LMFDB - Embedded newform 15.11.c.a.11.8

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			11.8
Root			$2.70449i$ of defining polynomial
Character	$\chi$	$=$	15.11
Dual form			15.11.c.a.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.94055i q^{2} +(182.813 - 160.089i) q^{3} +999.591 q^{4} -1397.54i q^{5} +(790.929 + 903.195i) q^{6} -5515.83 q^{7} +9997.66i q^{8} +(7791.87 - 58532.7i) q^{9} +O(q^{10})$	\(q+4.94055i q^{2} +(182.813 - 160.089i) q^{3} +999.591 q^{4} -1397.54i q^{5} +(790.929 + 903.195i) q^{6} -5515.83 q^{7} +9997.66i q^{8} +(7791.87 - 58532.7i) q^{9} +6904.63 q^{10} -76762.6i q^{11} +(182738. - 160024. i) q^{12} +449930. q^{13} -27251.2i q^{14} +(-223732. - 255488. i) q^{15} +974187. q^{16} -1.42045e6i q^{17} +(289184. + 38496.1i) q^{18} -1.48186e6 q^{19} -1.39697e6i q^{20} +(-1.00836e6 + 883025. i) q^{21} +379250. q^{22} +8.24828e6i q^{23} +(1.60052e6 + 1.82770e6i) q^{24} -1.95312e6 q^{25} +2.22291e6i q^{26} +(-7.94600e6 - 1.19479e7i) q^{27} -5.51357e6 q^{28} +3.07336e7i q^{29} +(1.26225e6 - 1.10536e6i) q^{30} -1.77120e7 q^{31} +1.50506e7i q^{32} +(-1.22889e7 - 1.40332e7i) q^{33} +7.01779e6 q^{34} +7.70860e6i q^{35} +(7.78868e6 - 5.85087e7i) q^{36} +7.18733e7 q^{37} -7.32120e6i q^{38} +(8.22529e7 - 7.20290e7i) q^{39} +1.39722e7 q^{40} -2.33115e7i q^{41} +(-4.36263e6 - 4.98187e6i) q^{42} -1.37592e7 q^{43} -7.67312e7i q^{44} +(-8.18019e7 - 1.08895e7i) q^{45} -4.07511e7 q^{46} +4.03553e8i q^{47} +(1.78094e8 - 1.55957e8i) q^{48} -2.52051e8 q^{49} -9.64952e6i q^{50} +(-2.27398e8 - 2.59675e8i) q^{51} +4.49746e8 q^{52} +4.99095e8i q^{53} +(5.90292e7 - 3.92576e7i) q^{54} -1.07279e8 q^{55} -5.51454e7i q^{56} +(-2.70902e8 + 2.37229e8i) q^{57} -1.51841e8 q^{58} +7.43569e8i q^{59} +(-2.23640e8 - 2.55384e8i) q^{60} -1.54609e9 q^{61} -8.75072e7i q^{62} +(-4.29786e7 + 3.22856e8i) q^{63} +9.23209e8 q^{64} -6.28797e8i q^{65} +(6.93316e7 - 6.07138e7i) q^{66} +1.83019e9 q^{67} -1.41987e9i q^{68} +(1.32046e9 + 1.50789e9i) q^{69} -3.80848e7 q^{70} -3.45433e9i q^{71} +(5.85189e8 + 7.79004e7i) q^{72} +8.31400e8 q^{73} +3.55094e8i q^{74} +(-3.57056e8 + 3.12674e8i) q^{75} -1.48125e9 q^{76} +4.23409e8i q^{77} +(3.55863e8 + 4.06375e8i) q^{78} +4.69267e8 q^{79} -1.36147e9i q^{80} +(-3.36536e9 - 9.12157e8i) q^{81} +1.15172e8 q^{82} +1.59991e9i q^{83} +(-1.00795e9 + 8.82663e8i) q^{84} -1.98513e9 q^{85} -6.79781e7i q^{86} +(4.92012e9 + 5.61849e9i) q^{87} +7.67447e8 q^{88} -6.09726e9i q^{89} +(5.38000e7 - 4.04146e8i) q^{90} -2.48174e9 q^{91} +8.24491e9i q^{92} +(-3.23798e9 + 2.83550e9i) q^{93} -1.99377e9 q^{94} +2.07096e9i q^{95} +(2.40944e9 + 2.75144e9i) q^{96} -2.89804e9 q^{97} -1.24527e9i q^{98} +(-4.49312e9 - 5.98124e8i) 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 $

$2$			4.94055i			0.154392i	0.997016	+	0.0771961i	$0.0245968\pi$
$2$			4.94055i			0.154392i	−0.997016	+	0.0771961i	$0.975403\pi$
$3$	182.813	−	160.089i	0.752315	−	0.658803i
$3$	182.813	−	160.089i	0.752315	−	0.658803i
$4$	999.591			0.976163
$5$		−	1397.54i		−	0.447214i
$5$		−	1397.54i		−	0.447214i
$6$	790.929	+	903.195i	0.101714	+	0.116152i
$7$	−5515.83			−0.328186			−0.164093	−	0.986445i	$-0.552470\pi$
$7$	−5515.83			−0.328186			−0.164093	+	0.986445i	$0.552470\pi$
$8$			9997.66i			0.305104i
$9$	7791.87	−	58532.7i	0.131956	−	0.991256i
$10$	6904.63			0.0690463
$11$		−	76762.6i		−	0.476636i	−0.971187	−	0.238318i	$-0.923404\pi$
$11$		−	76762.6i		−	0.476636i	0.971187	−	0.238318i	$-0.0765960\pi$
$12$	182738.	−	160024.i	0.734382	−	0.643100i
$13$	449930.			1.21179			0.605897	−	0.795543i	$-0.292814\pi$
$13$	449930.			1.21179			0.605897	+	0.795543i	$0.292814\pi$
$14$		−	27251.2i		−	0.0506694i
$15$	−223732.	−	255488.i	−0.294626	−	0.336446i
$16$	974187.			0.929057
$17$		−	1.42045e6i		−	1.00042i	−0.865906	−	0.500208i	$-0.833257\pi$
$17$		−	1.42045e6i		−	1.00042i	0.865906	−	0.500208i	$-0.166743\pi$
$18$	289184.	+	38496.1i	0.153042	+	0.0203730i
$19$	−1.48186e6			−0.598465			−0.299232	−	0.954180i	$-0.596731\pi$
$19$	−1.48186e6			−0.598465			−0.299232	+	0.954180i	$0.596731\pi$
$20$		−	1.39697e6i		−	0.436553i
$21$	−1.00836e6	+	883025.i	−0.246900	+	0.216210i
$22$	379250.			0.0735889
$23$			8.24828e6i			1.28152i	0.767743	+	0.640758i	$0.221380\pi$
$23$			8.24828e6i			1.28152i	−0.767743	+	0.640758i	$0.778620\pi$
$24$	1.60052e6	+	1.82770e6i	0.201004	+	0.229535i
$25$	−1.95312e6			−0.200000
$26$			2.22291e6i			0.187092i
$27$	−7.94600e6	−	1.19479e7i	−0.553770	−	0.832670i
$28$	−5.51357e6			−0.320363
$29$			3.07336e7i			1.49839i	0.662352	+	0.749193i	$0.269558\pi$
$29$			3.07336e7i			1.49839i	−0.662352	+	0.749193i	$0.730442\pi$
$30$	1.26225e6	−	1.10536e6i	0.0519446	−	0.0454880i
$31$	−1.77120e7			−0.618671			−0.309335	−	0.950953i	$-0.600107\pi$
$31$	−1.77120e7			−0.618671			−0.309335	+	0.950953i	$0.600107\pi$
$32$			1.50506e7i			0.448544i
$33$	−1.22889e7	−	1.40332e7i	−0.314009	−	0.358580i
$34$	7.01779e6			0.154456
$35$			7.70860e6i			0.146769i
$36$	7.78868e6	−	5.85087e7i	0.128811	−	0.967627i
$37$	7.18733e7			1.03648			0.518238	−	0.855237i	$-0.326588\pi$
$37$	7.18733e7			1.03648			0.518238	+	0.855237i	$0.326588\pi$
$38$		−	7.32120e6i		−	0.0923983i
$39$	8.22529e7	−	7.20290e7i	0.911650	−	0.798334i
$40$	1.39722e7			0.136447
$41$		−	2.33115e7i		−	0.201210i	−0.994926	−	0.100605i	$-0.967922\pi$
$41$		−	2.33115e7i		−	0.201210i	0.994926	−	0.100605i	$-0.0320779\pi$
$42$	−4.36263e6	−	4.98187e6i	−0.0333812	−	0.0381194i
$43$	−1.37592e7			−0.0935947			−0.0467973	−	0.998904i	$-0.514901\pi$
$43$	−1.37592e7			−0.0935947			−0.0467973	+	0.998904i	$0.514901\pi$
$44$		−	7.67312e7i		−	0.465274i
$45$	−8.18019e7	−	1.08895e7i	−0.443303	−	0.0590125i
$46$	−4.07511e7			−0.197856
$47$			4.03553e8i			1.75959i	0.475354	+	0.879795i	$0.342320\pi$
$47$			4.03553e8i			1.75959i	−0.475354	+	0.879795i	$0.657680\pi$
$48$	1.78094e8	−	1.55957e8i	0.698944	−	0.612066i
$49$	−2.52051e8			−0.892294
$50$		−	9.64952e6i		−	0.0308785i
$51$	−2.27398e8	−	2.59675e8i	−0.659077	−	0.752627i
$52$	4.49746e8			1.18291
$53$			4.99095e8i			1.19345i	0.802447	+	0.596724i	$0.203531\pi$
$53$			4.99095e8i			1.19345i	−0.802447	+	0.596724i	$0.796469\pi$
$54$	5.90292e7	−	3.92576e7i	0.128558	−	0.0854978i
$55$	−1.07279e8			−0.213158
$56$		−	5.51454e7i		−	0.100131i
$57$	−2.70902e8	+	2.37229e8i	−0.450234	+	0.394271i
$58$	−1.51841e8			−0.231339
$59$			7.43569e8i			1.04007i	0.854146	+	0.520033i	$0.174080\pi$
$59$			7.43569e8i			1.04007i	−0.854146	+	0.520033i	$0.825920\pi$
$60$	−2.23640e8	−	2.55384e8i	−0.287603	−	0.328426i
$61$	−1.54609e9			−1.83057			−0.915283	−	0.402811i	$-0.868033\pi$
$61$	−1.54609e9			−1.83057			−0.915283	+	0.402811i	$0.868033\pi$
$62$		−	8.75072e7i		−	0.0955180i
$63$	−4.29786e7	+	3.22856e8i	−0.0433061	+	0.325317i
$64$	9.23209e8			0.859806
$65$		−	6.28797e8i		−	0.541931i
$66$	6.93316e7	−	6.07138e7i	0.0553620	−	0.0484806i
$67$	1.83019e9			1.35557			0.677786	−	0.735259i	$-0.262939\pi$
$67$	1.83019e9			1.35557			0.677786	+	0.735259i	$0.262939\pi$
$68$		−	1.41987e9i		−	0.976568i
$69$	1.32046e9	+	1.50789e9i	0.844268	+	0.964104i
$70$	−3.80848e7			−0.0226601
$71$		−	3.45433e9i		−	1.91457i	−0.289139	−	0.957287i	$-0.593369\pi$
$71$		−	3.45433e9i		−	1.91457i	0.289139	−	0.957287i	$-0.406631\pi$
$72$	5.85189e8	+	7.79004e7i	0.302436	+	0.0402603i
$73$	8.31400e8			0.401048			0.200524	−	0.979689i	$-0.435736\pi$
$73$	8.31400e8			0.401048			0.200524	+	0.979689i	$0.435736\pi$
$74$			3.55094e8i			0.160024i
$75$	−3.57056e8	+	3.12674e8i	−0.150463	+	0.131761i
$76$	−1.48125e9			−0.584199
$77$			4.23409e8i			0.156425i
$78$	3.55863e8	+	4.06375e8i	0.123257	+	0.140752i
$79$	4.69267e8			0.152505			0.0762526	−	0.997089i	$-0.475704\pi$
$79$	4.69267e8			0.152505			0.0762526	+	0.997089i	$0.475704\pi$
$80$		−	1.36147e9i		−	0.415487i
$81$	−3.36536e9	−	9.12157e8i	−0.965175	−	0.261604i
$82$	1.15172e8			0.0310653
