LMFDB - Embedded newform 42.12.f.a.5.7

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			5.7
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.7

$q$-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} +(-76.1744 - 413.938i) 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} +(-165542. + 63062.9i) q^{9} +(255107. - 147286. i) q^{10} +(-727772. + 420179. i) q^{11} +(328083. - 279488. 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} +(5.59664e6 + 901021. i) q^{18} +(2.84416e6 + 1.64208e6i) q^{19} -9.42630e6 q^{20} +(-1.29012e7 + 1.35586e7i) q^{21} +2.68915e7 q^{22} +(-3.04590e7 - 1.75855e7i) q^{23} +(-1.35639e7 + 2.49608e6i) 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} +(-8.03998e7 - 9.43789e7i) q^{30} +(-2.70586e7 + 1.56223e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(2.29366e8 + 2.69245e8i) 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} +(-4.77827e8 + 8.79315e7i) q^{39} +(2.61229e8 + 1.50821e8i) q^{40} +6.02276e7 q^{41} +(5.74467e8 - 1.69328e8i) q^{42} +7.98515e8 q^{43} +(-7.45238e8 - 4.30263e8i) q^{44} +(2.59195e8 - 1.60997e9i) 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} +(3.53431e9 - 3.01082e9i) q^{51} +(1.02368e9 - 5.91025e8i) q^{52} +(-3.07329e9 + 1.77436e9i) q^{53} +(-5.33540e7 - 2.38529e9i) 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} +(7.18042e8 + 3.90190e9i) q^{60} +(1.76873e8 + 1.02118e8i) q^{61} +9.99828e8 q^{62} +(6.59517e9 + 4.30748e9i) q^{63} -1.07374e9 q^{64} +(9.20253e9 + 5.31309e9i) q^{65} +(-2.04844e9 - 1.11314e10i) 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} +(2.06645e9 + 5.42448e9i) q^{72} +(-1.30790e10 + 7.55117e9i) q^{73} +(-1.55345e10 + 8.96884e9i) q^{74} +(-1.15055e10 + 9.80138e9i) 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} +(2.34272e10 - 2.08791e10i) q^{81} +(-1.66908e9 - 9.63641e8i) q^{82} +5.81737e10 q^{83} +(-1.86293e10 - 4.49892e9i) q^{84} -1.01546e11 q^{85} +(-2.21291e10 - 1.27762e10i) q^{86} +(-3.65395e10 + 6.72413e9i) 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} +(8.52784e9 + 1.00106e10i) q^{93} +(-7.35775e10 + 4.24800e10i) q^{94} +(-2.61815e10 + 1.51159e10i) q^{95} +(-9.15827e9 - 1.07506e10i) 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
$3$	−76.1744	−	413.938i	−0.180985	−	0.983486i
$3$	−76.1744	−	413.938i	−0.180985	−	0.983486i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	−4602.68	+	7972.08i	−0.658683	+	1.14087i	0.322274	+	0.946646i	$0.395553\pi$
$5$	−4602.68	+	7972.08i	−0.658683	+	1.14087i	−0.980957	+	0.194225i	$0.937781\pi$
$6$	−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
$9$	−165542.	+	63062.9i	−0.934489	+	0.355992i
$10$	255107.	−	147286.i	0.806718	−	0.465759i
$11$	−727772.	+	420179.i	−1.36250	+	0.786638i	−0.989956	−	0.141378i	$-0.954847\pi$
$11$	−727772.	+	420179.i	−1.36250	+	0.786638i	−0.372541	+	0.928016i	$0.621513\pi$
$12$	328083.	−	279488.i	0.380616	−	0.324240i
$13$		−	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	$0.224536\pi$
$17$	5.51557e6	+	9.55325e6i	0.942153	+	1.63186i	0.180801	+	0.983520i	$0.442131\pi$
$18$	5.59664e6	+	901021.i	0.698117	+	0.112392i
$19$	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
$21$	−1.29012e7	+	1.35586e7i	−0.689326	+	0.724451i
$22$	2.68915e7			1.11247
$23$	−3.04590e7	−	1.75855e7i	−0.986764	−	0.569708i	−0.0824583	−	0.996595i	$-0.526277\pi$
$23$	−3.04590e7	−	1.75855e7i	−0.986764	−	0.569708i	−0.904305	+	0.426886i	$0.859610\pi$
$24$	−1.35639e7	+	2.49608e6i	−0.347715	+	0.0639878i
$25$	−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	$-0.869155\pi$
$29$		−	8.82728e7i		−	0.799168i	0.916697	−	0.399584i	$-0.130845\pi$
$30$	−8.03998e7	−	9.43789e7i	−0.604071	−	0.709101i
$31$	−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
$33$	2.29366e8	+	2.69245e8i	1.02024	+	1.19763i
$34$		−	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
$39$	−4.77827e8	+	8.79315e7i	−0.848038	+	0.156059i
$40$	2.61229e8	+	1.50821e8i	0.403359	+	0.232879i
$41$	6.02276e7			0.0811866			0.0405933	−	0.999176i	$-0.487075\pi$
$41$	6.02276e7			0.0811866			0.0405933	+	0.999176i	$0.487075\pi$
$42$	5.74467e8	−	1.69328e8i	0.678256	−	0.199921i
$43$	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
$45$	2.59195e8	−	1.60997e9i	0.209391	−	1.30062i
$46$	5.62737e8	+	9.74689e8i	0.402845	+	0.697747i
$47$	1.32750e9	−	2.29930e9i	0.844299	−	1.46237i	−0.0419305	−	0.999121i	$-0.513351\pi$
$47$	1.32750e9	−	2.29930e9i	0.844299	−	1.46237i	0.886229	−	0.463247i	$-0.153316\pi$
$48$	4.15831e8	+	1.47849e8i	0.235554	+	0.0837514i
$49$	−6.11284e8	+	1.88047e9i	−0.309146	+	0.951014i
$50$			1.14914e9i			0.520042i
$51$	3.53431e9	−	3.01082e9i	1.43439	−	1.22194i
$52$	1.02368e9	−	5.91025e8i	0.373377	−	0.215569i
$53$	−3.07329e9	+	1.77436e9i	−1.00945	+	0.582808i	−0.911031	−	0.412337i	$-0.864713\pi$
$53$	−3.07329e9	+	1.77436e9i	−1.00945	+	0.582808i	−0.0984216	+	0.995145i	$0.531379\pi$
$54$	−5.33540e7	−	2.38529e9i	−0.0158125	−	0.706930i
$55$		−	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	$-0.990873\pi$
$59$	−2.88094e9	−	4.98993e9i	−0.524624	−	0.908675i	0.474965	−	0.880005i	$-0.342461\pi$
$60$	7.18042e8	+	3.90190e9i	0.119211	+	0.647805i
$61$	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
$63$	6.59517e9	+	4.30748e9i	0.837245	+	0.546828i
$64$	−1.07374e9			−0.125000
$65$	9.20253e9	+	5.31309e9i	0.983748	+	0.567967i
$66$	−2.04844e9	−	1.11314e10i	−0.201341	−	1.09410i
$67$	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	$-0.943798\pi$
$71$		−	5.34061e9i		−	0.351294i	0.984453	−	0.175647i	$-0.0562017\pi$
$72$	2.06645e9	+	5.42448e9i	0.125862	+	0.330392i
$73$	−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
$75$	−1.15055e10	+	9.80138e9i	−0.559848	+	0.476925i
$76$			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
$81$	2.34272e10	−	2.08791e10i	0.746540	−	0.665341i
$82$	−1.66908e9	−	9.63641e8i	−0.0497164	−	0.0287038i
$83$	5.81737e10			1.62105			0.810526	−	0.585703i	$-0.199181\pi$
