LMFDB - Embedded newform 3.43.b.b.2.4

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			2.4
Root			$-59345.7i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.43.b.b.2.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.13644e6i q^{2} +(-3.48827e9 - 9.86159e9i) q^{3} -1.66350e11 q^{4} +7.27116e14i q^{5} +(-2.10687e16 + 7.45250e15i) q^{6} -7.17356e17 q^{7} -9.04079e18i q^{8} +(-8.50829e19 + 6.87998e19i) q^{9} +O(q^{10})$	\(q-2.13644e6i q^{2} +(-3.48827e9 - 9.86159e9i) q^{3} -1.66350e11 q^{4} +7.27116e14i q^{5} +(-2.10687e16 + 7.45250e15i) q^{6} -7.17356e17 q^{7} -9.04079e18i q^{8} +(-8.50829e19 + 6.87998e19i) q^{9} +1.55344e21 q^{10} +5.19263e21i q^{11} +(5.80275e20 + 1.64048e21i) q^{12} +2.30240e23 q^{13} +1.53259e24i q^{14} +(7.17052e24 - 2.53638e24i) q^{15} -2.00468e25 q^{16} -3.57260e25i q^{17} +(1.46987e26 + 1.81775e26i) q^{18} +1.20200e27 q^{19} -1.20956e26i q^{20} +(2.50233e27 + 7.07428e27i) q^{21} +1.10938e28 q^{22} -4.53948e28i q^{23} +(-8.91565e28 + 3.15367e28i) q^{24} -3.01324e29 q^{25} -4.91894e29i q^{26} +(9.75267e29 + 5.99061e29i) q^{27} +1.19333e29 q^{28} +3.09807e30i q^{29} +(-5.41883e30 - 1.53194e31i) q^{30} +2.88102e31 q^{31} +3.06700e30i q^{32} +(5.12076e31 - 1.81133e31i) q^{33} -7.63267e31 q^{34} -5.21601e32i q^{35} +(1.41536e31 - 1.14449e31i) q^{36} -7.76398e29 q^{37} -2.56801e33i q^{38} +(-8.03138e32 - 2.27053e33i) q^{39} +6.57370e33 q^{40} -1.18439e33i q^{41} +(1.51138e34 - 5.34610e33i) q^{42} +1.46050e33 q^{43} -8.63796e32i q^{44} +(-5.00254e34 - 6.18652e34i) q^{45} -9.69834e34 q^{46} +4.50924e34i q^{47} +(6.99285e34 + 1.97693e35i) q^{48} +2.02627e35 q^{49} +6.43762e35i q^{50} +(-3.52316e35 + 1.24622e35i) q^{51} -3.83005e34 q^{52} +2.22416e36i q^{53} +(1.27986e36 - 2.08361e36i) q^{54} -3.77564e36 q^{55} +6.48547e36i q^{56} +(-4.19290e36 - 1.18536e37i) q^{57} +6.61885e36 q^{58} -3.90010e36i q^{59} +(-1.19282e36 + 4.21927e35i) q^{60} +2.78638e37 q^{61} -6.15514e37i q^{62} +(6.10348e37 - 4.93540e37i) q^{63} -8.16141e37 q^{64} +1.67411e38i q^{65} +(-3.86981e37 - 1.09402e38i) q^{66} +3.05468e38 q^{67} +5.94304e36i q^{68} +(-4.47665e38 + 1.58349e38i) q^{69} -1.11437e39 q^{70} +3.64924e38i q^{71} +(6.22004e38 + 7.69217e38i) q^{72} +1.42617e39 q^{73} +1.65873e36i q^{74} +(1.05110e39 + 2.97153e39i) q^{75} -1.99953e38 q^{76} -3.72497e39i q^{77} +(-4.85086e39 + 1.71586e39i) q^{78} +3.60695e38 q^{79} -1.45763e40i q^{80} +(2.50570e39 - 1.17074e40i) q^{81} -2.53039e39 q^{82} +7.96913e39i q^{83} +(-4.16264e38 - 1.17681e39i) q^{84} +2.59770e40 q^{85} -3.12027e39i q^{86} +(3.05519e40 - 1.08069e40i) q^{87} +4.69455e40 q^{88} +6.40863e40i q^{89} +(-1.32172e41 + 1.06877e41i) q^{90} -1.65164e41 q^{91} +7.55144e39i q^{92} +(-1.00498e41 - 2.84114e41i) q^{93} +9.63373e40 q^{94} +8.73994e41i q^{95} +(3.02455e40 - 1.06985e40i) q^{96} +5.27229e41 q^{97} -4.32901e41i q^{98} +(-3.57252e41 - 4.41804e41i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16987205196 q^{3} - 34999503561888 q^{4} - 47\!\cdots\!88 q^{6}+ \cdots - 10\!\cdots\!60 q^{9}+O(q^{10}) $ 12 * q + 16987205196 * q^3 - 34999503561888 * q^4 - 47900661722006688 * q^6 - 41814621990917832 * q^7 - 10479496382139999060 * q^9	$ 12 q + 16987205196 q^{3} - 34999503561888 q^{4} - 47\!\cdots\!88 q^{6}+ \cdots - 45\!\cdots\!60 q^{99}+O(q^{100}) $ 12 * q + 16987205196 * q^3 - 34999503561888 * q^4 - 47900661722006688 * q^6 - 41814621990917832 * q^7 - 10479496382139999060 * q^9 - 1558337248111507093440 * q^10 + 49376377527162340879584 * q^12 + 104159867930333479443192 * q^13 - 448128019361693763840960 * q^15 + 30189980873605037368521216 * q^16 + 467763252053696004788775360 * q^18 + 1742192007122001281517876120 * q^19 + 9102775482298327940265250872 * q^21 - 4314702866032998614435578560 * q^22 + 213252820822149659960046027264 * q^24 - 1475565424466319180916113000660 * q^25 + 4679803843175845084152852300204 * q^27 - 12573192134196153529744555207488 * q^28 + 62452866934923176992747679887680 * q^30 - 82582711039551011868572590242696 * q^31 + 43265764437015443353441835054400 * q^33 - 263315485295738664634172504653056 * q^34 - 2405201397348598443590828900669856 * q^36 - 100843038556324004682477979351752 * q^37 - 10984759746962485956654149987757192 * q^39 + 14264689156939495925288444850785280 * q^40 - 2831182046378653470535212831685440 * q^42 - 71435403459183756447962146838987688 * q^43 + 171247471703495918987972144910848640 * q^45 - 368252835390302858087002506036095616 * q^46 + 393051873841281316858605019336751616 * q^48 + 503454865894447043110675471056528228 * q^49 - 26481340521925644924949289315966208 * q^51 + 6191863526932890484747245480405187008 * q^52 - 7762950205729260582930120693521404128 * q^54 + 7333373720922934220673629457367543680 * q^55 - 7646344343294849001862320271635263592 * q^57 - 40828097874719028971304350423217887040 * q^58 + 67409911106604936995672440638418037760 * q^60 - 86088392913854728749325031191744820616 * q^61 + 100834020234866427922563192954676937592 * q^63 - 141458640188438187587490744757105434624 * q^64 - 410927857618739095889759252898209949120 * q^66 + 637588020068292666249059312571603583128 * q^67 - 900977595682723671847728174824987261568 * q^69 + 1299257312773585175235999395827621799040 * q^70 - 1002862304292335428089280868557297904640 * q^72 + 4764698373378852277054437745609397085912 * q^73 + 10291654382848945060344626042064329363820 * q^75 - 10850719004897690517175553392098488304192 * q^76 - 1154864387471236146792590220220273542720 * q^78 - 16476824590026301016342599143867688625160 * q^79 - 29934898097734077284676557689524616295988 * q^81 + 12117774709574398821091222390193736370560 * q^82 - 115502524985324999123004799396029534507072 * q^84 + 179892388106464049414097141341403281134080 * q^85 - 108737363241821037303405571455850394882880 * q^87 + 262137413065538961600854476553505008040960 * q^88 - 246742532847586844558695609281104739341760 * q^90 + 85532425294904148246865639238250304747824 * q^91 + 153993445971229900791562733419639364858232 * q^93 + 711306705503600048406114202903471029729024 * q^94 - 1719405066055622809595776412409802129711104 * q^96 + 1090171163442244899022729083217627459542168 * q^97 - 4562402641239113129658705054315657608741760 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	2.13644e6i		−	1.01874i	−0.860549	−	0.509368i	$-0.829879\pi$
$2$		−	2.13644e6i		−	1.01874i	0.860549	−	0.509368i	$-0.170121\pi$
$3$	−3.48827e9	−	9.86159e9i	−0.333475	−	0.942759i
$3$	−3.48827e9	−	9.86159e9i	−0.333475	−	0.942759i
$4$	−1.66350e11			−0.0378237
$5$			7.27116e14i			1.52487i	0.647063	+	0.762436i	$0.275997\pi$
$5$			7.27116e14i			1.52487i	−0.647063	+	0.762436i	$0.724003\pi$
$6$	−2.10687e16	+	7.45250e15i	−0.960423	+	0.339723i
$7$	−7.17356e17			−1.28433			−0.642164	−	0.766567i	$-0.721963\pi$
$7$	−7.17356e17			−1.28433			−0.642164	+	0.766567i	$0.721963\pi$
$8$		−	9.04079e18i		−	0.980204i
$9$	−8.50829e19	+	6.87998e19i	−0.777588	+	0.628774i
$10$	1.55344e21			1.55344
$11$			5.19263e21i			0.701683i	0.936435	+	0.350842i	$0.114104\pi$
$11$			5.19263e21i			0.701683i	−0.936435	+	0.350842i	$0.885896\pi$
$12$	5.80275e20	+	1.64048e21i	0.0126133	+	0.0356586i
$13$	2.30240e23			0.931900			0.465950	−	0.884811i	$-0.345713\pi$
$13$	2.30240e23			0.931900			0.465950	+	0.884811i	$0.345713\pi$
$14$			1.53259e24i			1.30839i
$15$	7.17052e24	−	2.53638e24i	1.43759	−	0.508507i
$16$	−2.00468e25			−1.03639
$17$		−	3.57260e25i		−	0.517080i	−0.966001	−	0.258540i	$-0.916759\pi$
$17$		−	3.57260e25i		−	0.517080i	0.966001	−	0.258540i	$-0.0832413\pi$
$18$	1.46987e26	+	1.81775e26i	0.640555	+	0.792158i
$19$	1.20200e27			1.68298			0.841491	−	0.540272i	$-0.181679\pi$
$19$	1.20200e27			1.68298			0.841491	+	0.540272i	$0.181679\pi$
$20$		−	1.20956e26i		−	0.0576764i
$21$	2.50233e27	+	7.07428e27i	0.428292	+	1.21081i
$22$	1.10938e28			0.714830
$23$		−	4.53948e28i		−	1.15006i	−0.818132	−	0.575031i	$-0.804990\pi$
$23$		−	4.53948e28i		−	1.15006i	0.818132	−	0.575031i	$-0.195010\pi$
$24$	−8.91565e28	+	3.15367e28i	−0.924096	+	0.326874i
$25$	−3.01324e29			−1.32524
$26$		−	4.91894e29i		−	0.949361i
$27$	9.75267e29	+	5.99061e29i	0.852088	+	0.523398i
$28$	1.19333e29			0.0485781
$29$			3.09807e30i			0.603577i	0.953375	+	0.301789i	$0.0975837\pi$
