LMFDB - Embedded newform 126.9.n.d.19.8

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			19.8
Root			$4.08415 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.19
Dual form			126.9.n.d.73.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.65685 - 9.79796i) q^{2} +(-64.0000 - 110.851i) q^{4} +(254.021 + 146.659i) q^{5} +(-1180.12 - 2090.96i) q^{7} -1448.15 q^{8} +O(q^{10})$	\(q+(5.65685 - 9.79796i) q^{2} +(-64.0000 - 110.851i) q^{4} +(254.021 + 146.659i) q^{5} +(-1180.12 - 2090.96i) q^{7} -1448.15 q^{8} +(2873.92 - 1659.26i) q^{10} +(-9846.02 - 17053.8i) q^{11} +27364.3i q^{13} +(-27162.9 - 265.506i) q^{14} +(-8192.00 + 14189.0i) q^{16} +(41400.9 - 23902.8i) q^{17} +(72270.1 + 41725.2i) q^{19} -37544.8i q^{20} -222790. q^{22} +(-64660.1 + 111995. i) q^{23} +(-152295. - 263782. i) q^{25} +(268114. + 154796. i) q^{26} +(-156258. + 264639. i) q^{28} -710274. q^{29} +(-384515. + 222000. i) q^{31} +(92681.9 + 160530. i) q^{32} -540859. i q^{34} +(6883.50 - 704224. i) q^{35} +(176834. - 306285. i) q^{37} +(817643. - 472066. i) q^{38} +(-367862. - 212385. i) q^{40} +3.55628e6i q^{41} -6.52843e6 q^{43} +(-1.26029e6 + 2.18289e6i) q^{44} +(731546. + 1.26707e6i) q^{46} +(-965165. - 557238. i) q^{47} +(-2.97944e6 + 4.93517e6i) q^{49} -3.44603e6 q^{50} +(3.03337e6 - 1.75132e6i) q^{52} +(5.98041e6 + 1.03584e7i) q^{53} -5.77604e6i q^{55} +(1.70899e6 + 3.02804e6i) q^{56} +(-4.01792e6 + 6.95924e6i) q^{58} +(-1.01480e7 + 5.85894e6i) q^{59} +(1.13956e7 + 6.57926e6i) q^{61} +5.02328e6i q^{62} +2.09715e6 q^{64} +(-4.01323e6 + 6.95112e6i) q^{65} +(-7.88693e6 - 1.36606e7i) q^{67} +(-5.29931e6 - 3.05956e6i) q^{68} +(-6.86102e6 - 4.05114e6i) q^{70} -2.41198e7 q^{71} +(1.51799e7 - 8.76413e6i) q^{73} +(-2.00065e6 - 3.46522e6i) q^{74} -1.06816e7i q^{76} +(-2.40394e7 + 4.07132e7i) q^{77} +(3.57217e6 - 6.18718e6i) q^{79} +(-4.16188e6 + 2.40287e6i) q^{80} +(3.48443e7 + 2.01173e7i) q^{82} +6.34086e7i q^{83} +1.40223e7 q^{85} +(-3.69304e7 + 6.39653e7i) q^{86} +(1.42586e7 + 2.46965e7i) q^{88} +(7.67936e7 + 4.43368e7i) q^{89} +(5.72177e7 - 3.22931e7i) q^{91} +1.65530e7 q^{92} +(-1.09196e7 + 6.30443e6i) q^{94} +(1.22388e7 + 2.11982e7i) q^{95} +6.52152e7i q^{97} +(3.15003e7 + 5.71099e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	254.021	+	146.659i	0.406434	+	0.234655i	0.689256	−	0.724517i	$-0.257937\pi$
$5$	254.021	+	146.659i	0.406434	+	0.234655i	−0.282822	+	0.959172i	$0.591271\pi$
$6$		0			0
$7$	−1180.12	−	2090.96i	−0.491511	−	0.870871i
$7$	−1180.12	−	2090.96i	−0.491511	−	0.870871i
$8$	−1448.15			−0.353553
$9$		0			0
$10$	2873.92	−	1659.26i	0.287392	−	0.165926i
$11$	−9846.02	−	17053.8i	−0.672496	−	1.16480i	−0.977194	−	0.212348i	$-0.931889\pi$
$11$	−9846.02	−	17053.8i	−0.672496	−	1.16480i	0.304698	−	0.952449i	$-0.401445\pi$
$12$		0			0
$13$			27364.3i			0.958101i	0.877787	+	0.479050i	$0.159019\pi$
$13$			27364.3i			0.958101i	−0.877787	+	0.479050i	$0.840981\pi$
$14$	−27162.9	−	265.506i	−0.707073	−	0.00691135i
$15$		0			0
$16$	−8192.00	+	14189.0i	−0.125000	+	0.216506i
$17$	41400.9	−	23902.8i	0.495694	−	0.286189i	−0.231239	−	0.972897i	$-0.574278\pi$
$17$	41400.9	−	23902.8i	0.495694	−	0.286189i	0.726934	+	0.686708i	$0.240945\pi$
$18$		0			0
$19$	72270.1	+	41725.2i	0.554555	+	0.320172i	0.750957	−	0.660351i	$-0.229593\pi$
$19$	72270.1	+	41725.2i	0.554555	+	0.320172i	−0.196402	+	0.980523i	$0.562926\pi$
$20$		−	37544.8i		−	0.234655i
$21$		0			0
$22$	−222790.			−0.951053
$23$	−64660.1	+	111995.i	−0.231060	+	0.400208i	−0.958120	−	0.286366i	$-0.907553\pi$
$23$	−64660.1	+	111995.i	−0.231060	+	0.400208i	0.727060	+	0.686574i	$0.240886\pi$
$24$		0			0
$25$	−152295.	−	263782.i	−0.389874	−	0.675282i
$26$	268114.	+	154796.i	0.586714	+	0.338740i
$27$		0			0
$28$	−156258.	+	264639.i	−0.254220	+	0.430548i
$29$	−710274.			−1.00423			−0.502116	−	0.864800i	$-0.667445\pi$
$29$	−710274.			−1.00423			−0.502116	+	0.864800i	$0.667445\pi$
$30$		0			0
$31$	−384515.	+	222000.i	−0.416358	+	0.240384i	−0.693518	−	0.720440i	$-0.743940\pi$
$31$	−384515.	+	222000.i	−0.416358	+	0.240384i	0.277160	+	0.960824i	$0.410607\pi$
$32$	92681.9	+	160530.i	0.0883883	+	0.153093i
$33$		0			0
$34$		−	540859.i		−	0.404733i
$35$	6883.50	−	704224.i	0.00458709	−	0.469287i
$36$		0			0
$37$	176834.	−	306285.i	0.0943537	−	0.163425i	−0.814985	−	0.579482i	$-0.803255\pi$
$37$	176834.	−	306285.i	0.0943537	−	0.163425i	0.909339	+	0.416057i	$0.136588\pi$
$38$	817643.	−	472066.i	0.392129	−	0.226396i
$39$		0			0
$40$	−367862.	−	212385.i	−0.143696	−	0.0829630i
$41$			3.55628e6i			1.25852i	0.777195	+	0.629260i	$0.216642\pi$
$41$			3.55628e6i			1.25852i	−0.777195	+	0.629260i	$0.783358\pi$
$42$		0			0
$43$	−6.52843e6			−1.90957			−0.954784	−	0.297300i	$-0.903914\pi$
$43$	−6.52843e6			−1.90957			−0.954784	+	0.297300i	$0.903914\pi$
$44$	−1.26029e6	+	2.18289e6i	−0.336248	+	0.582399i
$45$		0			0
$46$	731546.	+	1.26707e6i	0.163384	+	0.282990i
$47$	−965165.	−	557238.i	−0.197793	−	0.114196i	0.397833	−	0.917458i	$-0.369762\pi$
$47$	−965165.	−	557238.i	−0.197793	−	0.114196i	−0.595625	+	0.803262i	$0.703096\pi$
$48$		0			0
$49$	−2.97944e6	+	4.93517e6i	−0.516833	+	0.856086i
$50$	−3.44603e6			−0.551365
$51$		0			0
$52$	3.03337e6	−	1.75132e6i	0.414870	−	0.239525i
$53$	5.98041e6	+	1.03584e7i	0.757927	+	1.31277i	0.943906	+	0.330215i	$0.107121\pi$
$53$	5.98041e6	+	1.03584e7i	0.757927	+	1.31277i	−0.185978	+	0.982554i	$0.559545\pi$
$54$		0			0
$55$		−	5.77604e6i		−	0.631218i
$56$	1.70899e6	+	3.02804e6i	0.173776	+	0.307899i
$57$		0			0
$58$	−4.01792e6	+	6.95924e6i	−0.355050	+	0.614964i
$59$	−1.01480e7	+	5.85894e6i	−0.837474	+	0.483516i	−0.856405	−	0.516305i	$-0.827307\pi$
$59$	−1.01480e7	+	5.85894e6i	−0.837474	+	0.483516i	0.0189306	+	0.999821i	$0.493974\pi$
$60$		0			0
$61$	1.13956e7	+	6.57926e6i	0.823035	+	0.475180i	0.851462	−	0.524416i	$-0.175716\pi$
$61$	1.13956e7	+	6.57926e6i	0.823035	+	0.475180i	−0.0284268	+	0.999596i	$0.509050\pi$
$62$			5.02328e6i			0.339955i
$63$		0			0
$64$	2.09715e6			0.125000
$65$	−4.01323e6	+	6.95112e6i	−0.224823	+	0.389405i
$66$		0			0
$67$	−7.88693e6	−	1.36606e7i	−0.391389	−	0.677906i	0.601244	−	0.799066i	$-0.294672\pi$
$67$	−7.88693e6	−	1.36606e7i	−0.391389	−	0.677906i	−0.992633	+	0.121160i	$0.961339\pi$
$68$	−5.29931e6	−	3.05956e6i	−0.247847	−	0.143095i
$69$		0			0
$70$	−6.86102e6	−	4.05114e6i	−0.285757	−	0.168727i
$71$	−2.41198e7			−0.949161			−0.474580	−	0.880212i	$-0.657400\pi$
$71$	−2.41198e7			−0.949161			−0.474580	+	0.880212i	$0.657400\pi$
$72$		0			0
$73$	1.51799e7	−	8.76413e6i	0.534537	−	0.308615i	−0.208325	−	0.978060i	$-0.566801\pi$
$73$	1.51799e7	−	8.76413e6i	0.534537	−	0.308615i	0.742862	+	0.669445i	$0.233468\pi$
$74$	−2.00065e6	−	3.46522e6i	−0.0667181	−	0.115559i
$75$		0			0
$76$		−	1.06816e7i		−	0.320172i
$77$	−2.40394e7	+	4.07132e7i	−0.683849	+	1.15817i
$78$		0			0
$79$	3.57217e6	−	6.18718e6i	0.0917115	−	0.158849i	−0.816520	−	0.577317i	$-0.804100\pi$
$79$	3.57217e6	−	6.18718e6i	0.0917115	−	0.158849i	0.908231	+	0.418468i	$0.137433\pi$
$80$	−4.16188e6	+	2.40287e6i	−0.101609	+	0.0586637i
$81$		0			0
$82$	3.48443e7	+	2.01173e7i	0.770683	+	0.444954i
$83$			6.34086e7i			1.33609i	0.744121	+	0.668045i	$0.232869\pi$
$83$			6.34086e7i			1.33609i	−0.744121	+	0.668045i	$0.767131\pi$
$84$		0			0
$85$	1.40223e7			0.268623
$86$	−3.69304e7	+	6.39653e7i	−0.675134	+	1.16937i
$87$		0			0
$88$	1.42586e7	+	2.46965e7i	0.237763	+	0.411818i
$89$	7.67936e7	+	4.43368e7i	1.22395	+	0.706650i	0.965758	−	0.259443i	$-0.0835391\pi$
