LMFDB - Embedded newform 126.10.g.d.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,10,Mod(37,126)]

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, 2]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, 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:	$64.8945153566$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 373x^{4} - 756x^{3} + 139129x^{2} - 140994x + 142884 $ x^6 + 373x^4 - 756x^3 + 139129x^2 - 140994x + 142884
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 5^{2}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.2
Root			$-9.90063 - 17.1484i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.10.g.d.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.00000 - 13.8564i) q^{2} +(-128.000 + 221.703i) q^{4} +(-236.226 - 409.156i) q^{5} +(-844.647 - 6296.04i) q^{7} +4096.00 q^{8} +(-3779.62 + 6546.49i) q^{10} +(-9180.32 + 15900.8i) q^{11} -4756.67 q^{13} +(-80483.4 + 62072.1i) q^{14} +(-32768.0 - 56755.8i) q^{16} +(-131390. + 227575. i) q^{17} +(-358465. - 620880. i) q^{19} +120948. q^{20} +293770. q^{22} +(129911. + 225012. i) q^{23} +(864957. - 1.49815e6i) q^{25} +(38053.4 + 65910.4i) q^{26} +(1.50396e6 + 618633. i) q^{28} -4.40930e6 q^{29} +(3.01245e6 - 5.21771e6i) q^{31} +(-524288. + 908093. i) q^{32} +4.20449e6 q^{34} +(-2.37653e6 + 1.83288e6i) q^{35} +(2.28440e6 + 3.95669e6i) q^{37} +(-5.73544e6 + 9.93407e6i) q^{38} +(-967582. - 1.67590e6i) q^{40} -1.47923e7 q^{41} -2.14447e7 q^{43} +(-2.35016e6 - 4.07060e6i) q^{44} +(2.07857e6 - 3.60020e6i) q^{46} +(1.90435e7 + 3.29843e7i) q^{47} +(-3.89267e7 + 1.06359e7i) q^{49} -2.76786e7 q^{50} +(608854. - 1.05457e6i) q^{52} +(1.58740e6 - 2.74946e6i) q^{53} +8.67452e6 q^{55} +(-3.45967e6 - 2.57886e7i) q^{56} +(3.52744e7 + 6.10970e7i) q^{58} +(2.67921e7 - 4.64052e7i) q^{59} +(3.06950e7 + 5.31654e7i) q^{61} -9.63983e7 q^{62} +1.67772e7 q^{64} +(1.12365e6 + 1.94622e6i) q^{65} +(-1.17564e8 + 2.03626e8i) q^{67} +(-3.36359e7 - 5.82591e7i) q^{68} +(4.44094e7 + 1.82672e7i) q^{70} +2.74423e8 q^{71} +(-1.16701e8 + 2.02133e8i) q^{73} +(3.65504e7 - 6.33071e7i) q^{74} +1.83534e8 q^{76} +(1.07866e8 + 4.43691e7i) q^{77} +(2.75465e7 + 4.77119e7i) q^{79} +(-1.54813e7 + 2.68144e7i) q^{80} +(1.18338e8 + 2.04968e8i) q^{82} -9.49452e7 q^{83} +1.24151e8 q^{85} +(1.71558e8 + 2.97147e8i) q^{86} +(-3.76026e7 + 6.51296e7i) q^{88} +(3.49353e8 + 6.05097e8i) q^{89} +(4.01771e6 + 2.99482e7i) q^{91} -6.65144e7 q^{92} +(3.04696e8 - 5.27749e8i) q^{94} +(-1.69358e8 + 2.93336e8i) q^{95} +1.52006e9 q^{97} +(4.58789e8 + 4.54298e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 48 q^{2} - 768 q^{4} - 361 q^{5} + 12509 q^{7} + 24576 q^{8} - 5776 q^{10} - 37799 q^{11} - 441172 q^{13} - 38752 q^{14} - 196608 q^{16} + 781816 q^{17} - 620154 q^{19} + 184832 q^{20} + 1209568 q^{22}+ \cdots + 2185772400 q^{98}+O(q^{100}) $ 6 * q - 48 * q^2 - 768 * q^4 - 361 * q^5 + 12509 * q^7 + 24576 * q^8 - 5776 * q^10 - 37799 * q^11 - 441172 * q^13 - 38752 * q^14 - 196608 * q^16 + 781816 * q^17 - 620154 * q^19 + 184832 * q^20 + 1209568 * q^22 - 1204784 * q^23 - 4020946 * q^25 + 3529376 * q^26 - 2582272 * q^28 + 10561070 * q^29 + 12838457 * q^31 - 3145728 * q^32 - 25018112 * q^34 + 20450416 * q^35 + 8014770 * q^37 - 9922464 * q^38 - 1478656 * q^40 - 13006056 * q^41 - 45086976 * q^43 - 9676544 * q^44 - 19276544 * q^46 + 21473082 * q^47 - 92935311 * q^49 + 128670272 * q^50 + 56470016 * q^52 - 13685715 * q^53 + 610214782 * q^55 + 51236864 * q^56 - 84488560 * q^58 + 92528141 * q^59 - 7516114 * q^61 - 410830624 * q^62 + 100663296 * q^64 - 79637616 * q^65 - 137325404 * q^67 + 200144896 * q^68 + 33639760 * q^70 - 16380692 * q^71 + 394016164 * q^73 + 128236320 * q^74 + 317518848 * q^76 - 140332213 * q^77 + 35090117 * q^79 - 23658496 * q^80 + 104048448 * q^82 - 1913896010 * q^83 - 823798640 * q^85 + 360695808 * q^86 - 154824704 * q^88 + 855499686 * q^89 - 1675912546 * q^91 + 616849408 * q^92 + 343569312 * q^94 + 2705508088 * q^95 + 4021139590 * q^97 + 2185772400 * q^98

Character values

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

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−8.00000	−	13.8564i	−0.353553	−	0.612372i
$2$	−8.00000	−	13.8564i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	−236.226	−	409.156i	−0.169030	−	0.292768i	0.769049	−	0.639189i	$-0.220730\pi$
$5$	−236.226	−	409.156i	−0.169030	−	0.292768i	−0.938079	+	0.346421i	$0.887397\pi$
$6$		0			0
$7$	−844.647	−	6296.04i	−0.132964	−	0.991121i
$7$	−844.647	−	6296.04i	−0.132964	−	0.991121i
$8$	4096.00			0.353553
$9$		0			0
$10$	−3779.62	+	6546.49i	−0.119522	+	0.207018i
$11$	−9180.32	+	15900.8i	−0.189056	+	0.327455i	−0.944936	−	0.327256i	$-0.893876\pi$
$11$	−9180.32	+	15900.8i	−0.189056	+	0.327455i	0.755880	+	0.654710i	$0.227209\pi$
$12$		0			0
$13$	−4756.67			−0.0461911			−0.0230956	−	0.999733i	$-0.507352\pi$
$13$	−4756.67			−0.0461911			−0.0230956	+	0.999733i	$0.507352\pi$
$14$	−80483.4	+	62072.1i	−0.559925	+	0.431838i
$15$		0			0
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	−131390.	+	227575.i	−0.381543	+	0.660851i	−0.991283	−	0.131750i	$-0.957940\pi$
$17$	−131390.	+	227575.i	−0.381543	+	0.660851i	0.609740	+	0.792601i	$0.291274\pi$
$18$		0			0
$19$	−358465.	−	620880.i	−0.631038	−	1.09299i	−0.987340	−	0.158619i	$-0.949296\pi$
$19$	−358465.	−	620880.i	−0.631038	−	1.09299i	0.356302	−	0.934371i	$-0.384038\pi$
$20$	120948.			0.169030
$21$		0			0
$22$	293770.			0.267366
$23$	129911.	+	225012.i	0.0967989	+	0.167661i	0.910358	−	0.413822i	$-0.135806\pi$
$23$	129911.	+	225012.i	0.0967989	+	0.167661i	−0.813559	+	0.581482i	$0.802473\pi$
$24$		0			0
$25$	864957.	−	1.49815e6i	0.442858	−	0.767052i
$26$	38053.4	+	65910.4i	0.0163310	+	0.0282862i
$27$		0			0
$28$	1.50396e6	+	618633.i	0.462409	+	0.190205i
$29$	−4.40930e6			−1.15765			−0.578826	−	0.815451i	$-0.696489\pi$
$29$	−4.40930e6			−1.15765			−0.578826	+	0.815451i	$0.696489\pi$
$30$		0			0
$31$	3.01245e6	−	5.21771e6i	0.585857	−	1.01473i	−0.408911	−	0.912574i	$-0.634091\pi$
$31$	3.01245e6	−	5.21771e6i	0.585857	−	1.01473i	0.994768	−	0.102160i	$-0.0325755\pi$
$32$	−524288.	+	908093.i	−0.0883883	+	0.153093i
$33$		0			0
$34$	4.20449e6			0.539583
$35$	−2.37653e6	+	1.83288e6i	−0.267694	+	0.206456i
$36$		0			0
$37$	2.28440e6	+	3.95669e6i	0.200384	+	0.347076i	0.948652	−	0.316321i	$-0.102448\pi$
$37$	2.28440e6	+	3.95669e6i	0.200384	+	0.347076i	−0.748268	+	0.663397i	$0.769114\pi$
$38$	−5.73544e6	+	9.93407e6i	−0.446211	+	0.772861i
$39$		0			0
$40$	−967582.	−	1.67590e6i	−0.0597610	−	0.103509i
$41$	−1.47923e7			−0.817537			−0.408769	−	0.912638i	$-0.634042\pi$
$41$	−1.47923e7			−0.817537			−0.408769	+	0.912638i	$0.634042\pi$
$42$		0			0
$43$	−2.14447e7			−0.956561			−0.478281	−	0.878207i	$-0.658740\pi$
$43$	−2.14447e7			−0.956561			−0.478281	+	0.878207i	$0.658740\pi$
$44$	−2.35016e6	−	4.07060e6i	−0.0945280	−	0.163727i
$45$		0			0
$46$	2.07857e6	−	3.60020e6i	0.0684471	−	0.118554i
$47$	1.90435e7	+	3.29843e7i	0.569254	+	0.985977i	0.996640	+	0.0819078i	$0.0261013\pi$
$47$	1.90435e7	+	3.29843e7i	0.569254	+	0.985977i	−0.427386	+	0.904069i	$0.640565\pi$
$48$		0			0
$49$	−3.89267e7	+	1.06359e7i	−0.964641	+	0.263567i
$50$	−2.76786e7			−0.626296
$51$		0			0
$52$	608854.	−	1.05457e6i	0.0115478	−	0.0200013i
$53$	1.58740e6	−	2.74946e6i	0.0276341	−	0.0478637i	−0.851878	−	0.523741i	$-0.824536\pi$
$53$	1.58740e6	−	2.74946e6i	0.0276341	−	0.0478637i	0.879512	+	0.475877i	$0.157869\pi$
$54$		0			0
$55$	8.67452e6			0.127824
$56$	−3.45967e6	−	2.57886e7i	−0.0470099	−	0.350414i
$57$		0			0
$58$	3.52744e7	+	6.10970e7i	0.409292	+	0.708915i
$59$	2.67921e7	−	4.64052e7i	0.287854	−	0.498577i	−0.685443	−	0.728126i	$-0.740392\pi$
$59$	2.67921e7	−	4.64052e7i	0.287854	−	0.498577i	0.973297	+	0.229548i	$0.0737249\pi$
$60$		0			0
$61$	3.06950e7	+	5.31654e7i	0.283847	+	0.491637i	0.972329	−	0.233616i	$-0.0750560\pi$
