LMFDB - Embedded newform 3.43.b.b.2.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,43,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, 43, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 43);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 43 $
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:	$33.5183121516$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 33864221333 x^{10} + \cdots + 25\!\cdots\!00 $ x^12 + 33864221333x^10 + 431067677694832840128x^8 + 2571749156180178266268142478336x^6 + 7347696986799808047021630608244043939840x^4 + 8856020548466312086094523118699705898743155916800*x^2 + 2517175751433570113519145367463712046356978756810178560000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{73}\cdot 3^{104}\cdot 5^{6}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.3
Root			$-74991.2i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.43.b.b.2.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69968e6i q^{2} +(-4.62216e9 + 9.38374e9i) q^{3} -2.89024e12 q^{4} +1.56653e14i q^{5} +(2.53331e16 + 1.24784e16i) q^{6} +1.13686e17 q^{7} -4.07061e18i q^{8} +(-6.66902e19 - 8.67463e19i) q^{9} +O(q^{10})$	\(q-2.69968e6i q^{2} +(-4.62216e9 + 9.38374e9i) q^{3} -2.89024e12 q^{4} +1.56653e14i q^{5} +(2.53331e16 + 1.24784e16i) q^{6} +1.13686e17 q^{7} -4.07061e18i q^{8} +(-6.66902e19 - 8.67463e19i) q^{9} +4.22913e20 q^{10} -3.96998e21i q^{11} +(1.33591e22 - 2.71212e22i) q^{12} +2.02902e23 q^{13} -3.06915e23i q^{14} +(-1.46999e24 - 7.24076e23i) q^{15} -2.37007e25 q^{16} +8.78401e25i q^{17} +(-2.34188e26 + 1.80042e26i) q^{18} -9.58686e26 q^{19} -4.52764e26i q^{20} +(-5.25473e26 + 1.06680e27i) q^{21} -1.07177e28 q^{22} +1.43753e28i q^{23} +(3.81976e28 + 1.88150e28i) q^{24} +2.02834e29 q^{25} -5.47771e29i q^{26} +(1.12226e30 - 2.24848e29i) q^{27} -3.28578e29 q^{28} +5.25287e30i q^{29} +(-1.95477e30 + 3.96851e30i) q^{30} -3.30069e31 q^{31} +4.60817e31i q^{32} +(3.72532e31 + 1.83499e31i) q^{33} +2.37140e32 q^{34} +1.78092e31i q^{35} +(1.92750e32 + 2.50717e32i) q^{36} +8.82106e32 q^{37} +2.58815e33i q^{38} +(-9.37846e32 + 1.90398e33i) q^{39} +6.37673e32 q^{40} +9.69173e33i q^{41} +(2.88001e33 + 1.41861e33i) q^{42} +8.56460e32 q^{43} +1.14742e34i q^{44} +(1.35891e34 - 1.04472e34i) q^{45} +3.88088e34 q^{46} +1.68830e34i q^{47} +(1.09549e35 - 2.22402e35i) q^{48} -2.99049e35 q^{49} -5.47586e35i q^{50} +(-8.24269e35 - 4.06011e35i) q^{51} -5.86434e35 q^{52} +2.29223e36i q^{53} +(-6.07019e35 - 3.02974e36i) q^{54} +6.21909e35 q^{55} -4.62769e35i q^{56} +(4.43120e36 - 8.99606e36i) q^{57} +1.41811e37 q^{58} +2.54386e37i q^{59} +(4.24862e36 + 2.09275e36i) q^{60} -3.80073e37 q^{61} +8.91081e37i q^{62} +(-7.58171e36 - 9.86180e36i) q^{63} +2.01690e37 q^{64} +3.17852e37i q^{65} +(4.95388e37 - 1.00572e38i) q^{66} +1.78920e38 q^{67} -2.53878e38i q^{68} +(-1.34894e38 - 6.64450e37i) q^{69} +4.80791e37 q^{70} -5.34024e38i q^{71} +(-3.53111e38 + 2.71470e38i) q^{72} -2.20906e39 q^{73} -2.38141e39i q^{74} +(-9.37529e38 + 1.90334e39i) q^{75} +2.77083e39 q^{76} -4.51329e38i q^{77} +(5.14014e39 + 2.53188e39i) q^{78} -3.32093e39 q^{79} -3.71279e39i q^{80} +(-3.07734e39 + 1.15703e40i) q^{81} +2.61646e40 q^{82} +2.39370e40i q^{83} +(1.51874e39 - 3.08329e39i) q^{84} -1.37604e40 q^{85} -2.31217e39i q^{86} +(-4.92916e40 - 2.42796e40i) q^{87} -1.61602e40 q^{88} +2.41519e40i q^{89} +(-2.82042e40 - 3.66862e40i) q^{90} +2.30670e40 q^{91} -4.15480e40i q^{92} +(1.52563e41 - 3.09728e41i) q^{93} +4.55786e40 q^{94} -1.50181e41i q^{95} +(-4.32419e41 - 2.12997e41i) q^{96} +3.93809e41 q^{97} +8.07337e41i q^{98} +(-3.44381e41 + 2.64759e41i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16987205196 q^{3} - 34999503561888 q^{4} - 47\!\cdots\!88 q^{6}+ \cdots - 10\!\cdots\!60 q^{9}+O(q^{10}) $ 12 * q + 16987205196 * q^3 - 34999503561888 * q^4 - 47900661722006688 * q^6 - 41814621990917832 * q^7 - 10479496382139999060 * q^9	$ 12 q + 16987205196 q^{3} - 34999503561888 q^{4} - 47\!\cdots\!88 q^{6}+ \cdots - 45\!\cdots\!60 q^{99}+O(q^{100}) $ 12 * q + 16987205196 * q^3 - 34999503561888 * q^4 - 47900661722006688 * q^6 - 41814621990917832 * q^7 - 10479496382139999060 * q^9 - 1558337248111507093440 * q^10 + 49376377527162340879584 * q^12 + 104159867930333479443192 * q^13 - 448128019361693763840960 * q^15 + 30189980873605037368521216 * q^16 + 467763252053696004788775360 * q^18 + 1742192007122001281517876120 * q^19 + 9102775482298327940265250872 * q^21 - 4314702866032998614435578560 * q^22 + 213252820822149659960046027264 * q^24 - 1475565424466319180916113000660 * q^25 + 4679803843175845084152852300204 * q^27 - 12573192134196153529744555207488 * q^28 + 62452866934923176992747679887680 * q^30 - 82582711039551011868572590242696 * q^31 + 43265764437015443353441835054400 * q^33 - 263315485295738664634172504653056 * q^34 - 2405201397348598443590828900669856 * q^36 - 100843038556324004682477979351752 * q^37 - 10984759746962485956654149987757192 * q^39 + 14264689156939495925288444850785280 * q^40 - 2831182046378653470535212831685440 * q^42 - 71435403459183756447962146838987688 * q^43 + 171247471703495918987972144910848640 * q^45 - 368252835390302858087002506036095616 * q^46 + 393051873841281316858605019336751616 * q^48 + 503454865894447043110675471056528228 * q^49 - 26481340521925644924949289315966208 * q^51 + 6191863526932890484747245480405187008 * q^52 - 7762950205729260582930120693521404128 * q^54 + 7333373720922934220673629457367543680 * q^55 - 7646344343294849001862320271635263592 * q^57 - 40828097874719028971304350423217887040 * q^58 + 67409911106604936995672440638418037760 * q^60 - 86088392913854728749325031191744820616 * q^61 + 100834020234866427922563192954676937592 * q^63 - 141458640188438187587490744757105434624 * q^64 - 410927857618739095889759252898209949120 * q^66 + 637588020068292666249059312571603583128 * q^67 - 900977595682723671847728174824987261568 * q^69 + 1299257312773585175235999395827621799040 * q^70 - 1002862304292335428089280868557297904640 * q^72 + 4764698373378852277054437745609397085912 * q^73 + 10291654382848945060344626042064329363820 * q^75 - 10850719004897690517175553392098488304192 * q^76 - 1154864387471236146792590220220273542720 * q^78 - 16476824590026301016342599143867688625160 * q^79 - 29934898097734077284676557689524616295988 * q^81 + 12117774709574398821091222390193736370560 * q^82 - 115502524985324999123004799396029534507072 * q^84 + 179892388106464049414097141341403281134080 * q^85 - 108737363241821037303405571455850394882880 * q^87 + 262137413065538961600854476553505008040960 * q^88 - 246742532847586844558695609281104739341760 * q^90 + 85532425294904148246865639238250304747824 * q^91 + 153993445971229900791562733419639364858232 * q^93 + 711306705503600048406114202903471029729024 * q^94 - 1719405066055622809595776412409802129711104 * q^96 + 1090171163442244899022729083217627459542168 * q^97 - 4562402641239113129658705054315657608741760 * 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 $

$2$		−	2.69968e6i		−	1.28731i	−0.765316	−	0.643654i	$-0.777417\pi$
$2$		−	2.69968e6i		−	1.28731i	0.765316	−	0.643654i	$-0.222583\pi$
$3$	−4.62216e9	+	9.38374e9i	−0.441874	+	0.897077i
$3$	−4.62216e9	+	9.38374e9i	−0.441874	+	0.897077i
$4$	−2.89024e12			−0.657163
$5$			1.56653e14i			0.328525i	0.986417	+	0.164263i	$0.0525244\pi$
$5$			1.56653e14i			0.328525i	−0.986417	+	0.164263i	$0.947476\pi$
$6$	2.53331e16	+	1.24784e16i	1.15481	+	0.568829i
$7$	1.13686e17			0.203538			0.101769	−	0.994808i	$-0.467550\pi$
$7$	1.13686e17			0.203538			0.101769	+	0.994808i	$0.467550\pi$
$8$		−	4.07061e18i		−	0.441337i
$9$	−6.66902e19	−	8.67463e19i	−0.609494	−	0.792791i
$10$	4.22913e20			0.422913
$11$		−	3.96998e21i		−	0.536465i	−0.963354	−	0.268233i	$-0.913560\pi$
$11$		−	3.96998e21i		−	0.536465i	0.963354	−	0.268233i	$-0.0864396\pi$
$12$	1.33591e22	−	2.71212e22i	0.290384	−	0.589526i
$13$	2.02902e23			0.821251			0.410625	−	0.911804i	$-0.365310\pi$
$13$	2.02902e23			0.821251			0.410625	+	0.911804i	$0.365310\pi$
$14$		−	3.06915e23i		−	0.262017i
$15$	−1.46999e24	−	7.24076e23i	−0.294712	−	0.145167i
$16$	−2.37007e25			−1.22530
$17$			8.78401e25i			1.27135i	0.771957	+	0.635675i	$0.219278\pi$
$17$			8.78401e25i			1.27135i	−0.771957	+	0.635675i	$0.780722\pi$
$18$	−2.34188e26	+	1.80042e26i	−1.02057	+	0.784607i
$19$	−9.58686e26			−1.34230			−0.671152	−	0.741320i	$-0.734200\pi$
$19$	−9.58686e26			−1.34230			−0.671152	+	0.741320i	$0.734200\pi$
$20$		−	4.52764e26i		−	0.215895i
$21$	−5.25473e26	+	1.06680e27i	−0.0899384	+	0.182590i
$22$	−1.07177e28			−0.690596
$23$			1.43753e28i			0.364194i	0.983281	+	0.182097i	$0.0582885\pi$
$23$			1.43753e28i			0.364194i	−0.983281	+	0.182097i	$0.941712\pi$
