LMFDB - Embedded newform 15.11.c.a.11.1

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			11.1
Root			$-55.5349i$ of defining polynomial
Character	$\chi$	$=$	15.11
Dual form			15.11.c.a.11.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-57.7709i q^{2} +(-60.6159 + 235.318i) q^{3} -2313.48 q^{4} +1397.54i q^{5} +(13594.6 + 3501.84i) q^{6} +22792.7 q^{7} +74494.6i q^{8} +(-51700.4 - 28528.1i) q^{9} +O(q^{10})$	\(q-57.7709i q^{2} +(-60.6159 + 235.318i) q^{3} -2313.48 q^{4} +1397.54i q^{5} +(13594.6 + 3501.84i) q^{6} +22792.7 q^{7} +74494.6i q^{8} +(-51700.4 - 28528.1i) q^{9} +80737.3 q^{10} +163555. i q^{11} +(140234. - 544405. i) q^{12} +376456. q^{13} -1.31675e6i q^{14} +(-328867. - 84713.4i) q^{15} +1.93462e6 q^{16} +1.43334e6i q^{17} +(-1.64809e6 + 2.98678e6i) q^{18} +1.20261e6 q^{19} -3.23319e6i q^{20} +(-1.38160e6 + 5.36354e6i) q^{21} +9.44873e6 q^{22} +4.68186e6i q^{23} +(-1.75299e7 - 4.51556e6i) q^{24} -1.95312e6 q^{25} -2.17482e7i q^{26} +(9.84705e6 - 1.04368e7i) q^{27} -5.27305e7 q^{28} +3.09100e7i q^{29} +(-4.89397e6 + 1.89990e7i) q^{30} +3.58223e7 q^{31} -3.54822e7i q^{32} +(-3.84875e7 - 9.91404e6i) q^{33} +8.28052e7 q^{34} +3.18537e7i q^{35} +(1.19608e8 + 6.59992e7i) q^{36} -8.77542e7 q^{37} -6.94757e7i q^{38} +(-2.28192e7 + 8.85870e7i) q^{39} -1.04109e8 q^{40} -6.35454e7i q^{41} +(3.09857e8 + 7.98163e7i) q^{42} -1.28943e8 q^{43} -3.78381e8i q^{44} +(3.98692e7 - 7.22535e7i) q^{45} +2.70475e8 q^{46} -2.23200e8i q^{47} +(-1.17269e8 + 4.55251e8i) q^{48} +2.37031e8 q^{49} +1.12834e8i q^{50} +(-3.37290e8 - 8.68831e7i) q^{51} -8.70924e8 q^{52} +8.77462e6i q^{53} +(-6.02944e8 - 5.68873e8i) q^{54} -2.28575e8 q^{55} +1.69793e9i q^{56} +(-7.28972e7 + 2.82995e8i) q^{57} +1.78570e9 q^{58} +3.20486e8i q^{59} +(7.60829e8 + 1.95983e8i) q^{60} -3.58980e8 q^{61} -2.06949e9i q^{62} +(-1.17839e9 - 6.50232e8i) q^{63} -6.87918e7 q^{64} +5.26113e8i q^{65} +(-5.72743e8 + 2.22346e9i) q^{66} -2.46701e8 q^{67} -3.31600e9i q^{68} +(-1.10173e9 - 2.83795e8i) q^{69} +1.84022e9 q^{70} -1.70232e9i q^{71} +(2.12519e9 - 3.85140e9i) q^{72} +1.99947e9 q^{73} +5.06964e9i q^{74} +(1.18391e8 - 4.59606e8i) q^{75} -2.78221e9 q^{76} +3.72786e9i q^{77} +(5.11775e9 + 1.31829e9i) q^{78} +1.11937e9 q^{79} +2.70371e9i q^{80} +(1.85908e9 + 2.94983e9i) q^{81} -3.67108e9 q^{82} +3.65141e9i q^{83} +(3.19631e9 - 1.24084e10i) q^{84} -2.00315e9 q^{85} +7.44918e9i q^{86} +(-7.27368e9 - 1.87364e9i) q^{87} -1.21840e10 q^{88} -5.52281e9i q^{89} +(-4.17415e9 - 2.30328e9i) q^{90} +8.58044e9 q^{91} -1.08314e10i q^{92} +(-2.17140e9 + 8.42965e9i) q^{93} -1.28945e10 q^{94} +1.68069e9i q^{95} +(8.34961e9 + 2.15079e9i) q^{96} +1.19590e10 q^{97} -1.36935e10i q^{98} +(4.66591e9 - 8.45586e9i) 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 $

$2$		−	57.7709i		−	1.80534i	−0.430331	−	0.902671i	$-0.641603\pi$
$2$		−	57.7709i		−	1.80534i	0.430331	−	0.902671i	$-0.358397\pi$
$3$	−60.6159	+	235.318i	−0.249448	+	0.968388i
$3$	−60.6159	+	235.318i	−0.249448	+	0.968388i
$4$	−2313.48			−2.25926
$5$			1397.54i			0.447214i
$5$			1397.54i			0.447214i
$6$	13594.6	+	3501.84i	1.74827	+	0.450340i
$7$	22792.7			1.35614			0.678071	−	0.734996i	$-0.262816\pi$
$7$	22792.7			1.35614			0.678071	+	0.734996i	$0.262816\pi$
$8$			74494.6i			2.27339i
$9$	−51700.4	−	28528.1i	−0.875551	−	0.483126i
$10$	80737.3			0.807373
$11$			163555.i			1.01555i	0.861490	+	0.507774i	$0.169531\pi$
$11$			163555.i			1.01555i	−0.861490	+	0.507774i	$0.830469\pi$
$12$	140234.	−	544405.i	0.563569	−	2.18784i
$13$	376456.			1.01391			0.506953	−	0.861974i	$-0.330772\pi$
$13$	376456.			1.01391			0.506953	+	0.861974i	$0.330772\pi$
$14$		−	1.31675e6i		−	2.44830i
$15$	−328867.	−	84713.4i	−0.433076	−	0.111557i
$16$	1.93462e6			1.84499
$17$			1.43334e6i			1.00949i	0.863267	+	0.504747i	$0.168414\pi$
$17$			1.43334e6i			1.00949i	−0.863267	+	0.504747i	$0.831586\pi$
$18$	−1.64809e6	+	2.98678e6i	−0.872207	+	1.58067i
$19$	1.20261e6			0.485686			0.242843	−	0.970066i	$-0.421920\pi$
$19$	1.20261e6			0.485686			0.242843	+	0.970066i	$0.421920\pi$
$20$		−	3.23319e6i		−	1.01037i
$21$	−1.38160e6	+	5.36354e6i	−0.338287	+	1.31327i
$22$	9.44873e6			1.83341
$23$			4.68186e6i			0.727410i	0.931514	+	0.363705i	$0.118488\pi$
$23$			4.68186e6i			0.727410i	−0.931514	+	0.363705i	$0.881512\pi$
$24$	−1.75299e7	−	4.51556e6i	−2.20153	−	0.567094i
$25$	−1.95312e6			−0.200000
$26$		−	2.17482e7i		−	1.83045i
$27$	9.84705e6	−	1.04368e7i	0.686258	−	0.727358i
$28$	−5.27305e7			−3.06388
$29$			3.09100e7i			1.50698i	0.657458	+	0.753492i	$0.271632\pi$
$29$			3.09100e7i			1.50698i	−0.657458	+	0.753492i	$0.728368\pi$
$30$	−4.89397e6	+	1.89990e7i	−0.201398	+	0.781851i
$31$	3.58223e7			1.25125			0.625627	−	0.780122i	$-0.284843\pi$
$31$	3.58223e7			1.25125			0.625627	+	0.780122i	$0.284843\pi$
$32$		−	3.54822e7i		−	1.05745i
$33$	−3.84875e7	−	9.91404e6i	−0.983444	−	0.253327i
$34$	8.28052e7			1.82248
$35$			3.18537e7i			0.606485i
$36$	1.19608e8	+	6.59992e7i	1.97810	+	1.09151i
$37$	−8.77542e7			−1.26549			−0.632746	−	0.774360i	$-0.718072\pi$
$37$	−8.77542e7			−1.26549			−0.632746	+	0.774360i	$0.718072\pi$
$38$		−	6.94757e7i		−	0.876830i
$39$	−2.28192e7	+	8.85870e7i	−0.252917	+	0.981854i
$40$	−1.04109e8			−1.01669
$41$		−	6.35454e7i		−	0.548486i	−0.961660	−	0.274243i	$-0.911573\pi$
$41$		−	6.35454e7i		−	0.548486i	0.961660	−	0.274243i	$-0.0884272\pi$
$42$	3.09857e8	+	7.98163e7i	2.37091	+	0.610725i
$43$	−1.28943e8			−0.877115			−0.438558	−	0.898703i	$-0.644510\pi$
$43$	−1.28943e8			−0.877115			−0.438558	+	0.898703i	$0.644510\pi$
$44$		−	3.78381e8i		−	2.29439i
$45$	3.98692e7	−	7.22535e7i	0.216060	−	0.391558i
$46$	2.70475e8			1.31322
$47$		−	2.23200e8i		−	0.973205i	−0.873623	−	0.486603i	$-0.838236\pi$
$47$		−	2.23200e8i		−	0.973205i	0.873623	−	0.486603i	$-0.161764\pi$
$48$	−1.17269e8	+	4.55251e8i	−0.460231	+	1.78667i
$49$	2.37031e8			0.839122
$50$			1.12834e8i			0.361068i
$51$	−3.37290e8	−	8.68831e7i	−0.977582	−	0.251817i
$52$	−8.70924e8			−2.29068
$53$			8.77462e6i			0.0209821i	0.999945	+	0.0104910i	$0.00333946\pi$
$53$			8.77462e6i			0.0209821i	−0.999945	+	0.0104910i	$0.996661\pi$
$54$	−6.02944e8	−	5.68873e8i	−1.31313	−	1.23893i
$55$	−2.28575e8			−0.454167
$56$			1.69793e9i			3.08305i
$57$	−7.28972e7	+	2.82995e8i	−0.121154	+	0.470333i
$58$	1.78570e9			2.72062
$59$			3.20486e8i			0.448279i	0.974557	+	0.224140i	$0.0719572\pi$
$59$			3.20486e8i			0.448279i	−0.974557	+	0.224140i	$0.928043\pi$
$60$	7.60829e8	+	1.95983e8i	0.978432	+	0.252036i
$61$	−3.58980e8			−0.425032			−0.212516	−	0.977158i	$-0.568166\pi$
$61$	−3.58980e8			−0.425032			−0.212516	+	0.977158i	$0.568166\pi$
$62$		−	2.06949e9i		−	2.25894i
$63$	−1.17839e9	−	6.50232e8i	−1.18737	−	0.655187i
$64$	−6.87918e7			−0.0640674
$65$			5.26113e8i			0.453432i
$66$	−5.72743e8	+	2.22346e9i	−0.457341	+	1.77545i
$67$	−2.46701e8			−0.182725			−0.0913624	−	0.995818i	$-0.529122\pi$
$67$	−2.46701e8			−0.182725			−0.0913624	+	0.995818i	$0.529122\pi$
$68$		−	3.31600e9i		−	2.28071i
$69$	−1.10173e9	−	2.83795e8i	−0.704415	−	0.181451i
$70$	1.84022e9			1.09491
$71$		−	1.70232e9i		−	0.943519i	−0.881727	−	0.471759i	$-0.843619\pi$
$71$		−	1.70232e9i		−	0.943519i	0.881727	−	0.471759i	$-0.156381\pi$
$72$	2.12519e9	−	3.85140e9i	1.09833	−	1.99047i
$73$	1.99947e9			0.964496			0.482248	−	0.876035i	$-0.339820\pi$
$73$	1.99947e9			0.964496			0.482248	+	0.876035i	$0.339820\pi$
$74$			5.06964e9i			2.28465i
$75$	1.18391e8	−	4.59606e8i	0.0498897	−	0.193678i
$76$	−2.78221e9			−1.09729
$77$			3.72786e9i			1.37723i
$78$	5.11775e9	+	1.31829e9i	1.77258	+	0.456602i
$79$	1.11937e9			0.363780			0.181890	−	0.983319i	$-0.441779\pi$
$79$	1.11937e9			0.363780			0.181890	+	0.983319i	$0.441779\pi$
$80$			2.70371e9i			0.825107i
$81$	1.85908e9	+	2.94983e9i	0.533179	+	0.846002i