$61$	3.06950e7	+	5.31654e7i	0.283847	+	0.491637i	−0.688482	+	0.725253i	$0.741723\pi$
$62$	−9.63983e7			−0.828527
$63$		0			0
$64$	1.67772e7			0.125000
$65$	1.12365e6	+	1.94622e6i	0.00780767	+	0.0135233i
$66$		0			0
$67$	−1.17564e8	+	2.03626e8i	−0.712750	+	1.23452i	0.251072	+	0.967969i	$0.419217\pi$
$67$	−1.17564e8	+	2.03626e8i	−0.712750	+	1.23452i	−0.963821	+	0.266550i	$0.914116\pi$
$68$	−3.36359e7	−	5.82591e7i	−0.190771	−	0.330426i
$69$		0			0
$70$	4.44094e7	+	1.82672e7i	0.221072	+	0.0909348i
$71$	2.74423e8			1.28162			0.640808	−	0.767701i	$-0.278600\pi$
$71$	2.74423e8			1.28162			0.640808	+	0.767701i	$0.278600\pi$
$72$		0			0
$73$	−1.16701e8	+	2.02133e8i	−0.480975	+	0.833073i	−0.999762	−	0.0218304i	$-0.993051\pi$
$73$	−1.16701e8	+	2.02133e8i	−0.480975	+	0.833073i	0.518787	+	0.854904i	$0.326384\pi$
$74$	3.65504e7	−	6.33071e7i	0.141693	−	0.245420i
$75$		0			0
$76$	1.83534e8			0.631038
$77$	1.07866e8	+	4.43691e7i	0.349685	+	0.143838i
$78$		0			0
$79$	2.75465e7	+	4.77119e7i	0.0795691	+	0.137818i	0.903064	−	0.429506i	$-0.141312\pi$
$79$	2.75465e7	+	4.77119e7i	0.0795691	+	0.137818i	−0.823495	+	0.567324i	$0.807979\pi$
$80$	−1.54813e7	+	2.68144e7i	−0.0422574	+	0.0731920i
$81$		0			0
$82$	1.18338e8	+	2.04968e8i	0.289043	+	0.500637i
$83$	−9.49452e7			−0.219595			−0.109797	−	0.993954i	$-0.535020\pi$
$83$	−9.49452e7			−0.219595			−0.109797	+	0.993954i	$0.535020\pi$
$84$		0			0
$85$	1.24151e8			0.257968
$86$	1.71558e8	+	2.97147e8i	0.338195	+	0.585772i
$87$		0			0
$88$	−3.76026e7	+	6.51296e7i	−0.0668414	+	0.115773i
$89$	3.49353e8	+	6.05097e8i	0.590214	+	1.02228i	0.994203	+	0.107517i	$0.0342899\pi$
$89$	3.49353e8	+	6.05097e8i	0.590214	+	1.02228i	−0.403990	+	0.914764i	$0.632377\pi$
$90$		0			0
$91$	4.01771e6	+	2.99482e7i	0.00614175	+	0.0457810i
$92$	−6.65144e7			−0.0967989
$93$		0			0
$94$	3.04696e8	−	5.27749e8i	0.402523	−	0.697191i
$95$	−1.69358e8	+	2.93336e8i	−0.213328	+	0.369496i
$96$		0			0
$97$	1.52006e9			1.74336			0.871681	−	0.490073i	$-0.163030\pi$
$97$	1.52006e9			1.74336			0.871681	+	0.490073i	$0.163030\pi$
$98$	4.58789e8	+	4.54298e8i	0.502453	+	0.497535i
$99$		0			0
$100$	2.21429e8	+	3.83526e8i	0.221429	+	0.383526i
$101$	−1.32352e8	+	2.29241e8i	−0.126557	+	0.219202i	−0.922340	−	0.386378i	$-0.873726\pi$
$101$	−1.32352e8	+	2.29241e8i	−0.126557	+	0.219202i	0.795784	+	0.605581i	$0.207059\pi$
$102$		0			0
$103$	7.58840e8	+	1.31435e9i	0.664328	+	1.15065i	0.979467	+	0.201605i	$0.0646156\pi$
$103$	7.58840e8	+	1.31435e9i	0.664328	+	1.15065i	−0.315139	+	0.949046i	$0.602051\pi$
$104$	−1.94833e7			−0.0163310
$105$		0			0
$106$	−5.07969e7			−0.0390805
$107$	1.12273e9	+	1.94462e9i	0.828031	+	1.43419i	0.899581	+	0.436755i	$0.143872\pi$
$107$	1.12273e9	+	1.94462e9i	0.828031	+	1.43419i	−0.0715494	+	0.997437i	$0.522794\pi$
$108$		0			0
$109$	−4.82619e8	+	8.35921e8i	−0.327481	+	0.567213i	−0.982011	−	0.188822i	$-0.939533\pi$
$109$	−4.82619e8	+	8.35921e8i	−0.327481	+	0.567213i	0.654531	+	0.756035i	$0.272866\pi$
$110$	−6.93962e7	−	1.20198e8i	−0.0451927	−	0.0782761i
$111$		0			0
$112$	−3.29660e8	+	2.54247e8i	−0.197963	+	0.152678i
$113$	−1.82803e9			−1.05470			−0.527352	−	0.849647i	$-0.676815\pi$
$113$	−1.82803e9			−1.05470			−0.527352	+	0.849647i	$0.676815\pi$
$114$		0			0
$115$	6.13767e7	−	1.06308e8i	0.0327238	−	0.0566792i
$116$	5.64390e8	−	9.77552e8i	0.289413	−	0.501278i
$117$		0			0
$118$	−8.57346e8			−0.407087
$119$	1.54380e9	+	6.35019e8i	0.705715	+	0.290285i
$120$		0			0
$121$	1.01042e9	+	1.75009e9i	0.428516	+	0.742211i
$122$	4.91121e8	−	8.50646e8i	0.200710	−	0.347640i
$123$		0			0
$124$	7.71187e8	+	1.33573e9i	0.292929	+	0.507367i
$125$	−1.74006e9			−0.637484
$126$		0			0
$127$	1.83082e9			0.624495			0.312248	−	0.950001i	$-0.398918\pi$
$127$	1.83082e9			0.624495			0.312248	+	0.950001i	$0.398918\pi$
$128$	−1.34218e8	−	2.32472e8i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	1.79784e7	−	3.11395e7i	0.00552085	−	0.00956240i
$131$	−1.50918e9	−	2.61397e9i	−0.447734	−	0.775498i	0.550504	−	0.834832i	$-0.314435\pi$
$131$	−1.50918e9	−	2.61397e9i	−0.447734	−	0.775498i	−0.998238	+	0.0593346i	$0.981102\pi$
$132$		0			0
$133$	−3.60631e9	+	2.78134e9i	−0.999380	+	0.770763i
$134$	3.76204e9			1.00798
$135$		0			0
$136$	−5.38174e8	+	9.32146e8i	−0.134896	+	0.233646i
$137$	−1.19334e9	+	2.06692e9i	−0.289414	+	0.501280i	−0.973670	−	0.227962i	$-0.926794\pi$
$137$	−1.19334e9	+	2.06692e9i	−0.289414	+	0.501280i	0.684256	+	0.729242i	$0.260127\pi$
$138$		0			0
$139$	−2.56337e8			−0.0582432			−0.0291216	−	0.999576i	$-0.509271\pi$
$139$	−2.56337e8			−0.0582432			−0.0291216	+	0.999576i	$0.509271\pi$
$140$	−1.02158e8	−	7.61493e8i	−0.0224749	−	0.167529i
$141$		0			0
$142$	−2.19538e9	−	3.80252e9i	−0.453120	−	0.784826i
$143$	4.36678e7	−	7.56348e7i	0.00873271	−	0.0151255i
$144$		0			0
$145$	1.04159e9	+	1.80409e9i	0.195678	+	0.338924i
$146$	3.73444e9			0.680202
$147$		0			0
$148$	−1.16961e9			−0.200384
$149$	2.64724e8	+	4.58516e8i	0.0440003	+	0.0762107i	0.887187	−	0.461410i	$-0.152656\pi$
$149$	2.64724e8	+	4.58516e8i	0.0440003	+	0.0762107i	−0.843187	+	0.537621i	$0.819323\pi$
$150$		0			0
$151$	1.73725e9	−	3.00900e9i	0.271935	−	0.471006i	−0.697422	−	0.716661i	$-0.745670\pi$
$151$	1.73725e9	−	3.00900e9i	0.271935	−	0.471006i	0.969357	+	0.245655i	$0.0790029\pi$
$152$	−1.46827e9	−	2.54312e9i	−0.223106	−	0.386430i
$153$		0			0
$154$	−2.48132e8	−	1.84959e9i	−0.0355500	−	0.264992i
$155$	−2.84648e9			−0.396109
$156$		0			0
$157$	−2.75151e8	+	4.76575e8i	−0.0361429	+	0.0626013i	−0.883531	−	0.468373i	$-0.844840\pi$
$157$	−2.75151e8	+	4.76575e8i	−0.0361429	+	0.0626013i	0.847388	+	0.530974i	$0.178174\pi$
$158$	4.40744e8	−	7.63391e8i	0.0562639	−	0.0974519i
$159$		0			0
$160$	4.95402e8			0.0597610
$161$	1.30696e9	−	1.00798e9i	0.153301	−	0.118232i
$162$		0			0
$163$	3.08057e8	+	5.33571e8i	0.0341812	+	0.0592035i	0.882610	−	0.470106i	$-0.155784\pi$
$163$	3.08057e8	+	5.33571e8i	0.0341812	+	0.0592035i	−0.848429	+	0.529310i	$0.822451\pi$
$164$	1.89341e9	−	3.27948e9i	0.204384	−	0.354004i
$165$		0			0
$166$	7.59562e8	+	1.31560e9i	0.0776384	+	0.134474i
$167$	−1.61177e10			−1.60354			−0.801771	−	0.597632i	$-0.796109\pi$
$167$	−1.61177e10			−1.60354			−0.801771	+	0.597632i	$0.796109\pi$
$168$		0			0
$169$	−1.05819e10			−0.997866
$170$	−9.93210e8	−	1.72029e9i	−0.0912055	−	0.157973i
$171$		0			0
$172$	2.74493e9	−	4.75435e9i	0.239140	−	0.414203i
$173$	−1.79049e9	−	3.10122e9i	−0.151973	−	0.263224i	0.779980	−	0.625804i	$-0.215229\pi$
$173$	−1.79049e9	−	3.10122e9i	−0.151973	−	0.263224i	−0.931953	+	0.362580i	$0.881896\pi$
$174$		0			0
$175$	−1.01630e10	−	4.18040e9i	−0.819126	−	0.336935i
$176$	1.20328e9			0.0945280
$177$		0			0
$178$	5.58965e9	−	9.68155e9i	0.417344	−	0.722861i
$179$	−1.26580e10	+	2.19243e10i	−0.921566	+	1.59620i	−0.124572	+	0.992211i	$0.539756\pi$
$179$	−1.26580e10	+	2.19243e10i	−0.921566	+	1.59620i	−0.796993	+	0.603988i	$0.793577\pi$
$180$		0			0
$181$	−8.79219e9			−0.608896			−0.304448	−	0.952529i	$-0.598472\pi$
$181$	−8.79219e9			−0.608896			−0.304448	+	0.952529i	$0.598472\pi$
$182$	3.82833e8	−	2.95257e8i	0.0258636	−	0.0199471i
$183$		0			0
$184$	5.32115e8	+	9.21650e8i	0.0342236	+	0.0592770i
$185$	1.07927e9	−	1.86935e9i	0.0677418	−	0.117332i
$186$		0			0
$187$	−2.41241e9	−	4.17841e9i	−0.144266	−	0.249876i
$188$	−9.75027e9			−0.569254
$189$		0			0
$190$	5.41944e9			0.301692
$191$	−1.12283e9	−	1.94480e9i	−0.0610468	−	0.105736i	0.833887	−	0.551936i	$-0.186111\pi$
$191$	−1.12283e9	−	1.94480e9i	−0.0610468	−	0.105736i	−0.894934	+	0.446199i	$0.852777\pi$
$192$		0			0
$193$	1.28006e10	−	2.21713e10i	0.664085	−	1.15023i	−0.315448	−	0.948943i	$-0.602155\pi$
$193$	1.28006e10	−	2.21713e10i	0.664085	−	1.15023i	0.979533	−	0.201286i	$-0.0645119\pi$
$194$	−1.21605e10	−	2.10626e10i	−0.616372	−	1.06759i
$195$		0			0
$196$	2.62462e9	−	9.99155e9i	0.127033	−	0.483594i
$197$	3.17764e10			1.50317			0.751583	−	0.659638i	$-0.229290\pi$