$24$	3.81976e28	+	1.88150e28i	0.395913	+	0.195015i
$25$	2.02834e29			0.892071
$26$		−	5.47771e29i		−	1.05720i
$27$	1.12226e30	−	2.24848e29i	0.980514	−	0.196449i
$28$	−3.28578e29			−0.133758
$29$			5.25287e30i			1.02338i	0.859169	+	0.511692i	$0.170981\pi$
$29$			5.25287e30i			1.02338i	−0.859169	+	0.511692i	$0.829019\pi$
$30$	−1.95477e30	+	3.96851e30i	−0.186875	+	0.379386i
$31$	−3.30069e31			−1.58493			−0.792463	−	0.609920i	$-0.791202\pi$
$31$	−3.30069e31			−1.58493			−0.792463	+	0.609920i	$0.791202\pi$
$32$			4.60817e31i			1.13600i
$33$	3.72532e31	+	1.83499e31i	0.481251	+	0.237050i
$34$	2.37140e32			1.63662
$35$			1.78092e31i			0.0668675i
$36$	1.92750e32	+	2.50717e32i	0.400537	+	0.520993i
$37$	8.82106e32			1.03106			0.515531	−	0.856871i	$-0.327595\pi$
$37$	8.82106e32			1.03106			0.515531	+	0.856871i	$0.327595\pi$
$38$			2.58815e33i			1.72796i
$39$	−9.37846e32	+	1.90398e33i	−0.362890	+	0.736725i
$40$	6.37673e32			0.144990
$41$			9.69173e33i			1.31202i	0.754752	+	0.656010i	$0.227757\pi$
$41$			9.69173e33i			1.31202i	−0.754752	+	0.656010i	$0.772243\pi$
$42$	2.88001e33	+	1.41861e33i	0.235049	+	0.115778i
$43$	8.56460e32			0.0426451			0.0213226	−	0.999773i	$-0.493212\pi$
$43$	8.56460e32			0.0426451			0.0213226	+	0.999773i	$0.493212\pi$
$44$			1.14742e34i			0.352545i
$45$	1.35891e34	−	1.04472e34i	0.260452	−	0.200234i
$46$	3.88088e34			0.468830
$47$			1.68830e34i			0.129836i	0.997891	+	0.0649178i	$0.0206785\pi$
$47$			1.68830e34i			0.129836i	−0.997891	+	0.0649178i	$0.979321\pi$
$48$	1.09549e35	−	2.22402e35i	0.541428	−	1.09919i
$49$	−2.99049e35			−0.958572
$50$		−	5.47586e35i		−	1.14837i
$51$	−8.24269e35	−	4.06011e35i	−1.14050	−	0.561777i
$52$	−5.86434e35			−0.539696
$53$			2.29223e36i			1.41405i	0.707190	+	0.707024i	$0.249963\pi$
$53$			2.29223e36i			1.41405i	−0.707190	+	0.707024i	$0.750037\pi$
$54$	−6.07019e35	−	3.02974e36i	−0.252891	−	1.26222i
$55$	6.21909e35			0.176242
$56$		−	4.62769e35i		−	0.0898289i
$57$	4.43120e36	−	8.99606e36i	0.593129	−	1.20415i
$58$	1.41811e37			1.31741
$59$			2.54386e37i			1.65045i	0.564808	+	0.825223i	$0.308950\pi$
$59$			2.54386e37i			1.65045i	−0.564808	+	0.825223i	$0.691050\pi$
$60$	4.24862e36	+	2.09275e36i	0.193674	+	0.0953983i
$61$	−3.80073e37			−1.22445			−0.612224	−	0.790685i	$-0.709725\pi$
$61$	−3.80073e37			−1.22445			−0.612224	+	0.790685i	$0.709725\pi$
$62$			8.91081e37i			2.04029i
$63$	−7.58171e36	−	9.86180e36i	−0.124055	−	0.161363i
$64$	2.01690e37			0.237086
$65$			3.17852e37i			0.269802i
$66$	4.95388e37	−	1.00572e38i	0.305157	−	0.619518i
$67$	1.78920e38			0.803688			0.401844	−	0.915708i	$-0.368369\pi$
$67$	1.78920e38			0.803688			0.401844	+	0.915708i	$0.368369\pi$
$68$		−	2.53878e38i		−	0.835485i
$69$	−1.34894e38	−	6.64450e37i	−0.326710	−	0.160928i
$70$	4.80791e37			0.0860791
$71$		−	5.34024e38i		−	0.709799i	−0.934904	−	0.354900i	$-0.884515\pi$
$71$		−	5.34024e38i		−	0.709799i	0.934904	−	0.354900i	$-0.115485\pi$
$72$	−3.53111e38	+	2.71470e38i	−0.349887	+	0.268992i
$73$	−2.20906e39			−1.63843			−0.819213	−	0.573489i	$-0.805589\pi$
$73$	−2.20906e39			−1.63843			−0.819213	+	0.573489i	$0.805589\pi$
$74$		−	2.38141e39i		−	1.32729i
$75$	−9.37529e38	+	1.90334e39i	−0.394183	+	0.800257i
$76$	2.77083e39			0.882113
$77$		−	4.51329e38i		−	0.109191i
$78$	5.14014e39	+	2.53188e39i	0.948393	+	0.467151i
$79$	−3.32093e39			−0.468912			−0.234456	−	0.972127i	$-0.575331\pi$
$79$	−3.32093e39			−0.468912			−0.234456	+	0.972127i	$0.575331\pi$
$80$		−	3.71279e39i		−	0.402542i
$81$	−3.07734e39	+	1.15703e40i	−0.257034	+	0.966402i
$82$	2.61646e40			1.68897
$83$			2.39370e40i			1.19793i	0.800776	+	0.598964i	$0.204421\pi$
$83$			2.39370e40i			1.19793i	−0.800776	+	0.598964i	$0.795579\pi$
$84$	1.51874e39	−	3.08329e39i	0.0591042	−	0.119991i
$85$	−1.37604e40			−0.417671
$86$		−	2.31217e39i		−	0.0548974i
$87$	−4.92916e40	−	2.42796e40i	−0.918055	−	0.452207i
$88$	−1.61602e40			−0.236762
$89$			2.41519e40i			0.279100i	0.990215	+	0.139550i	$0.0445656\pi$
$89$			2.41519e40i			0.279100i	−0.990215	+	0.139550i	$0.955434\pi$
$90$	−2.82042e40	−	3.66862e40i	−0.257763	−	0.335282i
$91$	2.30670e40			0.167156
$92$		−	4.15480e40i		−	0.239335i
$93$	1.52563e41	−	3.09728e41i	0.700338	−	1.42180i
$94$	4.55786e40			0.167138
$95$		−	1.50181e41i		−	0.440980i
$96$	−4.32419e41	−	2.12997e41i	−1.01908	−	0.501970i
$97$	3.93809e41			0.746586			0.373293	−	0.927714i	$-0.378229\pi$
$97$	3.93809e41			0.746586			0.373293	+	0.927714i	$0.378229\pi$
$98$			8.07337e41i			1.23398i
$99$	−3.44381e41	+	2.64759e41i	−0.425305	+	0.326972i
$100$	−5.86237e41			−0.586237
$101$			5.51034e41i			0.447126i	0.974690	+	0.223563i	$0.0717688\pi$
$101$			5.51034e41i			0.447126i	−0.974690	+	0.223563i	$0.928231\pi$
$102$	−1.09610e42	+	2.22526e42i	−0.723181	+	1.46817i
$103$	2.90760e42			1.56298			0.781489	−	0.623919i	$-0.214460\pi$
$103$	2.90760e42			1.56298			0.781489	+	0.623919i	$0.214460\pi$
$104$		−	8.25935e41i		−	0.362448i
$105$	−1.67117e41	−	8.23169e40i	−0.0599853	−	0.0295470i
$106$	6.18828e42			1.82032
$107$		−	4.45044e42i		−	1.07484i	−0.843315	−	0.537419i	$-0.819399\pi$
$107$		−	4.45044e42i		−	1.07484i	0.843315	−	0.537419i	$-0.180601\pi$
$108$	−3.24359e42	+	6.49864e41i	−0.644358	+	0.129099i
$109$	−1.50074e42			−0.245668			−0.122834	−	0.992427i	$-0.539198\pi$
$109$	−1.50074e42			−0.245668			−0.122834	+	0.992427i	$0.539198\pi$
$110$		−	1.67896e42i		−	0.226878i
$111$	−4.07724e42	+	8.27745e42i	−0.455600	+	0.924941i
$112$	−2.69443e42			−0.249395
$113$		−	3.40065e42i		−	0.261165i	−0.991437	−	0.130583i	$-0.958315\pi$
$113$		−	3.40065e42i		−	0.261165i	0.991437	−	0.130583i	$-0.0416848\pi$
$114$	−2.42865e43	−	1.19628e43i	−1.55011	−	0.763541i
$115$	−2.25194e42			−0.119647
$116$		−	1.51820e43i		−	0.672531i
$117$	−1.35316e43	−	1.76010e43i	−0.500547	−	0.651080i
$118$	6.86761e43			2.12463
$119$			9.98614e42i			0.258769i
$120$	−2.94743e42	+	5.98376e42i	−0.0640674	+	0.130067i
$121$	3.90030e43			0.712205
$122$			1.02608e44i			1.57624i
$123$	−9.09447e43	−	4.47968e43i	−1.17698	−	0.579748i
$124$	9.53977e43			1.04156
$125$			6.73932e43i			0.621593i
$126$	−2.66237e43	+	2.04682e43i	−0.207724	+	0.159698i
$127$	−5.70877e43			−0.377280			−0.188640	−	0.982046i	$-0.560408\pi$
$127$	−5.70877e43			−0.377280			−0.188640	+	0.982046i	$0.560408\pi$
$128$			1.48220e44i			0.830800i
$129$	−3.95870e42	+	8.03680e42i	−0.0188438	+	0.0382560i
$130$	8.58099e43			0.347318
$131$		−	1.67593e44i		−	0.577510i	−0.957403	−	0.288755i	$-0.906759\pi$
$131$		−	1.67593e44i		−	0.577510i	0.957403	−	0.288755i	$-0.0932414\pi$
$132$	−1.07671e44	−	5.30355e43i	−0.316260	−	0.155781i
$133$	−1.08989e44			−0.273210
$134$		−	4.83026e44i		−	1.03459i
$135$	3.52232e43	+	1.75805e44i	0.0645385	+	0.322124i
$136$	3.57563e44			0.561093
$137$		−	1.14562e45i		−	1.54138i	−0.637213	−	0.770688i	$-0.719913\pi$
$137$		−	1.14562e45i		−	1.54138i	0.637213	−	0.770688i	$-0.280087\pi$
$138$	−1.79380e44	+	3.64171e44i	−0.207164	+	0.420576i
$139$	−1.40165e44			−0.139101			−0.0695504	−	0.997578i	$-0.522156\pi$
$139$	−1.40165e44			−0.139101			−0.0695504	+	0.997578i	$0.522156\pi$
$140$		−	5.14727e43i		−	0.0439429i
$141$	−1.58425e44	−	7.80358e43i	−0.116472	−	0.0573710i
$142$	−1.44170e45			−0.913731
$143$		−	8.05516e44i		−	0.440572i
$144$	1.58061e45	+	2.05595e45i	0.746813	+	0.971406i
$145$	−8.22878e44			−0.336207
$146$			5.96375e45i			2.10916i
$147$	1.38225e45	−	2.80620e45i	0.423568	−	0.859913i
$148$	−2.54949e45			−0.677576
$149$		−	7.09141e44i		−	0.163614i	−0.996648	−	0.0818071i	$-0.973931\pi$
$149$		−	7.09141e44i		−	0.163614i	0.996648	−	0.0818071i	$-0.0260691\pi$
$150$	5.13841e45	+	2.53103e45i	1.03018	+	0.507436i
$151$	3.69736e45			0.644727			0.322364	−	0.946616i	$-0.395523\pi$
$151$	3.69736e45			0.644727			0.322364	+	0.946616i	$0.395523\pi$
$152$			3.90244e45i			0.592407i
$153$	7.61981e45	−	5.85807e45i	1.00791	−	0.774881i
$154$	−1.21844e45			−0.140563
$155$		−	5.17063e45i		−	0.520688i
$156$	2.71059e45	−	5.50295e45i	0.238478	−	0.484149i
$157$	−2.56798e46			−1.97560			−0.987802	−	0.155718i	$-0.950231\pi$
$157$	−2.56798e46			−1.97560			−0.987802	+	0.155718i	$0.950231\pi$
$158$			8.96546e45i			0.603634i
$159$	−2.15097e46	−	1.05950e46i	−1.26851	−	0.624832i
$160$	−7.21884e45			−0.373205
$161$			1.63426e45i			0.0741274i
$162$	3.12360e46	+	8.30784e45i	1.24406	+	0.330882i
$163$	−2.03050e46			−0.710662			−0.355331	−	0.934740i	$-0.615632\pi$
$163$	−2.03050e46			−0.710662			−0.355331	+	0.934740i	$0.615632\pi$
$164$		−	2.80114e46i		−	0.862212i
$165$	−2.87456e45	+	5.83583e45i	−0.0778770	+	0.158103i
$166$	6.46224e46			1.54210
$167$		−	6.30298e46i		−	1.32587i	−0.748678	−	0.662933i	$-0.769311\pi$
$167$		−	6.30298e46i		−	1.32587i	0.748678	−	0.662933i	$-0.230689\pi$
$168$	4.34251e45	+	2.13900e45i	0.0805834	+	0.0396931i
