LMFDB - Embedded newform 3.41.b.a.2.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,41,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, 41, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 41);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 41 $
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:	$30.4026855589$
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} + 249659905422 x^{10} + \cdots + 12\!\cdots\!00 $ x^12 + 249659905422x^10 + 21357900831219724160448x^8 + 757005714875983264074654770397184x^6 + 10196659004511185116272142565764285511761920x^4 + 42071301184141474816096210166597335428414342325862400*x^2 + 12606130133749306378798090199763505554693706712963960799232000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{63}\cdot 3^{98}\cdot 5^{6}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.10
Root			$229859. i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.41.b.a.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.37915e6i q^{2} +(-3.48296e9 + 1.63234e8i) q^{3} -8.02549e11 q^{4} -4.92196e13i q^{5} +(-2.25124e14 - 4.80353e15i) q^{6} +5.39353e16 q^{7} +4.09556e17i q^{8} +(1.21044e19 - 1.13707e18i) q^{9} +O(q^{10})$	\(q+1.37915e6i q^{2} +(-3.48296e9 + 1.63234e8i) q^{3} -8.02549e11 q^{4} -4.92196e13i q^{5} +(-2.25124e14 - 4.80353e15i) q^{6} +5.39353e16 q^{7} +4.09556e17i q^{8} +(1.21044e19 - 1.13707e18i) q^{9} +6.78814e19 q^{10} +2.19593e20i q^{11} +(2.79525e21 - 1.31003e20i) q^{12} +5.75209e21 q^{13} +7.43849e22i q^{14} +(8.03431e21 + 1.71430e23i) q^{15} -1.44725e24 q^{16} +6.05210e24i q^{17} +(1.56820e24 + 1.66938e25i) q^{18} +3.89743e25 q^{19} +3.95012e25i q^{20} +(-1.87854e26 + 8.80406e24i) q^{21} -3.02853e26 q^{22} -2.93005e27i q^{23} +(-6.68534e25 - 1.42647e27i) q^{24} +6.67237e27 q^{25} +7.93300e27i q^{26} +(-4.19735e28 + 5.93623e27i) q^{27} -4.32857e28 q^{28} +2.25230e29i q^{29} +(-2.36428e29 + 1.10805e28i) q^{30} -5.05825e29 q^{31} -1.54567e30i q^{32} +(-3.58451e28 - 7.64836e29i) q^{33} -8.34676e30 q^{34} -2.65467e30i q^{35} +(-9.71436e30 + 9.12558e29i) q^{36} -3.44493e31 q^{37} +5.37515e31i q^{38} +(-2.00343e31 + 9.38935e29i) q^{39} +2.01582e31 q^{40} -2.84139e31i q^{41} +(-1.21421e31 - 2.59080e32i) q^{42} -3.37498e31 q^{43} -1.76235e32i q^{44} +(-5.59664e31 - 5.95773e32i) q^{45} +4.04098e33 q^{46} +4.50279e33i q^{47} +(5.04073e33 - 2.36241e32i) q^{48} -3.45779e33 q^{49} +9.20222e33i q^{50} +(-9.87907e32 - 2.10792e34i) q^{51} -4.61633e33 q^{52} +1.59114e34i q^{53} +(-8.18697e33 - 5.78878e34i) q^{54} +1.08083e34 q^{55} +2.20895e34i q^{56} +(-1.35746e35 + 6.36193e33i) q^{57} -3.10627e35 q^{58} +4.55972e35i q^{59} +(-6.44793e33 - 1.37581e35i) q^{60} +2.97372e35 q^{61} -6.97609e35i q^{62} +(6.52853e35 - 6.13284e34i) q^{63} +5.40443e35 q^{64} -2.83116e35i q^{65} +(1.05482e36 - 4.94358e34i) q^{66} +1.49190e36 q^{67} -4.85711e36i q^{68} +(4.78283e35 + 1.02052e37i) q^{69} +3.66120e36 q^{70} +8.37384e36i q^{71} +(4.65696e35 + 4.95742e36i) q^{72} -1.01281e37 q^{73} -4.75109e37i q^{74} +(-2.32396e37 + 1.08916e36i) q^{75} -3.12788e37 q^{76} +1.18438e37i q^{77} +(-1.29493e36 - 2.76303e37i) q^{78} -9.72628e37 q^{79} +7.12333e37i q^{80} +(1.45223e38 - 2.75271e37i) q^{81} +3.91871e37 q^{82} +3.08704e38i q^{83} +(1.50762e38 - 7.06569e36i) q^{84} +2.97882e38 q^{85} -4.65462e37i q^{86} +(-3.67652e37 - 7.84469e38i) q^{87} -8.99359e37 q^{88} -4.83862e38i q^{89} +(8.21662e38 - 7.71862e37i) q^{90} +3.10240e38 q^{91} +2.35151e39i q^{92} +(1.76177e39 - 8.25677e37i) q^{93} -6.21004e39 q^{94} -1.91830e39i q^{95} +(2.52306e38 + 5.38351e39i) q^{96} -7.78530e39 q^{97} -4.76882e39i q^{98} +(2.49694e38 + 2.65804e39i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots - 23\!\cdots\!20 q^{9}+O(q^{10}) $ 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9	$ 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots + 54\!\cdots\!80 q^{99}+O(q^{100}) $ 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9 - 129384136354706290080 * q^10 - 4708039830028985428272 * q^12 + 704368845864154901976 * q^13 + 320935800901459838631840 * q^15 + 6054431850962872672227456 * q^16 + 10227710367381761273509920 * q^18 + 37616619688417835612151720 * q^19 - 179163719456723608834234728 * q^21 + 846315150249292772829325920 * q^22 - 18213480358094369517645250944 * q^24 + 8842265325510151276196474700 * q^25 - 70717074113738779393083858252 * q^27 + 469404222007499612173589889696 * q^28 - 207809636542026559976510503200 * q^30 - 914600368399753689553849145016 * q^31 + 157344642221562801276041757600 * q^33 - 14575908480758621487300381842304 * q^34 + 41100171486790863962401658870544 * q^36 + 5673106137824212681873457220696 * q^37 - 9206461430638842876438079090008 * q^39 + 50495897877443363581635475618560 * q^40 - 939238658319640212873301303645920 * q^42 + 1012654832326802922602871229857576 * q^43 + 196109968512215856818385626472000 * q^45 - 3082500781506234684371181468390336 * q^46 + 6532128822166367998693520969705088 * q^48 + 8498166150175390075155260408801892 * q^49 + 27565453699222767413826960590504832 * q^51 - 57328509042562386918101767400001504 * q^52 - 102847607224782098537542351912875792 * q^54 - 9637639495259752880102706884884800 * q^55 - 40307213604482059940636368892395464 * q^57 + 772129436848561910287203884295052320 * q^58 - 114385571579949295944121547557720320 * q^60 - 494443282701607071691140418439862696 * q^61 + 1379291076525018665154441723571240776 * q^63 - 6231783699524672226208093043936541696 * q^64 + 2652084094607847915810184973553481440 * q^66 + 5401062423529881431761320436868275176 * q^67 + 7110274695178254111533494284632123328 * q^69 + 516103243900107216646679160954379200 * q^70 - 27544975046740790141119542770107057920 * q^72 + 30000154498324943042431295514883418136 * q^73 + 43820294796704764666539599709819928500 * q^75 - 215478934792040263381331019050660960352 * q^76 + 234946633516471169601955850003339878560 * q^78 - 128704557118405295534397879672035334840 * q^79 + 473157359902659920298963194247360443532 * q^81 - 639159997421964256448917103585883414720 * q^82 + 1283288903941350744781821238287455403552 * q^84 - 1077142486191382871466217243736209678080 * q^85 + 1076668306862385320797179121273520148960 * q^87 - 2918662713596496795370587920448329114880 * q^88 + 6571793457940570799819318674019816438880 * q^90 - 9859184204686878150356379414618151910256 * q^91 + 11506410044121210986218054652959643683416 * q^93 - 16857264118330945289191940748512432348544 * q^94 + 53068562519213731340201280418423192237056 * q^96 - 41841010071967618660163746722085070705064 * q^97 + 54341076855402233475300783474292013590080 * 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 $

$2$			1.37915e6i			1.31526i	0.753340	+	0.657631i	$0.228441\pi$
$2$			1.37915e6i			1.31526i	−0.753340	+	0.657631i	$0.771559\pi$
$3$	−3.48296e9	+	1.63234e8i	−0.998904	+	0.0468150i
$3$	−3.48296e9	+	1.63234e8i	−0.998904	+	0.0468150i
$4$	−8.02549e11			−0.729914
$5$		−	4.92196e13i		−	0.516105i	−0.966131	−	0.258053i	$-0.916919\pi$
$5$		−	4.92196e13i		−	0.516105i	0.966131	−	0.258053i	$-0.0830808\pi$
$6$	−2.25124e14	−	4.80353e15i	−0.0615740	−	1.31382i
$7$	5.39353e16			0.675946			0.337973	−	0.941156i	$-0.390259\pi$
$7$	5.39353e16			0.675946			0.337973	+	0.941156i	$0.390259\pi$
$8$			4.09556e17i			0.355233i
$9$	1.21044e19	−	1.13707e18i	0.995617	−	0.0935274i
$10$	6.78814e19			0.678814
$11$			2.19593e20i			0.326412i	0.986592	+	0.163206i	$0.0521835\pi$
$11$			2.19593e20i			0.326412i	−0.986592	+	0.163206i	$0.947817\pi$
$12$	2.79525e21	−	1.31003e20i	0.729114	−	0.0341710i
$13$	5.75209e21			0.302662			0.151331	−	0.988483i	$-0.451644\pi$
$13$	5.75209e21			0.302662			0.151331	+	0.988483i	$0.451644\pi$
$14$			7.43849e22i			0.889046i
$15$	8.03431e21	+	1.71430e23i	0.0241615	+	0.515540i
$16$	−1.44725e24			−1.19714
$17$			6.05210e24i			1.48911i	0.667560	+	0.744556i	$0.267339\pi$
$17$			6.05210e24i			1.48911i	−0.667560	+	0.744556i	$0.732661\pi$
$18$	1.56820e24	+	1.66938e25i	0.123013	+	1.30950i
$19$	3.89743e25			1.03683			0.518414	−	0.855130i	$-0.326523\pi$
$19$	3.89743e25			1.03683			0.518414	+	0.855130i	$0.326523\pi$
$20$			3.95012e25i			0.376713i
$21$	−1.87854e26	+	8.80406e24i	−0.675205	+	0.0316444i
$22$	−3.02853e26			−0.429317
$23$		−	2.93005e27i		−	1.70733i	−0.520822	−	0.853666i	$-0.674374\pi$
$23$		−	2.93005e27i		−	1.70733i	0.520822	−	0.853666i	$-0.325626\pi$
$24$	−6.68534e25	−	1.42647e27i	−0.0166303	−	0.354844i
$25$	6.67237e27			0.733635
$26$			7.93300e27i			0.398080i
$27$	−4.19735e28	+	5.93623e27i	−0.990147	+	0.140035i
$28$	−4.32857e28			−0.493383
$29$			2.25230e29i			1.27253i	0.771472	+	0.636264i	$0.219521\pi$
