LMFDB - Embedded newform 547.3.b.b.546.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,3,Mod(546,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("547.546");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	547.b (of order $2$, degree $1$, 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:	$14.9046704605$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			546.4
Character	$\chi$	$=$	547.546
Dual form			547.3.b.b.546.85

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.76304i q^{2} -4.52828i q^{3} -10.1605 q^{4} +3.85159i q^{5} -17.0401 q^{6} -7.12637i q^{7} +23.1820i q^{8} -11.5053 q^{9} +O(q^{10})$	\(q-3.76304i q^{2} -4.52828i q^{3} -10.1605 q^{4} +3.85159i q^{5} -17.0401 q^{6} -7.12637i q^{7} +23.1820i q^{8} -11.5053 q^{9} +14.4937 q^{10} -3.33472 q^{11} +46.0093i q^{12} -18.1207 q^{13} -26.8168 q^{14} +17.4411 q^{15} +46.5930 q^{16} +27.0483i q^{17} +43.2948i q^{18} +23.2002 q^{19} -39.1339i q^{20} -32.2702 q^{21} +12.5487i q^{22} -17.8669i q^{23} +104.975 q^{24} +10.1653 q^{25} +68.1889i q^{26} +11.3446i q^{27} +72.4072i q^{28} -50.9671 q^{29} -65.6314i q^{30} -9.91155i q^{31} -82.6032i q^{32} +15.1005i q^{33} +101.784 q^{34} +27.4479 q^{35} +116.899 q^{36} -42.3987i q^{37} -87.3033i q^{38} +82.0555i q^{39} -89.2876 q^{40} +2.94026i q^{41} +121.434i q^{42} +41.9270i q^{43} +33.8823 q^{44} -44.3136i q^{45} -67.2338 q^{46} -7.50138 q^{47} -210.986i q^{48} -1.78519 q^{49} -38.2522i q^{50} +122.482 q^{51} +184.114 q^{52} -76.3180 q^{53} +42.6902 q^{54} -12.8440i q^{55} +165.204 q^{56} -105.057i q^{57} +191.791i q^{58} +89.9803i q^{59} -177.209 q^{60} +36.1711i q^{61} -37.2975 q^{62} +81.9909i q^{63} -124.467 q^{64} -69.7935i q^{65} +56.8239 q^{66} -117.849 q^{67} -274.823i q^{68} -80.9062 q^{69} -103.287i q^{70} +4.68380i q^{71} -266.716i q^{72} -73.1662 q^{73} -159.548 q^{74} -46.0311i q^{75} -235.725 q^{76} +23.7645i q^{77} +308.778 q^{78} -54.7711i q^{79} +179.457i q^{80} -52.1760 q^{81} +11.0643 q^{82} -79.8829i q^{83} +327.880 q^{84} -104.179 q^{85} +157.773 q^{86} +230.793i q^{87} -77.3056i q^{88} -54.8937i q^{89} -166.754 q^{90} +129.135i q^{91} +181.536i q^{92} -44.8822 q^{93} +28.2280i q^{94} +89.3578i q^{95} -374.050 q^{96} +175.452 q^{97} +6.71772i q^{98} +38.3669 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 192 q^{4} - 306 q^{9}+O(q^{10}) $ 88 * q - 192 * q^4 - 306 * q^9	$ 88 q - 192 q^{4} - 306 q^{9} - 4 q^{10} - 32 q^{11} + 26 q^{13} - 26 q^{14} + 22 q^{15} + 236 q^{16} - 12 q^{19} - 16 q^{21} - 2 q^{24} - 544 q^{25} - 96 q^{29} + 26 q^{34} + 10 q^{35} + 364 q^{36} + 44 q^{40} + 124 q^{44} - 288 q^{46} - 310 q^{47} - 694 q^{49} + 86 q^{51} - 316 q^{52} + 24 q^{53} - 266 q^{54} + 158 q^{56} - 80 q^{60} + 40 q^{62} - 652 q^{64} + 528 q^{66} + 28 q^{67} + 16 q^{69} + 94 q^{73} - 614 q^{74} - 28 q^{76} - 98 q^{78} + 928 q^{81} - 772 q^{82} + 358 q^{84} + 74 q^{85} - 410 q^{86} - 214 q^{90} + 656 q^{93} - 724 q^{96} + 346 q^{97} + 50 q^{99}+O(q^{100}) $ 88 * q - 192 * q^4 - 306 * q^9 - 4 * q^10 - 32 * q^11 + 26 * q^13 - 26 * q^14 + 22 * q^15 + 236 * q^16 - 12 * q^19 - 16 * q^21 - 2 * q^24 - 544 * q^25 - 96 * q^29 + 26 * q^34 + 10 * q^35 + 364 * q^36 + 44 * q^40 + 124 * q^44 - 288 * q^46 - 310 * q^47 - 694 * q^49 + 86 * q^51 - 316 * q^52 + 24 * q^53 - 266 * q^54 + 158 * q^56 - 80 * q^60 + 40 * q^62 - 652 * q^64 + 528 * q^66 + 28 * q^67 + 16 * q^69 + 94 * q^73 - 614 * q^74 - 28 * q^76 - 98 * q^78 + 928 * q^81 - 772 * q^82 + 358 * q^84 + 74 * q^85 - 410 * q^86 - 214 * q^90 + 656 * q^93 - 724 * q^96 + 346 * q^97 + 50 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	3.76304i		−	1.88152i	−0.339075	−	0.940759i	$-0.610114\pi$
$2$		−	3.76304i		−	1.88152i	0.339075	−	0.940759i	$-0.389886\pi$
$3$		−	4.52828i		−	1.50943i	−0.656056	−	0.754713i	$-0.727776\pi$
$3$		−	4.52828i		−	1.50943i	0.656056	−	0.754713i	$-0.272224\pi$
$4$	−10.1605			−2.54011
$5$			3.85159i			0.770318i	0.922850	+	0.385159i	$0.125853\pi$
$5$			3.85159i			0.770318i	−0.922850	+	0.385159i	$0.874147\pi$
$6$	−17.0401			−2.84001
$7$		−	7.12637i		−	1.01805i	−0.860751	−	0.509027i	$-0.830005\pi$
$7$		−	7.12637i		−	1.01805i	0.860751	−	0.509027i	$-0.169995\pi$
$8$			23.1820i			2.89775i
$9$	−11.5053			−1.27836
$10$	14.4937			1.44937
$11$	−3.33472			−0.303156			−0.151578	−	0.988445i	$-0.548436\pi$
$11$	−3.33472			−0.303156			−0.151578	+	0.988445i	$0.548436\pi$
$12$			46.0093i			3.83411i
$13$	−18.1207			−1.39390			−0.696950	−	0.717120i	$-0.745460\pi$
$13$	−18.1207			−1.39390			−0.696950	+	0.717120i	$0.745460\pi$
$14$	−26.8168			−1.91549
$15$	17.4411			1.16274
$16$	46.5930			2.91206
$17$			27.0483i			1.59108i	0.605904	+	0.795538i	$0.292812\pi$
$17$			27.0483i			1.59108i	−0.605904	+	0.795538i	$0.707188\pi$
$18$			43.2948i			2.40527i
$19$	23.2002			1.22106			0.610532	−	0.791991i	$-0.290956\pi$
$19$	23.2002			1.22106			0.610532	+	0.791991i	$0.290956\pi$
$20$		−	39.1339i		−	1.95670i
$21$	−32.2702			−1.53668
$22$			12.5487i			0.570395i
$23$		−	17.8669i		−	0.776821i	−0.921486	−	0.388411i	$-0.873024\pi$
$23$		−	17.8669i		−	0.776821i	0.921486	−	0.388411i	$-0.126976\pi$
$24$	104.975			4.37394
$25$	10.1653			0.406610
$26$			68.1889i			2.62265i
$27$			11.3446i			0.420171i
$28$			72.4072i			2.58597i
$29$	−50.9671			−1.75749			−0.878743	−	0.477295i	$-0.841617\pi$
$29$	−50.9671			−1.75749			−0.878743	+	0.477295i	$0.841617\pi$
$30$		−	65.6314i		−	2.18771i
$31$		−	9.91155i		−	0.319727i	−0.987139	−	0.159864i	$-0.948895\pi$
$31$		−	9.91155i		−	0.319727i	0.987139	−	0.159864i	$-0.0511055\pi$
$32$		−	82.6032i		−	2.58135i
$33$			15.1005i			0.457592i
$34$	101.784			2.99364
$35$	27.4479			0.784225
$36$	116.899			3.24719
$37$		−	42.3987i		−	1.14591i	−0.819587	−	0.572955i	$-0.805797\pi$
$37$		−	42.3987i		−	1.14591i	0.819587	−	0.572955i	$-0.194203\pi$
$38$		−	87.3033i		−	2.29746i
$39$			82.0555i			2.10399i
$40$	−89.2876			−2.23219
$41$			2.94026i			0.0717137i	0.999357	+	0.0358569i	$0.0114160\pi$
$41$			2.94026i			0.0717137i	−0.999357	+	0.0358569i	$0.988584\pi$
$42$			121.434i			2.89128i
$43$			41.9270i			0.975046i	0.873110	+	0.487523i	$0.162099\pi$
$43$			41.9270i			0.975046i	−0.873110	+	0.487523i	$0.837901\pi$
$44$	33.8823			0.770052
$45$		−	44.3136i		−	0.984747i
$46$	−67.2338			−1.46160
$47$	−7.50138			−0.159604			−0.0798019	−	0.996811i	$-0.525429\pi$
$47$	−7.50138			−0.159604			−0.0798019	+	0.996811i	$0.525429\pi$
$48$		−	210.986i		−	4.39554i
$49$	−1.78519			−0.0364324
$50$		−	38.2522i		−	0.765045i
$51$	122.482			2.40161
$52$	184.114			3.54066