$29$			3.09807e30i			0.603577i	−0.953375	+	0.301789i	$0.902416\pi$
$30$	−5.41883e30	−	1.53194e31i	−0.518035	−	1.46452i
$31$	2.88102e31			1.38341			0.691705	−	0.722180i	$-0.256860\pi$
$31$	2.88102e31			1.38341			0.691705	+	0.722180i	$0.256860\pi$
$32$			3.06700e30i			0.0756074i
$33$	5.12076e31	−	1.81133e31i	0.661518	−	0.233994i
$34$	−7.63267e31			−0.526768
$35$		−	5.21601e32i		−	1.95844i
$36$	1.41536e31	−	1.14449e31i	0.0294113	−	0.0237826i
$37$	−7.76398e29			−0.000907504			−0.000453752	−	1.00000i	$-0.500144\pi$
$37$	−7.76398e29			−0.000907504			−0.000453752		1.00000i	$0.500144\pi$
$38$		−	2.56801e33i		−	1.71451i
$39$	−8.03138e32	−	2.27053e33i	−0.310766	−	0.878557i
$40$	6.57370e33			1.49469
$41$		−	1.18439e33i		−	0.160337i	−0.996781	−	0.0801686i	$-0.974454\pi$
$41$		−	1.18439e33i		−	0.160337i	0.996781	−	0.0801686i	$-0.0255459\pi$
$42$	1.51138e34	−	5.34610e33i	1.23350	−	0.436317i
$43$	1.46050e33			0.0727215			0.0363608	−	0.999339i	$-0.488423\pi$
$43$	1.46050e33			0.0727215			0.0363608	+	0.999339i	$0.488423\pi$
$44$		−	8.63796e32i		−	0.0265403i
$45$	−5.00254e34	−	6.18652e34i	−0.958800	−	1.18572i
$46$	−9.69834e34			−1.17161
$47$			4.50924e34i			0.346775i	0.984854	+	0.173388i	$0.0554713\pi$
$47$			4.50924e34i			0.346775i	−0.984854	+	0.173388i	$0.944529\pi$
$48$	6.99285e34	+	1.97693e35i	0.345612	+	0.977069i
$49$	2.02627e35			0.649500
$50$			6.43762e35i			1.35007i
$51$	−3.52316e35	+	1.24622e35i	−0.487481	+	0.172433i
$52$	−3.83005e34			−0.0352479
$53$			2.22416e36i			1.37206i	0.727575	+	0.686028i	$0.240647\pi$
$53$			2.22416e36i			1.37206i	−0.727575	+	0.686028i	$0.759353\pi$
$54$	1.27986e36	−	2.08361e36i	0.533204	−	0.868053i
$55$	−3.77564e36			−1.06998
$56$			6.48547e36i			1.25890i
$57$	−4.19290e36	−	1.18536e37i	−0.561233	−	1.58665i
$58$	6.61885e36			0.614886
$59$		−	3.90010e36i		−	0.253037i	−0.991964	−	0.126518i	$-0.959620\pi$
$59$		−	3.90010e36i		−	0.253037i	0.991964	−	0.126518i	$-0.0403802\pi$
$60$	−1.19282e36	+	4.21927e35i	−0.0543749	+	0.0192336i
$61$	2.78638e37			0.897666			0.448833	−	0.893616i	$-0.351840\pi$
$61$	2.78638e37			0.897666			0.448833	+	0.893616i	$0.351840\pi$
$62$		−	6.15514e37i		−	1.40933i
$63$	6.10348e37	−	4.93540e37i	0.998679	−	0.807552i
$64$	−8.16141e37			−0.959369
$65$			1.67411e38i			1.42103i
$66$	−3.86981e37	−	1.09402e38i	−0.238378	−	0.673912i
$67$	3.05468e38			1.37213			0.686064	−	0.727541i	$-0.259337\pi$
$67$	3.05468e38			1.37213			0.686064	+	0.727541i	$0.259337\pi$
$68$			5.94304e36i			0.0195579i
$69$	−4.47665e38	+	1.58349e38i	−1.08423	+	0.383517i
$70$	−1.11437e39			−1.99513
$71$			3.64924e38i			0.485039i	0.970147	+	0.242519i	$0.0779738\pi$
$71$			3.64924e38i			0.485039i	−0.970147	+	0.242519i	$0.922026\pi$
$72$	6.22004e38	+	7.69217e38i	0.616326	+	0.762195i
$73$	1.42617e39			1.05777			0.528885	−	0.848693i	$-0.322610\pi$
$73$	1.42617e39			1.05777			0.528885	+	0.848693i	$0.322610\pi$
$74$			1.65873e36i			0.000924507i
$75$	1.05110e39	+	2.97153e39i	0.441934	+	1.24938i
$76$	−1.99953e38			−0.0636566
$77$		−	3.72497e39i		−	0.901192i
$78$	−4.85086e39	+	1.71586e39i	−0.895018	+	0.316588i
$79$	3.60695e38			0.0509298			0.0254649	−	0.999676i	$-0.491893\pi$
$79$	3.60695e38			0.0509298			0.0254649	+	0.999676i	$0.491893\pi$
$80$		−	1.45763e40i		−	1.58037i
$81$	2.50570e39	−	1.17074e40i	0.209288	−	0.977854i
$82$	−2.53039e39			−0.163341
$83$			7.96913e39i			0.398815i	0.979917	+	0.199407i	$0.0639017\pi$
$83$			7.96913e39i			0.398815i	−0.979917	+	0.199407i	$0.936098\pi$
$84$	−4.16264e38	−	1.17681e39i	−0.0161996	−	0.0457974i
$85$	2.59770e40			0.788481
$86$		−	3.12027e39i		−	0.0740841i
$87$	3.05519e40	−	1.08069e40i	0.569028	−	0.201278i
$88$	4.69455e40			0.687792
$89$			6.40863e40i			0.740585i	0.928915	+	0.370292i	$0.120743\pi$
$89$			6.40863e40i			0.740585i	−0.928915	+	0.370292i	$0.879257\pi$
$90$	−1.32172e41	+	1.06877e41i	−1.20794	+	0.976764i
$91$	−1.65164e41			−1.19687
$92$			7.55144e39i			0.0434996i
$93$	−1.00498e41	−	2.84114e41i	−0.461333	−	1.30422i
$94$	9.63373e40			0.353272
$95$			8.73994e41i			2.56633i
$96$	3.02455e40	−	1.06985e40i	0.0712795	−	0.0252132i
$97$	5.27229e41			0.999523			0.499761	−	0.866163i	$-0.333421\pi$
$97$	5.27229e41			0.999523			0.499761	+	0.866163i	$0.333421\pi$
$98$		−	4.32901e41i		−	0.661669i
$99$	−3.57252e41	−	4.41804e41i	−0.441200	−	0.545621i
$100$	5.01254e40			0.0501254
$101$		−	1.71112e42i		−	1.38845i	−0.719756	−	0.694227i	$-0.755746\pi$
$101$		−	1.71112e42i		−	1.38845i	0.719756	−	0.694227i	$-0.244254\pi$
$102$	2.66248e41	+	7.52703e41i	0.175664	+	0.496615i
$103$	2.09347e42			1.12535			0.562673	−	0.826680i	$-0.309773\pi$
$103$	2.09347e42			1.12535			0.562673	+	0.826680i	$0.309773\pi$
$104$		−	2.08155e42i		−	0.913452i
$105$	−5.14382e42	+	1.81949e42i	−1.84633	+	0.653091i
$106$	4.75179e42			1.39776
$107$		−	3.85687e42i		−	0.931486i	−0.884920	−	0.465743i	$-0.845787\pi$
$107$		−	3.85687e42i		−	0.931486i	0.884920	−	0.465743i	$-0.154213\pi$
$108$	−1.62236e41	−	9.96541e40i	−0.0322292	−	0.0197969i
$109$	−8.60429e42			−1.40851			−0.704253	−	0.709949i	$-0.748718\pi$
$109$	−8.60429e42			−1.40851			−0.704253	+	0.709949i	$0.748718\pi$
$110$			8.06646e42i			1.09002i
$111$	2.70829e39	+	7.65652e39i	0.000302630	+	0.000855557i
$112$	1.43807e43			1.33107
$113$			8.77386e42i			0.673819i	0.941537	+	0.336909i	$0.109382\pi$
$113$			8.77386e42i			0.673819i	−0.941537	+	0.336909i	$0.890618\pi$
$114$	−2.53247e43	+	8.95791e42i	−1.61637	+	0.571748i
$115$	3.30073e43			1.75370
$116$		−	5.15365e41i		−	0.0228295i
$117$	−1.95895e43	+	1.58404e43i	−0.724635	+	0.585954i
$118$	−8.33234e42			−0.257778
$119$			2.56283e43i			0.664100i
$120$	−2.29308e43	−	6.48271e43i	−0.498441	−	1.40913i
$121$	2.78003e43			0.507641
$122$		−	5.95296e43i		−	0.914484i
$123$	−1.16800e43	+	4.13148e42i	−0.151159	+	0.0534685i
$124$	−4.79259e42			−0.0523257
$125$		−	5.37704e43i		−	0.495944i
$126$	−1.05442e44	−	1.30397e44i	−0.822683	−	1.01739i
$127$	2.84926e44			1.88301			0.941507	−	0.336994i	$-0.109410\pi$
$127$	2.84926e44			1.88301			0.941507	+	0.336994i	$0.109410\pi$
$128$			1.87853e44i			1.05295i
$129$	−5.09461e42	−	1.44028e43i	−0.0242508	−	0.0685589i
$130$	3.57664e44			1.44765
$131$			1.92184e44i			0.662247i	0.943587	+	0.331123i	$0.107428\pi$
$131$			1.92184e44i			0.662247i	−0.943587	+	0.331123i	$0.892572\pi$
$132$	−8.51841e42	+	3.01316e42i	−0.0250211	+	0.00885052i
$133$	−8.62263e44			−2.16150
$134$		−	6.52615e44i		−	1.39784i
$135$	−4.35587e44	+	7.09132e44i	−0.798115	+	1.29933i
$136$	−3.22991e44			−0.506844
$137$			8.44852e43i			0.113671i	0.998384	+	0.0568354i	$0.0181010\pi$
$137$			8.44852e43i			0.113671i	−0.998384	+	0.0568354i	$0.981899\pi$
$138$	3.38304e44	+	9.56411e44i	0.390703	+	1.10455i
$139$	5.21481e44			0.517520			0.258760	−	0.965942i	$-0.416686\pi$
$139$	5.21481e44			0.517520			0.258760	+	0.965942i	$0.416686\pi$
$140$			8.67686e43i			0.0740754i
$141$	4.44682e44	−	1.57294e44i	0.326925	−	0.115641i
$142$	7.79639e44			0.494127
$143$			1.19555e45i			0.653899i
$144$	1.70564e45	−	1.37921e45i	0.805887	−	0.651657i
$145$	−2.25265e45			−0.920378
$146$		−	3.04693e45i		−	1.07759i
$147$	−7.06817e44	−	1.99822e45i	−0.216592	−	0.612322i
$148$	1.29154e41			3.43252e−5
$149$			1.48633e45i			0.342927i	0.985190	+	0.171464i	$0.0548496\pi$
$149$			1.48633e45i			0.342927i	−0.985190	+	0.171464i	$0.945150\pi$
$150$	6.34852e45	−	2.24562e45i	1.27279	−	0.450214i
$151$	−6.65776e45			−1.16095			−0.580473	−	0.814279i	$-0.697132\pi$
$151$	−6.65776e45			−1.16095			−0.580473	+	0.814279i	$0.697132\pi$
$152$		−	1.08670e46i		−	1.64966i
$153$	2.45794e45	+	3.03968e45i	0.325126	+	0.402075i
$154$	−7.95819e45			−0.918077
$155$			2.09484e46i			2.10952i
$156$	1.33602e44	+	3.77703e44i	0.0117543	+	0.0332303i
$157$	7.07911e45			0.544610			0.272305	−	0.962211i	$-0.412214\pi$
$157$	7.07911e45			0.544610			0.272305	+	0.962211i	$0.412214\pi$
$158$		−	7.70606e44i		−	0.0518840i
$159$	2.19337e46	−	7.75846e45i	1.29352	−	0.457547i
$160$	−2.23006e45			−0.115292
$161$			3.25642e46i			1.47706i
$162$	−2.50122e46	−	5.35329e45i	−0.996176	−	0.213209i
$163$	−4.31606e46			−1.51059			−0.755297	−	0.655382i	$-0.772508\pi$
$163$	−4.31606e46			−1.51059			−0.755297	+	0.655382i	$0.772508\pi$
$164$			1.97024e44i			0.00606455i
$165$	1.31705e46	+	3.72339e46i	0.356811	+	1.00873i
