LMFDB - Embedded newform 126.9.n.d.73.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("126.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			73.10
Root			$40.6850 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.73
Dual form			126.9.n.d.19.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.65685 + 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(565.865 - 326.703i) q^{5} +(2120.69 + 1125.82i) q^{7} -1448.15 q^{8} +O(q^{10})$	\(q+(5.65685 + 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(565.865 - 326.703i) q^{5} +(2120.69 + 1125.82i) q^{7} -1448.15 q^{8} +(6402.04 + 3696.22i) q^{10} +(13880.2 - 24041.2i) q^{11} -6765.74i q^{13} +(965.728 + 27147.0i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(-84547.9 - 48813.8i) q^{17} +(67716.2 - 39095.9i) q^{19} +83635.8i q^{20} +314072. q^{22} +(-46841.9 - 81132.5i) q^{23} +(18156.6 - 31448.1i) q^{25} +(66290.4 - 38272.8i) q^{26} +(-260523. + 163029. i) q^{28} -305473. q^{29} +(-1.10538e6 - 638191. i) q^{31} +(92681.9 - 160530. i) q^{32} -1.10453e6i q^{34} +(1.56783e6 - 55774.1i) q^{35} +(-1.39624e6 - 2.41836e6i) q^{37} +(766121. + 442320. i) q^{38} +(-819461. + 473116. i) q^{40} -2.12414e6i q^{41} +5.96500e6 q^{43} +(1.77666e6 + 3.07727e6i) q^{44} +(529955. - 917909. i) q^{46} +(3.70738e6 - 2.14046e6i) q^{47} +(3.22987e6 + 4.77503e6i) q^{49} +410836. q^{50} +(749990. + 433007. i) q^{52} +(1.11299e6 - 1.92776e6i) q^{53} -1.81387e7i q^{55} +(-3.07109e6 - 1.63036e6i) q^{56} +(-1.72802e6 - 2.99301e6i) q^{58} +(1.57427e7 + 9.08906e6i) q^{59} +(-4.28000e6 + 2.47106e6i) q^{61} -1.44406e7i q^{62} +2.09715e6 q^{64} +(-2.21038e6 - 3.82850e6i) q^{65} +(-1.58826e7 + 2.75094e7i) q^{67} +(1.08221e7 - 6.24816e6i) q^{68} +(9.41548e6 + 1.50461e7i) q^{70} +2.29883e7 q^{71} +(-1.88605e6 - 1.08891e6i) q^{73} +(1.57966e7 - 2.73606e7i) q^{74} +1.00086e7i q^{76} +(5.65015e7 - 3.53573e7i) q^{77} +(-7.82277e6 - 1.35494e7i) q^{79} +(-9.27114e6 - 5.35269e6i) q^{80} +(2.08123e7 - 1.20160e7i) q^{82} +1.88638e7i q^{83} -6.37903e7 q^{85} +(3.37432e7 + 5.84449e7i) q^{86} +(-2.01006e7 + 3.48153e7i) q^{88} +(6.59498e7 - 3.80762e7i) q^{89} +(7.61699e6 - 1.43480e7i) q^{91} +1.19915e7 q^{92} +(4.19442e7 + 2.42165e7i) q^{94} +(2.55455e7 - 4.42461e7i) q^{95} +1.44142e8i q^{97} +(-2.85146e7 + 5.86578e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 1280 q^{4} + 4186 q^{7}+O(q^{10}) $ 20 * q - 1280 * q^4 + 4186 * q^7	$ 20 q - 1280 q^{4} + 4186 q^{7} - 17664 q^{10} - 163840 q^{16} - 250890 q^{19} + 420864 q^{22} + 258962 q^{25} - 1189888 q^{28} + 342762 q^{31} - 4806598 q^{37} + 2260992 q^{40} + 6968252 q^{43} - 4357632 q^{46} - 26046538 q^{49} + 2075904 q^{52} + 2455296 q^{58} - 15410424 q^{61} + 41943040 q^{64} - 70041074 q^{67} - 25804800 q^{70} + 220264098 q^{73} + 12860578 q^{79} + 12085248 q^{82} + 29161632 q^{85} - 26935296 q^{88} - 311022894 q^{91} + 332230656 q^{94}+O(q^{100}) $ 20 * q - 1280 * q^4 + 4186 * q^7 - 17664 * q^10 - 163840 * q^16 - 250890 * q^19 + 420864 * q^22 + 258962 * q^25 - 1189888 * q^28 + 342762 * q^31 - 4806598 * q^37 + 2260992 * q^40 + 6968252 * q^43 - 4357632 * q^46 - 26046538 * q^49 + 2075904 * q^52 + 2455296 * q^58 - 15410424 * q^61 + 41943040 * q^64 - 70041074 * q^67 - 25804800 * q^70 + 220264098 * q^73 + 12860578 * q^79 + 12085248 * q^82 + 29161632 * q^85 - 26935296 * q^88 - 311022894 * q^91 + 332230656 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	5.65685	+	9.79796i	0.353553	+	0.612372i
$2$	5.65685	+	9.79796i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−64.0000	+	110.851i	−0.250000	+	0.433013i
$5$	565.865	−	326.703i	0.905385	−	0.522724i	0.0264413	−	0.999650i	$-0.491582\pi$
$5$	565.865	−	326.703i	0.905385	−	0.522724i	0.878943	+	0.476926i	$0.158249\pi$
$6$		0			0
$7$	2120.69	+	1125.82i	0.883254	+	0.468895i
$7$	2120.69	+	1125.82i	0.883254	+	0.468895i
$8$	−1448.15			−0.353553
$9$		0			0
$10$	6402.04	+	3696.22i	0.640204	+	0.369622i
$11$	13880.2	−	24041.2i	0.948034	−	1.64204i	0.198475	−	0.980106i	$-0.436401\pi$
$11$	13880.2	−	24041.2i	0.948034	−	1.64204i	0.749559	−	0.661937i	$-0.230265\pi$
$12$		0			0
$13$		−	6765.74i		−	0.236887i	−0.992961	−	0.118444i	$-0.962210\pi$
$13$		−	6765.74i		−	0.236887i	0.992961	−	0.118444i	$-0.0377905\pi$
$14$	965.728	+	27147.0i	0.0251387	+	0.706660i
$15$		0			0
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	−84547.9	−	48813.8i	−1.01230	−	0.584449i	−0.100433	−	0.994944i	$-0.532023\pi$
$17$	−84547.9	−	48813.8i	−1.01230	−	0.584449i	−0.911863	+	0.410495i	$0.865356\pi$
$18$		0			0
$19$	67716.2	−	39095.9i	0.519610	−	0.299997i	−0.217165	−	0.976135i	$-0.569681\pi$
$19$	67716.2	−	39095.9i	0.519610	−	0.299997i	0.736775	+	0.676138i	$0.236348\pi$
$20$			83635.8i			0.522724i
$21$		0			0
$22$	314072.			1.34072
$23$	−46841.9	−	81132.5i	−0.167387	−	0.289924i	0.770113	−	0.637907i	$-0.220200\pi$
$23$	−46841.9	−	81132.5i	−0.167387	−	0.289924i	−0.937501	+	0.347984i	$0.886866\pi$
$24$		0			0
$25$	18156.6	−	31448.1i	0.0464808	−	0.0805072i
$26$	66290.4	−	38272.8i	0.145063	−	0.0837523i
$27$		0			0
$28$	−260523.	+	163029.i	−0.423851	+	0.265236i
$29$	−305473.			−0.431897			−0.215949	−	0.976405i	$-0.569284\pi$
$29$	−305473.			−0.431897			−0.215949	+	0.976405i	$0.569284\pi$
$30$		0			0
$31$	−1.10538e6	−	638191.i	−1.19692	−	0.691041i	−0.237051	−	0.971497i	$-0.576181\pi$
$31$	−1.10538e6	−	638191.i	−1.19692	−	0.691041i	−0.959867	+	0.280457i	$0.909514\pi$
$32$	92681.9	−	160530.i	0.0883883	−	0.153093i
$33$		0			0
$34$		−	1.10453e6i		−	0.826536i
$35$	1.56783e6	−	55774.1i	1.04479	−	0.0371672i
$36$		0			0
$37$	−1.39624e6	−	2.41836e6i	−0.744994	−	1.29037i	−0.950197	−	0.311649i	$-0.899119\pi$
$37$	−1.39624e6	−	2.41836e6i	−0.744994	−	1.29037i	0.205203	−	0.978719i	$-0.434215\pi$
$38$	766121.	+	442320.i	0.367420	+	0.212130i
$39$		0			0
$40$	−819461.	+	473116.i	−0.320102	+	0.184811i
$41$		−	2.12414e6i		−	0.751707i	−0.926679	−	0.375853i	$-0.877350\pi$
$41$		−	2.12414e6i		−	0.751707i	0.926679	−	0.375853i	$-0.122650\pi$
$42$		0			0
$43$	5.96500e6			1.74477			0.872383	−	0.488824i	$-0.162574\pi$
$43$	5.96500e6			1.74477			0.872383	+	0.488824i	$0.162574\pi$
$44$	1.77666e6	+	3.07727e6i	0.474017	+	0.821022i
$45$		0			0
$46$	529955.	−	917909.i	0.118361	−	0.205007i
$47$	3.70738e6	−	2.14046e6i	0.759758	−	0.438647i	−0.0694505	−	0.997585i	$-0.522125\pi$
$47$	3.70738e6	−	2.14046e6i	0.759758	−	0.438647i	0.829209	+	0.558939i	$0.188791\pi$
$48$		0			0
$49$	3.22987e6	+	4.77503e6i	0.560274	+	0.828307i
$50$	410836.			0.0657338
$51$		0			0
$52$	749990.	+	433007.i	0.102575	+	0.0592218i
$53$	1.11299e6	−	1.92776e6i	0.141055	−	0.244315i	−0.786839	−	0.617158i	$-0.788284\pi$
$53$	1.11299e6	−	1.92776e6i	0.141055	−	0.244315i	0.927894	+	0.372843i	$0.121617\pi$
$54$		0			0
$55$		−	1.81387e7i		−	1.98224i
$56$	−3.07109e6	−	1.63036e6i	−0.312277	−	0.165780i
$57$		0			0
$58$	−1.72802e6	−	2.99301e6i	−0.152699	−	0.264482i
$59$	1.57427e7	+	9.08906e6i	1.29919	+	0.750085i	0.980264	−	0.197695i	$-0.0633456\pi$
$59$	1.57427e7	+	9.08906e6i	1.29919	+	0.750085i	0.318923	+	0.947781i	$0.396679\pi$
$60$		0			0
$61$	−4.28000e6	+	2.47106e6i	−0.309118	+	0.178469i	−0.646532	−	0.762887i	$-0.723781\pi$
$61$	−4.28000e6	+	2.47106e6i	−0.309118	+	0.178469i	0.337414	+	0.941356i	$0.390448\pi$
$62$		−	1.44406e7i		−	0.977279i
$63$		0			0
$64$	2.09715e6			0.125000
$65$	−2.21038e6	−	3.82850e6i	−0.123827	−	0.214474i
$66$		0			0
$67$	−1.58826e7	+	2.75094e7i	−0.788173	+	1.36516i	0.138911	+	0.990305i	$0.455640\pi$
$67$	−1.58826e7	+	2.75094e7i	−0.788173	+	1.36516i	−0.927085	+	0.374852i	$0.877694\pi$
$68$	1.08221e7	−	6.24816e6i	0.506148	−	0.292225i
$69$		0			0
