LMFDB - Embedded newform 3.43.b.b.2.8

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			2.8
Root			$52282.8i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.43.b.b.2.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.88218e6i q^{2} +(9.19591e9 - 4.98540e9i) q^{3} +8.55436e11 q^{4} +4.92433e14i q^{5} +(9.38344e15 + 1.73084e16i) q^{6} -8.30626e17 q^{7} +9.88801e18i q^{8} +(5.97105e19 - 9.16906e19i) q^{9} +O(q^{10})$	\(q+1.88218e6i q^{2} +(9.19591e9 - 4.98540e9i) q^{3} +8.55436e11 q^{4} +4.92433e14i q^{5} +(9.38344e15 + 1.73084e16i) q^{6} -8.30626e17 q^{7} +9.88801e18i q^{8} +(5.97105e19 - 9.16906e19i) q^{9} -9.26849e20 q^{10} -6.44887e21i q^{11} +(7.86651e21 - 4.26469e21i) q^{12} -2.92823e23 q^{13} -1.56339e24i q^{14} +(2.45498e24 + 4.52837e24i) q^{15} -1.48488e25 q^{16} +1.05183e26i q^{17} +(1.72578e26 + 1.12386e26i) q^{18} -7.89747e26 q^{19} +4.21245e26i q^{20} +(-7.63836e27 + 4.14100e27i) q^{21} +1.21380e28 q^{22} -3.44261e28i q^{23} +(4.92957e28 + 9.09293e28i) q^{24} -1.51168e28 q^{25} -5.51147e29i q^{26} +(9.19780e28 - 1.14086e30i) q^{27} -7.10547e29 q^{28} +3.85463e30i q^{29} +(-8.52322e30 + 4.62072e30i) q^{30} -7.97342e29 q^{31} +1.55398e31i q^{32} +(-3.21502e31 - 5.93033e31i) q^{33} -1.97973e32 q^{34} -4.09028e32i q^{35} +(5.10785e31 - 7.84354e31i) q^{36} -7.71994e32 q^{37} -1.48645e33i q^{38} +(-2.69278e33 + 1.45984e33i) q^{39} -4.86919e33 q^{40} +1.17299e33i q^{41} +(-7.79413e33 - 1.43768e34i) q^{42} -2.26903e34 q^{43} -5.51660e33i q^{44} +(4.51515e34 + 2.94034e34i) q^{45} +6.47961e34 q^{46} -9.68223e34i q^{47} +(-1.36548e35 + 7.40272e34i) q^{48} +3.77966e35 q^{49} -2.84526e34i q^{50} +(5.24379e35 + 9.67253e35i) q^{51} -2.50492e35 q^{52} +1.63507e36i q^{53} +(2.14731e36 + 1.73119e35i) q^{54} +3.17564e36 q^{55} -8.21324e36i q^{56} +(-7.26244e36 + 3.93721e36i) q^{57} -7.25512e36 q^{58} -1.67791e37i q^{59} +(2.10008e36 + 3.87373e36i) q^{60} -1.58648e37 q^{61} -1.50074e36i q^{62} +(-4.95971e37 + 7.61606e37i) q^{63} -9.45544e37 q^{64} -1.44196e38i q^{65} +(1.11620e38 - 6.05126e37i) q^{66} +1.30465e38 q^{67} +8.99772e37i q^{68} +(-1.71628e38 - 3.16579e38i) q^{69} +7.69865e38 q^{70} +1.38596e39i q^{71} +(9.06638e38 + 5.90418e38i) q^{72} -2.56350e38 q^{73} -1.45303e39i q^{74} +(-1.39013e38 + 7.53635e37i) q^{75} -6.75578e38 q^{76} +5.35660e39i q^{77} +(-2.74769e39 - 5.06830e39i) q^{78} +1.85997e39 q^{79} -7.31204e39i q^{80} +(-4.84182e39 - 1.09498e40i) q^{81} -2.20778e39 q^{82} +1.31402e40i q^{83} +(-6.53413e39 + 3.54236e39i) q^{84} -5.17956e40 q^{85} -4.27074e40i q^{86} +(1.92169e40 + 3.54469e40i) q^{87} +6.37665e40 q^{88} +3.99517e40i q^{89} +(-5.53427e40 + 8.49834e40i) q^{90} +2.43227e41 q^{91} -2.94493e40i q^{92} +(-7.33228e39 + 3.97507e39i) q^{93} +1.82237e41 q^{94} -3.88898e41i q^{95} +(7.74721e40 + 1.42903e41i) q^{96} -2.91048e41 q^{97} +7.11401e41i q^{98} +(-5.91301e41 - 3.85066e41i) 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 $

$2$			1.88218e6i			0.897495i	0.893659	+	0.448747i	$0.148130\pi$
$2$			1.88218e6i			0.897495i	−0.893659	+	0.448747i	$0.851870\pi$
$3$	9.19591e9	−	4.98540e9i	0.879120	−	0.476600i
$3$	9.19591e9	−	4.98540e9i	0.879120	−	0.476600i
$4$	8.55436e11			0.194504
$5$			4.92433e14i			1.03271i	0.856375	+	0.516354i	$0.172711\pi$
$5$			4.92433e14i			1.03271i	−0.856375	+	0.516354i	$0.827289\pi$
$6$	9.38344e15	+	1.73084e16i	0.427746	+	0.789006i
$7$	−8.30626e17			−1.48712			−0.743561	−	0.668668i	$-0.766865\pi$
$7$	−8.30626e17			−1.48712			−0.743561	+	0.668668i	$0.766865\pi$
$8$			9.88801e18i			1.07206i
$9$	5.97105e19	−	9.16906e19i	0.545705	−	0.837977i
$10$	−9.26849e20			−0.926849
$11$		−	6.44887e21i		−	0.871440i	−0.900082	−	0.435720i	$-0.856494\pi$
$11$		−	6.44887e21i		−	0.871440i	0.900082	−	0.435720i	$-0.143506\pi$
$12$	7.86651e21	−	4.26469e21i	0.170992	−	0.0927004i
$13$	−2.92823e23			−1.18521			−0.592605	−	0.805493i	$-0.701901\pi$
$13$	−2.92823e23			−1.18521			−0.592605	+	0.805493i	$0.701901\pi$
$14$		−	1.56339e24i		−	1.33468i
$15$	2.45498e24	+	4.52837e24i	0.492188	+	0.907874i
$16$	−1.48488e25			−0.767665
$17$			1.05183e26i			1.52236i	0.648540	+	0.761181i	$0.275380\pi$
$17$			1.05183e26i			1.52236i	−0.648540	+	0.761181i	$0.724620\pi$
$18$	1.72578e26	+	1.12386e26i	0.752080	+	0.489768i
$19$	−7.89747e26			−1.10576			−0.552882	−	0.833260i	$-0.686472\pi$
$19$	−7.89747e26			−1.10576			−0.552882	+	0.833260i	$0.686472\pi$
$20$			4.21245e26i			0.200865i
$21$	−7.63836e27	+	4.14100e27i	−1.30736	+	0.708762i
$22$	1.21380e28			0.782113
$23$		−	3.44261e28i		−	0.872173i	−0.899905	−	0.436087i	$-0.856364\pi$
$23$		−	3.44261e28i		−	0.872173i	0.899905	−	0.436087i	$-0.143636\pi$
$24$	4.92957e28	+	9.09293e28i	0.510944	+	0.942470i
$25$	−1.51168e28			−0.0664845
$26$		−	5.51147e29i		−	1.06372i
$27$	9.19780e28	−	1.14086e30i	0.0803609	−	0.996766i
$28$	−7.10547e29			−0.289251
$29$			3.85463e30i			0.750974i	0.926828	+	0.375487i	$0.122525\pi$
$29$			3.85463e30i			0.750974i	−0.926828	+	0.375487i	$0.877475\pi$
$30$	−8.52322e30	+	4.62072e30i	−0.814812	+	0.441736i
$31$	−7.97342e29			−0.0382868			−0.0191434	−	0.999817i	$-0.506094\pi$
$31$	−7.97342e29			−0.0382868			−0.0191434	+	0.999817i	$0.506094\pi$
$32$			1.55398e31i			0.383085i
$33$	−3.21502e31	−	5.93033e31i	−0.415328	−	0.766101i
$34$	−1.97973e32			−1.36631
$35$		−	4.09028e32i		−	1.53576i
$36$	5.10785e31	−	7.84354e31i	0.106142	−	0.162990i
$37$	−7.71994e32			−0.902355			−0.451178	−	0.892434i	$-0.648996\pi$
$37$	−7.71994e32			−0.902355			−0.451178	+	0.892434i	$0.648996\pi$
$38$		−	1.48645e33i		−	0.992417i
$39$	−2.69278e33	+	1.45984e33i	−1.04194	+	0.564871i
$40$	−4.86919e33			−1.10712
$41$			1.17299e33i			0.158793i	0.996843	+	0.0793967i	$0.0252994\pi$
$41$			1.17299e33i			0.158793i	−0.996843	+	0.0793967i	$0.974701\pi$
$42$	−7.79413e33	−	1.43768e34i	−0.636110	−	1.17335i
$43$	−2.26903e34			−1.12980			−0.564902	−	0.825158i	$-0.691086\pi$
$43$	−2.26903e34			−1.12980			−0.564902	+	0.825158i	$0.691086\pi$
$44$		−	5.51660e33i		−	0.169498i
$45$	4.51515e34	+	2.94034e34i	0.865385	+	0.563554i
$46$	6.47961e34			0.782771
$47$		−	9.68223e34i		−	0.744596i	−0.928113	−	0.372298i	$-0.878570\pi$
$47$		−	9.68223e34i		−	0.744596i	0.928113	−	0.372298i	$-0.121430\pi$
$48$	−1.36548e35	+	7.40272e34i	−0.674870	+	0.365869i
$49$	3.77966e35			1.21153
$50$		−	2.84526e34i		−	0.0596695i
$51$	5.24379e35	+	9.67253e35i	0.725557	+	1.33834i
$52$	−2.50492e35			−0.230528
$53$			1.63507e36i			1.00866i	0.863512	+	0.504328i	$0.168260\pi$
$53$			1.63507e36i			1.00866i	−0.863512	+	0.504328i	$0.831740\pi$
$54$	2.14731e36	+	1.73119e35i	0.894592	+	0.0721235i
$55$	3.17564e36			0.899943
$56$		−	8.21324e36i		−	1.59428i
$57$	−7.26244e36	+	3.93721e36i	−0.972100	+	0.527007i
$58$	−7.25512e36			−0.673995
$59$		−	1.67791e37i		−	1.08862i	−0.838885	−	0.544309i	$-0.816792\pi$
$59$		−	1.67791e37i		−	1.08862i	0.838885	−	0.544309i	$-0.183208\pi$
$60$	2.10008e36	+	3.87373e36i	0.0957323	+	0.176585i
$61$	−1.58648e37			−0.511104			−0.255552	−	0.966795i	$-0.582257\pi$
$61$	−1.58648e37			−0.511104			−0.255552	+	0.966795i	$0.582257\pi$
$62$		−	1.50074e36i		−	0.0343622i
$63$	−4.95971e37	+	7.61606e37i	−0.811531	+	1.24617i
$64$	−9.45544e37			−1.11148
$65$		−	1.44196e38i		−	1.22398i
$66$	1.11620e38	−	6.05126e37i	0.687571	−	0.372755i
$67$	1.30465e38			0.586035			0.293018	−	0.956107i	$-0.405341\pi$
$67$	1.30465e38			0.586035			0.293018	+	0.956107i	$0.405341\pi$
$68$			8.99772e37i			0.296105i
$69$	−1.71628e38	−	3.16579e38i	−0.415678	−	0.766745i
$70$	7.69865e38			1.37834
$71$			1.38596e39i			1.84216i	0.389377	+	0.921078i	$0.372690\pi$
$71$			1.38596e39i			1.84216i	−0.389377	+	0.921078i	$0.627310\pi$
$72$	9.06638e38	+	5.90418e38i	0.898362	+	0.585029i
$73$	−2.56350e38			−0.190131			−0.0950657	−	0.995471i	$-0.530306\pi$
$73$	−2.56350e38			−0.190131			−0.0950657	+	0.995471i	$0.530306\pi$
