LMFDB - Embedded newform 117.8.q.b.10.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,8,Mod(10,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.10"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	117.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$36.5490479816$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 1279 x^{12} + 629380 x^{10} + 148562016 x^{8} + 16872573312 x^{6} + 790180980480 x^{4} + \cdots + 4669637050368 $ x^14 + 1279x^12 + 629380x^10 + 148562016x^8 + 16872573312x^6 + 790180980480x^4 + 10484997239808x^2 + 4669637050368
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{7}\cdot 13^{4} $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.4
Root			$-0.679146i$ of defining polynomial
Character	$\chi$	$=$	117.10
Dual form			117.8.q.b.82.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.588158 + 0.339573i) q^{2} +(-63.7694 + 110.452i) q^{4} -439.155i q^{5} +(-1128.14 - 651.329i) q^{7} -173.548i q^{8} +(149.125 + 258.293i) q^{10} +(-497.807 + 287.409i) q^{11} +(-7892.42 - 676.938i) q^{13} +884.695 q^{14} +(-8103.55 - 14035.8i) q^{16} +(5634.27 - 9758.85i) q^{17} +(35549.9 + 20524.7i) q^{19} +(48505.5 + 28004.7i) q^{20} +(195.193 - 338.083i) q^{22} +(22132.8 + 38335.2i) q^{23} -114732. q^{25} +(4871.86 - 2281.91i) q^{26} +(143881. - 83069.7i) q^{28} +(-72756.1 - 126017. i) q^{29} +122045. i q^{31} +(28770.4 + 16610.6i) q^{32} +7652.99i q^{34} +(-286035. + 495427. i) q^{35} +(36374.8 - 21001.0i) q^{37} -27878.6 q^{38} -76214.6 q^{40} +(75942.3 - 43845.3i) q^{41} +(-374876. + 649305. i) q^{43} -73311.5i q^{44} +(-26035.2 - 15031.4i) q^{46} +940126. i q^{47} +(436688. + 756366. i) q^{49} +(67480.7 - 38960.0i) q^{50} +(578064. - 828564. i) q^{52} +924214. q^{53} +(126217. + 218614. i) q^{55} +(-113037. + 195786. i) q^{56} +(85584.1 + 49412.0i) q^{58} +(-547626. - 316172. i) q^{59} +(32203.2 - 55777.7i) q^{61} +(-41443.3 - 71781.9i) q^{62} +2.05195e6 q^{64} +(-297281. + 3.46600e6i) q^{65} +(-1.68358e6 + 972013. i) q^{67} +(718588. + 1.24463e6i) q^{68} -388519. i q^{70} +(4.09113e6 + 2.36202e6i) q^{71} +1.92731e6i q^{73} +(-14262.8 + 24703.8i) q^{74} +(-4.53399e6 + 2.61770e6i) q^{76} +748791. q^{77} -1.50287e6 q^{79} +(-6.16388e6 + 3.55872e6i) q^{80} +(-29777.4 + 51575.9i) q^{82} +1.87974e6i q^{83} +(-4.28565e6 - 2.47432e6i) q^{85} -509191. i q^{86} +(49879.3 + 86393.4i) q^{88} +(-3.78860e6 + 2.18735e6i) q^{89} +(8.46281e6 + 5.90424e6i) q^{91} -5.64559e6 q^{92} +(-319241. - 552942. i) q^{94} +(9.01354e6 - 1.56119e7i) q^{95} +(-1.53602e6 - 886819. i) q^{97} +(-513683. - 296575. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{2} + 383 q^{4} - 2772 q^{7} - 509 q^{10} - 6516 q^{11} + 5109 q^{13} + 47916 q^{14} - 633 q^{16} + 38403 q^{17} + 43254 q^{19} - 89409 q^{20} - 125882 q^{22} + 68550 q^{23} + 39380 q^{25} - 361959 q^{26}+ \cdots - 16173003 q^{98}+O(q^{100}) $ 14 * q + 3 * q^2 + 383 * q^4 - 2772 * q^7 - 509 * q^10 - 6516 * q^11 + 5109 * q^13 + 47916 * q^14 - 633 * q^16 + 38403 * q^17 + 43254 * q^19 - 89409 * q^20 - 125882 * q^22 + 68550 * q^23 + 39380 * q^25 - 361959 * q^26 - 234780 * q^28 - 221583 * q^29 + 878067 * q^32 - 659616 * q^35 - 565347 * q^37 - 953640 * q^38 - 77182 * q^40 - 1716057 * q^41 - 882692 * q^43 - 3267480 * q^46 + 2653979 * q^49 - 145128 * q^50 + 4962178 * q^52 + 1791210 * q^53 + 2453536 * q^55 + 7457952 * q^56 - 14978127 * q^58 + 1189032 * q^59 + 3858525 * q^61 - 1904142 * q^62 + 14570922 * q^64 - 10424661 * q^65 + 4674330 * q^67 - 9569619 * q^68 + 25203126 * q^71 - 8640105 * q^74 + 12934506 * q^76 - 19599336 * q^77 - 30688440 * q^79 - 29127963 * q^80 - 37359719 * q^82 - 22436313 * q^85 + 27045536 * q^88 - 2123160 * q^89 + 37205532 * q^91 + 47685588 * q^92 + 19138810 * q^94 + 43420386 * q^95 - 68556288 * q^97 - 16173003 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.588158	+	0.339573i	−0.0519863	+	0.0300143i	−0.525768	−	0.850628i	$-0.676222\pi$
$2$	−0.588158	+	0.339573i	−0.0519863	+	0.0300143i	0.473782	+	0.880642i	$0.342889\pi$
$3$		0			0
$3$		0			0
$4$	−63.7694	+	110.452i	−0.498198	+	0.862905i
$5$		−	439.155i		−	1.57117i	−0.618754	−	0.785585i	$-0.712362\pi$
$5$		−	439.155i		−	1.57117i	0.618754	−	0.785585i	$-0.287638\pi$
$6$		0			0
$7$	−1128.14	−	651.329i	−1.24313	−	0.717724i	−0.273403	−	0.961899i	$-0.588149\pi$
$7$	−1128.14	−	651.329i	−1.24313	−	0.717724i	−0.969731	+	0.244175i	$0.921483\pi$
$8$		−	173.548i		−	0.119841i
$9$		0			0
$10$	149.125	+	258.293i	0.0471576	+	0.0816793i
$11$	−497.807	+	287.409i	−0.112768	+	0.0651067i	−0.555323	−	0.831635i	$-0.687405\pi$
$11$	−497.807	+	287.409i	−0.112768	+	0.0651067i	0.442555	+	0.896741i	$0.354072\pi$
$12$		0			0
$13$	−7892.42	−	676.938i	−0.996342	−	0.0854568i
$13$	−7892.42	−	676.938i	−0.996342	−	0.0854568i
$14$	884.695			0.0861679
$15$		0			0
$16$	−8103.55	−	14035.8i	−0.494601	−	0.856675i
$17$	5634.27	−	9758.85i	0.278142	−	0.481756i	−0.692781	−	0.721148i	$-0.743615\pi$
$17$	5634.27	−	9758.85i	0.278142	−	0.481756i	0.970923	+	0.239392i	$0.0769481\pi$
$18$		0			0
$19$	35549.9	+	20524.7i	1.18905	+	0.686499i	0.958091	−	0.286464i	$-0.0924800\pi$
$19$	35549.9	+	20524.7i	1.18905	+	0.686499i	0.230960	+	0.972963i	$0.425813\pi$
$20$	48505.5	+	28004.7i	1.35577	+	0.782754i
$21$		0			0
$22$	195.193	−	338.083i	0.00390826	−	0.00676931i
$23$	22132.8	+	38335.2i	0.379306	+	0.656977i	0.990961	−	0.134147i	$-0.0428294\pi$
$23$	22132.8	+	38335.2i	0.379306	+	0.656977i	−0.611655	+	0.791124i	$0.709496\pi$
$24$		0			0
$25$	−114732.			−1.46857
$26$	4871.86	−	2281.91i	0.0543610	−	0.0254619i
$27$		0			0
$28$	143881.	−	83069.7i	1.23865	−	0.715138i
$29$	−72756.1	−	126017.i	−0.553957	−	0.959482i	−0.997984	−	0.0634685i	$-0.979784\pi$
$29$	−72756.1	−	126017.i	−0.553957	−	0.959482i	0.444027	−	0.896014i	$-0.353550\pi$
$30$		0			0
$31$			122045.i			0.735793i	0.929867	+	0.367896i	$0.119922\pi$
$31$			122045.i			0.735793i	−0.929867	+	0.367896i	$0.880078\pi$
$32$	28770.4	+	16610.6i	0.155210	+	0.0896107i
$33$		0			0
$34$			7652.99i			0.0333930i
$35$	−286035.	+	495427.i	−1.12767	+	1.95318i
$36$		0			0
$37$	36374.8	−	21001.0i	0.118058	−	0.0681608i	−0.439808	−	0.898092i	$-0.644954\pi$
$37$	36374.8	−	21001.0i	0.118058	−	0.0681608i	0.557866	+	0.829931i	$0.311620\pi$
$38$	−27878.6			−0.0824191
$39$		0			0
$40$	−76214.6			−0.188290
$41$	75942.3	−	43845.3i	0.172084	−	0.0993526i	−0.411484	−	0.911417i	$-0.634989\pi$
$41$	75942.3	−	43845.3i	0.172084	−	0.0993526i	0.583568	+	0.812064i	$0.301656\pi$
$42$		0			0
$43$	−374876.	+	649305.i	−0.719032	+	1.24540i	0.242352	+	0.970188i	$0.422081\pi$
$43$	−374876.	+	649305.i	−0.719032	+	1.24540i	−0.961384	+	0.275212i	$0.911252\pi$
$44$		−	73311.5i		−	0.129744i
$45$		0			0
$46$	−26035.2	−	15031.4i	−0.0394374	−	0.0227692i
$47$			940126.i			1.32082i	0.750905	+	0.660410i	$0.229617\pi$
$47$			940126.i			1.32082i	−0.750905	+	0.660410i	$0.770383\pi$
$48$		0			0
$49$	436688.	+	756366.i	0.530255	+	0.918429i
$50$	67480.7	−	38960.0i	0.0763457	−	0.0440782i
$51$		0			0
$52$	578064.	−	828564.i	0.570117	−	0.817174i
$53$	924214.			0.852721			0.426360	−	0.904553i	$-0.359796\pi$
$53$	924214.			0.852721			0.426360	+	0.904553i	$0.359796\pi$
$54$		0			0
$55$	126217.	+	218614.i	0.102294	+	0.177178i
$56$	−113037.	+	195786.i	−0.0860127	+	0.148978i
$57$		0			0
$58$	85584.1	+	49412.0i	0.0575964	+	0.0332533i
$59$	−547626.	−	316172.i	−0.347138	−	0.200420i	0.316286	−	0.948664i	$-0.397564\pi$
$59$	−547626.	−	316172.i	−0.347138	−	0.200420i	−0.663424	+	0.748244i	$0.730897\pi$
$60$		0			0
$61$	32203.2	−	55777.7i	0.0181654	−	0.0314634i	−0.856800	−	0.515649i	$-0.827551\pi$
$61$	32203.2	−	55777.7i	0.0181654	−	0.0314634i	0.874965	+	0.484186i	$0.160884\pi$
$62$	−41443.3	−	71781.9i	−0.0220843	−	0.0382511i
$63$		0			0
$64$	2.05195e6			0.978444