$53$	−76.3180			−1.43996			−0.719981	−	0.693994i	$-0.755850\pi$
$53$	−76.3180			−1.43996			−0.719981	+	0.693994i	$0.755850\pi$
$54$	42.6902			0.790559
$55$		−	12.8440i		−	0.233527i
$56$	165.204			2.95007
$57$		−	105.057i		−	1.84311i
$58$			191.791i			3.30674i
$59$			89.9803i			1.52509i	0.646935	+	0.762545i	$0.276051\pi$
$59$			89.9803i			1.52509i	−0.646935	+	0.762545i	$0.723949\pi$
$60$	−177.209			−2.95349
$61$			36.1711i			0.592969i	0.955038	+	0.296484i	$0.0958143\pi$
$61$			36.1711i			0.592969i	−0.955038	+	0.296484i	$0.904186\pi$
$62$	−37.2975			−0.601573
$63$			81.9909i			1.30144i
$64$	−124.467			−1.94479
$65$		−	69.7935i		−	1.07375i
$66$	56.8239			0.860968
$67$	−117.849			−1.75895			−0.879473	−	0.475948i	$-0.842105\pi$
$67$	−117.849			−1.75895			−0.879473	+	0.475948i	$0.842105\pi$
$68$		−	274.823i		−	4.04151i
$69$	−80.9062			−1.17255
$70$		−	103.287i		−	1.47553i
$71$			4.68380i			0.0659691i	0.999456	+	0.0329845i	$0.0105012\pi$
$71$			4.68380i			0.0659691i	−0.999456	+	0.0329845i	$0.989499\pi$
$72$		−	266.716i		−	3.70438i
$73$	−73.1662			−1.00228			−0.501138	−	0.865367i	$-0.667085\pi$
$73$	−73.1662			−1.00228			−0.501138	+	0.865367i	$0.667085\pi$
$74$	−159.548			−2.15605
$75$		−	46.0311i		−	0.613748i
$76$	−235.725			−3.10164
$77$			23.7645i			0.308629i
$78$	308.778			3.95869
$79$		−	54.7711i		−	0.693305i	−0.937994	−	0.346652i	$-0.887318\pi$
$79$		−	54.7711i		−	0.693305i	0.937994	−	0.346652i	$-0.112682\pi$
$80$			179.457i			2.24321i
$81$	−52.1760			−0.644148
$82$	11.0643			0.134931
$83$		−	79.8829i		−	0.962444i	−0.876599	−	0.481222i	$-0.840193\pi$
$83$		−	79.8829i		−	0.962444i	0.876599	−	0.481222i	$-0.159807\pi$
$84$	327.880			3.90333
$85$	−104.179			−1.22563
$86$	157.773			1.83457
$87$			230.793i			2.65279i
$88$		−	77.3056i		−	0.878472i
$89$		−	54.8937i		−	0.616784i	−0.951259	−	0.308392i	$-0.900209\pi$
$89$		−	54.8937i		−	0.616784i	0.951259	−	0.308392i	$-0.0997908\pi$
$90$	−166.754			−1.85282
$91$			129.135i			1.41906i
$92$			181.536i			1.97321i
$93$	−44.8822			−0.482604
$94$			28.2280i			0.300298i
$95$			89.3578i			0.940608i
$96$	−374.050			−3.89635
$97$	175.452			1.80878			0.904390	−	0.426708i	$-0.140327\pi$
$97$	175.452			1.80878			0.904390	+	0.426708i	$0.140327\pi$
$98$			6.71772i			0.0685482i
$99$	38.3669			0.387545
$100$	−103.284			−1.03284
$101$			104.657i			1.03621i	0.855316	+	0.518106i	$0.173363\pi$
$101$			104.657i			1.03621i	−0.855316	+	0.518106i	$0.826637\pi$
$102$		−	460.905i		−	4.51868i
$103$		−	153.617i		−	1.49143i	−0.666264	−	0.745716i	$-0.732108\pi$
$103$		−	153.617i		−	1.49143i	0.666264	−	0.745716i	$-0.267892\pi$
$104$		−	420.074i		−	4.03918i
$105$		−	124.292i		−	1.18373i
$106$			287.187i			2.70932i
$107$		−	21.1139i		−	0.197326i	−0.995121	−	0.0986632i	$-0.968543\pi$
$107$		−	21.1139i		−	0.197326i	0.995121	−	0.0986632i	$-0.0314566\pi$
$108$		−	115.266i		−	1.06728i
$109$			188.518i			1.72952i	0.502182	+	0.864762i	$0.332531\pi$
$109$			188.518i			1.72952i	−0.502182	+	0.864762i	$0.667469\pi$
$110$	−48.3324			−0.439385
$111$	−191.993			−1.72967
$112$		−	332.039i		−	2.96463i
$113$	−0.619774			−0.00548472			−0.00274236	−	0.999996i	$-0.500873\pi$
$113$	−0.619774			−0.00548472			−0.00274236	+	0.999996i	$0.500873\pi$
$114$	−395.334			−3.46784
$115$	68.8159			0.598400
$116$	517.849			4.46422
$117$	208.484			1.78191
$118$	338.599			2.86949
$119$	192.756			1.61980
$120$			404.319i			3.36933i
$121$	−109.880			−0.908096
$122$	136.113			1.11568
$123$	13.3143			0.108247
$124$			100.706i			0.812144i
$125$			135.442i			1.08354i
$126$	308.535			2.44869
$127$	44.2644			0.348538			0.174269	−	0.984698i	$-0.444244\pi$
$127$	44.2644			0.348538			0.174269	+	0.984698i	$0.444244\pi$
$128$			137.961i			1.07782i
$129$	189.857			1.47176
$130$	−262.636			−2.02027
$131$	−34.9397			−0.266716			−0.133358	−	0.991068i	$-0.542576\pi$
$131$	−34.9397			−0.266716			−0.133358	+	0.991068i	$0.542576\pi$
$132$		−	153.428i		−	1.16234i
$133$		−	165.333i		−	1.24311i
$134$			443.472i			3.30949i
$135$	−43.6948			−0.323665
$136$	−627.034			−4.61055
$137$	71.2736			0.520245			0.260123	−	0.965576i	$-0.416237\pi$
$137$	71.2736			0.520245			0.260123	+	0.965576i	$0.416237\pi$
$138$			304.453i			2.20618i
$139$	−33.2178			−0.238977			−0.119489	−	0.992836i	$-0.538126\pi$
$139$	−33.2178			−0.238977			−0.119489	+	0.992836i	$0.538126\pi$
$140$	−278.883			−1.99202
$141$			33.9683i			0.240910i
$142$	17.6253			0.124122
$143$	60.4275			0.422570
$144$	−536.066			−3.72268
$145$		−	196.304i		−	1.35382i
$146$			275.327i			1.88580i
$147$			8.08382i			0.0549919i
$148$			430.790i			2.91074i
$149$	−37.0133			−0.248411			−0.124206	−	0.992256i	$-0.539638\pi$
$149$	−37.0133			−0.248411			−0.124206	+	0.992256i	$0.539638\pi$
$150$	−173.217			−1.15478
$151$			78.6673i			0.520975i	0.965477	+	0.260488i	$0.0838833\pi$
$151$			78.6673i			0.520975i	−0.965477	+	0.260488i	$0.916117\pi$
$152$			537.828i			3.53834i
$153$		−	311.198i		−	2.03398i
$154$	89.4266			0.580692
$155$	38.1752			0.246292
$156$		−	833.721i		−	5.34437i
$157$	174.649			1.11241			0.556207	−	0.831044i	$-0.312256\pi$
$157$	174.649			1.11241			0.556207	+	0.831044i	$0.312256\pi$
$158$	−206.106			−1.30447
$159$			345.589i			2.17352i
$160$	318.154			1.98846
$161$	−127.326			−0.790846
$162$			196.340i			1.21198i
$163$		−	33.1720i		−	0.203509i	−0.994810	−	0.101755i	$-0.967554\pi$
$163$		−	33.1720i		−	0.203509i	0.994810	−	0.101755i	$-0.0324457\pi$
$164$		−	29.8744i		−	0.182161i
$165$	−58.1611			−0.352491
$166$	−300.602			−1.81086
$167$	−162.387			−0.972378			−0.486189	−	0.873854i	$-0.661613\pi$
$167$	−162.387			−0.972378			−0.486189	+	0.873854i	$0.661613\pi$
$168$		−	748.088i		−	4.45290i
$169$	159.359			0.942956
$170$			392.029i			2.30606i
$171$	−266.925			−1.56097
$172$		−	425.997i		−	2.47673i
$173$			77.8816i			0.450183i	0.974338	+	0.225091i	$0.0722680\pi$
$173$			77.8816i			0.450183i	−0.974338	+	0.225091i	$0.927732\pi$
$174$	868.483			4.99128
$175$		−	72.4414i		−	0.413951i
$176$	−155.375			−0.882811
$177$	407.456			2.30201
$178$	−206.567			−1.16049
$179$	208.336			1.16389			0.581945	−	0.813228i	$-0.302292\pi$
$179$	208.336			1.16389			0.581945	+	0.813228i	$0.302292\pi$
$180$			450.247i			2.50137i
$181$	−190.774			−1.05400			−0.527001	−	0.849865i	$-0.676684\pi$
$181$	−190.774			−1.05400			−0.527001	+	0.849865i	$0.676684\pi$
$182$	485.939			2.67000
$183$	163.793			0.895042
$184$	414.191			2.25104
$185$	163.302			0.882715
$186$			168.893i			0.908029i
$187$		−	90.1985i		−	0.482345i
$188$	76.2174			0.405412
$189$	80.8459			0.427756
$190$	336.257			1.76977