$74$		−	1.45303e39i		−	0.809859i
$75$	−1.39013e38	+	7.53635e37i	−0.0584479	+	0.0316865i
$76$	−6.75578e38			−0.215075
$77$			5.35660e39i			1.29594i
$78$	−2.74769e39	−	5.06830e39i	−0.506969	−	0.935138i
$79$	1.85997e39			0.262626			0.131313	−	0.991341i	$-0.458081\pi$
$79$	1.85997e39			0.262626			0.131313	+	0.991341i	$0.458081\pi$
$80$		−	7.31204e39i		−	0.792773i
$81$	−4.84182e39	−	1.09498e40i	−0.404411	−	0.914577i
$82$	−2.20778e39			−0.142516
$83$			1.31402e40i			0.657601i	0.944399	+	0.328801i	$0.106644\pi$
$83$			1.31402e40i			0.657601i	−0.944399	+	0.328801i	$0.893356\pi$
$84$	−6.53413e39	+	3.54236e39i	−0.254286	+	0.137857i
$85$	−5.17956e40			−1.57215
$86$		−	4.27074e40i		−	1.01399i
$87$	1.92169e40	+	3.54469e40i	0.357914	+	0.660197i
$88$	6.37665e40			0.934236
$89$			3.99517e40i			0.461684i	0.972991	+	0.230842i	$0.0741481\pi$
$89$			3.99517e40i			0.461684i	−0.972991	+	0.230842i	$0.925852\pi$
$90$	−5.53427e40	+	8.49834e40i	−0.505787	+	0.776678i
$91$	2.43227e41			1.76255
$92$		−	2.94493e40i		−	0.169641i
$93$	−7.33228e39	+	3.97507e39i	−0.0336587	+	0.0182475i
$94$	1.82237e41			0.668271
$95$		−	3.88898e41i		−	1.14193i
$96$	7.74721e40	+	1.42903e41i	0.182578	+	0.336778i
$97$	−2.91048e41			−0.551770			−0.275885	−	0.961191i	$-0.588971\pi$
$97$	−2.91048e41			−0.551770			−0.275885	+	0.961191i	$0.588971\pi$
$98$			7.11401e41i			1.08734i
$99$	−5.91301e41	−	3.85066e41i	−0.730247	−	0.475549i
$100$	−1.29315e40			−0.0129315
$101$			3.02343e41i			0.245330i	0.992448	+	0.122665i	$0.0391441\pi$
$101$			3.02343e41i			0.245330i	−0.992448	+	0.122665i	$0.960856\pi$
$102$	−1.82055e42	+	9.86977e41i	−1.20115	+	0.651184i
$103$	1.81534e42			0.975835			0.487918	−	0.872890i	$-0.337757\pi$
$103$	1.81534e42			0.975835			0.487918	+	0.872890i	$0.337757\pi$
$104$		−	2.89544e42i		−	1.27062i
$105$	−2.03917e42	−	3.76138e42i	−0.731944	−	1.35012i
$106$	−3.07750e42			−0.905264
$107$			1.29454e42i			0.312648i	0.987706	+	0.156324i	$0.0499644\pi$
$107$			1.29454e42i			0.312648i	−0.987706	+	0.156324i	$0.950036\pi$
$108$	7.86813e40	−	9.75932e41i	0.0156305	−	0.193875i
$109$	1.08437e43			1.77509			0.887546	−	0.460718i	$-0.152408\pi$
$109$	1.08437e43			1.77509			0.887546	+	0.460718i	$0.152408\pi$
$110$			5.97713e42i			0.807694i
$111$	−7.09918e42	+	3.84870e42i	−0.793279	+	0.430062i
$112$	1.23338e43			1.14161
$113$			1.84191e43i			1.41456i	0.706934	+	0.707280i	$0.250078\pi$
$113$			1.84191e43i			1.41456i	−0.706934	+	0.707280i	$0.749922\pi$
$114$	−7.41054e42	−	1.36692e43i	−0.472986	−	0.872454i
$115$	1.69525e43			0.900700
$116$			3.29739e42i			0.146067i
$117$	−1.74846e43	+	2.68492e43i	−0.646776	+	0.993179i
$118$	3.15812e43			0.977028
$119$		−	8.73677e43i		−	2.26394i
$120$	−4.47766e43	+	2.42748e43i	−0.973296	+	0.527655i
$121$	1.31757e43			0.240592
$122$		−	2.98605e43i		−	0.458713i
$123$	5.84781e42	+	1.07867e43i	0.0756809	+	0.139598i
$124$	−6.82075e41			−0.00744692
$125$			1.04522e44i			0.964048i
$126$	−1.43348e44	−	9.33508e43i	−1.11843	−	0.728344i
$127$	−1.25030e44			−0.826296			−0.413148	−	0.910664i	$-0.635571\pi$
$127$	−1.25030e44			−0.826296			−0.413148	+	0.910664i	$0.635571\pi$
$128$		−	1.09624e44i		−	0.614463i
$129$	−2.08658e44	+	1.13120e44i	−0.993235	+	0.538465i
$130$	2.71403e44			1.09851
$131$		−	2.25553e43i		−	0.0777232i	−0.999245	−	0.0388616i	$-0.987627\pi$
$131$		−	2.25553e43i		−	0.0777232i	0.999245	−	0.0388616i	$-0.0123731\pi$
$132$	−2.75025e43	−	5.07301e43i	−0.0807828	−	0.149009i
$133$	6.55984e44			1.64441
$134$			2.45559e44i			0.525964i
$135$	5.61797e44	+	4.52930e43i	1.02937	+	0.0829893i
$136$	−1.04005e45			−1.63206
$137$			4.97612e44i			0.669512i	0.942305	+	0.334756i	$0.108654\pi$
$137$			4.97612e44i			0.669512i	−0.942305	+	0.334756i	$0.891346\pi$
$138$	5.95859e44	−	3.23035e44i	0.688150	−	0.373068i
$139$	2.00466e45			1.98943			0.994715	−	0.102670i	$-0.0327387\pi$
$139$	2.00466e45			1.98943			0.994715	+	0.102670i	$0.0327387\pi$
$140$		−	3.49897e44i		−	0.298711i
$141$	−4.82698e44	−	8.90369e44i	−0.354874	−	0.654589i
$142$	−2.60864e45			−1.65333
$143$			1.88838e45i			1.03284i
$144$	−8.86629e44	+	1.36150e45i	−0.418919	+	0.643286i
$145$	−1.89815e45			−0.775537
$146$		−	4.82498e44i		−	0.170642i
$147$	3.47574e45	−	1.88431e45i	1.06508	−	0.577416i
$148$	−6.60391e44			−0.175511
$149$		−	3.65934e45i		−	0.844289i	−0.906528	−	0.422145i	$-0.861277\pi$
$149$		−	3.65934e45i		−	0.844289i	0.906528	−	0.422145i	$-0.138723\pi$
$150$	−1.41848e44	−	2.61648e44i	−0.0284385	−	0.0524567i
$151$	−7.93845e45			−1.38427			−0.692134	−	0.721769i	$-0.743329\pi$
$151$	−7.93845e45			−1.38427			−0.692134	+	0.721769i	$0.743329\pi$
$152$		−	7.80903e45i		−	1.18545i
$153$	9.64429e45	+	6.28053e45i	1.27570	+	0.830761i
$154$	−1.00821e46			−1.16310
$155$		−	3.92638e44i		−	0.0395391i
$156$	−2.30350e45	+	1.24880e45i	−0.202662	+	0.109869i
$157$	1.95402e46			1.50327			0.751634	−	0.659580i	$-0.229266\pi$
$157$	1.95402e46			1.50327			0.751634	+	0.659580i	$0.229266\pi$
$158$			3.50080e45i			0.235705i
$159$	8.15149e45	+	1.50360e46i	0.480726	+	0.886731i
$160$	−7.65231e45			−0.395615
$161$			2.85952e46i			1.29703i
$162$	2.06095e46	−	9.11319e45i	0.820828	−	0.362957i
$163$	−4.16484e45			−0.145767			−0.0728834	−	0.997340i	$-0.523220\pi$
$163$	−4.16484e45			−0.145767			−0.0728834	+	0.997340i	$0.523220\pi$
$164$			1.00342e45i			0.0308859i
$165$	2.92029e46	−	1.58318e46i	0.791158	−	0.428912i
$166$	−2.47323e46			−0.590193
$167$		−	4.07078e45i		−	0.0856312i	−0.999083	−	0.0428156i	$-0.986367\pi$
$167$		−	4.07078e45i		−	0.0856312i	0.999083	−	0.0428156i	$-0.0136328\pi$
$168$	−4.09463e46	−	7.55282e46i	−0.759836	−	1.40157i
$169$	2.47047e46			0.404724
$170$		−	9.74887e46i		−	1.41100i
$171$	−4.71562e46	+	7.24124e46i	−0.603421	+	0.926605i
$172$	−1.94101e46			−0.219751
$173$			1.30529e47i			1.30839i	0.756325	+	0.654196i	$0.226993\pi$
$173$			1.30529e47i			1.30839i	−0.756325	+	0.654196i	$0.773007\pi$
$174$	−6.67175e46	+	3.61697e46i	−0.592523	+	0.321226i
$175$	1.25564e46			0.0988706
$176$			9.57580e46i			0.668974i
$177$	−8.36503e46	−	1.54299e47i	−0.518835	−	0.957026i
$178$	−7.51964e46			−0.414359
$179$		−	3.36377e47i		−	1.64783i	−0.566714	−	0.823915i	$-0.691785\pi$
$179$		−	3.36377e47i		−	1.64783i	0.566714	−	0.823915i	$-0.308215\pi$
$180$	3.86242e46	+	2.51528e46i	0.168321	+	0.109613i
$181$	2.72379e47			1.05663			0.528315	−	0.849048i	$-0.322824\pi$
$181$	2.72379e47			1.05663			0.528315	+	0.849048i	$0.322824\pi$
$182$			4.57797e47i			1.58188i
$183$	−1.45892e47	+	7.90926e46i	−0.449322	+	0.243592i
$184$	3.40405e47			0.935022
$185$		−	3.80155e47i		−	0.931869i
$186$	−7.48181e45	−	1.38007e46i	−0.0163770	−	0.0302085i
$187$	6.78311e47			1.32665
$188$		−	8.28253e46i		−	0.144827i
$189$	−7.63993e46	+	9.47628e47i	−0.119507	+	1.48231i
$190$	7.31976e47			1.02488
$191$		−	1.74639e47i		−	0.218999i	−0.993987	−	0.109499i	$-0.965075\pi$
$191$		−	1.74639e47i		−	0.218999i	0.993987	−	0.109499i	$-0.0349248\pi$
$192$	−8.69514e47	+	4.71392e47i	−0.977126	+	0.529732i
$193$	−1.39456e48			−1.40519			−0.702595	−	0.711590i	$-0.747975\pi$
$193$	−1.39456e48			−1.40519			−0.702595	+	0.711590i	$0.747975\pi$
$194$		−	5.47805e47i		−	0.495211i
$195$	−7.18875e47	−	1.32601e48i	−0.583346	−	1.07602i
$196$	3.23326e47			0.235647
$197$			1.63413e48i			1.07028i	0.844764	+	0.535139i	$0.179741\pi$
$197$			1.63413e48i			1.07028i	−0.844764	+	0.535139i	$0.820259\pi$
$198$	7.24764e47	−	1.11294e48i	0.426803	−	0.655393i
$199$	−1.78142e48			−0.943740			−0.471870	−	0.881668i	$-0.656421\pi$
$199$	−1.78142e48			−0.943740			−0.471870	+	0.881668i	$0.656421\pi$
$200$		−	1.49475e47i		−	0.0712754i
$201$	1.19975e48	−	6.50421e47i	0.515196	−	0.279304i
$202$	−5.69064e47			−0.220182
$203$		−	3.20176e48i		−	1.11679i
$204$	4.48573e47	+	8.27423e47i	0.141123	+	0.260312i
$205$	−5.77618e47			−0.163987
$206$			3.41680e48i			0.875807i
