LMFDB - Embedded newform 15.11.c.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,11,Mod(11,15)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 11, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("15.11");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	15.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.53035879011$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 11554 x^{12} + 52224391 x^{10} + 115670558124 x^{8} + 127683454012911 x^{6} + \cdots + 62\!\cdots\!00 $ x^14 + 11554x^12 + 52224391x^10 + 115670558124x^8 + 127683454012911x^6 + 62207430110604450x^4 + 9049402196955729225x^2 + 62911149236536050000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{20}\cdot 5^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.5
Root			$-29.7613i$ of defining polynomial
Character	$\chi$	$=$	15.11
Dual form			15.11.c.a.11.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-27.5253i q^{2} +(-80.1400 + 229.405i) q^{3} +266.360 q^{4} -1397.54i q^{5} +(6314.43 + 2205.87i) q^{6} -24115.7 q^{7} -35517.5i q^{8} +(-46204.2 - 36769.0i) q^{9} +O(q^{10})$	\(q-27.5253i q^{2} +(-80.1400 + 229.405i) q^{3} +266.360 q^{4} -1397.54i q^{5} +(6314.43 + 2205.87i) q^{6} -24115.7 q^{7} -35517.5i q^{8} +(-46204.2 - 36769.0i) q^{9} -38467.7 q^{10} +218929. i q^{11} +(-21346.1 + 61104.3i) q^{12} -435784. q^{13} +663792. i q^{14} +(320603. + 111999. i) q^{15} -704876. q^{16} -1.40198e6i q^{17} +(-1.01208e6 + 1.27178e6i) q^{18} -3.96480e6 q^{19} -372249. i q^{20} +(1.93264e6 - 5.53227e6i) q^{21} +6.02608e6 q^{22} +1.21648e6i q^{23} +(8.14789e6 + 2.84637e6i) q^{24} -1.95312e6 q^{25} +1.19951e7i q^{26} +(1.21378e7 - 7.65279e6i) q^{27} -6.42347e6 q^{28} +1.00025e6i q^{29} +(3.08280e6 - 8.82468e6i) q^{30} +5.09524e7 q^{31} -1.69680e7i q^{32} +(-5.02234e7 - 1.75450e7i) q^{33} -3.85900e7 q^{34} +3.37028e7i q^{35} +(-1.23069e7 - 9.79379e6i) q^{36} +9.23155e6 q^{37} +1.09132e8i q^{38} +(3.49238e7 - 9.99710e7i) q^{39} -4.96372e7 q^{40} +4.72120e7i q^{41} +(-1.52277e8 - 5.31963e7i) q^{42} -7.55356e7 q^{43} +5.83140e7i q^{44} +(-5.13862e7 + 6.45723e7i) q^{45} +3.34839e7 q^{46} +1.53639e8i q^{47} +(5.64887e7 - 1.61702e8i) q^{48} +2.99094e8 q^{49} +5.37603e7i q^{50} +(3.21622e8 + 1.12355e8i) q^{51} -1.16076e8 q^{52} -3.89040e8i q^{53} +(-2.10645e8 - 3.34096e8i) q^{54} +3.05963e8 q^{55} +8.56531e8i q^{56} +(3.17739e8 - 9.09545e8i) q^{57} +2.75322e7 q^{58} -1.11064e8i q^{59} +(8.53958e7 + 2.98321e7i) q^{60} -6.20166e7 q^{61} -1.40248e9i q^{62} +(1.11425e9 + 8.86712e8i) q^{63} -1.18884e9 q^{64} +6.09027e8i q^{65} +(-4.82930e8 + 1.38241e9i) q^{66} -8.74334e8 q^{67} -3.73432e8i q^{68} +(-2.79066e8 - 9.74887e7i) q^{69} +9.27678e8 q^{70} +1.83375e9i q^{71} +(-1.30594e9 + 1.64106e9i) q^{72} +7.05499e7 q^{73} -2.54101e8i q^{74} +(1.56523e8 - 4.48056e8i) q^{75} -1.05606e9 q^{76} -5.27964e9i q^{77} +(-2.75173e9 - 9.61285e8i) q^{78} -6.40192e8 q^{79} +9.85094e8i q^{80} +(7.82866e8 + 3.39776e9i) q^{81} +1.29952e9 q^{82} -3.98887e9i q^{83} +(5.14777e8 - 1.47358e9i) q^{84} -1.95933e9 q^{85} +2.07914e9i q^{86} +(-2.29463e8 - 8.01602e7i) q^{87} +7.77582e9 q^{88} -3.01940e9i q^{89} +(1.77737e9 + 1.41442e9i) q^{90} +1.05093e10 q^{91} +3.24022e8i q^{92} +(-4.08333e9 + 1.16887e10i) q^{93} +4.22896e9 q^{94} +5.54098e9i q^{95} +(3.89255e9 + 1.35982e9i) q^{96} -1.02491e10 q^{97} -8.23264e9i q^{98} +(8.04981e9 - 1.01154e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9}+O(q^{10}) $ 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9	\( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9} + 31250 q^{10} + 43756 q^{12} + 699408 q^{13} - 343750 q^{15} + 2871906 q^{16} - 3243880 q^{18} + 3814644 q^{19} - 2191008 q^{21} - 10493420 q^{22} + 9454542 q^{24} - 27343750 q^{25} + 13322636 q^{27} - 10989172 q^{28} + 20875000 q^{30} + 105444308 q^{31} - 187570700 q^{33} + 84960772 q^{34} + 80968490 q^{36} - 152902928 q^{37} - 262995952 q^{39} - 228656250 q^{40} + 1025108820 q^{42} - 82568592 q^{43} + 284500000 q^{45} + 302816052 q^{46} - 534917396 q^{48} + 1339929050 q^{49} - 519773324 q^{51} - 2117624528 q^{52} - 3171778694 q^{54} - 414437500 q^{55} + 2459677832 q^{57} + 2203542020 q^{58} + 918156250 q^{60} - 2372907732 q^{61} + 253855908 q^{63} + 5663115830 q^{64} + 915786920 q^{66} - 7807415008 q^{67} - 1032380604 q^{69} - 95812500 q^{70} + 2313658920 q^{72} + 10465834068 q^{73} - 85937500 q^{75} - 4927934540 q^{76} - 4082143640 q^{78} - 8333919076 q^{79} - 4284635426 q^{81} + 14404193720 q^{82} + 13837595568 q^{84} + 4711812500 q^{85} - 11735627260 q^{87} - 14973492180 q^{88} - 9226281250 q^{90} + 4013221984 q^{91} - 9561672552 q^{93} - 47501516708 q^{94} + 43132239458 q^{96} + 31262487532 q^{97} + 36258312560 q^{99}+O(q^{100}) \) 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9 + 31250 * q^10 + 43756 * q^12 + 699408 * q^13 - 343750 * q^15 + 2871906 * q^16 - 3243880 * q^18 + 3814644 * q^19 - 2191008 * q^21 - 10493420 * q^22 + 9454542 * q^24 - 27343750 * q^25 + 13322636 * q^27 - 10989172 * q^28 + 20875000 * q^30 + 105444308 * q^31 - 187570700 * q^33 + 84960772 * q^34 + 80968490 * q^36 - 152902928 * q^37 - 262995952 * q^39 - 228656250 * q^40 + 1025108820 * q^42 - 82568592 * q^43 + 284500000 * q^45 + 302816052 * q^46 - 534917396 * q^48 + 1339929050 * q^49 - 519773324 * q^51 - 2117624528 * q^52 - 3171778694 * q^54 - 414437500 * q^55 + 2459677832 * q^57 + 2203542020 * q^58 + 918156250 * q^60 - 2372907732 * q^61 + 253855908 * q^63 + 5663115830 * q^64 + 915786920 * q^66 - 7807415008 * q^67 - 1032380604 * q^69 - 95812500 * q^70 + 2313658920 * q^72 + 10465834068 * q^73 - 85937500 * q^75 - 4927934540 * q^76 - 4082143640 * q^78 - 8333919076 * q^79 - 4284635426 * q^81 + 14404193720 * q^82 + 13837595568 * q^84 + 4711812500 * q^85 - 11735627260 * q^87 - 14973492180 * q^88 - 9226281250 * q^90 + 4013221984 * q^91 - 9561672552 * q^93 - 47501516708 * q^94 + 43132239458 * q^96 + 31262487532 * q^97 + 36258312560 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	27.5253i		−	0.860164i	−0.902790	−	0.430082i	$-0.858485\pi$
$2$		−	27.5253i		−	0.860164i	0.902790	−	0.430082i	$-0.141515\pi$
$3$	−80.1400	+	229.405i	−0.329794	+	0.944053i
$3$	−80.1400	+	229.405i	−0.329794	+	0.944053i
$4$	266.360			0.260117
$5$		−	1397.54i		−	0.447214i
$5$		−	1397.54i		−	0.447214i
$6$	6314.43	+	2205.87i	0.812041	+	0.283677i
$7$	−24115.7			−1.43486			−0.717432	−	0.696629i	$-0.754682\pi$
$7$	−24115.7			−1.43486			−0.717432	+	0.696629i	$0.754682\pi$
$8$		−	35517.5i		−	1.08391i
$9$	−46204.2	−	36769.0i	−0.782472	−	0.622686i
$10$	−38467.7			−0.384677
$11$			218929.i			1.35938i	0.733500	+	0.679689i	$0.237885\pi$
$11$			218929.i			1.35938i	−0.733500	+	0.679689i	$0.762115\pi$
$12$	−21346.1	+	61104.3i	−0.0857851	+	0.245564i
$13$	−435784.			−1.17369			−0.586847	−	0.809698i	$-0.699631\pi$
$13$	−435784.			−1.17369			−0.586847	+	0.809698i	$0.699631\pi$
$14$			663792.i			1.23422i
$15$	320603.	+	111999.i	0.422193	+	0.147488i
$16$	−704876.			−0.672222
$17$		−	1.40198e6i		−	0.987412i	−0.869629	−	0.493706i	$-0.835642\pi$
$17$		−	1.40198e6i		−	0.987412i	0.869629	−	0.493706i	$-0.164358\pi$
$18$	−1.01208e6	+	1.27178e6i	−0.535613	+	0.673054i
$19$	−3.96480e6			−1.60123			−0.800615	−	0.599180i	$-0.795494\pi$
$19$	−3.96480e6			−1.60123			−0.800615	+	0.599180i	$0.795494\pi$
$20$		−	372249.i		−	0.116328i
$21$	1.93264e6	−	5.53227e6i	0.473210	−	1.35459i
$22$	6.02608e6			1.16929
$23$			1.21648e6i			0.189002i	0.995525	+	0.0945009i	$0.0301255\pi$
$23$			1.21648e6i			0.189002i	−0.995525	+	0.0945009i	$0.969874\pi$
$24$	8.14789e6	+	2.84637e6i	1.02327	+	0.357467i
$25$	−1.95312e6			−0.200000
$26$			1.19951e7i			1.00957i
$27$	1.21378e7	−	7.65279e6i	0.845903	−	0.533336i
$28$	−6.42347e6			−0.373233
$29$			1.00025e6i			0.0487663i	0.999703	+	0.0243831i	$0.00776216\pi$
$29$			1.00025e6i			0.0487663i	−0.999703	+	0.0243831i	$0.992238\pi$
$30$	3.08280e6	−	8.82468e6i	0.126864	−	0.363156i
$31$	5.09524e7			1.77974			0.889870	−	0.456215i	$-0.150795\pi$
$31$	5.09524e7			1.77974			0.889870	+	0.456215i	$0.150795\pi$
$32$		−	1.69680e7i		−	0.505687i
$33$	−5.02234e7	−	1.75450e7i	−1.28333	−	0.448315i
$34$	−3.85900e7			−0.849336
$35$			3.37028e7i			0.641690i
$36$	−1.23069e7	−	9.79379e6i	−0.203534	−	0.161971i
$37$	9.23155e6			0.133127			0.0665635	−	0.997782i	$-0.478797\pi$
$37$	9.23155e6			0.133127			0.0665635	+	0.997782i	$0.478797\pi$
$38$			1.09132e8i			1.37732i
$39$	3.49238e7	−	9.99710e7i	0.387077	−	1.10803i
$40$	−4.96372e7			−0.484738
$41$			4.72120e7i			0.407505i	0.979022	+	0.203753i	$0.0653138\pi$