$82$	−3.67108e9			−0.990204
$83$			3.65141e9i			0.926981i	0.886102	+	0.463490i	$0.153403\pi$
$83$			3.65141e9i			0.926981i	−0.886102	+	0.463490i	$0.846597\pi$
$84$	3.19631e9	−	1.24084e10i	0.764279	−	2.96702i
$85$	−2.00315e9			−0.451459
$86$			7.44918e9i			1.58349i
$87$	−7.27368e9	−	1.87364e9i	−1.45934	−	0.375914i
$88$	−1.21840e10			−2.30874
$89$		−	5.52281e9i		−	0.989032i	−0.869169	−	0.494516i	$-0.835345\pi$
$89$		−	5.52281e9i		−	0.989032i	0.869169	−	0.494516i	$-0.164655\pi$
$90$	−4.17415e9	−	2.30328e9i	−0.706897	−	0.390063i
$91$	8.58044e9			1.37500
$92$		−	1.08314e10i		−	1.64341i
$93$	−2.17140e9	+	8.42965e9i	−0.312123	+	1.21170i
$94$	−1.28945e10			−1.75697
$95$			1.68069e9i			0.217205i
$96$	8.34961e9	+	2.15079e9i	1.02402	+	0.263780i
$97$	1.19590e10			1.39263			0.696317	−	0.717734i	$-0.254821\pi$
$97$	1.19590e10			1.39263			0.696317	+	0.717734i	$0.254821\pi$
$98$		−	1.36935e10i		−	1.51490i
$99$	4.66591e9	−	8.45586e9i	0.490637	−	0.889164i
$100$	4.51852e9			0.451852
$101$			1.70503e9i			0.162228i	0.996705	+	0.0811139i	$0.0258478\pi$
$101$			1.70503e9i			0.162228i	−0.996705	+	0.0811139i	$0.974152\pi$
$102$	−5.01932e9	+	1.94856e10i	−0.454615	+	1.76487i
$103$	−3.80941e9			−0.328603			−0.164302	−	0.986410i	$-0.552537\pi$
$103$	−3.80941e9			−0.328603			−0.164302	+	0.986410i	$0.552537\pi$
$104$			2.80439e10i			2.30501i
$105$	−7.49577e9	−	1.93084e9i	−0.587313	−	0.151287i
$106$	5.06918e8			0.0378798
$107$		−	5.69825e9i		−	0.406278i	−0.979150	−	0.203139i	$-0.934886\pi$
$107$		−	5.69825e9i		−	0.406278i	0.979150	−	0.203139i	$-0.0651143\pi$
$108$	−2.27810e10	+	2.41453e10i	−1.55043	+	1.64329i
$109$	2.51815e10			1.63662			0.818311	−	0.574775i	$-0.194911\pi$
$109$	2.51815e10			1.63662			0.818311	+	0.574775i	$0.194911\pi$
$110$			1.32050e10i			0.819926i
$111$	5.31930e9	−	2.06502e10i	0.315675	−	1.22549i
$112$	4.40951e10			2.50207
$113$		−	2.50785e10i		−	1.36116i	−0.732673	−	0.680580i	$-0.761728\pi$
$113$		−	2.50785e10i		−	1.36116i	0.732673	−	0.680580i	$-0.238272\pi$
$114$	1.63489e10	+	4.21134e9i	0.849111	+	0.218724i
$115$	−6.54310e9			−0.325308
$116$		−	7.15096e10i		−	3.40467i
$117$	−1.94629e10	−	1.07396e10i	−0.887726	−	0.489844i
$118$	1.85148e10			0.809297
$119$			3.26696e10i			1.36902i
$120$	6.31069e9	−	2.44988e10i	0.253612	−	0.984553i
$121$	−8.12806e8			−0.0313372
$122$			2.07386e10i			0.767327i
$123$	1.49534e10	+	3.85187e9i	0.531147	+	0.136819i
$124$	−8.28743e10			−2.82691
$125$		−	2.72958e9i		−	0.0894427i
$126$	−3.75645e10	+	6.80768e10i	−1.18284	+	2.14361i
$127$	−5.77643e10			−1.74840			−0.874200	−	0.485566i	$-0.838614\pi$
$127$	−5.77643e10			−1.74840			−0.874200	+	0.485566i	$0.838614\pi$
$128$		−	3.23596e10i		−	0.941788i
$129$	7.81602e9	−	3.03427e10i	0.218795	−	0.849388i
$130$	3.03941e10			0.818600
$131$			9.59792e9i			0.248783i	0.992233	+	0.124391i	$0.0396979\pi$
$131$			9.59792e9i			0.248783i	−0.992233	+	0.124391i	$0.960302\pi$
$132$	8.90401e10	+	2.29360e10i	2.22186	+	0.572331i
$133$	2.74106e10			0.658660
$134$			1.42522e10i			0.329881i
$135$	1.45859e10	+	1.37617e10i	0.325285	+	0.306904i
$136$	−1.06776e11			−2.29498
$137$			3.71888e10i			0.770565i	0.922799	+	0.385282i	$0.125896\pi$
$137$			3.71888e10i			0.770565i	−0.922799	+	0.385282i	$0.874104\pi$
$138$	−1.63951e10	+	6.36478e10i	−0.327581	+	1.27171i
$139$	6.29126e10			1.21245			0.606224	−	0.795294i	$-0.292683\pi$
$139$	6.29126e10			1.21245			0.606224	+	0.795294i	$0.292683\pi$
$140$		−	7.36931e10i		−	1.37021i
$141$	5.25230e10	+	1.35295e10i	0.942441	+	0.242764i
$142$	−9.83449e10			−1.70337
$143$			6.15712e10i			1.02967i
$144$	−1.00020e11	−	5.51909e10i	−1.61539	−	0.891364i
$145$	−4.31980e10			−0.673943
$146$		−	1.15511e11i		−	1.74125i
$147$	−1.43679e10	+	5.57778e10i	−0.209318	+	0.812596i
$148$	2.03018e11			2.85907
$149$		−	1.38441e10i		−	0.188509i	−0.995548	−	0.0942546i	$-0.969953\pi$
$149$		−	1.38441e10i		−	0.188509i	0.995548	−	0.0942546i	$-0.0300468\pi$
$150$	−2.65519e10	−	6.83953e9i	−0.349654	−	0.0900679i
$151$	−1.20208e11			−1.53125			−0.765627	−	0.643285i	$-0.777571\pi$
$151$	−1.20208e11			−1.53125			−0.765627	+	0.643285i	$0.777571\pi$
$152$			8.95877e10i			1.10416i
$153$	4.08904e10	−	7.41041e10i	0.487712	−	0.883863i
$154$	2.15362e11			2.48637
$155$			5.00632e10i			0.559578i
$156$	5.27919e10	−	2.04944e11i	0.571405	−	2.21826i
$157$	−1.29245e11			−1.35493			−0.677465	−	0.735555i	$-0.736922\pi$
$157$	−1.29245e11			−1.35493			−0.677465	+	0.735555i	$0.736922\pi$
$158$		−	6.46671e10i		−	0.656747i
$159$	−2.06483e9	−	5.31882e8i	−0.0203188	−	0.00523395i
$160$	4.95879e10			0.472907
$161$			1.06712e11i			0.986471i
$162$	1.70414e11	−	1.07401e11i	1.52732	−	0.962571i
$163$	−1.59289e10			−0.138435			−0.0692177	−	0.997602i	$-0.522050\pi$
$163$	−1.59289e10			−0.138435			−0.0692177	+	0.997602i	$0.522050\pi$
$164$			1.47011e11i			1.23917i
$165$	1.38553e10	−	5.37879e10i	0.113291	−	0.439810i
$166$	2.10946e11			1.67352
$167$			1.79802e10i			0.138424i	0.997602	+	0.0692120i	$0.0220485\pi$
$167$			1.79802e10i			0.138424i	−0.997602	+	0.0692120i	$0.977952\pi$
$168$	−3.99554e11	−	1.02922e11i	−2.98559	−	0.769061i
$169$	3.86059e9			0.0280040
$170$			1.15724e11i			0.815039i
$171$	−6.21753e10	−	3.43081e10i	−0.425243	−	0.234647i
$172$	2.98308e11			1.98163
$173$			2.30223e10i			0.148566i	0.997237	+	0.0742828i	$0.0236667\pi$
$173$			2.30223e10i			0.148566i	−0.997237	+	0.0742828i	$0.976333\pi$
$174$	−1.08242e11	+	4.20207e11i	−0.678654	+	2.63462i
$175$	−4.45170e10			−0.271228
$176$			3.16416e11i			1.87368i
$177$	−7.54162e10	−	1.94265e10i	−0.434108	−	0.111823i
$178$	−3.19058e11			−1.78554
$179$		−	3.11169e11i		−	1.69329i	−0.532158	−	0.846645i	$-0.678619\pi$
$179$		−	3.11169e11i		−	1.69329i	0.532158	−	0.846645i	$-0.321381\pi$
$180$	−9.22367e10	+	1.67157e11i	−0.488136	+	0.884632i
$181$	1.40782e11			0.724692			0.362346	−	0.932044i	$-0.381976\pi$
$181$	1.40782e11			0.724692			0.362346	+	0.932044i	$0.381976\pi$
$182$		−	4.95700e11i		−	2.48234i
$183$	2.17599e10	−	8.44746e10i	0.106023	−	0.411596i
$184$	−3.48773e11			−1.65369
$185$		−	1.22640e11i		−	0.565945i
$186$	4.86989e11	+	1.25444e11i	2.18753	+	0.563489i
$187$	−2.34429e11			−1.02519
$188$			5.16369e11i			2.19872i
$189$	2.24441e11	−	2.37883e11i	0.930663	−	0.986401i
$190$	9.70953e10			0.392130
$191$		−	1.25467e10i		−	0.0493585i	−0.999695	−	0.0246793i	$-0.992144\pi$
$191$		−	1.25467e10i		−	0.0493585i	0.999695	−	0.0246793i	$-0.00785645\pi$
$192$	4.16988e9	−	1.61880e10i	0.0159815	−	0.0620421i
$193$	2.42774e11			0.906600			0.453300	−	0.891358i	$-0.350247\pi$
$193$	2.42774e11			0.906600			0.453300	+	0.891358i	$0.350247\pi$
$194$		−	6.90884e11i		−	2.51418i
$195$	−1.23804e11	−	3.18908e10i	−0.439098	−	0.113108i
$196$	−5.48367e11			−1.89579
$197$			2.02762e11i			0.683371i	0.939814	+	0.341685i	$0.110998\pi$
$197$			2.02762e11i			0.683371i	−0.939814	+	0.341685i	$0.889002\pi$
$198$	−4.88503e11	−	2.69554e11i	−1.60524	−	0.885768i
$199$	−4.80280e11			−1.53897			−0.769483	−	0.638667i	$-0.779486\pi$
$199$	−4.80280e11			−1.53897			−0.769483	+	0.638667i	$0.779486\pi$
$200$		−	1.45497e11i		−	0.454679i
$201$	1.49540e10	−	5.80533e10i	0.0455804	−	0.176949i
$202$	9.85012e10			0.292877
$203$			7.04521e11i			2.04368i
$204$	7.80315e11	+	2.01002e11i	2.20861	+	0.568919i
$205$	8.88075e10			0.245290
$206$			2.20073e11i			0.593241i
$207$	1.33564e11	−	2.42054e11i	0.351430	−	0.636885i
$208$	7.28298e11			1.87065
$209$			1.96692e11i			0.493238i
$210$	−1.11547e11	+	4.33038e11i	−0.273124	+	1.06030i
$211$	8.57949e10			0.205139			0.102570	−	0.994726i	$-0.467294\pi$
$211$	8.57949e10			0.205139			0.102570	+	0.994726i	$0.467294\pi$
$212$		−	2.02999e10i		−	0.0474040i
$213$	4.00588e11	+	1.03188e11i	0.913692	+	0.235359i
$214$	−3.29193e11			−0.733470
$215$		−	1.80204e11i		−	0.392258i