$207$	−3.15655e48	−	2.05560e48i	−0.730861	−	0.475950i
$208$	4.34808e48			0.909844
$209$			5.09298e48i			0.963607i
$210$	7.07961e48	−	3.83809e48i	1.21173	−	0.656916i
$211$	−7.55246e48			−1.16992			−0.584961	−	0.811062i	$-0.698890\pi$
$211$	−7.55246e48			−1.16992			−0.584961	+	0.811062i	$0.698890\pi$
$212$			1.39870e48i			0.196187i
$213$	6.90959e48	+	1.27452e49i	0.877972	+	1.61948i
$214$	−2.43656e48			−0.280600
$215$		−	1.11735e49i		−	1.16676i
$216$	1.12808e49	+	9.09480e47i	1.06859	+	0.0861518i
$217$	6.62293e47			0.0569372
$218$			2.04098e49i			1.59314i
$219$	−2.35737e48	+	1.27801e48i	−0.167148	+	0.0906166i
$220$	2.71656e48			0.175042
$221$		−	3.08000e49i		−	1.80432i
$222$	−7.24395e48	−	1.33620e49i	−0.385979	−	0.711963i
$223$	−1.11341e49			−0.539825			−0.269912	−	0.962885i	$-0.586995\pi$
$223$	−1.11341e49			−0.539825			−0.269912	+	0.962885i	$0.586995\pi$
$224$		−	1.29078e49i		−	0.569695i
$225$	−9.02634e47	+	1.38607e48i	−0.0362809	+	0.0557125i
$226$	−3.46681e49			−1.26956
$227$		−	4.40667e48i		−	0.147085i	−0.997292	−	0.0735423i	$-0.976570\pi$
$227$		−	4.40667e48i		−	0.147085i	0.997292	−	0.0735423i	$-0.0234304\pi$
$228$	−6.21255e48	+	3.36803e48i	−0.189077	+	0.102505i
$229$	4.91606e48			0.136481			0.0682405	−	0.997669i	$-0.478261\pi$
$229$	4.91606e48			0.136481			0.0682405	+	0.997669i	$0.478261\pi$
$230$			3.19078e49i			0.808373i
$231$	2.67048e49	+	4.92588e49i	0.617644	+	1.13929i
$232$	−3.81147e49			−0.805090
$233$		−	8.79537e48i		−	0.169738i	−0.996392	−	0.0848691i	$-0.972953\pi$
$233$		−	8.79537e48i		−	0.169738i	0.996392	−	0.0848691i	$-0.0270472\pi$
$234$	−5.05350e49	−	3.29093e49i	−0.891373	−	0.580478i
$235$	4.76785e49			0.768949
$236$		−	1.43534e49i		−	0.211740i
$237$	1.71041e49	−	9.27270e48i	0.230880	−	0.125167i
$238$	1.64442e50			2.03187
$239$			4.98896e49i			0.564487i	0.959343	+	0.282244i	$0.0910787\pi$
$239$			4.98896e49i			0.564487i	−0.959343	+	0.282244i	$0.908921\pi$
$240$	−3.64535e49	−	6.72409e49i	−0.377835	−	0.696943i
$241$	6.95055e49			0.660178			0.330089	−	0.943950i	$-0.392921\pi$
$241$	6.95055e49			0.660178			0.330089	+	0.943950i	$0.392921\pi$
$242$			2.47991e49i			0.215930i
$243$	−9.91141e49	−	7.65548e49i	−0.791414	−	0.611281i
$244$	−1.35714e49			−0.0994115
$245$			1.86123e50i			1.25116i
$246$	−2.03025e49	+	1.10066e49i	−0.125289	+	0.0679232i
$247$	2.31256e50			1.31056
$248$		−	7.88413e48i		−	0.0410458i
$249$	6.55093e49	+	1.20836e50i	0.313413	+	0.578110i
$250$	−1.96730e50			−0.865228
$251$		−	1.21709e50i		−	0.492238i	−0.969240	−	0.246119i	$-0.920845\pi$
$251$		−	1.21709e50i		−	0.492238i	0.969240	−	0.246119i	$-0.0791554\pi$
$252$	−4.24271e49	+	6.51505e49i	−0.157846	+	0.242385i
$253$	−2.22009e50			−0.760047
$254$		−	2.35329e50i		−	0.741596i
$255$	−4.76307e50	+	2.58222e50i	−1.38211	+	0.749288i
$256$	−2.09522e50			−0.560004
$257$		−	5.07659e50i		−	1.25019i	−0.780548	−	0.625095i	$-0.785060\pi$
$257$		−	5.07659e50i		−	1.25019i	0.780548	−	0.625095i	$-0.214940\pi$
$258$	−2.12913e50	−	3.92733e50i	−0.483269	−	0.891423i
$259$	6.41238e50			1.34191
$260$		−	1.23350e50i		−	0.238068i
$261$	3.53434e50	+	2.30162e50i	0.629299	+	0.409811i
$262$	4.24531e49			0.0697562
$263$			1.23808e49i			0.0187792i	0.999956	+	0.00938961i	$0.00298885\pi$
$263$			1.23808e49i			0.0187792i	−0.999956	+	0.00938961i	$0.997011\pi$
$264$	5.86391e50	−	3.17902e50i	0.821306	−	0.445257i
$265$	−8.05164e50			−1.04165
$266$			1.23468e51i			1.47585i
$267$	1.99175e50	+	3.67392e50i	0.220039	+	0.405876i
$268$	1.11605e50			0.113986
$269$			6.35282e50i			0.600024i	0.953935	+	0.300012i	$0.0969907\pi$
$269$			6.35282e50i			0.600024i	−0.953935	+	0.300012i	$0.903009\pi$
$270$	−8.52497e49	+	1.05740e51i	−0.0744825	+	0.923852i
$271$	7.46160e50			0.603221			0.301611	−	0.953431i	$-0.402476\pi$
$271$	7.46160e50			0.603221			0.301611	+	0.953431i	$0.402476\pi$
$272$		−	1.56184e51i		−	1.16866i
$273$	2.23669e51	−	1.21258e51i	1.54950	−	0.840032i
$274$	−9.36596e50			−0.600884
$275$			9.74865e49i			0.0579373i
$276$	−1.46817e50	−	2.70813e50i	−0.0808508	−	0.149135i
$277$	−3.16076e51			−1.61330			−0.806651	−	0.591028i	$-0.798722\pi$
$277$	−3.16076e51			−1.61330			−0.806651	+	0.591028i	$0.798722\pi$
$278$			3.77313e51i			1.78550i
$279$	−4.76097e49	+	7.31088e49i	−0.0208933	+	0.0320835i
$280$	4.04447e51			1.64643
$281$		−	3.61642e51i		−	1.36599i	−0.730424	−	0.682994i	$-0.760678\pi$
$281$		−	3.61642e51i		−	1.36599i	0.730424	−	0.682994i	$-0.239322\pi$
$282$	1.67584e51	−	9.08526e50i	0.587490	−	0.318498i
$283$	−2.54998e51			−0.829892			−0.414946	−	0.909846i	$-0.636200\pi$
$283$	−2.54998e51			−0.829892			−0.414946	+	0.909846i	$0.636200\pi$
$284$			1.18560e51i			0.358306i
$285$	−1.93881e51	−	3.57627e51i	−0.544244	−	1.00389i
$286$	−3.55428e51			−0.926968
$287$		−	9.74314e50i		−	0.236145i
$288$	1.42485e51	+	9.27889e50i	0.321017	+	0.209052i
$289$	−6.28975e51			−1.31759
$290$		−	3.57266e51i		−	0.696040i
$291$	−2.67645e51	+	1.45099e51i	−0.485072	+	0.262973i
$292$	−2.19291e50			−0.0369812
$293$			7.19452e51i			1.12923i	0.825355	+	0.564614i	$0.190975\pi$
$293$			7.19452e51i			1.12923i	−0.825355	+	0.564614i	$0.809025\pi$
$294$	3.54662e51	+	6.54198e51i	0.518228	+	0.955906i
$295$	8.26256e51			1.12422
$296$		−	7.63348e51i		−	0.967379i
$297$	−7.35726e51	−	5.93155e50i	−0.868622	−	0.0700297i
$298$	6.88755e51			0.757745
$299$			1.00808e52i			1.03371i
$300$	−1.18917e50	+	6.44686e49i	−0.0113683	+	0.00616314i
$301$	1.88472e52			1.68016
$302$		−	1.49416e52i		−	1.24237i
$303$	1.50730e51	+	2.78031e51i	0.116924	+	0.215675i
$304$	1.17268e52			0.848856
$305$		−	7.81238e51i		−	0.527821i
$306$	−1.18211e52	+	1.81523e52i	−0.745603	+	1.14494i
$307$	−2.11177e52			−1.24377			−0.621886	−	0.783108i	$-0.713633\pi$
$307$	−2.11177e52			−1.24377			−0.621886	+	0.783108i	$0.713633\pi$
$308$			4.58223e51i			0.252065i
$309$	1.66937e52	−	9.05020e51i	0.857877	−	0.465083i
$310$	7.39016e50			0.0354861
$311$			4.34343e51i			0.194924i	0.995239	+	0.0974618i	$0.0310724\pi$
$311$			4.34343e51i			0.194924i	−0.995239	+	0.0974618i	$0.968928\pi$
$312$	−1.44349e52	−	2.66262e52i	−0.605576	−	1.11703i
$313$	9.77326e51			0.383361			0.191681	−	0.981457i	$-0.438606\pi$
$313$	9.77326e51			0.383361			0.191681	+	0.981457i	$0.438606\pi$
$314$			3.67782e52i			1.34918i
$315$	−3.75040e52	−	2.44233e52i	−1.28693	−	0.838074i
$316$	1.59109e51			0.0510816
$317$			3.86976e52i			1.16262i	0.813681	+	0.581312i	$0.197460\pi$
$317$			3.86976e52i			1.16262i	−0.813681	+	0.581312i	$0.802540\pi$
$318$	−2.83004e52	+	1.53426e52i	−0.795836	+	0.431449i
$319$	2.48580e52			0.654429
$320$		−	4.65617e52i		−	1.14784i
$321$	6.45380e51	+	1.19045e52i	0.149008	+	0.274855i
$322$	−5.38213e52			−1.16408
$323$		−	8.30679e52i		−	1.68337i
$324$	−4.14187e51	−	9.36684e51i	−0.0786595	−	0.177889i
$325$	4.42656e51			0.0787981
$326$		−	7.83899e51i		−	0.130825i
$327$	9.97177e52	−	5.40602e52i	1.56052	−	0.846009i
$328$	−1.15985e52			−0.170236
$329$			8.04231e52i			1.10730i
$330$	2.97984e52	+	5.49652e52i	0.384947	+	0.710060i
$331$	−5.71507e50			−0.00692842			−0.00346421	−	0.999994i	$-0.501103\pi$
$331$	−5.71507e50			−0.00692842			−0.00346421	+	0.999994i	$0.501103\pi$
$332$			1.12406e52i			0.127906i
$333$	−4.60961e52	+	7.07846e52i	−0.492420	+	0.756153i
$334$	7.66195e51			0.0768535
$335$			6.42454e52i			0.605203i
$336$	1.13420e53	−	6.14889e52i	1.00361	−	0.544092i
$337$	4.28497e52			0.356221			0.178111	−	0.984010i	$-0.443001\pi$
$337$	4.28497e52			0.356221			0.178111	+	0.984010i	$0.443001\pi$
$338$			4.64987e52i			0.363237i
$339$	9.18266e52	+	1.69380e53i	0.674179	+	1.24357i
$340$	−4.43078e52			−0.305790
$341$			5.14196e51i			0.0333647i
$342$	−1.36293e53	−	8.87566e52i	−0.831623	−	0.541567i
$343$	−5.48151e52			−0.314575
$344$		−	2.24362e53i		−	1.21122i
$345$	1.55894e53	−	8.45152e52i	0.791824	−	0.429273i
$346$	−2.45679e53			−1.17427
