LMFDB - Embedded newform 3.27.b.a.2.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,27,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, 27, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 27);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 27 $
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:	$12.8487876219$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2728193x^{6} + 2071419806976x^{4} + 503906274711956480x^{2} + 26754716118873014272000 $ x^8 + 2728193x^6 + 2071419806976x^4 + 503906274711956480*x^2 + 26754716118873014272000
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{33}\cdot 3^{38}\cdot 5^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.3
Root			$-575.513i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.27.b.a.2.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6906.16i q^{2} +(618315. + 1.46954e6i) q^{3} +1.94139e7 q^{4} +1.04255e9i q^{5} +(1.01489e10 - 4.27018e9i) q^{6} -1.82788e11 q^{7} -5.97540e11i q^{8} +(-1.77724e12 + 1.81728e12i) q^{9} +O(q^{10})$	\(q-6906.16i q^{2} +(618315. + 1.46954e6i) q^{3} +1.94139e7 q^{4} +1.04255e9i q^{5} +(1.01489e10 - 4.27018e9i) q^{6} -1.82788e11 q^{7} -5.97540e11i q^{8} +(-1.77724e12 + 1.81728e12i) q^{9} +7.19999e12 q^{10} +2.00553e13i q^{11} +(1.20039e13 + 2.85295e13i) q^{12} -1.77823e14 q^{13} +1.26236e15i q^{14} +(-1.53207e15 + 6.44622e14i) q^{15} -2.82386e15 q^{16} +1.19613e16i q^{17} +(1.25504e16 + 1.22739e16i) q^{18} -3.24857e15 q^{19} +2.02399e16i q^{20} +(-1.13020e17 - 2.68614e17i) q^{21} +1.38505e17 q^{22} -1.64173e17i q^{23} +(8.78109e17 - 3.69467e17i) q^{24} +4.03212e17 q^{25} +1.22808e18i q^{26} +(-3.76946e18 - 1.48808e18i) q^{27} -3.54862e18 q^{28} +1.21188e19i q^{29} +(4.45186e18 + 1.05807e19i) q^{30} +2.60244e18 q^{31} -2.05982e19i q^{32} +(-2.94720e19 + 1.24005e19i) q^{33} +8.26067e19 q^{34} -1.90565e20i q^{35} +(-3.45031e19 + 3.52804e19i) q^{36} -2.51577e19 q^{37} +2.24351e19i q^{38} +(-1.09951e20 - 2.61319e20i) q^{39} +6.22963e20 q^{40} +1.30238e21i q^{41} +(-1.85509e21 + 7.80536e20i) q^{42} +1.35087e21 q^{43} +3.89350e20i q^{44} +(-1.89460e21 - 1.85286e21i) q^{45} -1.13380e21 q^{46} -1.28484e21i q^{47} +(-1.74603e21 - 4.14978e21i) q^{48} +2.40239e22 q^{49} -2.78465e21i q^{50} +(-1.75777e22 + 7.39586e21i) q^{51} -3.45224e21 q^{52} -4.21845e22i q^{53} +(-1.02769e22 + 2.60325e22i) q^{54} -2.09085e22 q^{55} +1.09223e23i q^{56} +(-2.00864e21 - 4.77390e21i) q^{57} +8.36943e22 q^{58} -3.86894e22i q^{59} +(-2.97434e22 + 1.25146e22i) q^{60} -1.13641e23 q^{61} -1.79729e22i q^{62} +(3.24858e23 - 3.32176e23i) q^{63} -3.31760e23 q^{64} -1.85389e23i q^{65} +(8.56395e22 + 2.03538e23i) q^{66} +4.68597e23 q^{67} +2.32216e23i q^{68} +(2.41258e23 - 1.01510e23i) q^{69} -1.31607e24 q^{70} +5.64254e23i q^{71} +(1.08590e24 + 1.06197e24i) q^{72} -1.49767e24 q^{73} +1.73743e23i q^{74} +(2.49312e23 + 5.92537e23i) q^{75} -6.30673e22 q^{76} -3.66586e24i q^{77} +(-1.80471e24 + 7.59338e23i) q^{78} +4.28960e24 q^{79} -2.94400e24i q^{80} +(-1.43920e23 - 6.45948e24i) q^{81} +8.99442e24 q^{82} +1.38291e25i q^{83} +(-2.19416e24 - 5.21485e24i) q^{84} -1.24702e25 q^{85} -9.32932e24i q^{86} +(-1.78091e25 + 7.49323e24i) q^{87} +1.19838e25 q^{88} +2.05341e25i q^{89} +(-1.27961e25 + 1.30844e25i) q^{90} +3.25040e25 q^{91} -3.18723e24i q^{92} +(1.60913e24 + 3.82440e24i) q^{93} -8.87333e24 q^{94} -3.38678e24i q^{95} +(3.02699e25 - 1.27362e25i) q^{96} -3.14676e25 q^{97} -1.65913e26i q^{98} +(-3.64460e25 - 3.56430e25i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 1261080 q^{3} - 248848672 q^{4} + 4268261088 q^{6} - 83723264240 q^{7} + 3535237525320 q^{9}+O(q^{10}) $ 8 * q - 1261080 * q^3 - 248848672 * q^4 + 4268261088 * q^6 - 83723264240 * q^7 + 3535237525320 * q^9	$ 8 q - 1261080 q^{3} - 248848672 q^{4} + 4268261088 q^{6} - 83723264240 q^{7} + 3535237525320 q^{9} - 19160376580800 q^{10} + 361652147111520 q^{12} - 397915354631600 q^{13} - 719893807027200 q^{15} + 14\!\cdots\!24 q^{16}+ \cdots + 12\!\cdots\!20 q^{99}+O(q^{100}) $ 8 * q - 1261080 * q^3 - 248848672 * q^4 + 4268261088 * q^6 - 83723264240 * q^7 + 3535237525320 * q^9 - 19160376580800 * q^10 + 361652147111520 * q^12 - 397915354631600 * q^13 - 719893807027200 * q^15 + 14708338775335424 * q^16 - 21900893760832320 * q^18 + 16320401555362000 * q^19 + 194580840365988048 * q^21 - 772248680481769920 * q^22 - 462343148304920064 * q^24 + 1971388854053049800 * q^25 - 7894649015962792920 * q^27 + 15321751531929304000 * q^28 + 7398480599799681600 * q^30 - 9272518953250081904 * q^31 - 65168600178932490240 * q^33 + 221246262521511042816 * q^34 - 1016435634925989724704 * q^36 + 879374467120740709840 * q^37 - 1582238541124790450928 * q^39 + 4129217584783179033600 * q^40 - 6703469261814514512960 * q^42 + 6748593942335676212560 * q^43 - 16831420952659929907200 * q^45 + 36160927581299221074816 * q^46 - 66488551077760679646720 * q^48 + 45841873858091621647512 * q^49 - 62114113806050924347392 * q^51 + 99815113130579384624320 * q^52 - 65423424830500017302112 * q^54 + 31541176921532063385600 * q^55 - 68601650728105742286960 * q^57 + 179274146475296123858880 * q^58 + 132515345363297827507200 * q^60 - 319050283467071524566704 * q^61 + 658789337835295522626960 * q^63 - 1937027849517856838066176 * q^64 + 3327191890146340029253440 * q^66 - 3016122636770760226629680 * q^67 + 2874694883813365556256768 * q^69 - 3079956143630742638371200 * q^70 + 4816528692447953902187520 * q^72 - 1734362529074066854728560 * q^73 + 551279759153288953055400 * q^75 - 4252629668197637559664448 * q^76 - 2905541033044787133422400 * q^78 + 5851464318766097144790160 * q^79 - 7387002303358032367832952 * q^81 + 19281076716095151109326720 * q^82 - 58831332525651421466918208 * q^84 + 36766362882842005714329600 * q^85 - 66105320167985812595481600 * q^87 + 166743215953906759732730880 * q^88 - 112582289830354559315755200 * q^90 + 57658591275235919126596256 * q^91 - 721851591602497641585840 * q^93 - 128592383810221185199398144 * q^94 + 66451111218720743421763584 * q^96 + 87088434574088023884109840 * q^97 + 126385397236902706353285120 * 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 $

$2$		−	6906.16i		−	0.843037i	−0.906820	−	0.421518i	$-0.861497\pi$
$2$		−	6906.16i		−	0.843037i	0.906820	−	0.421518i	$-0.138503\pi$
$3$	618315.	+	1.46954e6i	0.387823	+	0.921734i
$3$	618315.	+	1.46954e6i	0.387823	+	0.921734i
$4$	1.94139e7			0.289289
$5$			1.04255e9i			0.854054i	0.904239	+	0.427027i	$0.140439\pi$
$5$			1.04255e9i			0.854054i	−0.904239	+	0.427027i	$0.859561\pi$
$6$	1.01489e10	−	4.27018e9i	0.777055	−	0.326949i
$7$	−1.82788e11			−1.88657			−0.943284	−	0.331986i	$-0.892281\pi$
$7$	−1.82788e11			−1.88657			−0.943284	+	0.331986i	$0.892281\pi$
$8$		−	5.97540e11i		−	1.08692i
$9$	−1.77724e12	+	1.81728e12i	−0.699187	+	0.714939i
$10$	7.19999e12			0.719999
$11$			2.00553e13i			0.580929i	0.956886	+	0.290465i	$0.0938099\pi$
$11$			2.00553e13i			0.580929i	−0.956886	+	0.290465i	$0.906190\pi$
$12$	1.20039e13	+	2.85295e13i	0.112193	+	0.266648i
$13$	−1.77823e14			−0.587118			−0.293559	−	0.955941i	$-0.594840\pi$
$13$	−1.77823e14			−0.587118			−0.293559	+	0.955941i	$0.594840\pi$
$14$			1.26236e15i			1.59045i
$15$	−1.53207e15	+	6.44622e14i	−0.787211	+	0.331222i
$16$	−2.82386e15			−0.627022
$17$			1.19613e16i			1.20766i	0.797115	+	0.603828i	$0.206359\pi$
$17$			1.19613e16i			1.20766i	−0.797115	+	0.603828i	$0.793641\pi$
$18$	1.25504e16	+	1.22739e16i	0.602719	+	0.589440i
$19$	−3.24857e15			−0.0772494			−0.0386247	−	0.999254i	$-0.512298\pi$
$19$	−3.24857e15			−0.0772494			−0.0386247	+	0.999254i	$0.512298\pi$
$20$			2.02399e16i			0.247069i
$21$	−1.13020e17	−	2.68614e17i	−0.731654	−	1.73891i
$22$	1.38505e17			0.489745
$23$		−	1.64173e17i		−	0.325716i	−0.986650	−	0.162858i	$-0.947929\pi$
$23$		−	1.64173e17i		−	0.325716i	0.986650	−	0.162858i	$-0.0520712\pi$
$24$	8.78109e17	−	3.69467e17i	1.00185	−	0.421532i
$25$	4.03212e17			0.270591
$26$			1.22808e18i			0.494962i
$27$	−3.76946e18	−	1.48808e18i	−0.930144	−	0.367195i
$28$	−3.54862e18			−0.545764
$29$			1.21188e19i			1.18110i	0.807002	+	0.590549i	$0.201089\pi$
$29$			1.21188e19i			1.18110i	−0.807002	+	0.590549i	$0.798911\pi$
$30$	4.45186e18	+	1.05807e19i	0.279232	+	0.663648i
$31$	2.60244e18			0.106581			0.0532904	−	0.998579i	$-0.483029\pi$
$31$	2.60244e18			0.106581			0.0532904	+	0.998579i	$0.483029\pi$
$32$		−	2.05982e19i		−	0.558315i
$33$	−2.94720e19	+	1.24005e19i	−0.535462	+	0.225298i
$34$	8.26067e19			1.01810
$35$		−	1.90565e20i		−	1.61123i
$36$	−3.45031e19	+	3.52804e19i	−0.202267	+	0.206824i
