LMFDB - Embedded newform 13.14.e.a.10.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,14,Mod(4,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 14, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.4"); S:= CuspForms(chi, 14); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	13.e (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:	$13.9400207637$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.5
Character	$\chi$	$=$	13.10
Dual form			13.14.e.a.4.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-77.2063 + 44.5751i) q^{2} +(-1229.77 - 2130.03i) q^{3} +(-122.125 + 211.526i) q^{4} +52376.5i q^{5} +(189892. + 109634. i) q^{6} +(240349. + 138765. i) q^{7} -752093. i q^{8} +(-2.22751e6 + 3.85817e6i) q^{9} +(-2.33469e6 - 4.04379e6i) q^{10} +(-442330. + 255379. i) q^{11} +600742. q^{12} +(-1.01162e7 - 1.41611e7i) q^{13} -2.47419e7 q^{14} +(1.11563e8 - 6.44111e7i) q^{15} +(3.25242e7 + 5.63335e7i) q^{16} +(-2.88760e7 + 5.00148e7i) q^{17} -3.97166e8i q^{18} +(-7.66910e6 - 4.42776e6i) q^{19} +(-1.10790e7 - 6.39647e6i) q^{20} -6.82599e8i q^{21} +(2.27671e7 - 3.94338e7i) q^{22} +(-6.11385e7 - 1.05895e8i) q^{23} +(-1.60198e9 + 9.24902e8i) q^{24} -1.52259e9 q^{25} +(1.41227e9 + 6.42393e8i) q^{26} +7.03603e9 q^{27} +(-5.87051e7 + 3.38934e7i) q^{28} +(-1.59098e9 - 2.75565e9i) q^{29} +(-5.74226e9 + 9.94589e9i) q^{30} -6.44076e9i q^{31} +(3.13569e8 + 1.81039e8i) q^{32} +(1.08793e9 + 6.28117e8i) q^{33} -5.14861e9i q^{34} +(-7.26805e9 + 1.25886e10i) q^{35} +(-5.44070e8 - 9.42356e8i) q^{36} +(6.28084e9 - 3.62624e9i) q^{37} +7.89470e8 q^{38} +(-1.77228e10 + 3.89628e10i) q^{39} +3.93920e10 q^{40} +(-1.09022e10 + 6.29436e9i) q^{41} +(3.04269e10 + 5.27010e10i) q^{42} +(2.75756e10 - 4.77623e10i) q^{43} -1.24753e8i q^{44} +(-2.02077e11 - 1.16669e11i) q^{45} +(9.44056e9 + 5.45051e9i) q^{46} -9.82051e9i q^{47} +(7.99946e10 - 1.38555e11i) q^{48} +(-9.93280e9 - 1.72041e10i) q^{49} +(1.17554e11 - 6.78697e10i) q^{50} +1.42044e11 q^{51} +(4.23089e9 - 4.10433e8i) q^{52} +1.96740e11 q^{53} +(-5.43226e11 + 3.13631e11i) q^{54} +(-1.33759e10 - 2.31677e10i) q^{55} +(1.04365e11 - 1.80765e11i) q^{56} +2.17805e10i q^{57} +(2.45667e11 + 1.41836e11i) q^{58} +(1.79313e10 + 1.03526e10i) q^{59} +3.14648e10i q^{60} +(-8.84591e10 + 1.53216e11i) q^{61} +(2.87097e11 + 4.97267e11i) q^{62} +(-1.07076e12 + 6.18204e11i) q^{63} -5.65155e11 q^{64} +(7.41708e11 - 5.29854e11i) q^{65} -1.11993e11 q^{66} +(2.80090e10 - 1.61710e10i) q^{67} +(-7.05296e9 - 1.22161e10i) q^{68} +(-1.50373e11 + 2.60453e11i) q^{69} -1.29589e12i q^{70} +(-5.64453e11 - 3.25887e11i) q^{71} +(2.90170e12 + 1.67530e12i) q^{72} -1.91527e12i q^{73} +(-3.23280e11 + 5.59938e11i) q^{74} +(1.87244e12 + 3.24316e12i) q^{75} +(1.87317e9 - 1.08148e9i) q^{76} -1.41751e11 q^{77} +(-3.68455e11 - 3.79817e12i) q^{78} +6.28561e11 q^{79} +(-2.95055e12 + 1.70350e12i) q^{80} +(-5.10133e12 - 8.83576e12i) q^{81} +(5.61143e11 - 9.71929e11i) q^{82} +1.81049e12i q^{83} +(1.44388e11 + 8.33623e10i) q^{84} +(-2.61960e12 - 1.51243e12i) q^{85} +4.91673e12i q^{86} +(-3.91308e12 + 6.77765e12i) q^{87} +(1.92069e11 + 3.32673e11i) q^{88} +(7.28167e12 - 4.20407e12i) q^{89} +2.08022e13 q^{90} +(-4.66358e11 - 4.80739e12i) q^{91} +2.98661e10 q^{92} +(-1.37190e13 + 7.92067e12i) q^{93} +(4.37750e11 + 7.58205e11i) q^{94} +(2.31910e11 - 4.01680e11i) q^{95} -8.90547e11i q^{96} +(-4.23464e12 - 2.44487e12i) q^{97} +(1.53375e12 + 8.85511e11i) q^{98} -2.27544e12i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - 730 q^{3} + 65535 q^{4} - 382584 q^{6} + 438984 q^{7} - 9117071 q^{9} + 3893475 q^{10} - 5364528 q^{11} + 27694876 q^{12} - 1794135 q^{13} + 61125588 q^{14} - 113380170 q^{15} - 350182521 q^{16}+ \cdots + 86959564160763 q^{98}+O(q^{100}) $ 30 * q - 3 * q^2 - 730 * q^3 + 65535 * q^4 - 382584 * q^6 + 438984 * q^7 - 9117071 * q^9 + 3893475 * q^10 - 5364528 * q^11 + 27694876 * q^12 - 1794135 * q^13 + 61125588 * q^14 - 113380170 * q^15 - 350182521 * q^16 - 23524899 * q^17 + 92116746 * q^19 + 959687745 * q^20 - 128185362 * q^22 + 417086886 * q^23 - 4232784354 * q^24 - 11926991364 * q^25 + 5442553119 * q^26 + 5605403288 * q^27 + 22569369732 * q^28 - 8810189577 * q^29 - 9936679242 * q^30 + 9137241117 * q^32 + 12085621392 * q^33 + 1059240720 * q^35 + 55900963715 * q^36 - 72651649419 * q^37 - 45168847944 * q^38 - 41492436530 * q^39 + 137282090274 * q^40 - 3909896103 * q^41 - 34124964786 * q^42 + 138326640480 * q^43 - 259122942393 * q^45 - 288578831832 * q^46 + 630595691198 * q^48 + 114277635303 * q^49 - 553717814136 * q^50 - 178343342508 * q^51 - 1243882821894 * q^52 + 938994404670 * q^53 + 1180281528282 * q^54 - 140610123120 * q^55 + 932974200720 * q^56 - 768032047215 * q^58 - 1420851272556 * q^59 + 284498233437 * q^61 + 2574083847030 * q^62 - 3219361289664 * q^63 - 4989806279958 * q^64 - 931161533727 * q^65 + 12037245084948 * q^66 + 2624227676622 * q^67 - 3124046642277 * q^68 + 1206986427996 * q^69 - 1317657850698 * q^71 - 2571404508735 * q^72 + 1723434230073 * q^74 + 1909848151684 * q^75 - 5741418039246 * q^76 - 8153714196816 * q^77 - 13064083856250 * q^78 + 10732970056200 * q^79 + 11699811454875 * q^80 + 26873856445 * q^81 - 924448017327 * q^82 + 5758359493380 * q^84 - 14711656818213 * q^85 - 6442966126134 * q^87 - 11094606812688 * q^88 + 18293004024660 * q^89 + 53932182551466 * q^90 + 2271787574784 * q^91 - 48706576133844 * q^92 - 50634402753492 * q^93 + 3529466920146 * q^94 + 11308314514950 * q^95 - 4972913690148 * q^97 + 86959564160763 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−77.2063	+	44.5751i	−0.853017	+	0.492490i	−0.861668	−	0.507473i	$-0.830580\pi$
$2$	−77.2063	+	44.5751i	−0.853017	+	0.492490i	0.00865056	+	0.999963i	$0.497246\pi$
$3$	−1229.77	−	2130.03i	−0.973949	−	1.68693i	−0.683360	−	0.730081i	$-0.739482\pi$
$3$	−1229.77	−	2130.03i	−0.973949	−	1.68693i	−0.290589	−	0.956848i	$-0.593851\pi$
$4$	−122.125	+	211.526i	−0.0149078	+	0.0258211i
$5$			52376.5i			1.49910i	0.661946	+	0.749551i	$0.269731\pi$
$5$			52376.5i			1.49910i	−0.661946	+	0.749551i	$0.730269\pi$
$6$	189892.	+	109634.i	1.66159	+	0.959320i
$7$	240349.	+	138765.i	0.772155	+	0.445804i	0.833643	−	0.552304i	$-0.186251\pi$
$7$	240349.	+	138765.i	0.772155	+	0.445804i	−0.0614875	+	0.998108i	$0.519584\pi$
$8$		−	752093.i		−	1.01435i
$9$	−2.22751e6	+	3.85817e6i	−1.39715	+	2.41994i
$10$	−2.33469e6	−	4.04379e6i	−0.738292	−	1.27876i
$11$	−442330.	+	255379.i	−0.0752825	+	0.0434644i	−0.537169	−	0.843475i	$-0.680506\pi$
$11$	−442330.	+	255379.i	−0.0752825	+	0.0434644i	0.461886	+	0.886939i	$0.347173\pi$
$12$	600742.			0.0580778
$13$	−1.01162e7	−	1.41611e7i	−0.581283	−	0.813701i
$13$	−1.01162e7	−	1.41611e7i	−0.581283	−	0.813701i
$14$	−2.47419e7			−0.878216
$15$	1.11563e8	−	6.44111e7i	2.52888	−	1.46005i
$16$	3.25242e7	+	5.63335e7i	0.484648	+	0.839434i
$17$	−2.88760e7	+	5.00148e7i	−0.290148	+	0.502551i	−0.973845	−	0.227215i	$-0.927038\pi$
$17$	−2.88760e7	+	5.00148e7i	−0.290148	+	0.502551i	0.683696	+	0.729767i	$0.260371\pi$
$18$		−	3.97166e8i		−	2.75234i
$19$	−7.66910e6	−	4.42776e6i	−0.0373978	−	0.0215916i	0.481185	−	0.876619i	$-0.340207\pi$
$19$	−7.66910e6	−	4.42776e6i	−0.0373978	−	0.0215916i	−0.518582	+	0.855028i	$0.673540\pi$
$20$	−1.10790e7	−	6.39647e6i	−0.0387085	−	0.0223483i
$21$		−	6.82599e8i		−	1.73676i
$22$	2.27671e7	−	3.94338e7i	0.0428115	−	0.0741517i
$23$	−6.11385e7	−	1.05895e8i	−0.0861160	−	0.149157i	0.819750	−	0.572721i	$-0.194112\pi$
$23$	−6.11385e7	−	1.05895e8i	−0.0861160	−	0.149157i	−0.905866	+	0.423564i	$0.860779\pi$
$24$	−1.60198e9	+	9.24902e8i	−1.71113	+	0.987922i
$25$	−1.52259e9			−1.24731
$26$	1.41227e9	+	6.42393e8i	0.896584	+	0.407825i
$27$	7.03603e9			3.49513
$28$	−5.87051e7	+	3.38934e7i	−0.0230223	+	0.0132919i
$29$	−1.59098e9	−	2.75565e9i	−0.496680	−	0.860276i	0.503312	−	0.864105i	$-0.332115\pi$
$29$	−1.59098e9	−	2.75565e9i	−0.496680	−	0.860276i	−0.999993	+	0.00382901i	$0.998781\pi$
$30$	−5.74226e9	+	9.94589e9i	−1.43812	+	2.49089i
$31$		−	6.44076e9i		−	1.30343i	−0.758466	−	0.651713i	$-0.774051\pi$
$31$		−	6.44076e9i		−	1.30343i	0.758466	−	0.651713i	$-0.225949\pi$
$32$	3.13569e8	+	1.81039e8i	0.0516248	+	0.0298056i
$33$	1.08793e9	+	6.28117e8i	0.146643	+	0.0846642i
$34$		−	5.14861e9i		−	0.571580i
$35$	−7.26805e9	+	1.25886e10i	−0.668306	+	1.15754i
$36$	−5.44070e8	−	9.42356e8i	−0.0416570	−	0.0721521i
$37$	6.28084e9	−	3.62624e9i	0.402445	−	0.232352i	−0.285094	−	0.958500i	$-0.592025\pi$
$37$	6.28084e9	−	3.62624e9i	0.402445	−	0.232352i	0.687538	+	0.726148i	$0.258691\pi$
$38$	7.89470e8			0.0425346
$39$	−1.77228e10	+	3.89628e10i	−0.806516	+	1.77309i
$40$	3.93920e10			1.52061
$41$	−1.09022e10	+	6.29436e9i	−0.358441	+	0.206946i	−0.668397	−	0.743805i	$-0.733019\pi$
$41$	−1.09022e10	+	6.29436e9i	−0.358441	+	0.206946i	0.309956	+	0.950751i	$0.399686\pi$
$42$	3.04269e10	+	5.27010e10i	0.855337	+	1.48149i
$43$	2.75756e10	−	4.77623e10i	0.665241	−	1.15223i	−0.313978	−	0.949430i	$-0.601662\pi$
$43$	2.75756e10	−	4.77623e10i	0.665241	−	1.15223i	0.979220	−	0.202802i	$-0.0650047\pi$
$44$		−	1.24753e8i		−	0.00259184i
$45$	−2.02077e11	−	1.16669e11i	−3.62774	−	2.09448i
$46$	9.44056e9	+	5.45051e9i	0.146917	+	0.0848225i
$47$		−	9.82051e9i		−	0.132892i	−0.997790	−	0.0664459i	$-0.978834\pi$
$47$		−	9.82051e9i		−	0.132892i	0.997790	−	0.0664459i	$-0.0211660\pi$
$48$	7.99946e10	−	1.38555e11i	0.944044	−	1.63513i
$49$	−9.93280e9	−	1.72041e10i	−0.102517	−	0.177565i
$50$	1.17554e11	−	6.78697e10i	1.06397	−	0.614286i
$51$	1.42044e11			1.13036
$52$	4.23089e9	−	4.10433e8i	0.0296763	−	0.00287886i
$53$	1.96740e11			1.21927			0.609635	−	0.792682i	$-0.291316\pi$
$53$	1.96740e11			1.21927			0.609635	+	0.792682i	$0.291316\pi$
$54$	−5.43226e11	+	3.13631e11i	−2.98140	+	1.72131i
$55$	−1.33759e10	−	2.31677e10i	−0.0651575	−	0.112856i