$197$	3.17764e10			1.50317			0.751583	+	0.659638i	$0.229290\pi$
$198$		0			0
$199$	1.23578e10	−	2.14043e10i	0.558602	−	0.967527i	−0.439012	−	0.898481i	$-0.644671\pi$
$199$	1.23578e10	−	2.14043e10i	0.558602	−	0.967527i	0.997614	−	0.0690456i	$-0.0219954\pi$
$200$	3.54286e9	−	6.13642e9i	0.156574	−	0.271194i
$201$		0			0
$202$	4.23527e9			0.178978
$203$	3.72430e9	+	2.77611e10i	0.153926	+	1.14737i
$204$		0			0
$205$	3.49432e9	+	6.05234e9i	0.138188	+	0.239349i
$206$	1.21414e10	−	2.10296e10i	0.469751	−	0.813632i
$207$		0			0
$208$	1.55867e8	+	2.69969e8i	0.00577389	+	0.0100007i
$209$	1.31633e10			0.477206
$210$		0			0
$211$	−3.48794e10			−1.21143			−0.605715	−	0.795681i	$-0.707113\pi$
$211$	−3.48794e10			−1.21143			−0.605715	+	0.795681i	$0.707113\pi$
$212$	4.06375e8	+	7.03862e8i	0.0138171	+	0.0239318i
$213$		0			0
$214$	1.79636e10	−	3.11139e10i	0.585506	−	1.01413i
$215$	5.06581e9	+	8.77424e9i	0.161687	+	0.280051i
$216$		0			0
$217$	−3.53954e10	−	1.45594e10i	−1.08362	−	0.445732i
$218$	1.54438e10			0.463127
$219$		0			0
$220$	−1.11034e9	+	1.92316e9i	−0.0319561	+	0.0553496i
$221$	6.24981e8	−	1.08250e9i	0.0176239	−	0.0305254i
$222$		0			0
$223$	−1.39097e9			−0.0376656			−0.0188328	−	0.999823i	$-0.505995\pi$
$223$	−1.39097e9			−0.0376656			−0.0188328	+	0.999823i	$0.505995\pi$
$224$	6.16024e9	+	2.53392e9i	0.163486	+	0.0672477i
$225$		0			0
$226$	1.46243e10	+	2.53300e10i	0.372894	+	0.645872i
$227$	1.56676e10	−	2.71370e10i	0.391638	−	0.678337i	−0.601028	−	0.799228i	$-0.705242\pi$
$227$	1.56676e10	−	2.71370e10i	0.391638	−	0.678337i	0.992666	+	0.120891i	$0.0385751\pi$
$228$		0			0
$229$	1.97249e10	+	3.41646e10i	0.473976	+	0.820950i	0.999556	−	0.0297938i	$-0.00948505\pi$
$229$	1.97249e10	+	3.41646e10i	0.473976	+	0.820950i	−0.525580	+	0.850744i	$0.676152\pi$
$230$	−1.96405e9			−0.0462784
$231$		0			0
$232$	−1.80605e10			−0.409292
$233$	−4.18668e10	−	7.25154e10i	−0.930610	−	1.61186i	−0.782280	−	0.622926i	$-0.785944\pi$
$233$	−4.18668e10	−	7.25154e10i	−0.930610	−	1.61186i	−0.148330	−	0.988938i	$-0.547390\pi$
$234$		0			0
$235$	8.99714e9	−	1.55835e10i	0.192442	−	0.333319i
$236$	6.85877e9	+	1.18797e10i	0.143927	+	0.249289i
$237$		0			0
$238$	−3.55131e9	−	2.64716e10i	−0.0717451	−	0.534792i
$239$	1.03880e9			0.0205941			0.0102970	−	0.999947i	$-0.496722\pi$
$239$	1.03880e9			0.0205941			0.0102970	+	0.999947i	$0.496722\pi$
$240$		0			0
$241$	−5.20820e10	+	9.02087e10i	−0.994515	+	1.72255i	−0.406675	+	0.913573i	$0.633312\pi$
$241$	−5.20820e10	+	9.02087e10i	−0.994515	+	1.72255i	−0.587840	+	0.808977i	$0.700021\pi$
$242$	1.61667e10	−	2.80015e10i	0.303006	−	0.524822i
$243$		0			0
$244$	−1.57159e10			−0.283847
$245$	1.35472e10	+	1.34146e10i	0.240217	+	0.237865i
$246$		0			0
$247$	1.70510e9	+	2.95332e9i	0.0291484	+	0.0504864i
$248$	1.23390e10	−	2.13718e10i	0.207132	−	0.358763i
$249$		0			0
$250$	1.39205e10	+	2.41110e10i	0.225385	+	0.390378i
$251$	−1.03278e11			−1.64238			−0.821192	−	0.570653i	$-0.806690\pi$
$251$	−1.03278e11			−1.64238			−0.821192	+	0.570653i	$0.806690\pi$
$252$		0			0
$253$	−4.77049e9			−0.0732016
$254$	−1.46466e10	−	2.53686e10i	−0.220792	−	0.382424i
$255$		0			0
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	4.81885e9	+	8.34650e9i	0.0689040	+	0.119345i	0.898419	−	0.439139i	$-0.144716\pi$
$257$	4.81885e9	+	8.34650e9i	0.0689040	+	0.119345i	−0.829515	+	0.558484i	$0.811383\pi$
$258$		0			0
$259$	2.29820e10	−	1.77247e10i	0.317350	−	0.244754i
$260$	−5.75309e8			−0.00780767
$261$		0			0
$262$	−2.41469e10	+	4.18236e10i	−0.316596	+	0.548360i
$263$	−7.32630e10	+	1.26895e11i	−0.944243	+	1.63548i	−0.186983	+	0.982363i	$0.559871\pi$
$263$	−7.32630e10	+	1.26895e11i	−0.944243	+	1.63548i	−0.757260	+	0.653114i	$0.773462\pi$
$264$		0			0
$265$	−1.49994e9			−0.0186839
$266$	6.73898e10	+	2.77198e10i	0.825328	+	0.339487i
$267$		0			0
$268$	−3.00963e10	−	5.21284e10i	−0.356375	−	0.617259i
$269$	−2.07463e10	+	3.59336e10i	−0.241576	+	0.418423i	−0.961164	−	0.275980i	$-0.910998\pi$
$269$	−2.07463e10	+	3.59336e10i	−0.241576	+	0.418423i	0.719587	+	0.694402i	$0.244331\pi$
$270$		0			0
$271$	5.97704e10	+	1.03525e11i	0.673170	+	1.16596i	0.977000	+	0.213238i	$0.0684009\pi$
$271$	5.97704e10	+	1.03525e11i	0.673170	+	1.16596i	−0.303831	+	0.952726i	$0.598266\pi$
$272$	1.72216e10			0.190771
$273$		0			0
$274$	3.81867e10			0.409294
$275$	1.58812e10	+	2.75070e10i	0.167450	+	0.290032i
$276$		0			0
$277$	3.09368e10	−	5.35842e10i	0.315731	−	0.546862i	−0.663862	−	0.747855i	$-0.731084\pi$
$277$	3.09368e10	−	5.35842e10i	0.315731	−	0.546862i	0.979593	+	0.200994i	$0.0644171\pi$
$278$	2.05070e9	+	3.55191e9i	0.0205921	+	0.0356665i
$279$		0			0
$280$	−9.73429e9	+	7.50749e9i	−0.0946440	+	0.0729934i
$281$	1.12291e11			1.07440			0.537199	−	0.843456i	$-0.319482\pi$
$281$	1.12291e11			1.07440			0.537199	+	0.843456i	$0.319482\pi$
$282$		0			0
$283$	5.97566e10	−	1.03502e11i	0.553793	−	0.959197i	−0.444204	−	0.895926i	$-0.646513\pi$
$283$	5.97566e10	−	1.03502e11i	0.553793	−	0.959197i	0.997996	−	0.0632710i	$-0.0201533\pi$
$284$	−3.51261e10	+	6.08402e10i	−0.320404	+	0.554956i
$285$		0			0
$286$	−1.39737e9			−0.0123499
$287$	1.24943e10	+	9.31328e10i	0.108703	+	0.810278i
$288$		0			0
$289$	2.47671e10	+	4.28980e10i	0.208851	+	0.361740i
$290$	1.66655e10	−	2.88654e10i	0.138365	−	0.239655i
$291$		0			0
$292$	−2.98755e10	−	5.17459e10i	−0.240488	−	0.416537i
$293$	−1.77567e11			−1.40753			−0.703765	−	0.710433i	$-0.748499\pi$
$293$	−1.77567e11			−1.40753			−0.703765	+	0.710433i	$0.748499\pi$
$294$		0			0
$295$	−2.53159e10			−0.194623
$296$	9.35689e9	+	1.62066e10i	0.0708466	+	0.122710i
$297$		0			0
$298$	4.23559e9	−	7.33625e9i	0.0311129	−	0.0538891i
$299$	−6.17944e8	−	1.07031e9i	−0.00447125	−	0.00774443i
$300$		0			0
$301$	1.81132e10	+	1.35017e11i	0.127188	+	0.948068i
$302$	−5.55920e10			−0.384575
$303$		0			0
$304$	−2.34924e10	+	4.06900e10i	−0.157760	+	0.273248i
$305$	1.45019e10	−	2.51181e10i	0.0959570	−	0.166202i
$306$		0			0
$307$	1.52250e11			0.978218			0.489109	−	0.872223i	$-0.337322\pi$
$307$	1.52250e11			0.978218			0.489109	+	0.872223i	$0.337322\pi$
$308$	−2.36436e10	+	1.82349e10i	−0.149705	+	0.115459i
$309$		0			0
$310$	2.27718e10	+	3.94419e10i	0.140046	+	0.242566i
$311$	−7.63392e10	+	1.32223e11i	−0.462728	+	0.801469i	−0.999096	−	0.0425158i	$-0.986463\pi$
$311$	−7.63392e10	+	1.32223e11i	−0.462728	+	0.801469i	0.536368	+	0.843984i	$0.319796\pi$
$312$		0			0
$313$	1.24943e11	+	2.16408e11i	0.735806	+	1.27445i	0.954369	+	0.298630i	$0.0965298\pi$
$313$	1.24943e11	+	2.16408e11i	0.735806	+	1.27445i	−0.218563	+	0.975823i	$0.570137\pi$
$314$	8.80483e9			0.0511137
$315$		0			0
$316$	−1.41038e10			−0.0795691
$317$	−6.17450e10	−	1.06945e11i	−0.343428	−	0.594834i	0.641639	−	0.767007i	$-0.278255\pi$
$317$	−6.17450e10	−	1.06945e11i	−0.343428	−	0.594834i	−0.985067	+	0.172173i	$0.944921\pi$
$318$		0			0
$319$	4.04787e10	−	7.01112e10i	0.218861	−	0.379079i
$320$	−3.96322e9	−	6.86449e9i	−0.0211287	−	0.0365960i
$321$		0			0
$322$	−2.44227e10	−	1.00459e10i	−0.126602	−	0.0520760i
$323$	1.88395e11			0.963072
$324$		0			0
$325$	−4.11432e9	+	7.12621e9i	−0.0204561	+	0.0354310i
$326$	4.92891e9	−	8.53713e9i	0.0241697	−	0.0418632i
$327$		0			0
$328$	−6.05892e10			−0.289043
$329$	1.91586e11	−	1.47759e11i	0.901532	−	0.695299i
$330$		0			0
$331$	−2.06815e10	−	3.58213e10i	−0.0947011	−	0.164027i	0.814783	−	0.579766i	$-0.196856\pi$
$331$	−2.06815e10	−	3.58213e10i	−0.0947011	−	0.164027i	−0.909484	+	0.415739i	$0.863523\pi$
$332$	1.21530e10	−	2.10496e10i	0.0548986	−	0.0950872i
$333$		0			0
$334$	1.28942e11	+	2.23334e11i	0.566938	+	0.981965i
$335$	1.11087e11			0.481903
$336$		0			0
$337$	−3.30223e11			−1.39468			−0.697338	−	0.716743i	$-0.745632\pi$
$337$	−3.30223e11			−1.39468			−0.697338	+	0.716743i	$0.745632\pi$
$338$	8.46550e10	+	1.46627e11i	0.352799	+	0.611066i
$339$		0			0
$340$	−1.58914e10	+	2.75246e10i	−0.0644920	+	0.111703i
$341$	5.53104e10	+	9.58005e10i	0.221520	+	0.383683i
