LMFDB - Embedded newform 126.3.c.b.55.2

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			55.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.55
Dual form			126.3.c.b.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +2.00000 q^{4} +1.01461i q^{5} +(-2.24264 + 6.63103i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q-1.41421 q^{2} +2.00000 q^{4} +1.01461i q^{5} +(-2.24264 + 6.63103i) q^{7} -2.82843 q^{8} -1.43488i q^{10} +10.2426 q^{11} +8.95743i q^{13} +(3.17157 - 9.37769i) q^{14} +4.00000 q^{16} +30.4085i q^{17} +16.1318i q^{19} +2.02922i q^{20} -14.4853 q^{22} +6.72792 q^{23} +23.9706 q^{25} -12.6677i q^{26} +(-4.48528 + 13.2621i) q^{28} -30.0000 q^{29} -50.1785i q^{31} -5.65685 q^{32} -43.0041i q^{34} +(-6.72792 - 2.27541i) q^{35} +30.9117 q^{37} -22.8138i q^{38} -2.86976i q^{40} -7.10228i q^{41} -74.4264 q^{43} +20.4853 q^{44} -9.51472 q^{46} -58.2954i q^{47} +(-38.9411 - 29.7420i) q^{49} -33.8995 q^{50} +17.9149i q^{52} +70.9706 q^{53} +10.3923i q^{55} +(6.34315 - 18.7554i) q^{56} +42.4264 q^{58} -0.492372i q^{59} -2.86976i q^{61} +70.9631i q^{62} +8.00000 q^{64} -9.08831 q^{65} +27.0294 q^{67} +60.8170i q^{68} +(9.51472 + 3.21792i) q^{70} -50.6102 q^{71} +70.6149i q^{73} -43.7157 q^{74} +32.2636i q^{76} +(-22.9706 + 67.9193i) q^{77} +133.823 q^{79} +4.05845i q^{80} +10.0441i q^{82} -104.415i q^{83} -30.8528 q^{85} +105.255 q^{86} -28.9706 q^{88} +144.970i q^{89} +(-59.3970 - 20.0883i) q^{91} +13.4558 q^{92} +82.4421i q^{94} -16.3675 q^{95} +100.705i q^{97} +(55.0711 + 42.0616i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$			1.01461i			0.202922i	0.994839	+	0.101461i	$0.0323518\pi$
$5$			1.01461i			0.202922i	−0.994839	+	0.101461i	$0.967648\pi$
$6$		0			0
$7$	−2.24264	+	6.63103i	−0.320377	+	0.947290i
$7$	−2.24264	+	6.63103i	−0.320377	+	0.947290i
$8$	−2.82843			−0.353553
$9$		0			0
$10$		−	1.43488i		−	0.143488i
$11$	10.2426			0.931149			0.465575	−	0.885009i	$-0.345848\pi$
$11$	10.2426			0.931149			0.465575	+	0.885009i	$0.345848\pi$
$12$		0			0
$13$			8.95743i			0.689033i	0.938780	+	0.344516i	$0.111957\pi$
$13$			8.95743i			0.689033i	−0.938780	+	0.344516i	$0.888043\pi$
$14$	3.17157	−	9.37769i	0.226541	−	0.669835i
$15$		0			0
$16$	4.00000			0.250000
$17$			30.4085i			1.78873i	0.447333	+	0.894367i	$0.352374\pi$
$17$			30.4085i			1.78873i	−0.447333	+	0.894367i	$0.647626\pi$
$18$		0			0
$19$			16.1318i			0.849043i	0.905418	+	0.424521i	$0.139558\pi$
$19$			16.1318i			0.849043i	−0.905418	+	0.424521i	$0.860442\pi$
$20$			2.02922i			0.101461i
$21$		0			0
$22$	−14.4853			−0.658422
$23$	6.72792			0.292518			0.146259	−	0.989246i	$-0.453277\pi$
$23$	6.72792			0.292518			0.146259	+	0.989246i	$0.453277\pi$
$24$		0			0
$25$	23.9706			0.958823
$26$		−	12.6677i		−	0.487220i
$27$		0			0
$28$	−4.48528	+	13.2621i	−0.160189	+	0.473645i
$29$	−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
$31$		−	50.1785i		−	1.61866i	−0.587354	−	0.809330i	$-0.699830\pi$
$31$		−	50.1785i		−	1.61866i	0.587354	−	0.809330i	$-0.300170\pi$
$32$	−5.65685			−0.176777
$33$		0			0
$34$		−	43.0041i		−	1.26483i
$35$	−6.72792	−	2.27541i	−0.192226	−	0.0650117i
$36$		0			0
$37$	30.9117			0.835451			0.417726	−	0.908573i	$-0.362827\pi$
$37$	30.9117			0.835451			0.417726	+	0.908573i	$0.362827\pi$
$38$		−	22.8138i		−	0.600364i
$39$		0			0
$40$		−	2.86976i		−	0.0717439i
$41$		−	7.10228i		−	0.173226i	−0.996242	−	0.0866132i	$-0.972396\pi$
$41$		−	7.10228i		−	0.173226i	0.996242	−	0.0866132i	$-0.0276044\pi$
$42$		0			0
$43$	−74.4264			−1.73085			−0.865423	−	0.501041i	$-0.832950\pi$
$43$	−74.4264			−1.73085			−0.865423	+	0.501041i	$0.832950\pi$
$44$	20.4853			0.465575
$45$		0			0
$46$	−9.51472			−0.206842
$47$		−	58.2954i		−	1.24033i	−0.784472	−	0.620164i	$-0.787066\pi$
$47$		−	58.2954i		−	1.24033i	0.784472	−	0.620164i	$-0.212934\pi$
$48$		0			0
$49$	−38.9411	−	29.7420i	−0.794717	−	0.606980i
$50$	−33.8995			−0.677990
$51$		0			0
$52$			17.9149i			0.344516i
$53$	70.9706			1.33907			0.669534	−	0.742782i	$-0.266494\pi$
$53$	70.9706			1.33907			0.669534	+	0.742782i	$0.266494\pi$
$54$		0			0
$55$			10.3923i			0.188951i
$56$	6.34315	−	18.7554i	0.113270	−	0.334918i
$57$		0			0
$58$	42.4264			0.731490
$59$		−	0.492372i		−	0.00834529i	−0.999991	−	0.00417265i	$-0.998672\pi$
$59$		−	0.492372i		−	0.00834529i	0.999991	−	0.00417265i	$-0.00132820\pi$
$60$		0			0
$61$		−	2.86976i		−	0.0470452i	−0.999723	−	0.0235226i	$-0.992512\pi$
$61$		−	2.86976i		−	0.0470452i	0.999723	−	0.0235226i	$-0.00748816\pi$
$62$			70.9631i			1.14457i
$63$		0			0
$64$	8.00000			0.125000
$65$	−9.08831			−0.139820
$66$		0			0
$67$	27.0294			0.403424			0.201712	−	0.979445i	$-0.435349\pi$
$67$	27.0294			0.403424			0.201712	+	0.979445i	$0.435349\pi$
$68$			60.8170i			0.894367i
$69$		0			0
$70$	9.51472	+	3.21792i	0.135925	+	0.0459702i
$71$	−50.6102			−0.712819			−0.356410	−	0.934330i	$-0.615999\pi$
$71$	−50.6102			−0.712819			−0.356410	+	0.934330i	$0.615999\pi$
$72$		0			0
$73$			70.6149i			0.967328i	0.875254	+	0.483664i	$0.160694\pi$
$73$			70.6149i			0.967328i	−0.875254	+	0.483664i	$0.839306\pi$
$74$	−43.7157			−0.590753
$75$		0			0
$76$			32.2636i			0.424521i
$77$	−22.9706	+	67.9193i	−0.298319	+	0.882068i
$78$		0			0
$79$	133.823			1.69397			0.846983	−	0.531619i	$-0.178416\pi$
$79$	133.823			1.69397			0.846983	+	0.531619i	$0.178416\pi$
$80$			4.05845i			0.0507306i
$81$		0			0
$82$			10.0441i			0.122490i
$83$		−	104.415i		−	1.25802i	−0.777398	−	0.629009i	$-0.783461\pi$
$83$		−	104.415i		−	1.25802i	0.777398	−	0.629009i	$-0.216539\pi$
$84$		0			0
$85$	−30.8528			−0.362974
$86$	105.255			1.22389
$87$		0			0
$88$	−28.9706			−0.329211
$89$			144.970i			1.62888i	0.580250	+	0.814438i	$0.302955\pi$
$89$			144.970i			1.62888i	−0.580250	+	0.814438i	$0.697045\pi$
$90$		0			0
$91$	−59.3970	−	20.0883i	−0.652714	−	0.220750i
$92$	13.4558			0.146259
