LMFDB - Embedded newform 126.3.c.b.55.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,3,Mod(55,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("126.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.c (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:	$3.43325133094$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.3
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.55
Dual form			126.3.c.b.55.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +2.00000 q^{4} -5.91359i q^{5} +(6.24264 + 3.16693i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+1.41421 q^{2} +2.00000 q^{4} -5.91359i q^{5} +(6.24264 + 3.16693i) q^{7} +2.82843 q^{8} -8.36308i q^{10} +1.75736 q^{11} -18.7554i q^{13} +(8.82843 + 4.47871i) q^{14} +4.00000 q^{16} +23.4803i q^{17} +23.0600i q^{19} -11.8272i q^{20} +2.48528 q^{22} -18.7279 q^{23} -9.97056 q^{25} -26.5241i q^{26} +(12.4853 + 6.33386i) q^{28} -30.0000 q^{29} -8.60927i q^{31} +5.65685 q^{32} +33.2061i q^{34} +(18.7279 - 36.9164i) q^{35} -70.9117 q^{37} +32.6118i q^{38} -16.7262i q^{40} +41.3951i q^{41} +10.4264 q^{43} +3.51472 q^{44} -26.4853 q^{46} +38.6995i q^{47} +(28.9411 + 39.5400i) q^{49} -14.1005 q^{50} -37.5108i q^{52} +37.0294 q^{53} -10.3923i q^{55} +(17.6569 + 8.95743i) q^{56} -42.4264 q^{58} -97.4872i q^{59} -16.7262i q^{61} -12.1753i q^{62} +8.00000 q^{64} -110.912 q^{65} +60.9706 q^{67} +46.9606i q^{68} +(26.4853 - 52.2077i) q^{70} +110.610 q^{71} +56.7585i q^{73} -100.284 q^{74} +46.1200i q^{76} +(10.9706 + 5.56543i) q^{77} -69.8234 q^{79} -23.6544i q^{80} +58.5416i q^{82} +6.43583i q^{83} +138.853 q^{85} +14.7452 q^{86} +4.97056 q^{88} -42.0915i q^{89} +(59.3970 - 117.083i) q^{91} -37.4558 q^{92} +54.7293i q^{94} +136.368 q^{95} -51.7153i q^{97} +(40.9289 + 55.9180i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} + 8 q^{7}+O(q^{10}) $ 4 * q + 8 * q^4 + 8 * q^7	$ 4 q + 8 q^{4} + 8 q^{7} + 24 q^{11} + 24 q^{14} + 16 q^{16} - 24 q^{22} - 24 q^{23} + 28 q^{25} + 16 q^{28} - 120 q^{29} + 24 q^{35} - 80 q^{37} - 128 q^{43} + 48 q^{44} - 72 q^{46} - 20 q^{49} - 96 q^{50} + 216 q^{53} + 48 q^{56} + 32 q^{64} - 240 q^{65} + 176 q^{67} + 72 q^{70} + 120 q^{71} - 288 q^{74} - 24 q^{77} + 128 q^{79} + 216 q^{85} + 240 q^{86} - 48 q^{88} - 48 q^{92} + 240 q^{95} + 192 q^{98}+O(q^{100}) $ 4 * q + 8 * q^4 + 8 * q^7 + 24 * q^11 + 24 * q^14 + 16 * q^16 - 24 * q^22 - 24 * q^23 + 28 * q^25 + 16 * q^28 - 120 * q^29 + 24 * q^35 - 80 * q^37 - 128 * q^43 + 48 * q^44 - 72 * q^46 - 20 * q^49 - 96 * q^50 + 216 * q^53 + 48 * q^56 + 32 * q^64 - 240 * q^65 + 176 * q^67 + 72 * q^70 + 120 * q^71 - 288 * q^74 - 24 * q^77 + 128 * q^79 + 216 * q^85 + 240 * q^86 - 48 * q^88 - 48 * q^92 + 240 * q^95 + 192 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$-1$

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
$3$		0			0
$3$		0			0
$4$	2.00000			0.500000
$5$		−	5.91359i		−	1.18272i	−0.806408	−	0.591359i	$-0.798592\pi$
$5$		−	5.91359i		−	1.18272i	0.806408	−	0.591359i	$-0.201408\pi$
$6$		0			0
$7$	6.24264	+	3.16693i	0.891806	+	0.452418i
$7$	6.24264	+	3.16693i	0.891806	+	0.452418i
$8$	2.82843			0.353553
$9$		0			0
$10$		−	8.36308i		−	0.836308i
$11$	1.75736			0.159760			0.0798800	−	0.996804i	$-0.474546\pi$
$11$	1.75736			0.159760			0.0798800	+	0.996804i	$0.474546\pi$
$12$		0			0
$13$		−	18.7554i		−	1.44272i	−0.692559	−	0.721361i	$-0.743517\pi$
$13$		−	18.7554i		−	1.44272i	0.692559	−	0.721361i	$-0.256483\pi$
$14$	8.82843	+	4.47871i	0.630602	+	0.319908i
$15$		0			0
$16$	4.00000			0.250000
$17$			23.4803i			1.38119i	0.723240	+	0.690597i	$0.242652\pi$
$17$			23.4803i			1.38119i	−0.723240	+	0.690597i	$0.757348\pi$
$18$		0			0
$19$			23.0600i			1.21369i	0.794822	+	0.606843i	$0.207564\pi$
$19$			23.0600i			1.21369i	−0.794822	+	0.606843i	$0.792436\pi$
$20$		−	11.8272i		−	0.591359i
$21$		0			0
$22$	2.48528			0.112967
$23$	−18.7279			−0.814257			−0.407129	−	0.913371i	$-0.633470\pi$
$23$	−18.7279			−0.814257			−0.407129	+	0.913371i	$0.633470\pi$
$24$		0			0
$25$	−9.97056			−0.398823
$26$		−	26.5241i		−	1.02016i
$27$		0			0
$28$	12.4853	+	6.33386i	0.445903	+	0.226209i
$29$	−30.0000			−1.03448			−0.517241	−	0.855840i	$-0.673041\pi$
$29$	−30.0000			−1.03448			−0.517241	+	0.855840i	$0.673041\pi$
$30$		0			0
$31$		−	8.60927i		−	0.277718i	−0.990312	−	0.138859i	$-0.955656\pi$
$31$		−	8.60927i		−	0.277718i	0.990312	−	0.138859i	$-0.0443435\pi$
$32$	5.65685			0.176777
$33$		0			0
$34$			33.2061i			0.976651i
$35$	18.7279	−	36.9164i	0.535083	−	1.05476i
$36$		0			0
$37$	−70.9117			−1.91653			−0.958266	−	0.285878i	$-0.907715\pi$
$37$	−70.9117			−1.91653			−0.958266	+	0.285878i	$0.907715\pi$
$38$			32.6118i			0.858205i
$39$		0			0
$40$		−	16.7262i		−	0.418154i
$41$			41.3951i			1.00964i	0.863225	+	0.504819i	$0.168441\pi$
$41$			41.3951i			1.00964i	−0.863225	+	0.504819i	$0.831559\pi$
$42$		0			0
$43$	10.4264			0.242475			0.121237	−	0.992624i	$-0.461314\pi$
$43$	10.4264			0.242475			0.121237	+	0.992624i	$0.461314\pi$
$44$	3.51472			0.0798800
$45$		0			0
$46$	−26.4853			−0.575767
$47$			38.6995i			0.823393i	0.911321	+	0.411696i	$0.135064\pi$
$47$			38.6995i			0.823393i	−0.911321	+	0.411696i	$0.864936\pi$
$48$		0			0
$49$	28.9411	+	39.5400i	0.590635	+	0.806939i
$50$	−14.1005			−0.282010
$51$		0			0
$52$		−	37.5108i		−	0.721361i
$53$	37.0294			0.698669			0.349334	−	0.936998i	$-0.386408\pi$
$53$	37.0294			0.698669			0.349334	+	0.936998i	$0.386408\pi$
$54$		0			0
$55$		−	10.3923i		−	0.188951i
$56$	17.6569	+	8.95743i	0.315301	+	0.159954i
$57$		0			0
$58$	−42.4264			−0.731490
$59$		−	97.4872i		−	1.65233i	−0.563431	−	0.826163i	$-0.690519\pi$
$59$		−	97.4872i		−	1.65233i	0.563431	−	0.826163i	$-0.309481\pi$
$60$		0			0
$61$		−	16.7262i		−	0.274199i	−0.990557	−	0.137100i	$-0.956222\pi$
$61$		−	16.7262i		−	0.274199i	0.990557	−	0.137100i	$-0.0437781\pi$
$62$		−	12.1753i		−	0.196376i
$63$		0			0
$64$	8.00000			0.125000
$65$	−110.912			−1.70633
$66$		0			0
$67$	60.9706			0.910008			0.455004	−	0.890489i	$-0.349638\pi$
$67$	60.9706			0.910008			0.455004	+	0.890489i	$0.349638\pi$
$68$			46.9606i			0.690597i
$69$		0			0