$191$	−108.095			−0.565942			−0.282971	−	0.959128i	$-0.591320\pi$
$191$	−108.095			−0.565942			−0.282971	+	0.959128i	$0.591320\pi$
$192$			563.620i			2.93552i
$193$	−39.6843			−0.205618			−0.102809	−	0.994701i	$-0.532783\pi$
$193$	−39.6843			−0.205618			−0.102809	+	0.994701i	$0.532783\pi$
$194$		−	660.231i		−	3.40325i
$195$	−316.044			−1.62074
$196$	18.1383			0.0925424
$197$		−	18.1632i		−	0.0921991i	−0.998937	−	0.0460995i	$-0.985321\pi$
$197$		−	18.1632i		−	0.0921991i	0.998937	−	0.0460995i	$-0.0146791\pi$
$198$		−	144.376i		−	0.729172i
$199$	85.1300			0.427789			0.213895	−	0.976857i	$-0.431385\pi$
$199$	85.1300			0.427789			0.213895	+	0.976857i	$0.431385\pi$
$200$			235.651i			1.17826i
$201$			533.655i			2.65500i
$202$	393.830			1.94965
$203$			363.211i			1.78922i
$204$	−1244.47			−6.10036
$205$	−11.3247			−0.0552424
$206$	−578.068			−2.80616
$207$			205.564i			0.993061i
$208$	−844.298			−4.05912
$209$	−77.3663			−0.370174
$210$	−467.714			−2.22721
$211$		−	73.8479i		−	0.349990i	−0.984569	−	0.174995i	$-0.944009\pi$
$211$		−	73.8479i		−	0.349990i	0.984569	−	0.174995i	$-0.0559909\pi$
$212$	775.425			3.65767
$213$	21.2096			0.0995754
$214$	−79.4525			−0.371273
$215$	−161.486			−0.751096
$216$	−262.991			−1.21755
$217$	−70.6334			−0.325499
$218$	709.401			3.25413
$219$			331.317i			1.51286i
$220$			130.501i			0.593185i
$221$		−	490.134i		−	2.21780i
$222$			722.476i			3.25440i
$223$		−	237.399i		−	1.06457i	−0.846565	−	0.532286i	$-0.821333\pi$
$223$		−	237.399i		−	1.06457i	0.846565	−	0.532286i	$-0.178667\pi$
$224$	−588.661			−2.62795
$225$	−116.954			−0.519796
$226$			2.33223i			0.0103196i
$227$	−234.089			−1.03123			−0.515614	−	0.856821i	$-0.672436\pi$
$227$	−234.089			−1.03123			−0.515614	+	0.856821i	$0.672436\pi$
$228$			1067.43i			4.68170i
$229$		−	311.775i		−	1.36146i	−0.732533	−	0.680731i	$-0.761662\pi$
$229$		−	311.775i		−	1.36146i	0.732533	−	0.680731i	$-0.238338\pi$
$230$		−	258.957i		−	1.12590i
$231$	107.612			0.465853
$232$		−	1181.52i		−	5.09276i
$233$	−383.432			−1.64563			−0.822816	−	0.568308i	$-0.807598\pi$
$233$	−383.432			−1.64563			−0.822816	+	0.568308i	$0.807598\pi$
$234$		−	784.532i		−	3.35270i
$235$		−	28.8922i		−	0.122946i
$236$		−	914.241i		−	3.87390i
$237$	−248.019			−1.04649
$238$		−	725.349i		−	3.04768i
$239$	162.793			0.681142			0.340571	−	0.940219i	$-0.389380\pi$
$239$	162.793			0.681142			0.340571	+	0.940219i	$0.389380\pi$
$240$	812.632			3.38596
$241$		−	353.483i		−	1.46673i	−0.679833	−	0.733367i	$-0.737948\pi$
$241$		−	353.483i		−	1.46673i	0.679833	−	0.733367i	$-0.262052\pi$
$242$			413.481i			1.70860i
$243$			338.369i			1.39246i
$244$		−	367.515i		−	1.50621i
$245$		−	6.87581i		−	0.0280645i
$246$		−	50.1023i		−	0.203668i
$247$	−420.404			−1.70204
$248$	229.770			0.926491
$249$	−361.732			−1.45274
$250$	509.674			2.03870
$251$			450.271i			1.79391i	0.442124	+	0.896954i	$0.354225\pi$
$251$			450.271i			1.79391i	−0.442124	+	0.896954i	$0.645775\pi$
$252$		−	833.065i		−	3.30581i
$253$			59.5811i			0.235498i
$254$		−	166.569i		−	0.655782i
$255$			471.751i			1.85000i
$256$	21.2838			0.0831400
$257$			154.133i			0.599738i	0.953980	+	0.299869i	$0.0969430\pi$
$257$			154.133i			0.599738i	−0.953980	+	0.299869i	$0.903057\pi$
$258$		−	714.439i		−	2.76914i
$259$	−302.149			−1.16660
$260$			709.133i			2.72744i
$261$	586.391			2.24671
$262$			131.480i			0.501830i
$263$	−439.477			−1.67101			−0.835507	−	0.549479i	$-0.814826\pi$
$263$	−439.477			−1.67101			−0.835507	+	0.549479i	$0.814826\pi$
$264$	−350.061			−1.32599
$265$		−	293.946i		−	1.10923i
$266$	−622.156			−2.33893
$267$	−248.574			−0.930989
$268$	1197.40			4.46792
$269$	−457.866			−1.70210			−0.851052	−	0.525081i	$-0.824035\pi$
$269$	−457.866			−1.70210			−0.851052	+	0.525081i	$0.824035\pi$
$270$			164.425i			0.608982i
$271$			376.006i			1.38748i	0.720227	+	0.693738i	$0.244037\pi$
$271$			376.006i			1.38748i	−0.720227	+	0.693738i	$0.755963\pi$
$272$			1260.26i			4.63331i
$273$	584.758			2.14197
$274$		−	268.205i		−	0.978851i
$275$	−33.8983			−0.123266
$276$	822.044			2.97842
$277$	−426.869			−1.54104			−0.770521	−	0.637415i	$-0.780004\pi$
$277$	−426.869			−1.54104			−0.770521	+	0.637415i	$0.780004\pi$
$278$			125.000i			0.449640i
$279$			114.035i			0.408728i
$280$			636.297i			2.27249i
$281$		−	89.1475i		−	0.317251i	−0.987339	−	0.158625i	$-0.949294\pi$
$281$		−	89.1475i		−	0.317251i	0.987339	−	0.158625i	$-0.0507062\pi$
$282$	127.824			0.453277
$283$		−	392.619i		−	1.38735i	−0.720290	−	0.693673i	$-0.755991\pi$
$283$		−	392.619i		−	1.38735i	0.720290	−	0.693673i	$-0.244009\pi$
$284$		−	47.5896i		−	0.167569i
$285$	404.637			1.41978
$286$		−	227.391i		−	0.795073i
$287$	20.9534			0.0730084
$288$			950.373i			3.29991i
$289$	−442.610			−1.53152
$290$	−738.701			−2.54724
$291$		−	794.493i		−	2.73022i
$292$	743.401			2.54590
$293$	−241.736			−0.825039			−0.412520	−	0.910949i	$-0.635351\pi$
$293$	−241.736			−0.825039			−0.412520	+	0.910949i	$0.635351\pi$
$294$	30.4197			0.103468
$295$	−346.567			−1.17480
$296$	982.887			3.32056
$297$		−	37.8311i		−	0.127377i
$298$			139.282i			0.467391i
$299$			323.760i			1.08281i
$300$			467.697i			1.55899i
$301$	298.787			0.992649
$302$	296.028			0.980225
$303$	473.918			1.56409
$304$	1080.97			3.55582
$305$	−139.316			−0.456774
$306$	−1171.05			−3.82696
$307$		−	82.3919i		−	0.268378i	−0.990956	−	0.134189i	$-0.957157\pi$
$307$		−	82.3919i		−	0.268378i	0.990956	−	0.134189i	$-0.0428429\pi$
$308$		−	241.458i		−	0.783954i
$309$	−695.622			−2.25121
$310$		−	143.655i		−	0.463403i
$311$	−110.538			−0.355427			−0.177713	−	0.984082i	$-0.556870\pi$
$311$	−110.538			−0.355427			−0.177713	+	0.984082i	$0.556870\pi$
$312$	−1902.21			−6.09683
$313$	−114.095			−0.364521			−0.182261	−	0.983250i	$-0.558341\pi$
$313$	−114.095			−0.364521			−0.182261	+	0.983250i	$0.558341\pi$
$314$		−	657.211i		−	2.09303i
$315$	−315.795			−1.00253
$316$			556.499i			1.76107i
$317$	432.946			1.36576			0.682881	−	0.730530i	$-0.260727\pi$
$317$	432.946			1.36576			0.682881	+	0.730530i	$0.260727\pi$
$318$	1300.46			4.08951
$319$	169.961			0.532793
$320$		−	479.395i		−	1.49811i
$321$	−95.6097			−0.297849
$322$			479.133i			1.48799i
$323$			627.527i			1.94281i
$324$	530.132			1.63621
$325$	−184.201			−0.566774
$326$	−124.828			−0.382907
$327$	853.662			2.61059
$328$	−68.1612			−0.207809
$329$			53.4576i			0.162485i
$330$			218.862i			0.663219i
$331$		−	437.359i		−	1.32133i	−0.750683	−	0.660663i	$-0.770275\pi$
$331$		−	437.359i		−	1.32133i	0.750683	−	0.660663i	$-0.229725\pi$