$29$			2.25230e29i			1.27253i	−0.771472	+	0.636264i	$0.780479\pi$
$30$	−2.36428e29	+	1.10805e28i	−0.678070	+	0.0317787i
$31$	−5.05825e29			−0.752950			−0.376475	−	0.926427i	$-0.622864\pi$
$31$	−5.05825e29			−0.752950			−0.376475	+	0.926427i	$0.622864\pi$
$32$		−	1.54567e30i		−	1.21932i
$33$	−3.58451e28	−	7.64836e29i	−0.0152810	−	0.326054i
$34$	−8.34676e30			−1.95857
$35$		−	2.65467e30i		−	0.348859i
$36$	−9.71436e30	+	9.12558e29i	−0.726715	+	0.0682670i
$37$	−3.44493e31			−1.48986			−0.744931	−	0.667141i	$-0.767518\pi$
$37$	−3.44493e31			−1.48986			−0.744931	+	0.667141i	$0.767518\pi$
$38$			5.37515e31i			1.36370i
$39$	−2.00343e31	+	9.38935e29i	−0.302330	+	0.0141691i
$40$	2.01582e31			0.183338
$41$		−	2.84139e31i		−	0.157708i	−0.996886	−	0.0788541i	$-0.974874\pi$
$41$		−	2.84139e31i		−	0.157708i	0.996886	−	0.0788541i	$-0.0251261\pi$
$42$	−1.21421e31	−	2.59080e32i	−0.0416207	−	0.888071i
$43$	−3.37498e31			−0.0722608			−0.0361304	−	0.999347i	$-0.511503\pi$
$43$	−3.37498e31			−0.0722608			−0.0361304	+	0.999347i	$0.511503\pi$
$44$		−	1.76235e32i		−	0.238253i
$45$	−5.59664e31	−	5.95773e32i	−0.0482700	−	0.513843i
$46$	4.04098e33			2.24559
$47$			4.50279e33i			1.62751i	0.581205	+	0.813757i	$0.302581\pi$
$47$			4.50279e33i			1.62751i	−0.581205	+	0.813757i	$0.697419\pi$
$48$	5.04073e33	−	2.36241e32i	1.19583	−	0.0560441i
$49$	−3.45779e33			−0.543097
$50$			9.20222e33i			0.964923i
$51$	−9.87907e32	−	2.10792e34i	−0.0697128	−	1.48748i
$52$	−4.61633e33			−0.220918
$53$			1.59114e34i			0.520224i	0.965578	+	0.260112i	$0.0837595\pi$
$53$			1.59114e34i			0.520224i	−0.965578	+	0.260112i	$0.916241\pi$
$54$	−8.18697e33	−	5.78878e34i	−0.184182	−	1.30230i
$55$	1.08083e34			0.168463
$56$			2.20895e34i			0.240119i
$57$	−1.35746e35	+	6.36193e33i	−1.03569	+	0.0485391i
$58$	−3.10627e35			−1.67371
$59$			4.55972e35i			1.74541i	0.488245	+	0.872707i	$0.337637\pi$
$59$			4.55972e35i			1.74541i	−0.488245	+	0.872707i	$0.662363\pi$
$60$	−6.44793e33	−	1.37581e35i	−0.0176358	−	0.376300i
$61$	2.97372e35			0.584391			0.292196	−	0.956359i	$-0.405614\pi$
$61$	2.97372e35			0.584391			0.292196	+	0.956359i	$0.405614\pi$
$62$		−	6.97609e35i		−	0.990327i
$63$	6.52853e35	−	6.13284e34i	0.672983	−	0.0632194i
$64$	5.40443e35			0.406584
$65$		−	2.83116e35i		−	0.156206i
$66$	1.05482e36	−	4.94358e34i	0.428846	−	0.0200985i
$67$	1.49190e36			0.448996			0.224498	−	0.974475i	$-0.427926\pi$
$67$	1.49190e36			0.448996			0.224498	+	0.974475i	$0.427926\pi$
$68$		−	4.85711e36i		−	1.08692i
$69$	4.78283e35	+	1.02052e37i	0.0799287	+	1.70546i
$70$	3.66120e36			0.458841
$71$			8.37384e36i			0.790237i	0.918630	+	0.395119i	$0.129297\pi$
$71$			8.37384e36i			0.790237i	−0.918630	+	0.395119i	$0.870703\pi$
$72$	4.65696e35	+	4.95742e36i	0.0332240	+	0.353676i
$73$	−1.01281e37			−0.548368			−0.274184	−	0.961677i	$-0.588408\pi$
$73$	−1.01281e37			−0.548368			−0.274184	+	0.961677i	$0.588408\pi$
$74$		−	4.75109e37i		−	1.95956i
$75$	−2.32396e37	+	1.08916e36i	−0.732831	+	0.0343451i
$76$	−3.12788e37			−0.756795
$77$			1.18438e37i			0.220637i
$78$	−1.29493e36	−	2.76303e37i	−0.0186361	−	0.397644i
$79$	−9.72628e37			−1.08494			−0.542469	−	0.840076i	$-0.682511\pi$
$79$	−9.72628e37			−1.08494			−0.542469	+	0.840076i	$0.682511\pi$
$80$			7.12333e37i			0.617850i
$81$	1.45223e38	−	2.75271e37i	0.982505	−	0.186235i
$82$	3.91871e37			0.207428
$83$			3.08704e38i			1.28227i	0.767428	+	0.641136i	$0.221536\pi$
$83$			3.08704e38i			1.28227i	−0.767428	+	0.641136i	$0.778464\pi$
$84$	1.50762e38	−	7.06569e36i	0.492842	−	0.0230977i
$85$	2.97882e38			0.768539
$86$		−	4.65462e37i		−	0.0950418i
$87$	−3.67652e37	−	7.84469e38i	−0.0595734	−	1.27113i
$88$	−8.99359e37			−0.115952
$89$		−	4.83862e38i		−	0.497647i	−0.968549	−	0.248824i	$-0.919956\pi$
$89$		−	4.83862e38i		−	0.497647i	0.968549	−	0.248824i	$-0.0800440\pi$
$90$	8.21662e38	−	7.71862e37i	0.675838	−	0.0634877i
$91$	3.10240e38			0.204583
$92$			2.35151e39i			1.24621i
$93$	1.76177e39	−	8.25677e37i	0.752125	−	0.0352494i
$94$	−6.21004e39			−2.14061
$95$		−	1.91830e39i		−	0.535112i
$96$	2.52306e38	+	5.38351e39i	0.0570824	+	1.21798i
$97$	−7.78530e39			−1.43166			−0.715831	−	0.698273i	$-0.753952\pi$
$97$	−7.78530e39			−1.43166			−0.715831	+	0.698273i	$0.753952\pi$
$98$		−	4.76882e39i		−	0.714315i
$99$	2.49694e38	+	2.65804e39i	0.0305284	+	0.324981i
$100$	−5.35491e39			−0.535491
$101$		−	1.65661e40i		−	1.35767i	−0.734293	−	0.678833i	$-0.762486\pi$
$101$		−	1.65661e40i		−	1.35767i	0.734293	−	0.678833i	$-0.237514\pi$
$102$	2.90715e40	−	1.36247e39i	1.95643	−	0.0916906i
$103$	6.78762e39			0.375814			0.187907	−	0.982187i	$-0.439830\pi$
$103$	6.78762e39			0.375814			0.187907	+	0.982187i	$0.439830\pi$
$104$			2.35580e39i			0.107516i
$105$	4.33333e38	+	9.24613e39i	0.0163319	+	0.348477i
$106$	−2.19442e40			−0.684231
$107$			3.91632e40i			1.01205i	0.862518	+	0.506026i	$0.168886\pi$
$107$			3.91632e40i			1.01205i	−0.862518	+	0.506026i	$0.831114\pi$
$108$	3.36858e40	−	4.76412e39i	0.722722	−	0.102213i
$109$	6.14356e39			0.109620			0.0548100	−	0.998497i	$-0.482545\pi$
$109$	6.14356e39			0.109620			0.0548100	+	0.998497i	$0.482545\pi$
$110$			1.49063e40i			0.221573i
$111$	1.19986e41	−	5.62330e39i	1.48823	−	0.0697479i
$112$	−7.80580e40			−0.809202
$113$			6.15450e40i			0.534101i	0.963682	+	0.267051i	$0.0860491\pi$
$113$			6.15450e40i			0.534101i	−0.963682	+	0.267051i	$0.913951\pi$
$114$	−8.77407e39	−	1.87215e41i	−0.0638416	−	1.36220i
$115$	−1.44216e41			−0.881163
$116$		−	1.80759e41i		−	0.928836i
$117$	6.96254e40	−	6.54055e39i	0.301336	−	0.0283072i
$118$	−6.28855e41			−2.29568
$119$			3.26421e41i			1.00656i
$120$	−7.02103e40	+	3.29050e39i	−0.183137	+	0.00858296i
$121$	4.04371e41			0.893455
$122$			4.10122e41i			0.768628i
$123$	4.63811e39	+	9.89646e40i	0.00738311	+	0.157535i
$124$	4.05949e41			0.549589
$125$		−	7.76062e41i		−	0.894738i
$126$	8.45812e40	+	9.00383e41i	0.0831501	+	0.885149i
$127$	8.82928e41			0.741056			0.370528	−	0.928821i	$-0.379177\pi$
$127$	8.82928e41			0.741056			0.370528	+	0.928821i	$0.379177\pi$
$128$		−	9.54129e41i		−	0.684554i
$129$	1.17549e41	−	5.50912e39i	0.0721815	−	0.00338289i
$130$	3.90460e41			0.205451
$131$		−	3.17130e42i		−	1.43157i	−0.698323	−	0.715783i	$-0.746070\pi$
$131$		−	3.17130e42i		−	1.43157i	0.698323	−	0.715783i	$-0.253930\pi$
$132$	2.87675e40	+	6.13818e41i	0.0111538	+	0.237991i
$133$	2.10209e42			0.700839
$134$			2.05755e42i			0.590547i
$135$	2.92179e41	+	2.06592e42i	0.0722726	+	0.511020i
$136$	−2.47867e42			−0.528982
$137$			5.39384e42i			0.994229i	0.867685	+	0.497115i	$0.165607\pi$
$137$			5.39384e42i			0.994229i	−0.867685	+	0.497115i	$0.834393\pi$
$138$	−1.40746e43	+	6.59625e41i	−2.24313	+	0.105127i
$139$	9.90151e42			1.36586			0.682929	−	0.730485i	$-0.260706\pi$
$139$	9.90151e42			1.36586			0.682929	+	0.730485i	$0.260706\pi$
$140$			2.13051e42i			0.254637i
$141$	−7.35008e41	−	1.56830e43i	−0.0761921	−	1.62573i
$142$	−1.15488e43			−1.03937
$143$			1.26312e42i			0.0987925i
$144$	−1.75181e43	+	1.64563e42i	−1.19189	+	0.111965i
$145$	1.10858e43			0.656758
$146$		−	1.39682e43i		−	0.721247i
$147$	1.20434e43	−	5.64429e41i	0.542502	−	0.0254251i
$148$	2.76473e43			1.08747
$149$			2.80166e43i			0.963141i	0.876407	+	0.481571i	$0.159934\pi$
$149$			2.80166e43i			0.963141i	−0.876407	+	0.481571i	$0.840066\pi$
$150$	−1.50211e42	−	3.20510e43i	−0.0451729	−	0.963865i
$151$	3.78370e43			0.996273			0.498136	−	0.867099i	$-0.334018\pi$
$151$	3.78370e43			0.996273			0.498136	+	0.867099i	$0.334018\pi$
$152$			1.59622e43i			0.368316i
$153$	6.88169e42	+	7.32569e43i	0.139273	+	1.48259i
$154$	−1.63344e43			−0.290195
$155$			2.48965e43i			0.388602i
$156$	1.60785e43	−	7.53542e41i	0.220675	−	0.0103423i
$157$	−2.54079e43			−0.306885			−0.153443	−	0.988158i	$-0.549036\pi$
$157$	−2.54079e43			−0.306885			−0.153443	+	0.988158i	$0.549036\pi$
$158$		−	1.34140e44i		−	1.42698i
$159$	−2.59728e42	−	5.54187e43i	−0.0243543	−	0.519654i
$160$	−7.60773e43			−0.629297
$161$		−	1.58033e44i		−	1.15406i
$162$	3.79641e43	+	2.00285e44i	0.244948	+	1.29225i
$163$	3.84121e43			0.219137			0.109568	−	0.993979i	$-0.465053\pi$
$163$	3.84121e43			0.219137			0.109568	+	0.993979i	$0.465053\pi$
$164$			2.28036e43i			0.115113i
$165$	−3.76449e43	+	1.76428e42i	−0.168278	+	0.00788659i
$166$	−4.25749e44			−1.68652
$167$			5.27479e43i			0.185300i	0.995699	+	0.0926500i	$0.0295338\pi$
$167$			5.27479e43i			0.185300i	−0.995699	+	0.0926500i	$0.970466\pi$
$168$	−3.60576e42	−	7.69369e43i	−0.0112412	−	0.239855i
$169$	−3.28102e44			−0.908396
$170$			4.10825e44i			1.01083i
$171$	4.71760e44	−	4.43167e43i	1.03228	−	0.0969718i
$172$	2.70859e43			0.0527442
$173$			2.89150e44i			0.501419i	0.968062	+	0.250710i	$0.0806639\pi$
