LMFDB - Embedded newform 162.8.c.a.55.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,8,Mod(55,162)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("162.55"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-8,0,-64,-210] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$50.6063741284$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 2)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	162.55
Dual form			162.8.c.a.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 + 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-105.000 - 181.865i) q^{5} +(-508.000 + 879.882i) q^{7} +512.000 q^{8} +1680.00 q^{10} +(546.000 - 945.700i) q^{11} +(-691.000 - 1196.85i) q^{13} +(-4064.00 - 7039.05i) q^{14} +(-2048.00 + 3547.24i) q^{16} -14706.0 q^{17} -39940.0 q^{19} +(-6720.00 + 11639.4i) q^{20} +(4368.00 + 7565.60i) q^{22} +(34356.0 + 59506.3i) q^{23} +(17012.5 - 29466.5i) q^{25} +11056.0 q^{26} +65024.0 q^{28} +(-51285.0 + 88828.2i) q^{29} +(-113776. - 197066. i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(58824.0 - 101886. i) q^{34} +213360. q^{35} +160526. q^{37} +(159760. - 276712. i) q^{38} +(-53760.0 - 93115.1i) q^{40} +(5421.00 + 9389.45i) q^{41} +(315374. - 546244. i) q^{43} -69888.0 q^{44} -549696. q^{46} +(236328. - 409332. i) q^{47} +(-104357. - 180751. i) q^{49} +(136100. + 235732. i) q^{50} +(-44224.0 + 76598.2i) q^{52} +1.49402e6 q^{53} -229320. q^{55} +(-260096. + 450499. i) q^{56} +(-410280. - 710626. i) q^{58} +(1.32033e6 + 2.28688e6i) q^{59} +(-413851. + 716811. i) q^{61} +1.82042e6 q^{62} +262144. q^{64} +(-145110. + 251338. i) q^{65} +(63002.0 + 109123. i) q^{67} +(470592. + 815089. i) q^{68} +(-853440. + 1.47820e6i) q^{70} +1.41473e6 q^{71} +980282. q^{73} +(-642104. + 1.11216e6i) q^{74} +(1.27808e6 + 2.21370e6i) q^{76} +(554736. + 960831. i) q^{77} +(1.78340e6 - 3.08894e6i) q^{79} +860160. q^{80} -86736.0 q^{82} +(2.83645e6 - 4.91287e6i) q^{83} +(1.54413e6 + 2.67451e6i) q^{85} +(2.52299e6 + 4.36995e6i) q^{86} +(279552. - 484198. i) q^{88} +1.19512e7 q^{89} +1.40411e6 q^{91} +(2.19878e6 - 3.80841e6i) q^{92} +(1.89062e6 + 3.27466e6i) q^{94} +(4.19370e6 + 7.26370e6i) q^{95} +(-4.34107e6 + 7.51896e6i) q^{97} +1.66970e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} - 64 q^{4} - 210 q^{5} - 1016 q^{7} + 1024 q^{8} + 3360 q^{10} + 1092 q^{11} - 1382 q^{13} - 8128 q^{14} - 4096 q^{16} - 29412 q^{17} - 79880 q^{19} - 13440 q^{20} + 8736 q^{22} + 68712 q^{23}+ \cdots + 3339408 q^{98}+O(q^{100}) $ 2 * q - 8 * q^2 - 64 * q^4 - 210 * q^5 - 1016 * q^7 + 1024 * q^8 + 3360 * q^10 + 1092 * q^11 - 1382 * q^13 - 8128 * q^14 - 4096 * q^16 - 29412 * q^17 - 79880 * q^19 - 13440 * q^20 + 8736 * q^22 + 68712 * q^23 + 34025 * q^25 + 22112 * q^26 + 130048 * q^28 - 102570 * q^29 - 227552 * q^31 - 32768 * q^32 + 117648 * q^34 + 426720 * q^35 + 321052 * q^37 + 319520 * q^38 - 107520 * q^40 + 10842 * q^41 + 630748 * q^43 - 139776 * q^44 - 1099392 * q^46 + 472656 * q^47 - 208713 * q^49 + 272200 * q^50 - 88448 * q^52 + 2988036 * q^53 - 458640 * q^55 - 520192 * q^56 - 820560 * q^58 + 2640660 * q^59 - 827702 * q^61 + 3640832 * q^62 + 524288 * q^64 - 290220 * q^65 + 126004 * q^67 + 941184 * q^68 - 1706880 * q^70 + 2829456 * q^71 + 1960564 * q^73 - 1284208 * q^74 + 2556160 * q^76 + 1109472 * q^77 + 3566800 * q^79 + 1720320 * q^80 - 173472 * q^82 + 5672892 * q^83 + 3088260 * q^85 + 5045984 * q^86 + 559104 * q^88 + 23902380 * q^89 + 2808224 * q^91 + 4397568 * q^92 + 3781248 * q^94 + 8387400 * q^95 - 8682146 * q^97 + 3339408 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	−105.000	−	181.865i	−0.375659	−	0.650661i	0.614766	−	0.788709i	$-0.289250\pi$
$5$	−105.000	−	181.865i	−0.375659	−	0.650661i	−0.990425	+	0.138048i	$0.955917\pi$
$6$		0			0
$7$	−508.000	+	879.882i	−0.559784	+	0.969575i	0.437730	+	0.899107i	$0.355783\pi$
$7$	−508.000	+	879.882i	−0.559784	+	0.969575i	−0.997514	+	0.0704680i	$0.977551\pi$
$8$	512.000			0.353553
$9$		0			0
$10$	1680.00			0.531263
$11$	546.000	−	945.700i	0.123685	−	0.214229i	−0.797533	−	0.603275i	$-0.793862\pi$
$11$	546.000	−	945.700i	0.123685	−	0.214229i	0.921218	+	0.389046i	$0.127195\pi$
$12$		0			0
$13$	−691.000	−	1196.85i	−0.0872321	−	0.151090i	0.819108	−	0.573639i	$-0.194469\pi$
$13$	−691.000	−	1196.85i	−0.0872321	−	0.151090i	−0.906340	+	0.422549i	$0.861136\pi$
$14$	−4064.00	−	7039.05i	−0.395827	−	0.685593i
$15$		0			0
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−14706.0			−0.725978			−0.362989	−	0.931793i	$-0.618244\pi$
$17$	−14706.0			−0.725978			−0.362989	+	0.931793i	$0.618244\pi$
$18$		0			0
$19$	−39940.0			−1.33589			−0.667945	−	0.744211i	$-0.732826\pi$
$19$	−39940.0			−1.33589			−0.667945	+	0.744211i	$0.732826\pi$
$20$	−6720.00	+	11639.4i	−0.187830	+	0.325331i
$21$		0			0
$22$	4368.00	+	7565.60i	0.0874587	+	0.151483i
$23$	34356.0	+	59506.3i	0.588783	+	1.01980i	0.994392	+	0.105755i	$0.0337260\pi$
$23$	34356.0	+	59506.3i	0.588783	+	1.01980i	−0.405609	+	0.914047i	$0.632941\pi$
$24$		0			0
$25$	17012.5	−	29466.5i	0.217760	−	0.377171i
$26$	11056.0			0.123365
$27$		0			0
$28$	65024.0			0.559784
$29$	−51285.0	+	88828.2i	−0.390479	+	0.676329i	−0.992513	−	0.122141i	$-0.961024\pi$
$29$	−51285.0	+	88828.2i	−0.390479	+	0.676329i	0.602034	+	0.798470i	$0.294357\pi$
$30$		0			0
$31$	−113776.	−	197066.i	−0.685938	−	1.18808i	−0.973141	−	0.230209i	$-0.926059\pi$
$31$	−113776.	−	197066.i	−0.685938	−	1.18808i	0.287203	−	0.957870i	$-0.407274\pi$
$32$	−16384.0	−	28377.9i	−0.0883883	−	0.153093i
$33$		0			0
$34$	58824.0	−	101886.i	0.256672	−	0.444569i
$35$	213360.			0.841153
$36$		0			0
$37$	160526.			0.521002			0.260501	−	0.965474i	$-0.416112\pi$
$37$	160526.			0.521002			0.260501	+	0.965474i	$0.416112\pi$
$38$	159760.	−	276712.i	0.472308	−	0.818062i
$39$		0			0
$40$	−53760.0	−	93115.1i	−0.132816	−	0.230043i
$41$	5421.00	+	9389.45i	0.0122839	+	0.0212763i	0.872102	−	0.489324i	$-0.162756\pi$
$41$	5421.00	+	9389.45i	0.0122839	+	0.0212763i	−0.859818	+	0.510600i	$0.829423\pi$
$42$		0			0
$43$	315374.	−	546244.i	0.604904	−	1.04772i	−0.387163	−	0.922011i	$-0.626545\pi$
$43$	315374.	−	546244.i	0.604904	−	1.04772i	0.992067	−	0.125713i	$-0.0401218\pi$
$44$	−69888.0			−0.123685
$45$		0			0
$46$	−549696.			−0.832665
$47$	236328.	−	409332.i	0.332026	−	0.575087i	−0.650883	−	0.759178i	$-0.725601\pi$
$47$	236328.	−	409332.i	0.332026	−	0.575087i	0.982909	+	0.184092i	$0.0589343\pi$
$48$		0			0
$49$	−104357.	−	180751.i	−0.126717	−	0.219479i
$50$	136100.	+	235732.i	0.153980	+	0.266700i
$51$		0			0
$52$	−44224.0	+	76598.2i	−0.0436160	+	0.0755452i
$53$	1.49402e6			1.37845			0.689224	−	0.724548i	$-0.257952\pi$
$53$	1.49402e6			1.37845			0.689224	+	0.724548i	$0.257952\pi$
$54$		0			0
$55$	−229320.			−0.185854
$56$	−260096.	+	450499.i	−0.197914	+	0.342796i
$57$		0			0
$58$	−410280.	−	710626.i	−0.276110	−	0.478237i
$59$	1.32033e6	+	2.28688e6i	0.836952	+	1.44964i	0.892431	+	0.451183i	$0.148998\pi$
$59$	1.32033e6	+	2.28688e6i	0.836952	+	1.44964i	−0.0554795	+	0.998460i	$0.517669\pi$
$60$		0			0
$61$	−413851.	+	716811.i	−0.233448	+	0.404343i	−0.958820	−	0.284013i	$-0.908334\pi$
$61$	−413851.	+	716811.i	−0.233448	+	0.404343i	0.725373	+	0.688356i	$0.241667\pi$
$62$	1.82042e6			0.970063
$63$		0			0
$64$	262144.			0.125000
$65$	−145110.	+	251338.i	−0.0655391	+	0.113517i
$66$		0			0
$67$	63002.0	+	109123.i	0.0255913	+	0.0443255i	0.878537	−	0.477674i	$-0.158520\pi$
$67$	63002.0	+	109123.i	0.0255913	+	0.0443255i	−0.852946	+	0.521999i	$0.825186\pi$
$68$	470592.	+	815089.i	0.181494	+	0.314358i
$69$		0			0
$70$	−853440.	+	1.47820e6i	−0.297392	+	0.515099i
$71$	1.41473e6			0.469104			0.234552	−	0.972104i	$-0.424638\pi$
$71$	1.41473e6			0.469104			0.234552	+	0.972104i	$0.424638\pi$
$72$		0			0
