LMFDB - Embedded newform 117.8.q.b.82.4

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			82.4
Root			$0.679146i$ of defining polynomial
Character	$\chi$	$=$	117.82
Dual form			117.8.q.b.10.4

$q$-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 $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

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

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	0.473782	−	0.880642i	$-0.342889\pi$
$2$	−0.588158	−	0.339573i	−0.0519863	−	0.0300143i	−0.525768	+	0.850628i	$0.676222\pi$
$3$		0			0
$3$		0			0
$4$	−63.7694	−	110.452i	−0.498198	−	0.862905i
$5$			439.155i			1.57117i	0.618754	+	0.785585i	$0.287638\pi$
$5$			439.155i			1.57117i	−0.618754	+	0.785585i	$0.712362\pi$
$6$		0			0
$7$	−1128.14	+	651.329i	−1.24313	+	0.717724i	−0.969731	−	0.244175i	$-0.921483\pi$
$7$	−1128.14	+	651.329i	−1.24313	+	0.717724i	−0.273403	+	0.961899i	$0.588149\pi$
$8$			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	0.442555	−	0.896741i	$-0.354072\pi$
$11$	−497.807	−	287.409i	−0.112768	−	0.0651067i	−0.555323	+	0.831635i	$0.687405\pi$
$12$		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	0.970923	−	0.239392i	$-0.0769481\pi$
$17$	5634.27	+	9758.85i	0.278142	+	0.481756i	−0.692781	+	0.721148i	$0.743615\pi$
$18$		0			0
$19$	35549.9	−	20524.7i	1.18905	−	0.686499i	0.230960	−	0.972963i	$-0.425813\pi$
$19$	35549.9	−	20524.7i	1.18905	−	0.686499i	0.958091	+	0.286464i	$0.0924800\pi$
$20$	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	−0.611655	−	0.791124i	$-0.709496\pi$
$23$	22132.8	−	38335.2i	0.379306	−	0.656977i	0.990961	+	0.134147i	$0.0428294\pi$
$24$		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	0.444027	+	0.896014i	$0.353550\pi$
$29$	−72756.1	+	126017.i	−0.553957	+	0.959482i	−0.997984	+	0.0634685i	$0.979784\pi$
$30$		0			0
$31$		−	122045.i		−	0.735793i	−0.929867	−	0.367896i	$-0.880078\pi$
$31$		−	122045.i		−	0.735793i	0.929867	−	0.367896i	$-0.119922\pi$
$32$	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	0.557866	−	0.829931i	$-0.311620\pi$
$37$	36374.8	+	21001.0i	0.118058	+	0.0681608i	−0.439808	+	0.898092i	$0.644954\pi$
$38$	−27878.6			−0.0824191
$39$		0			0
$40$	−76214.6			−0.188290
$41$	75942.3	+	43845.3i	0.172084	+	0.0993526i	0.583568	−	0.812064i	$-0.301656\pi$
$41$	75942.3	+	43845.3i	0.172084	+	0.0993526i	−0.411484	+	0.911417i	$0.634989\pi$
$42$		0			0
$43$	−374876.	−	649305.i	−0.719032	−	1.24540i	−0.961384	−	0.275212i	$-0.911252\pi$
$43$	−374876.	−	649305.i	−0.719032	−	1.24540i	0.242352	−	0.970188i	$-0.422081\pi$
$44$			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	$-0.770383\pi$
$47$		−	940126.i		−	1.32082i	0.750905	−	0.660410i	$-0.229617\pi$
$48$		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	−0.663424	−	0.748244i	$-0.730897\pi$
$59$	−547626.	+	316172.i	−0.347138	+	0.200420i	0.316286	+	0.948664i	$0.397564\pi$
$60$		0			0
$61$	32203.2	+	55777.7i	0.0181654	+	0.0314634i	0.874965	−	0.484186i	$-0.160884\pi$
$61$	32203.2	+	55777.7i	0.0181654	+	0.0314634i	−0.856800	+	0.515649i	$0.827551\pi$
$62$	−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	0.117444	−	0.993079i	$-0.462530\pi$
$67$	−1.68358e6	−	972013.i	−0.683866	−	0.394830i	−0.801310	+	0.598249i	$0.795863\pi$
$68$	718588.	−	1.24463e6i	0.277140	−	0.480020i
$69$		0			0
$70$			388519.i			0.135384i
$71$	4.09113e6	−	2.36202e6i	1.35656	−	0.783211i	0.367402	−	0.930062i	$-0.380247\pi$