$166$	1.70256e46			0.406287
$167$		−	5.67100e46i		−	1.19293i	−0.802640	−	0.596464i	$-0.796572\pi$
$167$		−	5.67100e46i		−	1.19293i	0.802640	−	0.596464i	$-0.203428\pi$
$168$	6.39570e46	−	2.26231e46i	1.18684	−	0.419813i
$169$	−8.03065e45			−0.131562
$170$		−	5.54984e46i		−	0.803254i
$171$	−1.02270e47	+	8.26974e46i	−1.30867	+	1.05821i
$172$	−2.42954e44			−0.00275060
$173$		−	1.07288e47i		−	1.07543i	−0.843127	−	0.537714i	$-0.819288\pi$
$173$		−	1.07288e47i		−	1.07543i	0.843127	−	0.537714i	$-0.180712\pi$
$174$	−2.30883e46	−	6.52724e46i	−0.205049	−	0.579689i
$175$	2.16157e47			1.70204
$176$		−	1.04095e47i		−	0.727219i
$177$	−3.84612e46	+	1.36046e46i	−0.238552	+	0.0843814i
$178$	1.36917e47			0.754461
$179$			2.70557e47i			1.32540i	0.748887	+	0.662698i	$0.230589\pi$
$179$			2.70557e47i			1.32540i	−0.748887	+	0.662698i	$0.769411\pi$
$180$	8.32175e45	+	1.02913e46i	0.0362654	+	0.0448485i
$181$	−4.69197e46			−0.182014			−0.0910070	−	0.995850i	$-0.529009\pi$
$181$	−4.69197e46			−0.182014			−0.0910070	+	0.995850i	$0.529009\pi$
$182$			3.52863e47i			1.21929i
$183$	−9.71966e46	−	2.74782e47i	−0.299349	−	0.846282i
$184$	−4.10404e47			−1.12730
$185$		−	5.64532e44i		−	0.00138383i
$186$	−6.06995e47	+	2.14708e47i	−1.32866	+	0.469977i
$187$	1.85512e47			0.362826
$188$		−	7.50114e45i		−	0.0131163i
$189$	−6.99614e47	−	4.29740e47i	−1.09436	−	0.672215i
$190$	1.86724e48			2.61442
$191$			1.26327e48i			1.58415i	0.610422	+	0.792076i	$0.291000\pi$
$191$			1.26327e48i			1.58415i	−0.610422	+	0.792076i	$0.709000\pi$
$192$	2.84692e47	+	8.04845e47i	0.319926	+	0.904454i
$193$	−1.04891e48			−1.05690			−0.528452	−	0.848963i	$-0.677227\pi$
$193$	−1.04891e48			−1.05690			−0.528452	+	0.848963i	$0.677227\pi$
$194$		−	1.12640e48i		−	1.01825i
$195$	1.65094e48	−	5.83974e47i	1.33969	−	0.473878i
$196$	−3.37071e46			−0.0245665
$197$		−	2.93719e48i		−	1.92372i	−0.273545	−	0.961859i	$-0.588196\pi$
$197$		−	2.93719e48i		−	1.92372i	0.273545	−	0.961859i	$-0.411804\pi$
$198$	−9.43890e47	+	7.63249e47i	−0.555844	+	0.449466i
$199$	1.88201e48			0.997028			0.498514	−	0.866882i	$-0.333879\pi$
$199$	1.88201e48			0.997028			0.498514	+	0.866882i	$0.333879\pi$
$200$			2.72420e48i			1.29900i
$201$	−1.06555e48	−	3.01240e48i	−0.457571	−	1.29359i
$202$	−3.65571e48			−1.41447
$203$		−	2.22242e48i		−	0.775191i
$204$	5.86079e46	−	2.07309e46i	0.0184384	−	0.00652207i
$205$	8.61190e47			0.244494
$206$		−	4.47259e48i		−	1.14643i
$207$	3.12315e48	+	3.86232e48i	0.723129	+	0.894275i
$208$	−4.61556e48			−0.965815
$209$			6.24155e48i			1.18092i
$210$	3.88723e48	+	1.09895e49i	0.665327	+	1.88093i
$211$	6.01374e48			0.931564			0.465782	−	0.884899i	$-0.345773\pi$
$211$	6.01374e48			0.931564			0.465782	+	0.884899i	$0.345773\pi$
$212$		−	3.69989e47i		−	0.0518963i
$213$	3.59873e48	−	1.27295e48i	0.457275	−	0.161749i
$214$	−8.24000e48			−0.948938
$215$			1.06195e48i			0.110891i
$216$	5.41598e48	−	8.81718e48i	0.513037	−	0.835220i
$217$	−2.06672e49			−1.77675
$218$			1.83826e49i			1.43490i
$219$	−4.97487e48	−	1.40643e49i	−0.352740	−	0.997222i
$220$	6.28080e47			0.0404705
$221$		−	8.22554e48i		−	0.481867i
$222$	1.63577e46	−	5.78610e45i	0.000871587	−	0.000308300i
$223$	5.63802e48			0.273353			0.136677	−	0.990616i	$-0.456358\pi$
$223$	5.63802e48			0.273353			0.136677	+	0.990616i	$0.456358\pi$
$224$		−	2.20013e48i		−	0.0971047i
$225$	2.56375e49	−	2.07310e49i	1.03049	−	0.833274i
$226$	1.87449e49			0.686444
$227$			1.22643e49i			0.409353i	0.978830	+	0.204677i	$0.0656143\pi$
$227$			1.22643e49i			0.409353i	−0.978830	+	0.204677i	$0.934386\pi$
$228$	6.97492e47	+	1.97186e48i	0.0212279	+	0.0600128i
$229$	−1.00652e49			−0.279432			−0.139716	−	0.990192i	$-0.544619\pi$
$229$	−1.00652e49			−0.279432			−0.139716	+	0.990192i	$0.544619\pi$
$230$		−	7.05182e49i		−	1.78656i
$231$	−3.67341e49	+	1.29937e49i	−0.849606	+	0.300525i
$232$	2.80090e49			0.591629
$233$			1.30888e49i			0.252595i	0.991992	+	0.126298i	$0.0403094\pi$
$233$			1.30888e49i			0.252595i	−0.991992	+	0.126298i	$0.959691\pi$
$234$	3.38422e49	+	4.18518e49i	0.596933	+	0.738212i
$235$	−3.27874e49			−0.528788
$236$			6.48783e47i			0.00957078i
$237$	−1.25820e48	−	3.55703e48i	−0.0169838	−	0.0480145i
$238$	5.47535e49			0.676543
$239$			9.12653e49i			1.03264i	0.856395	+	0.516321i	$0.172699\pi$
$239$			9.12653e49i			1.03264i	−0.856395	+	0.516321i	$0.827301\pi$
$240$	−1.43746e50	+	5.08461e49i	−1.48991	+	0.527014i
$241$	−1.31700e49			−0.125092			−0.0625458	−	0.998042i	$-0.519922\pi$
$241$	−1.31700e49			−0.125092			−0.0625458	+	0.998042i	$0.519922\pi$
$242$		−	5.93938e49i		−	0.517152i
$243$	−1.24194e50	+	1.61283e49i	−0.991673	+	0.128783i
$244$	−4.63516e48			−0.0339530
$245$			1.47333e50i			0.990405i
$246$	8.82667e48	+	2.49536e49i	0.0544703	+	0.153992i
$247$	2.76748e50			1.56837
$248$		−	2.60467e50i		−	1.35602i
$249$	7.85883e49	−	2.77985e49i	0.375986	−	0.132995i
$250$	−1.14877e50			−0.505236
$251$			2.45524e50i			0.992994i	0.868039	+	0.496497i	$0.165381\pi$
$251$			2.45524e50i			0.992994i	−0.868039	+	0.496497i	$0.834619\pi$
$252$	−1.01532e49	+	8.21006e48i	−0.0377738	+	0.0305446i
$253$	2.35718e50			0.806979
$254$		−	6.08728e50i		−	1.91829i
$255$	−9.06147e49	−	2.56174e50i	−0.262939	−	0.743347i
$256$	4.23946e49			0.113311
$257$			4.52151e50i			1.11349i	0.830682	+	0.556747i	$0.187951\pi$
$257$			4.52151e50i			1.11349i	−0.830682	+	0.556747i	$0.812049\pi$
$258$	−3.07708e49	+	1.08843e49i	−0.0698434	+	0.0247052i
$259$	5.56954e47			0.00116553
$260$		−	2.78489e49i		−	0.0537486i
$261$	−2.13146e50	−	2.63593e50i	−0.379513	−	0.469335i
$262$	4.10590e50			0.674655
$263$		−	6.20036e50i		−	0.940473i	−0.882541	−	0.470236i	$-0.844169\pi$
$263$		−	6.20036e50i		−	0.940473i	0.882541	−	0.470236i	$-0.155831\pi$
$264$	−1.63758e50	−	4.62957e50i	−0.229362	−	0.648422i
$265$	−1.61722e51			−2.09221
$266$			1.84218e51i			2.20200i
$267$	6.31993e50	−	2.23550e50i	0.698193	−	0.246967i
$268$	−5.08147e49			−0.0518990
$269$			2.78786e50i			0.263314i	0.991295	+	0.131657i	$0.0420297\pi$
$269$			2.78786e50i			0.263314i	−0.991295	+	0.131657i	$0.957970\pi$
$270$	1.51502e51	+	9.30607e50i	1.32367	+	0.813069i
$271$	−2.02394e50			−0.163623			−0.0818113	−	0.996648i	$-0.526070\pi$
$271$	−2.02394e50			−0.163623			−0.0818113	+	0.996648i	$0.526070\pi$
$272$			7.16191e50i			0.535898i
$273$	5.76136e50	+	1.62878e51i	0.399125	+	1.12836i
$274$	1.80498e50			0.115801
$275$		−	1.56466e51i		−	0.929896i
$276$	7.44692e49	−	2.63415e49i	0.0410097	−	0.0145061i
$277$	8.83785e50			0.451098			0.225549	−	0.974232i	$-0.427582\pi$
$277$	8.83785e50			0.451098			0.225549	+	0.974232i	$0.427582\pi$
$278$		−	1.11411e51i		−	0.527217i
$279$	−2.45126e51	+	1.98214e51i	−1.07572	+	0.869851i
$280$	−4.71569e51			−1.91967
$281$		−	4.53059e51i		−	1.71128i	−0.517569	−	0.855642i	$-0.673163\pi$
$281$		−	4.53059e51i		−	1.71128i	0.517569	−	0.855642i	$-0.326837\pi$
$282$	−3.36051e50	−	9.50039e50i	−0.117808	−	0.333051i
$283$	−2.02053e51			−0.657581			−0.328791	−	0.944403i	$-0.606641\pi$
$283$	−2.02053e51			−0.657581			−0.328791	+	0.944403i	$0.606641\pi$
$284$		−	6.07052e49i		−	0.0183460i
$285$	8.61897e51	−	3.04873e51i	2.41943	−	0.855808i
$286$	2.55422e51			0.666150
$287$			8.49631e50i			0.205926i
$288$	−2.11009e50	−	2.60949e50i	−0.0475399	−	0.0587914i
$289$	3.49735e51			0.732629
$290$			4.81267e51i			0.937623i
$291$	−1.83912e51	−	5.19932e51i	−0.333316	−	0.942309i
$292$	−2.37244e50			−0.0400088
$293$			2.82430e51i			0.443294i	0.975127	+	0.221647i	$0.0711432\pi$
$293$			2.82430e51i			0.443294i	−0.975127	+	0.221647i	$0.928857\pi$
$294$	−4.26909e51	+	1.51008e51i	−0.623795	+	0.220650i
$295$	2.83582e51			0.385848
$296$			7.01925e48i			0.000889539i
$297$	−3.11070e51	+	5.06420e51i	−0.367259	+	0.597896i
$298$	3.17545e51			0.349353
$299$		−	1.04517e52i		−	1.07174i
$300$	−1.74851e50	−	4.94316e50i	−0.0167156	−	0.0472561i
$301$	−1.04770e51			−0.0933983
$302$			1.42239e52i			1.18270i
$303$	−1.68744e52	+	5.96885e51i	−1.30898	+	0.463015i
$304$	−2.40962e52			−1.74423
$305$			2.02602e52i			1.36883i
$306$	6.49410e51	−	5.25126e51i	0.409609	−	0.331218i
$307$	2.15551e52			1.26953			0.634766	−	0.772705i	$-0.281097\pi$
$307$	2.15551e52			1.26953			0.634766	+	0.772705i	$0.281097\pi$
$308$			6.19650e50i			0.0340864i
