LMFDB - Embedded newform 3.19.b.b.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,19,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 19, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	3.b (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:	$6.16158413129$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.601940665.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 123x^{2} - 1744x + 16016 $ x^4 - x^3 + 123x^2 - 1744x + 16016
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11}\cdot 3^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.4
Root			$-6.07949 + 12.9551i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.19.b.b.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+932.767i q^{2} +(-4234.02 - 19222.2i) q^{3} -607911. q^{4} -1.14247e6i q^{5} +(1.79299e7 - 3.94936e6i) q^{6} -9.81043e6 q^{7} -3.22520e8i q^{8} +(-3.51567e8 + 1.62775e8i) q^{9} +O(q^{10})$	\(q+932.767i q^{2} +(-4234.02 - 19222.2i) q^{3} -607911. q^{4} -1.14247e6i q^{5} +(1.79299e7 - 3.94936e6i) q^{6} -9.81043e6 q^{7} -3.22520e8i q^{8} +(-3.51567e8 + 1.62775e8i) q^{9} +1.06566e9 q^{10} -2.16393e9i q^{11} +(2.57391e9 + 1.16854e10i) q^{12} -1.47189e10 q^{13} -9.15085e9i q^{14} +(-2.19608e10 + 4.83724e9i) q^{15} +1.41476e11 q^{16} -1.36506e10i q^{17} +(-1.51831e11 - 3.27930e11i) q^{18} -2.38919e11 q^{19} +6.94520e11i q^{20} +(4.15376e10 + 1.88578e11i) q^{21} +2.01844e12 q^{22} +5.70649e11i q^{23} +(-6.19955e12 + 1.36556e12i) q^{24} +2.50946e12 q^{25} -1.37293e13i q^{26} +(4.61743e12 + 6.06870e12i) q^{27} +5.96387e12 q^{28} +1.35326e13i q^{29} +(-4.51202e12 - 2.04843e13i) q^{30} -1.17012e13 q^{31} +4.74176e13i q^{32} +(-4.15954e13 + 9.16211e12i) q^{33} +1.27329e13 q^{34} +1.12081e13i q^{35} +(2.13721e14 - 9.89525e13i) q^{36} -1.26080e14 q^{37} -2.22856e14i q^{38} +(6.23201e13 + 2.82930e14i) q^{39} -3.68470e14 q^{40} -3.28662e14i q^{41} +(-1.75900e14 + 3.87449e13i) q^{42} +8.40904e14 q^{43} +1.31547e15i q^{44} +(1.85965e14 + 4.01654e14i) q^{45} -5.32283e14 q^{46} -9.97479e14i q^{47} +(-5.99013e14 - 2.71948e15i) q^{48} -1.53217e15 q^{49} +2.34074e15i q^{50} +(-2.62395e14 + 5.77971e13i) q^{51} +8.94778e15 q^{52} -5.45882e15i q^{53} +(-5.66068e15 + 4.30699e15i) q^{54} -2.47222e15 q^{55} +3.16406e15i q^{56} +(1.01159e15 + 4.59255e15i) q^{57} -1.26228e16 q^{58} +8.03632e14i q^{59} +(1.33502e16 - 2.94061e15i) q^{60} +1.04106e16 q^{61} -1.09145e16i q^{62} +(3.44902e15 - 1.59689e15i) q^{63} -7.14245e15 q^{64} +1.68159e16i q^{65} +(-8.54612e15 - 3.87989e16i) q^{66} -1.50639e16 q^{67} +8.29836e15i q^{68} +(1.09691e16 - 2.41614e15i) q^{69} -1.04546e16 q^{70} +4.47214e16i q^{71} +(5.24981e16 + 1.13387e17i) q^{72} -3.92287e16 q^{73} -1.17603e17i q^{74} +(-1.06251e16 - 4.82374e16i) q^{75} +1.45241e17 q^{76} +2.12290e16i q^{77} +(-2.63908e17 + 5.81302e16i) q^{78} -7.20817e16 q^{79} -1.61632e17i q^{80} +(9.71035e16 - 1.14452e17i) q^{81} +3.06565e17 q^{82} +1.02835e17i q^{83} +(-2.52512e16 - 1.14639e17i) q^{84} -1.55954e16 q^{85} +7.84368e17i q^{86} +(2.60126e17 - 5.72973e16i) q^{87} -6.97910e17 q^{88} -5.12684e17i q^{89} +(-3.74650e17 + 1.73462e17i) q^{90} +1.44399e17 q^{91} -3.46904e17i q^{92} +(4.95431e16 + 2.24923e17i) q^{93} +9.30416e17 q^{94} +2.72957e17i q^{95} +(9.11471e17 - 2.00767e17i) q^{96} -7.28759e17 q^{97} -1.42916e18i q^{98} +(3.52232e17 + 7.60764e17i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 15876 q^{3} - 1053536 q^{4} + 22698144 q^{6} - 95744152 q^{7} - 885341340 q^{9}+O(q^{10}) $ 4 * q + 15876 * q^3 - 1053536 * q^4 + 22698144 * q^6 - 95744152 * q^7 - 885341340 * q^9	$ 4 q + 15876 q^{3} - 1053536 q^{4} + 22698144 q^{6} - 95744152 q^{7} - 885341340 q^{9} + 1461136320 q^{10} + 7123171104 q^{12} - 5426221528 q^{13} - 68287821120 q^{15} + 201224008192 q^{16} - 624067623360 q^{18} + 191416649480 q^{19} - 843499414296 q^{21} + 6661732766400 q^{22} - 16917300997632 q^{24} + 11407599454180 q^{25} - 4632207691356 q^{27} + 5750860980032 q^{28} - 17181499602240 q^{30} + 35728415085608 q^{31} + 12242871023040 q^{33} - 97283346838272 q^{34} + 412657454022048 q^{36} - 475299833502232 q^{37} + 416909545005096 q^{39} - 967003294602240 q^{40} + 149151729948480 q^{42} + 15\!\cdots\!92 q^{43}+ \cdots + 30\!\cdots\!60 q^{99}+O(q^{100}) $ 4 * q + 15876 * q^3 - 1053536 * q^4 + 22698144 * q^6 - 95744152 * q^7 - 885341340 * q^9 + 1461136320 * q^10 + 7123171104 * q^12 - 5426221528 * q^13 - 68287821120 * q^15 + 201224008192 * q^16 - 624067623360 * q^18 + 191416649480 * q^19 - 843499414296 * q^21 + 6661732766400 * q^22 - 16917300997632 * q^24 + 11407599454180 * q^25 - 4632207691356 * q^27 + 5750860980032 * q^28 - 17181499602240 * q^30 + 35728415085608 * q^31 + 12242871023040 * q^33 - 97283346838272 * q^34 + 412657454022048 * q^36 - 475299833502232 * q^37 + 416909545005096 * q^39 - 967003294602240 * q^40 + 149151729948480 * q^42 + 1599607324574792 * q^43 - 221242601301120 * q^45 + 571461969379968 * q^46 - 2192825065342464 * q^48 - 3423787444328244 * q^49 - 4987666703736576 * q^51 + 19843921097419328 * q^52 - 14022277970462496 * q^54 - 84999034592640 * q^55 + 10169351626464648 * q^57 - 15931261886420160 * q^58 + 24723268055608320 * q^60 - 2207268745883992 * q^61 + 13833182825583912 * q^63 - 53493367589593088 * q^64 + 14857554290281920 * q^66 - 41331536078929912 * q^67 + 81420525478583424 * q^69 + 4599036429482880 * q^70 - 4994921842560000 * q^72 - 45389954762456248 * q^73 + 56512911509383140 * q^75 + 344787912869857856 * q^76 - 685829939469704640 * q^78 - 177365384029892440 * q^79 - 72782527872717756 * q^81 + 887840438080579200 * q^82 - 125687415484822464 * q^84 - 258438267155888640 * q^85 + 858898556077746240 * q^87 - 494740797131842560 * q^88 - 688243478411603520 * q^90 - 625122143135405552 * q^91 + 818827434766827432 * q^93 + 1164172551956805888 * q^94 + 1176359757688184832 * q^96 - 3491564534514760312 * q^97 + 3027708259671116160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			932.767i			1.82181i	0.412615	+	0.910906i	$0.364616\pi$
$2$			932.767i			1.82181i	−0.412615	+	0.910906i	$0.635384\pi$
$3$	−4234.02	−	19222.2i	−0.215111	−	0.976590i
$3$	−4234.02	−	19222.2i	−0.215111	−	0.976590i
$4$	−607911.			−2.31900
$5$		−	1.14247e6i		−	0.584944i	−0.956274	−	0.292472i	$-0.905522\pi$
$5$		−	1.14247e6i		−	0.584944i	0.956274	−	0.292472i	$-0.0944779\pi$
$6$	1.79299e7	−	3.94936e6i	1.77916	−	0.391891i
$7$	−9.81043e6			−0.243112			−0.121556	−	0.992585i	$-0.538788\pi$
$7$	−9.81043e6			−0.243112			−0.121556	+	0.992585i	$0.538788\pi$
$8$		−	3.22520e8i		−	2.40296i
$9$	−3.51567e8	+	1.62775e8i	−0.907455	+	0.420150i
$10$	1.06566e9			1.06566
$11$		−	2.16393e9i		−	0.917716i	−0.888510	−	0.458858i	$-0.848259\pi$
$11$		−	2.16393e9i		−	0.917716i	0.888510	−	0.458858i	$-0.151741\pi$
$12$	2.57391e9	+	1.16854e10i	0.498841	+	2.26471i
$13$	−1.47189e10			−1.38799			−0.693993	−	0.719982i	$-0.744150\pi$
$13$	−1.47189e10			−1.38799			−0.693993	+	0.719982i	$0.744150\pi$
$14$		−	9.15085e9i		−	0.442903i
$15$	−2.19608e10	+	4.83724e9i	−0.571251	+	0.125828i
$16$	1.41476e11			2.05875
$17$		−	1.36506e10i		−	0.115110i	−0.998342	−	0.0575549i	$-0.981670\pi$
$17$		−	1.36506e10i		−	0.115110i	0.998342	−	0.0575549i	$-0.0183304\pi$
$18$	−1.51831e11	−	3.27930e11i	−0.765434	−	1.65321i
$19$	−2.38919e11			−0.740402			−0.370201	−	0.928952i	$-0.620711\pi$
$19$	−2.38919e11			−0.740402			−0.370201	+	0.928952i	$0.620711\pi$
$20$			6.94520e11i			1.35648i
$21$	4.15376e10	+	1.88578e11i	0.0522959	+	0.237420i
$22$	2.01844e12			1.67190
$23$			5.70649e11i			0.316824i	0.987373	+	0.158412i	$0.0506375\pi$
$23$			5.70649e11i			0.316824i	−0.987373	+	0.158412i	$0.949363\pi$
$24$	−6.19955e12	+	1.36556e12i	−2.34671	+	0.516903i
$25$	2.50946e12			0.657840
$26$		−	1.37293e13i		−	2.52865i
$27$	4.61743e12	+	6.06870e12i	0.605517	+	0.795832i
$28$	5.96387e12			0.563775
$29$			1.35326e13i			0.932823i	0.884568	+	0.466411i	$0.154453\pi$
$29$			1.35326e13i			0.932823i	−0.884568	+	0.466411i	$0.845547\pi$
$30$	−4.51202e12	−	2.04843e13i	−0.229235	−	1.04071i
$31$	−1.17012e13			−0.442562			−0.221281	−	0.975210i	$-0.571024\pi$
$31$	−1.17012e13			−0.442562			−0.221281	+	0.975210i	$0.571024\pi$
$32$			4.74176e13i			1.34769i
$33$	−4.15954e13	+	9.16211e12i	−0.896232	+	0.197410i
$34$	1.27329e13			0.209708
$35$			1.12081e13i			0.142207i
$36$	2.13721e14	−	9.89525e13i	2.10438	−	0.974326i
$37$	−1.26080e14			−0.970132			−0.485066	−	0.874478i	$-0.661204\pi$
$37$	−1.26080e14			−0.970132			−0.485066	+	0.874478i	$0.661204\pi$