$70$	26.4853	−	52.2077i	0.378361	−	0.745824i
$71$	110.610			1.55789			0.778945	−	0.627092i	$-0.215755\pi$
$71$	110.610			1.55789			0.778945	+	0.627092i	$0.215755\pi$
$72$		0			0
$73$			56.7585i			0.777514i	0.921340	+	0.388757i	$0.127095\pi$
$73$			56.7585i			0.777514i	−0.921340	+	0.388757i	$0.872905\pi$
$74$	−100.284			−1.35519
$75$		0			0
$76$			46.1200i			0.606843i
$77$	10.9706	+	5.56543i	0.142475	+	0.0722783i
$78$		0			0
$79$	−69.8234			−0.883840			−0.441920	−	0.897054i	$-0.645703\pi$
$79$	−69.8234			−0.883840			−0.441920	+	0.897054i	$0.645703\pi$
$80$		−	23.6544i		−	0.295680i
$81$		0			0
$82$			58.5416i			0.713922i
$83$			6.43583i			0.0775401i	0.999248	+	0.0387701i	$0.0123440\pi$
$83$			6.43583i			0.0775401i	−0.999248	+	0.0387701i	$0.987656\pi$
$84$		0			0
$85$	138.853			1.63356
$86$	14.7452			0.171455
$87$		0			0
$88$	4.97056			0.0564837
$89$		−	42.0915i		−	0.472938i	−0.971639	−	0.236469i	$-0.924010\pi$
$89$		−	42.0915i		−	0.472938i	0.971639	−	0.236469i	$-0.0759901\pi$
$90$		0			0
$91$	59.3970	−	117.083i	0.652714	−	1.28663i
$92$	−37.4558			−0.407129
$93$		0			0
$94$			54.7293i			0.582227i
$95$	136.368			1.43545
$96$		0			0
$97$		−	51.7153i		−	0.533148i	−0.963814	−	0.266574i	$-0.914108\pi$
$97$		−	51.7153i		−	0.533148i	0.963814	−	0.266574i	$-0.0858916\pi$
$98$	40.9289	+	55.9180i	0.417642	+	0.570592i
$99$		0			0
$100$	−19.9411			−0.199411
$101$			6.60991i			0.0654447i	0.999464	+	0.0327223i	$0.0104177\pi$
$101$			6.60991i			0.0654447i	−0.999464	+	0.0327223i	$0.989582\pi$
$102$		0			0
$103$		−	175.871i		−	1.70748i	−0.520696	−	0.853742i	$-0.674327\pi$
$103$		−	175.871i		−	1.70748i	0.520696	−	0.853742i	$-0.325673\pi$
$104$		−	53.0482i		−	0.510079i
$105$		0			0
$106$	52.3675			0.494033
$107$	46.2426			0.432174			0.216087	−	0.976374i	$-0.430670\pi$
$107$	46.2426			0.432174			0.216087	+	0.976374i	$0.430670\pi$
$108$		0			0
$109$	−35.9411			−0.329735			−0.164868	−	0.986316i	$-0.552720\pi$
$109$	−35.9411			−0.329735			−0.164868	+	0.986316i	$0.552720\pi$
$110$		−	14.6969i		−	0.133609i
$111$		0			0
$112$	24.9706	+	12.6677i	0.222951	+	0.113105i
$113$	73.0294			0.646278			0.323139	−	0.946351i	$-0.395262\pi$
$113$	73.0294			0.646278			0.323139	+	0.946351i	$0.395262\pi$
$114$		0			0
$115$			110.749i			0.963037i
$116$	−60.0000			−0.517241
$117$		0			0
$118$		−	137.868i		−	1.16837i
$119$	−74.3604	+	146.579i	−0.624877	+	1.23176i
$120$		0			0
$121$	−117.912			−0.974477
$122$		−	23.6544i		−	0.193888i
$123$		0			0
$124$		−	17.2185i		−	0.138859i
$125$		−	88.8780i		−	0.711024i
$126$		0			0
$127$	89.9411			0.708198			0.354099	−	0.935208i	$-0.384788\pi$
$127$	89.9411			0.708198			0.354099	+	0.935208i	$0.384788\pi$
$128$	11.3137			0.0883883
$129$		0			0
$130$	−156.853			−1.20656
$131$			12.1753i			0.0929415i	0.998920	+	0.0464708i	$0.0147974\pi$
$131$			12.1753i			0.0929415i	−0.998920	+	0.0464708i	$0.985203\pi$
$132$		0			0
$133$	−73.0294	+	143.955i	−0.549094	+	1.08237i
$134$	86.2254			0.643473
$135$		0			0
$136$			66.4123i			0.488326i
$137$	−165.765			−1.20996			−0.604980	−	0.796241i	$-0.706819\pi$
$137$	−165.765			−1.20996			−0.604980	+	0.796241i	$0.706819\pi$
$138$		0			0
$139$			220.514i			1.58643i	0.608941	+	0.793215i	$0.291594\pi$
$139$			220.514i			1.58643i	−0.608941	+	0.793215i	$0.708406\pi$
$140$	37.4558	−	73.8329i	0.267542	−	0.527378i
$141$		0			0
$142$	156.426			1.10159
$143$		−	32.9600i		−	0.230489i
$144$		0			0
$145$			177.408i			1.22350i
$146$			80.2687i			0.549786i
$147$		0			0
$148$	−141.823			−0.958266
$149$	−210.853			−1.41512			−0.707560	−	0.706653i	$-0.750204\pi$
$149$	−210.853			−1.41512			−0.707560	+	0.706653i	$0.750204\pi$
$150$		0			0
$151$	−72.3675			−0.479255			−0.239628	−	0.970865i	$-0.577025\pi$
$151$	−72.3675			−0.479255			−0.239628	+	0.970865i	$0.577025\pi$
$152$			65.2236i			0.429103i
$153$		0			0
$154$	15.5147	+	7.87071i	0.100745	+	0.0511085i
$155$	−50.9117			−0.328463
$156$		0			0
$157$		−	233.674i		−	1.48837i	−0.667974	−	0.744184i	$-0.732838\pi$
$157$		−	233.674i		−	1.48837i	0.667974	−	0.744184i	$-0.267162\pi$
$158$	−98.7452			−0.624969
$159$		0			0
$160$		−	33.4523i		−	0.209077i
$161$	−116.912	−	59.3100i	−0.726160	−	0.368385i
$162$		0			0
$163$	−73.0883			−0.448395			−0.224197	−	0.974544i	$-0.571976\pi$
$163$	−73.0883			−0.448395			−0.224197	+	0.974544i	$0.571976\pi$
$164$			82.7903i			0.504819i
$165$		0			0
$166$			9.10164i			0.0548292i
$167$		−	39.3958i		−	0.235903i	−0.993019	−	0.117951i	$-0.962367\pi$
$167$		−	39.3958i		−	0.235903i	0.993019	−	0.117951i	$-0.0376327\pi$
$168$		0			0
$169$	−182.765			−1.08145
$170$	196.368			1.15510
$171$		0			0
$172$	20.8528			0.121237
$173$			23.8284i			0.137737i	0.997626	+	0.0688683i	$0.0219388\pi$
$173$			23.8284i			0.137737i	−0.997626	+	0.0688683i	$0.978061\pi$
$174$		0			0
$175$	−62.2426	−	31.5761i	−0.355672	−	0.180435i
$176$	7.02944			0.0399400
$177$		0			0
$178$		−	59.5263i		−	0.334417i
$179$	12.9045			0.0720924			0.0360462	−	0.999350i	$-0.488524\pi$
$179$	12.9045			0.0720924			0.0360462	+	0.999350i	$0.488524\pi$
$180$		0			0
$181$		−	65.3678i		−	0.361148i	−0.983561	−	0.180574i	$-0.942204\pi$
$181$		−	65.3678i		−	0.361148i	0.983561	−	0.180574i	$-0.0577955\pi$
$182$	84.0000	−	165.581i	0.461538	−	0.909783i
$183$		0			0
$184$	−52.9706			−0.287883
$185$			419.343i			2.26672i
$186$		0			0
$187$			41.2633i			0.220659i
$188$			77.3989i			0.411696i
$189$		0			0
$190$	192.853			1.01501
$191$	100.066			0.523906			0.261953	−	0.965081i	$-0.415633\pi$
$191$	100.066			0.523906			0.261953	+	0.965081i	$0.415633\pi$
$192$		0			0
$193$	78.9117			0.408869			0.204434	−	0.978880i	$-0.434464\pi$
$193$	78.9117			0.408869			0.204434	+	0.978880i	$0.434464\pi$
$194$		−	73.1365i		−	0.376992i
$195$		0			0
$196$	57.8823	+	79.0800i	0.295318	+	0.403469i
$197$	183.941			0.933711			0.466856	−	0.884334i	$-0.345387\pi$
$197$	183.941			0.933711			0.466856	+	0.884334i	$0.345387\pi$
$198$		0			0
$199$		−	170.029i		−	0.854419i	−0.904153	−	0.427210i	$-0.859497\pi$
$199$		−	170.029i		−	0.854419i	0.904153	−	0.427210i	$-0.140503\pi$
$200$	−28.2010			−0.141005
$201$		0			0
$202$			9.34783i			0.0462764i