$89$	7.67936e7	+	4.43368e7i	1.22395	+	0.706650i	0.258195	+	0.966093i	$0.416872\pi$
$90$		0			0
$91$	5.72177e7	−	3.22931e7i	0.834382	−	0.470917i
$92$	1.65530e7			0.231060
$93$		0			0
$94$	−1.09196e7	+	6.30443e6i	−0.139861	+	0.0807485i
$95$	1.22388e7	+	2.11982e7i	0.150260	+	0.260258i
$96$		0			0
$97$			6.52152e7i			0.736651i	0.929697	+	0.368325i	$0.120069\pi$
$97$			6.52152e7i			0.736651i	−0.929697	+	0.368325i	$0.879931\pi$
$98$	3.15003e7	+	5.71099e7i	0.341516	+	0.619166i
$99$		0			0
$100$	−1.94937e7	+	3.37641e7i	−0.194937	+	0.337641i
$101$	−1.53138e8	+	8.84145e7i	−1.47163	+	0.849646i	−0.999492	−	0.0318791i	$-0.989851\pi$
$101$	−1.53138e8	+	8.84145e7i	−1.47163	+	0.849646i	−0.472138	+	0.881525i	$0.656518\pi$
$102$		0			0
$103$	−9.89388e7	−	5.71223e7i	−0.879059	−	0.507525i	−0.00871065	−	0.999962i	$-0.502773\pi$
$103$	−9.89388e7	−	5.71223e7i	−0.879059	−	0.507525i	−0.870348	+	0.492437i	$0.836106\pi$
$104$		−	3.96278e7i		−	0.338740i
$105$		0			0
$106$	1.35321e8			1.07187
$107$	−7.14037e6	+	1.23675e7i	−0.0544736	+	0.0943510i	−0.891976	−	0.452082i	$-0.850681\pi$
$107$	−7.14037e6	+	1.23675e7i	−0.0544736	+	0.0943510i	0.837503	+	0.546433i	$0.184015\pi$
$108$		0			0
$109$	−1.01815e8	−	1.76349e8i	−0.721283	−	1.24930i	−0.960486	−	0.278329i	$-0.910220\pi$
$109$	−1.01815e8	−	1.76349e8i	−0.721283	−	1.24930i	0.239203	−	0.970970i	$-0.423114\pi$
$110$	−5.65934e7	−	3.26742e7i	−0.386540	−	0.223169i
$111$		0			0
$112$	3.93361e7	+	384494.i	0.249988	+	0.00244353i
$113$	−8.03050e7			−0.492525			−0.246263	−	0.969203i	$-0.579203\pi$
$113$	−8.03050e7			−0.492525			−0.246263	+	0.969203i	$0.579203\pi$
$114$		0			0
$115$	−3.28501e7	+	1.89660e7i	−0.187822	+	0.108439i
$116$	4.54576e7	+	7.87348e7i	0.251058	+	0.434845i
$117$		0			0
$118$			1.32573e8i			0.683795i
$119$	−9.88378e7	−	5.83595e7i	−0.492873	−	0.291020i
$120$		0			0
$121$	−8.67086e7	+	1.50184e8i	−0.404502	+	0.700618i
$122$	1.28927e8	−	7.44358e7i	0.581974	−	0.336003i
$123$		0			0
$124$	4.92179e7	+	2.84160e7i	0.208179	+	0.120192i
$125$		−	2.03919e8i		−	0.835253i
$126$		0			0
$127$	−3.26436e8			−1.25483			−0.627413	−	0.778687i	$-0.715886\pi$
$127$	−3.26436e8			−1.25483			−0.627413	+	0.778687i	$0.715886\pi$
$128$	1.18633e7	−	2.05478e7i	0.0441942	−	0.0765466i
$129$		0			0
$130$	4.54045e7	+	7.86429e7i	0.158974	+	0.275351i
$131$	1.32553e8	+	7.65293e7i	0.450094	+	0.259862i	0.707870	−	0.706343i	$-0.249656\pi$
$131$	1.32553e8	+	7.65293e7i	0.450094	+	0.259862i	−0.257776	+	0.966205i	$0.582990\pi$
$132$		0			0
$133$	1.95839e6	−	2.00355e8i	0.00625881	−	0.640314i
$134$	−1.78461e8			−0.553508
$135$		0			0
$136$	−5.99549e7	+	3.46150e7i	−0.175254	+	0.101183i
$137$	6.64691e7	+	1.15128e8i	0.188685	+	0.326812i	0.944812	−	0.327613i	$-0.106244\pi$
$137$	6.64691e7	+	1.15128e8i	0.188685	+	0.326812i	−0.756127	+	0.654425i	$0.772911\pi$
$138$		0			0
$139$		−	5.38269e8i		−	1.44192i	−0.692978	−	0.720958i	$-0.743702\pi$
$139$		−	5.38269e8i		−	1.44192i	0.692978	−	0.720958i	$-0.256298\pi$
$140$	−7.85047e7	+	4.43073e7i	−0.204354	+	0.115336i
$141$		0			0
$142$	−1.36442e8	+	2.36325e8i	−0.335579	+	0.581240i
$143$	4.66666e8	−	2.69429e8i	1.11599	−	0.644319i
$144$		0			0
$145$	−1.80425e8	−	1.04168e8i	−0.408154	−	0.235648i
$146$		−	1.98310e8i		−	0.436448i
$147$		0			0
$148$	−4.52695e7			−0.0943537
$149$	2.76227e8	−	4.78439e8i	0.560429	−	0.970691i	−0.437030	−	0.899447i	$-0.643970\pi$
$149$	2.76227e8	−	4.78439e8i	0.560429	−	0.970691i	0.997459	−	0.0712445i	$-0.0226971\pi$
$150$		0			0
$151$	−2.57729e7	−	4.46400e7i	−0.0495742	−	0.0858650i	0.840173	−	0.542318i	$-0.182453\pi$
$151$	−2.57729e7	−	4.46400e7i	−0.0495742	−	0.0858650i	−0.889748	+	0.456453i	$0.849120\pi$
$152$	−1.04658e8	−	6.04245e7i	−0.196065	−	0.113198i
$153$		0			0
$154$	2.62919e8	+	4.65845e8i	0.467454	+	0.828245i
$155$	−1.30233e8			−0.225629
$156$		0			0
$157$	−1.43245e8	+	8.27027e7i	−0.235766	+	0.136120i	−0.613229	−	0.789905i	$-0.710130\pi$
$157$	−1.43245e8	+	8.27027e7i	−0.235766	+	0.136120i	0.377463	+	0.926025i	$0.376796\pi$
$158$	−4.04145e7	−	6.99999e7i	−0.0648498	−	0.112323i
$159$		0			0
$160$			5.43706e7i			0.0829630i
$161$	3.10483e8	+	3.03485e6i	0.462098	+	0.00451682i
$162$		0			0
$163$	6.57420e7	−	1.13868e8i	0.0931306	−	0.161307i	−0.815696	−	0.578480i	$-0.803646\pi$
$163$	6.57420e7	−	1.13868e8i	0.0931306	−	0.161307i	0.908827	+	0.417174i	$0.136979\pi$
$164$	3.94218e8	−	2.27602e8i	0.544955	−	0.314630i
$165$		0			0
$166$	6.21275e8	+	3.58693e8i	0.818184	+	0.472379i
$167$		−	1.02034e9i		−	1.31184i	−0.754832	−	0.655918i	$-0.772282\pi$
$167$		−	1.02034e9i		−	1.31184i	0.754832	−	0.655918i	$-0.227718\pi$
$168$		0			0
$169$	6.69250e7			0.0820430
$170$	7.93219e7	−	1.37390e8i	0.0949725	−	0.164497i
$171$		0			0
$172$	4.17820e8	+	7.23685e8i	0.477392	+	0.826867i
$173$	1.16632e8	+	6.73374e7i	0.130206	+	0.0751747i	0.563688	−	0.825988i	$-0.309382\pi$
$173$	1.16632e8	+	6.73374e7i	0.130206	+	0.0751747i	−0.433482	+	0.901162i	$0.642715\pi$
$174$		0			0
$175$	−3.71832e8	+	6.29736e8i	−0.396456	+	0.671439i
$176$	3.22634e8			0.336248
$177$		0			0
$178$	8.68820e8	−	5.01613e8i	0.865465	−	0.499677i
$179$	−6.71392e8	−	1.16289e9i	−0.653979	−	1.13273i	−0.982149	−	0.188107i	$-0.939765\pi$
$179$	−6.71392e8	−	1.16289e9i	−0.653979	−	1.13273i	0.328169	−	0.944619i	$-0.393568\pi$
$180$		0			0
$181$		−	1.66215e9i		−	1.54866i	−0.632784	−	0.774328i	$-0.718088\pi$
$181$		−	1.66215e9i		−	1.54866i	0.632784	−	0.774328i	$-0.281912\pi$
$182$	7.26540e6	−	7.43295e8i	0.00662177	−	0.677447i
$183$		0			0
$184$	9.36379e7	−	1.62186e8i	0.0816921	−	0.141495i
$185$	8.98392e7	−	5.18687e7i	0.0766971	−	0.0442811i
$186$		0			0
$187$	−8.15267e8	−	4.70695e8i	−0.666705	−	0.384922i
$188$			1.42653e8i			0.114196i
$189$		0			0
$190$	2.76932e8			0.212500
$191$	4.00858e8	−	6.94306e8i	0.301201	−	0.521696i	−0.675207	−	0.737628i	$-0.735946\pi$
$191$	4.00858e8	−	6.94306e8i	0.301201	−	0.521696i	0.976408	+	0.215932i	$0.0692790\pi$
$192$		0			0
$193$	−5.88128e8	−	1.01867e9i	−0.423879	−	0.734181i	0.572436	−	0.819950i	$-0.305999\pi$
$193$	−5.88128e8	−	1.01867e9i	−0.423879	−	0.734181i	−0.996315	+	0.0857690i	$0.972665\pi$
$194$	6.38976e8	+	3.68913e8i	0.451105	+	0.260445i
$195$		0			0
$196$	7.37754e8	+	1.44239e7i	0.499904	+	0.00977366i
$197$	3.83159e8			0.254398			0.127199	−	0.991877i	$-0.459401\pi$
$197$	3.83159e8			0.254398			0.127199	+	0.991877i	$0.459401\pi$
$198$		0			0
$199$	1.90479e9	−	1.09973e9i	1.21460	−	0.701252i	0.250846	−	0.968027i	$-0.419291\pi$
$199$	1.90479e9	−	1.09973e9i	1.21460	−	0.701252i	0.963759	+	0.266775i	$0.0859580\pi$
$200$	2.20546e8	+	3.81997e8i	0.137841	+	0.238748i
$201$		0			0
$202$			2.00059e9i			1.20158i
$203$	8.38208e8	+	1.48516e9i	0.493592	+	0.874557i
$204$		0			0
$205$	−5.21561e8	+	9.03370e8i	−0.295318	+	0.511506i
$206$	−1.11936e9	+	6.46266e8i	−0.621588	+	0.358874i
$207$		0			0
$208$	−3.88271e8	−	2.24168e8i	−0.207435	−	0.119763i
$209$		−	1.64331e9i		−	0.861258i
$210$		0			0
$211$	8.01623e8			0.404427			0.202213	−	0.979341i	$-0.435187\pi$
$211$	8.01623e8			0.404427			0.202213	+	0.979341i	$0.435187\pi$
$212$	7.65493e8	−	1.32587e9i	0.378964	−	0.656384i
$213$		0			0
$214$	8.07841e7	+	1.39922e8i	0.0385186	+	0.0667162i
$215$	−1.65836e9	−	9.57455e8i	−0.776114	−	0.448089i
$216$		0			0
$217$	9.17967e8	+	5.42020e8i	0.413988	+	0.244442i
$218$	−2.30381e9			−1.02005
$219$		0			0
$220$	−6.40281e8	+	3.69666e8i	−0.273325	+	0.157804i
$221$	6.54084e8	+	1.13291e9i	0.274198	+	0.474925i
$222$		0			0
