LMFDB - Embedded newform 15.11.c.a.11.4

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			11.4
Root			$-42.9372i$ of defining polynomial
Character	$\chi$	$=$	15.11
Dual form			15.11.c.a.11.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-40.7012i q^{2} +(230.652 + 76.4761i) q^{3} -632.586 q^{4} -1397.54i q^{5} +(3112.67 - 9387.81i) q^{6} +19744.7 q^{7} -15931.0i q^{8} +(47351.8 + 35278.8i) q^{9} +O(q^{10})$	\(q-40.7012i q^{2} +(230.652 + 76.4761i) q^{3} -632.586 q^{4} -1397.54i q^{5} +(3112.67 - 9387.81i) q^{6} +19744.7 q^{7} -15931.0i q^{8} +(47351.8 + 35278.8i) q^{9} -56881.6 q^{10} -185244. i q^{11} +(-145907. - 48377.7i) q^{12} -529553. q^{13} -803633. i q^{14} +(106879. - 322346. i) q^{15} -1.29618e6 q^{16} +976612. i q^{17} +(1.43589e6 - 1.92727e6i) q^{18} +3.17224e6 q^{19} +884066. i q^{20} +(4.55416e6 + 1.51000e6i) q^{21} -7.53966e6 q^{22} -3.78168e6i q^{23} +(1.21834e6 - 3.67452e6i) q^{24} -1.95312e6 q^{25} +2.15534e7i q^{26} +(8.22381e6 + 1.17584e7i) q^{27} -1.24902e7 q^{28} +1.38573e7i q^{29} +(-1.31199e7 - 4.35009e6i) q^{30} +1.07567e7 q^{31} +3.64427e7i q^{32} +(1.41668e7 - 4.27270e7i) q^{33} +3.97492e7 q^{34} -2.75941e7i q^{35} +(-2.99541e7 - 2.23169e7i) q^{36} +6.04245e7 q^{37} -1.29114e8i q^{38} +(-1.22143e8 - 4.04982e7i) q^{39} -2.22643e7 q^{40} +2.08471e8i q^{41} +(6.14588e7 - 1.85360e8i) q^{42} -1.84104e7 q^{43} +1.17183e8i q^{44} +(4.93036e7 - 6.61761e7i) q^{45} -1.53919e8 q^{46} +1.02781e7i q^{47} +(-2.98966e8 - 9.91268e7i) q^{48} +1.07378e8 q^{49} +7.94945e7i q^{50} +(-7.46875e7 + 2.25258e8i) q^{51} +3.34988e8 q^{52} +5.68407e8i q^{53} +(4.78581e8 - 3.34719e8i) q^{54} -2.58887e8 q^{55} -3.14553e8i q^{56} +(7.31683e8 + 2.42601e8i) q^{57} +5.64010e8 q^{58} +4.19257e8i q^{59} +(-6.76099e7 + 2.03912e8i) q^{60} -1.42840e9 q^{61} -4.37812e8i q^{62} +(9.34947e8 + 6.96569e8i) q^{63} +1.55972e8 q^{64} +7.40073e8i q^{65} +(-1.73904e9 - 5.76604e8i) q^{66} -9.29430e8 q^{67} -6.17791e8i q^{68} +(2.89209e8 - 8.72254e8i) q^{69} -1.12311e9 q^{70} -1.16381e9i q^{71} +(5.62027e8 - 7.54362e8i) q^{72} +1.44576e9 q^{73} -2.45935e9i q^{74} +(-4.50492e8 - 1.49367e8i) q^{75} -2.00671e9 q^{76} -3.65759e9i q^{77} +(-1.64832e9 + 4.97135e9i) q^{78} +3.58653e9 q^{79} +1.81147e9i q^{80} +(9.97601e8 + 3.34103e9i) q^{81} +8.48502e9 q^{82} -5.61799e9i q^{83} +(-2.88090e9 - 9.55204e8i) q^{84} +1.36486e9 q^{85} +7.49324e8i q^{86} +(-1.05976e9 + 3.19622e9i) q^{87} -2.95113e9 q^{88} +1.07490e10i q^{89} +(-2.69345e9 - 2.00671e9i) q^{90} -1.04559e10 q^{91} +2.39224e9i q^{92} +(2.48107e9 + 8.22635e8i) q^{93} +4.18333e8 q^{94} -4.43334e9i q^{95} +(-2.78699e9 + 8.40558e9i) q^{96} +3.53316e9 q^{97} -4.37042e9i q^{98} +(6.53519e9 - 8.77164e9i) 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 $

$2$		−	40.7012i		−	1.27191i	−0.771725	−	0.635956i	$-0.780606\pi$
$2$		−	40.7012i		−	1.27191i	0.771725	−	0.635956i	$-0.219394\pi$
$3$	230.652	+	76.4761i	0.949186	+	0.314717i
$3$	230.652	+	76.4761i	0.949186	+	0.314717i
$4$	−632.586			−0.617760
$5$		−	1397.54i		−	0.447214i
$5$		−	1397.54i		−	0.447214i
$6$	3112.67	−	9387.81i	0.400292	−	1.20728i
$7$	19744.7			1.17479			0.587395	−	0.809300i	$-0.300153\pi$
$7$	19744.7			1.17479			0.587395	+	0.809300i	$0.300153\pi$
$8$		−	15931.0i		−	0.486176i
$9$	47351.8	+	35278.8i	0.801907	+	0.597449i
$10$	−56881.6			−0.568816
$11$		−	185244.i		−	1.15022i	−0.818076	−	0.575110i	$-0.804959\pi$
$11$		−	185244.i		−	1.15022i	0.818076	−	0.575110i	$-0.195041\pi$
$12$	−145907.	−	48377.7i	−0.586369	−	0.194419i
$13$	−529553.			−1.42624			−0.713120	−	0.701042i	$-0.752719\pi$
$13$	−529553.			−1.42624			−0.713120	+	0.701042i	$0.752719\pi$
$14$		−	803633.i		−	1.49423i
$15$	106879.	−	322346.i	0.140746	−	0.424489i
$16$	−1.29618e6			−1.23613
$17$			976612.i			0.687824i	0.939002	+	0.343912i	$0.111752\pi$
$17$			976612.i			0.687824i	−0.939002	+	0.343912i	$0.888248\pi$
$18$	1.43589e6	−	1.92727e6i	0.759903	−	1.01995i
$19$	3.17224e6			1.28114			0.640572	−	0.767898i	$-0.278697\pi$
$19$	3.17224e6			1.28114			0.640572	+	0.767898i	$0.278697\pi$
$20$			884066.i			0.276271i
$21$	4.55416e6	+	1.51000e6i	1.11509	+	0.369726i
$22$	−7.53966e6			−1.46298
$23$		−	3.78168e6i		−	0.587552i	−0.955874	−	0.293776i	$-0.905088\pi$
$23$		−	3.78168e6i		−	0.587552i	0.955874	−	0.293776i	$-0.0949119\pi$
$24$	1.21834e6	−	3.67452e6i	0.153008	−	0.461471i
$25$	−1.95312e6			−0.200000
$26$			2.15534e7i			1.81405i
$27$	8.22381e6	+	1.17584e7i	0.573131	+	0.819464i
$28$	−1.24902e7			−0.725738
$29$			1.38573e7i			0.675600i	0.941218	+	0.337800i	$0.109683\pi$
$29$			1.38573e7i			0.675600i	−0.941218	+	0.337800i	$0.890317\pi$
$30$	−1.31199e7	−	4.35009e6i	−0.539912	−	0.179016i
$31$	1.07567e7			0.375727			0.187864	−	0.982195i	$-0.439844\pi$
$31$	1.07567e7			0.375727			0.187864	+	0.982195i	$0.439844\pi$
$32$			3.64427e7i			1.08608i
$33$	1.41668e7	−	4.27270e7i	0.361994	−	1.09177i
$34$	3.97492e7			0.874851
$35$		−	2.75941e7i		−	0.525382i
$36$	−2.99541e7	−	2.23169e7i	−0.495386	−	0.369080i
$37$	6.04245e7			0.871373			0.435687	−	0.900098i	$-0.356506\pi$
$37$	6.04245e7			0.871373			0.435687	+	0.900098i	$0.356506\pi$
$38$		−	1.29114e8i		−	1.62950i
$39$	−1.22143e8	−	4.04982e7i	−1.35377	−	0.448862i
$40$	−2.22643e7			−0.217425
$41$			2.08471e8i			1.79940i	0.436513	+	0.899698i	$0.356213\pi$
$41$			2.08471e8i			1.79940i	−0.436513	+	0.899698i	$0.643787\pi$
$42$	6.14588e7	−	1.85360e8i	0.470259	−	1.41830i
$43$	−1.84104e7			−0.125233			−0.0626167	−	0.998038i	$-0.519945\pi$
$43$	−1.84104e7			−0.125233			−0.0626167	+	0.998038i	$0.519945\pi$
$44$			1.17183e8i			0.710560i
$45$	4.93036e7	−	6.61761e7i	0.267187	−	0.358624i
$46$	−1.53919e8			−0.747314
$47$			1.02781e7i			0.0448152i	0.999749	+	0.0224076i	$0.00713316\pi$
$47$			1.02781e7i			0.0448152i	−0.999749	+	0.0224076i	$0.992867\pi$
$48$	−2.98966e8	−	9.91268e7i	−1.17332	−	0.389032i
$49$	1.07378e8			0.380134
$50$			7.94945e7i			0.254382i
$51$	−7.46875e7	+	2.25258e8i	−0.216470	+	0.652873i
$52$	3.34988e8			0.881074
$53$			5.68407e8i			1.35919i	0.733587	+	0.679595i	$0.237845\pi$
$53$			5.68407e8i			1.35919i	−0.733587	+	0.679595i	$0.762155\pi$
$54$	4.78581e8	−	3.34719e8i	1.04229	−	0.728972i
$55$	−2.58887e8			−0.514394
$56$		−	3.14553e8i		−	0.571155i
$57$	7.31683e8	+	2.42601e8i	1.21604	+	0.403197i
$58$	5.64010e8			0.859303
$59$			4.19257e8i			0.586436i	0.956046	+	0.293218i	$0.0947261\pi$
$59$			4.19257e8i			0.586436i	−0.956046	+	0.293218i	$0.905274\pi$
$60$	−6.76099e7	+	2.03912e8i	−0.0869469	+	0.262232i
$61$	−1.42840e9			−1.69122			−0.845609	−	0.533803i	$-0.820762\pi$
$61$	−1.42840e9			−1.69122			−0.845609	+	0.533803i	$0.820762\pi$
$62$		−	4.37812e8i		−	0.477892i
$63$	9.34947e8	+	6.96569e8i	0.942073	+	0.701878i
$64$	1.55972e8			0.145260
$65$			7.40073e8i			0.637834i
$66$	−1.73904e9	−	5.76604e8i	−1.38864	−	0.460424i
$67$	−9.29430e8			−0.688403			−0.344201	−	0.938896i	$-0.611850\pi$
$67$	−9.29430e8			−0.688403			−0.344201	+	0.938896i	$0.611850\pi$
$68$		−	6.17791e8i		−	0.424910i
$69$	2.89209e8	−	8.72254e8i	0.184912	−	0.557696i
$70$	−1.12311e9			−0.668240
$71$		−	1.16381e9i		−	0.645047i	−0.946561	−	0.322524i	$-0.895469\pi$
$71$		−	1.16381e9i		−	0.645047i	0.946561	−	0.322524i	$-0.104531\pi$
$72$	5.62027e8	−	7.54362e8i	0.290465	−	0.389868i
$73$	1.44576e9			0.697401			0.348700	−	0.937234i	$-0.386623\pi$
$73$	1.44576e9			0.697401			0.348700	+	0.937234i	$0.386623\pi$
$74$		−	2.45935e9i		−	1.10831i
$75$	−4.50492e8	−	1.49367e8i	−0.189837	−	0.0629433i
$76$	−2.00671e9			−0.791439
$77$		−	3.65759e9i		−	1.35127i
$78$	−1.64832e9	+	4.97135e9i	−0.570912	+	1.72187i
$79$	3.58653e9			1.16557			0.582785	−	0.812626i	$-0.301963\pi$
$79$	3.58653e9			1.16557			0.582785	+	0.812626i	$0.301963\pi$
$80$			1.81147e9i			0.552815i
$81$	9.97601e8	+	3.34103e9i	0.286109	+	0.958197i
