LMFDB - Embedded newform 637.2.u.j.30.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(30,637)] 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("637.30"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,20,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			30.1
Character	$\chi$	$=$	637.30
Dual form			637.2.u.j.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.30510 + 1.33085i) q^{2} -3.18962 q^{3} +(2.54233 - 4.40345i) q^{4} +(0.285259 + 0.164694i) q^{5} +(7.35241 - 4.24492i) q^{6} +8.21047i q^{8} +7.17371 q^{9} -0.876736 q^{10} -0.475456i q^{11} +(-8.10909 + 14.0454i) q^{12} +(-2.74029 + 2.34325i) q^{13} +(-0.909869 - 0.525313i) q^{15} +(-5.84226 - 10.1191i) q^{16} +(-0.626291 + 1.08477i) q^{17} +(-16.5361 + 9.54714i) q^{18} -3.53646i q^{19} +(1.45045 - 0.837416i) q^{20} +(0.632762 + 1.09598i) q^{22} +(0.661804 + 1.14628i) q^{23} -26.1883i q^{24} +(-2.44575 - 4.23617i) q^{25} +(3.19812 - 9.04835i) q^{26} -13.3126 q^{27} +(-2.96691 + 5.13883i) q^{29} +2.79646 q^{30} +(-4.20156 + 2.42577i) q^{31} +(12.7131 + 7.33989i) q^{32} +1.51653i q^{33} -3.33400i q^{34} +(18.2380 - 31.5891i) q^{36} +(4.04936 - 2.33790i) q^{37} +(4.70650 + 8.15190i) q^{38} +(8.74049 - 7.47409i) q^{39} +(-1.35222 + 2.34211i) q^{40} +(4.89872 + 2.82828i) q^{41} +(-2.42505 - 4.20031i) q^{43} +(-2.09365 - 1.20877i) q^{44} +(2.04636 + 1.18147i) q^{45} +(-3.05105 - 1.76153i) q^{46} +(-1.99991 - 1.15465i) q^{47} +(18.6346 + 32.2761i) q^{48} +(11.2754 + 6.50987i) q^{50} +(1.99763 - 3.46000i) q^{51} +(3.35167 + 18.0241i) q^{52} +(6.39223 + 11.0717i) q^{53} +(30.6868 - 17.7170i) q^{54} +(0.0783050 - 0.135628i) q^{55} +11.2800i q^{57} -15.7941i q^{58} +(-1.48597 - 0.857925i) q^{59} +(-4.62638 + 2.67104i) q^{60} -5.82573 q^{61} +(6.45669 - 11.1833i) q^{62} -15.7042 q^{64} +(-1.16761 + 0.217124i) q^{65} +(-2.01827 - 3.49575i) q^{66} -9.79117i q^{67} +(3.18448 + 5.51569i) q^{68} +(-2.11091 - 3.65620i) q^{69} +(10.6965 - 6.17565i) q^{71} +58.8995i q^{72} +(7.97326 - 4.60336i) q^{73} +(-6.22279 + 10.7782i) q^{74} +(7.80103 + 13.5118i) q^{75} +(-15.5726 - 8.99086i) q^{76} +(-10.2008 + 28.8609i) q^{78} +(-5.52226 + 9.56484i) q^{79} -3.84875i q^{80} +20.9409 q^{81} -15.0561 q^{82} -8.18192i q^{83} +(-0.357311 + 0.206293i) q^{85} +(11.1800 + 6.45476i) q^{86} +(9.46332 - 16.3910i) q^{87} +3.90372 q^{88} +(9.43265 - 5.44595i) q^{89} -6.28944 q^{90} +6.73011 q^{92} +(13.4014 - 7.73730i) q^{93} +6.14666 q^{94} +(0.582435 - 1.00881i) q^{95} +(-40.5499 - 23.4115i) q^{96} +(13.0900 - 7.55751i) q^{97} -3.41078i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 20 q^{4} + 56 q^{9} - 12 q^{15} - 28 q^{16} - 24 q^{18} + 8 q^{22} + 24 q^{23} + 20 q^{25} - 24 q^{29} - 48 q^{30} + 60 q^{32} + 92 q^{36} + 52 q^{39} + 12 q^{43} + 24 q^{46} + 12 q^{50} - 36 q^{53}+ \cdots + 84 q^{95}+O(q^{100}) $ 32 * q + 20 * q^4 + 56 * q^9 - 12 * q^15 - 28 * q^16 - 24 * q^18 + 8 * q^22 + 24 * q^23 + 20 * q^25 - 24 * q^29 - 48 * q^30 + 60 * q^32 + 92 * q^36 + 52 * q^39 + 12 * q^43 + 24 * q^46 + 12 * q^50 - 36 * q^53 - 276 * q^60 + 32 * q^64 + 12 * q^65 - 48 * q^71 + 24 * q^74 - 156 * q^78 - 48 * q^79 + 128 * q^81 + 12 * q^85 + 48 * q^86 - 112 * q^88 + 168 * q^92 + 48 * q^93 + 84 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.30510	+	1.33085i	−1.62995	+	0.941054i	−0.645850	+	0.763465i	$0.723497\pi$
$2$	−2.30510	+	1.33085i	−1.62995	+	0.941054i	−0.984105	+	0.177590i	$0.943170\pi$
$3$	−3.18962			−1.84153			−0.920765	−	0.390117i	$-0.872435\pi$
$3$	−3.18962			−1.84153			−0.920765	+	0.390117i	$0.872435\pi$
$4$	2.54233	−	4.40345i	1.27117	−	2.20173i
$5$	0.285259	+	0.164694i	0.127572	+	0.0736536i	0.562428	−	0.826846i	$-0.309867\pi$
$5$	0.285259	+	0.164694i	0.127572	+	0.0736536i	−0.434856	+	0.900500i	$0.643201\pi$
$6$	7.35241	−	4.24492i	3.00161	−	1.73298i
$7$		0			0
$7$		0			0
$8$			8.21047i			2.90284i
$9$	7.17371			2.39124
$10$	−0.876736			−0.277248
$11$		−	0.475456i		−	0.143355i	−0.997428	−	0.0716777i	$-0.977165\pi$
$11$		−	0.475456i		−	0.143355i	0.997428	−	0.0716777i	$-0.0228353\pi$
$12$	−8.10909	+	14.0454i	−2.34089	+	4.05455i
$13$	−2.74029	+	2.34325i	−0.760019	+	0.649901i
$13$	−2.74029	+	2.34325i	−0.760019	+	0.649901i
$14$		0			0
$15$	−0.909869	−	0.525313i	−0.234927	−	0.135635i
$16$	−5.84226	−	10.1191i	−1.46056	−	2.52977i
$17$	−0.626291	+	1.08477i	−0.151898	+	0.263095i	−0.931925	−	0.362651i	$-0.881872\pi$
$17$	−0.626291	+	1.08477i	−0.151898	+	0.263095i	0.780027	+	0.625746i	$0.215205\pi$
$18$	−16.5361	+	9.54714i	−3.89760	+	2.25028i
$19$		−	3.53646i		−	0.811319i	−0.914024	−	0.405659i	$-0.867042\pi$
$19$		−	3.53646i		−	0.811319i	0.914024	−	0.405659i	$-0.132958\pi$
$20$	1.45045	−	0.837416i	0.324330	−	0.187252i
$21$		0			0
$22$	0.632762	+	1.09598i	0.134905	+	0.233663i
$23$	0.661804	+	1.14628i	0.137996	+	0.239016i	0.926738	−	0.375709i	$-0.122601\pi$
$23$	0.661804	+	1.14628i	0.137996	+	0.239016i	−0.788742	+	0.614724i	$0.789267\pi$
$24$		−	26.1883i		−	5.34567i
$25$	−2.44575	−	4.23617i	−0.489150	−	0.847233i
$26$	3.19812	−	9.04835i	0.627204	−	1.77453i
$27$	−13.3126			−2.56200
$28$		0			0
$29$	−2.96691	+	5.13883i	−0.550941	+	0.954258i	0.447266	+	0.894401i	$0.352398\pi$
$29$	−2.96691	+	5.13883i	−0.550941	+	0.954258i	−0.998207	+	0.0598566i	$0.980936\pi$
$30$	2.79646			0.510561
$31$	−4.20156	+	2.42577i	−0.754623	+	0.435682i	−0.827362	−	0.561669i	$-0.810159\pi$
$31$	−4.20156	+	2.42577i	−0.754623	+	0.435682i	0.0727391	+	0.997351i	$0.476826\pi$
$32$	12.7131	+	7.33989i	2.24737	+	1.29752i
$33$			1.51653i			0.263993i
$34$		−	3.33400i		−	0.571777i
$35$		0			0
$36$	18.2380	−	31.5891i	3.03966	−	5.26485i
$37$	4.04936	−	2.33790i	0.665710	−	0.384348i	−0.128739	−	0.991678i	$-0.541093\pi$
$37$	4.04936	−	2.33790i	0.665710	−	0.384348i	0.794449	+	0.607331i	$0.207760\pi$
$38$	4.70650	+	8.15190i	0.763495	+	1.32241i
$39$	8.74049	−	7.47409i	1.39960	−	1.19681i
$40$	−1.35222	+	2.34211i	−0.213805	+	0.370320i
$41$	4.89872	+	2.82828i	0.765052	+	0.441703i	0.831107	−	0.556113i	$-0.187708\pi$
$41$	4.89872	+	2.82828i	0.765052	+	0.441703i	−0.0660547	+	0.997816i	$0.521041\pi$
$42$		0			0
$43$	−2.42505	−	4.20031i	−0.369817	−	0.640541i	0.619720	−	0.784823i	$-0.287246\pi$
$43$	−2.42505	−	4.20031i	−0.369817	−	0.640541i	−0.989537	+	0.144282i	$0.953913\pi$
$44$	−2.09365	−	1.20877i	−0.315629	−	0.182229i
$45$	2.04636	+	1.18147i	0.305054	+	0.176123i
$46$	−3.05105	−	1.76153i	−0.449853	−	0.259723i
$47$	−1.99991	−	1.15465i	−0.291717	−	0.168423i	0.346999	−	0.937865i	$-0.387201\pi$
$47$	−1.99991	−	1.15465i	−0.291717	−	0.168423i	−0.638716	+	0.769443i	$0.720534\pi$
$48$	18.6346	+	32.2761i	2.68967	+	4.65865i
$49$		0			0
$50$	11.2754	+	6.50987i	1.59459	+	0.920634i
$51$	1.99763	−	3.46000i	0.279725	−	0.484497i
$52$	3.35167	+	18.0241i	0.464793	+	2.49949i
$53$	6.39223	+	11.0717i	0.878040	+	1.52081i	0.853488	+	0.521112i	$0.174483\pi$
$53$	6.39223	+	11.0717i	0.878040	+	1.52081i	0.0245517	+	0.999699i	$0.492184\pi$
$54$	30.6868	−	17.7170i	4.17595	−	2.41098i
$55$	0.0783050	−	0.135628i	0.0105586	−	0.0182881i
$56$		0			0
$57$			11.2800i			1.49407i
$58$		−	15.7941i		−	2.07386i
$59$	−1.48597	−	0.857925i	−0.193457	−	0.111692i	0.400143	−	0.916453i	$-0.368960\pi$
$59$	−1.48597	−	0.857925i	−0.193457	−	0.111692i	−0.593600	+	0.804760i	$0.702294\pi$
$60$	−4.62638	+	2.67104i	−0.597264	+	0.344830i
$61$	−5.82573			−0.745908			−0.372954	−	0.927850i	$-0.621655\pi$
$61$	−5.82573			−0.745908			−0.372954	+	0.927850i	$0.621655\pi$
$62$	6.45669	−	11.1833i	0.820000	−	1.42028i
$63$		0			0
$64$	−15.7042			−1.96302
$65$	−1.16761	+	0.217124i	−0.144824	+	0.0269309i
$66$	−2.01827	−	3.49575i	−0.248432	−	0.430297i
$67$		−	9.79117i		−	1.19618i	−0.801428	−	0.598091i	$-0.795926\pi$
$67$		−	9.79117i		−	1.19618i	0.801428	−	0.598091i	$-0.204074\pi$
$68$	3.18448	+	5.51569i	0.386175	+	0.668875i
$69$	−2.11091	−	3.65620i	−0.254123	−	0.440154i
$70$		0			0
$71$	10.6965	−	6.17565i	1.26945	−	0.732915i	0.294562	−	0.955632i	$-0.404826\pi$
$71$	10.6965	−	6.17565i	1.26945	−	0.732915i	0.974883	+	0.222718i	$0.0714928\pi$
