LMFDB - Embedded newform 126.10.g.d.109.1

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			109.1
Root			$9.39252 + 16.2683i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.10.g.d.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.00000 - 13.8564i) q^{2} +(-128.000 + 221.703i) q^{4} +(-1070.48 - 1854.13i) q^{5} +(1163.76 + 6244.94i) q^{7} +4096.00 q^{8} +(-17127.7 + 29666.1i) q^{10} +(-38719.2 + 67063.6i) q^{11} -92014.0 q^{13} +(77222.3 - 66085.1i) q^{14} +(-32768.0 - 56755.8i) q^{16} +(328781. - 569465. i) q^{17} +(371263. + 643047. i) q^{19} +548087. q^{20} +1.23901e6 q^{22} +(-3231.59 - 5597.28i) q^{23} +(-1.31530e6 + 2.27817e6i) q^{25} +(736112. + 1.27498e6i) q^{26} +(-1.53348e6 - 541344. i) q^{28} +2.55350e6 q^{29} +(-431646. + 747632. i) q^{31} +(-524288. + 908093. i) q^{32} -1.05210e7 q^{34} +(1.03331e7 - 8.84286e6i) q^{35} +(3.87152e6 + 6.70567e6i) q^{37} +(5.94021e6 - 1.02888e7i) q^{38} +(-4.38470e6 - 7.59451e6i) q^{40} -2.13515e7 q^{41} +1.01098e7 q^{43} +(-9.91211e6 - 1.71683e7i) q^{44} +(-51705.5 + 89556.5i) q^{46} +(1.31759e7 + 2.28213e7i) q^{47} +(-3.76449e7 + 1.45352e7i) q^{49} +4.20897e7 q^{50} +(1.17778e7 - 2.03997e7i) q^{52} +(-1.19254e7 + 2.06555e7i) q^{53} +1.65793e8 q^{55} +(4.76676e6 + 2.55793e7i) q^{56} +(-2.04280e7 - 3.53823e7i) q^{58} +(7.76530e7 - 1.34499e8i) q^{59} +(-4.28559e7 - 7.42286e7i) q^{61} +1.38127e7 q^{62} +1.67772e7 q^{64} +(9.84994e7 + 1.70606e8i) q^{65} +(1.11224e8 - 1.92646e8i) q^{67} +(8.41678e7 + 1.45783e8i) q^{68} +(-2.05195e8 - 7.24373e7i) q^{70} -2.65826e8 q^{71} +(1.87429e8 - 3.24637e8i) q^{73} +(6.19443e7 - 1.07291e8i) q^{74} -1.90087e8 q^{76} +(-4.63868e8 - 1.63753e8i) q^{77} +(-4.81092e6 - 8.33275e6i) q^{79} +(-7.01551e7 + 1.21512e8i) q^{80} +(1.70812e8 + 2.95855e8i) q^{82} -5.90221e8 q^{83} -1.40782e9 q^{85} +(-8.08785e7 - 1.40086e8i) q^{86} +(-1.58594e8 + 2.74692e8i) q^{88} +(-2.74589e8 - 4.75603e8i) q^{89} +(-1.07082e8 - 5.74622e8i) q^{91} +1.65458e6 q^{92} +(2.10814e8 - 3.65140e8i) q^{94} +(7.94862e8 - 1.37674e9i) q^{95} +6.67265e8 q^{97} +(5.02565e8 + 4.05342e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1070.48	−	1854.13i	−0.765975	−	1.32671i	−0.939730	−	0.341918i	$-0.888923\pi$
$5$	−1070.48	−	1854.13i	−0.765975	−	1.32671i	0.173755	−	0.984789i	$-0.444410\pi$
$6$		0			0
$7$	1163.76	+	6244.94i	0.183199	+	0.983076i
$7$	1163.76	+	6244.94i	0.183199	+	0.983076i
$8$	4096.00			0.353553
$9$		0			0
$10$	−17127.7	+	29666.1i	−0.541626	+	0.938124i
$11$	−38719.2	+	67063.6i	−0.797368	+	1.38108i	0.123956	+	0.992288i	$0.460442\pi$
$11$	−38719.2	+	67063.6i	−0.797368	+	1.38108i	−0.921324	+	0.388795i	$0.872892\pi$
$12$		0			0
$13$	−92014.0			−0.893530			−0.446765	−	0.894651i	$-0.647424\pi$
$13$	−92014.0			−0.893530			−0.446765	+	0.894651i	$0.647424\pi$
$14$	77222.3	−	66085.1i	0.537238	−	0.459756i
$15$		0			0
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	328781.	−	569465.i	0.954742	−	1.65366i	0.219785	−	0.975548i	$-0.429464\pi$
$17$	328781.	−	569465.i	0.954742	−	1.65366i	0.734957	−	0.678113i	$-0.237202\pi$
$18$		0			0
$19$	371263.	+	643047.i	0.653568	+	1.13201i	0.982251	+	0.187573i	$0.0600621\pi$
$19$	371263.	+	643047.i	0.653568	+	1.13201i	−0.328682	+	0.944441i	$0.606605\pi$
$20$	548087.			0.765975
$21$		0			0
$22$	1.23901e6			1.12765
$23$	−3231.59	−	5597.28i	−0.00240792	−	0.00417063i	0.864819	−	0.502084i	$-0.167433\pi$
$23$	−3231.59	−	5597.28i	−0.00240792	−	0.00417063i	−0.867227	+	0.497913i	$0.834100\pi$
$24$		0			0
$25$	−1.31530e6	+	2.27817e6i	−0.673435	+	1.16642i
$26$	736112.	+	1.27498e6i	0.315910	+	0.547173i
$27$		0			0
$28$	−1.53348e6	−	541344.i	−0.471484	−	0.166442i
$29$	2.55350e6			0.670416			0.335208	−	0.942144i	$-0.391193\pi$
$29$	2.55350e6			0.670416			0.335208	+	0.942144i	$0.391193\pi$
$30$		0			0
$31$	−431646.	+	747632.i	−0.0839460	+	0.145399i	−0.904942	−	0.425536i	$-0.860086\pi$
$31$	−431646.	+	747632.i	−0.0839460	+	0.145399i	0.820996	+	0.570934i	$0.193419\pi$
$32$	−524288.	+	908093.i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−1.05210e7			−1.35021
$35$	1.03331e7	−	8.84286e6i	1.16393	−	0.996062i
$36$		0			0
$37$	3.87152e6	+	6.70567e6i	0.339605	+	0.588213i	0.984358	−	0.176178i	$-0.0563733\pi$
$37$	3.87152e6	+	6.70567e6i	0.339605	+	0.588213i	−0.644754	+	0.764390i	$0.723040\pi$
$38$	5.94021e6	−	1.02888e7i	0.462143	−	0.800454i
$39$		0			0
$40$	−4.38470e6	−	7.59451e6i	−0.270813	−	0.469062i
$41$	−2.13515e7			−1.18005			−0.590025	−	0.807385i	$-0.700882\pi$
$41$	−2.13515e7			−1.18005			−0.590025	+	0.807385i	$0.700882\pi$
$42$		0			0
$43$	1.01098e7			0.450957			0.225478	−	0.974248i	$-0.427606\pi$
$43$	1.01098e7			0.450957			0.225478	+	0.974248i	$0.427606\pi$
$44$	−9.91211e6	−	1.71683e7i	−0.398684	−	0.690541i
$45$		0			0
$46$	−51705.5	+	89556.5i	−0.00170265	+	0.00294908i
$47$	1.31759e7	+	2.28213e7i	0.393857	+	0.682180i	0.992955	−	0.118496i	$-0.0378072\pi$
$47$	1.31759e7	+	2.28213e7i	0.393857	+	0.682180i	−0.599098	+	0.800676i	$0.704474\pi$
$48$		0			0
$49$	−3.76449e7	+	1.45352e7i	−0.932876	+	0.360196i
$50$	4.20897e7			0.952380
$51$		0			0
$52$	1.17778e7	−	2.03997e7i	0.223382	−	0.386910i
$53$	−1.19254e7	+	2.06555e7i	−0.207603	+	0.359578i	−0.950959	−	0.309317i	$-0.899899\pi$
$53$	−1.19254e7	+	2.06555e7i	−0.207603	+	0.359578i	0.743356	+	0.668896i	$0.233233\pi$
$54$		0			0
$55$	1.65793e8			2.44306
$56$	4.76676e6	+	2.55793e7i	0.0647705	+	0.347570i
$57$		0			0
$58$	−2.04280e7	−	3.53823e7i	−0.237028	−	0.410544i
$59$	7.76530e7	−	1.34499e8i	0.834303	−	1.44506i	−0.0602929	−	0.998181i	$-0.519203\pi$
$59$	7.76530e7	−	1.34499e8i	0.834303	−	1.44506i	0.894596	−	0.446875i	$-0.147463\pi$
$60$		0			0
$61$	−4.28559e7	−	7.42286e7i	−0.396302	−	0.686415i	0.596964	−	0.802268i	$-0.296373\pi$
$61$	−4.28559e7	−	7.42286e7i	−0.396302	−	0.686415i	−0.993266	+	0.115853i	$0.963040\pi$
$62$	1.38127e7			0.118718
$63$		0			0
$64$	1.67772e7			0.125000
$65$	9.84994e7	+	1.70606e8i	0.684421	+	1.18545i
$66$		0			0
$67$	1.11224e8	−	1.92646e8i	0.674317	−	1.16795i	−0.302352	−	0.953196i	$-0.597772\pi$
$67$	1.11224e8	−	1.92646e8i	0.674317	−	1.16795i	0.976668	−	0.214754i	$-0.0688950\pi$
$68$	8.41678e7	+	1.45783e8i	0.477371	+	0.826831i
$69$		0			0
$70$	−2.05195e8	−	7.24373e7i	−1.02147	−	0.360596i
$71$	−2.65826e8			−1.24147			−0.620734	−	0.784022i	$-0.713165\pi$
$71$	−2.65826e8			−1.24147			−0.620734	+	0.784022i	$0.713165\pi$
$72$		0			0
$73$	1.87429e8	−	3.24637e8i	0.772475	−	1.33797i	−0.163728	−	0.986505i	$-0.552352\pi$
$73$	1.87429e8	−	3.24637e8i	0.772475	−	1.33797i	0.936203	−	0.351460i	$-0.114315\pi$
$74$	6.19443e7	−	1.07291e8i	0.240137	−	0.415929i
$75$		0			0
$76$	−1.90087e8			−0.653568
$77$	−4.63868e8	−	1.63753e8i	−1.50379	−	0.530861i
$78$		0			0
$79$	−4.81092e6	−	8.33275e6i	−0.0138965	−	0.0240695i	0.858994	−	0.511986i	$-0.171090\pi$
$79$	−4.81092e6	−	8.33275e6i	−0.0138965	−	0.0240695i	−0.872890	+	0.487917i	$0.837757\pi$
$80$	−7.01551e7	+	1.21512e8i	−0.191494	+	0.331677i
$81$		0			0
$82$	1.70812e8	+	2.95855e8i	0.417211	+	0.722630i
$83$	−5.90221e8			−1.36510			−0.682548	−	0.730841i	$-0.739128\pi$
$83$	−5.90221e8			−1.36510			−0.682548	+	0.730841i	$0.739128\pi$
$84$		0			0
$85$	−1.40782e9			−2.92523
$86$	−8.08785e7	−	1.40086e8i	−0.159437	−	0.276153i
$87$		0			0
$88$	−1.58594e8	+	2.74692e8i	−0.281912	+	0.488286i
$89$	−2.74589e8	−	4.75603e8i	−0.463904	−	0.803506i	0.535247	−	0.844696i	$-0.320219\pi$
$89$	−2.74589e8	−	4.75603e8i	−0.463904	−	0.803506i	−0.999151	+	0.0411896i	$0.986885\pi$