$37$	−2.51577e19			−0.103288			−0.0516438	−	0.998666i	$-0.516446\pi$
$37$	−2.51577e19			−0.103288			−0.0516438	+	0.998666i	$0.516446\pi$
$38$			2.24351e19i			0.0651240i
$39$	−1.09951e20	−	2.61319e20i	−0.227698	−	0.541167i
$40$	6.22963e20			0.928287
$41$			1.30238e21i			1.40782i	0.710290	+	0.703909i	$0.248564\pi$
$41$			1.30238e21i			1.40782i	−0.710290	+	0.703909i	$0.751436\pi$
$42$	−1.85509e21	+	7.80536e20i	−1.46597	+	0.616811i
$43$	1.35087e21			0.786183			0.393091	−	0.919499i	$-0.371406\pi$
$43$	1.35087e21			0.786183			0.393091	+	0.919499i	$0.371406\pi$
$44$			3.89350e20i			0.168057i
$45$	−1.89460e21	−	1.85286e21i	−0.610597	−	0.597144i
$46$	−1.13380e21			−0.274590
$47$		−	1.28484e21i		−	0.235276i	−0.993057	−	0.117638i	$-0.962468\pi$
$47$		−	1.28484e21i		−	0.235276i	0.993057	−	0.117638i	$-0.0375323\pi$
$48$	−1.74603e21	−	4.14978e21i	−0.243173	−	0.577948i
$49$	2.40239e22			2.55914
$50$		−	2.78465e21i		−	0.228118i
$51$	−1.75777e22	+	7.39586e21i	−1.11314	+	0.468356i
$52$	−3.45224e21			−0.169847
$53$		−	4.21845e22i		−	1.62019i	−0.586298	−	0.810096i	$-0.699415\pi$
$53$		−	4.21845e22i		−	1.62019i	0.586298	−	0.810096i	$-0.300585\pi$
$54$	−1.02769e22	+	2.60325e22i	−0.309559	+	0.784145i
$55$	−2.09085e22			−0.496145
$56$			1.09223e23i			2.05055i
$57$	−2.00864e21	−	4.77390e21i	−0.0299591	−	0.0712034i
$58$	8.36943e22			0.995708
$59$		−	3.86894e22i		−	0.368567i	−0.982873	−	0.184283i	$-0.941004\pi$
$59$		−	3.86894e22i		−	0.368567i	0.982873	−	0.184283i	$-0.0589964\pi$
$60$	−2.97434e22	+	1.25146e22i	−0.227732	+	0.0958189i
$61$	−1.13641e23			−0.701856			−0.350928	−	0.936402i	$-0.614134\pi$
$61$	−1.13641e23			−0.701856			−0.350928	+	0.936402i	$0.614134\pi$
$62$		−	1.79729e22i		−	0.0898516i
$63$	3.24858e23	−	3.32176e23i	1.31906	−	1.34878i
$64$	−3.31760e23			−1.09770
$65$		−	1.85389e23i		−	0.501431i
$66$	8.56395e22	+	2.03538e23i	0.189934	+	0.451414i
$67$	4.68597e23			0.854726			0.427363	−	0.904080i	$-0.359443\pi$
$67$	4.68597e23			0.854726			0.427363	+	0.904080i	$0.359443\pi$
$68$			2.32216e23i			0.349362i
$69$	2.41258e23	−	1.01510e23i	0.300223	−	0.126320i
$70$	−1.31607e24			−1.35833
$71$			5.64254e23i			0.484302i	0.970239	+	0.242151i	$0.0778529\pi$
$71$			5.64254e23i			0.484302i	−0.970239	+	0.242151i	$0.922147\pi$
$72$	1.08590e24	+	1.06197e24i	0.777080	+	0.759959i
$73$	−1.49767e24			−0.895814			−0.447907	−	0.894080i	$-0.647831\pi$
$73$	−1.49767e24			−0.895814			−0.447907	+	0.894080i	$0.647831\pi$
$74$			1.73743e23i			0.0870753i
$75$	2.49312e23	+	5.92537e23i	0.104941	+	0.249413i
$76$	−6.30673e22			−0.0223474
$77$		−	3.66586e24i		−	1.09596i
$78$	−1.80471e24	+	7.59338e23i	−0.456223	+	0.191958i
$79$	4.28960e24			0.918892			0.459446	−	0.888206i	$-0.348048\pi$
$79$	4.28960e24			0.918892			0.459446	+	0.888206i	$0.348048\pi$
$80$		−	2.94400e24i		−	0.535511i
$81$	−1.43920e23	−	6.45948e24i	−0.0222748	−	0.999752i
$82$	8.99442e24			1.18684
$83$			1.38291e25i			1.55876i	0.626550	+	0.779381i	$0.284466\pi$
$83$			1.38291e25i			1.55876i	−0.626550	+	0.779381i	$0.715534\pi$
$84$	−2.19416e24	−	5.21485e24i	−0.211660	−	0.503049i
$85$	−1.24702e25			−1.03140
$86$		−	9.32932e24i		−	0.662781i
$87$	−1.78091e25	+	7.49323e24i	−1.08866	+	0.458056i
$88$	1.19838e25			0.631423
$89$			2.05341e25i			0.934126i	0.884224	+	0.467063i	$0.154688\pi$
$89$			2.05341e25i			0.934126i	−0.884224	+	0.467063i	$0.845312\pi$
$90$	−1.27961e25	+	1.30844e25i	−0.503414	+	0.514755i
$91$	3.25040e25			1.10764
$92$		−	3.18723e24i		−	0.0942261i
$93$	1.60913e24	+	3.82440e24i	0.0413345	+	0.0982392i
$94$	−8.87333e24			−0.198347
$95$		−	3.38678e24i		−	0.0659752i
$96$	3.02699e25	−	1.27362e25i	0.514618	−	0.216527i
$97$	−3.14676e25			−0.467554			−0.233777	−	0.972290i	$-0.575109\pi$
$97$	−3.14676e25			−0.467554			−0.233777	+	0.972290i	$0.575109\pi$
$98$		−	1.65913e26i		−	2.15745i
$99$	−3.64460e25	−	3.56430e25i	−0.415329	−	0.406178i
$100$	7.82791e24			0.0782791
$101$			8.23542e25i			0.723615i	0.932253	+	0.361808i	$0.117840\pi$
$101$			8.23542e25i			0.723615i	−0.932253	+	0.361808i	$0.882160\pi$
$102$	5.10769e25	+	1.21394e26i	0.394841	+	0.938415i
$103$	3.23565e25			0.220332			0.110166	−	0.993913i	$-0.464862\pi$
$103$	3.23565e25			0.220332			0.110166	+	0.993913i	$0.464862\pi$
$104$			1.06257e26i			0.638149i
$105$	2.80043e26	−	1.17829e26i	1.48513	−	0.624872i
$106$	−2.91332e26			−1.36588
$107$			2.11400e26i			0.877235i	0.898674	+	0.438617i	$0.144532\pi$
$107$			2.11400e26i			0.877235i	−0.898674	+	0.438617i	$0.855468\pi$
$108$	−7.31798e25	−	2.88894e25i	−0.269081	−	0.106226i
$109$	−4.44000e26			−1.44823			−0.724116	−	0.689678i	$-0.757752\pi$
$109$	−4.44000e26			−1.44823			−0.724116	+	0.689678i	$0.757752\pi$
$110$			1.44398e26i			0.418269i
$111$	−1.55554e25	−	3.69703e25i	−0.0400573	−	0.0952037i
$112$	5.16167e26			1.18292
$113$		−	3.62279e26i		−	0.739645i	−0.929103	−	0.369822i	$-0.879419\pi$
$113$		−	3.62279e26i		−	0.739645i	0.929103	−	0.369822i	$-0.120581\pi$
$114$	−3.29693e25	+	1.38720e25i	−0.0600270	+	0.0252566i
$115$	1.71158e26			0.278179
$116$			2.35273e26i			0.341679i
$117$	3.16035e26	−	3.23155e26i	0.410505	−	0.419753i
$118$	−2.67195e26			−0.310715
$119$		−	2.18638e27i		−	2.27832i
$120$	3.85187e26	+	9.15470e26i	0.360011	+	0.855634i
$121$	7.89604e26			0.662521
$122$			7.84824e26i			0.591691i
$123$	−1.91390e27	+	8.05279e26i	−1.29763	+	0.545984i
$124$	5.05235e25			0.0308327
$125$			1.97388e27i			1.08515i
$126$	−2.29406e27	−	2.24352e27i	−1.13707	−	1.11202i
$127$	2.03638e27			0.910775			0.455388	−	0.890293i	$-0.349501\pi$
$127$	2.03638e27			0.910775			0.455388	+	0.890293i	$0.349501\pi$
$128$			9.08866e26i			0.367088i
$129$	8.35263e26	+	1.98516e27i	0.304900	+	0.724651i
$130$	−1.28033e27			−0.422724
$131$			1.06949e27i			0.319632i	0.987147	+	0.159816i	$0.0510901\pi$
$131$			1.06949e27i			0.319632i	−0.987147	+	0.159816i	$0.948910\pi$
$132$	−5.72167e26	+	2.40741e26i	−0.154904	+	0.0651762i
$133$	5.93798e26			0.145736
$134$		−	3.23620e27i		−	0.720565i
$135$	1.55139e27	−	3.92984e27i	0.313605	−	0.794394i
$136$	7.14736e27			1.31262
$137$			1.02973e27i			0.171931i	0.996298	+	0.0859657i	$0.0273975\pi$
$137$			1.02973e27i			0.171931i	−0.996298	+	0.0859657i	$0.972602\pi$
$138$	−7.01046e26	−	1.66617e27i	−0.106492	−	0.253099i
$139$	−1.19179e28			−1.64818			−0.824092	−	0.566456i	$-0.808314\pi$
$139$	−1.19179e28			−1.64818			−0.824092	+	0.566456i	$0.808314\pi$
$140$		−	3.69960e27i		−	0.466112i
$141$	1.88813e27	−	7.94438e26i	0.216862	−	0.0912455i
$142$	3.89682e27			0.408284
$143$		−	3.56630e27i		−	0.341074i
$144$	5.01867e27	−	5.13173e27i	0.438406	−	0.448283i
$145$	−1.26344e28			−1.00872
$146$			1.03431e28i			0.755204i
$147$	1.48543e28	+	3.53041e28i	0.992493	+	2.35885i
$148$	−4.88408e26			−0.0298800
$149$		−	2.75606e27i		−	0.154478i	−0.997013	−	0.0772390i	$-0.975390\pi$
$149$		−	2.75606e27i		−	0.154478i	0.997013	−	0.0772390i	$-0.0246104\pi$
$150$	4.09215e27	−	1.72179e27i	0.210264	−	0.0884694i
$151$	−6.47428e27			−0.305134			−0.152567	−	0.988293i	$-0.548754\pi$
$151$	−6.47428e27			−0.305134			−0.152567	+	0.988293i	$0.548754\pi$
$152$			1.94115e27i			0.0839637i
$153$	−2.17370e28	−	2.12581e28i	−0.863400	−	0.844377i
$154$	−2.53170e28			−0.923937
$155$			2.71317e27i			0.0910259i
$156$	−2.13457e27	−	5.07322e27i	−0.0658705	−	0.156554i
$157$	2.34823e28			0.666877			0.333438	−	0.942772i	$-0.391791\pi$
$157$	2.34823e28			0.666877			0.333438	+	0.942772i	$0.391791\pi$
$158$		−	2.96246e28i		−	0.774659i
$159$	6.19918e28	−	2.60833e28i	1.49339	−	0.628347i
$160$	2.14746e28			0.476832
$161$			3.00087e28i			0.614485i
$162$	−4.46102e28	+	9.93931e26i	−0.842827	+	0.0187785i
$163$	1.16159e28			0.202589			0.101294	−	0.994856i	$-0.467702\pi$
$163$	1.16159e28			0.202589			0.101294	+	0.994856i	$0.467702\pi$
$164$			2.52842e28i			0.407267i
$165$	−1.29281e28	−	3.07260e28i	−0.192416	−	0.457314i
$166$	9.55062e28			1.31409
$167$		−	8.16140e28i		−	1.03860i	−0.854591	−	0.519302i	$-0.826192\pi$
$167$		−	8.16140e28i		−	1.03860i	0.854591	−	0.519302i	$-0.173808\pi$
$168$	−1.60508e29	+	6.75341e28i	−1.89006	+	0.795248i
$169$	−6.01121e28			−0.655292
$170$			8.61214e28i			0.869511i
$171$	5.77348e27	−	5.90355e27i	0.0540118	−	0.0552286i
$172$	2.62256e28			0.227434
$173$			6.03281e28i			0.485199i	0.970126	+	0.242600i	$0.0780002\pi$
$173$			6.03281e28i			0.485199i	−0.970126	+	0.242600i	$0.922000\pi$
$174$	5.17494e28	+	1.22992e29i	0.386158	+	0.917778i
$175$	−7.37022e28			−0.510489
$176$		−	5.66332e28i		−	0.364256i
$177$	5.68557e28	−	2.39222e28i	0.339721	−	0.142939i
$178$	1.41812e29			0.787503