$72$			58.8995i			6.94138i
$73$	7.97326	−	4.60336i	0.933200	−	0.538783i	0.0453775	−	0.998970i	$-0.485551\pi$
$73$	7.97326	−	4.60336i	0.933200	−	0.538783i	0.887822	+	0.460187i	$0.152218\pi$
$74$	−6.22279	+	10.7782i	−0.723384	+	1.25294i
$75$	7.80103	+	13.5118i	0.900785	+	1.56021i
$76$	−15.5726	−	8.99086i	−1.78630	−	1.03132i
$77$		0			0
$78$	−10.2008	+	28.8609i	−1.15501	+	3.26785i
$79$	−5.52226	+	9.56484i	−0.621303	+	1.07613i	0.367941	+	0.929849i	$0.380063\pi$
$79$	−5.52226	+	9.56484i	−0.621303	+	1.07613i	−0.989243	+	0.146279i	$0.953270\pi$
$80$		−	3.84875i		−	0.430303i
$81$	20.9409			2.32677
$82$	−15.0561			−1.66267
$83$		−	8.18192i		−	0.898083i	−0.893511	−	0.449041i	$-0.851766\pi$
$83$		−	8.18192i		−	0.898083i	0.893511	−	0.449041i	$-0.148234\pi$
$84$		0			0
$85$	−0.357311	+	0.206293i	−0.0387558	+	0.0223757i
$86$	11.1800	+	6.45476i	1.20557	+	0.696035i
$87$	9.46332	−	16.3910i	1.01457	−	1.75729i
$88$	3.90372			0.416138
$89$	9.43265	−	5.44595i	0.999859	−	0.577269i	0.0916527	−	0.995791i	$-0.470785\pi$
$89$	9.43265	−	5.44595i	0.999859	−	0.577269i	0.908207	+	0.418522i	$0.137452\pi$
$90$	−6.28944			−0.662966
$91$		0			0
$92$	6.73011			0.701662
$93$	13.4014	−	7.73730i	1.38966	−	0.802321i
$94$	6.14666			0.633979
$95$	0.582435	−	1.00881i	0.0597565	−	0.103501i
$96$	−40.5499	−	23.4115i	−4.13861	−	2.38942i
$97$	13.0900	−	7.55751i	1.32909	−	0.767349i	0.343928	−	0.938996i	$-0.388242\pi$
$97$	13.0900	−	7.55751i	1.32909	−	0.767349i	0.985158	+	0.171647i	$0.0549089\pi$
$98$		0			0
$99$		−	3.41078i		−	0.342796i
$100$	−24.8717			−2.48717
$101$	2.62563			0.261259			0.130630	−	0.991431i	$-0.458300\pi$
$101$	2.62563			0.261259			0.130630	+	0.991431i	$0.458300\pi$
$102$			10.6342i			1.05294i
$103$	6.88087	−	11.9180i	0.677992	−	1.17432i	−0.297593	−	0.954693i	$-0.596184\pi$
$103$	6.88087	−	11.9180i	0.677992	−	1.17432i	0.975585	−	0.219624i	$-0.0704830\pi$
$104$	−19.2392	−	22.4991i	−1.88656	−	2.20621i
$105$		0			0
$106$	−29.4695	−	17.0142i	−2.86233	−	1.65257i
$107$	−5.78003	−	10.0113i	−0.558777	−	0.967830i	−0.997599	−	0.0692558i	$-0.977938\pi$
$107$	−5.78003	−	10.0113i	−0.558777	−	0.967830i	0.438822	−	0.898574i	$-0.355396\pi$
$108$	−33.8450	+	58.6212i	−3.25673	+	5.64083i
$109$	2.89099	−	1.66911i	0.276907	−	0.159872i	−0.355116	−	0.934822i	$-0.615558\pi$
$109$	2.89099	−	1.66911i	0.276907	−	0.159872i	0.632022	+	0.774950i	$0.282225\pi$
$110$			0.416849i			0.0397450i
$111$	−12.9159	+	7.45701i	−1.22593	+	0.707788i
$112$		0			0
$113$	−4.04779	−	7.01097i	−0.380784	−	0.659537i	0.610391	−	0.792100i	$-0.291012\pi$
$113$	−4.04779	−	7.01097i	−0.380784	−	0.659537i	−0.991174	+	0.132564i	$0.957679\pi$
$114$	−15.0120	−	26.0015i	−1.40600	−	2.43526i
$115$			0.435982i			0.0406555i
$116$	15.0857	+	26.1293i	1.40068	+	2.42604i
$117$	−19.6580	+	16.8098i	−1.81738	+	1.55407i
$118$	4.56708			0.420434
$119$		0			0
$120$	4.31307	−	7.47046i	0.393728	−	0.681957i
$121$	10.7739			0.979449
$122$	13.4289	−	7.75318i	1.21580	−	0.701940i
$123$	−15.6251	−	9.02115i	−1.40887	−	0.813410i
$124$			24.6685i			2.21530i
$125$		−	3.25815i		−	0.291418i
$126$		0			0
$127$	−2.80212	+	4.85342i	−0.248648	+	0.430671i	−0.963151	−	0.268961i	$-0.913320\pi$
$127$	−2.80212	+	4.85342i	−0.248648	+	0.430671i	0.714503	+	0.699633i	$0.246653\pi$
$128$	10.7737	−	6.22017i	0.952265	−	0.549791i
$129$	7.73500	+	13.3974i	0.681028	+	1.17958i
$130$	2.40251	−	2.05441i	0.210714	−	0.180184i
$131$	2.95143	−	5.11203i	0.257868	−	0.446640i	−0.707803	−	0.706410i	$-0.750313\pi$
$131$	2.95143	−	5.11203i	0.257868	−	0.446640i	0.965671	+	0.259770i	$0.0836467\pi$
$132$	6.67795	+	3.85552i	0.581241	+	0.335580i
$133$		0			0
$134$	13.0306	+	22.5697i	1.12567	+	1.94972i
$135$	−3.79753	−	2.19250i	−0.326839	−	0.188701i
$136$	−8.90646	−	5.14215i	−0.763723	−	0.440936i
$137$	−17.0289	−	9.83163i	−1.45488	−	0.839973i	−0.456123	−	0.889917i	$-0.650762\pi$
$137$	−17.0289	−	9.83163i	−1.45488	−	0.839973i	−0.998752	+	0.0499439i	$0.984096\pi$
$138$	9.73171	+	5.61861i	0.828419	+	0.478288i
$139$	−5.42353	−	9.39384i	−0.460018	−	0.796775i	0.538943	−	0.842342i	$-0.318824\pi$
$139$	−5.42353	−	9.39384i	−0.460018	−	0.796775i	−0.998961	+	0.0455674i	$0.985490\pi$
$140$		0			0
$141$	6.37895	+	3.68289i	0.537205	+	0.310155i
$142$	−16.4377	+	28.4710i	−1.37943	+	2.38923i
$143$	1.11411	+	1.30289i	0.0931668	+	0.108953i
$144$	−41.9106	−	72.5914i	−3.49255	−	6.04928i
$145$	−1.69267	+	0.977266i	−0.140569	+	0.0811575i
$146$	−12.2528	+	21.2225i	−1.01405	+	1.75638i
$147$		0			0
$148$		−	23.7749i		−	1.95428i
$149$			1.09142i			0.0894123i	0.999000	+	0.0447061i	$0.0142351\pi$
$149$			1.09142i			0.0894123i	−0.999000	+	0.0447061i	$0.985765\pi$
$150$	−35.9644	−	20.7640i	−2.93648	−	1.69538i
$151$	9.38756	−	5.41991i	0.763949	−	0.441066i	−0.0667628	−	0.997769i	$-0.521267\pi$
$151$	9.38756	−	5.41991i	0.763949	−	0.441066i	0.830712	+	0.556703i	$0.187934\pi$
$152$	29.0360			2.35513
$153$	−4.49283	+	7.78181i	−0.363224	+	0.629122i
$154$		0			0
$155$	−1.59804			−0.128358
$156$	−10.6906	−	57.4900i	−0.855931	−	4.60288i
$157$	6.35834	+	11.0130i	0.507450	+	0.878930i	0.999963	+	0.00862444i	$0.00274528\pi$
$157$	6.35834	+	11.0130i	0.507450	+	0.878930i	−0.492512	+	0.870305i	$0.663921\pi$
$158$		−	29.3972i		−	2.33872i
$159$	−20.3888	−	35.3145i	−1.61694	−	2.80062i
$160$	2.41768	+	4.18754i	0.191134	+	0.331054i
$161$		0			0
$162$	−48.2710	+	27.8693i	−3.79253	+	2.18962i
$163$		−	0.377572i		−	0.0295737i	−0.999891	−	0.0147869i	$-0.995293\pi$
$163$		−	0.377572i		−	0.0295737i	0.999891	−	0.0147869i	$-0.00470698\pi$
$164$	24.9084	−	14.3809i	1.94502	−	1.12296i
$165$	−0.249763	+	0.432603i	−0.0194441	+	0.0336781i
$166$	10.8889	+	18.8602i	0.845145	+	1.46383i
$167$	13.2407	+	7.64452i	1.02460	+	0.591551i	0.915432	−	0.402473i	$-0.131849\pi$
$167$	13.2407	+	7.64452i	1.02460	+	0.591551i	0.109164	+	0.994024i	$0.465183\pi$
$168$		0			0
$169$	2.01834	−	12.8424i	0.155257	−	0.987874i
$170$	0.549092	−	0.951055i	0.0421134	−	0.0729426i
$171$		−	25.3695i		−	1.94005i
$172$	−24.6611			−1.88039
$173$	2.29597			0.174559			0.0872797	−	0.996184i	$-0.472183\pi$
$173$	2.29597			0.174559			0.0872797	+	0.996184i	$0.472183\pi$
$174$			50.3771i			3.81908i
$175$		0			0
$176$	−4.81118	+	2.77774i	−0.362656	+	0.209380i
$177$	4.73968	+	2.73646i	0.356256	+	0.205685i
$178$	−14.4955	+	25.1069i	−1.08648	+	1.88184i
$179$	−20.9969			−1.56939			−0.784693	−	0.619885i	$-0.787179\pi$
$179$	−20.9969			−1.56939			−0.784693	+	0.619885i	$0.787179\pi$
$180$	10.4051	−	6.00738i	0.775549	−	0.447764i
$181$	15.3035			1.13750			0.568750	−	0.822511i	$-0.307427\pi$
$181$	15.3035			1.13750			0.568750	+	0.822511i	$0.307427\pi$
$182$		0			0
$183$	18.5819			1.37361
$184$	−9.41149	+	5.43372i	−0.693824	+	0.400580i
$185$	1.54015			0.113234
$186$	−20.5944	+	35.6706i	−1.51006	+	2.61549i
$187$	0.515760	+	0.297774i	0.0377161	+	0.0217754i
$188$	−10.1689	+	5.87100i	−0.741641	+	0.428187i
$189$		0			0
$190$			3.10054i			0.224937i
$191$	13.4772			0.975174			0.487587	−	0.873074i	$-0.337877\pi$
$191$	13.4772			0.975174			0.487587	+	0.873074i	$0.337877\pi$
$192$	50.0905			3.61497
$193$			9.46693i			0.681444i	0.940164	+	0.340722i	$0.110672\pi$
$193$			9.46693i			0.681444i	−0.940164	+	0.340722i	$0.889328\pi$
$194$	−20.1158	+	34.8417i	−1.44423	+	2.50149i
$195$	3.72424	−	0.692544i	0.266699	−	0.0495941i
$196$		0			0
$197$	1.18502	+	0.684169i	0.0844289	+	0.0487450i	0.541620	−	0.840623i	$-0.317811\pi$
$197$	1.18502	+	0.684169i	0.0844289	+	0.0487450i	−0.457191	+	0.889368i	$0.651144\pi$
$198$	4.53925	+	7.86221i	0.322590	+	0.558743i
$199$	5.79370	−	10.0350i	0.410705	−	0.711361i	−0.584262	−	0.811565i	$-0.698616\pi$
$199$	5.79370	−	10.0350i	0.410705	−	0.711361i	0.994967	+	0.100204i	$0.0319494\pi$
$200$	34.7809	−	20.0808i	2.45938	−	1.41993i
$201$			31.2302i			2.20281i
$202$	−6.05234	+	3.49432i	−0.425841	+	0.245859i
$203$		0			0
$204$	−10.1573	−	17.5930i	−0.711154	−	1.23175i
$205$	0.931604	+	1.61358i	0.0650660	+	0.112698i
$206$			36.6297i			2.55211i
