LMFDB - Embedded newform 279.2.y.d.235.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [279,2,Mod(10,279)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(279, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([0, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("279.10"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	279.y (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.22782621639$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 93)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			235.3
Character	$\chi$	$=$	279.235
Dual form			279.2.y.d.19.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.08748 - 1.51664i) q^{2} +(1.43933 - 4.42980i) q^{4} +(1.93212 + 3.34652i) q^{5} +(-2.07563 - 2.30522i) q^{7} +(-2.11916 - 6.52210i) q^{8} +(9.10873 + 4.05547i) q^{10} +(-1.06351 + 0.226056i) q^{11} +(-0.249014 + 2.36921i) q^{13} +(-7.82901 - 1.66411i) q^{14} +(-6.77896 - 4.92520i) q^{16} +(-1.60951 - 0.342112i) q^{17} +(-0.0767990 - 0.730694i) q^{19} +(17.6054 - 3.74214i) q^{20} +(-1.87721 + 2.08485i) q^{22} +(0.222870 + 0.685924i) q^{23} +(-4.96614 + 8.60161i) q^{25} +(3.07343 + 5.32333i) q^{26} +(-13.1992 + 5.87665i) q^{28} +(-7.88779 + 5.73082i) q^{29} +(3.03814 - 4.66580i) q^{31} -7.90522 q^{32} +(-3.87868 + 1.72690i) q^{34} +(3.70411 - 11.4001i) q^{35} +(1.16410 - 2.01628i) q^{37} +(-1.26852 - 1.40883i) q^{38} +(17.7319 - 19.6933i) q^{40} +(-3.77729 - 1.68176i) q^{41} +(0.791467 + 7.53030i) q^{43} +(-0.529359 + 5.03651i) q^{44} +(1.50554 + 1.09384i) q^{46} +(1.30356 + 0.947094i) q^{47} +(-0.274100 + 2.60789i) q^{49} +(2.67885 + 25.4875i) q^{50} +(10.1367 + 4.51315i) q^{52} +(2.07659 - 2.30629i) q^{53} +(-2.81133 - 3.12230i) q^{55} +(-10.6363 + 18.4226i) q^{56} +(-7.77400 + 23.9259i) q^{58} +(9.44332 - 4.20444i) q^{59} +13.5425 q^{61} +(-0.734283 - 14.3475i) q^{62} +(-2.94405 + 2.13898i) q^{64} +(-8.40972 + 3.74425i) q^{65} +(-1.32349 - 2.29235i) q^{67} +(-3.83210 + 6.63740i) q^{68} +(-9.55759 - 29.4152i) q^{70} +(5.02644 - 5.58243i) q^{71} +(1.71580 - 0.364705i) q^{73} +(-0.627942 - 5.97447i) q^{74} +(-3.34737 - 0.711505i) q^{76} +(2.72856 + 1.98242i) q^{77} +(-10.7922 - 2.29395i) q^{79} +(3.38457 - 32.2020i) q^{80} +(-10.4356 + 2.21816i) q^{82} +(-9.96558 - 4.43696i) q^{83} +(-1.96488 - 6.04727i) q^{85} +(13.0729 + 14.5190i) q^{86} +(3.72811 + 6.45728i) q^{88} +(-1.89815 + 5.84191i) q^{89} +(5.97839 - 4.34356i) q^{91} +3.35929 q^{92} +4.15756 q^{94} +(2.29690 - 1.66880i) q^{95} +(3.74552 - 11.5275i) q^{97} +(3.38306 + 5.85963i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{4} + 6 q^{5} - q^{7} + 22 q^{8} + 24 q^{10} + 22 q^{11} - 8 q^{13} - 10 q^{14} - 2 q^{16} + 17 q^{17} + 5 q^{19} + 22 q^{20} - 37 q^{22} - 26 q^{23} - 8 q^{25} - 4 q^{26} - 36 q^{28} - 2 q^{29}+ \cdots + 14 q^{98}+O(q^{100}) $ 24 * q - 4 * q^4 + 6 * q^5 - q^7 + 22 * q^8 + 24 * q^10 + 22 * q^11 - 8 * q^13 - 10 * q^14 - 2 * q^16 + 17 * q^17 + 5 * q^19 + 22 * q^20 - 37 * q^22 - 26 * q^23 - 8 * q^25 - 4 * q^26 - 36 * q^28 - 2 * q^29 - 36 * q^32 + 40 * q^34 - 9 * q^35 - 13 * q^37 + q^38 - 27 * q^40 - 36 * q^41 - 11 * q^43 + 38 * q^44 - 23 * q^46 + 13 * q^47 - 22 * q^49 - 71 * q^50 + 9 * q^52 + 20 * q^53 + 26 * q^55 - 28 * q^56 + 40 * q^58 + 16 * q^59 + 70 * q^61 + 2 * q^62 + 34 * q^64 - 94 * q^65 + 4 * q^67 - 51 * q^68 - 43 * q^70 + 5 * q^71 - 12 * q^73 - 74 * q^74 + 71 * q^76 - 25 * q^77 - 29 * q^79 + 113 * q^80 - 60 * q^82 + 11 * q^83 + 16 * q^85 + 144 * q^86 + 26 * q^88 + 27 * q^89 - 81 * q^91 - 28 * q^92 - 80 * q^94 + 56 * q^95 - 21 * q^97 + 14 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/279\mathbb{Z}\right)^\times$.

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{13}{15}\right)$	$1$

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 $

$2$	2.08748	−	1.51664i	1.47607	−	1.07243i	0.497273	−	0.867594i	$-0.334335\pi$
$2$	2.08748	−	1.51664i	1.47607	−	1.07243i	0.978797	−	0.204834i	$-0.0656653\pi$
$3$		0			0
$3$		0			0
$4$	1.43933	−	4.42980i	0.719665	−	2.21490i
$5$	1.93212	+	3.34652i	0.864068	+	1.49661i	0.867969	+	0.496618i	$0.165425\pi$
$5$	1.93212	+	3.34652i	0.864068	+	1.49661i	−0.00390072	+	0.999992i	$0.501242\pi$
$6$		0			0
$7$	−2.07563	−	2.30522i	−0.784513	−	0.871290i	0.209804	−	0.977743i	$-0.432717\pi$
$7$	−2.07563	−	2.30522i	−0.784513	−	0.871290i	−0.994318	+	0.106453i	$0.966051\pi$
$8$	−2.11916	−	6.52210i	−0.749236	−	2.30591i
$9$		0			0
$10$	9.10873	+	4.05547i	2.88043	+	1.28245i
$11$	−1.06351	+	0.226056i	−0.320661	+	0.0681585i	−0.365430	−	0.930839i	$-0.619078\pi$
$11$	−1.06351	+	0.226056i	−0.320661	+	0.0681585i	0.0447693	+	0.998997i	$0.485745\pi$
$12$		0			0
$13$	−0.249014	+	2.36921i	−0.0690639	+	0.657099i	0.904153	+	0.427209i	$0.140503\pi$
$13$	−0.249014	+	2.36921i	−0.0690639	+	0.657099i	−0.973217	+	0.229890i	$0.926163\pi$
$14$	−7.82901	−	1.66411i	−2.09239	−	0.444752i
$15$		0			0
$16$	−6.77896	−	4.92520i	−1.69474	−	1.23130i
$17$	−1.60951	−	0.342112i	−0.390364	−	0.0829744i	0.00854849	−	0.999963i	$-0.497279\pi$
$17$	−1.60951	−	0.342112i	−0.390364	−	0.0829744i	−0.398912	+	0.916989i	$0.630612\pi$
$18$		0			0
$19$	−0.0767990	−	0.730694i	−0.0176189	−	0.167633i	0.982174	−	0.187973i	$-0.0601917\pi$
$19$	−0.0767990	−	0.730694i	−0.0176189	−	0.167633i	−0.999793	+	0.0203402i	$0.993525\pi$
$20$	17.6054	−	3.74214i	3.93668	−	0.836767i
$21$		0			0
$22$	−1.87721	+	2.08485i	−0.400222	+	0.444492i
$23$	0.222870	+	0.685924i	0.0464717	+	0.143025i	0.971600	−	0.236630i	$-0.0760428\pi$
$23$	0.222870	+	0.685924i	0.0464717	+	0.143025i	−0.925128	+	0.379655i	$0.876043\pi$
$24$		0			0
$25$	−4.96614	+	8.60161i	−0.993229	+	1.72032i
$26$	3.07343	+	5.32333i	0.602748	+	1.04399i
$27$		0			0
$28$	−13.1992	+	5.87665i	−2.49441	+	1.11058i
$29$	−7.88779	+	5.73082i	−1.46473	+	1.06419i	−0.482626	+	0.875826i	$0.660317\pi$
$29$	−7.88779	+	5.73082i	−1.46473	+	1.06419i	−0.982100	+	0.188360i	$0.939683\pi$
$30$		0			0
$31$	3.03814	−	4.66580i	0.545667	−	0.838002i
$31$	3.03814	−	4.66580i	0.545667	−	0.838002i
$32$	−7.90522			−1.39746
$33$		0			0
$34$	−3.87868	+	1.72690i	−0.665188	+	0.296161i
$35$	3.70411	−	11.4001i	0.626109	−	1.92697i
$36$		0			0
$37$	1.16410	−	2.01628i	0.191377	−	0.331475i	−0.754330	−	0.656496i	$-0.772038\pi$
$37$	1.16410	−	2.01628i	0.191377	−	0.331475i	0.945707	+	0.325021i	$0.105371\pi$
$38$	−1.26852	−	1.40883i	−0.205781	−	0.228543i
$39$		0			0
$40$	17.7319	−	19.6933i	2.80366	−	3.11378i
$41$	−3.77729	−	1.68176i	−0.589913	−	0.262646i	0.0899964	−	0.995942i	$-0.471314\pi$
$41$	−3.77729	−	1.68176i	−0.589913	−	0.262646i	−0.679910	+	0.733296i	$0.737981\pi$
$42$		0			0
$43$	0.791467	+	7.53030i	0.120698	+	1.14836i	0.872378	+	0.488833i	$0.162577\pi$
$43$	0.791467	+	7.53030i	0.120698	+	1.14836i	−0.751680	+	0.659528i	$0.770756\pi$
$44$	−0.529359	+	5.03651i	−0.0798038	+	0.759282i
$45$		0			0
$46$	1.50554	+	1.09384i	0.221979	+	0.161277i
$47$	1.30356	+	0.947094i	0.190144	+	0.138148i	0.678785	−	0.734337i	$-0.262507\pi$
$47$	1.30356	+	0.947094i	0.190144	+	0.138148i	−0.488640	+	0.872485i	$0.662507\pi$
$48$		0			0
$49$	−0.274100	+	2.60789i	−0.0391572	+	0.372556i
$50$	2.67885	+	25.4875i	0.378846	+	3.60448i
$51$		0			0
$52$	10.1367	+	4.51315i	1.40571	+	0.625861i
$53$	2.07659	−	2.30629i	0.285241	−	0.316793i	−0.583447	−	0.812151i	$-0.698297\pi$
$53$	2.07659	−	2.30629i	0.285241	−	0.316793i	0.868689	+	0.495358i	$0.164963\pi$
$54$		0			0
$55$	−2.81133	−	3.12230i	−0.379080	−	0.421010i
$56$	−10.6363	+	18.4226i	−1.42133	+	2.46182i
$57$		0			0
$58$	−7.77400	+	23.9259i	−1.02078	+	3.14163i
$59$	9.44332	−	4.20444i	1.22942	−	0.547371i	0.313824	−	0.949481i	$-0.398390\pi$
$59$	9.44332	−	4.20444i	1.22942	−	0.547371i	0.915591	+	0.402110i	$0.131723\pi$
$60$		0			0
$61$	13.5425			1.73395			0.866973	−	0.498355i	$-0.166063\pi$
$61$	13.5425			1.73395			0.866973	+	0.498355i	$0.166063\pi$