$82$	8.48502e9			2.28867
$83$		−	5.61799e9i		−	1.42623i	−0.701046	−	0.713116i	$-0.747283\pi$
$83$		−	5.61799e9i		−	1.42623i	0.701046	−	0.713116i	$-0.252717\pi$
$84$	−2.88090e9	−	9.55204e8i	−0.688860	−	0.228402i
$85$	1.36486e9			0.307604
$86$			7.49324e8i			0.159286i
$87$	−1.05976e9	+	3.19622e9i	−0.212622	+	0.641270i
$88$	−2.95113e9			−0.559210
$89$			1.07490e10i			1.92495i	0.271374	+	0.962474i	$0.412522\pi$
$89$			1.07490e10i			1.92495i	−0.271374	+	0.962474i	$0.587478\pi$
$90$	−2.69345e9	−	2.00671e9i	−0.456138	−	0.339839i
$91$	−1.04559e10			−1.67553
$92$			2.39224e9i			0.362966i
$93$	2.48107e9	+	8.22635e8i	0.356635	+	0.118248i
$94$	4.18333e8			0.0570010
$95$		−	4.43334e9i		−	0.572945i
$96$	−2.78699e9	+	8.40558e9i	−0.341806	+	1.03089i
$97$	3.53316e9			0.411439			0.205719	−	0.978611i	$-0.434047\pi$
$97$	3.53316e9			0.411439			0.205719	+	0.978611i	$0.434047\pi$
$98$		−	4.37042e9i		−	0.483496i
$99$	6.53519e9	−	8.77164e9i	0.687198	−	0.922370i
$100$	1.23552e9			0.123552
$101$			2.87829e9i			0.273860i	0.990581	+	0.136930i	$0.0437235\pi$
$101$			2.87829e9i			0.273860i	−0.990581	+	0.136930i	$0.956276\pi$
$102$	9.16825e9	+	3.03987e9i	0.830396	+	0.275330i
$103$	−5.48096e9			−0.472793			−0.236396	−	0.971657i	$-0.575966\pi$
$103$	−5.48096e9			−0.472793			−0.236396	+	0.971657i	$0.575966\pi$
$104$			8.43632e9i			0.693404i
$105$	2.11029e9	−	6.36463e9i	0.165347	−	0.498685i
$106$	2.31348e10			1.72877
$107$		−	7.49637e9i		−	0.534481i	−0.963630	−	0.267240i	$-0.913888\pi$
$107$		−	7.49637e9i		−	0.534481i	0.963630	−	0.267240i	$-0.0861118\pi$
$108$	−5.20226e9	−	7.43820e9i	−0.354057	−	0.506232i
$109$	−2.19466e10			−1.42638			−0.713188	−	0.700973i	$-0.752749\pi$
$109$	−2.19466e10			−1.42638			−0.713188	+	0.700973i	$0.752749\pi$
$110$			1.05370e10i			0.654264i
$111$	1.39370e10	+	4.62103e9i	0.827095	+	0.274236i
$112$	−2.55927e10			−1.45220
$113$		−	3.59489e10i		−	1.95116i	−0.219636	−	0.975582i	$-0.570487\pi$
$113$		−	3.59489e10i		−	1.95116i	0.219636	−	0.975582i	$-0.429513\pi$
$114$	9.87413e9	−	2.97804e10i	0.512831	−	1.54670i
$115$	−5.28507e9			−0.262761
$116$		−	8.76595e9i		−	0.417358i
$117$	−2.50753e10	−	1.86820e10i	−1.14371	−	0.852106i
$118$	1.70643e10			0.745895
$119$			1.92829e10i			0.808049i
$120$	−5.13530e9	−	1.70269e9i	−0.206376	−	0.0684271i
$121$	−8.37798e9			−0.323007
$122$			5.81374e10i			2.15108i
$123$	−1.59431e10	+	4.80843e10i	−0.566300	+	1.70796i
$124$	−6.80457e9			−0.232109
$125$			2.72958e9i			0.0894427i
$126$	2.83512e10	−	3.80535e10i	0.892727	−	1.19823i
$127$	−1.50898e10			−0.456735			−0.228368	−	0.973575i	$-0.573339\pi$
$127$	−1.50898e10			−0.456735			−0.228368	+	0.973575i	$0.573339\pi$
$128$			3.09690e10i			0.901318i
$129$	−4.24639e9	−	1.40795e9i	−0.118870	−	0.0394131i
$130$	3.01218e10			0.811269
$131$		−	1.81444e10i		−	0.470312i	−0.971958	−	0.235156i	$-0.924440\pi$
$131$		−	1.81444e10i		−	0.470312i	0.971958	−	0.235156i	$-0.0755601\pi$
$132$	−8.96169e9	+	2.70285e10i	−0.223625	+	0.674453i
$133$	6.26349e10			1.50508
$134$			3.78289e10i			0.875588i
$135$	1.64329e10	−	1.14931e10i	0.366475	−	0.256312i
$136$	1.55584e10			0.334403
$137$		−	5.93315e10i		−	1.22937i	−0.788772	−	0.614685i	$-0.789283\pi$
$137$		−	5.93315e10i		−	1.22937i	0.788772	−	0.614685i	$-0.210717\pi$
$138$	−3.55017e10	−	1.17711e10i	−0.709340	−	0.235192i
$139$	6.31026e10			1.21611			0.608056	−	0.793894i	$-0.291950\pi$
$139$	6.31026e10			1.21611			0.608056	+	0.793894i	$0.291950\pi$
$140$			1.74556e10i			0.324560i
$141$	−7.86033e8	+	2.37068e9i	−0.0141041	+	0.0425380i
$142$	−4.73686e10			−0.820443
$143$			9.80966e10i			1.64049i
$144$	−6.13764e10	−	4.57276e10i	−0.991263	−	0.738526i
$145$	1.93662e10			0.302137
$146$		−	5.88442e10i		−	0.887032i
$147$	2.47670e10	+	8.21188e9i	0.360817	+	0.119634i
$148$	−3.82237e10			−0.538299
$149$			1.68157e9i			0.0228973i	0.999934	+	0.0114486i	$0.00364429\pi$
$149$			1.68157e9i			0.0228973i	−0.999934	+	0.0114486i	$0.996356\pi$
$150$	−6.07943e9	+	1.83356e10i	−0.0800584	+	0.241456i
$151$	7.57190e10			0.964539			0.482270	−	0.876023i	$-0.339813\pi$
$151$	7.57190e10			0.964539			0.482270	+	0.876023i	$0.339813\pi$
$152$		−	5.05370e10i		−	0.622861i
$153$	−3.44537e10	+	4.62443e10i	−0.410940	+	0.551571i
$154$	−1.48868e11			−1.71869
$155$		−	1.50330e10i		−	0.168030i
$156$	7.72656e10	+	2.56186e10i	0.836303	+	0.277289i
$157$	−9.44099e10			−0.989736			−0.494868	−	0.868968i	$-0.664784\pi$
$157$	−9.44099e10			−0.989736			−0.494868	+	0.868968i	$0.664784\pi$
$158$		−	1.45976e11i		−	1.48250i
$159$	−4.34696e10	+	1.31104e11i	−0.427760	+	1.29012i
$160$	5.09302e10			0.485708
$161$		−	7.46683e10i		−	0.690250i
$162$	1.35984e11	−	4.06035e10i	1.21874	−	0.363906i
$163$	−2.36461e10			−0.205505			−0.102752	−	0.994707i	$-0.532765\pi$
$163$	−2.36461e10			−0.205505			−0.102752	+	0.994707i	$0.532765\pi$
$164$		−	1.31876e11i		−	1.11159i
$165$	−5.97127e10	−	1.97987e10i	−0.488256	−	0.161888i
$166$	−2.28659e11			−1.81404
$167$		−	2.29421e10i		−	0.176624i	−0.996093	−	0.0883122i	$-0.971853\pi$
$167$		−	2.29421e10i		−	0.176624i	0.996093	−	0.0883122i	$-0.0281473\pi$
$168$	2.40558e10	−	7.25524e10i	0.179752	−	0.542132i
$169$	1.42568e11			1.03416
$170$		−	5.55513e10i		−	0.391245i
$171$	1.50211e11	+	1.11913e11i	1.02736	+	0.765418i
$172$	1.16461e10			0.0773642
$173$		−	5.42785e10i		−	0.350266i	−0.984545	−	0.175133i	$-0.943965\pi$
$173$		−	5.42785e10i		−	0.350266i	0.984545	−	0.175133i	$-0.0560355\pi$
$174$	1.30090e11	+	4.31333e10i	0.815638	+	0.270437i
$175$	−3.85639e10			−0.234958
$176$			2.40110e11i			1.42183i
$177$	−3.20632e10	+	9.67026e10i	−0.184561	+	0.556636i
$178$	4.37498e11			2.44836
$179$		−	5.30518e10i		−	0.288692i	−0.989527	−	0.144346i	$-0.953892\pi$
$179$		−	5.30518e10i		−	0.288692i	0.989527	−	0.144346i	$-0.0461078\pi$
$180$	−3.11888e10	+	4.18621e10i	−0.165058	+	0.221543i
$181$	−2.22110e11			−1.14334			−0.571670	−	0.820483i	$-0.693704\pi$
$181$	−2.22110e11			−1.14334			−0.571670	+	0.820483i	$0.693704\pi$
$182$			4.25566e11i			2.13113i
$183$	−3.29463e11	−	1.09238e11i	−1.60528	−	0.532254i
$184$	−6.02461e10			−0.285654
$185$		−	8.44458e10i		−	0.389690i
$186$	3.34822e10	−	1.00982e11i	0.150401	−	0.453608i
$187$	1.80912e11			0.791149
$188$		−	6.50181e9i		−	0.0276850i
$189$	1.62377e11	+	2.32166e11i	0.673309	+	0.962698i
$190$	−1.80442e11			−0.728735
$191$			2.96902e11i			1.16801i	0.811751	+	0.584004i	$0.198515\pi$
$191$			2.96902e11i			1.16801i	−0.811751	+	0.584004i	$0.801485\pi$
$192$	3.59752e10	+	1.19281e10i	0.137879	+	0.0457157i
$193$	−1.84299e11			−0.688236			−0.344118	−	0.938926i	$-0.611822\pi$
$193$	−1.84299e11			−0.688236			−0.344118	+	0.938926i	$0.611822\pi$
$194$		−	1.43804e11i		−	0.523314i
$195$	−5.65979e10	+	1.70699e11i	−0.200737	+	0.605423i
$196$	−6.79260e10			−0.234831
$197$		−	4.05812e11i		−	1.36771i	−0.729619	−	0.683854i	$-0.760302\pi$
$197$		−	4.05812e11i		−	1.36771i	0.729619	−	0.683854i	$-0.239698\pi$
$198$	−3.57016e11	−	2.65990e11i	−1.17317	−	0.874056i
$199$	2.54202e11			0.814542			0.407271	−	0.913307i	$-0.366480\pi$
$199$	2.54202e11			0.814542			0.407271	+	0.913307i	$0.366480\pi$
$200$			3.11153e10i			0.0972352i
$201$	−2.14375e11	−	7.10792e10i	−0.653422	−	0.216652i
$202$	1.17150e11			0.348325
$203$			2.73609e11i			0.793688i
$204$	4.72463e10	−	1.42495e11i	0.133726	−	0.403318i
$205$	2.91347e11			0.804714
$206$			2.23082e11i			0.601351i
$207$	1.33413e11	−	1.79070e11i	0.351032	−	0.471162i
$208$	6.86396e11			1.76302
$209$		−	5.87639e11i		−	1.47360i
$210$	−2.59048e11	−	8.58912e10i	−0.634284	−	0.210306i
$211$	−4.47122e11			−1.06909			−0.534545	−	0.845140i	$-0.679517\pi$
$211$	−4.47122e11			−1.06909			−0.534545	+	0.845140i	$0.679517\pi$
$212$		−	3.59566e11i		−	0.839653i
$213$	8.90039e10	−	2.68436e11i	0.203007	−	0.612269i
$214$	−3.05111e11			−0.679813
$215$			2.57293e10i			0.0560061i