$169$	−1.98717e46			−0.325547
$170$			3.71487e46i			0.537671i
$171$	6.39350e46	+	8.31625e46i	0.818126	+	1.06417i
$172$	−2.47537e45			−0.0280248
$173$			7.00523e46i			0.702189i	0.936340	+	0.351095i	$0.114190\pi$
$173$			7.00523e46i			0.702189i	−0.936340	+	0.351095i	$0.885810\pi$
$174$	−6.55472e46	+	1.33072e47i	−0.582130	+	1.18182i
$175$	2.30592e46			0.181571
$176$			9.40914e46i			0.657331i
$177$	−2.38709e47	−	1.17581e47i	−1.48058	−	0.729289i
$178$	6.52023e46			0.359288
$179$		−	1.86398e47i		−	0.913120i	−0.889693	−	0.456560i	$-0.849081\pi$
$179$		−	1.86398e47i		−	0.913120i	0.889693	−	0.456560i	$-0.150919\pi$
$180$	−3.92756e46	+	3.01949e46i	−0.171159	+	0.131587i
$181$	3.16307e47			1.22704			0.613520	−	0.789679i	$-0.289753\pi$
$181$	3.16307e47			1.22704			0.613520	+	0.789679i	$0.289753\pi$
$182$		−	6.22736e46i		−	0.215181i
$183$	1.75676e47	−	3.56650e47i	0.541052	−	1.09842i
$184$	5.85163e46			0.160732
$185$			1.38185e47i			0.338730i
$186$	−8.36168e47	−	4.11872e47i	−1.83030	−	0.901552i
$187$	3.48723e47			0.682035
$188$		−	4.87957e46i		−	0.0853232i
$189$	1.27585e47	−	2.55620e46i	0.199572	−	0.0399850i
$190$	−4.05441e47			−0.567678
$191$			6.34977e47i			0.796265i	0.917328	+	0.398132i	$0.130341\pi$
$191$			6.34977e47i			0.796265i	−0.917328	+	0.398132i	$0.869659\pi$
$192$	−9.32245e46	+	1.89261e47i	−0.104762	+	0.212684i
$193$	−4.76080e47			−0.479707			−0.239854	−	0.970809i	$-0.577099\pi$
$193$	−4.76080e47			−0.479707			−0.239854	+	0.970809i	$0.577099\pi$
$194$		−	1.06316e48i		−	0.961086i
$195$	−2.98264e47	−	1.46916e47i	−0.242033	−	0.119218i
$196$	8.64322e47			0.629939
$197$			2.44114e48i			1.59883i	0.600778	+	0.799416i	$0.294858\pi$
$197$			2.44114e48i			1.59883i	−0.600778	+	0.799416i	$0.705142\pi$
$198$	7.14764e47	+	9.29719e47i	0.420914	+	0.547498i
$199$	1.24000e48			0.656913			0.328457	−	0.944519i	$-0.393472\pi$
$199$	1.24000e48			0.656913			0.328457	+	0.944519i	$0.393472\pi$
$200$		−	8.25656e47i		−	0.393704i
$201$	−8.26996e47	+	1.67894e48i	−0.355129	+	0.720970i
$202$	1.48762e48			0.575589
$203$			5.97175e47i			0.208298i
$204$	2.38233e48	+	1.17347e48i	0.749494	+	0.369179i
$205$	−1.51824e48			−0.431032
$206$		−	7.84959e48i		−	2.01204i
$207$	1.24701e48	−	9.58693e47i	0.288729	−	0.221974i
$208$	−4.80893e48			−1.00628
$209$			3.80596e48i			0.720099i
$210$	−2.22229e47	+	4.51162e47i	−0.0380361	+	0.0772196i
$211$	−4.27054e48			−0.661532			−0.330766	−	0.943713i	$-0.607307\pi$
$211$	−4.27054e48			−0.661532			−0.330766	+	0.943713i	$0.607307\pi$
$212$		−	6.62507e48i		−	0.929261i
$213$	5.01115e48	+	2.46835e48i	0.636745	+	0.313642i
$214$	−1.20148e49			−1.38365
$215$			1.34167e47i			0.0140100i
$216$	−9.15270e47	−	4.56828e48i	−0.0867002	−	0.432737i
$217$	−3.75241e48			−0.322593
$218$			4.05152e48i			0.316251i
$219$	1.02106e49	−	2.07292e49i	0.723978	−	1.46979i
$220$	−1.79746e48			−0.115820
$221$			1.78229e49i			1.04410i
$222$	2.23465e49	+	1.10072e49i	1.19068	+	0.586497i
$223$	3.31089e49			1.60525			0.802626	−	0.596483i	$-0.203436\pi$
$223$	3.31089e49			1.60525			0.802626	+	0.596483i	$0.203436\pi$
$224$			5.23882e48i			0.231220i
$225$	−1.35270e49	−	1.75951e49i	−0.543712	−	0.707226i
$226$	−9.18068e48			−0.336200
$227$			2.36882e49i			0.790658i	0.918540	+	0.395329i	$0.129369\pi$
$227$			2.36882e49i			0.790658i	−0.918540	+	0.395329i	$0.870631\pi$
$228$	−1.28072e49	+	2.60007e49i	−0.389783	+	0.791323i
$229$	−3.19209e49			−0.886196			−0.443098	−	0.896473i	$-0.646121\pi$
$229$	−3.19209e49			−0.886196			−0.443098	+	0.896473i	$0.646121\pi$
$230$			6.07951e48i			0.154022i
$231$	4.23515e48	+	2.08611e48i	0.0979530	+	0.0482488i
$232$	2.13824e49			0.451657
$233$			2.48211e49i			0.479012i	0.970895	+	0.239506i	$0.0769854\pi$
$233$			2.48211e49i			0.479012i	−0.970895	+	0.239506i	$0.923015\pi$
$234$	−4.75171e49	+	3.65309e49i	−0.838141	+	0.644359i
$235$	−2.64477e48			−0.0426542
$236$		−	7.35236e49i		−	1.08461i
$237$	1.53499e49	−	3.11628e49i	0.207200	−	0.420650i
$238$	2.69594e49			0.333115
$239$		−	1.31357e50i		−	1.48626i	−0.669144	−	0.743132i	$-0.733339\pi$
$239$		−	1.31357e50i		−	1.48626i	0.669144	−	0.743132i	$-0.266661\pi$
$240$	3.48399e49	+	1.71611e49i	0.361111	+	0.177873i
$241$	7.31187e49			0.694498			0.347249	−	0.937773i	$-0.387116\pi$
$241$	7.31187e49			0.694498			0.347249	+	0.937773i	$0.387116\pi$
$242$		−	1.05296e50i		−	0.916828i
$243$	−9.43484e49	−	8.23566e49i	−0.753361	−	0.657608i
$244$	1.09850e50			0.804662
$245$		−	4.68469e49i		−	0.314915i
$246$	−1.20937e50	+	2.45522e50i	−0.746315	+	1.51514i
$247$	−1.94519e50			−1.10237
$248$			1.34358e50i			0.699486i
$249$	−2.24619e50	−	1.10641e50i	−1.07463	−	0.529334i
$250$	1.81940e50			0.800182
$251$			3.06669e50i			1.24029i	0.784489	+	0.620143i	$0.212926\pi$
$251$			3.06669e50i			1.24029i	−0.784489	+	0.620143i	$0.787074\pi$
$252$	2.19129e49	+	2.85029e49i	0.0815247	+	0.106042i
$253$	5.70696e49			0.195377
$254$			1.54118e50i			0.485676i
$255$	6.36028e49	−	1.29124e50i	0.184558	−	0.374683i
$256$	4.88850e50			1.30658
$257$			3.02017e49i			0.0743766i	0.999308	+	0.0371883i	$0.0118401\pi$
$257$			3.02017e49i			0.0743766i	−0.999308	+	0.0371883i	$0.988160\pi$
$258$	2.16968e49	+	1.06872e49i	0.0492472	+	0.0242578i
$259$	1.00283e50			0.209861
$260$		−	9.18667e49i		−	0.177304i
$261$	4.55667e50	−	3.50315e50i	0.811329	−	0.623747i
$262$	−4.52449e50			−0.743434
$263$			6.09818e50i			0.924973i	0.886626	+	0.462487i	$0.153043\pi$
$263$			6.09818e50i			0.924973i	−0.886626	+	0.462487i	$0.846957\pi$
$264$	7.46952e49	−	1.51643e50i	0.104619	−	0.212393i
$265$	−3.59084e50			−0.464550
$266$			2.94235e50i			0.351706i
$267$	−2.26635e50	−	1.11634e50i	−0.250374	−	0.123327i
$268$	−5.17120e50			−0.528154
$269$		−	6.65208e50i		−	0.628289i	−0.949375	−	0.314145i	$-0.898282\pi$
$269$		−	6.65208e50i		−	0.628289i	0.949375	−	0.314145i	$-0.101718\pi$
$270$	4.74618e50	−	9.50913e49i	0.414672	−	0.0830810i
$271$	−9.00609e50			−0.728083			−0.364042	−	0.931383i	$-0.618603\pi$
$271$	−9.00609e50			−0.728083			−0.364042	+	0.931383i	$0.618603\pi$
$272$		−	2.08187e51i		−	1.55779i
$273$	−1.06619e50	+	2.16455e50i	−0.0738620	+	0.149952i
$274$	−3.09281e51			−1.98423
$275$		−	8.05244e50i		−	0.478565i
$276$	3.89876e50	+	1.92042e50i	0.214702	+	0.105756i
$277$	3.69045e51			1.88367			0.941835	−	0.336077i	$-0.109100\pi$
$277$	3.69045e51			1.88367			0.941835	+	0.336077i	$0.109100\pi$
$278$			3.78402e50i			0.179066i
$279$	2.20124e51	+	2.86323e51i	0.966003	+	1.25651i
$280$	7.24942e49			0.0295111
$281$		−	5.95944e50i		−	0.225098i	−0.993646	−	0.112549i	$-0.964098\pi$
$281$		−	5.95944e50i		−	0.225098i	0.993646	−	0.112549i	$-0.0359016\pi$
$282$	−2.10672e50	+	4.27698e50i	−0.0738542	+	0.149936i
$283$	−4.18906e50			−0.136333			−0.0681665	−	0.997674i	$-0.521715\pi$
$283$	−4.18906e50			−0.136333			−0.0681665	+	0.997674i	$0.521715\pi$
$284$			1.54346e51i			0.466454i
$285$	1.40926e51	+	6.94161e50i	0.395593	+	0.194858i
$286$	−2.17464e51			−0.567153
$287$			1.10181e51i			0.267046i
$288$	3.99742e51	−	3.07320e51i	0.900612	−	0.692387i
$289$	−2.94218e51			−0.616332
$290$			2.22151e51i			0.432803i
$291$	−1.82025e51	+	3.69541e51i	−0.329897	+	0.669745i
$292$	6.38469e51			1.07671
$293$			5.91428e51i			0.928286i	0.885760	+	0.464143i	$0.153638\pi$
$293$			5.91428e51i			0.928286i	−0.885760	+	0.464143i	$0.846362\pi$
$294$	−7.57585e51	−	3.73164e51i	−1.10697	−	0.545263i
$295$	−3.98503e51			−0.542213
$296$		−	3.59071e51i		−	0.455045i
$297$	−8.92642e50	−	4.45534e51i	−0.105388	−	0.526012i
$298$	−1.91445e51			−0.210622
$299$			2.91678e51i			0.299094i
$300$	2.70968e51	−	5.50109e51i	0.259043	−	0.525899i
$301$	9.73671e49			0.00867992
$302$		−	9.98170e51i		−	0.829963i
$303$	−5.17076e51	−	2.54697e51i	−0.401106	−	0.197573i
$304$	2.27216e52			1.64472
$305$		−	5.95395e51i		−	0.402262i
$306$	−1.58149e52	−	2.05710e52i	−0.997511	−	1.29750i
$307$	2.14532e52			1.26353			0.631765	−	0.775160i	$-0.282331\pi$
$307$	2.14532e52			1.26353			0.631765	+	0.775160i	$0.282331\pi$
$308$			1.30445e51i			0.0717565i
$309$	−1.34394e52	+	2.72842e52i	−0.690640	+	1.40211i
$310$	−1.39591e52			−0.670286
$311$		−	1.45720e52i		−	0.653960i	−0.945031	−	0.326980i	$-0.893969\pi$
$311$		−	1.45720e52i		−	0.653960i	0.945031	−	0.326980i	$-0.106031\pi$
$312$	7.75036e51	+	3.81760e51i	0.325144	+	0.160156i
$313$	−2.12172e52			−0.832256			−0.416128	−	0.909306i	$-0.636613\pi$
$313$	−2.12172e52			−0.832256			−0.416128	+	0.909306i	$0.636613\pi$
$314$			6.93274e52i			2.54321i
$315$	1.54488e51	−	1.18770e51i	0.0530119	−	0.0407553i
$316$	9.59828e51			0.308152
$317$		−	3.63197e52i		−	1.09118i	−0.838051	−	0.545592i	$-0.816305\pi$
$317$		−	3.63197e52i		−	1.09118i	0.838051	−	0.545592i	$-0.183695\pi$
$318$	−2.86032e52	+	5.80692e52i	−0.804351	+	1.63296i
$319$	2.08538e52			0.549010
$320$			3.15954e51i			0.0778887i