$70$	9.41548e6	+	1.50461e7i	0.392148	+	0.626658i
$71$	2.29883e7			0.904633			0.452317	−	0.891857i	$-0.350598\pi$
$71$	2.29883e7			0.904633			0.452317	+	0.891857i	$0.350598\pi$
$72$		0			0
$73$	−1.88605e6	−	1.08891e6i	−0.0664143	−	0.0383443i	0.466425	−	0.884561i	$-0.345542\pi$
$73$	−1.88605e6	−	1.08891e6i	−0.0664143	−	0.0383443i	−0.532839	+	0.846216i	$0.678875\pi$
$74$	1.57966e7	−	2.73606e7i	0.526791	−	0.912428i
$75$		0			0
$76$			1.00086e7i			0.299997i
$77$	5.65015e7	−	3.53573e7i	1.60730	−	1.00581i
$78$		0			0
$79$	−7.82277e6	−	1.35494e7i	−0.200841	−	0.347867i	0.747959	−	0.663745i	$-0.231034\pi$
$79$	−7.82277e6	−	1.35494e7i	−0.200841	−	0.347867i	−0.948800	+	0.315879i	$0.897701\pi$
$80$	−9.27114e6	−	5.35269e6i	−0.226346	−	0.130681i
$81$		0			0
$82$	2.08123e7	−	1.20160e7i	0.460324	−	0.265768i
$83$			1.88638e7i			0.397481i	0.980052	+	0.198741i	$0.0636851\pi$
$83$			1.88638e7i			0.397481i	−0.980052	+	0.198741i	$0.936315\pi$
$84$		0			0
$85$	−6.37903e7			−1.22202
$86$	3.37432e7	+	5.84449e7i	0.616868	+	1.06845i
$87$		0			0
$88$	−2.01006e7	+	3.48153e7i	−0.335181	+	0.580550i
$89$	6.59498e7	−	3.80762e7i	1.05112	−	0.606866i	0.128160	−	0.991754i	$-0.459093\pi$
$89$	6.59498e7	−	3.80762e7i	1.05112	−	0.606866i	0.922964	+	0.384887i	$0.125760\pi$
$90$		0			0
$91$	7.61699e6	−	1.43480e7i	0.111075	−	0.209232i
$92$	1.19915e7			0.167387
$93$		0			0
$94$	4.19442e7	+	2.42165e7i	0.537230	+	0.310170i
$95$	2.55455e7	−	4.42461e7i	0.313632	−	0.543226i
$96$		0			0
$97$			1.44142e8i			1.62818i	0.580735	+	0.814092i	$0.302765\pi$
$97$			1.44142e8i			1.62818i	−0.580735	+	0.814092i	$0.697235\pi$
$98$	−2.85146e7	+	5.86578e7i	−0.309146	+	0.635947i
$99$		0			0
$100$	2.32404e6	+	4.02536e6i	0.0232404	+	0.0402536i
$101$	1.00997e8	+	5.83108e7i	0.970564	+	0.560356i	0.899408	−	0.437110i	$-0.143998\pi$
$101$	1.00997e8	+	5.83108e7i	0.970564	+	0.560356i	0.0711561	+	0.997465i	$0.477331\pi$
$102$		0			0
$103$	1.72245e8	−	9.94459e7i	1.53038	−	0.883564i	0.531033	−	0.847351i	$-0.321804\pi$
$103$	1.72245e8	−	9.94459e7i	1.53038	−	0.883564i	0.999344	−	0.0362123i	$-0.0115292\pi$
$104$			9.79783e6i			0.0837523i
$105$		0			0
$106$	2.51842e7			0.199482
$107$	−7.65995e7	−	1.32674e8i	−0.584374	−	1.01216i	−0.994953	−	0.100340i	$-0.968007\pi$
$107$	−7.65995e7	−	1.32674e8i	−0.584374	−	1.01216i	0.410580	−	0.911825i	$-0.365326\pi$
$108$		0			0
$109$	−7.41080e6	+	1.28359e7i	−0.0525000	+	0.0909327i	−0.891081	−	0.453844i	$-0.850052\pi$
$109$	−7.41080e6	+	1.28359e7i	−0.0525000	+	0.0909327i	0.838581	+	0.544777i	$0.183386\pi$
$110$	1.77723e8	−	1.02608e8i	1.21387	−	0.700828i
$111$		0			0
$112$	−1.39852e6	−	3.93131e7i	−0.00888787	−	0.249842i
$113$	1.54533e8			0.947780			0.473890	−	0.880584i	$-0.342849\pi$
$113$	1.54533e8			0.947780			0.473890	+	0.880584i	$0.342849\pi$
$114$		0			0
$115$	−5.30124e7	−	3.06067e7i	−0.303100	−	0.174995i
$116$	1.95503e7	−	3.38620e7i	0.107974	−	0.187017i
$117$		0			0
$118$			2.05662e8i			1.06078i
$119$	−1.24345e8	−	1.98705e8i	−0.620068	−	0.990878i
$120$		0			0
$121$	−2.78139e8	−	4.81750e8i	−1.29754	−	2.24740i
$122$	−4.84227e7	−	2.79568e7i	−0.218579	−	0.126197i
$123$		0			0
$124$	1.41488e8	−	8.16884e7i	0.598459	−	0.345520i
$125$			2.31509e8i			0.948261i
$126$		0			0
$127$	−4.05583e8			−1.55907			−0.779534	−	0.626360i	$-0.784544\pi$
$127$	−4.05583e8			−1.55907			−0.779534	+	0.626360i	$0.784544\pi$
$128$	1.18633e7	+	2.05478e7i	0.0441942	+	0.0765466i
$129$		0			0
$130$	2.50076e7	−	4.33145e7i	0.0875587	−	0.151656i
$131$	−2.62492e8	+	1.51550e8i	−0.891313	+	0.514600i	−0.874372	−	0.485256i	$-0.838726\pi$
$131$	−2.62492e8	+	1.51550e8i	−0.891313	+	0.514600i	−0.0169415	+	0.999856i	$0.505393\pi$
$132$		0			0
$133$	1.87620e8	−	6.67439e6i	0.599615	−	0.0213307i
$134$	−3.59382e8			−1.11465
$135$		0			0
$136$	1.22439e8	+	7.06899e7i	0.357901	+	0.206634i
$137$	−4.17078e7	+	7.22400e7i	−0.118395	+	0.205067i	−0.919132	−	0.393950i	$-0.871108\pi$
$137$	−4.17078e7	+	7.22400e7i	−0.118395	+	0.205067i	0.800736	+	0.599017i	$0.204442\pi$
$138$		0			0
$139$		−	4.40378e8i		−	1.17969i	−0.807518	−	0.589843i	$-0.799190\pi$
$139$		−	4.40378e8i		−	1.17969i	0.807518	−	0.589843i	$-0.200810\pi$
$140$	−9.41587e7	+	1.77366e8i	−0.245103	+	0.461698i
$141$		0			0
$142$	1.30041e8	+	2.25238e8i	0.319836	+	0.553973i
$143$	−1.62656e8	−	9.39096e7i	−0.388979	−	0.224577i
$144$		0			0
$145$	−1.72856e8	+	9.97987e7i	−0.391033	+	0.225763i
$146$		−	2.46392e7i		−	0.0542270i
$147$		0			0
$148$	3.57437e8			0.744994
$149$	2.24155e8	+	3.88248e8i	0.454782	+	0.787705i	0.998676	−	0.0514488i	$-0.0163839\pi$
$149$	2.24155e8	+	3.88248e8i	0.454782	+	0.787705i	−0.543894	+	0.839154i	$0.683051\pi$
$150$		0			0
$151$	−6.40664e7	+	1.10966e8i	−0.123232	+	0.213444i	−0.921040	−	0.389467i	$-0.872659\pi$
$151$	−6.40664e7	+	1.10966e8i	−0.123232	+	0.213444i	0.797809	+	0.602911i	$0.205992\pi$
$152$	−9.80635e7	+	5.66170e7i	−0.183710	+	0.106065i
$153$		0			0
$154$	6.66051e8	+	3.53588e8i	1.18420	+	0.628659i
$155$	−8.33994e8			−1.44489
$156$		0			0
$157$	−5.55619e8	−	3.20787e8i	−0.914489	−	0.527980i	−0.0326160	−	0.999468i	$-0.510384\pi$
$157$	−5.55619e8	−	3.20787e8i	−0.914489	−	0.527980i	−0.881873	+	0.471488i	$0.843717\pi$
$158$	8.85045e7	−	1.53294e8i	0.142016	−	0.245979i
$159$		0			0
$160$		−	1.21118e8i		−	0.184811i
$161$	−7.99676e6	−	2.24792e8i	−0.0119017	−	0.334563i
$162$		0			0
$163$	−1.94108e8	−	3.36205e8i	−0.274975	−	0.476270i	0.695154	−	0.718861i	$-0.255336\pi$
$163$	−1.94108e8	−	3.36205e8i	−0.274975	−	0.476270i	−0.970129	+	0.242591i	$0.922003\pi$
$164$	2.35464e8	+	1.35945e8i	0.325499	+	0.187927i
$165$		0			0
$166$	−1.84827e8	+	1.06710e8i	−0.243406	+	0.140531i
$167$			8.17453e8i			1.05099i	0.850798	+	0.525493i	$0.176119\pi$
$167$			8.17453e8i			1.05099i	−0.850798	+	0.525493i	$0.823881\pi$
$168$		0			0
$169$	7.69956e8			0.943884
$170$	−3.60853e8	−	6.25015e8i	−0.432050	−	0.748333i
$171$		0			0
$172$	−3.81760e8	+	6.61228e8i	−0.436191	+	0.755505i
$173$	−2.71005e8	+	1.56465e8i	−0.302547	+	0.174676i	−0.643586	−	0.765373i	$-0.722554\pi$
$173$	−2.71005e8	+	1.56465e8i	−0.302547	+	0.174676i	0.341040	+	0.940049i	$0.389221\pi$
$174$		0			0
$175$	7.39094e7	−	4.62508e7i	0.0788038	−	0.0493136i
$176$	−4.54825e8			−0.474017
$177$		0			0
$178$	7.46137e8	+	4.30783e8i	0.743256	+	0.429119i
$179$	−5.83564e8	+	1.01076e9i	−0.568429	+	0.984548i	0.428293	+	0.903640i	$0.359115\pi$
$179$	−5.83564e8	+	1.01076e9i	−0.568429	+	0.984548i	−0.996722	+	0.0809079i	$0.974218\pi$
$180$		0			0
$181$		−	4.82102e7i		−	0.0449184i	−0.999748	−	0.0224592i	$-0.992850\pi$
$181$		−	4.82102e7i		−	0.0449184i	0.999748	−	0.0224592i	$-0.00714959\pi$
$182$	1.83670e8	−	6.53386e6i	0.167399	−	0.00595503i
$183$		0			0
$184$	6.78343e7	+	1.17492e8i	0.0591804	+	0.102503i
$185$	−1.58017e9	−	9.12310e8i	−1.34901	−	0.778853i
$186$		0			0
$187$	−2.34708e9	+	1.35509e9i	−1.91938	+	1.10816i
$188$			5.47957e8i			0.438647i
$189$		0			0
$190$	5.78028e8			0.443542
$191$	1.84184e8	+	3.19017e8i	0.138395	+	0.239706i	0.926889	−	0.375335i	$-0.122472\pi$
$191$	1.84184e8	+	3.19017e8i	0.138395	+	0.239706i	−0.788494	+	0.615042i	$0.789139\pi$
$192$		0			0
$193$	−1.07633e8	+	1.86426e8i	−0.0775742	+	0.134362i	−0.902203	−	0.431312i	$-0.858051\pi$
$193$	−1.07633e8	+	1.86426e8i	−0.0775742	+	0.134362i	0.824629	+	0.565674i	$0.191384\pi$
$194$	−1.41230e9	+	8.15390e8i	−0.997055	+	0.575650i
$195$		0			0
$196$	−7.36029e8	+	5.24333e7i	−0.498736	+	0.0355290i
$197$	−1.24242e9			−0.824901			−0.412450	−	0.910980i	$-0.635327\pi$
$197$	−1.24242e9			−0.824901			−0.412450	+	0.910980i	$0.635327\pi$
$198$		0			0
$199$	6.63293e7	+	3.82952e7i	0.0422954	+	0.0244193i	0.520999	−	0.853558i	$-0.325560\pi$
