LMFDB - Embedded newform 162.8.c.l.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,8,Mod(55,162)]

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

lf = mfeigenbasis(mf)

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")

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

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.l.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	0.990425	−	0.138048i	$-0.0440829\pi$
$5$	105.000	+	181.865i	0.375659	+	0.650661i	−0.614766	+	0.788709i	$0.710750\pi$
$6$		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	−0.921218	−	0.389046i	$-0.872805\pi$
$11$	−546.000	+	945.700i	−0.123685	+	0.214229i	0.797533	+	0.603275i	$0.206138\pi$
$12$		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	$-0.381756\pi$
$17$	14706.0			0.725978			0.362989	+	0.931793i	$0.381756\pi$
$18$		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	$-0.966274\pi$
$23$	−34356.0	−	59506.3i	−0.588783	−	1.01980i	0.405609	−	0.914047i	$-0.367059\pi$
$24$		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	−0.602034	−	0.798470i	$-0.705643\pi$
$29$	51285.0	−	88828.2i	0.390479	−	0.676329i	0.992513	+	0.122141i	$0.0389762\pi$
$30$		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	0.859818	−	0.510600i	$-0.170577\pi$
$41$	−5421.00	−	9389.45i	−0.0122839	−	0.0212763i	−0.872102	+	0.489324i	$0.837244\pi$
$42$		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	−0.982909	−	0.184092i	$-0.941066\pi$
$47$	−236328.	+	409332.i	−0.332026	+	0.575087i	0.650883	+	0.759178i	$0.274399\pi$
$48$		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	$-0.742048\pi$
$53$	−1.49402e6			−1.37845			−0.689224	+	0.724548i	$0.742048\pi$
$54$		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	$-0.851002\pi$
$59$	−1.32033e6	−	2.28688e6i	−0.836952	−	1.44964i	0.0554795	−	0.998460i	$-0.482331\pi$
$60$		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	$-0.575362\pi$
$71$	−1.41473e6			−0.469104			−0.234552	+	0.972104i	$0.575362\pi$
$72$		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	$0.349949\pi$
$83$	−2.83645e6	+	4.91287e6i	−0.544504	+	0.943109i	−0.998638	+	0.0521754i	$0.983385\pi$
$84$		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	$-0.855339\pi$
$89$	−1.19512e7			−1.79699			−0.898496	+	0.438982i	$0.855339\pi$
$90$		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	−0.513156	−	0.858295i	$-0.671524\pi$
$101$	5.03977e6	−	8.72914e6i	0.486727	−	0.843037i	0.999884	+	0.0152586i	$0.00485716\pi$
$102$		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	$-0.751152\pi$
$107$	−1.79856e7			−1.41932			−0.709661	+	0.704543i	$0.751152\pi$
$108$		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	$-0.984725\pi$
$113$	−8.29748e6	−	1.43717e7i	−0.540968	−	0.936984i	0.457881	−	0.889014i	$-0.348609\pi$
$114$		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	0.932686	−	0.360689i	$-0.117459\pi$
$131$	3.96191e6	+	6.86224e6i	0.153977	+	0.266696i	−0.778709	+	0.627385i	$0.784125\pi$
$132$		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	−0.863392	−	0.504535i	$-0.831664\pi$
$137$	157827.	−	273364.i	0.00524396	−	0.00908280i	0.868635	+	0.495452i	$0.164997\pi$
$138$		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	0.969121	−	0.246587i	$-0.0793090\pi$
$149$	1.09430e7	+	1.89539e7i	0.271010	+	0.469403i	−0.698111	+	0.715990i	$0.745976\pi$
$150$		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	$0.0932431\pi$