$203$	−187.279	−	95.0079i	−0.922558	−	0.468019i
$204$		0			0
$205$	244.794			1.19412
$206$		−	248.719i		−	1.20737i
$207$		0			0
$208$		−	75.0215i		−	0.360680i
$209$			40.5247i			0.193898i
$210$		0			0
$211$	21.5736			0.102245			0.0511223	−	0.998692i	$-0.483720\pi$
$211$	21.5736			0.102245			0.0511223	+	0.998692i	$0.483720\pi$
$212$	74.0589			0.349334
$213$		0			0
$214$	65.3970			0.305593
$215$		−	61.6575i		−	0.286779i
$216$		0			0
$217$	27.2649	−	53.7446i	0.125645	−	0.247671i
$218$	−50.8284			−0.233158
$219$		0			0
$220$		−	20.7846i		−	0.0944755i
$221$	440.382			1.99268
$222$		0			0
$223$			119.359i			0.535240i	0.963525	+	0.267620i	$0.0862372\pi$
$223$			119.359i			0.535240i	−0.963525	+	0.267620i	$0.913763\pi$
$224$	35.3137	+	17.9149i	0.157650	+	0.0799770i
$225$		0			0
$226$	103.279			0.456988
$227$		−	169.843i		−	0.748207i	−0.927387	−	0.374103i	$-0.877951\pi$
$227$		−	169.843i		−	0.748207i	0.927387	−	0.374103i	$-0.122049\pi$
$228$		0			0
$229$			110.011i			0.480396i	0.970724	+	0.240198i	$0.0772124\pi$
$229$			110.011i			0.480396i	−0.970724	+	0.240198i	$0.922788\pi$
$230$			156.623i			0.680970i
$231$		0			0
$232$	−84.8528			−0.365745
$233$	−57.2649			−0.245772			−0.122886	−	0.992421i	$-0.539215\pi$
$233$	−57.2649			−0.245772			−0.122886	+	0.992421i	$0.539215\pi$
$234$		0			0
$235$	228.853			0.973842
$236$		−	194.974i		−	0.826163i
$237$		0			0
$238$	−105.161	+	207.294i	−0.441855	+	0.870983i
$239$	−281.522			−1.17792			−0.588958	−	0.808164i	$-0.700462\pi$
$239$	−281.522			−1.17792			−0.588958	+	0.808164i	$0.700462\pi$
$240$		0			0
$241$		−	168.306i		−	0.698366i	−0.937055	−	0.349183i	$-0.886459\pi$
$241$		−	168.306i		−	0.698366i	0.937055	−	0.349183i	$-0.113541\pi$
$242$	−166.752			−0.689059
$243$		0			0
$244$		−	33.4523i		−	0.137100i
$245$	233.823	−	171.146i	0.954381	−	0.698555i
$246$		0			0
$247$	432.500			1.75101
$248$		−	24.3507i		−	0.0981882i
$249$		0			0
$250$		−	125.692i		−	0.502770i
$251$			106.096i			0.422695i	0.977411	+	0.211348i	$0.0677852\pi$
$251$			106.096i			0.422695i	−0.977411	+	0.211348i	$0.932215\pi$
$252$		0			0
$253$	−32.9117			−0.130086
$254$	127.196			0.500771
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	290.462i		−	1.13020i	−0.825021	−	0.565102i	$-0.808837\pi$
$257$		−	290.462i		−	1.13020i	0.825021	−	0.565102i	$-0.191163\pi$
$258$		0			0
$259$	−442.676	−	224.572i	−1.70917	−	0.867074i
$260$	−221.823			−0.853167
$261$		0			0
$262$			17.2185i			0.0657196i
$263$	89.0223			0.338488			0.169244	−	0.985574i	$-0.445867\pi$
$263$	89.0223			0.338488			0.169244	+	0.985574i	$0.445867\pi$
$264$		0			0
$265$		−	218.977i		−	0.826328i
$266$	−103.279	+	203.584i	−0.388268	+	0.765352i
$267$		0			0
$268$	121.941			0.455004
$269$			191.498i			0.711888i	0.934507	+	0.355944i	$0.115841\pi$
$269$			191.498i			0.711888i	−0.934507	+	0.355944i	$0.884159\pi$
$270$		0			0
$271$			217.440i			0.802362i	0.915999	+	0.401181i	$0.131400\pi$
$271$			217.440i			0.802362i	−0.915999	+	0.401181i	$0.868600\pi$
$272$			93.9211i			0.345298i
$273$		0			0
$274$	−234.426			−0.855571
$275$	−17.5219			−0.0637159
$276$		0			0
$277$	290.676			1.04937			0.524686	−	0.851296i	$-0.324183\pi$
$277$	290.676			1.04937			0.524686	+	0.851296i	$0.324183\pi$
$278$			311.854i			1.12178i
$279$		0			0
$280$	52.9706	−	104.415i	0.189181	−	0.372912i
$281$	−18.8528			−0.0670919			−0.0335459	−	0.999437i	$-0.510680\pi$
$281$	−18.8528			−0.0670919			−0.0335459	+	0.999437i	$0.510680\pi$
$282$		0			0
$283$			401.734i			1.41955i	0.704426	+	0.709777i	$0.251204\pi$
$283$			401.734i			1.41955i	−0.704426	+	0.709777i	$0.748796\pi$
$284$	221.220			0.778945
$285$		0			0
$286$		−	46.6124i		−	0.162980i
$287$	−131.095	+	258.415i	−0.456779	+	0.900401i
$288$		0			0
$289$	−262.324			−0.907695
$290$			250.892i			0.865146i
$291$		0			0
$292$			113.517i			0.388757i
$293$		−	280.893i		−	0.958679i	−0.877629	−	0.479340i	$-0.840876\pi$
$293$		−	280.893i		−	0.958679i	0.877629	−	0.479340i	$-0.159124\pi$
$294$		0			0
$295$	−576.500			−1.95424
$296$	−200.569			−0.677596
$297$		0			0
$298$	−298.191			−1.00064
$299$			351.249i			1.17475i
$300$		0			0
$301$	65.0883	+	33.0197i	0.216240	+	0.109700i
$302$	−102.343			−0.338885
$303$		0			0
$304$			92.2401i			0.303421i
$305$	−98.9117			−0.324301
$306$		0			0
$307$		−	152.318i		−	0.496151i	−0.968741	−	0.248076i	$-0.920202\pi$
$307$		−	152.318i		−	0.496151i	0.968741	−	0.248076i	$-0.0797982\pi$
$308$	21.9411	+	11.1309i	0.0712374	+	0.0361392i
$309$		0			0
$310$	−72.0000			−0.232258
$311$		−	283.156i		−	0.910470i	−0.890371	−	0.455235i	$-0.849555\pi$
$311$		−	283.156i		−	0.910470i	0.890371	−	0.455235i	$-0.150445\pi$
$312$		0			0
$313$		−	48.5819i		−	0.155214i	−0.996984	−	0.0776069i	$-0.975272\pi$
$313$		−	48.5819i		−	0.155214i	0.996984	−	0.0776069i	$-0.0247279\pi$
$314$		−	330.465i		−	1.05244i
$315$		0			0
$316$	−139.647			−0.441920
$317$	578.029			1.82343			0.911717	−	0.410819i	$-0.134757\pi$
$317$	578.029			1.82343			0.911717	+	0.410819i	$0.134757\pi$
$318$		0			0
$319$	−52.7208			−0.165269
$320$		−	47.3087i		−	0.147840i
$321$		0			0
$322$	−165.338	−	83.8770i	−0.513472	−	0.260488i
$323$	−541.456			−1.67633
$324$		0			0
$325$			187.002i			0.575390i
$326$	−103.362			−0.317063
$327$		0			0
$328$			117.083i			0.356961i
$329$	−122.558	+	241.587i	−0.372518	+	0.734307i
$330$		0			0
$331$	332.368			1.00413			0.502066	−	0.864829i	$-0.332574\pi$
$331$	332.368			1.00413			0.502066	+	0.864829i	$0.332574\pi$
$332$			12.8717i			0.0387701i
$333$		0			0
$334$		−	55.7141i		−	0.166809i
$335$		−	360.555i		−	1.07628i
$336$		0			0
$337$	88.1766			0.261652			0.130826	−	0.991405i	$-0.458237\pi$
$337$	88.1766			0.261652			0.130826	+	0.991405i	$0.458237\pi$
$338$	−258.468			−0.764698
$339$		0			0
$340$	277.706			0.816781
$341$		−	15.1296i		−	0.0443683i
$342$		0			0
$343$	55.4487	+	338.488i	0.161658	+	0.986847i
$344$	29.4903			0.0857277
$345$		0			0
$346$			33.6985i			0.0973945i
$347$	320.080			0.922422			0.461211	−	0.887291i	$-0.347415\pi$
$347$	320.080			0.922422			0.461211	+	0.887291i	$0.347415\pi$
$348$		0			0
$349$			333.046i			0.954287i	0.878825	+	0.477143i	$0.158328\pi$