$199$	6.63293e7	+	3.82952e7i	0.0422954	+	0.0244193i	−0.478703	+	0.877977i	$0.658893\pi$
$200$	−2.62935e7	+	4.55417e7i	−0.0164335	+	0.0284636i
$201$		0			0
$202$			1.31942e9i			0.792462i
$203$	−6.47814e8	−	3.43907e8i	−0.381475	−	0.202515i
$204$		0			0
$205$	−6.93963e8	−	1.20198e9i	−0.392935	−	0.680584i
$206$	1.94873e9	+	1.12510e9i	1.08214	+	0.624774i
$207$		0			0
$208$	−9.59988e7	+	5.54249e7i	−0.0512876	+	0.0296109i
$209$		−	2.17063e9i		−	1.13763i
$210$		0			0
$211$	−2.38976e8			−0.120566			−0.0602829	−	0.998181i	$-0.519200\pi$
$211$	−2.38976e8			−0.120566			−0.0602829	+	0.998181i	$0.519200\pi$
$212$	1.42463e8	+	2.46753e8i	0.0705276	+	0.122157i
$213$		0			0
$214$	8.66624e8	−	1.50104e9i	0.413215	−	0.715709i
$215$	3.37539e9	−	1.94878e9i	1.57968	−	0.912031i
$216$		0			0
$217$	−1.62568e9	−	2.59786e9i	−0.733156	−	1.17159i
$218$	−1.67687e8			−0.0742462
$219$		0			0
$220$	2.01070e9	+	1.16088e9i	0.858335	+	0.495560i
$221$	−3.30261e8	+	5.72029e8i	−0.138449	+	0.239800i
$222$		0			0
$223$			1.46166e9i			0.591055i	0.955334	+	0.295527i	$0.0954954\pi$
$223$			1.46166e9i			0.591055i	−0.955334	+	0.295527i	$0.904505\pi$
$224$	3.77277e8	−	2.36091e8i	0.149854	−	0.0937752i
$225$		0			0
$226$	8.74171e8	+	1.51411e9i	0.335091	+	0.580394i
$227$	−1.93853e9	−	1.11921e9i	−0.730079	−	0.421512i	0.0883718	−	0.996088i	$-0.471834\pi$
$227$	−1.93853e9	−	1.11921e9i	−0.730079	−	0.421512i	−0.818451	+	0.574576i	$0.805167\pi$
$228$		0			0
$229$	8.57629e8	−	4.95153e8i	0.311859	−	0.180052i	−0.335899	−	0.941898i	$-0.609040\pi$
$229$	8.57629e8	−	4.95153e8i	0.311859	−	0.180052i	0.647758	+	0.761846i	$0.275707\pi$
$230$		−	6.92551e8i		−	0.247480i
$231$		0			0
$232$	4.42372e8			0.152699
$233$	1.52722e9	+	2.64522e9i	0.518176	+	0.897507i	0.999777	+	0.0211162i	$0.00672201\pi$
$233$	1.52722e9	+	2.64522e9i	0.518176	+	0.897507i	−0.481601	+	0.876390i	$0.659945\pi$
$234$		0			0
$235$	1.39858e9	−	2.42242e9i	0.458582	−	0.794288i
$236$	−2.01507e9	+	1.16340e9i	−0.649593	+	0.375043i
$237$		0			0
$238$	1.24350e9	−	2.34237e9i	0.387559	−	0.730041i
$239$	6.41304e9			1.96550			0.982748	−	0.184948i	$-0.0592115\pi$
$239$	6.41304e9			1.96550			0.982748	+	0.184948i	$0.0592115\pi$
$240$		0			0
$241$	4.46600e9	+	2.57845e9i	1.32389	+	0.764346i	0.984346	−	0.176245i	$-0.0563952\pi$
$241$	4.46600e9	+	2.57845e9i	1.32389	+	0.764346i	0.339540	+	0.940592i	$0.389729\pi$
$242$	3.14678e9	−	5.45038e9i	0.917497	−	1.58915i
$243$		0			0
$244$		−	6.32591e8i		−	0.178469i
$245$	3.38768e9	+	1.64682e9i	0.940240	+	0.457068i
$246$		0			0
$247$	−2.64513e8	−	4.58150e8i	−0.0710655	−	0.123089i
$248$	1.60076e9	+	9.24199e8i	0.423174	+	0.244320i
$249$		0			0
$250$	−2.26832e9	+	1.30961e9i	−0.580689	+	0.335261i
$251$			5.54506e9i			1.39705i	0.715586	+	0.698524i	$0.246160\pi$
$251$			5.54506e9i			1.39705i	−0.715586	+	0.698524i	$0.753840\pi$
$252$		0			0
$253$	−2.60069e9			−0.634756
$254$	−2.29433e9	−	3.97389e9i	−0.551214	−	0.954730i
$255$		0			0
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	−4.04193e8	+	2.33361e8i	−0.0926522	+	0.0534928i	−0.545610	−	0.838039i	$-0.683702\pi$
$257$	−4.04193e8	+	2.33361e8i	−0.0926522	+	0.0534928i	0.452958	+	0.891532i	$0.350369\pi$
$258$		0			0
$259$	−2.38363e8	−	6.70050e9i	−0.0529713	−	1.48905i
$260$	5.65858e8			0.123827
$261$		0			0
$262$	−2.96975e9	−	1.71459e9i	−0.630254	−	0.363877i
$263$	3.52006e9	−	6.09692e9i	0.735744	−	1.27435i	−0.218652	−	0.975803i	$-0.570166\pi$
$263$	3.52006e9	−	6.09692e9i	0.735744	−	1.27435i	0.954396	−	0.298544i	$-0.0965008\pi$
$264$		0			0
$265$		−	1.45447e9i		−	0.294932i
$266$	1.12673e9	+	1.80054e9i	0.225058	+	0.359646i
$267$		0			0
$268$	−2.03297e9	−	3.52121e9i	−0.394087	−	0.682578i
$269$	−1.82792e9	−	1.05535e9i	−0.349098	−	0.201552i	0.315190	−	0.949029i	$-0.397932\pi$
$269$	−1.82792e9	−	1.05535e9i	−0.349098	−	0.201552i	−0.664288	+	0.747477i	$0.731265\pi$
$270$		0			0
$271$	−7.02504e9	+	4.05591e9i	−1.30248	+	0.751988i	−0.980829	−	0.194869i	$-0.937572\pi$
$271$	−7.02504e9	+	4.05591e9i	−1.30248	+	0.751988i	−0.321653	+	0.946858i	$0.604238\pi$
$272$			1.59953e9i			0.292225i
$273$		0			0
$274$	−9.43740e8			−0.167436
$275$	−5.04033e8	−	8.73010e8i	−0.0881308	−	0.152647i
$276$		0			0
$277$	−9.53708e7	+	1.65187e8i	−0.0161993	+	0.0280580i	−0.874011	−	0.485905i	$-0.838490\pi$
$277$	−9.53708e7	+	1.65187e8i	−0.0161993	+	0.0280580i	0.857812	+	0.513963i	$0.171823\pi$
$278$	4.31481e9	−	2.49116e9i	0.722407	−	0.417082i
$279$		0			0
$280$	−2.27047e9	+	8.07695e7i	−0.369388	+	0.0131406i
$281$	8.10613e9			1.30014			0.650068	−	0.759876i	$-0.274741\pi$
$281$	8.10613e9			1.30014			0.650068	+	0.759876i	$0.274741\pi$
$282$		0			0
$283$	5.32236e9	+	3.07287e9i	0.829771	+	0.479069i	0.853774	−	0.520643i	$-0.174308\pi$
$283$	5.32236e9	+	3.07287e9i	0.829771	+	0.479069i	−0.0240029	+	0.999712i	$0.507641\pi$
$284$	−1.47125e9	+	2.54828e9i	−0.226158	+	0.391718i
$285$		0			0
$286$		−	2.12493e9i		−	0.317600i
$287$	2.39140e9	−	4.50465e9i	0.352472	−	0.663948i
$288$		0			0
$289$	1.27769e9	+	2.21303e9i	0.183162	+	0.317245i
$290$	−1.95565e9	−	1.12909e9i	−0.276502	−	0.159639i
$291$		0			0
$292$	2.41414e8	−	1.39381e8i	0.0332071	−	0.0191722i
$293$		−	9.76338e9i		−	1.32474i	−0.749178	−	0.662368i	$-0.769551\pi$
$293$		−	9.76338e9i		−	1.32474i	0.749178	−	0.662368i	$-0.230449\pi$
$294$		0			0
$295$	1.18777e10			1.56835
$296$	2.02197e9	+	3.50216e9i	0.263395	+	0.456214i
$297$		0			0
$298$	−2.53602e9	+	4.39252e9i	−0.321579	+	0.556992i
$299$	−5.48921e8	+	3.16920e8i	−0.0686792	+	0.0396519i
$300$		0			0
$301$	1.26499e10	+	6.71551e9i	1.54107	+	0.818112i
$302$	−1.44966e9			−0.174276
$303$		0			0
$304$	−1.10946e9	−	6.40548e8i	−0.129903	−	0.0749993i
$305$	−1.61460e9	+	2.79657e9i	−0.186580	+	0.323167i
$306$		0			0
$307$			6.84209e9i			0.770257i	0.922863	+	0.385128i	$0.125843\pi$
$307$			6.84209e9i			0.770257i	−0.922863	+	0.385128i	$0.874157\pi$
$308$	3.03308e8	+	8.52613e9i	0.0337040	+	0.947435i
$309$		0			0
$310$	−4.71778e9	−	8.17144e9i	−0.510847	−	0.884813i
$311$	−3.27953e8	−	1.89344e8i	−0.0350566	−	0.0202399i	0.482369	−	0.875968i	$-0.339776\pi$
$311$	−3.27953e8	−	1.89344e8i	−0.0350566	−	0.0202399i	−0.517426	+	0.855728i	$0.673110\pi$
$312$		0			0
$313$	−1.00983e10	+	5.83026e9i	−1.05213	+	0.607450i	−0.923246	−	0.384209i	$-0.874474\pi$
$313$	−1.00983e10	+	5.83026e9i	−1.05213	+	0.607450i	−0.128888	+	0.991659i	$0.541141\pi$
$314$		−	7.25857e9i		−	0.746677i
$315$		0			0
$316$	2.00263e9			0.200841
$317$	−1.50709e9	−	2.61035e9i	−0.149246	−	0.258501i	0.781703	−	0.623651i	$-0.214351\pi$
$317$	−1.50709e9	−	2.61035e9i	−0.149246	−	0.258501i	−0.930949	+	0.365150i	$0.881018\pi$
$318$		0			0
$319$	−4.24001e9	+	7.34392e9i	−0.409453	+	0.709194i
$320$	1.18671e9	−	6.85145e8i	0.113173	−	0.0653405i
$321$		0			0
$322$	2.15727e9	−	1.34997e9i	0.200669	−	0.125574i
$323$	−7.63368e9			−0.701333
$324$		0			0
$325$	−2.12770e8	−	1.22843e8i	−0.0190711	−	0.0110107i
$326$	2.19608e9	−	3.80372e9i	0.194436	−	0.336774i
$327$		0			0
$328$			3.07609e9i			0.265768i
$329$	1.02720e10	−	3.65415e8i	0.876739	−	0.0311891i
$330$		0			0
$331$	−7.73255e9	−	1.33932e10i	−0.644185	−	1.11576i	−0.984489	−	0.175446i	$-0.943863\pi$
$331$	−7.73255e9	−	1.33932e10i	−0.644185	−	1.11576i	0.340304	−	0.940315i	$-0.389470\pi$
$332$	−2.09107e9	−	1.20728e9i	−0.172114	−	0.0993703i
$333$		0			0
$334$	−8.00937e9	+	4.62421e9i	−0.643595	+	0.371580i
$335$			2.07555e10i			1.64799i
$336$		0			0
$337$	1.53486e10			1.19001			0.595003	−	0.803723i	$-0.297151\pi$
$337$	1.53486e10			1.19001			0.595003	+	0.803723i	$0.297151\pi$
$338$	4.35553e9	+	7.54399e9i	0.333714	+	0.578009i
$339$		0			0
$340$	4.08258e9	−	7.07124e9i	0.305506	−	0.529151i
$341$	−3.06857e10	+	1.77164e10i	−2.26944	+	1.31026i
$342$		0			0