$216$	1.87323e11	−	1.31014e11i	0.398403	−	0.278643i
$217$	2.12389e11			0.441401
$218$			8.93251e11i			1.81422i
$219$	3.33468e11	+	1.10566e11i	0.661963	+	0.219484i
$220$	1.63768e11			0.317772
$221$		−	5.17168e11i		−	0.981002i
$222$	1.88081e11	−	5.67254e11i	0.348804	−	1.05199i
$223$	1.43897e11			0.260931			0.130466	−	0.991453i	$-0.458353\pi$
$223$	1.43897e11			0.260931			0.130466	+	0.991453i	$0.458353\pi$
$224$			7.19550e11i			1.27591i
$225$	−9.24840e10	−	6.89038e10i	−0.160381	−	0.119490i
$226$	−1.46316e12			−2.48171
$227$			4.10636e11i			0.681283i	0.940193	+	0.340642i	$0.110644\pi$
$227$			4.10636e11i			0.681283i	−0.940193	+	0.340642i	$0.889356\pi$
$228$	−4.62853e11	−	1.53466e11i	−0.751222	−	0.249079i
$229$	−7.27787e11			−1.15565			−0.577825	−	0.816160i	$-0.696099\pi$
$229$	−7.27787e11			−1.15565			−0.577825	+	0.816160i	$0.696099\pi$
$230$			2.15108e11i			0.334209i
$231$	2.79719e11	−	8.43631e11i	0.425267	−	1.28260i
$232$	2.20761e11			0.328460
$233$			5.00183e11i			0.728366i	0.931327	+	0.364183i	$0.118652\pi$
$233$			5.00183e11i			0.728366i	−0.931327	+	0.364183i	$0.881348\pi$
$234$	−7.60379e11	+	1.02059e12i	−1.08380	+	1.45470i
$235$	1.43642e10			0.0200420
$236$		−	2.65216e11i		−	0.362276i
$237$	8.27240e11	+	2.74284e11i	1.10634	+	0.366825i
$238$	7.84837e11			1.02777
$239$		−	7.08173e11i		−	0.908134i	−0.890968	−	0.454067i	$-0.849973\pi$
$239$		−	7.08173e11i		−	0.908134i	0.890968	−	0.454067i	$-0.150027\pi$
$240$	−1.38534e11	+	4.17818e11i	−0.173980	+	0.524724i
$241$	1.25267e11			0.154082			0.0770411	−	0.997028i	$-0.475453\pi$
$241$	1.25267e11			0.154082			0.0770411	+	0.997028i	$0.475453\pi$
$242$			3.40994e11i			0.410837i
$243$	−2.54100e10	+	8.46908e11i	−0.0299898	+	0.999550i
$244$	9.03583e11			1.04477
$245$		−	1.50066e11i		−	0.170001i
$246$	1.95709e12	+	6.48902e11i	2.17238	+	0.720283i
$247$	−1.67987e12			−1.82722
$248$		−	1.71366e11i		−	0.182670i
$249$	4.29642e11	−	1.29580e12i	0.448859	−	1.35376i
$250$	1.11097e11			0.113763
$251$			1.33024e12i			1.33524i	0.744500	+	0.667622i	$0.232688\pi$
$251$			1.33024e12i			1.33524i	−0.744500	+	0.667622i	$0.767312\pi$
$252$	−5.91435e11	−	4.40640e11i	−0.581975	−	0.433592i
$253$	−7.00535e11			−0.675814
$254$			6.14172e11i			0.580927i
$255$	3.14807e11	+	1.04379e11i	0.291973	+	0.0968082i
$256$	1.42019e12			1.29166
$257$		−	1.45172e11i		−	0.129485i	−0.997902	−	0.0647423i	$-0.979377\pi$
$257$		−	1.45172e11i		−	0.129485i	0.997902	−	0.0647423i	$-0.0206225\pi$
$258$	−5.73054e10	+	1.72833e11i	−0.0501299	+	0.151192i
$259$	1.19306e12			1.02368
$260$		−	4.68160e11i		−	0.394028i
$261$	−4.88869e11	+	6.56169e11i	−0.403636	+	0.541768i
$262$	−7.38498e11			−0.598195
$263$		−	1.97480e12i		−	1.56944i	−0.619851	−	0.784720i	$-0.712807\pi$
$263$		−	1.97480e12i		−	1.56944i	0.619851	−	0.784720i	$-0.287193\pi$
$264$	−6.80684e11	−	2.25691e11i	−0.530794	−	0.175993i
$265$	7.94373e11			0.607848
$266$		−	2.54931e12i		−	1.91432i
$267$	−8.22044e11	+	2.47929e12i	−0.605813	+	1.82713i
$268$	5.87944e11			0.425267
$269$		−	2.96228e11i		−	0.210313i	−0.994456	−	0.105156i	$-0.966466\pi$
$269$		−	2.96228e11i		−	0.210313i	0.994456	−	0.105156i	$-0.0335343\pi$
$270$	−4.67784e11	−	6.68837e11i	−0.326006	−	0.466124i
$271$	−5.40742e11			−0.369950			−0.184975	−	0.982743i	$-0.559220\pi$
$271$	−5.40742e11			−0.369950			−0.184975	+	0.982743i	$0.559220\pi$
$272$		−	1.26586e12i		−	0.850242i
$273$	−2.41167e12	−	7.99625e11i	−1.59039	−	0.527319i
$274$	−2.41486e12			−1.56365
$275$			3.61805e11i			0.230044i
$276$	−1.82949e11	+	5.51775e11i	−0.114231	+	0.344522i
$277$	−1.64463e12			−1.00849			−0.504243	−	0.863562i	$-0.668228\pi$
$277$	−1.64463e12			−1.00849			−0.504243	+	0.863562i	$0.668228\pi$
$278$		−	2.56835e12i		−	1.54679i
$279$	5.09351e11	+	3.79485e11i	0.301298	+	0.224478i
$280$	−4.39602e11			−0.255428
$281$			8.54442e11i			0.487698i	0.969813	+	0.243849i	$0.0784102\pi$
$281$			8.54442e11i			0.487698i	−0.969813	+	0.243849i	$0.921590\pi$
$282$	9.64893e10	+	3.19925e10i	0.0541046	+	0.0179392i
$283$	2.33223e12			1.28481			0.642405	−	0.766365i	$-0.277937\pi$
$283$	2.33223e12			1.28481			0.642405	+	0.766365i	$0.277937\pi$
$284$			7.36212e11i			0.398484i
$285$	3.39045e11	−	1.02256e12i	0.180315	−	0.543831i
$286$	3.99265e12			2.08656
$287$			4.11620e12i			2.11391i
$288$	−1.28565e12	+	1.72563e12i	−0.648875	+	0.870932i
$289$	1.06222e12			0.526898
$290$		−	7.88227e11i		−	0.384292i
$291$	8.14932e11	+	2.70203e11i	0.390532	+	0.129487i
$292$	−9.14568e11			−0.430826
$293$		−	1.17484e12i		−	0.544053i	−0.962290	−	0.272026i	$-0.912306\pi$
$293$		−	1.17484e12i		−	0.544053i	0.962290	−	0.272026i	$-0.0876938\pi$
$294$	3.34233e11	−	1.00805e12i	0.152164	−	0.458928i
$295$	5.85930e11			0.262262
$296$		−	9.62623e11i		−	0.423641i
$297$	2.17818e12	−	1.52341e12i	0.942564	−	0.659227i
$298$	6.84419e10			0.0291233
$299$			2.00260e12i			0.837990i
$300$	2.84975e11	+	9.44878e10i	0.117274	+	0.0388839i
$301$	−3.63508e11			−0.147123
$302$		−	3.08185e12i		−	1.22681i
$303$	−2.20121e11	+	6.63885e11i	−0.0861882	+	0.259944i
$304$	−4.11179e12			−1.58366
$305$			1.99624e12i			0.756335i
$306$	1.88220e12	+	1.40230e12i	0.701549	+	0.522679i
$307$	4.27396e12			1.56725			0.783626	−	0.621232i	$-0.213368\pi$
$307$	4.27396e12			1.56725			0.783626	+	0.621232i	$0.213368\pi$
$308$			2.31374e12i			0.834759i
$309$	−1.26420e12	−	4.19163e11i	−0.448768	−	0.148796i
$310$	−6.11861e11			−0.213720
$311$			2.14814e11i			0.0738347i	0.999318	+	0.0369174i	$0.0117538\pi$
$311$			2.14814e11i			0.0738347i	−0.999318	+	0.0369174i	$0.988246\pi$
$312$	−6.45177e11	+	1.94585e12i	−0.218226	+	0.658169i
$313$	−5.53675e12			−1.84303			−0.921517	−	0.388339i	$-0.873049\pi$
$313$	−5.53675e12			−1.84303			−0.921517	+	0.388339i	$0.873049\pi$
$314$			3.84260e12i			1.25886i
$315$	9.73485e11	−	1.30663e12i	0.313889	−	0.421308i
$316$	−2.26879e12			−0.720043
$317$		−	2.95252e12i		−	0.922352i	−0.887309	−	0.461176i	$-0.847428\pi$
$317$		−	2.95252e12i		−	0.922352i	0.887309	−	0.461176i	$-0.152572\pi$
$318$	5.33610e12	+	1.76926e12i	1.64092	+	0.544073i
$319$	2.56699e12			0.777089
$320$		−	2.17977e11i		−	0.0649622i
$321$	5.73294e11	−	1.72905e12i	0.168210	−	0.507322i
$322$	−3.03909e12			−0.877938
$323$			3.09804e12i			0.881201i
$324$	−6.31068e11	−	2.11349e12i	−0.176747	−	0.591935i
$325$	1.03428e12			0.285248
$326$			9.62425e11i			0.261384i
$327$	−5.06202e12	−	1.67839e12i	−1.35390	−	0.448904i
$328$	3.32116e12			0.874823
$329$			2.02939e11i			0.0526485i
$330$	−8.05828e11	+	2.43038e12i	−0.205908	+	0.621018i
$331$	−3.72688e12			−0.938006			−0.469003	−	0.883197i	$-0.655387\pi$
$331$	−3.72688e12			−0.938006			−0.469003	+	0.883197i	$0.655387\pi$
$332$			3.55386e12i			0.881069i
$333$	2.86121e12	+	2.13170e12i	0.698760	+	0.520601i
$334$	−9.33770e11			−0.224651
$335$			1.29892e12i			0.307863i
$336$	−5.90301e12	−	1.95723e12i	−1.37840	−	0.457031i
$337$	3.46582e12			0.797363			0.398681	−	0.917090i	$-0.369468\pi$
$337$	3.46582e12			0.797363			0.398681	+	0.917090i	$0.369468\pi$
$338$		−	5.80268e12i		−	1.31536i
$339$	2.74924e12	−	8.29170e12i	0.614064	−	1.85202i
$340$	−8.63389e11			−0.190025
$341$		−	1.99263e12i		−	0.432169i
$342$	4.55498e12	−	6.11377e12i	0.973544	−	1.30671i
$343$	−3.45724e12			−0.728213
$344$			2.93296e11i			0.0608855i
$345$	−1.21901e12	−	4.04181e11i	−0.249409	−	0.0826953i
$346$	−2.20920e12			−0.445507
$347$		−	3.62931e12i		−	0.721401i	−0.932682	−	0.360701i	$-0.882538\pi$
$347$		−	3.62931e12i		−	0.721401i	0.932682	−	0.360701i	$-0.117462\pi$
$348$	6.70386e11	−	2.02188e12i	0.131350	−	0.396151i
$349$	6.29091e12			1.21503			0.607514	−	0.794309i	$-0.292167\pi$
$349$	6.29091e12			1.21503			0.607514	+	0.794309i	$0.292167\pi$
$350$			1.56960e12i			0.298846i
$351$	−4.35494e12	−	6.22670e12i	−0.817423	−	1.16875i
$352$	6.75079e12			1.24923