$71$	4.09113e6	−	2.36202e6i	1.35656	−	0.783211i	0.989159	+	0.146851i	$0.0469139\pi$
$72$		0			0
$73$		−	1.92731e6i		−	0.579857i	−0.957048	−	0.289928i	$-0.906368\pi$
$73$		−	1.92731e6i		−	0.579857i	0.957048	−	0.289928i	$-0.0936315\pi$
$74$	−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	$-0.942253\pi$
$83$		−	1.87974e6i		−	0.360848i	0.983589	−	0.180424i	$-0.0577470\pi$
$84$		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	0.187355	−	0.982292i	$-0.440008\pi$
$89$	−3.78860e6	−	2.18735e6i	−0.569657	−	0.328892i	−0.757012	+	0.653400i	$0.773342\pi$
$90$		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	−0.583001	−	0.812471i	$-0.698122\pi$
$97$	−1.53602e6	+	886819.i	−0.170881	+	0.0986583i	0.412120	+	0.911130i	$0.364788\pi$
$98$	−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	−0.533746	−	0.845645i	$-0.679216\pi$
$101$	4.81973e6	−	8.34802e6i	0.465477	−	0.806229i	0.999223	+	0.0394154i	$0.0125496\pi$
$102$		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	0.0980299	+	0.995183i	$0.468746\pi$
$107$	−1.03003e7	+	1.78406e7i	−0.812839	+	1.40788i	−0.910869	+	0.412695i	$0.864587\pi$
$108$		0			0
$109$			1.05713e7i			0.781872i	0.920418	+	0.390936i	$0.127849\pi$
$109$			1.05713e7i			0.781872i	−0.920418	+	0.390936i	$0.872151\pi$
$110$	−148471.	+	85719.8i	−0.0106357	+	0.00614054i
$111$		0			0
$112$		−	2.11123e7i		−	1.41995i
$113$	1.34036e7	+	2.32157e7i	0.873868	+	1.51358i	0.857964	+	0.513711i	$0.171730\pi$
$113$	1.34036e7	+	2.32157e7i	0.873868	+	1.51358i	0.0159047	+	0.999874i	$0.494937\pi$
$114$		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	−0.940095	−	0.340912i	$-0.889264\pi$
$127$	−4.03532e6	+	6.98938e6i	−0.174810	+	0.302779i	0.765286	+	0.643691i	$0.222598\pi$
$128$	−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	−0.848680	−	0.528906i	$-0.822602\pi$
$137$	−2.45282e7	+	1.41614e7i	−0.814975	+	0.470526i	0.0337058	+	0.999432i	$0.489269\pi$
$138$		0			0
$139$	4.44074e6	+	7.69159e6i	0.140250	+	0.242920i	0.927591	−	0.373598i	$-0.121876\pi$
$139$	4.44074e6	+	7.69159e6i	0.140250	+	0.242920i	−0.787341	+	0.616518i	$0.788543\pi$
$140$	−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	0.156902	−	0.987614i	$-0.449849\pi$
$149$	4.40391e7	−	2.54260e7i	1.09065	−	0.629689i	0.933750	+	0.357926i	$0.116516\pi$
$150$		0			0
$151$			9.76974e6i			0.230921i	0.993312	+	0.115461i	$0.0368344\pi$
$151$			9.76974e6i			0.230921i	−0.993312	+	0.115461i	$0.963166\pi$
$152$	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	−0.333409	−	0.942782i	$-0.608199\pi$
$163$	1.74920e7	−	1.00990e7i	0.316361	−	0.182651i	0.649769	+	0.760132i	$0.274866\pi$
$164$		−	1.11839e7i		−	0.197989i
$165$		0			0
$166$	−638309.	+	1.10558e6i	−0.0108306	+	0.0187591i
$167$	5.86371e6	+	3.38542e6i	0.0974238	+	0.0562477i	0.547920	−	0.836531i	$-0.315420\pi$
$167$	5.86371e6	+	3.38542e6i	0.0974238	+	0.0562477i	−0.450497	+	0.892778i	$0.648753\pi$
$168$		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	−0.986179	−	0.165684i	$-0.947017\pi$
$173$	−4.33522e7	−	7.50883e7i	−0.636576	−	1.10258i	0.349603	−	0.936898i	$-0.386316\pi$
$174$		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	−0.412320	−	0.911039i	$-0.635281\pi$
$179$	4.47221e7	−	7.74609e7i	0.582823	−	1.00948i	0.995143	−	0.0984398i	$-0.0313852\pi$
$180$		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	0.945702	+	0.325034i	$0.105376\pi$