$38$		−	2.22856e14i		−	1.34887i
$39$	6.23201e13	+	2.82930e14i	0.298571	+	1.35549i
$40$	−3.68470e14			−1.40560
$41$		−	3.28662e14i		−	1.00391i	−0.864894	−	0.501955i	$-0.832614\pi$
$41$		−	3.28662e14i		−	1.00391i	0.864894	−	0.501955i	$-0.167386\pi$
$42$	−1.75900e14	+	3.87449e13i	−0.432535	+	0.0952733i
$43$	8.40904e14			1.67313			0.836566	−	0.547866i	$-0.184560\pi$
$43$	8.40904e14			1.67313			0.836566	+	0.547866i	$0.184560\pi$
$44$			1.31547e15i			2.12818i
$45$	1.85965e14	+	4.01654e14i	0.245764	+	0.530811i
$46$	−5.32283e14			−0.577194
$47$		−	9.97479e14i		−	0.891298i	−0.895208	−	0.445649i	$-0.852973\pi$
$47$		−	9.97479e14i		−	0.891298i	0.895208	−	0.445649i	$-0.147027\pi$
$48$	−5.99013e14	−	2.71948e15i	−0.442859	−	2.01055i
$49$	−1.53217e15			−0.940897
$50$			2.34074e15i			1.19846i
$51$	−2.62395e14	+	5.77971e13i	−0.112415	+	0.0247613i
$52$	8.94778e15			3.21873
$53$		−	5.45882e15i		−	1.65431i	−0.561977	−	0.827153i	$-0.689959\pi$
$53$		−	5.45882e15i		−	1.65431i	0.561977	−	0.827153i	$-0.310041\pi$
$54$	−5.66068e15	+	4.30699e15i	−1.44986	+	1.10314i
$55$	−2.47222e15			−0.536813
$56$			3.16406e15i			0.584188i
$57$	1.01159e15	+	4.59255e15i	0.159268	+	0.723069i
$58$	−1.26228e16			−1.69943
$59$			8.03632e14i			0.0927660i	0.998924	+	0.0463830i	$0.0147695\pi$
$59$			8.03632e14i			0.0927660i	−0.998924	+	0.0463830i	$0.985231\pi$
$60$	1.33502e16	−	2.94061e15i	1.32473	−	0.291794i
$61$	1.04106e16			0.890243			0.445121	−	0.895470i	$-0.353161\pi$
$61$	1.04106e16			0.890243			0.445121	+	0.895470i	$0.353161\pi$
$62$		−	1.09145e16i		−	0.806265i
$63$	3.44902e15	−	1.59689e15i	0.220613	−	0.102143i
$64$	−7.14245e15			−0.396486
$65$			1.68159e16i			0.811894i
$66$	−8.54612e15	−	3.87989e16i	−0.359645	−	1.63276i
$67$	−1.50639e16			−0.553685			−0.276843	−	0.960915i	$-0.589288\pi$
$67$	−1.50639e16			−0.553685			−0.276843	+	0.960915i	$0.589288\pi$
$68$			8.29836e15i			0.266939i
$69$	1.09691e16	−	2.41614e15i	0.309407	−	0.0681523i
$70$	−1.04546e16			−0.259074
$71$			4.47214e16i			0.975417i	0.873007	+	0.487709i	$0.162167\pi$
$71$			4.47214e16i			0.975417i	−0.873007	+	0.487709i	$0.837833\pi$
$72$	5.24981e16	+	1.13387e17i	1.00960	+	2.18058i
$73$	−3.92287e16			−0.666344			−0.333172	−	0.942866i	$-0.608119\pi$
$73$	−3.92287e16			−0.666344			−0.333172	+	0.942866i	$0.608119\pi$
$74$		−	1.17603e17i		−	1.76740i
$75$	−1.06251e16	−	4.82374e16i	−0.141508	−	0.642440i
$76$	1.45241e17			1.71699
$77$			2.12290e16i			0.223107i
$78$	−2.63908e17	+	5.81302e16i	−2.46945	+	0.543939i
$79$	−7.20817e16			−0.601425			−0.300712	−	0.953715i	$-0.597224\pi$
$79$	−7.20817e16			−0.601425			−0.300712	+	0.953715i	$0.597224\pi$
$80$		−	1.61632e17i		−	1.20425i
$81$	9.71035e16	−	1.14452e17i	0.646948	−	0.762534i
$82$	3.06565e17			1.82893
$83$			1.02835e17i			0.550093i	0.961431	+	0.275047i	$0.0886933\pi$
$83$			1.02835e17i			0.550093i	−0.961431	+	0.275047i	$0.911307\pi$
$84$	−2.52512e16	−	1.14639e17i	−0.121274	−	0.550577i
$85$	−1.55954e16			−0.0673328
$86$			7.84368e17i			3.04813i
$87$	2.60126e17	−	5.72973e16i	0.910985	−	0.200660i
$88$	−6.97910e17			−2.20524
$89$		−	5.12684e17i		−	1.46332i	−0.681669	−	0.731661i	$-0.738746\pi$
$89$		−	5.12684e17i		−	1.46332i	0.681669	−	0.731661i	$-0.261254\pi$
$90$	−3.74650e17	+	1.73462e17i	−0.967037	+	0.447736i
$91$	1.44399e17			0.337435
$92$		−	3.46904e17i		−	0.734715i
$93$	4.95431e16	+	2.24923e17i	0.0951999	+	0.432202i
$94$	9.30416e17			1.62378
$95$			2.72957e17i			0.433094i
$96$	9.11471e17	−	2.00767e17i	1.31614	−	0.289902i
$97$	−7.28759e17			−0.958602			−0.479301	−	0.877651i	$-0.659110\pi$
$97$	−7.28759e17			−0.958602			−0.479301	+	0.877651i	$0.659110\pi$
$98$		−	1.42916e18i		−	1.71414i
$99$	3.52232e17	+	7.60764e17i	0.385578	+	0.832785i
$100$	−1.52553e18			−1.52553
$101$		−	1.15126e18i		−	1.05264i	−0.850286	−	0.526321i	$-0.823571\pi$
$101$		−	1.15126e18i		−	1.05264i	0.850286	−	0.526321i	$-0.176429\pi$
$102$	−5.39112e16	−	2.44754e17i	−0.0451105	−	0.204799i
$103$	−1.83618e18			−1.40728			−0.703638	−	0.710559i	$-0.748442\pi$
$103$	−1.83618e18			−1.40728			−0.703638	+	0.710559i	$0.748442\pi$
$104$			4.74714e18i			3.33528i
$105$	2.15445e17	−	4.74554e16i	0.138878	−	0.0305902i
$106$	5.09181e18			3.01383
$107$			1.30924e18i			0.712140i	0.934459	+	0.356070i	$0.115883\pi$
$107$			1.30924e18i			0.712140i	−0.934459	+	0.356070i	$0.884117\pi$
$108$	−2.80699e18	−	3.68923e18i	−1.40419	−	1.84553i
$109$	9.37377e17			0.431594			0.215797	−	0.976438i	$-0.430765\pi$
$109$	9.37377e17			0.431594			0.215797	+	0.976438i	$0.430765\pi$
$110$		−	2.30601e18i		−	0.977971i
$111$	5.33826e17	+	2.42354e18i	0.208686	+	0.947420i
$112$	−1.38794e18			−0.500506
$113$			5.05201e17i			0.168174i	0.996458	+	0.0840868i	$0.0267973\pi$
$113$			5.05201e17i			0.168174i	−0.996458	+	0.0840868i	$0.973203\pi$
$114$	−4.28378e18	+	9.43576e17i	−1.31730	+	0.290157i
$115$	6.51949e17			0.185325
$116$		−	8.22661e18i		−	2.16321i
$117$	5.17467e18	−	2.39586e18i	1.25953	−	0.583162i
$118$	−7.49601e17			−0.169002
$119$			1.33918e17i			0.0279845i
$120$	1.56011e18	+	7.08280e18i	0.302360	+	1.37269i
$121$	8.77344e17			0.157798
$122$			9.71069e18i			1.62185i
$123$	−6.31761e18	+	1.39156e18i	−0.980408	+	0.215952i
$124$	7.11328e18			1.02630
$125$		−	7.22516e18i		−	0.969744i
$126$	1.48953e18	+	3.21713e18i	0.186086	+	0.401915i
$127$	−8.86372e18			−1.03129			−0.515647	−	0.856801i	$-0.672448\pi$
$127$	−8.86372e18			−1.03129			−0.515647	+	0.856801i	$0.672448\pi$
$128$			5.76799e18i			0.625366i
$129$	−3.56041e18	−	1.61640e19i	−0.359909	−	1.63396i
$130$	−1.56853e19			−1.47912
$131$			1.50395e19i			1.32371i	0.749632	+	0.661855i	$0.230231\pi$
$131$			1.50395e19i			1.32371i	−0.749632	+	0.661855i	$0.769769\pi$
$132$	2.52863e19	−	5.56975e18i	2.07836	−	0.457794i
$133$	2.34389e18			0.180000
$134$		−	1.40511e19i		−	1.00871i
$135$	6.93330e18	−	5.27527e18i	0.465518	−	0.354194i
$136$	−4.40260e18			−0.276604
$137$		−	7.91047e18i		−	0.465283i	−0.972563	−	0.232641i	$-0.925263\pi$
$137$		−	7.91047e18i		−	0.465283i	0.972563	−	0.232641i	$-0.0747369\pi$
$138$	2.25370e18	+	1.02317e19i	0.124161	+	0.563682i
$139$	2.96560e19			1.53102			0.765508	−	0.643426i	$-0.222488\pi$
$139$	2.96560e19			1.53102			0.765508	+	0.643426i	$0.222488\pi$
$140$		−	6.81354e18i		−	0.329777i
$141$	−1.91738e19	+	4.22335e18i	−0.870433	+	0.191728i
$142$	−4.17147e19			−1.77703
$143$			3.18506e19i			1.27378i
$144$	−4.97383e19	+	2.30287e19i	−1.86822	+	0.864983i
$145$	1.54606e19			0.545649
$146$		−	3.65913e19i		−	1.21395i
$147$	6.48724e18	+	2.94517e19i	0.202397	+	0.918870i
$148$	7.66454e19			2.24973
$149$		−	3.76072e19i		−	1.03895i	−0.854486	−	0.519475i	$-0.826128\pi$
$149$		−	3.76072e19i		−	1.03895i	0.854486	−	0.519475i	$-0.173872\pi$
$150$	4.49943e19	−	9.91076e18i	1.17040	−	0.257802i
$151$	−3.02438e19			−0.741044			−0.370522	−	0.928824i	$-0.620821\pi$
$151$	−3.02438e19			−0.741044			−0.370522	+	0.928824i	$0.620821\pi$
$152$			7.70561e19i			1.77916i
$153$	2.22198e18	+	4.79910e18i	0.0483633	+	0.104457i
$154$	−1.98018e19			−0.406459
$155$			1.33682e19i			0.258874i
$156$	−3.78851e19	−	1.71996e20i	−0.692384	−	3.14338i
$157$	−1.60317e19			−0.276620			−0.138310	−	0.990389i	$-0.544167\pi$
$157$	−1.60317e19			−0.276620			−0.138310	+	0.990389i	$0.544167\pi$
$158$		−	6.72354e19i		−	1.09568i
$159$	−1.04931e20	+	2.31128e19i	−1.61558	+	0.355859i
$160$	5.41731e19			0.788323
$161$		−	5.59831e18i		−	0.0770237i
$162$	1.06757e20	+	9.05749e19i	1.38919	+	1.17862i
$163$	4.78329e19			0.588895			0.294448	−	0.955668i	$-0.404864\pi$
$163$	4.78329e19			0.588895			0.294448	+	0.955668i	$0.404864\pi$
$164$			1.99797e20i			2.32806i
$165$	1.04674e19	+	4.75215e19i	0.115474	+	0.524246i
$166$	−9.59207e19			−1.00217
$167$		−	1.25413e20i		−	1.24135i	−0.784067	−	0.620676i	$-0.786858\pi$
$167$		−	1.25413e20i		−	1.24135i	0.784067	−	0.620676i	$-0.213142\pi$
$168$	6.08203e19	−	1.33967e19i	0.570512	−	0.125665i
$169$	1.04190e20			0.926503
$170$		−	1.45469e19i		−	0.122668i
$171$	8.39958e19	−	3.88899e19i	0.671881	−	0.311080i
$172$	−5.11195e20			−3.87999
$173$		−	1.32712e19i		−	0.0956085i	−0.998857	−	0.0478042i	$-0.984778\pi$
$173$		−	1.32712e19i		−	0.0956085i	0.998857	−	0.0478042i	$-0.0152224\pi$
$174$	5.34451e19	+	2.42637e20i	0.365565	+	1.65964i
$175$	−2.46189e19			−0.159929
$176$		−	3.06144e20i		−	1.88935i
$177$	1.54476e19	−	3.40260e18i	0.0905943	−	0.0199550i
$178$	4.78215e20			2.66590
$179$			3.08776e19i			0.163669i	0.996646	+	0.0818345i	$0.0260779\pi$
$179$			3.08776e19i			0.163669i	−0.996646	+	0.0818345i	$0.973922\pi$
