e14i	−0.663425	+	0.317419i
$526$	−2.57477e14			−0.278815
$527$	2.98488e14	+	1.72332e14i	0.319866	+	0.184675i
$528$	−2.40507e14	+	2.82324e14i	−0.255060	+	0.299407i
$529$	1.42097e14	+	2.46120e14i	0.149135	+	0.258309i
$530$	5.22678e14	−	9.05304e14i	0.542896	−	0.940324i
$531$	−7.91596e14	+	6.44363e14i	−0.813736	+	0.662385i
$532$	1.20988e14	−	8.78902e13i	0.123091	−	0.0894184i
$533$			6.95234e13i			0.0700054i
$534$	−1.10962e14	−	2.04196e13i	−0.110585	−	0.0203503i
$535$	−1.76057e15	+	1.01646e15i	−1.73663	+	1.00264i
$536$	−2.36840e14	+	1.36740e14i	−0.231232	+	0.133502i
$537$	1.35437e15	+	2.49237e14i	1.30882	+	0.240854i
$538$			1.19921e15i			1.14708i
$539$	3.45258e14	+	1.62540e15i	0.326893	+	1.53894i
$540$	−3.64931e14	+	6.00646e14i	−0.342015	+	0.562928i
$541$	−5.20436e14	+	9.01421e14i	−0.482816	+	0.836263i	−0.999805	−	0.0197294i	$-0.993720\pi$
$541$	−5.20436e14	+	9.01421e14i	−0.482816	+	0.836263i	0.516989	+	0.855992i	$0.327053\pi$
$542$	3.37861e14	+	5.85192e14i	0.310271	+	0.537406i
$543$	−6.27004e14	+	7.36021e14i	−0.569995	+	0.669100i
$544$	3.20554e14	+	1.85072e14i	0.288474	+	0.166551i
$545$	1.35079e15			1.20339
$546$	−5.70222e14	−	3.90893e14i	−0.502904	−	0.344745i
$547$	1.48817e13			0.0129934			0.00649668	−	0.999979i	$-0.497932\pi$
$547$	1.48817e13			0.0129934			0.00649668	+	0.999979i	$0.497932\pi$
$548$	−3.74196e14	−	2.16042e14i	−0.323449	−	0.186743i
$549$	−1.28797e13	+	3.38095e13i	−0.0110219	+	0.0289329i
$550$	−4.82845e14	−	8.36313e14i	−0.409085	−	0.708556i
$551$	−1.44951e14	+	2.51062e14i	−0.121587	+	0.210595i
$552$	−4.57039e14	+	1.62500e14i	−0.379567	+	0.134955i
$553$	−1.36035e15	+	1.42885e14i	−1.11857	+	0.117489i
$554$		−	1.55871e14i		−	0.126900i
$555$	3.93067e14	−	2.13596e15i	0.316851	−	1.72179i
$556$	6.08698e14	−	3.51432e14i	0.485837	−	0.280498i
$557$	−4.84175e14	+	2.79539e14i	−0.382647	+	0.220922i	−0.678969	−	0.734166i	$-0.737573\pi$
$557$	−4.84175e14	+	2.79539e14i	−0.382647	+	0.220922i	0.296322	+	0.955088i	$0.404240\pi$
$558$	−2.81520e13	−	1.74865e14i	−0.0220304	−	0.136840i
$559$		−	9.21762e14i		−	0.714256i
$560$	1.74606e14	−	3.92100e14i	0.133976	−	0.300859i
$561$	−1.30709e15	−	3.67623e15i	−0.993135	−	2.79323i
$562$	4.02599e13	−	6.97321e13i	0.0302916	−	0.0524666i
$563$	−7.60339e13	−	1.31695e14i	−0.0566514	−	0.0981232i	0.836309	−	0.548259i	$-0.184709\pi$
$563$	−7.60339e13	−	1.31695e14i	−0.0566514	−	0.0981232i	−0.892960	+	0.450135i	$0.851376\pi$
$564$	−8.71059e14	−	7.42041e14i	−0.642707	−	0.547511i
$565$	−1.39875e15	−	8.07571e14i	−1.02206	−	0.590084i
$566$	−1.30860e15			−0.946928
$567$	1.13303e15	+	8.14534e14i	0.811957	+	0.583717i
$568$	−1.75001e14			−0.124201
$569$	−2.07398e15	−	1.19741e15i	−1.45776	−	0.841640i	−0.458862	−	0.888508i	$-0.651743\pi$
$569$	−2.07398e15	−	1.19741e15i	−1.45776	−	0.841640i	−0.998901	+	0.0468676i	$0.985076\pi$
$570$	3.09955e14	+	2.64045e14i	0.215768	+	0.183809i
$571$	9.90432e14	+	1.71548e15i	0.682851	+	1.18273i	0.974107	+	0.226088i	$0.0725937\pi$
$571$	9.90432e14	+	1.71548e15i	0.682851	+	1.18273i	−0.291256	+	0.956645i	$0.594073\pi$
$572$	4.96673e14	−	8.60262e14i	0.339150	−	0.587425i
$573$	7.31828e14	+	2.05830e15i	0.494947	+	1.39206i
$574$	8.95237e12	+	8.52319e13i	0.00599684	+	0.0570935i
$575$		−	1.26302e15i		−	0.837985i
$576$	−3.02332e13	−	1.87792e14i	−0.0198683	−	0.123411i
$577$	1.65366e15	−	9.54744e14i	1.07642	−	0.621469i	0.146489	−	0.989212i	$-0.453203\pi$
$577$	1.65366e15	−	9.54744e14i	1.07642	−	0.621469i	0.929928	+	0.367743i	$0.119869\pi$
$578$	−2.42250e15	+	1.39863e15i	−1.56192	+	0.901778i
$579$	−1.90996e14	+	1.03789e15i	−0.121981	+	0.662856i
$580$			8.32086e14i			0.526398i
$581$	1.52035e15	+	2.09288e15i	0.952741	+	1.31152i
$582$	−1.96085e14	+	6.97183e13i	−0.121722	+	0.0432783i
$583$	1.49110e15	−	2.58266e15i	0.916918	−	1.58815i
$584$	−2.47437e14	−	4.28573e14i	−0.150728	−	0.261068i
$585$	6.70117e14	−	1.75908e15i	0.404384	−	1.06152i
$586$	4.67338e14	+	2.69818e14i	0.279379	+	0.161300i
$587$	2.28937e15			1.35584			0.677918	−	0.735138i	$-0.262883\pi$
$587$	2.28937e15			1.35584			0.677918	+	0.735138i	$0.262883\pi$
$588$	−7.49396e14	−	4.05787e14i	−0.439679	−	0.238080i
$589$	−1.02612e14			−0.0596437
$590$	1.46989e15	+	8.48643e14i	0.846447	+	0.488696i
$591$	−1.23338e15	+	1.44783e15i	−0.703665	+	0.826011i
$592$	2.93891e14	+	5.09034e14i	0.166118	+	0.287725i
$593$	−4.28615e14	+	7.42384e14i	−0.240031	+	0.415745i	−0.960723	−	0.277510i	$-0.910491\pi$
$593$	−4.28615e14	+	7.42384e14i	−0.240031	+	0.415745i	0.720692	+	0.693255i	$0.243824\pi$
$594$	−1.04108e15	+	1.71353e15i	−0.577642	+	0.950751i
$595$	2.65387e15	+	3.65326e15i	1.45893	+	2.00834i