$56$	1.04365e11	−	1.80765e11i	0.452200	−	0.783234i
$57$			2.17805e10i			0.0841165i
$58$	2.45667e11	+	1.41836e11i	0.847354	+	0.489220i
$59$	1.79313e10	+	1.03526e10i	0.0553444	+	0.0319531i	0.527417	−	0.849607i	$-0.323161\pi$
$59$	1.79313e10	+	1.03526e10i	0.0553444	+	0.0319531i	−0.472072	+	0.881560i	$0.656494\pi$
$60$			3.14648e10i			0.0870646i
$61$	−8.84591e10	+	1.53216e11i	−0.219836	+	0.380767i	−0.954758	−	0.297385i	$-0.903885\pi$
$61$	−8.84591e10	+	1.53216e11i	−0.219836	+	0.380767i	0.734922	+	0.678152i	$0.237219\pi$
$62$	2.87097e11	+	4.97267e11i	0.641924	+	1.11184i
$63$	−1.07076e12	+	6.18204e11i	−2.15764	+	1.24571i
$64$	−5.65155e11			−1.02801
$65$	7.41708e11	−	5.29854e11i	1.21982	−	0.871403i
$66$	−1.11993e11			−0.166785
$67$	2.80090e10	−	1.61710e10i	0.0378278	−	0.0218399i	−0.480967	−	0.876739i	$-0.659714\pi$
$67$	2.80090e10	−	1.61710e10i	0.0378278	−	0.0218399i	0.518795	+	0.854899i	$0.326381\pi$
$68$	−7.05296e9	−	1.22161e10i	−0.00865095	−	0.0149839i
$69$	−1.50373e11	+	2.60453e11i	−0.167745	+	0.290543i
$70$		−	1.29589e12i		−	1.31654i
$71$	−5.64453e11	−	3.25887e11i	−0.522936	−	0.301917i	0.215199	−	0.976570i	$-0.430960\pi$
$71$	−5.64453e11	−	3.25887e11i	−0.522936	−	0.301917i	−0.738135	+	0.674653i	$0.764293\pi$
$72$	2.90170e12	+	1.67530e12i	2.45466	+	1.41720i
$73$		−	1.91527e12i		−	1.48126i	−0.671914	−	0.740629i	$-0.734527\pi$
$73$		−	1.91527e12i		−	1.48126i	0.671914	−	0.740629i	$-0.265473\pi$
$74$	−3.23280e11	+	5.59938e11i	−0.228862	+	0.396400i
$75$	1.87244e12	+	3.24316e12i	1.21481	+	2.10412i
$76$	1.87317e9	−	1.08148e9i	0.00111504	−	0.000643768i
$77$	−1.41751e11			−0.0775064
$78$	−3.68455e11	−	3.79817e12i	−0.185255	−	1.90967i
$79$	6.28561e11			0.290919			0.145459	−	0.989364i	$-0.453534\pi$
$79$	6.28561e11			0.290919			0.145459	+	0.989364i	$0.453534\pi$
$80$	−2.95055e12	+	1.70350e12i	−1.25840	+	0.726536i
$81$	−5.10133e12	−	8.83576e12i	−2.00692	−	3.47609i
$82$	5.61143e11	−	9.71929e11i	0.203837	−	0.353057i
$83$			1.81049e12i			0.607837i	0.952698	+	0.303919i	$0.0982951\pi$
$83$			1.81049e12i			0.607837i	−0.952698	+	0.303919i	$0.901705\pi$
$84$	1.44388e11	+	8.33623e10i	0.0448451	+	0.0258913i
$85$	−2.61960e12	−	1.51243e12i	−0.753376	−	0.434962i
$86$			4.91673e12i			1.31050i
$87$	−3.91308e12	+	6.77765e12i	−0.967483	+	1.67573i
$88$	1.92069e11	+	3.32673e11i	0.0440880	+	0.0763626i
$89$	7.28167e12	−	4.20407e12i	1.55309	−	0.896675i	0.555199	−	0.831718i	$-0.312642\pi$
$89$	7.28167e12	−	4.20407e12i	1.55309	−	0.896675i	0.997888	−	0.0649575i	$-0.0206912\pi$
$90$	2.08022e13			4.12603
$91$	−4.66358e11	−	4.80739e12i	−0.0860895	−	0.887442i
$92$	2.98661e10			0.00513521
$93$	−1.37190e13	+	7.92067e12i	−2.19879	+	1.26947i
$94$	4.37750e11	+	7.58205e11i	0.0654478	+	0.113359i
$95$	2.31910e11	−	4.01680e11i	0.0323680	−	0.0560631i
$96$		−	8.90547e11i		−	0.116117i
$97$	−4.23464e12	−	2.44487e12i	−0.516179	−	0.298016i	0.219191	−	0.975682i	$-0.429658\pi$
$97$	−4.23464e12	−	2.44487e12i	−0.516179	−	0.298016i	−0.735370	+	0.677666i	$0.762992\pi$
$98$	1.53375e12	+	8.85511e11i	0.174898	+	0.100977i
$99$		−	2.27544e12i		−	0.242906i
$100$	1.85946e11	−	3.22068e11i	0.0185946	−	0.0322068i
$101$	2.30401e12	+	3.99066e12i	0.215971	+	0.374072i	0.953572	−	0.301164i	$-0.0973751\pi$
$101$	2.30401e12	+	3.99066e12i	0.215971	+	0.374072i	−0.737602	+	0.675236i	$0.764042\pi$
$102$	−1.09667e13	+	6.33161e12i	−0.964215	+	0.556690i
$103$	−1.12611e13			−0.929263			−0.464632	−	0.885504i	$-0.653813\pi$
$103$	−1.12611e13			−0.929263			−0.464632	+	0.885504i	$0.653813\pi$
$104$	−1.06505e13	+	7.60836e12i	−0.825376	+	0.589623i
$105$	3.57521e13			2.60358
$106$	−1.51896e13	+	8.76971e12i	−1.04006	+	0.600478i
$107$	6.96037e12	+	1.20557e13i	0.448372	+	0.776602i	0.998280	−	0.0586225i	$-0.0186708\pi$
$107$	6.96037e12	+	1.20557e13i	0.448372	+	0.776602i	−0.549909	+	0.835225i	$0.685337\pi$
$108$	−8.59274e11	+	1.48831e12i	−0.0521047	+	0.0902480i
$109$		−	2.65647e13i		−	1.51716i	−0.651578	−	0.758581i	$-0.725893\pi$
$109$		−	2.65647e13i		−	1.51716i	0.651578	−	0.758581i	$-0.274107\pi$
$110$	2.06540e12	+	1.19246e12i	0.111161	+	0.0641788i
$111$	−1.54480e13	−	8.91890e12i	−0.783921	−	0.452597i
$112$			1.80529e13i			0.864232i
$113$	−2.66216e12	+	4.61099e12i	−0.120288	+	0.208346i	−0.919881	−	0.392197i	$-0.871715\pi$
$113$	−2.66216e12	+	4.61099e12i	−0.120288	+	0.208346i	0.799593	+	0.600542i	$0.205049\pi$
$114$	−9.70868e11	−	1.68159e12i	−0.0414265	−	0.0717529i
$115$	5.54641e12	−	3.20222e12i	0.223602	−	0.129097i
$116$	7.77191e11			0.0296177
$117$	7.71700e13	−	7.48615e12i	2.78125	−	0.269805i
$118$	−1.84588e12			−0.0629463
$119$	−1.38806e13	+	8.01400e12i	−0.448079	+	0.258698i
$120$	−4.84431e13	−	8.39060e13i	−1.48100	−	2.56516i
$121$	−1.71309e13	+	2.96716e13i	−0.496222	+	0.859481i
$122$		−	1.57723e13i		−	0.433067i
$123$	2.68143e13	+	1.54813e13i	0.698206	+	0.403109i
$124$	1.36239e12	+	7.86577e11i	0.0336559	+	0.0194312i
$125$		−	1.58119e13i		−	0.370740i
$126$	5.51130e13	−	9.54585e13i	1.22700	−	2.12523i
$127$	−3.26610e13	−	5.65706e13i	−0.690726	−	1.19637i	−0.971600	−	0.236628i	$-0.923958\pi$
$127$	−3.26610e13	−	5.65706e13i	−0.690726	−	1.19637i	0.280875	−	0.959744i	$-0.409375\pi$
$128$	4.10648e13	−	2.37088e13i	0.825286	−	0.476479i
$129$	−1.35647e14			−2.59165
$130$	−3.36463e13	+	7.39697e13i	−0.611372	+	1.34407i
$131$	5.19907e13			0.898798			0.449399	−	0.893331i	$-0.351638\pi$
$131$	5.19907e13			0.898798			0.449399	+	0.893331i	$0.351638\pi$
$132$	−2.65726e11	+	1.53417e11i	−0.00437224	+	0.00252432i
$133$	−1.22884e12	−	2.12841e12i	−0.0192513	−	0.0333442i
$134$	−1.44165e12	+	2.49700e12i	−0.0215118	+	0.0372596i
$135$			3.68522e14i			5.23955i
$136$	3.76158e13	+	2.17175e13i	0.509761	+	0.294311i
$137$	3.74702e13	+	2.16334e13i	0.484175	+	0.279538i	0.722155	−	0.691732i	$-0.243152\pi$
$137$	3.74702e13	+	2.16334e13i	0.484175	+	0.279538i	−0.237980	+	0.971270i	$0.576485\pi$
$138$		−	2.68115e13i		−	0.330451i
$139$	5.34124e13	−	9.25130e13i	0.628125	−	1.08794i	−0.359803	−	0.933028i	$-0.617156\pi$
$139$	5.34124e13	−	9.25130e13i	0.628125	−	1.08794i	0.987928	−	0.154916i	$-0.0495106\pi$
$140$	−1.77522e12	−	3.07477e12i	−0.0199260	−	0.0345128i
$141$	−2.09180e13	+	1.20770e13i	−0.224179	+	0.129430i
$142$	5.81058e13			0.594764
$143$	8.09117e12	+	3.68040e12i	0.0791275	+	0.0359924i
$144$	−2.89792e14			−2.70851
$145$	1.44331e14	−	8.33298e13i	1.28964	−	0.744575i
$146$	8.53732e13	+	1.47871e14i	0.729505	+	1.26354i
$147$	−2.44301e13	+	4.23143e13i	−0.199693	+	0.345879i
$148$			1.77142e12i			0.0138554i
$149$	7.61300e12	+	4.39537e12i	0.0569961	+	0.0329067i	0.528227	−	0.849103i	$-0.322857\pi$
$149$	7.61300e12	+	4.39537e12i	0.0569961	+	0.0329067i	−0.471231	+	0.882010i	$0.656190\pi$
$150$	−2.89128e14	−	1.66928e14i	−2.07251	−	1.19657i
$151$			9.65175e13i			0.662607i	0.943524	+	0.331304i	$0.107488\pi$
$151$			9.65175e13i			0.662607i	−0.943524	+	0.331304i	$0.892512\pi$
$152$	−3.33008e12	+	5.76787e12i	−0.0219014	+	0.0379343i
$153$	−1.28644e14	−	2.22817e14i	−0.810763	−	1.40428i
$154$	1.09441e13	−	6.31858e12i	0.0661143	−	0.0381711i
$155$	3.37344e14			1.95397
$156$	−6.07726e12	−	8.50717e12i	−0.0337597	−	0.0472580i
$157$	2.03625e14			1.08513			0.542566	−	0.840013i	$-0.317453\pi$
$157$	2.03625e14			1.08513			0.542566	+	0.840013i	$0.317453\pi$
$158$	−4.85289e13	+	2.80182e13i	−0.248159	+	0.143274i
$159$	−2.41945e14	−	4.19062e14i	−1.18751	−	2.05682i
$160$	−9.48219e12	+	1.64236e13i	−0.0446816	+	0.0773908i
$161$		−	3.39356e13i		−	0.153563i
$162$	7.87709e14	+	4.54784e14i	3.42388	+	1.97678i
$163$	−2.18113e14	−	1.25927e14i	−0.910881	−	0.525897i	−0.0301664	−	0.999545i	$-0.509604\pi$
$163$	−2.18113e14	−	1.25927e14i	−0.910881	−	0.525897i	−0.880714	+	0.473648i	$0.842937\pi$
$164$		−	3.07479e12i		−	0.0123404i
$165$	−3.28985e13	+	5.69819e13i	−0.126920	+	0.219832i
$166$	−8.07025e13	−	1.39781e14i	−0.299354	−	0.518496i
$167$	1.80997e14	−	1.04499e14i	0.645676	−	0.372781i	−0.141122	−	0.989992i	$-0.545071\pi$
$167$	1.80997e14	−	1.04499e14i	0.645676	−	0.372781i	0.786798	+	0.617211i	$0.211737\pi$
$168$	−5.13378e14			−1.76168
$169$	−9.81981e13	+	2.86514e14i	−0.324220	+	0.945982i
$170$	2.69666e14			0.856857
$171$	3.41660e13	−	1.97258e13i	0.104501	−	0.0603336i
$172$	6.73532e12	+	1.16659e13i	0.0198346	+	0.0343545i
$173$	−1.43930e14	+	2.49295e14i	−0.408181	+	0.706990i	−0.994686	−	0.102955i	$-0.967170\pi$
$173$	−1.43930e14	+	2.49295e14i	−0.408181	+	0.706990i	0.586505	+	0.809946i	$0.300503\pi$
$174$		−	6.97703e14i		−	1.90590i
$175$	−3.65953e14	−	2.11283e14i	−0.963116	−	0.556055i
$176$	−2.87728e13	−	1.66120e13i	−0.0729710	−	0.0421298i
$177$		−	5.09256e13i		−	0.124483i
$178$	−3.74794e14	+	6.49162e14i	−0.883207	+	1.52976i
$179$	−2.21596e14	−	3.83815e14i	−0.503520	−	0.872122i	−0.999992	−	0.00406946i	$-0.998705\pi$
$179$	−2.21596e14	−	3.83815e14i	−0.503520	−	0.872122i	0.496472	−	0.868053i	$-0.334629\pi$
$180$	4.93573e13	−	2.84964e13i	0.108163	−	0.0624481i
$181$	−4.30196e14			−0.909402			−0.454701	−	0.890644i	$-0.650254\pi$
$181$	−4.30196e14			−0.909402			−0.454701	+	0.890644i	$0.650254\pi$
$182$	2.50295e14	+	3.50373e14i	0.510492	+	0.714605i
$183$	4.35138e14			0.856436
$184$	−7.96429e13	+	4.59818e13i	−0.151297	+	0.0873515i
$185$	1.89930e14	+	3.28968e14i	0.348319	+	0.603306i
$186$	7.06129e14	−	1.22305e15i	1.25040	−	2.16576i
$187$		−	2.94974e13i		−	0.0504444i
$188$	2.07730e12	+	1.19933e12i	0.00343141	+	0.00198113i
$189$	1.69110e15	+	9.76358e14i	2.69878	+	1.55814i
$190$			4.13497e13i			0.0637637i
$191$	−3.40822e14	+	5.90320e14i	−0.507937	+	0.879773i	0.492020	+	0.870584i	$0.336259\pi$
$191$	−3.40822e14	+	5.90320e14i	−0.507937	+	0.879773i	−0.999958	+	0.00918975i	$0.997075\pi$
$192$	6.95012e14	+	1.20380e15i	1.00123	+	1.73418i
$193$	−6.82719e14	+	3.94168e14i	−0.950866	+	0.548983i	−0.893350	−	0.449362i	$-0.851651\pi$