$349$			333.046i			0.954287i	−0.878825	+	0.477143i	$0.841672\pi$
$350$	−88.0244	−	44.6553i	−0.251498	−	0.127587i
$351$		0			0
$352$	9.94113			0.0282418
$353$		−	655.712i		−	1.85754i	−0.370654	−	0.928771i	$-0.620866\pi$
$353$		−	655.712i		−	1.85754i	0.370654	−	0.928771i	$-0.379134\pi$
$354$		0			0
$355$		−	654.103i		−	1.84254i
$356$		−	84.1829i		−	0.236469i
$357$		0			0
$358$	18.2498			0.0509770
$359$	97.7574			0.272305			0.136152	−	0.990688i	$-0.456526\pi$
$359$	97.7574			0.272305			0.136152	+	0.990688i	$0.456526\pi$
$360$		0			0
$361$	−170.765			−0.473032
$362$		−	92.4440i		−	0.255370i
$363$		0			0
$364$	118.794	−	234.166i	0.326357	−	0.643314i
$365$	335.647			0.919580
$366$		0			0
$367$			321.057i			0.874815i	0.899263	+	0.437408i	$0.144103\pi$
$367$			321.057i			0.874815i	−0.899263	+	0.437408i	$0.855897\pi$
$368$	−74.9117			−0.203564
$369$		0			0
$370$			593.040i			1.60281i
$371$	231.161	+	117.270i	0.623077	+	0.316091i
$372$		0			0
$373$	187.470			0.502601			0.251300	−	0.967909i	$-0.419142\pi$
$373$	187.470			0.502601			0.251300	+	0.967909i	$0.419142\pi$
$374$			58.3551i			0.156030i
$375$		0			0
$376$			109.459i			0.291113i
$377$			562.662i			1.49247i
$378$		0			0
$379$	−357.103			−0.942223			−0.471112	−	0.882074i	$-0.656147\pi$
$379$	−357.103			−0.942223			−0.471112	+	0.882074i	$0.656147\pi$
$380$	272.735			0.717724
$381$		0			0
$382$	141.515			0.370457
$383$			622.230i			1.62462i	0.583225	+	0.812311i	$0.301791\pi$
$383$			622.230i			1.62462i	−0.583225	+	0.812311i	$0.698209\pi$
$384$		0			0
$385$	32.9117	−	64.8754i	0.0854849	−	0.168508i
$386$	111.598			0.289114
$387$		0			0
$388$		−	103.431i		−	0.266574i
$389$	−227.470			−0.584756			−0.292378	−	0.956303i	$-0.594447\pi$
$389$	−227.470			−0.584756			−0.292378	+	0.956303i	$0.594447\pi$
$390$		0			0
$391$		−	439.737i		−	1.12465i
$392$	81.8579	+	111.836i	0.208821	+	0.285296i
$393$		0			0
$394$	260.132			0.660234
$395$			412.907i			1.04533i
$396$		0			0
$397$		−	720.329i		−	1.81443i	−0.420666	−	0.907216i	$-0.638204\pi$
$397$		−	720.329i		−	1.81443i	0.420666	−	0.907216i	$-0.361796\pi$
$398$		−	240.458i		−	0.604166i
$399$		0			0
$400$	−39.8823			−0.0997056
$401$	−697.176			−1.73859			−0.869296	−	0.494291i	$-0.835428\pi$
$401$	−697.176			−1.73859			−0.869296	+	0.494291i	$0.835428\pi$
$402$		0			0
$403$	−161.470			−0.400670
$404$			13.2198i			0.0327223i
$405$		0			0
$406$	−264.853	−	134.361i	−0.652347	−	0.330939i
$407$	−124.617			−0.306185
$408$		0			0
$409$		−	102.386i		−	0.250333i	−0.992136	−	0.125166i	$-0.960053\pi$
$409$		−	102.386i		−	0.250333i	0.992136	−	0.125166i	$-0.0399465\pi$
$410$	346.191			0.844368
$411$		0			0
$412$		−	351.742i		−	0.853742i
$413$	308.735	−	608.578i	0.747543	−	1.47355i
$414$		0			0
$415$	38.0589			0.0917081
$416$		−	106.096i		−	0.255040i
$417$		0			0
$418$			57.3106i			0.137107i
$419$			391.426i			0.934191i	0.884207	+	0.467095i	$0.154700\pi$
$419$			391.426i			0.934191i	−0.884207	+	0.467095i	$0.845300\pi$
$420$		0			0
$421$	354.441			0.841902			0.420951	−	0.907083i	$-0.361696\pi$
$421$	354.441			0.841902			0.420951	+	0.907083i	$0.361696\pi$
$422$	30.5097			0.0722978
$423$		0			0
$424$	104.735			0.247017
$425$		−	234.112i		−	0.550851i
$426$		0			0
$427$	52.9706	−	104.415i	0.124053	−	0.244533i
$428$	92.4853			0.216087
$429$		0			0
$430$		−	87.1969i		−	0.202783i
$431$	−585.286			−1.35797			−0.678987	−	0.734151i	$-0.737581\pi$
$431$	−585.286			−1.35797			−0.678987	+	0.734151i	$0.737581\pi$
$432$		0			0
$433$			392.207i			0.905789i	0.891564	+	0.452895i	$0.149609\pi$
$433$			392.207i			0.905789i	−0.891564	+	0.452895i	$0.850391\pi$
$434$	38.5584	−	76.0063i	0.0888443	−	0.175130i
$435$		0			0
$436$	−71.8823			−0.164868
$437$		−	431.866i		−	0.988252i
$438$		0			0
$439$			392.513i			0.894106i	0.894507	+	0.447053i	$0.147527\pi$
$439$			392.513i			0.894106i	−0.894507	+	0.447053i	$0.852473\pi$
$440$		−	29.3939i		−	0.0668043i
$441$		0			0
$442$	622.794			1.40904
$443$	814.742			1.83915			0.919574	−	0.392918i	$-0.128534\pi$
$443$	814.742			1.83915			0.919574	+	0.392918i	$0.128534\pi$
$444$		0			0
$445$	−248.912			−0.559352
$446$			168.798i			0.378472i
$447$		0			0
$448$	49.9411	+	25.3354i	0.111476	+	0.0565523i
$449$	−180.323			−0.401610			−0.200805	−	0.979631i	$-0.564356\pi$
$449$	−180.323			−0.401610			−0.200805	+	0.979631i	$0.564356\pi$
$450$		0			0
$451$			72.7461i			0.161300i
$452$	146.059			0.323139
$453$		0			0
$454$		−	240.194i		−	0.529062i
$455$	−692.382	−	351.249i	−1.52172	−	0.771977i
$456$		0			0
$457$	280.177			0.613078			0.306539	−	0.951858i	$-0.400829\pi$
$457$	280.177			0.613078			0.306539	+	0.951858i	$0.400829\pi$
$458$			155.579i			0.339691i
$459$		0			0
$460$			221.499i			0.481519i
$461$			406.297i			0.881338i	0.897670	+	0.440669i	$0.145259\pi$
$461$			406.297i			0.881338i	−0.897670	+	0.440669i	$0.854741\pi$
$462$		0			0
$463$	457.470			0.988056			0.494028	−	0.869446i	$-0.335524\pi$
$463$	457.470			0.988056			0.494028	+	0.869446i	$0.335524\pi$
$464$	−120.000			−0.258621
$465$		0			0
$466$	−80.9848			−0.173787
$467$		−	643.711i		−	1.37840i	−0.724573	−	0.689198i	$-0.757963\pi$
$467$		−	643.711i		−	1.37840i	0.724573	−	0.689198i	$-0.242037\pi$
$468$		0			0
$469$	380.617	+	193.089i	0.811551	+	0.411705i
$470$	323.647			0.688610
$471$		0			0
$472$		−	275.735i		−	0.584185i
$473$	18.3229			0.0387377
$474$		0			0
$475$		−	229.921i		−	0.484045i
$476$	−148.721	+	293.158i	−0.312439	+	0.615878i
$477$		0			0
$478$	−398.132			−0.832912
$479$			168.535i			0.351847i	0.984404	+	0.175924i	$0.0562912\pi$
$479$			168.535i			0.351847i	−0.984404	+	0.175924i	$0.943709\pi$
$480$		0			0
$481$			1329.98i			2.76502i
$482$		−	238.021i		−	0.493819i
$483$		0			0
$484$	−235.823			−0.487238
$485$	−305.823			−0.630564
$486$		0			0
$487$	−2.77965			−0.00570771			−0.00285385	−	0.999996i	$-0.500908\pi$
$487$	−2.77965			−0.00570771			−0.00285385	+	0.999996i	$0.500908\pi$
$488$		−	47.3087i		−	0.0969441i
$489$		0			0
$490$	330.676	−	242.037i	0.674849	−	0.493953i
$491$	247.477			0.504027			0.252014	−	0.967724i	$-0.418907\pi$
$491$	247.477			0.504027			0.252014	+	0.967724i	$0.418907\pi$
$492$		0			0
