LMFDB - Embedded newform 126.9.n.d.19.4

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			19.4
Root			$-63.1006 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.19
Dual form			126.9.n.d.73.4

$q$-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 $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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	$-0.123008\pi$
$5$	664.367	+	383.572i	1.06299	+	0.613716i	0.136730	+	0.990608i	$0.456341\pi$
$6$		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	$-0.111523\pi$
$11$	2523.72	+	4371.21i	0.172374	+	0.298560i	−0.766876	+	0.641796i	$0.778190\pi$
$12$		0			0
$13$			28279.2i			0.990133i	0.868855	+	0.495066i	$0.164856\pi$
$13$			28279.2i			0.990133i	−0.868855	+	0.495066i	$0.835144\pi$
$14$	−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	$-0.696459\pi$
$17$	−13520.1	+	7805.85i	−0.161877	+	0.0934598i	0.416873	+	0.908965i	$0.363126\pi$
$18$		0			0
$19$	107562.	+	62100.9i	0.825361	+	0.476522i	0.852262	−	0.523116i	$-0.175230\pi$
$19$	107562.	+	62100.9i	0.825361	+	0.476522i	−0.0269006	+	0.999638i	$0.508564\pi$
$20$		−	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	$-0.729362\pi$
$23$	89789.7	−	155520.i	0.320860	−	0.555745i	0.980666	+	0.195691i	$0.0626949\pi$
$24$		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	$-0.483981\pi$
$29$	71160.2			0.100611			0.0503055	+	0.998734i	$0.483981\pi$
$30$		0			0
$31$	845366.	−	488072.i	0.915372	−	0.528490i	0.0332165	−	0.999448i	$-0.489425\pi$
$31$	845366.	−	488072.i	0.915372	−	0.528490i	0.882156	+	0.470958i	$0.156092\pi$
$32$	−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	−0.614714	−	0.788750i	$-0.710729\pi$
$37$	704161.	−	1.21964e6i	0.375720	−	0.650767i	0.990435	+	0.137983i	$0.0440620\pi$
$38$	−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	$-0.330811\pi$
$47$	66978.0	+	38669.8i	0.0137259	+	0.00792465i	−0.493121	+	0.869961i	$0.664144\pi$
$48$		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	$-0.294999\pi$
$53$	−3.09571e6	−	5.36192e6i	−0.392334	−	0.679543i	−0.992757	+	0.120140i	$0.961666\pi$
$54$		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	$-0.874969\pi$
$59$	−1.27750e7	+	7.37564e6i	−1.05427	+	0.608684i	−0.130429	+	0.991458i	$0.541636\pi$
$60$		0			0
$61$	−2.14523e6	−	1.23855e6i	−0.154937	−	0.0894529i	0.420527	−	0.907280i	$-0.361845\pi$
$61$	−2.14523e6	−	1.23855e6i	−0.154937	−	0.0894529i	−0.575464	+	0.817827i	$0.695179\pi$
$62$			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	0.818045	−	0.575155i	$-0.195058\pi$
$67$	−1.79499e6	−	3.10901e6i	−0.0890763	−	0.154285i	−0.907121	+	0.420870i	$0.861725\pi$
$68$	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	$-0.743388\pi$
$71$	−3.51834e7			−1.38454			−0.692268	+	0.721641i	$0.743388\pi$
$72$		0			0
$73$	333640.	−	192627.i	0.0117486	−	0.00678307i	−0.494114	−	0.869397i	$-0.664508\pi$
$73$	333640.	−	192627.i	0.0117486	−	0.00678307i	0.505863	+	0.862614i	$0.331174\pi$
$74$	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	−0.565599	−	0.824680i	$-0.691355\pi$
$79$	1.68028e7	−	2.91034e7i	0.431394	−	0.747197i	0.996994	+	0.0774833i	$0.0246885\pi$
