LMFDB - Embedded newform 3.43.b.b.2.7

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			2.7
Root			$19978.7i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.43.b.b.2.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+719233. i q^{2} +(5.62540e9 + 8.81895e9i) q^{3} +3.88075e12 q^{4} +4.30398e14i q^{5} +(-6.34288e15 + 4.04597e15i) q^{6} +6.12563e17 q^{7} +5.95439e18i q^{8} +(-4.61287e19 + 9.92202e19i) q^{9} +O(q^{10})$	\(q+719233. i q^{2} +(5.62540e9 + 8.81895e9i) q^{3} +3.88075e12 q^{4} +4.30398e14i q^{5} +(-6.34288e15 + 4.04597e15i) q^{6} +6.12563e17 q^{7} +5.95439e18i q^{8} +(-4.61287e19 + 9.92202e19i) q^{9} -3.09557e20 q^{10} +4.42160e21i q^{11} +(2.18308e22 + 3.42241e22i) q^{12} +2.30355e23 q^{13} +4.40576e23i q^{14} +(-3.79566e24 + 2.42116e24i) q^{15} +1.27851e25 q^{16} -5.34470e25i q^{17} +(-7.13625e25 - 3.31773e25i) q^{18} +4.65475e26 q^{19} +1.67027e27i q^{20} +(3.44591e27 + 5.40216e27i) q^{21} -3.18016e27 q^{22} -6.08212e28i q^{23} +(-5.25114e28 + 3.34958e28i) q^{24} +4.21311e28 q^{25} +1.65679e29i q^{26} +(-1.13451e30 + 1.51346e29i) q^{27} +2.37720e30 q^{28} +2.44634e30i q^{29} +(-1.74138e30 - 2.72996e30i) q^{30} -1.07051e31 q^{31} +3.53832e31i q^{32} +(-3.89939e31 + 2.48733e31i) q^{33} +3.84408e31 q^{34} +2.63646e32i q^{35} +(-1.79014e32 + 3.85049e32i) q^{36} -1.66606e33 q^{37} +3.34785e32i q^{38} +(1.29584e33 + 2.03149e33i) q^{39} -2.56276e33 q^{40} +1.33033e34i q^{41} +(-3.88541e33 + 2.47841e33i) q^{42} -3.17268e33 q^{43} +1.71591e34i q^{44} +(-4.27042e34 - 1.98537e34i) q^{45} +4.37446e34 q^{46} -2.20119e35i q^{47} +(7.19215e34 + 1.12751e35i) q^{48} +6.32601e34 q^{49} +3.03021e34i q^{50} +(4.71346e35 - 3.00660e35i) q^{51} +8.93949e35 q^{52} -2.97294e36i q^{53} +(-1.08853e35 - 8.15978e35i) q^{54} -1.90305e36 q^{55} +3.64744e36i q^{56} +(2.61848e36 + 4.10500e36i) q^{57} -1.75949e36 q^{58} +4.22305e36i q^{59} +(-1.47300e37 + 9.39592e36i) q^{60} -8.94271e36 q^{61} -7.69947e36i q^{62} +(-2.82568e37 + 6.07787e37i) q^{63} +3.07809e37 q^{64} +9.91442e37i q^{65} +(-1.78897e37 - 2.80457e37i) q^{66} -9.08617e37 q^{67} -2.07414e38i q^{68} +(5.36379e38 - 3.42144e38i) q^{69} -1.89623e38 q^{70} -2.90702e38i q^{71} +(-5.90795e38 - 2.74668e38i) q^{72} +1.55476e39 q^{73} -1.19828e39i q^{74} +(2.37004e38 + 3.71552e38i) q^{75} +1.80639e39 q^{76} +2.70851e39i q^{77} +(-1.46111e39 + 9.32009e38i) q^{78} -6.10044e39 q^{79} +5.50270e39i q^{80} +(-7.71679e39 - 9.15381e39i) q^{81} -9.56816e39 q^{82} +1.82245e40i q^{83} +(1.33727e40 + 2.09644e40i) q^{84} +2.30035e40 q^{85} -2.28190e39i q^{86} +(-2.15741e40 + 1.37616e40i) q^{87} -2.63279e40 q^{88} -7.51499e40i q^{89} +(1.42795e40 - 3.07143e40i) q^{90} +1.41107e41 q^{91} -2.36032e41i q^{92} +(-6.02205e40 - 9.44079e40i) q^{93} +1.58317e41 q^{94} +2.00340e41i q^{95} +(-3.12042e41 + 1.99044e41i) q^{96} +3.76825e41 q^{97} +4.54987e40i q^{98} +(-4.38712e41 - 2.03963e41i) 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 $

$2$			719233.i			0.342957i	0.985188	+	0.171479i	$0.0548544\pi$
$2$			719233.i			0.342957i	−0.985188	+	0.171479i	$0.945146\pi$
$3$	5.62540e9	+	8.81895e9i	0.537783	+	0.843083i
$3$	5.62540e9	+	8.81895e9i	0.537783	+	0.843083i
$4$	3.88075e12			0.882380
$5$			4.30398e14i			0.902610i	0.892370	+	0.451305i	$0.149041\pi$
$5$			4.30398e14i			0.902610i	−0.892370	+	0.451305i	$0.850959\pi$
$6$	−6.34288e15	+	4.04597e15i	−0.289141	+	0.184436i
$7$	6.12563e17			1.09671			0.548355	−	0.836246i	$-0.315254\pi$
$7$	6.12563e17			1.09671			0.548355	+	0.836246i	$0.315254\pi$
$8$			5.95439e18i			0.645576i
$9$	−4.61287e19	+	9.92202e19i	−0.421579	+	0.906792i
$10$	−3.09557e20			−0.309557
$11$			4.42160e21i			0.597493i	0.954332	+	0.298747i	$0.0965686\pi$
$11$			4.42160e21i			0.597493i	−0.954332	+	0.298747i	$0.903431\pi$
$12$	2.18308e22	+	3.42241e22i	0.474529	+	0.743920i
$13$	2.30355e23			0.932367			0.466183	−	0.884688i	$-0.345629\pi$
$13$	2.30355e23			0.932367			0.466183	+	0.884688i	$0.345629\pi$
$14$			4.40576e23i			0.376125i
$15$	−3.79566e24	+	2.42116e24i	−0.760976	+	0.485408i
$16$	1.27851e25			0.660976
$17$		−	5.34470e25i		−	0.773563i	−0.922171	−	0.386781i	$-0.873587\pi$
$17$		−	5.34470e25i		−	0.773563i	0.922171	−	0.386781i	$-0.126413\pi$
$18$	−7.13625e25	−	3.31773e25i	−0.310991	−	0.144584i
$19$	4.65475e26			0.651735			0.325867	−	0.945416i	$-0.394344\pi$
$19$	4.65475e26			0.651735			0.325867	+	0.945416i	$0.394344\pi$
$20$			1.67027e27i			0.796446i
$21$	3.44591e27	+	5.40216e27i	0.589792	+	0.924618i
$22$	−3.18016e27			−0.204915
$23$		−	6.08212e28i		−	1.54089i	−0.637509	−	0.770443i	$-0.720035\pi$
$23$		−	6.08212e28i		−	1.54089i	0.637509	−	0.770443i	$-0.279965\pi$
$24$	−5.25114e28	+	3.34958e28i	−0.544274	+	0.347180i
$25$	4.21311e28			0.185295
$26$			1.65679e29i			0.319762i
$27$	−1.13451e30	+	1.51346e29i	−0.991219	+	0.132231i
$28$	2.37720e30			0.967716
$29$			2.44634e30i			0.476605i	0.971191	+	0.238302i	$0.0765909\pi$
$29$			2.44634e30i			0.476605i	−0.971191	+	0.238302i	$0.923409\pi$
$30$	−1.74138e30	−	2.72996e30i	−0.166474	−	0.260982i
$31$	−1.07051e31			−0.514039			−0.257019	−	0.966406i	$-0.582740\pi$
$31$	−1.07051e31			−0.514039			−0.257019	+	0.966406i	$0.582740\pi$
$32$			3.53832e31i			0.872262i
$33$	−3.89939e31	+	2.48733e31i	−0.503737	+	0.321322i
$34$	3.84408e31			0.265299
$35$			2.63646e32i			0.989902i
$36$	−1.79014e32	+	3.85049e32i	−0.371993	+	0.800135i
$37$	−1.66606e33			−1.94739			−0.973697	−	0.227845i	$-0.926832\pi$
$37$	−1.66606e33			−1.94739			−0.973697	+	0.227845i	$0.926832\pi$
$38$			3.34785e32i			0.223517i
$39$	1.29584e33	+	2.03149e33i	0.501411	+	0.786063i
$40$	−2.56276e33			−0.582703
$41$			1.33033e34i			1.80093i	0.434924	+	0.900467i	$0.356775\pi$
$41$			1.33033e34i			1.80093i	−0.434924	+	0.900467i	$0.643225\pi$
$42$	−3.88541e33	+	2.47841e33i	−0.317104	+	0.202273i
$43$	−3.17268e33			−0.157975			−0.0789876	−	0.996876i	$-0.525169\pi$
$43$	−3.17268e33			−0.157975			−0.0789876	+	0.996876i	$0.525169\pi$
$44$			1.71591e34i			0.527217i
$45$	−4.27042e34	−	1.98537e34i	−0.818480	−	0.380522i
$46$	4.37446e34			0.528458
$47$		−	2.20119e35i		−	1.69279i	−0.532559	−	0.846393i	$-0.678770\pi$
$47$		−	2.20119e35i		−	1.69279i	0.532559	−	0.846393i	$-0.321230\pi$
$48$	7.19215e34	+	1.12751e35i	0.355461	+	0.557258i
$49$	6.32601e34			0.202774
$50$			3.03021e34i			0.0635481i
$51$	4.71346e35	−	3.00660e35i	0.652178	−	0.416009i
$52$	8.93949e35			0.822702
$53$		−	2.97294e36i		−	1.83397i	−0.398922	−	0.916985i	$-0.630615\pi$
$53$		−	2.97294e36i		−	1.83397i	0.398922	−	0.916985i	$-0.369385\pi$
$54$	−1.08853e35	−	8.15978e35i	−0.0453495	−	0.339946i
$55$	−1.90305e36			−0.539304
$56$			3.64744e36i			0.708010i
$57$	2.61848e36	+	4.10500e36i	0.350492	+	0.549467i
$58$	−1.75949e36			−0.163455
$59$			4.22305e36i			0.273989i	0.990572	+	0.136995i	$0.0437443\pi$
$59$			4.22305e36i			0.273989i	−0.990572	+	0.136995i	$0.956256\pi$
$60$	−1.47300e37	+	9.39592e36i	−0.671470	+	0.428315i
$61$	−8.94271e36			−0.288100			−0.144050	−	0.989570i	$-0.546013\pi$
$61$	−8.94271e36			−0.288100			−0.144050	+	0.989570i	$0.546013\pi$
$62$		−	7.69947e36i		−	0.176293i
$63$	−2.82568e37	+	6.07787e37i	−0.462350	+	0.994488i
$64$	3.07809e37			0.361827
$65$			9.91442e37i			0.841564i
$66$	−1.78897e37	−	2.80457e37i	−0.110200	−	0.172760i
$67$	−9.08617e37			−0.408141			−0.204070	−	0.978956i	$-0.565417\pi$
$67$	−9.08617e37			−0.408141			−0.204070	+	0.978956i	$0.565417\pi$
$68$		−	2.07414e38i		−	0.682577i
$69$	5.36379e38	−	3.42144e38i	1.29910	−	0.828662i
$70$	−1.89623e38			−0.339494
$71$		−	2.90702e38i		−	0.386387i	−0.981161	−	0.193194i	$-0.938115\pi$
$71$		−	2.90702e38i		−	0.386387i	0.981161	−	0.193194i	$-0.0618845\pi$
$72$	−5.90795e38	−	2.74668e38i	−0.585403	−	0.272161i
$73$	1.55476e39			1.15314			0.576571	−	0.817047i	$-0.304391\pi$
$73$	1.55476e39			1.15314			0.576571	+	0.817047i	$0.304391\pi$
