LMFDB - Embedded newform 126.9.n.c.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,9,Mod(19,126)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("126.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	126.n (of order $6$, degree $2$, 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:	$51.3297048677$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 2 x^{11} + 6683 x^{10} + 105006 x^{9} + 34690411 x^{8} + 548172728 x^{7} + \cdots + 30\!\cdots\!24 $ x^12 - 2x^11 + 6683x^10 + 105006x^9 + 34690411x^8 + 548172728x^7 + 69245553226x^6 + 2257669296800x^5 + 109555419264148x^4 + 2043640985398464x^3 + 35697604660076192x^2 + 112120335940899328*x + 305636965993402624
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{6}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.1
Root			$-12.6321 - 21.8795i$ of defining polynomial
Character	$\chi$	$=$	126.73
Dual form			126.9.n.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(-607.249 + 350.595i) q^{5} +(-2120.49 + 1126.19i) q^{7} +1448.15 q^{8} +O(q^{10})$	\(q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(-607.249 + 350.595i) q^{5} +(-2120.49 + 1126.19i) q^{7} +1448.15 q^{8} +(6870.24 + 3966.53i) q^{10} +(-25.6528 + 44.4320i) q^{11} +32507.4i q^{13} +(23029.7 + 14405.8i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(125645. + 72541.4i) q^{17} +(-172719. + 99719.4i) q^{19} -89752.4i q^{20} +580.457 q^{22} +(94405.8 + 163516. i) q^{23} +(50521.7 - 87506.1i) q^{25} +(318506. - 183889. i) q^{26} +(10872.1 - 307136. i) q^{28} -45136.7 q^{29} +(-1.36356e6 - 787254. i) q^{31} +(-92681.9 + 160530. i) q^{32} -1.64142e6i q^{34} +(892831. - 1.42731e6i) q^{35} +(1.70067e6 + 2.94564e6i) q^{37} +(1.95409e6 + 1.12820e6i) q^{38} +(-879390. + 507716. i) q^{40} -3.93773e6i q^{41} -1.55052e6 q^{43} +(-3283.56 - 5687.29i) q^{44} +(1.06808e6 - 1.84997e6i) q^{46} +(-164462. + 94952.3i) q^{47} +(3.22819e6 - 4.77616e6i) q^{49} -1.14317e6 q^{50} +(-3.60348e6 - 2.08047e6i) q^{52} +(-1.00262e6 + 1.73659e6i) q^{53} -35975.0i q^{55} +(-3.07080e6 + 1.63090e6i) q^{56} +(255331. + 442247. i) q^{58} +(-1.11644e7 - 6.44579e6i) q^{59} +(1.13103e7 - 6.53000e6i) q^{61} +1.78135e7i q^{62} +2.09715e6 q^{64} +(-1.13969e7 - 1.97401e7i) q^{65} +(-8.75755e6 + 1.51685e7i) q^{67} +(-1.60826e7 + 9.28530e6i) q^{68} +(-1.90354e7 - 673822. i) q^{70} -8.61402e6 q^{71} +(-3.32550e7 - 1.91998e7i) q^{73} +(1.92409e7 - 3.33262e7i) q^{74} -2.55282e7i q^{76} +(4357.82 - 123108. i) q^{77} +(-8.02831e6 - 1.39054e7i) q^{79} +(9.94917e6 + 5.74415e6i) q^{80} +(-3.85817e7 + 2.22751e7i) q^{82} -2.28342e7i q^{83} -1.01731e8 q^{85} +(8.77106e6 + 1.51919e7i) q^{86} +(-37149.2 + 64344.4i) q^{88} +(-9.09745e7 + 5.25241e7i) q^{89} +(-3.66095e7 - 6.89317e7i) q^{91} -2.41679e7 q^{92} +(1.86068e6 + 1.07426e6i) q^{94} +(6.99223e7 - 1.21109e8i) q^{95} -6.95869e7i q^{97} +(-6.50580e7 - 4.61168e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 768 q^{4} + 1122 q^{5} - 4434 q^{7}+O(q^{10}) $ 12 * q - 768 * q^4 + 1122 * q^5 - 4434 * q^7	$ 12 q - 768 q^{4} + 1122 q^{5} - 4434 q^{7} + 4224 q^{10} - 9606 q^{11} + 19968 q^{14} - 98304 q^{16} + 227388 q^{17} + 315408 q^{19} + 557568 q^{22} + 663480 q^{23} + 601008 q^{25} + 585984 q^{26} + 398592 q^{28} - 5944884 q^{29} - 3214278 q^{31} + 1019784 q^{35} + 1607760 q^{37} + 986880 q^{38} - 540672 q^{40} + 12627648 q^{43} - 1229568 q^{44} - 4608768 q^{46} + 7830240 q^{47} + 16477242 q^{49} + 16565760 q^{50} - 4283904 q^{52} + 33200358 q^{53} + 8110080 q^{56} + 5576064 q^{58} + 29657382 q^{59} + 58344096 q^{61} + 25165824 q^{64} - 30909216 q^{65} + 7977444 q^{67} - 29105664 q^{68} - 59774976 q^{70} - 117213264 q^{71} - 170286636 q^{73} + 80311296 q^{74} + 3340686 q^{77} + 35420490 q^{79} - 18382848 q^{80} + 154232832 q^{82} + 416634600 q^{85} + 71958528 q^{86} - 35684352 q^{88} - 78064092 q^{89} + 335513292 q^{91} - 169850880 q^{92} - 18456576 q^{94} + 250727796 q^{95} + 150533376 q^{98}+O(q^{100}) $ 12 * q - 768 * q^4 + 1122 * q^5 - 4434 * q^7 + 4224 * q^10 - 9606 * q^11 + 19968 * q^14 - 98304 * q^16 + 227388 * q^17 + 315408 * q^19 + 557568 * q^22 + 663480 * q^23 + 601008 * q^25 + 585984 * q^26 + 398592 * q^28 - 5944884 * q^29 - 3214278 * q^31 + 1019784 * q^35 + 1607760 * q^37 + 986880 * q^38 - 540672 * q^40 + 12627648 * q^43 - 1229568 * q^44 - 4608768 * q^46 + 7830240 * q^47 + 16477242 * q^49 + 16565760 * q^50 - 4283904 * q^52 + 33200358 * q^53 + 8110080 * q^56 + 5576064 * q^58 + 29657382 * q^59 + 58344096 * q^61 + 25165824 * q^64 - 30909216 * q^65 + 7977444 * q^67 - 29105664 * q^68 - 59774976 * q^70 - 117213264 * q^71 - 170286636 * q^73 + 80311296 * q^74 + 3340686 * q^77 + 35420490 * q^79 - 18382848 * q^80 + 154232832 * q^82 + 416634600 * q^85 + 71958528 * q^86 - 35684352 * q^88 - 78064092 * q^89 + 335513292 * q^91 - 169850880 * q^92 - 18456576 * q^94 + 250727796 * q^95 + 150533376 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−5.65685	−	9.79796i	−0.353553	−	0.612372i
$2$	−5.65685	−	9.79796i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−64.0000	+	110.851i	−0.250000	+	0.433013i
$5$	−607.249	+	350.595i	−0.971598	+	0.560953i	−0.899723	−	0.436461i	$-0.856232\pi$
$5$	−607.249	+	350.595i	−0.971598	+	0.560953i	−0.0718752	+	0.997414i	$0.522898\pi$
$6$		0			0
$7$	−2120.49	+	1126.19i	−0.883171	+	0.469050i
$7$	−2120.49	+	1126.19i	−0.883171	+	0.469050i
$8$	1448.15			0.353553
$9$		0			0
$10$	6870.24	+	3966.53i	0.687024	+	0.396653i
$11$	−25.6528	+	44.4320i	−0.00175212	+	0.00303476i	−0.866900	−	0.498482i	$-0.833891\pi$
$11$	−25.6528	+	44.4320i	−0.00175212	+	0.00303476i	0.865148	+	0.501517i	$0.167224\pi$
$12$		0			0
$13$			32507.4i			1.13817i	0.822278	+	0.569086i	$0.192703\pi$
$13$			32507.4i			1.13817i	−0.822278	+	0.569086i	$0.807297\pi$
$14$	23029.7	+	14405.8i	0.599482	+	0.374996i
$15$		0			0
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	125645.	+	72541.4i	1.50436	+	0.868541i	0.999987	+	0.00505344i	$0.00160857\pi$
$17$	125645.	+	72541.4i	1.50436	+	0.868541i	0.504370	+	0.863488i	$0.331725\pi$
$18$		0			0
$19$	−172719.	+	99719.4i	−1.32534	+	0.765183i	−0.984574	−	0.174967i	$-0.944018\pi$
$19$	−172719.	+	99719.4i	−1.32534	+	0.765183i	−0.340762	+	0.940150i	$0.610685\pi$
$20$		−	89752.4i		−	0.560953i
$21$		0			0
$22$	580.457			0.00247787
$23$	94405.8	+	163516.i	0.337355	+	0.584316i	0.983934	−	0.178531i	$-0.0571344\pi$
$23$	94405.8	+	163516.i	0.337355	+	0.584316i	−0.646579	+	0.762847i	$0.723801\pi$
$24$		0			0
$25$	50521.7	−	87506.1i	0.129335	−	0.224016i
$26$	318506.	−	183889.i	0.696986	−	0.402405i
$27$		0			0
$28$	10872.1	−	307136.i	0.0176881	−	0.499687i
$29$	−45136.7			−0.0638171			−0.0319086	−	0.999491i	$-0.510159\pi$
$29$	−45136.7			−0.0638171			−0.0319086	+	0.999491i	$0.510159\pi$
$30$		0			0
$31$	−1.36356e6	−	787254.i	−1.47648	−	0.852448i	−0.476836	−	0.878992i	$-0.658216\pi$
$31$	−1.36356e6	−	787254.i	−1.47648	−	0.852448i	−0.999648	+	0.0265444i	$0.991550\pi$
$32$	−92681.9	+	160530.i	−0.0883883	+	0.153093i
$33$		0			0
$34$		−	1.64142e6i		−	1.22830i
$35$	892831.	−	1.42731e6i	0.594973	−	0.951146i
$36$		0			0
$37$	1.70067e6	+	2.94564e6i	0.907429	+	1.57171i	0.817622	+	0.575755i	$0.195292\pi$
$37$	1.70067e6	+	2.94564e6i	0.907429	+	1.57171i	0.0898070	+	0.995959i	$0.471375\pi$
$38$	1.95409e6	+	1.12820e6i	0.937154	+	0.541066i
$39$		0			0
$40$	−879390.	+	507716.i	−0.343512	+	0.198327i
$41$		−	3.93773e6i		−	1.39351i	−0.717309	−	0.696755i	$-0.754627\pi$
$41$		−	3.93773e6i		−	1.39351i	0.717309	−	0.696755i	$-0.245373\pi$
$42$		0			0
$43$	−1.55052e6			−0.453527			−0.226764	−	0.973950i	$-0.572814\pi$
$43$	−1.55052e6			−0.453527			−0.226764	+	0.973950i	$0.572814\pi$
$44$	−3283.56	−	5687.29i	−0.000876061	−	0.00151738i
$45$		0			0
$46$	1.06808e6	−	1.84997e6i	0.238546	−	0.413174i
$47$	−164462.	+	94952.3i	−0.0337035	+	0.0194587i	−0.516757	−	0.856132i	$-0.672861\pi$
$47$	−164462.	+	94952.3i	−0.0337035	+	0.0194587i	0.483054	+	0.875591i	$0.339528\pi$
$48$		0			0
$49$	3.22819e6	−	4.77616e6i	0.559984	−	0.828504i
$50$	−1.14317e6			−0.182908
$51$		0			0
$52$	−3.60348e6	−	2.08047e6i	−0.492843	−	0.284543i