$191$	7.26412e7	+	1.25818e8i	0.754339	+	1.30655i	−0.191364	+	0.981519i	$0.561291\pi$
$192$		0			0
$193$	−7.90017e7	−	4.56117e7i	−0.791017	−	0.456694i	0.0493033	−	0.998784i	$-0.484300\pi$
$193$	−7.90017e7	−	4.56117e7i	−0.791017	−	0.456694i	−0.840321	+	0.542090i	$0.817633\pi$
$194$	1.20456e6			0.0118446
$195$		0			0
$196$	−1.11389e8			−1.05669
$197$	−1.47447e8	−	8.51285e7i	−1.37405	−	0.793311i	−0.382619	−	0.923906i	$-0.624978\pi$
$197$	−1.47447e8	−	8.51285e7i	−1.37405	−	0.793311i	−0.991436	+	0.130595i	$0.958311\pi$
$198$		0			0
$199$	−6.97613e7	−	1.20830e8i	−0.627521	−	1.08690i	−0.988047	−	0.154150i	$-0.950736\pi$
$199$	−6.97613e7	−	1.20830e8i	−0.627521	−	1.08690i	0.360526	−	0.932749i	$-0.382597\pi$
$200$		−	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	−0.977644	−	0.210269i	$-0.932566\pi$
$211$	−4.18539e7	+	7.24931e7i	−0.306724	+	0.531261i	0.670920	+	0.741530i	$0.265899\pi$
$212$	−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	0.230277	−	0.973125i	$-0.426037\pi$
$223$	−8.23600e7	−	4.75506e7i	−0.497335	−	0.287137i	−0.727612	+	0.685988i	$0.759370\pi$
$224$	−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	−0.722793	−	0.691064i	$-0.757142\pi$
$227$	−8.55988e7	+	4.94205e7i	−0.485710	+	0.280425i	0.237083	+	0.971489i	$0.423809\pi$
$228$		0			0
$229$		−	8.72426e7i		−	0.480070i	−0.970764	−	0.240035i	$-0.922841\pi$
$229$		−	8.72426e7i		−	0.480070i	0.970764	−	0.240035i	$-0.0771589\pi$
$230$	−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	$-0.581006\pi$
$239$		−	4.08512e8i		−	1.93558i	0.251750	−	0.967792i	$-0.418994\pi$
$240$		0			0
$241$	1.89875e8	−	1.09624e8i	0.873792	−	0.504484i	0.00518518	−	0.999987i	$-0.498349\pi$
$241$	1.89875e8	−	1.09624e8i	0.873792	−	0.504484i	0.868606	+	0.495503i	$0.165016\pi$
$242$			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	0.850820	−	0.525458i	$-0.176106\pi$
$251$	−7.42822e6	−	1.28661e7i	−0.0296501	−	0.0513556i	−0.880470	+	0.474102i	$0.842773\pi$
$252$		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	−0.115579	+	0.993298i	$0.536872\pi$
$257$	−2.49812e8	+	4.32688e8i	−0.918011	+	1.59004i	−0.802432	+	0.596744i	$0.796461\pi$
$258$		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	−0.839165	−	0.543878i	$-0.816956\pi$
$263$	1.51725e7	−	2.62796e7i	0.0514295	−	0.0890785i	0.890594	+	0.454799i	$0.150289\pi$
$264$		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	0.939503	−	0.342541i	$-0.111288\pi$
$269$	5.52630e7	+	9.57183e7i	0.173102	+	0.299821i	−0.766401	+	0.642363i	$0.777954\pi$
$270$		0			0
$271$	4.36530e7	+	2.52031e7i	0.133236	+	0.0769238i	0.565136	−	0.824997i	$-0.308824\pi$
$271$	4.36530e7	+	2.52031e7i	0.133236	+	0.0769238i	−0.431901	+	0.901921i	$0.642157\pi$
$272$	−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	−0.942184	−	0.335097i	$-0.891231\pi$
$277$	−2.69297e8	−	4.66436e8i	−0.761294	−	1.31860i	0.180889	−	0.983503i	$-0.442102\pi$
$278$		−	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	$0.0617839\pi$
$281$			1.43482e8i			0.385766i	−0.981222	+	0.192883i	$0.938216\pi$
$282$		0			0
$283$	5.06236e7	−	8.76826e7i	0.132770	−	0.229964i	−0.791973	−	0.610556i	$-0.790946\pi$
$283$	5.06236e7	−	8.76826e7i	0.132770	−	0.229964i	0.924743	+	0.380591i	$0.124279\pi$
$284$	−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	−0.159252	−	0.987238i	$-0.550908\pi$