$309$	−7.30260e51	−	2.06450e52i	−0.375275	−	1.06093i
$310$	4.47550e52			2.14905
$311$		−	1.35097e52i		−	0.606284i	−0.952945	−	0.303142i	$-0.901964\pi$
$311$		−	1.35097e52i		−	0.606284i	0.952945	−	0.303142i	$-0.0980356\pi$
$312$	−2.05274e52	+	7.26099e51i	−0.861165	+	0.304614i
$313$	−6.40636e51			−0.251293			−0.125646	−	0.992075i	$-0.540100\pi$
$313$	−6.40636e51			−0.251293			−0.125646	+	0.992075i	$0.540100\pi$
$314$		−	1.51241e52i		−	0.554814i
$315$	3.58861e52	+	4.43794e52i	1.23141	+	1.52286i
$316$	−6.00018e49			−0.00192635
$317$		−	1.49860e52i		−	0.450237i	−0.974331	−	0.225118i	$-0.927723\pi$
$317$		−	1.49860e52i		−	0.450237i	0.974331	−	0.225118i	$-0.0722769\pi$
$318$	−1.65755e52	−	4.68602e52i	−0.466120	−	1.31775i
$319$	−1.60871e52			−0.423520
$320$		−	5.93429e52i		−	1.46292i
$321$	−3.80349e52	+	1.34538e52i	−0.878166	+	0.310628i
$322$	6.95717e52			1.50473
$323$		−	4.29427e52i		−	0.870235i
$324$	−4.16824e50	+	1.94753e51i	−0.00791603	+	0.0369861i
$325$	−6.93767e52			−1.23499
$326$			9.22103e52i			1.53890i
$327$	3.00141e52	+	8.48520e52i	0.469702	+	1.32788i
$328$	−1.07078e52			−0.157163
$329$		−	3.23473e52i		−	0.445373i
$330$	7.95481e52	−	2.81380e52i	1.02763	−	0.363496i
$331$	−4.37137e52			−0.529944			−0.264972	−	0.964256i	$-0.585363\pi$
$331$	−4.37137e52			−0.529944			−0.264972	+	0.964256i	$0.585363\pi$
$332$		−	1.32567e51i		−	0.0150847i
$333$	6.60582e49	−	5.34160e49i	0.000705664	−	0.000570614i
$334$	−1.21158e53			−1.21528
$335$			2.22110e53i			2.09232i
$336$	−5.01637e52	−	1.41816e53i	−0.443879	−	1.25488i
$337$	6.31139e52			0.524683			0.262342	−	0.964975i	$-0.415505\pi$
$337$	6.31139e52			0.524683			0.262342	+	0.964975i	$0.415505\pi$
$338$			1.71570e52i			0.134027i
$339$	8.65242e52	−	3.06056e52i	0.635249	−	0.224702i
$340$	−4.32128e51			−0.0298233
$341$			1.49601e53i			0.970715i
$342$	1.76678e53	+	2.18494e53i	1.07804	+	1.33319i
$343$	7.84405e52			0.450157
$344$		−	1.32040e52i		−	0.0712819i
$345$	−1.15138e53	−	3.25504e53i	−0.584815	−	1.65331i
$346$	−2.29214e53			−1.09558
$347$		−	2.10203e53i		−	0.945627i	−0.881162	−	0.472814i	$-0.843238\pi$
$347$		−	2.10203e53i		−	0.945627i	0.881162	−	0.472814i	$-0.156762\pi$
$348$	−5.08232e51	+	1.79773e51i	−0.0215227	+	0.00761308i
$349$	−1.71927e53			−0.685504			−0.342752	−	0.939426i	$-0.611359\pi$
$349$	−1.71927e53			−0.685504			−0.342752	+	0.939426i	$0.611359\pi$
$350$		−	4.61807e53i		−	1.73393i
$351$	2.24545e53	+	1.37927e53i	0.794061	+	0.487755i
$352$	−1.59258e52			−0.0530524
$353$		−	1.77688e52i		−	0.0557686i	−0.999611	−	0.0278843i	$-0.991123\pi$
$353$		−	1.77688e52i		−	0.0557686i	0.999611	−	0.0278843i	$-0.00887700\pi$
$354$	2.90655e52	+	8.21702e52i	0.0859624	+	0.243022i
$355$	−2.65342e53			−0.739623
$356$		−	1.06608e52i		−	0.0280117i
$357$	2.52736e53	−	8.93984e52i	0.626086	−	0.221461i
$358$	5.78031e53			1.35023
$359$		−	2.55854e53i		−	0.563649i	−0.959466	−	0.281825i	$-0.909060\pi$
$359$		−	2.55854e53i		−	0.563649i	0.959466	−	0.281825i	$-0.0909396\pi$
$360$	−5.59310e53	+	4.52269e53i	−1.16225	+	0.939819i
$361$	9.34712e53			1.83243
$362$			1.00241e53i			0.185424i
$363$	−9.69749e52	−	2.74155e53i	−0.169286	−	0.478583i
$364$	2.74751e52			0.0452699
$365$			1.03699e54i			1.61297i
$366$	−5.87056e53	+	2.07655e53i	−0.862138	+	0.304958i
$367$	−9.25599e53			−1.28362			−0.641808	−	0.766865i	$-0.721816\pi$
$367$	−9.25599e53			−1.28362			−0.641808	+	0.766865i	$0.721816\pi$
$368$			9.10018e53i			1.19192i
$369$	8.14859e52	+	1.00772e53i	0.100816	+	0.124676i
$370$	−1.20609e51			−0.00140976
$371$		−	1.59551e54i		−	1.76217i
$372$	1.67179e52	+	4.72626e52i	0.0174493	+	0.0493305i
$373$	−2.80838e53			−0.277058			−0.138529	−	0.990358i	$-0.544237\pi$
$373$	−2.80838e53			−0.277058			−0.138529	+	0.990358i	$0.544237\pi$
$374$		−	3.96336e53i		−	0.369624i
$375$	−5.30262e53	+	1.87566e53i	−0.467556	+	0.165385i
$376$	4.07670e53			0.339910
$377$			7.13297e53i			0.562474i
$378$	−9.18116e53	+	1.49469e54i	−0.684810	+	1.11487i
$379$	2.57918e53			0.181995			0.0909973	−	0.995851i	$-0.470995\pi$
$379$	2.57918e53			0.181995			0.0909973	+	0.995851i	$0.470995\pi$
$380$		−	1.45389e53i		−	0.0970682i
$381$	−9.93898e53	−	2.80982e54i	−0.627939	−	1.77523i
$382$	2.69892e54			1.61383
$383$		−	4.26971e53i		−	0.241671i	−0.992673	−	0.120835i	$-0.961443\pi$
$383$		−	4.26971e53i		−	0.241671i	0.992673	−	0.120835i	$-0.0385573\pi$
$384$	1.85253e54	−	6.55281e53i	0.992679	−	0.351133i
$385$	2.70848e54			1.37420
$386$			2.24094e54i			1.07671i
$387$	−1.24263e53	+	1.00482e53i	−0.0565474	+	0.0457254i
$388$	−8.77048e52			−0.0378057
$389$		−	1.11523e53i		−	0.0455430i	−0.999741	−	0.0227715i	$-0.992751\pi$
$389$		−	1.11523e53i		−	0.0455430i	0.999741	−	0.0227715i	$-0.00724902\pi$
$390$	−1.24763e54	−	3.52714e54i	−0.482757	−	1.36479i
$391$	−1.62178e54			−0.594674
$392$		−	1.83191e54i		−	0.636643i
$393$	1.89524e54	−	6.70389e53i	0.624339	−	0.220843i
$394$	−6.27515e54			−1.95976
$395$			2.62267e53i			0.0776614i
$396$	5.94290e52	+	7.34943e52i	0.0166878	+	0.0206374i
$397$	−5.82360e54			−1.55093			−0.775463	−	0.631394i	$-0.782483\pi$
$397$	−5.82360e54			−1.55093			−0.775463	+	0.631394i	$0.782483\pi$
$398$		−	4.02081e54i		−	1.01571i
$399$	3.00781e54	+	8.50329e54i	0.720807	+	2.03777i
$400$	6.04057e54			1.37347
$401$			4.43513e54i			0.956918i	0.878110	+	0.478459i	$0.158804\pi$
$401$			4.43513e54i			0.956918i	−0.878110	+	0.478459i	$0.841196\pi$
$402$	−6.43582e54	+	2.27650e54i	−1.31782	+	0.466144i
$403$	6.63325e54			1.28920
$404$			2.84646e53i			0.0525165i
$405$	8.51262e54	+	1.82193e54i	1.49110	+	0.319137i
$406$	−4.74807e54			−0.789716
$407$		−	4.03155e51i		−	0.000636780i
$408$	1.12668e54	+	3.18521e54i	0.169020	+	0.477831i
$409$	−1.10033e55			−1.56796			−0.783980	−	0.620786i	$-0.786814\pi$
$409$	−1.10033e55			−1.56796			−0.783980	+	0.620786i	$0.786814\pi$
$410$		−	1.83989e54i		−	0.249075i
$411$	8.33158e53	−	2.94707e53i	0.107164	−	0.0379064i
$412$	−3.48250e53			−0.0425648
$413$			2.79776e54i			0.324982i
$414$	8.25164e54	−	6.67244e54i	0.911030	−	0.736678i
$415$	−5.79448e54			−0.608142
$416$			7.06144e53i			0.0704585i
$417$	−1.81907e54	−	5.14263e54i	−0.172580	−	0.487897i
$418$	1.33347e55			1.20305
$419$		−	5.67630e54i		−	0.487047i	−0.969895	−	0.243524i	$-0.921697\pi$
$419$		−	5.67630e54i		−	0.487047i	0.969895	−	0.243524i	$-0.0783033\pi$
$420$	8.55677e53	−	3.02672e53i	0.0698352	−	0.0247023i
$421$	−1.72259e55			−1.33739			−0.668693	−	0.743538i	$-0.733146\pi$
$421$	−1.72259e55			−1.33739			−0.668693	+	0.743538i	$0.733146\pi$
$422$		−	1.28480e55i		−	0.949018i
$423$	−3.10234e54	−	3.83659e54i	−0.218043	−	0.269648i
$424$	2.01081e55			1.34490
$425$			1.07651e55i			0.685253i
$426$	−2.71959e54	−	7.68848e54i	−0.164779	−	0.465842i
$427$	−1.99883e55			−1.15290
$428$			6.41593e53i			0.0352323i
$429$	1.17900e55	−	4.17040e54i	0.616469	−	0.218059i
$430$	2.26880e54			0.112969
$431$		−	5.94563e54i		−	0.281952i	−0.990013	−	0.140976i	$-0.954976\pi$
$431$		−	5.94563e54i		−	0.281952i	0.990013	−	0.140976i	$-0.0450241\pi$
$432$	−1.95509e55	−	1.20092e55i	−0.883099	−	0.542446i
$433$	4.34540e55			1.86975			0.934877	−	0.354972i	$-0.115510\pi$
$433$	4.34540e55			1.86975			0.934877	+	0.354972i	$0.115510\pi$
$434$			4.41543e55i			1.81004i
$435$	7.85786e54	+	2.22147e55i	0.306923	+	0.867695i
$436$	1.43133e54			0.0532749
$437$		−	5.45646e55i		−	1.93553i
$438$	−3.00476e55	+	1.06285e55i	−1.01591	+	0.359349i
$439$	1.23238e55			0.397182			0.198591	−	0.980082i	$-0.436363\pi$
$439$	1.23238e55			0.397182			0.198591	+	0.980082i	$0.436363\pi$
$440$			3.41348e55i			1.04880i
$441$	−1.72401e55	+	1.39407e55i	−0.505044	+	0.408389i
$442$	−1.75734e55			−0.490895
$443$			5.56284e55i			1.48190i	0.671562	+	0.740948i	$0.265624\pi$
$443$			5.56284e55i			1.48190i	−0.671562	+	0.740948i	$0.734376\pi$
$444$	−4.50525e50	−	1.27367e51i	−1.14466e−5	−	3.23603e-5i
$445$	−4.65981e55			−1.12930
$446$		−	1.20453e55i		−	0.278475i
$447$	1.46575e55	−	5.18470e54i	0.323298	−	0.114358i
$448$	5.85464e55			1.23215
$449$		−	1.31335e55i		−	0.263758i	−0.991266	−	0.131879i	$-0.957899\pi$
$449$		−	1.31335e55i		−	0.263758i	0.991266	−	0.131879i	$-0.0421010\pi$
$450$	−4.42907e55	−	5.47732e55i	−0.848886	−	1.04980i
$451$	6.15011e54			0.112506
$452$		−	1.45954e54i		−	0.0254863i
$453$	2.32241e55	+	6.56561e55i	0.387147	+	1.09449i