$53$	−1.00262e6	+	1.73659e6i	−0.127067	+	0.220087i	−0.922539	−	0.385904i	$-0.873890\pi$
$53$	−1.00262e6	+	1.73659e6i	−0.127067	+	0.220087i	0.795472	+	0.605991i	$0.207223\pi$
$54$		0			0
$55$		−	35975.0i		−	0.00393143i
$56$	−3.07080e6	+	1.63090e6i	−0.312248	+	0.165834i
$57$		0			0
$58$	255331.	+	442247.i	0.0225628	+	0.0390799i
$59$	−1.11644e7	−	6.44579e6i	−0.921359	−	0.531947i	−0.0372907	−	0.999304i	$-0.511873\pi$
$59$	−1.11644e7	−	6.44579e6i	−0.921359	−	0.531947i	−0.884068	+	0.467357i	$0.845206\pi$
$60$		0			0
$61$	1.13103e7	−	6.53000e6i	0.816873	−	0.471622i	−0.0324640	−	0.999473i	$-0.510335\pi$
$61$	1.13103e7	−	6.53000e6i	0.816873	−	0.471622i	0.849337	+	0.527851i	$0.177002\pi$
$62$			1.78135e7i			1.20554i
$63$		0			0
$64$	2.09715e6			0.125000
$65$	−1.13969e7	−	1.97401e7i	−0.638461	−	1.10585i
$66$		0			0
$67$	−8.75755e6	+	1.51685e7i	−0.434593	+	0.752738i	−0.997262	−	0.0739444i	$-0.976441\pi$
$67$	−8.75755e6	+	1.51685e7i	−0.434593	+	0.752738i	0.562669	+	0.826682i	$0.309775\pi$
$68$	−1.60826e7	+	9.28530e6i	−0.752179	+	0.434271i
$69$		0			0
$70$	−1.90354e7	−	673822.i	−0.792810	−	0.0280642i
$71$	−8.61402e6			−0.338979			−0.169489	−	0.985532i	$-0.554212\pi$
$71$	−8.61402e6			−0.338979			−0.169489	+	0.985532i	$0.554212\pi$
$72$		0			0
$73$	−3.32550e7	−	1.91998e7i	−1.17102	−	0.676091i	−0.217102	−	0.976149i	$-0.569661\pi$
$73$	−3.32550e7	−	1.91998e7i	−1.17102	−	0.676091i	−0.953921	+	0.300058i	$0.902994\pi$
$74$	1.92409e7	−	3.33262e7i	0.641650	−	1.11137i
$75$		0			0
$76$		−	2.55282e7i		−	0.765183i
$77$	4357.82	−	123108.i	0.000123967	−	0.00350205i
$78$		0			0
$79$	−8.02831e6	−	1.39054e7i	−0.206118	−	0.357007i	0.744370	−	0.667767i	$-0.232750\pi$
$79$	−8.02831e6	−	1.39054e7i	−0.206118	−	0.357007i	−0.950488	+	0.310760i	$0.899416\pi$
$80$	9.94917e6	+	5.74415e6i	0.242900	+	0.140238i
$81$		0			0
$82$	−3.85817e7	+	2.22751e7i	−0.853347	+	0.492680i
$83$		−	2.28342e7i		−	0.481141i	−0.970632	−	0.240571i	$-0.922665\pi$
$83$		−	2.28342e7i		−	0.481141i	0.970632	−	0.240571i	$-0.0773346\pi$
$84$		0			0
$85$	−1.01731e8			−1.94884
$86$	8.77106e6	+	1.51919e7i	0.160346	+	0.277727i
$87$		0			0
$88$	−37149.2	+	64344.4i	−0.000619469	+	0.00107295i
$89$	−9.09745e7	+	5.25241e7i	−1.44997	+	0.837142i	−0.998479	−	0.0551329i	$-0.982442\pi$
$89$	−9.09745e7	+	5.25241e7i	−1.44997	+	0.837142i	−0.451493	+	0.892275i	$0.649108\pi$
$90$		0			0
$91$	−3.66095e7	−	6.89317e7i	−0.533860	−	1.00520i
$92$	−2.41679e7			−0.337355
$93$		0			0
$94$	1.86068e6	+	1.07426e6i	0.0238320	+	0.0137594i
$95$	6.99223e7	−	1.21109e8i	0.858463	−	1.48690i
$96$		0			0
$97$		−	6.95869e7i		−	0.786033i	−0.919531	−	0.393017i	$-0.871432\pi$
$97$		−	6.95869e7i		−	0.786033i	0.919531	−	0.393017i	$-0.128568\pi$
$98$	−6.50580e7	−	4.61168e6i	−0.705337	−	0.0499982i
$99$		0			0
$100$	6.46677e6	+	1.12008e7i	0.0646677	+	0.112008i
$101$	7.51605e7	+	4.33939e7i	0.722277	+	0.417007i	0.815590	−	0.578630i	$-0.196412\pi$
$101$	7.51605e7	+	4.33939e7i	0.722277	+	0.417007i	−0.0933130	+	0.995637i	$0.529746\pi$
$102$		0			0
$103$	−6.28284e7	+	3.62740e7i	−0.558222	+	0.322290i	−0.752432	−	0.658670i	$-0.771119\pi$
$103$	−6.28284e7	+	3.62740e7i	−0.558222	+	0.322290i	0.194209	+	0.980960i	$0.437786\pi$
$104$			4.70757e7i			0.402405i
$105$		0			0
$106$	2.26867e7			0.179700
$107$	5.75474e7	+	9.96751e7i	0.439027	+	0.760417i	0.997615	−	0.0690288i	$-0.0219900\pi$
$107$	5.75474e7	+	9.96751e7i	0.439027	+	0.760417i	−0.558588	+	0.829445i	$0.688657\pi$
$108$		0			0
$109$	5.59443e7	−	9.68983e7i	0.396323	−	0.686452i	−0.596946	−	0.802282i	$-0.703619\pi$
$109$	5.59443e7	−	9.68983e7i	0.396323	−	0.686452i	0.993269	+	0.115830i	$0.0369526\pi$
$110$	−352482.	+	203505.i	−0.00240750	+	0.00138997i
$111$		0			0
$112$	3.33506e7	+	2.08619e7i	0.211949	+	0.132581i
$113$	−1.68762e7			−0.103505			−0.0517523	−	0.998660i	$-0.516481\pi$
$113$	−1.68762e7			−0.103505			−0.0517523	+	0.998660i	$0.516481\pi$
$114$		0			0
$115$	−1.14656e8	−	6.61965e7i	−0.655547	−	0.378480i
$116$	2.88875e6	−	5.00345e6i	0.0159543	−	0.0276336i
$117$		0			0
$118$			1.45852e8i			0.752287i
$119$	−3.48126e8	−	1.23231e7i	−1.73599	−	0.0614514i
$120$		0			0
$121$	1.07178e8	+	1.85638e8i	0.499994	+	0.866015i
$122$	−1.27961e8	−	7.38785e7i	−0.577616	−	0.333487i
$123$		0			0
$124$	1.74536e8	−	1.00768e8i	0.738242	−	0.426224i
$125$		−	2.03052e8i		−	0.831701i
$126$		0			0
$127$	1.74028e8			0.668966			0.334483	−	0.942402i	$-0.391438\pi$
$127$	1.74028e8			0.668966			0.334483	+	0.942402i	$0.391438\pi$
$128$	−1.18633e7	−	2.05478e7i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.28942e8	+	2.23333e8i	−0.451460	+	0.781952i
$131$	3.12000e8	−	1.80133e8i	1.05942	−	0.611659i	0.134151	−	0.990961i	$-0.457169\pi$
$131$	3.12000e8	−	1.80133e8i	1.05942	−	0.611659i	0.925273	+	0.379302i	$0.123836\pi$
$132$		0			0
$133$	2.53947e8	−	4.05969e8i	0.811590	−	1.29744i
$134$	1.98161e8			0.614608
$135$		0			0
$136$	1.81954e8	+	1.05051e8i	0.531871	+	0.307076i
$137$	1.00301e8	−	1.73727e8i	0.284725	−	0.493157i	−0.687818	−	0.725883i	$-0.741431\pi$
$137$	1.00301e8	−	1.73727e8i	0.284725	−	0.493157i	0.972542	+	0.232726i	$0.0747645\pi$
$138$		0			0
$139$			9.12135e6i			0.0244343i	0.999925	+	0.0122171i	$0.00388893\pi$
$139$			9.12135e6i			0.0244343i	−0.999925	+	0.0122171i	$0.996111\pi$
$140$	1.01078e8	+	1.90319e8i	0.263115	+	0.495417i
$141$		0			0
$142$	4.87283e7	+	8.43998e7i	0.119847	+	0.207581i
$143$	−1.44437e6	−	833905.i	−0.00345409	−	0.00199422i
$144$		0			0
$145$	2.74092e7	−	1.58247e7i	0.0620046	−	0.0357984i
$146$			4.34441e8i			0.956136i
$147$		0			0
$148$	−4.35371e8			−0.907429
$149$	−1.72687e8	−	2.99103e8i	−0.350361	−	0.606843i	0.635952	−	0.771729i	$-0.280608\pi$
$149$	−1.72687e8	−	2.99103e8i	−0.350361	−	0.606843i	−0.986313	+	0.164886i	$0.947274\pi$
$150$		0			0
$151$	3.09151e7	−	5.35465e7i	0.0594651	−	0.102997i	−0.834760	−	0.550613i	$-0.814394\pi$
$151$	3.09151e7	−	5.35465e7i	0.0594651	−	0.102997i	0.894225	+	0.447617i	$0.147727\pi$
$152$	−2.50124e8	+	1.44409e8i	−0.468577	+	0.270533i
$153$		0			0
$154$	−1.23086e6	+	653705.i	−0.00218839	+	0.00116225i
$155$	1.10403e9			1.91273
$156$		0			0
$157$	4.16486e8	+	2.40458e8i	0.685491	+	0.395769i	0.801921	−	0.597430i	$-0.203812\pi$
$157$	4.16486e8	+	2.40458e8i	0.685491	+	0.395769i	−0.116429	+	0.993199i	$0.537145\pi$
$158$	−9.08299e7	+	1.57322e8i	−0.145747	+	0.252442i
$159$		0			0
$160$		−	1.29975e8i		−	0.198327i
$161$	−3.84337e8	−	2.40415e8i	−0.572016	−	0.357815i
$162$		0			0
$163$	5.44041e8	+	9.42307e8i	0.770693	+	1.33488i	0.937184	+	0.348836i	$0.113423\pi$
$163$	5.44041e8	+	9.42307e8i	0.770693	+	1.33488i	−0.166491	+	0.986043i	$0.553244\pi$
$164$	4.36502e8	+	2.52014e8i	0.603407	+	0.348377i
$165$		0			0
$166$	−2.23728e8	+	1.29170e8i	−0.294638	+	0.170109i
$167$			1.46053e9i			1.87778i	0.344213	+	0.938892i	$0.388146\pi$
$167$			1.46053e9i			1.87778i	−0.344213	+	0.938892i	$0.611854\pi$
$168$		0			0
$169$	−2.40998e8			−0.295438
$170$	5.75476e8	+	9.96754e8i	0.689019	+	1.19342i
$171$		0			0
$172$	9.92332e7	−	1.71877e8i	0.113382	−	0.196383i
$173$	1.11558e9	−	6.44083e8i	1.24543	−	0.719047i	0.275233	−	0.961378i	$-0.411245\pi$
$173$	1.11558e9	−	6.44083e8i	1.24543	−	0.719047i	0.970194	+	0.242330i	$0.0779117\pi$
$174$		0			0
$175$	−8.58246e6	+	2.42453e8i	−0.00915081	+	0.258509i
$176$	840591.			0.000876061
$177$		0			0
$178$	1.02926e9	+	5.94243e8i	1.02529	+	0.591949i
$179$	4.98256e8	−	8.63005e8i	0.485334	−	0.840622i	−0.514524	−	0.857476i	$-0.672031\pi$
$179$	4.98256e8	−	8.63005e8i	0.485334	−	0.840622i	0.999858	+	0.0168533i	$0.00536483\pi$
$180$		0			0
$181$		−	1.19990e9i		−	1.11797i	−0.829177	−	0.558987i	$-0.811190\pi$
$181$		−	1.19990e9i		−	1.11797i	0.829177	−	0.558987i	$-0.188810\pi$
$182$	−4.68295e8	+	7.48634e8i	−0.426810	+	0.682314i
$183$		0			0
$184$	1.36714e8	+	2.36796e8i	0.119273	+	0.206587i
$185$	−2.06546e9	−	1.19249e9i	−1.76331	−	1.01805i
$186$		0			0
$187$	−6.44632e6	+	3.72178e6i	−0.00527163	+	0.00304358i
$188$		−	2.43078e7i		−	0.0194587i
$189$		0			0
$190$	−1.58216e9			−1.21405
$191$	−4.85771e8	−	8.41379e8i	−0.365004	−	0.632206i	0.623773	−	0.781606i	$-0.285599\pi$