$83$	5.81737e10			1.62105			0.810526	+	0.585703i	$0.199181\pi$
$84$	−1.86293e10	−	4.49892e9i	−0.486028	−	0.117374i
$85$	−1.01546e11			−2.48232
$86$	−2.21291e10	−	1.27762e10i	−0.507250	−	0.292861i
$87$	−3.65395e10	+	6.72413e9i	−0.785971	+	0.144637i
$88$	1.37684e10	+	2.38476e10i	0.278118	+	0.481715i
$89$	4.18851e9	−	7.25471e9i	0.0795086	−	0.137713i	−0.823529	−	0.567274i	$-0.807998\pi$
$89$	4.18851e9	−	7.25471e9i	0.0795086	−	0.137713i	0.903038	+	0.429561i	$0.141332\pi$
$90$	−3.29426e10	+	4.04698e10i	−0.588063	+	0.722432i
$91$	−4.15292e10	+	3.01684e10i	−0.697632	+	0.506787i
$92$		−	3.60152e10i		−	0.569708i
$93$	8.52784e9	+	1.00106e10i	0.127111	+	0.149212i
$94$	−7.35775e10	+	4.24800e10i	−1.03405	+	0.597009i
$95$	−2.61815e10	+	1.51159e10i	−0.347149	+	0.200426i
$96$	−9.15827e9	−	1.07506e10i	−0.114636	−	0.134568i
$97$			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	$0.0434584\pi$
$101$	6.47712e10	+	1.12187e11i	0.613217	+	1.06212i	−0.377477	+	0.926019i	$0.623208\pi$
$102$	−1.46119e11	+	2.68893e10i	−1.31040	+	0.241145i
$103$	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
$105$	−4.87102e10	−	1.65256e11i	−0.372459	−	1.26362i
$106$	1.13559e11			0.824215
$107$	1.91254e11	+	1.10421e11i	1.31826	+	0.761097i	0.983448	−	0.181188i	$-0.0579942\pi$
$107$	1.91254e11	+	1.10421e11i	1.31826	+	0.761097i	0.334811	+	0.942285i	$0.391328\pi$
$108$	−3.66861e10	+	6.69569e10i	−0.240254	+	0.438495i
$109$	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	$0.147838\pi$
$113$			1.75457e11i			0.895856i	−0.894070	+	0.447928i	$0.852162\pi$
$114$	−3.36711e10	+	2.86838e10i	−0.163787	+	0.139528i
$115$	2.80387e11	−	1.61881e11i	1.29993	−	0.750514i
$116$	7.82812e10	−	4.51957e10i	0.346050	−	0.199792i
$117$	7.27963e10	+	1.91093e11i	0.306964	+	0.805789i
$118$			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
$123$	−4.58780e9	−	2.49305e10i	−0.0146935	−	0.0798458i
$124$	−2.77080e10	−	1.59972e10i	−0.0848763	−	0.0490034i
$125$	−1.18910e11			−0.348508
$126$	−1.13851e11	−	2.24895e11i	−0.319373	−	0.630873i
$127$	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
$129$	−6.08264e10	−	3.30535e11i	−0.149916	−	0.814657i
$130$	−1.70019e11	−	2.94481e11i	−0.401614	−	0.695615i
$131$	−2.95885e10	+	5.12489e10i	−0.0670087	+	0.116063i	−0.897583	−	0.440845i	$-0.854679\pi$
$131$	−2.95885e10	+	5.12489e10i	−0.0670087	+	0.116063i	0.830575	+	0.556907i	$0.188012\pi$
$132$	−1.21334e11	+	3.41257e11i	−0.263528	+	0.741183i
$133$	−1.52551e10	−	1.45238e11i	−0.0317857	−	0.302619i
$134$		−	2.67070e11i		−	0.534009i
$135$	−6.86172e11	+	1.53482e10i	−1.31704	+	0.0294593i
$136$	3.13041e11	−	1.80734e11i	0.576949	−	0.333102i
$137$	3.65425e11	−	2.10978e11i	0.646898	−	0.373487i	−0.140369	−	0.990099i	$-0.544829\pi$
$137$	3.65425e11	−	2.10978e11i	0.646898	−	0.373487i	0.787267	+	0.616613i	$0.211496\pi$
$138$	3.60595e11	−	3.07185e11i	0.613316	−	0.522474i
$139$		−	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
$144$	2.95246e10	−	1.83391e11i	0.0397366	−	0.246822i
$145$	7.03718e11	+	4.06292e11i	0.911748	+	0.526398i
$146$	4.83275e11			0.602911
$147$	8.24960e11	+	1.09790e11i	0.991260	+	0.131922i
$148$	5.74006e11			0.664472
$149$	2.06360e11	+	1.19142e11i	0.230198	+	0.132905i	0.610663	−	0.791890i	$-0.290903\pi$
$149$	2.06360e11	+	1.19142e11i	0.230198	+	0.132905i	−0.380465	+	0.924795i	$0.624236\pi$
$150$	4.75673e11	−	8.75351e10i	0.511454	−	0.0941197i
$151$	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
$156$	−3.22626e11	−	3.78721e11i	−0.279585	−	0.328196i
$157$	−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
$159$	9.68582e11	+	1.13699e12i	0.755879	+	0.887304i
$160$			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
$165$	−3.20214e12	+	5.89270e11i	−2.03835	+	0.375105i
$166$	−1.61216e12	−	9.30779e11i	−0.992687	−	0.573128i
$167$	4.42690e11			0.263730			0.131865	−	0.991268i	$-0.457904\pi$
$167$	4.42690e11			0.263730			0.131865	+	0.991268i	$0.457904\pi$
$168$	4.44289e11	+	4.22747e11i	0.256132	+	0.243714i
$169$	4.59648e11			0.256477
$170$	2.81412e12	+	1.62473e12i	1.52010	+	0.877633i
$171$	−5.74382e11	−	9.24716e10i	−0.300415	−	0.0483648i
$172$	4.08840e11	+	7.08131e11i	0.207084	+	0.358680i
$173$	1.54860e12	−	2.68225e12i	0.759776	−	1.31597i	−0.183189	−	0.983078i	$-0.558642\pi$
$173$	1.54860e12	−	2.68225e12i	0.759776	−	1.31597i	0.942965	−	0.332893i	$-0.108025\pi$
$174$	1.12020e12	+	3.98287e11i	0.532444	+	0.189311i
$175$	−6.49595e11	+	1.45875e12i	−0.299180	+	0.671847i
$176$		−	8.81180e11i		−	0.393319i
$177$	−1.84607e12	+	1.57263e12i	−0.798720	+	0.680416i
$178$	−2.32151e11	+	1.34032e11i	−0.0973778	+	0.0562211i
$179$	−2.83357e12	+	1.63596e12i	−1.15250	+	0.665398i	−0.949496	−	0.313779i	$-0.898405\pi$
$179$	−2.83357e12	+	1.63596e12i	−1.15250	+	0.665398i	−0.203007	+	0.979177i	$0.565071\pi$
$180$	1.56045e12	−	5.94450e11i	0.615532	−	0.234486i
$181$			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
$186$	−7.61613e10	−	4.13867e11i	−0.0250849	−	0.136314i
$187$	−8.02816e12	−	4.63506e12i	−2.56736	−	1.48227i
$188$	2.71872e12			0.844299
$189$	1.28065e12	−	3.05811e12i	0.386269	−	0.922386i
$190$	9.67419e11			0.283446
$191$	−4.49491e12	−	2.59514e12i	−1.27949	−	0.738715i	−0.302737	−	0.953074i	$-0.597900\pi$
$191$	−4.49491e12	−	2.59514e12i	−1.27949	−	0.738715i	−0.976755	+	0.214359i	$0.931234\pi$
$192$	8.17916e10	+	4.44462e11i	0.0226231	+	0.122936i
$193$	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	$-0.817459\pi$
$197$		−	4.51891e12i		−	1.08510i	0.840024	−	0.542549i	$-0.182541\pi$
$198$	−4.45167e12	+	1.69585e12i	−1.03959	+	0.396032i
$199$	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
$201$	2.67398e12	−	2.27792e12i	0.574884	−	0.489734i
$202$		−	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
$207$	6.15124e12	+	9.90308e11i	1.12493	+	0.181106i
$208$	1.04825e12	+	6.05209e11i	0.186689	+	0.107785i
$209$	−2.75987e12			−0.478722
$210$	−1.29419e12	+	5.35906e12i	−0.218672	+	0.905488i
$211$	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