$73$	980282.			0.294931			0.147466	−	0.989067i	$-0.452888\pi$
$73$	980282.			0.294931			0.147466	+	0.989067i	$0.452888\pi$
$74$	−642104.	+	1.11216e6i	−0.184202	+	0.319047i
$75$		0			0
$76$	1.27808e6	+	2.21370e6i	0.333972	+	0.578457i
$77$	554736.	+	960831.i	0.138474	+	0.239844i
$78$		0			0
$79$	1.78340e6	−	3.08894e6i	0.406962	−	0.704879i	−0.587586	−	0.809162i	$-0.699921\pi$
$79$	1.78340e6	−	3.08894e6i	0.406962	−	0.704879i	0.994548	+	0.104283i	$0.0332548\pi$
$80$	860160.			0.187830
$81$		0			0
$82$	−86736.0			−0.0173720
$83$	2.83645e6	−	4.91287e6i	0.544504	−	0.943109i	−0.454134	−	0.890934i	$-0.650051\pi$
$83$	2.83645e6	−	4.91287e6i	0.544504	−	0.943109i	0.998638	−	0.0521754i	$-0.0166155\pi$
$84$		0			0
$85$	1.54413e6	+	2.67451e6i	0.272720	+	0.472366i
$86$	2.52299e6	+	4.36995e6i	0.427732	+	0.740853i
$87$		0			0
$88$	279552.	−	484198.i	0.0437294	−	0.0757415i
$89$	1.19512e7			1.79699			0.898496	−	0.438982i	$-0.144661\pi$
$89$	1.19512e7			1.79699			0.898496	+	0.438982i	$0.144661\pi$
$90$		0			0
$91$	1.40411e6			0.195325
$92$	2.19878e6	−	3.80841e6i	0.294391	−	0.509901i
$93$		0			0
$94$	1.89062e6	+	3.27466e6i	0.234778	+	0.406648i
$95$	4.19370e6	+	7.26370e6i	0.501839	+	0.869211i
$96$		0			0
$97$	−4.34107e6	+	7.51896e6i	−0.482943	+	0.836482i	−0.999808	−	0.0195848i	$-0.993766\pi$
$97$	−4.34107e6	+	7.51896e6i	−0.482943	+	0.836482i	0.516865	+	0.856067i	$0.327099\pi$
$98$	1.66970e6			0.179204
$99$		0			0
$100$	−2.17760e6			−0.217760
$101$	−5.03977e6	+	8.72914e6i	−0.486727	+	0.843037i	−0.999884	−	0.0152586i	$-0.995143\pi$
$101$	−5.03977e6	+	8.72914e6i	−0.486727	+	0.843037i	0.513156	+	0.858295i	$0.328476\pi$
$102$		0			0
$103$	−1.87400e6	−	3.24586e6i	−0.168981	−	0.292684i	0.769081	−	0.639152i	$-0.220714\pi$
$103$	−1.87400e6	−	3.24586e6i	−0.168981	−	0.292684i	−0.938062	+	0.346468i	$0.887381\pi$
$104$	−353792.	−	612786.i	−0.0308412	−	0.0534185i
$105$		0			0
$106$	−5.97607e6	+	1.03509e7i	−0.487355	+	0.844123i
$107$	1.79856e7			1.41932			0.709661	−	0.704543i	$-0.248848\pi$
$107$	1.79856e7			1.41932			0.709661	+	0.704543i	$0.248848\pi$
$108$		0			0
$109$	1.22570e7			0.906552			0.453276	−	0.891370i	$-0.350255\pi$
$109$	1.22570e7			0.906552			0.453276	+	0.891370i	$0.350255\pi$
$110$	917280.	−	1.58878e6i	0.0657094	−	0.113812i
$111$		0			0
$112$	−2.08077e6	−	3.60400e6i	−0.139946	−	0.242394i
$113$	8.29748e6	+	1.43717e7i	0.540968	+	0.936984i	0.998849	+	0.0479706i	$0.0152754\pi$
$113$	8.29748e6	+	1.43717e7i	0.540968	+	0.936984i	−0.457881	+	0.889014i	$0.651391\pi$
$114$		0			0
$115$	7.21476e6	−	1.24963e7i	0.442364	−	0.766196i
$116$	6.56448e6			0.390479
$117$		0			0
$118$	−2.11253e7			−1.18363
$119$	7.47065e6	−	1.29395e7i	0.406391	−	0.703890i
$120$		0			0
$121$	9.14735e6	+	1.58437e7i	0.469404	+	0.813031i
$122$	−3.31081e6	−	5.73449e6i	−0.165072	−	0.285914i
$123$		0			0
$124$	−7.28166e6	+	1.26122e7i	−0.342969	+	0.594040i
$125$	−2.35515e7			−1.07853
$126$		0			0
$127$	1.16826e6			0.0506087			0.0253043	−	0.999680i	$-0.491945\pi$
$127$	1.16826e6			0.0506087			0.0253043	+	0.999680i	$0.491945\pi$
$128$	−1.04858e6	+	1.81619e6i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.16088e6	−	2.01070e6i	−0.0463432	−	0.0802687i
$131$	−3.96191e6	−	6.86224e6i	−0.153977	−	0.266696i	0.778709	−	0.627385i	$-0.215875\pi$
$131$	−3.96191e6	−	6.86224e6i	−0.153977	−	0.266696i	−0.932686	+	0.360689i	$0.882541\pi$
$132$		0			0
$133$	2.02895e7	−	3.51425e7i	0.747810	−	1.29524i
$134$	−1.00803e6			−0.0361916
$135$		0			0
$136$	−7.52947e6			−0.256672
$137$	−157827.	+	273364.i	−0.00524396	+	0.00908280i	−0.868635	−	0.495452i	$-0.835003\pi$
$137$	−157827.	+	273364.i	−0.00524396	+	0.00908280i	0.863392	+	0.504535i	$0.168336\pi$
$138$		0			0
$139$	−1.96019e7	−	3.39515e7i	−0.619079	−	1.07228i	−0.989654	−	0.143474i	$-0.954173\pi$
$139$	−1.96019e7	−	3.39515e7i	−0.619079	−	1.07228i	0.370575	−	0.928803i	$-0.379161\pi$
$140$	−6.82752e6	−	1.18256e7i	−0.210288	−	0.364230i
$141$		0			0
$142$	−5.65891e6	+	9.80152e6i	−0.165853	+	0.287266i
$143$	−1.50914e6			−0.0431573
$144$		0			0
$145$	2.15397e7			0.586748
$146$	−3.92113e6	+	6.79159e6i	−0.104274	+	0.180608i
$147$		0			0
$148$	−5.13683e6	−	8.89725e6i	−0.130250	−	0.225600i
$149$	−1.09430e7	−	1.89539e7i	−0.271010	−	0.469403i	0.698111	−	0.715990i	$-0.254024\pi$
$149$	−1.09430e7	−	1.89539e7i	−0.271010	−	0.469403i	−0.969121	+	0.246587i	$0.920691\pi$
$150$		0			0
$151$	1.47077e7	−	2.54745e7i	0.347637	−	0.602125i	−0.638192	−	0.769877i	$-0.720317\pi$
$151$	1.47077e7	−	2.54745e7i	0.347637	−	0.602125i	0.985829	+	0.167752i	$0.0536508\pi$
$152$	−2.04493e7			−0.472308
$153$		0			0
$154$	−8.87578e6			−0.195832
$155$	−2.38930e7	+	4.13838e7i	−0.515358	+	0.892626i
$156$		0			0
$157$	−3.02775e7	−	5.24421e7i	−0.624412	−	1.08151i	−0.988654	−	0.150209i	$-0.952005\pi$
$157$	−3.02775e7	−	5.24421e7i	−0.624412	−	1.08151i	0.364243	−	0.931304i	$-0.381328\pi$
$158$	1.42672e7	+	2.47115e7i	0.287766	+	0.498425i
$159$		0			0
$160$	−3.44064e6	+	5.95936e6i	−0.0664078	+	0.115022i
$161$	−6.98114e7			−1.31837
$162$		0			0
$163$	5.70853e7			1.03245			0.516223	−	0.856454i	$-0.327337\pi$
$163$	5.70853e7			1.03245			0.516223	+	0.856454i	$0.327337\pi$
$164$	346944.	−	600925.i	0.00614194	−	0.0106382i
$165$		0			0
$166$	2.26916e7	+	3.93029e7i	0.385023	+	0.666879i
$167$	−4.38633e7	−	7.59734e7i	−0.728775	−	1.26227i	−0.957401	−	0.288760i	$-0.906757\pi$
$167$	−4.38633e7	−	7.59734e7i	−0.728775	−	1.26227i	0.228627	−	0.973514i	$-0.426576\pi$
$168$		0			0
$169$	3.04193e7	−	5.26878e7i	0.484781	−	0.839666i
$170$	−2.47061e7			−0.385685
$171$		0			0
$172$	−4.03679e7			−0.604904
$173$	4.28477e6	−	7.42144e6i	0.0629167	−	0.108975i	−0.832851	−	0.553497i	$-0.813293\pi$
$173$	4.28477e6	−	7.42144e6i	0.0629167	−	0.108975i	0.895768	+	0.444522i	$0.146626\pi$
$174$		0			0
$175$	1.72847e7	+	2.99380e7i	0.243797	+	0.422269i
$176$	2.23642e6	+	3.87359e6i	0.0309213	+	0.0535573i
$177$		0			0
$178$	−4.78048e7	+	8.28003e7i	−0.635333	+	1.10043i
$179$	−1.88041e7			−0.245056			−0.122528	−	0.992465i	$-0.539100\pi$
$179$	−1.88041e7			−0.245056			−0.122528	+	0.992465i	$0.539100\pi$
$180$		0			0
$181$	−5.99625e7			−0.751631			−0.375816	−	0.926694i	$-0.622637\pi$
$181$	−5.99625e7			−0.751631			−0.375816	+	0.926694i	$0.622637\pi$
$182$	−5.61645e6	+	9.72797e6i	−0.0690577	+	0.119611i
$183$		0			0
$184$	1.75903e7	+	3.04672e7i	0.208166	+	0.360554i
$185$	−1.68552e7	−	2.91941e7i	−0.195719	−	0.338996i
$186$		0			0
$187$	−8.02948e6	+	1.39075e7i	−0.0897928	+	0.155526i
$188$	−3.02500e7			−0.332026
$189$		0			0
$190$	−6.70992e7			−0.709708
$191$	4.69931e7	−	8.13944e7i	0.487997	−	0.845235i	−0.511908	−	0.859040i	$-0.671061\pi$
$191$	4.69931e7	−	8.13944e7i	0.487997	−	0.845235i	0.999905	+	0.0138052i	$0.00439446\pi$
$192$		0			0
$193$	1.75973e7	+	3.04794e7i	0.176196	+	0.305180i	0.940574	−	0.339588i	$-0.110288\pi$
$193$	1.75973e7	+	3.04794e7i	0.176196	+	0.305180i	−0.764379	+	0.644767i	$0.776954\pi$
$194$	−3.47286e7	−	6.01517e7i	−0.341492	−	0.591482i
$195$		0			0
$196$	−6.67882e6	+	1.15680e7i	−0.0633583	+	0.109740i
$197$	−1.02985e8			−0.959718			−0.479859	−	0.877346i	$-0.659312\pi$
$197$	−1.02985e8			−0.959718			−0.479859	+	0.877346i	$0.659312\pi$
$198$		0			0
$199$	8.36376e7			0.752342			0.376171	−	0.926550i	$-0.377240\pi$
$199$	8.36376e7			0.752342			0.376171	+	0.926550i	$0.377240\pi$
$200$	8.71040e6	−	1.50869e7i	0.0769898	−	0.133350i
$201$		0			0
$202$	−4.03182e7	−	6.98331e7i	−0.344168	−	0.596117i
$203$	−5.21056e7	−	9.02495e7i	−0.437168	−	0.757196i
$204$		0			0
$205$	1.13841e6	−	1.97178e6i	0.00922912	−	0.0159853i
$206$	2.99839e7			0.238975
$207$		0			0
$208$	5.66067e6			0.0436160
$209$	−2.18072e7	+	3.77712e7i	−0.165230	+	0.286187i
$210$		0			0
$211$	4.87005e7	+	8.43518e7i	0.356899	+	0.618167i	0.987441	−	0.157988i	$-0.0505008\pi$