$321$	4.17618e52	+	2.05706e52i	0.964213	+	0.474944i
$322$	4.41199e51			0.0954249
$323$		−	8.42110e52i		−	1.70654i
$324$	8.89424e51	−	3.34408e52i	0.168913	−	0.635084i
$325$	4.11553e52			0.732614
$326$			5.48170e52i			0.914842i
$327$	6.93667e51	−	1.40826e52i	0.108555	−	0.220383i
$328$	3.94513e52			0.579042
$329$			1.91935e51i			0.0264265i
$330$	1.57549e52	+	7.76041e51i	0.203527	+	0.100252i
$331$	−8.36929e52			−1.01461			−0.507307	−	0.861765i	$-0.669359\pi$
$331$	−8.36929e52			−1.01461			−0.507307	+	0.861765i	$0.669359\pi$
$332$		−	6.91837e52i		−	0.787234i
$333$	−5.88278e52	−	7.65195e52i	−0.628426	−	0.817416i
$334$	−1.70160e53			−1.70680
$335$			2.80283e52i			0.264032i
$336$	1.24541e52	−	2.52838e52i	0.110201	−	0.223727i
$337$	−1.17005e53			−0.972691			−0.486345	−	0.873767i	$-0.661670\pi$
$337$	−1.17005e53			−0.972691			−0.486345	+	0.873767i	$0.661670\pi$
$338$			5.36472e52i			0.419080i
$339$	3.19109e52	+	1.57184e52i	0.234285	+	0.115402i
$340$	3.97708e52			0.274478
$341$			1.31037e53i			0.850258i
$342$	2.24512e53	−	1.72604e53i	1.36991	−	1.05318i
$343$	−6.94644e52			−0.398645
$344$		−	3.48631e51i		−	0.0188208i
$345$	1.04088e52	−	2.11316e52i	0.0528689	−	0.107332i
$346$	1.89119e53			0.903934
$347$		−	4.91463e52i		−	0.221091i	−0.993871	−	0.110546i	$-0.964740\pi$
$347$		−	4.91463e52i		−	0.221091i	0.993871	−	0.110546i	$-0.0352598\pi$
$348$	1.42464e53	+	7.01738e52i	0.603312	+	0.297174i
$349$	−1.71290e53			−0.682966			−0.341483	−	0.939888i	$-0.610929\pi$
$349$	−1.71290e53			−0.682966			−0.341483	+	0.939888i	$0.610929\pi$
$350$		−	6.22526e52i		−	0.233738i
$351$	2.27708e53	−	4.56221e52i	0.805248	−	0.161334i
$352$	1.82943e53			0.609426
$353$			3.76460e53i			1.18154i	0.806839	+	0.590772i	$0.201177\pi$
$353$			3.76460e53i			1.18154i	−0.806839	+	0.590772i	$0.798823\pi$
$354$	−3.17432e53	+	6.44439e53i	−0.938821	+	1.90596i
$355$	8.36565e52			0.233187
$356$		−	6.98045e52i		−	0.183414i
$357$	−9.37074e52	−	4.61576e52i	−0.232135	−	0.114343i
$358$	−5.03215e53			−1.17547
$359$			9.52529e52i			0.209843i	0.994481	+	0.104922i	$0.0334591\pi$
$359$			9.52529e52i			0.209843i	−0.994481	+	0.104922i	$0.966541\pi$
$360$	−4.25266e52	−	5.53158e52i	−0.0883706	−	0.114947i
$361$	4.08983e53			0.801778
$362$		−	8.53928e53i		−	1.57958i
$363$	−1.80278e53	+	3.65994e53i	−0.314705	+	0.638903i
$364$	−6.66691e52			−0.109849
$365$		−	3.46055e53i		−	0.538264i
$366$	−9.62842e53	−	4.74269e53i	−1.41401	−	0.696501i
$367$	4.09709e53			0.568182			0.284091	−	0.958797i	$-0.408308\pi$
$367$	4.09709e53			0.568182			0.284091	+	0.958797i	$0.408308\pi$
$368$		−	3.40705e53i		−	0.446247i
$369$	8.40723e53	−	6.46344e53i	1.04016	−	0.799669i
$370$	3.73054e53			0.436049
$371$			2.60593e53i			0.287813i
$372$	−4.40944e53	+	8.95187e53i	−0.460237	+	0.934356i
$373$	1.90141e53			0.187582			0.0937909	−	0.995592i	$-0.470101\pi$
$373$	1.90141e53			0.187582			0.0937909	+	0.995592i	$0.470101\pi$
$374$		−	9.41441e53i		−	0.877990i
$375$	−6.32401e53	−	3.11502e53i	−0.557617	−	0.274666i
$376$	6.87240e52			0.0573012
$377$			1.06582e54i			0.840455i
$378$	−6.90092e52	−	3.44438e53i	−0.0514730	−	0.256911i
$379$	−1.76335e53			−0.124427			−0.0622137	−	0.998063i	$-0.519816\pi$
$379$	−1.76335e53			−0.124427			−0.0622137	+	0.998063i	$0.519816\pi$
$380$			4.34058e53i			0.289796i
$381$	2.63868e53	−	5.35696e53i	0.166710	−	0.338449i
$382$	1.71424e54			1.02504
$383$			2.47941e54i			1.40338i	0.712484	+	0.701688i	$0.247570\pi$
$383$			2.47941e54i			1.40338i	−0.712484	+	0.701688i	$0.752430\pi$
$384$	−1.39085e54	−	6.85095e53i	−0.745291	−	0.367109i
$385$	7.07020e52			0.0358721
$386$			1.28526e54i			0.617531i
$387$	−5.71175e52	−	7.42947e52i	−0.0259920	−	0.0338087i
$388$	−1.13820e54			−0.490629
$389$			8.09266e53i			0.330483i	0.986253	+	0.165242i	$0.0528404\pi$
$389$			8.09266e53i			0.330483i	−0.986253	+	0.165242i	$0.947160\pi$
$390$	−3.96627e53	+	8.05218e53i	−0.153471	+	0.311571i
$391$	−1.26273e54			−0.463018
$392$			1.21731e54i			0.423053i
$393$	1.57265e54	+	7.74644e53i	0.518071	+	0.255187i
$394$	6.59031e54			2.05819
$395$		−	5.20234e53i		−	0.154049i
$396$	9.95342e53	−	7.65215e53i	0.279495	−	0.214874i
$397$	−1.54684e54			−0.411949			−0.205975	−	0.978557i	$-0.566036\pi$
$397$	−1.54684e54			−0.411949			−0.205975	+	0.978557i	$0.566036\pi$
$398$		−	3.34761e54i		−	0.845650i
$399$	5.03763e53	−	1.02272e54i	0.120725	−	0.245091i
$400$	−4.80730e54			−1.09305
$401$		−	9.09178e54i		−	1.96163i	−0.194943	−	0.980814i	$-0.562452\pi$
$401$		−	9.09178e54i		−	1.96163i	0.194943	−	0.980814i	$-0.437548\pi$
$402$	4.53260e54	+	2.23263e54i	0.928111	+	0.457161i
$403$	−6.69716e54			−1.30162
$404$		−	1.59262e54i		−	0.293835i
$405$	−1.81252e54	−	4.82075e53i	−0.317487	−	0.0844421i
$406$	1.61218e54			0.268144
$407$		−	3.50194e54i		−	0.553129i
$408$	−1.65271e54	+	3.35528e54i	−0.247933	+	0.503344i
$409$	−7.90939e54			−1.12708			−0.563538	−	0.826090i	$-0.690560\pi$
$409$	−7.90939e54			−1.12708			−0.563538	+	0.826090i	$0.690560\pi$
$410$			4.09876e54i			0.554871i
$411$	1.07502e55	+	5.29524e54i	1.38273	+	0.681094i
$412$	−8.40365e54			−1.02713
$413$			2.89200e54i			0.335929i
$414$	−2.58817e54	−	3.36652e54i	−0.285749	−	0.371684i
$415$	−3.74981e54			−0.393549
$416$			9.35007e54i			0.932943i
$417$	6.47866e53	−	1.31527e54i	0.0614651	−	0.124784i
$418$	1.02749e55			0.926990
$419$		−	1.69265e55i		−	1.45235i	−0.687509	−	0.726176i	$-0.741296\pi$
$419$		−	1.69265e55i		−	1.45235i	0.687509	−	0.726176i	$-0.258704\pi$
$420$	4.83007e53	+	2.37915e53i	0.0394201	+	0.0194172i
$421$	2.06572e55			1.60379			0.801895	−	0.597465i	$-0.203825\pi$
$421$	2.06572e55			1.60379			0.801895	+	0.597465i	$0.203825\pi$
$422$			1.15291e55i			0.851596i
$423$	1.46453e54	−	1.12593e54i	0.102932	−	0.0791340i
$424$	9.33076e54			0.624071
$425$			1.78169e55i			1.13414i
$426$	6.66375e54	−	1.35285e55i	0.403754	−	0.819687i
$427$	−4.32088e54			−0.249222
$428$			1.28628e55i			0.706345i
$429$	7.55875e54	+	3.72322e54i	0.395227	+	0.194678i
$430$	3.62208e53			0.0180352
$431$		−	2.14228e54i		−	0.101591i	−0.998709	−	0.0507954i	$-0.983824\pi$
$431$		−	2.14228e54i		−	0.101591i	0.998709	−	0.0507954i	$-0.0161756\pi$
$432$	−2.65984e55	+	5.32907e54i	−1.20142	+	0.240709i
$433$	−4.44788e55			−1.91385			−0.956923	−	0.290340i	$-0.906232\pi$
$433$	−4.44788e55			−1.91385			−0.956923	+	0.290340i	$0.906232\pi$
$434$			1.01303e55i			0.415277i
$435$	3.80348e54	−	7.72167e54i	0.148561	−	0.301604i
$436$	4.33749e54			0.161444
$437$		−	1.37814e55i		−	0.488859i
$438$	−5.59623e55	−	2.75654e55i	−1.89208	−	0.931984i
$439$	1.70979e55			0.551047			0.275524	−	0.961294i	$-0.411149\pi$
$439$	1.70979e55			0.551047			0.275524	+	0.961294i	$0.411149\pi$
$440$		−	2.53155e54i		−	0.0777822i
$441$	1.99437e55	+	2.59414e55i	0.584244	+	0.759947i
$442$	4.81162e55			1.34408
$443$		−	2.36090e55i		−	0.628926i	−0.949270	−	0.314463i	$-0.898176\pi$
$443$		−	2.36090e55i		−	0.628926i	0.949270	−	0.314463i	$-0.101824\pi$
$444$	1.17842e55	−	2.39238e55i	0.299403	−	0.607838i
$445$	−3.78346e54			−0.0916915
$446$		−	8.93836e55i		−	2.06645i
$447$	6.65439e54	+	3.27776e54i	0.146774	+	0.0722969i
$448$	2.29293e54			0.0482561
$449$			1.87014e55i			0.375578i	0.982209	+	0.187789i	$0.0601322\pi$
$449$			1.87014e55i			0.375578i	−0.982209	+	0.187789i	$0.939868\pi$
$450$	−4.75011e55	+	3.65186e55i	−0.910418	+	0.699925i
$451$	3.84760e55			0.703853
$452$			9.82869e54i			0.171628i
$453$	−1.70898e55	+	3.46951e55i	−0.284888	+	0.578370i
$454$	6.39505e55			1.01782
$455$			3.61352e54i			0.0549150i
$456$	−3.66195e55	−	1.80377e55i	−0.531435	−	0.261770i
$457$	−4.32413e55			−0.599320			−0.299660	−	0.954046i	$-0.596873\pi$
$457$	−4.32413e55			−0.599320			−0.299660	+	0.954046i	$0.596873\pi$
$458$			8.61762e55i			1.14081i
$459$	1.97507e55	+	9.85793e55i	0.249756	+	1.24658i
$460$	6.50862e54			0.0786275
$461$			4.25946e55i			0.491626i	0.969317	+	0.245813i	$0.0790549\pi$
$461$			4.25946e55i			0.491626i	−0.969317	+	0.245813i	$0.920945\pi$
$462$	5.63185e54	−	1.14336e55i	0.0621111	−	0.126096i
$463$	−1.32730e56			−1.39884			−0.699419	−	0.714712i	$-0.746558\pi$
$463$	−1.32730e56			−1.39884			−0.699419	+	0.714712i	$0.746558\pi$
$464$		−	1.24497e56i		−	1.25395i
$465$	4.85198e55	+	2.38995e55i	0.467097	+	0.230079i
$466$	6.70090e55			0.616636
$467$			1.06762e56i			0.939205i	0.882878	+	0.469602i	$0.155603\pi$
$467$			1.06762e56i			0.939205i	−0.882878	+	0.469602i	$0.844397\pi$
$468$	3.91094e55	+	5.08710e55i	0.328941	+	0.427866i
$469$	2.03406e55			0.163581
$470$			7.14003e54i			0.0549092i
$471$	1.18696e56	−	2.40973e56i	0.872968	−	1.77227i
$472$	1.03551e56			0.728402
$473$		−	3.40013e54i		−	0.0228776i
$474$	−8.41296e55	−	4.14398e55i	−0.541506	−	0.266731i
$475$	−1.94454e56			−1.19743
$476$		−	2.88623e55i		−	0.170053i
$477$	1.98842e56	−	1.52869e56i	1.12104	−	0.861854i