$347$		−	3.55888e53i		−	1.60101i	−0.599324	−	0.800507i	$-0.704564\pi$
$347$		−	3.55888e53i		−	1.60101i	0.599324	−	0.800507i	$-0.295436\pi$
$348$	1.64388e52	+	3.03225e52i	0.0696156	+	0.128411i
$349$	−9.17752e52			−0.365924			−0.182962	−	0.983120i	$-0.558569\pi$
$349$	−9.17752e52			−0.365924			−0.182962	+	0.983120i	$0.558569\pi$
$350$			2.36335e52i			0.0887358i
$351$	−2.69333e52	+	3.34070e53i	−0.0952446	+	1.18138i
$352$	1.00214e53			0.333836
$353$			2.78254e53i			0.873319i	0.899627	+	0.436660i	$0.143839\pi$
$353$			2.78254e53i			0.873319i	−0.899627	+	0.436660i	$0.856161\pi$
$354$	2.90418e53	−	1.57445e53i	0.858925	−	0.465651i
$355$	−6.82495e53			−1.90241
$356$			3.41761e52i			0.0897992i
$357$	−4.35563e53	−	8.03425e53i	−1.07899	−	1.99027i
$358$	6.33122e53			1.47892
$359$			2.59283e53i			0.571204i	0.958348	+	0.285602i	$0.0921935\pi$
$359$			2.59283e53i			0.571204i	−0.958348	+	0.285602i	$0.907806\pi$
$360$	−2.90742e53	+	4.46459e53i	−0.604164	+	0.927745i
$361$	1.13605e53			0.222714
$362$			5.12666e53i			0.948319i
$363$	1.21163e53	−	6.56863e52i	0.211509	−	0.114666i
$364$	2.08065e53			0.342823
$365$		−	1.26235e53i		−	0.196350i
$366$	−1.48867e53	−	2.74595e53i	−0.218622	−	0.403264i
$367$	3.65825e53			0.507325			0.253662	−	0.967293i	$-0.418365\pi$
$367$	3.65825e53			0.507325			0.253662	+	0.967293i	$0.418365\pi$
$368$			5.11186e53i			0.669537i
$369$	1.07552e53	+	7.00397e52i	0.133065	+	0.0866544i
$370$	7.15522e53			0.836347
$371$		−	1.35813e54i		−	1.50000i
$372$	−6.27230e51	+	3.40042e51i	−0.00654674	+	0.00354920i
$373$	9.89881e53			0.976557			0.488279	−	0.872688i	$-0.337625\pi$
$373$	9.89881e53			0.976557			0.488279	+	0.872688i	$0.337625\pi$
$374$			1.27671e54i			1.19066i
$375$	5.21086e53	+	9.61178e53i	0.459465	+	0.847515i
$376$	9.57380e53			0.798252
$377$		−	1.12873e54i		−	0.890063i
$378$	−1.78361e54	−	1.43797e53i	−1.33037	−	0.107256i
$379$	−1.29508e54			−0.913850			−0.456925	−	0.889505i	$-0.651049\pi$
$379$	−1.29508e54			−0.913850			−0.456925	+	0.889505i	$0.651049\pi$
$380$		−	3.32677e53i		−	0.222110i
$381$	−1.14976e54	+	6.23324e53i	−0.726413	+	0.393812i
$382$	3.28703e53			0.196550
$383$			3.76689e53i			0.213210i	0.994301	+	0.106605i	$0.0339981\pi$
$383$			3.76689e53i			0.213210i	−0.994301	+	0.106605i	$0.966002\pi$
$384$	−5.46519e53	−	1.00809e54i	−0.292853	−	0.540187i
$385$	−2.63777e54			−1.33832
$386$		−	2.62482e54i		−	1.26115i
$387$	−1.35485e54	+	2.08049e54i	−0.616541	+	0.946751i
$388$	−2.48973e53			−0.107321
$389$		−	9.48331e53i		−	0.387274i	−0.981073	−	0.193637i	$-0.937972\pi$
$389$		−	9.48331e53i		−	0.387274i	0.981073	−	0.193637i	$-0.0620284\pi$
$390$	2.49580e54	−	1.35305e54i	0.965724	−	0.523550i
$391$	3.62103e54			1.32776
$392$			3.73733e54i			1.29884i
$393$	−1.12447e53	−	2.07416e53i	−0.0370429	−	0.0683281i
$394$	−3.07573e54			−0.960568
$395$			9.15911e53i			0.271215i
$396$	−5.05820e53	−	3.29399e53i	−0.142036	−	0.0924961i
$397$	−1.72863e54			−0.460365			−0.230183	−	0.973147i	$-0.573932\pi$
$397$	−1.72863e54			−0.460365			−0.230183	+	0.973147i	$0.573932\pi$
$398$		−	3.35296e54i		−	0.847001i
$399$	6.03237e54	−	3.27035e54i	1.44563	−	0.783724i
$400$	2.24467e53			0.0510378
$401$			1.98877e54i			0.429095i	0.976714	+	0.214548i	$0.0688277\pi$
$401$			1.98877e54i			0.429095i	−0.976714	+	0.214548i	$0.931172\pi$
$402$	1.22421e54	+	2.25814e54i	0.250674	+	0.462385i
$403$	2.33480e53			0.0453779
$404$			2.58635e53i			0.0477175i
$405$	5.39204e54	−	2.38427e54i	0.944491	−	0.417639i
$406$	6.02629e54			1.00231
$407$			4.97849e54i			0.786349i
$408$	−9.56421e54	+	5.18507e54i	−1.43478	+	0.777841i
$409$	−6.09384e54			−0.868364			−0.434182	−	0.900825i	$-0.642963\pi$
$409$	−6.09384e54			−0.868364			−0.434182	+	0.900825i	$0.642963\pi$
$410$		−	1.08718e54i		−	0.147177i
$411$	2.48079e54	+	4.57599e54i	0.319089	+	0.588582i
$412$	1.55291e54			0.189803
$413$			1.39371e55i			1.61891i
$414$	3.86901e54	−	5.94120e54i	0.427162	−	0.655944i
$415$	−6.47068e54			−0.679109
$416$		−	4.55042e54i		−	0.454037i
$417$	1.84346e55	−	9.99401e54i	1.74895	−	0.948162i
$418$	−9.58592e54			−0.864832
$419$		−	1.03417e55i		−	0.887357i	−0.896186	−	0.443678i	$-0.853673\pi$
$419$		−	1.03417e55i		−	0.887357i	0.896186	−	0.443678i	$-0.146327\pi$
$420$	−1.74438e54	−	3.21762e54i	−0.142366	−	0.262603i
$421$	−7.44772e54			−0.578228			−0.289114	−	0.957295i	$-0.593361\pi$
$421$	−7.44772e54			−0.578228			−0.289114	+	0.957295i	$0.593361\pi$
$422$		−	1.42151e55i		−	1.05000i
$423$	−8.87770e54	−	5.78131e54i	−0.623954	−	0.406330i
$424$	−1.61676e55			−1.08134
$425$		−	1.59003e54i		−	0.101213i
$426$	−2.39888e55	+	1.30051e55i	−1.45347	+	0.787975i
$427$	1.31777e55			0.760074
$428$			1.10739e54i			0.0608112i
$429$	9.41434e54	+	1.73654e55i	0.492251	+	0.907991i
$430$	2.10305e55			1.04716
$431$		−	2.36573e55i		−	1.12187i	−0.827860	−	0.560935i	$-0.810442\pi$
$431$		−	2.36573e55i		−	1.12187i	0.827860	−	0.560935i	$-0.189558\pi$
$432$	−1.36576e54	+	1.69404e55i	−0.0616903	+	0.765182i
$433$	1.32858e55			0.571667			0.285834	−	0.958279i	$-0.407730\pi$
$433$	1.32858e55			0.571667			0.285834	+	0.958279i	$0.407730\pi$
$434$			1.24656e54i			0.0511008i
$435$	−1.74552e55	+	9.46304e54i	−0.681790	+	0.369621i
$436$	9.27609e54			0.345262
$437$			2.71879e55i			0.964418i
$438$	−2.40545e54	−	4.43701e54i	−0.0813279	−	0.150015i
$439$	−2.01281e55			−0.648705			−0.324352	−	0.945936i	$-0.605146\pi$
$439$	−2.01281e55			−0.648705			−0.324352	+	0.945936i	$0.605146\pi$
$440$			3.14008e55i			0.964793i
$441$	2.25686e55	−	3.46559e55i	0.661140	−	1.01524i
$442$	5.79713e55			1.61937
$443$			2.52393e55i			0.672357i	0.941798	+	0.336178i	$0.109134\pi$
$443$			2.52393e55i			0.672357i	−0.941798	+	0.336178i	$0.890866\pi$
$444$	−6.07290e54	+	3.29231e54i	−0.154296	+	0.0836487i
$445$	−1.96735e55			−0.476785
$446$		−	2.09564e55i		−	0.484490i
$447$	−1.82433e55	−	3.36510e55i	−0.402388	−	0.742232i
$448$	7.85394e55			1.65291
$449$		−	7.37329e55i		−	1.48077i	−0.672182	−	0.740386i	$-0.734643\pi$
$449$		−	7.37329e55i		−	1.48077i	0.672182	−	0.740386i	$-0.265357\pi$
$450$	−2.60884e54	−	1.69892e54i	−0.0500017	−	0.0325619i
$451$	7.56445e54			0.138379
$452$			1.57564e55i			0.275137i
$453$	−7.30013e55	+	3.95764e55i	−1.21694	+	0.659742i
$454$	8.29415e54			0.132008
$455$			1.19773e56i			1.82020i
$456$	−3.89311e55	−	7.18111e55i	−0.564983	−	1.04215i
$457$	−9.17486e55			−1.27163			−0.635813	−	0.771843i	$-0.719335\pi$
$457$	−9.17486e55			−1.27163			−0.635813	+	0.771843i	$0.719335\pi$
$458$			9.25293e54i			0.122491i
$459$	1.19999e56	+	9.67452e54i	1.51744	+	0.122338i
$460$	1.45018e55			0.175189
$461$		−	4.10595e55i		−	0.473908i	−0.971521	−	0.236954i	$-0.923851\pi$
$461$		−	4.10595e55i		−	0.473908i	0.971521	−	0.236954i	$-0.0761491\pi$
$462$	−9.27141e55	+	5.02633e55i	−1.02250	+	0.554332i
$463$	−1.40269e56			−1.47830			−0.739149	−	0.673541i	$-0.764772\pi$
$463$	−1.40269e56			−1.47830			−0.739149	+	0.673541i	$0.764772\pi$
$464$		−	5.72367e55i		−	0.576497i
$465$	−1.95746e54	−	3.61066e54i	−0.0188443	−	0.0347596i
$466$	1.65545e55			0.152339
$467$		−	1.79216e56i		−	1.57660i	−0.615290	−	0.788301i	$-0.710961\pi$
$467$		−	1.79216e56i		−	1.57660i	0.615290	−	0.788301i	$-0.289039\pi$
$468$	−1.49570e55	+	2.29677e55i	−0.125800	+	0.193177i
$469$	−1.08368e56			−0.871506
$470$			8.97397e55i			0.690128i
$471$	1.79690e56	−	9.74158e55i	1.32155	−	0.716457i
$472$	1.65911e56			1.16706
$473$			1.46327e56i			0.984557i
$474$	1.74529e55	+	3.21931e55i	0.112337	+	0.207213i
$475$	1.19385e55			0.0735162
$476$		−	7.47374e55i		−	0.440344i
$477$	1.49921e56	+	9.76310e55i	0.845231	+	0.550429i
$478$	−9.39013e55			−0.506624
$479$		−	6.51468e55i		−	0.336393i	−0.985753	−	0.168197i	$-0.946206\pi$
$479$		−	6.51468e55i		−	0.336393i	0.985753	−	0.168197i	$-0.0537943\pi$
$480$	−7.03700e55	+	3.81498e55i	−0.347793	+	0.188550i
$481$	2.26058e56			1.06948