$454$	2.62019e55			0.417023
$455$		−	1.20093e56i		−	1.82507i
$456$	−1.07166e56	+	3.79071e55i	−1.55524	+	0.550122i
$457$	1.77206e55			0.245606			0.122803	−	0.992431i	$-0.460812\pi$
$457$	1.77206e55			0.245606			0.122803	+	0.992431i	$0.460812\pi$
$458$			2.15037e55i			0.284667i
$459$	2.14021e55	−	3.48424e55i	0.270638	−	0.440598i
$460$	−5.49077e54			−0.0663314
$461$		−	1.44665e56i		−	1.66972i	−0.550460	−	0.834861i	$-0.685548\pi$
$461$		−	1.44665e56i		−	1.66972i	0.550460	−	0.834861i	$-0.314452\pi$
$462$	2.77603e55	+	7.84804e55i	0.306156	+	0.865525i
$463$	1.12959e56			1.19048			0.595238	−	0.803549i	$-0.297058\pi$
$463$	1.12959e56			1.19048			0.595238	+	0.803549i	$0.297058\pi$
$464$		−	6.21062e55i		−	0.625543i
$465$	2.06584e56	−	7.30735e55i	1.98877	−	0.703474i
$466$	2.79635e55			0.257328
$467$			2.05563e56i			1.80838i	0.427131	+	0.904190i	$0.359524\pi$
$467$			2.05563e56i			1.80838i	−0.427131	+	0.904190i	$0.640476\pi$
$468$	3.25872e54	−	2.63506e54i	0.0274084	−	0.0221630i
$469$	−2.19129e56			−1.76226
$470$			7.00484e55i			0.538695i
$471$	−2.46938e55	−	6.98113e55i	−0.181614	−	0.513436i
$472$	−3.52599e55			−0.248027
$473$			7.58382e54i			0.0510275i
$474$	−7.59940e54	+	2.68808e54i	−0.0489141	+	0.0173020i
$475$	−3.62192e56			−2.23035
$476$		−	4.26328e54i		−	0.0251187i
$477$	−1.53021e56	−	1.89238e56i	−0.862713	−	1.06690i
$478$	1.94983e56			1.05199
$479$			2.80412e56i			1.44794i	0.689830	+	0.723972i	$0.257685\pi$
$479$			2.80412e56i			1.44794i	−0.689830	+	0.723972i	$0.742315\pi$
$480$	7.77906e54	+	2.19920e55i	0.0384469	+	0.108692i
$481$	−1.78758e53			−0.000845703
$482$			2.81370e55i			0.127435i
$483$	3.21135e56	−	1.13593e56i	1.39251	−	0.492562i
$484$	−4.62459e54			−0.0192009
$485$			3.83357e56i			1.52415i
$486$	3.44572e55	+	2.65333e56i	0.131195	+	1.01025i
$487$	−2.41714e56			−0.881440			−0.440720	−	0.897645i	$-0.645277\pi$
$487$	−2.41714e56			−0.881440			−0.440720	+	0.897645i	$0.645277\pi$
$488$		−	2.51911e56i		−	0.879895i
$489$	1.50556e56	+	4.25632e56i	0.503746	+	1.42413i
$490$	3.14769e56			1.00896
$491$		−	2.68654e56i		−	0.825053i	−0.910946	−	0.412526i	$-0.864646\pi$
$491$		−	2.68654e56i		−	0.825053i	0.910946	−	0.412526i	$-0.135354\pi$
$492$	1.94297e54	−	6.87273e53i	0.00571741	−	0.00202238i
$493$	1.10682e56			0.312097
$494$		−	5.91257e56i		−	1.59776i
$495$	3.21243e56	−	2.59763e56i	0.832002	−	0.672773i
$496$	−5.77551e56			−1.43376
$497$		−	2.61780e56i		−	0.622949i
$498$	−5.93899e55	−	1.67900e56i	−0.135487	−	0.383031i
$499$	−4.16921e56			−0.911890			−0.455945	−	0.890008i	$-0.650699\pi$
$499$	−4.16921e56			−0.911890			−0.455945	+	0.890008i	$0.650699\pi$
$500$			8.94473e54i			0.0187585i
$501$	−5.59251e56	+	1.97820e56i	−1.12464	+	0.397812i
$502$	5.24549e56			1.01160
$503$			5.45303e56i			1.00858i	0.863535	+	0.504290i	$0.168246\pi$
$503$			5.45303e56i			1.00858i	−0.863535	+	0.504290i	$0.831754\pi$
$504$	−4.46199e56	−	5.51803e56i	−0.791566	−	0.978909i
$505$	1.24418e57			2.11722
$506$		−	5.03599e56i		−	0.822099i
$507$	2.80131e55	+	7.91950e55i	0.0438726	+	0.124031i
$508$	−4.73975e55			−0.0712226
$509$		−	9.31700e56i		−	1.34339i	−0.740827	−	0.671696i	$-0.765566\pi$
$509$		−	9.31700e56i		−	1.34339i	0.740827	−	0.671696i	$-0.234434\pi$
$510$	−5.47302e56	+	1.93593e56i	−0.757275	+	0.267865i
$511$	−1.02307e57			−1.35852
$512$			7.35612e56i			0.937518i
$513$	1.17227e57	+	7.20072e56i	1.43405	+	0.880869i
$514$	9.65996e56			1.13436
$515$			1.52220e57i			1.71601i
$516$	8.47490e53	+	2.39592e54i	0.000917257	+	0.00259315i
$517$	−2.34148e56			−0.243326
$518$		−	1.18990e54i		−	0.00118737i
$519$	−1.05803e57	+	3.74248e56i	−1.01387	+	0.358629i
$520$	1.51353e57			1.39290
$521$			6.71722e55i			0.0593742i	0.999559	+	0.0296871i	$0.00945108\pi$
$521$			6.71722e55i			0.0593742i	−0.999559	+	0.0296871i	$0.990549\pi$
$522$	−5.63151e56	+	4.55375e56i	−0.478128	+	0.386624i
$523$	−5.13804e54			−0.00419046			−0.00209523	−	0.999998i	$-0.500667\pi$
$523$	−5.13804e54			−0.00419046			−0.00209523	+	0.999998i	$0.500667\pi$
$524$		−	3.19699e55i		−	0.0250486i
$525$	−7.54013e56	−	2.13165e57i	−0.567588	−	1.60461i
$526$	−1.32467e57			−0.958094
$527$		−	1.02927e57i		−	0.715333i
$528$	−1.02655e57	+	3.63113e56i	−0.685593	+	0.242510i
$529$	−5.02680e56			−0.322643
$530$			3.45510e57i			2.13141i
$531$	2.68326e56	+	3.31832e56i	0.159103	+	0.196758i
$532$	1.43438e56			0.0817560
$533$		−	2.72694e56i		−	0.149418i
$534$	−4.77603e56	−	1.35022e57i	−0.251594	−	0.711275i
$535$	2.80440e57			1.42040
$536$		−	2.76167e57i		−	1.34497i
$537$	2.66812e57	−	9.43777e56i	1.24953	−	0.441987i
$538$	5.95611e56			0.268247
$539$			1.05217e57i			0.455743i
$540$	7.24601e55	−	1.17965e56i	0.0301877	−	0.0491454i
$541$	−2.83251e57			−1.13508			−0.567542	−	0.823344i	$-0.692106\pi$
$541$	−2.83251e57			−1.13508			−0.567542	+	0.823344i	$0.692106\pi$
$542$			4.32405e56i			0.166688i
$543$	1.63668e56	+	4.62702e56i	0.0606972	+	0.171595i
$544$	1.09572e56			0.0390950
$545$		−	6.25632e57i		−	2.14779i
$546$	3.47979e57	−	1.23088e57i	1.14950	−	0.406604i
$547$	9.20507e56			0.292613			0.146306	−	0.989239i	$-0.453261\pi$
$547$	9.20507e56			0.292613			0.146306	+	0.989239i	$0.453261\pi$
$548$		−	1.40542e55i		−	0.00429945i
$549$	−2.37074e57	+	1.91703e57i	−0.698014	+	0.564428i
$550$	−3.34282e57			−0.947319
$551$			3.72388e57i			1.01581i
$552$	1.43160e57	+	4.04724e57i	0.375925	+	1.06277i
$553$	−2.58747e56			−0.0654105
$554$		−	1.88816e57i		−	0.459550i
$555$	−5.56718e54	+	1.96924e54i	−0.00130462	+	0.000461472i
$556$	−8.67486e55			−0.0195745
$557$		−	6.21919e57i		−	1.35137i	−0.737190	−	0.675686i	$-0.763848\pi$
$557$		−	6.21919e57i		−	1.35137i	0.737190	−	0.675686i	$-0.236152\pi$
$558$	4.23472e57	+	5.23698e57i	0.886149	+	1.09588i
$559$	3.36264e56			0.0677692
$560$			1.04564e58i			2.02971i
$561$	−6.47116e56	−	1.82944e57i	−0.120994	−	0.342057i
$562$	−9.67935e57			−1.74335
$563$		−	4.91519e57i		−	0.852834i	−0.904527	−	0.426417i	$-0.859776\pi$
$563$		−	4.91519e57i		−	0.852834i	0.904527	−	0.426417i	$-0.140224\pi$
$564$	−7.39731e55	+	2.61660e55i	−0.0123655	+	0.00437397i
$565$	−6.37961e57			−1.02749
$566$			4.31674e57i			0.669902i
$567$	−1.79748e57	+	8.39836e57i	−0.268794	+	1.25589i
$568$	3.29920e57			0.475437
$569$			4.79293e57i			0.665646i	0.942989	+	0.332823i	$0.108001\pi$
$569$			4.79293e57i			0.665646i	−0.942989	+	0.332823i	$0.891999\pi$
$570$	−6.51344e57	−	1.84140e58i	−0.871843	−	2.46476i
$571$	6.89407e57			0.889442			0.444721	−	0.895669i	$-0.353303\pi$
$571$	6.89407e57			0.889442			0.444721	+	0.895669i	$0.353303\pi$
$572$		−	1.98880e56i		−	0.0247329i
$573$	1.24579e58	−	4.40664e57i	1.49347	−	0.528276i
$574$	1.81519e57			0.209784
$575$			1.36785e58i			1.52410i
$576$	6.94397e57	−	5.61503e57i	0.745994	−	0.603226i
$577$	5.24748e57			0.543574			0.271787	−	0.962357i	$-0.412385\pi$
$577$	5.24748e57			0.543574			0.271787	+	0.962357i	$0.412385\pi$
$578$		−	7.47189e57i		−	0.746355i
$579$	3.65889e57	+	1.03439e58i	0.352451	+	0.996405i
$580$	3.74730e56			0.0348121
$581$		−	5.71671e57i		−	0.512209i
$582$	−1.11081e58	+	3.92917e57i	−0.959965	+	0.339561i
$583$	−1.15492e58			−0.962749
$584$		−	1.28937e58i		−	1.03683i
$585$	−1.15178e58	−	1.42438e58i	−0.893506	−	1.10498i
$586$	6.03397e57			0.451599
$587$		−	8.91021e57i		−	0.643410i	−0.946840	−	0.321705i	$-0.895744\pi$
$587$		−	8.91021e57i		−	0.643410i	0.946840	−	0.321705i	$-0.104256\pi$
$588$	1.17579e56	+	3.32405e56i	0.00819233	+	0.0231603i
$589$	3.46299e58			2.32825
$590$		−	6.05858e57i		−	0.393078i
$591$	−2.89654e58	+	1.02457e58i	−1.81360	+	0.641513i
$592$	1.55643e55			0.000940530
$593$			1.08094e58i			0.630451i	0.949017	+	0.315226i	$0.102080\pi$
$593$			1.08094e58i			0.630451i	−0.949017	+	0.315226i	$0.897920\pi$
$594$	1.08194e58	+	6.64584e57i	0.609098	+	0.374141i
$595$	−1.86347e58			−1.01267
$596$		−	2.47251e56i		−	0.0129708i
$597$	−6.56496e57	−	1.85596e58i	−0.332484	−	0.939957i
$598$	−2.23294e58			−1.09182
$599$			1.89633e58i			0.895261i	0.894219	+	0.447630i	$0.147732\pi$
$599$			1.89633e58i			0.895261i	−0.894219	+	0.447630i	$0.852268\pi$
$600$	2.68650e58	−	9.50276e57i	1.22465	−	0.433185i
$601$	2.88502e58			1.26994			0.634972	−	0.772535i	$-0.281012\pi$
$601$	2.88502e58			1.26994			0.634972	+	0.772535i	$0.281012\pi$
$602$			2.23835e57i			0.0951483i
