LMFDB - Embedded newform 3.19.b.b.2.3

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			2.3
Root			$6.57949 + 5.90892i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.19.b.b.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+425.442i q^{2} +(12172.0 + 15468.1i) q^{3} +81143.0 q^{4} +787628. i q^{5} +(-6.58078e6 + 5.17849e6i) q^{6} -3.80616e7 q^{7} +1.46049e8i q^{8} +(-9.11041e7 + 3.76556e8i) q^{9} +O(q^{10})$	\(q+425.442i q^{2} +(12172.0 + 15468.1i) q^{3} +81143.0 q^{4} +787628. i q^{5} +(-6.58078e6 + 5.17849e6i) q^{6} -3.80616e7 q^{7} +1.46049e8i q^{8} +(-9.11041e7 + 3.76556e8i) q^{9} -3.35090e8 q^{10} -3.08486e9i q^{11} +(9.87675e8 + 1.25513e9i) q^{12} +1.20058e10 q^{13} -1.61930e10i q^{14} +(-1.21831e10 + 9.58703e9i) q^{15} -4.08641e10 q^{16} +1.44261e11i q^{17} +(-1.60203e11 - 3.87595e10i) q^{18} +3.34627e11 q^{19} +6.39105e10i q^{20} +(-4.63287e11 - 5.88742e11i) q^{21} +1.31243e12 q^{22} -1.92274e12i q^{23} +(-2.25910e12 + 1.77771e12i) q^{24} +3.19434e12 q^{25} +5.10776e12i q^{26} +(-6.93353e12 + 3.17425e12i) q^{27} -3.08844e12 q^{28} -1.09466e13i q^{29} +(-4.07873e12 - 5.18321e12i) q^{30} +2.95654e13 q^{31} +2.09005e13i q^{32} +(4.77169e13 - 3.75489e13i) q^{33} -6.13745e13 q^{34} -2.99784e13i q^{35} +(-7.39246e12 + 3.05549e13i) q^{36} -1.11570e14 q^{37} +1.42364e14i q^{38} +(1.46135e14 + 1.85707e14i) q^{39} -1.15032e14 q^{40} -3.22853e14i q^{41} +(2.50475e14 - 1.97102e14i) q^{42} -4.11004e13 q^{43} -2.50315e14i q^{44} +(-2.96586e14 - 7.17562e13i) q^{45} +8.18014e14 q^{46} +8.18748e14i q^{47} +(-4.97399e14 - 6.32091e14i) q^{48} -1.79725e14 q^{49} +1.35901e15i q^{50} +(-2.23144e15 + 1.75594e15i) q^{51} +9.74185e14 q^{52} -7.04145e14i q^{53} +(-1.35046e15 - 2.94982e15i) q^{54} +2.42972e15 q^{55} -5.55886e15i q^{56} +(4.07309e15 + 5.17605e15i) q^{57} +4.65713e15 q^{58} -3.09091e15i q^{59} +(-9.88575e14 + 7.77921e14i) q^{60} -1.15143e16 q^{61} +1.25784e16i q^{62} +(3.46757e15 - 1.43324e16i) q^{63} -1.96042e16 q^{64} +9.45609e15i q^{65} +(1.59749e16 + 2.03008e16i) q^{66} -5.60191e15 q^{67} +1.17057e16i q^{68} +(2.97411e16 - 2.34036e16i) q^{69} +1.27541e16 q^{70} -5.38702e16i q^{71} +(-5.49956e16 - 1.33056e16i) q^{72} +1.65337e16 q^{73} -4.74665e16i q^{74} +(3.88816e16 + 4.94104e16i) q^{75} +2.71527e16 q^{76} +1.17415e17i q^{77} +(-7.90074e16 + 6.21718e16i) q^{78} -1.66010e16 q^{79} -3.21857e16i q^{80} +(-1.33495e17 - 6.86117e16i) q^{81} +1.37355e17 q^{82} +4.84222e16i q^{83} +(-3.75925e16 - 4.77723e16i) q^{84} -1.13624e17 q^{85} -1.74859e16i q^{86} +(1.69323e17 - 1.33242e17i) q^{87} +4.50539e17 q^{88} -5.03152e16i q^{89} +(3.05281e16 - 1.26180e17i) q^{90} -4.56960e17 q^{91} -1.56017e17i q^{92} +(3.59871e17 + 4.57321e17i) q^{93} -3.48330e17 q^{94} +2.63562e17i q^{95} +(-3.23291e17 + 2.54401e17i) q^{96} -1.01702e18 q^{97} -7.64624e16i q^{98} +(1.16162e18 + 2.81043e17i) 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 $

$2$			425.442i			0.830942i	0.909607	+	0.415471i	$0.136383\pi$
$2$			425.442i			0.830942i	−0.909607	+	0.415471i	$0.863617\pi$
$3$	12172.0	+	15468.1i	0.618403	+	0.785861i
$3$	12172.0	+	15468.1i	0.618403	+	0.785861i
$4$	81143.0			0.309536
$5$			787628.i			0.403266i	0.979461	+	0.201633i	$0.0646248\pi$
$5$			787628.i			0.403266i	−0.979461	+	0.201633i	$0.935375\pi$
$6$	−6.58078e6	+	5.17849e6i	−0.653005	+	0.513857i
$7$	−3.80616e7			−0.943203			−0.471602	−	0.881812i	$-0.656324\pi$
$7$	−3.80616e7			−0.943203			−0.471602	+	0.881812i	$0.656324\pi$
$8$			1.46049e8i			1.08815i
$9$	−9.11041e7	+	3.76556e8i	−0.235156	+	0.971958i
$10$	−3.35090e8			−0.335090
$11$		−	3.08486e9i		−	1.30828i	−0.756374	−	0.654140i	$-0.773031\pi$
$11$		−	3.08486e9i		−	1.30828i	0.756374	−	0.654140i	$-0.226969\pi$
$12$	9.87675e8	+	1.25513e9i	0.191418	+	0.243252i
$13$	1.20058e10			1.13214			0.566070	−	0.824357i	$-0.308463\pi$
$13$	1.20058e10			1.13214			0.566070	+	0.824357i	$0.308463\pi$
$14$		−	1.61930e10i		−	0.783747i
$15$	−1.21831e10	+	9.58703e9i	−0.316911	+	0.249381i
$16$	−4.08641e10			−0.594651
$17$			1.44261e11i			1.21649i	0.793751	+	0.608243i	$0.208126\pi$
$17$			1.44261e11i			1.21649i	−0.793751	+	0.608243i	$0.791874\pi$
$18$	−1.60203e11	−	3.87595e10i	−0.807640	−	0.195401i
$19$	3.34627e11			1.03700			0.518500	−	0.855078i	$-0.326491\pi$
$19$	3.34627e11			1.03700			0.518500	+	0.855078i	$0.326491\pi$
$20$			6.39105e10i			0.124825i
$21$	−4.63287e11	−	5.88742e11i	−0.583280	−	0.741227i
$22$	1.31243e12			1.08710
$23$		−	1.92274e12i		−	1.06750i	−0.845641	−	0.533752i	$-0.820781\pi$
$23$		−	1.92274e12i		−	1.06750i	0.845641	−	0.533752i	$-0.179219\pi$
$24$	−2.25910e12	+	1.77771e12i	−0.855133	+	0.672914i
$25$	3.19434e12			0.837377
$26$			5.10776e12i			0.940742i
$27$	−6.93353e12	+	3.17425e12i	−0.909245	+	0.416262i
$28$	−3.08844e12			−0.291955
$29$		−	1.09466e13i		−	0.754564i	−0.926098	−	0.377282i	$-0.876859\pi$
$29$		−	1.09466e13i		−	0.754564i	0.926098	−	0.377282i	$-0.123141\pi$
$30$	−4.07873e12	−	5.18321e12i	−0.207221	−	0.263334i
$31$	2.95654e13			1.11822			0.559111	−	0.829093i	$-0.311142\pi$
$31$	2.95654e13			1.11822			0.559111	+	0.829093i	$0.311142\pi$
$32$			2.09005e13i			0.594028i
$33$	4.77169e13	−	3.75489e13i	1.02813	−	0.809044i
$34$	−6.13745e13			−1.01083
$35$		−	2.99784e13i		−	0.380361i
$36$	−7.39246e12	+	3.05549e13i	−0.0727892	+	0.300856i
$37$	−1.11570e14			−0.858483			−0.429241	−	0.903190i	$-0.641219\pi$
$37$	−1.11570e14			−0.858483			−0.429241	+	0.903190i	$0.641219\pi$
$38$			1.42364e14i			0.861686i
$39$	1.46135e14	+	1.85707e14i	0.700119	+	0.889705i
$40$	−1.15032e14			−0.438813
$41$		−	3.22853e14i		−	0.986165i	−0.869982	−	0.493083i	$-0.835870\pi$
$41$		−	3.22853e14i		−	0.986165i	0.869982	−	0.493083i	$-0.164130\pi$
$42$	2.50475e14	−	1.97102e14i	0.615916	−	0.484671i
$43$	−4.11004e13			−0.0817769			−0.0408884	−	0.999164i	$-0.513019\pi$
$43$	−4.11004e13			−0.0817769			−0.0408884	+	0.999164i	$0.513019\pi$
$44$		−	2.50315e14i		−	0.404960i
$45$	−2.96586e14	−	7.17562e13i	−0.391957	−	0.0948302i
$46$	8.18014e14			0.887034
$47$			8.18748e14i			0.731593i	0.930695	+	0.365796i	$0.119203\pi$
$47$			8.18748e14i			0.731593i	−0.930695	+	0.365796i	$0.880797\pi$
$48$	−4.97399e14	−	6.32091e14i	−0.367734	−	0.467313i
$49$	−1.79725e14			−0.110368
$50$			1.35901e15i			0.695811i
$51$	−2.23144e15	+	1.75594e15i	−0.955990	+	0.752279i
$52$	9.74185e14			0.350438
$53$		−	7.04145e14i		−	0.213393i	−0.994292	−	0.106696i	$-0.965973\pi$
$53$		−	7.04145e14i		−	0.213393i	0.994292	−	0.106696i	$-0.0340273\pi$
$54$	−1.35046e15	−	2.94982e15i	−0.345889	−	0.755529i
$55$	2.42972e15			0.527584
$56$		−	5.55886e15i		−	1.02634i
$57$	4.07309e15	+	5.17605e15i	0.641284	+	0.814938i
$58$	4.65713e15			0.626999
$59$		−	3.09091e15i		−	0.356794i	−0.983959	−	0.178397i	$-0.942909\pi$
$59$		−	3.09091e15i		−	0.356794i	0.983959	−	0.178397i	$-0.0570912\pi$
$60$	−9.88575e14	+	7.77921e14i	−0.0980954	+	0.0771923i
$61$	−1.15143e16			−0.984618			−0.492309	−	0.870421i	$-0.663847\pi$
$61$	−1.15143e16			−0.984618			−0.492309	+	0.870421i	$0.663847\pi$
$62$			1.25784e16i			0.929178i
$63$	3.46757e15	−	1.43324e16i	0.221800	−	0.916754i
$64$	−1.96042e16			−1.08825
$65$			9.45609e15i			0.456553i
$66$	1.59749e16	+	2.03008e16i	0.672268	+	0.854313i
$67$	−5.60191e15			−0.205903			−0.102952	−	0.994686i	$-0.532829\pi$
$67$	−5.60191e15			−0.205903			−0.102952	+	0.994686i	$0.532829\pi$
$68$			1.17057e16i			0.376547i
$69$	2.97411e16	−	2.34036e16i	0.838910	−	0.660148i
$70$	1.27541e16			0.316058
$71$		−	5.38702e16i		−	1.17496i	−0.809238	−	0.587481i	$-0.800120\pi$
$71$		−	5.38702e16i		−	1.17496i	0.809238	−	0.587481i	$-0.199880\pi$
$72$	−5.49956e16	−	1.33056e16i	−1.05763	−	0.255884i
$73$	1.65337e16			0.280844			0.140422	−	0.990092i	$-0.455154\pi$
$73$	1.65337e16			0.280844			0.140422	+	0.990092i	$0.455154\pi$
$74$		−	4.74665e16i		−	0.713349i