$207$	4.74759	+	8.22306i	0.329980	+	0.571542i
$208$	39.7210	+	14.0393i	2.75416	+	0.973452i
$209$	−1.68143			−0.116307
$210$		0			0
$211$	2.79738	−	4.84521i	0.192580	−	0.333558i	−0.753525	−	0.657420i	$-0.771648\pi$
$211$	2.79738	−	4.84521i	0.192580	−	0.333558i	0.946104	+	0.323862i	$0.104981\pi$
$212$	65.0047			4.46454
$213$	−34.1179	+	19.6980i	−2.33772	+	1.34968i
$214$	26.6471	+	15.3847i	1.82156	+	1.05168i
$215$		−	1.59757i		−	0.108953i
$216$		−	109.302i		−	7.43709i
$217$		0			0
$218$	−4.44269	+	7.69496i	−0.300897	+	0.521168i
$219$	−25.4317	+	14.6830i	−1.71852	+	0.992185i
$220$	−0.398155	−	0.689624i	−0.0268436	−	0.0464945i
$221$	−0.825667	−	4.44013i	−0.0555404	−	0.298676i
$222$	19.8484	−	34.3784i	1.33213	−	2.30732i
$223$	12.2239	+	7.05747i	0.818573	+	0.472603i	0.849924	−	0.526905i	$-0.176648\pi$
$223$	12.2239	+	7.05747i	0.818573	+	0.472603i	−0.0313511	+	0.999508i	$0.509981\pi$
$224$		0			0
$225$	−17.5451	−	30.3890i	−1.16967	−	2.02593i
$226$	18.6611	+	10.7740i	1.24132	+	0.716676i
$227$	−20.3410	−	11.7439i	−1.35008	−	0.779469i	−0.361819	−	0.932248i	$-0.617844\pi$
$227$	−20.3410	−	11.7439i	−1.35008	−	0.779469i	−0.988260	+	0.152780i	$0.951177\pi$
$228$	49.6708	+	28.6775i	3.28953	+	1.89921i
$229$	−19.8075	−	11.4358i	−1.30891	−	0.755702i	−0.326999	−	0.945025i	$-0.606037\pi$
$229$	−19.8075	−	11.4358i	−1.30891	−	0.755702i	−0.981915	+	0.189323i	$0.939371\pi$
$230$	−0.580227	−	1.00498i	−0.0382590	−	0.0662666i
$231$		0			0
$232$	−42.1923	−	24.3597i	−2.77006	−	1.59929i
$233$	−0.483750	+	0.837879i	−0.0316915	+	0.0548913i	−0.881436	−	0.472303i	$-0.843423\pi$
$233$	−0.483750	+	0.837879i	−0.0316915	+	0.0548913i	0.849745	+	0.527194i	$0.176756\pi$
$234$	22.9424	−	64.9102i	1.49979	−	4.24331i
$235$	−0.380328	−	0.658747i	−0.0248099	−	0.0429719i
$236$	−7.55566	+	4.36226i	−0.491832	+	0.283959i
$237$	17.6139	−	30.5082i	1.14415	−	1.98172i
$238$		0			0
$239$		−	1.96824i		−	0.127315i	−0.997972	−	0.0636574i	$-0.979723\pi$
$239$		−	1.96824i		−	0.127315i	0.997972	−	0.0636574i	$-0.0202765\pi$
$240$			12.2761i			0.792417i
$241$	1.88984	+	1.09110i	0.121735	+	0.0702839i	0.559631	−	0.828742i	$-0.310943\pi$
$241$	1.88984	+	1.09110i	0.121735	+	0.0702839i	−0.437896	+	0.899026i	$0.644276\pi$
$242$	−24.8350	+	14.3385i	−1.59646	+	0.921715i
$243$	−26.8561			−1.72282
$244$	−14.8109	+	25.6533i	−0.948174	+	1.64229i
$245$		0			0
$246$	48.0233			3.06185
$247$	8.28681	+	9.69091i	0.527277	+	0.616618i
$248$	−19.9167	−	34.4968i	−1.26471	−	2.19055i
$249$			26.0973i			1.65385i
$250$	4.33612	+	7.51037i	0.274240	+	0.474998i
$251$	12.5057	+	21.6606i	0.789355	+	1.36720i	0.926363	+	0.376633i	$0.122918\pi$
$251$	12.5057	+	21.6606i	0.789355	+	1.36720i	−0.137008	+	0.990570i	$0.543749\pi$
$252$		0			0
$253$	0.545005	−	0.314659i	0.0342642	−	0.0197824i
$254$		−	14.9168i		−	0.935966i
$255$	1.13969	−	0.657998i	0.0713699	−	0.0412055i
$256$	−0.852070	+	1.47583i	−0.0532544	+	0.0922393i
$257$	1.16560	+	2.01887i	0.0727080	+	0.125934i	0.900087	−	0.435710i	$-0.143503\pi$
$257$	1.16560	+	2.01887i	0.0727080	+	0.125934i	−0.827379	+	0.561644i	$0.810169\pi$
$258$	−35.6599	−	20.5883i	−2.22009	−	1.28177i
$259$		0			0
$260$	−2.01237	+	5.69353i	−0.124802	+	0.353097i
$261$	−21.2837	+	36.8645i	−1.31743	+	2.28185i
$262$			15.7117i			0.970671i
$263$	3.87270			0.238801			0.119400	−	0.992846i	$-0.461903\pi$
$263$	3.87270			0.238801			0.119400	+	0.992846i	$0.461903\pi$
$264$	−12.4514			−0.766331
$265$			4.21106i			0.258683i
$266$		0			0
$267$	−30.0866	+	17.3705i	−1.84127	+	1.06306i
$268$	−43.1149	−	24.8924i	−2.63366	−	1.52055i
$269$	−7.52413	+	13.0322i	−0.458754	+	0.794586i	−0.998895	−	0.0469888i	$-0.985037\pi$
$269$	−7.52413	+	13.0322i	−0.458754	+	0.794586i	0.540141	+	0.841574i	$0.318371\pi$
$270$	11.6716			0.710310
$271$	11.5962	−	6.69507i	0.704419	−	0.406696i	−0.104572	−	0.994517i	$-0.533347\pi$
$271$	11.5962	−	6.69507i	0.704419	−	0.406696i	0.808991	+	0.587821i	$0.200014\pi$
$272$	14.6358			0.887427
$273$		0			0
$274$	52.3378			3.16184
$275$	−2.01411	+	1.16285i	−0.121455	+	0.0701223i
$276$	−21.4665			−1.29213
$277$	4.18657	−	7.25135i	0.251547	−	0.435692i	−0.712405	−	0.701768i	$-0.752394\pi$
$277$	4.18657	−	7.25135i	0.251547	−	0.435692i	0.963952	+	0.266077i	$0.0857275\pi$
$278$	25.0036	+	14.4358i	1.49962	+	0.865804i
$279$	−30.1408	+	17.4018i	−1.80448	+	1.04182i
$280$		0			0
$281$		−	17.7474i		−	1.05872i	−0.848397	−	0.529360i	$-0.822432\pi$
$281$		−	17.7474i		−	1.05872i	0.848397	−	0.529360i	$-0.177568\pi$
$282$	−19.6055			−1.16749
$283$	21.7772			1.29452			0.647261	−	0.762269i	$-0.275915\pi$
$283$	21.7772			1.29452			0.647261	+	0.762269i	$0.275915\pi$
$284$		−	62.8022i		−	3.72663i
$285$	−1.85775	+	3.21771i	−0.110044	+	0.190601i
$286$	−4.30209	−	1.52057i	−0.254388	−	0.0899130i
$287$		0			0
$288$	91.1997	+	52.6542i	5.37400	+	3.10268i
$289$	7.71552	+	13.3637i	0.453854	+	0.786098i
$290$	2.60119	−	4.50540i	0.152747	−	0.264566i
$291$	−41.7521	+	24.1056i	−2.44755	+	1.41310i
$292$		−	46.8132i		−	2.73953i
$293$	23.8412	−	13.7648i	1.39282	−	0.804145i	0.399194	−	0.916867i	$-0.369290\pi$
$293$	23.8412	−	13.7648i	1.39282	−	0.804145i	0.993627	+	0.112721i	$0.0359567\pi$
$294$		0			0
$295$	−0.282591	−	0.489462i	−0.0164531	−	0.0284976i
$296$	19.1952	+	33.2471i	1.11570	+	1.93245i
$297$			6.32954i			0.367277i
$298$	−1.45251	−	2.51583i	−0.0841418	−	0.145738i
$299$	−4.49955	−	1.59036i	−0.260216	−	0.0919728i
$300$	79.3313			4.58019
$301$		0			0
$302$	−14.4262	+	24.9869i	−0.830135	+	1.43784i
$303$	−8.37476			−0.481117
$304$	−35.7857	+	20.6609i	−2.05245	+	1.18498i
$305$	−1.66184	−	0.959465i	−0.0951568	−	0.0549388i
$306$		−	23.9172i		−	1.36725i
$307$			26.1419i			1.49200i	0.665946	+	0.746000i	$0.268028\pi$
$307$			26.1419i			1.49200i	−0.665946	+	0.746000i	$0.731972\pi$
$308$		0			0
$309$	−21.9474	+	38.0140i	−1.24854	+	2.16254i
$310$	3.68366	−	2.12676i	0.209218	−	0.120792i
$311$	−1.21810	−	2.10981i	−0.0690720	−	0.119636i	0.829421	−	0.558624i	$-0.188671\pi$
$311$	−1.21810	−	2.10981i	−0.0690720	−	0.119636i	−0.898493	+	0.438988i	$0.855337\pi$
$312$	61.3658	+	71.7635i	3.47416	+	4.06281i
$313$	8.12125	−	14.0664i	0.459040	−	0.795081i	−0.539870	−	0.841748i	$-0.681527\pi$
$313$	8.12125	−	14.0664i	0.459040	−	0.795081i	0.998910	+	0.0466674i	$0.0148601\pi$
$314$	−29.3132	−	16.9240i	−1.65424	−	0.955077i
$315$		0			0
$316$	28.0789	+	48.6340i	1.57956	+	2.73588i
$317$	−23.0444	−	13.3047i	−1.29430	−	0.747266i	−0.314888	−	0.949129i	$-0.601967\pi$
$317$	−23.0444	−	13.3047i	−1.29430	−	0.747266i	−0.979414	+	0.201863i	$0.935300\pi$
$318$	93.9966	+	54.2690i	5.27107	+	3.04325i
$319$	2.44329	+	1.41063i	0.136798	+	0.0789803i
$320$	−4.47976	−	2.58639i	−0.250426	−	0.144584i
$321$	18.4361	+	31.9323i	1.02900	+	1.78229i
$322$		0			0
$323$	3.83624	+	2.21485i	0.213454	+	0.123238i
$324$	53.2389	−	92.2124i	2.95771	−	5.12291i
$325$	16.6285	+	5.87730i	0.922381	+	0.326014i
$326$	0.502492	+	0.870343i	0.0278305	+	0.0482038i
$327$	−9.22117	+	5.32385i	−0.509932	+	0.294409i
$328$	−23.2215	+	40.2208i	−1.28219	+	2.22082i
$329$		0			0
$330$		−	1.32959i		−	0.0731917i
$331$		−	16.6976i		−	0.917785i	−0.888492	−	0.458892i	$-0.848246\pi$
$331$		−	16.6976i		−	0.917785i	0.888492	−	0.458892i	$-0.151754\pi$
$332$	−36.0287	−	20.8012i	−1.97733	−	1.14161i
$333$	29.0489	−	16.7714i	1.59187	−	0.919066i
$334$	−40.6949			−2.22673
$335$	1.61255	−	2.79302i	0.0881031	−	0.152599i
$336$		0			0
$337$	−23.6180			−1.28655			−0.643276	−	0.765634i	$-0.722425\pi$
$337$	−23.6180			−1.28655			−0.643276	+	0.765634i	$0.722425\pi$
$338$	12.4388	+	32.2891i	0.676581	+	1.75630i
$339$	12.9109	+	22.3624i	0.701225	+	1.21456i
$340$			2.09787i			0.113773i
$341$	1.15335	+	1.99766i	0.0624573	+	0.108179i
$342$	33.7631	+	58.4793i	1.82570	+	3.16220i
$343$		0			0
$344$	34.4865	−	19.9108i	1.85939	−	1.07352i
$345$		−	1.39062i		−	0.0748684i
$346$	−5.29245	+	3.05560i	−0.284524	+	0.164270i
$347$	7.45040	−	12.9045i	0.399958	−	0.692748i	−0.593762	−	0.804641i	$-0.702358\pi$
$347$	7.45040	−	12.9045i	0.399958	−	0.692748i	0.993720	+	0.111893i	$0.0356913\pi$
