LMFDB - Embedded newform 1050.3.f.b.601.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(601,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("1050.601");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.f (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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			601.6
Root			$-1.01575 - 1.40294i$ of defining polynomial
Character	$\chi$	$=$	1050.601
Dual form			1050.3.f.b.601.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(6.70141 - 2.02265i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(6.70141 - 2.02265i) q^{7} +2.82843 q^{8} -3.00000 q^{9} -5.00806 q^{11} -3.46410i q^{12} +9.06929i q^{13} +(9.47723 - 2.86045i) q^{14} +4.00000 q^{16} -19.7410i q^{17} -4.24264 q^{18} -25.6863i q^{19} +(-3.50333 - 11.6072i) q^{21} -7.08246 q^{22} +40.9686 q^{23} -4.89898i q^{24} +12.8259i q^{26} +5.19615i q^{27} +(13.4028 - 4.04529i) q^{28} -22.3071 q^{29} -15.9015i q^{31} +5.65685 q^{32} +8.67421i q^{33} -27.9179i q^{34} -6.00000 q^{36} +44.7506 q^{37} -36.3259i q^{38} +15.7085 q^{39} +27.0829i q^{41} +(-4.95445 - 16.4150i) q^{42} +30.6690 q^{43} -10.0161 q^{44} +57.9383 q^{46} -58.1430i q^{47} -6.92820i q^{48} +(40.8178 - 27.1092i) q^{49} -34.1924 q^{51} +18.1386i q^{52} -65.6199 q^{53} +7.34847i q^{54} +(18.9545 - 5.72091i) q^{56} -44.4900 q^{57} -31.5469 q^{58} -32.5746i q^{59} +83.5349i q^{61} -22.4881i q^{62} +(-20.1042 + 6.06794i) q^{63} +8.00000 q^{64} +12.2672i q^{66} -72.0585 q^{67} -39.4819i q^{68} -70.9597i q^{69} -24.8675 q^{71} -8.48528 q^{72} -67.8725i q^{73} +63.2870 q^{74} -51.3726i q^{76} +(-33.5610 + 10.1295i) q^{77} +22.2151 q^{78} +30.4452 q^{79} +9.00000 q^{81} +38.3009i q^{82} -72.4623i q^{83} +(-7.00665 - 23.2144i) q^{84} +43.3725 q^{86} +38.6370i q^{87} -14.1649 q^{88} -113.756i q^{89} +(18.3440 + 60.7770i) q^{91} +81.9372 q^{92} -27.5422 q^{93} -82.2267i q^{94} -9.79796i q^{96} -103.804i q^{97} +(57.7251 - 38.3381i) q^{98} +15.0242 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 8 * q + 16 * q^4 - 24 * q^9	$ 8 q + 16 q^{4} - 24 q^{9} - 16 q^{11} + 32 q^{14} + 32 q^{16} - 96 q^{22} - 144 q^{29} - 48 q^{36} + 48 q^{37} - 48 q^{39} + 48 q^{42} + 64 q^{43} - 32 q^{44} + 128 q^{46} - 24 q^{49} - 128 q^{53} + 64 q^{56} - 144 q^{57} - 224 q^{58} + 64 q^{64} + 192 q^{67} + 176 q^{71} - 160 q^{74} - 192 q^{77} + 96 q^{78} - 288 q^{79} + 72 q^{81} - 64 q^{86} - 192 q^{88} + 64 q^{91} - 336 q^{93} + 48 q^{99}+O(q^{100}) $ 8 * q + 16 * q^4 - 24 * q^9 - 16 * q^11 + 32 * q^14 + 32 * q^16 - 96 * q^22 - 144 * q^29 - 48 * q^36 + 48 * q^37 - 48 * q^39 + 48 * q^42 + 64 * q^43 - 32 * q^44 + 128 * q^46 - 24 * q^49 - 128 * q^53 + 64 * q^56 - 144 * q^57 - 224 * q^58 + 64 * q^64 + 192 * q^67 + 176 * q^71 - 160 * q^74 - 192 * q^77 + 96 * q^78 - 288 * q^79 + 72 * q^81 - 64 * q^86 - 192 * q^88 + 64 * q^91 - 336 * q^93 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	6.70141	−	2.02265i	0.957344	−	0.288949i
$7$	6.70141	−	2.02265i	0.957344	−	0.288949i
$8$	2.82843			0.353553
$9$	−3.00000			−0.333333
$10$		0			0
$11$	−5.00806			−0.455278			−0.227639	−	0.973746i	$-0.573101\pi$
$11$	−5.00806			−0.455278			−0.227639	+	0.973746i	$0.573101\pi$
$12$		−	3.46410i		−	0.288675i
$13$			9.06929i			0.697638i	0.937190	+	0.348819i	$0.113417\pi$
$13$			9.06929i			0.697638i	−0.937190	+	0.348819i	$0.886583\pi$
$14$	9.47723	−	2.86045i	0.676945	−	0.204318i
$15$		0			0
$16$	4.00000			0.250000
$17$		−	19.7410i		−	1.16123i	−0.814177	−	0.580617i	$-0.802812\pi$
$17$		−	19.7410i		−	1.16123i	0.814177	−	0.580617i	$-0.197188\pi$
$18$	−4.24264			−0.235702
$19$		−	25.6863i		−	1.35191i	−0.736942	−	0.675956i	$-0.763731\pi$
$19$		−	25.6863i		−	1.35191i	0.736942	−	0.675956i	$-0.236269\pi$
$20$		0			0
$21$	−3.50333	−	11.6072i	−0.166825	−	0.552723i
$22$	−7.08246			−0.321930
$23$	40.9686			1.78124			0.890621	−	0.454746i	$-0.150270\pi$
$23$	40.9686			1.78124			0.890621	+	0.454746i	$0.150270\pi$
$24$		−	4.89898i		−	0.204124i
$25$		0			0
$26$			12.8259i			0.493304i
$27$			5.19615i			0.192450i
$28$	13.4028	−	4.04529i	0.478672	−	0.144475i
$29$	−22.3071			−0.769209			−0.384604	−	0.923081i	$-0.625662\pi$
$29$	−22.3071			−0.769209			−0.384604	+	0.923081i	$0.625662\pi$
$30$		0			0
$31$		−	15.9015i		−	0.512952i	−0.966551	−	0.256476i	$-0.917439\pi$
$31$		−	15.9015i		−	0.512952i	0.966551	−	0.256476i	$-0.0825614\pi$
$32$	5.65685			0.176777
$33$			8.67421i			0.262855i
$34$		−	27.9179i		−	0.821116i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	44.7506			1.20948			0.604738	−	0.796424i	$-0.293278\pi$
$37$	44.7506			1.20948			0.604738	+	0.796424i	$0.293278\pi$
$38$		−	36.3259i		−	0.955946i
$39$	15.7085			0.402781
$40$		0			0
$41$			27.0829i			0.660557i	0.943883	+	0.330279i	$0.107143\pi$
$41$			27.0829i			0.660557i	−0.943883	+	0.330279i	$0.892857\pi$
$42$	−4.95445	−	16.4150i	−0.117963	−	0.390834i
$43$	30.6690			0.713233			0.356616	−	0.934251i	$-0.383930\pi$
$43$	30.6690			0.713233			0.356616	+	0.934251i	$0.383930\pi$
$44$	−10.0161			−0.227639
$45$		0			0
$46$	57.9383			1.25953
$47$		−	58.1430i		−	1.23709i	−0.785751	−	0.618543i	$-0.787723\pi$
$47$		−	58.1430i		−	1.23709i	0.785751	−	0.618543i	$-0.212277\pi$
$48$		−	6.92820i		−	0.144338i
$49$	40.8178	−	27.1092i	0.833016	−	0.553248i
$50$		0			0
$51$	−34.1924			−0.670438
$52$			18.1386i			0.348819i
$53$	−65.6199			−1.23811			−0.619055	−	0.785347i	$-0.712484\pi$
$53$	−65.6199			−1.23811			−0.619055	+	0.785347i	$0.712484\pi$
$54$			7.34847i			0.136083i
$55$		0			0
$56$	18.9545	−	5.72091i	0.338472	−	0.102159i
$57$	−44.4900			−0.780526
$58$	−31.5469			−0.543913
$59$		−	32.5746i		−	0.552112i	−0.961142	−	0.276056i	$-0.910973\pi$
$59$		−	32.5746i		−	0.552112i	0.961142	−	0.276056i	$-0.0890275\pi$
$60$		0			0
$61$			83.5349i			1.36943i	0.728813	+	0.684713i	$0.240072\pi$
$61$			83.5349i			1.36943i	−0.728813	+	0.684713i	$0.759928\pi$
$62$		−	22.4881i		−	0.362712i
$63$	−20.1042	+	6.06794i	−0.319115	+	0.0963165i
$64$	8.00000			0.125000
$65$		0			0
$66$			12.2672i			0.185866i
$67$	−72.0585			−1.07550			−0.537750	−	0.843104i	$-0.680726\pi$
$67$	−72.0585			−1.07550			−0.537750	+	0.843104i	$0.680726\pi$
$68$		−	39.4819i		−	0.580617i
$69$		−	70.9597i		−	1.02840i
$70$		0			0
$71$	−24.8675			−0.350246			−0.175123	−	0.984547i	$-0.556032\pi$
$71$	−24.8675			−0.350246			−0.175123	+	0.984547i	$0.556032\pi$