$332$			811.646i			2.44472i
$333$			487.809i			1.46489i
$334$			611.069i			1.82955i
$335$		−	453.908i		−	1.35495i
$336$	−1503.56			−4.47489
$337$			402.488i			1.19433i	0.802119	+	0.597164i	$0.203706\pi$
$337$			402.488i			1.19433i	−0.802119	+	0.597164i	$0.796294\pi$
$338$		−	599.676i		−	1.77419i
$339$			2.80651i			0.00827878i
$340$	1058.51			3.11325
$341$			33.0522i			0.0969274i
$342$			1004.45i			2.93699i
$343$		−	336.470i		−	0.980963i
$344$	−971.952			−2.82544
$345$		−	311.618i		−	0.903239i
$346$	293.071			0.847027
$347$	−100.950			−0.290922			−0.145461	−	0.989364i	$-0.546466\pi$
$347$	−100.950			−0.290922			−0.145461	+	0.989364i	$0.546466\pi$
$348$		−	2344.96i		−	6.73840i
$349$	373.527			1.07028			0.535140	−	0.844764i	$-0.320259\pi$
$349$	373.527			1.07028			0.535140	+	0.844764i	$0.320259\pi$
$350$	−272.600			−0.778856
$351$		−	205.572i		−	0.585676i
$352$			275.458i			0.782553i
$353$	555.254			1.57296			0.786479	−	0.617617i	$-0.211902\pi$
$353$	555.254			1.57296			0.786479	+	0.617617i	$0.211902\pi$
$354$		−	1533.27i		−	4.33128i
$355$	−18.0401			−0.0508172
$356$			557.745i			1.56670i
$357$		−	872.853i		−	2.44497i
$358$		−	783.978i		−	2.18988i
$359$		−	363.772i		−	1.01329i	−0.862154	−	0.506646i	$-0.830885\pi$
$359$		−	363.772i		−	1.01329i	0.862154	−	0.506646i	$-0.169115\pi$
$360$	1027.28			2.85355
$361$	177.251			0.490999
$362$			717.891i			1.98313i
$363$			497.565i			1.37070i
$364$		−	1312.07i		−	3.60458i
$365$		−	281.806i		−	0.772071i
$366$		−	616.358i		−	1.68404i
$367$	−422.020			−1.14992			−0.574960	−	0.818182i	$-0.694982\pi$
$367$	−422.020			−1.14992			−0.574960	+	0.818182i	$0.694982\pi$
$368$		−	832.472i		−	2.26215i
$369$		−	33.8286i		−	0.0916763i
$370$		−	614.513i		−	1.66085i
$371$			543.870i			1.46596i
$372$	456.024			1.22587
$373$		−	120.491i		−	0.323032i	−0.986870	−	0.161516i	$-0.948362\pi$
$373$		−	120.491i		−	0.323032i	0.986870	−	0.161516i	$-0.0516383\pi$
$374$	−339.420			−0.907541
$375$	613.319			1.63552
$376$		−	173.897i		−	0.462492i
$377$	923.559			2.44976
$378$		−	304.226i		−	0.804831i
$379$	65.7673			0.173529			0.0867643	−	0.996229i	$-0.472347\pi$
$379$	65.7673			0.173529			0.0867643	+	0.996229i	$0.472347\pi$
$380$		−	907.916i		−	2.38925i
$381$		−	200.441i		−	0.526093i
$382$			406.765i			1.06483i
$383$	30.2487			0.0789784			0.0394892	−	0.999220i	$-0.487427\pi$
$383$	30.2487			0.0789784			0.0394892	+	0.999220i	$0.487427\pi$
$384$	624.724			1.62688
$385$	−91.5310			−0.237743
$386$			149.333i			0.386874i
$387$		−	482.382i		−	1.24646i
$388$	−1782.67			−4.59450
$389$		−	680.565i		−	1.74952i	−0.484552	−	0.874762i	$-0.661017\pi$
$389$		−	680.565i		−	1.74952i	0.484552	−	0.874762i	$-0.338983\pi$
$390$			1189.29i			3.04945i
$391$	483.269			1.23598
$392$		−	41.3842i		−	0.105572i
$393$			158.217i			0.402587i
$394$	−68.3489			−0.173474
$395$	210.956			0.534065
$396$	−389.825			−0.984407
$397$			21.9440i			0.0552746i	0.999618	+	0.0276373i	$0.00879835\pi$
$397$			21.9440i			0.0552746i	−0.999618	+	0.0276373i	$0.991202\pi$
$398$		−	320.348i		−	0.804893i
$399$	−748.676			−1.87638
$400$	473.630			1.18407
$401$	−644.893			−1.60821			−0.804106	−	0.594486i	$-0.797355\pi$
$401$	−644.893			−1.60821			−0.804106	+	0.594486i	$0.797355\pi$
$402$	2008.16			4.99543
$403$			179.604i			0.445668i
$404$		−	1063.37i		−	2.63210i
$405$		−	200.961i		−	0.496199i
$406$	1366.78			3.36644
$407$			141.388i			0.347390i
$408$			2839.38i			6.95927i
$409$	−76.5622			−0.187194			−0.0935969	−	0.995610i	$-0.529836\pi$
$409$	−76.5622			−0.187194			−0.0935969	+	0.995610i	$0.529836\pi$
$410$			42.6152i			0.103940i
$411$		−	322.746i		−	0.785271i
$412$			1560.82i			3.78841i
$413$	641.233			1.55262
$414$	773.544			1.86846
$415$	307.676			0.741388
$416$			1496.83i			3.59814i
$417$			150.420i			0.360718i
$418$			291.132i			0.696489i
$419$	708.119			1.69002			0.845011	−	0.534749i	$-0.179594\pi$
$419$	708.119			1.69002			0.845011	+	0.534749i	$0.179594\pi$
$420$			1262.86i			3.00681i
$421$			115.189i			0.273608i	0.990598	+	0.136804i	$0.0436830\pi$
$421$			115.189i			0.273608i	−0.990598	+	0.136804i	$0.956317\pi$
$422$	−277.892			−0.658513
$423$	86.3055			0.204032
$424$		−	1769.21i		−	4.17265i
$425$			274.953i			0.646948i
$426$		−	79.8124i		−	0.187353i
$427$	257.769			0.603674
$428$			214.527i			0.501231i
$429$		−	273.632i		−	0.637837i
$430$			607.676i			1.41320i
$431$		−	474.217i		−	1.10027i	−0.835075	−	0.550136i	$-0.814576\pi$
$431$		−	474.217i		−	1.10027i	0.835075	−	0.550136i	$-0.185424\pi$
$432$			528.579i			1.22356i
$433$			480.043i			1.10864i	0.832302	+	0.554322i	$0.187022\pi$
$433$			480.043i			1.10864i	−0.832302	+	0.554322i	$0.812978\pi$
$434$			265.796i			0.612433i
$435$	−888.921			−2.04350
$436$		−	1915.43i		−	4.39319i
$437$		−	414.516i		−	0.948549i
$438$	1246.76			2.84648
$439$	−584.929			−1.33241			−0.666206	−	0.745768i	$-0.732083\pi$
$439$	−584.929			−1.33241			−0.666206	+	0.745768i	$0.732083\pi$
$440$	297.749			0.676703
$441$	20.5391			0.0465739
$442$	−1844.39			−4.17283
$443$	−101.286			−0.228636			−0.114318	−	0.993444i	$-0.536468\pi$
$443$	−101.286			−0.228636			−0.114318	+	0.993444i	$0.536468\pi$
$444$	1950.73			4.39355
$445$	211.428			0.475120
$446$	−893.343			−2.00301
$447$			167.606i			0.374958i
$448$			886.997i			1.97990i
$449$	−56.2120			−0.125194			−0.0625969	−	0.998039i	$-0.519938\pi$
$449$	−56.2120			−0.125194			−0.0625969	+	0.998039i	$0.519938\pi$
$450$			440.103i			0.978006i
$451$		−	9.80496i		−	0.0217405i
$452$	6.29718			0.0139318
$453$	356.227			0.786373
$454$			880.884i			1.94027i
$455$	−497.374			−1.09313
$456$	2435.43			5.34087
$457$		−	0.415496i		−	0.000909182i	−1.00000		0.000454591i	$-0.999855\pi$
$457$		−	0.415496i		−	0.000909182i	1.00000		0.000454591i	$-0.000144701\pi$
$458$	−1173.22			−2.56162
$459$	−306.852			−0.668524
$460$	−699.201			−1.52000
$461$		−	452.616i		−	0.981813i	−0.871212	−	0.490906i	$-0.836666\pi$
$461$		−	452.616i		−	0.981813i	0.871212	−	0.490906i	$-0.163334\pi$
$462$		−	404.948i		−	0.876511i
$463$			129.538i			0.279779i	0.990167	+	0.139890i	$0.0446748\pi$
$463$			129.538i			0.279779i	−0.990167	+	0.139890i	$0.955325\pi$
$464$	−2374.71			−5.11791
$465$		−	172.868i		−	0.371759i
$466$			1442.87i			3.09629i
$467$	3.66176			0.00784103			0.00392052	−	0.999992i	$-0.498752\pi$
$467$	3.66176			0.00784103			0.00392052	+	0.999992i	$0.498752\pi$
$468$	−2118.29			−4.52626
$469$			839.839i			1.79070i
$470$	−108.723			−0.231325
$471$		−	790.859i		−	1.67911i
$472$	−2085.93			−4.41933
$473$		−	139.815i		−	0.295592i