$213$	−2.21068e12	+	4.06818e11i	−0.345492	+	0.0635788i
$214$	−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
$219$	4.12200e12	+	4.83869e12i	0.552924	+	0.649060i
$220$	6.86019e12	−	3.96073e12i	0.897453	−	0.518145i
$221$	1.10278e13	−	6.36688e12i	1.40711	−	0.812398i
$222$	4.89587e12	+	5.74711e12i	0.609380	+	0.715333i
$223$		−	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	0.989168	−	0.146786i	$-0.0468928\pi$
$227$	3.33701e12	+	5.77986e12i	0.367464	+	0.636466i	−0.621704	+	0.783252i	$0.713559\pi$
$228$	1.39206e12	−	2.56172e11i	0.149629	−	0.0275354i
$229$	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
$231$	3.69209e12	−	1.52884e13i	0.369323	−	1.52931i
$232$	−2.89252e12			−0.282549
$233$	−3.91014e12	−	2.25752e12i	−0.373022	−	0.215364i	0.301756	−	0.953385i	$-0.402427\pi$
$233$	−3.91014e12	−	2.25752e12i	−0.373022	−	0.215364i	−0.674778	+	0.738021i	$0.735761\pi$
$234$	1.04009e12	−	6.46045e12i	0.0969132	−	0.601971i
$235$	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	$-0.939071\pi$
$239$		−	4.58710e12i		−	0.380496i	0.981736	−	0.190248i	$-0.0609292\pi$
$240$	−3.09261e12	+	2.63454e12i	−0.250705	+	0.213571i
$241$	−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
$243$	−1.04272e13	−	8.10695e12i	−0.789466	−	0.613795i
$244$			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
$249$	−4.43134e12	−	2.40803e13i	−0.293386	−	1.59428i
$250$	3.29533e12	+	1.90256e12i	0.213417	+	0.123216i
$251$	4.09853e12			0.259671			0.129835	−	0.991536i	$-0.458555\pi$
$251$	4.09853e12			0.259671			0.129835	+	0.991536i	$0.458555\pi$
$252$	−4.43194e11	+	8.05409e12i	−0.0274720	+	0.499245i
$253$	2.95563e13			1.79262
$254$	−1.03210e11	−	5.95885e10i	−0.00612545	−	0.00353653i
$255$	7.73519e12	+	4.20336e13i	0.449262	+	2.44133i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	6.55417e11	−	1.13522e12i	0.0364658	−	0.0631606i	−0.847217	−	0.531248i	$-0.821723\pi$
$257$	6.55417e11	−	1.13522e12i	0.0364658	−	0.0631606i	0.883682	+	0.468087i	$0.155057\pi$
$258$	−3.60290e12	+	1.01333e13i	−0.196220	+	0.551877i
$259$	−2.47898e13	+	2.60381e12i	−1.32167	+	0.138823i
$260$			1.08812e13i			0.567967i
$261$	5.56674e12	+	1.46129e13i	0.284497	+	0.746814i
$262$	1.63996e12	−	9.46833e11i	0.0820686	−	0.0473823i
$263$	6.96817e12	−	4.02308e12i	0.341478	−	0.197152i	−0.319448	−	0.947604i	$-0.603497\pi$
$263$	6.96817e12	−	4.02308e12i	0.341478	−	0.197152i	0.660925	+	0.750452i	$0.270164\pi$
$264$	8.82263e12	−	7.51585e12i	0.423425	−	0.360709i
$265$		−	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	$-0.865531\pi$
$269$	−1.87377e13	−	3.24547e13i	−0.811108	−	1.40488i	0.100980	−	0.994888i	$-0.467802\pi$
$270$	1.92613e13	+	1.05534e13i	0.816932	+	0.447602i
$271$	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
$273$	1.56513e13	+	1.48925e13i	0.624678	+	0.594390i
$274$	−1.35026e13			−0.528190
$275$	2.61348e13	+	1.50889e13i	1.00205	+	0.578533i
$276$	−1.49080e13	+	2.74343e12i	−0.560300	+	0.103109i
$277$	−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	$0.0136402\pi$
$281$			2.51624e12i			0.0856776i	−0.999082	+	0.0428388i	$0.986360\pi$
$282$	2.31888e13	+	2.72206e13i	0.774297	+	0.908924i
$283$	−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
$285$	8.25141e12	+	9.68608e12i	0.259945	+	0.305142i
$286$		−	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
$291$	6.39606e12	−	1.17703e12i	0.179681	−	0.0330655i
$292$	−1.33929e13	−	7.73240e12i	−0.369206	−	0.213161i
$293$	−1.68636e13			−0.456224			−0.228112	−	0.973635i	$-0.573255\pi$
$293$	−1.68636e13			−0.456224			−0.228112	+	0.973635i	$0.573255\pi$
$294$	−2.11053e13	−	1.62420e13i	−0.560379	−	0.431249i
$295$	5.30402e13			1.38224
$296$	−1.59073e13	−	9.18409e12i	−0.406904	−	0.234926i
$297$	−5.49490e13	−	3.01069e13i	−1.37975	−	0.755972i
$298$	−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
$303$	4.15045e13	−	3.53570e13i	0.933601	−	0.795319i
$304$	−2.98232e12	+	1.72184e12i	−0.0658794	+	0.0380355i
$305$	−1.62818e12	+	9.40032e11i	−0.0353227	+	0.0203936i
$306$	2.22610e13	+	5.84358e13i	0.474326	+	1.24512i
$307$		−	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	0.520704	−	0.853737i	$-0.325670\pi$
$311$	−2.45767e13	−	4.25681e13i	−0.479006	−	0.829663i	−0.999710	+	0.0240743i	$0.992336\pi$
$312$	2.88134e12	+	1.56574e13i	0.0551752	+	0.299827i
$313$	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
$315$	−6.46951e13	+	3.27512e13i	−1.17534	+	0.595003i
$316$	3.14987e13			0.562360
$317$	7.06341e13	+	4.07806e13i	1.23933	+	0.715530i	0.968958	−	0.247225i	$-0.0795187\pi$
$317$	7.06341e13	+	4.07806e13i	1.23933	+	0.715530i	0.270376	+	0.962755i	$0.412852\pi$
$318$	−8.65031e12	−	4.70065e13i	−0.149170	−	0.810604i
$319$	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
$324$	3.05105e13	+	1.00854e13i	0.474736	+	0.156926i
$325$	−3.58996e13	+	2.07267e13i	−0.549201	+	0.317081i
$326$	2.04079e13	−	1.17825e13i	0.306974	−	0.177232i
$327$	4.70143e13	−	4.00507e13i	0.695372	−	0.592376i
$328$		−	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
$333$	−1.57834e13	+	9.80378e13i	−0.211231	+	1.31205i
$334$	−1.22682e13	−	7.08303e12i	−0.161501	−	0.0932425i
$335$	−7.68273e13			−0.994877
$336$	−5.54854e12	−	1.88241e13i	−0.0706826	−	0.239800i
$337$	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
$339$	7.26281e13	−	1.33653e13i	0.881061	−	0.162136i
$340$	−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
$345$	−8.83671e13	−	1.03731e14i	−0.973387	−	1.14263i
$346$	−8.58321e13	+	4.95552e13i	−0.930532	+	0.537243i
$347$	2.47703e13	−	1.43011e13i	0.264313	−	0.152601i	−0.361987	−	0.932183i	$-0.617902\pi$
$347$	2.47703e13	−	1.43011e13i	0.264313	−	0.152601i	0.626301	+	0.779582i	$0.284568\pi$
$348$	−2.46712e13	−	2.89608e13i	−0.259122	−	0.304176i
$349$			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	0.756700	−	0.653763i	$-0.226811\pi$
$353$	−1.93426e13	−	3.35024e13i	−0.187825	−	0.325323i	−0.944525	+	0.328440i	$0.893477\pi$
$354$	7.63219e13	−	1.40450e13i	0.729678	−	0.134278i
$355$	4.25758e13	+	2.45812e13i	0.400781	+	0.231391i