$74$		−	1.19828e39i		−	0.667873i
$75$	2.37004e38	+	3.71552e38i	0.0996483	+	0.156219i
$76$	1.80639e39			0.575078
$77$			2.70851e39i			0.655277i
$78$	−1.46111e39	+	9.32009e38i	−0.269586	+	0.171962i
$79$	−6.10044e39			−0.861375			−0.430688	−	0.902501i	$-0.641729\pi$
$79$	−6.10044e39			−0.861375			−0.430688	+	0.902501i	$0.641729\pi$
$80$			5.50270e39i			0.596603i
$81$	−7.71679e39	−	9.15381e39i	−0.644542	−	0.764569i
$82$	−9.56816e39			−0.617643
$83$			1.82245e40i			0.912046i	0.889968	+	0.456023i	$0.150727\pi$
$83$			1.82245e40i			0.912046i	−0.889968	+	0.456023i	$0.849273\pi$
$84$	1.33727e40	+	2.09644e40i	0.520421	+	0.815865i
$85$	2.30035e40			0.698226
$86$		−	2.28190e39i		−	0.0541787i
$87$	−2.15741e40	+	1.37616e40i	−0.401817	+	0.256310i
$88$	−2.63279e40			−0.385727
$89$		−	7.51499e40i		−	0.868437i	−0.900808	−	0.434219i	$-0.857025\pi$
$89$		−	7.51499e40i		−	0.868437i	0.900808	−	0.434219i	$-0.142975\pi$
$90$	1.42795e40	−	3.07143e40i	0.130503	−	0.280703i
$91$	1.41107e41			1.02254
$92$		−	2.36032e41i		−	1.35965i
$93$	−6.02205e40	−	9.44079e40i	−0.276441	−	0.433377i
$94$	1.58317e41			0.580553
$95$			2.00340e41i			0.588262i
$96$	−3.12042e41	+	1.99044e41i	−0.735390	+	0.469088i
$97$	3.76825e41			0.714386			0.357193	−	0.934031i	$-0.383734\pi$
$97$	3.76825e41			0.714386			0.357193	+	0.934031i	$0.383734\pi$
$98$			4.54987e40i			0.0695427i
$99$	−4.38712e41	−	2.03963e41i	−0.541802	−	0.251891i
$100$	1.63500e41			0.163500
$101$			4.93112e41i			0.400126i	0.979783	+	0.200063i	$0.0641147\pi$
$101$			4.93112e41i			0.400126i	−0.979783	+	0.200063i	$0.935885\pi$
$102$	2.16245e41	+	3.39008e41i	0.142673	+	0.223669i
$103$	−1.64471e42			−0.884114			−0.442057	−	0.896987i	$-0.645751\pi$
$103$	−1.64471e42			−0.884114			−0.442057	+	0.896987i	$0.645751\pi$
$104$			1.37162e42i			0.601913i
$105$	−2.32508e42	+	1.48311e42i	−0.834570	+	0.532353i
$106$	2.13823e42			0.628973
$107$			6.41007e41i			0.154812i	0.997000	+	0.0774058i	$0.0246637\pi$
$107$			6.41007e41i			0.154812i	−0.997000	+	0.0774058i	$0.975336\pi$
$108$	−4.40275e42	+	5.87337e41i	−0.874632	+	0.116678i
$109$	1.04740e43			1.71457			0.857286	−	0.514841i	$-0.172149\pi$
$109$	1.04740e43			1.71457			0.857286	+	0.514841i	$0.172149\pi$
$110$		−	1.36874e42i		−	0.184958i
$111$	−9.37224e42	−	1.46929e43i	−1.04728	−	1.64182i
$112$	7.83170e42			0.724899
$113$		−	9.77601e42i		−	0.750783i	−0.926866	−	0.375391i	$-0.877508\pi$
$113$		−	9.77601e42i		−	0.750783i	0.926866	−	0.375391i	$-0.122492\pi$
$114$	−2.95245e42	+	1.88330e42i	−0.188443	+	0.120204i
$115$	2.61773e43			1.39082
$116$			9.49362e42i			0.420547i
$117$	−1.06260e43	+	2.28558e43i	−0.393066	+	0.845462i
$118$	−3.03736e42			−0.0939666
$119$		−	3.27396e43i		−	0.848375i
$120$	−1.44165e43	−	2.26008e43i	−0.313368	−	0.491267i
$121$	3.52131e43			0.643002
$122$		−	6.43189e42i		−	0.0988058i
$123$	−1.17321e44	+	7.48363e43i	−1.51834	+	0.968512i
$124$	−4.15439e43			−0.453578
$125$			1.15994e44i			1.06986i
$126$	−4.37140e43	−	2.03232e43i	−0.341067	−	0.158566i
$127$	2.09138e44			1.38215			0.691074	−	0.722784i	$-0.257138\pi$
$127$	2.09138e44			1.38215			0.691074	+	0.722784i	$0.257138\pi$
$128$			1.77755e44i			0.996353i
$129$	−1.78476e43	−	2.79797e43i	−0.0849563	−	0.133186i
$130$	−7.13078e43			−0.288620
$131$		−	3.11970e44i		−	1.07502i	−0.843258	−	0.537510i	$-0.819365\pi$
$131$		−	3.11970e44i		−	1.07502i	0.843258	−	0.537510i	$-0.180635\pi$
$132$	−1.51325e44	+	9.65270e43i	−0.444487	+	0.283528i
$133$	2.85133e44			0.714764
$134$		−	6.53507e43i		−	0.139975i
$135$	−6.51392e43	−	4.88291e44i	−0.119353	−	0.894684i
$136$	3.18244e44			0.499393
$137$		−	9.85372e44i		−	1.32577i	−0.748721	−	0.662885i	$-0.769332\pi$
$137$		−	9.85372e44i		−	1.32577i	0.748721	−	0.662885i	$-0.230668\pi$
$138$	2.46081e44	+	3.85782e44i	0.284196	+	0.445534i
$139$	−9.83575e44			−0.976106			−0.488053	−	0.872814i	$-0.662293\pi$
$139$	−9.83575e44			−0.976106			−0.488053	+	0.872814i	$0.662293\pi$
$140$			1.02314e45i			0.873470i
$141$	1.94122e45	−	1.23826e45i	1.42716	−	0.910351i
$142$	2.09083e44			0.132514
$143$			1.01854e45i			0.557083i
$144$	−5.89762e44	+	1.26854e45i	−0.278653	+	0.599367i
$145$	−1.05290e45			−0.430188
$146$			1.11823e45i			0.395478i
$147$	3.55863e44	+	5.57887e44i	0.109048	+	0.170955i
$148$	−6.46556e45			−1.71834
$149$		−	1.00621e45i		−	0.232154i	−0.993240	−	0.116077i	$-0.962968\pi$
$149$		−	1.00621e45i		−	0.232154i	0.993240	−	0.116077i	$-0.0370319\pi$
$150$	−2.67233e44	+	1.70461e44i	−0.0535763	+	0.0341751i
$151$	2.37605e45			0.414324			0.207162	−	0.978307i	$-0.433577\pi$
$151$	2.37605e45			0.414324			0.207162	+	0.978307i	$0.433577\pi$
$152$			2.77162e45i			0.420744i
$153$	5.30302e45	+	2.46544e45i	0.701460	+	0.326118i
$154$	−1.94805e45			−0.224732
$155$		−	4.60746e45i		−	0.463977i
$156$	5.02882e45	+	7.88369e45i	0.442435	+	0.693606i
$157$	−1.24226e46			−0.955699			−0.477850	−	0.878442i	$-0.658584\pi$
$157$	−1.24226e46			−0.955699			−0.477850	+	0.878442i	$0.658584\pi$
$158$		−	4.38764e45i		−	0.295415i
$159$	2.62182e46	−	1.67240e46i	1.54619	−	0.986278i
$160$	−1.52288e46			−0.787313
$161$		−	3.72568e46i		−	1.68991i
$162$	6.58372e45	−	5.55017e45i	0.262214	−	0.221050i
$163$	3.15531e46			1.10434			0.552170	−	0.833732i	$-0.313800\pi$
$163$	3.15531e46			1.10434			0.552170	+	0.833732i	$0.313800\pi$
$164$			5.16267e46i			1.58911i
$165$	−1.07054e46	−	1.67829e46i	−0.290028	−	0.454678i
$166$	−1.31077e46			−0.312793
$167$			1.26220e45i			0.0265512i	0.999912	+	0.0132756i	$0.00422587\pi$
$167$			1.26220e45i			0.0265512i	−0.999912	+	0.0132756i	$0.995774\pi$
$168$	−3.21666e46	+	2.05183e46i	−0.596911	+	0.380756i
$169$	−7.97759e45			−0.130693
$170$			1.65449e46i			0.239462i
$171$	−2.14718e46	+	4.61845e46i	−0.274758	+	0.590988i
$172$	−1.23124e46			−0.139394
$173$		−	8.47519e45i		−	0.0849535i	−0.999097	−	0.0424768i	$-0.986475\pi$
$173$		−	8.47519e45i		−	0.0849535i	0.999097	−	0.0424768i	$-0.0135248\pi$
$174$	−9.89781e45	−	1.55168e46i	−0.0879033	−	0.137806i
$175$	2.58080e46			0.203215
$176$			5.65307e46i			0.394929i
$177$	−3.72428e46	+	2.37563e46i	−0.230996	+	0.147347i
$178$	5.40503e46			0.297837
$179$			1.07332e47i			0.525793i	0.964824	+	0.262896i	$0.0846778\pi$
$179$			1.07332e47i			0.525793i	−0.964824	+	0.262896i	$0.915322\pi$
$180$	−1.65724e47	−	7.70474e46i	−0.722210	−	0.335765i
$181$	1.37701e47			0.534179			0.267089	−	0.963672i	$-0.413938\pi$
$181$	1.37701e47			0.534179			0.267089	+	0.963672i	$0.413938\pi$
$182$			1.01489e47i			0.350686i
$183$	−5.03063e46	−	7.88653e46i	−0.154935	−	0.242892i
$184$	3.62153e47			0.994759
$185$		−	7.17068e47i		−	1.75774i
$186$	6.79013e46	−	4.33126e46i	0.148630	−	0.0948075i
$187$	2.36321e47			0.462199
$188$		−	8.54226e47i		−	1.49368i
$189$	−6.94959e47	+	9.27092e46i	−1.08708	+	0.145019i
$190$	−1.44091e47			−0.201749
$191$			1.03491e48i			1.29778i	0.760882	+	0.648891i	$0.224767\pi$
$191$			1.03491e48i			1.29778i	−0.760882	+	0.648891i	$0.775233\pi$
$192$	1.73155e47	+	2.71455e47i	0.194585	+	0.305050i
$193$	1.24003e48			1.24947			0.624737	−	0.780835i	$-0.285206\pi$
$193$	1.24003e48			1.24947			0.624737	+	0.780835i	$0.285206\pi$
$194$			2.71025e47i			0.245004i
$195$	−8.74348e47	+	5.57726e47i	−0.709508	+	0.452579i
$196$	2.45497e47			0.178924
$197$			9.09881e47i			0.595928i	0.954577	+	0.297964i	$0.0963075\pi$
$197$			9.09881e47i			0.595928i	−0.954577	+	0.297964i	$0.903692\pi$
$198$	1.46697e47	−	3.15536e47i	0.0863877	−	0.185815i
$199$	−2.30862e48			−1.22303			−0.611516	−	0.791232i	$-0.709440\pi$
$199$	−2.30862e48			−1.22303			−0.611516	+	0.791232i	$0.709440\pi$
$200$			2.50865e47i			0.119622i
$201$	−5.11133e47	−	8.01305e47i	−0.219491	−	0.344097i
$202$	−3.54663e47			−0.137226
$203$			1.49854e48i			0.522697i
$204$	1.82918e48	−	1.16679e48i	0.575469	−	0.367078i
$205$	−5.72571e48			−1.62554
$206$		−	1.18293e48i		−	0.303213i