$223$			1.04630e9i			0.423095i	0.977368	+	0.211548i	$0.0678503\pi$
$223$			1.04630e9i			0.423095i	−0.977368	+	0.211548i	$0.932150\pi$
$224$	2.26286e8	−	3.83239e8i	0.0898805	−	0.152222i
$225$		0			0
$226$	−4.54273e8	+	7.86825e8i	−0.174134	+	0.301609i
$227$	−1.84193e9	+	1.06344e9i	−0.693697	+	0.400506i	−0.804996	−	0.593281i	$-0.797832\pi$
$227$	−1.84193e9	+	1.06344e9i	−0.693697	+	0.400506i	0.111299	+	0.993787i	$0.464499\pi$
$228$		0			0
$229$	−4.04718e9	−	2.33664e9i	−1.47167	−	0.849670i	−0.472179	−	0.881503i	$-0.656532\pi$
$229$	−4.04718e9	−	2.33664e9i	−1.47167	−	0.849670i	−0.999493	+	0.0318328i	$0.989866\pi$
$230$			4.29152e8i			0.153356i
$231$		0			0
$232$	1.02859e9			0.355050
$233$	−1.30399e9	+	2.25857e9i	−0.442435	+	0.766320i	−0.997870	−	0.0652405i	$-0.979219\pi$
$233$	−1.30399e9	+	2.25857e9i	−0.442435	+	0.766320i	0.555435	+	0.831560i	$0.312552\pi$
$234$		0			0
$235$	−1.63448e8	−	2.83101e8i	−0.0535931	−	0.0928260i
$236$	1.29894e9	+	7.49944e8i	0.418737	+	0.241758i
$237$		0			0
$238$	−1.13091e9	+	6.38278e8i	−0.352470	+	0.198931i
$239$	2.50883e9			0.768917			0.384459	−	0.923142i	$-0.374388\pi$
$239$	2.50883e9			0.768917			0.384459	+	0.923142i	$0.374388\pi$
$240$		0			0
$241$	−1.39883e9	+	8.07613e8i	−0.414664	+	0.239406i	−0.692792	−	0.721138i	$-0.743619\pi$
$241$	−1.39883e9	+	8.07613e8i	−0.414664	+	0.239406i	0.278128	+	0.960544i	$0.410286\pi$
$242$	9.80996e8	+	1.69914e9i	0.286026	+	0.495412i
$243$		0			0
$244$		−	1.68429e9i		−	0.475180i
$245$	−1.48063e9	+	8.16675e8i	−0.410943	+	0.226665i
$246$		0			0
$247$	−1.14178e9	+	1.97762e9i	−0.306757	+	0.531319i
$248$	5.56837e8	−	3.21490e8i	0.147205	−	0.0849887i
$249$		0			0
$250$	−1.99799e9	−	1.15354e9i	−0.511486	−	0.295307i
$251$			7.67075e9i			1.93260i	0.257411	+	0.966302i	$0.417131\pi$
$251$			7.67075e9i			1.93260i	−0.257411	+	0.966302i	$0.582869\pi$
$252$		0			0
$253$	2.54658e9			0.621549
$254$	−1.84660e9	+	3.19841e9i	−0.443648	+	0.768421i
$255$		0			0
$256$	−1.34218e8	−	2.32472e8i	−0.0312500	−	0.0541266i
$257$	9.62997e7	+	5.55987e7i	0.0220746	+	0.0127448i	0.510997	−	0.859583i	$-0.329276\pi$
$257$	9.62997e7	+	5.55987e7i	0.0220746	+	0.0127448i	−0.488922	+	0.872327i	$0.662610\pi$
$258$		0			0
$259$	−8.49116e8	−	8.29976e6i	−0.188698	−	0.00184445i
$260$	1.02739e9			0.224823
$261$		0			0
$262$	1.49966e9	−	8.65830e8i	0.318264	−	0.183750i
$263$	1.92395e9	+	3.33238e9i	0.402135	+	0.696518i	0.993983	−	0.109532i	$-0.0349351\pi$
$263$	1.92395e9	+	3.33238e9i	0.402135	+	0.696518i	−0.591849	+	0.806049i	$0.701602\pi$
$264$		0			0
$265$			3.50833e9i			0.711405i
$266$	−1.95199e9	−	1.15257e9i	−0.389898	−	0.230218i
$267$		0			0
$268$	−1.00953e9	+	1.74855e9i	−0.195695	+	0.338953i
$269$	−3.56338e9	+	2.05732e9i	−0.680539	+	0.392909i	−0.800058	−	0.599922i	$-0.795198\pi$
$269$	−3.56338e9	+	2.05732e9i	−0.680539	+	0.392909i	0.119519	+	0.992832i	$0.461865\pi$
$270$		0			0
$271$	−5.46088e9	−	3.15284e9i	−1.01248	−	0.584554i	−0.100561	−	0.994931i	$-0.532064\pi$
$271$	−5.46088e9	−	3.15284e9i	−1.01248	−	0.584554i	−0.911916	+	0.410377i	$0.865397\pi$
$272$			7.83247e8i			0.143095i
$273$		0			0
$274$	1.50402e9			0.266841
$275$	−2.99899e9	+	5.19440e9i	−0.524378	+	0.908249i
$276$		0			0
$277$	8.46807e7	+	1.46671e8i	0.0143835	+	0.0249130i	0.873128	−	0.487492i	$-0.162088\pi$
$277$	8.46807e7	+	1.46671e8i	0.0143835	+	0.0249130i	−0.858744	+	0.512405i	$0.828755\pi$
$278$	−5.27394e9	−	3.04491e9i	−0.882990	−	0.509795i
$279$		0			0
$280$	−9.96838e6	+	1.01983e9i	−0.00162178	+	0.165918i
$281$	−4.27204e9			−0.685188			−0.342594	−	0.939484i	$-0.611306\pi$
$281$	−4.27204e9			−0.685188			−0.342594	+	0.939484i	$0.611306\pi$
$282$		0			0
$283$	7.97705e9	−	4.60555e9i	1.24364	−	0.718019i	0.273811	−	0.961784i	$-0.411716\pi$
$283$	7.97705e9	−	4.60555e9i	1.24364	−	0.718019i	0.969834	+	0.243765i	$0.0783825\pi$
$284$	1.54367e9	+	2.67371e9i	0.237290	+	0.410999i
$285$		0			0
$286$		−	6.09649e9i		−	0.911205i
$287$	7.43604e9	−	4.19683e9i	1.09601	−	0.618577i
$288$		0			0
$289$	−2.34519e9	+	4.06199e9i	−0.336191	+	0.582301i
$290$	−2.04127e9	+	1.17853e9i	−0.288609	+	0.166628i
$291$		0			0
$292$	−1.94303e9	−	1.12181e9i	−0.267269	−	0.154308i
$293$		−	6.22459e9i		−	0.844578i	−0.906461	−	0.422289i	$-0.861227\pi$
$293$		−	6.22459e9i		−	0.844578i	0.906461	−	0.422289i	$-0.138773\pi$
$294$		0			0
$295$	−3.43707e9			−0.453837
$296$	−2.56083e8	+	4.43549e8i	−0.0333591	+	0.0577796i
$297$		0			0
$298$	−3.12515e9	−	5.41292e9i	−0.396283	−	0.686383i
$299$	−3.06466e9	−	1.76938e9i	−0.383440	−	0.221379i
$300$		0			0
$301$	7.70433e9	+	1.36507e10i	0.938575	+	1.66299i
$302$	−5.83174e8			−0.0701085
$303$		0			0
$304$	−1.18407e9	+	6.83625e8i	−0.138639	+	0.0800431i
$305$	1.92982e9	+	3.34254e9i	0.223006	+	0.386258i
$306$		0			0
$307$		−	9.75323e9i		−	1.09798i	−0.835829	−	0.548991i	$-0.815012\pi$
$307$		−	9.75323e9i		−	1.09798i	0.835829	−	0.548991i	$-0.184988\pi$
$308$	6.05162e9	+	5.91522e7i	0.672464	+	0.00657306i
$309$		0			0
$310$	−7.36711e8	+	1.27602e9i	−0.0797720	+	0.138169i
$311$	−1.41768e10	+	8.18496e9i	−1.51543	+	0.874933i	−0.515592	+	0.856834i	$0.672428\pi$
$311$	−1.41768e10	+	8.18496e9i	−1.51543	+	0.874933i	−0.999836	+	0.0180989i	$0.994239\pi$
$312$		0			0
$313$	1.41041e10	+	8.14301e9i	1.46950	+	0.848414i	0.999415	−	0.0342090i	$-0.0108912\pi$
$313$	1.41041e10	+	8.14301e9i	1.46950	+	0.848414i	0.470081	+	0.882623i	$0.344225\pi$
$314$			1.87135e9i			0.192502i
$315$		0			0
$316$	−9.14475e8			−0.0917115
$317$	5.18198e9	−	8.97545e9i	0.513167	−	0.888831i	−0.486717	−	0.873560i	$-0.661806\pi$
$317$	5.18198e9	−	8.97545e9i	0.513167	−	0.888831i	0.999883	−	0.0152710i	$-0.00486110\pi$
$318$		0			0
$319$	6.99337e9	+	1.21129e10i	0.675342	+	1.16973i
$320$	5.32721e8	+	3.07567e8i	0.0508043	+	0.0293319i
$321$		0			0
$322$	1.78609e9	−	3.02493e9i	0.166142	−	0.281379i
$323$	3.98939e9			0.366519
$324$		0			0
$325$	7.21821e9	−	4.16744e9i	0.646988	−	0.373539i
$326$	−7.43785e8	−	1.28827e9i	−0.0658533	−	0.114061i
$327$		0			0
$328$		−	5.15004e9i		−	0.444954i
$329$	−2.61542e7	+	2.67573e9i	−0.00223233	+	0.228380i
$330$		0			0
$331$	−1.08132e9	+	1.87289e9i	−0.0900825	+	0.156027i	−0.907546	−	0.419953i	$-0.862046\pi$
$331$	−1.08132e9	+	1.87289e9i	−0.0900825	+	0.156027i	0.817463	+	0.575981i	$0.195380\pi$
$332$	7.02892e9	−	4.05815e9i	0.578544	−	0.334022i
$333$		0			0
$334$	−9.99726e9	−	5.77192e9i	−0.803332	−	0.463804i
$335$		−	4.62677e9i		−	0.367365i
$336$		0			0
$337$	1.73513e9			0.134528			0.0672640	−	0.997735i	$-0.478573\pi$
$337$	1.73513e9			0.134528			0.0672640	+	0.997735i	$0.478573\pi$
$338$	3.78585e8	−	6.55729e8i	0.0290066	−	0.0502409i
$339$		0			0
$340$	−8.97425e8	−	1.55439e9i	−0.0671557	−	0.116317i
$341$	7.57188e9	+	4.37163e9i	0.559998	+	0.323315i
$342$		0			0
$343$	1.38353e10	+	4.05808e8i	0.999570	+	0.0293186i
$344$	9.45418e9			0.675134
$345$		0			0
$346$	1.31954e9	−	7.61836e8i	0.0920699	−	0.0531566i
$347$	−4.70131e8	−	8.14291e8i	−0.0324266	−	0.0561645i	0.849357	−	0.527819i	$-0.176990\pi$
$347$	−4.70131e8	−	8.14291e8i	−0.0324266	−	0.0561645i	−0.881783	+	0.471655i	$0.843657\pi$
$348$		0			0
$349$			1.33733e9i			0.0901437i	0.998984	+	0.0450719i	$0.0143517\pi$
$349$			1.33733e9i			0.0901437i	−0.998984	+	0.0450719i	$0.985648\pi$
$350$	4.06673e9	+	7.20552e9i	0.271002	+	0.480168i
$351$		0			0
$352$	1.82509e9	−	3.16116e9i	0.118882	−	0.205909i
$353$	−1.04605e9	+	6.03937e8i	−0.0673679	+	0.0388949i	−0.533306	−	0.845923i	$-0.679050\pi$
$353$	−1.04605e9	+	6.03937e8i	−0.0673679	+	0.0388949i	0.465938	+	0.884818i	$0.345717\pi$
$354$		0			0