$80$	−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	$-0.469596\pi$
$89$	−4.51130e7	−	2.60460e7i	−0.719021	−	0.415127i	−0.814392	+	0.580315i	$0.802930\pi$
$90$		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	$0.304380\pi$
$97$			1.44662e8i			1.63406i	−0.576598	+	0.817028i	$0.695620\pi$
$98$	−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	$-0.815548\pi$
$101$	−8.12614e7	+	4.69163e7i	−0.780906	+	0.450857i	0.0558450	+	0.998439i	$0.482215\pi$
$102$		0			0
$103$	−1.52669e8	−	8.81435e7i	−1.35645	−	0.783144i	−0.367302	−	0.930102i	$-0.619719\pi$
$103$	−1.52669e8	−	8.81435e7i	−1.35645	−	0.783144i	−0.989143	+	0.146958i	$0.953052\pi$
$104$			4.09526e7i			0.350065i
$105$		0			0
$106$	7.00478e7			0.554844
$107$	−8.92457e7	+	1.54578e8i	−0.680851	+	1.17927i	0.293870	+	0.955845i	$0.405057\pi$
$107$	−8.92457e7	+	1.54578e8i	−0.680851	+	1.17927i	−0.974721	+	0.223424i	$0.928277\pi$
$108$		0			0
$109$	1.18770e8	+	2.05716e8i	0.841400	+	1.45735i	0.888712	+	0.458467i	$0.151601\pi$
$109$	1.18770e8	+	2.05716e8i	0.841400	+	1.45735i	−0.0473118	+	0.998880i	$0.515065\pi$
$110$	−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	$-0.264675\pi$
$113$	2.19712e8			1.34753			0.673766	+	0.738945i	$0.264675\pi$
$114$		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	$-0.321452\pi$
$131$	1.90353e7	+	1.09900e7i	0.0646360	+	0.0373176i	−0.467334	+	0.884081i	$0.654785\pi$
$132$		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	−0.864135	−	0.503259i	$-0.832134\pi$
$137$	−3.05741e8	−	5.29559e8i	−0.867903	−	1.50325i	−0.00376775	−	0.999993i	$-0.501199\pi$
$138$		0			0
$139$			1.49082e8i			0.399360i	0.979861	+	0.199680i	$0.0639903\pi$
$139$			1.49082e8i			0.399360i	−0.979861	+	0.199680i	$0.936010\pi$
$140$	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	−0.254644	−	0.967035i	$-0.581958\pi$
$149$	3.50024e8	−	6.06260e8i	0.710155	−	1.23002i	0.964799	−	0.262990i	$-0.0847085\pi$
$150$		0			0
$151$	4.86258e8	+	8.42224e8i	0.935318	+	1.62002i	0.774066	+	0.633105i	$0.218220\pi$
$151$	4.86258e8	+	8.42224e8i	0.935318	+	1.62002i	0.161252	+	0.986913i	$0.448447\pi$
$152$	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	−0.512743	−	0.858542i	$-0.671371\pi$
$157$	−1.55513e7	+	8.97854e6i	−0.0255957	+	0.0147777i	0.487148	+	0.873320i	$0.338037\pi$
$158$	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	0.348192	+	0.937423i	$0.386796\pi$
$163$	−4.50185e8	+	7.79744e8i	−0.637736	+	1.10459i	−0.985928	+	0.167168i	$0.946538\pi$
$164$	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	$-0.381590\pi$
$173$	−2.34309e8	−	1.35278e8i	−0.261580	−	0.151023i	−0.625055	+	0.780581i	$0.714924\pi$
$174$		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	$-0.308015\pi$
$179$	−4.41046e8	−	7.63914e8i	−0.429608	−	0.744102i	−0.996838	+	0.0794568i	$0.974681\pi$
$180$		0			0
$181$		−	4.95902e8i		−	0.462042i	−0.972949	−	0.231021i	$-0.925793\pi$
$181$		−	4.95902e8i		−	0.462042i	0.972949	−	0.231021i	$-0.0742067\pi$
$182$	−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	−0.400184	−	0.916435i	$-0.631054\pi$
$191$	7.89952e8	−	1.36824e9i	0.593564	−	1.02808i	0.993748	−	0.111648i	$-0.0356129\pi$
$192$		0			0