$207$	6.03469e48	+	2.80561e48i	1.39726	+	0.649605i
$208$	2.94511e48			0.616272
$209$			2.05814e48i			0.389407i
$210$	−1.06670e48	−	1.67228e48i	−0.182574	−	0.286222i
$211$	4.13084e48			0.639892			0.319946	−	0.947436i	$-0.396335\pi$
$211$	4.13084e48			0.639892			0.319946	+	0.947436i	$0.396335\pi$
$212$		−	1.15372e49i		−	1.61826i
$213$	2.56369e48	−	1.63531e48i	0.325757	−	0.207792i
$214$	−4.61034e47			−0.0530938
$215$		−	1.36552e48i		−	0.142590i
$216$	−9.01174e47	−	6.75531e48i	−0.0853650	−	0.639907i
$217$	−6.55756e48			−0.563752
$218$			7.53324e48i			0.588025i
$219$	8.74613e48	+	1.37113e49i	0.620140	+	0.972194i
$220$	−7.38526e48			−0.475871
$221$		−	1.23118e49i		−	0.721244i
$222$	1.05676e49	−	6.74083e48i	0.563072	−	0.359171i
$223$	−2.57057e49			−1.24631			−0.623156	−	0.782097i	$-0.714150\pi$
$223$	−2.57057e49			−1.24631			−0.623156	+	0.782097i	$0.714150\pi$
$224$			2.16744e49i			0.956619i
$225$	−1.94346e48	+	4.18026e48i	−0.0781163	+	0.168024i
$226$	7.03123e48			0.257486
$227$			2.24668e49i			0.749890i	0.927047	+	0.374945i	$0.122338\pi$
$227$			2.24668e49i			0.749890i	−0.927047	+	0.374945i	$0.877662\pi$
$228$	1.01617e49	+	1.59305e49i	0.309267	+	0.484839i
$229$	−1.22686e49			−0.340603			−0.170302	−	0.985392i	$-0.554474\pi$
$229$	−1.22686e49			−0.340603			−0.170302	+	0.985392i	$0.554474\pi$
$230$			1.88276e49i			0.476991i
$231$	−2.38862e49	+	1.52364e49i	−0.552453	+	0.352397i
$232$	−1.45664e49			−0.307684
$233$		−	8.48032e49i		−	1.63658i	−0.574804	−	0.818291i	$-0.694922\pi$
$233$		−	8.48032e49i		−	1.63658i	0.574804	−	0.818291i	$-0.305078\pi$
$234$	−1.64387e49	−	7.64255e48i	−0.289957	−	0.134805i
$235$	9.47387e49			1.52793
$236$			1.63886e49i			0.241763i
$237$	−3.43174e49	−	5.37995e49i	−0.463233	−	0.726211i
$238$	2.35474e49			0.290956
$239$		−	1.10383e49i		−	0.124895i	−0.998048	−	0.0624476i	$-0.980109\pi$
$239$		−	1.10383e49i		−	0.124895i	0.998048	−	0.0624476i	$-0.0198906\pi$
$240$	−4.85280e49	+	3.09549e49i	−0.502986	+	0.320843i
$241$	1.16885e50			1.11020			0.555102	−	0.831783i	$-0.312679\pi$
$241$	1.16885e50			1.11020			0.555102	+	0.831783i	$0.312679\pi$
$242$			2.53265e49i			0.220522i
$243$	3.73169e49	−	1.19548e50i	0.297971	−	0.954575i
$244$	−3.47044e49			−0.254213
$245$			2.72270e49i			0.183026i
$246$	−5.38247e49	−	8.43812e49i	−0.332158	−	0.520725i
$247$	1.07224e50			0.607656
$248$		−	6.37424e49i		−	0.331851i
$249$	−1.60721e50	+	1.02520e50i	−0.768931	+	0.490483i
$250$	−8.34270e49			−0.366916
$251$		−	1.03748e50i		−	0.419596i	−0.977745	−	0.209798i	$-0.932719\pi$
$251$		−	1.03748e50i		−	0.419596i	0.977745	−	0.209798i	$-0.0672806\pi$
$252$	−1.09657e50	+	2.35867e50i	−0.407969	+	0.877517i
$253$	2.68927e50			0.920669
$254$			1.50419e50i			0.474017i
$255$	1.29404e50	+	2.02866e50i	0.375494	+	0.588663i
$256$	7.52809e48			0.0201208
$257$			3.77243e50i			0.929020i	0.885568	+	0.464510i	$0.153770\pi$
$257$			3.77243e50i			0.929020i	−0.885568	+	0.464510i	$0.846230\pi$
$258$	2.01239e49	−	1.28366e49i	0.0456772	−	0.0291364i
$259$	−1.02057e51			−2.13573
$260$			3.84754e50i			0.742579i
$261$	−2.42726e50	−	1.12846e50i	−0.432181	−	0.200926i
$262$	2.24379e50			0.368685
$263$		−	1.30517e51i		−	1.97969i	−0.142160	−	0.989844i	$-0.545405\pi$
$263$		−	1.30517e51i		−	1.97969i	0.142160	−	0.989844i	$-0.454595\pi$
$264$	−1.48105e50	−	2.32185e50i	−0.207438	−	0.325200i
$265$	1.27955e51			1.65536
$266$			2.05077e50i			0.245133i
$267$	6.62743e50	−	4.22748e50i	0.732165	−	0.467031i
$268$	−3.52612e50			−0.360135
$269$			2.32608e50i			0.219698i	0.993948	+	0.109849i	$0.0350367\pi$
$269$			2.32608e50i			0.219698i	−0.993948	+	0.109849i	$0.964963\pi$
$270$	3.51195e50	−	4.68503e49i	0.306838	−	0.0409329i
$271$	−1.06179e51			−0.858388			−0.429194	−	0.903212i	$-0.641202\pi$
$271$	−1.06179e51			−0.858388			−0.429194	+	0.903212i	$0.641202\pi$
$272$		−	6.83326e50i		−	0.511306i
$273$	7.93782e50	+	1.24441e51i	0.549903	+	0.862083i
$274$	7.08712e50			0.454682
$275$			1.86287e50i			0.110712i
$276$	2.08155e51	−	1.32777e51i	1.14630	−	0.731195i
$277$	−2.52875e51			−1.29072			−0.645359	−	0.763879i	$-0.723292\pi$
$277$	−2.52875e51			−1.29072			−0.645359	+	0.763879i	$0.723292\pi$
$278$		−	7.07420e50i		−	0.334762i
$279$	4.93814e50	−	1.06216e51i	0.216708	−	0.466126i
$280$	−1.56985e51			−0.639057
$281$			1.17617e51i			0.444259i	0.975017	+	0.222130i	$0.0713008\pi$
$281$			1.17617e51i			0.444259i	−0.975017	+	0.222130i	$0.928699\pi$
$282$	8.90595e50	+	1.39619e51i	0.312211	+	0.489454i
$283$	−1.91704e51			−0.623903			−0.311951	−	0.950098i	$-0.600983\pi$
$283$	−1.91704e51			−0.623903			−0.311951	+	0.950098i	$0.600983\pi$
$284$		−	1.12814e51i		−	0.340940i
$285$	−1.76678e51	+	1.12699e51i	−0.495954	+	0.316357i
$286$	−7.32565e50			−0.191056
$287$			8.14910e51i			1.97510i
$288$	−3.51072e51	−	1.63218e51i	−0.790960	−	0.367727i
$289$	1.91712e51			0.401600
$290$		−	7.57280e50i		−	0.147536i
$291$	2.11979e51	+	3.32320e51i	0.384185	+	0.602287i
$292$	6.03363e51			1.01751
$293$			2.78723e51i			0.437474i	0.975784	+	0.218737i	$0.0701937\pi$
$293$			2.78723e51i			0.437474i	−0.975784	+	0.218737i	$0.929806\pi$
$294$	−4.01251e50	+	2.55949e50i	−0.0586303	+	0.0373989i
$295$	−1.81759e51			−0.247306
$296$		−	9.92035e51i		−	1.25719i
$297$	−6.69193e50	−	5.01635e51i	−0.0790071	−	0.592247i
$298$	7.23697e50			0.0796187
$299$		−	1.40105e52i		−	1.43667i
$300$	9.19755e50	+	1.44190e51i	0.0879277	+	0.137844i
$301$	−1.94347e51			−0.173253
$302$			1.70894e51i			0.142096i
$303$	−4.34873e51	+	2.77395e51i	−0.337340	+	0.215181i
$304$	5.95116e51			0.430781
$305$		−	3.84893e51i		−	0.260042i
$306$	−1.77323e51	+	3.81411e51i	−0.111844	+	0.240571i
$307$	2.54221e52			1.49729			0.748644	−	0.662972i	$-0.230705\pi$
$307$	2.54221e52			1.49729			0.748644	+	0.662972i	$0.230705\pi$
$308$			1.05110e52i			0.578204i
$309$	−9.25217e51	−	1.45046e52i	−0.475462	−	0.745382i
$310$	3.31384e51			0.159124
$311$			6.95034e51i			0.311916i	0.987764	+	0.155958i	$0.0498465\pi$
$311$			6.95034e51i			0.311916i	−0.987764	+	0.155958i	$0.950154\pi$
$312$	−1.20963e52	+	7.71591e51i	−0.507463	+	0.323699i
$313$	9.58372e51			0.375927			0.187963	−	0.982176i	$-0.439811\pi$
$313$	9.58372e51			0.375927			0.187963	+	0.982176i	$0.439811\pi$
$314$		−	8.93477e51i		−	0.327764i
$315$	−2.61590e52	−	1.21617e52i	−0.897635	−	0.417322i
$316$	−2.36743e52			−0.760061
$317$			5.10910e52i			1.53497i	0.641067	+	0.767485i	$0.278492\pi$
$317$			5.10910e52i			1.53497i	−0.641067	+	0.767485i	$0.721508\pi$
$318$	1.20284e52	+	1.88570e52i	0.338251	+	0.530277i
$319$	−1.08167e52			−0.284768
$320$			1.32480e52i			0.326589i
$321$	−5.65301e51	+	3.60592e51i	−0.130519	+	0.0832551i
$322$	2.67963e52			0.579565
$323$		−	2.48782e52i		−	0.504158i
$324$	−2.99469e52	−	3.55236e52i	−0.568732	−	0.674640i
$325$	9.70510e51			0.172762
$326$			2.26940e52i			0.378741i
$327$	5.89204e52	+	9.23696e52i	0.922067	+	1.44553i
$328$	−7.92129e52			−1.16264
$329$		−	1.34837e53i		−	1.85650i
$330$	1.20708e52	−	7.69969e51i	0.155935	−	0.0994673i
$331$	3.43408e52			0.416316			0.208158	−	0.978095i	$-0.433253\pi$
$331$	3.43408e52			0.416316			0.208158	+	0.978095i	$0.433253\pi$
$332$			7.07249e52i			0.804772i
$333$	7.68532e52	−	1.65307e53i	0.820981	−	1.76588i
$334$	−9.07819e50			−0.00910591
$335$		−	3.91067e52i		−	0.368392i
$336$	4.40564e52	+	6.90673e52i	0.389838	+	0.611150i
$337$	−1.06037e53			−0.881512			−0.440756	−	0.897627i	$-0.645290\pi$
$337$	−1.06037e53			−0.881512			−0.440756	+	0.897627i	$0.645290\pi$
$338$		−	5.73775e51i		−	0.0448220i
$339$	8.62141e52	−	5.49940e52i	0.632973	−	0.403758i
$340$	8.92707e52			0.616101
$341$		−	4.73337e52i		−	0.307135i
$342$	−3.32175e52	−	1.54432e52i	−0.202683	−	0.0942301i
$343$	−1.52353e53			−0.874326
$344$		−	1.88914e52i		−	0.101985i
$345$	1.47258e53	+	2.30857e53i	0.747959	+	1.17258i
$346$	6.09564e51			0.0291354
$347$			1.19367e53i			0.536990i	0.963281	+	0.268495i	$0.0865262\pi$