$355$	−6.12694e9	−	3.53739e9i	−0.385771	−	0.222725i
$356$		−	1.13502e10i		−	0.706650i
$357$		0			0
$358$	−1.51919e10			−0.924866
$359$	1.58025e10	−	2.73707e10i	0.951366	−	1.64781i	0.208893	−	0.977939i	$-0.433014\pi$
$359$	1.58025e10	−	2.73707e10i	0.951366	−	1.64781i	0.742473	−	0.669876i	$-0.233653\pi$
$360$		0			0
$361$	−5.00980e9	−	8.67723e9i	−0.294979	−	0.510919i
$362$	−1.62857e10	−	9.40253e9i	−0.948355	−	0.547533i
$363$		0			0
$364$	−7.24167e9	−	4.27590e9i	−0.412509	−	0.243569i
$365$	5.14136e9			0.289672
$366$		0			0
$367$	2.60965e8	−	1.50668e8i	0.0143853	−	0.00830533i	−0.492790	−	0.870148i	$-0.664023\pi$
$367$	2.60965e8	−	1.50668e8i	0.0143853	−	0.00830533i	0.507175	+	0.861843i	$0.330690\pi$
$368$	−1.05939e9	−	1.83492e9i	−0.0577651	−	0.100052i
$369$		0			0
$370$		−	1.17365e9i		−	0.0626229i
$371$	1.46014e10	−	2.47289e10i	0.770722	−	1.30530i
$372$		0			0
$373$	−1.65408e10	+	2.86496e10i	−0.854520	+	1.48007i	0.0225698	+	0.999745i	$0.492815\pi$
$373$	−1.65408e10	+	2.86496e10i	−0.854520	+	1.48007i	−0.877090	+	0.480327i	$0.840518\pi$
$374$	−9.22370e9	+	5.32530e9i	−0.471432	+	0.272181i
$375$		0			0
$376$	1.39771e9	+	8.06967e8i	0.0699303	+	0.0403743i
$377$		−	1.94362e10i		−	0.962156i
$378$		0			0
$379$	2.26256e10			1.09659			0.548294	−	0.836285i	$-0.315277\pi$
$379$	2.26256e10			1.09659			0.548294	+	0.836285i	$0.315277\pi$
$380$	1.56656e9	−	2.71336e9i	0.0751300	−	0.130129i
$381$		0			0
$382$	−4.53519e9	−	7.85518e9i	−0.212981	−	0.368895i
$383$	−2.09715e10	−	1.21079e10i	−0.974616	−	0.562695i	−0.0739756	−	0.997260i	$-0.523569\pi$
$383$	−2.09715e10	−	1.21079e10i	−0.974616	−	0.562695i	−0.900640	+	0.434565i	$0.856902\pi$
$384$		0			0
$385$	−1.20775e10	+	6.81641e9i	−0.549709	+	0.310251i
$386$	−1.33078e10			−0.599456
$387$		0			0
$388$	7.22918e9	−	4.17377e9i	0.318979	−	0.184163i
$389$	5.38937e9	+	9.33466e9i	0.235364	+	0.407662i	0.959378	−	0.282123i	$-0.0910385\pi$
$389$	5.38937e9	+	9.33466e9i	0.235364	+	0.407662i	−0.724015	+	0.689785i	$0.757705\pi$
$390$		0			0
$391$			6.18224e9i			0.264508i
$392$	4.31469e9	−	7.14689e9i	0.182728	−	0.302672i
$393$		0			0
$394$	2.16747e9	−	3.75417e9i	0.0899433	−	0.155786i
$395$	1.81481e9	−	1.04778e9i	0.0745493	−	0.0430411i
$396$		0			0
$397$	−1.11612e10	−	6.44391e9i	−0.449312	−	0.259410i	0.258228	−	0.966084i	$-0.416862\pi$
$397$	−1.11612e10	−	6.44391e9i	−0.449312	−	0.259410i	−0.707540	+	0.706674i	$0.750195\pi$
$398$		−	2.48841e10i		−	0.991721i
$399$		0			0
$400$	4.99039e9			0.194937
$401$	3.32886e9	−	5.76576e9i	0.128742	−	0.222987i	−0.794448	−	0.607333i	$-0.792240\pi$
$401$	3.32886e9	−	5.76576e9i	0.128742	−	0.222987i	0.923189	+	0.384346i	$0.125573\pi$
$402$		0			0
$403$	−6.07487e9	−	1.05220e10i	−0.230312	−	0.398913i
$404$	1.96017e10	+	1.13171e10i	0.735815	+	0.424823i
$405$		0			0
$406$	1.92931e10	+	1.88582e8i	0.710065	+	0.00694060i
$407$	−6.96444e9			−0.253810
$408$		0			0
$409$	−3.21707e10	+	1.85737e10i	−1.14965	+	0.663752i	−0.948803	−	0.315870i	$-0.897704\pi$
$409$	−3.21707e10	+	1.85737e10i	−1.14965	+	0.663752i	−0.200850	+	0.979622i	$0.564370\pi$
$410$	5.90079e9	+	1.02205e10i	0.208821	+	0.361689i
$411$		0			0
$412$			1.46233e10i			0.507525i
$413$	2.42266e10	+	1.43048e10i	0.832708	+	0.491679i
$414$		0			0
$415$	−9.29945e9	+	1.61071e10i	−0.313520	+	0.543032i
$416$	−4.39279e9	+	2.53618e9i	−0.146679	+	0.0846849i
$417$		0			0
$418$	−1.61011e10	−	9.29595e9i	−0.527411	−	0.304501i
$419$		−	3.13974e10i		−	1.01868i	−0.860566	−	0.509339i	$-0.829890\pi$
$419$		−	3.13974e10i		−	1.01868i	0.860566	−	0.509339i	$-0.170110\pi$
$420$		0			0
$421$	9.64445e8			0.0307008			0.0153504	−	0.999882i	$-0.495114\pi$
$421$	9.64445e8			0.0307008			0.0153504	+	0.999882i	$0.495114\pi$
$422$	4.53466e9	−	7.85426e9i	0.142987	−	0.247660i
$423$		0			0
$424$	−8.66056e9	−	1.50005e10i	−0.267968	−	0.464134i
$425$	−1.26103e10	−	7.28054e9i	−0.386517	−	0.223156i
$426$		0			0
$427$	3.08800e8	−	3.15921e10i	0.00928893	−	0.950314i
$428$	1.82794e9			0.0544736
$429$		0			0
$430$	−1.87622e10	+	1.08324e10i	−0.548795	+	0.316847i
$431$	3.21242e10	+	5.56407e10i	0.930943	+	1.61244i	0.781713	+	0.623638i	$0.214346\pi$
$431$	3.21242e10	+	5.56407e10i	0.930943	+	1.61244i	0.149230	+	0.988803i	$0.452321\pi$
$432$		0			0
$433$		−	4.85656e9i		−	0.138158i	−0.997611	−	0.0690792i	$-0.977994\pi$
$433$		−	4.85656e9i		−	0.138158i	0.997611	−	0.0690792i	$-0.0220061\pi$
$434$	1.05035e10	−	5.92807e9i	0.296057	−	0.167092i
$435$		0			0
$436$	−1.30323e10	+	2.25726e10i	−0.360641	+	0.624649i
$437$	−9.34599e9	+	5.39591e9i	−0.256271	+	0.147958i
$438$		0			0
$439$	1.97737e10	+	1.14163e10i	0.532389	+	0.307375i	0.741989	−	0.670412i	$-0.233883\pi$
$439$	1.97737e10	+	1.14163e10i	0.532389	+	0.307375i	−0.209600	+	0.977787i	$0.567216\pi$
$440$			8.36460e9i			0.223169i
$441$		0			0
$442$	1.48002e10			0.387775
$443$	−1.83252e10	+	3.17402e10i	−0.475811	+	0.824129i	−0.999616	−	0.0277093i	$-0.991179\pi$
$443$	−1.83252e10	+	3.17402e10i	−0.475811	+	0.824129i	0.523805	+	0.851838i	$0.324512\pi$
$444$		0			0
$445$	1.30048e10	+	2.25250e10i	0.331637	+	0.574413i
$446$	1.02516e10	+	5.91878e9i	0.259092	+	0.149587i
$447$		0			0
$448$	−2.47489e9	−	4.38506e9i	−0.0614389	−	0.108859i
$449$	−7.21152e10			−1.77436			−0.887179	−	0.461425i	$-0.847338\pi$
$449$	−7.21152e10			−1.77436			−0.887179	+	0.461425i	$0.847338\pi$
$450$		0			0
$451$	6.06480e10	−	3.50152e10i	1.46592	−	0.846350i
$452$	5.13952e9	+	8.90190e9i	0.123131	+	0.213270i
$453$		0			0
$454$			2.40629e10i			0.566401i
$455$	1.92706e10	+	1.88362e8i	0.449624	+	0.00439490i
$456$		0			0
$457$	3.00998e10	−	5.21344e10i	0.690080	−	1.19525i	−0.281732	−	0.959493i	$-0.590909\pi$
$457$	3.00998e10	−	5.21344e10i	0.690080	−	1.19525i	0.971811	−	0.235760i	$-0.0757578\pi$
$458$	−4.57887e10	+	2.64361e10i	−1.04063	+	0.600808i
$459$		0			0
$460$	4.20481e9	+	2.42765e9i	0.0939108	+	0.0542194i
$461$		−	8.97724e10i		−	1.98765i	−0.110972	−	0.993824i	$-0.535396\pi$
$461$		−	8.97724e10i		−	1.98765i	0.110972	−	0.993824i	$-0.464604\pi$
$462$		0			0
$463$	−3.64822e10			−0.793883			−0.396942	−	0.917844i	$-0.629928\pi$
$463$	−3.64822e10			−0.793883			−0.396942	+	0.917844i	$0.629928\pi$
$464$	5.81857e9	−	1.00781e10i	0.125529	−	0.217423i
$465$		0			0
$466$	1.47529e10	+	2.55528e10i	0.312849	+	0.541870i
$467$	−7.40477e9	−	4.27515e9i	−0.155684	−	0.0898842i	0.420134	−	0.907462i	$-0.361983\pi$
$467$	−7.40477e9	−	4.27515e9i	−0.155684	−	0.0898842i	−0.575818	+	0.817578i	$0.695316\pi$
$468$		0			0
$469$	−1.92562e10	+	3.26124e10i	−0.397996	+	0.674048i
$470$	−3.69841e9			−0.0757921
$471$		0			0
$472$	1.46958e10	−	8.48465e9i	0.296092	−	0.170949i
$473$	6.42791e10	+	1.11335e11i	1.28418	+	2.22426i
$474$		0			0
$475$		−	2.54181e10i		−	0.499308i
$476$	−1.43602e8	+	1.46913e10i	−0.00279725	+	0.286176i
$477$		0			0
$478$	1.41921e10	−	2.45814e10i	0.271853	−	0.470864i
$479$	−7.84934e10	+	4.53182e10i	−1.49105	+	0.860856i	−0.999947	−	0.0102484i	$-0.996738\pi$
$479$	−7.84934e10	+	4.53182e10i	−1.49105	+	0.860856i	−0.491098	+	0.871104i	$0.663404\pi$
$480$		0			0
$481$	8.38129e9	+	4.83894e9i	0.156578	+	0.0904003i
$482$			1.82742e10i			0.338571i
$483$		0			0
$484$	2.21974e10			0.404502
$485$	−9.56441e9	+	1.65660e10i	−0.172859	+	0.299400i
$486$		0			0
$487$	−2.00698e10	−	3.47619e10i	−0.356802	−	0.617999i	0.630623	−	0.776090i	$-0.282800\pi$
$487$	−2.00698e10	−	3.47619e10i	−0.356802	−	0.617999i	−0.987425	+	0.158090i	$0.949466\pi$
$488$	−1.65026e10	−	9.52779e9i	−0.290987	−	0.168001i
$489$		0			0
$490$	−3.73952e8	+	1.91270e10i	−0.00648682	+	0.331789i