$65$	−297281.	+	3.46600e6i	−0.134267	+	1.56542i
$66$		0			0
$67$	−1.68358e6	+	972013.i	−0.683866	+	0.394830i	−0.801310	−	0.598249i	$-0.795863\pi$
$67$	−1.68358e6	+	972013.i	−0.683866	+	0.394830i	0.117444	+	0.993079i	$0.462530\pi$
$68$	718588.	+	1.24463e6i	0.277140	+	0.480020i
$69$		0			0
$70$		−	388519.i		−	0.135384i
$71$	4.09113e6	+	2.36202e6i	1.35656	+	0.783211i	0.989159	−	0.146851i	$-0.0469139\pi$
$71$	4.09113e6	+	2.36202e6i	1.35656	+	0.783211i	0.367402	+	0.930062i	$0.380247\pi$
$72$		0			0
$73$			1.92731e6i			0.579857i	0.957048	+	0.289928i	$0.0936315\pi$
$73$			1.92731e6i			0.579857i	−0.957048	+	0.289928i	$0.906368\pi$
$74$	−14262.8	+	24703.8i	−0.00409159	+	0.00708685i
$75$		0			0
$76$	−4.53399e6	+	2.61770e6i	−1.18477	+	0.684025i
$77$	748791.			0.186915
$78$		0			0
$79$	−1.50287e6			−0.342947			−0.171474	−	0.985189i	$-0.554853\pi$
$79$	−1.50287e6			−0.342947			−0.171474	+	0.985189i	$0.554853\pi$
$80$	−6.16388e6	+	3.55872e6i	−1.34598	+	0.777103i
$81$		0			0
$82$	−29777.4	+	51575.9i	−0.00596400	+	0.0103300i
$83$			1.87974e6i			0.360848i	0.983589	+	0.180424i	$0.0577470\pi$
$83$			1.87974e6i			0.360848i	−0.983589	+	0.180424i	$0.942253\pi$
$84$		0			0
$85$	−4.28565e6	−	2.47432e6i	−0.756921	−	0.437008i
$86$		−	509191.i		−	0.0863250i
$87$		0			0
$88$	49879.3	+	86393.4i	0.00780244	+	0.0135142i
$89$	−3.78860e6	+	2.18735e6i	−0.569657	+	0.328892i	−0.757012	−	0.653400i	$-0.773342\pi$
$89$	−3.78860e6	+	2.18735e6i	−0.569657	+	0.328892i	0.187355	+	0.982292i	$0.440008\pi$
$90$		0			0
$91$	8.46281e6	+	5.90424e6i	1.17725	+	0.821333i
$92$	−5.64559e6			−0.755879
$93$		0			0
$94$	−319241.	−	552942.i	−0.0396435	−	0.0686645i
$95$	9.01354e6	−	1.56119e7i	1.07861	−	1.86820i
$96$		0			0
$97$	−1.53602e6	−	886819.i	−0.170881	−	0.0986583i	0.412120	−	0.911130i	$-0.364788\pi$
$97$	−1.53602e6	−	886819.i	−0.170881	−	0.0986583i	−0.583001	+	0.812471i	$0.698122\pi$
$98$	−513683.	−	296575.i	−0.0551320	−	0.0318305i
$99$		0			0
$100$	7.31641e6	−	1.26724e7i	0.731641	−	1.26724i
$101$	4.81973e6	+	8.34802e6i	0.465477	+	0.806229i	0.999223	−	0.0394154i	$-0.0125496\pi$
$101$	4.81973e6	+	8.34802e6i	0.465477	+	0.806229i	−0.533746	+	0.845645i	$0.679216\pi$
$102$		0			0
$103$	7.14668e6			0.644427			0.322214	−	0.946667i	$-0.395573\pi$
$103$	7.14668e6			0.644427			0.322214	+	0.946667i	$0.395573\pi$
$104$	−117481.	+	1.36971e6i	−0.0102412	+	0.119402i
$105$		0			0
$106$	−543583.	+	313838.i	−0.0443298	+	0.0255938i
$107$	−1.03003e7	−	1.78406e7i	−0.812839	−	1.40788i	−0.910869	−	0.412695i	$-0.864587\pi$
$107$	−1.03003e7	−	1.78406e7i	−0.812839	−	1.40788i	0.0980299	−	0.995183i	$-0.468746\pi$
$108$		0			0
$109$		−	1.05713e7i		−	0.781872i	−0.920418	−	0.390936i	$-0.872151\pi$
$109$		−	1.05713e7i		−	0.781872i	0.920418	−	0.390936i	$-0.127849\pi$
$110$	−148471.	−	85719.8i	−0.0106357	−	0.00614054i
$111$		0			0
$112$			2.11123e7i			1.41995i
$113$	1.34036e7	−	2.32157e7i	0.873868	−	1.51358i	0.0159047	−	0.999874i	$-0.494937\pi$
$113$	1.34036e7	−	2.32157e7i	0.873868	−	1.51358i	0.857964	−	0.513711i	$-0.171730\pi$
$114$		0			0
$115$	1.68351e7	−	9.71976e6i	1.03222	−	0.595954i
$116$	1.85584e7			1.10392
$117$		0			0
$118$	429454.			0.0240619
$119$	−1.27124e7	+	7.33953e6i	−0.691536	+	0.399258i
$120$		0			0
$121$	−9.57838e6	+	1.65902e7i	−0.491522	+	0.851341i
$122$			43741.4i			0.00218089i
$123$		0			0
$124$	−1.34801e7	−	7.78276e6i	−0.634919	−	0.366571i
$125$			1.60763e7i			0.736209i
$126$		0			0
$127$	−4.03532e6	−	6.98938e6i	−0.174810	−	0.302779i	0.765286	−	0.643691i	$-0.222598\pi$
$127$	−4.03532e6	−	6.98938e6i	−0.174810	−	0.302779i	−0.940095	+	0.340912i	$0.889264\pi$
$128$	−4.88947e6	+	2.82294e6i	−0.206076	+	0.118978i
$129$		0			0
$130$	−1.00211e6	−	2.13950e6i	−0.0400050	−	0.0854104i
$131$	−1.26390e7			−0.491206			−0.245603	−	0.969370i	$-0.578986\pi$
$131$	−1.26390e7			−0.491206			−0.245603	+	0.969370i	$0.578986\pi$
$132$		0			0
$133$	−2.67367e7	−	4.63094e7i	−0.985434	−	1.70682i
$134$	660139.	−	1.14339e6i	0.0237011	−	0.0410515i
$135$		0			0
$136$	−1.69363e6	−	977818.i	−0.0577341	−	0.0333328i
$137$	−2.45282e7	−	1.41614e7i	−0.814975	−	0.470526i	0.0337058	−	0.999432i	$-0.489269\pi$
$137$	−2.45282e7	−	1.41614e7i	−0.814975	−	0.470526i	−0.848680	+	0.528906i	$0.822602\pi$
$138$		0			0
$139$	4.44074e6	−	7.69159e6i	0.140250	−	0.242920i	−0.787341	−	0.616518i	$-0.788543\pi$
$139$	4.44074e6	−	7.69159e6i	0.140250	−	0.242920i	0.927591	+	0.373598i	$0.121876\pi$
$140$	−3.64805e7	−	6.31861e7i	−1.12360	−	1.94614i
$141$		0			0
$142$	−3.20831e6			−0.0940301
$143$	4.12346e6	−	1.93137e6i	0.117919	−	0.0552317i
$144$		0			0
$145$	−5.53411e7	+	3.19512e7i	−1.50751	+	0.870361i
$146$	−654461.	−	1.13356e6i	−0.0174040	−	0.0301446i
$147$		0			0
$148$			5.35689e6i			0.135830i
$149$	4.40391e7	+	2.54260e7i	1.09065	+	0.629689i	0.933750	−	0.357926i	$-0.116516\pi$
$149$	4.40391e7	+	2.54260e7i	1.09065	+	0.629689i	0.156902	+	0.987614i	$0.449849\pi$
$150$		0			0
$151$		−	9.76974e6i		−	0.230921i	−0.993312	−	0.115461i	$-0.963166\pi$
$151$		−	9.76974e6i		−	0.230921i	0.993312	−	0.115461i	$-0.0368344\pi$
$152$	3.56203e6	−	6.16961e6i	0.0822706	−	0.142497i
$153$		0			0
$154$	−440407.	+	254269.i	−0.00971699	+	0.00561011i
$155$	5.35969e7			1.15606
$156$		0			0
$157$	6.53474e7			1.34766			0.673828	−	0.738888i	$-0.264649\pi$
$157$	6.53474e7			1.34766			0.673828	+	0.738888i	$0.264649\pi$
$158$	883927.	−	510335.i	0.0178286	−	0.0102933i
$159$		0			0
$160$	7.29462e6	−	1.26347e7i	0.140794	−	0.243862i
$161$		−	5.76631e7i		−	1.08895i
$162$		0			0
$163$	1.74920e7	+	1.00990e7i	0.316361	+	0.182651i	0.649769	−	0.760132i	$-0.274866\pi$
$163$	1.74920e7	+	1.00990e7i	0.316361	+	0.182651i	−0.333409	+	0.942782i	$0.608199\pi$
$164$			1.11839e7i			0.197989i
$165$		0			0
$166$	−638309.	−	1.10558e6i	−0.0108306	−	0.0187591i
$167$	5.86371e6	−	3.38542e6i	0.0974238	−	0.0562477i	−0.450497	−	0.892778i	$-0.648753\pi$
$167$	5.86371e6	−	3.38542e6i	0.0974238	−	0.0562477i	0.547920	+	0.836531i	$0.315420\pi$
$168$		0			0
$169$	6.18320e7	+	1.06853e7i	0.985394	+	0.170288i
$170$	3.36085e6			0.0524660
$171$		0			0
$172$	−4.78112e7	−	8.28115e7i	−0.716441	−	1.24091i
$173$	−4.33522e7	+	7.50883e7i	−0.636576	+	1.10258i	0.349603	+	0.936898i	$0.386316\pi$
$173$	−4.33522e7	+	7.50883e7i	−0.636576	+	1.10258i	−0.986179	+	0.165684i	$0.947017\pi$
$174$		0			0
$175$	1.29434e8	+	7.47285e7i	1.82563	+	1.05403i
$176$	8.06800e6	+	4.65806e6i	0.111550	+	0.0644037i
$177$		0			0
$178$	1.48553e6	−	2.57301e6i	0.0197429	−	0.0341957i
$179$	4.47221e7	+	7.74609e7i	0.582823	+	1.00948i	0.995143	+	0.0984398i	$0.0313852\pi$
$179$	4.47221e7	+	7.74609e7i	0.582823	+	1.00948i	−0.412320	+	0.911039i	$0.635281\pi$
$180$		0			0
$181$	−2.55748e7			−0.320581			−0.160290	−	0.987070i	$-0.551243\pi$
$181$	−2.55748e7			−0.320581			−0.160290	+	0.987070i	$0.551243\pi$
$182$	−6.98239e6	−	598883.i	−0.0858527	−	0.00736364i
$183$		0			0
$184$	6.65300e6	−	3.84111e6i	0.0787328	−	0.0454564i
$185$	−9.22271e6	−	1.59742e7i	−0.107092	−	0.185489i
$186$		0			0
$187$			6.47736e6i			0.0724356i
$188$	−1.03839e8	−	5.99512e7i	−1.13974	−	0.658030i
$189$		0			0
$190$			1.22430e7i			0.129494i
$191$	7.26412e7	−	1.25818e8i	0.754339	−	1.30655i	−0.191364	−	0.981519i	$-0.561291\pi$
$191$	7.26412e7	−	1.25818e8i	0.754339	−	1.30655i	0.945702	−	0.325034i	$-0.105376\pi$
$192$		0			0
$193$	−7.90017e7	+	4.56117e7i	−0.791017	+	0.456694i	−0.840321	−	0.542090i	$-0.817633\pi$
$193$	−7.90017e7	+	4.56117e7i	−0.791017	+	0.456694i	0.0493033	+	0.998784i	$0.484300\pi$
$194$	1.20456e6			0.0118446
$195$		0			0
$196$	−1.11389e8			−1.05669
$197$	−1.47447e8	+	8.51285e7i	−1.37405	+	0.793311i	−0.991436	−	0.130595i	$-0.958311\pi$
$197$	−1.47447e8	+	8.51285e7i	−1.37405	+	0.793311i	−0.382619	+	0.923906i	$0.624978\pi$
$198$		0			0
$199$	−6.97613e7	+	1.20830e8i	−0.627521	+	1.08690i	0.360526	+	0.932749i	$0.382597\pi$