$348$	−48.1178	−	83.3426i	−2.57939	−	4.46763i
$349$	−18.8539	−	10.8853i	−1.00923	−	0.582677i	−0.0982611	−	0.995161i	$-0.531328\pi$
$349$	−18.8539	−	10.8853i	−1.00923	−	0.582677i	−0.910965	+	0.412484i	$0.864661\pi$
$350$		0			0
$351$	36.4802	−	31.1947i	1.94717	−	1.66505i
$352$	3.48979	−	6.04450i	0.186007	−	0.322173i
$353$		−	26.4436i		−	1.40745i	−0.710472	−	0.703725i	$-0.751519\pi$
$353$		−	26.4436i		−	1.40745i	0.710472	−	0.703725i	$-0.248481\pi$
$354$	−14.5673			−0.774242
$355$	4.06838			0.215927
$356$		−	55.3817i		−	2.93522i
$357$		0			0
$358$	48.4001	−	27.9438i	2.55803	−	1.47688i
$359$	−19.5600	−	11.2930i	−1.03234	−	0.596021i	−0.114685	−	0.993402i	$-0.536586\pi$
$359$	−19.5600	−	11.2930i	−1.03234	−	0.596021i	−0.917654	+	0.397381i	$0.869919\pi$
$360$	−9.70042	+	16.8016i	−0.511257	+	0.885523i
$361$	6.49347			0.341762
$362$	−35.2761	+	20.3667i	−1.85407	+	1.07045i
$363$	−34.3648			−1.80369
$364$		0			0
$365$	3.03259			0.158733
$366$	−42.8332	+	24.7297i	−2.23893	+	1.29264i
$367$	8.71276			0.454802			0.227401	−	0.973801i	$-0.426977\pi$
$367$	8.71276			0.454802			0.227401	+	0.973801i	$0.426977\pi$
$368$	7.73286	−	13.3937i	0.403103	−	0.698195i
$369$	35.1420	+	20.2892i	1.82942	+	1.05622i
$370$	−3.55021	+	2.04972i	−0.184567	+	0.106560i
$371$		0			0
$372$		−	78.6832i		−	4.07954i
$373$	−17.0503			−0.882830			−0.441415	−	0.897303i	$-0.645523\pi$
$373$	−17.0503			−0.882830			−0.441415	+	0.897303i	$0.645523\pi$
$374$	−1.58517			−0.0819673
$375$			10.3923i			0.536655i
$376$	9.48020	−	16.4202i	0.488904	−	0.846807i
$377$	−3.91140	−	21.0341i	−0.201448	−	1.08331i
$378$		0			0
$379$	7.09232	+	4.09475i	0.364308	+	0.210333i	0.670969	−	0.741486i	$-0.265878\pi$
$379$	7.09232	+	4.09475i	0.364308	+	0.210333i	−0.306661	+	0.951819i	$0.599212\pi$
$380$	−2.96149	−	5.12945i	−0.151921	−	0.263135i
$381$	8.93772	−	15.4806i	0.457893	−	0.793094i
$382$	−31.0663	+	17.9361i	−1.58949	+	0.917692i
$383$			14.5796i			0.744980i	0.928036	+	0.372490i	$0.121496\pi$
$383$			14.5796i			0.744980i	−0.928036	+	0.372490i	$0.878504\pi$
$384$	−34.3639	+	19.8400i	−1.75363	+	1.01246i
$385$		0			0
$386$	−12.5991	−	21.8222i	−0.641276	−	1.11072i
$387$	−17.3966	−	30.1318i	−0.884318	−	1.53168i
$388$		−	76.8548i		−	3.90171i
$389$	4.96404	+	8.59798i	0.251687	+	0.435935i	0.963990	−	0.265937i	$-0.0856813\pi$
$389$	4.96404	+	8.59798i	0.251687	+	0.435935i	−0.712303	+	0.701872i	$0.752348\pi$
$390$	−7.66310	+	6.55280i	−0.388036	+	0.331814i
$391$	−1.65793			−0.0838450
$392$		0			0
$393$	−9.41397	+	16.3055i	−0.474872	+	0.822502i
$394$	−3.64211			−0.183487
$395$	−3.15055	+	1.81897i	−0.158521	+	0.0915224i
$396$	−15.0192	−	8.67135i	−0.754744	−	0.435752i
$397$		−	15.2826i		−	0.767013i	−0.923538	−	0.383506i	$-0.874716\pi$
$397$		−	15.2826i		−	0.767013i	0.923538	−	0.383506i	$-0.125284\pi$
$398$			30.8422i			1.54598i
$399$		0			0
$400$	−28.5774	+	49.4975i	−1.42887	+	2.47488i
$401$	10.8597	−	6.26986i	0.542308	−	0.313102i	−0.203706	−	0.979032i	$-0.565299\pi$
$401$	10.8597	−	6.26986i	0.542308	−	0.313102i	0.746014	+	0.665931i	$0.231965\pi$
$402$	−41.5627	−	71.9887i	−2.07296	−	3.59047i
$403$	5.82929	−	16.4926i	0.290377	−	0.821556i
$404$	6.67522	−	11.5618i	0.332104	−	0.575222i
$405$	5.97359	+	3.44886i	0.296830	+	0.171375i
$406$		0			0
$407$	−1.11157	−	1.92529i	−0.0550983	−	0.0954331i
$408$	28.4083	+	16.4015i	1.40642	+	0.811996i
$409$	−21.1905	−	12.2344i	−1.04780	−	0.604950i	−0.125770	−	0.992059i	$-0.540140\pi$
$409$	−21.1905	−	12.2344i	−1.04780	−	0.604950i	−0.922034	+	0.387110i	$0.873474\pi$
$410$	−4.29488	−	2.47965i	−0.212109	−	0.122461i
$411$	54.3157	+	31.3592i	2.67920	+	1.54684i
$412$	−34.9869	−	60.5991i	−1.72368	−	2.98551i
$413$		0			0
$414$	−21.8874	−	12.6367i	−1.07570	−	0.621059i
$415$	1.34752	−	2.33397i	0.0661470	−	0.114570i
$416$	−52.0366	+	9.67650i	−2.55131	+	0.474429i
$417$	17.2990	+	29.9628i	0.847137	+	1.46729i
$418$	3.87587	−	2.23773i	0.189575	−	0.109451i
$419$	7.17785	−	12.4324i	0.350661	−	0.607362i	−0.635705	−	0.771932i	$-0.719290\pi$
$419$	7.17785	−	12.4324i	0.350661	−	0.607362i	0.986365	+	0.164570i	$0.0526237\pi$
$420$		0			0
$421$		−	20.6225i		−	1.00508i	−0.864555	−	0.502539i	$-0.832399\pi$
$421$		−	20.6225i		−	1.00508i	0.864555	−	0.502539i	$-0.167601\pi$
$422$			14.8916i			0.724912i
$423$	−14.3467	−	8.28310i	−0.697563	−	0.402738i
$424$	−90.9036	+	52.4832i	−4.41467	+	2.54881i
$425$	6.12701			0.297204
$426$	52.4302	−	90.8118i	2.54025	−	4.39985i
$427$		0			0
$428$	−58.7791			−2.84119
$429$	−3.55360	−	4.15572i	−0.171570	−	0.200640i
$430$	2.12613	+	3.68256i	0.102531	+	0.177589i
$431$			13.8304i			0.666188i	0.942894	+	0.333094i	$0.108093\pi$
$431$			13.8304i			0.666188i	−0.942894	+	0.333094i	$0.891907\pi$
$432$	77.7754	+	134.711i	3.74197	+	6.48128i
$433$	−8.06097	−	13.9620i	−0.387386	−	0.670972i	0.604711	−	0.796445i	$-0.293288\pi$
$433$	−8.06097	−	13.9620i	−0.387386	−	0.670972i	−0.992097	+	0.125473i	$0.959955\pi$
$434$		0			0
$435$	5.39900	−	3.11711i	0.258862	−	0.149454i
$436$		−	16.9738i		−	0.812897i
$437$	4.05376	−	2.34044i	0.193918	−	0.111959i
$438$	39.0818	−	67.6917i	1.86740	−	3.23443i
$439$	−4.81164	−	8.33400i	−0.229647	−	0.397760i	0.728057	−	0.685517i	$-0.240424\pi$
$439$	−4.81164	−	8.33400i	−0.229647	−	0.397760i	−0.957703	+	0.287757i	$0.907090\pi$
$440$	1.11357	+	0.642921i	0.0530874	+	0.0306500i
$441$		0			0
$442$	7.81241	+	9.13613i	0.371598	+	0.434561i
$443$	2.27061	−	3.93281i	0.107880	−	0.186853i	−0.807031	−	0.590509i	$-0.798927\pi$
$443$	2.27061	−	3.93281i	0.107880	−	0.186853i	0.914911	+	0.403655i	$0.132260\pi$
$444$			75.8329i			3.59887i
$445$	3.58767			0.170072
$446$	−37.5698			−1.77898
$447$		−	3.48121i		−	0.164655i
$448$		0			0
$449$	−8.25996	+	4.76889i	−0.389812	+	0.225058i	−0.682079	−	0.731279i	$-0.738924\pi$
$449$	−8.25996	+	4.76889i	−0.389812	+	0.225058i	0.292267	+	0.956337i	$0.405590\pi$
$450$	80.8865	+	46.6999i	3.81303	+	2.20145i
$451$	1.34472	−	2.32913i	0.0633205	−	0.109674i
$452$	−41.1633			−1.93616
$453$	−29.9428	+	17.2875i	−1.40684	+	0.812237i
$454$	62.5175			2.93409
$455$		0			0
$456$	−92.6139			−4.33704
$457$	23.1927	−	13.3903i	1.08491	−	0.626372i	0.152692	−	0.988274i	$-0.451206\pi$
$457$	23.1927	−	13.3903i	1.08491	−	0.626372i	0.932216	+	0.361902i	$0.117872\pi$
$458$	60.8776			2.84463
$459$	8.33754	−	14.4410i	0.389163	−	0.674050i
$460$	1.91982	+	1.10841i	0.0895123	+	0.0516799i
$461$	−8.87870	+	5.12612i	−0.413522	+	0.238747i	−0.692302	−	0.721608i	$-0.743403\pi$
$461$	−8.87870	+	5.12612i	−0.413522	+	0.238747i	0.278780	+	0.960355i	$0.410070\pi$
$462$		0			0
$463$			8.39526i			0.390161i	0.980787	+	0.195080i	$0.0624968\pi$
$463$			8.39526i			0.390161i	−0.980787	+	0.195080i	$0.937503\pi$
$464$	69.3338			3.21874
$465$	5.09716			0.236375
$466$		−	2.57520i		−	0.119294i
$467$	−5.46029	+	9.45750i	−0.252672	+	0.437641i	−0.964261	−	0.264956i	$-0.914643\pi$
$467$	−5.46029	+	9.45750i	−0.252672	+	0.437641i	0.711589	+	0.702596i	$0.247976\pi$
$468$	24.0439	+	129.299i	1.11143	+	5.97686i
$469$		0			0
$470$	1.75339	+	1.01232i	0.0808779	+	0.0466949i
$471$	−20.2807	−	35.1272i	−0.934485	−	1.61858i
$472$	7.04397	−	12.2005i	0.324225	−	0.561574i
$473$	−1.99706	+	1.15300i	−0.0918250	+	0.0530152i
$474$			93.7662i			4.30682i
$475$	−14.9810	+	8.64930i	−0.687376	+	0.396857i
$476$		0			0
$477$	45.8560	+	79.4249i	2.09960	+	3.63662i
$478$	2.61944	+	4.53700i	0.119810	+	0.207517i
$479$			28.3667i			1.29611i	0.761595	+	0.648053i	$0.224417\pi$
$479$			28.3667i			1.29611i	−0.761595	+	0.648053i	$0.775583\pi$
$480$	−7.71148	−	13.3567i	−0.351979	−	0.609646i
$481$	−5.61812	+	15.8952i	−0.256164	+	0.724757i
$482$	−5.80837			−0.264564
$483$		0			0
$484$	27.3910	−	47.4425i	1.24504	−	2.15648i
$485$	4.97872			0.226072
$486$	61.9060	−	35.7415i	2.80811	−	1.62127i
$487$	27.1818	+	15.6934i	1.23172	+	0.711136i	0.967389	−	0.253295i	$-0.0815144\pi$
$487$	27.1818	+	15.6934i	1.23172	+	0.711136i	0.264335	+	0.964431i	$0.414848\pi$
$488$		−	47.8320i		−	2.16525i
$489$			1.20431i			0.0544609i