$90$		0			0
$91$	−1.07082e8	−	5.74622e8i	−0.163693	−	0.878407i
$92$	1.65458e6			0.00240792
$93$		0			0
$94$	2.10814e8	−	3.65140e8i	0.278499	−	0.482374i
$95$	7.94862e8	−	1.37674e9i	1.00123	−	1.73419i
$96$		0			0
$97$	6.67265e8			0.765289			0.382644	−	0.923896i	$-0.375013\pi$
$97$	6.67265e8			0.765289			0.382644	+	0.923896i	$0.375013\pi$
$98$	5.02565e8	+	4.05342e8i	0.550396	+	0.443919i
$99$		0			0
$100$	−3.36717e8	−	5.83211e8i	−0.336717	−	0.583211i
$101$	7.45596e8	−	1.29141e9i	0.712947	−	1.23486i	−0.250799	−	0.968039i	$-0.580693\pi$
$101$	7.45596e8	−	1.29141e9i	0.712947	−	1.23486i	0.963746	−	0.266821i	$-0.0859734\pi$
$102$		0			0
$103$	−5.17697e8	−	8.96677e8i	−0.453219	−	0.784998i	0.545365	−	0.838199i	$-0.316391\pi$
$103$	−5.17697e8	−	8.96677e8i	−0.453219	−	0.784998i	−0.998584	+	0.0532006i	$0.983058\pi$
$104$	−3.76889e8			−0.315910
$105$		0			0
$106$	3.81614e8			0.293595
$107$	6.40566e8	+	1.10949e9i	0.472429	+	0.818272i	0.999502	−	0.0315484i	$-0.0100438\pi$
$107$	6.40566e8	+	1.10949e9i	0.472429	+	0.818272i	−0.527073	+	0.849820i	$0.676710\pi$
$108$		0			0
$109$	−9.66590e7	+	1.67418e8i	−0.0655878	+	0.113601i	−0.896955	−	0.442123i	$-0.854226\pi$
$109$	−9.66590e7	+	1.67418e8i	−0.0655878	+	0.113601i	0.831367	+	0.555724i	$0.187559\pi$
$110$	−1.32634e9	−	2.29729e9i	−0.863751	−	1.49606i
$111$		0			0
$112$	3.16303e8	−	2.70684e8i	0.189942	−	0.162548i
$113$	−2.50261e9			−1.44391			−0.721955	−	0.691940i	$-0.756756\pi$
$113$	−2.50261e9			−1.44391			−0.721955	+	0.691940i	$0.756756\pi$
$114$		0			0
$115$	−6.91872e6	+	1.19836e7i	−0.00368880	+	0.00638920i
$116$	−3.26848e8	+	5.66117e8i	−0.167604	+	0.290299i
$117$		0			0
$118$	−2.48490e9			−1.17988
$119$	3.93889e9	+	1.39049e9i	1.80058	+	0.635635i
$120$		0			0
$121$	−1.81937e9	−	3.15125e9i	−0.771593	−	1.33644i
$122$	−6.85694e8	+	1.18766e9i	−0.280228	+	0.485369i
$123$		0			0
$124$	−1.10501e8	−	1.91394e8i	−0.0419730	−	0.0726993i
$125$	1.45046e9			0.531386
$126$		0			0
$127$	1.61401e9			0.550540			0.275270	−	0.961367i	$-0.411233\pi$
$127$	1.61401e9			0.550540			0.275270	+	0.961367i	$0.411233\pi$
$128$	−1.34218e8	−	2.32472e8i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	1.57599e9	−	2.72969e9i	0.483959	−	0.838241i
$131$	−1.67488e9	−	2.90098e9i	−0.496893	−	0.860644i	0.503101	−	0.864228i	$-0.332192\pi$
$131$	−1.67488e9	−	2.90098e9i	−0.496893	−	0.860644i	−0.999994	+	0.00358415i	$0.998859\pi$
$132$		0			0
$133$	−3.58373e9	+	3.06687e9i	−0.993122	+	0.849891i
$134$	−3.55918e9			−0.953628
$135$		0			0
$136$	1.34669e9	−	2.33253e9i	0.337552	−	0.584658i
$137$	−2.61593e9	+	4.53093e9i	−0.634430	+	1.09887i	0.352205	+	0.935923i	$0.385432\pi$
$137$	−2.61593e9	+	4.53093e9i	−0.634430	+	1.09887i	−0.986636	+	0.162943i	$0.947901\pi$
$138$		0			0
$139$	4.86927e9			1.10636			0.553181	−	0.833061i	$-0.313414\pi$
$139$	4.86927e9			1.10636			0.553181	+	0.833061i	$0.313414\pi$
$140$	6.37842e8	+	3.42277e9i	0.140326	+	0.753011i
$141$		0			0
$142$	2.12661e9	+	3.68340e9i	0.438925	+	0.760240i
$143$	3.56271e9	−	6.17079e9i	0.712472	−	1.23404i
$144$		0			0
$145$	−2.73347e9	−	4.73451e9i	−0.513522	−	0.889446i
$146$	−5.99773e9			−1.09244
$147$		0			0
$148$	−1.98222e9			−0.339605
$149$	4.28903e8	+	7.42882e8i	0.0712888	+	0.123476i	0.899466	−	0.436990i	$-0.143955\pi$
$149$	4.28903e8	+	7.42882e8i	0.0712888	+	0.123476i	−0.828178	+	0.560466i	$0.810622\pi$
$150$		0			0
$151$	7.13023e8	−	1.23499e9i	0.111611	−	0.193316i	−0.804809	−	0.593534i	$-0.797732\pi$
$151$	7.13023e8	−	1.23499e9i	0.111611	−	0.193316i	0.916420	+	0.400218i	$0.131066\pi$
$152$	1.52069e9	+	2.63392e9i	0.231071	+	0.400227i
$153$		0			0
$154$	1.44191e9	+	7.73756e9i	0.206584	+	1.10856i
$155$	1.84828e9			0.257202
$156$		0			0
$157$	5.43197e9	−	9.40846e9i	0.713525	−	1.23586i	−0.250001	−	0.968246i	$-0.580431\pi$
$157$	5.43197e9	−	9.40846e9i	0.713525	−	1.23586i	0.963526	−	0.267616i	$-0.0862359\pi$
$158$	−7.69746e7	+	1.33324e8i	−0.00982632	+	0.0170197i
$159$		0			0
$160$	2.24496e9			0.270813
$161$	3.11939e7	−	2.66950e7i	0.00365892	−	0.00313122i
$162$		0			0
$163$	4.46717e9	+	7.73737e9i	0.495665	+	0.858518i	0.999988	−	0.00499805i	$-0.00159094\pi$
$163$	4.46717e9	+	7.73737e9i	0.495665	+	0.858518i	−0.504322	+	0.863516i	$0.668258\pi$
$164$	2.73299e9	−	4.73367e9i	0.295012	−	0.510976i
$165$		0			0
$166$	4.72177e9	+	8.17834e9i	0.482634	+	0.835947i
$167$	1.45791e10			1.45046			0.725231	−	0.688505i	$-0.241733\pi$
$167$	1.45791e10			1.45046			0.725231	+	0.688505i	$0.241733\pi$
$168$		0			0
$169$	−2.13792e9			−0.201605
$170$	1.12625e10	+	1.95073e10i	1.03423	+	1.79133i
$171$		0			0
$172$	−1.29406e9	+	2.24137e9i	−0.112739	+	0.195270i
$173$	−1.95829e9	−	3.39186e9i	−0.166215	−	0.287892i	0.770871	−	0.636991i	$-0.219821\pi$
$173$	−1.95829e9	−	3.39186e9i	−0.166215	−	0.287892i	−0.937086	+	0.349099i	$0.886488\pi$
$174$		0			0
$175$	−1.57577e10	−	5.56274e9i	−1.27005	−	0.448350i
$176$	5.07500e9			0.398684
$177$		0			0
$178$	−4.39343e9	+	7.60964e9i	−0.328030	+	0.568165i
$179$	2.25086e9	−	3.89861e9i	0.163874	−	0.283838i	−0.772381	−	0.635160i	$-0.780934\pi$
$179$	2.25086e9	−	3.89861e9i	0.163874	−	0.283838i	0.936255	+	0.351322i	$0.114268\pi$
$180$		0			0
$181$	6.07935e9			0.421021			0.210510	−	0.977592i	$-0.432487\pi$
$181$	6.07935e9			0.421021			0.210510	+	0.977592i	$0.432487\pi$
$182$	−7.10554e9	+	6.08075e9i	−0.480038	+	0.410805i
$183$		0			0
$184$	−1.32366e7	−	2.29265e7i	−0.000851327	−	0.00147454i
$185$	8.28879e9	−	1.43566e10i	0.520257	−	0.901112i
$186$		0			0
$187$	2.54602e10	+	4.40984e10i	1.52256	+	2.63716i
$188$	−6.74604e9			−0.393857
$189$		0			0
$190$	−2.54356e10			−1.41596
$191$	−4.49180e9	−	7.78003e9i	−0.244214	−	0.422991i	0.717696	−	0.696356i	$-0.245197\pi$
$191$	−4.49180e9	−	7.78003e9i	−0.244214	−	0.422991i	−0.961910	+	0.273365i	$0.911863\pi$
$192$		0			0
$193$	6.07803e9	−	1.05275e10i	0.315322	−	0.546154i	−0.664184	−	0.747569i	$-0.731221\pi$
$193$	6.07803e9	−	1.05275e10i	0.315322	−	0.546154i	0.979506	+	0.201415i	$0.0645540\pi$
$194$	−5.33812e9	−	9.24589e9i	−0.270570	−	0.468642i
$195$		0			0
$196$	1.59606e9	−	1.02065e10i	0.0772495	−	0.493996i
$197$	2.25902e10			1.06862			0.534308	−	0.845290i	$-0.320572\pi$
$197$	2.25902e10			1.06862			0.534308	+	0.845290i	$0.320572\pi$
$198$		0			0
$199$	−1.40098e9	+	2.42658e9i	−0.0633278	+	0.109687i	−0.895951	−	0.444153i	$-0.853505\pi$
$199$	−1.40098e9	+	2.42658e9i	−0.0633278	+	0.109687i	0.832623	+	0.553840i	$0.186838\pi$
$200$	−5.38748e9	+	9.33138e9i	−0.238095	+	0.412393i
$201$		0			0
$202$	−2.38591e10			−1.00826
$203$	2.97166e9	+	1.59464e10i	0.122819	+	0.659070i
$204$		0			0
$205$	2.28564e10	+	3.95884e10i	0.903888	+	1.56558i
$206$	−8.28315e9	+	1.43468e10i	−0.320474	+	0.555077i
$207$		0			0
$208$	3.01512e9	+	5.22233e9i	0.111691	+	0.193455i
$209$	−5.75001e10			−2.08454
$210$		0			0
$211$	1.43493e9			0.0498380			0.0249190	−	0.999689i	$-0.492067\pi$
$211$	1.43493e9			0.0498380			0.0249190	+	0.999689i	$0.492067\pi$
$212$	−3.05291e9	−	5.28780e9i	−0.103801	−	0.179789i
$213$		0			0
$214$	1.02491e10	−	1.77519e10i	0.334058	−	0.578605i
$215$	−1.08224e10	−	1.87449e10i	−0.345421	−	0.598287i
$216$		0			0
$217$	−5.17125e9	−	1.82554e9i	−0.158317	−	0.0558884i
$218$	3.09309e9			0.0927552
$219$		0			0
$220$	−2.12215e10	+	3.67567e10i	−0.610764	+	1.05787i
$221$	−3.02524e10	+	5.23987e10i	−0.853090	+	1.47760i
$222$		0			0
$223$	−2.50519e9			−0.0678372			−0.0339186	−	0.999425i	$-0.510799\pi$
$223$	−2.50519e9			−0.0678372			−0.0339186	+	0.999425i	$0.510799\pi$