$493$		−	704.409i		−	1.42882i
$494$	611.647			1.23815
$495$		0			0
$496$		−	34.4371i		−	0.0694296i
$497$	690.500	+	350.295i	1.38934	+	0.704818i
$498$		0			0
$499$	−483.426			−0.968789			−0.484394	−	0.874850i	$-0.660960\pi$
$499$	−483.426			−0.968789			−0.484394	+	0.874850i	$0.660960\pi$
$500$		−	177.756i		−	0.355512i
$501$		0			0
$502$			150.043i			0.298891i
$503$			58.7033i			0.116706i	0.998296	+	0.0583532i	$0.0185849\pi$
$503$			58.7033i			0.116706i	−0.998296	+	0.0583532i	$0.981415\pi$
$504$		0			0
$505$	39.0883			0.0774026
$506$	−46.5442			−0.0919845
$507$		0			0
$508$	179.882			0.354099
$509$			68.8793i			0.135323i	0.997708	+	0.0676614i	$0.0215537\pi$
$509$			68.8793i			0.135323i	−0.997708	+	0.0676614i	$0.978446\pi$
$510$		0			0
$511$	−179.750	+	354.323i	−0.351762	+	0.693392i
$512$	22.6274			0.0441942
$513$		0			0
$514$		−	410.776i		−	0.799175i
$515$	−1040.03			−2.01947
$516$		0			0
$517$			68.0089i			0.131545i
$518$	−626.039	−	317.593i	−1.20857	−	0.613114i
$519$		0			0
$520$	−313.706			−0.603280
$521$			292.720i			0.561843i	0.959731	+	0.280922i	$0.0906401\pi$
$521$			292.720i			0.561843i	−0.959731	+	0.280922i	$0.909360\pi$
$522$		0			0
$523$		−	493.056i		−	0.942746i	−0.881934	−	0.471373i	$-0.843759\pi$
$523$		−	493.056i		−	0.942746i	0.881934	−	0.471373i	$-0.156241\pi$
$524$			24.3507i			0.0464708i
$525$		0			0
$526$	125.897			0.239347
$527$	202.148			0.383583
$528$		0			0
$529$	−178.265			−0.336985
$530$		−	309.680i		−	0.584302i
$531$		0			0
$532$	−146.059	+	287.911i	−0.274547	+	0.541186i
$533$	776.382			1.45663
$534$		0			0
$535$		−	273.460i		−	0.511140i
$536$	172.451			0.321737
$537$		0			0
$538$			270.819i			0.503381i
$539$	50.8600	+	69.4860i	0.0943598	+	0.128916i
$540$		0			0
$541$	−1037.85			−1.91840			−0.959198	−	0.282736i	$-0.908758\pi$
$541$	−1037.85			−1.91840			−0.959198	+	0.282736i	$0.908758\pi$
$542$			307.507i			0.567356i
$543$		0			0
$544$			132.825i			0.244163i
$545$			212.541i			0.389984i
$546$		0			0
$547$	−130.530			−0.238629			−0.119314	−	0.992857i	$-0.538070\pi$
$547$	−130.530			−0.238629			−0.119314	+	0.992857i	$0.538070\pi$
$548$	−331.529			−0.604980
$549$		0			0
$550$	−24.7797			−0.0450539
$551$		−	691.801i		−	1.25554i
$552$		0			0
$553$	−435.882	−	221.126i	−0.788214	−	0.399866i
$554$	411.078			0.742018
$555$		0			0
$556$			441.028i			0.793215i
$557$	−665.147			−1.19416			−0.597080	−	0.802182i	$-0.703673\pi$
$557$	−665.147			−1.19416			−0.597080	+	0.802182i	$0.703673\pi$
$558$		0			0
$559$		−	195.551i		−	0.349823i
$560$	74.9117	−	147.666i	0.133771	−	0.263689i
$561$		0			0
$562$	−26.6619			−0.0474411
$563$			829.295i			1.47299i	0.676441	+	0.736497i	$0.263521\pi$
$563$			829.295i			1.47299i	−0.676441	+	0.736497i	$0.736479\pi$
$564$		0			0
$565$		−	431.866i		−	0.764365i
$566$			568.137i			1.00378i
$567$		0			0
$568$	312.853			0.550797
$569$	−706.971			−1.24248			−0.621240	−	0.783621i	$-0.713371\pi$
$569$	−706.971			−1.24248			−0.621240	+	0.783621i	$0.713371\pi$
$570$		0			0
$571$	−366.912			−0.642577			−0.321289	−	0.946981i	$-0.604116\pi$
$571$	−366.912			−0.642577			−0.321289	+	0.946981i	$0.604116\pi$
$572$		−	65.9199i		−	0.115245i
$573$		0			0
$574$	−185.397	+	365.454i	−0.322991	+	0.636679i
$575$	186.728			0.324744
$576$		0			0
$577$			390.357i			0.676528i	0.941051	+	0.338264i	$0.109840\pi$
$577$			390.357i			0.676528i	−0.941051	+	0.338264i	$0.890160\pi$
$578$	−370.982			−0.641837
$579$		0			0
$580$			354.815i			0.611751i
$581$	−20.3818	+	40.1766i	−0.0350806	+	0.0691507i
$582$		0			0
$583$	65.0740			0.111619
$584$			160.537i			0.274893i
$585$		0			0
$586$		−	397.243i		−	0.677889i
$587$		−	702.499i		−	1.19676i	−0.801212	−	0.598381i	$-0.795811\pi$
$587$		−	702.499i		−	1.19676i	0.801212	−	0.598381i	$-0.204189\pi$
$588$		0			0
$589$	198.530			0.337063
$590$	−815.294			−1.38185
$591$		0			0
$592$	−283.647			−0.479133
$593$			942.519i			1.58941i	0.606997	+	0.794704i	$0.292374\pi$
$593$			942.519i			1.58941i	−0.606997	+	0.794704i	$0.707626\pi$
$594$		0			0
$595$	866.808	+	439.737i	1.45682	+	0.739054i
$596$	−421.706			−0.707560
$597$		0			0
$598$			496.742i			0.830672i
$599$	952.109			1.58950			0.794749	−	0.606939i	$-0.207603\pi$
$599$	952.109			1.58950			0.794749	+	0.606939i	$0.207603\pi$
$600$		0			0
$601$		−	729.804i		−	1.21432i	−0.794581	−	0.607158i	$-0.792310\pi$
$601$		−	729.804i		−	1.21432i	0.794581	−	0.607158i	$-0.207690\pi$
$602$	92.0488	+	46.6969i	0.152905	+	0.0775696i
$603$		0			0
$604$	−144.735			−0.239628
$605$			697.282i			1.15253i
$606$		0			0
$607$			1006.34i			1.65789i	0.559332	+	0.828944i	$0.311058\pi$
$607$			1006.34i			1.65789i	−0.559332	+	0.828944i	$0.688942\pi$
$608$			130.447i			0.214551i
$609$		0			0
$610$	−139.882			−0.229315
$611$	725.823			1.18793
$612$		0			0
$613$	−199.588			−0.325592			−0.162796	−	0.986660i	$-0.552051\pi$
$613$	−199.588			−0.325592			−0.162796	+	0.986660i	$0.552051\pi$
$614$		−	215.411i		−	0.350832i
$615$		0			0
$616$	31.0294	+	15.7414i	0.0503725	+	0.0255542i
$617$	353.294			0.572599			0.286299	−	0.958140i	$-0.407575\pi$
$617$	353.294			0.572599			0.286299	+	0.958140i	$0.407575\pi$
$618$		0			0
$619$			56.2064i			0.0908020i	0.998969	+	0.0454010i	$0.0144566\pi$
$619$			56.2064i			0.0908020i	−0.998969	+	0.0454010i	$0.985543\pi$
$620$	−101.823			−0.164231
$621$		0			0
$622$		−	400.443i		−	0.643799i
$623$	133.301	−	262.762i	0.213966	−	0.421769i
$624$		0			0
$625$	−774.852			−1.23976
$626$		−	68.7052i		−	0.109753i
$627$		0			0
$628$		−	467.348i		−	0.744184i
$629$		−	1665.03i		−	2.64710i
$630$		0			0
$631$	807.322			1.27943			0.639716	−	0.768611i	$-0.279052\pi$
$631$	807.322			1.27943			0.639716	+	0.768611i	$0.279052\pi$
$632$	−197.490			−0.312485
$633$		0			0
$634$	817.456			1.28936
$635$		−	531.875i		−	0.837599i
$636$		0			0
$637$	741.588	−	542.802i	1.16419	−	0.852122i
$638$	−74.5584			−0.116863
$639$		0			0
$640$		−	66.9046i		−	0.104539i
$641$	−1016.35			−1.58557			−0.792786	−	0.609500i	$-0.791370\pi$
$641$	−1016.35			−1.58557			−0.792786	+	0.609500i	$0.791370\pi$
$642$		0			0
$643$			404.688i			0.629375i	0.949195	+	0.314687i	$0.101900\pi$