$199$	−6.97613e7	+	1.20830e8i	−0.627521	+	1.08690i	−0.988047	+	0.154150i	$0.950736\pi$
$200$			1.99116e7i			0.175995i
$201$		0			0
$202$	−5.66952e6	−	3.27330e6i	−0.0483968	−	0.0279419i
$203$			1.89553e8i			1.59035i
$204$		0			0
$205$	−1.92549e7	−	3.33504e7i	−0.156100	−	0.270373i
$206$	−4.20337e6	+	2.42682e6i	−0.0335014	+	0.0193420i
$207$		0			0
$208$	5.44553e7	+	1.16262e8i	0.419583	+	0.895808i
$209$	−2.35960e7			−0.178783
$210$		0			0
$211$	−4.18539e7	−	7.24931e7i	−0.306724	−	0.531261i	0.670920	−	0.741530i	$-0.265899\pi$
$211$	−4.18539e7	−	7.24931e7i	−0.306724	−	0.531261i	−0.977644	+	0.210269i	$0.932566\pi$
$212$	−5.89365e7	+	1.02081e8i	−0.424824	+	0.735817i
$213$		0			0
$214$	1.21163e7	+	6.99538e6i	0.0845130	+	0.0487936i
$215$	2.85146e8	+	1.64629e8i	1.95673	+	1.12972i
$216$		0			0
$217$	7.94917e7	−	1.37684e8i	0.528096	−	0.914689i
$218$	3.58973e6	+	6.21759e6i	0.0234673	+	0.0406466i
$219$		0			0
$220$	−3.21951e7			−0.203850
$221$	−5.10742e7	+	7.32069e7i	−0.318294	+	0.456225i
$222$		0			0
$223$	−8.23600e7	+	4.75506e7i	−0.497335	+	0.287137i	−0.727612	−	0.685988i	$-0.759370\pi$
$223$	−8.23600e7	+	4.75506e7i	−0.497335	+	0.287137i	0.230277	+	0.973125i	$0.426037\pi$
$224$	−2.16379e7	−	3.74779e7i	−0.128631	−	0.222796i
$225$		0			0
$226$			1.82060e7i			0.104914i
$227$	−8.55988e7	−	4.94205e7i	−0.485710	−	0.280425i	0.237083	−	0.971489i	$-0.423809\pi$
$227$	−8.55988e7	−	4.94205e7i	−0.485710	−	0.280425i	−0.722793	+	0.691064i	$0.757142\pi$
$228$		0			0
$229$			8.72426e7i			0.480070i	0.970764	+	0.240035i	$0.0771589\pi$
$229$			8.72426e7i			0.480070i	−0.970764	+	0.240035i	$0.922841\pi$
$230$	−6.60113e6	+	1.14335e7i	−0.0357743	+	0.0619629i
$231$		0			0
$232$	−2.18701e7	+	1.26267e7i	−0.114985	+	0.0663867i
$233$	2.42490e8			1.25588			0.627940	−	0.778262i	$-0.283898\pi$
$233$	2.42490e8			1.25588			0.627940	+	0.778262i	$0.283898\pi$
$234$		0			0
$235$	4.12861e8			2.07523
$236$	6.98436e7	−	4.03242e7i	0.345887	−	0.199698i
$237$		0			0
$238$	4.98462e6	−	8.63361e6i	0.0239669	−	0.0415119i
$239$			4.08512e8i			1.93558i	0.251750	+	0.967792i	$0.418994\pi$
$239$			4.08512e8i			1.93558i	−0.251750	+	0.967792i	$0.581006\pi$
$240$		0			0
$241$	1.89875e8	+	1.09624e8i	0.873792	+	0.504484i	0.868606	−	0.495503i	$-0.165016\pi$
$241$	1.89875e8	+	1.09624e8i	0.873792	+	0.504484i	0.00518518	+	0.999987i	$0.498349\pi$
$242$		−	1.30102e7i		−	0.0590108i
$243$		0			0
$244$	4.10716e6	+	7.11381e6i	0.0181000	+	0.0313500i
$245$	3.32162e8	−	1.91774e8i	1.44301	−	0.833121i
$246$		0			0
$247$	−2.66681e8	−	1.86055e8i	−1.12604	−	0.785600i
$248$	2.11807e7			0.0881780
$249$		0			0
$250$	−5.45908e6	−	9.45541e6i	−0.0220968	−	0.0382728i
$251$	−7.42822e6	+	1.28661e7i	−0.0296501	+	0.0513556i	−0.880470	−	0.474102i	$-0.842773\pi$
$251$	−7.42822e6	+	1.28661e7i	−0.0296501	+	0.0513556i	0.850820	+	0.525458i	$0.176106\pi$
$252$		0			0
$253$	−2.20358e7	−	1.27223e7i	−0.0855473	−	0.0493907i
$254$	4.74681e6	+	2.74057e6i	0.0181754	+	0.0104936i
$255$		0			0
$256$	−1.29407e8	+	2.24140e8i	−0.482080	+	0.834987i
$257$	−2.49812e8	−	4.32688e8i	−0.918011	−	1.59004i	−0.802432	−	0.596744i	$-0.796461\pi$
$257$	−2.49812e8	−	4.32688e8i	−0.918011	−	1.59004i	−0.115579	−	0.993298i	$-0.536872\pi$
$258$		0			0
$259$	−5.47143e7			−0.195682
$260$	−3.63868e8	−	2.53860e8i	−1.28392	−	0.895750i
$261$		0			0
$262$	7.43374e6	−	4.29187e6i	0.0255360	−	0.0147432i
$263$	1.51725e7	+	2.62796e7i	0.0514295	+	0.0890785i	0.890594	−	0.454799i	$-0.150289\pi$
$263$	1.51725e7	+	2.62796e7i	0.0514295	+	0.0890785i	−0.839165	+	0.543878i	$0.816956\pi$
$264$		0			0
$265$		−	4.05873e8i		−	1.33977i
$266$	3.14508e7	+	1.81581e7i	0.102458	+	0.0591542i
$267$		0			0
$268$		−	2.47939e8i		−	0.786815i
$269$	5.52630e7	−	9.57183e7i	0.173102	−	0.299821i	−0.766401	−	0.642363i	$-0.777954\pi$
$269$	5.52630e7	−	9.57183e7i	0.173102	−	0.299821i	0.939503	+	0.342541i	$0.111288\pi$
$270$		0			0
$271$	4.36530e7	−	2.52031e7i	0.133236	−	0.0769238i	−0.431901	−	0.901921i	$-0.642157\pi$
$271$	4.36530e7	−	2.52031e7i	0.133236	−	0.0769238i	0.565136	+	0.824997i	$0.308824\pi$
$272$	−1.82630e8			−0.550278
$273$		0			0
$274$	1.92353e7			0.0564900
$275$	5.71145e7	−	3.29751e7i	0.165608	−	0.0956140i
$276$		0			0
$277$	−2.69297e8	+	4.66436e8i	−0.761294	+	1.31860i	0.180889	+	0.983503i	$0.442102\pi$
$277$	−2.69297e8	+	4.66436e8i	−0.761294	+	1.31860i	−0.942184	+	0.335097i	$0.891231\pi$
$278$			6.03182e6i			0.0168380i
$279$		0			0
$280$	8.59804e7	+	4.96408e7i	0.234070	+	0.135140i
$281$		−	1.43482e8i		−	0.385766i	−0.981222	−	0.192883i	$-0.938216\pi$
$281$		−	1.43482e8i		−	0.385766i	0.981222	−	0.192883i	$-0.0617839\pi$
$282$		0			0
$283$	5.06236e7	+	8.76826e7i	0.132770	+	0.229964i	0.924743	−	0.380591i	$-0.124279\pi$
$283$	5.06236e7	+	8.76826e7i	0.132770	+	0.229964i	−0.791973	+	0.610556i	$0.790946\pi$
$284$	−5.21778e8	+	3.01249e8i	−1.35167	+	0.780389i
$285$		0			0
$286$	−1.76940e6	+	2.53616e6i	−0.00447245	+	0.00641056i
$287$	−1.14231e8			−0.285231
$288$		0			0
$289$	1.41679e8	+	2.45396e8i	0.345274	+	0.598032i
$290$	2.16995e7	−	3.75847e7i	0.0522465	−	0.0904937i
$291$		0			0
$292$	−2.12875e8	−	1.22903e8i	−0.500361	−	0.288884i
$293$	2.65267e8	+	1.53152e8i	0.616094	+	0.355702i	0.775347	−	0.631536i	$-0.217575\pi$
$293$	2.65267e8	+	1.53152e8i	0.616094	+	0.355702i	−0.159252	+	0.987238i	$0.550908\pi$
$294$		0			0
$295$	−1.38849e8	+	2.40493e8i	−0.314894	+	0.545413i
$296$	−3.64469e6	−	6.31279e6i	−0.00816845	−	0.0141482i
$297$		0			0
$298$	−3.45359e7			−0.0755986
$299$	−1.48731e8	−	3.17540e8i	−0.321775	−	0.686988i
$300$		0			0
$301$	8.45822e8	−	4.88336e8i	1.78771	−	1.03213i
$302$	3.31754e6	+	5.74615e6i	0.00693094	+	0.0120047i
$303$		0			0
$304$		−	6.65293e8i		−	1.35817i
$305$	−2.44951e7	−	1.41422e7i	−0.0494344	−	0.0285409i
$306$		0			0
$307$			8.86416e6i			0.0174845i	0.999962	+	0.00874225i	$0.00278278\pi$
$307$			8.86416e6i			0.0174845i	−0.999962	+	0.00874225i	$0.997217\pi$
$308$	−4.77499e7	+	8.27053e7i	−0.0931205	+	0.161289i
$309$		0			0
$310$	−3.15234e7	+	1.82001e7i	−0.0600990	+	0.0346982i
$311$	3.95364e8			0.745309			0.372654	−	0.927970i	$-0.378448\pi$
$311$	3.95364e8			0.745309			0.372654	+	0.927970i	$0.378448\pi$
$312$		0			0
$313$	−8.88408e8			−1.63760			−0.818799	−	0.574080i	$-0.805360\pi$
$313$	−8.88408e8			−1.63760			−0.818799	+	0.574080i	$0.805360\pi$
$314$	−3.84346e7	+	2.21902e7i	−0.0700597	+	0.0404490i
$315$		0			0
$316$	9.58373e7	−	1.65995e8i	0.170856	−	0.295931i
$317$		−	3.40256e8i		−	0.599928i	−0.953951	−	0.299964i	$-0.903025\pi$
$317$		−	3.40256e8i		−	0.599928i	0.953951	−	0.299964i	$-0.0969746\pi$
$318$		0			0
$319$	7.24369e7	+	4.18215e7i	0.124937	+	0.0721326i
$320$		−	9.01123e8i		−	1.53730i
$321$		0			0
$322$	1.95808e7	+	3.39150e7i	0.0326840	+	0.0566104i
$323$	4.00595e8	−	2.31284e8i	0.661450	−	0.381888i
$324$		0			0
$325$	9.05516e8	+	7.76666e7i	1.46320	+	0.125500i
$326$	−1.37174e7			−0.0219286
$327$		0			0
$328$	−7.60927e6	−	1.31796e7i	−0.0119065	−	0.0206227i
$329$	6.12331e8	−	1.06059e9i	0.947984	−	1.64196i
$330$		0			0
$331$	−4.75802e8	−	2.74704e8i	−0.721154	−	0.416359i	0.0940230	−	0.995570i	$-0.470027\pi$
$331$	−4.75802e8	−	2.74704e8i	−0.721154	−	0.416359i	−0.815177	+	0.579211i	$0.803361\pi$
$332$	−2.07621e8	−	1.19870e8i	−0.311377	−	0.179774i
$333$		0			0
$334$	−2.29919e6	+	3.98232e6i	−0.00337647	+	0.00584821i
$335$	4.26865e8	+	7.39351e8i	0.620345	+	1.07447i
$336$		0			0
$337$	−6.88538e8			−0.979993			−0.489997	−	0.871724i	$-0.663002\pi$
$337$	−6.88538e8			−0.979993			−0.489997	+	0.871724i	$0.663002\pi$
$338$	−3.99954e7	+	1.47118e7i	−0.0563381	+	0.0207233i
$339$		0			0
$340$	5.46586e8	−	3.15572e8i	0.754193	−	0.435434i
$341$	−3.50769e7	−	6.07550e7i	−0.0479050	−	0.0829739i
$342$		0			0
$343$		−	6.49158e7i		−	0.0868602i