$353$			7.17912e12i			1.30978i	0.755725	+	0.654889i	$0.227285\pi$
$353$			7.17912e12i			1.30978i	−0.755725	+	0.654889i	$0.772715\pi$
$354$	3.93591e12	+	1.30501e12i	0.707992	+	0.234745i
$355$	−1.62648e12			−0.288474
$356$		−	6.79968e12i		−	1.18916i
$357$	−1.47468e12	+	4.44764e12i	−0.254307	+	0.766989i
$358$	−2.15927e12			−0.367191
$359$		−	4.64354e12i		−	0.778713i	−0.921087	−	0.389356i	$-0.872697\pi$
$359$		−	4.64354e12i		−	0.778713i	0.921087	−	0.389356i	$-0.127303\pi$
$360$	−1.05425e12	−	7.85456e11i	−0.174354	−	0.129900i
$361$	3.93203e12			0.641328
$362$			9.04015e12i			1.45423i
$363$	−1.93240e12	−	6.40716e11i	−0.306594	−	0.101656i
$364$	6.61424e12			1.03508
$365$		−	2.02051e12i		−	0.311887i
$366$	−4.44612e12	+	1.34095e13i	−0.676981	+	2.04177i
$367$	−4.37186e12			−0.656653			−0.328326	−	0.944564i	$-0.606485\pi$
$367$	−4.37186e12			−0.656653			−0.328326	+	0.944564i	$0.606485\pi$
$368$			4.90174e12i			0.726292i
$369$	−7.35461e12	+	9.87148e12i	−1.07505	+	1.44295i
$370$	−3.43704e12			−0.495651
$371$			1.12230e13i			1.59676i
$372$	−1.56949e12	−	5.20387e11i	−0.220315	−	0.0730486i
$373$	−5.71591e10			−0.00791664			−0.00395832	−	0.999992i	$-0.501260\pi$
$373$	−5.71591e10			−0.00791664			−0.00395832	+	0.999992i	$0.501260\pi$
$374$		−	7.36332e12i		−	1.00627i
$375$	−2.08747e11	+	6.29582e11i	−0.0281491	+	0.0848977i
$376$	1.63741e11			0.0217881
$377$		−	7.33819e12i		−	0.963568i
$378$	9.44944e12	−	6.60892e12i	1.22447	−	0.856390i
$379$	−1.37212e12			−0.175468			−0.0877339	−	0.996144i	$-0.527963\pi$
$379$	−1.37212e12			−0.175468			−0.0877339	+	0.996144i	$0.527963\pi$
$380$			2.80447e12i			0.353942i
$381$	−3.48049e12	−	1.15401e12i	−0.433527	−	0.143742i
$382$	1.20842e13			1.48560
$383$		−	9.41244e12i		−	1.14211i	−0.820912	−	0.571055i	$-0.806534\pi$
$383$		−	9.41244e12i		−	1.14211i	0.820912	−	0.571055i	$-0.193466\pi$
$384$	−2.36839e12	+	7.14308e12i	−0.283660	+	0.855518i
$385$	−5.11164e12			−0.604306
$386$			7.50120e12i			0.875375i
$387$	−8.71764e11	−	6.49495e11i	−0.100426	−	0.0748206i
$388$	−2.23503e12			−0.254170
$389$			3.70707e12i			0.416181i	0.978110	+	0.208091i	$0.0667249\pi$
$389$			3.70707e12i			0.416181i	−0.978110	+	0.208091i	$0.933275\pi$
$390$	6.94767e12	+	2.30360e12i	0.770045	+	0.255320i
$391$	3.69324e12			0.404132
$392$		−	1.71065e12i		−	0.184812i
$393$	1.38761e12	−	4.18504e12i	0.148015	−	0.446413i
$394$	−1.65170e13			−1.73960
$395$		−	5.01232e12i		−	0.521259i
$396$	−4.13407e12	+	5.54882e12i	−0.424523	+	0.569803i
$397$	7.96834e12			0.808008			0.404004	−	0.914757i	$-0.367618\pi$
$397$	7.96834e12			0.808008			0.404004	+	0.914757i	$0.367618\pi$
$398$		−	1.03463e13i		−	1.03603i
$399$	1.44469e13	+	4.79008e12i	1.42860	+	0.473672i
$400$	2.53160e12			0.247227
$401$			1.29017e13i			1.24430i	0.782897	+	0.622151i	$0.213741\pi$
$401$			1.29017e13i			1.24430i	−0.782897	+	0.622151i	$0.786259\pi$
$402$	−2.89301e12	+	8.72531e12i	−0.275562	+	0.831095i
$403$	−5.69627e12			−0.535877
$404$		−	1.82077e12i		−	0.169180i
$405$	4.66923e12	−	1.39419e12i	0.428519	−	0.127952i
$406$	1.11362e13			1.00950
$407$		−	1.11933e13i		−	1.00227i
$408$	3.58858e12	+	1.18985e12i	0.317411	+	0.105242i
$409$	1.74210e12			0.152215			0.0761073	−	0.997100i	$-0.475751\pi$
$409$	1.74210e12			0.152215			0.0761073	+	0.997100i	$0.475751\pi$
$410$		−	1.18582e13i		−	1.02353i
$411$	4.53745e12	−	1.36849e13i	0.386903	−	1.16690i
$412$	3.46718e12			0.292072
$413$			8.27811e12i			0.688939i
$414$	−7.28834e12	−	5.43007e12i	−0.599276	−	0.446482i
$415$	−7.85137e12			−0.637830
$416$		−	1.92983e13i		−	1.54901i
$417$	1.45548e13	+	4.82585e12i	1.15432	+	0.382731i
$418$	−2.39176e13			−1.87429
$419$		−	1.54669e13i		−	1.19766i	−0.800875	−	0.598831i	$-0.795632\pi$
$419$		−	1.54669e13i		−	1.19766i	0.800875	−	0.598831i	$-0.204368\pi$
$420$	−1.33494e12	+	4.02618e12i	−0.102144	+	0.308068i
$421$	−6.44816e12			−0.487557			−0.243778	−	0.969831i	$-0.578387\pi$
$421$	−6.44816e12			−0.487557			−0.243778	+	0.969831i	$0.578387\pi$
$422$			1.81984e13i			1.35979i
$423$	−3.62600e11	+	4.86689e11i	−0.0267748	+	0.0359376i
$424$	9.05531e12			0.660806
$425$		−	1.90744e12i		−	0.137565i
$426$	−1.09257e13	−	3.62256e12i	−0.778753	−	0.258207i
$427$	−2.82033e13			−1.98683
$428$			4.74210e12i			0.330181i
$429$	−7.50205e12	+	2.26262e13i	−0.516290	+	1.55713i
$430$	1.04721e12			0.0712348
$431$		−	8.43322e11i		−	0.0567031i	−0.999598	−	0.0283516i	$-0.990974\pi$
$431$		−	8.43322e11i		−	0.0567031i	0.999598	−	0.0283516i	$-0.00902579\pi$
$432$	−1.06595e13	−	1.52410e13i	−0.708466	−	1.01297i
$433$	−1.62030e12			−0.106453			−0.0532264	−	0.998582i	$-0.516951\pi$
$433$	−1.62030e12			−0.106453			−0.0532264	+	0.998582i	$0.516951\pi$
$434$		−	8.64448e12i		−	0.561423i
$435$	4.46686e12	+	1.48105e12i	0.286784	+	0.0950877i
$436$	1.38831e13			0.881157
$437$		−	1.19964e13i		−	0.752738i
$438$	4.50018e12	−	1.35725e13i	0.279164	−	0.841958i
$439$	2.89110e12			0.177313			0.0886564	−	0.996062i	$-0.471743\pi$
$439$	2.89110e12			0.177313			0.0886564	+	0.996062i	$0.471743\pi$
$440$			4.12433e12i			0.250086i
$441$	5.08456e12	+	3.78817e12i	0.304832	+	0.227110i
$442$	−2.10493e13			−1.24775
$443$			1.20898e13i			0.708602i	0.935132	+	0.354301i	$0.115281\pi$
$443$			1.20898e13i			0.708602i	−0.935132	+	0.354301i	$0.884719\pi$
$444$	−8.81637e12	−	2.92320e12i	−0.510946	−	0.169412i
$445$	1.50222e13			0.860863
$446$		−	5.85676e12i		−	0.331882i
$447$	−1.28600e11	+	3.87858e11i	−0.00720615	+	0.0217337i
$448$	3.07962e12			0.170650
$449$			8.99212e12i			0.492754i	0.969174	+	0.246377i	$0.0792401\pi$
$449$			8.99212e12i			0.492754i	−0.969174	+	0.246377i	$0.920760\pi$
$450$	−2.80447e12	+	3.76421e12i	−0.151981	+	0.203991i
$451$	3.86181e13			2.06970
$452$			2.27408e13i			1.20535i
$453$	1.74647e13	+	5.79069e12i	0.915527	+	0.303557i
$454$	1.67134e13			0.866532
$455$			1.46125e13i			0.749322i
$456$	3.86487e12	−	1.16565e13i	0.196025	−	0.591211i
$457$	8.53120e12			0.427986			0.213993	−	0.976835i	$-0.431353\pi$
$457$	8.53120e12			0.427986			0.213993	+	0.976835i	$0.431353\pi$
$458$			2.96218e13i			1.46989i
$459$	−1.14834e13	+	8.03147e12i	−0.563647	+	0.394213i
$460$	3.34326e12			0.162323
$461$			3.91720e12i			0.188136i	0.995566	+	0.0940679i	$0.0299871\pi$
$461$			3.91720e12i			0.188136i	−0.995566	+	0.0940679i	$0.970013\pi$
$462$	−3.43368e13	−	1.13849e13i	−1.63136	−	0.540902i
$463$	2.72142e13			1.27906			0.639528	−	0.768767i	$-0.279130\pi$
$463$	2.72142e13			1.27906			0.639528	+	0.768767i	$0.279130\pi$
$464$		−	1.79616e13i		−	0.835131i
$465$	1.14967e12	−	3.46740e12i	0.0528819	−	0.159492i
$466$	2.03580e13			0.926417
$467$			1.54618e13i			0.696108i	0.937474	+	0.348054i	$0.113157\pi$
$467$			1.54618e13i			0.696108i	−0.937474	+	0.348054i	$0.886843\pi$
$468$	1.58623e13	+	1.18180e13i	0.706539	+	0.526397i
$469$	−1.83513e13			−0.808729
$470$		−	5.84638e11i		−	0.0254916i
$471$	−2.17759e13	−	7.22011e12i	−0.939443	−	0.311486i
$472$	6.67919e12			0.285111
$473$			3.41042e12i			0.144046i
$474$	1.11637e13	−	3.36696e13i	0.466568	−	1.40717i
$475$	−6.19578e12			−0.256229
$476$		−	1.21981e13i		−	0.499180i
$477$	−2.00527e13	+	2.69151e13i	−0.812047	+	1.08994i
$478$	−2.88235e13			−1.15507
$479$			1.92741e13i			0.764359i	0.924088	+	0.382179i	$0.124826\pi$
$479$			1.92741e13i			0.764359i	−0.924088	+	0.382179i	$0.875174\pi$
$480$	1.17471e13	+	3.89494e12i	0.461027	+	0.152860i
$481$	−3.19980e13			−1.24279
$482$		−	5.09852e12i		−	0.195979i
$483$	5.71034e12	−	1.72224e13i	0.217233	−	0.655176i
$484$	5.29979e12			0.199541
$485$		−	4.93775e12i		−	0.184001i
$486$	3.44701e13	+	1.03422e12i	1.27134	+	0.0381444i
$487$	−1.99147e13			−0.726993			−0.363496	−	0.931596i	$-0.618417\pi$
$487$	−1.99147e13			−0.726993			−0.363496	+	0.931596i	$0.618417\pi$
$488$			2.27558e13i			0.822229i
$489$	−5.45403e12	−	1.80836e12i	−0.195062	−	0.0646758i
$490$	−6.10785e12			−0.216226
