LMFDB - Embedded newform 126.9.n.d.73.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("126.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$51.3297048677$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} - 26382 x^{18} + 177344 x^{17} + 298653216 x^{16} - 1823810808 x^{15} + \cdots + 42\!\cdots\!32 $ x^20 - 8x^19 - 26382x^18 + 177344x^17 + 298653216x^16 - 1823810808x^15 - 1891249463672x^14 + 11806020599312x^13 + 7316478649605270x^12 - 52687155135219848x^11 - 17677778016929268548x^10 + 159557587043375632176x^9 + 25942214297922759947412x^8 - 305008424965479773875688x^7 - 20749002299789629192234200x^6 + 325395581603349554951740400x^5 + 6083917772973420120813872017x^4 - 144252792084909643404755532432x^3 + 1061914206438596097569355774114x^2 - 3448453709078208081753932409840*x + 4271031984253419377206782621732
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{40}\cdot 3^{18}\cdot 7^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.7
Root			$-64.5148 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.73
Dual form			126.9.n.d.19.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.65685 + 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(-664.367 + 383.572i) q^{5} +(1667.57 - 1727.43i) q^{7} -1448.15 q^{8} +O(q^{10})$	\(q+(5.65685 + 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(-664.367 + 383.572i) q^{5} +(1667.57 - 1727.43i) q^{7} -1448.15 q^{8} +(-7516.45 - 4339.62i) q^{10} +(-2523.72 + 4371.21i) q^{11} -28279.2i q^{13} +(26358.5 + 6566.95i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(13520.1 + 7805.85i) q^{17} +(107562. - 62100.9i) q^{19} -98194.5i q^{20} -57105.3 q^{22} +(-89789.7 - 155520. i) q^{23} +(98942.8 - 171374. i) q^{25} +(277078. - 159971. i) q^{26} +(84763.4 + 295408. i) q^{28} -71160.2 q^{29} +(845366. + 488072. i) q^{31} +(92681.9 - 160530. i) q^{32} +176626. i q^{34} +(-445283. + 1.78728e6i) q^{35} +(704161. + 1.21964e6i) q^{37} +(1.21692e6 + 702591. i) q^{38} +(962105. - 555472. i) q^{40} +3.98966e6i q^{41} +2.21621e6 q^{43} +(-323036. - 559515. i) q^{44} +(1.01585e6 - 1.75951e6i) q^{46} +(-66978.0 + 38669.8i) q^{47} +(-203229. - 5.76122e6i) q^{49} +2.23882e6 q^{50} +(3.13478e6 + 1.80987e6i) q^{52} +(3.09571e6 - 5.36192e6i) q^{53} -3.87212e6i q^{55} +(-2.41490e6 + 2.50159e6i) q^{56} +(-402543. - 697225. i) q^{58} +(1.27750e7 + 7.37564e6i) q^{59} +(-2.14523e6 + 1.23855e6i) q^{61} +1.10438e7i q^{62} +2.09715e6 q^{64} +(1.08471e7 + 1.87877e7i) q^{65} +(-1.79499e6 + 3.10901e6i) q^{67} +(-1.73058e6 + 999149. i) q^{68} +(-2.00306e7 + 5.74752e6i) q^{70} +3.51834e7 q^{71} +(333640. + 192627. i) q^{73} +(-7.96667e6 + 1.37987e7i) q^{74} +1.58978e7i q^{76} +(3.34249e6 + 1.16489e7i) q^{77} +(1.68028e7 + 2.91034e7i) q^{79} +(1.08850e7 + 6.28445e6i) q^{80} +(-3.90906e7 + 2.25689e7i) q^{82} +7.92564e7i q^{83} -1.19764e7 q^{85} +(1.25368e7 + 2.17144e7i) q^{86} +(3.65474e6 - 6.33019e6i) q^{88} +(4.51130e7 - 2.60460e7i) q^{89} +(-4.88503e7 - 4.71575e7i) q^{91} +2.29862e7 q^{92} +(-757770. - 437499. i) q^{94} +(-4.76403e7 + 8.25155e7i) q^{95} -1.44662e8i q^{97} +(5.52985e7 - 3.45816e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 1280 q^{4} + 4186 q^{7}+O(q^{10}) $ 20 * q - 1280 * q^4 + 4186 * q^7	$ 20 q - 1280 q^{4} + 4186 q^{7} - 17664 q^{10} - 163840 q^{16} - 250890 q^{19} + 420864 q^{22} + 258962 q^{25} - 1189888 q^{28} + 342762 q^{31} - 4806598 q^{37} + 2260992 q^{40} + 6968252 q^{43} - 4357632 q^{46} - 26046538 q^{49} + 2075904 q^{52} + 2455296 q^{58} - 15410424 q^{61} + 41943040 q^{64} - 70041074 q^{67} - 25804800 q^{70} + 220264098 q^{73} + 12860578 q^{79} + 12085248 q^{82} + 29161632 q^{85} - 26935296 q^{88} - 311022894 q^{91} + 332230656 q^{94}+O(q^{100}) $ 20 * q - 1280 * q^4 + 4186 * q^7 - 17664 * q^10 - 163840 * q^16 - 250890 * q^19 + 420864 * q^22 + 258962 * q^25 - 1189888 * q^28 + 342762 * q^31 - 4806598 * q^37 + 2260992 * q^40 + 6968252 * q^43 - 4357632 * q^46 - 26046538 * q^49 + 2075904 * q^52 + 2455296 * q^58 - 15410424 * q^61 + 41943040 * q^64 - 70041074 * q^67 - 25804800 * q^70 + 220264098 * q^73 + 12860578 * q^79 + 12085248 * q^82 + 29161632 * q^85 - 26935296 * q^88 - 311022894 * q^91 + 332230656 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	5.65685	+	9.79796i	0.353553	+	0.612372i
$2$	5.65685	+	9.79796i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−64.0000	+	110.851i	−0.250000	+	0.433013i
$5$	−664.367	+	383.572i	−1.06299	+	0.613716i	−0.926257	−	0.376893i	$-0.876992\pi$
$5$	−664.367	+	383.572i	−1.06299	+	0.613716i	−0.136730	+	0.990608i	$0.543659\pi$
$6$		0			0
$7$	1667.57	−	1727.43i	0.694531	−	0.719463i
$7$	1667.57	−	1727.43i	0.694531	−	0.719463i
$8$	−1448.15			−0.353553
$9$		0			0
$10$	−7516.45	−	4339.62i	−0.751645	−	0.433962i
$11$	−2523.72	+	4371.21i	−0.172374	+	0.298560i	−0.939249	−	0.343236i	$-0.888477\pi$
$11$	−2523.72	+	4371.21i	−0.172374	+	0.298560i	0.766876	+	0.641796i	$0.221810\pi$
$12$		0			0
$13$		−	28279.2i		−	0.990133i	−0.868855	−	0.495066i	$-0.835144\pi$
$13$		−	28279.2i		−	0.990133i	0.868855	−	0.495066i	$-0.164856\pi$
$14$	26358.5	+	6566.95i	0.686133	+	0.170943i
$15$		0			0
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	13520.1	+	7805.85i	0.161877	+	0.0934598i	0.578750	−	0.815505i	$-0.303541\pi$
$17$	13520.1	+	7805.85i	0.161877	+	0.0934598i	−0.416873	+	0.908965i	$0.636874\pi$
$18$		0			0
$19$	107562.	−	62100.9i	0.825361	−	0.476522i	−0.0269006	−	0.999638i	$-0.508564\pi$
$19$	107562.	−	62100.9i	0.825361	−	0.476522i	0.852262	+	0.523116i	$0.175230\pi$
$20$		−	98194.5i		−	0.613716i
$21$		0			0
$22$	−57105.3			−0.243773
$23$	−89789.7	−	155520.i	−0.320860	−	0.555745i	0.659806	−	0.751436i	$-0.270638\pi$
$23$	−89789.7	−	155520.i	−0.320860	−	0.555745i	−0.980666	+	0.195691i	$0.937305\pi$
$24$		0			0
$25$	98942.8	−	171374.i	0.253293	−	0.438717i
$26$	277078.	−	159971.i	0.606330	−	0.350065i
$27$		0			0
$28$	84763.4	+	295408.i	0.137904	+	0.480606i
$29$	−71160.2			−0.100611			−0.0503055	−	0.998734i	$-0.516019\pi$
$29$	−71160.2			−0.100611			−0.0503055	+	0.998734i	$0.516019\pi$
$30$		0			0
$31$	845366.	+	488072.i	0.915372	+	0.528490i	0.882156	−	0.470958i	$-0.156092\pi$
$31$	845366.	+	488072.i	0.915372	+	0.528490i	0.0332165	+	0.999448i	$0.489425\pi$
$32$	92681.9	−	160530.i	0.0883883	−	0.153093i
$33$		0			0
$34$			176626.i			0.132172i
$35$	−445283.	+	1.78728e6i	−0.296732	+	1.19102i
$36$		0			0
$37$	704161.	+	1.21964e6i	0.375720	+	0.650767i	0.990435	−	0.137983i	$-0.0440620\pi$
$37$	704161.	+	1.21964e6i	0.375720	+	0.650767i	−0.614714	+	0.788750i	$0.710729\pi$
$38$	1.21692e6	+	702591.i	0.583618	+	0.336952i
$39$		0			0
$40$	962105.	−	555472.i	0.375822	−	0.216981i
$41$			3.98966e6i			1.41189i	0.708267	+	0.705945i	$0.249477\pi$
$41$			3.98966e6i			1.41189i	−0.708267	+	0.705945i	$0.750523\pi$
$42$		0			0
$43$	2.21621e6			0.648243			0.324121	−	0.946016i	$-0.394931\pi$
$43$	2.21621e6			0.648243			0.324121	+	0.946016i	$0.394931\pi$
$44$	−323036.	−	559515.i	−0.0861868	−	0.149280i
$45$		0			0
$46$	1.01585e6	−	1.75951e6i	0.226882	−	0.392971i
$47$	−66978.0	+	38669.8i	−0.0137259	+	0.00792465i	−0.506847	−	0.862036i	$-0.669189\pi$
$47$	−66978.0	+	38669.8i	−0.0137259	+	0.00792465i	0.493121	+	0.869961i	$0.335856\pi$
$48$		0			0
$49$	−203229.	−	5.76122e6i	−0.0352535	−	0.999378i
$50$	2.23882e6			0.358211
$51$		0			0
$52$	3.13478e6	+	1.80987e6i	0.428740	+	0.247533i
$53$	3.09571e6	−	5.36192e6i	0.392334	−	0.679543i	−0.600423	−	0.799683i	$-0.705001\pi$
$53$	3.09571e6	−	5.36192e6i	0.392334	−	0.679543i	0.992757	+	0.120140i	$0.0383343\pi$
$54$		0			0
$55$		−	3.87212e6i		−	0.423153i
$56$	−2.41490e6	+	2.50159e6i	−0.245554	+	0.254369i
$57$		0			0
$58$	−402543.	−	697225.i	−0.0355714	−	0.0616114i
$59$	1.27750e7	+	7.37564e6i	1.05427	+	0.608684i	0.923842	−	0.382774i	$-0.125031\pi$
$59$	1.27750e7	+	7.37564e6i	1.05427	+	0.608684i	0.130429	+	0.991458i	$0.458364\pi$