$193$	−8.26070e8	−	1.43079e9i	−0.595371	−	1.03121i	−0.993494	−	0.113881i	$-0.963672\pi$
$193$	−8.26070e8	−	1.43079e9i	−0.595371	−	1.03121i	0.398124	−	0.917332i	$-0.369661\pi$
$194$	−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	$-0.442524\pi$
$197$	5.40965e8			0.359174			0.179587	+	0.983742i	$0.442524\pi$
$198$		0			0
$199$	−1.18428e8	+	6.83742e7i	−0.0755163	+	0.0435994i	−0.537283	−	0.843402i	$-0.680549\pi$
$199$	−1.18428e8	+	6.83742e7i	−0.0755163	+	0.0435994i	0.461766	+	0.887002i	$0.347216\pi$
$200$	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	$0.0598540\pi$
$223$			9.24549e8i			0.373861i	−0.982373	+	0.186931i	$0.940146\pi$
$224$	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	$-0.896859\pi$
$227$	−3.04346e9	+	1.75714e9i	−1.14621	+	0.661765i	−0.198249	+	0.980152i	$0.563526\pi$
$228$		0			0
$229$	2.54322e9	+	1.46833e9i	0.924789	+	0.533927i	0.885160	−	0.465288i	$-0.154049\pi$
$229$	2.54322e9	+	1.46833e9i	0.924789	+	0.533927i	0.0396290	+	0.999214i	$0.487382\pi$
$230$			1.55861e9i			0.556964i
$231$		0			0
$232$	1.03051e8			0.0355714
$233$	−1.94715e9	+	3.37256e9i	−0.660657	+	1.14429i	0.319787	+	0.947490i	$0.396389\pi$
$233$	−1.94715e9	+	3.37256e9i	−0.660657	+	1.14429i	−0.980443	+	0.196801i	$0.936945\pi$
$234$		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	$-0.510610\pi$
$239$	−2.17474e8			−0.0666525			−0.0333262	+	0.999445i	$0.510610\pi$
$240$		0			0
$241$	2.28371e9	−	1.31850e9i	0.676977	−	0.390853i	−0.121738	−	0.992562i	$-0.538847\pi$
$241$	2.28371e9	−	1.31850e9i	0.676977	−	0.390853i	0.798715	+	0.601710i	$0.205514\pi$
$242$	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	$-0.294023\pi$
$257$	9.30785e8	+	5.37389e8i	0.213362	+	0.123185i	−0.389511	+	0.921022i	$0.627356\pi$
$258$		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	−0.998608	−	0.0527463i	$-0.983203\pi$
$263$	−2.60739e9	−	4.51614e9i	−0.544984	−	0.943939i	0.453624	−	0.891193i	$-0.350131\pi$
$264$		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	$-0.912254\pi$
$269$	−6.32340e9	+	3.65082e9i	−1.20765	+	0.697237i	−0.245405	+	0.969421i	$0.578921\pi$
$270$		0			0
$271$	−5.76676e9	−	3.32944e9i	−1.06919	−	0.617296i	−0.141229	−	0.989977i	$-0.545105\pi$
$271$	−5.76676e9	−	3.32944e9i	−1.06919	−	0.617296i	−0.927960	+	0.372681i	$0.878439\pi$
$272$		−	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	−0.992469	−	0.122499i	$-0.960909\pi$
$277$	−3.54607e9	−	6.14198e9i	−0.602322	−	1.04325i	0.390147	−	0.920753i	$-0.372424\pi$
$278$	−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	$-0.467590\pi$
$281$	1.26746e9			0.203287			0.101643	+	0.994821i	$0.467590\pi$
$282$		0			0
$283$	7.86397e9	−	4.54027e9i	1.22602	−	0.707841i	0.259822	−	0.965656i	$-0.416336\pi$
$283$	7.86397e9	−	4.54027e9i	1.22602	−	0.707841i	0.966194	+	0.257816i	$0.0830027\pi$
$284$	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	$-0.950104\pi$
$307$		−	2.77342e9i		−	0.312221i	0.987740	−	0.156110i	$-0.0498956\pi$
$308$	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	$-0.369020\pi$
$311$	1.30379e10	−	7.52746e9i	1.39369	−	0.804650i	0.993722	+	0.111877i	$0.0356863\pi$
$312$		0			0