$356$	8.57807e12			0.0795086
$357$	−2.00687e14	−	4.84651e13i	−1.83165	−	0.442337i
$358$	1.04702e14			0.941015
$359$	1.53290e14	+	8.85022e13i	1.35674	+	0.783312i	0.989182	−	0.146690i	$-0.0468621\pi$
$359$	1.53290e14	+	8.85022e13i	1.35674	+	0.783312i	0.367554	+	0.930002i	$0.380195\pi$
$360$	−5.27556e13	−	8.49329e12i	−0.459838	−	0.0740307i
$361$	−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
$366$	−2.09394e12	+	1.78380e12i	−0.0166655	+	0.0141971i
$367$	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
$369$	−9.97019e12	+	3.79813e12i	−0.0758680	+	0.0289018i
$370$		−	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
$375$	9.05788e12	+	4.92213e13i	0.0630746	+	0.342753i
$376$	−7.53433e13	−	4.34995e13i	−0.517025	−	0.298505i
$377$	−1.01897e14			−0.689105
$378$	−8.44201e13	+	6.42584e13i	−0.562653	+	0.428277i
$379$	−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
$381$	−2.83695e11	−	1.54162e12i	−0.00181036	−	0.00983763i
$382$	8.30444e13	+	1.43837e14i	0.522350	+	0.904737i
$383$	1.58093e13	−	2.73824e13i	0.0980208	−	0.169777i	−0.812845	−	0.582481i	$-0.802082\pi$
$383$	1.58093e13	−	2.73824e13i	0.0980208	−	0.169777i	0.910865	+	0.412704i	$0.135416\pi$
$384$	4.84472e12	−	1.36260e13i	0.0296106	−	0.0832809i
$385$	−2.78307e14	+	2.02173e14i	−1.67683	+	1.21812i
$386$		−	8.02354e13i		−	0.476580i
$387$	−1.32188e14	+	5.03567e13i	−0.774071	+	0.294881i
$388$	−1.37028e13	+	7.91130e12i	−0.0791104	+	0.0456744i
$389$	1.31115e14	−	7.56991e13i	0.746326	−	0.430892i	−0.0780387	−	0.996950i	$-0.524866\pi$
$389$	1.31115e14	−	7.56991e13i	0.746326	−	0.430892i	0.824365	+	0.566059i	$0.191532\pi$
$390$	−1.08946e14	+	9.28091e13i	−0.611442	+	0.520877i
$391$		−	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
$396$	1.50502e14	+	2.42298e13i	0.776637	+	0.125033i
$397$	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
$399$	−5.89574e13	+	1.73781e13i	−0.291869	+	0.0860302i
$400$	3.76551e13			0.183863
$401$	−1.88222e14	−	1.08670e14i	−0.906515	−	0.523377i	−0.0272071	−	0.999630i	$-0.508661\pi$
$401$	−1.88222e14	−	1.08670e14i	−0.906515	−	0.523377i	−0.879308	+	0.476253i	$0.841995\pi$
$402$	−1.10550e14	+	2.03439e13i	−0.525190	+	0.0966474i
$403$	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
$408$	−9.86585e13	−	1.15812e14i	−0.432020	−	0.507135i
$409$	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
$411$	−1.15168e14	−	1.35192e14i	−0.484397	−	0.568619i
$412$			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
$417$	−2.84123e14	+	5.22853e13i	−1.10346	+	0.203063i
$418$	7.64837e13	+	4.41579e13i	0.293156	+	0.169254i
$419$	4.42084e14			1.67235			0.836175	−	0.548462i	$-0.184786\pi$
$419$	4.42084e14			1.67235			0.836175	+	0.548462i	$0.184786\pi$
$420$	1.21611e14	−	1.27808e14i	0.454047	−	0.477183i
$421$	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
$423$	−7.47565e13	+	4.64346e14i	−0.268397	+	1.66713i
$424$	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
$429$	3.10802e14	−	2.64767e14i	1.03269	−	0.879729i
$430$	2.03706e14	−	1.17610e14i	0.668233	−	0.385805i
$431$	6.86139e13	−	3.96143e13i	0.222222	−	0.128300i	−0.384757	−	0.923018i	$-0.625715\pi$
$431$	6.86139e13	−	3.96143e13i	0.222222	−	0.128300i	0.606979	+	0.794718i	$0.292381\pi$
$432$	−7.81613e13	+	1.74830e12i	−0.249937	+	0.00559058i
$433$			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
$438$	−3.68132e13	−	2.00046e14i	−0.109118	−	0.592955i
$439$	−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
$441$	−1.73946e13	−	3.49845e14i	−0.0496595	−	0.998766i
$442$	−4.07480e14			−1.14890
$443$	2.43370e14	+	1.40510e14i	0.677714	+	0.391278i	0.798993	−	0.601340i	$-0.205366\pi$
$443$	2.43370e14	+	1.40510e14i	0.677714	+	0.391278i	−0.121279	+	0.992618i	$0.538700\pi$
$444$	−4.37245e13	−	2.37603e14i	−0.120259	−	0.653499i
$445$	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	$-0.771103\pi$
$449$		−	5.09422e14i		−	1.31742i	0.752399	−	0.658708i	$-0.228897\pi$
$450$	−7.24682e13	−	1.90231e14i	−0.185131	−	0.485974i
$451$	−4.38319e13	+	2.53064e13i	−0.110616	+	0.0638644i
$452$	−1.55597e14	+	8.98337e13i	−0.387917	+	0.223964i
$453$	5.01842e14	−	4.27511e14i	1.23602	−	1.05295i
$454$		−	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
$459$	−3.95205e14	+	7.21300e14i	−0.905426	+	1.65252i
$460$	2.87116e14	+	1.65766e14i	0.649964	+	0.375257i
$461$	−9.30351e13			−0.208109			−0.104055	−	0.994572i	$-0.533182\pi$
$461$	−9.30351e13			−0.208109			−0.104055	+	0.994572i	$0.533182\pi$
$462$	−3.46933e14	+	3.64611e14i	−0.766857	+	0.805933i
$463$	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
$465$	−1.19056e14	+	2.19091e13i	−0.253957	+	0.0467341i
$466$	7.22406e13	+	1.25124e14i	0.152286	+	0.263766i
$467$	8.21526e13	−	1.42292e14i	0.171151	−	0.296442i	−0.767672	−	0.640843i	$-0.778585\pi$
$467$	8.21526e13	−	1.42292e14i	0.171151	−	0.296442i	0.938822	+	0.344402i	$0.111918\pi$
$468$	−1.32191e14	+	1.62396e14i	−0.272176	+	0.334367i
$469$	1.50971e14	−	3.39024e14i	0.307215	−	0.689891i
$470$		−	7.82088e14i		−	1.57296i
$471$	5.74050e14	+	6.73860e14i	1.14113	+	1.33954i
$472$	−1.63510e14	+	9.44026e13i	−0.321265	+	0.185482i
$473$	−5.81136e14	+	3.35519e14i	−1.12860	+	0.651600i
$474$	2.68662e14	+	3.15375e14i	0.515734	+	0.605405i
$475$		−	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	0.778044	−	0.628210i	$-0.216212\pi$
$479$	−8.55545e13	−	1.48185e14i	−0.155024	−	0.268509i	−0.933068	+	0.359701i	$0.882879\pi$
$480$	1.27857e14	−	2.35288e13i	0.229034	−	0.0421476i
$481$	−5.60380e14	−	3.23535e14i	−0.992395	−	0.572959i
$482$	2.14925e14			0.376295
$483$	6.31394e14	−	1.86108e14i	1.09293	−	0.322148i
$484$	4.30992e14			0.737598
$485$	−1.23183e14	−	7.11195e13i	−0.208435	−	0.120340i
$486$	1.59256e14	+	3.91502e14i	0.266438	+	0.654989i
$487$	−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	$0.226532\pi$
$491$			8.25959e14i			1.30620i	−0.757271	+	0.653101i	$0.773468\pi$
$492$	1.97596e13	−	1.68329e13i	0.0309009	−	0.0263239i