$343$	1.47375e9	+	1.37626e10i	0.106475	+	0.994315i
$344$	−8.63825e9			−0.616868
$345$		0			0
$346$	−3.06607e9	−	1.77020e9i	−0.213933	−	0.123514i
$347$	3.88941e9	−	6.73665e9i	0.268266	−	0.464650i	−0.700148	−	0.713998i	$-0.746883\pi$
$347$	3.88941e9	−	6.73665e9i	0.268266	−	0.464650i	0.968414	+	0.249347i	$0.0802161\pi$
$348$		0			0
$349$			1.49476e10i			1.00756i	0.863833	+	0.503778i	$0.168057\pi$
$349$			1.49476e10i			1.00756i	−0.863833	+	0.503778i	$0.831943\pi$
$350$	8.71258e8	+	4.62527e8i	0.0580597	+	0.0308223i
$351$		0			0
$352$	−2.57288e9	−	4.45636e9i	−0.167590	−	0.290275i
$353$	−1.99572e10	−	1.15223e10i	−1.28529	−	0.742061i	−0.307478	−	0.951555i	$-0.599485\pi$
$353$	−1.99572e10	−	1.15223e10i	−1.28529	−	0.742061i	−0.977810	+	0.209494i	$0.932818\pi$
$354$		0			0
$355$	1.30083e10	−	7.51032e9i	0.819041	−	0.472874i
$356$			9.74750e9i			0.606866i
$357$		0			0
$358$	−1.32045e10			−0.803880
$359$	3.05292e9	+	5.28781e9i	0.183796	+	0.318345i	0.943170	−	0.332310i	$-0.107828\pi$
$359$	3.05292e9	+	5.28781e9i	0.183796	+	0.318345i	−0.759374	+	0.650655i	$0.774495\pi$
$360$		0			0
$361$	−5.43480e9	+	9.41334e9i	−0.320003	+	0.554262i
$362$	4.72362e8	−	2.72718e8i	0.0275068	−	0.0158811i
$363$		0			0
$364$	1.10301e9	+	1.76263e9i	0.0628311	+	0.100405i
$365$	−1.42300e9			−0.0801740
$366$		0			0
$367$	1.35256e10	+	7.80898e9i	0.745574	+	0.430457i	0.824092	−	0.566455i	$-0.191686\pi$
$367$	1.35256e10	+	7.80898e9i	0.745574	+	0.430457i	−0.0785184	+	0.996913i	$0.525019\pi$
$368$	−7.67457e8	+	1.32927e9i	−0.0418469	+	0.0724809i
$369$		0			0
$370$		−	2.06432e10i		−	1.10146i
$371$	4.53063e9	−	2.83516e9i	0.239146	−	0.149652i
$372$		0			0
$373$	−5.50571e9	−	9.53617e9i	−0.284432	−	0.492650i	0.688040	−	0.725673i	$-0.258472\pi$
$373$	−5.50571e9	−	9.53617e9i	−0.284432	−	0.492650i	−0.972471	+	0.233023i	$0.925138\pi$
$374$	−2.65542e10	−	1.53311e10i	−1.35721	−	0.783584i
$375$		0			0
$376$	−5.36886e9	+	3.09971e9i	−0.268615	+	0.155085i
$377$			2.06675e9i			0.102311i
$378$		0			0
$379$	−3.66496e10			−1.77629			−0.888143	−	0.459567i	$-0.848005\pi$
$379$	−3.66496e10			−1.77629			−0.888143	+	0.459567i	$0.848005\pi$
$380$	3.26982e9	+	5.66350e9i	0.156816	+	0.271613i
$381$		0			0
$382$	−2.08381e9	+	3.60926e9i	−0.0978598	+	0.169498i
$383$	−5.83120e9	+	3.36664e9i	−0.270996	+	0.156460i	−0.629340	−	0.777130i	$-0.716675\pi$
$383$	−5.83120e9	+	3.36664e9i	−0.270996	+	0.156460i	0.358344	+	0.933590i	$0.383341\pi$
$384$		0			0
$385$	2.04209e10	−	3.84667e10i	0.929464	−	1.75082i
$386$	−2.43546e9			−0.109706
$387$		0			0
$388$	−1.59783e10	−	9.22509e9i	−0.705025	−	0.407046i
$389$	1.84833e9	−	3.20140e9i	0.0807199	−	0.139811i	−0.822839	−	0.568274i	$-0.807611\pi$
$389$	1.84833e9	−	3.20140e9i	0.0807199	−	0.139811i	0.903559	+	0.428463i	$0.140945\pi$
$390$		0			0
$391$			9.14611e9i			0.391318i
$392$	−4.67735e9	−	6.91498e9i	−0.198087	−	0.292851i
$393$		0			0
$394$	−7.02816e9	−	1.21731e10i	−0.291647	−	0.505147i
$395$	−8.85327e9	−	5.11144e9i	−0.363677	−	0.209969i
$396$		0			0
$397$	4.27969e10	−	2.47088e10i	1.72286	−	0.994694i	0.809993	−	0.586439i	$-0.199471\pi$
$397$	4.27969e10	−	2.47088e10i	1.72286	−	0.994694i	0.912868	−	0.408255i	$-0.133863\pi$
$398$			8.66522e8i			0.0345340i
$399$		0			0
$400$	−5.94955e8			−0.0232404
$401$	−1.47061e9	−	2.54716e9i	−0.0568747	−	0.0985098i	0.836186	−	0.548446i	$-0.184780\pi$
$401$	−1.47061e9	−	2.54716e9i	−0.0568747	−	0.0985098i	−0.893061	+	0.449936i	$0.851447\pi$
$402$		0			0
$403$	−4.31783e9	+	7.47870e9i	−0.163699	+	0.283535i
$404$	−1.29277e10	+	7.46379e9i	−0.485282	+	0.280178i
$405$		0			0
$406$	−2.95004e8	−	8.29268e9i	−0.0108573	−	0.305205i
$407$	−7.75201e10			−2.82512
$408$		0			0
$409$	2.16429e10	+	1.24956e10i	0.773434	+	0.446542i	0.834098	−	0.551616i	$-0.185989\pi$
$409$	2.16429e10	+	1.24956e10i	0.773434	+	0.446542i	−0.0606645	+	0.998158i	$0.519322\pi$
$410$	7.85130e9	−	1.35988e10i	0.277847	−	0.481245i
$411$		0			0
$412$			2.54581e10i			0.883564i
$413$	2.31528e10	+	3.69985e10i	0.795799	+	1.27170i
$414$		0			0
$415$	6.16285e9	+	1.06744e10i	0.207773	+	0.359873i
$416$	−1.08610e9	−	6.27061e8i	−0.0362658	−	0.0209381i
$417$		0			0
$418$	2.12678e10	−	1.22790e10i	0.696653	−	0.402213i
$419$			5.50593e10i			1.78638i	0.449676	+	0.893192i	$0.351540\pi$
$419$			5.50593e10i			1.78638i	−0.449676	+	0.893192i	$0.648460\pi$
$420$		0			0
$421$	9.98403e9			0.317817			0.158909	−	0.987293i	$-0.449202\pi$
$421$	9.98403e9			0.317817			0.158909	+	0.987293i	$0.449202\pi$
$422$	−1.35185e9	−	2.34148e9i	−0.0426265	−	0.0738312i
$423$		0			0
$424$	−1.61179e9	+	2.79170e9i	−0.0498706	+	0.0863783i
$425$	−3.07020e9	+	1.77258e9i	−0.0941047	+	0.0543314i
$426$		0			0
$427$	−1.18585e10	+	4.21855e8i	−0.356713	+	0.0126897i
$428$	1.96095e10			0.584374
$429$		0			0
$430$	3.81882e10	+	2.20480e10i	1.11700	+	0.644903i
$431$	2.10447e10	−	3.64504e10i	0.609864	−	1.05631i	−0.381399	−	0.924411i	$-0.624557\pi$
$431$	2.10447e10	−	3.64504e10i	0.609864	−	1.05631i	0.991262	−	0.131904i	$-0.0421092\pi$
$432$		0			0
$433$			2.50235e9i			0.0711863i	0.999366	+	0.0355932i	$0.0113321\pi$
$433$			2.50235e9i			0.0711863i	−0.999366	+	0.0355932i	$0.988668\pi$
$434$	1.62575e10	−	3.06241e10i	0.458242	−	0.863185i
$435$		0			0
$436$	−9.48583e8	−	1.64299e9i	−0.0262500	−	0.0454663i
$437$	−6.34390e9	−	3.66265e9i	−0.173953	−	0.100432i
$438$		0			0
$439$	−4.15377e10	+	2.39818e10i	−1.11837	+	0.645689i	−0.940983	−	0.338453i	$-0.890097\pi$
$439$	−4.15377e10	+	2.39818e10i	−1.11837	+	0.645689i	−0.177383	+	0.984142i	$0.556763\pi$
$440$			2.62677e10i			0.700828i
$441$		0			0
$442$	−7.47296e9			−0.195796
$443$	−1.02730e10	−	1.77934e10i	−0.266737	−	0.462002i	0.701280	−	0.712886i	$-0.252612\pi$
$443$	−1.02730e10	−	1.77934e10i	−0.266737	−	0.462002i	−0.968017	+	0.250884i	$0.919279\pi$
$444$		0			0
$445$	2.48792e10	−	4.30920e10i	0.634447	−	1.09889i
$446$	−1.43213e10	+	8.26842e9i	−0.361946	+	0.208969i
$447$		0			0
$448$	4.44741e9	+	2.36101e9i	0.110407	+	0.0586119i
$449$	6.58561e10			1.62036			0.810178	−	0.586184i	$-0.199370\pi$
$449$	6.58561e10			1.62036			0.810178	+	0.586184i	$0.199370\pi$
$450$		0			0
$451$	−5.10669e10	−	2.94835e10i	−1.23433	−	0.712644i
$452$	−9.89012e9	+	1.71302e10i	−0.236945	+	0.410401i
$453$		0			0
$454$		−	2.53249e10i		−	0.596107i
$455$	−3.77353e8	−	1.06076e10i	−0.00880444	−	0.247497i
$456$		0			0
$457$	−7.45983e9	−	1.29208e10i	−0.171027	−	0.296227i	0.767752	−	0.640747i	$-0.221375\pi$
$457$	−7.45983e9	−	1.29208e10i	−0.171027	−	0.296227i	−0.938779	+	0.344520i	$0.888042\pi$
$458$	9.70297e9	+	5.60201e9i	0.220517	+	0.127316i
$459$		0			0
$460$	6.78558e9	−	3.91766e9i	0.151550	−	0.0874974i
$461$			1.31092e10i			0.290251i	0.989413	+	0.145125i	$0.0463586\pi$
$461$			1.31092e10i			0.290251i	−0.989413	+	0.145125i	$0.953641\pi$
$462$		0			0
$463$	−3.12775e10			−0.680626			−0.340313	−	0.940312i	$-0.610533\pi$
$463$	−3.12775e10			−0.680626			−0.340313	+	0.940312i	$0.610533\pi$
$464$	2.50243e9	+	4.33434e9i	0.0539872	+	0.0935085i
$465$		0			0
$466$	−1.72785e10	+	2.99272e10i	−0.366406	+	0.634633i
$467$	8.08128e10	−	4.66573e10i	1.69908	−	0.980962i	0.752438	−	0.658663i	$-0.228878\pi$
$467$	8.08128e10	−	4.66573e10i	1.69908	−	0.980962i	0.946638	−	0.322299i	$-0.104456\pi$
$468$		0			0
$469$	−6.46527e10	+	4.04581e10i	−1.33627	+	0.836208i
$470$	3.16464e10			0.648533
$471$		0			0
$472$	−2.27979e10	−	1.31624e10i	−0.459332	−	0.265195i
$473$	8.27953e10	−	1.43406e11i	1.65410	−	2.86498i
$474$		0			0
$475$		−	2.83939e9i		−	0.0557765i
$476$	2.99847e10	−	1.06668e9i	0.584080	−	0.0207780i
$477$		0			0
$478$	3.62776e10	+	6.28347e10i	0.694908	+	1.20362i
$479$	−6.05959e10	−	3.49850e10i	−1.15107	−	0.664570i	−0.201921	−	0.979402i	$-0.564718\pi$