$193$	−6.82719e14	+	3.94168e14i	−0.950866	+	0.548983i	−0.0575162	+	0.998345i	$0.518318\pi$
$194$	4.35921e14			0.587080
$195$	−2.04073e15	−	9.28260e14i	−2.65804	−	1.20905i
$196$	4.85217e12			0.00611324
$197$	−8.15687e14	+	4.70937e14i	−0.994244	+	0.574027i	−0.906540	−	0.422120i	$-0.861286\pi$
$197$	−8.15687e14	+	4.70937e14i	−0.994244	+	0.574027i	−0.0877039	+	0.996147i	$0.527953\pi$
$198$	1.01428e14	+	1.75679e14i	0.119629	+	0.207203i
$199$	4.94138e14	−	8.55871e14i	0.564031	−	0.976930i	−0.433108	−	0.901342i	$-0.642583\pi$
$199$	4.94138e14	−	8.55871e14i	0.564031	−	0.976930i	0.997139	−	0.0755883i	$-0.0240835\pi$
$200$			1.14513e15i			1.26520i
$201$	−6.88892e13	−	3.97732e13i	−0.0736846	−	0.0425418i
$202$	−3.55768e14	−	2.05403e14i	−0.368454	−	0.212727i
$203$		−	8.83091e14i		−	0.885689i
$204$	−1.73471e13	+	3.00460e13i	−0.0168512	+	0.0291871i
$205$	−3.29677e14	−	5.71017e14i	−0.310233	−	0.537339i
$206$	8.69428e14	−	5.01964e14i	0.792678	−	0.457653i
$207$	5.44748e14			0.481269
$208$	4.68721e14	−	1.03046e15i	0.401331	−	0.882308i
$209$	4.52303e12			0.00375386
$210$	−2.76029e15	+	1.59365e15i	−2.22090	+	1.28224i
$211$	−2.86872e14	−	4.96876e14i	−0.223796	−	0.387626i	0.732162	−	0.681131i	$-0.238512\pi$
$211$	−2.86872e14	−	4.96876e14i	−0.223796	−	0.387626i	−0.955957	+	0.293505i	$0.905178\pi$
$212$	−2.40269e13	+	4.16157e13i	−0.0181766	+	0.0314829i
$213$			1.60307e15i			1.17621i
$214$	−1.07477e15	−	6.20519e14i	−0.764937	−	0.441637i
$215$	2.50162e15	+	1.44431e15i	1.72731	+	0.997265i
$216$		−	5.29175e15i		−	3.54527i
$217$	8.93755e14	−	1.54803e15i	0.581073	−	1.00645i
$218$	1.18412e15	+	2.05096e15i	0.747187	+	1.29417i
$219$	−4.07957e15	+	2.35534e15i	−2.49878	+	1.44267i
$220$	6.53410e12			0.00388543
$221$	1.00038e15	−	9.70455e13i	0.577585	−	0.0560307i
$222$	1.59024e15			0.891598
$223$	1.64027e15	−	9.47011e14i	0.893170	−	0.515672i	0.0181916	−	0.999835i	$-0.494209\pi$
$223$	1.64027e15	−	9.47011e14i	0.893170	−	0.515672i	0.874978	+	0.484163i	$0.160876\pi$
$224$	5.02440e13	+	8.70251e13i	0.0265749	+	0.0460291i
$225$	3.39160e15	−	5.87442e15i	1.74268	−	3.01841i
$226$		−	4.74663e14i		−	0.236963i
$227$	1.39279e15	+	8.04130e14i	0.675645	+	0.390084i	0.798212	−	0.602376i	$-0.205779\pi$
$227$	1.39279e15	+	8.04130e14i	0.675645	+	0.390084i	−0.122567	+	0.992460i	$0.539113\pi$
$228$	−4.60715e12	−	2.65994e12i	−0.00217198	−	0.00125399i
$229$			7.60189e14i			0.348330i	0.984716	+	0.174165i	$0.0557226\pi$
$229$			7.60189e14i			0.348330i	−0.984716	+	0.174165i	$0.944277\pi$
$230$	−2.85478e14	+	4.94463e14i	−0.127158	+	0.220243i
$231$	1.74322e14	+	3.01934e14i	0.0754873	+	0.130748i
$232$	−2.07251e15	+	1.19656e15i	−0.872618	+	0.503806i
$233$	−2.83788e15			−1.16193			−0.580966	−	0.813928i	$-0.697325\pi$
$233$	−2.83788e15			−1.16193			−0.580966	+	0.813928i	$0.697325\pi$
$234$	−5.62431e15	+	4.01784e15i	−2.23958	+	1.59989i
$235$	5.14364e14			0.199218
$236$	−4.37972e12	+	2.52863e12i	−0.00165013	+	0.000952702i
$237$	−7.72987e14	−	1.33885e15i	−0.283340	−	0.490759i
$238$	7.14449e14	−	1.23746e15i	0.254813	−	0.441348i
$239$		−	4.74023e15i		−	1.64518i	−0.568635	−	0.822590i	$-0.692528\pi$
$239$		−	4.74023e15i		−	1.64518i	0.568635	−	0.822590i	$-0.307472\pi$
$240$	7.25700e15	+	4.18983e15i	2.45123	+	1.41522i
$241$	2.30662e14	+	1.33173e14i	0.0758342	+	0.0437829i	0.537438	−	0.843304i	$-0.319392\pi$
$241$	2.30662e14	+	1.33173e14i	0.0758342	+	0.0437829i	−0.461603	+	0.887086i	$0.652726\pi$
$242$		−	3.05445e15i		−	0.977536i
$243$	−6.93809e15	+	1.20171e16i	−2.16172	+	3.74420i
$244$	−2.16061e13	−	3.74229e13i	−0.00655454	−	0.0113528i
$245$	9.01091e14	−	5.20245e14i	0.266188	−	0.153684i
$246$	−2.76031e15			−0.794109
$247$	1.48806e13	+	1.53395e14i	0.00416957	+	0.0429815i
$248$	−4.84405e15			−1.32213
$249$	3.85638e15	−	2.22648e15i	1.02538	−	0.592003i
$250$	7.04817e14	+	1.22078e15i	0.182585	+	0.316247i
$251$	−1.96430e15	+	3.40226e15i	−0.495824	+	0.858793i	−0.999988	−	0.00481503i	$-0.998467\pi$
$251$	−1.96430e15	+	3.40226e15i	−0.495824	+	0.858793i	0.504164	+	0.863608i	$0.331801\pi$
$252$		−	3.01992e14i		−	0.0742835i
$253$	5.40868e13	+	3.12270e13i	0.0129661	+	0.00748596i
$254$	5.04327e15	+	2.91174e15i	1.17840	+	0.680351i
$255$			7.43975e15i			1.69452i
$256$	2.01236e14	−	3.48550e14i	0.0446833	−	0.0773937i
$257$	−2.39979e15	−	4.15656e15i	−0.519527	−	0.899847i	−0.999742	−	0.0226962i	$-0.992775\pi$
$257$	−2.39979e15	−	4.15656e15i	−0.519527	−	0.899847i	0.480216	−	0.877150i	$-0.340558\pi$
$258$	1.04728e16	−	6.04645e15i	2.21072	−	1.27636i
$259$	2.01279e15			0.414333
$260$	2.14970e13	+	2.21599e14i	0.00431570	+	0.0444878i
$261$	1.41757e16			2.77575
$262$	−4.01401e15	+	2.31749e15i	−0.766690	+	0.442649i
$263$	−6.36577e14	−	1.10258e15i	−0.118615	−	0.205447i	0.800604	−	0.599193i	$-0.204512\pi$
$263$	−6.36577e14	−	1.10258e15i	−0.118615	−	0.205447i	−0.919219	+	0.393747i	$0.871179\pi$
$264$	4.72402e14	−	8.18224e14i	0.0858789	−	0.148747i
$265$			1.03046e16i			1.82781i
$266$	1.89748e14	+	1.09551e14i	0.0328433	+	0.0189621i
$267$	−1.79096e16	−	1.03401e16i	−3.02526	−	1.74663i
$268$			7.89951e12i			0.00130234i
$269$	6.08744e15	−	1.05438e16i	0.979591	−	1.69670i	0.315723	−	0.948851i	$-0.397753\pi$
$269$	6.08744e15	−	1.05438e16i	0.979591	−	1.69670i	0.663868	−	0.747850i	$-0.268914\pi$
$270$	−1.64269e16	−	2.84522e16i	−2.58043	−	4.46943i
$271$	−1.03173e15	+	5.95668e14i	−0.158221	+	0.0913490i	−0.577020	−	0.816730i	$-0.695785\pi$
$271$	−1.03173e15	+	5.95668e14i	−0.158221	+	0.0913490i	0.418799	+	0.908079i	$0.362451\pi$
$272$	−3.75668e15			−0.562478
$273$	−9.66635e15	+	6.90534e15i	−1.41321	+	1.00955i
$274$	−3.85724e15			−0.550679
$275$	6.73488e14	−	3.88839e14i	0.0939004	−	0.0542134i
$276$	−3.67285e13	−	6.36156e13i	−0.00500143	−	0.00866273i
$277$	6.96849e15	−	1.20698e16i	0.926873	−	1.60539i	0.138353	−	0.990383i	$-0.455819\pi$
$277$	6.96849e15	−	1.20698e16i	0.926873	−	1.60539i	0.788520	−	0.615009i	$-0.210848\pi$
$278$			9.52345e15i			1.23738i
$279$	2.48495e16	+	1.43469e16i	3.15421	+	1.82109i
$280$	9.46782e15	+	5.46625e15i	1.17415	+	0.677894i
$281$		−	1.01873e16i		−	1.23444i	−0.786791	−	0.617220i	$-0.788259\pi$
$281$		−	1.01873e16i		−	1.23444i	0.786791	−	0.617220i	$-0.211741\pi$
$282$	1.07667e15	−	1.86484e15i	0.127486	−	0.220812i
$283$	4.76573e15	+	8.25449e15i	0.551465	+	0.955165i	0.998169	+	0.0604836i	$0.0192643\pi$
$283$	4.76573e15	+	8.25449e15i	0.551465	+	0.955165i	−0.446704	+	0.894682i	$0.647402\pi$
$284$	1.37867e14	−	7.95978e13i	0.0155917	−	0.00900185i
$285$	−1.14079e15			−0.126099
$286$	−7.88743e14	+	7.65149e13i	−0.0852230	+	0.00826736i
$287$	−3.49376e15			−0.369029
$288$	−1.39696e15	+	8.06535e14i	−0.144256	+	0.0832860i
$289$	3.28464e15	+	5.68916e15i	0.331628	+	0.574397i
$290$	−7.42886e15	+	1.28672e16i	−0.733391	+	1.27027i
$291$			1.20265e16i			1.16101i
$292$	4.05130e14	+	2.33902e14i	0.0382477	+	0.0220823i
$293$	−1.63794e16	−	9.45665e15i	−1.51237	−	0.873168i	−0.999895	−	0.0144659i	$-0.995395\pi$
$293$	−1.63794e16	−	9.45665e15i	−1.51237	−	0.873168i	−0.512475	−	0.858702i	$-0.671271\pi$
$294$		−	4.35590e15i		−	0.393387i
$295$	−5.42235e14	+	9.39179e14i	−0.0479010	+	0.0829670i
$296$	−2.72727e15	−	4.72377e15i	−0.235685	−	0.408219i
$297$	−3.11225e15	+	1.79686e15i	−0.263122	+	0.151914i
$298$	−7.83696e14			−0.0648249
$299$	−8.81097e14	+	1.93705e15i	−0.0713117	+	0.156775i
$300$	−9.14686e14			−0.0724409
$301$	1.32555e16	−	7.65307e15i	1.02734	−	0.593135i
$302$	−4.30228e15	−	7.45176e15i	−0.326327	−	0.565215i
$303$	5.66681e15	−	9.81520e15i	0.420689	−	0.728655i
$304$		−	5.76036e14i		−	0.0418573i
$305$	−8.02489e15	−	4.63317e15i	−0.570808	−	0.329556i
$306$	1.98642e16	+	1.14686e16i	1.38319	+	0.798585i
$307$			3.13601e15i			0.213785i	0.994271	+	0.106893i	$0.0340901\pi$
$307$			3.13601e15i			0.213785i	−0.994271	+	0.106893i	$0.965910\pi$
$308$	1.73114e13	−	2.99842e13i	0.00115545	−	0.00200130i
$309$	1.38486e16	+	2.39864e16i	0.905055	+	1.56760i
$310$	−2.60451e16	+	1.50372e16i	−1.66677	+	0.962309i
$311$	−2.53361e16			−1.58780			−0.793902	−	0.608045i	$-0.791954\pi$
$311$	−2.53361e16			−1.58780			−0.793902	+	0.608045i	$0.791954\pi$
$312$	2.93036e16	+	1.33292e16i	1.79853	+	0.818088i
$313$	9.59573e15			0.576819			0.288410	−	0.957507i	$-0.406873\pi$
$313$	9.59573e15			0.576819			0.288410	+	0.957507i	$0.406873\pi$
$314$	−1.57211e16	+	9.07658e15i	−0.925636	+	0.534416i
$315$	−3.23794e16	−	5.60827e16i	−1.86745	−	3.23452i
$316$	−7.67629e13	+	1.32957e14i	−0.00433696	+	0.00751184i
$317$			1.87096e16i			1.03557i	0.855511	+	0.517785i	$0.173243\pi$
$317$			1.87096e16i			1.03557i	−0.855511	+	0.517785i	$0.826757\pi$
$318$	3.73594e16	+	2.15695e16i	2.02593	+	1.16967i
$319$	1.40747e15	+	8.12606e14i	0.0747827	+	0.0431758i
$320$		−	2.96008e16i		−	1.54109i
$321$	1.71193e16	−	2.96516e16i	0.873382	−	1.51274i
$322$	1.51268e15	+	2.62005e15i	0.0756284	+	0.130992i
$323$	4.42906e14	−	2.55712e14i	0.0217018	−	0.0125295i
$324$	2.49200e15			0.119675
$325$	1.54029e16	+	2.15616e16i	0.725039	+	1.01494i
$326$	2.24529e16			1.03600
$327$	−5.65835e16	+	3.26685e16i	−2.55935	+	1.47764i
$328$	4.73395e15	+	8.19944e15i	0.209915	+	0.363583i
$329$	1.36275e15	−	2.36035e15i	0.0592437	−	0.102613i
$330$		−	5.86582e15i		−	0.250028i
$331$	−3.52893e16	−	2.03743e16i	−1.47489	−	0.851530i	−0.475294	−	0.879827i	$-0.657658\pi$
$331$	−3.52893e16	−	2.03743e16i	−1.47489	−	0.851530i	−0.999600	+	0.0282972i	$0.990992\pi$
$332$	−3.82965e14	−	2.21105e14i	−0.0156950	−	0.00906153i
$333$			3.23100e16i			1.29852i
$334$	−9.31608e15	+	1.61359e16i	−0.367182	+	0.635978i
$335$	8.46979e14	+	1.46701e15i	0.0327402	+	0.0567077i
$336$	3.84532e16	−	2.22010e16i	1.45790	−	0.841718i
$337$	1.08634e16			0.403991			0.201995	−	0.979386i	$-0.435257\pi$
$337$	1.08634e16			0.403991			0.201995	+	0.979386i	$0.435257\pi$
$338$	−5.18989e15	−	2.64979e16i	−0.189321	−	0.966614i
$339$	1.30954e16			0.468619