$342$		0			0
$343$	9.98433e10	+	2.36101e11i	0.389489	+	0.921031i
$344$	−8.78377e10			−0.338195
$345$		0			0
$346$	−2.86479e10	+	4.96196e10i	−0.107461	+	0.186128i
$347$	2.66746e11	−	4.62018e11i	0.987679	−	1.71071i	0.358315	−	0.933601i	$-0.383352\pi$
$347$	2.66746e11	−	4.62018e11i	0.987679	−	1.71071i	0.629365	−	0.777110i	$-0.283315\pi$
$348$		0			0
$349$	−8.45986e10			−0.305245			−0.152623	−	0.988285i	$-0.548772\pi$
$349$	−8.45986e10			−0.305245			−0.152623	+	0.988285i	$0.548772\pi$
$350$	2.33787e10	+	1.74266e11i	0.0832748	+	0.620735i
$351$		0			0
$352$	−9.62626e9	−	1.66732e10i	−0.0334207	−	0.0578864i
$353$	8.39073e10	−	1.45332e11i	0.287616	−	0.498166i	−0.685624	−	0.727956i	$-0.740471\pi$
$353$	8.39073e10	−	1.45332e11i	0.287616	−	0.498166i	0.973240	+	0.229790i	$0.0738038\pi$
$354$		0			0
$355$	−6.48259e10	−	1.12282e11i	−0.216631	−	0.375216i
$356$	−1.78869e11			−0.590214
$357$		0			0
$358$	4.05056e11			1.30329
$359$	3.83450e10	+	6.64156e10i	0.121838	+	0.211030i	0.920493	−	0.390760i	$-0.127788\pi$
$359$	3.83450e10	+	6.64156e10i	0.121838	+	0.211030i	−0.798654	+	0.601790i	$0.794454\pi$
$360$		0			0
$361$	−9.56505e10	+	1.65672e11i	−0.296418	+	0.513412i
$362$	7.03375e10	+	1.21828e11i	0.215277	+	0.372871i
$363$		0			0
$364$	−7.15387e9	−	2.94264e9i	−0.0213592	−	0.00878578i
$365$	1.10272e11			0.325196
$366$		0			0
$367$	1.33542e11	−	2.31301e11i	0.384255	−	0.665550i	−0.607410	−	0.794388i	$-0.707792\pi$
$367$	1.33542e11	−	2.31301e11i	0.384255	−	0.665550i	0.991666	+	0.128838i	$0.0411249\pi$
$368$	8.51384e9	−	1.47464e10i	0.0241997	−	0.0419151i
$369$		0			0
$370$	−3.45366e10			−0.0958014
$371$	−1.86515e10	−	7.67203e9i	−0.0511130	−	0.0210246i
$372$		0			0
$373$	−2.85297e11	−	4.94149e11i	−0.763146	−	1.32181i	−0.941221	−	0.337791i	$-0.890320\pi$
$373$	−2.85297e11	−	4.94149e11i	−0.763146	−	1.32181i	0.178075	−	0.984017i	$-0.443013\pi$
$374$	−3.85985e10	+	6.68546e10i	−0.102011	+	0.176689i
$375$		0			0
$376$	7.80021e10	+	1.35104e11i	0.201262	+	0.348596i
$377$	2.09736e10			0.0534733
$378$		0			0
$379$	1.64654e10			0.0409918			0.0204959	−	0.999790i	$-0.493476\pi$
$379$	1.64654e10			0.0409918			0.0204959	+	0.999790i	$0.493476\pi$
$380$	−4.33556e10	−	7.50940e10i	−0.106664	−	0.184748i
$381$		0			0
$382$	−1.79652e10	+	3.11167e10i	−0.0431666	+	0.0747668i
$383$	1.38378e11	+	2.39678e11i	0.328605	+	0.569160i	0.982235	−	0.187654i	$-0.0600883\pi$
$383$	1.38378e11	+	2.39678e11i	0.328605	+	0.569160i	−0.653631	+	0.756814i	$0.726755\pi$
$384$		0			0
$385$	−7.32691e9	−	5.46152e10i	−0.0169960	−	0.126689i
$386$	−4.09620e11			−0.939158
$387$		0			0
$388$	−1.94568e11	+	3.37001e11i	−0.435841	+	0.754898i
$389$	1.92123e11	−	3.32767e11i	0.425409	−	0.736829i	−0.571050	−	0.820915i	$-0.693464\pi$
$389$	1.92123e11	−	3.32767e11i	0.425409	−	0.736829i	0.996458	+	0.0840861i	$0.0267971\pi$
$390$		0			0
$391$	−6.82761e10			−0.147732
$392$	−1.59444e11	+	4.35645e10i	−0.341052	+	0.0931849i
$393$		0			0
$394$	−2.54211e11	−	4.40307e11i	−0.531450	−	0.920498i
$395$	1.30144e10	−	2.25416e10i	0.0268991	−	0.0465906i
$396$		0			0
$397$	−1.76876e11	−	3.06359e11i	−0.357365	−	0.618974i	0.630155	−	0.776470i	$-0.282991\pi$
$397$	−1.76876e11	−	3.06359e11i	−0.357365	−	0.618974i	−0.987520	+	0.157495i	$0.949658\pi$
$398$	−3.95450e11			−0.789983
$399$		0			0
$400$	−1.13372e11			−0.221429
$401$	−1.74594e11	−	3.02406e11i	−0.337195	−	0.584038i	0.646709	−	0.762737i	$-0.276145\pi$
$401$	−1.74594e11	−	3.02406e11i	−0.337195	−	0.584038i	−0.983904	+	0.178698i	$0.942811\pi$
$402$		0			0
$403$	−1.43292e10	+	2.48190e10i	−0.0270614	+	0.0468717i
$404$	−3.38821e10	−	5.86856e10i	−0.0632783	−	0.109601i
$405$		0			0
$406$	3.54875e11	−	2.73694e11i	0.648199	−	0.499918i
$407$	−8.38860e10			−0.151536
$408$		0			0
$409$	5.06068e11	−	8.76535e11i	0.894240	−	1.54887i	0.0594971	−	0.998228i	$-0.481050\pi$
$409$	5.06068e11	−	8.76535e11i	0.894240	−	1.54887i	0.834743	−	0.550640i	$-0.185616\pi$
$410$	5.59091e10	−	9.68375e10i	0.0977137	−	0.169245i
$411$		0			0
$412$	−3.88526e11			−0.664328
$413$	−3.14799e11	−	1.29488e11i	−0.532425	−	0.219005i
$414$		0			0
$415$	2.24285e10	+	3.88474e10i	0.0371180	+	0.0642903i
$416$	2.49387e9	−	4.31951e9i	0.00408276	−	0.00707154i
$417$		0			0
$418$	−1.05306e11	−	1.82396e11i	−0.168718	−	0.292228i
$419$	−5.26641e11			−0.834741			−0.417371	−	0.908736i	$-0.637048\pi$
$419$	−5.26641e11			−0.834741			−0.417371	+	0.908736i	$0.637048\pi$
$420$		0			0
$421$	−4.25683e10			−0.0660414			−0.0330207	−	0.999455i	$-0.510513\pi$
$421$	−4.25683e10			−0.0660414			−0.0330207	+	0.999455i	$0.510513\pi$
$422$	2.79036e11	+	4.83304e11i	0.428305	+	0.741847i
$423$		0			0
$424$	6.50200e9	−	1.12618e10i	0.00977013	−	0.0169224i
$425$	2.27294e11	+	3.93684e11i	0.337938	+	0.585326i
$426$		0			0
$427$	3.08805e11	−	2.38163e11i	0.449530	−	0.346696i
$428$	−5.74836e11			−0.828031
$429$		0			0
$430$	8.10529e10	−	1.40388e11i	0.114330	−	0.198026i
$431$	1.40950e11	−	2.44132e11i	0.196751	−	0.340782i	−0.750722	−	0.660618i	$-0.770294\pi$
$431$	1.40950e11	−	2.44132e11i	0.196751	−	0.340782i	0.947473	+	0.319836i	$0.103628\pi$
$432$		0			0
$433$	5.58015e10			0.0762870			0.0381435	−	0.999272i	$-0.487856\pi$
$433$	5.58015e10			0.0762870			0.0381435	+	0.999272i	$0.487856\pi$
$434$	8.14226e10	+	6.06928e11i	0.110164	+	0.821171i
$435$		0			0
$436$	−1.23551e11	−	2.13996e11i	−0.163740	−	0.283607i
$437$	9.31370e10	−	1.61318e11i	0.122168	−	0.211600i
$438$		0			0
$439$	−3.79583e11	−	6.57457e11i	−0.487772	−	0.844846i	0.512129	−	0.858908i	$-0.328857\pi$
$439$	−3.79583e11	−	6.57457e11i	−0.487772	−	0.844846i	−0.999901	+	0.0140628i	$0.995524\pi$
$440$	3.55308e10			0.0451927
$441$		0			0
$442$	−1.99994e10			−0.0249239
$443$	−7.29381e11	−	1.26333e12i	−0.899783	−	1.55847i	−0.827771	−	0.561066i	$-0.810391\pi$
$443$	−7.29381e11	−	1.26333e12i	−0.899783	−	1.55847i	−0.0720122	−	0.997404i	$-0.522942\pi$
$444$		0			0
$445$	1.65053e11	−	2.85879e11i	0.199527	−	0.345591i
$446$	1.11277e10	+	1.92738e10i	0.0133168	+	0.0230654i
$447$		0			0
$448$	−1.41708e10	−	1.05630e11i	−0.0166205	−	0.123890i
$449$	−9.76798e11			−1.13422			−0.567109	−	0.823643i	$-0.691938\pi$
$449$	−9.76798e11			−1.13422			−0.567109	+	0.823643i	$0.691938\pi$
$450$		0			0
$451$	1.35798e11	−	2.35209e11i	0.154560	−	0.267706i
$452$	2.33988e11	−	4.05279e11i	0.263676	−	0.456700i
$453$		0			0
$454$	−5.01362e11			−0.553860
$455$	1.13044e10	−	8.71843e9i	0.0123651	−	0.00953645i
$456$		0			0
$457$	2.46280e9	+	4.26570e9i	0.00264123	+	0.00457475i	0.867343	−	0.497711i	$-0.165826\pi$
$457$	2.46280e9	+	4.26570e9i	0.00264123	+	0.00457475i	−0.864702	+	0.502286i	$0.832493\pi$
$458$	3.15599e11	−	5.46634e11i	0.335152	−	0.580500i
$459$		0			0
$460$	1.57124e10	+	2.72147e10i	0.0163619	+	0.0283396i
$461$	−1.45140e11			−0.149670			−0.0748348	−	0.997196i	$-0.523843\pi$
$461$	−1.45140e11			−0.149670			−0.0748348	+	0.997196i	$0.523843\pi$
$462$		0			0
$463$	−1.06638e12			−1.07844			−0.539221	−	0.842164i	$-0.681281\pi$
$463$	−1.06638e12			−1.07844			−0.539221	+	0.842164i	$0.681281\pi$
$464$	1.44484e11	+	2.50253e11i	0.144707	+	0.250639i
$465$		0			0
$466$	−6.69868e11	+	1.16025e12i	−0.658041	+	1.13976i
$467$	7.14697e11	+	1.23789e12i	0.695338	+	1.20436i	0.970067	+	0.242839i	$0.0780787\pi$
$467$	7.14697e11	+	1.23789e12i	0.695338	+	1.20436i	−0.274729	+	0.961522i	$0.588588\pi$
$468$		0			0
$469$	1.38134e12	+	5.68194e11i	1.31833	+	0.542274i
$470$	−2.87909e11			−0.272154
$471$		0			0
$472$	1.09740e11	−	1.90076e11i	0.101772	−	0.176274i
$473$	1.96870e11	−	3.40988e11i	0.180844	−	0.313230i
$474$		0			0
$475$	−1.24023e12			−1.11784
$476$	−3.38391e11	+	2.60982e11i	−0.302126	+	0.233012i
$477$		0			0
$478$	−8.31042e9	−	1.43941e10i	−0.00728111	−	0.0126113i
$479$	1.89417e10	−	3.28080e10i	0.0164403	−	0.0284754i	−0.857688	−	0.514170i	$-0.828100\pi$
$479$	1.89417e10	−	3.28080e10i	0.0164403	−	0.0284754i	0.874129	+	0.485695i	$0.161433\pi$
$480$		0			0