$490$		0			0
$491$	−11.3251	+	19.6156i	−0.511093	+	0.885239i	0.488824	+	0.872382i	$0.337426\pi$
$491$	−11.3251	+	19.6156i	−0.511093	+	0.885239i	−0.999917	+	0.0128567i	$0.995907\pi$
$492$	−79.4484	+	45.8696i	−3.58181	+	2.06796i
$493$	−3.71630	−	6.43681i	−0.167374	−	0.289900i
$494$	−31.9991	−	11.3100i	−1.43971	−	0.508862i
$495$	0.561737	−	0.972957i	0.0252482	−	0.0437311i
$496$	49.0932	+	28.3440i	2.20435	+	1.27268i
$497$		0			0
$498$	−34.7316	−	60.1569i	−1.55636	−	2.69570i
$499$	11.5703	+	6.68014i	0.517960	+	0.299044i	0.736100	−	0.676873i	$-0.236666\pi$
$499$	11.5703	+	6.68014i	0.517960	+	0.299044i	−0.218140	+	0.975918i	$0.569999\pi$
$500$	−14.3471	−	8.28331i	−0.641622	−	0.370441i
$501$	−42.2329	−	24.3832i	−1.88683	−	1.08936i
$502$	−57.6540	−	33.2866i	−2.57322	−	1.48565i
$503$	1.18389	+	2.05056i	0.0527871	+	0.0914299i	0.891212	−	0.453588i	$-0.149856\pi$
$503$	1.18389	+	2.05056i	0.0527871	+	0.0914299i	−0.838424	+	0.545018i	$0.816523\pi$
$504$		0			0
$505$	0.748984	+	0.432426i	0.0333293	+	0.0192427i
$506$	−0.837528	+	1.45064i	−0.0372327	+	0.0644889i
$507$	−6.43776	+	40.9623i	−0.285911	+	1.81920i
$508$	14.2479	+	24.6780i	0.632147	+	1.09491i
$509$	9.30452	−	5.37197i	0.412416	−	0.238108i	−0.279412	−	0.960171i	$-0.590139\pi$
$509$	9.30452	−	5.37197i	0.412416	−	0.238108i	0.691827	+	0.722063i	$0.256806\pi$
$510$	−1.75140	+	3.03351i	−0.0775532	+	0.134326i
$511$		0			0
$512$			20.3448i			0.899120i
$513$			47.0793i			2.07860i
$514$	−5.37365	−	3.10248i	−0.237021	−	0.136844i
$515$	3.92566	−	2.26648i	0.172985	−	0.0998731i
$516$	78.6598			3.46280
$517$	−0.548984	+	0.950868i	−0.0241443	+	0.0418191i
$518$		0			0
$519$	−7.32328			−0.321456
$520$	−1.78269	−	9.58665i	−0.0781761	−	0.420402i
$521$	−5.82202	−	10.0840i	−0.255067	−	0.441790i	0.709846	−	0.704357i	$-0.248764\pi$
$521$	−5.82202	−	10.0840i	−0.255067	−	0.441790i	−0.964914	+	0.262567i	$0.915431\pi$
$522$		−	113.302i		−	4.95909i
$523$	−16.2553	−	28.1549i	−0.710793	−	1.23113i	−0.964560	−	0.263864i	$-0.915003\pi$
$523$	−16.2553	−	28.1549i	−0.710793	−	1.23113i	0.253767	−	0.967265i	$-0.418330\pi$
$524$	−15.0071	−	25.9930i	−0.655587	−	1.13551i
$525$		0			0
$526$	−8.92696	+	5.15398i	−0.389234	+	0.224724i
$527$		−	6.07696i		−	0.264717i
$528$	15.3459	−	8.85994i	0.667843	−	0.385579i
$529$	10.6240	−	18.4014i	0.461914	−	0.800059i
$530$	−5.60429	−	9.70692i	−0.243435	−	0.421642i
$531$	−10.6599	−	6.15450i	−0.462600	−	0.267082i
$532$		0			0
$533$	−20.0513	+	3.72864i	−0.868517	+	0.161506i
$534$	46.2352	−	80.0817i	2.00079	−	3.46547i
$535$		−	3.80776i		−	0.164624i
$536$	80.3902			3.47233
$537$	66.9724			2.89007
$538$		−	40.0540i		−	1.72685i
$539$		0			0
$540$	−19.3092	+	11.1482i	−0.830934	+	0.479740i
$541$	20.0972	+	11.6031i	0.864048	+	0.498858i	0.865366	−	0.501141i	$-0.167086\pi$
$541$	20.0972	+	11.6031i	0.864048	+	0.498858i	−0.00131774	+	0.999999i	$0.500419\pi$
$542$	−17.8203	+	30.8656i	−0.765447	+	1.32579i
$543$	−48.8124			−2.09474
$544$	−15.9242	+	9.19382i	−0.682743	+	0.394182i
$545$	1.09957			0.0471006
$546$		0			0
$547$	−17.4876			−0.747714			−0.373857	−	0.927486i	$-0.621965\pi$
$547$	−17.4876			−0.747714			−0.373857	+	0.927486i	$0.621965\pi$
$548$	−86.5862	+	49.9906i	−3.69878	+	2.13549i
$549$	−41.7921			−1.78364
$550$	3.09516	−	5.36097i	0.131978	−	0.228592i
$551$	18.1733	+	10.4923i	0.774207	+	0.446989i
$552$	30.0191	−	17.3315i	1.27770	−	0.737679i
$553$		0			0
$554$			22.2868i			0.946876i
$555$	−4.91251			−0.208525
$556$	−55.1537			−2.33904
$557$			31.1727i			1.32083i	0.750900	+	0.660415i	$0.229620\pi$
$557$			31.1727i			1.32083i	−0.750900	+	0.660415i	$0.770380\pi$
$558$	46.3184	−	80.2258i	1.96081	−	3.39623i
$559$	16.4877	+	5.82755i	0.697356	+	0.246479i
$560$		0			0
$561$	−1.64508	−	0.949787i	−0.0694553	−	0.0401000i
$562$	23.6192	+	40.9096i	0.996314	+	1.72567i
$563$	−10.7537	+	18.6259i	−0.453213	+	0.784988i	−0.998584	−	0.0532069i	$-0.983056\pi$
$563$	−10.7537	+	18.6259i	−0.453213	+	0.784988i	0.545370	+	0.838195i	$0.316389\pi$
$564$	32.4349	−	18.7263i	1.36575	−	0.788519i
$565$		−	2.66659i		−	0.112184i
$566$	−50.1987	+	28.9823i	−2.11001	+	1.21822i
$567$		0			0
$568$	50.7050	+	87.8236i	2.12753	+	3.68500i
$569$	4.39588	+	7.61389i	0.184285	+	0.319191i	0.943335	−	0.331841i	$-0.107670\pi$
$569$	4.39588	+	7.61389i	0.184285	+	0.319191i	−0.759050	+	0.651032i	$0.774336\pi$
$570$		−	9.88955i		−	0.414228i
$571$	9.76184	+	16.9080i	0.408520	+	0.707578i	0.994724	−	0.102586i	$-0.0327115\pi$
$571$	9.76184	+	16.9080i	0.408520	+	0.707578i	−0.586204	+	0.810164i	$0.699378\pi$
$572$	8.56964	−	1.59357i	0.358315	−	0.0666306i
$573$	−42.9871			−1.79581
$574$		0			0
$575$	3.23722	−	5.60702i	0.135001	−	0.233829i
$576$	−112.657			−4.69405
$577$	26.5530	−	15.3304i	1.10542	−	0.638212i	0.167778	−	0.985825i	$-0.446341\pi$
$577$	26.5530	−	15.3304i	1.10542	−	0.638212i	0.937638	+	0.347612i	$0.113007\pi$
$578$	−35.5701	−	20.5364i	−1.47952	−	0.854203i
$579$		−	30.1959i		−	1.25490i
$580$			9.93815i			0.412659i
$581$		0			0
$582$	64.1620	−	111.132i	2.65960	−	4.60656i
$583$	5.26409	−	3.03922i	0.218016	−	0.125872i
$584$	37.7958	+	65.4643i	1.56400	+	2.70893i
$585$	−8.37611	+	1.55758i	−0.346309	+	0.0643981i
$586$	−36.6377	+	63.4583i	−1.51349	+	2.62144i
$587$	−2.24386	−	1.29550i	−0.0926142	−	0.0534708i	0.452978	−	0.891522i	$-0.350362\pi$
$587$	−2.24386	−	1.29550i	−0.0926142	−	0.0534708i	−0.545592	+	0.838051i	$0.683695\pi$
$588$		0			0
$589$	8.57864	+	14.8586i	0.353477	+	0.612240i
$590$	1.30280	+	0.752173i	0.0536355	+	0.0309665i
$591$	−3.77976	−	2.18224i	−0.155478	−	0.0897655i
$592$	−47.3148	−	27.3172i	−1.94462	−	1.12273i
$593$	15.3406	+	8.85689i	0.629962	+	0.363709i	0.780737	−	0.624859i	$-0.214844\pi$
$593$	15.3406	+	8.85689i	0.629962	+	0.363709i	−0.150775	+	0.988568i	$0.548177\pi$
$594$	−8.42368	−	14.5902i	−0.345628	−	0.598645i
$595$		0			0
$596$	4.80600	+	2.77474i	0.196861	+	0.113658i
$597$	−18.4797	+	32.0078i	−0.756325	+	1.30999i
$598$	12.4885	−	2.32230i	0.510691	−	0.0949658i
$599$	−17.3049	−	29.9729i	−0.707057	−	1.22466i	−0.965944	−	0.258752i	$-0.916689\pi$
$599$	−17.3049	−	29.9729i	−0.707057	−	1.22466i	0.258886	−	0.965908i	$-0.416644\pi$
$600$	−110.938	+	64.0502i	−4.52903	+	2.61484i
$601$	−18.9080	+	32.7496i	−0.771272	+	1.33588i	0.165594	+	0.986194i	$0.447046\pi$
$601$	−18.9080	+	32.7496i	−0.771272	+	1.33588i	−0.936866	+	0.349688i	$0.886287\pi$
$602$		0			0
$603$		−	70.2390i		−	2.86035i
$604$		−	55.1169i		−	2.24267i
$605$	3.07336	+	1.77441i	0.124950	+	0.0721399i
$606$	19.3047	−	11.1456i	0.784199	−	0.452758i
$607$	−39.1728			−1.58998			−0.794988	−	0.606625i	$-0.792523\pi$
$607$	−39.1728			−1.58998			−0.794988	+	0.606625i	$0.792523\pi$
$608$	25.9572	−	44.9592i	1.05270	−	1.82334i
$609$		0			0
$610$	5.10762			0.206802
$611$	8.18595	−	1.52222i	0.331168	−	0.0615825i
$612$	22.8445	+	39.5679i	0.923436	+	1.59944i
$613$			21.4325i			0.865649i	0.901478	+	0.432825i	$0.142483\pi$
$613$			21.4325i			0.865649i	−0.901478	+	0.432825i	$0.857517\pi$
$614$	−34.7911	−	60.2599i	−1.40405	−	2.43189i
$615$	−2.97147	−	5.14673i	−0.119821	−	0.207536i
$616$		0			0
$617$	32.2102	−	18.5966i	1.29673	−	0.748669i	0.316895	−	0.948461i	$-0.397360\pi$
$617$	32.2102	−	18.5966i	1.29673	−	0.748669i	0.979838	+	0.199792i	$0.0640265\pi$
$618$		−	116.835i		−	4.69979i
$619$	−26.6037	+	15.3597i	−1.06929	+	0.617357i	−0.927988	−	0.372609i	$-0.878463\pi$
$619$	−26.6037	+	15.3597i	−1.06929	+	0.617357i	−0.141305	+	0.989966i	$0.545130\pi$
$620$	−4.06276	+	7.03691i	−0.163164	+	0.282609i
$621$	−8.81030	−	15.2599i	−0.353545	−	0.612358i
$622$	5.61569	+	3.24222i	0.225169	+	0.130001i
$623$		0			0
$624$	−126.695	−	44.7802i	−5.07187	−	1.79264i
$625$	−11.6922	+	20.2514i	−0.467686	+	0.810056i
$626$			43.2327i			1.72793i
$627$	5.36313			0.214183
$628$	64.6601			2.58022
$629$			5.85682i			0.233527i
$630$		0			0
$631$	−12.1022	+	6.98719i	−0.481779	+	0.278155i	−0.721158	−	0.692771i	$-0.756390\pi$
$631$	−12.1022	+	6.98719i	−0.481779	+	0.278155i	0.239378	+	0.970926i	$0.423056\pi$
$632$	−78.5318	−	45.3404i	−3.12383	−	1.80354i
