LMFDB - Embedded newform 637.2.q.j.491.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
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			491.16
Character	$\chi$	$=$	637.491
Dual form			637.2.q.j.589.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.30510 - 1.33085i) q^{2} +(1.59481 + 2.76230i) q^{3} +(2.54233 - 4.40345i) q^{4} +0.329389i q^{5} +(7.35241 + 4.24492i) q^{6} -8.21047i q^{8} +(-3.58685 + 6.21261i) q^{9} +O(q^{10})$	\(q+(2.30510 - 1.33085i) q^{2} +(1.59481 + 2.76230i) q^{3} +(2.54233 - 4.40345i) q^{4} +0.329389i q^{5} +(7.35241 + 4.24492i) q^{6} -8.21047i q^{8} +(-3.58685 + 6.21261i) q^{9} +(0.438368 + 0.759275i) q^{10} +(0.411757 - 0.237728i) q^{11} +16.2182 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} +19.0943i q^{18} +(-3.06266 - 1.76823i) q^{19} +(1.45045 + 0.837416i) q^{20} +(0.632762 - 1.09598i) q^{22} +(0.661804 + 1.14628i) q^{23} +(22.6798 - 13.0942i) q^{24} +4.89150 q^{25} +(-9.43517 - 1.75452i) q^{26} -13.3126 q^{27} +(-2.96691 - 5.13883i) q^{29} +(-1.39823 + 2.42180i) q^{30} +4.85154i q^{31} +(-12.7131 - 7.33989i) q^{32} +(1.31335 + 0.758263i) q^{33} +3.33400i q^{34} +(18.2380 + 31.5891i) q^{36} +(-4.04936 + 2.33790i) q^{37} -9.41300 q^{38} +(2.10251 - 11.3065i) q^{39} +2.70444 q^{40} +(4.89872 - 2.82828i) q^{41} +(-2.42505 + 4.20031i) q^{43} -2.41754i q^{44} +(-2.04636 - 1.18147i) q^{45} +(3.05105 + 1.76153i) q^{46} -2.30929i q^{47} +(18.6346 - 32.2761i) q^{48} +(11.2754 - 6.50987i) q^{50} -3.99527 q^{51} +(-17.2851 + 6.10939i) q^{52} -12.7845 q^{53} +(-30.6868 + 17.7170i) q^{54} +(0.0783050 + 0.135628i) q^{55} -11.2800i q^{57} +(-13.6781 - 7.89703i) q^{58} +(1.48597 + 0.857925i) q^{59} +5.34209i q^{60} +(2.91286 - 5.04523i) q^{61} +(6.45669 + 11.1833i) q^{62} -15.7042 q^{64} +(0.771841 - 0.902620i) q^{65} +4.03654 q^{66} +(8.47940 - 4.89559i) q^{67} +(3.18448 + 5.51569i) q^{68} +(-2.11091 + 3.65620i) q^{69} +(10.6965 + 6.17565i) q^{71} +(51.0085 + 29.4498i) q^{72} -9.20673i 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} +11.0445 q^{79} +(3.33311 - 1.92437i) q^{80} +(-10.4705 - 18.1354i) q^{81} +(7.52804 - 13.0390i) q^{82} +8.18192i q^{83} +(-0.357311 - 0.206293i) q^{85} +12.9095i q^{86} +(9.46332 - 16.3910i) q^{87} +(-1.95186 - 3.38072i) q^{88} +(-9.43265 + 5.44595i) q^{89} -6.28944 q^{90} +6.73011 q^{92} +(-13.4014 + 7.73730i) q^{93} +(-3.07333 - 5.32316i) q^{94} +(0.582435 - 1.00881i) q^{95} -46.8230i q^{96} +(13.0900 + 7.55751i) q^{97} +3.41078i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 20 q^{4} - 28 q^{9}+O(q^{10}) $ 32 * q + 20 * q^4 - 28 * q^9	$ 32 q + 20 q^{4} - 28 q^{9} - 12 q^{15} - 28 q^{16} + 8 q^{22} + 24 q^{23} - 40 q^{25} - 24 q^{29} + 24 q^{30} - 60 q^{32} + 92 q^{36} - 32 q^{39} + 12 q^{43} - 24 q^{46} + 12 q^{50} + 72 q^{53} - 132 q^{58} + 32 q^{64} + 48 q^{67} - 48 q^{71} + 72 q^{72} + 24 q^{74} - 156 q^{78} + 96 q^{79} - 64 q^{81} + 12 q^{85} + 56 q^{88} + 168 q^{92} - 48 q^{93} + 84 q^{95}+O(q^{100}) $ 32 * q + 20 * q^4 - 28 * q^9 - 12 * q^15 - 28 * q^16 + 8 * q^22 + 24 * q^23 - 40 * q^25 - 24 * q^29 + 24 * q^30 - 60 * q^32 + 92 * q^36 - 32 * q^39 + 12 * q^43 - 24 * q^46 + 12 * q^50 + 72 * q^53 - 132 * q^58 + 32 * q^64 + 48 * q^67 - 48 * q^71 + 72 * q^72 + 24 * q^74 - 156 * q^78 + 96 * q^79 - 64 * q^81 + 12 * q^85 + 56 * q^88 + 168 * q^92 - 48 * q^93 + 84 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	2.30510	−	1.33085i	1.62995	−	0.941054i	0.645850	−	0.763465i	$-0.276503\pi$
$2$	2.30510	−	1.33085i	1.62995	−	0.941054i	0.984105	−	0.177590i	$-0.0568300\pi$
$3$	1.59481	+	2.76230i	0.920765	+	1.59481i	0.798234	+	0.602348i	$0.205768\pi$
$3$	1.59481	+	2.76230i	0.920765	+	1.59481i	0.122532	+	0.992465i	$0.460899\pi$
$4$	2.54233	−	4.40345i	1.27117	−	2.20173i
$5$			0.329389i			0.147307i	0.997284	+	0.0736536i	$0.0234659\pi$
$5$			0.329389i			0.147307i	−0.997284	+	0.0736536i	$0.976534\pi$
$6$	7.35241	+	4.24492i	3.00161	+	1.73298i
$7$		0			0
$7$		0			0
$8$		−	8.21047i		−	2.90284i
$9$	−3.58685	+	6.21261i	−1.19562	+	2.07087i
$10$	0.438368	+	0.759275i	0.138624	+	0.240104i
$11$	0.411757	−	0.237728i	0.124149	−	0.0716777i	−0.436639	−	0.899637i	$-0.643831\pi$
$11$	0.411757	−	0.237728i	0.124149	−	0.0716777i	0.560789	+	0.827959i	$0.310498\pi$
$12$	16.2182			4.68179
$13$	−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	$0.215205\pi$
$18$			19.0943i			4.50057i
$19$	−3.06266	−	1.76823i	−0.702623	−	0.405659i	0.105701	−	0.994398i	$-0.466291\pi$
$19$	−3.06266	−	1.76823i	−0.702623	−	0.405659i	−0.808324	+	0.588739i	$0.799625\pi$
$20$	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	$0.789267\pi$
$24$	22.6798	−	13.0942i	4.62949	−	2.67284i
$25$	4.89150			0.978301
$26$	−9.43517	−	1.75452i	−1.85039	−	0.344090i
$27$	−13.3126			−2.56200
$28$		0			0
$29$	−2.96691	−	5.13883i	−0.550941	−	0.954258i	−0.998207	−	0.0598566i	$-0.980936\pi$
$29$	−2.96691	−	5.13883i	−0.550941	−	0.954258i	0.447266	−	0.894401i	$-0.352398\pi$
$30$	−1.39823	+	2.42180i	−0.255280	+	0.442159i
$31$			4.85154i			0.871363i	0.900101	+	0.435682i	$0.143493\pi$
$31$			4.85154i			0.871363i	−0.900101	+	0.435682i	$0.856507\pi$
$32$	−12.7131	−	7.33989i	−2.24737	−	1.29752i
$33$	1.31335	+	0.758263i	0.228625	+	0.131997i
$34$			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	−0.794449	−	0.607331i	$-0.792240\pi$
$37$	−4.04936	+	2.33790i	−0.665710	+	0.384348i	0.128739	+	0.991678i	$0.458907\pi$
$38$	−9.41300			−1.52699
$39$	2.10251	−	11.3065i	0.336671	−	1.81049i
$40$	2.70444			0.427609
$41$	4.89872	−	2.82828i	0.765052	−	0.441703i	−0.0660547	−	0.997816i	$-0.521041\pi$
$41$	4.89872	−	2.82828i	0.765052	−	0.441703i	0.831107	+	0.556113i	$0.187708\pi$
$42$		0			0
$43$	−2.42505	+	4.20031i	−0.369817	+	0.640541i	−0.989537	−	0.144282i	$-0.953913\pi$
$43$	−2.42505	+	4.20031i	−0.369817	+	0.640541i	0.619720	+	0.784823i	$0.287246\pi$
$44$		−	2.41754i		−	0.364457i
$45$	−2.04636	−	1.18147i	−0.305054	−	0.176123i
$46$	3.05105	+	1.76153i	0.449853	+	0.259723i
$47$		−	2.30929i		−	0.336845i	−0.985715	−	0.168423i	$-0.946133\pi$
$47$		−	2.30929i		−	0.336845i	0.985715	−	0.168423i	$-0.0538673\pi$
$48$	18.6346	−	32.2761i	2.68967	−	4.65865i
$49$		0			0
$50$	11.2754	−	6.50987i	1.59459	−	0.920634i
$51$	−3.99527			−0.559449
$52$	−17.2851	+	6.10939i	−2.39701	+	0.847220i
$53$	−12.7845			−1.75608			−0.878040	−	0.478587i	$-0.841149\pi$
$53$	−12.7845			−1.75608			−0.878040	+	0.478587i	$0.841149\pi$
$54$	−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
$58$	−13.6781	−	7.89703i	−1.79602	−	1.03693i
$59$	1.48597	+	0.857925i	0.193457	+	0.111692i	0.593600	−	0.804760i	$-0.297706\pi$
$59$	1.48597	+	0.857925i	0.193457	+	0.111692i	−0.400143	+	0.916453i	$0.631040\pi$
$60$			5.34209i			0.689661i
$61$	2.91286	−	5.04523i	0.372954	−	0.645975i	−0.617064	−	0.786913i	$-0.711678\pi$
$61$	2.91286	−	5.04523i	0.372954	−	0.645975i	0.990019	+	0.140937i	$0.0450116\pi$
$62$	6.45669	+	11.1833i	0.820000	+	1.42028i
$63$		0			0
$64$	−15.7042			−1.96302