$93$		0			0
$94$			82.4421i			0.877044i
$95$	−16.3675			−0.172290
$96$		0			0
$97$			100.705i			1.03820i	0.854714	+	0.519099i	$0.173732\pi$
$97$			100.705i			1.03820i	−0.854714	+	0.519099i	$0.826268\pi$
$98$	55.0711	+	42.0616i	0.561950	+	0.429200i
$99$		0			0
$100$	47.9411			0.479411
$101$		−	138.882i		−	1.37507i	−0.726150	−	0.687536i	$-0.758692\pi$
$101$		−	138.882i		−	1.37507i	0.726150	−	0.687536i	$-0.241308\pi$
$102$		0			0
$103$		−	78.8760i		−	0.765787i	−0.923793	−	0.382893i	$-0.874928\pi$
$103$		−	78.8760i		−	0.765787i	0.923793	−	0.382893i	$-0.125072\pi$
$104$		−	25.3354i		−	0.243610i
$105$		0			0
$106$	−100.368			−0.946864
$107$	37.7574			0.352873			0.176436	−	0.984312i	$-0.443543\pi$
$107$	37.7574			0.352873			0.176436	+	0.984312i	$0.443543\pi$
$108$		0			0
$109$	31.9411			0.293038			0.146519	−	0.989208i	$-0.453193\pi$
$109$	31.9411			0.293038			0.146519	+	0.989208i	$0.453193\pi$
$110$		−	14.6969i		−	0.133609i
$111$		0			0
$112$	−8.97056	+	26.5241i	−0.0800943	+	0.236823i
$113$	106.971			0.946642			0.473321	−	0.880890i	$-0.343055\pi$
$113$	106.971			0.946642			0.473321	+	0.880890i	$0.343055\pi$
$114$		0			0
$115$			6.82623i			0.0593585i
$116$	−60.0000			−0.517241
$117$		0			0
$118$			0.696320i			0.00590101i
$119$	−201.640	−	68.1953i	−1.69445	−	0.573070i
$120$		0			0
$121$	−16.0883			−0.132961
$122$			4.05845i			0.0332660i
$123$		0			0
$124$		−	100.357i		−	0.809330i
$125$			49.6861i			0.397489i
$126$		0			0
$127$	22.0589			0.173692			0.0868460	−	0.996222i	$-0.472321\pi$
$127$	22.0589			0.173692			0.0868460	+	0.996222i	$0.472321\pi$
$128$	−11.3137			−0.0883883
$129$		0			0
$130$	12.8528			0.0988678
$131$		−	70.9631i		−	0.541703i	−0.962621	−	0.270852i	$-0.912695\pi$
$131$		−	70.9631i		−	0.541703i	0.962621	−	0.270852i	$-0.0873052\pi$
$132$		0			0
$133$	−106.971	−	36.1779i	−0.804290	−	0.272014i
$134$	−38.2254			−0.285264
$135$		0			0
$136$		−	86.0082i		−	0.632413i
$137$	105.765			0.772004			0.386002	−	0.922498i	$-0.373856\pi$
$137$	105.765			0.772004			0.386002	+	0.922498i	$0.373856\pi$
$138$		0			0
$139$		−	181.322i		−	1.30447i	−0.758015	−	0.652237i	$-0.773831\pi$
$139$		−	181.322i		−	1.30447i	0.758015	−	0.652237i	$-0.226169\pi$
$140$	−13.4558	−	4.55082i	−0.0961132	−	0.0325059i
$141$		0			0
$142$	71.5736			0.504039
$143$			91.7477i			0.641592i
$144$		0			0
$145$		−	30.4384i		−	0.209920i
$146$		−	99.8646i		−	0.684004i
$147$		0			0
$148$	61.8234			0.417726
$149$	−41.1472			−0.276156			−0.138078	−	0.990421i	$-0.544092\pi$
$149$	−41.1472			−0.276156			−0.138078	+	0.990421i	$0.544092\pi$
$150$		0			0
$151$	80.3675			0.532235			0.266118	−	0.963941i	$-0.414259\pi$
$151$	80.3675			0.532235			0.266118	+	0.963941i	$0.414259\pi$
$152$		−	45.6277i		−	0.300182i
$153$		0			0
$154$	32.4853	−	96.0523i	0.210943	−	0.623716i
$155$	50.9117			0.328463
$156$		0			0
$157$			57.3106i			0.365036i	0.983203	+	0.182518i	$0.0584248\pi$
$157$			57.3106i			0.365036i	−0.983203	+	0.182518i	$0.941575\pi$
$158$	−189.255			−1.19782
$159$		0			0
$160$		−	5.73951i		−	0.0358719i
$161$	−15.0883	+	44.6131i	−0.0937162	+	0.277100i
$162$		0			0
$163$	−174.912			−1.07308			−0.536539	−	0.843876i	$-0.680269\pi$
$163$	−174.912			−1.07308			−0.536539	+	0.843876i	$0.680269\pi$
$164$		−	14.2046i		−	0.0866132i
$165$		0			0
$166$			147.666i			0.889552i
$167$			196.163i			1.17463i	0.809359	+	0.587315i	$0.199815\pi$
$167$			196.163i			1.17463i	−0.809359	+	0.587315i	$0.800185\pi$
$168$		0			0
$169$	88.7645			0.525234
$170$	43.6325			0.256662
$171$		0			0
$172$	−148.853			−0.865423
$173$		−	38.5254i		−	0.222690i	−0.993782	−	0.111345i	$-0.964484\pi$
$173$		−	38.5254i		−	0.222690i	0.993782	−	0.111345i	$-0.0355159\pi$
$174$		0			0
$175$	−53.7574	+	158.950i	−0.307185	+	0.908283i
$176$	40.9706			0.232787
$177$		0			0
$178$		−	205.019i		−	1.15179i
$179$	191.095			1.06757			0.533786	−	0.845619i	$-0.320769\pi$
$179$	191.095			1.06757			0.533786	+	0.845619i	$0.320769\pi$
$180$		0			0
$181$		−	120.793i		−	0.667367i	−0.942685	−	0.333683i	$-0.891708\pi$
$181$		−	120.793i		−	0.667367i	0.942685	−	0.333683i	$-0.108292\pi$
$182$	84.0000	+	28.4091i	0.461538	+	0.156094i
$183$		0			0
$184$	−19.0294			−0.103421
$185$			31.3634i			0.169532i
$186$		0			0
$187$			311.463i			1.66558i
$188$		−	116.591i		−	0.620164i
$189$		0			0
$190$	23.1472			0.121827
$191$	−112.066			−0.586733			−0.293367	−	0.956000i	$-0.594776\pi$
$191$	−112.066			−0.586733			−0.293367	+	0.956000i	$0.594776\pi$
$192$		0			0
$193$	−22.9117			−0.118713			−0.0593567	−	0.998237i	$-0.518905\pi$
$193$	−22.9117			−0.118713			−0.0593567	+	0.998237i	$0.518905\pi$
$194$		−	142.419i		−	0.734116i
$195$		0			0
$196$	−77.8823	−	59.4841i	−0.397358	−	0.303490i
$197$	116.059			0.589131			0.294566	−	0.955631i	$-0.404825\pi$
$197$	116.059			0.589131			0.294566	+	0.955631i	$0.404825\pi$
$198$		0			0
$199$		−	163.101i		−	0.819604i	−0.912174	−	0.409802i	$-0.865598\pi$
$199$		−	163.101i		−	0.819604i	0.912174	−	0.409802i	$-0.134402\pi$
$200$	−67.7990			−0.338995
$201$		0			0
$202$			196.409i			0.972323i
$203$	67.2792	−	198.931i	0.331425	−	0.979955i
$204$		0			0
$205$	7.20606			0.0351515
$206$			111.548i			0.541493i
$207$		0			0
$208$			35.8297i			0.172258i
$209$			165.232i			0.790586i
$210$		0			0
$211$	106.426			0.504391			0.252195	−	0.967676i	$-0.418847\pi$
$211$	106.426			0.504391			0.252195	+	0.967676i	$0.418847\pi$
$212$	141.941			0.669534
$213$		0			0
$214$	−53.3970			−0.249519
$215$		−	75.5139i		−	0.351228i
$216$		0			0
$217$	332.735	+	112.532i	1.53334	+	0.518582i
$218$	−45.1716			−0.207209
$219$		0			0
$220$			20.7846i			0.0944755i
$221$	−272.382			−1.23250
$222$		0			0
$223$			57.0047i			0.255627i	0.991798	+	0.127813i	$0.0407958\pi$
$223$			57.0047i			0.255627i	−0.991798	+	0.127813i	$0.959204\pi$
$224$	12.6863	−	37.5108i	0.0566352	−	0.167459i
$225$		0			0
$226$	−151.279			−0.669377