$167$	4.38633e7	+	7.59734e7i	0.728775	+	1.26227i	−0.228627	+	0.973514i	$0.573424\pi$
$168$		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	−0.895768	−	0.444522i	$-0.853374\pi$
$173$	−4.28477e6	+	7.42144e6i	−0.0629167	+	0.108975i	0.832851	+	0.553497i	$0.186707\pi$
$174$		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	$-0.460900\pi$
$179$	1.88041e7			0.245056			0.122528	+	0.992465i	$0.460900\pi$
$180$		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	−0.999905	−	0.0138052i	$-0.995606\pi$
$191$	−4.69931e7	+	8.13944e7i	−0.487997	+	0.845235i	0.511908	+	0.859040i	$0.328939\pi$
$192$		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	$-0.340688\pi$
$197$	1.02985e8			0.959718			0.479859	+	0.877346i	$0.340688\pi$
$198$		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	$-0.657934\pi$
$227$	9.22704e7	−	1.59817e8i	0.523567	−	0.906844i	0.999624	−	0.0274298i	$-0.00873228\pi$
$228$		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	$-0.600194\pi$
$233$	−1.19556e8			−0.619193			−0.309597	+	0.950868i	$0.600194\pi$
$234$		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	$-0.778748\pi$
$239$	−1.98105e8	−	3.43127e8i	−0.938646	−	1.62578i	−0.170646	−	0.985332i	$-0.554585\pi$
$240$		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	$-0.546847\pi$
$251$	−7.34775e7			−0.293290			−0.146645	+	0.989189i	$0.546847\pi$
$252$		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	0.989941	−	0.141482i	$-0.0451868\pi$
$257$	1.01351e8	+	1.75544e8i	0.372443	+	0.645091i	−0.617498	+	0.786573i	$0.711853\pi$
$258$		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	−0.966623	−	0.256203i	$-0.917529\pi$
$263$	−7.71270e7	+	1.33588e8i	−0.261434	+	0.452816i	0.705189	+	0.709019i	$0.250862\pi$
$264$		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	$-0.932070\pi$
$269$	−6.24018e8			−1.95463			−0.977315	+	0.211793i	$0.932070\pi$
$270$		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	−0.998301	−	0.0582682i	$-0.981442\pi$
$281$	−1.66885e8	+	2.89053e8i	−0.448689	+	0.777152i	0.549612	+	0.835420i	$0.314775\pi$
$282$		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	0.602690	−	0.797976i	$-0.294096\pi$
$293$	−1.67800e8	−	2.90638e8i	−0.389722	−	0.675019i	−0.992412	+	0.122957i	$0.960762\pi$
$294$		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	$-0.898368\pi$
$311$	−3.96031e8	−	6.85945e8i	−0.746565	−	1.29309i	0.202895	−	0.979200i	$-0.434965\pi$
$312$		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	−0.842797	−	0.538231i	$-0.819093\pi$
$317$	2.53655e7	−	4.39343e7i	0.0447235	−	0.0774633i	0.887521	+	0.460768i	$0.152426\pi$
$318$		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	$0.174580\pi$
$347$	6.83502e8	+	1.18386e9i	0.878187	+	1.52106i	0.0248578	+	0.999691i	$0.492087\pi$
$348$		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	−0.852143	−	0.523310i	$-0.824697\pi$
$353$	2.24198e7	−	3.88322e7i	0.0271281	−	0.0469873i	0.879271	+	0.476322i	$0.158030\pi$
$354$		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	$-0.427057\pi$
$359$	3.98281e8			0.454317			0.227158	+	0.973858i	$0.427057\pi$
$360$		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	0.810345	−	0.585953i	$-0.199280\pi$
$383$	−1.12455e8	−	1.94778e8i	−0.102278	−	0.177151i	−0.912623	+	0.408802i	$0.865947\pi$
$384$		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	−0.997564	−	0.0697544i	$-0.977778\pi$