$65$	0.771841	−	0.902620i	0.0957351	−	0.111956i
$66$	4.03654			0.496864
$67$	8.47940	−	4.89559i	1.03592	−	0.598091i	0.117248	−	0.993103i	$-0.462593\pi$
$67$	8.47940	−	4.89559i	1.03592	−	0.598091i	0.918676	+	0.395012i	$0.129259\pi$
$68$	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	0.974883	−	0.222718i	$-0.0714928\pi$
$71$	10.6965	+	6.17565i	1.26945	+	0.732915i	0.294562	+	0.955632i	$0.404826\pi$
$72$	51.0085	+	29.4498i	6.01141	+	3.47069i
$73$		−	9.20673i		−	1.07757i	−0.842445	−	0.538783i	$-0.818884\pi$
$73$		−	9.20673i		−	1.07757i	0.842445	−	0.538783i	$-0.181116\pi$
$74$	−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
$79$	11.0445			1.24261			0.621303	−	0.783571i	$-0.286604\pi$
$79$	11.0445			1.24261			0.621303	+	0.783571i	$0.286604\pi$
$80$	3.33311	−	1.92437i	0.372654	−	0.215152i
$81$	−10.4705	−	18.1354i	−1.16339	−	2.01504i
$82$	7.52804	−	13.0390i	0.831333	−	1.43991i
$83$			8.18192i			0.898083i	0.893511	+	0.449041i	$0.148234\pi$
$83$			8.18192i			0.898083i	−0.893511	+	0.449041i	$0.851766\pi$
$84$		0			0
$85$	−0.357311	−	0.206293i	−0.0387558	−	0.0223757i
$86$			12.9095i			1.39207i
$87$	9.46332	−	16.3910i	1.01457	−	1.75729i
$88$	−1.95186	−	3.38072i	−0.208069	−	0.360386i
$89$	−9.43265	+	5.44595i	−0.999859	+	0.577269i	−0.908207	−	0.418522i	$-0.862548\pi$
$89$	−9.43265	+	5.44595i	−0.999859	+	0.577269i	−0.0916527	+	0.995791i	$0.529215\pi$
$90$	−6.28944			−0.662966
$91$		0			0
$92$	6.73011			0.701662
$93$	−13.4014	+	7.73730i	−1.38966	+	0.802321i
$94$	−3.07333	−	5.32316i	−0.316990	−	0.549042i
$95$	0.582435	−	1.00881i	0.0597565	−	0.103501i
$96$		−	46.8230i		−	4.77885i
$97$	13.0900	+	7.55751i	1.32909	+	0.767349i	0.985158	−	0.171647i	$-0.0549089\pi$
$97$	13.0900	+	7.55751i	1.32909	+	0.767349i	0.343928	+	0.938996i	$0.388242\pi$
$98$		0			0
$99$			3.41078i			0.342796i
$100$	12.4358	−	21.5395i	1.24358	−	2.15395i
$101$	−1.31281	−	2.27386i	−0.130630	−	0.226257i	0.793290	−	0.608844i	$-0.208367\pi$
$101$	−1.31281	−	2.27386i	−0.130630	−	0.226257i	−0.923919	+	0.382587i	$0.875033\pi$
$102$	−9.20951	+	5.31711i	−0.911877	+	0.526472i
$103$	−13.7617			−1.35598			−0.677992	−	0.735069i	$-0.737150\pi$
$103$	−13.7617			−1.35598			−0.677992	+	0.735069i	$0.737150\pi$
$104$	−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
$109$		−	3.33823i		−	0.319744i	−0.987138	−	0.159872i	$-0.948892\pi$
$109$		−	3.33823i		−	0.319744i	0.987138	−	0.159872i	$-0.0511082\pi$
$110$	0.361002	+	0.208425i	0.0344202	+	0.0198725i
$111$	−12.9159	−	7.45701i	−1.22593	−	0.707788i
$112$		0			0
$113$	−4.04779	+	7.01097i	−0.380784	+	0.659537i	−0.991174	−	0.132564i	$-0.957679\pi$
$113$	−4.04779	+	7.01097i	−0.380784	+	0.659537i	0.610391	+	0.792100i	$0.291012\pi$
$114$	−15.0120	−	26.0015i	−1.40600	−	2.43526i
$115$	−0.377571	+	0.217991i	−0.0352087	+	0.0203277i
$116$	−30.1715			−2.80135
$117$	24.3867	−	8.61944i	2.25455	−	0.796867i
$118$	4.56708			0.420434
$119$		0			0
$120$	4.31307	+	7.47046i	0.393728	+	0.681957i
$121$	−5.38697	+	9.33051i	−0.489725	+	0.848228i
$122$		−	15.5064i		−	1.40388i
$123$	15.6251	+	9.02115i	1.40887	+	0.813410i
$124$	21.3635	+	12.3342i	1.91850	+	1.10765i
$125$			3.25815i			0.291418i
$126$		0			0
$127$	−2.80212	−	4.85342i	−0.248648	−	0.430671i	0.714503	−	0.699633i	$-0.246653\pi$
$127$	−2.80212	−	4.85342i	−0.248648	−	0.430671i	−0.963151	+	0.268961i	$0.913320\pi$
$128$	−10.7737	+	6.22017i	−0.952265	+	0.549791i
$129$	−15.4700			−1.36206
$130$	0.577919	−	3.10784i	0.0506869	−	0.272575i
$131$	−5.90287			−0.515736			−0.257868	−	0.966180i	$-0.583020\pi$
$131$	−5.90287			−0.515736			−0.257868	+	0.966180i	$0.583020\pi$
$132$	6.67795	−	3.85552i	0.581241	−	0.335580i
$133$		0			0
$134$	13.0306	−	22.5697i	1.12567	−	1.94972i
$135$		−	4.38501i		−	0.377401i
$136$	8.90646	+	5.14215i	0.763723	+	0.440936i
$137$	17.0289	+	9.83163i	1.45488	+	0.839973i	0.998752	−	0.0499439i	$-0.0159043\pi$
$137$	17.0289	+	9.83163i	1.45488	+	0.839973i	0.456123	+	0.889917i	$0.349238\pi$
$138$			11.2372i			0.956575i
$139$	−5.42353	+	9.39384i	−0.460018	+	0.796775i	−0.998961	−	0.0455674i	$-0.985490\pi$
$139$	−5.42353	+	9.39384i	−0.460018	+	0.796775i	0.538943	+	0.842342i	$0.318824\pi$
$140$		0			0
$141$	6.37895	−	3.68289i	0.537205	−	0.310155i
$142$	32.8755			2.75885
$143$	−1.68539	−	0.313407i	−0.140939	−	0.0262084i
$144$	83.8213			6.98511
$145$	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
$149$	0.945194	+	0.545708i	0.0774333	+	0.0447061i	0.538217	−	0.842806i	$-0.319098\pi$
$149$	0.945194	+	0.545708i	0.0774333	+	0.0447061i	−0.460783	+	0.887513i	$0.652432\pi$
$150$	35.9644	+	20.7640i	2.93648	+	1.69538i
$151$		−	10.8398i		−	0.882132i	−0.897475	−	0.441066i	$-0.854600\pi$
$151$		−	10.8398i		−	0.882132i	0.897475	−	0.441066i	$-0.145400\pi$
$152$	−14.5180	+	25.1459i	−1.17757	+	2.03960i
$153$	−4.49283	−	7.78181i	−0.363224	−	0.629122i
$154$		0			0
$155$	−1.59804			−0.128358
$156$	−44.4425	−	38.0033i	−3.55825	−	3.04270i
$157$	−12.7167			−1.01490			−0.507450	−	0.861681i	$-0.669412\pi$
$157$	−12.7167			−1.01490			−0.507450	+	0.861681i	$0.669412\pi$
$158$	25.4588	−	14.6986i	2.02539	−	1.16936i
$159$	−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
$163$	−0.326987	−	0.188786i	−0.0256116	−	0.0147869i	0.487140	−	0.873324i	$-0.338040\pi$
$163$	−0.326987	−	0.188786i	−0.0256116	−	0.0147869i	−0.512751	+	0.858537i	$0.671374\pi$
$164$		−	28.7617i		−	2.24591i
$165$	−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	0.109164	−	0.994024i	$-0.465183\pi$
$167$	13.2407	−	7.64452i	1.02460	−	0.591551i	0.915432	+	0.402473i	$0.131849\pi$
$168$		0			0
$169$	2.01834	+	12.8424i	0.155257	+	0.987874i
$170$	−1.09818			−0.0842268
$171$	21.9706	−	12.6848i	1.68014	−	0.970027i
$172$	12.3306	+	21.3572i	0.940197	+	1.62847i
$173$	−1.14799	+	1.98837i	−0.0872797	+	0.151173i	−0.906360	−	0.422505i	$-0.861151\pi$
$173$	−1.14799	+	1.98837i	−0.0872797	+	0.151173i	0.819081	+	0.573678i	$0.194484\pi$
$174$		−	50.3771i		−	3.81908i
$175$		0			0
$176$	−4.81118	−	2.77774i	−0.362656	−	0.209380i
$177$			5.47292i			0.411369i
$178$	−14.4955	+	25.1069i	−1.08648	+	1.88184i
$179$	10.4985	+	18.1839i	0.784693	+	1.35913i	0.929183	+	0.369621i	$0.120512\pi$
$179$	10.4985	+	18.1839i	0.784693	+	1.35913i	−0.144490	+	0.989506i	$0.546154\pi$
$180$	−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
$185$	−0.770077	−	1.33381i	−0.0566172	−	0.0980638i
$186$	−20.5944	+	35.6706i	−1.51006	+	2.61549i
$187$			0.595548i			0.0435508i
$188$	−10.1689	−	5.87100i	−0.741641	−	0.428187i
$189$		0			0
$190$		−	3.10054i		−	0.224937i
$191$	−6.73859	+	11.6716i	−0.487587	+	0.844525i	−0.999898	−	0.0142745i	$-0.995456\pi$
$191$	−6.73859	+	11.6716i	−0.487587	+	0.844525i	0.512311	+	0.858800i	$0.328789\pi$
$192$	−25.0452	−	43.3796i	−1.80748	−	3.13065i
$193$	−8.19860	+	4.73346i	−0.590148	+	0.340722i	−0.765156	−	0.643845i	$-0.777338\pi$
$193$	−8.19860	+	4.73346i	−0.590148	+	0.340722i	0.175008	+	0.984567i	$0.444005\pi$
$194$	40.2317			2.88847
$195$	3.72424	+	0.692544i	0.266699	+	0.0495941i
$196$		0			0