$596$		−	2.44003e14i		−	0.132905i
$597$	2.44401e15	+	4.49756e14i	1.31900	+	0.242727i
$598$	1.12513e15	−	6.49593e14i	0.601652	−	0.347364i
$599$	−9.62635e14	+	5.55777e14i	−0.510052	+	0.294478i	−0.732855	−	0.680385i	$-0.761813\pi$
$599$	−9.62635e14	+	5.55777e14i	−0.510052	+	0.294478i	0.222803	+	0.974863i	$0.428479\pi$
$600$	4.87089e14	+	8.96360e13i	0.255727	+	0.0470599i
$601$		−	2.24302e15i		−	1.16687i	−0.812159	−	0.583436i	$-0.801708\pi$
$601$		−	2.24302e15i		−	1.16687i	0.812159	−	0.583436i	$-0.198292\pi$
$602$	−1.18693e14	−	1.13003e15i	−0.0611850	−	0.582517i
$603$	−1.14661e15	+	9.33342e14i	−0.585691	+	0.476756i
$604$	−8.01961e14	+	1.38904e15i	−0.405929	+	0.703090i
$605$	−1.93723e15	−	3.35537e15i	−0.971686	−	1.68301i
$606$	1.13142e15	−	1.32815e15i	0.562375	−	0.660155i
$607$	−1.34809e15	−	7.78320e14i	−0.664020	−	0.383372i	0.129787	−	0.991542i	$-0.458571\pi$
$607$	−1.34809e15	−	7.78320e14i	−0.664020	−	0.383372i	−0.793807	+	0.608170i	$0.791904\pi$
$608$	−1.10198e14			−0.0537903
$609$	1.64715e15	+	1.27638e14i	0.796779	+	0.0617428i
$610$	6.01620e13			0.0288409
$611$	2.65418e15	+	1.53239e15i	1.26097	+	0.728020i
$612$	1.86994e15	+	7.12352e14i	0.880432	+	0.335399i
$613$	−1.17082e15	−	2.02791e15i	−0.546331	−	0.946273i	−0.998522	−	0.0543516i	$-0.982691\pi$
$613$	−1.17082e15	−	2.02791e15i	−0.546331	−	0.946273i	0.452191	−	0.891921i	$-0.350643\pi$
$614$	5.66330e14	−	9.80913e14i	0.261905	−	0.453633i
$615$	−2.19864e14	+	7.81728e13i	−0.100772	+	0.0358296i
$616$	4.98119e14	−	1.11859e15i	0.226276	−	0.508132i
$617$		−	1.40288e15i		−	0.631613i	−0.948824	−	0.315807i	$-0.897725\pi$
$617$		−	1.40288e15i		−	0.631613i	0.948824	−	0.315807i	$-0.102275\pi$
$618$	−8.46672e13	+	4.60089e14i	−0.0377815	+	0.205308i
$619$	2.05159e15	−	1.18449e15i	0.907385	−	0.523879i	0.0277962	−	0.999614i	$-0.491151\pi$
$619$	2.05159e15	−	1.18449e15i	0.907385	−	0.523879i	0.879589	+	0.475735i	$0.157818\pi$
$620$	−2.55063e14	+	1.47261e14i	−0.111813	+	0.0645553i
$621$	−2.29975e15	+	1.26005e15i	−0.999257	+	0.547499i
$622$			1.57291e15i			0.677417i
$623$	3.70464e14	−	3.89119e13i	0.158147	−	0.0166111i
$624$	1.70669e14	+	4.80013e14i	0.0722170	+	0.203113i
$625$	1.42403e15	−	2.46649e15i	0.597281	−	1.03452i
$626$	4.70420e14	+	8.14792e14i	0.195581	+	0.338757i
$627$	8.84243e14	+	7.53272e14i	0.364418	+	0.310442i
$628$	−1.86516e15	−	1.07685e15i	−0.761971	−	0.439924i
$629$	−6.18354e15			−2.50414
$630$	5.95015e14	−	2.24282e15i	0.238866	−	0.900371i
$631$	3.35628e14			0.133566			0.0667830	−	0.997768i	$-0.478726\pi$
$631$	3.35628e14			0.133566			0.0667830	+	0.997768i	$0.478726\pi$
$632$	8.72919e14	+	5.03980e14i	0.344374	+	0.198824i
$633$	2.12627e15	+	1.81133e15i	0.831567	+	0.708398i
$634$	−1.30498e15	−	2.26029e15i	−0.505956	−	0.876342i
$635$	1.71417e13	−	2.96903e13i	0.00658868	−	0.0114119i
$636$	5.12379e14	+	1.44109e15i	0.195244	+	0.549131i
$637$	2.17071e15	+	7.05632e14i	0.820039	+	0.266570i
$638$			2.37379e15i			0.889054i
$639$	−9.34046e14	+	1.50375e14i	−0.346828	+	0.0558369i
$640$	−2.73919e14	+	1.58147e14i	−0.100840	+	0.0582199i
$641$	1.20432e15	−	6.95314e14i	0.439565	−	0.253783i	−0.263848	−	0.964564i	$-0.584992\pi$
$641$	1.20432e15	−	6.95314e14i	0.439565	−	0.253783i	0.703413	+	0.710781i	$0.251659\pi$
$642$	5.38319e14	−	2.92527e15i	0.194804	−	1.05858i
$643$			1.89024e15i			0.678198i	0.940751	+	0.339099i	$0.110122\pi$
$643$			1.89024e15i			0.678198i	−0.940751	+	0.339099i	$0.889878\pi$
$644$	1.29570e15	−	9.41245e14i	0.460926	−	0.334835i
$645$	2.91502e15	−	1.03644e15i	1.02817	−	0.365565i
$646$	5.79648e14	−	1.00398e15i	0.202715	−	0.351112i
$647$	1.39531e15	+	2.41675e15i	0.483836	+	0.838029i	0.999828	−	0.0185649i	$-0.00590972\pi$
$647$	1.39531e15	+	2.41675e15i	0.483836	+	0.838029i	−0.515991	+	0.856594i	$0.672576\pi$
$648$	−3.22732e14	−	9.76337e14i	−0.110963	−	0.335689i
$649$	4.19333e15	+	2.42102e15i	1.42960	+	0.825377i
$650$	−1.32651e15			−0.448421
$651$	2.52383e14	+	5.27497e14i	0.0845989	+	0.176817i
$652$	−7.54081e14			−0.250643
$653$	−3.65749e15	−	2.11165e15i	−1.20548	−	0.695985i	−0.243712	−	0.969848i	$-0.578365\pi$
$653$	−3.65749e15	−	2.11165e15i	−1.20548	−	0.695985i	−0.961769	+	0.273863i	$0.911699\pi$
$654$	−1.28162e15	+	1.50446e15i	−0.418873	+	0.491702i
$655$	−2.72373e14	−	4.71765e14i	−0.0882750	−	0.152897i
$656$	3.15766e13	−	5.46923e13i	0.0101483	−	0.0175774i
$657$	−1.68893e15	−	2.07484e15i	−0.538271	−	0.661263i
$658$	3.45120e15	+	1.53686e15i	1.09076	+	0.485725i
$659$			2.31572e13i			0.00725800i	0.999993	+	0.00362900i	$0.00115515\pi$
$659$			2.31572e13i			0.00725800i	−0.999993	+	0.00362900i	$0.998845\pi$