$224$	−6.28113e9	−	2.21734e9i	−0.166695	−	0.0588460i
$225$		0			0
$226$	2.00209e10	+	3.46772e10i	0.510499	+	0.884210i
$227$	3.25982e9	−	5.64618e9i	0.0814850	−	0.141136i	−0.822403	−	0.568905i	$-0.807367\pi$
$227$	3.25982e9	−	5.64618e9i	0.0814850	−	0.141136i	0.903888	+	0.427769i	$0.140700\pi$
$228$		0			0
$229$	2.69070e9	+	4.66043e9i	0.0646556	+	0.111987i	0.896541	−	0.442960i	$-0.146072\pi$
$229$	2.69070e9	+	4.66043e9i	0.0646556	+	0.111987i	−0.831886	+	0.554947i	$0.812738\pi$
$230$	2.21399e8			0.00521676
$231$		0			0
$232$	1.04591e10			0.237028
$233$	−2.78378e10	−	4.82164e10i	−0.618775	−	1.07175i	−0.989710	−	0.143091i	$-0.954296\pi$
$233$	−2.78378e10	−	4.82164e10i	−0.618775	−	1.07175i	0.370935	−	0.928659i	$-0.379037\pi$
$234$		0			0
$235$	2.82090e10	−	4.88595e10i	0.603369	−	1.04507i
$236$	1.98792e10	+	3.44317e10i	0.417152	+	0.722528i
$237$		0			0
$238$	−1.22439e10	−	6.57029e10i	−0.247357	−	1.32736i
$239$	9.46283e10			1.87599			0.937995	−	0.346648i	$-0.112680\pi$
$239$	9.46283e10			1.87599			0.937995	+	0.346648i	$0.112680\pi$
$240$		0			0
$241$	1.39422e10	−	2.41485e10i	0.266228	−	0.461120i	−0.701657	−	0.712515i	$-0.747556\pi$
$241$	1.39422e10	−	2.41485e10i	0.266228	−	0.461120i	0.967885	+	0.251395i	$0.0808893\pi$
$242$	−2.91100e10	+	5.04200e10i	−0.545598	+	0.945004i
$243$		0			0
$244$	2.19422e10			0.396302
$245$	6.72484e10	+	5.42389e10i	1.19243	+	0.961753i
$246$		0			0
$247$	−3.41614e10	−	5.91694e10i	−0.583983	−	1.01149i
$248$	−1.76802e9	+	3.06230e9i	−0.0296794	+	0.0514062i
$249$		0			0
$250$	−1.16037e10	−	2.00981e10i	−0.187873	−	0.325406i
$251$	−3.03736e10			−0.483019			−0.241509	−	0.970398i	$-0.577642\pi$
$251$	−3.03736e10			−0.483019			−0.241509	+	0.970398i	$0.577642\pi$
$252$		0			0
$253$	5.00498e8			0.00767998
$254$	−1.29121e10	−	2.23643e10i	−0.194645	−	0.337135i
$255$		0			0
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	4.50692e10	+	7.80621e10i	0.644437	+	1.11620i	0.984431	+	0.175771i	$0.0562417\pi$
$257$	4.50692e10	+	7.80621e10i	0.644437	+	1.11620i	−0.339994	+	0.940428i	$0.610425\pi$
$258$		0			0
$259$	−3.73710e10	+	3.19812e10i	−0.516043	+	0.441617i
$260$	−5.04317e10			−0.684421
$261$		0			0
$262$	−2.67981e10	+	4.64156e10i	−0.351356	+	0.608567i
$263$	4.06474e10	−	7.04033e10i	0.523880	−	0.907386i	−0.475734	−	0.879589i	$-0.657817\pi$
$263$	4.06474e10	−	7.04033e10i	0.523880	−	0.907386i	0.999614	−	0.0277971i	$-0.00884922\pi$
$264$		0			0
$265$	5.10639e10			0.636074
$266$	7.11656e10	+	2.51226e10i	0.871571	+	0.307679i
$267$		0			0
$268$	2.84735e10	+	4.93175e10i	0.337158	+	0.583975i
$269$	5.35167e10	−	9.26936e10i	0.623166	−	1.07935i	−0.365727	−	0.930722i	$-0.619179\pi$
$269$	5.35167e10	−	9.26936e10i	0.623166	−	1.07935i	0.988892	−	0.148633i	$-0.0474872\pi$
$270$		0			0
$271$	3.35168e10	+	5.80527e10i	0.377485	+	0.653824i	0.990696	−	0.136096i	$-0.0434555\pi$
$271$	3.35168e10	+	5.80527e10i	0.377485	+	0.653824i	−0.613210	+	0.789920i	$0.710122\pi$
$272$	−4.30939e10			−0.477371
$273$		0			0
$274$	8.37098e10			0.897220
$275$	−1.01855e11	−	1.76418e11i	−1.07395	−	1.86014i
$276$		0			0
$277$	7.05918e10	−	1.22269e11i	0.720436	−	1.24783i	−0.240389	−	0.970677i	$-0.577275\pi$
$277$	7.05918e10	−	1.22269e11i	0.720436	−	1.24783i	0.960825	−	0.277155i	$-0.0893916\pi$
$278$	−3.89542e10	−	6.74706e10i	−0.391158	−	0.677506i
$279$		0			0
$280$	4.23246e10	−	3.62204e10i	0.411511	−	0.352161i
$281$	7.98623e10			0.764123			0.382061	−	0.924137i	$-0.375214\pi$
$281$	7.98623e10			0.764123			0.382061	+	0.924137i	$0.375214\pi$
$282$		0			0
$283$	−4.40429e10	+	7.62846e10i	−0.408166	+	0.706965i	−0.994684	−	0.102971i	$-0.967165\pi$
$283$	−4.40429e10	+	7.62846e10i	−0.408166	+	0.706965i	0.586518	+	0.809936i	$0.300498\pi$
$284$	3.40258e10	−	5.89343e10i	0.310367	−	0.537571i
$285$		0			0
$286$	−1.14007e11			−1.00759
$287$	−2.48480e10	−	1.33339e11i	−0.216184	−	1.16008i
$288$		0			0
$289$	−1.56899e11	−	2.71758e11i	−1.32306	−	2.29162i
$290$	−4.37356e10	+	7.57522e10i	−0.363115	+	0.628933i
$291$		0			0
$292$	4.79819e10	+	8.31070e10i	0.386237	+	0.668983i
$293$	7.12696e10			0.564937			0.282469	−	0.959277i	$-0.408847\pi$
$293$	7.12696e10			0.564937			0.282469	+	0.959277i	$0.408847\pi$
$294$		0			0
$295$	−3.32505e11			−2.55622
$296$	1.58577e10	+	2.74664e10i	0.120068	+	0.207965i
$297$		0			0
$298$	6.86245e9	−	1.18861e10i	0.0504088	−	0.0873105i
$299$	2.97352e8	+	5.15028e8i	0.00215154	+	0.00372658i
$300$		0			0
$301$	1.17654e10	+	6.31351e10i	0.0826147	+	0.443325i
$302$	−2.28167e10			−0.157842
$303$		0			0
$304$	2.43311e10	−	4.21427e10i	0.163392	−	0.283003i
$305$	−9.17529e10	+	1.58921e11i	−0.607115	+	1.05155i
$306$		0			0
$307$	−1.31777e10			−0.0846677			−0.0423338	−	0.999104i	$-0.513479\pi$
$307$	−1.31777e10			−0.0846677			−0.0423338	+	0.999104i	$0.513479\pi$
$308$	9.56795e10	−	8.18803e10i	0.605816	−	0.518443i
$309$		0			0
$310$	−1.47862e10	−	2.56105e10i	−0.0909346	−	0.157503i
$311$	−1.10435e11	+	1.91279e11i	−0.669400	+	1.15943i	0.308673	+	0.951168i	$0.400115\pi$
$311$	−1.10435e11	+	1.91279e11i	−0.669400	+	1.15943i	−0.978072	+	0.208266i	$0.933218\pi$
$312$		0			0
$313$	1.50518e10	+	2.60704e10i	0.0886417	+	0.153532i	0.906937	−	0.421266i	$-0.138414\pi$
$313$	1.50518e10	+	2.60704e10i	0.0886417	+	0.153532i	−0.818296	+	0.574798i	$0.805081\pi$
$314$	−1.73823e11			−1.00908
$315$		0			0
$316$	2.46319e9			0.0138965
$317$	−4.56593e10	−	7.90843e10i	−0.253959	−	0.439869i	0.710654	−	0.703542i	$-0.248399\pi$
$317$	−4.56593e10	−	7.90843e10i	−0.253959	−	0.439869i	−0.964612	+	0.263673i	$0.915066\pi$
$318$		0			0
$319$	−9.88693e10	+	1.71247e11i	−0.534568	+	0.925900i
$320$	−1.79597e10	−	3.11071e10i	−0.0957468	−	0.165838i
$321$		0			0
$322$	−6.19448e8	−	2.18675e8i	−0.00321110	−	0.00113357i
$323$	4.88257e11			2.49596
$324$		0			0
$325$	1.21026e11	−	2.09624e11i	0.601734	−	1.04223i
$326$	7.14748e10	−	1.23798e11i	0.350488	−	0.607064i
$327$		0			0
$328$	−8.74556e10			−0.417211
$329$	−1.27184e11	+	1.08841e11i	−0.598481	+	0.512166i
$330$		0			0
$331$	−7.24179e10	−	1.25432e11i	−0.331604	−	0.574356i	0.651222	−	0.758887i	$-0.274257\pi$
$331$	−7.24179e10	−	1.25432e11i	−0.331604	−	0.574356i	−0.982827	+	0.184531i	$0.940923\pi$
$332$	7.55483e10	−	1.30853e11i	0.341274	−	0.591104i
$333$		0			0
$334$	−1.16633e11	−	2.02014e11i	−0.512816	−	0.888223i
$335$	−4.76255e11			−2.06604
$336$		0			0
$337$	4.40381e11			1.85992			0.929959	−	0.367664i	$-0.119842\pi$
$337$	4.40381e11			1.85992			0.929959	+	0.367664i	$0.119842\pi$
$338$	1.71034e10	+	2.96239e10i	0.0712781	+	0.123457i
$339$		0			0
$340$	1.80200e11	−	3.12116e11i	0.731308	−	1.26666i
$341$	−3.34259e10	−	5.78954e10i	−0.133872	−	0.231873i
$342$		0			0
$343$	−1.34581e11	−	2.18175e11i	−0.525002	−	0.851101i
$344$	4.14098e10			0.159437
$345$		0			0
$346$	−3.13326e10	+	5.42697e10i	−0.117531	+	0.203571i
$347$	6.60794e10	−	1.14453e11i	0.244672	−	0.423784i	−0.717368	−	0.696695i	$-0.754653\pi$
$347$	6.60794e10	−	1.14453e11i	0.244672	−	0.423784i	0.962039	+	0.272911i	$0.0879865\pi$
$348$		0			0
$349$	1.26079e11			0.454911			0.227456	−	0.973788i	$-0.426959\pi$
$349$	1.26079e11			0.454911			0.227456	+	0.973788i	$0.426959\pi$
$350$	4.89823e10	+	2.62847e11i	0.174475	+	0.936262i
$351$		0			0
$352$	−4.06000e10	−	7.03213e10i	−0.140956	−	0.244143i
$353$	−1.44777e11	+	2.50762e11i	−0.496266	+	0.859557i	−0.999991	−	0.00430667i	$-0.998629\pi$
$353$	−1.44777e11	+	2.50762e11i	−0.496266	+	0.859557i	0.503725	+	0.863864i	$0.331962\pi$
$354$		0			0
$355$	2.84562e11	+	4.92876e11i	0.950933	+	1.64706i
$356$	1.40590e11			0.463904