$197$	1.18502	−	0.684169i	0.0844289	−	0.0487450i	−0.457191	−	0.889368i	$-0.651144\pi$
$197$	1.18502	−	0.684169i	0.0844289	−	0.0487450i	0.541620	+	0.840623i	$0.317811\pi$
$198$	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	$0.0319494\pi$
$200$		−	40.1616i		−	2.83985i
$201$	27.0461	+	15.6151i	1.90769	+	1.10140i
$202$	−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
$206$	−31.7222	+	18.3148i	−2.21019	+	1.27605i
$207$	−9.49517			−0.659960
$208$	−7.70210	+	41.4191i	−0.534045	+	2.87190i
$209$	−1.68143			−0.116307
$210$		0			0
$211$	2.79738	+	4.84521i	0.192580	+	0.333558i	0.946104	−	0.323862i	$-0.104981\pi$
$211$	2.79738	+	4.84521i	0.192580	+	0.333558i	−0.753525	+	0.657420i	$0.771648\pi$
$212$	−32.5024	+	56.2957i	−2.23227	+	3.86641i
$213$			39.3960i			2.69937i
$214$	−26.6471	−	15.3847i	−1.82156	−	1.05168i
$215$	−1.38353	−	0.798784i	−0.0943563	−	0.0544766i
$216$			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
$220$	0.796310			0.0536872
$221$	4.25810	−	1.50502i	0.286431	−	0.101238i
$222$	−39.6967			−2.66427
$223$	12.2239	−	7.05747i	0.818573	−	0.472603i	−0.0313511	−	0.999508i	$-0.509981\pi$
$223$	12.2239	−	7.05747i	0.818573	−	0.472603i	0.849924	+	0.526905i	$0.176648\pi$
$224$		0			0
$225$	−17.5451	+	30.3890i	−1.16967	+	2.02593i
$226$			21.5480i			1.43335i
$227$	20.3410	+	11.7439i	1.35008	+	0.779469i	0.988260	−	0.152780i	$-0.0488225\pi$
$227$	20.3410	+	11.7439i	1.35008	+	0.779469i	0.361819	+	0.932248i	$0.382156\pi$
$228$	−49.6708	−	28.6775i	−3.28953	−	1.89921i
$229$		−	22.8717i		−	1.51140i	−0.654916	−	0.755702i	$-0.727296\pi$
$229$		−	22.8717i		−	1.51140i	0.654916	−	0.755702i	$-0.272704\pi$
$230$	−0.580227	+	1.00498i	−0.0382590	+	0.0662666i
$231$		0			0
$232$	−42.1923	+	24.3597i	−2.77006	+	1.59929i
$233$	0.967499			0.0633830			0.0316915	−	0.999498i	$-0.489911\pi$
$233$	0.967499			0.0633830			0.0316915	+	0.999498i	$0.489911\pi$
$234$	44.7427	−	52.3238i	2.92492	−	3.42051i
$235$	0.760656			0.0496197
$236$	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	$0.0202765\pi$
$239$			1.96824i			0.127315i	−0.997972	+	0.0636574i	$0.979723\pi$
$240$	10.6314	+	6.13803i	0.686253	+	0.396208i
$241$	−1.88984	−	1.09110i	−0.121735	−	0.0702839i	0.437896	−	0.899026i	$-0.355724\pi$
$241$	−1.88984	−	1.09110i	−0.121735	−	0.0702839i	−0.559631	+	0.828742i	$0.689057\pi$
$242$			28.6770i			1.84343i
$243$	13.4280	−	23.2580i	0.861409	−	1.49200i
$244$	−14.8109	−	25.6533i	−0.948174	−	1.64229i
$245$		0			0
$246$	48.0233			3.06185
$247$	4.24917	+	12.0220i	0.270368	+	0.764944i
$248$	39.8335			2.52943
$249$	−22.6009	+	13.0486i	−1.43227	+	0.826924i
$250$	4.33612	+	7.51037i	0.274240	+	0.474998i
$251$	12.5057	−	21.6606i	0.789355	−	1.36720i	−0.137008	−	0.990570i	$-0.543749\pi$
$251$	12.5057	−	21.6606i	0.789355	−	1.36720i	0.926363	−	0.376633i	$-0.122918\pi$
$252$		0			0
$253$	0.545005	+	0.314659i	0.0342642	+	0.0197824i
$254$	−12.9184	−	7.45842i	−0.810570	−	0.467983i
$255$		−	1.31600i		−	0.0824109i
$256$	−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
$261$	42.5674			2.63486
$262$	−13.6067	+	7.85584i	−0.840626	+	0.485336i
$263$	−1.93635	−	3.35385i	−0.119400	−	0.206807i	0.800130	−	0.599827i	$-0.204764\pi$
$263$	−1.93635	−	3.35385i	−0.119400	−	0.206807i	−0.919530	+	0.393019i	$0.871431\pi$
$264$	6.22570	−	10.7832i	0.383165	−	0.663662i
$265$		−	4.21106i		−	0.258683i
$266$		0			0
$267$	−30.0866	−	17.3705i	−1.84127	−	1.06306i
$268$		−	49.7849i		−	3.04109i
$269$	−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	$0.318371\pi$
$270$	−5.83580	−	10.1079i	−0.355155	−	0.615147i
$271$	−11.5962	+	6.69507i	−0.704419	+	0.406696i	−0.808991	−	0.587821i	$-0.799986\pi$
$271$	−11.5962	+	6.69507i	−0.704419	+	0.406696i	0.104572	+	0.994517i	$0.466653\pi$
$272$	14.6358			0.887427
$273$		0			0
$274$	52.3378			3.16184
$275$	2.01411	−	1.16285i	0.121455	−	0.0701223i
$276$	10.7333	+	18.5905i	0.646066	+	1.11902i
$277$	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	$0.0857275\pi$
$278$			28.8717i			1.73161i
$279$	−30.1408	−	17.4018i	−1.80448	−	1.04182i
$280$		0			0
$281$			17.7474i			1.05872i	0.848397	+	0.529360i	$0.177568\pi$
$281$			17.7474i			1.05872i	−0.848397	+	0.529360i	$0.822432\pi$
$282$	9.80277	−	16.9789i	0.583746	−	1.01108i
$283$	−10.8886	−	18.8596i	−0.647261	−	1.12109i	−0.983774	−	0.179410i	$-0.942581\pi$
$283$	−10.8886	−	18.8596i	−0.647261	−	1.12109i	0.336514	−	0.941679i	$-0.390752\pi$
$284$	54.3883	−	31.4011i	3.22735	−	1.86331i
$285$	3.71550			0.220087
$286$	−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
$291$			48.2112i			2.82619i
$292$	−40.5414	−	23.4066i	−2.37251	−	1.36977i
$293$	23.8412	+	13.7648i	1.39282	+	0.804145i	0.993627	−	0.112721i	$-0.0359567\pi$
$293$	23.8412	+	13.7648i	1.39282	+	0.804145i	0.399194	+	0.916867i	$0.369290\pi$
$294$		0			0
$295$	−0.282591	+	0.489462i	−0.0164531	+	0.0284976i
$296$	19.1952	+	33.2471i	1.11570	+	1.93245i
$297$	−5.48154	+	3.16477i	−0.318071	+	0.183638i
$298$	2.90503			0.168284
$299$	0.872485	−	4.69190i	0.0504571	−	0.271340i
$300$	79.3313			4.58019
$301$		0			0
$302$	−14.4262	−	24.9869i	−0.830135	−	1.43784i
$303$	4.18738	−	7.25275i	0.240559	−	0.416660i
$304$			41.3218i			2.36997i
$305$	1.66184	+	0.959465i	0.0951568	+	0.0549388i
$306$	−20.7129	−	11.9586i	−1.18408	−	0.683627i
$307$		−	26.1419i		−	1.49200i	−0.665946	−	0.746000i	$-0.731972\pi$
$307$		−	26.1419i		−	1.49200i	0.665946	−	0.746000i	$-0.268028\pi$
$308$		0			0
$309$	−21.9474	−	38.0140i	−1.24854	−	2.16254i
$310$	−3.68366	+	2.12676i	−0.209218	+	0.120792i
$311$	2.43620			0.138144			0.0690720	−	0.997612i	$-0.477996\pi$
$311$	2.43620			0.138144			0.0690720	+	0.997612i	$0.477996\pi$
$312$	−92.8320	−	17.2626i	−5.25558	−	0.977303i
$313$	−16.2425			−0.918080			−0.459040	−	0.888416i	$-0.651807\pi$
$313$	−16.2425			−0.918080			−0.459040	+	0.888416i	$0.651807\pi$
$314$	−29.3132	+	16.9240i	−1.65424	+	0.955077i
$315$		0			0
$316$	28.0789	−	48.6340i	1.57956	−	2.73588i
$317$		−	26.6094i		−	1.49453i	−0.664525	−	0.747266i	$-0.731366\pi$
$317$		−	26.6094i		−	1.49453i	0.664525	−	0.747266i	$-0.268634\pi$
$318$	−93.9966	−	54.2690i	−5.27107	−	3.04325i
$319$	−2.44329	−	1.41063i	−0.136798	−	0.0789803i
$320$		−	5.17278i		−	0.289167i
$321$	18.4361	−	31.9323i	1.02900	−	1.78229i
$322$		0			0
$323$	3.83624	−	2.21485i	0.213454	−	0.123238i
$324$	−106.478			−5.91543
$325$	−13.4041	−	11.4620i	−0.743527	−	0.635799i
$326$	−1.00498			−0.0556610
$327$	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
$331$	−14.4606	−	8.34882i	−0.794825	−	0.458892i	0.0468334	−	0.998903i	$-0.485087\pi$
$331$	−14.4606	−	8.34882i	−0.794825	−	0.458892i	−0.841658	+	0.540010i	$0.818420\pi$
$332$	36.0287	+	20.8012i	1.97733	+	1.14161i
$333$		−	33.5428i		−	1.83813i
$334$	20.3475	−	35.2428i	1.11336	−	1.92840i
$335$	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	$0.722425\pi$
$338$	21.7438	+	26.9169i	1.18271	+	1.46408i
$339$	−25.8218			−1.40245
$340$	−1.81681	+	1.04893i	−0.0985301	+	0.0568864i