$481$	−1.08661e10	−	1.88207e10i	−0.00925598	−	0.0160318i
$482$	1.66663e12			1.40646
$483$		0			0
$484$	−5.17334e11			−0.428516
$485$	−3.59078e11	−	6.21941e11i	−0.294680	−	0.510401i
$486$		0			0
$487$	−1.20656e12	+	2.08982e12i	−0.972002	+	1.68356i	−0.282511	+	0.959264i	$0.591167\pi$
$487$	−1.20656e12	+	2.08982e12i	−0.972002	+	1.68356i	−0.689492	+	0.724293i	$0.742166\pi$
$488$	1.25727e11	+	2.17765e11i	0.100355	+	0.173820i
$489$		0			0
$490$	7.75006e10	−	2.95033e11i	0.0607327	−	0.231200i
$491$	8.41135e11			0.653129			0.326564	−	0.945175i	$-0.394109\pi$
$491$	8.41135e11			0.653129			0.326564	+	0.945175i	$0.394109\pi$
$492$		0			0
$493$	5.79338e11	−	1.00344e12i	0.441694	−	0.765036i
$494$	2.72816e10	−	4.72532e10i	0.0206110	−	0.0356993i
$495$		0			0
$496$	−3.94848e11			−0.292929
$497$	−2.31790e11	−	1.72778e12i	−0.170409	−	1.27024i
$498$		0			0
$499$	6.91862e11	+	1.19834e12i	0.499536	+	0.865222i	1.00000		0.000535723i	$-0.000170526\pi$
$499$	6.91862e11	+	1.19834e12i	0.499536	+	0.865222i	−0.500464	+	0.865757i	$0.666837\pi$
$500$	2.22728e11	−	3.85776e11i	0.159371	−	0.276039i
$501$		0			0
$502$	8.26221e11	+	1.43106e12i	0.580670	+	1.00575i
$503$	2.11862e11			0.147570			0.0737850	−	0.997274i	$-0.476492\pi$
$503$	2.11862e11			0.147570			0.0737850	+	0.997274i	$0.476492\pi$
$504$		0			0
$505$	1.25060e11			0.0855673
$506$	3.81639e10	+	6.61019e10i	0.0258807	+	0.0448267i
$507$		0			0
$508$	−2.34345e11	+	4.05898e11i	−0.156124	+	0.270414i
$509$	7.15423e11	+	1.23915e12i	0.472425	+	0.818264i	0.999502	−	0.0315537i	$-0.0100455\pi$
$509$	7.15423e11	+	1.23915e12i	0.472425	+	0.818264i	−0.527077	+	0.849817i	$0.676712\pi$
$510$		0			0
$511$	1.37121e12	+	5.64026e11i	0.889629	+	0.365936i
$512$	6.87195e10			0.0441942
$513$		0			0
$514$	7.71017e10	−	1.33544e11i	0.0487225	−	0.0843899i
$515$	3.58516e11	−	6.20967e11i	0.224582	−	0.388988i
$516$		0			0
$517$	−6.99301e11			−0.430484
$518$	−4.29456e11	−	1.76651e11i	−0.262081	−	0.107803i
$519$		0			0
$520$	4.60247e9	+	7.97172e9i	0.00276043	+	0.00478120i
$521$	−8.48406e11	+	1.46948e12i	−0.504469	+	0.873765i	0.495518	+	0.868598i	$0.334978\pi$
$521$	−8.48406e11	+	1.46948e12i	−0.504469	+	0.873765i	−0.999987	+	0.00516763i	$0.998355\pi$
$522$		0			0
$523$	1.37685e12	+	2.38478e12i	0.804694	+	1.39377i	0.916498	+	0.400040i	$0.131004\pi$
$523$	1.37685e12	+	2.38478e12i	0.804694	+	1.39377i	−0.111804	+	0.993730i	$0.535663\pi$
$524$	7.72700e11			0.447734
$525$		0			0
$526$	2.34442e12			1.33536
$527$	7.91613e11	+	1.37111e12i	0.447059	+	0.774329i
$528$		0			0
$529$	8.66823e11	−	1.50138e12i	0.481260	−	0.833567i
$530$	1.19995e10	+	2.07838e10i	0.00660577	+	0.0114415i
$531$		0			0
$532$	−1.55022e11	−	1.15554e12i	−0.0839054	−	0.625435i
$533$	7.03620e10			0.0377630
$534$		0			0
$535$	5.30434e11	−	9.18739e11i	0.279924	−	0.484842i
$536$	−4.81541e11	+	8.34054e11i	−0.251995	+	0.436468i
$537$		0			0
$538$	6.63880e11			0.341641
$539$	1.88241e11	−	7.16606e11i	0.0960651	−	0.365705i
$540$		0			0
$541$	6.28572e11	+	1.08872e12i	0.315477	+	0.546422i	0.979539	−	0.201256i	$-0.0645022\pi$
$541$	6.28572e11	+	1.08872e12i	0.315477	+	0.546422i	−0.664062	+	0.747678i	$0.731169\pi$
$542$	9.56327e11	−	1.65641e12i	0.476003	−	0.824461i
$543$		0			0
$544$	−1.37773e11	−	2.38629e11i	−0.0674478	−	0.116823i
$545$	4.56029e11			0.221416
$546$		0			0
$547$	−8.97132e11			−0.428463			−0.214231	−	0.976783i	$-0.568725\pi$
$547$	−8.97132e11			−0.428463			−0.214231	+	0.976783i	$0.568725\pi$
$548$	−3.05494e11	−	5.29131e11i	−0.144707	−	0.250640i
$549$		0			0
$550$	2.54098e11	−	4.40111e11i	0.118405	−	0.205083i
$551$	1.58058e12	+	2.73764e12i	0.730523	+	1.26530i
$552$		0			0
$553$	2.77129e11	−	2.13734e11i	0.126014	−	0.0971874i
$554$	−9.89978e11			−0.446511
$555$		0			0
$556$	3.28112e10	−	5.68306e10i	0.0145608	−	0.0252200i
$557$	−2.06688e12	+	3.57995e12i	−0.909846	+	1.57590i	−0.0955680	+	0.995423i	$0.530467\pi$
$557$	−2.06688e12	+	3.57995e12i	−0.909846	+	1.57590i	−0.814277	+	0.580476i	$0.802867\pi$
$558$		0			0
$559$	1.02006e11			0.0441846
$560$	1.81901e11	+	7.48223e10i	0.0781608	+	0.0321503i
$561$		0			0
$562$	−8.98325e11	−	1.55595e12i	−0.379857	−	0.657932i
$563$	−1.41705e11	+	2.45439e11i	−0.0594424	+	0.102957i	−0.894215	−	0.447637i	$-0.852266\pi$
$563$	−1.41705e11	+	2.45439e11i	−0.0594424	+	0.102957i	0.834773	+	0.550594i	$0.185599\pi$
$564$		0			0
$565$	4.31829e11	+	7.47950e11i	0.178276	+	0.308784i
$566$	−1.91221e12			−0.783181
$567$		0			0
$568$	1.12404e12			0.453120
$569$	9.87499e11	+	1.71040e12i	0.394940	+	0.684057i	0.993094	−	0.117325i	$-0.0374319\pi$
$569$	9.87499e11	+	1.71040e12i	0.394940	+	0.684057i	−0.598153	+	0.801382i	$0.704099\pi$
$570$		0			0
$571$	−1.33664e12	+	2.31512e12i	−0.526200	+	0.911406i	0.473334	+	0.880883i	$0.343051\pi$
$571$	−1.33664e12	+	2.31512e12i	−0.526200	+	0.911406i	−0.999534	+	0.0305227i	$0.990283\pi$
$572$	1.11790e10	+	1.93625e10i	0.00436635	+	0.00756275i
$573$		0			0
$574$	1.19053e12	−	9.18188e11i	0.457760	−	0.353043i
$575$	4.49469e11			0.171473
$576$		0			0
$577$	5.79597e11	−	1.00389e12i	0.217688	−	0.377047i	−0.736412	−	0.676533i	$-0.763482\pi$
$577$	5.79597e11	−	1.00389e12i	0.217688	−	0.377047i	0.954101	+	0.299486i	$0.0968150\pi$
$578$	3.96274e11	−	6.86367e11i	0.147680	−	0.255789i
$579$		0			0
$580$	−5.33295e11			−0.195678
$581$	8.01952e10	+	5.97779e11i	0.0291982	+	0.217645i
$582$		0			0
$583$	2.91457e10	+	5.04818e10i	0.0104488	+	0.0180978i
$584$	−4.78008e11	+	8.27935e11i	−0.170050	+	0.294536i
$585$		0			0
$586$	1.42054e12	+	2.46044e12i	0.497637	+	0.861933i
$587$	−8.46356e10			−0.0294226			−0.0147113	−	0.999892i	$-0.504683\pi$
$587$	−8.46356e10			−0.0294226			−0.0147113	+	0.999892i	$0.504683\pi$
$588$		0			0
$589$	−4.31943e12			−1.47879
$590$	2.02528e11	+	3.50788e11i	0.0688098	+	0.119182i
$591$		0			0
$592$	1.49710e11	−	2.59306e11i	0.0500961	−	0.0867690i
$593$	−1.12629e12	−	1.95080e12i	−0.374029	−	0.647837i	0.616152	−	0.787627i	$-0.288691\pi$
$593$	−1.12629e12	−	1.95080e12i	−0.374029	−	0.647837i	−0.990181	+	0.139790i	$0.955357\pi$
$594$		0			0
$595$	−1.04864e11	−	7.81662e11i	−0.0343005	−	0.255678i
$596$	−1.35539e11			−0.0440003
$597$		0			0
$598$	−9.88710e9	+	1.71250e10i	−0.00316165	+	0.00547614i
$599$	−2.00374e12	+	3.47058e12i	−0.635947	+	1.10149i	0.350366	+	0.936613i	$0.386057\pi$
$599$	−2.00374e12	+	3.47058e12i	−0.635947	+	1.10149i	−0.986314	+	0.164880i	$0.947276\pi$
$600$		0			0
$601$	−4.08150e11			−0.127610			−0.0638050	−	0.997962i	$-0.520324\pi$
$601$	−4.08150e11			−0.127610			−0.0638050	+	0.997962i	$0.520324\pi$
$602$	1.72595e12	−	1.33112e12i	0.535603	−	0.413079i
$603$		0			0
$604$	4.44736e11	+	7.70305e11i	0.135968	+	0.235503i
$605$	4.77374e11	−	8.26836e11i	0.144864	−	0.250911i
$606$		0			0
$607$	2.48423e12	+	4.30280e12i	0.742749	+	1.28648i	0.951239	+	0.308454i	$0.0998116\pi$
$607$	2.48423e12	+	4.30280e12i	0.742749	+	1.28648i	−0.208491	+	0.978024i	$0.566855\pi$
$608$	7.51756e11			0.223106
$609$		0			0
$610$	−4.64062e11			−0.135704
$611$	−9.05837e10	−	1.56896e11i	−0.0262945	−	0.0455434i
$612$		0			0
$613$	−1.52442e12	+	2.64038e12i	−0.436047	+	0.755256i	−0.997380	−	0.0723339i	$-0.976955\pi$
$613$	−1.52442e12	+	2.64038e12i	−0.436047	+	0.755256i	0.561333	+	0.827590i	$0.310289\pi$
$614$	−1.21800e12	−	2.10964e12i	−0.345852	−	0.599034i
$615$		0			0
$616$	4.41820e11	+	1.81736e11i	0.123632	+	0.0508543i
$617$	−4.69271e12			−1.30359			−0.651794	−	0.758396i	$-0.725983\pi$
$617$	−4.69271e12			−1.30359			−0.651794	+	0.758396i	$0.725983\pi$
$618$		0			0
$619$	−5.14323e11	+	8.90834e11i	−0.140808	+	0.243887i	−0.927801	−	0.373075i	$-0.878303\pi$
$619$	−5.14323e11	+	8.90834e11i	−0.140808	+	0.243887i	0.786993	+	0.616962i	$0.211637\pi$
$620$	3.64349e11	−	6.31071e11i	0.0990273	−	0.171520i
$621$		0			0
$622$	2.44285e12			0.654396
$623$	3.51464e12	−	2.71063e12i	0.934726	−	0.720900i
$624$		0			0
$625$	−1.27832e12	−	2.21412e12i	−0.335104	−	0.580418i
$626$	1.99909e12	−	3.46253e12i	0.520293	−	0.901175i