$389$	−5.08941e8	+	8.81512e8i	−0.438373	+	0.759284i	0.559191	+	0.829039i	$0.311112\pi$
$390$		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	0.807878	−	0.589350i	$-0.200616\pi$
$401$	−1.37456e8	−	2.38081e8i	−0.106453	−	0.184382i	−0.914331	+	0.404968i	$0.867283\pi$
$402$		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	0.989490	−	0.144598i	$-0.0461890\pi$
$419$	5.56399e8	+	9.63711e8i	0.369519	+	0.640026i	−0.619971	+	0.784625i	$0.712856\pi$
$420$		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	$-0.595404\pi$
$431$	−9.81508e8			−0.590505			−0.295252	+	0.955419i	$0.595404\pi$
$432$		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	−0.999998	−	0.00207637i	$-0.999339\pi$
$443$	−9.11627e8	+	1.57899e9i	−0.498201	+	0.862909i	0.501797	+	0.864985i	$0.332672\pi$
$444$		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	$-0.339963\pi$
$449$	1.84846e9			0.963713			0.481856	+	0.876250i	$0.339963\pi$
$450$		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	$-0.628165\pi$
$461$	1.26390e9	−	2.18915e9i	0.600843	−	1.04069i	0.992694	−	0.120661i	$-0.0385015\pi$
$462$		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	$-0.293761\pi$
$467$	2.65667e9			1.20706			0.603529	+	0.797341i	$0.293761\pi$
$468$		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	−0.968971	−	0.247173i	$-0.920498\pi$
$479$	−6.50467e8	+	1.12664e9i	−0.270428	+	0.468394i	0.698544	+	0.715567i	$0.253832\pi$
$480$		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	0.930979	−	0.365073i	$-0.118956\pi$
$491$	3.91672e8	+	6.78396e8i	0.149327	+	0.258641i	−0.781652	+	0.623715i	$0.785623\pi$
$492$		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	$-0.657410\pi$
$503$	−2.70927e9			−0.949215			−0.474607	+	0.880198i	$0.657410\pi$
$504$		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	$-0.966540\pi$
$509$	−1.74972e9	−	3.03060e9i	−0.588106	−	1.01863i	0.406374	−	0.913707i	$-0.366793\pi$
$510$		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	$-0.568410\pi$
$521$	−1.37683e9			−0.426530			−0.213265	+	0.976994i	$0.568410\pi$
$522$		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	$-0.741465\pi$
$557$	−5.61106e9			−1.37579			−0.687894	+	0.725811i	$0.741465\pi$
$558$		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	$-0.876334\pi$
$563$	−3.34845e9	−	5.79968e9i	−0.790795	−	1.36970i	0.134680	−	0.990889i	$-0.456999\pi$
$564$		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	−0.956013	−	0.293323i	$-0.905239\pi$
$569$	−9.84251e8	+	1.70477e9i	−0.223982	+	0.387948i	0.732032	+	0.681271i	$0.238572\pi$
$570$		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	−0.836075	−	0.548616i	$-0.815155\pi$
$587$	2.79705e8	−	4.84464e8i	0.0570778	−	0.0988617i	0.893152	+	0.449754i	$0.148488\pi$
$588$		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	$-0.596258\pi$
$593$	−3.02459e9			−0.595628			−0.297814	+	0.954624i	$0.596258\pi$
$594$		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	$0.0131706\pi$
$599$	2.81623e9	+	4.87785e9i	0.535395	+	0.927331i	−0.463749	+	0.885967i	$0.653496\pi$
$600$		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	$-0.977417\pi$
$617$	−3.26806e9	−	5.66044e9i	−0.560133	−	0.970179i	0.437351	−	0.899291i	$-0.355917\pi$
$618$		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	−0.644075	−	0.764963i	$-0.722757\pi$
$641$	2.27009e9	−	3.93191e9i	0.340440	−	0.589659i	0.984514	+	0.175304i	$0.0560908\pi$
$642$		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	$-0.869666\pi$