$313$	−1.14520e10	−	6.61182e9i	−1.19318	−	0.688880i	−0.234150	−	0.972200i	$-0.575231\pi$
$313$	−1.14520e10	−	6.61182e9i	−1.19318	−	0.688880i	−0.959025	+	0.283320i	$0.908564\pi$
$314$		−	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	$-0.786587\pi$
$317$	1.47764e9	−	2.55935e9i	0.146329	−	0.253450i	0.929868	+	0.367893i	$0.119921\pi$
$318$		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	−0.659115	−	0.752042i	$-0.729069\pi$
$331$	3.86192e9	−	6.68905e9i	0.321730	−	0.557253i	0.980845	+	0.194789i	$0.0624023\pi$
$332$	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	$-0.260443\pi$
$347$	−4.20981e9	−	7.29161e9i	−0.290365	−	0.502927i	−0.973896	+	0.226994i	$0.927110\pi$
$348$		0			0
$349$		−	1.69363e10i		−	1.14161i	−0.821087	−	0.570803i	$-0.806632\pi$
$349$		−	1.69363e10i		−	1.14161i	0.821087	−	0.570803i	$-0.193368\pi$
$350$	−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	0.647491	−	0.762073i	$-0.275818\pi$
$353$	2.53285e10	−	1.46234e10i	1.63121	−	0.941780i	0.983720	−	0.179707i	$-0.0575150\pi$
$354$		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	$-0.882536\pi$
$359$	−2.55730e9	+	4.42937e9i	−0.153959	+	0.266664i	0.778721	+	0.627371i	$0.215869\pi$
$360$		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	−0.271820	−	0.962348i	$-0.587625\pi$
$367$	7.72247e9	−	4.45857e9i	0.425688	−	0.245771i	0.697508	+	0.716577i	$0.254292\pi$
$368$	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	0.0209000	−	0.999782i	$-0.493347\pi$
$373$	1.69622e10	−	2.93793e10i	0.876286	−	1.51777i	0.855386	−	0.517991i	$-0.173320\pi$
$374$	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	$-0.338544\pi$
$383$	−6.10111e8	−	3.52248e8i	−0.0283540	−	0.0163702i	−0.514110	+	0.857724i	$0.671878\pi$
$384$		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	−0.828616	−	0.559817i	$-0.810871\pi$
$389$	−2.05882e10	−	3.56598e10i	−0.899124	−	1.55733i	−0.0705080	−	0.997511i	$-0.522462\pi$
$390$		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	0.344672	−	0.938723i	$-0.387990\pi$
$397$	−7.35159e9	−	4.24444e9i	−0.295951	−	0.170867i	−0.640622	+	0.767856i	$0.721324\pi$
$398$		−	1.54713e9i		−	0.0616588i
$399$		0			0
$400$	−3.24216e9			−0.126647
$401$	1.67749e10	−	2.90550e10i	0.648757	−	1.12368i	−0.334663	−	0.942338i	$-0.608622\pi$
$401$	1.67749e10	−	2.90550e10i	0.648757	−	1.12368i	0.983420	−	0.181342i	$-0.0580442\pi$
$402$		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	−0.107117	−	0.994246i	$-0.534162\pi$
$409$	1.95983e10	−	1.13151e10i	0.700367	−	0.404357i	0.807484	+	0.589890i	$0.200829\pi$
$410$	−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	$-0.172764\pi$
$431$	−6.60998e8	−	1.14488e9i	−0.0191554	−	0.0331781i	−0.875444	+	0.483319i	$0.839431\pi$
$432$		0			0
$433$		−	1.53701e9i		−	0.0437246i	−0.999761	−	0.0218623i	$-0.993040\pi$
$433$		−	1.53701e9i		−	0.0437246i	0.999761	−	0.0218623i	$-0.00695954\pi$
$434$	−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	0.851040	−	0.525101i	$-0.175972\pi$
$439$	3.05231e10	+	1.76225e10i	0.821809	+	0.474472i	−0.0292309	+	0.999573i	$0.509306\pi$
$440$			5.60743e9i			0.149607i
$441$		0			0
$442$	4.99485e9			0.130868
$443$	−3.28022e10	+	5.68150e10i	−0.851702	+	1.47519i	0.0279697	+	0.999609i	$0.491096\pi$