$179$		−	4.70459e28i		−	0.242903i	−0.992597	−	0.121451i	$-0.961245\pi$
$179$		−	4.70459e28i		−	0.242903i	0.992597	−	0.121451i	$-0.0387549\pi$
$180$	−3.67815e28	−	3.59711e28i	−0.176639	−	0.172747i
$181$	9.02584e28			0.403335			0.201668	−	0.979454i	$-0.435364\pi$
$181$	9.02584e28			0.403335			0.201668	+	0.979454i	$0.435364\pi$
$182$		−	2.24477e29i		−	0.933780i
$183$	−7.02661e28	−	1.67001e29i	−0.272196	−	0.646925i
$184$	−9.80996e28			−0.354026
$185$		−	2.62281e28i		−	0.0882133i
$186$	2.64119e28	−	1.11129e28i	0.0828192	−	0.0348465i
$187$	−2.39887e29			−0.701562
$188$		−	2.49438e28i		−	0.0680629i
$189$	6.89011e29	+	2.72002e29i	1.75478	+	0.692739i
$190$	−2.33896e28			−0.0556195
$191$			3.87159e29i			0.859916i	0.902849	+	0.429958i	$0.141472\pi$
$191$			3.87159e29i			0.859916i	−0.902849	+	0.429958i	$0.858528\pi$
$192$	−2.05132e29	−	4.87535e29i	−0.425714	−	1.01179i
$193$	−8.50418e29			−1.64963			−0.824817	−	0.565400i	$-0.808722\pi$
$193$	−8.50418e29			−1.64963			−0.824817	+	0.565400i	$0.808722\pi$
$194$			2.17320e29i			0.394165i
$195$	2.72437e29	−	1.14629e29i	0.462186	−	0.194466i
$196$	4.66397e29			0.740332
$197$			1.10042e30i			1.63493i	0.575977	+	0.817466i	$0.304622\pi$
$197$			1.10042e30i			1.63493i	−0.575977	+	0.817466i	$0.695378\pi$
$198$	−2.46156e29	+	2.51702e29i	−0.342423	+	0.350137i
$199$	−1.76150e29			−0.229505			−0.114753	−	0.993394i	$-0.536608\pi$
$199$	−1.76150e29			−0.229505			−0.114753	+	0.993394i	$0.536608\pi$
$200$		−	2.40935e29i		−	0.294110i
$201$	2.89740e29	+	6.88623e29i	0.331482	+	0.787830i
$202$	5.68751e29			0.610034
$203$		−	2.21517e30i		−	2.22822i
$204$	−3.41251e29	+	1.43582e29i	−0.322019	+	0.135490i
$205$	−1.35779e30			−1.20235
$206$		−	2.23459e29i		−	0.185748i
$207$	2.98347e29	+	2.91774e29i	0.232867	+	0.227736i
$208$	5.02148e29			0.368136
$209$		−	6.51508e28i		−	0.0448764i
$210$	−8.13746e29	−	1.93402e30i	−0.526790	−	1.25202i
$211$	2.90897e30			1.77038			0.885191	−	0.465228i	$-0.154028\pi$
$211$	2.90897e30			1.77038			0.885191	+	0.465228i	$0.154028\pi$
$212$		−	8.18964e29i		−	0.468704i
$213$	−8.29194e29	+	3.48886e29i	−0.446397	+	0.187823i
$214$	1.45996e30			0.739541
$215$			1.40835e30i			0.671443i
$216$	−8.89185e29	+	2.25240e30i	−0.399111	+	1.01099i
$217$	−4.75695e29			−0.201072
$218$			3.06633e30i			1.22091i
$219$	−9.26029e29	−	2.20088e30i	−0.347417	−	0.825703i
$220$	−4.05916e29			−0.143530
$221$		−	2.12700e30i		−	0.709036i
$222$	−2.55322e29	+	1.07428e29i	−0.0802602	+	0.0337698i
$223$	−2.33027e30			−0.690944			−0.345472	−	0.938429i	$-0.612281\pi$
$223$	−2.33027e30			−0.690944			−0.345472	+	0.938429i	$0.612281\pi$
$224$			3.76510e30i			1.05330i
$225$	−7.16605e29	+	7.32749e29i	−0.189194	+	0.193456i
$226$	−2.50195e30			−0.623547
$227$		−	6.02266e29i		−	0.141727i	−0.997486	−	0.0708634i	$-0.977425\pi$
$227$		−	6.02266e29i		−	0.141727i	0.997486	−	0.0708634i	$-0.0225755\pi$
$228$	−3.89954e28	−	9.26800e28i	−0.00866684	−	0.0205984i
$229$	2.90554e30			0.610050			0.305025	−	0.952344i	$-0.401335\pi$
$229$	2.90554e30			0.610050			0.305025	+	0.952344i	$0.401335\pi$
$230$		−	1.18204e30i		−	0.234515i
$231$	5.38713e30	−	2.26665e30i	1.01019	−	0.425039i
$232$	7.24146e30			1.28376
$233$		−	8.98718e29i		−	0.150659i	−0.997159	−	0.0753297i	$-0.975999\pi$
$233$		−	8.98718e29i		−	0.150659i	0.997159	−	0.0753297i	$-0.0240009\pi$
$234$	−2.23176e30	−	2.18259e30i	−0.353868	−	0.346071i
$235$	1.33951e30			0.200939
$236$		−	7.51112e29i		−	0.106622i
$237$	2.65232e30	+	6.30374e30i	0.356367	+	0.846974i
$238$	−1.50995e31			−1.92071
$239$		−	1.49139e31i		−	1.79646i	−0.439524	−	0.898231i	$-0.644853\pi$
$239$		−	1.49139e31i		−	1.79646i	0.439524	−	0.898231i	$-0.355147\pi$
$240$	4.32634e30	−	1.82032e30i	0.493599	−	0.207683i
$241$	−9.48024e30			−1.02470			−0.512351	−	0.858776i	$-0.671225\pi$
$241$	−9.48024e30			−1.02470			−0.512351	+	0.858776i	$0.671225\pi$
$242$		−	5.45313e30i		−	0.558529i
$243$	9.40349e30	−	4.20549e30i	0.912867	−	0.408258i
$244$	−2.20622e30			−0.203040
$245$			2.50460e31i			2.18565i
$246$	5.56138e30	+	1.32177e31i	0.460284	+	1.09395i
$247$	5.77671e29			0.0453545
$248$		−	1.55506e30i		−	0.115845i
$249$	−2.03225e31	+	8.55076e30i	−1.43676	+	0.604524i
$250$	1.36319e31			0.914824
$251$			9.53997e30i			0.607839i	0.952698	+	0.303919i	$0.0982954\pi$
$251$			9.53997e30i			0.607839i	−0.952698	+	0.303919i	$0.901705\pi$
$252$	6.30675e30	−	6.44883e30i	0.381591	−	0.390188i
$253$	3.29252e30			0.189218
$254$		−	1.40636e31i		−	0.767817i
$255$	−7.71053e30	−	1.83255e31i	−0.400002	−	0.950680i
$256$	−1.59873e31			−0.788234
$257$			2.95289e31i			1.38394i	0.721927	+	0.691970i	$0.243257\pi$
$257$			2.95289e31i			1.38394i	−0.721927	+	0.691970i	$0.756743\pi$
$258$	1.37098e31	−	5.76845e30i	0.610908	−	0.257041i
$259$	4.59852e30			0.194859
$260$		−	3.59913e30i		−	0.145059i
$261$	−2.20232e31	−	2.15380e31i	−0.844412	−	0.825808i
$262$	7.38607e30			0.269462
$263$		−	4.55126e31i		−	1.58018i	−0.612989	−	0.790092i	$-0.710033\pi$
$263$		−	4.55126e31i		−	1.58018i	0.612989	−	0.790092i	$-0.289967\pi$
$264$	7.40976e30	+	1.76107e31i	0.244880	+	0.582004i
$265$	4.39793e31			1.38373
$266$		−	4.10086e30i		−	0.122861i
$267$	−3.01757e31	+	1.26965e31i	−0.861016	+	0.362275i
$268$	9.09728e30			0.247263
$269$			1.57251e31i			0.407206i	0.979054	+	0.203603i	$0.0652652\pi$
$269$			1.57251e31i			0.407206i	−0.979054	+	0.203603i	$0.934735\pi$
$270$	−2.71401e31	−	1.07141e31i	−0.669703	−	0.264380i
$271$	1.74298e31			0.409913			0.204957	−	0.978771i	$-0.434295\pi$
$271$	1.74298e31			0.409913			0.204957	+	0.978771i	$0.434295\pi$
$272$		−	3.37771e31i		−	0.757227i
$273$	2.00977e31	+	4.77659e31i	0.429567	+	1.02095i
$274$	7.11146e30			0.144944
$275$			8.08652e30i			0.157194i
$276$	4.68376e30	−	1.97071e30i	0.0868514	−	0.0365430i
$277$	−3.68085e31			−0.651195			−0.325598	−	0.945508i	$-0.605565\pi$
$277$	−3.68085e31			−0.651195			−0.325598	+	0.945508i	$0.605565\pi$
$278$			8.23065e31i			1.38948i
$279$	−4.62517e30	+	4.72936e30i	−0.0745200	+	0.0761988i
$280$	−1.13870e32			−1.75128
$281$			3.00160e31i			0.440728i	0.975418	+	0.220364i	$0.0707245\pi$
$281$			3.00160e31i			0.440728i	−0.975418	+	0.220364i	$0.929276\pi$
$282$	−5.48651e30	−	1.30397e31i	−0.0769233	−	0.182823i
$283$	1.14970e32			1.53944			0.769719	−	0.638382i	$-0.220396\pi$
$283$	1.14970e32			1.53944			0.769719	+	0.638382i	$0.220396\pi$
$284$			1.09544e31i			0.140103i
$285$	4.97702e30	−	2.09410e30i	0.0608115	−	0.0255867i
$286$	−2.46294e31			−0.287538
$287$		−	2.38059e32i		−	2.65595i
$288$	3.74327e31	+	3.66079e31i	0.399161	+	0.390367i
$289$	−4.49724e31			−0.458432
$290$			8.72553e31i			0.850389i
$291$	−1.94569e31	−	4.62430e31i	−0.181328	−	0.430960i
$292$	−2.90755e31			−0.259150
$293$			6.05334e31i			0.516079i	0.966134	+	0.258039i	$0.0830764\pi$
$293$			6.05334e31i			0.516079i	−0.966134	+	0.258039i	$0.916924\pi$
$294$	2.43816e32	−	1.02586e32i	1.98859	−	0.836708i
$295$	4.03355e31			0.314776
$296$			1.50327e31i			0.112265i
$297$	2.98438e31	−	7.55975e31i	0.213314	−	0.540348i
$298$	−1.90338e31			−0.130231
$299$			2.91937e31i			0.191234i
$300$	4.84011e30	+	1.15034e31i	0.0303584	+	0.0721525i
$301$	−2.46922e32			−1.48319
$302$			4.47124e31i			0.257239i
$303$	−1.21023e32	+	5.09208e31i	−0.666981	+	0.280634i
$304$	9.17349e30			0.0484371
$305$		−	1.18476e32i		−	0.599424i
$306$	−1.46812e32	+	1.50119e32i	−0.711841	+	0.727877i
$307$	8.33385e31			0.387300			0.193650	−	0.981071i	$-0.437967\pi$
$307$	8.33385e31			0.387300			0.193650	+	0.981071i	$0.437967\pi$
$308$		−	7.11685e31i		−	0.317050i
$309$	2.00065e31	+	4.75493e31i	0.0854499	+	0.203088i
$310$	1.87376e31			0.0767381
$311$			4.43574e32i			1.74213i	0.491165	+	0.871067i	$0.336571\pi$
$311$			4.43574e32i			1.74213i	−0.491165	+	0.871067i	$0.663429\pi$
$312$	−1.56148e32	+	6.57000e31i	−0.588204	+	0.247489i
$313$	3.26202e32			1.17872			0.589360	−	0.807871i	$-0.299380\pi$
$313$	3.26202e32			1.17872			0.589360	+	0.807871i	$0.299380\pi$
$314$		−	1.62173e32i		−	0.562202i
$315$	3.46309e32	+	3.38679e32i	1.15193	+	1.12655i
$316$	8.32777e31			0.265826
$317$		−	2.02393e32i		−	0.620047i	−0.950729	−	0.310023i	$-0.899663\pi$
$317$		−	2.02393e32i		−	0.620047i	0.950729	−	0.310023i	$-0.100337\pi$
$318$	−1.80135e32	−	4.28125e32i	−0.529719	−	1.25898i
$319$	−2.43046e32			−0.686134
$320$		−	3.45876e32i		−	0.937498i
$321$	−3.10661e32	+	1.30712e32i	−0.808577	+	0.340212i
$322$	2.07245e32			0.518033
$323$		−	3.88571e31i		−	0.0932906i
$324$	−2.79404e30	−	1.25404e32i	−0.00644388	−	0.289218i
$325$	−7.17006e31			−0.158869
$326$		−	8.02215e31i		−	0.170790i
$327$	−2.74532e32	−	6.52476e32i	−0.561657	−	1.33488i