$647$	−1.26393e10			−1.83468			−0.917338	+	0.398109i	$0.869666\pi$
$648$		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	$0.0975029\pi$
$653$	5.25022e9	+	9.09365e9i	0.737873	+	1.27803i	−0.215579	+	0.976486i	$0.569164\pi$
$654$		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	$0.394683\pi$
$659$	−4.82409e9	+	8.35557e9i	−0.656624	+	1.13731i	−0.981484	+	0.191543i	$0.938651\pi$
$660$		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	$0.348095\pi$
$677$	−4.35652e9	+	7.54572e9i	−0.539610	+	0.934631i	−0.998925	+	0.0463581i	$0.985238\pi$
$678$		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	$-0.159308\pi$
$683$	1.46109e10			1.75470			0.877351	+	0.479849i	$0.159308\pi$
$684$		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	$-0.477032\pi$
$701$	1.31502e9			0.144185			0.0720923	+	0.997398i	$0.477032\pi$
$702$		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	$-0.420114\pi$
$719$	4.95034e9			0.496689			0.248344	+	0.968672i	$0.420114\pi$
$720$		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	0.825588	−	0.564273i	$-0.190843\pi$
$743$	−8.48381e8	−	1.46944e9i	−0.0758805	−	0.131429i	−0.901469	+	0.432844i	$0.857510\pi$
$744$		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	0.985314	−	0.170755i	$-0.0546205\pi$
$761$	4.19167e9	+	7.26019e9i	0.344779	+	0.597175i	−0.640535	+	0.767929i	$0.721287\pi$
$762$		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	$-0.430456\pi$
$773$	5.56680e9			0.433488			0.216744	+	0.976228i	$0.430456\pi$
$774$		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	0.966087	−	0.258217i	$-0.0831350\pi$
$797$	3.70774e9	+	6.42199e9i	0.259421	+	0.449330i	−0.706666	+	0.707547i	$0.749802\pi$
$798$		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	$-0.655721\pi$
$809$	−1.41542e10			−0.939863			−0.469932	+	0.882703i	$0.655721\pi$
$810$		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	−0.964689	−	0.263391i	$-0.915159\pi$
$821$	−4.03132e9	+	6.98245e9i	−0.254241	+	0.440359i	0.710448	+	0.703750i	$0.248492\pi$
$822$		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	$-0.445356\pi$
$827$	5.55722e9			0.341655			0.170828	+	0.985301i	$0.445356\pi$
$828$		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	−0.977056	−	0.212984i	$-0.931682\pi$
$839$	−5.20178e9	+	9.00975e9i	−0.304078	+	0.526679i	0.672977	+	0.739663i	$0.265015\pi$
$840$		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	−0.767088	−	0.641542i	$-0.778295\pi$
$857$	3.17017e9	−	5.49090e9i	0.172048	−	0.297996i	0.939136	+	0.343546i	$0.111628\pi$
$858$		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	$-0.774946\pi$
$863$	−2.87111e10			−1.52059			−0.760295	+	0.649578i	$0.774946\pi$
$864$		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	$-0.599951\pi$
$881$	−1.25378e10			−0.617738			−0.308869	+	0.951105i	$0.599951\pi$
$882$		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	$-0.886692\pi$
$887$	−1.60134e10	−	2.77360e10i	−0.770462	−	1.33448i	0.166848	−	0.985983i	$-0.446641\pi$
$888$		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	−0.999805	−	0.0197638i	$-0.993709\pi$
$911$	−1.10172e10	+	1.90823e10i	−0.482786	+	0.836211i	0.517018	+	0.855974i	$0.327042\pi$
$912$		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	−0.968502	−	0.249007i	$-0.919896\pi$
$929$	−6.56399e9	+	1.13692e10i	−0.268604	+	0.465236i	0.699898	+	0.714243i	$0.253229\pi$