$633$	−8.92260	+	15.4544i	−0.354642	+	0.614257i
$634$	70.8263			2.81287
$635$	−1.59866	+	0.922988i	−0.0634409	+	0.0366276i
$636$	−207.341			−8.22159
$637$		0			0
$638$	−7.50938			−0.297299
$639$	76.7338	−	44.3023i	3.03554	−	1.75257i
$640$	4.09771			0.161976
$641$	−14.5449	+	25.1925i	−0.574489	+	0.995045i	0.421608	+	0.906778i	$0.361466\pi$
$641$	−14.5449	+	25.1925i	−0.574489	+	0.995045i	−0.996097	+	0.0882663i	$0.971867\pi$
$642$	−84.9944	−	49.0715i	−3.35446	−	1.93670i
$643$	11.7654	−	6.79275i	0.463982	−	0.267880i	−0.249735	−	0.968314i	$-0.580344\pi$
$643$	11.7654	−	6.79275i	0.463982	−	0.267880i	0.713717	+	0.700434i	$0.247010\pi$
$644$		0			0
$645$			5.09564i			0.200641i
$646$	−11.7906			−0.463893
$647$	−30.1526			−1.18542			−0.592710	−	0.805416i	$-0.701942\pi$
$647$	−30.1526			−1.18542			−0.592710	+	0.805416i	$0.701942\pi$
$648$			171.935i			6.75425i
$649$	−0.407905	+	0.706513i	−0.0160117	+	0.0277331i
$650$	−46.1521	+	8.58224i	−1.81024	+	0.336623i
$651$		0			0
$652$	−1.66262	−	0.959914i	−0.0651132	−	0.0375931i
$653$	−13.0045	−	22.5245i	−0.508906	−	0.881451i	−0.999947	−	0.0103145i	$-0.996717\pi$
$653$	−13.0045	−	22.5245i	−0.508906	−	0.881451i	0.491041	−	0.871137i	$-0.336617\pi$
$654$	14.1705	−	24.5440i	0.554111	−	0.959748i
$655$	1.68385	−	0.972169i	0.0657933	−	0.0379858i
$656$		−	66.0941i		−	2.58054i
$657$	57.1978	−	33.0232i	2.23150	−	1.28836i
$658$		0			0
$659$	−6.75204	−	11.6949i	−0.263022	−	0.455568i	0.704021	−	0.710179i	$-0.251386\pi$
$659$	−6.75204	−	11.6949i	−0.263022	−	0.455568i	−0.967044	+	0.254611i	$0.918053\pi$
$660$	1.26996	+	2.19964i	0.0494333	+	0.0856210i
$661$		−	43.3094i		−	1.68454i	−0.539056	−	0.842270i	$-0.681219\pi$
$661$		−	43.3094i		−	1.68454i	0.539056	−	0.842270i	$-0.318781\pi$
$662$	22.2221	+	38.4898i	0.863686	+	1.49595i
$663$	2.63357	+	14.1624i	0.102279	+	0.550021i
$664$	67.1775			2.60699
$665$		0			0
$666$	−44.6405	+	77.3195i	−1.72978	+	2.99607i
$667$	−7.85404			−0.304110
$668$	67.3246	−	38.8699i	2.60487	−	1.50392i
$669$	−38.9897	−	22.5107i	−1.50743	−	0.870314i
$670$			8.58427i			0.331639i
$671$			2.76988i			0.106930i
$672$		0			0
$673$	−5.58760	+	9.67801i	−0.215386	+	0.373060i	−0.953392	−	0.301735i	$-0.902434\pi$
$673$	−5.58760	+	9.67801i	−0.215386	+	0.373060i	0.738006	+	0.674794i	$0.235768\pi$
$674$	54.4418	−	31.4320i	2.09702	−	1.21072i
$675$	32.5592	+	56.3942i	1.25320	+	2.17061i
$676$	−51.4194	−	41.5373i	−1.97767	−	1.59759i
$677$	0.948300	−	1.64250i	0.0364461	−	0.0631265i	−0.847227	−	0.531231i	$-0.821730\pi$
$677$	0.948300	−	1.64250i	0.0364461	−	0.0631265i	0.883673	+	0.468105i	$0.155063\pi$
$678$	−59.5220	−	34.3650i	−2.28593	−	1.31978i
$679$		0			0
$680$	−1.69377	−	2.93369i	−0.0649530	−	0.112502i
$681$	64.8801	+	37.4586i	2.48621	+	1.43542i
$682$	−5.31717	−	3.06987i	−0.203605	−	0.117551i
$683$	33.9929	+	19.6258i	1.30070	+	0.750961i	0.980525	−	0.196396i	$-0.0629237\pi$
$683$	33.9929	+	19.6258i	1.30070	+	0.750961i	0.320179	+	0.947357i	$0.396257\pi$
$684$	−111.713	−	64.4978i	−4.27147	−	2.46613i
$685$	−3.23843	−	5.60912i	−0.123734	−	0.214314i
$686$		0			0
$687$	63.1784	+	36.4760i	2.41040	+	1.39165i
$688$	−28.3355	+	49.0786i	−1.08028	+	1.87110i
$689$	−43.4602	−	15.3609i	−1.65570	−	0.585205i
$690$	1.85071	+	3.20552i	0.0704552	+	0.122032i
$691$	11.2115	−	6.47294i	0.426504	−	0.246242i	−0.271352	−	0.962480i	$-0.587471\pi$
$691$	11.2115	−	6.47294i	0.426504	−	0.246242i	0.697856	+	0.716238i	$0.254137\pi$
$692$	5.83712	−	10.1102i	0.221894	−	0.384332i
$693$		0			0
$694$			39.6615i			1.50553i
$695$		−	3.57290i		−	0.135528i
$696$	134.577	+	77.6984i	5.10115	+	2.94515i
$697$	−6.13605	+	3.54265i	−0.232420	+	0.134188i
$698$	57.9469			2.19332
$699$	1.54298	−	2.67252i	0.0583609	−	0.101084i
$700$		0			0
$701$	37.5032			1.41647			0.708237	−	0.705974i	$-0.249491\pi$
$701$	37.5032			1.41647			0.708237	+	0.705974i	$0.249491\pi$
$702$	−42.5752	+	120.457i	−1.60690	+	4.54635i
$703$	−8.26787	−	14.3204i	−0.311829	−	0.540103i
$704$			7.46665i			0.281410i
$705$	1.21310	+	2.10116i	0.0456881	+	0.0791341i
$706$	35.1925	+	60.9552i	1.32449	+	2.29408i
$707$		0			0
$708$	24.0997	−	13.9140i	0.905723	−	0.522919i
$709$			11.6762i			0.438509i	0.975668	+	0.219255i	$0.0703625\pi$
$709$			11.6762i			0.438509i	−0.975668	+	0.219255i	$0.929637\pi$
$710$	−9.37803	+	5.41441i	−0.351951	+	0.203199i
$711$	−39.6151	+	68.6153i	−1.48568	+	2.57328i
$712$	44.7138	+	77.4466i	1.67572	+	2.90243i
$713$	−5.56122	−	3.21077i	−0.208269	−	0.120244i
$714$		0			0
$715$	0.103233	+	0.555148i	0.00386069	+	0.0207614i
$716$	−53.3812	+	92.4590i	−1.99495	+	3.45536i
$717$			6.27795i			0.234454i
$718$	60.1172			2.24355
$719$	26.8073			0.999742			0.499871	−	0.866100i	$-0.333381\pi$
$719$	26.8073			0.999742			0.499871	+	0.866100i	$0.333381\pi$
$720$		−	27.6098i		−	1.02896i
$721$		0			0
$722$	−14.9681	+	8.64185i	−0.557056	+	0.321616i
$723$	−6.02788	−	3.48020i	−0.224179	−	0.129430i
$724$	38.9066	−	67.3882i	1.44595	−	2.50446i
$725$	29.0253			1.07797
$726$	79.2145	−	45.7345i	2.93993	−	1.69737i
$727$	−14.1968			−0.526532			−0.263266	−	0.964723i	$-0.584800\pi$
$727$	−14.1968			−0.526532			−0.263266	+	0.964723i	$0.584800\pi$
$728$		0			0
$729$	22.8380			0.845851
$730$	−6.99044	+	4.03593i	−0.258728	+	0.149377i
$731$	6.07515			0.224697
$732$	47.2414	−	81.8245i	1.74609	−	3.02432i
$733$	−0.226967	−	0.131039i	−0.00838322	−	0.00484005i	0.495803	−	0.868435i	$-0.334874\pi$
$733$	−0.226967	−	0.131039i	−0.00838322	−	0.00484005i	−0.504186	+	0.863595i	$0.668207\pi$
$734$	−20.0838	+	11.5954i	−0.741307	+	0.427994i
$735$		0			0
$736$			19.4303i			0.716209i
$737$	−4.65527			−0.171479
$738$	−108.008			−3.97583
$739$		−	16.2783i		−	0.598808i	−0.954127	−	0.299404i	$-0.903212\pi$
$739$		−	16.2783i		−	0.598808i	0.954127	−	0.299404i	$-0.0967878\pi$
$740$	3.91559	−	6.78199i	0.143940	−	0.249311i
$741$	−26.4318	−	30.9104i	−0.970997	−	1.13552i
$742$		0			0
$743$	−1.03251	−	0.596118i	−0.0378790	−	0.0218695i	0.480941	−	0.876753i	$-0.340295\pi$
$743$	−1.03251	−	0.596118i	−0.0378790	−	0.0218695i	−0.518820	+	0.854884i	$0.673628\pi$
$744$	63.5269	+	110.032i	2.32901	+	4.03396i
$745$	−0.179750	+	0.311336i	−0.00658553	+	0.0114065i
$746$	39.3027	−	22.6914i	1.43897	−	0.830792i
$747$		−	58.6947i		−	2.14753i
$748$	2.62247	−	1.51408i	0.0958869	−	0.0553603i
$749$		0			0
$750$	−13.8306	−	23.9553i	−0.505022	−	0.874723i
$751$	2.57029	+	4.45188i	0.0937913	+	0.162451i	0.909104	−	0.416570i	$-0.136768\pi$
$751$	2.57029	+	4.45188i	0.0937913	+	0.162451i	−0.815312	+	0.579022i	$0.803435\pi$
$752$			26.9830i			0.983968i
$753$	−39.8886	−	69.0891i	−1.45362	−	2.51775i
$754$	37.0095	+	43.2803i	1.34780	+	1.57617i
$755$	3.57052			0.129944
$756$		0			0
$757$	−7.40225	+	12.8211i	−0.269039	+	0.465990i	−0.968614	−	0.248570i	$-0.920040\pi$
$757$	−7.40225	+	12.8211i	−0.269039	+	0.465990i	0.699575	+	0.714560i	$0.253373\pi$
$758$	−21.7980			−0.791740
$759$	−1.73836	+	1.00364i	−0.0630985	+	0.0364299i
$760$	8.28278	+	4.78207i	0.300448	+	0.173464i
$761$		−	18.9564i		−	0.687170i	−0.939122	−	0.343585i	$-0.888359\pi$
$761$		−	18.9564i		−	0.687170i	0.939122	−	0.343585i	$-0.111641\pi$
$762$			47.5791i			1.72361i
$763$		0			0
$764$	34.2635	−	59.3461i	1.23961	−	2.14707i
$765$	−2.56324	+	1.47989i	−0.0926742	+	0.0535055i
$766$	−19.4032	−	33.6074i	−0.701067	−	1.21428i
$767$	6.08231	−	1.13104i	0.219620	−	0.0408395i
$768$	2.71778	−	4.70734i	0.0980696	−	0.169862i
$769$	36.8803	+	21.2928i	1.32994	+	0.767839i	0.985290	−	0.170893i	$-0.0546653\pi$
$769$	36.8803	+	21.2928i	1.32994	+	0.767839i	0.344647	+	0.938732i	$0.387999\pi$
$770$		0			0
$771$	−3.71782	−	6.43945i	−0.133894	−	0.231911i
$772$	41.6872	+	24.0681i	1.50035	+	0.866230i
$773$	−13.7119	−	7.91657i	−0.493183	−	0.284739i	0.232711	−	0.972546i	$-0.425240\pi$
$773$	−13.7119	−	7.91657i	−0.493183	−	0.284739i	−0.725894	+	0.687807i	$0.758574\pi$
$774$	80.2019	+	46.3046i	2.88280	+	1.66438i
$775$	20.5519	+	11.8657i	0.738248	+	0.426228i
$776$	62.0507	+	107.475i	2.22749	+	3.85813i
$777$		0			0