$60$		0			0
$61$	−2.14523e6	+	1.23855e6i	−0.154937	+	0.0894529i	−0.575464	−	0.817827i	$-0.695179\pi$
$61$	−2.14523e6	+	1.23855e6i	−0.154937	+	0.0894529i	0.420527	+	0.907280i	$0.361845\pi$
$62$			1.10438e7i			0.747398i
$63$		0			0
$64$	2.09715e6			0.125000
$65$	1.08471e7	+	1.87877e7i	0.607660	+	1.05250i
$66$		0			0
$67$	−1.79499e6	+	3.10901e6i	−0.0890763	+	0.154285i	−0.907121	−	0.420870i	$-0.861725\pi$
$67$	−1.79499e6	+	3.10901e6i	−0.0890763	+	0.154285i	0.818045	+	0.575155i	$0.195058\pi$
$68$	−1.73058e6	+	999149.i	−0.0809385	+	0.0467299i
$69$		0			0
$70$	−2.00306e7	+	5.74752e6i	−0.834260	+	0.239380i
$71$	3.51834e7			1.38454			0.692268	−	0.721641i	$-0.256612\pi$
$71$	3.51834e7			1.38454			0.692268	+	0.721641i	$0.256612\pi$
$72$		0			0
$73$	333640.	+	192627.i	0.0117486	+	0.00678307i	0.505863	−	0.862614i	$-0.331174\pi$
$73$	333640.	+	192627.i	0.0117486	+	0.00678307i	−0.494114	+	0.869397i	$0.664508\pi$
$74$	−7.96667e6	+	1.37987e7i	−0.265674	+	0.460162i
$75$		0			0
$76$			1.58978e7i			0.476522i
$77$	3.34249e6	+	1.16489e7i	0.0950839	+	0.331375i
$78$		0			0
$79$	1.68028e7	+	2.91034e7i	0.431394	+	0.747197i	0.996994	−	0.0774833i	$-0.0246885\pi$
$79$	1.68028e7	+	2.91034e7i	0.431394	+	0.747197i	−0.565599	+	0.824680i	$0.691355\pi$
$80$	1.08850e7	+	6.28445e6i	0.265747	+	0.153429i
$81$		0			0
$82$	−3.90906e7	+	2.25689e7i	−0.864603	+	0.499179i
$83$			7.92564e7i			1.67002i	0.550233	+	0.835011i	$0.314539\pi$
$83$			7.92564e7i			1.67002i	−0.550233	+	0.835011i	$0.685461\pi$
$84$		0			0
$85$	−1.19764e7			−0.229431
$86$	1.25368e7	+	2.17144e7i	0.229188	+	0.396966i
$87$		0			0
$88$	3.65474e6	−	6.33019e6i	0.0609433	−	0.105557i
$89$	4.51130e7	−	2.60460e7i	0.719021	−	0.415127i	−0.0953709	−	0.995442i	$-0.530404\pi$
$89$	4.51130e7	−	2.60460e7i	0.719021	−	0.415127i	0.814392	+	0.580315i	$0.197070\pi$
$90$		0			0
$91$	−4.88503e7	−	4.71575e7i	−0.712364	−	0.687678i
$92$	2.29862e7			0.320860
$93$		0			0
$94$	−757770.	−	437499.i	−0.00970568	−	0.00560358i
$95$	−4.76403e7	+	8.25155e7i	−0.584898	+	1.01307i
$96$		0			0
$97$		−	1.44662e8i		−	1.63406i	−0.576598	−	0.817028i	$-0.695620\pi$
$97$		−	1.44662e8i		−	1.63406i	0.576598	−	0.817028i	$-0.304380\pi$
$98$	5.52985e7	−	3.45816e7i	0.599528	−	0.374922i
$99$		0			0
$100$	1.26647e7	+	2.19359e7i	0.126647	+	0.219359i
$101$	8.12614e7	+	4.69163e7i	0.780906	+	0.450857i	0.836751	−	0.547583i	$-0.184452\pi$
$101$	8.12614e7	+	4.69163e7i	0.780906	+	0.450857i	−0.0558450	+	0.998439i	$0.517785\pi$
$102$		0			0
$103$	−1.52669e8	+	8.81435e7i	−1.35645	+	0.783144i	−0.989143	−	0.146958i	$-0.953052\pi$
$103$	−1.52669e8	+	8.81435e7i	−1.35645	+	0.783144i	−0.367302	+	0.930102i	$0.619719\pi$
$104$			4.09526e7i			0.350065i
$105$		0			0
$106$	7.00478e7			0.554844
$107$	8.92457e7	+	1.54578e8i	0.680851	+	1.17927i	0.974721	+	0.223424i	$0.0717233\pi$
$107$	8.92457e7	+	1.54578e8i	0.680851	+	1.17927i	−0.293870	+	0.955845i	$0.594943\pi$
$108$		0			0
$109$	1.18770e8	−	2.05716e8i	0.841400	−	1.45735i	−0.0473118	−	0.998880i	$-0.515065\pi$
$109$	1.18770e8	−	2.05716e8i	0.841400	−	1.45735i	0.888712	−	0.458467i	$-0.151601\pi$
$110$	3.79389e7	−	2.19040e7i	0.259127	−	0.149607i
$111$		0			0
$112$	−3.81712e7	−	9.50996e6i	−0.242585	−	0.0604375i
$113$	−2.19712e8			−1.34753			−0.673766	−	0.738945i	$-0.735325\pi$
$113$	−2.19712e8			−1.34753			−0.673766	+	0.738945i	$0.735325\pi$
$114$		0			0
$115$	1.19307e8	+	6.88817e7i	0.682139	+	0.393833i
$116$	4.55425e6	−	7.88820e6i	0.0251527	−	0.0435658i
$117$		0			0
$118$			1.66892e8i			0.860809i
$119$	3.60298e7	−	1.03383e7i	0.179669	−	0.0515538i
$120$		0			0
$121$	9.44411e7	+	1.63577e8i	0.440575	+	0.763098i
$122$	−2.42705e7	−	1.40126e7i	−0.109557	−	0.0632527i
$123$		0			0
$124$	−1.08207e8	+	6.24732e7i	−0.457686	+	0.264245i
$125$		−	1.47859e8i		−	0.605631i
$126$		0			0
$127$	3.52796e8			1.35615			0.678076	−	0.734992i	$-0.262814\pi$
$127$	3.52796e8			1.35615			0.678076	+	0.734992i	$0.262814\pi$
$128$	1.18633e7	+	2.05478e7i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.22721e8	+	2.12559e8i	−0.429680	+	0.744228i
$131$	−1.90353e7	+	1.09900e7i	−0.0646360	+	0.0373176i	−0.531970	−	0.846763i	$-0.678548\pi$
$131$	−1.90353e7	+	1.09900e7i	−0.0646360	+	0.0373176i	0.467334	+	0.884081i	$0.345215\pi$
$132$		0			0
$133$	7.20919e7	−	2.89363e8i	0.230399	−	0.924776i
$134$	−4.06159e7			−0.125973
$135$		0			0
$136$	−1.95792e7	−	1.13041e7i	−0.0572322	−	0.0330430i
$137$	3.05741e8	−	5.29559e8i	0.867903	−	1.50325i	0.00376775	−	0.999993i	$-0.498801\pi$
$137$	3.05741e8	−	5.29559e8i	0.867903	−	1.50325i	0.864135	−	0.503259i	$-0.167866\pi$
$138$		0			0
$139$		−	1.49082e8i		−	0.399360i	−0.979861	−	0.199680i	$-0.936010\pi$
$139$		−	1.49082e8i		−	0.399360i	0.979861	−	0.199680i	$-0.0639903\pi$
$140$	−1.69624e8	−	1.63746e8i	−0.441545	−	0.426244i
$141$		0			0
$142$	1.99027e8	+	3.44725e8i	0.489507	+	0.847851i
$143$	1.23614e8	+	7.13688e7i	0.295614	+	0.170673i
$144$		0			0
$145$	4.72765e7	−	2.72951e7i	0.106948	−	0.0617465i
$146$			4.35866e6i			0.00959270i
$147$		0			0
$148$	−1.80265e8			−0.375720
$149$	−3.50024e8	−	6.06260e8i	−0.710155	−	1.23002i	−0.964799	−	0.262990i	$-0.915292\pi$
$149$	−3.50024e8	−	6.06260e8i	−0.710155	−	1.23002i	0.254644	−	0.967035i	$-0.418042\pi$
$150$		0			0
$151$	4.86258e8	−	8.42224e8i	0.935318	−	1.62002i	0.161252	−	0.986913i	$-0.448447\pi$
$151$	4.86258e8	−	8.42224e8i	0.935318	−	1.62002i	0.774066	−	0.633105i	$-0.218220\pi$
$152$	−1.55766e8	+	8.99317e7i	−0.291809	+	0.168476i
$153$		0			0
$154$	−9.52270e7	+	9.86454e7i	−0.169308	+	0.175386i
$155$	−7.48843e8			−1.29737
$156$		0			0
$157$	−1.55513e7	−	8.97854e6i	−0.0255957	−	0.0147777i	0.487148	−	0.873320i	$-0.338037\pi$
$157$	−1.55513e7	−	8.97854e6i	−0.0255957	−	0.0147777i	−0.512743	+	0.858542i	$0.671371\pi$
$158$	−1.90102e8	+	3.29267e8i	−0.305042	+	0.528348i
$159$		0			0
$160$			1.42201e8i			0.216981i
$161$	−4.18381e8	−	1.04235e8i	−0.622685	−	0.155136i
$162$		0			0
$163$	−4.50185e8	−	7.79744e8i	−0.637736	−	1.10459i	−0.985928	−	0.167168i	$-0.946538\pi$
$163$	−4.50185e8	−	7.79744e8i	−0.637736	−	1.10459i	0.348192	−	0.937423i	$-0.386796\pi$
$164$	−4.42259e8	−	2.55339e8i	−0.611366	−	0.352973i
$165$		0			0
$166$	−7.76551e8	+	4.48342e8i	−1.02268	+	0.590442i
$167$			2.27161e8i			0.292057i	0.989280	+	0.146029i	$0.0466492\pi$
$167$			2.27161e8i			0.292057i	−0.989280	+	0.146029i	$0.953351\pi$
$168$		0			0
$169$	1.60184e7			0.0196369
$170$	−6.77489e7	−	1.17345e8i	−0.0811160	−	0.140497i
$171$		0			0
$172$	−1.41838e8	+	2.45670e8i	−0.162061	+	0.280697i
$173$	2.34309e8	−	1.35278e8i	0.261580	−	0.151023i	−0.363475	−	0.931604i	$-0.618410\pi$
$173$	2.34309e8	−	1.35278e8i	0.261580	−	0.151023i	0.625055	+	0.780581i	$0.285076\pi$
$174$		0			0
$175$	−1.31043e8	−	4.56694e8i	−0.139721	−	0.486938i
$176$	8.26973e7			0.0861868
$177$		0			0
$178$	5.10396e8	+	2.94677e8i	0.508425	+	0.293539i
$179$	4.41046e8	−	7.63914e8i	0.429608	−	0.744102i	−0.567231	−	0.823559i	$-0.691985\pi$
$179$	4.41046e8	−	7.63914e8i	0.429608	−	0.744102i	0.996838	+	0.0794568i	$0.0253186\pi$
$180$		0			0
$181$			4.95902e8i			0.462042i	0.972949	+	0.231021i	$0.0742067\pi$
$181$			4.95902e8i			0.462042i	−0.972949	+	0.231021i	$0.925793\pi$
$182$	1.85708e8	−	7.45396e8i	0.169256	−	0.679363i
$183$		0			0
$184$	1.30029e8	+	2.25218e8i	0.113441	+	0.196486i
$185$	−9.35641e8	−	5.40193e8i	−0.798771	−	0.461171i
$186$		0			0
$187$	−6.82421e7	+	3.93996e7i	−0.0558067	+	0.0322200i
$188$		−	9.89946e6i		−	0.00792465i
$189$		0			0
$190$	−1.07798e9			−0.827171
$191$	−7.89952e8	−	1.36824e9i	−0.593564	−	1.02808i	−0.993748	−	0.111648i	$-0.964387\pi$
$191$	−7.89952e8	−	1.36824e9i	−0.593564	−	1.02808i	0.400184	−	0.916435i	$-0.368946\pi$
$192$		0			0
$193$	−8.26070e8	+	1.43079e9i	−0.595371	+	1.03121i	0.398124	+	0.917332i	$0.369661\pi$
$193$	−8.26070e8	+	1.43079e9i	−0.595371	+	1.03121i	−0.993494	+	0.113881i	$0.963672\pi$