$41$			4.72120e7i			0.407505i	−0.979022	+	0.203753i	$0.934686\pi$
$42$	−1.52277e8	−	5.31963e7i	−1.16517	−	0.407038i
$43$	−7.55356e7			−0.513818			−0.256909	−	0.966436i	$-0.582704\pi$
$43$	−7.55356e7			−0.513818			−0.256909	+	0.966436i	$0.582704\pi$
$44$			5.83140e7i			0.353598i
$45$	−5.13862e7	+	6.45723e7i	−0.278474	+	0.349932i
$46$	3.34839e7			0.162573
$47$			1.53639e8i			0.669905i	0.942235	+	0.334953i	$0.108720\pi$
$47$			1.53639e8i			0.669905i	−0.942235	+	0.334953i	$0.891280\pi$
$48$	5.64887e7	−	1.61702e8i	0.221695	−	0.634613i
$49$	2.99094e8			1.05883
$50$			5.37603e7i			0.172033i
$51$	3.21622e8	+	1.12355e8i	0.932169	+	0.325643i
$52$	−1.16076e8			−0.305298
$53$		−	3.89040e8i		−	0.930283i	−0.885236	−	0.465141i	$-0.846003\pi$
$53$		−	3.89040e8i		−	0.930283i	0.885236	−	0.465141i	$-0.153997\pi$
$54$	−2.10645e8	−	3.34096e8i	−0.458757	−	0.727616i
$55$	3.05963e8			0.607933
$56$			8.56531e8i			1.55526i
$57$	3.17739e8	−	9.09545e8i	0.528076	−	1.51165i
$58$	2.75322e7			0.0419470
$59$		−	1.11064e8i		−	0.155350i	−0.996979	−	0.0776751i	$-0.975250\pi$
$59$		−	1.11064e8i		−	0.155350i	0.996979	−	0.0776751i	$-0.0247497\pi$
$60$	8.53958e7	+	2.98321e7i	0.109820	+	0.0383643i
$61$	−6.20166e7			−0.0734275			−0.0367138	−	0.999326i	$-0.511689\pi$
$61$	−6.20166e7			−0.0734275			−0.0367138	+	0.999326i	$0.511689\pi$
$62$		−	1.40248e9i		−	1.53087i
$63$	1.11425e9	+	8.86712e8i	1.12274	+	0.893470i
$64$	−1.18884e9			−1.10720
$65$			6.09027e8i			0.524892i
$66$	−4.82930e8	+	1.38241e9i	−0.385625	+	1.10387i
$67$	−8.74334e8			−0.647595			−0.323798	−	0.946126i	$-0.604960\pi$
$67$	−8.74334e8			−0.647595			−0.323798	+	0.946126i	$0.604960\pi$
$68$		−	3.73432e8i		−	0.256843i
$69$	−2.79066e8	−	9.74887e7i	−0.178428	−	0.0623317i
$70$	9.27678e8			0.551959
$71$			1.83375e9i			1.01636i	0.861251	+	0.508180i	$0.169681\pi$
$71$			1.83375e9i			1.01636i	−0.861251	+	0.508180i	$0.830319\pi$
$72$	−1.30594e9	+	1.64106e9i	−0.674935	+	0.848127i
$73$	7.05499e7			0.0340316			0.0170158	−	0.999855i	$-0.494583\pi$
$73$	7.05499e7			0.0340316			0.0170158	+	0.999855i	$0.494583\pi$
$74$		−	2.54101e8i		−	0.114511i
$75$	1.56523e8	−	4.48056e8i	0.0659588	−	0.188811i
$76$	−1.05606e9			−0.416507
$77$		−	5.27964e9i		−	1.95052i
$78$	−2.75173e9	−	9.61285e8i	−0.953087	−	0.332950i
$79$	−6.40192e8			−0.208053			−0.104027	−	0.994575i	$-0.533173\pi$
$79$	−6.40192e8			−0.208053			−0.104027	+	0.994575i	$0.533173\pi$
$80$			9.85094e8i			0.300627i
$81$	7.82866e8	+	3.39776e9i	0.224524	+	0.974469i
$82$	1.29952e9			0.350521
$83$		−	3.98887e9i		−	1.01265i	−0.862343	−	0.506325i	$-0.831004\pi$
$83$		−	3.98887e9i		−	1.01265i	0.862343	−	0.506325i	$-0.168996\pi$
$84$	5.14777e8	−	1.47358e9i	0.123090	−	0.352351i
$85$	−1.95933e9			−0.441584
$86$			2.07914e9i			0.441968i
$87$	−2.29463e8	−	8.01602e7i	−0.0460379	−	0.0160828i
$88$	7.77582e9			1.47344
$89$		−	3.01940e9i		−	0.540718i	−0.962760	−	0.270359i	$-0.912858\pi$
$89$		−	3.01940e9i		−	0.540718i	0.962760	−	0.270359i	$-0.0871424\pi$
$90$	1.77737e9	+	1.41442e9i	0.300999	+	0.239533i
$91$	1.05093e10			1.68409
$92$			3.24022e8i			0.0491626i
$93$	−4.08333e9	+	1.16887e10i	−0.586948	+	1.68017i
$94$	4.22896e9			0.576229
$95$			5.54098e9i			0.716091i
$96$	3.89255e9	+	1.35982e9i	0.477395	+	0.166773i
$97$	−1.02491e10			−1.19351			−0.596754	−	0.802424i	$-0.703543\pi$
$97$	−1.02491e10			−1.19351			−0.596754	+	0.802424i	$0.703543\pi$
$98$		−	8.23264e9i		−	0.910770i
$99$	8.04981e9	−	1.01154e10i	0.846466	−	1.06368i
$100$	−5.20234e8			−0.0520234
$101$		−	1.14343e10i		−	1.08793i	−0.839106	−	0.543967i	$-0.816921\pi$
$101$		−	1.14343e10i		−	1.08793i	0.839106	−	0.543967i	$-0.183079\pi$
$102$	3.09260e9	−	8.85272e9i	0.280106	−	0.801818i
$103$	−1.84678e10			−1.59305			−0.796525	−	0.604606i	$-0.793331\pi$
$103$	−1.84678e10			−1.59305			−0.796525	+	0.604606i	$0.793331\pi$
$104$			1.54780e10i			1.27218i
$105$	−7.73158e9	−	2.70094e9i	−0.605790	−	0.211626i
$106$	−1.07084e10			−0.800196
$107$			1.27274e10i			0.907449i	0.891142	+	0.453724i	$0.149905\pi$
$107$			1.27274e10i			0.907449i	−0.891142	+	0.453724i	$0.850095\pi$
$108$	3.23302e9	−	2.03840e9i	0.220034	−	0.138730i
$109$	−7.89967e9			−0.513425			−0.256712	−	0.966488i	$-0.582639\pi$
$109$	−7.89967e9			−0.513425			−0.256712	+	0.966488i	$0.582639\pi$
$110$		−	8.42171e9i		−	0.522922i
$111$	−7.39816e8	+	2.11776e9i	−0.0439045	+	0.125679i
$112$	1.69986e10			0.964546
$113$			1.24747e10i			0.677074i	0.940953	+	0.338537i	$0.109932\pi$
$113$			1.24747e10i			0.677074i	−0.940953	+	0.338537i	$0.890068\pi$
$114$	−2.50355e10	−	8.74585e9i	−1.30026	−	0.454232i
$115$	1.70008e9			0.0845242
$116$			2.66427e8i			0.0126849i
$117$	2.01351e10	+	1.60234e10i	0.918382	+	0.730843i
$118$	−3.05706e9			−0.133627
$119$			3.38099e10i			1.41680i
$120$	3.97793e9	−	1.13870e10i	0.159864	−	0.457619i
$121$	−2.19926e10			−0.847910
$122$			1.70702e9i			0.0631597i
$123$	−1.08307e10	−	3.78357e9i	−0.384706	−	0.134393i
$124$	1.35717e10			0.462941
$125$			2.72958e9i			0.0894427i
$126$	2.44070e10	−	3.06700e10i	0.768531	−	0.965741i
$127$	−1.29905e10			−0.393194			−0.196597	−	0.980484i	$-0.562989\pi$
$127$	−1.29905e10			−0.393194			−0.196597	+	0.980484i	$0.562989\pi$
$128$			1.53479e10i			0.446683i
$129$	6.05342e9	−	1.73282e10i	0.169454	−	0.485072i
$130$	1.67636e10			0.451493
$131$		−	4.93423e10i		−	1.27898i	−0.768801	−	0.639488i	$-0.779146\pi$
$131$		−	4.93423e10i		−	1.27898i	0.768801	−	0.639488i	$-0.220854\pi$
$132$	−1.33775e10	−	4.67328e9i	−0.333815	−	0.116614i
$133$	9.56142e10			2.29755
$134$			2.40663e10i			0.557038i
$135$	−1.06951e10	−	1.69631e10i	−0.238515	−	0.378299i
$136$	−4.97949e10			−1.07026
$137$			2.13856e10i			0.443117i	0.975147	+	0.221559i	$0.0711144\pi$
$137$			2.13856e10i			0.443117i	−0.975147	+	0.221559i	$0.928886\pi$
$138$	−2.68340e9	+	7.68138e9i	−0.0536155	+	0.153477i
$139$	3.80392e10			0.733090			0.366545	−	0.930400i	$-0.380541\pi$
$139$	3.80392e10			0.733090			0.366545	+	0.930400i	$0.380541\pi$
$140$			8.97707e9i			0.166915i
$141$	−3.52456e10	−	1.23127e10i	−0.632426	−	0.220931i
$142$	5.04743e10			0.874236
$143$		−	9.54059e10i		−	1.59549i
$144$	3.25682e10	+	2.59176e10i	0.525994	+	0.418583i
$145$	1.39789e9			0.0218089
$146$		−	1.94190e9i		−	0.0292727i
$147$	−2.39694e10	+	6.86136e10i	−0.349197	+	0.999594i
$148$	2.45892e9			0.0346286
$149$		−	3.55299e10i		−	0.483797i	−0.970302	−	0.241898i	$-0.922230\pi$
$149$		−	3.55299e10i		−	0.483797i	0.970302	−	0.241898i	$-0.0777701\pi$
$150$	−1.23329e10	−	4.30835e9i	−0.162408	−	0.0567354i
$151$	−6.10213e9			−0.0777315			−0.0388657	−	0.999244i	$-0.512374\pi$
$151$	−6.10213e9			−0.0777315			−0.0388657	+	0.999244i	$0.512374\pi$
$152$			1.40820e11i			1.73559i
$153$	−5.15495e10	+	6.47775e10i	−0.614848	+	0.772622i
$154$	−1.45324e11			−1.67777
$155$		−	7.12082e10i		−	0.795924i
$156$	9.30229e9	−	2.66283e10i	0.100686	−	0.288217i
$157$	−1.48553e11			−1.55734			−0.778668	−	0.627436i	$-0.784104\pi$
$157$	−1.48553e11			−1.55734			−0.778668	+	0.627436i	$0.784104\pi$
$158$			1.76214e10i			0.178960i
$159$	8.92477e10	+	3.11777e10i	0.878236	+	0.306802i
$160$	−2.37135e10			−0.226150
$161$		−	2.93363e10i		−	0.271192i
$162$	9.35243e10	−	2.15486e10i	0.838203	−	0.193127i
$163$	1.30154e11			1.13115			0.565573	−	0.824698i	$-0.308655\pi$
$163$	1.30154e11			1.13115			0.565573	+	0.824698i	$0.308655\pi$
$164$			1.25754e10i			0.105999i
$165$	−2.45199e10	+	7.01894e10i	−0.200493	+	0.573920i
$166$	−1.09795e11			−0.871045
$167$		−	1.61088e11i		−	1.24017i	−0.784536	−	0.620083i	$-0.787099\pi$
$167$		−	1.61088e11i		−	1.24017i	0.784536	−	0.620083i	$-0.212901\pi$
$168$	−1.96492e11	−	6.86424e10i	−1.46825	−	0.512916i
$169$	5.20495e10			0.377558
$170$			5.39311e10i			0.379835i
$171$	1.83190e11	+	1.45782e11i	1.25292	+	0.997063i
$172$	−2.01197e10			−0.133653
$173$			1.51842e11i			0.979854i	0.871763	+	0.489927i	$0.162977\pi$
$173$			1.51842e11i			0.979854i	−0.871763	+	0.489927i	$0.837023\pi$
$174$	−2.20643e9	+	6.31602e9i	−0.0138339	+	0.0396002i
$175$	4.71011e10			0.286973
$176$		−	1.54318e11i		−	0.913804i
$177$	2.54785e10	+	8.90064e9i	0.146659	+	0.0512336i
$178$	−8.31098e10			−0.465106
$179$		−	2.98641e11i		−	1.62512i	−0.582880	−	0.812558i	$-0.698074\pi$
$179$		−	2.98641e11i		−	1.62512i	0.582880	−	0.812558i	$-0.301926\pi$
$180$	−1.36872e10	+	1.71995e10i	−0.0724358	+	0.0910233i
$181$	5.00350e10			0.257561			0.128781	−	0.991673i	$-0.458894\pi$
$181$	5.00350e10			0.257561			0.128781	+	0.991673i	$0.458894\pi$
$182$		−	2.89270e11i		−	1.44859i
$183$	4.97001e9	−	1.42269e10i	0.0242160	−	0.0693194i