$75$	3.88816e16	+	4.94104e16i	0.517836	+	0.658062i
$76$	2.71527e16			0.320989
$77$			1.17415e17i			1.23397i
$78$	−7.90074e16	+	6.21718e16i	−0.739293	+	0.581758i
$79$	−1.66010e16			−0.138513			−0.0692565	−	0.997599i	$-0.522063\pi$
$79$	−1.66010e16			−0.138513			−0.0692565	+	0.997599i	$0.522063\pi$
$80$		−	3.21857e16i		−	0.239802i
$81$	−1.33495e17	−	6.86117e16i	−0.889404	−	0.457123i
$82$	1.37355e17			0.819446
$83$			4.84222e16i			0.259025i	0.991578	+	0.129512i	$0.0413412\pi$
$83$			4.84222e16i			0.259025i	−0.991578	+	0.129512i	$0.958659\pi$
$84$	−3.75925e16	−	4.77723e16i	−0.180546	−	0.229436i
$85$	−1.13624e17			−0.490567
$86$		−	1.74859e16i		−	0.0679518i
$87$	1.69323e17	−	1.33242e17i	0.592983	−	0.466625i
$88$	4.50539e17			1.42360
$89$		−	5.03152e16i		−	0.143611i	−0.997419	−	0.0718057i	$-0.977124\pi$
$89$		−	5.03152e16i		−	0.143611i	0.997419	−	0.0718057i	$-0.0228762\pi$
$90$	3.05281e16	−	1.26180e17i	0.0787983	−	0.325693i
$91$	−4.56960e17			−1.06784
$92$		−	1.56017e17i		−	0.330431i
$93$	3.59871e17	+	4.57321e17i	0.691512	+	0.878768i
$94$	−3.48330e17			−0.607911
$95$			2.63562e17i			0.418186i
$96$	−3.23291e17	+	2.54401e17i	−0.466823	+	0.367348i
$97$	−1.01702e18			−1.33778			−0.668891	−	0.743360i	$-0.733231\pi$
$97$	−1.01702e18			−1.33778			−0.668891	+	0.743360i	$0.733231\pi$
$98$		−	7.64624e16i		−	0.0917093i
$99$	1.16162e18	+	2.81043e17i	1.27159	+	0.307649i
$100$	2.59198e17			0.259198
$101$		−	4.94174e17i		−	0.451843i	−0.974146	−	0.225921i	$-0.927461\pi$
$101$		−	4.94174e17i		−	0.451843i	0.974146	−	0.225921i	$-0.0725393\pi$
$102$	−7.47052e17	−	9.49348e17i	−0.625100	−	0.794372i
$103$	1.21075e18			0.927939			0.463970	−	0.885851i	$-0.346425\pi$
$103$	1.21075e18			0.927939			0.463970	+	0.885851i	$0.346425\pi$
$104$			1.75343e18i			1.23194i
$105$	4.63709e17	−	3.64898e17i	0.298911	−	0.235217i
$106$	2.99573e17			0.177317
$107$		−	3.26862e18i		−	1.77791i	−0.457993	−	0.888956i	$-0.651432\pi$
$107$		−	3.26862e18i		−	1.77791i	0.457993	−	0.888956i	$-0.348568\pi$
$108$	−5.62608e17	+	2.57568e17i	−0.281444	+	0.128848i
$109$	−6.74802e17			−0.310698			−0.155349	−	0.987860i	$-0.549650\pi$
$109$	−6.74802e17			−0.310698			−0.155349	+	0.987860i	$0.549650\pi$
$110$			1.03370e18i			0.438392i
$111$	−1.35803e18	−	1.72578e18i	−0.530888	−	0.674648i
$112$	1.55536e18			0.560877
$113$			5.04400e18i			1.67907i	0.543305	+	0.839536i	$0.317173\pi$
$113$			5.04400e18i			1.67907i	−0.543305	+	0.839536i	$0.682827\pi$
$114$	−2.20211e18	+	1.73286e18i	−0.677166	+	0.532869i
$115$	1.51440e18			0.430488
$116$		−	8.88239e17i		−	0.233565i
$117$	−1.09378e18	+	4.52085e18i	−0.266229	+	1.10039i
$118$	1.31500e18			0.296475
$119$		−	5.49080e18i		−	1.14739i
$120$	−1.40017e18	−	1.77933e18i	−0.271363	−	0.344846i
$121$	−3.95642e18			−0.711596
$122$		−	4.89865e18i		−	0.818160i
$123$	4.99392e18	−	3.92977e18i	0.774989	−	0.609848i
$124$	2.39903e18			0.346130
$125$			5.52051e18i			0.740951i
$126$	6.09759e18	+	1.47525e18i	0.761769	+	0.184302i
$127$	5.82269e17			0.0677471			0.0338735	−	0.999426i	$-0.489216\pi$
$127$	5.82269e17			0.0677471			0.0338735	+	0.999426i	$0.489216\pi$
$128$		−	2.86153e18i		−	0.310247i
$129$	−5.00276e17	−	6.35746e17i	−0.0505710	−	0.0642653i
$130$	−4.02302e18			−0.379369
$131$			1.29504e19i			1.13984i	0.821702	+	0.569918i	$0.193025\pi$
$131$			1.29504e19i			1.13984i	−0.821702	+	0.569918i	$0.806975\pi$
$132$	3.87189e18	−	3.04684e18i	0.318242	−	0.250428i
$133$	−1.27365e19			−0.978101
$134$		−	2.38329e18i		−	0.171094i
$135$	−2.50012e18	−	5.46105e18i	−0.167864	−	0.366667i
$136$	−2.10691e19			−1.32372
$137$			8.52718e18i			0.501557i	0.968045	+	0.250778i	$0.0806866\pi$
$137$			8.52718e18i			0.501557i	−0.968045	+	0.250778i	$0.919313\pi$
$138$	9.95689e18	+	1.26531e19i	0.548544	+	0.697085i
$139$	1.94254e19			1.00285			0.501425	−	0.865201i	$-0.332809\pi$
$139$	1.94254e19			1.00285			0.501425	+	0.865201i	$0.332809\pi$
$140$		−	2.43254e18i		−	0.117736i
$141$	−1.26645e19	+	9.96582e18i	−0.574930	+	0.452419i
$142$	2.29187e19			0.976324
$143$		−	3.70361e19i		−	1.48116i
$144$	3.72289e18	−	1.53876e19i	0.139836	−	0.577976i
$145$	8.62183e18			0.304290
$146$			7.03415e18i			0.233365i
$147$	−2.18761e18	−	2.78000e18i	−0.0682519	−	0.0867339i
$148$	−9.05312e18			−0.265731
$149$		−	2.52538e19i		−	0.697669i	−0.937184	−	0.348835i	$-0.886578\pi$
$149$		−	2.52538e19i		−	0.697669i	0.937184	−	0.348835i	$-0.113422\pi$
$150$	−2.10213e19	+	1.65419e19i	−0.546811	+	0.430292i
$151$	4.93498e19			1.20918			0.604592	−	0.796535i	$-0.293336\pi$
$151$	4.93498e19			1.20918			0.604592	+	0.796535i	$0.293336\pi$
$152$			4.88719e19i			1.12841i
$153$	−5.43222e19	−	1.31427e19i	−1.18237	−	0.286064i
$154$	−4.99531e19			−1.02536
$155$			2.32865e19i			0.450941i
$156$	1.18578e19	+	1.50688e19i	0.216712	+	0.275396i
$157$	4.64830e19			0.802043			0.401021	−	0.916069i	$-0.368655\pi$
$157$	4.64830e19			0.802043			0.401021	+	0.916069i	$0.368655\pi$
$158$		−	7.06277e18i		−	0.115096i
$159$	1.08918e19	−	8.57087e18i	0.167697	−	0.131963i
$160$	−1.64618e19			−0.239551
$161$			7.31826e19i			1.00687i
$162$	2.91903e19	−	5.67943e19i	0.379842	−	0.739042i
$163$	−5.33167e19			−0.656409			−0.328205	−	0.944607i	$-0.606444\pi$
$163$	−5.33167e19			−0.656409			−0.328205	+	0.944607i	$0.606444\pi$
$164$		−	2.61973e19i		−	0.305254i
$165$	2.95746e19	+	3.75832e19i	0.326260	+	0.414608i
$166$	−2.06008e19			−0.215234
$167$		−	1.72019e20i		−	1.70266i	−0.524631	−	0.851330i	$-0.675797\pi$
$167$		−	1.72019e20i		−	1.70266i	0.524631	−	0.851330i	$-0.324203\pi$
$168$	8.59850e19	−	6.76625e19i	0.806564	−	0.634694i
$169$	3.16833e19			0.281741
$170$		−	4.83403e19i		−	0.407633i
$171$	−3.04859e19	+	1.26006e20i	−0.243856	+	1.00792i
$172$	−3.33502e18			−0.0253129
$173$			4.28816e19i			0.308927i	0.987998	+	0.154464i	$0.0493649\pi$
$173$			4.28816e19i			0.308927i	−0.987998	+	0.154464i	$0.950635\pi$
$174$	5.66868e19	+	7.20370e19i	0.387738	+	0.492734i
$175$	−1.21582e20			−0.789816
$176$			1.26060e20i			0.777970i
$177$	4.78105e19	−	3.76226e19i	0.280391	−	0.220643i
$178$	2.14062e19			0.119333
$179$			1.99405e20i			1.05696i	0.848946	+	0.528479i	$0.177238\pi$
$179$			1.99405e20i			1.05696i	−0.848946	+	0.528479i	$0.822762\pi$
$180$	−2.40659e19	−	5.82251e18i	−0.121325	−	0.0293534i
$181$	−3.50663e20			−1.68183			−0.840917	−	0.541164i	$-0.817984\pi$
$181$	−3.50663e20			−1.68183			−0.840917	+	0.541164i	$0.817984\pi$
$182$		−	1.94410e20i		−	0.887311i
$183$	−1.40152e20	−	1.78104e20i	−0.608890	−	0.773773i
$184$	2.80814e20			1.16160
$185$		−	8.78756e19i		−	0.346197i
$186$	−1.94563e20	+	1.53104e20i	−0.730205	+	0.574606i
$187$	4.45023e20			1.59151
$188$			6.64357e19i			0.226454i
$189$	2.63902e20	−	1.20817e20i	0.857603	−	0.392619i
$190$	−1.12130e20			−0.347488
$191$			3.95689e20i			1.16964i	0.811162	+	0.584822i	$0.198836\pi$
$191$			3.95689e20i			1.16964i	−0.811162	+	0.584822i	$0.801164\pi$
$192$	−2.38623e20	−	3.03240e20i	−0.672979	−	0.855216i
$193$	5.57447e20			1.50033			0.750167	−	0.661248i	$-0.229973\pi$
$193$	5.57447e20			1.50033			0.750167	+	0.661248i	$0.229973\pi$
$194$		−	4.32685e20i		−	1.11162i
$195$	−1.46268e20	+	1.15100e20i	−0.358787	+	0.282334i
$196$	−1.45834e19			−0.0341629
$197$		−	6.09641e20i		−	1.36420i	−0.731259	−	0.682100i	$-0.761067\pi$
$197$		−	6.09641e20i		−	1.36420i	0.731259	−	0.682100i	$-0.238933\pi$
$198$	−1.19568e20	+	4.94203e20i	−0.255639	+	1.05662i
$199$	−7.93685e20			−1.62170			−0.810850	−	0.585255i	$-0.800995\pi$
$199$	−7.93685e20			−1.62170			−0.810850	+	0.585255i	$0.800995\pi$
$200$			4.66529e20i			0.911190i
$201$	−6.81866e19	−	8.66510e19i	−0.127331	−	0.161811i
$202$	2.10242e20			0.375455
$203$			4.16645e20i			0.711708i
$204$	−1.81066e20	+	1.42483e20i	−0.295913	+	0.232858i
$205$	2.54288e20			0.397687
$206$			5.15104e20i			0.771063i
$207$	7.24019e20	+	1.75169e20i	1.03757	+	0.251030i