$347$			1.19367e53i			0.536990i	−0.963281	+	0.268495i	$0.913474\pi$
$348$	−8.37238e52	+	5.34054e52i	−0.354556	+	0.226163i
$349$	−1.24426e53			−0.496110			−0.248055	−	0.968746i	$-0.579791\pi$
$349$	−1.24426e53			−0.496110			−0.248055	+	0.968746i	$0.579791\pi$
$350$			1.85619e52i			0.0696939i
$351$	−2.61340e53	+	3.48633e52i	−0.924179	+	0.123288i
$352$	−1.56450e53			−0.521171
$353$			2.66027e53i			0.834942i	0.908690	+	0.417471i	$0.137084\pi$
$353$			2.66027e53i			0.834942i	−0.908690	+	0.417471i	$0.862916\pi$
$354$	−1.70863e52	−	2.67863e52i	−0.0505336	−	0.0792217i
$355$	1.25118e53			0.348757
$356$		−	2.91638e53i		−	0.766292i
$357$	2.88729e53	−	1.84174e53i	0.715250	−	0.456241i
$358$	−7.71966e52			−0.180324
$359$			2.19050e53i			0.482569i	0.970454	+	0.241285i	$0.0775687\pi$
$359$			2.19050e53i			0.482569i	−0.970454	+	0.241285i	$0.922431\pi$
$360$	1.18217e53	−	2.54277e53i	0.245655	−	0.528391i
$361$	−2.93428e53			−0.575242
$362$			9.90390e52i			0.183200i
$363$	1.98088e53	+	3.10543e53i	0.345795	+	0.542104i
$364$	5.47600e53			0.902266
$365$			6.69165e53i			1.04084i
$366$	5.67226e52	−	3.61820e52i	0.0833015	−	0.0531361i
$367$	6.25855e53			0.867933			0.433967	−	0.900929i	$-0.357114\pi$
$367$	6.25855e53			0.867933			0.433967	+	0.900929i	$0.357114\pi$
$368$		−	7.77607e53i		−	1.01849i
$369$	−1.31996e54	−	6.13664e53i	−1.63307	−	0.759236i
$370$	5.15739e53			0.602829
$371$		−	1.82111e54i		−	2.01133i
$372$	−2.33701e53	−	3.66373e53i	−0.243926	−	0.382404i
$373$	2.16622e53			0.213707			0.106853	−	0.994275i	$-0.465922\pi$
$373$	2.16622e53			0.213707			0.106853	+	0.994275i	$0.465922\pi$
$374$			1.69970e53i			0.158514i
$375$	−1.02295e54	+	6.52515e53i	−0.901980	+	0.575352i
$376$	1.31067e54			1.09282
$377$			5.63525e53i			0.444370i
$378$	−6.66795e52	−	4.99838e53i	−0.0497353	−	0.372822i
$379$	7.82952e52			0.0552474			0.0276237	−	0.999618i	$-0.491206\pi$
$379$	7.82952e52			0.0552474			0.0276237	+	0.999618i	$0.491206\pi$
$380$			7.77468e53i			0.519071i
$381$	1.17648e54	+	1.84438e54i	0.743295	+	1.16527i
$382$	−7.44341e53			−0.445083
$383$			4.34768e53i			0.246084i	0.992401	+	0.123042i	$0.0392650\pi$
$383$			4.34768e53i			0.246084i	−0.992401	+	0.123042i	$0.960735\pi$
$384$	−1.56762e54	+	9.99945e53i	−0.840009	+	0.535822i
$385$	−1.16574e54			−0.591460
$386$			8.91867e53i			0.428516i
$387$	1.46352e53	−	3.14794e53i	0.0665990	−	0.143251i
$388$	1.46236e54			0.630360
$389$			9.99232e53i			0.408061i	0.978965	+	0.204030i	$0.0654041\pi$
$389$			9.99232e53i			0.408061i	−0.978965	+	0.204030i	$0.934596\pi$
$390$	−4.01135e53	−	6.28860e53i	−0.155215	−	0.243331i
$391$	−3.25071e54			−1.19197
$392$			3.76675e53i			0.130906i
$393$	2.75125e54	−	1.75496e54i	0.906331	−	0.578127i
$394$	−6.54416e53			−0.204378
$395$		−	2.62562e54i		−	0.777486i
$396$	−1.70253e54	−	7.91529e53i	−0.478076	−	0.222263i
$397$	1.73946e54			0.463248			0.231624	−	0.972805i	$-0.425596\pi$
$397$	1.73946e54			0.463248			0.231624	+	0.972805i	$0.425596\pi$
$398$		−	1.66044e54i		−	0.419447i
$399$	1.60399e54	+	2.51457e54i	0.384388	+	0.602606i
$400$	5.38652e53			0.122475
$401$			1.67477e54i			0.361346i	0.983543	+	0.180673i	$0.0578275\pi$
$401$			1.67477e54i			0.361346i	−0.983543	+	0.180673i	$0.942172\pi$
$402$	5.76325e53	−	3.67624e53i	0.118010	−	0.0752760i
$403$	−2.46597e54			−0.479272
$404$			1.91365e54i			0.353063i
$405$	3.93978e54	−	3.32129e54i	0.690108	−	0.581771i
$406$	−1.07780e54			−0.179263
$407$		−	7.36664e54i		−	1.16356i
$408$	1.79025e54	+	2.80658e54i	0.268565	+	0.421030i
$409$	6.73242e54			0.959360			0.479680	−	0.877444i	$-0.340753\pi$
$409$	6.73242e54			0.959360			0.479680	+	0.877444i	$0.340753\pi$
$410$		−	4.11812e54i		−	0.557491i
$411$	8.68995e54	−	5.54311e54i	1.11773	−	0.712977i
$412$	−6.38272e54			−0.780125
$413$			2.58688e54i			0.300487i
$414$	−2.01789e54	+	4.34035e54i	−0.222787	+	0.479201i
$415$	−7.84381e54			−0.823222
$416$			8.15068e54i			0.813268i
$417$	−5.53300e54	−	8.67410e54i	−0.524933	−	0.822938i
$418$	−1.48029e54			−0.133550
$419$			1.05921e55i			0.908837i	0.890788	+	0.454419i	$0.150153\pi$
$419$			1.05921e55i			0.908837i	−0.890788	+	0.454419i	$0.849847\pi$
$420$	−9.02306e54	+	5.75560e54i	−0.736408	+	0.469737i
$421$	−1.98883e55			−1.54410			−0.772049	−	0.635564i	$-0.780768\pi$
$421$	−1.98883e55			−1.54410			−0.772049	+	0.635564i	$0.780768\pi$
$422$			2.97104e54i			0.219456i
$423$	2.18402e55	+	1.01538e55i	1.53500	+	0.713643i
$424$	1.77020e55			1.18397
$425$		−	2.25178e54i		−	0.143337i
$426$	1.17617e54	+	1.84389e54i	0.0712639	+	0.111721i
$427$	−5.47798e54			−0.315962
$428$			2.48759e54i			0.136603i
$429$	−8.98242e54	+	5.72968e54i	−0.469667	+	0.299590i
$430$	9.82124e53			0.0489023
$431$		−	1.50529e55i		−	0.713833i	−0.934136	−	0.356917i	$-0.883828\pi$
$431$		−	1.50529e55i		−	0.713833i	0.934136	−	0.356917i	$-0.116172\pi$
$432$	−1.45049e55	+	1.93498e54i	−0.655172	+	0.0874014i
$433$	−1.26409e55			−0.543916			−0.271958	−	0.962309i	$-0.587671\pi$
$433$	−1.26409e55			−0.543916			−0.271958	+	0.962309i	$0.587671\pi$
$434$		−	4.71641e54i		−	0.193343i
$435$	−5.92298e54	−	9.28546e54i	−0.231348	−	0.362685i
$436$	4.06469e55			1.51290
$437$		−	2.83108e55i		−	1.00425i
$438$	−9.86164e54	+	6.29051e54i	−0.333421	+	0.212681i
$439$	4.03133e55			1.29925			0.649626	−	0.760254i	$-0.274925\pi$
$439$	4.03133e55			1.29925			0.649626	+	0.760254i	$0.274925\pi$
$440$		−	1.13315e55i		−	0.348161i
$441$	−2.91811e54	+	6.27668e54i	−0.0854852	+	0.183874i
$442$	8.85502e54			0.247356
$443$			5.68553e55i			1.51458i	0.653078	+	0.757291i	$0.273477\pi$
$443$			5.68553e55i			1.51458i	−0.653078	+	0.757291i	$0.726523\pi$
$444$	−3.63713e55	−	5.70194e55i	−0.924096	−	1.44871i
$445$	3.23444e55			0.783860
$446$		−	1.84884e55i		−	0.427432i
$447$	8.87368e54	−	5.66031e54i	0.195725	−	0.124848i
$448$	1.88552e55			0.396820
$449$		−	1.67758e54i		−	0.0336907i	−0.999858	−	0.0168453i	$-0.994638\pi$
$449$		−	1.67758e54i		−	0.0336907i	0.999858	−	0.0168453i	$-0.00536229\pi$
$450$	−3.00658e54	−	1.39780e54i	−0.0576249	−	0.0267905i
$451$	−5.88218e55			−1.07605
$452$		−	3.79383e55i		−	0.662476i
$453$	1.33663e55	+	2.09543e55i	0.222817	+	0.349310i
$454$	−1.61588e55			−0.257180
$455$			6.07321e55i			0.922952i
$456$	−2.44428e55	+	1.55915e55i	−0.354722	+	0.226269i
$457$	−7.28018e55			−1.00903			−0.504513	−	0.863404i	$-0.668328\pi$
$457$	−7.28018e55			−1.00903			−0.504513	+	0.863404i	$0.668328\pi$
$458$		−	8.82396e54i		−	0.116812i
$459$	8.08900e54	+	6.06362e55i	0.102289	+	0.766770i
$460$	1.01588e56			1.22723
$461$			6.63328e55i			0.765612i	0.923829	+	0.382806i	$0.125042\pi$
$461$			6.63328e55i			0.765612i	−0.923829	+	0.382806i	$0.874958\pi$
$462$	−1.09586e55	−	1.71798e55i	−0.120857	−	0.189468i
$463$	−6.10716e55			−0.643633			−0.321817	−	0.946802i	$-0.604293\pi$
$463$	−6.10716e55			−0.643633			−0.321817	+	0.946802i	$0.604293\pi$
$464$			3.12767e55i			0.315024i
$465$	4.06330e55	−	2.59188e55i	0.391171	−	0.249519i
$466$	6.09932e55			0.561277
$467$		−	4.26288e55i		−	0.375015i	−0.982263	−	0.187508i	$-0.939959\pi$
$467$		−	4.26288e55i		−	0.375015i	0.982263	−	0.187508i	$-0.0600409\pi$
$468$	−4.12368e55	+	8.86978e55i	−0.346834	+	0.746019i
$469$	−5.56585e55			−0.447612
$470$			6.81392e55i			0.524013i
$471$	−6.98823e55	−	1.09555e56i	−0.513959	−	0.805734i
$472$	−2.51457e55			−0.176881
$473$		−	1.40283e55i		−	0.0943891i
$474$	3.86944e55	−	2.46822e55i	0.249059	−	0.158869i
$475$	1.96110e55			0.120763
$476$		−	1.27054e56i		−	0.748589i
$477$	2.94975e56	+	1.37138e56i	1.66303	+	0.773163i
$478$	7.93910e54			0.0428337
$479$		−	3.72427e56i		−	1.92307i	−0.274676	−	0.961537i	$-0.588571\pi$
$479$		−	3.72427e56i		−	1.92307i	0.274676	−	0.961537i	$-0.411429\pi$
$480$	−8.56683e55	−	1.34302e56i	−0.423403	−	0.663770i
$481$	−3.83784e56			−1.81569
$482$			8.40679e55i			0.380752i
$483$	3.28566e56	−	2.09585e56i	1.42473	−	0.908803i