$344$	1.12686e8	+	6.50591e7i	0.149250	+	0.0861694i
$345$		0			0
$346$		−	5.88850e7i		−	0.0764255i
$347$	−3.43577e8	+	5.95094e8i	−0.441440	+	0.764596i	−0.997797	−	0.0663474i	$-0.978865\pi$
$347$	−3.43577e8	+	5.95094e8i	−0.441440	+	0.764596i	0.556357	+	0.830943i	$0.312199\pi$
$348$		0			0
$349$	−8.95711e8	+	5.17139e8i	−1.12792	+	0.651206i	−0.943411	−	0.331625i	$-0.892403\pi$
$349$	−8.95711e8	+	5.17139e8i	−1.12792	+	0.651206i	−0.184510	+	0.982831i	$0.559070\pi$
$350$	−1.01503e8			−0.126544
$351$		0			0
$352$	−1.90961e7			−0.0233370
$353$	−9.29168e8	+	5.36455e8i	−1.12430	+	0.649116i	−0.942496	−	0.334219i	$-0.891528\pi$
$353$	−9.29168e8	+	5.36455e8i	−1.12430	+	0.649116i	−0.181806	+	0.983334i	$0.558194\pi$
$354$		0			0
$355$	1.03729e9	−	1.79664e9i	1.23056	−	2.13139i
$356$		−	5.57943e8i		−	0.655413i
$357$		0			0
$358$	−5.26073e7	−	3.03728e7i	−0.0605976	−	0.0349860i
$359$			6.57582e8i			0.750100i	0.927005	+	0.375050i	$0.122374\pi$
$359$			6.57582e8i			0.750100i	−0.927005	+	0.375050i	$0.877626\pi$
$360$		0			0
$361$	3.95593e8	+	6.85188e8i	0.442562	+	0.766539i
$362$	1.50420e7	−	8.68452e6i	0.0166658	−	0.00962201i
$363$		0			0
$364$	−1.19180e9	+	5.58223e8i	−1.29524	+	0.606670i
$365$	8.46387e8			0.911054
$366$		0			0
$367$	4.47343e8	+	7.74821e8i	0.472400	+	0.818220i	0.999501	−	0.0315822i	$-0.0100546\pi$
$367$	4.47343e8	+	7.74821e8i	0.472400	+	0.818220i	−0.527102	+	0.849802i	$0.676721\pi$
$368$	3.58709e8	−	6.21303e8i	0.375211	−	0.649884i
$369$		0			0
$370$	1.08488e7	+	6.26357e6i	0.0111346	+	0.00642859i
$371$	−1.04264e9	−	6.01967e8i	−1.06005	−	0.612018i
$372$		0			0
$373$	−3.42088e8	+	5.92515e8i	−0.341317	+	0.591178i	−0.984677	−	0.174385i	$-0.944206\pi$
$373$	−3.42088e8	+	5.92515e8i	−0.341317	+	0.591178i	0.643361	+	0.765563i	$0.277540\pi$
$374$	−2.19954e6	−	3.80971e6i	−0.00217410	−	0.00376566i
$375$		0			0
$376$	1.63157e8			0.158288
$377$	4.88916e8	+	1.04383e9i	0.469937	+	1.00331i
$378$		0			0
$379$	−9.87024e8	+	5.69859e8i	−0.931302	+	0.537687i	−0.887223	−	0.461341i	$-0.847369\pi$
$379$	−9.87024e8	+	5.69859e8i	−0.931302	+	0.537687i	−0.0440788	+	0.999028i	$0.514035\pi$
$380$	1.14958e9	+	1.99112e9i	1.07472	+	1.86147i
$381$		0			0
$382$			9.86680e7i			0.0905638i
$383$	−1.16426e9	−	6.72186e8i	−1.05890	−	0.611355i	−0.133771	−	0.991012i	$-0.542709\pi$
$383$	−1.16426e9	−	6.72186e8i	−1.05890	−	0.611355i	−0.925127	+	0.379657i	$0.876042\pi$
$384$		0			0
$385$		−	3.28835e8i		−	0.293674i
$386$	3.09770e7	−	5.36537e7i	0.0274147	−	0.0474837i
$387$		0			0
$388$	1.95901e8	−	1.13104e8i	0.170265	−	0.0983028i
$389$	−4.06758e8			−0.350359			−0.175179	−	0.984537i	$-0.556051\pi$
$389$	−4.06758e8			−0.350359			−0.175179	+	0.984537i	$0.556051\pi$
$390$		0			0
$391$	4.98810e8			0.422004
$392$	1.31266e8	−	7.57864e7i	0.110065	−	0.0635463i
$393$		0			0
$394$	5.78147e7	−	1.00138e8i	0.0476213	−	0.0824826i
$395$			6.59995e8i			0.538829i
$396$		0			0
$397$	1.70506e8	+	9.84416e7i	0.136764	+	0.0789609i	0.566821	−	0.823841i	$-0.308173\pi$
$397$	1.70506e8	+	9.84416e7i	0.136764	+	0.0789609i	−0.430057	+	0.902802i	$0.641506\pi$
$398$		−	9.47562e7i		−	0.0753385i
$399$		0			0
$400$	9.29739e8	+	1.61036e9i	0.726359	+	1.25809i
$401$	−8.66177e8	+	5.00088e8i	−0.670813	+	0.387294i	−0.796385	−	0.604791i	$-0.793257\pi$
$401$	−8.66177e8	+	5.00088e8i	−0.670813	+	0.387294i	0.125572	+	0.992085i	$0.459923\pi$
$402$		0			0
$403$	8.26171e7	−	9.63233e8i	0.0628785	−	0.733101i
$404$	−1.22940e9			−0.927599
$405$		0			0
$406$	−6.43670e7	−	1.11487e8i	−0.0477333	−	0.0826766i
$407$	−1.20718e7	+	2.09089e7i	−0.00887544	+	0.0153727i
$408$		0			0
$409$	1.40643e9	+	8.12004e8i	1.01645	+	0.586850i	0.913075	−	0.407793i	$-0.133701\pi$
$409$	1.40643e9	+	8.12004e8i	1.01645	+	0.586850i	0.103379	+	0.994642i	$0.467035\pi$
$410$	2.26498e7	+	1.30769e7i	0.0162301	+	0.00937045i
$411$		0			0
$412$	−4.55739e8	+	7.89363e8i	−0.321053	+	0.556079i
$413$	4.11864e8	+	7.13370e8i	0.287693	+	0.498299i
$414$		0			0
$415$	8.25497e8			0.566953
$416$	−2.15823e8	−	1.50573e8i	−0.146985	−	0.102547i
$417$		0			0
$418$	1.38781e7	−	8.01255e6i	0.00929425	−	0.00536604i
$419$	−9.59601e7	−	1.66208e8i	−0.0637297	−	0.110383i	0.832400	−	0.554175i	$-0.186966\pi$
$419$	−9.59601e7	−	1.66208e8i	−0.0637297	−	0.110383i	−0.896130	+	0.443792i	$0.853633\pi$
$420$		0			0
$421$		−	1.17016e9i		−	0.764292i	−0.924102	−	0.382146i	$-0.875185\pi$
$421$		−	1.17016e9i		−	0.764292i	0.924102	−	0.382146i	$-0.124815\pi$
$422$	4.92334e7	+	2.84249e7i	0.0318909	+	0.0184122i
$423$		0			0
$424$		−	1.60396e8i		−	0.102191i
$425$	−6.46433e8	+	1.11966e9i	−0.408472	+	0.707495i
$426$		0			0
$427$	−7.26592e7	+	4.19498e7i	−0.0451641	+	0.0260755i
$428$	2.62736e9			1.61982
$429$		0			0
$430$	−2.23614e8			−0.135631
$431$	1.83241e8	−	1.05794e8i	0.110243	−	0.0636491i	−0.443864	−	0.896094i	$-0.646393\pi$
$431$	1.83241e8	−	1.05794e8i	0.110243	−	0.0636491i	0.554108	+	0.832445i	$0.313059\pi$
$432$		0			0
$433$	−5.87978e8	+	1.01841e9i	−0.348060	+	0.602857i	−0.985905	−	0.167308i	$-0.946493\pi$
$433$	−5.87978e8	+	1.01841e9i	−0.348060	+	0.602857i	0.637845	+	0.770165i	$0.279826\pi$
$434$			1.07973e8i			0.0634017i
$435$		0			0
$436$	1.16762e9	+	6.74125e8i	0.674681	+	0.389527i
$437$			1.81708e9i			1.04157i
$438$		0			0
$439$	−1.21215e9	−	2.09950e9i	−0.683802	−	1.18438i	−0.973812	−	0.227356i	$-0.926992\pi$
$439$	−1.21215e9	−	2.09950e9i	−0.683802	−	1.18438i	0.290010	−	0.957024i	$-0.406341\pi$
$440$	3.79401e7	−	2.19047e7i	0.0212331	−	0.0122590i
$441$		0			0
$442$	5.18059e6	−	6.04006e7i	0.00285366	−	0.0332708i
$443$	−8.11271e7			−0.0443356			−0.0221678	−	0.999754i	$-0.507057\pi$
$443$	−8.11271e7			−0.0443356			−0.0221678	+	0.999754i	$0.507057\pi$
$444$		0			0
$445$	9.60586e8	+	1.66378e9i	0.516745	+	0.895028i
$446$	3.22938e7	−	5.59345e7i	0.0172364	−	0.0298543i
$447$		0			0
$448$	−2.31487e9	−	1.33649e9i	−1.21634	−	0.702253i
$449$	2.29405e7	+	1.32447e7i	0.0119603	+	0.00690525i	0.505968	−	0.862552i	$-0.331135\pi$
$449$	2.29405e7	+	1.32447e7i	0.0119603	+	0.00690525i	−0.494008	+	0.869457i	$0.664469\pi$
$450$		0			0
$451$	−2.52030e7	+	4.36529e7i	−0.0129370	+	0.0224076i
$452$	1.70947e9	+	2.96090e9i	0.870719	+	1.50813i
$453$		0			0
$454$	6.71275e7			0.0336670
$455$	2.59288e9	−	3.71649e9i	1.29045	−	1.84966i
$456$		0			0
$457$	−2.28711e9	+	1.32046e9i	−1.12094	+	0.647172i	−0.941640	−	0.336623i	$-0.890715\pi$
$457$	−2.28711e9	+	1.32046e9i	−1.12094	+	0.647172i	−0.179296	+	0.983795i	$0.557382\pi$
$458$	−2.96252e7	−	5.13124e7i	−0.0144090	−	0.0249570i
$459$		0			0
$460$			2.47929e9i			1.18761i
$461$	1.91120e8	+	1.10343e8i	0.0908558	+	0.0524556i	0.544740	−	0.838605i	$-0.316629\pi$
$461$	1.91120e8	+	1.10343e8i	0.0908558	+	0.0524556i	−0.453884	+	0.891061i	$0.649962\pi$
$462$		0			0
$463$		−	1.40461e9i		−	0.657691i	−0.944384	−	0.328845i	$-0.893341\pi$
$463$		−	1.40461e9i		−	0.657691i	0.944384	−	0.328845i	$-0.106659\pi$
$464$	−1.17916e9	+	2.04237e9i	−0.547976	+	0.949122i
$465$		0			0
$466$	−1.42622e8	+	8.23431e7i	−0.0652885	+	0.0376944i
$467$	−1.70943e9			−0.776681			−0.388341	−	0.921516i	$-0.626952\pi$
$467$	−1.70943e9			−0.776681			−0.388341	+	0.921516i	$0.626952\pi$
$468$		0			0
$469$	2.53240e9			1.13352
$470$	−2.42827e8	+	1.40197e8i	−0.107884	+	0.0622866i
$471$		0			0
$472$	−5.48711e7	+	9.50395e7i	−0.0240185	+	0.0416013i
$473$		−	4.30971e8i		−	0.187255i
$474$		0			0
$475$	−4.07872e9	−	2.35485e9i	−1.74621	−	1.00817i
$476$		−	1.87215e9i		−	0.795640i
$477$		0			0
$478$	−1.38720e8	−	2.40269e8i	−0.0580952	−	0.100624i
$479$	1.87473e9	−	1.08237e9i	0.779405	−	0.449990i	−0.0568141	−	0.998385i	$-0.518094\pi$
$479$	1.87473e9	−	1.08237e9i	0.779405	−	0.449990i	0.836220	+	0.548395i	$0.184761\pi$
$480$		0			0
$481$	−3.01302e8	+	1.41125e8i	−0.123451	+	0.0578226i
$482$	−1.48902e8			−0.0605669
$483$		0			0
$484$	−1.22161e9	−	2.11590e9i	−0.489751	−	0.848274i