$83$			1.59991e9i			0.406166i	0.979162	+	0.203083i	$0.0650962\pi$
$83$			1.59991e9i			0.406166i	−0.979162	+	0.203083i	$0.934904\pi$
$84$	−1.00795e9	+	8.82663e8i	−0.241014	+	0.211056i
$85$	−1.98513e9			−0.447399
$86$		−	6.79781e7i		−	0.0144503i
$87$	4.92012e9	+	5.61849e9i	0.987142	+	1.12726i
$88$	7.67447e8			0.145424
$89$		−	6.09726e9i		−	1.09190i	−0.837816	−	0.545952i	$-0.816168\pi$
$89$		−	6.09726e9i		−	1.09190i	0.837816	−	0.545952i	$-0.183832\pi$
$90$	5.38000e7	−	4.04146e8i	0.00911107	−	0.0684426i
$91$	−2.48174e9			−0.397694
$92$			8.24491e9i			1.25097i
$93$	−3.23798e9	+	2.83550e9i	−0.465435	+	0.407582i
$94$	−1.99377e9			−0.271667
$95$			2.07096e9i			0.267642i
$96$	2.40944e9	+	2.75144e9i	0.295502	+	0.337446i
$97$	−2.89804e9			−0.337478			−0.168739	−	0.985661i	$-0.553969\pi$
$97$	−2.89804e9			−0.337478			−0.168739	+	0.985661i	$0.553969\pi$
$98$		−	1.24527e9i		−	0.137763i
$99$	−4.49312e9	−	5.98124e8i	−0.472468	−	0.0628949i
$100$	−1.95233e9			−0.195233
$101$		−	6.76431e9i		−	0.643601i	−0.946807	−	0.321801i	$-0.895712\pi$
$101$		−	6.76431e9i		−	0.643601i	0.946807	−	0.321801i	$-0.104288\pi$
$102$	1.28294e9	−	1.12347e9i	0.116200	−	0.101756i
$103$	7.52661e9			0.649252			0.324626	−	0.945842i	$-0.394762\pi$
$103$	7.52661e9			0.649252			0.324626	+	0.945842i	$0.394762\pi$
$104$			4.49825e9i			0.369723i
$105$	1.23406e9	+	1.40923e9i	0.0966922	+	0.110417i
$106$	−2.46580e9			−0.184259
$107$		−	1.43017e10i		−	1.01969i	−0.860266	−	0.509846i	$-0.829702\pi$
$107$		−	1.43017e10i		−	1.01969i	0.860266	−	0.509846i	$-0.170298\pi$
$108$	−7.94275e9	−	1.19430e10i	−0.540570	−	0.812821i
$109$	1.92202e10			1.24918			0.624590	−	0.780953i	$-0.285266\pi$
$109$	1.92202e10			1.24918			0.624590	+	0.780953i	$0.285266\pi$
$110$		−	5.30018e8i		−	0.0329099i
$111$	1.31393e10	−	1.15061e10i	0.779756	−	0.682834i
$112$	−5.37345e9			−0.304904
$113$			5.99003e9i			0.325115i	0.986699	+	0.162557i	$0.0519742\pi$
$113$			5.99003e9i			0.325115i	−0.986699	+	0.162557i	$0.948026\pi$
$114$	−1.17204e9	−	1.33841e9i	−0.0608723	−	0.0695127i
$115$	1.15273e10			0.573112
$116$			3.07210e10i			1.46267i
$117$	3.50580e9	−	2.63356e10i	0.159903	−	1.20120i
$118$	−3.67364e9			−0.160578
$119$			7.83494e9i			0.328323i
$120$	2.55429e9	−	2.23679e9i	0.102651	−	0.0898916i
$121$	2.00449e10			0.772819
$122$		−	7.63854e9i		−	0.282625i
$123$	−3.73192e9	−	4.26163e9i	−0.132558	−	0.151374i
$124$	−1.77048e10			−0.603923
$125$			2.72958e9i			0.0894427i
$126$	−1.59509e9	−	2.12338e8i	−0.0502264	−	0.00668613i
$127$	−5.13070e10			−1.55295			−0.776477	−	0.630146i	$-0.782995\pi$
$127$	−5.13070e10			−1.55295			−0.776477	+	0.630146i	$0.782995\pi$
$128$			1.99730e10i			0.581291i
$129$	−2.51536e9	+	2.20270e9i	−0.0704127	+	0.0616605i
$130$	3.10660e9			0.0836699
$131$			3.64957e10i			0.945987i	0.881066	+	0.472993i	$0.156827\pi$
$131$			3.64957e10i			0.945987i	−0.881066	+	0.472993i	$0.843173\pi$
$132$	−1.22838e10	−	1.40274e10i	−0.306524	−	0.350033i
$133$	8.17367e9			0.196408
$134$			9.04217e9i			0.209290i
$135$	−1.66977e10	+	1.11049e10i	−0.372381	+	0.247654i
$136$	1.42011e10			0.305231
$137$			1.26506e9i			0.0262125i	0.999914	+	0.0131063i	$0.00417197\pi$
$137$			1.26506e9i			0.0262125i	−0.999914	+	0.0131063i	$0.995828\pi$
$138$	−7.44981e9	+	6.52381e9i	−0.148850	+	0.130348i
$139$	−7.45779e10			−1.43726			−0.718631	−	0.695391i	$-0.755231\pi$
$139$	−7.45779e10			−1.43726			−0.718631	+	0.695391i	$0.755231\pi$
$140$			7.70545e9i			0.143271i
$141$	6.46045e10	+	7.37746e10i	1.15922	+	1.32377i
$142$	1.70663e10			0.295595
$143$		−	3.45378e10i		−	0.577584i
$144$	7.59074e9	−	5.70218e10i	0.122595	−	0.920933i
$145$	4.29515e10			0.670099
$146$			4.10758e9i			0.0619187i
$147$	−4.60781e10	+	4.03506e10i	−0.671286	+	0.587846i
$148$	7.18439e10			1.01177
$149$		−	1.09401e11i		−	1.48967i	−0.667250	−	0.744834i	$-0.732529\pi$
$149$		−	1.09401e11i		−	1.48967i	0.667250	−	0.744834i	$-0.267471\pi$
$150$	−1.54478e9	−	1.76405e9i	−0.0203428	−	0.0232303i
$151$	−4.87351e10			−0.620807			−0.310404	−	0.950605i	$-0.600464\pi$
$151$	−4.87351e10			−0.620807			−0.310404	+	0.950605i	$0.600464\pi$
$152$		−	1.48151e10i		−	0.182594i
$153$	−8.31425e10	−	1.10679e10i	−0.991667	−	0.132011i
$154$	−2.09188e9			−0.0241509
$155$			2.47533e10i			0.276678i
$156$	8.22193e10	−	7.19996e10i	0.889920	−	0.779304i
$157$	1.94261e10			0.203651			0.101826	−	0.994802i	$-0.467532\pi$
$157$	1.94261e10			0.203651			0.101826	+	0.994802i	$0.467532\pi$
$158$			2.31844e9i			0.0235456i
$159$	7.98997e10	+	9.12408e10i	0.786248	+	0.897849i
$160$	2.10339e10			0.200595
$161$		−	4.54961e10i		−	0.420576i
$162$	4.50656e9	−	1.66267e10i	0.0403897	−	0.149016i
$163$	2.30635e10			0.200441			0.100221	−	0.994965i	$-0.468045\pi$
$163$	2.30635e10			0.200441			0.100221	+	0.994965i	$0.468045\pi$
$164$		−	2.33019e10i		−	0.196414i
$165$	−1.96120e10	+	1.71742e10i	−0.160362	+	0.140429i
$166$	−7.90442e9			−0.0627089
$167$		−	5.87169e10i		−	0.452044i	−0.974122	−	0.226022i	$-0.927428\pi$
$167$		−	5.87169e10i		−	0.452044i	0.974122	−	0.226022i	$-0.0725721\pi$
$168$	−8.82818e9	−	1.00813e10i	−0.0659667	−	0.0753301i
$169$	6.45789e10			0.468443
$170$		−	9.80766e9i		−	0.0690750i
$171$	−1.15464e10	+	8.67371e10i	−0.0789710	+	0.593231i
$172$	−1.37536e10			−0.0913637
$173$		−	2.00408e11i		−	1.29326i	−0.762804	−	0.646629i	$-0.776178\pi$
$173$		−	2.00408e11i		−	1.29326i	0.762804	−	0.646629i	$-0.223822\pi$
$174$	−2.77585e10	+	2.43081e10i	−0.174040	+	0.152407i
$175$	1.07731e10			0.0656373
$176$		−	7.47812e10i		−	0.442822i
$177$	1.19037e11	+	1.35934e11i	0.685199	+	0.782457i
$178$	3.01238e10			0.168582
$179$			2.40658e11i			1.30959i	0.755806	+	0.654796i	$0.227245\pi$
$179$			2.40658e11i			1.30959i	−0.755806	+	0.654796i	$0.772755\pi$
$180$	−8.17684e10	−	1.08850e10i	−0.432736	−	0.0576058i
$181$	−2.73793e11			−1.40938			−0.704691	−	0.709514i	$-0.748914\pi$
$181$	−2.73793e11			−1.40938			−0.704691	+	0.709514i	$0.748914\pi$
$182$		−	1.22612e10i		−	0.0614009i
$183$	−2.82645e11	+	2.47512e11i	−1.37716	+	1.20598i
$184$	−8.24635e10			−0.390996
$185$		−	1.00446e11i		−	0.463526i
$186$	−1.40090e10	−	1.59974e10i	−0.0629276	−	0.0718596i
$187$	−1.09037e11			−0.476833
$188$			4.03388e11i			1.71765i
$189$	4.38287e10	+	6.59025e10i	0.181740	+	0.273271i
$190$	−1.02317e10			−0.0413218
$191$		−	1.15427e11i		−	0.454088i	−0.973885	−	0.227044i	$-0.927094\pi$
$191$		−	1.15427e11i		−	0.454088i	0.973885	−	0.227044i	$-0.0729061\pi$
$192$	1.68774e11	−	1.47796e11i	0.646845	−	0.566443i
$193$	3.82211e11			1.42730			0.713652	−	0.700500i	$-0.247040\pi$
$193$	3.82211e11			1.42730			0.713652	+	0.700500i	$0.247040\pi$
$194$		−	1.43179e10i		−	0.0521039i
$195$	−1.00664e11	−	1.14952e11i	−0.357026	−	0.407702i
$196$	−2.51948e11			−0.871024
$197$			1.38791e11i			0.467768i	0.972265	+	0.233884i	$0.0751435\pi$
$197$			1.38791e11i			0.467768i	−0.972265	+	0.233884i	$0.924856\pi$
$198$	2.95506e9	−	2.21985e10i	0.00971049	−	0.0729454i
$199$	2.19040e11			0.701872			0.350936	−	0.936399i	$-0.385863\pi$
$199$	2.19040e11			0.701872			0.350936	+	0.936399i	$0.385863\pi$
$200$		−	1.95267e10i		−	0.0610209i
$201$	3.34582e11	−	2.92994e11i	1.01982	−	0.893056i
$202$	3.34194e10			0.0993670
$203$		−	1.69521e11i		−	0.491750i
$204$	−2.27305e11	−	2.59569e11i	−0.643367	−	0.734687i
$205$	−3.25788e10			−0.0899841
$206$			3.71856e10i			0.100239i
$207$	4.82794e11	+	6.42695e10i	1.27031	+	0.169104i
$208$	4.38316e11			1.12583
$209$			1.13751e11i			0.285250i
$210$	−6.96237e9	+	6.09696e9i	−0.0170475	+	0.0149285i
$211$	−6.66760e11			−1.59425			−0.797126	−	0.603813i	$-0.793648\pi$
$211$	−6.66760e11			−1.59425			−0.797126	+	0.603813i	$0.793648\pi$
$212$			4.98890e11i			1.16500i
$213$	−5.53001e11	−	6.31495e11i	−1.26133	−	1.44036i
$214$	7.06584e10			0.157433
$215$			1.92291e10i			0.0418568i
$216$	1.19451e11	−	7.94414e10i	0.254051	−	0.168958i
$217$	9.76964e10			0.203039