$627$		0			0
$628$	−7.04386e10	−	1.22003e11i	−0.0180714	−	0.0313006i
$629$	−1.20059e12			−0.305821
$630$		0			0
$631$	−5.01733e12			−1.25991			−0.629956	−	0.776631i	$-0.716927\pi$
$631$	−5.01733e12			−1.25991			−0.629956	+	0.776631i	$0.716927\pi$
$632$	1.12830e11	+	1.95428e11i	0.0281319	+	0.0487259i
$633$		0			0
$634$	−9.87920e11	+	1.71113e12i	−0.242840	+	0.420611i
$635$	−4.32488e11	−	7.49091e11i	−0.105558	−	0.182832i
$636$		0			0
$637$	1.85162e11	−	5.05914e10i	0.0445578	−	0.0121744i
$638$	−1.29532e12			−0.309516
$639$		0			0
$640$	−6.34115e10	+	1.09832e11i	−0.0149403	+	0.0258773i
$641$	1.21201e12	−	2.09927e12i	0.283561	−	0.491142i	−0.688698	−	0.725048i	$-0.741817\pi$
$641$	1.21201e12	−	2.09927e12i	0.283561	−	0.491142i	0.972259	+	0.233906i	$0.0751508\pi$
$642$		0			0
$643$	4.20461e12			0.970011			0.485006	−	0.874511i	$-0.338818\pi$
$643$	4.20461e12			0.970011			0.485006	+	0.874511i	$0.338818\pi$
$644$	5.61812e10	+	4.18777e11i	0.0128708	+	0.0959394i
$645$		0			0
$646$	−1.50716e12	−	2.61048e12i	−0.340497	−	0.589759i
$647$	−2.75204e12	+	4.76668e12i	−0.617427	+	1.06942i	0.372526	+	0.928022i	$0.378492\pi$
$647$	−2.75204e12	+	4.76668e12i	−0.617427	+	1.06942i	−0.989953	+	0.141394i	$0.954842\pi$
$648$		0			0
$649$	4.91919e11	+	8.52029e11i	0.108841	+	0.188518i
$650$	1.31658e11			0.0289293
$651$		0			0
$652$	−1.57725e11			−0.0341812
$653$	−3.08839e12	−	5.34925e12i	−0.664696	−	1.15129i	−0.979368	−	0.202087i	$-0.935228\pi$
$653$	−3.08839e12	−	5.34925e12i	−0.664696	−	1.15129i	0.314672	−	0.949201i	$-0.398106\pi$
$654$		0			0
$655$	−7.13015e11	+	1.23498e12i	−0.151361	+	0.262164i
$656$	4.84713e11	+	8.39548e11i	0.102192	+	0.177002i
$657$		0			0
$658$	−3.58009e12	−	1.47262e12i	−0.744522	−	0.306248i
$659$	4.17021e12			0.861338			0.430669	−	0.902510i	$-0.358278\pi$
$659$	4.17021e12			0.861338			0.430669	+	0.902510i	$0.358278\pi$
$660$		0			0
$661$	1.86979e12	−	3.23857e12i	0.380966	−	0.659852i	−0.610235	−	0.792221i	$-0.708925\pi$
$661$	1.86979e12	−	3.23857e12i	0.380966	−	0.659852i	0.991201	+	0.132368i	$0.0422582\pi$
$662$	−3.30903e11	+	5.73141e11i	−0.0669638	+	0.115985i
$663$		0			0
$664$	−3.88896e11			−0.0776384
$665$	1.98990e12	+	8.18518e11i	0.394580	+	0.162305i
$666$		0			0
$667$	−5.72816e11	−	9.92146e11i	−0.112059	−	0.194093i
$668$	2.06307e12	−	3.57335e12i	0.400885	−	0.694354i
$669$		0			0
$670$	−8.88692e11	−	1.53926e12i	−0.170379	−	0.295104i
$671$	−1.12716e12			−0.214652
$672$		0			0
$673$	−8.78180e12			−1.65012			−0.825060	−	0.565044i	$-0.808859\pi$
$673$	−8.78180e12			−1.65012			−0.825060	+	0.565044i	$0.808859\pi$
$674$	2.64179e12	+	4.57571e12i	0.493092	+	0.854061i
$675$		0			0
$676$	1.35448e12	−	2.34603e12i	0.249467	−	0.432089i
$677$	−5.38955e12	−	9.33497e12i	−0.986060	−	1.70791i	−0.637130	−	0.770757i	$-0.719878\pi$
$677$	−5.38955e12	−	9.33497e12i	−0.986060	−	1.70791i	−0.348930	−	0.937149i	$-0.613455\pi$
$678$		0			0
$679$	−1.28391e12	−	9.57036e12i	−0.231804	−	1.72788i
$680$	5.08524e11			0.0912055
$681$		0			0
$682$	8.84967e11	−	1.53281e12i	0.156638	−	0.271305i
$683$	−2.95973e12	+	5.12640e12i	−0.520426	+	0.901404i	0.479292	+	0.877656i	$0.340894\pi$
$683$	−2.95973e12	+	5.12640e12i	−0.520426	+	0.901404i	−0.999718	+	0.0237489i	$0.992440\pi$
$684$		0			0
$685$	1.12759e12			0.195678
$686$	2.47277e12	−	3.27228e12i	0.426309	−	0.564146i
$687$		0			0
$688$	7.02701e11	+	1.21711e12i	0.119570	+	0.207102i
$689$	−7.55075e9	+	1.30783e10i	−0.00127645	+	0.00221088i
$690$		0			0
$691$	3.71733e12	+	6.43860e12i	0.620268	+	1.07434i	0.989436	+	0.144973i	$0.0463097\pi$
$691$	3.71733e12	+	6.43860e12i	0.620268	+	1.07434i	−0.369167	+	0.929363i	$0.620357\pi$
$692$	9.16732e11			0.151973
$693$		0			0
$694$	−8.53589e12			−1.39679
$695$	6.05535e10	+	1.04882e11i	0.00984482	+	0.0170517i
$696$		0			0
$697$	1.94356e12	−	3.36635e12i	0.311925	−	0.540270i
$698$	6.76789e11	+	1.17223e12i	0.107920	+	0.186924i
$699$		0			0
$700$	2.22767e12	−	1.71807e12i	0.350679	−	0.270458i
$701$	−3.36697e12			−0.526634			−0.263317	−	0.964709i	$-0.584816\pi$
$701$	−3.36697e12			−0.526634			−0.263317	+	0.964709i	$0.584816\pi$
$702$		0			0
$703$	1.63775e12	−	2.83667e12i	0.252900	−	0.438036i
$704$	−1.54020e11	+	2.66771e11i	−0.0236320	+	0.0409318i
$705$		0			0
$706$	−2.68503e12			−0.406751
$707$	1.55510e12	+	6.39667e11i	0.234084	+	0.0962868i
$708$		0			0
$709$	−5.85825e12	−	1.01468e13i	−0.870682	−	1.50807i	−0.861293	−	0.508109i	$-0.830345\pi$
$709$	−5.85825e12	−	1.01468e13i	−0.870682	−	1.50807i	−0.00938941	−	0.999956i	$-0.502989\pi$
$710$	−1.03721e12	+	1.79651e12i	−0.153181	+	0.265318i
$711$		0			0
$712$	1.43095e12	+	2.47848e12i	0.208672	+	0.361431i
$713$	1.56540e12			0.226841
$714$		0			0
$715$	−4.12619e10			−0.00590435
$716$	−3.24045e12	−	5.61262e12i	−0.460783	−	0.798099i
$717$		0			0
$718$	6.13521e11	−	1.06265e12i	0.0861527	−	0.149221i
$719$	6.42536e12	+	1.11291e13i	0.896639	+	1.55302i	0.831763	+	0.555131i	$0.187332\pi$
$719$	6.42536e12	+	1.11291e13i	0.896639	+	1.55302i	0.0648756	+	0.997893i	$0.479335\pi$
$720$		0			0
$721$	7.63425e12	−	5.88785e12i	1.05210	−	0.811425i
$722$	3.06082e12			0.419199
$723$		0			0
$724$	1.12540e12	−	1.94925e12i	0.152224	−	0.263660i
$725$	−3.81385e12	+	6.60578e12i	−0.512676	+	0.887980i
$726$		0			0
$727$	1.03159e13			1.36963			0.684817	−	0.728715i	$-0.259882\pi$
$727$	1.03159e13			1.36963			0.684817	+	0.728715i	$0.259882\pi$
$728$	1.64565e10	+	1.22668e11i	0.00217144	+	0.0161860i
$729$		0			0
$730$	−8.82172e11	−	1.52797e12i	−0.114974	−	0.199141i
$731$	2.81763e12	−	4.88028e12i	0.364969	−	0.632145i
$732$		0			0
$733$	5.28862e12	+	9.16015e12i	0.676666	+	1.17202i	0.975979	+	0.217865i	$0.0699091\pi$
$733$	5.28862e12	+	9.16015e12i	0.676666	+	1.17202i	−0.299313	+	0.954155i	$0.596758\pi$
$734$	−4.27334e12			−0.543419
$735$		0			0
$736$	−2.72443e11			−0.0342236
$737$	−2.15855e12	−	3.73871e12i	−0.269499	−	0.466786i
$738$		0			0
$739$	3.62845e12	−	6.28466e12i	0.447529	−	0.775143i	−0.550696	−	0.834706i	$-0.685637\pi$
$739$	3.62845e12	−	6.28466e12i	0.447529	−	0.775143i	0.998225	+	0.0595632i	$0.0189708\pi$
$740$	2.76293e11	+	4.78553e11i	0.0338709	+	0.0586661i
$741$		0			0
$742$	4.29054e10	+	3.19819e11i	0.00519630	+	0.0387335i
$743$	−7.60678e12			−0.915696			−0.457848	−	0.889031i	$-0.651380\pi$
$743$	−7.60678e12			−0.915696			−0.457848	+	0.889031i	$0.651380\pi$
$744$		0			0
$745$	1.25069e11	−	2.16627e11i	0.0148747	−	0.0257637i
$746$	−4.56475e12	+	7.90639e12i	−0.539626	+	0.934659i
$747$		0			0
$748$	1.23515e12			0.144266
$749$	1.12951e13	−	8.71125e12i	1.31136	−	1.01137i
$750$		0			0
$751$	1.65083e11	+	2.85933e11i	0.0189375	+	0.0328008i	0.875339	−	0.483510i	$-0.160638\pi$
$751$	1.65083e11	+	2.85933e11i	0.0189375	+	0.0328008i	−0.856401	+	0.516311i	$0.827305\pi$
$752$	1.24803e12	−	2.16166e12i	0.142314	−	0.246494i
$753$		0			0
$754$	−1.67789e11	−	2.90619e11i	−0.0189057	−	0.0327455i
$755$	−1.64153e12			−0.183861
$756$		0			0
$757$	−9.46308e12			−1.04737			−0.523686	−	0.851911i	$-0.675443\pi$
$757$	−9.46308e12			−1.04737			−0.523686	+	0.851911i	$0.675443\pi$
$758$	−1.31723e11	−	2.28152e11i	−0.0144928	−	0.0251022i
$759$		0			0
$760$	−6.93689e11	+	1.20150e12i	−0.0754230	+	0.130636i
$761$	−5.21569e12	−	9.03383e12i	−0.563742	−	0.976430i	−0.997165	−	0.0752395i	$-0.976028\pi$
$761$	−5.21569e12	−	9.03383e12i	−0.563742	−	0.976430i	0.433423	−	0.901190i	$-0.357305\pi$
$762$		0			0
$763$	5.67064e12	+	2.33253e12i	0.605720	+	0.249154i
$764$	5.74888e11			0.0610468
$765$		0			0
$766$	2.21405e12	−	3.83485e12i	0.232358	−	0.402457i
$767$	−1.27441e11	+	2.20734e11i	−0.0132963	+	0.0230298i
$768$		0			0
$769$	−5.48400e12			−0.565496			−0.282748	−	0.959194i	$-0.591246\pi$
$769$	−5.48400e12			−0.565496			−0.282748	+	0.959194i	$0.591246\pi$
$770$	−6.98155e11	+	5.38446e11i	−0.0715721	+	0.0551993i
$771$		0			0
$772$	3.27696e12	+	5.67586e12i	0.332042	+	0.575114i
$773$	6.72970e12	−	1.16562e13i	0.677935	−	1.17422i	−0.297666	−	0.954670i	$-0.596208\pi$