$216$	7.77485e11	+	7.33552e11i	1.65357	+	1.56013i
$217$	8.16487e11			1.69688
$218$		−	1.45476e12i		−	2.95466i
$219$	−1.21200e11	+	4.70512e11i	−0.240592	+	0.934007i
$220$	5.28804e11			1.02608
$221$			5.39588e11i			1.02353i
$222$	−1.19298e12	−	3.07301e11i	−2.21242	−	0.569901i
$223$	1.42066e10			0.0257611			0.0128806	−	0.999917i	$-0.495900\pi$
$223$	1.42066e10			0.0257611			0.0128806	+	0.999917i	$0.495900\pi$
$224$		−	8.08734e11i		−	1.43405i
$225$	1.00977e11	+	5.57189e10i	0.175110	+	0.0966251i
$226$	−1.44881e12			−2.45736
$227$		−	1.06042e11i		−	0.175933i	−0.996123	−	0.0879667i	$-0.971963\pi$
$227$		−	1.06042e11i		−	0.175933i	0.996123	−	0.0879667i	$-0.0280369\pi$
$228$	1.68646e11	−	6.54705e11i	0.273717	−	1.06260i
$229$	9.57619e11			1.52060			0.760301	−	0.649571i	$-0.225052\pi$
$229$	9.57619e11			1.52060			0.760301	+	0.649571i	$0.225052\pi$
$230$			3.78001e11i			0.587292i
$231$	−8.77233e11	−	2.25968e11i	−1.33369	−	0.343547i
$232$	−2.30262e12			−3.42597
$233$		−	7.32591e11i		−	1.06680i	−0.845864	−	0.533398i	$-0.820915\pi$
$233$		−	7.32591e11i		−	1.06680i	0.845864	−	0.533398i	$-0.179085\pi$
$234$	−6.20435e11	+	1.12439e12i	−0.884335	+	1.60265i
$235$	3.11931e11			0.435231
$236$		−	7.41438e11i		−	1.01278i
$237$	−6.78517e10	+	2.63408e11i	−0.0907443	+	0.352280i
$238$	1.88735e12			2.47154
$239$		−	7.60948e11i		−	0.975810i	−0.872897	−	0.487905i	$-0.837761\pi$
$239$		−	7.60948e11i		−	0.975810i	0.872897	−	0.487905i	$-0.162239\pi$
$240$	−6.36232e11	−	1.63888e11i	−0.799023	−	0.205821i
$241$	6.72439e11			0.827119			0.413559	−	0.910477i	$-0.364285\pi$
$241$	6.72439e11			0.827119			0.413559	+	0.910477i	$0.364285\pi$
$242$			4.69566e10i			0.0565744i
$243$	−8.06838e11	+	2.58669e11i	−0.952259	+	0.305291i
$244$	8.30494e11			0.960257
$245$			3.31261e11i			0.375267i
$246$	2.22526e11	−	8.63872e11i	0.247005	−	0.958902i
$247$	4.52729e11			0.492440
$248$			2.66857e12i			2.84459i
$249$	−8.59245e11	−	2.21334e11i	−0.897677	−	0.231234i
$250$	−1.57690e11			−0.161475
$251$			1.02911e12i			1.03298i	0.856294	+	0.516490i	$0.172761\pi$
$251$			1.02911e12i			1.03298i	−0.856294	+	0.516490i	$0.827239\pi$
$252$	2.72619e12	+	1.50430e12i	2.68258	+	1.48024i
$253$	−7.65742e11			−0.738720
$254$			3.33710e12i			3.15646i
$255$	1.21423e11	−	4.71378e11i	0.112616	−	0.437188i
$256$	−1.93989e12			−1.76432
$257$		−	7.10033e11i		−	0.633305i	−0.948542	−	0.316652i	$-0.897441\pi$
$257$		−	7.10033e11i		−	0.633305i	0.948542	−	0.316652i	$-0.102559\pi$
$258$	−1.75293e12	−	4.51539e11i	−1.53344	−	0.395000i
$259$	−2.00015e12			−1.71619
$260$		−	1.21715e12i		−	1.02442i
$261$	8.81802e11	−	1.59806e12i	0.728062	−	1.31944i
$262$	5.54481e11			0.449138
$263$			6.83503e11i			0.543202i	0.962410	+	0.271601i	$0.0875532\pi$
$263$			6.83503e11i			0.543202i	−0.962410	+	0.271601i	$0.912447\pi$
$264$	7.38542e11	−	2.86711e12i	0.575911	−	2.23576i
$265$	−1.22629e10			−0.00938348
$266$		−	1.58354e12i		−	1.18911i
$267$	1.29962e12	+	3.34771e11i	0.957767	+	0.246712i
$268$	5.70739e11			0.412823
$269$		−	2.17686e12i		−	1.54550i	−0.634710	−	0.772750i	$-0.718881\pi$
$269$		−	2.17686e12i		−	1.54550i	0.634710	−	0.772750i	$-0.281119\pi$
$270$	7.95025e11	−	8.42639e11i	0.554066	−	0.587250i
$271$	1.11446e12			0.762461			0.381230	−	0.924480i	$-0.375500\pi$
$271$	1.11446e12			0.762461			0.381230	+	0.924480i	$0.375500\pi$
$272$			2.77296e12i			1.86251i
$273$	−5.20112e11	+	2.01913e12i	−0.342991	+	1.33153i
$274$	2.14843e12			1.39113
$275$		−	3.19443e11i		−	0.203110i
$276$	2.54883e12	+	6.56555e11i	1.59146	+	0.409945i
$277$	5.18557e11			0.317979			0.158989	−	0.987280i	$-0.449176\pi$
$277$	5.18557e11			0.317979			0.158989	+	0.987280i	$0.449176\pi$
$278$		−	3.63452e12i		−	2.18888i
$279$	−1.85203e12	−	1.02194e12i	−1.09554	−	0.604513i
$280$	−2.37293e12			−1.37878
$281$		−	5.72439e11i		−	0.326736i	−0.986565	−	0.163368i	$-0.947764\pi$
$281$		−	5.72439e11i		−	0.326736i	0.986565	−	0.163368i	$-0.0522359\pi$
$282$	7.81610e11	−	3.03430e12i	0.438273	−	1.70143i
$283$	−1.55478e12			−0.856519			−0.428259	−	0.903656i	$-0.640873\pi$
$283$	−1.55478e12			−0.856519			−0.428259	+	0.903656i	$0.640873\pi$
$284$			3.93830e12i			2.13165i
$285$	−3.95498e11	−	1.01877e11i	−0.210339	−	0.0541815i
$286$	3.55703e12			1.85891
$287$		−	1.44837e12i		−	0.743824i
$288$	−1.01224e12	+	1.83444e12i	−0.510882	+	0.925853i
$289$	−3.84612e10			−0.0190780
$290$			2.49559e12i			1.21670i
$291$	−7.24907e11	+	2.81418e12i	−0.347390	+	1.34861i
$292$	−4.62574e12			−2.17905
$293$			2.78877e12i			1.29144i	0.763574	+	0.645721i	$0.223443\pi$
$293$			2.78877e12i			1.29144i	−0.763574	+	0.645721i	$0.776557\pi$
$294$	3.22233e12	+	8.30045e11i	1.46701	+	0.377890i
$295$	−4.47892e11			−0.200477
$296$		−	6.53721e12i		−	2.87696i
$297$	1.70699e12	+	1.61053e12i	0.738667	+	0.696928i
$298$	−7.99785e11			−0.340324
$299$			1.76251e12i			0.737525i
$300$	−2.73894e11	+	1.06329e12i	−0.112714	+	0.437568i
$301$	−2.93896e12			−1.18949
$302$			6.94451e12i			2.76444i
$303$	−4.01225e11	−	1.03352e11i	−0.157100	−	0.0404675i
$304$	2.32658e12			0.896088
$305$		−	5.01690e11i		−	0.190080i
$306$	−4.28106e12	−	2.36227e12i	−1.59568	−	0.880488i
$307$	1.83275e12			0.672065			0.336033	−	0.941850i	$-0.390915\pi$
$307$	1.83275e12			0.672065			0.336033	+	0.941850i	$0.390915\pi$
$308$		−	8.62433e12i		−	3.11151i
$309$	2.30911e11	−	8.96424e11i	0.0819695	−	0.318215i
$310$	2.89220e12			1.01023
$311$			7.46300e11i			0.256514i	0.991741	+	0.128257i	$0.0409383\pi$
$311$			7.46300e11i			0.256514i	−0.991741	+	0.128257i	$0.959062\pi$
$312$	−6.59925e12	−	1.69991e12i	−2.23214	−	0.574980i
$313$	2.49278e12			0.829780			0.414890	−	0.909872i	$-0.363820\pi$
$313$	2.49278e12			0.829780			0.414890	+	0.909872i	$0.363820\pi$
$314$			7.46663e12i			2.44611i
$315$	9.08726e11	−	1.64685e12i	0.293009	−	0.531009i
$316$	−2.58964e12			−0.821873
$317$		−	3.19392e12i		−	0.997765i	−0.866670	−	0.498883i	$-0.833744\pi$
$317$		−	3.19392e12i		−	0.997765i	0.866670	−	0.498883i	$-0.166256\pi$
$318$	−3.07273e10	+	1.19287e11i	−0.00944906	+	0.0366824i
$319$	−5.05548e12			−1.53041
$320$		−	9.61395e10i		−	0.0286518i
$321$	1.34090e12	+	3.45405e11i	0.393434	+	0.101345i
$322$	6.16486e12			1.78092
$323$			1.72374e12i			0.490297i
$324$	−4.30095e12	−	6.82437e12i	−1.20459	−	1.91134i
$325$	−7.35266e11			−0.202781
$326$			9.20226e11i			0.249923i
$327$	−1.52640e12	+	5.92566e12i	−0.408253	+	1.58489i
$328$	4.73379e12			1.24692
$329$		−	5.08732e12i		−	1.31981i
$330$	−3.10738e12	−	8.00433e11i	−0.794007	−	0.204529i
$331$	9.29417e11			0.233922			0.116961	−	0.993137i	$-0.462685\pi$
$331$	9.29417e11			0.233922			0.116961	+	0.993137i	$0.462685\pi$
$332$		−	8.44748e12i		−	2.09429i
$333$	4.53693e12	+	2.50346e12i	1.10800	+	0.611391i
$334$	1.03873e12			0.249903
$335$		−	3.44776e11i		−	0.0817170i
$336$	−2.67287e12	+	1.03764e13i	−0.624138	+	2.42298i
$337$	−4.16411e12			−0.958017			−0.479008	−	0.877810i	$-0.659004\pi$
$337$	−4.16411e12			−0.958017			−0.479008	+	0.877810i	$0.659004\pi$
$338$		−	2.23030e11i		−	0.0505568i
$339$	5.90143e12	+	1.52016e12i	1.31813	+	0.339539i
$340$	4.63425e12			1.01996
$341$			5.85892e12i			1.27071i
$342$	−1.98201e12	+	3.59193e12i	−0.423619	+	0.767709i
$343$	−1.03579e12			−0.218174
$344$		−	9.60558e12i		−	1.99403i
$345$	3.96616e11	−	1.53971e12i	0.0811474	−	0.315024i
$346$	1.33002e12			0.268212
$347$		−	4.93791e12i		−	0.981513i	−0.871297	−	0.490756i	$-0.836721\pi$
$347$		−	4.93791e12i		−	0.981513i	0.871297	−	0.490756i	$-0.163279\pi$
$348$	1.68275e13	+	4.33462e12i	3.29704	+	0.849288i
$349$	2.92683e12			0.565289			0.282644	−	0.959225i	$-0.408788\pi$
$349$	2.92683e12			0.565289			0.282644	+	0.959225i	$0.408788\pi$
$350$			2.57179e12i			0.489660i
$351$	3.70698e12	−	3.92899e12i	0.695800	−	0.737472i
$352$	5.80329e12			1.07389