$357$		0			0
$358$	−7.20276e10			−0.231753
$359$	1.05817e11	+	1.83280e11i	0.336225	+	0.582359i	0.983719	−	0.179711i	$-0.0575164\pi$
$359$	1.05817e11	+	1.83280e11i	0.336225	+	0.582359i	−0.647494	+	0.762070i	$0.724183\pi$
$360$		0			0
$361$	−1.14329e11	+	1.98024e11i	−0.354303	+	0.613671i
$362$	−4.86348e10	−	8.42379e10i	−0.148853	−	0.257821i
$363$		0			0
$364$	1.41102e11	+	4.98112e10i	0.421285	+	0.148721i
$365$	−8.02558e11			−2.36678
$366$		0			0
$367$	3.00433e11	−	5.20365e11i	0.864471	−	1.49731i	−0.00310083	−	0.999995i	$-0.500987\pi$
$367$	3.00433e11	−	5.20365e11i	0.864471	−	1.49731i	0.867572	−	0.497312i	$-0.165680\pi$
$368$	−2.11786e8	+	3.66823e8i	−0.000601979	+	0.00104266i
$369$		0			0
$370$	−2.65241e11			−0.735755
$371$	−1.42871e11	−	5.04356e10i	−0.391525	−	0.138215i
$372$		0			0
$373$	7.00479e10	+	1.21326e11i	0.187372	+	0.324538i	0.944373	−	0.328875i	$-0.106670\pi$
$373$	7.00479e10	+	1.21326e11i	0.187372	+	0.324538i	−0.757001	+	0.653414i	$0.773336\pi$
$374$	4.07364e11	−	7.05575e11i	1.07661	−	1.86475i
$375$		0			0
$376$	5.39683e10	+	9.34759e10i	0.139249	+	0.241187i
$377$	−2.34958e11			−0.599037
$378$		0			0
$379$	−5.87185e11			−1.46183			−0.730917	−	0.682466i	$-0.760907\pi$
$379$	−5.87185e11			−1.46183			−0.730917	+	0.682466i	$0.760907\pi$
$380$	2.03485e11	+	3.52446e11i	0.500617	+	0.867094i
$381$		0			0
$382$	−7.18689e10	+	1.24481e11i	−0.172685	+	0.299100i
$383$	1.94963e11	+	3.37685e11i	0.462975	+	0.801895i	0.999108	−	0.0422381i	$-0.0134488\pi$
$383$	1.94963e11	+	3.37685e11i	0.462975	+	0.801895i	−0.536133	+	0.844134i	$0.680115\pi$
$384$		0			0
$385$	1.92943e11	+	1.03537e12i	0.447565	+	2.40171i
$386$	−1.94497e11			−0.445933
$387$		0			0
$388$	−8.54099e10	+	1.47934e11i	−0.191322	+	0.331380i
$389$	6.76642e10	−	1.17198e11i	0.149826	−	0.259506i	−0.781337	−	0.624109i	$-0.785462\pi$
$389$	6.76642e10	−	1.17198e11i	0.149826	−	0.259506i	0.931163	+	0.364603i	$0.118795\pi$
$390$		0			0
$391$	−4.24994e9			−0.00919575
$392$	−1.54194e11	+	5.95363e10i	−0.329822	+	0.127349i
$393$		0			0
$394$	−1.80721e11	−	3.13019e11i	−0.377813	−	0.654391i
$395$	−1.03000e10	+	1.78401e10i	−0.0212888	+	0.0368732i
$396$		0			0
$397$	−3.85624e11	−	6.67920e11i	−0.779124	−	1.34948i	−0.932447	−	0.361306i	$-0.882331\pi$
$397$	−3.85624e11	−	6.67920e11i	−0.779124	−	1.34948i	0.153324	−	0.988176i	$-0.451002\pi$
$398$	4.48315e10			0.0895590
$399$		0			0
$400$	1.72399e11			0.336717
$401$	−5.59446e10	−	9.68988e10i	−0.108046	−	0.187141i	0.806933	−	0.590643i	$-0.201126\pi$
$401$	−5.59446e10	−	9.68988e10i	−0.108046	−	0.187141i	−0.914979	+	0.403502i	$0.867793\pi$
$402$		0			0
$403$	3.97175e10	−	6.87926e10i	0.0750082	−	0.129918i
$404$	1.90873e11	+	3.30601e11i	0.356474	+	0.617430i
$405$		0			0
$406$	1.97187e11	−	1.68748e11i	0.360173	−	0.308228i
$407$	−5.99608e11			−1.08316
$408$		0			0
$409$	−5.18709e11	+	8.98430e11i	−0.916576	+	1.58756i	−0.111999	+	0.993708i	$0.535725\pi$
$409$	−5.18709e11	+	8.98430e11i	−0.916576	+	1.58756i	−0.804577	+	0.593848i	$0.797608\pi$
$410$	3.65702e11	−	6.33414e11i	0.639145	−	1.10703i
$411$		0			0
$412$	2.65061e11			0.453219
$413$	9.30307e11	+	3.28414e11i	1.57344	+	0.555451i
$414$		0			0
$415$	6.31821e11	+	1.09435e12i	1.04563	+	1.81108i
$416$	4.82418e10	−	8.35573e10i	0.0789776	−	0.136793i
$417$		0			0
$418$	4.60000e11	+	7.96744e11i	0.736996	+	1.27651i
$419$	3.17331e11			0.502978			0.251489	−	0.967860i	$-0.419080\pi$
$419$	3.17331e11			0.502978			0.251489	+	0.967860i	$0.419080\pi$
$420$		0			0
$421$	−7.33305e11			−1.13767			−0.568833	−	0.822453i	$-0.692605\pi$
$421$	−7.33305e11			−1.13767			−0.568833	+	0.822453i	$0.692605\pi$
$422$	−1.14795e10	−	1.98830e10i	−0.0176204	−	0.0305194i
$423$		0			0
$424$	−4.88466e10	+	8.46048e10i	−0.0733986	+	0.127130i
$425$	8.64892e11	+	1.49804e12i	1.28591	+	2.22727i
$426$		0			0
$427$	4.13679e11	−	3.54017e11i	0.602196	−	0.515345i
$428$	−3.27970e11			−0.472429
$429$		0			0
$430$	−1.73158e11	+	2.99918e11i	−0.244250	+	0.423053i
$431$	6.55600e11	−	1.13553e12i	0.915148	−	1.58508i	0.108463	−	0.994100i	$-0.465407\pi$
$431$	6.55600e11	−	1.13553e12i	0.915148	−	1.58508i	0.806685	−	0.590982i	$-0.201260\pi$
$432$		0			0
$433$	5.23536e11			0.715734			0.357867	−	0.933773i	$-0.383504\pi$
$433$	5.23536e11			0.715734			0.357867	+	0.933773i	$0.383504\pi$
$434$	1.60746e10	+	8.62592e10i	0.0217489	+	0.116708i
$435$		0			0
$436$	−2.47447e10	−	4.28591e10i	−0.0327939	−	0.0568007i
$437$	2.39954e9	−	4.15613e9i	0.00314747	−	0.00545159i
$438$		0			0
$439$	2.15186e11	+	3.72714e11i	0.276519	+	0.478945i	0.970517	−	0.241032i	$-0.0774859\pi$
$439$	2.15186e11	+	3.72714e11i	0.276519	+	0.478945i	−0.693998	+	0.719977i	$0.744153\pi$
$440$	6.79087e11			0.863751
$441$		0			0
$442$	9.68078e11			1.20645
$443$	9.97795e10	+	1.72823e11i	0.123091	+	0.213199i	0.920985	−	0.389598i	$-0.127386\pi$
$443$	9.97795e10	+	1.72823e11i	0.123091	+	0.213199i	−0.797894	+	0.602797i	$0.794053\pi$
$444$		0			0
$445$	−5.87886e11	+	1.01825e12i	−0.710678	+	1.23093i
$446$	2.00415e10	+	3.47129e10i	0.0239841	+	0.0415417i
$447$		0			0
$448$	1.95247e10	+	1.04773e11i	0.0228998	+	0.122884i
$449$	1.34444e11			0.156111			0.0780555	−	0.996949i	$-0.475129\pi$
$449$	1.34444e11			0.156111			0.0780555	+	0.996949i	$0.475129\pi$
$450$		0			0
$451$	8.26711e11	−	1.43191e12i	0.940934	−	1.62975i
$452$	3.20334e11	−	5.54835e11i	0.360977	−	0.625231i
$453$		0			0
$454$	−1.04314e11			−0.115237
$455$	−9.50794e11	+	8.13667e11i	−1.04000	+	0.890011i
$456$		0			0
$457$	−1.05963e11	−	1.83534e11i	−0.113640	−	0.196831i	0.803595	−	0.595176i	$-0.202918\pi$
$457$	−1.05963e11	−	1.83534e11i	−0.113640	−	0.196831i	−0.917235	+	0.398346i	$0.869584\pi$
$458$	4.30513e10	−	7.45670e10i	0.0457184	−	0.0791866i
$459$		0			0
$460$	−1.77119e9	−	3.06780e9i	−0.00184440	−	0.00319460i
$461$	1.04842e12			1.08114			0.540570	−	0.841299i	$-0.318209\pi$
$461$	1.04842e12			1.08114			0.540570	+	0.841299i	$0.318209\pi$
$462$		0			0
$463$	4.22312e11			0.427089			0.213545	−	0.976933i	$-0.431499\pi$
$463$	4.22312e11			0.427089			0.213545	+	0.976933i	$0.431499\pi$
$464$	−8.36730e10	−	1.44926e11i	−0.0838020	−	0.145149i
$465$		0			0
$466$	−4.45404e11	+	7.71463e11i	−0.437540	+	0.757841i
$467$	2.43784e10	+	4.22246e10i	0.0237180	+	0.0410808i	0.877641	−	0.479319i	$-0.159116\pi$
$467$	2.43784e10	+	4.22246e10i	0.0237180	+	0.0410808i	−0.853923	+	0.520400i	$0.825783\pi$
$468$		0			0
$469$	1.33250e12	+	4.70396e11i	1.27172	+	0.448937i
$470$	−9.02689e11			−0.853292
$471$		0			0
$472$	3.18067e11	−	5.50907e11i	0.294971	−	0.510904i
$473$	−3.91443e11	+	6.78000e11i	−0.359579	+	0.622808i
$474$		0			0
$475$	−1.95329e12			−1.76054
$476$	−8.12455e11	+	6.95279e11i	−0.725384	+	0.620766i
$477$		0			0
$478$	−7.57027e11	−	1.31121e12i	−0.663263	−	1.14881i
$479$	−2.01070e11	+	3.48263e11i	−0.174517	+	0.302272i	−0.939994	−	0.341191i	$-0.889170\pi$
$479$	−2.01070e11	+	3.48263e11i	−0.174517	+	0.302272i	0.765477	+	0.643463i	$0.222503\pi$
$480$		0			0
$481$	−3.56234e11	−	6.17016e11i	−0.303447	−	0.525586i
$482$	−4.46149e11			−0.376503
$483$		0			0
$484$	9.31520e11			0.771593
$485$	−7.14295e11	−	1.23720e12i	−0.586192	−	1.01531i
$486$		0			0
$487$	−4.97415e11	+	8.61548e11i	−0.400718	+	0.694063i	−0.993813	−	0.111069i	$-0.964572\pi$
$487$	−4.97415e11	+	8.61548e11i	−0.400718	+	0.694063i	0.593095	+	0.805132i	$0.297906\pi$
$488$	−1.75538e11	−	3.04040e11i	−0.140114	−	0.242684i
$489$		0			0
$490$	2.13569e11	−	1.36573e12i	0.167361	−	1.07025i
$491$	−1.77339e11			−0.137702			−0.0688508	−	0.997627i	$-0.521933\pi$