$773$	6.72970e12	−	1.16562e13i	0.677935	−	1.17422i	0.975602	−	0.219548i	$-0.0704584\pi$
$774$		0			0
$775$	−5.21128e12	−	9.02619e12i	−0.518903	−	0.898767i
$776$	6.22616e12			0.616372
$777$		0			0
$778$	−6.14794e12			−0.601619
$779$	5.30251e12	+	9.18422e12i	0.515897	+	0.893560i
$780$		0			0
$781$	−2.51929e12	+	4.36354e12i	−0.242297	+	0.419671i
$782$	5.46209e11	+	9.46061e11i	0.0522310	+	0.0904667i
$783$		0			0
$784$	1.87920e12	+	1.86080e12i	0.177644	+	0.175905i
$785$	2.59991e11			0.0244369
$786$		0			0
$787$	−2.47549e12	+	4.28767e12i	−0.230025	+	0.398414i	−0.957815	−	0.287385i	$-0.907214\pi$
$787$	−2.47549e12	+	4.28767e12i	−0.230025	+	0.398414i	0.727790	+	0.685800i	$0.240547\pi$
$788$	−4.06738e12	+	7.04491e12i	−0.375792	+	0.650890i
$789$		0			0
$790$	−4.16461e11			−0.0380410
$791$	1.54404e12	+	1.15094e13i	0.140238	+	1.04534i
$792$		0			0
$793$	−1.46006e11	−	2.52890e11i	−0.0131112	−	0.0227093i
$794$	−2.83002e12	+	4.90174e12i	−0.252695	+	0.437681i
$795$		0			0
$796$	3.16360e12	+	5.47951e12i	0.279301	+	0.483764i
$797$	1.45639e13			1.27854			0.639269	−	0.768983i	$-0.279237\pi$
$797$	1.45639e13			1.27854			0.639269	+	0.768983i	$0.279237\pi$
$798$		0			0
$799$	−1.00085e13			−0.868779
$800$	9.06973e11	+	1.57092e12i	0.0782870	+	0.135597i
$801$		0			0
$802$	−2.79351e12	+	4.83850e12i	−0.238433	+	0.412978i
$803$	−2.14271e12	−	3.71128e12i	−0.181863	−	0.314995i
$804$		0			0
$805$	−7.21159e11	−	2.96638e11i	−0.0605270	−	0.0248969i
$806$	4.58535e11			0.0382706
$807$		0			0
$808$	−5.42114e11	+	9.38969e11i	−0.0447445	+	0.0774997i
$809$	−2.00228e12	+	3.46805e12i	−0.164345	+	0.284654i	−0.936422	−	0.350875i	$-0.885884\pi$
$809$	−2.00228e12	+	3.46805e12i	−0.164345	+	0.284654i	0.772078	+	0.635528i	$0.219218\pi$
$810$		0			0
$811$	−1.23992e13			−1.00646			−0.503232	−	0.864151i	$-0.667856\pi$
$811$	−1.23992e13			−1.00646			−0.503232	+	0.864151i	$0.667856\pi$
$812$	−6.63142e12	−	2.72774e12i	−0.535309	−	0.220191i
$813$		0			0
$814$	6.71088e11	+	1.16236e12i	0.0535759	+	0.0927962i
$815$	1.45542e11	−	2.52087e11i	0.0115553	−	0.0200143i
$816$		0			0
$817$	7.68719e12	+	1.33146e13i	0.603627	+	1.04551i
$818$	−1.61942e13			−1.26465
$819$		0			0
$820$	−1.78909e12			−0.138188
$821$	−8.94969e12	−	1.55013e13i	−0.687486	−	1.19076i	−0.972649	−	0.232281i	$-0.925381\pi$
$821$	−8.94969e12	−	1.55013e13i	−0.687486	−	1.19076i	0.285163	−	0.958479i	$-0.407952\pi$
$822$		0			0
$823$	−3.60489e12	+	6.24385e12i	−0.273900	+	0.474410i	−0.969857	−	0.243674i	$-0.921647\pi$
$823$	−3.60489e12	+	6.24385e12i	−0.273900	+	0.474410i	0.695957	+	0.718084i	$0.254981\pi$
$824$	3.10821e12	+	5.38357e12i	0.234875	+	0.406816i
$825$		0			0
$826$	7.24155e11	+	5.39789e12i	0.0541279	+	0.403472i
$827$	−1.78205e13			−1.32478			−0.662391	−	0.749159i	$-0.730458\pi$
$827$	−1.78205e13			−1.32478			−0.662391	+	0.749159i	$0.730458\pi$
$828$		0			0
$829$	−1.00826e12	+	1.74636e12i	−0.0741442	+	0.128422i	−0.900714	−	0.434413i	$-0.856956\pi$
$829$	−1.00826e12	+	1.74636e12i	−0.0741442	+	0.128422i	0.826570	+	0.562835i	$0.190289\pi$
$830$	3.58857e11	−	6.21558e11i	0.0262464	−	0.0454601i
$831$		0			0
$832$	−7.98038e10			−0.00577389
$833$	2.69414e12	−	1.02562e13i	0.193873	−	0.738046i
$834$		0			0
$835$	3.80743e12	+	6.59467e12i	0.271046	+	0.469466i
$836$	−1.68490e12	+	2.91833e12i	−0.119302	+	0.206636i
$837$		0			0
$838$	4.21313e12	+	7.29736e12i	0.295126	+	0.511172i
$839$	2.75875e13			1.92214			0.961068	−	0.276312i	$-0.0891124\pi$
$839$	2.75875e13			1.92214			0.961068	+	0.276312i	$0.0891124\pi$
$840$		0			0
$841$	4.93474e12			0.340159
$842$	3.40546e11	+	5.89843e11i	0.0233492	+	0.0404419i
$843$		0			0
$844$	4.46457e12	−	7.73286e12i	0.302858	−	0.524565i
$845$	2.49972e12	+	4.32963e12i	0.168669	+	0.292143i
$846$		0			0
$847$	1.01652e13	−	7.83985e12i	0.678644	−	0.523398i
$848$	−2.08064e11			−0.0138171
$849$		0			0
$850$	3.63670e12	−	6.29895e12i	0.238958	−	0.413888i
$851$	−5.93536e11	+	1.02803e12i	−0.0387940	+	0.0671931i
$852$		0			0
$853$	−7.06363e12			−0.456833			−0.228416	−	0.973564i	$-0.573355\pi$
$853$	−7.06363e12			−0.456833			−0.228416	+	0.973564i	$0.573355\pi$
$854$	−5.77053e12	−	2.37362e12i	−0.371240	−	0.152704i
$855$		0			0
$856$	4.59868e12	+	7.96516e12i	0.292753	+	0.507063i
$857$	1.41223e13	−	2.44605e13i	0.894317	−	1.54900i	0.0596684	−	0.998218i	$-0.480996\pi$
$857$	1.41223e13	−	2.44605e13i	0.894317	−	1.54900i	0.834648	−	0.550783i	$-0.185671\pi$
$858$		0			0
$859$	1.15007e13	+	1.99198e13i	0.720702	+	1.24829i	0.960719	+	0.277523i	$0.0895136\pi$
$859$	1.15007e13	+	1.99198e13i	0.720702	+	1.24829i	−0.240017	+	0.970769i	$0.577153\pi$
$860$	−2.59369e12			−0.161687
$861$		0			0
$862$	−4.51039e12			−0.278247
$863$	3.17233e12	+	5.49463e12i	0.194684	+	0.337202i	0.946797	−	0.321832i	$-0.104299\pi$
$863$	3.17233e12	+	5.49463e12i	0.194684	+	0.337202i	−0.752113	+	0.659034i	$0.770965\pi$
$864$		0			0
$865$	−8.45922e11	+	1.46518e12i	−0.0513757	+	0.0889854i
$866$	−4.46412e11	−	7.73209e11i	−0.0269715	−	0.0467161i
$867$		0			0
$868$	7.75846e12	−	5.98365e12i	0.463913	−	0.357789i
$869$	−1.01154e12			−0.0601721
$870$		0			0
$871$	5.59213e11	−	9.68585e11i	0.0329227	−	0.0570238i
$872$	−1.97681e12	+	3.42393e12i	−0.115782	+	0.200540i
$873$		0			0
$874$	−2.98039e12			−0.172771
$875$	1.46974e12	+	1.09555e13i	0.0847624	+	0.631824i
$876$		0			0
$877$	−1.36489e12	−	2.36406e12i	−0.0779113	−	0.134946i	0.824437	−	0.565953i	$-0.191492\pi$
$877$	−1.36489e12	−	2.36406e12i	−0.0779113	−	0.134946i	−0.902349	+	0.431007i	$0.858158\pi$
$878$	−6.07333e12	+	1.05193e13i	−0.344907	+	0.597396i
$879$		0			0
$880$	−2.84247e11	−	4.92330e11i	−0.0159780	−	0.0276748i
$881$	−1.05136e13			−0.587974			−0.293987	−	0.955809i	$-0.594982\pi$
$881$	−1.05136e13			−0.587974			−0.293987	+	0.955809i	$0.594982\pi$
$882$		0			0
$883$	2.11154e13			1.16890			0.584448	−	0.811431i	$-0.301311\pi$
$883$	2.11154e13			1.16890			0.584448	+	0.811431i	$0.301311\pi$
$884$	1.59995e11	+	2.77120e11i	0.00881194	+	0.0152627i
$885$		0			0
$886$	−1.16701e13	+	2.02132e13i	−0.636243	+	1.10200i
$887$	1.36875e13	+	2.37075e13i	0.742453	+	1.28597i	0.951375	+	0.308034i	$0.0996711\pi$
$887$	1.36875e13	+	2.37075e13i	0.742453	+	1.28597i	−0.208922	+	0.977932i	$0.566996\pi$
$888$		0			0
$889$	−1.54640e12	−	1.15269e13i	−0.0830354	−	0.618950i
$890$	−5.28168e12			−0.282174
$891$		0			0
$892$	1.78044e11	−	3.08381e11i	0.00941640	−	0.0163097i
$893$	1.36529e13	−	2.36474e13i	0.718442	−	1.24438i
$894$		0			0
$895$	1.19606e13			0.623088
$896$	−1.35029e12	+	1.04140e12i	−0.0699907	+	0.0539797i
$897$		0			0
$898$	7.81438e12	+	1.35349e13i	0.401006	+	0.694563i
$899$	−1.32828e13	+	2.30064e13i	−0.678219	+	1.17471i
$900$		0			0
$901$	4.17138e11	+	7.22505e11i	0.0210872	+	0.0365241i
$902$	−4.34553e12			−0.218581
$903$		0			0
$904$	−7.48762e12			−0.372894
$905$	2.07694e12	+	3.59737e12i	0.102922	+	0.178265i
$906$		0			0
$907$	−7.43436e12	+	1.28767e13i	−0.364763	+	0.631788i	−0.988738	−	0.149656i	$-0.952183\pi$
$907$	−7.43436e12	+	1.28767e13i	−0.364763	+	0.631788i	0.623975	+	0.781444i	$0.285517\pi$
$908$	4.01090e12	+	6.94708e12i	0.195819	+	0.339169i
$909$		0			0
$910$	−2.11241e11	−	8.68910e10i	−0.0102116	−	0.00420038i
$911$	−3.26369e12			−0.156992			−0.0784958	−	0.996914i	$-0.525012\pi$
$911$	−3.26369e12			−0.156992			−0.0784958	+	0.996914i	$0.525012\pi$
$912$		0			0
$913$	8.71627e11	−	1.50970e12i	0.0415157	−	0.0719073i
$914$	3.94049e10	−	6.82512e10i	0.00186764	−	0.00323484i
$915$		0			0
$916$	−1.00992e13			−0.473976
$917$	−1.51830e13	+	1.17097e13i	−0.709079	+	0.546872i
$918$		0			0
$919$	−1.93299e13	−	3.34804e13i	−0.893944	−	1.54836i	−0.835106	−	0.550089i	$-0.814594\pi$
$919$	−1.93299e13	−	3.34804e13i	−0.893944	−	1.54836i	−0.0588382	−	0.998268i	$-0.518740\pi$
$920$	2.51399e11	−	4.35436e11i	0.0115696	−	0.0200391i
$921$		0			0
$922$	1.16112e12	+	2.01112e12i	0.0529162	+	0.0916535i
$923$	−1.30534e12			−0.0591992
$924$		0			0