$353$		−	2.88243e12i		−	0.525879i	−0.964812	−	0.262939i	$-0.915308\pi$
$353$		−	2.88243e12i		−	0.525879i	0.964812	−	0.262939i	$-0.0846919\pi$
$354$	−1.12229e12	+	4.35686e12i	−0.201878	+	0.783714i
$355$	2.37907e12			0.421954
$356$			1.27769e13i			2.23448i
$357$	−7.68775e12	−	1.98030e12i	−1.32574	−	0.341499i
$358$	−1.79765e13			−3.05697
$359$		−	6.03965e12i		−	1.01284i	−0.862288	−	0.506419i	$-0.830969\pi$
$359$		−	6.03965e12i		−	1.01284i	0.862288	−	0.506419i	$-0.169031\pi$
$360$	5.38250e12	+	2.97004e12i	0.890166	+	0.491190i
$361$	−4.68480e12			−0.764109
$362$		−	8.13310e12i		−	1.30832i
$363$	4.92690e10	−	1.91268e11i	0.00781701	−	0.0303466i
$364$	−1.98507e13			−3.10648
$365$			2.79434e12i			0.431336i
$366$	−4.88018e12	−	1.25709e12i	−0.743071	−	0.191409i
$367$	6.07725e12			0.912803			0.456401	−	0.889774i	$-0.349138\pi$
$367$	6.07725e12			0.912803			0.456401	+	0.889774i	$0.349138\pi$
$368$			9.05761e12i			1.34207i
$369$	−1.81283e12	+	3.28533e12i	−0.264987	+	0.480227i
$370$	−7.08504e12			−1.02172
$371$			1.99997e11i			0.0284547i
$372$	5.02351e12	−	1.95018e13i	0.705167	−	2.73754i
$373$	6.69297e12			0.926989			0.463494	−	0.886100i	$-0.346595\pi$
$373$	6.69297e12			0.926989			0.463494	+	0.886100i	$0.346595\pi$
$374$			1.35432e13i			1.85082i
$375$	6.42319e11	+	1.65456e11i	0.0866153	+	0.0223113i
$376$	1.66272e13			2.21248
$377$			1.16362e13i			1.52794i
$378$	−1.37427e13	−	1.29662e13i	−1.78079	−	1.68017i
$379$	6.64278e12			0.849481			0.424740	−	0.905315i	$-0.360365\pi$
$379$	6.64278e12			0.849481			0.424740	+	0.905315i	$0.360365\pi$
$380$		−	3.88826e12i		−	0.490724i
$381$	3.50144e12	−	1.35930e13i	0.436135	−	1.69313i
$382$	−7.24834e11			−0.0891090
$383$		−	1.54067e13i		−	1.86946i	−0.355357	−	0.934731i	$-0.615641\pi$
$383$		−	1.54067e13i		−	1.86946i	0.355357	−	0.934731i	$-0.384359\pi$
$384$	7.61480e12	+	1.96151e12i	0.912016	+	0.234927i
$385$	−5.20984e12			−0.615915
$386$		−	1.40253e13i		−	1.63672i
$387$	6.66642e12	+	3.67851e12i	0.767959	+	0.423757i
$388$	−2.76670e13			−3.14632
$389$		−	4.59169e12i		−	0.515495i	−0.966212	−	0.257748i	$-0.917020\pi$
$389$		−	4.59169e12i		−	0.515495i	0.966212	−	0.257748i	$-0.0829803\pi$
$390$	−1.84236e12	+	7.15228e12i	−0.204198	+	0.792723i
$391$	−6.71068e12			−0.734316
$392$			1.76575e13i			1.90765i
$393$	−2.25857e12	−	5.81787e11i	−0.240918	−	0.0620585i
$394$	1.17138e13			1.23372
$395$			1.56437e12i			0.162687i
$396$	−1.07945e13	+	1.95625e13i	−1.10848	+	2.00885i
$397$	−1.82048e13			−1.84600			−0.923002	−	0.384795i	$-0.874272\pi$
$397$	−1.82048e13			−1.84600			−0.923002	+	0.384795i	$0.874272\pi$
$398$			2.77462e13i			2.77836i
$399$	−1.66152e12	+	6.45023e12i	−0.164302	+	0.637838i
$400$	−3.77855e12			−0.368999
$401$			1.48693e13i			1.43406i	0.697040	+	0.717032i	$0.254500\pi$
$401$			1.48693e13i			1.43406i	−0.697040	+	0.717032i	$0.745500\pi$
$402$	−3.35380e12	−	8.63909e11i	−0.319453	−	0.0822882i
$403$	1.34855e13			1.26865
$404$		−	3.94456e12i		−	0.366515i
$405$	−4.12251e12	+	2.59814e12i	−0.378344	+	0.238445i
$406$	4.07008e13			3.68955
$407$		−	1.43526e13i		−	1.28517i
$408$	6.47232e12	−	2.51263e13i	0.572478	−	2.22243i
$409$	2.27420e13			1.98706			0.993531	−	0.113557i	$-0.0362244\pi$
$409$	2.27420e13			1.98706			0.993531	+	0.113557i	$0.0362244\pi$
$410$		−	5.13049e12i		−	0.442833i
$411$	−8.75120e12	−	2.25423e12i	−0.746206	−	0.192216i
$412$	8.81300e12			0.742400
$413$			7.30473e12i			0.607930i
$414$	−1.39837e13	−	7.71615e12i	−1.14979	−	0.634452i
$415$	−5.10301e12			−0.414558
$416$		−	1.33575e13i		−	1.07216i
$417$	−3.81350e12	+	1.48045e13i	−0.302443	+	1.17412i
$418$	1.13631e13			0.890462
$419$		−	5.10264e12i		−	0.395116i	−0.980291	−	0.197558i	$-0.936699\pi$
$419$		−	5.10264e12i		−	0.395116i	0.980291	−	0.197558i	$-0.0633011\pi$
$420$	1.73413e13	+	4.46697e12i	1.32689	+	0.341796i
$421$	2.18158e13			1.64953			0.824765	−	0.565475i	$-0.191307\pi$
$421$	2.18158e13			1.64953			0.824765	+	0.565475i	$0.191307\pi$
$422$		−	4.95645e12i		−	0.370347i
$423$	−6.36746e12	+	1.15395e13i	−0.470181	+	0.852091i
$424$	−6.53661e11			−0.0477006
$425$		−	2.79949e12i		−	0.201899i
$426$	5.96127e12	−	2.31424e13i	0.424904	−	1.64953i
$427$	−8.18212e12			−0.576403
$428$			1.31828e13i			0.917887i
$429$	−1.44888e13	−	3.73220e12i	−0.997119	−	0.256849i
$430$	−1.04105e13			−0.708159
$431$			7.51221e12i			0.505105i	0.967583	+	0.252552i	$0.0812700\pi$
$431$			7.51221e12i			0.505105i	−0.967583	+	0.252552i	$0.918730\pi$
$432$	1.90503e13	−	2.01912e13i	1.26614	−	1.34197i
$433$	−2.24414e13			−1.47438			−0.737192	−	0.675684i	$-0.763849\pi$
$433$	−2.24414e13			−1.47438			−0.737192	+	0.675684i	$0.763849\pi$
$434$		−	4.71692e13i		−	3.06345i
$435$	2.61849e12	−	1.01653e13i	0.168114	−	0.652639i
$436$	−5.82569e13			−3.69755
$437$			5.63044e12i			0.353293i
$438$	2.71819e13	+	7.00182e12i	1.68620	+	0.434351i
$439$	−5.77280e12			−0.354049			−0.177025	−	0.984206i	$-0.556647\pi$
$439$	−5.77280e12			−0.354049			−0.177025	+	0.984206i	$0.556647\pi$
$440$		−	1.70276e13i		−	1.03250i
$441$	−1.22546e13	−	6.76204e12i	−0.734694	−	0.405401i
$442$	3.11725e13			1.84782
$443$			3.21997e13i			1.88727i	0.330991	+	0.943634i	$0.392617\pi$
$443$			3.21997e13i			1.88727i	−0.330991	+	0.943634i	$0.607383\pi$
$444$	−1.23061e13	+	4.77738e13i	−0.713191	+	2.76869i
$445$	7.71837e12			0.442309
$446$		−	8.20727e11i		−	0.0465077i
$447$	3.25776e12	+	8.39172e11i	0.182550	+	0.0470233i
$448$	−1.56795e12			−0.0868845
$449$			8.59517e11i			0.0471002i	0.999723	+	0.0235501i	$0.00749693\pi$
$449$			8.59517e11i			0.0471002i	−0.999723	+	0.0235501i	$0.992503\pi$
$450$	3.21893e12	−	5.83356e12i	0.174441	−	0.316134i
$451$	1.03932e13			0.557013
$452$			5.80187e13i			3.07522i
$453$	7.28650e12	−	2.82870e13i	0.381969	−	1.48285i
$454$	−6.12614e12			−0.317620
$455$			1.19915e13i			0.614919i
$456$	−2.10816e13	−	5.43044e12i	−1.06925	−	0.275430i
$457$	−3.09485e13			−1.55260			−0.776298	−	0.630366i	$-0.782905\pi$
$457$	−3.09485e13			−1.55260			−0.776298	+	0.630366i	$0.782905\pi$
$458$		−	5.53225e13i		−	2.74521i
$459$	1.49594e13	+	1.41141e13i	0.734264	+	0.692773i
$460$	1.51373e13			0.734954
$461$			2.65915e13i			1.27714i	0.769563	+	0.638571i	$0.220474\pi$
$461$			2.65915e13i			1.27714i	−0.769563	+	0.638571i	$0.779526\pi$
$462$	−1.30544e13	+	5.06786e13i	−0.620220	+	2.40777i
$463$	3.80490e13			1.78829			0.894146	−	0.447776i	$-0.147784\pi$
$463$	3.80490e13			1.78829			0.894146	+	0.447776i	$0.147784\pi$
$464$			5.97989e13i			2.78038i
$465$	−1.17808e13	−	3.03463e12i	−0.541888	−	0.139586i
$466$	−4.23225e13			−1.92593
$467$		−	2.57553e13i		−	1.15953i	−0.814783	−	0.579766i	$-0.803144\pi$
$467$		−	2.57553e13i		−	1.15953i	0.814783	−	0.579766i	$-0.196856\pi$
$468$	4.50271e13	+	2.48458e13i	2.00560	+	1.10668i
$469$	−5.62299e12			−0.247801
$470$		−	1.80206e13i		−	0.785740i
$471$	7.83434e12	−	3.04138e13i	0.337985	−	1.31210i
$472$	−2.38744e13			−1.01912
$473$		−	2.10893e13i		−	0.890752i
$474$	1.52174e13	+	3.91986e12i	0.635986	+	0.163824i
$475$	−2.34884e12			−0.0971372
$476$		−	7.55805e13i		−	3.09297i
$477$	2.50323e11	−	4.53651e11i	0.0101370	−	0.0183709i
$478$	−4.39607e13			−1.76167
$479$			1.01416e13i			0.402188i	0.979572	+	0.201094i	$0.0644497\pi$
$479$			1.01416e13i			0.402188i	−0.979572	+	0.201094i	$0.935550\pi$
$480$	−3.00582e12	+	1.16689e13i	−0.117966	+	0.457957i
$481$	−3.30356e13			−1.28309
$482$		−	3.88475e13i		−	1.49323i
$483$	−2.51113e13	−	6.46846e12i	−0.955287	−	0.246074i
$484$	1.88041e12			0.0707989
$485$			1.67132e13i			0.622805i
$486$	1.49436e13	+	4.66118e13i	0.551154	+	1.71915i
$487$	4.13730e13			1.51033			0.755165	−	0.655534i	$-0.227557\pi$
$487$	4.13730e13			1.51033			0.755165	+	0.655534i	$0.227557\pi$
$488$		−	2.67421e13i		−	0.966264i
$489$	9.65544e11	−	3.74836e12i	0.0345325	−	0.134059i
$490$	1.91373e13			0.677485