$62$	−0.734283	−	14.3475i	−0.0932540	−	1.82214i
$63$		0			0
$64$	−2.94405	+	2.13898i	−0.368006	+	0.267372i
$65$	−8.40972	+	3.74425i	−1.04310	+	0.464417i
$66$		0			0
$67$	−1.32349	−	2.29235i	−0.161690	−	0.280055i	0.773785	−	0.633448i	$-0.218361\pi$
$67$	−1.32349	−	2.29235i	−0.161690	−	0.280055i	−0.935475	+	0.353393i	$0.885028\pi$
$68$	−3.83210	+	6.63740i	−0.464711	+	0.804903i
$69$		0			0
$70$	−9.55759	−	29.4152i	−1.14235	−	3.51579i
$71$	5.02644	−	5.58243i	0.596529	−	0.662513i	−0.366967	−	0.930234i	$-0.619604\pi$
$71$	5.02644	−	5.58243i	0.596529	−	0.662513i	0.963496	+	0.267721i	$0.0862706\pi$
$72$		0			0
$73$	1.71580	−	0.364705i	0.200819	−	0.0426855i	−0.106404	−	0.994323i	$-0.533934\pi$
$73$	1.71580	−	0.364705i	0.200819	−	0.0426855i	0.307223	+	0.951638i	$0.400600\pi$
$74$	−0.627942	−	5.97447i	−0.0729968	−	0.694518i
$75$		0			0
$76$	−3.34737	−	0.711505i	−0.383969	−	0.0816152i
$77$	2.72856	+	1.98242i	0.310948	+	0.225917i
$78$		0			0
$79$	−10.7922	−	2.29395i	−1.21421	−	0.258089i	−0.444089	−	0.895983i	$-0.646473\pi$
$79$	−10.7922	−	2.29395i	−1.21421	−	0.258089i	−0.770125	+	0.637893i	$0.779806\pi$
$80$	3.38457	−	32.2020i	0.378406	−	3.60029i
$81$		0			0
$82$	−10.4356	+	2.21816i	−1.15242	+	0.244955i
$83$	−9.96558	−	4.43696i	−1.09386	−	0.487020i	−0.221145	−	0.975241i	$-0.570979\pi$
$83$	−9.96558	−	4.43696i	−1.09386	−	0.487020i	−0.872720	+	0.488221i	$0.837646\pi$
$84$		0			0
$85$	−1.96488	−	6.04727i	−0.213121	−	0.655918i
$86$	13.0729	+	14.5190i	1.40969	+	1.56562i
$87$		0			0
$88$	3.72811	+	6.45728i	0.397418	+	0.688348i
$89$	−1.89815	+	5.84191i	−0.201204	+	0.619241i	0.798644	+	0.601803i	$0.205551\pi$
$89$	−1.89815	+	5.84191i	−0.201204	+	0.619241i	−0.999848	+	0.0174376i	$0.994449\pi$
$90$		0			0
$91$	5.97839	−	4.34356i	0.626706	−	0.455328i
$92$	3.35929			0.350230
$93$		0			0
$94$	4.15756			0.428820
$95$	2.29690	−	1.66880i	0.235657	−	0.171215i
$96$		0			0
$97$	3.74552	−	11.5275i	0.380300	−	1.17044i	−0.559532	−	0.828809i	$-0.689019\pi$
$97$	3.74552	−	11.5275i	0.380300	−	1.17044i	0.939833	−	0.341636i	$-0.110981\pi$
$98$	3.38306	+	5.85963i	0.341740	+	0.591912i
$99$		0			0
$100$	30.9555	+	34.3796i	3.09555	+	3.43796i
$101$	−2.98732	−	9.19401i	−0.297249	−	0.914838i	−0.982457	−	0.186491i	$-0.940289\pi$
$101$	−2.98732	−	9.19401i	−0.297249	−	0.914838i	0.685208	−	0.728348i	$-0.259711\pi$
$102$		0			0
$103$	−5.10625	−	2.27345i	−0.503134	−	0.224010i	0.139444	−	0.990230i	$-0.455468\pi$
$103$	−5.10625	−	2.27345i	−0.503134	−	0.224010i	−0.642578	+	0.766220i	$0.722135\pi$
$104$	15.9799	−	3.39663i	1.56696	−	0.333067i
$105$		0			0
$106$	0.837025	−	7.96376i	0.0812991	−	0.773509i
$107$	−4.09493	−	0.870403i	−0.395871	−	0.0841451i	0.00567462	−	0.999984i	$-0.498194\pi$
$107$	−4.09493	−	0.870403i	−0.395871	−	0.0841451i	−0.401546	+	0.915839i	$0.631527\pi$
$108$		0			0
$109$	4.42032	+	3.21155i	0.423390	+	0.307611i	0.779000	−	0.627023i	$-0.215727\pi$
$109$	4.42032	+	3.21155i	0.423390	+	0.307611i	−0.355610	+	0.934634i	$0.615727\pi$
$110$	−10.6040	−	2.25395i	−1.01105	−	0.214906i
$111$		0			0
$112$	2.71693	+	25.8499i	0.256726	+	2.44258i
$113$	−14.3351	+	3.04703i	−1.34854	+	0.286640i	−0.824889	−	0.565295i	$-0.808762\pi$
$113$	−14.3351	+	3.04703i	−1.34854	+	0.286640i	−0.523647	+	0.851935i	$0.675429\pi$
$114$		0			0
$115$	−1.86485	+	2.07113i	−0.173898	+	0.193133i
$116$	14.0332	+	43.1899i	1.30295	+	4.01008i
$117$		0			0
$118$	13.3361	−	23.0988i	1.22769	−	2.12642i
$119$	2.55210	+	4.42037i	0.233951	+	0.405215i
$120$		0			0
$121$	−8.96905	+	3.99328i	−0.815368	+	0.363025i
$122$	28.2698	−	20.5392i	2.55942	−	1.85953i
$123$		0			0
$124$	−16.2957	−	20.1740i	−1.46339	−	1.81168i
$125$	−19.0595			−1.70473
$126$		0			0
$127$	−12.8112	+	5.70393i	−1.13681	+	0.506142i	−0.886824	−	0.462107i	$-0.847094\pi$
$127$	−12.8112	+	5.70393i	−1.13681	+	0.506142i	−0.249989	+	0.968249i	$0.580427\pi$
$128$	1.98412	−	6.10649i	0.175373	−	0.539742i
$129$		0			0
$130$	−11.8764	+	20.5706i	−1.04163	+	1.80416i
$131$	9.25965	+	10.2839i	0.809020	+	0.898507i	0.996486	−	0.0837638i	$-0.0266941\pi$
$131$	9.25965	+	10.2839i	0.809020	+	0.898507i	−0.187466	+	0.982271i	$0.560027\pi$
$132$		0			0
$133$	−1.52500	+	1.69369i	−0.132234	+	0.146861i
$134$	−6.23943	−	2.77797i	−0.539005	−	0.239980i
$135$		0			0
$136$	1.17952	+	11.2224i	0.101143	+	0.962312i
$137$	0.591136	−	5.62428i	0.0505041	−	0.480515i	−0.939813	−	0.341690i	$-0.889001\pi$
$137$	0.591136	−	5.62428i	0.0505041	−	0.480515i	0.990317	−	0.138825i	$-0.0443326\pi$
$138$		0			0
$139$	4.57543	+	3.32425i	0.388083	+	0.281959i	0.764670	−	0.644423i	$-0.222902\pi$
$139$	4.57543	+	3.32425i	0.388083	+	0.281959i	−0.376586	+	0.926382i	$0.622902\pi$
$140$	−45.1686	−	32.8169i	−3.81745	−	2.77354i
$141$		0			0
$142$	2.02604	−	19.2765i	0.170022	−	1.61765i
$143$	−0.270745	−	2.57597i	−0.0226408	−	0.215413i
$144$		0			0
$145$	−34.4184	−	15.3241i	−2.85830	−	1.27260i
$146$	3.02857	−	3.36357i	0.250646	−	0.278371i
$147$		0			0
$148$	−7.25620	−	8.05883i	−0.596456	−	0.662432i
$149$	8.43564	−	14.6110i	0.691075	−	1.19698i	−0.280411	−	0.959880i	$-0.590471\pi$
$149$	8.43564	−	14.6110i	0.691075	−	1.19698i	0.971486	−	0.237097i	$-0.0761959\pi$
$150$		0			0
$151$	1.39505	−	4.29351i	0.113527	−	0.349401i	−0.878110	−	0.478459i	$-0.841195\pi$
$151$	1.39505	−	4.29351i	0.113527	−	0.349401i	0.991637	+	0.129058i	$0.0411954\pi$
$152$	−4.60291	+	2.04935i	−0.373345	+	0.166224i
$153$		0			0
$154$	8.70243			0.701261
$155$	21.4842	+	1.15236i	1.72566	+	0.0925596i
$156$		0			0
$157$	6.36232	−	4.62249i	0.507768	−	0.368915i	−0.304208	−	0.952606i	$-0.598392\pi$
$157$	6.36232	−	4.62249i	0.507768	−	0.368915i	0.811976	+	0.583690i	$0.198392\pi$
$158$	−26.0075	+	11.5793i	−2.06905	+	0.921199i
$159$		0			0
$160$	−15.2738	−	26.4550i	−1.20750	−	2.09145i
$161$	1.11861	−	1.93749i	0.0881587	−	0.152695i
$162$		0			0
$163$	4.02379	+	12.3839i	0.315167	+	0.969986i	0.975685	+	0.219175i	$0.0703367\pi$
$163$	4.02379	+	12.3839i	0.315167	+	0.969986i	−0.660518	+	0.750810i	$0.729663\pi$
$164$	−12.8866	+	14.3120i	−1.00628	+	1.11758i
$165$		0			0
$166$	−27.5322	+	5.85215i	−2.13691	+	0.454215i
$167$	2.22382	+	21.1583i	0.172085	+	1.63728i	0.650760	+	0.759284i	$0.274451\pi$
$167$	2.22382	+	21.1583i	0.172085	+	1.63728i	−0.478675	+	0.877992i	$0.658883\pi$
$168$		0			0
$169$	7.16479	+	1.52292i	0.551138	+	0.117148i
$170$	−13.2732	−	9.64352i	−1.01801	−	0.739625i
$171$		0			0
$172$	34.4969	+	7.33255i	2.63037	+	0.559101i
$173$	−1.32757	+	12.6309i	−0.100933	+	0.960313i	0.820466	+	0.571695i	$0.193714\pi$
$173$	−1.32757	+	12.6309i	−0.100933	+	0.960313i	−0.921399	+	0.388618i	$0.872953\pi$
$174$		0			0
$175$	30.1364	−	6.40570i	2.27810	−	0.484225i
$176$	8.32287	+	3.70558i	0.627360	+	0.279319i
$177$		0			0
$178$	4.89773	+	15.0737i	0.367100	+	1.12982i
$179$	−10.2337	−	11.3656i	−0.764900	−	0.849507i	0.227344	−	0.973814i	$-0.426996\pi$
$179$	−10.2337	−	11.3656i	−0.764900	−	0.849507i	−0.992244	+	0.124307i	$0.960329\pi$
$180$		0			0
$181$	8.52389	+	14.7638i	0.633576	+	1.09739i	0.986815	+	0.161853i	$0.0517469\pi$
$181$	8.52389	+	14.7638i	0.633576	+	1.09739i	−0.353239	+	0.935533i	$0.614920\pi$
$182$	5.89215	−	18.1342i	0.436755	−	1.34419i
$183$		0			0
$184$	4.00137	−	2.90716i	0.294985	−	0.214319i
$185$	8.99671			0.661451
$186$		0			0
$187$	1.78907			0.130830
$188$	6.07169	−	4.41134i	0.442823	−	0.321730i
$189$		0			0
$190$	2.26376	−	6.96715i	0.164231	−	0.505450i
$191$	−4.80846	−	8.32850i	−0.347928	−	0.602629i	0.637953	−	0.770075i	$-0.279781\pi$
$191$	−4.80846	−	8.32850i	−0.347928	−	0.602629i	−0.985881	+	0.167446i	$0.946448\pi$
$192$		0			0
$193$	6.62768	+	7.36079i	0.477071	+	0.529841i	0.932856	−	0.360249i	$-0.117308\pi$
$193$	6.62768	+	7.36079i	0.477071	+	0.529841i	−0.455785	+	0.890090i	$0.650642\pi$
$194$	−9.66444	−	29.7441i	−0.693867	−	2.13550i
$195$		0			0
$196$	11.1579	+	4.96782i	0.796994	+	0.354844i