$194$	1.41739e9	−	8.18331e8i	1.00065	−	0.577726i
$195$		0			0
$196$	6.51645e8	+	3.46190e8i	0.441557	+	0.234579i
$197$	−5.40965e8			−0.359174			−0.179587	−	0.983742i	$-0.557476\pi$
$197$	−5.40965e8			−0.359174			−0.179587	+	0.983742i	$0.557476\pi$
$198$		0			0
$199$	−1.18428e8	−	6.83742e7i	−0.0755163	−	0.0435994i	0.461766	−	0.887002i	$-0.347216\pi$
$199$	−1.18428e8	−	6.83742e7i	−0.0755163	−	0.0435994i	−0.537283	+	0.843402i	$0.680549\pi$
$200$	−1.43284e8	+	2.48176e8i	−0.0895528	+	0.155110i
$201$		0			0
$202$			1.06159e9i			0.637607i
$203$	−1.18665e8	+	1.22924e8i	−0.0698774	+	0.0723859i
$204$		0			0
$205$	−1.53032e9	−	2.65060e9i	−0.866499	−	1.50082i
$206$	−1.72725e9	−	9.97230e8i	−0.959151	−	0.553766i
$207$		0			0
$208$	−4.01252e8	+	2.31663e8i	−0.214370	+	0.123767i
$209$			6.26901e8i			0.328560i
$210$		0			0
$211$	8.90323e8			0.449177			0.224589	−	0.974454i	$-0.427896\pi$
$211$	8.90323e8			0.449177			0.224589	+	0.974454i	$0.427896\pi$
$212$	3.96250e8	+	6.86326e8i	0.196167	+	0.339771i
$213$		0			0
$214$	−1.00970e9	+	1.74885e9i	−0.481435	+	0.833869i
$215$	−1.47238e9	+	8.50077e8i	−0.689073	+	0.397837i
$216$		0			0
$217$	2.25282e9	−	6.46416e8i	1.01598	−	0.291523i
$218$	2.68747e9			1.18992
$219$		0			0
$220$	4.29229e8	+	2.47816e8i	0.183231	+	0.105788i
$221$	2.20743e8	−	3.82338e8i	0.0925376	−	0.160280i
$222$		0			0
$223$		−	9.24549e8i		−	0.373861i	−0.982373	−	0.186931i	$-0.940146\pi$
$223$		−	9.24549e8i		−	0.373861i	0.982373	−	0.186931i	$-0.0598540\pi$
$224$	−1.22751e8	−	4.27796e8i	−0.0487564	−	0.169920i
$225$		0			0
$226$	−1.24288e9	−	2.15273e9i	−0.476425	−	0.825192i
$227$	3.04346e9	+	1.75714e9i	1.14621	+	0.661765i	0.947961	−	0.318387i	$-0.103141\pi$
$227$	3.04346e9	+	1.75714e9i	1.14621	+	0.661765i	0.198249	+	0.980152i	$0.436474\pi$
$228$		0			0
$229$	2.54322e9	−	1.46833e9i	0.924789	−	0.533927i	0.0396290	−	0.999214i	$-0.487382\pi$
$229$	2.54322e9	−	1.46833e9i	0.924789	−	0.533927i	0.885160	+	0.465288i	$0.154049\pi$
$230$			1.55861e9i			0.556964i
$231$		0			0
$232$	1.03051e8			0.0355714
$233$	1.94715e9	+	3.37256e9i	0.660657	+	1.14429i	0.980443	+	0.196801i	$0.0630554\pi$
$233$	1.94715e9	+	3.37256e9i	0.660657	+	1.14429i	−0.319787	+	0.947490i	$0.603611\pi$
$234$		0			0
$235$	2.96653e7	−	5.13818e7i	0.00972697	−	0.0168476i
$236$	−1.63520e9	+	9.44082e8i	−0.527136	+	0.304342i
$237$		0			0
$238$	3.05110e8	+	2.94536e8i	0.0950929	+	0.0917976i
$239$	2.17474e8			0.0666525			0.0333262	−	0.999445i	$-0.489390\pi$
$239$	2.17474e8			0.0666525			0.0333262	+	0.999445i	$0.489390\pi$
$240$		0			0
$241$	2.28371e9	+	1.31850e9i	0.676977	+	0.390853i	0.798715	−	0.601710i	$-0.205514\pi$
$241$	2.28371e9	+	1.31850e9i	0.676977	+	0.390853i	−0.121738	+	0.992562i	$0.538847\pi$
$242$	−1.06848e9	+	1.85066e9i	−0.311533	+	0.539592i
$243$		0			0
$244$		−	3.17069e8i		−	0.0894529i
$245$	2.34486e9	+	3.74961e9i	0.650808	+	1.04069i
$246$		0			0
$247$	−1.75616e9	−	3.04176e9i	−0.471821	−	0.817217i
$248$	−1.22422e9	−	7.06804e8i	−0.323633	−	0.186850i
$249$		0			0
$250$	1.44872e9	−	8.36417e8i	0.370871	−	0.214123i
$251$		−	1.72673e9i		−	0.435041i	−0.976056	−	0.217520i	$-0.930203\pi$
$251$		−	1.72673e9i		−	0.435041i	0.976056	−	0.217520i	$-0.0697969\pi$
$252$		0			0
$253$	9.06417e8			0.221231
$254$	1.99571e9	+	3.45668e9i	0.479472	+	0.830470i
$255$		0			0
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	−9.30785e8	+	5.37389e8i	−0.213362	+	0.123185i	−0.602873	−	0.797837i	$-0.705977\pi$
$257$	−9.30785e8	+	5.37389e8i	−0.213362	+	0.123185i	0.389511	+	0.921022i	$0.372644\pi$
$258$		0			0
$259$	3.28108e9	+	8.17449e8i	0.729152	+	0.181661i
$260$	−2.77686e9			−0.607660
$261$		0			0
$262$	−2.15360e8	−	1.24338e8i	−0.0457046	−	0.0263876i
$263$	2.60739e9	−	4.51614e9i	0.544984	−	0.943939i	−0.453624	−	0.891193i	$-0.649869\pi$
$263$	2.60739e9	−	4.51614e9i	0.544984	−	0.943939i	0.998608	−	0.0527463i	$-0.0167975\pi$
$264$		0			0
$265$			4.74971e9i			0.963127i
$266$	3.24298e9	−	9.30532e8i	0.647766	−	0.185868i
$267$		0			0
$268$	−2.29758e8	−	3.97953e8i	−0.0445381	−	0.0771423i
$269$	6.32340e9	+	3.65082e9i	1.20765	+	0.697237i	0.962245	−	0.272183i	$-0.0877456\pi$
$269$	6.32340e9	+	3.65082e9i	1.20765	+	0.697237i	0.245405	+	0.969421i	$0.421079\pi$
$270$		0			0
$271$	−5.76676e9	+	3.32944e9i	−1.06919	+	0.617296i	−0.927960	−	0.372681i	$-0.878439\pi$
$271$	−5.76676e9	+	3.32944e9i	−1.06919	+	0.617296i	−0.141229	+	0.989977i	$0.545105\pi$
$272$		−	2.55782e8i		−	0.0467299i
$273$		0			0
$274$	6.91813e9			1.22740
$275$	4.99408e8	+	8.65000e8i	0.0873222	+	0.151247i
$276$		0			0
$277$	−3.54607e9	+	6.14198e9i	−0.602322	+	1.04325i	0.390147	+	0.920753i	$0.372424\pi$
$277$	−3.54607e9	+	6.14198e9i	−0.602322	+	1.04325i	−0.992469	+	0.122499i	$0.960909\pi$
$278$	1.46070e9	−	8.43333e8i	0.244557	−	0.141195i
$279$		0			0
$280$	6.44838e8	−	2.58826e9i	0.104910	−	0.421090i
$281$	−1.26746e9			−0.203287			−0.101643	−	0.994821i	$-0.532410\pi$
$281$	−1.26746e9			−0.203287			−0.101643	+	0.994821i	$0.532410\pi$
$282$		0			0
$283$	7.86397e9	+	4.54027e9i	1.22602	+	0.707841i	0.966194	−	0.257816i	$-0.0830027\pi$
$283$	7.86397e9	+	4.54027e9i	1.22602	+	0.707841i	0.259822	+	0.965656i	$0.416336\pi$
$284$	−2.25174e9	+	3.90012e9i	−0.346134	+	0.599521i
$285$		0			0
$286$			1.61489e9i			0.241368i
$287$	6.89187e9	+	6.65304e9i	1.01580	+	0.980601i
$288$		0			0
$289$	−3.36602e9	−	5.83011e9i	−0.482531	−	0.835767i
$290$	5.34872e8	+	3.08809e8i	0.0756237	+	0.0436614i
$291$		0			0
$292$	−4.27059e7	+	2.46563e7i	−0.00587431	+	0.00339153i
$293$			7.62166e9i			1.03414i	0.855943	+	0.517070i	$0.172977\pi$
$293$			7.62166e9i			1.03414i	−0.855943	+	0.517070i	$0.827023\pi$
$294$		0			0
$295$	−1.13164e10			−1.49424
$296$	−1.01973e9	−	1.76623e9i	−0.132837	−	0.230081i
$297$		0			0
$298$	3.96007e9	−	6.85905e9i	0.502155	−	0.869759i
$299$	−4.39799e9	+	2.53918e9i	−0.550262	+	0.317694i
$300$		0			0
$301$	3.69569e9	−	3.82835e9i	0.450225	−	0.466386i
$302$	1.10028e10			1.32274
$303$		0			0
$304$	−1.76229e9	−	1.01746e9i	−0.206340	−	0.119131i
$305$	9.50147e8	−	1.64570e9i	0.109797	−	0.190174i
$306$		0			0
$307$			2.77342e9i			0.312221i	0.987740	+	0.156110i	$0.0498956\pi$
$307$			2.77342e9i			0.312221i	−0.987740	+	0.156110i	$0.950104\pi$
$308$	−1.50521e9	−	3.75008e8i	−0.167261	−	0.0416713i
$309$		0			0
$310$	−4.23610e9	−	7.33714e9i	−0.458690	−	0.794474i
$311$	−1.30379e10	−	7.52746e9i	−1.39369	−	0.804650i	−0.399973	−	0.916527i	$-0.630980\pi$
$311$	−1.30379e10	−	7.52746e9i	−1.39369	−	0.804650i	−0.993722	+	0.111877i	$0.964314\pi$
$312$		0			0
$313$	−1.14520e10	+	6.61182e9i	−1.19318	+	0.688880i	−0.959025	−	0.283320i	$-0.908564\pi$
$313$	−1.14520e10	+	6.61182e9i	−1.19318	+	0.688880i	−0.234150	+	0.972200i	$0.575231\pi$
$314$		−	2.03161e8i		−	0.0208988i
$315$		0			0
$316$	−4.30153e9			−0.431394
$317$	−1.47764e9	−	2.55935e9i	−0.146329	−	0.253450i	0.783539	−	0.621343i	$-0.213413\pi$
$317$	−1.47764e9	−	2.55935e9i	−0.146329	−	0.253450i	−0.929868	+	0.367893i	$0.880079\pi$
$318$		0			0
$319$	1.79589e8	−	3.11057e8i	0.0173427	−	0.0300384i
$320$	−1.39328e9	+	8.04409e8i	−0.132873	+	0.0767144i
$321$		0			0
$322$	−1.34543e9	−	4.68892e9i	−0.125152	−	0.436164i
$323$	1.93900e9			0.178143
$324$		0			0
$325$	−4.84631e9	−	2.79802e9i	−0.434388	−	0.250794i
$326$	5.09327e9	−	8.82179e9i	0.450947	−	0.781064i
$327$		0			0
$328$		−	5.77765e9i		−	0.499179i
$329$	−4.48911e7	+	1.80184e8i	−0.00383157	+	0.0153792i
$330$		0			0
$331$	3.86192e9	+	6.68905e9i	0.321730	+	0.557253i	0.980845	−	0.194789i	$-0.0624023\pi$
$331$	3.86192e9	+	6.68905e9i	0.321730	+	0.557253i	−0.659115	+	0.752042i	$0.729069\pi$
$332$	−8.78568e9	−	5.07241e9i	−0.723141	−	0.417505i
$333$		0			0
$334$	−2.22572e9	+	1.28502e9i	−0.178848	+	0.103258i
$335$		−	2.75403e9i		−	0.218670i
$336$		0			0
$337$	1.36239e10			1.05629			0.528145	−	0.849154i	$-0.322888\pi$
$337$	1.36239e10			1.05629			0.528145	+	0.849154i	$0.322888\pi$
$338$	9.06140e7	+	1.56948e8i	0.00694270	+	0.0120251i