$603$	−2.59901e58	+	2.10161e58i	−1.06695	+	0.862758i
$604$	1.10752e57			0.0439113
$605$			2.02140e58i			0.774088i
$606$	1.27521e58	+	3.60512e58i	0.471690	+	1.33350i
$607$	6.03978e57			0.215804			0.107902	−	0.994162i	$-0.465587\pi$
$607$	6.03978e57			0.215804			0.107902	+	0.994162i	$0.465587\pi$
$608$			3.68654e57i			0.127246i
$609$	−2.19166e58	+	7.75239e57i	−0.730818	+	0.258507i
$610$	4.32849e58			1.39447
$611$			1.03820e58i			0.323160i
$612$	−4.08880e56	−	5.05652e56i	−0.0122975	−	0.0152080i
$613$	1.31791e58			0.383015			0.191507	−	0.981491i	$-0.438662\pi$
$613$	1.31791e58			0.383015			0.191507	+	0.981491i	$0.438662\pi$
$614$		−	4.60512e58i		−	1.29332i
$615$	−3.00406e57	−	8.49270e57i	−0.0815327	−	0.230499i
$616$	−3.36766e58			−0.883352
$617$		−	3.27470e58i		−	0.830202i	−0.909775	−	0.415101i	$-0.863746\pi$
$617$		−	3.27470e58i		−	0.830202i	0.909775	−	0.415101i	$-0.136254\pi$
$618$	−4.41069e58	+	1.56016e58i	−1.08081	+	0.382306i
$619$	−5.06522e58			−1.19976			−0.599880	−	0.800090i	$-0.704785\pi$
$619$	−5.06522e58			−1.19976			−0.599880	+	0.800090i	$0.704785\pi$
$620$		−	3.48477e57i		−	0.0797900i
$621$	2.71942e58	−	4.42720e58i	0.601940	−	0.979955i
$622$	−2.88626e58			−0.617643
$623$		−	4.59727e58i		−	0.951154i
$624$	1.61003e58	+	4.55167e58i	0.322075	+	0.910531i
$625$	−2.94158e58			−0.568985
$626$			1.36868e58i			0.256001i
$627$	6.15516e58	−	2.17722e58i	1.11332	−	0.393807i
$628$	−1.17761e57			−0.0205992
$629$			2.77376e55i			0.000469252i
$630$	9.48141e58	−	7.66686e58i	1.55139	−	1.25449i
$631$	1.15422e59			1.82672			0.913362	−	0.407148i	$-0.133477\pi$
$631$	1.15422e59			1.82672			0.913362	+	0.407148i	$0.133477\pi$
$632$		−	3.26097e57i		−	0.0499215i
$633$	−2.09775e58	−	5.93050e58i	−0.310654	−	0.878240i
$634$	−3.20167e58			−0.458673
$635$			2.07174e59i			2.87136i
$636$	−3.64868e57	+	1.29062e57i	−0.0489257	+	0.0173061i
$637$	4.66527e58			0.605269
$638$			3.43692e58i			0.431455i
$639$	−2.51067e58	−	3.10488e58i	−0.304980	−	0.377161i
$640$	−1.36591e59			−1.60562
$641$		−	1.46357e59i		−	1.66493i	−0.554078	−	0.832465i	$-0.686929\pi$
$641$		−	1.46357e59i		−	1.66493i	0.554078	−	0.832465i	$-0.313071\pi$
$642$	2.87433e58	+	8.12595e58i	0.316448	+	0.894620i
$643$	−2.32480e58			−0.247717			−0.123858	−	0.992300i	$-0.539527\pi$
$643$	−2.32480e58			−0.247717			−0.123858	+	0.992300i	$0.539527\pi$
$644$		−	5.41708e57i		−	0.0558678i
$645$	1.04725e58	−	3.70437e57i	0.104544	−	0.0369794i
$646$	−9.17448e58			−0.886540
$647$			1.03073e58i			0.0964176i	0.998837	+	0.0482088i	$0.0153513\pi$
$647$			1.03073e58i			0.0964176i	−0.998837	+	0.0482088i	$0.984649\pi$
$648$	−1.05844e59	−	2.26535e58i	−0.958496	−	0.205144i
$649$	2.02518e58			0.177551
$650$			1.48219e59i			1.25813i
$651$	7.20927e58	+	2.03811e59i	0.592503	+	1.67505i
$652$	7.17979e57			0.0571363
$653$		−	1.68043e59i		−	1.29492i	−0.762100	−	0.647460i	$-0.775831\pi$
$653$		−	1.68043e59i		−	1.29492i	0.762100	−	0.647460i	$-0.224169\pi$
$654$	1.81282e59	−	6.41234e58i	1.35276	−	0.478502i
$655$	−1.39740e59			−1.00984
$656$			2.37432e58i			0.166172i
$657$	−1.21343e59	+	9.81202e58i	−0.822510	+	0.665098i
$658$	−6.91082e58			−0.453718
$659$			1.35087e59i			0.859055i	0.903054	+	0.429528i	$0.141320\pi$
$659$			1.35087e59i			0.859055i	−0.903054	+	0.429528i	$0.858680\pi$
$660$	−2.19091e57	−	6.19387e57i	−0.0134959	−	0.0381539i
$661$	1.83751e59			1.09648			0.548238	−	0.836322i	$-0.315299\pi$
$661$	1.83751e59			1.09648			0.548238	+	0.836322i	$0.315299\pi$
$662$			9.33920e58i			0.539873i
$663$	−8.11170e58	+	2.86929e58i	−0.454284	+	0.160691i
$664$	7.20472e58			0.390920
$665$		−	6.26965e59i		−	3.29601i
$666$	−1.14120e56	−	1.41130e56i	−0.000581306	−	0.000718886i
$667$	1.40636e59			0.694151
$668$			9.43374e57i			0.0451210i
$669$	−1.96669e58	−	5.55998e58i	−0.0911566	−	0.257706i
$670$	4.74527e59			2.13152
$671$			1.44687e59i			0.629877i
$672$	−2.16968e58	+	7.67465e57i	−0.0915463	+	0.0323820i
$673$	−1.14509e59			−0.468298			−0.234149	−	0.972201i	$-0.575230\pi$
$673$	−1.14509e59			−0.468298			−0.234149	+	0.972201i	$0.575230\pi$
$674$		−	1.34839e59i		−	0.534514i
$675$	−2.93871e59	−	1.80511e59i	−1.12922	−	0.693626i
$676$	1.33590e57			0.00497616
$677$			3.43532e59i			1.24052i	0.784395	+	0.620262i	$0.212974\pi$
$677$			3.43532e59i			1.24052i	−0.784395	+	0.620262i	$0.787026\pi$
$678$	−6.53871e58	−	1.84854e59i	−0.228912	−	0.647151i
$679$	−3.78211e59			−1.28372
$680$		−	2.34852e59i		−	0.772872i
$681$	1.20945e59	−	4.27811e58i	0.385922	−	0.136509i
$682$	3.19614e59			0.988903
$683$			3.14711e58i			0.0944227i	0.998885	+	0.0472114i	$0.0150334\pi$
$683$			3.14711e58i			0.0944227i	−0.998885	+	0.0472114i	$0.984967\pi$
$684$	1.70126e58	−	1.37568e58i	0.0494986	−	0.0400256i
$685$	−6.14305e58			−0.173333
$686$		−	1.67584e59i		−	0.458591i
$687$	3.51100e58	+	9.92586e58i	0.0931836	+	0.263437i
$688$	−2.92782e58			−0.0753681
$689$			5.12089e59i			1.27862i
$690$	−6.95422e59	+	2.45987e59i	−1.68429	+	0.595772i
$691$	5.83430e59			1.37072			0.685362	−	0.728203i	$-0.259644\pi$
$691$	5.83430e59			1.37072			0.685362	+	0.728203i	$0.259644\pi$
$692$			1.78474e58i			0.0406767i
$693$	2.56277e59	+	3.16931e59i	0.566646	+	0.700756i
$694$	−4.49087e59			−0.963345
$695$			3.79177e59i			0.789153i
$696$	−9.77028e58	−	2.76213e59i	−0.197294	−	0.557763i
$697$	−4.23136e58			−0.0829071
$698$			3.67313e59i			0.698348i
$699$	1.29076e59	−	4.56572e58i	0.238136	−	0.0842343i
$700$	−3.59578e58			−0.0643775
$701$		−	3.33564e59i		−	0.579563i	−0.957093	−	0.289781i	$-0.906417\pi$
$701$		−	3.33564e59i		−	0.579563i	0.957093	−	0.289781i	$-0.0935826\pi$
$702$	2.94675e59	−	4.79728e59i	0.496893	−	0.808939i
$703$	−9.33232e56			−0.00152731
$704$		−	4.23792e59i		−	0.673173i
$705$	1.14371e59	+	3.23336e59i	0.176338	+	0.498519i
$706$	−3.79621e58			−0.0568135
$707$			1.22748e60i			1.78323i
$708$	6.39803e57	−	2.26313e57i	0.00902294	−	0.00319162i
$709$	1.41570e58			0.0193821			0.00969106	−	0.999953i	$-0.496915\pi$
$709$	1.41570e58			0.0193821			0.00969106	+	0.999953i	$0.496915\pi$
$710$			5.66888e59i			0.753480i
$711$	−3.06890e58	+	2.48158e58i	−0.0396024	+	0.0320233i
$712$	5.79390e59			0.725924
$713$		−	1.30783e60i		−	1.59101i
$714$	−1.90995e59	−	5.39956e59i	−0.225610	−	0.637817i
$715$	−8.69302e59			−0.997112
$716$		−	4.50073e58i		−	0.0501314i
$717$	9.00021e59	−	3.18358e59i	0.973532	−	0.344361i
$718$	−5.46618e59			−0.574210
$719$		−	1.87268e60i		−	1.91054i	−0.295729	−	0.955272i	$-0.595563\pi$
$719$		−	1.87268e60i		−	1.91054i	0.295729	−	0.955272i	$-0.404437\pi$
$720$	1.00285e60	+	1.24020e60i	0.993693	+	1.22888i
$721$	−1.50177e60			−1.44531
$722$		−	1.99696e60i		−	1.86676i
$723$	4.59406e58	+	1.29877e59i	0.0417150	+	0.117931i
$724$	7.80511e57			0.00688445
$725$		−	9.33521e59i		−	0.799882i
$726$	−5.85717e59	+	2.07182e59i	−0.487550	+	0.172458i
$727$	−1.13110e60			−0.914700			−0.457350	−	0.889287i	$-0.651201\pi$
$727$	−1.13110e60			−0.914700			−0.457350	+	0.889287i	$0.651201\pi$
$728$			1.49321e60i			1.17317i
$729$	5.92273e59	+	1.16849e60i	0.452109	+	0.891963i
$730$	2.21547e60			1.64319
$731$		−	5.21777e58i		−	0.0376028i
$732$	1.61687e58	+	4.57101e58i	0.0113225	+	0.0320095i
$733$	1.19118e60			0.810575			0.405287	−	0.914189i	$-0.367172\pi$
$733$	1.19118e60			0.810575			0.405287	+	0.914189i	$0.367172\pi$
$734$			1.97749e60i			1.30767i
$735$	1.45294e60	−	5.13938e59i	0.933713	−	0.330276i
$736$	1.39226e59			0.0869532
$737$			1.58618e60i			0.962799i
$738$	2.15293e59	−	1.74090e59i	0.127012	−	0.102705i
$739$	1.01276e60			0.580731			0.290366	−	0.956916i	$-0.406223\pi$
$739$	1.01276e60			0.580731			0.290366	+	0.956916i	$0.406223\pi$
$740$			9.39101e55i			5.23415e-5i
$741$	−9.65372e59	−	2.72918e60i	−0.523013	−	1.47860i
$742$	−3.40873e60			−1.79519
$743$			1.88526e60i			0.965177i	0.875847	+	0.482589i	$0.160303\pi$
$743$			1.88526e60i			0.965177i	−0.875847	+	0.482589i	$0.839697\pi$
$744$	−2.56862e60	+	9.08579e59i	−1.27840	+	0.452200i
$745$	−1.08073e60			−0.522921
$746$			5.99994e59i			0.282249i
$747$	−5.48275e59	−	6.78037e59i	−0.250764	−	0.310114i
$748$	−3.08600e58			−0.0137234
$749$			2.76675e60i			1.19633i
$750$	4.00724e59	+	1.13287e60i	0.168484	+	0.476316i
$751$	−1.65912e60			−0.678327			−0.339163	−	0.940727i	$-0.610144\pi$
$751$	−1.65912e60			−0.678327			−0.339163	+	0.940727i	$0.610144\pi$