$208$	−4.90606e20			−0.673228
$209$		−	1.03228e21i		−	1.35669i
$210$	1.55243e20	+	1.97282e20i	0.195451	+	0.248378i
$211$	−9.70884e20			−1.17118			−0.585592	−	0.810606i	$-0.699138\pi$
$211$	−9.70884e20			−1.17118			−0.585592	+	0.810606i	$0.699138\pi$
$212$		−	5.71365e19i		−	0.0660527i
$213$	8.33270e20	−	6.55710e20i	0.923357	−	0.726600i
$214$	1.39061e21			1.47734
$215$		−	3.23719e19i		−	0.0329778i
$216$	−4.63595e20	−	1.01263e21i	−0.452954	−	0.989393i
$217$	−1.12531e21			−1.05471
$218$		−	2.87089e20i		−	0.258172i
$219$	2.01249e20	+	2.55746e20i	0.173675	+	0.220704i
$220$	1.97155e20			0.163306
$221$			1.73196e21i			1.37723i
$222$	7.34218e20	−	5.77764e20i	0.560593	−	0.441137i
$223$	5.41092e20			0.396759			0.198380	−	0.980125i	$-0.436432\pi$
$223$	5.41092e20			0.396759			0.198380	+	0.980125i	$0.436432\pi$
$224$		−	7.95507e20i		−	0.560289i
$225$	−2.91017e20	+	1.20285e21i	−0.196914	+	0.813895i
$226$	−2.14593e21			−1.39521
$227$			1.06343e19i			0.00664471i	0.999994	+	0.00332235i	$0.00105754\pi$
$227$			1.06343e19i			0.00664471i	−0.999994	+	0.00332235i	$0.998942\pi$
$228$	3.30503e20	+	4.20000e20i	0.198500	+	0.252253i
$229$	8.33519e20			0.481278			0.240639	−	0.970615i	$-0.422643\pi$
$229$	8.33519e20			0.481278			0.240639	+	0.970615i	$0.422643\pi$
$230$			6.44291e20i			0.357710i
$231$	−1.81618e21	+	1.42917e21i	−0.969732	+	0.763093i
$232$	1.59873e21			0.821078
$233$		−	6.48594e20i		−	0.320457i	−0.987080	−	0.160228i	$-0.948777\pi$
$233$		−	6.48594e20i		−	0.320457i	0.987080	−	0.160228i	$-0.0512231\pi$
$234$	−1.92336e21	−	4.65338e20i	−0.914362	−	0.221221i
$235$	−6.44869e20			−0.295026
$236$		−	2.50806e20i		−	0.110441i
$237$	−2.02068e20	−	2.56786e20i	−0.0856568	−	0.108852i
$238$	2.33602e21			0.953418
$239$		−	1.26828e21i		−	0.498466i	−0.968444	−	0.249233i	$-0.919821\pi$
$239$		−	1.26828e21i		−	0.498466i	0.968444	−	0.249233i	$-0.0801785\pi$
$240$	4.97852e20	−	3.91766e20i	0.188451	−	0.148295i
$241$	1.90001e21			0.692791			0.346396	−	0.938089i	$-0.387405\pi$
$241$	1.90001e21			0.692791			0.346396	+	0.938089i	$0.387405\pi$
$242$		−	1.68323e21i		−	0.591295i
$243$	−5.63609e20	−	2.90005e21i	−0.190775	−	0.981634i
$244$	−9.34302e20			−0.304775
$245$		−	1.41556e20i		−	0.0445076i
$246$	1.67189e21	+	2.12462e21i	0.506748	+	0.643971i
$247$	4.01746e21			1.17403
$248$			4.31799e21i			1.21679i
$249$	−7.48999e20	+	5.89396e20i	−0.203558	+	0.160182i
$250$	−2.34866e21			−0.615687
$251$			1.52328e20i			0.0385227i	0.999814	+	0.0192614i	$0.00613146\pi$
$251$			1.52328e20i			0.0385227i	−0.999814	+	0.0192614i	$0.993869\pi$
$252$	2.81369e20	−	1.16297e21i	0.0686550	−	0.283768i
$253$	−5.93137e21			−1.39659
$254$			2.47722e20i			0.0562939i
$255$	−1.38303e21	−	1.75754e21i	−0.303368	−	0.385518i
$256$	−3.92172e21			−0.830456
$257$			2.25211e21i			0.460459i	0.973136	+	0.230229i	$0.0739477\pi$
$257$			2.25211e21i			0.460459i	−0.973136	+	0.230229i	$0.926052\pi$
$258$	2.70473e20	−	2.12838e20i	0.0534007	−	0.0420216i
$259$	4.24654e21			0.809724
$260$			7.67296e20i			0.141320i
$261$	4.12200e21	+	9.97278e20i	0.733405	+	0.177440i
$262$	−5.50965e21			−0.947136
$263$		−	9.39971e20i		−	0.156139i	−0.996948	−	0.0780697i	$-0.975124\pi$
$263$		−	9.39971e20i		−	0.156139i	0.996948	−	0.0780697i	$-0.0248757\pi$
$264$	5.48398e21	+	6.96899e21i	0.880360	+	1.11875i
$265$	5.54605e20			0.0860539
$266$		−	5.41862e21i		−	0.812745i
$267$	7.78281e20	−	6.12438e20i	0.112859	−	0.0888097i
$268$	−4.54556e20			−0.0637345
$269$		−	6.52766e20i		−	0.0885089i	−0.999020	−	0.0442545i	$-0.985909\pi$
$269$		−	6.52766e20i		−	0.0885089i	0.999020	−	0.0442545i	$-0.0140912\pi$
$270$	2.32336e21	−	1.06366e21i	0.304679	−	0.139485i
$271$	8.01941e21			1.01723			0.508615	−	0.860994i	$-0.330158\pi$
$271$	8.01941e21			1.01723			0.508615	+	0.860994i	$0.330158\pi$
$272$		−	5.89508e21i		−	0.723385i
$273$	−5.56212e21	−	7.06830e21i	−0.660354	−	0.839172i
$274$	−3.62782e21			−0.416764
$275$		−	9.85407e21i		−	1.09552i
$276$	2.41329e21	−	1.89904e21i	0.259673	−	0.204340i
$277$	−7.20753e21			−0.750704			−0.375352	−	0.926882i	$-0.622478\pi$
$277$	−7.20753e21			−0.750704			−0.375352	+	0.926882i	$0.622478\pi$
$278$			8.26437e21i			0.833310i
$279$	−2.69353e21	+	1.11330e22i	−0.262956	+	1.08687i
$280$	4.37831e21			0.413889
$281$			2.02613e22i			1.85486i	0.373999	+	0.927429i	$0.377986\pi$
$281$			2.02613e22i			1.85486i	−0.373999	+	0.927429i	$0.622014\pi$
$282$	−4.23988e21	−	5.38800e21i	−0.375934	−	0.477733i
$283$	2.45641e21			0.210971			0.105485	−	0.994421i	$-0.466360\pi$
$283$	2.45641e21			0.210971			0.105485	+	0.994421i	$0.466360\pi$
$284$		−	4.37119e21i		−	0.363693i
$285$	−4.07680e21	+	3.20808e21i	−0.328636	+	0.258608i
$286$	1.57567e22			1.23075
$287$			1.22883e22i			0.930154i
$288$	−7.87021e21	−	1.90412e21i	−0.577370	−	0.139689i
$289$	−6.74804e21			−0.479840
$290$			3.66809e21i			0.252847i
$291$	−1.23792e22	−	1.57314e22i	−0.827288	−	1.05131i
$292$	1.34160e21			0.0869314
$293$		−	1.07510e22i		−	0.675521i	−0.941232	−	0.337761i	$-0.890331\pi$
$293$		−	1.07510e22i		−	0.675521i	0.941232	−	0.337761i	$-0.109669\pi$
$294$	1.18273e21	−	9.30703e20i	0.0720708	−	0.0567133i
$295$	2.43449e21			0.143883
$296$		−	1.62946e22i		−	0.934156i
$297$	9.79209e21	+	2.13890e22i	0.544587	+	1.18955i
$298$	1.07440e22			0.579722
$299$		−	2.30840e22i		−	1.20856i
$300$	3.15497e21	+	4.00931e21i	0.160289	+	0.203694i
$301$	1.56435e21			0.0771322
$302$			2.09955e22i			1.00476i
$303$	7.64394e21	−	6.01510e21i	0.355086	−	0.279421i
$304$	−1.36742e22			−0.616653
$305$		−	9.06896e21i		−	0.397062i
$306$	5.59147e21	−	2.31110e22i	0.237702	−	0.982484i
$307$	1.38184e22			0.570444			0.285222	−	0.958461i	$-0.407933\pi$
$307$	1.38184e22			0.570444			0.285222	+	0.958461i	$0.407933\pi$
$308$			9.52738e21i			0.381959i
$309$	1.47373e22	+	1.87280e22i	0.573840	+	0.729231i
$310$	−9.90707e21			−0.374705
$311$		−	1.09800e22i		−	0.403422i	−0.979445	−	0.201711i	$-0.935350\pi$
$311$		−	1.09800e22i		−	0.403422i	0.979445	−	0.201711i	$-0.0646501\pi$
$312$	−2.71222e22	+	2.13428e22i	−0.968131	+	0.761833i
$313$	−3.70789e22			−1.28596			−0.642981	−	0.765882i	$-0.722303\pi$
$313$	−3.70789e22			−1.28596			−0.642981	+	0.765882i	$0.722303\pi$
$314$			1.97758e22i			0.666451i
$315$	1.12886e22	+	2.73116e21i	0.369695	+	0.0894441i
$316$	−1.34706e21			−0.0428748
$317$			1.41066e22i			0.436405i	0.975903	+	0.218203i	$0.0700194\pi$
$317$			1.41066e22i			0.436405i	−0.975903	+	0.218203i	$0.929981\pi$
$318$	3.64641e21	+	4.63383e21i	0.109653	+	0.139346i
$319$	−3.37686e22			−0.987181
$320$		−	1.54408e22i		−	0.438855i
$321$	5.05593e22	−	3.97857e22i	1.39719	−	1.09947i
$322$	−3.11350e22			−0.836653
$323$			4.82735e22i			1.26150i
$324$	−1.08322e22	−	5.56736e21i	−0.275303	−	0.141496i
$325$	3.83505e22			0.948028
$326$		−	2.26832e22i		−	0.545438i
$327$	−8.21371e21	−	1.04379e22i	−0.192136	−	0.244165i
$328$	4.71522e22			1.07309
$329$		−	3.11629e22i		−	0.690040i
$330$	−1.59895e22	+	1.25823e22i	−0.344515	+	0.271103i
$331$	5.37767e21			0.112757			0.0563784	−	0.998409i	$-0.482045\pi$
$331$	5.37767e21			0.112757			0.0563784	+	0.998409i	$0.482045\pi$
$332$			3.92912e21i			0.0801775i
$333$	1.01645e22	−	4.20124e22i	0.201877	−	0.834409i
$334$	7.31841e22			1.41481
$335$		−	4.41222e21i		−	0.0830337i
$336$	1.89318e22	+	2.40584e22i	0.346848	+	0.440771i
$337$	−7.51619e22			−1.34069			−0.670346	−	0.742049i	$-0.733854\pi$
$337$	−7.51619e22			−1.34069			−0.670346	+	0.742049i	$0.733854\pi$
$338$			1.34794e22i			0.234110i
$339$	−7.80211e22	+	6.13957e22i	−1.31952	+	1.03834i
$340$	−9.21977e21			−0.151848
$341$		−	9.12049e22i		−	1.46295i
$342$	−5.36082e22	−	1.29700e22i	−0.837522	−	0.202630i
$343$	6.88207e22			1.04730
$344$		−	6.00267e21i		−	0.0889853i
$345$	1.84334e22	+	2.34249e22i	0.266215	+	0.338304i
$346$	−1.82436e22			−0.256700
$347$			1.33632e23i			1.83208i	0.401082	+	0.916042i	$0.368634\pi$