$227$			287.418i			1.26616i	0.774086	+	0.633080i	$0.218210\pi$
$227$			287.418i			1.26616i	−0.774086	+	0.633080i	$0.781790\pi$
$228$		0			0
$229$		−	139.405i		−	0.608754i	−0.952552	−	0.304377i	$-0.901552\pi$
$229$		−	139.405i		−	0.608754i	0.952552	−	0.304377i	$-0.0984482\pi$
$230$		−	9.65375i		−	0.0419728i
$231$		0			0
$232$	84.8528			0.365745
$233$	−362.735			−1.55680			−0.778401	−	0.627767i	$-0.783969\pi$
$233$	−362.735			−1.55680			−0.778401	+	0.627767i	$0.783969\pi$
$234$		0			0
$235$	59.1472			0.251690
$236$		−	0.984744i		−	0.00417265i
$237$		0			0
$238$	285.161	+	96.4427i	1.19816	+	0.405222i
$239$	−18.4781			−0.0773144			−0.0386572	−	0.999253i	$-0.512308\pi$
$239$	−18.4781			−0.0773144			−0.0386572	+	0.999253i	$0.512308\pi$
$240$		0			0
$241$			178.104i			0.739021i	0.929227	+	0.369510i	$0.120475\pi$
$241$			178.104i			0.739021i	−0.929227	+	0.369510i	$0.879525\pi$
$242$	22.7523			0.0940178
$243$		0			0
$244$		−	5.73951i		−	0.0235226i
$245$	30.1766	−	39.5101i	0.123170	−	0.161266i
$246$		0			0
$247$	−144.500			−0.585018
$248$			141.926i			0.572283i
$249$		0			0
$250$		−	70.2668i		−	0.281067i
$251$			50.6709i			0.201876i	0.994893	+	0.100938i	$0.0321844\pi$
$251$			50.6709i			0.201876i	−0.994893	+	0.100938i	$0.967816\pi$
$252$		0			0
$253$	68.9117			0.272378
$254$	−31.1960			−0.122819
$255$		0			0
$256$	16.0000			0.0625000
$257$			187.584i			0.729898i	0.931028	+	0.364949i	$0.118914\pi$
$257$			187.584i			0.729898i	−0.931028	+	0.364949i	$0.881086\pi$
$258$		0			0
$259$	−69.3238	+	204.976i	−0.267659	+	0.791414i
$260$	−18.1766			−0.0699101
$261$		0			0
$262$			100.357i			0.383042i
$263$	402.978			1.53223			0.766117	−	0.642701i	$-0.222186\pi$
$263$	402.978			1.53223			0.766117	+	0.642701i	$0.222186\pi$
$264$		0			0
$265$			72.0076i			0.271727i
$266$	151.279	+	51.1632i	0.568719	+	0.192343i
$267$		0			0
$268$	54.0589			0.201712
$269$		−	480.538i		−	1.78639i	−0.449674	−	0.893193i	$-0.648460\pi$
$269$		−	480.538i		−	1.78639i	0.449674	−	0.893193i	$-0.351540\pi$
$270$		0			0
$271$			37.3068i			0.137664i	0.997628	+	0.0688318i	$0.0219272\pi$
$271$			37.3068i			0.137664i	−0.997628	+	0.0688318i	$0.978073\pi$
$272$			121.634i			0.447184i
$273$		0			0
$274$	−149.574			−0.545889
$275$	245.522			0.892807
$276$		0			0
$277$	−82.6762			−0.298470			−0.149235	−	0.988802i	$-0.547681\pi$
$277$	−82.6762			−0.298470			−0.149235	+	0.988802i	$0.547681\pi$
$278$			256.428i			0.922403i
$279$		0			0
$280$	19.0294	+	6.43583i	0.0679623	+	0.0229851i
$281$	150.853			0.536843			0.268421	−	0.963302i	$-0.413498\pi$
$281$	150.853			0.536843			0.268421	+	0.963302i	$0.413498\pi$
$282$		0			0
$283$		−	284.158i		−	1.00409i	−0.864841	−	0.502046i	$-0.832581\pi$
$283$		−	284.158i		−	1.00409i	0.864841	−	0.502046i	$-0.167419\pi$
$284$	−101.220			−0.356410
$285$		0			0
$286$		−	129.751i		−	0.453674i
$287$	47.0955	+	15.9279i	0.164096	+	0.0554978i
$288$		0			0
$289$	−635.676			−2.19957
$290$			43.0463i			0.148436i
$291$		0			0
$292$			141.230i			0.483664i
$293$		−	537.237i		−	1.83357i	−0.399379	−	0.916786i	$-0.630774\pi$
$293$		−	537.237i		−	1.83357i	0.399379	−	0.916786i	$-0.369226\pi$
$294$		0			0
$295$	0.499567			0.00169345
$296$	−87.4315			−0.295377
$297$		0			0
$298$	58.1909			0.195272
$299$			60.2649i			0.201555i
$300$		0			0
$301$	166.912	−	493.524i	0.554524	−	1.63961i
$302$	−113.657			−0.376347
$303$		0			0
$304$			64.5273i			0.212261i
$305$	2.91169			0.00954652
$306$		0			0
$307$			34.7430i			0.113169i	0.998398	+	0.0565847i	$0.0180211\pi$
$307$			34.7430i			0.113169i	−0.998398	+	0.0565847i	$0.981979\pi$
$308$	−45.9411	+	135.839i	−0.149159	+	0.441034i
$309$		0			0
$310$	−72.0000			−0.232258
$311$		−	89.1664i		−	0.286709i	−0.989671	−	0.143354i	$-0.954211\pi$
$311$		−	89.1664i		−	0.286709i	0.989671	−	0.143354i	$-0.0457888\pi$
$312$		0			0
$313$		−	519.700i		−	1.66038i	−0.557479	−	0.830191i	$-0.688231\pi$
$313$		−	519.700i		−	1.66038i	0.557479	−	0.830191i	$-0.311769\pi$
$314$		−	81.0495i		−	0.258119i
$315$		0			0
$316$	267.647			0.846983
$317$	−542.029			−1.70987			−0.854935	−	0.518736i	$-0.826403\pi$
$317$	−542.029			−1.70987			−0.854935	+	0.518736i	$0.826403\pi$
$318$		0			0
$319$	−307.279			−0.963258
$320$			8.11689i			0.0253653i
$321$		0			0
$322$	21.3381	−	63.0924i	0.0662674	−	0.195939i
$323$	−490.544			−1.51871
$324$		0			0
$325$			214.715i			0.660660i
$326$	247.362			0.758781
$327$		0			0
$328$			20.0883i			0.0612448i
$329$	386.558	+	130.736i	1.17495	+	0.397373i
$330$		0			0
$331$	179.632			0.542696			0.271348	−	0.962481i	$-0.412531\pi$
$331$	179.632			0.542696			0.271348	+	0.962481i	$0.412531\pi$
$332$		−	208.831i		−	0.629009i
$333$		0			0
$334$		−	277.417i		−	0.830588i
$335$			27.4244i			0.0818638i
$336$		0			0
$337$	291.823			0.865945			0.432972	−	0.901407i	$-0.357465\pi$
$337$	291.823			0.865945			0.432972	+	0.901407i	$0.357465\pi$
$338$	−125.532			−0.371396
$339$		0			0
$340$	−61.7056			−0.181487
$341$		−	513.960i		−	1.50721i
$342$		0			0
$343$	284.551	−	191.519i	0.829596	−	0.558365i
$344$	210.510			0.611947
$345$		0			0
$346$			54.4831i			0.157466i
$347$	−452.080			−1.30283			−0.651413	−	0.758724i	$-0.725823\pi$
$347$	−452.080			−1.30283			−0.651413	+	0.758724i	$0.725823\pi$
$348$		0			0
$349$		−	235.067i		−	0.673543i	−0.941586	−	0.336772i	$-0.890665\pi$
$349$		−	235.067i		−	0.673543i	0.941586	−	0.336772i	$-0.109335\pi$
$350$	76.0244	−	224.789i	0.217213	−	0.642253i
$351$		0			0
$352$	−57.9411			−0.164605
$353$		−	25.2458i		−	0.0715179i	−0.999360	−	0.0357590i	$-0.988615\pi$
$353$		−	25.2458i		−	0.0715179i	0.999360	−	0.0357590i	$-0.0113849\pi$
$354$		0			0
$355$		−	51.3497i		−	0.144647i
$356$			289.940i			0.814438i
$357$		0			0
$358$	−270.250			−0.754888
$359$	106.243			0.295941			0.147970	−	0.988992i	$-0.452726\pi$
$359$	106.243			0.295941			0.147970	+	0.988992i	$0.452726\pi$
$360$		0			0
$361$	100.765			0.279126