$72$	−8.48528			−0.117851
$73$		−	67.8725i		−	0.929760i	−0.885374	−	0.464880i	$-0.846098\pi$
$73$		−	67.8725i		−	0.929760i	0.885374	−	0.464880i	$-0.153902\pi$
$74$	63.2870			0.855229
$75$		0			0
$76$		−	51.3726i		−	0.675956i
$77$	−33.5610	+	10.1295i	−0.435858	+	0.131552i
$78$	22.2151			0.284809
$79$	30.4452			0.385383			0.192691	−	0.981259i	$-0.438278\pi$
$79$	30.4452			0.385383			0.192691	+	0.981259i	$0.438278\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$			38.3009i			0.467085i
$83$		−	72.4623i		−	0.873040i	−0.899695	−	0.436520i	$-0.856211\pi$
$83$		−	72.4623i		−	0.873040i	0.899695	−	0.436520i	$-0.143789\pi$
$84$	−7.00665	−	23.2144i	−0.0834125	−	0.276362i
$85$		0			0
$86$	43.3725			0.504332
$87$			38.6370i			0.444103i
$88$	−14.1649			−0.160965
$89$		−	113.756i		−	1.27815i	−0.769143	−	0.639076i	$-0.779317\pi$
$89$		−	113.756i		−	1.27815i	0.769143	−	0.639076i	$-0.220683\pi$
$90$		0			0
$91$	18.3440	+	60.7770i	0.201582	+	0.667880i
$92$	81.9372			0.890621
$93$	−27.5422			−0.296153
$94$		−	82.2267i		−	0.874752i
$95$		0			0
$96$		−	9.79796i		−	0.102062i
$97$		−	103.804i		−	1.07014i	−0.844806	−	0.535072i	$-0.820284\pi$
$97$		−	103.804i		−	1.07014i	0.844806	−	0.535072i	$-0.179716\pi$
$98$	57.7251	−	38.3381i	0.589032	−	0.391206i
$99$	15.0242			0.151759
$100$		0			0
$101$			155.379i			1.53841i	0.639003	+	0.769204i	$0.279347\pi$
$101$			155.379i			1.53841i	−0.639003	+	0.769204i	$0.720653\pi$
$102$	−48.3553			−0.474071
$103$			65.9471i			0.640264i	0.947373	+	0.320132i	$0.103727\pi$
$103$			65.9471i			0.640264i	−0.947373	+	0.320132i	$0.896273\pi$
$104$			25.6518i			0.246652i
$105$		0			0
$106$	−92.8005			−0.875476
$107$	136.269			1.27354			0.636771	−	0.771053i	$-0.280270\pi$
$107$	136.269			1.27354			0.636771	+	0.771053i	$0.280270\pi$
$108$			10.3923i			0.0962250i
$109$	166.003			1.52296			0.761482	−	0.648186i	$-0.224472\pi$
$109$	166.003			1.52296			0.761482	+	0.648186i	$0.224472\pi$
$110$		0			0
$111$		−	77.5104i		−	0.698292i
$112$	26.8056	−	8.09058i	0.239336	−	0.0722374i
$113$	25.5037			0.225696			0.112848	−	0.993612i	$-0.464003\pi$
$113$	25.5037			0.225696			0.112848	+	0.993612i	$0.464003\pi$
$114$	−62.9184			−0.551915
$115$		0			0
$116$	−44.6141			−0.384604
$117$		−	27.2079i		−	0.232546i
$118$		−	46.0674i		−	0.390402i
$119$	−39.9290	−	132.292i	−0.335538	−	1.11170i
$120$		0			0
$121$	−95.9194			−0.792722
$122$			118.136i			0.968330i
$123$	46.9089			0.381373
$124$		−	31.8030i		−	0.256476i
$125$		0			0
$126$	−28.4317	+	8.58136i	−0.225648	+	0.0681060i
$127$	230.306			1.81344			0.906718	−	0.421738i	$-0.138580\pi$
$127$	230.306			1.81344			0.906718	+	0.421738i	$0.138580\pi$
$128$	11.3137			0.0883883
$129$		−	53.1203i		−	0.411785i
$130$		0			0
$131$			40.9127i			0.312311i	0.987733	+	0.156155i	$0.0499101\pi$
$131$			40.9127i			0.312311i	−0.987733	+	0.156155i	$0.950090\pi$
$132$			17.3484i			0.131427i
$133$	−51.9543	−	172.135i	−0.390634	−	1.29424i
$134$	−101.906			−0.760493
$135$		0			0
$136$		−	55.8359i		−	0.410558i
$137$	−158.300			−1.15547			−0.577737	−	0.816223i	$-0.696064\pi$
$137$	−158.300			−1.15547			−0.577737	+	0.816223i	$0.696064\pi$
$138$		−	100.352i		−	0.727189i
$139$			141.584i			1.01859i	0.860592	+	0.509296i	$0.170094\pi$
$139$			141.584i			1.01859i	−0.860592	+	0.509296i	$0.829906\pi$
$140$		0			0
$141$	−100.707			−0.714232
$142$	−35.1679			−0.247661
$143$		−	45.4195i		−	0.317619i
$144$	−12.0000			−0.0833333
$145$		0			0
$146$		−	95.9861i		−	0.657439i
$147$	−46.9545	−	70.6985i	−0.319418	−	0.480942i
$148$	89.5013			0.604738
$149$	−121.456			−0.815139			−0.407569	−	0.913174i	$-0.633624\pi$
$149$	−121.456			−0.815139			−0.407569	+	0.913174i	$0.633624\pi$
$150$		0			0
$151$	−219.093			−1.45094			−0.725472	−	0.688251i	$-0.758379\pi$
$151$	−219.093			−1.45094			−0.725472	+	0.688251i	$0.758379\pi$
$152$		−	72.6519i		−	0.477973i
$153$			59.2229i			0.387078i
$154$	−47.4625	+	14.3253i	−0.308198	+	0.0930215i
$155$		0			0
$156$	31.4169			0.201391
$157$			57.2815i			0.364850i	0.983220	+	0.182425i	$0.0583947\pi$
$157$			57.2815i			0.364850i	−0.983220	+	0.182425i	$0.941605\pi$
$158$	43.0560			0.272507
$159$			113.657i			0.714824i
$160$		0			0
$161$	274.547	−	82.8649i	1.70526	−	0.514689i
$162$	12.7279			0.0785674
$163$	8.52297			0.0522882			0.0261441	−	0.999658i	$-0.491677\pi$
$163$	8.52297			0.0522882			0.0261441	+	0.999658i	$0.491677\pi$
$164$			54.1657i			0.330279i
$165$		0			0
$166$		−	102.477i		−	0.617333i
$167$			258.148i			1.54580i	0.634529	+	0.772899i	$0.281194\pi$
$167$			258.148i			1.54580i	−0.634529	+	0.772899i	$0.718806\pi$
$168$	−9.90890	−	32.8301i	−0.0589816	−	0.195417i
$169$	86.7480			0.513301
$170$		0			0
$171$			77.0589i			0.450637i
$172$	61.3380			0.356616
$173$			327.250i			1.89162i	0.324725	+	0.945808i	$0.394728\pi$
$173$			327.250i			1.89162i	−0.324725	+	0.945808i	$0.605272\pi$
$174$			54.6409i			0.314028i
$175$		0			0
$176$	−20.0322			−0.113819
$177$	−56.4208			−0.318762
$178$		−	160.875i		−	0.903791i
$179$	−167.569			−0.936141			−0.468071	−	0.883691i	$-0.655051\pi$
$179$	−167.569			−0.936141			−0.468071	+	0.883691i	$0.655051\pi$
$180$		0			0
$181$			147.957i			0.817442i	0.912659	+	0.408721i	$0.134025\pi$
$181$			147.957i			0.817442i	−0.912659	+	0.408721i	$0.865975\pi$
$182$	25.9423	+	85.9517i	0.142540	+	0.472262i
$183$	144.687			0.790638
$184$	115.877			0.629764
$185$		0			0
$186$	−38.9506			−0.209412
$187$			98.8638i			0.528684i
$188$		−	116.286i		−	0.618543i
$189$	10.5100	+	34.8216i	0.0556083	+	0.184241i
$190$		0			0
$191$	49.4939			0.259130			0.129565	−	0.991571i	$-0.458642\pi$
$191$	49.4939			0.259130			0.129565	+	0.991571i	$0.458642\pi$
$192$		−	13.8564i		−	0.0721688i
$193$	−172.674			−0.894686			−0.447343	−	0.894362i	$-0.647630\pi$
$193$	−172.674			−0.894686			−0.447343	+	0.894362i	$0.647630\pi$
$194$		−	146.801i		−	0.756707i
$195$		0			0
$196$	81.6356	−	54.2183i	0.416508	−	0.276624i
$197$	−75.6444			−0.383982			−0.191991	−	0.981397i	$-0.561494\pi$
$197$	−75.6444			−0.383982			−0.191991	+	0.981397i	$0.561494\pi$
$198$	21.2474			0.107310
$199$			147.620i			0.741808i	0.928671	+	0.370904i	$0.120952\pi$
$199$			147.620i			0.741808i	−0.928671	+	0.370904i	$0.879048\pi$
$200$		0			0
$201$			124.809i			0.620940i
$202$			219.739i			1.08782i
$203$	−149.489	+	45.1193i	−0.736398	+	0.222262i