$184$	4.32063e10			0.204861
$185$		−	1.29015e10i		−	0.0595362i
$186$	3.21735e11	+	1.12395e11i	1.44522	+	0.504871i
$187$	3.06935e11			1.34227
$188$			4.09234e10i			0.174254i
$189$	−2.92712e11	+	1.84553e11i	−1.21376	+	0.765265i
$190$	1.52517e11			0.615956
$191$			4.67558e11i			1.83937i	0.392660	+	0.919684i	$0.371555\pi$
$191$			4.67558e11i			1.83937i	−0.392660	+	0.919684i	$0.628445\pi$
$192$	9.52738e10	−	2.72726e11i	0.365147	−	1.04525i
$193$	4.65772e10			0.173935			0.0869675	−	0.996211i	$-0.472282\pi$
$193$	4.65772e10			0.173935			0.0869675	+	0.996211i	$0.472282\pi$
$194$			2.82108e11i			1.02661i
$195$	−1.39714e11	−	4.88074e10i	−0.495526	−	0.173106i
$196$	7.96667e10			0.275421
$197$			1.04345e11i			0.351675i	0.984419	+	0.175837i	$0.0562633\pi$
$197$			1.04345e11i			0.351675i	−0.984419	+	0.175837i	$0.943737\pi$
$198$	−2.78430e11	−	2.21573e11i	−0.914935	−	0.728100i
$199$	−5.99954e10			−0.192244			−0.0961219	−	0.995370i	$-0.530644\pi$
$199$	−5.99954e10			−0.192244			−0.0961219	+	0.995370i	$0.530644\pi$
$200$			6.93701e10i			0.216782i
$201$	7.00691e10	−	2.00577e11i	0.213573	−	0.611364i
$202$	−3.14732e11			−0.935803
$203$		−	2.41218e10i		−	0.0699729i
$204$	8.56672e10	+	2.99269e10i	0.242473	+	0.0847053i
$205$	6.59808e10			0.182242
$206$			5.08331e11i			1.37028i
$207$	4.47288e10	−	5.62065e10i	0.117689	−	0.147889i
$208$	3.07174e11			0.788983
$209$		−	8.68011e11i		−	2.17668i
$210$	−7.43441e10	+	2.12814e11i	−0.182033	+	0.521079i
$211$	−7.49985e11			−1.79325			−0.896624	−	0.442792i	$-0.853988\pi$
$211$	−7.49985e11			−1.79325			−0.896624	+	0.442792i	$0.853988\pi$
$212$		−	1.03625e11i		−	0.241983i
$213$	−4.20670e11	−	1.46956e11i	−0.959497	−	0.335189i
$214$	3.50326e11			0.780555
$215$			1.05564e11i			0.229787i
$216$	−2.71808e11	−	4.31104e11i	−0.578087	−	0.916881i
$217$	−1.22876e12			−2.55368
$218$			2.17441e11i			0.441630i
$219$	−5.65387e9	+	1.61845e10i	−0.0112234	+	0.0321276i
$220$	8.14963e10			0.158134
$221$			6.10962e11i			1.15892i
$222$	5.82920e10	+	2.03636e10i	0.108104	+	0.0377651i
$223$	1.06490e12			1.93101			0.965503	−	0.260394i	$-0.0838523\pi$
$223$	1.06490e12			1.93101			0.965503	+	0.260394i	$0.0838523\pi$
$224$			4.09197e11i			0.725591i
$225$	9.02425e10	+	7.18145e10i	0.156494	+	0.124537i
$226$	3.43368e11			0.582395
$227$		−	3.01663e10i		−	0.0500487i	−0.999687	−	0.0250244i	$-0.992034\pi$
$227$		−	3.01663e10i		−	0.0500487i	0.999687	−	0.0250244i	$-0.00796633\pi$
$228$	8.46330e10	−	2.42266e11i	0.137362	−	0.393205i
$229$	−8.11842e11			−1.28912			−0.644561	−	0.764553i	$-0.722960\pi$
$229$	−8.11842e11			−1.28912			−0.644561	+	0.764553i	$0.722960\pi$
$230$		−	4.67952e10i		−	0.0727047i
$231$	1.21118e12	+	4.23110e11i	1.84140	+	0.643271i
$232$	3.55265e10			0.0528581
$233$			5.24222e11i			0.763371i	0.924292	+	0.381685i	$0.124656\pi$
$233$			5.24222e11i			0.763371i	−0.924292	+	0.381685i	$0.875344\pi$
$234$	4.41047e11	−	5.54223e11i	0.628645	−	0.789960i
$235$	2.14718e11			0.299591
$236$		−	2.95829e10i		−	0.0404093i
$237$	5.13049e10	−	1.46863e11i	0.0686147	−	0.196413i
$238$	9.30626e11			1.21868
$239$		−	1.66440e11i		−	0.213437i	−0.994289	−	0.106718i	$-0.965966\pi$
$239$		−	1.66440e11i		−	0.213437i	0.994289	−	0.106718i	$-0.0340343\pi$
$240$	−2.25985e11	−	7.89454e10i	−0.283808	−	0.0991449i
$241$	−1.21763e12			−1.49772			−0.748862	−	0.662726i	$-0.769399\pi$
$241$	−1.21763e12			−1.49772			−0.748862	+	0.662726i	$0.769399\pi$
$242$			6.05352e11i			0.729342i
$243$	−8.42202e11	−	9.27034e10i	−0.993997	−	0.109412i
$244$	−1.65187e10			−0.0190998
$245$		−	4.17997e11i		−	0.473524i
$246$	−1.04144e11	+	2.98117e11i	−0.115600	+	0.330911i
$247$	1.72780e12			1.87935
$248$		−	1.80970e12i		−	1.92907i
$249$	9.15065e11	+	3.19668e11i	0.955995	+	0.333966i
$250$	7.51323e10			0.0769354
$251$		−	1.64602e12i		−	1.65222i	−0.563512	−	0.826108i	$-0.690550\pi$
$251$		−	1.64602e12i		−	1.65222i	0.563512	−	0.826108i	$-0.309450\pi$
$252$	2.96791e11	+	2.36185e11i	0.292044	+	0.232407i
$253$	−2.66323e11			−0.256925
$254$			3.57567e11i			0.338212i
$255$	1.57021e11	−	4.49480e11i	0.145632	−	0.416879i
$256$	−7.94919e11			−0.722974
$257$		−	1.27887e11i		−	0.114067i	−0.998372	−	0.0570336i	$-0.981836\pi$
$257$		−	1.27887e11i		−	0.114067i	0.998372	−	0.0570336i	$-0.0181642\pi$
$258$	−4.76964e11	−	1.66622e11i	−0.417241	−	0.145759i
$259$	−2.22626e11			−0.191019
$260$			1.62220e11i			0.136533i
$261$	3.67783e10	−	4.62158e10i	0.0303661	−	0.0381582i
$262$	−1.35816e12			−1.10013
$263$			2.48857e12i			1.97775i	0.148741	+	0.988876i	$0.452478\pi$
$263$			2.48857e12i			1.97775i	−0.148741	+	0.988876i	$0.547522\pi$
$264$	−6.23154e11	+	1.78381e12i	−0.485932	+	1.39101i
$265$	−5.43700e11			−0.416035
$266$		−	2.63180e12i		−	1.97627i
$267$	6.92666e11	+	2.41975e11i	0.510467	+	0.178326i
$268$	−2.32888e11			−0.168451
$269$			1.03039e12i			0.731547i	0.930704	+	0.365773i	$0.119196\pi$
$269$			1.03039e12i			0.731547i	−0.930704	+	0.365773i	$0.880804\pi$
$270$	−4.66913e11	+	2.94385e11i	−0.325400	+	0.205162i
$271$	1.62656e12			1.11282			0.556409	−	0.830909i	$-0.312179\pi$
$271$	1.62656e12			1.11282			0.556409	+	0.830909i	$0.312179\pi$
$272$			9.88224e11i			0.663760i
$273$	−8.42212e11	+	2.41088e12i	−0.555403	+	1.58987i
$274$	5.88644e11			0.381154
$275$		−	4.27596e11i		−	0.271876i
$276$	−7.43322e10	−	2.59671e10i	−0.0464121	−	0.0162135i
$277$	1.37251e12			0.841624			0.420812	−	0.907148i	$-0.361745\pi$
$277$	1.37251e12			0.841624			0.420812	+	0.907148i	$0.361745\pi$
$278$		−	1.04704e12i		−	0.630578i
$279$	−2.35421e12	−	1.87347e12i	−1.39260	−	1.10822i
$280$	1.19704e12			0.695533
$281$			6.12902e11i			0.349832i	0.984583	+	0.174916i	$0.0559654\pi$
$281$			6.12902e11i			0.349832i	−0.984583	+	0.174916i	$0.944035\pi$
$282$	−3.38909e11	+	9.70145e11i	−0.190037	+	0.543990i
$283$	−9.61960e11			−0.529938			−0.264969	−	0.964257i	$-0.585362\pi$
$283$	−9.61960e11			−0.529938			−0.264969	+	0.964257i	$0.585362\pi$
$284$			4.88437e11i			0.264373i
$285$	−1.27113e12	−	4.44054e11i	−0.676028	−	0.236163i
$286$	−2.62607e12			−1.37239
$287$		−	1.13855e12i		−	0.584714i
$288$	−6.23897e11	+	7.83994e11i	−0.314884	+	0.395685i
$289$	5.04362e10			0.0250180
$290$		−	3.84774e10i		−	0.0187593i
$291$	8.21359e11	−	2.35118e12i	0.393612	−	1.12673i
$292$	1.87917e10			0.00885220
$293$		−	3.28624e12i		−	1.52181i	−0.648862	−	0.760906i	$-0.724755\pi$
$293$		−	3.28624e12i		−	1.52181i	0.648862	−	0.760906i	$-0.275245\pi$
$294$	1.88861e12	+	6.59764e11i	0.859815	+	0.300367i
$295$	−1.55216e11			−0.0694748
$296$		−	3.27882e11i		−	0.144297i
$297$	1.67542e12	+	2.65732e12i	0.725006	+	1.14990i
$298$	−9.77971e11			−0.416145
$299$		−	5.30123e11i		−	0.221830i
$300$	4.16916e10	−	1.19344e11i	0.0171570	−	0.0491129i
$301$	1.82160e12			0.737259
$302$			1.67963e11i			0.0668618i
$303$	2.62309e12	+	9.16345e11i	1.02707	+	0.358795i
$304$	2.79469e12			1.07638
$305$			8.66708e10i			0.0328378i
$306$	1.78302e12	+	1.41891e12i	0.664582	+	0.528870i
$307$	−4.36270e11			−0.159979			−0.0799896	−	0.996796i	$-0.525489\pi$
$307$	−4.36270e11			−0.159979			−0.0799896	+	0.996796i	$0.525489\pi$
$308$		−	1.40629e12i		−	0.507364i
$309$	1.48001e12	−	4.23661e12i	0.525379	−	1.50392i
$310$	−1.96002e12			−0.684625
$311$			1.17043e11i			0.0402295i	0.999798	+	0.0201148i	$0.00640316\pi$
$311$			1.17043e11i			0.0402295i	−0.999798	+	0.0201148i	$0.993597\pi$
$312$	−3.55072e12	−	1.24040e12i	−1.20100	−	0.419556i
$313$	2.82819e12			0.941428			0.470714	−	0.882286i	$-0.343996\pi$
$313$	2.82819e12			0.941428			0.470714	+	0.882286i	$0.343996\pi$
$314$			4.08895e12i			1.33957i
$315$	1.23922e12	−	1.55721e12i	0.399572	−	0.502104i
$316$	−1.70521e11			−0.0541182
$317$			4.21635e12i			1.31717i	0.752508	+	0.658583i	$0.228844\pi$
$317$			4.21635e12i			1.31717i	−0.752508	+	0.658583i	$0.771156\pi$
$318$	8.58173e11	−	2.45657e12i	0.263900	−	0.755428i
$319$	−2.18984e11			−0.0662918
$320$			1.66146e12i			0.495153i
$321$	−2.91974e12	−	1.01998e12i	−0.856680	−	0.299271i
$322$	−8.07490e11			−0.233269
$323$			5.55859e12i			1.58107i
$324$	2.08524e11	+	9.05028e11i	0.0584025	+	0.253476i
$325$	8.51141e11			0.234739
$326$		−	3.58251e12i		−	0.972971i
$327$	6.33080e11	−	1.81222e12i	0.169324	−	0.484700i
$328$	1.67685e12			0.441698
$329$		−	3.70513e12i		−	0.961222i
$330$	1.93198e12	+	6.74916e11i	0.493666	+	0.172457i
$331$	−3.65692e12			−0.920398			−0.460199	−	0.887816i	$-0.652222\pi$
$331$	−3.65692e12			−0.920398			−0.460199	+	0.887816i	$0.652222\pi$
$332$		−	1.06247e12i		−	0.263408i
$333$	−4.26536e11	−	3.39435e11i	−0.104168	−	0.0828963i
$334$	−4.43398e12			−1.06675
$335$			1.22192e12i			0.289613i