$211$	4.87005e7	+	8.43518e7i	0.356899	+	0.618167i	−0.630542	+	0.776155i	$0.717167\pi$
$212$	−4.78086e7	−	8.28069e7i	−0.344612	−	0.596885i
$213$		0			0
$214$	−7.19423e7	+	1.24608e8i	−0.501806	+	0.869153i
$215$	−1.32457e8			−0.908951
$216$		0			0
$217$	2.31193e8			1.53591
$218$	−4.90281e7	+	8.49192e7i	−0.320514	+	0.555147i
$219$		0			0
$220$	7.33824e6	+	1.27102e7i	0.0464636	+	0.0804773i
$221$	1.01618e7	+	1.76008e7i	0.0633286	+	0.109688i
$222$		0			0
$223$	7.32286e6	−	1.26836e7i	0.0442195	−	0.0765904i	−0.843069	−	0.537806i	$-0.819253\pi$
$223$	7.32286e6	−	1.26836e7i	0.0442195	−	0.0765904i	0.887288	+	0.461216i	$0.152587\pi$
$224$	3.32923e7			0.197914
$225$		0			0
$226$	−1.32760e8			−0.765045
$227$	−9.22704e7	+	1.59817e8i	−0.523567	+	0.906844i	0.476057	+	0.879414i	$0.342066\pi$
$227$	−9.22704e7	+	1.59817e8i	−0.523567	+	0.906844i	−0.999624	+	0.0274298i	$0.991268\pi$
$228$		0			0
$229$	4.37730e6	+	7.58171e6i	0.0240870	+	0.0417199i	0.877818	−	0.478995i	$-0.158999\pi$
$229$	4.37730e6	+	7.58171e6i	0.0240870	+	0.0417199i	−0.853731	+	0.520715i	$0.825665\pi$
$230$	5.77181e7	+	9.99706e7i	0.312798	+	0.541783i
$231$		0			0
$232$	−2.62579e7	+	4.54801e7i	−0.138055	+	0.239118i
$233$	1.19556e8			0.619193			0.309597	−	0.950868i	$-0.399806\pi$
$233$	1.19556e8			0.619193			0.309597	+	0.950868i	$0.399806\pi$
$234$		0			0
$235$	−9.92578e7			−0.498915
$236$	8.45011e7	−	1.46360e8i	0.418476	−	0.724822i
$237$		0			0
$238$	5.97652e7	+	1.03516e8i	0.287362	+	0.497725i
$239$	1.98105e8	+	3.43127e8i	0.938646	+	1.62578i	0.768000	+	0.640450i	$0.221252\pi$
$239$	1.98105e8	+	3.43127e8i	0.938646	+	1.62578i	0.170646	+	0.985332i	$0.445415\pi$
$240$		0			0
$241$	1.28303e8	−	2.22228e8i	0.590443	−	1.02268i	−0.403730	−	0.914878i	$-0.632287\pi$
$241$	1.28303e8	−	2.22228e8i	0.590443	−	1.02268i	0.994173	−	0.107799i	$-0.0343801\pi$
$242$	−1.46358e8			−0.663837
$243$		0			0
$244$	5.29729e7			0.233448
$245$	−2.19149e7	+	3.79577e7i	−0.0952045	+	0.164899i
$246$		0			0
$247$	2.75985e7	+	4.78021e7i	0.116532	+	0.201840i
$248$	−5.82533e7	−	1.00898e8i	−0.242516	−	0.420049i
$249$		0			0
$250$	9.42060e7	−	1.63170e8i	0.381319	−	0.660464i
$251$	7.34775e7			0.293290			0.146645	−	0.989189i	$-0.453153\pi$
$251$	7.34775e7			0.293290			0.146645	+	0.989189i	$0.453153\pi$
$252$		0			0
$253$	7.50335e7			0.291295
$254$	−4.67302e6	+	8.09391e6i	−0.0178929	+	0.0309914i
$255$		0			0
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	−1.01351e8	−	1.75544e8i	−0.372443	−	0.645091i	0.617498	−	0.786573i	$-0.288147\pi$
$257$	−1.01351e8	−	1.75544e8i	−0.372443	−	0.645091i	−0.989941	+	0.141482i	$0.954813\pi$
$258$		0			0
$259$	−8.15472e7	+	1.41244e8i	−0.291649	+	0.505150i
$260$	1.85741e7			0.0655391
$261$		0			0
$262$	6.33906e7			0.217756
$263$	7.71270e7	−	1.33588e8i	0.261434	−	0.452816i	−0.705189	−	0.709019i	$-0.749138\pi$
$263$	7.71270e7	−	1.33588e8i	0.261434	−	0.452816i	0.966623	+	0.256203i	$0.0824714\pi$
$264$		0			0
$265$	−1.56872e8	−	2.71710e8i	−0.517827	−	0.896902i
$266$	1.62316e8	+	2.81140e8i	0.528781	+	0.915876i
$267$		0			0
$268$	4.03213e6	−	6.98385e6i	0.0127957	−	0.0221627i
$269$	6.24018e8			1.95463			0.977315	−	0.211793i	$-0.0679302\pi$
$269$	6.24018e8			1.95463			0.977315	+	0.211793i	$0.0679302\pi$
$270$		0			0
$271$	−3.87983e8			−1.18419			−0.592094	−	0.805869i	$-0.701698\pi$
$271$	−3.87983e8			−1.18419			−0.592094	+	0.805869i	$0.701698\pi$
$272$	3.01179e7	−	5.21657e7i	0.0907472	−	0.157179i
$273$		0			0
$274$	−1.26262e6	−	2.18692e6i	−0.00370804	−	0.00642251i
$275$	−1.85776e7	−	3.21774e7i	−0.0538674	−	0.0933011i
$276$		0			0
$277$	−2.26976e8	+	3.93134e8i	−0.641654	+	1.11138i	0.343409	+	0.939186i	$0.388418\pi$
$277$	−2.26976e8	+	3.93134e8i	−0.641654	+	1.11138i	−0.985063	+	0.172192i	$0.944915\pi$
$278$	3.13630e8			0.875510
$279$		0			0
$280$	1.09240e8			0.297392
$281$	1.66885e8	−	2.89053e8i	0.448689	−	0.777152i	−0.549612	−	0.835420i	$-0.685225\pi$
$281$	1.66885e8	−	2.89053e8i	0.448689	−	0.777152i	0.998301	+	0.0582682i	$0.0185579\pi$
$282$		0			0
$283$	−2.68847e8	−	4.65657e8i	−0.705104	−	1.22128i	−0.966654	−	0.256086i	$-0.917567\pi$
$283$	−2.68847e8	−	4.65657e8i	−0.705104	−	1.22128i	0.261550	−	0.965190i	$-0.415766\pi$
$284$	−4.52713e7	−	7.84122e7i	−0.117276	−	0.203128i
$285$		0			0
$286$	6.03658e6	−	1.04557e7i	0.0152584	−	0.0264284i
$287$	−1.10155e7			−0.0275053
$288$		0			0
$289$	−1.94072e8			−0.472956
$290$	−8.61588e7	+	1.49231e8i	−0.207447	+	0.359308i
$291$		0			0
$292$	−3.13690e7	−	5.43327e7i	−0.0737329	−	0.127709i
$293$	1.67800e8	+	2.90638e8i	0.389722	+	0.675019i	0.992412	−	0.122957i	$-0.0392376\pi$
$293$	1.67800e8	+	2.90638e8i	0.389722	+	0.675019i	−0.602690	+	0.797976i	$0.705904\pi$
$294$		0			0
$295$	2.77269e8	−	4.80245e8i	0.628818	−	1.08914i
$296$	8.21893e7			0.184202
$297$		0			0
$298$	1.75088e8			0.383266
$299$	4.74800e7	−	8.22378e7i	0.102722	−	0.177919i
$300$		0			0
$301$	3.20420e8	+	5.54984e8i	0.677231	+	1.17300i
$302$	1.17662e8	+	2.03796e8i	0.245817	+	0.425767i
$303$		0			0
$304$	8.17971e7	−	1.41677e8i	0.166986	−	0.289229i
$305$	1.73817e8			0.350787
$306$		0			0
$307$	2.15029e8			0.424143			0.212072	−	0.977254i	$-0.431979\pi$
$307$	2.15029e8			0.424143			0.212072	+	0.977254i	$0.431979\pi$
$308$	3.55031e7	−	6.14932e7i	0.0692371	−	0.119922i
$309$		0			0
$310$	−1.91144e8	−	3.31071e8i	−0.364413	−	0.631182i
$311$	3.96031e8	+	6.85945e8i	0.746565	+	1.29309i	0.949460	+	0.313888i	$0.101632\pi$
$311$	3.96031e8	+	6.85945e8i	0.746565	+	1.29309i	−0.202895	+	0.979200i	$0.565035\pi$
$312$		0			0
$313$	5.92287e7	−	1.02587e8i	0.109176	−	0.189098i	−0.806261	−	0.591560i	$-0.798512\pi$
$313$	5.92287e7	−	1.02587e8i	0.109176	−	0.189098i	0.915437	+	0.402462i	$0.131845\pi$
$314$	4.84440e8			0.883051
$315$		0			0
$316$	−2.28275e8			−0.406962
$317$	−2.53655e7	+	4.39343e7i	−0.0447235	+	0.0774633i	−0.887521	−	0.460768i	$-0.847574\pi$
$317$	−2.53655e7	+	4.39343e7i	−0.0447235	+	0.0774633i	0.842797	+	0.538231i	$0.180907\pi$
$318$		0			0
$319$	5.60032e7	+	9.70004e7i	0.0965930	+	0.167304i
$320$	−2.75251e7	−	4.76749e7i	−0.0469574	−	0.0813327i
$321$		0			0
$322$	2.79246e8	−	4.83668e8i	0.466112	−	0.807331i
$323$	5.87358e8			0.969826
$324$		0			0
$325$	−4.70226e7			−0.0759826
$326$	−2.28341e8	+	3.95499e8i	−0.365025	+	0.632242i
$327$		0			0
$328$	2.77555e6	+	4.80740e6i	0.00434301	+	0.00752232i
$329$	2.40109e8	+	4.15881e8i	0.371726	+	0.643849i
$330$		0			0
$331$	−1.36878e8	+	2.37080e8i	−0.207461	+	0.359334i	−0.950914	−	0.309455i	$-0.899853\pi$
$331$	−1.36878e8	+	2.37080e8i	−0.207461	+	0.359334i	0.743453	+	0.668788i	$0.233187\pi$
$332$	−3.63065e8			−0.544504
$333$		0			0
$334$	7.01812e8			1.03064
$335$	1.32304e7	−	2.29158e7i	0.0192272	−	0.0333025i
$336$		0			0
$337$	4.59256e7	+	7.95455e7i	0.0653658	+	0.113217i	0.896856	−	0.442322i	$-0.145845\pi$
$337$	4.59256e7	+	7.95455e7i	0.0653658	+	0.113217i	−0.831490	+	0.555539i	$0.812512\pi$
$338$	2.43354e8	+	4.21502e8i	0.342792	+	0.593733i
$339$		0			0
$340$	9.88243e7	−	1.71169e8i	0.136360	−	0.236183i
$341$	−2.48487e8			−0.339362
$342$		0			0
$343$	−6.24667e8			−0.835833
$344$	1.61471e8	−	2.79677e8i	0.213866	−	0.370426i
$345$		0			0
$346$	3.42782e7	+	5.93715e7i	0.0444889	+	0.0770570i
$347$	−6.83502e8	−	1.18386e9i	−0.878187	−	1.52106i	−0.853329	−	0.521373i	$-0.825420\pi$
$347$	−6.83502e8	−	1.18386e9i	−0.878187	−	1.52106i	−0.0248578	−	0.999691i	$-0.507913\pi$
$348$		0			0
$349$	−5.65716e8	+	9.79849e8i	−0.712377	+	1.23387i	0.251586	+	0.967835i	$0.419048\pi$
$349$	−5.65716e8	+	9.79849e8i	−0.712377	+	1.23387i	−0.963963	+	0.266038i	$0.914285\pi$
$350$	−2.76555e8			−0.344781
$351$		0			0
$352$	−3.57827e7			−0.0437294
$353$	−2.24198e7	+	3.88322e7i	−0.0271281	+	0.0469873i	−0.879271	−	0.476322i	$-0.841970\pi$
$353$	−2.24198e7	+	3.88322e7i	−0.0271281	+	0.0469873i	0.852143	+	0.523310i	$0.175303\pi$