$197$	22.0638	−	4.68980i	1.57198	−	0.334134i	0.662232	−	0.749298i	$-0.269609\pi$
$197$	22.0638	−	4.68980i	1.57198	−	0.334134i	0.909747	+	0.415164i	$0.136276\pi$
$198$		0			0
$199$	0.832137	−	7.91725i	0.0589886	−	0.561239i	−0.924616	−	0.380901i	$-0.875614\pi$
$199$	0.832137	−	7.91725i	0.0589886	−	0.561239i	0.983605	−	0.180339i	$-0.0577194\pi$
$200$	66.6246	+	14.1615i	4.71107	+	1.00137i
$201$		0			0
$202$	−20.1800	−	14.6616i	−1.41986	−	1.03159i
$203$	29.5829	+	6.28804i	2.07631	+	0.441334i
$204$		0			0
$205$	−1.67012	−	15.8901i	−0.116646	−	1.10982i
$206$	−14.1072	+	2.99858i	−0.982895	+	0.208921i
$207$		0			0
$208$	13.3569	−	14.8343i	0.926132	−	1.02857i
$209$	0.246855	+	0.759740i	0.0170753	+	0.0525523i
$210$		0			0
$211$	−3.67864	+	6.37160i	−0.253248	+	0.438639i	−0.964418	−	0.264381i	$-0.914832\pi$
$211$	−3.67864	+	6.37160i	−0.253248	+	0.438639i	0.711170	+	0.703020i	$0.248166\pi$
$212$	−7.22749	−	12.5184i	−0.496386	−	0.859766i
$213$		0			0
$214$	−9.86816	+	4.39359i	−0.674573	+	0.300339i
$215$	−23.6711	+	17.1981i	−1.61436	+	1.17290i
$216$		0			0
$217$	−17.0617	+	2.68087i	−1.15823	+	0.181990i
$218$	14.0981			0.954844
$219$		0			0
$220$	−17.8776	+	7.95961i	−1.20531	+	0.536637i
$221$	1.21132	−	3.72807i	0.0814825	−	0.250777i
$222$		0			0
$223$	11.7266	−	20.3111i	0.785271	−	1.36013i	−0.143566	−	0.989641i	$-0.545857\pi$
$223$	11.7266	−	20.3111i	0.785271	−	1.36013i	0.928837	−	0.370489i	$-0.120810\pi$
$224$	16.4083	+	18.2232i	1.09632	+	1.21759i
$225$		0			0
$226$	−25.3030	+	28.1019i	−1.68313	+	1.86931i
$227$	−2.64310	−	1.17678i	−0.175429	−	0.0781059i	0.317143	−	0.948378i	$-0.397276\pi$
$227$	−2.64310	−	1.17678i	−0.175429	−	0.0781059i	−0.492572	+	0.870272i	$0.663943\pi$
$228$		0			0
$229$	−0.632597	−	6.01876i	−0.0418032	−	0.397731i	−0.995338	−	0.0964479i	$-0.969252\pi$
$229$	−0.632597	−	6.01876i	−0.0418032	−	0.397731i	0.953535	−	0.301283i	$-0.0974148\pi$
$230$	−0.751678	+	7.15174i	−0.0495642	+	0.471572i
$231$		0			0
$232$	54.0925	+	39.3005i	3.55134	+	2.58020i
$233$	18.9279	+	13.7519i	1.24001	+	0.900917i	0.997599	−	0.0692572i	$-0.0220629\pi$
$233$	18.9279	+	13.7519i	1.24001	+	0.900917i	0.242407	+	0.970175i	$0.422063\pi$
$234$		0			0
$235$	−0.650836	+	6.19230i	−0.0424559	+	0.403941i
$236$	−5.03277	−	47.8836i	−0.327605	−	3.11696i
$237$		0			0
$238$	12.0316	+	5.35680i	0.779891	+	0.347230i
$239$	6.93759	−	7.70498i	0.448755	−	0.498393i	−0.475740	−	0.879586i	$-0.657820\pi$
$239$	6.93759	−	7.70498i	0.448755	−	0.498393i	0.924496	+	0.381192i	$0.124486\pi$
$240$		0			0
$241$	5.54025	+	6.15307i	0.356879	+	0.396354i	0.894673	−	0.446722i	$-0.147409\pi$
$241$	5.54025	+	6.15307i	0.356879	+	0.396354i	−0.537794	+	0.843076i	$0.680742\pi$
$242$	−12.6663	+	21.9387i	−0.814222	+	1.41027i
$243$		0			0
$244$	19.4922	−	59.9908i	1.24786	−	3.84052i
$245$	−9.25696	+	4.12146i	−0.591405	+	0.263311i
$246$		0			0
$247$	1.75029			0.111368
$248$	−36.8691	−	9.92752i	−2.34119	−	0.630398i
$249$		0			0
$250$	−39.7863	+	28.9064i	−2.51631	+	1.82820i
$251$	6.31041	−	2.80958i	0.398310	−	0.177339i	−0.197799	−	0.980243i	$-0.563379\pi$
$251$	6.31041	−	2.80958i	0.398310	−	0.177339i	0.596109	+	0.802904i	$0.296713\pi$
$252$		0			0
$253$	−0.392082	−	0.679107i	−0.0246500	−	0.0426951i
$254$	−18.0924	+	31.3369i	−1.13522	+	1.96625i
$255$		0			0
$256$	−7.36860	−	22.6782i	−0.460538	−	1.41739i
$257$	−16.5146	+	18.3413i	−1.03015	+	1.14410i	−0.0407094	+	0.999171i	$0.512962\pi$
$257$	−16.5146	+	18.3413i	−1.03015	+	1.14410i	−0.989442	+	0.144928i	$0.953705\pi$
$258$		0			0
$259$	−7.06421	+	1.50154i	−0.438949	+	0.0933014i
$260$	4.48192	+	42.6426i	0.277957	+	2.64458i
$261$		0			0
$262$	34.9263	+	7.42381i	2.15775	+	0.458645i
$263$	−19.0727	−	13.8571i	−1.17607	−	0.854467i	−0.184349	−	0.982861i	$-0.559018\pi$
$263$	−19.0727	−	13.8571i	−1.17607	−	0.854467i	−0.991723	+	0.128394i	$0.959018\pi$
$264$		0			0
$265$	11.7302	+	2.49334i	0.720583	+	0.153165i
$266$	−0.614693	+	5.84842i	−0.0376893	+	0.358589i
$267$		0			0
$268$	−12.0596	+	2.56335i	−0.736657	+	0.156581i
$269$	−0.864697	−	0.384988i	−0.0527215	−	0.0234731i	0.380207	−	0.924902i	$-0.375853\pi$
$269$	−0.864697	−	0.384988i	−0.0527215	−	0.0234731i	−0.432928	+	0.901428i	$0.642520\pi$
$270$		0			0
$271$	9.65333	+	29.7099i	0.586398	+	1.80475i	0.593582	+	0.804774i	$0.297713\pi$
$271$	9.65333	+	29.7099i	0.586398	+	1.80475i	−0.00718389	+	0.999974i	$0.502287\pi$
$272$	9.22584	+	10.2463i	0.559399	+	0.621275i
$273$		0			0
$274$	−7.29604	−	12.6371i	−0.440770	−	0.763436i
$275$	3.33710	−	10.2705i	0.201235	−	0.619337i
$276$		0			0
$277$	−22.3794	+	16.2596i	−1.34465	+	0.976942i	−0.345387	+	0.938460i	$0.612252\pi$
$277$	−22.3794	+	16.2596i	−1.34465	+	0.976942i	−0.999259	+	0.0384820i	$0.987748\pi$
$278$	14.5928			0.875219
$279$		0			0
$280$	−82.2021			−4.91251
$281$	−6.69071	+	4.86109i	−0.399134	+	0.289988i	−0.769188	−	0.639022i	$-0.779339\pi$
$281$	−6.69071	+	4.86109i	−0.399134	+	0.289988i	0.370054	+	0.929010i	$0.379339\pi$
$282$		0			0
$283$	0.254844	−	0.784328i	0.0151489	−	0.0466234i	−0.943196	−	0.332236i	$-0.892197\pi$
$283$	0.254844	−	0.784328i	0.0151489	−	0.0466234i	0.958345	+	0.285612i	$0.0921970\pi$
$284$	−17.4943	−	30.3011i	−1.03810	−	1.79804i
$285$		0			0
$286$	−4.47199	−	4.96665i	−0.264435	−	0.293684i
$287$	3.96343	+	12.1982i	0.233954	+	0.720035i
$288$		0			0
$289$	−13.0568	−	5.81326i	−0.768046	−	0.341956i
$290$	−95.0889	+	20.2118i	−5.58381	+	1.18688i
$291$		0			0
$292$	0.854034	−	8.12559i	0.0499786	−	0.475514i
$293$	−3.44829	−	0.732958i	−0.201452	−	0.0428198i	0.106081	−	0.994358i	$-0.466170\pi$
$293$	−3.44829	−	0.732958i	−0.201452	−	0.0428198i	−0.307532	+	0.951538i	$0.599503\pi$
$294$		0			0
$295$	32.3158	+	23.4788i	1.88150	+	1.36699i
$296$	−15.6173	−	3.31956i	−0.907738	−	0.192946i
$297$		0			0
$298$	−4.55037	−	43.2939i	−0.263596	−	2.50795i
$299$	−1.68059	+	0.357221i	−0.0971912	+	0.0206586i
$300$		0			0
$301$	15.7162	−	17.4546i	0.905867	−	1.00607i
$302$	−3.59959	−	11.0784i	−0.207133	−	0.637490i
$303$		0			0
$304$	−3.07820	+	5.33160i	−0.176547	+	0.305788i
$305$	26.1658	+	45.3204i	1.49825	+	2.59504i
$306$		0			0
$307$	−8.13923	+	3.62382i	−0.464530	+	0.206822i	−0.625636	−	0.780115i	$-0.715161\pi$
$307$	−8.13923	+	3.62382i	−0.464530	+	0.206822i	0.161106	+	0.986937i	$0.448494\pi$
$308$	12.7090	−	9.23363i	0.724163	−	0.526135i
$309$		0			0
$310$	46.5956	−	30.1784i	2.64645	−	1.71402i
$311$	26.1174			1.48098			0.740491	−	0.672066i	$-0.234593\pi$
$311$	26.1174			1.48098			0.740491	+	0.672066i	$0.234593\pi$
$312$		0			0
$313$	−4.63794	+	2.06494i	−0.262152	+	0.116717i	−0.533604	−	0.845734i	$-0.679163\pi$
$313$	−4.63794	+	2.06494i	−0.262152	+	0.116717i	0.271452	+	0.962452i	$0.412496\pi$
$314$	6.27053	−	19.2987i	0.353867	−	1.08909i
$315$		0			0
$316$	−25.6952	+	44.5054i	−1.44547	+	2.50362i
$317$	−3.73508	−	4.14823i	−0.209783	−	0.232988i	0.629066	−	0.777352i	$-0.283438\pi$
$317$	−3.73508	−	4.14823i	−0.209783	−	0.232988i	−0.838849	+	0.544364i	$0.816771\pi$
$318$		0			0
$319$	7.09327	−	7.87787i	0.397147	−	0.441076i
$320$	−12.8464	−	5.71957i	−0.718134	−	0.319734i
$321$		0			0
$322$	−0.603402	−	5.74099i	−0.0336263	−	0.319933i
$323$	−0.126370	+	1.20233i	−0.00703144	+	0.0668997i
$324$		0			0
$325$	−19.1423	−	13.9077i	−1.06183	−	0.771462i
$326$	27.1816	+	19.7486i	1.50545	+	1.09377i
$327$		0			0
$328$	−2.96392	+	28.1998i	−0.163655	+	1.55707i
$329$	−0.522453	−	4.97081i	−0.0288038	−	0.274049i
$330$		0			0
$331$	−3.37335	−	1.50191i	−0.185416	−	0.0825527i	0.311929	−	0.950106i	$-0.399025\pi$
$331$	−3.37335	−	1.50191i	−0.185416	−	0.0825527i	−0.497345	+	0.867553i	$0.665692\pi$
$332$	−33.9986	+	37.7593i	−1.86592	+	2.07231i
$333$		0			0
$334$	36.7317	+	40.7947i	2.00987	+	2.23219i
$335$	5.11427	−	8.85818i	0.279422	−	0.483974i
$336$		0			0
$337$	−10.1823	+	31.3380i	−0.554668	+	1.70709i	0.142151	+	0.989845i	$0.454598\pi$