$362$			170.828i			0.471900i
$363$		0			0
$364$	−118.794	−	40.1766i	−0.326357	−	0.110375i
$365$	−71.6468			−0.196292
$366$		0			0
$367$			286.416i			0.780426i	0.920725	+	0.390213i	$0.127599\pi$
$367$			286.416i			0.780426i	−0.920725	+	0.390213i	$0.872401\pi$
$368$	26.9117			0.0731296
$369$		0			0
$370$		−	44.3545i		−	0.119877i
$371$	−159.161	+	470.608i	−0.429007	+	1.26849i
$372$		0			0
$373$	−423.470			−1.13531			−0.567654	−	0.823267i	$-0.692149\pi$
$373$	−423.470			−1.13531			−0.567654	+	0.823267i	$0.692149\pi$
$374$		−	440.476i		−	1.17774i
$375$		0			0
$376$			164.884i			0.438522i
$377$		−	268.723i		−	0.712793i
$378$		0			0
$379$	101.103			0.266761			0.133381	−	0.991065i	$-0.457417\pi$
$379$	101.103			0.266761			0.133381	+	0.991065i	$0.457417\pi$
$380$	−32.7351			−0.0861449
$381$		0			0
$382$	158.485			0.414883
$383$			220.394i			0.575442i	0.957714	+	0.287721i	$0.0928976\pi$
$383$			220.394i			0.575442i	−0.957714	+	0.287721i	$0.907102\pi$
$384$		0			0
$385$	−68.9117	−	23.3062i	−0.178991	−	0.0605356i
$386$	32.4020			0.0839431
$387$		0			0
$388$			201.410i			0.519099i
$389$	383.470			0.985784			0.492892	−	0.870090i	$-0.335940\pi$
$389$	383.470			0.985784			0.492892	+	0.870090i	$0.335940\pi$
$390$		0			0
$391$			204.586i			0.523238i
$392$	110.142	+	84.1232i	0.280975	+	0.214600i
$393$		0			0
$394$	−164.132			−0.416579
$395$			135.779i			0.343744i
$396$		0			0
$397$			485.178i			1.22211i	0.791588	+	0.611056i	$0.209255\pi$
$397$			485.178i			1.22211i	−0.791588	+	0.611056i	$0.790745\pi$
$398$			230.660i			0.579548i
$399$		0			0
$400$	95.8823			0.239706
$401$	253.176			0.631361			0.315680	−	0.948866i	$-0.397767\pi$
$401$	253.176			0.631361			0.315680	+	0.948866i	$0.397767\pi$
$402$		0			0
$403$	449.470			1.11531
$404$		−	277.765i		−	0.687536i
$405$		0			0
$406$	−95.1472	+	281.331i	−0.234353	+	0.692933i
$407$	316.617			0.777930
$408$		0			0
$409$		−	5.39135i		−	0.0131818i	−0.999978	−	0.00659089i	$-0.997902\pi$
$409$		−	5.39135i		−	0.0131818i	0.999978	−	0.00659089i	$-0.00209796\pi$
$410$	−10.1909			−0.0248559
$411$		0			0
$412$		−	157.752i		−	0.382893i
$413$	3.26494	+	1.10421i	0.00790541	+	0.00267364i
$414$		0			0
$415$	105.941			0.255280
$416$		−	50.6709i		−	0.121805i
$417$		0			0
$418$		−	233.674i		−	0.559028i
$419$			294.431i			0.702700i	0.936244	+	0.351350i	$0.114277\pi$
$419$			294.431i			0.702700i	−0.936244	+	0.351350i	$0.885723\pi$
$420$		0			0
$421$	−290.441			−0.689883			−0.344941	−	0.938624i	$-0.612101\pi$
$421$	−290.441			−0.689883			−0.344941	+	0.938624i	$0.612101\pi$
$422$	−150.510			−0.356658
$423$		0			0
$424$	−200.735			−0.473432
$425$			728.909i			1.71508i
$426$		0			0
$427$	19.0294	+	6.43583i	0.0445654	+	0.0150722i
$428$	75.5147			0.176436
$429$		0			0
$430$			106.793i			0.248355i
$431$	−50.7136			−0.117665			−0.0588325	−	0.998268i	$-0.518738\pi$
$431$	−50.7136			−0.117665			−0.0588325	+	0.998268i	$0.518738\pi$
$432$		0			0
$433$			724.761i			1.67381i	0.547347	+	0.836906i	$0.315638\pi$
$433$			724.761i			1.67381i	−0.547347	+	0.836906i	$0.684362\pi$
$434$	−470.558	−	159.145i	−1.08424	−	0.366693i
$435$		0			0
$436$	63.8823			0.146519
$437$			108.534i			0.248361i
$438$		0			0
$439$			371.728i			0.846761i	0.905952	+	0.423381i	$0.139157\pi$
$439$			371.728i			0.846761i	−0.905952	+	0.423381i	$0.860843\pi$
$440$		−	29.3939i		−	0.0668043i
$441$		0			0
$442$	385.206			0.871507
$443$	229.258			0.517512			0.258756	−	0.965943i	$-0.416687\pi$
$443$	229.258			0.517512			0.258756	+	0.965943i	$0.416687\pi$
$444$		0			0
$445$	−147.088			−0.330536
$446$		−	80.6168i		−	0.180755i
$447$		0			0
$448$	−17.9411	+	53.0482i	−0.0400472	+	0.118411i
$449$	600.323			1.33702			0.668511	−	0.743702i	$-0.266932\pi$
$449$	600.323			1.33702			0.668511	+	0.743702i	$0.266932\pi$
$450$		0			0
$451$		−	72.7461i		−	0.161300i
$452$	213.941			0.473321
$453$		0			0
$454$		−	406.471i		−	0.895311i
$455$	20.3818	−	60.2649i	0.0447952	−	0.132450i
$456$		0			0
$457$	483.823			1.05869			0.529347	−	0.848405i	$-0.322437\pi$
$457$	483.823			1.05869			0.529347	+	0.848405i	$0.322437\pi$
$458$			197.148i			0.430454i
$459$		0			0
$460$			13.6525i			0.0296793i
$461$			274.661i			0.595794i	0.954598	+	0.297897i	$0.0962852\pi$
$461$			274.661i			0.595794i	−0.954598	+	0.297897i	$0.903715\pi$
$462$		0			0
$463$	−153.470			−0.331469			−0.165734	−	0.986170i	$-0.552999\pi$
$463$	−153.470			−0.331469			−0.165734	+	0.986170i	$0.552999\pi$
$464$	−120.000			−0.258621
$465$		0			0
$466$	512.985			1.10083
$467$		−	61.7420i		−	0.132210i	−0.997813	−	0.0661049i	$-0.978943\pi$
$467$		−	61.7420i		−	0.132210i	0.997813	−	0.0661049i	$-0.0210572\pi$
$468$		0			0
$469$	−60.6173	+	179.233i	−0.129248	+	0.382160i
$470$	−83.6468			−0.177972
$471$		0			0
$472$			1.39264i			0.00295051i
$473$	−762.323			−1.61168
$474$		0			0
$475$			386.689i			0.814082i
$476$	−403.279	−	136.391i	−0.847225	−	0.286535i
$477$		0			0
$478$	26.1320			0.0546695
$479$			556.514i			1.16182i	0.813966	+	0.580912i	$0.197304\pi$
$479$			556.514i			1.16182i	−0.813966	+	0.580912i	$0.802696\pi$
$480$		0			0
$481$			276.889i			0.575653i
$482$		−	251.877i		−	0.522567i
$483$		0			0
$484$	−32.1766			−0.0664806
$485$	−102.177			−0.210673
$486$		0			0
$487$	−325.220			−0.667804			−0.333902	−	0.942608i	$-0.608365\pi$
$487$	−325.220			−0.667804			−0.333902	+	0.942608i	$0.608365\pi$
$488$			8.11689i			0.0166330i
$489$		0			0
$490$	−42.6762	+	55.8758i	−0.0870943	+	0.114032i
$491$	−643.477			−1.31054			−0.655272	−	0.755393i	$-0.727446\pi$
$491$	−643.477			−1.31054			−0.655272	+	0.755393i	$0.727446\pi$
$492$		0			0
$493$		−	912.255i		−	1.85042i
$494$	204.353			0.413671
$495$		0			0
$496$		−	200.714i		−	0.404665i
$497$	113.500	−	335.598i	0.228371	−	0.675247i
$498$		0			0
$499$	755.426			1.51388			0.756939	−	0.653485i	$-0.226694\pi$
$499$	755.426			1.51388			0.756939	+	0.653485i	$0.226694\pi$