$354$		0			0
$355$	−1.48546e8	−	2.57290e8i	−0.176223	−	0.305227i
$356$	−3.82438e8	−	6.62402e8i	−0.449248	−	0.778120i
$357$		0			0
$358$	7.52162e7	−	1.30278e8i	0.0866405	−	0.150066i
$359$	−3.98281e8			−0.454317			−0.227158	−	0.973858i	$-0.572943\pi$
$359$	−3.98281e8			−0.454317			−0.227158	+	0.973858i	$0.572943\pi$
$360$		0			0
$361$	7.01332e8			0.784600
$362$	2.39850e8	−	4.15432e8i	0.265742	−	0.460278i
$363$		0			0
$364$	−4.49316e7	−	7.78238e7i	−0.0488311	−	0.0845780i
$365$	−1.02930e8	−	1.78279e8i	−0.110794	−	0.191900i
$366$		0			0
$367$	−8.17359e8	+	1.41571e9i	−0.863140	+	1.49500i	0.00574132	+	0.999984i	$0.498172\pi$
$367$	−8.17359e8	+	1.41571e9i	−0.863140	+	1.49500i	−0.868882	+	0.495020i	$0.835161\pi$
$368$	−2.81444e8			−0.294391
$369$		0			0
$370$	2.69684e8			0.276789
$371$	−7.58961e8	+	1.31456e9i	−0.771633	+	1.33651i
$372$		0			0
$373$	7.73166e8	+	1.33916e9i	0.771421	+	1.33614i	0.936784	+	0.349908i	$0.113787\pi$
$373$	7.73166e8	+	1.33916e9i	0.771421	+	1.33614i	−0.165363	+	0.986233i	$0.552879\pi$
$374$	−6.42358e7	−	1.11260e8i	−0.0634931	−	0.109973i
$375$		0			0
$376$	1.21000e8	−	2.09578e8i	0.117389	−	0.203324i
$377$	1.41752e8			0.136249
$378$		0			0
$379$	−1.05688e9			−0.997216			−0.498608	−	0.866828i	$-0.666155\pi$
$379$	−1.05688e9			−0.997216			−0.498608	+	0.866828i	$0.666155\pi$
$380$	2.68397e8	−	4.64877e8i	0.250920	−	0.434606i
$381$		0			0
$382$	3.75944e8	+	6.51155e8i	0.345066	+	0.597671i
$383$	1.12455e8	+	1.94778e8i	0.102278	+	0.177151i	0.912623	−	0.408802i	$-0.134053\pi$
$383$	1.12455e8	+	1.94778e8i	0.102278	+	0.177151i	−0.810345	+	0.585953i	$0.800720\pi$
$384$		0			0
$385$	1.16495e8	−	2.01774e8i	0.104038	−	0.180200i
$386$	−2.81556e8			−0.249178
$387$		0			0
$388$	5.55657e8			0.482943
$389$	5.08941e8	−	8.81512e8i	0.438373	−	0.759284i	−0.559191	−	0.829039i	$-0.688888\pi$
$389$	5.08941e8	−	8.81512e8i	0.438373	−	0.759284i	0.997564	+	0.0697544i	$0.0222215\pi$
$390$		0			0
$391$	−5.05239e8	−	8.75100e8i	−0.427443	−	0.740353i
$392$	−5.34305e7	−	9.25444e7i	−0.0448011	−	0.0775977i
$393$		0			0
$394$	4.11941e8	−	7.13503e8i	0.339311	−	0.587705i
$395$	−7.49028e8			−0.611517
$396$		0			0
$397$	−1.47565e9			−1.18363			−0.591817	−	0.806072i	$-0.701589\pi$
$397$	−1.47565e9			−1.18363			−0.591817	+	0.806072i	$0.701589\pi$
$398$	−3.34550e8	+	5.79458e8i	−0.265993	+	0.460714i
$399$		0			0
$400$	6.96832e7	+	1.20695e8i	0.0544400	+	0.0942928i
$401$	1.37456e8	+	2.38081e8i	0.106453	+	0.184382i	0.914331	−	0.404968i	$-0.132717\pi$
$401$	1.37456e8	+	2.38081e8i	0.106453	+	0.184382i	−0.807878	+	0.589350i	$0.799384\pi$
$402$		0			0
$403$	−1.57238e8	+	2.72345e8i	−0.119672	+	0.207277i
$404$	6.45090e8			0.486727
$405$		0			0
$406$	8.33689e8			0.618248
$407$	8.76472e7	−	1.51809e8i	0.0644403	−	0.111614i
$408$		0			0
$409$	8.17136e8	+	1.41532e9i	0.590558	+	1.02288i	0.994157	+	0.107941i	$0.0344258\pi$
$409$	8.17136e8	+	1.41532e9i	0.590558	+	1.02288i	−0.403599	+	0.914936i	$0.632241\pi$
$410$	9.10728e6	+	1.57743e7i	0.00652597	+	0.0113033i
$411$		0			0
$412$	−1.19936e8	+	2.07735e8i	−0.0844906	+	0.146342i
$413$	−2.68291e9			−1.87405
$414$		0			0
$415$	−1.19131e9			−0.818192
$416$	−2.26427e7	+	3.92183e7i	−0.0154206	+	0.0267093i
$417$		0			0
$418$	−1.74458e8	−	3.02170e8i	−0.116835	−	0.202365i
$419$	−5.56399e8	−	9.63711e8i	−0.369519	−	0.640026i	0.619971	−	0.784625i	$-0.287144\pi$
$419$	−5.56399e8	−	9.63711e8i	−0.369519	−	0.640026i	−0.989490	+	0.144598i	$0.953811\pi$
$420$		0			0
$421$	−4.61264e8	+	7.98933e8i	−0.301274	+	0.521823i	−0.976425	−	0.215857i	$-0.930745\pi$
$421$	−4.61264e8	+	7.98933e8i	−0.301274	+	0.521823i	0.675150	+	0.737680i	$0.264079\pi$
$422$	−7.79208e8			−0.504731
$423$		0			0
$424$	7.64937e8			0.487355
$425$	−2.50186e8	+	4.33335e8i	−0.158089	+	0.273818i
$426$		0			0
$427$	−4.20473e8	−	7.28280e8i	−0.261361	−	0.452690i
$428$	−5.75538e8	−	9.96861e8i	−0.354830	−	0.614584i
$429$		0			0
$430$	5.29828e8	−	9.17690e8i	0.321363	−	0.556617i
$431$	9.81508e8			0.590505			0.295252	−	0.955419i	$-0.404596\pi$
$431$	9.81508e8			0.590505			0.295252	+	0.955419i	$0.404596\pi$
$432$		0			0
$433$	2.84998e9			1.68707			0.843537	−	0.537071i	$-0.180469\pi$
$433$	2.84998e9			1.68707			0.843537	+	0.537071i	$0.180469\pi$
$434$	−9.24771e8	+	1.60175e9i	−0.543026	+	0.940548i
$435$		0			0
$436$	−3.92225e8	−	6.79354e8i	−0.226638	−	0.392548i
$437$	−1.37218e9	−	2.37668e9i	−0.786549	−	1.36234i
$438$		0			0
$439$	5.28109e8	−	9.14712e8i	0.297919	−	0.516011i	−0.677741	−	0.735301i	$-0.737041\pi$
$439$	5.28109e8	−	9.14712e8i	0.297919	−	0.516011i	0.975660	+	0.219290i	$0.0703742\pi$
$440$	−1.17412e8			−0.0657094
$441$		0			0
$442$	−1.62590e8			−0.0895601
$443$	9.11627e8	−	1.57899e9i	0.498201	−	0.862909i	−0.501797	−	0.864985i	$-0.667328\pi$
$443$	9.11627e8	−	1.57899e9i	0.498201	−	0.862909i	0.999998	+	0.00207637i	$0.000660931\pi$
$444$		0			0
$445$	−1.25487e9	−	2.17351e9i	−0.675057	−	1.16923i
$446$	5.85829e7	+	1.01469e8i	0.0312679	+	0.0541576i
$447$		0			0
$448$	−1.33169e8	+	2.30656e8i	−0.0699730	+	0.121197i
$449$	−1.84846e9			−0.963713			−0.481856	−	0.876250i	$-0.660037\pi$
$449$	−1.84846e9			−0.963713			−0.481856	+	0.876250i	$0.660037\pi$
$450$		0			0
$451$	1.18395e7			0.00607735
$452$	5.31039e8	−	9.19786e8i	0.270484	−	0.468492i
$453$		0			0
$454$	−7.38164e8	−	1.27854e9i	−0.370218	−	0.641236i
$455$	−1.47432e8	−	2.55359e8i	−0.0733755	−	0.127090i
$456$		0			0
$457$	1.49033e9	−	2.58133e9i	0.730425	−	1.26513i	−0.226276	−	0.974063i	$-0.572655\pi$
$457$	1.49033e9	−	2.58133e9i	0.730425	−	1.26513i	0.956702	−	0.291071i	$-0.0940114\pi$
$458$	−7.00369e7			−0.0340642
$459$		0			0
$460$	−9.23489e8			−0.442364
$461$	−1.26390e9	+	2.18915e9i	−0.600843	+	1.04069i	0.391851	+	0.920029i	$0.371835\pi$
$461$	−1.26390e9	+	2.18915e9i	−0.600843	+	1.04069i	−0.992694	+	0.120661i	$0.961498\pi$
$462$		0			0
$463$	4.45145e8	+	7.71014e8i	0.208434	+	0.361018i	0.951221	−	0.308509i	$-0.0998300\pi$
$463$	4.45145e8	+	7.71014e8i	0.208434	+	0.361018i	−0.742787	+	0.669527i	$0.766497\pi$
$464$	−2.10063e8	−	3.63840e8i	−0.0976197	−	0.169082i
$465$		0			0
$466$	−4.78225e8	+	8.28310e8i	−0.218918	+	0.379177i
$467$	−2.65667e9			−1.20706			−0.603529	−	0.797341i	$-0.706239\pi$
$467$	−2.65667e9			−1.20706			−0.603529	+	0.797341i	$0.706239\pi$
$468$		0			0
$469$	−1.28020e8			−0.0573024
$470$	3.97031e8	−	6.87678e8i	0.176393	−	0.305522i
$471$		0			0
$472$	6.76009e8	+	1.17088e9i	0.295907	+	0.512526i
$473$	−3.44388e8	−	5.96498e8i	−0.149635	−	0.259176i
$474$		0			0
$475$	−6.79479e8	+	1.17689e9i	−0.290903	+	0.503859i
$476$	−9.56243e8			−0.406391
$477$		0			0
$478$	−3.16967e9			−1.32745
$479$	6.50467e8	−	1.12664e9i	0.270428	−	0.468394i	−0.698544	−	0.715567i	$-0.746168\pi$
$479$	6.50467e8	−	1.12664e9i	0.270428	−	0.468394i	0.968971	+	0.247173i	$0.0795016\pi$
$480$		0			0
$481$	−1.10923e8	−	1.92125e8i	−0.0454481	−	0.0787184i
$482$	1.02643e9	+	1.77782e9i	0.417506	+	0.723142i
$483$		0			0
$484$	5.85431e8	−	1.01400e9i	0.234702	−	0.406516i
$485$	1.82325e9			0.725689
$486$		0			0
$487$	−1.07447e9			−0.421542			−0.210771	−	0.977535i	$-0.567598\pi$
$487$	−1.07447e9			−0.421542			−0.210771	+	0.977535i	$0.567598\pi$
$488$	−2.11892e8	+	3.67007e8i	−0.0825362	+	0.142957i
$489$		0			0
$490$	−1.75319e8	−	3.03661e8i	−0.0673198	−	0.116601i
$491$	−3.91672e8	−	6.78396e8i	−0.149327	−	0.258641i	0.781652	−	0.623715i	$-0.214377\pi$
$491$	−3.91672e8	−	6.78396e8i	−0.149327	−	0.258641i	−0.930979	+	0.365073i	$0.881044\pi$
$492$		0			0
$493$	7.54197e8	−	1.30631e9i	0.283479	−	0.491000i
$494$	−4.41577e8			−0.164802
$495$		0			0
$496$	9.32053e8			0.342969
$497$	−7.18682e8	+	1.24479e9i	−0.262597	+	0.454831i
$498$		0			0
$499$	3.11594e8	+	5.39697e8i	0.112263	+	0.194445i	0.916682	−	0.399617i	$-0.130857\pi$
$499$	3.11594e8	+	5.39697e8i	0.112263	+	0.194445i	−0.804419	+	0.594062i	$0.797523\pi$