$180$	−1.13050e20	−	2.44170e20i	−0.569927	−	1.23095i
$181$	6.94280e18			0.0332987			0.0166494	−	0.999861i	$-0.494700\pi$
$181$	6.94280e18			0.0332987			0.0166494	+	0.999861i	$0.494700\pi$
$182$			1.34690e20i			0.614743i
$183$	−4.40789e19	−	2.00115e20i	−0.191501	−	0.869402i
$184$	1.84046e20			0.761317
$185$			1.44043e20i			0.567473i
$186$	−2.09800e20	+	4.62122e19i	−0.787390	+	0.173436i
$187$	−2.95389e19			−0.105638
$188$			6.06379e20i			2.06692i
$189$	−4.52990e19	−	5.95365e19i	−0.147208	−	0.193476i
$190$	−2.54606e20			−0.789016
$191$		−	3.84936e19i		−	0.113786i	−0.998380	−	0.0568930i	$-0.981881\pi$
$191$		−	3.84936e19i		−	0.113786i	0.998380	−	0.0568930i	$-0.0181194\pi$
$192$	3.02413e19	+	1.37294e20i	0.0852884	+	0.387204i
$193$	−5.08300e20			−1.36806			−0.684028	−	0.729455i	$-0.739774\pi$
$193$	−5.08300e20			−1.36806			−0.684028	+	0.729455i	$0.739774\pi$
$194$		−	6.79762e20i		−	1.74639i
$195$	3.23238e20	−	7.11989e19i	0.792887	−	0.174647i
$196$	9.31422e20			2.18194
$197$			6.30050e20i			1.40987i	0.709272	+	0.704935i	$0.249024\pi$
$197$			6.30050e20i			1.40987i	−0.709272	+	0.704935i	$0.750976\pi$
$198$	−7.09616e20	+	3.28551e20i	−1.51718	+	0.702451i
$199$	1.14335e19			0.0233615			0.0116807	−	0.999932i	$-0.496282\pi$
$199$	1.14335e19			0.0233615			0.0116807	+	0.999932i	$0.496282\pi$
$200$		−	8.09352e20i		−	1.58077i
$201$	6.37807e19	+	2.89561e20i	0.119104	+	0.540723i
$202$	1.07386e21			1.91771
$203$		−	1.32761e20i		−	0.226780i
$204$	1.59513e20	−	3.51355e19i	0.260690	−	0.0574215i
$205$	−3.75486e20			−0.587231
$206$		−	1.71272e21i		−	2.56379i
$207$	−9.28872e19	−	2.00621e20i	−0.133114	−	0.287504i
$208$	−2.08237e21			−2.85751
$209$			5.17002e20i			0.679479i
$210$	4.42649e19	+	2.00960e20i	0.0557296	+	0.253009i
$211$	6.41724e20			0.774117			0.387058	−	0.922055i	$-0.373491\pi$
$211$	6.41724e20			0.774117			0.387058	+	0.922055i	$0.373491\pi$
$212$			3.31847e21i			3.83633i
$213$	8.59645e20	−	1.89352e20i	0.952582	−	0.209823i
$214$	−1.22122e21			−1.29738
$215$		−	9.60707e20i		−	0.978690i
$216$	1.95728e21	−	1.48921e21i	1.91236	−	1.45504i
$217$	1.14794e20			0.107592
$218$			8.74355e20i			0.786284i
$219$	1.66095e20	+	7.54063e20i	0.143338	+	0.650744i
$220$	1.50289e21			1.24487
$221$			2.00922e20i			0.159771i
$222$	−2.26060e21	+	4.97935e20i	−1.72602	+	0.380186i
$223$	−8.65729e20			−0.634802			−0.317401	−	0.948291i	$-0.602810\pi$
$223$	−8.65729e20			−0.634802			−0.317401	+	0.948291i	$0.602810\pi$
$224$		−	4.65187e20i		−	0.327639i
$225$	−8.82242e20	+	4.08477e20i	−0.596960	+	0.276391i
$226$	−4.71235e20			−0.306381
$227$		−	2.48692e21i		−	1.55392i	−0.629547	−	0.776962i	$-0.716760\pi$
$227$		−	2.48692e21i		−	1.55392i	0.629547	−	0.776962i	$-0.283240\pi$
$228$	−6.14955e20	−	2.79186e21i	−0.369343	−	1.67679i
$229$	−4.47185e20			−0.258207			−0.129103	−	0.991631i	$-0.541210\pi$
$229$	−4.47185e20			−0.258207			−0.129103	+	0.991631i	$0.541210\pi$
$230$			6.08117e20i			0.337627i
$231$	4.08069e20	−	8.98843e19i	0.217884	−	0.0479928i
$232$	4.36454e21			2.24154
$233$		−	2.20802e21i		−	1.09094i	−0.838131	−	0.545468i	$-0.816352\pi$
$233$		−	2.20802e21i		−	1.09094i	0.838131	−	0.545468i	$-0.183648\pi$
$234$	2.23478e21	+	4.82676e21i	1.06241	+	2.29463i
$235$	−1.13959e21			−0.521360
$236$		−	4.88537e20i		−	0.215124i
$237$	3.05196e20	+	1.38557e21i	0.129373	+	0.587345i
$238$	−1.24915e20			−0.0509825
$239$			1.30522e21i			0.512983i	0.966547	+	0.256491i	$0.0825665\pi$
$239$			1.30522e21i			0.512983i	−0.966547	+	0.256491i	$0.917434\pi$
$240$	−3.10693e21	+	6.84355e20i	−1.17606	+	0.259048i
$241$	1.77386e21			0.646795			0.323398	−	0.946263i	$-0.395175\pi$
$241$	1.77386e21			0.646795			0.323398	+	0.946263i	$0.395175\pi$
$242$			8.18358e20i			0.287478i
$243$	−2.61116e21	−	1.38195e21i	−0.883848	−	0.467774i
$244$	−6.32874e21			−2.06447
$245$			1.75046e21i			0.550372i
$246$	−1.29800e21	−	5.89286e21i	−0.393423	−	1.78612i
$247$	3.51662e21			1.02767
$248$			3.77387e21i			1.06346i
$249$	1.97671e21	−	4.35404e20i	0.537215	−	0.118331i
$250$	6.73939e21			1.76669
$251$			4.95925e21i			1.25416i	0.778956	+	0.627079i	$0.215750\pi$
$251$			4.95925e21i			1.25416i	−0.778956	+	0.627079i	$0.784250\pi$
$252$	−2.09670e21	+	9.70767e20i	−0.511600	+	0.236870i
$253$	1.23484e21			0.290755
$254$		−	8.26779e21i		−	1.87882i
$255$	6.60314e19	+	2.99778e20i	0.0144840	+	0.0657565i
$256$	−7.25254e21			−1.53579
$257$		−	7.24122e20i		−	0.148052i	−0.997256	−	0.0740259i	$-0.976415\pi$
$257$		−	7.24122e20i		−	0.148052i	0.997256	−	0.0740259i	$-0.0235847\pi$
$258$	1.50773e22	−	3.32103e21i	2.97677	−	0.655686i
$259$	1.23690e21			0.235850
$260$		−	1.02226e22i		−	1.88278i
$261$	−2.20276e21	−	4.75761e21i	−0.391925	−	0.846494i
$262$	−1.40284e22			−2.41155
$263$			1.13671e22i			1.88821i	0.329650	+	0.944103i	$0.393069\pi$
$263$			1.13671e22i			1.88821i	−0.329650	+	0.944103i	$0.606931\pi$
$264$	2.95497e21	+	1.34154e22i	0.474370	+	2.15361i
$265$	−6.23653e21			−0.967676
$266$			2.18631e21i			0.327927i
$267$	−9.85492e21	+	2.17072e21i	−1.42906	+	0.314776i
$268$	9.15748e21			1.28399
$269$		−	9.09091e21i		−	1.23264i	−0.787495	−	0.616321i	$-0.788623\pi$
$269$		−	9.09091e21i		−	1.23264i	0.787495	−	0.616321i	$-0.211377\pi$
$270$	4.92060e21	+	6.46716e21i	0.645275	+	0.848085i
$271$	5.59132e21			0.709235			0.354618	−	0.935011i	$-0.384611\pi$
$271$	5.59132e21			0.709235			0.354618	+	0.935011i	$0.384611\pi$
$272$		−	1.93124e21i		−	0.236982i
$273$	−6.11387e20	−	2.77566e21i	−0.0725860	−	0.329536i
$274$	7.37863e21			0.847658
$275$		−	5.43029e21i		−	0.603710i
$276$	−6.66826e21	+	1.46880e21i	−0.717515	+	0.158045i
$277$	−3.61235e21			−0.376246			−0.188123	−	0.982145i	$-0.560240\pi$
$277$	−3.61235e21			−0.376246			−0.188123	+	0.982145i	$0.560240\pi$
$278$			2.76622e22i			2.78922i
$279$	4.11374e21	−	1.90466e21i	0.401605	−	0.185942i
$280$	3.61484e21			0.341718
$281$		−	3.75694e20i		−	0.0343936i	−0.999852	−	0.0171968i	$-0.994526\pi$
$281$		−	3.75694e20i		−	0.0343936i	0.999852	−	0.0171968i	$-0.00547418\pi$
$282$	−3.93940e21	−	1.78847e22i	−0.349292	−	1.58576i
$283$	4.33569e21			0.372375			0.186187	−	0.982514i	$-0.440387\pi$
$283$	4.33569e21			0.372375			0.186187	+	0.982514i	$0.440387\pi$
$284$		−	2.71866e22i		−	2.26199i
$285$	5.24684e21	−	1.15571e21i	0.422955	−	0.0931632i
$286$	−2.97092e22			−2.32058
$287$			3.22431e21i			0.244062i
$288$	−7.71838e21	−	1.66704e22i	−0.566231	−	1.22297i
$289$	1.38767e22			0.986750
$290$			1.44211e22i			0.994070i
$291$	3.08558e21	+	1.40084e22i	0.206205	+	0.936160i
$292$	2.38476e22			1.54525
$293$		−	1.01590e22i		−	0.638326i	−0.947700	−	0.319163i	$-0.896598\pi$
$293$		−	1.01590e22i		−	0.638326i	0.947700	−	0.319163i	$-0.103402\pi$
$294$	−2.74716e22	+	6.05109e21i	−1.67401	+	0.368729i
$295$	9.18125e20			0.0542630
$296$			4.06633e22i			2.33119i
$297$	1.31322e22	−	9.99178e21i	0.730348	−	0.555693i
$298$	3.50788e22			1.89277
$299$		−	8.39932e21i		−	0.439748i
$300$	6.45913e21	+	2.93240e22i	0.328158	+	1.48982i
$301$	−8.24963e21			−0.406758
$302$		−	2.82105e22i		−	1.35004i
$303$	−2.21297e22	+	4.87446e21i	−1.02800	+	0.226434i
$304$	−3.38013e22			−1.52430
$305$		−	1.18938e22i		−	0.520742i
$306$	−4.47645e21	+	2.07259e21i	−0.190301	+	0.0881089i
$307$	−3.56186e22			−1.47039			−0.735194	−	0.677857i	$-0.762909\pi$
$307$	−3.56186e22			−1.47039			−0.735194	+	0.677857i	$0.762909\pi$
$308$		−	1.29054e22i		−	0.517385i
$309$	7.77441e21	+	3.52954e22i	0.302720	+	1.37433i
$310$	−1.24695e22			−0.471620
$311$		−	9.62119e21i		−	0.353497i	−0.984256	−	0.176748i	$-0.943442\pi$
$311$		−	9.62119e21i		−	0.353497i	0.984256	−	0.176748i	$-0.0565579\pi$
$312$	9.12505e22	−	2.00995e22i	3.25720	−	0.717454i
$313$	−2.06842e22			−0.717364			−0.358682	−	0.933460i	$-0.616774\pi$
$313$	−2.06842e22			−0.717364			−0.358682	+	0.933460i	$0.616774\pi$
$314$		−	1.49539e22i		−	0.503949i
$315$	−1.82440e21	−	3.94040e21i	−0.0597481	−	0.129046i
$316$	4.38193e22			1.39470
$317$			4.70774e22i			1.45640i	0.685367	+	0.728198i	$0.259642\pi$
$317$			4.70774e22i			1.45640i	−0.685367	+	0.728198i	$0.740358\pi$
$318$	−2.15588e22	−	9.78758e22i	−0.648308	−	2.94328i
$319$	2.92835e22			0.856066
$320$			8.16003e21i			0.231922i
$321$	2.51665e22	−	5.54335e21i	0.695468	−	0.153189i
$322$	5.22192e21			0.140323
$323$			3.26139e21i			0.0852275i
$324$	−5.90303e22	+	6.95768e22i	−1.50027	+	1.76831i
$325$	−3.69365e22			−0.913072
$326$			4.46170e22i			1.07286i
$327$	−3.96888e21	−	1.80185e22i	−0.0928406	−	0.421491i
$328$	−1.06000e23			−2.41236
$329$			9.78570e21i			0.216685i