$485$	−3.89451e8	+	6.74549e8i	−0.155009	+	0.268483i
$486$		0			0
$487$	3.13354e9	+	1.80915e9i	1.22937	+	0.709779i	0.966899	−	0.255160i	$-0.0821282\pi$
$487$	3.13354e9	+	1.80915e9i	1.22937	+	0.709779i	0.262474	+	0.964939i	$0.415462\pi$
$488$	−9.68011e6	−	5.58881e6i	−0.00377060	−	0.00217696i
$489$		0			0
$490$	−1.30242e8	+	2.25587e8i	−0.0500111	+	0.0866218i
$491$	8.96441e8	+	1.55268e9i	0.341772	+	0.591966i	0.984762	−	0.173908i	$-0.0556397\pi$
$491$	8.96441e8	+	1.55268e9i	0.341772	+	0.591966i	−0.642990	+	0.765875i	$0.722306\pi$
$492$		0			0
$493$	−1.63971e9			−0.616315
$494$	2.20029e8	+	1.88721e7i	0.0821176	+	0.00704328i
$495$		0			0
$496$	1.71300e9	−	9.89001e8i	0.630335	−	0.363924i
$497$	−3.07690e9	−	5.32935e9i	−1.12426	−	1.94727i
$498$		0			0
$499$			1.87794e9i			0.676596i	0.941039	+	0.338298i	$0.109851\pi$
$499$			1.87794e9i			0.676596i	−0.941039	+	0.338298i	$0.890149\pi$
$500$	−1.77566e9	−	1.02518e9i	−0.635279	−	0.366778i
$501$		0			0
$502$		−	1.00897e7i		−	0.00355971i
$503$	−5.65977e7	+	9.80300e7i	−0.0198294	+	0.0343456i	−0.875770	−	0.482729i	$-0.839646\pi$
$503$	−5.65977e7	+	9.80300e7i	−0.0198294	+	0.0343456i	0.855940	+	0.517074i	$0.172979\pi$
$504$		0			0
$505$	3.66608e9	−	2.11661e9i	1.26672	−	0.731343i
$506$	1.72807e7			0.00592971
$507$		0			0
$508$	1.02932e9			0.348359
$509$	−4.69915e9	+	2.71305e9i	−1.57945	+	0.911898i	−0.584517	+	0.811381i	$0.698716\pi$
$509$	−4.69915e9	+	2.71305e9i	−1.57945	+	0.911898i	−0.994935	+	0.100516i	$0.967950\pi$
$510$		0			0
$511$	1.25531e9	−	2.17426e9i	0.416177	−	0.720840i
$512$		−	8.98445e8i		−	0.295833i
$513$		0			0
$514$	2.93858e8	+	1.69659e8i	0.0954480	+	0.0551069i
$515$		−	3.13850e9i		−	1.01250i
$516$		0			0
$517$	−2.70200e8	−	4.68001e8i	−0.0859942	−	0.148946i
$518$	3.21807e7	−	1.85795e7i	0.0101728	−	0.00587327i
$519$		0			0
$520$	6.01517e8	+	5.15925e7i	0.187602	+	0.0160907i
$521$	2.65903e9			0.823741			0.411871	−	0.911242i	$-0.364876\pi$
$521$	2.65903e9			0.823741			0.411871	+	0.911242i	$0.364876\pi$
$522$		0			0
$523$	−2.02223e9	−	3.50260e9i	−0.618122	−	1.07062i	−0.989828	−	0.142268i	$-0.954560\pi$
$523$	−2.02223e9	−	3.50260e9i	−0.618122	−	1.07062i	0.371706	−	0.928350i	$-0.378773\pi$
$524$	8.05983e8	−	1.39600e9i	0.244718	−	0.423864i
$525$		0			0
$526$	−1.78477e7	−	1.03044e7i	−0.00534726	−	0.00308724i
$527$	1.19102e9	+	6.87637e8i	0.354473	+	0.204655i
$528$		0			0
$529$	7.22687e8	−	1.25173e9i	0.212254	−	0.367634i
$530$	1.37824e8	+	2.38717e8i	0.0402122	+	0.0696496i
$531$		0			0
$532$	6.81994e9			1.96377
$533$	−6.29049e8	+	2.94637e8i	−0.179945	+	0.0842835i
$534$		0			0
$535$	−7.83478e9	+	4.52341e9i	−2.21202	+	1.27711i
$536$	1.68691e8	+	2.92181e8i	0.0473168	+	0.0819551i
$537$		0			0
$538$			7.50633e7i			0.0207821i
$539$	−4.34772e8	−	2.51016e8i	−0.119592	−	0.0690463i
$540$		0			0
$541$			6.97904e9i			1.89498i	0.319782	+	0.947491i	$0.396390\pi$
$541$			6.97904e9i			1.89498i	−0.319782	+	0.947491i	$0.603610\pi$
$542$	−1.71166e7	+	2.96467e7i	−0.00461763	+	0.00799796i
$543$		0			0
$544$	3.24200e8	−	1.87177e8i	0.0863410	−	0.0498490i
$545$	−4.64244e9			−1.22845
$546$		0			0
$547$	5.47434e7			0.0143013			0.00715065	−	0.999974i	$-0.497724\pi$
$547$	5.47434e7			0.0143013			0.00715065	+	0.999974i	$0.497724\pi$
$548$	3.12830e9	−	1.80612e9i	0.812038	−	0.468830i
$549$		0			0
$550$	−2.23949e7	+	3.87891e7i	−0.00573957	+	0.00994123i
$551$		−	5.97320e9i		−	1.52116i
$552$		0			0
$553$	1.69544e9	+	9.78866e8i	0.426330	+	0.246142i
$554$		−	3.65784e8i		−	0.0913989i
$555$		0			0
$556$	5.66366e8	+	9.80975e8i	0.139745	+	0.242045i
$557$	−1.87977e8	+	1.08528e8i	−0.0460905	+	0.0266103i	−0.522868	−	0.852414i	$-0.675138\pi$
$557$	−1.87977e8	+	1.08528e8i	−0.0460905	+	0.0266103i	0.476778	+	0.879024i	$0.341805\pi$
$558$		0			0
$559$	3.39822e9	−	4.87082e9i	0.822830	−	1.17940i
$560$	9.27158e9			2.23098
$561$		0			0
$562$	4.87225e7	+	8.43899e7i	0.0115785	+	0.0200546i
$563$	−2.39971e9	+	4.15643e9i	−0.566735	+	0.981614i	0.430151	+	0.902757i	$0.358460\pi$
$563$	−2.39971e9	+	4.15643e9i	−0.566735	+	0.981614i	−0.996886	+	0.0788572i	$0.974873\pi$
$564$		0			0
$565$	−1.01953e10	−	5.88625e9i	−2.37810	−	1.37300i
$566$	−5.95493e7	−	3.43808e7i	−0.0138044	−	0.00797000i
$567$		0			0
$568$	4.09923e8	−	7.10008e8i	0.0938607	−	0.162571i
$569$	−2.61206e9	−	4.52422e9i	−0.594415	−	1.02956i	−0.993629	−	0.112699i	$-0.964050\pi$
$569$	−2.61206e9	−	4.52422e9i	−0.594415	−	1.02956i	0.399214	−	0.916858i	$-0.369283\pi$
$570$		0			0
$571$	−9.53468e8			−0.214328			−0.107164	−	0.994241i	$-0.534177\pi$
$571$	−9.53468e8			−0.214328			−0.107164	+	0.994241i	$0.534177\pi$
$572$	−4.96273e7	+	5.78605e8i	−0.0110875	+	0.129270i
$573$		0			0
$574$	6.71858e7	−	3.87897e7i	0.0148281	−	0.00856101i
$575$	−2.53935e9	−	4.39829e9i	−0.557039	−	0.964820i
$576$		0			0
$577$			7.41729e6i			0.00160742i	1.00000		0.000803711i	$0.000255829\pi$
$577$			7.41729e6i			0.00160742i	−1.00000		0.000803711i	$0.999744\pi$
$578$	−1.66659e8	−	9.62209e7i	−0.0358990	−	0.0207263i
$579$		0			0
$580$		−	8.15004e9i		−	1.73445i
$581$	1.22433e9	−	2.12060e9i	0.258989	−	0.448583i
$582$		0			0
$583$	−4.60080e8	+	2.65627e8i	−0.0961597	+	0.0555178i
$584$	3.34481e8			0.0694906
$585$		0			0
$586$	−2.08025e8			−0.0427046
$587$	−5.20465e9	+	3.00490e9i	−1.06208	+	0.613193i	−0.926007	−	0.377505i	$-0.876782\pi$
$587$	−5.20465e9	+	3.00490e9i	−1.06208	+	0.613193i	−0.136074	+	0.990699i	$0.543449\pi$
$588$		0			0
$589$	−2.50495e9	+	4.33870e9i	−0.505121	+	0.874895i
$590$		−	1.88597e8i		−	0.0378053i
$591$		0			0
$592$	−5.89531e8	−	3.40366e8i	−0.116783	−	0.0674248i
$593$		−	1.00461e9i		−	0.197836i	−0.995096	−	0.0989178i	$-0.968462\pi$
$593$		−	1.00461e9i		−	0.197836i	0.995096	−	0.0989178i	$-0.0315381\pi$
$594$		0			0
$595$	3.22320e9	+	5.58274e9i	0.627303	+	1.08652i
$596$	−5.61669e9	+	3.24280e9i	−1.08672	+	0.627420i
$597$		0			0
$598$	1.95305e8	+	1.36259e8i	0.0373474	+	0.0260561i
$599$	4.70768e9			0.894979			0.447489	−	0.894289i	$-0.352318\pi$
$599$	4.70768e9			0.894979			0.447489	+	0.894289i	$0.352318\pi$
$600$		0			0
$601$	−3.02639e9	−	5.24187e9i	−0.568676	−	0.984975i	−0.996697	−	0.0812066i	$-0.974123\pi$
$601$	−3.02639e9	−	5.24187e9i	−0.568676	−	0.984975i	0.428022	−	0.903768i	$-0.359211\pi$
$602$	−3.31651e8	+	5.74437e8i	−0.0619575	+	0.107314i
$603$		0			0
$604$	1.07909e9	+	6.23010e8i	0.199263	+	0.115045i
$605$	7.28569e9	+	4.20640e9i	1.33760	+	0.772265i
$606$		0			0
$607$	3.56363e9	−	6.17239e9i	0.646744	−	1.12019i	−0.337152	−	0.941450i	$-0.609464\pi$
$607$	3.56363e9	−	6.17239e9i	0.646744	−	1.12019i	0.983896	−	0.178743i	$-0.0572031\pi$
$608$	6.81855e8	+	1.18101e9i	0.123035	+	0.213103i
$609$		0			0
$610$	1.92093e7			0.00342655
$611$	6.36406e8	−	7.41987e9i	0.112873	−	1.31599i
$612$		0			0
$613$	−8.66562e8	+	5.00310e8i	−0.151946	+	0.0877258i	−0.574045	−	0.818824i	$-0.694627\pi$
$613$	−8.66562e8	+	5.00310e8i	−0.151946	+	0.0877258i	0.422100	+	0.906549i	$0.361293\pi$
$614$	−3.01003e6	−	5.21352e6i	−0.000524785	−	0.000908954i
$615$		0			0
$616$		−	1.29951e8i		−	0.0224000i
$617$	3.21958e9	+	1.85882e9i	0.551825	+	0.318596i	0.749858	−	0.661599i	$-0.230122\pi$
$617$	3.21958e9	+	1.85882e9i	0.551825	+	0.318596i	−0.198033	+	0.980195i	$0.563455\pi$
$618$		0			0
$619$			8.30664e9i			1.40769i	0.710352	+	0.703847i	$0.248536\pi$
$619$			8.30664e9i			1.40769i	−0.710352	+	0.703847i	$0.751464\pi$
$620$	−3.41784e9	+	5.91987e9i	−0.575945	+	0.997565i
$621$		0			0
$622$	−2.32537e8	+	1.34255e8i	−0.0387458	+	0.0223699i
$623$	5.69874e9			0.944214
$624$		0			0
$625$	−1.90347e9			−0.311864
$626$	5.22524e8	−	3.01680e8i	0.0851327	−	0.0491514i
$627$		0			0
$628$	−4.16716e9	+	7.21773e9i	−0.671400	+	1.16290i
$629$		−	4.73302e8i		−	0.0758335i
$630$		0			0
$631$	6.78879e9	+	3.91951e9i	1.07570	+	0.621053i	0.929732	−	0.368237i	$-0.120038\pi$