$173$			2.89150e44i			0.501419i	−0.968062	+	0.250710i	$0.919336\pi$
$174$	1.08190e45	−	5.07048e43i	1.67187	−	0.0783546i
$175$	3.59876e44			0.495898
$176$		−	3.17807e44i		−	0.390760i
$177$	−7.44301e43	−	1.58813e45i	−0.0817115	−	1.74350i
$178$	6.67320e44			0.654537
$179$			2.25416e43i			0.0197662i	0.999951	+	0.00988312i	$0.00314594\pi$
$179$			2.25416e43i			0.0197662i	−0.999951	+	0.00988312i	$0.996854\pi$
$180$	4.49158e43	+	4.78137e44i	0.0352330	+	0.375062i
$181$	−1.60109e45			−1.12420			−0.562101	−	0.827069i	$-0.690007\pi$
$181$	−1.60109e45			−1.12420			−0.562101	+	0.827069i	$0.690007\pi$
$182$			4.27869e44i			0.269081i
$183$	−1.03574e45	+	4.85412e43i	−0.583751	+	0.0273583i
$184$	1.20002e45			0.606501
$185$			1.69558e45i			0.768926i
$186$	1.13873e44	+	2.42975e45i	0.0463622	+	0.989241i
$187$	−1.32900e45			−0.486064
$188$		−	3.61371e45i		−	1.18795i
$189$	−2.26385e45	+	3.20172e44i	−0.669286	+	0.0946558i
$190$	2.64563e45			0.703813
$191$			2.81966e45i			0.675350i	0.941263	+	0.337675i	$0.109641\pi$
$191$			2.81966e45i			0.675350i	−0.941263	+	0.337675i	$0.890359\pi$
$192$	−1.88234e45	+	8.82186e43i	−0.406139	+	0.0190342i
$193$	−7.64121e45			−1.48599			−0.742995	−	0.669297i	$-0.766596\pi$
$193$	−7.64121e45			−1.48599			−0.742995	+	0.669297i	$0.766596\pi$
$194$		−	1.07371e46i		−	1.88301i
$195$	4.62140e43	+	9.86081e44i	0.00731277	+	0.156034i
$196$	2.77505e45			0.396414
$197$		−	9.28857e44i		−	0.119846i	−0.998203	−	0.0599231i	$-0.980914\pi$
$197$		−	9.28857e44i		−	0.119846i	0.998203	−	0.0599231i	$-0.0190855\pi$
$198$	−3.66584e45	+	3.44366e44i	−0.427435	+	0.0401529i
$199$	1.72349e46			1.81697			0.908486	−	0.417915i	$-0.137239\pi$
$199$	1.72349e46			1.81697			0.908486	+	0.417915i	$0.137239\pi$
$200$			2.73271e45i			0.260612i
$201$	−5.19621e45	+	2.43528e44i	−0.448503	+	0.0210197i
$202$	2.28472e46			1.78569
$203$			1.21479e46i			0.860160i
$204$	7.92844e44	+	1.69171e46i	0.0508844	+	1.08573i
$205$	−1.39852e45			−0.0813940
$206$			9.36116e45i			0.494294i
$207$	−3.33168e45	−	3.54664e46i	−0.159682	−	1.69985i
$208$	−8.32472e45			−0.362329
$209$			8.55851e45i			0.338433i
$210$	−1.27518e46	+	5.97632e44i	−0.458338	+	0.0214807i
$211$	1.43413e46			0.468749			0.234375	−	0.972146i	$-0.424696\pi$
$211$	1.43413e46			0.468749			0.234375	+	0.972146i	$0.424696\pi$
$212$		−	1.27697e46i		−	0.379719i
$213$	−1.36689e45	−	2.91658e46i	−0.0369950	−	0.789371i
$214$	−5.40120e46			−1.33111
$215$			1.66115e45i			0.0372942i
$216$	−2.43122e45	−	1.71905e46i	−0.0497450	−	0.351733i
$217$	−2.72818e46			−0.508954
$218$			8.47290e45i			0.144179i
$219$	3.52759e46	−	1.65325e45i	0.547767	−	0.0256718i
$220$	−8.67420e45			−0.122963
$221$			3.48122e46i			0.450698i
$222$	7.75538e45	+	1.65479e47i	0.0917368	+	1.95741i
$223$	−6.91711e46			−0.747872			−0.373936	−	0.927454i	$-0.621992\pi$
$223$	−6.91711e46			−0.747872			−0.373936	+	0.927454i	$0.621992\pi$
$224$		−	8.33661e46i		−	0.824194i
$225$	8.07649e46	−	7.58699e45i	0.730420	−	0.0686150i
$226$	−8.48799e46			−0.702483
$227$		−	1.58759e45i		−	0.0120288i	−0.999982	−	0.00601440i	$-0.998086\pi$
$227$		−	1.58759e45i		−	0.0120288i	0.999982	−	0.00601440i	$-0.00191445\pi$
$228$	1.08943e47	−	5.10576e45i	0.755966	−	0.0354294i
$229$	2.60363e47			1.65527			0.827636	−	0.561265i	$-0.189685\pi$
$229$	2.60363e47			1.65527			0.827636	+	0.561265i	$0.189685\pi$
$230$		−	1.98896e47i		−	1.15896i
$231$	−1.93331e45	−	4.12516e46i	−0.0103291	−	0.220395i
$232$	−9.22445e46			−0.452044
$233$			1.26626e47i			0.569384i	0.958619	+	0.284692i	$0.0918913\pi$
$233$			1.26626e47i			0.569384i	−0.958619	+	0.284692i	$0.908109\pi$
$234$	9.02041e45	+	9.60240e46i	0.0372314	+	0.396335i
$235$	2.21626e47			0.839969
$236$		−	3.65940e47i		−	1.27400i
$237$	3.38763e47	−	1.58766e46i	1.08375	−	0.0507914i
$238$	−4.50185e47			−1.32389
$239$			4.85091e47i			1.31179i	0.754850	+	0.655897i	$0.227709\pi$
$239$			4.85091e47i			1.31179i	−0.754850	+	0.655897i	$0.772291\pi$
$240$	−1.16277e46	−	2.48103e47i	−0.0289247	−	0.617173i
$241$	−5.71937e47			−1.30920			−0.654602	−	0.755973i	$-0.727164\pi$
$241$	−5.71937e47			−1.30920			−0.654602	+	0.755973i	$0.727164\pi$
$242$			5.57690e47i			1.17513i
$243$	−5.01313e47	+	1.19581e47i	−0.972709	+	0.232027i
$244$	−2.38656e47			−0.426556
$245$			1.70191e47i			0.280295i
$246$	−1.36487e47	+	6.39667e45i	−0.207200	+	0.00971072i
$247$	2.24184e47			0.313809
$248$		−	2.07164e47i		−	0.267473i
$249$	−5.03909e46	−	1.07520e48i	−0.0600295	−	1.28087i
$250$	1.07031e48			1.17682
$251$		−	1.04596e48i		−	1.06180i	−0.847436	−	0.530898i	$-0.821855\pi$
$251$		−	1.04596e48i		−	1.06180i	0.847436	−	0.530898i	$-0.178145\pi$
$252$	−5.23946e47	+	4.92191e46i	−0.491220	+	0.0461448i
$253$	6.43419e47			0.557293
$254$			1.21769e48i			0.974683i
$255$	−1.03751e48	+	4.86244e46i	−0.767696	+	0.0359792i
$256$	1.91011e48			1.30695
$257$		−	4.07243e47i		−	0.257746i	−0.991661	−	0.128873i	$-0.958864\pi$
$257$		−	4.07243e47i		−	0.257746i	0.991661	−	0.128873i	$-0.0411359\pi$
$258$	7.59791e45	+	1.62118e47i	0.00444939	+	0.0949376i
$259$	−1.85803e48			−1.00707
$260$			2.27214e47i			0.114017i
$261$	2.56104e47	+	2.72627e48i	0.119016	+	1.26695i
$262$	4.37371e48			1.88288
$263$		−	1.95587e48i		−	0.780233i	−0.920765	−	0.390117i	$-0.872435\pi$
$263$		−	1.95587e48i		−	0.780233i	0.920765	−	0.390117i	$-0.127565\pi$
$264$	3.13243e47	−	1.46806e46i	0.115825	−	0.00542831i
$265$	7.83152e47			0.268490
$266$			2.89910e48i			0.921788i
$267$	7.89827e46	+	1.68527e48i	0.0232974	+	0.497102i
$268$	−1.19732e48			−0.327728
$269$		−	3.91909e48i		−	0.995724i	−0.867256	−	0.497862i	$-0.834119\pi$
$269$		−	3.91909e48i		−	0.995724i	0.867256	−	0.497862i	$-0.165881\pi$
$270$	−2.84922e48	+	4.02960e47i	−0.672125	+	0.0950574i
$271$	−3.29742e48			−0.722418			−0.361209	−	0.932485i	$-0.617636\pi$
$271$	−3.29742e48			−0.722418			−0.361209	+	0.932485i	$0.617636\pi$
$272$		−	8.75891e48i		−	1.78268i
$273$	−1.08055e48	+	5.06417e46i	−0.204359	+	0.00957757i
$274$	−7.43892e48			−1.30767
$275$			1.46521e48i			0.239467i
$276$	−3.83846e47	−	8.19021e48i	−0.0583411	−	1.24484i
$277$	5.09477e47			0.0720327			0.0360163	−	0.999351i	$-0.488533\pi$
$277$	5.09477e47			0.0720327			0.0360163	+	0.999351i	$0.488533\pi$
$278$			1.36557e49i			1.79646i
$279$	−6.12269e48	+	5.75160e47i	−0.749650	+	0.0704214i
$280$	1.08724e48			0.123926
$281$			1.31370e49i			1.39435i	0.716902	+	0.697174i	$0.245559\pi$
$281$			1.31370e49i			1.39435i	−0.716902	+	0.697174i	$0.754441\pi$
$282$	2.16293e49	−	1.01369e48i	2.13826	−	0.100213i
$283$	4.62045e48			0.425554			0.212777	−	0.977101i	$-0.431749\pi$
$283$	4.62045e48			0.425554			0.212777	+	0.977101i	$0.431749\pi$
$284$		−	6.72042e48i		−	0.576806i
$285$	3.13132e47	+	6.68137e48i	0.0250513	+	0.534526i
$286$	−1.74204e48			−0.129938
$287$		−	1.53251e48i		−	0.106602i
$288$	−1.75754e48	−	1.87094e49i	−0.114040	−	1.21397i
$289$	−2.01099e49			−1.21746
$290$			1.52890e49i			0.863809i
$291$	2.71159e49	−	1.27082e48i	1.43009	−	0.0670233i
$292$	8.12832e48			0.400262
$293$		−	2.66809e49i		−	1.22701i	−0.789691	−	0.613505i	$-0.789759\pi$
$293$		−	2.66809e49i		−	1.22701i	0.789691	−	0.613505i	$-0.210241\pi$
$294$	7.78433e47	+	1.66096e49i	0.0334407	+	0.713532i
$295$	2.24428e49			0.900817
$296$		−	1.41089e49i		−	0.529249i
$297$	−1.30356e48	−	9.21710e48i	−0.0457089	−	0.323195i
$298$	−3.86392e49			−1.26678
$299$		−	1.68539e49i		−	0.516745i
$300$	1.86509e49	−	8.74102e47i	0.534904	−	0.0250690i
$301$	−1.82031e48			−0.0488444
$302$			5.21831e49i			1.31036i
$303$	2.70415e48	+	5.76991e49i	0.0635591	+	1.35618i
$304$	−5.64057e49			−1.24123
$305$		−	1.46366e49i		−	0.301607i
$306$	−1.01032e50	+	9.49089e48i	−1.94999	+	0.183180i
$307$	5.35320e49			0.967934			0.483967	−	0.875086i	$-0.339195\pi$
$307$	5.35320e49			0.967934			0.483967	+	0.875086i	$0.339195\pi$
$308$		−	9.50526e48i		−	0.161046i
$309$	−2.36410e49	+	1.10797e48i	−0.375402	+	0.0175937i
$310$	−3.43361e49			−0.511113
$311$		−	7.51843e49i		−	1.04935i	−0.851303	−	0.524674i	$-0.824187\pi$
$311$		−	7.51843e49i		−	1.04935i	0.851303	−	0.524674i	$-0.175813\pi$
$312$	−3.84547e47	−	8.20517e48i	−0.00503335	−	0.107398i
$313$	9.48806e49			1.16491			0.582453	−	0.812864i	$-0.302093\pi$
$313$	9.48806e49			1.16491			0.582453	+	0.812864i	$0.302093\pi$
$314$		−	3.50414e49i		−	0.403635i
$315$	−3.01856e48	−	3.21332e49i	−0.0326279	−	0.347330i
$316$	7.80582e49			0.791912
$317$			7.19460e49i			0.685206i	0.939480	+	0.342603i	$0.111309\pi$
$317$			7.19460e49i			0.685206i	−0.939480	+	0.342603i	$0.888691\pi$
$318$	7.64308e49	−	3.58204e48i	0.683481	−	0.0320323i
$319$	−4.94591e49			−0.415368
$320$		−	2.66004e49i		−	0.209840i
$321$	−6.39276e48	−	1.36404e50i	−0.0473792	−	1.01094i
$322$	2.17951e50			1.51790