$330$	−4.43265e22	+	9.76368e21i	−0.955077	+	0.210372i
$331$	6.94207e22			1.45558			0.727791	−	0.685799i	$-0.240547\pi$
$331$	6.94207e22			1.45558			0.727791	+	0.685799i	$0.240547\pi$
$332$		−	6.25143e22i		−	1.27566i
$333$	4.43255e22	−	2.05226e22i	0.880350	−	0.407601i
$334$	1.16981e23			2.26151
$335$			1.72100e22i			0.323875i
$336$	5.87658e21	+	2.66793e22i	0.107664	+	0.488789i
$337$	−7.20588e22			−1.28534			−0.642670	−	0.766143i	$-0.722173\pi$
$337$	−7.20588e22			−1.28534			−0.642670	+	0.766143i	$0.722173\pi$
$338$			9.71853e22i			1.68791i
$339$	9.71107e21	−	2.13903e21i	0.164237	−	0.0361759i
$340$	9.48063e21			0.156145
$341$			2.53205e22i			0.406146i
$342$	3.62752e22	+	7.83486e22i	0.566729	+	1.22404i
$343$	3.10067e22			0.471854
$344$		−	2.71209e23i		−	4.02048i
$345$	−2.76037e21	−	1.25319e22i	−0.0398653	−	0.180986i
$346$	1.23790e22			0.174181
$347$		−	7.97053e22i		−	1.09275i	−0.837540	−	0.546376i	$-0.816007\pi$
$347$		−	7.97053e22i		−	1.09275i	0.837540	−	0.546376i	$-0.183993\pi$
$348$	−1.58134e23	+	3.48317e22i	−2.11257	+	0.465330i
$349$	−2.86134e22			−0.372513			−0.186256	−	0.982501i	$-0.559635\pi$
$349$	−2.86134e22			−0.372513			−0.186256	+	0.982501i	$0.559635\pi$
$350$		−	2.29637e22i		−	0.291360i
$351$	−6.79635e22	−	8.93245e22i	−0.840449	−	1.10460i
$352$	1.02608e23			1.23679
$353$			4.43974e22i			0.521657i	0.965385	+	0.260829i	$0.0839957\pi$
$353$			4.43974e22i			0.521657i	−0.965385	+	0.260829i	$0.916004\pi$
$354$	3.17383e21	+	1.44090e22i	0.0363542	+	0.165046i
$355$	5.10928e22			0.570565
$356$			3.11666e23i			3.39344i
$357$	2.57421e21	−	5.67014e20i	0.0273294	−	0.00601977i
$358$	−2.88016e22			−0.298174
$359$		−	4.97330e22i		−	0.502105i	−0.967973	−	0.251052i	$-0.919223\pi$
$359$		−	4.97330e22i		−	0.502105i	0.967973	−	0.251052i	$-0.0807767\pi$
$360$	1.29542e23	−	5.99775e22i	1.27552	−	0.590563i
$361$	−4.70452e22			−0.451805
$362$			6.47602e21i			0.0606640i
$363$	−3.71470e21	−	1.68645e22i	−0.0339441	−	0.154104i
$364$	−8.77815e22			−0.782511
$365$			4.48176e22i			0.389774i
$366$	1.86661e23	−	4.11153e22i	1.58389	−	0.348878i
$367$	−6.92177e22			−0.573090			−0.286545	−	0.958067i	$-0.592507\pi$
$367$	−6.92177e22			−0.573090			−0.286545	+	0.958067i	$0.592507\pi$
$368$			8.07332e22i			0.652262i
$369$	5.34978e22	+	1.15547e23i	0.421792	+	0.911003i
$370$	−1.34358e23			−1.03383
$371$			5.35533e22i			0.402181i
$372$	−3.01178e22	−	1.36733e23i	−0.220768	−	1.00227i
$373$	8.88028e22			0.635400			0.317700	−	0.948191i	$-0.397090\pi$
$373$	8.88028e22			0.635400			0.317700	+	0.948191i	$0.397090\pi$
$374$		−	2.75529e22i		−	0.192453i
$375$	−1.38884e23	+	3.05915e22i	−0.947042	+	0.208602i
$376$	−3.21707e23			−2.14176
$377$		−	1.99185e23i		−	1.29474i
$378$	5.55337e22	−	4.22534e22i	0.352477	−	0.268186i
$379$	2.92079e23			1.81028			0.905142	−	0.425109i	$-0.139764\pi$
$379$	2.92079e23			1.81028			0.905142	+	0.425109i	$0.139764\pi$
$380$		−	1.65934e23i		−	1.00434i
$381$	3.75292e22	+	1.70380e23i	0.221842	+	1.00715i
$382$	3.59056e22			0.207297
$383$		−	1.19044e23i		−	0.671306i	−0.941986	−	0.335653i	$-0.891043\pi$
$383$		−	1.19044e23i		−	0.671306i	0.941986	−	0.335653i	$-0.108957\pi$
$384$	1.10873e23	−	2.44218e22i	0.610726	−	0.134523i
$385$	2.42535e22			0.130505
$386$		−	4.74126e23i		−	2.49234i
$387$	−2.95634e23	+	1.36878e23i	−1.51829	+	0.702966i
$388$	4.43020e23			2.22299
$389$			3.20490e23i			1.57133i	0.618650	+	0.785666i	$0.287680\pi$
$389$			3.20490e23i			1.57133i	−0.618650	+	0.785666i	$0.712320\pi$
$390$	6.64120e22	+	3.01506e23i	0.318174	+	1.44449i
$391$	7.78971e21			0.0364696
$392$			4.94156e23i			2.26094i
$393$	2.89093e23	−	6.36778e22i	1.29272	−	0.284744i
$394$	−5.87690e23			−2.56852
$395$			8.23511e22i			0.351800i
$396$	−2.14126e23	−	4.62477e23i	−0.894154	−	1.93123i
$397$	−3.68991e23			−1.50626			−0.753132	−	0.657870i	$-0.771458\pi$
$397$	−3.68991e23			−1.50626			−0.753132	+	0.657870i	$0.771458\pi$
$398$			1.06648e22i			0.0425602i
$399$	−9.92411e21	−	4.50548e22i	−0.0387200	−	0.175786i
$400$	3.55029e23			1.35433
$401$		−	4.34713e23i		−	1.62145i	−0.585429	−	0.810724i	$-0.699074\pi$
$401$		−	4.34713e23i		−	1.62145i	0.585429	−	0.810724i	$-0.300926\pi$
$402$	−2.70093e23	+	5.94926e22i	−0.985096	+	0.216984i
$403$	1.72228e23			0.614270
$404$			6.99863e23i			2.44107i
$405$	−1.30758e23	−	1.10938e23i	−0.446040	−	0.378429i
$406$	1.23835e23			0.413150
$407$			2.72828e23i			0.890305i
$408$	1.86407e22	+	8.46277e22i	0.0595006	+	0.270129i
$409$	1.61875e22			0.0505440			0.0252720	−	0.999681i	$-0.491955\pi$
$409$	1.61875e22			0.0505440			0.0252720	+	0.999681i	$0.491955\pi$
$410$		−	3.50241e23i		−	1.06982i
$411$	−1.52057e23	+	3.34931e22i	−0.454391	+	0.100087i
$412$	1.11623e24			3.26347
$413$		−	7.88397e21i		−	0.0225525i
$414$	1.87133e23	−	8.66422e22i	0.523778	−	0.242508i
$415$	1.17485e23			0.321774
$416$		−	6.97934e23i		−	1.87057i
$417$	−1.25564e23	−	5.70055e23i	−0.329338	−	1.49518i
$418$	−4.82243e23			−1.23788
$419$		−	1.48601e23i		−	0.373333i	−0.982423	−	0.186666i	$-0.940232\pi$
$419$		−	1.48601e23i		−	0.373333i	0.982423	−	0.186666i	$-0.0597684\pi$
$420$	−1.30971e23	+	2.88487e22i	−0.322057	+	0.0709386i
$421$	−2.10694e23			−0.507123			−0.253562	−	0.967319i	$-0.581602\pi$
$421$	−2.10694e23			−0.507123			−0.253562	+	0.967319i	$0.581602\pi$
$422$			5.98580e23i			1.41029i
$423$	1.62364e23	+	3.50680e23i	0.374479	+	0.808813i
$424$	−1.76058e24			−3.97523
$425$		−	3.42557e22i		−	0.0757238i
$426$	1.76621e23	+	8.01848e23i	0.382257	+	1.73543i
$427$	−1.02133e23			−0.216428
$428$		−	7.95901e23i		−	1.65145i
$429$	6.12239e23	−	1.34856e23i	1.24396	−	0.274003i
$430$	8.96116e23			1.78299
$431$			1.45530e23i			0.283567i	0.989898	+	0.141783i	$0.0452837\pi$
$431$			1.45530e23i			0.283567i	−0.989898	+	0.141783i	$0.954716\pi$
$432$	6.53256e23	+	8.58576e23i	1.24661	+	1.63842i
$433$	2.76937e23			0.517594			0.258797	−	0.965932i	$-0.416674\pi$
$433$	2.76937e23			0.517594			0.258797	+	0.965932i	$0.416674\pi$
$434$			1.07076e23i			0.196012i
$435$	−6.54605e22	−	2.97187e23i	−0.117375	−	0.532876i
$436$	−5.69842e23			−1.00087
$437$		−	1.36339e23i		−	0.234577i
$438$	−7.03365e23	+	1.54928e23i	−1.18553	+	0.261134i
$439$	7.04854e23			1.16391			0.581954	−	0.813222i	$-0.302288\pi$
$439$	7.04854e23			1.16391			0.581954	+	0.813222i	$0.302288\pi$
$440$			7.97341e23i			1.28994i
$441$	5.38659e23	−	2.49398e23i	0.853821	−	0.395318i
$442$	−1.87413e23			−0.291072
$443$			1.22387e24i			1.86252i	0.364351	+	0.931262i	$0.381291\pi$
$443$			1.22387e24i			1.86252i	−0.364351	+	0.931262i	$0.618709\pi$
$444$	−3.24519e23	−	1.47329e24i	−0.483941	−	2.19706i
$445$	−5.85726e23			−0.855962
$446$		−	8.07524e23i		−	1.15649i
$447$	−7.22894e23	+	1.59230e23i	−1.01463	+	0.223489i
$448$	7.00705e22			0.0963903
$449$		−	4.92165e23i		−	0.663580i	−0.943353	−	0.331790i	$-0.892347\pi$
$449$		−	4.92165e23i		−	0.663580i	0.943353	−	0.331790i	$-0.107653\pi$
$450$	−3.81014e23	−	8.22927e23i	−0.503533	−	1.08755i
$451$	−7.11200e23			−0.921304
$452$		−	3.07117e23i		−	0.389994i
$453$	1.28053e23	+	5.81353e23i	0.159407	+	0.723696i
$454$	2.31972e24			2.83096
$455$		−	1.64971e23i		−	0.197381i
$456$	1.48119e24	−	3.26257e23i	1.73751	−	0.382716i
$457$	−1.39981e24			−1.60999			−0.804994	−	0.593284i	$-0.797831\pi$
$457$	−1.39981e24			−1.60999			−0.804994	+	0.593284i	$0.797831\pi$
$458$		−	4.17120e23i		−	0.470404i
$459$	8.28415e22	−	6.30308e22i	0.0916080	−	0.0697009i
$460$	−3.96327e23			−0.429767
$461$			1.15752e24i			1.23090i	0.788177	+	0.615449i	$0.211025\pi$
$461$			1.15752e24i			1.23090i	−0.788177	+	0.615449i	$0.788975\pi$
$462$	8.38411e22	+	3.80634e23i	0.0874338	+	0.396944i
$463$	1.06888e23			0.109320			0.0546602	−	0.998505i	$-0.482592\pi$
$463$	1.06888e23			0.109320			0.0546602	+	0.998505i	$0.482592\pi$
$464$			1.91454e24i			1.92045i
$465$	2.56967e23	−	5.66015e22i	0.252814	−	0.0556867i
$466$	2.05957e24			1.98748
$467$		−	1.19933e24i		−	1.13524i	−0.823291	−	0.567619i	$-0.807865\pi$
$467$		−	1.19933e24i		−	1.13524i	0.823291	−	0.567619i	$-0.192135\pi$
$468$	−3.14574e24	+	1.45647e24i	−2.92085	+	1.35235i
$469$	1.47783e23			0.134607
$470$		−	1.06297e24i		−	0.949819i
$471$	6.78788e22	+	3.08165e23i	0.0595039	+	0.270144i
$472$	2.59187e23			0.222913
$473$		−	1.81965e24i		−	1.53546i
$474$	−1.29241e24	+	2.84677e23i	−1.07003	+	0.235693i
$475$	−5.99557e23			−0.487066
$476$		−	8.14105e22i		−	0.0648960i
$477$	8.88557e23	+	1.91914e24i	0.695056	+	1.50121i
$478$	−1.21747e24			−0.934557
$479$			8.59327e23i			0.647350i	0.946168	+	0.323675i	$0.104918\pi$