$491$		−	3.18944e13i		−	1.11765i	−0.829284	−	0.558827i	$-0.811252\pi$
$491$		−	3.18944e13i		−	1.11765i	0.829284	−	0.558827i	$-0.188748\pi$
$492$	1.00854e13	−	3.04175e13i	0.349837	−	1.05511i
$493$	−1.35332e13			−0.464694
$494$			6.83726e13i			2.32406i
$495$	−1.22587e13	−	9.13320e12i	−0.412496	−	0.307324i
$496$	−1.39427e13			−0.464449
$497$		−	2.29791e13i		−	0.757795i
$498$	−5.27406e13	−	1.74869e13i	−1.72186	−	0.570909i
$499$	−4.45141e13			−1.43878			−0.719390	−	0.694606i	$-0.755579\pi$
$499$	−4.45141e13			−1.43878			−0.719390	+	0.694606i	$0.755579\pi$
$500$		−	1.72669e12i		−	0.0552541i
$501$	1.75452e12	−	5.29164e12i	0.0555867	−	0.167649i
$502$	5.41423e13			1.69831
$503$		−	4.51648e13i		−	1.40268i	−0.712825	−	0.701342i	$-0.752585\pi$
$503$		−	4.51648e13i		−	1.40268i	0.712825	−	0.701342i	$-0.247415\pi$
$504$	1.10971e13	−	1.48947e13i	0.341236	−	0.458013i
$505$	4.02254e12			0.122474
$506$			2.85126e13i			0.859576i
$507$	3.28836e13	+	1.09030e13i	0.981611	+	0.325468i
$508$	9.54559e12			0.282153
$509$		−	3.71099e13i		−	1.08618i	−0.839676	−	0.543088i	$-0.817255\pi$
$509$		−	3.71099e13i		−	1.08618i	0.839676	−	0.543088i	$-0.182745\pi$
$510$	4.24835e12	−	1.28130e13i	0.123131	−	0.371365i
$511$	2.85461e13			0.819300
$512$		−	2.60912e13i		−	0.741556i
$513$	2.60879e13	+	3.73005e13i	0.734263	+	1.04985i
$514$	−5.90869e12			−0.164693
$515$			7.65988e12i			0.211439i
$516$	2.68621e12	+	8.90652e11i	0.0734330	+	0.0243478i
$517$	1.90397e12			0.0515474
$518$		−	4.85591e13i		−	1.30203i
$519$	4.15101e12	−	1.25195e13i	0.110234	−	0.332467i
$520$	1.17901e13			0.310100
$521$			4.37403e13i			1.13944i	0.821837	+	0.569722i	$0.192949\pi$
$521$			4.37403e13i			1.13944i	−0.821837	+	0.569722i	$0.807051\pi$
$522$	2.67069e13	+	1.98976e13i	0.689081	+	0.513390i
$523$	1.38360e13			0.353592			0.176796	−	0.984247i	$-0.443427\pi$
$523$	1.38360e13			0.353592			0.176796	+	0.984247i	$0.443427\pi$
$524$			1.14779e13i			0.290540i
$525$	−8.89484e12	−	2.94922e12i	−0.223019	−	0.0739452i
$526$	−8.03767e13			−1.99619
$527$			1.05052e13i			0.258434i
$528$	−1.83627e13	+	5.53818e13i	−0.447472	+	1.34958i
$529$	2.71254e13			0.654783
$530$		−	3.23319e13i		−	0.773130i
$531$	−1.47909e13	+	1.98526e13i	−0.350366	+	0.470267i
$532$	−3.96220e13			−0.929775
$533$		−	1.10397e14i		−	2.56637i
$534$	1.00910e14	+	3.34582e13i	2.32395	+	0.770541i
$535$	−1.04765e13			−0.239027
$536$			1.48068e13i			0.334685i
$537$	4.05719e12	−	1.22365e13i	0.0908561	−	0.274022i
$538$	−1.20568e13			−0.267499
$539$		−	1.98912e13i		−	0.437237i
$540$	−1.03952e13	+	7.27039e12i	−0.226394	+	0.158339i
$541$	2.12263e13			0.458025			0.229012	−	0.973424i	$-0.426450\pi$
$541$	2.12263e13			0.458025			0.229012	+	0.973424i	$0.426450\pi$
$542$			2.20088e13i			0.470544i
$543$	−5.12302e13	−	1.69861e13i	−1.08524	−	0.359828i
$544$	−3.55903e13			−0.747029
$545$			3.06712e13i			0.637895i
$546$	−3.25457e13	+	9.81578e13i	−0.670703	+	2.02284i
$547$	4.88587e13			0.997713			0.498857	−	0.866685i	$-0.333753\pi$
$547$	4.88587e13			0.997713			0.498857	+	0.866685i	$0.333753\pi$
$548$			3.75323e13i			0.759456i
$549$	−6.76371e13	−	5.03921e13i	−1.35620	−	1.01042i
$550$	1.47259e13			0.292596
$551$			4.39587e13i			0.865540i
$552$	−1.38959e13	−	4.60739e12i	−0.271138	−	0.0898999i
$553$	7.08149e13			1.36930
$554$			6.69384e13i			1.28270i
$555$	6.45809e12	−	1.94776e13i	0.122642	−	0.369888i
$556$	−3.99178e13			−0.751265
$557$			1.80997e13i			0.337595i	0.985651	+	0.168797i	$0.0539883\pi$
$557$			1.80997e13i			0.337595i	−0.985651	+	0.168797i	$0.946012\pi$
$558$	1.54455e13	−	2.07312e13i	0.285516	−	0.383225i
$559$	9.74927e12			0.178613
$560$			3.57669e13i			0.649442i
$561$	4.17276e13	+	1.38354e13i	0.750947	+	0.248988i
$562$	3.47768e13			0.620309
$563$			4.11767e13i			0.727963i	0.931406	+	0.363981i	$0.118583\pi$
$563$			4.11767e13i			0.727963i	−0.931406	+	0.363981i	$0.881417\pi$
$564$	4.97234e11	−	1.49966e12i	0.00871294	−	0.0262782i
$565$	−5.02401e13			−0.872587
$566$		−	9.49245e13i		−	1.63417i
$567$	1.96973e13	+	6.59676e13i	0.336118	+	1.12568i
$568$	−1.85407e13			−0.313606
$569$		−	1.66251e13i		−	0.278743i	−0.990240	−	0.139371i	$-0.955492\pi$
$569$		−	1.66251e13i		−	0.278743i	0.990240	−	0.139371i	$-0.0445082\pi$
$570$	−4.16193e13	−	1.37995e13i	−0.691705	−	0.229345i
$571$	−5.15118e13			−0.848645			−0.424323	−	0.905511i	$-0.639488\pi$
$571$	−5.15118e13			−0.848645			−0.424323	+	0.905511i	$0.639488\pi$
$572$		−	6.20545e13i		−	1.01343i
$573$	−2.27059e13	+	6.84810e13i	−0.367591	+	1.10866i
$574$	1.67534e14			2.68871
$575$			7.38610e12i			0.117510i
$576$	7.38554e12	+	5.50249e12i	0.116485	+	0.0867854i
$577$	1.98553e13			0.310455			0.155227	−	0.987879i	$-0.450389\pi$
$577$	1.98553e13			0.310455			0.155227	+	0.987879i	$0.450389\pi$
$578$		−	4.32338e13i		−	0.670168i
$579$	−4.25090e13	−	1.40945e13i	−0.653263	−	0.216599i
$580$	−1.22508e13			−0.186648
$581$		−	1.10926e14i		−	1.67552i
$582$	1.09976e13	−	3.31687e13i	0.164696	−	0.496722i
$583$	1.05294e14			1.56337
$584$		−	2.30324e13i		−	0.339059i
$585$	−2.61089e13	+	3.50438e13i	−0.381073	+	0.511484i
$586$	−4.78174e13			−0.691987
$587$		−	4.26345e13i		−	0.611745i	−0.952072	−	0.305873i	$-0.901052\pi$
$587$		−	4.26345e13i		−	0.611745i	0.952072	−	0.305873i	$-0.0989481\pi$
$588$	−1.56673e13	−	5.19472e12i	−0.222898	−	0.0739053i
$589$	3.41230e13			0.481360
$590$		−	2.38480e13i		−	0.333574i
$591$	3.10349e13	−	9.36013e13i	0.430441	−	1.29821i
$592$	−7.83209e13			−1.07713
$593$		−	4.39739e13i		−	0.599683i	−0.953989	−	0.299841i	$-0.903066\pi$
$593$		−	4.39739e13i		−	0.599683i	0.953989	−	0.299841i	$-0.0969337\pi$
$594$	−6.20047e13	−	8.86543e13i	−0.838479	−	1.19886i
$595$	2.69487e13			0.361371
$596$		−	1.06374e12i		−	0.0141450i
$597$	5.86322e13	+	1.94404e13i	0.773152	+	0.256350i
$598$	8.15083e13			1.06585
$599$			8.56316e13i			1.11045i	0.831699	+	0.555226i	$0.187368\pi$
$599$			8.56316e13i			1.11045i	−0.831699	+	0.555226i	$0.812632\pi$
$600$	−2.37958e12	+	7.17680e12i	−0.0306015	+	0.0922943i
$601$	−1.19046e14			−1.51825			−0.759126	−	0.650944i	$-0.774373\pi$
$601$	−1.19046e14			−1.51825			−0.759126	+	0.650944i	$0.774373\pi$
$602$			1.47952e13i			0.187128i
$603$	−4.40102e13	−	3.27891e13i	−0.552035	−	0.411286i
$604$	−4.78988e13			−0.595854
$605$			1.17086e13i			0.144453i
$606$	2.70209e13	+	8.95918e12i	0.330626	+	0.109624i
$607$	−1.02499e14			−1.24388			−0.621939	−	0.783065i	$-0.713655\pi$
$607$	−1.02499e14			−1.24388			−0.621939	+	0.783065i	$0.713655\pi$
$608$			1.15605e14i			1.39142i
$609$	−2.09246e13	+	6.31085e13i	−0.249787	+	0.753358i
$610$	8.12495e13			0.961992
$611$		−	5.44283e12i		−	0.0639173i
$612$	2.17949e13	−	2.92535e13i	0.253862	−	0.340738i
$613$	−5.79613e13			−0.669631			−0.334816	−	0.942284i	$-0.608674\pi$
$613$	−5.79613e13			−0.669631			−0.334816	+	0.942284i	$0.608674\pi$
$614$		−	1.73955e14i		−	1.99341i
$615$	6.71999e13	+	2.22811e13i	0.763823	+	0.253257i
$616$	−5.82692e13			−0.656954
$617$			4.22216e12i			0.0472182i	0.999721	+	0.0236091i	$0.00751570\pi$
$617$			4.22216e12i			0.0472182i	−0.999721	+	0.0236091i	$0.992484\pi$
$618$	−1.70604e13	+	5.14542e13i	−0.189255	+	0.570793i
$619$	−1.28881e14			−1.41820			−0.709098	−	0.705110i	$-0.750897\pi$
$619$	−1.28881e14			−1.41820			−0.709098	+	0.705110i	$0.750897\pi$
$620$			9.50967e12i			0.103802i
$621$	4.44666e13	−	3.10998e13i	0.481477	−	0.336744i
$622$	8.74318e12			0.0939113
$623$			2.12236e14i			2.26141i
$624$	1.58319e14	+	5.24929e13i	1.67344	+	0.554853i
$625$	3.81470e12			0.0400000
$626$			2.25352e14i			2.34418i
$627$	4.49403e13	−	1.35540e14i	0.463766	−	1.39872i
$628$	5.97224e13			0.611419
$629$			5.90112e13i			0.599351i
$630$	−5.31813e13	−	3.96220e13i	−0.535866	−	0.399239i
$631$	1.03893e14			1.03858			0.519288	−	0.854599i	$-0.326197\pi$
$631$	1.03893e14			1.03858			0.519288	+	0.854599i	$0.326197\pi$