$341$	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
$345$	−1.20431	−	0.695309i	−0.0648379	−	0.0374342i
$346$			6.11119i			0.328540i
$347$	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	−0.910965	−	0.412484i	$-0.864661\pi$
$349$	−18.8539	+	10.8853i	−1.00923	+	0.582677i	−0.0982611	+	0.995161i	$0.531328\pi$
$350$		0			0
$351$	36.4802	+	31.1947i	1.94717	+	1.66505i
$352$	−6.97959			−0.372013
$353$	22.9008	−	13.2218i	1.21889	−	0.703725i	0.254208	−	0.967150i	$-0.418185\pi$
$353$	22.9008	−	13.2218i	1.21889	−	0.703725i	0.964680	+	0.263424i	$0.0848519\pi$
$354$	7.28364	+	12.6156i	0.387121	+	0.670513i
$355$	−2.03419	+	3.52332i	−0.107964	+	0.186998i
$356$			55.3817i			2.93522i
$357$		0			0
$358$	48.4001	+	27.9438i	2.55803	+	1.47688i
$359$		−	22.5860i		−	1.19204i	−0.802969	−	0.596021i	$-0.796748\pi$
$359$		−	22.5860i		−	1.19204i	0.802969	−	0.596021i	$-0.203252\pi$
$360$	−9.70042	+	16.8016i	−0.511257	+	0.885523i
$361$	−3.24673	−	5.62351i	−0.170881	−	0.295974i
$362$	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
$367$	−4.35638	−	7.54547i	−0.227401	−	0.393870i	0.729636	−	0.683836i	$-0.239690\pi$
$367$	−4.35638	−	7.54547i	−0.227401	−	0.393870i	−0.957037	+	0.289965i	$0.906356\pi$
$368$	7.73286	−	13.3937i	0.403103	−	0.698195i
$369$			40.5785i			2.11243i
$370$	−3.55021	−	2.04972i	−0.184567	−	0.106560i
$371$		0			0
$372$			78.6832i			4.07954i
$373$	8.52514	−	14.7660i	0.441415	−	0.764554i	−0.556380	−	0.830928i	$-0.687810\pi$
$373$	8.52514	−	14.7660i	0.441415	−	0.764554i	0.997795	+	0.0663747i	$0.0211433\pi$
$374$	0.792586	+	1.37280i	0.0409837	+	0.0709858i
$375$	−8.99998	+	5.19614i	−0.464757	+	0.268327i
$376$	−18.9604			−0.977808
$377$	−3.91140	+	21.0341i	−0.201448	+	1.08331i
$378$		0			0
$379$	7.09232	−	4.09475i	0.364308	−	0.210333i	−0.306661	−	0.951819i	$-0.599212\pi$
$379$	7.09232	−	4.09475i	0.364308	−	0.210333i	0.670969	+	0.741486i	$0.265878\pi$
$380$	−2.96149	−	5.12945i	−0.151921	−	0.263135i
$381$	8.93772	−	15.4806i	0.457893	−	0.793094i
$382$			35.8722i			1.83538i
$383$	12.6263	+	7.28978i	0.645172	+	0.372490i	0.786604	−	0.617458i	$-0.211837\pi$
$383$	12.6263	+	7.28978i	0.645172	+	0.372490i	−0.141432	+	0.989948i	$0.545171\pi$
$384$	−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
$388$	66.5582	−	38.4274i	3.37898	−	1.95086i
$389$	−9.92809			−0.503374			−0.251687	−	0.967809i	$-0.580985\pi$
$389$	−9.92809			−0.503374			−0.251687	+	0.967809i	$0.580985\pi$
$390$	9.50644	−	3.36003i	0.481377	−	0.170142i
$391$	−1.65793			−0.0838450
$392$		0			0
$393$	−9.41397	−	16.3055i	−0.474872	−	0.822502i
$394$	1.82106	−	3.15416i	0.0917435	−	0.158904i
$395$			3.63794i			0.183045i
$396$	15.0192	+	8.67135i	0.754744	+	0.435752i
$397$	−13.2351	−	7.64131i	−0.664252	−	0.383506i	0.129643	−	0.991561i	$-0.458617\pi$
$397$	−13.2351	−	7.64131i	−0.664252	−	0.383506i	−0.793895	+	0.608054i	$0.791950\pi$
$398$		−	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	−0.746014	−	0.665931i	$-0.768035\pi$
$401$	−10.8597	+	6.26986i	−0.542308	+	0.313102i	0.203706	+	0.979032i	$0.434701\pi$
$402$	83.1254			4.14592
$403$	11.3684	−	13.2946i	0.566300	−	0.662252i
$404$	−13.3504			−0.664209
$405$	5.97359	−	3.44886i	0.296830	−	0.171375i
$406$		0			0
$407$	−1.11157	+	1.92529i	−0.0550983	+	0.0954331i
$408$			32.8030i			1.62399i
$409$	21.1905	+	12.2344i	1.04780	+	0.604950i	0.922034	−	0.387110i	$-0.126526\pi$
$409$	21.1905	+	12.2344i	1.04780	+	0.604950i	0.125770	+	0.992059i	$0.459860\pi$
$410$	4.29488	+	2.47965i	0.212109	+	0.122461i
$411$			62.7184i			3.09367i
$412$	−34.9869	+	60.5991i	−1.72368	+	2.98551i
$413$		0			0
$414$	−21.8874	+	12.6367i	−1.07570	+	0.621059i
$415$	−2.69503			−0.132294
$416$	17.6382	+	49.9033i	0.864785	+	2.44671i
$417$	−34.5981			−1.69427
$418$	−3.87587	+	2.23773i	−0.189575	+	0.109451i
$419$	7.17785	+	12.4324i	0.350661	+	0.607362i	0.986365	−	0.164570i	$-0.0526237\pi$
$419$	7.17785	+	12.4324i	0.350661	+	0.607362i	−0.635705	+	0.771932i	$0.719290\pi$
$420$		0			0
$421$			20.6225i			1.00508i	0.864555	+	0.502539i	$0.167601\pi$
$421$			20.6225i			1.00508i	−0.864555	+	0.502539i	$0.832399\pi$
$422$	12.8965	+	7.44581i	0.627793	+	0.362456i
$423$	14.3467	+	8.28310i	0.697563	+	0.402738i
$424$			104.966i			5.09762i
$425$	−3.06351	+	5.30615i	−0.148602	+	0.257386i
$426$	52.4302	+	90.8118i	2.54025	+	4.39985i
$427$		0			0
$428$	−58.7791			−2.84119
$429$	−1.82216	−	5.15537i	−0.0879745	−	0.248904i
$430$	−4.25225			−0.205062
$431$	−11.9775	+	6.91521i	−0.576935	+	0.333094i	−0.759915	−	0.650023i	$-0.774759\pi$
$431$	−11.9775	+	6.91521i	−0.576935	+	0.333094i	0.182979	+	0.983117i	$0.441426\pi$
$432$	77.7754	+	134.711i	3.74197	+	6.48128i
$433$	−8.06097	+	13.9620i	−0.387386	+	0.670972i	−0.992097	−	0.125473i	$-0.959955\pi$
$433$	−8.06097	+	13.9620i	−0.387386	+	0.670972i	0.604711	+	0.796445i	$0.293288\pi$
$434$		0			0
$435$	5.39900	+	3.11711i	0.258862	+	0.149454i
$436$	−14.6997	−	8.48689i	−0.703989	−	0.406448i
$437$		−	4.68088i		−	0.223917i
$438$	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
$443$	−4.54121			−0.215760			−0.107880	−	0.994164i	$-0.534406\pi$
$443$	−4.54121			−0.215760			−0.107880	+	0.994164i	$0.534406\pi$
$444$	−65.6732	+	37.9164i	−3.11671	+	1.79943i
$445$	−1.79383	−	3.10701i	−0.0850359	−	0.147286i
$446$	18.7849	−	32.5364i	0.889491	−	1.54064i
$447$			3.48121i			0.164655i
$448$		0			0
$449$	−8.25996	−	4.76889i	−0.389812	−	0.225058i	0.292267	−	0.956337i	$-0.405590\pi$
$449$	−8.25996	−	4.76889i	−0.389812	−	0.225058i	−0.682079	+	0.731279i	$0.738924\pi$
$450$			93.3997i			4.40291i
$451$	1.34472	−	2.32913i	0.0633205	−	0.109674i
$452$	20.5817	+	35.6485i	0.968079	+	1.67676i
$453$	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	−0.932216	−	0.361902i	$-0.882128\pi$
$457$	−23.1927	+	13.3903i	−1.08491	+	0.626372i	−0.152692	+	0.988274i	$0.548794\pi$
$458$	−30.4388	−	52.7216i	−1.42231	−	2.46352i
$459$	8.33754	−	14.4410i	0.389163	−	0.674050i
$460$			2.21682i			0.103360i
$461$	−8.87870	−	5.12612i	−0.413522	−	0.238747i	0.278780	−	0.960355i	$-0.410070\pi$
$461$	−8.87870	−	5.12612i	−0.413522	−	0.238747i	−0.692302	+	0.721608i	$0.743403\pi$
$462$		0			0
$463$		−	8.39526i		−	0.390161i	−0.980787	−	0.195080i	$-0.937503\pi$
$463$		−	8.39526i		−	0.390161i	0.980787	−	0.195080i	$-0.0624968\pi$
$464$	−34.6669	+	60.0448i	−1.60937	+	2.78751i
$465$	−2.54858	−	4.41427i	−0.118188	−	0.204707i
$466$	2.23019	−	1.28760i	0.103311	−	0.0596469i
$467$	10.9206			0.505344			0.252672	−	0.967552i	$-0.418691\pi$
$467$	10.9206			0.505344			0.252672	+	0.967552i	$0.418691\pi$
$468$	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
$473$			2.30601i			0.106030i
$474$	81.2039	+	46.8831i	3.72982	+	2.15341i
$475$	−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
$479$	−24.5663	+	14.1833i	−1.12246	+	0.648053i	−0.942028	−	0.335534i	$-0.891083\pi$
$479$	−24.5663	+	14.1833i	−1.12246	+	0.648053i	−0.180433	+	0.983587i	$0.557750\pi$
$480$	15.4230			0.703959
$481$	16.5747	+	3.08215i	0.755740	+	0.140534i