$218$			9.49584e10i			0.192864i
$219$	1.51990e11	−	1.33098e11i	0.301714	−	0.264212i
$220$	−1.07235e11			−0.208077
$221$		−	6.39102e11i		−	1.21230i
$222$	5.68467e10	+	6.49156e10i	0.105424	+	0.120388i
$223$	3.27596e11			0.594038			0.297019	−	0.954872i	$-0.404008\pi$
$223$	3.27596e11			0.594038			0.297019	+	0.954872i	$0.404008\pi$
$224$		−	8.30167e10i		−	0.147206i
$225$	−1.52185e10	+	1.14322e11i	−0.0263912	+	0.198251i
$226$	−2.95940e10			−0.0501952
$227$			2.93173e11i			0.486401i	0.969976	+	0.243201i	$0.0781974\pi$
$227$			2.93173e11i			0.486401i	−0.969976	+	0.243201i	$0.921803\pi$
$228$	−2.70791e11	+	2.37132e11i	−0.439502	+	0.384872i
$229$	6.68388e11			1.06133			0.530666	−	0.847581i	$-0.321942\pi$
$229$	6.68388e11			1.06133			0.530666	+	0.847581i	$0.321942\pi$
$230$			5.69514e10i			0.0884840i
$231$	6.77833e10	+	7.74046e10i	0.103054	+	0.117681i
$232$	−3.07264e11			−0.457164
$233$		−	2.04654e11i		−	0.298017i	−0.988836	−	0.149009i	$-0.952392\pi$
$233$		−	2.04654e11i		−	0.298017i	0.988836	−	0.149009i	$-0.0476082\pi$
$234$	1.30113e11	+	1.73206e10i	0.185456	+	0.0246878i
$235$	5.63982e11			0.786912
$236$			7.43264e11i			1.01527i
$237$	8.57879e10	−	7.51246e10i	0.114732	−	0.100471i
$238$	−3.87089e10			−0.0506905
$239$			4.49686e11i			0.576660i	0.957531	+	0.288330i	$0.0931000\pi$
$239$			4.49686e11i			0.576660i	−0.957531	+	0.288330i	$0.906900\pi$
$240$	−2.17956e11	−	2.48893e11i	−0.273724	−	0.312577i
$241$	−7.08685e11			−0.871702			−0.435851	−	0.900019i	$-0.643553\pi$
$241$	−7.08685e11			−0.871702			−0.435851	+	0.900019i	$0.643553\pi$
$242$			9.90330e10i			0.119317i
$243$	−7.61256e11	+	3.72004e11i	−0.898462	+	0.439052i
$244$	−1.54546e12			−1.78693
$245$			3.52252e11i			0.399046i
$246$	2.10548e10	−	1.84377e10i	0.0233709	−	0.0204660i
$247$	−6.66733e11			−0.725216
$248$		−	1.77079e11i		−	0.188759i
$249$	2.56128e11	+	2.92483e11i	0.267584	+	0.305565i
$250$	−1.34856e10			−0.0138093
$251$			6.04034e11i			0.606307i	0.952942	+	0.303154i	$0.0980396\pi$
$251$			6.04034e11i			0.606307i	−0.952942	+	0.303154i	$0.901960\pi$
$252$	−4.29610e10	+	3.22724e11i	−0.0422739	+	0.317562i
$253$	6.33160e11			0.610817
$254$		−	2.53485e11i		−	0.239764i
$255$	−3.62908e11	+	3.17799e11i	−0.336585	+	0.294748i
$256$	8.46689e11			0.770059
$257$		−	1.94288e12i		−	1.73293i	−0.499237	−	0.866465i	$-0.666386\pi$
$257$		−	1.94288e12i		−	1.73293i	0.499237	−	0.866465i	$-0.333614\pi$
$258$	−1.08826e10	−	1.24272e10i	−0.00951991	−	0.0108712i
$259$	−3.96441e11			−0.340157
$260$		−	6.28540e11i		−	0.529013i
$261$	1.79892e12	+	2.39472e11i	1.48528	+	0.197721i
$262$	−1.80309e11			−0.146053
$263$			5.84830e11i			0.464784i	0.972622	+	0.232392i	$0.0746552\pi$
$263$			5.84830e11i			0.464784i	−0.972622	+	0.232392i	$0.925345\pi$
$264$	1.40299e11	−	1.22860e11i	0.109404	−	0.0958056i
$265$	6.97506e11			0.533726
$266$			4.03825e10i			0.0303239i
$267$	−9.76106e11	−	1.11466e12i	−0.719351	−	0.821456i
$268$	1.82944e12			1.32326
$269$		−	5.38851e11i		−	0.382567i	−0.981535	−	0.191284i	$-0.938735\pi$
$269$		−	5.38851e11i		−	0.382567i	0.981535	−	0.191284i	$-0.0612650\pi$
$270$	−5.48642e10	−	8.24958e10i	−0.0382358	−	0.0574928i
$271$	4.83044e11			0.330476			0.165238	−	0.986254i	$-0.447161\pi$
$271$	4.83044e11			0.330476			0.165238	+	0.986254i	$0.447161\pi$
$272$		−	1.38378e12i		−	0.929443i
$273$	−4.53693e11	+	3.97300e11i	−0.299191	+	0.262002i
$274$	−6.25011e9			−0.00404701
$275$			1.49927e11i			0.0953271i
$276$	1.31992e12	+	1.50727e12i	0.824143	+	0.941123i
$277$	9.99573e10			0.0612937			0.0306468	−	0.999530i	$-0.490243\pi$
$277$	9.99573e10			0.0612937			0.0306468	+	0.999530i	$0.490243\pi$
$278$		−	3.68456e11i		−	0.221902i
$279$	−1.38010e11	+	1.03673e12i	−0.0816373	+	0.613261i
$280$	−7.70680e10			−0.0447800
$281$		−	3.57850e11i		−	0.204253i	−0.994771	−	0.102127i	$-0.967435\pi$
$281$		−	3.57850e11i		−	0.204253i	0.994771	−	0.102127i	$-0.0325647\pi$
$282$	−3.64487e11	+	3.19182e11i	−0.204379	+	0.178975i
$283$	−2.89162e12			−1.59297			−0.796487	−	0.604655i	$-0.793311\pi$
$283$	−2.89162e12			−1.59297			−0.796487	+	0.604655i	$0.793311\pi$
$284$		−	3.45292e12i		−	1.86894i
$285$	3.31538e11	+	3.78597e11i	0.176323	+	0.201351i
$286$	1.70636e11			0.0891745
$287$			1.28582e11i			0.0660345i
$288$	8.80953e11	+	1.17272e11i	0.444621	+	0.0591880i
$289$	−1.67443e9			−0.000830573
$290$			2.12204e11i			0.103458i
$291$	−5.29797e11	+	4.63944e11i	−0.253889	+	0.222331i
$292$	8.31060e11			0.391488
$293$		−	1.25594e12i		−	0.581607i	−0.956783	−	0.290804i	$-0.906077\pi$
$293$		−	1.25594e12i		−	0.581607i	0.956783	−	0.290804i	$-0.0939226\pi$
$294$	−1.99354e11	−	2.27651e11i	−0.0907589	−	0.103641i
$295$	1.03917e12			0.465132
$296$			7.18565e11i			0.316233i
$297$	−9.17152e11	+	6.09956e11i	−0.396880	+	0.263947i
$298$	5.40501e11			0.229993
$299$			3.71115e12i			1.55293i
$300$	−3.56910e11	+	3.12546e11i	−0.146876	+	0.128620i
$301$	7.58934e10			0.0307165
$302$		−	2.40778e11i		−	0.0958479i
$303$	−1.08289e12	−	1.23660e12i	−0.424007	−	0.484191i
$304$	−1.44361e12			−0.556008
$305$			2.16073e12i			0.818654i
$306$	5.46817e10	−	4.10770e11i	0.0203814	−	0.153106i
$307$	−3.70465e12			−1.35849			−0.679244	−	0.733913i	$-0.737692\pi$
$307$	−3.70465e12			−1.35849			−0.679244	+	0.733913i	$0.737692\pi$
$308$			4.23236e11i			0.152697i
$309$	1.37596e12	−	1.20493e12i	0.488442	−	0.427729i
$310$	−1.22295e11			−0.0427169
$311$			8.49329e11i			0.291927i	0.989290	+	0.145963i	$0.0466282\pi$
$311$			8.49329e11i			0.291927i	−0.989290	+	0.145963i	$0.953372\pi$
$312$	7.20122e11	+	8.22337e11i	0.243575	+	0.278149i
$313$	−3.83784e11			−0.127751			−0.0638756	−	0.997958i	$-0.520346\pi$
$313$	−3.83784e11			−0.127751			−0.0638756	+	0.997958i	$0.520346\pi$
$314$			9.59755e10i			0.0314422i
$315$	4.51205e11	+	6.00644e10i	0.145486	+	0.0193671i
$316$	4.69075e11			0.148870
$317$			5.14367e12i			1.60685i	0.595403	+	0.803427i	$0.296992\pi$
$317$			5.14367e12i			1.60685i	−0.595403	+	0.803427i	$0.703008\pi$
$318$	−4.50780e11	+	3.94749e11i	−0.138621	+	0.121391i
$319$	2.35919e12			0.714184
$320$		−	1.29022e12i		−	0.384517i
$321$	−2.28955e12	−	2.61453e12i	−0.671777	−	0.767130i
$322$	2.24776e11			0.0649337
$323$			2.10490e12i			0.598713i
$324$	−3.36398e12	−	9.11784e11i	−0.942168	−	0.255368i
$325$	−8.78770e11			−0.242359
$326$			1.13946e11i			0.0309466i
$327$	3.51369e12	−	3.07695e12i	0.939777	−	0.822965i
$328$	2.33060e11			0.0613902
$329$		−	2.22593e12i		−	0.577473i
$330$	−8.48502e10	−	9.68939e10i	−0.0216812	−	0.0247586i
$331$	−4.35171e10			−0.0109527			−0.00547634	−	0.999985i	$-0.501743\pi$
$331$	−4.35171e10			−0.0109527			−0.00547634	+	0.999985i	$0.501743\pi$
$332$			1.59925e12i			0.396484i
$333$	5.60027e11	−	4.20693e12i	0.136769	−	1.02741i
$334$	2.90094e11			0.0697921
$335$		−	2.55777e12i		−	0.606231i
$336$	−9.82334e11	+	8.60231e11i	−0.229384	+	0.200872i
$337$	3.95468e12			0.909833			0.454916	−	0.890534i	$-0.349669\pi$
$337$	3.95468e12			0.909833			0.454916	+	0.890534i	$0.349669\pi$
$338$			3.19055e11i			0.0723240i
$339$	9.58939e11	+	1.09505e12i	0.214187	+	0.244589i
$340$	−1.98432e12			−0.436735
$341$			1.35962e12i			0.294880i
$342$	−4.28529e11	−	5.70458e10i	−0.0915904	−	0.0121925i
$343$	2.94835e12			0.621025
$344$		−	1.37560e11i		−	0.0285561i
$345$	2.10734e12	−	1.84540e12i	0.431161	−	0.377568i
$346$	9.90129e11			0.199669
$347$		−	5.55283e12i		−	1.10374i	−0.833930	−	0.551870i	$-0.813914\pi$
$347$		−	5.55283e12i		−	1.10374i	0.833930	−	0.551870i	$-0.186086\pi$
$348$	4.91811e12	+	5.61619e12i	0.963611	+	1.10039i
$349$	4.15329e12			0.802168			0.401084	−	0.916041i	$-0.368634\pi$
$349$	4.15329e12			0.802168			0.401084	+	0.916041i	$0.368634\pi$
$350$			5.32251e10i			0.0101339i
$351$	−3.57515e12	−	5.37572e12i	−0.671055	−	1.00902i
$352$	1.15533e12			0.213792
$353$		−	7.61709e11i		−	0.138968i	−0.997583	−	0.0694842i	$-0.977865\pi$