$632$		−	5.71370e13i		−	0.566672i
$633$	−1.03130e14	−	3.41942e13i	−1.01476	−	0.336460i
$634$	−1.20171e14			−1.17315
$635$			2.10886e13i			0.204258i
$636$	2.74983e13	−	8.29348e13i	0.264253	−	0.796987i
$637$	−5.68625e13			−0.542162
$638$		−	1.04479e14i		−	0.988388i
$639$	4.10579e13	−	5.51086e13i	0.385383	−	0.517268i
$640$	4.32806e13			0.403082
$641$			2.02512e13i			0.187138i	0.995613	+	0.0935689i	$0.0298275\pi$
$641$			2.02512e13i			0.187138i	−0.995613	+	0.0935689i	$0.970172\pi$
$642$	−7.03745e13	−	2.33337e13i	−0.645268	−	0.213948i
$643$	−5.67698e13			−0.516491			−0.258245	−	0.966079i	$-0.583144\pi$
$643$	−5.67698e13			−0.516491			−0.258245	+	0.966079i	$0.583144\pi$
$644$			4.72341e13i			0.426409i
$645$	−1.96768e12	+	5.93451e12i	−0.0176261	+	0.0531602i
$646$	1.26094e14			1.12081
$647$			1.87106e14i			1.65031i	0.564904	+	0.825156i	$0.308913\pi$
$647$			1.87106e14i			1.65031i	−0.564904	+	0.825156i	$0.691087\pi$
$648$	5.32259e13	−	1.58928e13i	0.465852	−	0.139099i
$649$	7.76650e13			0.674530
$650$		−	4.20966e13i		−	0.362810i
$651$	4.89879e13	+	1.62427e13i	0.418971	+	0.138916i
$652$	1.49582e13			0.126953
$653$			1.71948e13i			0.144821i	0.997375	+	0.0724103i	$0.0230691\pi$
$653$			1.71948e13i			0.144821i	−0.997375	+	0.0724103i	$0.976931\pi$
$654$	−6.83124e13	+	2.06030e14i	−0.570966	+	1.72204i
$655$	−2.53576e13			−0.210330
$656$		−	2.70216e14i		−	2.22429i
$657$	6.84594e13	+	5.10047e13i	0.559250	+	0.416661i
$658$	8.25986e12			0.0669643
$659$			1.26487e14i			1.01770i	0.860856	+	0.508848i	$0.169929\pi$
$659$			1.26487e14i			1.01770i	−0.860856	+	0.508848i	$0.830071\pi$
$660$	3.77734e13	+	1.25243e13i	0.301625	+	0.100008i
$661$	1.52484e14			1.20842			0.604209	−	0.796826i	$-0.293489\pi$
$661$	1.52484e14			1.20842			0.604209	+	0.796826i	$0.293489\pi$
$662$			1.51688e14i			1.19306i
$663$	3.95510e13	−	1.19286e14i	0.308738	−	0.931153i
$664$	−8.95002e13			−0.693400
$665$		−	8.75349e13i		−	0.673090i
$666$	8.67628e13	−	1.16455e14i	0.662159	−	0.888761i
$667$	5.24040e13			0.396950
$668$			1.45128e13i			0.109111i
$669$	3.31901e13	+	1.10047e13i	0.247672	+	0.0821194i
$670$	5.28675e13			0.391575
$671$			2.64602e14i			1.94527i
$672$	−5.50284e13	+	1.65966e14i	−0.401551	+	1.21108i
$673$	6.82057e13			0.494021			0.247011	−	0.969013i	$-0.420552\pi$
$673$	6.82057e13			0.494021			0.247011	+	0.969013i	$0.420552\pi$
$674$		−	1.41063e14i		−	1.01417i
$675$	−1.60621e13	−	2.29656e13i	−0.114626	−	0.163893i
$676$	−9.01865e13			−0.638863
$677$		−	1.57815e14i		−	1.10970i	−0.831951	−	0.554849i	$-0.812776\pi$
$677$		−	1.57815e14i		−	1.10970i	0.831951	−	0.554849i	$-0.187224\pi$
$678$	−3.37482e14	−	1.11897e14i	−2.35560	−	0.781035i
$679$	6.97613e13			0.483354
$680$		−	2.17435e13i		−	0.149550i
$681$	−3.14039e13	+	9.47141e13i	−0.214411	+	0.646664i
$682$	−8.11022e13			−0.549681
$683$			6.87530e13i			0.462581i	0.972885	+	0.231291i	$0.0742948\pi$
$683$			6.87530e13i			0.462581i	−0.972885	+	0.231291i	$0.925705\pi$
$684$	−9.50215e13	−	7.07944e13i	−0.634660	−	0.472844i
$685$	−8.29183e13			−0.549791
$686$			1.40714e14i			0.926223i
$687$	−1.67865e14	−	5.56583e13i	−1.09693	−	0.363703i
$688$	2.38631e13			0.154805
$689$		−	3.01002e14i		−	1.93853i
$690$	−1.64507e13	+	4.96152e13i	−0.105181	+	0.317226i
$691$	−8.09259e13			−0.513685			−0.256843	−	0.966453i	$-0.582682\pi$
$691$	−8.09259e13			−0.513685			−0.256843	+	0.966453i	$0.582682\pi$
$692$			3.43358e13i			0.216380i
$693$	1.29035e14	−	1.73194e14i	0.807314	−	1.08359i
$694$	−1.47717e14			−0.917558
$695$		−	8.81886e13i		−	0.543862i
$696$	5.09191e13	+	1.68830e13i	0.311770	+	0.103372i
$697$	−2.03595e14			−1.23767
$698$		−	2.56048e14i		−	1.54541i
$699$	−3.82521e13	+	1.15368e14i	−0.229229	+	0.691354i
$700$	2.43950e13			0.145148
$701$		−	2.76968e14i		−	1.63621i	−0.575066	−	0.818107i	$-0.695024\pi$
$701$		−	2.76968e14i		−	1.63621i	0.575066	−	0.818107i	$-0.304976\pi$
$702$	−2.53434e14	+	1.77251e14i	−1.48655	+	1.03969i
$703$	1.91681e14			1.11635
$704$		−	2.88928e13i		−	0.167081i
$705$	3.31312e12	+	1.09851e12i	0.0190236	+	0.00630755i
$706$	2.92199e14			1.66592
$707$			5.68311e13i			0.321728i
$708$	2.02827e13	−	6.11727e13i	0.114014	−	0.343868i
$709$	2.95688e13			0.165045			0.0825225	−	0.996589i	$-0.473702\pi$
$709$	2.95688e13			0.165045			0.0825225	+	0.996589i	$0.473702\pi$
$710$			6.61996e13i			0.366913i
$711$	1.69828e14	+	1.26528e14i	0.934679	+	0.696369i
$712$	1.71243e14			0.935863
$713$		−	4.06786e13i		−	0.220759i
$714$	1.81024e14	+	6.00213e13i	0.975542	+	0.323455i
$715$	1.37094e14			0.733650
$716$			3.35598e13i			0.178342i
$717$	5.41583e13	−	1.63342e14i	0.285805	−	0.861988i
$718$	−1.88998e14			−0.990454
$719$		−	6.92492e13i		−	0.360388i	−0.983631	−	0.180194i	$-0.942327\pi$
$719$		−	6.92492e13i		−	0.360388i	0.983631	−	0.180194i	$-0.0576725\pi$
$720$	−6.39063e13	+	8.57761e13i	−0.330279	+	0.443306i
$721$	−1.08220e14			−0.555432
$722$		−	1.60038e14i		−	0.815713i
$723$	2.88932e13	+	9.57996e12i	0.146253	+	0.0484922i
$724$	1.40504e14			0.706310
$725$		−	2.70651e13i		−	0.135120i
$726$	−2.60779e13	+	7.86509e13i	−0.129297	+	0.389961i
$727$	−1.70669e14			−0.840392			−0.420196	−	0.907433i	$-0.638039\pi$
$727$	−1.70669e14			−0.840392			−0.420196	+	0.907433i	$0.638039\pi$
$728$			1.66573e14i			0.814604i
$729$	−7.06291e13	+	1.93398e14i	−0.343041	+	0.939320i
$730$	−8.22373e13			−0.396693
$731$		−	1.79798e13i		−	0.0861386i
$732$	2.08413e14	+	6.91026e13i	0.991677	+	0.328805i
$733$	−2.36538e14			−1.11784			−0.558922	−	0.829220i	$-0.688785\pi$
$733$	−2.36538e14			−1.11784			−0.558922	+	0.829220i	$0.688785\pi$
$734$			1.77940e14i			0.835204i
$735$	1.14765e13	−	3.46130e13i	0.0535021	−	0.161362i
$736$	1.37815e14			0.638126
$737$			1.72171e14i			0.791815i
$738$	4.01781e14	+	2.99341e14i	1.83530	+	1.36737i
$739$	2.15365e14			0.977131			0.488565	−	0.872527i	$-0.337520\pi$
$739$	2.15365e14			0.977131			0.488565	+	0.872527i	$0.337520\pi$
$740$			5.34192e13i			0.240735i
$741$	−3.87465e14	−	1.28470e14i	−1.73437	−	0.575056i
$742$	4.56791e14			2.03094
$743$			1.47180e14i			0.649988i	0.945716	+	0.324994i	$0.105362\pi$
$743$			1.47180e14i			0.649988i	−0.945716	+	0.324994i	$0.894638\pi$
$744$	1.31054e13	−	3.95259e13i	0.0574891	−	0.173387i
$745$	2.35006e12			0.0102400
$746$			2.32644e12i			0.0100693i
$747$	1.98196e14	−	2.66022e14i	0.852101	−	1.14371i
$748$	−1.14442e14			−0.488740
$749$		−	1.48014e14i		−	0.627903i
$750$	2.56247e13	+	8.49626e12i	0.107982	+	0.0358032i
$751$	−1.31605e14			−0.550900			−0.275450	−	0.961315i	$-0.588827\pi$
$751$	−1.31605e14			−0.550900			−0.275450	+	0.961315i	$0.588827\pi$
$752$		−	1.33223e13i		−	0.0553976i
$753$	−1.01732e14	+	3.06822e14i	−0.420224	+	1.26740i
$754$	−2.98673e14			−1.22557
$755$		−	1.05820e14i		−	0.431355i
$756$	−1.02717e14	−	1.46865e14i	−0.415943	−	0.594716i
$757$	−2.21460e14			−0.890875			−0.445437	−	0.895313i	$-0.646952\pi$
$757$	−2.21460e14			−0.890875			−0.445437	+	0.895313i	$0.646952\pi$
$758$			5.58471e13i			0.223180i
$759$	−1.61580e14	−	5.35742e13i	−0.641473	−	0.212690i
$760$	−7.06276e13			−0.278552
$761$			1.56272e14i			0.612290i	0.951985	+	0.306145i	$0.0990392\pi$
$761$			1.56272e14i			0.612290i	−0.951985	+	0.306145i	$0.900961\pi$
$762$	−4.69695e13	+	1.41660e14i	−0.182827	+	0.551408i
$763$	−4.33328e14			−1.67569
$764$		−	1.87816e14i		−	0.721548i
$765$	6.46284e13	+	4.81504e13i	0.246670	+	0.183778i
$766$	−3.83097e14			−1.45266
$767$		−	2.22019e14i		−	0.836398i
$768$	3.27570e14	+	1.08611e14i	1.22602	+	0.406506i
$769$	3.83535e14			1.42618			0.713089	−	0.701074i	$-0.247296\pi$
$769$	3.83535e14			1.42618			0.713089	+	0.701074i	$0.247296\pi$
$770$			2.08050e14i			0.768624i
$771$	1.11022e13	−	3.34843e13i	0.0407510	−	0.122905i
$772$	1.16585e14			0.425164
$773$		−	8.09240e13i		−	0.293211i	−0.989195	−	0.146605i	$-0.953165\pi$