$340$	6.39836e14	−	3.69409e14i	0.0224624	−	0.0129687i
$341$	1.64484e15	+	2.84894e15i	0.0566526	+	0.0981251i
$342$	−1.75856e15	+	3.04591e15i	−0.0594274	+	0.102931i
$343$		−	3.24030e16i		−	1.07442i
$344$	−3.59217e16	−	2.07394e16i	−1.16876	−	0.674786i
$345$	−1.36416e16	−	7.87600e15i	−0.435554	−	0.251467i
$346$		−	2.56628e16i		−	0.804100i
$347$	8.05399e15	−	1.39499e16i	0.247668	−	0.428973i	−0.715211	−	0.698909i	$-0.753669\pi$
$347$	8.05399e15	−	1.39499e16i	0.247668	−	0.428973i	0.962878	+	0.269936i	$0.0870025\pi$
$348$	−9.55768e14	−	1.65544e15i	−0.0288461	−	0.0499629i
$349$	−5.93243e15	+	3.42509e15i	−0.175739	+	0.101463i	−0.585289	−	0.810825i	$-0.699019\pi$
$349$	−5.93243e15	+	3.42509e15i	−0.175739	+	0.101463i	0.409550	+	0.912288i	$0.365686\pi$
$350$	3.76719e16			1.09541
$351$	−7.11782e16	−	9.96379e16i	−2.03166	−	2.84399i
$352$	−1.84935e14			−0.00518192
$353$	−1.27550e16	+	7.36410e15i	−0.350869	+	0.202574i	−0.665068	−	0.746783i	$-0.731597\pi$
$353$	−1.27550e16	+	7.36410e15i	−0.350869	+	0.202574i	0.314199	+	0.949357i	$0.398264\pi$
$354$	2.27001e15	+	3.93177e15i	0.0613065	+	0.106186i
$355$	1.70688e16	−	2.95641e16i	0.452605	−	0.783934i
$356$			2.05369e15i			0.0534699i
$357$	3.41401e16	+	1.97108e16i	0.872812	+	0.503918i
$358$	3.42172e16	+	1.97553e16i	0.859023	+	0.495957i
$359$			6.57551e16i			1.62112i	0.585655	+	0.810561i	$0.300837\pi$
$359$			6.57551e16i			1.62112i	−0.585655	+	0.810561i	$0.699163\pi$
$360$	−8.77462e16	+	1.51981e17i	−2.12453	+	3.67979i
$361$	−2.09873e16	−	3.63510e16i	−0.499068	−	0.864410i
$362$	3.32139e16	−	1.91760e16i	0.775735	−	0.447871i
$363$	8.42685e16			1.93318
$364$	1.07384e15	+	4.88454e14i	0.0241981	+	0.0110069i
$365$	1.00315e17			2.22056
$366$	−3.35954e16	+	1.93963e16i	−0.730554	+	0.421786i
$367$	4.05926e16	+	7.03084e16i	0.867196	+	1.50203i	0.864850	+	0.502031i	$0.167414\pi$
$367$	4.05926e16	+	7.03084e16i	0.867196	+	1.50203i	0.00234679	+	0.999997i	$0.499253\pi$
$368$	3.97696e15	−	6.88829e15i	0.0834718	−	0.144577i
$369$		−	5.60831e16i		−	1.15654i
$370$	−2.93276e16	−	1.69323e16i	−0.594244	−	0.343087i
$371$	4.72863e16	+	2.73007e16i	0.941466	+	0.543555i
$372$		−	3.86924e15i		−	0.0757001i
$373$	2.13638e16	−	3.70032e16i	0.410744	−	0.711430i	−0.584227	−	0.811590i	$-0.698602\pi$
$373$	2.13638e16	−	3.70032e16i	0.410744	−	0.711430i	0.994971	+	0.100161i	$0.0319357\pi$
$374$	1.31485e15	+	2.27738e15i	0.0248434	+	0.0430300i
$375$	−3.36798e16	+	1.94450e16i	−0.625412	+	0.361082i
$376$	−7.38594e15			−0.134798
$377$	−2.29283e16	+	5.04069e16i	−0.411295	+	0.904213i
$378$	−1.74085e17			−3.06948
$379$	−4.19571e15	+	2.42240e15i	−0.0727195	+	0.0419846i	−0.535919	−	0.844269i	$-0.680035\pi$
$379$	−4.19571e15	+	2.42240e15i	−0.0727195	+	0.0419846i	0.463199	+	0.886254i	$0.346701\pi$
$380$	5.66440e13	+	9.81103e13i	0.000965074	+	0.00167156i
$381$	−8.03312e16	+	1.39138e17i	−1.34546	+	2.33041i
$382$		−	6.07686e16i		−	1.00062i
$383$	−5.31262e16	−	3.06724e16i	−0.860037	−	0.496542i	0.00398779	−	0.999992i	$-0.498731\pi$
$383$	−5.31262e16	−	3.06724e16i	−0.860037	−	0.496542i	−0.864025	+	0.503450i	$0.832064\pi$
$384$	−1.01001e17	−	5.83127e16i	−1.60757	−	0.928133i
$385$		−	7.42444e15i		−	0.116190i
$386$	3.51401e16	−	6.08645e16i	0.540737	−	0.936583i
$387$	1.22850e17	+	2.12782e17i	1.85889	+	3.21969i
$388$	1.03431e15	−	5.97159e14i	0.0153902	−	0.00888554i
$389$	−7.28750e16			−1.06637			−0.533183	−	0.846000i	$-0.679004\pi$
$389$	−7.28750e16			−1.06637			−0.533183	+	0.846000i	$0.679004\pi$
$390$	1.98935e17	−	1.92984e16i	2.86280	−	0.277716i
$391$	7.06175e15			0.0999456
$392$	−1.29391e16	+	7.47039e15i	−0.180113	+	0.103988i
$393$	−6.39367e16	−	1.10742e17i	−0.875384	−	1.51621i
$394$	4.19841e16	−	7.27186e16i	0.565405	−	0.979310i
$395$			3.29218e16i			0.436117i
$396$	4.81317e14	+	2.77888e14i	0.00627209	+	0.00362119i
$397$	−4.20912e15	−	2.43013e15i	−0.0539576	−	0.0311524i	0.472779	−	0.881181i	$-0.343251\pi$
$397$	−4.20912e15	−	2.43013e15i	−0.0539576	−	0.0311524i	−0.526736	+	0.850029i	$0.676584\pi$
$398$			8.81049e16i			1.11112i
$399$	−3.02238e15	+	5.23492e15i	−0.0374995	+	0.0649511i
$400$	−4.95210e16	−	8.57730e16i	−0.604505	−	1.04703i
$401$	−2.85846e16	+	1.65033e16i	−0.343316	+	0.198213i	−0.661737	−	0.749736i	$-0.730181\pi$
$401$	−2.85846e16	+	1.65033e16i	−0.343316	+	0.198213i	0.318422	+	0.947949i	$0.396847\pi$
$402$	7.09158e15			0.0838057
$403$	−9.12082e16	+	6.51564e16i	−1.06060	+	0.757659i
$404$	−1.12551e15			−0.0128786
$405$	4.62786e17	−	2.67190e17i	5.21102	−	3.00858i
$406$	3.93638e16	+	6.81802e16i	0.436193	+	0.755508i
$407$	−1.85214e15	+	3.20799e15i	−0.0201980	+	0.0349840i
$408$		−	1.06830e17i		−	1.14658i
$409$	−6.41067e15	−	3.70120e15i	−0.0677176	−	0.0390968i	0.465759	−	0.884912i	$-0.345781\pi$
$409$	−6.41067e15	−	3.70120e15i	−0.0677176	−	0.0390968i	−0.533477	+	0.845815i	$0.679115\pi$
$410$	5.09062e16	+	2.93907e16i	0.529268	+	0.305573i
$411$		−	1.06417e17i		−	1.08902i
$412$	1.37526e15	−	2.38202e15i	0.0138533	−	0.0239946i
$413$	2.87318e15	+	4.97649e15i	0.0284897	+	0.0493456i
$414$	−4.20579e16	+	2.42822e16i	−0.410531	+	0.237020i
$415$	−9.48268e16			−0.911210
$416$	−6.08430e14	−	6.27192e15i	−0.00575577	−	0.0593327i
$417$	−2.62740e17			−2.44705
$418$	−3.49206e14	+	2.01614e14i	−0.00320211	+	0.00184874i
$419$	4.05161e15	+	7.01759e15i	0.0365794	+	0.0633573i	0.883735	−	0.467987i	$-0.155020\pi$
$419$	4.05161e15	+	7.01759e15i	0.0365794	+	0.0633573i	−0.847156	+	0.531344i	$0.821687\pi$
$420$	−4.36622e15	+	7.56252e15i	−0.0388138	+	0.0672274i
$421$			1.07619e17i			0.942008i	0.882131	+	0.471004i	$0.156108\pi$
$421$			1.07619e17i			0.942008i	−0.882131	+	0.471004i	$0.843892\pi$
$422$	4.42966e16	+	2.55747e16i	0.381803	+	0.220434i
$423$	3.78892e16	+	2.18753e16i	0.321590	+	0.185670i
$424$		−	1.47967e17i		−	1.23676i
$425$	4.39665e16	−	7.61521e16i	0.361904	−	0.626836i
$426$	−7.14568e16	−	1.23767e17i	−0.579270	−	1.00333i
$427$	−4.25221e16	+	2.45501e16i	−0.339495	+	0.196007i
$428$	−3.40014e15			−0.0267370
$429$	−2.11095e15	−	2.17605e16i	−0.0163495	−	0.168537i
$430$	−2.57521e17			−1.96457
$431$	9.12098e14	−	5.26600e14i	0.00685392	−	0.00395711i	−0.496569	−	0.867997i	$-0.665407\pi$
$431$	9.12098e14	−	5.26600e14i	0.00685392	−	0.00395711i	0.503423	+	0.864040i	$0.332074\pi$
$432$	2.28841e17	+	3.96364e17i	1.69391	+	2.93393i
$433$	−1.61318e16	+	2.79412e16i	−0.117628	+	0.203738i	−0.918827	−	0.394660i	$-0.870863\pi$
$433$	−1.61318e16	+	2.79412e16i	−0.117628	+	0.203738i	0.801199	+	0.598398i	$0.204196\pi$
$434$			1.59357e17i			1.14469i
$435$	−3.54989e17	−	2.04953e17i	−2.51209	−	1.45036i
$436$	5.61913e15	+	3.24421e15i	0.0391748	+	0.0226176i
$437$			1.08283e15i			0.00743754i
$438$	2.09979e17	−	3.63694e17i	1.42100	−	2.46125i
$439$	9.97463e16	+	1.72766e17i	0.665086	+	1.15196i	0.979262	+	0.202598i	$0.0649383\pi$
$439$	9.97463e16	+	1.72766e17i	0.665086	+	1.15196i	−0.314176	+	0.949365i	$0.601728\pi$
$440$	−1.74243e16	+	1.00599e16i	−0.114475	+	0.0660924i
$441$	8.85018e16			0.572930
$442$	−7.29099e16	+	5.20846e16i	−0.465095	+	0.332250i
$443$	2.57262e17			1.61716			0.808578	−	0.588390i	$-0.200238\pi$
$443$	2.57262e17			1.61716			0.808578	+	0.588390i	$0.200238\pi$
$444$	3.77316e15	−	2.17844e15i	0.0233731	−	0.0134945i
$445$	2.20195e17	+	3.81388e17i	1.34421	+	2.32824i
$446$	−8.44262e16	+	1.46230e17i	−0.507926	+	0.879754i
$447$		−	2.16212e16i		−	0.128198i
$448$	−1.35834e17	−	7.84240e16i	−0.793784	−	0.458292i
$449$	−2.36139e17	−	1.36335e17i	−1.36009	−	0.785247i	−0.370452	−	0.928851i	$-0.620797\pi$
$449$	−2.36139e17	−	1.36335e17i	−1.36009	−	0.785247i	−0.989635	+	0.143605i	$0.954131\pi$
$450$			6.04723e17i			3.43301i
$451$	3.21490e15	−	5.56837e15i	0.0179895	−	0.0311588i
$452$	−6.50231e14	−	1.12623e15i	−0.00358647	−	0.00621195i
$453$	2.05585e17	−	1.18695e17i	1.11777	−	0.645346i
$454$	−1.43377e17			−0.768449
$455$	2.51794e17	−	2.44262e16i	1.33037	−	0.129057i
$456$	1.63810e16			0.0853234
$457$	1.28511e17	−	7.41956e16i	0.659908	−	0.380998i	−0.132334	−	0.991205i	$-0.542247\pi$
$457$	1.28511e17	−	7.41956e16i	0.659908	−	0.380998i	0.792242	+	0.610207i	$0.208914\pi$
$458$	−3.38855e16	−	5.86914e16i	−0.171549	−	0.297131i
$459$	−2.03173e17	+	3.51905e17i	−1.01410	+	1.75648i
$460$			1.56428e15i			0.00769820i
$461$	6.23372e16	+	3.59904e16i	0.302476	+	0.174635i	0.643555	−	0.765400i	$-0.277459\pi$
$461$	6.23372e16	+	3.59904e16i	0.302476	+	0.174635i	−0.341078	+	0.940035i	$0.610792\pi$
$462$	−2.69175e16	−	1.55408e16i	−0.128784	−	0.0743534i
$463$		−	1.23919e17i		−	0.584602i	−0.956326	−	0.292301i	$-0.905579\pi$
$463$		−	1.23919e17i		−	0.584602i	0.956326	−	0.292301i	$-0.0944209\pi$
$464$	1.03490e17	−	1.79251e17i	0.481430	−	0.833861i
$465$	−4.14857e17	−	7.18553e17i	−1.90307	−	3.29621i
$466$	2.19102e17	−	1.26499e17i	0.991149	−	0.572240i
$467$	1.41979e17			0.633381			0.316691	−	0.948529i	$-0.397428\pi$
$467$	1.41979e17			0.633381			0.316691	+	0.948529i	$0.397428\pi$
$468$	−7.84085e15	+	1.72377e16i	−0.0344957	+	0.0758371i
$469$	8.97589e15			0.0389452
$470$	−3.97121e16	+	2.29278e16i	−0.169937	+	0.0981130i
$471$	−2.50412e17	−	4.33726e17i	−1.05686	−	1.83054i
$472$	7.78615e15	−	1.34860e16i	0.0324116	−	0.0561385i
$473$			2.81689e16i			0.115657i
$474$	1.19359e17	+	6.89119e16i	0.483388	+	0.279084i
$475$	1.16769e16	+	6.74167e15i	0.0466465	+	0.0269314i
$476$		−	3.91483e15i		−	0.0154265i
$477$	−4.38241e17	+	7.59056e17i	−1.70351	+	2.95056i
$478$	2.11296e17	+	3.65976e17i	0.810234	+	1.40337i
$479$	−9.68364e15	+	5.59085e15i	−0.0366317	+	0.0211493i	−0.518204	−	0.855257i	$-0.673399\pi$
$479$	−9.68364e15	+	5.59085e15i	−0.0366317	+	0.0211493i	0.481572	+	0.876406i	$0.340066\pi$
$480$	4.66437e16			0.174071
$481$	−1.14890e17	−	5.22595e16i	−0.422999	−	0.192408i
$482$	−2.37447e16			−0.0862505
$483$	−7.22838e16	+	4.17331e16i	−0.259051	+	0.149563i
$484$	−4.18422e15	−	7.24728e15i	−0.0147952	−	0.0256260i