$491$	3.33248e10			0.573379			0.286689	−	0.958024i	$-0.407445\pi$
$491$	3.33248e10			0.573379			0.286689	+	0.958024i	$0.407445\pi$
$492$		0			0
$493$	−2.94060e10	+	1.69775e10i	−0.497792	+	0.287400i
$494$	1.29178e10	+	2.23742e10i	0.216910	+	0.375699i
$495$		0			0
$496$		−	7.27449e9i		−	0.120192i
$497$	2.84642e10	+	5.04335e10i	0.466523	+	0.826597i
$498$		0			0
$499$	5.21701e10	−	9.03612e10i	0.841432	−	1.45740i	−0.0472517	−	0.998883i	$-0.515046\pi$
$499$	5.21701e10	−	9.03612e10i	0.841432	−	1.45740i	0.888684	−	0.458520i	$-0.151620\pi$
$500$	−2.26047e10	+	1.30508e10i	−0.361675	+	0.208813i
$501$		0			0
$502$	7.51577e10	+	4.33923e10i	1.18347	+	0.683279i
$503$			5.93676e10i			0.927423i	0.885986	+	0.463711i	$0.153483\pi$
$503$			5.93676e10i			0.927423i	−0.885986	+	0.463711i	$0.846517\pi$
$504$		0			0
$505$	−5.18672e10			−0.797494
$506$	1.44056e10	−	2.49513e10i	0.219751	−	0.380619i
$507$		0			0
$508$	2.08919e10	+	3.61859e10i	0.313707	+	0.543356i
$509$	−2.93270e10	−	1.69319e10i	−0.436914	−	0.252253i	0.265374	−	0.964146i	$-0.414505\pi$
$509$	−2.93270e10	−	1.69319e10i	−0.436914	−	0.252253i	−0.702288	+	0.711893i	$0.747838\pi$
$510$		0			0
$511$	−3.62396e10	−	2.13979e10i	−0.531495	−	0.313825i
$512$	−3.03700e9			−0.0441942
$513$		0			0
$514$	1.08951e9	−	6.29027e8i	0.0156091	−	0.00901191i
$515$	−1.67550e10	−	2.90206e10i	−0.238186	−	0.412551i
$516$		0			0
$517$			2.19463e10i			0.307184i
$518$	−4.88465e9	+	8.27265e9i	−0.0678444	+	0.114902i
$519$		0			0
$520$	5.81178e9	−	1.00663e10i	0.0794869	−	0.137675i
$521$	−7.52763e10	+	4.34608e10i	−1.02166	+	0.589857i	−0.914585	−	0.404394i	$-0.867483\pi$
$521$	−7.52763e10	+	4.34608e10i	−1.02166	+	0.589857i	−0.107077	+	0.994251i	$0.534149\pi$
$522$		0			0
$523$	−1.16722e9	−	6.73896e8i	−0.0156008	−	0.00900712i	0.492179	−	0.870494i	$-0.336200\pi$
$523$	−1.16722e9	−	6.73896e8i	−0.0156008	−	0.00900712i	−0.507780	+	0.861487i	$0.669534\pi$
$524$		−	1.95915e10i		−	0.259862i
$525$		0			0
$526$	4.35341e10			0.568704
$527$	−1.06128e10	+	1.83820e10i	−0.137591	+	0.238314i
$528$		0			0
$529$	3.07936e10	+	5.33361e10i	0.393222	+	0.681081i
$530$	3.43745e10	+	1.98461e10i	0.435645	+	0.251520i
$531$		0			0
$532$	−2.23349e10	+	1.26056e10i	−0.278829	+	0.157368i
$533$	−9.73151e10			−1.20579
$534$		0			0
$535$	−3.62761e9	+	2.09440e9i	−0.0442798	+	0.0255650i
$536$	1.14215e10	+	1.97826e10i	0.138377	+	0.239676i
$537$		0			0
$538$			4.65518e10i			0.555658i
$539$	1.13499e11	+	2.21902e9i	1.34474	+	0.0262910i
$540$		0			0
$541$	−2.82020e10	+	4.88474e10i	−0.329224	+	0.570233i	−0.982358	−	0.187010i	$-0.940120\pi$
$541$	−2.82020e10	+	4.88474e10i	−0.329224	+	0.570233i	0.653134	+	0.757242i	$0.273454\pi$
$542$	−6.17828e10	+	3.56703e10i	−0.715929	+	0.413342i
$543$		0			0
$544$	7.67422e9	+	4.43072e9i	0.0876272	+	0.0505916i
$545$		−	5.97284e10i		−	0.677010i
$546$		0			0
$547$	−9.05773e10			−1.01174			−0.505872	−	0.862609i	$-0.668829\pi$
$547$	−9.05773e10			−1.01174			−0.505872	+	0.862609i	$0.668829\pi$
$548$	8.50805e9	−	1.47364e10i	0.0943426	−	0.163406i
$549$		0			0
$550$	3.39297e10	+	5.87680e10i	0.370791	+	0.642229i
$551$	−5.13316e10	−	2.96363e10i	−0.556902	−	0.321527i
$552$		0			0
$553$	−1.71527e10	−	1.67661e8i	−0.183414	−	0.00179280i
$554$	1.91611e9			0.0203414
$555$		0			0
$556$	−5.96678e10	+	3.44492e10i	−0.624368	+	0.360479i
$557$	8.50601e10	+	1.47328e11i	0.883701	+	1.53061i	0.847196	+	0.531281i	$0.178289\pi$
$557$	8.50601e10	+	1.47328e11i	0.883701	+	1.53061i	0.0365050	+	0.999333i	$0.488378\pi$
$558$		0			0
$559$		−	1.78646e11i		−	1.82956i
$560$	9.93582e9	+	5.86667e9i	0.101030	+	0.0596540i
$561$		0			0
$562$	−2.41663e10	+	4.18573e10i	−0.242251	+	0.419590i
$563$	−1.07954e11	+	6.23275e10i	−1.07450	+	0.620364i	−0.929408	−	0.369054i	$-0.879682\pi$
$563$	−1.07954e11	+	6.23275e10i	−1.07450	+	0.620364i	−0.145094	+	0.989418i	$0.546348\pi$
$564$		0			0
$565$	−2.03992e10	−	1.17775e10i	−0.200179	−	0.115573i
$566$		−	1.04212e11i		−	1.01543i
$567$		0			0
$568$	3.49292e10			0.335579
$569$	6.46031e10	−	1.11896e11i	0.616317	−	1.06749i	−0.373835	−	0.927495i	$-0.621957\pi$
$569$	6.46031e10	−	1.11896e11i	0.616317	−	1.06749i	0.990152	−	0.139997i	$-0.0447093\pi$
$570$		0			0
$571$	−5.09591e10	−	8.82638e10i	−0.479377	−	0.830306i	0.520343	−	0.853957i	$-0.325804\pi$
$571$	−5.09591e10	−	8.82638e10i	−0.479377	−	0.830306i	−0.999720	+	0.0236516i	$0.992471\pi$
$572$	−5.97332e10	−	3.44870e10i	−0.557997	−	0.322160i
$573$		0			0
$574$	9.44215e8	−	9.65989e10i	0.00869808	−	0.889866i
$575$	3.93896e10			0.360338
$576$		0			0
$577$	−1.37255e11	+	7.92444e10i	−1.23830	+	0.714933i	−0.968747	−	0.248053i	$-0.920209\pi$
$577$	−1.37255e11	+	7.92444e10i	−1.23830	+	0.714933i	−0.269553	+	0.962985i	$0.586876\pi$
$578$	2.65328e10	+	4.59562e10i	0.237723	+	0.411749i
$579$		0			0
$580$			2.66671e10i			0.235648i
$581$	1.32585e11	−	7.48297e10i	1.16356	−	0.656703i
$582$		0			0
$583$	1.17766e11	−	2.03977e11i	1.01941	−	1.76566i
$584$	−2.19829e10	+	1.26918e10i	−0.188987	+	0.109112i
$585$		0			0
$586$	−6.09882e10	−	3.52116e10i	−0.517196	−	0.298604i
$587$		−	1.98747e11i		−	1.67397i	−0.547227	−	0.836984i	$-0.684317\pi$
$587$		−	1.98747e11i		−	1.67397i	0.547227	−	0.836984i	$-0.315683\pi$
$588$		0			0
$589$	−3.70519e10			−0.307857
$590$	−1.94430e10	+	3.36763e10i	−0.160456	+	0.277918i
$591$		0			0
$592$	2.89725e9	+	5.01818e9i	0.0235884	+	0.0408563i
$593$	7.00747e9	+	4.04576e9i	0.0566686	+	0.0327176i	0.528067	−	0.849203i	$-0.322917\pi$
$593$	7.00747e9	+	4.04576e9i	0.0566686	+	0.0327176i	−0.471398	+	0.881921i	$0.656250\pi$
$594$		0			0
$595$	−1.65480e10	−	2.93200e10i	−0.132031	−	0.233936i
$596$	−7.07140e10			−0.560429
$597$		0			0
$598$	−3.46726e10	+	2.00183e10i	−0.271133	+	0.156539i
$599$	9.11259e10	+	1.57835e11i	0.707839	+	1.22601i	0.965657	+	0.259820i	$0.0836631\pi$
$599$	9.11259e10	+	1.57835e11i	0.707839	+	1.22601i	−0.257818	+	0.966193i	$0.583004\pi$
$600$		0			0
$601$			2.47060e11i			1.89367i	0.321713	+	0.946837i	$0.395741\pi$
$601$			2.47060e11i			1.89367i	−0.321713	+	0.946837i	$0.604259\pi$
$602$	1.77331e11	+	1.73334e9i	1.35020	+	0.0131977i
$603$		0			0
$604$	−3.29893e9	+	5.71392e9i	−0.0247871	+	0.0429325i
$605$	−4.40517e10	+	2.54332e10i	−0.328807	+	0.189837i
$606$		0			0
$607$	3.95009e10	+	2.28059e10i	0.290973	+	0.167993i	0.638380	−	0.769721i	$-0.279605\pi$
$607$	3.95009e10	+	2.28059e10i	0.290973	+	0.167993i	−0.347408	+	0.937714i	$0.612938\pi$
$608$			1.54687e10i			0.113198i
$609$		0			0
$610$	4.36668e10			0.315379
$611$	1.52484e10	−	2.64111e10i	0.109411	−	0.189505i
$612$		0			0
$613$	2.26313e10	+	3.91986e10i	0.160276	+	0.277606i	0.934968	−	0.354733i	$-0.115428\pi$
$613$	2.26313e10	+	3.91986e10i	0.160276	+	0.277606i	−0.774692	+	0.632339i	$0.782095\pi$
$614$	−9.55617e10	−	5.51726e10i	−0.672373	−	0.388195i
$615$		0			0
$616$	3.48127e10	−	5.89589e10i	0.241777	−	0.409475i
$617$	3.39761e10			0.234440			0.117220	−	0.993106i	$-0.462602\pi$
$617$	3.39761e10			0.234440			0.117220	+	0.993106i	$0.462602\pi$
$618$		0			0
$619$	−3.85975e10	+	2.22843e10i	−0.262904	+	0.151787i	−0.625658	−	0.780097i	$-0.715170\pi$
$619$	−3.85975e10	+	2.22843e10i	−0.262904	+	0.151787i	0.362755	+	0.931885i	$0.381836\pi$
$620$	8.33493e9	+	1.44365e10i	0.0564073	+	0.0977003i
$621$		0			0
$622$			1.85204e11i			1.23734i
$623$	2.08096e9	−	2.12895e11i	0.0138138	−	1.41323i
$624$		0			0
$625$	−2.95834e10	+	5.12400e10i	−0.193878	+	0.335807i
$626$	1.59570e11	−	9.21277e10i	1.03909	−	0.599919i
$627$		0			0