$773$		−	8.09240e13i		−	0.293211i	0.989195	−	0.146605i	$-0.0468347\pi$
$774$	−2.64352e13	+	3.54818e13i	−0.0951652	+	0.127732i
$775$	−2.10093e13			−0.0751454
$776$		−	5.62869e13i		−	0.200032i
$777$	2.75183e14	+	9.12409e13i	0.971664	+	0.322170i
$778$	1.50882e14			0.529346
$779$			6.61320e14i			2.30528i
$780$	3.58031e13	−	1.07982e14i	0.124007	−	0.374006i
$781$	−2.15590e14			−0.741946
$782$		−	1.50319e14i		−	0.514020i
$783$	−1.62940e14	+	1.13960e14i	−0.553629	+	0.387207i
$784$	−1.39182e14			−0.469895
$785$			1.31942e14i			0.442623i
$786$	−1.70336e14	−	5.64775e13i	−0.567798	−	0.188262i
$787$	1.83977e14			0.609384			0.304692	−	0.952451i	$-0.401447\pi$
$787$	1.83977e14			0.609384			0.304692	+	0.952451i	$0.401447\pi$
$788$			2.56711e14i			0.844915i
$789$	1.51025e14	−	4.55492e14i	0.493929	−	1.48969i
$790$	−2.04007e14			−0.662996
$791$		−	7.09801e14i		−	2.29221i
$792$	−1.39741e14	−	1.04112e14i	−0.448434	−	0.334099i
$793$	7.56412e14			2.41208
$794$		−	3.24321e14i		−	1.02771i
$795$	1.83224e14	+	6.07506e13i	0.576961	+	0.191300i
$796$	−1.60805e14			−0.503191
$797$		−	3.84261e14i		−	1.19491i	−0.801903	−	0.597455i	$-0.796179\pi$
$797$		−	3.84261e14i		−	1.19491i	0.801903	−	0.597455i	$-0.203821\pi$
$798$	1.94962e14	−	5.88005e14i	0.602469	−	1.81705i
$799$	−1.00378e13			−0.0308250
$800$		−	7.11771e13i		−	0.217215i
$801$	−3.79212e14	+	5.08986e14i	−1.15006	+	1.54363i
$802$	5.25115e14			1.58264
$803$		−	2.67819e14i		−	0.802165i
$804$	1.35611e14	+	4.49637e13i	0.403658	+	0.133839i
$805$	−1.04352e14			−0.308689
$806$			2.31845e14i			0.681589i
$807$	2.26544e13	−	6.83257e13i	0.0661889	−	0.199626i
$808$	4.58541e13			0.133144
$809$			4.20380e14i			1.21311i	0.795042	+	0.606554i	$0.207449\pi$
$809$			4.20380e14i			1.21311i	−0.795042	+	0.606554i	$0.792551\pi$
$810$	−5.67452e13	−	1.90043e14i	−0.162744	−	0.545038i
$811$	5.36324e14			1.52870			0.764351	−	0.644800i	$-0.223060\pi$
$811$	5.36324e14			1.52870			0.764351	+	0.644800i	$0.223060\pi$
$812$		−	1.73081e14i		−	0.490309i
$813$	−1.24723e14	−	4.13538e13i	−0.351152	−	0.116430i
$814$	−4.55580e14			−1.27480
$815$			3.30465e13i			0.0919046i
$816$	9.68084e13	−	2.91974e14i	0.267585	−	0.807037i
$817$	−5.84021e13			−0.160442
$818$		−	7.09055e13i		−	0.193604i
$819$	−4.95104e14	−	3.68870e14i	−1.34362	−	1.00105i
$820$	−1.84302e14			−0.497120
$821$			6.41082e14i			1.71869i	0.511395	+	0.859346i	$0.329129\pi$
$821$			6.41082e14i			1.71869i	−0.511395	+	0.859346i	$0.670871\pi$
$822$	−5.56993e14	−	1.84679e14i	−1.48420	−	0.492107i
$823$	−4.41310e14			−1.16881			−0.584405	−	0.811462i	$-0.698672\pi$
$823$	−4.41310e14			−1.16881			−0.584405	+	0.811462i	$0.698672\pi$
$824$			8.73173e13i			0.229860i
$825$	−2.76695e13	+	8.34511e13i	−0.0723987	+	0.218355i
$826$	3.36929e14			0.876270
$827$			5.12469e14i			1.32477i	0.749164	+	0.662385i	$0.230456\pi$
$827$			5.12469e14i			1.32477i	−0.749164	+	0.662385i	$0.769544\pi$
$828$	−8.43953e13	+	1.13277e14i	−0.216854	+	0.291065i
$829$	7.09580e14			1.81229			0.906147	−	0.422964i	$-0.139010\pi$
$829$	7.09580e14			1.81229			0.906147	+	0.422964i	$0.139010\pi$
$830$			3.19560e14i			0.811264i
$831$	−3.79338e14	−	1.25775e14i	−0.957240	−	0.317387i
$832$	−8.25953e13			−0.207176
$833$			1.04867e14i			0.261465i
$834$	1.96418e14	−	5.92396e14i	0.486800	−	1.46819i
$835$	−3.20626e13			−0.0789888
$836$			3.71732e14i			0.910329i
$837$	8.84614e13	+	1.26482e14i	0.215341	+	0.307895i
$838$	−6.29523e14			−1.52332
$839$		−	2.57072e14i		−	0.618365i	−0.951003	−	0.309182i	$-0.899945\pi$
$839$		−	2.57072e14i		−	0.618365i	0.951003	−	0.309182i	$-0.100055\pi$
$840$	−1.01395e14	−	3.36190e13i	−0.242449	−	0.0803875i
$841$	2.28682e14			0.543565
$842$			2.62448e14i			0.620129i
$843$	−6.53445e13	+	1.97079e14i	−0.153487	+	0.462916i
$844$	2.82843e14			0.660440
$845$		−	1.99245e14i		−	0.462491i
$846$	1.98088e13	+	1.47583e13i	0.0457095	+	0.0340552i
$847$	−1.65421e14			−0.379466
$848$		−	7.36758e14i		−	1.68014i
$849$	5.37934e14	+	1.78360e14i	1.21952	+	0.404351i
$850$	−7.76352e13			−0.174970
$851$		−	2.28506e14i		−	0.511977i
$852$	−5.63026e13	+	1.69809e14i	−0.125410	+	0.378235i
$853$	−1.44468e14			−0.319908			−0.159954	−	0.987124i	$-0.551135\pi$
$853$	−1.44468e14			−0.319908			−0.159954	+	0.987124i	$0.551135\pi$
$854$			1.14791e15i			2.52707i
$855$	1.56403e14	−	2.09926e14i	0.342305	−	0.459448i
$856$	−1.19425e14			−0.259852
$857$			8.06575e14i			1.74478i	0.488810	+	0.872390i	$0.337431\pi$
$857$			8.06575e14i			1.74478i	−0.488810	+	0.872390i	$0.662569\pi$
$858$	9.20913e14	+	3.05342e14i	1.98053	+	0.656675i
$859$	3.62973e14			0.776084			0.388042	−	0.921642i	$-0.373152\pi$
$859$	3.62973e14			0.776084			0.388042	+	0.921642i	$0.373152\pi$
$860$		−	1.62760e13i		−	0.0345983i
$861$	−3.14791e14	+	9.49411e14i	−0.665284	+	2.00650i
$862$	−3.43242e13			−0.0721214
$863$		−	5.40656e14i		−	1.12945i	−0.825279	−	0.564725i	$-0.808982\pi$
$863$		−	5.40656e14i		−	1.12945i	0.825279	−	0.564725i	$-0.191018\pi$
$864$	−4.28508e14	+	2.99697e14i	−0.889999	+	0.622464i
$865$	−7.58565e13			−0.156644
$866$			6.59483e13i			0.135399i
$867$	2.45004e14	+	8.12348e13i	0.500124	+	0.165824i
$868$	−1.34354e14			−0.272680
$869$		−	6.64383e14i		−	1.34066i
$870$	6.02806e13	−	1.81806e14i	0.120943	−	0.364765i
$871$	4.92182e14			0.981828
$872$			3.49631e14i			0.693470i
$873$	1.67302e14	+	1.24646e14i	0.329936	+	0.245814i
$874$	−4.88268e14			−0.957416
$875$			5.38947e13i			0.105076i
$876$	−2.10947e14	−	6.99427e13i	−0.408934	−	0.135588i
$877$	3.10352e14			0.598214			0.299107	−	0.954220i	$-0.403311\pi$
$877$	3.10352e14			0.598214			0.299107	+	0.954220i	$0.403311\pi$
$878$		−	1.17671e14i		−	0.225526i
$879$	8.98473e13	−	2.70980e14i	0.171222	−	0.516407i
$880$	3.35563e14			0.635860
$881$		−	1.00799e15i		−	1.89922i	−0.313437	−	0.949609i	$-0.601480\pi$
$881$		−	1.00799e15i		−	1.89922i	0.313437	−	0.949609i	$-0.398520\pi$
$882$	1.54183e14	−	2.06947e14i	0.288864	−	0.387719i
$883$	−4.44352e14			−0.827797			−0.413899	−	0.910323i	$-0.635833\pi$
$883$	−4.44352e14			−0.827797			−0.413899	+	0.910323i	$0.635833\pi$
$884$			3.27153e14i			0.606024i
$885$	1.35146e14	+	4.48096e13i	0.248935	+	0.0825382i
$886$	4.92071e14			0.901279
$887$		−	6.56148e13i		−	0.119504i	−0.998213	−	0.0597521i	$-0.980969\pi$
$887$		−	6.56148e13i		−	0.119504i	0.998213	−	0.0597521i	$-0.0190310\pi$
$888$	7.36177e13	−	2.22031e14i	0.133327	−	0.402114i
$889$	−2.97944e14			−0.536569
$890$		−	6.11422e14i		−	1.09494i
$891$	6.18906e14	−	1.84800e14i	1.10214	−	0.329089i
$892$	−9.10270e13			−0.161193
$893$			3.26047e13i			0.0574147i
$894$	1.57863e13	+	5.23417e12i	0.0276434	+	0.00916559i
$895$	−7.41421e13			−0.129107
$896$			6.11475e14i			1.05886i
$897$	−1.53151e14	+	4.61905e14i	−0.263729	+	0.795408i
$898$	3.65990e14			0.626740
$899$			1.49060e14i			0.253841i
$900$	5.85041e13	+	4.35876e13i	0.0990771	+	0.0738160i
$901$	−5.55113e14			−0.934884
$902$		−	1.57180e15i		−	2.63248i
$903$	−8.38438e13	−	2.77997e13i	−0.139647	−	0.0463021i
$904$	−5.72703e14			−0.948609
$905$			3.10409e14i			0.511318i
$906$	2.35688e14	−	7.10835e14i	0.386097	−	1.16447i
$907$	−1.11481e15			−1.81620			−0.908098	−	0.418758i	$-0.862466\pi$
$907$	−1.11481e15			−1.81620			−0.908098	+	0.418758i	$0.862466\pi$
$908$		−	2.59763e14i		−	0.420869i
$909$	−1.01543e14	+	1.36292e14i	−0.163617	+	0.219610i
$910$	5.94747e14			0.953071
$911$			5.55231e14i			0.884875i	0.896799	+	0.442438i	$0.145886\pi$
$911$			5.55231e14i			0.884875i	−0.896799	+	0.442438i	$0.854114\pi$
$912$	−9.48393e14	−	3.14454e14i	−1.50319	−	0.498405i
$913$	−1.04070e15			−1.64048
$914$		−	3.47230e14i		−	0.544360i
$915$	−1.52665e14	+	4.60438e14i	−0.238031	+	0.717903i
$916$	4.60387e14			0.713914
$917$		−	3.58256e14i		−	0.552518i
$918$	3.26890e14	+	4.67388e14i	0.501405	+	0.716909i
$919$	−5.46948e14			−0.834389			−0.417195	−	0.908817i	$-0.636987\pi$