$485$	1.28054e17	−	2.21796e17i	0.446757	−	0.773805i
$486$		−	1.23706e18i		−	4.25849i
$487$	−1.88120e17	−	1.08611e17i	−0.638995	−	0.368924i	0.145232	−	0.989398i	$-0.453607\pi$
$487$	−1.88120e17	−	1.08611e17i	−0.638995	−	0.368924i	−0.784227	+	0.620474i	$0.786940\pi$
$488$	1.15232e17	+	6.65294e16i	0.386230	+	0.222990i
$489$			6.19448e17i			2.04879i
$490$	−4.63799e16	+	8.03324e16i	−0.151375	+	0.262190i
$491$	2.33397e17	+	4.04255e17i	0.751736	+	1.30204i	0.946981	+	0.321290i	$0.104117\pi$
$491$	2.33397e17	+	4.04255e17i	0.751736	+	1.30204i	−0.195245	+	0.980755i	$0.562550\pi$
$492$	−6.54939e15	+	3.78129e15i	−0.0208175	+	0.0120190i
$493$	1.83765e17			0.576443
$494$	−7.98648e15	−	1.11798e16i	−0.0247246	−	0.0346105i
$495$	1.19180e17			0.364140
$496$	3.62831e17	−	2.09480e17i	1.09414	−	0.631702i
$497$	−9.04437e16	−	1.56653e17i	−0.269192	−	0.466254i
$498$	−1.98491e17	+	3.43797e17i	−0.583110	+	1.00998i
$499$		−	3.59799e17i		−	1.04329i	−0.853162	−	0.521647i	$-0.825318\pi$
$499$		−	3.59799e17i		−	1.04329i	0.853162	−	0.521647i	$-0.174682\pi$
$500$	3.34463e15	+	1.93103e15i	0.00957290	+	0.00552692i
$501$	−4.45170e17	−	2.57019e17i	−1.25771	−	0.726140i
$502$		−	3.50235e17i		−	0.976753i
$503$	−1.58710e16	+	2.74893e16i	−0.0436929	+	0.0756784i	−0.887045	−	0.461683i	$-0.847246\pi$
$503$	−1.58710e16	+	2.74893e16i	−0.0436929	+	0.0756784i	0.843352	+	0.537362i	$0.180579\pi$
$504$	4.64947e17	+	8.05312e17i	1.26359	+	2.18860i
$505$	−2.09017e17	+	1.20676e17i	−0.560773	+	0.323762i
$506$	−5.56779e15			−0.0147470
$507$	7.31044e17	−	1.43183e17i	1.91158	−	0.374402i
$508$	1.59549e16			0.0411888
$509$	−3.87993e17	+	2.24008e17i	−0.988913	+	0.570949i	−0.904949	−	0.425519i	$-0.860091\pi$
$509$	−3.87993e17	+	2.24008e17i	−0.988913	+	0.570949i	−0.0839641	+	0.996469i	$0.526758\pi$
$510$	−3.31628e17	−	5.74396e17i	−0.834535	−	1.44546i
$511$	2.65773e17	−	4.60332e17i	0.660351	−	1.14376i
$512$			4.24325e17i			1.04098i
$513$	−5.39600e16	−	3.11538e16i	−0.130710	−	0.0754655i
$514$	3.70558e17	+	2.13942e17i	0.886330	+	0.511723i
$515$		−	5.89817e17i		−	1.39306i
$516$	1.65658e16	−	2.86928e16i	0.0386358	−	0.0669191i
$517$	2.50796e15	+	4.34391e15i	0.00577606	+	0.0100044i
$518$	−1.55400e17	+	8.97202e16i	−0.353433	+	0.204055i
$519$	7.08006e17			1.59019
$520$	−3.98499e17	−	5.57834e17i	−0.883905	−	1.23732i
$521$	−8.47953e17			−1.85749			−0.928745	−	0.370719i	$-0.879111\pi$
$521$	−8.47953e17			−1.85749			−0.928745	+	0.370719i	$0.879111\pi$
$522$	−1.09445e18	+	6.31883e17i	−2.36777	+	1.36703i
$523$	−1.00796e17	−	1.74584e17i	−0.215369	−	0.373030i	0.738018	−	0.674782i	$-0.235762\pi$
$523$	−1.00796e17	−	1.74584e17i	−0.215369	−	0.373030i	−0.953387	+	0.301751i	$0.902429\pi$
$524$	−6.34935e15	+	1.09974e16i	−0.0133991	+	0.0232079i
$525$			1.03932e18i			2.16628i
$526$	9.82954e16	+	5.67509e16i	0.202361	+	0.116833i
$527$	3.22133e17	+	1.85984e17i	0.655038	+	0.378187i
$528$			8.17158e16i			0.164129i
$529$	2.44542e17	−	4.23560e17i	0.485168	−	0.840336i
$530$	−4.59326e17	−	7.95577e17i	−0.900178	−	1.55915i
$531$	−7.98845e16	+	4.61213e16i	−0.154649	+	0.0892868i
$532$	6.00287e14			0.00114798
$533$	1.99424e17	+	9.07111e16i	0.376748	+	0.171370i
$534$	1.84364e18			3.44079
$535$	−6.31436e17	+	3.64560e17i	−1.16421	+	0.672155i
$536$	−1.21621e16	−	2.10653e16i	−0.0221532	−	0.0383705i
$537$	−5.45024e17	+	9.44010e17i	−0.980806	+	1.69881i
$538$			1.08539e18i			1.92975i
$539$	8.78715e15	+	5.07326e15i	0.0154355	+	0.00891170i
$540$	−7.79522e16	−	4.50057e16i	−0.135291	−	0.0781103i
$541$			3.64670e17i			0.625343i	0.949861	+	0.312671i	$0.101224\pi$
$541$			3.64670e17i			0.625343i	−0.949861	+	0.312671i	$0.898776\pi$
$542$	5.31039e16	−	9.19786e16i	0.0899769	−	0.155845i
$543$	5.29043e17	+	9.16329e17i	0.885711	+	1.53410i
$544$	−1.81093e16	+	1.04554e16i	−0.0299577	+	0.0172961i
$545$	1.39136e18			2.27438
$546$	4.38497e17	−	9.64014e17i	0.708296	−	1.55715i
$547$	−6.78076e17			−1.08233			−0.541166	−	0.840916i	$-0.682017\pi$
$547$	−6.78076e17			−1.08233			−0.541166	+	0.840916i	$0.682017\pi$
$548$	−9.15208e15	+	5.28395e15i	−0.0144360	+	0.00833461i
$549$	−3.94088e17	−	6.82580e17i	−0.614289	−	1.06398i
$550$	−3.46650e16	+	6.00416e16i	−0.0533991	+	0.0924900i
$551$			2.81778e16i			0.0428965i
$552$	1.95885e17	+	1.13094e17i	0.294712	+	0.170152i
$553$	1.51074e17	+	8.72226e16i	0.224634	+	0.129693i
$554$			1.24248e18i			1.82590i
$555$	4.67141e17	−	8.09111e17i	0.678490	−	1.17518i
$556$	1.30460e16	+	2.25963e16i	0.0187279	+	0.0324377i
$557$	4.52148e17	−	2.61048e17i	0.641537	−	0.370391i	−0.143669	−	0.989626i	$-0.545890\pi$
$557$	4.52148e17	−	2.61048e17i	0.641537	−	0.370391i	0.785206	+	0.619234i	$0.212557\pi$
$558$	−2.55805e18			−3.58746
$559$	−9.55327e17	+	9.26749e16i	−1.32427	+	0.128465i
$560$	−9.45548e17			−1.29557
$561$	−6.28302e16	+	3.62750e16i	−0.0850962	+	0.0491303i
$562$	4.54101e17	+	7.86527e17i	0.607949	+	1.05300i
$563$	4.72036e17	−	8.17590e17i	0.624699	−	1.08201i	−0.363900	−	0.931438i	$-0.618555\pi$
$563$	4.72036e17	−	8.17590e17i	0.624699	−	1.08201i	0.988599	−	0.150572i	$-0.0481115\pi$
$564$		−	5.89960e15i		−	0.00771806i
$565$	−2.41507e17	−	1.39434e17i	−0.312331	−	0.180325i
$566$	−7.35889e17	−	4.24866e17i	−0.940818	−	0.543182i
$567$		−	2.83155e18i		−	3.57878i
$568$	−2.45097e17	+	4.24521e17i	−0.306249	+	0.530439i
$569$	−5.18722e17	−	8.98453e17i	−0.640774	−	1.10985i	−0.985260	−	0.171062i	$-0.945280\pi$
$569$	−5.18722e17	−	8.98453e17i	−0.640774	−	1.10985i	0.344486	−	0.938791i	$-0.388053\pi$
$570$	8.80759e16	−	5.08506e16i	0.107565	−	0.0621026i
$571$	5.24173e17			0.632908			0.316454	−	0.948608i	$-0.397508\pi$
$571$	5.24173e17			0.632908			0.316454	+	0.948608i	$0.397508\pi$
$572$	−1.76663e15	+	1.26203e15i	−0.00210898	+	0.00150659i
$573$	1.67653e18			1.97882
$574$	2.69740e17	−	1.55735e17i	0.314788	−	0.181743i
$575$	9.30890e16	+	1.61235e17i	0.107413	+	0.186045i
$576$	1.25889e18	−	2.18046e18i	1.43629	−	2.48773i
$577$		−	1.27349e18i		−	1.43666i	−0.695702	−	0.718330i	$-0.744907\pi$
$577$		−	1.27349e18i		−	1.43666i	0.695702	−	0.718330i	$-0.255093\pi$
$578$	−5.07189e17	−	2.92826e17i	−0.565769	−	0.326647i
$579$	1.67918e18	+	9.69473e17i	1.85219	+	1.06936i
$580$			4.07065e16i			0.0443999i
$581$	−2.51233e17	+	4.35148e17i	−0.270976	+	0.469345i
$582$	−5.36084e17	−	9.28524e17i	−0.571786	−	0.990362i
$583$	−8.70241e16	+	5.02434e16i	−0.0917897	+	0.0529948i
$584$	−1.44046e18			−1.50251
$585$	3.92098e17	+	4.04189e18i	0.404466	+	4.16938i
$586$	1.68612e18			1.72010
$587$	−9.72648e17	+	5.61559e17i	−0.981314	+	0.566562i	−0.902667	−	0.430340i	$-0.858394\pi$
$587$	−9.72648e17	+	5.61559e17i	−0.981314	+	0.566562i	−0.0786478	+	0.996902i	$0.525060\pi$
$588$	−5.96705e15	−	1.03352e16i	−0.00595398	−	0.0103126i
$589$	−2.85181e16	+	4.93948e16i	−0.0281431	+	0.0487452i
$590$		−	9.66807e16i		−	0.0943630i
$591$	2.00622e18	+	1.15829e18i	1.93669	+	1.11815i
$592$	4.08558e17	+	2.35881e17i	0.390088	+	0.225217i
$593$		−	3.88920e17i		−	0.367286i	−0.982993	−	0.183643i	$-0.941211\pi$
$593$		−	3.88920e17i		−	0.367286i	0.982993	−	0.183643i	$-0.0587891\pi$
$594$	1.60190e17	−	2.77457e17i	0.149632	−	0.259170i
$595$	−4.19745e17	−	7.27019e17i	−0.387815	−	0.671716i
$596$	−1.85947e15	+	1.07357e15i	−0.00169937	+	0.000981134i
$597$	−2.43071e18			−2.19735
$598$	−1.83179e16	−	1.88827e17i	−0.0163801	−	0.168852i
$599$	−6.55013e17			−0.579396			−0.289698	−	0.957118i	$-0.593555\pi$
$599$	−6.55013e17			−0.579396			−0.289698	+	0.957118i	$0.593555\pi$
$600$	2.43916e18	−	1.40825e18i	2.13431	−	1.23224i
$601$	4.06426e16	+	7.03950e16i	0.0351801	+	0.0609337i	0.883079	−	0.469224i	$-0.155466\pi$
$601$	4.06426e16	+	7.03950e16i	0.0351801	+	0.0609337i	−0.847899	+	0.530157i	$0.822133\pi$
$602$	−6.82272e17	+	1.18173e18i	−0.584226	+	1.01191i
$603$			1.44084e17i			0.122055i
$604$	−2.04160e16	−	1.17872e16i	−0.0171092	−	0.00987802i
$605$	−1.55410e18	−	8.97257e17i	−1.28845	−	0.743887i
$606$			1.01039e18i			0.828740i
$607$	−5.50980e17	+	9.54326e17i	−0.447105	+	0.774409i	−0.998196	−	0.0600364i	$-0.980878\pi$
$607$	−5.50980e17	+	9.54326e17i	−0.447105	+	0.774409i	0.551091	+	0.834445i	$0.314212\pi$
$608$	−1.60319e15	−	2.77681e15i	−0.00128710	−	0.00222933i
$609$	−1.88101e18	+	1.08600e18i	−1.49409	+	0.862616i
$610$	8.26096e17			0.649212
$611$	−1.39069e17	+	9.93467e16i	−0.108134	+	0.0772477i
$612$	6.28423e16			0.0483468
$613$	8.60868e17	−	4.97022e17i	0.655305	−	0.378340i	−0.135181	−	0.990821i	$-0.543162\pi$
$613$	8.60868e17	−	4.97022e17i	0.655305	−	0.378340i	0.790486	+	0.612481i	$0.209828\pi$
$614$	−1.39788e17	−	2.42120e17i	−0.105287	−	0.182363i
$615$	−8.10854e17	+	1.40444e18i	−0.604302	+	1.04668i
$616$			1.06610e17i			0.0786184i
$617$	5.75774e17	+	3.32423e17i	0.420144	+	0.242570i	0.695139	−	0.718875i	$-0.255343\pi$
$617$	5.75774e17	+	3.32423e17i	0.420144	+	0.242570i	−0.274995	+	0.961446i	$0.588676\pi$
$618$	−2.13839e18	−	1.23460e18i	−1.54406	−	0.891461i
$619$			2.60096e18i			1.85842i	0.369546	+	0.929212i	$0.379513\pi$
$619$			2.60096e18i			1.85842i	−0.369546	+	0.929212i	$0.620487\pi$
$620$	−4.11981e16	+	7.13573e16i	−0.0291294	+	0.0504536i
$621$	−4.30172e17	−	7.45080e17i	−0.300986	−	0.521324i
$622$	1.95611e18	−	1.12936e18i	1.35442	−	0.781977i
$623$	2.33352e18			1.59897
$624$	−2.77133e18	+	2.68843e17i	−1.87927	+	0.182305i
$625$	−1.03046e18			−0.691531
$626$	−7.40851e17	+	4.27730e17i	−0.492037	+	0.284078i
$627$	−5.56229e15	−	9.63417e15i	−0.00365607	−	0.00633250i
$628$	−2.48676e16	+	4.30720e16i	−0.0161769	+	0.0280193i
$629$			4.18846e17i			0.269666i
$630$	4.99978e18	+	2.88662e18i	3.18594	+	1.83940i
$631$	−1.88535e18	−	1.08851e18i	−1.18905	−	0.686499i	−0.230960	−	0.972963i	$-0.574187\pi$
$631$	−1.88535e18	−	1.08851e18i	−1.18905	−	0.686499i	−0.958091	+	0.286464i	$0.907520\pi$
$632$		−	4.72737e17i		−	0.295093i
$633$	−7.05573e17	+	1.22209e18i	−0.435931	+	0.755055i