$491$	−1.77339e11			−0.137702			−0.0688508	+	0.997627i	$0.521933\pi$
$492$		0			0
$493$	8.39540e11	−	1.45413e12i	0.640074	−	1.10864i
$494$	−5.46583e11	+	9.46710e11i	−0.412938	+	0.715230i
$495$		0			0
$496$	5.65767e10			0.0419730
$497$	−3.09358e11	−	1.66007e12i	−0.227435	−	1.22046i
$498$		0			0
$499$	5.12949e10	+	8.88454e10i	0.0370358	+	0.0641479i	0.883949	−	0.467583i	$-0.154875\pi$
$499$	5.12949e10	+	8.88454e10i	0.0370358	+	0.0641479i	−0.846913	+	0.531731i	$0.821542\pi$
$500$	−1.85659e11	+	3.21570e11i	−0.132846	+	0.230097i
$501$		0			0
$502$	2.42988e11	+	4.20868e11i	0.170773	+	0.295787i
$503$	−2.35796e12			−1.64241			−0.821203	−	0.570637i	$-0.806696\pi$
$503$	−2.35796e12			−1.64241			−0.821203	+	0.570637i	$0.806696\pi$
$504$		0			0
$505$	−3.19259e12			−2.18440
$506$	−4.00399e9	−	6.93511e9i	−0.00271528	−	0.00470301i
$507$		0			0
$508$	−2.06593e11	+	3.57829e11i	−0.137635	+	0.238391i
$509$	3.05373e11	+	5.28922e11i	0.201651	+	0.349270i	0.949061	−	0.315094i	$-0.102036\pi$
$509$	3.05373e11	+	5.28922e11i	0.201651	+	0.349270i	−0.747409	+	0.664364i	$0.768703\pi$
$510$		0			0
$511$	2.24546e12	+	7.92684e11i	1.45684	+	0.514288i
$512$	6.87195e10			0.0441942
$513$		0			0
$514$	7.21107e11	−	1.24899e12i	0.455686	−	0.789271i
$515$	−1.10837e12	+	1.91975e12i	−0.694308	+	1.20258i
$516$		0			0
$517$	−2.04063e12			−1.25620
$518$	7.42112e11	+	2.61978e11i	0.452883	+	0.159875i
$519$		0			0
$520$	4.03453e11	+	6.98802e11i	0.241979	+	0.419121i
$521$	3.24713e11	−	5.62419e11i	0.193077	−	0.334418i	−0.753192	−	0.657801i	$-0.771487\pi$
$521$	3.24713e11	−	5.62419e11i	0.193077	−	0.334418i	0.946268	+	0.323383i	$0.104820\pi$
$522$		0			0
$523$	−8.23475e11	−	1.42630e12i	−0.481274	−	0.833591i	0.518495	−	0.855081i	$-0.326493\pi$
$523$	−8.23475e11	−	1.42630e12i	−0.481274	−	0.833591i	−0.999769	+	0.0214893i	$0.993159\pi$
$524$	8.57538e11			0.496893
$525$		0			0
$526$	−1.30072e12			−0.740878
$527$	2.83833e11	+	4.91614e11i	0.160293	+	0.277636i
$528$		0			0
$529$	9.00555e11	−	1.55981e12i	0.499988	−	0.866005i
$530$	−4.08511e11	−	7.07562e11i	−0.224886	−	0.389514i
$531$		0			0
$532$	−2.21216e11	−	1.18708e12i	−0.119733	−	0.642507i
$533$	1.96463e12			1.05441
$534$		0			0
$535$	1.37143e12	−	2.37538e12i	0.723738	−	1.25355i
$536$	4.55576e11	−	7.89080e11i	0.238407	−	0.412933i
$537$		0			0
$538$	−1.71253e12			−0.881290
$539$	4.82796e11	−	3.08740e12i	0.246385	−	1.57559i
$540$		0			0
$541$	−2.50530e11	−	4.33931e11i	−0.125740	−	0.217788i	0.796282	−	0.604925i	$-0.206797\pi$
$541$	−2.50530e11	−	4.33931e11i	−0.125740	−	0.217788i	−0.922022	+	0.387138i	$0.873464\pi$
$542$	5.36268e11	−	9.28844e11i	0.266923	−	0.462323i
$543$		0			0
$544$	3.44751e11	+	5.97127e11i	0.168776	+	0.292329i
$545$	4.13887e11			0.200954
$546$		0			0
$547$	1.31820e12			0.629560			0.314780	−	0.949165i	$-0.398069\pi$
$547$	1.31820e12			0.629560			0.314780	+	0.949165i	$0.398069\pi$
$548$	−6.69679e11	−	1.15992e12i	−0.317215	−	0.549433i
$549$		0			0
$550$	−1.62968e12	+	2.82268e12i	−0.759398	+	1.31532i
$551$	9.48020e11	+	1.64202e12i	0.438163	+	0.758920i
$552$		0			0
$553$	4.64388e10	−	3.97412e10i	0.0211163	−	0.0180708i
$554$	−2.25894e12			−1.01885
$555$		0			0
$556$	−6.23267e11	+	1.07953e12i	−0.276591	+	0.479069i
$557$	1.04867e12	−	1.81635e12i	0.461625	−	0.799558i	−0.537417	−	0.843317i	$-0.680600\pi$
$557$	1.04867e12	−	1.81635e12i	0.461625	−	0.799558i	0.999042	+	0.0437586i	$0.0139332\pi$
$558$		0			0
$559$	−9.30244e11			−0.402943
$560$	−8.40480e11	−	2.96703e11i	−0.361145	−	0.127490i
$561$		0			0
$562$	−6.38898e11	−	1.10660e12i	−0.270158	−	0.467928i
$563$	1.77041e12	−	3.06644e12i	0.742654	−	1.28631i	−0.208629	−	0.977995i	$-0.566900\pi$
$563$	1.77041e12	−	3.06644e12i	0.742654	−	1.28631i	0.951283	−	0.308319i	$-0.0997666\pi$
$564$		0			0
$565$	2.67900e12	+	4.64016e12i	1.10600	+	1.91565i
$566$	1.40937e12			0.577234
$567$		0			0
$568$	−1.08882e12			−0.438925
$569$	−1.16613e12	−	2.01979e12i	−0.466381	−	0.807795i	0.532882	−	0.846190i	$-0.321109\pi$
$569$	−1.16613e12	−	2.01979e12i	−0.466381	−	0.807795i	−0.999263	+	0.0383943i	$0.987776\pi$
$570$		0			0
$571$	5.78780e11	−	1.00248e12i	0.227851	−	0.394649i	−0.729320	−	0.684173i	$-0.760163\pi$
$571$	5.78780e11	−	1.00248e12i	0.227851	−	0.394649i	0.957171	+	0.289523i	$0.0934968\pi$
$572$	9.12053e11	+	1.57972e12i	0.356236	+	0.617019i
$573$		0			0
$574$	−1.64881e12	+	1.41101e12i	−0.633968	+	0.542534i
$575$	1.70021e10			0.00648629
$576$		0			0
$577$	−1.85995e12	+	3.22152e12i	−0.698570	+	1.20996i	0.270393	+	0.962750i	$0.412846\pi$
$577$	−1.85995e12	+	3.22152e12i	−0.698570	+	1.20996i	−0.968962	+	0.247208i	$0.920487\pi$
$578$	−2.51039e12	+	4.34813e12i	−0.935548	+	1.62042i
$579$		0			0
$580$	1.39954e12			0.513522
$581$	−6.86875e11	−	3.68589e12i	−0.250084	−	1.34199i
$582$		0			0
$583$	−9.23486e11	−	1.59953e12i	−0.331072	−	0.573433i
$584$	7.67710e11	−	1.32971e12i	0.273111	−	0.473042i
$585$		0			0
$586$	−5.70157e11	−	9.87541e11i	−0.199735	−	0.345952i
$587$	−4.35998e12			−1.51570			−0.757849	−	0.652429i	$-0.773750\pi$
$587$	−4.35998e12			−1.51570			−0.757849	+	0.652429i	$0.773750\pi$
$588$		0			0
$589$	−6.41017e11			−0.219458
$590$	2.66004e12	+	4.60732e12i	0.903761	+	1.56536i
$591$		0			0
$592$	2.53724e11	−	4.39463e11i	0.0849012	−	0.147053i
$593$	6.15758e11	+	1.06652e12i	0.204486	+	0.354180i	0.949969	−	0.312345i	$-0.101114\pi$
$593$	6.15758e11	+	1.06652e12i	0.204486	+	0.354180i	−0.745483	+	0.666525i	$0.767781\pi$
$594$		0			0
$595$	−1.63836e12	−	8.79172e12i	−0.535899	−	2.87573i
$596$	−2.19598e11			−0.0712888
$597$		0			0
$598$	4.75763e9	−	8.24045e9i	0.00152137	−	0.00263509i
$599$	2.54603e12	−	4.40985e12i	0.808058	−	1.39960i	−0.106150	−	0.994350i	$-0.533852\pi$
$599$	2.54603e12	−	4.40985e12i	0.808058	−	1.39960i	0.914207	−	0.405247i	$-0.132814\pi$
$600$		0			0
$601$	−1.32105e12			−0.413033			−0.206516	−	0.978443i	$-0.566213\pi$
$601$	−1.32105e12			−0.413033			−0.206516	+	0.978443i	$0.566213\pi$
$602$	7.80703e11	−	6.68107e11i	0.242271	−	0.207330i
$603$		0			0
$604$	1.82534e11	+	3.16158e11i	0.0558055	+	0.0966580i
$605$	−3.89522e12	+	6.74671e12i	−1.18204	+	2.04735i
$606$		0			0
$607$	−5.11679e11	−	8.86255e11i	−0.152985	−	0.264978i	0.779338	−	0.626603i	$-0.215555\pi$
$607$	−5.11679e11	−	8.86255e11i	−0.152985	−	0.264978i	−0.932324	+	0.361625i	$0.882222\pi$
$608$	−7.78596e11			−0.231071
$609$		0			0
$610$	2.93609e12			0.858590
$611$	−1.21236e12	−	2.09988e12i	−0.351923	−	0.609548i
$612$		0			0
$613$	2.65817e12	−	4.60408e12i	0.760344	−	1.31695i	−0.182330	−	0.983237i	$-0.558364\pi$
$613$	2.65817e12	−	4.60408e12i	0.760344	−	1.31695i	0.942674	−	0.333716i	$-0.108303\pi$
$614$	1.05422e11	+	1.82596e11i	0.0299345	+	0.0518482i
$615$		0			0
$616$	−1.90000e12	−	6.70732e11i	−0.531669	−	0.187688i
$617$	1.84099e10			0.00511409			0.00255705	−	0.999997i	$-0.499186\pi$
$617$	1.84099e10			0.00511409			0.00255705	+	0.999997i	$0.499186\pi$
$618$		0			0
$619$	1.01330e12	−	1.75509e12i	0.277415	−	0.480498i	−0.693326	−	0.720624i	$-0.743856\pi$
$619$	1.01330e12	−	1.75509e12i	0.277415	−	0.480498i	0.970742	+	0.240126i	$0.0771888\pi$
$620$	−2.36579e11	+	4.09767e11i	−0.0643005	+	0.111372i
$621$		0			0
$622$	3.53392e12			0.946674
$623$	2.65055e12	−	2.26828e12i	0.704921	−	0.603254i
$624$		0			0
$625$	1.01626e12	+	1.76021e12i	0.266406	+	0.461429i
$626$	2.40828e11	−	4.17127e11i	0.0626791	−	0.108563i
$627$		0			0
$628$	1.39059e12	+	2.40856e12i	0.356763	+	0.617931i
$629$	5.09152e12			1.29694
$630$		0			0