$660$	3.27899e15	+	6.03413e14i	1.01918	+	0.187553i
$661$	−1.46509e15	+	8.45872e14i	−0.451604	+	0.260734i	−0.708507	−	0.705704i	$-0.750631\pi$
$661$	−1.46509e15	+	8.45872e14i	−0.451604	+	0.260734i	0.256904	+	0.966437i	$0.417298\pi$
$662$	−4.98637e14	+	2.87888e14i	−0.152428	+	0.0880046i
$663$	−5.27098e15	−	9.69986e14i	−1.59796	−	0.294063i
$664$		−	1.90623e15i		−	0.573128i
$665$	−1.22806e15	−	5.46869e14i	−0.366186	−	0.163066i
$666$	2.00601e15	+	2.46437e15i	0.593232	+	0.728781i
$667$	−1.55233e15	+	2.68871e15i	−0.455293	+	0.788590i
$668$	−2.26657e14	−	3.92582e14i	−0.0659324	−	0.114198i
$669$	1.29038e15	−	1.51474e15i	0.372284	−	0.437012i
$670$	2.12910e15	+	1.22924e15i	0.609235	+	0.351742i
$671$	1.71631e14			0.0487104
$672$	2.71041e14	+	5.66493e14i	0.0762964	+	0.159464i
$673$	−5.74393e15			−1.60371			−0.801856	−	0.597518i	$-0.796154\pi$
$673$	−5.74393e15			−1.60371			−0.801856	+	0.597518i	$0.796154\pi$
$674$	1.74738e15	+	1.00885e15i	0.483903	+	0.279382i
$675$	2.67680e15	+	5.98744e13i	0.735267	+	0.0164464i
$676$	2.35340e14	+	4.07620e14i	0.0641192	+	0.111058i
$677$	−2.33437e14	+	4.04325e14i	−0.0630860	+	0.109268i	−0.895843	−	0.444370i	$-0.853428\pi$
$677$	−2.33437e14	+	4.04325e14i	−0.0630860	+	0.109268i	0.832757	+	0.553638i	$0.186761\pi$
$678$	2.22657e15	−	7.91659e14i	0.596862	−	0.212215i
$679$	5.55899e14	−	4.03827e14i	0.147813	−	0.107377i
$680$		−	3.32745e15i		−	0.877633i
$681$	5.08389e14	−	2.76263e15i	0.133011	−	0.722791i
$682$	−7.27646e14	+	4.20107e14i	−0.188845	+	0.109030i
$683$	−1.47584e15	+	8.52077e14i	−0.379949	+	0.219364i	−0.677796	−	0.735250i	$-0.737065\pi$
$683$	−1.47584e15	+	8.52077e14i	−0.379949	+	0.219364i	0.297847	+	0.954614i	$0.403732\pi$
$684$	−5.88167e14	+	9.46909e13i	−0.150208	+	0.0241824i
$685$			3.88427e15i			0.984036i
$686$	2.75203e15	+	5.85549e14i	0.691625	+	0.147157i
$687$	4.03519e14	+	1.13491e15i	0.100601	+	0.282944i
$688$	−4.18652e14	+	7.25126e14i	−0.103542	+	0.179340i
$689$	−2.04823e15	−	3.54764e15i	−0.502542	−	0.870429i
$690$	3.31941e15	+	2.82775e15i	0.807961	+	0.688288i
$691$	−5.31316e15	−	3.06755e15i	−1.28299	−	0.740735i	−0.305597	−	0.952161i	$-0.598856\pi$
$691$	−5.31316e15	−	3.06755e15i	−1.28299	−	0.740735i	−0.977394	+	0.211426i	$0.932189\pi$
$692$	−3.17153e15			−0.759776
$693$	1.69747e15	−	6.39835e15i	0.403430	−	1.52067i
$694$	−9.15273e14			−0.215811
$695$	−5.47196e15	−	3.15924e15i	−1.28005	−	0.739036i
$696$	−9.26746e14	−	7.89479e14i	−0.215085	−	0.183227i
$697$	3.32190e14	+	5.75369e14i	0.0764902	+	0.132485i
$698$	−6.50019e12	+	1.12587e13i	−0.00148498	+	0.00257206i
$699$	6.36620e14	+	1.79052e15i	0.144297	+	0.405840i
$700$	−1.62622e15	+	1.70811e14i	−0.365714	+	0.0384129i
$701$		−	5.47613e15i		−	1.22187i	−0.791681	−	0.610935i	$-0.790794\pi$
$701$		−	5.47613e15i		−	1.22187i	0.791681	−	0.610935i	$-0.209206\pi$
$702$	1.32339e15	+	2.41536e15i	0.292977	+	0.534721i
$703$	1.59430e15	−	9.20470e14i	0.350200	−	0.202188i
$704$	−7.81439e14	+	4.51164e14i	−0.170312	+	0.0983297i
$705$	−1.86172e15	+	1.01167e16i	−0.402600	+	2.18776i
$706$			1.23793e15i			0.265625i
$707$	−2.34332e15	+	5.26221e15i	−0.498912	+	1.12037i
$708$	−2.33981e15	+	8.31922e14i	−0.494309	+	0.175752i
$709$	−8.60445e14	+	1.49033e15i	−0.180372	+	0.312413i	−0.942007	−	0.335593i	$-0.891063\pi$
$709$	−8.60445e14	+	1.49033e15i	−0.180372	+	0.312413i	0.761635	+	0.648006i	$0.224397\pi$
$710$	7.86597e14	+	1.36243e15i	0.163618	+	0.283395i
$711$	5.09215e15	+	1.93985e15i	1.05104	+	0.400391i
$712$	−2.37722e14	−	1.37249e14i	−0.0486889	−	0.0281106i
$713$	−1.09891e15			−0.223341
$714$	−6.58683e15	−	5.10417e14i	−1.32842	−	0.102940i
$715$	−8.92979e15			−1.78714
$716$	2.90157e15	+	1.67522e15i	0.576252	+	0.332699i
$717$	−1.25199e15	+	1.46968e15i	−0.246744	+	0.289646i
$718$	−2.83207e15	−	4.90529e15i	−0.553885	−	0.959357i
$719$	−1.96809e15	+	3.40883e15i	−0.381976	+	0.661602i	−0.991345	−	0.131285i	$-0.958090\pi$
$719$	−1.96809e15	+	3.40883e15i	−0.381976	+	0.661602i	0.609369	+	0.792887i	$0.291423\pi$
$720$	−1.32611e15	+	1.07946e15i	−0.255418	+	0.207912i
$721$	−1.61343e14	−	1.53608e15i	−0.0308393	−	0.293609i
$722$		−	3.38255e15i		−	0.641637i
$723$	−2.78017e15	−	5.11618e14i	−0.523373	−	0.0963130i
$724$	−2.03722e15	+	1.17619e15i	−0.380606	+	0.219743i
$725$	2.74525e15	−	1.58497e15i	0.509005	−	0.293874i
$726$	5.57512e15	+	1.02595e15i	1.02589	+	0.188789i
$727$		−	3.60355e14i		−	0.0658100i	−0.999458	−	0.0329050i	$-0.989524\pi$
$727$		−	3.60355e14i		−	0.0658100i	0.999458	−	0.0329050i	$-0.0104759\pi$
$728$	−9.88559e14	−	1.36083e15i	−0.179176	−	0.246650i
$729$	−2.56149e15	−	4.93376e15i	−0.460777	−	0.887516i