$337$	−10.1823	+	31.3380i	−0.554668	+	1.70709i	−0.696819	+	0.717247i	$0.745402\pi$
$338$	17.2661	−	7.68735i	0.939151	−	0.418137i
$339$		0			0
$340$	−29.6163			−1.60617
$341$	−2.17637	+	5.64892i	−0.117857	+	0.305906i
$342$		0			0
$343$	−10.9862	+	7.98192i	−0.593198	+	0.430983i
$344$	47.4362	−	21.1199i	2.55759	−	1.13871i
$345$		0			0
$346$	16.3853	+	28.3803i	0.880882	+	1.52573i
$347$	−3.85451	+	6.67621i	−0.206921	+	0.358398i	−0.950743	−	0.309980i	$-0.899678\pi$
$347$	−3.85451	+	6.67621i	−0.206921	+	0.358398i	0.743822	+	0.668378i	$0.233011\pi$
$348$		0			0
$349$	7.90757	+	24.3370i	0.423283	+	1.30273i	0.904629	+	0.426199i	$0.140148\pi$
$349$	7.90757	+	24.3370i	0.423283	+	1.30273i	−0.481347	+	0.876530i	$0.659852\pi$
$350$	53.1940	−	59.0779i	2.84334	−	3.15785i
$351$		0			0
$352$	8.40729	−	1.78702i	0.448110	−	0.0952487i
$353$	−0.834879	−	7.94335i	−0.0444362	−	0.422782i	−0.994014	−	0.109251i	$-0.965155\pi$
$353$	−0.834879	−	7.94335i	−0.0444362	−	0.422782i	0.949578	−	0.313531i	$-0.101512\pi$
$354$		0			0
$355$	28.3934	+	6.03520i	1.50697	+	0.320315i
$356$	23.1464	+	16.8169i	1.22676	+	0.891291i
$357$		0			0
$358$	−38.6001	−	8.20471i	−2.04008	−	0.433632i
$359$	0.493090	−	4.69143i	0.0260243	−	0.247604i	−0.973774	−	0.227518i	$-0.926939\pi$
$359$	0.493090	−	4.69143i	0.0260243	−	0.247604i	0.999798	−	0.0200868i	$-0.00639427\pi$
$360$		0			0
$361$	18.0568	−	3.83809i	0.950357	−	0.202005i
$362$	40.1849	+	17.8915i	2.11207	+	0.940354i
$363$		0			0
$364$	−10.6362	−	32.7349i	−0.557489	−	1.71577i
$365$	4.53562	+	5.03732i	0.237405	+	0.263665i
$366$		0			0
$367$	−12.2456	−	21.2100i	−0.639217	−	1.10716i	−0.985605	−	0.169064i	$-0.945925\pi$
$367$	−12.2456	−	21.2100i	−0.639217	−	1.10716i	0.346389	−	0.938091i	$-0.387408\pi$
$368$	1.86749	−	5.74753i	0.0973495	−	0.299611i
$369$		0			0
$370$	18.7804	−	13.6448i	0.976349	−	0.709359i
$371$	−9.62671			−0.499794
$372$		0			0
$373$	1.58686			0.0821647			0.0410824	−	0.999156i	$-0.486919\pi$
$373$	1.58686			0.0821647			0.0410824	+	0.999156i	$0.486919\pi$
$374$	3.73464	−	2.71338i	0.193114	−	0.140305i
$375$		0			0
$376$	3.41458	−	10.5090i	0.176094	−	0.541961i
$377$	−11.6133	−	20.1149i	−0.598116	−	1.03597i
$378$		0			0
$379$	5.13571	+	5.70379i	0.263804	+	0.292984i	0.860465	−	0.509509i	$-0.170173\pi$
$379$	5.13571	+	5.70379i	0.263804	+	0.292984i	−0.596661	+	0.802493i	$0.703506\pi$
$380$	−4.08643	−	12.5768i	−0.209630	−	0.645174i
$381$		0			0
$382$	−22.6689	−	10.0928i	−1.15984	−	0.516395i
$383$	−11.4719	+	2.43842i	−0.586185	+	0.124598i	−0.491451	−	0.870905i	$-0.663533\pi$
$383$	−11.4719	+	2.43842i	−0.586185	+	0.124598i	−0.0947341	+	0.995503i	$0.530200\pi$
$384$		0			0
$385$	−1.36230	+	12.9614i	−0.0694294	+	0.660577i
$386$	24.9988	+	5.31366i	1.27241	+	0.270458i
$387$		0			0
$388$	−45.6736	−	33.1838i	−2.31873	−	1.68465i
$389$	−4.50941	−	0.958505i	−0.228636	−	0.0485981i	0.0921688	−	0.995743i	$-0.470620\pi$
$389$	−4.50941	−	0.958505i	−0.228636	−	0.0485981i	−0.320805	+	0.947145i	$0.603953\pi$
$390$		0			0
$391$	−0.124049	−	1.18025i	−0.00627344	−	0.0596878i
$392$	17.5898	−	3.73882i	0.888418	−	0.188839i
$393$		0			0
$394$	38.9449	−	43.2527i	1.96202	−	2.17904i
$395$	−13.1750	−	40.5484i	−0.662905	−	2.04021i
$396$		0			0
$397$	−16.0539	+	27.8062i	−0.805723	+	1.39555i	0.110079	+	0.993923i	$0.464890\pi$
$397$	−16.0539	+	27.8062i	−0.805723	+	1.39555i	−0.915802	+	0.401630i	$0.868444\pi$
$398$	−10.2706	−	17.7891i	−0.514817	−	0.891689i
$399$		0			0
$400$	76.0300	−	33.8507i	3.80150	−	1.69254i
$401$	1.99995	−	1.45305i	0.0998725	−	0.0725616i	−0.536728	−	0.843755i	$-0.680340\pi$
$401$	1.99995	−	1.45305i	0.0998725	−	0.0725616i	0.636601	+	0.771194i	$0.280340\pi$
$402$		0			0
$403$	10.2977	+	8.35984i	0.512965	+	0.416433i
$404$	−45.0274			−2.24019
$405$		0			0
$406$	71.2904	−	31.7405i	3.53808	−	1.57526i
$407$	−0.782241	+	2.40749i	−0.0387743	+	0.119335i
$408$		0			0
$409$	−10.1579	+	17.5939i	−0.502274	+	0.869965i	0.497722	+	0.867336i	$0.334170\pi$
$409$	−10.1579	+	17.5939i	−0.502274	+	0.869965i	−0.999997	+	0.00262811i	$0.999163\pi$
$410$	−27.5860	−	30.6373i	−1.36237	−	1.51307i
$411$		0			0
$412$	−17.4205	+	19.3474i	−0.858246	+	0.953179i
$413$	−29.2929	−	13.0421i	−1.44141	−	0.641758i
$414$		0			0
$415$	−4.40626	−	41.9228i	−0.216295	−	2.05791i
$416$	1.96851	−	18.7291i	0.0965140	−	0.918269i
$417$		0			0
$418$	1.66756	+	1.21155i	0.0815629	+	0.0592589i
$419$	−11.4035	−	8.28511i	−0.557096	−	0.404754i	0.273299	−	0.961929i	$-0.411885\pi$
$419$	−11.4035	−	8.28511i	−0.557096	−	0.404754i	−0.830395	+	0.557175i	$0.811885\pi$
$420$		0			0
$421$	0.806922	−	7.67735i	0.0393270	−	0.374171i	−0.957103	−	0.289748i	$-0.906429\pi$
$421$	0.806922	−	7.67735i	0.0393270	−	0.374171i	0.996430	−	0.0844233i	$-0.0269048\pi$
$422$	1.98434	+	18.8797i	0.0965962	+	0.919052i
$423$		0			0
$424$	−19.4424	−	8.65633i	−0.944209	−	0.420389i
$425$	10.9358	−	12.1454i	0.530463	−	0.589139i
$426$		0			0
$427$	−28.1093	−	31.2185i	−1.36030	−	1.51077i
$428$	−9.74966	+	16.8869i	−0.471268	+	0.816259i
$429$		0			0
$430$	−23.3296	+	71.8012i	−1.12505	+	3.46256i
$431$	−23.9510	+	10.6637i	−1.15368	+	0.513652i	−0.892237	−	0.451567i	$-0.850865\pi$
$431$	−23.9510	+	10.6637i	−1.15368	+	0.513652i	−0.261444	+	0.965219i	$0.584199\pi$
$432$		0			0
$433$	22.6643			1.08918			0.544589	−	0.838703i	$-0.316685\pi$
$433$	22.6643			1.08918			0.544589	+	0.838703i	$0.316685\pi$
$434$	−31.5501	+	31.4728i	−1.51445	+	1.51074i
$435$		0			0
$436$	20.5888	−	14.9587i	0.986027	−	0.716390i
$437$	0.484084	−	0.215528i	0.0231569	−	0.0103101i
$438$		0			0
$439$	−11.0343	−	19.1119i	−0.526636	−	0.912161i	−0.999518	−	0.0310352i	$-0.990120\pi$
$439$	−11.0343	−	19.1119i	−0.526636	−	0.912161i	0.472882	−	0.881126i	$-0.343214\pi$
$440$	−14.4063	+	24.9524i	−0.686793	+	1.18956i
$441$		0			0
$442$	−3.12554	−	9.61941i	−0.148667	−	0.457549i
$443$	2.84672	−	3.16160i	0.135252	−	0.150212i	−0.671714	−	0.740811i	$-0.734442\pi$
$443$	2.84672	−	3.16160i	0.135252	−	0.150212i	0.806966	+	0.590598i	$0.201108\pi$
$444$		0			0
$445$	−23.2175	+	4.93504i	−1.10062	+	0.233943i
$446$	−6.32559	−	60.1839i	−0.299525	−	2.84979i
$447$		0			0
$448$	11.0416	+	2.34695i	0.521664	+	0.110883i
$449$	25.7852	+	18.7340i	1.21688	+	0.884113i	0.995837	−	0.0911522i	$-0.0290550\pi$
$449$	25.7852	+	18.7340i	1.21688	+	0.884113i	0.221040	+	0.975265i	$0.429055\pi$
$450$		0			0
$451$	4.39736	+	0.934688i	0.207064	+	0.0440127i
$452$	−7.13526	+	67.8874i	−0.335614	+	3.19316i
$453$		0			0
$454$	−7.30217	+	1.55212i	−0.342708	+	0.0728448i
$455$	26.0868	+	11.6146i	1.22297	+	0.544500i
$456$		0			0
$457$	−2.55831	−	7.87366i	−0.119673	−	0.368314i	0.873220	−	0.487326i	$-0.162028\pi$
$457$	−2.55831	−	7.87366i	−0.119673	−	0.368314i	−0.992893	+	0.119011i	$0.962028\pi$
$458$	−10.4488	−	11.6046i	−0.488242	−	0.542247i
$459$		0			0
$460$	6.49054	+	11.2419i	0.302623	+	0.524158i
$461$	3.47956	−	10.7090i	0.162059	−	0.498767i	−0.836748	−	0.547587i	$-0.815546\pi$
$461$	3.47956	−	10.7090i	0.162059	−	0.498767i	0.998808	+	0.0488209i	$0.0155464\pi$
$462$		0			0
$463$	16.5630	−	12.0337i	0.769746	−	0.559253i	−0.132138	−	0.991231i	$-0.542184\pi$
$463$	16.5630	−	12.0337i	0.769746	−	0.559253i	0.901884	+	0.431978i	$0.142184\pi$
$464$	81.6965			3.79266
$465$		0			0
$466$	60.3682			2.79650
$467$	−19.3637	+	14.0685i	−0.896045	+	0.651015i	−0.937447	−	0.348128i	$-0.886817\pi$
$467$	−19.3637	+	14.0685i	−0.896045	+	0.651015i	0.0414023	+	0.999143i	$0.486817\pi$
$468$		0			0
$469$	−2.53730	+	7.80900i	−0.117162	+	0.360586i
$470$	8.03289	+	13.9134i	0.370529	+	0.641776i
$471$		0			0
$472$	−47.4336	−	52.6804i	−2.18331	−	2.42481i
$473$	−2.54401	−	7.82965i	−0.116974	−	0.360007i
$474$		0			0
$475$	6.66654	+	2.96814i	0.305882	+	0.136187i
$476$	23.2547	−	4.94293i	1.06588	−	0.226559i
$477$		0			0
$478$	2.79638	−	26.6058i	0.127904	−	1.21692i
$479$	16.4014	+	3.48622i	0.749399	+	0.159290i	0.566751	−	0.823889i	$-0.308200\pi$