$631$	6.78879e9	+	3.91951e9i	1.07570	+	0.621053i	0.145963	+	0.989290i	$0.453372\pi$
$632$			2.60821e8i			0.0410991i
$633$		0			0
$634$	1.15542e8	+	2.00124e8i	0.0180064	+	0.0311880i
$635$	−3.06942e9	+	1.77213e9i	−0.475717	+	0.274655i
$636$		0			0
$637$	−2.93451e9	−	6.26517e9i	−0.449830	−	0.960384i
$638$	−5.68058e7			−0.00866004
$639$		0			0
$640$	1.23971e9	+	2.14724e9i	0.186935	+	0.323780i
$641$	−6.36068e8	+	1.10170e9i	−0.0953895	+	0.165220i	−0.909771	−	0.415110i	$-0.863743\pi$
$641$	−6.36068e8	+	1.10170e9i	−0.0953895	+	0.165220i	0.814382	+	0.580330i	$0.197076\pi$
$642$		0			0
$643$	4.91826e9	+	2.83956e9i	0.729581	+	0.421224i	0.818269	−	0.574836i	$-0.194934\pi$
$643$	4.91826e9	+	2.83956e9i	0.729581	+	0.421224i	−0.0886881	+	0.996059i	$0.528267\pi$
$644$	6.36899e9	+	3.67714e9i	0.939659	+	0.542512i
$645$		0			0
$646$	−1.57076e8	+	2.72063e8i	−0.0229242	+	0.0397059i
$647$	4.91513e9	+	8.51325e9i	0.713460	+	1.23575i	0.963551	+	0.267526i	$0.0862063\pi$
$647$	4.91513e9	+	8.51325e9i	0.713460	+	1.23575i	−0.250091	+	0.968222i	$0.580460\pi$
$648$		0			0
$649$	3.63483e8			0.0521948
$650$	−5.58960e8	+	2.61808e8i	−0.0798332	+	0.0373927i
$651$		0			0
$652$	−2.23091e9	+	1.28801e9i	−0.315221	+	0.181993i
$653$	−1.92707e9	−	3.33778e9i	−0.270832	−	0.469096i	0.698243	−	0.715861i	$-0.253966\pi$
$653$	−1.92707e9	−	3.33778e9i	−0.270832	−	0.469096i	−0.969075	+	0.246765i	$0.920632\pi$
$654$		0			0
$655$			5.55049e9i			0.771769i
$656$	−1.23080e9	−	7.10605e8i	−0.170226	−	0.0982799i
$657$		0			0
$658$			8.31725e8i			0.113812i
$659$	−2.45749e9	+	4.25650e9i	−0.334498	+	0.579367i	−0.983388	−	0.181515i	$-0.941900\pi$
$659$	−2.45749e9	+	4.25650e9i	−0.334498	+	0.579367i	0.648891	+	0.760882i	$0.275233\pi$
$660$		0			0
$661$	1.10777e10	−	6.39573e9i	1.49192	−	0.861360i	0.491962	−	0.870616i	$-0.336280\pi$
$661$	1.10777e10	−	6.39573e9i	1.49192	−	0.861360i	0.999957	+	0.00925625i	$0.00294640\pi$
$662$	3.73129e8			0.0499869
$663$		0			0
$664$	3.26225e8			0.0432443
$665$	−2.03370e10	+	1.17416e10i	−2.68171	+	1.54828i
$666$		0			0
$667$	3.22060e9	−	5.57824e9i	0.420239	−	0.727875i
$668$			8.63544e8i			0.112090i
$669$		0			0
$670$	−5.02127e8	−	2.89903e8i	−0.0644989	−	0.0372384i
$671$			3.70220e7i			0.00473076i
$672$		0			0
$673$	−5.49257e9	−	9.51341e9i	−0.694581	−	1.20305i	−0.970322	−	0.241818i	$-0.922256\pi$
$673$	−5.49257e9	−	9.51341e9i	−0.694581	−	1.20305i	0.275741	−	0.961232i	$-0.411077\pi$
$674$	4.04969e8	−	2.33809e8i	0.0509462	−	0.0294138i
$675$		0			0
$676$	−5.12321e9	+	6.14806e9i	−0.637864	+	0.765464i
$677$	−3.14306e9			−0.389307			−0.194653	−	0.980872i	$-0.562358\pi$
$677$	−3.14306e9			−0.389307			−0.194653	+	0.980872i	$0.562358\pi$
$678$		0			0
$679$	1.15522e9	+	2.00090e9i	0.141619	+	0.245291i
$680$	−4.29414e8	+	7.43766e8i	−0.0523715	+	0.0907100i
$681$		0			0
$682$	4.12615e7	+	2.38223e7i	0.00498081	+	0.00287567i
$683$	1.33989e10	+	7.73584e9i	1.60915	+	0.929042i	0.989561	+	0.144113i	$0.0460328\pi$
$683$	1.33989e10	+	7.73584e9i	1.60915	+	0.929042i	0.619586	+	0.784929i	$0.287301\pi$
$684$		0			0
$685$	−6.21904e9	+	1.07717e10i	−0.739276	+	1.28046i
$686$	2.20436e7	+	3.81807e7i	0.00260705	+	0.00451554i
$687$		0			0
$688$	1.21513e10			1.42254
$689$	−7.29428e9	−	6.25635e8i	−0.849601	−	0.0728708i
$690$		0			0
$691$	−4.00359e9	+	2.31148e9i	−0.461612	+	0.266512i	−0.712722	−	0.701447i	$-0.752538\pi$
$691$	−4.00359e9	+	2.31148e9i	−0.461612	+	0.266512i	0.251110	+	0.967959i	$0.419204\pi$
$692$	−5.52909e9	−	9.57666e9i	−0.634282	−	1.09861i
$693$		0			0
$694$		−	4.66678e8i		−	0.0529980i
$695$	−3.37780e9	−	1.95017e9i	−0.381669	−	0.220357i
$696$		0			0
$697$		−	9.88145e8i		−	0.110537i
$698$	3.51213e8	−	6.08319e8i	0.0390910	−	0.0677076i
$699$		0			0
$700$	−1.65078e10	+	9.53079e9i	−1.81906	+	1.05023i
$701$	1.41767e10			1.55440			0.777200	−	0.629253i	$-0.216639\pi$
$701$	1.41767e10			1.55440			0.777200	+	0.629253i	$0.216639\pi$
$702$		0			0
$703$	1.72416e9			0.187169
$704$	−1.02147e9	+	5.89747e8i	−0.110337	+	0.0637033i
$705$		0			0
$706$	3.64332e8	−	6.31041e8i	0.0389655	−	0.0674902i
$707$		−	1.25569e10i		−	1.33634i
$708$		0			0
$709$	7.07624e9	+	4.08547e9i	0.745660	+	0.430507i	0.824124	−	0.566410i	$-0.191668\pi$
$709$	7.07624e9	+	4.08547e9i	0.745660	+	0.430507i	−0.0784635	+	0.996917i	$0.525001\pi$
$710$			1.40895e9i			0.147737i
$711$		0			0
$712$	3.79610e8	+	6.57504e8i	0.0394147	+	0.0682682i
$713$	−4.67864e9	+	2.70121e9i	−0.483399	+	0.279091i
$714$		0			0
$715$	−8.48170e8	−	1.81084e9i	−0.0867784	−	0.185271i
$716$	−1.14076e10			−1.16145
$717$		0			0
$718$	−2.23297e8	−	3.86762e8i	−0.0225137	−	0.0389949i
$719$	7.71168e9	−	1.33570e10i	0.773745	−	1.34017i	−0.161752	−	0.986831i	$-0.551714\pi$
$719$	7.71168e9	−	1.33570e10i	0.773745	−	1.34017i	0.935497	−	0.353334i	$-0.114952\pi$
$720$		0			0
$721$	−8.06242e9	−	4.65484e9i	−0.801110	−	0.462521i
$722$	−4.65343e8	−	2.68666e8i	−0.0460143	−	0.0265664i
$723$		0			0
$724$	1.63089e9	−	2.82479e9i	0.159713	−	0.276631i
$725$	8.34748e9	+	1.44583e10i	0.813527	+	1.40907i
$726$		0			0
$727$	5.70391e9			0.550557			0.275279	−	0.961365i	$-0.411230\pi$
$727$	5.70391e9			0.550557			0.275279	+	0.961365i	$0.411230\pi$
$728$	1.02467e9	−	1.46870e9i	0.0984292	−	0.141083i
$729$		0			0
$730$	−4.97809e8	+	2.87410e8i	−0.0473623	+	0.0273446i
$731$	4.22431e9	+	7.31672e9i	0.399986	+	0.692796i
$732$		0			0
$733$		−	1.66495e10i		−	1.56148i	−0.624854	−	0.780742i	$-0.714841\pi$
$733$		−	1.66495e10i		−	1.56148i	0.624854	−	0.780742i	$-0.285159\pi$
$734$	−5.26217e8	−	3.03811e8i	−0.0491166	−	0.0283575i
$735$		0			0
$736$			1.47056e9i			0.135959i
$737$	5.58730e8	−	9.67749e8i	0.0514122	−	0.0890485i
$738$		0			0
$739$	−4.26718e9	+	2.46366e9i	−0.388943	+	0.224556i	−0.681702	−	0.731630i	$-0.738760\pi$
$739$	−4.26718e9	+	2.46366e9i	−0.388943	+	0.224556i	0.292759	+	0.956186i	$0.405427\pi$
$740$	2.35251e9			0.213412
$741$		0			0
$742$	8.17647e8			0.0734772
$743$	8.58753e9	−	4.95801e9i	0.768082	−	0.443452i	−0.0641082	−	0.997943i	$-0.520420\pi$
$743$	8.58753e9	−	4.95801e9i	0.768082	−	0.443452i	0.832190	+	0.554491i	$0.187087\pi$
$744$		0			0
$745$	1.11660e10	−	1.93400e10i	0.989348	−	1.71360i
$746$		−	4.64656e8i		−	0.0409775i
$747$		0			0
$748$	−7.15436e8	−	4.13057e8i	−0.0625051	−	0.0360873i
$749$			2.68354e10i			2.33358i
$750$		0			0
$751$	1.12646e10	+	1.95109e10i	0.970456	+	1.68088i	0.694180	+	0.719801i	$0.255767\pi$
$751$	1.12646e10	+	1.95109e10i	0.970456	+	1.68088i	0.276276	+	0.961078i	$0.410900\pi$
$752$	1.31954e10	−	7.61835e9i	1.13151	−	0.653279i
$753$		0			0
$754$	−6.42017e8	−	4.47915e8i	−0.0545439	−	0.0380536i
$755$	−4.29043e9			−0.362816
$756$		0			0
$757$	1.10819e10	+	1.91944e10i	0.928493	+	1.60820i	0.785846	+	0.618423i	$0.212228\pi$
$757$	1.10819e10	+	1.91944e10i	0.928493	+	1.60820i	0.142647	+	0.989774i	$0.454439\pi$
$758$	3.87017e8	−	6.70333e8i	0.0322766	−	0.0559047i
$759$		0			0
$760$	−2.70942e9	−	1.56428e9i	−0.223887	−	0.129261i
$761$	−6.64485e9	−	3.83641e9i	−0.546561	−	0.315557i	0.201173	−	0.979556i	$-0.435525\pi$
$761$	−6.64485e9	−	3.83641e9i	−0.546561	−	0.315557i	−0.747734	+	0.663999i	$0.768858\pi$
$762$		0			0
$763$	−6.88540e9	+	1.19259e10i	−0.561168	+	0.971972i
$764$	9.26457e9	+	1.60467e10i	0.751620	+	1.30184i
$765$		0			0
$766$	9.13025e8			0.0733976
$767$	4.10807e9	+	2.86607e9i	0.328741	+	0.229352i
$768$		0			0
$769$	−7.77528e9	+	4.48906e9i	−0.616558	+	0.355970i	−0.775528	−	0.631314i	$-0.782516\pi$
$769$	−7.77528e9	+	4.48906e9i	−0.616558	+	0.355970i	0.158970	+	0.987283i	$0.449183\pi$
$770$	1.11664e8	+	1.93407e8i	0.00881443	+	0.0152670i
$771$		0			0
$772$		−	1.16345e10i		−	0.910097i
$773$	−9.70027e9	−	5.60045e9i	−0.755363	−	0.436109i	0.0722655	−	0.997385i	$-0.476977\pi$
$773$	−9.70027e9	−	5.60045e9i	−0.755363	−	0.436109i	−0.827628	+	0.561276i	$0.810310\pi$