$328$	7.78222e32			1.53018
$329$			2.34854e32i			0.443865i
$330$	−2.12198e32	+	8.92832e31i	−0.385532	+	0.162214i
$331$	1.37471e32			0.240131			0.120066	−	0.992766i	$-0.461690\pi$
$331$	1.37471e32			0.240131			0.120066	+	0.992766i	$0.461690\pi$
$332$			2.68477e32i			0.450933i
$333$	4.47112e31	−	4.57185e31i	0.0722174	−	0.0738443i
$334$	−5.63639e32			−0.875582
$335$			4.88534e32i			0.729982i
$336$	3.19153e32	+	7.58528e32i	0.458763	+	1.09034i
$337$	5.38851e32			0.745212			0.372606	−	0.927990i	$-0.378464\pi$
$337$	5.38851e32			0.745212			0.372606	+	0.927990i	$0.378464\pi$
$338$			4.15144e32i			0.552435i
$339$	5.32384e32	−	2.24002e32i	0.681756	−	0.286851i
$340$	−2.42096e32			−0.298374
$341$			5.21927e31i			0.0619160i
$342$	−4.07708e31	−	3.98726e31i	−0.0465597	−	0.0455339i
$343$	−2.67536e33			−2.94143
$344$		−	8.07198e32i		−	0.854516i
$345$	1.05829e32	+	2.51523e32i	0.107884	+	0.256407i
$346$	4.16635e32			0.409041
$347$			4.22062e31i			0.0399110i	0.999801	+	0.0199555i	$0.00635246\pi$
$347$			4.22062e31i			0.0399110i	−0.999801	+	0.0199555i	$0.993648\pi$
$348$	−3.45744e32	+	1.45473e32i	−0.314937	+	0.132511i
$349$	9.56464e32			0.839341			0.419670	−	0.907677i	$-0.362146\pi$
$349$	9.56464e32			0.839341			0.419670	+	0.907677i	$0.362146\pi$
$350$			5.08999e32i			0.430361i
$351$	6.70298e32	+	2.64615e32i	0.546104	+	0.215587i
$352$	4.13102e32			0.324342
$353$		−	1.63888e33i		−	1.24016i	−0.784539	−	0.620079i	$-0.787100\pi$
$353$		−	1.63888e33i		−	1.24016i	0.784539	−	0.620079i	$-0.212900\pi$
$354$	−1.65211e32	−	3.92655e32i	−0.120502	−	0.286397i
$355$	−5.88261e32			−0.413620
$356$			3.98647e32i			0.270233i
$357$	3.21298e33	−	1.35187e33i	2.10001	−	0.883586i
$358$	−3.24907e32			−0.204776
$359$		−	1.00603e33i		−	0.611484i	−0.952114	−	0.305742i	$-0.901095\pi$
$359$		−	1.00603e33i		−	0.611484i	0.952114	−	0.305742i	$-0.0989045\pi$
$360$	−1.10715e33	+	1.13210e33i	−0.649046	+	0.663668i
$361$	−1.75790e33			−0.994033
$362$		−	6.23339e32i		−	0.340026i
$363$	4.88224e32	+	1.16036e33i	0.256941	+	0.610668i
$364$	6.31028e32			0.320428
$365$		−	1.56139e33i		−	0.765074i
$366$	−1.15333e33	+	4.85268e32i	−0.545381	+	0.229471i
$367$	2.89094e33			1.31941			0.659706	−	0.751524i	$-0.270681\pi$
$367$	2.89094e33			1.31941			0.659706	+	0.751524i	$0.270681\pi$
$368$			4.63600e32i			0.204231i
$369$	−2.36678e33	−	2.31464e33i	−1.00650	−	0.984328i
$370$	−1.81135e32			−0.0743670
$371$			7.71080e33i			3.05660i
$372$	3.12394e31	+	7.42464e31i	0.0119576	+	0.0284196i
$373$	−1.41727e33			−0.523887			−0.261943	−	0.965083i	$-0.584363\pi$
$373$	−1.41727e33			−0.523887			−0.261943	+	0.965083i	$0.584363\pi$
$374$			1.65670e33i			0.591443i
$375$	−2.90070e33	+	1.22048e33i	−1.00022	+	0.420847i
$376$	−7.67745e32			−0.255726
$377$		−	2.15501e33i		−	0.693444i
$378$	1.87849e33	−	4.75842e33i	0.584004	−	1.47934i
$379$	7.08401e32			0.212799			0.106399	−	0.994323i	$-0.466068\pi$
$379$	7.08401e32			0.212799			0.106399	+	0.994323i	$0.466068\pi$
$380$		−	6.57506e31i		−	0.0190859i
$381$	1.25913e33	+	2.99255e33i	0.353219	+	0.839492i
$382$	2.67378e33			0.724940
$383$		−	4.75619e33i		−	1.24645i	−0.782042	−	0.623225i	$-0.785822\pi$
$383$		−	4.75619e33i		−	1.24645i	0.782042	−	0.623225i	$-0.214178\pi$
$384$	−1.33562e33	+	5.61965e32i	−0.338357	+	0.142365i
$385$	3.82183e33			0.936012
$386$			5.87312e33i			1.39070i
$387$	−2.40082e33	+	2.45491e33i	−0.549689	+	0.562073i
$388$	−6.10909e32			−0.135258
$389$		−	3.55104e33i		−	0.760345i	−0.924916	−	0.380172i	$-0.875865\pi$
$389$		−	3.55104e33i		−	0.760345i	0.924916	−	0.380172i	$-0.124135\pi$
$390$	−7.91645e32	−	1.88149e33i	−0.163942	−	0.389640i
$391$	1.96372e33			0.393352
$392$		−	1.43552e34i		−	2.78158i
$393$	−1.57166e33	+	6.61282e32i	−0.294616	+	0.123961i
$394$	7.59971e33			1.37831
$395$			4.47211e33i			0.784783i
$396$	−7.07558e32	−	6.91969e32i	−0.120150	−	0.117503i
$397$	−1.15977e34			−1.90588			−0.952938	−	0.303164i	$-0.901957\pi$
$397$	−1.15977e34			−1.90588			−0.952938	+	0.303164i	$0.901957\pi$
$398$			1.21652e33i			0.193481i
$399$	3.67154e32	+	8.72611e32i	0.0565198	+	0.134330i
$400$	−1.13861e33			−0.169667
$401$			4.69837e33i			0.677752i	0.940831	+	0.338876i	$0.110047\pi$
$401$			4.69837e33i			0.677752i	−0.940831	+	0.338876i	$0.889953\pi$
$402$	4.75573e33	−	2.00099e33i	0.664169	−	0.279452i
$403$	−4.62775e32			−0.0625756
$404$			1.59881e33i			0.209334i
$405$	6.73431e33	−	1.50043e32i	0.853842	−	0.0190239i
$406$	−1.52983e34			−1.87847
$407$		−	5.04544e32i		−	0.0600028i
$408$	4.41932e33	+	1.05033e34i	0.509065	+	1.20989i
$409$	1.30144e34			1.45218			0.726089	−	0.687601i	$-0.241336\pi$
$409$	1.30144e34			1.45218			0.726089	+	0.687601i	$0.241336\pi$
$410$			9.37710e33i			1.01363i
$411$	−1.51323e33	+	6.36696e32i	−0.158475	+	0.0666789i
$412$	6.28166e32			0.0637398
$413$			7.07196e33i			0.695327i
$414$	2.01504e33	−	2.06043e33i	0.191990	−	0.196315i
$415$	−1.44175e34			−1.33127
$416$			3.66284e33i			0.327797i
$417$	−7.36898e33	−	1.75138e34i	−0.639203	−	1.51919i
$418$	−4.49942e32			−0.0378325
$419$		−	1.08310e34i		−	0.882848i	−0.897299	−	0.441424i	$-0.854474\pi$
$419$		−	1.08310e34i		−	0.882848i	0.897299	−	0.441424i	$-0.145526\pi$
$420$	5.43672e33	−	2.28752e33i	0.429632	−	0.180769i
$421$	7.21830e33			0.553054			0.276527	−	0.961006i	$-0.410816\pi$
$421$	7.21830e33			0.553054			0.276527	+	0.961006i	$0.410816\pi$
$422$		−	2.00898e34i		−	1.49250i
$423$	2.33492e33	+	2.28348e33i	0.168208	+	0.164502i
$424$	−2.52069e34			−1.76102
$425$			4.82295e33i			0.326781i
$426$	2.40946e33	+	5.72654e33i	0.158342	+	0.376329i
$427$	2.07722e34			1.32410
$428$			4.10409e33i			0.253775i
$429$	5.24082e33	−	2.20509e33i	0.314380	−	0.132276i
$430$	9.72625e33			0.566051
$431$		−	3.64644e33i		−	0.205904i	−0.994686	−	0.102952i	$-0.967171\pi$
$431$		−	3.64644e33i		−	0.205904i	0.994686	−	0.102952i	$-0.0328288\pi$
$432$	1.06444e34	+	4.20212e33i	0.583221	+	0.230239i
$433$	1.68552e34			0.896174			0.448087	−	0.893990i	$-0.352105\pi$
$433$	1.68552e34			0.896174			0.448087	+	0.893990i	$0.352105\pi$
$434$			3.28522e33i			0.169511i
$435$	−7.81205e33	−	1.85668e34i	−0.391205	−	0.929773i
$436$	−8.61976e33			−0.418958
$437$			5.33325e32i			0.0251613i
$438$	−1.51996e34	+	6.39530e33i	−0.696097	+	0.292885i
$439$	1.11671e34			0.496480			0.248240	−	0.968699i	$-0.420148\pi$
$439$	1.11671e34			0.496480			0.248240	+	0.968699i	$0.420148\pi$
$440$			1.24937e34i			0.539269i
$441$	−4.26962e34	+	4.36581e34i	−1.78932	+	1.82963i
$442$	−1.46894e34			−0.597744
$443$		−	3.64304e34i		−	1.43951i	−0.694227	−	0.719756i	$-0.744254\pi$
$443$		−	3.64304e34i		−	1.43951i	0.694227	−	0.719756i	$-0.255746\pi$
$444$	−3.01990e32	−	7.17737e32i	−0.0115881	−	0.0275414i
$445$	−2.14078e34			−0.797795
$446$			1.60932e34i			0.582491i
$447$	4.05014e33	−	1.70411e33i	0.142388	−	0.0599101i
$448$	6.06417e34			2.07089
$449$			1.73953e34i			0.577072i	0.957469	+	0.288536i	$0.0931685\pi$
$449$			1.73953e34i			0.577072i	−0.957469	+	0.288536i	$0.906831\pi$
$450$	5.06048e33	+	4.94898e33i	0.163091	+	0.159497i
$451$	−2.61195e34			−0.817843
$452$		−	7.03324e33i		−	0.213971i
$453$	−4.00314e33	−	9.51422e33i	−0.118338	−	0.281253i
$454$	−4.15934e33			−0.119481
$455$			3.38869e34i			0.945984i
$456$	−2.85260e33	+	1.20024e33i	−0.0773922	+	0.0325630i
$457$	2.59048e34			0.683076			0.341538	−	0.939868i	$-0.389052\pi$
$457$	2.59048e34			0.683076			0.341538	+	0.939868i	$0.389052\pi$
$458$		−	2.00661e34i		−	0.514294i
$459$	1.77994e34	−	4.50877e34i	0.443445	−	1.12329i
$460$	3.32283e33			0.0804742
$461$			1.24046e34i			0.292060i	0.989280	+	0.146030i	$0.0466496\pi$
$461$			1.24046e34i			0.292060i	−0.989280	+	0.146030i	$0.953350\pi$
$462$	−1.56539e34	−	3.72043e34i	−0.358324	−	0.851624i
$463$	5.33047e34			1.18635			0.593175	−	0.805073i	$-0.297874\pi$
$463$	5.33047e34			1.18635			0.593175	+	0.805073i	$0.297874\pi$
$464$		−	3.42218e34i		−	0.740574i
$465$	−3.98712e33	+	1.67759e33i	−0.0839016	+	0.0353019i
$466$	−6.20669e33			−0.127011
$467$		−	8.65230e33i		−	0.172192i	−0.996287	−	0.0860958i	$-0.972561\pi$
$467$		−	8.65230e33i		−	0.172192i	0.996287	−	0.0860958i	$-0.0274391\pi$
$468$	6.13546e33	−	6.27369e33i	0.118755	−	0.121430i
$469$	−8.56538e34			−1.61250
$470$		−	9.25086e33i		−	0.169399i
$471$	1.45195e34	+	3.45083e34i	0.258630	+	0.614683i
$472$	−2.31185e34			−0.400602
$473$			2.70920e34i			0.456717i
$474$	4.35346e34	−	1.83173e34i	0.714030	−	0.300430i
$475$	−1.30986e33			−0.0209030
$476$		−	4.24462e34i		−	0.659095i
$477$	7.66609e34	+	7.49719e34i	1.15834	+	1.13282i
$478$	−1.02998e35			−1.51448
$479$			3.25576e34i			0.465897i	0.972489	+	0.232949i	$0.0748374\pi$