$443$	−3.28022e10	+	5.68150e10i	−0.851702	+	1.47519i	−0.879671	+	0.475582i	$0.842238\pi$
$444$		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	$-0.262441\pi$
$449$	5.51880e10			1.35787			0.678937	+	0.734196i	$0.262441\pi$
$450$		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	−0.519305	−	0.854589i	$-0.673809\pi$
$457$	2.09559e10	−	3.62968e10i	0.480444	−	0.832153i	0.999748	+	0.0224363i	$0.00714231\pi$
$458$	−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	$-0.110381\pi$
$467$	5.30982e10	+	3.06562e10i	1.11638	+	0.644542i	0.175906	+	0.984407i	$0.443715\pi$
$468$		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	$-0.557703\pi$
$479$	3.06068e10	−	1.76709e10i	0.581402	−	0.335672i	0.761690	+	0.647941i	$0.224370\pi$
$480$		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	0.964083	−	0.265600i	$-0.0855700\pi$
$487$	1.41762e10	+	2.45539e10i	0.252026	+	0.436521i	−0.712058	+	0.702121i	$0.752237\pi$
$488$	−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	$-0.643671\pi$
$491$	−5.07023e10			−0.872372			−0.436186	+	0.899857i	$0.643671\pi$
$492$		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	−0.999998	−	0.00189664i	$-0.999396\pi$
$499$	−3.08989e10	+	5.35184e10i	−0.498357	+	0.863179i	0.501642	+	0.865076i	$0.332730\pi$
$500$	−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	$-0.453940\pi$
$509$	−4.30042e10	−	2.48285e10i	−0.640677	−	0.369895i	−0.784875	+	0.619654i	$0.787273\pi$
$510$		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	$-0.418425\pi$
$521$	8.97396e10	−	5.18112e10i	1.21796	−	0.703190i	0.964481	+	0.264151i	$0.0850918\pi$
$522$		0			0
$523$	1.08458e11	+	6.26180e10i	1.44962	+	0.836936i	0.998458	−	0.0555075i	$-0.0176777\pi$
$523$	1.08458e11	+	6.26180e10i	1.44962	+	0.836936i	0.451158	+	0.892444i	$0.351011\pi$
$524$		−	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	−0.713534	−	0.700620i	$-0.752907\pi$
$541$	2.14145e10	−	3.70910e10i	0.249988	−	0.432992i	0.963522	+	0.267629i	$0.0862401\pi$
$542$	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	$-0.144771\pi$
$557$	6.61578e9	+	1.14589e10i	0.0687322	+	0.119048i	−0.829611	+	0.558341i	$0.811438\pi$
$558$		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	$-0.448997\pi$
$563$	1.09939e11	−	6.34731e10i	1.09425	−	0.631765i	0.934705	+	0.355425i	$0.115664\pi$
$564$		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	$-0.714976\pi$
$569$	3.80836e10	−	6.59628e10i	0.363320	−	0.629289i	0.988505	+	0.151188i	$0.0483098\pi$
$570$		0			0
$571$	−1.57055e10	−	2.72028e10i	−0.147743	−	0.255899i	0.782650	−	0.622462i	$-0.213868\pi$
$571$	−1.57055e10	−	2.72028e10i	−0.147743	−	0.255899i	−0.930393	+	0.366563i	$0.880534\pi$
$572$	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	0.163885	−	0.986479i	$-0.447597\pi$
$577$	1.21942e11	−	7.04032e10i	1.10014	−	0.635168i	0.936259	+	0.351311i	$0.114264\pi$
$578$	−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	$-0.187135\pi$
$593$	9.49497e10	+	5.48192e10i	0.767847	+	0.443317i	−0.0642590	+	0.997933i	$0.520468\pi$
$594$		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	−0.939469	−	0.342634i	$-0.888681\pi$