$479$	16.4014	+	3.48622i	0.749399	+	0.159290i	0.182647	+	0.983178i	$0.441533\pi$
$480$		0			0
$481$	4.48711	+	3.26008i	0.204595	+	0.148647i
$482$	20.8972	+	4.44183i	0.951839	+	0.202320i
$483$		0			0
$484$	4.78001	+	45.4787i	0.217273	+	2.06721i
$485$	45.8140	−	9.73806i	2.08030	−	0.442182i
$486$		0			0
$487$	−2.46520	+	2.73788i	−0.111709	+	0.124065i	−0.796406	−	0.604763i	$-0.793268\pi$
$487$	−2.46520	+	2.73788i	−0.111709	+	0.124065i	0.684697	+	0.728828i	$0.259935\pi$
$488$	−28.6988	−	88.3259i	−1.29913	−	3.99832i
$489$		0			0
$490$	−13.0729	+	22.6430i	−0.590574	+	1.02290i
$491$	−1.93176	−	3.34591i	−0.0871791	−	0.150999i	0.819139	−	0.573596i	$-0.194452\pi$
$491$	−1.93176	−	3.34591i	−0.0871791	−	0.150999i	−0.906318	+	0.422597i	$0.861119\pi$
$492$		0			0
$493$	14.6561	−	6.52531i	0.660077	−	0.293885i
$494$	3.65369	−	2.65456i	0.164387	−	0.119434i
$495$		0			0
$496$	−43.5755	+	16.6658i	−1.95660	+	0.748316i
$497$	−23.3017			−1.04523
$498$		0			0
$499$	−24.9120	+	11.0915i	−1.11522	+	0.496526i	−0.879788	−	0.475366i	$-0.842316\pi$
$499$	−24.9120	+	11.0915i	−1.11522	+	0.496526i	−0.235427	+	0.971892i	$0.575649\pi$
$500$	−27.4329	+	84.4297i	−1.22684	+	3.77581i
$501$		0			0
$502$	8.91173	−	15.4356i	0.397750	−	0.688923i
$503$	6.93122	+	7.69790i	0.309048	+	0.343232i	0.877581	−	0.479428i	$-0.159156\pi$
$503$	6.93122	+	7.69790i	0.309048	+	0.343232i	−0.568534	+	0.822660i	$0.692489\pi$
$504$		0			0
$505$	24.9961	−	27.7610i	1.11231	−	1.23535i
$506$	−1.84842	−	0.822972i	−0.0821725	−	0.0365856i
$507$		0			0
$508$	6.82768	+	64.9610i	0.302929	+	2.88218i
$509$	2.99643	−	28.5091i	0.132814	−	1.26364i	−0.701626	−	0.712545i	$-0.747542\pi$
$509$	2.99643	−	28.5091i	0.132814	−	1.26364i	0.834440	−	0.551098i	$-0.185791\pi$
$510$		0			0
$511$	−4.40209	−	3.19831i	−0.194737	−	0.141485i
$512$	−39.3876	−	28.6167i	−1.74070	−	1.26469i
$513$		0			0
$514$	−6.65665	+	63.3338i	−0.293612	+	2.79353i
$515$	−2.25772	−	21.4808i	−0.0994869	−	0.946555i
$516$		0			0
$517$	−1.60045	−	0.712566i	−0.0703877	−	0.0313386i
$518$	−12.4691	+	13.8483i	−0.547860	+	0.608460i
$519$		0			0
$520$	42.2419	+	46.9144i	1.85243	+	2.05733i
$521$	−4.39356	+	7.60986i	−0.192485	+	0.333394i	−0.946073	−	0.323953i	$-0.894988\pi$
$521$	−4.39356	+	7.60986i	−0.192485	+	0.333394i	0.753588	+	0.657347i	$0.228321\pi$
$522$		0			0
$523$	11.3608	−	34.9649i	0.496773	−	1.52891i	−0.317403	−	0.948291i	$-0.602811\pi$
$523$	11.3608	−	34.9649i	0.496773	−	1.52891i	0.814176	−	0.580618i	$-0.197189\pi$
$524$	58.8832	−	26.2165i	2.57233	−	1.14527i
$525$		0			0
$526$	−60.8301			−2.65232
$527$	−6.48616	+	6.47027i	−0.282541	+	0.281849i
$528$		0			0
$529$	18.1866	−	13.2133i	0.790720	−	0.574492i
$530$	28.2681	−	12.5858i	1.22789	−	0.546692i
$531$		0			0
$532$	5.30771	+	9.19323i	0.230119	+	0.398577i
$533$	4.92502	−	8.53039i	0.213327	−	0.369492i
$534$		0			0
$535$	−4.99905	−	15.3855i	−0.216128	−	0.665172i
$536$	−12.1463	+	13.4898i	−0.524639	+	0.582670i
$537$		0			0
$538$	−2.38892	+	0.507781i	−0.102994	+	0.0218920i
$539$	−0.298021	−	2.83548i	−0.0128367	−	0.122133i
$540$		0			0
$541$	−5.92038	−	1.25842i	−0.254537	−	0.0541035i	0.0788758	−	0.996884i	$-0.474867\pi$
$541$	−5.92038	−	1.25842i	−0.254537	−	0.0541035i	−0.333413	+	0.942781i	$0.608200\pi$
$542$	65.2104	+	47.3781i	2.80103	+	2.03506i
$543$		0			0
$544$	12.7235	+	2.70447i	0.545517	+	0.115953i
$545$	−2.20696	+	20.9978i	−0.0945357	+	0.899447i
$546$		0			0
$547$	3.80881	−	0.809587i	0.162853	−	0.0346155i	−0.125764	−	0.992060i	$-0.540138\pi$
$547$	3.80881	−	0.809587i	0.162853	−	0.0346155i	0.288617	+	0.957445i	$0.406805\pi$
$548$	−24.0636	−	10.7138i	−1.02795	−	0.457671i
$549$		0			0
$550$	−8.61060	−	26.5007i	−0.367157	−	1.12999i
$551$	4.79325	+	5.32344i	0.204199	+	0.226786i
$552$		0			0
$553$	17.1125	+	29.6397i	0.727696	+	1.26041i
$554$	−22.0565	+	67.8830i	−0.937091	+	2.88407i
$555$		0			0
$556$	21.3113	−	15.4836i	0.903801	−	0.656650i
$557$	−36.1880			−1.53334			−0.766668	−	0.642044i	$-0.778087\pi$
$557$	−36.1880			−1.53334			−0.766668	+	0.642044i	$0.778087\pi$
$558$		0			0
$559$	−18.0379			−0.762923
$560$	−81.2577	+	59.0372i	−3.43377	+	2.49478i
$561$		0			0
$562$	−6.59419	+	20.2948i	−0.278159	+	0.856085i
$563$	5.47949	+	9.49076i	0.230933	+	0.399988i	0.958083	−	0.286491i	$-0.0924888\pi$
$563$	5.47949	+	9.49076i	0.230933	+	0.399988i	−0.727150	+	0.686479i	$0.759155\pi$
$564$		0			0
$565$	−37.8941	−	42.0856i	−1.59422	−	1.77056i
$566$	−0.657564	−	2.02377i	−0.0276395	−	0.0850655i
$567$		0			0
$568$	−47.0610	−	20.9529i	−1.97464	−	0.879164i
$569$	5.61416	−	1.19333i	0.235358	−	0.0500269i	−0.0887226	−	0.996056i	$-0.528278\pi$
$569$	5.61416	−	1.19333i	0.235358	−	0.0500269i	0.324081	+	0.946030i	$0.394945\pi$
$570$		0			0
$571$	2.17507	−	20.6944i	0.0910238	−	0.866033i	−0.849793	−	0.527117i	$-0.823273\pi$
$571$	2.17507	−	20.6944i	0.0910238	−	0.866033i	0.940816	−	0.338916i	$-0.110060\pi$
$572$	−11.8007	−	2.50832i	−0.493412	−	0.104878i
$573$		0			0
$574$	26.7738	+	19.4523i	1.11752	+	0.811924i
$575$	−7.00686	−	1.48935i	−0.292206	−	0.0621103i
$576$		0			0
$577$	−0.234062	−	2.22695i	−0.00974414	−	0.0927093i	0.988569	−	0.150770i	$-0.0481751\pi$
$577$	−0.234062	−	2.22695i	−0.00974414	−	0.0927093i	−0.998313	+	0.0580602i	$0.981508\pi$
$578$	−36.0724	+	7.66742i	−1.50041	+	0.318923i
$579$		0			0
$580$	−117.422	+	130.410i	−4.87569	+	5.41500i
$581$	10.4567	+	32.1823i	0.433816	+	1.33515i
$582$		0			0
$583$	−1.68712	+	2.92219i	−0.0698736	+	0.121025i
$584$	−6.01470	−	10.4178i	−0.248890	−	0.431090i
$585$		0			0
$586$	−8.30987	+	3.69979i	−0.343278	+	0.152837i
$587$	−8.76402	+	6.36744i	−0.361730	+	0.262812i	−0.753773	−	0.657135i	$-0.771768\pi$
$587$	−8.76402	+	6.36744i	−0.361730	+	0.262812i	0.392043	+	0.919947i	$0.371768\pi$
$588$		0			0
$589$	−3.64260	−	1.86163i	−0.150091	−	0.0767070i
$590$	103.068			4.24322
$591$		0			0
$592$	−17.8220	+	7.93486i	−0.732480	+	0.326121i
$593$	−2.39504	+	7.37117i	−0.0983524	+	0.302698i	−0.988113	−	0.153730i	$-0.950871\pi$
$593$	−2.39504	+	7.37117i	−0.0983524	+	0.302698i	0.889760	+	0.456428i	$0.150871\pi$
$594$		0			0
$595$	−9.86191	+	17.0813i	−0.404299	+	0.700267i
$596$	−52.5820	−	58.3982i	−2.15384	−	2.39208i
$597$		0			0
$598$	−2.96642	+	3.29455i	−0.121306	+	0.134724i
$599$	7.29277	+	3.24695i	0.297974	+	0.132667i	0.550278	−	0.834981i	$-0.314522\pi$
$599$	7.29277	+	3.24695i	0.297974	+	0.132667i	−0.252304	+	0.967648i	$0.581188\pi$
$600$		0			0
$601$	−2.68517	−	25.5477i	−0.109531	−	1.04211i	−0.901863	−	0.432023i	$-0.857800\pi$
$601$	−2.68517	−	25.5477i	−0.109531	−	1.04211i	0.792332	−	0.610090i	$-0.208867\pi$
$602$	6.33484	−	60.2719i	0.258189	−	2.45650i
$603$		0			0
$604$	−17.0115	−	12.3596i	−0.692187	−	0.502903i
$605$	−30.6928	−	22.2996i	−1.24784	−	0.906609i
$606$		0			0
$607$	1.84497	−	17.5537i	0.0748850	−	0.712483i	−0.891086	−	0.453834i	$-0.850056\pi$
$607$	1.84497	−	17.5537i	0.0748850	−	0.712483i	0.965971	−	0.258649i	$-0.0832774\pi$
$608$	0.607113	+	5.77630i	0.0246217	+	0.234260i
$609$		0			0
$610$	123.355	+	54.9213i	4.99451	+	2.22370i
$611$	−2.56846	+	2.85257i	−0.103909	+	0.115403i
$612$		0			0
$613$	−28.3742	−	31.5127i	−1.14602	−	1.27279i	−0.956766	−	0.290859i	$-0.906059\pi$
$613$	−28.3742	−	31.5127i	−1.14602	−	1.27279i	−0.189256	−	0.981928i	$-0.560608\pi$
$614$	−11.4944	+	19.9089i	−0.463877	+	0.803459i
$615$		0			0
$616$	7.14726	−	21.9970i	0.287971	−	0.886285i
$617$	−31.1398	+	13.8643i	−1.25364	+	0.558157i	−0.922709	−	0.385498i	$-0.874030\pi$
$617$	−31.1398	+	13.8643i	−1.25364	+	0.558157i	−0.330932	+	0.943655i	$0.607363\pi$
$618$		0			0
$619$	−6.20601			−0.249441			−0.124720	−	0.992192i	$-0.539803\pi$
$619$	−6.20601			−0.249441			−0.124720	+	0.992192i	$0.539803\pi$
$620$	36.0276	−	93.5123i	1.44690	−	3.75554i
$621$		0			0
$622$	54.5195	−	39.6107i	2.18603	−	1.58825i
$623$	17.4067	−	7.74997i	0.697385	−	0.310496i