$634$	−8.33983e17	−	1.44450e18i	−0.510008	−	0.883359i
$635$	2.96297e18	−	1.71067e18i	1.79348	−	1.03547i
$636$	1.18190e17			0.0708125
$637$	−1.43146e17	+	3.14700e17i	−0.0848934	+	0.186634i
$638$	−1.44888e17			−0.0850545
$639$	2.51465e18	−	1.45184e18i	1.46124	−	0.843649i
$640$	1.24178e18	+	2.15083e18i	0.714291	+	1.23719i
$641$	1.65638e18	−	2.86893e18i	0.943152	−	1.63359i	0.183743	−	0.982974i	$-0.441179\pi$
$641$	1.65638e18	−	2.86893e18i	0.943152	−	1.63359i	0.759409	−	0.650613i	$-0.225488\pi$
$642$			3.05238e18i			1.72053i
$643$	4.68739e17	+	2.70627e17i	0.261553	+	0.151008i	0.625043	−	0.780590i	$-0.285081\pi$
$643$	4.68739e17	+	2.70627e17i	0.261553	+	0.151008i	−0.363490	+	0.931598i	$0.618415\pi$
$644$	7.17829e15	+	4.14438e15i	0.00396518	+	0.00228930i
$645$		−	7.10469e18i		−	3.88514i
$646$	−2.27968e16	+	3.94852e16i	−0.0123413	+	0.0213758i
$647$	−4.19678e17	−	7.26903e17i	−0.224925	−	0.389582i	0.731372	−	0.681979i	$-0.238880\pi$
$647$	−4.19678e17	−	7.26903e17i	−0.224925	−	0.389582i	−0.956297	+	0.292397i	$0.905547\pi$
$648$	−6.64531e18	+	3.83667e18i	−3.52596	+	2.03572i
$649$	−1.05754e16			−0.00555529
$650$	−2.15031e18	−	9.78103e17i	−1.11832	−	0.508684i
$651$	−4.39646e18			−2.26374
$652$	5.32740e16	−	3.07577e16i	0.0271585	−	0.0156800i
$653$	9.07631e17	+	1.57206e18i	0.458114	+	0.793477i	0.998861	−	0.0477080i	$-0.0151917\pi$
$653$	9.07631e17	+	1.57206e18i	0.458114	+	0.793477i	−0.540747	+	0.841185i	$0.681858\pi$
$654$	2.91240e18	−	5.04442e18i	1.45544	−	2.52090i
$655$			2.72309e18i			1.34739i
$656$	−7.09167e17	−	4.09438e17i	−0.347435	−	0.200592i
$657$	7.38942e18	+	4.26629e18i	3.58456	+	2.06955i
$658$			2.42978e17i			0.116708i
$659$	5.42089e16	−	9.38925e16i	0.0257819	−	0.0446556i	−0.852847	−	0.522162i	$-0.825126\pi$
$659$	5.42089e16	−	9.38925e16i	0.0257819	−	0.0446556i	0.878628	+	0.477506i	$0.158459\pi$
$660$	−8.03545e15	−	1.39178e16i	−0.00378421	−	0.00655444i
$661$	2.03525e18	−	1.17505e18i	0.949093	−	0.547959i	0.0562939	−	0.998414i	$-0.482072\pi$
$661$	2.03525e18	−	1.17505e18i	0.949093	−	0.547959i	0.892799	+	0.450455i	$0.148738\pi$
$662$	3.63274e18			1.67748
$663$	−1.43695e18	−	2.01150e18i	−0.657058	−	0.919774i
$664$	1.36165e18			0.616558
$665$	1.11479e17	−	6.43623e16i	0.0499863	−	0.0288596i
$666$	−1.44022e18	−	2.49454e18i	−0.639509	−	1.10766i
$667$	−1.94540e17	+	3.36953e17i	−0.0855442	+	0.148167i
$668$			5.10476e16i			0.0222294i
$669$	−4.03432e18	−	2.32921e18i	−1.73980	−	1.00448i
$670$	−1.30784e17	−	7.55083e16i	−0.0558559	−	0.0322484i
$671$		−	9.03625e16i		−	0.0382201i
$672$	1.23577e17	−	2.14042e17i	0.0517652	−	0.0896600i
$673$	2.75049e17	+	4.76398e17i	0.114107	+	0.197639i	0.917422	−	0.397915i	$-0.130266\pi$
$673$	2.75049e17	+	4.76398e17i	0.114107	+	0.197639i	−0.803316	+	0.595554i	$0.796933\pi$
$674$	−8.38723e17	+	4.84237e17i	−0.344611	+	0.198961i
$675$	−1.07130e19			−4.35950
$676$	−4.86129e16	−	5.57620e16i	−0.0195929	−	0.0224742i
$677$	8.63789e17			0.344811			0.172406	−	0.985026i	$-0.444846\pi$
$677$	8.63789e17			0.344811			0.172406	+	0.985026i	$0.444846\pi$
$678$	−1.01105e18	+	5.83727e17i	−0.399740	+	0.230790i
$679$	−6.78528e17	−	1.17524e18i	−0.265714	−	0.460230i
$680$	−1.13748e18	+	1.97018e18i	−0.441202	+	0.764185i
$681$		−	3.95558e18i		−	1.51969i
$682$	−2.53984e17	−	1.46638e17i	−0.0966512	−	0.0558016i
$683$	−5.69615e17	−	3.28867e17i	−0.214707	−	0.123961i	0.388790	−	0.921326i	$-0.372893\pi$
$683$	−5.69615e17	−	3.28867e17i	−0.214707	−	0.123961i	−0.603497	+	0.797365i	$0.706227\pi$
$684$			9.63603e15i			0.00359777i
$685$	−1.13308e18	+	1.96256e18i	−0.419057	+	0.725827i
$686$	1.44437e18	+	2.50172e18i	0.529140	+	0.916498i
$687$	1.61922e18	−	9.34858e17i	0.587608	−	0.339256i
$688$	3.58749e18			1.28963
$689$	−1.99027e18	−	2.78606e18i	−0.708741	−	0.992121i
$690$	1.40429e18			0.495380
$691$	−6.07261e17	+	3.50602e17i	−0.212211	+	0.122520i	−0.602338	−	0.798241i	$-0.705764\pi$
$691$	−6.07261e17	+	3.50602e17i	−0.212211	+	0.122520i	0.390128	+	0.920761i	$0.372431\pi$
$692$	−3.51549e16	−	6.08901e16i	−0.0121702	−	0.0210794i
$693$	3.15753e17	−	5.46900e17i	0.108288	−	0.187561i
$694$			1.43603e18i			0.487895i
$695$	4.84551e18	+	2.79755e18i	1.63094	+	0.941623i
$696$	5.09742e18	+	2.94300e18i	1.69977	+	0.981363i
$697$		−	7.27025e17i		−	0.240180i
$698$	3.05348e17	−	5.28877e17i	0.0999388	−	0.173099i
$699$	3.48995e18	+	6.04477e18i	1.13166	+	1.96010i
$700$	8.93840e16	−	5.16059e16i	0.0287159	−	0.0165791i
$701$	−5.86940e17			−0.186821			−0.0934107	−	0.995628i	$-0.529777\pi$
$701$	−5.86940e17			−0.186821			−0.0934107	+	0.995628i	$0.529777\pi$
$702$	9.93677e18	+	4.51990e18i	3.13368	+	1.42540i
$703$	−6.42245e16			−0.0200674
$704$	2.49985e17	−	1.44329e17i	0.0773912	−	0.0446819i
$705$	−6.32550e17	−	1.09561e18i	−0.194029	−	0.336067i
$706$	6.56510e17	−	1.13711e18i	0.199531	−	0.345598i
$707$			1.27887e18i			0.385123i
$708$	1.07721e16	+	6.21927e15i	0.00321428	+	0.00185577i
$709$	−4.62330e18	−	2.66927e18i	−1.36695	−	0.789207i	−0.376410	−	0.926453i	$-0.622842\pi$
$709$	−4.62330e18	−	2.66927e18i	−1.36695	−	0.789207i	−0.990537	+	0.137246i	$0.956175\pi$
$710$			3.04338e18i			0.891613i
$711$	−1.40013e18	+	2.42510e18i	−0.406458	+	0.704006i
$712$	−3.16185e18	−	5.47649e18i	−0.909540	−	1.57537i
$713$	−6.82044e17	+	3.93779e17i	−0.194415	+	0.112246i
$714$	−3.51444e18			−0.992698
$715$	−1.92766e17	+	4.23787e17i	−0.0539562	+	0.118620i
$716$	1.08249e17			0.0300255
$717$	−1.00968e19	+	5.82940e18i	−2.77530	+	1.60232i
$718$	−2.93104e18	−	5.07671e18i	−0.798385	−	1.38284i
$719$	2.78355e17	−	4.82125e17i	0.0751383	−	0.130143i	−0.826008	−	0.563658i	$-0.809393\pi$
$719$	2.78355e17	−	4.82125e17i	0.0751383	−	0.130143i	0.901146	+	0.433515i	$0.142727\pi$
$720$		−	1.51783e19i		−	4.06033i
$721$	−2.70659e18	−	1.56265e18i	−0.717536	−	0.414269i
$722$	3.24070e18	+	1.87102e18i	0.851426	+	0.491571i
$723$		−	6.55088e17i		−	0.170569i
$724$	5.25376e16	−	9.09978e16i	0.0135572	−	0.0234817i
$725$	2.42241e18	+	4.19574e18i	0.619513	+	1.07303i
$726$	−6.50606e18	+	3.75627e18i	−1.64903	+	0.952071i
$727$	5.08339e18			1.27697			0.638483	−	0.769636i	$-0.279562\pi$
$727$	5.08339e18			1.27697			0.638483	+	0.769636i	$0.279562\pi$
$728$	−3.61560e18	+	3.50744e17i	−0.900175	+	0.0873246i
$729$	1.78627e19			4.40777
$730$	−7.74495e18	+	4.47155e18i	−1.89417	+	1.09360i
$731$	1.59255e18	+	2.75837e18i	0.386037	+	0.668636i
$732$	−5.31411e16	+	9.20431e16i	−0.0127676	+	0.0221141i
$733$			2.47373e18i			0.589084i	0.955639	+	0.294542i	$0.0951671\pi$
$733$			2.47373e18i			0.589084i	−0.955639	+	0.294542i	$0.904833\pi$
$734$	−6.26801e18	−	3.61884e18i	−1.47947	−	0.854171i
$735$	−2.21627e18	−	1.27957e18i	−0.518508	−	0.299361i
$736$		−	4.42739e16i		−	0.0102670i
$737$	−8.25947e15	+	1.43058e16i	−0.00189851	+	0.00328832i
$738$	2.49991e18	+	4.32997e18i	0.569584	+	0.986549i
$739$	−3.70111e17	+	2.13684e17i	−0.0835879	+	0.0482595i	−0.541211	−	0.840887i	$-0.682034\pi$
$739$	−3.70111e17	+	2.13684e17i	−0.0835879	+	0.0482595i	0.457623	+	0.889146i	$0.348701\pi$
$740$	−9.27806e16			−0.0207707
$741$	3.08436e17	−	2.20337e17i	0.0684457	−	0.0488955i
$742$	−4.86773e18			−1.07078
$743$	7.46881e18	−	4.31212e18i	1.62864	−	0.940294i	0.644136	−	0.764911i	$-0.277217\pi$
$743$	7.46881e18	−	4.31212e18i	1.62864	−	0.940294i	0.984500	−	0.175383i	$-0.0561163\pi$
$744$	5.95708e18	+	1.03180e19i	1.28768	+	2.23033i
$745$	−2.30214e17	+	3.98742e17i	−0.0493305	+	0.0854430i
$746$			3.80917e18i			0.809149i
$747$	−6.98516e18	−	4.03288e18i	−1.47093	−	0.849242i
$748$	6.23948e15	+	3.60236e15i	0.00130253	+	0.000752016i
$749$			3.86344e18i			0.799544i
$750$	1.73353e18	−	3.00256e18i	0.355658	−	0.616018i
$751$	−2.79973e18	−	4.84928e18i	−0.569451	−	0.986319i	−0.996620	−	0.0821469i	$-0.973822\pi$
$751$	−2.79973e18	−	4.84928e18i	−0.569451	−	0.986319i	0.427169	−	0.904172i	$-0.359511\pi$
$752$	5.53224e17	−	3.19404e17i	0.111554	−	0.0644057i
$753$	9.66254e18			1.93163
$754$	−4.76677e17	−	4.91376e18i	−0.0944735	−	0.973868i
$755$	−5.05525e18			−0.993316
$756$	−4.13051e17	+	2.38475e17i	−0.0804659	+	0.0464570i
$757$	−5.50018e17	−	9.52660e17i	−0.106232	−	0.183999i	0.808009	−	0.589170i	$-0.200545\pi$
$757$	−5.50018e17	−	9.52660e17i	−0.106232	−	0.183999i	−0.914241	+	0.405171i	$0.867212\pi$
$758$	2.15957e17	−	3.74048e17i	0.0413540	−	0.0716272i
$759$		−	1.53608e17i		−	0.0291638i
$760$	−3.02101e17	−	1.74418e17i	−0.0568674	−	0.0328324i
$761$	5.24199e18	+	3.02647e18i	0.978354	+	0.564853i	0.901773	−	0.432210i	$-0.142266\pi$
$761$	5.24199e18	+	3.02647e18i	0.978354	+	0.564853i	0.0765814	+	0.997063i	$0.475599\pi$
$762$		−	1.43231e19i		−	2.65051i
$763$	3.68626e18	−	6.38479e18i	0.676358	−	1.17149i
$764$	−8.32456e16	−	1.44186e17i	−0.0151445	−	0.0262310i
$765$	1.16704e19	−	6.73790e18i	2.10516	−	1.21542i
$766$	5.46891e18			0.978168
$767$	−3.47928e16	−	3.58657e17i	−0.00617049	−	0.0636077i
$768$	−9.89895e17			−0.174077
$769$	−6.58829e18	+	3.80375e18i	−1.14882	+	0.663271i	−0.948599	−	0.316480i	$-0.897499\pi$
$769$	−6.58829e18	+	3.80375e18i	−1.14882	+	0.663271i	−0.200220	+	0.979751i	$0.564166\pi$
$770$	3.30945e17	+	5.73213e17i	0.0572224	+	0.0991121i
$771$	−5.90239e18	+	1.02232e19i	−1.01199	+	1.75281i
$772$		−	1.92551e17i		−	0.0327365i
$773$	1.24237e18	+	7.17282e17i	0.209452	+	0.120927i	0.601057	−	0.799206i	$-0.294747\pi$
$773$	1.24237e18	+	7.17282e17i	0.209452	+	0.120927i	−0.391605	+	0.920133i	$0.628080\pi$
$774$	−1.89696e19	−	1.09521e19i	−3.17133	−	1.83097i
$775$			9.80666e18i			1.62577i
$776$	−1.83877e18	+	3.18484e18i	−0.302292	+	0.523585i
$777$	−2.47527e18	−	4.28729e18i	−0.403539	−	0.698951i
$778$	5.62641e18	−	3.24841e18i	0.909629	−	0.525174i
$779$	1.11480e17			0.0178732
$780$	4.45576e17	−	3.18306e17i	0.0708446	−	0.0506092i
$781$	3.32899e17			0.0524906
$782$	−5.45212e17	+	3.14778e17i	−0.0852553	+	0.0492222i