$479$			3.25576e34i			0.465897i	−0.972489	+	0.232949i	$0.925163\pi$
$480$	1.32781e34	+	3.15578e34i	0.184926	+	0.439512i
$481$	4.47363e33			0.0606420
$482$			6.54720e34i			0.863861i
$483$	−4.40991e34	+	1.85548e34i	−0.566392	+	0.238311i
$484$	1.53293e34			0.191660
$485$		−	3.28065e34i		−	0.399316i
$486$	−2.90437e34	−	6.49419e34i	−0.344176	−	0.769580i
$487$	−1.32385e34			−0.152744			−0.0763718	−	0.997079i	$-0.524334\pi$
$487$	−1.32385e34			−0.152744			−0.0763718	+	0.997079i	$0.524334\pi$
$488$			6.79052e34i			0.762860i
$489$	7.18230e33	+	1.70701e34i	0.0785685	+	0.186733i
$490$	1.72972e35			1.84258
$491$		−	5.47725e34i		−	0.568203i	−0.958794	−	0.284101i	$-0.908305\pi$
$491$		−	5.47725e34i		−	0.568203i	0.958794	−	0.284101i	$-0.0916952\pi$
$492$	−3.71562e34	+	1.56336e34i	−0.375392	+	0.157947i
$493$	−1.44957e35			−1.42636
$494$		−	3.98949e33i		−	0.0382355i
$495$	3.71595e34	−	3.79966e34i	0.346898	−	0.354713i
$496$	−7.34893e33			−0.0668286
$497$		−	1.03139e35i		−	0.913668i
$498$	5.90529e34	+	1.40350e35i	0.509635	+	1.21124i
$499$	−7.35107e33			−0.0618079			−0.0309039	−	0.999522i	$-0.509839\pi$
$499$	−7.35107e33			−0.0618079			−0.0309039	+	0.999522i	$0.509839\pi$
$500$			3.83207e34i			0.313924i
$501$	1.19935e35	−	5.04631e34i	0.957317	−	0.402794i
$502$	6.58845e34			0.512430
$503$		−	2.09921e35i		−	1.59101i	−0.605949	−	0.795503i	$-0.707207\pi$
$503$		−	2.09921e35i		−	1.59101i	0.605949	−	0.795503i	$-0.292793\pi$
$504$	−1.98488e35	−	1.94115e35i	−1.46601	−	1.43371i
$505$	−8.58581e34			−0.618007
$506$		−	2.27387e34i		−	0.159517i
$507$	−3.71682e34	−	8.83373e34i	−0.254137	−	0.604005i
$508$	3.95341e34			0.263478
$509$			2.02711e35i			1.31688i	0.752633	+	0.658441i	$0.228784\pi$
$509$			2.02711e35i			1.31688i	−0.752633	+	0.658441i	$0.771216\pi$
$510$	−1.26559e35	+	5.32501e34i	−0.801458	+	0.337216i
$511$	2.73755e35			1.69002
$512$			1.71404e35i			1.03160i
$513$	1.22453e34	+	4.83412e33i	0.0718530	+	0.0283656i
$514$	2.03931e35			1.16671
$515$			3.37332e34i			0.188176i
$516$	1.62157e34	+	3.85397e34i	0.0882042	+	0.209634i
$517$	2.57679e34			0.136679
$518$		−	3.17581e34i		−	0.164273i
$519$	−8.86547e34	+	3.73018e34i	−0.447225	+	0.188171i
$520$	−1.10777e35			−0.545014
$521$			1.85639e35i			0.890796i	0.895333	+	0.445398i	$0.146938\pi$
$521$			1.85639e35i			0.890796i	−0.895333	+	0.445398i	$0.853062\pi$
$522$	−1.48745e35	+	1.52096e35i	−0.696186	+	0.711871i
$523$	−1.31184e35			−0.598906			−0.299453	−	0.954111i	$-0.596804\pi$
$523$	−1.31184e35			−0.598906			−0.299453	+	0.954111i	$0.596804\pi$
$524$			2.07630e34i			0.0924662i
$525$	−4.55712e34	−	1.08309e35i	−0.197979	−	0.470535i
$526$	−3.14317e35			−1.33215
$527$			3.11286e34i			0.128713i
$528$	8.32248e34	−	3.50171e34i	0.335747	−	0.141267i
$529$	2.27100e35			0.893909
$530$		−	3.03728e35i		−	1.16654i
$531$	7.03095e34	+	6.87604e34i	0.263503	+	0.257697i
$532$	1.15279e34			0.0421599
$533$		−	2.31593e35i		−	0.826555i
$534$	8.76843e34	+	2.08398e35i	0.305411	+	0.725868i
$535$	−2.20394e35			−0.749206
$536$		−	2.80005e35i		−	0.929017i
$537$	6.91360e34	−	2.90892e34i	0.223892	−	0.0942033i
$538$	1.08600e35			0.343290
$539$			4.81805e35i			1.48668i
$540$	3.01185e34	−	7.62934e34i	0.0907225	−	0.229810i
$541$	4.02730e35			1.18427			0.592134	−	0.805840i	$-0.298286\pi$
$541$	4.02730e35			1.18427			0.592134	+	0.805840i	$0.298286\pi$
$542$		−	1.20373e35i		−	0.345572i
$543$	5.58081e34	+	1.32639e35i	0.156423	+	0.371768i
$544$	2.46382e35			0.674253
$545$		−	4.62891e35i		−	1.23687i
$546$	3.29879e35	−	1.38798e35i	0.860697	−	0.362141i
$547$	−6.57248e35			−1.67453			−0.837267	−	0.546795i	$-0.815848\pi$
$547$	−6.57248e35			−1.67453			−0.837267	+	0.546795i	$0.815848\pi$
$548$			1.99910e34i			0.0497379i
$549$	2.01968e35	−	2.06518e35i	0.490729	−	0.501784i
$550$	5.58468e34			0.132521
$551$		−	3.93687e34i		−	0.0912390i
$552$	−6.06564e34	−	1.44161e35i	−0.137299	−	0.326318i
$553$	−7.84086e35			−1.73355
$554$			2.54205e35i			0.548981i
$555$	3.85432e34	−	1.62172e34i	0.0813092	−	0.0342111i
$556$	−2.31372e35			−0.476802
$557$			6.22563e35i			1.25333i	0.779288	+	0.626665i	$0.215581\pi$
$557$			6.22563e35i			1.25333i	−0.779288	+	0.626665i	$0.784419\pi$
$558$	3.26617e34	+	3.19421e34i	0.0642384	+	0.0628231i
$559$	−2.40216e35			−0.461582
$560$			5.38128e35i			1.01028i
$561$	−1.48326e35	−	3.52524e35i	−0.272082	−	0.646654i
$562$	2.07295e35			0.371550
$563$			2.87438e35i			0.503426i	0.967802	+	0.251713i	$0.0809939\pi$
$563$			2.87438e35i			0.503426i	−0.967802	+	0.251713i	$0.919006\pi$
$564$	3.66560e34	−	1.54231e34i	0.0627359	−	0.0263964i
$565$	3.77693e35			0.631697
$566$		−	7.94003e35i		−	1.29780i
$567$	2.63067e34	+	1.18071e36i	0.0420230	+	1.88610i
$568$	3.37164e35			0.526396
$569$			3.47987e35i			0.531011i	0.964109	+	0.265506i	$0.0855389\pi$
$569$			3.47987e35i			0.531011i	−0.964109	+	0.265506i	$0.914461\pi$
$570$	−1.44622e34	−	3.43721e34i	−0.0215705	−	0.0512664i
$571$	1.25721e36			1.83289			0.916446	−	0.400159i	$-0.131045\pi$
$571$	1.25721e36			1.83289			0.916446	+	0.400159i	$0.131045\pi$
$572$		−	6.92356e34i		−	0.0986691i
$573$	−5.68947e35	+	2.39386e35i	−0.792613	+	0.333495i
$574$	−1.64407e36			−2.23906
$575$		−	6.61963e34i		−	0.0881357i
$576$	5.89617e35	−	6.02901e35i	0.767499	−	0.784790i
$577$	3.83337e35			0.487860			0.243930	−	0.969793i	$-0.421563\pi$
$577$	3.83337e35			0.487860			0.243930	+	0.969793i	$0.421563\pi$
$578$			3.10587e35i			0.386475i
$579$	−5.25826e35	−	1.24972e36i	−0.639765	−	1.52052i
$580$	−2.45283e35			−0.291812
$581$		−	2.52780e36i		−	2.94071i
$582$	−3.19361e35	+	1.34372e35i	−0.363315	+	0.152866i
$583$	8.46020e35			0.941217
$584$			8.94915e35i			0.973677i
$585$	3.36904e35	+	3.29481e35i	0.358492	+	0.350594i
$586$	4.18053e35			0.435073
$587$			5.19443e35i			0.528740i	0.964421	+	0.264370i	$0.0851641\pi$
$587$			5.19443e35i			0.528740i	−0.964421	+	0.264370i	$0.914836\pi$
$588$	2.88380e35	+	6.85390e35i	0.287118	+	0.682390i
$589$	−8.45421e33			−0.00823330
$590$		−	2.78564e35i		−	0.265368i
$591$	−1.61712e36	+	6.80409e35i	−1.50697	+	0.634063i
$592$	7.10417e34			0.0647636
$593$		−	1.58590e36i		−	1.41437i	−0.707028	−	0.707186i	$-0.749964\pi$
$593$		−	1.58590e36i		−	1.41437i	0.707028	−	0.707186i	$-0.250036\pi$
$594$	−5.22088e35	−	2.06106e35i	−0.455533	−	0.179832i
$595$	2.27941e36			1.94581
$596$		−	5.35058e34i		−	0.0446888i
$597$	−1.08916e35	−	2.58860e35i	−0.0890073	−	0.211543i
$598$	2.01616e35			0.161217
$599$			1.07011e36i			0.837294i	0.908149	+	0.418647i	$0.137496\pi$
$599$			1.07011e36i			0.837294i	−0.908149	+	0.418647i	$0.862504\pi$
$600$	3.54064e35	−	1.48974e35i	0.271091	−	0.114063i
$601$	−1.49432e36			−1.11963			−0.559815	−	0.828617i	$-0.689128\pi$
$601$	−1.49432e36			−1.11963			−0.559815	+	0.828617i	$0.689128\pi$
$602$			1.70529e36i			1.25038i
$603$	−8.32809e35	+	8.51571e35i	−0.597613	+	0.611077i
$604$	−1.25691e35			−0.0882721
$605$			8.23200e35i			0.565829i
$606$	3.51667e35	+	8.35803e35i	0.236585	+	0.562289i
$607$	−1.90838e36			−1.25664			−0.628321	−	0.777954i	$-0.716258\pi$
$607$	−1.90838e36			−1.25664			−0.628321	+	0.777954i	$0.716258\pi$
$608$			6.69146e34i			0.0431295i
$609$	3.25528e36	−	1.36967e36i	2.05383	−	0.864155i
$610$	−8.18216e35			−0.505336
$611$			2.28475e35i			0.138135i
$612$	−4.22000e35	−	4.12703e35i	−0.249772	−	0.244269i
$613$	1.44907e36			0.839657			0.419828	−	0.907604i	$-0.362090\pi$
$613$	1.44907e36			0.839657			0.419828	+	0.907604i	$0.362090\pi$
$614$		−	5.75549e35i		−	0.326508i
$615$	−8.39541e35	−	1.99533e36i	−0.466300	−	1.10825i
$616$	−2.19049e36			−1.19122
$617$			2.71381e36i			1.44501i	0.691364	+	0.722506i	$0.257010\pi$
$617$			2.71381e36i			1.44501i	−0.691364	+	0.722506i	$0.742990\pi$
$618$	3.28383e35	−	1.38168e35i	0.171210	−	0.0720374i
$619$	−1.00442e36			−0.512787			−0.256394	−	0.966572i	$-0.582534\pi$
$619$	−1.00442e36			−0.512787			−0.256394	+	0.966572i	$0.582534\pi$
$620$			5.26731e34i			0.0263328i
$621$	−2.44302e35	+	6.18842e35i	−0.119601	+	0.302962i
$622$	3.06339e36			1.46868
$623$		−	3.75338e36i		−	1.76229i
$624$	3.10486e35	+	7.37927e35i	0.142772	+	0.339324i
$625$	−1.45703e36			−0.656189
$626$		−	2.25280e36i		−	0.993704i
$627$	9.57419e34	−	4.02837e34i	0.0413641	−	0.0174041i
$628$	4.55883e35			0.192920
$629$		−	3.00919e35i		−	0.124736i
$630$	2.33897e36	−	2.39167e36i	0.949725	−	0.971121i
$631$	2.02638e36			0.806010			0.403005	−	0.915198i	$-0.367966\pi$
$631$	2.02638e36			0.806010			0.403005	+	0.915198i	$0.367966\pi$
$632$		−	2.56320e36i		−	0.998760i
$633$	1.79866e36	+	4.27485e36i	0.686594	+	1.63182i
$634$	−1.39776e36			−0.522722