$353$		−	7.61709e11i		−	0.138968i	0.997583	−	0.0694842i	$-0.0221353\pi$
$354$	−6.71588e11	+	5.88110e11i	−0.120805	+	0.105789i
$355$	−4.82757e12			−0.856224
$356$		−	6.09477e12i		−	1.06588i
$357$	1.25429e12	+	1.43233e12i	0.216300	+	0.247002i
$358$	−1.18899e12			−0.202191
$359$			9.96528e12i			1.67116i	0.549372	+	0.835578i	$0.314867\pi$
$359$			9.96528e12i			1.67116i	−0.549372	+	0.835578i	$0.685133\pi$
$360$	1.08869e11	−	8.17827e11i	0.0180050	−	0.135254i
$361$	−3.93516e12			−0.641840
$362$		−	1.35269e12i		−	0.217598i
$363$	3.66446e12	−	3.20898e12i	0.581403	−	0.509136i
$364$	−2.48072e12			−0.388214
$365$		−	1.16192e12i		−	0.179354i
$366$	−1.22285e12	−	1.39642e12i	−0.186195	−	0.212623i
$367$	4.63111e12			0.695593			0.347796	−	0.937570i	$-0.386930\pi$
$367$	4.63111e12			0.695593			0.347796	+	0.937570i	$0.386930\pi$
$368$			8.03537e12i			1.19060i
$369$	−1.36448e12	−	1.81640e11i	−0.199451	−	0.0265509i
$370$	4.96259e11			0.0715648
$371$		−	2.75292e12i		−	0.391673i
$372$	−3.23665e12	+	2.83434e12i	−0.454341	+	0.397867i
$373$	−1.30203e13			−1.80334			−0.901668	−	0.432430i	$-0.857656\pi$
$373$	−1.30203e13			−1.80334			−0.901668	+	0.432430i	$0.857656\pi$
$374$		−	5.38704e11i		−	0.0736194i
$375$	4.36976e11	+	4.99001e11i	0.0589252	+	0.0672891i
$376$	−4.03458e12			−0.536858
$377$			1.38280e13i			1.81573i
$378$	−3.25595e11	+	2.16538e11i	−0.0421909	+	0.0280592i
$379$	7.47154e12			0.955463			0.477732	−	0.878506i	$-0.341459\pi$
$379$	7.47154e12			0.955463			0.477732	+	0.878506i	$0.341459\pi$
$380$			2.07011e12i			0.261262i
$381$	−9.37957e12	+	8.21371e12i	−1.16831	+	1.02309i
$382$	5.70272e11			0.0701076
$383$		−	1.14597e13i		−	1.39053i	−0.718753	−	0.695266i	$-0.755287\pi$
$383$		−	1.14597e13i		−	1.39053i	0.718753	−	0.695266i	$-0.244713\pi$
$384$	3.19746e12	+	3.65132e12i	0.382956	+	0.437314i
$385$	5.91733e11			0.0699555
$386$			1.88833e12i			0.220365i
$387$	−1.07210e11	+	8.05363e11i	−0.0123504	+	0.0927762i
$388$	−2.89685e12			−0.329433
$389$		−	1.92602e12i		−	0.216229i	−0.994138	−	0.108114i	$-0.965519\pi$
$389$		−	1.92602e12i		−	0.216229i	0.994138	−	0.108114i	$-0.0344813\pi$
$390$	5.67926e11	−	4.97334e11i	0.0629461	−	0.0551220i
$391$	1.17162e13			1.28205
$392$		−	2.51992e12i		−	0.272243i
$393$	5.84257e12	+	6.67187e12i	0.623219	+	0.711680i
$394$	−6.85704e11			−0.0722197
$395$		−	6.55820e11i		−	0.0682024i
$396$	−4.49128e12	−	5.97880e11i	−0.461205	−	0.0613957i
$397$	1.93350e12			0.196061			0.0980304	−	0.995183i	$-0.468746\pi$
$397$	1.93350e12			0.196061			0.0980304	+	0.995183i	$0.468746\pi$
$398$			1.08218e12i			0.108364i
$399$	1.49425e12	−	1.30852e12i	0.147761	−	0.129394i
$400$	−1.90271e12			−0.185811
$401$		−	1.66814e13i		−	1.60883i	−0.594069	−	0.804414i	$-0.702479\pi$
$401$		−	1.66814e13i		−	1.60883i	0.594069	−	0.804414i	$-0.297521\pi$
$402$	1.44755e12	+	1.65302e12i	0.137881	+	0.157452i
$403$	−7.96917e12			−0.749701
$404$		−	6.76154e12i		−	0.628260i
$405$	−1.27478e12	+	4.70323e12i	−0.116993	+	0.431639i
$406$	8.37529e11			0.0759224
$407$		−	5.51718e12i		−	0.494021i
$408$	2.59615e12	−	2.27345e12i	0.229630	−	0.201087i
$409$	−7.66089e12			−0.669365			−0.334682	−	0.942331i	$-0.608629\pi$
$409$	−7.66089e12			−0.669365			−0.334682	+	0.942331i	$0.608629\pi$
$410$		−	1.60957e11i		−	0.0138928i
$411$	2.02523e11	+	2.31269e11i	0.0172689	+	0.0197201i
$412$	7.52353e12			0.633776
$413$		−	4.10140e12i		−	0.341336i
$414$	−3.17527e11	+	2.38527e12i	−0.0261083	+	0.196126i
$415$	2.23594e12			0.181643
$416$			6.77173e12i			0.543542i
$417$	−1.36338e13	+	1.19391e13i	−1.08127	+	0.946874i
$418$	−5.61994e11			−0.0440403
$419$		−	1.40555e13i		−	1.08837i	−0.838966	−	0.544184i	$-0.816839\pi$
$419$		−	1.40555e13i		−	1.08837i	0.838966	−	0.544184i	$-0.183161\pi$
$420$	1.23356e12	+	1.40865e12i	0.0943873	+	0.107785i
$421$	1.26332e13			0.955216			0.477608	−	0.878573i	$-0.341504\pi$
$421$	1.26332e13			0.955216			0.477608	+	0.878573i	$0.341504\pi$
$422$		−	3.29416e12i		−	0.246140i
$423$	2.36210e13	+	3.14443e12i	1.74420	+	0.232188i
$424$	−4.98978e12			−0.364126
$425$			2.77431e12i			0.200083i
$426$	3.11993e12	−	2.73213e12i	0.222381	−	0.194739i
$427$	8.52796e12			0.600767
$428$		−	1.42959e13i		−	0.995386i
$429$	−5.52914e12	−	6.31395e12i	−0.380514	−	0.434525i
$430$	−9.50023e10			−0.00646237
$431$			1.68808e13i			1.13503i	0.823363	+	0.567515i	$0.192095\pi$
$431$			1.68808e13i			1.13503i	−0.823363	+	0.567515i	$0.807905\pi$
$432$	−7.74089e12	−	1.16395e13i	−0.514484	−	0.773598i
$433$	−5.41352e12			−0.355664			−0.177832	−	0.984061i	$-0.556908\pi$
$433$	−5.41352e12			−0.355664			−0.177832	+	0.984061i	$0.556908\pi$
$434$			4.82674e11i			0.0313477i
$435$	7.85208e12	−	6.87608e12i	0.504125	−	0.441463i
$436$	1.92123e13			1.21940
$437$		−	1.22228e13i		−	0.766943i
$438$	6.57579e11	+	7.50917e11i	0.0407922	+	0.0465823i
$439$	−3.52336e12			−0.216090			−0.108045	−	0.994146i	$-0.534459\pi$
$439$	−3.52336e12			−0.216090			−0.108045	+	0.994146i	$0.534459\pi$
$440$		−	1.07254e12i		−	0.0650354i
$441$	−1.96395e12	+	1.47532e13i	−0.117743	+	0.884491i
$442$	3.15752e12			0.187169
$443$			2.39026e13i			1.40096i	0.713670	+	0.700482i	$0.247032\pi$
$443$			2.39026e13i			1.40096i	−0.713670	+	0.700482i	$0.752968\pi$
$444$	1.31340e13	−	1.15014e13i	0.761169	−	0.666557i
$445$	−8.52118e12			−0.488315
$446$			1.61850e12i			0.0917148i
$447$	−1.75139e13	−	1.99999e13i	−0.981398	−	1.12070i
$448$	−5.09226e12			−0.282176
$449$			1.51612e13i			0.830810i	0.909637	+	0.415405i	$0.136360\pi$
$449$			1.51612e13i			0.830810i	−0.909637	+	0.415405i	$0.863640\pi$
$450$	−5.64812e11	−	7.51878e10i	−0.0306084	−	0.00407460i
$451$	−1.78945e12			−0.0959041
$452$			5.98758e12i			0.317365i
$453$	−8.90938e12	+	7.80196e12i	−0.467043	+	0.408990i
$454$	−1.44844e12			−0.0750966
$455$			3.46834e12i			0.177854i
$456$	−2.37174e12	−	2.70839e12i	−0.120294	−	0.137368i
$457$	−3.51782e13			−1.76479			−0.882395	−	0.470510i	$-0.844070\pi$
$457$	−3.51782e13			−1.76479			−0.882395	+	0.470510i	$0.844070\pi$
$458$			3.30221e12i			0.163861i
$459$	−1.69714e13	+	1.12869e13i	−0.833015	+	0.554000i
$460$	1.15226e13			0.559451
$461$			2.62076e13i			1.25870i	0.777121	+	0.629352i	$0.216679\pi$
$461$			2.62076e13i			1.25870i	−0.777121	+	0.629352i	$0.783321\pi$
$462$	−3.82421e11	+	3.34887e11i	−0.0181691	+	0.0159107i
$463$	−1.57165e13			−0.738671			−0.369336	−	0.929296i	$-0.620415\pi$
$463$	−1.57165e13			−0.738671			−0.369336	+	0.929296i	$0.620415\pi$
$464$			2.99403e13i			1.39209i
$465$	3.96274e12	+	4.52521e12i	0.182276	+	0.208149i
$466$	1.01110e12			0.0460115
$467$		−	1.91543e13i		−	0.862345i	−0.902270	−	0.431172i	$-0.858100\pi$
$467$		−	1.91543e13i		−	0.862345i	0.902270	−	0.431172i	$-0.141900\pi$
$468$	3.50436e12	−	2.63248e13i	0.156092	−	1.17256i
$469$	−1.00950e13			−0.444880
$470$			2.78638e12i			0.121493i
$471$	3.55133e12	−	3.10991e12i	0.153210	−	0.134166i
$472$	−7.43394e12			−0.317329
$473$			1.05619e12i			0.0446106i
$474$	3.71157e11	+	4.23840e11i	0.0155119	+	0.0177137i
$475$	2.89425e12			0.119693
$476$			7.83173e12i			0.320496i
$477$	2.92133e13	+	3.88888e12i	1.18301	+	0.157483i
$478$	−2.22170e12			−0.0890318
$479$		−	1.41157e13i		−	0.559791i	−0.960030	−	0.279896i	$-0.909700\pi$
$479$		−	1.41157e13i		−	0.559791i	0.960030	−	0.279896i	$-0.0902999\pi$
$480$	3.84526e12	−	3.36730e12i	0.150910	−	0.132153i
$481$	3.23380e13			1.25599
$482$		−	3.50130e12i		−	0.134584i
$483$	−7.28344e12	−	8.31726e12i	−0.277077	−	0.316406i
$484$	2.00367e13			0.754397
$485$			4.05013e12i			0.150925i
$486$	−1.83790e12	−	3.76103e12i	−0.0677863	−	0.138716i
$487$	−9.86654e12			−0.360181			−0.180090	−	0.983650i	$-0.557639\pi$
$487$	−9.86654e12			−0.360181			−0.180090	+	0.983650i	$0.557639\pi$
$488$		−	1.54573e13i		−	0.558514i
$489$	4.21630e12	−	3.69222e12i	0.150795	−	0.132051i
$490$	−1.74032e12			−0.0616096
$491$		−	9.49971e12i		−	0.332891i	−0.986051	−	0.166446i	$-0.946771\pi$