$624$		0			0
$625$	−11.9944	−	20.7750i	−0.479777	−	0.830999i
$626$	−6.54981	+	11.3446i	−0.261783	+	0.453422i
$627$		0			0
$628$	−11.3193	−	34.8371i	−0.451687	−	1.39015i
$629$	−2.56343	+	2.84698i	−0.102211	+	0.113516i
$630$		0			0
$631$	−20.2648	+	4.30743i	−0.806731	+	0.171476i	−0.592776	−	0.805368i	$-0.701968\pi$
$631$	−20.2648	+	4.30743i	−0.806731	+	0.171476i	−0.213955	+	0.976843i	$0.568635\pi$
$632$	7.90897	+	75.2488i	0.314602	+	2.99324i
$633$		0			0
$634$	−14.0883	−	2.99456i	−0.559517	−	0.118929i
$635$	−43.8411	−	31.8524i	−1.73978	−	1.26403i
$636$		0			0
$637$	−6.11037	−	1.29880i	−0.242102	−	0.0514603i
$638$	2.85913	−	27.2028i	0.113194	−	1.07697i
$639$		0			0
$640$	24.2690	−	5.15854i	0.959318	−	0.203909i
$641$	36.0859	+	16.0665i	1.42531	+	0.634588i	0.967132	−	0.254274i	$-0.0818363\pi$
$641$	36.0859	+	16.0665i	1.42531	+	0.634588i	0.458176	+	0.888862i	$0.348503\pi$
$642$		0			0
$643$	9.75533	+	30.0238i	0.384713	+	1.18402i	0.936689	+	0.350163i	$0.113874\pi$
$643$	9.75533	+	30.0238i	0.384713	+	1.18402i	−0.551976	+	0.833860i	$0.686126\pi$
$644$	−6.97263	−	7.74389i	−0.274760	−	0.305152i
$645$		0			0
$646$	1.55971	+	2.70151i	0.0613662	+	0.106289i
$647$	8.38234	−	25.7982i	0.329544	−	1.01423i	−0.639804	−	0.768538i	$-0.720984\pi$
$647$	8.38234	−	25.7982i	0.329544	−	1.01423i	0.969348	−	0.245693i	$-0.0790157\pi$
$648$		0			0
$649$	−9.09263	+	6.60619i	−0.356917	+	0.259315i
$650$	−61.0523			−2.39467
$651$		0			0
$652$	60.6500			2.37524
$653$	−0.429357	+	0.311946i	−0.0168020	+	0.0122074i	−0.596155	−	0.802870i	$-0.703305\pi$
$653$	−0.429357	+	0.311946i	−0.0168020	+	0.0122074i	0.579353	+	0.815077i	$0.303305\pi$
$654$		0			0
$655$	−16.5245	+	50.8573i	−0.645667	+	1.98716i
$656$	17.3231	+	30.0045i	0.676353	+	1.17148i
$657$		0			0
$658$	−8.62954	−	9.58408i	−0.336415	−	0.373626i
$659$	4.88814	+	15.0442i	0.190415	+	0.586037i	1.00000		0.000966277i	$-0.000307576\pi$
$659$	4.88814	+	15.0442i	0.190415	+	0.586037i	−0.809585	+	0.587003i	$0.800308\pi$
$660$		0			0
$661$	36.5859	+	16.2891i	1.42303	+	0.633573i	0.966624	−	0.256200i	$-0.0824707\pi$
$661$	36.5859	+	16.2891i	1.42303	+	0.633573i	0.456403	+	0.889773i	$0.349137\pi$
$662$	−9.31967	+	1.98096i	−0.362219	+	0.0769921i
$663$		0			0
$664$	−7.81967	+	74.3992i	−0.303462	+	2.88725i
$665$	−8.61444	−	1.83106i	−0.334054	−	0.0710053i
$666$		0			0
$667$	−5.68886	−	4.13320i	−0.220274	−	0.160038i
$668$	96.9277	+	20.6026i	3.75025	+	0.797139i
$669$		0			0
$670$	−2.75875	−	26.2478i	−0.106580	−	1.01404i
$671$	−14.4026	+	3.06138i	−0.556008	+	0.118183i
$672$		0			0
$673$	−9.68290	+	10.7539i	−0.373248	+	0.414534i	−0.900280	−	0.435312i	$-0.856638\pi$
$673$	−9.68290	+	10.7539i	−0.373248	+	0.414534i	0.527032	+	0.849846i	$0.323305\pi$
$674$	26.2732	+	80.8605i	1.01200	+	3.11463i
$675$		0			0
$676$	17.0587	−	29.5466i	0.656105	−	1.13641i
$677$	−13.1537	−	22.7829i	−0.505538	−	0.875618i	−0.999979	−	0.00640672i	$-0.997961\pi$
$677$	−13.1537	−	22.7829i	−0.505538	−	0.875618i	0.494441	−	0.869211i	$-0.335373\pi$
$678$		0			0
$679$	−34.3478	+	15.2926i	−1.31815	+	0.586877i
$680$	−35.2770	+	25.6302i	−1.35281	+	0.982875i
$681$		0			0
$682$	4.02427	+	15.0928i	0.154097	+	0.577932i
$683$	−4.22266			−0.161575			−0.0807877	−	0.996731i	$-0.525744\pi$
$683$	−4.22266			−0.161575			−0.0807877	+	0.996731i	$0.525744\pi$
$684$		0			0
$685$	19.9639	−	8.88852i	0.762783	−	0.339613i
$686$	−10.8277	+	33.3242i	−0.413403	+	1.27232i
$687$		0			0
$688$	31.7230	−	54.9458i	1.20943	−	2.09479i
$689$	4.94696	+	5.49416i	0.188464	+	0.209311i
$690$		0			0
$691$	−23.4319	+	26.0237i	−0.891391	+	0.989990i	−0.999992	−	0.00409566i	$-0.998696\pi$
$691$	−23.4319	+	26.0237i	−0.891391	+	0.989990i	0.108601	+	0.994085i	$0.465363\pi$
$692$	54.0417	+	24.0609i	2.05436	+	0.914659i
$693$		0			0
$694$	2.07921	+	19.7824i	0.0789257	+	0.750928i
$695$	−2.28440	+	21.7346i	−0.0866523	+	0.824441i
$696$		0			0
$697$	5.50424	+	3.99906i	0.208488	+	0.151475i
$698$	53.4174	+	38.8100i	2.02188	+	1.46898i
$699$		0			0
$700$	15.0003	−	142.718i	0.566958	−	5.39425i
$701$	−1.63569	−	15.5626i	−0.0617793	−	0.587791i	−0.980995	−	0.194035i	$-0.937842\pi$
$701$	−1.63569	−	15.5626i	−0.0617793	−	0.587791i	0.919215	−	0.393755i	$-0.128824\pi$
$702$		0			0
$703$	−1.56269	−	0.695753i	−0.0589379	−	0.0262408i
$704$	2.64750	−	2.94035i	0.0997814	−	0.110818i
$705$		0			0
$706$	−13.7900	−	15.3154i	−0.518994	−	0.576401i
$707$	−14.9936	+	25.9697i	−0.563894	+	0.976693i
$708$		0			0
$709$	11.5303	−	35.4865i	0.433028	−	1.33272i	−0.462067	−	0.886845i	$-0.652892\pi$
$709$	11.5303	−	35.4865i	0.433028	−	1.33272i	0.895094	−	0.445877i	$-0.147108\pi$
$710$	68.4238	−	30.4643i	2.56790	−	1.14330i
$711$		0			0
$712$	42.1240			1.57866
$713$	3.87750	+	1.04407i	0.145213	+	0.0391007i
$714$		0			0
$715$	8.09742	−	5.88312i	0.302826	−	0.220016i
$716$	−65.0771	+	28.9742i	−2.43204	+	1.08282i
$717$		0			0
$718$	−6.08591	−	10.5411i	−0.227124	−	0.393391i
$719$	17.7379	−	30.7229i	0.661511	−	1.14577i	−0.318708	−	0.947853i	$-0.603249\pi$
$719$	17.7379	−	30.7229i	0.661511	−	1.14577i	0.980219	−	0.197917i	$-0.0634176\pi$
$720$		0			0
$721$	5.35788	+	16.4899i	0.199538	+	0.614114i
$722$	31.8721	−	35.3976i	1.18616	−	1.31736i
$723$		0			0
$724$	77.6694	−	16.5091i	2.88656	−	0.613558i
$725$	−10.1224	−	96.3078i	−0.375935	−	3.57678i
$726$		0			0
$727$	7.11776	+	1.51293i	0.263983	+	0.0561114i	0.338002	−	0.941146i	$-0.390249\pi$
$727$	7.11776	+	1.51293i	0.263983	+	0.0561114i	−0.0740185	+	0.997257i	$0.523582\pi$
$728$	−40.9983	−	29.7870i	−1.51950	−	1.10398i
$729$		0			0
$730$	17.1078	+	3.63638i	0.633189	+	0.134588i
$731$	1.30233	−	12.3909i	0.0481686	−	0.458293i
$732$		0			0
$733$	−2.43273	+	0.517093i	−0.0898550	+	0.0190993i	−0.252620	−	0.967566i	$-0.581292\pi$
$733$	−2.43273	+	0.517093i	−0.0898550	+	0.0190993i	0.162765	+	0.986665i	$0.447959\pi$
$734$	−57.7305	−	25.7033i	−2.13087	−	0.948725i
$735$		0			0
$736$	−1.76184	−	5.42238i	−0.0649422	−	0.199872i
$737$	1.92575	+	2.13876i	0.0709358	+	0.0787822i
$738$		0			0
$739$	6.27959	+	10.8766i	0.230998	+	0.400101i	0.958102	−	0.286427i	$-0.0924675\pi$
$739$	6.27959	+	10.8766i	0.230998	+	0.400101i	−0.727104	+	0.686528i	$0.759134\pi$
$740$	12.9492	−	39.8536i	0.476023	−	1.46505i
$741$		0			0
$742$	−20.0956	+	14.6003i	−0.737731	+	0.535993i
$743$	16.9054			0.620198			0.310099	−	0.950704i	$-0.399638\pi$
$743$	16.9054			0.620198			0.310099	+	0.950704i	$0.399638\pi$
$744$		0			0
$745$	65.1946			2.38854
$746$	3.31255	−	2.40671i	0.121281	−	0.0881157i
$747$		0			0
$748$	2.57506	−	7.92522i	0.0941535	−	0.289775i
$749$	6.49307	+	11.2463i	0.237252	+	0.410932i
$750$		0			0
$751$	28.2436	+	31.3677i	1.03062	+	1.14462i	0.989362	+	0.145474i	$0.0464707\pi$
$751$	28.2436	+	31.3677i	1.03062	+	1.14462i	0.0412605	+	0.999148i	$0.486863\pi$
$752$	−4.17217	−	12.8406i	−0.152143	−	0.468249i
$753$		0			0
$754$	−54.7496	−	24.3761i	−1.99386	−	0.887724i
$755$	17.0637	−	3.62701i	0.621013	−	0.132000i
$756$		0			0
$757$	−1.15362	+	10.9760i	−0.0419290	+	0.398928i	0.953350	+	0.301868i	$0.0976103\pi$
$757$	−1.15362	+	10.9760i	−0.0419290	+	0.398928i	−0.995279	+	0.0970593i	$0.969056\pi$
$758$	19.3713	+	4.11749i	0.703597	+	0.149554i
$759$		0			0
$760$	−15.7515	−	11.4442i	−0.571369	−	0.415124i
$761$	−14.8990	−	3.16687i	−0.540087	−	0.114799i	−0.0702120	−	0.997532i	$-0.522368\pi$
$761$	−14.8990	−	3.16687i	−0.540087	−	0.114799i	−0.469875	+	0.882733i	$0.655701\pi$
$762$		0			0
$763$	−1.77162	−	16.8558i	−0.0641368	−	0.610221i
$764$	−43.8145	+	9.31307i	−1.58515	+	0.336935i
$765$		0			0
$766$	−20.2491	+	22.4889i	−0.731629	+	0.812556i
$767$	7.60966	+	23.4201i	0.274769	+	0.845652i
$768$		0			0
$769$	−7.88074	+	13.6498i	−0.284187	+	0.492226i	−0.972412	−	0.233271i	$-0.925057\pi$
$769$	−7.88074	+	13.6498i	−0.284187	+	0.492226i	0.688225	+	0.725498i	$0.258390\pi$
$770$	16.8141	+	29.1229i	0.605938	+	1.04952i