$479$			8.59327e23i			0.647350i	−0.946168	+	0.323675i	$0.895082\pi$
$480$	−2.29370e23	−	1.04133e24i	−0.169577	−	0.769868i
$481$	1.85576e24			1.34653
$482$			1.65460e24i			1.17834i
$483$	−1.07612e23	+	2.37034e22i	−0.0752205	+	0.0165686i
$484$	−5.33347e23			−0.365933
$485$			8.32585e23i			0.560729i
$486$	1.28904e24	−	2.43561e24i	0.852195	−	1.61020i
$487$	9.68317e23			0.628430			0.314215	−	0.949352i	$-0.398259\pi$
$487$	9.68317e23			0.628430			0.314215	+	0.949352i	$0.398259\pi$
$488$		−	3.35764e24i		−	2.13922i
$489$	−2.02526e23	−	9.19454e23i	−0.126678	−	0.575109i
$490$	−1.63277e24			−1.00267
$491$		−	1.67063e24i		−	1.00727i	−0.863916	−	0.503635i	$-0.831996\pi$
$491$		−	1.67063e24i		−	1.00727i	0.863916	−	0.503635i	$-0.168004\pi$
$492$	3.84054e24	−	8.45946e23i	2.27356	−	0.500791i
$493$	1.84728e23			0.107377
$494$			3.28019e24i			1.87222i
$495$	8.69149e23	−	4.02415e23i	0.487133	−	0.225542i
$496$	−1.65544e24			−0.911125
$497$		−	4.38736e23i		−	0.237135i
$498$	4.06131e23	+	1.84381e24i	0.215577	+	0.978705i
$499$	3.00033e23			0.156410			0.0782050	−	0.996937i	$-0.475081\pi$
$499$	3.00033e23			0.156410			0.0782050	+	0.996937i	$0.475081\pi$
$500$			4.39225e24i			2.24883i
$501$	−2.41072e24	+	5.31002e23i	−1.21229	+	0.267028i
$502$	−4.62582e24			−2.28484
$503$		−	3.08864e24i		−	1.49850i	−0.662289	−	0.749248i	$-0.730415\pi$
$503$		−	3.08864e24i		−	1.49850i	0.662289	−	0.749248i	$-0.269585\pi$
$504$	−5.15029e23	−	1.11238e24i	−0.245447	−	0.530124i
$505$	−1.31528e24			−0.615737
$506$			1.15182e24i			0.529700i
$507$	−4.41144e23	−	2.00277e24i	−0.199301	−	0.904813i
$508$	5.38835e24			2.39157
$509$			3.85870e24i			1.68260i	0.540569	+	0.841299i	$0.318209\pi$
$509$			3.85870e24i			1.68260i	−0.540569	+	0.841299i	$0.681791\pi$
$510$	−2.79624e23	+	6.15919e22i	−0.119796	+	0.0263871i
$511$	3.84851e23			0.161996
$512$		−	5.25289e24i		−	2.17254i
$513$	−1.10319e24	−	1.44992e24i	−0.448326	−	0.589236i
$514$	6.75437e23			0.269722
$515$			2.09777e24i			0.823178i
$516$	2.16441e24	+	9.82630e24i	0.834627	+	3.78916i
$517$	−2.15847e24			−0.817958
$518$			1.15374e24i			0.429675i
$519$	−2.55103e23	+	5.61907e22i	−0.0933702	+	0.0205664i
$520$	5.42346e24			1.95095
$521$		−	1.16274e24i		−	0.411097i	−0.978647	−	0.205549i	$-0.934102\pi$
$521$		−	1.16274e24i		−	0.411097i	0.978647	−	0.205549i	$-0.0658979\pi$
$522$	4.43774e24	−	2.05467e24i	1.54215	−	0.714014i
$523$	1.12148e24			0.383069			0.191534	−	0.981486i	$-0.438654\pi$
$523$	1.12148e24			0.383069			0.191534	+	0.981486i	$0.438654\pi$
$524$		−	9.14270e24i		−	3.06968i
$525$	1.04237e23	+	4.73230e23i	0.0344023	+	0.156185i
$526$	−1.06029e25			−3.43996
$527$			1.59728e23i			0.0509432i
$528$	−5.88476e24	+	1.29622e24i	−1.84512	+	0.406419i
$529$	2.91851e24			0.899622
$530$		−	5.81723e24i		−	1.76292i
$531$	−1.30811e23	−	2.82530e23i	−0.0389756	−	0.0841810i
$532$	−1.42488e24			−0.417420
$533$			4.83754e24i			1.39341i
$534$	−2.02477e24	−	9.19235e24i	−0.573463	−	2.60349i
$535$	1.49577e24			0.416562
$536$			4.85840e24i			1.33049i
$537$	5.93536e23	−	1.30737e23i	0.159837	−	0.0352070i
$538$	8.47970e24			2.24564
$539$			3.31550e24i			0.863476i
$540$	−4.21483e24	+	3.20690e24i	−1.07953	+	0.821375i
$541$	2.23337e24			0.562582			0.281291	−	0.959622i	$-0.409237\pi$
$541$	2.23337e24			0.562582			0.281291	+	0.959622i	$0.409237\pi$
$542$			5.21540e24i			1.29209i
$543$	−2.93960e22	−	1.33456e23i	−0.00716291	−	0.0325192i
$544$	6.47279e23			0.155132
$545$		−	1.07092e24i		−	0.252459i
$546$	2.58905e24	−	5.70282e23i	0.600352	−	0.132238i
$547$	2.13233e24			0.486372			0.243186	−	0.969980i	$-0.421808\pi$
$547$	2.13233e24			0.486372			0.243186	+	0.969980i	$0.421808\pi$
$548$			4.80886e24i			1.07899i
$549$	−3.66003e24	+	1.69459e24i	−0.807855	+	0.374035i
$550$	5.06519e24			1.09985
$551$		−	3.23319e24i		−	0.690664i
$552$	−7.79255e23	−	3.53777e24i	−0.163768	−	0.743495i
$553$	7.07152e23			0.146213
$554$		−	3.36949e24i		−	0.685450i
$555$	2.76882e24	−	6.09880e23i	0.554188	−	0.122070i
$556$	−1.80282e25			−3.55042
$557$			4.28440e24i			0.830221i	0.909771	+	0.415111i	$0.136257\pi$
$557$			4.28440e24i			0.830221i	−0.909771	+	0.415111i	$0.863743\pi$
$558$	1.77660e24	+	3.83717e24i	0.338752	+	0.731649i
$559$	−1.23772e25			−2.32228
$560$			1.58568e24i			0.292768i
$561$	1.25069e23	+	5.67804e23i	0.0227239	+	0.103165i
$562$	3.50435e23			0.0626587
$563$		−	6.48683e24i		−	1.14145i	−0.821141	−	0.570725i	$-0.806662\pi$
$563$		−	6.48683e24i		−	1.14145i	0.821141	−	0.570725i	$-0.193338\pi$
$564$	1.16559e25	−	2.56742e24i	2.01853	−	0.444616i
$565$	5.77176e23			0.0983722
$566$			4.04419e24i			0.678396i
$567$	−9.52627e23	+	1.12283e24i	−0.157281	+	0.185381i
$568$	1.44236e25			2.34389
$569$		−	1.13256e25i		−	1.81155i	−0.423762	−	0.905774i	$-0.639291\pi$
$569$		−	1.13256e25i		−	1.81155i	0.423762	−	0.905774i	$-0.360709\pi$
$570$	1.07801e24	+	4.89409e24i	0.169726	+	0.770545i
$571$	3.22177e23			0.0499309			0.0249654	−	0.999688i	$-0.492052\pi$
$571$	3.22177e23			0.0499309			0.0249654	+	0.999688i	$0.492052\pi$
$572$		−	1.93623e25i		−	2.95388i
$573$	−7.39933e23	+	1.62983e23i	−0.111122	+	0.0244766i
$574$	−3.00754e24			−0.444635
$575$			1.43202e24i			0.208420i
$576$	2.51105e24	−	1.16261e24i	0.359793	−	0.166583i
$577$	1.04474e25			1.47375			0.736877	−	0.676027i	$-0.236300\pi$
$577$	1.04474e25			1.47375			0.736877	+	0.676027i	$0.236300\pi$
$578$			1.29438e25i			1.79767i
$579$	2.15215e24	+	9.77065e24i	0.294284	+	1.33603i
$580$	−9.39866e24			−1.26536
$581$		−	1.00885e24i		−	0.133734i
$582$	−1.30665e25	+	2.87813e24i	−1.70551	+	0.375667i
$583$	−1.18125e25			−1.51818
$584$			1.26521e25i			1.60120i
$585$	−2.73720e24	−	5.91190e24i	−0.341117	−	0.736757i
$586$	9.47598e24			1.16291
$587$			1.94521e24i			0.235084i	0.993068	+	0.117542i	$0.0375015\pi$
$587$			1.94521e24i			0.235084i	−0.993068	+	0.117542i	$0.962498\pi$
$588$	−3.94367e24	−	1.79040e25i	−0.469358	−	2.13086i
$589$	2.79563e24			0.327674
$590$			8.56397e23i			0.0988569i
$591$	1.21110e25	−	2.66765e24i	1.37686	−	0.303278i
$592$	−1.78373e25			−1.99726
$593$		−	1.02435e25i		−	1.12968i	−0.825200	−	0.564841i	$-0.808937\pi$
$593$		−	1.02435e25i		−	1.12968i	0.825200	−	0.564841i	$-0.191063\pi$
$594$	9.32000e24	+	1.22493e25i	1.01237	+	1.33056i
$595$	1.52998e23			0.0163694
$596$			2.28618e25i			2.40932i
$597$	−4.84096e22	−	2.19777e23i	−0.00502531	−	0.0228146i
$598$	7.83461e24			0.801137
$599$			8.10173e24i			0.816086i	0.912963	+	0.408043i	$0.133789\pi$
$599$			8.10173e24i			0.816086i	−0.912963	+	0.408043i	$0.866211\pi$
$600$	−1.55575e25	+	3.42682e24i	−1.54376	+	0.340040i
$601$	−4.00759e24			−0.391754			−0.195877	−	0.980628i	$-0.562755\pi$
$601$	−4.00759e24			−0.391754			−0.195877	+	0.980628i	$0.562755\pi$
$602$		−	7.69499e24i		−	0.741036i
$603$	5.29595e24	−	2.45201e24i	0.502444	−	0.232631i
$604$	1.83856e25			1.71848
$605$		−	1.00234e24i		−	0.0923031i
$606$	−4.54673e24	−	2.06419e25i	−0.412521	−	1.87282i
$607$	1.18663e25			1.06076			0.530378	−	0.847761i	$-0.322050\pi$
$607$	1.18663e25			1.06076			0.530378	+	0.847761i	$0.322050\pi$
$608$		−	1.13289e25i		−	0.997832i
$609$	−2.55195e24	+	5.62112e23i	−0.221471	+	0.0487828i
$610$	1.10942e25			0.948695
$611$			1.46818e25i			1.23711i
$612$	−1.35076e24	−	2.91743e24i	−0.112154	−	0.242235i
$613$	−1.12607e25			−0.921345			−0.460673	−	0.887570i	$-0.652392\pi$
$613$	−1.12607e25			−0.921345			−0.460673	+	0.887570i	$0.652392\pi$
$614$		−	3.32239e25i		−	2.67877i
$615$	1.58982e24	+	7.21768e24i	0.126320	+	0.573484i
$616$	6.84679e24			0.536119
$617$		−	2.90545e23i		−	0.0224206i	−0.999937	−	0.0112103i	$-0.996432\pi$
$617$		−	2.90545e23i		−	0.0224206i	0.999937	−	0.0112103i	$-0.00356842\pi$
$618$	−3.29224e25	+	7.25172e24i	−2.50377	+	0.551499i
$619$	−1.42594e25			−1.06877			−0.534385	−	0.845241i	$-0.679457\pi$
$619$	−1.42594e25			−1.06877			−0.534385	+	0.845241i	$0.679457\pi$
$620$		−	8.12670e24i		−	0.600329i
$621$	−3.46310e24	+	2.63493e24i	−0.252139	+	0.191843i
$622$	8.97433e24			0.644004
$623$			5.02965e24i			0.355750i
$624$	8.81681e24	+	4.00278e25i	0.614682	+	2.79062i
$625$	1.31831e24			0.0905936
$626$		−	1.92935e25i		−	1.30690i
$627$	9.93793e24	−	2.18900e24i	0.663572	−	0.146163i
$628$	9.74587e24			0.641481
$629$			1.72107e24i			0.111672i
$630$	3.67548e24	−	1.70174e24i	0.235098	−	0.108850i
$631$	−1.34151e25			−0.845923			−0.422961	−	0.906148i	$-0.639009\pi$
$631$	−1.34151e25			−0.845923			−0.422961	+	0.906148i	$0.639009\pi$
$632$			2.32478e25i			1.44520i
$633$	−2.71708e24	−	1.23354e25i	−0.166521	−	0.755995i
$634$	−4.39123e25			−2.65328