$774$		0			0
$775$		−	1.40026e10i		−	1.08057i
$776$	−1.53906e8	+	2.66573e8i	−0.0118233	+	0.0204786i
$777$		0			0
$778$	2.39238e8	−	1.38124e8i	0.0182138	−	0.0105158i
$779$	3.59965e9			0.272822
$780$		0			0
$781$	−2.71546e9			−0.203969
$782$	−2.93379e8	+	1.69382e8i	−0.0219384	+	0.0126662i
$783$		0			0
$784$	7.07745e9	−	1.22585e10i	0.524530	−	0.908513i
$785$		−	2.86976e10i		−	2.11740i
$786$		0			0
$787$	−9.57297e8	−	5.52696e8i	−0.0700060	−	0.0404180i	0.464588	−	0.885527i	$-0.346202\pi$
$787$	−9.57297e8	−	5.52696e8i	−0.0700060	−	0.0404180i	−0.534594	+	0.845109i	$0.679536\pi$
$788$		−	2.17144e10i		−	1.58090i
$789$		0			0
$790$	−2.24116e8	−	3.88181e8i	−0.0161726	−	0.0280117i
$791$	−3.02421e10	+	1.74603e10i	−2.17267	+	1.25439i
$792$		0			0
$793$	−2.91920e8	+	4.18421e8i	−0.0207877	+	0.0297960i
$794$	−1.33712e8			−0.00947982
$795$		0			0
$796$	−8.89727e9	−	1.54105e10i	−0.625260	−	1.08298i
$797$	7.49691e9	−	1.29850e10i	0.524540	−	0.908529i	−0.475052	−	0.879958i	$-0.657571\pi$
$797$	7.49691e9	−	1.29850e10i	0.524540	−	0.908529i	0.999592	−	0.0285717i	$-0.00909588\pi$
$798$		0			0
$799$	9.17454e9	+	5.29693e9i	0.636313	+	0.367375i
$800$	−3.30089e9	−	1.90577e9i	−0.227938	−	0.131600i
$801$		0			0
$802$	3.39632e8	−	5.88261e8i	0.0232487	−	0.0402679i
$803$	−5.53925e8	−	9.59426e8i	−0.0377526	−	0.0653894i
$804$		0			0
$805$	−2.53230e10			−1.71092
$806$	2.78496e8	+	5.94588e8i	0.0187347	+	0.0399985i
$807$		0			0
$808$	1.44878e9	−	8.36455e8i	0.0966192	−	0.0557831i
$809$	7.66062e9	+	1.32686e10i	0.508679	+	0.881059i	0.999949	+	0.0100514i	$0.00319951\pi$
$809$	7.66062e9	+	1.32686e10i	0.508679	+	0.881059i	−0.491270	+	0.871007i	$0.663467\pi$
$810$		0			0
$811$		−	1.14391e10i		−	0.753041i	−0.926408	−	0.376521i	$-0.877120\pi$
$811$		−	1.14391e10i		−	0.753041i	0.926408	−	0.376521i	$-0.122880\pi$
$812$	−2.09364e10	−	1.20877e10i	−1.37232	−	0.792311i
$813$		0			0
$814$		−	1.63970e7i		−	0.00106556i
$815$	4.43503e9	−	7.68170e9i	0.286976	−	0.497056i
$816$		0			0
$817$	−2.66536e10	+	1.53885e10i	−1.70993	+	0.987229i
$818$	−1.10294e9			−0.0704555
$819$		0			0
$820$	4.91149e9			0.311075
$821$	−1.88617e10	+	1.08898e10i	−1.18954	+	0.686782i	−0.958202	−	0.286091i	$-0.907644\pi$
$821$	−1.88617e10	+	1.08898e10i	−1.18954	+	0.686782i	−0.231339	+	0.972873i	$0.574311\pi$
$822$		0			0
$823$	−1.08157e9	+	1.87333e9i	−0.0676324	+	0.117143i	−0.897859	−	0.440284i	$-0.854878\pi$
$823$	−1.08157e9	+	1.87333e9i	−0.0676324	+	0.117143i	0.830226	+	0.557426i	$0.188211\pi$
$824$		−	1.24029e9i		−	0.0772287i
$825$		0			0
$826$	−4.84482e8	−	2.79716e8i	−0.0299122	−	0.0172698i
$827$		−	2.27847e10i		−	1.40079i	−0.713755	−	0.700395i	$-0.753007\pi$
$827$		−	2.27847e10i		−	1.40079i	0.713755	−	0.700395i	$-0.246993\pi$
$828$		0			0
$829$	4.91919e9	+	8.52030e9i	0.299884	+	0.519414i	0.976109	−	0.217281i	$-0.0697187\pi$
$829$	4.91919e9	+	8.52030e9i	0.299884	+	0.519414i	−0.676225	+	0.736695i	$0.736385\pi$
$830$	−4.85523e8	+	2.80317e8i	−0.0294738	+	0.0170167i
$831$		0			0
$832$	−1.61948e10	−	1.38904e9i	−0.974865	−	0.0836148i
$833$	9.84168e9			0.589945
$834$		0			0
$835$	−1.48672e9	−	2.57508e9i	−0.0883746	−	0.153069i
$836$	1.50470e9	−	2.60622e9i	0.0890692	−	0.154272i
$837$		0			0
$838$	1.12879e8	+	6.51709e7i	0.00662614	+	0.00382560i
$839$	1.81235e10	+	1.04636e10i	1.05944	+	0.611666i	0.925276	−	0.379294i	$-0.123833\pi$
$839$	1.81235e10	+	1.04636e10i	1.05944	+	0.611666i	0.134160	+	0.990960i	$0.457166\pi$
$840$		0			0
$841$	−1.96195e9	+	3.39821e9i	−0.113737	+	0.196999i
$842$	3.97356e8	+	6.88240e8i	0.0229397	+	0.0397327i
$843$		0			0
$844$	1.06760e10			0.611237
$845$	4.69253e9	−	2.71539e10i	0.267552	−	1.54822i
$846$		0			0
$847$	2.16114e10	−	1.24774e10i	1.22206	−	0.705555i
$848$	−7.48941e9	−	1.29720e10i	−0.421757	−	0.730504i
$849$		0			0
$850$		−	8.78045e8i		−	0.0490400i
$851$	1.61016e9	+	9.29625e8i	0.0895602	+	0.0517076i
$852$		0			0
$853$		−	2.52741e10i		−	1.39429i	−0.716928	−	0.697147i	$-0.754452\pi$
$853$		−	2.52741e10i		−	1.39429i	0.716928	−	0.697147i	$-0.245548\pi$
$854$	2.84901e7	−	4.93462e7i	0.00156528	−	0.00271114i
$855$		0			0
$856$	−3.09620e9	+	1.78759e9i	−0.168721	+	0.0974114i
$857$	2.67167e10			1.44994			0.724969	−	0.688782i	$-0.241854\pi$
$857$	2.67167e10			1.44994			0.724969	+	0.688782i	$0.241854\pi$
$858$		0			0
$859$	−8.51182e9			−0.458191			−0.229095	−	0.973404i	$-0.573577\pi$
$859$	−8.51182e9			−0.458191			−0.229095	+	0.973404i	$0.573577\pi$
$860$	−3.63671e10	+	2.09966e10i	−1.94968	+	1.12565i
$861$		0			0
$862$	−7.18499e7	+	1.24448e8i	−0.00382077	+	0.00661776i
$863$		−	5.94525e9i		−	0.314871i	−0.987529	−	0.157435i	$-0.949677\pi$
$863$		−	5.94525e9i		−	0.314871i	0.987529	−	0.157435i	$-0.0503226\pi$
$864$		0			0
$865$	3.29754e10	+	1.90384e10i	1.73234	+	1.00017i
$866$		−	7.98646e8i		−	0.0417871i
$867$		0			0
$868$	1.01383e10	+	1.75600e10i	0.526193	+	0.911393i
$869$	7.48140e8	−	4.31939e8i	0.0386735	−	0.0223282i
$870$		0			0
$871$	1.39455e10	−	6.53186e9i	0.715105	−	0.334945i
$872$	−1.83463e9			−0.0937002
$873$		0			0
$874$	−6.17032e8	−	1.06873e9i	−0.0312621	−	0.0541475i
$875$	1.04710e10	−	1.81363e10i	0.528395	−	0.915207i
$876$		0			0
$877$	9.21976e9	+	5.32303e9i	0.461552	+	0.266477i	0.712697	−	0.701472i	$-0.247474\pi$
$877$	9.21976e9	+	5.32303e9i	0.461552	+	0.266477i	−0.251144	+	0.967950i	$0.580807\pi$
$878$	1.42587e9	+	8.23226e8i	0.0710966	+	0.0410477i
$879$		0			0
$880$	2.04561e9	−	3.54310e9i	0.101189	−	0.175265i
$881$	1.91599e9	+	3.31860e9i	0.0944014	+	0.163508i	0.909359	−	0.416013i	$-0.136573\pi$
$881$	1.91599e9	+	3.31860e9i	0.0944014	+	0.163508i	−0.814957	+	0.579521i	$0.803240\pi$
$882$		0			0
$883$	−1.75487e10			−0.857792			−0.428896	−	0.903354i	$-0.641097\pi$
$883$	−1.75487e10			−0.857792			−0.428896	+	0.903354i	$0.641097\pi$
$884$	−4.82886e9	−	1.03096e10i	−0.235105	−	0.501948i
$885$		0			0
$886$	4.77155e7	−	2.75486e7i	0.00230485	−	0.00133070i
$887$	−5.37291e9	−	9.30616e9i	−0.258510	−	0.447752i	0.707333	−	0.706880i	$-0.249898\pi$
$887$	−5.37291e9	−	9.30616e9i	−0.258510	−	0.447752i	−0.965843	+	0.259128i	$0.916565\pi$
$888$		0			0
$889$			1.05133e10i			0.501860i
$890$	−1.12995e9	−	6.52378e8i	−0.0537273	−	0.0310195i
$891$		0			0
$892$		−	1.21291e10i		−	0.572204i
$893$	−1.92958e10	+	3.34214e10i	−0.906741	+	1.57052i
$894$		0			0
$895$	3.40174e10	−	1.96399e10i	1.58606	−	0.915714i
$896$	7.35465e9			0.341573
$897$		0			0
$898$	−1.79902e7			−0.000829025
$899$	1.53798e10	−	8.87954e9i	0.705980	−	0.407598i
$900$		0			0
$901$	5.20727e9	−	9.01926e9i	0.237178	−	0.410803i
$902$		−	3.42331e7i		−	0.00155319i
$903$		0			0
$904$	−4.02904e9	−	2.32616e9i	−0.181389	−	0.104725i
$905$			1.12313e10i			0.503687i
$906$		0			0
$907$	−1.03600e10	−	1.79440e10i	−0.461034	−	0.798534i	0.537979	−	0.842958i	$-0.319188\pi$
$907$	−1.03600e10	−	1.79440e10i	−0.461034	−	0.798534i	−0.999013	+	0.0444245i	$0.985855\pi$
$908$	1.09172e10	−	6.30303e9i	0.483960	−	0.279415i
$909$		0			0
$910$	−2.63003e8	+	3.06635e9i	−0.0115695	+	0.134889i
$911$	3.76677e10			1.65065			0.825325	−	0.564658i	$-0.190992\pi$
$911$	3.76677e10			1.65065			0.825325	+	0.564658i	$0.190992\pi$
$912$		0			0
$913$	−5.40254e8	−	9.35747e8i	−0.0234936	−	0.0406921i
$914$	8.96788e8	−	1.55328e9i	0.0388489	−	0.0672882i
$915$		0			0
$916$	−9.63610e9	−	5.56341e9i	−0.414255	−	0.239170i
$917$	1.42585e10	+	8.23217e9i	0.610636	+	0.352551i
$918$		0			0
$919$	−7.80748e9	+	1.35229e10i	−0.331823	+	0.574734i	−0.982869	−	0.184304i	$-0.940997\pi$
$919$	−7.80748e9	+	1.35229e10i	−0.331823	+	0.574734i	0.651046	+	0.759038i	$0.274330\pi$
$920$	−1.68685e9	−	2.92170e9i	−0.0714197	−	0.123703i
$921$		0			0
$922$	−1.49878e8			−0.00629768
$923$	−3.06900e10	−	2.14115e10i	−1.28467	−	0.896273i
$924$		0			0
$925$	−4.17337e9	+	2.40950e9i	−0.173377	+	0.100099i