$191$	−4.85771e8	−	8.41379e8i	−0.365004	−	0.632206i	−0.988777	+	0.149400i	$0.952266\pi$
$192$		0			0
$193$	−3.82023e8	+	6.61684e8i	−0.275335	+	0.476894i	−0.970219	−	0.242227i	$-0.922122\pi$
$193$	−3.82023e8	+	6.61684e8i	−0.275335	+	0.476894i	0.694885	+	0.719121i	$0.255455\pi$
$194$	−6.81810e8	+	3.93643e8i	−0.481345	+	0.277905i
$195$		0			0
$196$	3.22839e8	+	6.63524e8i	0.218757	+	0.449606i
$197$	−3.44781e8			−0.228917			−0.114459	−	0.993428i	$-0.536513\pi$
$197$	−3.44781e8			−0.228917			−0.114459	+	0.993428i	$0.536513\pi$
$198$		0			0
$199$	3.73493e8	+	2.15637e8i	0.238161	+	0.137502i	0.614331	−	0.789048i	$-0.289426\pi$
$199$	3.73493e8	+	2.15637e8i	0.238161	+	0.137502i	−0.376170	+	0.926551i	$0.622759\pi$
$200$	7.31632e7	−	1.26722e8i	0.0457270	−	0.0792015i
$201$		0			0
$202$		−	9.81892e8i		−	0.589737i
$203$	9.57120e7	−	5.08324e7i	0.0563615	−	0.0299335i
$204$		0			0
$205$	1.38055e9	+	2.39118e9i	0.781693	+	1.35393i
$206$	7.10822e8	+	4.10393e8i	0.394723	+	0.227893i
$207$		0			0
$208$	4.61246e8	−	2.66300e8i	0.246422	−	0.142272i
$209$		−	1.02323e7i		−	0.00536278i
$210$		0			0
$211$	−3.27153e9			−1.65052			−0.825260	−	0.564753i	$-0.808971\pi$
$211$	−3.27153e9			−1.65052			−0.825260	+	0.564753i	$0.808971\pi$
$212$	−1.28336e8	−	2.22284e8i	−0.0635337	−	0.110044i
$213$		0			0
$214$	6.51075e8	−	1.12769e9i	0.310439	−	0.537696i
$215$	9.41551e8	−	5.43605e8i	0.440646	−	0.254407i
$216$		0			0
$217$	3.77803e9	+	1.33736e8i	1.70383	+	0.0603128i
$218$	−1.26587e9			−0.560486
$219$		0			0
$220$	3.98788e6	+	2.30240e6i	0.00170236	+	0.000982857i
$221$	−2.35813e9	+	4.08440e9i	−0.988550	+	1.71222i
$222$		0			0
$223$		−	1.21483e9i		−	0.491244i	−0.969366	−	0.245622i	$-0.921008\pi$
$223$		−	1.21483e9i		−	0.491244i	0.969366	−	0.245622i	$-0.0789922\pi$
$224$	1.57445e7	−	4.44780e8i	0.00625369	−	0.176666i
$225$		0			0
$226$	9.54660e7	+	1.65352e8i	0.0365944	+	0.0633834i
$227$	−1.72294e9	−	9.94740e8i	−0.648884	−	0.374633i	0.139145	−	0.990272i	$-0.455565\pi$
$227$	−1.72294e9	−	9.94740e8i	−0.648884	−	0.374633i	−0.788028	+	0.615639i	$0.788898\pi$
$228$		0			0
$229$	3.20267e9	−	1.84906e9i	1.16458	−	0.672371i	0.212183	−	0.977230i	$-0.431943\pi$
$229$	3.20267e9	−	1.84906e9i	1.16458	−	0.672371i	0.952398	+	0.304859i	$0.0986092\pi$
$230$			1.49785e9i			0.535252i
$231$		0			0
$232$	−6.53649e7			−0.0225628
$233$	−1.03108e9	−	1.78588e9i	−0.349839	−	0.605939i	0.636381	−	0.771374i	$-0.280430\pi$
$233$	−1.03108e9	−	1.78588e9i	−0.349839	−	0.605939i	−0.986221	+	0.165435i	$0.947097\pi$
$234$		0			0
$235$	6.65797e7	−	1.15319e8i	0.0218308	−	0.0378121i
$236$	1.42905e9	−	8.25062e8i	0.460680	−	0.265973i
$237$		0			0
$238$	1.84856e9	+	3.48063e9i	0.576136	+	1.08480i
$239$	4.45572e9			1.36561			0.682804	−	0.730601i	$-0.260760\pi$
$239$	4.45572e9			1.36561			0.682804	+	0.730601i	$0.260760\pi$
$240$		0			0
$241$	−5.05448e9	−	2.91820e9i	−1.49833	−	0.865063i	−0.498334	−	0.866985i	$-0.666055\pi$
$241$	−5.05448e9	−	2.91820e9i	−1.49833	−	0.865063i	−0.999998	+	0.00192224i	$0.999388\pi$
$242$	1.21258e9	−	2.10025e9i	0.353549	−	0.612365i
$243$		0			0
$244$			1.67168e9i			0.471622i
$245$	−2.85818e8	+	4.03211e9i	−0.0793279	+	1.11910i
$246$		0			0
$247$	−3.24162e9	−	5.61464e9i	−0.870911	−	1.50846i
$248$	−1.97465e9	−	1.14007e9i	−0.522016	−	0.301386i
$249$		0			0
$250$	−1.98949e9	+	1.14864e9i	−0.509311	+	0.294051i
$251$			1.66381e9i			0.419189i	0.977788	+	0.209594i	$0.0672143\pi$
$251$			1.66381e9i			0.419189i	−0.977788	+	0.209594i	$0.932786\pi$
$252$		0			0
$253$	−9.68710e6			−0.00236435
$254$	−9.84451e8	−	1.70512e9i	−0.236515	−	0.409657i
$255$		0			0
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	7.47093e9	−	4.31334e9i	1.71255	−	0.988738i	0.781445	−	0.623974i	$-0.214483\pi$
$257$	7.47093e9	−	4.31334e9i	1.71255	−	0.988738i	0.931100	−	0.364764i	$-0.118850\pi$
$258$		0			0
$259$	−6.92361e9	−	4.33095e9i	−1.53863	−	0.962463i
$260$	2.91761e9			0.638461
$261$		0			0
$262$	−3.52988e9	−	2.03798e9i	−0.749126	−	0.432508i
$263$	3.91054e9	−	6.77325e9i	0.817360	−	1.41571i	−0.0902601	−	0.995918i	$-0.528770\pi$
$263$	3.91054e9	−	6.77325e9i	0.817360	−	1.41571i	0.907621	−	0.419792i	$-0.137897\pi$
$264$		0			0
$265$		−	1.40606e9i		−	0.285115i
$266$	−5.41421e9	−	1.91654e8i	−1.08146	−	0.0382818i
$267$		0			0
$268$	−1.12097e9	−	1.94157e9i	−0.217297	−	0.376369i
$269$	−4.64217e9	−	2.68016e9i	−0.886567	−	0.511860i	−0.0137489	−	0.999905i	$-0.504377\pi$
$269$	−4.64217e9	−	2.68016e9i	−0.886567	−	0.511860i	−0.872818	+	0.488046i	$0.837710\pi$
$270$		0			0
$271$	−4.60881e9	+	2.66090e9i	−0.854499	+	0.493345i	−0.862166	−	0.506626i	$-0.830893\pi$
$271$	−4.60881e9	+	2.66090e9i	−0.854499	+	0.493345i	0.00766747	+	0.999971i	$0.497559\pi$
$272$		−	2.37704e9i		−	0.434271i
$273$		0			0
$274$	−2.26956e9			−0.402661
$275$	2.59205e6	+	4.48956e6i	0.000453223	+	0.000785005i
$276$		0			0
$277$	−1.02775e8	+	1.78011e8i	−0.0174569	+	0.0302363i	−0.874622	−	0.484806i	$-0.838890\pi$
$277$	−1.02775e8	+	1.78011e8i	−0.0174569	+	0.0302363i	0.857165	+	0.515042i	$0.172224\pi$
$278$	8.93706e7	−	5.15981e7i	0.0149629	−	0.00863883i
$279$		0			0
$280$	1.29296e9	−	2.06697e9i	0.210355	−	0.336281i
$281$	−5.51900e9			−0.885188			−0.442594	−	0.896722i	$-0.645942\pi$
$281$	−5.51900e9			−0.885188			−0.442594	+	0.896722i	$0.645942\pi$
$282$		0			0
$283$	−6.16234e9	−	3.55783e9i	−0.960726	−	0.554675i	−0.0643297	−	0.997929i	$-0.520491\pi$
$283$	−6.16234e9	−	3.55783e9i	−0.960726	−	0.554675i	−0.896396	+	0.443253i	$0.853824\pi$
$284$	5.51297e8	−	9.54875e8i	0.0847447	−	0.146782i
$285$		0			0
$286$			1.88691e7i			0.00282025i
$287$	4.43463e9	+	8.34993e9i	0.653626	+	1.23071i
$288$		0			0
$289$	7.03664e9	+	1.21878e10i	1.00873	+	1.74717i
$290$	−3.10100e8	−	1.79036e8i	−0.0438439	−	0.0253133i
$291$		0			0
$292$	4.25664e9	−	2.45757e9i	0.585512	−	0.338045i
$293$			1.66605e9i			0.226056i	0.993592	+	0.113028i	$0.0360550\pi$
$293$			1.66605e9i			0.226056i	−0.993592	+	0.113028i	$0.963945\pi$
$294$		0			0
$295$	9.03946e9			1.19359
$296$	2.46283e9	+	4.26575e9i	0.320825	+	0.555685i
$297$		0			0
$298$	−1.95374e9	+	3.38397e9i	−0.247743	+	0.429103i
$299$	−5.31546e9	+	3.06888e9i	−0.665053	+	0.383968i
$300$		0			0
$301$	3.28787e9	−	1.74618e9i	0.400542	−	0.212727i
$302$	−6.99528e8			−0.0840964
$303$		0			0
$304$	2.82983e9	+	1.63380e9i	0.331334	+	0.191296i
$305$	−4.57878e9	+	7.93067e9i	−0.529115	+	0.916454i
$306$		0			0
$307$		−	3.39536e9i		−	0.382237i	−0.981567	−	0.191118i	$-0.938789\pi$
$307$		−	3.39536e9i		−	0.382237i	0.981567	−	0.191118i	$-0.0612115\pi$
$308$	1.33677e7	+	8.36196e6i	0.00148544	+	0.000929192i
$309$		0			0
$310$	−6.24534e9	−	1.08172e10i	−0.676253	−	1.17130i
$311$	−5.73107e9	−	3.30884e9i	−0.612625	−	0.353699i	0.161367	−	0.986894i	$-0.448410\pi$
$311$	−5.73107e9	−	3.30884e9i	−0.612625	−	0.353699i	−0.773992	+	0.633195i	$0.781743\pi$
$312$		0			0
$313$	−1.38453e10	+	7.99362e9i	−1.44254	+	0.832848i	−0.998018	−	0.0629220i	$-0.979958\pi$
$313$	−1.38453e10	+	7.99362e9i	−1.44254	+	0.832848i	−0.444517	+	0.895770i	$0.646625\pi$
$314$		−	5.44095e9i		−	0.559701i
$315$		0			0
$316$	2.05525e9			0.206118
$317$	6.95619e9	+	1.20485e10i	0.688866	+	1.19315i	0.972205	+	0.234131i	$0.0752244\pi$
$317$	6.95619e9	+	1.20485e10i	0.688866	+	1.19315i	−0.283339	+	0.959020i	$0.591442\pi$
$318$		0			0
$319$	1.15788e6	−	2.00551e6i	0.000111815	−	0.000193670i
$320$	−1.27349e9	+	7.35252e8i	−0.121450	+	0.0701191i
$321$		0			0
$322$	−1.81442e8	+	5.12571e9i	−0.0168777	+	0.476794i
$323$	−2.89352e10			−2.65837
$324$		0			0
$325$	2.84459e9	+	1.64233e9i	0.254969	+	0.147206i
$326$	6.15512e9	−	1.06610e10i	0.544962	−	0.943902i
$327$		0			0
$328$		−	5.70244e9i		−	0.492680i
$329$	2.41807e8	−	3.86562e8i	0.0206388	−	0.0329940i
$330$		0			0
$331$	9.12792e9	+	1.58100e10i	0.760431	+	1.31710i	0.942629	+	0.333843i	$0.108346\pi$
$331$	9.12792e9	+	1.58100e10i	0.760431	+	1.31710i	−0.182198	+	0.983262i	$0.558321\pi$
$332$	2.53120e9	+	1.46139e9i	0.208340	+	0.120285i
$333$		0			0
$334$	1.43102e10	−	8.26202e9i	1.14990	−	0.663897i
$335$		−	1.22814e10i		−	0.975145i
$336$		0			0
$337$	7.27644e9			0.564156			0.282078	−	0.959391i	$-0.408976\pi$