$631$	−2.70186e12			−0.678471			−0.339235	−	0.940702i	$-0.610168\pi$
$631$	−2.70186e12			−0.678471			−0.339235	+	0.940702i	$0.610168\pi$
$632$	−1.97055e10	−	3.41309e10i	−0.00491316	−	0.00850984i
$633$		0			0
$634$	−7.30549e11	+	1.26535e12i	−0.179576	+	0.311034i
$635$	−1.72777e12	−	2.99258e12i	−0.421699	−	0.730405i
$636$		0			0
$637$	3.46386e12	−	1.33744e12i	0.833553	−	0.321846i
$638$	3.16382e12			0.755994
$639$		0			0
$640$	−2.87355e11	+	4.97714e11i	−0.0677032	+	0.117265i
$641$	−3.23955e12	+	5.61107e12i	−0.757920	+	1.31276i	0.185989	+	0.982552i	$0.440451\pi$
$641$	−3.23955e12	+	5.61107e12i	−0.757920	+	1.31276i	−0.943909	+	0.330205i	$0.892882\pi$
$642$		0			0
$643$	6.59134e12			1.52063			0.760317	−	0.649553i	$-0.225044\pi$
$643$	6.59134e12			1.52063			0.760317	+	0.649553i	$0.225044\pi$
$644$	1.92553e9	+	1.03327e10i	0.000441127	+	0.00236716i
$645$		0			0
$646$	−3.90606e12	−	6.76549e12i	−0.882454	−	1.52845i
$647$	−1.44155e12	+	2.49683e12i	−0.323414	+	0.560170i	−0.981190	−	0.193044i	$-0.938164\pi$
$647$	−1.44155e12	+	2.49683e12i	−0.323414	+	0.560170i	0.657776	+	0.753214i	$0.271497\pi$
$648$		0			0
$649$	6.01332e12	+	1.04154e13i	1.33049	+	2.30448i
$650$	−3.87284e12			−0.850980
$651$		0			0
$652$	−2.28719e12			−0.495665
$653$	2.99660e12	+	5.19027e12i	0.644941	+	1.11707i	0.984315	+	0.176419i	$0.0564514\pi$
$653$	2.99660e12	+	5.19027e12i	0.644941	+	1.11707i	−0.339374	+	0.940651i	$0.610215\pi$
$654$		0			0
$655$	−3.58586e12	+	6.21089e12i	−0.761215	+	1.31846i
$656$	6.99645e11	+	1.21182e12i	0.147506	+	0.255488i
$657$		0			0
$658$	2.52561e12	+	8.91583e11i	0.525231	+	0.185415i
$659$	7.08700e11			0.146379			0.0731894	−	0.997318i	$-0.476682\pi$
$659$	7.08700e11			0.146379			0.0731894	+	0.997318i	$0.476682\pi$
$660$		0			0
$661$	4.19907e12	−	7.27301e12i	0.855553	−	1.48186i	−0.0205788	−	0.999788i	$-0.506551\pi$
$661$	4.19907e12	−	7.27301e12i	0.855553	−	1.48186i	0.876131	−	0.482072i	$-0.160116\pi$
$662$	−1.15869e12	+	2.00691e12i	−0.234480	+	0.406131i
$663$		0			0
$664$	−2.41754e12			−0.482634
$665$	9.52269e12	+	3.36167e12i	1.88826	+	0.666588i
$666$		0			0
$667$	−8.25186e9	−	1.42926e10i	−0.00161431	−	0.00279606i
$668$	−1.86612e12	+	3.23222e12i	−0.362616	+	0.628069i
$669$		0			0
$670$	3.81004e12	+	6.59919e12i	0.730455	+	1.26518i
$671$	6.63738e12			1.26399
$672$		0			0
$673$	−1.06217e13			−1.99584			−0.997920	−	0.0644576i	$-0.979468\pi$
$673$	−1.06217e13			−1.99584			−0.997920	+	0.0644576i	$0.979468\pi$
$674$	−3.52305e12	−	6.10209e12i	−0.657580	−	1.13896i
$675$		0			0
$676$	2.73654e11	−	4.73982e11i	0.0504012	−	0.0872975i
$677$	−1.12868e12	−	1.95492e12i	−0.206500	−	0.357669i	0.744110	−	0.668058i	$-0.232874\pi$
$677$	−1.12868e12	−	1.95492e12i	−0.206500	−	0.357669i	−0.950610	+	0.310389i	$0.899541\pi$
$678$		0			0
$679$	7.76536e11	+	4.16703e12i	0.140200	+	0.752337i
$680$	−5.76641e12			−1.03423
$681$		0			0
$682$	−5.34815e11	+	9.26326e11i	−0.0946616	+	0.163959i
$683$	−3.16248e12	+	5.47758e12i	−0.556077	+	0.963153i	0.441742	+	0.897142i	$0.354361\pi$
$683$	−3.16248e12	+	5.47758e12i	−0.556077	+	0.963153i	−0.997819	+	0.0660110i	$0.978973\pi$
$684$		0			0
$685$	1.12012e13			1.94383
$686$	−1.94647e12	+	3.61021e12i	−0.335574	+	0.622406i
$687$		0			0
$688$	−3.31278e11	−	5.73791e11i	−0.0563696	−	0.0976350i
$689$	1.09731e12	−	1.90059e12i	0.185499	−	0.321294i
$690$		0			0
$691$	1.78903e12	+	3.09869e12i	0.298515	+	0.517043i	0.975796	−	0.218681i	$-0.0701754\pi$
$691$	1.78903e12	+	3.09869e12i	0.298515	+	0.517043i	−0.677282	+	0.735724i	$0.736842\pi$
$692$	1.00264e12			0.166215
$693$		0			0
$694$	−2.11454e12			−0.346018
$695$	−5.21247e12	−	9.02826e12i	−0.847446	−	1.46782i
$696$		0			0
$697$	−7.01995e12	+	1.21589e13i	−1.12664	+	1.95140i
$698$	−1.00863e12	−	1.74700e12i	−0.160835	−	0.278575i
$699$		0			0
$700$	3.25026e12	−	2.78150e12i	0.511655	−	0.437862i
$701$	1.11407e12			0.174253			0.0871264	−	0.996197i	$-0.472232\pi$
$701$	1.11407e12			0.174253			0.0871264	+	0.996197i	$0.472232\pi$
$702$		0			0
$703$	−2.87471e12	+	4.97914e12i	−0.443910	+	0.768874i
$704$	−6.49600e11	+	1.12514e12i	−0.0996710	+	0.172635i
$705$		0			0
$706$	4.63287e12			0.701826
$707$	8.93247e12	+	3.15331e12i	1.34457	+	0.474656i
$708$		0			0
$709$	−1.06699e12	−	1.84808e12i	−0.158582	−	0.274672i	0.775776	−	0.631009i	$-0.217359\pi$
$709$	−1.06699e12	−	1.84808e12i	−0.158582	−	0.274672i	−0.934357	+	0.356337i	$0.884025\pi$
$710$	4.55300e12	−	7.88602e12i	0.672411	−	1.16465i
$711$		0			0
$712$	−1.12472e12	−	1.94807e12i	−0.164015	−	0.284082i
$713$	5.57961e9			0.000808539
$714$		0			0
$715$	−1.52553e13			−2.18294
$716$	5.76221e11	+	9.98043e11i	0.0819370	+	0.141919i
$717$		0			0
$718$	1.69307e12	−	2.93248e12i	0.237747	−	0.411790i
$719$	−5.08025e12	−	8.79926e12i	−0.708933	−	1.22791i	−0.965253	−	0.261317i	$-0.915843\pi$
$719$	−5.08025e12	−	8.79926e12i	−0.708933	−	1.22791i	0.256320	−	0.966592i	$-0.417490\pi$
$720$		0			0
$721$	4.99722e12	−	4.27650e12i	0.688684	−	0.589359i
$722$	3.65853e12			0.501060
$723$		0			0
$724$	−7.78156e11	+	1.34781e12i	−0.105255	+	0.182307i
$725$	−3.35862e12	+	5.81730e12i	−0.451481	+	0.781989i
$726$		0			0
$727$	−4.40678e12			−0.585082			−0.292541	−	0.956253i	$-0.594501\pi$
$727$	−4.40678e12			−0.585082			−0.292541	+	0.956253i	$0.594501\pi$
$728$	−4.38609e11	−	2.35365e12i	−0.0578744	−	0.310564i
$729$		0			0
$730$	6.42047e12	+	1.11206e13i	0.836784	+	1.44935i
$731$	3.32391e12	−	5.75718e12i	0.430547	−	0.745730i
$732$		0			0
$733$	2.66792e12	+	4.62096e12i	0.341353	+	0.591241i	0.984684	−	0.174347i	$-0.0557814\pi$
$733$	2.66792e12	+	4.62096e12i	0.341353	+	0.591241i	−0.643331	+	0.765588i	$0.722448\pi$
$734$	−9.61386e12			−1.22255
$735$		0			0
$736$	6.77714e9			0.000851327
$737$	8.61304e12	+	1.49182e13i	1.07536	+	1.86257i
$738$		0			0
$739$	−2.08742e12	+	3.61551e12i	−0.257460	+	0.445933i	−0.965561	−	0.260178i	$-0.916219\pi$
$739$	−2.08742e12	+	3.61551e12i	−0.257460	+	0.445933i	0.708101	+	0.706111i	$0.249552\pi$
$740$	2.12193e12	+	3.67529e12i	0.260129	+	0.450556i
$741$		0			0
$742$	4.44107e11	+	2.38316e12i	0.0537861	+	0.288626i
$743$	−8.87391e12			−1.06823			−0.534116	−	0.845411i	$-0.679355\pi$
$743$	−8.87391e12			−1.06823			−0.534116	+	0.845411i	$0.679355\pi$
$744$		0			0
$745$	9.18266e11	−	1.59048e12i	0.109211	−	0.189159i
$746$	1.12077e12	−	1.94122e12i	0.132492	−	0.229483i
$747$		0			0
$748$	−1.30356e13			−1.52256
$749$	−6.18325e12	+	5.29148e12i	−0.717875	+	0.614340i
$750$		0			0
$751$	−1.31241e12	−	2.27317e12i	−0.150554	−	0.260766i	0.780878	−	0.624684i	$-0.214772\pi$
$751$	−1.31241e12	−	2.27317e12i	−0.150554	−	0.260766i	−0.931431	+	0.363918i	$0.881439\pi$
$752$	8.63493e11	−	1.49561e12i	0.0984642	−	0.170545i
$753$		0			0
$754$	1.87966e12	+	3.25567e12i	0.211791	+	0.366833i
$755$	−3.05311e12			−0.341965
$756$		0			0
$757$	−8.31291e12			−0.920071			−0.460036	−	0.887900i	$-0.652163\pi$
$757$	−8.31291e12			−0.920071			−0.460036	+	0.887900i	$0.652163\pi$
$758$	4.69748e12	+	8.13627e12i	0.516837	+	0.895187i
$759$		0			0
$760$	3.25575e12	−	5.63913e12i	0.353990	−	0.613128i
$761$	−1.69837e12	−	2.94166e12i	−0.183570	−	0.317952i	0.759524	−	0.650480i	$-0.225432\pi$
$761$	−1.69837e12	−	2.94166e12i	−0.183570	−	0.317952i	−0.943094	+	0.332527i	$0.892099\pi$
$762$		0			0
$763$	−1.15801e12	−	4.08795e11i	−0.123694	−	0.0436662i
$764$	2.29980e12			0.244214
$765$		0			0
$766$	3.11940e12	−	5.40297e12i	0.327372	−	0.567026i
$767$	−7.14516e12	+	1.23758e13i	−0.745475	+	1.29120i
$768$		0			0
$769$	4.79457e12			0.494403			0.247201	−	0.968964i	$-0.420489\pi$