$479$	−6.05959e10	−	3.49850e10i	−1.15107	−	0.664570i	−0.949147	+	0.314832i	$0.898052\pi$
$480$		0			0
$481$	−1.63620e10	+	9.44659e9i	−0.305672	+	0.176480i
$482$			5.83436e10i			1.08095i
$483$		0			0
$484$	7.12035e10			1.29754
$485$	4.70916e10	+	8.15650e10i	0.851091	+	1.47413i
$486$		0			0
$487$	−2.00394e10	+	3.47092e10i	−0.356261	+	0.617062i	−0.987333	−	0.158662i	$-0.949282\pi$
$487$	−2.00394e10	+	3.47092e10i	−0.356261	+	0.617062i	0.631072	+	0.775724i	$0.282615\pi$
$488$	6.19810e9	−	3.57848e9i	0.109290	−	0.0630985i
$489$		0			0
$490$	3.02820e9	+	4.25082e10i	0.0525292	+	0.737375i
$491$	−6.13480e10			−1.05554			−0.527770	−	0.849387i	$-0.676972\pi$
$491$	−6.13480e10			−1.05554			−0.527770	+	0.849387i	$0.676972\pi$
$492$		0			0
$493$	2.58271e10	+	1.49113e10i	0.437208	+	0.252422i
$494$	2.99262e9	−	5.18337e9i	0.0502509	−	0.0870371i
$495$		0			0
$496$			2.09122e10i			0.345520i
$497$	4.87510e10	+	2.58806e10i	0.799021	+	0.424178i
$498$		0			0
$499$	1.57072e10	+	2.72056e10i	0.253335	+	0.438790i	0.964442	−	0.264294i	$-0.0851390\pi$
$499$	1.57072e10	+	2.72056e10i	0.253335	+	0.438790i	−0.711107	+	0.703084i	$0.751806\pi$
$500$	−2.56631e10	−	1.48166e10i	−0.410609	−	0.237065i
$501$		0			0
$502$	−5.43303e10	+	3.13676e10i	−0.855514	+	0.493931i
$503$			5.45243e10i			0.851763i	0.904779	+	0.425881i	$0.140036\pi$
$503$			5.45243e10i			0.851763i	−0.904779	+	0.425881i	$0.859964\pi$
$504$		0			0
$505$	7.62012e10			1.17165
$506$	−1.47117e10	−	2.54815e10i	−0.224420	−	0.388707i
$507$		0			0
$508$	2.59573e10	−	4.49594e10i	0.389767	−	0.675096i
$509$	−6.70138e10	+	3.86904e10i	−0.998373	+	0.576411i	−0.907767	−	0.419476i	$-0.862214\pi$
$509$	−6.70138e10	+	3.86904e10i	−0.998373	+	0.576411i	−0.0906066	+	0.995887i	$0.528881\pi$
$510$		0			0
$511$	−2.77381e9	−	4.43259e9i	−0.0406812	−	0.0650091i
$512$	−3.03700e9			−0.0441942
$513$		0			0
$514$	−4.57292e9	−	2.64018e9i	−0.0655150	−	0.0378251i
$515$	6.49784e10	−	1.12546e11i	0.923720	−	1.59993i
$516$		0			0
$517$		−	1.18840e11i		−	1.66341i
$518$	6.43029e10	−	4.02392e10i	0.893123	−	0.558896i
$519$		0			0
$520$	3.20098e9	+	5.54425e9i	0.0437793	+	0.0758280i
$521$	−4.97137e10	−	2.87022e10i	−0.674722	−	0.389551i	0.123141	−	0.992389i	$-0.460703\pi$
$521$	−4.97137e10	−	2.87022e10i	−0.674722	−	0.389551i	−0.797864	+	0.602838i	$0.794037\pi$
$522$		0			0
$523$	−2.15576e10	+	1.24463e10i	−0.288133	+	0.166354i	−0.637100	−	0.770781i	$-0.719866\pi$
$523$	−2.15576e10	+	1.24463e10i	−0.288133	+	0.166354i	0.348966	+	0.937135i	$0.386533\pi$
$524$		−	3.87967e10i		−	0.514600i
$525$		0			0
$526$	7.96498e10			1.04050
$527$	6.23050e10	+	1.07915e11i	0.807756	+	1.39907i
$528$		0			0
$529$	3.47672e10	−	6.02185e10i	0.443963	−	0.768966i
$530$	1.42509e10	−	8.22773e9i	0.180608	−	0.104274i
$531$		0			0
$532$	−1.12678e10	+	2.12251e10i	−0.140667	+	0.264974i
$533$	−1.43714e10			−0.178070
$534$		0			0
$535$	−8.66900e10	−	5.00505e10i	−1.05817	−	0.610932i
$536$	2.30004e10	−	3.98379e10i	0.278661	−	0.482656i
$537$		0			0
$538$		−	2.38798e10i		−	0.285037i
$539$	1.59628e11	−	1.13716e10i	1.89128	−	0.134731i
$540$		0			0
$541$	6.51069e10	+	1.12768e11i	0.760043	+	1.31643i	0.942828	+	0.333280i	$0.108155\pi$
$541$	6.51069e10	+	1.12768e11i	0.760043	+	1.31643i	−0.182785	+	0.983153i	$0.558511\pi$
$542$	−7.94793e10	−	4.58874e10i	−0.920994	−	0.531736i
$543$		0			0
$544$	−1.56721e10	+	9.04831e9i	−0.178950	+	0.103317i
$545$			9.68451e9i			0.109772i
$546$		0			0
$547$	−1.36767e11			−1.52768			−0.763839	−	0.645407i	$-0.776688\pi$
$547$	−1.36767e11			−1.52768			−0.763839	+	0.645407i	$0.776688\pi$
$548$	−5.33860e9	−	9.24673e9i	−0.0591977	−	0.102533i
$549$		0			0
$550$	5.70248e9	−	9.87698e9i	0.0623179	−	0.107938i
$551$	−2.06854e10	+	1.19427e10i	−0.224418	+	0.129568i
$552$		0			0
$553$	−1.33549e9	−	3.75412e10i	−0.0142804	−	0.401428i
$554$	−2.15799e9			−0.0229093
$555$		0			0
$556$	4.88165e10	+	2.81842e10i	0.510819	+	0.294922i
$557$	1.82963e10	−	3.16901e10i	0.190083	−	0.329233i	−0.755195	−	0.655500i	$-0.772458\pi$
$557$	1.82963e10	−	3.16901e10i	0.190083	−	0.329233i	0.945277	+	0.326268i	$0.105791\pi$
$558$		0			0
$559$		−	4.03577e10i		−	0.413313i
$560$	−1.36351e10	−	2.17890e10i	−0.138645	−	0.221557i
$561$		0			0
$562$	4.58552e10	+	7.94236e10i	0.459667	+	0.796167i
$563$	7.96758e10	+	4.60008e10i	0.793035	+	0.457859i	0.841030	−	0.540988i	$-0.181950\pi$
$563$	7.96758e10	+	4.60008e10i	0.793035	+	0.457859i	−0.0479946	+	0.998848i	$0.515283\pi$
$564$		0			0
$565$	8.74449e10	−	5.04863e10i	0.858106	−	0.495428i
$566$			6.95310e10i			0.677506i
$567$		0			0
$568$	−3.32905e10			−0.319836
$569$	−5.98155e10	−	1.03603e11i	−0.570643	−	0.988383i	−0.996500	−	0.0835923i	$-0.973361\pi$
$569$	−5.98155e10	−	1.03603e11i	−0.570643	−	0.988383i	0.425857	−	0.904790i	$-0.359973\pi$
$570$		0			0
$571$	2.22070e10	−	3.84636e10i	0.208903	−	0.361831i	−0.742466	−	0.669883i	$-0.766344\pi$
$571$	2.22070e10	−	3.84636e10i	0.208903	−	0.361831i	0.951369	+	0.308053i	$0.0996774\pi$
$572$	2.08200e10	−	1.20204e10i	0.194490	−	0.112289i
$573$		0			0
$574$	5.76642e10	−	2.05134e9i	0.531201	−	0.0188969i
$575$	−3.40195e9			−0.0311212
$576$		0			0
$577$	−1.38340e11	−	7.98709e10i	−1.24809	−	0.720585i	−0.277362	−	0.960766i	$-0.589460\pi$
$577$	−1.38340e11	−	7.98709e10i	−1.24809	−	0.720585i	−0.970728	+	0.240181i	$0.922793\pi$
$578$	−1.44554e10	+	2.50375e10i	−0.129515	+	0.224326i
$579$		0			0
$580$		−	2.55485e10i		−	0.225763i
$581$	−2.12372e10	+	4.00043e10i	−0.186377	+	0.351077i
$582$		0			0
$583$	−3.08971e10	−	5.35153e10i	−0.267450	−	0.463238i
$584$	2.73129e9	+	1.57691e9i	0.0234810	+	0.0135568i
$585$		0			0
$586$	9.56612e10	−	5.52300e10i	0.811232	−	0.468365i
$587$			6.45369e10i			0.543571i	0.962358	+	0.271785i	$0.0876141\pi$
$587$			6.45369e10i			0.543571i	−0.962358	+	0.271785i	$0.912386\pi$
$588$		0			0
$589$	−9.98026e10			−0.829241
$590$	6.71903e10	+	1.16377e11i	0.554496	+	0.960415i
$591$		0			0
$592$	−2.28760e10	+	3.96224e10i	−0.186249	+	0.322592i
$593$	−1.42839e11	+	8.24683e10i	−1.15512	+	0.666912i	−0.950131	−	0.311852i	$-0.899051\pi$
$593$	−1.42839e11	+	8.24683e10i	−1.15512	+	0.666912i	−0.204994	+	0.978763i	$0.565718\pi$
$594$		0			0
$595$	−1.35280e11	−	7.18163e10i	−1.07936	−	0.573001i
$596$	−5.73836e10			−0.454782
$597$		0			0
$598$	−6.21033e9	−	3.58554e9i	−0.0485635	−	0.0280382i
$599$	−2.47750e10	+	4.29116e10i	−0.192445	+	0.333325i	−0.946060	−	0.323992i	$-0.894975\pi$
$599$	−2.47750e10	+	4.29116e10i	−0.192445	+	0.333325i	0.753615	+	0.657316i	$0.228308\pi$
$600$		0			0
$601$			7.98491e10i			0.612029i	0.952027	+	0.306014i	$0.0989956\pi$
$601$			7.98491e10i			0.612029i	−0.952027	+	0.306014i	$0.901004\pi$
$602$	5.76057e9	+	1.61932e11i	0.0438611	+	1.23296i
$603$		0			0
$604$	−8.20050e9	−	1.42037e10i	−0.0616158	−	0.106722i
$605$	−3.14778e11	−	1.81737e11i	−2.34954	−	1.35651i
$606$		0			0
$607$	8.48948e9	−	4.90140e9i	0.0625355	−	0.0361049i	−0.468406	−	0.883513i	$-0.655172\pi$
$607$	8.48948e9	−	4.90140e9i	0.0625355	−	0.0361049i	0.530942	+	0.847408i	$0.321838\pi$
$608$		−	1.44939e10i		−	0.106065i
$609$		0			0
$610$	−3.65343e10			−0.263865
$611$	−1.44818e10	−	2.50832e10i	−0.103910	−	0.179977i
$612$		0			0
$613$	8.89832e10	−	1.54123e11i	0.630182	−	1.09151i	−0.357332	−	0.933977i	$-0.616314\pi$
$613$	8.89832e10	−	1.54123e11i	0.630182	−	1.09151i	0.987514	−	0.157530i	$-0.0503531\pi$
$614$	−6.70386e10	+	3.87047e10i	−0.471684	+	0.272327i
$615$		0			0
$616$	−8.18229e10	+	5.12029e10i	−0.568267	+	0.355608i
$617$	−2.41894e10			−0.166911			−0.0834553	−	0.996512i	$-0.526596\pi$
$617$	−2.41894e10			−0.166911			−0.0834553	+	0.996512i	$0.526596\pi$
$618$		0			0