$500$	7.53648e8	+	1.30536e9i	0.269633	+	0.467019i
$501$		0			0
$502$	−2.93910e8	+	5.09067e8i	−0.103694	+	0.179602i
$503$	2.70927e9			0.949215			0.474607	−	0.880198i	$-0.342590\pi$
$503$	2.70927e9			0.949215			0.474607	+	0.880198i	$0.342590\pi$
$504$		0			0
$505$	2.11670e9			0.731375
$506$	−3.00134e8	+	5.19847e8i	−0.102988	+	0.178381i
$507$		0			0
$508$	−3.73842e7	−	6.47513e7i	−0.0126522	−	0.0219142i
$509$	1.74972e9	+	3.03060e9i	0.588106	+	1.01863i	0.994480	+	0.104923i	$0.0334596\pi$
$509$	1.74972e9	+	3.03060e9i	0.588106	+	1.01863i	−0.406374	+	0.913707i	$0.633207\pi$
$510$		0			0
$511$	−4.97983e8	+	8.62532e8i	−0.165098	+	0.285958i
$512$	1.34218e8			0.0441942
$513$		0			0
$514$	1.62161e9			0.526714
$515$	−3.93539e8	+	6.81630e8i	−0.126959	+	0.219899i
$516$		0			0
$517$	−2.58070e8	−	4.46991e8i	−0.0821336	−	0.142260i
$518$	−6.52378e8	−	1.12995e9i	−0.206227	−	0.357195i
$519$		0			0
$520$	−7.42963e7	+	1.28685e8i	−0.0231716	+	0.0401343i
$521$	1.37683e9			0.426530			0.213265	−	0.976994i	$-0.431590\pi$
$521$	1.37683e9			0.426530			0.213265	+	0.976994i	$0.431590\pi$
$522$		0			0
$523$	−2.86154e9			−0.874669			−0.437334	−	0.899299i	$-0.644077\pi$
$523$	−2.86154e9			−0.874669			−0.437334	+	0.899299i	$0.644077\pi$
$524$	−2.53562e8	+	4.39183e8i	−0.0769884	+	0.133348i
$525$		0			0
$526$	6.17016e8	+	1.06870e9i	0.184862	+	0.320190i
$527$	1.67319e9	+	2.89805e9i	0.497976	+	0.862519i
$528$		0			0
$529$	−6.58257e8	+	1.14013e9i	−0.193331	+	0.334858i
$530$	2.50995e9			0.732318
$531$		0			0
$532$	−2.59706e9			−0.747810
$533$	7.49182e6	−	1.29762e7i	0.00214310	−	0.00371196i
$534$		0			0
$535$	−1.88848e9	−	3.27095e9i	−0.533182	−	0.923498i
$536$	3.22570e7	+	5.58708e7i	0.00904789	+	0.0156714i
$537$		0			0
$538$	−2.49607e9	+	4.32333e9i	−0.691066	+	1.19696i
$539$	−2.27915e8			−0.0626919
$540$		0			0
$541$	5.34467e9			1.45121			0.725605	−	0.688111i	$-0.241560\pi$
$541$	5.34467e9			1.45121			0.725605	+	0.688111i	$0.241560\pi$
$542$	1.55193e9	−	2.68803e9i	0.418673	−	0.725164i
$543$		0			0
$544$	2.40943e8	+	4.17326e8i	0.0641680	+	0.111142i
$545$	−1.28699e9	−	2.22913e9i	−0.340555	−	0.589858i
$546$		0			0
$547$	1.68567e9	−	2.91967e9i	0.440370	−	0.762743i	−0.557347	−	0.830280i	$-0.688181\pi$
$547$	1.68567e9	−	2.91967e9i	0.440370	−	0.762743i	0.997717	+	0.0675365i	$0.0215139\pi$
$548$	2.02019e7			0.00524396
$549$		0			0
$550$	2.97242e8			0.0761801
$551$	2.04832e9	−	3.54780e9i	0.521636	−	0.903501i
$552$		0			0
$553$	1.81193e9	+	3.13836e9i	0.455622	+	0.789160i
$554$	−1.81581e9	−	3.14507e9i	−0.453718	−	0.785863i
$555$		0			0
$556$	−1.25452e9	+	2.17289e9i	−0.309540	+	0.536138i
$557$	5.61106e9			1.37579			0.687894	−	0.725811i	$-0.258535\pi$
$557$	5.61106e9			1.37579			0.687894	+	0.725811i	$0.258535\pi$
$558$		0			0
$559$	−8.71694e8			−0.211068
$560$	−4.36961e8	+	7.56839e8i	−0.105144	+	0.182115i
$561$		0			0
$562$	1.33508e9	+	2.31243e9i	0.317271	+	0.549529i
$563$	3.34845e9	+	5.79968e9i	0.790795	+	1.36970i	0.925475	+	0.378809i	$0.123666\pi$
$563$	3.34845e9	+	5.79968e9i	0.790795	+	1.36970i	−0.134680	+	0.990889i	$0.543001\pi$
$564$		0			0
$565$	1.74247e9	−	3.01805e9i	0.406440	−	0.703974i
$566$	4.30156e9			0.997168
$567$		0			0
$568$	7.24341e8			0.165853
$569$	9.84251e8	−	1.70477e9i	0.223982	−	0.387948i	−0.732032	−	0.681271i	$-0.761428\pi$
$569$	9.84251e8	−	1.70477e9i	0.223982	−	0.387948i	0.956013	+	0.293323i	$0.0947610\pi$
$570$		0			0
$571$	−5.14629e8	−	8.91363e8i	−0.115682	−	0.200368i	0.802370	−	0.596827i	$-0.203572\pi$
$571$	−5.14629e8	−	8.91363e8i	−0.115682	−	0.200368i	−0.918052	+	0.396459i	$0.870239\pi$
$572$	4.82926e7	+	8.36453e7i	0.0107893	+	0.0186877i
$573$		0			0
$574$	4.40619e7	−	7.63174e7i	0.00972459	−	0.0168435i
$575$	2.33793e9			0.512853
$576$		0			0
$577$	3.31179e9			0.717708			0.358854	−	0.933394i	$-0.383168\pi$
$577$	3.31179e9			0.717708			0.358854	+	0.933394i	$0.383168\pi$
$578$	7.76289e8	−	1.34457e9i	0.167215	−	0.289625i
$579$		0			0
$580$	−6.89270e8	−	1.19385e9i	−0.146687	−	0.254069i
$581$	2.88183e9	+	4.99147e9i	0.609610	+	1.05587i
$582$		0			0
$583$	8.15734e8	−	1.41289e9i	0.170494	−	0.295304i
$584$	5.01904e8			0.104274
$585$		0			0
$586$	−2.68480e9			−0.551151
$587$	−2.79705e8	+	4.84464e8i	−0.0570778	+	0.0988617i	−0.893152	−	0.449754i	$-0.851512\pi$
$587$	−2.79705e8	+	4.84464e8i	−0.0570778	+	0.0988617i	0.836075	+	0.548616i	$0.184845\pi$
$588$		0			0
$589$	4.54421e9	+	7.87081e9i	0.916337	+	1.58714i
$590$	2.21815e9	+	3.84196e9i	0.444641	+	0.770141i
$591$		0			0
$592$	−3.28757e8	+	5.69424e8i	−0.0651252	+	0.112800i
$593$	3.02459e9			0.595628			0.297814	−	0.954624i	$-0.403742\pi$
$593$	3.02459e9			0.595628			0.297814	+	0.954624i	$0.403742\pi$
$594$		0			0
$595$	−3.13767e9			−0.610658
$596$	−7.00354e8	+	1.21305e9i	−0.135505	+	0.234702i
$597$		0			0
$598$	3.79840e8	+	6.57902e8i	0.0726351	+	0.125808i
$599$	−2.81623e9	−	4.87785e9i	−0.535395	−	0.927331i	−0.999144	−	0.0413648i	$-0.986829\pi$
$599$	−2.81623e9	−	4.87785e9i	−0.535395	−	0.927331i	0.463749	−	0.885967i	$-0.346504\pi$
$600$		0			0
$601$	−1.70396e8	+	2.95134e8i	−0.0320183	+	0.0554573i	−0.881591	−	0.472015i	$-0.843527\pi$
$601$	−1.70396e8	+	2.95134e8i	−0.0320183	+	0.0554573i	0.849572	+	0.527472i	$0.176860\pi$
$602$	−5.12672e9			−0.957749
$603$		0			0
$604$	−1.88259e9			−0.347637
$605$	1.92094e9	−	3.32717e9i	0.352672	−	0.610846i
$606$		0			0
$607$	−1.92710e9	−	3.33783e9i	−0.349739	−	0.605765i	0.636464	−	0.771306i	$-0.280396\pi$
$607$	−1.92710e9	−	3.33783e9i	−0.349739	−	0.605765i	−0.986203	+	0.165541i	$0.947063\pi$
$608$	6.54377e8	+	1.13341e9i	0.118077	+	0.204515i
$609$		0			0
$610$	−6.95270e8	+	1.20424e9i	−0.124022	+	0.214812i
$611$	−6.53211e8			−0.115853
$612$		0			0
$613$	9.22245e9			1.61709			0.808545	−	0.588434i	$-0.200255\pi$
$613$	9.22245e9			1.61709			0.808545	+	0.588434i	$0.200255\pi$
$614$	−8.60116e8	+	1.48976e9i	−0.149957	+	0.259734i
$615$		0			0
$616$	2.84025e8	+	4.91945e8i	0.0489580	+	0.0847978i
$617$	3.26806e9	+	5.66044e9i	0.560133	+	0.970179i	0.997484	+	0.0708885i	$0.0225835\pi$
$617$	3.26806e9	+	5.66044e9i	0.560133	+	0.970179i	−0.437351	+	0.899291i	$0.644083\pi$
$618$		0			0
$619$	−6.82793e8	+	1.18263e9i	−0.115710	+	0.200416i	−0.918063	−	0.396434i	$-0.870248\pi$
$619$	−6.82793e8	+	1.18263e9i	−0.115710	+	0.200416i	0.802353	+	0.596849i	$0.203581\pi$
$620$	3.05830e9			0.515358
$621$		0			0
$622$	−6.33649e9			−1.05580
$623$	−6.07120e9	+	1.05156e10i	−1.00593	+	1.74232i
$624$		0			0
$625$	1.14381e9	+	1.98113e9i	0.187401	+	0.324588i
$626$	4.73830e8	+	8.20697e8i	0.0771991	+	0.133713i
$627$		0			0
$628$	−1.93776e9	+	3.35630e9i	−0.312206	+	0.540756i
$629$	−2.36070e9			−0.378236
$630$		0			0
$631$	1.54079e9			0.244141			0.122070	−	0.992521i	$-0.461047\pi$
$631$	1.54079e9			0.244141			0.122070	+	0.992521i	$0.461047\pi$
$632$	9.13101e8	−	1.58154e9i	0.143883	−	0.249212i
$633$		0			0
$634$	−2.02924e8	−	3.51474e8i	−0.0316243	−	0.0547749i
$635$	−1.22667e8	−	2.12465e8i	−0.0190116	−	0.0329291i
$636$		0			0
$637$	−1.44221e8	+	2.49798e8i	−0.0221075	+	0.0382913i
$638$	−8.96052e8			−0.136603
$639$		0			0
$640$	4.40402e8			0.0664078
$641$	−2.27009e9	+	3.93191e9i	−0.340440	+	0.589659i	−0.984514	−	0.175304i	$-0.943909\pi$
$641$	−2.27009e9	+	3.93191e9i	−0.340440	+	0.589659i	0.644075	+	0.764963i	$0.277243\pi$
$642$		0			0
$643$	−5.70269e9	−	9.87735e9i	−0.845944	−	1.46522i	−0.884799	−	0.465973i	$-0.845705\pi$
$643$	−5.70269e9	−	9.87735e9i	−0.845944	−	1.46522i	0.0388554	−	0.999245i	$-0.487629\pi$
$644$	2.23396e9	+	3.86934e9i	0.329591	+	0.570869i
$645$		0			0
$646$	−2.34943e9	+	4.06933e9i	−0.342885	+	0.593895i
$647$	1.26393e10			1.83468			0.917338	−	0.398109i	$-0.130334\pi$
$647$	1.26393e10			1.83468			0.917338	+	0.398109i	$0.130334\pi$
$648$		0			0
$649$	2.88360e9			0.414075