$599$	−9.86732e10	−	1.70907e11i	−0.766464	−	1.32755i	0.173005	−	0.984921i	$-0.444652\pi$
$600$		0			0
$601$		−	6.14321e10i		−	0.470866i	−0.971891	−	0.235433i	$-0.924349\pi$
$601$		−	6.14321e10i		−	0.470866i	0.971891	−	0.235433i	$-0.0756508\pi$
$602$	−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	0.748628	−	0.662990i	$-0.230713\pi$
$607$	7.44988e10	+	4.30119e10i	0.548775	+	0.316836i	−0.199853	+	0.979826i	$0.564046\pi$
$608$		−	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	0.979403	−	0.201914i	$-0.0647160\pi$
$613$	4.44561e10	+	7.70002e10i	0.314839	+	0.545318i	−0.664564	+	0.747231i	$0.731383\pi$
$614$	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	$-0.0990539\pi$
$617$	2.75927e11			1.90394			0.951971	+	0.306189i	$0.0990539\pi$
$618$		0			0
$619$	−1.88747e11	+	1.08973e11i	−1.28564	+	0.742262i	−0.977873	−	0.209201i	$-0.932914\pi$
$619$	−1.88747e11	+	1.08973e11i	−1.28564	+	0.742262i	−0.307763	+	0.951463i	$0.599580\pi$
$620$	−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	−0.668976	−	0.743284i	$-0.733267\pi$
$641$	−1.65141e11	−	2.86033e11i	−0.978191	−	1.69428i	−0.309215	−	0.950992i	$-0.600066\pi$
$642$		0			0
$643$			1.72066e11i			1.00659i	0.864116	+	0.503293i	$0.167878\pi$
$643$			1.72066e11i			1.00659i	−0.864116	+	0.503293i	$0.832122\pi$
$644$	−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	$-0.466424\pi$
$647$	1.78588e11	−	1.03108e11i	1.01914	−	0.588402i	0.913856	+	0.406039i	$0.133090\pi$
$648$		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	$-0.792829\pi$
$653$	2.30745e10	−	3.99662e10i	0.126905	−	0.219806i	0.922476	+	0.386054i	$0.126162\pi$
$654$		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	$-0.485936\pi$
$659$	1.66601e10			0.0883357			0.0441679	+	0.999024i	$0.485936\pi$
$660$		0			0
$661$	−8.05750e9	+	4.65200e9i	−0.0422080	+	0.0243688i	−0.520956	−	0.853584i	$-0.674424\pi$
$661$	−8.05750e9	+	4.65200e9i	−0.0422080	+	0.0243688i	0.478748	+	0.877953i	$0.341091\pi$
$662$	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	$-0.395055\pi$
$677$	−7.01094e10	−	4.04777e10i	−0.333750	−	0.192691i	−0.657505	+	0.753450i	$0.728388\pi$
$678$		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	$-0.319367\pi$
$683$	−1.00435e11	−	1.73959e11i	−0.461534	−	0.799400i	−0.999038	+	0.0438612i	$0.986034\pi$
$684$		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	−0.252400	−	0.967623i	$-0.581220\pi$
$691$	−2.77367e11	−	1.60138e11i	−1.21659	−	0.702397i	−0.964186	+	0.265226i	$0.914553\pi$
$692$			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	$-0.462637\pi$
$701$	5.65576e10			0.234217			0.117109	+	0.993119i	$0.462637\pi$
$702$		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	−0.359323	−	0.933213i	$-0.616992\pi$
$709$	1.58821e11	−	2.75086e11i	0.628525	−	1.08864i	0.987848	−	0.155423i	$-0.0496742\pi$
$710$	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	$-0.144648\pi$
$719$	2.58599e11	+	1.49302e11i	0.967633	+	0.558663i	0.0691194	+	0.997608i	$0.477981\pi$
$720$		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	$0.0122957\pi$
$727$			2.15756e10i			0.0772371i	−0.999254	+	0.0386185i	$0.987704\pi$