$619$	4.35106e10	+	2.51209e10i	0.296369	+	0.171109i	0.640810	−	0.767699i	$-0.278598\pi$
$619$	4.35106e10	+	2.51209e10i	0.296369	+	0.171109i	−0.344442	+	0.938808i	$0.611932\pi$
$620$	5.33756e10	−	9.24493e10i	0.361224	−	0.625658i
$621$		0			0
$622$		−	4.28436e9i		−	0.0286236i
$623$	1.82726e11	−	6.50029e9i	1.21297	−	0.0431500i
$624$		0			0
$625$	8.27270e10	+	1.43287e11i	0.542160	+	0.939049i
$626$	−1.14249e11	−	6.59618e10i	−0.743971	−	0.429532i
$627$		0			0
$628$	7.11192e10	−	4.10607e10i	0.457244	−	0.263990i
$629$			2.72623e11i			1.74165i
$630$		0			0
$631$	−9.14077e10			−0.576587			−0.288294	−	0.957542i	$-0.593088\pi$
$631$	−9.14077e10			−0.576587			−0.288294	+	0.957542i	$0.593088\pi$
$632$	1.13286e10	+	1.96217e10i	0.0710080	+	0.122989i
$633$		0			0
$634$	1.70508e10	−	2.95328e10i	0.105533	−	0.182788i
$635$	−2.29506e11	+	1.32505e11i	−1.41156	+	0.814962i
$636$		0			0
$637$	3.23066e10	−	2.18524e10i	0.196215	−	0.132722i
$638$	−9.59406e10			−0.579055
$639$		0			0
$640$	1.34260e10	+	7.75153e9i	0.0800254	+	0.0462027i
$641$	9.72074e10	−	1.68368e11i	0.575794	−	0.997305i	−0.420161	−	0.907450i	$-0.638026\pi$
$641$	9.72074e10	−	1.68368e11i	0.575794	−	0.997305i	0.995955	−	0.0898549i	$-0.0286403\pi$
$642$		0			0
$643$			2.71299e11i			1.58710i	0.608506	+	0.793550i	$0.291769\pi$
$643$			2.71299e11i			1.58710i	−0.608506	+	0.793550i	$0.708231\pi$
$644$	2.54303e10	+	1.35003e10i	0.147846	+	0.0784872i
$645$		0			0
$646$	−4.31826e10	−	7.47945e10i	−0.247958	−	0.429477i
$647$	−2.38580e11	−	1.37744e11i	−1.36150	−	0.786061i	−0.371675	−	0.928363i	$-0.621216\pi$
$647$	−2.38580e11	−	1.37744e11i	−1.36150	−	0.786061i	−0.989823	+	0.142302i	$0.954550\pi$
$648$		0			0
$649$	4.37023e11	−	2.52315e11i	2.46335	−	1.42221i
$650$		−	2.77961e9i		−	0.0155715i
$651$		0			0
$652$	4.96916e10			0.274975
$653$	−7.33889e9	−	1.27113e10i	−0.0403624	−	0.0699098i	0.845138	−	0.534547i	$-0.179518\pi$
$653$	−7.33889e9	−	1.27113e10i	−0.0403624	−	0.0699098i	−0.885501	+	0.464638i	$0.846185\pi$
$654$		0			0
$655$	−9.90233e10	+	1.71513e11i	−0.537988	+	0.931822i
$656$	−3.01394e10	+	1.74010e10i	−0.162749	+	0.0939633i
$657$		0			0
$658$	6.16874e10	+	9.85773e10i	0.329073	+	0.525864i
$659$	−1.85183e11			−0.981883			−0.490941	−	0.871193i	$-0.663347\pi$
$659$	−1.85183e11			−0.981883			−0.490941	+	0.871193i	$0.663347\pi$
$660$		0			0
$661$	2.46702e11	+	1.42433e11i	1.29231	+	0.746116i	0.979063	−	0.203556i	$-0.0652498\pi$
$661$	2.46702e11	+	1.42433e11i	1.29231	+	0.746116i	0.313247	+	0.949672i	$0.398583\pi$
$662$	8.74838e10	−	1.51526e11i	0.455507	−	0.788962i
$663$		0			0
$664$		−	2.73177e10i		−	0.140531i
$665$	1.03987e11	−	6.50727e10i	0.531732	−	0.332746i
$666$		0			0
$667$	1.43089e10	+	2.47838e10i	0.0722942	+	0.125217i
$668$	−9.06157e10	−	5.23170e10i	−0.455090	−	0.262747i
$669$		0			0
$670$	−2.03362e11	+	1.17411e11i	−1.00918	+	0.582652i
$671$			1.37195e11i			0.676780i
$672$		0			0
$673$	−2.03429e10			−0.0991635			−0.0495817	−	0.998770i	$-0.515789\pi$
$673$	−2.03429e10			−0.0991635			−0.0495817	+	0.998770i	$0.515789\pi$
$674$	8.68248e10	+	1.50385e11i	0.420731	+	0.728727i
$675$		0			0
$676$	−4.92772e10	+	8.53505e10i	−0.235971	+	0.408714i
$677$	−2.36996e11	+	1.36830e11i	−1.12820	+	0.651366i	−0.943481	−	0.331425i	$-0.892471\pi$
$677$	−2.36996e11	+	1.36830e11i	−1.12820	+	0.651366i	−0.184718	+	0.982792i	$0.559137\pi$
$678$		0			0
$679$	−1.62278e11	+	3.05681e11i	−0.763448	+	1.43810i
$680$	9.23783e10			0.432050
$681$		0			0
$682$	−3.47169e11	−	2.00438e11i	−1.60473	−	0.926494i
$683$	−8.12982e8	+	1.40813e9i	−0.00373592	+	0.00647081i	−0.867887	−	0.496761i	$-0.834523\pi$
$683$	−8.12982e8	+	1.40813e9i	−0.00373592	+	0.00647081i	0.864151	+	0.503232i	$0.167856\pi$
$684$		0			0
$685$			5.45042e10i			0.247553i
$686$	−1.26509e11	+	9.22928e10i	−0.571247	+	0.416746i
$687$		0			0
$688$	−4.88653e10	−	8.46372e10i	−0.218096	−	0.377753i
$689$	−1.30427e10	−	7.53022e9i	−0.0578751	−	0.0334142i
$690$		0			0
$691$	2.02262e10	−	1.16776e10i	0.0887162	−	0.0512203i	−0.454986	−	0.890499i	$-0.650356\pi$
$691$	2.02262e10	−	1.16776e10i	0.0887162	−	0.0512203i	0.543702	+	0.839278i	$0.317022\pi$
$692$		−	4.00550e10i		−	0.174676i
$693$		0			0
$694$	8.80072e10			0.379385
$695$	−1.43873e11	−	2.49195e11i	−0.616650	−	1.06807i
$696$		0			0
$697$	−1.03687e11	+	1.79592e11i	−0.439334	+	0.760950i
$698$	−1.46456e11	+	8.45562e10i	−0.616999	+	0.356225i
$699$		0			0
$700$	3.96756e8	+	1.11530e10i	0.00165246	+	0.0464515i
$701$	2.58500e11			1.07050			0.535252	−	0.844693i	$-0.320217\pi$
$701$	2.58500e11			1.07050			0.535252	+	0.844693i	$0.320217\pi$
$702$		0			0
$703$	−1.89096e11	−	1.09175e11i	−0.774214	−	0.446992i
$704$	2.91088e10	−	5.04180e10i	0.118504	−	0.205255i
$705$		0			0
$706$		−	2.60719e11i		−	1.04943i
$707$	1.48537e11	+	2.37364e11i	0.594506	+	0.950029i
$708$		0			0
$709$	−1.09246e11	−	1.89220e11i	−0.432336	−	0.748828i	0.564738	−	0.825270i	$-0.308977\pi$
$709$	−1.09246e11	−	1.89220e11i	−0.432336	−	0.748828i	−0.997074	+	0.0764424i	$0.975644\pi$
$710$	1.47172e11	+	8.49696e10i	0.579149	+	0.334372i
$711$		0			0
$712$	−9.55056e10	+	5.51402e10i	−0.371628	+	0.214560i
$713$			1.19576e11i			0.462686i
$714$		0			0
$715$	−1.22722e11			−0.469568
$716$	−7.46962e10	−	1.29378e11i	−0.284215	−	0.492274i
$717$		0			0
$718$	−3.45398e10	+	5.98247e10i	−0.129964	+	0.225104i
$719$	2.52373e11	−	1.45708e11i	0.944337	−	0.545213i	0.0530201	−	0.998593i	$-0.483115\pi$
$719$	2.52373e11	−	1.45708e11i	0.944337	−	0.545213i	0.891317	+	0.453380i	$0.149782\pi$
$720$		0			0
$721$	4.77237e11	−	1.69772e10i	1.76601	−	0.0628240i
$722$	−1.22975e11			−0.452553
$723$		0			0
$724$	5.34416e9	+	3.08545e9i	0.0194503	+	0.0112296i
$725$	−5.54634e9	+	9.60654e9i	−0.0200750	+	0.0347708i
$726$		0			0
$727$		−	5.02509e10i		−	0.179890i	−0.995947	−	0.0899448i	$-0.971331\pi$
$727$		−	5.02509e10i		−	0.179890i	0.995947	−	0.0899448i	$-0.0286691\pi$
$728$	−1.10306e10	+	2.07782e10i	−0.0392711	+	0.0739745i
$729$		0			0
$730$	−8.04970e9	−	1.39425e10i	−0.0283458	−	0.0490963i
$731$	−5.04329e11	−	2.91174e11i	−1.76622	−	1.01973i
$732$		0			0
$733$	−1.41107e10	+	8.14684e9i	−0.0488803	+	0.0282211i	−0.524241	−	0.851570i	$-0.675651\pi$
$733$	−1.41107e10	+	8.14684e9i	−0.0488803	+	0.0282211i	0.475361	+	0.879791i	$0.342318\pi$
$734$			1.76697e11i			0.608759i
$735$		0			0
$736$	−1.73656e10			−0.0591804
$737$	4.40906e11	+	7.63671e11i	1.49443	+	2.58843i
$738$		0			0
$739$	−1.84732e11	+	3.19966e11i	−0.619391	+	1.07282i	0.370206	+	0.928950i	$0.379287\pi$
$739$	−1.84732e11	+	3.19966e11i	−0.619391	+	1.07282i	−0.989597	+	0.143867i	$0.954046\pi$
$740$	2.02261e11	−	1.16776e11i	0.674506	−	0.389426i
$741$		0			0
$742$	5.34079e10	+	2.83528e10i	0.176193	+	0.0935363i
$743$	4.71388e11			1.54676			0.773380	−	0.633942i	$-0.218564\pi$
$743$	4.71388e11			1.54676			0.773380	+	0.633942i	$0.218564\pi$
$744$		0			0
$745$	2.53683e11	+	1.46464e11i	0.823505	+	0.475451i
$746$	6.22900e10	−	1.07889e11i	0.201124	−	0.348356i
$747$		0			0
$748$		−	3.46902e11i		−	1.10816i
$749$	−1.30769e10	−	3.67598e11i	−0.0415507	−	1.16801i
$750$		0			0
$751$	4.80229e10	+	8.31780e10i	0.150969	+	0.261486i	0.931584	−	0.363526i	$-0.118427\pi$
$751$	4.80229e10	+	8.31780e10i	0.150969	+	0.261486i	−0.780615	+	0.625012i	$0.785094\pi$
$752$	−6.07417e10	−	3.50692e10i	−0.189940	−	0.109662i
$753$		0			0
$754$	−2.02499e10	+	1.16913e10i	−0.0626524	+	0.0361724i
$755$			8.37226e10i			0.257665i
$756$		0			0
$757$	5.08191e11			1.54754			0.773772	−	0.633464i	$-0.218367\pi$
$757$	5.08191e11			1.54754			0.773772	+	0.633464i	$0.218367\pi$
$758$	−2.07322e11	−	3.59092e11i	−0.628012	−	1.08775i
$759$		0			0
$760$	−3.69938e10	+	6.40752e10i	−0.110885	+	0.192059i