$337$	7.27644e9			0.564156			0.282078	+	0.959391i	$0.408976\pi$
$338$	1.36329e9	+	2.36128e9i	0.104453	+	0.180918i
$339$		0			0
$340$	6.51077e9	−	1.12770e10i	0.487210	−	0.843873i
$341$	6.99585e7	−	4.03905e7i	0.00517396	−	0.00298719i
$342$		0			0
$343$	−1.46651e9	+	1.37634e10i	−0.105952	+	0.994371i
$344$	−2.24539e9			−0.160346
$345$		0			0
$346$	−1.26214e10	−	7.28697e9i	−0.880650	−	0.508443i
$347$	−5.18756e8	+	8.98512e8i	−0.0357804	+	0.0619735i	−0.883361	−	0.468693i	$-0.844725\pi$
$347$	−5.18756e8	+	8.98512e8i	−0.0357804	+	0.0619735i	0.847581	+	0.530667i	$0.178058\pi$
$348$		0			0
$349$			1.93298e10i			1.30294i	0.758673	+	0.651471i	$0.225848\pi$
$349$			1.93298e10i			1.30294i	−0.758673	+	0.651471i	$0.774152\pi$
$350$	2.42410e9	−	1.28743e9i	0.161539	−	0.0857931i
$351$		0			0
$352$	−4.75510e6	−	8.23608e6i	−0.000309734	−	0.000536475i
$353$	1.20662e10	+	6.96642e9i	0.777090	+	0.448653i	0.835398	−	0.549646i	$-0.185237\pi$
$353$	1.20662e10	+	6.96642e9i	0.777090	+	0.448653i	−0.0583081	+	0.998299i	$0.518571\pi$
$354$		0			0
$355$	5.23086e9	−	3.02004e9i	0.329351	−	0.190151i
$356$		−	1.34462e10i		−	0.837142i
$357$		0			0
$358$	−1.12742e10			−0.686365
$359$	8.46599e9	+	1.46635e10i	0.509683	+	0.882796i	0.999937	+	0.0112169i	$0.00357051\pi$
$359$	8.46599e9	+	1.46635e10i	0.509683	+	0.882796i	−0.490254	+	0.871579i	$0.663096\pi$
$360$		0			0
$361$	1.13961e10	−	1.97387e10i	0.671010	−	1.16222i
$362$	−1.17566e10	+	6.78767e9i	−0.684616	+	0.395263i
$363$		0			0
$364$	9.98417e9	+	3.53424e8i	0.568730	+	0.0201321i
$365$	2.69254e10			1.51702
$366$		0			0
$367$	−6.87587e9	−	3.96979e9i	−0.379021	−	0.218828i	0.298371	−	0.954450i	$-0.403557\pi$
$367$	−6.87587e9	−	3.96979e9i	−0.379021	−	0.218828i	−0.677392	+	0.735622i	$0.736890\pi$
$368$	1.54674e9	−	2.67904e9i	0.0843388	−	0.146079i
$369$		0			0
$370$			2.69830e10i			1.43974i
$371$	1.70322e8	−	4.81158e9i	0.00899033	−	0.253976i
$372$		0			0
$373$	−8.14272e8	−	1.41036e9i	−0.0420663	−	0.0728610i	0.844226	−	0.535988i	$-0.180061\pi$
$373$	−8.14272e8	−	1.41036e9i	−0.0420663	−	0.0728610i	−0.886292	+	0.463127i	$0.846727\pi$
$374$	7.29318e7	+	4.21072e7i	0.00372761	+	0.00215214i
$375$		0			0
$376$	−2.38167e8	+	1.37506e8i	−0.0119160	+	0.00687969i
$377$		−	1.46727e9i		−	0.0726349i
$378$		0			0
$379$	2.09430e10			1.01504			0.507518	−	0.861641i	$-0.330563\pi$
$379$	2.09430e10			1.01504			0.507518	+	0.861641i	$0.330563\pi$
$380$	8.95006e9	+	1.55020e10i	0.429231	+	0.743451i
$381$		0			0
$382$	−5.49587e9	+	9.51912e9i	−0.258097	+	0.447037i
$383$	8.12348e9	−	4.69009e9i	0.377526	−	0.217965i	−0.299215	−	0.954186i	$-0.596725\pi$
$383$	8.12348e9	−	4.69009e9i	0.377526	−	0.217965i	0.676741	+	0.736221i	$0.263392\pi$
$384$		0			0
$385$	4.05147e7	+	7.62848e7i	0.00184404	+	0.00347213i
$386$	8.64420e9			0.389382
$387$		0			0
$388$	7.71380e9	+	4.45356e9i	0.340362	+	0.196508i
$389$	−7.05904e8	+	1.22266e9i	−0.0308281	+	0.0533959i	−0.881028	−	0.473064i	$-0.843148\pi$
$389$	−7.05904e8	+	1.22266e9i	−0.0308281	+	0.0533959i	0.850200	+	0.526460i	$0.176481\pi$
$390$		0			0
$391$			2.73933e10i			1.17203i
$392$	4.67492e9	−	6.91662e9i	0.197984	−	0.292920i
$393$		0			0
$394$	1.95038e9	+	3.37815e9i	0.0809344	+	0.140183i
$395$	9.75036e9	+	5.62937e9i	0.400527	+	0.231245i
$396$		0			0
$397$	−1.27200e10	+	7.34391e9i	−0.512066	+	0.295641i	−0.733682	−	0.679493i	$-0.762200\pi$
$397$	−1.27200e10	+	7.34391e9i	−0.512066	+	0.295641i	0.221617	+	0.975134i	$0.428867\pi$
$398$		−	4.87930e9i		−	0.194458i
$399$		0			0
$400$	−1.65549e9			−0.0646677
$401$	9.91295e9	+	1.71697e10i	0.383376	+	0.664027i	0.991542	−	0.129783i	$-0.0414279\pi$
$401$	9.91295e9	+	1.71697e10i	0.383376	+	0.664027i	−0.608166	+	0.793810i	$0.708095\pi$
$402$		0			0
$403$	2.55915e10	−	4.43258e10i	0.970233	−	1.68049i
$404$	−9.62054e9	+	5.55442e9i	−0.361139	+	0.208503i
$405$		0			0
$406$	−1.03948e9	−	6.50231e8i	−0.0382572	−	0.0239311i
$407$	−1.74508e8			−0.00635971
$408$		0			0
$409$	−2.31685e10	−	1.33763e10i	−0.827950	−	0.478017i	0.0252003	−	0.999682i	$-0.491978\pi$
$409$	−2.31685e10	−	1.33763e10i	−0.827950	−	0.478017i	−0.853150	+	0.521665i	$0.825311\pi$
$410$	1.56191e10	−	2.70531e10i	0.552740	−	0.957374i
$411$		0			0
$412$		−	9.28614e9i		−	0.322290i
$413$	3.09333e10	+	1.09499e9i	1.06323	+	0.0376366i
$414$		0			0
$415$	8.00555e9	+	1.38660e10i	0.269897	+	0.467476i
$416$	−5.21840e9	−	3.01284e9i	−0.174246	−	0.100601i
$417$		0			0
$418$	−1.00256e8	+	5.78828e7i	−0.00328402	+	0.00189603i
$419$			3.90074e10i			1.26558i	0.774322	+	0.632792i	$0.218091\pi$
$419$			3.90074e10i			1.26558i	−0.774322	+	0.632792i	$0.781909\pi$
$420$		0			0
$421$	6.65431e9			0.211824			0.105912	−	0.994376i	$-0.466224\pi$
$421$	6.65431e9			0.211824			0.105912	+	0.994376i	$0.466224\pi$
$422$	1.85066e10	+	3.20543e10i	0.583547	+	1.01073i
$423$		0			0
$424$	−1.45195e9	+	2.51485e9i	−0.0449251	+	0.0778125i
$425$	1.26956e10	−	7.32983e9i	0.389134	−	0.224666i
$426$		0			0
$427$	−1.66294e10	+	2.65844e10i	−0.500225	+	0.799677i
$428$	−1.47321e10			−0.439027
$429$		0			0
$430$	−1.06524e10	−	6.15018e9i	−0.311584	−	0.179893i
$431$	−7.33104e9	+	1.26977e10i	−0.212450	+	0.367974i	−0.952481	−	0.304599i	$-0.901478\pi$
$431$	−7.33104e9	+	1.26977e10i	−0.212450	+	0.367974i	0.740031	+	0.672573i	$0.234811\pi$
$432$		0			0
$433$			3.73328e10i			1.06204i	0.847361	+	0.531018i	$0.178190\pi$
$433$			3.73328e10i			1.06204i	−0.847361	+	0.531018i	$0.821810\pi$
$434$	−2.00614e10	−	3.77735e10i	−0.565461	−	1.06470i
$435$		0			0
$436$	7.16087e9	+	1.24030e10i	0.198162	+	0.343226i
$437$	−3.26114e10	−	1.88282e10i	−0.894218	−	0.516277i
$438$		0			0
$439$	1.30334e10	−	7.52486e9i	0.350914	−	0.202600i	−0.314174	−	0.949366i	$-0.601727\pi$
$439$	1.30334e10	−	7.52486e9i	0.350914	−	0.202600i	0.665088	+	0.746765i	$0.268394\pi$
$440$		−	5.20974e7i		−	0.00138997i
$441$		0			0
$442$	5.33584e10			1.39802
$443$	−3.20575e10	−	5.55252e10i	−0.832367	−	1.44170i	−0.896157	−	0.443738i	$-0.853652\pi$
$443$	−3.20575e10	−	5.55252e10i	−0.832367	−	1.44170i	0.0637900	−	0.997963i	$-0.479681\pi$
$444$		0			0
$445$	3.68294e10	−	6.37905e10i	0.939194	−	1.62673i
$446$	−1.19029e10	+	6.87214e9i	−0.300824	+	0.173681i
$447$		0			0
$448$	−4.44700e9	+	2.36179e9i	−0.110396	+	0.0586313i
$449$	−3.80094e10			−0.935203			−0.467602	−	0.883939i	$-0.654882\pi$
$449$	−3.80094e10			−0.935203			−0.467602	+	0.883939i	$0.654882\pi$
$450$		0			0
$451$	1.74961e8	+	1.01014e8i	0.00422897	+	0.00244160i
$452$	1.08007e9	−	1.87074e9i	0.0258762	−	0.0448188i
$453$		0			0
$454$			2.25084e10i			0.529811i
$455$	4.63982e10	+	2.90236e10i	1.08257	+	0.677182i
$456$		0			0
$457$	−2.07070e10	−	3.58656e10i	−0.474737	−	0.822268i	0.524845	−	0.851198i	$-0.324123\pi$
$457$	−2.07070e10	−	3.58656e10i	−0.474737	−	0.822268i	−0.999581	+	0.0289299i	$0.990790\pi$
$458$	−3.62340e10	−	2.09197e10i	−0.823483	−	0.475438i
$459$		0			0
$460$	1.46759e10	−	8.47315e9i	0.327774	−	0.189240i
$461$		−	2.71417e10i		−	0.600944i	−0.953791	−	0.300472i	$-0.902856\pi$
$461$		−	2.71417e10i		−	0.600944i	0.953791	−	0.300472i	$-0.0971442\pi$
$462$		0			0
$463$	−5.33868e10			−1.16174			−0.580871	−	0.813996i	$-0.697288\pi$
$463$	−5.33868e10			−1.16174			−0.580871	+	0.813996i	$0.697288\pi$
$464$	3.69759e8	+	6.40442e8i	0.00797714	+	0.0138168i
$465$		0			0
$466$	−1.16653e10	+	2.02049e10i	−0.247374	+	0.428464i
$467$	−3.79032e10	+	2.18835e10i	−0.796909	+	0.460096i	−0.842389	−	0.538869i	$-0.818852\pi$
$467$	−3.79032e10	+	2.18835e10i	−0.796909	+	0.460096i	0.0454800	+	0.998965i	$0.485518\pi$
$468$		0			0
$469$	1.48770e9	−	4.20274e10i	0.0307486	−	0.868643i
$470$	−1.50653e9			−0.0308735
$471$		0			0
$472$	−1.61678e10	−	9.33451e9i	−0.325750	−	0.188072i
$473$	3.97752e7	−	6.88926e7i	0.000794635	−	0.00137635i
$474$		0			0
$475$			2.01520e10i			0.395861i
$476$	2.36461e10	−	3.78015e10i	0.460608	−	0.736345i
$477$		0			0
$478$	−2.52054e10	−	4.36570e10i	−0.482816	−	0.836261i
$479$	−8.72178e10	−	5.03552e10i	−1.65677	−	0.956539i	−0.974189	−	0.225732i	$-0.927522\pi$
$479$	−8.72178e10	−	5.03552e10i	−1.65677	−	0.956539i	−0.682585	−	0.730806i	$-0.739144\pi$
$480$		0			0
$481$	−9.57551e10	+	5.52843e10i	−1.78888	+	1.03281i