$339$		0			0
$340$	7.66492e8	−	1.32760e9i	0.0573577	−	0.0993465i
$341$	−4.26694e9	+	2.46352e9i	−0.315572	+	0.182196i
$342$		0			0
$343$	−1.02910e10	−	9.25616e9i	−0.743500	−	0.668736i
$344$	−3.20942e9			−0.229188
$345$		0			0
$346$	2.65091e9	+	1.53050e9i	0.184965	+	0.106790i
$347$	4.20981e9	−	7.29161e9i	0.290365	−	0.502927i	−0.683531	−	0.729922i	$-0.739557\pi$
$347$	4.20981e9	−	7.29161e9i	0.290365	−	0.502927i	0.973896	+	0.226994i	$0.0728899\pi$
$348$		0			0
$349$			1.69363e10i			1.14161i	0.821087	+	0.570803i	$0.193368\pi$
$349$			1.69363e10i			1.14161i	−0.821087	+	0.570803i	$0.806632\pi$
$350$	3.73338e9	−	3.86740e9i	0.248789	−	0.257720i
$351$		0			0
$352$	4.67807e8	+	8.10265e8i	0.0304716	+	0.0527784i
$353$	−2.53285e10	−	1.46234e10i	−1.63121	−	0.941780i	−0.983720	−	0.179707i	$-0.942485\pi$
$353$	−2.53285e10	−	1.46234e10i	−1.63121	−	0.941780i	−0.647491	−	0.762073i	$-0.724182\pi$
$354$		0			0
$355$	−2.33747e10	+	1.34954e10i	−1.47174	+	0.849711i
$356$			6.66778e9i			0.415127i
$357$		0			0
$358$	9.97973e9			0.607557
$359$	2.55730e9	+	4.42937e9i	0.153959	+	0.266664i	0.932679	−	0.360707i	$-0.117464\pi$
$359$	2.55730e9	+	4.42937e9i	0.153959	+	0.266664i	−0.778721	+	0.627371i	$0.784131\pi$
$360$		0			0
$361$	−7.78741e8	+	1.34882e9i	−0.0458527	+	0.0794191i
$362$	−4.85883e9	+	2.80525e9i	−0.282942	+	0.163357i
$363$		0			0
$364$	8.35389e9	−	2.39704e9i	0.475864	−	0.136543i
$365$	−2.95546e8			−0.0166515
$366$		0			0
$367$	7.72247e9	+	4.45857e9i	0.425688	+	0.245771i	0.697508	−	0.716577i	$-0.254292\pi$
$367$	7.72247e9	+	4.45857e9i	0.425688	+	0.245771i	−0.271820	+	0.962348i	$0.587625\pi$
$368$	−1.47111e9	+	2.54805e9i	−0.0802149	+	0.138936i
$369$		0			0
$370$		−	1.22232e10i		−	0.652194i
$371$	−4.10004e9	−	1.42890e10i	−0.216418	−	0.754234i
$372$		0			0
$373$	1.69622e10	+	2.93793e10i	0.876286	+	1.51777i	0.855386	+	0.517991i	$0.173320\pi$
$373$	1.69622e10	+	2.93793e10i	0.876286	+	1.51777i	0.0209000	+	0.999782i	$0.493347\pi$
$374$	−7.72071e8	−	4.45756e8i	−0.0394613	−	0.0227830i
$375$		0			0
$376$	9.69945e7	−	5.59998e7i	0.00485284	−	0.00280179i
$377$			2.01235e9i			0.0996182i
$378$		0			0
$379$	4.48233e9			0.217244			0.108622	−	0.994083i	$-0.465356\pi$
$379$	4.48233e9			0.217244			0.108622	+	0.994083i	$0.465356\pi$
$380$	−6.09796e9	−	1.05620e10i	−0.292449	−	0.506537i
$381$		0			0
$382$	8.93729e9	−	1.54798e10i	0.419713	−	0.726964i
$383$	6.10111e8	−	3.52248e8i	0.0283540	−	0.0163702i	−0.485756	−	0.874094i	$-0.661456\pi$
$383$	6.10111e8	−	3.52248e8i	0.0283540	−	0.0163702i	0.514110	+	0.857724i	$0.328122\pi$
$384$		0			0
$385$	−6.68881e9	−	6.45702e9i	−0.304443	−	0.293893i
$386$	−1.86918e10			−0.841981
$387$		0			0
$388$	1.60359e10	+	9.25836e9i	0.707567	+	0.408514i
$389$	2.05882e10	−	3.56598e10i	0.899124	−	1.55733i	0.0705080	−	0.997511i	$-0.477538\pi$
$389$	2.05882e10	−	3.56598e10i	0.899124	−	1.55733i	0.828616	−	0.559817i	$-0.189129\pi$
$390$		0			0
$391$		−	2.80354e9i		−	0.119950i
$392$	2.94307e8	+	8.34313e9i	0.0124640	+	0.353334i
$393$		0			0
$394$	−3.06016e9	−	5.30035e9i	−0.126987	−	0.219948i
$395$	−2.23265e10	−	1.28902e10i	−0.917133	−	0.529507i
$396$		0			0
$397$	−7.35159e9	+	4.24444e9i	−0.295951	+	0.170867i	−0.640622	−	0.767856i	$-0.721324\pi$
$397$	−7.35159e9	+	4.24444e9i	−0.295951	+	0.170867i	0.344672	+	0.938723i	$0.387990\pi$
$398$		−	1.54713e9i		−	0.0616588i
$399$		0			0
$400$	−3.24216e9			−0.126647
$401$	−1.67749e10	−	2.90550e10i	−0.648757	−	1.12368i	−0.983420	−	0.181342i	$-0.941956\pi$
$401$	−1.67749e10	−	2.90550e10i	−0.648757	−	1.12368i	0.334663	−	0.942338i	$-0.391378\pi$
$402$		0			0
$403$	1.38023e10	−	2.39062e10i	0.523276	−	0.906340i
$404$	−1.04015e10	+	6.00529e9i	−0.390453	+	0.225428i
$405$		0			0
$406$	−1.87568e9	−	4.67306e8i	−0.0690325	−	0.0171988i
$407$	−7.10842e9			−0.259057
$408$		0			0
$409$	1.95983e10	+	1.13151e10i	0.700367	+	0.404357i	0.807484	−	0.589890i	$-0.200829\pi$
$409$	1.95983e10	+	1.13151e10i	0.700367	+	0.404357i	−0.107117	+	0.994246i	$0.534162\pi$
$410$	1.73136e10	−	2.99881e10i	0.612707	−	1.06124i
$411$		0			0
$412$		−	2.25647e10i		−	0.783144i
$413$	3.40441e10	−	9.76851e9i	1.17015	−	0.335759i
$414$		0			0
$415$	−3.04006e10	−	5.26553e10i	−1.02492	−	1.77521i
$416$	−4.53965e9	−	2.62097e9i	−0.151583	−	0.0875162i
$417$		0			0
$418$	−6.14235e9	+	3.54629e9i	−0.201201	+	0.116163i
$419$			3.35474e10i			1.08844i	0.838944	+	0.544218i	$0.183174\pi$
$419$			3.35474e10i			1.08844i	−0.838944	+	0.544218i	$0.816826\pi$
$420$		0			0
$421$	3.27977e10			1.04403			0.522017	−	0.852935i	$-0.325180\pi$
$421$	3.27977e10			1.04403			0.522017	+	0.852935i	$0.325180\pi$
$422$	5.03643e9	+	8.72335e9i	0.158808	+	0.275064i
$423$		0			0
$424$	−4.48306e9	+	7.76489e9i	−0.138711	+	0.240255i
$425$	2.67544e9	−	1.54467e9i	0.0820048	−	0.0473455i
$426$		0			0
$427$	−1.43781e9	+	5.77111e9i	−0.0432505	+	0.173599i
$428$	−2.28469e10			−0.680851
$429$		0			0
$430$	−1.66580e10	−	9.61753e9i	−0.487248	−	0.281313i
$431$	6.60998e8	−	1.14488e9i	0.0191554	−	0.0331781i	−0.856289	−	0.516497i	$-0.827236\pi$
$431$	6.60998e8	−	1.14488e9i	0.0191554	−	0.0331781i	0.875444	+	0.483319i	$0.160569\pi$
$432$		0			0
$433$			1.53701e9i			0.0437246i	0.999761	+	0.0218623i	$0.00695954\pi$
$433$			1.53701e9i			0.0437246i	−0.999761	+	0.0218623i	$0.993040\pi$
$434$	1.90774e10	+	1.84163e10i	0.537725	+	0.519091i
$435$		0			0
$436$	1.52026e10	+	2.63317e10i	0.420700	+	0.728674i
$437$	−1.93159e10	−	1.11520e10i	−0.529650	−	0.305794i
$438$		0			0
$439$	3.05231e10	−	1.76225e10i	0.821809	−	0.474472i	−0.0292309	−	0.999573i	$-0.509306\pi$
$439$	3.05231e10	−	1.76225e10i	0.821809	−	0.474472i	0.851040	+	0.525101i	$0.175972\pi$
$440$			5.60743e9i			0.149607i
$441$		0			0
$442$	4.99485e9			0.130868
$443$	3.28022e10	+	5.68150e10i	0.851702	+	1.47519i	0.879671	+	0.475582i	$0.157762\pi$
$443$	3.28022e10	+	5.68150e10i	0.851702	+	1.47519i	−0.0279697	+	0.999609i	$0.508904\pi$
$444$		0			0
$445$	−1.99811e10	+	3.46082e10i	−0.509540	+	0.882549i
$446$	9.05870e9	−	5.23004e9i	0.228942	−	0.132180i
$447$		0			0
$448$	3.49715e9	−	3.62268e9i	0.0868164	−	0.0899329i
$449$	−5.51880e10			−1.35787			−0.678937	−	0.734196i	$-0.737559\pi$
$449$	−5.51880e10			−1.35787			−0.678937	+	0.734196i	$0.737559\pi$
$450$		0			0
$451$	−1.74397e10	−	1.00688e10i	−0.421534	−	0.243373i
$452$	1.40615e10	−	2.43553e10i	0.336883	−	0.583499i
$453$		0			0
$454$			3.97596e10i			0.935877i
$455$	5.05428e10	+	1.25922e10i	1.17927	+	0.293804i
$456$		0			0
$457$	2.09559e10	+	3.62968e10i	0.480444	+	0.832153i	0.999748	−	0.0224363i	$-0.00714231\pi$
$457$	2.09559e10	+	3.62968e10i	0.480444	+	0.832153i	−0.519305	+	0.854589i	$0.673809\pi$
$458$	2.87733e10	+	1.66123e10i	0.653924	+	0.377543i
$459$		0			0
$460$	−1.52712e10	+	8.81685e9i	−0.341070	+	0.196917i
$461$			5.47469e10i			1.21215i	0.795408	+	0.606074i	$0.207257\pi$
$461$			5.47469e10i			1.21215i	−0.795408	+	0.606074i	$0.792743\pi$
$462$		0			0
$463$	−5.59007e10			−1.21645			−0.608223	−	0.793766i	$-0.708117\pi$
$463$	−5.59007e10			−1.21645			−0.608223	+	0.793766i	$0.708117\pi$
$464$	5.82945e8	+	1.00969e9i	0.0125764	+	0.0217829i
$465$		0			0
$466$	−2.20295e10	+	3.81562e10i	−0.467155	+	0.809136i
$467$	−5.30982e10	+	3.06562e10i	−1.11638	+	0.644542i	−0.940474	−	0.339865i	$-0.889619\pi$
$467$	−5.30982e10	+	3.06562e10i	−1.11638	+	0.644542i	−0.175906	+	0.984407i	$0.556285\pi$
$468$		0			0
$469$	2.37733e9	+	8.28520e9i	0.0491358	+	0.171243i
$470$	6.71249e8			0.0137560
$471$		0			0
$472$	−1.85002e10	−	1.06811e10i	−0.372741	−	0.215202i
$473$	−5.59310e9	+	9.68754e9i	−0.111740	+	0.193539i
$474$		0			0
$475$		−	2.45777e10i		−	0.482800i
$476$	−1.15990e9	+	4.65560e9i	−0.0225939	+	0.0906876i
$477$		0			0
$478$	1.23022e9	+	2.13080e9i	0.0235652	+	0.0408161i
$479$	−3.06068e10	−	1.76709e10i	−0.581402	−	0.335672i	0.180288	−	0.983614i	$-0.442297\pi$
$479$	−3.06068e10	−	1.76709e10i	−0.581402	−	0.335672i	−0.761690	+	0.647941i	$0.775630\pi$