$635$			2.12302e36i			0.777851i
$636$	1.20350e36	−	5.06378e35i	0.432021	−	0.181774i
$637$	−4.27201e36			−1.50252
$638$			1.67851e36i			0.578436i
$639$	−1.02541e36	−	1.00281e36i	−0.346246	−	0.338617i
$640$	−9.47535e35			−0.313513
$641$			1.44958e36i			0.469989i	0.971997	+	0.234994i	$0.0755072\pi$
$641$			1.44958e36i			0.469989i	−0.971997	+	0.234994i	$0.924493\pi$
$642$	9.02715e35	+	2.14547e36i	0.286811	+	0.681660i
$643$	2.15306e36			0.670368			0.335184	−	0.942153i	$-0.391202\pi$
$643$	2.15306e36			0.670368			0.335184	+	0.942153i	$0.391202\pi$
$644$			5.82586e35i			0.177764i
$645$	−2.06962e36	+	8.70800e35i	−0.618892	+	0.260401i
$646$	−2.68353e35			−0.0786474
$647$		−	3.21045e36i		−	0.922167i	−0.887357	−	0.461084i	$-0.847461\pi$
$647$		−	3.21045e36i		−	0.922167i	0.887357	−	0.461084i	$-0.152539\pi$
$648$	−3.85979e36	+	8.59977e34i	−1.08665	+	0.0242109i
$649$	7.75927e35			0.214111
$650$			4.95175e35i			0.133932i
$651$	−2.94129e35	−	6.99053e35i	−0.0779803	−	0.185335i
$652$	2.25510e35			0.0586068
$653$			4.55451e36i			1.16030i	0.814510	+	0.580150i	$0.197006\pi$
$653$			4.55451e36i			1.16030i	−0.814510	+	0.580150i	$0.802994\pi$
$654$	−4.50610e36	+	1.89596e36i	−1.12536	+	0.473498i
$655$	−1.11499e36			−0.272983
$656$		−	3.67773e36i		−	0.882733i
$657$	2.66171e36	−	2.72168e36i	0.626342	−	0.640452i
$658$	1.62194e36			0.374194
$659$			6.29692e36i			1.42435i	0.702000	+	0.712177i	$0.252291\pi$
$659$			6.29692e36i			1.42435i	−0.702000	+	0.712177i	$0.747709\pi$
$660$	−2.50984e35	−	5.96511e35i	−0.0556640	−	0.132296i
$661$	1.81650e36			0.395018			0.197509	−	0.980301i	$-0.436715\pi$
$661$	1.81650e36			0.395018			0.197509	+	0.980301i	$0.436715\pi$
$662$		−	9.49399e35i		−	0.202439i
$663$	3.12572e36	−	1.31516e36i	0.653543	−	0.274980i
$664$	8.26346e36			1.69425
$665$			6.19062e35i			0.124467i
$666$	−3.15739e35	−	3.08783e35i	−0.0622535	−	0.0608819i
$667$	1.98957e36			0.384702
$668$		−	1.58444e36i		−	0.300457i
$669$	−1.44084e36	−	3.42443e36i	−0.267964	−	0.636867i
$670$	3.37389e36			0.615402
$671$		−	2.27911e36i		−	0.407729i
$672$	−5.53297e36	+	2.32802e36i	−0.970863	+	0.408494i
$673$	−9.54076e36			−1.64205			−0.821027	−	0.570890i	$-0.806598\pi$
$673$	−9.54076e36			−1.64205			−0.821027	+	0.570890i	$0.806598\pi$
$674$		−	3.72139e36i		−	0.628241i
$675$	−1.51989e36	−	6.00011e35i	−0.251689	−	0.0993597i
$676$	−1.16701e36			−0.189569
$677$		−	1.04767e37i		−	1.66945i	−0.550667	−	0.834725i	$-0.685627\pi$
$677$		−	1.04767e37i		−	1.66945i	0.550667	−	0.834725i	$-0.314373\pi$
$678$	−1.54699e36	−	3.67672e36i	−0.241826	−	0.574745i
$679$	5.75190e36			0.882072
$680$			7.45146e36i			1.12105i
$681$	8.85055e35	−	3.72390e35i	0.130634	−	0.0549649i
$682$	3.60451e35			0.0521974
$683$		−	7.24061e36i		−	1.02874i	−0.857568	−	0.514370i	$-0.828026\pi$
$683$		−	7.24061e36i		−	1.02874i	0.857568	−	0.514370i	$-0.171974\pi$
$684$	1.12086e35	−	1.14611e35i	0.0156250	−	0.0159770i
$685$	−1.07354e36			−0.146839
$686$			1.84764e37i			2.47973i
$687$	1.79654e36	+	4.26981e36i	0.236591	+	0.562304i
$688$	−3.81466e36			−0.492954
$689$			7.50139e36i			0.951244i
$690$	1.73706e36	−	7.30873e35i	0.216160	−	0.0909502i
$691$	2.45929e36			0.300327			0.150164	−	0.988661i	$-0.452020\pi$
$691$	2.45929e36			0.300327			0.150164	+	0.988661i	$0.452020\pi$
$692$			1.17120e36i			0.140363i
$693$	6.66188e36	+	6.51510e36i	0.783547	+	0.766283i
$694$	2.91482e35			0.0336464
$695$		−	1.24249e37i		−	1.40764i
$696$	4.47750e36	+	1.06416e37i	0.497870	+	1.18328i
$697$	−1.55781e37			−1.70016
$698$		−	6.60549e36i		−	0.707595i
$699$	1.32070e36	−	5.55691e35i	0.138868	−	0.0584292i
$700$	−1.43085e36			−0.147679
$701$			1.29219e37i			1.30915i	0.755995	+	0.654577i	$0.227153\pi$
$701$			1.29219e37i			1.30915i	−0.755995	+	0.654577i	$0.772847\pi$
$702$	1.82747e36	−	4.62918e36i	0.181748	−	0.460386i
$703$	8.17264e34			0.00797890
$704$		−	6.65354e36i		−	0.637688i
$705$	8.28239e35	+	1.96847e36i	0.0779286	+	0.185212i
$706$	−1.13184e37			−1.04550
$707$		−	1.50533e37i		−	1.36515i
$708$	1.10379e36	−	4.64424e35i	0.0982775	−	0.0413506i
$709$	2.66702e36			0.233144			0.116572	−	0.993182i	$-0.462809\pi$
$709$	2.66702e36			0.233144			0.116572	+	0.993182i	$0.462809\pi$
$710$			4.06262e36i			0.348697i
$711$	−7.62364e36	+	7.79539e36i	−0.642477	+	0.656951i
$712$	1.22699e37			1.01532
$713$		−	4.27250e35i		−	0.0347151i
$714$	−9.33624e36	−	2.21893e37i	−0.744895	−	1.77038i
$715$	3.71803e36			0.291296
$716$		−	9.13344e35i		−	0.0702692i
$717$	2.19166e37	−	9.22147e36i	1.65586	−	0.696709i
$718$	−6.94783e36			−0.515503
$719$			6.85917e36i			0.499800i	0.968272	+	0.249900i	$0.0803977\pi$
$719$			6.85917e36i			0.499800i	−0.968272	+	0.249900i	$0.919602\pi$
$720$	5.35007e36	+	5.23220e36i	0.382858	+	0.374422i
$721$	−5.91438e36			−0.415672
$722$			1.21403e37i			0.838006i
$723$	−5.86177e36	−	1.39316e37i	−0.397403	−	0.944503i
$724$	1.75227e36			0.116681
$725$			4.88645e36i			0.319594i
$726$	8.01360e36	−	3.37175e36i	0.514816	−	0.216610i
$727$	1.97236e37			1.24463			0.622313	−	0.782768i	$-0.286193\pi$
$727$	1.97236e37			1.24463			0.622313	+	0.782768i	$0.286193\pi$
$728$		−	1.94224e37i		−	1.20391i
$729$	1.19945e37	+	1.12185e37i	0.730336	+	0.683088i
$730$	−1.07832e37			−0.644986
$731$			1.61582e37i			0.949438i
$732$	−1.36414e36	−	3.24213e36i	−0.0787434	−	0.187149i
$733$	−3.71159e36			−0.210479			−0.105239	−	0.994447i	$-0.533561\pi$
$733$	−3.71159e36			−0.210479			−0.105239	+	0.994447i	$0.533561\pi$
$734$		−	1.99653e37i		−	1.11231i
$735$	−3.68062e37	+	1.54863e37i	−2.01458	+	0.847643i
$736$	−3.38166e36			−0.181852
$737$			9.39783e36i			0.496535i
$738$	−1.59852e37	+	1.63454e37i	−0.829825	+	0.848519i
$739$	−2.02049e37			−1.03057			−0.515287	−	0.857018i	$-0.672315\pi$
$739$	−2.02049e37			−1.03057			−0.515287	+	0.857018i	$0.672315\pi$
$740$		−	5.09189e35i		−	0.0255192i
$741$	3.57183e35	+	8.48912e35i	0.0175895	+	0.0418048i
$742$	5.32520e37			2.57683
$743$			3.45294e37i			1.64185i	0.571033	+	0.820927i	$0.306543\pi$
$743$			3.45294e37i			1.64185i	−0.571033	+	0.820927i	$0.693457\pi$
$744$	2.28523e36	−	9.61518e35i	0.106778	−	0.0449272i
$745$	2.87332e36			0.131933
$746$			9.78788e36i			0.441656i
$747$	−2.51314e37	−	2.45777e37i	−1.11442	−	1.08987i
$748$	−4.65714e36			−0.202955
$749$		−	3.86413e37i		−	1.65496i
$750$	8.42883e36	+	2.00327e37i	0.354790	+	0.843225i
$751$	2.44251e37			1.01046			0.505229	−	0.862986i	$-0.331408\pi$
$751$	2.44251e37			1.01046			0.505229	+	0.862986i	$0.331408\pi$
$752$			3.62822e36i			0.147523i
$753$	−1.40194e37	+	5.89870e36i	−0.560266	+	0.235734i
$754$	−1.48828e37			−0.584598
$755$		−	6.74974e36i		−	0.260601i
$756$	1.33764e37	+	5.28062e36i	0.507639	+	0.200402i
$757$	−3.68388e37			−1.37423			−0.687114	−	0.726550i	$-0.741123\pi$
$757$	−3.68388e37			−1.37423			−0.687114	+	0.726550i	$0.741123\pi$
$758$		−	4.89233e36i		−	0.179397i
$759$	2.03581e36	+	4.83850e36i	0.0733829	+	0.174408i
$760$	−2.02374e36			−0.0717096
$761$		−	3.62230e37i		−	1.26178i	−0.775872	−	0.630891i	$-0.782690\pi$
$761$		−	3.62230e37i		−	1.26178i	0.775872	−	0.630891i	$-0.217310\pi$
$762$	2.06670e37	−	8.69572e36i	0.707723	−	0.297777i
$763$	8.11577e37			2.73219
$764$			7.51626e36i			0.248764i
$765$	2.21626e37	−	2.26619e37i	0.721144	−	0.737390i
$766$	−3.28470e37			−1.05080
$767$			6.87989e36i			0.216392i
$768$	−9.88517e36	−	2.34940e37i	−0.305695	−	0.726542i
$769$	2.47123e37			0.751399			0.375699	−	0.926742i	$-0.377403\pi$
$769$	2.47123e37			0.751399			0.375699	+	0.926742i	$0.377403\pi$
$770$		−	2.63941e37i		−	0.789092i
$771$	−4.33940e37	+	1.82582e37i	−1.27562	+	0.536723i
$772$	−1.65099e37			−0.477221
$773$			2.44726e37i			0.695579i	0.937573	+	0.347789i	$0.113068\pi$
$773$			2.44726e37i			0.695579i	−0.937573	+	0.347789i	$0.886932\pi$
$774$	1.69540e37	+	1.65804e37i	0.473848	+	0.463408i
$775$	1.04934e36			0.0288398
$776$			1.88032e37i			0.508193i
$777$	2.84333e36	+	6.75771e36i	0.0755708	+	0.179608i
$778$	−2.45240e37			−0.640998
$779$		−	4.23086e36i		−	0.108753i
$780$	5.28907e36	−	2.22539e36i	0.133705	−	0.0562570i
$781$	−1.13163e37			−0.281345
$782$		−	1.35618e37i		−	0.331610i
$783$	1.80337e37	−	4.56813e37i	0.433693	−	1.09859i
$784$	−6.78400e37			−1.60464
$785$			2.44814e37i			0.569549i
$786$	4.56692e36	+	1.08541e37i	0.104503	+	0.248372i
$787$	−5.75180e37			−1.29459			−0.647295	−	0.762240i	$-0.724100\pi$
$787$	−5.75180e37			−1.29459			−0.647295	+	0.762240i	$0.724100\pi$
$788$			2.13635e37i			0.472968i
$789$	6.68827e37	−	2.81411e37i	1.45651	−	0.612831i
$790$	3.08851e37			0.661601
$791$			6.62201e37i			1.39539i
$792$	−2.12981e37	+	2.17779e37i	−0.441483	+	0.451428i