$482$	−5.80837			−0.264564
$483$		0			0
$484$	27.3910	+	47.4425i	1.24504	+	2.15648i
$485$	−2.48936	+	4.31170i	−0.113036	+	0.195784i
$486$		−	71.4829i		−	3.24253i
$487$	−27.1818	−	15.6934i	−1.23172	−	0.711136i	−0.264335	−	0.964431i	$-0.585152\pi$
$487$	−27.1818	−	15.6934i	−1.23172	−	0.711136i	−0.967389	+	0.253295i	$0.918486\pi$
$488$	−41.4237	−	23.9160i	−1.87516	−	1.08263i
$489$		−	1.20431i		−	0.0544609i
$490$		0			0
$491$	−11.3251	−	19.6156i	−0.511093	−	0.885239i	−0.999917	−	0.0128567i	$-0.995907\pi$
$491$	−11.3251	−	19.6156i	−0.511093	−	0.885239i	0.488824	−	0.872382i	$-0.337426\pi$
$492$	79.4484	−	45.8696i	3.58181	−	2.06796i
$493$	7.43259			0.334747
$494$	25.7943	+	22.0570i	1.16054	+	0.992393i
$495$	−1.12347			−0.0504964
$496$	49.0932	−	28.3440i	2.20435	−	1.27268i
$497$		0			0
$498$	−34.7316	+	60.1569i	−1.55636	+	2.69570i
$499$			13.3603i			0.598089i	0.954239	+	0.299044i	$0.0966678\pi$
$499$			13.3603i			0.598089i	−0.954239	+	0.299044i	$0.903332\pi$
$500$	14.3471	+	8.28331i	0.641622	+	0.370441i
$501$	42.2329	+	24.3832i	1.88683	+	1.08936i
$502$		−	66.5731i		−	2.97130i
$503$	1.18389	−	2.05056i	0.0527871	−	0.0914299i	−0.838424	−	0.545018i	$-0.816523\pi$
$503$	1.18389	−	2.05056i	0.0527871	−	0.0914299i	0.891212	+	0.453588i	$0.149856\pi$
$504$		0			0
$505$	0.748984	−	0.432426i	0.0333293	−	0.0192427i
$506$	1.67506			0.0744654
$507$	−32.2555	+	26.0564i	−1.43252	+	1.15721i
$508$	−28.4957			−1.26429
$509$	−9.30452	+	5.37197i	−0.412416	+	0.238108i	−0.691827	−	0.722063i	$-0.743194\pi$
$509$	−9.30452	+	5.37197i	−0.412416	+	0.238108i	0.279412	+	0.960171i	$0.409861\pi$
$510$	−1.75140	−	3.03351i	−0.0775532	−	0.134326i
$511$		0			0
$512$		−	20.3448i		−	0.899120i
$513$	40.7719	+	23.5396i	1.80012	+	1.03930i
$514$	5.37365	+	3.10248i	0.237021	+	0.136844i
$515$		−	4.53296i		−	0.199746i
$516$	−39.3299	+	68.1214i	−1.73140	+	2.99888i
$517$	−0.548984	−	0.950868i	−0.0241443	−	0.0418191i
$518$		0			0
$519$	−7.32328			−0.321456
$520$	−7.41094	−	6.33718i	−0.324991	−	0.277904i
$521$	11.6440			0.510135			0.255067	−	0.966923i	$-0.417902\pi$
$521$	11.6440			0.510135			0.255067	+	0.966923i	$0.417902\pi$
$522$	98.1223	−	56.6510i	4.29470	−	2.47955i
$523$	−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
$527$	−5.26280	−	3.03848i	−0.229251	−	0.132358i
$528$		−	17.7199i		−	0.771159i
$529$	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
$534$	−92.4704			−4.00158
$535$	3.29761	−	1.90388i	0.142568	−	0.0823118i
$536$	−40.1951	−	69.6199i	−1.73616	−	3.00712i
$537$	−33.4862	+	57.9998i	−1.44504	+	2.50287i
$538$			40.0540i			1.72685i
$539$		0			0
$540$	−19.3092	−	11.1482i	−0.830934	−	0.479740i
$541$			23.2063i			0.997717i	0.866684	+	0.498858i	$0.166247\pi$
$541$			23.2063i			0.997717i	−0.866684	+	0.498858i	$0.833753\pi$
$542$	−17.8203	+	30.8656i	−0.765447	+	1.32579i
$543$	24.4062	+	42.2728i	1.04737	+	1.81410i
$544$	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
$549$	20.8960	+	36.1930i	0.891821	+	1.54468i
$550$	3.09516	−	5.36097i	0.131978	−	0.228592i
$551$			20.9847i			0.893978i
$552$	30.0191	+	17.3315i	1.27770	+	0.737679i
$553$		0			0
$554$		−	22.2868i		−	0.946876i
$555$	2.45626	−	4.25436i	0.104262	−	0.180588i
$556$	27.5769	+	47.7645i	1.16952	+	2.02567i
$557$	−26.9964	+	15.5864i	−1.14387	+	0.660415i	−0.947387	−	0.320091i	$-0.896286\pi$
$557$	−26.9964	+	15.5864i	−1.14387	+	0.660415i	−0.196486	+	0.980507i	$0.562953\pi$
$558$	−92.6368			−3.92163
$559$	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	$0.316389\pi$
$564$		−	37.4526i		−	1.57704i
$565$	−2.30934	−	1.33330i	−0.0971545	−	0.0560922i
$566$	−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	$0.774336\pi$
$570$	8.56460	−	4.94478i	0.358732	−	0.207114i
$571$	−19.5237			−0.817041			−0.408520	−	0.912749i	$-0.633955\pi$
$571$	−19.5237			−0.817041			−0.408520	+	0.912749i	$0.633955\pi$
$572$	−5.66490	+	6.62474i	−0.236861	+	0.276994i
$573$	−42.9871			−1.79581
$574$		0			0
$575$	3.23722	+	5.60702i	0.135001	+	0.233829i
$576$	56.3286	−	97.5640i	2.34703	−	4.06517i
$577$		−	30.6608i		−	1.27642i	−0.769860	−	0.638212i	$-0.779674\pi$
$577$		−	30.6608i		−	1.27642i	0.769860	−	0.638212i	$-0.220326\pi$
$578$	35.5701	+	20.5364i	1.47952	+	0.854203i
$579$	−26.1505	−	15.0980i	−1.08678	−	0.627450i
$580$		−	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
$584$	−75.5916			−3.12800
$585$	2.83915	+	8.03271i	0.117384	+	0.332112i
$586$	73.2754			3.02698
$587$	−2.24386	+	1.29550i	−0.0926142	+	0.0534708i	−0.545592	−	0.838051i	$-0.683695\pi$
$587$	−2.24386	+	1.29550i	−0.0926142	+	0.0534708i	0.452978	+	0.891522i	$0.350362\pi$
$588$		0			0
$589$	8.57864	−	14.8586i	0.353477	−	0.612240i
$590$			1.50435i			0.0619329i
$591$	3.77976	+	2.18224i	0.155478	+	0.0897655i
$592$	47.3148	+	27.3172i	1.94462	+	1.12273i
$593$			17.7138i			0.727417i	0.931513	+	0.363709i	$0.118490\pi$
$593$			17.7138i			0.727417i	−0.931513	+	0.363709i	$0.881510\pi$
$594$	−8.42368	+	14.5902i	−0.345628	+	0.598645i
$595$		0			0
$596$	4.80600	−	2.77474i	0.196861	−	0.113658i
$597$	36.9595			1.51265
$598$	−4.23306	−	11.9765i	−0.173103	−	0.489754i
$599$	34.6097			1.41411			0.707057	−	0.707156i	$-0.250022\pi$
$599$	34.6097			1.41411			0.707057	+	0.707156i	$0.250022\pi$
$600$	110.938	−	64.0502i	4.52903	−	2.61484i
$601$	−18.9080	−	32.7496i	−0.771272	−	1.33588i	−0.936866	−	0.349688i	$-0.886287\pi$
$601$	−18.9080	−	32.7496i	−0.771272	−	1.33588i	0.165594	−	0.986194i	$-0.447046\pi$
$602$		0			0
$603$			70.2390i			2.86035i
$604$	−47.7326	−	27.5585i	−1.94221	−	1.12134i
$605$	−3.07336	−	1.77441i	−0.124950	−	0.0721399i
$606$		−	22.2911i		−	0.905515i
$607$	19.5864	−	33.9247i	0.794988	−	1.37696i	−0.127858	−	0.991792i	$-0.540810\pi$
$607$	19.5864	−	33.9247i	0.794988	−	1.37696i	0.922847	−	0.385168i	$-0.125856\pi$
$608$	25.9572	+	44.9592i	1.05270	+	1.82334i
$609$		0			0
$610$	5.10762			0.206802
$611$	−5.41126	+	6.32813i	−0.218916	+	0.256009i
$612$	−45.6891			−1.84687
$613$	−18.5611	+	10.7162i	−0.749674	+	0.432825i	−0.825576	−	0.564291i	$-0.809150\pi$
$613$	−18.5611	+	10.7162i	−0.749674	+	0.432825i	0.0759019	+	0.997115i	$0.475816\pi$
$614$	−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	0.979838	−	0.199792i	$-0.0640265\pi$
$617$	32.2102	+	18.5966i	1.29673	+	0.748669i	0.316895	+	0.948461i	$0.397360\pi$
$618$	−101.182	−	58.4174i	−4.07014	−	2.34989i
$619$			30.7193i			1.23471i	0.786683	+	0.617357i	$0.211797\pi$
$619$			30.7193i			1.23471i	−0.786683	+	0.617357i	$0.788203\pi$
$620$	−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
$625$	23.3843			0.935373
$626$	−37.4406	+	21.6164i	−1.49643	+	0.863963i
$627$	−2.68157	−	4.64461i	−0.107091	−	0.185488i
$628$	−32.3300	+	55.9972i	−1.29011	+	2.23453i
$629$		−	5.85682i		−	0.233527i
$630$		0			0
$631$	−12.1022	−	6.98719i	−0.481779	−	0.278155i	0.239378	−	0.970926i	$-0.423056\pi$
$631$	−12.1022	−	6.98719i	−0.481779	−	0.278155i	−0.721158	+	0.692771i	$0.756390\pi$
$632$		−	90.6808i		−	3.60709i
$633$	−8.92260	+	15.4544i	−0.354642	+	0.614257i