$761$	3.00390e11	−	1.73430e11i	0.895667	−	0.517113i	0.0198748	−	0.999802i	$-0.493673\pi$
$761$	3.00390e11	−	1.73430e11i	0.895667	−	0.517113i	0.875792	+	0.482689i	$0.160340\pi$
$762$		0			0
$763$	−3.01669e10	+	1.88777e10i	−0.0890087	+	0.0556996i
$764$	−4.71512e10			−0.138395
$765$		0			0
$766$	−6.59725e10	−	3.80892e10i	−0.191623	−	0.110634i
$767$	6.14942e10	−	1.06511e11i	0.177686	−	0.307761i
$768$		0			0
$769$		−	2.21968e11i		−	0.634724i	−0.948304	−	0.317362i	$-0.897203\pi$
$769$		−	2.21968e11i		−	0.634724i	0.948304	−	0.317362i	$-0.102797\pi$
$770$	4.92413e11	−	1.75171e10i	1.40077	−	0.0498309i
$771$		0			0
$772$	−1.37771e10	−	2.38626e10i	−0.0387871	−	0.0671812i
$773$	3.27357e11	+	1.88999e11i	0.916860	+	0.529349i	0.882632	−	0.470065i	$-0.155769\pi$
$773$	3.27357e11	+	1.88999e11i	0.916860	+	0.529349i	0.0342281	+	0.999414i	$0.489103\pi$
$774$		0			0
$775$	−4.01398e10	+	2.31747e10i	−0.111267	+	0.0642403i
$776$		−	2.08740e11i		−	0.575650i
$777$		0			0
$778$	4.18229e10			0.114155
$779$	−8.30454e10	−	1.43839e11i	−0.225510	−	0.390595i
$780$		0			0
$781$	3.19081e11	−	5.52664e11i	0.857623	−	1.48545i
$782$	−8.96132e10	+	5.17382e10i	−0.239632	+	0.138352i
$783$		0			0
$784$	4.12936e10	−	8.49455e10i	0.109300	−	0.224841i
$785$	−4.19207e11			−1.10395
$786$		0			0
$787$	−2.86479e8	−	1.65399e8i	−0.000746783	−	0.000431156i	0.499627	−	0.866241i	$-0.333471\pi$
$787$	−2.86479e8	−	1.65399e8i	−0.000746783	−	0.000431156i	−0.500373	+	0.865810i	$0.666804\pi$
$788$	7.95146e10	−	1.37723e11i	0.206225	−	0.357193i
$789$		0			0
$790$		−	1.15659e11i		−	0.296941i
$791$	3.27717e11	+	1.73976e11i	0.837130	+	0.444410i
$792$		0			0
$793$	1.67185e10	+	2.89574e10i	0.0422771	+	0.0732261i
$794$	4.84192e11	+	2.79548e11i	1.21825	+	0.703355i
$795$		0			0
$796$	−8.49015e9	+	4.90179e9i	−0.0211477	+	0.0122096i
$797$		−	4.05700e11i		−	1.00548i	−0.864439	−	0.502738i	$-0.832326\pi$
$797$		−	4.05700e11i		−	1.00548i	0.864439	−	0.502738i	$-0.167674\pi$
$798$		0			0
$799$	−4.17935e11			−1.02547
$800$	−3.36557e9	−	5.82934e9i	−0.00821673	−	0.0142318i
$801$		0			0
$802$	1.66380e10	−	2.88179e10i	0.0402165	−	0.0696569i
$803$	−5.23573e10	+	3.02285e10i	−0.125926	+	0.0727034i
$804$		0			0
$805$	−7.79653e10	−	1.24590e11i	−0.185660	−	0.296687i
$806$	−9.77013e10			−0.231505
$807$		0			0
$808$	−1.46260e11	−	8.44431e10i	−0.343146	−	0.198116i
$809$	3.98666e11	−	6.90510e11i	0.930712	−	1.61204i	0.148605	−	0.988897i	$-0.452522\pi$
$809$	3.98666e11	−	6.90510e11i	0.930712	−	1.61204i	0.782107	−	0.623144i	$-0.214145\pi$
$810$		0			0
$811$			6.69434e11i			1.54748i	0.633504	+	0.773739i	$0.281616\pi$
$811$			6.69434e11i			1.54748i	−0.633504	+	0.773739i	$0.718384\pi$
$812$	7.95826e10	−	4.98009e10i	0.183060	−	0.114555i
$813$		0			0
$814$	−4.38520e11	−	7.59539e11i	−0.998831	−	1.73003i
$815$	−2.19678e11	−	1.26831e11i	−0.497916	−	0.287472i
$816$		0			0
$817$	4.03927e11	−	2.33207e11i	0.906598	−	0.523425i
$818$			2.82742e11i			0.631506i
$819$		0			0
$820$	1.77655e11			0.392935
$821$	2.05956e11	+	3.56727e11i	0.453318	+	0.785169i	0.998590	−	0.0530899i	$-0.0169070\pi$
$821$	2.05956e11	+	3.56727e11i	0.453318	+	0.785169i	−0.545272	+	0.838259i	$0.683574\pi$
$822$		0			0
$823$	2.43752e11	−	4.22191e11i	0.531311	−	0.920258i	−0.468021	−	0.883717i	$-0.655033\pi$
$823$	2.43752e11	−	4.22191e11i	0.531311	−	0.920258i	0.999332	−	0.0365405i	$-0.0116338\pi$
$824$	−2.49438e11	+	1.44013e11i	−0.541070	+	0.312387i
$825$		0			0
$826$	−2.31538e11	+	4.36146e11i	−0.497395	+	0.936939i
$827$	2.20022e11			0.470376			0.235188	−	0.971950i	$-0.424429\pi$
$827$	2.20022e11			0.470376			0.235188	+	0.971950i	$0.424429\pi$
$828$		0			0
$829$	5.08634e11	+	2.93660e11i	1.07693	+	0.621766i	0.930067	−	0.367391i	$-0.119749\pi$
$829$	5.08634e11	+	2.93660e11i	1.07693	+	0.621766i	0.146863	+	0.989157i	$0.453082\pi$
$830$	−6.97247e10	+	1.20767e11i	−0.146918	+	0.254469i
$831$		0			0
$832$		−	1.41888e10i		−	0.0296109i
$833$	−3.99917e10	−	5.61381e11i	−0.0830596	−	1.16594i
$834$		0			0
$835$	2.67064e11	+	4.62569e11i	0.549376	+	0.951547i
$836$	2.40617e11	+	1.38920e11i	0.492608	+	0.284408i
$837$		0			0
$838$	−5.39469e11	+	3.11463e11i	−1.09393	+	0.631582i
$839$		−	2.54607e11i		−	0.513834i	−0.966433	−	0.256917i	$-0.917293\pi$
$839$		−	2.54607e11i		−	0.513834i	0.966433	−	0.256917i	$-0.0827067\pi$
$840$		0			0
$841$	−4.06933e11			−0.813465
$842$	5.64782e10	+	9.78231e10i	0.112365	+	0.194623i
$843$		0			0
$844$	1.52945e10	−	2.64908e10i	0.0301415	−	0.0522066i
$845$	4.35691e11	−	2.51546e11i	0.854578	−	0.493391i
$846$		0			0
$847$	−4.74833e10	−	1.33478e12i	−0.0922587	−	2.59343i
$848$	−3.64706e10			−0.0705276
$849$		0			0
$850$	−3.47354e10	−	2.00545e10i	−0.0665421	−	0.0384181i
$851$	−1.30805e11	+	2.26561e11i	−0.249405	+	0.431983i
$852$		0			0
$853$			8.69174e11i			1.64176i	0.571099	+	0.820881i	$0.306517\pi$
$853$			8.69174e11i			1.64176i	−0.571099	+	0.820881i	$0.693483\pi$
$854$	−7.12153e10	−	1.13803e11i	−0.133888	−	0.213955i
$855$		0			0
$856$	1.10928e11	+	1.92133e11i	0.206607	+	0.357854i
$857$	−2.04031e11	−	1.17797e11i	−0.378245	−	0.218380i	0.298810	−	0.954313i	$-0.403410\pi$
$857$	−2.04031e11	−	1.17797e11i	−0.378245	−	0.218380i	−0.677054	+	0.735933i	$0.736744\pi$
$858$		0			0
$859$	−5.48368e11	+	3.16600e11i	−1.00716	+	0.581485i	−0.910359	−	0.413819i	$-0.864195\pi$
$859$	−5.48368e11	+	3.16600e11i	−1.00716	+	0.581485i	−0.0968021	+	0.995304i	$0.530861\pi$
$860$			4.98888e11i			0.912031i
$861$		0			0
$862$	4.76186e11			0.862478
$863$	1.38463e11	+	2.39825e11i	0.249626	+	0.432365i	0.963422	−	0.267989i	$-0.0863589\pi$
$863$	1.38463e11	+	2.39825e11i	0.249626	+	0.432365i	−0.713796	+	0.700354i	$0.753026\pi$
$864$		0			0
$865$	−1.02235e11	+	1.77076e11i	−0.182614	+	0.316297i
$866$	−2.45179e10	+	1.41554e10i	−0.0435925	+	0.0251682i
$867$		0			0
$868$	3.92020e11	−	1.39457e10i	0.690604	−	0.0245675i
$869$	−4.34325e11			−0.761616
$870$		0			0
$871$	1.86122e11	+	1.07457e11i	0.323388	+	0.186708i
$872$	1.07320e10	−	1.85883e10i	0.0185616	−	0.0321495i
$873$		0			0
$874$		−	8.28764e10i		−	0.142032i
$875$	−2.60637e11	+	4.90960e11i	−0.444635	+	0.837555i
$876$		0			0
$877$	−2.05639e11	−	3.56178e11i	−0.347623	−	0.602100i	0.638204	−	0.769867i	$-0.279678\pi$
$877$	−2.05639e11	−	3.56178e11i	−0.347623	−	0.602100i	−0.985827	+	0.167767i	$0.946344\pi$
$878$	−4.69945e11	−	2.71323e11i	−0.790805	−	0.456571i
$879$		0			0
$880$	−2.57370e11	+	1.48593e11i	−0.429168	+	0.247780i
$881$			8.49897e11i			1.41079i	0.708814	+	0.705395i	$0.249231\pi$
$881$			8.49897e11i			1.41079i	−0.708814	+	0.705395i	$0.750769\pi$
$882$		0			0
$883$	−2.23996e11			−0.368466			−0.184233	−	0.982883i	$-0.558980\pi$
$883$	−2.23996e11			−0.368466			−0.184233	+	0.982883i	$0.558980\pi$
$884$	−4.22734e10	−	7.32197e10i	−0.0692243	−	0.119900i
$885$		0			0
$886$	1.16226e11	−	2.01309e11i	0.188612	−	0.326685i
$887$	4.79045e11	−	2.76577e11i	0.773894	−	0.446808i	−0.0603680	−	0.998176i	$-0.519227\pi$
$887$	4.79045e11	−	2.76577e11i	0.773894	−	0.446808i	0.834262	+	0.551368i	$0.185894\pi$
$888$		0			0
$889$	−8.60117e11	−	4.56613e11i	−1.37705	−	0.731040i
$890$	5.62951e11			0.897244
$891$		0			0
$892$	−1.62027e11	−	9.35464e10i	−0.255934	−	0.147764i
$893$	1.67366e11	−	2.89887e11i	0.263186	−	0.455851i
$894$		0			0
$895$			7.62607e11i			1.18853i
$896$	2.02528e9	+	5.69315e10i	0.00314234	+	0.0883325i
$897$		0			0
$898$	3.72538e11	+	6.45255e11i	0.572882	+	0.992261i
$899$	3.37663e11	+	1.94950e11i	0.516946	+	0.298459i
$900$		0			0
$901$	−1.88203e11	+	1.08659e11i	−0.285579	+	0.164879i
$902$		−	6.67135e11i		−	1.00783i
$903$		0			0
$904$	−2.23788e11			−0.335091
$905$	−1.57504e10	−	2.72805e10i	−0.0234800	−	0.0406685i
$906$		0			0