$323$			2.35876e50i			1.54395i
$324$	−1.16549e50	+	2.20919e49i	−0.717145	+	0.135935i
$325$	3.83801e49			0.222044
$326$			5.29761e49i			0.288222i
$327$	−2.13978e49	+	1.00284e48i	−0.109500	+	0.00513186i
$328$	1.16371e49			0.0560232
$329$			2.42859e50i			1.10011i
$330$	−2.43321e48	−	5.19181e49i	−0.0103729	−	0.221330i
$331$	2.91862e49			0.117116			0.0585582	−	0.998284i	$-0.481350\pi$
$331$	2.91862e49			0.117116			0.0585582	+	0.998284i	$0.481350\pi$
$332$		−	2.47750e50i		−	0.935948i
$333$	−4.16988e50	+	3.91714e49i	−1.48333	+	0.139343i
$334$	−7.27473e49			−0.243718
$335$		−	7.34305e49i		−	0.231729i
$336$	2.71873e50	−	1.27417e49i	0.808314	−	0.0378828i
$337$	−1.25336e50			−0.351138			−0.175569	−	0.984467i	$-0.556176\pi$
$337$	−1.25336e50			−0.351138			−0.175569	+	0.984467i	$0.556176\pi$
$338$		−	4.52503e50i		−	1.19478i
$339$	−1.00462e49	−	2.14359e50i	−0.0250040	−	0.533516i
$340$	−2.39065e50			−0.560968
$341$		−	1.11076e50i		−	0.245772i
$342$	6.11195e49	+	6.50629e50i	0.127543	+	1.35772i
$343$	−5.29892e50			−1.04305
$344$		−	1.38225e49i		−	0.0256694i
$345$	5.02298e50	−	2.35409e49i	0.880197	−	0.0412516i
$346$	−3.98782e50			−0.659498
$347$		−	3.21902e50i		−	0.502497i	−0.967923	−	0.251249i	$-0.919159\pi$
$347$		−	3.21902e50i		−	0.502497i	0.967923	−	0.251249i	$-0.0808412\pi$
$348$	2.95059e49	+	6.29575e50i	0.0434835	+	0.927818i
$349$	1.74668e50			0.243055			0.121527	−	0.992588i	$-0.461221\pi$
$349$	1.74668e50			0.243055			0.121527	+	0.992588i	$0.461221\pi$
$350$			4.96324e50i			0.652236i
$351$	−2.41435e50	+	3.41457e49i	−0.299680	+	0.0423832i
$352$	3.39419e50			0.398000
$353$			4.50717e50i			0.499356i	0.968329	+	0.249678i	$0.0803247\pi$
$353$			4.50717e50i			0.499356i	−0.968329	+	0.249678i	$0.919675\pi$
$354$	2.19028e51	−	1.02650e50i	2.29316	−	0.107472i
$355$	4.12157e50			0.407846
$356$			3.88324e50i			0.363240i
$357$	−5.32830e49	−	1.13691e51i	−0.0471221	−	1.00546i
$358$	−3.10883e49			−0.0259978
$359$		−	3.54644e50i		−	0.280481i	−0.990117	−	0.140241i	$-0.955212\pi$
$359$		−	3.54644e50i		−	0.280481i	0.990117	−	0.140241i	$-0.0447876\pi$
$360$	2.44003e50	−	2.29214e49i	0.182534	−	0.0171471i
$361$	1.05992e50			0.0750116
$362$		−	2.20815e51i		−	1.47862i
$363$	−1.40841e51	+	6.60071e49i	−0.892476	+	0.0418271i
$364$	−2.48983e50			−0.149328
$365$			4.98503e50i			0.283016i
$366$	−6.69457e49	−	1.42844e51i	−0.0359833	−	0.767785i
$367$	−1.94434e51			−0.989578			−0.494789	−	0.869013i	$-0.664755\pi$
$367$	−1.94434e51			−0.989578			−0.494789	+	0.869013i	$0.664755\pi$
$368$			4.24052e51i			2.04391i
$369$	−3.23088e49	−	3.43933e50i	−0.0147500	−	0.157017i
$370$	−2.33847e51			−1.01134
$371$			8.58184e50i			0.351643i
$372$	−1.41391e51	+	6.62647e49i	−0.548987	+	0.0257290i
$373$	3.70930e51			1.36494			0.682472	−	0.730912i	$-0.260905\pi$
$373$	3.70930e51			1.36494			0.682472	+	0.730912i	$0.260905\pi$
$374$		−	1.83290e51i		−	0.639301i
$375$	1.26680e50	+	2.70299e51i	0.0418872	+	0.893757i
$376$	−1.84415e51			−0.578147
$377$			1.29554e51i			0.385146i
$378$	−4.41566e50	−	3.12219e51i	−0.124497	−	0.880286i
$379$	4.60053e51			1.23034			0.615168	−	0.788396i	$-0.289088\pi$
$379$	4.60053e51			1.23034			0.615168	+	0.788396i	$0.289088\pi$
$380$			1.53953e51i			0.390586i
$381$	−3.07521e51	+	1.44124e50i	−0.740244	+	0.0346925i
$382$	−3.88874e51			−0.888263
$383$		−	2.47639e51i		−	0.536839i	−0.963302	−	0.268420i	$-0.913499\pi$
$383$		−	2.47639e51i		−	0.536839i	0.963302	−	0.268420i	$-0.0865014\pi$
$384$	1.55746e50	+	3.32319e51i	0.0320474	+	0.683803i
$385$	5.82949e50			0.113872
$386$		−	1.05384e52i		−	1.95447i
$387$	−4.08521e50	+	3.83761e49i	−0.0719440	+	0.00675836i
$388$	6.24809e51			1.04499
$389$		−	2.87226e51i		−	0.456281i	−0.973628	−	0.228140i	$-0.926735\pi$
$389$		−	2.87226e51i		−	0.456281i	0.973628	−	0.228140i	$-0.0732645\pi$
$390$	−1.35996e51	+	6.37362e49i	−0.205226	+	0.00961821i
$391$	1.77329e52			2.54241
$392$		−	1.41616e51i		−	0.192926i
$393$	5.17664e50	+	1.10455e52i	0.0670188	+	1.43000i
$394$	1.28103e51			0.157629
$395$			4.78724e51i			0.559943i
$396$	−2.00392e50	−	2.13321e51i	−0.0222831	−	0.237208i
$397$	−2.27883e51			−0.240936			−0.120468	−	0.992717i	$-0.538440\pi$
$397$	−2.27883e51			−0.240936			−0.120468	+	0.992717i	$0.538440\pi$
$398$			2.37696e52i			2.38980i
$399$	−7.32150e51	+	3.43132e50i	−0.700071	+	0.0328098i
$400$	−9.65661e51			−0.878264
$401$		−	2.26183e52i		−	1.95692i	−0.206432	−	0.978461i	$-0.566185\pi$
$401$		−	2.26183e52i		−	1.95692i	0.206432	−	0.978461i	$-0.433815\pi$
$402$	−3.35862e50	−	7.16637e51i	−0.0276465	−	0.589900i
$403$	−2.90955e51			−0.227890
$404$			1.32951e52i			0.990980i
$405$	−1.35488e51	−	7.14782e51i	−0.0961168	−	0.507076i
$406$	−1.67538e52			−1.13134
$407$		−	7.56485e51i		−	0.486309i
$408$	8.63313e51	−	4.04603e50i	0.528402	−	0.0247643i
$409$	−2.07287e52			−1.20811			−0.604053	−	0.796944i	$-0.706448\pi$
$409$	−2.07287e52			−1.20811			−0.604053	+	0.796944i	$0.706448\pi$
$410$		−	1.92878e51i		−	0.107054i
$411$	−8.80457e50	−	1.87865e52i	−0.0465449	−	0.993139i
$412$	−5.44740e51			−0.274312
$413$			2.45930e52i			1.17981i
$414$	4.89135e52	−	4.59489e51i	2.23574	−	0.210024i
$415$	1.51943e52			0.661787
$416$		−	8.89083e51i		−	0.369042i
$417$	−3.44866e52	+	1.61626e51i	−1.36436	+	0.0639426i
$418$	−1.18035e52			−0.445128
$419$		−	1.57114e52i		−	0.564852i	−0.959289	−	0.282426i	$-0.908861\pi$
$419$		−	1.57114e52i		−	0.564852i	0.959289	−	0.282426i	$-0.0911392\pi$
$420$	−3.47771e50	−	7.42047e51i	−0.0119209	−	0.254358i
$421$	1.39208e52			0.455013			0.227507	−	0.973777i	$-0.426943\pi$
$421$	1.39208e52			0.455013			0.227507	+	0.973777i	$0.426943\pi$
$422$			1.97789e52i			0.616528i
$423$	5.12001e51	+	5.45035e52i	0.152217	+	1.62038i
$424$	−6.51660e51			−0.184801
$425$			4.03819e52i			1.09247i
$426$	4.02240e52	−	1.88515e51i	1.03823	−	0.0486581i
$427$	1.60388e52			0.395017
$428$		−	3.14304e52i		−	0.738711i
$429$	−2.06184e50	−	4.39940e51i	−0.00462497	−	0.0986842i
$430$	−2.29099e51			−0.0490516
$431$		−	2.35434e52i		−	0.481199i	−0.970625	−	0.240599i	$-0.922656\pi$
$431$		−	2.35434e52i		−	0.481199i	0.970625	−	0.240599i	$-0.0773440\pi$
$432$	6.07462e52	−	8.59122e51i	1.18534	−	0.167641i
$433$	3.12129e51			0.0581536			0.0290768	−	0.999577i	$-0.490743\pi$
$433$	3.12129e51			0.0581536			0.0290768	+	0.999577i	$0.490743\pi$
$434$		−	3.76257e52i		−	0.669407i
$435$	−3.86113e52	+	1.80957e51i	−0.656038	+	0.0307461i
$436$	−4.93051e51			−0.0800133
$437$		−	1.14197e53i		−	1.77021i
$438$	2.28009e51	+	4.86508e52i	0.0337652	+	0.720457i
$439$	−1.93419e52			−0.273658			−0.136829	−	0.990595i	$-0.543691\pi$
$439$	−1.93419e52			−0.273658			−0.136829	+	0.990595i	$0.543691\pi$
$440$			4.42661e51i			0.0598436i
$441$	−4.18544e52	+	3.93177e51i	−0.540716	+	0.0507944i
$442$	−4.80113e52			−0.592786
$443$			1.63741e53i			1.93233i	0.257920	+	0.966166i	$0.416963\pi$
$443$			1.63741e53i			1.93233i	−0.257920	+	0.966166i	$0.583037\pi$
$444$	−9.62944e52	+	4.51297e51i	−1.08628	+	0.0509100i
$445$	−2.38155e52			−0.256839
$446$		−	9.53975e52i		−	0.983648i
$447$	−4.57326e51	−	9.75807e52i	−0.0450895	−	0.962085i
$448$	2.91489e52			0.274829
$449$			1.35291e53i			1.21995i	0.792420	+	0.609975i	$0.208821\pi$
$449$			1.35291e53i			1.21995i	−0.792420	+	0.609975i	$0.791179\pi$
$450$	1.04636e52	+	1.11387e53i	0.0902467	+	0.960693i
$451$	6.23951e51			0.0514778
$452$		−	4.93929e52i		−	0.389848i
$453$	−1.31785e53	+	6.17629e51i	−0.995181	+	0.0466405i
$454$	2.18953e51			0.0158210
$455$		−	1.52699e52i		−	0.105587i
$456$	−2.60557e51	−	5.55956e52i	−0.0172427	−	0.367912i
$457$	3.02271e53			1.91457			0.957287	−	0.289141i	$-0.0933695\pi$
$457$	3.02271e53			1.91457			0.957287	+	0.289141i	$0.0933695\pi$
$458$			3.59080e53i			2.17712i
$459$	−3.59266e52	−	2.54027e53i	−0.208527	−	1.47444i
$460$	1.15740e53			0.643173
$461$		−	1.80944e53i		−	0.962776i	−0.876507	−	0.481388i	$-0.840133\pi$
$461$		−	1.80944e53i		−	0.962776i	0.876507	−	0.481388i	$-0.159867\pi$
$462$	5.68922e52	−	2.66633e51i	0.289877	−	0.0135855i
$463$	2.11666e53			1.03284			0.516419	−	0.856336i	$-0.327265\pi$
$463$	2.11666e53			1.03284			0.516419	+	0.856336i	$0.327265\pi$
$464$		−	3.25965e53i		−	1.52339i
$465$	−4.06395e51	−	8.67136e52i	−0.0181924	−	0.388176i
$466$	−1.74637e53			−0.748889
$467$			1.47795e53i			0.607185i	0.952802	+	0.303592i	$0.0981861\pi$
$467$			1.47795e53i			0.607185i	−0.952802	+	0.303592i	$0.901814\pi$
$468$	−5.58778e52	+	5.24911e51i	−0.219949	+	0.0206618i
$469$	8.04658e52			0.303497
$470$			3.05656e53i			1.10478i
$471$	8.84948e52	−	4.14743e51i	0.306549	−	0.0143668i
$472$	−1.86746e53			−0.620029
$473$		−	7.41124e51i		−	0.0235868i
$474$	2.18962e52	+	4.67205e53i	0.0668040	+	1.42541i
$475$	2.60051e53			0.760653