$347$			1.33632e23i			1.83208i	−0.401082	+	0.916042i	$0.631366\pi$
$348$	1.37394e22	−	1.08117e22i	0.183550	−	0.144437i
$349$	−2.64641e22			−0.344531			−0.172265	−	0.985051i	$-0.555109\pi$
$349$	−2.64641e22			−0.344531			−0.172265	+	0.985051i	$0.555109\pi$
$350$		−	5.17260e22i		−	0.656291i
$351$	−8.32425e22	+	3.81093e22i	−1.02939	+	0.471267i
$352$	6.44750e22			0.777154
$353$			9.99960e22i			1.17493i	0.809251	+	0.587463i	$0.199873\pi$
$353$			9.99960e22i			1.17493i	−0.809251	+	0.587463i	$0.800127\pi$
$354$	1.60062e22	+	2.03406e22i	0.183341	+	0.232988i
$355$	4.24297e22			0.473822
$356$		−	4.08273e21i		−	0.0444529i
$357$	8.49322e22	−	6.68341e22i	0.901693	−	0.709552i
$358$	−8.48351e22			−0.878271
$359$		−	5.93683e22i		−	0.599383i	−0.954036	−	0.299692i	$-0.903116\pi$
$359$		−	5.93683e22i		−	0.599383i	0.954036	−	0.299692i	$-0.0968838\pi$
$360$	1.04799e22	−	4.33161e22i	0.103189	−	0.426507i
$361$	7.84788e21			0.0753681
$362$		−	1.49187e23i		−	1.39751i
$363$	−4.81576e22	−	6.11983e22i	−0.440053	−	0.559216i
$364$	−3.70791e22			−0.330534
$365$			1.30224e22i			0.113255i
$366$	7.57729e22	−	5.96265e22i	0.642960	−	0.505952i
$367$	−2.37011e22			−0.196234			−0.0981171	−	0.995175i	$-0.531282\pi$
$367$	−2.37011e22			−0.196234			−0.0981171	+	0.995175i	$0.531282\pi$
$368$			7.85710e22i			0.634793i
$369$	1.21572e23	+	2.94132e22i	0.958511	+	0.231902i
$370$	3.73860e22			0.287669
$371$			2.68009e22i			0.201273i
$372$	2.92010e22	+	3.71084e22i	0.214048	+	0.272010i
$373$	−3.66833e21			−0.0262476			−0.0131238	−	0.999914i	$-0.504178\pi$
$373$	−3.66833e21			−0.0262476			−0.0131238	+	0.999914i	$0.504178\pi$
$374$			1.89332e23i			1.32245i
$375$	−8.53919e22	+	6.71958e22i	−0.582285	+	0.458206i
$376$	−1.19577e23			−0.796081
$377$		−	1.31422e23i		−	0.854273i
$378$	5.14006e22	+	1.12275e23i	0.326244	+	0.712618i
$379$	−1.36680e22			−0.0847133			−0.0423566	−	0.999103i	$-0.513487\pi$
$379$	−1.36680e22			−0.0847133			−0.0423566	+	0.999103i	$0.513487\pi$
$380$			2.13862e22i			0.129444i
$381$	7.08740e21	+	9.00661e21i	0.0418950	+	0.0532398i
$382$	−1.68343e23			−0.971906
$383$		−	2.33776e23i		−	1.31829i	−0.752015	−	0.659146i	$-0.770918\pi$
$383$		−	2.33776e23i		−	1.31829i	0.752015	−	0.659146i	$-0.229082\pi$
$384$	4.42624e22	−	3.48306e22i	0.243811	−	0.191858i
$385$	−9.24791e22			−0.497619
$386$			2.37162e23i			1.24669i
$387$	3.74442e21	−	1.54766e22i	0.0192303	−	0.0794836i
$388$	−8.25244e22			−0.414092
$389$		−	6.57142e22i		−	0.322190i	−0.986939	−	0.161095i	$-0.948497\pi$
$389$		−	6.57142e22i		−	0.322190i	0.986939	−	0.161095i	$-0.0515026\pi$
$390$	−4.89683e22	−	6.22285e22i	−0.234603	−	0.298131i
$391$	2.77375e23			1.29861
$392$		−	2.62486e22i		−	0.120097i
$393$	−2.00318e23	+	1.57633e23i	−0.895752	+	0.704877i
$394$	2.59367e23			1.13357
$395$		−	1.30754e22i		−	0.0558575i
$396$	9.42575e22	+	2.28047e22i	0.393604	+	0.0952286i
$397$	3.05894e23			1.24870			0.624348	−	0.781146i	$-0.285365\pi$
$397$	3.05894e23			1.24870			0.624348	+	0.781146i	$0.285365\pi$
$398$		−	3.37667e23i		−	1.34754i
$399$	−1.55028e23	−	1.97009e23i	−0.604861	−	0.768652i
$400$	−1.30534e23			−0.497947
$401$			1.87752e23i			0.700301i	0.936693	+	0.350151i	$0.113870\pi$
$401$			1.87752e23i			0.700301i	−0.936693	+	0.350151i	$0.886130\pi$
$402$	3.68650e22	−	2.90095e22i	0.134456	−	0.105805i
$403$	3.54955e23			1.26598
$404$		−	4.00988e22i		−	0.139862i
$405$	5.40405e22	−	1.05144e23i	0.184342	−	0.358666i
$406$	−1.77258e23			−0.591387
$407$			3.44177e23i			1.12314i
$408$	−2.56453e23	−	3.25899e23i	−0.818591	−	1.04026i
$409$	−4.15170e23			−1.29633			−0.648166	−	0.761499i	$-0.724464\pi$
$409$	−4.15170e23			−1.29633			−0.648166	+	0.761499i	$0.724464\pi$
$410$			1.08185e23i			0.330454i
$411$	−1.31899e23	+	1.03793e23i	−0.394154	+	0.310164i
$412$	9.82440e22			0.287231
$413$			1.17645e23i			0.336530i
$414$	−7.45244e22	+	3.08028e23i	−0.208591	+	0.862159i
$415$	−3.81387e22			−0.104456
$416$			2.50927e23i			0.672522i
$417$	2.36446e23	+	3.00474e23i	0.620165	+	0.788101i
$418$	4.39174e23			1.12733
$419$		−	4.77936e23i		−	1.20072i	−0.799728	−	0.600362i	$-0.795023\pi$
$419$		−	4.77936e23i		−	1.20072i	0.799728	−	0.600362i	$-0.204977\pi$
$420$	3.76268e22	−	2.96089e22i	0.0925238	−	0.0728080i
$421$	−7.31647e23			−1.76101			−0.880507	−	0.474034i	$-0.842797\pi$
$421$	−7.31647e23			−1.76101			−0.880507	+	0.474034i	$0.842797\pi$
$422$		−	4.13055e23i		−	0.973185i
$423$	−3.08305e23	−	7.45913e22i	−0.711077	−	0.172038i
$424$	1.02840e23			0.232203
$425$			4.60817e23i			1.01866i
$426$	2.78966e23	+	3.54508e23i	0.603762	+	0.767255i
$427$	4.38252e23			0.928694
$428$		−	2.65226e23i		−	0.550328i
$429$	5.72878e23	−	4.50804e23i	1.16398	−	0.915951i
$430$	1.37724e22			0.0274026
$431$			1.55731e23i			0.303446i	0.988423	+	0.151723i	$0.0484821\pi$
$431$			1.55731e23i			0.303446i	−0.988423	+	0.151723i	$0.951518\pi$
$432$	2.83333e23	−	1.29713e23i	0.540684	−	0.247531i
$433$	−8.73394e23			−1.63237			−0.816186	−	0.577790i	$-0.803915\pi$
$433$	−8.73394e23			−1.63237			−0.816186	+	0.577790i	$0.803915\pi$
$434$		−	4.78753e23i		−	0.876403i
$435$	1.04945e23	+	1.33363e23i	0.188174	+	0.239130i
$436$	−5.47555e22			−0.0961722
$437$		−	6.43400e23i		−	1.10700i
$438$	−1.08805e23	+	8.56198e22i	−0.183393	+	0.144314i
$439$	5.44754e23			0.899538			0.449769	−	0.893145i	$-0.351506\pi$
$439$	5.44754e23			0.899538			0.449769	+	0.893145i	$0.351506\pi$
$440$			3.54857e23i			0.574090i
$441$	1.63737e22	−	6.76765e22i	0.0259536	−	0.107273i
$442$	−7.36849e23			−1.14440
$443$			1.37168e23i			0.208747i	0.994538	+	0.104374i	$0.0332838\pi$
$443$			1.37168e23i			0.208747i	−0.994538	+	0.104374i	$0.966716\pi$
$444$	−1.10195e23	−	1.40035e23i	−0.164329	−	0.208828i
$445$	3.96297e22			0.0579136
$446$			2.30203e23i			0.329684i
$447$	3.90628e23	−	3.07389e23i	0.548271	−	0.431441i
$448$	7.46169e23			1.02644
$449$			1.27019e24i			1.71259i	0.516490	+	0.856294i	$0.327239\pi$
$449$			1.27019e24i			1.71259i	−0.516490	+	0.856294i	$0.672761\pi$
$450$	−5.11742e23	−	1.23811e23i	−0.676299	−	0.163624i
$451$	−9.95954e23			−1.29018
$452$			4.09286e23i			0.519733i
$453$	6.00687e23	+	7.63348e23i	0.747764	+	0.950252i
$454$	−4.52428e21			−0.00552137
$455$		−	3.59914e23i		−	0.430622i
$456$	−7.55955e23	+	5.94869e23i	−0.886773	+	0.697811i
$457$	3.24758e23			0.373520			0.186760	−	0.982406i	$-0.440201\pi$
$457$	3.24758e23			0.373520			0.186760	+	0.982406i	$0.440201\pi$
$458$			3.54614e23i			0.399914i
$459$	−4.57918e23	−	1.00024e24i	−0.506377	−	1.10608i
$460$	1.22883e23			0.133252
$461$		−	1.03509e24i		−	1.10070i	−0.834933	−	0.550351i	$-0.814494\pi$
$461$		−	1.03509e24i		−	1.10070i	0.834933	−	0.550351i	$-0.185506\pi$
$462$	−6.08031e23	−	7.72681e23i	−0.634086	−	0.805791i
$463$	1.05861e24			1.08270			0.541349	−	0.840798i	$-0.317914\pi$
$463$	1.05861e24			1.08270			0.541349	+	0.840798i	$0.317914\pi$
$464$			4.47322e23i			0.448703i
$465$	−3.60199e23	+	2.83444e23i	−0.354377	+	0.278863i
$466$	2.75939e23			0.266281
$467$		−	1.79684e24i		−	1.70082i	−0.526124	−	0.850408i	$-0.676355\pi$
$467$		−	1.79684e24i		−	1.70082i	0.526124	−	0.850408i	$-0.323645\pi$
$468$	−8.87523e22	+	3.66836e23i	−0.0824075	+	0.340611i
$469$	2.13218e23			0.194209
$470$		−	2.74354e23i		−	0.245149i
$471$	5.65792e23	+	7.19004e23i	0.495985	+	0.630294i
$472$	4.51423e23			0.388245
$473$			1.26789e23i			0.106987i
$474$	1.09248e23	−	8.59682e22i	0.0904496	−	0.0711758i
$475$	1.06891e24			0.868359
$476$		−	4.45540e23i		−	0.355160i
$477$	2.65150e23	+	6.41505e22i	0.207409	+	0.0501805i
$478$	5.39582e23			0.414196
$479$			1.34665e24i			1.01446i	0.861812	+	0.507229i	$0.169330\pi$
$479$			1.34665e24i			1.01446i	−0.861812	+	0.507229i	$0.830670\pi$
$480$	−2.00374e23	−	2.54633e23i	−0.148139	−	0.188254i
$481$	−1.33948e24			−0.971923
$482$			8.08344e23i			0.575669i
$483$	−1.13200e24	+	8.90780e23i	−0.791263	+	0.622654i