$484$	1.36653e56			0.567372
$485$			1.62185e56i			0.644812i
$486$	8.59828e55	+	2.68396e55i	0.327378	+	0.102191i
$487$	−6.78807e53			−0.00247536			−0.00123768	−	0.999999i	$-0.500394\pi$
$487$	−6.78807e53			−0.00247536			−0.00123768	+	0.999999i	$0.500394\pi$
$488$		−	5.32484e55i		−	0.185990i
$489$	1.77499e56	+	2.78265e56i	0.593895	+	0.931050i
$490$	−1.95826e55			−0.0627700
$491$			1.83621e56i			0.563911i	0.959427	+	0.281956i	$0.0909831\pi$
$491$			1.83621e56i			0.563911i	−0.959427	+	0.281956i	$0.909017\pi$
$492$	−4.55294e56	+	2.90421e56i	−1.33975	+	0.854596i
$493$	1.30749e56			0.368684
$494$			7.71193e55i			0.208400i
$495$	8.77853e55	−	1.88821e56i	0.227359	−	0.489036i
$496$	−1.36866e56			−0.339767
$497$		−	1.78073e56i		−	0.423755i
$498$	−7.37360e55	−	1.15596e56i	−0.168215	−	0.263710i
$499$	−5.07875e56			−1.11083			−0.555413	−	0.831575i	$-0.687440\pi$
$499$	−5.07875e56			−1.11083			−0.555413	+	0.831575i	$0.687440\pi$
$500$			4.50145e56i			0.944023i
$501$	−1.11313e55	+	7.10040e54i	−0.0223849	+	0.0142788i
$502$	7.46189e55			0.143903
$503$		−	1.90538e56i		−	0.352414i	−0.984353	−	0.176207i	$-0.943617\pi$
$503$		−	1.90538e56i		−	0.352414i	0.984353	−	0.176207i	$-0.0563828\pi$
$504$	−3.61899e56	−	1.68252e56i	−0.642017	−	0.298482i
$505$	−2.12235e56			−0.361158
$506$			1.93421e56i			0.315750i
$507$	−4.48771e55	−	7.03540e55i	−0.0702843	−	0.110185i
$508$	8.11611e56			1.21958
$509$			4.15768e56i			0.599485i	0.954020	+	0.299742i	$0.0969007\pi$
$509$			4.15768e56i			0.599485i	−0.954020	+	0.299742i	$0.903099\pi$
$510$	−1.45908e56	+	9.30714e55i	−0.201886	+	0.128778i
$511$	9.52387e56			1.26466
$512$			7.87191e56i			1.00325i
$513$	−5.28086e56	+	7.04479e55i	−0.646012	+	0.0861794i
$514$	−2.71325e56			−0.318614
$515$		−	7.07881e56i		−	0.798011i
$516$	−6.92621e55	−	1.08582e56i	−0.0749638	−	0.117521i
$517$	9.73277e56			1.01143
$518$		−	7.34025e56i		−	0.732463i
$519$	7.47423e55	−	4.76763e55i	0.0716229	−	0.0456866i
$520$	−5.90343e56			−0.543293
$521$		−	2.00330e57i		−	1.77073i	−0.464894	−	0.885366i	$-0.653908\pi$
$521$		−	2.00330e57i		−	1.77073i	0.464894	−	0.885366i	$-0.346092\pi$
$522$	8.11629e55	−	1.74577e56i	0.0689092	−	0.148220i
$523$	9.89621e56			0.807111			0.403556	−	0.914955i	$-0.367774\pi$
$523$	9.89621e56			0.807111			0.403556	+	0.914955i	$0.367774\pi$
$524$		−	1.21068e57i		−	0.948576i
$525$	1.45180e56	+	2.27599e56i	0.109285	+	0.171327i
$526$	9.38722e56			0.678948
$527$			5.72156e56i			0.397641i
$528$	−4.98542e56	+	3.18008e56i	−0.332958	+	0.212386i
$529$	−2.14121e57			−1.37433
$530$			9.20292e56i			0.567718i
$531$	−4.19012e56	−	1.94804e56i	−0.248451	−	0.115508i
$532$	1.10653e57			0.630694
$533$			3.06447e57i			1.67913i
$534$	3.04055e56	+	4.76667e56i	0.160172	+	0.251101i
$535$	−2.75888e56			−0.139735
$536$		−	5.41025e56i		−	0.263486i
$537$	−9.46554e56	+	6.03784e56i	−0.443287	+	0.282762i
$538$	−1.67299e56			−0.0753470
$539$			2.79711e56i			0.121156i
$540$	−2.52789e56	−	1.89494e57i	−0.105315	−	0.789452i
$541$	−1.81112e57			−0.725779			−0.362890	−	0.931832i	$-0.618210\pi$
$541$	−1.81112e57			−0.725779			−0.362890	+	0.931832i	$0.618210\pi$
$542$		−	7.63675e56i		−	0.294390i
$543$	7.74622e56	+	1.21438e57i	0.287272	+	0.450357i
$544$	1.89112e57			0.674750
$545$			4.50799e57i			1.54759i
$546$	−8.95024e56	+	5.70914e56i	−0.295658	+	0.188593i
$547$	−1.19436e57			−0.379666			−0.189833	−	0.981816i	$-0.560795\pi$
$547$	−1.19436e57			−0.379666			−0.189833	+	0.981816i	$0.560795\pi$
$548$		−	3.82398e57i		−	1.16983i
$549$	4.12516e56	−	8.87298e56i	0.121457	−	0.261246i
$550$	−1.33984e56			−0.0379696
$551$			1.13871e57i			0.310620i
$552$	2.03725e57	+	3.19381e57i	0.534964	+	0.838664i
$553$	−3.73691e57			−0.944679
$554$		−	1.81876e57i		−	0.442661i
$555$	6.32379e57	−	4.03380e57i	1.48192	−	0.945282i
$556$	−3.81701e57			−0.861296
$557$		−	2.13279e57i		−	0.463435i	−0.972783	−	0.231717i	$-0.925566\pi$
$557$		−	2.13279e57i		−	0.463435i	0.972783	−	0.231717i	$-0.0744344\pi$
$558$	7.63943e56	+	3.55167e56i	0.159861	+	0.0743215i
$559$	−7.30842e56			−0.147291
$560$			3.37075e57i			0.654301i
$561$	1.32940e57	+	2.08410e57i	0.248563	+	0.389672i
$562$	−8.45938e56			−0.152362
$563$		−	5.72379e57i		−	0.993134i	−0.867999	−	0.496567i	$-0.834594\pi$
$563$		−	5.72379e57i		−	0.993134i	0.867999	−	0.496567i	$-0.165406\pi$
$564$	7.53337e57	−	4.80536e57i	1.25930	−	0.803276i
$565$	4.20758e57			0.677664
$566$		−	1.37880e57i		−	0.213972i
$567$	−4.72702e57	−	5.60729e57i	−0.706876	−	0.838510i
$568$	1.73095e57			0.249442
$569$			1.52530e56i			0.0211835i	0.999944	+	0.0105917i	$0.00337152\pi$
$569$			1.52530e56i			0.0211835i	−0.999944	+	0.0105917i	$0.996628\pi$
$570$	−8.10569e56	−	1.27073e57i	−0.108497	−	0.170091i
$571$	1.14312e57			0.147480			0.0737401	−	0.997277i	$-0.476506\pi$
$571$	1.14312e57			0.147480			0.0737401	+	0.997277i	$0.476506\pi$
$572$			3.95269e57i			0.491559i
$573$	−9.12681e57	+	5.82178e57i	−1.09414	+	0.697925i
$574$	−5.86110e57			−0.677376
$575$		−	2.56247e57i		−	0.285518i
$576$	−1.41988e57	+	3.05408e57i	−0.152539	+	0.328102i
$577$	4.13058e57			0.427877			0.213938	−	0.976847i	$-0.431371\pi$
$577$	4.13058e57			0.427877			0.213938	+	0.976847i	$0.431371\pi$
$578$			1.37885e57i			0.137732i
$579$	6.97564e57	+	1.09357e58i	0.671945	+	1.05341i
$580$	−4.08604e57			−0.379590
$581$			1.11637e58i			1.00025i
$582$	−2.39015e57	+	1.52462e57i	−0.206559	+	0.131759i
$583$	1.31451e58			1.09579
$584$			9.25763e57i			0.744440i
$585$	−9.83711e57	−	4.57340e57i	−0.763123	−	0.354786i
$586$	−2.00467e57			−0.150035
$587$		−	2.28951e58i		−	1.65326i	−0.562743	−	0.826632i	$-0.690254\pi$
$587$		−	2.28951e58i		−	1.65326i	0.562743	−	0.826632i	$-0.309746\pi$
$588$	1.38102e57	+	2.16502e57i	0.0962221	+	0.150848i
$589$	−4.98296e57			−0.335017
$590$		−	1.30727e57i		−	0.0848152i
$591$	−8.02419e57	+	5.11844e57i	−0.502417	+	0.320480i
$592$	−2.13008e58			−1.28718
$593$			2.13601e58i			1.24582i	0.782294	+	0.622910i	$0.214050\pi$
$593$			2.13601e58i			1.24582i	−0.782294	+	0.622910i	$0.785950\pi$
$594$	3.60793e57	−	4.81306e56i	0.203115	−	0.0270960i
$595$	1.40911e58			0.765752
$596$		−	3.90484e57i		−	0.204848i
$597$	−1.29869e58	−	2.03596e58i	−0.657726	−	1.03112i
$598$	1.00768e58			0.492716
$599$		−	2.46588e58i		−	1.16415i	−0.813135	−	0.582075i	$-0.802241\pi$
$599$		−	2.46588e58i		−	1.16415i	0.813135	−	0.582075i	$-0.197759\pi$
$600$	−2.21236e57	+	1.41122e57i	−0.100851	+	0.0643305i
$601$	3.63876e58			1.60173			0.800865	−	0.598844i	$-0.204373\pi$
$601$	3.63876e58			1.60173			0.800865	+	0.598844i	$0.204373\pi$
$602$		−	1.39781e57i		−	0.0594183i
$603$	4.19134e57	−	9.01532e57i	0.172064	−	0.370099i
$604$	9.22088e57			0.365592
$605$			1.51557e58i			0.580380i
$606$	−1.99512e57	−	3.12775e57i	−0.0737978	−	0.115693i
$607$	3.56364e58			1.27330			0.636651	−	0.771152i	$-0.280319\pi$
$607$	3.56364e58			1.27330			0.636651	+	0.771152i	$0.280319\pi$
$608$			1.64700e58i			0.568483i
$609$	−1.32155e58	+	8.42986e57i	−0.440677	+	0.281098i
$610$	2.76828e57			0.0891831
$611$		−	5.07054e58i		−	1.57830i
$612$	2.05797e58	+	9.56776e57i	0.618955	+	0.287760i
$613$	−5.75115e58			−1.67142			−0.835709	−	0.549172i	$-0.814943\pi$
$613$	−5.75115e58			−1.67142			−0.835709	+	0.549172i	$0.814943\pi$
$614$			1.82844e58i			0.513505i
$615$	−3.22094e58	−	5.04947e58i	−0.874189	−	1.37047i
$616$	−1.61275e58			−0.423031
$617$			3.67234e58i			0.931009i	0.885045	+	0.465505i	$0.154127\pi$
$617$			3.67234e58i			0.931009i	−0.885045	+	0.465505i	$0.845873\pi$
$618$	1.04322e58	−	6.65447e57i	0.255634	−	0.163063i
$619$	2.95029e58			0.698814			0.349407	−	0.936971i	$-0.386383\pi$
$619$	2.95029e58			0.698814			0.349407	+	0.936971i	$0.386383\pi$
$620$		−	1.78804e58i		−	0.409404i
$621$	9.20507e57	+	6.90023e58i	0.203753	+	1.52736i
$622$	−4.99891e57			−0.106974
$623$		−	4.60341e58i		−	0.952424i