$204$	−68.3847			−0.335219
$205$		0			0
$206$			93.2634i			0.452735i
$207$	−122.906			−0.593747
$208$			36.2772i			0.174409i
$209$			128.638i			0.615495i
$210$		0			0
$211$	156.882			0.743518			0.371759	−	0.928329i	$-0.378755\pi$
$211$	156.882			0.743518			0.371759	+	0.928329i	$0.378755\pi$
$212$	−131.240			−0.619055
$213$			43.0717i			0.202215i
$214$	192.713			0.900530
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	−32.1631	−	106.563i	−0.148217	−	0.491072i
$218$	234.764			1.07690
$219$	−117.559			−0.536797
$220$		0			0
$221$	179.037			0.810120
$222$		−	109.616i		−	0.493767i
$223$			60.4029i			0.270865i	0.990787	+	0.135433i	$0.0432424\pi$
$223$			60.4029i			0.270865i	−0.990787	+	0.135433i	$0.956758\pi$
$224$	37.9089	−	11.4418i	0.169236	−	0.0510795i
$225$		0			0
$226$	36.0677			0.159592
$227$		−	313.611i		−	1.38155i	−0.723071	−	0.690773i	$-0.757270\pi$
$227$		−	313.611i		−	1.38155i	0.723071	−	0.690773i	$-0.242730\pi$
$228$	−88.9800			−0.390263
$229$			110.368i			0.481957i	0.970530	+	0.240979i	$0.0774684\pi$
$229$			110.368i			0.481957i	−0.970530	+	0.240979i	$0.922532\pi$
$230$		0			0
$231$	17.5449	+	58.1294i	0.0759517	+	0.251643i
$232$	−63.0939			−0.271956
$233$	−38.4067			−0.164835			−0.0824177	−	0.996598i	$-0.526264\pi$
$233$	−38.4067			−0.164835			−0.0824177	+	0.996598i	$0.526264\pi$
$234$		−	38.4777i		−	0.164435i
$235$		0			0
$236$		−	65.1492i		−	0.276056i
$237$		−	52.7327i		−	0.222501i
$238$	−56.4681	−	187.090i	−0.237261	−	0.786091i
$239$	−125.129			−0.523552			−0.261776	−	0.965129i	$-0.584308\pi$
$239$	−125.129			−0.523552			−0.261776	+	0.965129i	$0.584308\pi$
$240$		0			0
$241$		−	154.625i		−	0.641598i	−0.947147	−	0.320799i	$-0.896049\pi$
$241$		−	154.625i		−	0.641598i	0.947147	−	0.320799i	$-0.103951\pi$
$242$	−135.650			−0.560539
$243$		−	15.5885i		−	0.0641500i
$244$			167.070i			0.684713i
$245$		0			0
$246$	66.3392			0.269671
$247$	232.957			0.943144
$248$		−	44.9763i		−	0.181356i
$249$	−125.508			−0.504050
$250$		0			0
$251$		−	152.655i		−	0.608185i	−0.952642	−	0.304093i	$-0.901647\pi$
$251$		−	152.655i		−	0.608185i	0.952642	−	0.304093i	$-0.0983532\pi$
$252$	−40.2085	+	12.1359i	−0.159557	+	0.0481582i
$253$	−205.173			−0.810960
$254$	325.702			1.28229
$255$		0			0
$256$	16.0000			0.0625000
$257$			20.1517i			0.0784113i	0.999231	+	0.0392057i	$0.0124827\pi$
$257$			20.1517i			0.0784113i	−0.999231	+	0.0392057i	$0.987517\pi$
$258$		−	75.1234i		−	0.291176i
$259$	299.892	−	90.5147i	1.15789	−	0.349478i
$260$		0			0
$261$	66.9212			0.256403
$262$			57.8593i			0.220837i
$263$	320.699			1.21939			0.609693	−	0.792637i	$-0.291293\pi$
$263$	320.699			1.21939			0.609693	+	0.792637i	$0.291293\pi$
$264$			24.5344i			0.0929332i
$265$		0			0
$266$	−73.4745	−	243.435i	−0.276220	−	0.915169i
$267$	−197.030			−0.737942
$268$	−144.117			−0.537750
$269$			39.2134i			0.145775i	0.997340	+	0.0728874i	$0.0232214\pi$
$269$			39.2134i			0.145775i	−0.997340	+	0.0728874i	$0.976779\pi$
$270$		0			0
$271$			299.071i			1.10358i	0.833982	+	0.551792i	$0.186056\pi$
$271$			299.071i			1.10358i	−0.833982	+	0.551792i	$0.813944\pi$
$272$		−	78.9639i		−	0.290308i
$273$	105.269	−	31.7727i	0.385600	−	0.116383i
$274$	−223.870			−0.817044
$275$		0			0
$276$		−	141.919i		−	0.514200i
$277$	438.966			1.58472			0.792358	−	0.610056i	$-0.208853\pi$
$277$	438.966			1.58472			0.792358	+	0.610056i	$0.208853\pi$
$278$			200.230i			0.720253i
$279$			47.7045i			0.170984i
$280$		0			0
$281$	−199.479			−0.709889			−0.354944	−	0.934887i	$-0.615500\pi$
$281$	−199.479			−0.709889			−0.354944	+	0.934887i	$0.615500\pi$
$282$	−142.421			−0.505038
$283$			541.179i			1.91229i	0.292889	+	0.956147i	$0.405384\pi$
$283$			541.179i			1.91229i	−0.292889	+	0.956147i	$0.594616\pi$
$284$	−49.7349			−0.175123
$285$		0			0
$286$		−	64.2329i		−	0.224591i
$287$	54.7790	+	181.493i	0.190868	+	0.632381i
$288$	−16.9706			−0.0589256
$289$	−100.706			−0.348462
$290$		0			0
$291$	−179.794			−0.617848
$292$		−	135.745i		−	0.464880i
$293$			378.757i			1.29269i	0.763047	+	0.646343i	$0.223702\pi$
$293$			378.757i			1.29269i	−0.763047	+	0.646343i	$0.776298\pi$
$294$	−66.4036	−	99.9828i	−0.225863	−	0.340078i
$295$		0			0
$296$	126.574			0.427615
$297$		−	26.0226i		−	0.0876183i
$298$	−171.764			−0.576390
$299$			371.556i			1.24266i
$300$		0			0
$301$	205.526	−	62.0326i	0.682810	−	0.206088i
$302$	−309.844			−1.02597
$303$	269.125			0.888200
$304$		−	102.745i		−	0.337978i
$305$		0			0
$306$			83.7538i			0.273705i
$307$			140.210i			0.456710i	0.973578	+	0.228355i	$0.0733346\pi$
$307$			140.210i			0.456710i	−0.973578	+	0.228355i	$0.926665\pi$
$308$	−67.1221	+	20.2591i	−0.217929	+	0.0657761i
$309$	114.224			0.369656
$310$		0			0
$311$			249.886i			0.803491i	0.915751	+	0.401745i	$0.131596\pi$
$311$			249.886i			0.803491i	−0.915751	+	0.401745i	$0.868404\pi$
$312$	44.4303			0.142405
$313$			517.894i			1.65461i	0.561750	+	0.827307i	$0.310128\pi$
$313$			517.894i			1.65461i	−0.561750	+	0.827307i	$0.689872\pi$
$314$			81.0082i			0.257988i
$315$		0			0
$316$	60.8904			0.192691
$317$	180.043			0.567959			0.283980	−	0.958830i	$-0.408345\pi$
$317$	180.043			0.567959			0.283980	+	0.958830i	$0.408345\pi$
$318$			160.735i			0.505457i
$319$	111.715			0.350204
$320$		0			0
$321$		−	236.025i		−	0.735280i
$322$	388.268	−	117.189i	1.20580	−	0.363940i
$323$	−507.073			−1.56988
$324$	18.0000			0.0555556
$325$		0			0
$326$	12.0533			0.0369733
$327$		−	287.526i		−	0.879283i
$328$			76.6019i			0.233542i
$329$	−117.603	−	389.640i	−0.357455	−	1.18432i
$330$		0			0
$331$	81.0283			0.244799			0.122399	−	0.992481i	$-0.460941\pi$
$331$	81.0283			0.244799			0.122399	+	0.992481i	$0.460941\pi$
$332$		−	144.925i		−	0.436520i
$333$	−134.252			−0.403159
$334$			365.077i			1.09304i
$335$		0			0
$336$	−14.0133	−	46.4287i	−0.0417063	−	0.138181i
$337$	372.937			1.10664			0.553318	−	0.832970i	$-0.313361\pi$
$337$	372.937			1.10664			0.553318	+	0.832970i	$0.313361\pi$
$338$	122.680			0.362959
$339$		−	44.1737i		−	0.130306i
$340$		0			0
$341$			79.6356i			0.233536i
$342$			108.978i			0.318649i
$343$	218.705	−	264.230i	0.637623	−	0.770349i
$344$	86.7451			0.252166
$345$		0			0
$346$			462.801i			1.33758i
$347$	−415.231			−1.19663			−0.598316	−	0.801260i	$-0.704163\pi$
$347$	−415.231			−1.19663			−0.598316	+	0.801260i	$0.704163\pi$