$484$	−3.21036e23			−0.220265
$485$		−	8.01036e23i		−	0.539482i
$486$	1.23380e24	−	2.39783e23i	0.815680	−	0.158523i
$487$	−2.88392e24			−1.87164			−0.935819	−	0.352480i	$-0.885338\pi$
$487$	−2.88392e24			−1.87164			−0.935819	+	0.352480i	$0.885338\pi$
$488$		−	1.68164e24i		−	1.07141i
$489$	−6.48972e23	−	8.24708e23i	−0.405926	−	0.515847i
$490$	6.02240e22			0.0369832
$491$			1.45684e24i			0.878372i	0.898396	+	0.439186i	$0.144733\pi$
$491$			1.45684e24i			0.878372i	−0.898396	+	0.439186i	$0.855267\pi$
$492$	4.05222e23	−	3.18874e23i	0.239887	−	0.188770i
$493$	1.57916e24			0.917918
$494$			1.70920e24i			0.975549i
$495$	−2.21357e23	+	9.14926e23i	−0.124064	+	0.512790i
$496$	−1.20816e24			−0.664953
$497$			2.05039e24i			1.10823i
$498$	−2.50754e23	−	3.18656e23i	−0.133102	−	0.169144i
$499$	−6.62415e23			−0.345323			−0.172661	−	0.984981i	$-0.555237\pi$
$499$	−6.62415e23			−0.345323			−0.172661	+	0.984981i	$0.555237\pi$
$500$			4.47951e23i			0.229351i
$501$	2.66081e24	−	2.09382e24i	1.33805	−	1.05293i
$502$	−6.48069e22			−0.0320101
$503$		−	3.54934e23i		−	0.172201i	−0.996286	−	0.0861006i	$-0.972559\pi$
$503$		−	3.54934e23i		−	0.172201i	0.996286	−	0.0861006i	$-0.0274406\pi$
$504$	2.09322e24	+	5.06435e23i	0.997564	+	0.241351i
$505$	3.89225e23			0.182213
$506$		−	2.52345e24i		−	1.16049i
$507$	3.85650e23	+	4.90081e23i	0.174229	+	0.221409i
$508$	4.72471e22			0.0209702
$509$		−	2.66614e24i		−	1.16258i	−0.813697	−	0.581290i	$-0.802548\pi$
$509$		−	2.66614e24i		−	1.16258i	0.813697	−	0.581290i	$-0.197452\pi$
$510$	7.47733e23	−	5.88399e23i	0.320343	−	0.252081i
$511$	−6.29301e23			−0.264893
$512$		−	2.41860e24i		−	1.00031i
$513$	−2.32015e24	+	1.06219e24i	−0.942886	+	0.431663i
$514$	−9.58141e23			−0.382614
$515$			9.53621e23i			0.374206i
$516$	−4.05939e22	−	5.15864e22i	−0.0156536	−	0.0198924i
$517$	2.52572e24			0.957128
$518$			1.80665e24i			0.672833i
$519$	−6.63297e23	+	5.21956e23i	−0.242774	+	0.191042i
$520$	−1.38105e24			−0.496797
$521$		−	6.76943e23i		−	0.239339i	−0.992814	−	0.119669i	$-0.961817\pi$
$521$		−	6.76943e23i		−	0.239339i	0.992814	−	0.119669i	$-0.0381834\pi$
$522$	−4.24284e23	+	1.75367e24i	−0.147442	+	0.609416i
$523$	1.41522e24			0.483404			0.241702	−	0.970351i	$-0.422294\pi$
$523$	1.41522e24			0.483404			0.241702	+	0.970351i	$0.422294\pi$
$524$			1.05084e24i			0.352820i
$525$	−1.47990e24	−	1.88064e24i	−0.488425	−	0.620686i
$526$	3.99903e23			0.129743
$527$			4.26512e24i			1.36030i
$528$	−1.94991e24	+	1.53440e24i	−0.611377	+	0.481099i
$529$	−4.52773e23			−0.139566
$530$			2.35952e23i			0.0715058i
$531$	1.16390e24	+	2.81594e23i	0.346789	+	0.0839022i
$532$	−1.03347e24			−0.302758
$533$		−	3.87610e24i		−	1.11648i
$534$	2.60557e23	+	3.31113e23i	0.0737957	+	0.0937789i
$535$	2.57446e24			0.716971
$536$		−	8.18152e23i		−	0.224053i
$537$	−3.08441e24	+	2.42716e24i	−0.830623	+	0.653626i
$538$	2.77714e23			0.0735458
$539$			5.54425e23i			0.144392i
$540$	−2.02868e23	−	4.43126e23i	−0.0519600	−	0.113497i
$541$	5.91029e24			1.48879			0.744395	−	0.667740i	$-0.232738\pi$
$541$	5.91029e24			1.48879			0.744395	+	0.667740i	$0.232738\pi$
$542$			3.41179e24i			0.845258i
$543$	−4.26828e24	−	5.42410e24i	−1.04005	−	1.32169i
$544$	−3.01512e24			−0.722627
$545$		−	5.31493e23i		−	0.125294i
$546$	3.00715e24	−	2.36636e24i	0.697303	−	0.548716i
$547$	−2.74589e24			−0.626321			−0.313160	−	0.949700i	$-0.601388\pi$
$547$	−2.74589e24			−0.626321			−0.313160	+	0.949700i	$0.601388\pi$
$548$			6.91921e23i			0.155250i
$549$	1.04900e24	−	4.33577e24i	0.231538	−	0.957007i
$550$	4.19234e24			0.910316
$551$		−	3.66302e24i		−	0.782483i
$552$	3.41807e24	+	4.34365e24i	0.718339	+	0.912859i
$553$	6.31862e23			0.130646
$554$		−	3.06639e24i		−	0.623791i
$555$	1.35927e24	−	1.06962e24i	0.272063	−	0.214089i
$556$	1.57623e24			0.310418
$557$			2.11583e24i			0.410001i	0.978762	+	0.205000i	$0.0657196\pi$
$557$			2.11583e24i			0.410001i	−0.978762	+	0.205000i	$0.934280\pi$
$558$	−4.73646e24	−	1.14594e24i	−0.903122	−	0.218501i
$559$	−4.93443e23			−0.0925829
$560$			1.22504e24i			0.226182i
$561$	5.41683e24	+	6.88366e24i	0.984192	+	1.25070i
$562$	−8.62001e24			−1.54128
$563$		−	3.02777e23i		−	0.0532779i	−0.999645	−	0.0266389i	$-0.991520\pi$
$563$		−	3.02777e23i		−	0.0532779i	0.999645	−	0.0266389i	$-0.00848044\pi$
$564$	−1.02763e24	+	8.08657e23i	−0.177962	+	0.140040i
$565$	−3.97280e24			−0.677112
$566$			1.04506e24i			0.175304i
$567$	5.08103e24	+	2.61147e24i	0.838888	+	0.431160i
$568$	7.86768e24			1.27853
$569$			7.60979e24i			1.21720i	0.793477	+	0.608600i	$0.208269\pi$
$569$			7.60979e24i			1.21720i	−0.793477	+	0.608600i	$0.791731\pi$
$570$	−1.36485e24	−	1.73444e24i	−0.214888	−	0.273078i
$571$	−8.38957e24			−1.30021			−0.650106	−	0.759843i	$-0.725276\pi$
$571$	−8.38957e24			−1.30021			−0.650106	+	0.759843i	$0.725276\pi$
$572$		−	3.00522e24i		−	0.458471i
$573$	−6.12056e24	+	4.81634e24i	−0.919178	+	0.723311i
$574$	−5.22796e24			−0.772904
$575$		−	6.14188e24i		−	0.893904i
$576$	1.78603e24	−	7.38210e24i	0.255909	−	1.05774i
$577$	−3.94794e24			−0.556915			−0.278457	−	0.960449i	$-0.589823\pi$
$577$	−3.94794e24			−0.556915			−0.278457	+	0.960449i	$0.589823\pi$
$578$		−	2.87090e24i		−	0.398719i
$579$	6.78526e24	+	8.62265e24i	0.927811	+	1.17905i
$580$	6.99602e23			0.0941887
$581$		−	1.84303e24i		−	0.244313i
$582$	6.69281e24	−	5.26665e24i	0.873578	−	0.687428i
$583$	−2.17219e24			−0.279177
$584$			2.41473e24i			0.305600i
$585$	−3.56075e24	−	8.61489e23i	−0.443750	−	0.107361i
$586$	4.57391e24			0.561319
$587$		−	1.94436e23i		−	0.0234981i	−0.999931	−	0.0117491i	$-0.996260\pi$
$587$		−	1.94436e23i		−	0.0234981i	0.999931	−	0.0117491i	$-0.00373993\pi$
$588$	−1.77510e23	−	2.25578e23i	−0.0211264	−	0.0268473i
$589$	9.89338e24			1.15960
$590$			1.03573e24i			0.119558i
$591$	9.42999e24	−	7.42057e24i	1.07207	−	0.843626i
$592$	4.55921e24			0.510498
$593$			1.07663e25i			1.18733i	0.804711	+	0.593666i	$0.202320\pi$
$593$			1.07663e25i			1.18733i	−0.804711	+	0.593666i	$0.797680\pi$
$594$	−9.09976e24	+	4.16597e24i	−0.988444	+	0.452520i
$595$	4.32471e24			0.462705
$596$		−	2.04917e24i		−	0.215954i
$597$	−9.66075e24	−	1.22768e25i	−1.00286	−	1.27443i
$598$	9.82089e24			1.00425
$599$		−	1.06993e25i		−	1.07774i	−0.842388	−	0.538871i	$-0.818851\pi$
$599$		−	1.06993e25i		−	1.07774i	0.842388	−	0.538871i	$-0.181149\pi$
$600$	−7.21632e24	+	5.67861e24i	−0.716069	+	0.563483i
$601$	−1.69522e25			−1.65713			−0.828563	−	0.559896i	$-0.810841\pi$
$601$	−1.69522e25			−1.65713			−0.828563	+	0.559896i	$0.810841\pi$
$602$			6.65541e23i			0.0640923i
$603$	5.10357e23	−	2.10944e24i	0.0484193	−	0.200129i
$604$	4.00439e24			0.374286
$605$		−	3.11619e24i		−	0.286962i
$606$	2.55908e24	+	3.25205e24i	0.232183	+	0.295056i
$607$	−7.82318e24			−0.699335			−0.349667	−	0.936874i	$-0.613705\pi$
$607$	−7.82318e24			−0.699335			−0.349667	+	0.936874i	$0.613705\pi$
$608$			6.99387e24i			0.616006i
$609$	−6.44470e24	+	5.07141e24i	−0.559303	+	0.440122i
$610$	3.85832e24			0.329936
$611$			9.82970e24i			0.828265i
$612$	−4.40787e24	−	1.06644e24i	−0.365987	−	0.0885471i
$613$	1.87651e25			1.53534			0.767672	−	0.640843i	$-0.221415\pi$
$613$	1.87651e25			1.53534			0.767672	+	0.640843i	$0.221415\pi$
$614$			5.87894e24i			0.474006i
$615$	3.09520e24	+	3.93335e24i	0.245931	+	0.312526i
$616$	−1.71483e25			−1.34275
$617$		−	4.89772e24i		−	0.377944i	−0.981983	−	0.188972i	$-0.939485\pi$
$617$		−	4.89772e24i		−	0.377944i	0.981983	−	0.188972i	$-0.0605155\pi$
$618$	−7.96769e24	+	6.26986e24i	−0.605949	+	0.476828i
$619$	3.82122e24			0.286409			0.143204	−	0.989693i	$-0.454259\pi$
$619$	3.82122e24			0.286409			0.143204	+	0.989693i	$0.454259\pi$
$620$			1.88954e24i			0.139582i
$621$	6.10324e24	+	1.33314e25i	0.444361	+	0.970623i
$622$	4.67136e24			0.335220
$623$			1.91508e24i			0.135455i
$624$	−5.97166e24	−	7.58874e24i	−0.416326	−	0.529064i