$500$			99.3722i			0.198744i
$501$		0			0
$502$		−	71.6594i		−	0.142748i
$503$		−	509.409i		−	1.01274i	−0.862316	−	0.506371i	$-0.830987\pi$
$503$		−	509.409i		−	1.01274i	0.862316	−	0.506371i	$-0.169013\pi$
$504$		0			0
$505$	140.912			0.279033
$506$	−97.4558			−0.192600
$507$		0			0
$508$	44.1177			0.0868460
$509$		−	769.433i		−	1.51166i	−0.654770	−	0.755828i	$-0.727234\pi$
$509$		−	769.433i		−	1.51166i	0.654770	−	0.755828i	$-0.272766\pi$
$510$		0			0
$511$	−468.250	−	158.364i	−0.916340	−	0.309910i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$		−	265.283i		−	0.516116i
$515$	80.0286			0.155395
$516$		0			0
$517$		−	597.099i		−	1.15493i
$518$	98.0387	−	289.880i	0.189264	−	0.559615i
$519$		0			0
$520$	25.7056			0.0494339
$521$			535.207i			1.02727i	0.858009	+	0.513635i	$0.171701\pi$
$521$			535.207i			1.02727i	−0.858009	+	0.513635i	$0.828299\pi$
$522$		0			0
$523$		−	839.466i		−	1.60510i	−0.596586	−	0.802549i	$-0.703477\pi$
$523$		−	839.466i		−	1.60510i	0.596586	−	0.802549i	$-0.296523\pi$
$524$		−	141.926i		−	0.270852i
$525$		0			0
$526$	−569.897			−1.08345
$527$	1525.85			2.89535
$528$		0			0
$529$	−483.735			−0.914433
$530$		−	101.834i		−	0.192140i
$531$		0			0
$532$	−213.941	−	72.3557i	−0.402145	−	0.136007i
$533$	63.6182			0.119359
$534$		0			0
$535$			38.3091i			0.0716057i
$536$	−76.4508			−0.142632
$537$		0			0
$538$			679.583i			1.26317i
$539$	−398.860	−	304.637i	−0.740000	−	0.565189i
$540$		0			0
$541$	285.852			0.528377			0.264188	−	0.964471i	$-0.414896\pi$
$541$	285.852			0.528377			0.264188	+	0.964471i	$0.414896\pi$
$542$		−	52.7598i		−	0.0973428i
$543$		0			0
$544$		−	172.016i		−	0.316207i
$545$			32.4078i			0.0594639i
$546$		0			0
$547$	−741.470			−1.35552			−0.677761	−	0.735283i	$-0.737049\pi$
$547$	−741.470			−1.35552			−0.677761	+	0.735283i	$0.737049\pi$
$548$	211.529			0.386002
$549$		0			0
$550$	−347.220			−0.631310
$551$		−	483.954i		−	0.878320i
$552$		0			0
$553$	−300.118	+	887.387i	−0.542708	+	1.60468i
$554$	116.922			0.211050
$555$		0			0
$556$		−	362.644i		−	0.652237i
$557$	−834.853			−1.49884			−0.749419	−	0.662096i	$-0.769667\pi$
$557$	−834.853			−1.49884			−0.749419	+	0.662096i	$0.769667\pi$
$558$		0			0
$559$		−	666.669i		−	1.19261i
$560$	−26.9117	−	9.10164i	−0.0480566	−	0.0162529i
$561$		0			0
$562$	−213.338			−0.379605
$563$		−	417.781i		−	0.742062i	−0.928620	−	0.371031i	$-0.879004\pi$
$563$		−	417.781i		−	0.742062i	0.928620	−	0.371031i	$-0.120996\pi$
$564$		0			0
$565$			108.534i			0.192095i
$566$			401.861i			0.710001i
$567$		0			0
$568$	143.147			0.252020
$569$	−673.029			−1.18283			−0.591414	−	0.806368i	$-0.701430\pi$
$569$	−673.029			−1.18283			−0.591414	+	0.806368i	$0.701430\pi$
$570$		0			0
$571$	−265.088			−0.464253			−0.232126	−	0.972686i	$-0.574568\pi$
$571$	−265.088			−0.464253			−0.232126	+	0.972686i	$0.574568\pi$
$572$			183.495i			0.320796i
$573$		0			0
$574$	−66.6030	−	22.5254i	−0.116033	−	0.0392429i
$575$	161.272			0.280473
$576$		0			0
$577$		−	468.740i		−	0.812375i	−0.913790	−	0.406188i	$-0.866858\pi$
$577$		−	468.740i		−	0.812375i	0.913790	−	0.406188i	$-0.133142\pi$
$578$	898.982			1.55533
$579$		0			0
$580$		−	60.8767i		−	0.104960i
$581$	692.382	+	234.166i	1.19171	+	0.403040i
$582$		0			0
$583$	726.926			1.24687
$584$		−	199.729i		−	0.342002i
$585$		0			0
$586$			759.767i			1.29653i
$587$		−	120.530i		−	0.205332i	−0.994716	−	0.102666i	$-0.967263\pi$
$587$		−	120.530i		−	0.205332i	0.994716	−	0.102666i	$-0.0327372\pi$
$588$		0			0
$589$	809.470			1.37431
$590$	−0.706494			−0.00119745
$591$		0			0
$592$	123.647			0.208863
$593$			561.468i			0.946826i	0.880841	+	0.473413i	$0.156978\pi$
$593$			561.468i			0.946826i	−0.880841	+	0.473413i	$0.843022\pi$
$594$		0			0
$595$	69.1918	−	204.586i	0.116289	−	0.343842i
$596$	−82.2944			−0.138078
$597$		0			0
$598$		−	85.2274i		−	0.142521i
$599$	−940.109			−1.56946			−0.784732	−	0.619835i	$-0.787199\pi$
$599$	−940.109			−1.56946			−0.784732	+	0.619835i	$0.787199\pi$
$600$		0			0
$601$		−	563.527i		−	0.937649i	−0.883291	−	0.468824i	$-0.844678\pi$
$601$		−	563.527i		−	0.937649i	0.883291	−	0.468824i	$-0.155322\pi$
$602$	−236.049	+	697.948i	−0.392108	+	1.15938i
$603$		0			0
$604$	160.735			0.266118
$605$		−	16.3234i		−	0.0269808i
$606$		0			0
$607$			306.589i			0.505089i	0.967585	+	0.252544i	$0.0812674\pi$
$607$			306.589i			0.505089i	−0.967585	+	0.252544i	$0.918733\pi$
$608$		−	91.2553i		−	0.150091i
$609$		0			0
$610$	−4.11775			−0.00675041
$611$	522.177			0.854626
$612$		0			0
$613$	275.588			0.449572			0.224786	−	0.974408i	$-0.427832\pi$
$613$	275.588			0.449572			0.224786	+	0.974408i	$0.427832\pi$
$614$		−	49.1340i		−	0.0800228i
$615$		0			0
$616$	64.9706	−	192.105i	0.105472	−	0.311858i
$617$	−461.294			−0.747639			−0.373820	−	0.927501i	$-0.621952\pi$
$617$	−461.294			−0.747639			−0.373820	+	0.927501i	$0.621952\pi$
$618$		0			0
$619$			374.904i			0.605660i	0.953045	+	0.302830i	$0.0979315\pi$
$619$			374.904i			0.605660i	−0.953045	+	0.302830i	$0.902068\pi$
$620$	101.823			0.164231
$621$		0			0
$622$			126.100i			0.202734i
$623$	−961.301	−	325.116i	−1.54302	−	0.521855i
$624$		0			0
$625$	548.852			0.878163
$626$			734.966i			1.17407i
$627$		0			0
$628$			114.621i			0.182518i
$629$			939.978i			1.49440i
$630$		0			0
$631$	−1127.32			−1.78656			−0.893282	−	0.449496i	$-0.851603\pi$
$631$	−1127.32			−1.78656			−0.893282	+	0.449496i	$0.851603\pi$
$632$	−378.510			−0.598908
$633$		0			0
$634$	766.544			1.20906
$635$			22.3812i			0.0352460i
$636$		0			0
$637$	266.412	−	348.812i	0.418229	−	0.547586i
$638$	434.558			0.681126
$639$		0			0
$640$		−	11.4790i		−	0.0179360i
$641$	884.352			1.37964			0.689822	−	0.723979i	$-0.257689\pi$
$641$	884.352			1.37964			0.689822	+	0.723979i	$0.257689\pi$
$642$		0			0
$643$			300.765i			0.467753i	0.972266	+	0.233876i	$0.0751411\pi$