$480$		0			0
$481$	3.44905e10	−	1.99131e10i	0.644346	−	0.372013i
$482$			2.98343e10i			0.552749i
$483$		0			0
$484$	−2.41769e10			−0.440575
$485$	5.54883e10	+	9.61085e10i	1.00285	+	1.73698i
$486$		0			0
$487$	1.41762e10	−	2.45539e10i	0.252026	−	0.436521i	−0.712058	−	0.702121i	$-0.752237\pi$
$487$	1.41762e10	−	2.45539e10i	0.252026	−	0.436521i	0.964083	+	0.265600i	$0.0855700\pi$
$488$	3.10663e9	−	1.79361e9i	0.0547785	−	0.0316264i
$489$		0			0
$490$	−2.34740e10	+	4.41858e10i	−0.407195	+	0.766476i
$491$	5.07023e10			0.872372			0.436186	−	0.899857i	$-0.356329\pi$
$491$	5.07023e10			0.872372			0.436186	+	0.899857i	$0.356329\pi$
$492$		0			0
$493$	−9.62096e8	−	5.55466e8i	−0.0162866	−	0.00940308i
$494$	1.98687e10	−	3.44136e10i	0.333628	−	0.577860i
$495$		0			0
$496$		−	1.59931e10i		−	0.264245i
$497$	5.86707e10	−	6.07768e10i	0.961603	−	0.996122i
$498$		0			0
$499$	−3.08989e10	−	5.35184e10i	−0.498357	−	0.863179i	0.501642	−	0.865076i	$-0.332730\pi$
$499$	−3.08989e10	−	5.35184e10i	−0.498357	−	0.863179i	−0.999998	+	0.00189664i	$0.999396\pi$
$500$	1.63904e10	+	9.46298e9i	0.262246	+	0.151408i
$501$		0			0
$502$	1.69185e10	−	9.76787e9i	0.266407	−	0.153810i
$503$			1.17222e11i			1.83121i	0.402082	+	0.915604i	$0.368287\pi$
$503$			1.17222e11i			1.83121i	−0.402082	+	0.915604i	$0.631713\pi$
$504$		0			0
$505$	−7.19832e10			−1.10679
$506$	5.12747e9	+	8.88104e9i	0.0782170	+	0.135476i
$507$		0			0
$508$	−2.25789e10	+	3.91078e10i	−0.339038	+	0.587231i
$509$	4.30042e10	−	2.48285e10i	0.640677	−	0.369895i	−0.144198	−	0.989549i	$-0.546060\pi$
$509$	4.30042e10	−	2.48285e10i	0.640677	−	0.369895i	0.784875	+	0.619654i	$0.212727\pi$
$510$		0			0
$511$	8.89118e8	−	2.55121e8i	0.0130399	−	0.00374164i
$512$	−3.03700e9			−0.0441942
$513$		0			0
$514$	−1.05306e10	−	6.07986e9i	−0.150870	−	0.0871047i
$515$	6.76188e10	−	1.17119e11i	0.961255	−	1.66494i
$516$		0			0
$517$		−	3.90367e8i		−	0.00546400i
$518$	1.05513e10	+	3.67721e10i	0.146550	+	0.510739i
$519$		0			0
$520$	−1.57083e10	−	2.72076e10i	−0.214840	−	0.372114i
$521$	−8.97396e10	−	5.18112e10i	−1.21796	−	0.703190i	−0.253479	−	0.967341i	$-0.581575\pi$
$521$	−8.97396e10	−	5.18112e10i	−1.21796	−	0.703190i	−0.964481	+	0.264151i	$0.914908\pi$
$522$		0			0
$523$	1.08458e11	−	6.26180e10i	1.44962	−	0.836936i	0.451158	−	0.892444i	$-0.351011\pi$
$523$	1.08458e11	−	6.26180e10i	1.44962	−	0.836936i	0.998458	+	0.0555075i	$0.0176777\pi$
$524$		−	2.81345e9i		−	0.0373176i
$525$		0			0
$526$	5.89986e10			0.770723
$527$	7.61964e9	+	1.31976e10i	0.0987852	+	0.171101i
$528$		0			0
$529$	2.30311e10	−	3.98911e10i	0.294098	−	0.509393i
$530$	−4.65374e10	+	2.68684e10i	−0.589792	+	0.340517i
$531$		0			0
$532$	2.74624e10	+	2.65107e10i	0.342840	+	0.330960i
$533$	1.12824e11			1.39796
$534$		0			0
$535$	−1.18584e11	−	6.84643e10i	−1.44747	−	0.835698i
$536$	2.59942e9	−	4.50232e9i	0.0314932	−	0.0545479i
$537$		0			0
$538$			8.26085e10i			0.986043i
$539$	2.56964e10	+	1.36514e10i	0.304451	+	0.161741i
$540$		0			0
$541$	2.14145e10	+	3.70910e10i	0.249988	+	0.432992i	0.963522	−	0.267629i	$-0.0862401\pi$
$541$	2.14145e10	+	3.70910e10i	0.249988	+	0.432992i	−0.713534	+	0.700620i	$0.752907\pi$
$542$	−6.52434e10	−	3.76683e10i	−0.756031	−	0.436494i
$543$		0			0
$544$	2.50614e9	−	1.44692e9i	0.0286161	−	0.0165215i
$545$			1.82228e11i			2.06552i
$546$		0			0
$547$	−4.63137e10			−0.517321			−0.258660	−	0.965968i	$-0.583281\pi$
$547$	−4.63137e10			−0.517321			−0.258660	+	0.965968i	$0.583281\pi$
$548$	3.91348e10	+	6.77835e10i	0.433952	+	0.751626i
$549$		0			0
$550$	−5.65016e9	+	9.78636e9i	−0.0617461	+	0.106947i
$551$	−7.65413e9	+	4.41911e9i	−0.0830404	+	0.0479434i
$552$		0			0
$553$	7.82940e10	+	1.95061e10i	0.837197	+	0.208579i
$554$	−8.02384e10			−0.851811
$555$		0			0
$556$	1.65259e10	+	9.54122e9i	0.172928	+	0.0998401i
$557$	−6.61578e9	+	1.14589e10i	−0.0687322	+	0.119048i	−0.898343	−	0.439294i	$-0.855229\pi$
$557$	−6.61578e9	+	1.14589e10i	−0.0687322	+	0.119048i	0.829611	+	0.558341i	$0.188562\pi$
$558$		0			0
$559$		−	6.26727e10i		−	0.641846i
$560$	2.90074e10	−	8.32330e9i	0.294956	−	0.0846337i
$561$		0			0
$562$	−7.16984e9	−	1.24185e10i	−0.0718727	−	0.124487i
$563$	−1.09939e11	−	6.34731e10i	−1.09425	−	0.631765i	−0.159545	−	0.987191i	$-0.551003\pi$
$563$	−1.09939e11	−	6.34731e10i	−1.09425	−	0.631765i	−0.934705	+	0.355425i	$0.884336\pi$
$564$		0			0
$565$	1.45969e11	−	8.42753e10i	1.43241	−	0.827002i
$566$			1.02735e11i			1.00104i
$567$		0			0
$568$	−5.09510e10			−0.489507
$569$	−3.80836e10	−	6.59628e10i	−0.363320	−	0.629289i	0.625185	−	0.780477i	$-0.285024\pi$
$569$	−3.80836e10	−	6.59628e10i	−0.363320	−	0.629289i	−0.988505	+	0.151188i	$0.951690\pi$
$570$		0			0
$571$	−1.57055e10	+	2.72028e10i	−0.147743	+	0.255899i	−0.930393	−	0.366563i	$-0.880534\pi$
$571$	−1.57055e10	+	2.72028e10i	−0.147743	+	0.255899i	0.782650	+	0.622462i	$0.213868\pi$
$572$	−1.58226e10	+	9.13521e9i	−0.147807	+	0.0853364i
$573$		0			0
$574$	−2.61999e10	+	1.05162e11i	−0.241353	+	0.968744i
$575$	−3.55362e10			−0.325087
$576$		0			0
$577$	1.21942e11	+	7.04032e10i	1.10014	+	0.635168i	0.936259	−	0.351311i	$-0.114264\pi$
$577$	1.21942e11	+	7.04032e10i	1.10014	+	0.635168i	0.163885	+	0.986479i	$0.447597\pi$
$578$	3.80821e10	−	6.59602e10i	0.341201	−	0.590977i
$579$		0			0
$580$			6.98754e9i			0.0617465i
$581$	1.36910e11	+	1.32166e11i	1.20152	+	1.15988i
$582$		0			0
$583$	1.56254e10	+	2.70640e10i	0.135256	+	0.234271i
$584$	−4.83162e8	−	2.78954e8i	−0.00415376	−	0.00239818i
$585$		0			0
$586$	−7.46767e10	+	4.31146e10i	−0.633278	+	0.365623i
$587$		−	1.27088e11i		−	1.07041i	−0.844722	−	0.535205i	$-0.820234\pi$
$587$		−	1.27088e11i		−	1.07041i	0.844722	−	0.535205i	$-0.179766\pi$
$588$		0			0
$589$	1.21239e11			1.00735
$590$	−6.40150e10	−	1.10877e11i	−0.528292	−	0.915028i
$591$		0			0
$592$	1.15370e10	−	1.99826e10i	0.0939301	−	0.162692i
$593$	−9.49497e10	+	5.48192e10i	−0.767847	+	0.443317i	−0.832106	−	0.554617i	$-0.812865\pi$
$593$	−9.49497e10	+	5.48192e10i	−0.767847	+	0.443317i	0.0642590	+	0.997933i	$0.479532\pi$
$594$		0			0
$595$	−1.99715e10	+	2.06884e10i	−0.159347	+	0.165067i
$596$	8.96062e10			0.710155
$597$		0			0
$598$	−4.97576e10	−	2.87275e10i	−0.389094	−	0.224643i
$599$	9.86732e10	−	1.70907e11i	0.766464	−	1.32755i	−0.173005	−	0.984921i	$-0.555348\pi$
$599$	9.86732e10	−	1.70907e11i	0.766464	−	1.32755i	0.939469	−	0.342634i	$-0.111319\pi$
$600$		0			0
$601$			6.14321e10i			0.470866i	0.971891	+	0.235433i	$0.0756508\pi$
$601$			6.14321e10i			0.470866i	−0.971891	+	0.235433i	$0.924349\pi$
$602$	5.84160e10	+	1.45538e10i	0.444781	+	0.110813i
$603$		0			0
$604$	6.22411e10	+	1.07805e11i	0.467659	+	0.810009i
$605$	−1.25487e11	−	7.24500e10i	−0.936650	−	0.540775i
$606$		0			0
$607$	7.44988e10	−	4.30119e10i	0.548775	−	0.316836i	−0.199853	−	0.979826i	$-0.564046\pi$
$607$	7.44988e10	−	4.30119e10i	0.548775	−	0.316836i	0.748628	+	0.662990i	$0.230713\pi$
$608$		−	2.30225e10i		−	0.168476i
$609$		0			0
$610$	2.14994e10			0.155277
$611$	1.09355e9	+	1.89408e9i	0.00784646	+	0.0135905i
$612$		0			0
$613$	4.44561e10	−	7.70002e10i	0.314839	−	0.545318i	−0.664564	−	0.747231i	$-0.731383\pi$
$613$	4.44561e10	−	7.70002e10i	0.314839	−	0.545318i	0.979403	+	0.201914i	$0.0647160\pi$
$614$	−2.71738e10	+	1.56888e10i	−0.191195	+	0.110387i
$615$		0			0
$616$	−4.84044e9	−	1.68693e10i	−0.0336172	−	0.117159i
$617$	−2.75927e11			−1.90394			−0.951971	−	0.306189i	$-0.900946\pi$
$617$	−2.75927e11			−1.90394			−0.951971	+	0.306189i	$0.900946\pi$
$618$		0			0
$619$	−1.88747e11	−	1.08973e11i	−1.28564	−	0.742262i	−0.307763	−	0.951463i	$-0.599580\pi$
$619$	−1.88747e11	−	1.08973e11i	−1.28564	−	0.742262i	−0.977873	+	0.209201i	$0.932914\pi$
$620$	4.79260e10	−	8.30102e10i	0.324343	−	0.561778i
$621$		0			0
$622$		−	1.70327e11i		−	1.13795i
$623$	3.02364e10	−	1.21363e11i	0.200714	−	0.805628i
$624$		0			0