$925$	7.90362e12			0.354967
$926$	8.53102e12	+	1.47762e13i	0.381287	+	0.660408i
$927$		0			0
$928$	2.31174e12	−	4.00405e12i	0.102323	−	0.177229i
$929$	6.61021e12	+	1.14492e13i	0.291169	+	0.504319i	0.974086	−	0.226176i	$-0.0726226\pi$
$929$	6.61021e12	+	1.14492e13i	0.291169	+	0.504319i	−0.682918	+	0.730495i	$0.739289\pi$
$930$		0			0
$931$	2.05575e13	+	2.03562e13i	0.896801	+	0.888023i
$932$	2.14358e13			0.930610
$933$		0			0
$934$	1.14352e13	−	1.98063e13i	0.491678	−	0.851612i
$935$	−1.13975e12	+	1.97410e12i	−0.0487704	+	0.0844728i
$936$		0			0
$937$	4.49241e12			0.190393			0.0951966	−	0.995458i	$-0.469652\pi$
$937$	4.49241e12			0.190393			0.0951966	+	0.995458i	$0.469652\pi$
$938$	−3.17760e12	−	2.36860e13i	−0.134025	−	0.999030i
$939$		0			0
$940$	2.30327e12	+	3.98938e12i	0.0962208	+	0.166659i
$941$	−1.26286e13	+	2.18734e13i	−0.525052	+	0.909416i	0.474523	+	0.880243i	$0.342621\pi$
$941$	−1.26286e13	+	2.18734e13i	−0.525052	+	0.909416i	−0.999574	+	0.0291730i	$0.990713\pi$
$942$		0			0
$943$	−1.92168e12	−	3.32844e12i	−0.0791367	−	0.137069i
$944$	−3.51169e12			−0.143927
$945$		0			0
$946$	−6.29982e12			−0.255752
$947$	−1.14172e13	−	1.97752e13i	−0.461303	−	0.799000i	0.537724	−	0.843121i	$-0.319284\pi$
$947$	−1.14172e13	−	1.97752e13i	−0.461303	−	0.799000i	−0.999026	+	0.0441216i	$0.985951\pi$
$948$		0			0
$949$	5.55110e11	−	9.61479e11i	0.0222168	−	0.0384806i
$950$	9.92182e12	+	1.71851e13i	0.395216	+	0.684535i
$951$		0			0
$952$	6.32340e12	+	2.60104e12i	0.249508	+	0.102631i
$953$	−2.31698e13			−0.909923			−0.454961	−	0.890511i	$-0.650347\pi$
$953$	−2.31698e13			−0.909923			−0.454961	+	0.890511i	$0.650347\pi$
$954$		0			0
$955$	−5.30483e11	+	9.18823e11i	−0.0206374	+	0.0357451i
$956$	−1.32967e11	+	2.30305e11i	−0.00514852	+	0.00891750i
$957$		0			0
$958$	−6.06135e11			−0.0232501
$959$	1.40214e13	+	5.76748e12i	0.535311	+	0.220192i
$960$		0			0
$961$	−4.92987e12	−	8.53879e12i	−0.186458	−	0.322954i
$962$	−1.73858e11	+	3.01131e11i	−0.00654496	+	0.0113362i
$963$		0			0
$964$	−1.33330e13	−	2.30934e13i	−0.497257	−	0.861275i
$965$	−1.20954e13			−0.449000
$966$		0			0
$967$	3.31795e13			1.22026			0.610128	−	0.792303i	$-0.291118\pi$
$967$	3.31795e13			1.22026			0.610128	+	0.792303i	$0.291118\pi$
$968$	4.13867e12	+	7.16839e12i	0.151503	+	0.262411i
$969$		0			0
$970$	−5.74524e12	+	9.95105e12i	−0.208370	+	0.360908i
$971$	5.44888e12	+	9.43773e12i	0.196707	+	0.340707i	0.947459	−	0.319878i	$-0.103642\pi$
$971$	5.44888e12	+	9.43773e12i	0.196707	+	0.340707i	−0.750752	+	0.660585i	$0.770308\pi$
$972$		0			0
$973$	2.16514e11	+	1.61391e12i	0.00774424	+	0.0577260i
$974$	3.86098e13			1.37462
$975$		0			0
$976$	2.01163e12	−	3.48425e12i	0.0709617	−	0.122909i
$977$	2.66655e13	−	4.61860e13i	0.936320	−	1.62175i	0.164056	−	0.986451i	$-0.447542\pi$
$977$	2.66655e13	−	4.61860e13i	0.936320	−	1.62175i	0.772264	−	0.635302i	$-0.219124\pi$
$978$		0			0
$979$	−1.28287e13			−0.446334
$980$	−4.70810e12	+	1.28639e12i	−0.163053	+	0.0445506i
$981$		0			0
$982$	−6.72908e12	−	1.16551e13i	−0.230916	−	0.399958i
$983$	1.45566e13	−	2.52127e13i	0.497242	−	0.861249i	−0.502753	−	0.864430i	$-0.667679\pi$
$983$	1.45566e13	−	2.52127e13i	0.497242	−	0.861249i	0.999995	+	0.00318165i	$0.00101275\pi$
$984$		0			0
$985$	−7.50642e12	−	1.30015e13i	−0.254080	−	0.440079i
$986$	−1.85388e13			−0.624649
$987$		0			0
$988$	−8.73012e11			−0.0291484
$989$	−2.78591e12	−	4.82533e12i	−0.0925941	−	0.160378i
$990$		0			0
$991$	−1.69110e13	+	2.92907e13i	−0.556978	+	0.964714i	0.440769	+	0.897621i	$0.354706\pi$
$991$	−1.69110e13	+	2.92907e13i	−0.556978	+	0.964714i	−0.997747	+	0.0670930i	$0.978628\pi$
$992$	3.15878e12	+	5.47117e12i	0.103566	+	0.179381i
$993$		0			0
$994$	−2.20865e13	+	1.70340e13i	−0.717609	+	0.553450i
$995$	−1.16769e13			−0.377681
$996$		0			0
$997$	1.09049e13	−	1.88878e13i	0.349537	−	0.605416i	−0.636630	−	0.771169i	$-0.719672\pi$
$997$	1.09049e13	−	1.88878e13i	0.349537	−	0.605416i	0.986167	+	0.165753i	$0.0530056\pi$
$998$	1.10698e13	−	1.91734e13i	0.353225	−	0.611804i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.10.g.d.109.2		6
3.2	odd	2		42.10.e.d.25.2	✓	6
7.2	even	3	inner	126.10.g.d.37.2		6
21.2	odd	6		42.10.e.d.37.2	yes	6
21.11	odd	6		294.10.a.r.1.2		3
21.17	even	6		294.10.a.u.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.10.e.d.25.2	✓	6	3.2	odd	2
42.10.e.d.37.2	yes	6	21.2	odd	6
126.10.g.d.37.2		6	7.2	even	3	inner
126.10.g.d.109.2		6	1.1	even	1	trivial
294.10.a.r.1.2		3	21.11	odd	6
294.10.a.u.1.2		3	21.17	even	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 - 13.8564i) q^{2} +(-128.000 + 221.703i) q^{4} +(-236.226 - 409.156i) q^{5} +(-844.647 - 6296.04i) q^{7} +4096.00 q^{8} +(-3779.62 + 6546.49i) q^{10} +(-9180.32 + 15900.8i) q^{11} -4756.67 q^{13} +(-80483.4 + 62072.1i) q^{14} +(-32768.0 - 56755.8i) q^{16} +(-131390. + 227575. i) q^{17} +(-358465. - 620880. i) q^{19} +120948. q^{20} +293770. q^{22} +(129911. + 225012. i) q^{23} +(864957. - 1.49815e6i) q^{25} +(38053.4 + 65910.4i) q^{26} +(1.50396e6 + 618633. i) q^{28} -4.40930e6 q^{29} +(3.01245e6 - 5.21771e6i) q^{31} +(-524288. + 908093. i) q^{32} +4.20449e6 q^{34} +(-2.37653e6 + 1.83288e6i) q^{35} +(2.28440e6 + 3.95669e6i) q^{37} +(-5.73544e6 + 9.93407e6i) q^{38} +(-967582. - 1.67590e6i) q^{40} -1.47923e7 q^{41} -2.14447e7 q^{43} +(-2.35016e6 - 4.07060e6i) q^{44} +(2.07857e6 - 3.60020e6i) q^{46} +(1.90435e7 + 3.29843e7i) q^{47} +(-3.89267e7 + 1.06359e7i) q^{49} -2.76786e7 q^{50} +(608854. - 1.05457e6i) q^{52} +(1.58740e6 - 2.74946e6i) q^{53} +8.67452e6 q^{55} +(-3.45967e6 - 2.57886e7i) q^{56} +(3.52744e7 + 6.10970e7i) q^{58} +(2.67921e7 - 4.64052e7i) q^{59} +(3.06950e7 + 5.31654e7i) q^{61} -9.63983e7 q^{62} +1.67772e7 q^{64} +(1.12365e6 + 1.94622e6i) q^{65} +(-1.17564e8 + 2.03626e8i) q^{67} +(-3.36359e7 - 5.82591e7i) q^{68} +(4.44094e7 + 1.82672e7i) q^{70} +2.74423e8 q^{71} +(-1.16701e8 + 2.02133e8i) q^{73} +(3.65504e7 - 6.33071e7i) q^{74} +1.83534e8 q^{76} +(1.07866e8 + 4.43691e7i) q^{77} +(2.75465e7 + 4.77119e7i) q^{79} +(-1.54813e7 + 2.68144e7i) q^{80} +(1.18338e8 + 2.04968e8i) q^{82} -9.49452e7 q^{83} +1.24151e8 q^{85} +(1.71558e8 + 2.97147e8i) q^{86} +(-3.76026e7 + 6.51296e7i) q^{88} +(3.49353e8 + 6.05097e8i) q^{89} +(4.01771e6 + 2.99482e7i) q^{91} -6.65144e7 q^{92} +(3.04696e8 - 5.27749e8i) q^{94} +(-1.69358e8 + 2.93336e8i) q^{95} +1.52006e9 q^{97} +(4.58789e8 + 4.54298e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} - 768 q^{4} - 361 q^{5} + 12509 q^{7} + 24576 q^{8} - 5776 q^{10} - 37799 q^{11} - 441172 q^{13} - 38752 q^{14} - 196608 q^{16} + 781816 q^{17} - 620154 q^{19} + 184832 q^{20} + 1209568 q^{22}+ \cdots + 2185772400 q^{98}+O(q^{100}) \) 6 * q - 48 * q^2 - 768 * q^4 - 361 * q^5 + 12509 * q^7 + 24576 * q^8 - 5776 * q^10 - 37799 * q^11 - 441172 * q^13 - 38752 * q^14 - 196608 * q^16 + 781816 * q^17 - 620154 * q^19 + 184832 * q^20 + 1209568 * q^22 - 1204784 * q^23 - 4020946 * q^25 + 3529376 * q^26 - 2582272 * q^28 + 10561070 * q^29 + 12838457 * q^31 - 3145728 * q^32 - 25018112 * q^34 + 20450416 * q^35 + 8014770 * q^37 - 9922464 * q^38 - 1478656 * q^40 - 13006056 * q^41 - 45086976 * q^43 - 9676544 * q^44 - 19276544 * q^46 + 21473082 * q^47 - 92935311 * q^49 + 128670272 * q^50 + 56470016 * q^52 - 13685715 * q^53 + 610214782 * q^55 + 51236864 * q^56 - 84488560 * q^58 + 92528141 * q^59 - 7516114 * q^61 - 410830624 * q^62 + 100663296 * q^64 - 79637616 * q^65 - 137325404 * q^67 + 200144896 * q^68 + 33639760 * q^70 - 16380692 * q^71 + 394016164 * q^73 + 128236320 * q^74 + 317518848 * q^76 - 140332213 * q^77 + 35090117 * q^79 - 23658496 * q^80 + 104048448 * q^82 - 1913896010 * q^83 - 823798640 * q^85 + 360695808 * q^86 - 154824704 * q^88 + 855499686 * q^89 - 1675912546 * q^91 + 616849408 * q^92 + 343569312 * q^94 + 2705508088 * q^95 + 4021139590 * q^97 + 2185772400 * q^98

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