$476$		−	2.61969e53i		−	0.734702i
$477$	1.80924e52	+	1.92597e53i	0.0486552	+	0.517944i
$478$	−6.69015e53			−1.72535
$479$			9.58337e52i			0.237033i	0.992952	+	0.118516i	$0.0378138\pi$
$479$			9.58337e52i			0.237033i	−0.992952	+	0.118516i	$0.962186\pi$
$480$	2.64974e53	−	1.24184e52i	0.628607	−	0.0294605i
$481$	−1.98155e53			−0.450925
$482$		−	7.88789e53i		−	1.72195i
$483$	2.57963e52	+	5.50422e53i	0.0540275	+	1.15280i
$484$	−3.24528e53			−0.652146
$485$			3.83190e53i			0.738889i
$486$	−1.64921e53	−	6.91386e53i	−0.305176	−	1.27937i
$487$	2.13753e53			0.379605			0.189803	−	0.981822i	$-0.439215\pi$
$487$	2.13753e53			0.379605			0.189803	+	0.981822i	$0.439215\pi$
$488$			1.21791e53i			0.207595i
$489$	−1.33788e53	+	6.27015e51i	−0.218897	+	0.0102589i
$490$	−2.34720e53			−0.368662
$491$		−	1.17512e54i		−	1.77195i	−0.463734	−	0.885975i	$-0.653491\pi$
$491$		−	1.17512e54i		−	1.77195i	0.463734	−	0.885975i	$-0.346509\pi$
$492$	−3.72232e51	−	7.94240e52i	−0.00538904	−	0.114987i
$493$	−1.36312e54			−1.89494
$494$			3.09183e53i			0.412741i
$495$	1.30828e53	−	1.22899e52i	0.167724	−	0.0157559i
$496$	7.32056e53			0.901386
$497$			4.51645e53i			0.534158i
$498$	1.48287e54	−	6.94967e52i	1.68467	−	0.0789546i
$499$	7.55269e53			0.824310			0.412155	−	0.911114i	$-0.364776\pi$
$499$	7.55269e53			0.824310			0.412155	+	0.911114i	$0.364776\pi$
$500$			6.22828e53i			0.653083i
$501$	−8.61024e51	−	1.83719e53i	−0.00867482	−	0.185097i
$502$	1.44254e54			1.39654
$503$			1.44044e54i			1.34009i	0.742318	+	0.670047i	$0.233726\pi$
$503$			1.44044e54i			1.34009i	−0.742318	+	0.670047i	$0.766274\pi$
$504$	2.51174e52	+	2.67380e53i	0.0224577	+	0.239066i
$505$	−8.15378e53			−0.700699
$506$			8.87373e53i			0.732986i
$507$	1.14277e54	−	5.35574e52i	0.907400	−	0.0425265i
$508$	−7.08594e53			−0.540908
$509$		−	1.97937e54i		−	1.45268i	−0.687334	−	0.726341i	$-0.741219\pi$
$509$		−	1.97937e54i		−	1.45268i	0.687334	−	0.726341i	$-0.258781\pi$
$510$	−6.70605e52	−	1.43089e54i	−0.0473220	−	1.00972i
$511$	−5.46263e53			−0.370667
$512$			1.58526e54i			1.03443i
$513$	−1.63589e54	+	2.31361e53i	−1.02661	+	0.145192i
$514$	5.61650e53			0.339003
$515$		−	3.34084e53i		−	0.193960i
$516$	−9.43392e52	+	4.42134e51i	−0.0526863	+	0.00246922i
$517$	−9.88784e53			−0.531240
$518$		−	2.56251e54i		−	1.32456i
$519$	−4.71990e52	−	1.00710e54i	−0.0234739	−	0.500869i
$520$	1.15952e53			0.0554894
$521$		−	2.44544e53i		−	0.112617i	−0.998413	−	0.0563084i	$-0.982067\pi$
$521$		−	2.44544e53i		−	0.112617i	0.998413	−	0.0563084i	$-0.0179330\pi$
$522$	−3.75995e54	+	3.53206e53i	−1.66637	+	0.156537i
$523$	4.06306e54			1.73309			0.866543	−	0.499103i	$-0.166337\pi$
$523$	4.06306e54			1.73309			0.866543	+	0.499103i	$0.166337\pi$
$524$			2.54513e54i			1.04492i
$525$	−1.25343e54	+	5.87440e52i	−0.495354	+	0.0232155i
$526$	2.69744e54			1.02621
$527$		−	3.06130e54i		−	1.12123i
$528$	5.18769e52	+	1.10691e54i	0.0182934	+	0.390332i
$529$	−5.63998e54			−1.91498
$530$			1.08009e54i			0.353135i
$531$	5.18475e53	+	5.51926e54i	0.163244	+	1.73776i
$532$	−1.68703e54			−0.511553
$533$		−	1.63439e53i		−	0.0477323i
$534$	−2.32425e54	+	1.08929e53i	−0.653819	+	0.0306421i
$535$	1.92760e54			0.522325
$536$			6.11015e53i			0.159498i
$537$	−3.67955e51	−	7.85115e52i	−0.000925356	−	0.0197446i
$538$	5.40502e54			1.30964
$539$		−	7.59309e53i		−	0.177273i
$540$	−2.34488e53	−	1.65800e54i	−0.0527528	−	0.373001i
$541$	−3.89611e54			−0.844668			−0.422334	−	0.906440i	$-0.638789\pi$
$541$	−3.89611e54			−0.844668			−0.422334	+	0.906440i	$0.638789\pi$
$542$		−	4.54765e54i		−	0.950169i
$543$	5.57653e54	−	2.61352e53i	1.12297	−	0.0526295i
$544$	9.35455e54			1.81570
$545$		−	3.02384e53i		−	0.0565755i
$546$	−6.98426e52	−	1.49025e54i	−0.0125970	−	0.268786i
$547$	4.78615e54			0.832223			0.416112	−	0.909314i	$-0.363393\pi$
$547$	4.78615e54			0.832223			0.416112	+	0.909314i	$0.363393\pi$
$548$		−	4.32882e54i		−	0.725702i
$549$	3.59951e54	−	3.38134e53i	0.581830	−	0.0546566i
$550$	−2.02075e54			−0.314962
$551$			8.77820e54i			1.31939i
$552$	−4.17962e54	+	1.95884e53i	−0.605836	+	0.0283933i
$553$	−5.24590e54			−0.733360
$554$			7.02647e53i			0.0947418i
$555$	−2.76777e53	−	5.90565e54i	−0.0359973	−	0.768083i
$556$	−7.94645e54			−0.996959
$557$			1.04373e55i			1.26324i	0.775280	+	0.631618i	$0.217609\pi$
$557$			1.04373e55i			1.26324i	−0.775280	+	0.631618i	$0.782391\pi$
$558$	−7.93234e53	−	8.44413e54i	−0.0926226	−	0.985986i
$559$	−1.94132e53			−0.0218706
$560$			3.84198e54i			0.417633i
$561$	4.62886e54	−	2.16938e53i	0.485531	−	0.0227551i
$562$	−1.81180e55			−1.83393
$563$		−	3.11876e53i		−	0.0304659i	−0.999884	−	0.0152330i	$-0.995151\pi$
$563$		−	3.11876e53i		−	0.0304659i	0.999884	−	0.0152330i	$-0.00484899\pi$
$564$	5.89880e53	+	1.25864e55i	0.0556137	+	1.18664i
$565$	3.02922e54			0.275653
$566$			6.37230e54i			0.559716i
$567$	7.83264e54	−	1.48468e54i	0.664120	−	0.125885i
$568$	−3.42956e54			−0.280719
$569$		−	6.48098e54i		−	0.512148i	−0.966657	−	0.256074i	$-0.917571\pi$
$569$		−	6.48098e54i		−	0.512148i	0.966657	−	0.256074i	$-0.0824291\pi$
$570$	−9.21463e54	+	4.31857e53i	−0.703041	+	0.0329490i
$571$	−1.66814e54			−0.122888			−0.0614442	−	0.998111i	$-0.519571\pi$
$571$	−1.66814e54			−0.122888			−0.0614442	+	0.998111i	$0.519571\pi$
$572$		−	1.01372e54i		−	0.0721101i
$573$	−4.60264e53	−	9.82076e54i	−0.0316165	−	0.674610i
$574$	2.11357e54			0.140210
$575$		−	1.95504e55i		−	1.25256i
$576$	6.54173e54	−	6.14524e53i	0.404802	−	0.0380268i
$577$	−8.58415e54			−0.513075			−0.256538	−	0.966534i	$-0.582582\pi$
$577$	−8.58415e54			−0.513075			−0.256538	+	0.966534i	$0.582582\pi$
$578$		−	2.77346e55i		−	1.60127i
$579$	2.66140e55	−	1.24730e54i	1.48436	−	0.0695667i
$580$	−8.89687e54			−0.479377
$581$			1.66500e55i			0.866746i
$582$	1.75266e54	+	3.73970e55i	0.0881532	+	1.88095i
$583$	−3.49403e54			−0.169807
$584$		−	4.14804e54i		−	0.194799i
$585$	−3.21923e53	−	3.42694e54i	−0.0146095	−	0.155521i
$586$	3.67971e55			1.61384
$587$			8.79766e54i			0.372911i	0.982463	+	0.186455i	$0.0597000\pi$
$587$			8.79766e54i			0.372911i	−0.982463	+	0.186455i	$0.940300\pi$
$588$	−9.66539e54	+	4.52982e53i	−0.395980	+	0.0185581i
$589$	−1.97142e55			−0.780679
$590$			3.09520e55i			1.18481i
$591$	1.51621e53	+	3.23517e54i	0.00561060	+	0.119715i
$592$	4.98569e55			1.78357
$593$		−	1.89933e55i		−	0.656910i	−0.944520	−	0.328455i	$-0.893472\pi$
$593$		−	1.89933e55i		−	0.656910i	0.944520	−	0.328455i	$-0.106528\pi$
$594$	1.27118e55	−	1.79780e54i	0.425087	−	0.0601192i
$595$	1.60663e55			0.519491
$596$		−	2.24847e55i		−	0.703011i
$597$	−6.00286e55	+	2.81333e54i	−1.81498	+	0.0850616i
$598$	2.32441e55			0.679655
$599$			3.37089e55i			0.953252i	0.879106	+	0.476626i	$0.158140\pi$
$599$			3.37089e55i			0.953252i	−0.879106	+	0.476626i	$0.841860\pi$
$600$	−4.46071e53	−	9.51793e54i	−0.0122005	−	0.260326i
$601$	−4.50788e55			−1.19257			−0.596283	−	0.802774i	$-0.703356\pi$
$601$	−4.50788e55			−1.19257			−0.596283	+	0.802774i	$0.703356\pi$
$602$		−	2.51048e54i		−	0.0642432i
$603$	1.80585e55	−	1.69640e54i	0.447028	−	0.0419934i
$604$	−3.03661e55			−0.727194
$605$		−	1.99030e55i		−	0.461117i
$606$	−7.95758e55	+	3.72943e54i	−1.78373	+	0.0835969i
$607$	4.11803e55			0.893133			0.446566	−	0.894751i	$-0.352647\pi$
$607$	4.11803e55			0.893133			0.446566	+	0.894751i	$0.352647\pi$
$608$		−	6.02414e55i		−	1.26422i
$609$	−1.98294e54	−	4.23105e55i	−0.0402684	−	0.859217i
$610$	2.01860e55			0.396693
$611$			2.59004e55i			0.492587i
$612$	−5.52289e54	−	5.87922e55i	−0.101657	−	1.08216i
$613$	−8.47769e55			−1.51032			−0.755159	−	0.655542i	$-0.772440\pi$
$613$	−8.47769e55			−1.51032			−0.755159	+	0.655542i	$0.772440\pi$
$614$			7.38288e55i			1.27309i
$615$	4.87100e54	−	2.28286e53i	0.0813048	−	0.00381046i
$616$	−4.85071e54			−0.0783775
$617$			1.03563e56i			1.61996i	0.586460	+	0.809978i	$0.300521\pi$
$617$			1.03563e56i			1.61996i	−0.586460	+	0.809978i	$0.699479\pi$
$618$	−1.52806e54	−	3.26046e55i	−0.0231404	−	0.493752i
$619$	1.56701e55			0.229752			0.114876	−	0.993380i	$-0.463353\pi$
$619$	1.56701e55			0.229752			0.114876	+	0.993380i	$0.463353\pi$
$620$		−	1.99807e55i		−	0.283646i
$621$	1.73934e55	+	1.22984e56i	0.239085	+	1.69051i
$622$	1.03691e56			1.38017
$623$		−	2.60972e55i		−	0.336383i
$624$	2.89947e55	−	1.35888e54i	0.361932	−	0.0169624i
$625$	2.24874e55			0.271856
$626$			1.30855e56i			1.53216i
$627$	−1.39704e54	−	2.98090e55i	−0.0158437	−	0.338062i
$628$	2.03911e55			0.224000
$629$		−	2.08491e56i		−	2.21857i
$630$	4.43165e55	−	4.16306e54i	0.456830	−	0.0429142i
$631$	7.98242e55			0.797164			0.398582	−	0.917133i	$-0.369502\pi$
$631$	7.98242e55			0.797164			0.398582	+	0.917133i	$0.369502\pi$
$632$		−	3.98346e55i		−	0.385406i