$478$	−3.54621e56			−1.91328
$479$			1.34227e56i			0.693099i	0.938032	+	0.346550i	$0.112647\pi$
$479$			1.34227e56i			0.693099i	−0.938032	+	0.346550i	$0.887353\pi$
$480$	3.33667e55	−	6.77397e55i	0.164910	−	0.334794i
$481$	1.78981e56			0.846760
$482$		−	1.97397e56i		−	0.894033i
$483$	−1.53355e55	−	7.55383e54i	−0.0664980	−	0.0327550i
$484$	−1.12728e56			−0.468035
$485$			6.16914e55i			0.245272i
$486$	−2.22337e56	+	2.54711e56i	−0.846544	+	0.969808i
$487$	1.15629e55			0.0421656			0.0210828	−	0.999778i	$-0.493289\pi$
$487$	1.15629e55			0.0421656			0.0210828	+	0.999778i	$0.493289\pi$
$488$			1.54713e56i			0.540393i
$489$	9.38530e55	−	1.90537e56i	0.314023	−	0.637519i
$490$	−1.26472e56			−0.405393
$491$		−	5.79804e56i		−	1.78061i	−0.455360	−	0.890307i	$-0.650489\pi$
$491$		−	5.79804e56i		−	1.78061i	0.455360	−	0.890307i	$-0.349511\pi$
$492$	2.62852e56	+	1.29473e56i	0.773470	+	0.380989i
$493$	−4.61413e56			−1.30108
$494$			5.25140e56i			1.41909i
$495$	−4.14752e55	−	5.39483e55i	−0.107419	−	0.139723i
$496$	7.82288e56			1.94201
$497$		−	6.07108e55i		−	0.144471i
$498$	−2.98695e56	+	6.06400e56i	−0.681416	+	1.38338i
$499$	−3.23365e56			−0.707264			−0.353632	−	0.935385i	$-0.615053\pi$
$499$	−3.23365e56			−0.707264			−0.353632	+	0.935385i	$0.615053\pi$
$500$		−	1.94782e56i		−	0.408488i
$501$	5.91455e56	+	2.91334e56i	1.18940	+	0.585867i
$502$	8.27909e56			1.59663
$503$			6.08610e56i			1.12567i	0.826569	+	0.562836i	$0.190290\pi$
$503$			6.08610e56i			1.12567i	−0.826569	+	0.562836i	$0.809710\pi$
$504$	−4.01436e55	+	3.08622e55i	−0.0712155	+	0.0547502i
$505$	−8.63211e55			−0.146892
$506$		−	1.54070e56i		−	0.251511i
$507$	9.18502e55	−	1.86471e56i	0.143851	−	0.292041i
$508$	1.64997e56			0.247935
$509$		−	7.62610e56i		−	1.09959i	−0.835301	−	0.549793i	$-0.814707\pi$
$509$		−	7.62610e56i		−	1.09959i	0.835301	−	0.549793i	$-0.185293\pi$
$510$	−3.48594e56	−	1.71707e56i	−0.482332	−	0.237583i
$511$	−2.51138e56			−0.333483
$512$		−	6.67863e56i		−	0.851174i
$513$	−1.07589e57	+	2.15559e56i	−1.31615	+	0.263695i
$514$	8.15350e55			0.0957456
$515$			4.55484e56i			0.513478i
$516$	1.14416e55	−	2.32282e55i	0.0123834	−	0.0251404i
$517$	6.70250e55			0.0696522
$518$		−	2.70731e56i		−	0.270155i
$519$	−6.57353e56	−	3.23793e56i	−0.629918	−	0.310279i
$520$	1.29385e56			0.119073
$521$			1.62710e57i			1.43821i	0.694900	+	0.719106i	$0.255448\pi$
$521$			1.62710e57i			1.43821i	−0.694900	+	0.719106i	$0.744552\pi$
$522$	−9.45739e56	−	1.23016e57i	−0.802955	−	1.04443i
$523$	−7.94532e56			−0.648002			−0.324001	−	0.946057i	$-0.605028\pi$
$523$	−7.94532e56			−0.648002			−0.324001	+	0.946057i	$0.605028\pi$
$524$			4.84384e56i			0.379519i
$525$	−1.06584e56	+	2.16382e56i	−0.0802314	+	0.162883i
$526$	1.64631e57			1.19073
$527$		−	2.89933e57i		−	2.01500i
$528$	−8.82929e56	−	4.34906e56i	−0.589676	−	0.290458i
$529$	1.35136e57			0.867363
$530$			9.69413e56i			0.598020i
$531$	2.20671e57	−	1.69651e57i	1.30846	−	1.00594i
$532$	3.15003e56			0.179544
$533$			1.96647e57i			1.07750i
$534$	−3.01376e56	+	6.11842e56i	−0.158760	+	0.322309i
$535$	6.97174e56			0.353112
$536$		−	7.28313e56i		−	0.354697i
$537$	1.74911e57	+	8.61562e56i	0.819138	+	0.403484i
$538$	−1.79585e57			−0.808802
$539$			1.18722e57i			0.514241i
$540$	−1.01803e56	−	5.08118e56i	−0.0424124	−	0.211688i
$541$	−6.42279e55			−0.0257384			−0.0128692	−	0.999917i	$-0.504097\pi$
$541$	−6.42279e55			−0.0257384			−0.0128692	+	0.999917i	$0.504097\pi$
$542$			2.43136e57i			0.937268i
$543$	−1.46202e57	+	2.96814e57i	−0.542197	+	1.10075i
$544$	−4.04782e57			−1.44426
$545$		−	2.35096e56i		−	0.0807083i
$546$	5.84359e56	+	2.87839e56i	0.193034	+	0.0950831i
$547$	1.74843e57			0.555796			0.277898	−	0.960611i	$-0.410362\pi$
$547$	1.74843e57			0.555796			0.277898	+	0.960611i	$0.410362\pi$
$548$			3.31111e57i			1.01294i
$549$	2.53471e57	+	3.29699e57i	0.746293	+	0.970730i
$550$	−2.17390e57			−0.616061
$551$		−	5.03585e57i		−	1.37369i
$552$	−2.70472e56	+	5.49102e56i	−0.0710234	+	0.144189i
$553$	−3.77542e56			−0.0954416
$554$		−	9.96305e57i		−	2.42486i
$555$	−1.29669e57	−	6.38711e56i	−0.303866	−	0.149676i
$556$	4.05110e56			0.0914119
$557$			2.32535e57i			0.505277i	0.967561	+	0.252638i	$0.0812983\pi$
$557$			2.32535e57i			0.505277i	−0.967561	+	0.252638i	$0.918702\pi$
$558$	7.72980e57	−	5.94264e57i	1.61752	−	1.24354i
$559$	1.73777e56			0.0350223
$560$		−	4.22091e56i		−	0.0819327i
$561$	−1.61185e57	+	3.27233e57i	−0.301374	+	0.611838i
$562$	−1.60886e57			−0.289771
$563$		−	1.00315e58i		−	1.74057i	−0.492549	−	0.870285i	$-0.663935\pi$
$563$		−	1.00315e58i		−	1.74057i	0.492549	−	0.870285i	$-0.336065\pi$
$564$	4.57886e56	+	2.25542e56i	0.0765414	+	0.0377021i
$565$	5.32723e56			0.0857993
$566$			1.13091e57i			0.175503i
$567$	−3.49849e56	+	1.31537e57i	−0.0523163	+	0.196700i
$568$	−2.17380e57			−0.313260
$569$			1.25269e58i			1.73975i	0.493276	+	0.869873i	$0.335799\pi$
$569$			1.25269e58i			1.73975i	−0.493276	+	0.869873i	$0.664201\pi$
$570$	1.87401e57	−	3.80455e57i	0.250842	−	0.509251i
$571$	−1.26105e58			−1.62695			−0.813474	−	0.581601i	$-0.802427\pi$
$571$	−1.26105e58			−1.62695			−0.813474	+	0.581601i	$0.802427\pi$
$572$			2.32813e57i			0.289528i
$573$	−5.95846e57	−	2.93497e57i	−0.714311	−	0.351849i
$574$	2.97454e57			0.343771
$575$			2.91579e57i			0.324887i
$576$	−1.34508e57	−	1.74959e57i	−0.144502	−	0.187959i
$577$	−2.36858e57			−0.245355			−0.122678	−	0.992447i	$-0.539148\pi$
$577$	−2.36858e57			−0.245355			−0.122678	+	0.992447i	$0.539148\pi$
$578$			7.94296e57i			0.793410i
$579$	2.20052e57	−	4.46741e57i	0.211970	−	0.430334i
$580$	2.37831e57			0.220943
$581$			2.72130e57i			0.243824i
$582$	9.97642e57	+	4.91410e57i	0.862168	+	0.424679i
$583$	9.10008e57			0.758588
$584$			8.99221e57i			0.723097i
$585$	2.75725e57	−	2.11976e57i	0.213896	−	0.164442i
$586$	1.59667e58			1.19499
$587$		−	7.95656e57i		−	0.574547i	−0.957849	−	0.287273i	$-0.907251\pi$
$587$		−	7.95656e57i		−	0.574547i	0.957849	−	0.287273i	$-0.0927488\pi$
$588$	−3.99504e57	+	8.11058e57i	−0.278354	+	0.565103i
$589$	3.16432e58			2.12745
$590$			1.07583e58i			0.697995i
$591$	−2.29071e58	−	1.12834e58i	−1.43427	−	0.706483i
$592$	−2.09066e58			−1.26336
$593$		−	1.38586e58i		−	0.808295i	−0.914694	−	0.404148i	$-0.867568\pi$
$593$		−	1.38586e58i		−	0.808295i	0.914694	−	0.404148i	$-0.132432\pi$
$594$	−1.20280e58	+	2.40985e57i	−0.677139	+	0.135667i
$595$	−1.56436e57			−0.0850120
$596$			2.04958e57i			0.107521i
$597$	−5.73149e57	+	1.16359e58i	−0.290273	+	0.589302i
$598$	7.87437e57			0.385027
$599$		−	2.16138e58i		−	1.02039i	−0.860058	−	0.510196i	$-0.829573\pi$
$599$		−	2.16138e58i		−	1.02039i	0.860058	−	0.510196i	$-0.170427\pi$
$600$	7.74775e57	+	3.81632e57i	0.353182	+	0.173968i
$601$	4.42294e57			0.194692			0.0973458	−	0.995251i	$-0.468965\pi$
$601$	4.42294e57			0.194692			0.0973458	+	0.995251i	$0.468965\pi$
$602$		−	2.62860e56i		−	0.0111737i
$603$	−1.19322e58	−	1.55206e58i	−0.489843	−	0.637156i
$604$	−1.06862e58			−0.423691
$605$			6.10993e57i			0.233977i
$606$	−6.87600e57	+	1.39594e58i	−0.254338	+	0.516347i
$607$	−1.45277e58			−0.519080			−0.259540	−	0.965732i	$-0.583571\pi$
$607$	−1.45277e58			−0.519080			−0.259540	+	0.965732i	$0.583571\pi$
$608$		−	4.41779e58i		−	1.52486i
$609$	−5.60374e57	−	2.76024e57i	−0.186859	−	0.0920415i
$610$	−1.60738e58			−0.517835
$611$			3.42558e57i			0.106628i
$612$	−2.20230e58	+	1.69312e58i	−0.662365	+	0.509223i
$613$	3.88200e58			1.12820			0.564099	−	0.825707i	$-0.309224\pi$
$613$	3.88200e58			1.12820			0.564099	+	0.825707i	$0.309224\pi$
$614$		−	5.79167e58i		−	1.62655i
$615$	7.01755e57	−	1.42468e58i	0.190462	−	0.386669i
$616$	−1.83718e57			−0.0481901
$617$			4.97953e58i			1.26241i	0.775616	+	0.631205i	$0.217439\pi$
$617$			4.97953e58i			1.26241i	−0.775616	+	0.631205i	$0.782561\pi$
$618$	7.36586e58	+	3.62821e58i	1.80495	+	0.889067i
$619$	−2.13853e57			−0.0506537			−0.0253268	−	0.999679i	$-0.508063\pi$
$619$	−2.13853e57			−0.0506537			−0.0253268	+	0.999679i	$0.508063\pi$
$620$			1.49443e58i			0.342177i
$621$	3.23226e57	+	1.61328e58i	0.0715456	+	0.357097i
$622$	−3.93398e58			−0.841849
$623$			2.74572e57i			0.0568076i
$624$	2.22276e58	−	4.51257e58i	0.444649	−	0.902709i
$625$	3.55616e58			0.687862
$626$			5.72797e58i			1.07137i
$627$	−3.57142e58	−	1.75918e58i	−0.645984	−	0.318193i
$628$	7.42208e58			1.29829
$629$			7.74842e58i			1.31084i
$630$	−3.20641e57	−	4.17069e57i	−0.0524647	−	0.0682427i
$631$	−3.67082e58			−0.580961			−0.290481	−	0.956881i	$-0.593815\pi$
$631$	−3.67082e58			−0.580961			−0.290481	+	0.956881i	$0.593815\pi$
$632$			1.35182e58i			0.206948i
$633$	1.97391e58	−	4.00736e58i	0.292314	−	0.593445i
$634$	−9.80518e58			−1.40469
$635$		−	8.94295e57i		−	0.123946i
$636$	6.21680e58	+	3.06222e58i	0.833618	+	0.410616i