$293$	2.65267e8	−	1.53152e8i	0.616094	−	0.355702i	0.775347	+	0.631536i	$0.217575\pi$
$294$		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	$-0.997217\pi$
$307$		−	8.86416e6i		−	0.0174845i	0.999962	−	0.00874225i	$-0.00278278\pi$
$308$	−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	$0.0969746\pi$
$317$			3.40256e8i			0.599928i	−0.953951	+	0.299964i	$0.903025\pi$
$318$		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	−0.815177	−	0.579211i	$-0.803361\pi$
$331$	−4.75802e8	+	2.74704e8i	−0.721154	+	0.416359i	0.0940230	+	0.995570i	$0.470027\pi$
$332$	−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	0.556357	−	0.830943i	$-0.312199\pi$
$347$	−3.43577e8	−	5.95094e8i	−0.441440	−	0.764596i	−0.997797	+	0.0663474i	$0.978865\pi$
$348$		0			0
$349$	−8.95711e8	−	5.17139e8i	−1.12792	−	0.651206i	−0.184510	−	0.982831i	$-0.559070\pi$
$349$	−8.95711e8	−	5.17139e8i	−1.12792	−	0.651206i	−0.943411	+	0.331625i	$0.892403\pi$
$350$	−1.01503e8			−0.126544
$351$		0			0
$352$	−1.90961e7			−0.0233370
$353$	−9.29168e8	−	5.36455e8i	−1.12430	−	0.649116i	−0.181806	−	0.983334i	$-0.558194\pi$
$353$	−9.29168e8	−	5.36455e8i	−1.12430	−	0.649116i	−0.942496	+	0.334219i	$0.891528\pi$
$354$		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	$-0.877626\pi$
$359$		−	6.57582e8i		−	0.750100i	0.927005	−	0.375050i	$-0.122374\pi$
$360$		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	−0.527102	−	0.849802i	$-0.676721\pi$
$367$	4.47343e8	−	7.74821e8i	0.472400	−	0.818220i	0.999501	+	0.0315822i	$0.0100546\pi$
$368$	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	0.643361	−	0.765563i	$-0.277540\pi$
$373$	−3.42088e8	−	5.92515e8i	−0.341317	−	0.591178i	−0.984677	+	0.174385i	$0.944206\pi$
$374$	−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	−0.0440788	−	0.999028i	$-0.514035\pi$
$379$	−9.87024e8	−	5.69859e8i	−0.931302	−	0.537687i	−0.887223	+	0.461341i	$0.847369\pi$
$380$	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	−0.925127	−	0.379657i	$-0.876042\pi$
$383$	−1.16426e9	+	6.72186e8i	−1.05890	+	0.611355i	−0.133771	+	0.991012i	$0.542709\pi$
$384$		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	−0.430057	−	0.902802i	$-0.641506\pi$
$397$	1.70506e8	−	9.84416e7i	0.136764	−	0.0789609i	0.566821	+	0.823841i	$0.308173\pi$
$398$			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	0.125572	−	0.992085i	$-0.459923\pi$
$401$	−8.66177e8	−	5.00088e8i	−0.670813	−	0.387294i	−0.796385	+	0.604791i	$0.793257\pi$
$402$		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	0.103379	−	0.994642i	$-0.467035\pi$
$409$	1.40643e9	−	8.12004e8i	1.01645	−	0.586850i	0.913075	+	0.407793i	$0.133701\pi$
$410$	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	−0.896130	−	0.443792i	$-0.853633\pi$
$419$	−9.59601e7	+	1.66208e8i	−0.0637297	+	0.110383i	0.832400	+	0.554175i	$0.186966\pi$
$420$		0			0
$421$			1.17016e9i			0.764292i	0.924102	+	0.382146i	$0.124815\pi$
$421$			1.17016e9i			0.764292i	−0.924102	+	0.382146i	$0.875185\pi$
$422$	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	0.554108	−	0.832445i	$-0.313059\pi$
$431$	1.83241e8	+	1.05794e8i	0.110243	+	0.0636491i	−0.443864	+	0.896094i	$0.646393\pi$
$432$		0			0
$433$	−5.87978e8	−	1.01841e9i	−0.348060	−	0.602857i	0.637845	−	0.770165i	$-0.279826\pi$
$433$	−5.87978e8	−	1.01841e9i	−0.348060	−	0.602857i	−0.985905	+	0.167308i	$0.946493\pi$