$491$		−	9.49971e12i		−	0.332891i	0.986051	−	0.166446i	$-0.0532291\pi$
$492$	−3.73039e12	−	4.25989e12i	−0.129398	−	0.147765i
$493$	4.36555e13			1.49901
$494$		−	3.29403e12i		−	0.111968i
$495$	−8.35904e11	+	6.27933e12i	−0.0281275	+	0.211294i
$496$	−1.72548e13			−0.574780
$497$			1.90535e13i			0.628337i
$498$	−1.44503e12	+	1.26541e12i	−0.0471769	+	0.0413129i
$499$	1.62883e13			0.526468			0.263234	−	0.964732i	$-0.415211\pi$
$499$	1.62883e13			0.526468			0.263234	+	0.964732i	$0.415211\pi$
$500$			2.72846e12i			0.0873107i
$501$	−9.39995e12	−	1.07342e13i	−0.297808	−	0.340080i
$502$	−2.98426e12			−0.0936092
$503$			1.24997e13i			0.388203i	0.980981	+	0.194101i	$0.0621791\pi$
$503$			1.24997e13i			0.388203i	−0.980981	+	0.194101i	$0.937821\pi$
$504$	−3.22780e12	−	4.29685e11i	−0.0992555	−	0.0132129i
$505$	−9.45341e12			−0.287827
$506$			3.12816e12i			0.0943054i
$507$	1.18058e13	−	1.03384e13i	0.352417	−	0.308612i
$508$	−5.12861e13			−1.51594
$509$		−	6.53479e13i		−	1.91268i	−0.292253	−	0.956341i	$-0.594405\pi$
$509$		−	6.53479e13i		−	1.91268i	0.292253	−	0.956341i	$-0.405595\pi$
$510$	−1.57010e12	−	1.79296e12i	−0.0455068	−	0.0519662i
$511$	−4.58586e12			−0.131618
$512$			2.46355e13i			0.700182i
$513$	1.17748e13	+	1.77051e13i	0.331412	+	0.498323i
$514$	9.59892e12			0.267551
$515$		−	1.05188e13i		−	0.290354i
$516$	−2.51433e12	+	2.20180e12i	−0.0687343	+	0.0601907i
$517$	3.09778e13			0.838683
$518$		−	1.95864e12i		−	0.0525176i
$519$	−3.20832e13	−	3.66372e13i	−0.852003	−	0.972938i
$520$	6.28650e12			0.165345
$521$		−	5.07986e13i		−	1.32331i	−0.749807	−	0.661657i	$-0.769853\pi$
$521$		−	5.07986e13i		−	1.32331i	0.749807	−	0.661657i	$-0.230147\pi$
$522$	−1.18313e12	+	8.88766e12i	−0.0305266	+	0.229316i
$523$	6.59187e13			1.68461			0.842307	−	0.538999i	$-0.181197\pi$
$523$	6.59187e13			1.68461			0.842307	+	0.538999i	$0.181197\pi$
$524$			3.64808e13i			0.923437i
$525$	1.96946e12	−	1.72466e12i	0.0493799	−	0.0432421i
$526$	−2.88939e12			−0.0717591
$527$			2.51590e13i			0.618928i
$528$	−1.19717e13	−	1.36709e13i	−0.291733	−	0.333141i
$529$	−2.66076e13			−0.642286
$530$			3.44607e12i			0.0824032i
$531$	4.35230e13	+	5.79379e12i	1.03097	+	0.137243i
$532$	8.17033e12			0.191726
$533$		−	1.04885e13i		−	0.243826i
$534$	5.50702e12	−	4.82250e12i	0.126827	−	0.111062i
$535$	−1.99872e13			−0.456020
$536$			1.82976e13i			0.413591i
$537$	3.85268e13	+	4.39954e13i	0.862763	+	0.985225i
$538$	2.66222e12			0.0590654
$539$			1.93481e13i			0.425299i
$540$	−1.66909e13	+	1.11003e13i	−0.363505	+	0.241750i
$541$	−6.93652e13			−1.49677			−0.748386	−	0.663264i	$-0.769171\pi$
$541$	−6.93652e13			−1.49677			−0.748386	+	0.663264i	$0.769171\pi$
$542$			2.38651e12i			0.0510230i
$543$	−5.00527e13	+	4.38312e13i	−1.06030	+	0.928506i
$544$	2.13786e13			0.448730
$545$		−	2.68610e13i		−	0.558651i
$546$	−1.96288e12	−	2.24149e12i	−0.0404511	−	0.0461928i
$547$	−9.67192e12			−0.197504			−0.0987520	−	0.995112i	$-0.531485\pi$
$547$	−9.67192e12			−0.197504			−0.0987520	+	0.995112i	$0.531485\pi$
$548$			1.26454e12i			0.0255877i
$549$	−1.20469e13	+	9.04967e13i	−0.241554	+	1.81456i
$550$	−7.40722e11			−0.0147178
$551$		−	4.55428e13i		−	0.896731i
$552$	−1.50754e13	+	1.32015e13i	−0.294152	+	0.257590i
$553$	−2.58840e12			−0.0500501
$554$			4.93844e11i			0.00946327i
$555$	−1.60803e13	−	1.83628e13i	−0.305372	−	0.348717i
$556$	−7.45474e13			−1.40300
$557$		−	4.20154e13i		−	0.783669i	−0.920036	−	0.391834i	$-0.871841\pi$
$557$		−	4.20154e13i		−	0.783669i	0.920036	−	0.391834i	$-0.128159\pi$
$558$	−5.12203e12	−	6.81844e11i	−0.0946827	−	0.0126042i
$559$	−6.19069e12			−0.113417
$560$			7.50962e12i			0.136357i
$561$	−1.99334e13	+	1.74557e13i	−0.358729	+	0.314140i
$562$	1.76797e12			0.0315351
$563$			2.90627e13i			0.513800i	0.966438	+	0.256900i	$0.0827012\pi$
$563$			2.90627e13i			0.513800i	−0.966438	+	0.256900i	$0.917299\pi$
$564$	6.45781e13	+	7.37444e13i	1.13159	+	1.29221i
$565$	8.37132e12			0.145396
$566$		−	1.42862e13i		−	0.245943i
$567$	1.85627e13	+	5.03130e12i	0.316757	+	0.0858549i
$568$	3.45352e13			0.584145
$569$		−	2.07825e13i		−	0.348448i	−0.984706	−	0.174224i	$-0.944258\pi$
$569$		−	2.07825e13i		−	0.348448i	0.984706	−	0.174224i	$-0.0557416\pi$
$570$	−1.87048e12	+	1.63798e12i	−0.0310870	+	0.0272229i
$571$	−2.91011e13			−0.479435			−0.239717	−	0.970843i	$-0.577055\pi$
$571$	−2.91011e13			−0.479435			−0.239717	+	0.970843i	$0.577055\pi$
$572$		−	3.45237e13i		−	0.563816i
$573$	−1.84786e13	−	2.11015e13i	−0.299155	−	0.341617i
$574$	−6.35267e11			−0.0101952
$575$		−	1.61099e13i		−	0.256303i
$576$	7.19352e12	−	5.40379e13i	0.113456	−	0.852287i
$577$	1.02857e13			0.160825			0.0804124	−	0.996762i	$-0.474376\pi$
$577$	1.02857e13			0.160825			0.0804124	+	0.996762i	$0.474376\pi$
$578$		−	8.27261e9i		−	0.000128234i
$579$	6.98730e13	−	6.11879e13i	1.07378	−	0.940313i
$580$	4.29340e13			0.654125
$581$		−	8.82480e12i		−	0.133298i
$582$	−2.29214e12	−	2.61749e12i	−0.0343263	−	0.0391986i
$583$	3.83118e13			0.568840
$584$			8.31206e12i			0.122361i
$585$	−3.68051e13	−	4.89950e12i	−0.537192	−	0.0715110i
$586$	6.20502e12			0.0897957
$587$			3.11526e13i			0.446996i	0.974704	+	0.223498i	$0.0717477\pi$
$587$			3.11526e13i			0.446996i	−0.974704	+	0.223498i	$0.928252\pi$
$588$	−4.60592e13	+	4.03341e13i	−0.655285	+	0.573834i
$589$	2.62467e13			0.370253
$590$			5.13407e12i			0.0718128i
$591$	2.22189e13	+	2.53727e13i	0.308167	+	0.351909i
$592$	7.00180e13			0.962945
$593$		−	3.66027e13i		−	0.499160i	−0.968354	−	0.249580i	$-0.919707\pi$
$593$		−	3.66027e13i		−	0.499160i	0.968354	−	0.249580i	$-0.0802926\pi$
$594$	−3.01352e12	−	4.53124e12i	−0.0407513	−	0.0612752i
$595$	1.09497e13			0.146830
$596$		−	1.09356e14i		−	1.45416i
$597$	4.00433e13	−	3.50659e13i	0.528029	−	0.462396i
$598$	−1.83351e13			−0.239761
$599$			8.96289e13i			1.16229i	0.813801	+	0.581144i	$0.197395\pi$
$599$			8.96289e13i			1.16229i	−0.813801	+	0.581144i	$0.802605\pi$
$600$	−3.12601e12	−	3.56972e12i	−0.0402008	−	0.0459069i
$601$	−1.73929e13			−0.221820			−0.110910	−	0.993830i	$-0.535377\pi$
$601$	−1.73929e13			−0.221820			−0.110910	+	0.993830i	$0.535377\pi$
$602$			3.74955e11i			0.00474239i
$603$	1.42606e13	−	1.07126e14i	0.178876	−	1.34372i
$604$	−4.87151e13			−0.606009
$605$		−	2.80136e13i		−	0.345615i
$606$	6.10949e12	−	5.35009e12i	0.0747553	−	0.0654633i
$607$	−2.05879e13			−0.249844			−0.124922	−	0.992167i	$-0.539868\pi$
$607$	−2.05879e13			−0.249844			−0.124922	+	0.992167i	$0.539868\pi$
$608$		−	2.23029e13i		−	0.268437i
$609$	−2.71385e13	−	3.09906e13i	−0.323966	−	0.369951i
$610$	−1.06752e13			−0.126394
$611$			1.81571e14i			2.13226i
$612$	−8.31085e13	−	1.10634e13i	−0.968029	−	0.128864i
$613$	1.11168e14			1.28433			0.642164	−	0.766567i	$-0.278037\pi$
$613$	1.11168e14			1.28433			0.642164	+	0.766567i	$0.278037\pi$
$614$		−	1.83030e13i		−	0.209740i
$615$	−5.95581e12	+	5.21551e12i	−0.0676964	+	0.0592818i
$616$	−4.23310e12			−0.0477260
$617$			5.43384e13i			0.607689i	0.952722	+	0.303845i	$0.0982703\pi$
$617$			5.43384e13i			0.607689i	−0.952722	+	0.303845i	$0.901730\pi$
$618$	5.95302e12	+	6.79800e12i	0.0660381	+	0.0754117i
$619$	−7.92716e13			−0.872297			−0.436148	−	0.899875i	$-0.643658\pi$
$619$	−7.92716e13			−0.872297			−0.436148	+	0.899875i	$0.643658\pi$
$620$			2.47432e13i			0.270083i
$621$	9.85496e13	−	6.55408e13i	1.06708	−	0.709666i
$622$	−4.19616e12			−0.0450713
$623$			3.36314e13i			0.358348i
$624$	8.01298e13	−	7.01697e13i	0.846976	−	0.741698i
$625$	3.81470e12			0.0400000
$626$		−	1.89610e12i		−	0.0197238i
$627$	1.82104e13	+	2.07952e13i	0.187923	+	0.214598i
$628$	1.94181e13			0.198797
$629$		−	1.02092e14i		−	1.03691i
$630$	−2.96751e11	+	2.22920e12i	−0.00299013	+	0.0224619i
$631$	−4.25559e13			−0.425415			−0.212708	−	0.977116i	$-0.568228\pi$
$631$	−4.25559e13			−0.425415			−0.212708	+	0.977116i	$0.568228\pi$