$625$	7.83732e24			0.538577
$626$		−	1.57749e25i		−	1.06856i
$627$	1.59674e25	−	1.25649e25i	1.06617	−	0.838978i
$628$	3.77177e24			0.248261
$629$		−	1.60951e25i		−	1.04433i
$630$	−1.16195e24	+	4.80263e24i	−0.0743228	+	0.307195i
$631$	−9.88067e24			−0.623049			−0.311524	−	0.950238i	$-0.600840\pi$
$631$	−9.88067e24			−0.623049			−0.311524	+	0.950238i	$0.600840\pi$
$632$		−	2.42456e24i		−	0.150723i
$633$	−1.18176e25	−	1.50177e25i	−0.724264	−	0.920388i
$634$	−6.00156e24			−0.362627
$635$			4.58612e23i			0.0273201i
$636$	8.83793e23	−	6.95467e23i	0.0519083	−	0.0408472i
$637$	−2.15773e24			−0.124952
$638$		−	1.43666e25i		−	0.820290i
$639$	2.02852e25	+	4.90780e24i	1.14201	+	0.276299i
$640$	2.25382e24			0.125112
$641$			1.80423e25i			0.987574i	0.869583	+	0.493787i	$0.164388\pi$
$641$			1.80423e25i			0.987574i	−0.869583	+	0.493787i	$0.835612\pi$
$642$	1.69265e25	+	2.15101e25i	0.913592	+	1.16098i
$643$	3.02845e24			0.161184			0.0805920	−	0.996747i	$-0.474319\pi$
$643$	3.02845e24			0.161184			0.0805920	+	0.996747i	$0.474319\pi$
$644$			5.93826e24i			0.311664i
$645$	5.00732e23	−	3.94031e23i	0.0259160	−	0.0203936i
$646$	−2.05376e25			−1.04823
$647$		−	1.83814e23i		−	0.00925209i	−0.999989	−	0.00462604i	$-0.998527\pi$
$647$		−	1.83814e23i		−	0.00925209i	0.999989	−	0.00462604i	$-0.00147252\pi$
$648$	1.00206e25	−	1.94967e25i	0.497417	−	0.967803i
$649$	−9.53501e24			−0.466787
$650$			1.63159e25i			0.787756i
$651$	−1.36973e25	−	1.74064e25i	−0.652236	−	0.828857i
$652$	−4.32628e24			−0.203182
$653$			3.87281e25i			1.79394i	0.442092	+	0.896970i	$0.354237\pi$
$653$			3.87281e25i			1.79394i	−0.442092	+	0.896970i	$0.645763\pi$
$654$	4.44073e24	−	3.49446e24i	0.202887	−	0.159654i
$655$	−1.02001e25			−0.459656
$656$			1.31931e25i			0.586424i
$657$	−1.50629e24	+	6.22588e24i	−0.0660421	+	0.272969i
$658$	1.32580e25			0.573383
$659$		−	4.07856e25i		−	1.73996i	−0.493090	−	0.869978i	$-0.664133\pi$
$659$		−	4.07856e25i		−	1.73996i	0.493090	−	0.869978i	$-0.335867\pi$
$660$	2.39977e24	+	3.04961e24i	0.100989	+	0.128336i
$661$	−6.61984e24			−0.274811			−0.137406	−	0.990515i	$-0.543876\pi$
$661$	−6.61984e24			−0.274811			−0.137406	+	0.990515i	$0.543876\pi$
$662$			2.28789e24i			0.0936943i
$663$	−2.67902e25	+	2.10815e25i	−1.08231	+	0.851685i
$664$	−7.07200e24			−0.281857
$665$		−	1.00316e25i		−	0.394435i
$666$	1.78738e25	+	4.32440e24i	0.693345	+	0.167748i
$667$	−2.10474e25			−0.805501
$668$		−	1.39581e25i		−	0.527035i
$669$	6.58618e24	+	8.36967e24i	0.245357	+	0.311798i
$670$	1.87715e24			0.0689961
$671$			3.55198e25i			1.28816i
$672$	1.23050e25	−	9.68293e24i	0.440309	−	0.346484i
$673$	4.79308e25			1.69231			0.846153	−	0.532941i	$-0.178913\pi$
$673$	4.79308e25			1.69231			0.846153	+	0.532941i	$0.178913\pi$
$674$		−	3.19770e25i		−	1.11404i
$675$	−2.21481e25	+	1.01396e25i	−0.761381	+	0.348568i
$676$	2.57088e24			0.0872090
$677$		−	4.80922e25i		−	1.60982i	−0.593399	−	0.804909i	$-0.702214\pi$
$677$		−	4.80922e25i		−	1.60982i	0.593399	−	0.804909i	$-0.297786\pi$
$678$	−2.61203e25	−	3.31935e25i	−0.862802	−	1.09644i
$679$	3.87096e25			1.26180
$680$		−	1.65946e25i		−	0.533810i
$681$	−1.64492e23	+	1.29441e23i	−0.00522182	+	0.00410911i
$682$	3.88024e25			1.21562
$683$			2.51210e25i			0.776695i	0.921513	+	0.388347i	$0.126954\pi$
$683$			2.51210e25i			0.776695i	−0.921513	+	0.388347i	$0.873046\pi$
$684$	−2.47372e24	+	1.02245e25i	−0.0754823	+	0.311988i
$685$	−6.71624e24			−0.202261
$686$			2.92792e25i			0.870247i
$687$	1.01456e25	+	1.28930e25i	0.297624	+	0.378218i
$688$	1.67953e24			0.0486287
$689$		−	8.45381e24i		−	0.241590i
$690$	−9.96596e24	+	7.84232e24i	−0.281111	+	0.221209i
$691$	−1.30800e25			−0.364171			−0.182085	−	0.983283i	$-0.558285\pi$
$691$	−1.30800e25			−0.364171			−0.182085	+	0.983283i	$0.558285\pi$
$692$			3.47954e24i			0.0956241i
$693$	−4.42132e25	−	1.06970e25i	−1.19937	−	0.290176i
$694$	−5.68527e25			−1.52236
$695$			1.53000e25i			0.404415i
$696$	1.94598e25	+	2.47294e25i	0.507757	+	0.645253i
$697$	4.65749e25			1.19966
$698$		−	1.12589e25i		−	0.286285i
$699$	1.00325e25	−	7.89470e24i	0.251835	−	0.198172i
$700$	−9.86552e24			−0.244477
$701$		−	1.51612e24i		−	0.0370913i	−0.999828	−	0.0185456i	$-0.994096\pi$
$701$		−	1.51612e24i		−	0.0370913i	0.999828	−	0.0185456i	$-0.00590360\pi$
$702$	−1.62133e25	−	3.54149e25i	−0.391595	−	0.855365i
$703$	−3.73343e25			−0.890246
$704$			6.04762e25i			1.42374i
$705$	−7.84936e24	−	9.97490e24i	−0.182445	−	0.231850i
$706$	−4.25425e25			−0.976295
$707$			1.88091e25i			0.426180i
$708$	3.87949e24	−	3.05281e24i	0.0867911	−	0.0682969i
$709$	4.79750e25			1.05974			0.529869	−	0.848079i	$-0.322241\pi$
$709$	4.79750e25			1.05974			0.529869	+	0.848079i	$0.322241\pi$
$710$			1.80514e25i			0.393718i
$711$	1.51242e24	−	6.25121e24i	0.0325721	−	0.134629i
$712$	7.34847e24			0.156270
$713$		−	5.68465e25i		−	1.19371i
$714$	2.84340e25	+	3.61337e25i	0.589596	+	0.749254i
$715$	2.91707e25			0.597299
$716$			1.61803e25i			0.327167i
$717$	1.96180e25	−	1.54376e25i	0.391725	−	0.308253i
$718$	2.52578e25			0.498053
$719$		−	1.66163e25i		−	0.323574i	−0.986826	−	0.161787i	$-0.948274\pi$
$719$		−	1.66163e25i		−	0.323574i	0.986826	−	0.161787i	$-0.0517257\pi$
$720$	1.21197e25	+	2.93225e24i	0.233078	+	0.0563909i
$721$	−4.60832e25			−0.875235
$722$			3.33882e24i			0.0626265i
$723$	2.31270e25	+	2.93895e25i	0.428424	+	0.544438i
$724$	−2.84539e25			−0.520589
$725$		−	3.49671e25i		−	0.631855i
$726$	2.60363e25	−	2.04883e25i	0.464676	−	0.365659i
$727$	−3.23199e25			−0.569718			−0.284859	−	0.958569i	$-0.591947\pi$
$727$	−3.23199e25			−0.569718			−0.284859	+	0.958569i	$0.591947\pi$
$728$		−	6.67384e25i		−	1.16197i
$729$	3.79981e25	−	4.40175e25i	0.653452	−	0.756968i
$730$	−5.54029e24			−0.0941081
$731$		−	5.92917e24i		−	0.0994805i
$732$	−1.13724e25	−	1.44519e25i	−0.188474	−	0.239511i
$733$	−3.49733e25			−0.572533			−0.286266	−	0.958150i	$-0.592414\pi$
$733$	−3.49733e25			−0.572533			−0.286266	+	0.958150i	$0.592414\pi$
$734$		−	1.00835e25i		−	0.163059i
$735$	2.18961e24	−	1.72303e24i	0.0349768	−	0.0275236i
$736$	4.01862e25			0.634127
$737$			1.72811e25i			0.269379i
$738$	−1.25136e25	+	5.17219e25i	−0.192697	+	0.796467i
$739$	−6.36670e25			−0.968533			−0.484267	−	0.874920i	$-0.660914\pi$
$739$	−6.36670e25			−0.968533			−0.484267	+	0.874920i	$0.660914\pi$
$740$		−	7.13050e24i		−	0.107160i
$741$	4.89006e25	+	6.21425e25i	0.726023	+	0.922624i
$742$	−1.14022e25			−0.167246
$743$			4.64497e25i			0.673107i	0.941664	+	0.336553i	$0.109261\pi$
$743$			4.64497e25i			0.673107i	−0.941664	+	0.336553i	$0.890739\pi$
$744$	−6.67911e25	+	5.25587e25i	−0.956230	+	0.752468i
$745$	1.98906e25			0.281346
$746$		−	1.56066e24i		−	0.0218102i
$747$	−1.82337e25	−	4.41146e24i	−0.251761	−	0.0609112i
$748$	3.61105e25			0.492628
$749$			1.24409e26i			1.67693i
$750$	−2.85879e25	−	3.63293e25i	−0.380743	−	0.483844i
$751$	8.14117e25			1.07134			0.535670	−	0.844427i	$-0.320059\pi$
$751$	8.14117e25			1.07134			0.535670	+	0.844427i	$0.320059\pi$
$752$		−	3.34574e25i		−	0.435042i
$753$	−2.35623e24	+	1.85414e24i	−0.0302735	+	0.0238226i
$754$	5.59125e25			0.709851
$755$			3.88693e25i			0.487623i
$756$	2.14138e25	−	9.80346e24i	0.265459	−	0.121530i
$757$	−1.58931e26			−1.94691			−0.973455	−	0.228879i	$-0.926494\pi$
$757$	−1.58931e26			−1.94691			−0.973455	+	0.228879i	$0.926494\pi$
$758$		−	5.81494e24i		−	0.0703918i
$759$	−7.21968e25	−	9.17471e25i	−0.863658	−	1.09753i
$760$	−3.84929e25			−0.455049
$761$		−	9.42509e25i		−	1.10109i	−0.834805	−	0.550546i	$-0.814420\pi$
$761$		−	9.42509e25i		−	1.10109i	0.834805	−	0.550546i	$-0.185580\pi$
$762$	−3.83179e24	+	3.01528e24i	−0.0442392	+	0.0348123i
$763$	2.56841e25			0.293051
$764$			3.21074e25i			0.362047i
$765$	1.03516e25	−	4.27857e25i	0.115360	−	0.476811i
$766$	9.94583e25			1.09542