$348$			77.2739i			0.222051i
$349$			536.207i			1.53641i	0.640203	+	0.768206i	$0.278850\pi$
$349$			536.207i			1.53641i	−0.640203	+	0.768206i	$0.721150\pi$
$350$		0			0
$351$	−47.1254			−0.134260
$352$	−28.3298			−0.0804825
$353$		−	416.230i		−	1.17912i	−0.807724	−	0.589560i	$-0.799301\pi$
$353$		−	416.230i		−	1.17912i	0.807724	−	0.589560i	$-0.200699\pi$
$354$	−79.7911			−0.225399
$355$		0			0
$356$		−	227.511i		−	0.639076i
$357$	−229.137	+	69.1590i	−0.641840	+	0.193723i
$358$	−236.979			−0.661952
$359$	−270.563			−0.753659			−0.376829	−	0.926283i	$-0.622986\pi$
$359$	−270.563			−0.753659			−0.376829	+	0.926283i	$0.622986\pi$
$360$		0			0
$361$	−298.787			−0.827664
$362$			209.243i			0.578019i
$363$			166.137i			0.457678i
$364$	36.6879	+	121.554i	0.100791	+	0.333940i
$365$		0			0
$366$	204.618			0.559066
$367$			605.024i			1.64857i	0.566178	+	0.824283i	$0.308422\pi$
$367$			605.024i			1.64857i	−0.566178	+	0.824283i	$0.691578\pi$
$368$	163.874			0.445311
$369$		−	81.2486i		−	0.220186i
$370$		0			0
$371$	−439.746	+	132.726i	−1.18530	+	0.357751i
$372$	−55.0844			−0.148076
$373$	21.5124			0.0576739			0.0288370	−	0.999584i	$-0.490820\pi$
$373$	21.5124			0.0576739			0.0288370	+	0.999584i	$0.490820\pi$
$374$			139.815i			0.373836i
$375$		0			0
$376$		−	164.453i		−	0.437376i
$377$		−	202.309i		−	0.536629i
$378$	14.8634	+	49.2451i	0.0393210	+	0.130278i
$379$	449.862			1.18697			0.593486	−	0.804844i	$-0.297751\pi$
$379$	449.862			1.18697			0.593486	+	0.804844i	$0.297751\pi$
$380$		0			0
$381$		−	398.902i		−	1.04699i
$382$	69.9949			0.183233
$383$			560.756i			1.46412i	0.681242	+	0.732058i	$0.261440\pi$
$383$			560.756i			1.46412i	−0.681242	+	0.732058i	$0.738560\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−244.199			−0.632639
$387$	−92.0071			−0.237744
$388$		−	207.608i		−	0.535072i
$389$	−582.222			−1.49671			−0.748357	−	0.663296i	$-0.769157\pi$
$389$	−582.222			−1.49671			−0.748357	+	0.663296i	$0.769157\pi$
$390$		0			0
$391$		−	808.759i		−	2.06844i
$392$	115.450	−	76.6763i	0.294516	−	0.195603i
$393$	70.8629			0.180313
$394$	−106.977			−0.271516
$395$		0			0
$396$	30.0483			0.0758796
$397$		−	726.563i		−	1.83013i	−0.403304	−	0.915066i	$-0.632138\pi$
$397$		−	726.563i		−	1.83013i	0.403304	−	0.915066i	$-0.367862\pi$
$398$			208.766i			0.524538i
$399$	−298.146	+	89.9875i	−0.747232	+	0.225533i
$400$		0			0
$401$	−32.7962			−0.0817860			−0.0408930	−	0.999164i	$-0.513020\pi$
$401$	−32.7962			−0.0817860			−0.0408930	+	0.999164i	$0.513020\pi$
$402$			176.507i			0.439071i
$403$	144.215			0.357855
$404$			310.758i			0.769204i
$405$		0			0
$406$	−211.409	+	63.8083i	−0.520712	+	0.157163i
$407$	−224.114			−0.550648
$408$	−96.7106			−0.237036
$409$		−	637.739i		−	1.55926i	−0.626238	−	0.779632i	$-0.715406\pi$
$409$		−	637.739i		−	1.55926i	0.626238	−	0.779632i	$-0.284594\pi$
$410$		0			0
$411$			274.184i			0.667114i
$412$			131.894i			0.320132i
$413$	−65.8869	−	218.296i	−0.159532	−	0.528561i
$414$	−173.815			−0.419843
$415$		0			0
$416$			51.3037i			0.123326i
$417$	245.231			0.588084
$418$			181.922i			0.435221i
$419$			344.535i			0.822280i	0.911572	+	0.411140i	$0.134869\pi$
$419$			344.535i			0.822280i	−0.911572	+	0.411140i	$0.865131\pi$
$420$		0			0
$421$	290.412			0.689814			0.344907	−	0.938637i	$-0.387910\pi$
$421$	290.412			0.689814			0.344907	+	0.938637i	$0.387910\pi$
$422$	221.865			0.525746
$423$			174.429i			0.412362i
$424$	−185.601			−0.437738
$425$		0			0
$426$			60.9126i			0.142987i
$427$	168.962	+	559.802i	0.395695	+	1.31101i
$428$	272.538			0.636771
$429$	−78.6689			−0.183377
$430$		0			0
$431$	−214.780			−0.498329			−0.249164	−	0.968461i	$-0.580156\pi$
$431$	−214.780			−0.498329			−0.249164	+	0.968461i	$0.580156\pi$
$432$			20.7846i			0.0481125i
$433$		−	425.041i		−	0.981619i	−0.871267	−	0.490809i	$-0.836701\pi$
$433$		−	425.041i		−	0.981619i	0.871267	−	0.490809i	$-0.163299\pi$
$434$	−45.4855	−	150.702i	−0.104805	−	0.347240i
$435$		0			0
$436$	332.006			0.761482
$437$		−	1052.33i		−	2.40808i
$438$	−166.253			−0.379573
$439$			204.200i			0.465149i	0.972579	+	0.232574i	$0.0747149\pi$
$439$			204.200i			0.465149i	−0.972579	+	0.232574i	$0.925285\pi$
$440$		0			0
$441$	−122.453	+	81.3275i	−0.277672	+	0.184416i
$442$	253.196			0.572841
$443$	−276.367			−0.623854			−0.311927	−	0.950106i	$-0.600974\pi$
$443$	−276.367			−0.623854			−0.311927	+	0.950106i	$0.600974\pi$
$444$		−	155.021i		−	0.349146i
$445$		0			0
$446$			85.4227i			0.191531i
$447$			210.367i			0.470620i
$448$	53.6113	−	16.1812i	0.119668	−	0.0361187i
$449$	195.290			0.434945			0.217472	−	0.976066i	$-0.430219\pi$
$449$	195.290			0.434945			0.217472	+	0.976066i	$0.430219\pi$
$450$		0			0
$451$		−	135.632i		−	0.300737i
$452$	51.0074			0.112848
$453$			379.480i			0.837703i
$454$		−	443.513i		−	0.976901i
$455$		0			0
$456$	−125.837			−0.275958
$457$	−10.3428			−0.0226319			−0.0113159	−	0.999936i	$-0.503602\pi$
$457$	−10.3428			−0.0226319			−0.0113159	+	0.999936i	$0.503602\pi$
$458$			156.084i			0.340795i
$459$	102.577			0.223479
$460$		0			0
$461$		−	527.572i		−	1.14441i	−0.820111	−	0.572204i	$-0.806088\pi$
$461$		−	527.572i		−	1.14441i	0.820111	−	0.572204i	$-0.193912\pi$
$462$	24.8122	+	82.2074i	0.0537060	+	0.177938i
$463$	−797.897			−1.72332			−0.861660	−	0.507486i	$-0.830575\pi$
$463$	−797.897			−1.72332			−0.861660	+	0.507486i	$0.830575\pi$
$464$	−89.2282			−0.192302
$465$		0			0
$466$	−54.3152			−0.116556
$467$			169.651i			0.363278i	0.983365	+	0.181639i	$0.0581403\pi$
$467$			169.651i			0.363278i	−0.983365	+	0.181639i	$0.941860\pi$
$468$		−	54.4157i		−	0.116273i
$469$	−482.894	+	145.749i	−1.02962	+	0.310765i
$470$		0			0
$471$	99.2144			0.210646
$472$		−	92.1348i		−	0.195201i
$473$	−153.592			−0.324719
$474$		−	74.5753i		−	0.157332i
$475$		0			0
$476$	−79.8580	−	264.585i	−0.167769	−	0.555850i
$477$	196.860			0.412704
$478$	−176.959			−0.370207
$479$			704.272i			1.47030i	0.677906	+	0.735148i	$0.262887\pi$
$479$			704.272i			1.47030i	−0.677906	+	0.735148i	$0.737113\pi$
$480$		0			0
$481$			405.857i			0.843777i
$482$		−	218.673i		−	0.453678i
$483$	−143.526	−	475.530i	−0.297156	−	0.984534i
$484$	−191.839			−0.396361
$485$		0			0
$486$		−	22.0454i		−	0.0453609i
$487$	66.7966			0.137159			0.0685797	−	0.997646i	$-0.478153\pi$
$487$	66.7966			0.137159			0.0685797	+	0.997646i	$0.478153\pi$