$643$			404.688i			0.629375i	−0.949195	+	0.314687i	$0.898100\pi$
$644$	−233.823	−	118.620i	−0.363080	−	0.184193i
$645$		0			0
$646$	−765.734			−1.18535
$647$		−	940.604i		−	1.45379i	−0.686747	−	0.726896i	$-0.740962\pi$
$647$		−	940.604i		−	1.45379i	0.686747	−	0.726896i	$-0.259038\pi$
$648$		0			0
$649$		−	171.320i		−	0.263975i
$650$			264.460i			0.406862i
$651$		0			0
$652$	−146.177			−0.224197
$653$	−731.970			−1.12093			−0.560467	−	0.828177i	$-0.689378\pi$
$653$	−731.970			−1.12093			−0.560467	+	0.828177i	$0.689378\pi$
$654$		0			0
$655$	72.0000			0.109924
$656$			165.581i			0.252409i
$657$		0			0
$658$	−173.324	+	341.655i	−0.263410	+	0.519233i
$659$	−904.316			−1.37225			−0.686127	−	0.727481i	$-0.740691\pi$
$659$	−904.316			−1.37225			−0.686127	+	0.727481i	$0.740691\pi$
$660$		0			0
$661$			335.881i			0.508141i	0.967186	+	0.254070i	$0.0817695\pi$
$661$			335.881i			0.508141i	−0.967186	+	0.254070i	$0.918231\pi$
$662$	470.039			0.710028
$663$		0			0
$664$			18.2033i			0.0274146i
$665$	851.294	+	431.866i	1.28014	+	0.649423i
$666$		0			0
$667$	561.838			0.842335
$668$		−	78.7916i		−	0.117951i
$669$		0			0
$670$		−	509.902i		−	0.761047i
$671$		−	29.3939i		−	0.0438061i
$672$		0			0
$673$	1191.44			1.77034			0.885171	−	0.465266i	$-0.154041\pi$
$673$	1191.44			1.77034			0.885171	+	0.465266i	$0.154041\pi$
$674$	124.701			0.185016
$675$		0			0
$676$	−365.529			−0.540723
$677$			1211.07i			1.78888i	0.447186	+	0.894441i	$0.352426\pi$
$677$			1211.07i			1.78888i	−0.447186	+	0.894441i	$0.647574\pi$
$678$		0			0
$679$	163.779	−	322.840i	0.241206	−	0.475464i
$680$	392.735			0.577552
$681$		0			0
$682$		−	21.3965i		−	0.0313731i
$683$	1233.89			1.80657			0.903287	−	0.429038i	$-0.141147\pi$
$683$	1233.89			1.80657			0.903287	+	0.429038i	$0.141147\pi$
$684$		0			0
$685$			980.264i			1.43104i
$686$	78.4163	+	478.695i	0.114309	+	0.697806i
$687$		0			0
$688$	41.7056			0.0606186
$689$		−	694.501i		−	1.00798i
$690$		0			0
$691$			86.7045i			0.125477i	0.998030	+	0.0627384i	$0.0199834\pi$
$691$			86.7045i			0.125477i	−0.998030	+	0.0627384i	$0.980017\pi$
$692$			47.6569i			0.0688683i
$693$		0			0
$694$	452.662			0.652251
$695$	1304.03			1.87630
$696$		0			0
$697$	−971.970			−1.39450
$698$			470.998i			0.674783i
$699$		0			0
$700$	−124.485	−	63.1521i	−0.177836	−	0.0902173i
$701$	149.147			0.212763			0.106382	−	0.994325i	$-0.466073\pi$
$701$	149.147			0.212763			0.106382	+	0.994325i	$0.466073\pi$
$702$		0			0
$703$		−	1635.22i		−	2.32607i
$704$	14.0589			0.0199700
$705$		0			0
$706$		−	927.317i		−	1.31348i
$707$	−20.9331	+	41.2633i	−0.0296084	+	0.0583639i
$708$		0			0
$709$	189.647			0.267485			0.133742	−	0.991016i	$-0.457301\pi$
$709$	189.647			0.267485			0.133742	+	0.991016i	$0.457301\pi$
$710$		−	925.042i		−	1.30288i
$711$		0			0
$712$		−	119.053i		−	0.167209i
$713$			161.234i			0.226134i
$714$		0			0
$715$	−194.912			−0.272604
$716$	25.8091			0.0360462
$717$		0			0
$718$	138.250			0.192548
$719$		−	12.0064i		−	0.0166987i	−0.999965	−	0.00834937i	$-0.997342\pi$
$719$		−	12.0064i		−	0.0166987i	0.999965	−	0.00834937i	$-0.00265772\pi$
$720$		0			0
$721$	556.971	−	1097.90i	0.772497	−	1.52274i
$722$	−241.497			−0.334484
$723$		0			0
$724$		−	130.736i		−	0.180574i
$725$	299.117			0.412575
$726$		0			0
$727$			417.169i			0.573823i	0.957957	+	0.286911i	$0.0926286\pi$
$727$			417.169i			0.573823i	−0.957957	+	0.286911i	$0.907371\pi$
$728$	168.000	−	331.161i	0.230769	−	0.454892i
$729$		0			0
$730$	474.676			0.650241
$731$			244.815i			0.334904i
$732$		0			0
$733$		−	1286.99i		−	1.75578i	−0.478859	−	0.877892i	$-0.658949\pi$
$733$		−	1286.99i		−	1.75578i	0.478859	−	0.877892i	$-0.341051\pi$
$734$			454.043i			0.618588i
$735$		0			0
$736$	−105.941			−0.143942
$737$	107.147			0.145383
$738$		0			0
$739$	1333.47			1.80443			0.902213	−	0.431292i	$-0.141942\pi$
$739$	1333.47			1.80443			0.902213	+	0.431292i	$0.141942\pi$
$740$			838.685i			1.13336i
$741$		0			0
$742$	326.912	+	165.844i	0.440582	+	0.223510i
$743$	776.476			1.04506			0.522528	−	0.852622i	$-0.324989\pi$
$743$	776.476			1.04506			0.522528	+	0.852622i	$0.324989\pi$
$744$		0			0
$745$			1246.90i			1.67369i
$746$	265.123			0.355392
$747$		0			0
$748$			82.5266i			0.110330i
$749$	288.676	+	146.447i	0.385415	+	0.195524i
$750$		0			0
$751$	48.8385			0.0650313			0.0325157	−	0.999471i	$-0.489648\pi$
$751$	48.8385			0.0650313			0.0325157	+	0.999471i	$0.489648\pi$
$752$			154.798i			0.205848i
$753$		0			0
$754$			795.724i			1.05534i
$755$			427.952i			0.566824i
$756$		0			0
$757$	−1279.47			−1.69019			−0.845093	−	0.534620i	$-0.820455\pi$
$757$	−1279.47			−1.69019			−0.845093	+	0.534620i	$0.820455\pi$
$758$	−505.019			−0.666252
$759$		0			0
$760$	385.706			0.507507
$761$		−	1316.12i		−	1.72947i	−0.502231	−	0.864734i	$-0.667487\pi$
$761$		−	1316.12i		−	1.72947i	0.502231	−	0.864734i	$-0.332513\pi$
$762$		0			0
$763$	−224.368	−	113.823i	−0.294060	−	0.149178i
$764$	200.132			0.261953
$765$		0			0
$766$			879.966i			1.14878i
$767$	−1828.41			−2.38385
$768$		0			0
$769$			110.324i			0.143464i	0.997424	+	0.0717320i	$0.0228526\pi$
$769$			110.324i			0.143464i	−0.997424	+	0.0717320i	$0.977147\pi$
$770$	46.5442	−	91.7477i	0.0604470	−	0.119153i
$771$		0			0
$772$	157.823			0.204434
$773$		−	717.634i		−	0.928375i	−0.885737	−	0.464187i	$-0.846346\pi$
$773$		−	717.634i		−	0.928375i	0.885737	−	0.464187i	$-0.153654\pi$
$774$		0			0
$775$			85.8392i			0.110760i
$776$		−	146.273i		−	0.188496i
$777$		0			0
$778$	−321.691			−0.413485
$779$	−954.573			−1.22538
$780$		0			0
$781$	194.382			0.248888
$782$		−	621.882i		−	0.795245i
$783$		0			0
$784$	115.765	+	158.160i	0.147659	+	0.201735i
$785$	−1381.85			−1.76032
$786$		0			0
$787$			347.191i			0.441158i	0.975369	+	0.220579i	$0.0707946\pi$
$787$			347.191i			0.441158i	−0.975369	+	0.220579i	$0.929205\pi$
$788$	367.882			0.466856
$789$		0			0
$790$			583.939i			0.739163i
$791$	455.897	+	231.279i	0.576355	+	0.292388i
$792$		0			0
$793$	−313.706			−0.395593
$794$		−	1018.70i		−	1.28300i
$795$		0			0
$796$		−	340.059i		−	0.427210i
$797$			361.246i			0.453257i	0.973981	+	0.226629i	$0.0727704\pi$