$482$			1.30822e56i			0.592506i
$483$	1.42558e56	+	2.62959e56i	0.618163	+	1.14024i
$484$	1.12710e55			0.0467960
$485$		−	1.43322e56i		−	0.569817i
$486$	1.44090e56	−	1.86551e56i	0.548621	−	0.710289i
$487$	−2.24454e56			−0.818501			−0.409251	−	0.912422i	$-0.634210\pi$
$487$	−2.24454e56			−0.818501			−0.409251	+	0.912422i	$0.634210\pi$
$488$		−	1.56872e56i		−	0.547934i
$489$	−3.82995e55	+	2.07634e55i	−0.128147	+	0.0694724i
$490$	−3.50318e56			−1.12291
$491$			4.34489e56i			1.33434i	0.744904	+	0.667172i	$0.232495\pi$
$491$			4.34489e56i			1.33434i	−0.744904	+	0.667172i	$0.767505\pi$
$492$	5.00243e54	+	9.22731e54i	0.0147202	+	0.0271524i
$493$	−4.05442e56			−1.14325
$494$			4.35267e56i			1.17622i
$495$	1.89619e56	−	2.91176e56i	0.491103	−	0.754131i
$496$	1.18396e55			0.0293914
$497$		−	1.15122e57i		−	2.73951i
$498$	−2.27436e56	+	1.23300e56i	−0.518851	+	0.281286i
$499$	4.58058e56			1.00186			0.500932	−	0.865487i	$-0.332991\pi$
$499$	4.58058e56			1.00186			0.500932	+	0.865487i	$0.332991\pi$
$500$			8.94121e55i			0.187511i
$501$	−2.02945e55	−	3.74345e55i	−0.0408118	−	0.0752801i
$502$	2.29079e56			0.441781
$503$			6.70353e56i			1.23987i	0.784653	+	0.619935i	$0.212841\pi$
$503$			6.70353e56i			1.23987i	−0.784653	+	0.619935i	$0.787159\pi$
$504$	−7.53077e56	−	4.90417e56i	−1.33597	−	0.870010i
$505$	−1.48884e56			−0.253354
$506$		−	4.17862e56i		−	0.682138i
$507$	2.27182e56	−	1.23163e56i	0.355801	−	0.192891i
$508$	−1.06955e56			−0.160717
$509$			8.45746e56i			1.21946i	0.792610	+	0.609729i	$0.208722\pi$
$509$			8.45746e56i			1.21946i	−0.792610	+	0.609729i	$0.791278\pi$
$510$	−4.86020e56	−	8.96497e56i	−0.672482	−	1.24044i
$511$	2.12931e56			0.282749
$512$		−	8.76491e56i		−	1.11706i
$513$	−7.26394e55	+	9.00990e56i	−0.0888602	+	1.10219i
$514$	9.55506e56			1.12204
$515$			8.93934e56i			1.00775i
$516$	−1.78494e56	+	9.67673e55i	−0.193188	+	0.104733i
$517$	−6.24395e56			−0.648871
$518$			1.20693e57i			1.20436i
$519$	6.50738e56	+	1.20033e57i	0.623579	+	1.15023i
$520$	1.42581e57			1.31218
$521$		−	1.93613e57i		−	1.71136i	−0.517502	−	0.855682i	$-0.673138\pi$
$521$		−	1.93613e57i		−	1.71136i	0.517502	−	0.855682i	$-0.326862\pi$
$522$	−4.33207e56	+	6.65227e56i	−0.367803	+	0.564793i
$523$	9.61573e56			0.784236			0.392118	−	0.919915i	$-0.371742\pi$
$523$	9.61573e56			0.784236			0.392118	+	0.919915i	$0.371742\pi$
$524$		−	1.92946e55i		−	0.0151174i
$525$	1.15468e56	−	6.25988e55i	0.0869191	−	0.0471217i
$526$	−2.33029e55			−0.0168542
$527$		−	8.38668e55i		−	0.0582864i
$528$	4.77392e56	+	8.80582e56i	0.318833	+	0.588109i
$529$	3.72852e56			0.239314
$530$		−	1.51546e57i		−	0.934873i
$531$	−1.53848e57	−	1.00189e57i	−0.912236	−	0.594064i
$532$	5.61153e56			0.319843
$533$		−	3.43478e56i		−	0.188203i
$534$	−6.91499e56	+	3.74884e56i	−0.364271	+	0.197483i
$535$	−6.37474e56			−0.322874
$536$			1.29004e57i			0.628265i
$537$	−1.67697e57	−	3.09329e57i	−0.785355	−	1.44864i
$538$	−1.19572e57			−0.538518
$539$		−	2.43746e57i		−	1.05578i
$540$	4.80581e56	+	3.87453e55i	0.200216	+	0.0161417i
$541$	−1.98075e57			−0.793754			−0.396877	−	0.917872i	$-0.629906\pi$
$541$	−1.98075e57			−0.793754			−0.396877	+	0.917872i	$0.629906\pi$
$542$			1.40441e57i			0.541388i
$543$	2.50477e57	−	1.35792e57i	0.928905	−	0.503590i
$544$	−1.63452e57			−0.583195
$545$			5.33980e57i			1.83315i
$546$	2.28230e57	+	4.20986e57i	0.753924	+	1.39066i
$547$	−3.19526e57			−1.01572			−0.507858	−	0.861441i	$-0.669562\pi$
$547$	−3.19526e57			−1.01572			−0.507858	+	0.861441i	$0.669562\pi$
$548$			4.25675e56i			0.130223i
$549$	−9.47298e56	+	1.45466e57i	−0.278912	+	0.428293i
$550$	−1.83487e56			−0.0519984
$551$		−	3.04419e57i		−	0.830400i
$552$	3.13034e57	−	1.69706e57i	0.821997	−	0.445632i
$553$	−1.54494e57			−0.390556
$554$		−	5.94912e57i		−	1.44793i
$555$	−1.89523e57	−	3.49587e57i	−0.444129	−	0.819225i
$556$	1.71485e57			0.386951
$557$			1.18866e57i			0.258284i	0.991626	+	0.129142i	$0.0412223\pi$
$557$			1.18866e57i			0.258284i	−0.991626	+	0.129142i	$0.958778\pi$
$558$	−1.37604e56	−	8.96102e55i	−0.0287947	−	0.0187516i
$559$	6.64426e57			1.33906
$560$			6.07357e57i			1.17895i
$561$	6.23769e57	−	3.38166e57i	1.16628	−	0.632280i
$562$	6.80677e57			1.22597
$563$			6.72390e57i			1.16666i	0.812235	+	0.583331i	$0.198251\pi$
$563$			6.72390e57i			1.16666i	−0.812235	+	0.583331i	$0.801749\pi$
$564$	−4.12917e56	−	7.61654e56i	−0.0690243	−	0.127320i
$565$	−9.07018e57			−1.46083
$566$		−	4.79953e57i		−	0.744823i
$567$	4.02174e57	+	9.09518e57i	0.601409	+	1.36009i
$568$	−1.37044e58			−1.97490
$569$			2.60538e57i			0.361837i	0.983498	+	0.180919i	$0.0579070\pi$
$569$			2.60538e57i			0.361837i	−0.983498	+	0.180919i	$0.942093\pi$
$570$	6.73119e57	−	3.64920e57i	0.900990	−	0.488456i
$571$	9.61585e57			1.24059			0.620297	−	0.784367i	$-0.287012\pi$
$571$	9.61585e57			1.24059			0.620297	+	0.784367i	$0.287012\pi$
$572$			1.61539e57i			0.200891i
$573$	−8.70648e56	−	1.60597e57i	−0.104375	−	0.192526i
$574$	1.83384e57			0.211939
$575$			5.20413e56i			0.0579860i
$576$	−5.64589e57	+	8.66975e57i	−0.606542	+	0.931396i
$577$	−7.05107e57			−0.730404			−0.365202	−	0.930928i	$-0.619000\pi$
$577$	−7.05107e57			−0.730404			−0.365202	+	0.930928i	$0.619000\pi$
$578$		−	1.18385e58i		−	1.18253i
$579$	−1.28243e58	+	6.95246e57i	−1.23533	+	0.669713i
$580$	−1.62375e57			−0.150845
$581$		−	1.09146e58i		−	0.977933i
$582$	−2.73103e57	−	5.03757e57i	−0.236017	−	0.435350i
$583$	1.05444e58			0.878984
$584$		−	2.53479e57i		−	0.203832i
$585$	−1.32214e58	−	8.61002e57i	−1.02566	−	0.667930i
$586$	−1.35414e58			−1.01348
$587$		−	5.18573e57i		−	0.374464i	−0.982316	−	0.187232i	$-0.940048\pi$
$587$		−	5.18573e57i		−	0.374464i	0.982316	−	0.187232i	$-0.0599516\pi$
$588$	2.97327e57	−	1.61191e57i	0.207162	−	0.112310i
$589$	6.29698e56			0.0423362
$590$			1.55517e58i			1.00898i
$591$	8.14680e57	+	1.50273e58i	0.510094	+	0.940902i
$592$	1.14632e58			0.692706
$593$		−	2.55630e58i		−	1.49095i	−0.666532	−	0.745476i	$-0.732222\pi$
$593$		−	2.55630e58i		−	1.49095i	0.666532	−	0.745476i	$-0.267778\pi$
$594$	1.11643e57	−	1.38477e58i	0.0628513	−	0.779583i
$595$	4.30227e58			2.33799
$596$		−	3.13033e57i		−	0.164217i
$597$	−1.63818e58	+	8.88111e57i	−0.829661	+	0.449786i
$598$	−1.89738e58			−0.927748
$599$			3.75023e58i			1.77050i	0.465118	+	0.885249i	$0.346012\pi$
$599$			3.75023e58i			1.77050i	−0.465118	+	0.885249i	$0.653988\pi$
$600$	−7.45195e56	−	1.37456e57i	−0.0339698	−	0.0626597i
$601$	−6.94744e57			−0.305816			−0.152908	−	0.988240i	$-0.548864\pi$
$601$	−6.94744e57			−0.305816			−0.152908	+	0.988240i	$0.548864\pi$
$602$			3.54738e58i			1.50793i
$603$	7.79015e57	−	1.19624e58i	0.319803	−	0.491084i
$604$	−6.79084e57			−0.269245
$605$			6.48816e57i			0.248461i
$606$	−5.23306e57	+	2.83701e57i	−0.193567	+	0.104939i
$607$	3.78358e58			1.35189			0.675943	−	0.736954i	$-0.263736\pi$
$607$	3.78358e58			1.35189			0.675943	+	0.736954i	$0.263736\pi$
$608$		−	1.22725e58i		−	0.423602i
$609$	−1.59621e58	−	2.94431e58i	−0.532262	−	0.981794i
$610$	1.47043e58			0.473716
$611$			2.83518e58i			0.882503i
$612$	8.25007e57	+	5.37259e57i	0.248129	+	0.161586i
$613$	5.00494e58			1.45455			0.727276	−	0.686345i	$-0.240786\pi$
$613$	5.00494e58			1.45455			0.727276	+	0.686345i	$0.240786\pi$
$614$		−	3.97473e58i		−	1.11628i
$615$	−5.31172e57	+	2.87966e57i	−0.144164	+	0.0781562i
$616$	−5.29662e58			−1.38932
$617$		−	6.14033e57i		−	0.155669i	−0.996966	−	0.0778347i	$-0.975199\pi$
$617$		−	6.14033e57i		−	0.155669i	0.996966	−	0.0778347i	$-0.0248007\pi$
$618$	1.70341e58	+	3.14206e58i	0.417409	+	0.769939i
$619$	−1.65937e58			−0.393042			−0.196521	−	0.980500i	$-0.562964\pi$
$619$	−1.65937e58			−0.393042			−0.196521	+	0.980500i	$0.562964\pi$
$620$		−	3.35876e56i		−	0.00769049i
$621$	−3.92753e58	−	3.16644e57i	−0.869353	−	0.0700887i
$622$	−8.17512e57			−0.174943