$728$	−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	0.481904	−	0.876224i	$-0.339945\pi$
$733$	−1.03855e10	−	5.99605e9i	−0.0359758	−	0.0207706i	−0.517880	+	0.855453i	$0.673279\pi$
$734$			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	0.974429	+	0.224698i	$0.0721394\pi$
$739$	2.03348e11	+	3.52209e11i	0.681808	+	1.18093i	−0.292620	+	0.956229i	$0.594527\pi$
$740$	−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	$-0.569513\pi$
$743$	−1.32051e11			−0.433299			−0.216650	+	0.976249i	$0.569513\pi$
$744$		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	−0.837560	−	0.546345i	$-0.816019\pi$
$751$	1.72943e10	−	2.99547e10i	0.0543681	−	0.0941683i	0.891929	+	0.452176i	$0.149352\pi$
$752$	−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	$-0.438749\pi$
$761$	−1.88879e11	−	1.09050e11i	−0.563179	−	0.325151i	−0.754420	+	0.656392i	$0.772082\pi$
$762$		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	$-0.914473\pi$
$769$		−	1.85675e11i		−	0.530942i	0.964119	−	0.265471i	$-0.0855275\pi$
$770$	−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	$-0.700440\pi$
$773$	−6.54917e10	+	3.78116e10i	−0.183429	+	0.105903i	0.405474	+	0.914107i	$0.367107\pi$
$774$		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	−0.981292	−	0.192524i	$-0.938333\pi$
$787$	−5.00701e11	+	2.89080e11i	−1.30521	+	0.753562i	−0.323915	+	0.946086i	$0.604999\pi$
$788$	−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	$-0.0736406\pi$
$809$	1.23410e11	+	2.13752e11i	0.288108	+	0.499017i	−0.685250	+	0.728308i	$0.740307\pi$
$810$		0			0
$811$		−	3.79882e11i		−	0.878143i	−0.898452	−	0.439071i	$-0.855307\pi$
$811$		−	3.79882e11i		−	0.878143i	0.898452	−	0.439071i	$-0.144693\pi$
$812$	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	−0.0589976	−	0.998258i	$-0.518790\pi$
$821$	3.79375e11	−	6.57097e11i	0.835018	−	1.44629i	0.894016	−	0.448036i	$-0.147876\pi$
$822$		0			0
$823$	−3.26699e11	−	5.65860e11i	−0.712113	−	1.23342i	−0.964063	−	0.265675i	$-0.914405\pi$
$823$	−3.26699e11	−	5.65860e11i	−0.712113	−	1.23342i	0.251950	−	0.967740i	$-0.418928\pi$
$824$	−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	$-0.448642\pi$
$827$	1.50289e11			0.321296			0.160648	+	0.987012i	$0.448642\pi$
$828$		0			0
$829$	5.29912e11	−	3.05945e11i	1.12198	−	0.647776i	0.180075	−	0.983653i	$-0.442366\pi$
$829$	5.29912e11	−	3.05945e11i	1.12198	−	0.647776i	0.941906	+	0.335877i	$0.109033\pi$
$830$	−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	$-0.884647\pi$
$853$		−	3.75369e11i		−	0.709026i	0.935051	−	0.354513i	$-0.115353\pi$
$854$	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	$-0.739731\pi$
$857$	−2.12580e11	+	1.22733e11i	−0.394093	+	0.227530i	0.289839	+	0.957075i	$0.406398\pi$
$858$		0			0
$859$	−1.67139e11	−	9.64979e10i	−0.306977	−	0.177233i	0.338596	−	0.940932i	$-0.390048\pi$
$859$	−1.67139e11	−	9.64979e10i	−0.306977	−	0.177233i	−0.645573	+	0.763699i	$0.723381\pi$
$860$		−	2.17620e11i		−	0.397837i
$861$		0			0
$862$	1.49567e10			0.0270898
$863$	−3.98230e11	+	6.89754e11i	−0.717944	+	1.24352i	0.243869	+	0.969808i	$0.421583\pi$
$863$	−3.98230e11	+	6.89754e11i	−0.717944	+	1.24352i	−0.961813	+	0.273707i	$0.911750\pi$