$493$	8.43293e14	−	4.86875e14i	1.30413	−	0.752939i
$494$	−1.05061e14	+	6.06568e13i	−0.160673	+	0.0927643i
$495$	4.87842e14	+	1.28060e15i	0.737821	+	1.93680i
$496$		−	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
$501$	−3.37216e13	−	1.83246e14i	−0.0477310	−	0.259374i
$502$	−1.13582e14	−	6.55765e13i	−0.159015	−	0.0918074i
$503$	−6.87652e14			−0.952236			−0.476118	−	0.879381i	$-0.657956\pi$
$503$	−6.87652e14			−0.952236			−0.476118	+	0.879381i	$0.657956\pi$
$504$	1.41148e14	−	2.16110e14i	0.193333	−	0.296011i
$505$	−1.19249e15			−1.61566
$506$	−8.19088e14	−	4.72901e14i	−1.09775	−	0.633785i
$507$	−3.50134e13	−	1.90266e14i	−0.0464184	−	0.252241i
$508$	1.90683e12	+	3.30273e12i	0.00250070	+	0.00433135i
$509$	−8.97516e13	+	1.55454e14i	−0.116438	+	0.201676i	−0.918354	−	0.395761i	$-0.870481\pi$
$509$	−8.97516e13	+	1.55454e14i	−0.116438	+	0.201676i	0.801916	+	0.597437i	$0.203814\pi$
$510$	4.58174e14	−	1.28863e15i	0.588024	−	1.65384i
$511$	6.13480e14	+	2.73189e14i	0.778907	+	0.346855i
$512$			3.51844e13i			0.0441942i
$513$	5.47571e12	+	2.44802e14i	0.00680449	+	0.304208i
$514$	−3.63269e13	+	2.09733e13i	−0.0446613	+	0.0257852i
$515$	−2.76903e14	+	1.59870e14i	−0.336813	+	0.194459i
$516$	2.61979e14	−	2.23176e14i	0.315278	−	0.268580i
$517$			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	0.751569	−	0.659654i	$-0.229297\pi$
$521$	−1.71293e14	−	2.96687e14i	−0.195493	−	0.338604i	−0.947062	+	0.321051i	$0.895964\pi$
$522$	7.95357e13	−	4.94031e14i	0.0898202	−	0.557913i
$523$	−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
$525$	6.53313e14	+	1.57773e14i	0.714899	+	0.172646i
$526$	−2.57477e14			−0.278815
$527$	−2.98488e14	−	1.72332e14i	−0.319866	−	0.184675i
$528$	−3.64754e14	+	6.71233e13i	−0.386824	+	0.0711847i
$529$	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
$534$	7.31650e13	+	8.58861e13i	0.0729166	+	0.0855945i
$535$	−1.76057e15	+	1.01646e15i	−1.73663	+	1.00264i
$536$	2.36840e14	−	1.36740e14i	0.231232	−	0.133502i
$537$	8.93032e14	+	1.04830e15i	0.862995	+	1.01304i
$538$			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
$543$	9.50915e14	−	1.74991e14i	0.864456	−	0.159080i
$544$	3.20554e14	+	1.85072e14i	0.288474	+	0.166551i
$545$	−1.35079e15			−1.20339
$546$	−1.95463e14	−	6.63133e14i	−0.172387	−	0.584845i
$547$	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
$549$	−3.57198e13	−	5.75064e12i	−0.0305676	−	0.00492117i
$550$	−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
$555$	1.65326e15	−	1.40838e15i	1.33269	−	1.13530i
$556$	6.08698e14	−	3.51432e14i	0.485837	−	0.280498i
$557$	4.84175e14	−	2.79539e14i	0.382647	−	0.220922i	−0.296322	−	0.955088i	$-0.595760\pi$
$557$	4.84175e14	−	2.79539e14i	0.382647	−	0.220922i	0.678969	+	0.734166i	$0.262427\pi$
$558$	−1.65513e14	+	6.30520e13i	−0.129522	+	0.0493414i
$559$		−	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	0.892960	−	0.450135i	$-0.148624\pi$
$563$	7.60339e13	+	1.31695e14i	0.0566514	+	0.0981232i	−0.836309	+	0.548259i	$0.815291\pi$
$564$	−2.07097e14	−	1.12538e15i	−0.152805	−	0.830356i
$565$	−1.39875e15	−	8.07571e14i	−1.02206	−	0.590084i
$566$	1.30860e15			0.946928
$567$	−1.36342e15	−	2.97159e14i	−0.977063	−	0.212952i
$568$	−1.75001e14			−0.124201
$569$	2.07398e15	+	1.19741e15i	1.45776	+	0.841640i	0.998901	−	0.0468676i	$-0.0149239\pi$
$569$	2.07398e15	+	1.19741e15i	1.45776	+	0.841640i	0.458862	+	0.888508i	$0.348257\pi$
$570$	−7.36925e13	−	4.00451e14i	−0.0512993	−	0.278765i
$571$	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
$576$	1.77749e14	−	6.77133e13i	0.116811	−	0.0444990i
$577$	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
$579$	8.03341e14	−	6.84353e14i	0.513059	−	0.437067i
$580$			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
$585$	−1.85846e15	−	2.99200e14i	−1.12149	−	0.180553i
$586$	4.67338e14	+	2.69818e14i	0.279379	+	0.161300i
$587$	−2.28937e15			−1.35584			−0.677918	−	0.735138i	$-0.737117\pi$
$587$	−2.28937e15			−1.35584			−0.677918	+	0.735138i	$0.737117\pi$
$588$	3.25017e14	+	7.87795e14i	0.190691	+	0.462209i
$589$	−1.02612e14			−0.0596437
$590$	−1.46989e15	−	8.48643e14i	−0.846447	−	0.488696i
$591$	−1.87055e15	+	3.44225e14i	−1.06718	+	0.196386i
$592$	2.93891e14	+	5.09034e14i	0.166118	+	0.287725i
$593$	4.28615e14	−	7.42384e14i	0.240031	−	0.415745i	−0.720692	−	0.693255i	$-0.756176\pi$
$593$	4.28615e14	−	7.42384e14i	0.240031	−	0.415745i	0.960723	+	0.277510i	$0.0895091\pi$
$594$	1.04108e15	+	1.71353e15i	0.577642	+	0.950751i
$595$	2.65387e15	+	3.65326e15i	1.45893	+	2.00834i
$596$			2.44003e14i			0.132905i
$597$	−1.61151e15	−	1.89170e15i	−0.869708	−	1.02092i
$598$	1.12513e15	−	6.49593e14i	0.601652	−	0.347364i
$599$	9.62635e14	−	5.55777e14i	0.510052	−	0.294478i	−0.222803	−	0.974863i	$-0.571521\pi$
$599$	9.62635e14	−	5.55777e14i	0.510052	−	0.294478i	0.732855	+	0.680385i	$0.238187\pi$
$600$	3.21172e14	+	3.77014e14i	0.168619	+	0.197936i
$601$		−	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
$606$	−1.71592e15	+	3.15770e14i	−0.852899	+	0.156954i
$607$	−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
$609$	1.19686e15	+	1.13883e15i	0.578958	+	0.550887i
$610$	6.01620e13			0.0288409
$611$	−2.65418e15	−	1.53239e15i	−1.26097	−	0.728020i
$612$	3.18057e14	−	1.97560e15i	0.149752	−	0.930176i
$613$	−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	$0.102275\pi$
$617$			1.40288e15i			0.631613i	−0.948824	+	0.315807i	$0.897725\pi$
$618$	−3.56115e14	+	3.03368e14i	−0.158911	+	0.135373i
$619$	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
$621$	−5.86412e13	−	2.62167e15i	−0.0254800	−	1.13913i
$622$			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
$627$	2.10231e14	+	1.14241e15i	0.0866414	+	0.470816i
$628$	−1.86516e15	−	1.07685e15i	−0.761971	−	0.439924i
$629$	6.18354e15			2.50414
$630$	2.31690e15	+	1.27493e14i	0.930111	+	0.0511814i
$631$	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
$633$	−5.05526e14	−	2.74707e15i	−0.197707	−	1.07436i
$634$	−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