$491$		−	1.99323e13i		−	0.698474i	−0.937034	−	0.349237i	$-0.886441\pi$
$491$		−	1.99323e13i		−	0.698474i	0.937034	−	0.349237i	$-0.113559\pi$
$492$	−3.45944e13	−	8.91123e12i	−1.20000	−	0.309109i
$493$	−4.43044e13			−1.52129
$494$		−	2.61546e13i		−	0.889022i
$495$	1.18174e13	+	6.52081e12i	0.397646	+	0.219420i
$496$	6.93025e13			2.30856
$497$		−	3.88005e13i		−	1.27955i
$498$	−1.27867e13	+	4.96394e13i	−0.417456	+	1.62061i
$499$	−1.69667e13			−0.548397			−0.274199	−	0.961673i	$-0.588413\pi$
$499$	−1.69667e13			−0.548397			−0.274199	+	0.961673i	$0.588413\pi$
$500$			6.31482e12i			0.202074i
$501$	−4.23106e12	−	1.08988e12i	−0.134048	−	0.0345296i
$502$	5.94524e13			1.86488
$503$		−	9.99088e12i		−	0.310287i	−0.987892	−	0.155144i	$-0.950416\pi$
$503$		−	9.99088e12i		−	0.310287i	0.987892	−	0.155144i	$-0.0495840\pi$
$504$	4.84387e13	−	8.77838e13i	1.48950	−	2.69936i
$505$	−2.38285e12			−0.0725505
$506$			4.42376e13i			1.33364i
$507$	−2.34013e11	+	9.08467e11i	−0.00698555	+	0.0271187i
$508$	1.33637e14			3.95009
$509$			3.35082e13i			0.980758i	0.871509	+	0.490379i	$0.163142\pi$
$509$			3.35082e13i			0.980758i	−0.871509	+	0.490379i	$0.836858\pi$
$510$	−2.72319e13	−	7.01471e12i	−0.789274	−	0.203310i
$511$	4.55733e13			1.30799
$512$			7.89329e13i			2.24341i
$513$	1.18421e13	−	1.25514e13i	0.333306	−	0.353268i
$514$	−4.10193e13			−1.14333
$515$		−	5.32381e12i		−	0.146956i
$516$	−1.80822e13	+	7.01973e13i	−0.494314	+	1.91899i
$517$	3.65054e13			0.988337
$518$			1.15551e14i			3.09830i
$519$	−5.41757e12	−	1.39552e12i	−0.143869	−	0.0370594i
$520$	−3.91926e13			−1.03083
$521$		−	2.36567e13i		−	0.616263i	−0.951344	−	0.308131i	$-0.900296\pi$
$521$		−	2.36567e13i		−	0.616263i	0.951344	−	0.308131i	$-0.0997036\pi$
$522$	−9.23213e13	−	5.09425e13i	−2.38204	−	1.31440i
$523$	−4.80871e13			−1.22891			−0.614455	−	0.788952i	$-0.710624\pi$
$523$	−4.80871e13			−1.22891			−0.614455	+	0.788952i	$0.710624\pi$
$524$		−	2.22046e13i		−	0.562065i
$525$	2.69844e12	−	1.04757e13i	0.0676575	−	0.262654i
$526$	3.94866e13			0.980666
$527$			5.13455e13i			1.26313i
$528$	−7.44585e13	−	1.91799e13i	−1.81445	−	0.467386i
$529$	1.95067e13			0.470875
$530$			7.08439e11i			0.0169404i
$531$	9.14284e12	−	1.65692e13i	0.216575	−	0.392491i
$532$	−6.34140e13			−1.48808
$533$		−	2.39221e13i		−	0.556112i
$534$	1.93400e13	−	7.50802e13i	0.445400	−	1.72910i
$535$	7.96355e12			0.181693
$536$		−	1.83779e13i		−	0.415405i
$537$	7.32238e13	+	1.88618e13i	1.63976	+	0.422388i
$538$	−1.25759e14			−2.79016
$539$			3.87676e13i			0.852168i
$540$	−3.37441e13	−	3.18374e13i	−0.734902	−	0.693375i
$541$	5.88648e12			0.127019			0.0635096	−	0.997981i	$-0.479771\pi$
$541$	5.88648e12			0.127019			0.0635096	+	0.997981i	$0.479771\pi$
$542$		−	6.43833e13i		−	1.37650i
$543$	−8.53362e12	+	3.31285e13i	−0.180773	+	0.701783i
$544$	5.08579e13			1.06749
$545$			3.51922e13i			0.731920i
$546$	1.16647e14	+	3.00473e13i	2.40387	+	0.619217i
$547$	3.71451e12			0.0758516			0.0379258	−	0.999281i	$-0.487925\pi$
$547$	3.71451e12			0.0758516			0.0379258	+	0.999281i	$0.487925\pi$
$548$		−	8.60356e13i		−	1.74091i
$549$	1.85594e13	+	1.02410e13i	0.372137	+	0.205344i
$550$	−1.84545e13			−0.366682
$551$			3.71725e13i			0.731921i
$552$	2.11412e13	−	8.20727e13i	0.412510	−	1.60141i
$553$	2.55135e13			0.493337
$554$		−	2.99576e13i		−	0.574060i
$555$	2.88595e13	+	7.43395e12i	0.548054	+	0.141174i
$556$	−1.45547e14			−2.73924
$557$		−	2.27483e13i		−	0.424301i	−0.977237	−	0.212150i	$-0.931953\pi$
$557$		−	2.27483e13i		−	0.424301i	0.977237	−	0.212150i	$-0.0680467\pi$
$558$	−5.90386e13	+	1.06993e14i	−1.09135	+	1.97782i
$559$	−4.85415e13			−0.889312
$560$			6.16248e13i			1.11896i
$561$	1.42102e13	−	5.51655e13i	0.255732	−	0.992781i
$562$	−3.30703e13			−0.589871
$563$		−	9.93082e13i		−	1.75567i	−0.478962	−	0.877836i	$-0.658987\pi$
$563$		−	9.93082e13i		−	1.75567i	0.478962	−	0.877836i	$-0.341013\pi$
$564$	−1.21511e14	−	3.13002e13i	−2.12922	−	0.548468i
$565$	3.50483e13			0.608730
$566$			8.98211e13i			1.54631i
$567$	4.23734e13	+	6.72345e13i	0.723067	+	1.14730i
$568$	1.26814e14			2.14499
$569$			1.10963e14i			1.86044i	0.367000	+	0.930221i	$0.380385\pi$
$569$			1.10963e14i			1.86044i	−0.367000	+	0.930221i	$0.619615\pi$
$570$	−5.88552e12	+	2.28483e13i	−0.0978162	+	0.379734i
$571$	−7.79615e13			−1.28440			−0.642199	−	0.766538i	$-0.721978\pi$
$571$	−7.79615e13			−1.28440			−0.642199	+	0.766538i	$0.721978\pi$
$572$		−	1.42444e14i		−	2.32629i
$573$	2.95246e12	+	7.60529e11i	0.0477982	+	0.0123124i
$574$	−8.36738e13			−1.34286
$575$		−	9.14426e12i		−	0.145482i
$576$	3.55657e12	+	1.96250e12i	0.0560943	+	0.0309526i
$577$	−3.64321e13			−0.569646			−0.284823	−	0.958580i	$-0.591935\pi$
$577$	−3.64321e13			−0.569646			−0.284823	+	0.958580i	$0.591935\pi$
$578$			2.22194e12i			0.0344424i
$579$	−1.47160e13	+	5.71292e13i	−0.226150	+	0.877941i
$580$	9.99377e13			1.52261
$581$			8.32255e13i			1.25712i
$582$	1.62578e14	+	4.18786e13i	2.43470	+	0.627158i
$583$	−1.43513e12			−0.0213083
$584$			1.48950e14i			2.19268i
$585$	1.50090e13	−	2.72003e13i	0.219065	−	0.397003i
$586$	1.61110e14			2.33149
$587$		−	1.21698e14i		−	1.74620i	−0.487541	−	0.873100i	$-0.662106\pi$
$587$		−	1.21698e14i		−	1.74620i	0.487541	−	0.873100i	$-0.337894\pi$
$588$	3.32398e13	−	1.29041e14i	0.472903	−	1.83586i
$589$	4.30802e13			0.607717
$590$			2.58752e13i			0.361929i
$591$	−4.77137e13	−	1.22906e13i	−0.661768	−	0.170466i
$592$	−1.69771e14			−2.33483
$593$			7.44533e13i			1.01534i	0.861552	+	0.507669i	$0.169493\pi$
$593$			7.44533e13i			1.01534i	−0.861552	+	0.507669i	$0.830507\pi$
$594$	9.30421e13	−	9.86144e13i	1.25819	−	1.33355i
$595$	−4.56571e13			−0.612243
$596$			3.20280e13i			0.425891i
$597$	2.91126e13	−	1.13019e14i	0.383893	−	1.49032i
$598$	1.01822e14			1.33148
$599$		−	1.04530e14i		−	1.35552i	−0.735284	−	0.677759i	$-0.762951\pi$
$599$		−	1.04530e14i		−	1.35552i	0.735284	−	0.677759i	$-0.237049\pi$
$600$	3.42382e13	+	8.81945e12i	0.440306	+	0.113419i
$601$	−2.22177e13			−0.283352			−0.141676	−	0.989913i	$-0.545249\pi$
$601$	−2.22177e13			−0.283352			−0.141676	+	0.989913i	$0.545249\pi$
$602$			1.69787e14i			2.14744i
$603$	1.27546e13	+	7.03792e12i	0.159985	+	0.0882790i
$604$	2.78098e14			3.45950
$605$		−	1.13593e12i		−	0.0140144i
$606$	−5.97075e12	+	2.31791e13i	−0.0730576	+	0.283618i
$607$	−7.54396e13			−0.915495			−0.457748	−	0.889082i	$-0.651344\pi$
$607$	−7.54396e13			−0.915495			−0.457748	+	0.889082i	$0.651344\pi$
$608$		−	4.26711e13i		−	0.513590i
$609$	−1.65787e14	−	4.27052e13i	−1.97908	−	0.509793i
$610$	−2.89831e13			−0.343159
$611$		−	8.40249e13i		−	0.986738i
$612$	−9.45991e13	+	1.71439e14i	−1.10187	+	1.99688i
$613$	5.56443e13			0.642863			0.321432	−	0.946933i	$-0.395836\pi$
$613$	5.56443e13			0.642863			0.321432	+	0.946933i	$0.395836\pi$
$614$		−	1.05880e14i		−	1.21331i
$615$	−5.38315e12	+	2.08980e13i	−0.0611872	+	0.237536i
$616$	−2.77705e14			−3.13098
$617$			5.63180e13i			0.629828i	0.949120	+	0.314914i	$0.101976\pi$
$617$			5.63180e13i			0.629828i	−0.949120	+	0.314914i	$0.898024\pi$
$618$	−5.17873e13	−	1.33399e13i	−0.574487	−	0.147983i
$619$	3.81737e13			0.420059			0.210030	−	0.977695i	$-0.432644\pi$
$619$	3.81737e13			0.420059			0.210030	+	0.977695i	$0.432644\pi$
$620$		−	1.15820e14i		−	1.26423i
$621$	4.88636e13	+	4.61025e13i	0.529088	+	0.499191i
$622$	4.31145e13			0.463096
$623$		−	1.25880e14i		−	1.34127i
$624$	−4.41465e13	+	1.71382e14i	−0.466630	+	1.81151i
$625$	3.81470e12			0.0400000
$626$		−	1.44010e14i		−	1.49804i
$627$	−4.62853e13	−	1.19227e13i	−0.477645	−	0.123037i
$628$	2.99007e14			3.06114
$629$		−	1.25781e14i		−	1.27751i
$630$	−9.51402e13	−	5.24980e13i	−0.958652	−	0.528981i
$631$	−9.94107e13			−0.993771			−0.496885	−	0.867816i	$-0.665523\pi$
$631$	−9.94107e13			−0.993771			−0.496885	+	0.867816i	$0.665523\pi$