$637$	−6.06776e58			−0.787228
$638$		−	5.62986e58i		−	0.706745i
$639$	−4.63246e58	+	3.56142e58i	−0.562722	+	0.432619i
$640$	−2.32190e58			−0.272939
$641$			1.19584e59i			1.36036i	0.733045	+	0.680180i	$0.238098\pi$
$641$			1.19584e59i			1.36036i	−0.733045	+	0.680180i	$0.761902\pi$
$642$	5.55342e58	−	1.12743e59i	0.611399	−	1.24124i
$643$	7.02159e58			0.748178			0.374089	−	0.927393i	$-0.377955\pi$
$643$	7.02159e58			0.748178			0.374089	+	0.927393i	$0.377955\pi$
$644$		−	4.72341e57i		−	0.0487138i
$645$	−1.25899e57	−	6.20141e56i	−0.0125680	−	0.00619066i
$646$	−2.27343e59			−2.19684
$647$		−	1.38164e59i		−	1.29242i	−0.763159	−	0.646211i	$-0.776353\pi$
$647$		−	1.38164e59i		−	1.29242i	0.763159	−	0.646211i	$-0.223647\pi$
$648$	4.70981e58	+	1.25267e58i	0.426509	+	0.113438i
$649$	1.00991e59			0.885406
$650$		−	1.11106e59i		−	0.943100i
$651$	1.73442e58	−	3.52116e58i	0.142546	−	0.289391i
$652$	5.86862e58			0.467021
$653$			9.34180e58i			0.719869i	0.932978	+	0.359935i	$0.117201\pi$
$653$			9.34180e58i			0.719869i	−0.932978	+	0.359935i	$0.882799\pi$
$654$	−3.80185e58	−	1.87268e58i	−0.283702	−	0.139743i
$655$	2.62540e58			0.189727
$656$		−	2.29701e59i		−	1.60762i
$657$	1.47323e59	+	1.91628e59i	0.998611	+	1.29893i
$658$	5.18163e57			0.0340191
$659$		−	2.34227e59i		−	1.48951i	−0.667340	−	0.744754i	$-0.732567\pi$
$659$		−	2.34227e59i		−	1.48951i	0.667340	−	0.744754i	$-0.267433\pi$
$660$	8.30816e57	−	1.68669e58i	0.0511779	−	0.103899i
$661$	−1.09940e59			−0.656030			−0.328015	−	0.944673i	$-0.606380\pi$
$661$	−1.09940e59			−0.656030			−0.328015	+	0.944673i	$0.606380\pi$
$662$			2.25944e59i			1.30612i
$663$	−1.67246e59	−	8.23804e58i	−0.936636	−	0.461360i
$664$	9.74384e58			0.528689
$665$		−	1.70734e58i		−	0.0897564i
$666$	−2.06578e59	+	1.58816e59i	−1.05227	+	0.808978i
$667$	−7.55116e58			−0.372710
$668$			1.82171e59i			0.871311i
$669$	−1.53035e59	+	3.10686e59i	−0.709319	+	1.44003i
$670$	7.56675e58			0.339890
$671$			1.50888e59i			0.656873i
$672$	−4.91598e58	−	2.42147e58i	−0.207422	−	0.102170i
$673$	3.29152e59			1.34611			0.673054	−	0.739593i	$-0.264982\pi$
$673$	3.29152e59			1.34611			0.673054	+	0.739593i	$0.264982\pi$
$674$			3.15875e59i			1.25215i
$675$	2.27632e59	−	4.56068e58i	0.874688	−	0.175247i
$676$	5.74339e58			0.213938
$677$		−	1.99293e59i		−	0.719665i	−0.933017	−	0.359833i	$-0.882834\pi$
$677$		−	1.99293e59i		−	0.719665i	0.933017	−	0.359833i	$-0.117166\pi$
$678$	4.24346e58	−	8.61492e58i	0.148558	−	0.301597i
$679$	4.47704e58			0.151959
$680$			5.60133e58i			0.184333i
$681$	−2.22284e59	−	1.09491e59i	−0.709281	−	0.349371i
$682$	3.53757e59			1.09454
$683$		−	5.96639e59i		−	1.79010i	−0.445968	−	0.895049i	$-0.647140\pi$
$683$		−	5.96639e59i		−	1.79010i	0.445968	−	0.895049i	$-0.352860\pi$
$684$	−1.84787e59	−	2.40359e59i	−0.537642	−	0.699331i
$685$	1.79465e59			0.506381
$686$			1.87532e59i			0.513179i
$687$	1.47544e59	−	2.99537e59i	0.391587	−	0.794986i
$688$	−2.02987e58			−0.0522531
$689$			4.65097e59i			1.16129i
$690$	−5.70485e58	−	2.81005e58i	−0.138170	−	0.0680586i
$691$	−1.04125e59			−0.244633			−0.122317	−	0.992491i	$-0.539032\pi$
$691$	−1.04125e59			−0.244633			−0.122317	+	0.992491i	$0.539032\pi$
$692$		−	2.02468e59i		−	0.461453i
$693$	−3.91511e58	+	3.00992e58i	−0.0865658	+	0.0665514i
$694$	−1.32679e59			−0.284613
$695$		−	2.19573e58i		−	0.0456981i
$696$	−9.88329e58	+	2.00647e59i	−0.199576	+	0.405171i
$697$	−8.51323e59			−1.66804
$698$			4.62430e59i			0.879188i
$699$	−2.32914e59	−	1.14727e59i	−0.429710	−	0.211663i
$700$	−6.66466e58			−0.119322
$701$		−	4.47369e59i		−	0.777298i	−0.921386	−	0.388649i	$-0.872942\pi$
$701$		−	4.47369e59i		−	0.777298i	0.921386	−	0.388649i	$-0.127058\pi$
$702$	−1.23165e59	−	6.14740e59i	−0.207687	−	1.03660i
$703$	−8.45662e59			−1.38400
$704$		−	8.00706e58i		−	0.127188i
$705$	1.22245e58	−	2.48178e58i	0.0188478	−	0.0382641i
$706$	1.01632e60			1.52101
$707$			6.26446e58i			0.0910072i
$708$	6.89926e59	+	3.39838e59i	0.972981	+	0.479262i
$709$	3.58169e59			0.490362			0.245181	−	0.969477i	$-0.421153\pi$
$709$	3.58169e59			0.490362			0.245181	+	0.969477i	$0.421153\pi$
$710$		−	2.25846e59i		−	0.300184i
$711$	2.21474e59	+	2.88079e59i	0.285799	+	0.371749i
$712$	9.83128e58			0.123177
$713$		−	4.74484e59i		−	0.577220i
$714$	−1.24611e59	+	2.52980e59i	−0.147195	+	0.298830i
$715$	1.26186e59			0.144739
$716$			5.38734e59i			0.600069i
$717$	1.23262e60	+	6.07152e59i	1.33329	+	0.656742i
$718$	2.57152e59			0.270133
$719$			4.31952e59i			0.440685i	0.975423	+	0.220343i	$0.0707175\pi$
$719$			4.31952e59i			0.440685i	−0.975423	+	0.220343i	$0.929282\pi$
$720$	−3.22071e59	+	2.47607e59i	−0.319131	+	0.245347i
$721$	3.30552e59			0.318126
$722$		−	1.10412e60i		−	1.03214i
$723$	−3.37967e59	+	6.86127e59i	−0.306881	+	0.623018i
$724$	−9.14201e59			−0.806366
$725$			1.06546e60i			0.912932i
$726$	9.88067e59	+	4.86694e59i	0.822465	+	0.405123i
$727$	−1.67194e60			−1.35207			−0.676033	−	0.736872i	$-0.736302\pi$
$727$	−1.67194e60			−1.35207			−0.676033	+	0.736872i	$0.736302\pi$
$728$		−	9.38968e58i		−	0.0737721i
$729$	1.20891e60	−	5.04676e59i	0.922815	−	0.385243i
$730$	−9.34239e59			−0.692912
$731$			7.52315e58i			0.0542169i
$732$	−5.07744e59	+	1.03080e60i	−0.355559	+	0.721844i
$733$	−6.74532e59			−0.459007			−0.229503	−	0.973308i	$-0.573710\pi$
$733$	−6.74532e59			−0.459007			−0.229503	+	0.973308i	$0.573710\pi$
$734$		−	1.10608e60i		−	0.731426i
$735$	4.39600e59	+	2.16534e59i	0.282503	+	0.139153i
$736$	−6.62439e59			−0.413725
$737$		−	7.10307e59i		−	0.431151i
$738$	−1.74492e60	−	2.26968e60i	−1.02942	−	1.33900i
$739$	1.10644e60			0.634446			0.317223	−	0.948351i	$-0.397250\pi$
$739$	1.10644e60			0.634446			0.317223	+	0.948351i	$0.397250\pi$
$740$		−	3.99386e59i		−	0.222601i
$741$	8.99099e59	−	1.82532e60i	0.487108	−	0.988909i
$742$	7.03518e59			0.370504
$743$			2.45523e60i			1.25698i	0.777819	+	0.628488i	$0.216326\pi$
$743$			2.45523e60i			1.25698i	−0.777819	+	0.628488i	$0.783674\pi$
$744$	−1.26078e60	−	6.21025e59i	−0.627493	−	0.309085i
$745$	1.11089e59			0.0537514
$746$		−	5.13321e59i		−	0.241476i
$747$	2.07645e60	−	1.59637e60i	0.949706	−	0.730130i
$748$	−1.00789e60			−0.448209
$749$		−	5.05950e59i		−	0.218771i
$750$	−8.40958e59	+	1.70728e60i	−0.353580	+	0.717825i
$751$	2.61001e60			1.06710			0.533549	−	0.845769i	$-0.320858\pi$
$751$	2.61001e60			1.06710			0.533549	+	0.845769i	$0.320858\pi$
$752$		−	4.00139e59i		−	0.159087i
$753$	−2.87770e60	−	1.41747e60i	−1.11263	−	0.548051i
$754$	2.87737e60			1.08193
$755$			5.79203e59i			0.211809i
$756$	−3.68749e59	+	7.38802e58i	−0.131152	+	0.0262767i
$757$	−1.44876e60			−0.501168			−0.250584	−	0.968095i	$-0.580623\pi$
$757$	−1.44876e60			−0.501168			−0.250584	+	0.968095i	$0.580623\pi$
$758$			4.76050e59i			0.160177i
$759$	−2.63785e59	+	5.35527e59i	−0.0863322	+	0.175269i
$760$	−6.11328e59			−0.194621
$761$			2.77473e60i			0.859295i	0.902997	+	0.429647i	$0.141362\pi$
$761$			2.77473e60i			0.859295i	−0.902997	+	0.429647i	$0.858638\pi$
$762$	−1.44621e60	−	7.12361e59i	−0.435689	−	0.214608i
$763$	−1.70613e59			−0.0500030
$764$		−	1.83523e60i		−	0.523276i
$765$	9.17685e59	+	1.19367e60i	0.254568	+	0.331125i
$766$	6.69362e60			1.80658
$767$			5.16154e60i			1.35543i
$768$	−2.25954e60	+	4.58724e60i	−0.577345	+	1.17210i
$769$	−4.86078e59			−0.120852			−0.0604258	−	0.998173i	$-0.519246\pi$
$769$	−4.86078e59			−0.120852			−0.0604258	+	0.998173i	$0.519246\pi$
$770$		−	1.90873e59i		−	0.0461784i
$771$	−2.83405e59	−	1.39597e59i	−0.0667215	−	0.0328651i
$772$	1.37598e60			0.315246
$773$			9.44348e59i			0.210554i	0.994443	+	0.105277i	$0.0335729\pi$
$773$			9.44348e59i			0.210554i	−0.994443	+	0.105277i	$0.966427\pi$
$774$	−2.00572e59	+	1.54199e59i	−0.0435222	+	0.0334597i
$775$	−6.69490e60			−1.41387
$776$		−	1.60304e60i		−	0.329496i
$777$	−4.63523e59	+	9.41027e59i	−0.0927320	+	0.188261i
$778$	2.18476e60			0.425434
$779$		−	9.29133e60i		−	1.76113i
$780$	8.62053e59	+	4.24623e59i	0.159055	+	0.0783460i
$781$	−2.12006e60			−0.380783
$782$			3.40896e60i			0.596047i
$783$	1.18110e60	+	5.89508e60i	0.201043	+	1.00344i
$784$	7.08769e60			1.17454
$785$		−	4.02283e60i		−	0.649035i
$786$	2.09129e60	−	4.24566e60i	0.328504	−	0.666918i
$787$	7.45701e60			1.14050			0.570250	−	0.821471i	$-0.306846\pi$
$787$	7.45701e60			1.14050			0.570250	+	0.821471i	$0.306846\pi$
$788$		−	7.05548e60i		−	1.05069i
$789$	−5.72237e60	−	2.81868e60i	−0.829772	−	0.408722i
$790$	−1.40447e60			−0.198309
$791$		−	3.86605e59i		−	0.0531571i
$792$	1.07773e60	+	1.40184e60i	0.144305	+	0.187702i
$793$	−7.71175e60			−1.00558
$794$			4.17596e60i			0.530306i
$795$	1.65974e60	−	3.36955e60i	0.205273	−	0.416737i
$796$	−3.58390e60			−0.431699
$797$		−	1.68074e61i		−	1.97186i	−0.167165	−	0.985929i	$-0.553461\pi$