$907$	6.49965e10	−	1.12577e11i	0.0960420	−	0.166350i	−0.814001	−	0.580863i	$-0.802715\pi$
$907$	6.49965e10	−	1.12577e11i	0.0960420	−	0.166350i	0.910043	+	0.414514i	$0.136048\pi$
$908$	2.48132e11	−	1.43259e11i	0.365040	−	0.210756i
$909$		0			0
$910$	1.01798e11	−	6.37027e10i	0.148447	−	0.0928949i
$911$	1.39320e10			0.0202274			0.0101137	−	0.999949i	$-0.496781\pi$
$911$	1.39320e10			0.0202274			0.0101137	+	0.999949i	$0.496781\pi$
$912$		0			0
$913$	4.53507e11	+	2.61833e11i	0.652681	+	0.376826i
$914$	8.43983e10	−	1.46182e11i	0.120934	−	0.209464i
$915$		0			0
$916$			1.26759e11i			0.180052i
$917$	−7.27281e11	+	2.58723e10i	−1.02855	+	0.0365896i
$918$		0			0
$919$	−2.24911e11	−	3.89558e11i	−0.315318	−	0.546147i	0.664187	−	0.747567i	$-0.268778\pi$
$919$	−2.24911e11	−	3.89558e11i	−0.315318	−	0.546147i	−0.979505	+	0.201419i	$0.935445\pi$
$920$	7.67701e10	+	4.43233e10i	0.107162	+	0.0618700i
$921$		0			0
$922$	−1.28444e11	+	7.41570e10i	−0.177742	+	0.102619i
$923$		−	1.55532e11i		−	0.214296i
$924$		0			0
$925$	−1.01404e11			−0.138512
$926$	−1.76932e11	−	3.06456e11i	−0.240638	−	0.416797i
$927$		0			0
$928$	−2.83118e10	+	4.90375e10i	−0.0381747	+	0.0661205i
$929$	−9.32448e11	+	5.38349e11i	−1.25188	+	0.722771i	−0.971482	−	0.237113i	$-0.923799\pi$
$929$	−9.32448e11	+	5.38349e11i	−1.25188	+	0.722771i	−0.280395	+	0.959885i	$0.590465\pi$
$930$		0			0
$931$	4.05398e11	+	1.97072e11i	0.539614	+	0.262316i
$932$	−3.90968e11			−0.518176
$933$		0			0
$934$	9.14293e11	+	5.27867e11i	1.20143	+	0.693645i
$935$	−8.85421e11	+	1.53359e12i	−1.15852	+	2.00661i
$936$		0			0
$937$			1.17387e11i			0.152287i	0.997097	+	0.0761433i	$0.0242606\pi$
$937$			1.17387e11i			0.152287i	−0.997097	+	0.0761433i	$0.975739\pi$
$938$	−7.62138e11	−	4.04598e11i	−0.984515	−	0.522652i
$939$		0			0
$940$	1.79019e11	+	3.10070e11i	0.229291	+	0.397144i
$941$	1.22577e12	+	7.07698e11i	1.56333	+	0.902588i	0.996917	+	0.0784643i	$0.0250017\pi$
$941$	1.22577e12	+	7.07698e11i	1.56333	+	0.902588i	0.566411	+	0.824123i	$0.308332\pi$
$942$		0			0
$943$	−1.72337e11	+	9.94988e10i	−0.217937	+	0.125826i
$944$		−	2.97830e11i		−	0.375043i
$945$		0			0
$946$	1.87344e12			2.33925
$947$	−7.92418e11	−	1.37251e12i	−0.985268	−	1.70654i	−0.640737	−	0.767760i	$-0.721371\pi$
$947$	−7.92418e11	−	1.37251e12i	−0.985268	−	1.70654i	−0.344531	−	0.938775i	$-0.611962\pi$
$948$		0			0
$949$	−7.36728e9	+	1.27605e10i	−0.00908328	+	0.0157327i
$950$	2.78203e10	−	1.60620e10i	0.0341560	−	0.0197200i
$951$		0			0
$952$	1.80070e11	+	2.87755e11i	0.219227	+	0.350328i
$953$	−8.80951e11			−1.06802			−0.534011	−	0.845478i	$-0.679316\pi$
$953$	−8.80951e11			−1.06802			−0.534011	+	0.845478i	$0.679316\pi$
$954$		0			0
$955$	2.08447e11	+	1.20347e11i	0.250601	+	0.144684i
$956$	−4.10435e11	+	7.10893e11i	−0.491374	+	0.851085i
$957$		0			0
$958$		−	7.91621e11i		−	0.939843i
$959$	−1.69779e11	+	1.06243e11i	−0.200728	+	0.125611i
$960$		0			0
$961$	3.88129e11	+	6.72259e11i	0.455074	+	0.788212i
$962$	−1.85115e11	−	1.06876e11i	−0.216143	−	0.124790i
$963$		0			0
$964$	−5.71648e11	+	3.30041e11i	−0.661943	+	0.382173i
$965$			1.40656e11i			0.162200i
$966$		0			0
$967$	−9.07089e11			−1.03739			−0.518697	−	0.854958i	$-0.673583\pi$
$967$	−9.07089e11			−1.03739			−0.518697	+	0.854958i	$0.673583\pi$
$968$	4.02788e11	+	6.97649e11i	0.458749	+	0.794576i
$969$		0			0
$970$	−5.32780e11	+	9.22802e11i	−0.601812	+	1.04237i
$971$	−8.42948e10	+	4.86676e10i	−0.0948252	+	0.0547474i	−0.546663	−	0.837353i	$-0.684102\pi$
$971$	−8.42948e10	+	4.86676e10i	−0.0948252	+	0.0547474i	0.451838	+	0.892100i	$0.350769\pi$
$972$		0			0
$973$	4.95786e11	−	9.33906e11i	0.553150	−	1.04196i
$974$	−4.53439e11			−0.503829
$975$		0			0
$976$	7.01235e10	+	4.04858e10i	0.0772795	+	0.0446174i
$977$	−5.91684e11	+	1.02483e12i	−0.649398	+	1.12479i	0.333868	+	0.942620i	$0.391646\pi$
$977$	−5.91684e11	+	1.02483e12i	−0.649398	+	1.12479i	−0.983267	+	0.182171i	$0.941687\pi$
$978$		0			0
$979$		−	2.11401e12i		−	2.30132i
$980$	−3.99363e11	+	2.70133e11i	−0.432976	+	0.292869i
$981$		0			0
$982$	−3.47037e11	−	6.01086e11i	−0.373190	−	0.646384i
$983$	−6.45965e11	−	3.72948e11i	−0.691823	−	0.399424i	0.112471	−	0.993655i	$-0.464123\pi$
$983$	−6.45965e11	−	3.72948e11i	−0.691823	−	0.399424i	−0.804295	+	0.594231i	$0.797457\pi$
$984$		0			0
$985$	−7.03040e11	+	4.05900e11i	−0.746853	+	0.431196i
$986$			3.37404e11i			0.356979i
$987$		0			0
$988$	6.77153e10			0.0710655
$989$	−2.79412e11	−	4.83956e11i	−0.292052	−	0.505848i
$990$		0			0
$991$	−1.51209e11	+	2.61902e11i	−0.156778	+	0.271547i	−0.933705	−	0.358044i	$-0.883444\pi$
$991$	−1.51209e11	+	2.61902e11i	−0.156778	+	0.271547i	0.776927	+	0.629590i	$0.216777\pi$
$992$	−2.04897e11	+	1.18297e11i	−0.211587	+	0.122160i
$993$		0			0
$994$	2.22004e10	+	6.24063e11i	0.0227413	+	0.639268i
$995$	5.00446e10			0.0510581
$996$		0			0
$997$	−1.35948e12	−	7.84897e11i	−1.37592	−	0.794387i	−0.384254	−	0.923228i	$-0.625541\pi$
$997$	−1.35948e12	−	7.84897e11i	−1.37592	−	0.794387i	−0.991665	+	0.128840i	$0.958875\pi$
$998$	−1.77706e11	+	3.07797e11i	−0.179135	+	0.310271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.n.d.73.10	yes	20
3.2	odd	2	inner	126.9.n.d.73.1	yes	20
7.5	odd	6	inner	126.9.n.d.19.10	yes	20
21.5	even	6	inner	126.9.n.d.19.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.n.d.19.1	✓	20	21.5	even	6	inner
126.9.n.d.19.10	yes	20	7.5	odd	6	inner
126.9.n.d.73.1	yes	20	3.2	odd	2	inner
126.9.n.d.73.10	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(5.65685 + 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(565.865 - 326.703i) q^{5} +(2120.69 + 1125.82i) q^{7} -1448.15 q^{8} +O(q^{10})\)	\(q+(5.65685 + 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(565.865 - 326.703i) q^{5} +(2120.69 + 1125.82i) q^{7} -1448.15 q^{8} +(6402.04 + 3696.22i) q^{10} +(13880.2 - 24041.2i) q^{11} -6765.74i q^{13} +(965.728 + 27147.0i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(-84547.9 - 48813.8i) q^{17} +(67716.2 - 39095.9i) q^{19} +83635.8i q^{20} +314072. q^{22} +(-46841.9 - 81132.5i) q^{23} +(18156.6 - 31448.1i) q^{25} +(66290.4 - 38272.8i) q^{26} +(-260523. + 163029. i) q^{28} -305473. q^{29} +(-1.10538e6 - 638191. i) q^{31} +(92681.9 - 160530. i) q^{32} -1.10453e6i q^{34} +(1.56783e6 - 55774.1i) q^{35} +(-1.39624e6 - 2.41836e6i) q^{37} +(766121. + 442320. i) q^{38} +(-819461. + 473116. i) q^{40} -2.12414e6i q^{41} +5.96500e6 q^{43} +(1.77666e6 + 3.07727e6i) q^{44} +(529955. - 917909. i) q^{46} +(3.70738e6 - 2.14046e6i) q^{47} +(3.22987e6 + 4.77503e6i) q^{49} +410836. q^{50} +(749990. + 433007. i) q^{52} +(1.11299e6 - 1.92776e6i) q^{53} -1.81387e7i q^{55} +(-3.07109e6 - 1.63036e6i) q^{56} +(-1.72802e6 - 2.99301e6i) q^{58} +(1.57427e7 + 9.08906e6i) q^{59} +(-4.28000e6 + 2.47106e6i) q^{61} -1.44406e7i q^{62} +2.09715e6 q^{64} +(-2.21038e6 - 3.82850e6i) q^{65} +(-1.58826e7 + 2.75094e7i) q^{67} +(1.08221e7 - 6.24816e6i) q^{68} +(9.41548e6 + 1.50461e7i) q^{70} +2.29883e7 q^{71} +(-1.88605e6 - 1.08891e6i) q^{73} +(1.57966e7 - 2.73606e7i) q^{74} +1.00086e7i q^{76} +(5.65015e7 - 3.53573e7i) q^{77} +(-7.82277e6 - 1.35494e7i) q^{79} +(-9.27114e6 - 5.35269e6i) q^{80} +(2.08123e7 - 1.20160e7i) q^{82} +1.88638e7i q^{83} -6.37903e7 q^{85} +(3.37432e7 + 5.84449e7i) q^{86} +(-2.01006e7 + 3.48153e7i) q^{88} +(6.59498e7 - 3.80762e7i) q^{89} +(7.61699e6 - 1.43480e7i) q^{91} +1.19915e7 q^{92} +(4.19442e7 + 2.42165e7i) q^{94} +(2.55455e7 - 4.42461e7i) q^{95} +1.44142e8i q^{97} +(-2.85146e7 + 5.86578e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 1280 q^{4} + 4186 q^{7}+O(q^{10}) \) 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

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