$624$	1.65674e58	+	2.59728e58i	0.331420	+	0.519568i
$625$	−4.03443e58			−0.780371
$626$			6.89293e57i			0.128927i
$627$	−1.81507e58	+	1.15779e58i	−0.328303	+	0.209417i
$628$	−4.82092e58			−0.843290
$629$			8.90458e58i			1.50643i
$630$	8.74707e57	−	1.88144e58i	0.143124	−	0.307850i
$631$	4.27246e57			0.0676179			0.0338089	−	0.999428i	$-0.489236\pi$
$631$	4.27246e57			0.0676179			0.0338089	+	0.999428i	$0.489236\pi$
$632$		−	3.63244e58i		−	0.556083i
$633$	2.32376e58	+	3.64297e58i	0.344123	+	0.539483i
$634$	−3.67463e58			−0.526429
$635$			9.00125e58i			1.24754i
$636$	1.01746e59	−	6.49015e58i	1.36433	−	0.870272i
$637$	1.45723e58			0.189060
$638$		−	7.77975e57i		−	0.0976632i
$639$	2.88435e58	+	1.34097e58i	0.350373	+	0.162893i
$640$	−7.65056e58			−0.899319
$641$			3.02499e58i			0.344116i	0.985087	+	0.172058i	$0.0550417\pi$
$641$			3.02499e58i			0.344116i	−0.985087	+	0.172058i	$0.944958\pi$
$642$	−2.59350e57	−	4.06583e57i	−0.0285529	−	0.0447625i
$643$	−3.12986e58			−0.333499			−0.166750	−	0.985999i	$-0.553327\pi$
$643$	−3.12986e58			−0.333499			−0.166750	+	0.985999i	$0.553327\pi$
$644$		−	1.44584e59i		−	1.49114i
$645$	1.20424e58	−	7.68157e57i	0.120215	−	0.0766825i
$646$	1.78932e58			0.172904
$647$		−	1.33263e59i		−	1.24658i	−0.781990	−	0.623291i	$-0.785795\pi$
$647$		−	1.33263e59i		−	1.24658i	0.781990	−	0.623291i	$-0.214205\pi$
$648$	5.45053e58	−	4.59488e58i	0.493587	−	0.416101i
$649$	−1.86726e58			−0.163707
$650$			6.98023e57i			0.0592501i
$651$	−3.68889e58	−	5.78308e58i	−0.303176	−	0.475290i
$652$	1.22450e59			0.974447
$653$		−	1.75356e59i		−	1.35127i	−0.737236	−	0.675636i	$-0.763869\pi$
$653$		−	1.75356e59i		−	1.35127i	0.737236	−	0.675636i	$-0.236131\pi$
$654$	−6.64353e58	+	4.23775e58i	−0.495754	+	0.316230i
$655$	1.34272e59			0.970324
$656$			1.70084e59i			1.19037i
$657$	−7.17190e58	+	1.54263e59i	−0.486140	+	1.04566i
$658$	9.69790e58			0.636698
$659$			1.29676e59i			0.824644i	0.911038	+	0.412322i	$0.135282\pi$
$659$			1.29676e59i			0.824644i	−0.911038	+	0.412322i	$0.864718\pi$
$660$	−4.15450e58	−	6.51302e58i	−0.255915	−	0.401199i
$661$	−2.06767e59			−1.23382			−0.616908	−	0.787035i	$-0.711615\pi$
$661$	−2.06767e59			−1.23382			−0.616908	+	0.787035i	$0.711615\pi$
$662$			2.46991e58i			0.142778i
$663$	1.08577e59	−	6.92586e58i	0.608069	−	0.387873i
$664$	−1.08516e59			−0.588795
$665$			1.22721e59i			0.645154i
$666$	1.18894e59	+	5.52754e58i	0.605622	+	0.281561i
$667$	1.48789e59			0.734393
$668$			4.89830e57i			0.0234282i
$669$	−1.44605e59	−	2.26697e59i	−0.670245	−	1.05075i
$670$	2.81268e58			0.126343
$671$		−	3.95411e58i		−	0.172138i
$672$	−1.91146e59	+	1.21927e59i	−0.806509	+	0.514453i
$673$	−2.05299e59			−0.839597			−0.419799	−	0.907617i	$-0.637899\pi$
$673$	−2.05299e59			−0.839597			−0.419799	+	0.907617i	$0.637899\pi$
$674$		−	7.62651e58i		−	0.302321i
$675$	−4.77982e58	+	6.37639e57i	−0.183668	+	0.0245017i
$676$	−3.09590e58			−0.115321
$677$			3.54435e59i			1.27990i	0.768418	+	0.639948i	$0.221044\pi$
$677$			3.54435e59i			1.27990i	−0.768418	+	0.639948i	$0.778956\pi$
$678$	3.95535e58	+	6.20081e58i	0.138472	+	0.217082i
$679$	2.30829e59			0.783475
$680$			1.36972e59i			0.450758i
$681$	−1.98133e59	+	1.26385e59i	−0.632220	+	0.403278i
$682$	3.40440e58			0.105334
$683$		−	7.60473e58i		−	0.228165i	−0.993471	−	0.114082i	$-0.963607\pi$
$683$		−	7.60473e58i		−	0.228165i	0.993471	−	0.114082i	$-0.0363928\pi$
$684$	−8.33266e58	+	1.79231e59i	−0.242441	+	0.521476i
$685$	4.24102e59			1.19665
$686$		−	1.09577e59i		−	0.299856i
$687$	−6.90156e58	−	1.08196e59i	−0.183171	−	0.287157i
$688$	−4.05631e58			−0.104418
$689$		−	6.84830e59i		−	1.70993i
$690$	−1.66040e59	+	1.05913e59i	−0.402144	+	0.256518i
$691$	2.44786e59			0.575105			0.287552	−	0.957765i	$-0.407158\pi$
$691$	2.44786e59			0.575105			0.287552	+	0.957765i	$0.407158\pi$
$692$		−	3.28901e58i		−	0.0749613i
$693$	−2.68739e59	−	1.24940e59i	−0.594200	−	0.276251i
$694$	−8.58528e58			−0.184164
$695$		−	4.23329e59i		−	0.881043i
$696$	−8.19420e58	−	1.28461e59i	−0.165467	−	0.259404i
$697$	7.11020e59			1.39314
$698$		−	8.94915e58i		−	0.170145i
$699$	7.47875e59	−	4.77052e59i	1.37977	−	0.880126i
$700$	1.00154e59			0.179313
$701$			3.33137e59i			0.578822i	0.957205	+	0.289411i	$0.0934594\pi$
$701$			3.33137e59i			0.578822i	−0.957205	+	0.289411i	$0.906541\pi$
$702$	−2.50749e58	−	1.87964e59i	−0.0422824	−	0.316954i
$703$	−7.75509e59			−1.26918
$704$			1.36101e59i			0.216189i
$705$	5.32943e59	+	8.35496e59i	0.821692	+	1.28817i
$706$	−1.91335e59			−0.286349
$707$			3.02062e59i			0.438822i
$708$	−1.44530e59	+	9.21924e58i	−0.203826	+	0.130016i
$709$	−1.03252e60			−1.41360			−0.706802	−	0.707412i	$-0.749863\pi$
$709$	−1.03252e60			−1.41360			−0.706802	+	0.707412i	$0.749863\pi$
$710$			8.99887e58i			0.119609i
$711$	2.81406e59	−	6.05287e59i	0.363138	−	0.781088i
$712$	4.47472e59			0.560642
$713$			6.51098e59i			0.792075i
$714$	1.32464e59	+	2.07664e59i	0.156471	+	0.245300i
$715$	−4.38376e59			−0.502829
$716$			4.16528e59i			0.463949i
$717$	9.73460e58	−	6.20947e58i	0.105297	−	0.0671665i
$718$	−1.57548e59			−0.165501
$719$		−	6.56960e59i		−	0.670243i	−0.942175	−	0.335122i	$-0.891223\pi$
$719$		−	6.56960e59i		−	0.670243i	0.942175	−	0.335122i	$-0.108777\pi$
$720$	−5.45979e59	−	2.53832e59i	−0.540995	−	0.251515i
$721$	−1.00749e60			−0.969617
$722$		−	2.11043e59i		−	0.197283i
$723$	6.57527e59	+	1.03081e60i	0.597048	+	0.935994i
$724$	5.34382e59			0.471349
$725$			1.03067e59i			0.0883123i
$726$	−2.23353e59	+	1.42471e59i	−0.185918	+	0.118593i
$727$	−1.39086e60			−1.12477			−0.562383	−	0.826877i	$-0.690115\pi$
$727$	−1.39086e60			−1.12477			−0.562383	+	0.826877i	$0.690115\pi$
$728$			8.40204e59i			0.660125i
$729$	1.26421e60	−	3.43408e59i	0.965030	−	0.262139i
$730$	−4.81285e59			−0.356963
$731$			1.69570e59i			0.122204i
$732$	−1.95226e59	−	3.06057e59i	−0.136712	−	0.214323i
$733$	3.51755e59			0.239363			0.119681	−	0.992812i	$-0.461813\pi$
$733$	3.51755e59			0.239363			0.119681	+	0.992812i	$0.461813\pi$
$734$			4.50136e59i			0.297664i
$735$	−2.40114e59	+	1.53163e59i	−0.154306	+	0.0984281i
$736$	2.15205e60			1.34406
$737$		−	4.01754e59i		−	0.243861i
$738$	4.41367e59	−	9.49355e59i	0.260385	−	0.560074i
$739$	−7.02043e59			−0.402560			−0.201280	−	0.979534i	$-0.564510\pi$
$739$	−7.02043e59			−0.402560			−0.201280	+	0.979534i	$0.564510\pi$
$740$		−	2.78276e60i		−	1.55099i
$741$	6.03180e59	+	9.45606e59i	0.326787	+	0.512304i
$742$	1.30980e60			0.689801
$743$		−	6.49360e58i		−	0.0332445i	−0.999862	−	0.0166223i	$-0.994709\pi$
$743$		−	6.49360e58i		−	0.0332445i	0.999862	−	0.0166223i	$-0.00529128\pi$
$744$	5.62141e59	−	3.58576e59i	0.279778	−	0.178464i
$745$	4.33069e59			0.209544
$746$			1.55802e59i			0.0732922i
$747$	−1.80824e60	−	8.40676e59i	−0.827036	−	0.384500i
$748$	9.17103e59			0.407835
$749$			3.92658e59i			0.169784i
$750$	−4.69310e59	−	7.35738e59i	−0.197321	−	0.309341i
$751$	−2.42708e60			−0.992306			−0.496153	−	0.868235i	$-0.665254\pi$
$751$	−2.42708e60			−0.992306			−0.496153	+	0.868235i	$0.665254\pi$
$752$		−	2.81425e60i		−	1.11889i
$753$	9.14947e59	−	5.83623e59i	0.353754	−	0.225651i
$754$	−4.05306e59			−0.152400
$755$			1.02265e60i			0.373974i
$756$	−2.69696e60	+	3.59781e59i	−0.959218	+	0.127962i
$757$	7.77243e59			0.268871			0.134435	−	0.990922i	$-0.457078\pi$
$757$	7.77243e59			0.268871			0.134435	+	0.990922i	$0.457078\pi$
$758$			5.63125e58i			0.0189475i
$759$	1.51282e60	+	2.37165e60i	0.495120	+	0.776201i
$760$	−1.19290e60			−0.379768
$761$			1.04787e60i			0.324510i	0.986749	+	0.162255i	$0.0518767\pi$
$761$			1.04787e60i			0.324510i	−0.986749	+	0.162255i	$0.948123\pi$
$762$	−1.32654e60	+	8.46166e59i	−0.399636	+	0.254918i
$763$	6.41598e60			1.88039
$764$			4.01622e60i			1.14514i
$765$	−1.06112e60	+	2.28241e60i	−0.294357	+	0.633145i
$766$	−3.12699e59			−0.0843962
$767$			9.72799e59i			0.255459i