$336$	−1.36227e12	+	3.89956e12i	−0.318102	+	0.910583i
$337$	−3.50041e12			−0.805322			−0.402661	−	0.915349i	$-0.631915\pi$
$337$	−3.50041e12			−0.805322			−0.402661	+	0.915349i	$0.631915\pi$
$338$		−	1.43268e12i		−	0.324762i
$339$	−2.86175e12	−	9.99718e11i	−0.639194	−	0.223295i
$340$	−5.21888e11			−0.114864
$341$			1.11550e13i			2.41934i
$342$	4.01268e12	−	5.04236e12i	0.857638	−	1.07771i
$343$	−4.00774e11			−0.0844167
$344$			2.68284e12i			0.556932i
$345$	−1.36245e11	+	3.90007e11i	−0.0278756	+	0.0797953i
$346$	4.17949e12			0.842836
$347$		−	6.85033e12i		−	1.36165i	−0.732448	−	0.680823i	$-0.761622\pi$
$347$		−	6.85033e12i		−	1.36165i	0.732448	−	0.680823i	$-0.238378\pi$
$348$	−6.11197e10	−	2.13515e10i	−0.0119753	−	0.00418342i
$349$	−5.11040e12			−0.987024			−0.493512	−	0.869739i	$-0.664287\pi$
$349$	−5.11040e12			−0.987024			−0.493512	+	0.869739i	$0.664287\pi$
$350$		−	1.29647e12i		−	0.246844i
$351$	−5.28946e12	+	3.33497e12i	−0.992832	+	0.625974i
$352$	3.71480e12			0.687420
$353$		−	2.89458e12i		−	0.528095i	−0.964510	−	0.264047i	$-0.914942\pi$
$353$		−	2.89458e12i		−	0.528095i	0.964510	−	0.264047i	$-0.0850575\pi$
$354$	2.44992e11	−	7.01304e11i	0.0440693	−	0.126151i
$355$	2.56274e12			0.454530
$356$		−	8.04248e11i		−	0.140650i
$357$	−7.75615e12	−	2.70952e12i	−1.33753	−	0.467253i
$358$	−8.22017e12			−1.39787
$359$			5.87330e12i			0.984940i	0.870329	+	0.492470i	$0.163906\pi$
$359$			5.87330e12i			0.984940i	−0.870329	+	0.492470i	$0.836094\pi$
$360$	2.29345e12	+	1.82511e12i	0.379294	+	0.301840i
$361$	9.58859e12			1.56394
$362$		−	1.37723e12i		−	0.221545i
$363$	1.76249e12	−	5.04521e12i	0.279636	−	0.800472i
$364$	2.79925e12			0.438061
$365$		−	9.85964e10i		−	0.0152194i
$366$	−3.91599e11	−	1.36801e11i	−0.0596261	−	0.0208297i
$367$	−1.26759e12			−0.190392			−0.0951960	−	0.995459i	$-0.530348\pi$
$367$	−1.26759e12			−0.190392			−0.0951960	+	0.995459i	$0.530348\pi$
$368$		−	8.57467e11i		−	0.127051i
$369$	1.73594e12	−	2.18139e12i	0.253748	−	0.318861i
$370$	−3.55117e11			−0.0512109
$371$			9.38199e12i			1.33483i
$372$	−1.08764e12	+	3.11341e12i	−0.152675	+	0.437041i
$373$	6.12110e10			0.00847785			0.00423892	−	0.999991i	$-0.498651\pi$
$373$	6.12110e10			0.00847785			0.00423892	+	0.999991i	$0.498651\pi$
$374$		−	8.44847e12i		−	1.15457i
$375$	−6.26178e11	−	2.18748e11i	−0.0844387	−	0.0294977i
$376$	5.45689e12			0.726116
$377$		−	4.35894e11i		−	0.0572367i
$378$	5.07986e12	+	8.05697e12i	0.658253	+	1.04403i
$379$	8.02388e12			1.02610			0.513049	−	0.858360i	$-0.328516\pi$
$379$	8.02388e12			1.02610			0.513049	+	0.858360i	$0.328516\pi$
$380$			1.47590e12i			0.186268i
$381$	1.04106e12	−	2.98008e12i	0.129673	−	0.371196i
$382$	1.28696e13			1.58216
$383$			3.43547e12i			0.416862i	0.978037	+	0.208431i	$0.0668357\pi$
$383$			3.43547e12i			0.416862i	−0.978037	+	0.208431i	$0.933164\pi$
$384$	−3.52089e12	−	1.22998e12i	−0.421693	−	0.147314i
$385$	−7.37852e12			−0.872300
$386$		−	1.28205e12i		−	0.149613i
$387$	3.49006e12	+	2.77737e12i	0.402048	+	0.319948i
$388$	−2.72994e12			−0.310452
$389$		−	1.43402e13i		−	1.60993i	−0.593322	−	0.804965i	$-0.702184\pi$
$389$		−	1.43402e13i		−	1.60993i	0.593322	−	0.804965i	$-0.297816\pi$
$390$	−1.34344e12	+	3.84566e12i	−0.148900	+	0.426234i
$391$	1.70549e12			0.186623
$392$		−	1.06231e13i		−	1.14768i
$393$	1.13194e13	+	3.95429e12i	1.20742	+	0.421799i
$394$	2.87213e12			0.302498
$395$			8.94695e11i			0.0930442i
$396$	2.14415e12	−	2.69435e12i	0.220180	−	0.276680i
$397$	−7.76634e12			−0.787524			−0.393762	−	0.919212i	$-0.628827\pi$
$397$	−7.76634e12			−0.787524			−0.393762	+	0.919212i	$0.628827\pi$
$398$			1.65139e12i			0.165361i
$399$	−7.66252e12	+	2.19344e13i	−0.757717	+	2.16900i
$400$	1.37671e12			0.134444
$401$		−	1.13589e13i		−	1.09551i	−0.836640	−	0.547754i	$-0.815483\pi$
$401$		−	1.13589e13i		−	1.09551i	0.836640	−	0.547754i	$-0.184517\pi$
$402$	−5.52092e12	−	1.92867e12i	−0.525873	−	0.183708i
$403$	−2.22043e13			−2.08887
$404$		−	3.04564e12i		−	0.282991i
$405$	4.74852e12	−	1.09409e12i	0.435796	−	0.100410i
$406$	−6.63960e11			−0.0601882
$407$			2.02106e12i			0.180970i
$408$	3.99057e12	−	1.14232e13i	0.352967	−	1.01039i
$409$	9.79320e12			0.855673			0.427837	−	0.903856i	$-0.359276\pi$
$409$	9.79320e12			0.855673			0.427837	+	0.903856i	$0.359276\pi$
$410$		−	1.81614e12i		−	0.156758i
$411$	−4.90596e12	−	1.71384e12i	−0.418326	−	0.146138i
$412$	−4.91909e12			−0.414380
$413$			2.67838e12i			0.222906i
$414$	−1.54710e12	−	1.23117e12i	−0.127208	−	0.101232i
$415$	−5.57461e12			−0.452871
$416$			7.39440e12i			0.593521i
$417$	−3.04846e12	+	8.72637e12i	−0.241769	+	0.692076i
$418$	−2.38922e13			−1.87230
$419$		−	1.97848e13i		−	1.53201i	−0.642833	−	0.766006i	$-0.722241\pi$
$419$		−	1.97848e13i		−	1.53201i	0.642833	−	0.766006i	$-0.277759\pi$
$420$	−2.05938e12	−	7.19423e11i	−0.157576	−	0.0550475i
$421$	9.74675e12			0.736970			0.368485	−	0.929634i	$-0.379877\pi$
$421$	9.74675e12			0.736970			0.368485	+	0.929634i	$0.379877\pi$
$422$			2.06435e13i			1.54249i
$423$	5.64917e12	−	7.09878e12i	0.417141	−	0.524182i
$424$	−1.38177e13			−1.00834
$425$			2.73825e12i			0.197482i
$426$	−4.04501e12	+	1.15791e13i	−0.288318	+	0.825325i
$427$	1.49558e12			0.105358
$428$			3.39008e12i			0.236043i
$429$	2.18866e13	+	7.64583e12i	1.50623	+	0.526185i
$430$	2.90568e12			0.197654
$431$		−	1.81943e12i		−	0.122334i	−0.998128	−	0.0611671i	$-0.980518\pi$
$431$		−	1.81943e12i		−	0.122334i	0.998128	−	0.0611671i	$-0.0194823\pi$
$432$	−8.55563e12	+	5.39427e12i	−0.568635	+	0.358520i
$433$	1.88176e13			1.23631			0.618153	−	0.786058i	$-0.287881\pi$
$433$	1.88176e13			1.23631			0.618153	+	0.786058i	$0.287881\pi$
$434$			3.38218e13i			2.19659i
$435$	−1.12027e11	+	3.20684e11i	−0.00719246	+	0.0205888i
$436$	−2.10416e12			−0.133551
$437$		−	4.82310e12i		−	0.302635i
$438$	4.45482e11	+	1.55624e11i	0.0276350	+	0.00965398i
$439$	−1.31625e13			−0.807266			−0.403633	−	0.914921i	$-0.632253\pi$
$439$	−1.31625e13			−0.807266			−0.403633	+	0.914921i	$0.632253\pi$
$440$		−	1.08670e13i		−	0.658943i
$441$	−1.38194e13	−	1.09974e13i	−0.828506	−	0.659320i
$442$	1.68169e13			0.996861
$443$		−	1.22492e12i		−	0.0717943i	−0.999355	−	0.0358972i	$-0.988571\pi$
$443$		−	1.22492e12i		−	0.0717943i	0.999355	−	0.0358972i	$-0.0114289\pi$
$444$	−1.97057e11	+	5.64087e11i	−0.0114203	+	0.0326912i
$445$	−4.21974e12			−0.241817
$446$		−	2.93116e13i		−	1.66098i
$447$	8.15074e12	+	2.84737e12i	0.456730	+	0.159553i
$448$	2.86698e13			1.58867
$449$			2.63416e12i			0.144348i	0.997392	+	0.0721741i	$0.0229937\pi$
$449$			2.63416e12i			0.144348i	−0.997392	+	0.0721741i	$0.977006\pi$
$450$	1.97671e12	−	2.48395e12i	0.107123	−	0.134611i
$451$	−1.03361e13			−0.553954
$452$			3.32275e12i			0.176119i
$453$	4.89025e11	−	1.39986e12i	0.0256354	−	0.0733826i
$454$	−8.30336e11			−0.0430501
$455$		−	1.46871e13i		−	0.753148i
$456$	−3.23048e13	−	1.12853e13i	−1.63848	−	0.572386i
$457$	2.23624e13			1.12186			0.560928	−	0.827864i	$-0.310444\pi$
$457$	2.23624e13			1.12186			0.560928	+	0.827864i	$0.310444\pi$
$458$			2.23462e13i			1.10886i
$459$	−1.07291e13	−	1.70170e13i	−0.526623	−	0.835255i
$460$	4.52834e11			0.0219862
$461$		−	9.31576e12i		−	0.447418i	−0.974656	−	0.223709i	$-0.928183\pi$
$461$		−	9.31576e12i		−	0.447418i	0.974656	−	0.223709i	$-0.0718165\pi$
$462$	1.16462e13	−	3.33379e13i	0.553319	−	1.58390i
$463$	−7.64194e12			−0.359169			−0.179584	−	0.983743i	$-0.557475\pi$
$463$	−7.64194e12			−0.359169			−0.179584	+	0.983743i	$0.557475\pi$
$464$		−	7.05053e11i		−	0.0327817i
$465$	1.63355e13	+	5.70662e12i	0.751394	+	0.262491i
$466$	1.44293e13			0.656624
$467$			2.60999e13i			1.17504i	0.809209	+	0.587521i	$0.199896\pi$
$467$			2.60999e13i			1.17504i	−0.809209	+	0.587521i	$0.800104\pi$
$468$	5.36317e12	+	4.26798e12i	0.238887	+	0.190105i
$469$	2.10852e13			0.929210
$470$		−	5.91016e12i		−	0.257697i
$471$	1.19050e13	−	3.40787e13i	0.513600	−	1.47021i
$472$	−3.94470e12			−0.168385
$473$		−	1.65370e13i		−	0.698474i
$474$	−4.04244e12	−	1.41218e12i	−0.168948	−	0.0590200i
$475$	7.74375e12			0.320246
$476$			9.00560e12i			0.368534i
$477$	−1.43046e13	+	1.79753e13i	−0.579274	+	0.727920i
$478$	−4.58131e12			−0.183591
$479$			4.08677e13i			1.62070i	0.585946	+	0.810350i	$0.300723\pi$
$479$			4.08677e13i			1.62070i	−0.585946	+	0.810350i	$0.699277\pi$
$480$	1.90040e12	−	5.44000e12i	0.0745829	−	0.213498i
$481$	−4.02296e12			−0.156250
$482$			3.35157e13i			1.28829i
$483$	6.72990e12	+	2.35101e12i	0.256019	+	0.0894374i
$484$	−5.85795e12			−0.220556
$485$			1.43235e13i			0.533753i