$919$	−5.46948e14			−0.834389			−0.417195	+	0.908817i	$0.636987\pi$
$920$			8.41965e13i			0.127748i
$921$	9.85799e14	+	3.26856e14i	1.48761	+	0.493241i
$922$	1.59435e14			0.239292
$923$			6.16301e14i			0.919992i
$924$	−1.76946e14	+	5.33669e14i	−0.262713	+	0.792342i
$925$	−1.18017e14			−0.174275
$926$		−	1.10765e15i		−	1.62685i
$927$	−2.59533e14	−	1.93362e14i	−0.379136	−	0.282470i
$928$	−5.04998e14			−0.733753
$929$			2.61566e13i			0.0378009i	0.999821	+	0.0189004i	$0.00601656\pi$
$929$			2.61566e13i			0.0378009i	−0.999821	+	0.0189004i	$0.993983\pi$
$930$	−1.41127e14	−	4.67928e13i	−0.202860	−	0.0672612i
$931$	3.40630e14			0.487006
$932$		−	3.16409e14i		−	0.449955i
$933$	−1.64281e13	+	4.95473e13i	−0.0232370	+	0.0700829i
$934$	6.29315e14			0.885388
$935$		−	2.52832e14i		−	0.353813i
$936$	−2.97623e14	+	3.99475e14i	−0.414273	+	0.556045i
$937$	1.17449e15			1.62612			0.813060	−	0.582181i	$-0.197800\pi$
$937$	1.17449e15			1.62612			0.813060	+	0.582181i	$0.197800\pi$
$938$			7.46920e14i			1.02863i
$939$	−1.27706e15	−	4.23429e14i	−1.74938	−	0.580033i
$940$	−9.08656e12			−0.0123811
$941$		−	1.26169e15i		−	1.71004i	−0.518596	−	0.855020i	$-0.673545\pi$
$941$		−	1.26169e15i		−	1.71004i	0.518596	−	0.855020i	$-0.326455\pi$
$942$	−2.93867e14	+	8.86303e14i	−0.396183	+	1.19489i
$943$	7.88372e14			1.05724
$944$		−	5.43432e14i		−	0.724912i
$945$	3.24462e14	−	2.26928e14i	0.430532	−	0.301113i
$946$	1.38808e14			0.183214
$947$		−	3.87359e13i		−	0.0508585i	−0.999677	−	0.0254293i	$-0.991905\pi$
$947$		−	3.87359e13i		−	0.0508585i	0.999677	−	0.0254293i	$-0.00809526\pi$
$948$	−5.23300e14	−	1.73508e14i	−0.683454	−	0.226609i
$949$	−7.65608e14			−0.994661
$950$			2.52175e14i			0.325900i
$951$	2.25797e14	−	6.81005e14i	0.290280	−	0.875483i
$952$	3.07196e14			0.392854
$953$			1.07685e15i			1.36990i	0.728590	+	0.684950i	$0.240176\pi$
$953$			1.07685e15i			1.36990i	−0.728590	+	0.684950i	$0.759824\pi$
$954$	1.09548e15	+	8.16169e14i	1.38631	+	1.03285i
$955$	4.14932e14			0.522349
$956$			4.47980e14i			0.561008i
$957$	5.92081e14	+	1.96313e14i	0.737602	+	0.244563i
$958$	7.84480e14			0.972197
$959$		−	1.17148e15i		−	1.44425i
$960$	1.66700e13	−	5.02769e13i	0.0204447	−	0.0616612i
$961$	−7.03921e14			−0.858829
$962$			1.30235e15i			1.58072i
$963$	2.64463e14	−	3.54967e14i	0.319325	−	0.428604i
$964$	−7.92423e13			−0.0951857
$965$			2.57566e14i			0.307788i
$966$	−7.00972e14	−	2.32418e14i	−0.833326	−	0.276302i
$967$	−1.41897e15			−1.67819			−0.839095	−	0.543985i	$-0.816915\pi$
$967$	−1.41897e15			−1.67819			−0.839095	+	0.543985i	$0.816915\pi$
$968$			1.33470e14i			0.157038i
$969$	−2.36926e14	+	7.14570e14i	−0.277329	+	0.836423i
$970$	−2.00972e14			−0.234033
$971$		−	8.50172e14i		−	0.984942i	−0.870329	−	0.492471i	$-0.836094\pi$
$971$		−	8.50172e14i		−	0.984942i	0.870329	−	0.492471i	$-0.163906\pi$
$972$	1.60740e13	−	5.35742e14i	0.0185265	−	0.617482i
$973$	1.24594e15			1.42868
$974$			8.10554e14i			0.924670i
$975$	2.38560e14	+	7.90980e13i	0.270753	+	0.0897723i
$976$	1.85146e15			2.09057
$977$		−	1.22334e14i		−	0.137428i	−0.997636	−	0.0687139i	$-0.978110\pi$
$977$		−	1.22334e14i		−	0.137428i	0.997636	−	0.0687139i	$-0.0218896\pi$
$978$	−7.36026e13	+	2.21985e14i	−0.0822619	+	0.248102i
$979$	1.99119e15			2.21411
$980$			9.49295e13i			0.105020i
$981$	−1.03921e15	−	7.74247e14i	−1.14382	−	0.852187i
$982$	−1.29814e15			−1.42156
$983$		−	4.35724e14i		−	0.474727i	−0.971421	−	0.237363i	$-0.923717\pi$
$983$		−	4.35724e14i		−	0.474727i	0.971421	−	0.237363i	$-0.0762832\pi$
$984$	7.66032e14	+	2.53989e14i	0.830369	+	0.275321i
$985$	−5.67139e14			−0.611658
$986$			5.50818e14i			0.591049i
$987$	−1.55200e13	+	4.68083e13i	−0.0165694	+	0.0499732i
$988$	1.06266e15			1.12878
$989$			6.96222e13i			0.0735811i
$990$	−3.71732e14	+	4.98945e14i	−0.390890	+	0.524659i
$991$	−2.05146e13			−0.0214632			−0.0107316	−	0.999942i	$-0.503416\pi$
$991$	−2.05146e13			−0.0214632			−0.0107316	+	0.999942i	$0.503416\pi$
$992$			3.92005e14i			0.408068i
$993$	−8.59613e14	−	2.85018e14i	−0.890342	−	0.295206i
$994$	−9.35278e14			−0.963849
$995$		−	3.55258e14i		−	0.364274i
$996$	−2.71785e14	+	8.19705e14i	−0.277287	+	0.836298i
$997$	6.81845e14			0.692165			0.346083	−	0.938204i	$-0.387512\pi$
$997$	6.81845e14			0.692165			0.346083	+	0.938204i	$0.387512\pi$
$998$			1.81177e15i			1.83000i
$999$	4.96919e14	+	7.10496e14i	0.499411	+	0.714059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.11.c.a.11.4	✓	14
3.2	odd	2	inner	15.11.c.a.11.11	yes	14
4.3	odd	2		240.11.l.b.161.1		14
5.2	odd	4		75.11.d.d.74.21		28
5.3	odd	4		75.11.d.d.74.8		28
5.4	even	2		75.11.c.g.26.11		14
12.11	even	2		240.11.l.b.161.2		14
15.2	even	4		75.11.d.d.74.7		28
15.8	even	4		75.11.d.d.74.22		28
15.14	odd	2		75.11.c.g.26.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.11.c.a.11.4	✓	14	1.1	even	1	trivial
15.11.c.a.11.11	yes	14	3.2	odd	2	inner
75.11.c.g.26.4		14	15.14	odd	2
75.11.c.g.26.11		14	5.4	even	2
75.11.d.d.74.7		28	15.2	even	4
75.11.d.d.74.8		28	5.3	odd	4
75.11.d.d.74.21		28	5.2	odd	4
75.11.d.d.74.22		28	15.8	even	4
240.11.l.b.161.1		14	4.3	odd	2
240.11.l.b.161.2		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)

\(f(q)\)	\(=\)	\(q-40.7012i q^{2} +(230.652 + 76.4761i) q^{3} -632.586 q^{4} -1397.54i q^{5} +(3112.67 - 9387.81i) q^{6} +19744.7 q^{7} -15931.0i q^{8} +(47351.8 + 35278.8i) q^{9} +O(q^{10})\)	\(q-40.7012i q^{2} +(230.652 + 76.4761i) q^{3} -632.586 q^{4} -1397.54i q^{5} +(3112.67 - 9387.81i) q^{6} +19744.7 q^{7} -15931.0i q^{8} +(47351.8 + 35278.8i) q^{9} -56881.6 q^{10} -185244. i q^{11} +(-145907. - 48377.7i) q^{12} -529553. q^{13} -803633. i q^{14} +(106879. - 322346. i) q^{15} -1.29618e6 q^{16} +976612. i q^{17} +(1.43589e6 - 1.92727e6i) q^{18} +3.17224e6 q^{19} +884066. i q^{20} +(4.55416e6 + 1.51000e6i) q^{21} -7.53966e6 q^{22} -3.78168e6i q^{23} +(1.21834e6 - 3.67452e6i) q^{24} -1.95312e6 q^{25} +2.15534e7i q^{26} +(8.22381e6 + 1.17584e7i) q^{27} -1.24902e7 q^{28} +1.38573e7i q^{29} +(-1.31199e7 - 4.35009e6i) q^{30} +1.07567e7 q^{31} +3.64427e7i q^{32} +(1.41668e7 - 4.27270e7i) q^{33} +3.97492e7 q^{34} -2.75941e7i q^{35} +(-2.99541e7 - 2.23169e7i) q^{36} +6.04245e7 q^{37} -1.29114e8i q^{38} +(-1.22143e8 - 4.04982e7i) q^{39} -2.22643e7 q^{40} +2.08471e8i q^{41} +(6.14588e7 - 1.85360e8i) q^{42} -1.84104e7 q^{43} +1.17183e8i q^{44} +(4.93036e7 - 6.61761e7i) q^{45} -1.53919e8 q^{46} +1.02781e7i q^{47} +(-2.98966e8 - 9.91268e7i) q^{48} +1.07378e8 q^{49} +7.94945e7i q^{50} +(-7.46875e7 + 2.25258e8i) q^{51} +3.34988e8 q^{52} +5.68407e8i q^{53} +(4.78581e8 - 3.34719e8i) q^{54} -2.58887e8 q^{55} -3.14553e8i q^{56} +(7.31683e8 + 2.42601e8i) q^{57} +5.64010e8 q^{58} +4.19257e8i q^{59} +(-6.76099e7 + 2.03912e8i) q^{60} -1.42840e9 q^{61} -4.37812e8i q^{62} +(9.34947e8 + 6.96569e8i) q^{63} +1.55972e8 q^{64} +7.40073e8i q^{65} +(-1.73904e9 - 5.76604e8i) q^{66} -9.29430e8 q^{67} -6.17791e8i q^{68} +(2.89209e8 - 8.72254e8i) q^{69} -1.12311e9 q^{70} -1.16381e9i q^{71} +(5.62027e8 - 7.54362e8i) q^{72} +1.44576e9 q^{73} -2.45935e9i q^{74} +(-4.50492e8 - 1.49367e8i) q^{75} -2.00671e9 q^{76} -3.65759e9i q^{77} +(-1.64832e9 + 4.97135e9i) q^{78} +3.58653e9 q^{79} +1.81147e9i q^{80} +(9.97601e8 + 3.34103e9i) q^{81} +8.48502e9 q^{82} -5.61799e9i q^{83} +(-2.88090e9 - 9.55204e8i) q^{84} +1.36486e9 q^{85} +7.49324e8i q^{86} +(-1.05976e9 + 3.19622e9i) q^{87} -2.95113e9 q^{88} +1.07490e10i q^{89} +(-2.69345e9 - 2.00671e9i) q^{90} -1.04559e10 q^{91} +2.39224e9i q^{92} +(2.48107e9 + 8.22635e8i) q^{93} +4.18333e8 q^{94} -4.43334e9i q^{95} +(-2.78699e9 + 8.40558e9i) q^{96} +3.53316e9 q^{97} -4.37042e9i q^{98} +(6.53519e9 - 8.77164e9i) 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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