$730$	−2.22436e15	+	3.85271e15i	−0.397127	+	0.687844i
$731$	−4.40427e15	−	7.62841e15i	−0.780419	−	1.35173i
$732$	−5.70814e13	+	6.70062e13i	−0.0100389	+	0.0117843i
$733$	6.57007e15	+	3.79323e15i	1.14683	+	0.662121i	0.948112	−	0.317936i	$-0.102990\pi$
$733$	6.57007e15	+	3.79323e15i	1.14683	+	0.662121i	0.198715	+	0.980057i	$0.436323\pi$
$734$	4.80471e15			0.832413
$735$	2.09240e14	+	7.65816e15i	0.0359803	+	1.31687i
$736$	−1.18015e15			−0.201422
$737$	6.07393e15	+	3.50678e15i	1.02896	+	0.594070i
$738$	1.21540e14	−	3.19046e14i	0.0204366	−	0.0536467i
$739$	−1.42616e15	−	2.47018e15i	−0.238025	−	0.412272i	0.722122	−	0.691765i	$-0.243167\pi$
$739$	−1.42616e15	−	2.47018e15i	−0.238025	−	0.412272i	−0.960148	+	0.279493i	$0.909833\pi$
$740$	2.64197e15	−	4.57602e15i	0.437676	−	0.758077i
$741$	1.50341e15	−	5.34537e14i	0.247216	−	0.0878978i
$742$	−2.96784e15	−	4.08546e15i	−0.484416	−	0.666837i
$743$			4.12866e15i			0.668914i	0.942411	+	0.334457i	$0.108553\pi$
$743$			4.12866e15i			0.668914i	−0.942411	+	0.334457i	$0.891447\pi$
$744$	7.79891e13	−	4.23799e14i	0.0125425	−	0.0681568i
$745$	−1.89962e15	+	1.09675e15i	−0.303255	+	0.175084i
$746$	−6.51105e15	+	3.75916e15i	−1.03178	+	0.595699i
$747$	−1.63799e15	−	1.01743e16i	−0.257660	−	1.60044i
$748$		−	9.49260e15i		−	1.48227i
$749$	1.02583e15	+	9.76647e15i	0.159010	+	1.51387i
$750$	5.36521e14	+	1.50899e15i	0.0825562	+	0.232193i
$751$	−1.11037e15	+	1.92322e15i	−0.169609	+	0.293772i	−0.938282	−	0.345870i	$-0.887584\pi$
$751$	−1.11037e15	+	1.92322e15i	−0.169609	+	0.293772i	0.768673	+	0.639642i	$0.220917\pi$
$752$	−1.39198e15	−	2.41099e15i	−0.211075	−	0.365592i
$753$	−1.31314e15	−	1.11864e15i	−0.197669	−	0.168391i
$754$	2.82386e15	+	1.63036e15i	0.421989	+	0.243635i
$755$	1.44186e16			2.13903
$756$	1.93342e15	+	2.79068e15i	0.284745	+	0.410999i
$757$	1.13162e16			1.65452			0.827259	−	0.561821i	$-0.189899\pi$
$757$	1.13162e16			1.65452			0.827259	+	0.561821i	$0.189899\pi$
$758$	−6.65028e14	−	3.83954e14i	−0.0965293	−	0.0557312i
$759$	9.46965e15	+	8.06703e15i	1.36460	+	1.16248i
$760$	4.95319e14	+	8.57917e14i	0.0708614	+	0.122736i
$761$	3.52244e15	−	6.10104e15i	0.500297	−	0.866540i	−0.499703	−	0.866197i	$-0.666558\pi$
$761$	3.52244e15	−	6.10104e15i	0.500297	−	0.866540i	1.00000		0.000342847i	$-0.000109131\pi$
$762$	1.68040e13	+	4.72618e13i	0.00236951	+	0.00666435i
$763$	2.65439e15	−	5.96077e15i	0.371604	−	0.834483i
$764$			5.31484e15i			0.738715i
$765$	−2.85921e15	−	1.77598e16i	−0.394556	−	2.45076i
$766$	−8.76238e14	+	5.05896e14i	−0.120050	+	0.0693111i
$767$	5.76010e15	−	3.32560e15i	0.783530	−	0.452371i
$768$	8.37546e13	−	4.55129e14i	0.0113115	−	0.0614679i
$769$			1.35117e16i			1.81182i	0.423475	+	0.905908i	$0.360810\pi$
$769$			1.35117e16i			1.81182i	−0.423475	+	0.905908i	$0.639190\pi$
$770$	−1.09474e16	+	1.14987e15i	−1.45752	+	0.153091i
$771$	−5.19835e14	+	1.84828e14i	−0.0687173	+	0.0244325i
$772$	−1.28377e15	+	2.22355e15i	−0.168497	+	0.291845i
$773$	−7.51186e15	−	1.30109e16i	−0.978950	−	1.69559i	−0.666232	−	0.745745i	$-0.732094\pi$
$773$	−7.51186e15	−	1.30109e16i	−0.978950	−	1.69559i	−0.312718	−	0.949846i	$-0.601239\pi$
$774$	−1.61141e15	+	4.23001e15i	−0.208512	+	0.547351i
$775$	9.71694e14	+	5.61008e14i	0.124845	+	0.0720791i
$776$	−5.06323e14			−0.0645934
$777$	−8.65316e15	−	5.93183e15i	−1.09612	−	0.751403i
$778$	−4.84474e15			−0.609373
$779$	−1.71297e14	−	9.88983e13i	−0.0213941	−	0.0123519i
$780$	2.96989e15	−	3.48626e15i	0.368316	−	0.432355i
$781$	2.24401e15	+	3.88675e15i	0.276341	+	0.478636i
$782$	6.20764e15	−	1.07519e16i	0.759083	−	1.31477i
$783$	−5.62477e15	−	3.41741e15i	−0.682991	−	0.414961i
$784$	−1.38715e15	−	1.54101e15i	−0.167257	−	0.185809i
$785$			1.93610e16i			2.31816i
$786$	7.83860e14	+	1.44249e14i	0.0931997	+	0.0171510i
$787$	−1.07047e14	+	6.18039e13i	−0.0126391	+	0.00729717i	−0.506306	−	0.862354i	$-0.668989\pi$
$787$	−1.07047e14	+	6.18039e13i	−0.0126391	+	0.00729717i	0.493667	+	0.869651i	$0.335656\pi$
$788$	−4.00741e15	+	2.31368e15i	−0.469861	+	0.271275i
$789$	−3.33061e15	−	6.12911e14i	−0.387793	−	0.0713631i
$790$		−	9.06117e15i		−	1.04770i
$791$	−6.31230e15	+	4.58550e15i	−0.724798	+	0.526521i
$792$	−3.78315e15	+	3.07950e15i	−0.431385	+	0.351150i
$793$	1.17879e14	−	2.04173e14i	0.0133486	−	0.0231204i
$794$	6.61196e14	+	1.14523e15i	0.0743563	+	0.128789i
$795$	8.91616e15	−	1.04664e16i	0.995769	−	1.16890i
$796$	5.23599e15	+	3.02300e15i	0.580734	+	0.335287i
$797$	8.35758e15			0.920577			0.460288	−	0.887769i	$-0.347746\pi$
$797$	8.35758e15			0.920577			0.460288	+	0.887769i	$0.347746\pi$
$798$	1.77426e15	−	8.48904e14i	0.194090	−	0.0928630i
$799$	2.92877e16			3.18183