$482$			6.60314e10i			1.22338i
$483$		0			0
$484$	−2.74376e10			−0.499994
$485$	2.43969e10	+	4.22566e10i	0.440927	+	0.763708i
$486$		0			0
$487$	2.26332e10	−	3.92018e10i	0.402374	−	0.696932i	−0.591638	−	0.806204i	$-0.701519\pi$
$487$	2.26332e10	−	3.92018e10i	0.402374	−	0.696932i	0.994012	+	0.109272i	$0.0348519\pi$
$488$	1.63791e10	−	9.45645e9i	0.288808	−	0.166744i
$489$		0			0
$490$	4.11233e10	−	2.00086e10i	0.713351	−	0.347082i
$491$	−1.02274e11			−1.75969			−0.879847	−	0.475256i	$-0.842355\pi$
$491$	−1.02274e11			−1.75969			−0.879847	+	0.475256i	$0.842355\pi$
$492$		0			0
$493$	−5.67121e9	−	3.27428e9i	−0.0960038	−	0.0554278i
$494$	−3.66747e10	+	6.35224e10i	−0.615827	+	1.06664i
$495$		0			0
$496$			2.57967e10i			0.426224i
$497$	1.82660e10	−	9.70102e9i	0.299376	−	0.158998i
$498$		0			0
$499$	−2.36190e10	−	4.09093e10i	−0.380942	−	0.659811i	0.610255	−	0.792205i	$-0.291067\pi$
$499$	−2.36190e10	−	4.09093e10i	−0.380942	−	0.659811i	−0.991197	+	0.132394i	$0.957734\pi$
$500$	2.25086e10	+	1.29953e10i	0.360137	+	0.207925i
$501$		0			0
$502$	1.63020e10	−	9.41195e9i	0.256700	−	0.148206i
$503$		−	4.64077e10i		−	0.724966i	−0.931990	−	0.362483i	$-0.881929\pi$
$503$		−	4.64077e10i		−	0.724966i	0.931990	−	0.362483i	$-0.118071\pi$
$504$		0			0
$505$	−6.08548e10			−0.935684
$506$	5.47985e7	+	9.49138e7i	0.000835923	+	0.00144786i
$507$		0			0
$508$	−1.11378e10	+	1.92912e10i	−0.167242	+	0.289671i
$509$	4.70380e10	−	2.71574e10i	0.700773	−	0.404591i	−0.106862	−	0.994274i	$-0.534080\pi$
$509$	4.70380e10	−	2.71574e10i	0.700773	−	0.404591i	0.807635	+	0.589682i	$0.200747\pi$
$510$		0			0
$511$	9.21396e10	+	3.26160e9i	1.35133	+	0.0478351i
$512$	3.03700e9			0.0441942
$513$		0			0
$514$	−8.45239e10	−	4.87999e10i	−1.21095	−	0.699144i
$515$	2.54350e10	−	4.40547e10i	0.361579	−	0.626272i
$516$		0			0
$517$		−	9.74318e6i		−	0.000136376i
$518$	−3.26858e9	+	9.23368e10i	−0.0453983	+	1.28250i
$519$		0			0
$520$	−1.65045e10	−	2.85867e10i	−0.225730	−	0.390976i
$521$	9.49506e10	+	5.48197e10i	1.28868	+	0.744023i	0.978420	−	0.206628i	$-0.0662488\pi$
$521$	9.49506e10	+	5.48197e10i	1.28868	+	0.744023i	0.310265	+	0.950650i	$0.399582\pi$
$522$		0			0
$523$	−2.93392e10	+	1.69390e10i	−0.392140	+	0.226402i	−0.683087	−	0.730337i	$-0.739363\pi$
$523$	−2.93392e10	+	1.69390e10i	−0.392140	+	0.226402i	0.290947	+	0.956739i	$0.406030\pi$
$524$			4.61141e10i			0.611659i
$525$		0			0
$526$	−8.84854e10			−1.15592
$527$	−1.14217e11	−	1.97830e11i	−1.48077	−	2.56477i
$528$		0			0
$529$	2.13306e10	−	3.69457e10i	0.272383	−	0.471781i
$530$	−1.37765e10	+	7.95387e9i	−0.174597	+	0.100803i
$531$		0			0
$532$	2.87496e10	+	5.41324e10i	0.358909	+	0.675788i
$533$	1.28005e11			1.58605
$534$		0			0
$535$	−6.98912e10	−	4.03517e10i	−0.853115	−	0.492546i
$536$	−1.26823e10	+	2.19664e10i	−0.153652	+	0.266133i
$537$		0			0
$538$			6.06450e10i			0.723879i
$539$	1.29402e8	+	2.65957e8i	0.00153315	+	0.00315106i
$540$		0			0
$541$	5.67999e10	+	9.83803e10i	0.663068	+	1.14847i	0.979805	+	0.199955i	$0.0640794\pi$
$541$	5.67999e10	+	9.83803e10i	0.663068	+	1.14847i	−0.316737	+	0.948513i	$0.602587\pi$
$542$	5.21427e10	+	3.01046e10i	0.604222	+	0.348848i
$543$		0			0
$544$	−2.32901e10	+	1.34466e10i	−0.265935	+	0.153538i
$545$			7.84552e10i			0.889274i
$546$		0			0
$547$	−1.34000e11			−1.49678			−0.748388	−	0.663261i	$-0.769172\pi$
$547$	−1.34000e11			−1.49678			−0.748388	+	0.663261i	$0.769172\pi$
$548$	1.28386e10	+	2.22371e10i	0.142362	+	0.246579i
$549$		0			0
$550$	2.93257e7	−	5.07935e7i	0.000320477	−	0.000555083i
$551$	7.79596e9	−	4.50100e9i	0.0845792	−	0.0488318i
$552$		0			0
$553$	3.26841e10	+	2.04450e10i	0.349491	+	0.218618i
$554$	2.32553e9			0.0246878
$555$		0			0
$556$	−1.01111e9	−	5.83766e8i	−0.0105804	−	0.00610857i
$557$	8.00384e10	−	1.38631e11i	0.831530	−	1.44025i	−0.0652955	−	0.997866i	$-0.520799\pi$
$557$	8.00384e10	−	1.38631e11i	0.831530	−	1.44025i	0.896825	−	0.442385i	$-0.145868\pi$
$558$		0			0
$559$		−	5.04033e10i		−	0.516192i
$560$	−2.75662e10	−	9.75798e8i	−0.280301	−	0.00992220i
$561$		0			0
$562$	3.12202e10	+	5.40750e10i	0.312961	+	0.542065i
$563$	−1.99832e10	−	1.15373e10i	−0.198899	−	0.114834i	0.397243	−	0.917713i	$-0.369967\pi$
$563$	−1.99832e10	−	1.15373e10i	−0.198899	−	0.114834i	−0.596142	+	0.802879i	$0.703300\pi$
$564$		0			0
$565$	1.02480e10	−	5.91671e9i	0.100565	−	0.0580612i
$566$			8.05044e10i			0.784430i
$567$		0			0
$568$	−1.24744e10			−0.119847
$569$	−2.13235e10	−	3.69333e10i	−0.203427	−	0.352346i	0.746203	−	0.665718i	$-0.231875\pi$
$569$	−2.13235e10	−	3.69333e10i	−0.203427	−	0.352346i	−0.949630	+	0.313372i	$0.898541\pi$
$570$		0			0
$571$	4.78333e10	−	8.28497e10i	0.449972	−	0.779375i	−0.548411	−	0.836209i	$-0.684767\pi$
$571$	4.78333e10	−	8.28497e10i	0.449972	−	0.779375i	0.998384	+	0.0568339i	$0.0181006\pi$
$572$	1.84879e8	−	1.06740e8i	0.00172704	−	0.000997109i
$573$		0			0
$574$	5.67262e10	−	9.06846e10i	0.522560	−	0.835384i
$575$	1.90782e10			0.174528
$576$		0			0
$577$	−2.78602e10	−	1.60851e10i	−0.251351	−	0.145118i	0.369032	−	0.929417i	$-0.379689\pi$
$577$	−2.78602e10	−	1.60851e10i	−0.251351	−	0.145118i	−0.620383	+	0.784299i	$0.713023\pi$
$578$	7.96104e10	−	1.37889e11i	0.713278	−	1.23543i
$579$		0			0
$580$			4.05112e9i			0.0357984i
$581$	2.57156e10	+	4.84197e10i	0.225679	+	0.424930i
$582$		0			0
$583$	−5.14402e7	−	8.90970e7i	−0.000445275	−	0.000771238i
$584$	−4.81584e10	−	2.78043e10i	−0.414019	−	0.239034i
$585$		0			0
$586$	1.63238e10	−	9.42457e9i	0.138431	−	0.0799229i
$587$		−	4.64261e10i		−	0.391030i	−0.980701	−	0.195515i	$-0.937362\pi$
$587$		−	4.64261e10i		−	0.391030i	0.980701	−	0.195515i	$-0.0626378\pi$
$588$		0			0
$589$	3.14018e11			2.60912
$590$	−5.11349e10	−	8.85683e10i	−0.421997	−	0.730920i
$591$		0			0
$592$	2.78638e10	−	4.82614e10i	0.226857	−	0.392928i
$593$	−1.44787e11	+	8.35927e10i	−1.17087	+	0.676004i	−0.953886	−	0.300170i	$-0.902957\pi$
$593$	−1.44787e11	+	8.35927e10i	−1.17087	+	0.676004i	−0.216988	+	0.976174i	$0.569623\pi$
$594$		0			0
$595$	2.15719e11	−	1.14568e11i	1.72116	−	0.914105i
$596$	4.42080e10			0.350361
$597$		0			0
$598$	6.01376e10	+	3.47204e10i	0.470263	+	0.271507i
$599$	−5.41914e10	+	9.38622e10i	−0.420943	+	0.729094i	−0.996032	−	0.0889966i	$-0.971634\pi$
$599$	−5.41914e10	+	9.38622e10i	−0.420943	+	0.729094i	0.575089	+	0.818091i	$0.304967\pi$
$600$		0			0
$601$			3.09111e9i			0.0236928i	0.999930	+	0.0118464i	$0.00377092\pi$
$601$			3.09111e9i			0.0236928i	−0.999930	+	0.0118464i	$0.996229\pi$
$602$	−3.57080e10	−	2.23365e10i	−0.271881	−	0.170071i
$603$		0			0
$604$	3.95713e9	+	6.85395e9i	0.0297326	+	0.0514983i
$605$	−1.30168e11	−	7.51523e10i	−0.971586	−	0.560946i
$606$		0			0
$607$	−5.77092e10	+	3.33184e10i	−0.425100	+	0.245431i	−0.697257	−	0.716821i	$-0.745596\pi$
$607$	−5.77092e10	+	3.33184e10i	−0.425100	+	0.245431i	0.272157	+	0.962253i	$0.412263\pi$
$608$		−	3.69687e10i		−	0.270533i
$609$		0			0
$610$	1.03606e11			0.748282
$611$	−3.08665e9	−	5.34623e9i	−0.0221474	−	0.0383604i
$612$		0			0
$613$	−9.80316e10	+	1.69796e11i	−0.694263	+	1.20250i	0.276165	+	0.961110i	$0.410936\pi$
$613$	−9.80316e10	+	1.69796e11i	−0.694263	+	1.20250i	−0.970428	+	0.241389i	$0.922397\pi$
$614$	−3.32676e10	+	1.92071e10i	−0.234071	+	0.135141i
$615$		0			0
$616$	6.31079e6	−	1.78279e8i	4.38289e−5	−	0.00123816i
$617$	9.94637e10			0.686315			0.343158	−	0.939278i	$-0.388503\pi$
$617$	9.94637e10			0.686315			0.343158	+	0.939278i	$0.388503\pi$
$618$		0			0
$619$	−1.59483e11	−	9.20774e10i	−1.08630	−	0.627177i	−0.153713	−	0.988116i	$-0.549123\pi$
$619$	−1.59483e11	−	9.20774e10i	−1.08630	−	0.627177i	−0.932590	+	0.360938i	$0.882456\pi$
$620$	−7.06579e10	+	1.22383e11i	−0.478183	+	0.828237i
$621$		0			0
$622$			7.48704e10i			0.500206i
$623$	1.33759e11	−	2.13832e11i	0.887912	−	1.41945i
$624$		0			0
$625$	9.09241e10	+	1.57485e11i	0.595880	+	1.03209i
$626$	1.56642e11	+	9.04374e10i	1.02003	+	0.588913i
$627$		0			0
$628$	−5.33102e10	+	3.07787e10i	−0.342746	+	0.197884i
$629$			4.93476e11i			3.15256i
$630$		0			0
$631$	−4.06646e10			−0.256507			−0.128253	−	0.991741i	$-0.540937\pi$