$474$			933.303i			1.96899i
$475$	235.836			0.496497
$476$	−1958.49			−4.11448
$477$	878.060			1.84080
$478$		−	612.596i		−	1.28158i
$479$	−740.424			−1.54577			−0.772886	−	0.634545i	$-0.781187\pi$
$479$	−740.424			−1.54577			−0.772886	+	0.634545i	$0.781187\pi$
$480$		−	1440.69i		−	3.00143i
$481$			768.293i			1.59728i
$482$	−1330.17			−2.75969
$483$			576.568i			1.19372i
$484$	1116.43			2.30667
$485$			675.768i			1.39334i
$486$	1273.29			2.61995
$487$		−	834.245i		−	1.71303i	−0.516124	−	0.856514i	$-0.672625\pi$
$487$		−	834.245i		−	1.71303i	0.516124	−	0.856514i	$-0.327375\pi$
$488$	−838.519			−1.71828
$489$	−150.212			−0.307182
$490$	−25.8739			−0.0528039
$491$			145.617i			0.296573i	0.988944	+	0.148287i	$0.0473758\pi$
$491$			145.617i			0.296573i	−0.988944	+	0.148287i	$0.952624\pi$
$492$	−135.280			−0.274958
$493$		−	1378.57i		−	2.79630i
$494$			1582.00i			3.20242i
$495$			147.774i			0.298533i
$496$		−	461.809i		−	0.931066i
$497$	33.3785			0.0671600
$498$			1361.21i			2.73335i
$499$	−354.742			−0.710906			−0.355453	−	0.934694i	$-0.615673\pi$
$499$	−354.742			−0.710906			−0.355453	+	0.934694i	$0.615673\pi$
$500$		−	1376.15i		−	2.75231i
$501$			735.334i			1.46773i
$502$	1694.39			3.37527
$503$			65.4383i			0.130096i	0.997882	+	0.0650480i	$0.0207200\pi$
$503$			65.4383i			0.130096i	−0.997882	+	0.0650480i	$0.979280\pi$
$504$	−1900.72			−3.77126
$505$	−403.098			−0.798213
$506$	224.206			0.443095
$507$		−	721.624i		−	1.42332i
$508$	−449.746			−0.885327
$509$	468.105			0.919657			0.459828	−	0.888008i	$-0.347911\pi$
$509$	468.105			0.919657			0.459828	+	0.888008i	$0.347911\pi$
$510$	1775.22			3.48082
$511$			521.409i			1.02037i
$512$			471.751i			0.921388i
$513$			263.198i			0.513056i
$514$	580.007			1.12842
$515$	591.672			1.14888
$516$	−1929.03			−3.73844
$517$	25.0150			0.0483849
$518$			1137.00i			2.19497i
$519$	352.669			0.679517
$520$	1617.95			3.11145
$521$	23.2900			0.0447026			0.0223513	−	0.999750i	$-0.492885\pi$
$521$	23.2900			0.0447026			0.0223513	+	0.999750i	$0.492885\pi$
$522$		−	2206.61i		−	4.22723i
$523$		−	956.185i		−	1.82827i	−0.405411	−	0.914135i	$-0.632871\pi$
$523$		−	956.185i		−	1.82827i	0.405411	−	0.914135i	$-0.367129\pi$
$524$	355.004			0.677488
$525$	−328.035			−0.624828
$526$			1653.77i			3.14405i
$527$	268.090			0.508711
$528$			703.579i			1.33254i
$529$	209.774			0.396549
$530$	−1106.13			−2.08703
$531$		−	1035.25i		−	1.94962i
$532$			1679.86i			3.15764i
$533$		−	53.2796i		−	0.0999617i
$534$			935.393i			1.75167i
$535$	81.3222			0.152004
$536$		−	2731.99i		−	5.09699i
$537$		−	943.405i		−	1.75681i
$538$			1722.97i			3.20254i
$539$	5.95310			0.0110447
$540$	443.959			0.822146
$541$			458.584i			0.847660i	0.905742	+	0.423830i	$0.139315\pi$
$541$			458.584i			0.847660i	−0.905742	+	0.423830i	$0.860685\pi$
$542$	1414.93			2.61056
$543$			863.879i			1.59094i
$544$	2234.27			4.10712
$545$	−726.094			−1.33228
$546$		−	2200.47i		−	4.03016i
$547$	−532.189	−	126.428i	−0.972923	−	0.231129i
$547$	−532.189	−	126.428i	−0.972923	−	0.231129i
$548$	−724.172			−1.32148
$549$		−	416.159i		−	0.758030i
$550$			127.561i			0.231928i
$551$	−1182.45			−2.14601
$552$		−	1875.57i		−	3.39777i
$553$	−390.319			−0.705821
$554$			1606.32i			2.89950i
$555$		−	739.478i		−	1.33239i
$556$	337.508			0.607029
$557$	388.034			0.696650			0.348325	−	0.937374i	$-0.386751\pi$
$557$	388.034			0.696650			0.348325	+	0.937374i	$0.386751\pi$
$558$	429.119			0.769030
$559$		−	759.746i		−	1.35912i
$560$	1278.88			2.28371
$561$	−408.444			−0.728064
$562$	−335.465			−0.596913
$563$	−354.961			−0.630481			−0.315241	−	0.949012i	$-0.602085\pi$
$563$	−354.961			−0.630481			−0.315241	+	0.949012i	$0.602085\pi$
$564$		−	345.133i		−	0.611939i
$565$		−	2.38711i		−	0.00422498i
$566$	−1477.44			−2.61032
$567$			371.826i			0.655777i
$568$	−108.580			−0.191162
$569$			609.891i			1.07186i	0.844261	+	0.535932i	$0.180040\pi$
$569$			609.891i			1.07186i	−0.844261	+	0.535932i	$0.819960\pi$
$570$		−	1522.66i		−	2.67134i
$571$	514.679			0.901364			0.450682	−	0.892685i	$-0.351181\pi$
$571$	514.679			0.901364			0.450682	+	0.892685i	$0.351181\pi$
$572$	−613.970			−1.07337
$573$			489.483i			0.854247i
$574$		−	78.8485i		−	0.137367i
$575$		−	181.621i		−	0.315863i
$576$	1432.03			2.48616
$577$		−	993.006i		−	1.72098i	−0.509466	−	0.860491i	$-0.670157\pi$
$577$		−	993.006i		−	1.72098i	0.509466	−	0.860491i	$-0.329843\pi$
$578$			1665.56i			2.88159i
$579$			179.701i			0.310365i
$580$			1994.54i			3.43887i
$581$	−569.275			−0.979819
$582$	−2989.71			−5.13696
$583$	254.499			0.436534
$584$		−	1696.14i		−	2.90435i
$585$			802.994i			1.37264i
$586$			909.664i			1.55233i
$587$	−466.703			−0.795065			−0.397532	−	0.917588i	$-0.630133\pi$
$587$	−466.703			−0.795065			−0.397532	+	0.917588i	$0.630133\pi$
$588$		−	82.1352i		−	0.139686i
$589$		−	229.950i		−	0.390408i
$590$			1304.15i			2.21042i
$591$	−82.2481			−0.139168
$592$		−	1975.48i		−	3.33696i
$593$	882.081			1.48749			0.743744	−	0.668464i	$-0.233048\pi$
$593$	882.081			1.48749			0.743744	+	0.668464i	$0.233048\pi$
$594$	−142.360			−0.239663
$595$			742.418i			1.24776i
$596$	376.072			0.630993
$597$		−	385.492i		−	0.645716i
$598$	1218.32			2.03733
$599$	1145.04			1.91159			0.955794	−	0.294039i	$-0.0949995\pi$
$599$	1145.04			1.91159			0.955794	+	0.294039i	$0.0949995\pi$
$600$	1067.09			1.77849
$601$	−831.853			−1.38411			−0.692057	−	0.721843i	$-0.743295\pi$
$601$	−831.853			−1.38411			−0.692057	+	0.721843i	$0.743295\pi$
$602$		−	1124.35i		−	1.86769i
$603$	1355.89			2.24858
$604$		−	799.295i		−	1.32334i
$605$		−	423.211i		−	0.699523i
$606$		−	1783.37i		−	2.94286i
$607$	473.269			0.779686			0.389843	−	0.920881i	$-0.372529\pi$
$607$	473.269			0.779686			0.389843	+	0.920881i	$0.372529\pi$
$608$		−	1916.41i		−	3.15199i
$609$	1644.72			2.70069
$610$			524.252i			0.859430i
$611$	135.930			0.222472
$612$			3161.92i			5.16653i
$613$	264.869			0.432086			0.216043	−	0.976384i	$-0.430685\pi$
$613$	264.869			0.432086			0.216043	+	0.976384i	$0.430685\pi$
$614$	−310.044			−0.504958
$615$			51.2813i			0.0833842i
$616$	−550.908			−0.894332
$617$		−	168.463i		−	0.273035i	−0.990638	−	0.136517i	$-0.956409\pi$
$617$		−	168.463i		−	0.273035i	0.990638	−	0.136517i	$-0.0435910\pi$
$618$			2617.65i			4.23568i
$619$			1065.77i			1.72176i	0.508812	+	0.860878i	$0.330085\pi$
$619$			1065.77i			1.72176i	−0.508812	+	0.860878i	$0.669915\pi$
$620$	−387.878			−0.625609
$621$	202.693			0.326398
$622$			415.957i			0.668742i
$623$	−391.193			−0.627919
$624$			3823.21i			6.12694i