$634$	−35.4131	−	61.3374i	−1.40644	−	2.43602i
$635$	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
$640$	−2.04885	−	3.54872i	−0.0809881	−	0.140276i
$641$	−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	$0.971867\pi$
$642$		−	98.1431i		−	3.87340i
$643$	11.7654	+	6.79275i	0.463982	+	0.267880i	0.713717	−	0.700434i	$-0.247010\pi$
$643$	11.7654	+	6.79275i	0.463982	+	0.267880i	−0.249735	+	0.968314i	$0.580344\pi$
$644$		0			0
$645$		−	5.09564i		−	0.200641i
$646$	5.89528	−	10.2109i	0.231947	−	0.401744i
$647$	15.0763	+	26.1129i	0.592710	+	1.02660i	0.993866	+	0.110593i	$0.0352751\pi$
$647$	15.0763	+	26.1129i	0.592710	+	1.02660i	−0.401156	+	0.916010i	$0.631392\pi$
$648$	−148.900	+	85.9675i	−5.84935	+	3.37712i
$649$	0.815811			0.0320234
$650$	−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
$655$		−	1.94434i		−	0.0759716i
$656$	−57.2392	−	33.0471i	−2.23482	−	1.29027i
$657$	57.1978	+	33.0232i	2.23150	+	1.28836i
$658$		0			0
$659$	−6.75204	+	11.6949i	−0.263022	+	0.455568i	−0.967044	−	0.254611i	$-0.918053\pi$
$659$	−6.75204	+	11.6949i	−0.263022	+	0.455568i	0.704021	+	0.710179i	$0.251386\pi$
$660$	1.26996	+	2.19964i	0.0494333	+	0.0856210i
$661$	37.5070	−	21.6547i	1.45885	−	0.842270i	0.459899	−	0.887971i	$-0.347886\pi$
$661$	37.5070	−	21.6547i	1.45885	−	0.842270i	0.998955	+	0.0457012i	$0.0145522\pi$
$662$	−44.4442			−1.72737
$663$	10.9482	+	9.36192i	0.425192	+	0.363587i
$664$	67.1775			2.60699
$665$		0			0
$666$	−44.6405	−	77.3195i	−1.72978	−	2.99607i
$667$	3.92702	−	6.80180i	0.152055	−	0.263367i
$668$		−	77.7397i		−	3.00784i
$669$	38.9897	+	22.5107i	1.50743	+	0.870314i
$670$	7.43419	+	4.29213i	0.287208	+	0.165820i
$671$		−	2.76988i		−	0.106930i
$672$		0			0
$673$	−5.58760	−	9.67801i	−0.215386	−	0.373060i	0.738006	−	0.674794i	$-0.235768\pi$
$673$	−5.58760	−	9.67801i	−0.215386	−	0.373060i	−0.953392	+	0.301735i	$0.902434\pi$
$674$	−54.4418	+	31.4320i	−2.09702	+	1.21072i
$675$	−65.1184			−2.50641
$676$	61.6820	+	23.7619i	2.37239	+	0.913919i
$677$	−1.89660			−0.0728922			−0.0364461	−	0.999336i	$-0.511604\pi$
$677$	−1.89660			−0.0728922			−0.0364461	+	0.999336i	$0.511604\pi$
$678$	−59.5220	+	34.3650i	−2.28593	+	1.31978i
$679$		0			0
$680$	−1.69377	+	2.93369i	−0.0649530	+	0.112502i
$681$			74.9171i			2.87083i
$682$	5.31717	+	3.06987i	0.203605	+	0.117551i
$683$	−33.9929	−	19.6258i	−1.30070	−	0.750961i	−0.320179	−	0.947357i	$-0.603743\pi$
$683$	−33.9929	−	19.6258i	−1.30070	−	0.750961i	−0.980525	+	0.196396i	$0.937076\pi$
$684$		−	128.996i		−	4.93227i
$685$	−3.23843	+	5.60912i	−0.123734	+	0.214314i
$686$		0			0
$687$	63.1784	−	36.4760i	2.41040	−	1.39165i
$688$	56.6710			2.16056
$689$	35.0331	+	29.9572i	1.33465	+	1.14128i
$690$	−3.70141			−0.140910
$691$	−11.2115	+	6.47294i	−0.426504	+	0.246242i	−0.697856	−	0.716238i	$-0.745863\pi$
$691$	−11.2115	+	6.47294i	−0.426504	+	0.246242i	0.271352	+	0.962480i	$0.412529\pi$
$692$	5.83712	+	10.1102i	0.221894	+	0.384332i
$693$		0			0
$694$		−	39.6615i		−	1.50553i
$695$	−3.09422	−	1.78645i	−0.117371	−	0.0677640i
$696$	−134.577	−	77.6984i	−5.10115	−	2.94515i
$697$			7.08531i			0.268375i
$698$	−28.9735	+	50.1835i	−1.09666	+	1.89947i
$699$	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	$0.249491\pi$
$702$	125.606	+	23.3572i	4.74070	+	0.881559i
$703$	16.5357			0.623657
$704$	−6.46631	+	3.73333i	−0.243708	+	0.140705i
$705$	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
$709$	10.1119	+	5.83811i	0.379760	+	0.219255i	0.677714	−	0.735326i	$-0.262971\pi$
$709$	10.1119	+	5.83811i	0.379760	+	0.219255i	−0.297954	+	0.954580i	$0.596304\pi$
$710$			10.8288i			0.406398i
$711$	−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
$716$	106.762			3.98990
$717$	−5.43686	+	3.13897i	−0.203043	+	0.117227i
$718$	−30.0586	−	52.0630i	−1.12178	−	1.94297i
$719$	−13.4036	+	23.2158i	−0.499871	+	0.865802i	−1.00000		0.000149098i	$-0.999953\pi$
$719$	−13.4036	+	23.2158i	−0.499871	+	0.865802i	0.500129	+	0.865951i	$0.333286\pi$
$720$			27.6098i			1.02896i
$721$		0			0
$722$	−14.9681	−	8.64185i	−0.557056	−	0.321616i
$723$		−	6.96040i		−	0.258860i
$724$	38.9066	−	67.3882i	1.44595	−	2.50446i
$725$	−14.5126	−	25.1366i	−0.538986	−	0.933551i
$726$	−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
$731$	−3.03757	−	5.26123i	−0.112349	−	0.194594i
$732$	47.2414	−	81.8245i	1.74609	−	3.02432i
$733$		−	0.262079i		−	0.00968011i	−0.999988	−	0.00484005i	$-0.998459\pi$
$733$		−	0.262079i		−	0.00968011i	0.999988	−	0.00484005i	$-0.00154064\pi$
$734$	−20.0838	−	11.5954i	−0.741307	−	0.427994i
$735$		0			0
$736$		−	19.4303i		−	0.716209i
$737$	2.32764	−	4.03158i	0.0857396	−	0.148505i
$738$	54.0040	+	93.5376i	1.98791	+	3.44317i
$739$	14.0974	−	8.13916i	0.518583	−	0.299404i	−0.217772	−	0.976000i	$-0.569879\pi$
$739$	14.0974	−	8.13916i	0.518583	−	0.299404i	0.736355	+	0.676596i	$0.236546\pi$
$740$	−7.83117			−0.287880
$741$	−26.4318	+	30.9104i	−0.970997	+	1.13552i
$742$		0			0
$743$	−1.03251	+	0.596118i	−0.0378790	+	0.0218695i	−0.518820	−	0.854884i	$-0.673628\pi$
$743$	−1.03251	+	0.596118i	−0.0378790	+	0.0218695i	0.480941	+	0.876753i	$0.340295\pi$
$744$	63.5269	+	110.032i	2.32901	+	4.03396i
$745$	−0.179750	+	0.311336i	−0.00658553	+	0.0114065i
$746$		−	45.3828i		−	1.66158i
$747$	−50.8311	−	29.3474i	−1.85981	−	1.07376i
$748$	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	$0.803435\pi$
$752$	−23.3680	+	13.4915i	−0.852142	+	0.491984i
$753$	79.7772			2.90724
$754$	18.9771	+	53.6913i	0.691104	+	1.95532i
$755$	3.57052			0.129944
$756$		0			0
$757$	−7.40225	−	12.8211i	−0.269039	−	0.465990i	0.699575	−	0.714560i	$-0.253373\pi$
$757$	−7.40225	−	12.8211i	−0.269039	−	0.465990i	−0.968614	+	0.248570i	$0.920040\pi$
$758$	10.8990	−	18.8776i	0.395870	−	0.685667i
$759$			2.00729i			0.0728599i
$760$	−8.28278	−	4.78207i	−0.300448	−	0.173464i
$761$	−16.4167	−	9.47821i	−0.595106	−	0.343585i	0.172008	−	0.985096i	$-0.444975\pi$
$761$	−16.4167	−	9.47821i	−0.595106	−	0.343585i	−0.767114	+	0.641511i	$0.778308\pi$
$762$		−	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
$766$	38.8065			1.40213
$767$	−2.06165	−	5.83296i	−0.0744418	−	0.210616i
$768$	−5.43557			−0.196139
$769$	36.8803	−	21.2928i	1.32994	−	0.767839i	0.344647	−	0.938732i	$-0.387999\pi$
$769$	36.8803	−	21.2928i	1.32994	−	0.767839i	0.985290	+	0.170893i	$0.0546653\pi$
$770$		0			0
$771$	−3.71782	+	6.43945i	−0.133894	+	0.231911i
$772$			48.1362i			1.73246i
$773$	13.7119	+	7.91657i	0.493183	+	0.284739i	0.725894	−	0.687807i	$-0.241426\pi$
$773$	13.7119	+	7.91657i	0.493183	+	0.284739i	−0.232711	+	0.972546i	$0.574760\pi$
$774$	−80.2019	−	46.3046i	−2.88280	−	1.66438i
$775$			23.7313i			0.852455i
$776$	62.0507	−	107.475i	2.22749	−	3.85813i
$777$		0			0
$778$	−22.8853	+	13.2128i	−0.820477	+	0.473702i
$779$	−20.0042			−0.716724
$780$	12.5179	−	14.6389i	0.448211	−	0.524155i
$781$	5.87250			0.210135
$782$	−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
$786$	−43.4003	−	25.0572i	−1.54804	−	0.893760i