$783$	−1.11942e19	−	1.93889e19i	−1.73596	−	3.00677i
$784$	6.46112e17	−	1.11910e18i	0.0993695	−	0.172113i
$785$			1.06651e19i			1.62672i
$786$	9.87263e18	+	5.69996e18i	1.49343	+	0.862235i
$787$	−5.83213e17	−	3.36718e17i	−0.0874966	−	0.0505162i	0.455613	−	0.890178i	$-0.349420\pi$
$787$	−5.83213e17	−	3.36718e17i	−0.0874966	−	0.0505162i	−0.543110	+	0.839662i	$0.682753\pi$
$788$		−	2.30052e17i		−	0.0342300i
$789$	−1.56569e18	+	2.71185e18i	−0.231049	+	0.400189i
$790$	−1.46749e18	−	2.54177e18i	−0.214783	−	0.372015i
$791$	−1.27969e18	+	7.38831e17i	−0.185763	+	0.107250i
$792$	−1.71135e18			−0.246391
$793$	3.06457e18	−	2.97290e17i	0.437617	−	0.0424526i
$794$	4.33294e17			0.0613690
$795$	2.19490e19	−	1.26722e19i	3.08339	−	1.78019i
$796$	1.20693e17	+	2.09046e17i	0.0168169	+	0.0291278i
$797$	4.42772e18	−	7.66904e18i	0.611929	−	1.05989i	−0.378986	−	0.925403i	$-0.623727\pi$
$797$	4.42772e18	−	7.66904e18i	0.611929	−	1.05989i	0.990915	−	0.134490i	$-0.0429396\pi$
$798$		−	5.38892e17i		−	0.0738725i
$799$	4.91171e17	+	2.83578e17i	0.0667849	+	0.0385583i
$800$	−4.77438e17	−	2.75649e17i	−0.0643920	−	0.0371767i
$801$			3.74585e19i			5.01117i
$802$	1.47127e18	−	2.54832e18i	0.195236	−	0.338159i
$803$	4.89120e17	+	8.47181e17i	0.0643820	+	0.111513i
$804$	1.68262e16	−	9.71459e15i	0.00219695	−	0.00126841i
$805$	1.77743e18			0.230207
$806$	4.13750e18	−	9.09610e18i	0.531570	−	1.16863i
$807$	−2.99446e19			−3.81629
$808$	3.00135e18	−	1.73283e18i	0.379439	−	0.219069i
$809$	−4.26585e18	−	7.38866e18i	−0.534983	−	0.926618i	−0.999164	−	0.0408773i	$-0.986985\pi$
$809$	−4.26585e18	−	7.38866e18i	−0.534983	−	0.926618i	0.464181	−	0.885740i	$-0.346349\pi$
$810$	−2.38200e19	+	4.12574e19i	−2.96339	+	5.13275i
$811$			9.18511e18i			1.13357i	0.823865	+	0.566786i	$0.191813\pi$
$811$			9.18511e18i			1.13357i	−0.823865	+	0.566786i	$0.808187\pi$
$812$	1.86797e17	+	1.07847e17i	0.0228694	+	0.0132037i
$813$	2.53758e18	+	1.46507e18i	0.308199	+	0.177939i
$814$		−	3.30236e17i		−	0.0397893i
$815$	6.59564e18	−	1.14240e19i	0.788374	−	1.36550i
$816$	4.61985e18	+	8.00182e18i	0.547825	+	0.948861i
$817$	−4.22959e17	+	2.44196e17i	−0.0497571	+	0.0287273i
$818$	6.59925e17			0.0770191
$819$	1.95865e19	+	8.90924e18i	2.26784	+	1.03156i
$820$	1.61047e17			0.0184996
$821$	1.19187e18	−	6.88128e17i	0.135831	−	0.0784222i	−0.430545	−	0.902569i	$-0.641678\pi$
$821$	1.19187e18	−	6.88128e17i	0.135831	−	0.0784222i	0.566376	+	0.824147i	$0.308345\pi$
$822$	4.74353e18	+	8.21603e18i	0.536333	+	0.928956i
$823$	−2.17626e17	+	3.76940e17i	−0.0244125	+	0.0422837i	−0.877974	−	0.478709i	$-0.841105\pi$
$823$	−2.17626e17	+	3.76940e17i	−0.0244125	+	0.0422837i	0.853561	+	0.520993i	$0.174438\pi$
$824$			8.46939e18i			0.942596i
$825$	−1.65647e18	−	9.56366e17i	−0.182909	−	0.105602i
$826$	−4.43655e17	−	2.56144e17i	−0.0486044	−	0.0280617i
$827$		−	5.57312e18i		−	0.605777i	−0.953026	−	0.302888i	$-0.902049\pi$
$827$		−	5.57312e18i		−	0.605777i	0.953026	−	0.302888i	$-0.0979509\pi$
$828$	−6.65272e16	+	1.15228e17i	−0.00717467	+	0.0124269i
$829$	3.13110e17	+	5.42323e17i	0.0335037	+	0.0580302i	0.882291	−	0.470704i	$-0.156000\pi$
$829$	3.13110e17	+	5.42323e17i	0.0335037	+	0.0580302i	−0.848787	+	0.528734i	$0.822667\pi$
$830$	7.32123e18	−	4.22691e18i	0.777278	−	0.448762i
$831$	−3.42786e19			−3.61091
$832$	5.71725e18	+	8.00322e18i	0.597566	+	0.836494i
$833$	1.14728e18			0.118981
$834$	2.02852e19	−	1.17117e19i	2.08737	−	1.20515i
$835$	5.47328e18	+	9.48000e18i	0.558837	+	0.967935i
$836$	−5.52374e14	+	9.56740e14i	−5.59619e−5	+	9.69289e-5i
$837$		−	4.53174e19i		−	4.55564i
$838$	−6.25619e17	−	3.61201e17i	−0.0624056	−	0.0360299i
$839$	2.75443e18	+	1.59027e18i	0.272634	+	0.157405i	0.630084	−	0.776527i	$-0.283020\pi$
$839$	2.75443e18	+	1.59027e18i	0.272634	+	0.157405i	−0.357450	+	0.933932i	$0.616354\pi$
$840$		−	2.68889e19i		−	2.64094i
$841$	6.78979e16	−	1.17603e17i	0.00661732	−	0.0114615i
$842$	−4.79712e18	−	8.30885e18i	−0.463929	−	0.803549i
$843$	−2.16993e19	+	1.25281e19i	−2.08241	+	1.20228i
$844$	1.40137e17			0.0133452
$845$	−1.50066e19	−	5.14327e18i	−1.41812	−	0.486039i
$846$	−3.90038e18			−0.365763
$847$	−8.23479e18	+	4.75436e18i	−0.766321	+	0.442435i
$848$	6.39881e18	+	1.10831e19i	0.590916	+	1.02350i
$849$	1.17215e19	−	2.03023e19i	1.07420	−	1.86056i
$850$			7.83923e18i			0.712936i
$851$	−7.68002e17	−	4.43406e17i	−0.0693139	−	0.0400184i
$852$	−3.39091e17	−	1.95774e17i	−0.0303710	−	0.0175347i
$853$			4.56956e18i			0.406168i	0.979161	+	0.203084i	$0.0650964\pi$
$853$			4.56956e18i			0.406168i	−0.979161	+	0.203084i	$0.934904\pi$
$854$	2.18865e18	−	3.79085e18i	0.193063	−	0.334395i
$855$	1.03317e18	+	1.78950e18i	0.0904463	+	0.156658i
$856$	9.06702e18	−	5.23485e18i	0.787744	−	0.454804i
$857$	−7.06659e18			−0.609305			−0.304653	−	0.952464i	$-0.598540\pi$
$857$	−7.06659e18			−0.609305			−0.304653	+	0.952464i	$0.598540\pi$
$858$	1.13295e18	+	1.58595e18i	0.0969493	+	0.135713i
$859$	1.56558e19			1.32959			0.664797	−	0.747024i	$-0.268518\pi$
$859$	1.56558e19			1.32959			0.664797	+	0.747024i	$0.268518\pi$
$860$	−6.11020e17	+	3.52772e17i	−0.0515009	+	0.0297341i
$861$	4.29653e18	+	7.44180e18i	0.359416	+	0.622526i
$862$	−4.69465e16	+	8.13136e16i	−0.00389767	+	0.00675097i
$863$			1.00569e19i			0.828692i	0.910119	+	0.414346i	$0.135990\pi$
$863$			1.00569e19i			0.828692i	−0.910119	+	0.414346i	$0.864010\pi$
$864$	2.20628e18	+	1.27380e18i	0.180435	+	0.104174i
$865$	−1.30572e19	−	7.53857e18i	−1.05985	−	0.611905i
$866$		−	2.87631e18i		−	0.231723i
$867$	8.07871e18	−	1.39927e19i	0.645978	−	1.11887i
$868$	2.18299e17	+	3.78106e17i	0.0173250	+	0.0300079i
$869$	−2.78032e17	+	1.60522e17i	−0.0219011	+	0.0126446i
$870$	3.65432e19			2.85714
$871$	−5.12344e17	−	2.33048e17i	−0.0397598	−	0.0180854i
$872$	−1.99791e19			−1.53893
$873$	1.88655e19	−	1.08920e19i	1.44236	−	0.832749i
$874$	−4.82670e16	−	8.36009e16i	−0.00366291	−	0.00634435i
$875$	2.19415e18	−	3.80037e18i	0.165277	−	0.286269i
$876$		−	1.15058e18i		−	0.0860283i
$877$	−6.86318e18	−	3.96246e18i	−0.509364	−	0.294081i	0.223208	−	0.974771i	$-0.428347\pi$
$877$	−6.86318e18	−	3.96246e18i	−0.509364	−	0.294081i	−0.732572	+	0.680689i	$0.761680\pi$
$878$	−1.54021e19	−	8.89240e18i	−1.13466	−	0.655096i
$879$			4.65181e19i			3.40168i
$880$	8.70078e17	−	1.50702e18i	0.0631569	−	0.109391i
$881$	−8.07540e18	−	1.39870e19i	−0.581863	−	1.00782i	−0.995259	−	0.0972648i	$-0.968991\pi$
$881$	−8.07540e18	−	1.39870e19i	−0.581863	−	1.00782i	0.413395	−	0.910552i	$-0.364343\pi$
$882$	−6.83290e18	+	3.94497e18i	−0.488719	+	0.282162i
$883$	1.70818e19			1.21280			0.606399	−	0.795161i	$-0.292614\pi$
$883$	1.70818e19			1.21280			0.606399	+	0.795161i	$0.292614\pi$
$884$	−1.01644e17	+	2.23459e17i	−0.00716375	+	0.0157492i
$885$	2.66730e18			0.186613
$886$	−1.98623e19	+	1.14675e19i	−1.37946	+	0.796432i
$887$	1.13206e19	+	1.96078e19i	0.780486	+	1.35184i	0.931659	+	0.363335i	$0.118362\pi$
$887$	1.13206e19	+	1.96078e19i	0.780486	+	1.35184i	−0.151172	+	0.988507i	$0.548305\pi$
$888$	−6.70784e18	+	1.16183e19i	−0.459091	+	0.795168i
$889$		−	1.81289e19i		−	1.23171i
$890$	−3.40008e19	−	1.96304e19i	−2.29326	−	1.32402i
$891$	4.51294e18	+	2.60555e18i	0.302172	+	0.174459i
$892$			4.62614e17i			0.0307502i
$893$	−4.34828e16	+	7.53145e16i	−0.00286935	+	0.00496986i
$894$	9.63766e17	+	1.66929e18i	0.0631361	+	0.109355i
$895$	2.01029e19	−	1.16064e19i	1.30740	−	0.754828i
$896$	1.31598e19			0.849666
$897$	5.20951e18	−	5.05367e17i	0.333923	−	0.0323934i
$898$	2.43086e19			1.54690
$899$	−1.77485e19	+	1.02471e19i	−1.12131	+	0.647386i
$900$	8.28396e17	+	1.43482e18i	0.0519591	+	0.0899958i
$901$	−5.68108e18	+	9.83991e18i	−0.353769	+	0.612746i
$902$			5.73218e17i			0.0354387i
$903$	−3.26025e19	−	1.88231e19i	−2.00115	−	1.15537i
$904$	3.46789e18	+	2.00219e18i	0.211335	+	0.122014i
$905$		−	2.25322e19i		−	1.36329i
$906$	−1.05816e19	+	1.83279e19i	−0.635652	+	1.10098i
$907$	1.20112e19	+	2.08040e19i	0.716373	+	1.24080i	0.962427	+	0.271539i	$0.0875326\pi$
$907$	1.20112e19	+	2.08040e19i	0.716373	+	1.24080i	−0.246054	+	0.969256i	$0.579134\pi$
$908$	−3.40189e17	+	1.96408e17i	−0.0201448	+	0.0116306i
$909$	−2.05288e19			−1.20698
$910$	−1.83513e19	+	1.31096e19i	−1.07127	+	0.765280i
$911$	−3.99309e18			−0.231441			−0.115720	−	0.993282i	$-0.536918\pi$
$911$	−3.99309e18			−0.231441			−0.115720	+	0.993282i	$0.536918\pi$
$912$	−1.22697e18	+	7.08393e17i	−0.0706103	+	0.0407669i
$913$	−4.62361e17	−	8.00832e17i	−0.0264193	−	0.0457595i
$914$	−6.61455e18	+	1.14567e19i	−0.375275	+	0.649996i
$915$			2.27910e19i			1.28388i
$916$	−1.60800e17	−	9.28379e16i	−0.00899426	−	0.00519284i
$917$	1.24959e19	+	7.21451e18i	0.694012	+	0.400688i
$918$		−	3.62258e19i		−	1.99774i
$919$	7.22636e18	−	1.25164e19i	0.395703	−	0.685377i	−0.597488	−	0.801878i	$-0.703834\pi$
$919$	7.22636e18	−	1.25164e19i	0.395703	−	0.685377i	0.993191	+	0.116501i	$0.0371677\pi$
$920$	−2.40837e18	−	4.17141e18i	−0.130949	−	0.226810i
$921$	6.67978e18	−	3.85658e18i	0.360641	−	0.208216i
$922$	−6.41710e18			−0.344023
$923$	1.09523e18	+	1.12900e19i	0.0583034	+	0.601013i
$924$	−8.51561e16			−0.00450140
$925$	−9.56315e18	+	5.52129e18i	−0.501972	+	0.289814i
$926$	5.52368e18	+	9.56730e18i	0.287910	+	0.498675i
$927$	2.50843e19	−	4.34472e19i	1.29832	−	2.24876i
$928$		−	1.15212e18i		−	0.0592154i
$929$	−1.26205e19	−	7.28643e18i	−0.644130	−	0.371888i	0.142074	−	0.989856i	$-0.454623\pi$
$929$	−1.26205e19	−	7.28643e18i	−0.644130	−	0.371888i	−0.786204	+	0.617968i	$0.787956\pi$
$930$	6.40591e19	+	3.69845e19i	3.24670	+	1.87448i
$931$			1.75920e17i			0.00885406i
$932$	3.46576e17	−	6.00287e17i	0.0173219	−	0.0300024i
$933$	3.11576e19	+	5.39665e19i	1.54644	+	2.67851i
$934$	−1.09617e19	+	6.32874e18i	−0.540285	+	0.311934i
$935$	1.54497e18			0.0756213
$936$	−5.63028e18	−	5.80390e19i	−0.273676	−	2.82115i