$625$	9.53641e10	+	1.65176e11i	0.624978	+	1.08249i
$626$	−1.29565e11	−	7.48042e10i	−0.843703	−	0.487112i
$627$		0			0
$628$	1.99056e9	−	1.14925e9i	0.0127979	−	0.00738885i
$629$			2.19863e10i			0.140459i
$630$		0			0
$631$	−1.15606e11			−0.729227			−0.364614	−	0.931159i	$-0.618799\pi$
$631$	−1.15606e11			−0.729227			−0.364614	+	0.931159i	$0.618799\pi$
$632$	−2.43331e10	−	4.21462e10i	−0.152521	−	0.264174i
$633$		0			0
$634$	1.67176e10	−	2.89557e10i	0.103471	−	0.179216i
$635$	−2.34386e11	+	1.35323e11i	−1.44157	+	0.832292i
$636$		0			0
$637$	−1.62923e11	+	5.74716e9i	−0.989517	+	0.0349056i
$638$	4.06363e9			0.0245262
$639$		0			0
$640$	−1.57631e10	−	9.10085e9i	−0.0939556	−	0.0542453i
$641$	1.65141e11	−	2.86033e11i	0.978191	−	1.69428i	0.309215	−	0.950992i	$-0.399934\pi$
$641$	1.65141e11	−	2.86033e11i	0.978191	−	1.69428i	0.668976	−	0.743284i	$-0.266733\pi$
$642$		0			0
$643$		−	1.72066e11i		−	1.00659i	−0.864116	−	0.503293i	$-0.832122\pi$
$643$		−	1.72066e11i		−	1.00659i	0.864116	−	0.503293i	$-0.167878\pi$
$644$	3.83310e10	−	3.97070e10i	0.222847	−	0.230847i
$645$		0			0
$646$	1.09686e10	+	1.89983e10i	0.0629830	+	0.109090i
$647$	−1.78588e11	−	1.03108e11i	−1.01914	−	0.588402i	−0.105287	−	0.994442i	$-0.533576\pi$
$647$	−1.78588e11	−	1.03108e11i	−1.01914	−	0.588402i	−0.913856	+	0.406039i	$0.866910\pi$
$648$		0			0
$649$	−6.44810e10	+	3.72281e10i	−0.363457	+	0.209842i
$650$		−	6.33120e10i		−	0.354677i
$651$		0			0
$652$	1.15247e11			0.637736
$653$	−2.30745e10	−	3.99662e10i	−0.126905	−	0.219806i	0.795571	−	0.605861i	$-0.207171\pi$
$653$	−2.30745e10	−	3.99662e10i	−0.126905	−	0.219806i	−0.922476	+	0.386054i	$0.873838\pi$
$654$		0			0
$655$	8.43095e9	−	1.46028e10i	0.0458048	−	0.0793363i
$656$	5.66092e10	−	3.26833e10i	0.305683	−	0.176486i
$657$		0			0
$658$	−2.01938e9	+	5.79435e8i	−0.0107725	+	0.00309102i
$659$	−1.66601e10			−0.0883357			−0.0441679	−	0.999024i	$-0.514064\pi$
$659$	−1.66601e10			−0.0883357			−0.0441679	+	0.999024i	$0.514064\pi$
$660$		0			0
$661$	−8.05750e9	−	4.65200e9i	−0.0422080	−	0.0243688i	0.478748	−	0.877953i	$-0.341091\pi$
$661$	−8.05750e9	−	4.65200e9i	−0.0422080	−	0.0243688i	−0.520956	+	0.853584i	$0.674424\pi$
$662$	−4.36927e10	+	7.56779e10i	−0.227498	+	0.394037i
$663$		0			0
$664$		−	1.14776e11i		−	0.590442i
$665$	6.30962e10	+	2.19896e11i	0.322639	+	1.12442i
$666$		0			0
$667$	6.38946e9	+	1.10669e10i	0.0322820	+	0.0559141i
$668$	−2.51811e10	−	1.45383e10i	−0.126465	−	0.0730144i
$669$		0			0
$670$	2.69839e10	−	1.55791e10i	0.133907	−	0.0773115i
$671$		−	1.25030e10i		−	0.0616773i
$672$		0			0
$673$	−1.10631e11			−0.539282			−0.269641	−	0.962961i	$-0.586905\pi$
$673$	−1.10631e11			−0.539282			−0.269641	+	0.962961i	$0.586905\pi$
$674$	7.70687e10	+	1.33487e11i	0.373455	+	0.646843i
$675$		0			0
$676$	−1.02518e9	+	1.77566e9i	−0.00490923	+	0.00850304i
$677$	7.01094e10	−	4.04777e10i	0.333750	−	0.192691i	−0.323755	−	0.946141i	$-0.604945\pi$
$677$	7.01094e10	−	4.04777e10i	0.333750	−	0.192691i	0.657505	+	0.753450i	$0.271612\pi$
$678$		0			0
$679$	−2.49893e11	−	2.41234e11i	−1.17564	−	1.13490i
$680$	1.73437e10			0.0811160
$681$		0			0
$682$	−4.82749e10	−	2.78715e10i	−0.223143	−	0.128832i
$683$	1.00435e11	−	1.73959e11i	0.461534	−	0.799400i	−0.537504	−	0.843261i	$-0.680633\pi$
$683$	1.00435e11	−	1.73959e11i	0.461534	−	0.799400i	0.999038	+	0.0438612i	$0.0139659\pi$
$684$		0			0
$685$			4.69095e11i			2.13058i
$686$	3.24768e10	−	1.53192e11i	0.146648	−	0.691733i
$687$		0			0
$688$	−1.81552e10	−	3.14458e10i	−0.0810303	−	0.140349i
$689$	−1.51631e11	−	8.75440e10i	−0.672838	−	0.388463i
$690$		0			0
$691$	−2.77367e11	+	1.60138e11i	−1.21659	+	0.702397i	−0.964186	−	0.265226i	$-0.914553\pi$
$691$	−2.77367e11	+	1.60138e11i	−1.21659	+	0.702397i	−0.252400	+	0.967623i	$0.581220\pi$
$692$			3.46313e10i			0.151023i
$693$		0			0
$694$	9.52571e10			0.410639
$695$	5.71836e10	+	9.90448e10i	0.245094	+	0.424515i
$696$		0			0
$697$	−3.11427e10	+	5.39408e10i	−0.131955	+	0.228553i
$698$	−1.65941e11	+	9.58061e10i	−0.699088	+	0.403619i
$699$		0			0
$700$	5.90119e10	+	1.47022e10i	0.245780	+	0.0612337i
$701$	−5.65576e10			−0.234217			−0.117109	−	0.993119i	$-0.537363\pi$
$701$	−5.65576e10			−0.234217			−0.117109	+	0.993119i	$0.537363\pi$
$702$		0			0
$703$	1.51482e11	+	8.74580e10i	0.620210	+	0.358078i
$704$	−5.29263e9	+	9.16710e9i	−0.0215467	+	0.0373200i
$705$		0			0
$706$		−	3.30890e11i		−	1.33188i
$707$	2.16554e11	−	6.21373e10i	0.866738	−	0.248699i
$708$		0			0
$709$	1.58821e11	+	2.75086e11i	0.628525	+	1.08864i	0.987848	+	0.155423i	$0.0496742\pi$
$709$	1.58821e11	+	2.75086e11i	0.628525	+	1.08864i	−0.359323	+	0.933213i	$0.616992\pi$
$710$	−2.64454e11	−	1.52683e11i	−1.04068	−	0.600836i
$711$		0			0
$712$	−6.53306e10	+	3.77187e10i	−0.254212	+	0.146770i
$713$		−	1.75295e11i		−	0.678285i
$714$		0			0
$715$	−1.09500e11			−0.418978
$716$	5.64539e10	+	9.77810e10i	0.214804	+	0.372051i
$717$		0			0
$718$	−2.89326e10	+	5.01126e10i	−0.108865	+	0.188560i
$719$	−2.58599e11	+	1.49302e11i	−0.967633	+	0.558663i	−0.898514	−	0.438945i	$-0.855352\pi$
$719$	−2.58599e11	+	1.49302e11i	−0.967633	+	0.558663i	−0.0691194	+	0.997608i	$0.522019\pi$
$720$		0			0
$721$	−1.02324e11	+	4.10711e11i	−0.378650	+	1.51983i
$722$	−1.76209e10			−0.0648454
$723$		0			0
$724$	−5.49714e10	−	3.17377e10i	−0.200070	−	0.115511i
$725$	−7.04079e9	+	1.21950e10i	−0.0254841	+	0.0441398i
$726$		0			0
$727$		−	2.15756e10i		−	0.0772371i	−0.999254	−	0.0386185i	$-0.987704\pi$
$727$		−	2.15756e10i		−	0.0772371i	0.999254	−	0.0386185i	$-0.0122957\pi$
$728$	7.07428e10	+	6.82913e10i	0.251859	+	0.243131i
$729$		0			0
$730$	−1.67186e9	−	2.89574e9i	−0.00588719	−	0.0101969i
$731$	2.99635e10	+	1.72994e10i	0.104936	+	0.0605846i
$732$		0			0
$733$	−1.03855e10	+	5.99605e9i	−0.0359758	+	0.0207706i	−0.517880	−	0.855453i	$-0.673279\pi$
$733$	−1.03855e10	+	5.99605e9i	−0.0359758	+	0.0207706i	0.481904	+	0.876224i	$0.339945\pi$
$734$			1.00886e11i			0.347573i
$735$		0			0
$736$	−3.32875e10			−0.113441
$737$	−9.06009e9	−	1.56925e10i	−0.0307088	−	0.0531892i
$738$		0			0
$739$	2.03348e11	−	3.52209e11i	0.681808	−	1.18093i	−0.292620	−	0.956229i	$-0.594527\pi$
$739$	2.03348e11	−	3.52209e11i	0.681808	−	1.18093i	0.974429	−	0.224698i	$-0.0721394\pi$
$740$	1.19762e11	−	6.91447e10i	0.399386	−	0.230585i
$741$		0			0
$742$	1.16810e11	−	1.21003e11i	0.385357	−	0.399190i
$743$	1.32051e11			0.433299			0.216650	−	0.976249i	$-0.430487\pi$
$743$	1.32051e11			0.433299			0.216650	+	0.976249i	$0.430487\pi$
$744$		0			0
$745$	4.65089e11	+	2.68519e11i	1.50977	+	0.871666i
$746$	−1.91905e11	+	3.32389e11i	−0.619628	+	1.07323i
$747$		0			0
$748$		−	1.00863e10i		−	0.0322200i
$749$	4.15846e11	+	1.03604e11i	1.32131	+	0.329192i
$750$		0			0
$751$	1.72943e10	+	2.99547e10i	0.0543681	+	0.0941683i	0.891929	−	0.452176i	$-0.149352\pi$
$751$	1.72943e10	+	2.99547e10i	0.0543681	+	0.0941683i	−0.837560	+	0.546345i	$0.816019\pi$
$752$	1.09737e9	+	6.33566e8i	0.00343148	+	0.00198116i
$753$		0			0
$754$	−1.97170e10	+	1.13836e10i	−0.0610035	+	0.0352204i
$755$			7.46061e11i			2.29608i
$756$		0			0
$757$	−2.94290e10			−0.0896173			−0.0448086	−	0.998996i	$-0.514268\pi$
$757$	−2.94290e10			−0.0896173			−0.0448086	+	0.998996i	$0.514268\pi$
$758$	2.53559e10	+	4.39177e10i	0.0768073	+	0.133034i
$759$		0			0
$760$	6.89906e10	−	1.19495e11i	0.206793	−	0.358176i
$761$	1.88879e11	−	1.09050e11i	0.563179	−	0.325151i	−0.191242	−	0.981543i	$-0.561251\pi$
$761$	1.88879e11	−	1.09050e11i	0.563179	−	0.325151i	0.754420	+	0.656392i	$0.227918\pi$
$762$		0			0
$763$	−1.57303e11	−	5.48214e11i	−0.464129	−	1.61753i
$764$	2.02228e11			0.593564
$765$		0			0
$766$	6.90262e9	+	3.98523e9i	0.0200493	+	0.0115755i
$767$	2.08577e11	−	3.61266e11i	0.602678	−	1.04387i
$768$		0			0
$769$			1.85675e11i			0.530942i	0.964119	+	0.265471i	$0.0855275\pi$
$769$			1.85675e11i			0.530942i	−0.964119	+	0.265471i	$0.914473\pi$