$926$	4.76967e8	+	8.26131e8i	0.0197401	+	0.0341909i
$927$		0			0
$928$		−	4.83408e9i		−	0.198562i
$929$	−2.38983e10	−	1.37977e10i	−0.977941	−	0.564615i	−0.0762934	−	0.997085i	$-0.524309\pi$
$929$	−2.38983e10	−	1.37977e10i	−0.977941	−	0.564615i	−0.901648	+	0.432471i	$0.857642\pi$
$930$		0			0
$931$			3.58516e10i			1.45608i
$932$	−1.54634e10	+	2.67835e10i	−0.625677	+	1.08370i
$933$		0			0
$934$	1.00542e9	−	5.80477e8i	0.0403768	−	0.0233115i
$935$	2.84457e9			0.113809
$936$		0			0
$937$	−3.75571e9			−0.149143			−0.0745715	−	0.997216i	$-0.523759\pi$
$937$	−3.75571e9			−0.149143			−0.0745715	+	0.997216i	$0.523759\pi$
$938$	−1.48945e9	+	8.59935e8i	−0.0589273	+	0.0340217i
$939$		0			0
$940$	−2.63279e10	+	4.56013e10i	−1.03388	+	1.79073i
$941$			3.77084e10i			1.47528i	0.675193	+	0.737641i	$0.264060\pi$
$941$			3.77084e10i			1.47528i	−0.675193	+	0.737641i	$0.735940\pi$
$942$		0			0
$943$	3.36164e9	+	1.94084e9i	0.130545	+	0.0753701i
$944$			1.02485e10i			0.396512i
$945$		0			0
$946$	1.46346e8	+	2.53479e8i	0.00562033	+	0.00973470i
$947$	3.96761e10	−	2.29070e10i	1.51811	−	0.876483i	0.518340	−	0.855174i	$-0.326550\pi$
$947$	3.96761e10	−	2.29070e10i	1.51811	−	0.876483i	0.999773	−	0.0213086i	$-0.00678325\pi$
$948$		0			0
$949$	1.30467e9	−	1.52111e10i	0.0495527	−	0.577736i
$950$	3.19857e9			0.121039
$951$		0			0
$952$	1.27376e9	+	2.20622e9i	0.0478475	+	0.0828743i
$953$	−9.15154e9	+	1.58509e10i	−0.342507	+	0.593239i	−0.984898	−	0.173138i	$-0.944609\pi$
$953$	−9.15154e9	+	1.58509e10i	−0.342507	+	0.593239i	0.642391	+	0.766377i	$0.277943\pi$
$954$		0			0
$955$	−5.52538e10	−	3.19008e10i	−2.05282	−	1.18519i
$956$	−4.51209e10	−	2.60506e10i	−1.67023	−	0.964305i
$957$		0			0
$958$	−7.35089e8	+	1.27321e9i	−0.0270123	+	0.0467866i
$959$	1.84474e10	+	3.19519e10i	0.675415	+	1.16985i
$960$		0			0
$961$	1.26175e10			0.458609
$962$	1.29291e8	−	1.85318e8i	0.00468225	−	0.00671127i
$963$		0			0
$964$	−2.42164e10	+	1.39813e10i	−0.870643	+	0.502666i
$965$	2.00306e10	+	3.46940e10i	0.717544	+	1.24282i
$966$		0			0
$967$		−	2.62013e10i		−	0.931816i	−0.884833	−	0.465908i	$-0.845728\pi$
$967$		−	2.62013e10i		−	0.931816i	0.884833	−	0.465908i	$-0.154272\pi$
$968$	2.87920e9	+	1.66231e9i	0.102026	+	0.0589045i
$969$		0			0
$970$		−	5.28988e8i		−	0.0186099i
$971$	1.52480e9	−	2.64103e9i	0.0534497	−	0.0925777i	−0.838063	−	0.545574i	$-0.816312\pi$
$971$	1.52480e9	−	2.64103e9i	0.0534497	−	0.0925777i	0.891512	+	0.452996i	$0.149645\pi$
$972$		0			0
$973$	−1.00195e10	+	5.78477e9i	−0.348700	+	0.201322i
$974$	−2.45735e9			−0.0852141
$975$		0			0
$976$	−1.04384e9			−0.0359385
$977$	−3.81568e10	+	2.20298e10i	−1.30900	+	0.755754i	−0.981930	−	0.189245i	$-0.939396\pi$
$977$	−3.81568e10	+	2.20298e10i	−1.30900	+	0.755754i	−0.327074	+	0.944999i	$0.606063\pi$
$978$		0			0
$979$	1.25733e9	−	2.17775e9i	0.0428261	−	0.0741770i
$980$			4.89172e10i			1.66024i
$981$		0			0
$982$	−1.05450e9	−	6.08814e8i	−0.0355349	−	0.0205161i
$983$		−	3.19323e10i		−	1.07224i	−0.844141	−	0.536122i	$-0.819889\pi$
$983$		−	3.19323e10i		−	1.07224i	0.844141	−	0.536122i	$-0.180111\pi$
$984$		0			0
$985$	3.73846e10	+	6.47521e10i	1.24643	+	2.15887i
$986$	9.64408e8	−	5.56801e8i	0.0320399	−	0.0184983i
$987$		0			0
$988$	3.75561e10	−	1.75907e10i	1.23889	−	0.580277i
$989$	−3.31883e10			−1.09093
$990$		0			0
$991$	−1.83299e10	−	3.17483e10i	−0.598277	−	1.03625i	−0.993075	−	0.117478i	$-0.962519\pi$
$991$	−1.83299e10	−	3.17483e10i	−0.598277	−	1.03625i	0.394798	−	0.918768i	$-0.370814\pi$
$992$	−2.02724e9	+	3.51129e9i	−0.0659349	+	0.114203i
$993$		0			0
$994$	3.61941e9	+	2.08966e9i	0.116892	+	0.0674876i
$995$	5.30632e10	+	3.06360e10i	1.70770	+	0.985943i
$996$		0			0
$997$	−2.93042e10	+	5.07563e10i	−0.936476	+	1.62202i	−0.164495	+	0.986378i	$0.552600\pi$
$997$	−2.93042e10	+	5.07563e10i	−0.936476	+	1.62202i	−0.771981	+	0.635646i	$0.780734\pi$
$998$	−6.37697e8	−	1.10452e9i	−0.0203076	−	0.0351737i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.8.q.b.10.4		14
3.2	odd	2		13.8.e.a.10.4	yes	14
12.11	even	2		208.8.w.a.49.7		14
13.4	even	6	inner	117.8.q.b.82.4		14
39.2	even	12		169.8.a.g.1.8		14
39.11	even	12		169.8.a.g.1.7		14
39.17	odd	6		13.8.e.a.4.4	✓	14
39.23	odd	6		169.8.b.d.168.7		14
39.29	odd	6		169.8.b.d.168.8		14
156.95	even	6		208.8.w.a.17.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.8.e.a.4.4	✓	14	39.17	odd	6
13.8.e.a.10.4	yes	14	3.2	odd	2
117.8.q.b.10.4		14	1.1	even	1	trivial
117.8.q.b.82.4		14	13.4	even	6	inner
169.8.a.g.1.7		14	39.11	even	12
169.8.a.g.1.8		14	39.2	even	12
169.8.b.d.168.7		14	39.23	odd	6
169.8.b.d.168.8		14	39.29	odd	6
208.8.w.a.17.7		14	156.95	even	6
208.8.w.a.49.7		14	12.11	even	2

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	117.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.588158 + 0.339573i) q^{2} +(-63.7694 + 110.452i) q^{4} -439.155i q^{5} +(-1128.14 - 651.329i) q^{7} -173.548i q^{8} +(149.125 + 258.293i) q^{10} +(-497.807 + 287.409i) q^{11} +(-7892.42 - 676.938i) q^{13} +884.695 q^{14} +(-8103.55 - 14035.8i) q^{16} +(5634.27 - 9758.85i) q^{17} +(35549.9 + 20524.7i) q^{19} +(48505.5 + 28004.7i) q^{20} +(195.193 - 338.083i) q^{22} +(22132.8 + 38335.2i) q^{23} -114732. q^{25} +(4871.86 - 2281.91i) q^{26} +(143881. - 83069.7i) q^{28} +(-72756.1 - 126017. i) q^{29} +122045. i q^{31} +(28770.4 + 16610.6i) q^{32} +7652.99i q^{34} +(-286035. + 495427. i) q^{35} +(36374.8 - 21001.0i) q^{37} -27878.6 q^{38} -76214.6 q^{40} +(75942.3 - 43845.3i) q^{41} +(-374876. + 649305. i) q^{43} -73311.5i q^{44} +(-26035.2 - 15031.4i) q^{46} +940126. i q^{47} +(436688. + 756366. i) q^{49} +(67480.7 - 38960.0i) q^{50} +(578064. - 828564. i) q^{52} +924214. q^{53} +(126217. + 218614. i) q^{55} +(-113037. + 195786. i) q^{56} +(85584.1 + 49412.0i) q^{58} +(-547626. - 316172. i) q^{59} +(32203.2 - 55777.7i) q^{61} +(-41443.3 - 71781.9i) q^{62} +2.05195e6 q^{64} +(-297281. + 3.46600e6i) q^{65} +(-1.68358e6 + 972013. i) q^{67} +(718588. + 1.24463e6i) q^{68} -388519. i q^{70} +(4.09113e6 + 2.36202e6i) q^{71} +1.92731e6i q^{73} +(-14262.8 + 24703.8i) q^{74} +(-4.53399e6 + 2.61770e6i) q^{76} +748791. q^{77} -1.50287e6 q^{79} +(-6.16388e6 + 3.55872e6i) q^{80} +(-29777.4 + 51575.9i) q^{82} +1.87974e6i q^{83} +(-4.28565e6 - 2.47432e6i) q^{85} -509191. i q^{86} +(49879.3 + 86393.4i) q^{88} +(-3.78860e6 + 2.18735e6i) q^{89} +(8.46281e6 + 5.90424e6i) q^{91} -5.64559e6 q^{92} +(-319241. - 552942. i) q^{94} +(9.01354e6 - 1.56119e7i) q^{95} +(-1.53602e6 - 886819. i) q^{97} +(-513683. - 296575. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{2} + 383 q^{4} - 2772 q^{7} - 509 q^{10} - 6516 q^{11} + 5109 q^{13} + 47916 q^{14} - 633 q^{16} + 38403 q^{17} + 43254 q^{19} - 89409 q^{20} - 125882 q^{22} + 68550 q^{23} + 39380 q^{25} - 361959 q^{26}+ \cdots - 16173003 q^{98}+O(q^{100}) \) 14 * q + 3 * q^2 + 383 * q^4 - 2772 * q^7 - 509 * q^10 - 6516 * q^11 + 5109 * q^13 + 47916 * q^14 - 633 * q^16 + 38403 * q^17 + 43254 * q^19 - 89409 * q^20 - 125882 * q^22 + 68550 * q^23 + 39380 * q^25 - 361959 * q^26 - 234780 * q^28 - 221583 * q^29 + 878067 * q^32 - 659616 * q^35 - 565347 * q^37 - 953640 * q^38 - 77182 * q^40 - 1716057 * q^41 - 882692 * q^43 - 3267480 * q^46 + 2653979 * q^49 - 145128 * q^50 + 4962178 * q^52 + 1791210 * q^53 + 2453536 * q^55 + 7457952 * q^56 - 14978127 * q^58 + 1189032 * q^59 + 3858525 * q^61 - 1904142 * q^62 + 14570922 * q^64 - 10424661 * q^65 + 4674330 * q^67 - 9569619 * q^68 + 25203126 * q^71 - 8640105 * q^74 + 12934506 * q^76 - 19599336 * q^77 - 30688440 * q^79 - 29127963 * q^80 - 37359719 * q^82 - 22436313 * q^85 + 27045536 * q^88 - 2123160 * q^89 + 37205532 * q^91 + 47685588 * q^92 + 19138810 * q^94 + 43420386 * q^95 - 68556288 * q^97 - 16173003 * q^98

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