$488$			236.273i			0.484165i
$489$		−	14.7622i		−	0.0301886i
$490$		0			0
$491$	546.122			1.11227			0.556133	−	0.831094i	$-0.312285\pi$
$491$	546.122			1.11227			0.556133	+	0.831094i	$0.312285\pi$
$492$	93.8178			0.190687
$493$			440.363i			0.893231i
$494$	329.450			0.666904
$495$		0			0
$496$		−	63.6060i		−	0.128238i
$497$	−166.647	+	50.2981i	−0.335306	+	0.101203i
$498$	−177.496			−0.356417
$499$	714.060			1.43098			0.715491	−	0.698622i	$-0.246203\pi$
$499$	714.060			1.43098			0.715491	+	0.698622i	$0.246203\pi$
$500$		0			0
$501$	447.126			0.892467
$502$		−	215.886i		−	0.430052i
$503$		−	878.751i		−	1.74702i	−0.486807	−	0.873510i	$-0.661838\pi$
$503$		−	878.751i		−	1.74702i	0.486807	−	0.873510i	$-0.338162\pi$
$504$	−56.8634	+	17.1627i	−0.112824	+	0.0340530i
$505$		0			0
$506$	−290.158			−0.573435
$507$		−	150.252i		−	0.296355i
$508$	460.613			0.906718
$509$		−	510.558i		−	1.00306i	−0.865140	−	0.501530i	$-0.832771\pi$
$509$		−	510.558i		−	1.00306i	0.865140	−	0.501530i	$-0.167229\pi$
$510$		0			0
$511$	−137.282	−	454.841i	−0.268654	−	0.890100i
$512$	22.6274			0.0441942
$513$	133.470			0.260175
$514$			28.4988i			0.0554452i
$515$		0			0
$516$		−	106.241i		−	0.205893i
$517$			291.184i			0.563218i
$518$	424.112	−	128.007i	0.818749	−	0.247118i
$519$	566.813			1.09213
$520$		0			0
$521$			17.2889i			0.0331841i	0.999862	+	0.0165921i	$0.00528166\pi$
$521$			17.2889i			0.0331841i	−0.999862	+	0.0165921i	$0.994718\pi$
$522$	94.6408			0.181304
$523$			287.840i			0.550364i	0.961392	+	0.275182i	$0.0887381\pi$
$523$			287.840i			0.550364i	−0.961392	+	0.275182i	$0.911262\pi$
$524$			81.8254i			0.156155i
$525$		0			0
$526$	453.536			0.862237
$527$	−313.911			−0.595657
$528$			34.6968i			0.0657137i
$529$	1149.42			2.17282
$530$		0			0
$531$			97.7238i			0.184037i
$532$	−103.909	−	344.269i	−0.195317	−	0.647122i
$533$	−245.622			−0.460830
$534$	−278.643			−0.521804
$535$		0			0
$536$	−203.812			−0.380247
$537$			290.239i			0.540481i
$538$			55.4562i			0.103078i
$539$	−204.418	+	135.764i	−0.379254	+	0.251882i
$540$		0			0
$541$	−228.274			−0.421949			−0.210974	−	0.977492i	$-0.567664\pi$
$541$	−228.274			−0.421949			−0.210974	+	0.977492i	$0.567664\pi$
$542$			422.950i			0.780351i
$543$	256.269			0.471950
$544$		−	111.672i		−	0.205279i
$545$		0			0
$546$	148.873	−	44.9334i	0.272661	−	0.0822955i
$547$	−876.996			−1.60328			−0.801642	−	0.597805i	$-0.796040\pi$
$547$	−876.996			−1.60328			−0.801642	+	0.597805i	$0.796040\pi$
$548$	−316.600			−0.577737
$549$		−	250.605i		−	0.456475i
$550$		0			0
$551$			572.986i			1.03990i
$552$		−	200.704i		−	0.363595i
$553$	204.026	−	61.5799i	0.368944	−	0.111356i
$554$	620.792			1.12056
$555$		0			0
$556$			283.168i			0.509296i
$557$	−561.224			−1.00758			−0.503792	−	0.863825i	$-0.668062\pi$
$557$	−561.224			−1.00758			−0.503792	+	0.863825i	$0.668062\pi$
$558$			67.4644i			0.120904i
$559$			278.146i			0.497578i
$560$		0			0
$561$	171.237			0.305236
$562$	−282.105			−0.501967
$563$		−	890.386i		−	1.58150i	−0.612137	−	0.790752i	$-0.709690\pi$
$563$		−	890.386i		−	1.58150i	0.612137	−	0.790752i	$-0.290310\pi$
$564$	−201.413			−0.357116
$565$		0			0
$566$			765.343i			1.35220i
$567$	60.3127	−	18.2038i	0.106372	−	0.0321055i
$568$	−70.3358			−0.123831
$569$	138.453			0.243327			0.121663	−	0.992571i	$-0.461177\pi$
$569$	138.453			0.243327			0.121663	+	0.992571i	$0.461177\pi$
$570$		0			0
$571$	476.343			0.834225			0.417113	−	0.908855i	$-0.363042\pi$
$571$	476.343			0.834225			0.417113	+	0.908855i	$0.363042\pi$
$572$		−	90.8390i		−	0.158810i
$573$		−	85.7259i		−	0.149609i
$574$	77.4693	+	256.670i	0.134964	+	0.447161i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$		−	678.464i		−	1.17585i	−0.808916	−	0.587924i	$-0.799945\pi$
$577$		−	678.464i		−	1.17585i	0.808916	−	0.587924i	$-0.200055\pi$
$578$	−142.419			−0.246400
$579$			299.081i			0.516547i
$580$		0			0
$581$	−146.566	−	485.600i	−0.252264	−	0.835800i
$582$	−254.267			−0.436885
$583$	328.628			0.563684
$584$		−	191.972i		−	0.328720i
$585$		0			0
$586$			535.643i			0.914067i
$587$		−	48.9046i		−	0.0833128i	−0.999132	−	0.0416564i	$-0.986737\pi$
$587$		−	48.9046i		−	0.0833128i	0.999132	−	0.0416564i	$-0.0132635\pi$
$588$	−93.9089	−	141.397i	−0.159709	−	0.240471i
$589$	−408.451			−0.693465
$590$		0			0
$591$			131.020i			0.221692i
$592$	179.003			0.302369
$593$			487.761i			0.822531i	0.911516	+	0.411266i	$0.134913\pi$
$593$			487.761i			0.822531i	−0.911516	+	0.411266i	$0.865087\pi$
$594$		−	36.8015i		−	0.0619555i
$595$		0			0
$596$	−242.911			−0.407569
$597$	255.685			0.428283
$598$			525.459i			0.878695i
$599$	−1083.77			−1.80931			−0.904653	−	0.426149i	$-0.859870\pi$
$599$	−1083.77			−1.80931			−0.904653	+	0.426149i	$0.859870\pi$
$600$		0			0
$601$		−	274.481i		−	0.456707i	−0.973578	−	0.228353i	$-0.926666\pi$
$601$		−	274.481i		−	0.456707i	0.973578	−	0.228353i	$-0.0733342\pi$
$602$	290.657	−	87.7273i	0.482819	−	0.145726i
$603$	216.175			0.358500
$604$	−438.185			−0.725472
$605$		0			0
$606$	380.600			0.628052
$607$			941.550i			1.55115i	0.631253	+	0.775577i	$0.282541\pi$
$607$			941.550i			1.55115i	−0.631253	+	0.775577i	$0.717459\pi$
$608$		−	145.304i		−	0.238986i
$609$	78.1489	+	258.922i	0.128323	+	0.425159i
$610$		0			0
$611$	527.316			0.863038
$612$			118.446i			0.193539i
$613$	658.706			1.07456			0.537281	−	0.843404i	$-0.319452\pi$
$613$	658.706			1.07456			0.537281	+	0.843404i	$0.319452\pi$
$614$			198.287i			0.322942i
$615$		0			0
$616$	−94.9249	+	28.6506i	−0.154099	+	0.0465108i
$617$	−355.965			−0.576929			−0.288464	−	0.957491i	$-0.593145\pi$
$617$	−355.965			−0.576929			−0.288464	+	0.957491i	$0.593145\pi$
$618$	161.537			0.261387
$619$		−	214.933i		−	0.347226i	−0.984814	−	0.173613i	$-0.944456\pi$
$619$		−	214.933i		−	0.347226i	0.984814	−	0.173613i	$-0.0555442\pi$
$620$		0			0
$621$			212.879i			0.342800i
$622$			353.392i			0.568154i
$623$	−230.087	−	762.323i	−0.369322	−	1.22363i
$624$	62.8339			0.100695
$625$		0			0
$626$			732.413i			1.16999i
$627$	222.808			0.355356
$628$			114.563i			0.182425i
$629$		−	883.421i		−	1.40448i
$630$		0			0
$631$	589.714			0.934570			0.467285	−	0.884107i	$-0.345232\pi$
$631$	589.714			0.934570			0.467285	+	0.884107i	$0.345232\pi$
$632$	86.1121			0.136253
$633$		−	271.728i		−	0.429270i
$634$	254.619			0.401608
$635$		0			0