$643$			300.765i			0.467753i	−0.972266	+	0.233876i	$0.924859\pi$
$644$	−30.1766	+	89.2261i	−0.0468581	+	0.138550i
$645$		0			0
$646$	693.734			1.07389
$647$		−	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
$649$		−	5.04319i		−	0.00777071i
$650$		−	303.652i		−	0.467157i
$651$		0			0
$652$	−349.823			−0.536539
$653$	455.970			0.698269			0.349135	−	0.937073i	$-0.386476\pi$
$653$	455.970			0.698269			0.349135	+	0.937073i	$0.386476\pi$
$654$		0			0
$655$	72.0000			0.109924
$656$		−	28.4091i		−	0.0433066i
$657$		0			0
$658$	−546.676	−	184.888i	−0.830815	−	0.280985i
$659$	−403.684			−0.612571			−0.306285	−	0.951940i	$-0.599086\pi$
$659$	−403.684			−0.612571			−0.306285	+	0.951940i	$0.599086\pi$
$660$		0			0
$661$			1153.41i			1.74495i	0.488663	+	0.872473i	$0.337485\pi$
$661$			1153.41i			1.74495i	−0.488663	+	0.872473i	$0.662515\pi$
$662$	−254.039			−0.383744
$663$		0			0
$664$			295.331i			0.444776i
$665$	36.7065	−	108.534i	0.0551977	−	0.163208i
$666$		0			0
$667$	−201.838			−0.302605
$668$			392.326i			0.587315i
$669$		0			0
$670$		−	38.7839i		−	0.0578865i
$671$		−	29.3939i		−	0.0438061i
$672$		0			0
$673$	−607.440			−0.902585			−0.451293	−	0.892376i	$-0.649037\pi$
$673$	−607.440			−0.902585			−0.451293	+	0.892376i	$0.649037\pi$
$674$	−412.701			−0.612315
$675$		0			0
$676$	177.529			0.262617
$677$		−	1137.59i		−	1.68034i	−0.542326	−	0.840168i	$-0.682456\pi$
$677$		−	1137.59i		−	1.68034i	0.542326	−	0.840168i	$-0.317544\pi$
$678$		0			0
$679$	−667.779	−	225.845i	−0.983474	−	0.332615i
$680$	87.2649			0.128331
$681$		0			0
$682$			726.849i			1.06576i
$683$	818.111			1.19782			0.598910	−	0.800817i	$-0.295601\pi$
$683$	818.111			1.19782			0.598910	+	0.800817i	$0.295601\pi$
$684$		0			0
$685$			107.310i			0.156657i
$686$	−402.416	+	270.849i	−0.586613	+	0.394823i
$687$		0			0
$688$	−297.706			−0.432712
$689$			635.714i			0.922661i
$690$		0			0
$691$		−	204.280i		−	0.295630i	−0.989015	−	0.147815i	$-0.952776\pi$
$691$		−	204.280i		−	0.295630i	0.989015	−	0.147815i	$-0.0472239\pi$
$692$		−	77.0508i		−	0.111345i
$693$		0			0
$694$	639.338			0.921236
$695$	183.971			0.264707
$696$		0			0
$697$	215.970			0.309856
$698$			332.434i			0.476267i
$699$		0			0
$700$	−107.515	+	317.899i	−0.153592	+	0.454142i
$701$	318.853			0.454854			0.227427	−	0.973795i	$-0.426969\pi$
$701$	318.853			0.454854			0.227427	+	0.973795i	$0.426969\pi$
$702$		0			0
$703$			498.662i			0.709334i
$704$	81.9411			0.116394
$705$		0			0
$706$			35.7030i			0.0505708i
$707$	920.933	+	311.463i	1.30259	+	0.440542i
$708$		0			0
$709$	−217.647			−0.306977			−0.153489	−	0.988150i	$-0.549051\pi$
$709$	−217.647			−0.306977			−0.153489	+	0.988150i	$0.549051\pi$
$710$			72.6194i			0.102281i
$711$		0			0
$712$		−	410.037i		−	0.575895i
$713$		−	337.597i		−	0.473488i
$714$		0			0
$715$	−93.0883			−0.130193
$716$	382.191			0.533786
$717$		0			0
$718$	−150.250			−0.209262
$719$			1207.36i			1.67922i	0.543192	+	0.839609i	$0.317216\pi$
$719$			1207.36i			1.67922i	−0.543192	+	0.839609i	$0.682784\pi$
$720$		0			0
$721$	523.029	+	176.891i	0.725422	+	0.245341i
$722$	−142.503			−0.197372
$723$		0			0
$724$		−	241.587i		−	0.333683i
$725$	−719.117			−0.991885
$726$		0			0
$727$		−	123.231i		−	0.169506i	−0.996402	−	0.0847528i	$-0.972990\pi$
$727$		−	123.231i		−	0.169506i	0.996402	−	0.0847528i	$-0.0270100\pi$
$728$	168.000	+	56.8183i	0.230769	+	0.0780471i
$729$		0			0
$730$	101.324			0.138800
$731$		−	2263.19i		−	3.09603i
$732$		0			0
$733$			375.779i			0.512659i	0.966589	+	0.256330i	$0.0825133\pi$
$733$			375.779i			0.512659i	−0.966589	+	0.256330i	$0.917487\pi$
$734$		−	405.054i		−	0.551844i
$735$		0			0
$736$	−38.0589			−0.0517104
$737$	276.853			0.375648
$738$		0			0
$739$	722.530			0.977713			0.488856	−	0.872364i	$-0.337414\pi$
$739$	722.530			0.977713			0.488856	+	0.872364i	$0.337414\pi$
$740$			62.7267i			0.0847659i
$741$		0			0
$742$	225.088	−	665.540i	0.303354	−	0.896954i
$743$	−1268.48			−1.70724			−0.853618	−	0.520899i	$-0.825597\pi$
$743$	−1268.48			−1.70724			−0.853618	+	0.520899i	$0.825597\pi$
$744$		0			0
$745$		−	41.7484i		−	0.0560382i
$746$	598.877			0.802784
$747$		0			0
$748$			622.926i			0.832789i
$749$	−84.6762	+	250.370i	−0.113052	+	0.334273i
$750$		0			0
$751$	439.161			0.584769			0.292384	−	0.956301i	$-0.405551\pi$
$751$	439.161			0.584769			0.292384	+	0.956301i	$0.405551\pi$
$752$		−	233.182i		−	0.310082i
$753$		0			0
$754$			380.031i			0.504020i
$755$			81.5419i			0.108002i
$756$		0			0
$757$	−668.530			−0.883131			−0.441565	−	0.897229i	$-0.645577\pi$
$757$	−668.530			−0.883131			−0.441565	+	0.897229i	$0.645577\pi$
$758$	−142.981			−0.188629
$759$		0			0
$760$	46.2944			0.0609136
$761$			880.116i			1.15653i	0.815851	+	0.578263i	$0.196269\pi$
$761$			880.116i			1.15653i	−0.815851	+	0.578263i	$0.803731\pi$
$762$		0			0
$763$	−71.6325	+	211.803i	−0.0938827	+	0.277592i
$764$	−224.132			−0.293367
$765$		0			0
$766$		−	311.685i		−	0.406899i
$767$	4.41039			0.00575018
$768$		0			0
$769$			1163.41i			1.51289i	0.654059	+	0.756444i	$0.273065\pi$
$769$			1163.41i			1.51289i	−0.654059	+	0.756444i	$0.726935\pi$
$770$	97.4558	+	32.9600i	0.126566	+	0.0428051i
$771$		0			0
$772$	−45.8234			−0.0593567
$773$			536.371i			0.693883i	0.937887	+	0.346941i	$0.112780\pi$
$773$			536.371i			0.693883i	−0.937887	+	0.346941i	$0.887220\pi$
$774$		0			0
$775$		−	1202.81i		−	1.55201i
$776$		−	284.837i		−	0.367058i
$777$		0			0
$778$	−542.309			−0.697055
$779$	114.573			0.147077
$780$		0			0
$781$	−518.382			−0.663741
$782$		−	289.328i		−	0.369985i
$783$		0			0
$784$	−155.765	−	118.968i	−0.198679	−	0.151745i
$785$	−58.1481			−0.0740740
$786$		0			0
$787$			83.9192i			0.106632i	0.998578	+	0.0533159i	$0.0169790\pi$
$787$			83.9192i			0.106632i	−0.998578	+	0.0533159i	$0.983021\pi$
$788$	232.118			0.294566
$789$		0			0
$790$		−	192.020i		−	0.243064i