$787$	−44.4043	−	25.6368i	−1.58284	−	0.913854i	−0.994442	−	0.105284i	$-0.966425\pi$
$787$	−44.4043	−	25.6368i	−1.58284	−	0.913854i	−0.588400	−	0.808570i	$-0.700242\pi$
$788$		−	6.95755i		−	0.247852i
$789$	6.17622	−	10.6975i	0.219879	−	0.380842i
$790$	4.84156	+	8.38583i	0.172255	+	0.298355i
$791$		0			0
$792$	28.0041			0.995084
$793$	−19.8043	+	6.99980i	−0.703272	+	0.248570i
$794$	−40.6778			−1.44360
$795$	11.6322	−	6.71585i	0.412551	−	0.238187i
$796$	−29.4590	−	51.0246i	−1.04415	−	1.80852i
$797$	−25.8457	+	44.7660i	−0.915501	+	1.58569i	−0.109335	+	0.994005i	$0.534872\pi$
$797$	−25.8457	+	44.7660i	−0.915501	+	1.58569i	−0.806166	+	0.591689i	$0.798461\pi$
$798$		0			0
$799$	2.50505	+	1.44629i	0.0886223	+	0.0511661i
$800$	−62.1860	−	35.9031i	−2.19861	−	1.26937i
$801$		−	78.1352i		−	2.76077i
$802$	−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
$807$	−47.9983			−1.68962
$808$	−18.6695	+	10.7788i	−0.656789	+	0.379197i
$809$	3.85493	+	6.67694i	0.135532	+	0.234749i	0.925801	−	0.378012i	$-0.123392\pi$
$809$	3.85493	+	6.67694i	0.135532	+	0.234749i	−0.790268	+	0.612761i	$0.790059\pi$
$810$	9.17983	−	15.8999i	0.322546	−	0.558667i
$811$		−	27.3184i		−	0.959278i	−0.877466	−	0.479639i	$-0.840768\pi$
$811$		−	27.3184i		−	0.959278i	0.877466	−	0.479639i	$-0.159232\pi$
$812$		0			0
$813$	−36.9875	−	21.3548i	−1.29721	−	0.748944i
$814$			5.91733i			0.207402i
$815$	0.0621840	−	0.107706i	0.00217821	−	0.00377277i
$816$	23.3414	+	40.4285i	0.817112	+	1.41528i
$817$	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	0.194239	−	0.980954i	$-0.437776\pi$
$821$	32.6900	−	18.8736i	1.14089	−	0.658693i	0.946651	+	0.322261i	$0.104443\pi$
$822$	83.4689	+	144.572i	2.91131	+	5.04254i
$823$	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	$0.0216887\pi$
$824$			112.990i			3.93621i
$825$	6.42426	+	3.70905i	0.223664	+	0.129132i
$826$		0			0
$827$			14.9309i			0.519198i	0.965717	+	0.259599i	$0.0835903\pi$
$827$			14.9309i			0.519198i	−0.965717	+	0.259599i	$0.916410\pi$
$828$	−24.1399	+	41.8115i	−0.838920	+	1.45305i
$829$	−7.77493	−	13.4666i	−0.270034	−	0.467713i	0.698836	−	0.715282i	$-0.253702\pi$
$829$	−7.77493	−	13.4666i	−0.270034	−	0.467713i	−0.968870	+	0.247569i	$0.920368\pi$
$830$	−6.21233	+	3.58669i	−0.215633	+	0.124496i
$831$	26.7072			0.926462
$832$	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
$837$		−	64.5865i		−	2.23243i
$838$	33.0914	+	19.1053i	1.14312	+	0.659982i
$839$	−49.3577	−	28.4967i	−1.70402	−	0.983814i	−0.941604	−	0.336723i	$-0.890681\pi$
$839$	−49.3577	−	28.4967i	−1.70402	−	0.983814i	−0.762413	−	0.647091i	$-0.775985\pi$
$840$		0			0
$841$	−3.10508	+	5.37815i	−0.107072	+	0.185454i
$842$	27.4455	+	47.5369i	0.945833	+	1.63823i
$843$	−49.0236	+	28.3038i	−1.68846	+	0.974833i
$844$	28.4475			0.979205
$845$	−4.23013	+	0.664820i	−0.145521	+	0.0228705i
$846$	44.0943			1.51599
$847$		0			0
$848$	74.6901	+	129.367i	2.56487	+	4.44248i
$849$	34.7306	−	60.1551i	1.19195	−	2.06452i
$850$			16.3083i			0.559370i
$851$	−5.35976	−	3.09446i	−0.183730	−	0.106077i
$852$	173.478	+	100.158i	5.94327	+	3.43135i
$853$			53.4201i			1.82907i	0.404509	+	0.914534i	$0.367443\pi$
$853$			53.4201i			1.82907i	−0.404509	+	0.914534i	$0.632557\pi$
$854$		0			0
$855$	4.17822	+	7.23688i	0.142892	+	0.247496i
$856$	−82.1976	+	47.4568i	−2.80946	+	1.62204i
$857$	−32.6515			−1.11535			−0.557676	−	0.830058i	$-0.688307\pi$
$857$	−32.6515			−1.11535			−0.557676	+	0.830058i	$0.688307\pi$
$858$	−11.0613	−	9.45864i	−0.377626	−	0.322913i
$859$	34.7647			1.18616			0.593078	−	0.805145i	$-0.297913\pi$
$859$	34.7647			1.18616			0.593078	+	0.805145i	$0.297913\pi$
$860$	−7.03481	+	4.06155i	−0.239885	+	0.138498i
$861$		0			0
$862$	−18.4062	+	31.8805i	−0.626919	+	1.08586i
$863$		−	23.3318i		−	0.794224i	−0.917770	−	0.397112i	$-0.870012\pi$
$863$		−	23.3318i		−	0.794224i	0.917770	−	0.397112i	$-0.129988\pi$
$864$	169.243	+	97.7127i	5.75777	+	3.32425i
$865$	−0.654946	−	0.378133i	−0.0222688	−	0.0128569i
$866$			42.9118i			1.45820i
$867$	−24.6096	+	42.6251i	−0.835786	+	1.44762i
$868$		0			0
$869$	4.54766	−	2.62559i	0.154269	−	0.0890671i
$870$	16.5937			0.562578
$871$	−34.7076	−	6.45406i	−1.17602	−	0.218688i
$872$	−27.4084			−0.928167
$873$	−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
$877$	−4.25311	−	2.45553i	−0.143617	−	0.0829175i	0.426470	−	0.904502i	$-0.359757\pi$
$877$	−4.25311	−	2.45553i	−0.143617	−	0.0829175i	−0.570087	+	0.821584i	$0.693090\pi$
$878$	−22.1826	−	12.8072i	−0.748628	−	0.432220i
$879$			87.8088i			2.96172i
$880$	0.914956	−	1.58475i	0.0308431	−	0.0534219i
$881$	4.78761	+	8.29238i	0.161299	+	0.279378i	0.935335	−	0.353764i	$-0.115098\pi$
$881$	4.78761	+	8.29238i	0.161299	+	0.279378i	−0.774036	+	0.633142i	$0.781765\pi$
$882$		0			0
$883$	16.6962			0.561871			0.280935	−	0.959727i	$-0.409355\pi$
$883$	16.6962			0.561871			0.280935	+	0.959727i	$0.409355\pi$
$884$	4.19824	−	22.5766i	0.141202	−	0.759334i
$885$	−1.80272			−0.0605977
$886$	−10.4680	+	6.04368i	−0.351678	+	0.203042i
$887$	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
$891$	−8.62258	−	4.97825i	−0.288867	−	0.166778i
$892$		−	71.7698i		−	2.40303i
$893$	−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
$898$	−25.3868			−0.847167
$899$	24.9313	−	14.3941i	0.831505	−	0.480070i
$900$	89.2110	+	154.518i	2.97370	+	5.15060i
$901$	8.00679	−	13.8682i	0.266745	−	0.462016i
$902$		−	7.15851i		−	0.238352i
$903$		0			0
$904$	57.5634	+	33.2342i	1.91453	+	1.10535i
$905$			5.04080i			0.167562i
$906$	46.0142	−	79.6989i	1.52872	−	2.64782i
$907$	−18.3270	−	31.7432i	−0.608537	−	1.05402i	−0.991482	−	0.130246i	$-0.958423\pi$
$907$	−18.3270	−	31.7432i	−0.608537	−	1.05402i	0.382945	−	0.923771i	$-0.374910\pi$
$908$	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
$913$	1.94507	+	3.36897i	0.0643725	+	0.111496i
$914$	−35.6410	+	61.7321i	−1.17890	+	2.04192i
$915$			6.12067i			0.202343i
$916$	−100.714	−	58.1475i	−3.32770	−	1.92125i
$917$		0			0
$918$		−	44.3841i		−	1.46489i
$919$	−11.8826	+	20.5812i	−0.391970	+	0.678912i	−0.992709	−	0.120533i	$-0.961540\pi$
$919$	−11.8826	+	20.5812i	−0.391970	+	0.678912i	0.600739	+	0.799445i	$0.294873\pi$
$920$	1.78981	+	3.10004i	0.0590082	+	0.102205i
$921$	72.2118	−	41.6915i	2.37946	−	1.37378i
$922$	−27.2884			−0.898696
$923$	−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
$928$			87.1071i			2.85943i
$929$	−17.1279	−	9.88880i	−0.561949	−	0.324441i	0.191979	−	0.981399i	$-0.438510\pi$
$929$	−17.1279	−	9.88880i	−0.561949	−	0.324441i	−0.753927	+	0.656958i	$0.771843\pi$
$930$	−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
$934$	25.1731	−	14.5337i	0.823688	−	0.475556i
$935$	−0.196167			−0.00641534
$936$	−70.7697	−	200.227i	−2.31318	−	6.54461i
$937$	−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
$940$	1.93384	−	3.34951i	0.0630749	−	0.109249i
$941$			8.84647i			0.288387i	0.989550	+	0.144193i	$0.0460587\pi$
$941$			8.84647i			0.288387i	−0.989550	+	0.144193i	$0.953941\pi$