$631$	−4.06646e10			−0.256507			−0.128253	+	0.991741i	$0.540937\pi$
$632$	−1.16262e10	−	2.01372e10i	−0.0728737	−	0.126221i
$633$		0			0
$634$	7.87003e10	−	1.36313e11i	0.487102	−	0.843685i
$635$	−1.05678e11	+	6.10134e10i	−0.649967	+	0.375258i
$636$		0			0
$637$	1.55260e11	+	1.04940e11i	0.942980	+	0.637358i
$638$	−2.61999e7			−0.000158131
$639$		0			0
$640$	1.44079e10	+	8.31842e9i	0.0858780	+	0.0495817i
$641$	1.38149e11	−	2.39281e11i	0.818304	−	1.41734i	−0.0886267	−	0.996065i	$-0.528248\pi$
$641$	1.38149e11	−	2.39281e11i	0.818304	−	1.41734i	0.906931	−	0.421279i	$-0.138419\pi$
$642$		0			0
$643$		−	7.00082e10i		−	0.409548i	−0.978809	−	0.204774i	$-0.934354\pi$
$643$		−	7.00082e10i		−	0.409548i	0.978809	−	0.204774i	$-0.0656460\pi$
$644$	5.12479e10	−	2.72176e10i	0.297942	−	0.158237i
$645$		0			0
$646$	1.63682e11	+	2.83505e11i	0.939876	+	1.62791i
$647$	9.44301e10	+	5.45192e10i	0.538882	+	0.311123i	0.744626	−	0.667482i	$-0.232628\pi$
$647$	9.44301e10	+	5.45192e10i	0.538882	+	0.311123i	−0.205744	+	0.978606i	$0.565961\pi$
$648$		0			0
$649$	5.72799e8	−	3.30705e8i	0.00322867	−	0.00186407i
$650$		−	3.71616e10i		−	0.208181i
$651$		0			0
$652$	−1.39274e11			−0.770693
$653$	7.94409e10	+	1.37596e11i	0.436910	+	0.756750i	0.997449	−	0.0713779i	$-0.0227396\pi$
$653$	7.94409e10	+	1.37596e11i	0.436910	+	0.756750i	−0.560540	+	0.828128i	$0.689406\pi$
$654$		0			0
$655$	−1.26308e11	+	2.18772e11i	−0.686223	+	1.18857i
$656$	−5.58722e10	+	3.22578e10i	−0.301704	+	0.174189i
$657$		0			0
$658$	−5.15538e9	−	1.82492e8i	−0.0275015	−	0.000973511i
$659$	1.48506e11			0.787412			0.393706	−	0.919236i	$-0.371193\pi$
$659$	1.48506e11			0.787412			0.393706	+	0.919236i	$0.371193\pi$
$660$		0			0
$661$	1.98165e11	+	1.14411e11i	1.03806	+	0.599323i	0.919283	−	0.393598i	$-0.128770\pi$
$661$	1.98165e11	+	1.14411e11i	1.03806	+	0.599323i	0.118776	+	0.992921i	$0.462103\pi$
$662$	1.03271e11	−	1.78870e11i	0.537706	−	0.931334i
$663$		0			0
$664$		−	3.30674e10i		−	0.170109i
$665$	−1.18782e10	+	3.35557e11i	−0.0607384	+	1.71585i
$666$		0			0
$667$	−4.26116e9	−	7.38055e9i	−0.0215290	−	0.0372894i
$668$	−1.61902e11	−	9.34741e10i	−0.813104	−	0.469446i
$669$		0			0
$670$	−1.20333e11	+	6.94742e10i	−0.597152	+	0.344766i
$671$			6.70052e8i			0.00330536i
$672$		0			0
$673$	−1.83564e11			−0.894805			−0.447402	−	0.894333i	$-0.647651\pi$
$673$	−1.83564e11			−0.894805			−0.447402	+	0.894333i	$0.647651\pi$
$674$	−4.11618e10	−	7.12943e10i	−0.199459	−	0.345474i
$675$		0			0
$676$	1.54238e10	−	2.67149e10i	0.0738594	−	0.127928i
$677$	−9.02613e10	+	5.21124e10i	−0.429682	+	0.248077i	−0.699211	−	0.714915i	$-0.746465\pi$
$677$	−9.02613e10	+	5.21124e10i	−0.429682	+	0.248077i	0.269529	+	0.962992i	$0.413132\pi$
$678$		0			0
$679$	7.83681e10	+	1.47559e11i	0.368689	+	0.694202i
$680$	−1.47322e11			−0.689019
$681$		0			0
$682$	−7.91490e8	−	4.56967e8i	−0.00365854	−	0.00211226i
$683$	−5.73559e10	+	9.93434e10i	−0.263570	+	0.456516i	−0.967188	−	0.254062i	$-0.918233\pi$
$683$	−5.73559e10	+	9.93434e10i	−0.263570	+	0.456516i	0.703618	+	0.710578i	$0.251567\pi$
$684$		0			0
$685$			1.40661e11i			0.638868i
$686$	1.43149e11	−	6.34887e10i	0.646385	−	0.286681i
$687$		0			0
$688$	1.27018e10	+	2.20002e10i	0.0566909	+	0.0981915i
$689$	−5.64520e10	−	3.25926e10i	−0.250497	−	0.144625i
$690$		0			0
$691$	−3.02268e10	+	1.74514e10i	−0.132581	+	0.0765454i	−0.564823	−	0.825212i	$-0.691056\pi$
$691$	−3.02268e10	+	1.74514e10i	−0.132581	+	0.0765454i	0.432243	+	0.901757i	$0.357722\pi$
$692$			1.64885e11i			0.719047i
$693$		0			0
$694$	1.17381e10			0.0506012
$695$	−3.19790e9	−	5.53893e9i	−0.0137065	−	0.0237403i
$696$		0			0
$697$	2.85648e11	−	4.94757e11i	1.21032	−	2.09634i
$698$	1.89392e11	−	1.09346e11i	0.797886	−	0.460660i
$699$		0			0
$700$	−2.63270e10	−	1.64684e10i	−0.109650	−	0.0685897i
$701$	4.04644e11			1.67572			0.837858	−	0.545888i	$-0.183808\pi$
$701$	4.04644e11			1.67572			0.837858	+	0.545888i	$0.183808\pi$
$702$		0			0
$703$	−5.87476e11	−	3.39179e11i	−2.40530	−	1.38870i
$704$	−5.37978e7	+	9.31806e7i	−0.000219015	+	0.000379345i
$705$		0			0
$706$		−	1.57632e11i		−	0.634491i
$707$	−2.08247e11	−	7.37161e9i	−0.833492	−	0.0295043i
$708$		0			0
$709$	−8.03552e10	−	1.39179e11i	−0.318001	−	0.550795i	0.662070	−	0.749442i	$-0.269678\pi$
$709$	−8.03552e10	−	1.39179e11i	−0.318001	−	0.550795i	−0.980071	+	0.198648i	$0.936345\pi$
$710$	−5.91804e10	−	3.41678e10i	−0.232887	−	0.134457i
$711$		0			0
$712$	−1.31745e11	+	7.60631e10i	−0.512643	+	0.295974i
$713$		−	2.97285e11i		−	1.15031i
$714$		0			0
$715$	1.16945e9			0.00447465
$716$	6.37768e10	+	1.10465e11i	0.242667	+	0.420311i
$717$		0			0
$718$	9.57817e10	−	1.65899e11i	0.360400	−	0.624231i
$719$	−2.86258e11	+	1.65271e11i	−1.07113	+	0.618416i	−0.928489	−	0.371359i	$-0.878892\pi$
$719$	−2.86258e11	+	1.65271e11i	−1.07113	+	0.618416i	−0.142639	+	0.989775i	$0.545559\pi$
$720$		0			0
$721$	9.23759e10	−	1.47676e11i	0.341836	−	0.546471i
$722$	−2.57865e11			−0.948952
$723$		0			0
$724$	1.33011e11	+	7.67937e10i	0.484097	+	0.279493i
$725$	−2.28038e9	+	3.94973e9i	−0.00825382	+	0.0142960i
$726$		0			0
$727$			5.22460e11i			1.87032i	0.354230	+	0.935158i	$0.384743\pi$
$727$			5.22460e11i			1.87032i	−0.354230	+	0.935158i	$0.615257\pi$
$728$	−5.30162e10	−	9.98237e10i	−0.188748	−	0.355393i
$729$		0			0
$730$	−1.52313e11	−	2.63814e11i	−0.536347	−	0.928981i
$731$	−1.94816e11	−	1.12477e11i	−0.682267	−	0.393907i
$732$		0			0
$733$	−2.59008e11	+	1.49539e11i	−0.897218	+	0.518009i	−0.876297	−	0.481772i	$-0.839993\pi$
$733$	−2.59008e11	+	1.49539e11i	−0.897218	+	0.518009i	−0.0209215	+	0.999781i	$0.506660\pi$
$734$			8.98260e10i			0.309470i
$735$		0			0
$736$	−3.49988e10			−0.119273
$737$	−4.49311e8	−	7.78230e8i	−0.00152292	−	0.00263778i
$738$		0			0
$739$	1.58713e11	−	2.74898e11i	0.532149	−	0.921710i	−0.467146	−	0.884180i	$-0.654718\pi$
$739$	1.58713e11	−	2.74898e11i	0.532149	−	0.921710i	0.999296	−	0.0375297i	$-0.0119489\pi$
$740$	2.64379e11	−	1.52639e11i	0.881657	−	0.509025i
$741$		0			0
$742$	−4.81071e10	+	2.55496e10i	−0.158706	+	0.0842885i
$743$	2.55243e11			0.837526			0.418763	−	0.908096i	$-0.362464\pi$
$743$	2.55243e11			0.837526			0.418763	+	0.908096i	$0.362464\pi$
$744$		0			0
$745$	2.09729e11	+	1.21087e11i	0.680820	+	0.393072i
$746$	−9.21244e9	+	1.59564e10i	−0.0297454	+	0.0515205i
$747$		0			0
$748$		−	9.52776e8i		−	0.00304358i
$749$	−2.34282e11	−	1.46551e11i	−0.744409	−	0.465653i
$750$		0			0
$751$	−2.78274e10	−	4.81985e10i	−0.0874810	−	0.151521i	0.818965	−	0.573844i	$-0.194548\pi$
$751$	−2.78274e10	−	4.81985e10i	−0.0874810	−	0.151521i	−0.906446	+	0.422322i	$0.861215\pi$
$752$	2.69455e9	+	1.55570e9i	0.00842587	+	0.00486468i
$753$		0			0
$754$	−1.43763e10	+	8.30015e9i	−0.0444796	+	0.0256803i
$755$			4.33547e10i			0.133428i
$756$		0			0
$757$	1.51282e11			0.460684			0.230342	−	0.973110i	$-0.426015\pi$
$757$	1.51282e11			0.460684			0.230342	+	0.973110i	$0.426015\pi$
$758$	−1.18471e11	−	2.05199e11i	−0.358870	−	0.621581i
$759$		0			0
$760$	1.01258e11	−	1.75385e11i	0.303512	−	0.525699i
$761$	−3.45291e11	+	1.99354e11i	−1.02955	+	0.594411i	−0.916856	−	0.399219i	$-0.869281\pi$
$761$	−3.45291e11	+	1.99354e11i	−1.02955	+	0.594411i	−0.112694	+	0.993630i	$0.535948\pi$
$762$		0			0
$763$	−9.50363e9	+	2.68476e11i	−0.0280409	+	0.792150i
$764$	1.24357e11			0.365004
$765$		0			0
$766$	−9.19067e10	−	5.30623e10i	−0.266951	−	0.154124i
$767$	2.09536e11	−	3.62926e11i	0.605448	−	1.04867i
$768$		0			0
$769$		−	5.28713e10i		−	0.151187i	−0.997139	−	0.0755936i	$-0.975915\pi$
$769$		−	5.28713e10i		−	0.151187i	0.997139	−	0.0755936i	$-0.0240852\pi$
$770$	5.18250e8	−	8.28494e8i	0.00147427	−	0.00235682i
$771$		0			0
$772$	−4.88990e10	−	8.46956e10i	−0.137667	−	0.238447i
$773$	2.30293e10	+	1.32960e10i	0.0645005	+	0.0372394i	0.531903	−	0.846805i	$-0.321477\pi$
$773$	2.30293e10	+	1.32960e10i	0.0645005	+	0.0372394i	−0.467403	+	0.884044i	$0.654810\pi$
$774$		0			0
$775$	−1.37779e11	+	7.95467e10i	−0.381923	+	0.220504i
$776$		−	1.00773e11i		−	0.277905i
$777$		0			0
$778$	1.59728e10			0.0435976
$779$	3.92668e11	+	6.80120e11i	1.06629	+	1.84687i