$633$	−4.99503e55	+	2.34099e54i	−0.468235	+	0.0219445i
$634$	−9.92244e55			−0.901226
$635$		−	4.34574e55i		−	0.382463i
$636$	2.08444e54	+	4.44763e55i	0.0177765	+	0.379303i
$637$	−1.98895e55			−0.164375
$638$		−	6.82117e55i		−	0.546318i
$639$	9.52168e54	+	1.01360e56i	0.0739088	+	0.786774i
$640$	−4.69619e55			−0.353302
$641$		−	1.21501e56i		−	0.885969i	−0.896529	−	0.442985i	$-0.853920\pi$
$641$		−	1.21501e56i		−	0.885969i	0.896529	−	0.442985i	$-0.146080\pi$
$642$	1.88122e56	−	8.81659e54i	1.32965	−	0.0623160i
$643$	1.48311e56			1.01614			0.508072	−	0.861315i	$-0.330358\pi$
$643$	1.48311e56			1.01614			0.508072	+	0.861315i	$0.330358\pi$
$644$			1.26829e56i			0.842368i
$645$	−2.71157e53	−	5.78574e54i	−0.00174593	−	0.0372533i
$646$	−3.25310e56			−2.03070
$647$		−	1.11424e56i		−	0.674364i	−0.941439	−	0.337182i	$-0.890526\pi$
$647$		−	1.11424e56i		−	0.674364i	0.941439	−	0.337182i	$-0.109474\pi$
$648$	1.12739e55	+	5.94770e55i	0.0661568	+	0.349019i
$649$	−1.00129e56			−0.569723
$650$			5.29320e55i			0.292046i
$651$	9.50214e55	−	4.45331e54i	0.508396	−	0.0238267i
$652$	−3.08276e55			−0.159951
$653$			2.87225e56i			1.44530i	0.691213	+	0.722651i	$0.257077\pi$
$653$			2.87225e56i			1.44530i	−0.691213	+	0.722651i	$0.742923\pi$
$654$	−1.38306e54	−	2.95108e55i	−0.00674975	−	0.144021i
$655$	−1.56090e56			−0.738839
$656$			4.11221e55i			0.188799i
$657$	−1.22595e56	+	1.15164e55i	−0.545964	+	0.0512874i
$658$	−3.34940e56			−1.44693
$659$			1.81493e55i			0.0760593i	0.999277	+	0.0380296i	$0.0121081\pi$
$659$			1.81493e55i			0.0760593i	−0.999277	+	0.0380296i	$0.987892\pi$
$660$	3.02119e55	−	1.41592e54i	0.122829	−	0.00575654i
$661$	2.14598e55			0.0846440			0.0423220	−	0.999104i	$-0.486524\pi$
$661$	2.14598e55			0.0846440			0.0423220	+	0.999104i	$0.486524\pi$
$662$			4.02522e55i			0.154039i
$663$	−5.68253e54	−	1.21249e56i	−0.0210994	−	0.450204i
$664$	−1.26431e56			−0.455505
$665$		−	1.03464e56i		−	0.361707i
$666$	−5.40234e55	−	5.75089e56i	−0.183272	−	1.95097i
$667$	6.59936e56			2.17263
$668$		−	4.23328e55i		−	0.135253i
$669$	2.40920e56	−	1.12911e55i	0.747052	−	0.0350116i
$670$	1.01272e56			0.304785
$671$			6.53010e55i			0.190752i
$672$	1.36082e55	+	2.90361e56i	0.0385846	+	0.823290i
$673$	5.09730e56			1.40294			0.701470	−	0.712699i	$-0.252527\pi$
$673$	5.09730e56			1.40294			0.701470	+	0.712699i	$0.252527\pi$
$674$		−	1.72857e56i		−	0.461838i
$675$	−2.80063e56	+	3.96087e55i	−0.726406	+	0.102734i
$676$	2.63318e56			0.663051
$677$			1.61926e56i			0.395860i	0.980216	+	0.197930i	$0.0634219\pi$
$677$			1.61926e56i			0.395860i	−0.980216	+	0.197930i	$0.936578\pi$
$678$	2.95633e56	−	1.38553e55i	0.701713	−	0.0328868i
$679$	−4.19902e56			−0.967727
$680$			1.21999e56i			0.273011i
$681$	2.59149e53	+	5.52953e54i	0.000563128	+	0.0120156i
$682$	1.53190e56			0.323254
$683$			7.57766e56i			1.55282i	0.630229	+	0.776410i	$0.282961\pi$
$683$			7.57766e56i			1.55282i	−0.630229	+	0.776410i	$0.717039\pi$
$684$	−3.78611e56	+	3.55663e55i	−0.753478	+	0.0707811i
$685$	2.65483e56			0.513127
$686$		−	7.30802e56i		−	1.37188i
$687$	−9.06834e56	+	4.25000e55i	−1.65346	+	0.0774916i
$688$	4.88445e55			0.0865062
$689$			9.15236e55i			0.157452i
$690$	3.24665e55	+	6.92746e56i	0.0542567	+	1.15769i
$691$	−2.89353e56			−0.469750			−0.234875	−	0.972026i	$-0.575468\pi$
$691$	−2.89353e56			−0.469750			−0.234875	+	0.972026i	$0.575468\pi$
$692$		−	2.32057e56i		−	0.365993i
$693$	1.34673e55	+	1.43362e56i	0.0206356	+	0.219670i
$694$	4.43951e56			0.660915
$695$		−	4.87349e56i		−	0.704927i
$696$	3.21284e56	−	1.50574e55i	0.451548	−	0.0211624i
$697$	1.71964e56			0.234845
$698$			2.40893e56i			0.319680i
$699$	−2.06697e55	−	4.41034e56i	−0.0266557	−	0.568760i
$700$	−2.88818e56			−0.361963
$701$		−	1.26479e57i		−	1.54049i	−0.637751	−	0.770243i	$-0.720135\pi$
$701$		−	1.26479e57i		−	1.54049i	0.637751	−	0.770243i	$-0.279865\pi$
$702$	−4.70921e55	−	3.32976e56i	−0.0557450	−	0.394158i
$703$	−1.34264e57			−1.54473
$704$			1.18678e56i			0.132714i
$705$	−7.71914e56	+	3.61768e55i	−0.839048	+	0.0393231i
$706$	−6.21608e56			−0.656783
$707$		−	8.93497e56i		−	0.917709i
$708$	5.97339e55	+	1.27456e57i	0.0596424	+	1.27261i
$709$	1.45309e57			1.41048			0.705239	−	0.708969i	$-0.250840\pi$
$709$	1.45309e57			1.41048			0.705239	+	0.708969i	$0.250840\pi$
$710$			5.68428e56i			0.536424i
$711$	−1.17731e57	+	1.10595e56i	−1.08018	+	0.101471i
$712$	1.98169e56			0.176781
$713$			1.48209e57i			1.28554i
$714$	1.56798e57	−	7.34854e55i	1.32244	−	0.0619779i
$715$	6.21703e55			0.0509873
$716$		−	1.80907e55i		−	0.0144277i
$717$	−7.91833e55	−	1.68955e57i	−0.0614116	−	1.31036i
$718$	4.89108e56			0.368906
$719$			1.31015e57i			0.961045i	0.876982	+	0.480523i	$0.159553\pi$
$719$			1.31015e57i			0.961045i	−0.876982	+	0.480523i	$0.840447\pi$
$720$	8.09975e55	+	8.62234e56i	0.0577859	+	0.615142i
$721$	3.66092e56			0.254030
$722$			1.46179e56i			0.0986600i
$723$	1.99204e57	−	9.33595e55i	1.30777	−	0.0612904i
$724$	1.28495e57			0.820571
$725$			1.50282e57i			0.933571i
$726$	−9.10338e55	−	1.94241e57i	−0.0550136	−	1.17384i
$727$	−6.53644e56			−0.384285			−0.192142	−	0.981367i	$-0.561544\pi$
$727$	−6.53644e56			−0.384285			−0.192142	+	0.981367i	$0.561544\pi$
$728$			1.27061e56i			0.0726748i
$729$	1.72653e57	−	4.98328e56i	0.960781	−	0.277310i
$730$	−6.87511e56			−0.372240
$731$		−	2.04257e56i		−	0.107604i
$732$	8.31229e56	−	3.89567e55i	0.426088	−	0.0199692i
$733$	−1.72547e57			−0.860651			−0.430325	−	0.902674i	$-0.641601\pi$
$733$	−1.72547e57			−0.860651			−0.430325	+	0.902674i	$0.641601\pi$
$734$		−	2.68153e57i		−	1.30155i
$735$	−2.77810e55	−	5.92770e56i	−0.0131220	−	0.279988i
$736$	−4.52888e57			−2.08178
$737$			3.27610e56i			0.146557i
$738$	4.74336e56	−	4.45587e55i	0.206518	−	0.0194002i
$739$	4.69133e56			0.198796			0.0993979	−	0.995048i	$-0.468308\pi$
$739$	4.69133e56			0.198796			0.0993979	+	0.995048i	$0.468308\pi$
$740$		−	1.36079e57i		−	0.561250i
$741$	−7.80823e56	+	3.65944e55i	−0.313465	+	0.0146910i
$742$	−1.18357e57			−0.462503
$743$		−	2.04139e57i		−	0.776514i	−0.921551	−	0.388257i	$-0.873077\pi$
$743$		−	2.04139e57i		−	0.776514i	0.921551	−	0.388257i	$-0.126923\pi$
$744$	3.38161e55	+	7.21543e56i	0.0125218	+	0.267180i
$745$	1.37897e57			0.497083
$746$			5.11568e57i			1.79526i
$747$	3.51019e56	+	3.73666e57i	0.119927	+	1.27665i
$748$	1.06659e57			0.354785
$749$			2.11228e57i			0.684092i
$750$	−3.72784e57	+	1.74710e56i	−1.17553	+	0.0550926i
$751$	−3.33553e57			−1.02416			−0.512078	−	0.858939i	$-0.671124\pi$
$751$	−3.33553e57			−1.02416			−0.512078	+	0.858939i	$0.671124\pi$
$752$		−	6.51668e57i		−	1.94836i
$753$	1.70736e56	+	3.64304e57i	0.0497080	+	1.06063i
$754$	−1.78675e57			−0.506568
$755$		−	1.86233e57i		−	0.514182i
$756$	1.81685e57	−	2.56954e56i	0.488521	−	0.0690907i
$757$	4.96840e57			1.30106			0.650532	−	0.759479i	$-0.274546\pi$
$757$	4.96840e57			1.30106			0.650532	+	0.759479i	$0.274546\pi$
$758$			6.34483e57i			1.61821i
$759$	−2.24100e57	+	1.05028e56i	−0.556682	+	0.0260897i
$760$	7.85653e56			0.190090
$761$		−	5.68523e57i		−	1.33985i	−0.742430	−	0.669923i	$-0.766327\pi$
$761$		−	5.68523e57i		−	1.33985i	0.742430	−	0.669923i	$-0.233673\pi$
$762$	−1.98769e56	−	4.24118e57i	−0.0456298	−	0.973614i
$763$	3.31354e56			0.0740972
$764$		−	2.26291e57i		−	0.492948i
$765$	3.60568e57	−	3.38714e56i	0.765170	−	0.0718794i
$766$	3.41533e57			0.706085
$767$			2.62279e57i			0.528271i
$768$	−6.65285e57	+	3.11795e56i	−1.30552	+	0.0611850i
$769$	3.56826e57			0.682228			0.341114	−	0.940022i	$-0.389196\pi$
$769$	3.56826e57			0.682228			0.341114	+	0.940022i	$0.389196\pi$
$770$			8.03976e56i			0.149771i
$771$	6.64759e55	+	1.41841e57i	0.0120664	+	0.257463i
$772$	6.13245e57			1.08465
$773$		−	4.57545e57i		−	0.788577i	−0.918987	−	0.394289i	$-0.870991\pi$
$773$		−	4.57545e57i		−	0.788577i	0.918987	−	0.394289i	$-0.129009\pi$
$774$	−5.29265e55	−	5.63412e56i	−0.00888901	−	0.0946253i
$775$	−3.37505e57			−0.552391
$776$		−	3.18852e57i		−	0.508574i
$777$	6.47146e57	−	3.03294e56i	1.00596	−	0.0471458i
$778$	3.96129e57			0.600129
$779$		−	1.10741e57i		−	0.163516i
$780$	−3.70891e55	−	7.91378e56i	−0.00533769	−	0.113892i
$781$	−1.83884e57			−0.257943
$782$			2.44564e58i			3.34393i
$783$	−1.33702e57	−	9.45370e57i	−0.178198	−	1.25999i
$784$	5.00430e57			0.650163
$785$			1.25057e57i			0.158385i
$786$	−1.52334e58	+	7.13937e56i	−1.88082	+	0.0881473i
$787$	4.35653e57			0.524380			0.262190	−	0.965016i	$-0.415555\pi$
$787$	4.35653e57			0.524380			0.262190	+	0.965016i	$0.415555\pi$
$788$			7.45453e56i			0.0874774i
$789$	3.19264e56	+	6.81221e57i	0.0365266	+	0.779378i
$790$	−6.60234e57			−0.736471
$791$			3.31944e57i			0.361024i