$770$	2.54280e10	−	1.02063e11i	0.0723352	−	0.290340i
$771$		0			0
$772$	−1.05737e11	−	1.83142e11i	−0.297685	−	0.515606i
$773$	6.54917e10	+	3.78116e10i	0.183429	+	0.105903i	0.588903	−	0.808204i	$-0.299560\pi$
$773$	6.54917e10	+	3.78116e10i	0.183429	+	0.105903i	−0.405474	+	0.914107i	$0.632893\pi$
$774$		0			0
$775$	1.67286e11	−	9.65824e10i	0.463716	−	0.267726i
$776$			2.09493e11i			0.577726i
$777$		0			0
$778$	4.65857e11			1.27155
$779$	2.47762e11	+	4.29136e11i	0.672797	+	1.16532i
$780$		0			0
$781$	−8.87930e10	+	1.53794e11i	−0.238657	+	0.413367i
$782$	2.74690e10	−	1.58592e10i	0.0734540	−	0.0424087i
$783$		0			0
$784$	−8.00808e10	+	5.00795e10i	−0.211965	+	0.132555i
$785$	1.37757e10			0.0362772
$786$		0			0
$787$	−5.00701e11	−	2.89080e11i	−1.30521	−	0.753562i	−0.323915	−	0.946086i	$-0.604999\pi$
$787$	−5.00701e11	−	2.89080e11i	−1.30521	−	0.753562i	−0.981292	+	0.192524i	$0.938333\pi$
$788$	3.46218e10	−	5.99667e10i	0.0897934	−	0.155527i
$789$		0			0
$790$		−	2.91672e11i		−	0.748836i
$791$	−3.66384e11	+	3.79537e11i	−0.935903	+	0.969500i
$792$		0			0
$793$	3.50252e10	+	6.06654e10i	0.0885702	+	0.153408i
$794$	−8.31738e10	−	4.80204e10i	−0.209269	−	0.120821i
$795$		0			0
$796$	1.51587e10	−	8.75190e9i	0.0377582	−	0.0217997i
$797$			4.43180e11i			1.09836i	0.835703	+	0.549182i	$0.185061\pi$
$797$			4.43180e11i			1.09836i	−0.835703	+	0.549182i	$0.814939\pi$
$798$		0			0
$799$	−1.20740e9			−0.00296254
$800$	−1.83404e10	−	3.17665e10i	−0.0447764	−	0.0775550i
$801$		0			0
$802$	1.89786e11	−	3.28719e11i	0.458741	−	0.794562i
$803$	−1.68403e9	+	9.72275e8i	−0.00405030	+	0.00233844i
$804$		0			0
$805$	3.17940e11	−	9.12288e10i	0.757115	−	0.217244i
$806$	3.12310e11			0.740024
$807$		0			0
$808$	−1.17679e11	−	6.79421e10i	−0.276092	−	0.159402i
$809$	−1.23410e11	+	2.13752e11i	−0.288108	+	0.499017i	−0.973358	−	0.229290i	$-0.926359\pi$
$809$	−1.23410e11	+	2.13752e11i	−0.288108	+	0.499017i	0.685250	+	0.728308i	$0.259693\pi$
$810$		0			0
$811$			3.79882e11i			0.878143i	0.898452	+	0.439071i	$0.144693\pi$
$811$			3.79882e11i			0.878143i	−0.898452	+	0.439071i	$0.855307\pi$
$812$	−6.03178e9	−	2.10213e10i	−0.0138746	−	0.0483543i
$813$		0			0
$814$	−4.02113e10	−	6.96480e10i	−0.0915905	−	0.158639i
$815$	5.98176e11	+	3.45357e11i	1.35581	+	0.782777i
$816$		0			0
$817$	2.38380e11	−	1.37629e11i	0.535034	−	0.308902i
$818$			2.56031e11i			0.571847i
$819$		0			0
$820$	3.91763e11			0.866499
$821$	−3.79375e11	−	6.57097e11i	−0.835018	−	1.44629i	−0.894016	−	0.448036i	$-0.852124\pi$
$821$	−3.79375e11	−	6.57097e11i	−0.835018	−	1.44629i	0.0589976	−	0.998258i	$-0.481210\pi$
$822$		0			0
$823$	−3.26699e11	+	5.65860e11i	−0.712113	+	1.23342i	0.251950	+	0.967740i	$0.418928\pi$
$823$	−3.26699e11	+	5.65860e11i	−0.712113	+	1.23342i	−0.964063	+	0.265675i	$0.914405\pi$
$824$	2.21088e11	−	1.27645e11i	0.479576	−	0.276883i
$825$		0			0
$826$	2.88294e11	+	2.78304e11i	0.619320	+	0.597859i
$827$	−1.50289e11			−0.321296			−0.160648	−	0.987012i	$-0.551358\pi$
$827$	−1.50289e11			−0.321296			−0.160648	+	0.987012i	$0.551358\pi$
$828$		0			0
$829$	5.29912e11	+	3.05945e11i	1.12198	+	0.647776i	0.941906	−	0.335877i	$-0.109033\pi$
$829$	5.29912e11	+	3.05945e11i	1.12198	+	0.647776i	0.180075	+	0.983653i	$0.442366\pi$
$830$	3.43943e11	−	5.95727e11i	0.724727	−	1.25526i
$831$		0			0
$832$		−	5.93057e10i		−	0.123767i
$833$	4.22235e10	−	7.94788e10i	0.0876949	−	0.165071i
$834$		0			0
$835$	−8.71327e10	−	1.50918e11i	−0.179240	−	0.310453i
$836$	−6.94928e10	−	4.01217e10i	−0.142270	−	0.0821399i
$837$		0			0
$838$	−3.28696e11	+	1.89773e11i	−0.666529	+	0.384821i
$839$		−	2.75074e11i		−	0.555139i	−0.960706	−	0.277569i	$-0.910471\pi$
$839$		−	2.75074e11i		−	0.555139i	0.960706	−	0.277569i	$-0.0895288\pi$
$840$		0			0
$841$	−4.95183e11			−0.989877
$842$	1.85532e11	+	3.21350e11i	0.369122	+	0.639338i
$843$		0			0
$844$	−5.69807e10	+	9.86934e10i	−0.112294	+	0.194499i
$845$	−1.06421e10	+	6.14423e9i	−0.0208738	+	0.0120515i
$846$		0			0
$847$	4.40054e11	+	1.09635e11i	0.855013	+	0.213018i
$848$	−1.01440e11			−0.196167
$849$		0			0
$850$	3.02691e10	+	1.74759e10i	0.0579861	+	0.0334783i
$851$	1.26453e11	−	2.19023e11i	0.241107	−	0.417610i
$852$		0			0
$853$			3.75369e11i			0.709026i	0.935051	+	0.354513i	$0.115353\pi$
$853$			3.75369e11i			0.709026i	−0.935051	+	0.354513i	$0.884647\pi$
$854$	−6.46786e10	+	1.85587e10i	−0.121599	+	0.0348912i
$855$		0			0
$856$	−1.29242e11	−	2.23853e11i	−0.240717	−	0.416935i
$857$	2.12580e11	+	1.22733e11i	0.394093	+	0.227530i	0.683932	−	0.729546i	$-0.260269\pi$
$857$	2.12580e11	+	1.22733e11i	0.394093	+	0.227530i	−0.289839	+	0.957075i	$0.593602\pi$
$858$		0			0
$859$	−1.67139e11	+	9.64979e10i	−0.306977	+	0.177233i	−0.645573	−	0.763699i	$-0.723381\pi$
$859$	−1.67139e11	+	9.64979e10i	−0.306977	+	0.177233i	0.338596	+	0.940932i	$0.390048\pi$
$860$		−	2.17620e11i		−	0.397837i
$861$		0			0
$862$	1.49567e10			0.0270898
$863$	3.98230e11	+	6.89754e11i	0.717944	+	1.24352i	0.961813	+	0.273707i	$0.0882500\pi$
$863$	3.98230e11	+	6.89754e11i	0.717944	+	1.24352i	−0.243869	+	0.969808i	$0.578417\pi$
$864$		0			0
$865$	−1.03778e11	+	1.79749e11i	−0.185371	+	0.321072i
$866$	−1.50596e10	+	8.69466e9i	−0.0267758	+	0.0154590i
$867$		0			0
$868$	−7.25241e10	+	2.91098e11i	−0.127763	+	0.512815i
$869$	−1.69623e11			−0.297444
$870$		0			0
$871$	8.79202e10	+	5.07608e10i	0.152762	+	0.0881973i
$872$	−1.71998e11	+	2.97909e11i	−0.297480	+	0.515250i
$873$		0			0
$874$		−	2.52342e11i		−	0.432458i
$875$	−2.55416e11	−	2.46565e11i	−0.435729	−	0.420629i
$876$		0			0
$877$	−3.95942e11	−	6.85792e11i	−0.669319	−	1.15929i	−0.978095	−	0.208160i	$-0.933253\pi$
$877$	−3.95942e11	−	6.85792e11i	−0.669319	−	1.15929i	0.308776	−	0.951135i	$-0.400081\pi$
$878$	3.45330e11	+	1.99376e11i	0.581107	+	0.335502i
$879$		0			0
$880$	−5.49413e10	+	3.17204e10i	−0.0916154	+	0.0528942i
$881$			5.78522e11i			0.960320i	0.877181	+	0.480160i	$0.159421\pi$
$881$			5.78522e11i			0.960320i	−0.877181	+	0.480160i	$0.840579\pi$
$882$		0			0
$883$	−8.90230e11			−1.46440			−0.732199	−	0.681090i	$-0.761506\pi$
$883$	−8.90230e11			−1.46440			−0.732199	+	0.681090i	$0.761506\pi$
$884$	2.82551e10	+	4.89393e10i	0.0462688	+	0.0801399i
$885$		0			0
$886$	−3.71114e11	+	6.42788e11i	−0.602244	+	1.04312i
$887$	−5.27870e11	+	3.04766e11i	−0.852771	+	0.492347i	−0.861585	−	0.507614i	$-0.830528\pi$
$887$	−5.27870e11	+	3.04766e11i	−0.852771	+	0.492347i	0.00881401	+	0.999961i	$0.497194\pi$
$888$		0			0
$889$	5.88311e11	−	6.09430e11i	0.941890	−	0.975701i
$890$	−4.52120e11			−0.720598
$891$		0			0
$892$	1.02487e11	+	5.91712e10i	0.161887	+	0.0934654i
$893$	−4.80286e9	+	8.31879e9i	−0.00755255	+	0.0130814i
$894$		0			0
$895$			6.76692e11i			1.05463i
$896$	5.52777e10	+	1.37719e10i	0.0857666	+	0.0213679i
$897$		0			0
$898$	−3.12191e11	−	5.40730e11i	−0.480081	−	0.831525i
$899$	−6.01564e10	−	3.47313e10i	−0.0920965	−	0.0531719i
$900$		0			0
$901$	8.37087e10	−	4.83293e10i	0.127020	−	0.0733349i
$902$		−	2.27831e11i		−	0.344181i
$903$		0			0
$904$	3.18176e11			0.476425
$905$	−1.90214e11	−	3.29461e11i	−0.283563	−	0.491145i
$906$		0			0
$907$	2.03801e11	−	3.52994e11i	0.301147	−	0.521601i	−0.675249	−	0.737590i	$-0.735964\pi$
$907$	2.03801e11	−	3.52994e11i	0.301147	−	0.521601i	0.976396	+	0.215988i	$0.0692973\pi$
$908$	−3.89563e11	+	2.24914e11i	−0.573105	+	0.330882i
$909$		0			0
$910$	1.62535e11	+	5.66449e11i	0.237018	+	0.826029i
$911$	−2.27629e11			−0.330487			−0.165243	−	0.986253i	$-0.552841\pi$
$911$	−2.27629e11			−0.330487			−0.165243	+	0.986253i	$0.552841\pi$
$912$		0			0
$913$	−3.46447e11	−	2.00021e11i	−0.498601	−	0.287868i
$914$	−2.37089e11	+	4.10651e11i	−0.339725	+	0.588421i
$915$		0			0
$916$			3.75893e11i			0.533927i
$917$	−1.27582e10	+	5.12088e10i	−0.0180431	+	0.0724215i
$918$		0			0
$919$	−6.31609e11	−	1.09398e12i	−0.885496	−	1.53372i	−0.845144	−	0.534538i	$-0.820486\pi$