$797$			361.246i			0.453257i	−0.973981	+	0.226629i	$0.927230\pi$
$798$		0			0
$799$	−908.674			−1.13726
$800$	−56.4020			−0.0705025
$801$		0			0
$802$	−985.955			−1.22937
$803$			99.7451i			0.124216i
$804$		0			0
$805$	−350.735	+	691.368i	−0.435696	+	0.858842i
$806$	−228.353			−0.283317
$807$		0			0
$808$			18.6957i			0.0231382i
$809$	113.147			0.139861			0.0699303	−	0.997552i	$-0.477722\pi$
$809$	113.147			0.139861			0.0699303	+	0.997552i	$0.477722\pi$
$810$		0			0
$811$		−	134.182i		−	0.165453i	−0.996572	−	0.0827264i	$-0.973637\pi$
$811$		−	134.182i		−	0.165453i	0.996572	−	0.0827264i	$-0.0263628\pi$
$812$	−374.558	−	190.016i	−0.461279	−	0.234010i
$813$		0			0
$814$	−176.235			−0.216506
$815$			432.214i			0.530324i
$816$		0			0
$817$			240.433i			0.294288i
$818$		−	144.796i		−	0.177012i
$819$		0			0
$820$	489.588			0.597058
$821$	−491.677			−0.598876			−0.299438	−	0.954116i	$-0.596799\pi$
$821$	−491.677			−0.598876			−0.299438	+	0.954116i	$0.596799\pi$
$822$		0			0
$823$	−941.852			−1.14441			−0.572207	−	0.820110i	$-0.693912\pi$
$823$	−941.852			−1.14441			−0.572207	+	0.820110i	$0.693912\pi$
$824$		−	497.438i		−	0.603687i
$825$		0			0
$826$	436.617	−	860.659i	0.528592	−	1.04196i
$827$	−966.978			−1.16926			−0.584630	−	0.811300i	$-0.698760\pi$
$827$	−966.978			−1.16926			−0.584630	+	0.811300i	$0.698760\pi$
$828$		0			0
$829$			1185.53i			1.43007i	0.699088	+	0.715035i	$0.253589\pi$
$829$			1185.53i			1.43007i	−0.699088	+	0.715035i	$0.746411\pi$
$830$	53.8234			0.0648474
$831$		0			0
$832$		−	150.043i		−	0.180340i
$833$	−928.410	+	679.546i	−1.11454	+	0.815781i
$834$		0			0
$835$	−232.971			−0.279007
$836$			81.0495i			0.0969491i
$837$		0			0
$838$			553.560i			0.660573i
$839$			1376.91i			1.64113i	0.571550	+	0.820567i	$0.306342\pi$
$839$			1376.91i			1.64113i	−0.571550	+	0.820567i	$0.693658\pi$
$840$		0			0
$841$	59.0000			0.0701546
$842$	501.255			0.595315
$843$		0			0
$844$	43.1472			0.0511223
$845$			1080.79i			1.27905i
$846$		0			0
$847$	−736.080	−	373.418i	−0.869044	−	0.440871i
$848$	148.118			0.174667
$849$		0			0
$850$		−	331.084i		−	0.389510i
$851$	1328.03			1.56055
$852$		0			0
$853$			175.006i			0.205165i	0.994725	+	0.102582i	$0.0327105\pi$
$853$			175.006i			0.205165i	−0.994725	+	0.102582i	$0.967289\pi$
$854$	74.9117	−	147.666i	0.0877186	−	0.172911i
$855$		0			0
$856$	130.794			0.152797
$857$		−	61.7471i		−	0.0720503i	−0.999351	−	0.0360252i	$-0.988530\pi$
$857$		−	61.7471i		−	0.0720503i	0.999351	−	0.0360252i	$-0.0114696\pi$
$858$		0			0
$859$			191.306i			0.222708i	0.993781	+	0.111354i	$0.0355188\pi$
$859$			191.306i			0.222708i	−0.993781	+	0.111354i	$0.964481\pi$
$860$		−	123.315i		−	0.143390i
$861$		0			0
$862$	−827.720			−0.960232
$863$	494.507			0.573009			0.286504	−	0.958079i	$-0.407507\pi$
$863$	494.507			0.573009			0.286504	+	0.958079i	$0.407507\pi$
$864$		0			0
$865$	140.912			0.162904
$866$			554.664i			0.640490i
$867$		0			0
$868$	54.5299	−	107.489i	0.0628224	−	0.123835i
$869$	−122.705			−0.141202
$870$		0			0
$871$		−	1143.53i		−	1.31289i
$872$	−101.657			−0.116579
$873$		0			0
$874$		−	610.751i		−	0.698800i
$875$	281.470	−	554.833i	0.321680	−	0.634095i
$876$		0			0
$877$	−454.353			−0.518077			−0.259038	−	0.965867i	$-0.583406\pi$
$877$	−454.353			−0.518077			−0.259038	+	0.965867i	$0.583406\pi$
$878$			555.097i			0.632229i
$879$		0			0
$880$		−	41.5692i		−	0.0472377i
$881$			143.493i			0.162875i	0.996678	+	0.0814375i	$0.0259511\pi$
$881$			143.493i			0.162875i	−0.996678	+	0.0814375i	$0.974049\pi$
$882$		0			0
$883$	−927.986			−1.05095			−0.525473	−	0.850810i	$-0.676112\pi$
$883$	−927.986			−1.05095			−0.525473	+	0.850810i	$0.676112\pi$
$884$	880.764			0.996339
$885$		0			0
$886$	1152.22			1.30047
$887$			958.265i			1.08034i	0.841555	+	0.540172i	$0.181641\pi$
$887$			958.265i			1.08034i	−0.841555	+	0.540172i	$0.818359\pi$
$888$		0			0
$889$	561.470	+	284.837i	0.631575	+	0.320402i
$890$	−352.014			−0.395522
$891$		0			0
$892$			238.717i			0.267620i
$893$	−892.410			−0.999340
$894$		0			0
$895$		−	76.3122i		−	0.0852650i
$896$	70.6274	+	35.8297i	0.0788252	+	0.0399885i
$897$		0			0
$898$	−255.015			−0.283981
$899$			258.278i			0.287295i
$900$		0			0
$901$			869.462i			0.964996i
$902$			102.879i			0.114056i
$903$		0			0
$904$	206.558			0.228494
$905$	−386.558			−0.427136
$906$		0			0
$907$	−552.721			−0.609394			−0.304697	−	0.952449i	$-0.598555\pi$
$907$	−552.721			−0.609394			−0.304697	+	0.952449i	$0.598555\pi$
$908$		−	339.686i		−	0.374103i
$909$		0			0
$910$	−979.176	−	496.742i	−1.07602	−	0.545870i
$911$	−142.742			−0.156687			−0.0783437	−	0.996926i	$-0.524963\pi$
$911$	−142.742			−0.156687			−0.0783437	+	0.996926i	$0.524963\pi$
$912$		0			0
$913$			11.3101i			0.0123878i
$914$	396.230			0.433512
$915$		0			0
$916$			220.021i			0.240198i
$917$	−38.5584	+	76.0063i	−0.0420485	+	0.0828858i
$918$		0			0
$919$	1086.45			1.18221			0.591107	−	0.806593i	$-0.298691\pi$
$919$	1086.45			1.18221			0.591107	+	0.806593i	$0.298691\pi$
$920$			313.246i			0.340485i
$921$		0			0
$922$			574.591i			0.623200i
$923$		−	2074.54i		−	2.24760i
$924$		0			0
$925$	707.029			0.764356
$926$	646.960			0.698661
$927$		0			0
$928$	−169.706			−0.182872
$929$		−	1550.75i		−	1.66927i	−0.550806	−	0.834633i	$-0.685680\pi$
$929$		−	1550.75i		−	1.66927i	0.550806	−	0.834633i	$-0.314320\pi$
$930$		0			0
$931$	−911.793	+	667.383i	−0.979370	+	0.716845i
$932$	−114.530			−0.122886
$933$		0			0
$934$		−	910.345i		−	0.974673i
$935$	244.014			0.260978
$936$		0			0
$937$		−	759.317i		−	0.810370i	−0.914235	−	0.405185i	$-0.867207\pi$
$937$		−	759.317i		−	0.810370i	0.914235	−	0.405185i	$-0.132793\pi$
$938$	538.274	+	273.070i	0.573853	+	0.291119i
$939$		0			0
$940$	457.706			0.486921
$941$			36.3519i			0.0386312i	0.999813	+	0.0193156i	$0.00614873\pi$
$941$			36.3519i			0.0386312i	−0.999813	+	0.0193156i	$0.993851\pi$
$942$		0			0
$943$		−	775.245i		−	0.822105i
$944$		−	389.949i		−	0.413081i
$945$		0			0
$946$	25.9126			0.0273917
$947$	−92.5370			−0.0977160			−0.0488580	−	0.998806i	$-0.515558\pi$
$947$	−92.5370			−0.0977160			−0.0488580	+	0.998806i	$0.515558\pi$