$942$	−93.4982	−	53.9812i	−3.04634	−	1.75880i
$943$	6.48399	+	3.74353i	0.211148	+	0.121906i
$944$		−	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	−0.747444	−	0.664324i	$-0.768719\pi$
$947$	−16.7975	+	9.69803i	−0.545845	+	0.315144i	0.201600	+	0.979468i	$0.435386\pi$
$948$	179.122			5.81761
$949$	−21.5737	+	25.2291i	−0.700311	+	0.818970i
$950$	−46.0437			−1.49386
$951$	73.5030	−	42.4370i	2.38350	−	1.37611i
$952$		0			0
$953$	−16.9408	+	29.3423i	−0.548767	+	0.950492i	0.449593	+	0.893234i	$0.351569\pi$
$953$	−16.9408	+	29.3423i	−0.548767	+	0.950492i	−0.998359	+	0.0572580i	$0.981764\pi$
$954$		−	244.110i		−	7.90335i
$955$	−3.84449	−	2.21961i	−0.124405	−	0.0718251i
$956$	8.66705	+	5.00392i	0.280312	+	0.161838i
$957$		−	8.99879i		−	0.290889i
$958$	−37.7518	+	65.3881i	−1.21971	+	2.11259i
$959$		0			0
$960$	14.2888	−	8.24962i	0.461168	−	0.266255i
$961$	7.46252			0.240726
$962$	42.3082	−	14.9538i	1.36407	−	0.482129i
$963$	82.9285			2.67233
$964$	−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	$0.00183962\pi$
$967$			0.359435i			0.0115586i	−0.999983	+	0.00577932i	$0.998160\pi$
$968$	76.6079	+	44.2296i	2.46227	+	1.42159i
$969$	12.2362	+	7.06455i	0.393082	+	0.226946i
$970$			13.2519i			0.425492i
$971$	9.73847	−	16.8675i	0.312523	−	0.541305i	−0.666385	−	0.745608i	$-0.732159\pi$
$971$	9.73847	−	16.8675i	0.312523	−	0.541305i	0.978908	+	0.204303i	$0.0654927\pi$
$972$	−68.2771	−	118.259i	−2.18999	−	3.79317i
$973$		0			0
$974$	−83.5424			−2.67687
$975$	10.2844	−	55.3059i	0.329366	−	1.77121i
$976$	−68.0708			−2.17889
$977$	−51.3063	+	29.6217i	−1.64143	+	0.947682i	−0.661108	+	0.750291i	$0.729914\pi$
$977$	−51.3063	+	29.6217i	−1.64143	+	0.947682i	−0.980325	+	0.197391i	$0.936753\pi$
$978$	−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
$982$	−52.2109	−	30.1440i	−1.66612	−	0.961933i
$983$			21.5982i			0.688874i	0.938809	+	0.344437i	$0.111930\pi$
$983$			21.5982i			0.688874i	−0.938809	+	0.344437i	$0.888070\pi$
$984$	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
$989$	−6.41963			−0.204132
$990$	−2.58972	+	1.49518i	−0.0823068	+	0.0475198i
$991$	−1.86780	−	3.23512i	−0.0593325	−	0.102767i	0.834833	−	0.550503i	$-0.185564\pi$
$991$	−1.86780	−	3.23512i	−0.0593325	−	0.102767i	−0.894166	+	0.447736i	$0.852231\pi$
$992$	35.6098	−	61.6780i	1.13061	−	1.95828i
$993$		−	53.2592i		−	1.69013i
$994$		0			0
$995$	3.30541	+	1.90838i	0.104789	+	0.0604997i
$996$			132.696i			4.20463i
$997$	−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	$0.224160\pi$
$998$	17.7806	+	30.7968i	0.562834	+	0.974857i
$999$	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.q.j.491.16	yes	32
7.2	even	3		637.2.u.j.361.1		32
7.3	odd	6		637.2.k.j.569.15		32
7.4	even	3		637.2.k.j.569.16		32
7.5	odd	6		637.2.u.j.361.2		32
7.6	odd	2	inner	637.2.q.j.491.15	✓	32
13.2	odd	12		8281.2.a.cx.1.31		32
13.4	even	6	inner	637.2.q.j.589.16	yes	32
13.11	odd	12		8281.2.a.cx.1.1		32
91.4	even	6		637.2.u.j.30.1		32
91.17	odd	6		637.2.u.j.30.2		32
91.30	even	6		637.2.k.j.459.2		32
91.41	even	12		8281.2.a.cx.1.32		32
91.69	odd	6	inner	637.2.q.j.589.15	yes	32
91.76	even	12		8281.2.a.cx.1.2		32
91.82	odd	6		637.2.k.j.459.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.k.j.459.1		32	91.82	odd	6
637.2.k.j.459.2		32	91.30	even	6
637.2.k.j.569.15		32	7.3	odd	6
637.2.k.j.569.16		32	7.4	even	3
637.2.q.j.491.15	✓	32	7.6	odd	2	inner
637.2.q.j.491.16	yes	32	1.1	even	1	trivial
637.2.q.j.589.15	yes	32	91.69	odd	6	inner
637.2.q.j.589.16	yes	32	13.4	even	6	inner
637.2.u.j.30.1		32	91.4	even	6
637.2.u.j.30.2		32	91.17	odd	6
637.2.u.j.361.1		32	7.2	even	3
637.2.u.j.361.2		32	7.5	odd	6
8281.2.a.cx.1.1		32	13.11	odd	12
8281.2.a.cx.1.2		32	91.76	even	12
8281.2.a.cx.1.31		32	13.2	odd	12
8281.2.a.cx.1.32		32	91.41	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.30510 - 1.33085i) q^{2} +(1.59481 + 2.76230i) q^{3} +(2.54233 - 4.40345i) q^{4} +0.329389i q^{5} +(7.35241 + 4.24492i) q^{6} -8.21047i q^{8} +(-3.58685 + 6.21261i) q^{9} +O(q^{10})\)	\(q+(2.30510 - 1.33085i) q^{2} +(1.59481 + 2.76230i) q^{3} +(2.54233 - 4.40345i) q^{4} +0.329389i q^{5} +(7.35241 + 4.24492i) q^{6} -8.21047i q^{8} +(-3.58685 + 6.21261i) q^{9} +(0.438368 + 0.759275i) q^{10} +(0.411757 - 0.237728i) q^{11} +16.2182 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} +19.0943i q^{18} +(-3.06266 - 1.76823i) q^{19} +(1.45045 + 0.837416i) q^{20} +(0.632762 - 1.09598i) q^{22} +(0.661804 + 1.14628i) q^{23} +(22.6798 - 13.0942i) q^{24} +4.89150 q^{25} +(-9.43517 - 1.75452i) q^{26} -13.3126 q^{27} +(-2.96691 - 5.13883i) q^{29} +(-1.39823 + 2.42180i) q^{30} +4.85154i q^{31} +(-12.7131 - 7.33989i) q^{32} +(1.31335 + 0.758263i) q^{33} +3.33400i q^{34} +(18.2380 + 31.5891i) q^{36} +(-4.04936 + 2.33790i) q^{37} -9.41300 q^{38} +(2.10251 - 11.3065i) q^{39} +2.70444 q^{40} +(4.89872 - 2.82828i) q^{41} +(-2.42505 + 4.20031i) q^{43} -2.41754i q^{44} +(-2.04636 - 1.18147i) q^{45} +(3.05105 + 1.76153i) q^{46} -2.30929i q^{47} +(18.6346 - 32.2761i) q^{48} +(11.2754 - 6.50987i) q^{50} -3.99527 q^{51} +(-17.2851 + 6.10939i) q^{52} -12.7845 q^{53} +(-30.6868 + 17.7170i) q^{54} +(0.0783050 + 0.135628i) q^{55} -11.2800i q^{57} +(-13.6781 - 7.89703i) q^{58} +(1.48597 + 0.857925i) q^{59} +5.34209i q^{60} +(2.91286 - 5.04523i) q^{61} +(6.45669 + 11.1833i) q^{62} -15.7042 q^{64} +(0.771841 - 0.902620i) q^{65} +4.03654 q^{66} +(8.47940 - 4.89559i) q^{67} +(3.18448 + 5.51569i) q^{68} +(-2.11091 + 3.65620i) q^{69} +(10.6965 + 6.17565i) q^{71} +(51.0085 + 29.4498i) q^{72} -9.20673i 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} +11.0445 q^{79} +(3.33311 - 1.92437i) q^{80} +(-10.4705 - 18.1354i) q^{81} +(7.52804 - 13.0390i) q^{82} +8.18192i q^{83} +(-0.357311 - 0.206293i) q^{85} +12.9095i q^{86} +(9.46332 - 16.3910i) q^{87} +(-1.95186 - 3.38072i) q^{88} +(-9.43265 + 5.44595i) q^{89} -6.28944 q^{90} +6.73011 q^{92} +(-13.4014 + 7.73730i) q^{93} +(-3.07333 - 5.32316i) q^{94} +(0.582435 - 1.00881i) q^{95} -46.8230i q^{96} +(13.0900 + 7.55751i) q^{97} +3.41078i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4} - 28 q^{9}+O(q^{10}) \) 32 * q + 20 * q^4 - 28 * q^9	\( 32 q + 20 q^{4} - 28 q^{9} - 12 q^{15} - 28 q^{16} + 8 q^{22} + 24 q^{23} - 40 q^{25} - 24 q^{29} + 24 q^{30} - 60 q^{32} + 92 q^{36} - 32 q^{39} + 12 q^{43} - 24 q^{46} + 12 q^{50} + 72 q^{53} - 132 q^{58} + 32 q^{64} + 48 q^{67} - 48 q^{71} + 72 q^{72} + 24 q^{74} - 156 q^{78} + 96 q^{79} - 64 q^{81} + 12 q^{85} + 56 q^{88} + 168 q^{92} - 48 q^{93} + 84 q^{95}+O(q^{100}) \) 32 * q + 20 * q^4 - 28 * q^9 - 12 * q^15 - 28 * q^16 + 8 * q^22 + 24 * q^23 - 40 * q^25 - 24 * q^29 + 24 * q^30 - 60 * q^32 + 92 * q^36 - 32 * q^39 + 12 * q^43 - 24 * q^46 + 12 * q^50 + 72 * q^53 - 132 * q^58 + 32 * q^64 + 48 * q^67 - 48 * q^71 + 72 * q^72 + 24 * q^74 - 156 * q^78 + 96 * q^79 - 64 * q^81 + 12 * q^85 + 56 * q^88 + 168 * q^92 - 48 * q^93 + 84 * q^95

Introduction

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