$434$		−	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	0.290010	+	0.957024i	$0.406341\pi$
$439$	−1.21215e9	+	2.09950e9i	−0.683802	+	1.18438i	−0.973812	+	0.227356i	$0.926992\pi$
$440$	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	−0.494008	−	0.869457i	$-0.664469\pi$
$449$	2.29405e7	−	1.32447e7i	0.0119603	−	0.00690525i	0.505968	+	0.862552i	$0.331135\pi$
$450$		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	−0.179296	−	0.983795i	$-0.557382\pi$
$457$	−2.28711e9	−	1.32046e9i	−1.12094	−	0.647172i	−0.941640	+	0.336623i	$0.890715\pi$
$458$	−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	−0.453884	−	0.891061i	$-0.649962\pi$
$461$	1.91120e8	−	1.10343e8i	0.0908558	−	0.0524556i	0.544740	+	0.838605i	$0.316629\pi$
$462$		0			0
$463$			1.40461e9i			0.657691i	0.944384	+	0.328845i	$0.106659\pi$
$463$			1.40461e9i			0.657691i	−0.944384	+	0.328845i	$0.893341\pi$
$464$	−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	0.836220	−	0.548395i	$-0.184761\pi$
$479$	1.87473e9	+	1.08237e9i	0.779405	+	0.449990i	−0.0568141	+	0.998385i	$0.518094\pi$
$480$		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	0.262474	−	0.964939i	$-0.415462\pi$
$487$	3.13354e9	−	1.80915e9i	1.22937	−	0.709779i	0.966899	+	0.255160i	$0.0821282\pi$
$488$	−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	−0.642990	−	0.765875i	$-0.722306\pi$
$491$	8.96441e8	−	1.55268e9i	0.341772	−	0.591966i	0.984762	+	0.173908i	$0.0556397\pi$
$492$		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	$-0.890149\pi$
$499$		−	1.87794e9i		−	0.676596i	0.941039	−	0.338298i	$-0.109851\pi$
$500$	−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	0.855940	−	0.517074i	$-0.172979\pi$
$503$	−5.65977e7	−	9.80300e7i	−0.0198294	−	0.0343456i	−0.875770	+	0.482729i	$0.839646\pi$
$504$		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	−0.994935	−	0.100516i	$-0.967950\pi$
$509$	−4.69915e9	−	2.71305e9i	−1.57945	−	0.911898i	−0.584517	−	0.811381i	$-0.698716\pi$
$510$		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	0.371706	+	0.928350i	$0.378773\pi$
$523$	−2.02223e9	+	3.50260e9i	−0.618122	+	1.07062i	−0.989828	+	0.142268i	$0.954560\pi$
$524$	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	$-0.603610\pi$
$541$		−	6.97904e9i		−	1.89498i	0.319782	−	0.947491i	$-0.396390\pi$
$542$	−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	0.476778	−	0.879024i	$-0.341805\pi$
$557$	−1.87977e8	−	1.08528e8i	−0.0460905	−	0.0266103i	−0.522868	+	0.852414i	$0.675138\pi$
$558$		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	−0.996886	−	0.0788572i	$-0.974873\pi$
$563$	−2.39971e9	−	4.15643e9i	−0.566735	−	0.981614i	0.430151	−	0.902757i	$-0.358460\pi$
$564$		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	0.399214	+	0.916858i	$0.369283\pi$
$569$	−2.61206e9	+	4.52422e9i	−0.594415	+	1.02956i	−0.993629	+	0.112699i	$0.964050\pi$
$570$		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	$-0.999744\pi$
$577$		−	7.41729e6i		−	0.00160742i	1.00000		0.000803711i	$-0.000255829\pi$
$578$	−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	−0.136074	−	0.990699i	$-0.543449\pi$
$587$	−5.20465e9	−	3.00490e9i	−1.06208	−	0.613193i	−0.926007	+	0.377505i	$0.876782\pi$
$588$		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	$0.0315381\pi$
$593$			1.00461e9i			0.197836i	−0.995096	+	0.0989178i	$0.968462\pi$