$486$	−2.55169e12	+	2.31818e13i	−0.0941122	+	0.855000i
$487$	5.24504e12			0.191471			0.0957357	−	0.995407i	$-0.469480\pi$
$487$	5.24504e12			0.191471			0.0957357	+	0.995407i	$0.469480\pi$
$488$			2.20267e12i			0.0795887i
$489$	−1.04305e13	+	2.98579e13i	−0.373045	+	1.06786i
$490$	−1.15055e13			−0.407309
$491$			3.09503e13i			1.08457i	0.840194	+	0.542285i	$0.182441\pi$
$491$			3.09503e13i			1.08457i	−0.840194	+	0.542285i	$0.817559\pi$
$492$	−2.88486e12	−	1.00779e12i	−0.100069	−	0.0349579i
$493$	1.40234e12			0.0481524
$494$		−	4.75581e13i		−	1.61655i
$495$	−1.41368e13	−	1.12500e13i	−0.475690	−	0.378551i
$496$	−3.59151e13			−1.19638
$497$		−	4.42221e13i		−	1.45834i
$498$	8.79894e12	−	2.51874e13i	0.287266	−	0.822313i
$499$	2.83274e12			0.0915595			0.0457798	−	0.998952i	$-0.485423\pi$
$499$	2.83274e12			0.0915595			0.0457798	+	0.998952i	$0.485423\pi$
$500$			7.27050e11i			0.0232656i
$501$	3.69543e13	+	1.29096e13i	1.17078	+	0.409000i
$502$	−4.53071e13			−1.42118
$503$		−	1.23847e13i		−	0.384634i	−0.981333	−	0.192317i	$-0.938400\pi$
$503$		−	1.23847e13i		−	0.384634i	0.981333	−	0.192317i	$-0.0616001\pi$
$504$	3.14938e13	−	3.95753e13i	0.968439	−	1.21695i
$505$	−1.59799e13			−0.486539
$506$			7.33061e12i			0.220998i
$507$	−4.17125e12	+	1.19404e13i	−0.124516	+	0.356434i
$508$	−3.46015e12			−0.102277
$509$			1.15213e13i			0.337220i	0.985683	+	0.168610i	$0.0539279\pi$
$509$			1.15213e13i			0.337220i	−0.985683	+	0.168610i	$0.946072\pi$
$510$	−1.23721e13	−	4.32204e12i	−0.358584	−	0.125267i
$511$	−1.70136e12			−0.0488306
$512$			3.75966e13i			1.06856i
$513$	−4.81239e13	+	3.03418e13i	−1.35449	+	0.853994i
$514$	−3.52012e12			−0.0981165
$515$			2.58096e13i			0.712434i
$516$	1.61239e12	−	4.61555e12i	0.0440780	−	0.126175i
$517$	−3.36362e13			−0.910655
$518$			6.12783e12i			0.164308i
$519$	−3.48333e13	−	1.21686e13i	−0.925034	−	0.323150i
$520$	2.16311e13			0.568935
$521$		−	5.60633e13i		−	1.46046i	−0.683200	−	0.730231i	$-0.739412\pi$
$521$		−	5.60633e13i		−	1.46046i	0.683200	−	0.730231i	$-0.260588\pi$
$522$	−1.27210e12	−	1.01233e12i	−0.0328223	−	0.0261198i
$523$	−5.51546e13			−1.40953			−0.704763	−	0.709442i	$-0.748947\pi$
$523$	−5.51546e13			−1.40953			−0.704763	+	0.709442i	$0.748947\pi$
$524$		−	1.31428e13i		−	0.332684i
$525$	−3.77468e12	+	1.08052e13i	−0.0946419	+	0.270917i
$526$	6.84987e13			1.70119
$527$		−	7.14345e13i		−	1.75734i
$528$	3.54013e13	+	1.23670e13i	0.862679	+	0.301367i
$529$	3.99467e13			0.964278
$530$			1.49655e13i			0.357859i
$531$	−4.08370e12	+	5.13160e12i	−0.0967345	+	0.121557i
$532$	2.54678e13			0.597631
$533$		−	2.05743e13i		−	0.478286i
$534$	6.66042e12	−	1.90658e13i	0.153389	−	0.439085i
$535$	1.77871e13			0.405823
$536$			3.10542e13i			0.701933i
$537$	6.85097e13	+	2.39331e13i	1.53420	+	0.535954i
$538$	2.83619e13			0.629251
$539$			6.54804e13i			1.43935i
$540$	−2.84875e12	−	4.51829e12i	−0.0620419	−	0.0984022i
$541$	−4.10912e13			−0.886671			−0.443336	−	0.896356i	$-0.646205\pi$
$541$	−4.10912e13			−0.886671			−0.443336	+	0.896356i	$0.646205\pi$
$542$		−	4.47715e13i		−	0.957206i
$543$	−4.00980e12	+	1.14783e13i	−0.0849423	+	0.243152i
$544$	−2.37889e13			−0.499321
$545$			1.10401e13i			0.229610i
$546$	6.63600e13	+	2.31821e13i	1.36755	+	0.477738i
$547$	−8.84674e11			−0.0180654			−0.00903268	−	0.999959i	$-0.502875\pi$
$547$	−8.84674e11			−0.0180654			−0.00903268	+	0.999959i	$0.502875\pi$
$548$			5.69627e12i			0.115262i
$549$	2.86543e12	+	2.28029e12i	0.0574549	+	0.0457223i
$550$	−1.17697e13			−0.233858
$551$		−	3.96580e12i		−	0.0780860i
$552$	−3.46255e12	+	9.91174e12i	−0.0675618	+	0.193399i
$553$	1.54387e13			0.298528
$554$		−	3.77788e13i		−	0.723935i
$555$	2.95966e12	+	1.03392e12i	0.0562053	+	0.0196347i
$556$	1.01321e13			0.190689
$557$		−	4.89810e13i		−	0.913591i	−0.889572	−	0.456795i	$-0.848997\pi$
$557$		−	4.89810e13i		−	0.913591i	0.889572	−	0.456795i	$-0.151003\pi$
$558$	−5.15677e13	+	6.48004e13i	−0.953251	+	1.19786i
$559$	3.29172e13			0.603065
$560$		−	2.37563e13i		−	0.431358i
$561$	−2.45978e13	+	7.04124e13i	−0.442672	+	1.26717i
$562$	1.68703e13			0.300913
$563$		−	8.08485e13i		−	1.42932i	−0.699471	−	0.714661i	$-0.746581\pi$
$563$		−	8.08485e13i		−	1.42932i	0.699471	−	0.714661i	$-0.253419\pi$
$564$	−9.38803e12	−	3.27960e12i	−0.164505	−	0.0574679i
$565$	1.74339e13			0.302797
$566$			2.64782e13i			0.455834i
$567$	−1.88794e13	−	8.19396e13i	−0.322161	−	1.39823i
$568$	6.51300e13			1.10164
$569$		−	4.70230e13i		−	0.788405i	−0.919024	−	0.394203i	$-0.871021\pi$
$569$		−	4.70230e13i		−	0.788405i	0.919024	−	0.394203i	$-0.128979\pi$
$570$	−1.22227e13	+	3.49881e13i	−0.203139	+	0.581495i
$571$	3.94741e13			0.650327			0.325164	−	0.945658i	$-0.394581\pi$
$571$	3.94741e13			0.650327			0.325164	+	0.945658i	$0.394581\pi$
$572$		−	2.54123e13i		−	0.415016i
$573$	−1.07260e14	−	3.74701e13i	−1.73646	−	0.606613i
$574$	−3.13390e13			−0.502950
$575$		−	2.37594e12i		−	0.0378004i
$576$	5.49295e13	+	4.37125e13i	0.866349	+	0.689435i
$577$	2.72198e12			0.0425605			0.0212802	−	0.999774i	$-0.493226\pi$
$577$	2.72198e12			0.0425605			0.0212802	+	0.999774i	$0.493226\pi$
$578$		−	1.38827e12i		−	0.0215196i
$579$	−3.73270e12	+	1.06850e13i	−0.0573628	+	0.164204i
$580$	3.72343e11			0.00567288
$581$			9.61945e13i			1.45301i
$582$	−6.47169e13	−	2.26081e13i	−0.969177	−	0.338571i
$583$	8.51723e13			1.26461
$584$		−	2.50575e12i		−	0.0368871i
$585$	2.23933e13	−	2.81396e13i	0.326843	−	0.410713i
$586$	−9.04546e13			−1.30901
$587$			1.01511e14i			1.45654i	0.685293	+	0.728268i	$0.259674\pi$
$587$			1.01511e14i			1.45654i	−0.685293	+	0.728268i	$0.740326\pi$
$588$	−6.38449e12	+	1.82759e13i	−0.0908321	+	0.260012i
$589$	−2.02016e14			−2.84977
$590$			4.27237e12i			0.0597597i
$591$	−2.39373e13	−	8.36222e12i	−0.331999	−	0.115980i
$592$	−6.50709e12			−0.0894908
$593$		−	3.33265e13i		−	0.454481i	−0.973839	−	0.227241i	$-0.927030\pi$
$593$		−	3.33265e13i		−	0.454481i	0.973839	−	0.227241i	$-0.0729704\pi$
$594$	7.31433e13	−	4.61164e13i	0.989105	−	0.623624i
$595$	4.72507e13			0.633613
$596$		−	9.46375e12i		−	0.125844i
$597$	4.80803e12	−	1.37632e13i	0.0634009	−	0.181488i
$598$	−1.45918e13			−0.190810
$599$			8.32579e13i			1.07967i	0.841771	+	0.539835i	$0.181513\pi$
$599$			8.32579e13i			1.07967i	−0.841771	+	0.539835i	$0.818487\pi$
$600$	−1.59138e13	−	5.55932e12i	−0.204653	−	0.0714933i
$601$	−2.42358e13			−0.309091			−0.154545	−	0.987986i	$-0.549391\pi$
$601$	−2.42358e13			−0.309091			−0.154545	+	0.987986i	$0.549391\pi$
$602$		−	5.01400e13i		−	0.634164i
$603$	4.03979e13	+	3.21484e13i	0.506725	+	0.403249i
$604$	−1.62536e12			−0.0202193
$605$			3.07356e13i			0.379197i
$606$	2.52226e13	−	7.22011e13i	0.308622	−	0.883447i
$607$	−7.69672e13			−0.934033			−0.467016	−	0.884249i	$-0.654671\pi$
$607$	−7.69672e13			−0.934033			−0.467016	+	0.884249i	$0.654671\pi$
$608$			6.72749e13i			0.809720i
$609$	5.53366e12	+	1.93312e12i	0.0660581	+	0.0230767i
$610$	2.38564e12			0.0282459
$611$		−	6.69536e13i		−	0.786264i
$612$	−1.37307e13	+	1.72541e13i	−0.159932	+	0.200972i
$613$	1.31289e14			1.51679			0.758396	−	0.651794i	$-0.225983\pi$
$613$	1.31289e14			1.51679			0.758396	+	0.651794i	$0.225983\pi$
$614$			1.20084e13i			0.137608i
$615$	−5.28770e12	+	1.51363e13i	−0.0601023	+	0.172046i
$616$	−1.87520e14			−2.11419
$617$			4.12100e13i			0.460869i	0.973088	+	0.230434i	$0.0740147\pi$
$617$			4.12100e13i			0.460869i	−0.973088	+	0.230434i	$0.925985\pi$
$618$	−1.16614e14	−	4.07377e13i	−1.29362	−	0.451912i
$619$	1.33201e14			1.46574			0.732868	−	0.680371i	$-0.238181\pi$
$619$	1.33201e14			1.46574			0.732868	+	0.680371i	$0.238181\pi$
$620$		−	1.89670e13i		−	0.207033i
$621$	9.30947e12	+	1.47654e13i	0.100802	+	0.159877i
$622$	3.22165e12			0.0346040
$623$			7.28151e13i			0.775857i
$624$	−2.46169e13	+	7.04672e13i	−0.260202	+	0.744841i
$625$	3.81470e12			0.0400000
$626$		−	7.78467e13i		−	0.809783i
$627$	1.99126e14	+	6.95624e13i	2.05490	+	0.717855i
$628$	−3.95685e13			−0.405090
$629$		−	1.29425e13i		−	0.131451i
$630$	−4.28626e13	−	3.41098e13i	−0.431892	−	0.343697i
$631$	−3.77275e13			−0.377148			−0.188574	−	0.982059i	$-0.560386\pi$
$631$	−3.77275e13			−0.377148			−0.188574	+	0.982059i	$0.560386\pi$
$632$			2.27380e13i			0.225511i
$633$	6.01038e13	−	1.72050e14i	0.591403	−	1.69292i
$634$	1.16056e14			1.13298
$635$			1.81548e13i			0.175842i
$636$	2.37720e13	+	8.30448e12i	0.228444	+	0.0798045i
$637$	−1.30340e14			−1.24275
$638$			6.02760e12i			0.0570219i
$639$	6.74250e13	−	8.47267e13i	0.632873	−	0.795272i
$640$	2.14494e13			0.199763