$632$			8.33871e13i			0.827015i
$633$	−5.20054e12	+	2.01891e13i	−0.0511717	+	0.198655i
$634$	−1.84516e14			−1.80131
$635$		−	8.07280e13i		−	0.781908i
$636$	4.77694e12	+	1.23050e12i	0.0459055	+	0.0118248i
$637$	8.92318e13			0.850790
$638$			2.92060e14i			2.76292i
$639$	−4.85640e13	+	8.80109e13i	−0.455838	+	0.826099i
$640$	4.52239e13			0.421180
$641$		−	3.43268e13i		−	0.317207i	−0.987342	−	0.158603i	$-0.949301\pi$
$641$		−	3.43268e13i		−	0.317207i	0.987342	−	0.158603i	$-0.0506991\pi$
$642$	1.99544e13	−	7.74653e13i	0.182963	−	0.710284i
$643$	5.99929e13			0.545814			0.272907	−	0.962040i	$-0.412015\pi$
$643$	5.99929e13			0.545814			0.272907	+	0.962040i	$0.412015\pi$
$644$		−	2.46877e14i		−	2.22869i
$645$	4.24052e13	+	1.09232e13i	0.379858	+	0.0978480i
$646$	9.95822e13			0.885154
$647$			1.85855e14i			1.63928i	0.572882	+	0.819638i	$0.305825\pi$
$647$			1.85855e14i			1.63928i	−0.572882	+	0.819638i	$0.694175\pi$
$648$	−2.19746e14	+	1.38491e14i	−1.92330	+	1.21213i
$649$	−5.24170e13			−0.455249
$650$			4.24770e13i			0.366089i
$651$	−4.94921e13	+	1.92134e14i	−0.423283	+	1.64324i
$652$	3.68512e13			0.312761
$653$			9.87637e13i			0.831824i	0.909405	+	0.415912i	$0.136538\pi$
$653$			9.87637e13i			0.831824i	−0.909405	+	0.415912i	$0.863462\pi$
$654$	3.42331e14	+	8.81815e13i	2.86126	+	0.737036i
$655$	−1.34135e13			−0.111259
$656$		−	1.22936e14i		−	1.01195i
$657$	−1.03373e14	−	5.70410e13i	−0.844466	−	0.465973i
$658$	−2.93899e14			−2.38270
$659$			1.09217e14i			0.878744i	0.898305	+	0.439372i	$0.144799\pi$
$659$			1.09217e14i			0.878744i	−0.898305	+	0.439372i	$0.855201\pi$
$660$	−3.20540e13	+	1.24437e14i	−0.255954	+	0.993644i
$661$	1.58083e14			1.25279			0.626394	−	0.779507i	$-0.284530\pi$
$661$	1.58083e14			1.25279			0.626394	+	0.779507i	$0.284530\pi$
$662$		−	5.36933e13i		−	0.422309i
$663$	−1.26975e14	−	3.27077e13i	−0.991176	−	0.255318i
$664$	−2.72011e14			−2.10739
$665$			3.83075e13i			0.294562i
$666$	1.44627e14	−	2.62103e14i	1.10377	−	2.00032i
$667$	−1.44716e14			−1.09619
$668$		−	4.15968e13i		−	0.312736i
$669$	−8.61145e11	+	3.34307e12i	−0.00642607	+	0.0249468i
$670$	−1.99180e13			−0.147527
$671$		−	5.87130e13i		−	0.431640i
$672$	1.90310e14	+	4.90222e13i	1.38872	+	0.357723i
$673$	−1.74713e13			−0.126546			−0.0632732	−	0.997996i	$-0.520154\pi$
$673$	−1.74713e13			−0.126546			−0.0632732	+	0.997996i	$0.520154\pi$
$674$			2.40565e14i			1.72955i
$675$	−1.92325e13	+	2.03844e13i	−0.137252	+	0.145472i
$676$	−8.93140e12			−0.0632683
$677$		−	1.05352e14i		−	0.740800i	−0.928872	−	0.370400i	$-0.879221\pi$
$677$		−	1.05352e14i		−	0.740800i	0.928872	−	0.370400i	$-0.120779\pi$
$678$	8.78209e13	−	3.40931e14i	0.612984	−	2.37968i
$679$	2.72578e14			1.88861
$680$		−	1.49224e14i		−	1.02635i
$681$	2.49536e13	+	6.42783e12i	0.170372	+	0.0438863i
$682$	3.38475e14			2.29406
$683$			3.94453e13i			0.265394i	0.991157	+	0.132697i	$0.0423637\pi$
$683$			3.94453e13i			0.265394i	−0.991157	+	0.132697i	$0.957636\pi$
$684$	1.43841e14	+	7.93711e13i	0.960735	+	0.530130i
$685$	−5.19729e13			−0.344607
$686$			5.98387e13i			0.393878i
$687$	−5.80470e13	+	2.25345e14i	−0.379311	+	1.47253i
$688$	−2.49456e14			−1.61827
$689$			3.30326e12i			0.0212739i
$690$	−8.89505e13	−	2.29129e13i	−0.568726	−	0.146499i
$691$	1.05489e14			0.669602			0.334801	−	0.942289i	$-0.391331\pi$
$691$	1.05489e14			0.669602			0.334801	+	0.942289i	$0.391331\pi$
$692$		−	5.32617e13i		−	0.335648i
$693$	1.06349e14	−	1.92732e14i	0.665374	−	1.20583i
$694$	−2.85268e14			−1.77197
$695$			8.79230e13i			0.542223i
$696$	1.39576e14	−	5.41850e14i	0.854602	−	3.31767i
$697$	9.10820e13			0.553693
$698$		−	1.69086e14i		−	1.02054i
$699$	1.72392e14	+	4.44067e13i	1.03307	+	0.266111i
$700$	1.02989e14			0.612775
$701$		−	1.43922e14i		−	0.850231i	−0.905139	−	0.425116i	$-0.860233\pi$
$701$		−	1.43922e14i		−	0.850231i	0.905139	−	0.425116i	$-0.139767\pi$
$702$	−2.26982e14	−	2.14156e14i	−1.33139	−	1.25616i
$703$	−1.05534e14			−0.614632
$704$		−	1.12512e13i		−	0.0650635i
$705$	−1.89080e13	+	7.34031e13i	−0.108568	+	0.421472i
$706$	−1.66521e14			−0.949391
$707$			3.88622e13i			0.220004i
$708$	1.74474e14	+	4.49430e13i	0.980763	+	0.252636i
$709$	2.68307e14			1.49762			0.748810	−	0.662785i	$-0.230626\pi$
$709$	2.68307e14			1.49762			0.748810	+	0.662785i	$0.230626\pi$
$710$		−	1.37441e14i		−	0.761772i
$711$	−5.78719e13	−	3.19335e13i	−0.318508	−	0.175751i
$712$	4.11420e14			2.24846
$713$			1.67715e14i			0.910174i
$714$	−1.14404e14	+	4.44129e14i	−0.616523	+	2.39341i
$715$	−8.60484e13			−0.460482
$716$			7.19884e14i			3.82558i
$717$	1.79065e14	+	4.61256e13i	0.944963	+	0.243414i
$718$	−3.48916e14			−1.82852
$719$		−	1.59359e14i		−	0.829339i	−0.909972	−	0.414670i	$-0.863897\pi$
$719$		−	1.59359e14i		−	0.829339i	0.909972	−	0.414670i	$-0.136103\pi$
$720$	7.71316e13	−	1.39783e14i	0.398630	−	0.722423i
$721$	−8.68267e13			−0.445632
$722$			2.70645e14i			1.37948i
$723$	−4.07605e13	+	1.58237e14i	−0.206323	+	0.800972i
$724$	−3.25696e14			−1.63727
$725$		−	6.03710e13i		−	0.301397i
$726$	−1.10497e13	−	2.84632e12i	−0.0547859	−	0.0141124i
$727$	−1.98820e14			−0.979012			−0.489506	−	0.872000i	$-0.662823\pi$
$727$	−1.98820e14			−0.979012			−0.489506	+	0.872000i	$0.662823\pi$
$728$			6.39196e14i			3.12592i
$729$	−1.19623e13	−	2.05543e14i	−0.0581003	−	0.998311i
$730$	1.61432e14			0.778709
$731$		−	1.84819e14i		−	0.885442i
$732$	−5.03412e13	+	1.95430e14i	−0.239534	+	0.929901i
$733$	1.04627e14			0.494450			0.247225	−	0.968958i	$-0.420481\pi$
$733$	1.04627e14			0.494450			0.247225	+	0.968958i	$0.420481\pi$
$734$		−	3.51089e14i		−	1.64792i
$735$	−7.79518e13	−	2.00797e13i	−0.363404	−	0.0936096i
$736$	1.66123e14			0.769201
$737$		−	4.03492e13i		−	0.185566i
$738$	1.89796e14	+	1.04729e14i	0.866974	+	0.478393i
$739$	−1.65463e14			−0.750720			−0.375360	−	0.926879i	$-0.622481\pi$
$739$	−1.65463e14			−0.750720			−0.375360	+	0.926879i	$0.622481\pi$
$740$			2.83726e14i			1.27862i
$741$	−2.74426e13	+	1.06535e14i	−0.122838	+	0.476873i
$742$	1.15540e13			0.0513705
$743$		−	2.78996e13i		−	0.123212i	−0.998101	−	0.0616062i	$-0.980378\pi$
$743$		−	2.78996e13i		−	0.123212i	0.998101	−	0.0616062i	$-0.0196223\pi$
$744$	−6.27963e14	−	1.61758e14i	−2.75467	−	0.709579i
$745$	1.93477e13			0.0843039
$746$		−	3.86659e14i		−	1.67353i
$747$	1.04168e14	−	1.88780e14i	0.447848	−	0.811619i
$748$	5.42348e14			2.31617
$749$		−	1.29878e14i		−	0.550970i
$750$	9.55854e12	−	3.71074e13i	0.0402796	−	0.156370i
$751$	2.51925e14			1.05456			0.527280	−	0.849692i	$-0.323212\pi$
$751$	2.51925e14			1.05456			0.527280	+	0.849692i	$0.323212\pi$
$752$		−	4.31806e14i		−	1.79556i
$753$	−2.42167e14	−	6.23802e13i	−1.00032	−	0.257675i
$754$	6.72236e14			2.75845
$755$		−	1.67995e14i		−	0.684798i
$756$	−5.19239e14	+	5.50337e14i	−2.10261	+	2.22854i
$757$	−4.29105e14			−1.72617			−0.863086	−	0.505056i	$-0.831472\pi$
$757$	−4.29105e14			−1.72617			−0.863086	+	0.505056i	$0.831472\pi$
$758$		−	3.83759e14i		−	1.53360i
$759$	4.64161e13	−	1.80193e14i	0.184272	−	0.715367i
$760$	−1.25203e14			−0.493794
$761$			3.81777e14i			1.49584i	0.663787	+	0.747922i	$0.268948\pi$
$761$			3.81777e14i			1.49584i	−0.663787	+	0.747922i	$0.731052\pi$
$762$	−7.85280e14	−	2.02281e14i	−3.05668	−	0.787374i
$763$	5.73953e14			2.21949
$764$			2.90265e13i			0.111514i
$765$	1.03564e14	+	5.71460e13i	0.395276	+	0.218112i
$766$	−8.90061e14			−3.37502
$767$			1.20649e14i			0.454513i
$768$	1.17588e14	−	4.56491e14i	0.440106	−	1.70854i
$769$	−8.31056e13			−0.309028			−0.154514	−	0.987991i	$-0.549381\pi$
$769$	−8.31056e13			−0.309028			−0.154514	+	0.987991i	$0.549381\pi$
$770$			3.00977e14i			1.11194i
$771$	1.67084e14	+	4.30393e13i	0.613285	+	0.157977i
$772$	−5.61653e14			−2.04824
$773$		−	2.07385e14i		−	0.751416i	−0.926738	−	0.375708i	$-0.877400\pi$