$628$	1.83354e10	+	1.05859e10i	0.117883	+	0.0680598i
$629$		−	1.69073e10i		−	0.108012i
$630$		0			0
$631$	1.19363e11			0.752924			0.376462	−	0.926432i	$-0.377141\pi$
$631$	1.19363e11			0.752924			0.376462	+	0.926432i	$0.377141\pi$
$632$	−5.17305e9	+	8.95999e9i	−0.0324249	+	0.0561616i
$633$		0			0
$634$	−5.86274e10	−	1.01546e11i	−0.362864	−	0.628498i
$635$	−8.29218e10	−	4.78749e10i	−0.510004	−	0.294451i
$636$		0			0
$637$	−1.35047e11	−	8.15303e10i	−0.820217	−	0.495178i
$638$	1.58242e11			0.955078
$639$		0			0
$640$	6.02705e9	−	3.47972e9i	0.0359240	−	0.0207408i
$641$	−8.05963e10	−	1.39597e11i	−0.477401	−	0.826882i	0.522264	−	0.852784i	$-0.325088\pi$
$641$	−8.05963e10	−	1.39597e11i	−0.477401	−	0.826882i	−0.999664	+	0.0259018i	$0.991754\pi$
$642$		0			0
$643$		−	5.72715e10i		−	0.335039i	−0.985869	−	0.167519i	$-0.946424\pi$
$643$		−	5.72715e10i		−	0.335039i	0.985869	−	0.167519i	$-0.0535756\pi$
$644$	−1.95345e10	−	3.46117e10i	−0.113569	−	0.201224i
$645$		0			0
$646$	2.25674e10	−	3.90879e10i	0.129584	−	0.224446i
$647$	−4.30146e10	+	2.48345e10i	−0.245470	+	0.141722i	−0.617688	−	0.786423i	$-0.711931\pi$
$647$	−4.30146e10	+	2.48345e10i	−0.245470	+	0.141722i	0.372218	+	0.928145i	$0.378597\pi$
$648$		0			0
$649$	1.99834e11	+	1.15374e11i	1.12640	+	0.650325i
$650$		−	9.42984e10i		−	0.528264i
$651$		0			0
$652$	−1.68299e10			−0.0931306
$653$	1.75732e11	−	3.04377e11i	0.966492	−	1.67401i	0.260939	−	0.965355i	$-0.415968\pi$
$653$	1.75732e11	−	3.04377e11i	0.966492	−	1.67401i	0.705553	−	0.708657i	$-0.250699\pi$
$654$		0			0
$655$	2.24475e10	+	3.88801e10i	0.121956	+	0.211233i
$656$	−5.04599e10	−	2.91330e10i	−0.272478	−	0.157315i
$657$		0			0
$658$	2.60687e10	+	1.53925e10i	0.139065	+	0.0821117i
$659$	−7.49500e10			−0.397402			−0.198701	−	0.980060i	$-0.563672\pi$
$659$	−7.49500e10			−0.397402			−0.198701	+	0.980060i	$0.563672\pi$
$660$		0			0
$661$	9.13344e10	−	5.27319e10i	0.478441	−	0.276228i	−0.241326	−	0.970444i	$-0.577582\pi$
$661$	9.13344e10	−	5.27319e10i	0.478441	−	0.276228i	0.719767	+	0.694216i	$0.244249\pi$
$662$	1.22337e10	+	2.11894e10i	0.0636979	+	0.110328i
$663$		0			0
$664$		−	9.18254e10i		−	0.472379i
$665$	2.98813e10	−	5.06071e10i	0.152797	−	0.258777i
$666$		0			0
$667$	4.59264e10	−	7.95469e10i	0.232038	−	0.401902i
$668$	−1.13106e11	+	6.53019e10i	−0.568042	+	0.327959i
$669$		0			0
$670$	−4.53329e10	−	2.61729e10i	−0.224964	−	0.129883i
$671$		−	2.59118e11i		−	1.27823i
$672$		0			0
$673$	−1.87077e11			−0.911929			−0.455965	−	0.889998i	$-0.650706\pi$
$673$	−1.87077e11			−0.911929			−0.455965	+	0.889998i	$0.650706\pi$
$674$	9.81538e9	−	1.70007e10i	0.0475628	−	0.0823812i
$675$		0			0
$676$	−4.28320e9	−	7.41872e9i	−0.0205108	−	0.0355257i
$677$	−2.65310e11	−	1.53177e11i	−1.26299	−	0.729185i	−0.289334	−	0.957228i	$-0.593434\pi$
$677$	−2.65310e11	−	1.53177e11i	−1.26299	−	0.729185i	−0.973651	+	0.228043i	$0.926767\pi$
$678$		0			0
$679$	1.36362e11	−	7.69617e10i	0.641528	−	0.362072i
$680$	−2.03064e10			−0.0949725
$681$		0			0
$682$	8.56661e10	−	4.94593e10i	0.395978	−	0.228618i
$683$	1.68227e11	+	2.91377e11i	0.773057	+	1.33897i	0.935880	+	0.352319i	$0.114607\pi$
$683$	1.68227e11	+	2.91377e11i	0.773057	+	1.33897i	−0.162823	+	0.986655i	$0.552060\pi$
$684$		0			0
$685$			3.89932e10i			0.177104i
$686$	8.22406e10	−	1.33262e11i	0.371355	−	0.601743i
$687$		0			0
$688$	5.34809e10	−	9.26317e10i	0.238696	−	0.413434i
$689$	−2.83450e11	+	1.63650e11i	−1.25776	+	0.726171i
$690$		0			0
$691$	2.51262e11	+	1.45066e11i	1.10208	+	0.636289i	0.936768	−	0.349952i	$-0.113802\pi$
$691$	2.51262e11	+	1.45066e11i	1.10208	+	0.636289i	0.165317	+	0.986240i	$0.447135\pi$
$692$		−	1.72384e10i		−	0.0751747i
$693$		0			0
$694$	−1.06379e10			−0.0458581
$695$	7.89421e10	−	1.36732e11i	0.338353	−	0.586044i
$696$		0			0
$697$	8.50050e10	+	1.47233e11i	0.360175	+	0.623841i
$698$	1.31031e10	+	7.56506e9i	0.0552015	+	0.0318706i
$699$		0			0
$700$	9.36043e10	+	9.14944e8i	0.389856	+	0.00381068i
$701$	3.91859e11			1.62277			0.811386	−	0.584510i	$-0.198713\pi$
$701$	3.91859e11			1.62277			0.811386	+	0.584510i	$0.198713\pi$
$702$		0			0
$703$	2.55596e10	−	1.47569e10i	0.104649	−	0.0604188i
$704$	−2.06486e10	−	3.57644e10i	−0.0840620	−	0.145600i
$705$		0			0
$706$			1.36655e10i			0.0550057i
$707$	3.65593e11	+	2.15867e11i	1.46325	+	0.863989i
$708$		0			0
$709$	−1.48776e11	+	2.57687e11i	−0.588772	+	1.01978i	0.405621	+	0.914041i	$0.367055\pi$
$709$	−1.48776e11	+	2.57687e11i	−0.588772	+	1.01978i	−0.994394	+	0.105742i	$0.966278\pi$
$710$	−6.93184e10	+	4.00210e10i	−0.272782	+	0.157490i
$711$		0			0
$712$	−1.11209e11	−	6.42065e10i	−0.432733	−	0.249838i
$713$		−	5.74182e10i		−	0.222173i
$714$		0			0
$715$	1.58057e11			0.604770
$716$	−8.59382e10	+	1.48849e11i	−0.326990	+	0.566363i
$717$		0			0
$718$	−1.78785e11	−	3.09664e11i	−0.672717	−	1.16518i
$719$	2.77663e11	+	1.60309e11i	1.03897	+	0.599849i	0.919541	−	0.392994i	$-0.128561\pi$
$719$	2.77663e11	+	1.60309e11i	1.03897	+	0.599849i	0.119428	+	0.992843i	$0.461894\pi$
$720$		0			0
$721$	−2.68106e9	+	2.74288e11i	−0.00992122	+	1.01500i
$722$	−1.13359e11			−0.417164
$723$		0			0
$724$	−1.84251e11	+	1.06377e11i	−0.670588	+	0.387164i
$725$	1.08171e11	+	1.87358e11i	0.391524	+	0.678140i
$726$		0			0
$727$		−	4.99101e11i		−	1.78670i	−0.449364	−	0.893349i	$-0.648349\pi$
$727$		−	4.99101e11i		−	1.78670i	0.449364	−	0.893349i	$-0.351651\pi$
$728$	−8.28601e10	+	4.67655e10i	−0.294999	+	0.166494i
$729$		0			0
$730$	2.90839e10	−	5.03749e10i	0.102415	−	0.177387i
$731$	−2.70283e11	+	1.56048e11i	−0.946562	+	0.546498i
$732$		0			0
$733$	3.43929e11	+	1.98568e11i	1.19139	+	0.687848i	0.958621	−	0.284685i	$-0.0918890\pi$
$733$	3.43929e11	+	1.98568e11i	1.19139	+	0.687848i	0.232766	+	0.972533i	$0.425222\pi$
$734$		−	3.40923e9i		−	0.0117455i
$735$		0			0
$736$	−2.39713e10			−0.0816921
$737$	−1.55310e11	+	2.69004e11i	−0.526415	+	0.911778i
$738$		0			0
$739$	−1.33494e10	−	2.31219e10i	−0.0447595	−	0.0775257i	0.842778	−	0.538262i	$-0.180919\pi$
$739$	−1.33494e10	−	2.31219e10i	−0.0447595	−	0.0775257i	−0.887537	+	0.460736i	$0.847585\pi$
$740$	−1.14994e10	−	6.63919e9i	−0.0383485	−	0.0221405i
$741$		0			0
$742$	−1.59695e11	−	2.82952e11i	−0.526837	−	0.933462i
$743$	−2.98139e11			−0.978281			−0.489141	−	0.872205i	$-0.662690\pi$
$743$	−2.98139e11			−0.978281			−0.489141	+	0.872205i	$0.662690\pi$
$744$		0			0
$745$	1.40335e11	−	8.10224e10i	0.455555	−	0.263015i
$746$	1.87138e11	+	3.24133e11i	0.604237	+	1.04657i
$747$		0			0
$748$			1.20498e11i			0.384922i
$749$	3.42864e10	+	3.35136e8i	0.108942	+	0.00106486i
$750$		0			0
$751$	3.87148e10	−	6.70559e10i	0.121707	−	0.210803i	−0.798734	−	0.601685i	$-0.794496\pi$
$751$	3.87148e10	−	6.70559e10i	0.121707	−	0.210803i	0.920441	+	0.390881i	$0.127830\pi$
$752$	1.58133e10	−	9.12979e9i	0.0494482	−	0.0285489i
$753$		0			0
$754$	−1.90435e11	−	1.09948e11i	−0.589198	−	0.340173i
$755$		−	1.51193e10i		−	0.0465313i
$756$		0			0
$757$	−5.03553e11			−1.53342			−0.766711	−	0.641992i	$-0.778108\pi$
$757$	−5.03553e11			−1.53342			−0.766711	+	0.641992i	$0.778108\pi$
$758$	1.27990e11	−	2.21685e11i	0.387703	−	0.671521i
$759$		0			0
$760$	−1.77236e10	−	3.06982e10i	−0.0531249	−	0.0920150i
$761$	−8.89472e10	−	5.13537e10i	−0.265212	−	0.153120i	0.361498	−	0.932373i	$-0.382266\pi$
$761$	−8.89472e10	−	5.13537e10i	−0.265212	−	0.153120i	−0.626710	+	0.779253i	$0.715599\pi$
$762$		0			0
$763$	−2.48584e11	+	4.21003e11i	−0.733459	+	1.24219i
$764$	−1.02620e11			−0.301201
$765$		0			0