$641$			9.57378e13i			0.884695i	0.896844	+	0.442347i	$0.145854\pi$
$641$			9.57378e13i			0.884695i	−0.896844	+	0.442347i	$0.854146\pi$
$642$	−2.80751e13	+	8.03665e13i	−0.257423	+	0.736885i
$643$	1.53187e14			1.39370			0.696849	−	0.717218i	$-0.254585\pi$
$643$	1.53187e14			1.39370			0.696849	+	0.717218i	$0.254585\pi$
$644$		−	7.81403e12i		−	0.0705416i
$645$	−2.42170e13	−	8.45992e12i	−0.216931	−	0.0757823i
$646$	1.53002e14			1.35998
$647$			1.03278e14i			0.910935i	0.890252	+	0.455468i	$0.150528\pi$
$647$			1.03278e14i			0.910935i	−0.890252	+	0.455468i	$0.849472\pi$
$648$	1.20680e14	−	2.78054e13i	1.05623	−	0.243363i
$649$	2.43151e13			0.211180
$650$		−	2.34279e13i		−	0.201914i
$651$	9.84725e13	−	2.81883e14i	0.842190	−	2.41081i
$652$	3.46677e13			0.294230
$653$			4.61490e13i			0.388684i	0.980934	+	0.194342i	$0.0622572\pi$
$653$			4.61490e13i			0.388684i	−0.980934	+	0.194342i	$0.937743\pi$
$654$	−4.98819e13	−	1.74257e13i	−0.416922	−	0.145647i
$655$	−6.89579e13			−0.571976
$656$		−	3.32786e13i		−	0.273934i
$657$	−3.25970e12	−	2.59405e12i	−0.0266287	−	0.0211910i
$658$	−1.01985e14			−0.826809
$659$		−	1.66936e14i		−	1.34315i	−0.740939	−	0.671573i	$-0.765619\pi$
$659$		−	1.66936e14i		−	1.34315i	0.740939	−	0.671573i	$-0.234381\pi$
$660$	−6.53111e12	+	1.86956e13i	−0.0521516	+	0.149287i
$661$	−9.89499e9			−7.84166e−5			−3.92083e−5	−	1.00000i	$-0.500012\pi$
$661$	−9.89499e9			−7.84166e−5			−3.92083e−5		1.00000i	$0.500012\pi$
$662$			1.00658e14i			0.791693i
$663$	−1.40158e14	−	4.89625e13i	−1.09408	−	0.382205i
$664$	−1.41675e14			−1.09762
$665$		−	1.33625e14i		−	1.02749i
$666$	−9.34303e12	+	1.17405e13i	−0.0713045	+	0.0896017i
$667$	−1.21679e12			−0.00921691
$668$		−	4.29073e13i		−	0.322589i
$669$	−8.53409e13	+	2.44293e14i	−0.636834	+	1.82297i
$670$	3.36336e13			0.249115
$671$		−	1.35772e13i		−	0.0998158i
$672$	−9.38717e13	−	3.27930e13i	−0.684997	−	0.239296i
$673$	−1.95710e14			−1.41755			−0.708773	−	0.705436i	$-0.750751\pi$
$673$	−1.95710e14			−1.41755			−0.708773	+	0.705436i	$0.750751\pi$
$674$			9.63497e13i			0.692709i
$675$	−2.37066e13	+	1.49469e13i	−0.169181	+	0.106667i
$676$	1.38639e13			0.0982092
$677$		−	8.39435e13i		−	0.590261i	−0.955457	−	0.295130i	$-0.904637\pi$
$677$		−	8.39435e13i		−	0.590261i	0.955457	−	0.295130i	$-0.0953631\pi$
$678$	−2.75175e13	+	7.87703e13i	−0.192070	+	0.549812i
$679$	2.47164e14			1.71252
$680$			6.95905e13i			0.478636i
$681$	6.92030e12	+	2.41753e12i	0.0472486	+	0.0165058i
$682$	3.07044e14			2.08103
$683$			1.05484e14i			0.709717i	0.934920	+	0.354858i	$0.115471\pi$
$683$			1.05484e14i			0.709717i	−0.934920	+	0.354858i	$0.884529\pi$
$684$	4.87946e13	+	3.88304e13i	0.325905	+	0.259353i
$685$	2.98873e13			0.198168
$686$			1.10314e13i			0.0726122i
$687$	6.50610e13	−	1.86240e14i	0.425145	−	1.21700i
$688$	5.32432e13			0.345400
$689$			1.69538e14i			1.09187i
$690$	1.07351e13	+	3.75017e12i	0.0686371	+	0.0239776i
$691$	−2.96033e14			−1.87910			−0.939551	−	0.342409i	$-0.888757\pi$
$691$	−2.96033e14			−1.87910			−0.939551	+	0.342409i	$0.888757\pi$
$692$			4.04447e13i			0.254877i
$693$	−1.94127e14	+	2.43941e14i	−1.21456	+	1.52623i
$694$	−1.88557e14			−1.17124
$695$		−	5.31614e13i		−	0.327848i
$696$	−2.84709e12	+	8.14994e12i	−0.0174323	+	0.0499009i
$697$	6.61905e13			0.402375
$698$			1.40665e14i			0.849003i
$699$	−1.20259e14	−	4.20111e13i	−0.720662	−	0.251755i
$700$	1.25458e13			0.0746465
$701$		−	3.27773e14i		−	1.93635i	−0.250276	−	0.968175i	$-0.580521\pi$
$701$		−	3.27773e14i		−	1.93635i	0.250276	−	0.968175i	$-0.419479\pi$
$702$	9.17958e13	+	1.45594e14i	0.538440	+	0.853998i
$703$	−3.66013e13			−0.213167
$704$		−	2.60272e14i		−	1.50510i
$705$	−1.72075e13	+	4.92573e13i	−0.0988033	+	0.282829i
$706$	−7.96740e13			−0.454248
$707$			2.75747e14i			1.56104i
$708$	6.78647e12	+	2.37078e12i	0.0381485	+	0.0133267i
$709$	−4.95628e13			−0.276646			−0.138323	−	0.990387i	$-0.544171\pi$
$709$	−4.95628e13			−0.276646			−0.138323	+	0.990387i	$0.544171\pi$
$710$		−	7.05400e13i		−	0.390970i
$711$	2.95795e13	+	2.35392e13i	0.162796	+	0.129552i
$712$	−1.07242e14			−0.586089
$713$			6.19826e13i			0.336374i
$714$	−7.45803e13	+	2.13490e14i	−0.401914	+	1.15050i
$715$	−1.33334e14			−0.713527
$716$		−	7.95460e13i		−	0.422721i
$717$	3.81822e13	+	1.33385e13i	0.201495	+	0.0703902i
$718$	1.61664e14			0.847211
$719$			5.69586e13i			0.296425i	0.988956	+	0.148213i	$0.0473520\pi$
$719$			5.69586e13i			0.296425i	−0.988956	+	0.148213i	$0.952648\pi$
$720$	3.62209e13	−	4.55154e13i	0.187196	−	0.235232i
$721$	4.45365e14			2.28581
$722$		−	2.63928e14i		−	1.34524i
$723$	9.75812e13	−	2.79331e14i	0.493940	−	1.41393i
$724$	1.33273e13			0.0669962
$725$		−	1.95362e12i		−	0.00975325i
$726$	−1.38871e14	−	4.85129e13i	−0.688537	−	0.240533i
$727$	−2.81767e14			−1.38745			−0.693726	−	0.720239i	$-0.744032\pi$
$727$	−2.81767e14			−1.38745			−0.693726	+	0.720239i	$0.744032\pi$
$728$		−	3.73263e14i		−	1.82540i
$729$	8.87607e13	−	1.85776e14i	0.431105	−	0.902302i
$730$	−2.71389e12			−0.0130912
$731$			1.05900e14i			0.507350i
$732$	1.32381e12	−	3.78948e12i	0.00629899	−	0.0180312i
$733$	−1.04493e14			−0.493819			−0.246909	−	0.969039i	$-0.579415\pi$
$733$	−1.04493e14			−0.493819			−0.246909	+	0.969039i	$0.579415\pi$
$734$			3.48908e13i			0.163768i
$735$	9.58904e13	+	3.34982e13i	0.447032	+	0.156166i
$736$	2.06413e13			0.0955757
$737$		−	1.91417e14i		−	0.880327i
$738$	−6.00434e13	−	4.77822e13i	−0.274273	−	0.218265i
$739$	−2.65253e13			−0.120348			−0.0601740	−	0.998188i	$-0.519166\pi$
$739$	−2.65253e13			−0.120348			−0.0601740	+	0.998188i	$0.519166\pi$
$740$		−	3.43644e12i		−	0.0154864i
$741$	−1.38466e14	+	3.96365e14i	−0.619800	+	1.77421i
$742$	2.58242e14			1.14817
$743$			1.68581e14i			0.744499i	0.928133	+	0.372249i	$0.121413\pi$
$743$			1.68581e14i			0.744499i	−0.928133	+	0.372249i	$0.878587\pi$
$744$	4.15155e14	+	1.45030e14i	1.82115	+	0.636197i
$745$	−4.96546e13			−0.216361
$746$		−	1.68485e12i		−	0.00729234i
$747$	−1.46667e14	+	1.84302e14i	−0.630563	+	0.792369i
$748$	8.17553e13			0.349147
$749$		−	3.06932e14i		−	1.30206i
$750$	−6.02110e12	+	1.72357e13i	−0.0253729	+	0.0726311i
$751$	1.56240e14			0.654021			0.327011	−	0.945021i	$-0.393959\pi$
$751$	1.56240e14			0.654021			0.327011	+	0.945021i	$0.393959\pi$
$752$		−	1.08297e14i		−	0.450325i
$753$	3.77605e14	+	1.31912e14i	1.55978	+	0.544891i
$754$	−1.19981e13			−0.0492329
$755$			8.52799e12i			0.0347626i
$756$	−7.79667e13	+	4.91575e13i	−0.315719	+	0.199059i
$757$	−1.61527e14			−0.649779			−0.324890	−	0.945752i	$-0.605327\pi$
$757$	−1.61527e14			−0.649779			−0.324890	+	0.945752i	$0.605327\pi$
$758$		−	2.20859e14i		−	0.882612i
$759$	2.13431e13	−	6.10958e13i	0.0847323	−	0.242551i
$760$	1.96802e14			0.776177
$761$			3.55804e14i			1.39408i	0.717033	+	0.697039i	$0.245500\pi$
$761$			3.55804e14i			1.39408i	−0.717033	+	0.697039i	$0.754500\pi$
$762$	−8.20276e13	−	2.86554e13i	−0.319290	−	0.111540i
$763$	1.90507e14			0.736694
$764$			1.24539e14i			0.478451i
$765$	9.05293e13	+	7.20427e13i	0.345527	+	0.274968i
$766$	9.45622e13			0.358570
$767$			4.83998e13i			0.182334i
$768$	6.37048e13	−	1.82358e14i	0.238433	−	0.682526i
$769$	1.37014e13			0.0509489			0.0254744	−	0.999675i	$-0.491890\pi$
$769$	1.37014e13			0.0509489			0.0254744	+	0.999675i	$0.491890\pi$
$770$			2.03096e14i			0.750321i
$771$	2.93379e13	+	1.02489e13i	0.107685	+	0.0376187i
$772$	1.24063e13			0.0452435
$773$			6.08347e13i			0.220421i	0.993908	+	0.110211i	$0.0351526\pi$
$773$			6.08347e13i			0.220421i	−0.993908	+	0.110211i	$0.964847\pi$
$774$	7.64478e13	−	9.60648e13i	0.275208	−	0.345828i
$775$	−9.95165e13			−0.355948
$776$			3.64021e14i			1.29365i
$777$	1.78412e13	−	5.10714e13i	0.0629969	−	0.180332i
$778$	−3.94718e14			−1.38481
$779$		−	1.87186e14i		−	0.652509i
$780$	−3.72142e13	−	1.30003e13i	−0.128895	−	0.0450279i
$781$	−4.01461e14			−1.38162
$782$		−	4.69439e13i		−	0.160526i
$783$	7.65472e12	+	1.21408e13i	0.0260088	+	0.0412515i
$784$	−2.10824e14			−0.711770
$785$			2.07609e14i			0.696462i
$786$	1.08843e14	−	3.11568e14i	0.362817	−	1.03858i
$787$	−8.80368e13			−0.291602			−0.145801	−	0.989314i	$-0.546576\pi$
$787$	−8.80368e13			−0.291602			−0.145801	+	0.989314i	$0.546576\pi$
$788$			2.77934e13i			0.0914766i
$789$	−5.70891e14	−	1.99434e14i	−1.86710	−	0.652251i
$790$	2.46267e13			0.0800333
$791$		−	3.00836e14i		−	0.971509i
$792$	−3.59275e14	−	2.85909e14i	−1.15293	−	0.917492i
$793$	2.70259e13			0.0861814
$794$			2.13770e14i			0.677400i
$795$	4.35721e13	−	1.24727e14i	0.137206	−	0.392759i
$796$	−1.59804e13			−0.0500059