$792$	−1.08862e57	+	1.02264e56i	−0.115444	+	0.0108447i
$793$	1.71051e57			0.176873
$794$		−	3.14285e57i		−	0.316894i
$795$	−2.72769e57	+	1.27837e56i	−0.268196	+	0.0125694i
$796$	−1.38319e58			−1.32623
$797$		−	1.01655e58i		−	0.950527i	−0.879844	−	0.475263i	$-0.842353\pi$
$797$		−	1.01655e58i		−	0.950527i	0.879844	−	0.475263i	$-0.157647\pi$
$798$	−4.73232e56	−	1.00975e58i	−0.0431535	−	0.920777i
$799$	−2.72513e58			−2.42355
$800$		−	1.03133e58i		−	0.894535i
$801$	−5.50188e56	−	5.85685e57i	−0.0465437	−	0.495466i
$802$	3.11941e58			2.57386
$803$		−	2.22407e57i		−	0.178994i
$804$	4.17022e57	−	1.95443e56i	0.327369	−	0.0153426i
$805$	−7.77832e57			−0.595618
$806$		−	4.01271e57i		−	0.299735i
$807$	6.39727e56	+	1.36500e58i	0.0466148	+	0.994633i
$808$	6.78475e57			0.482288
$809$			2.07322e58i			1.43772i	0.695155	+	0.718860i	$0.255336\pi$
$809$			2.07322e58i			1.43772i	−0.695155	+	0.718860i	$0.744664\pi$
$810$	9.85794e57	−	1.86858e57i	0.666938	−	0.126419i
$811$	−9.48084e57			−0.625792			−0.312896	−	0.949787i	$-0.601299\pi$
$811$	−9.48084e57			−0.625792			−0.312896	+	0.949787i	$0.601299\pi$
$812$		−	9.74926e57i		−	0.627843i
$813$	1.14848e58	−	5.38251e56i	0.721626	−	0.0338200i
$814$	1.04331e58			0.639623
$815$		−	1.89063e57i		−	0.113098i
$816$	1.42975e57	+	3.05070e58i	0.0834560	+	1.78072i
$817$	−1.31538e57			−0.0749220
$818$		−	2.85880e58i		−	1.58898i
$819$	3.75526e57	−	3.52766e56i	0.203687	−	0.0191341i
$820$	1.12238e57			0.0594107
$821$			1.82148e58i			0.940939i	0.882416	+	0.470469i	$0.155915\pi$
$821$			1.82148e58i			0.940939i	−0.882416	+	0.470469i	$0.844085\pi$
$822$	2.59095e58	−	1.21428e57i	1.30624	−	0.0612187i
$823$	−8.22694e57			−0.404801			−0.202400	−	0.979303i	$-0.564874\pi$
$823$	−8.22694e57			−0.404801			−0.202400	+	0.979303i	$0.564874\pi$
$824$			2.77991e57i			0.133502i
$825$	−2.39172e56	−	5.10327e57i	−0.0112107	−	0.239205i
$826$	−3.39175e58			−1.55175
$827$		−	1.59628e57i		−	0.0712850i	−0.999365	−	0.0356425i	$-0.988652\pi$
$827$		−	1.59628e57i		−	0.0712850i	0.999365	−	0.0356425i	$-0.0113478\pi$
$828$	2.67384e57	+	2.84635e58i	0.116554	+	1.24074i
$829$	1.05730e58			0.449893			0.224946	−	0.974371i	$-0.427779\pi$
$829$	1.05730e58			0.449893			0.224946	+	0.974371i	$0.427779\pi$
$830$			2.09552e58i			0.870423i
$831$	−1.77449e57	+	8.31639e55i	−0.0719537	+	0.00337221i
$832$	3.10868e57			0.123058
$833$		−	2.09269e58i		−	0.808733i
$834$	−2.22907e57	−	4.75622e58i	−0.0841013	−	1.79449i
$835$	2.59623e57			0.0956343
$836$		−	6.86862e57i		−	0.247027i
$837$	2.12312e58	−	3.00269e57i	0.745531	−	0.105439i
$838$	2.16684e58			0.742928
$839$		−	1.81513e58i		−	0.607670i	−0.952725	−	0.303835i	$-0.901733\pi$
$839$		−	1.81513e58i		−	0.607670i	0.952725	−	0.303835i	$-0.0982671\pi$
$840$	−3.78681e57	+	1.77474e56i	−0.123791	+	0.00580162i
$841$	−1.94017e58			−0.619326
$842$			1.91990e58i			0.598461i
$843$	−2.14441e57	−	4.57558e58i	−0.0652764	−	1.39282i
$844$	−1.15096e58			−0.342147
$845$			1.61491e58i			0.468828i
$846$	−7.51686e58	+	7.06127e57i	−2.13122	+	0.200205i
$847$	2.18099e58			0.603928
$848$		−	2.30278e58i		−	0.622781i
$849$	−1.60928e58	+	7.54213e56i	−0.425088	+	0.0199223i
$850$	−5.56927e58			−1.43688
$851$			1.00938e59i			2.54369i
$852$	1.09700e57	+	2.34070e58i	0.0270032	+	0.576173i
$853$	−1.57273e58			−0.378157			−0.189079	−	0.981962i	$-0.560550\pi$
$853$	−1.57273e58			−0.378157			−0.189079	+	0.981962i	$0.560550\pi$
$854$			2.21200e58i			0.519551i
$855$	−2.18125e57	−	2.32199e58i	−0.0500476	−	0.532767i
$856$	−1.60395e58			−0.359514
$857$		−	2.48359e58i		−	0.543830i	−0.962321	−	0.271915i	$-0.912343\pi$
$857$		−	2.48359e58i		−	0.543830i	0.962321	−	0.271915i	$-0.0876570\pi$
$858$	6.06744e57	−	2.84359e56i	0.129796	−	0.00608305i
$859$	7.97374e58			1.66647			0.833237	−	0.552916i	$-0.186485\pi$
$859$	7.97374e58			1.66647			0.833237	+	0.552916i	$0.186485\pi$
$860$		−	1.33316e57i		−	0.0272216i
$861$	2.50158e56	+	5.33768e57i	0.00499058	+	0.106485i
$862$	3.24700e58			0.632903
$863$		−	5.20595e58i		−	0.991480i	−0.868471	−	0.495740i	$-0.834897\pi$
$863$		−	5.20595e58i		−	0.991480i	0.868471	−	0.495740i	$-0.165103\pi$
$864$	9.17545e57	+	6.48771e58i	0.170747	+	1.20730i
$865$	1.42319e58			0.258785
$866$			4.30474e57i			0.0764872i
$867$	7.00420e58	−	3.28262e57i	1.21612	−	0.0569952i
$868$	2.18950e58			0.371493
$869$		−	2.13583e58i		−	0.354137i
$870$	−2.49567e57	−	5.32508e58i	−0.0404392	−	0.862862i
$871$	8.58151e57			0.135894
$872$			2.51613e57i			0.0389407i
$873$	−9.42362e58	+	8.85247e57i	−1.42539	+	0.133900i
$874$	1.57494e59			2.32829
$875$		−	4.18571e58i		−	0.604795i
$876$	−2.83106e58	+	1.32682e57i	−0.399823	+	0.0187382i
$877$	−5.67389e58			−0.783230			−0.391615	−	0.920129i	$-0.628083\pi$
$877$	−5.67389e58			−0.783230			−0.391615	+	0.920129i	$0.628083\pi$
$878$		−	2.66754e58i		−	0.359932i
$879$	4.35523e57	+	9.29286e58i	0.0574425	+	1.22567i
$880$	−1.56424e58			−0.201673
$881$		−	9.54440e58i		−	1.20290i	−0.798910	−	0.601451i	$-0.794589\pi$
$881$		−	9.54440e58i		−	1.20290i	0.798910	−	0.601451i	$-0.205411\pi$
$882$	−5.42251e57	−	5.77236e58i	−0.0668080	−	0.711184i
$883$	1.39324e59			1.67807			0.839036	−	0.544076i	$-0.183120\pi$
$883$	1.39324e59			1.67807			0.839036	+	0.544076i	$0.183120\pi$
$884$		−	2.79385e58i		−	0.328971i
$885$	−7.81674e58	+	3.66342e57i	−0.899830	+	0.0421718i
$886$	−2.25823e59			−2.54152
$887$			1.44700e59i			1.59220i	0.605167	+	0.796098i	$0.293106\pi$
$887$			1.44700e59i			1.59220i	−0.605167	+	0.796098i	$0.706894\pi$
$888$	2.30306e57	+	4.91409e58i	0.0247768	+	0.528669i
$889$	4.76210e58			0.500914
$890$		−	3.28453e58i		−	0.337810i
$891$	6.04478e57	+	3.18900e58i	0.0607892	+	0.320701i
$892$	5.55132e58			0.545883
$893$			1.75493e59i			1.68745i
$894$	1.34579e59	−	6.30722e57i	1.26539	−	0.0593045i
$895$	1.10949e57			0.0102015
$896$		−	5.14612e58i		−	0.462721i
$897$	2.75112e57	+	5.87014e58i	0.0241914	+	0.516178i
$898$	−1.86587e59			−1.60456
$899$		−	1.13927e59i		−	0.958150i
$900$	−6.48178e58	+	6.08893e57i	−0.533144	+	0.0500831i
$901$	−9.62972e58			−0.774672
$902$			8.60524e57i			0.0677068i
$903$	6.34006e57	−	2.97136e56i	0.0487908	−	0.00228665i
$904$	−2.52061e58			−0.189731
$905$			7.88051e58i			0.580206i
$906$	−8.51804e57	−	1.81752e59i	−0.0613445	−	1.30892i
$907$	−1.05800e59			−0.745314			−0.372657	−	0.927969i	$-0.621553\pi$
$907$	−1.05800e59			−0.745314			−0.372657	+	0.927969i	$0.621553\pi$
$908$			1.27412e57i			0.00877999i
$909$	−1.88369e58	−	2.00522e59i	−0.126979	−	1.35171i
$910$	2.10595e58			0.138874
$911$		−	2.09761e59i		−	1.35319i	−0.736357	−	0.676593i	$-0.763456\pi$
$911$		−	2.09761e59i		−	1.35319i	0.736357	−	0.676593i	$-0.236544\pi$
$912$	1.96459e59	−	9.20732e57i	1.23987	−	0.0581081i
$913$	−6.77893e58			−0.418548
$914$			4.16877e59i			2.51817i
$915$	2.38918e57	+	5.09786e58i	0.0141198	+	0.301277i
$916$	−2.08954e59			−1.20821
$917$		−	1.71045e59i		−	0.967661i
$918$	3.50343e59	−	4.95483e58i	1.93927	−	0.274268i
$919$	3.09625e59			1.67697			0.838487	−	0.544921i	$-0.183440\pi$
$919$	3.09625e59			1.67697			0.838487	+	0.544921i	$0.183440\pi$
$920$		−	5.90645e58i		−	0.313018i
$921$	−1.86450e59	+	8.73823e57i	−0.966873	+	0.0453139i
$922$	2.49549e59			1.26630
$923$			4.81670e58i			0.239175i
$924$	1.55158e57	+	3.31065e58i	0.00753937	+	0.160869i
$925$	−2.29859e59			−1.09302
$926$			2.91920e59i			1.35845i
$927$	8.21599e58	−	7.71803e57i	0.374167	−	0.0351489i
$928$	3.48132e59			1.55162
$929$			2.84934e58i			0.124288i	0.998067	+	0.0621440i	$0.0197938\pi$
$929$			2.84934e58i			0.124288i	−0.998067	+	0.0621440i	$0.980206\pi$
$930$	1.19591e59	−	5.60481e57i	0.510553	−	0.0239278i
$931$	−1.34765e59			−0.563098
$932$		−	1.01624e59i		−	0.415602i
$933$	1.22726e58	+	2.61864e59i	0.0491252	+	1.04820i
$934$	−2.03831e59			−0.798607
$935$			6.54130e58i			0.250860i
$936$	2.67872e57	+	2.85155e58i	0.0100557	+	0.107044i
$937$	2.58554e59			0.950078			0.475039	−	0.879965i	$-0.342434\pi$
$937$	2.58554e59			0.950078			0.475039	+	0.879965i	$0.342434\pi$
$938$			1.10975e59i			0.399178i
$939$	−3.30466e59	+	1.54877e58i	−1.16363	+	0.0545351i
$940$	−1.77866e59			−0.613105
$941$		−	3.55530e59i		−	1.19973i	−0.800101	−	0.599865i	$-0.795221\pi$
$941$		−	3.55530e59i		−	1.19973i	0.800101	−	0.599865i	$-0.204779\pi$
$942$	5.71994e57	+	1.22048e59i	0.0188962	+	0.403192i
$943$	−8.32541e58			−0.269260
$944$		−	6.59907e59i		−	2.08950i
$945$	1.57588e58	+	1.11426e59i	0.0488524	+	0.345422i
$946$	1.02212e58			0.0310228
$947$		−	3.80294e59i		−	1.13011i	−0.825054	−	0.565053i	$-0.808856\pi$
$947$		−	3.80294e59i		−	1.13011i	0.825054	−	0.565053i	$-0.191144\pi$
$948$	−2.71874e59	+	1.27417e58i	−0.791044	+	0.0370734i
$949$	−5.82579e58			−0.165970
$950$			3.58650e59i			1.00046i
$951$	−1.17440e58	−	2.50585e59i	−0.0320779	−	0.684455i