$636$			227.314i			0.357412i
$637$	245.861	+	370.189i	0.385967	+	0.581144i
$638$	157.989			0.247631
$639$	74.6024			0.116749
$640$		0			0
$641$	−675.508			−1.05383			−0.526917	−	0.849917i	$-0.676652\pi$
$641$	−675.508			−1.05383			−0.526917	+	0.849917i	$0.676652\pi$
$642$		−	333.789i		−	0.519921i
$643$		−	733.747i		−	1.14113i	−0.821252	−	0.570565i	$-0.806724\pi$
$643$		−	733.747i		−	1.14113i	0.821252	−	0.570565i	$-0.193276\pi$
$644$	549.095	−	165.730i	0.852631	−	0.257345i
$645$		0			0
$646$	−717.109			−1.11008
$647$			645.060i			0.997002i	0.866889	+	0.498501i	$0.166116\pi$
$647$			645.060i			0.997002i	−0.866889	+	0.498501i	$0.833884\pi$
$648$	25.4558			0.0392837
$649$			163.135i			0.251364i
$650$		0			0
$651$	−184.572	+	55.7082i	−0.283520	+	0.0855732i
$652$	17.0459			0.0261441
$653$	610.744			0.935289			0.467644	−	0.883917i	$-0.345103\pi$
$653$	610.744			0.935289			0.467644	+	0.883917i	$0.345103\pi$
$654$		−	406.623i		−	0.621747i
$655$		0			0
$656$			108.331i			0.165139i
$657$			203.617i			0.309920i
$658$	−166.315	−	551.035i	−0.252759	−	0.837439i
$659$	220.888			0.335187			0.167594	−	0.985856i	$-0.446400\pi$
$659$	220.888			0.335187			0.167594	+	0.985856i	$0.446400\pi$
$660$		0			0
$661$		−	306.043i		−	0.463000i	−0.972835	−	0.231500i	$-0.925637\pi$
$661$		−	306.043i		−	0.463000i	0.972835	−	0.231500i	$-0.0743634\pi$
$662$	114.591			0.173099
$663$		−	310.100i		−	0.467723i
$664$		−	204.954i		−	0.308666i
$665$		0			0
$666$	−189.861			−0.285076
$667$	−913.888			−1.37015
$668$			516.297i			0.772899i
$669$	104.621			0.156384
$670$		0			0
$671$		−	418.348i		−	0.623469i
$672$	−19.8178	−	65.6601i	−0.0294908	−	0.0977085i
$673$	1025.63			1.52397			0.761986	−	0.647594i	$-0.224225\pi$
$673$	1025.63			1.52397			0.761986	+	0.647594i	$0.224225\pi$
$674$	527.412			0.782510
$675$		0			0
$676$	173.496			0.256651
$677$			622.692i			0.919781i	0.887976	+	0.459891i	$0.152111\pi$
$677$			622.692i			0.919781i	−0.887976	+	0.459891i	$0.847889\pi$
$678$		−	62.4711i		−	0.0921402i
$679$	−209.959	−	695.634i	−0.309218	−	1.02450i
$680$		0			0
$681$	−543.190			−0.797636
$682$			112.622i			0.165135i
$683$	−170.676			−0.249891			−0.124946	−	0.992164i	$-0.539876\pi$
$683$	−170.676			−0.249891			−0.124946	+	0.992164i	$0.539876\pi$
$684$			154.118i			0.225319i
$685$		0			0
$686$	309.295	−	373.677i	0.450867	−	0.544719i
$687$	191.163			0.278258
$688$	122.676			0.178308
$689$		−	595.126i		−	0.863753i
$690$		0			0
$691$			1353.09i			1.95816i	0.203481	+	0.979079i	$0.434774\pi$
$691$			1353.09i			1.95816i	−0.203481	+	0.979079i	$0.565226\pi$
$692$			654.499i			0.945808i
$693$	100.683	−	30.3886i	0.145286	−	0.0438508i
$694$	−587.226			−0.846147
$695$		0			0
$696$			109.282i			0.157014i
$697$	534.642			0.767061
$698$			758.312i			1.08641i
$699$			66.5223i			0.0951678i
$700$		0			0
$701$	−631.426			−0.900750			−0.450375	−	0.892840i	$-0.648710\pi$
$701$	−631.426			−0.900750			−0.450375	+	0.892840i	$0.648710\pi$
$702$	−66.6454			−0.0949365
$703$		−	1149.48i		−	1.63510i
$704$	−40.0644			−0.0569097
$705$		0			0
$706$		−	588.638i		−	0.833764i
$707$	314.277	+	1041.26i	0.444522	+	1.47279i
$708$	−112.842			−0.159381
$709$	−294.907			−0.415947			−0.207974	−	0.978134i	$-0.566687\pi$
$709$	−294.907			−0.415947			−0.207974	+	0.978134i	$0.566687\pi$
$710$		0			0
$711$	−91.3357			−0.128461
$712$		−	321.749i		−	0.451895i
$713$		−	651.462i		−	0.913692i
$714$	−324.049	+	97.8056i	−0.453850	+	0.136983i
$715$		0			0
$716$	−335.139			−0.468071
$717$			216.730i			0.302273i
$718$	−382.634			−0.532917
$719$		−	884.788i		−	1.23058i	−0.788301	−	0.615290i	$-0.789039\pi$
$719$		−	884.788i		−	1.23058i	0.788301	−	0.615290i	$-0.210961\pi$
$720$		0			0
$721$	133.388	+	441.939i	0.185004	+	0.612953i
$722$	−422.548			−0.585247
$723$	−267.818			−0.370427
$724$			295.914i			0.408721i
$725$		0			0
$726$			234.954i			0.323627i
$727$		−	361.739i		−	0.497578i	−0.968558	−	0.248789i	$-0.919967\pi$
$727$		−	361.739i		−	0.497578i	0.968558	−	0.248789i	$-0.0800325\pi$
$728$	51.8846	+	171.903i	0.0712700	+	0.236131i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	605.436i		−	0.828230i
$732$	289.374			0.395319
$733$		−	819.923i		−	1.11859i	−0.828970	−	0.559293i	$-0.811073\pi$
$733$		−	819.923i		−	1.11859i	0.828970	−	0.559293i	$-0.188927\pi$
$734$			855.633i			1.16571i
$735$		0			0
$736$	231.753			0.314882
$737$	360.873			0.489651
$738$		−	114.903i		−	0.155695i
$739$	−802.663			−1.08615			−0.543074	−	0.839685i	$-0.682740\pi$
$739$	−802.663			−1.08615			−0.543074	+	0.839685i	$0.682740\pi$
$740$		0			0
$741$		−	403.493i		−	0.544525i
$742$	−621.894	+	187.703i	−0.838132	+	0.252968i
$743$	1061.48			1.42865			0.714323	−	0.699816i	$-0.246735\pi$
$743$	1061.48			1.42865			0.714323	+	0.699816i	$0.246735\pi$
$744$	−77.9012			−0.104706
$745$		0			0
$746$	30.4231			0.0407816
$747$			217.387i			0.291013i
$748$			197.728i			0.264342i
$749$	913.194	−	275.624i	1.21922	−	0.367989i
$750$		0			0
$751$	−1044.41			−1.39069			−0.695346	−	0.718675i	$-0.744749\pi$
$751$	−1044.41			−1.39069			−0.695346	+	0.718675i	$0.744749\pi$
$752$		−	232.572i		−	0.309272i
$753$	−264.405			−0.351136
$754$		−	286.108i		−	0.379454i
$755$		0			0
$756$	21.0200	+	69.6431i	0.0278042	+	0.0921205i
$757$	1267.83			1.67481			0.837406	−	0.546581i	$-0.184071\pi$
$757$	1267.83			1.67481			0.837406	+	0.546581i	$0.184071\pi$
$758$	636.202			0.839316
$759$			355.370i			0.468208i
$760$		0			0
$761$			257.020i			0.337740i	0.985638	+	0.168870i	$0.0540118\pi$
$761$			257.020i			0.337740i	−0.985638	+	0.168870i	$0.945988\pi$
$762$		−	564.133i		−	0.740332i
$763$	1112.45	−	335.765i	1.45800	−	0.440060i
$764$	98.9878			0.129565
$765$		0			0
$766$			793.029i			1.03529i
$767$	295.428			0.385174
$768$		−	27.7128i		−	0.0360844i
$769$		−	1192.50i		−	1.55071i	−0.631524	−	0.775357i	$-0.717570\pi$
$769$		−	1192.50i		−	1.55071i	0.631524	−	0.775357i	$-0.282430\pi$
$770$		0			0
$771$	34.9038			0.0452708
$772$	−345.349			−0.447343
$773$			1121.01i			1.45021i	0.688639	+	0.725104i	$0.258208\pi$
$773$			1121.01i			1.45021i	−0.688639	+	0.725104i	$0.741792\pi$
$774$	−130.118			−0.168111
$775$		0			0
$776$		−	293.602i		−	0.378353i
$777$	−156.776	−	519.429i	−0.201771	−	0.668506i
$778$	−823.386			−1.05834
$779$	695.659			0.893015
$780$		0			0
$781$	124.538			0.159459
$782$		−	1143.76i		−	1.46261i