$632$			4.69157e12i			0.0465300i
$633$	−1.21892e14	+	1.06741e14i	−1.19938	+	1.05030i
$634$	−2.54126e13			−0.248086
$635$			7.17038e13i			0.694502i
$636$	7.98670e13	+	9.12034e13i	0.767506	+	0.876447i
$637$	−1.13405e14			−1.08128
$638$			1.16557e13i			0.110264i
$639$	−2.02191e14	−	2.69157e13i	−1.89783	−	0.252639i
$640$	2.79131e13			0.259961
$641$			9.84752e13i			0.909990i	0.890494	+	0.454995i	$0.150359\pi$
$641$			9.84752e13i			0.909990i	−0.890494	+	0.454995i	$0.849641\pi$
$642$	1.29172e13	−	1.13116e13i	0.118439	−	0.103717i
$643$	6.54316e12			0.0595296			0.0297648	−	0.999557i	$-0.490524\pi$
$643$	6.54316e12			0.0595296			0.0297648	+	0.999557i	$0.490524\pi$
$644$		−	4.54775e13i		−	0.410551i
$645$	3.07837e12	+	3.51532e12i	0.0275754	+	0.0314895i
$646$	−1.03994e13			−0.0924367
$647$			1.12859e14i			0.995440i	0.867338	+	0.497720i	$0.165829\pi$
$647$			1.12859e14i			0.995440i	−0.867338	+	0.497720i	$0.834171\pi$
$648$	9.11944e12	−	3.36457e13i	0.0798166	−	0.294479i
$649$	5.70783e13			0.495733
$650$		−	4.34161e12i		−	0.0374183i
$651$	1.78601e13	−	1.56401e13i	0.152749	−	0.133763i
$652$	2.30541e13			0.195663
$653$			9.10523e13i			0.766875i	0.923567	+	0.383438i	$0.125260\pi$
$653$			9.10523e13i			0.766875i	−0.923567	+	0.383438i	$0.874740\pi$
$654$	1.52018e13	+	1.73596e13i	0.127059	+	0.145094i
$655$	5.10043e13			0.423058
$656$		−	2.27097e13i		−	0.186936i
$657$	6.47816e12	−	4.86641e13i	0.0529206	−	0.397541i
$658$	1.09973e13			0.0891574
$659$			4.01991e13i			0.323436i	0.986837	+	0.161718i	$0.0517035\pi$
$659$			4.01991e13i			0.323436i	−0.986837	+	0.161718i	$0.948296\pi$
$660$	−1.96039e13	+	1.71672e13i	−0.156539	+	0.137082i
$661$	2.35135e13			0.186342			0.0931710	−	0.995650i	$-0.470300\pi$
$661$	2.35135e13			0.186342			0.0931710	+	0.995650i	$0.470300\pi$
$662$		−	2.14999e11i		−	0.00169101i
$663$	−1.02313e14	−	1.16836e14i	−0.798665	−	0.912029i
$664$	−1.59953e13			−0.123923
$665$		−	1.14231e13i		−	0.0878363i
$666$	2.07846e13	+	2.76684e12i	0.158624	+	0.0211161i
$667$	−2.53500e14			−1.92021
$668$		−	5.86929e13i		−	0.441269i
$669$	5.98886e13	−	5.24446e13i	0.446903	−	0.391354i
$670$	1.26368e13			0.0935973
$671$			1.18682e14i			0.872513i
$672$	−1.32901e13	−	1.51765e13i	−0.0969797	−	0.110745i
$673$	3.86676e13			0.280074			0.140037	−	0.990146i	$-0.455278\pi$
$673$	3.86676e13			0.280074			0.140037	+	0.990146i	$0.455278\pi$
$674$			1.95383e13i			0.140471i
$675$	1.55195e13	+	2.33357e13i	0.110754	+	0.166534i
$676$	6.45525e13			0.457277
$677$		−	2.73795e14i		−	1.92523i	−0.270881	−	0.962613i	$-0.587315\pi$
$677$		−	2.73795e14i		−	1.92523i	0.270881	−	0.962613i	$-0.412685\pi$
$678$	−5.41016e12	+	4.73769e12i	−0.0377626	+	0.0330688i
$679$	1.59851e13			0.110756
$680$		−	1.98467e13i		−	0.136503i
$681$	4.69339e13	+	5.35957e13i	0.320443	+	0.365927i
$682$	−6.71728e12			−0.0455273
$683$		−	5.50715e13i		−	0.370530i	−0.982689	−	0.185265i	$-0.940686\pi$
$683$		−	5.50715e13i		−	0.370530i	0.982689	−	0.185265i	$-0.0593143\pi$
$684$	−1.15417e13	+	8.67016e13i	−0.0770885	+	0.579091i
$685$	1.76798e12			0.0117226
$686$			1.45665e13i			0.0958815i
$687$	1.22190e14	−	1.07002e14i	0.798456	−	0.699209i
$688$	−1.34040e13			−0.0869548
$689$			2.24558e14i			1.44621i
$690$	9.11730e12	+	1.04114e13i	0.0582936	+	0.0665679i
$691$	2.33019e14			1.47911			0.739557	−	0.673094i	$-0.235035\pi$
$691$	2.33019e14			1.47911			0.739557	+	0.673094i	$0.235035\pi$
$692$		−	2.00326e14i		−	1.26243i
$693$	2.47833e13	+	3.29915e12i	0.155057	+	0.0206412i
$694$	2.74341e13			0.170409
$695$			1.04226e14i			0.642763i
$696$	−5.61718e13	+	4.91897e13i	−0.343931	+	0.301181i
$697$	−3.31127e13			−0.201294
$698$			2.05196e13i			0.123848i
$699$	−3.27629e13	−	3.74134e13i	−0.196335	−	0.224203i
$700$	1.07687e13			0.0640727
$701$		−	3.13777e14i		−	1.85366i	−0.375475	−	0.926832i	$-0.622521\pi$
$701$		−	3.13777e14i		−	1.85366i	0.375475	−	0.926832i	$-0.377479\pi$
$702$	2.65590e13	−	1.76632e13i	0.155785	−	0.103606i
$703$	−1.06506e14			−0.620294
$704$		−	7.08680e13i		−	0.409814i
$705$	1.03103e14	−	9.02875e13i	0.592006	−	0.518420i
$706$	3.76327e12			0.0214556
$707$			3.73108e13i			0.211221i
$708$	1.18989e14	+	1.35878e14i	0.668866	+	0.763806i
$709$	2.62044e14			1.46266			0.731329	−	0.682024i	$-0.238900\pi$
$709$	2.62044e14			1.46266			0.731329	+	0.682024i	$0.238900\pi$
$710$		−	2.38509e13i		−	0.132194i
$711$	3.65647e12	−	2.74674e13i	0.0201240	−	0.151172i
$712$	6.09583e13			0.333145
$713$		−	1.46094e14i		−	0.792837i
$714$	−7.07648e12	+	6.19688e12i	−0.0381352	+	0.0333951i
$715$	−4.82681e13			−0.258303
$716$			2.40560e14i			1.27837i
$717$	7.19899e13	+	8.22082e13i	0.379905	+	0.433830i
$718$	−4.92340e13			−0.258014
$719$		−	2.80403e14i		−	1.45928i	−0.683833	−	0.729638i	$-0.739688\pi$
$719$		−	2.80403e14i		−	1.45928i	0.683833	−	0.729638i	$-0.260312\pi$
$720$	−7.96903e13	−	1.06084e13i	−0.411854	−	0.0548260i
$721$	−4.15155e13			−0.213076
$722$		−	1.94419e13i		−	0.0990952i
$723$	−1.29557e14	+	1.13453e14i	−0.655795	+	0.574280i
$724$	−2.73681e14			−1.37579
$725$		−	6.00266e13i		−	0.299677i
$726$	1.58541e13	+	1.81045e13i	0.0786066	+	0.0897641i
$727$	−1.50248e14			−0.739840			−0.369920	−	0.929064i	$-0.620615\pi$
$727$	−1.50248e14			−0.739840			−0.369920	+	0.929064i	$0.620615\pi$
$728$		−	2.48116e13i		−	0.121338i
$729$	−7.96134e13	+	1.89876e14i	−0.386677	+	0.922215i
$730$	5.74051e12			0.0276909
$731$			1.95442e13i			0.0936335i
$732$	−2.82529e14	+	2.47411e14i	−1.34434	+	1.17724i
$733$	2.65643e14			1.25539			0.627694	−	0.778460i	$-0.283999\pi$
$733$	2.65643e14			1.25539			0.627694	+	0.778460i	$0.283999\pi$
$734$			2.28803e13i			0.107394i
$735$	5.63917e13	+	6.43961e13i	0.262893	+	0.300208i
$736$	−1.24142e14			−0.574816
$737$		−	1.40490e14i		−	0.646114i
$738$	8.97402e11	−	6.74130e12i	0.00409926	−	0.0307937i
$739$	−1.11745e13			−0.0506999			−0.0253500	−	0.999679i	$-0.508070\pi$
$739$	−1.11745e13			−0.0506999			−0.0253500	+	0.999679i	$0.508070\pi$
$740$		−	1.00405e14i		−	0.452477i
$741$	−1.21887e14	+	1.06737e14i	−0.545591	+	0.477775i
$742$	1.36009e13			0.0604713
$743$			1.72434e14i			0.761517i	0.924674	+	0.380759i	$0.124337\pi$
$743$			1.72434e14i			0.761517i	−0.924674	+	0.380759i	$0.875663\pi$
$744$	−2.83484e13	−	3.23722e13i	−0.124355	−	0.142006i
$745$	−1.52892e14			−0.666200
$746$		−	6.43274e13i		−	0.278421i
$747$	9.36467e13	+	1.24662e13i	0.402615	+	0.0535960i
$748$	−1.08993e14			−0.465467
$749$			7.88858e13i			0.334649i
$750$	−2.46534e12	+	2.15890e12i	−0.0103889	+	0.00909759i
$751$	−8.67803e13			−0.363263			−0.181632	−	0.983367i	$-0.558138\pi$
$751$	−8.67803e13			−0.363263			−0.181632	+	0.983367i	$0.558138\pi$
$752$			3.93136e14i			1.63476i
$753$	9.66994e13	+	1.10425e14i	0.399437	+	0.456134i
$754$	−6.83179e13			−0.280335
$755$			6.81093e13i			0.277633i
$756$	4.38108e13	+	6.58756e13i	0.177408	+	0.266757i
$757$	4.22941e14			1.70138			0.850689	−	0.525669i	$-0.176185\pi$
$757$	4.22941e14			1.70138			0.850689	+	0.525669i	$0.176185\pi$
$758$			3.69135e13i			0.147516i
$759$	1.15750e14	−	1.01362e14i	0.459526	−	0.402408i
$760$	−2.07047e13			−0.0816586
$761$		−	2.50798e14i		−	0.982654i	−0.870975	−	0.491327i	$-0.836512\pi$
$761$		−	2.50798e14i		−	0.982654i	0.870975	−	0.491327i	$-0.163488\pi$
$762$	−4.05802e13	−	4.63403e13i	−0.157957	−	0.180378i
$763$	−1.06015e14			−0.409964
$764$		−	1.15380e14i		−	0.443264i
$765$	−1.54679e13	+	1.16195e14i	−0.0590370	+	0.443487i
$766$	5.66175e13			0.214687
$767$			3.34554e14i			1.26035i
$768$	1.54785e14	−	1.35546e14i	0.579327	−	0.507317i
$769$	6.46104e13			0.240254			0.120127	−	0.992759i	$-0.461670\pi$
$769$	6.46104e13			0.240254			0.120127	+	0.992759i	$0.461670\pi$
$770$			2.92349e12i			0.0108006i
$771$	−3.11035e14	−	3.55184e14i	−1.14166	−	1.30371i
$772$	3.82055e14			1.39328
$773$		−	2.45543e14i		−	0.889673i	−0.895612	−	0.444836i	$-0.853262\pi$