$791$	−239.897	+	709.325i	−0.303283	+	0.896745i
$792$		0			0
$793$	25.7056			0.0324157
$794$		−	686.146i		−	0.864163i
$795$		0			0
$796$		−	326.202i		−	0.409802i
$797$			1005.57i			1.26169i	0.775908	+	0.630846i	$0.217292\pi$
$797$			1005.57i			1.26169i	−0.775908	+	0.630846i	$0.782708\pi$
$798$		0			0
$799$	1772.67			2.21862
$800$	−135.598			−0.169497
$801$		0			0
$802$	−358.045			−0.446440
$803$			723.283i			0.900727i
$804$		0			0
$805$	−45.2649	−	15.3088i	−0.0562297	−	0.0190171i
$806$	−635.647			−0.788644
$807$		0			0
$808$			392.819i			0.486162i
$809$	282.853			0.349633			0.174816	−	0.984601i	$-0.444067\pi$
$809$	282.853			0.349633			0.174816	+	0.984601i	$0.444067\pi$
$810$		0			0
$811$		−	923.997i		−	1.13933i	−0.821877	−	0.569665i	$-0.807073\pi$
$811$		−	923.997i		−	1.13933i	0.821877	−	0.569665i	$-0.192927\pi$
$812$	134.558	−	397.862i	0.165712	−	0.489978i
$813$		0			0
$814$	−447.765			−0.550079
$815$		−	177.467i		−	0.217752i
$816$		0			0
$817$		−	1200.63i		−	1.46956i
$818$			7.62452i			0.00932093i
$819$		0			0
$820$	14.4121			0.0175758
$821$	−1272.32			−1.54972			−0.774862	−	0.632131i	$-0.782181\pi$
$821$	−1272.32			−1.54972			−0.774862	+	0.632131i	$0.782181\pi$
$822$		0			0
$823$	381.852			0.463976			0.231988	−	0.972719i	$-0.425477\pi$
$823$	381.852			0.463976			0.231988	+	0.972719i	$0.425477\pi$
$824$			223.095i			0.270747i
$825$		0			0
$826$	−4.61732	−	1.56159i	−0.00558997	−	0.00189055i
$827$	−653.022			−0.789628			−0.394814	−	0.918761i	$-0.629191\pi$
$827$	−653.022			−0.789628			−0.394814	+	0.918761i	$0.629191\pi$
$828$		0			0
$829$			215.580i			0.260048i	0.991511	+	0.130024i	$0.0415054\pi$
$829$			215.580i			0.260048i	−0.991511	+	0.130024i	$0.958495\pi$
$830$	−149.823			−0.180510
$831$		0			0
$832$			71.6594i			0.0861291i
$833$	904.410	−	1184.14i	1.08573	−	1.42154i
$834$		0			0
$835$	−199.029			−0.238359
$836$			330.465i			0.395293i
$837$		0			0
$838$		−	416.389i		−	0.496884i
$839$		−	632.267i		−	0.753596i	−0.926295	−	0.376798i	$-0.877025\pi$
$839$		−	632.267i		−	0.753596i	0.926295	−	0.376798i	$-0.122975\pi$
$840$		0			0
$841$	59.0000			0.0701546
$842$	410.745			0.487821
$843$		0			0
$844$	212.853			0.252195
$845$			90.0615i			0.106582i
$846$		0			0
$847$	36.0803	−	106.682i	0.0425978	−	0.125953i
$848$	283.882			0.334767
$849$		0			0
$850$		−	1030.83i		−	1.21274i
$851$	207.971			0.244385
$852$		0			0
$853$		−	919.650i		−	1.07814i	−0.842262	−	0.539068i	$-0.818776\pi$
$853$		−	919.650i		−	1.07814i	0.842262	−	0.539068i	$-0.181224\pi$
$854$	−26.9117	−	9.10164i	−0.0315125	−	0.0106577i
$855$		0			0
$856$	−106.794			−0.124759
$857$			527.150i			0.615111i	0.951530	+	0.307556i	$0.0995110\pi$
$857$			527.150i			0.615111i	−0.951530	+	0.307556i	$0.900489\pi$
$858$		0			0
$859$			239.804i			0.279166i	0.990210	+	0.139583i	$0.0445762\pi$
$859$			239.804i			0.279166i	−0.990210	+	0.139583i	$0.955424\pi$
$860$		−	151.028i		−	0.175614i
$861$		0			0
$862$	71.7199			0.0832018
$863$	−362.507			−0.420054			−0.210027	−	0.977696i	$-0.567355\pi$
$863$	−362.507			−0.420054			−0.210027	+	0.977696i	$0.567355\pi$
$864$		0			0
$865$	39.0883			0.0451888
$866$		−	1024.97i		−	1.18356i
$867$		0			0
$868$	665.470	+	225.065i	0.766671	+	0.259291i
$869$	1370.70			1.57734
$870$		0			0
$871$			242.114i			0.277973i
$872$	−90.3431			−0.103605
$873$		0			0
$874$		−	153.490i		−	0.175617i
$875$	−329.470	−	111.428i	−0.376537	−	0.127346i
$876$		0			0
$877$	−861.647			−0.982493			−0.491247	−	0.871020i	$-0.663459\pi$
$877$	−861.647			−0.982493			−0.491247	+	0.871020i	$0.663459\pi$
$878$		−	525.703i		−	0.598750i
$879$		0			0
$880$			41.5692i			0.0472377i
$881$		−	334.553i		−	0.379742i	−0.981809	−	0.189871i	$-0.939193\pi$
$881$		−	334.553i		−	0.379742i	0.981809	−	0.189871i	$-0.0608071\pi$
$882$		0			0
$883$	−1488.01			−1.68518			−0.842590	−	0.538555i	$-0.818970\pi$
$883$	−1488.01			−1.68518			−0.842590	+	0.538555i	$0.818970\pi$
$884$	−544.764			−0.616248
$885$		0			0
$886$	−324.219			−0.365936
$887$		−	801.498i		−	0.903606i	−0.892118	−	0.451803i	$-0.850781\pi$
$887$		−	801.498i		−	0.903606i	0.892118	−	0.451803i	$-0.149219\pi$
$888$		0			0
$889$	−49.4701	+	146.273i	−0.0556469	+	0.164537i
$890$	208.014			0.233724
$891$		0			0
$892$			114.009i			0.127813i
$893$	940.410			1.05309
$894$		0			0
$895$			193.888i			0.216634i
$896$	25.3726	−	75.0215i	0.0283176	−	0.0837294i
$897$		0			0
$898$	−848.985			−0.945417
$899$			1505.35i			1.67448i
$900$		0			0
$901$			2158.11i			2.39524i
$902$			102.879i			0.114056i
$903$		0			0
$904$	−302.558			−0.334689
$905$	122.558			0.135424
$906$		0			0
$907$	−807.279			−0.890054			−0.445027	−	0.895517i	$-0.646806\pi$
$907$	−807.279			−0.890054			−0.445027	+	0.895517i	$0.646806\pi$
$908$			574.837i			0.633080i
$909$		0			0
$910$	−28.8242	+	85.2274i	−0.0316750	+	0.0936565i
$911$	442.742			0.485996			0.242998	−	0.970027i	$-0.421869\pi$
$911$	442.742			0.485996			0.242998	+	0.970027i	$0.421869\pi$
$912$		0			0
$913$		−	1069.49i		−	1.17140i
$914$	−684.230			−0.748610
$915$		0			0
$916$		−	278.809i		−	0.304377i
$917$	470.558	+	159.145i	0.513150	+	0.173549i
$918$		0			0
$919$	−118.455			−0.128896			−0.0644478	−	0.997921i	$-0.520529\pi$
$919$	−118.455			−0.128896			−0.0644478	+	0.997921i	$0.520529\pi$
$920$		−	19.3075i		−	0.0209864i
$921$		0			0
$922$		−	388.430i		−	0.421290i
$923$		−	453.337i		−	0.491156i
$924$		0			0
$925$	740.971			0.801049
$926$	217.040			0.234384
$927$		0			0
$928$	169.706			0.182872
$929$		−	629.297i		−	0.677392i	−0.940896	−	0.338696i	$-0.890014\pi$
$929$		−	629.297i		−	0.677392i	0.940896	−	0.338696i	$-0.109986\pi$
$930$		0			0
$931$	479.793	−	628.191i	0.515352	−	0.674749i
$932$	−725.470			−0.778401
$933$		0			0
$934$			87.3164i			0.0934865i
$935$	−316.014			−0.337983
$936$		0			0
$937$			210.631i			0.224793i	0.993663	+	0.112397i	$0.0358527\pi$
$937$			210.631i			0.224793i	−0.993663	+	0.112397i	$0.964147\pi$