$639$	3.36795e14	+	8.84095e14i	0.125058	+	0.328280i
$640$	−2.73919e14	+	1.58147e14i	−0.100840	+	0.0582199i
$641$	−1.20432e15	+	6.95314e14i	−0.439565	+	0.253783i	−0.703413	−	0.710781i	$-0.748341\pi$
$641$	−1.20432e15	+	6.95314e14i	−0.439565	+	0.253783i	0.263848	+	0.964564i	$0.415008\pi$
$642$	−2.26420e15	+	1.92883e15i	−0.819355	+	0.697995i
$643$			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	0.515991	−	0.856594i	$-0.327424\pi$
$647$	−1.39531e15	−	2.41675e15i	−0.483836	−	0.838029i	−0.999828	+	0.0185649i	$0.994090\pi$
$648$	−6.84167e14	−	7.67663e14i	−0.235234	−	0.263942i
$649$	4.19333e15	+	2.42102e15i	1.42960	+	0.825377i
$650$	1.32651e15			0.448421
$651$	1.37272e14	−	5.68425e14i	0.0460138	−	0.190536i
$652$	−7.54081e14			−0.250643
$653$	3.65749e15	+	2.11165e15i	1.20548	+	0.695985i	0.961769	−	0.273863i	$-0.0883015\pi$
$653$	3.65749e15	+	2.11165e15i	1.20548	+	0.695985i	0.243712	+	0.969848i	$0.421635\pi$
$654$	−1.94371e15	+	3.57689e14i	−0.635263	+	0.116904i
$655$	−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	$-0.998845\pi$
$659$		−	2.31572e13i		−	0.00725800i	0.999993	−	0.00362900i	$-0.00115515\pi$
$660$	−2.16207e15	−	2.53799e15i	−0.672013	−	0.788856i
$661$	−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
$663$	−3.47552e15	−	4.07981e15i	−1.05365	−	1.23685i
$664$		−	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
$669$	−1.95699e15	+	3.60133e14i	−0.564606	+	0.103901i
$670$	2.12910e15	+	1.22924e15i	0.609235	+	0.351742i
$671$	−1.71631e14			−0.0487104
$672$	−1.47421e14	+	6.10446e14i	−0.0414980	+	0.171837i
$673$	−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
$675$	1.28655e15	−	2.34811e15i	0.353390	−	0.644983i
$676$	2.35340e14	+	4.07620e14i	0.0641192	+	0.111058i
$677$	2.33437e14	−	4.04325e14i	0.0630860	−	0.109268i	−0.832757	−	0.553638i	$-0.813239\pi$
$677$	2.33437e14	−	4.04325e14i	0.0630860	−	0.109268i	0.895843	+	0.444370i	$0.146572\pi$
$678$	−2.22657e15	−	7.91659e14i	−0.596862	−	0.212215i
$679$	5.55899e14	−	4.03827e14i	0.147813	−	0.107377i
$680$			3.32745e15i			0.877633i
$681$	2.13831e15	−	1.82159e15i	0.559450	−	0.476586i
$682$	−7.27646e14	+	4.20107e14i	−0.188845	+	0.109030i
$683$	1.47584e15	−	8.52077e14i	0.379949	−	0.219364i	−0.297847	−	0.954614i	$-0.596268\pi$
$683$	1.47584e15	−	8.52077e14i	0.379949	−	0.219364i	0.677796	+	0.735250i	$0.262935\pi$
$684$	−2.12079e14	−	5.56713e14i	−0.0541613	−	0.142175i
$685$			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
$690$	7.89197e14	+	4.28856e15i	0.192095	+	1.04386i
$691$	−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
$693$	−6.60969e15	−	3.63713e14i	−1.57090	−	0.0864422i
$694$	−9.15273e14			−0.215811
$695$	5.47196e15	+	3.15924e15i	1.28005	+	0.739036i
$696$	2.20336e14	+	1.19733e15i	0.0511370	+	0.277883i
$697$	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	$0.209206\pi$
$701$			5.47613e15i			1.22187i	−0.791681	+	0.610935i	$0.790794\pi$
$702$	−2.75345e15	+	6.15890e13i	−0.609570	+	0.0136348i
$703$	1.59430e15	−	9.20470e14i	0.350200	−	0.202188i
$704$	7.81439e14	−	4.51164e14i	0.170312	−	0.0983297i
$705$	7.83049e15	−	6.67066e15i	1.69336	−	1.44254i
$706$			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
$711$	−8.66120e14	+	5.37985e15i	−0.178770	+	1.11042i
$712$	−2.37722e14	−	1.37249e14i	−0.0486889	−	0.0281106i
$713$	1.09891e15			0.223341
$714$	4.78615e15	+	4.55409e15i	0.965263	+	0.918462i
$715$	−8.92979e15			−1.78714
$716$	−2.90157e15	−	1.67522e15i	−0.576252	−	0.332699i
$717$	−1.89878e15	+	3.49420e14i	−0.374213	+	0.0688640i
$718$	−2.83207e15	−	4.90529e15i	−0.553885	−	0.959357i
$719$	1.96809e15	−	3.40883e15i	0.381976	−	0.661602i	−0.609369	−	0.792887i	$-0.708577\pi$
$719$	1.96809e15	−	3.40883e15i	0.381976	−	0.661602i	0.991345	+	0.131285i	$0.0419104\pi$
$720$	1.32611e15	+	1.07946e15i	0.255418	+	0.207912i
$721$	−1.61343e14	−	1.53608e15i	−0.0308393	−	0.293609i
$722$			3.38255e15i			0.641637i
$723$	1.83316e15	+	2.15189e15i	0.345096	+	0.405098i
$724$	−2.03722e15	+	1.17619e15i	−0.380606	+	0.219743i
$725$	−2.74525e15	+	1.58497e15i	−0.509005	+	0.293874i
$726$	3.67606e15	+	4.31522e15i	0.676443	+	0.794056i
$727$		−	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
$732$	8.65698e13	−	1.59309e13i	0.0152249	−	0.00280175i
$733$	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
$735$	−4.67229e15	+	6.07132e15i	−0.803432	+	1.04401i
$736$	−1.18015e15			−0.201422
$737$	−6.07393e15	−	3.50678e15i	−1.02896	−	0.594070i
$738$	3.37072e14	+	5.42663e13i	0.0566778	+	0.00912473i
$739$	−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	$-0.891447\pi$
$743$		−	4.12866e15i		−	0.668914i	0.942411	−	0.334457i	$-0.108553\pi$
$744$	3.28026e14	−	2.79440e14i	0.0527543	−	0.0449405i
$745$	−1.89962e15	+	1.09675e15i	−0.303255	+	0.175084i
$746$	6.51105e15	−	3.75916e15i	1.03178	−	0.595699i
$747$	−9.63018e15	+	3.66860e15i	−1.51486	+	0.577081i
$748$		−	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
$753$	−3.12203e14	−	1.69654e15i	−0.0469964	−	0.255382i
$754$	2.82386e15	+	1.63036e15i	0.421989	+	0.243635i
$755$	−1.44186e16			−2.13903
$756$	3.36765e15	−	4.30060e14i	0.495972	−	0.0633373i
$757$	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
$759$	−2.25143e15	−	1.22345e16i	−0.324436	−	1.76301i
$760$	4.95319e14	+	8.57917e14i	0.0708614	+	0.122736i
$761$	−3.52244e15	+	6.10104e15i	−0.500297	+	0.866540i	0.499703	+	0.866197i	$0.333442\pi$
$761$	−3.52244e15	+	6.10104e15i	−0.500297	+	0.866540i	−1.00000		0.000342847i	$0.999891\pi$
$762$	−1.68040e13	+	4.72618e13i	−0.00236951	+	0.00666435i
$763$	2.65439e15	−	5.96077e15i	0.371604	−	0.834483i
$764$		−	5.31484e15i		−	0.738715i
$765$	1.68101e16	−	6.40377e15i	2.31970	−	0.883686i
$766$	−8.76238e14	+	5.05896e14i	−0.120050	+	0.0693111i
$767$	−5.76010e15	+	3.32560e15i	−0.783530	+	0.452371i
$768$	−3.52276e14	+	3.00098e14i	−0.0475770	+	0.0405300i
$769$			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	$0.267906\pi$
$773$	7.51186e15	+	1.30109e16i	0.978950	+	1.69559i	0.312718	+	0.949846i	$0.398761\pi$