$767$		−	3.71088e25i		−	0.403941i
$768$	−4.77352e25	−	6.06615e25i	−0.513556	−	0.652623i
$769$	1.11441e26			1.18497			0.592484	−	0.805583i	$-0.298148\pi$
$769$	1.11441e26			1.18497			0.592484	+	0.805583i	$0.298148\pi$
$770$		−	3.93445e25i		−	0.413492i
$771$	−3.48358e25	+	2.74127e25i	−0.361857	+	0.284749i
$772$	4.52330e25			0.464408
$773$			1.82886e26i			1.85595i	0.372644	+	0.927974i	$0.378451\pi$
$773$			1.82886e26i			1.85595i	−0.372644	+	0.927974i	$0.621549\pi$
$774$	6.58441e24	+	1.59303e24i	0.0660463	+	0.0159792i
$775$	9.44419e25			0.936374
$776$		−	1.48535e26i		−	1.45571i
$777$	5.16889e25	+	6.56859e25i	0.500736	+	0.636330i
$778$	2.79576e25			0.267721
$779$		−	1.08035e26i		−	1.02265i
$780$	−1.18686e25	+	9.33954e24i	−0.111058	+	0.0873925i
$781$	−1.66182e26			−1.53718
$782$			1.18007e26i			1.07907i
$783$	3.47471e25	+	7.58985e25i	0.314096	+	0.686084i
$784$	7.34429e24			0.0656304
$785$			3.66113e25i			0.323436i
$786$	−6.70636e25	−	8.52239e25i	−0.585712	−	0.744318i
$787$	6.95053e25			0.600130			0.300065	−	0.953919i	$-0.402992\pi$
$787$	6.95053e25			0.600130			0.300065	+	0.953919i	$0.402992\pi$
$788$		−	4.94681e25i		−	0.422269i
$789$	1.45396e25	−	1.14413e25i	0.122704	−	0.0965571i
$790$	5.56283e24			0.0464143
$791$		−	1.91983e26i		−	1.58371i
$792$	−4.10460e25	+	1.69653e26i	−0.334768	+	1.38368i
$793$	−1.38238e26			−1.11473
$794$			1.30140e26i			1.03759i
$795$	6.75066e24	+	8.57868e24i	0.0532160	+	0.0676264i
$796$	−6.44020e25			−0.501975
$797$			1.05855e26i			0.815805i	0.913026	+	0.407902i	$0.133740\pi$
$797$			1.05855e26i			0.815805i	−0.913026	+	0.407902i	$0.866260\pi$
$798$	8.38158e25	−	6.59556e25i	0.638705	−	0.502604i
$799$	−1.18113e26			−0.889973
$800$			6.67632e25i			0.497425i
$801$	1.89465e25	+	4.58392e24i	0.139584	+	0.0337710i
$802$	−7.98775e25			−0.581909
$803$		−	5.10042e25i		−	0.367423i
$804$	−5.53287e24	−	7.03112e24i	−0.0394136	−	0.0500864i
$805$	−5.76407e25			−0.406037
$806$			1.51013e26i			1.05196i
$807$	1.00971e25	−	7.94549e24i	0.0695557	−	0.0547342i
$808$	7.21735e25			0.491672
$809$		−	2.02650e26i		−	1.36524i	−0.730772	−	0.682621i	$-0.760840\pi$
$809$		−	2.02650e26i		−	1.36524i	0.730772	−	0.682621i	$-0.239160\pi$
$810$	4.47328e25	+	2.29911e25i	0.298030	+	0.153177i
$811$	2.26978e26			1.49553			0.747765	−	0.663963i	$-0.231127\pi$
$811$	2.26978e26			1.49553			0.747765	+	0.663963i	$0.231127\pi$
$812$			3.38078e25i			0.220299i
$813$	9.76125e25	+	1.24045e26i	0.629057	+	0.799401i
$814$	−1.46427e26			−0.933260
$815$		−	4.19937e25i		−	0.264707i
$816$	9.11858e25	−	7.17551e25i	0.568481	−	0.447344i
$817$	−1.37533e25			−0.0848026
$818$		−	1.76631e26i		−	1.07718i
$819$	4.16309e25	−	1.72071e26i	0.251108	−	1.03789i
$820$	2.06337e25			0.123098
$821$		−	5.58171e25i		−	0.329366i	−0.986347	−	0.164683i	$-0.947340\pi$
$821$		−	5.58171e25i		−	0.329366i	0.986347	−	0.164683i	$-0.0526601\pi$
$822$	−4.41579e25	−	5.61155e25i	−0.257728	−	0.327519i
$823$	2.42911e25			0.140233			0.0701163	−	0.997539i	$-0.477663\pi$
$823$	2.42911e25			0.140233			0.0701163	+	0.997539i	$0.477663\pi$
$824$			1.76829e26i			1.00974i
$825$	1.52424e26	−	1.19944e26i	0.860929	−	0.677475i
$826$	−5.00512e25			−0.279636
$827$			2.05744e26i			1.13704i	0.822668	+	0.568522i	$0.192485\pi$
$827$			2.05744e26i			1.13704i	−0.822668	+	0.568522i	$0.807515\pi$
$828$	5.87491e25	+	1.42138e25i	0.321165	+	0.0777028i
$829$	7.41110e24			0.0400767			0.0200383	−	0.999799i	$-0.493621\pi$
$829$	7.41110e24			0.0400767			0.0200383	+	0.999799i	$0.493621\pi$
$830$		−	1.62258e25i		−	0.0867967i
$831$	−8.77303e25	−	1.11487e26i	−0.464238	−	0.589949i
$832$	−2.35364e26			−1.23206
$833$		−	2.59272e25i		−	0.134261i
$834$	−1.27834e26	+	1.00594e26i	−0.654866	+	0.515321i
$835$	1.35487e26			0.686624
$836$		−	8.37620e25i		−	0.419943i
$837$	−2.04993e26	+	9.38478e25i	−1.01674	+	0.465473i
$838$	2.03334e26			0.997732
$839$			1.84372e26i			0.895030i	0.894276	+	0.447515i	$0.147691\pi$
$839$			1.84372e26i			0.895030i	−0.894276	+	0.447515i	$0.852309\pi$
$840$	5.32929e25	+	6.77242e25i	0.255950	+	0.325260i
$841$	9.06297e25			0.430633
$842$		−	3.11273e26i		−	1.46330i
$843$	−3.13404e26	+	2.46621e26i	−1.45766	+	1.14705i
$844$	−7.87805e25			−0.362524
$845$			2.49547e25i			0.113616i
$846$	3.17343e25	−	1.31166e26i	0.142954	−	0.590863i
$847$	1.50588e26			0.671180
$848$			2.87743e25i			0.126894i
$849$	2.98994e25	+	3.79960e25i	0.130465	+	0.165794i
$850$	−1.96051e26			−0.846445
$851$			2.14520e26i			0.916434i
$852$	6.76141e25	−	5.32063e25i	0.285812	−	0.224909i
$853$	−2.47408e26			−1.03484			−0.517418	−	0.855733i	$-0.673107\pi$
$853$	−2.47408e26			−1.03484			−0.517418	+	0.855733i	$0.673107\pi$
$854$			1.86451e26i			0.771691i
$855$	−9.92458e25	−	2.40116e25i	−0.406459	−	0.0983389i
$856$	4.77378e26			1.93463
$857$		−	4.86971e25i		−	0.195288i	−0.995221	−	0.0976441i	$-0.968869\pi$
$857$		−	4.86971e25i		−	0.195288i	0.995221	−	0.0976441i	$-0.0311307\pi$
$858$	1.91791e26	+	2.43726e26i	0.761102	+	0.967202i
$859$	2.00521e26			0.787448			0.393724	−	0.919229i	$-0.371186\pi$
$859$	2.00521e26			0.787448			0.393724	+	0.919229i	$0.371186\pi$
$860$		−	2.62675e24i		−	0.0102078i
$861$	−1.90077e26	+	1.49574e26i	−0.730972	+	0.575210i
$862$	−6.62547e25			−0.252146
$863$		−	3.11006e26i		−	1.17131i	−0.810561	−	0.585654i	$-0.800838\pi$
$863$		−	3.11006e26i		−	1.17131i	0.810561	−	0.585654i	$-0.199162\pi$
$864$	−6.63433e25	−	1.44914e26i	−0.247271	−	0.540116i
$865$	−3.37748e25			−0.124580
$866$		−	3.71578e26i		−	1.35641i
$867$	−8.21373e25	−	1.04379e26i	−0.296735	−	0.377088i
$868$	−9.13109e25			−0.326471
$869$			5.12117e25i			0.181214i
$870$	−5.67384e25	+	4.46481e25i	−0.198703	+	0.156361i
$871$	−6.72553e25			−0.233111
$872$		−	9.85540e25i		−	0.338085i
$873$	9.26550e25	−	3.82967e26i	0.314587	−	1.30027i
$874$	2.73730e26			0.919854
$875$		−	2.10120e26i		−	0.698867i
$876$	1.63300e25	+	2.07520e25i	0.0537586	+	0.0683160i
$877$	3.72610e26			1.21411			0.607056	−	0.794659i	$-0.292351\pi$
$877$	3.72610e26			1.21411			0.607056	+	0.794659i	$0.292351\pi$
$878$			2.31761e26i			0.747463i
$879$	1.66297e26	−	1.30861e26i	0.530866	−	0.417744i
$880$	−9.92883e25			−0.313729
$881$			2.24165e26i			0.701109i	0.936542	+	0.350554i	$0.114007\pi$
$881$			2.24165e26i			0.701109i	−0.936542	+	0.350554i	$0.885993\pi$
$882$	2.87924e25	+	6.96604e24i	0.0891376	+	0.0215660i
$883$	−4.76491e26			−1.46019			−0.730093	−	0.683348i	$-0.760523\pi$
$883$	−4.76491e26			−1.46019			−0.730093	+	0.683348i	$0.760523\pi$
$884$			1.40537e26i			0.426304i
$885$	2.96326e25	+	3.76569e25i	0.0889776	+	0.113072i
$886$	−5.83572e25			−0.173457
$887$			4.49426e26i			1.32235i	0.750233	+	0.661174i	$0.229942\pi$
$887$			4.49426e26i			1.32235i	−0.750233	+	0.661174i	$0.770058\pi$
$888$	2.52047e26	−	1.98339e26i	0.734117	−	0.577685i
$889$	−2.21621e25			−0.0638992
$890$			1.68601e25i			0.0481228i
$891$	−2.11657e26	+	4.11812e26i	−0.598044	+	1.16359i
$892$	4.39058e25			0.122811
$893$			2.73975e26i			0.758661i
$894$	1.30776e26	+	1.66189e26i	0.358502	+	0.455581i
$895$	−1.57057e26			−0.426235
$896$			1.08914e26i			0.292626i
$897$	3.57065e26	−	2.80979e26i	0.949764	−	0.747380i
$898$	−5.40394e26			−1.42306
$899$		−	3.23640e26i		−	0.843771i
$900$	−2.36140e25	+	9.76028e25i	−0.0609520	+	0.251930i
$901$	1.01580e26			0.259589
$902$		−	4.23721e26i		−	1.07206i
$903$	1.90413e25	+	2.41975e25i	0.0476988	+	0.0606152i
$904$	−7.36670e26			−1.82708
$905$		−	2.76192e26i		−	0.678226i
$906$	−3.24760e26	+	2.55557e26i	−0.789604	+	0.621348i
$907$	1.16539e26			0.280546			0.140273	−	0.990113i	$-0.455202\pi$
$907$	1.16539e26			0.280546			0.140273	+	0.990113i	$0.455202\pi$
$908$			8.62899e23i			0.00205678i
$909$	1.86084e26	+	4.50213e25i	0.439172	+	0.106253i
$910$	1.53123e26			0.357822
$911$			4.76112e26i			1.10165i	0.834620	+	0.550825i	$0.185687\pi$
$911$			4.76112e26i			1.10165i	−0.834620	+	0.550825i	$0.814313\pi$