$800$	1.04353e15	+	6.02481e14i	0.112592	+	0.0650053i
$801$	−1.38675e15	−	5.28279e14i	−0.148600	−	0.0566089i
$802$	3.47743e15	+	6.02309e15i	0.370083	+	0.641003i
$803$	−6.34569e15	+	1.09911e16i	−0.670723	+	1.16173i
$804$	−3.38916e15	+	1.20502e15i	−0.355782	+	0.126498i
$805$	−1.31517e16	−	5.85660e15i	−1.37122	−	0.610616i
$806$			1.15415e15i			0.119514i
$807$	−2.85467e15	+	1.55125e16i	−0.293597	+	1.59543i
$808$	3.67614e15	−	2.12242e15i	0.375517	−	0.216805i
$809$	−4.86789e15	+	2.81048e15i	−0.493883	+	0.285143i	−0.726184	−	0.687501i	$-0.758708\pi$
$809$	−4.86789e15	+	2.81048e15i	−0.493883	+	0.285143i	0.232301	+	0.972644i	$0.425375\pi$
$810$	−6.15040e15	+	6.90099e15i	−0.619777	+	0.695415i
$811$		−	2.25502e15i		−	0.225703i	−0.993612	−	0.112851i	$-0.964002\pi$
$811$		−	2.25502e15i		−	0.225703i	0.993612	−	0.112851i	$-0.0359984\pi$
$812$	3.67184e15	+	1.63511e15i	0.365027	+	0.162550i
$813$	2.97740e15	+	8.37404e15i	0.293994	+	0.826870i
$814$	7.53704e15	−	1.30545e16i	0.739208	−	1.28035i
$815$	3.38945e15	+	5.87070e15i	0.330189	+	0.571904i
$816$	3.70599e15	+	3.15707e15i	0.358598	+	0.305484i
$817$	2.27110e15	+	1.31122e15i	0.218281	+	0.126025i
$818$	6.91558e15			0.660215
$819$	−6.44564e15	−	6.41381e15i	−0.611230	−	0.608211i
$820$	−5.67723e14			−0.0534762
$821$	7.20379e15	+	4.15911e15i	0.674021	+	0.389146i	0.797599	−	0.603188i	$-0.206103\pi$
$821$	7.20379e15	+	4.15911e15i	0.674021	+	0.389146i	−0.123577	+	0.992335i	$0.539437\pi$
$822$	−4.32615e15	−	3.68538e15i	−0.402075	−	0.342521i
$823$	−1.38092e15	−	2.39183e15i	−0.127488	−	0.220816i	0.795215	−	0.606328i	$-0.207358\pi$
$823$	−1.38092e15	−	2.39183e15i	−0.127488	−	0.220816i	−0.922703	+	0.385512i	$0.874025\pi$
$824$	−5.69084e14	+	9.85682e14i	−0.0521887	+	0.0903935i
$825$	−4.25507e15	−	1.19676e16i	−0.387624	−	1.09021i
$826$	6.63334e15	−	4.81871e15i	0.600264	−	0.436055i
$827$		−	1.22872e15i		−	0.110452i	−0.998474	−	0.0552259i	$-0.982412\pi$
$827$		−	1.22872e15i		−	0.110452i	0.998474	−	0.0552259i	$-0.0175879\pi$
$828$	−6.29887e15	+	1.01408e15i	−0.562466	+	0.0905531i
$829$	−5.84225e15	+	3.37302e15i	−0.518239	+	0.299205i	−0.736214	−	0.676749i	$-0.763388\pi$
$829$	−5.84225e15	+	3.37302e15i	−0.518239	+	0.299205i	0.217975	+	0.975954i	$0.430055\pi$
$830$	−1.48405e16	+	8.56816e15i	−1.30773	+	0.755019i
$831$	3.71043e14	−	2.01628e15i	0.0324802	−	0.176500i
$832$			1.23947e15i			0.107785i
$833$	2.13362e16	−	4.53210e15i	1.84318	−	0.391519i
$834$	8.71041e15	−	3.09699e15i	0.747524	−	0.265783i
$835$	−2.03756e15	+	3.52916e15i	−0.173714	+	0.300882i
$836$	1.41305e15	+	2.44748e15i	0.119681	+	0.207293i
$837$	5.20946e13	−	2.32899e15i	0.00438331	−	0.195964i
$838$	−1.22514e16	−	7.07334e15i	−1.02410	−	0.591265i
$839$	2.06376e16			1.71383			0.856917	−	0.515454i	$-0.172377\pi$
$839$	2.06376e16			1.71383			0.856917	+	0.515454i	$0.172377\pi$
$840$	3.19200e15	−	4.65639e15i	0.263346	−	0.384161i
$841$	4.40841e15			0.361330
$842$	6.13579e15	+	3.54250e15i	0.499636	+	0.288465i
$843$	6.86777e14	−	8.06187e14i	0.0555603	−	0.0652205i
$844$	3.39785e15	+	5.88525e15i	0.273099	+	0.473022i
$845$	2.11561e15	−	3.66435e15i	0.168937	−	0.292607i
$846$	−9.50125e15	−	1.16722e16i	−0.753778	−	0.926012i
$847$	−1.86134e16	+	1.95507e15i	−1.46712	+	0.154100i
$848$			3.72111e15i			0.291404i
$849$	−1.69275e16	−	3.11506e15i	−1.31704	−	0.242367i
$850$	−1.09780e16	+	6.33818e15i	−0.848635	+	0.489960i
$851$	1.70739e16	−	9.85761e15i	1.31135	−	0.757110i
$852$	−2.26374e15	−	4.16581e14i	−0.172746	−	0.0317894i
$853$		−	4.18859e15i		−	0.317576i	−0.987313	−	0.158788i	$-0.949241\pi$
$853$		−	4.18859e15i		−	0.317576i	0.987313	−	0.158788i	$-0.0507587\pi$
$854$	1.18223e14	−	2.65483e14i	0.00890598	−	0.0199995i
$855$	3.38089e15	+	4.15340e15i	0.253056	+	0.310878i
$856$	3.61827e15	−	6.26703e15i	0.269089	−	0.466075i
$857$	2.60561e15	+	4.51305e15i	0.192537	+	0.333485i	0.946090	−	0.323903i	$-0.104995\pi$
$857$	2.60561e15	+	4.51305e15i	0.192537	+	0.333485i	−0.753553	+	0.657387i	$0.771662\pi$
$858$	8.47254e15	−	9.94566e15i	0.622062	−	0.730220i
$859$	2.16157e16	+	1.24798e16i	1.57691	+	0.910428i	0.995288	+	0.0969673i	$0.0309142\pi$
$859$	2.16157e16	+	1.24798e16i	1.57691	+	0.910428i	0.581620	+	0.813461i	$0.302419\pi$
$860$	7.52704e15			0.545610
$861$	−8.70863e13	+	1.12383e15i	−0.00627238	+	0.0809439i
$862$	−2.53531e15			−0.181444
$863$	−1.66155e16	−	9.59295e15i	−1.18155	−	0.682171i	−0.225180	−	0.974317i	$-0.572297\pi$
$863$	−1.66155e16	−	9.59295e15i	−1.18155	−	0.682171i	−0.956374	+	0.292147i	$0.905630\pi$
$864$	5.59458e13	−	2.50116e15i	0.00395313	−	0.176732i
$865$	1.42554e16	+	2.46911e16i	1.00090	+	1.73361i