$768$	4.23485e58	+	6.63899e58i	0.0108206	+	0.0169635i
$769$	−3.87606e60			−0.963691			−0.481845	−	0.876256i	$-0.660033\pi$
$769$	−3.87606e60			−0.963691			−0.481845	+	0.876256i	$0.660033\pi$
$770$		−	8.38437e59i		−	0.202845i
$771$	−3.32688e60	+	2.12214e60i	−0.783241	+	0.499611i
$772$	4.81223e60			1.10251
$773$		−	2.59645e60i		−	0.578909i	−0.957192	−	0.289455i	$-0.906526\pi$
$773$		−	2.59645e60i		−	0.578909i	0.957192	−	0.289455i	$-0.0934739\pi$
$774$	2.26410e59	+	1.05261e59i	0.0491288	+	0.0228406i
$775$	−4.51018e59			−0.0952486
$776$			2.24376e60i			0.461190i
$777$	−5.74109e60	−	9.00032e60i	−1.14856	−	1.80060i
$778$	−7.18681e59			−0.139947
$779$			6.19235e60i			1.17373i
$780$	−3.39313e60	+	2.16440e60i	−0.626056	+	0.399347i
$781$	1.28537e60			0.230864
$782$		−	2.33802e60i		−	0.408795i
$783$	−3.70244e59	−	2.77540e60i	−0.0630218	−	0.472420i
$784$	8.08788e59			0.134029
$785$		−	5.34668e60i		−	0.862624i
$786$	1.26222e60	+	1.97879e60i	0.198273	+	0.310833i
$787$	5.01310e60			0.766721			0.383360	−	0.923599i	$-0.374767\pi$
$787$	5.01310e60			0.766721			0.383360	+	0.923599i	$0.374767\pi$
$788$			3.53102e60i			0.525835i
$789$	1.15102e61	−	7.34211e60i	1.66904	−	1.06464i
$790$	1.88843e60			0.266644
$791$		−	5.98842e60i		−	0.823391i
$792$	1.21447e60	−	2.61226e60i	0.162615	−	0.349774i
$793$	−2.06000e60			−0.268614
$794$			1.25108e60i			0.158874i
$795$	7.19796e60	+	1.12843e61i	0.890225	+	1.39561i
$796$	−8.95918e60			−1.07918
$797$		−	1.13355e61i		−	1.32989i	−0.746894	−	0.664943i	$-0.768456\pi$
$797$		−	1.13355e61i		−	1.32989i	0.746894	−	0.664943i	$-0.231544\pi$
$798$	−1.80856e60	+	1.15364e60i	−0.206668	+	0.131829i
$799$	−1.17647e61			−1.30948
$800$			1.49073e60i			0.161625i
$801$	7.45639e60	+	3.46657e60i	0.787492	+	0.366115i
$802$	−1.20455e60			−0.123926
$803$			6.87452e60i			0.688995i
$804$	−1.98358e60	−	3.10966e60i	−0.193675	−	0.303624i
$805$	1.60353e61			1.52533
$806$		−	1.77361e60i		−	0.164370i
$807$	−2.05136e60	+	1.30851e60i	−0.185224	+	0.118150i
$808$	−2.93618e60			−0.258312
$809$		−	1.05487e61i		−	0.904231i	−0.891959	−	0.452116i	$-0.850669\pi$
$809$		−	1.05487e61i		−	0.904231i	0.891959	−	0.452116i	$-0.149331\pi$
$810$	2.38878e60	+	2.83362e60i	0.199522	+	0.236677i
$811$	−1.53279e61			−1.24752			−0.623758	−	0.781618i	$-0.714395\pi$
$811$	−1.53279e61			−1.24752			−0.623758	+	0.781618i	$0.714395\pi$
$812$			5.81544e60i			0.461218i
$813$	−5.97299e60	−	9.36387e60i	−0.461626	−	0.723692i
$814$	5.29834e60			0.399050
$815$			1.35804e61i			0.996788i
$816$	6.02622e60	−	3.84398e60i	0.431074	−	0.274972i
$817$	−1.47680e60			−0.102958
$818$			4.84218e60i			0.329019i
$819$	−6.50908e60	+	1.40006e61i	−0.431080	+	0.927227i
$820$	−2.22200e61			−1.43435
$821$			2.02514e61i			1.27424i	0.770766	+	0.637118i	$0.219874\pi$
$821$			2.02514e61i			1.27424i	−0.770766	+	0.637118i	$0.780126\pi$
$822$	3.98679e60	+	6.25010e60i	0.244520	+	0.383335i
$823$	−9.63699e59			−0.0576163			−0.0288081	−	0.999585i	$-0.509171\pi$
$823$	−9.63699e59			−0.0576163			−0.0288081	+	0.999585i	$0.509171\pi$
$824$		−	9.79325e60i		−	0.570763i
$825$	−1.64286e60	+	1.04794e60i	−0.0933397	+	0.0595392i
$826$	−1.86057e60			−0.103054
$827$		−	3.08026e60i		−	0.166330i	−0.996536	−	0.0831652i	$-0.973497\pi$
$827$		−	3.08026e60i		−	0.166330i	0.996536	−	0.0831652i	$-0.0265029\pi$
$828$	2.34191e61	+	1.08879e61i	1.23292	+	0.573199i
$829$	4.79284e60			0.246007			0.123004	−	0.992406i	$-0.460747\pi$
$829$	4.79284e60			0.246007			0.123004	+	0.992406i	$0.460747\pi$
$830$		−	5.64153e60i		−	0.282330i
$831$	−1.42253e61	−	2.23010e61i	−0.694126	−	1.08818i
$832$	7.09051e60			0.337356
$833$		−	3.38106e60i		−	0.156858i
$834$	6.23870e60	−	3.97952e60i	0.282233	−	0.180029i
$835$	−5.43250e59			−0.0239654
$836$			7.98715e60i			0.343605i
$837$	1.21451e61	−	1.62018e60i	0.509525	−	0.0679718i
$838$	−7.61816e60			−0.311692
$839$		−	3.37073e61i		−	1.34500i	−0.740096	−	0.672501i	$-0.765220\pi$
$839$		−	3.37073e61i		−	1.34500i	0.740096	−	0.672501i	$-0.234780\pi$
$840$	−8.83103e60	−	1.38444e61i	−0.343674	−	0.538778i
$841$	2.03615e61			0.772848
$842$		−	1.43044e61i		−	0.529559i
$843$	−1.03726e61	+	6.61641e60i	−0.374547	+	0.238915i
$844$	1.60308e61			0.564629
$845$		−	3.43354e60i		−	0.117964i
$846$	−7.30295e60	+	1.57082e61i	−0.244749	+	0.526440i
$847$	2.15703e61			0.705187
$848$		−	3.80094e61i		−	1.21221i
$849$	−1.07841e61	−	1.69063e61i	−0.335524	−	0.526002i
$850$	1.61955e60			0.0491584
$851$			1.01332e62i			3.00071i
$852$	9.94903e60	−	6.34625e60i	0.287441	−	0.183352i
$853$	1.56693e61			0.441691			0.220846	−	0.975309i	$-0.429118\pi$
$853$	1.56693e61			0.441691			0.220846	+	0.975309i	$0.429118\pi$
$854$		−	3.93994e60i		−	0.108361i
$855$	−1.98777e61	−	9.24141e60i	−0.533431	−	0.247999i
$856$	−3.81681e60			−0.0999427
$857$		−	2.42950e60i		−	0.0620753i	−0.999518	−	0.0310377i	$-0.990119\pi$
$857$		−	2.42950e60i		−	0.0620753i	0.999518	−	0.0310377i	$-0.00988118\pi$
$858$	−4.12097e60	−	6.46046e60i	−0.102746	−	0.161076i
$859$	9.74644e60			0.237132			0.118566	−	0.992946i	$-0.462170\pi$
$859$	9.74644e60			0.237132			0.118566	+	0.992946i	$0.462170\pi$
$860$		−	5.29923e60i		−	0.125819i
$861$	−7.18665e61	+	4.58420e61i	−1.66518	+	1.06218i
$862$	1.08265e61			0.244814
$863$		−	1.99435e61i		−	0.440123i	−0.975486	−	0.220061i	$-0.929374\pi$
$863$		−	1.99435e61i		−	0.440123i	0.975486	−	0.220061i	$-0.0706258\pi$
$864$	−5.35511e60	−	4.01426e61i	−0.115340	−	0.864603i
$865$	3.64771e60			0.0766799
$866$		−	9.09175e60i		−	0.186540i
$867$	1.07846e61	+	1.69070e61i	0.215974	+	0.338583i
$868$	−2.54482e61			−0.497443
$869$		−	2.69737e61i		−	0.514666i
$870$	6.67841e60	−	4.26000e60i	0.124385	−	0.0793424i
$871$	−2.09304e61			−0.380537
$872$			6.23662e61i			1.10689i
$873$	−1.73825e61	+	3.73886e61i	−0.301170	+	0.647799i
$874$	2.03620e61			0.344414
$875$			7.10539e61i			1.17333i
$876$	3.39416e61	+	5.32102e61i	0.547199	+	0.857845i
$877$	6.34279e61			0.998364			0.499182	−	0.866497i	$-0.333634\pi$
$877$	6.34279e61			0.998364			0.499182	+	0.866497i	$0.333634\pi$
$878$			2.89947e61i			0.445588i
$879$	−2.45804e61	+	1.56793e61i	−0.368827	+	0.235266i
$880$	−2.43307e61			−0.356467
$881$		−	3.47434e61i		−	0.497025i	−0.968629	−	0.248513i	$-0.920058\pi$
$881$		−	3.47434e61i		−	0.497025i	0.968629	−	0.248513i	$-0.0799417\pi$
$882$	−4.51439e60	−	2.09880e60i	−0.0630608	−	0.0293178i
$883$	−6.40001e61			−0.872984			−0.436492	−	0.899708i	$-0.643779\pi$
$883$	−6.40001e61			−0.872984			−0.436492	+	0.899708i	$0.643779\pi$
$884$		−	4.77789e61i		−	0.636412i
$885$	−1.02247e61	−	1.60293e61i	−0.132997	−	0.208499i
$886$	−4.08922e61			−0.519437
$887$		−	1.33017e62i		−	1.65011i	−0.565056	−	0.825053i	$-0.691145\pi$
$887$		−	1.33017e62i		−	1.65011i	0.565056	−	0.825053i	$-0.308855\pi$
$888$	8.74871e61	−	5.58059e61i	1.05992	−	0.676096i
$889$	1.28110e62			1.51582
$890$			2.32632e61i			0.268831i
$891$	4.04745e61	−	3.41206e61i	0.456825	−	0.385110i
$892$	−9.97573e61			−1.09972
$893$		−	1.02460e62i		−	1.10325i
$894$	4.07109e60	+	6.38225e60i	0.0428176	+	0.0671252i
$895$	−4.61954e61			−0.474586
$896$			1.08886e62i			1.09271i
$897$	1.23557e62	−	7.88144e61i	1.21123	−	0.772617i
$898$	1.20657e60			0.0115544
$899$		−	2.61883e61i		−	0.244993i
$900$	−7.54207e60	+	1.62225e61i	−0.0689283	+	0.148261i
$901$	−1.58894e62			−1.41869
$902$		−	4.23066e61i		−	0.369038i
$903$	−1.09328e61	−	1.71393e61i	−0.0931725	−	0.146067i
$904$	5.82101e61			0.484687
$905$			5.92662e61i			0.482155i
$906$	−1.50710e61	+	9.61346e60i	−0.119798	+	0.0764165i
$907$	2.56947e62			1.99568			0.997839	−	0.0657010i	$-0.0209283\pi$
$907$	2.56947e62			1.99568			0.997839	+	0.0657010i	$0.0209283\pi$
$908$			8.71879e61i			0.661688i
$909$	−4.89267e61	−	2.27466e61i	−0.362831	−	0.168685i
$910$	−4.36805e61			−0.316533
$911$			1.91875e62i			1.35873i	0.733802	+	0.679363i	$0.237744\pi$