$797$		−	2.80333e14i		−	0.871731i	−0.900012	−	0.435865i	$-0.856442\pi$
$797$		−	2.80333e14i		−	0.871731i	0.900012	−	0.435865i	$-0.143558\pi$
$798$	6.03749e14	+	2.10913e14i	1.86570	+	0.651761i
$799$	2.15400e14			0.661472
$800$			3.31407e13i			0.101137i
$801$	−1.11020e14	+	1.39509e14i	−0.336698	+	0.423097i
$802$	−3.12657e14			−0.942317
$803$			1.54454e13i			0.0462618i
$804$	1.86636e13	−	5.34256e13i	0.0555540	−	0.159026i
$805$	−4.09988e13			−0.121281
$806$			6.11178e14i			1.79677i
$807$	−2.36378e14	−	8.25758e13i	−0.690619	−	0.241260i
$808$	−4.06118e14			−1.17922
$809$		−	3.04518e14i		−	0.878759i	−0.898302	−	0.439379i	$-0.855198\pi$
$809$		−	3.04518e14i		−	0.878759i	0.898302	−	0.439379i	$-0.144802\pi$
$810$	−3.01151e13	−	1.30704e14i	−0.0863691	−	0.374856i
$811$	4.61813e14			1.31632			0.658161	−	0.752877i	$-0.271335\pi$
$811$	4.61813e14			1.31632			0.658161	+	0.752877i	$0.271335\pi$
$812$		−	6.42509e12i		−	0.0182012i
$813$	−1.30353e14	+	3.73141e14i	−0.367001	+	1.05056i
$814$	5.56301e13			0.155664
$815$		−	1.81895e14i		−	0.505864i
$816$	−2.26703e14	−	7.91963e13i	−0.626624	−	0.218904i
$817$	2.99484e14			0.822741
$818$		−	2.69560e14i		−	0.736020i
$819$	−4.85572e14	−	3.86415e14i	−1.31775	−	1.04866i
$820$	1.75746e13			0.0474043
$821$			2.35728e14i			0.631968i	0.948764	+	0.315984i	$0.102335\pi$
$821$			2.35728e14i			0.631968i	−0.948764	+	0.315984i	$0.897665\pi$
$822$	−4.71740e13	+	1.35038e14i	−0.125702	+	0.359829i
$823$	−6.77056e13			−0.179319			−0.0896593	−	0.995972i	$-0.528578\pi$
$823$	−6.77056e13			−0.179319			−0.0896593	+	0.995972i	$0.528578\pi$
$824$			6.55931e14i			1.72672i
$825$	9.80926e13	+	3.42676e13i	0.256665	+	0.0896630i
$826$	7.37232e13			0.191736
$827$			5.95756e14i			1.54007i	0.638001	+	0.770036i	$0.279762\pi$
$827$			5.95756e14i			1.54007i	−0.638001	+	0.770036i	$0.720238\pi$
$828$	1.19140e13	−	1.49712e13i	0.0306129	−	0.0384684i
$829$	5.82336e14			1.48731			0.743654	−	0.668565i	$-0.233091\pi$
$829$	5.82336e14			1.48731			0.743654	+	0.668565i	$0.233091\pi$
$830$			1.53443e14i			0.389543i
$831$	−1.09993e14	+	3.14861e14i	−0.277563	+	0.794537i
$832$	5.18079e14			1.29951
$833$		−	4.19325e14i		−	1.04550i
$834$	2.40196e14	+	8.39097e13i	0.595299	+	0.207961i
$835$	−2.25127e14			−0.554619
$836$		−	2.31203e14i		−	0.566191i
$837$	6.18450e14	−	3.89928e14i	1.50549	−	0.949200i
$838$	−5.44583e14			−1.31778
$839$			5.35480e14i			1.28805i	0.765003	+	0.644026i	$0.222737\pi$
$839$			5.35480e14i			1.28805i	−0.765003	+	0.644026i	$0.777263\pi$
$840$	−9.59306e13	+	2.74606e14i	−0.229383	+	0.656620i
$841$	4.19707e14			0.997622
$842$		−	2.68282e14i		−	0.633915i
$843$	−1.40603e14	−	4.91180e13i	−0.330260	−	0.115373i
$844$	−1.99766e14			−0.466455
$845$		−	7.27414e13i		−	0.168849i
$846$	−1.95396e14	−	1.55495e14i	−0.450882	−	0.358810i
$847$	5.30368e14			1.21663
$848$			2.74225e14i			0.625356i
$849$	7.70915e13	−	2.20678e14i	0.174770	−	0.500289i
$850$	7.53710e13			0.169867
$851$			1.12300e13i			0.0251612i
$852$	−1.12050e14	−	3.91433e13i	−0.249582	−	0.0871885i
$853$	−1.47772e14			−0.327225			−0.163612	−	0.986525i	$-0.552315\pi$
$853$	−1.47772e14			−0.327225			−0.163612	+	0.986525i	$0.552315\pi$
$854$		−	4.11661e13i		−	0.0906256i
$855$	2.03736e14	−	2.56016e14i	0.445900	−	0.560321i
$856$	4.52047e14			0.983591
$857$		−	8.21818e14i		−	1.77775i	−0.458146	−	0.888877i	$-0.651486\pi$
$857$		−	8.21818e14i		−	1.77775i	0.458146	−	0.888877i	$-0.348514\pi$
$858$	2.10453e14	−	6.02434e14i	0.452605	−	1.29561i
$859$	−6.19313e14			−1.32417			−0.662086	−	0.749428i	$-0.730328\pi$
$859$	−6.19313e14			−1.32417			−0.662086	+	0.749428i	$0.730328\pi$
$860$			2.81181e13i			0.0597714i
$861$	2.61190e14	+	9.12436e13i	0.552001	+	0.192835i
$862$	−5.00801e13			−0.105228
$863$			6.20768e14i			1.29681i	0.761297	+	0.648403i	$0.224563\pi$
$863$			6.20768e14i			1.29681i	−0.761297	+	0.648403i	$0.775437\pi$
$864$	−1.29853e14	−	2.05954e14i	−0.269701	−	0.427762i
$865$	2.12206e14			0.438204
$866$		−	5.17960e14i		−	1.06343i
$867$	−4.04196e12	+	1.15703e13i	−0.00825080	+	0.0236183i
$868$	−3.27291e14			−0.664257
$869$		−	1.40157e14i		−	0.282823i
$870$	8.82691e12	+	3.08358e12i	0.0177097	+	0.00618670i
$871$	3.81021e14			0.760078
$872$			2.80577e14i			0.556505i
$873$	4.73549e14	+	3.76848e14i	0.933886	+	0.743181i
$874$	−1.32757e14			−0.260316
$875$		−	6.58257e13i		−	0.128338i
$876$	−1.50596e12	+	4.31090e12i	−0.00291940	+	0.00835694i
$877$	−4.15719e14			−0.801313			−0.400656	−	0.916228i	$-0.631218\pi$
$877$	−4.15719e14			−0.801313			−0.400656	+	0.916228i	$0.631218\pi$
$878$			3.62302e14i			0.694381i
$879$	7.53879e14	+	2.63359e14i	1.43667	+	0.501885i
$880$	−2.15666e14			−0.408665
$881$		−	9.63563e14i		−	1.81552i	−0.419491	−	0.907759i	$-0.637792\pi$
$881$		−	9.63563e14i		−	1.81552i	0.419491	−	0.907759i	$-0.362208\pi$
$882$	−3.02706e14	+	3.80382e14i	−0.567124	+	0.712652i
$883$	−1.56289e14			−0.291156			−0.145578	−	0.989347i	$-0.546504\pi$
$883$	−1.56289e14			−0.291156			−0.145578	+	0.989347i	$0.546504\pi$
$884$			1.62736e14i			0.301455i
$885$	1.24390e13	−	3.56074e13i	0.0229124	−	0.0655878i
$886$	−3.37163e13			−0.0617549
$887$			4.22682e14i			0.769831i	0.922952	+	0.384916i	$0.125769\pi$
$887$			4.22682e14i			0.769831i	−0.922952	+	0.384916i	$0.874231\pi$
$888$	7.52176e13	+	2.62764e13i	0.136224	+	0.0475884i
$889$	3.13276e14			0.564180
$890$			1.16150e14i			0.208002i
$891$	−7.43870e14	+	1.71392e14i	−1.32467	+	0.305213i
$892$	2.83646e14			0.502288
$893$		−	6.09150e14i		−	1.07267i
$894$	7.83746e13	−	2.24351e14i	0.137242	−	0.392863i
$895$	−4.17364e14			−0.726774
$896$		−	3.70127e14i		−	0.640930i
$897$	1.21613e14	+	4.24841e13i	0.209419	+	0.0731583i
$898$	7.25061e13			0.124163
$899$			5.09653e13i			0.0867912i
$900$	2.40370e13	+	1.91285e13i	0.0407069	+	0.0323943i
$901$	−5.45428e14			−0.918572
$902$			2.84504e14i			0.476491i
$903$	−1.45983e14	+	4.17883e14i	−0.243144	+	0.696011i
$904$	4.43068e14			0.733886
$905$		−	6.99260e13i		−	0.115185i
$906$	−3.85315e13	−	1.34605e13i	−0.0631211	−	0.0220506i
$907$	−4.69868e14			−0.765490			−0.382745	−	0.923854i	$-0.625021\pi$
$907$	−4.69868e14			−0.765490			−0.382745	+	0.923854i	$0.625021\pi$
$908$		−	8.03510e12i		−	0.0130185i
$909$	−4.20428e14	+	5.28313e14i	−0.677442	+	0.851278i
$910$	−4.04267e14			−0.647831
$911$		−	4.83462e14i		−	0.770496i	−0.922813	−	0.385248i	$-0.874116\pi$
$911$		−	4.83462e14i		−	0.770496i	0.922813	−	0.385248i	$-0.125884\pi$
$912$	−2.23967e14	+	6.41116e14i	−0.354984	+	1.01616i
$913$	8.73280e14			1.37657
$914$		−	6.15531e14i		−	0.964981i
$915$	−1.98827e13	−	6.94580e12i	−0.0310006	−	0.0108297i
$916$	−2.16242e14			−0.335323
$917$			1.18993e15i			1.83516i
$918$	−4.68397e14	+	2.95321e14i	−0.718457	+	0.452982i
$919$	−6.42475e14			−0.980118			−0.490059	−	0.871689i	$-0.663025\pi$
$919$	−6.42475e14			−0.980118			−0.490059	+	0.871689i	$0.663025\pi$
$920$		−	6.03827e13i		−	0.0916164i
$921$	3.49627e13	−	1.00082e14i	0.0527602	−	0.151029i
$922$	−2.56419e14			−0.384853
$923$		−	7.99118e14i		−	1.19289i
$924$	3.22609e14	+	1.12700e14i	0.478979	+	0.167326i
$925$	−1.80304e13			−0.0266254
$926$			2.10346e14i			0.308944i
$927$	8.53290e14	+	6.79043e14i	1.24652	+	0.991970i
$928$	1.69723e13			0.0246605
$929$			1.29783e14i			0.187559i	0.995593	+	0.0937796i	$0.0298949\pi$
$929$			1.29783e14i			0.187559i	−0.995593	+	0.0937796i	$0.970105\pi$
$930$	1.57076e14	−	4.49639e14i	0.225785	−	0.646322i
$931$	−1.18585e15			−1.69543
$932$			1.39632e14i			0.198566i
$933$	−2.68503e13	−	9.37985e12i	−0.0379788	−	0.0132675i
$934$	7.18405e14			1.01073
$935$		−	4.28955e14i		−	0.600280i
$936$	5.69109e14	−	7.15147e14i	0.792167	−	0.995442i
$937$	−4.95593e14			−0.686163			−0.343081	−	0.939306i	$-0.611471\pi$
$937$	−4.95593e14			−0.686163			−0.343081	+	0.939306i	$0.611471\pi$
$938$		−	5.80376e14i		−	0.799274i
$939$	−2.26651e14	+	6.48801e14i	−0.310477	+	0.888758i
$940$	5.71922e13			0.0779287
$941$			1.14019e15i			1.54536i	0.634794	+	0.772682i	$0.281085\pi$
$941$			1.14019e15i			1.54536i	−0.634794	+	0.772682i	$0.718915\pi$
$942$	−9.38026e14	−	3.27689e14i	−1.26462	−	0.441781i
$943$	−5.74325e13			−0.0770192
$944$			7.82861e13i			0.104430i
$945$	2.57920e14	+	4.09077e14i	0.342237	+	0.542808i
$946$	−4.55184e14			−0.600802
$947$		−	5.62820e14i		−	0.738958i	−0.929239	−	0.369479i	$-0.879536\pi$
$947$		−	5.62820e14i		−	0.738958i	0.929239	−	0.369479i	$-0.120464\pi$
$948$	1.36656e13	−	3.91184e13i	0.0178479	−	0.0510905i
$949$	−3.07445e13			−0.0399426
$950$		−	2.13149e14i		−	0.275464i
$951$	−9.67251e14	−	3.37898e14i	−1.24347	−	0.434394i
$952$	1.20084e15			1.53568