$625$	−267.536			−0.428058
$626$			429.345i			0.685854i
$627$			350.336i			0.558749i
$628$	−1774.51			−2.82566
$629$	1146.81			1.82323
$630$			1188.35i			1.88627i
$631$	−1072.66			−1.69994			−0.849968	−	0.526834i	$-0.823379\pi$
$631$	−1072.66			−1.69994			−0.849968	+	0.526834i	$0.823379\pi$
$632$	1269.70			2.00903
$633$	−334.404			−0.528284
$634$		−	1629.19i		−	2.56971i
$635$			170.488i			0.268485i
$636$		−	3511.34i		−	5.52098i
$637$	32.3488			0.0507831
$638$		−	639.570i		−	1.00246i
$639$		−	53.8885i		−	0.0843325i
$640$	−531.368			−0.830262
$641$			87.2450i			0.136108i	0.997682	+	0.0680538i	$0.0216790\pi$
$641$			87.2450i			0.136108i	−0.997682	+	0.0680538i	$0.978321\pi$
$642$			359.783i			0.560409i
$643$	−227.586			−0.353944			−0.176972	−	0.984216i	$-0.556630\pi$
$643$	−227.586			−0.353944			−0.176972	+	0.984216i	$0.556630\pi$
$644$	1293.69			2.00884
$645$			731.251i			1.13372i
$646$	2361.41			3.65543
$647$	1202.88			1.85917			0.929586	−	0.368607i	$-0.120165\pi$
$647$	1202.88			1.85917			0.929586	+	0.368607i	$0.120165\pi$
$648$		−	1209.55i		−	1.86658i
$649$		−	300.059i		−	0.462341i
$650$			693.157i			1.06640i
$651$			319.847i			0.491317i
$652$			337.043i			0.516937i
$653$			565.314i			0.865719i	0.901461	+	0.432859i	$0.142495\pi$
$653$			565.314i			0.865719i	−0.901461	+	0.432859i	$0.857505\pi$
$654$		−	3212.36i		−	4.91187i
$655$		−	134.574i		−	0.205456i
$656$			136.996i			0.208835i
$657$	841.797			1.28127
$658$	201.163			0.305719
$659$		−	1134.24i		−	1.72116i	−0.509319	−	0.860578i	$-0.670103\pi$
$659$		−	1134.24i		−	1.72116i	0.509319	−	0.860578i	$-0.329897\pi$
$660$	590.943			0.895368
$661$	−816.943			−1.23592			−0.617960	−	0.786210i	$-0.712040\pi$
$661$	−816.943			−1.23592			−0.617960	+	0.786210i	$0.712040\pi$
$662$	−1645.80			−2.48610
$663$	−2219.46			−3.34760
$664$	1851.85			2.78893
$665$	636.797			0.957589
$666$	1835.64			2.75622
$667$			910.624i			1.36525i
$668$	1649.93			2.46995
$669$	−1075.01			−1.60689
$670$	−1708.07			−2.54936
$671$		−	120.620i		−	0.179762i
$672$			2665.62i			3.96669i
$673$	−720.708			−1.07089			−0.535445	−	0.844570i	$-0.679856\pi$
$673$	−720.708			−1.07089			−0.535445	+	0.844570i	$0.679856\pi$
$674$	1514.58			2.24715
$675$			115.321i			0.170846i
$676$	−1619.16			−2.39521
$677$	717.902			1.06042			0.530209	−	0.847867i	$-0.322114\pi$
$677$	717.902			1.06042			0.530209	+	0.847867i	$0.322114\pi$
$678$	10.5610			0.0155767
$679$		−	1250.33i		−	1.84143i
$680$		−	2415.08i		−	3.55159i
$681$			1060.02i			1.55656i
$682$	124.377			0.182371
$683$	574.164			0.840650			0.420325	−	0.907374i	$-0.361916\pi$
$683$	574.164			0.840650			0.420325	+	0.907374i	$0.361916\pi$
$684$	2712.08			3.96503
$685$			274.517i			0.400754i
$686$	−1266.15			−1.84570
$687$	−1411.80			−2.05503
$688$			1953.50i			2.83940i
$689$	1382.93			2.00716
$690$	−1172.63			−1.69946
$691$	−141.730			−0.205109			−0.102554	−	0.994727i	$-0.532702\pi$
$691$	−141.730			−0.205109			−0.102554	+	0.994727i	$0.532702\pi$
$692$		−	791.312i		−	1.14351i
$693$		−	273.417i		−	0.394541i
$694$			379.878i			0.547374i
$695$		−	127.942i		−	0.184089i
$696$	−5350.25			−7.68714
$697$	−79.5291			−0.114102
$698$		−	1405.60i		−	2.01375i
$699$			1736.29i			2.48396i
$700$			736.037i			1.05148i
$701$	427.412			0.609718			0.304859	−	0.952398i	$-0.401391\pi$
$701$	427.412			0.609718			0.304859	+	0.952398i	$0.401391\pi$
$702$	−773.576			−1.10196
$703$		−	983.659i		−	1.39923i
$704$	415.062			0.589577
$705$	−130.832			−0.185577
$706$		−	2089.44i		−	2.95955i
$707$	745.828			1.05492
$708$	−4139.94			−5.84737
$709$		−	1199.81i		−	1.69226i	−0.532979	−	0.846129i	$-0.678927\pi$
$709$		−	1199.81i		−	1.69226i	0.532979	−	0.846129i	$-0.321073\pi$
$710$			67.8856i			0.0956135i
$711$			630.157i			0.886296i
$712$	1272.55			1.78729
$713$	−177.089			−0.248371
$714$	−3284.58			−4.60025
$715$			232.742i			0.325513i
$716$	−2116.79			−2.95641
$717$		−	737.171i		−	1.02813i
$718$	−1368.89			−1.90653
$719$		−	35.1580i		−	0.0488984i	−0.999701	−	0.0244492i	$-0.992217\pi$
$719$		−	35.1580i		−	0.0488984i	0.999701	−	0.0244492i	$-0.00778320\pi$
$720$		−	2064.71i		−	2.86765i
$721$	−1094.74			−1.51836
$722$		−	667.001i		−	0.923824i
$723$	−1600.67			−2.21392
$724$	1938.35			2.67729
$725$	−518.094			−0.714612
$726$	1872.36			2.57900
$727$		−	1048.01i		−	1.44156i	−0.693165	−	0.720779i	$-0.743784\pi$
$727$		−	1048.01i		−	1.44156i	0.693165	−	0.720779i	$-0.256216\pi$
$728$	−2993.61			−4.11210
$729$	1062.64			1.45767
$730$	−1060.45			−1.45267
$731$	−1134.05			−1.55137
$732$	−1664.21			−2.27351
$733$			505.860i			0.690122i	0.938580	+	0.345061i	$0.112142\pi$
$733$			505.860i			0.690122i	−0.938580	+	0.345061i	$0.887858\pi$
$734$			1588.08i			2.16360i
$735$	−31.1355			−0.0423613
$736$	−1475.86			−2.00525
$737$	392.995			0.533236
$738$	−127.298			−0.172491
$739$			393.965i			0.533106i	0.963820	+	0.266553i	$0.0858847\pi$
$739$			393.965i			0.533106i	−0.963820	+	0.266553i	$0.914115\pi$
$740$	−1659.23			−2.24220
$741$			1903.71i			2.56910i
$742$	2046.61			2.75823
$743$	79.0216			0.106355			0.0531774	−	0.998585i	$-0.483065\pi$
$743$	79.0216			0.106355			0.0531774	+	0.998585i	$0.483065\pi$
$744$		−	1040.46i		−	1.39847i
$745$		−	142.560i		−	0.191356i
$746$	−453.412			−0.607791
$747$			919.075i			1.23035i
$748$			916.458i			1.22521i
$749$	−150.466			−0.200889
$750$		−	2307.94i		−	3.07726i
$751$	−1373.13			−1.82841			−0.914203	−	0.405255i	$-0.867183\pi$
$751$	−1373.13			−1.82841			−0.914203	+	0.405255i	$0.867183\pi$
$752$	−349.512			−0.464776
$753$	2038.95			2.70777
$754$		−	3475.39i		−	4.60927i
$755$	−302.994			−0.401317
$756$	−821.431			−1.08655
$757$	299.726			0.395939			0.197969	−	0.980208i	$-0.436565\pi$
$757$	299.726			0.395939			0.197969	+	0.980208i	$0.436565\pi$
$758$		−	247.485i		−	0.326497i
$759$	269.800			0.355467
$760$	−2071.49			−2.72565
$761$	876.854			1.15224			0.576120	−	0.817365i	$-0.304566\pi$
$761$	876.854			1.15224			0.576120	+	0.817365i	$0.304566\pi$
$762$	−754.268			−0.989853
$763$	1343.45			1.76075
$764$	1098.29			1.43756
$765$	1198.61			1.56681
$766$		−	113.827i		−	0.148599i
$767$		−	1630.51i		−	2.12582i
$768$		−	96.3791i		−	0.125494i
$769$			930.002i			1.20937i	0.796466	+	0.604683i	$0.206700\pi$
$769$			930.002i			1.20937i	−0.796466	+	0.604683i	$0.793300\pi$
$770$			344.435i			0.447318i
$771$	697.956			0.905260
$772$	403.210			0.522293
$773$		−	345.943i		−	0.447533i	−0.974643	−	0.223766i	$-0.928165\pi$
$773$		−	345.943i		−	0.447533i	0.974643	−	0.223766i	$-0.0718352\pi$
$774$	−1815.22			−2.34525
$775$		−	100.753i		−	0.130004i