$766$	−2.37265e11	+	1.36985e11i	−0.689158	+	0.397885i
$767$	−1.60326e11	−	2.77693e11i	−0.463257	−	0.802385i
$768$		0			0
$769$		−	5.28224e10i		−	0.151047i	−0.997144	−	0.0755236i	$-0.975937\pi$
$769$		−	5.28224e10i		−	0.151047i	0.997144	−	0.0755236i	$-0.0240628\pi$
$770$	−1.53358e9	+	1.56894e11i	−0.00436257	+	0.446317i
$771$		0			0
$772$	−7.52803e10	+	1.30389e11i	−0.211940	+	0.367090i
$773$	−3.29208e11	+	1.90068e11i	−0.922046	+	0.532344i	−0.884287	−	0.466943i	$-0.845355\pi$
$773$	−3.29208e11	+	1.90068e11i	−0.922046	+	0.532344i	−0.0377590	+	0.999287i	$0.512022\pi$
$774$		0			0
$775$	1.17119e11	+	6.76188e10i	0.324654	+	0.187439i
$776$		−	9.44417e10i		−	0.260445i
$777$		0			0
$778$	1.21947e11			0.332855
$779$	−1.48386e11	+	2.57013e11i	−0.402943	+	0.697918i
$780$		0			0
$781$	2.37484e11	+	4.11334e11i	0.638307	+	1.10558i
$782$	6.05733e10	+	3.49720e10i	0.161977	+	0.0935176i
$783$		0			0
$784$	−4.56173e10	−	8.27040e10i	−0.120744	−	0.218908i
$785$	−4.85164e10			−0.127765
$786$		0			0
$787$	4.12322e11	−	2.38054e11i	1.07482	−	0.620550i	0.145328	−	0.989384i	$-0.453576\pi$
$787$	4.12322e11	−	2.38054e11i	1.07482	−	0.620550i	0.929495	+	0.368834i	$0.120243\pi$
$788$	−2.45222e10	−	4.24736e10i	−0.0635995	−	0.110158i
$789$		0			0
$790$		−	2.37086e10i		−	0.0608693i
$791$	9.47694e10	+	1.67915e11i	0.242082	+	0.428926i
$792$		0			0
$793$	−1.80037e11	+	3.11833e11i	−0.455270	+	0.788551i
$794$	−1.26274e11	+	7.29045e10i	−0.317711	+	0.183431i
$795$		0			0
$796$	−2.43813e11	−	1.40766e11i	−0.607302	−	0.350626i
$797$			2.92025e11i			0.723746i	0.932227	+	0.361873i	$0.117863\pi$
$797$			2.92025e11i			0.723746i	−0.932227	+	0.361873i	$0.882137\pi$
$798$		0			0
$799$	−5.32782e10			−0.130726
$800$	2.82299e10	−	4.88956e10i	0.0689207	−	0.119374i
$801$		0			0
$802$	−3.76618e10	−	6.52322e10i	−0.0910340	−	0.157676i
$803$	−2.98923e11	−	1.72583e11i	−0.718948	−	0.415085i
$804$		0			0
$805$	7.84242e10	+	4.63061e10i	0.186753	+	0.110269i
$806$	−1.37459e11			−0.325711
$807$		0			0
$808$	2.21768e11	−	1.28038e11i	0.520300	−	0.300395i
$809$	2.54870e11	+	4.41447e11i	0.595009	+	1.03059i	0.993546	+	0.113434i	$0.0361850\pi$
$809$	2.54870e11	+	4.41447e11i	0.595009	+	1.03059i	−0.398536	+	0.917153i	$0.630482\pi$
$810$		0			0
$811$			2.98657e11i			0.690381i	0.938533	+	0.345191i	$0.112186\pi$
$811$			2.98657e11i			0.690381i	−0.938533	+	0.345191i	$0.887814\pi$
$812$	1.10986e11	−	1.87966e11i	0.255296	−	0.432371i
$813$		0			0
$814$	−3.93968e10	+	6.82373e10i	−0.0897353	+	0.155426i
$815$	3.33997e10	−	1.92833e10i	0.0757029	−	0.0437071i
$816$		0			0
$817$	−4.71811e11	−	2.72400e11i	−1.05896	−	0.611391i
$818$			4.20276e11i			0.938688i
$819$		0			0
$820$	1.33520e11			0.295318
$821$	−2.07864e11	+	3.60031e11i	−0.457516	+	0.792441i	−0.998829	−	0.0483802i	$-0.984594\pi$
$821$	−2.07864e11	+	3.60031e11i	−0.457516	+	0.792441i	0.541313	+	0.840821i	$0.317927\pi$
$822$		0			0
$823$	−1.28735e11	−	2.22976e11i	−0.280606	−	0.486025i	0.690928	−	0.722924i	$-0.257202\pi$
$823$	−1.28735e11	−	2.22976e11i	−0.280606	−	0.486025i	−0.971534	+	0.236899i	$0.923869\pi$
$824$	1.43279e11	+	8.27220e10i	0.310794	+	0.179437i
$825$		0			0
$826$	2.77204e11	−	1.56452e11i	0.595497	−	0.336093i
$827$	−2.54192e11			−0.543426			−0.271713	−	0.962378i	$-0.587590\pi$
$827$	−2.54192e11			−0.543426			−0.271713	+	0.962378i	$0.587590\pi$
$828$		0			0
$829$	−6.50967e11	+	3.75836e11i	−1.37829	+	0.795757i	−0.991954	−	0.126601i	$-0.959593\pi$
$829$	−6.50967e11	+	3.75836e11i	−1.37829	+	0.795757i	−0.386337	+	0.922358i	$0.626260\pi$
$830$	1.05211e11	+	1.82231e11i	0.221692	+	0.383982i
$831$		0			0
$832$			5.73871e10i			0.119763i
$833$	−5.38704e9	+	2.75537e11i	−0.0111885	+	0.572269i
$834$		0			0
$835$	1.49643e11	−	2.59188e11i	0.307829	−	0.533175i
$836$	−1.82163e11	+	1.05172e11i	−0.372936	+	0.215315i
$837$		0			0
$838$	−3.07630e11	−	1.77610e11i	−0.623811	−	0.360157i
$839$		−	2.44756e11i		−	0.493954i	−0.969021	−	0.246977i	$-0.920563\pi$
$839$		−	2.44756e11i		−	0.493954i	0.969021	−	0.246977i	$-0.0794372\pi$
$840$		0			0
$841$	4.24316e9			0.00848214
$842$	5.45572e9	−	9.44959e9i	0.0108544	−	0.0188003i
$843$		0			0
$844$	−5.13038e10	−	8.88609e10i	−0.101107	−	0.175122i
$845$	1.70004e10	+	9.81517e9i	0.0333451	+	0.0192518i
$846$		0			0
$847$	4.16355e11	+	4.06970e9i	0.808966	+	0.00790731i
$848$	−1.95966e11			−0.378964
$849$		0			0
$850$	−1.42669e11	+	8.23699e10i	−0.273309	+	0.157795i
$851$	2.28682e10	+	3.96089e10i	0.0436028	+	0.0755222i
$852$		0			0
$853$		−	1.02397e11i		−	0.193416i	−0.995313	−	0.0967078i	$-0.969169\pi$
$853$		−	1.02397e11i		−	0.193416i	0.995313	−	0.0967078i	$-0.0308312\pi$
$854$	−3.07791e11	−	1.81738e11i	−0.578662	−	0.341675i
$855$		0			0
$856$	1.03404e10	−	1.79100e10i	0.0192593	−	0.0333581i
$857$	7.52580e11	−	4.34502e11i	1.39518	−	0.805506i	0.401295	−	0.915949i	$-0.368560\pi$
$857$	7.52580e11	−	4.34502e11i	1.39518	−	0.805506i	0.993883	+	0.110442i	$0.0352267\pi$
$858$		0			0
$859$	−5.47218e11	−	3.15936e11i	−1.00505	−	0.580266i	−0.0953112	−	0.995448i	$-0.530385\pi$
$859$	−5.47218e11	−	3.15936e11i	−1.00505	−	0.580266i	−0.909738	+	0.415182i	$0.863718\pi$
$860$			2.45109e11i			0.448089i
$861$		0			0
$862$	7.26887e11			1.31655
$863$	1.45694e10	−	2.52350e10i	0.0262663	−	0.0454946i	−0.852593	−	0.522575i	$-0.824972\pi$
$863$	1.45694e10	−	2.52350e10i	0.0262663	−	0.0454946i	0.878860	+	0.477080i	$0.158305\pi$
$864$		0			0
$865$	1.97513e10	+	3.42103e10i	0.0352802	+	0.0611071i
$866$	−4.75844e10	−	2.74729e10i	−0.0846044	−	0.0488464i
$867$		0			0
$868$	1.33371e9	−	1.36447e11i	0.00234955	−	0.240373i
$869$	−1.40687e11			−0.246702
$870$		0			0
$871$	3.73812e11	−	2.15820e11i	0.649502	−	0.374990i
$872$	1.47444e11	+	2.55380e11i	0.255012	+	0.441694i
$873$		0			0
$874$			1.22096e11i			0.209244i
$875$	−4.26387e11	+	2.40649e11i	−0.727398	+	0.410536i
$876$		0			0
$877$	1.09627e10	−	1.89879e10i	0.0185318	−	0.0320980i	−0.856611	−	0.515963i	$-0.827434\pi$
$877$	1.09627e10	−	1.89879e10i	0.0185318	−	0.0320980i	0.875143	+	0.483865i	$0.160767\pi$
$878$	2.23713e11	−	1.29161e11i	0.376456	−	0.217347i
$879$		0			0
$880$	8.19560e10	+	4.73173e10i	0.136663	+	0.0789022i
$881$			1.09148e11i			0.181181i	0.995888	+	0.0905907i	$0.0288755\pi$
$881$			1.09148e11i			0.181181i	−0.995888	+	0.0905907i	$0.971124\pi$
$882$		0			0
$883$	2.59857e11			0.427457			0.213728	−	0.976893i	$-0.431439\pi$
$883$	2.59857e11			0.427457			0.213728	+	0.976893i	$0.431439\pi$
$884$	8.37227e10	−	1.45012e11i	0.137099	−	0.237462i
$885$		0			0
$886$	2.07326e11	+	3.59100e11i	0.336449	+	0.582747i
$887$	5.97593e11	+	3.45020e11i	0.965408	+	0.557379i	0.897833	−	0.440336i	$-0.145141\pi$
$887$	5.97593e11	+	3.45020e11i	0.965408	+	0.557379i	0.0675747	+	0.997714i	$0.478474\pi$
$888$		0			0
$889$	3.85234e11	+	6.82566e11i	0.616761	+	1.09279i
$890$	2.94265e11			0.469006
$891$		0			0
$892$	1.15984e11	−	6.69634e10i	0.183206	−	0.105774i
$893$	−4.65017e10	−	8.05433e10i	−0.0731245	−	0.126655i
$894$		0			0
$895$		−	3.93863e11i		−	0.613838i
$896$	−5.69648e10	−	5.56807e8i	−0.0883841	−	0.000863919i
$897$		0			0
$898$	−4.07945e11	+	7.06582e11i	−0.627331	+	1.08657i
$899$	2.73111e11	−	1.57681e11i	0.418120	−	0.241402i
$900$		0			0
$901$	4.95189e11	+	2.85897e11i	0.751400	+	0.433821i
$902$		−	7.92303e11i		−	1.19692i
$903$		0			0
$904$	1.16294e11			0.174134
$905$	2.43769e11	−	4.22221e11i	0.363400	−	0.629427i
$906$		0			0
$907$	−1.10593e11	−	1.91553e11i	−0.163417	−	0.283047i	0.772675	−	0.634802i	$-0.218918\pi$
$907$	−1.10593e11	−	1.91553e11i	−0.163417	−	0.283047i	−0.936092	+	0.351755i	$0.885585\pi$