$752$		−	9.03956e59i		−	0.359395i
$753$	2.42126e60	−	8.56455e59i	0.936153	−	0.331139i
$754$	1.52392e60			0.573012
$755$		−	4.84096e60i		−	1.77030i
$756$	1.16381e59	+	7.14875e58i	0.0413928	+	0.0254257i
$757$	−3.17570e60			−1.09856			−0.549282	−	0.835637i	$-0.685099\pi$
$757$	−3.17570e60			−1.09856			−0.549282	+	0.835637i	$0.685099\pi$
$758$		−	5.51028e59i		−	0.185404i
$759$	−8.22249e59	−	2.32456e60i	−0.269108	−	0.760787i
$760$	7.90159e60			2.51553
$761$			2.25357e60i			0.697901i	0.937141	+	0.348951i	$0.113462\pi$
$761$			2.25357e60i			0.697901i	−0.937141	+	0.348951i	$0.886538\pi$
$762$	−6.00303e60	+	2.12341e60i	−1.80849	+	0.639704i
$763$	6.17234e60			1.80898
$764$		−	2.10146e59i		−	0.0599185i
$765$	−2.21020e60	+	1.78721e60i	−0.613113	+	0.495776i
$766$	−9.12200e59			−0.246199
$767$		−	8.97957e59i		−	0.235805i
$768$	−1.47884e59	−	4.18078e59i	−0.0377864	−	0.106825i
$769$	6.98979e60			1.73784			0.868922	−	0.494948i	$-0.164813\pi$
$769$	6.98979e60			1.73784			0.868922	+	0.494948i	$0.164813\pi$
$770$		−	5.78652e60i		−	1.39995i
$771$	4.45893e60	−	1.57722e60i	1.04976	−	0.371323i
$772$	1.74487e59			0.0399760
$773$			2.04748e60i			0.456511i	0.973601	+	0.228255i	$0.0733021\pi$
$773$			2.04748e60i			0.456511i	−0.973601	+	0.228255i	$0.926698\pi$
$774$	2.14674e59	+	2.65482e59i	0.0465821	+	0.0576069i
$775$	−8.68120e60			−1.83335
$776$		−	4.76656e60i		−	0.979736i
$777$	−1.94281e57	−	5.49246e57i	−0.000388676	−	0.00109882i
$778$	−2.38262e59			−0.0463963
$779$		−	1.42364e60i		−	0.269845i
$780$	−2.74634e59	+	9.71444e58i	−0.0506720	+	0.0179238i
$781$	−1.89491e60			−0.340344
$782$			3.46483e60i			0.605816i
$783$	−1.85593e60	+	3.02144e60i	−0.315911	+	0.514301i
$784$	−4.06201e60			−0.673138
$785$			5.14733e60i			0.830461i
$786$	−1.43225e60	−	4.04907e60i	−0.224981	−	0.636037i
$787$	−9.53164e57			−0.00145780			−0.000728900	−	1.00000i	$-0.500232\pi$
$787$	−9.53164e57			−0.00145780			−0.000728900		1.00000i	$0.500232\pi$
$788$			4.88603e59i			0.0727622i
$789$	−6.11454e60	+	2.16285e60i	−0.886639	+	0.313624i
$790$	5.60320e59			0.0791165
$791$		−	6.29398e60i		−	0.865405i
$792$	−3.99426e60	+	3.22984e60i	−0.534819	+	0.432466i
$793$	6.41536e60			0.836535
$794$			1.24418e61i			1.57998i
$795$	5.64130e60	+	1.59484e61i	0.697701	+	1.97245i
$796$	−3.13073e59			−0.0377113
$797$		−	5.56964e59i		−	0.0653435i	−0.999466	−	0.0326718i	$-0.989598\pi$
$797$		−	5.56964e59i		−	0.0653435i	0.999466	−	0.0326718i	$-0.0104016\pi$
$798$	1.81668e61	−	6.42601e60i	2.07595	−	0.734313i
$799$	1.61097e60			0.179310
$800$		−	9.24160e59i		−	0.100198i
$801$	−4.40912e60	−	5.45265e60i	−0.465660	−	0.575870i
$802$	9.47541e60			0.974847
$803$			7.40558e60i			0.742220i
$804$	1.77255e59	+	5.01114e59i	0.0173070	+	0.0489282i
$805$	−2.36780e61			−2.25233
$806$		−	1.41716e61i		−	1.31335i
$807$	2.74927e60	−	9.72481e59i	0.248241	−	0.0878086i
$808$	−1.54699e61			−1.36097
$809$			1.17085e61i			1.00365i	0.864969	+	0.501826i	$0.167338\pi$
$809$			1.17085e61i			1.00365i	−0.864969	+	0.501826i	$0.832662\pi$
$810$	3.89246e60	−	1.81867e61i	0.325116	−	1.51904i
$811$	2.34143e60			0.190565			0.0952823	−	0.995450i	$-0.469625\pi$
$811$	2.34143e60			0.190565			0.0952823	+	0.995450i	$0.469625\pi$
$812$			3.69700e59i			0.0293206i
$813$	7.06006e59	+	1.99593e60i	0.0545641	+	0.154257i
$814$	−8.61318e57			−0.000648711
$815$		−	3.13828e61i		−	2.30346i
$816$	7.06278e60	−	2.49827e60i	0.505222	−	0.178709i
$817$	1.75552e60			0.122389
$818$			2.35080e61i			1.59734i
$819$	1.40526e61	−	1.13632e61i	0.930669	−	0.752558i
$820$	−1.43259e59			−0.00924767
$821$			1.15239e61i			0.725090i	0.931966	+	0.362545i	$0.118092\pi$
$821$			1.15239e61i			0.725090i	−0.931966	+	0.362545i	$0.881908\pi$
$822$	−6.29626e59	−	1.78000e60i	−0.0386166	−	0.109172i
$823$	8.97873e60			0.536807			0.268404	−	0.963307i	$-0.413504\pi$
$823$	8.97873e60			0.536807			0.268404	+	0.963307i	$0.413504\pi$
$824$		−	1.89267e61i		−	1.10307i
$825$	−1.54301e61	+	5.45797e60i	−0.876668	+	0.310097i
$826$	5.97726e60			0.331071
$827$			2.40762e60i			0.130009i	0.997885	+	0.0650044i	$0.0207062\pi$
$827$			2.40762e60i			0.130009i	−0.997885	+	0.0650044i	$0.979294\pi$
$828$	−5.19538e59	−	6.42499e59i	−0.0273514	−	0.0338248i
$829$	−2.02726e61			−1.04055			−0.520276	−	0.853998i	$-0.674171\pi$
$829$	−2.02726e61			−1.04055			−0.520276	+	0.853998i	$0.674171\pi$
$830$			1.23796e61i			0.619536i
$831$	−3.08288e60	−	8.71552e60i	−0.150430	−	0.425277i
$832$	−1.87908e61			−0.894036
$833$		−	7.23905e60i		−	0.335843i
$834$	−1.09869e61	+	3.88633e60i	−0.497038	+	0.175814i
$835$	4.12348e61			1.81906
$836$		−	1.03828e60i		−	0.0446668i
$837$	2.80977e61	+	1.72591e61i	1.17879	+	0.724074i
$838$	−1.21271e61			−0.496173
$839$		−	2.77679e61i		−	1.10801i	−0.832515	−	0.554003i	$-0.813100\pi$
$839$		−	2.77679e61i		−	1.10801i	0.832515	−	0.554003i	$-0.186900\pi$
$840$	1.64496e61	+	4.65042e61i	0.640162	+	1.80978i
$841$	1.67481e61			0.635695
$842$			3.68021e61i			1.36244i
$843$	−4.46788e61	+	1.58039e61i	−1.61333	+	0.570671i
$844$	−1.00039e60			−0.0352352
$845$		−	5.83921e60i		−	0.200615i
$846$	−8.19666e60	+	6.62799e60i	−0.274701	+	0.222128i
$847$	−1.99427e61			−0.651978
$848$		−	4.45871e61i		−	1.42199i
$849$	7.04814e60	+	1.99256e61i	0.219287	+	0.619941i
$850$	2.29991e61			0.698092
$851$			3.52444e58i			0.00104369i
$852$	−5.98650e59	+	2.11756e59i	−0.0172958	+	0.00611793i
$853$	1.30625e61			0.368210			0.184105	−	0.982907i	$-0.441061\pi$
$853$	1.30625e61			0.368210			0.184105	+	0.982907i	$0.441061\pi$
$854$			4.27039e61i			1.17450i
$855$	−6.01306e61	−	7.43620e61i	−1.61364	−	1.99555i
$856$	−3.48692e61			−0.913046
$857$			6.41360e61i			1.63872i	0.573280	+	0.819360i	$0.305671\pi$
$857$			6.41360e61i			1.63872i	−0.573280	+	0.819360i	$0.694329\pi$
$858$	−8.90982e60	−	2.51887e61i	−0.222145	−	0.628019i
$859$	3.48827e61			0.848699			0.424350	−	0.905498i	$-0.360503\pi$
$859$	3.48827e61			0.848699			0.424350	+	0.905498i	$0.360503\pi$
$860$		−	1.76656e59i		−	0.00419431i
$861$	8.37871e60	−	2.96374e60i	0.194138	−	0.0686711i
$862$	−1.27025e61			−0.287235
$863$		−	5.40809e61i		−	1.19349i	−0.802432	−	0.596743i	$-0.796461\pi$
$863$		−	5.40809e61i		−	1.19349i	0.802432	−	0.596743i	$-0.203539\pi$
$864$	−1.83732e60	+	2.99114e60i	−0.0395727	+	0.0644242i
$865$	7.80106e61			1.63989
$866$		−	9.28372e61i		−	1.90479i
$867$	−1.21997e61	−	3.44894e61i	−0.244314	−	0.690692i
$868$	3.43800e60			0.0672034
$869$			1.87296e60i			0.0357365i
$870$	4.74606e61	−	1.67879e61i	0.883952	−	0.312674i
$871$	7.03308e61			1.27869
$872$			7.77895e61i			1.38062i
$873$	−4.48582e61	+	3.62732e61i	−0.777217	+	0.628474i
$874$	−1.16574e62			−1.97180
$875$			3.85725e61i			0.636956i
$876$	8.27572e59	+	2.33960e60i	0.0133420	+	0.0377187i
$877$	5.70025e61			0.897227			0.448613	−	0.893726i	$-0.351918\pi$
$877$	5.70025e61			0.897227			0.448613	+	0.893726i	$0.351918\pi$
$878$		−	2.63291e61i		−	0.404624i
$879$	2.78521e61	−	9.85193e60i	0.417919	−	0.147827i
$880$	7.56894e61			1.10892
$881$		−	1.05231e62i		−	1.50539i	−0.658369	−	0.752696i	$-0.728753\pi$
$881$		−	1.05231e62i		−	1.50539i	0.658369	−	0.752696i	$-0.271247\pi$
$882$	2.97835e61	+	3.68325e61i	0.416040	+	0.514507i
$883$	−1.12382e62			−1.53292			−0.766462	−	0.642290i	$-0.777985\pi$
$883$	−1.12382e62			−1.53292			−0.766462	+	0.642290i	$0.777985\pi$
$884$			1.36832e60i			0.0182260i
$885$	−9.89212e60	−	2.79657e61i	−0.128671	−	0.363762i
$886$	1.18847e62			1.50966
$887$			1.08353e62i			1.34414i	0.740490	+	0.672068i	$0.234594\pi$
$887$			1.08353e62i			1.34414i	−0.740490	+	0.672068i	$0.765406\pi$
$888$	6.92210e58	−	2.44850e58i	0.000838620	−	0.000296639i
$889$	−2.04393e62			−2.41841
$890$			9.95544e61i			1.15046i
$891$	6.07921e61	+	1.30112e61i	0.686144	+	0.146853i
$892$	−9.37887e59			−0.0103392
$893$			5.42011e61i			0.583616i
$894$	−1.10768e61	−	3.13150e61i	−0.116500	−	0.329355i
$895$	−1.96726e62			−2.02106
$896$		−	1.34757e62i		−	1.35234i
$897$	−1.03070e62	+	3.64582e61i	−1.01040	+	0.357400i
$898$	−2.80589e61			−0.268700
$899$			8.92559e61i			0.834994i
$900$	−4.26481e60	+	3.44861e60i	−0.0389769	+	0.0315175i
$901$	7.94603e61			0.709463
$902$		−	1.31394e61i		−	0.114614i
$903$	3.65465e60	+	1.03320e61i	0.0311460	+	0.0880521i
$904$	7.93226e61			0.660480