$953$			3.36550e14i			0.428140i	0.976818	+	0.214070i	$0.0686720\pi$
$953$			3.36550e14i			0.428140i	−0.976818	+	0.214070i	$0.931328\pi$
$954$	4.94774e14	+	3.93738e14i	0.626131	+	0.498271i
$955$	6.53432e14			0.822590
$956$		−	4.43330e13i		−	0.0555185i
$957$	1.75494e13	−	5.02361e13i	0.0218627	−	0.0625830i
$958$	1.12489e15			1.39407
$959$		−	5.15730e14i		−	0.635813i
$960$	−3.81146e14	−	1.33149e14i	−0.467450	−	0.163299i
$961$	1.77652e15			2.16747
$962$			1.10733e14i			0.134401i
$963$	4.67975e14	−	5.88061e14i	0.565056	−	0.710053i
$964$	−3.24329e14			−0.389584
$965$		−	6.50936e13i		−	0.0777861i
$966$	6.47122e13	−	1.85242e14i	0.0769309	−	0.220219i
$967$	1.61188e14			0.190634			0.0953172	−	0.995447i	$-0.469613\pi$
$967$	1.61188e14			0.190634			0.0953172	+	0.995447i	$0.469613\pi$
$968$			7.81122e14i			0.919056i
$969$	−1.27517e15	−	4.45465e14i	−1.49262	−	0.521429i
$970$	3.94258e14			0.459115
$971$		−	1.34616e15i		−	1.55955i	−0.626060	−	0.779775i	$-0.715334\pi$
$971$		−	1.34616e15i		−	1.55955i	0.626060	−	0.779775i	$-0.284666\pi$
$972$	−2.24329e14	−	2.46925e13i	−0.258556	−	0.0284599i
$973$	−9.17343e14			−1.05188
$974$		−	1.44371e14i		−	0.164697i
$975$	−6.82104e13	+	1.95256e14i	−0.0774155	+	0.221606i
$976$	4.37140e13			0.0493596
$977$		−	1.10154e15i		−	1.23745i	−0.785609	−	0.618724i	$-0.787650\pi$
$977$		−	1.10154e15i		−	1.23745i	0.785609	−	0.618724i	$-0.212350\pi$
$978$	8.21846e14	+	2.87103e14i	0.918536	+	0.320880i
$979$	6.61035e14			0.735041
$980$		−	1.11338e14i		−	0.123172i
$981$	3.64998e14	+	2.90463e14i	0.401740	+	0.319702i
$982$	8.51916e14			0.932909
$983$			9.85641e14i			1.07387i	0.843624	+	0.536934i	$0.180418\pi$
$983$			9.85641e14i			1.07387i	−0.843624	+	0.536934i	$0.819582\pi$
$984$	−1.34383e14	+	3.84678e14i	−0.145669	+	0.416986i
$985$	1.45827e14			0.157274
$986$		−	3.85997e13i		−	0.0414190i
$987$	8.49975e14	+	2.96929e14i	0.907445	+	0.317006i
$988$	4.60217e14			0.488852
$989$		−	9.18876e13i		−	0.0971126i
$990$	−3.09658e14	+	3.89118e14i	−0.325616	+	0.409172i
$991$	−1.20714e15			−1.26296			−0.631481	−	0.775392i	$-0.717552\pi$
$991$	−1.20714e15			−1.26296			−0.631481	+	0.775392i	$0.717552\pi$
$992$		−	8.64562e14i		−	0.899991i
$993$	2.93066e14	−	8.38915e14i	0.303542	−	0.868904i
$994$	−1.21723e15			−1.25441
$995$			8.38461e13i			0.0859740i
$996$	2.43737e14	+	8.51467e13i	0.248671	+	0.0868703i
$997$	−1.43111e15			−1.45277			−0.726387	−	0.687286i	$-0.758802\pi$
$997$	−1.43111e15			−1.45277			−0.726387	+	0.687286i	$0.758802\pi$
$998$		−	7.79718e13i		−	0.0787563i
$999$	1.12051e14	−	7.06471e13i	0.112613	−	0.0710014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.11.c.a.11.5	✓	14
3.2	odd	2	inner	15.11.c.a.11.10	yes	14
4.3	odd	2		240.11.l.b.161.9		14
5.2	odd	4		75.11.d.d.74.20		28
5.3	odd	4		75.11.d.d.74.9		28
5.4	even	2		75.11.c.g.26.10		14
12.11	even	2		240.11.l.b.161.10		14
15.2	even	4		75.11.d.d.74.10		28
15.8	even	4		75.11.d.d.74.19		28
15.14	odd	2		75.11.c.g.26.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.11.c.a.11.5	✓	14	1.1	even	1	trivial
15.11.c.a.11.10	yes	14	3.2	odd	2	inner
75.11.c.g.26.5		14	15.14	odd	2
75.11.c.g.26.10		14	5.4	even	2
75.11.d.d.74.9		28	5.3	odd	4
75.11.d.d.74.10		28	15.2	even	4
75.11.d.d.74.19		28	15.8	even	4
75.11.d.d.74.20		28	5.2	odd	4
240.11.l.b.161.9		14	4.3	odd	2
240.11.l.b.161.10		14	12.11	even	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	15.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-27.5253i q^{2} +(-80.1400 + 229.405i) q^{3} +266.360 q^{4} -1397.54i q^{5} +(6314.43 + 2205.87i) q^{6} -24115.7 q^{7} -35517.5i q^{8} +(-46204.2 - 36769.0i) q^{9} +O(q^{10})\)	\(q-27.5253i q^{2} +(-80.1400 + 229.405i) q^{3} +266.360 q^{4} -1397.54i q^{5} +(6314.43 + 2205.87i) q^{6} -24115.7 q^{7} -35517.5i q^{8} +(-46204.2 - 36769.0i) q^{9} -38467.7 q^{10} +218929. i q^{11} +(-21346.1 + 61104.3i) q^{12} -435784. q^{13} +663792. i q^{14} +(320603. + 111999. i) q^{15} -704876. q^{16} -1.40198e6i q^{17} +(-1.01208e6 + 1.27178e6i) q^{18} -3.96480e6 q^{19} -372249. i q^{20} +(1.93264e6 - 5.53227e6i) q^{21} +6.02608e6 q^{22} +1.21648e6i q^{23} +(8.14789e6 + 2.84637e6i) q^{24} -1.95312e6 q^{25} +1.19951e7i q^{26} +(1.21378e7 - 7.65279e6i) q^{27} -6.42347e6 q^{28} +1.00025e6i q^{29} +(3.08280e6 - 8.82468e6i) q^{30} +5.09524e7 q^{31} -1.69680e7i q^{32} +(-5.02234e7 - 1.75450e7i) q^{33} -3.85900e7 q^{34} +3.37028e7i q^{35} +(-1.23069e7 - 9.79379e6i) q^{36} +9.23155e6 q^{37} +1.09132e8i q^{38} +(3.49238e7 - 9.99710e7i) q^{39} -4.96372e7 q^{40} +4.72120e7i q^{41} +(-1.52277e8 - 5.31963e7i) q^{42} -7.55356e7 q^{43} +5.83140e7i q^{44} +(-5.13862e7 + 6.45723e7i) q^{45} +3.34839e7 q^{46} +1.53639e8i q^{47} +(5.64887e7 - 1.61702e8i) q^{48} +2.99094e8 q^{49} +5.37603e7i q^{50} +(3.21622e8 + 1.12355e8i) q^{51} -1.16076e8 q^{52} -3.89040e8i q^{53} +(-2.10645e8 - 3.34096e8i) q^{54} +3.05963e8 q^{55} +8.56531e8i q^{56} +(3.17739e8 - 9.09545e8i) q^{57} +2.75322e7 q^{58} -1.11064e8i q^{59} +(8.53958e7 + 2.98321e7i) q^{60} -6.20166e7 q^{61} -1.40248e9i q^{62} +(1.11425e9 + 8.86712e8i) q^{63} -1.18884e9 q^{64} +6.09027e8i q^{65} +(-4.82930e8 + 1.38241e9i) q^{66} -8.74334e8 q^{67} -3.73432e8i q^{68} +(-2.79066e8 - 9.74887e7i) q^{69} +9.27678e8 q^{70} +1.83375e9i q^{71} +(-1.30594e9 + 1.64106e9i) q^{72} +7.05499e7 q^{73} -2.54101e8i q^{74} +(1.56523e8 - 4.48056e8i) q^{75} -1.05606e9 q^{76} -5.27964e9i q^{77} +(-2.75173e9 - 9.61285e8i) q^{78} -6.40192e8 q^{79} +9.85094e8i q^{80} +(7.82866e8 + 3.39776e9i) q^{81} +1.29952e9 q^{82} -3.98887e9i q^{83} +(5.14777e8 - 1.47358e9i) q^{84} -1.95933e9 q^{85} +2.07914e9i q^{86} +(-2.29463e8 - 8.01602e7i) q^{87} +7.77582e9 q^{88} -3.01940e9i q^{89} +(1.77737e9 + 1.41442e9i) q^{90} +1.05093e10 q^{91} +3.24022e8i q^{92} +(-4.08333e9 + 1.16887e10i) q^{93} +4.22896e9 q^{94} +5.54098e9i q^{95} +(3.89255e9 + 1.35982e9i) q^{96} -1.02491e10 q^{97} -8.23264e9i q^{98} +(8.04981e9 - 1.01154e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9}+O(q^{10}) \) 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9	\( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9} + 31250 q^{10} + 43756 q^{12} + 699408 q^{13} - 343750 q^{15} + 2871906 q^{16} - 3243880 q^{18} + 3814644 q^{19} - 2191008 q^{21} - 10493420 q^{22} + 9454542 q^{24} - 27343750 q^{25} + 13322636 q^{27} - 10989172 q^{28} + 20875000 q^{30} + 105444308 q^{31} - 187570700 q^{33} + 84960772 q^{34} + 80968490 q^{36} - 152902928 q^{37} - 262995952 q^{39} - 228656250 q^{40} + 1025108820 q^{42} - 82568592 q^{43} + 284500000 q^{45} + 302816052 q^{46} - 534917396 q^{48} + 1339929050 q^{49} - 519773324 q^{51} - 2117624528 q^{52} - 3171778694 q^{54} - 414437500 q^{55} + 2459677832 q^{57} + 2203542020 q^{58} + 918156250 q^{60} - 2372907732 q^{61} + 253855908 q^{63} + 5663115830 q^{64} + 915786920 q^{66} - 7807415008 q^{67} - 1032380604 q^{69} - 95812500 q^{70} + 2313658920 q^{72} + 10465834068 q^{73} - 85937500 q^{75} - 4927934540 q^{76} - 4082143640 q^{78} - 8333919076 q^{79} - 4284635426 q^{81} + 14404193720 q^{82} + 13837595568 q^{84} + 4711812500 q^{85} - 11735627260 q^{87} - 14973492180 q^{88} - 9226281250 q^{90} + 4013221984 q^{91} - 9561672552 q^{93} - 47501516708 q^{94} + 43132239458 q^{96} + 31262487532 q^{97} + 36258312560 q^{99}+O(q^{100}) \) 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9 + 31250 * q^10 + 43756 * q^12 + 699408 * q^13 - 343750 * q^15 + 2871906 * q^16 - 3243880 * q^18 + 3814644 * q^19 - 2191008 * q^21 - 10493420 * q^22 + 9454542 * q^24 - 27343750 * q^25 + 13322636 * q^27 - 10989172 * q^28 + 20875000 * q^30 + 105444308 * q^31 - 187570700 * q^33 + 84960772 * q^34 + 80968490 * q^36 - 152902928 * q^37 - 262995952 * q^39 - 228656250 * q^40 + 1025108820 * q^42 - 82568592 * q^43 + 284500000 * q^45 + 302816052 * q^46 - 534917396 * q^48 + 1339929050 * q^49 - 519773324 * q^51 - 2117624528 * q^52 - 3171778694 * q^54 - 414437500 * q^55 + 2459677832 * q^57 + 2203542020 * q^58 + 918156250 * q^60 - 2372907732 * q^61 + 253855908 * q^63 + 5663115830 * q^64 + 915786920 * q^66 - 7807415008 * q^67 - 1032380604 * q^69 - 95812500 * q^70 + 2313658920 * q^72 + 10465834068 * q^73 - 85937500 * q^75 - 4927934540 * q^76 - 4082143640 * q^78 - 8333919076 * q^79 - 4284635426 * q^81 + 14404193720 * q^82 + 13837595568 * q^84 + 4711812500 * q^85 - 11735627260 * q^87 - 14973492180 * q^88 - 9226281250 * q^90 + 4013221984 * q^91 - 9561672552 * q^93 - 47501516708 * q^94 + 43132239458 * q^96 + 31262487532 * q^97 + 36258312560 * q^99

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