$650$	1.88090e8	−	3.25782e8i	0.0268639	−	0.0465297i
$651$		0			0
$652$	−1.82673e9	−	3.16399e9i	−0.258112	−	0.447063i
$653$	−5.25022e9	−	9.09365e9i	−0.737873	−	1.27803i	−0.953451	−	0.301547i	$-0.902497\pi$
$653$	−5.25022e9	−	9.09365e9i	−0.737873	−	1.27803i	0.215579	−	0.976486i	$-0.430836\pi$
$654$		0			0
$655$	−8.32002e8	+	1.44107e9i	−0.115686	+	0.200374i
$656$	−4.44088e7			−0.00614194
$657$		0			0
$658$	−3.84175e9			−0.525700
$659$	4.82409e9	−	8.35557e9i	0.656624	−	1.13731i	−0.324861	−	0.945762i	$-0.605317\pi$
$659$	4.82409e9	−	8.35557e9i	0.656624	−	1.13731i	0.981484	−	0.191543i	$-0.0613493\pi$
$660$		0			0
$661$	3.29149e9	+	5.70103e9i	0.443290	+	0.767801i	0.997931	−	0.0642888i	$-0.0204779\pi$
$661$	3.29149e9	+	5.70103e9i	0.443290	+	0.767801i	−0.554641	+	0.832089i	$0.687145\pi$
$662$	−1.09503e9	−	1.89664e9i	−0.146697	−	0.254087i
$663$		0			0
$664$	1.45226e9	−	2.51539e9i	0.192511	−	0.333439i
$665$	−8.52160e9			−1.12369
$666$		0			0
$667$	−7.04779e9			−0.919629
$668$	−2.80725e9	+	4.86230e9i	−0.364387	+	0.631137i
$669$		0			0
$670$	1.05843e8	+	1.83326e8i	0.0135957	+	0.0235485i
$671$	4.51925e8	+	7.82758e8i	0.0577481	+	0.100023i
$672$		0			0
$673$	4.27324e9	−	7.40148e9i	0.540387	−	0.935978i	−0.458494	−	0.888697i	$-0.651611\pi$
$673$	4.27324e9	−	7.40148e9i	0.540387	−	0.935978i	0.998882	−	0.0472808i	$-0.0150556\pi$
$674$	−7.34810e8			−0.0924411
$675$		0			0
$676$	−3.89367e9			−0.484781
$677$	4.35652e9	−	7.54572e9i	0.539610	−	0.934631i	−0.459315	−	0.888273i	$-0.651905\pi$
$677$	4.35652e9	−	7.54572e9i	0.539610	−	0.934631i	0.998925	−	0.0463581i	$-0.0147615\pi$
$678$		0			0
$679$	−4.41053e9	−	7.63926e9i	−0.540688	−	0.936499i
$680$	7.90595e8	+	1.36935e9i	0.0964212	+	0.167006i
$681$		0			0
$682$	9.93947e8	−	1.72157e9i	0.119983	−	0.207816i
$683$	−1.46109e10			−1.75470			−0.877351	−	0.479849i	$-0.840692\pi$
$683$	−1.46109e10			−1.75470			−0.877351	+	0.479849i	$0.840692\pi$
$684$		0			0
$685$	6.62873e7			0.00787977
$686$	2.49867e9	−	4.32782e9i	0.295511	−	0.511841i
$687$		0			0
$688$	1.29177e9	+	2.23741e9i	0.151226	+	0.261931i
$689$	−1.03237e9	−	1.78811e9i	−0.120245	−	0.208270i
$690$		0			0
$691$	7.36738e9	−	1.27607e10i	0.849454	−	1.47130i	−0.0322413	−	0.999480i	$-0.510265\pi$
$691$	7.36738e9	−	1.27607e10i	0.849454	−	1.47130i	0.881696	−	0.471818i	$-0.156402\pi$
$692$	−5.48451e8			−0.0629167
$693$		0			0
$694$	1.09360e10			1.24194
$695$	−4.11640e9	+	7.12981e9i	−0.465126	+	0.805622i
$696$		0			0
$697$	−7.97212e7	−	1.38081e8i	−0.00891783	−	0.0154461i
$698$	−4.52573e9	−	7.83879e9i	−0.503726	−	0.872480i
$699$		0			0
$700$	1.10622e9	−	1.91603e9i	0.121899	−	0.211135i
$701$	−1.31502e9			−0.144185			−0.0720923	−	0.997398i	$-0.522968\pi$
$701$	−1.31502e9			−0.144185			−0.0720923	+	0.997398i	$0.522968\pi$
$702$		0			0
$703$	−6.41141e9			−0.696001
$704$	1.43131e8	−	2.47910e8i	0.0154607	−	0.0267787i
$705$		0			0
$706$	−1.79358e8	−	3.10657e8i	−0.0191825	−	0.0332250i
$707$	−5.12041e9	−	8.86880e9i	−0.544925	−	0.943837i
$708$		0			0
$709$	−3.32014e8	+	5.75065e8i	−0.0349860	+	0.0605976i	−0.882988	−	0.469395i	$-0.844472\pi$
$709$	−3.32014e8	+	5.75065e8i	−0.0349860	+	0.0605976i	0.848002	+	0.529993i	$0.177805\pi$
$710$	2.37674e9			0.249217
$711$		0			0
$712$	6.11901e9			0.635333
$713$	7.81778e9	−	1.35408e10i	0.807737	−	1.39904i
$714$		0			0
$715$	1.58460e8	+	2.74461e8i	0.0162125	+	0.0280808i
$716$	6.01730e8	+	1.04223e9i	0.0612641	+	0.106113i
$717$		0			0
$718$	1.59312e9	−	2.75937e9i	0.160625	−	0.278211i
$719$	−4.95034e9			−0.496689			−0.248344	−	0.968672i	$-0.579886\pi$
$719$	−4.95034e9			−0.496689			−0.248344	+	0.968672i	$0.579886\pi$
$720$		0			0
$721$	3.80796e9			0.378372
$722$	−2.80533e9	+	4.85897e9i	−0.277398	+	0.480467i
$723$		0			0
$724$	1.91880e9	+	3.32346e9i	0.187908	+	0.325466i
$725$	1.74497e9	+	3.02238e9i	0.170061	+	0.294555i
$726$		0			0
$727$	−4.40550e9	+	7.63056e9i	−0.425231	+	0.736522i	−0.996442	−	0.0842813i	$-0.973141\pi$
$727$	−4.40550e9	+	7.63056e9i	−0.425231	+	0.736522i	0.571211	+	0.820803i	$0.306474\pi$
$728$	7.18905e8			0.0690577
$729$		0			0
$730$	1.64687e9			0.156686
$731$	−4.63789e9	+	8.03306e9i	−0.439147	+	0.760624i
$732$		0			0
$733$	7.47069e7	+	1.29396e8i	0.00700643	+	0.0121355i	0.869507	−	0.493920i	$-0.164436\pi$
$733$	7.47069e7	+	1.29396e8i	0.00700643	+	0.0121355i	−0.862501	+	0.506055i	$0.831103\pi$
$734$	−6.53887e9	−	1.13257e10i	−0.610332	−	1.05713i
$735$		0			0
$736$	1.12578e9	−	1.94990e9i	0.104083	−	0.180277i
$737$	1.37596e8			0.0126611
$738$		0			0
$739$	−4.70806e9			−0.429127			−0.214564	−	0.976710i	$-0.568833\pi$
$739$	−4.70806e9			−0.429127			−0.214564	+	0.976710i	$0.568833\pi$
$740$	−1.07873e9	+	1.86842e9i	−0.0978596	+	0.169498i
$741$		0			0
$742$	−6.07169e9	−	1.05165e10i	−0.545627	−	0.945054i
$743$	8.48381e8	+	1.46944e9i	0.0758805	+	0.131429i	0.901469	−	0.432844i	$-0.142490\pi$
$743$	8.48381e8	+	1.46944e9i	0.0758805	+	0.131429i	−0.825588	+	0.564273i	$0.809157\pi$
$744$		0			0
$745$	−2.29804e9	+	3.98031e9i	−0.203615	+	0.352671i
$746$	−1.23707e10			−1.09095
$747$		0			0
$748$	1.02777e9			0.0897928
$749$	−9.13667e9	+	1.58252e10i	−0.794514	+	1.37614i
$750$		0			0
$751$	−5.33250e9	−	9.23616e9i	−0.459400	−	0.795704i	0.539529	−	0.841967i	$-0.318602\pi$
$751$	−5.33250e9	−	9.23616e9i	−0.459400	−	0.795704i	−0.998929	+	0.0462626i	$0.985269\pi$
$752$	9.67999e8	+	1.67662e9i	0.0830066	+	0.143772i
$753$		0			0
$754$	−5.67007e8	+	9.82085e8i	−0.0481713	+	0.0834352i
$755$	−6.17724e9			−0.522373
$756$		0			0
$757$	6.22876e9			0.521874			0.260937	−	0.965356i	$-0.415968\pi$
$757$	6.22876e9			0.521874			0.260937	+	0.965356i	$0.415968\pi$
$758$	4.22753e9	−	7.32229e9i	0.352569	−	0.610668i
$759$		0			0
$760$	2.14717e9	+	3.71902e9i	0.177427	+	0.307313i
$761$	−4.19167e9	−	7.26019e9i	−0.344779	−	0.597175i	0.640535	−	0.767929i	$-0.278713\pi$
$761$	−4.19167e9	−	7.26019e9i	−0.344779	−	0.597175i	−0.985314	+	0.170755i	$0.945379\pi$
$762$		0			0
$763$	−6.22657e9	+	1.07847e10i	−0.507473	+	0.878969i
$764$	−6.01511e9			−0.487997
$765$		0			0
$766$	−1.79928e9			−0.144643
$767$	1.82470e9	−	3.16047e9i	0.146018	−	0.252911i
$768$		0			0
$769$	5.93244e9	+	1.02753e10i	0.470426	+	0.814802i	0.999428	−	0.0338188i	$-0.0107669\pi$
$769$	5.93244e9	+	1.02753e10i	0.470426	+	0.814802i	−0.529002	+	0.848621i	$0.677434\pi$
$770$	9.31956e8	+	1.61420e9i	0.0735662	+	0.127420i
$771$		0			0
$772$	1.12623e9	−	1.95068e9i	0.0880978	−	0.152590i
$773$	−5.56680e9			−0.433488			−0.216744	−	0.976228i	$-0.569544\pi$
$773$	−5.56680e9			−0.433488			−0.216744	+	0.976228i	$0.569544\pi$
$774$		0			0
$775$	−7.74246e9			−0.597479
$776$	−2.22263e9	+	3.84971e9i	−0.170746	+	0.295741i
$777$		0			0
$778$	4.07153e9	+	7.05209e9i	0.309977	+	0.536895i
$779$	−2.16515e8	−	3.75015e8i	−0.0164099	−	0.0284228i
$780$		0			0
$781$	7.72441e8	−	1.33791e9i	0.0580212	−	0.100496i
$782$	8.08383e9			0.604496
$783$		0			0
$784$	8.54888e8			0.0633583
$785$	−6.35827e9	+	1.10128e10i	−0.469132	+	0.812561i
$786$		0			0
$787$	−6.73056e7	−	1.16577e8i	−0.00492198	−	0.00852512i	0.863554	−	0.504257i	$-0.168233\pi$
$787$	−6.73056e7	−	1.16577e8i	−0.00492198	−	0.00852512i	−0.868476	+	0.495731i	$0.834900\pi$
$788$	3.29553e9	+	5.70803e9i	0.239929	+	0.415570i
$789$		0			0
$790$	2.99611e9	−	5.18942e9i	0.216204	−	0.374476i
$791$	−1.68605e10			−1.21130
$792$		0			0
$793$	1.14388e9			0.0814565
$794$	5.90261e9	−	1.02236e10i	0.418478	−	0.724825i
$795$		0			0
$796$	−2.67640e9	−	4.63566e9i	−0.188086	−	0.325774i
$797$	−3.70774e9	−	6.42199e9i	−0.259421	−	0.449330i	0.706666	−	0.707547i	$-0.250198\pi$
$797$	−3.70774e9	−	6.42199e9i	−0.259421	−	0.449330i	−0.966087	+	0.258217i	$0.916865\pi$
$798$		0			0
$799$	−3.47544e9	+	6.01964e9i	−0.241044	+	0.417500i
$800$	−1.11493e9			−0.0769898
$801$		0			0
$802$	−2.19930e9			−0.150548