$793$	2.02081e37			0.412073
$794$			8.00954e37i			1.60672i
$795$	2.71930e37	+	6.46294e37i	0.536642	+	1.27543i
$796$	−3.41975e36			−0.0663934
$797$		−	9.65724e37i		−	1.84457i	−0.386512	−	0.922285i	$-0.626320\pi$
$797$		−	9.65724e37i		−	1.84457i	0.386512	−	0.922285i	$-0.373680\pi$
$798$	6.02639e36	−	2.53562e36i	0.113245	−	0.0476483i
$799$	1.53684e37			0.284133
$800$		−	8.30544e36i		−	0.151075i
$801$	−3.73162e37	−	3.64940e37i	−0.667843	−	0.653129i
$802$	3.24477e37			0.571369
$803$		−	3.00361e37i		−	0.520405i
$804$	5.62498e36	+	1.33688e37i	0.0958943	+	0.227911i
$805$	−3.12855e37			−0.524803
$806$			3.19600e36i			0.0527535i
$807$	−2.31087e37	+	9.72307e36i	−0.375336	+	0.157924i
$808$	4.92099e37			0.786511
$809$		−	4.97913e37i		−	0.783110i	−0.920155	−	0.391555i	$-0.871937\pi$
$809$		−	4.97913e37i		−	0.783110i	0.920155	−	0.391555i	$-0.128063\pi$
$810$	−1.03622e36	−	4.65082e37i	−0.0160379	−	0.719820i
$811$	−7.39902e37			−1.12695			−0.563473	−	0.826134i	$-0.690535\pi$
$811$	−7.39902e37			−1.12695			−0.563473	+	0.826134i	$0.690535\pi$
$812$		−	4.30050e37i		−	0.644601i
$813$	1.07771e37	+	2.56138e37i	0.158974	+	0.377831i
$814$	−3.48446e36			−0.0505846
$815$			1.21102e37i			0.173022i
$816$	4.96368e37	−	2.08848e37i	0.697962	−	0.293670i
$817$	−4.38839e36			−0.0607321
$818$		−	8.98792e37i		−	1.22424i
$819$	−5.77673e37	+	5.90687e37i	−0.774447	+	0.791894i
$820$	−2.63600e37			−0.347828
$821$		−	9.98209e37i		−	1.29646i	−0.761443	−	0.648232i	$-0.775509\pi$
$821$		−	9.98209e37i		−	1.29646i	0.761443	−	0.648232i	$-0.224491\pi$
$822$	4.39712e36	+	1.04506e37i	0.0562127	+	0.133600i
$823$	1.13685e38			1.43056			0.715282	−	0.698836i	$-0.246298\pi$
$823$	1.13685e38			1.43056			0.715282	+	0.698836i	$0.246298\pi$
$824$		−	1.93343e37i		−	0.239483i
$825$	−1.18835e37	+	5.00002e36i	−0.144891	+	0.0609635i
$826$	4.88400e37			0.586186
$827$			9.88322e37i			1.16769i	0.811866	+	0.583844i	$0.198452\pi$
$827$			9.88322e37i			1.16769i	−0.811866	+	0.583844i	$0.801548\pi$
$828$	5.79208e36	+	5.66446e36i	0.0673659	+	0.0658816i
$829$	2.48526e37			0.284553			0.142276	−	0.989827i	$-0.454558\pi$
$829$	2.48526e37			0.284553			0.142276	+	0.989827i	$0.454558\pi$
$830$			9.95697e37i			1.12231i
$831$	−2.27592e37	−	5.40916e37i	−0.252548	−	0.600229i
$832$	5.89948e37			0.644481
$833$			2.87357e38i			3.09056i
$834$	−1.20953e38	+	5.08913e37i	−1.28073	+	0.538872i
$835$	8.50864e37			0.887025
$836$		−	1.26483e36i		−	0.0129823i
$837$	−9.80981e36	−	3.87264e36i	−0.0991356	−	0.0391360i
$838$	−7.48005e37			−0.744273
$839$		−	9.09390e37i		−	0.890932i	−0.895299	−	0.445466i	$-0.853038\pi$
$839$		−	9.09390e37i		−	0.890932i	0.895299	−	0.445466i	$-0.146962\pi$
$840$	−7.04075e37	−	1.67337e38i	−0.679185	−	1.61421i
$841$	−4.15849e37			−0.394992
$842$		−	4.98507e37i		−	0.466245i
$843$	−4.41097e37	+	1.85593e37i	−0.406234	+	0.170924i
$844$	5.64744e37			0.512153
$845$		−	6.26697e37i		−	0.559655i
$846$	1.57700e37	−	1.61253e37i	0.138681	−	0.141806i
$847$	−1.44330e38			−1.24989
$848$			1.19123e38i			1.01590i
$849$	7.10879e37	+	1.68954e38i	0.597029	+	1.41895i
$850$	3.33080e37			0.275488
$851$			4.13020e36i			0.0336424i
$852$	−1.60979e37	+	6.77324e36i	−0.129138	+	0.0543352i
$853$	−1.98067e38			−1.56486			−0.782430	−	0.622738i	$-0.786020\pi$
$853$	−1.98067e38			−1.56486			−0.782430	+	0.622738i	$0.786020\pi$
$854$		−	1.43456e38i		−	1.11626i
$855$	6.15473e36	+	6.01912e36i	0.0471682	+	0.0461290i
$856$	1.26320e38			0.953482
$857$			8.03880e37i			0.597641i	0.954309	+	0.298821i	$0.0965933\pi$
$857$			8.03880e37i			0.597641i	−0.954309	+	0.298821i	$0.903407\pi$
$858$	−1.52287e37	−	3.61939e37i	−0.111514	−	0.265034i
$859$	2.25210e38			1.62434			0.812168	−	0.583423i	$-0.198287\pi$
$859$	2.25210e38			1.62434			0.812168	+	0.583423i	$0.198287\pi$
$860$			2.73414e37i			0.194241i
$861$	3.49837e38	−	1.47195e38i	2.44808	−	1.03004i
$862$	−2.51829e37			−0.173584
$863$		−	2.03964e38i		−	1.38488i	−0.721473	−	0.692442i	$-0.756535\pi$
$863$		−	2.03964e38i		−	1.38488i	0.721473	−	0.692442i	$-0.243465\pi$
$864$	−3.06517e37	+	7.76441e37i	−0.205011	+	0.519314i
$865$	−6.28949e37			−0.414387
$866$		−	1.16405e38i		−	0.755507i
$867$	−2.78071e37	−	6.60889e37i	−0.177790	−	0.422552i
$868$	−9.23508e36			−0.0581680
$869$			8.60290e37i			0.533811i
$870$	−1.28225e38	+	5.39512e37i	−0.783833	+	0.329800i
$871$	−8.33275e37			−0.501825
$872$			2.65307e38i			1.57411i
$873$	5.59255e37	−	5.71854e37i	0.326907	−	0.334272i
$874$	3.68323e36			0.0212119
$875$		−	3.60802e38i		−	2.04722i
$876$	−1.79778e37	−	4.27277e37i	−0.100504	−	0.238867i
$877$	−1.20583e38			−0.664187			−0.332094	−	0.943246i	$-0.607755\pi$
$877$	−1.20583e38			−0.664187			−0.332094	+	0.943246i	$0.607755\pi$
$878$		−	7.71217e37i		−	0.418550i
$879$	−8.89563e37	+	3.74287e37i	−0.475687	+	0.200147i
$880$	5.90427e37			0.311094
$881$			3.38133e37i			0.175550i	0.996140	+	0.0877751i	$0.0279757\pi$
$881$			3.38133e37i			0.175550i	−0.996140	+	0.0877751i	$0.972024\pi$
$882$	3.01510e38	+	2.94867e38i	1.54244	+	1.50846i
$883$	3.27626e37			0.165154			0.0825770	−	0.996585i	$-0.473685\pi$
$883$	3.27626e37			0.165154			0.0825770	+	0.996585i	$0.473685\pi$
$884$		−	4.12934e37i		−	0.205117i
$885$	2.49401e37	+	5.92748e37i	0.122077	+	0.290140i
$886$	−2.51594e38			−1.21356
$887$			3.21541e38i			1.52837i	0.644997	+	0.764185i	$0.276859\pi$
$887$			3.21541e38i			1.52837i	−0.644997	+	0.764185i	$0.723141\pi$
$888$	−2.20912e37	+	9.29495e36i	−0.103479	+	0.0435390i
$889$	−3.72226e38			−1.71824
$890$			1.47845e38i			0.672570i
$891$	1.29547e38	−	2.88634e36i	0.580785	−	0.0129401i
$892$	−4.52396e37			−0.199883
$893$			4.17390e36i			0.0181749i
$894$	−1.17688e37	−	2.79709e37i	−0.0505064	−	0.120038i
$895$	4.90476e37			0.207452
$896$		−	1.66130e38i		−	0.692537i
$897$	−4.29014e37	+	1.80509e37i	−0.176266	+	0.0741647i
$898$	1.20135e38			0.486493
$899$			3.15385e37i			0.125882i
$900$	−1.39121e37	+	1.42255e37i	−0.0547318	+	0.0559648i
$901$	5.04582e38			1.95663
$902$			1.80385e38i			0.689471i
$903$	−1.52676e38	−	3.62863e38i	−0.575214	−	1.36710i
$904$	−2.16476e38			−0.803933
$905$			9.40986e37i			0.344470i
$906$	−6.57067e37	+	2.76463e37i	−0.237106	+	0.0997633i
$907$	2.64704e38			0.941599			0.470800	−	0.882240i	$-0.343965\pi$
$907$	2.64704e38			0.941599			0.470800	+	0.882240i	$0.343965\pi$
$908$		−	1.16923e37i		−	0.0410001i
$909$	−1.49660e38	−	1.46363e38i	−0.517341	−	0.505942i
$910$	2.34028e38			0.797499
$911$			5.19318e37i			0.174459i	0.996188	+	0.0872297i	$0.0278014\pi$
$911$			5.19318e37i			0.174459i	−0.996188	+	0.0872297i	$0.972199\pi$
$912$	5.67210e36	+	1.34808e37i	0.0187850	+	0.0446461i
$913$	−2.77347e38			−0.905531
$914$		−	1.78902e38i		−	0.575858i
$915$	1.74106e38	−	7.32557e37i	0.552509	−	0.232470i
$916$	5.64078e37			0.176481
$917$		−	1.95490e38i		−	0.603008i
$918$	−3.11383e38	−	1.22925e38i	−0.946977	−	0.373840i
$919$	9.37364e37			0.281065			0.140532	−	0.990076i	$-0.455119\pi$
$919$	9.37364e37			0.281065			0.140532	+	0.990076i	$0.455119\pi$
$920$		−	1.02273e38i		−	0.302358i
$921$	5.15294e37	+	1.22469e38i	0.150204	+	0.356987i
$922$	8.56684e37			0.246217
$923$		−	1.00338e38i		−	0.284342i
$924$	1.04585e38	−	4.40045e37i	0.292236	−	0.122959i
$925$	−1.01439e37			−0.0279487
$926$		−	3.68131e38i		−	1.00014i
$927$	−5.75053e37	+	5.88008e37i	−0.154053	+	0.157524i
$928$	2.49626e38			0.659425
$929$			4.86704e38i			1.26783i	0.773403	+	0.633914i	$0.218553\pi$
$929$			4.86704e38i			1.26783i	−0.773403	+	0.633914i	$0.781447\pi$
$930$	1.15857e37	+	2.75356e37i	0.0297608	+	0.0707321i
$931$	−7.80432e37			−0.197692
$932$		−	1.74476e37i		−	0.0435842i
$933$	−6.51851e38	+	2.74268e38i	−1.60578	+	0.675639i
$934$	−5.97541e37			−0.145164
$935$		−	2.50094e38i		−	0.599173i
$936$	−1.93098e38	−	1.88843e38i	−0.456238	−	0.446186i
$937$	2.03446e38			0.474061			0.237031	−	0.971502i	$-0.423826\pi$
$937$	2.03446e38			0.474061			0.237031	+	0.971502i	$0.423826\pi$
$938$			5.91538e38i			1.35940i
$939$	2.01696e38	+	4.79368e38i	0.457134	+	1.08647i
$940$	2.60051e37			0.0581295
$941$		−	4.32737e38i		−	0.954023i	−0.878897	−	0.477011i	$-0.841720\pi$
$941$		−	4.32737e38i		−	0.954023i	0.878897	−	0.477011i	$-0.158280\pi$
$942$	2.38319e38	−	1.00274e38i	0.518200	−	0.218035i
$943$	2.13814e38			0.458548
$944$			1.09253e38i			0.231100i
$945$	−2.83575e38	+	7.18326e38i	−0.591636	+	1.49868i
$946$	1.87102e38			0.385029
$947$			1.52006e38i			0.308540i	0.988029	+	0.154270i	$0.0493026\pi$
$947$			1.52006e38i			0.308540i	−0.988029	+	0.154270i	$0.950697\pi$
$948$	5.14918e37	+	1.22380e38i	0.103093	+	0.245020i
$949$	2.66320e38			0.525949