$623$		−	3.31849e58i		−	0.686581i
$624$	3.99845e58	−	2.16769e58i	0.799863	−	0.433632i
$625$	−5.49074e58			−1.06206
$626$			1.83951e58i			0.344065i
$627$	2.53905e58	+	4.68346e58i	0.459255	+	0.847126i
$628$	1.67154e58			0.292391
$629$		−	8.12006e58i		−	1.37371i
$630$	4.59690e58	−	7.05894e58i	0.752166	−	1.15502i
$631$	−7.89703e58			−1.24982			−0.624910	−	0.780697i	$-0.714864\pi$
$631$	−7.89703e58			−1.24982			−0.624910	+	0.780697i	$0.714864\pi$
$632$			1.83914e58i			0.281551i
$633$	−6.94517e58	+	3.76520e58i	−1.02850	+	0.557584i
$634$	−7.28359e58			−1.04345
$635$		−	6.15689e58i		−	0.853322i
$636$	6.97307e57	+	1.28623e58i	0.0935029	+	0.172472i
$637$	−1.10677e59			−1.43592
$638$			4.67874e58i			0.587347i
$639$	1.27080e59	+	8.27566e58i	1.54369	+	1.00527i
$640$	5.39825e58			0.634561
$641$			1.37127e59i			1.55993i	0.625822	+	0.779966i	$0.284764\pi$
$641$			1.37127e59i			1.55993i	−0.625822	+	0.779966i	$0.715236\pi$
$642$	−2.24064e58	+	1.21472e58i	−0.246681	+	0.133734i
$643$	1.58546e59			1.68937			0.844685	−	0.535263i	$-0.179788\pi$
$643$	1.58546e59			1.68937			0.844685	+	0.535263i	$0.179788\pi$
$644$			2.44613e58i			0.252277i
$645$	−5.57043e58	−	1.02750e59i	−0.556077	−	1.02572i
$646$	1.56349e59			1.51082
$647$		−	1.72280e58i		−	0.161155i	−0.996748	−	0.0805776i	$-0.974324\pi$
$647$		−	1.72280e58i		−	0.161155i	0.996748	−	0.0805776i	$-0.0256765\pi$
$648$	1.08272e59	−	4.78760e58i	0.980482	−	0.433553i
$649$	−1.08206e59			−0.948665
$650$			8.33160e57i			0.0707209i
$651$	6.09039e57	−	3.30180e57i	0.0500546	−	0.0271362i
$652$	−3.56275e57			−0.0283522
$653$		−	2.41269e59i		−	1.85919i	−0.368582	−	0.929595i	$-0.620157\pi$
$653$		−	2.41269e59i		−	1.85919i	0.368582	−	0.929595i	$-0.379843\pi$
$654$	1.01751e59	+	1.87687e59i	0.759288	+	1.40056i
$655$	1.11070e58			0.0802653
$656$		−	1.74174e58i		−	0.121900i
$657$	−1.53068e58	+	2.35049e58i	−0.103756	+	0.159326i
$658$	−1.51371e59			−0.993800
$659$			1.43003e59i			0.909394i	0.890646	+	0.454697i	$0.150252\pi$
$659$			1.43003e59i			0.909394i	−0.890646	+	0.454697i	$0.849748\pi$
$660$	2.49812e58	−	1.35431e58i	0.153883	−	0.0834250i
$661$	1.51384e59			0.903337			0.451669	−	0.892186i	$-0.350829\pi$
$661$	1.51384e59			0.903337			0.451669	+	0.892186i	$0.350829\pi$
$662$		−	1.07568e57i		−	0.00621821i
$663$	−1.53551e59	−	2.83234e59i	−0.859938	−	1.58621i
$664$	−1.29931e59			−0.704988
$665$			3.23029e59i			1.69819i
$666$	−1.33229e59	−	8.67614e58i	−0.678643	−	0.441944i
$667$	1.32700e59			0.654980
$668$		−	3.48229e57i		−	0.0166556i
$669$	−1.02388e59	+	5.55079e58i	−0.474571	+	0.257280i
$670$	−1.20922e59			−0.543166
$671$			1.02310e59i			0.445396i
$672$	−6.43504e58	−	1.18699e59i	−0.271516	−	0.500830i
$673$	8.45019e58			0.345581			0.172791	−	0.984959i	$-0.444722\pi$
$673$	8.45019e58			0.345581			0.172791	+	0.984959i	$0.444722\pi$
$674$			8.06510e58i			0.319707i
$675$	−1.39042e57	+	1.72462e58i	−0.00534276	+	0.0662695i
$676$	2.11333e58			0.0787202
$677$		−	3.33262e59i		−	1.20344i	−0.798707	−	0.601720i	$-0.794482\pi$
$677$		−	3.33262e59i		−	1.20344i	0.798707	−	0.601720i	$-0.205518\pi$
$678$	−3.18805e59	+	1.72834e59i	−1.11610	+	0.605072i
$679$	2.41752e59			0.820550
$680$		−	5.12155e59i		−	1.68544i
$681$	−2.19690e58	−	4.05233e58i	−0.0701005	−	0.129305i
$682$	−9.67810e57			−0.0299446
$683$			1.32106e59i			0.396357i	0.980166	+	0.198179i	$0.0635026\pi$
$683$			1.32106e59i			0.396357i	−0.980166	+	0.198179i	$0.936497\pi$
$684$	−4.03391e58	+	6.19441e58i	−0.117368	+	0.180228i
$685$	−2.45040e59			−0.691410
$686$		−	1.03172e59i		−	0.282329i
$687$	4.52077e58	−	2.45085e58i	0.119983	−	0.0650468i
$688$	3.36924e59			0.867311
$689$		−	4.78787e59i		−	1.19547i
$690$	1.59073e59	+	2.93421e59i	0.385270	+	0.710657i
$691$	4.48891e58			0.105463			0.0527317	−	0.998609i	$-0.483207\pi$
$691$	4.48891e58			0.105463			0.0527317	+	0.998609i	$0.483207\pi$
$692$			1.11659e59i			0.254487i
$693$	4.91150e59	+	3.19846e59i	1.08597	+	0.707200i
$694$	6.69847e59			1.43690
$695$			9.87159e59i			2.05450i
$696$	−3.50499e59	+	1.90017e59i	−0.707771	+	0.383706i
$697$	−1.23378e59			−0.241741
$698$		−	1.72738e59i		−	0.328415i
$699$	−4.38484e58	−	8.08814e58i	−0.0808972	−	0.149220i
$700$	1.07412e58			0.0192307
$701$			2.67159e59i			0.464185i	0.972694	+	0.232092i	$0.0745572\pi$
$701$			2.67159e59i			0.464185i	−0.972694	+	0.232092i	$0.925443\pi$
$702$	−6.28782e59	−	5.06934e58i	−1.06028	−	0.0854815i
$703$	6.09680e59			0.997792
$704$			6.09770e59i			0.968590i
$705$	4.38447e59	−	2.37697e59i	0.675999	−	0.366481i
$706$	−5.23725e59			−0.783799
$707$		−	2.51134e59i		−	0.364836i
$708$	−7.15575e58	−	1.31993e59i	−0.100915	−	0.186145i
$709$	−5.90682e59			−0.808692			−0.404346	−	0.914606i	$-0.632501\pi$
$709$	−5.90682e59			−0.808692			−0.404346	+	0.914606i	$0.632501\pi$
$710$		−	1.28458e60i		−	1.70740i
$711$	1.11060e59	−	1.70542e59i	0.143316	−	0.220074i
$712$	−3.95043e59			−0.494953
$713$			2.74493e58i			0.0333927i
$714$	1.51219e60	−	8.19809e59i	1.78626	−	0.968390i
$715$	−9.29902e59			−1.06662
$716$		−	2.87749e59i		−	0.320509i
$717$	2.48720e59	+	4.58780e59i	0.269035	+	0.496252i
$718$	−4.88019e59			−0.512653
$719$			5.72423e59i			0.583997i	0.956419	+	0.291998i	$0.0943202\pi$
$719$			5.72423e59i			0.583997i	−0.956419	+	0.291998i	$0.905680\pi$
$720$	−6.70446e59	−	4.36606e59i	−0.664326	−	0.432620i
$721$	−1.50787e60			−1.45119
$722$			2.13826e59i			0.199884i
$723$	6.39166e59	−	3.46513e59i	0.580376	−	0.314641i
$724$	2.33002e59			0.205518
$725$		−	5.82698e58i		−	0.0499282i
$726$	1.23634e59	+	2.28050e59i	0.102912	+	0.189829i
$727$	1.57771e60			1.27586			0.637932	−	0.770093i	$-0.279790\pi$
$727$	1.57771e60			1.27586			0.637932	+	0.770093i	$0.279790\pi$
$728$			2.40503e60i			1.88956i
$729$	−1.29310e60	−	2.09868e59i	−0.987084	−	0.160202i
$730$	2.37598e59			0.176223
$731$		−	2.38664e60i		−	1.71997i
$732$	−1.24801e59	+	6.76587e58i	−0.0873947	+	0.0473795i
$733$	−1.86116e60			−1.26649			−0.633244	−	0.773953i	$-0.718277\pi$
$733$	−1.86116e60			−1.26649			−0.633244	+	0.773953i	$0.718277\pi$
$734$			6.88550e59i			0.455321i
$735$	9.27898e59	+	1.71157e60i	0.596302	+	1.09992i
$736$	5.34974e59			0.334117
$737$		−	8.41354e59i		−	0.510695i
$738$	−1.31827e59	+	2.02432e59i	−0.0777718	+	0.119425i
$739$	−1.40992e60			−0.808464			−0.404232	−	0.914657i	$-0.632461\pi$
$739$	−1.40992e60			−0.808464			−0.404232	+	0.914657i	$0.632461\pi$
$740$		−	3.25199e59i		−	0.181252i
$741$	2.12661e60	−	1.15291e60i	1.15214	−	0.624614i
$742$	2.55625e60			1.34624
$743$			8.46860e59i			0.433558i	0.976221	+	0.216779i	$0.0695550\pi$
$743$			8.46860e59i			0.433558i	−0.976221	+	0.216779i	$0.930445\pi$
$744$	−3.93055e58	−	7.25017e58i	−0.0195624	−	0.0360842i
$745$	1.80198e60			0.871904
$746$			1.86314e60i			0.876455i
$747$	1.20483e60	+	7.84609e59i	0.551055	+	0.358856i
$748$	5.80252e59			0.258038
$749$		−	1.07528e60i		−	0.464946i
$750$	−1.80911e60	+	9.80779e59i	−0.760640	+	0.412368i
$751$	−1.44434e60			−0.590515			−0.295257	−	0.955418i	$-0.595405\pi$
$751$	−1.44434e60			−0.590515			−0.295257	+	0.955418i	$0.595405\pi$
$752$			1.43770e60i			0.571600i
$753$	−6.06769e59	−	1.11923e60i	−0.234601	−	0.432736i
$754$	2.12447e60			0.798826
$755$		−	3.90916e60i		−	1.42954i
$756$	−6.53547e58	+	8.10635e59i	−0.0232444	+	0.288315i
$757$	1.24352e60			0.430170			0.215085	−	0.976595i	$-0.430997\pi$
$757$	1.24352e60			0.430170			0.215085	+	0.976595i	$0.430997\pi$
$758$		−	2.43759e60i		−	0.820175i
$759$	−2.04158e60	+	1.10681e60i	−0.668173	+	0.362238i
$760$	3.84543e60			1.22422
$761$		−	3.68413e59i		−	0.114092i	−0.998372	−	0.0570462i	$-0.981832\pi$
$761$		−	3.68413e59i		−	0.114092i	0.998372	−	0.0570462i	$-0.0181682\pi$
$762$	−1.17321e60	−	2.16406e60i	−0.353444	−	0.651952i
$763$	−9.00706e60			−2.63978
$764$		−	1.49393e59i		−	0.0425960i
$765$	−3.09274e60	+	4.74917e60i	−0.857933	+	1.31743i