$952$	−1.33688e59			−0.357564
$953$			2.95999e59i			0.775234i	0.921821	+	0.387617i	$0.126702\pi$
$953$			2.95999e59i			0.775234i	−0.921821	+	0.387617i	$0.873298\pi$
$954$	−2.65621e59	+	2.49522e58i	−0.681232	+	0.0639943i
$955$	1.38783e59			0.348552
$956$		−	3.89310e59i		−	0.957497i
$957$	1.72264e59	−	8.07340e57i	0.414912	−	0.0194454i
$958$	−1.32169e59			−0.311760
$959$			2.90918e59i			0.672045i
$960$	4.34209e57	+	9.26483e58i	0.00982368	+	0.209610i
$961$	−1.95444e59			−0.433066
$962$		−	2.73287e59i		−	0.593085i
$963$	4.45315e58	+	4.74046e59i	0.0946545	+	1.00761i
$964$	4.59008e59			0.955607
$965$			3.76098e59i			0.766928i
$966$	−7.59116e59	+	3.55770e58i	−1.51623	+	0.0710603i
$967$	9.40566e59			1.84018			0.920089	−	0.391709i	$-0.128116\pi$
$967$	9.40566e59			1.84018			0.920089	+	0.391709i	$0.128116\pi$
$968$			1.65613e59i			0.317385i
$969$	−3.85030e58	−	8.21548e59i	−0.0722802	−	1.54226i
$970$	−5.28477e59			−0.971833
$971$			7.90172e59i			1.42343i	0.702467	+	0.711717i	$0.252082\pi$
$971$			7.90172e59i			1.42343i	−0.702467	+	0.711717i	$0.747918\pi$
$972$	4.02328e59	−	9.59699e58i	0.709995	−	0.169360i
$973$	5.34041e59			0.923246
$974$			2.94797e59i			0.499280i
$975$	−1.33676e59	+	6.26493e57i	−0.221800	+	0.0103950i
$976$	−4.30373e59			−0.699598
$977$			2.31628e59i			0.368892i	0.982843	+	0.184446i	$0.0590491\pi$
$977$			2.31628e59i			0.368892i	−0.982843	+	0.184446i	$0.940951\pi$
$978$	−8.64749e57	−	1.84514e59i	−0.0134931	−	0.287906i
$979$	1.06253e59			0.162438
$980$		−	1.36587e59i		−	0.204592i
$981$	7.43639e58	−	6.98568e57i	0.109140	−	0.0102525i
$982$	1.62067e60			2.33058
$983$			1.31841e59i			0.185772i	0.995677	+	0.0928862i	$0.0296093\pi$
$983$			1.31841e59i			0.185772i	−0.995677	+	0.0928862i	$0.970391\pi$
$984$	−4.05316e58	+	1.89957e57i	−0.0559618	+	0.00262273i
$985$	−4.57180e58			−0.0618533
$986$		−	1.87995e60i		−	2.49234i
$987$	−3.96428e58	−	8.45869e59i	−0.0515017	−	1.09891i
$988$	−1.79918e59			−0.229053
$989$			9.88886e58i			0.123373i
$990$	1.69496e58	+	1.80432e59i	0.0207231	+	0.220602i
$991$	3.29149e59			0.394384			0.197192	−	0.980365i	$-0.436818\pi$
$991$	3.29149e59			0.394384			0.197192	+	0.980365i	$0.436818\pi$
$992$			7.81838e59i			0.918086i
$993$	−1.01654e59	+	4.76418e57i	−0.116988	+	0.00548281i
$994$	−6.22887e59			−0.702558
$995$		−	8.48298e59i		−	0.937749i
$996$	4.04412e58	+	8.62903e59i	0.0438164	+	0.934922i
$997$	−4.87393e59			−0.517578			−0.258789	−	0.965934i	$-0.583323\pi$
$997$	−4.87393e59			−0.517578			−0.258789	+	0.965934i	$0.583323\pi$
$998$			1.04163e60i			1.08418i
$999$	1.44596e60	−	2.04499e59i	1.47518	−	0.208632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.41.b.a.2.10	yes	12
3.2	odd	2	inner	3.41.b.a.2.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.41.b.a.2.3	✓	12	3.2	odd	2	inner
3.41.b.a.2.10	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:	\( k \)	\(=\)	\( 41 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.37915e6i q^{2} +(-3.48296e9 + 1.63234e8i) q^{3} -8.02549e11 q^{4} -4.92196e13i q^{5} +(-2.25124e14 - 4.80353e15i) q^{6} +5.39353e16 q^{7} +4.09556e17i q^{8} +(1.21044e19 - 1.13707e18i) q^{9} +O(q^{10})\)	\(q+1.37915e6i q^{2} +(-3.48296e9 + 1.63234e8i) q^{3} -8.02549e11 q^{4} -4.92196e13i q^{5} +(-2.25124e14 - 4.80353e15i) q^{6} +5.39353e16 q^{7} +4.09556e17i q^{8} +(1.21044e19 - 1.13707e18i) q^{9} +6.78814e19 q^{10} +2.19593e20i q^{11} +(2.79525e21 - 1.31003e20i) q^{12} +5.75209e21 q^{13} +7.43849e22i q^{14} +(8.03431e21 + 1.71430e23i) q^{15} -1.44725e24 q^{16} +6.05210e24i q^{17} +(1.56820e24 + 1.66938e25i) q^{18} +3.89743e25 q^{19} +3.95012e25i q^{20} +(-1.87854e26 + 8.80406e24i) q^{21} -3.02853e26 q^{22} -2.93005e27i q^{23} +(-6.68534e25 - 1.42647e27i) q^{24} +6.67237e27 q^{25} +7.93300e27i q^{26} +(-4.19735e28 + 5.93623e27i) q^{27} -4.32857e28 q^{28} +2.25230e29i q^{29} +(-2.36428e29 + 1.10805e28i) q^{30} -5.05825e29 q^{31} -1.54567e30i q^{32} +(-3.58451e28 - 7.64836e29i) q^{33} -8.34676e30 q^{34} -2.65467e30i q^{35} +(-9.71436e30 + 9.12558e29i) q^{36} -3.44493e31 q^{37} +5.37515e31i q^{38} +(-2.00343e31 + 9.38935e29i) q^{39} +2.01582e31 q^{40} -2.84139e31i q^{41} +(-1.21421e31 - 2.59080e32i) q^{42} -3.37498e31 q^{43} -1.76235e32i q^{44} +(-5.59664e31 - 5.95773e32i) q^{45} +4.04098e33 q^{46} +4.50279e33i q^{47} +(5.04073e33 - 2.36241e32i) q^{48} -3.45779e33 q^{49} +9.20222e33i q^{50} +(-9.87907e32 - 2.10792e34i) q^{51} -4.61633e33 q^{52} +1.59114e34i q^{53} +(-8.18697e33 - 5.78878e34i) q^{54} +1.08083e34 q^{55} +2.20895e34i q^{56} +(-1.35746e35 + 6.36193e33i) q^{57} -3.10627e35 q^{58} +4.55972e35i q^{59} +(-6.44793e33 - 1.37581e35i) q^{60} +2.97372e35 q^{61} -6.97609e35i q^{62} +(6.52853e35 - 6.13284e34i) q^{63} +5.40443e35 q^{64} -2.83116e35i q^{65} +(1.05482e36 - 4.94358e34i) q^{66} +1.49190e36 q^{67} -4.85711e36i q^{68} +(4.78283e35 + 1.02052e37i) q^{69} +3.66120e36 q^{70} +8.37384e36i q^{71} +(4.65696e35 + 4.95742e36i) q^{72} -1.01281e37 q^{73} -4.75109e37i q^{74} +(-2.32396e37 + 1.08916e36i) q^{75} -3.12788e37 q^{76} +1.18438e37i q^{77} +(-1.29493e36 - 2.76303e37i) q^{78} -9.72628e37 q^{79} +7.12333e37i q^{80} +(1.45223e38 - 2.75271e37i) q^{81} +3.91871e37 q^{82} +3.08704e38i q^{83} +(1.50762e38 - 7.06569e36i) q^{84} +2.97882e38 q^{85} -4.65462e37i q^{86} +(-3.67652e37 - 7.84469e38i) q^{87} -8.99359e37 q^{88} -4.83862e38i q^{89} +(8.21662e38 - 7.71862e37i) q^{90} +3.10240e38 q^{91} +2.35151e39i q^{92} +(1.76177e39 - 8.25677e37i) q^{93} -6.21004e39 q^{94} -1.91830e39i q^{95} +(2.52306e38 + 5.38351e39i) q^{96} -7.78530e39 q^{97} -4.76882e39i q^{98} +(2.49694e38 + 2.65804e39i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots - 23\!\cdots\!20 q^{9}+O(q^{10}) \) 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9	\( 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots + 54\!\cdots\!80 q^{99}+O(q^{100}) \) 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9 - 129384136354706290080 * q^10 - 4708039830028985428272 * q^12 + 704368845864154901976 * q^13 + 320935800901459838631840 * q^15 + 6054431850962872672227456 * q^16 + 10227710367381761273509920 * q^18 + 37616619688417835612151720 * q^19 - 179163719456723608834234728 * q^21 + 846315150249292772829325920 * q^22 - 18213480358094369517645250944 * q^24 + 8842265325510151276196474700 * q^25 - 70717074113738779393083858252 * q^27 + 469404222007499612173589889696 * q^28 - 207809636542026559976510503200 * q^30 - 914600368399753689553849145016 * q^31 + 157344642221562801276041757600 * q^33 - 14575908480758621487300381842304 * q^34 + 41100171486790863962401658870544 * q^36 + 5673106137824212681873457220696 * q^37 - 9206461430638842876438079090008 * q^39 + 50495897877443363581635475618560 * q^40 - 939238658319640212873301303645920 * q^42 + 1012654832326802922602871229857576 * q^43 + 196109968512215856818385626472000 * q^45 - 3082500781506234684371181468390336 * q^46 + 6532128822166367998693520969705088 * q^48 + 8498166150175390075155260408801892 * q^49 + 27565453699222767413826960590504832 * q^51 - 57328509042562386918101767400001504 * q^52 - 102847607224782098537542351912875792 * q^54 - 9637639495259752880102706884884800 * q^55 - 40307213604482059940636368892395464 * q^57 + 772129436848561910287203884295052320 * q^58 - 114385571579949295944121547557720320 * q^60 - 494443282701607071691140418439862696 * q^61 + 1379291076525018665154441723571240776 * q^63 - 6231783699524672226208093043936541696 * q^64 + 2652084094607847915810184973553481440 * q^66 + 5401062423529881431761320436868275176 * q^67 + 7110274695178254111533494284632123328 * q^69 + 516103243900107216646679160954379200 * q^70 - 27544975046740790141119542770107057920 * q^72 + 30000154498324943042431295514883418136 * q^73 + 43820294796704764666539599709819928500 * q^75 - 215478934792040263381331019050660960352 * q^76 + 234946633516471169601955850003339878560 * q^78 - 128704557118405295534397879672035334840 * q^79 + 473157359902659920298963194247360443532 * q^81 - 639159997421964256448917103585883414720 * q^82 + 1283288903941350744781821238287455403552 * q^84 - 1077142486191382871466217243736209678080 * q^85 + 1076668306862385320797179121273520148960 * q^87 - 2918662713596496795370587920448329114880 * q^88 + 6571793457940570799819318674019816438880 * q^90 - 9859184204686878150356379414618151910256 * q^91 + 11506410044121210986218054652959643683416 * q^93 - 16857264118330945289191940748512432348544 * q^94 + 53068562519213731340201280418423192237056 * q^96 - 41841010071967618660163746722085070705064 * q^97 + 54341076855402233475300783474292013590080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more