$938$	85.7258	−	253.474i	0.0913921	−	0.270228i
$939$		0			0
$940$	118.294			0.125845
$941$		−	178.422i		−	0.189609i	−0.995496	−	0.0948047i	$-0.969777\pi$
$941$		−	178.422i		−	0.189609i	0.995496	−	0.0948047i	$-0.0302226\pi$
$942$		0			0
$943$		−	47.7836i		−	0.0506719i
$944$		−	1.96949i		−	0.00208632i
$945$		0			0
$946$	1078.09			1.13963
$947$	−423.463			−0.447163			−0.223581	−	0.974685i	$-0.571775\pi$
$947$	−423.463			−0.447163			−0.223581	+	0.974685i	$0.571775\pi$
$948$		0			0
$949$	−632.528			−0.666521
$950$		−	546.860i		−	0.575643i
$951$		0			0
$952$	570.323	+	192.885i	0.599079	+	0.202611i
$953$	546.706			0.573669			0.286834	−	0.957980i	$-0.407397\pi$
$953$	546.706			0.573669			0.286834	+	0.957980i	$0.407397\pi$
$954$		0			0
$955$		−	113.704i		−	0.119061i
$956$	−36.9563			−0.0386572
$957$		0			0
$958$		−	787.030i		−	0.821534i
$959$	−237.192	+	701.328i	−0.247332	+	0.731311i
$960$		0			0
$961$	−1556.88			−1.62006
$962$		−	391.580i		−	0.407048i
$963$		0			0
$964$			356.208i			0.369510i
$965$		−	23.2465i		−	0.0240896i
$966$		0			0
$967$	1262.32			1.30540			0.652701	−	0.757616i	$-0.273636\pi$
$967$	1262.32			1.30540			0.652701	+	0.757616i	$0.273636\pi$
$968$	45.5046			0.0470089
$969$		0			0
$970$	144.500			0.148969
$971$		−	1080.93i		−	1.11322i	−0.830775	−	0.556608i	$-0.812102\pi$
$971$		−	1080.93i		−	1.11322i	0.830775	−	0.556608i	$-0.187898\pi$
$972$		0			0
$973$	1202.35	+	406.640i	1.23572	+	0.417924i
$974$	459.931			0.472208
$975$		0			0
$976$		−	11.4790i		−	0.0117613i
$977$	−1800.26			−1.84264			−0.921322	−	0.388801i	$-0.872889\pi$
$977$	−1800.26			−1.84264			−0.921322	+	0.388801i	$0.872889\pi$
$978$		0			0
$979$			1484.88i			1.51673i
$980$	60.3532	−	79.0203i	0.0615849	−	0.0806329i
$981$		0			0
$982$	910.014			0.926695
$983$			996.810i			1.01405i	0.861932	+	0.507025i	$0.169255\pi$
$983$			996.810i			1.01405i	−0.861932	+	0.507025i	$0.830745\pi$
$984$		0			0
$985$			117.755i			0.119548i
$986$			1290.12i			1.30844i
$987$		0			0
$988$	−288.999			−0.292509
$989$	−500.735			−0.506304
$990$		0			0
$991$	788.721			0.795884			0.397942	−	0.917411i	$-0.369725\pi$
$991$	788.721			0.795884			0.397942	+	0.917411i	$0.369725\pi$
$992$			283.852i			0.286142i
$993$		0			0
$994$	−160.514	+	474.607i	−0.161483	+	0.477471i
$995$	165.484			0.166316
$996$		0			0
$997$		−	1942.70i		−	1.94854i	−0.225379	−	0.974271i	$-0.572362\pi$
$997$		−	1942.70i		−	1.94854i	0.225379	−	0.974271i	$-0.427638\pi$
$998$	−1068.33			−1.07047
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.c.b.55.2		4
3.2	odd	2		42.3.c.a.13.3	✓	4
4.3	odd	2		1008.3.f.g.433.3		4
7.2	even	3		882.3.n.d.325.2		4
7.3	odd	6		882.3.n.d.19.2		4
7.4	even	3		882.3.n.a.19.2		4
7.5	odd	6		882.3.n.a.325.2		4
7.6	odd	2	inner	126.3.c.b.55.1		4
12.11	even	2		336.3.f.c.97.4		4
15.2	even	4		1050.3.h.a.349.5		8
15.8	even	4		1050.3.h.a.349.4		8
15.14	odd	2		1050.3.f.a.601.2		4
21.2	odd	6		294.3.g.c.31.1		4
21.5	even	6		294.3.g.b.31.1		4
21.11	odd	6		294.3.g.b.19.1		4
21.17	even	6		294.3.g.c.19.1		4
21.20	even	2		42.3.c.a.13.4	yes	4
24.5	odd	2		1344.3.f.f.769.3		4
24.11	even	2		1344.3.f.e.769.1		4
28.27	even	2		1008.3.f.g.433.2		4
84.83	odd	2		336.3.f.c.97.1		4
105.62	odd	4		1050.3.h.a.349.8		8
105.83	odd	4		1050.3.h.a.349.1		8
105.104	even	2		1050.3.f.a.601.1		4
168.83	odd	2		1344.3.f.e.769.4		4
168.125	even	2		1344.3.f.f.769.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.c.a.13.3	✓	4	3.2	odd	2
42.3.c.a.13.4	yes	4	21.20	even	2
126.3.c.b.55.1		4	7.6	odd	2	inner
126.3.c.b.55.2		4	1.1	even	1	trivial
294.3.g.b.19.1		4	21.11	odd	6
294.3.g.b.31.1		4	21.5	even	6
294.3.g.c.19.1		4	21.17	even	6
294.3.g.c.31.1		4	21.2	odd	6
336.3.f.c.97.1		4	84.83	odd	2
336.3.f.c.97.4		4	12.11	even	2
882.3.n.a.19.2		4	7.4	even	3
882.3.n.a.325.2		4	7.5	odd	6
882.3.n.d.19.2		4	7.3	odd	6
882.3.n.d.325.2		4	7.2	even	3
1008.3.f.g.433.2		4	28.27	even	2
1008.3.f.g.433.3		4	4.3	odd	2
1050.3.f.a.601.1		4	105.104	even	2
1050.3.f.a.601.2		4	15.14	odd	2
1050.3.h.a.349.1		8	105.83	odd	4
1050.3.h.a.349.4		8	15.8	even	4
1050.3.h.a.349.5		8	15.2	even	4
1050.3.h.a.349.8		8	105.62	odd	4
1344.3.f.e.769.1		4	24.11	even	2
1344.3.f.e.769.4		4	168.83	odd	2
1344.3.f.f.769.2		4	168.125	even	2
1344.3.f.f.769.3		4	24.5	odd	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)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +2.00000 q^{4} +1.01461i q^{5} +(-2.24264 + 6.63103i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q-1.41421 q^{2} +2.00000 q^{4} +1.01461i q^{5} +(-2.24264 + 6.63103i) q^{7} -2.82843 q^{8} -1.43488i q^{10} +10.2426 q^{11} +8.95743i q^{13} +(3.17157 - 9.37769i) q^{14} +4.00000 q^{16} +30.4085i q^{17} +16.1318i q^{19} +2.02922i q^{20} -14.4853 q^{22} +6.72792 q^{23} +23.9706 q^{25} -12.6677i q^{26} +(-4.48528 + 13.2621i) q^{28} -30.0000 q^{29} -50.1785i q^{31} -5.65685 q^{32} -43.0041i q^{34} +(-6.72792 - 2.27541i) q^{35} +30.9117 q^{37} -22.8138i q^{38} -2.86976i q^{40} -7.10228i q^{41} -74.4264 q^{43} +20.4853 q^{44} -9.51472 q^{46} -58.2954i q^{47} +(-38.9411 - 29.7420i) q^{49} -33.8995 q^{50} +17.9149i q^{52} +70.9706 q^{53} +10.3923i q^{55} +(6.34315 - 18.7554i) q^{56} +42.4264 q^{58} -0.492372i q^{59} -2.86976i q^{61} +70.9631i q^{62} +8.00000 q^{64} -9.08831 q^{65} +27.0294 q^{67} +60.8170i q^{68} +(9.51472 + 3.21792i) q^{70} -50.6102 q^{71} +70.6149i q^{73} -43.7157 q^{74} +32.2636i q^{76} +(-22.9706 + 67.9193i) q^{77} +133.823 q^{79} +4.05845i q^{80} +10.0441i q^{82} -104.415i q^{83} -30.8528 q^{85} +105.255 q^{86} -28.9706 q^{88} +144.970i q^{89} +(-59.3970 - 20.0883i) q^{91} +13.4558 q^{92} +82.4421i q^{94} -16.3675 q^{95} +100.705i q^{97} +(55.0711 + 42.0616i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} + 8 q^{7}+O(q^{10}) \) 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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