$766$	−7.08997e59			−0.191355
$767$			4.91330e60i			1.29024i
$768$	−1.92675e60	+	1.04455e60i	−0.492311	+	0.266898i
$769$	4.39336e60			1.09230			0.546152	−	0.837686i	$-0.316092\pi$
$769$	4.39336e60			1.09230			0.546152	+	0.837686i	$0.316092\pi$
$770$		−	4.96476e60i		−	1.20114i
$771$	−2.53088e60	−	4.66838e60i	−0.595841	−	1.09907i
$772$	−1.19296e60			−0.273314
$773$			4.70825e60i			1.04976i	0.851176	+	0.524880i	$0.175890\pi$
$773$			4.70825e60i			1.04976i	−0.851176	+	0.524880i	$0.824110\pi$
$774$	−3.91586e60	−	2.55008e60i	−0.849704	−	0.553342i
$775$	1.20533e58			0.00254548
$776$		−	2.87789e60i		−	0.591531i
$777$	5.89677e60	−	3.19683e60i	1.17970	−	0.639555i
$778$	1.78493e60			0.347576
$779$		−	9.26363e59i		−	0.175588i
$780$	−6.14951e59	−	1.13432e60i	−0.113463	−	0.209290i
$781$	8.93791e60			1.60533
$782$			6.81545e60i			1.19166i
$783$	4.39760e60	+	3.54542e59i	0.748546	+	0.0603490i
$784$	−5.61234e60			−0.930051
$785$			9.62225e60i			1.55244i
$786$	3.90395e59	−	2.11646e59i	0.0613241	−	0.0332458i
$787$	1.89867e59			0.0290389			0.0145195	−	0.999895i	$-0.495378\pi$
$787$	1.89867e59			0.0290389			0.0145195	+	0.999895i	$0.495378\pi$
$788$			1.39789e60i			0.208173i
$789$	6.17232e58	+	1.13853e59i	0.00895017	+	0.0165092i
$790$	−1.72391e60			−0.243414
$791$		−	1.52994e61i		−	2.10362i
$792$	3.80753e60	−	5.84679e60i	0.509818	−	0.782869i
$793$	4.64560e60			0.605766
$794$		−	3.25361e60i		−	0.413175i
$795$	−7.40421e60	+	4.01406e60i	−0.915733	+	0.496449i
$796$	−1.52389e60			−0.183561
$797$			9.97845e60i			1.17068i	0.810788	+	0.585340i	$0.199039\pi$
$797$			9.97845e60i			1.17068i	−0.810788	+	0.585340i	$0.800961\pi$
$798$	6.15539e60	+	1.13540e61i	0.703388	+	1.29745i
$799$	1.01841e61			1.13354
$800$		−	2.34912e59i		−	0.0254692i
$801$	3.66319e60	+	2.38554e60i	0.386881	+	0.251943i
$802$	−3.74324e60			−0.385111
$803$			1.65317e60i			0.165688i
$804$	1.02631e60	−	5.56394e59i	0.100207	−	0.0543257i
$805$	−1.40812e61			−1.33945
$806$			4.39453e59i			0.0407264i
$807$	3.16714e60	+	5.84200e60i	0.285971	+	0.527493i
$808$	−2.98957e60			−0.263008
$809$		−	1.08213e61i		−	0.927601i	−0.885940	−	0.463801i	$-0.846485\pi$
$809$		−	1.08213e61i		−	0.927601i	0.885940	−	0.463801i	$-0.153515\pi$
$810$	4.48764e60	+	1.01488e61i	0.374828	+	0.847675i
$811$	−2.20955e61			−1.79832			−0.899159	−	0.437622i	$-0.855821\pi$
$811$	−2.20955e61			−1.79832			−0.899159	+	0.437622i	$0.855821\pi$
$812$		−	2.73890e60i		−	0.217220i
$813$	6.86162e60	−	3.71991e60i	0.530304	−	0.287495i
$814$	−9.37043e60			−0.705744
$815$		−	2.05091e60i		−	0.150534i
$816$	−7.78640e60	−	1.43625e61i	−0.556985	−	1.02740i
$817$	1.79196e61			1.24930
$818$		−	1.14697e61i		−	0.779352i
$819$	1.45232e61	−	2.23016e61i	0.961834	−	1.47698i
$820$	−4.94115e59			−0.0318961
$821$		−	3.00432e60i		−	0.189034i	−0.995523	−	0.0945169i	$-0.969869\pi$
$821$		−	3.00432e60i		−	0.189034i	0.995523	−	0.0945169i	$-0.0301306\pi$
$822$	−8.61285e60	+	4.66931e60i	−0.528249	+	0.286381i
$823$	−1.22270e61			−0.731012			−0.365506	−	0.930809i	$-0.619104\pi$
$823$	−1.22270e61			−0.731012			−0.365506	+	0.930809i	$0.619104\pi$
$824$			1.79501e61i			1.04615i
$825$	4.86009e59	+	8.96477e59i	0.0276129	+	0.0509338i
$826$	−2.62322e61			−1.45296
$827$		−	2.35769e61i		−	1.27312i	−0.771226	−	0.636562i	$-0.780356\pi$
$827$		−	2.35769e61i		−	1.27312i	0.771226	−	0.636562i	$-0.219644\pi$
$828$	−2.70022e60	−	1.75843e60i	−0.142155	−	0.0925739i
$829$	1.03766e61			0.532609			0.266304	−	0.963889i	$-0.414197\pi$
$829$	1.03766e61			0.532609			0.266304	+	0.963889i	$0.414197\pi$
$830$		−	1.21790e61i		−	0.609497i
$831$	−2.90660e61	+	1.57576e61i	−1.41829	+	0.768900i
$832$	2.76878e61			1.31734
$833$			3.97556e61i			1.84439i
$834$	1.88106e61	+	3.46973e61i	0.850970	+	1.56967i
$835$	2.00459e60			0.0884319
$836$			4.35672e60i			0.187425i
$837$	−7.33379e58	+	9.09655e59i	−0.00307676	+	0.0381630i
$838$	1.94650e61			0.796398
$839$			3.71734e61i			1.48331i	0.670784	+	0.741653i	$0.265958\pi$
$839$			3.71734e61i			1.48331i	−0.670784	+	0.741653i	$0.734042\pi$
$840$	3.71926e61	−	2.01633e61i	1.44741	−	0.784688i
$841$	1.14879e61			0.436037
$842$		−	1.40180e61i		−	0.518956i
$843$	−1.80293e61	−	3.32563e61i	−0.651029	−	1.20087i
$844$	−6.46064e60			−0.227554
$845$			1.21654e61i			0.417961i
$846$	1.08815e61	−	1.67094e61i	0.364679	−	0.559995i
$847$	−1.09441e61			−0.357790
$848$		−	2.42788e61i		−	0.774310i
$849$	−2.34494e61	+	1.27127e61i	−0.729575	+	0.395526i
$850$	2.99273e60			0.0908385
$851$			2.65767e61i			0.787010i
$852$	5.91071e60	+	1.09027e61i	0.170769	+	0.314994i
$853$	4.28394e61			1.20757			0.603787	−	0.797146i	$-0.293658\pi$
$853$	4.28394e61			1.20757			0.603787	+	0.797146i	$0.293658\pi$
$854$			2.48029e61i			0.682162i
$855$	−3.56583e61	−	2.32213e61i	−0.956912	−	0.623158i
$856$	−1.28004e61			−0.335178
$857$		−	7.22157e61i		−	1.84516i	−0.385803	−	0.922581i	$-0.626076\pi$
$857$		−	7.22157e61i		−	1.84516i	0.385803	−	0.922581i	$-0.373924\pi$
$858$	−3.26848e61	+	1.77195e61i	−0.814917	+	0.441793i
$859$	5.81391e61			1.41453			0.707264	−	0.706949i	$-0.249929\pi$
$859$	5.81391e61			1.41453			0.707264	+	0.706949i	$0.249929\pi$
$860$		−	9.55819e60i		−	0.226939i
$861$	−4.85734e60	−	8.95970e60i	−0.112547	−	0.207600i
$862$	4.45273e61			1.00687
$863$		−	1.59365e61i		−	0.351695i	−0.984417	−	0.175847i	$-0.943734\pi$
$863$		−	1.59365e61i		−	0.351695i	0.984417	−	0.175847i	$-0.0562665\pi$
$864$	1.77287e61	+	1.42932e60i	0.381847	+	0.0307851i
$865$	−6.42767e61			−1.35119
$866$			2.50064e61i			0.513068i
$867$	−5.78400e61	+	3.13569e61i	−1.15832	+	0.627961i
$868$	5.66549e59			0.0110745
$869$		−	1.19947e61i		−	0.228863i
$870$	−1.78112e61	−	3.28539e61i	−0.331733	−	0.611903i
$871$	−3.82033e61			−0.694575
$872$			1.07223e62i			1.90301i
$873$	−1.73786e61	+	2.66864e61i	−0.301104	+	0.462371i
$874$	−5.11726e61			−0.865560
$875$		−	8.68190e61i		−	1.43366i
$876$	−2.01658e60	+	1.09325e60i	−0.0325110	+	0.0176252i
$877$	1.72753e61			0.271916			0.135958	−	0.990715i	$-0.456589\pi$
$877$	1.72753e61			0.271916			0.135958	+	0.990715i	$0.456589\pi$
$878$		−	3.78847e61i		−	0.582209i
$879$	3.58676e61	+	6.61601e61i	0.538190	+	0.992727i
$880$	−4.71544e61			−0.690854
$881$		−	1.11853e62i		−	1.60012i	−0.599917	−	0.800062i	$-0.704800\pi$
$881$		−	1.11853e62i		−	1.60012i	0.599917	−	0.800062i	$-0.295200\pi$
$882$	6.52288e61	+	4.24781e61i	0.911169	+	0.593369i
$883$	1.87178e61			0.255317			0.127659	−	0.991818i	$-0.459254\pi$
$883$	1.87178e61			0.255317			0.127659	+	0.991818i	$0.459254\pi$
$884$		−	2.63474e61i		−	0.350947i
$885$	7.59818e61	−	4.11922e61i	0.988327	−	0.535804i
$886$	−4.75050e61			−0.603436
$887$			9.78793e61i			1.21421i	0.794621	+	0.607106i	$0.207670\pi$
$887$			9.78793e61i			1.21421i	−0.794621	+	0.607106i	$0.792330\pi$
$888$	−3.80560e61	−	7.01968e61i	−0.461053	−	0.850443i
$889$	1.03853e62			1.22880
$890$		−	3.70292e61i		−	0.427912i
$891$	−7.06138e61	+	3.12243e61i	−0.796999	+	0.352420i
$892$	−9.52450e60			−0.104998
$893$			7.64651e61i			0.823347i
$894$	6.33373e61	−	3.43372e61i	0.666149	−	0.361141i
$895$	1.65643e62			1.70173
$896$			9.10565e61i			0.913782i
$897$	5.02566e61	+	9.27017e61i	0.492665	+	0.908755i
$898$	1.38779e62			1.32899
$899$		−	3.07346e60i		−	0.0287524i
$900$	−7.72145e59	+	1.18569e60i	−0.00705677	+	0.0108363i
$901$	−1.71982e62			−1.53554
$902$			1.42377e61i			0.124194i
$903$	1.73317e62	−	9.39608e61i	1.47706	−	0.800763i
$904$	−1.82128e62			−1.51649
$905$			1.34128e62i			1.09119i
$906$	−7.44900e61	−	1.37402e62i	−0.592114	−	1.09220i
$907$	−8.35887e61			−0.649224			−0.324612	−	0.945847i	$-0.605234\pi$
$907$	−8.35887e61			−0.649224			−0.324612	+	0.945847i	$0.605234\pi$
$908$		−	3.76962e60i		−	0.0286085i
$909$	2.77220e61	+	1.80530e61i	0.205581	+	0.133878i
$910$	−2.25435e62			−1.63362
$911$			5.79257e61i			0.410190i	0.978742	+	0.205095i	$0.0657504\pi$