$911$			1.91875e62i			1.35873i	−0.733802	+	0.679363i	$0.762256\pi$
$912$	3.34776e61	+	5.24830e61i	0.231667	+	0.363184i
$913$	−8.05817e61			−0.544942
$914$		−	5.23615e61i		−	0.346053i
$915$	3.39435e61	−	2.16518e61i	0.219237	−	0.139846i
$916$	−4.76112e61			−0.300542
$917$		−	1.91102e62i		−	1.17898i
$918$	−4.36115e61	+	5.81788e60i	−0.262969	+	0.0350807i
$919$	−1.87203e62			−1.10329			−0.551643	−	0.834081i	$-0.685999\pi$
$919$	−1.87203e62			−1.10329			−0.551643	+	0.834081i	$0.685999\pi$
$920$			1.55870e62i			0.897879i
$921$	1.43009e62	+	2.24196e62i	0.805216	+	1.26234i
$922$	−4.77087e61			−0.262572
$923$		−	6.69646e61i		−	0.360254i
$924$	−9.26964e61	+	5.91288e61i	−0.487474	+	0.310948i
$925$	−7.01929e61			−0.360842
$926$		−	4.39247e61i		−	0.220739i
$927$	7.58685e61	−	1.63189e62i	0.372724	−	0.801707i
$928$	−8.65591e61			−0.415724
$929$			2.77253e62i			1.30181i	0.759160	+	0.650904i	$0.225610\pi$
$929$			2.77253e62i			1.30181i	−0.759160	+	0.650904i	$0.774390\pi$
$930$	1.86417e61	+	2.92246e61i	0.0855742	+	0.134155i
$931$	2.94460e61			0.132155
$932$		−	3.29100e62i		−	1.44409i
$933$	−6.12947e61	+	3.90984e61i	−0.262971	+	0.167743i
$934$	3.06601e61			0.128614
$935$			1.01712e62i			0.417185i
$936$	−1.36093e62	−	6.32711e61i	−0.545810	−	0.253754i
$937$	−3.71382e62			−1.45643			−0.728214	−	0.685350i	$-0.759649\pi$
$937$	−3.71382e62			−1.45643			−0.728214	+	0.685350i	$0.759649\pi$
$938$		−	4.00314e61i		−	0.153512i
$939$	5.39122e61	+	8.45183e61i	0.202167	+	0.316937i
$940$	3.67657e62			1.34821
$941$			2.16683e62i			0.777040i	0.921440	+	0.388520i	$0.127014\pi$
$941$			2.16683e62i			0.777040i	−0.921440	+	0.388520i	$0.872986\pi$
$942$	7.87953e61	−	5.02617e61i	0.276332	−	0.176266i
$943$	8.09122e62			2.77503
$944$			5.39922e61i			0.181100i
$945$	−3.99019e61	−	2.99109e62i	−0.130896	−	0.981210i
$946$	1.00896e61			0.0323714
$947$		−	4.94607e62i		−	1.55207i	−0.630690	−	0.776035i	$-0.717228\pi$
$947$		−	4.94607e62i		−	1.55207i	0.630690	−	0.776035i	$-0.282772\pi$
$948$	−1.33177e62	−	2.08782e62i	−0.408748	−	0.640794i
$949$	3.58146e62			1.07515
$950$			1.41049e61i			0.0414165i
$951$	−4.50569e62	+	2.87407e62i	−1.29411	+	0.825480i
$952$	1.94944e62			0.547690
$953$		−	1.46378e61i		−	0.0402275i	−0.999798	−	0.0201138i	$-0.993597\pi$
$953$		−	1.46378e61i		−	0.0402275i	0.999798	−	0.0201138i	$-0.00640284\pi$
$954$	−9.86340e61	+	2.12156e62i	−0.265162	+	0.570348i
$955$	−4.45423e62			−1.17139
$956$		−	4.28368e61i		−	0.110205i
$957$	−6.08484e61	−	9.53921e61i	−0.153143	−	0.240083i
$958$	2.67862e62			0.659532
$959$		−	6.03602e62i		−	1.45399i
$960$	−1.16834e62	+	7.45254e61i	−0.275342	+	0.175634i
$961$	−3.19102e62			−0.735764
$962$		−	2.76030e62i		−	0.622702i
$963$	−6.36009e61	−	2.95689e61i	−0.140382	−	0.0652654i
$964$	4.53603e62			0.979622
$965$			5.33705e62i			1.12779i
$966$	1.50740e62	+	2.36316e62i	0.311680	+	0.488622i
$967$	−1.52198e62			−0.307931			−0.153966	−	0.988076i	$-0.549204\pi$
$967$	−1.52198e62			−0.307931			−0.153966	+	0.988076i	$0.549204\pi$
$968$			2.09673e62i			0.415106i
$969$	2.19400e62	−	1.39950e62i	0.425047	−	0.271127i
$970$	−1.16649e62			−0.221143
$971$			9.86698e62i			1.83055i	0.402835	+	0.915273i	$0.368025\pi$
$971$			9.86698e62i			1.83055i	−0.402835	+	0.915273i	$0.631975\pi$
$972$	1.44818e62	−	4.63935e62i	0.262924	−	0.842298i
$973$	−6.02502e62			−1.07051
$974$		−	4.88221e59i		−	0.000848942i
$975$	5.45951e61	+	8.55888e61i	0.0929087	+	0.145653i
$976$	−1.14334e62			−0.190427
$977$			4.52891e62i			0.738257i	0.929378	+	0.369128i	$0.120344\pi$
$977$			4.52891e62i			0.738257i	−0.929378	+	0.369128i	$0.879656\pi$
$978$	−2.00138e62	+	1.27663e62i	−0.319310	+	0.203680i
$979$	3.32283e62			0.518886
$980$			1.05661e62i			0.161498i
$981$	−4.83152e62	+	1.03923e63i	−0.722827	+	1.55476i
$982$	−1.32066e62			−0.193397
$983$		−	3.68267e62i		−	0.527885i	−0.964538	−	0.263942i	$-0.914977\pi$
$983$		−	3.68267e62i		−	0.527885i	0.964538	−	0.263942i	$-0.0850229\pi$
$984$	−4.45604e62	−	6.98574e62i	−0.625248	−	0.980202i
$985$	−3.91611e62			−0.537891
$986$			9.40392e61i			0.126443i
$987$	1.18912e63	−	7.58510e62i	1.56518	−	0.998392i
$988$	4.16111e62			0.536183
$989$			1.92966e62i			0.243422i
$990$	1.35806e62	+	6.31381e61i	0.167718	+	0.0779744i
$991$	−1.06443e63			−1.28697			−0.643486	−	0.765458i	$-0.722513\pi$
$991$	−1.06443e63			−1.28697			−0.643486	+	0.765458i	$0.722513\pi$
$992$		−	3.78781e62i		−	0.448376i
$993$	1.93181e62	+	3.02850e62i	0.223888	+	0.350989i
$994$	1.28076e62			0.145330
$995$		−	9.93626e62i		−	1.10392i
$996$	−6.23719e62	+	3.97856e62i	−0.678490	+	0.432792i
$997$	1.08807e63			1.15894			0.579469	−	0.814994i	$-0.303260\pi$
$997$	1.08807e63			1.15894			0.579469	+	0.814994i	$0.303260\pi$
$998$		−	3.65281e62i		−	0.380965i
$999$	1.89016e63	−	2.52152e62i	1.93029	−	0.257506i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.43.b.b.2.7	yes	12
3.2	odd	2	inner	3.43.b.b.2.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.43.b.b.2.6	✓	12	3.2	odd	2	inner
3.43.b.b.2.7	yes	12	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+719233. i q^{2} +(5.62540e9 + 8.81895e9i) q^{3} +3.88075e12 q^{4} +4.30398e14i q^{5} +(-6.34288e15 + 4.04597e15i) q^{6} +6.12563e17 q^{7} +5.95439e18i q^{8} +(-4.61287e19 + 9.92202e19i) q^{9} +O(q^{10})\)	\(q+719233. i q^{2} +(5.62540e9 + 8.81895e9i) q^{3} +3.88075e12 q^{4} +4.30398e14i q^{5} +(-6.34288e15 + 4.04597e15i) q^{6} +6.12563e17 q^{7} +5.95439e18i q^{8} +(-4.61287e19 + 9.92202e19i) q^{9} -3.09557e20 q^{10} +4.42160e21i q^{11} +(2.18308e22 + 3.42241e22i) q^{12} +2.30355e23 q^{13} +4.40576e23i q^{14} +(-3.79566e24 + 2.42116e24i) q^{15} +1.27851e25 q^{16} -5.34470e25i q^{17} +(-7.13625e25 - 3.31773e25i) q^{18} +4.65475e26 q^{19} +1.67027e27i q^{20} +(3.44591e27 + 5.40216e27i) q^{21} -3.18016e27 q^{22} -6.08212e28i q^{23} +(-5.25114e28 + 3.34958e28i) q^{24} +4.21311e28 q^{25} +1.65679e29i q^{26} +(-1.13451e30 + 1.51346e29i) q^{27} +2.37720e30 q^{28} +2.44634e30i q^{29} +(-1.74138e30 - 2.72996e30i) q^{30} -1.07051e31 q^{31} +3.53832e31i q^{32} +(-3.89939e31 + 2.48733e31i) q^{33} +3.84408e31 q^{34} +2.63646e32i q^{35} +(-1.79014e32 + 3.85049e32i) q^{36} -1.66606e33 q^{37} +3.34785e32i q^{38} +(1.29584e33 + 2.03149e33i) q^{39} -2.56276e33 q^{40} +1.33033e34i q^{41} +(-3.88541e33 + 2.47841e33i) q^{42} -3.17268e33 q^{43} +1.71591e34i q^{44} +(-4.27042e34 - 1.98537e34i) q^{45} +4.37446e34 q^{46} -2.20119e35i q^{47} +(7.19215e34 + 1.12751e35i) q^{48} +6.32601e34 q^{49} +3.03021e34i q^{50} +(4.71346e35 - 3.00660e35i) q^{51} +8.93949e35 q^{52} -2.97294e36i q^{53} +(-1.08853e35 - 8.15978e35i) q^{54} -1.90305e36 q^{55} +3.64744e36i q^{56} +(2.61848e36 + 4.10500e36i) q^{57} -1.75949e36 q^{58} +4.22305e36i q^{59} +(-1.47300e37 + 9.39592e36i) q^{60} -8.94271e36 q^{61} -7.69947e36i q^{62} +(-2.82568e37 + 6.07787e37i) q^{63} +3.07809e37 q^{64} +9.91442e37i q^{65} +(-1.78897e37 - 2.80457e37i) q^{66} -9.08617e37 q^{67} -2.07414e38i q^{68} +(5.36379e38 - 3.42144e38i) q^{69} -1.89623e38 q^{70} -2.90702e38i q^{71} +(-5.90795e38 - 2.74668e38i) q^{72} +1.55476e39 q^{73} -1.19828e39i q^{74} +(2.37004e38 + 3.71552e38i) q^{75} +1.80639e39 q^{76} +2.70851e39i q^{77} +(-1.46111e39 + 9.32009e38i) q^{78} -6.10044e39 q^{79} +5.50270e39i q^{80} +(-7.71679e39 - 9.15381e39i) q^{81} -9.56816e39 q^{82} +1.82245e40i q^{83} +(1.33727e40 + 2.09644e40i) q^{84} +2.30035e40 q^{85} -2.28190e39i q^{86} +(-2.15741e40 + 1.37616e40i) q^{87} -2.63279e40 q^{88} -7.51499e40i q^{89} +(1.42795e40 - 3.07143e40i) q^{90} +1.41107e41 q^{91} -2.36032e41i q^{92} +(-6.02205e40 - 9.44079e40i) q^{93} +1.58317e41 q^{94} +2.00340e41i q^{95} +(-3.12042e41 + 1.99044e41i) q^{96} +3.76825e41 q^{97} +4.54987e40i q^{98} +(-4.38712e41 - 2.03963e41i) 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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