$594$		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	0.428022	+	0.903768i	$0.359211\pi$
$601$	−3.02639e9	+	5.24187e9i	−0.568676	+	0.984975i	−0.996697	+	0.0812066i	$0.974123\pi$
$602$	−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	0.983896	+	0.178743i	$0.0572031\pi$
$607$	3.56363e9	+	6.17239e9i	0.646744	+	1.12019i	−0.337152	+	0.941450i	$0.609464\pi$
$608$	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	0.422100	−	0.906549i	$-0.361293\pi$
$613$	−8.66562e8	−	5.00310e8i	−0.151946	−	0.0877258i	−0.574045	+	0.818824i	$0.694627\pi$
$614$	−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	−0.198033	−	0.980195i	$-0.563455\pi$
$617$	3.21958e9	−	1.85882e9i	0.551825	−	0.318596i	0.749858	+	0.661599i	$0.230122\pi$
$618$		0			0
$619$		−	8.30664e9i		−	1.40769i	−0.710352	−	0.703847i	$-0.751464\pi$
$619$		−	8.30664e9i		−	1.40769i	0.710352	−	0.703847i	$-0.248536\pi$
$620$	−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	0.145963	−	0.989290i	$-0.453372\pi$
$631$	6.78879e9	−	3.91951e9i	1.07570	−	0.621053i	0.929732	+	0.368237i	$0.120038\pi$
$632$		−	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	0.814382	−	0.580330i	$-0.197076\pi$
$641$	−6.36068e8	−	1.10170e9i	−0.0953895	−	0.165220i	−0.909771	+	0.415110i	$0.863743\pi$
$642$		0			0
$643$	4.91826e9	−	2.83956e9i	0.729581	−	0.421224i	−0.0886881	−	0.996059i	$-0.528267\pi$
$643$	4.91826e9	−	2.83956e9i	0.729581	−	0.421224i	0.818269	+	0.574836i	$0.194934\pi$
$644$	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	−0.250091	−	0.968222i	$-0.580460\pi$
$647$	4.91513e9	−	8.51325e9i	0.713460	−	1.23575i	0.963551	−	0.267526i	$-0.0862063\pi$
$648$		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	−0.969075	−	0.246765i	$-0.920632\pi$
$653$	−1.92707e9	+	3.33778e9i	−0.270832	+	0.469096i	0.698243	+	0.715861i	$0.253966\pi$
$654$		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	0.648891	−	0.760882i	$-0.275233\pi$
$659$	−2.45749e9	−	4.25650e9i	−0.334498	−	0.579367i	−0.983388	+	0.181515i	$0.941900\pi$
$660$		0			0
$661$	1.10777e10	+	6.39573e9i	1.49192	+	0.861360i	0.999957	−	0.00925625i	$-0.00294640\pi$
$661$	1.10777e10	+	6.39573e9i	1.49192	+	0.861360i	0.491962	+	0.870616i	$0.336280\pi$
$662$	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	0.275741	+	0.961232i	$0.411077\pi$
$673$	−5.49257e9	+	9.51341e9i	−0.694581	+	1.20305i	−0.970322	+	0.241818i	$0.922256\pi$
$674$	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	0.619586	−	0.784929i	$-0.287301\pi$
$683$	1.33989e10	−	7.73584e9i	1.60915	−	0.929042i	0.989561	−	0.144113i	$-0.0460328\pi$
$684$		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	0.251110	−	0.967959i	$-0.419204\pi$
$691$	−4.00359e9	−	2.31148e9i	−0.461612	−	0.266512i	−0.712722	+	0.701447i	$0.752538\pi$
$692$	−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	−0.0784635	−	0.996917i	$-0.525001\pi$
$709$	7.07624e9	−	4.08547e9i	0.745660	−	0.430507i	0.824124	+	0.566410i	$0.191668\pi$
$710$		−	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	0.935497	+	0.353334i	$0.114952\pi$
$719$	7.71168e9	+	1.33570e10i	0.773745	+	1.34017i	−0.161752	+	0.986831i	$0.551714\pi$
$720$		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	$0.285159\pi$
$733$			1.66495e10i			1.56148i	−0.624854	+	0.780742i	$0.714841\pi$
$734$	−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	0.292759	−	0.956186i	$-0.405427\pi$