$866$	−2.73312e13	+	4.73390e13i	−0.00190682	+	0.00330271i
$867$	−3.46657e16	+	1.23254e16i	−2.40323	+	0.854469i
$868$	1.48617e14	+	1.41492e15i	0.0102379	+	0.0974706i
$869$		−	2.58498e16i		−	1.76949i
$870$	−1.98074e15	+	1.07635e16i	−0.134732	+	0.732146i
$871$	8.34336e15	−	4.81704e15i	0.563951	−	0.325597i
$872$	−4.16415e15	+	2.40418e15i	−0.279696	+	0.161483i
$873$	−2.70243e15	+	4.35073e14i	−0.180375	+	0.0290392i
$874$			3.69623e15i			0.245158i
$875$	−3.10767e15	−	4.27795e15i	−0.204829	−	0.281963i
$876$	−2.18053e15	−	6.13284e15i	−0.142820	−	0.401688i
$877$	1.07889e16	−	1.86870e16i	0.702233	−	1.21630i	−0.265448	−	0.964125i	$-0.585520\pi$
$877$	1.07889e16	−	1.86870e16i	0.702233	−	1.21630i	0.967681	−	0.252178i	$-0.0811467\pi$
$878$	−5.06100e15	−	8.76591e15i	−0.327353	−	0.566992i
$879$	5.40299e15	+	4.60271e15i	0.347292	+	0.295852i
$880$	7.02484e15	+	4.05579e15i	0.448726	+	0.259072i
$881$	−1.00275e16			−0.636537			−0.318268	−	0.948001i	$-0.603101\pi$
$881$	−1.00275e16			−0.636537			−0.318268	+	0.948001i	$0.603101\pi$
$882$	−8.72789e15	−	7.03298e15i	−0.550595	−	0.443672i
$883$	−1.47699e16			−0.925965			−0.462983	−	0.886367i	$-0.653221\pi$
$883$	−1.47699e16			−0.925965			−0.462983	+	0.886367i	$0.653221\pi$
$884$	−1.12924e16	−	6.51968e15i	−0.703557	−	0.406199i
$885$	1.69937e16	+	1.44767e16i	1.05221	+	0.896357i
$886$	−4.49631e15	−	7.78784e15i	−0.276676	−	0.479216i
$887$	−8.53323e14	+	1.47800e15i	−0.0521836	+	0.0903846i	−0.890937	−	0.454126i	$-0.849951\pi$
$887$	−8.53323e14	+	1.47800e15i	−0.0521836	+	0.0903846i	0.838754	+	0.544511i	$0.183285\pi$
$888$	2.58991e15	+	7.28423e15i	0.157403	+	0.442703i
$889$	−9.73330e13	−	1.33987e14i	−0.00587896	−	0.00809285i
$890$			2.46763e15i			0.148127i
$891$	−1.75459e16	+	1.96872e16i	−1.04676	+	1.17451i
$892$	4.19261e15	−	2.42060e15i	0.248587	−	0.143522i
$893$	−7.55124e15	+	4.35971e15i	−0.444975	+	0.256906i
$894$	5.80837e14	−	3.15632e15i	0.0340172	−	0.184852i
$895$		−	3.01193e16i		−	1.75314i
$896$	1.59603e14	+	1.51952e15i	0.00923312	+	0.0879048i
$897$	1.61005e16	−	5.72453e15i	0.925721	−	0.329141i
$898$	−8.15075e15	+	1.41175e16i	−0.465777	+	0.806749i
$899$	−1.37903e15	−	2.38854e15i	−0.0783239	−	0.135661i
$900$	6.08740e15	+	2.31898e15i	0.343635	+	0.130907i
$901$	−3.39019e16	−	1.95733e16i	−1.90212	−	1.09819i
$902$	−1.61961e15			−0.0903179
$903$	1.15462e15	−	1.49001e16i	0.0639963	−	0.825860i
$904$	5.74936e15			0.316733
$905$	1.83138e16	+	1.05735e16i	1.00279	+	0.578963i
$906$	−1.36803e16	+	1.60589e16i	−0.744547	+	0.874001i
$907$	9.76380e14	+	1.69114e15i	0.0528176	+	0.0914828i	0.891225	−	0.453561i	$-0.149846\pi$
$907$	9.76380e14	+	1.69114e15i	0.0528176	+	0.0914828i	−0.838408	+	0.545043i	$0.816513\pi$
$908$	3.41709e15	−	5.91858e15i	0.183732	−	0.318233i
$909$	1.77972e16	−	1.44870e16i	0.951152	−	0.774243i
$910$	−6.15100e15	+	1.38128e16i	−0.326752	+	0.733762i
$911$			3.59436e15i			0.189789i	0.995487	+	0.0948943i	$0.0302513\pi$
$911$			3.59436e15i			0.189789i	−0.995487	+	0.0948943i	$0.969749\pi$
$912$	−1.42547e15	−	2.62321e14i	−0.0748147	−	0.0137677i
$913$	−4.23371e16	+	2.44434e16i	−2.20868	+	1.27518i
$914$	1.42747e16	−	8.24152e15i	0.740225	−	0.427369i
$915$	7.78229e14	+	1.43213e14i	0.0401136	+	0.00738185i
$916$			2.93052e15i			0.150148i
$917$	−2.61704e15	+	2.74882e14i	−0.133284	+	0.0139996i
$918$	2.24930e16	+	1.36660e16i	1.13871	+	0.691840i
$919$	−9.53414e15	+	1.65136e16i	−0.479785	+	0.831011i	−0.999731	−	0.0231876i	$-0.992619\pi$
$919$	−9.53414e15	+	1.65136e16i	−0.479785	+	0.831011i	0.519947	+	0.854199i	$0.325952\pi$
$920$	5.30453e15	+	9.18771e15i	0.265347	+	0.459594i
$921$	9.66081e15	−	1.13405e16i	0.480381	−	0.563904i
$922$	2.57826e15	+	1.48856e15i	0.127440	+	0.0735778i
$923$	6.16491e15			0.302913
$924$	9.10619e15	−	1.32838e16i	0.444776	−	0.648825i
$925$	−2.01298e16			−0.977373
$926$	1.31456e16	+	7.58964e15i	0.634485	+	0.366320i
$927$	−2.19044e15	+	5.74996e15i	−0.105097	+	0.275884i
$928$	−1.48097e15	−	2.56512e15i	−0.0706371	−	0.122347i
$929$	−1.88793e16	+	3.27000e16i	−0.895159	+	1.55046i	−0.0615515	+	0.998104i	$0.519605\pi$
$929$	−1.88793e16	+	3.27000e16i	−0.895159	+	1.55046i	−0.833608	+	0.552357i	$0.813728\pi$
$930$	−3.64992e15	+	1.29773e15i	−0.172039	+	0.0611687i
$931$	−4.82646e15	+	4.34457e15i	−0.226155	+	0.203575i
$932$			4.62340e15i			0.215364i
$933$	−3.74423e15	+	2.03464e16i	−0.173386	+	0.942192i
$934$	−4.55336e15	+	2.62888e15i	−0.209616	+	0.121022i
$935$	−7.39021e16	+	4.26674e16i	−3.38215	+	1.95269i
$936$	1.06505e15	+	6.61550e15i	0.0484566	+	0.300986i
$937$		−	3.32141e16i		−	1.50229i	−0.660136	−	0.751146i	$-0.729501\pi$