$774$	4.46900e15	+	7.19478e14i	0.578276	+	0.0930984i
$775$	9.71694e14	+	5.61008e14i	0.124845	+	0.0720791i
$776$	5.06323e14			0.0645934
$777$	2.96616e15	+	1.00631e16i	0.375733	+	1.27472i
$778$	−4.84474e15			−0.609373
$779$	1.71297e14	+	9.88983e13i	0.0213941	+	0.0123519i
$780$	4.50414e15	−	8.28869e14i	0.558588	−	0.102793i
$781$	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
$786$	−5.16853e14	−	6.06718e14i	−0.0614530	−	0.0721379i
$787$	−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
$789$	−2.19610e15	−	2.57793e15i	−0.255699	−	0.300157i
$790$		−	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
$795$	−1.35223e16	+	2.48842e15i	−1.51018	+	0.277910i
$796$	5.23599e15	+	3.02300e15i	0.580734	+	0.335287i
$797$	−8.35758e15			−0.920577			−0.460288	−	0.887769i	$-0.652254\pi$
$797$	−8.35758e15			−0.920577			−0.460288	+	0.887769i	$0.652254\pi$
$798$	1.91193e15	+	4.61723e14i	0.209149	+	0.0505087i
$799$	2.92877e16			3.18183
$800$	−1.04353e15	−	6.02481e14i	−0.112592	−	0.0650053i
$801$	−2.35871e14	+	1.46510e15i	−0.0252752	+	0.156996i
$802$	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
$807$	−1.20069e16	+	1.02285e16i	−1.23488	+	1.05198i
$808$	3.67614e15	−	2.12242e15i	0.375517	−	0.216805i
$809$	4.86789e15	−	2.81048e15i	0.493883	−	0.285143i	−0.232301	−	0.972644i	$-0.574625\pi$
$809$	4.86789e15	−	2.81048e15i	0.493883	−	0.285143i	0.726184	+	0.687501i	$0.241292\pi$
$810$	2.90124e15	−	8.77690e15i	0.292358	−	0.884450i
$811$		−	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
$816$	8.81109e14	+	4.78802e15i	0.0852577	+	0.463297i
$817$	2.27110e15	+	1.31122e15i	0.218281	+	0.126025i
$818$	−6.91558e15			−0.660215
$819$	4.97232e15	−	7.61310e15i	0.471517	−	0.721938i
$820$	−5.67723e14			−0.0534762
$821$	−7.20379e15	−	4.15911e15i	−0.674021	−	0.389146i	0.123577	−	0.992335i	$-0.460563\pi$
$821$	−7.20379e15	−	4.15911e15i	−0.674021	−	0.389146i	−0.797599	+	0.603188i	$0.793897\pi$
$822$	1.02855e15	+	5.58924e15i	0.0955943	+	0.519467i
$823$	−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	$0.0175879\pi$
$827$			1.22872e15i			0.110452i	−0.998474	+	0.0552259i	$0.982412\pi$
$828$	2.27122e15	+	5.96202e15i	0.202812	+	0.532386i
$829$	−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
$831$	−1.56063e15	+	1.32947e15i	−0.136613	+	0.116379i
$832$			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
$837$	−2.04301e15	−	1.11938e15i	−0.171902	−	0.0941862i
$838$	−1.22514e16	−	7.07334e15i	−1.02410	−	0.591265i
$839$	−2.06376e16			−1.71383			−0.856917	−	0.515454i	$-0.827623\pi$
$839$	−2.06376e16			−1.71383			−0.856917	+	0.515454i	$0.827623\pi$
$840$	−5.41510e15	+	1.59613e15i	−0.446756	+	0.131684i
$841$	4.40841e15			0.361330
$842$	−6.13579e15	−	3.54250e15i	−0.499636	−	0.288465i
$843$	1.04157e15	−	1.91673e14i	0.0842628	−	0.0155063i
$844$	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
$849$	1.11615e16	+	1.31021e16i	0.868418	+	1.01941i
$850$	−1.09780e16	+	6.33818e15i	−0.848635	+	0.489960i
$851$	−1.70739e16	+	9.85761e15i	−1.31135	+	0.757110i
$852$	−1.49264e15	−	1.75216e15i	−0.113903	−	0.133708i
$853$		−	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	0.753553	−	0.657387i	$-0.228338\pi$
$857$	−2.60561e15	−	4.51305e15i	−0.192537	−	0.333485i	−0.946090	+	0.323903i	$0.895005\pi$
$858$	−1.28495e16	+	2.36461e15i	−0.943420	+	0.173612i
$859$	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
$861$	−7.77009e14	+	8.16603e14i	−0.0559640	+	0.0588157i
$862$	−2.53531e15			−0.181444
$863$	1.66155e16	+	9.59295e15i	1.18155	+	0.682171i	0.956374	−	0.292147i	$-0.0943695\pi$
$863$	1.66155e16	+	9.59295e15i	1.18155	+	0.682171i	0.225180	+	0.974317i	$0.427703\pi$
$864$	2.19404e15	+	1.20213e15i	0.155031	+	0.0849427i
$865$	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
$870$	−8.33109e15	+	7.09712e15i	−0.566691	+	0.482754i
$871$	8.34336e15	−	4.81704e15i	0.563951	−	0.325597i
$872$	4.16415e15	−	2.40418e15i	0.279696	−	0.161483i
$873$	−9.74432e14	−	2.55791e15i	−0.0650389	−	0.170729i
$874$			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
$879$	1.28457e15	+	6.98048e15i	0.0825696	+	0.448690i
$880$	7.02484e15	+	4.05579e15i	0.448726	+	0.259072i
$881$	1.00275e16			0.636537			0.318268	−	0.948001i	$-0.396899\pi$
$881$	1.00275e16			0.636537			0.318268	+	0.948001i	$0.396899\pi$
$882$	−5.11547e15	+	9.97351e15i	−0.322707	+	0.629174i
$883$	−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
$885$	−4.04030e15	−	2.19553e16i	−0.250165	−	1.35942i
$886$	−4.49631e15	−	7.78784e15i	−0.276676	−	0.479216i
$887$	8.53323e14	−	1.47800e15i	0.0521836	−	0.0903846i	−0.838754	−	0.544511i	$-0.816715\pi$
$887$	8.53323e14	−	1.47800e15i	0.0521836	−	0.0903846i	0.890937	+	0.454126i	$0.150049\pi$
$888$	−2.58991e15	+	7.28423e15i	−0.157403	+	0.442703i
$889$	−9.73330e13	−	1.33987e14i	−0.00587896	−	0.00809285i
$890$		−	2.46763e15i		−	0.148127i
$891$	−8.27669e15	+	2.50388e16i	−0.493775	+	1.49378i
$892$	4.19261e15	−	2.42060e15i	0.248587	−	0.143522i
$893$	7.55124e15	−	4.35971e15i	0.444975	−	0.256906i
$894$	−2.44303e15	+	2.08118e15i	−0.143078	+	0.121886i
$895$		−	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
$900$	−1.03540e15	+	6.43133e15i	−0.0584487	+	0.363051i
$901$	−3.39019e16	−	1.95733e16i	−1.90212	−	1.09819i
$902$	1.61961e15			0.0903179
$903$	−1.03018e16	+	1.08268e16i	−0.570993	+	0.600089i
$904$	5.74936e15			0.316733
$905$	−1.83138e16	−	1.05735e16i	−1.00279	−	0.578963i
$906$	−2.07476e16	+	3.81805e15i	−1.12918	+	0.207796i
$907$	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	$-0.969749\pi$
$911$		−	3.59436e15i		−	0.189789i	0.995487	−	0.0948943i	$-0.0302513\pi$
$912$	9.39912e14	+	1.10333e15i	0.0493305	+	0.0579076i
$913$	−4.23371e16	+	2.44434e16i	−2.20868	+	1.27518i
$914$	−1.42747e16	+	8.24152e15i	−0.740225	+	0.427369i
$915$	5.13140e14	+	6.02360e14i	0.0264497	+	0.0310485i
$916$			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
$921$	−1.46516e16	+	2.69624e15i	−0.728546	+	0.134070i