$905$		−	3.41160e61i		−	0.277548i
$906$	1.40271e62	−	4.96169e61i	1.11500	−	0.394401i
$907$	2.30658e62			1.79149			0.895747	−	0.444563i	$-0.146641\pi$
$907$	2.30658e62			1.79149			0.895747	+	0.444563i	$0.146641\pi$
$908$		−	2.04017e60i		−	0.0154833i
$909$	1.17725e62	+	1.45587e62i	0.873023	+	1.07965i
$910$	−2.56573e62			−1.85926
$911$		−	5.09186e60i		−	0.0360571i	−0.999837	−	0.0180285i	$-0.994261\pi$
$911$		−	5.09186e60i		−	0.0360571i	0.999837	−	0.0180285i	$-0.00573898\pi$
$912$	8.40541e61	+	2.37627e62i	0.581658	+	1.64439i
$913$	−4.13808e61			−0.279842
$914$		−	3.78591e61i		−	0.250208i
$915$	1.99798e62	−	7.06732e61i	1.29047	−	0.456470i
$916$	1.67435e60			0.0105692
$917$		−	1.37864e62i		−	0.850542i
$918$	−7.44389e61	−	4.57243e61i	−0.448853	−	0.275709i
$919$	8.15286e61			0.480490			0.240245	−	0.970712i	$-0.422772\pi$
$919$	8.15286e61			0.480490			0.240245	+	0.970712i	$0.422772\pi$
$920$		−	2.98412e62i		−	1.71898i
$921$	−7.51899e61	−	2.12567e62i	−0.423357	−	1.19686i
$922$	−3.09069e62			−1.70101
$923$			8.40198e61i			0.452008i
$924$	6.11073e60	−	2.16151e60i	0.0321353	−	0.0113670i
$925$	2.33947e59			0.00120266
$926$		−	2.41331e62i		−	1.21278i
$927$	−1.78119e62	+	1.44031e62i	−0.875056	+	0.707588i
$928$	−9.50176e60			−0.0456349
$929$			2.00651e62i			0.942130i	0.882098	+	0.471065i	$0.156130\pi$
$929$			2.00651e62i			0.942130i	−0.882098	+	0.471065i	$0.843870\pi$
$930$	−1.56118e62	−	4.41356e62i	−0.716655	−	2.02603i
$931$	2.43558e62			1.09310
$932$		−	2.17733e60i		−	0.00955409i
$933$	−1.33227e62	+	4.71253e61i	−0.571579	+	0.202181i
$934$	4.39173e62			1.84226
$935$			1.34889e62i			0.553263i
$936$	1.43210e62	+	1.77104e62i	0.574355	+	0.710290i
$937$	−2.70506e62			−1.06083			−0.530416	−	0.847738i	$-0.677964\pi$
$937$	−2.70506e62			−1.06083			−0.530416	+	0.847738i	$0.677964\pi$
$938$			4.68158e62i			1.79528i
$939$	2.23471e61	+	6.31768e61i	0.0837999	+	0.236908i
$940$	5.45420e60			0.0200007
$941$			2.30368e61i			0.0826113i	0.999147	+	0.0413057i	$0.0131517\pi$
$941$			2.30368e61i			0.0826113i	−0.999147	+	0.0413057i	$0.986848\pi$
$942$	−1.49148e62	+	5.27570e61i	−0.523056	+	0.185017i
$943$	−5.37652e61			−0.184398
$944$			7.81843e61i			0.262245i
$945$	3.12471e62	−	5.08701e62i	1.02504	−	1.66876i
$946$	1.62024e61			0.0519835
$947$			1.12155e62i			0.351940i	0.984396	+	0.175970i	$0.0563062\pi$
$947$			1.12155e62i			0.351940i	−0.984396	+	0.175970i	$0.943694\pi$
$948$	2.09303e59	+	5.91714e59i	0.000642391	+	0.00181609i
$949$	3.28361e62			0.985737
$950$			7.73803e62i			2.27214i
$951$	−1.47786e62	+	5.22752e61i	−0.424465	+	0.150143i
$952$	2.31700e62			0.650954
$953$		−	5.87297e62i		−	1.61401i	−0.590542	−	0.807007i	$-0.701086\pi$
$953$		−	5.87297e62i		−	1.61401i	0.590542	−	0.807007i	$-0.298914\pi$
$954$	−4.04296e62	+	3.26922e62i	−1.08688	+	0.878877i
$955$	−9.18547e62			−2.41563
$956$		−	1.51820e61i		−	0.0390584i
$957$	5.61162e61	+	1.58644e62i	0.141233	+	0.399277i
$958$	5.99086e62			1.47507
$959$		−	6.06060e61i		−	0.145991i
$960$	−5.85215e62	+	2.07004e62i	−1.37918	+	0.487846i
$961$	3.96326e62			0.913822
$962$			3.81906e59i			0.000861548i
$963$	2.65352e62	+	3.28154e62i	0.585694	+	0.724313i
$964$	2.19084e60			0.00473143
$965$		−	7.62680e62i		−	1.61164i
$966$	−2.42685e62	−	6.86088e62i	−0.501791	−	1.41860i
$967$	−1.68585e62			−0.341086			−0.170543	−	0.985350i	$-0.554552\pi$
$967$	−1.68585e62			−0.341086			−0.170543	+	0.985350i	$0.554552\pi$
$968$		−	2.51336e62i		−	0.497592i
$969$	−4.23484e62	+	1.49796e62i	−0.820422	+	0.290202i
$970$	8.19020e62			1.55270
$971$		−	9.90017e62i		−	1.83670i	−0.395766	−	0.918351i	$-0.629521\pi$
$971$		−	9.90017e62i		−	1.83670i	0.395766	−	0.918351i	$-0.370479\pi$
$972$	2.06597e61	−	2.68295e60i	0.0375088	−	0.00487104i
$973$	−3.74088e62			−0.664666
$974$			5.16408e62i			0.897955i
$975$	2.42005e62	+	6.84164e62i	0.411838	+	1.16430i
$976$	−5.58580e62			−0.930334
$977$			6.54803e62i			1.06739i	0.845676	+	0.533697i	$0.179198\pi$
$977$			6.54803e62i			1.06739i	−0.845676	+	0.533697i	$0.820802\pi$
$978$	9.09340e62	−	3.21654e62i	1.45081	−	0.513184i
$979$	−3.32776e62			−0.519656
$980$		−	2.45089e61i		−	0.0374608i
$981$	7.32078e62	−	5.91973e62i	1.09524	−	0.885631i
$982$	−5.73964e62			−0.840511
$983$		−	6.63799e62i		−	0.951509i	−0.879578	−	0.475754i	$-0.842175\pi$
$983$		−	6.63799e62i		−	0.951509i	0.879578	−	0.475754i	$-0.157825\pi$
$984$	3.73518e61	+	1.05596e62i	0.0524100	+	0.148167i
$985$	2.13568e63			2.93343
$986$		−	2.36465e62i		−	0.317945i
$987$	−3.18996e62	+	1.12836e62i	−0.419880	+	0.148521i
$988$	−4.60372e61			−0.0593216
$989$		−	6.62989e61i		−	0.0836343i
$990$	−5.54970e62	−	6.86318e62i	−0.685379	−	0.847591i
$991$	−5.83179e62			−0.705108			−0.352554	−	0.935792i	$-0.614687\pi$
$991$	−5.83179e62			−0.705108			−0.352554	+	0.935792i	$0.614687\pi$
$992$			8.83609e61i			0.104596i
$993$	1.52485e62	+	4.31087e62i	0.176723	+	0.499610i
$994$	−5.59279e62			−0.634621
$995$			1.36844e63i			1.52034i
$996$	−1.30732e61	+	4.62429e60i	−0.0142212	+	0.00503036i
$997$	−1.50217e63			−1.60000			−0.800001	−	0.599999i	$-0.795168\pi$
$997$	−1.50217e63			−1.60000			−0.800001	+	0.599999i	$0.795168\pi$
$998$			8.90729e62i			0.928976i
$999$	−7.57196e59	−	4.65110e59i	−0.000773273	−	0.000474985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.43.b.b.2.4	✓	12
3.2	odd	2	inner	3.43.b.b.2.9	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.43.b.b.2.4	✓	12	1.1	even	1	trivial
3.43.b.b.2.9	yes	12	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.13644e6i q^{2} +(-3.48827e9 - 9.86159e9i) q^{3} -1.66350e11 q^{4} +7.27116e14i q^{5} +(-2.10687e16 + 7.45250e15i) q^{6} -7.17356e17 q^{7} -9.04079e18i q^{8} +(-8.50829e19 + 6.87998e19i) q^{9} +O(q^{10})\)	\(q-2.13644e6i q^{2} +(-3.48827e9 - 9.86159e9i) q^{3} -1.66350e11 q^{4} +7.27116e14i q^{5} +(-2.10687e16 + 7.45250e15i) q^{6} -7.17356e17 q^{7} -9.04079e18i q^{8} +(-8.50829e19 + 6.87998e19i) q^{9} +1.55344e21 q^{10} +5.19263e21i q^{11} +(5.80275e20 + 1.64048e21i) q^{12} +2.30240e23 q^{13} +1.53259e24i q^{14} +(7.17052e24 - 2.53638e24i) q^{15} -2.00468e25 q^{16} -3.57260e25i q^{17} +(1.46987e26 + 1.81775e26i) q^{18} +1.20200e27 q^{19} -1.20956e26i q^{20} +(2.50233e27 + 7.07428e27i) q^{21} +1.10938e28 q^{22} -4.53948e28i q^{23} +(-8.91565e28 + 3.15367e28i) q^{24} -3.01324e29 q^{25} -4.91894e29i q^{26} +(9.75267e29 + 5.99061e29i) q^{27} +1.19333e29 q^{28} +3.09807e30i q^{29} +(-5.41883e30 - 1.53194e31i) q^{30} +2.88102e31 q^{31} +3.06700e30i q^{32} +(5.12076e31 - 1.81133e31i) q^{33} -7.63267e31 q^{34} -5.21601e32i q^{35} +(1.41536e31 - 1.14449e31i) q^{36} -7.76398e29 q^{37} -2.56801e33i q^{38} +(-8.03138e32 - 2.27053e33i) q^{39} +6.57370e33 q^{40} -1.18439e33i q^{41} +(1.51138e34 - 5.34610e33i) q^{42} +1.46050e33 q^{43} -8.63796e32i q^{44} +(-5.00254e34 - 6.18652e34i) q^{45} -9.69834e34 q^{46} +4.50924e34i q^{47} +(6.99285e34 + 1.97693e35i) q^{48} +2.02627e35 q^{49} +6.43762e35i q^{50} +(-3.52316e35 + 1.24622e35i) q^{51} -3.83005e34 q^{52} +2.22416e36i q^{53} +(1.27986e36 - 2.08361e36i) q^{54} -3.77564e36 q^{55} +6.48547e36i q^{56} +(-4.19290e36 - 1.18536e37i) q^{57} +6.61885e36 q^{58} -3.90010e36i q^{59} +(-1.19282e36 + 4.21927e35i) q^{60} +2.78638e37 q^{61} -6.15514e37i q^{62} +(6.10348e37 - 4.93540e37i) q^{63} -8.16141e37 q^{64} +1.67411e38i q^{65} +(-3.86981e37 - 1.09402e38i) q^{66} +3.05468e38 q^{67} +5.94304e36i q^{68} +(-4.47665e38 + 1.58349e38i) q^{69} -1.11437e39 q^{70} +3.64924e38i q^{71} +(6.22004e38 + 7.69217e38i) q^{72} +1.42617e39 q^{73} +1.65873e36i q^{74} +(1.05110e39 + 2.97153e39i) q^{75} -1.99953e38 q^{76} -3.72497e39i q^{77} +(-4.85086e39 + 1.71586e39i) q^{78} +3.60695e38 q^{79} -1.45763e40i q^{80} +(2.50570e39 - 1.17074e40i) q^{81} -2.53039e39 q^{82} +7.96913e39i q^{83} +(-4.16264e38 - 1.17681e39i) q^{84} +2.59770e40 q^{85} -3.12027e39i q^{86} +(3.05519e40 - 1.08069e40i) q^{87} +4.69455e40 q^{88} +6.40863e40i q^{89} +(-1.32172e41 + 1.06877e41i) q^{90} -1.65164e41 q^{91} +7.55144e39i q^{92} +(-1.00498e41 - 2.84114e41i) q^{93} +9.63373e40 q^{94} +8.73994e41i q^{95} +(3.02455e40 - 1.06985e40i) q^{96} +5.27229e41 q^{97} -4.32901e41i q^{98} +(-3.57252e41 - 4.41804e41i) 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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