$769$	4.79457e12			0.494403			0.247201	+	0.968964i	$0.420489\pi$
$770$	1.28029e13	−	1.09564e13i	1.31250	−	1.12321i
$771$		0			0
$772$	1.55598e12	+	2.69503e12i	0.157661	+	0.273077i
$773$	7.38674e12	−	1.27942e13i	0.744124	−	1.28886i	−0.206479	−	0.978451i	$-0.566201\pi$
$773$	7.38674e12	−	1.27942e13i	0.744124	−	1.28886i	0.950603	−	0.310409i	$-0.100466\pi$
$774$		0			0
$775$	−1.13549e12	−	1.96672e12i	−0.113064	−	0.195833i
$776$	2.73312e12			0.270570
$777$		0			0
$778$	−2.16526e12			−0.211885
$779$	−7.92702e12	−	1.37300e13i	−0.771243	−	1.33583i
$780$		0			0
$781$	1.02926e13	−	1.78273e13i	0.989907	−	1.71457i
$782$	3.39995e10	+	5.88889e10i	0.00325119	+	0.00563123i
$783$		0			0
$784$	2.05851e12	+	1.66028e12i	0.194594	+	0.156949i
$785$	−2.32593e13			−2.18617
$786$		0			0
$787$	1.02538e12	−	1.77602e12i	0.0952798	−	0.165029i	−0.814446	−	0.580240i	$-0.802959\pi$
$787$	1.02538e12	−	1.77602e12i	0.0952798	−	0.165029i	0.909725	+	0.415211i	$0.136292\pi$
$788$	−2.89154e12	+	5.00830e12i	−0.267154	+	0.462724i
$789$		0			0
$790$	3.29600e11			0.0301068
$791$	−2.91244e12	−	1.56286e13i	−0.264522	−	1.41947i
$792$		0			0
$793$	3.94334e12	+	6.83007e12i	0.354107	+	0.613332i
$794$	−6.16998e12	+	1.06867e13i	−0.550924	+	0.954228i
$795$		0			0
$796$	−3.58652e11	−	6.21203e11i	−0.0316639	−	0.0548435i
$797$	1.19235e13			1.04675			0.523373	−	0.852104i	$-0.324673\pi$
$797$	1.19235e13			1.04675			0.523373	+	0.852104i	$0.324673\pi$
$798$		0			0
$799$	1.73279e13			1.50413
$800$	−1.37919e12	−	2.38883e12i	−0.119048	−	0.206196i
$801$		0			0
$802$	−8.95113e11	+	1.55038e12i	−0.0764000	+	0.132329i
$803$	1.45142e13	+	2.51393e13i	1.23189	+	2.13370i
$804$		0			0
$805$	−8.28885e10	−	2.92610e10i	−0.00695685	−	0.00245588i
$806$	−1.27096e12			−0.106078
$807$		0			0
$808$	3.05396e12	−	5.28962e12i	0.252065	−	0.436589i
$809$	−1.92036e12	+	3.32616e12i	−0.157621	+	0.273007i	−0.934010	−	0.357246i	$-0.883716\pi$
$809$	−1.92036e12	+	3.32616e12i	−0.157621	+	0.273007i	0.776389	+	0.630254i	$0.217049\pi$
$810$		0			0
$811$	−7.57838e12			−0.615152			−0.307576	−	0.951524i	$-0.599518\pi$
$811$	−7.57838e12			−0.615152			−0.307576	+	0.951524i	$0.599518\pi$
$812$	−3.91574e12	−	1.38232e12i	−0.316090	−	0.111585i
$813$		0			0
$814$	4.79687e12	+	8.30842e12i	0.382955	+	0.663298i
$815$	9.56406e12	−	1.65654e13i	0.759334	−	1.31521i
$816$		0			0
$817$	3.75340e12	+	6.50108e12i	0.294731	+	0.510489i
$818$	1.65987e13			1.29623
$819$		0			0
$820$	−1.17025e13			−0.903888
$821$	6.60158e12	+	1.14343e13i	0.507112	+	0.878343i	0.999966	+	0.00823152i	$0.00262020\pi$
$821$	6.60158e12	+	1.14343e13i	0.507112	+	0.878343i	−0.492854	+	0.870112i	$0.664046\pi$
$822$		0			0
$823$	6.89186e11	−	1.19370e12i	0.0523645	−	0.0906980i	−0.838655	−	0.544663i	$-0.816658\pi$
$823$	6.89186e11	−	1.19370e12i	0.0523645	−	0.0906980i	0.891020	+	0.453965i	$0.149991\pi$
$824$	−2.12049e12	−	3.67279e12i	−0.160237	−	0.277539i
$825$		0			0
$826$	−2.89182e12	−	1.55180e13i	−0.216153	−	1.15991i
$827$	−1.26509e13			−0.940474			−0.470237	−	0.882540i	$-0.655832\pi$
$827$	−1.26509e13			−0.940474			−0.470237	+	0.882540i	$0.655832\pi$
$828$		0			0
$829$	−1.39141e12	+	2.40999e12i	−0.102320	+	0.177223i	−0.912640	−	0.408764i	$-0.865960\pi$
$829$	−1.39141e12	+	2.40999e12i	−0.102320	+	0.177223i	0.810320	+	0.585987i	$0.199293\pi$
$830$	1.01091e13	−	1.75095e13i	0.739371	−	1.28063i
$831$		0			0
$832$	−1.54374e12			−0.111691
$833$	−4.09963e12	+	2.62164e13i	−0.295013	+	1.88656i
$834$		0			0
$835$	−1.56067e13	−	2.70315e13i	−1.11102	−	1.92434i
$836$	7.36001e12	−	1.27479e13i	0.521135	−	0.902632i
$837$		0			0
$838$	−2.53865e12	−	4.39707e12i	−0.177830	−	0.308010i
$839$	−2.84268e12			−0.198061			−0.0990304	−	0.995084i	$-0.531574\pi$
$839$	−2.84268e12			−0.198061			−0.0990304	+	0.995084i	$0.531574\pi$
$840$		0			0
$841$	−7.98680e12			−0.550542
$842$	5.86644e12	+	1.01610e13i	0.402226	+	0.696676i
$843$		0			0
$844$	−1.83672e11	+	3.18128e11i	−0.0124595	+	0.0215805i
$845$	2.28860e12	+	3.96398e12i	0.154424	+	0.267471i
$846$		0			0
$847$	1.75620e13	−	1.50292e13i	1.17246	−	1.00337i
$848$	1.56309e12			0.103801
$849$		0			0
$850$	1.38383e13	−	2.39686e13i	0.909278	−	1.57491i
$851$	2.50224e10	−	4.33400e10i	0.00163548	−	0.00283273i
$852$		0			0
$853$	2.28579e12			0.147831			0.0739156	−	0.997265i	$-0.476450\pi$
$853$	2.28579e12			0.147831			0.0739156	+	0.997265i	$0.476450\pi$
$854$	−8.21483e12	−	2.89997e12i	−0.528492	−	0.186566i
$855$		0			0
$856$	2.62376e12	+	4.54448e12i	0.167029	+	0.289303i
$857$	−9.74082e12	+	1.68716e13i	−0.616853	+	1.06842i	0.373203	+	0.927750i	$0.378259\pi$
$857$	−9.74082e12	+	1.68716e13i	−0.616853	+	1.06842i	−0.990056	+	0.140671i	$0.955074\pi$
$858$		0			0
$859$	1.10241e13	+	1.90943e13i	0.690835	+	1.19656i	0.971565	+	0.236775i	$0.0760904\pi$
$859$	1.10241e13	+	1.90943e13i	0.690835	+	1.19656i	−0.280729	+	0.959787i	$0.590576\pi$
$860$	5.54105e12			0.345421
$861$		0			0
$862$	−2.09792e13			−1.29421
$863$	−1.12778e13	−	1.95337e13i	−0.692110	−	1.19877i	−0.971145	−	0.238489i	$-0.923348\pi$
$863$	−1.12778e13	−	1.95337e13i	−0.692110	−	1.19877i	0.279035	−	0.960281i	$-0.409985\pi$
$864$		0			0
$865$	−4.19263e12	+	7.26184e12i	−0.254632	+	0.441036i
$866$	−4.18829e12	−	7.25433e12i	−0.253050	−	0.438296i
$867$		0			0
$868$	1.06665e12	−	9.12810e11i	0.0637796	−	0.0545810i
$869$	7.45099e11			0.0443226
$870$		0			0
$871$	−1.02342e13	+	1.77262e13i	−0.602522	+	1.04360i
$872$	−3.95915e11	+	6.85745e11i	−0.0231888	+	0.0401642i
$873$		0			0
$874$	−7.67854e10			−0.00445120
$875$	1.68799e12	+	9.05802e12i	0.0973492	+	0.522393i
$876$		0			0
$877$	−1.54052e13	−	2.66826e13i	−0.879367	−	1.52311i	−0.852037	−	0.523481i	$-0.824633\pi$
$877$	−1.54052e13	−	2.66826e13i	−0.879367	−	1.52311i	−0.0273297	−	0.999626i	$-0.508700\pi$
$878$	3.44298e12	−	5.96342e12i	0.195528	−	0.338665i
$879$		0			0
$880$	−5.43270e12	−	9.40971e12i	−0.305382	−	0.528937i
$881$	1.72758e11			0.00966157			0.00483078	−	0.999988i	$-0.498462\pi$
$881$	1.72758e11			0.00966157			0.00483078	+	0.999988i	$0.498462\pi$
$882$		0			0
$883$	1.07928e13			0.597460			0.298730	−	0.954338i	$-0.403437\pi$
$883$	1.07928e13			0.597460			0.298730	+	0.954338i	$0.403437\pi$
$884$	−7.74462e12	−	1.34141e13i	−0.426545	−	0.738798i
$885$		0			0
$886$	1.59647e12	−	2.76517e12i	0.0870382	−	0.150755i
$887$	−1.17452e13	−	2.03432e13i	−0.637093	−	1.10348i	−0.986067	−	0.166346i	$-0.946803\pi$
$887$	−1.17452e13	−	2.03432e13i	−0.637093	−	1.10348i	0.348974	−	0.937132i	$-0.386530\pi$
$888$		0			0
$889$	1.87832e12	+	1.00794e13i	0.100858	+	0.541222i
$890$	1.88123e13			1.00505
$891$		0			0
$892$	3.20664e11	−	5.55406e11i	0.0169593	−	0.0293744i
$893$	−9.78343e12	+	1.69454e13i	−0.514825	+	0.891703i
$894$		0			0
$895$	−9.63803e12			−0.502093
$896$	1.29558e12	−	1.10872e12i	0.0671548	−	0.0574695i
$897$		0			0
$898$	−1.07555e12	−	1.86291e12i	−0.0551936	−	0.0955981i
$899$	−1.10221e12	+	1.90908e12i	−0.0562787	+	0.0974776i
$900$		0			0
$901$	7.84171e12	+	1.35822e13i	0.396414	+	0.686609i
$902$	−2.64547e13			−1.33068
$903$		0			0
$904$	−1.02507e13			−0.510499
$905$	−6.50783e12	−	1.12719e13i	−0.322491	−	0.558571i
$906$		0			0
$907$	−1.19812e13	+	2.07521e13i	−0.587852	+	1.01819i	0.406662	+	0.913579i	$0.366693\pi$
$907$	−1.19812e13	+	2.07521e13i	−0.587852	+	1.01819i	−0.994513	+	0.104610i	$0.966641\pi$
$908$	8.34515e11	+	1.44542e12i	0.0407425	+	0.0705681i
$909$		0			0
$910$	1.88809e13	+	6.66525e12i	0.912715	+	0.322204i
$911$	−7.80479e12			−0.375429			−0.187715	−	0.982224i	$-0.560108\pi$