$948$		0			0
$949$	1064.53			1.12174
$950$		−	325.158i		−	0.342271i
$951$		0			0
$952$	−210.323	+	414.588i	−0.220927	+	0.435492i
$953$	1361.29			1.42843			0.714215	−	0.699927i	$-0.246784\pi$
$953$	1361.29			1.42843			0.714215	+	0.699927i	$0.246784\pi$
$954$		0			0
$955$		−	591.750i		−	0.619633i
$956$	−563.044			−0.588958
$957$		0			0
$958$			238.344i			0.248794i
$959$	−1034.81	−	524.964i	−1.07905	−	0.547408i
$960$		0			0
$961$	886.881			0.922873
$962$			1880.87i			1.95517i
$963$		0			0
$964$		−	336.612i		−	0.349183i
$965$		−	466.651i		−	0.483577i
$966$		0			0
$967$	481.677			0.498115			0.249057	−	0.968489i	$-0.419879\pi$
$967$	481.677			0.498115			0.249057	+	0.968489i	$0.419879\pi$
$968$	−333.505			−0.344530
$969$		0			0
$970$	−432.500			−0.445876
$971$		−	1427.34i		−	1.46997i	−0.678082	−	0.734987i	$-0.737188\pi$
$971$		−	1427.34i		−	1.46997i	0.678082	−	0.734987i	$-0.262812\pi$
$972$		0			0
$973$	−698.352	+	1376.59i	−0.717730	+	1.41479i
$974$	−3.93102			−0.00403596
$975$		0			0
$976$		−	66.9046i		−	0.0685498i
$977$	1356.26			1.38819			0.694095	−	0.719883i	$-0.255805\pi$
$977$	1356.26			1.38819			0.694095	+	0.719883i	$0.255805\pi$
$978$		0			0
$979$		−	73.9698i		−	0.0755565i
$980$	467.647	−	342.292i	0.477191	−	0.349278i
$981$		0			0
$982$	349.986			0.356401
$983$			1315.51i			1.33826i	0.743146	+	0.669129i	$0.233333\pi$
$983$			1315.51i			1.33826i	−0.743146	+	0.669129i	$0.766667\pi$
$984$		0			0
$985$		−	1087.75i		−	1.10432i
$986$		−	996.184i		−	1.01033i
$987$		0			0
$988$	864.999			0.875505
$989$	−195.265			−0.197437
$990$		0			0
$991$	1043.28			1.05275			0.526377	−	0.850251i	$-0.323550\pi$
$991$	1043.28			1.05275			0.526377	+	0.850251i	$0.323550\pi$
$992$		−	48.7014i		−	0.0490941i
$993$		0			0
$994$	976.514	+	495.391i	0.982408	+	0.498382i
$995$	−1005.48			−1.01054
$996$		0			0
$997$		−	820.328i		−	0.822796i	−0.911456	−	0.411398i	$-0.865041\pi$
$997$		−	820.328i		−	0.822796i	0.911456	−	0.411398i	$-0.134959\pi$
$998$	−683.667			−0.685037
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.c.b.55.3		4
3.2	odd	2		42.3.c.a.13.2	yes	4
4.3	odd	2		1008.3.f.g.433.1		4
7.2	even	3		882.3.n.a.325.1		4
7.3	odd	6		882.3.n.a.19.1		4
7.4	even	3		882.3.n.d.19.1		4
7.5	odd	6		882.3.n.d.325.1		4
7.6	odd	2	inner	126.3.c.b.55.4		4
12.11	even	2		336.3.f.c.97.2		4
15.2	even	4		1050.3.h.a.349.3		8
15.8	even	4		1050.3.h.a.349.6		8
15.14	odd	2		1050.3.f.a.601.3		4
21.2	odd	6		294.3.g.b.31.2		4
21.5	even	6		294.3.g.c.31.2		4
21.11	odd	6		294.3.g.c.19.2		4
21.17	even	6		294.3.g.b.19.2		4
21.20	even	2		42.3.c.a.13.1	✓	4
24.5	odd	2		1344.3.f.f.769.1		4
24.11	even	2		1344.3.f.e.769.3		4
28.27	even	2		1008.3.f.g.433.4		4
84.83	odd	2		336.3.f.c.97.3		4
105.62	odd	4		1050.3.h.a.349.2		8
105.83	odd	4		1050.3.h.a.349.7		8
105.104	even	2		1050.3.f.a.601.4		4
168.83	odd	2		1344.3.f.e.769.2		4
168.125	even	2		1344.3.f.f.769.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.c.a.13.1	✓	4	21.20	even	2
42.3.c.a.13.2	yes	4	3.2	odd	2
126.3.c.b.55.3		4	1.1	even	1	trivial
126.3.c.b.55.4		4	7.6	odd	2	inner
294.3.g.b.19.2		4	21.17	even	6
294.3.g.b.31.2		4	21.2	odd	6
294.3.g.c.19.2		4	21.11	odd	6
294.3.g.c.31.2		4	21.5	even	6
336.3.f.c.97.2		4	12.11	even	2
336.3.f.c.97.3		4	84.83	odd	2
882.3.n.a.19.1		4	7.3	odd	6
882.3.n.a.325.1		4	7.2	even	3
882.3.n.d.19.1		4	7.4	even	3
882.3.n.d.325.1		4	7.5	odd	6
1008.3.f.g.433.1		4	4.3	odd	2
1008.3.f.g.433.4		4	28.27	even	2
1050.3.f.a.601.3		4	15.14	odd	2
1050.3.f.a.601.4		4	105.104	even	2
1050.3.h.a.349.2		8	105.62	odd	4
1050.3.h.a.349.3		8	15.2	even	4
1050.3.h.a.349.6		8	15.8	even	4
1050.3.h.a.349.7		8	105.83	odd	4
1344.3.f.e.769.2		4	168.83	odd	2
1344.3.f.e.769.3		4	24.11	even	2
1344.3.f.f.769.1		4	24.5	odd	2
1344.3.f.f.769.4		4	168.125	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +2.00000 q^{4} -5.91359i q^{5} +(6.24264 + 3.16693i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+1.41421 q^{2} +2.00000 q^{4} -5.91359i q^{5} +(6.24264 + 3.16693i) q^{7} +2.82843 q^{8} -8.36308i q^{10} +1.75736 q^{11} -18.7554i q^{13} +(8.82843 + 4.47871i) q^{14} +4.00000 q^{16} +23.4803i q^{17} +23.0600i q^{19} -11.8272i q^{20} +2.48528 q^{22} -18.7279 q^{23} -9.97056 q^{25} -26.5241i q^{26} +(12.4853 + 6.33386i) q^{28} -30.0000 q^{29} -8.60927i q^{31} +5.65685 q^{32} +33.2061i q^{34} +(18.7279 - 36.9164i) q^{35} -70.9117 q^{37} +32.6118i q^{38} -16.7262i q^{40} +41.3951i q^{41} +10.4264 q^{43} +3.51472 q^{44} -26.4853 q^{46} +38.6995i q^{47} +(28.9411 + 39.5400i) q^{49} -14.1005 q^{50} -37.5108i q^{52} +37.0294 q^{53} -10.3923i q^{55} +(17.6569 + 8.95743i) q^{56} -42.4264 q^{58} -97.4872i q^{59} -16.7262i q^{61} -12.1753i q^{62} +8.00000 q^{64} -110.912 q^{65} +60.9706 q^{67} +46.9606i q^{68} +(26.4853 - 52.2077i) q^{70} +110.610 q^{71} +56.7585i q^{73} -100.284 q^{74} +46.1200i q^{76} +(10.9706 + 5.56543i) q^{77} -69.8234 q^{79} -23.6544i q^{80} +58.5416i q^{82} +6.43583i q^{83} +138.853 q^{85} +14.7452 q^{86} +4.97056 q^{88} -42.0915i q^{89} +(59.3970 - 117.083i) q^{91} -37.4558 q^{92} +54.7293i q^{94} +136.368 q^{95} -51.7153i q^{97} +(40.9289 + 55.9180i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} + 8 q^{7}+O(q^{10}) \) 4 * q + 8 * q^4 + 8 * q^7	\( 4 q + 8 q^{4} + 8 q^{7} + 24 q^{11} + 24 q^{14} + 16 q^{16} - 24 q^{22} - 24 q^{23} + 28 q^{25} + 16 q^{28} - 120 q^{29} + 24 q^{35} - 80 q^{37} - 128 q^{43} + 48 q^{44} - 72 q^{46} - 20 q^{49} - 96 q^{50} + 216 q^{53} + 48 q^{56} + 32 q^{64} - 240 q^{65} + 176 q^{67} + 72 q^{70} + 120 q^{71} - 288 q^{74} - 24 q^{77} + 128 q^{79} + 216 q^{85} + 240 q^{86} - 48 q^{88} - 48 q^{92} + 240 q^{95} + 192 q^{98}+O(q^{100}) \) 4 * q + 8 * q^4 + 8 * q^7 + 24 * q^11 + 24 * q^14 + 16 * q^16 - 24 * q^22 - 24 * q^23 + 28 * q^25 + 16 * q^28 - 120 * q^29 + 24 * q^35 - 80 * q^37 - 128 * q^43 + 48 * q^44 - 72 * q^46 - 20 * q^49 - 96 * q^50 + 216 * q^53 + 48 * q^56 + 32 * q^64 - 240 * q^65 + 176 * q^67 + 72 * q^70 + 120 * q^71 - 288 * q^74 - 24 * q^77 + 128 * q^79 + 216 * q^85 + 240 * q^86 - 48 * q^88 - 48 * q^92 + 240 * q^95 + 192 * q^98

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