$803$	5.35234e8	−	9.27052e8i	0.0364787	−	0.0631829i
$804$		0			0
$805$	7.33020e9	+	1.26963e10i	0.495256	+	0.857809i
$806$	−1.25791e9	−	2.17876e9i	−0.0846206	−	0.146567i
$807$		0			0
$808$	−2.58036e9	+	4.46932e9i	−0.172084	+	0.298058i
$809$	1.41542e10			0.939863			0.469932	−	0.882703i	$-0.344279\pi$
$809$	1.41542e10			0.939863			0.469932	+	0.882703i	$0.344279\pi$
$810$		0			0
$811$	−2.63708e10			−1.73600			−0.868001	−	0.496563i	$-0.834595\pi$
$811$	−2.63708e10			−1.73600			−0.868001	+	0.496563i	$0.834595\pi$
$812$	−3.33476e9	+	5.77597e9i	−0.218584	+	0.378598i
$813$		0			0
$814$	7.01178e8	+	1.21448e9i	0.0455662	+	0.0789229i
$815$	−5.99396e9	−	1.03818e10i	−0.387848	−	0.671773i
$816$		0			0
$817$	−1.25960e10	+	2.18170e10i	−0.808084	+	1.39964i
$818$	−1.30742e10			−0.835176
$819$		0			0
$820$	−1.45716e8			−0.00922912
$821$	4.03132e9	−	6.98245e9i	0.254241	−	0.440359i	−0.710448	−	0.703750i	$-0.751508\pi$
$821$	4.03132e9	−	6.98245e9i	0.254241	−	0.440359i	0.964689	+	0.263391i	$0.0848409\pi$
$822$		0			0
$823$	1.17101e10	+	2.02825e10i	0.732253	+	1.26830i	0.955918	+	0.293633i	$0.0948643\pi$
$823$	1.17101e10	+	2.02825e10i	0.732253	+	1.26830i	−0.223666	+	0.974666i	$0.571802\pi$
$824$	−9.59486e8	−	1.66188e9i	−0.0597439	−	0.103479i
$825$		0			0
$826$	1.07316e10	−	1.85877e10i	0.662576	−	1.14762i
$827$	−5.55722e9			−0.341655			−0.170828	−	0.985301i	$-0.554644\pi$
$827$	−5.55722e9			−0.341655			−0.170828	+	0.985301i	$0.554644\pi$
$828$		0			0
$829$	2.84256e10			1.73288			0.866440	−	0.499281i	$-0.166403\pi$
$829$	2.84256e10			1.73288			0.866440	+	0.499281i	$0.166403\pi$
$830$	4.76523e9	−	8.25362e9i	0.289275	−	0.501039i
$831$		0			0
$832$	−1.81142e8	−	3.13746e8i	−0.0109040	−	0.0188863i
$833$	1.53467e9	+	2.65812e9i	0.0919934	+	0.159337i
$834$		0			0
$835$	−9.21128e9	+	1.59544e10i	−0.547542	+	0.948371i
$836$	2.79133e9			0.165230
$837$		0			0
$838$	8.90238e9			0.522579
$839$	5.20178e9	−	9.00975e9i	0.304078	−	0.526679i	−0.672977	−	0.739663i	$-0.734985\pi$
$839$	5.20178e9	−	9.00975e9i	0.304078	−	0.526679i	0.977056	+	0.212984i	$0.0683182\pi$
$840$		0			0
$841$	3.36464e9	+	5.82772e9i	0.195053	+	0.337841i
$842$	−3.69011e9	−	6.39146e9i	−0.213033	−	0.368984i
$843$		0			0
$844$	3.11683e9	−	5.39851e9i	0.178449	−	0.309083i
$845$	−1.27761e10			−0.728450
$846$		0			0
$847$	−1.85874e10			−1.05106
$848$	−3.05975e9	+	5.29964e9i	−0.172306	+	0.298443i
$849$		0			0
$850$	−2.00149e9	−	3.46668e9i	−0.111786	−	0.193619i
$851$	5.51503e9	+	9.55231e9i	0.306757	+	0.531319i
$852$		0			0
$853$	9.02901e9	−	1.56387e10i	0.498102	−	0.862739i	−0.501895	−	0.864928i	$-0.667364\pi$
$853$	9.02901e9	−	1.56387e10i	0.498102	−	0.862739i	0.999998	+	0.00218977i	$0.000697026\pi$
$854$	6.72756e9			0.369620
$855$		0			0
$856$	9.20861e9			0.501806
$857$	−3.17017e9	+	5.49090e9i	−0.172048	+	0.297996i	−0.939136	−	0.343546i	$-0.888372\pi$
$857$	−3.17017e9	+	5.49090e9i	−0.172048	+	0.297996i	0.767088	+	0.641542i	$0.221705\pi$
$858$		0			0
$859$	−6.07444e9	−	1.05212e10i	−0.326987	−	0.566358i	0.654926	−	0.755693i	$-0.272700\pi$
$859$	−6.07444e9	−	1.05212e10i	−0.326987	−	0.566358i	−0.981912	+	0.189336i	$0.939367\pi$
$860$	4.23863e9	+	7.34152e9i	0.227238	+	0.393587i
$861$		0			0
$862$	−3.92603e9	+	6.80009e9i	−0.208775	+	0.361609i
$863$	2.87111e10			1.52059			0.760295	−	0.649578i	$-0.225054\pi$
$863$	2.87111e10			1.52059			0.760295	+	0.649578i	$0.225054\pi$
$864$		0			0
$865$	−1.79960e9			−0.0945411
$866$	−1.13999e10	+	1.97452e10i	−0.596471	+	1.03312i
$867$		0			0
$868$	−7.39817e9	−	1.28140e10i	−0.383977	−	0.665068i
$869$	−1.94747e9	−	3.37312e9i	−0.100670	−	0.174366i
$870$		0			0
$871$	8.70688e7	−	1.50808e8i	0.00446477	−	0.00773320i
$872$	6.27560e9			0.320514
$873$		0			0
$874$	2.19549e10			1.11235
$875$	1.19642e10	−	2.07225e10i	0.603746	−	1.04572i
$876$		0			0
$877$	−1.23011e10	−	2.13061e10i	−0.615806	−	1.06661i	−0.990243	−	0.139355i	$-0.955497\pi$
$877$	−1.23011e10	−	2.13061e10i	−0.615806	−	1.06661i	0.374437	−	0.927253i	$-0.377836\pi$
$878$	4.22487e9	+	7.31770e9i	0.210660	+	0.364875i
$879$		0			0
$880$	4.69647e8	−	8.13453e8i	0.0232318	−	0.0402386i
$881$	1.25378e10			0.617738			0.308869	−	0.951105i	$-0.400049\pi$
$881$	1.25378e10			0.617738			0.308869	+	0.951105i	$0.400049\pi$
$882$		0			0
$883$	1.93097e10			0.943873			0.471937	−	0.881633i	$-0.343555\pi$
$883$	1.93097e10			0.943873			0.471937	+	0.881633i	$0.343555\pi$
$884$	6.50358e8	−	1.12645e9i	0.0316643	−	0.0548441i
$885$		0			0
$886$	7.29302e9	+	1.26319e10i	0.352281	+	0.610169i
$887$	1.60134e10	+	2.77360e10i	0.770462	+	1.33448i	0.937310	+	0.348496i	$0.113308\pi$
$887$	1.60134e10	+	2.77360e10i	0.770462	+	1.33448i	−0.166848	+	0.985983i	$0.553359\pi$
$888$		0			0
$889$	−5.93474e8	+	1.02793e9i	−0.0283299	+	0.0490689i
$890$	2.00780e10			0.954675
$891$		0			0
$892$	−9.37327e8			−0.0442195
$893$	−9.43894e9	+	1.63487e10i	−0.443551	+	0.768252i
$894$		0			0
$895$	1.97443e9	+	3.41981e9i	0.0920577	+	0.159449i
$896$	−1.06535e9	−	1.84525e9i	−0.0494784	−	0.0856991i
$897$		0			0
$898$	7.39384e9	−	1.28065e10i	0.340724	−	0.590151i
$899$	2.33400e10			1.07138
$900$		0			0
$901$	−2.19710e10			−1.00072
$902$	−4.73579e7	+	8.20262e7i	−0.00214867	+	0.00372160i
$903$		0			0
$904$	4.24831e9	+	7.35829e9i	0.191261	+	0.331274i
$905$	6.29606e9	+	1.09051e10i	0.282357	+	0.489057i
$906$		0			0
$907$	−1.16852e9	+	2.02393e9i	−0.0520008	+	0.0900679i	−0.890854	−	0.454290i	$-0.849893\pi$
$907$	−1.16852e9	+	2.02393e9i	−0.0520008	+	0.0900679i	0.838853	+	0.544357i	$0.183226\pi$
$908$	1.18106e10			0.523567
$909$		0			0
$910$	2.35891e9			0.103769
$911$	1.10172e10	−	1.90823e10i	0.482786	−	0.836211i	−0.517018	−	0.855974i	$-0.672958\pi$
$911$	1.10172e10	−	1.90823e10i	0.482786	−	0.836211i	0.999805	+	0.0197638i	$0.00629142\pi$
$912$		0			0
$913$	−3.09740e9	−	5.36485e9i	−0.134694	−	0.233297i
$914$	1.19226e10	+	2.06506e10i	0.516489	+	0.894585i
$915$		0			0
$916$	2.80148e8	−	4.85230e8i	0.0120435	−	0.0208599i
$917$	8.05061e9			0.344775
$918$		0			0
$919$	−1.43277e10			−0.608938			−0.304469	−	0.952522i	$-0.598479\pi$
$919$	−1.43277e10			−0.608938			−0.304469	+	0.952522i	$0.598479\pi$
$920$	3.69396e9	−	6.39812e9i	0.156399	−	0.270891i
$921$		0			0
$922$	−1.01112e10	−	1.75132e10i	−0.424860	−	0.735879i
$923$	−9.77577e8	−	1.69321e9i	−0.0409209	−	0.0708771i
$924$		0			0
$925$	2.73095e9	−	4.73014e9i	0.113453	−	0.196507i
$926$	−7.12233e9			−0.294770
$927$		0			0
$928$	3.36101e9			0.138055
$929$	6.56399e9	−	1.13692e10i	0.268604	−	0.465236i	−0.699898	−	0.714243i	$-0.746771\pi$
$929$	6.56399e9	−	1.13692e10i	0.268604	−	0.465236i	0.968502	+	0.249007i	$0.0801043\pi$
$930$		0			0
$931$	4.16800e9	+	7.21919e9i	0.169279	+	0.293200i
$932$	−3.82580e9	−	6.62648e9i	−0.154798	−	0.268119i
$933$		0			0
$934$	1.06267e10	−	1.84059e10i	0.426759	−	0.739169i
$935$	3.37238e9			0.134926
$936$		0			0
$937$	−3.87626e10			−1.53930			−0.769652	−	0.638463i	$-0.779571\pi$
$937$	−3.87626e10			−1.53930			−0.769652	+	0.638463i	$0.779571\pi$
$938$	5.12080e8	−	8.86949e8i	0.0202595	−	0.0350904i
$939$		0			0
$940$	3.17625e9	+	5.50142e9i	0.124729	+	0.216037i
$941$	1.03140e10	+	1.78643e10i	0.403517	+	0.698912i	0.994148	−	0.108030i	$-0.0344542\pi$
$941$	1.03140e10	+	1.78643e10i	0.403517	+	0.698912i	−0.590630	+	0.806942i	$0.701121\pi$
$942$		0			0
$943$	−3.72488e8	+	6.45168e8i	−0.0144651	+	0.0250543i
$944$	−1.08161e10			−0.418476
$945$		0			0
$946$	5.51021e9			0.211617
$947$	−1.05853e10	+	1.83342e10i	−0.405020	+	0.701516i	−0.994324	−	0.106396i	$-0.966069\pi$
$947$	−1.05853e10	+	1.83342e10i	−0.405020	+	0.701516i	0.589304	+	0.807912i	$0.299402\pi$
$948$		0			0
$949$	−6.77375e8	−	1.17325e9i	−0.0257275	−	0.0445613i
$950$	−5.43583e9	−	9.41514e9i	−0.205700	−	0.356282i
$951$		0			0
$952$	3.82497e9	−	6.62505e9i	0.143681	−	0.248863i