$773$		−	2.45543e14i		−	0.889673i	0.895612	−	0.444836i	$-0.146738\pi$
$774$	−3.97894e12	−	5.29676e11i	−0.0143239	−	0.00190680i
$775$	3.45938e13			0.123734
$776$		−	2.89736e13i		−	0.102966i
$777$	−7.24743e13	+	6.34659e13i	−0.255905	+	0.224097i
$778$	9.51563e12			0.0333841
$779$			3.45443e13i			0.120417i
$780$	−1.00622e14	−	1.14905e14i	−0.348515	−	0.397984i
$781$	−2.65164e14			−0.912554
$782$			5.78847e13i			0.197938i
$783$	3.67202e14	−	2.44209e14i	1.24766	−	0.829761i
$784$	−2.45545e14			−0.828992
$785$		−	2.71488e13i		−	0.0910755i
$786$	−3.29627e13	+	2.88655e13i	−0.109878	+	0.0962203i
$787$	1.30473e13			0.0432162			0.0216081	−	0.999767i	$-0.493121\pi$
$787$	1.30473e13			0.0432162			0.0216081	+	0.999767i	$0.493121\pi$
$788$			1.38734e14i			0.456617i
$789$	9.36251e13	+	1.06914e14i	0.306201	+	0.349664i
$790$	3.24012e12			0.0105299
$791$		−	3.30400e13i		−	0.106698i
$792$	5.97984e12	−	4.49207e13i	0.0191895	−	0.144152i
$793$	−6.95633e14			−2.21827
$794$			9.55254e12i			0.0302703i
$795$	1.27513e14	−	1.11663e14i	0.401530	−	0.351621i
$796$	2.18950e14			0.685142
$797$			1.67090e14i			0.519587i	0.965664	+	0.259794i	$0.0836545\pi$
$797$			1.67090e14i			0.519587i	−0.965664	+	0.259794i	$0.916345\pi$
$798$	6.46480e12	+	7.38242e12i	0.0199775	+	0.0228131i
$799$	5.73225e14			1.76032
$800$		−	2.93958e13i		−	0.0897087i
$801$	−3.56889e14	−	4.75091e13i	−1.08236	−	0.144083i
$802$	8.24152e13			0.248391
$803$		−	6.38205e13i		−	0.191154i
$804$	3.34445e14	−	2.92874e14i	0.995509	−	0.871768i
$805$	−6.35827e13			−0.188087
$806$		−	3.93721e13i		−	0.115748i
$807$	−8.62643e13	−	9.85088e13i	−0.252037	−	0.287811i
$808$	6.76273e13			0.196365
$809$			3.76357e14i			1.08607i	0.839710	+	0.543035i	$0.182725\pi$
$809$			3.76357e14i			1.08607i	−0.839710	+	0.543035i	$0.817275\pi$
$810$	−2.32366e13	−	6.29811e12i	−0.0666418	−	0.0180628i
$811$	3.47571e14			0.990694			0.495347	−	0.868695i	$-0.335041\pi$
$811$	3.47571e14			0.990694			0.495347	+	0.868695i	$0.335041\pi$
$812$		−	1.69452e14i		−	0.480028i
$813$	8.83066e13	−	7.73302e13i	0.248622	−	0.217719i
$814$	2.72579e13			0.0762730
$815$		−	3.22322e13i		−	0.0896401i
$816$	−2.21528e14	−	2.52973e14i	−0.612320	−	0.699234i
$817$	2.03892e13			0.0560131
$818$		−	3.78490e13i		−	0.103345i
$819$	−1.93374e13	+	1.45263e14i	−0.0524781	+	0.394216i
$820$	−3.25655e13			−0.0878391
$821$		−	3.67449e14i		−	0.985103i	−0.870283	−	0.492551i	$-0.836064\pi$
$821$		−	3.67449e14i		−	0.985103i	0.870283	−	0.492551i	$-0.163936\pi$
$822$	−1.14260e12	+	1.00058e12i	−0.00304463	+	0.00266619i
$823$	−1.36316e14			−0.361033			−0.180517	−	0.983572i	$-0.557777\pi$
$823$	−1.36316e14			−0.361033			−0.180517	+	0.983572i	$0.557777\pi$
$824$			7.52485e13i			0.198090i
$825$	2.40017e13	+	2.74085e13i	0.0628018	+	0.0717160i
$826$	2.02632e13			0.0526996
$827$		−	3.14441e14i		−	0.812851i	−0.913684	−	0.406426i	$-0.866775\pi$
$827$		−	3.14441e14i		−	0.812851i	0.913684	−	0.406426i	$-0.133225\pi$
$828$	4.82596e14	+	6.42432e13i	1.24003	+	0.165073i
$829$	2.65848e14			0.678985			0.339493	−	0.940609i	$-0.389745\pi$
$829$	2.65848e14			0.678985			0.339493	+	0.940609i	$0.389745\pi$
$830$			1.10468e13i			0.0280443i
$831$	1.82734e13	−	1.60021e13i	0.0461122	−	0.0403805i
$832$	4.15380e14			1.04191
$833$			3.58025e14i			0.892664i
$834$	−5.89859e13	−	6.73584e13i	−0.146190	−	0.166940i
$835$	−8.20594e13			−0.202160
$836$			1.13705e14i			0.278450i
$837$	1.40740e14	+	2.11621e14i	0.342601	+	0.515148i
$838$	6.94419e13			0.168036
$839$			1.80987e14i			0.435348i	0.976022	+	0.217674i	$0.0698470\pi$
$839$			1.80987e14i			0.435348i	−0.976022	+	0.217674i	$0.930153\pi$
$840$	−1.40890e13	+	1.23378e13i	−0.0336886	+	0.0295012i
$841$	−5.23848e14			−1.24516
$842$			6.24148e13i			0.147478i
$843$	−5.72879e13	−	6.54194e13i	−0.134563	−	0.153663i
$844$	−6.66487e14			−1.55625
$845$		−	9.02518e13i		−	0.209494i
$846$	−1.55352e13	+	1.16701e14i	−0.0358481	+	0.269291i
$847$	−1.10564e14			−0.253628
$848$			4.86212e14i			1.10878i
$849$	−5.28624e14	+	4.62917e14i	−1.19842	+	1.04946i
$850$	−1.37066e13			−0.0308913
$851$			5.92831e14i			1.32826i
$852$	−5.52775e14	−	6.31237e14i	−1.23126	−	1.40603i
$853$	−4.94420e14			−1.09484			−0.547420	−	0.836858i	$-0.684390\pi$
$853$	−4.94420e14			−1.09484			−0.547420	+	0.836858i	$0.684390\pi$
$854$			4.21329e13i			0.0927538i
$855$	1.21219e14	+	1.61366e13i	0.265301	+	0.0353169i
$856$	1.42984e14			0.311112
$857$			2.92460e14i			0.632649i	0.948651	+	0.316325i	$0.102449\pi$
$857$			2.92460e14i			0.632649i	−0.948651	+	0.316325i	$0.897551\pi$
$858$	3.11944e13	−	2.73170e13i	0.0670873	−	0.0587485i
$859$	−5.68576e13			−0.121569			−0.0607845	−	0.998151i	$-0.519360\pi$
$859$	−5.68576e13			−0.121569			−0.0607845	+	0.998151i	$0.519360\pi$
$860$			1.92212e13i			0.0408591i
$861$	2.05846e13	+	2.35064e13i	0.0435038	+	0.0496788i
$862$	−8.34005e13			−0.175240
$863$		−	2.51908e13i		−	0.0526244i	−0.999654	−	0.0263122i	$-0.991624\pi$
$863$		−	2.51908e13i		−	0.0526244i	0.999654	−	0.0263122i	$-0.00837640\pi$
$864$	1.79823e14	−	1.19592e14i	0.373489	−	0.248390i
$865$	−2.80079e14			−0.578363
$866$		−	2.67458e13i		−	0.0549118i
$867$	−3.06107e11	+	2.68058e11i	−0.000624853	+	0.000547185i
$868$	9.76565e13			0.198199
$869$		−	3.60222e13i		−	0.0726894i
$870$	3.39716e13	+	3.87936e13i	0.0681585	+	0.0778330i
$871$	8.23460e14			1.64267
$872$			1.92157e14i			0.381130i
$873$	−2.25811e13	+	1.69630e14i	−0.0445322	+	0.334527i
$874$	6.03873e13			0.118410
$875$		−	1.50559e13i		−	0.0293539i
$876$	1.51928e14	−	1.33044e14i	0.294522	−	0.257914i
$877$	−4.84836e14			−0.934538			−0.467269	−	0.884115i	$-0.654762\pi$
$877$	−4.84836e14			−0.934538			−0.467269	+	0.884115i	$0.654762\pi$
$878$		−	1.74074e13i		−	0.0333626i
$879$	−2.01062e14	−	2.29601e14i	−0.383165	−	0.437552i
$880$	−1.04510e14			−0.198036
$881$			5.56916e14i			1.04932i	0.851310	+	0.524662i	$0.175808\pi$
$881$			5.56916e14i			1.04932i	−0.851310	+	0.524662i	$0.824192\pi$
$882$	−7.28890e13	−	9.70298e12i	−0.136559	−	0.0181787i
$883$	6.32234e13			0.117781			0.0588903	−	0.998264i	$-0.481244\pi$
$883$	6.32234e13			0.117781			0.0588903	+	0.998264i	$0.481244\pi$
$884$		−	6.38841e14i		−	1.18340i
$885$	1.89973e14	−	1.66360e14i	0.349926	−	0.306430i
$886$	−1.18092e14			−0.216298
$887$		−	7.90226e14i		−	1.43924i	−0.694368	−	0.719620i	$-0.744316\pi$
$887$		−	7.90226e14i		−	1.43924i	0.694368	−	0.719620i	$-0.255684\pi$
$888$	1.15034e14	+	1.31363e14i	0.208335	+	0.237907i
$889$	2.83001e14			0.509658
$890$		−	4.20994e13i		−	0.0753920i
$891$	−7.00196e13	+	2.58334e14i	−0.124690	+	0.460037i
$892$	3.27462e14			0.579878
$893$		−	5.98008e14i		−	1.05305i
$894$	9.88103e13	−	8.65284e13i	0.173027	−	0.151520i
$895$	3.36330e14			0.585667
$896$		−	1.10168e14i		−	0.190772i
$897$	5.94116e14	+	6.78445e14i	1.02308	+	1.16830i
$898$	−7.49047e13			−0.128271
$899$		−	5.44354e14i		−	0.927007i
$900$	−1.52123e13	+	1.14275e14i	−0.0257621	+	0.193525i
$901$	7.08937e14			1.19394
$902$		−	8.84088e12i		−	0.0148068i
$903$	1.38743e13	−	1.21497e13i	0.0231085	−	0.0202361i
$904$	−5.98862e13			−0.0991939
$905$			3.82637e14i			0.630295i
$906$	−3.85460e13	−	4.40173e13i	−0.0631449	−	0.0721078i
$907$	−6.75301e14			−1.10017			−0.550087	−	0.835108i	$-0.685405\pi$
$907$	−6.75301e14			−1.10017			−0.550087	+	0.835108i	$0.685405\pi$
$908$			2.93053e14i			0.474807i
$909$	−3.95933e14	−	5.27066e13i	−0.637973	−	0.0849270i
$910$	−1.71355e13			−0.0274593
$911$		−	2.99762e14i		−	0.477733i	−0.971052	−	0.238866i	$-0.923224\pi$
$911$		−	2.99762e14i		−	0.477733i	0.971052	−	0.238866i	$-0.0767758\pi$
$912$	−2.63909e14	+	2.31106e14i	−0.418293	+	0.366300i
$913$	1.22813e14			0.193593
$914$		−	1.73800e14i		−	0.272470i
$915$	3.45909e14	+	3.95008e14i	0.539332	+	0.615886i
$916$	6.68115e14			1.03603
$917$		−	2.01304e14i		−	0.310460i
$918$	−5.57633e13	−	8.38479e13i	−0.0855333	−	0.128611i
$919$	1.05086e14			0.160313			0.0801563	−	0.996782i	$-0.474458\pi$