$783$		−	115.911i		−	0.148034i
$784$	163.271	−	108.437i	0.208254	−	0.138312i
$785$		0			0
$786$	100.215			0.127500
$787$		−	1207.04i		−	1.53372i	−0.641813	−	0.766861i	$-0.721817\pi$
$787$		−	1207.04i		−	1.53372i	0.641813	−	0.766861i	$-0.278183\pi$
$788$	−151.289			−0.191991
$789$		−	555.466i		−	0.704013i
$790$		0			0
$791$	170.911	−	51.5850i	0.216069	−	0.0652149i
$792$	42.4948			0.0536550
$793$	−757.603			−0.955363
$794$		−	1027.51i		−	1.29410i
$795$		0			0
$796$			295.240i			0.370904i
$797$		−	378.901i		−	0.475409i	−0.971338	−	0.237704i	$-0.923605\pi$
$797$		−	378.901i		−	0.475409i	0.971338	−	0.237704i	$-0.0763950\pi$
$798$	−421.642	+	127.262i	−0.528373	+	0.159476i
$799$	−1147.80			−1.43655
$800$		0			0
$801$			341.267i			0.426051i
$802$	−46.3808			−0.0578314
$803$			339.909i			0.423299i
$804$			249.618i			0.310470i
$805$		0			0
$806$	203.951			0.253041
$807$	67.9196			0.0841631
$808$			439.479i			0.543909i
$809$	−403.691			−0.499000			−0.249500	−	0.968375i	$-0.580266\pi$
$809$	−403.691			−0.499000			−0.249500	+	0.968375i	$0.580266\pi$
$810$		0			0
$811$		−	109.713i		−	0.135281i	−0.997710	−	0.0676407i	$-0.978453\pi$
$811$		−	109.713i		−	0.135281i	0.997710	−	0.0676407i	$-0.0215471\pi$
$812$	−298.977	+	90.2386i	−0.368199	+	0.111131i
$813$	518.006			0.637154
$814$	−316.945			−0.389367
$815$		0			0
$816$	−136.769			−0.167610
$817$		−	787.774i		−	0.964228i
$818$		−	901.899i		−	1.10257i
$819$	−55.0319	−	182.331i	−0.0671940	−	0.222627i
$820$		0			0
$821$	426.293			0.519236			0.259618	−	0.965711i	$-0.416403\pi$
$821$	426.293			0.519236			0.259618	+	0.965711i	$0.416403\pi$
$822$			387.754i			0.471721i
$823$	708.932			0.861400			0.430700	−	0.902495i	$-0.358267\pi$
$823$	708.932			0.861400			0.430700	+	0.902495i	$0.358267\pi$
$824$			186.527i			0.226367i
$825$		0			0
$826$	−93.1781	−	308.717i	−0.112806	−	0.373749i
$827$	813.963			0.984236			0.492118	−	0.870528i	$-0.336223\pi$
$827$	813.963			0.984236			0.492118	+	0.870528i	$0.336223\pi$
$828$	−245.811			−0.296874
$829$		−	92.7107i		−	0.111834i	−0.998435	−	0.0559172i	$-0.982192\pi$
$829$		−	92.7107i		−	0.111834i	0.998435	−	0.0559172i	$-0.0178083\pi$
$830$		0			0
$831$		−	760.312i		−	0.914936i
$832$			72.5543i			0.0872047i
$833$	−535.161	−	805.783i	−0.642450	−	0.967326i
$834$	346.809			0.415838
$835$		0			0
$836$			257.277i			0.307748i
$837$	82.6267			0.0987176
$838$			487.247i			0.581440i
$839$		−	852.206i		−	1.01574i	−0.861434	−	0.507870i	$-0.830433\pi$
$839$		−	852.206i		−	1.01574i	0.861434	−	0.507870i	$-0.169567\pi$
$840$		0			0
$841$	−343.395			−0.408318
$842$	410.704			0.487772
$843$			345.507i			0.409854i
$844$	313.764			0.371759
$845$		0			0
$846$			246.680i			0.291584i
$847$	−642.795	+	194.011i	−0.758908	+	0.229057i
$848$	−262.479			−0.309528
$849$	937.349			1.10406
$850$		0			0
$851$	1833.37			2.15437
$852$			86.1434i			0.101107i
$853$		−	1472.75i		−	1.72655i	−0.504733	−	0.863275i	$-0.668409\pi$
$853$		−	1472.75i		−	1.72655i	0.504733	−	0.863275i	$-0.331591\pi$
$854$	238.948	+	791.680i	0.279798	+	0.927025i
$855$		0			0
$856$	385.427			0.450265
$857$		−	882.824i		−	1.03013i	−0.857150	−	0.515066i	$-0.827767\pi$
$857$		−	882.824i		−	1.03013i	0.857150	−	0.515066i	$-0.172233\pi$
$858$	−111.255			−0.129667
$859$			700.963i			0.816023i	0.912977	+	0.408011i	$0.133778\pi$
$859$			700.963i			0.816023i	−0.912977	+	0.408011i	$0.866222\pi$
$860$		0			0
$861$	314.356	−	94.8801i	0.365105	−	0.110198i
$862$	−303.744			−0.352372
$863$	−1246.07			−1.44388			−0.721938	−	0.691957i	$-0.756749\pi$
$863$	−1246.07			−1.44388			−0.721938	+	0.691957i	$0.756749\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$		−	601.099i		−	0.694109i
$867$			174.427i			0.201185i
$868$	−64.3263	−	213.125i	−0.0741086	−	0.245536i
$869$	−152.471			−0.175456
$870$		0			0
$871$		−	653.519i		−	0.750309i
$872$	469.527			0.538449
$873$			311.412i			0.356715i
$874$		−	1488.22i		−	1.70277i
$875$		0			0
$876$	−235.117			−0.268399
$877$	−957.986			−1.09234			−0.546172	−	0.837673i	$-0.683916\pi$
$877$	−957.986			−1.09234			−0.546172	+	0.837673i	$0.683916\pi$
$878$			288.783i			0.328910i
$879$	656.026			0.746333
$880$		0			0
$881$		−	865.707i		−	0.982642i	−0.870979	−	0.491321i	$-0.836514\pi$
$881$		−	865.707i		−	0.982642i	0.870979	−	0.491321i	$-0.163486\pi$
$882$	−173.175	+	115.014i	−0.196344	+	0.130402i
$883$	−985.817			−1.11644			−0.558220	−	0.829693i	$-0.688516\pi$
$883$	−985.817			−1.11644			−0.558220	+	0.829693i	$0.688516\pi$
$884$	358.073			0.405060
$885$		0			0
$886$	−390.843			−0.441132
$887$		−	443.357i		−	0.499838i	−0.968267	−	0.249919i	$-0.919596\pi$
$887$		−	443.357i		−	0.499838i	0.968267	−	0.249919i	$-0.0804040\pi$
$888$		−	219.232i		−	0.246883i
$889$	1543.38	−	465.828i	1.73608	−	0.523991i
$890$		0			0
$891$	−45.0725			−0.0505864
$892$			120.806i			0.135433i
$893$	−1493.48			−1.67243
$894$			297.504i			0.332779i
$895$		0			0
$896$	75.8178	−	22.8836i	0.0846181	−	0.0255398i
$897$	643.554			0.717451
$898$	276.182			0.307552
$899$			354.716i			0.394567i
$900$		0			0
$901$			1295.40i			1.43774i
$902$		−	191.813i		−	0.212653i
$903$	−107.444	−	355.981i	−0.118985	−	0.394220i
$904$	72.1354			0.0797958
$905$		0			0
$906$			536.665i			0.592346i
$907$	−49.0514			−0.0540810			−0.0270405	−	0.999634i	$-0.508608\pi$
$907$	−49.0514			−0.0540810			−0.0270405	+	0.999634i	$0.508608\pi$
$908$		−	627.222i		−	0.690773i
$909$		−	466.138i		−	0.512803i
$910$		0			0
$911$	−290.836			−0.319249			−0.159624	−	0.987178i	$-0.551028\pi$
$911$	−290.836			−0.319249			−0.159624	+	0.987178i	$0.551028\pi$
$912$	−177.960			−0.195132
$913$			362.895i			0.397476i
$914$	−14.6269			−0.0160032
$915$		0			0
$916$			220.736i			0.240979i
$917$	82.7519	+	274.173i	0.0902420	+	0.298989i
$918$	145.066			0.158024
$919$	−721.872			−0.785498			−0.392749	−	0.919646i	$-0.628476\pi$
$919$	−721.872			−0.785498			−0.392749	+	0.919646i	$0.628476\pi$
$920$		0			0
$921$	242.851			0.263681
$922$		−	746.100i		−	0.809219i
$923$		−	225.530i		−	0.244345i
$924$	35.0897	+	116.259i	0.0379759	+	0.125821i
$925$		0			0
$926$	−1128.40			−1.21857
$927$		−	197.841i		−	0.213421i
$928$	−126.188			−0.135978
$929$		−	617.161i		−	0.664329i	−0.943222	−	0.332164i	$-0.892221\pi$
$929$		−	617.161i		−	0.664329i	0.943222	−	0.332164i	$-0.107779\pi$
$930$		0			0
$931$	−696.335	−	1048.46i	−0.747943	−	1.12616i