$937$	2.61977e19			1.26461			0.632305	−	0.774720i	$-0.282109\pi$
$937$	2.61977e19			1.26461			0.632305	+	0.774720i	$0.282109\pi$
$938$	−6.92995e17	+	4.00101e17i	−0.0332209	+	0.0191801i
$939$	−1.18006e19	−	2.04392e19i	−0.561793	−	0.973054i
$940$	−6.28166e16	+	1.08802e17i	−0.00296991	+	0.00514404i
$941$		−	6.79768e18i		−	0.319174i	−0.987184	−	0.159587i	$-0.948984\pi$
$941$		−	6.79768e18i		−	0.319174i	0.987184	−	0.159587i	$-0.0510163\pi$
$942$	3.86667e19	+	2.23242e19i	1.80304	+	1.04099i
$943$	1.33308e18	+	7.69656e17i	0.0617350	+	0.0356427i
$944$			1.34684e18i			0.0619440i
$945$	−5.11382e19	+	8.85739e19i	−2.33582	+	4.04575i
$946$	−1.25563e18	−	2.17482e18i	−0.0569600	−	0.0986576i
$947$	−1.03722e19	+	5.98839e18i	−0.467300	+	0.269796i	−0.715109	−	0.699013i	$-0.753623\pi$
$947$	−1.03722e19	+	5.98839e18i	−0.467300	+	0.269796i	0.247809	+	0.968809i	$0.420290\pi$
$948$	3.77603e17			0.0168959
$949$	−2.71223e19	+	1.93753e19i	−1.20530	+	0.861031i
$950$	−1.20204e18			−0.0530537
$951$	3.98520e19	−	2.30086e19i	1.74693	−	1.00859i
$952$	6.02727e18	+	1.04395e19i	0.262410	+	0.454508i
$953$	9.00173e18	−	1.55915e19i	0.389244	−	0.674191i	−0.603104	−	0.797663i	$-0.706069\pi$
$953$	9.00173e18	−	1.55915e19i	0.389244	−	0.674191i	0.992348	+	0.123472i	$0.0394028\pi$
$954$		−	7.81386e19i		−	3.35584i
$955$	−3.09189e19	−	1.78510e19i	−1.31887	−	0.761450i
$956$	1.00268e18	+	5.78900e17i	0.0424803	+	0.0245260i
$957$		−	3.99728e18i		−	0.168204i
$958$	4.98425e17	−	8.63298e17i	0.0208317	−	0.0360815i
$959$	6.00394e18	+	1.03991e19i	0.249239	+	0.431694i
$960$	−6.30506e19	+	3.64023e19i	−2.59972	+	1.50095i
$961$	−1.70659e19			−0.698918
$962$	1.11997e19	−	1.08647e18i	0.455584	−	0.0441956i
$963$	−6.20173e19			−2.50578
$964$	−5.63391e16	+	3.25274e16i	−0.00226104	+	0.00130541i
$965$	−2.06451e19	−	3.57584e19i	−0.822981	−	1.42545i
$966$	3.72051e18	−	6.44412e18i	0.147316	−	0.255160i
$967$		−	1.81053e19i		−	0.712089i	−0.934469	−	0.356044i	$-0.884125\pi$
$967$		−	1.81053e19i		−	0.712089i	0.934469	−	0.356044i	$-0.115875\pi$
$968$	2.23158e19	+	1.28840e19i	0.871812	+	0.503341i
$969$	−1.08935e18	−	6.28935e17i	−0.0422729	−	0.0244063i
$970$			2.28320e19i			0.880092i
$971$	−4.13840e18	+	7.16792e18i	−0.158456	+	0.274453i	−0.934312	−	0.356457i	$-0.883985\pi$
$971$	−4.13840e18	+	7.16792e18i	−0.158456	+	0.274453i	0.775856	+	0.630910i	$0.217318\pi$
$972$	−1.69463e18	−	2.93518e18i	−0.0644530	−	0.111636i
$973$	2.56752e19	−	1.48236e19i	0.970020	−	0.560041i
$974$	1.93654e19			0.726765
$975$	2.69847e19	−	5.93245e19i	1.00597	−	2.21159i
$976$	−1.15082e19			−0.426172
$977$	−1.43713e19	+	8.29726e18i	−0.528665	+	0.305225i	−0.740473	−	0.672086i	$-0.765398\pi$
$977$	−1.43713e19	+	8.29726e18i	−0.528665	+	0.305225i	0.211808	+	0.977311i	$0.432065\pi$
$978$	−2.76119e19	−	4.78253e19i	−1.00901	−	1.74765i
$979$	−2.14727e18	+	3.71918e18i	−0.0779468	+	0.135008i
$980$			2.54139e17i			0.00916437i
$981$	1.02491e20	+	5.91732e19i	3.67144	+	2.11971i
$982$	−3.60394e19	−	2.08074e19i	−1.28249	−	0.740444i
$983$		−	3.88258e19i		−	1.37253i	−0.727350	−	0.686267i	$-0.759248\pi$
$983$		−	3.88258e19i		−	1.37253i	0.727350	−	0.686267i	$-0.240752\pi$
$984$	1.16433e19	−	2.01669e19i	0.408893	−	0.708223i
$985$	−2.46660e19	−	4.27228e19i	−0.860525	−	1.49047i
$986$	−1.41878e19	+	8.19132e18i	−0.491716	+	0.283892i
$987$	−6.70347e18			−0.230801
$988$	−3.42644e16	−	1.55857e16i	−0.00117199	−	0.000533097i
$989$	−6.74371e18			−0.229152
$990$	−9.20143e18	+	5.31245e18i	−0.310618	+	0.179335i
$991$	2.05517e19	+	3.55965e19i	0.689237	+	1.19379i	0.972085	+	0.234628i	$0.0753872\pi$
$991$	2.05517e19	+	3.55965e19i	0.689237	+	1.19379i	−0.282849	+	0.959165i	$0.591279\pi$
$992$	1.16603e18	−	2.01962e18i	0.0388494	−	0.0672891i
$993$			1.00223e20i			3.31739i
$994$	1.39657e19	+	8.06307e18i	0.459251	+	0.265148i
$995$	4.48275e19	+	2.58812e19i	1.46452	+	0.845540i
$996$			1.08764e18i			0.0353019i
$997$	1.05975e19	−	1.83553e19i	0.341730	−	0.591894i	−0.643024	−	0.765846i	$-0.722320\pi$
$997$	1.05975e19	−	1.83553e19i	0.341730	−	0.591894i	0.984754	+	0.173952i	$0.0556538\pi$
$998$	1.60381e19	+	2.77788e19i	0.513811	+	0.889947i
$999$	4.41921e19	−	2.55143e19i	1.40660	−	0.812099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.14.e.a.10.5	yes	30
13.2	odd	12		169.14.a.f.1.9		30
13.4	even	6	inner	13.14.e.a.4.5	✓	30
13.11	odd	12		169.14.a.f.1.22		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.14.e.a.4.5	✓	30	13.4	even	6	inner
13.14.e.a.10.5	yes	30	1.1	even	1	trivial
169.14.a.f.1.9		30	13.2	odd	12
169.14.a.f.1.22		30	13.11	odd	12

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	13.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-77.2063 + 44.5751i) q^{2} +(-1229.77 - 2130.03i) q^{3} +(-122.125 + 211.526i) q^{4} +52376.5i q^{5} +(189892. + 109634. i) q^{6} +(240349. + 138765. i) q^{7} -752093. i q^{8} +(-2.22751e6 + 3.85817e6i) q^{9} +(-2.33469e6 - 4.04379e6i) q^{10} +(-442330. + 255379. i) q^{11} +600742. q^{12} +(-1.01162e7 - 1.41611e7i) q^{13} -2.47419e7 q^{14} +(1.11563e8 - 6.44111e7i) q^{15} +(3.25242e7 + 5.63335e7i) q^{16} +(-2.88760e7 + 5.00148e7i) q^{17} -3.97166e8i q^{18} +(-7.66910e6 - 4.42776e6i) q^{19} +(-1.10790e7 - 6.39647e6i) q^{20} -6.82599e8i q^{21} +(2.27671e7 - 3.94338e7i) q^{22} +(-6.11385e7 - 1.05895e8i) q^{23} +(-1.60198e9 + 9.24902e8i) q^{24} -1.52259e9 q^{25} +(1.41227e9 + 6.42393e8i) q^{26} +7.03603e9 q^{27} +(-5.87051e7 + 3.38934e7i) q^{28} +(-1.59098e9 - 2.75565e9i) q^{29} +(-5.74226e9 + 9.94589e9i) q^{30} -6.44076e9i q^{31} +(3.13569e8 + 1.81039e8i) q^{32} +(1.08793e9 + 6.28117e8i) q^{33} -5.14861e9i q^{34} +(-7.26805e9 + 1.25886e10i) q^{35} +(-5.44070e8 - 9.42356e8i) q^{36} +(6.28084e9 - 3.62624e9i) q^{37} +7.89470e8 q^{38} +(-1.77228e10 + 3.89628e10i) q^{39} +3.93920e10 q^{40} +(-1.09022e10 + 6.29436e9i) q^{41} +(3.04269e10 + 5.27010e10i) q^{42} +(2.75756e10 - 4.77623e10i) q^{43} -1.24753e8i q^{44} +(-2.02077e11 - 1.16669e11i) q^{45} +(9.44056e9 + 5.45051e9i) q^{46} -9.82051e9i q^{47} +(7.99946e10 - 1.38555e11i) q^{48} +(-9.93280e9 - 1.72041e10i) q^{49} +(1.17554e11 - 6.78697e10i) q^{50} +1.42044e11 q^{51} +(4.23089e9 - 4.10433e8i) q^{52} +1.96740e11 q^{53} +(-5.43226e11 + 3.13631e11i) q^{54} +(-1.33759e10 - 2.31677e10i) q^{55} +(1.04365e11 - 1.80765e11i) q^{56} +2.17805e10i q^{57} +(2.45667e11 + 1.41836e11i) q^{58} +(1.79313e10 + 1.03526e10i) q^{59} +3.14648e10i q^{60} +(-8.84591e10 + 1.53216e11i) q^{61} +(2.87097e11 + 4.97267e11i) q^{62} +(-1.07076e12 + 6.18204e11i) q^{63} -5.65155e11 q^{64} +(7.41708e11 - 5.29854e11i) q^{65} -1.11993e11 q^{66} +(2.80090e10 - 1.61710e10i) q^{67} +(-7.05296e9 - 1.22161e10i) q^{68} +(-1.50373e11 + 2.60453e11i) q^{69} -1.29589e12i q^{70} +(-5.64453e11 - 3.25887e11i) q^{71} +(2.90170e12 + 1.67530e12i) q^{72} -1.91527e12i q^{73} +(-3.23280e11 + 5.59938e11i) q^{74} +(1.87244e12 + 3.24316e12i) q^{75} +(1.87317e9 - 1.08148e9i) q^{76} -1.41751e11 q^{77} +(-3.68455e11 - 3.79817e12i) q^{78} +6.28561e11 q^{79} +(-2.95055e12 + 1.70350e12i) q^{80} +(-5.10133e12 - 8.83576e12i) q^{81} +(5.61143e11 - 9.71929e11i) q^{82} +1.81049e12i q^{83} +(1.44388e11 + 8.33623e10i) q^{84} +(-2.61960e12 - 1.51243e12i) q^{85} +4.91673e12i q^{86} +(-3.91308e12 + 6.77765e12i) q^{87} +(1.92069e11 + 3.32673e11i) q^{88} +(7.28167e12 - 4.20407e12i) q^{89} +2.08022e13 q^{90} +(-4.66358e11 - 4.80739e12i) q^{91} +2.98661e10 q^{92} +(-1.37190e13 + 7.92067e12i) q^{93} +(4.37750e11 + 7.58205e11i) q^{94} +(2.31910e11 - 4.01680e11i) q^{95} -8.90547e11i q^{96} +(-4.23464e12 - 2.44487e12i) q^{97} +(1.53375e12 + 8.85511e11i) q^{98} -2.27544e12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - 730 q^{3} + 65535 q^{4} - 382584 q^{6} + 438984 q^{7} - 9117071 q^{9} + 3893475 q^{10} - 5364528 q^{11} + 27694876 q^{12} - 1794135 q^{13} + 61125588 q^{14} - 113380170 q^{15} - 350182521 q^{16}+ \cdots + 86959564160763 q^{98}+O(q^{100}) \) 30 * q - 3 * q^2 - 730 * q^3 + 65535 * q^4 - 382584 * q^6 + 438984 * q^7 - 9117071 * q^9 + 3893475 * q^10 - 5364528 * q^11 + 27694876 * q^12 - 1794135 * q^13 + 61125588 * q^14 - 113380170 * q^15 - 350182521 * q^16 - 23524899 * q^17 + 92116746 * q^19 + 959687745 * q^20 - 128185362 * q^22 + 417086886 * q^23 - 4232784354 * q^24 - 11926991364 * q^25 + 5442553119 * q^26 + 5605403288 * q^27 + 22569369732 * q^28 - 8810189577 * q^29 - 9936679242 * q^30 + 9137241117 * q^32 + 12085621392 * q^33 + 1059240720 * q^35 + 55900963715 * q^36 - 72651649419 * q^37 - 45168847944 * q^38 - 41492436530 * q^39 + 137282090274 * q^40 - 3909896103 * q^41 - 34124964786 * q^42 + 138326640480 * q^43 - 259122942393 * q^45 - 288578831832 * q^46 + 630595691198 * q^48 + 114277635303 * q^49 - 553717814136 * q^50 - 178343342508 * q^51 - 1243882821894 * q^52 + 938994404670 * q^53 + 1180281528282 * q^54 - 140610123120 * q^55 + 932974200720 * q^56 - 768032047215 * q^58 - 1420851272556 * q^59 + 284498233437 * q^61 + 2574083847030 * q^62 - 3219361289664 * q^63 - 4989806279958 * q^64 - 931161533727 * q^65 + 12037245084948 * q^66 + 2624227676622 * q^67 - 3124046642277 * q^68 + 1206986427996 * q^69 - 1317657850698 * q^71 - 2571404508735 * q^72 + 1723434230073 * q^74 + 1909848151684 * q^75 - 5741418039246 * q^76 - 8153714196816 * q^77 - 13064083856250 * q^78 + 10732970056200 * q^79 + 11699811454875 * q^80 + 26873856445 * q^81 - 924448017327 * q^82 + 5758359493380 * q^84 - 14711656818213 * q^85 - 6442966126134 * q^87 - 11094606812688 * q^88 + 18293004024660 * q^89 + 53932182551466 * q^90 + 2271787574784 * q^91 - 48706576133844 * q^92 - 50634402753492 * q^93 + 3529466920146 * q^94 + 11308314514950 * q^95 - 4972913690148 * q^97 + 86959564160763 * q^98

Introduction

L-functions

Modular forms

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Database

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