$797$		−	1.68074e61i		−	1.97186i	0.167165	−	0.985929i	$-0.446539\pi$
$798$	−2.76102e60	−	1.36000e60i	−0.315507	−	0.155410i
$799$	−1.48300e60			−0.165066
$800$			9.34692e60i			1.01339i
$801$	2.09508e60	−	1.61069e60i	0.221268	−	0.170110i
$802$	−2.45449e61			−2.52522
$803$			8.76990e60i			0.878959i
$804$	2.39021e60	−	4.85252e60i	0.233378	−	0.473795i
$805$	−2.56012e59			−0.0243527
$806$			1.80802e61i			1.67559i
$807$	6.24214e60	+	3.07470e60i	0.563624	+	0.277625i
$808$	2.24304e60			0.197333
$809$			6.66039e59i			0.0570927i	0.999592	+	0.0285463i	$0.00908782\pi$
$809$			6.66039e59i			0.0570927i	−0.999592	+	0.0285463i	$0.990912\pi$
$810$	−1.30145e60	+	4.89322e60i	−0.108703	+	0.408704i
$811$	2.13914e61			1.74101			0.870506	−	0.492159i	$-0.163792\pi$
$811$	2.13914e61			1.74101			0.870506	+	0.492159i	$0.163792\pi$
$812$		−	1.72598e60i		−	0.136886i
$813$	4.16276e60	−	8.45108e60i	0.321721	−	0.653147i
$814$	−9.45412e60			−0.712047
$815$		−	3.18084e60i		−	0.233470i
$816$	1.95358e61	+	9.62276e60i	1.39745	+	0.688345i
$817$	−8.21076e59			−0.0572427
$818$			2.13528e61i			1.45090i
$819$	−1.53834e60	−	2.00098e60i	−0.101881	−	0.132520i
$820$	4.38807e60			0.283258
$821$			4.66180e59i			0.0293324i	0.999892	+	0.0146662i	$0.00466856\pi$
$821$			4.66180e59i			0.0293324i	−0.999892	+	0.0146662i	$0.995331\pi$
$822$	1.42955e61	−	2.90221e61i	0.876779	−	1.78000i
$823$	−8.85863e60			−0.529627			−0.264813	−	0.964300i	$-0.585310\pi$
$823$	−8.85863e60			−0.529627			−0.264813	+	0.964300i	$0.585310\pi$
$824$		−	1.18357e61i		−	0.689799i
$825$	7.55620e60	+	3.72197e60i	0.429310	+	0.211466i
$826$	7.80748e60			0.432444
$827$			3.29341e60i			0.177840i	0.996039	+	0.0889200i	$0.0283415\pi$
$827$			3.29341e60i			0.177840i	−0.996039	+	0.0889200i	$0.971658\pi$
$828$	−3.60414e60	+	2.77085e60i	−0.189742	+	0.145873i
$829$	−9.53526e60			−0.489427			−0.244713	−	0.969595i	$-0.578694\pi$
$829$	−9.53526e60			−0.489427			−0.244713	+	0.969595i	$0.578694\pi$
$830$			1.01233e61i			0.506619i
$831$	−1.70579e61	+	3.46303e61i	−0.832345	+	1.68980i
$832$	4.09233e60			0.194707
$833$		−	2.62685e61i		−	1.21868i
$834$	−3.55082e60	−	1.74903e60i	−0.160636	−	0.0791245i
$835$	9.87380e60			0.435581
$836$		−	1.10001e61i		−	0.473223i
$837$	−3.70423e61	+	7.42154e60i	−1.55404	+	0.311358i
$838$	−4.56961e61			−1.86963
$839$			3.25695e61i			1.29960i	0.760105	+	0.649800i	$0.225147\pi$
$839$			3.25695e61i			1.29960i	−0.760105	+	0.649800i	$0.774853\pi$
$840$	−3.35080e59	+	6.80267e59i	−0.0130402	+	0.0264737i
$841$	−1.24658e60			−0.0473155
$842$		−	5.57679e61i		−	2.06457i
$843$	5.59218e60	+	2.75455e60i	0.201931	+	0.0994652i
$844$	1.23429e61			0.434734
$845$		−	3.11296e60i		−	0.106950i
$846$	−3.03965e60	−	3.95378e60i	−0.101870	−	0.132506i
$847$	4.43407e60			0.144961
$848$		−	5.43275e61i		−	1.73263i
$849$	1.93625e60	−	3.93090e60i	0.0602421	−	0.122301i
$850$	4.81000e61			1.45998
$851$			1.26805e61i			0.375506i
$852$	−1.44834e61	−	7.13410e60i	−0.418445	−	0.206114i
$853$	6.82673e61			1.92434			0.962172	−	0.272442i	$-0.0878312\pi$
$853$	6.82673e61			1.92434			0.962172	+	0.272442i	$0.0878312\pi$
$854$			1.16650e61i			0.320826i
$855$	−1.30277e61	+	1.00156e61i	−0.349605	+	0.268775i
$856$	−1.81160e61			−0.474366
$857$		−	3.19362e61i		−	0.815993i	−0.912983	−	0.407997i	$-0.866228\pi$
$857$		−	3.19362e61i		−	0.815993i	0.912983	−	0.407997i	$-0.133772\pi$
$858$	1.00515e61	−	2.04062e61i	0.250610	−	0.508780i
$859$	−1.70391e61			−0.414564			−0.207282	−	0.978281i	$-0.566462\pi$
$859$	−1.70391e61			−0.414564			−0.207282	+	0.978281i	$0.566462\pi$
$860$		−	3.87774e59i		−	0.00920686i
$861$	−1.03391e61	−	5.09274e60i	−0.239561	−	0.118001i
$862$	−5.78348e60			−0.130779
$863$			7.38147e61i			1.62898i	0.580177	+	0.814491i	$0.302984\pi$
$863$			7.38147e61i			1.62898i	−0.580177	+	0.814491i	$0.697016\pi$
$864$	1.03614e61	+	5.17156e61i	0.223167	+	1.11387i
$865$	−1.09739e61			−0.230687
$866$			1.20079e62i			2.46371i
$867$	1.35992e61	−	2.76087e61i	0.272341	−	0.552898i
$868$	1.08453e61			0.211997
$869$			1.31840e61i			0.251555i
$870$	−2.08461e61	−	1.02682e61i	−0.388257	−	0.191244i
$871$	3.63032e61			0.660029
$872$			6.10893e60i			0.108422i
$873$	−2.62632e61	−	3.41615e61i	−0.455040	−	0.591886i
$874$	−3.72054e61			−0.629312
$875$			7.66164e60i			0.126518i
$876$	−2.95111e61	+	5.99123e61i	−0.475772	+	0.965895i
$877$	2.50109e61			0.393675			0.196837	−	0.980436i	$-0.436933\pi$
$877$	2.50109e61			0.393675			0.196837	+	0.980436i	$0.436933\pi$
$878$		−	4.61590e61i		−	0.709368i
$879$	−5.54981e61	−	2.73367e61i	−0.832744	−	0.410186i
$880$	−1.47397e61			−0.215950
$881$			1.27595e61i			0.182532i	0.995827	+	0.0912659i	$0.0290913\pi$
$881$			1.27595e61i			0.182532i	−0.995827	+	0.0912659i	$0.970909\pi$
$882$	7.00336e61	−	5.38415e61i	0.978286	−	0.752102i
$883$	9.99745e61			1.36369			0.681843	−	0.731498i	$-0.261179\pi$
$883$	9.99745e61			1.36369			0.681843	+	0.731498i	$0.261179\pi$
$884$		−	5.15124e61i		−	0.686143i
$885$	1.84195e61	−	3.73945e61i	0.239590	−	0.486407i
$886$	−6.37368e61			−0.809622
$887$			2.07075e60i			0.0256881i	0.999918	+	0.0128441i	$0.00408850\pi$
$887$			2.07075e60i			0.0256881i	−0.999918	+	0.0128441i	$0.995911\pi$
$888$	3.36943e61	+	1.65968e61i	0.408210	+	0.201073i
$889$	−6.49004e60			−0.0767910
$890$			1.02141e61i			0.118035i
$891$	4.59337e61	+	1.22170e61i	0.518441	+	0.137890i
$892$	−9.56926e61			−1.05491
$893$		−	1.61855e61i		−	0.174279i
$894$	8.84892e60	−	1.79647e61i	0.0930684	−	0.188944i
$895$	2.91998e61			0.299983
$896$			1.68504e61i			0.169100i
$897$	−2.73703e61	−	1.34818e61i	−0.268311	−	0.132162i
$898$	5.04878e61			0.483485
$899$		−	1.73381e62i		−	1.62199i
$900$	3.90963e61	+	5.08539e61i	0.357308	+	0.464763i
$901$	−2.01349e62			−1.79775
$902$		−	1.03873e62i		−	0.906076i
$903$	−4.50046e59	+	9.13667e59i	−0.00383543	+	0.00778655i
$904$	−1.38427e61			−0.115262
$905$			4.95504e61i			0.403113i
$906$	9.36657e61	+	4.61370e61i	0.744541	+	0.366739i
$907$	−2.16590e62			−1.68223			−0.841116	−	0.540855i	$-0.818101\pi$
$907$	−2.16590e62			−1.68223			−0.841116	+	0.540855i	$0.818101\pi$
$908$		−	6.84644e61i		−	0.519591i
$909$	4.78002e61	−	3.67486e61i	0.354477	−	0.272520i
$910$	9.75534e60			0.0706925
$911$			7.66051e61i			0.542465i	0.962514	+	0.271232i	$0.0874312\pi$
$911$			7.66051e61i			0.542465i	−0.962514	+	0.271232i	$0.912569\pi$
$912$	−1.05023e62	+	2.13213e62i	−0.726761	+	1.47544i
$913$	9.50295e61			0.642647
$914$			1.16738e62i			0.771509i
$915$	5.58703e61	+	2.75201e61i	0.360860	+	0.177749i
$916$	9.22589e61			0.582376
$917$		−	1.90529e61i		−	0.117546i
$918$	2.66133e62	−	5.33206e61i	1.60473	−	0.321513i
$919$	−1.48046e62			−0.872511			−0.436255	−	0.899823i	$-0.643696\pi$
$919$	−1.48046e62			−0.872511			−0.436255	+	0.899823i	$0.643696\pi$
$920$			9.16675e60i			0.0528045i
$921$	−9.91600e61	+	2.01311e62i	−0.558321	+	1.13348i
$922$	1.14992e62			0.632874
$923$		−	1.08355e62i		−	0.582923i
$924$	−1.22406e61	−	6.02936e60i	−0.0643711	−	0.0317074i
$925$	1.78921e62			0.919780
$926$			3.58328e62i			1.80073i
$927$	−1.93909e62	−	2.52224e62i	−0.952626	−	1.23911i
$928$	−2.42061e62			−1.16257
$929$			8.02744e59i			0.00376918i	0.999998	+	0.00188459i	$0.000599884\pi$
$929$			8.02744e59i			0.00376918i	−0.999998	+	0.00188459i	$0.999400\pi$
$930$	6.45210e61	−	1.30988e62i	0.296182	−	0.601298i
$931$	2.86694e62			1.28669
$932$		−	7.17387e61i		−	0.314789i
$933$	1.36740e62	+	6.73542e61i	0.586653	+	0.288968i
$934$	2.88222e62			1.20905
$935$			5.46285e61i			0.224066i
$936$	−7.16468e61	+	5.50818e61i	−0.287345	+	0.220910i
$937$	−6.48396e61			−0.254278			−0.127139	−	0.991885i	$-0.540579\pi$
$937$	−6.48396e61			−0.254278			−0.127139	+	0.991885i	$0.540579\pi$
$938$		−	5.49131e61i		−	0.210580i
$939$	9.80694e61	−	1.99097e62i	0.367753	−	0.746598i
$940$	7.64400e60			0.0280308
$941$			4.63115e62i			1.66076i	0.557199	+	0.830379i	$0.311876\pi$
$941$			4.63115e62i			1.66076i	−0.557199	+	0.830379i	$0.688124\pi$
$942$	−6.50551e62	−	3.20443e62i	−2.28146	−	1.12378i
$943$	−1.39322e62			−0.477830
$944$		−	6.02914e62i		−	2.02229i
$945$	4.00436e60	+	1.99865e61i	0.0131361	+	0.0655645i
$946$	−9.17926e60			−0.0294506
$947$		−	2.65145e62i		−	0.832020i	−0.909360	−	0.416010i	$-0.863428\pi$
$947$		−	2.65145e62i		−	0.832020i	0.909360	−	0.416010i	$-0.136572\pi$
$948$	−4.43648e61	+	9.00678e61i	−0.136164	+	0.276436i
$949$	−4.48222e62			−1.34556
$950$			5.24963e62i			1.54146i
$951$	3.40815e62	+	1.67876e62i	0.978877	+	0.482167i
$952$	4.06497e61			0.114204
$953$		−	1.92239e62i		−	0.528313i	−0.964480	−	0.264156i	$-0.914907\pi$
$953$		−	1.92239e62i		−	0.528313i	0.964480	−	0.264156i	$-0.0850935\pi$
$954$	−4.12698e62	−	5.36811e62i	−1.10947	−	1.44313i
$955$	−9.94711e61			−0.261593
$956$			3.79652e62i			0.976719i
$957$	−9.63895e61	+	1.95686e62i	−0.242593	+	0.492504i