$773$		−	2.07385e14i		−	0.751416i	0.926738	−	0.375708i	$-0.122600\pi$
$774$	2.12511e14	−	3.85126e14i	0.765026	−	1.38643i
$775$	−6.99655e13			−0.250251
$776$			8.90882e14i			3.16601i
$777$	1.21241e14	−	4.70673e14i	0.428100	−	1.66193i
$778$	−2.65266e14			−0.930645
$779$		−	7.64202e13i		−	0.266392i
$780$	2.86418e14	+	7.37789e13i	0.992037	+	0.255540i
$781$	2.78424e14			0.958188
$782$			3.87683e14i			1.32569i
$783$	3.22601e14	+	3.04372e14i	1.09612	+	1.03418i
$784$	4.58564e14			1.54818
$785$		−	1.80626e14i		−	0.605943i
$786$	−3.36104e13	+	1.30480e14i	−0.112037	+	0.434940i
$787$	−4.37710e14			−1.44982			−0.724908	−	0.688846i	$-0.758118\pi$
$787$	−4.37710e14			−1.44982			−0.724908	+	0.688846i	$0.758118\pi$
$788$		−	4.69087e14i		−	1.54391i
$789$	−1.60841e14	−	4.14312e13i	−0.526031	−	0.135501i
$790$	9.03750e13			0.293706
$791$		−	5.71606e14i		−	1.84593i
$792$	6.29916e14	+	3.47585e14i	2.02142	+	1.11541i
$793$	−1.35140e14			−0.430942
$794$			1.05171e15i			3.33267i
$795$	7.43327e11	−	2.88568e12i	0.00234069	−	0.00908685i
$796$	1.11112e15			3.47692
$797$			2.15396e14i			0.669801i	0.942254	+	0.334900i	$0.108703\pi$
$797$			2.15396e14i			0.669801i	−0.942254	+	0.334900i	$0.891297\pi$
$798$	3.72636e14	+	9.59877e13i	1.15152	+	0.296620i
$799$	3.19921e14			0.982445
$800$			6.93012e13i			0.211490i
$801$	−1.57555e14	+	2.85532e14i	−0.477827	+	0.865948i
$802$	8.59013e14			2.58898
$803$			3.27023e14i			0.979492i
$804$	−3.45959e13	+	1.34305e14i	−0.102978	+	0.399773i
$805$	−1.49135e14			−0.441163
$806$		−	7.79072e14i		−	2.29035i
$807$	5.12255e14	+	1.31952e14i	1.49664	+	0.385523i
$808$	−1.27016e14			−0.368808
$809$			5.05141e14i			1.45771i	0.684670	+	0.728853i	$0.259946\pi$
$809$			5.05141e14i			1.45771i	−0.684670	+	0.728853i	$0.740054\pi$
$810$	1.50097e14	+	2.38161e14i	0.430475	+	0.683040i
$811$	−2.11952e14			−0.604133			−0.302066	−	0.953287i	$-0.597676\pi$
$811$	−2.11952e14			−0.604133			−0.302066	+	0.953287i	$0.597676\pi$
$812$		−	1.62990e15i		−	4.61721i
$813$	−6.75540e13	+	2.62252e14i	−0.190195	+	0.738358i
$814$	−8.29165e14			−2.32017
$815$		−	2.22613e13i		−	0.0619102i
$816$	−6.52528e14	−	1.68085e14i	−1.80363	−	0.464600i
$817$	−1.55068e14			−0.426003
$818$		−	1.31383e15i		−	3.58733i
$819$	−4.43612e14	−	2.44784e14i	−1.20388	−	0.664298i
$820$	−2.05454e14			−0.554174
$821$			4.22723e14i			1.13329i	0.823963	+	0.566643i	$0.191758\pi$
$821$			4.22723e14i			1.13329i	−0.823963	+	0.566643i	$0.808242\pi$
$822$	−1.30229e14	+	5.05565e14i	−0.347016	+	1.34716i
$823$	−6.60077e14			−1.74822			−0.874108	−	0.485731i	$-0.838553\pi$
$823$	−6.60077e14			−1.74822			−0.874108	+	0.485731i	$0.838553\pi$
$824$		−	2.83780e14i		−	0.747044i
$825$	7.51709e13	+	1.93634e13i	0.196689	+	0.0506653i
$826$	4.22001e14			1.09752
$827$			7.44406e14i			1.92434i	0.272446	+	0.962171i	$0.412167\pi$
$827$			7.44406e14i			1.92434i	−0.272446	+	0.962171i	$0.587833\pi$
$828$	−3.08999e14	+	5.59988e14i	−0.793972	+	1.43889i
$829$	−1.68576e14			−0.430548			−0.215274	−	0.976554i	$-0.569065\pi$
$829$	−1.68576e14			−0.430548			−0.215274	+	0.976554i	$0.569065\pi$
$830$			2.94806e14i			0.748420i
$831$	−3.14328e13	+	1.22026e14i	−0.0793193	+	0.307927i
$832$	−2.58971e13			−0.0649583
$833$			3.39746e14i			0.847088i
$834$	8.55269e14	+	2.20310e14i	2.11969	+	0.546014i
$835$	−2.51280e13			−0.0619051
$836$		−	4.55044e14i		−	1.11435i
$837$	3.52744e14	−	3.73870e14i	0.858683	−	0.910110i
$838$	−2.94785e14			−0.713320
$839$		−	6.56779e14i		−	1.57983i	−0.613219	−	0.789913i	$-0.710126\pi$
$839$		−	6.56779e14i		−	1.57983i	0.613219	−	0.789913i	$-0.289874\pi$
$840$	1.43837e14	−	5.58394e14i	0.343934	−	1.33519i
$841$	−5.34718e14			−1.27100
$842$		−	1.26032e15i		−	2.97797i
$843$	1.34705e14	+	3.46989e13i	0.316408	+	0.0815039i
$844$	−1.98485e14			−0.463463
$845$			5.39534e12i			0.0125238i
$846$	6.66649e14	+	3.67854e14i	1.53832	+	0.848837i
$847$	−1.85260e13			−0.0424977
$848$			1.69755e13i			0.0387118i
$849$	9.42445e13	−	3.65868e14i	0.213657	−	0.829443i
$850$	−1.61729e14			−0.364496
$851$		−	4.10853e14i		−	0.920531i
$852$	−9.26753e14	−	2.38724e14i	−2.06427	−	0.531738i
$853$	2.96474e14			0.656510			0.328255	−	0.944589i	$-0.393539\pi$
$853$	2.96474e14			0.656510			0.328255	+	0.944589i	$0.393539\pi$
$854$			4.72689e14i			1.04061i
$855$	4.79470e13	−	8.68926e13i	0.104938	−	0.190174i
$856$	4.24489e14			0.923629
$857$			1.42555e14i			0.308375i	0.988042	+	0.154187i	$0.0492759\pi$
$857$			1.42555e14i			0.308375i	−0.988042	+	0.154187i	$0.950724\pi$
$858$	−2.15613e14	+	8.37034e14i	−0.463701	+	1.80014i
$859$	3.91074e14			0.836166			0.418083	−	0.908409i	$-0.362702\pi$
$859$	3.91074e14			0.836166			0.418083	+	0.908409i	$0.362702\pi$
$860$			4.16898e14i			0.886212i
$861$	3.40828e14	+	8.77944e13i	0.720311	+	0.185546i
$862$	4.33988e14			0.911887
$863$			4.75912e14i			0.994198i	0.867694	+	0.497099i	$0.165601\pi$
$863$			4.75912e14i			0.994198i	−0.867694	+	0.497099i	$0.834399\pi$
$864$	−3.70320e14	−	3.49395e14i	−0.769146	−	0.725684i
$865$	−3.21746e13			−0.0664405
$866$			1.29646e15i			2.66177i
$867$	2.33136e12	−	9.05062e12i	0.00475898	−	0.0184749i
$868$	−1.88893e15			−3.83369
$869$			1.83079e14i			0.369436i
$870$	−5.87257e14	−	1.51272e14i	−1.17824	−	0.303503i
$871$	−9.28722e13			−0.185266
$872$			1.87588e15i			3.72069i
$873$	−6.18286e14	−	3.41168e14i	−1.21932	−	0.672817i
$874$	3.25276e14			0.637815
$875$		−	6.22143e13i		−	0.121297i
$876$	2.80393e14	−	1.08852e15i	0.543560	−	2.11016i
$877$	7.43219e14			1.43258			0.716290	−	0.697802i	$-0.245839\pi$
$877$	7.43219e14			1.43258			0.716290	+	0.697802i	$0.245839\pi$
$878$			3.33500e14i			0.639180i
$879$	−6.56249e14	−	1.69044e14i	−1.25062	−	0.322148i
$880$	−4.42205e14			−0.837935
$881$			5.63352e14i			1.06145i	0.847544	+	0.530726i	$0.178081\pi$
$881$			5.63352e14i			1.06145i	−0.847544	+	0.530726i	$0.821919\pi$
$882$	−3.90650e14	+	7.07960e14i	−0.731888	+	1.32637i
$883$	5.43563e14			1.01262			0.506310	−	0.862352i	$-0.331009\pi$
$883$	5.43563e14			1.01262			0.506310	+	0.862352i	$0.331009\pi$
$884$		−	1.24833e15i		−	2.31242i
$885$	2.71494e13	−	1.05397e14i	0.0500085	−	0.194139i
$886$	1.86021e15			3.40716
$887$		−	4.52341e14i		−	0.823849i	−0.911218	−	0.411924i	$-0.864857\pi$
$887$		−	4.52341e14i		−	0.823849i	0.911218	−	0.411924i	$-0.135143\pi$
$888$	1.53833e15	+	3.96259e14i	2.78602	+	0.717653i
$889$	−1.31660e15			−2.37108
$890$		−	4.45897e14i		−	0.798518i
$891$	−4.82459e14	+	3.04062e14i	−0.859156	+	0.541469i
$892$	−3.28666e13			−0.0582011
$893$		−	2.68422e14i		−	0.472672i
$894$	4.84797e13	−	1.88204e14i	0.0848931	−	0.329565i
$895$	4.34872e14			0.757262
$896$		−	7.37562e14i		−	1.27720i
$897$	−4.14752e14	−	1.06836e14i	−0.714210	−	0.183974i
$898$	4.96551e13			0.0850320
$899$			1.10727e15i			1.88562i
$900$	−2.33609e14	−	1.28905e14i	−0.395619	−	0.218301i
$901$	−1.25770e13			−0.0211813
$902$		−	6.00423e14i		−	1.00560i
$903$	1.78148e14	−	6.91592e14i	0.296717	−	1.15189i
$904$	1.86821e15			3.09445
$905$			1.96749e14i			0.324092i
$906$	−1.63417e15	−	4.20948e14i	−2.67705	−	0.689584i
$907$	7.94455e14			1.29429			0.647147	−	0.762365i	$-0.275962\pi$
$907$	7.94455e14			1.29429			0.647147	+	0.762365i	$0.275962\pi$
$908$			2.45326e14i			0.397479i
$909$	4.86413e13	−	8.81508e13i	0.0783764	−	0.142039i
$910$	6.92762e14			1.11014
$911$		−	1.19682e15i		−	1.90738i	−0.300790	−	0.953690i	$-0.597250\pi$
$911$		−	1.19682e15i		−	1.90738i	0.300790	−	0.953690i	$-0.402750\pi$
$912$	−1.41028e14	+	5.47488e14i	−0.223528	+	0.867761i
$913$	−5.97207e14			−0.941393
$914$			1.78792e15i			2.80297i
$915$	1.18057e14	+	3.04104e13i	0.184071	+	0.0474151i
$916$	−2.21543e15			−3.43543
$917$			2.18762e14i			0.337385i
$918$	8.15387e14	−	8.64221e14i	1.25069	−	1.32560i
$919$	2.18883e14			0.333914			0.166957	−	0.985964i	$-0.446606\pi$