$635$			1.01265e25i			0.603249i
$636$	6.37884e25	−	1.40505e25i	3.74652	−	0.825235i
$637$	2.25518e25			1.30595
$638$			2.73147e25i			1.55959i
$639$	−7.27951e24	−	1.57226e25i	−0.409821	−	0.885147i
$640$	6.58975e24			0.365805
$641$		−	5.98895e24i		−	0.327815i	−0.986476	−	0.163907i	$-0.947590\pi$
$641$		−	5.98895e24i		−	0.327815i	0.986476	−	0.163907i	$-0.0524098\pi$
$642$	5.17066e24	+	2.34745e25i	0.279081	+	1.26701i
$643$	−1.54893e25			−0.824391			−0.412196	−	0.911095i	$-0.635238\pi$
$643$	−1.54893e25			−0.824391			−0.412196	+	0.911095i	$0.635238\pi$
$644$			3.40328e24i			0.178618i
$645$	−1.84669e25	+	4.06766e24i	−0.955778	+	0.210527i
$646$	−3.04212e24			−0.155268
$647$			1.51080e25i			0.760447i	0.924895	+	0.380223i	$0.124153\pi$
$647$			1.51080e25i			0.760447i	−0.924895	+	0.380223i	$0.875847\pi$
$648$	−3.69132e25	−	3.13178e25i	−1.83234	−	1.55459i
$649$	1.73900e24			0.0851328
$650$		−	3.44531e25i		−	1.66345i
$651$	−4.86039e23	−	2.20659e24i	−0.0231442	−	0.105073i
$652$	−2.90781e25			−1.36565
$653$			2.12528e25i			0.984457i	0.870466	+	0.492228i	$0.163818\pi$
$653$			2.12528e25i			0.984457i	−0.870466	+	0.492228i	$0.836182\pi$
$654$	1.68070e25	−	3.70204e24i	0.767877	−	0.169138i
$655$	1.71822e25			0.774297
$656$		−	4.64978e25i		−	2.06680i
$657$	1.37915e25	−	6.38544e24i	0.604677	−	0.279964i
$658$	−9.12778e24			−0.394759
$659$		−	4.11576e25i		−	1.75583i	−0.478820	−	0.877913i	$-0.658936\pi$
$659$		−	4.11576e25i		−	1.75583i	0.478820	−	0.877913i	$-0.341064\pi$
$660$	−6.36327e24	−	2.88889e25i	−0.267784	−	1.21572i
$661$	3.24714e25			1.34799			0.673996	−	0.738735i	$-0.264576\pi$
$661$	3.24714e25			1.34799			0.673996	+	0.738735i	$0.264576\pi$
$662$			6.47533e25i			2.65180i
$663$	3.86217e24	−	8.50709e23i	0.156030	−	0.0343684i
$664$	3.31662e25			1.32185
$665$		−	2.67783e24i		−	0.105290i
$666$	1.91428e25	+	4.13454e25i	0.742571	+	1.60383i
$667$	−7.72236e24			−0.295541
$668$			7.62400e25i			2.87869i
$669$	3.66552e24	+	1.66412e25i	0.136553	+	0.619941i
$670$	−1.60529e25			−0.590039
$671$		−	2.25278e25i		−	0.816990i
$672$	−8.94192e24	+	1.96961e24i	−0.319969	+	0.0704786i
$673$	1.10390e25			0.389758			0.194879	−	0.980827i	$-0.437569\pi$
$673$	1.10390e25			0.389758			0.194879	+	0.980827i	$0.437569\pi$
$674$		−	6.72141e25i		−	2.34165i
$675$	1.15873e25	+	1.52292e25i	0.398334	+	0.523530i
$676$	−6.33384e25			−2.14856
$677$		−	2.74075e25i		−	0.917427i	−0.888584	−	0.458714i	$-0.848310\pi$
$677$		−	2.74075e25i		−	0.917427i	0.888584	−	0.458714i	$-0.151690\pi$
$678$	1.99522e24	+	9.05817e24i	0.0659058	+	0.299208i
$679$	7.14944e24			0.233047
$680$			5.02984e24i			0.161798i
$681$	−4.78042e25	+	1.05297e25i	−1.51755	+	0.334266i
$682$	−2.36181e25			−0.739922
$683$		−	3.99739e25i		−	1.23592i	−0.786210	−	0.617960i	$-0.787959\pi$
$683$		−	3.99739e25i		−	1.23592i	0.786210	−	0.617960i	$-0.212041\pi$
$684$	−5.10620e25	+	2.36416e25i	−1.55809	+	0.721393i
$685$	−9.03747e24			−0.272165
$686$			2.89220e25i			0.859630i
$687$	1.89339e24	+	8.59589e24i	0.0555431	+	0.252162i
$688$	1.18968e26			3.44456
$689$			8.03477e25i			2.29615i
$690$	1.16894e25	−	2.57478e24i	0.329723	−	0.0726271i
$691$	−1.02801e25			−0.286218			−0.143109	−	0.989707i	$-0.545710\pi$
$691$	−1.02801e25			−0.286218			−0.143109	+	0.989707i	$0.545710\pi$
$692$			8.06773e24i			0.221716i
$693$	−3.45555e24	−	7.46342e24i	−0.0937385	−	0.202460i
$694$	7.43465e25			1.99079
$695$		−	3.38811e25i		−	0.895560i
$696$	−1.84796e25	−	8.38960e25i	−0.482179	−	2.18906i
$697$	−4.48644e24			−0.115560
$698$		−	2.66897e25i		−	0.678648i
$699$	−4.24430e25	+	9.34881e24i	−1.06540	+	0.234672i
$700$	1.49661e25			0.370874
$701$		−	2.02392e25i		−	0.495143i	−0.968870	−	0.247572i	$-0.920367\pi$
$701$		−	2.02392e25i		−	0.495143i	0.968870	−	0.247572i	$-0.0796325\pi$
$702$	8.33189e25	−	6.33941e25i	2.01238	−	1.53114i
$703$	3.01229e25			0.718288
$704$			1.54557e25i			0.363861i
$705$	4.82505e24	+	2.19054e25i	0.112150	+	0.509155i
$706$	−4.14124e25			−0.950361
$707$			1.12943e25i			0.255909i
$708$	−9.39075e24	+	2.06848e24i	−0.210088	+	0.0462755i
$709$	−8.66215e25			−1.91342			−0.956708	−	0.291048i	$-0.905996\pi$
$709$	−8.66215e25			−1.91342			−0.956708	+	0.291048i	$0.905996\pi$
$710$			4.76577e25i			1.03946i
$711$	2.53415e25	−	1.17331e25i	0.545766	−	0.252688i
$712$	−1.65351e26			−3.51631
$713$		−	6.67727e24i		−	0.140215i
$714$	5.28892e23	+	2.40114e24i	0.0109669	+	0.0497890i
$715$	3.63883e25			0.745088
$716$		−	1.87708e25i		−	0.379548i
$717$	2.50892e25	−	5.52633e24i	0.500973	−	0.110348i
$718$	4.63893e25			0.914740
$719$			8.53805e25i			1.66264i	0.555793	+	0.831320i	$0.312415\pi$
$719$			8.53805e25i			1.66264i	−0.555793	+	0.831320i	$0.687585\pi$
$720$	2.63096e25	+	5.68245e25i	0.505967	+	1.09281i
$721$	1.80137e25			0.342125
$722$		−	4.38822e25i		−	0.823103i
$723$	−7.51058e24	−	3.40976e25i	−0.139133	−	0.631653i
$724$	−4.22060e24			−0.0772196
$725$			3.39595e25i			0.613648i
$726$	1.57307e25	−	3.46495e24i	0.280748	−	0.0618397i
$727$	1.83358e25			0.323215			0.161607	−	0.986855i	$-0.448332\pi$
$727$	1.83358e25			0.323215			0.161607	+	0.986855i	$0.448332\pi$
$728$		−	4.65715e25i		−	0.810845i
$729$	−1.55084e25	+	5.60436e25i	−0.266698	+	0.963780i
$730$	−4.18044e25			−0.710095
$731$		−	1.14789e25i		−	0.192594i
$732$	2.67960e25	+	1.21652e26i	0.444090	+	2.01614i
$733$	9.99901e25			1.63690			0.818449	−	0.574580i	$-0.194834\pi$
$733$	9.99901e25			1.63690			0.818449	+	0.574580i	$0.194834\pi$
$734$		−	6.45640e25i		−	1.04406i
$735$	3.36476e25	−	7.41148e24i	0.537488	−	0.118391i
$736$	−2.70588e25			−0.426981
$737$			3.25971e25i			0.508126i
$738$	−1.07778e26	+	4.99010e25i	−1.65967	+	0.768426i
$739$	7.21830e24			0.109808			0.0549041	−	0.998492i	$-0.482515\pi$
$739$	7.21830e24			0.109808			0.0549041	+	0.998492i	$0.482515\pi$
$740$		−	8.75650e25i		−	1.31597i
$741$	−1.48894e25	−	6.75972e25i	−0.221062	−	1.00361i
$742$	−4.99528e25			−0.732697
$743$		−	4.78088e25i		−	0.692802i	−0.938087	−	0.346401i	$-0.887404\pi$
$743$		−	4.78088e25i		−	0.692802i	0.938087	−	0.346401i	$-0.112596\pi$
$744$	7.25421e25	−	1.59786e25i	1.03856	−	0.228762i
$745$	−4.29651e25			−0.607728
$746$			8.28324e25i			1.15758i
$747$	−1.67389e25	−	3.61532e25i	−0.231122	−	0.499185i
$748$	1.79570e25			0.244974
$749$		−	1.28442e25i		−	0.173129i
$750$	−2.85348e25	−	1.29546e26i	−0.380034	−	1.72533i
$751$	−1.09528e26			−1.44134			−0.720670	−	0.693278i	$-0.756166\pi$
$751$	−1.09528e26			−1.44134			−0.720670	+	0.693278i	$0.756166\pi$
$752$		−	1.41119e26i		−	1.83496i
$753$	9.53277e25	−	2.09976e25i	1.22480	−	0.269783i
$754$	1.85793e26			2.35878
$755$			3.45527e25i			0.433470i
$756$	2.75378e25	+	3.61929e25i	0.341375	+	0.448670i
$757$	−1.54885e26			−1.89734			−0.948670	−	0.316267i	$-0.897570\pi$
$757$	−1.54885e26			−1.89734			−0.948670	+	0.316267i	$0.897570\pi$
$758$			2.72441e26i			3.29800i
$759$	−5.22835e24	−	2.37364e25i	−0.0625445	−	0.283948i
$760$	8.80343e25			1.04071
$761$		−	2.98795e25i		−	0.349069i	−0.984651	−	0.174535i	$-0.944158\pi$
$761$		−	2.98795e25i		−	0.349069i	0.984651	−	0.174535i	$-0.0558421\pi$
$762$	−1.58925e26	+	3.50060e25i	−1.83484	+	0.404155i
$763$	−9.19607e24			−0.104926
$764$			2.34007e25i			0.263869i
$765$	5.48283e24	−	2.53854e24i	0.0611015	−	0.0282899i
$766$	1.11041e26			1.22299
$767$		−	1.18286e25i		−	0.128758i
$768$	3.07074e25	+	1.39410e26i	0.330364	+	1.49983i
$769$	3.57805e25			0.380461			0.190230	−	0.981739i	$-0.439077\pi$
$769$	3.57805e25			0.380461			0.190230	+	0.981739i	$0.439077\pi$
$770$			2.26229e25i			0.237756i
$771$	−1.39192e25	+	3.06595e24i	−0.144586	+	0.0318475i
$772$	3.09001e26			3.17252
$773$		−	1.13119e26i		−	1.14794i	−0.818876	−	0.573971i	$-0.805402\pi$
$773$		−	1.13119e26i		−	1.14794i	0.818876	−	0.573971i	$-0.194598\pi$
$774$	−1.27675e26	−	2.75758e26i	−1.28067	−	2.76604i
$775$	−2.93637e25			−0.291135
$776$			2.35039e26i			2.30348i
$777$	−5.23706e24	−	2.37759e25i	−0.0507339	−	0.230329i
$778$	−2.98943e26			−2.86267
$779$			7.85235e25i			0.743297i
$780$	−1.96500e26	+	4.32826e25i	−1.83870	+	0.405006i
$781$	9.67738e25			0.895155
$782$			7.26599e24i			0.0664407i
$783$	−8.21252e25	+	6.24858e25i	−0.742370	+	0.564840i
$784$	−2.16765e26			−1.93707
$785$			1.83158e25i			0.161807i
$786$	5.93966e25	+	2.69657e26i	0.518750	+	2.35510i
$787$	1.96409e26			1.69586			0.847928	−	0.530111i	$-0.177850\pi$
$787$	1.96409e26			1.69586			0.847928	+	0.530111i	$0.177850\pi$
$788$		−	3.83014e26i		−	3.26948i
$789$	2.18502e26	−	4.81288e25i	1.84400	−	0.406174i
$790$	−7.68145e25			−0.640913