$950$			9.04611e36i			0.0176220i
$951$	2.97425e38	−	1.25142e38i	0.571518	−	0.240468i
$952$	−1.30645e39			−2.47635
$953$			7.36063e38i			1.37628i	0.725577	+	0.688141i	$0.241573\pi$
$953$			7.36063e38i			1.37628i	−0.725577	+	0.688141i	$0.758427\pi$
$954$	5.17768e38	−	5.29432e38i	0.955006	−	0.976521i
$955$	−4.03632e38			−0.734415
$956$		−	2.89536e38i		−	0.519697i
$957$	−1.50279e38	−	3.57166e38i	−0.266098	−	0.632433i
$958$	2.24848e38			0.392768
$959$		−	1.88222e38i		−	0.324360i
$960$	5.08279e38	−	2.13860e38i	0.864123	−	0.363583i
$961$	−5.89444e38			−0.988641
$962$		−	3.08956e37i		−	0.0511235i
$963$	−3.84173e38	−	3.75708e38i	−0.627169	−	0.613351i
$964$	−1.84048e38			−0.296435
$965$		−	8.86601e38i		−	1.40888i
$966$	1.28143e38	+	3.04555e38i	0.200905	+	0.477489i
$967$	−1.18571e38			−0.183415			−0.0917075	−	0.995786i	$-0.529232\pi$
$967$	−1.18571e38			−0.183415			−0.0917075	+	0.995786i	$0.529232\pi$
$968$		−	4.71820e38i		−	0.720106i
$969$	5.71022e37	−	2.40259e37i	0.0859891	−	0.0361802i
$970$	−2.26567e38			−0.336638
$971$			8.77148e38i			1.28595i	0.765889	+	0.642973i	$0.222299\pi$
$971$			8.77148e38i			1.28595i	−0.765889	+	0.642973i	$0.777701\pi$
$972$	1.82558e38	−	8.16448e37i	0.264083	−	0.118105i
$973$	2.17844e39			3.10941
$974$			9.14272e37i			0.128768i
$975$	−4.43335e37	−	1.05367e38i	−0.0616130	−	0.146435i
$976$	3.20907e38			0.440080
$977$		−	3.71527e38i		−	0.502760i	−0.967888	−	0.251380i	$-0.919116\pi$
$977$		−	3.71527e38i		−	0.502760i	0.967888	−	0.251380i	$-0.0808844\pi$
$978$	1.17889e38	−	4.96021e37i	0.157423	−	0.0662361i
$979$	−4.11817e38			−0.542661
$980$			4.86241e38i			0.632284i
$981$	7.89094e38	−	8.06871e38i	1.01259	−	1.03540i
$982$	−3.78267e38			−0.479016
$983$		−	4.11799e38i		−	0.514623i	−0.966329	−	0.257311i	$-0.917163\pi$
$983$		−	4.11799e38i		−	0.514623i	0.966329	−	0.257311i	$-0.0828366\pi$
$984$	4.81186e38	+	1.14363e39i	0.593440	+	1.41042i
$985$	−1.14724e39			−1.39632
$986$			1.00109e39i			1.20247i
$987$	−3.45127e38	+	1.45214e38i	−0.409125	+	0.172141i
$988$	1.12148e37			0.0131206
$989$		−	2.21776e38i		−	0.256072i
$990$	−2.62411e38	−	2.56629e38i	−0.299036	−	0.292448i
$991$	−1.38403e39			−1.55664			−0.778318	−	0.627871i	$-0.783927\pi$
$991$	−1.38403e39			−1.55664			−0.778318	+	0.627871i	$0.783927\pi$
$992$		−	5.36057e37i		−	0.0595057i
$993$	8.50006e37	+	2.02020e38i	0.0931283	+	0.221337i
$994$	−7.12292e38			−0.770256
$995$		−	1.83645e38i		−	0.196010i
$996$	−3.94539e38	+	1.66003e38i	−0.415641	+	0.174882i
$997$	6.81486e38			0.708630			0.354315	−	0.935126i	$-0.384714\pi$
$997$	6.81486e38			0.708630			0.354315	+	0.935126i	$0.384714\pi$
$998$			5.07677e37i			0.0521063i
$999$	9.48309e37	+	3.74366e37i	0.0960724	+	0.0379267i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.27.b.a.2.3	✓	8
3.2	odd	2	inner	3.27.b.a.2.6	yes	8
4.3	odd	2		48.27.e.d.17.3		8
12.11	even	2		48.27.e.d.17.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.27.b.a.2.3	✓	8	1.1	even	1	trivial
3.27.b.a.2.6	yes	8	3.2	odd	2	inner
48.27.e.d.17.3		8	4.3	odd	2
48.27.e.d.17.4		8	12.11	even	2

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:	\( k \)	\(=\)	\( 27 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-6906.16i q^{2} +(618315. + 1.46954e6i) q^{3} +1.94139e7 q^{4} +1.04255e9i q^{5} +(1.01489e10 - 4.27018e9i) q^{6} -1.82788e11 q^{7} -5.97540e11i q^{8} +(-1.77724e12 + 1.81728e12i) q^{9} +O(q^{10})\)	\(q-6906.16i q^{2} +(618315. + 1.46954e6i) q^{3} +1.94139e7 q^{4} +1.04255e9i q^{5} +(1.01489e10 - 4.27018e9i) q^{6} -1.82788e11 q^{7} -5.97540e11i q^{8} +(-1.77724e12 + 1.81728e12i) q^{9} +7.19999e12 q^{10} +2.00553e13i q^{11} +(1.20039e13 + 2.85295e13i) q^{12} -1.77823e14 q^{13} +1.26236e15i q^{14} +(-1.53207e15 + 6.44622e14i) q^{15} -2.82386e15 q^{16} +1.19613e16i q^{17} +(1.25504e16 + 1.22739e16i) q^{18} -3.24857e15 q^{19} +2.02399e16i q^{20} +(-1.13020e17 - 2.68614e17i) q^{21} +1.38505e17 q^{22} -1.64173e17i q^{23} +(8.78109e17 - 3.69467e17i) q^{24} +4.03212e17 q^{25} +1.22808e18i q^{26} +(-3.76946e18 - 1.48808e18i) q^{27} -3.54862e18 q^{28} +1.21188e19i q^{29} +(4.45186e18 + 1.05807e19i) q^{30} +2.60244e18 q^{31} -2.05982e19i q^{32} +(-2.94720e19 + 1.24005e19i) q^{33} +8.26067e19 q^{34} -1.90565e20i q^{35} +(-3.45031e19 + 3.52804e19i) q^{36} -2.51577e19 q^{37} +2.24351e19i q^{38} +(-1.09951e20 - 2.61319e20i) q^{39} +6.22963e20 q^{40} +1.30238e21i q^{41} +(-1.85509e21 + 7.80536e20i) q^{42} +1.35087e21 q^{43} +3.89350e20i q^{44} +(-1.89460e21 - 1.85286e21i) q^{45} -1.13380e21 q^{46} -1.28484e21i q^{47} +(-1.74603e21 - 4.14978e21i) q^{48} +2.40239e22 q^{49} -2.78465e21i q^{50} +(-1.75777e22 + 7.39586e21i) q^{51} -3.45224e21 q^{52} -4.21845e22i q^{53} +(-1.02769e22 + 2.60325e22i) q^{54} -2.09085e22 q^{55} +1.09223e23i q^{56} +(-2.00864e21 - 4.77390e21i) q^{57} +8.36943e22 q^{58} -3.86894e22i q^{59} +(-2.97434e22 + 1.25146e22i) q^{60} -1.13641e23 q^{61} -1.79729e22i q^{62} +(3.24858e23 - 3.32176e23i) q^{63} -3.31760e23 q^{64} -1.85389e23i q^{65} +(8.56395e22 + 2.03538e23i) q^{66} +4.68597e23 q^{67} +2.32216e23i q^{68} +(2.41258e23 - 1.01510e23i) q^{69} -1.31607e24 q^{70} +5.64254e23i q^{71} +(1.08590e24 + 1.06197e24i) q^{72} -1.49767e24 q^{73} +1.73743e23i q^{74} +(2.49312e23 + 5.92537e23i) q^{75} -6.30673e22 q^{76} -3.66586e24i q^{77} +(-1.80471e24 + 7.59338e23i) q^{78} +4.28960e24 q^{79} -2.94400e24i q^{80} +(-1.43920e23 - 6.45948e24i) q^{81} +8.99442e24 q^{82} +1.38291e25i q^{83} +(-2.19416e24 - 5.21485e24i) q^{84} -1.24702e25 q^{85} -9.32932e24i q^{86} +(-1.78091e25 + 7.49323e24i) q^{87} +1.19838e25 q^{88} +2.05341e25i q^{89} +(-1.27961e25 + 1.30844e25i) q^{90} +3.25040e25 q^{91} -3.18723e24i q^{92} +(1.60913e24 + 3.82440e24i) q^{93} -8.87333e24 q^{94} -3.38678e24i q^{95} +(3.02699e25 - 1.27362e25i) q^{96} -3.14676e25 q^{97} -1.65913e26i q^{98} +(-3.64460e25 - 3.56430e25i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 1261080 q^{3} - 248848672 q^{4} + 4268261088 q^{6} - 83723264240 q^{7} + 3535237525320 q^{9}+O(q^{10}) \) 8 * q - 1261080 * q^3 - 248848672 * q^4 + 4268261088 * q^6 - 83723264240 * q^7 + 3535237525320 * q^9	\( 8 q - 1261080 q^{3} - 248848672 q^{4} + 4268261088 q^{6} - 83723264240 q^{7} + 3535237525320 q^{9} - 19160376580800 q^{10} + 361652147111520 q^{12} - 397915354631600 q^{13} - 719893807027200 q^{15} + 14\!\cdots\!24 q^{16}+ \cdots + 12\!\cdots\!20 q^{99}+O(q^{100}) \) 8 * q - 1261080 * q^3 - 248848672 * q^4 + 4268261088 * q^6 - 83723264240 * q^7 + 3535237525320 * q^9 - 19160376580800 * q^10 + 361652147111520 * q^12 - 397915354631600 * q^13 - 719893807027200 * q^15 + 14708338775335424 * q^16 - 21900893760832320 * q^18 + 16320401555362000 * q^19 + 194580840365988048 * q^21 - 772248680481769920 * q^22 - 462343148304920064 * q^24 + 1971388854053049800 * q^25 - 7894649015962792920 * q^27 + 15321751531929304000 * q^28 + 7398480599799681600 * q^30 - 9272518953250081904 * q^31 - 65168600178932490240 * q^33 + 221246262521511042816 * q^34 - 1016435634925989724704 * q^36 + 879374467120740709840 * q^37 - 1582238541124790450928 * q^39 + 4129217584783179033600 * q^40 - 6703469261814514512960 * q^42 + 6748593942335676212560 * q^43 - 16831420952659929907200 * q^45 + 36160927581299221074816 * q^46 - 66488551077760679646720 * q^48 + 45841873858091621647512 * q^49 - 62114113806050924347392 * q^51 + 99815113130579384624320 * q^52 - 65423424830500017302112 * q^54 + 31541176921532063385600 * q^55 - 68601650728105742286960 * q^57 + 179274146475296123858880 * q^58 + 132515345363297827507200 * q^60 - 319050283467071524566704 * q^61 + 658789337835295522626960 * q^63 - 1937027849517856838066176 * q^64 + 3327191890146340029253440 * q^66 - 3016122636770760226629680 * q^67 + 2874694883813365556256768 * q^69 - 3079956143630742638371200 * q^70 + 4816528692447953902187520 * q^72 - 1734362529074066854728560 * q^73 + 551279759153288953055400 * q^75 - 4252629668197637559664448 * q^76 - 2905541033044787133422400 * q^78 + 5851464318766097144790160 * q^79 - 7387002303358032367832952 * q^81 + 19281076716095151109326720 * q^82 - 58831332525651421466918208 * q^84 + 36766362882842005714329600 * q^85 - 66105320167985812595481600 * q^87 + 166743215953906759732730880 * q^88 - 112582289830354559315755200 * q^90 + 57658591275235919126596256 * q^91 - 721851591602497641585840 * q^93 - 128592383810221185199398144 * q^94 + 66451111218720743421763584 * q^96 + 87088434574088023884109840 * q^97 + 126385397236902706353285120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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