$771$		0			0
$772$	42.1462	−	18.7647i	1.51688	−	0.675357i
$773$	−17.2180	+	12.5096i	−0.619287	+	0.449939i	−0.852673	−	0.522446i	$-0.825020\pi$
$773$	−17.2180	+	12.5096i	−0.619287	+	0.449939i	0.233385	+	0.972384i	$0.425020\pi$
$774$		0			0
$775$	25.0455	+	49.3040i	0.899662	+	1.77105i
$776$	−83.1211			−2.98387
$777$		0			0
$778$	−10.8670	+	4.83830i	−0.389601	+	0.173461i
$779$	−0.938758	+	2.88920i	−0.0336345	+	0.103516i
$780$		0			0
$781$	−4.08373	+	7.07323i	−0.146127	+	0.253100i
$782$	−2.04897	−	2.27561i	−0.0732708	−	0.0813755i
$783$		0			0
$784$	14.7025	−	16.3288i	0.525090	−	0.583171i
$785$	27.7620	+	12.3604i	0.990869	+	0.441163i
$786$		0			0
$787$	−0.268859	−	2.55803i	−0.00958380	−	0.0911838i	0.988684	−	0.150010i	$-0.0479307\pi$
$787$	−0.268859	−	2.55803i	−0.00958380	−	0.0911838i	−0.998268	+	0.0588267i	$0.981264\pi$
$788$	10.9822	−	104.488i	0.391223	−	3.72224i
$789$		0			0
$790$	−88.9999	−	64.6622i	−3.16647	−	2.30058i
$791$	36.7785	+	26.7211i	1.30769	+	0.950093i
$792$		0			0
$793$	−3.37228	+	32.0851i	−0.119753	+	1.13937i
$794$	8.65984	+	82.3928i	0.307326	+	2.92401i
$795$		0			0
$796$	−33.8741	−	15.0817i	−1.20064	−	0.534558i
$797$	21.6032	−	23.9928i	0.765224	−	0.849867i	−0.227057	−	0.973882i	$-0.572910\pi$
$797$	21.6032	−	23.9928i	0.765224	−	0.849867i	0.992280	+	0.124015i	$0.0395770\pi$
$798$		0			0
$799$	−1.77409	−	1.97032i	−0.0627627	−	0.0697050i
$800$	39.2584	−	67.9976i	1.38800	−	2.40408i
$801$		0			0
$802$	1.97109	−	6.06640i	0.0696017	−	0.214212i
$803$	−1.74233	+	0.775736i	−0.0614855	+	0.0273751i
$804$		0			0
$805$	8.64513			0.304701
$806$	34.1751	+	1.83306i	1.20377	+	0.0645668i
$807$		0			0
$808$	−53.6337	+	38.9671i	−1.88683	+	1.37086i
$809$	8.45847	−	3.76596i	0.297384	−	0.132404i	−0.252621	−	0.967565i	$-0.581293\pi$
$809$	8.45847	−	3.76596i	0.297384	−	0.132404i	0.550005	+	0.835161i	$0.314626\pi$
$810$		0			0
$811$	24.7603	+	42.8861i	0.869452	+	1.50593i	0.862558	+	0.505958i	$0.168861\pi$
$811$	24.7603	+	42.8861i	0.869452	+	1.50593i	0.00689343	+	0.999976i	$0.497806\pi$
$812$	70.4343	−	121.996i	2.47176	−	4.28121i
$813$		0			0
$814$	2.01839	+	6.21196i	0.0707445	+	0.217729i
$815$	−33.6687	+	37.3929i	−1.17936	+	1.30982i
$816$		0			0
$817$	5.44156	−	1.15664i	0.190376	−	0.0404657i
$818$	5.47938	+	52.1328i	0.191582	+	1.82278i
$819$		0			0
$820$	−72.7940	−	15.4728i	−2.54208	−	0.540335i
$821$	−11.1586	−	8.10722i	−0.389439	−	0.282944i	0.375787	−	0.926706i	$-0.377373\pi$
$821$	−11.1586	−	8.10722i	−0.389439	−	0.282944i	−0.765226	+	0.643762i	$0.777373\pi$
$822$		0			0
$823$	−19.5004	−	4.14495i	−0.679742	−	0.144484i	−0.144914	−	0.989444i	$-0.546290\pi$
$823$	−19.5004	−	4.14495i	−0.679742	−	0.144484i	−0.534829	+	0.844961i	$0.679624\pi$
$824$	−4.00671	+	38.1213i	−0.139580	+	1.32802i
$825$		0			0
$826$	−80.9285	+	17.2019i	−2.81586	+	0.598530i
$827$	−28.0336	−	12.4814i	−0.974825	−	0.434020i	−0.143405	−	0.989664i	$-0.545805\pi$
$827$	−28.0336	−	12.4814i	−0.974825	−	0.434020i	−0.831420	+	0.555644i	$0.812472\pi$
$828$		0			0
$829$	−8.61884	−	26.5261i	−0.299345	−	0.921289i	−0.981727	−	0.190293i	$-0.939056\pi$
$829$	−8.61884	−	26.5261i	−0.299345	−	0.921289i	0.682382	−	0.730995i	$-0.260944\pi$
$830$	−72.7798	−	80.8302i	−2.52622	−	2.80566i
$831$		0			0
$832$	−4.33457	−	7.50769i	−0.150274	−	0.260282i
$833$	1.33336	−	4.10366i	0.0461981	−	0.142183i
$834$		0			0
$835$	−66.5099	+	48.3223i	−2.30167	+	1.67226i
$836$	3.72080			0.128687
$837$		0			0
$838$	−36.3701			−1.25638
$839$	−30.0289	+	21.8172i	−1.03671	+	0.753215i	−0.969641	−	0.244533i	$-0.921365\pi$
$839$	−30.0289	+	21.8172i	−1.03671	+	0.753215i	−0.0670707	+	0.997748i	$0.521365\pi$
$840$		0			0
$841$	20.4135	−	62.8264i	0.703915	−	2.16643i
$842$	−9.95936	−	17.2501i	−0.343222	−	0.594478i
$843$		0			0
$844$	22.9301	+	25.4665i	0.789287	+	0.876592i
$845$	8.74671	+	26.9196i	0.300896	+	0.926063i
$846$		0			0
$847$	27.8218	+	12.3870i	0.955967	+	0.425624i
$848$	−25.4360	+	5.40660i	−0.873477	+	0.185663i
$849$		0			0
$850$	4.40796	−	41.9389i	0.151192	−	1.43849i
$851$	1.64246	+	0.349116i	0.0563028	+	0.0119675i
$852$		0			0
$853$	14.9845	+	10.8868i	0.513058	+	0.372758i	0.813982	−	0.580890i	$-0.197295\pi$
$853$	14.9845	+	10.8868i	0.513058	+	0.372758i	−0.300924	+	0.953648i	$0.597295\pi$
$854$	−106.025	−	22.5363i	−3.62809	−	0.771175i
$855$		0			0
$856$	3.00094	+	28.5520i	0.102570	+	0.975889i
$857$	54.2375	−	11.5285i	1.85272	−	0.393807i	0.859605	−	0.510960i	$-0.170710\pi$
$857$	54.2375	−	11.5285i	1.85272	−	0.393807i	0.993114	+	0.117152i	$0.0373766\pi$
$858$		0			0
$859$	37.2700	−	41.3925i	1.27164	−	1.41230i	0.404259	−	0.914645i	$-0.367529\pi$
$859$	37.2700	−	41.3925i	1.27164	−	1.41230i	0.867378	−	0.497651i	$-0.165804\pi$
$860$	42.1135	+	129.612i	1.43606	+	4.41973i
$861$		0			0
$862$	−33.8243	+	58.5854i	−1.15206	+	1.99543i
$863$	−21.4622	−	37.1736i	−0.730581	−	1.26540i	−0.956635	−	0.291289i	$-0.905916\pi$
$863$	−21.4622	−	37.1736i	−0.730581	−	1.26540i	0.226054	−	0.974115i	$-0.427417\pi$
$864$		0			0
$865$	−44.8347	+	19.9617i	−1.52443	+	0.678719i
$866$	47.3113	−	34.3737i	1.60770	−	1.16807i
$867$		0			0
$868$	−12.6817	+	79.4387i	−0.430446	+	2.69633i
$869$	11.9962			0.406942
$870$		0			0
$871$	5.76062	−	2.56479i	0.195191	−	0.0869047i
$872$	11.5787	−	35.6356i	0.392104	−	1.20677i
$873$		0			0
$874$	0.683637	−	1.18409i	0.0231244	−	0.0400526i
$875$	39.5604	+	43.9363i	1.33739	+	1.48532i
$876$		0			0
$877$	0.430758	−	0.478406i	0.0145457	−	0.0161546i	−0.735828	−	0.677168i	$-0.763207\pi$
$877$	0.430758	−	0.478406i	0.0145457	−	0.0161546i	0.750374	+	0.661014i	$0.229874\pi$
$878$	−52.0197	−	23.1606i	−1.75558	−	0.781634i
$879$		0			0
$880$	3.67994	+	35.0123i	0.124051	+	1.18026i
$881$	0.975867	−	9.28476i	0.0328778	−	0.312811i	−0.965707	−	0.259633i	$-0.916398\pi$
$881$	0.975867	−	9.28476i	0.0328778	−	0.312811i	0.998585	−	0.0531780i	$-0.0169351\pi$
$882$		0			0
$883$	−33.4000	−	24.2665i	−1.12400	−	0.816632i	−0.139188	−	0.990266i	$-0.544449\pi$
$883$	−33.4000	−	24.2665i	−1.12400	−	0.816632i	−0.984810	+	0.173634i	$0.944449\pi$
$884$	−14.7711	−	10.7318i	−0.496806	−	0.360951i
$885$		0			0
$886$	1.14745	−	10.9172i	0.0385492	−	0.366771i
$887$	−3.21546	−	30.5931i	−0.107965	−	1.02722i	−0.905617	−	0.424097i	$-0.860591\pi$
$887$	−3.21546	−	30.5931i	−0.107965	−	1.02722i	0.797652	−	0.603118i	$-0.206075\pi$
$888$		0			0
$889$	39.7401	+	17.6934i	1.33284	+	0.593419i
$890$	−40.9814	+	45.5144i	−1.37370	+	1.52565i
$891$		0			0
$892$	−73.0955	−	81.1808i	−2.44742	−	2.71813i
$893$	0.591923	−	1.02524i	0.0198080	−	0.0343084i
$894$		0			0
$895$	18.2627	−	56.2069i	0.610456	−	1.87879i
$896$	−18.1951	+	8.10097i	−0.607855	+	0.270634i
$897$		0			0
$898$	82.2387			2.74434
$899$	2.77458	+	54.2139i	0.0925374	+	1.80814i
$900$		0			0
$901$	−4.13130	+	3.00157i	−0.137634	+	0.0999967i
$902$	10.5970	−	4.71808i	0.352841	−	0.157095i
$903$		0			0
$904$	50.2514	+	87.0381i	1.67134	+	2.89484i
$905$	−32.9383	+	57.0508i	−1.09491	+	1.89643i
$906$		0			0
$907$	9.94174	+	30.5975i	0.330110	+	1.01597i	0.969081	+	0.246743i	$0.0793604\pi$
$907$	9.94174	+	30.5975i	0.330110	+	1.01597i	−0.638971	+	0.769231i	$0.720640\pi$
$908$	−9.01721	+	10.0146i	−0.299246	+	0.332347i
$909$		0			0
$910$	72.0707	−	15.3191i	2.38912	−	0.507823i
$911$	1.81555	+	17.2738i	0.0601518	+	0.572306i	0.982541	+	0.186045i	$0.0595671\pi$
$911$	1.81555	+	17.2738i	0.0601518	+	0.572306i	−0.922389	+	0.386261i	$0.873766\pi$
$912$		0			0
$913$	11.6015	+	2.46598i	0.383954	+	0.0816119i
$914$	−17.2819	−	12.5561i	−0.571636	−	0.415318i
$915$		0			0
$916$	−27.5724	−	5.86069i	−0.911018	−	0.193643i
$917$	4.48701	−	42.6910i	0.148174	−	1.40978i
$918$		0			0
$919$	−46.9202	+	9.97320i	−1.54776	+	0.328986i	−0.901037	−	0.433743i	$-0.857193\pi$
$919$	−46.9202	+	9.97320i	−1.54776	+	0.328986i	−0.646719	+	0.762728i	$0.723859\pi$
$920$	17.4600	+	7.77369i	0.575639	+	0.256291i