$791$		−	4.95623e24i		−	0.0408850i
$792$	2.45362e26	−	1.13602e26i	2.00115	−	0.926530i
$793$	−1.53233e26			−1.23564
$794$		−	3.44182e26i		−	2.74413i
$795$	2.64056e25	+	1.19880e26i	0.208158	+	0.945023i
$796$	−6.95053e24			−0.0541752
$797$		−	1.17991e26i		−	0.909335i	−0.890661	−	0.454667i	$-0.849758\pi$
$797$		−	1.17991e26i		−	0.909335i	0.890661	−	0.454667i	$-0.150242\pi$
$798$	4.20257e25	−	9.25689e24i	0.320250	−	0.0705406i
$799$	−1.36162e25			−0.102597
$800$			1.18993e26i			0.886564i
$801$	8.34520e25	+	1.80243e26i	0.614814	+	1.32790i
$802$	4.05486e26			2.95397
$803$			8.48880e25i			0.611514i
$804$	−3.87730e25	−	1.76027e26i	−0.276201	−	1.25394i
$805$	−6.39590e24			−0.0450546
$806$			1.60649e26i			1.11908i
$807$	−1.74747e26	+	3.84911e25i	−1.20378	+	0.265154i
$808$	−3.71304e26			−2.52946
$809$			1.68951e26i			1.13821i	0.822264	+	0.569106i	$0.192711\pi$
$809$			1.68951e26i			1.13821i	−0.822264	+	0.569106i	$0.807289\pi$
$810$	1.03479e26	−	1.21967e26i	0.689426	−	0.812601i
$811$	7.99308e24			0.0526655			0.0263328	−	0.999653i	$-0.491617\pi$
$811$	7.99308e24			0.0526655			0.0263328	+	0.999653i	$0.491617\pi$
$812$			8.07066e25i			0.525902i
$813$	−2.36738e25	−	1.07477e26i	−0.152564	−	0.692632i
$814$	−2.54485e26			−1.62197
$815$		−	5.46476e25i		−	0.344471i
$816$	−3.71227e25	+	8.17691e24i	−0.231434	+	0.0509774i
$817$	−2.00908e26			−1.23879
$818$			1.50992e25i			0.0920816i
$819$	−5.07657e25	+	2.35044e25i	−0.306207	+	0.141773i
$820$	2.28262e26			1.36179
$821$		−	3.07541e26i		−	1.81474i	−0.420333	−	0.907370i	$-0.638087\pi$
$821$		−	3.07541e26i		−	1.81474i	0.420333	−	0.907370i	$-0.361913\pi$
$822$	−3.12413e25	−	1.41834e26i	−0.182340	−	0.827814i
$823$	1.77089e26			1.02234			0.511168	−	0.859481i	$-0.329213\pi$
$823$	1.77089e26			1.02234			0.511168	+	0.859481i	$0.329213\pi$
$824$			5.92204e26i			3.38163i
$825$	−1.04382e26	+	2.29920e25i	−0.589577	+	0.129865i
$826$	7.35391e24			0.0410864
$827$			7.12742e25i			0.393897i	0.980414	+	0.196949i	$0.0631032\pi$
$827$			7.12742e25i			0.393897i	−0.980414	+	0.196949i	$0.936897\pi$
$828$	5.64672e25	+	1.21960e26i	0.308690	+	0.666720i
$829$	5.99218e25			0.324036			0.162018	−	0.986788i	$-0.448200\pi$
$829$	5.99218e25			0.324036			0.162018	+	0.986788i	$0.448200\pi$
$830$			1.09587e26i			0.586212i
$831$	1.52948e25	+	6.94374e25i	0.0809346	+	0.367438i
$832$	1.05129e26			0.550316
$833$			2.09151e25i			0.108306i
$834$	5.31729e26	−	1.17122e26i	2.72393	−	0.599992i
$835$	−1.43281e26			−0.726121
$836$		−	3.14291e26i		−	1.57571i
$837$	−5.40294e25	−	7.10109e25i	−0.267979	−	0.352205i
$838$	1.38610e26			0.680142
$839$			2.28769e26i			1.11056i	0.831665	+	0.555278i	$0.187388\pi$
$839$			2.28769e26i			1.11056i	−0.831665	+	0.555278i	$0.812612\pi$
$840$	−1.53053e25	−	6.94853e25i	−0.0735071	−	0.333718i
$841$	2.73261e25			0.129842
$842$		−	1.96529e26i		−	0.923883i
$843$	−7.22168e24	+	1.59070e24i	−0.0335884	+	0.00739843i
$844$	−3.90111e26			−1.79517
$845$		−	1.19034e26i		−	0.541953i
$846$	−3.27103e26	+	1.51448e26i	−1.47350	+	0.682230i
$847$	−8.60713e24			−0.0383625
$848$		−	7.72292e26i		−	3.40580i
$849$	−1.83574e25	−	8.33415e25i	−0.0801018	−	0.363657i
$850$	3.19526e25			0.137954
$851$		−	7.19474e25i		−	0.307361i
$852$	−5.22587e26	+	1.15109e26i	−2.20903	+	0.486578i
$853$	1.08284e26			0.452923			0.226461	−	0.974020i	$-0.427284\pi$
$853$	1.08284e26			0.452923			0.226461	+	0.974020i	$0.427284\pi$
$854$		−	9.52661e25i		−	0.394292i
$855$	−4.44305e25	−	9.59627e25i	−0.181964	−	0.393013i
$856$	4.22256e26			1.71124
$857$			2.55259e26i			1.02366i	0.859088	+	0.511829i	$0.171032\pi$
$857$			2.55259e26i			1.02366i	−0.859088	+	0.511829i	$0.828968\pi$
$858$	1.25789e26	+	5.71076e26i	0.499181	+	2.26625i
$859$	4.68433e26			1.83954			0.919770	−	0.392457i	$-0.128375\pi$
$859$	4.68433e26			1.83954			0.919770	+	0.392457i	$0.128375\pi$
$860$			5.84025e26i			2.26958i
$861$	6.19785e25	−	1.36518e25i	0.238348	−	0.0525004i
$862$	−1.35745e26			−0.516606
$863$		−	4.14979e26i		−	1.56289i	−0.623974	−	0.781445i	$-0.714483\pi$
$863$		−	4.14979e26i		−	1.56289i	0.623974	−	0.781445i	$-0.285517\pi$
$864$	−2.87763e26	+	2.18947e26i	−1.07253	+	0.816049i
$865$	−1.51620e25			−0.0559256
$866$			2.58318e26i			0.942959i
$867$	−5.87545e25	−	2.66742e26i	−0.212260	−	0.963650i
$868$	−6.97843e25			−0.249506
$869$			1.55979e26i			0.551937i
$870$	2.77206e26	−	6.10594e25i	0.970799	−	0.213835i
$871$	2.21723e26			0.768507
$872$		−	3.02323e26i		−	1.03711i
$873$	2.56207e26	−	1.18623e26i	0.869887	−	0.402756i
$874$	1.27172e26			0.427356
$875$			7.08819e25i			0.235756i
$876$	−1.00971e26	−	4.58403e26i	−0.332400	−	1.50907i
$877$	−2.54490e26			−0.829227			−0.414614	−	0.909998i	$-0.636083\pi$
$877$	−2.54490e26			−0.829227			−0.414614	+	0.909998i	$0.636083\pi$
$878$			6.57465e26i			2.12042i
$879$	−1.95278e26	+	4.30135e25i	−0.623382	+	0.137311i
$880$	−3.49760e26			−1.10516
$881$			2.39637e26i			0.749498i	0.927126	+	0.374749i	$0.122271\pi$
$881$			2.39637e26i			0.749498i	−0.927126	+	0.374749i	$0.877729\pi$
$882$	2.32631e26	+	5.02444e26i	0.720194	+	1.55550i
$883$	−1.97871e26			−0.606368			−0.303184	−	0.952932i	$-0.598050\pi$
$883$	−1.97871e26			−0.606368			−0.303184	+	0.952932i	$0.598050\pi$
$884$		−	1.22143e26i		−	0.370508i
$885$	−3.88736e24	−	1.76484e25i	−0.0116725	−	0.0529926i
$886$	−1.14159e27			−3.39317
$887$			3.45748e25i			0.101730i	0.998706	+	0.0508648i	$0.0161978\pi$
$887$			3.45748e25i			0.101730i	−0.998706	+	0.0508648i	$0.983802\pi$
$888$	7.81640e26	−	1.72170e26i	2.27662	−	0.501464i
$889$	8.69569e25			0.250719
$890$		−	5.46346e26i		−	1.55940i
$891$	−2.47666e26	−	2.10125e26i	−0.699789	−	0.593714i
$892$	5.26286e26			1.47210
$893$			2.38316e26i			0.659919i
$894$	−1.48524e26	−	6.74292e26i	−0.407155	−	1.84846i
$895$	3.52767e25			0.0957373
$896$		−	5.65864e25i		−	0.152034i
$897$	−1.61454e26	+	3.55629e25i	−0.429453	+	0.0945944i
$898$	4.59075e26			1.20892
$899$		−	1.58347e26i		−	0.412832i
$900$	5.36325e26	−	2.48317e26i	1.38435	−	0.640951i
$901$	−7.45162e25			−0.190427
$902$		−	6.63384e26i		−	1.67844i
$903$	3.49291e25	+	1.58576e26i	0.0874980	+	0.397236i
$904$	1.62937e26			0.404115
$905$		−	7.93194e24i		−	0.0194779i
$906$	−5.42268e26	+	1.19444e26i	−1.31844	+	0.290409i
$907$	−1.75179e26			−0.421713			−0.210857	−	0.977517i	$-0.567625\pi$
$907$	−1.75179e26			−0.421713			−0.210857	+	0.977517i	$0.567625\pi$
$908$			1.51183e27i			3.60355i
$909$	1.87396e26	+	4.04744e26i	0.442267	+	0.955224i
$910$	1.53880e26			0.359591
$911$		−	1.77018e25i		−	0.0409593i	−0.999790	−	0.0204796i	$-0.993481\pi$
$911$		−	1.77018e25i		−	0.0409593i	0.999790	−	0.0204796i	$-0.00651933\pi$
$912$	1.43115e26	+	6.49736e26i	0.327894	+	1.48862i
$913$	2.22526e26			0.504829
$914$		−	1.30569e27i		−	2.93309i
$915$	−2.28626e26	+	5.03588e25i	−0.508552	+	0.112017i
$916$	2.71849e26			0.598781
$917$		−	1.47544e26i		−	0.321809i
$918$	5.87931e25	+	7.72718e25i	0.126982	+	0.166893i
$919$	−3.87242e26			−0.828214			−0.414107	−	0.910228i	$-0.635906\pi$
$919$	−3.87242e26			−0.828214			−0.414107	+	0.910228i	$0.635906\pi$
$920$		−	2.10267e26i		−	0.445328i
$921$	1.50810e26	+	6.84669e26i	0.316296	+	1.43596i
$922$	−1.07970e27			−2.24246
$923$		−	6.58249e26i		−	1.35386i
$924$	−2.48070e26	+	5.46416e25i	−0.505273	+	0.111295i
$925$	−3.16393e26			−0.638191
$926$			9.97020e25i			0.199161i
$927$	6.45538e26	−	2.98883e26i	1.27704	−	0.591267i
$928$	−6.41683e26			−1.25715
$929$			7.04714e26i			1.36732i	0.729799	+	0.683662i	$0.239614\pi$
$929$			7.04714e26i			1.36732i	−0.729799	+	0.683662i	$0.760386\pi$
$930$	5.27960e25	+	2.39691e26i	0.101451	+	0.460579i
$931$	3.66064e26			0.696642
$932$			1.34228e27i			2.52988i
$933$	−1.84941e26	+	4.07364e25i	−0.345221	+	0.0760409i
$934$	1.11870e27			2.06819
$935$			3.37473e25i			0.0617924i
$936$	−7.72714e26	−	1.66894e27i	−1.40132	−	3.02661i
$937$	−4.77743e26			−0.858100			−0.429050	−	0.903281i	$-0.641152\pi$
$937$	−4.77743e26			−0.858100			−0.429050	+	0.903281i	$0.641152\pi$
$938$			1.37847e26i			0.245229i
$939$	8.75774e25	+	3.97596e26i	0.154313	+	0.700570i
$940$	6.92769e26			1.20903
$941$		−	8.51491e26i		−	1.47188i	−0.677045	−	0.735941i	$-0.736740\pi$
$941$		−	8.51491e26i		−	1.47188i	0.677045	−	0.735941i	$-0.263260\pi$
$942$	−2.87447e26	+	6.33151e25i	−0.492152	+	0.108405i
$943$	1.87551e26			0.318063
$944$			1.13695e26i			0.190982i
$945$	−6.80186e25	+	5.17527e25i	−0.113173	+	0.0861086i
$946$	1.69731e27			2.79732
$947$			5.74303e26i			0.937543i	0.883319	+	0.468772i	$0.155303\pi$
$947$			5.74303e26i			0.937543i	−0.883319	+	0.468772i	$0.844697\pi$