$864$		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	0.308776	+	0.951135i	$0.400081\pi$
$877$	−3.95942e11	+	6.85792e11i	−0.669319	+	1.15929i	−0.978095	+	0.208160i	$0.933253\pi$
$878$	−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	$-0.169472\pi$
$887$	5.27870e11	+	3.04766e11i	0.852771	+	0.492347i	−0.00881401	+	0.999961i	$0.502806\pi$
$888$		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	0.976396	−	0.215988i	$-0.0692973\pi$
$907$	2.03801e11	+	3.52994e11i	0.301147	+	0.521601i	−0.675249	+	0.737590i	$0.735964\pi$
$908$	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	$-0.447159\pi$
$911$	2.27629e11			0.330487			0.165243	+	0.986253i	$0.447159\pi$
$912$		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	−0.0403516	+	0.999186i	$0.512848\pi$
$919$	−6.31609e11	+	1.09398e12i	−0.885496	+	1.53372i	−0.845144	+	0.534538i	$0.820486\pi$
$920$	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	−0.976778	−	0.214253i	$-0.931268\pi$
$929$	−1.22952e12	−	7.09863e11i	−1.65072	−	0.953041i	−0.673938	−	0.738788i	$-0.735398\pi$
$930$		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	$0.0848661\pi$
$937$			4.06177e11i			0.526935i	−0.964668	+	0.263467i	$0.915134\pi$
$938$	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	$-0.450097\pi$
$941$	8.54334e11	−	4.93250e11i	1.08961	−	0.629084i	0.933471	+	0.358652i	$0.116764\pi$
$942$		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	$-0.752289\pi$
$947$	2.02568e11	−	3.50858e11i	0.251867	−	0.436246i	0.964040	+	0.265758i	$0.0856222\pi$
$948$		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	$-0.498341\pi$
$953$	8.59856e9			0.0104245			0.00521224	+	0.999986i	$0.498341\pi$
$954$		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	$-0.461930\pi$
$971$	−6.05255e11	−	3.49444e11i	−0.680866	−	0.393098i	−0.800181	+	0.599758i	$0.795263\pi$
$972$		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	0.726704	+	0.686951i	$0.241051\pi$
$977$	8.73103e11	+	1.51226e12i	0.958269	+	1.65977i	0.231565	+	0.972819i	$0.425615\pi$
$978$		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	$-0.569450\pi$
$983$	4.86285e11	−	2.80757e11i	0.520807	−	0.300688i	0.737265	+	0.675604i	$0.236117\pi$
$984$		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	0.997561	−	0.0697966i	$-0.0222350\pi$
$991$	4.22767e11	+	7.32253e11i	0.438335	+	0.759218i	−0.559226	+	0.829015i	$0.688902\pi$
$992$	−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	0.00144368	−	0.999999i	$-0.499540\pi$
$997$	8.57819e11	−	4.95262e11i	0.868190	−	0.501250i	0.866746	+	0.498749i	$0.166207\pi$
$998$	−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.19.4	✓	20
3.2	odd	2	inner	126.9.n.d.19.7	yes	20
7.3	odd	6	inner	126.9.n.d.73.4	yes	20
21.17	even	6	inner	126.9.n.d.73.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.n.d.19.4	✓	20	1.1	even	1	trivial
126.9.n.d.19.7	yes	20	3.2	odd	2	inner
126.9.n.d.73.4	yes	20	7.3	odd	6	inner
126.9.n.d.73.7	yes	20	21.17	even	6	inner

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

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Database

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