$922$	2.57826e15	+	1.48856e15i	0.127440	+	0.0735778i
$923$	−6.16491e15			−0.302913
$924$	1.54483e16	−	4.55347e15i	0.754542	−	0.222406i
$925$	−2.01298e16			−0.977373
$926$	−1.31456e16	−	7.58964e15i	−0.634485	−	0.366320i
$927$	−6.07483e15	−	9.78005e14i	−0.291471	−	0.0469248i
$928$	−1.48097e15	−	2.56512e15i	−0.0706371	−	0.122347i
$929$	1.88793e16	−	3.27000e16i	0.895159	−	1.55046i	0.0615515	−	0.998104i	$-0.480395\pi$
$929$	1.88793e16	−	3.27000e16i	0.895159	−	1.55046i	0.833608	−	0.552357i	$-0.186272\pi$
$930$	3.64992e15	+	1.29773e15i	0.172039	+	0.0611687i
$931$	−4.82646e15	+	4.34457e15i	−0.226155	+	0.203575i
$932$		−	4.62340e15i		−	0.215364i
$933$	−1.57484e16	+	1.34158e16i	−0.729269	+	0.621252i
$934$	−4.55336e15	+	2.62888e15i	−0.209616	+	0.121022i
$935$	7.39021e16	−	4.26674e16i	3.38215	−	1.95269i
$936$	6.26172e15	−	2.38539e15i	0.284889	−	0.108528i
$937$		−	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	$0.0396504\pi$
$941$	1.36641e16	+	2.36669e16i	0.603724	+	1.04568i	−0.388528	+	0.921437i	$0.627016\pi$
$942$	−5.12678e15	−	2.78594e16i	−0.225198	−	1.22375i
$943$	−1.83447e15	−	1.05913e15i	−0.0801120	−	0.0462527i
$944$	6.04176e15			0.262312
$945$	1.84851e16	+	2.42849e16i	0.797896	+	1.04824i
$946$	2.14732e16			0.921502
$947$	1.88592e16	+	1.08884e16i	0.804634	+	0.464555i	0.845089	−	0.534626i	$-0.179547\pi$
$947$	1.88592e16	+	1.08884e16i	0.804634	+	0.464555i	−0.0404551	+	0.999181i	$0.512881\pi$
$948$	−2.39940e15	−	1.30385e16i	−0.101779	−	0.553073i
$949$	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	$0.0136163\pi$
$953$			2.07547e15i			0.0855274i	−0.999085	+	0.0427637i	$0.986384\pi$
$954$	−1.87988e16	+	7.16138e15i	−0.770220	+	0.293414i
$955$	4.13773e16	−	2.38892e16i	1.68556	−	0.973157i
$956$	4.06789e15	−	2.34860e15i	0.164760	−	0.0951240i
$957$	2.37670e16	−	2.02468e16i	0.957105	−	0.815342i
$958$			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
$963$	−3.86241e16	−	6.21822e15i	−1.50284	−	0.241948i
$964$	−5.95617e15	−	3.43880e15i	−0.230432	−	0.133040i
$965$	−2.30811e16			−0.887886
$966$	−2.04754e16	−	4.94474e15i	−0.783175	−	0.189134i
$967$	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
$969$	1.49961e16	−	2.75964e15i	0.563895	−	0.103770i
$970$	2.27582e15	+	3.94184e15i	0.0850931	+	0.147386i
$971$	−2.13970e16	+	3.70607e16i	−0.795512	+	1.37787i	0.127002	+	0.991903i	$0.459465\pi$
$971$	−2.13970e16	+	3.70607e16i	−0.795512	+	1.37787i	−0.922514	+	0.385965i	$0.873869\pi$
$972$	1.85060e15	−	1.33977e16i	0.0684144	−	0.495297i
$973$	−2.46939e16	+	1.79386e16i	−0.907755	+	0.659428i
$974$			2.41094e16i			0.881278i
$975$	1.13142e16	+	1.32814e16i	0.411242	+	0.482745i
$976$	−1.85465e14	+	1.07078e14i	−0.00670329	+	0.00387014i
$977$	4.27464e16	−	2.46796e16i	1.53631	−	0.886990i	0.537261	−	0.843416i	$-0.319459\pi$
$977$	4.27464e16	−	2.46796e16i	1.53631	−	0.886990i	0.999050	−	0.0435742i	$-0.0138745\pi$
$978$	−6.43179e15	−	7.55008e15i	−0.229863	−	0.269829i
$979$			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	$0.0955268\pi$
$983$	2.11127e16	+	3.65683e16i	0.733669	+	1.27075i	−0.221636	+	0.975129i	$0.571140\pi$
$984$	−8.16922e14	+	1.50333e14i	−0.0282298	+	0.00519495i
$985$	3.60251e16	+	2.07991e16i	1.23796	+	0.714735i
$986$	−3.11600e16			−1.06482
$987$	1.40489e16	+	4.76628e16i	0.477418	+	1.61970i
$988$	3.88203e15			0.131189
$989$	−2.43220e16	−	1.40423e16i	−0.817372	−	0.471910i
$990$	6.97012e15	−	4.32945e16i	0.232941	−	1.44690i
$991$	−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
$996$	1.90858e16	−	1.62589e16i	0.616998	−	0.525610i
$997$	−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
$999$	4.17838e16	−	9.34616e14i	1.32861	−	0.0297182i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.7	✓	60	1.1	even	1	trivial
42.12.f.a.5.27	yes	60	3.2	odd	2	inner
42.12.f.a.17.7	yes	60	21.17	even	6	inner
42.12.f.a.17.27	yes	60	7.3	odd	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} +(-76.1744 - 413.938i) 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} +(-165542. + 63062.9i) q^{9} +(255107. - 147286. i) q^{10} +(-727772. + 420179. i) q^{11} +(328083. - 279488. 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} +(5.59664e6 + 901021. i) q^{18} +(2.84416e6 + 1.64208e6i) q^{19} -9.42630e6 q^{20} +(-1.29012e7 + 1.35586e7i) q^{21} +2.68915e7 q^{22} +(-3.04590e7 - 1.75855e7i) q^{23} +(-1.35639e7 + 2.49608e6i) 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} +(-8.03998e7 - 9.43789e7i) q^{30} +(-2.70586e7 + 1.56223e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(2.29366e8 + 2.69245e8i) 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} +(-4.77827e8 + 8.79315e7i) q^{39} +(2.61229e8 + 1.50821e8i) q^{40} +6.02276e7 q^{41} +(5.74467e8 - 1.69328e8i) q^{42} +7.98515e8 q^{43} +(-7.45238e8 - 4.30263e8i) q^{44} +(2.59195e8 - 1.60997e9i) 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} +(3.53431e9 - 3.01082e9i) q^{51} +(1.02368e9 - 5.91025e8i) q^{52} +(-3.07329e9 + 1.77436e9i) q^{53} +(-5.33540e7 - 2.38529e9i) 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} +(7.18042e8 + 3.90190e9i) q^{60} +(1.76873e8 + 1.02118e8i) q^{61} +9.99828e8 q^{62} +(6.59517e9 + 4.30748e9i) q^{63} -1.07374e9 q^{64} +(9.20253e9 + 5.31309e9i) q^{65} +(-2.04844e9 - 1.11314e10i) 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} +(2.06645e9 + 5.42448e9i) q^{72} +(-1.30790e10 + 7.55117e9i) q^{73} +(-1.55345e10 + 8.96884e9i) q^{74} +(-1.15055e10 + 9.80138e9i) 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} +(2.34272e10 - 2.08791e10i) q^{81} +(-1.66908e9 - 9.63641e8i) q^{82} +5.81737e10 q^{83} +(-1.86293e10 - 4.49892e9i) q^{84} -1.01546e11 q^{85} +(-2.21291e10 - 1.27762e10i) q^{86} +(-3.65395e10 + 6.72413e9i) 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} +(8.52784e9 + 1.00106e10i) q^{93} +(-7.35775e10 + 4.24800e10i) q^{94} +(-2.61815e10 + 1.51159e10i) q^{95} +(-9.15827e9 - 1.07506e10i) 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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