$780$		0			0
$781$	2.20974e8	−	3.82738e8i	0.000593932	−	0.00102872i
$782$	2.68399e11	−	1.54960e11i	0.717717	−	0.414374i
$783$		0			0
$784$	−9.42141e10	−	6.67842e9i	−0.249374	−	0.0176770i
$785$	−3.37214e11			−0.888030
$786$		0			0
$787$	1.39157e11	+	8.03422e10i	0.362748	+	0.209433i	0.670286	−	0.742103i	$-0.266172\pi$
$787$	1.39157e11	+	8.03422e10i	0.362748	+	0.209433i	−0.307537	+	0.951536i	$0.599505\pi$
$788$	2.20660e10	−	3.82194e10i	0.0572293	−	0.0991240i
$789$		0			0
$790$		−	1.27378e11i		−	0.327029i
$791$	3.57858e10	−	1.90058e10i	0.0914124	−	0.0485489i
$792$		0			0
$793$	2.12273e11	+	3.67668e11i	0.536787	+	0.929743i
$794$	1.43911e11	+	8.30868e10i	0.362085	+	0.209050i
$795$		0			0
$796$	−4.78072e10	+	2.76015e10i	−0.119081	+	0.0687512i
$797$		−	4.30829e11i		−	1.06776i	−0.845562	−	0.533878i	$-0.820734\pi$
$797$		−	4.30829e11i		−	1.06776i	0.845562	−	0.533878i	$-0.179266\pi$
$798$		0			0
$799$	−2.75519e10			−0.0676028
$800$	9.36489e9	+	1.62205e10i	0.0228635	+	0.0396007i
$801$		0			0
$802$	1.12152e11	−	1.94253e11i	0.271088	−	0.469538i
$803$	1.70617e9	−	9.85057e8i	0.00410355	−	0.00236919i
$804$		0			0
$805$	3.17676e11	+	1.12452e10i	0.756487	+	0.0267784i
$806$	−5.79070e11			−1.37212
$807$		0			0
$808$	1.08844e11	+	6.28411e10i	0.255364	+	0.147434i
$809$	−2.79510e11	+	4.84126e11i	−0.652535	+	1.13022i	0.329971	+	0.943991i	$0.392961\pi$
$809$	−2.79510e11	+	4.84126e11i	−0.652535	+	1.13022i	−0.982506	+	0.186232i	$0.940372\pi$
$810$		0			0
$811$			1.62918e9i			0.00376605i	0.999998	+	0.00188303i	$0.000599387\pi$
$811$			1.62918e9i			0.00376605i	−0.999998	+	0.00188303i	$0.999401\pi$
$812$	−4.90731e8	+	1.38631e10i	−0.00112881	+	0.0318886i
$813$		0			0
$814$	9.87165e8	+	1.70982e9i	0.00224850	+	0.00389451i
$815$	−6.60737e11	−	3.81476e11i	−1.49761	−	0.864644i
$816$		0			0
$817$	2.67804e11	−	1.54617e11i	0.601076	−	0.347031i
$818$			3.02672e11i			0.676018i
$819$		0			0
$820$	−3.53420e11			−0.781693
$821$	1.12094e11	+	1.94153e11i	0.246723	+	0.427337i	0.962615	−	0.270874i	$-0.0873128\pi$
$821$	1.12094e11	+	1.94153e11i	0.246723	+	0.427337i	−0.715891	+	0.698212i	$0.753979\pi$
$822$		0			0
$823$	−3.77547e11	+	6.53931e11i	−0.822947	+	1.42539i	0.0805307	+	0.996752i	$0.474339\pi$
$823$	−3.77547e11	+	6.53931e11i	−0.822947	+	1.42539i	−0.903478	+	0.428634i	$0.858995\pi$
$824$	−9.09853e10	+	5.25304e10i	−0.197361	+	0.113947i
$825$		0			0
$826$	−1.64257e11	−	3.09278e11i	−0.352860	−	0.664398i
$827$	−4.00032e11			−0.855209			−0.427605	−	0.903966i	$-0.640642\pi$
$827$	−4.00032e11			−0.855209			−0.427605	+	0.903966i	$0.640642\pi$
$828$		0			0
$829$	−7.79461e11	−	4.50022e11i	−1.65035	−	0.952830i	−0.976927	−	0.213574i	$-0.931490\pi$
$829$	−7.79461e11	−	4.50022e11i	−1.65035	−	0.952830i	−0.673424	−	0.739257i	$-0.735177\pi$
$830$	9.05725e10	−	1.56876e11i	0.190846	−	0.330556i
$831$		0			0
$832$			6.81729e10i			0.142272i
$833$	7.52077e11	−	3.65925e11i	1.56200	−	0.759997i
$834$		0			0
$835$	−5.12056e11	−	8.86907e11i	−1.05335	−	1.82445i
$836$	1.13427e9	+	6.54869e8i	0.00232215	+	0.00134069i
$837$		0			0
$838$	3.82193e11	−	2.20659e11i	0.775008	−	0.447451i
$839$		−	9.73366e11i		−	1.96439i	−0.187855	−	0.982197i	$-0.560153\pi$
$839$		−	9.73366e11i		−	1.96439i	0.187855	−	0.982197i	$-0.439847\pi$
$840$		0			0
$841$	−4.98209e11			−0.995927
$842$	−3.76425e10	−	6.51987e10i	−0.0748910	−	0.129715i
$843$		0			0
$844$	2.09378e11	−	3.62653e11i	0.412630	−	0.714696i
$845$	1.46345e11	−	8.44926e10i	0.287047	−	0.165726i
$846$		0			0
$847$	−4.36334e11	−	2.72941e11i	−0.847785	−	0.530317i
$848$	3.28539e10			0.0635337
$849$		0			0
$850$	−1.43635e11	−	8.29275e10i	−0.275159	−	0.158863i
$851$	−3.21106e11	+	5.56172e11i	−0.612252	+	1.06045i
$852$		0			0
$853$		−	2.69191e11i		−	0.508469i	−0.967143	−	0.254235i	$-0.918176\pi$
$853$		−	2.69191e11i		−	0.508469i	0.967143	−	0.254235i	$-0.0818236\pi$
$854$	3.54543e11	+	1.25502e10i	0.666557	+	0.0235950i
$855$		0			0
$856$	8.33376e10	+	1.44345e11i	0.155219	+	0.268848i
$857$	5.28096e11	+	3.04897e11i	0.979016	+	0.565235i	0.901973	−	0.431793i	$-0.142119\pi$
$857$	5.28096e11	+	3.04897e11i	0.979016	+	0.565235i	0.0770431	+	0.997028i	$0.475452\pi$
$858$		0			0
$859$	9.14679e11	−	5.28090e11i	1.67995	−	0.969918i	0.718259	−	0.695776i	$-0.244939\pi$
$859$	9.14679e11	−	5.28090e11i	1.67995	−	0.969918i	0.961689	−	0.274142i	$-0.0883939\pi$
$860$			1.39163e11i			0.254407i
$861$		0			0
$862$	1.65882e11			0.300449
$863$	−1.32259e10	−	2.29080e10i	−0.0238442	−	0.0412994i	0.853857	−	0.520508i	$-0.174257\pi$
$863$	−1.32259e10	−	2.29080e10i	−0.0238442	−	0.0412994i	−0.877701	+	0.479208i	$0.840924\pi$
$864$		0			0
$865$	−4.51625e11	+	7.82238e11i	−0.806703	+	1.39725i
$866$	3.65785e11	−	2.11186e11i	0.650361	−	0.375486i
$867$		0			0
$868$	−2.56618e11	+	4.10240e11i	−0.452073	+	0.722701i
$869$	8.23795e8			0.00144457
$870$		0			0
$871$	−4.93088e11	−	2.84685e11i	−0.856746	−	0.494643i
$872$	8.10159e10	−	1.40324e11i	0.140121	−	0.242697i
$873$		0			0
$874$			4.26033e11i			0.730126i
$875$	2.28675e11	+	4.30571e11i	0.390110	+	0.734534i
$876$		0			0
$877$	−6.42769e10	−	1.11331e11i	−0.108657	−	0.188199i	0.806570	−	0.591139i	$-0.201322\pi$
$877$	−6.42769e10	−	1.11331e11i	−0.108657	−	0.188199i	−0.915226	+	0.402940i	$0.867988\pi$
$878$	−1.47456e11	−	8.51340e10i	−0.248134	−	0.143260i
$879$		0			0
$880$	−5.10448e8	+	2.94707e8i	−0.000851179	+	0.000491429i
$881$			1.98233e11i			0.329057i	0.986372	+	0.164529i	$0.0526103\pi$
$881$			1.98233e11i			0.329057i	−0.986372	+	0.164529i	$0.947390\pi$
$882$		0			0
$883$	9.19955e11			1.51330			0.756648	−	0.653823i	$-0.226836\pi$
$883$	9.19955e11			1.51330			0.756648	+	0.653823i	$0.226836\pi$
$884$	−3.01841e11	−	5.22803e11i	−0.494275	−	0.856109i
$885$		0			0
$886$	−3.62689e11	+	6.28196e11i	−0.588572	+	1.01944i
$887$	5.12659e11	−	2.95984e11i	0.828198	−	0.478161i	−0.0250371	−	0.999687i	$-0.507970\pi$
$887$	5.12659e11	−	2.95984e11i	0.828198	−	0.478161i	0.853235	+	0.521526i	$0.174637\pi$
$888$		0			0
$889$	−3.69026e11	+	1.95989e11i	−0.590812	+	0.313779i
$890$	−8.33355e11			−1.32822
$891$		0			0
$892$	1.34666e11	+	7.77494e10i	0.212715	+	0.122811i
$893$	1.89372e10	−	3.28002e10i	0.0297790	−	0.0515787i
$894$		0			0
$895$			6.98745e11i			1.08900i
$896$	4.82968e10	+	3.02112e10i	0.0749352	+	0.0468744i
$897$		0			0
$898$	2.15014e11	+	3.72415e11i	0.330644	+	0.572693i
$899$	6.15467e10	+	3.55340e10i	0.0942250	+	0.0544008i
$900$		0			0
$901$	−2.51950e11	+	1.45463e11i	−0.382309	+	0.220726i
$902$		−	2.28568e9i		−	0.00345294i
$903$		0			0
$904$	−2.44393e10			−0.0365944
$905$	4.20680e11	+	7.28639e11i	0.627130	+	1.08622i
$906$		0			0
$907$	3.14821e11	−	5.45286e11i	0.465195	−	0.805741i	−0.534016	−	0.845475i	$-0.679318\pi$
$907$	3.14821e11	−	5.45286e11i	0.465195	−	0.805741i	0.999210	+	0.0397339i	$0.0126510\pi$
$908$	2.20536e11	−	1.27327e11i	0.324442	−	0.187317i
$909$		0			0
$910$	2.19042e10	−	6.18790e11i	0.0319419	−	0.902355i
$911$	−6.13193e11			−0.890274			−0.445137	−	0.895462i	$-0.646845\pi$
$911$	−6.13193e11			−0.890274			−0.445137	+	0.895462i	$0.646845\pi$
$912$		0			0
$913$	1.01457e9	+	5.85760e8i	0.00146015	+	0.000843018i
$914$	−2.34273e11	+	4.05773e11i	−0.335690	+	0.581431i
$915$		0			0
$916$			4.73359e11i			0.672371i
$917$	−4.58730e11	+	7.33343e11i	−0.648754	+	1.03712i
$918$		0			0
$919$	−2.17693e11	−	3.77056e11i	−0.305199	−	0.528620i	0.672107	−	0.740454i	$-0.265390\pi$
$919$	−2.17693e11	−	3.77056e11i	−0.305199	−	0.528620i	−0.977306	+	0.211834i	$0.932056\pi$
$920$	−1.66039e11	−	9.58627e10i	−0.231771	−	0.133813i
$921$		0			0
$922$	−2.65934e11	+	1.53537e11i	−0.368002	+	0.212466i
$923$		−	2.80019e11i		−	0.385817i
$924$		0			0
$925$	3.43683e11			0.469451
$926$	3.02001e11	+	5.23081e11i	0.410738	+	0.711419i
$927$		0			0
$928$	4.18335e9	−	7.24578e9i	0.00564069	−	0.00976997i
$929$	1.98362e11	−	1.14524e11i	0.266315	−	0.153757i	−0.360897	−	0.932606i	$-0.617529\pi$
$929$	1.98362e11	−	1.14524e11i	0.266315	−	0.153757i	0.627212	+	0.778849i	$0.284196\pi$
$930$		0			0
$931$	−8.12950e10	+	1.14685e12i	−0.108209	+	1.52654i
$932$	2.63956e11			0.349839
$933$		0			0
$934$	4.28826e11	+	2.47583e11i	0.563500	+	0.325337i