$919$	2.18883e14			0.333914			0.166957	+	0.985964i	$0.446606\pi$
$920$		−	4.87425e14i		−	0.739552i
$921$	−1.11094e14	+	4.31280e14i	−0.167646	+	0.650820i
$922$	1.53622e15			2.30568
$923$		−	6.40850e14i		−	0.956639i
$924$	2.02946e15	+	5.22772e14i	3.01315	+	0.776162i
$925$	1.71395e14			0.253098
$926$		−	2.19813e15i		−	3.22848i
$927$	1.96948e14	+	1.08675e14i	0.287709	+	0.158757i
$928$	1.09675e15			1.59356
$929$		−	9.26545e14i		−	1.33902i	−0.742802	−	0.669511i	$-0.766504\pi$
$929$		−	9.26545e14i		−	1.33902i	0.742802	−	0.669511i	$-0.233496\pi$
$930$	−1.75313e14	+	6.80588e14i	−0.252000	+	0.978294i
$931$	2.85055e14			0.407550
$932$			1.69484e15i			2.41017i
$933$	−1.75618e14	−	4.52377e13i	−0.248405	−	0.0639871i
$934$	−1.48791e15			−2.09335
$935$		−	3.27625e14i		−	0.458479i
$936$	8.00040e14	−	1.44988e15i	1.11361	−	2.01815i
$937$	−1.29678e15			−1.79543			−0.897713	−	0.440581i	$-0.854772\pi$
$937$	−1.29678e15			−1.79543			−0.897713	+	0.440581i	$0.854772\pi$
$938$			3.24845e14i			0.447365i
$939$	−1.51102e14	+	5.86598e14i	−0.206987	+	0.803549i
$940$	−7.21647e14			−0.983299
$941$			2.81045e14i			0.380915i	0.981695	+	0.190458i	$0.0609972\pi$
$941$			2.81045e14i			0.380915i	−0.981695	+	0.190458i	$0.939003\pi$
$942$	−1.75704e15	−	4.52597e14i	−2.36879	−	0.610179i
$943$	2.97511e14			0.398974
$944$			6.20017e14i			0.827073i
$945$	3.32451e14	+	3.13665e14i	0.441132	+	0.416205i
$946$	−1.21835e15			−1.60811
$947$			1.33255e14i			0.174958i	0.996166	+	0.0874790i	$0.0278811\pi$
$947$			1.33255e14i			0.174958i	−0.996166	+	0.0874790i	$0.972119\pi$
$948$	1.56974e14	−	6.09391e14i	0.205015	−	0.795892i
$949$	7.52712e14			0.977908
$950$			1.35695e14i			0.175366i
$951$	7.51589e14	+	1.93603e14i	0.966224	+	0.248891i
$952$	−2.43371e15			−3.11232
$953$		−	8.93117e13i		−	0.113617i	−0.998385	−	0.0568086i	$-0.981908\pi$
$953$		−	8.93117e13i		−	0.113617i	0.998385	−	0.0568086i	$-0.0180925\pi$
$954$	−2.62079e13	−	1.44614e13i	−0.0331657	−	0.0183007i
$955$	1.75345e13			0.0220738
$956$			1.76044e15i			2.20461i
$957$	3.06443e14	−	1.18965e15i	0.381759	−	1.48203i
$958$	5.85891e14			0.726088
$959$			8.47632e14i			1.04500i
$960$	2.26234e13	+	5.82759e12i	0.0277461	+	0.00714715i
$961$	4.63611e14			0.565636
$962$			1.90850e15i			2.31641i
$963$	−1.62560e14	+	2.94602e14i	−0.196283	+	0.355717i
$964$	−1.55568e15			−1.86868
$965$			3.39287e14i			0.405444i
$966$	−3.73689e14	+	1.45070e15i	−0.444247	+	1.72462i
$967$	1.00441e15			1.18790			0.593951	−	0.804501i	$-0.297567\pi$
$967$	1.00441e15			1.18790			0.593951	+	0.804501i	$0.297567\pi$
$968$		−	6.05497e13i		−	0.0712418i
$969$	−4.05628e14	−	1.04486e14i	−0.474798	−	0.122304i
$970$	9.65540e14			1.12438
$971$		−	2.83236e14i		−	0.328135i	−0.986449	−	0.164068i	$-0.947539\pi$
$971$		−	2.83236e14i		−	0.328135i	0.986449	−	0.164068i	$-0.0524615\pi$
$972$	1.86661e15	−	5.98427e14i	2.15140	−	0.689731i
$973$	1.43395e15			1.64425
$974$		−	2.39016e15i		−	2.72666i
$975$	4.45688e13	−	1.73021e14i	0.0505834	−	0.196371i
$976$	−6.94489e14			−0.784181
$977$		−	8.97065e14i		−	1.00775i	−0.863778	−	0.503873i	$-0.831908\pi$
$977$		−	8.97065e14i		−	1.00775i	0.863778	−	0.503873i	$-0.168092\pi$
$978$	−2.16546e14	−	5.57804e13i	−0.242023	−	0.0623429i
$979$	9.03284e14			1.00441
$980$		−	7.66367e14i		−	0.847825i
$981$	−1.30189e15	−	7.18379e14i	−1.43295	−	0.790694i
$982$	−1.15151e15			−1.26099
$983$			8.51414e14i			0.927627i	0.885933	+	0.463814i	$0.153519\pi$
$983$			8.51414e14i			0.927627i	−0.885933	+	0.463814i	$0.846481\pi$
$984$	−2.86943e14	+	1.11395e15i	−0.311043	+	1.20751i
$985$	−2.83369e14			−0.305613
$986$			2.55951e15i			2.74645i
$987$	1.19714e15	+	3.08373e14i	1.27808	+	0.329223i
$988$	−1.04738e15			−1.11255
$989$		−	6.03695e14i		−	0.638022i
$990$	3.76713e14	−	6.82704e14i	0.396127	−	0.717887i
$991$	−1.17599e15			−1.23037			−0.615185	−	0.788383i	$-0.710919\pi$
$991$	−1.17599e15			−1.23037			−0.615185	+	0.788383i	$0.710919\pi$
$992$		−	1.27105e15i		−	1.32314i
$993$	−5.63375e13	+	2.18709e14i	−0.0583514	+	0.226527i
$994$	−2.24154e15			−2.31002
$995$		−	6.71212e14i		−	0.688247i
$996$	1.98785e15	+	5.12052e14i	2.02809	+	0.522417i
$997$	−4.42639e13			−0.0449339			−0.0224670	−	0.999748i	$-0.507152\pi$
$997$	−4.42639e13			−0.0449339			−0.0224670	+	0.999748i	$0.507152\pi$
$998$			9.80183e14i			0.990044i
$999$	−8.64120e14	+	9.15873e14i	−0.868454	+	0.920466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.11.c.a.11.1	✓	14
3.2	odd	2	inner	15.11.c.a.11.14	yes	14
4.3	odd	2		240.11.l.b.161.7		14
5.2	odd	4		75.11.d.d.74.28		28
5.3	odd	4		75.11.d.d.74.1		28
5.4	even	2		75.11.c.g.26.14		14
12.11	even	2		240.11.l.b.161.8		14
15.2	even	4		75.11.d.d.74.2		28
15.8	even	4		75.11.d.d.74.27		28
15.14	odd	2		75.11.c.g.26.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.11.c.a.11.1	✓	14	1.1	even	1	trivial
15.11.c.a.11.14	yes	14	3.2	odd	2	inner
75.11.c.g.26.1		14	15.14	odd	2
75.11.c.g.26.14		14	5.4	even	2
75.11.d.d.74.1		28	5.3	odd	4
75.11.d.d.74.2		28	15.2	even	4
75.11.d.d.74.27		28	15.8	even	4
75.11.d.d.74.28		28	5.2	odd	4
240.11.l.b.161.7		14	4.3	odd	2
240.11.l.b.161.8		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)

\(f(q)\)	\(=\)	\(q-57.7709i q^{2} +(-60.6159 + 235.318i) q^{3} -2313.48 q^{4} +1397.54i q^{5} +(13594.6 + 3501.84i) q^{6} +22792.7 q^{7} +74494.6i q^{8} +(-51700.4 - 28528.1i) q^{9} +O(q^{10})\)	\(q-57.7709i q^{2} +(-60.6159 + 235.318i) q^{3} -2313.48 q^{4} +1397.54i q^{5} +(13594.6 + 3501.84i) q^{6} +22792.7 q^{7} +74494.6i q^{8} +(-51700.4 - 28528.1i) q^{9} +80737.3 q^{10} +163555. i q^{11} +(140234. - 544405. i) q^{12} +376456. q^{13} -1.31675e6i q^{14} +(-328867. - 84713.4i) q^{15} +1.93462e6 q^{16} +1.43334e6i q^{17} +(-1.64809e6 + 2.98678e6i) q^{18} +1.20261e6 q^{19} -3.23319e6i q^{20} +(-1.38160e6 + 5.36354e6i) q^{21} +9.44873e6 q^{22} +4.68186e6i q^{23} +(-1.75299e7 - 4.51556e6i) q^{24} -1.95312e6 q^{25} -2.17482e7i q^{26} +(9.84705e6 - 1.04368e7i) q^{27} -5.27305e7 q^{28} +3.09100e7i q^{29} +(-4.89397e6 + 1.89990e7i) q^{30} +3.58223e7 q^{31} -3.54822e7i q^{32} +(-3.84875e7 - 9.91404e6i) q^{33} +8.28052e7 q^{34} +3.18537e7i q^{35} +(1.19608e8 + 6.59992e7i) q^{36} -8.77542e7 q^{37} -6.94757e7i q^{38} +(-2.28192e7 + 8.85870e7i) q^{39} -1.04109e8 q^{40} -6.35454e7i q^{41} +(3.09857e8 + 7.98163e7i) q^{42} -1.28943e8 q^{43} -3.78381e8i q^{44} +(3.98692e7 - 7.22535e7i) q^{45} +2.70475e8 q^{46} -2.23200e8i q^{47} +(-1.17269e8 + 4.55251e8i) q^{48} +2.37031e8 q^{49} +1.12834e8i q^{50} +(-3.37290e8 - 8.68831e7i) q^{51} -8.70924e8 q^{52} +8.77462e6i q^{53} +(-6.02944e8 - 5.68873e8i) q^{54} -2.28575e8 q^{55} +1.69793e9i q^{56} +(-7.28972e7 + 2.82995e8i) q^{57} +1.78570e9 q^{58} +3.20486e8i q^{59} +(7.60829e8 + 1.95983e8i) q^{60} -3.58980e8 q^{61} -2.06949e9i q^{62} +(-1.17839e9 - 6.50232e8i) q^{63} -6.87918e7 q^{64} +5.26113e8i q^{65} +(-5.72743e8 + 2.22346e9i) q^{66} -2.46701e8 q^{67} -3.31600e9i q^{68} +(-1.10173e9 - 2.83795e8i) q^{69} +1.84022e9 q^{70} -1.70232e9i q^{71} +(2.12519e9 - 3.85140e9i) q^{72} +1.99947e9 q^{73} +5.06964e9i q^{74} +(1.18391e8 - 4.59606e8i) q^{75} -2.78221e9 q^{76} +3.72786e9i q^{77} +(5.11775e9 + 1.31829e9i) q^{78} +1.11937e9 q^{79} +2.70371e9i q^{80} +(1.85908e9 + 2.94983e9i) q^{81} -3.67108e9 q^{82} +3.65141e9i q^{83} +(3.19631e9 - 1.24084e10i) q^{84} -2.00315e9 q^{85} +7.44918e9i q^{86} +(-7.27368e9 - 1.87364e9i) q^{87} -1.21840e10 q^{88} -5.52281e9i q^{89} +(-4.17415e9 - 2.30328e9i) q^{90} +8.58044e9 q^{91} -1.08314e10i q^{92} +(-2.17140e9 + 8.42965e9i) q^{93} -1.28945e10 q^{94} +1.68069e9i q^{95} +(8.34961e9 + 2.15079e9i) q^{96} +1.19590e10 q^{97} -1.36935e10i q^{98} +(4.66591e9 - 8.45586e9i) 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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