$739$	−4.26718e9	−	2.46366e9i	−0.388943	−	0.224556i	−0.681702	+	0.731630i	$0.738760\pi$
$740$	2.35251e9			0.213412
$741$		0			0
$742$	8.17647e8			0.0734772
$743$	8.58753e9	+	4.95801e9i	0.768082	+	0.443452i	0.832190	−	0.554491i	$-0.187087\pi$
$743$	8.58753e9	+	4.95801e9i	0.768082	+	0.443452i	−0.0641082	+	0.997943i	$0.520420\pi$
$744$		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	0.276276	−	0.961078i	$-0.410900\pi$
$751$	1.12646e10	−	1.95109e10i	0.970456	−	1.68088i	0.694180	−	0.719801i	$-0.255767\pi$
$752$	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	0.142647	−	0.989774i	$-0.454439\pi$
$757$	1.10819e10	−	1.91944e10i	0.928493	−	1.60820i	0.785846	−	0.618423i	$-0.212228\pi$
$758$	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	−0.747734	−	0.663999i	$-0.768858\pi$
$761$	−6.64485e9	+	3.83641e9i	−0.546561	+	0.315557i	0.201173	+	0.979556i	$0.435525\pi$
$762$		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	0.158970	−	0.987283i	$-0.449183\pi$
$769$	−7.77528e9	−	4.48906e9i	−0.616558	−	0.355970i	−0.775528	+	0.631314i	$0.782516\pi$
$770$	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	−0.827628	−	0.561276i	$-0.810310\pi$
$773$	−9.70027e9	+	5.60045e9i	−0.755363	+	0.436109i	0.0722655	+	0.997385i	$0.476977\pi$
$774$		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	−0.534594	−	0.845109i	$-0.679536\pi$
$787$	−9.57297e8	+	5.52696e8i	−0.0700060	+	0.0404180i	0.464588	+	0.885527i	$0.346202\pi$
$788$			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	0.999592	+	0.0285717i	$0.00909588\pi$
$797$	7.49691e9	+	1.29850e10i	0.524540	+	0.908529i	−0.475052	+	0.879958i	$0.657571\pi$
$798$		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	−0.491270	−	0.871007i	$-0.663467\pi$
$809$	7.66062e9	−	1.32686e10i	0.508679	−	0.881059i	0.999949	−	0.0100514i	$-0.00319951\pi$
$810$		0			0
$811$			1.14391e10i			0.753041i	0.926408	+	0.376521i	$0.122880\pi$
$811$			1.14391e10i			0.753041i	−0.926408	+	0.376521i	$0.877120\pi$
$812$	−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	−0.231339	−	0.972873i	$-0.574311\pi$
$821$	−1.88617e10	−	1.08898e10i	−1.18954	−	0.686782i	−0.958202	+	0.286091i	$0.907644\pi$
$822$		0			0
$823$	−1.08157e9	−	1.87333e9i	−0.0676324	−	0.117143i	0.830226	−	0.557426i	$-0.188211\pi$
$823$	−1.08157e9	−	1.87333e9i	−0.0676324	−	0.117143i	−0.897859	+	0.440284i	$0.854878\pi$
$824$			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	$0.246993\pi$
$827$			2.27847e10i			1.40079i	−0.713755	+	0.700395i	$0.753007\pi$
$828$		0			0
$829$	4.91919e9	−	8.52030e9i	0.299884	−	0.519414i	−0.676225	−	0.736695i	$-0.736385\pi$
$829$	4.91919e9	−	8.52030e9i	0.299884	−	0.519414i	0.976109	+	0.217281i	$0.0697187\pi$
$830$	−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	0.134160	−	0.990960i	$-0.457166\pi$
$839$	1.81235e10	−	1.04636e10i	1.05944	−	0.611666i	0.925276	+	0.379294i	$0.123833\pi$
$840$		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	$0.245548\pi$
$853$			2.52741e10i			1.39429i	−0.716928	+	0.697147i	$0.754452\pi$
$854$	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	$0.0503226\pi$
$863$			5.94525e9i			0.314871i	−0.987529	+	0.157435i	$0.949677\pi$
$864$		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	−0.251144	−	0.967950i	$-0.580807\pi$
$877$	9.21976e9	−	5.32303e9i	0.461552	−	0.266477i	0.712697	+	0.701472i	$0.247474\pi$
$878$	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	−0.814957	−	0.579521i	$-0.803240\pi$