$911$	−7.80479e12			−0.375429			−0.187715	+	0.982224i	$0.560108\pi$
$912$		0			0
$913$	2.28529e13	−	3.95823e13i	1.08848	−	1.88531i
$914$	−1.69541e12	+	2.93654e12i	−0.0803559	+	0.139180i
$915$		0			0
$916$	−1.37764e12			−0.0646556
$917$	1.61673e13	−	1.38356e13i	0.755048	−	0.646152i
$918$		0			0
$919$	−4.00028e12	−	6.92868e12i	−0.184999	−	0.320428i	0.758577	−	0.651583i	$-0.225895\pi$
$919$	−4.00028e12	−	6.92868e12i	−0.184999	−	0.320428i	−0.943576	+	0.331155i	$0.892562\pi$
$920$	−2.83391e10	+	4.90847e10i	−0.00130419	+	0.00225892i
$921$		0			0
$922$	−8.38738e12	−	1.45274e13i	−0.382241	−	0.662061i
$923$	2.44597e13			1.10929
$924$		0			0
$925$	−2.03689e13			−0.914806
$926$	−3.37849e12	−	5.85172e12i	−0.150999	−	0.261538i
$927$		0			0
$928$	−1.33877e12	+	2.31881e12i	−0.0592570	+	0.102636i
$929$	1.83611e12	+	3.18024e12i	0.0808778	+	0.140084i	0.903627	−	0.428320i	$-0.140894\pi$
$929$	1.83611e12	+	3.18024e12i	0.0808778	+	0.140084i	−0.822749	+	0.568404i	$0.807561\pi$
$930$		0			0
$931$	−2.33230e13	−	1.88111e13i	−1.01745	−	0.820616i
$932$	1.42529e13			0.618775
$933$		0			0
$934$	3.90054e11	−	6.75593e11i	0.0167712	−	0.0290485i
$935$	5.45094e13	−	9.44131e13i	2.33249	−	4.03999i
$936$		0			0
$937$	−4.58091e13			−1.94144			−0.970719	−	0.240218i	$-0.922781\pi$
$937$	−4.58091e13			−1.94144			−0.970719	+	0.240218i	$0.922781\pi$
$938$	−4.14204e12	−	2.22269e13i	−0.174703	−	0.937488i
$939$		0			0
$940$	7.22151e12	+	1.25080e13i	0.301684	+	0.522533i
$941$	−1.69377e13	+	2.93370e13i	−0.704210	+	1.21973i	0.262766	+	0.964860i	$0.415365\pi$
$941$	−1.69377e13	+	2.93370e13i	−0.704210	+	1.21973i	−0.966976	+	0.254868i	$0.917968\pi$
$942$		0			0
$943$	6.89992e10	+	1.19510e11i	0.00284146	+	0.00492155i
$944$	−1.01781e13			−0.417152
$945$		0			0
$946$	1.25262e13			0.508521
$947$	3.39394e12	+	5.87847e12i	0.137129	+	0.237514i	0.926409	−	0.376519i	$-0.122879\pi$
$947$	3.39394e12	+	5.87847e12i	0.137129	+	0.237514i	−0.789280	+	0.614034i	$0.789546\pi$
$948$		0			0
$949$	−1.72461e13	+	2.98711e13i	−0.690229	+	1.19551i
$950$	1.56264e13	+	2.70656e13i	0.622446	+	1.07811i
$951$		0			0
$952$	1.61337e13	+	5.69547e12i	0.636602	+	0.224731i
$953$	−5.28058e12			−0.207378			−0.103689	−	0.994610i	$-0.533065\pi$
$953$	−5.28058e12			−0.207378			−0.103689	+	0.994610i	$0.533065\pi$
$954$		0			0
$955$	−9.61679e12	+	1.66568e13i	−0.374124	+	0.648001i
$956$	−1.21124e13	+	2.09793e13i	−0.468998	+	0.812328i
$957$		0			0
$958$	6.43424e12			0.246804
$959$	−3.13397e13	−	1.10634e13i	−1.19649	−	0.422382i
$960$		0			0
$961$	1.28472e13	+	2.22520e13i	0.485906	+	0.841614i
$962$	−5.69975e12	+	9.87225e12i	−0.214569	+	0.371645i
$963$		0			0
$964$	3.56920e12	+	6.18203e12i	0.133114	+	0.230560i
$965$	−2.60257e13			−0.966116
$966$		0			0
$967$	4.33872e13			1.59567			0.797834	−	0.602878i	$-0.205979\pi$
$967$	4.33872e13			1.59567			0.797834	+	0.602878i	$0.205979\pi$
$968$	−7.45216e12	−	1.29075e13i	−0.272799	−	0.472502i
$969$		0			0
$970$	−1.14287e13	+	1.97951e13i	−0.414500	+	0.717935i
$971$	2.68045e13	+	4.64268e13i	0.967658	+	1.67603i	0.702297	+	0.711884i	$0.252158\pi$
$971$	2.68045e13	+	4.64268e13i	0.967658	+	1.67603i	0.265361	+	0.964149i	$0.414509\pi$
$972$		0			0
$973$	5.66667e12	+	3.04083e13i	0.202684	+	1.08764i
$974$	1.59173e13			0.566700
$975$		0			0
$976$	−2.80860e12	+	4.86464e12i	−0.0990755	+	0.171604i
$977$	5.27189e12	−	9.13119e12i	0.185115	−	0.320628i	−0.758500	−	0.651673i	$-0.774068\pi$
$977$	5.27189e12	−	9.13119e12i	0.185115	−	0.320628i	0.943615	+	0.331044i	$0.107401\pi$
$978$		0			0
$979$	4.25275e13			1.47961
$980$	−2.06327e13	+	7.96657e12i	−0.714560	+	0.275901i
$981$		0			0
$982$	1.41872e12	+	2.45729e12i	0.0486848	+	0.0843246i
$983$	−2.28178e13	+	3.95217e13i	−0.779442	+	1.35003i	0.152822	+	0.988254i	$0.451164\pi$
$983$	−2.28178e13	+	3.95217e13i	−0.779442	+	1.35003i	−0.932264	+	0.361779i	$0.882169\pi$
$984$		0			0
$985$	−2.41824e13	−	4.18851e13i	−0.818533	−	1.41774i
$986$	−2.68653e13			−0.905202
$987$		0			0
$988$	1.74907e13			0.583983
$989$	−3.26708e10	−	5.65874e10i	−0.00108587	−	0.00188077i
$990$		0			0
$991$	1.24239e13	−	2.15188e13i	0.409191	−	0.708739i	−0.585609	−	0.810594i	$-0.699144\pi$
$991$	1.24239e13	−	2.15188e13i	0.409191	−	0.708739i	0.994799	+	0.101855i	$0.0324778\pi$
$992$	−4.52613e11	−	7.83949e11i	−0.0148397	−	0.0257031i
$993$		0			0
$994$	−2.05277e13	+	1.75671e13i	−0.666963	+	0.570772i
$995$	5.99891e12			0.194030
$996$		0			0
$997$	7.52003e12	−	1.30251e13i	0.241041	−	0.417496i	−0.719970	−	0.694005i	$-0.755844\pi$
$997$	7.52003e12	−	1.30251e13i	0.241041	−	0.417496i	0.961011	+	0.276510i	$0.0891778\pi$
$998$	8.20719e11	−	1.42153e12i	0.0261883	−	0.0453594i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.10.g.d.109.1		6
3.2	odd	2		42.10.e.d.25.3	✓	6
7.2	even	3	inner	126.10.g.d.37.1		6
21.2	odd	6		42.10.e.d.37.3	yes	6
21.11	odd	6		294.10.a.r.1.1		3
21.17	even	6		294.10.a.u.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.10.e.d.25.3	✓	6	3.2	odd	2
42.10.e.d.37.3	yes	6	21.2	odd	6
126.10.g.d.37.1		6	7.2	even	3	inner
126.10.g.d.109.1		6	1.1	even	1	trivial
294.10.a.r.1.1		3	21.11	odd	6
294.10.a.u.1.3		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)

\(f(q)\)	\(=\)	\(q+(-8.00000 - 13.8564i) q^{2} +(-128.000 + 221.703i) q^{4} +(-1070.48 - 1854.13i) q^{5} +(1163.76 + 6244.94i) q^{7} +4096.00 q^{8} +(-17127.7 + 29666.1i) q^{10} +(-38719.2 + 67063.6i) q^{11} -92014.0 q^{13} +(77222.3 - 66085.1i) q^{14} +(-32768.0 - 56755.8i) q^{16} +(328781. - 569465. i) q^{17} +(371263. + 643047. i) q^{19} +548087. q^{20} +1.23901e6 q^{22} +(-3231.59 - 5597.28i) q^{23} +(-1.31530e6 + 2.27817e6i) q^{25} +(736112. + 1.27498e6i) q^{26} +(-1.53348e6 - 541344. i) q^{28} +2.55350e6 q^{29} +(-431646. + 747632. i) q^{31} +(-524288. + 908093. i) q^{32} -1.05210e7 q^{34} +(1.03331e7 - 8.84286e6i) q^{35} +(3.87152e6 + 6.70567e6i) q^{37} +(5.94021e6 - 1.02888e7i) q^{38} +(-4.38470e6 - 7.59451e6i) q^{40} -2.13515e7 q^{41} +1.01098e7 q^{43} +(-9.91211e6 - 1.71683e7i) q^{44} +(-51705.5 + 89556.5i) q^{46} +(1.31759e7 + 2.28213e7i) q^{47} +(-3.76449e7 + 1.45352e7i) q^{49} +4.20897e7 q^{50} +(1.17778e7 - 2.03997e7i) q^{52} +(-1.19254e7 + 2.06555e7i) q^{53} +1.65793e8 q^{55} +(4.76676e6 + 2.55793e7i) q^{56} +(-2.04280e7 - 3.53823e7i) q^{58} +(7.76530e7 - 1.34499e8i) q^{59} +(-4.28559e7 - 7.42286e7i) q^{61} +1.38127e7 q^{62} +1.67772e7 q^{64} +(9.84994e7 + 1.70606e8i) q^{65} +(1.11224e8 - 1.92646e8i) q^{67} +(8.41678e7 + 1.45783e8i) q^{68} +(-2.05195e8 - 7.24373e7i) q^{70} -2.65826e8 q^{71} +(1.87429e8 - 3.24637e8i) q^{73} +(6.19443e7 - 1.07291e8i) q^{74} -1.90087e8 q^{76} +(-4.63868e8 - 1.63753e8i) q^{77} +(-4.81092e6 - 8.33275e6i) q^{79} +(-7.01551e7 + 1.21512e8i) q^{80} +(1.70812e8 + 2.95855e8i) q^{82} -5.90221e8 q^{83} -1.40782e9 q^{85} +(-8.08785e7 - 1.40086e8i) q^{86} +(-1.58594e8 + 2.74692e8i) q^{88} +(-2.74589e8 - 4.75603e8i) q^{89} +(-1.07082e8 - 5.74622e8i) q^{91} +1.65458e6 q^{92} +(2.10814e8 - 3.65140e8i) q^{94} +(7.94862e8 - 1.37674e9i) q^{95} +6.67265e8 q^{97} +(5.02565e8 + 4.05342e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} - 768 q^{4} - 361 q^{5} + 12509 q^{7} + 24576 q^{8} - 5776 q^{10} - 37799 q^{11} - 441172 q^{13} - 38752 q^{14} - 196608 q^{16} + 781816 q^{17} - 620154 q^{19} + 184832 q^{20} + 1209568 q^{22}+ \cdots + 2185772400 q^{98}+O(q^{100}) \) 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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