$937$		−	3.32141e16i		−	1.50229i	0.660136	−	0.751146i	$-0.270499\pi$
$938$	9.60822e15	−	6.97978e15i	0.432043	−	0.313853i
$939$	4.14558e15	+	1.16596e16i	0.185321	+	0.521222i
$940$	−1.25134e16	+	2.16738e16i	−0.556125	+	0.963236i
$941$	−1.36641e16	−	2.36669e16i	−0.603724	−	1.04568i	−0.992252	−	0.124244i	$-0.960350\pi$
$941$	−1.36641e16	−	2.36669e16i	−0.603724	−	1.04568i	0.388528	−	0.921437i	$-0.372984\pi$
$942$	−2.15635e16	−	1.83696e16i	−0.947196	−	0.806900i
$943$	−1.83447e15	−	1.05913e15i	−0.0801120	−	0.0462527i
$944$	−6.04176e15			−0.262312
$945$	1.30358e16	−	2.75957e16i	0.562680	−	1.19115i
$946$	2.14732e16			0.921502
$947$	−1.88592e16	−	1.08884e16i	−0.804634	−	0.464555i	0.0404551	−	0.999181i	$-0.487119\pi$
$947$	−1.88592e16	−	1.08884e16i	−0.804634	−	0.464555i	−0.845089	+	0.534626i	$0.820453\pi$
$948$	1.00920e16	+	8.59720e15i	0.428086	+	0.364679i
$949$	8.71665e15	+	1.50977e16i	0.367609	+	0.636717i
$950$	1.88698e15	−	3.26834e15i	0.0791202	−	0.137040i
$951$	−1.15001e16	−	3.23446e16i	−0.479413	−	1.34837i
$952$	−1.46834e16	−	6.53867e15i	−0.608588	−	0.271011i
$953$		−	2.07547e15i		−	0.0855274i	−0.999085	−	0.0427637i	$-0.986384\pi$
$953$		−	2.07547e15i		−	0.0855274i	0.999085	−	0.0427637i	$-0.0136163\pi$
$954$	3.19748e15	+	1.98610e16i	0.131006	+	0.813737i
$955$	4.13773e16	−	2.38892e16i	1.68556	−	0.973157i
$956$	−4.06789e15	+	2.34860e15i	−0.164760	+	0.0951240i
$957$	−5.65068e15	+	3.07062e16i	−0.227554	+	1.23655i
$958$			5.47549e15i			0.219236i
$959$	1.71405e16	+	7.63286e15i	0.682373	+	0.303868i
$960$	−3.91975e15	+	1.39367e15i	−0.155155	+	0.0551656i
$961$	−1.22161e16	+	2.11589e16i	−0.480789	+	0.832752i
$962$	−1.03531e16	−	1.79322e16i	−0.405144	−	0.701729i
$963$	1.39269e16	−	3.65586e16i	0.541889	−	1.42247i
$964$	−5.95617e15	−	3.43880e15i	−0.230432	−	0.133040i
$965$	2.30811e16			0.887886
$966$	1.90012e16	−	9.09119e15i	0.726785	−	0.347733i
$967$	3.62794e16			1.37980			0.689898	−	0.723907i	$-0.257655\pi$
$967$	3.62794e16			1.37980			0.689898	+	0.723907i	$0.257655\pi$
$968$	1.19440e16	+	6.89587e15i	0.451685	+	0.260780i
$969$	9.88799e15	−	1.16072e16i	0.371815	−	0.436463i
$970$	2.27582e15	+	3.94184e15i	0.0850931	+	0.147386i
$971$	2.13970e16	−	3.70607e16i	0.795512	−	1.37787i	−0.127002	−	0.991903i	$-0.540535\pi$
$971$	2.13970e16	−	3.70607e16i	0.795512	−	1.37787i	0.922514	−	0.385965i	$-0.126131\pi$
$972$	−1.85060e15	−	1.33977e16i	−0.0684144	−	0.495297i
$973$	−2.46939e16	+	1.79386e16i	−0.907755	+	0.659428i
$974$		−	2.41094e16i		−	0.881278i
$975$	−1.71591e16	−	3.15768e15i	−0.623690	−	0.114774i
$976$	−1.85465e14	+	1.07078e14i	−0.00670329	+	0.00387014i
$977$	−4.27464e16	+	2.46796e16i	−1.53631	+	0.886990i	−0.537261	+	0.843416i	$0.680541\pi$
$977$	−4.27464e16	+	2.46796e16i	−1.53631	+	0.886990i	−0.999050	+	0.0435742i	$0.986126\pi$
$978$	−9.75446e15	−	1.79505e15i	−0.348610	−	0.0641525i
$979$			7.03970e15i			0.250178i
$980$	−5.76214e15	+	1.77258e16i	−0.203629	+	0.626417i
$981$	−2.01598e16	+	1.64102e16i	−0.708445	+	0.576678i
$982$	1.32153e16	−	2.28897e16i	0.461812	−	0.799882i
$983$	−2.11127e16	−	3.65683e16i	−0.733669	−	1.27075i	−0.955305	−	0.295622i	$-0.904473\pi$
$983$	−2.11127e16	−	3.65683e16i	−0.733669	−	1.27075i	0.221636	−	0.975129i	$-0.428860\pi$
$984$	5.38653e14	−	6.32308e14i	0.0186138	−	0.0218502i
$985$	3.60251e16	+	2.07991e16i	1.23796	+	0.714735i
$986$	3.11600e16			1.06482
$987$	4.09848e16	+	2.80955e16i	1.39277	+	0.954756i
$988$	3.88203e15			0.131189
$989$	2.43220e16	+	1.40423e16i	0.817372	+	0.471910i
$990$	4.09792e16	+	1.56110e16i	1.36953	+	0.521718i
$991$	−1.72245e16	−	2.98338e16i	−0.572456	−	0.991523i	−0.996313	−	0.0857940i	$-0.972657\pi$
$991$	−1.72245e16	−	2.98338e16i	−0.572456	−	0.991523i	0.423857	−	0.905729i	$-0.360676\pi$
$992$	5.24198e14	−	9.07937e14i	0.0173253	−	0.0300083i
$993$	−7.13545e15	+	2.53702e15i	−0.234531	+	0.0833877i
$994$	7.55784e15	−	7.93841e14i	0.247043	−	0.0259483i
$995$		−	5.43513e16i		−	1.76678i
$996$	4.53769e15	−	2.46582e16i	0.146693	−	0.797141i
$997$	−2.28243e16	+	1.31776e16i	−0.733795	+	0.423657i	−0.819809	−	0.572637i	$-0.805920\pi$
$997$	−2.28243e16	+	1.31776e16i	−0.733795	+	0.423657i	0.0860137	+	0.996294i	$0.472587\pi$
$998$	2.72684e16	−	1.57434e16i	0.871849	−	0.503362i
$999$	2.00825e16	+	3.66532e16i	0.638569	+	1.16547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.27	yes	60
3.2	odd	2	inner	42.12.f.a.5.7	✓	60
7.3	odd	6	inner	42.12.f.a.17.7	yes	60
21.17	even	6	inner	42.12.f.a.17.27	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.7	✓	60	3.2	odd	2	inner
42.12.f.a.5.27	yes	60	1.1	even	1	trivial
42.12.f.a.17.7	yes	60	7.3	odd	6	inner