$778$	−22.8853	−	13.2128i	−0.820477	−	0.473702i
$779$	10.0021	−	17.3241i	0.358362	−	0.620701i
$780$	6.41869	−	18.1602i	0.229826	−	0.650240i
$781$	−2.93625	−	5.08573i	−0.105067	−	0.181982i
$782$	3.82170	−	2.20646i	0.136664	−	0.0789027i
$783$	39.4971	−	68.4110i	1.41151	−	2.44481i
$784$		0			0
$785$			4.18873i			0.149502i
$786$		−	50.1144i		−	1.78752i
$787$	44.4043	+	25.6368i	1.58284	+	0.913854i	0.994442	+	0.105284i	$0.0335751\pi$
$787$	44.4043	+	25.6368i	1.58284	+	0.913854i	0.588400	+	0.808570i	$0.299758\pi$
$788$	6.02541	−	3.47877i	0.214646	−	0.123926i
$789$	−12.3524			−0.439759
$790$	4.84156	−	8.38583i	0.172255	−	0.298355i
$791$		0			0
$792$	28.0041			0.995084
$793$	15.9642	−	13.6511i	0.566904	−	0.484766i
$794$	20.3389	+	35.2280i	0.721801	+	1.25020i
$795$		−	13.4317i		−	0.476373i
$796$	−29.4590	−	51.0246i	−1.04415	−	1.80852i
$797$	−25.8457	−	44.7660i	−0.915501	−	1.58569i	−0.806166	−	0.591689i	$-0.798461\pi$
$797$	−25.8457	−	44.7660i	−0.915501	−	1.58569i	−0.109335	−	0.994005i	$-0.534872\pi$
$798$		0			0
$799$	2.50505	−	1.44629i	0.0886223	−	0.0511661i
$800$		−	71.8062i		−	2.53873i
$801$	67.6671	−	39.0676i	2.39090	−	1.38039i
$802$	−16.6885	+	28.9053i	−0.589291	+	1.02068i
$803$	−2.18870	−	3.79094i	−0.0772375	−	0.133779i
$804$	137.521	+	79.3975i	4.84997	+	2.80013i
$805$		0			0
$806$	8.51213	+	45.7751i	0.299827	+	1.61236i
$807$	23.9991	−	41.5677i	0.844810	−	1.46325i
$808$			21.5576i			0.758395i
$809$	−7.70987			−0.271065			−0.135532	−	0.990773i	$-0.543274\pi$
$809$	−7.70987			−0.271065			−0.135532	+	0.990773i	$0.543274\pi$
$810$	−18.3597			−0.645093
$811$			27.3184i			0.959278i	0.877466	+	0.479639i	$0.159232\pi$
$811$			27.3184i			0.959278i	−0.877466	+	0.479639i	$0.840768\pi$
$812$		0			0
$813$	−36.9875	+	21.3548i	−1.29721	+	0.748944i
$814$	5.12455	+	2.95866i	0.179616	+	0.103701i
$815$	0.0621840	−	0.107706i	0.00217821	−	0.00377277i
$816$	−46.6828			−1.63422
$817$	−14.8542	+	8.57608i	−0.519683	+	0.300039i
$818$	65.1285			2.27716
$819$		0			0
$820$	9.47379			0.330839
$821$	−32.6900	+	18.8736i	−1.14089	+	0.658693i	−0.946651	−	0.322261i	$-0.895557\pi$
$821$	−32.6900	+	18.8736i	−1.14089	+	0.658693i	−0.194239	+	0.980954i	$0.562224\pi$
$822$	−166.938			−5.82263
$823$	12.6192	−	21.8571i	0.439877	−	0.761889i	−0.557803	−	0.829974i	$-0.688355\pi$
$823$	12.6192	−	21.8571i	0.439877	−	0.761889i	0.997680	+	0.0680843i	$0.0216887\pi$
$824$	97.8525	+	56.4952i	3.40885	+	1.96810i
$825$	6.42426	−	3.70905i	0.223664	−	0.129132i
$826$		0			0
$827$		−	14.9309i		−	0.519198i	−0.965717	−	0.259599i	$-0.916410\pi$
$827$		−	14.9309i		−	0.519198i	0.965717	−	0.259599i	$-0.0835903\pi$
$828$	48.2798			1.67784
$829$	15.5499			0.540069			0.270034	−	0.962851i	$-0.412965\pi$
$829$	15.5499			0.540069			0.270034	+	0.962851i	$0.412965\pi$
$830$			7.17338i			0.248992i
$831$	−13.3536	+	23.1291i	−0.463231	+	0.802339i
$832$	43.0340	−	36.7989i	1.49193	−	1.27577i
$833$		0			0
$834$	−79.7521	−	46.0449i	−2.76159	−	1.59441i
$835$	2.51802	+	4.36134i	0.0871397	+	0.150930i
$836$	−4.27476	+	7.40410i	−0.147846	+	0.256076i
$837$	55.9335	−	32.2932i	1.93334	−	1.11622i
$838$			38.2106i			1.31996i
$839$	−49.3577	+	28.4967i	−1.70402	+	0.983814i	−0.762413	+	0.647091i	$0.775985\pi$
$839$	−49.3577	+	28.4967i	−1.70402	+	0.983814i	−0.941604	+	0.336723i	$0.890681\pi$
$840$		0			0
$841$	−3.10508	−	5.37815i	−0.107072	−	0.185454i
$842$	27.4455	+	47.5369i	0.945833	+	1.63823i
$843$			56.6075i			1.94967i
$844$	−14.2238	−	24.6363i	−0.489602	−	0.848016i
$845$	2.69082	−	3.33099i	0.0925669	−	0.114590i
$846$	44.0943			1.51599
$847$		0			0
$848$	74.6901	−	129.367i	2.56487	−	4.44248i
$849$	−69.4612			−2.38390
$850$	−14.1234	+	8.15415i	−0.484428	+	0.279685i
$851$	5.35976	+	3.09446i	0.183730	+	0.106077i
$852$			200.316i			6.86270i
$853$		−	53.4201i		−	1.82907i	−0.404509	−	0.914534i	$-0.632557\pi$
$853$		−	53.4201i		−	1.82907i	0.404509	−	0.914534i	$-0.367443\pi$
$854$		0			0
$855$	4.17822	−	7.23688i	0.142892	−	0.247496i
$856$	82.1976	−	47.4568i	2.80946	−	1.62204i
$857$	16.3257	+	28.2770i	0.557676	+	0.965924i	0.997690	+	0.0679326i	$0.0216403\pi$
$857$	16.3257	+	28.2770i	0.557676	+	0.965924i	−0.440014	+	0.897991i	$0.645026\pi$
$858$	13.7221	+	4.85004i	0.468464	+	0.165578i
$859$	−17.3823	+	30.1071i	−0.593078	+	1.02724i	0.400737	+	0.916193i	$0.368754\pi$
$859$	−17.3823	+	30.1071i	−0.593078	+	1.02724i	−0.993815	+	0.111048i	$0.964579\pi$
$860$	−7.03481	−	4.06155i	−0.239885	−	0.138498i
$861$		0			0
$862$	−18.4062	−	31.8805i	−0.626919	−	1.08586i
$863$	−20.2059	−	11.6659i	−0.687818	−	0.397112i	0.114976	−	0.993368i	$-0.463321\pi$
$863$	−20.2059	−	11.6659i	−0.687818	−	0.397112i	−0.802794	+	0.596256i	$0.796654\pi$
$864$	−169.243	−	97.7127i	−5.75777	−	3.32425i
$865$	0.654946	+	0.378133i	0.0222688	+	0.0128569i
$866$	37.1627	+	21.4559i	1.26284	+	0.729102i
$867$	−24.6096	−	42.6251i	−0.835786	−	1.44762i
$868$		0			0
$869$	4.54766	+	2.62559i	0.154269	+	0.0890671i
$870$	−8.29683	+	14.3705i	−0.281289	+	0.487207i
$871$	22.9432	+	26.8306i	0.777400	+	0.909121i
$872$	13.7042	+	23.7364i	0.464083	+	0.803816i
$873$	93.9037	−	54.2153i	3.17816	−	1.83491i
$874$	−6.22956	+	10.7899i	−0.210718	+	0.364974i
$875$		0			0
$876$			149.316i			5.04493i
$877$		−	4.91107i		−	0.165835i	−0.996556	−	0.0829175i	$-0.973576\pi$
$877$		−	4.91107i		−	0.165835i	0.996556	−	0.0829175i	$-0.0264238\pi$
$878$	22.1826	+	12.8072i	0.748628	+	0.432220i
$879$	−76.0446	+	43.9044i	−2.56492	+	1.48086i
$880$	−1.82991			−0.0616863
$881$	4.78761	−	8.29238i	0.161299	−	0.279378i	−0.774036	−	0.633142i	$-0.781765\pi$
$881$	4.78761	−	8.29238i	0.161299	−	0.279378i	0.935335	+	0.353764i	$0.115098\pi$
$882$		0			0
$883$	16.6962			0.561871			0.280935	−	0.959727i	$-0.409355\pi$
$883$	16.6962			0.561871			0.280935	+	0.959727i	$0.409355\pi$
$884$	−21.6510	−	7.65252i	−0.728203	−	0.257382i
$885$	0.901359	+	1.56120i	0.0302988	+	0.0524791i
$886$			12.0874i			0.406083i
$887$	15.3095	+	26.5169i	0.514043	+	0.890349i	0.999867	+	0.0162923i	$0.00518623\pi$
$887$	15.3095	+	26.5169i	0.514043	+	0.890349i	−0.485824	+	0.874057i	$0.661480\pi$
$888$	−61.2256	−	106.046i	−2.05460	−	3.55867i
$889$		0			0
$890$	−8.26994	+	4.77465i	−0.277209	+	0.160047i
$891$		−	9.95650i		−	0.333555i
$892$	62.1545	−	35.8849i	2.08109	−	1.20152i
$893$	−4.08336	+	7.07259i	−0.136644	+	0.236675i
$894$	4.63297	+	8.02454i	0.154950	+	0.268381i
$895$	−5.98957	−	3.45808i	−0.200209	−	0.115591i
$896$		0			0
$897$	14.3519	+	5.07264i	0.479195	+	0.169371i
$898$	12.6934	−	21.9856i	0.423584	−	0.733668i
$899$		−	28.7882i		−	0.960139i
$900$	−178.422			−5.94740
$901$	−16.0136			−0.533490
$902$			7.15851i			0.238352i
$903$		0			0
$904$	57.5634	−	33.2342i	1.91453	−	1.10535i
$905$	4.36546	+	2.52040i	0.145113	+	0.0837809i
$906$	46.0142	−	79.6989i	1.52872	−	2.64782i
$907$	36.6539			1.21707			0.608537	−	0.793526i	$-0.291757\pi$
$907$	36.6539			1.21707			0.608537	+	0.793526i	$0.291757\pi$
$908$	−103.427	+	59.7137i	−3.43235	+	1.98167i
$909$	18.8355			0.624733
$910$		0			0
$911$	−32.6958			−1.08326			−0.541630	−	0.840617i	$-0.682192\pi$
$911$	−32.6958			−1.08326			−0.541630	+	0.840617i	$0.682192\pi$
$912$	114.143	−	65.9005i	3.77965	−	2.18218i
$913$	−3.89015			−0.128745
$914$	−35.6410	+	61.7321i	−1.17890	+	2.04192i
$915$	5.30065	+	3.06033i	0.175234	+	0.101171i
$916$	−100.714	+	58.1475i	−3.32770	+	1.92125i
$917$		0			0
$918$			44.3841i			1.46489i
$919$	23.7652			0.783940			0.391970	−	0.919978i	$-0.371794\pi$
$919$	23.7652			0.783940			0.391970	+	0.919978i	$0.371794\pi$
$920$	−3.57962			−0.118016
$921$		−	83.3830i		−	2.74756i
$922$	13.6442	−	23.6325i	0.449348	−	0.778294i
$923$	−14.8405	+	41.9877i	−0.488480	+	1.38204i
$924$		0			0
$925$	−19.8074	−	11.4358i	−0.651264	−	0.376008i
$926$	−11.1729	−	19.3519i	−0.367163	−	0.635944i
$927$	49.3613	−	85.4963i	1.62124	−	2.80807i
$928$	−75.4369	+	43.5535i	−2.47634	+	1.42971i
$929$		−	19.7776i		−	0.648882i	−0.945906	−	0.324441i	$-0.894824\pi$
$929$		−	19.7776i		−	0.648882i	0.945906	−	0.324441i	$-0.105176\pi$