$776$			4067.32i			5.24139i
$777$			1368.21i			1.76089i
$778$	−2560.99			−3.29176
$779$			68.2148i			0.0875671i
$780$	3211.15			4.11686
$781$		−	15.6192i		−	0.0199990i
$782$		−	1818.56i		−	2.32552i
$783$		−	578.202i		−	0.738444i
$784$	−83.1772			−0.106093
$785$			672.676i			0.856913i
$786$	595.376			0.757476
$787$	833.158			1.05865			0.529325	−	0.848419i	$-0.322445\pi$
$787$	833.158			1.05865			0.529325	+	0.848419i	$0.322445\pi$
$788$			184.547i			0.234196i
$789$			1990.07i			2.52227i
$790$		−	793.835i		−	1.00485i
$791$			4.41674i			0.00558374i
$792$			889.422i			1.12301i
$793$		−	655.445i		−	0.826539i
$794$	82.5762			0.104000
$795$	−1331.07			−1.67430
$796$	−864.960			−1.08663
$797$	451.397			0.566371			0.283185	−	0.959065i	$-0.408609\pi$
$797$	451.397			0.566371			0.283185	+	0.959065i	$0.408609\pi$
$798$			2817.29i			3.53044i
$799$		−	202.899i		−	0.253942i
$800$		−	839.682i		−	1.04960i
$801$			631.568i			0.788474i
$802$			2426.76i			3.02588i
$803$	243.989			0.303846
$804$		−	5422.18i		−	6.74400i
$805$		−	490.408i		−	0.609203i
$806$	675.857			0.838532
$807$			2073.34i			2.56920i
$808$	−2426.17			−3.00269
$809$			785.927i			0.971479i	0.874104	+	0.485740i	$0.161450\pi$
$809$			785.927i			0.971479i	−0.874104	+	0.485740i	$0.838550\pi$
$810$	−756.223			−0.933608
$811$	42.1396			0.0519600			0.0259800	−	0.999662i	$-0.491729\pi$
$811$	42.1396			0.0519600			0.0259800	+	0.999662i	$0.491729\pi$
$812$		−	3690.38i		−	4.54481i
$813$	1702.66			2.09429
$814$	532.047			0.653621
$815$	127.765			0.156767
$816$	5706.81			6.99364
$817$			972.716i			1.19059i
$818$			288.107i			0.352209i
$819$		−	1485.73i		−	1.81408i
$820$	115.064			0.140322
$821$			1237.53i			1.50734i	0.657253	+	0.753670i	$0.271718\pi$
$821$			1237.53i			1.50734i	−0.657253	+	0.753670i	$0.728282\pi$
$822$	−1214.51			−1.47750
$823$	871.999			1.05954			0.529769	−	0.848142i	$-0.322279\pi$
$823$	871.999			1.05954			0.529769	+	0.848142i	$0.322279\pi$
$824$	3561.16			4.32180
$825$			153.501i			0.186062i
$826$		−	2412.99i		−	2.92129i
$827$			436.663i			0.528008i	0.964522	+	0.264004i	$0.0850433\pi$
$827$			436.663i			0.528008i	−0.964522	+	0.264004i	$0.914957\pi$
$828$		−	2088.62i		−	2.52249i
$829$	−847.562			−1.02239			−0.511195	−	0.859465i	$-0.670797\pi$
$829$	−847.562			−1.02239			−0.511195	+	0.859465i	$0.670797\pi$
$830$		−	1157.80i		−	1.39494i
$831$			1932.98i			2.32609i
$832$	2255.42			2.71085
$833$		−	48.2862i		−	0.0579667i
$834$	566.035			0.678698
$835$		−	625.449i		−	0.749040i
$836$	786.077			0.940283
$837$	112.443			0.134340
$838$		−	2664.68i		−	3.17981i
$839$	1329.11			1.58416			0.792082	−	0.610415i	$-0.208997\pi$
$839$	1329.11			1.58416			0.792082	+	0.610415i	$0.208997\pi$
$840$	2881.33			3.43015
$841$	1756.65			2.08876
$842$	433.460			0.514798
$843$	−403.684			−0.478866
$844$			750.328i			0.889014i
$845$			613.787i			0.726376i
$846$		−	324.771i		−	0.383890i
$847$			783.043i			0.924490i
$848$	−3555.88			−4.19326
$849$	−1777.89			−2.09410
$850$	1034.66			1.21724
$851$	−757.532			−0.890167
$852$	−215.499			−0.252933
$853$	−557.460			−0.653528			−0.326764	−	0.945106i	$-0.605958\pi$
$853$	−557.460			−0.653528			−0.326764	+	0.945106i	$0.605958\pi$
$854$		−	969.993i		−	1.13582i
$855$		−	1028.09i		−	1.20244i
$856$	489.463			0.571803
$857$		−	457.728i		−	0.534106i	−0.963682	−	0.267053i	$-0.913950\pi$
$857$		−	457.728i		−	0.534106i	0.963682	−	0.267053i	$-0.0860498\pi$
$858$	−1029.69			−1.20010
$859$	−606.085			−0.705570			−0.352785	−	0.935704i	$-0.614765\pi$
$859$	−606.085			−0.705570			−0.352785	+	0.935704i	$0.614765\pi$
$860$	1640.77			1.90787
$861$		−	94.8828i		−	0.110201i
$862$	−1784.50			−2.07018
$863$		−	32.4998i		−	0.0376591i	−0.999823	−	0.0188296i	$-0.994006\pi$
$863$		−	32.4998i		−	0.0376591i	0.999823	−	0.0188296i	$-0.00599399\pi$
$864$	937.101			1.08461
$865$	−299.968			−0.346784
$866$	1806.42			2.08593
$867$			2004.26i			2.31172i
$868$	717.667			0.826805
$869$			182.646i			0.210180i
$870$			3345.04i			3.84488i
$871$	2135.51			2.45180
$872$	−4370.23			−5.01173
$873$	−2018.62			−2.31228
$874$	−1559.84			−1.78471
$875$	965.211			1.10310
$876$		−	3366.33i		−	3.84284i
$877$		−	1364.78i		−	1.55620i	−0.628142	−	0.778098i	$-0.716184\pi$
$877$		−	1364.78i		−	1.55620i	0.628142	−	0.778098i	$-0.283816\pi$
$878$			2201.11i			2.50696i
$879$			1094.65i			1.24533i
$880$		−	598.440i		−	0.680045i
$881$		−	98.8107i		−	0.112157i	−0.998426	−	0.0560787i	$-0.982140\pi$
$881$		−	98.8107i		−	0.112157i	0.998426	−	0.0560787i	$-0.0178598\pi$
$882$		−	77.2893i		−	0.0876296i
$883$	764.435			0.865725			0.432863	−	0.901460i	$-0.357503\pi$
$883$	764.435			0.865725			0.432863	+	0.901460i	$0.357503\pi$
$884$			4979.98i			5.63346i
$885$			1569.35i			1.77328i
$886$			381.142i			0.430183i
$887$	847.853			0.955865			0.477933	−	0.878396i	$-0.341386\pi$
$887$	847.853			0.955865			0.477933	+	0.878396i	$0.341386\pi$
$888$		−	4450.78i		−	5.01214i
$889$		−	315.444i		−	0.354831i
$890$		−	795.612i		−	0.893947i
$891$	173.992			0.195278
$892$			2412.09i			2.70413i
$893$	−174.034			−0.194887
$894$	630.709			0.705491
$895$			802.426i			0.896566i
$896$	983.159			1.09728
$897$	1466.08			1.63442
$898$			211.528i			0.235555i
$899$			505.163i			0.561916i
$900$	1188.31			1.32034
$901$		−	2064.27i		−	2.29109i
$902$	−36.8964			−0.0409051
$903$		−	1352.99i		−	1.49833i
$904$		−	14.3676i		−	0.0158934i
$905$		−	734.785i		−	0.811917i
$906$		−	1340.50i		−	1.47958i
$907$	524.738			0.578542			0.289271	−	0.957247i	$-0.406587\pi$
$907$	524.738			0.578542			0.289271	+	0.957247i	$0.406587\pi$
$908$	2378.45			2.61943
$909$		−	1204.11i		−	1.32466i
$910$			1871.64i			2.05675i
$911$		−	48.8177i		−	0.0535869i	−0.999641	−	0.0267934i	$-0.991470\pi$
$911$		−	48.8177i		−	0.0535869i	0.999641	−	0.0267934i	$-0.00852964\pi$
$912$		−	4894.92i		−	5.36724i
$913$			266.387i			0.291771i
$914$	−1.56353			−0.00171064
$915$			630.862i			0.689467i
$916$			3167.77i			3.45827i
$917$			248.994i			0.271531i
$918$			1154.70i			1.25784i
$919$	98.1588			0.106810			0.0534052	−	0.998573i	$-0.482993\pi$
$919$	98.1588			0.106810			0.0534052	+	0.998573i	$0.482993\pi$
$920$			1595.29i			1.73401i
$921$	−373.093			−0.405096
$922$	−1703.21			−1.84730
$923$		−	84.8738i		−	0.0919543i
$924$	−1093.39			−1.18332
$925$		−	430.993i		−	0.465939i
$926$	487.456			0.526410
$927$			1767.41i			1.90659i
$928$			4210.04i			4.53669i
$929$		−	1276.72i		−	1.37429i	−0.726520	−	0.687146i	$-0.758863\pi$
$929$		−	1276.72i		−	1.37429i	0.726520	−	0.687146i	$-0.241137\pi$
$930$	−650.508			−0.699471