42.12.f.a.17.27	yes	60	21.17	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	42.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(27.7128 + 16.0000i) q^{2} +(320.393 + 272.938i) q^{3} +(512.000 + 886.810i) q^{4} +(4602.68 - 7972.08i) q^{5} +(4512.00 + 12690.2i) q^{6} +(-26134.7 - 35976.5i) q^{7} +32768.0i q^{8} +(28156.9 + 174895. i) q^{9} +(255107. - 147286. i) q^{10} +(727772. - 420179. i) q^{11} +(-78002.6 + 423872. i) q^{12} -1.15435e6i q^{13} +(-148642. - 1.41516e6i) q^{14} +(3.65055e6 - 1.29796e6i) q^{15} +(-524288. + 908093. i) q^{16} +(-5.51557e6 - 9.55325e6i) q^{17} +(-2.01801e6 + 5.29734e6i) q^{18} +(2.84416e6 + 1.64208e6i) q^{19} +9.42630e6 q^{20} +(1.44595e6 - 1.86598e7i) q^{21} +2.68915e7 q^{22} +(3.04590e7 + 1.75855e7i) q^{23} +(-8.94363e6 + 1.04987e7i) q^{24} +(-1.79553e7 - 3.10996e7i) q^{25} +(1.84695e7 - 3.19901e7i) q^{26} +(-3.87142e7 + 6.37203e7i) q^{27} +(1.85233e7 - 4.15964e7i) q^{28} +8.82728e7i q^{29} +(1.21934e8 + 2.24388e7i) q^{30} +(-2.70586e7 + 1.56223e7i) q^{31} +(-2.90590e7 + 1.67772e7i) q^{32} +(3.47856e8 + 6.40138e7i) q^{33} -3.52997e8i q^{34} +(-4.07097e8 + 4.27596e7i) q^{35} +(-1.40682e8 + 1.14516e8i) q^{36} +(2.80276e8 - 4.85453e8i) q^{37} +(5.25465e7 + 9.10131e7i) q^{38} +(3.15064e8 - 3.69845e8i) q^{39} +(2.61229e8 + 1.50821e8i) q^{40} -6.02276e7 q^{41} +(3.38628e8 - 4.93979e8i) q^{42} +7.98515e8 q^{43} +(7.45238e8 + 4.30263e8i) q^{44} +(1.52387e9 + 5.80517e8i) q^{45} +(5.62737e8 + 9.74689e8i) q^{46} +(-1.32750e9 + 2.29930e9i) q^{47} +(-4.15831e8 + 1.47849e8i) q^{48} +(-6.11284e8 + 1.88047e9i) q^{49} -1.14914e9i q^{50} +(8.40291e8 - 4.56621e9i) q^{51} +(1.02368e9 - 5.91025e8i) q^{52} +(3.07329e9 - 1.77436e9i) q^{53} +(-2.09240e9 + 1.14644e9i) q^{54} -7.73581e9i q^{55} +(1.17888e9 - 8.56381e8i) q^{56} +(4.63066e8 + 1.30239e9i) q^{57} +(-1.41237e9 + 2.44629e9i) q^{58} +(2.88094e9 + 4.98993e9i) q^{59} +(3.02012e9 + 2.57279e9i) q^{60} +(1.76873e8 + 1.02118e8i) q^{61} -9.99828e8 q^{62} +(5.55623e9 - 5.58381e9i) q^{63} -1.07374e9 q^{64} +(-9.20253e9 - 5.31309e9i) q^{65} +(8.61585e9 + 7.33970e9i) q^{66} +(4.17296e9 + 7.22778e9i) q^{67} +(5.64795e9 - 9.78253e9i) q^{68} +(4.95912e9 + 1.39477e10i) q^{69} +(-1.19660e10 - 5.32856e9i) q^{70} +5.34061e9i q^{71} +(-5.73096e9 + 9.22645e8i) q^{72} +(-1.30790e10 + 7.55117e9i) q^{73} +(1.55345e10 - 8.96884e9i) q^{74} +(2.73547e9 - 1.48648e10i) q^{75} +3.36297e9i q^{76} +(-3.41366e10 - 1.52014e10i) q^{77} +(1.46488e10 - 5.20840e9i) q^{78} +(1.53802e10 - 2.66394e10i) q^{79} +(4.82626e9 + 8.35933e9i) q^{80} +(-2.97954e10 + 9.84900e9i) q^{81} +(-1.66908e9 - 9.63641e8i) q^{82} -5.81737e10 q^{83} +(1.72880e10 - 8.27151e9i) q^{84} -1.01546e11 q^{85} +(2.21291e10 + 1.27762e10i) q^{86} +(-2.40930e10 + 2.82820e10i) q^{87} +(1.37684e10 + 2.38476e10i) q^{88} +(-4.18851e9 + 7.25471e9i) q^{89} +(3.29426e10 + 4.04698e10i) q^{90} +(-4.15292e10 + 3.01684e10i) q^{91} +3.60152e10i q^{92} +(-1.29333e10 - 2.38004e9i) q^{93} +(-7.35775e10 + 4.24800e10i) q^{94} +(2.61815e10 - 1.51159e10i) q^{95} +(-1.38894e10 - 2.55599e9i) q^{96} +1.54517e10i q^{97} +(-4.70278e10 + 4.23325e10i) q^{98} +(9.39790e10 + 1.15453e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30720 q^{4} - 95298 q^{7} - 91434 q^{9} + 245184 q^{10} - 8480820 q^{15} - 31457280 q^{16} + 12170496 q^{18} + 1649724 q^{19} + 43254216 q^{21} + 20705664 q^{22} + 4521984 q^{24} - 336132444 q^{25}+ \cdots + 288758042496 q^{99}+O(q^{100}) \) 60 * q + 30720 * q^4 - 95298 * q^7 - 91434 * q^9 + 245184 * q^10 - 8480820 * q^15 - 31457280 * q^16 + 12170496 * q^18 + 1649724 * q^19 + 43254216 * q^21 + 20705664 * q^22 + 4521984 * q^24 - 336132444 * q^25 + 28121088 * q^28 - 77109120 * q^30 - 275992974 * q^31 + 1056712914 * q^33 - 187256832 * q^36 + 555437556 * q^37 - 563926680 * q^39 + 251068416 * q^40 + 1167043776 * q^42 + 2546594304 * q^43 + 544480776 * q^45 - 452472192 * q^46 - 1309143414 * q^49 + 2007979044 * q^51 + 3219419136 * q^52 - 9840998592 * q^54 + 17053196256 * q^57 + 12235419456 * q^58 - 4342179840 * q^60 - 3056592000 * q^61 - 42499692960 * q^63 - 64424509440 * q^64 + 48796070400 * q^66 + 27979853436 * q^67 - 4966503360 * q^70 - 12462587904 * q^72 - 105678747168 * q^73 + 173211633504 * q^75 - 16600538880 * q^78 - 27787555926 * q^79 - 71399556486 * q^81 + 31231064832 * q^82 - 25272410112 * q^84 + 12868048152 * q^85 + 137017459998 * q^87 + 10601299968 * q^88 + 333571182180 * q^91 - 14607989424 * q^93 - 430917051648 * q^94 + 4630511616 * q^96 + 288758042496 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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