$958$	3.62371e62			0.892232
$959$		−	1.30240e62i		−	0.313729i
$960$	−2.96483e61	−	1.46039e61i	−0.0698721	−	0.0344170i
$961$	6.55753e62			1.51199
$962$		−	4.83192e62i		−	1.09004i
$963$	−3.86059e62	+	2.96801e62i	−0.852122	+	0.655108i
$964$	−2.11330e62			−0.456399
$965$		−	7.45793e61i		−	0.157596i
$966$	−2.03929e61	+	4.14010e61i	−0.0421658	+	0.0856035i
$967$	4.09346e62			0.828200			0.414100	−	0.910231i	$-0.364096\pi$
$967$	4.09346e62			0.828200			0.414100	+	0.910231i	$0.364096\pi$
$968$		−	1.58766e62i		−	0.314322i
$969$	7.90215e62	+	3.89237e62i	1.53090	+	0.754075i
$970$	1.66547e62			0.315741
$971$		−	3.32748e62i		−	0.617321i	−0.951172	−	0.308661i	$-0.900119\pi$
$971$		−	3.32748e62i		−	0.617321i	0.951172	−	0.308661i	$-0.0998807\pi$
$972$	2.72689e62	+	2.38030e62i	0.495081	+	0.432156i
$973$	−1.59348e61			−0.0283123
$974$		−	3.12162e61i		−	0.0542802i
$975$	−1.90227e62	+	3.86191e62i	−0.323723	+	0.657211i
$976$	9.00800e62			1.50031
$977$			6.87320e62i			1.12040i	0.828357	+	0.560200i	$0.189276\pi$
$977$			6.87320e62i			1.12040i	−0.828357	+	0.560200i	$0.810724\pi$
$978$	−5.14389e62	−	2.53373e62i	−0.820683	−	0.404245i
$979$	9.58823e61			0.149728
$980$			1.35399e62i			0.206951i
$981$	1.00085e62	+	1.30184e62i	0.149733	+	0.194764i
$982$	−1.56529e63			−2.29220
$983$		−	2.59367e62i		−	0.371784i	−0.982570	−	0.185892i	$-0.940483\pi$
$983$		−	2.59367e62i		−	0.371784i	0.982570	−	0.185892i	$-0.0595175\pi$
$984$	−1.82350e62	+	3.70201e62i	−0.255864	+	0.519446i
$985$	−3.82413e62			−0.525256
$986$			1.24567e63i			1.67489i
$987$	−1.80107e61	−	8.87154e60i	−0.0237066	−	0.0116772i
$988$	5.62206e62			0.724436
$989$			1.23119e61i			0.0155311i
$990$	−1.45643e62	+	1.11970e62i	−0.179867	+	0.138281i
$991$	−1.62922e63			−1.96985			−0.984925	−	0.172983i	$-0.944660\pi$
$991$	−1.62922e63			−1.96985			−0.984925	+	0.172983i	$0.944660\pi$
$992$		−	1.52101e63i		−	1.80048i
$993$	3.86842e62	−	7.85353e62i	0.448332	−	0.910187i
$994$	−1.63900e62			−0.185979
$995$			1.94250e62i			0.215812i
$996$	6.49202e62	+	3.19778e62i	0.706210	+	0.347859i
$997$	9.08022e62			0.967159			0.483580	−	0.875300i	$-0.339336\pi$
$997$	9.08022e62			0.967159			0.483580	+	0.875300i	$0.339336\pi$
$998$			8.72983e62i			0.910467i
$999$	9.89951e62	−	1.98340e62i	1.01097	−	0.202551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.43.b.b.2.3	✓	12
3.2	odd	2	inner	3.43.b.b.2.10	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.43.b.b.2.3	✓	12	1.1	even	1	trivial
3.43.b.b.2.10	yes	12	3.2	odd	2	inner

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:	\( k \)	\(=\)	\( 43 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.69968e6i q^{2} +(-4.62216e9 + 9.38374e9i) q^{3} -2.89024e12 q^{4} +1.56653e14i q^{5} +(2.53331e16 + 1.24784e16i) q^{6} +1.13686e17 q^{7} -4.07061e18i q^{8} +(-6.66902e19 - 8.67463e19i) q^{9} +O(q^{10})\)	\(q-2.69968e6i q^{2} +(-4.62216e9 + 9.38374e9i) q^{3} -2.89024e12 q^{4} +1.56653e14i q^{5} +(2.53331e16 + 1.24784e16i) q^{6} +1.13686e17 q^{7} -4.07061e18i q^{8} +(-6.66902e19 - 8.67463e19i) q^{9} +4.22913e20 q^{10} -3.96998e21i q^{11} +(1.33591e22 - 2.71212e22i) q^{12} +2.02902e23 q^{13} -3.06915e23i q^{14} +(-1.46999e24 - 7.24076e23i) q^{15} -2.37007e25 q^{16} +8.78401e25i q^{17} +(-2.34188e26 + 1.80042e26i) q^{18} -9.58686e26 q^{19} -4.52764e26i q^{20} +(-5.25473e26 + 1.06680e27i) q^{21} -1.07177e28 q^{22} +1.43753e28i q^{23} +(3.81976e28 + 1.88150e28i) q^{24} +2.02834e29 q^{25} -5.47771e29i q^{26} +(1.12226e30 - 2.24848e29i) q^{27} -3.28578e29 q^{28} +5.25287e30i q^{29} +(-1.95477e30 + 3.96851e30i) q^{30} -3.30069e31 q^{31} +4.60817e31i q^{32} +(3.72532e31 + 1.83499e31i) q^{33} +2.37140e32 q^{34} +1.78092e31i q^{35} +(1.92750e32 + 2.50717e32i) q^{36} +8.82106e32 q^{37} +2.58815e33i q^{38} +(-9.37846e32 + 1.90398e33i) q^{39} +6.37673e32 q^{40} +9.69173e33i q^{41} +(2.88001e33 + 1.41861e33i) q^{42} +8.56460e32 q^{43} +1.14742e34i q^{44} +(1.35891e34 - 1.04472e34i) q^{45} +3.88088e34 q^{46} +1.68830e34i q^{47} +(1.09549e35 - 2.22402e35i) q^{48} -2.99049e35 q^{49} -5.47586e35i q^{50} +(-8.24269e35 - 4.06011e35i) q^{51} -5.86434e35 q^{52} +2.29223e36i q^{53} +(-6.07019e35 - 3.02974e36i) q^{54} +6.21909e35 q^{55} -4.62769e35i q^{56} +(4.43120e36 - 8.99606e36i) q^{57} +1.41811e37 q^{58} +2.54386e37i q^{59} +(4.24862e36 + 2.09275e36i) q^{60} -3.80073e37 q^{61} +8.91081e37i q^{62} +(-7.58171e36 - 9.86180e36i) q^{63} +2.01690e37 q^{64} +3.17852e37i q^{65} +(4.95388e37 - 1.00572e38i) q^{66} +1.78920e38 q^{67} -2.53878e38i q^{68} +(-1.34894e38 - 6.64450e37i) q^{69} +4.80791e37 q^{70} -5.34024e38i q^{71} +(-3.53111e38 + 2.71470e38i) q^{72} -2.20906e39 q^{73} -2.38141e39i q^{74} +(-9.37529e38 + 1.90334e39i) q^{75} +2.77083e39 q^{76} -4.51329e38i q^{77} +(5.14014e39 + 2.53188e39i) q^{78} -3.32093e39 q^{79} -3.71279e39i q^{80} +(-3.07734e39 + 1.15703e40i) q^{81} +2.61646e40 q^{82} +2.39370e40i q^{83} +(1.51874e39 - 3.08329e39i) q^{84} -1.37604e40 q^{85} -2.31217e39i q^{86} +(-4.92916e40 - 2.42796e40i) q^{87} -1.61602e40 q^{88} +2.41519e40i q^{89} +(-2.82042e40 - 3.66862e40i) q^{90} +2.30670e40 q^{91} -4.15480e40i q^{92} +(1.52563e41 - 3.09728e41i) q^{93} +4.55786e40 q^{94} -1.50181e41i q^{95} +(-4.32419e41 - 2.12997e41i) q^{96} +3.93809e41 q^{97} +8.07337e41i q^{98} +(-3.44381e41 + 2.64759e41i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16987205196 q^{3} - 34999503561888 q^{4} - 47\!\cdots\!88 q^{6}+ \cdots - 10\!\cdots\!60 q^{9}+O(q^{10}) \) 12 * q + 16987205196 * q^3 - 34999503561888 * q^4 - 47900661722006688 * q^6 - 41814621990917832 * q^7 - 10479496382139999060 * q^9	\( 12 q + 16987205196 q^{3} - 34999503561888 q^{4} - 47\!\cdots\!88 q^{6}+ \cdots - 45\!\cdots\!60 q^{99}+O(q^{100}) \) 12 * q + 16987205196 * q^3 - 34999503561888 * q^4 - 47900661722006688 * q^6 - 41814621990917832 * q^7 - 10479496382139999060 * q^9 - 1558337248111507093440 * q^10 + 49376377527162340879584 * q^12 + 104159867930333479443192 * q^13 - 448128019361693763840960 * q^15 + 30189980873605037368521216 * q^16 + 467763252053696004788775360 * q^18 + 1742192007122001281517876120 * q^19 + 9102775482298327940265250872 * q^21 - 4314702866032998614435578560 * q^22 + 213252820822149659960046027264 * q^24 - 1475565424466319180916113000660 * q^25 + 4679803843175845084152852300204 * q^27 - 12573192134196153529744555207488 * q^28 + 62452866934923176992747679887680 * q^30 - 82582711039551011868572590242696 * q^31 + 43265764437015443353441835054400 * q^33 - 263315485295738664634172504653056 * q^34 - 2405201397348598443590828900669856 * q^36 - 100843038556324004682477979351752 * q^37 - 10984759746962485956654149987757192 * q^39 + 14264689156939495925288444850785280 * q^40 - 2831182046378653470535212831685440 * q^42 - 71435403459183756447962146838987688 * q^43 + 171247471703495918987972144910848640 * q^45 - 368252835390302858087002506036095616 * q^46 + 393051873841281316858605019336751616 * q^48 + 503454865894447043110675471056528228 * q^49 - 26481340521925644924949289315966208 * q^51 + 6191863526932890484747245480405187008 * q^52 - 7762950205729260582930120693521404128 * q^54 + 7333373720922934220673629457367543680 * q^55 - 7646344343294849001862320271635263592 * q^57 - 40828097874719028971304350423217887040 * q^58 + 67409911106604936995672440638418037760 * q^60 - 86088392913854728749325031191744820616 * q^61 + 100834020234866427922563192954676937592 * q^63 - 141458640188438187587490744757105434624 * q^64 - 410927857618739095889759252898209949120 * q^66 + 637588020068292666249059312571603583128 * q^67 - 900977595682723671847728174824987261568 * q^69 + 1299257312773585175235999395827621799040 * q^70 - 1002862304292335428089280868557297904640 * q^72 + 4764698373378852277054437745609397085912 * q^73 + 10291654382848945060344626042064329363820 * q^75 - 10850719004897690517175553392098488304192 * q^76 - 1154864387471236146792590220220273542720 * q^78 - 16476824590026301016342599143867688625160 * q^79 - 29934898097734077284676557689524616295988 * q^81 + 12117774709574398821091222390193736370560 * q^82 - 115502524985324999123004799396029534507072 * q^84 + 179892388106464049414097141341403281134080 * q^85 - 108737363241821037303405571455850394882880 * q^87 + 262137413065538961600854476553505008040960 * q^88 - 246742532847586844558695609281104739341760 * q^90 + 85532425294904148246865639238250304747824 * q^91 + 153993445971229900791562733419639364858232 * q^93 + 711306705503600048406114202903471029729024 * q^94 - 1719405066055622809595776412409802129711104 * q^96 + 1090171163442244899022729083217627459542168 * q^97 - 4562402641239113129658705054315657608741760 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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