$931$	−41.4167			−0.0444863
$932$	3895.84			4.18009
$933$			500.545i			0.536490i
$934$		−	13.7793i		−	0.0147531i
$935$	347.408			0.371559
$936$			4833.07i			5.16354i
$937$		−	1464.03i		−	1.56247i	−0.624237	−	0.781235i	$-0.714590\pi$
$937$		−	1464.03i		−	1.56247i	0.624237	−	0.781235i	$-0.285410\pi$
$938$	3160.35			3.36924
$939$			516.655i			0.550218i
$940$			293.558i			0.312296i
$941$	−997.237			−1.05976			−0.529881	−	0.848072i	$-0.677764\pi$
$941$	−997.237			−1.05976			−0.529881	+	0.848072i	$0.677764\pi$
$942$	−2976.03			−3.15927
$943$	52.5334			0.0557088
$944$			4192.45i			4.44116i
$945$			311.385i			0.329508i
$946$	−526.128			−0.556161
$947$	−80.7804			−0.0853014			−0.0426507	−	0.999090i	$-0.513580\pi$
$947$	−80.7804			−0.0853014			−0.0426507	+	0.999090i	$0.513580\pi$
$948$	2519.98			2.65821
$949$	1325.82			1.39707
$950$		−	887.461i		−	0.934169i
$951$		−	1960.50i		−	2.06151i
$952$			4468.48i			4.69378i
$953$	243.059			0.255046			0.127523	−	0.991836i	$-0.459297\pi$
$953$	243.059			0.255046			0.127523	+	0.991836i	$0.459297\pi$
$954$		−	3304.17i		−	3.46349i
$955$		−	416.337i		−	0.435955i
$956$	−1654.05			−1.73018
$957$		−	769.631i		−	0.804212i
$958$			2786.24i			2.90840i
$959$		−	507.922i		−	0.529637i
$960$	−2170.83			−2.26128
$961$	862.761			0.897774
$962$	2891.12			3.00532
$963$			242.922i			0.252255i
$964$			3591.54i			3.72567i
$965$		−	152.848i		−	0.158391i
$966$	2169.65			2.24601
$967$		−	1284.13i		−	1.32795i	−0.747754	−	0.663976i	$-0.768868\pi$
$967$		−	1284.13i		−	1.32795i	0.747754	−	0.663976i	$-0.231132\pi$
$968$		−	2547.23i		−	2.63144i
$969$	2841.61			2.93252
$970$	2542.94			2.62159
$971$			818.345i			0.842786i	0.906878	+	0.421393i	$0.138459\pi$
$971$			818.345i			0.842786i	−0.906878	+	0.421393i	$0.861541\pi$
$972$		−	3437.98i		−	3.53702i
$973$			236.723i			0.243292i
$974$	−3139.29			−3.22310
$975$			834.115i			0.855502i
$976$			1685.32i			1.72676i
$977$		−	571.134i		−	0.584580i	−0.956330	−	0.292290i	$-0.905583\pi$
$977$		−	571.134i		−	0.584580i	0.956330	−	0.292290i	$-0.0944172\pi$
$978$			565.254i			0.577969i
$979$			183.055i			0.186982i
$980$			69.8613i			0.0712870i
$981$		−	2168.95i		−	2.21096i
$982$	547.964			0.558008
$983$			798.393i			0.812201i	0.913829	+	0.406100i	$0.133112\pi$
$983$			798.393i			0.812201i	−0.913829	+	0.406100i	$0.866888\pi$
$984$			308.653i			0.313672i
$985$	69.9573			0.0710226
$986$	−5187.62			−5.26128
$987$	242.071			0.245259
$988$	4271.50			4.32338
$989$	749.105			0.757437
$990$	556.078			0.561695
$991$	−516.872			−0.521566			−0.260783	−	0.965397i	$-0.583981\pi$
$991$	−516.872			−0.521566			−0.260783	+	0.965397i	$0.583981\pi$
$992$	−818.725			−0.825328
$993$	−1980.48			−1.99444
$994$		−	125.605i		−	0.126363i
$995$			327.886i			0.329534i
$996$	3675.36			3.69012
$997$			1589.94i			1.59473i	0.603500	+	0.797363i	$0.293772\pi$
$997$			1589.94i			1.59473i	−0.603500	+	0.797363i	$0.706228\pi$
$998$			1334.91i			1.33758i
$999$	480.996			0.481478

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.3.b.b.546.4	✓	88
547.546	odd	2	inner	547.3.b.b.546.85	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.3.b.b.546.4	✓	88	1.1	even	1	trivial
547.3.b.b.546.85	yes	88	547.546	odd	2	inner

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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	547.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.76304i q^{2} -4.52828i q^{3} -10.1605 q^{4} +3.85159i q^{5} -17.0401 q^{6} -7.12637i q^{7} +23.1820i q^{8} -11.5053 q^{9} +O(q^{10})\)	\(q-3.76304i q^{2} -4.52828i q^{3} -10.1605 q^{4} +3.85159i q^{5} -17.0401 q^{6} -7.12637i q^{7} +23.1820i q^{8} -11.5053 q^{9} +14.4937 q^{10} -3.33472 q^{11} +46.0093i q^{12} -18.1207 q^{13} -26.8168 q^{14} +17.4411 q^{15} +46.5930 q^{16} +27.0483i q^{17} +43.2948i q^{18} +23.2002 q^{19} -39.1339i q^{20} -32.2702 q^{21} +12.5487i q^{22} -17.8669i q^{23} +104.975 q^{24} +10.1653 q^{25} +68.1889i q^{26} +11.3446i q^{27} +72.4072i q^{28} -50.9671 q^{29} -65.6314i q^{30} -9.91155i q^{31} -82.6032i q^{32} +15.1005i q^{33} +101.784 q^{34} +27.4479 q^{35} +116.899 q^{36} -42.3987i q^{37} -87.3033i q^{38} +82.0555i q^{39} -89.2876 q^{40} +2.94026i q^{41} +121.434i q^{42} +41.9270i q^{43} +33.8823 q^{44} -44.3136i q^{45} -67.2338 q^{46} -7.50138 q^{47} -210.986i q^{48} -1.78519 q^{49} -38.2522i q^{50} +122.482 q^{51} +184.114 q^{52} -76.3180 q^{53} +42.6902 q^{54} -12.8440i q^{55} +165.204 q^{56} -105.057i q^{57} +191.791i q^{58} +89.9803i q^{59} -177.209 q^{60} +36.1711i q^{61} -37.2975 q^{62} +81.9909i q^{63} -124.467 q^{64} -69.7935i q^{65} +56.8239 q^{66} -117.849 q^{67} -274.823i q^{68} -80.9062 q^{69} -103.287i q^{70} +4.68380i q^{71} -266.716i q^{72} -73.1662 q^{73} -159.548 q^{74} -46.0311i q^{75} -235.725 q^{76} +23.7645i q^{77} +308.778 q^{78} -54.7711i q^{79} +179.457i q^{80} -52.1760 q^{81} +11.0643 q^{82} -79.8829i q^{83} +327.880 q^{84} -104.179 q^{85} +157.773 q^{86} +230.793i q^{87} -77.3056i q^{88} -54.8937i q^{89} -166.754 q^{90} +129.135i q^{91} +181.536i q^{92} -44.8822 q^{93} +28.2280i q^{94} +89.3578i q^{95} -374.050 q^{96} +175.452 q^{97} +6.71772i q^{98} +38.3669 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 192 q^{4} - 306 q^{9}+O(q^{10}) \) 88 * q - 192 * q^4 - 306 * q^9	\( 88 q - 192 q^{4} - 306 q^{9} - 4 q^{10} - 32 q^{11} + 26 q^{13} - 26 q^{14} + 22 q^{15} + 236 q^{16} - 12 q^{19} - 16 q^{21} - 2 q^{24} - 544 q^{25} - 96 q^{29} + 26 q^{34} + 10 q^{35} + 364 q^{36} + 44 q^{40} + 124 q^{44} - 288 q^{46} - 310 q^{47} - 694 q^{49} + 86 q^{51} - 316 q^{52} + 24 q^{53} - 266 q^{54} + 158 q^{56} - 80 q^{60} + 40 q^{62} - 652 q^{64} + 528 q^{66} + 28 q^{67} + 16 q^{69} + 94 q^{73} - 614 q^{74} - 28 q^{76} - 98 q^{78} + 928 q^{81} - 772 q^{82} + 358 q^{84} + 74 q^{85} - 410 q^{86} - 214 q^{90} + 656 q^{93} - 724 q^{96} + 346 q^{97} + 50 q^{99}+O(q^{100}) \) 88 * q - 192 * q^4 - 306 * q^9 - 4 * q^10 - 32 * q^11 + 26 * q^13 - 26 * q^14 + 22 * q^15 + 236 * q^16 - 12 * q^19 - 16 * q^21 - 2 * q^24 - 544 * q^25 - 96 * q^29 + 26 * q^34 + 10 * q^35 + 364 * q^36 + 44 * q^40 + 124 * q^44 - 288 * q^46 - 310 * q^47 - 694 * q^49 + 86 * q^51 - 316 * q^52 + 24 * q^53 - 266 * q^54 + 158 * q^56 - 80 * q^60 + 40 * q^62 - 652 * q^64 + 528 * q^66 + 28 * q^67 + 16 * q^69 + 94 * q^73 - 614 * q^74 - 28 * q^76 - 98 * q^78 + 928 * q^81 - 772 * q^82 + 358 * q^84 + 74 * q^85 - 410 * q^86 - 214 * q^90 + 656 * q^93 - 724 * q^96 + 346 * q^97 + 50 * q^99

Introduction

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