$911$			5.79257e61i			0.410190i	−0.978742	+	0.205095i	$0.934250\pi$
$912$	1.07839e62	−	5.84628e61i	0.746247	−	0.404565i
$913$	8.47396e61			0.573060
$914$		−	1.72688e62i		−	1.14128i
$915$	−3.89478e61	−	7.18419e61i	−0.251559	−	0.464018i
$916$	4.20538e60			0.0265460
$917$			1.87350e61i			0.115584i
$918$	−1.82092e61	+	2.25860e62i	−0.109798	+	1.36189i
$919$	−8.65557e61			−0.510117			−0.255059	−	0.966926i	$-0.582095\pi$
$919$	−8.65557e61			−0.510117			−0.255059	+	0.966926i	$0.582095\pi$
$920$			1.67627e62i			0.965605i
$921$	−1.94196e62	+	1.05280e62i	−1.09342	+	0.592781i
$922$	7.72815e61			0.425330
$923$		−	4.05843e62i		−	2.18334i
$924$	2.28443e61	+	4.21378e61i	0.120134	+	0.221595i
$925$	1.16701e61			0.0599926
$926$		−	2.64013e62i		−	1.32677i
$927$	1.08395e62	−	1.66450e62i	0.532518	−	0.817728i
$928$	−5.99002e61			−0.287687
$929$			1.98220e62i			0.930719i	0.885122	+	0.465359i	$0.154075\pi$
$929$			1.98220e62i			0.930719i	−0.885122	+	0.465359i	$0.845925\pi$
$930$	6.79592e60	−	3.68429e60i	0.0311965	−	0.0169127i
$931$	−2.98498e62			−1.33967
$932$		−	7.52387e60i		−	0.0330147i
$933$	2.16537e61	+	3.99418e61i	0.0929005	+	0.171361i
$934$	3.37317e62			1.41499
$935$			3.34023e62i			1.37004i
$936$	−2.65485e62	−	1.72888e62i	−1.06475	−	0.693383i
$937$	3.18813e62			1.25027			0.625137	−	0.780515i	$-0.285043\pi$
$937$	3.18813e62			1.25027			0.625137	+	0.780515i	$0.285043\pi$
$938$		−	2.03968e62i		−	0.782172i
$939$	8.98740e61	−	4.87236e61i	0.337021	−	0.182710i
$940$	4.07859e61			0.149563
$941$		−	3.98416e62i		−	1.42875i	−0.699765	−	0.714373i	$-0.746712\pi$
$941$		−	3.98416e62i		−	1.42875i	0.699765	−	0.714373i	$-0.253288\pi$
$942$	1.83354e62	+	3.38209e62i	0.643017	+	1.18609i
$943$	4.03813e61			0.138495
$944$			2.49149e62i			0.835693i
$945$	−4.66643e62	−	3.76216e61i	−1.53080	−	0.123415i
$946$	−2.75414e62			−0.883635
$947$			5.08911e62i			1.59695i	0.602025	+	0.798477i	$0.294361\pi$
$947$			5.08911e62i			1.59695i	−0.602025	+	0.798477i	$0.705639\pi$
$948$	1.46315e61	−	7.93220e60i	0.0449069	−	0.0243455i
$949$	7.50654e61			0.225346
$950$			2.24704e61i			0.0659803i
$951$	1.92923e62	+	3.55859e62i	0.554106	+	1.02209i
$952$	8.63893e62			2.42708
$953$		−	1.03176e62i		−	0.283549i	−0.989899	−	0.141775i	$-0.954719\pi$
$953$		−	1.03176e62i		−	0.283549i	0.989899	−	0.141775i	$-0.0452808\pi$
$954$	−1.83759e62	+	2.82178e62i	−0.494007	+	0.758591i
$955$	8.59983e61			0.226162
$956$			4.26774e61i			0.109795i
$957$	2.28592e62	−	1.23927e62i	0.575322	−	0.311901i
$958$	1.22618e62			0.301911
$959$		−	4.13329e62i		−	0.995647i
$960$	−2.32129e62	−	4.28178e62i	−0.547058	−	1.00909i
$961$	−4.33066e62			−0.998534
$962$			4.25482e62i			0.959853i
$963$	1.18697e62	+	7.72976e61i	0.261992	+	0.170614i
$964$	5.94575e61			0.128407
$965$		−	6.86729e62i		−	1.45115i
$966$	−4.94936e62	+	2.68321e62i	−1.02336	+	0.554798i
$967$	7.49938e62			1.51729			0.758647	−	0.651502i	$-0.225861\pi$
$967$	7.49938e62			1.51729			0.758647	+	0.651502i	$0.225861\pi$
$968$			1.30282e62i			0.257929i
$969$	−4.14127e62	−	7.63885e62i	−0.802295	−	1.47989i
$970$	2.69758e62			0.511408
$971$			4.21444e61i			0.0781873i	0.999236	+	0.0390936i	$0.0124471\pi$
$971$			4.21444e61i			0.0781873i	−0.999236	+	0.0390936i	$0.987553\pi$
$972$	−8.47857e61	−	6.54878e61i	−0.153933	−	0.118896i
$973$	−1.66512e63			−2.95853
$974$		−	4.22463e62i		−	0.734600i
$975$	4.07063e61	−	2.20682e61i	0.0692730	−	0.0375552i
$976$	2.35574e62			0.392356
$977$			6.13398e62i			0.999899i	0.866054	+	0.499950i	$0.166648\pi$
$977$			6.13398e62i			0.999899i	−0.866054	+	0.499950i	$0.833352\pi$
$978$	−3.90805e61	−	7.20866e61i	−0.0623511	−	0.115011i
$979$	2.57643e62			0.402330
$980$			1.59216e62i			0.243355i
$981$	6.47483e62	−	9.94266e62i	0.968678	−	1.48749i
$982$	−8.17788e62			−1.19757
$983$			1.03432e63i			1.48263i	0.671159	+	0.741313i	$0.265797\pi$
$983$			1.03432e63i			1.48263i	−0.671159	+	0.741313i	$0.734203\pi$
$984$	−1.06659e62	+	5.78232e61i	−0.149658	+	0.0811345i
$985$	−8.04701e62			−1.10528
$986$		−	7.63115e62i		−	1.02606i
$987$	4.00942e62	+	7.39564e62i	0.527741	+	0.973454i
$988$	1.97825e62			0.254909
$989$			7.81139e62i			0.985386i
$990$	5.48047e62	+	3.56898e62i	0.676829	+	0.440763i
$991$	−1.24074e63			−1.50014			−0.750071	−	0.661357i	$-0.769981\pi$
$991$	−1.24074e63			−1.50014			−0.750071	+	0.661357i	$0.769981\pi$
$992$		−	1.23905e61i		−	0.0146671i
$993$	−5.25553e60	+	2.84919e60i	−0.00609091	+	0.00330208i
$994$	2.16680e63			2.45870
$995$		−	8.77232e62i		−	0.974607i
$996$	5.60390e61	+	1.03368e62i	0.0609599	+	0.112445i
$997$	4.30779e62			0.458834			0.229417	−	0.973328i	$-0.426318\pi$
$997$	4.30779e62			0.458834			0.229417	+	0.973328i	$0.426318\pi$
$998$			8.62148e62i			0.899168i
$999$	−7.10064e61	+	8.80736e62i	−0.0725141	+	0.899437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.43.b.b.2.8	yes	12
3.2	odd	2	inner	3.43.b.b.2.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.43.b.b.2.5	✓	12	3.2	odd	2	inner
3.43.b.b.2.8	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)

\(f(q)\)	\(=\)	\(q+1.88218e6i q^{2} +(9.19591e9 - 4.98540e9i) q^{3} +8.55436e11 q^{4} +4.92433e14i q^{5} +(9.38344e15 + 1.73084e16i) q^{6} -8.30626e17 q^{7} +9.88801e18i q^{8} +(5.97105e19 - 9.16906e19i) q^{9} +O(q^{10})\)	\(q+1.88218e6i q^{2} +(9.19591e9 - 4.98540e9i) q^{3} +8.55436e11 q^{4} +4.92433e14i q^{5} +(9.38344e15 + 1.73084e16i) q^{6} -8.30626e17 q^{7} +9.88801e18i q^{8} +(5.97105e19 - 9.16906e19i) q^{9} -9.26849e20 q^{10} -6.44887e21i q^{11} +(7.86651e21 - 4.26469e21i) q^{12} -2.92823e23 q^{13} -1.56339e24i q^{14} +(2.45498e24 + 4.52837e24i) q^{15} -1.48488e25 q^{16} +1.05183e26i q^{17} +(1.72578e26 + 1.12386e26i) q^{18} -7.89747e26 q^{19} +4.21245e26i q^{20} +(-7.63836e27 + 4.14100e27i) q^{21} +1.21380e28 q^{22} -3.44261e28i q^{23} +(4.92957e28 + 9.09293e28i) q^{24} -1.51168e28 q^{25} -5.51147e29i q^{26} +(9.19780e28 - 1.14086e30i) q^{27} -7.10547e29 q^{28} +3.85463e30i q^{29} +(-8.52322e30 + 4.62072e30i) q^{30} -7.97342e29 q^{31} +1.55398e31i q^{32} +(-3.21502e31 - 5.93033e31i) q^{33} -1.97973e32 q^{34} -4.09028e32i q^{35} +(5.10785e31 - 7.84354e31i) q^{36} -7.71994e32 q^{37} -1.48645e33i q^{38} +(-2.69278e33 + 1.45984e33i) q^{39} -4.86919e33 q^{40} +1.17299e33i q^{41} +(-7.79413e33 - 1.43768e34i) q^{42} -2.26903e34 q^{43} -5.51660e33i q^{44} +(4.51515e34 + 2.94034e34i) q^{45} +6.47961e34 q^{46} -9.68223e34i q^{47} +(-1.36548e35 + 7.40272e34i) q^{48} +3.77966e35 q^{49} -2.84526e34i q^{50} +(5.24379e35 + 9.67253e35i) q^{51} -2.50492e35 q^{52} +1.63507e36i q^{53} +(2.14731e36 + 1.73119e35i) q^{54} +3.17564e36 q^{55} -8.21324e36i q^{56} +(-7.26244e36 + 3.93721e36i) q^{57} -7.25512e36 q^{58} -1.67791e37i q^{59} +(2.10008e36 + 3.87373e36i) q^{60} -1.58648e37 q^{61} -1.50074e36i q^{62} +(-4.95971e37 + 7.61606e37i) q^{63} -9.45544e37 q^{64} -1.44196e38i q^{65} +(1.11620e38 - 6.05126e37i) q^{66} +1.30465e38 q^{67} +8.99772e37i q^{68} +(-1.71628e38 - 3.16579e38i) q^{69} +7.69865e38 q^{70} +1.38596e39i q^{71} +(9.06638e38 + 5.90418e38i) q^{72} -2.56350e38 q^{73} -1.45303e39i q^{74} +(-1.39013e38 + 7.53635e37i) q^{75} -6.75578e38 q^{76} +5.35660e39i q^{77} +(-2.74769e39 - 5.06830e39i) q^{78} +1.85997e39 q^{79} -7.31204e39i q^{80} +(-4.84182e39 - 1.09498e40i) q^{81} -2.20778e39 q^{82} +1.31402e40i q^{83} +(-6.53413e39 + 3.54236e39i) q^{84} -5.17956e40 q^{85} -4.27074e40i q^{86} +(1.92169e40 + 3.54469e40i) q^{87} +6.37665e40 q^{88} +3.99517e40i q^{89} +(-5.53427e40 + 8.49834e40i) q^{90} +2.43227e41 q^{91} -2.94493e40i q^{92} +(-7.33228e39 + 3.97507e39i) q^{93} +1.82237e41 q^{94} -3.88898e41i q^{95} +(7.74721e40 + 1.42903e41i) q^{96} -2.91048e41 q^{97} +7.11401e41i q^{98} +(-5.91301e41 - 3.85066e41i) 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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