$919$	−6.31609e11	−	1.09398e12i	−0.885496	−	1.53372i	−0.0403516	−	0.999186i	$-0.512848\pi$
$920$	−1.72774e11	−	9.97513e10i	−0.241173	−	0.139241i
$921$		0			0
$922$	−5.36408e11	+	3.09695e11i	−0.742287	+	0.428559i
$923$		−	9.94957e11i		−	1.37087i
$924$		0			0
$925$	2.78686e11			0.380670
$926$	−3.16222e11	−	5.47712e11i	−0.430079	−	0.744918i
$927$		0			0
$928$	−6.59527e9	+	1.14233e10i	−0.00889284	+	0.0154028i
$929$	1.22952e12	−	7.09863e11i	1.65072	−	0.953041i	0.673938	−	0.738788i	$-0.264602\pi$
$929$	1.22952e12	−	7.09863e11i	1.65072	−	0.953041i	0.976778	−	0.214253i	$-0.0687317\pi$
$930$		0			0
$931$	−3.79636e11	−	6.07067e11i	−0.505323	−	0.808049i
$932$	−4.98471e11			−0.660657
$933$		0			0
$934$	−6.00737e11	−	3.46836e11i	−0.789400	−	0.455760i
$935$	3.02252e10	−	5.23516e10i	0.0395478	−	0.0684988i
$936$		0			0
$937$		−	4.06177e11i		−	0.526935i	−0.964668	−	0.263467i	$-0.915134\pi$
$937$		−	4.06177e11i		−	0.526935i	0.964668	−	0.263467i	$-0.0848661\pi$
$938$	−6.77298e10	+	7.01612e10i	−0.0874921	+	0.0906328i
$939$		0			0
$940$	3.79716e9	+	6.57687e9i	0.00486348	+	0.00842380i
$941$	−8.54334e11	−	4.93250e11i	−1.08961	−	0.629084i	−0.156134	−	0.987736i	$-0.549903\pi$
$941$	−8.54334e11	−	4.93250e11i	−1.08961	−	0.629084i	−0.933471	+	0.358652i	$0.883236\pi$
$942$		0			0
$943$	6.20474e11	−	3.58231e11i	0.784651	−	0.453019i
$944$		−	2.41685e11i		−	0.304342i
$945$		0			0
$946$	−1.26557e11			−0.158024
$947$	−2.02568e11	−	3.50858e11i	−0.251867	−	0.436246i	0.712173	−	0.702004i	$-0.247711\pi$
$947$	−2.02568e11	−	3.50858e11i	−0.251867	−	0.436246i	−0.964040	+	0.265758i	$0.914378\pi$
$948$		0			0
$949$	5.44734e9	−	9.43507e9i	0.00671614	−	0.0116327i
$950$	2.40812e11	−	1.39033e11i	0.295653	−	0.170696i
$951$		0			0
$952$	−5.21767e10	+	1.49714e10i	−0.0635227	+	0.0182270i
$953$	−8.59856e9			−0.0104245			−0.00521224	−	0.999986i	$-0.501659\pi$
$953$	−8.59856e9			−0.0104245			−0.00521224	+	0.999986i	$0.501659\pi$
$954$		0			0
$955$	1.04964e12	+	6.06007e11i	1.26190	+	0.728559i
$956$	−1.39184e10	+	2.41073e10i	−0.0166631	+	0.0288614i
$957$		0			0
$958$		−	3.99846e11i		−	0.474713i
$959$	−4.04932e11	−	1.41122e12i	−0.478749	−	1.66848i
$960$		0			0
$961$	4.99831e10	+	8.65732e10i	0.0586043	+	0.101506i
$962$	3.90215e11	+	2.25291e11i	0.455621	+	0.263053i
$963$		0			0
$964$	−2.92315e11	+	1.68768e11i	−0.338488	+	0.195426i
$965$		−	1.26743e12i		−	1.46155i
$966$		0			0
$967$	−7.57902e10			−0.0866777			−0.0433388	−	0.999060i	$-0.513800\pi$
$967$	−7.57902e10			−0.0866777			−0.0433388	+	0.999060i	$0.513800\pi$
$968$	−1.36765e11	−	2.36884e11i	−0.155767	−	0.269796i
$969$		0			0
$970$	−6.27778e11	+	1.08734e12i	−0.709119	+	1.22823i
$971$	6.05255e11	−	3.49444e11i	0.680866	−	0.393098i	−0.119315	−	0.992856i	$-0.538070\pi$
$971$	6.05255e11	−	3.49444e11i	0.680866	−	0.393098i	0.800181	+	0.599758i	$0.204737\pi$
$972$		0			0
$973$	−2.57528e11	−	2.48604e11i	−0.287325	−	0.277368i
$974$	3.20771e11			0.356418
$975$		0			0
$976$	3.51475e10	+	2.02924e10i	0.0387342	+	0.0223632i
$977$	−8.73103e11	+	1.51226e12i	−0.958269	+	1.65977i	−0.231565	+	0.972819i	$0.574385\pi$
$977$	−8.73103e11	+	1.51226e12i	−0.958269	+	1.65977i	−0.726704	+	0.686951i	$0.758949\pi$
$978$		0			0
$979$			2.62932e11i			0.286228i
$980$	−5.65720e11	+	1.99560e10i	−0.613334	+	0.0216356i
$981$		0			0
$982$	2.86815e11	+	4.96779e11i	0.308430	+	0.534216i
$983$	−4.86285e11	−	2.80757e11i	−0.520807	−	0.300688i	0.216458	−	0.976292i	$-0.430550\pi$
$983$	−4.86285e11	−	2.80757e11i	−0.520807	−	0.300688i	−0.737265	+	0.675604i	$0.763883\pi$
$984$		0			0
$985$	3.59399e11	−	2.07499e11i	0.381797	−	0.220430i
$986$		−	1.25688e10i		−	0.0132980i
$987$		0			0
$988$	4.49578e11			0.471821
$989$	−1.98993e11	−	3.44666e11i	−0.207995	−	0.360258i
$990$		0			0
$991$	4.22767e11	−	7.32253e11i	0.438335	−	0.759218i	−0.559226	−	0.829015i	$-0.688902\pi$
$991$	4.22767e11	−	7.32253e11i	0.438335	−	0.759218i	0.997561	+	0.0697966i	$0.0222350\pi$
$992$	1.56700e11	−	9.04709e10i	0.161816	−	0.0934248i
$993$		0			0
$994$	9.27380e11	+	2.31047e11i	0.949975	+	0.236677i
$995$	1.04906e11			0.107030
$996$		0			0
$997$	8.57819e11	+	4.95262e11i	0.868190	+	0.501250i	0.866746	−	0.498749i	$-0.166207\pi$
$997$	8.57819e11	+	4.95262e11i	0.868190	+	0.501250i	0.00144368	+	0.999999i	$0.499540\pi$
$998$	3.49581e11	−	6.05491e11i	0.352391	−	0.610360i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.n.d.73.7	yes	20
3.2	odd	2	inner	126.9.n.d.73.4	yes	20
7.5	odd	6	inner	126.9.n.d.19.7	yes	20
21.5	even	6	inner	126.9.n.d.19.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.n.d.19.4	✓	20	21.5	even	6	inner
126.9.n.d.19.7	yes	20	7.5	odd	6	inner
126.9.n.d.73.4	yes	20	3.2	odd	2	inner
126.9.n.d.73.7	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(5.65685 + 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(-664.367 + 383.572i) q^{5} +(1667.57 - 1727.43i) q^{7} -1448.15 q^{8} +O(q^{10})\)	\(q+(5.65685 + 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(-664.367 + 383.572i) q^{5} +(1667.57 - 1727.43i) q^{7} -1448.15 q^{8} +(-7516.45 - 4339.62i) q^{10} +(-2523.72 + 4371.21i) q^{11} -28279.2i q^{13} +(26358.5 + 6566.95i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(13520.1 + 7805.85i) q^{17} +(107562. - 62100.9i) q^{19} -98194.5i q^{20} -57105.3 q^{22} +(-89789.7 - 155520. i) q^{23} +(98942.8 - 171374. i) q^{25} +(277078. - 159971. i) q^{26} +(84763.4 + 295408. i) q^{28} -71160.2 q^{29} +(845366. + 488072. i) q^{31} +(92681.9 - 160530. i) q^{32} +176626. i q^{34} +(-445283. + 1.78728e6i) q^{35} +(704161. + 1.21964e6i) q^{37} +(1.21692e6 + 702591. i) q^{38} +(962105. - 555472. i) q^{40} +3.98966e6i q^{41} +2.21621e6 q^{43} +(-323036. - 559515. i) q^{44} +(1.01585e6 - 1.75951e6i) q^{46} +(-66978.0 + 38669.8i) q^{47} +(-203229. - 5.76122e6i) q^{49} +2.23882e6 q^{50} +(3.13478e6 + 1.80987e6i) q^{52} +(3.09571e6 - 5.36192e6i) q^{53} -3.87212e6i q^{55} +(-2.41490e6 + 2.50159e6i) q^{56} +(-402543. - 697225. i) q^{58} +(1.27750e7 + 7.37564e6i) q^{59} +(-2.14523e6 + 1.23855e6i) q^{61} +1.10438e7i q^{62} +2.09715e6 q^{64} +(1.08471e7 + 1.87877e7i) q^{65} +(-1.79499e6 + 3.10901e6i) q^{67} +(-1.73058e6 + 999149. i) q^{68} +(-2.00306e7 + 5.74752e6i) q^{70} +3.51834e7 q^{71} +(333640. + 192627. i) q^{73} +(-7.96667e6 + 1.37987e7i) q^{74} +1.58978e7i q^{76} +(3.34249e6 + 1.16489e7i) q^{77} +(1.68028e7 + 2.91034e7i) q^{79} +(1.08850e7 + 6.28445e6i) q^{80} +(-3.90906e7 + 2.25689e7i) q^{82} +7.92564e7i q^{83} -1.19764e7 q^{85} +(1.25368e7 + 2.17144e7i) q^{86} +(3.65474e6 - 6.33019e6i) q^{88} +(4.51130e7 - 2.60460e7i) q^{89} +(-4.88503e7 - 4.71575e7i) q^{91} +2.29862e7 q^{92} +(-757770. - 437499. i) q^{94} +(-4.76403e7 + 8.25155e7i) q^{95} -1.44662e8i q^{97} +(5.52985e7 - 3.45816e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 1280 q^{4} + 4186 q^{7}+O(q^{10}) \) 20 * q - 1280 * q^4 + 4186 * q^7	\( 20 q - 1280 q^{4} + 4186 q^{7} - 17664 q^{10} - 163840 q^{16} - 250890 q^{19} + 420864 q^{22} + 258962 q^{25} - 1189888 q^{28} + 342762 q^{31} - 4806598 q^{37} + 2260992 q^{40} + 6968252 q^{43} - 4357632 q^{46} - 26046538 q^{49} + 2075904 q^{52} + 2455296 q^{58} - 15410424 q^{61} + 41943040 q^{64} - 70041074 q^{67} - 25804800 q^{70} + 220264098 q^{73} + 12860578 q^{79} + 12085248 q^{82} + 29161632 q^{85} - 26935296 q^{88} - 311022894 q^{91} + 332230656 q^{94}+O(q^{100}) \) 20 * q - 1280 * q^4 + 4186 * q^7 - 17664 * q^10 - 163840 * q^16 - 250890 * q^19 + 420864 * q^22 + 258962 * q^25 - 1189888 * q^28 + 342762 * q^31 - 4806598 * q^37 + 2260992 * q^40 + 6968252 * q^43 - 4357632 * q^46 - 26046538 * q^49 + 2075904 * q^52 + 2455296 * q^58 - 15410424 * q^61 + 41943040 * q^64 - 70041074 * q^67 - 25804800 * q^70 + 220264098 * q^73 + 12860578 * q^79 + 12085248 * q^82 + 29161632 * q^85 - 26935296 * q^88 - 311022894 * q^91 + 332230656 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more