$935$	2.60968e9	−	4.52010e9i	0.00341461	−	0.00591427i
$936$		0			0
$937$		−	5.11176e11i		−	0.663151i	−0.943429	−	0.331575i	$-0.892420\pi$
$937$		−	5.11176e11i		−	0.663151i	0.943429	−	0.331575i	$-0.107580\pi$
$938$	−4.20199e11	+	2.23166e11i	−0.542804	+	0.288282i
$939$		0			0
$940$	8.52220e9	+	1.47609e10i	0.0109154	+	0.0189061i
$941$	5.15843e11	+	2.97822e11i	0.657899	+	0.379838i	0.791476	−	0.611200i	$-0.209313\pi$
$941$	5.15843e11	+	2.97822e11i	0.657899	+	0.379838i	−0.133577	+	0.991038i	$0.542646\pi$
$942$		0			0
$943$	6.43880e11	−	3.71744e11i	0.814250	−	0.470108i
$944$			2.11216e11i			0.265973i
$945$		0			0
$946$	−9.00009e8			−0.00112378
$947$	−6.38604e11	−	1.10609e12i	−0.794020	−	1.37528i	−0.923460	−	0.383696i	$-0.874651\pi$
$947$	−6.38604e11	−	1.10609e12i	−0.794020	−	1.37528i	0.129439	−	0.991587i	$-0.458682\pi$
$948$		0			0
$949$	6.24134e11	−	1.08103e12i	0.769508	−	1.33283i
$950$	1.97448e11	−	1.13997e11i	0.242415	−	0.139958i
$951$		0			0
$952$	−5.04140e11	−	1.78458e10i	−0.613767	−	0.0217264i
$953$	5.58803e11			0.677466			0.338733	−	0.940883i	$-0.390002\pi$
$953$	5.58803e11			0.677466			0.338733	+	0.940883i	$0.390002\pi$
$954$		0			0
$955$	5.89967e11	+	3.40618e11i	0.709275	+	0.409500i
$956$	−2.85166e11	+	4.93922e11i	−0.341402	+	0.591326i
$957$		0			0
$958$			1.13941e12i			1.35275i
$959$	−1.70389e10	+	4.81346e11i	−0.0201450	+	0.569093i
$960$		0			0
$961$	8.13091e11	+	1.40832e12i	0.953335	+	1.65123i
$962$	1.08335e12	+	6.25470e11i	1.26493	+	0.730308i
$963$		0			0
$964$	6.46973e11	−	3.73530e11i	0.749166	−	0.432531i
$965$		−	5.35743e11i		−	0.617799i
$966$		0			0
$967$	6.89336e11			0.788361			0.394181	−	0.919033i	$-0.371028\pi$
$967$	6.89336e11			0.788361			0.394181	+	0.919033i	$0.371028\pi$
$968$	1.55211e11	+	2.68832e11i	0.176775	+	0.306182i
$969$		0			0
$970$	2.76019e11	−	4.78079e11i	0.311783	−	0.540023i
$971$	−1.15517e12	+	6.66940e11i	−1.29948	+	0.750257i	−0.980315	−	0.197441i	$-0.936737\pi$
$971$	−1.15517e12	+	6.66940e11i	−1.29948	+	0.750257i	−0.319168	+	0.947698i	$0.603404\pi$
$972$		0			0
$973$	−1.02724e10	−	1.93418e10i	−0.0114609	−	0.0215797i
$974$	−5.12130e11			−0.569042
$975$		0			0
$976$	−1.85308e11	−	1.06988e11i	−0.204218	−	0.117905i
$977$	5.40202e11	−	9.35657e11i	0.592895	−	1.02692i	−0.400945	−	0.916102i	$-0.631318\pi$
$977$	5.40202e11	−	9.35657e11i	0.592895	−	1.02692i	0.993840	−	0.110822i	$-0.0353484\pi$
$978$		0			0
$979$		−	5.38957e9i		−	0.00586710i
$980$	−4.28672e11	−	2.89738e11i	−0.464751	−	0.314124i
$981$		0			0
$982$	5.78547e11	+	1.00207e12i	0.622146	+	1.07759i
$983$	−4.68508e11	−	2.70493e11i	−0.501768	−	0.289696i	0.227675	−	0.973737i	$-0.426887\pi$
$983$	−4.68508e11	−	2.70493e11i	−0.501768	−	0.289696i	−0.729443	+	0.684041i	$0.760221\pi$
$984$		0			0
$985$	2.09368e11	−	1.20879e11i	0.222416	−	0.128412i
$986$			7.40884e10i			0.0783868i
$987$		0			0
$988$	8.29853e11			0.870911
$989$	−1.46378e11	−	2.53534e11i	−0.153000	−	0.265003i
$990$		0			0
$991$	−4.45266e11	+	7.71224e11i	−0.461663	+	0.799624i	−0.999044	−	0.0437158i	$-0.986080\pi$
$991$	−4.45266e11	+	7.71224e11i	−0.461663	+	0.799624i	0.537381	+	0.843340i	$0.319414\pi$
$992$	2.52755e11	−	1.45928e11i	0.261008	−	0.150693i
$993$		0			0
$994$	−1.98378e11	−	1.24092e11i	−0.203212	−	0.127116i
$995$	−3.02405e11			−0.308529
$996$		0			0
$997$	8.12579e11	+	4.69143e11i	0.822403	+	0.474815i	0.851245	−	0.524769i	$-0.175848\pi$
$997$	8.12579e11	+	4.69143e11i	0.822403	+	0.474815i	−0.0288411	+	0.999584i	$0.509182\pi$
$998$	−2.67218e11	+	4.62836e11i	−0.269367	+	0.466557i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.n.c.73.1		12
3.2	odd	2		42.9.g.b.31.6	yes	12
7.5	odd	6	inner	126.9.n.c.19.1		12
21.5	even	6		42.9.g.b.19.6	✓	12
21.11	odd	6		294.9.c.b.97.6		12
21.17	even	6		294.9.c.b.97.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.9.g.b.19.6	✓	12	21.5	even	6
42.9.g.b.31.6	yes	12	3.2	odd	2
126.9.n.c.19.1		12	7.5	odd	6	inner
126.9.n.c.73.1		12	1.1	even	1	trivial
294.9.c.b.97.1		12	21.17	even	6
294.9.c.b.97.6		12	21.11	odd	6

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(-607.249 + 350.595i) q^{5} +(-2120.49 + 1126.19i) q^{7} +1448.15 q^{8} +O(q^{10})\)	\(q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(-607.249 + 350.595i) q^{5} +(-2120.49 + 1126.19i) q^{7} +1448.15 q^{8} +(6870.24 + 3966.53i) q^{10} +(-25.6528 + 44.4320i) q^{11} +32507.4i q^{13} +(23029.7 + 14405.8i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(125645. + 72541.4i) q^{17} +(-172719. + 99719.4i) q^{19} -89752.4i q^{20} +580.457 q^{22} +(94405.8 + 163516. i) q^{23} +(50521.7 - 87506.1i) q^{25} +(318506. - 183889. i) q^{26} +(10872.1 - 307136. i) q^{28} -45136.7 q^{29} +(-1.36356e6 - 787254. i) q^{31} +(-92681.9 + 160530. i) q^{32} -1.64142e6i q^{34} +(892831. - 1.42731e6i) q^{35} +(1.70067e6 + 2.94564e6i) q^{37} +(1.95409e6 + 1.12820e6i) q^{38} +(-879390. + 507716. i) q^{40} -3.93773e6i q^{41} -1.55052e6 q^{43} +(-3283.56 - 5687.29i) q^{44} +(1.06808e6 - 1.84997e6i) q^{46} +(-164462. + 94952.3i) q^{47} +(3.22819e6 - 4.77616e6i) q^{49} -1.14317e6 q^{50} +(-3.60348e6 - 2.08047e6i) q^{52} +(-1.00262e6 + 1.73659e6i) q^{53} -35975.0i q^{55} +(-3.07080e6 + 1.63090e6i) q^{56} +(255331. + 442247. i) q^{58} +(-1.11644e7 - 6.44579e6i) q^{59} +(1.13103e7 - 6.53000e6i) q^{61} +1.78135e7i q^{62} +2.09715e6 q^{64} +(-1.13969e7 - 1.97401e7i) q^{65} +(-8.75755e6 + 1.51685e7i) q^{67} +(-1.60826e7 + 9.28530e6i) q^{68} +(-1.90354e7 - 673822. i) q^{70} -8.61402e6 q^{71} +(-3.32550e7 - 1.91998e7i) q^{73} +(1.92409e7 - 3.33262e7i) q^{74} -2.55282e7i q^{76} +(4357.82 - 123108. i) q^{77} +(-8.02831e6 - 1.39054e7i) q^{79} +(9.94917e6 + 5.74415e6i) q^{80} +(-3.85817e7 + 2.22751e7i) q^{82} -2.28342e7i q^{83} -1.01731e8 q^{85} +(8.77106e6 + 1.51919e7i) q^{86} +(-37149.2 + 64344.4i) q^{88} +(-9.09745e7 + 5.25241e7i) q^{89} +(-3.66095e7 - 6.89317e7i) q^{91} -2.41679e7 q^{92} +(1.86068e6 + 1.07426e6i) q^{94} +(6.99223e7 - 1.21109e8i) q^{95} -6.95869e7i q^{97} +(-6.50580e7 - 4.61168e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 768 q^{4} + 1122 q^{5} - 4434 q^{7}+O(q^{10}) \) 12 * q - 768 * q^4 + 1122 * q^5 - 4434 * q^7	\( 12 q - 768 q^{4} + 1122 q^{5} - 4434 q^{7} + 4224 q^{10} - 9606 q^{11} + 19968 q^{14} - 98304 q^{16} + 227388 q^{17} + 315408 q^{19} + 557568 q^{22} + 663480 q^{23} + 601008 q^{25} + 585984 q^{26} + 398592 q^{28} - 5944884 q^{29} - 3214278 q^{31} + 1019784 q^{35} + 1607760 q^{37} + 986880 q^{38} - 540672 q^{40} + 12627648 q^{43} - 1229568 q^{44} - 4608768 q^{46} + 7830240 q^{47} + 16477242 q^{49} + 16565760 q^{50} - 4283904 q^{52} + 33200358 q^{53} + 8110080 q^{56} + 5576064 q^{58} + 29657382 q^{59} + 58344096 q^{61} + 25165824 q^{64} - 30909216 q^{65} + 7977444 q^{67} - 29105664 q^{68} - 59774976 q^{70} - 117213264 q^{71} - 170286636 q^{73} + 80311296 q^{74} + 3340686 q^{77} + 35420490 q^{79} - 18382848 q^{80} + 154232832 q^{82} + 416634600 q^{85} + 71958528 q^{86} - 35684352 q^{88} - 78064092 q^{89} + 335513292 q^{91} - 169850880 q^{92} - 18456576 q^{94} + 250727796 q^{95} + 150533376 q^{98}+O(q^{100}) \) 12 * q - 768 * q^4 + 1122 * q^5 - 4434 * q^7 + 4224 * q^10 - 9606 * q^11 + 19968 * q^14 - 98304 * q^16 + 227388 * q^17 + 315408 * q^19 + 557568 * q^22 + 663480 * q^23 + 601008 * q^25 + 585984 * q^26 + 398592 * q^28 - 5944884 * q^29 - 3214278 * q^31 + 1019784 * q^35 + 1607760 * q^37 + 986880 * q^38 - 540672 * q^40 + 12627648 * q^43 - 1229568 * q^44 - 4608768 * q^46 + 7830240 * q^47 + 16477242 * q^49 + 16565760 * q^50 - 4283904 * q^52 + 33200358 * q^53 + 8110080 * q^56 + 5576064 * q^58 + 29657382 * q^59 + 58344096 * q^61 + 25165824 * q^64 - 30909216 * q^65 + 7977444 * q^67 - 29105664 * q^68 - 59774976 * q^70 - 117213264 * q^71 - 170286636 * q^73 + 80311296 * q^74 + 3340686 * q^77 + 35420490 * q^79 - 18382848 * q^80 + 154232832 * q^82 + 416634600 * q^85 + 71958528 * q^86 - 35684352 * q^88 - 78064092 * q^89 + 335513292 * q^91 - 169850880 * q^92 - 18456576 * q^94 + 250727796 * q^95 + 150533376 * q^98

Introduction

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