$881$	1.91599e9	−	3.31860e9i	0.0944014	−	0.163508i	0.909359	+	0.416013i	$0.136573\pi$
$882$		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	−0.965843	−	0.259128i	$-0.916565\pi$
$887$	−5.37291e9	+	9.30616e9i	−0.258510	+	0.447752i	0.707333	+	0.706880i	$0.249898\pi$
$888$		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	−0.999013	−	0.0444245i	$-0.985855\pi$
$907$	−1.03600e10	+	1.79440e10i	−0.461034	+	0.798534i	0.537979	+	0.842958i	$0.319188\pi$
$908$	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	0.651046	−	0.759038i	$-0.274330\pi$
$919$	−7.80748e9	−	1.35229e10i	−0.331823	−	0.574734i	−0.982869	+	0.184304i	$0.940997\pi$
$920$	−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	−0.901648	−	0.432471i	$-0.857642\pi$
$929$	−2.38983e10	+	1.37977e10i	−0.977941	+	0.564615i	−0.0762934	+	0.997085i	$0.524309\pi$
$930$		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	$-0.735940\pi$
$941$		−	3.77084e10i		−	1.47528i	0.675193	−	0.737641i	$-0.264060\pi$
$942$		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	0.999773	+	0.0213086i	$0.00678325\pi$
$947$	3.96761e10	+	2.29070e10i	1.51811	+	0.876483i	0.518340	+	0.855174i	$0.326550\pi$
$948$		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	0.642391	−	0.766377i	$-0.277943\pi$
$953$	−9.15154e9	−	1.58509e10i	−0.342507	−	0.593239i	−0.984898	+	0.173138i	$0.944609\pi$
$954$		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	$0.154272\pi$
$967$			2.62013e10i			0.931816i	−0.884833	+	0.465908i	$0.845728\pi$
$968$	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	0.891512	−	0.452996i	$-0.149645\pi$
$971$	1.52480e9	+	2.64103e9i	0.0534497	+	0.0925777i	−0.838063	+	0.545574i	$0.816312\pi$
$972$		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	−0.327074	−	0.944999i	$-0.606063\pi$
$977$	−3.81568e10	−	2.20298e10i	−1.30900	−	0.755754i	−0.981930	+	0.189245i	$0.939396\pi$
$978$		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	$0.180111\pi$
$983$			3.19323e10i			1.07224i	−0.844141	+	0.536122i	$0.819889\pi$
$984$		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	0.394798	+	0.918768i	$0.370814\pi$
$991$	−1.83299e10	+	3.17483e10i	−0.598277	+	1.03625i	−0.993075	+	0.117478i	$0.962519\pi$
$992$	−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	−0.771981	−	0.635646i	$-0.780734\pi$
$997$	−2.93042e10	−	5.07563e10i	−0.936476	−	1.62202i	−0.164495	−	0.986378i	$-0.552600\pi$
$998$	−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.82.4		14
3.2	odd	2		13.8.e.a.4.4	✓	14
12.11	even	2		208.8.w.a.17.7		14
13.10	even	6	inner	117.8.q.b.10.4		14
39.17	odd	6		169.8.b.d.168.8		14
39.20	even	12		169.8.a.g.1.8		14
39.23	odd	6		13.8.e.a.10.4	yes	14
39.32	even	12		169.8.a.g.1.7		14
39.35	odd	6		169.8.b.d.168.7		14
156.23	even	6		208.8.w.a.49.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.8.e.a.4.4	✓	14	3.2	odd	2
13.8.e.a.10.4	yes	14	39.23	odd	6
117.8.q.b.10.4		14	13.10	even	6	inner
117.8.q.b.82.4		14	1.1	even	1	trivial
169.8.a.g.1.7		14	39.32	even	12
169.8.a.g.1.8		14	39.20	even	12
169.8.b.d.168.7		14	39.35	odd	6
169.8.b.d.168.8		14	39.17	odd	6
208.8.w.a.17.7		14	12.11	even	2
208.8.w.a.49.7		14	156.23	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 $\F_{q}$
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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more