$919$	1.05086e14			0.160313			0.0801563	+	0.996782i	$0.474458\pi$
$920$			1.15246e14i			0.174859i
$921$	−6.77257e14	+	5.93075e14i	−1.02201	+	0.894976i
$922$	−1.29480e14			−0.194334
$923$		−	1.55421e15i		−	2.32007i
$924$	6.77556e13	+	7.73729e13i	0.100597	+	0.114876i
$925$	−1.40378e14			−0.207295
$926$		−	7.76483e13i		−	0.114045i
$927$	5.86463e13	−	4.40552e14i	0.0856727	−	0.643575i
$928$	−4.62560e14			−0.672091
$929$		−	2.55223e14i		−	0.368843i	−0.982847	−	0.184422i	$-0.940959\pi$
$929$		−	2.55223e14i		−	0.368843i	0.982847	−	0.184422i	$-0.0590412\pi$
$930$	−2.23571e13	+	1.95781e13i	−0.0321366	+	0.0281421i
$931$	3.73504e14			0.534006
$932$		−	2.04570e14i		−	0.290913i
$933$	1.35969e14	+	1.55268e14i	0.192323	+	0.219621i
$934$	9.46326e13			0.133139
$935$			1.52384e14i			0.213246i
$936$	2.63295e14	+	3.50498e13i	0.366490	+	0.0487872i
$937$	−6.60292e14			−0.914193			−0.457097	−	0.889417i	$-0.651111\pi$
$937$	−6.60292e14			−0.914193			−0.457097	+	0.889417i	$0.651111\pi$
$938$		−	4.98750e13i		−	0.0686861i
$939$	−7.01605e13	+	6.14397e13i	−0.0961092	+	0.0841629i
$940$	5.63752e14			0.768155
$941$		−	7.04381e14i		−	0.954684i	−0.878718	−	0.477342i	$-0.841600\pi$
$941$		−	7.04381e14i		−	0.954684i	0.878718	−	0.477342i	$-0.158400\pi$
$942$	1.53647e13	+	1.75455e13i	0.0207142	+	0.0236544i
$943$	1.92280e14			0.257855
$944$			7.24375e14i			0.966281i
$945$	9.21016e13	−	6.12525e13i	0.122210	−	0.0812765i
$946$	−5.21818e12			−0.00688752
$947$		−	2.35007e14i		−	0.308553i	−0.988028	−	0.154277i	$-0.950695\pi$
$947$		−	2.35007e14i		−	0.308553i	0.988028	−	0.154277i	$-0.0493047\pi$
$948$	8.57528e13	−	7.50939e13i	0.111997	−	0.0980760i
$949$	3.74072e14			0.485987
$950$			1.42992e13i			0.0184797i
$951$	8.23446e14	+	9.40327e14i	1.05860	+	1.20886i
$952$	−7.83310e13			−0.100173
$953$			4.57418e14i			0.581901i	0.956738	+	0.290950i	$0.0939715\pi$
$953$			4.57418e14i			0.581901i	−0.956738	+	0.290950i	$0.906029\pi$
$954$	−1.92132e13	+	1.44330e14i	−0.0243141	+	0.182648i
$955$	−1.61314e14			−0.203074
$956$			4.49502e14i			0.562914i
$957$	4.31290e14	−	3.77681e14i	0.537291	−	0.470507i
$958$	6.97396e13			0.0864275
$959$		−	6.97787e12i		−	0.00860260i
$960$	−2.06551e14	−	2.35869e14i	−0.253321	−	0.289278i
$961$	−5.05913e14			−0.617247
$962$			1.59768e14i			0.193916i
$963$	−8.37117e14	−	1.11437e14i	−1.01078	−	0.134554i
$964$	−7.08395e14			−0.850923
$965$		−	5.34156e14i		−	0.638310i
$966$	4.10919e13	−	3.59842e13i	0.0488506	−	0.0427786i
$967$	−1.35536e14			−0.160296			−0.0801478	−	0.996783i	$-0.525539\pi$
$967$	−1.35536e14			−0.160296			−0.0801478	+	0.996783i	$0.525539\pi$
$968$			2.00402e14i			0.235790i
$969$	3.36972e14	+	3.84802e14i	0.394434	+	0.450421i
$970$	−2.00099e13			−0.0233016
$971$			1.19058e15i			1.37931i	0.724137	+	0.689656i	$0.242238\pi$
$971$			1.19058e15i			1.37931i	−0.724137	+	0.689656i	$0.757762\pi$
$972$	−7.60945e14	+	3.71852e14i	−0.877045	+	0.428586i
$973$	4.11359e14			0.471690
$974$		−	4.87462e13i		−	0.0556091i
$975$	−1.60650e14	+	1.40682e14i	−0.182330	+	0.159667i
$976$	−1.50618e15			−1.70070
$977$			3.44556e14i			0.387067i	0.981094	+	0.193534i	$0.0619949\pi$
$977$			3.44556e14i			0.387067i	−0.981094	+	0.193534i	$0.938005\pi$
$978$	1.82416e13	+	2.08308e13i	0.0203877	+	0.0232816i
$979$	−4.68042e14			−0.520441
$980$			3.52108e14i			0.389534i
$981$	1.49761e14	−	1.12501e15i	0.164837	−	1.23826i
$982$	4.69338e13			0.0513959
$983$			1.41837e15i			1.54533i	0.634812	+	0.772667i	$0.281078\pi$
$983$			1.41837e15i			1.54533i	−0.634812	+	0.772667i	$0.718922\pi$
$984$	4.26063e13	−	3.73104e13i	0.0461848	−	0.0404441i
$985$	1.93966e14			0.209192
$986$			2.15682e14i			0.231435i
$987$	−3.56347e14	−	4.06928e14i	−0.380441	−	0.434442i
$988$	−6.66460e14			−0.707929
$989$		−	1.13490e14i		−	0.119943i
$990$	−3.10233e13	−	4.12983e12i	−0.0326222	−	0.00434266i
$991$	2.21394e14			0.231631			0.115816	−	0.993271i	$-0.463052\pi$
$991$	2.21394e14			0.231631			0.115816	+	0.993271i	$0.463052\pi$
$992$		−	2.66577e14i		−	0.277501i
$993$	−7.95548e12	+	6.96663e12i	−0.00823987	+	0.00721566i
$994$	−9.41348e13			−0.0970104
$995$		−	3.06118e14i		−	0.313887i
$996$	2.56023e14	+	2.92363e14i	0.261205	+	0.298281i
$997$	7.64114e14			0.775680			0.387840	−	0.921727i	$-0.373221\pi$
$997$	7.64114e14			0.775680			0.387840	+	0.921727i	$0.373221\pi$
$998$			8.04730e13i			0.0812826i
$999$	−5.71105e14	−	8.58735e14i	−0.573969	−	0.863041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.11.c.a.11.8	yes	14
3.2	odd	2	inner	15.11.c.a.11.7	✓	14
4.3	odd	2		240.11.l.b.161.6		14
5.2	odd	4		75.11.d.d.74.13		28
5.3	odd	4		75.11.d.d.74.16		28
5.4	even	2		75.11.c.g.26.7		14
12.11	even	2		240.11.l.b.161.5		14
15.2	even	4		75.11.d.d.74.15		28
15.8	even	4		75.11.d.d.74.14		28
15.14	odd	2		75.11.c.g.26.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.11.c.a.11.7	✓	14	3.2	odd	2	inner
15.11.c.a.11.8	yes	14	1.1	even	1	trivial
75.11.c.g.26.7		14	5.4	even	2
75.11.c.g.26.8		14	15.14	odd	2
75.11.d.d.74.13		28	5.2	odd	4
75.11.d.d.74.14		28	15.8	even	4
75.11.d.d.74.15		28	15.2	even	4
75.11.d.d.74.16		28	5.3	odd	4
240.11.l.b.161.5		14	12.11	even	2
240.11.l.b.161.6		14	4.3	odd	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)

\(f(q)\)	\(=\)	\(q+4.94055i q^{2} +(182.813 - 160.089i) q^{3} +999.591 q^{4} -1397.54i q^{5} +(790.929 + 903.195i) q^{6} -5515.83 q^{7} +9997.66i q^{8} +(7791.87 - 58532.7i) q^{9} +O(q^{10})\)	\(q+4.94055i q^{2} +(182.813 - 160.089i) q^{3} +999.591 q^{4} -1397.54i q^{5} +(790.929 + 903.195i) q^{6} -5515.83 q^{7} +9997.66i q^{8} +(7791.87 - 58532.7i) q^{9} +6904.63 q^{10} -76762.6i q^{11} +(182738. - 160024. i) q^{12} +449930. q^{13} -27251.2i q^{14} +(-223732. - 255488. i) q^{15} +974187. q^{16} -1.42045e6i q^{17} +(289184. + 38496.1i) q^{18} -1.48186e6 q^{19} -1.39697e6i q^{20} +(-1.00836e6 + 883025. i) q^{21} +379250. q^{22} +8.24828e6i q^{23} +(1.60052e6 + 1.82770e6i) q^{24} -1.95312e6 q^{25} +2.22291e6i q^{26} +(-7.94600e6 - 1.19479e7i) q^{27} -5.51357e6 q^{28} +3.07336e7i q^{29} +(1.26225e6 - 1.10536e6i) q^{30} -1.77120e7 q^{31} +1.50506e7i q^{32} +(-1.22889e7 - 1.40332e7i) q^{33} +7.01779e6 q^{34} +7.70860e6i q^{35} +(7.78868e6 - 5.85087e7i) q^{36} +7.18733e7 q^{37} -7.32120e6i q^{38} +(8.22529e7 - 7.20290e7i) q^{39} +1.39722e7 q^{40} -2.33115e7i q^{41} +(-4.36263e6 - 4.98187e6i) q^{42} -1.37592e7 q^{43} -7.67312e7i q^{44} +(-8.18019e7 - 1.08895e7i) q^{45} -4.07511e7 q^{46} +4.03553e8i q^{47} +(1.78094e8 - 1.55957e8i) q^{48} -2.52051e8 q^{49} -9.64952e6i q^{50} +(-2.27398e8 - 2.59675e8i) q^{51} +4.49746e8 q^{52} +4.99095e8i q^{53} +(5.90292e7 - 3.92576e7i) q^{54} -1.07279e8 q^{55} -5.51454e7i q^{56} +(-2.70902e8 + 2.37229e8i) q^{57} -1.51841e8 q^{58} +7.43569e8i q^{59} +(-2.23640e8 - 2.55384e8i) q^{60} -1.54609e9 q^{61} -8.75072e7i q^{62} +(-4.29786e7 + 3.22856e8i) q^{63} +9.23209e8 q^{64} -6.28797e8i q^{65} +(6.93316e7 - 6.07138e7i) q^{66} +1.83019e9 q^{67} -1.41987e9i q^{68} +(1.32046e9 + 1.50789e9i) q^{69} -3.80848e7 q^{70} -3.45433e9i q^{71} +(5.85189e8 + 7.79004e7i) q^{72} +8.31400e8 q^{73} +3.55094e8i q^{74} +(-3.57056e8 + 3.12674e8i) q^{75} -1.48125e9 q^{76} +4.23409e8i q^{77} +(3.55863e8 + 4.06375e8i) q^{78} +4.69267e8 q^{79} -1.36147e9i q^{80} +(-3.36536e9 - 9.12157e8i) q^{81} +1.15172e8 q^{82} +1.59991e9i q^{83} +(-1.00795e9 + 8.82663e8i) q^{84} -1.98513e9 q^{85} -6.79781e7i q^{86} +(4.92012e9 + 5.61849e9i) q^{87} +7.67447e8 q^{88} -6.09726e9i q^{89} +(5.38000e7 - 4.04146e8i) q^{90} -2.48174e9 q^{91} +8.24491e9i q^{92} +(-3.23798e9 + 2.83550e9i) q^{93} -1.99377e9 q^{94} +2.07096e9i q^{95} +(2.40944e9 + 2.75144e9i) q^{96} -2.89804e9 q^{97} -1.24527e9i q^{98} +(-4.49312e9 - 5.98124e8i) 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

Introduction

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