$948$	−1.85532e26	−	8.42303e26i	−0.300015	−	1.36205i
$949$	5.77403e26			0.924875
$950$		−	5.59247e26i		−	0.887343i
$951$	9.04932e26	−	1.99327e26i	1.42230	−	0.313286i
$952$	4.31914e25			0.0672457
$953$		−	5.35549e26i		−	0.825967i	−0.910738	−	0.412984i	$-0.864487\pi$
$953$		−	5.35549e26i		−	0.825967i	0.910738	−	0.412984i	$-0.135513\pi$
$954$	−1.79011e27	+	8.28817e26i	−2.73492	+	1.26626i
$955$	−4.39778e25			−0.0665584
$956$		−	7.93458e26i		−	1.18960i
$957$	−1.23987e26	−	5.62894e26i	−0.184149	−	0.836025i
$958$	−8.01552e26			−1.17935
$959$			7.76051e25i			0.113116i
$960$	1.56854e26	−	3.45498e25i	0.226493	−	0.0498889i
$961$	−5.62136e26			−0.804139
$962$			1.73099e27i			2.45312i
$963$	−2.13111e26	−	4.60285e26i	−0.299205	−	0.646234i
$964$	−1.07835e27			−1.49992
$965$			5.80717e26i			0.800237i
$966$	−2.21098e25	−	1.00377e26i	−0.0301849	−	0.137038i
$967$	1.92733e26			0.260686			0.130343	−	0.991469i	$-0.458392\pi$
$967$	1.92733e26			0.260686			0.130343	+	0.991469i	$0.458392\pi$
$968$		−	2.82961e26i		−	0.379183i
$969$	6.26911e25	−	1.38088e25i	0.0832323	−	0.0183334i
$970$	−7.76608e26			−1.02154
$971$		−	5.11685e26i		−	0.666852i	−0.942776	−	0.333426i	$-0.891795\pi$
$971$		−	5.11685e26i		−	0.666852i	0.942776	−	0.333426i	$-0.108205\pi$
$972$	1.58736e27	+	8.40102e26i	2.04964	+	1.08477i
$973$	−2.90938e26			−0.372208
$974$			9.03214e26i			1.14488i
$975$	1.56390e26	+	7.10001e26i	0.196412	+	0.891697i
$976$	1.47286e27			1.83279
$977$		−	8.34449e26i		−	1.02884i	−0.857538	−	0.514421i	$-0.828007\pi$
$977$		−	8.34449e26i		−	1.02884i	0.857538	−	0.514421i	$-0.171993\pi$
$978$	8.57637e26	−	1.88909e26i	1.04774	−	0.230783i
$979$	−1.10941e27			−1.34291
$980$		−	1.06412e27i		−	1.27631i
$981$	−3.29550e26	+	1.52581e26i	−0.391652	+	0.181334i
$982$	1.55831e27			1.83506
$983$			5.33273e25i			0.0622254i	0.999516	+	0.0311127i	$0.00990508\pi$
$983$			5.33273e25i			0.0622254i	−0.999516	+	0.0311127i	$0.990095\pi$
$984$	4.48807e26	+	2.03756e27i	0.518924	+	2.35588i
$985$	7.19813e26			0.824696
$986$			1.72309e26i			0.195621i
$987$	1.88103e26	−	4.14329e25i	0.211612	−	0.0466113i
$988$	−2.13779e27			−2.38316
$989$			4.79861e26i			0.530089i
$990$	3.75359e26	+	8.10714e26i	0.410894	+	0.887465i
$991$	−8.81591e26			−0.956322			−0.478161	−	0.878272i	$-0.658696\pi$
$991$	−8.81591e26			−0.956322			−0.478161	+	0.878272i	$0.658696\pi$
$992$		−	5.54842e26i		−	0.596436i
$993$	−2.93929e26	−	1.33442e27i	−0.313111	−	1.42151i
$994$	4.09239e26			0.432016
$995$		−	1.30624e25i		−	0.0136652i
$996$	−1.20166e27	+	2.64687e26i	−1.24580	+	0.274409i
$997$	5.47604e26			0.562613			0.281307	−	0.959618i	$-0.409232\pi$
$997$	5.47604e26			0.562613			0.281307	+	0.959618i	$0.409232\pi$
$998$			2.79861e26i			0.284950i
$999$	−5.82166e26	−	7.65141e26i	−0.587431	−	0.772062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.19.b.b.2.4	yes	4
3.2	odd	2	inner	3.19.b.b.2.1	✓	4
4.3	odd	2		48.19.e.b.17.4		4
12.11	even	2		48.19.e.b.17.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.19.b.b.2.1	✓	4	3.2	odd	2	inner
3.19.b.b.2.4	yes	4	1.1	even	1	trivial
48.19.e.b.17.3		4	12.11	even	2
48.19.e.b.17.4		4	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+932.767i q^{2} +(-4234.02 - 19222.2i) q^{3} -607911. q^{4} -1.14247e6i q^{5} +(1.79299e7 - 3.94936e6i) q^{6} -9.81043e6 q^{7} -3.22520e8i q^{8} +(-3.51567e8 + 1.62775e8i) q^{9} +O(q^{10})\)	\(q+932.767i q^{2} +(-4234.02 - 19222.2i) q^{3} -607911. q^{4} -1.14247e6i q^{5} +(1.79299e7 - 3.94936e6i) q^{6} -9.81043e6 q^{7} -3.22520e8i q^{8} +(-3.51567e8 + 1.62775e8i) q^{9} +1.06566e9 q^{10} -2.16393e9i q^{11} +(2.57391e9 + 1.16854e10i) q^{12} -1.47189e10 q^{13} -9.15085e9i q^{14} +(-2.19608e10 + 4.83724e9i) q^{15} +1.41476e11 q^{16} -1.36506e10i q^{17} +(-1.51831e11 - 3.27930e11i) q^{18} -2.38919e11 q^{19} +6.94520e11i q^{20} +(4.15376e10 + 1.88578e11i) q^{21} +2.01844e12 q^{22} +5.70649e11i q^{23} +(-6.19955e12 + 1.36556e12i) q^{24} +2.50946e12 q^{25} -1.37293e13i q^{26} +(4.61743e12 + 6.06870e12i) q^{27} +5.96387e12 q^{28} +1.35326e13i q^{29} +(-4.51202e12 - 2.04843e13i) q^{30} -1.17012e13 q^{31} +4.74176e13i q^{32} +(-4.15954e13 + 9.16211e12i) q^{33} +1.27329e13 q^{34} +1.12081e13i q^{35} +(2.13721e14 - 9.89525e13i) q^{36} -1.26080e14 q^{37} -2.22856e14i q^{38} +(6.23201e13 + 2.82930e14i) q^{39} -3.68470e14 q^{40} -3.28662e14i q^{41} +(-1.75900e14 + 3.87449e13i) q^{42} +8.40904e14 q^{43} +1.31547e15i q^{44} +(1.85965e14 + 4.01654e14i) q^{45} -5.32283e14 q^{46} -9.97479e14i q^{47} +(-5.99013e14 - 2.71948e15i) q^{48} -1.53217e15 q^{49} +2.34074e15i q^{50} +(-2.62395e14 + 5.77971e13i) q^{51} +8.94778e15 q^{52} -5.45882e15i q^{53} +(-5.66068e15 + 4.30699e15i) q^{54} -2.47222e15 q^{55} +3.16406e15i q^{56} +(1.01159e15 + 4.59255e15i) q^{57} -1.26228e16 q^{58} +8.03632e14i q^{59} +(1.33502e16 - 2.94061e15i) q^{60} +1.04106e16 q^{61} -1.09145e16i q^{62} +(3.44902e15 - 1.59689e15i) q^{63} -7.14245e15 q^{64} +1.68159e16i q^{65} +(-8.54612e15 - 3.87989e16i) q^{66} -1.50639e16 q^{67} +8.29836e15i q^{68} +(1.09691e16 - 2.41614e15i) q^{69} -1.04546e16 q^{70} +4.47214e16i q^{71} +(5.24981e16 + 1.13387e17i) q^{72} -3.92287e16 q^{73} -1.17603e17i q^{74} +(-1.06251e16 - 4.82374e16i) q^{75} +1.45241e17 q^{76} +2.12290e16i q^{77} +(-2.63908e17 + 5.81302e16i) q^{78} -7.20817e16 q^{79} -1.61632e17i q^{80} +(9.71035e16 - 1.14452e17i) q^{81} +3.06565e17 q^{82} +1.02835e17i q^{83} +(-2.52512e16 - 1.14639e17i) q^{84} -1.55954e16 q^{85} +7.84368e17i q^{86} +(2.60126e17 - 5.72973e16i) q^{87} -6.97910e17 q^{88} -5.12684e17i q^{89} +(-3.74650e17 + 1.73462e17i) q^{90} +1.44399e17 q^{91} -3.46904e17i q^{92} +(4.95431e16 + 2.24923e17i) q^{93} +9.30416e17 q^{94} +2.72957e17i q^{95} +(9.11471e17 - 2.00767e17i) q^{96} -7.28759e17 q^{97} -1.42916e18i q^{98} +(3.52232e17 + 7.60764e17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 15876 q^{3} - 1053536 q^{4} + 22698144 q^{6} - 95744152 q^{7} - 885341340 q^{9}+O(q^{10}) \) 4 * q + 15876 * q^3 - 1053536 * q^4 + 22698144 * q^6 - 95744152 * q^7 - 885341340 * q^9	\( 4 q + 15876 q^{3} - 1053536 q^{4} + 22698144 q^{6} - 95744152 q^{7} - 885341340 q^{9} + 1461136320 q^{10} + 7123171104 q^{12} - 5426221528 q^{13} - 68287821120 q^{15} + 201224008192 q^{16} - 624067623360 q^{18} + 191416649480 q^{19} - 843499414296 q^{21} + 6661732766400 q^{22} - 16917300997632 q^{24} + 11407599454180 q^{25} - 4632207691356 q^{27} + 5750860980032 q^{28} - 17181499602240 q^{30} + 35728415085608 q^{31} + 12242871023040 q^{33} - 97283346838272 q^{34} + 412657454022048 q^{36} - 475299833502232 q^{37} + 416909545005096 q^{39} - 967003294602240 q^{40} + 149151729948480 q^{42} + 15\!\cdots\!92 q^{43}+ \cdots + 30\!\cdots\!60 q^{99}+O(q^{100}) \) 4 * q + 15876 * q^3 - 1053536 * q^4 + 22698144 * q^6 - 95744152 * q^7 - 885341340 * q^9 + 1461136320 * q^10 + 7123171104 * q^12 - 5426221528 * q^13 - 68287821120 * q^15 + 201224008192 * q^16 - 624067623360 * q^18 + 191416649480 * q^19 - 843499414296 * q^21 + 6661732766400 * q^22 - 16917300997632 * q^24 + 11407599454180 * q^25 - 4632207691356 * q^27 + 5750860980032 * q^28 - 17181499602240 * q^30 + 35728415085608 * q^31 + 12242871023040 * q^33 - 97283346838272 * q^34 + 412657454022048 * q^36 - 475299833502232 * q^37 + 416909545005096 * q^39 - 967003294602240 * q^40 + 149151729948480 * q^42 + 1599607324574792 * q^43 - 221242601301120 * q^45 + 571461969379968 * q^46 - 2192825065342464 * q^48 - 3423787444328244 * q^49 - 4987666703736576 * q^51 + 19843921097419328 * q^52 - 14022277970462496 * q^54 - 84999034592640 * q^55 + 10169351626464648 * q^57 - 15931261886420160 * q^58 + 24723268055608320 * q^60 - 2207268745883992 * q^61 + 13833182825583912 * q^63 - 53493367589593088 * q^64 + 14857554290281920 * q^66 - 41331536078929912 * q^67 + 81420525478583424 * q^69 + 4599036429482880 * q^70 - 4994921842560000 * q^72 - 45389954762456248 * q^73 + 56512911509383140 * q^75 + 344787912869857856 * q^76 - 685829939469704640 * q^78 - 177365384029892440 * q^79 - 72782527872717756 * q^81 + 887840438080579200 * q^82 - 125687415484822464 * q^84 - 258438267155888640 * q^85 + 858898556077746240 * q^87 - 494740797131842560 * q^88 - 688243478411603520 * q^90 - 625122143135405552 * q^91 + 818827434766827432 * q^93 + 1164172551956805888 * q^94 + 1176359757688184832 * q^96 - 3491564534514760312 * q^97 + 3027708259671116160 * q^99

Introduction

L-functions

Modular forms

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