$930$	−11.7495	+	6.78357i	−0.385281	+	0.222442i
$931$		0			0
$932$	2.45971	+	4.26034i	0.0805704	+	0.139552i
$933$	3.88528	+	6.72950i	0.127198	+	0.220314i
$934$		−	29.0673i		−	0.951113i
$935$	0.0980834	+	0.169885i	0.00320767	+	0.00555585i
$936$	−138.016	−	161.402i	−4.51121	−	5.27558i
$937$	−37.9416			−1.23950			−0.619749	−	0.784800i	$-0.712765\pi$
$937$	−37.9416			−1.23950			−0.619749	+	0.784800i	$0.712765\pi$
$938$		0			0
$939$	−25.9037	+	44.8666i	−0.845336	+	1.46417i
$940$	−3.86768			−0.126150
$941$	−7.66127	+	4.42324i	−0.249750	+	0.144193i	−0.619650	−	0.784878i	$-0.712725\pi$
$941$	−7.66127	+	4.42324i	−0.249750	+	0.144193i	0.369900	+	0.929072i	$0.379392\pi$
$942$	93.4982	+	53.9812i	3.04634	+	1.75880i
$943$			7.48707i			0.243812i
$944$			20.0489i			0.652535i
$945$		0			0
$946$	3.06896	−	5.31559i	0.0997804	−	0.172825i
$947$	16.7975	−	9.69803i	0.545845	−	0.315144i	−0.201600	−	0.979468i	$-0.564614\pi$
$947$	16.7975	−	9.69803i	0.545845	−	0.315144i	0.747444	+	0.664324i	$0.231281\pi$
$948$	−89.5610	−	155.124i	−2.90881	−	5.03820i
$949$	−11.0622	+	31.2979i	−0.359094	+	1.01597i
$950$	23.0219	−	39.8750i	0.746928	−	1.29372i
$951$	73.5030	+	42.4370i	2.38350	+	1.37611i
$952$		0			0
$953$	−16.9408	−	29.3423i	−0.548767	−	0.950492i	−0.998359	−	0.0572580i	$-0.981764\pi$
$953$	−16.9408	−	29.3423i	−0.548767	−	0.950492i	0.449593	−	0.893234i	$-0.351569\pi$
$954$	−211.406	−	122.055i	−6.84451	−	3.95168i
$955$	3.84449	+	2.21961i	0.124405	+	0.0718251i
$956$	−8.66705	−	5.00392i	−0.280312	−	0.161838i
$957$	−7.79318	−	4.49939i	−0.251918	−	0.145445i
$958$	−37.7518	−	65.3881i	−1.21971	−	2.11259i
$959$		0			0
$960$	14.2888	+	8.24962i	0.461168	+	0.266255i
$961$	−3.73126	+	6.46273i	−0.120363	+	0.208475i
$962$	−8.20377	−	44.1169i	−0.264500	−	1.42239i
$963$	−41.4642	−	71.8182i	−1.33617	−	2.31431i
$964$	9.60921	−	5.54788i	0.309492	−	0.178685i
$965$	−1.55915	+	2.70053i	−0.0501908	+	0.0869330i
$966$		0			0
$967$		−	0.359435i		−	0.0115586i	−0.999983	−	0.00577932i	$-0.998160\pi$
$967$		−	0.359435i		−	0.0115586i	0.999983	−	0.00577932i	$-0.00183962\pi$
$968$			88.4592i			2.84319i
$969$	−12.2362	−	7.06455i	−0.393082	−	0.226946i
$970$	−11.4765	+	6.62594i	−0.368487	+	0.212746i
$971$	−19.4769			−0.625045			−0.312523	−	0.949910i	$-0.601174\pi$
$971$	−19.4769			−0.625045			−0.312523	+	0.949910i	$0.601174\pi$
$972$	−68.2771	+	118.259i	−2.18999	+	3.79317i
$973$		0			0
$974$	−83.5424			−2.67687
$975$	−53.0386	−	18.7464i	−1.69859	−	0.600365i
$976$	34.0354	+	58.9511i	1.08945	+	1.88698i
$977$			59.2434i			1.89536i	0.319217	+	0.947682i	$0.396580\pi$
$977$			59.2434i			1.89536i	−0.319217	+	0.947682i	$0.603420\pi$
$978$	−1.60276	−	2.77607i	−0.0512507	−	0.0887688i
$979$	−2.58931	−	4.48481i	−0.0827546	−	0.143335i
$980$		0			0
$981$	20.7391	−	11.9737i	0.662149	−	0.382292i
$982$		−	60.2879i		−	1.92387i
$983$	−18.7045	+	10.7991i	−0.596582	+	0.344437i	−0.767696	−	0.640814i	$-0.778597\pi$
$983$	−18.7045	+	10.7991i	−0.596582	+	0.344437i	0.171113	+	0.985251i	$0.445264\pi$
$984$	74.0679	−	128.289i	2.36120	−	4.08972i
$985$	0.225358	+	0.390331i	0.00718049	+	0.0124370i
$986$	17.1329	+	9.89168i	0.545622	+	0.315015i
$987$		0			0
$988$	63.7413	−	11.8530i	2.02788	−	0.377095i
$989$	3.20981	−	5.55956i	0.102066	−	0.176784i
$990$			2.99035i			0.0950397i
$991$	3.73559			0.118665			0.0593325	−	0.998238i	$-0.481103\pi$
$991$	3.73559			0.118665			0.0593325	+	0.998238i	$0.481103\pi$
$992$	−71.2196			−2.26122
$993$			53.2592i			1.69013i
$994$		0			0
$995$	3.30541	−	1.90838i	0.104789	−	0.0604997i
$996$	114.918	+	66.3480i	3.64132	+	2.10232i
$997$	−5.67223	+	9.82459i	−0.179641	+	0.311148i	−0.941758	−	0.336292i	$-0.890827\pi$
$997$	−5.67223	+	9.82459i	−0.179641	+	0.311148i	0.762116	+	0.647440i	$0.224160\pi$
$998$	−35.5611			−1.12567
$999$	−53.9073	+	31.1234i	−1.70555	+	0.984700i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.j.30.1		32
7.2	even	3		637.2.q.j.589.16	yes	32
7.3	odd	6		637.2.k.j.459.1		32
7.4	even	3		637.2.k.j.459.2		32
7.5	odd	6		637.2.q.j.589.15	yes	32
7.6	odd	2	inner	637.2.u.j.30.2		32
13.10	even	6		637.2.k.j.569.16		32
91.10	odd	6	inner	637.2.u.j.361.2		32
91.19	even	12		8281.2.a.cx.1.2		32
91.23	even	6		637.2.q.j.491.16	yes	32
91.33	even	12		8281.2.a.cx.1.32		32
91.58	odd	12		8281.2.a.cx.1.1		32
91.62	odd	6		637.2.k.j.569.15		32
91.72	odd	12		8281.2.a.cx.1.31		32
91.75	odd	6		637.2.q.j.491.15	✓	32
91.88	even	6	inner	637.2.u.j.361.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.k.j.459.1		32	7.3	odd	6
637.2.k.j.459.2		32	7.4	even	3
637.2.k.j.569.15		32	91.62	odd	6
637.2.k.j.569.16		32	13.10	even	6
637.2.q.j.491.15	✓	32	91.75	odd	6
637.2.q.j.491.16	yes	32	91.23	even	6
637.2.q.j.589.15	yes	32	7.5	odd	6
637.2.q.j.589.16	yes	32	7.2	even	3
637.2.u.j.30.1		32	1.1	even	1	trivial
637.2.u.j.30.2		32	7.6	odd	2	inner
637.2.u.j.361.1		32	91.88	even	6	inner
637.2.u.j.361.2		32	91.10	odd	6	inner
8281.2.a.cx.1.1		32	91.58	odd	12
8281.2.a.cx.1.2		32	91.19	even	12
8281.2.a.cx.1.31		32	91.72	odd	12
8281.2.a.cx.1.32		32	91.33	even	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.30510 + 1.33085i) q^{2} -3.18962 q^{3} +(2.54233 - 4.40345i) q^{4} +(0.285259 + 0.164694i) q^{5} +(7.35241 - 4.24492i) q^{6} +8.21047i q^{8} +7.17371 q^{9} -0.876736 q^{10} -0.475456i q^{11} +(-8.10909 + 14.0454i) q^{12} +(-2.74029 + 2.34325i) q^{13} +(-0.909869 - 0.525313i) q^{15} +(-5.84226 - 10.1191i) q^{16} +(-0.626291 + 1.08477i) q^{17} +(-16.5361 + 9.54714i) q^{18} -3.53646i q^{19} +(1.45045 - 0.837416i) q^{20} +(0.632762 + 1.09598i) q^{22} +(0.661804 + 1.14628i) q^{23} -26.1883i q^{24} +(-2.44575 - 4.23617i) q^{25} +(3.19812 - 9.04835i) q^{26} -13.3126 q^{27} +(-2.96691 + 5.13883i) q^{29} +2.79646 q^{30} +(-4.20156 + 2.42577i) q^{31} +(12.7131 + 7.33989i) q^{32} +1.51653i q^{33} -3.33400i q^{34} +(18.2380 - 31.5891i) q^{36} +(4.04936 - 2.33790i) q^{37} +(4.70650 + 8.15190i) q^{38} +(8.74049 - 7.47409i) q^{39} +(-1.35222 + 2.34211i) q^{40} +(4.89872 + 2.82828i) q^{41} +(-2.42505 - 4.20031i) q^{43} +(-2.09365 - 1.20877i) q^{44} +(2.04636 + 1.18147i) q^{45} +(-3.05105 - 1.76153i) q^{46} +(-1.99991 - 1.15465i) q^{47} +(18.6346 + 32.2761i) q^{48} +(11.2754 + 6.50987i) q^{50} +(1.99763 - 3.46000i) q^{51} +(3.35167 + 18.0241i) q^{52} +(6.39223 + 11.0717i) q^{53} +(30.6868 - 17.7170i) q^{54} +(0.0783050 - 0.135628i) q^{55} +11.2800i q^{57} -15.7941i q^{58} +(-1.48597 - 0.857925i) q^{59} +(-4.62638 + 2.67104i) q^{60} -5.82573 q^{61} +(6.45669 - 11.1833i) q^{62} -15.7042 q^{64} +(-1.16761 + 0.217124i) q^{65} +(-2.01827 - 3.49575i) q^{66} -9.79117i q^{67} +(3.18448 + 5.51569i) q^{68} +(-2.11091 - 3.65620i) q^{69} +(10.6965 - 6.17565i) q^{71} +58.8995i q^{72} +(7.97326 - 4.60336i) q^{73} +(-6.22279 + 10.7782i) q^{74} +(7.80103 + 13.5118i) q^{75} +(-15.5726 - 8.99086i) q^{76} +(-10.2008 + 28.8609i) q^{78} +(-5.52226 + 9.56484i) q^{79} -3.84875i q^{80} +20.9409 q^{81} -15.0561 q^{82} -8.18192i q^{83} +(-0.357311 + 0.206293i) q^{85} +(11.1800 + 6.45476i) q^{86} +(9.46332 - 16.3910i) q^{87} +3.90372 q^{88} +(9.43265 - 5.44595i) q^{89} -6.28944 q^{90} +6.73011 q^{92} +(13.4014 - 7.73730i) q^{93} +6.14666 q^{94} +(0.582435 - 1.00881i) q^{95} +(-40.5499 - 23.4115i) q^{96} +(13.0900 - 7.55751i) q^{97} -3.41078i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4} + 56 q^{9} - 12 q^{15} - 28 q^{16} - 24 q^{18} + 8 q^{22} + 24 q^{23} + 20 q^{25} - 24 q^{29} - 48 q^{30} + 60 q^{32} + 92 q^{36} + 52 q^{39} + 12 q^{43} + 24 q^{46} + 12 q^{50} - 36 q^{53}+ \cdots + 84 q^{95}+O(q^{100}) \) 32 * q + 20 * q^4 + 56 * q^9 - 12 * q^15 - 28 * q^16 - 24 * q^18 + 8 * q^22 + 24 * q^23 + 20 * q^25 - 24 * q^29 - 48 * q^30 + 60 * q^32 + 92 * q^36 + 52 * q^39 + 12 * q^43 + 24 * q^46 + 12 * q^50 - 36 * q^53 - 276 * q^60 + 32 * q^64 + 12 * q^65 - 48 * q^71 + 24 * q^74 - 156 * q^78 - 48 * q^79 + 128 * q^81 + 12 * q^85 + 48 * q^86 - 112 * q^88 + 168 * q^92 + 48 * q^93 + 84 * q^95

Introduction

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