$912$	−1.66443e26	−	2.11515e26i	−0.381340	−	0.484604i
$913$	1.49375e26			0.338877
$914$			1.38166e26i			0.310373i
$915$	1.40280e26	−	1.10388e26i	0.312036	−	0.245545i
$916$	6.76343e25			0.148973
$917$		−	4.92914e26i		−	1.07510i
$918$	4.25542e26	−	1.94818e26i	0.919091	−	0.420770i
$919$	4.11575e26			0.880258			0.440129	−	0.897935i	$-0.354933\pi$
$919$	4.11575e26			0.880258			0.440129	+	0.897935i	$0.354933\pi$
$920$			2.21177e26i			0.468435i
$921$	1.68198e26	+	2.13745e26i	0.352764	+	0.448290i
$922$	4.40371e26			0.914619
$923$		−	6.46754e26i		−	1.33022i
$924$	−1.47371e26	+	1.15968e26i	−0.300167	+	0.236205i
$925$	−3.56392e26			−0.718874
$926$			4.50378e26i			0.899659i
$927$	−1.10304e26	+	4.55916e26i	−0.218210	+	0.901918i
$928$	2.28789e26			0.448232
$929$		−	7.32748e26i		−	1.42172i	−0.703335	−	0.710858i	$-0.748307\pi$
$929$		−	7.32748e26i		−	1.42172i	0.703335	−	0.710858i	$-0.251693\pi$
$930$	−1.20589e26	−	1.53244e26i	−0.231719	−	0.294466i
$931$	−6.01407e25			−0.114452
$932$		−	5.26289e25i		−	0.0991930i
$933$	1.69840e26	−	1.33649e26i	0.317033	−	0.249477i
$934$	7.64451e26			1.41328
$935$			3.50513e26i			0.641799i
$936$	−6.60265e26	−	1.59745e26i	−1.19739	−	0.289697i
$937$	−1.07046e26			−0.192271			−0.0961354	−	0.995368i	$-0.530648\pi$
$937$	−1.07046e26			−0.192271			−0.0961354	+	0.995368i	$0.530648\pi$
$938$			9.07119e25i			0.161376i
$939$	−4.51326e26	−	5.73541e26i	−0.795243	−	1.01059i
$940$	−5.23266e25			−0.0913213
$941$		−	4.35108e26i		−	0.752125i	−0.926594	−	0.376063i	$-0.877278\pi$
$941$		−	4.35108e26i		−	0.752125i	0.926594	−	0.376063i	$-0.122722\pi$
$942$	−3.05895e26	+	2.40712e26i	−0.523738	+	0.412135i
$943$	−6.20761e26			−1.05274
$944$			1.26307e26i			0.212168i
$945$	9.51589e25	+	2.07856e26i	0.158330	+	0.345842i
$946$	−5.39413e25			−0.0889000
$947$			9.34157e26i			1.52500i	0.646988	+	0.762500i	$0.276028\pi$
$947$			9.34157e26i			1.52500i	−0.646988	+	0.762500i	$0.723972\pi$
$948$	−1.63964e25	−	2.08364e25i	−0.0265139	−	0.0336936i
$949$	1.98500e26			0.317955
$950$			4.54760e26i			0.721556i
$951$	−2.18203e26	+	1.71706e26i	−0.342954	+	0.269874i
$952$	8.01924e26			1.24853
$953$			9.70253e26i			1.49640i	0.663471	+	0.748202i	$0.269083\pi$
$953$			9.70253e26i			1.49640i	−0.663471	+	0.748202i	$0.730917\pi$
$954$	−2.72923e25	+	1.12806e26i	−0.0416970	+	0.172344i
$955$	−3.11656e26			−0.471677
$956$		−	1.02912e26i		−	0.154293i
$957$	−4.11032e26	−	5.22336e26i	−0.610476	−	0.775788i
$958$	−5.72920e26			−0.842955
$959$		−	3.24558e26i		−	0.473070i
$960$	2.38841e26	−	1.87946e26i	0.344879	−	0.271389i
$961$	1.75059e26			0.250422
$962$		−	5.69873e26i		−	0.807611i
$963$	1.23082e27	+	2.97785e26i	1.72805	+	0.418086i
$964$	1.54173e26			0.214444
$965$			4.39061e26i			0.605033i
$966$	−3.78975e26	−	4.81599e26i	−0.517389	−	0.657493i
$967$	5.26713e26			0.712419			0.356209	−	0.934406i	$-0.384069\pi$
$967$	5.26713e26			0.712419			0.356209	+	0.934406i	$0.384069\pi$
$968$		−	5.77830e26i		−	0.774322i
$969$	−7.46699e26	+	5.87586e26i	−0.991361	+	0.780113i
$970$	3.40795e26			0.448278
$971$			2.68098e26i			0.349398i	0.984622	+	0.174699i	$0.0558952\pi$
$971$			2.68098e26i			0.349398i	−0.984622	+	0.174699i	$0.944105\pi$
$972$	−4.57329e25	−	2.35319e26i	−0.0590517	−	0.303851i
$973$	−7.39361e26			−0.945891
$974$		−	1.22694e27i		−	1.55522i
$975$	4.66804e26	+	5.93210e26i	0.586263	+	0.745018i
$976$	4.70520e26			0.585504
$977$		−	8.62179e26i		−	1.06303i	−0.847048	−	0.531516i	$-0.821623\pi$
$977$		−	8.62179e26i		−	1.06303i	0.847048	−	0.531516i	$-0.178377\pi$
$978$	3.50866e26	−	2.76100e26i	0.428638	−	0.337300i
$979$	−1.55215e26			−0.187884
$980$		−	1.14863e25i		−	0.0137767i
$981$	6.14773e25	−	2.54101e26i	0.0730623	−	0.301985i
$982$	−6.19801e26			−0.729875
$983$		−	2.59448e26i		−	0.302739i	−0.988477	−	0.151370i	$-0.951632\pi$
$983$		−	2.59448e26i		−	0.302739i	0.988477	−	0.151370i	$-0.0483684\pi$
$984$	5.73938e26	+	7.29356e26i	0.663604	+	0.843303i
$985$	4.80171e26			0.550135
$986$			6.71841e26i			0.762736i
$987$	4.82031e26	−	3.79315e26i	0.542276	−	0.426723i
$988$	3.25989e26			0.363404
$989$			7.90254e25i			0.0872972i
$990$	−3.89248e26	−	9.41748e25i	−0.426098	−	0.103090i
$991$	−1.78293e27			−1.93407			−0.967033	−	0.254649i	$-0.918040\pi$
$991$	−1.78293e27			−1.93407			−0.967033	+	0.254649i	$0.918040\pi$
$992$			6.17931e26i			0.664255i
$993$	6.54572e25	+	8.31824e25i	0.0697291	+	0.0886111i
$994$	−8.72322e26			−0.920872
$995$		−	6.25128e26i		−	0.653976i
$996$	−6.07761e25	+	4.78254e25i	−0.0630084	+	0.0495820i
$997$	6.83380e26			0.702111			0.351056	−	0.936355i	$-0.385823\pi$
$997$	6.83380e26			0.702111			0.351056	+	0.936355i	$0.385823\pi$
$998$		−	2.81819e26i		−	0.286943i
$999$	7.73574e26	−	3.54150e26i	0.780571	−	0.357354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.19.b.b.2.3	yes	4
3.2	odd	2	inner	3.19.b.b.2.2	✓	4
4.3	odd	2		48.19.e.b.17.1		4
12.11	even	2		48.19.e.b.17.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.19.b.b.2.2	✓	4	3.2	odd	2	inner
3.19.b.b.2.3	yes	4	1.1	even	1	trivial
48.19.e.b.17.1		4	4.3	odd	2
48.19.e.b.17.2		4	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+425.442i q^{2} +(12172.0 + 15468.1i) q^{3} +81143.0 q^{4} +787628. i q^{5} +(-6.58078e6 + 5.17849e6i) q^{6} -3.80616e7 q^{7} +1.46049e8i q^{8} +(-9.11041e7 + 3.76556e8i) q^{9} +O(q^{10})\)	\(q+425.442i q^{2} +(12172.0 + 15468.1i) q^{3} +81143.0 q^{4} +787628. i q^{5} +(-6.58078e6 + 5.17849e6i) q^{6} -3.80616e7 q^{7} +1.46049e8i q^{8} +(-9.11041e7 + 3.76556e8i) q^{9} -3.35090e8 q^{10} -3.08486e9i q^{11} +(9.87675e8 + 1.25513e9i) q^{12} +1.20058e10 q^{13} -1.61930e10i q^{14} +(-1.21831e10 + 9.58703e9i) q^{15} -4.08641e10 q^{16} +1.44261e11i q^{17} +(-1.60203e11 - 3.87595e10i) q^{18} +3.34627e11 q^{19} +6.39105e10i q^{20} +(-4.63287e11 - 5.88742e11i) q^{21} +1.31243e12 q^{22} -1.92274e12i q^{23} +(-2.25910e12 + 1.77771e12i) q^{24} +3.19434e12 q^{25} +5.10776e12i q^{26} +(-6.93353e12 + 3.17425e12i) q^{27} -3.08844e12 q^{28} -1.09466e13i q^{29} +(-4.07873e12 - 5.18321e12i) q^{30} +2.95654e13 q^{31} +2.09005e13i q^{32} +(4.77169e13 - 3.75489e13i) q^{33} -6.13745e13 q^{34} -2.99784e13i q^{35} +(-7.39246e12 + 3.05549e13i) q^{36} -1.11570e14 q^{37} +1.42364e14i q^{38} +(1.46135e14 + 1.85707e14i) q^{39} -1.15032e14 q^{40} -3.22853e14i q^{41} +(2.50475e14 - 1.97102e14i) q^{42} -4.11004e13 q^{43} -2.50315e14i q^{44} +(-2.96586e14 - 7.17562e13i) q^{45} +8.18014e14 q^{46} +8.18748e14i q^{47} +(-4.97399e14 - 6.32091e14i) q^{48} -1.79725e14 q^{49} +1.35901e15i q^{50} +(-2.23144e15 + 1.75594e15i) q^{51} +9.74185e14 q^{52} -7.04145e14i q^{53} +(-1.35046e15 - 2.94982e15i) q^{54} +2.42972e15 q^{55} -5.55886e15i q^{56} +(4.07309e15 + 5.17605e15i) q^{57} +4.65713e15 q^{58} -3.09091e15i q^{59} +(-9.88575e14 + 7.77921e14i) q^{60} -1.15143e16 q^{61} +1.25784e16i q^{62} +(3.46757e15 - 1.43324e16i) q^{63} -1.96042e16 q^{64} +9.45609e15i q^{65} +(1.59749e16 + 2.03008e16i) q^{66} -5.60191e15 q^{67} +1.17057e16i q^{68} +(2.97411e16 - 2.34036e16i) q^{69} +1.27541e16 q^{70} -5.38702e16i q^{71} +(-5.49956e16 - 1.33056e16i) q^{72} +1.65337e16 q^{73} -4.74665e16i q^{74} +(3.88816e16 + 4.94104e16i) q^{75} +2.71527e16 q^{76} +1.17415e17i q^{77} +(-7.90074e16 + 6.21718e16i) q^{78} -1.66010e16 q^{79} -3.21857e16i q^{80} +(-1.33495e17 - 6.86117e16i) q^{81} +1.37355e17 q^{82} +4.84222e16i q^{83} +(-3.75925e16 - 4.77723e16i) q^{84} -1.13624e17 q^{85} -1.74859e16i q^{86} +(1.69323e17 - 1.33242e17i) q^{87} +4.50539e17 q^{88} -5.03152e16i q^{89} +(3.05281e16 - 1.26180e17i) q^{90} -4.56960e17 q^{91} -1.56017e17i q^{92} +(3.59871e17 + 4.57321e17i) q^{93} -3.48330e17 q^{94} +2.63562e17i q^{95} +(-3.23291e17 + 2.54401e17i) q^{96} -1.01702e18 q^{97} -7.64624e16i q^{98} +(1.16162e18 + 2.81043e17i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more