$932$	−76.8133			−0.0824177
$933$	432.815			0.463896
$934$			239.923i			0.256877i
$935$		0			0
$936$		−	76.9555i		−	0.0822174i
$937$		−	224.045i		−	0.239108i	−0.992828	−	0.119554i	$-0.961853\pi$
$937$		−	224.045i		−	0.239108i	0.992828	−	0.119554i	$-0.0381465\pi$
$938$	−682.915	+	206.120i	−0.728054	+	0.219744i
$939$	897.019			0.955292
$940$		0			0
$941$			522.371i			0.555124i	0.960708	+	0.277562i	$0.0895264\pi$
$941$			522.371i			0.555124i	−0.960708	+	0.277562i	$0.910474\pi$
$942$	140.310			0.148949
$943$			1109.55i			1.17661i
$944$		−	130.298i		−	0.138028i
$945$		0			0
$946$	−217.212			−0.229611
$947$	728.427			0.769194			0.384597	−	0.923084i	$-0.374340\pi$
$947$	728.427			0.769194			0.384597	+	0.923084i	$0.374340\pi$
$948$		−	105.465i		−	0.111250i
$949$	615.555			0.648636
$950$		0			0
$951$		−	311.844i		−	0.327911i
$952$	−112.936	−	374.179i	−0.118630	−	0.393045i
$953$	1169.38			1.22705			0.613527	−	0.789674i	$-0.289750\pi$
$953$	1169.38			1.22705			0.613527	+	0.789674i	$0.289750\pi$
$954$	278.402			0.291825
$955$		0			0
$956$	−250.258			−0.261776
$957$		−	193.496i		−	0.202190i
$958$			995.991i			1.03966i
$959$	−1060.83	+	320.185i	−1.10619	+	0.333874i
$960$		0			0
$961$	708.142			0.736880
$962$			573.968i			0.596640i
$963$	−408.807			−0.424514
$964$		−	309.250i		−	0.320799i
$965$		0			0
$966$	−202.977	−	672.501i	−0.210121	−	0.696170i
$967$	−771.440			−0.797767			−0.398883	−	0.917002i	$-0.630602\pi$
$967$	−771.440			−0.797767			−0.398883	+	0.917002i	$0.630602\pi$
$968$	−271.301			−0.280270
$969$			878.275i			0.906373i
$970$		0			0
$971$			1380.71i			1.42195i	0.703220	+	0.710973i	$0.251745\pi$
$971$			1380.71i			1.42195i	−0.703220	+	0.710973i	$0.748255\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	286.375	+	948.814i	0.294321	+	0.975143i
$974$	94.4647			0.0969864
$975$		0			0
$976$			334.140i			0.342356i
$977$	−974.771			−0.997718			−0.498859	−	0.866683i	$-0.666248\pi$
$977$	−974.771			−0.997718			−0.498859	+	0.866683i	$0.666248\pi$
$978$		−	20.8769i		−	0.0213466i
$979$			569.694i			0.581915i
$980$		0			0
$981$	−498.009			−0.507655
$982$	772.333			0.786490
$983$		−	206.961i		−	0.210540i	−0.994444	−	0.105270i	$-0.966429\pi$
$983$		−	206.961i		−	0.210540i	0.994444	−	0.105270i	$-0.0335708\pi$
$984$	132.678			0.134836
$985$		0			0
$986$			622.767i			0.631610i
$987$	−674.877	+	203.694i	−0.683766	+	0.206377i
$988$	465.913			0.471572
$989$	1256.47			1.27044
$990$		0			0
$991$	−413.701			−0.417459			−0.208729	−	0.977973i	$-0.566933\pi$
$991$	−413.701			−0.417459			−0.208729	+	0.977973i	$0.566933\pi$
$992$		−	89.9525i		−	0.0906779i
$993$		−	140.345i		−	0.141335i
$994$	−235.675	+	71.1322i	−0.237097	+	0.0715616i
$995$		0			0
$996$	−251.017			−0.252025
$997$		−	542.511i		−	0.544143i	−0.962277	−	0.272072i	$-0.912291\pi$
$997$		−	542.511i		−	0.544143i	0.962277	−	0.272072i	$-0.0877088\pi$
$998$	1009.83			1.01186
$999$			232.531i			0.232764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.f.b.601.6		8
5.2	odd	4		1050.3.h.b.349.11		16
5.3	odd	4		1050.3.h.b.349.6		16
5.4	even	2		210.3.f.a.181.4	yes	8
7.6	odd	2	inner	1050.3.f.b.601.8		8
15.14	odd	2		630.3.f.c.181.5		8
20.19	odd	2		1680.3.s.a.1441.4		8
35.13	even	4		1050.3.h.b.349.3		16
35.27	even	4		1050.3.h.b.349.14		16
35.34	odd	2		210.3.f.a.181.1	✓	8
105.104	even	2		630.3.f.c.181.7		8
140.139	even	2		1680.3.s.a.1441.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.f.a.181.1	✓	8	35.34	odd	2
210.3.f.a.181.4	yes	8	5.4	even	2
630.3.f.c.181.5		8	15.14	odd	2
630.3.f.c.181.7		8	105.104	even	2
1050.3.f.b.601.6		8	1.1	even	1	trivial
1050.3.f.b.601.8		8	7.6	odd	2	inner
1050.3.h.b.349.3		16	35.13	even	4
1050.3.h.b.349.6		16	5.3	odd	4
1050.3.h.b.349.11		16	5.2	odd	4
1050.3.h.b.349.14		16	35.27	even	4
1680.3.s.a.1441.4		8	20.19	odd	2
1680.3.s.a.1441.6		8	140.139	even	2

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(6.70141 - 2.02265i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(6.70141 - 2.02265i) q^{7} +2.82843 q^{8} -3.00000 q^{9} -5.00806 q^{11} -3.46410i q^{12} +9.06929i q^{13} +(9.47723 - 2.86045i) q^{14} +4.00000 q^{16} -19.7410i q^{17} -4.24264 q^{18} -25.6863i q^{19} +(-3.50333 - 11.6072i) q^{21} -7.08246 q^{22} +40.9686 q^{23} -4.89898i q^{24} +12.8259i q^{26} +5.19615i q^{27} +(13.4028 - 4.04529i) q^{28} -22.3071 q^{29} -15.9015i q^{31} +5.65685 q^{32} +8.67421i q^{33} -27.9179i q^{34} -6.00000 q^{36} +44.7506 q^{37} -36.3259i q^{38} +15.7085 q^{39} +27.0829i q^{41} +(-4.95445 - 16.4150i) q^{42} +30.6690 q^{43} -10.0161 q^{44} +57.9383 q^{46} -58.1430i q^{47} -6.92820i q^{48} +(40.8178 - 27.1092i) q^{49} -34.1924 q^{51} +18.1386i q^{52} -65.6199 q^{53} +7.34847i q^{54} +(18.9545 - 5.72091i) q^{56} -44.4900 q^{57} -31.5469 q^{58} -32.5746i q^{59} +83.5349i q^{61} -22.4881i q^{62} +(-20.1042 + 6.06794i) q^{63} +8.00000 q^{64} +12.2672i q^{66} -72.0585 q^{67} -39.4819i q^{68} -70.9597i q^{69} -24.8675 q^{71} -8.48528 q^{72} -67.8725i q^{73} +63.2870 q^{74} -51.3726i q^{76} +(-33.5610 + 10.1295i) q^{77} +22.2151 q^{78} +30.4452 q^{79} +9.00000 q^{81} +38.3009i q^{82} -72.4623i q^{83} +(-7.00665 - 23.2144i) q^{84} +43.3725 q^{86} +38.6370i q^{87} -14.1649 q^{88} -113.756i q^{89} +(18.3440 + 60.7770i) q^{91} +81.9372 q^{92} -27.5422 q^{93} -82.2267i q^{94} -9.79796i q^{96} -103.804i q^{97} +(57.7251 - 38.3381i) q^{98} +15.0242 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 8 * q + 16 * q^4 - 24 * q^9	\( 8 q + 16 q^{4} - 24 q^{9} - 16 q^{11} + 32 q^{14} + 32 q^{16} - 96 q^{22} - 144 q^{29} - 48 q^{36} + 48 q^{37} - 48 q^{39} + 48 q^{42} + 64 q^{43} - 32 q^{44} + 128 q^{46} - 24 q^{49} - 128 q^{53} + 64 q^{56} - 144 q^{57} - 224 q^{58} + 64 q^{64} + 192 q^{67} + 176 q^{71} - 160 q^{74} - 192 q^{77} + 96 q^{78} - 288 q^{79} + 72 q^{81} - 64 q^{86} - 192 q^{88} + 64 q^{91} - 336 q^{93} + 48 q^{99}+O(q^{100}) \) 8 * q + 16 * q^4 - 24 * q^9 - 16 * q^11 + 32 * q^14 + 32 * q^16 - 96 * q^22 - 144 * q^29 - 48 * q^36 + 48 * q^37 - 48 * q^39 + 48 * q^42 + 64 * q^43 - 32 * q^44 + 128 * q^46 - 24 * q^49 - 128 * q^53 + 64 * q^56 - 144 * q^57 - 224 * q^58 + 64 * q^64 + 192 * q^67 + 176 * q^71 - 160 * q^74 - 192 * q^77 + 96 * q^78 - 288 * q^79 + 72 * q^81 - 64 * q^86 - 192 * q^88 + 64 * q^91 - 336 * q^93 + 48 * q^99

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