$953$	−2.14876e10			−0.804196			−0.402098	−	0.915597i	$-0.631719\pi$
$953$	−2.14876e10			−0.804196			−0.402098	+	0.915597i	$0.631719\pi$
$954$		0			0
$955$	−1.97371e10			−0.733282
$956$	1.26787e10	−	2.19601e10i	0.469323	−	0.812891i
$957$		0			0
$958$	5.20374e9	+	9.01313e9i	0.191221	+	0.331205i
$959$	−1.60352e8	−	2.77738e8i	−0.00587097	−	0.0101688i
$960$		0			0
$961$	−1.21336e10	+	2.10161e10i	−0.441021	+	0.763871i
$962$	1.77478e9			0.0642733
$963$		0			0
$964$	−1.64228e10			−0.590443
$965$	3.69543e9	−	6.40067e9i	0.132379	−	0.229287i
$966$		0			0
$967$	−1.96313e10	−	3.40023e10i	−0.698161	−	1.20925i	−0.969103	−	0.246655i	$-0.920669\pi$
$967$	−1.96313e10	−	3.40023e10i	−0.698161	−	1.20925i	0.270943	−	0.962596i	$-0.412665\pi$
$968$	4.68344e9	+	8.11196e9i	0.165959	+	0.287450i
$969$		0			0
$970$	−7.29300e9	+	1.26319e10i	−0.256570	+	0.444392i
$971$	5.62647e10			1.97228			0.986140	−	0.165917i	$-0.0530585\pi$
$971$	5.62647e10			1.97228			0.986140	+	0.165917i	$0.0530585\pi$
$972$		0			0
$973$	3.98310e10			1.38620
$974$	4.29786e9	−	7.44412e9i	0.149038	−	0.258141i
$975$		0			0
$976$	−1.69513e9	−	2.93606e9i	−0.0583619	−	0.101086i
$977$	−4.21718e9	−	7.30438e9i	−0.144674	−	0.250583i	0.784577	−	0.620031i	$-0.212880\pi$
$977$	−4.21718e9	−	7.30438e9i	−0.144674	−	0.250583i	−0.929251	+	0.369448i	$0.879547\pi$
$978$		0			0
$979$	6.52535e9	−	1.13022e10i	0.222262	−	0.384968i
$980$	2.80510e9			0.0952045
$981$		0			0
$982$	6.26675e9			0.211180
$983$	−1.12115e10	+	1.94189e10i	−0.376466	+	0.652058i	−0.990545	−	0.137186i	$-0.956194\pi$
$983$	−1.12115e10	+	1.94189e10i	−0.376466	+	0.652058i	0.614079	+	0.789244i	$0.289527\pi$
$984$		0			0
$985$	1.08135e10	+	1.87295e10i	0.360527	+	0.624451i
$986$	6.03358e9	+	1.04505e10i	0.200450	+	0.347189i
$987$		0			0
$988$	1.76631e9	−	3.05933e9i	0.0582662	−	0.100920i
$989$	4.33400e10			1.42463
$990$		0			0
$991$	3.46728e10			1.13170			0.565849	−	0.824509i	$-0.308548\pi$
$991$	3.46728e10			1.13170			0.565849	+	0.824509i	$0.308548\pi$
$992$	−3.72821e9	+	6.45745e9i	−0.121258	+	0.210025i
$993$		0			0
$994$	−5.74945e9	−	9.95835e9i	−0.185684	−	0.321614i
$995$	−8.78194e9	−	1.52108e10i	−0.282625	−	0.489520i
$996$		0			0
$997$	1.48237e10	−	2.56754e10i	0.473722	−	0.820511i	−0.525825	−	0.850593i	$-0.676243\pi$
$997$	1.48237e10	−	2.56754e10i	0.473722	−	0.820511i	0.999547	+	0.0300818i	$0.00957679\pi$
$998$	−4.98550e9			−0.158764
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.8.c.a.55.1		2
3.2	odd	2		162.8.c.l.55.1		2
9.2	odd	6		2.8.a.a.1.1	✓	1
9.4	even	3	inner	162.8.c.a.109.1		2
9.5	odd	6		162.8.c.l.109.1		2
9.7	even	3		18.8.a.b.1.1		1
36.7	odd	6		144.8.a.i.1.1		1
36.11	even	6		16.8.a.b.1.1		1
45.2	even	12		50.8.b.c.49.1		2
45.7	odd	12		450.8.c.g.199.2		2
45.29	odd	6		50.8.a.g.1.1		1
45.34	even	6		450.8.a.c.1.1		1
45.38	even	12		50.8.b.c.49.2		2
45.43	odd	12		450.8.c.g.199.1		2
63.2	odd	6		98.8.c.d.67.1		2
63.11	odd	6		98.8.c.d.79.1		2
63.20	even	6		98.8.a.a.1.1		1
63.38	even	6		98.8.c.e.79.1		2
63.47	even	6		98.8.c.e.67.1		2
72.11	even	6		64.8.a.e.1.1		1
72.29	odd	6		64.8.a.c.1.1		1
72.43	odd	6		576.8.a.f.1.1		1
72.61	even	6		576.8.a.g.1.1		1
99.65	even	6		242.8.a.e.1.1		1
117.38	odd	6		338.8.a.d.1.1		1
117.47	even	12		338.8.b.d.337.1		2
117.83	even	12		338.8.b.d.337.2		2
144.11	even	12		256.8.b.f.129.2		2
144.29	odd	12		256.8.b.b.129.2		2
144.83	even	12		256.8.b.f.129.1		2
144.101	odd	12		256.8.b.b.129.1		2
153.101	odd	6		578.8.a.b.1.1		1
180.47	odd	12		400.8.c.j.49.2		2
180.83	odd	12		400.8.c.j.49.1		2
180.119	even	6		400.8.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.8.a.a.1.1	✓	1	9.2	odd	6
16.8.a.b.1.1		1	36.11	even	6
18.8.a.b.1.1		1	9.7	even	3
50.8.a.g.1.1		1	45.29	odd	6
50.8.b.c.49.1		2	45.2	even	12
50.8.b.c.49.2		2	45.38	even	12
64.8.a.c.1.1		1	72.29	odd	6
64.8.a.e.1.1		1	72.11	even	6
98.8.a.a.1.1		1	63.20	even	6
98.8.c.d.67.1		2	63.2	odd	6
98.8.c.d.79.1		2	63.11	odd	6
98.8.c.e.67.1		2	63.47	even	6
98.8.c.e.79.1		2	63.38	even	6
144.8.a.i.1.1		1	36.7	odd	6
162.8.c.a.55.1		2	1.1	even	1	trivial
162.8.c.a.109.1		2	9.4	even	3	inner
162.8.c.l.55.1		2	3.2	odd	2
162.8.c.l.109.1		2	9.5	odd	6
242.8.a.e.1.1		1	99.65	even	6
256.8.b.b.129.1		2	144.101	odd	12
256.8.b.b.129.2		2	144.29	odd	12
256.8.b.f.129.1		2	144.83	even	12
256.8.b.f.129.2		2	144.11	even	12
338.8.a.d.1.1		1	117.38	odd	6
338.8.b.d.337.1		2	117.47	even	12
338.8.b.d.337.2		2	117.83	even	12
400.8.a.l.1.1		1	180.119	even	6
400.8.c.j.49.1		2	180.83	odd	12
400.8.c.j.49.2		2	180.47	odd	12
450.8.a.c.1.1		1	45.34	even	6
450.8.c.g.199.1		2	45.43	odd	12
450.8.c.g.199.2		2	45.7	odd	12
576.8.a.f.1.1		1	72.43	odd	6
576.8.a.g.1.1		1	72.61	even	6
578.8.a.b.1.1		1	153.101	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-105.000 - 181.865i) q^{5} +(-508.000 + 879.882i) q^{7} +512.000 q^{8} +1680.00 q^{10} +(546.000 - 945.700i) q^{11} +(-691.000 - 1196.85i) q^{13} +(-4064.00 - 7039.05i) q^{14} +(-2048.00 + 3547.24i) q^{16} -14706.0 q^{17} -39940.0 q^{19} +(-6720.00 + 11639.4i) q^{20} +(4368.00 + 7565.60i) q^{22} +(34356.0 + 59506.3i) q^{23} +(17012.5 - 29466.5i) q^{25} +11056.0 q^{26} +65024.0 q^{28} +(-51285.0 + 88828.2i) q^{29} +(-113776. - 197066. i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(58824.0 - 101886. i) q^{34} +213360. q^{35} +160526. q^{37} +(159760. - 276712. i) q^{38} +(-53760.0 - 93115.1i) q^{40} +(5421.00 + 9389.45i) q^{41} +(315374. - 546244. i) q^{43} -69888.0 q^{44} -549696. q^{46} +(236328. - 409332. i) q^{47} +(-104357. - 180751. i) q^{49} +(136100. + 235732. i) q^{50} +(-44224.0 + 76598.2i) q^{52} +1.49402e6 q^{53} -229320. q^{55} +(-260096. + 450499. i) q^{56} +(-410280. - 710626. i) q^{58} +(1.32033e6 + 2.28688e6i) q^{59} +(-413851. + 716811. i) q^{61} +1.82042e6 q^{62} +262144. q^{64} +(-145110. + 251338. i) q^{65} +(63002.0 + 109123. i) q^{67} +(470592. + 815089. i) q^{68} +(-853440. + 1.47820e6i) q^{70} +1.41473e6 q^{71} +980282. q^{73} +(-642104. + 1.11216e6i) q^{74} +(1.27808e6 + 2.21370e6i) q^{76} +(554736. + 960831. i) q^{77} +(1.78340e6 - 3.08894e6i) q^{79} +860160. q^{80} -86736.0 q^{82} +(2.83645e6 - 4.91287e6i) q^{83} +(1.54413e6 + 2.67451e6i) q^{85} +(2.52299e6 + 4.36995e6i) q^{86} +(279552. - 484198. i) q^{88} +1.19512e7 q^{89} +1.40411e6 q^{91} +(2.19878e6 - 3.80841e6i) q^{92} +(1.89062e6 + 3.27466e6i) q^{94} +(4.19370e6 + 7.26370e6i) q^{95} +(-4.34107e6 + 7.51896e6i) q^{97} +1.66970e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} - 64 q^{4} - 210 q^{5} - 1016 q^{7} + 1024 q^{8} + 3360 q^{10} + 1092 q^{11} - 1382 q^{13} - 8128 q^{14} - 4096 q^{16} - 29412 q^{17} - 79880 q^{19} - 13440 q^{20} + 8736 q^{22} + 68712 q^{23}+ \cdots + 3339408 q^{98}+O(q^{100}) \) 2 * q - 8 * q^2 - 64 * q^4 - 210 * q^5 - 1016 * q^7 + 1024 * q^8 + 3360 * q^10 + 1092 * q^11 - 1382 * q^13 - 8128 * q^14 - 4096 * q^16 - 29412 * q^17 - 79880 * q^19 - 13440 * q^20 + 8736 * q^22 + 68712 * q^23 + 34025 * q^25 + 22112 * q^26 + 130048 * q^28 - 102570 * q^29 - 227552 * q^31 - 32768 * q^32 + 117648 * q^34 + 426720 * q^35 + 321052 * q^37 + 319520 * q^38 - 107520 * q^40 + 10842 * q^41 + 630748 * q^43 - 139776 * q^44 - 1099392 * q^46 + 472656 * q^47 - 208713 * q^49 + 272200 * q^50 - 88448 * q^52 + 2988036 * q^53 - 458640 * q^55 - 520192 * q^56 - 820560 * q^58 + 2640660 * q^59 - 827702 * q^61 + 3640832 * q^62 + 524288 * q^64 - 290220 * q^65 + 126004 * q^67 + 941184 * q^68 - 1706880 * q^70 + 2829456 * q^71 + 1960564 * q^73 - 1284208 * q^74 + 2556160 * q^76 + 1109472 * q^77 + 3566800 * q^79 + 1720320 * q^80 - 173472 * q^82 + 5672892 * q^83 + 3088260 * q^85 + 5045984 * q^86 + 559104 * q^88 + 23902380 * q^89 + 2808224 * q^91 + 4397568 * q^92 + 3781248 * q^94 + 8387400 * q^95 - 8682146 * q^97 + 3339408 * q^98

Introduction

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