$930$		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	0.590630	−	0.806942i	$-0.298879\pi$
$941$	−1.03140e10	−	1.78643e10i	−0.403517	−	0.698912i	−0.994148	+	0.108030i	$0.965546\pi$
$942$		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	−0.589304	−	0.807912i	$-0.700598\pi$
$947$	1.05853e10	−	1.83342e10i	0.405020	−	0.701516i	0.994324	+	0.106396i	$0.0339311\pi$
$948$		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	$-0.368281\pi$
$953$	2.14876e10			0.804196			0.402098	+	0.915597i	$0.368281\pi$
$954$		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	$-0.946941\pi$
$971$	−5.62647e10			−1.97228			−0.986140	+	0.165917i	$0.946941\pi$
$972$		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	0.929251	−	0.369448i	$-0.120453\pi$
$977$	4.21718e9	+	7.30438e9i	0.144674	+	0.250583i	−0.784577	+	0.620031i	$0.787120\pi$
$978$		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	−0.614079	−	0.789244i	$-0.710473\pi$
$983$	1.12115e10	−	1.94189e10i	0.376466	−	0.652058i	0.990545	+	0.137186i	$0.0438059\pi$
$984$		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.l.55.1		2
3.2	odd	2		162.8.c.a.55.1		2
9.2	odd	6		18.8.a.b.1.1		1
9.4	even	3	inner	162.8.c.l.109.1		2
9.5	odd	6		162.8.c.a.109.1		2
9.7	even	3		2.8.a.a.1.1	✓	1
36.7	odd	6		16.8.a.b.1.1		1
36.11	even	6		144.8.a.i.1.1		1
45.2	even	12		450.8.c.g.199.2		2
45.7	odd	12		50.8.b.c.49.1		2
45.29	odd	6		450.8.a.c.1.1		1
45.34	even	6		50.8.a.g.1.1		1
45.38	even	12		450.8.c.g.199.1		2
45.43	odd	12		50.8.b.c.49.2		2
63.16	even	3		98.8.c.d.67.1		2
63.25	even	3		98.8.c.d.79.1		2
63.34	odd	6		98.8.a.a.1.1		1
63.52	odd	6		98.8.c.e.79.1		2
63.61	odd	6		98.8.c.e.67.1		2
72.11	even	6		576.8.a.f.1.1		1
72.29	odd	6		576.8.a.g.1.1		1
72.43	odd	6		64.8.a.e.1.1		1
72.61	even	6		64.8.a.c.1.1		1
99.43	odd	6		242.8.a.e.1.1		1
117.25	even	6		338.8.a.d.1.1		1
117.34	odd	12		338.8.b.d.337.1		2
117.70	odd	12		338.8.b.d.337.2		2
144.43	odd	12		256.8.b.f.129.2		2
144.61	even	12		256.8.b.b.129.2		2
144.115	odd	12		256.8.b.f.129.1		2
144.133	even	12		256.8.b.b.129.1		2
153.16	even	6		578.8.a.b.1.1		1
180.7	even	12		400.8.c.j.49.2		2
180.43	even	12		400.8.c.j.49.1		2
180.79	odd	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	9.7	even	3
16.8.a.b.1.1		1	36.7	odd	6
18.8.a.b.1.1		1	9.2	odd	6
50.8.a.g.1.1		1	45.34	even	6
50.8.b.c.49.1		2	45.7	odd	12
50.8.b.c.49.2		2	45.43	odd	12
64.8.a.c.1.1		1	72.61	even	6
64.8.a.e.1.1		1	72.43	odd	6
98.8.a.a.1.1		1	63.34	odd	6
98.8.c.d.67.1		2	63.16	even	3
98.8.c.d.79.1		2	63.25	even	3
98.8.c.e.67.1		2	63.61	odd	6
98.8.c.e.79.1		2	63.52	odd	6
144.8.a.i.1.1		1	36.11	even	6
162.8.c.a.55.1		2	3.2	odd	2
162.8.c.a.109.1		2	9.5	odd	6
162.8.c.l.55.1		2	1.1	even	1	trivial
162.8.c.l.109.1		2	9.4	even	3	inner
242.8.a.e.1.1		1	99.43	odd	6
256.8.b.b.129.1		2	144.133	even	12
256.8.b.b.129.2		2	144.61	even	12
256.8.b.f.129.1		2	144.115	odd	12
256.8.b.f.129.2		2	144.43	odd	12
338.8.a.d.1.1		1	117.25	even	6
338.8.b.d.337.1		2	117.34	odd	12
338.8.b.d.337.2		2	117.70	odd	12
400.8.a.l.1.1		1	180.79	odd	6
400.8.c.j.49.1		2	180.43	even	12
400.8.c.j.49.2		2	180.7	even	12
450.8.a.c.1.1		1	45.29	odd	6
450.8.c.g.199.1		2	45.38	even	12
450.8.c.g.199.2		2	45.2	even	12
576.8.a.f.1.1		1	72.11	even	6
576.8.a.g.1.1		1	72.29	odd	6
578.8.a.b.1.1		1	153.16	even	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 $\F_{q}$

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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