$921$		0			0
$922$	−8.97818	−	27.6320i	−0.295680	−	0.910011i
$923$	11.9743	+	13.2988i	0.394138	+	0.437734i
$924$		0			0
$925$	11.5622	+	20.0263i	0.380162	+	0.658460i
$926$	16.3240	−	50.2401i	0.536440	−	1.65099i
$927$		0			0
$928$	62.3547	−	45.3034i	2.04689	−	1.48716i
$929$	36.7464			1.20561			0.602805	−	0.797888i	$-0.294050\pi$
$929$	36.7464			1.20561			0.602805	+	0.797888i	$0.294050\pi$
$930$		0			0
$931$	1.92662			0.0631424
$932$	88.1616	−	64.0532i	2.88783	−	2.09813i
$933$		0			0
$934$	−19.0843	+	58.7356i	−0.624459	+	1.92189i
$935$	3.45669	+	5.98716i	0.113046	+	0.195801i
$936$		0			0
$937$	20.0011	+	22.2135i	0.653407	+	0.725682i	0.975249	−	0.221111i	$-0.0709684\pi$
$937$	20.0011	+	22.2135i	0.653407	+	0.725682i	−0.321841	+	0.946794i	$0.604302\pi$
$938$	6.54690	+	20.1493i	0.213764	+	0.657898i
$939$		0			0
$940$	26.4939	+	11.7958i	0.864134	+	0.384737i
$941$	−11.8565	+	2.52017i	−0.386510	+	0.0821553i	−0.397069	−	0.917789i	$-0.629972\pi$
$941$	−11.8565	+	2.52017i	−0.386510	+	0.0821553i	0.0105582	+	0.999944i	$0.496639\pi$
$942$		0			0
$943$	0.311713	−	2.96575i	0.0101508	−	0.0965780i
$944$	−84.7236	−	18.0086i	−2.75752	−	0.586129i
$945$		0			0
$946$	−17.1853	−	12.4859i	−0.558743	−	0.405951i
$947$	−20.9933	−	4.46226i	−0.682191	−	0.145004i	−0.146235	−	0.989250i	$-0.546715\pi$
$947$	−20.9933	−	4.46226i	−0.682191	−	0.145004i	−0.535956	+	0.844246i	$0.680049\pi$
$948$		0			0
$949$	0.436803	+	4.15590i	0.0141792	+	0.134906i
$950$	18.4179	−	3.91484i	0.597554	−	0.127014i
$951$		0			0
$952$	23.4218	−	26.0125i	0.759105	−	0.843071i
$953$	0.178594	+	0.549655i	0.00578522	+	0.0178051i	0.953907	−	0.300101i	$-0.0970204\pi$
$953$	0.178594	+	0.549655i	0.00578522	+	0.0178051i	−0.948122	+	0.317906i	$0.897020\pi$
$954$		0			0
$955$	18.5810	−	32.1833i	0.601267	−	1.04143i
$956$	−24.1460	−	41.8221i	−0.780938	−	1.35262i
$957$		0			0
$958$	39.5249	−	17.5976i	1.27699	−	0.568553i
$959$	−14.1922	+	10.3112i	−0.458289	+	0.332967i
$960$		0			0
$961$	−12.5394	−	28.3507i	−0.404495	−	0.914540i
$962$	14.3111			0.461409
$963$		0			0
$964$	35.2311	−	15.6859i	1.13472	−	0.505209i
$965$	−11.8276	+	36.4016i	−0.380744	+	1.17181i
$966$		0			0
$967$	18.3533	−	31.7888i	0.590202	−	1.02226i	−0.404003	−	0.914758i	$-0.632381\pi$
$967$	18.3533	−	31.7888i	0.590202	−	1.02226i	0.994205	−	0.107502i	$-0.0342853\pi$
$968$	45.0514	+	50.0346i	1.44801	+	1.60817i
$969$		0			0
$970$	80.8665	−	89.8113i	2.59647	−	2.88367i
$971$	25.0672	+	11.1606i	0.804443	+	0.358161i	0.767413	−	0.641153i	$-0.221544\pi$
$971$	25.0672	+	11.1606i	0.804443	+	0.358161i	0.0370301	+	0.999314i	$0.488210\pi$
$972$		0			0
$973$	−1.83378	−	17.4473i	−0.0587884	−	0.559334i
$974$	−0.993666	+	9.45410i	−0.0318391	+	0.302929i
$975$		0			0
$976$	−91.8044	−	66.6998i	−2.93859	−	2.13501i
$977$	11.1842	+	8.12581i	0.357815	+	0.259968i	0.752140	−	0.659003i	$-0.229022\pi$
$977$	11.1842	+	8.12581i	0.357815	+	0.259968i	−0.394325	+	0.918971i	$0.629022\pi$
$978$		0			0
$979$	0.698105	−	6.64202i	0.0223115	−	0.212280i
$980$	4.93345	+	46.9386i	0.157593	+	1.49940i
$981$		0			0
$982$	−9.10705	−	4.05472i	−0.290618	−	0.129391i
$983$	8.13914	−	9.03943i	0.259598	−	0.288313i	−0.599230	−	0.800577i	$-0.704526\pi$
$983$	8.13914	−	9.03943i	0.259598	−	0.288313i	0.858828	+	0.512264i	$0.171193\pi$
$984$		0			0
$985$	58.3243	+	64.7757i	1.85837	+	2.06393i
$986$	20.6977	−	35.8494i	0.659149	−	1.14168i
$987$		0			0
$988$	2.51924	−	7.75343i	0.0801477	−	0.246669i
$989$	−4.98882	+	2.22117i	−0.158635	+	0.0706290i
$990$		0			0
$991$	−49.0596			−1.55843			−0.779214	−	0.626758i	$-0.784382\pi$
$991$	−49.0596			−1.55843			−0.779214	+	0.626758i	$0.784382\pi$
$992$	−24.0172	+	36.8842i	−0.762547	+	1.17107i
$993$		0			0
$994$	−48.6419	+	35.3404i	−1.54283	+	1.12093i
$995$	28.1031	−	12.5123i	0.890927	−	0.396666i
$996$		0			0
$997$	−28.6217	−	49.5742i	−0.906459	−	1.57003i	−0.818947	−	0.573869i	$-0.805442\pi$
$997$	−28.6217	−	49.5742i	−0.906459	−	1.57003i	−0.0875112	−	0.996164i	$-0.527891\pi$
$998$	−35.1814	+	60.9360i	−1.11365	+	1.92889i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.2.y.d.235.3		24
3.2	odd	2		93.2.m.b.49.1	yes	24
31.9	even	15		8649.2.a.bk.1.2		12
31.19	even	15	inner	279.2.y.d.19.3		24
31.22	odd	30		8649.2.a.bl.1.2		12
93.50	odd	30		93.2.m.b.19.1	✓	24
93.53	even	30		2883.2.a.s.1.11		12
93.71	odd	30		2883.2.a.t.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.b.19.1	✓	24	93.50	odd	30
93.2.m.b.49.1	yes	24	3.2	odd	2
279.2.y.d.19.3		24	31.19	even	15	inner
279.2.y.d.235.3		24	1.1	even	1	trivial
2883.2.a.s.1.11		12	93.53	even	30
2883.2.a.t.1.11		12	93.71	odd	30
8649.2.a.bk.1.2		12	31.9	even	15
8649.2.a.bl.1.2		12	31.22	odd	30

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:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	279.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.08748 - 1.51664i) q^{2} +(1.43933 - 4.42980i) q^{4} +(1.93212 + 3.34652i) q^{5} +(-2.07563 - 2.30522i) q^{7} +(-2.11916 - 6.52210i) q^{8} +(9.10873 + 4.05547i) q^{10} +(-1.06351 + 0.226056i) q^{11} +(-0.249014 + 2.36921i) q^{13} +(-7.82901 - 1.66411i) q^{14} +(-6.77896 - 4.92520i) q^{16} +(-1.60951 - 0.342112i) q^{17} +(-0.0767990 - 0.730694i) q^{19} +(17.6054 - 3.74214i) q^{20} +(-1.87721 + 2.08485i) q^{22} +(0.222870 + 0.685924i) q^{23} +(-4.96614 + 8.60161i) q^{25} +(3.07343 + 5.32333i) q^{26} +(-13.1992 + 5.87665i) q^{28} +(-7.88779 + 5.73082i) q^{29} +(3.03814 - 4.66580i) q^{31} -7.90522 q^{32} +(-3.87868 + 1.72690i) q^{34} +(3.70411 - 11.4001i) q^{35} +(1.16410 - 2.01628i) q^{37} +(-1.26852 - 1.40883i) q^{38} +(17.7319 - 19.6933i) q^{40} +(-3.77729 - 1.68176i) q^{41} +(0.791467 + 7.53030i) q^{43} +(-0.529359 + 5.03651i) q^{44} +(1.50554 + 1.09384i) q^{46} +(1.30356 + 0.947094i) q^{47} +(-0.274100 + 2.60789i) q^{49} +(2.67885 + 25.4875i) q^{50} +(10.1367 + 4.51315i) q^{52} +(2.07659 - 2.30629i) q^{53} +(-2.81133 - 3.12230i) q^{55} +(-10.6363 + 18.4226i) q^{56} +(-7.77400 + 23.9259i) q^{58} +(9.44332 - 4.20444i) q^{59} +13.5425 q^{61} +(-0.734283 - 14.3475i) q^{62} +(-2.94405 + 2.13898i) q^{64} +(-8.40972 + 3.74425i) q^{65} +(-1.32349 - 2.29235i) q^{67} +(-3.83210 + 6.63740i) q^{68} +(-9.55759 - 29.4152i) q^{70} +(5.02644 - 5.58243i) q^{71} +(1.71580 - 0.364705i) q^{73} +(-0.627942 - 5.97447i) q^{74} +(-3.34737 - 0.711505i) q^{76} +(2.72856 + 1.98242i) q^{77} +(-10.7922 - 2.29395i) q^{79} +(3.38457 - 32.2020i) q^{80} +(-10.4356 + 2.21816i) q^{82} +(-9.96558 - 4.43696i) q^{83} +(-1.96488 - 6.04727i) q^{85} +(13.0729 + 14.5190i) q^{86} +(3.72811 + 6.45728i) q^{88} +(-1.89815 + 5.84191i) q^{89} +(5.97839 - 4.34356i) q^{91} +3.35929 q^{92} +4.15756 q^{94} +(2.29690 - 1.66880i) q^{95} +(3.74552 - 11.5275i) q^{97} +(3.38306 + 5.85963i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{4} + 6 q^{5} - q^{7} + 22 q^{8} + 24 q^{10} + 22 q^{11} - 8 q^{13} - 10 q^{14} - 2 q^{16} + 17 q^{17} + 5 q^{19} + 22 q^{20} - 37 q^{22} - 26 q^{23} - 8 q^{25} - 4 q^{26} - 36 q^{28} - 2 q^{29}+ \cdots + 14 q^{98}+O(q^{100}) \) 24 * q - 4 * q^4 + 6 * q^5 - q^7 + 22 * q^8 + 24 * q^10 + 22 * q^11 - 8 * q^13 - 10 * q^14 - 2 * q^16 + 17 * q^17 + 5 * q^19 + 22 * q^20 - 37 * q^22 - 26 * q^23 - 8 * q^25 - 4 * q^26 - 36 * q^28 - 2 * q^29 - 36 * q^32 + 40 * q^34 - 9 * q^35 - 13 * q^37 + q^38 - 27 * q^40 - 36 * q^41 - 11 * q^43 + 38 * q^44 - 23 * q^46 + 13 * q^47 - 22 * q^49 - 71 * q^50 + 9 * q^52 + 20 * q^53 + 26 * q^55 - 28 * q^56 + 40 * q^58 + 16 * q^59 + 70 * q^61 + 2 * q^62 + 34 * q^64 - 94 * q^65 + 4 * q^67 - 51 * q^68 - 43 * q^70 + 5 * q^71 - 12 * q^73 - 74 * q^74 + 71 * q^76 - 25 * q^77 - 29 * q^79 + 113 * q^80 - 60 * q^82 + 11 * q^83 + 16 * q^85 + 144 * q^86 + 26 * q^88 + 27 * q^89 - 81 * q^91 - 28 * q^92 - 80 * q^94 + 56 * q^95 - 21 * q^97 + 14 * q^98

Introduction

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