$908$	2.35767e11	+	1.36120e11i	0.346849	+	0.200253i
$909$		0			0
$910$	1.10857e11	−	1.87747e11i	0.161658	−	0.273784i
$911$	−5.57854e11			−0.809929			−0.404964	−	0.914332i	$-0.632716\pi$
$911$	−5.57854e11			−0.809929			−0.404964	+	0.914332i	$0.632716\pi$
$912$		0			0
$913$	1.08136e12	−	6.24322e11i	1.55627	−	0.898515i
$914$	−3.40541e11	−	5.89834e11i	−0.487960	−	0.845171i
$915$		0			0
$916$			5.98180e11i			0.849670i
$917$	3.59193e9	−	3.67476e11i	0.00507985	−	0.519699i
$918$		0			0
$919$	1.76298e11	−	3.05357e11i	0.247164	−	0.428100i	−0.715574	−	0.698537i	$-0.753835\pi$
$919$	1.76298e11	−	3.05357e11i	0.247164	−	0.428100i	0.962738	+	0.270437i	$0.0871681\pi$
$920$	4.75720e10	−	2.74657e10i	0.0664049	−	0.0383389i
$921$		0			0
$922$	−8.79587e11	−	5.07830e11i	−1.21718	−	0.702739i
$923$		−	6.60021e11i		−	0.909392i
$924$		0			0
$925$	−1.07723e11			−0.147144
$926$	−2.06374e11	+	3.57451e11i	−0.280680	+	0.486152i
$927$		0			0
$928$	−6.58296e10	−	1.14020e11i	−0.0887624	−	0.153741i
$929$	−4.96997e11	−	2.86941e11i	−0.667253	−	0.385239i	0.127782	−	0.991802i	$-0.459214\pi$
$929$	−4.96997e11	−	2.86941e11i	−0.667253	−	0.385239i	−0.795035	+	0.606563i	$0.792548\pi$
$930$		0			0
$931$	−4.21245e11	+	2.32347e11i	−0.560707	+	0.309271i
$932$	3.33821e11			0.442435
$933$		0			0
$934$	−8.37754e10	+	4.83678e10i	−0.110085	+	0.0635578i
$935$	−1.38064e11	−	2.39133e11i	−0.180648	−	0.312891i
$936$		0			0
$937$		−	8.48860e11i		−	1.10123i	−0.834760	−	0.550615i	$-0.814393\pi$
$937$		−	8.48860e11i		−	1.10123i	0.834760	−	0.550615i	$-0.185607\pi$
$938$	2.10605e11	+	3.73155e11i	0.272055	+	0.482034i
$939$		0			0
$940$	−2.09214e10	+	3.62369e10i	−0.0267966	+	0.0464130i
$941$	−3.68293e11	+	2.12634e11i	−0.469715	+	0.271190i	−0.716121	−	0.697977i	$-0.754084\pi$
$941$	−3.68293e11	+	2.12634e11i	−0.469715	+	0.271190i	0.246405	+	0.969167i	$0.420751\pi$
$942$		0			0
$943$	−3.98284e11	−	2.29949e11i	−0.503670	−	0.290794i
$944$		−	1.91986e11i		−	0.241758i
$945$		0			0
$946$	1.45447e12			1.81610
$947$	3.53892e11	−	6.12958e11i	0.440018	−	0.762133i	−0.557672	−	0.830061i	$-0.688305\pi$
$947$	3.53892e11	−	6.12958e11i	0.440018	−	0.762133i	0.997690	+	0.0679279i	$0.0216388\pi$
$948$		0			0
$949$	2.39824e11	+	4.15388e11i	0.295684	+	0.512140i
$950$	−2.49045e11	−	1.43786e11i	−0.305762	−	0.176532i
$951$		0			0
$952$	1.43132e11	+	8.45136e10i	0.174257	+	0.102891i
$953$	1.11824e12			1.35570			0.677851	−	0.735199i	$-0.262911\pi$
$953$	1.11824e12			1.35570			0.677851	+	0.735199i	$0.262911\pi$
$954$		0			0
$955$	2.03653e11	−	1.17579e11i	0.244837	−	0.141357i
$956$	−1.60565e11	−	2.78107e11i	−0.192229	−	0.332951i
$957$		0			0
$958$			1.02543e12i			1.21743i
$959$	1.62287e11	−	2.74849e11i	0.191870	−	0.324952i
$960$		0			0
$961$	−3.27878e11	+	5.67901e11i	−0.384431	+	0.665854i
$962$	9.48235e10	−	5.47463e10i	0.110717	−	0.0639227i
$963$		0			0
$964$	1.79050e11	+	1.03374e11i	0.207332	+	0.119703i
$965$		−	3.45017e11i		−	0.397861i
$966$		0			0
$967$	−1.31325e12			−1.50190			−0.750952	−	0.660356i	$-0.770405\pi$
$967$	−1.31325e12			−1.50190			−0.750952	+	0.660356i	$0.770405\pi$
$968$	1.25568e11	−	2.17489e11i	0.143013	−	0.247706i
$969$		0			0
$970$	1.08209e11	+	1.87423e11i	0.122230	+	0.211708i
$971$	1.44855e12	+	8.36318e11i	1.62950	+	0.940794i	0.984241	+	0.176833i	$0.0565851\pi$
$971$	1.44855e12	+	8.36318e11i	1.62950	+	0.940794i	0.645262	+	0.763961i	$0.276748\pi$
$972$		0			0
$973$	−1.12550e12	+	6.35221e11i	−1.25572	+	0.708719i
$974$	−4.54128e11			−0.504594
$975$		0			0
$976$	−1.86706e11	+	1.07795e11i	−0.205759	+	0.118795i
$977$	−4.87813e11	−	8.44917e11i	−0.535396	−	0.927333i	−0.999144	−	0.0413657i	$-0.986829\pi$
$977$	−4.87813e11	−	8.44917e11i	−0.535396	−	0.927333i	0.463748	−	0.885967i	$-0.346504\pi$
$978$		0			0
$979$		−	1.74616e12i		−	1.90088i
$980$	1.85290e11	+	1.11862e11i	0.200885	+	0.121277i
$981$		0			0
$982$	1.88513e11	−	3.26515e11i	0.202720	−	0.351121i
$983$	8.75801e11	−	5.05644e11i	0.937975	−	0.541540i	0.0486500	−	0.998816i	$-0.484508\pi$
$983$	8.75801e11	−	5.05644e11i	0.937975	−	0.541540i	0.889325	+	0.457276i	$0.151175\pi$
$984$		0			0
$985$	9.73305e10	+	5.61938e10i	0.103396	+	0.0596957i
$986$			3.84158e11i			0.406446i
$987$		0			0
$988$	2.92296e11			0.306757
$989$	4.22129e11	−	7.31150e11i	0.441225	−	0.764225i
$990$		0			0
$991$	−1.10221e11	−	1.90909e11i	−0.114280	−	0.197939i	0.803211	−	0.595694i	$-0.203123\pi$
$991$	−1.10221e11	−	1.90909e11i	−0.114280	−	0.197939i	−0.917492	+	0.397755i	$0.869790\pi$
$992$	−7.12752e10	−	4.11507e10i	−0.0736023	−	0.0424943i
$993$		0			0
$994$	6.55163e11	+	6.40396e9i	0.671126	+	0.00655998i
$995$	6.45143e11			0.658209
$996$		0			0
$997$	4.24638e11	−	2.45165e11i	0.429772	−	0.248129i	−0.269477	−	0.963007i	$-0.586851\pi$
$997$	4.24638e11	−	2.45165e11i	0.429772	−	0.248129i	0.699250	+	0.714878i	$0.253518\pi$
$998$	−5.90237e11	−	1.02232e12i	−0.594982	−	1.03054i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.n.d.19.8	yes	20
3.2	odd	2	inner	126.9.n.d.19.3	✓	20
7.3	odd	6	inner	126.9.n.d.73.8	yes	20
21.17	even	6	inner	126.9.n.d.73.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.n.d.19.3	✓	20	3.2	odd	2	inner
126.9.n.d.19.8	yes	20	1.1	even	1	trivial
126.9.n.d.73.3	yes	20	21.17	even	6	inner
126.9.n.d.73.8	yes	20	7.3	odd	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)

\(f(q)\)	\(=\)	\(q+(5.65685 - 9.79796i) q^{2} +(-64.0000 - 110.851i) q^{4} +(254.021 + 146.659i) q^{5} +(-1180.12 - 2090.96i) q^{7} -1448.15 q^{8} +O(q^{10})\)	\(q+(5.65685 - 9.79796i) q^{2} +(-64.0000 - 110.851i) q^{4} +(254.021 + 146.659i) q^{5} +(-1180.12 - 2090.96i) q^{7} -1448.15 q^{8} +(2873.92 - 1659.26i) q^{10} +(-9846.02 - 17053.8i) q^{11} +27364.3i q^{13} +(-27162.9 - 265.506i) q^{14} +(-8192.00 + 14189.0i) q^{16} +(41400.9 - 23902.8i) q^{17} +(72270.1 + 41725.2i) q^{19} -37544.8i q^{20} -222790. q^{22} +(-64660.1 + 111995. i) q^{23} +(-152295. - 263782. i) q^{25} +(268114. + 154796. i) q^{26} +(-156258. + 264639. i) q^{28} -710274. q^{29} +(-384515. + 222000. i) q^{31} +(92681.9 + 160530. i) q^{32} -540859. i q^{34} +(6883.50 - 704224. i) q^{35} +(176834. - 306285. i) q^{37} +(817643. - 472066. i) q^{38} +(-367862. - 212385. i) q^{40} +3.55628e6i q^{41} -6.52843e6 q^{43} +(-1.26029e6 + 2.18289e6i) q^{44} +(731546. + 1.26707e6i) q^{46} +(-965165. - 557238. i) q^{47} +(-2.97944e6 + 4.93517e6i) q^{49} -3.44603e6 q^{50} +(3.03337e6 - 1.75132e6i) q^{52} +(5.98041e6 + 1.03584e7i) q^{53} -5.77604e6i q^{55} +(1.70899e6 + 3.02804e6i) q^{56} +(-4.01792e6 + 6.95924e6i) q^{58} +(-1.01480e7 + 5.85894e6i) q^{59} +(1.13956e7 + 6.57926e6i) q^{61} +5.02328e6i q^{62} +2.09715e6 q^{64} +(-4.01323e6 + 6.95112e6i) q^{65} +(-7.88693e6 - 1.36606e7i) q^{67} +(-5.29931e6 - 3.05956e6i) q^{68} +(-6.86102e6 - 4.05114e6i) q^{70} -2.41198e7 q^{71} +(1.51799e7 - 8.76413e6i) q^{73} +(-2.00065e6 - 3.46522e6i) q^{74} -1.06816e7i q^{76} +(-2.40394e7 + 4.07132e7i) q^{77} +(3.57217e6 - 6.18718e6i) q^{79} +(-4.16188e6 + 2.40287e6i) q^{80} +(3.48443e7 + 2.01173e7i) q^{82} +6.34086e7i q^{83} +1.40223e7 q^{85} +(-3.69304e7 + 6.39653e7i) q^{86} +(1.42586e7 + 2.46965e7i) q^{88} +(7.67936e7 + 4.43368e7i) q^{89} +(5.72177e7 - 3.22931e7i) q^{91} +1.65530e7 q^{92} +(-1.09196e7 + 6.30443e6i) q^{94} +(1.22388e7 + 2.11982e7i) q^{95} +6.52152e7i q^{97} +(3.15003e7 + 5.71099e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 1280 q^{4} + 4186 q^{7}+O(q^{10}) \) 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