LMFDB - Embedded newform 252.4.t.a.89.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(17,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 290 x^{14} + 1728 x^{13} + 29275 x^{12} - 246984 x^{11} - 955194 x^{10} + \cdots + 7375227456 $ x^16 - 4x^15 - 290x^14 + 1728x^13 + 29275x^12 - 246984x^11 - 955194x^10 + 14344616x^9 - 18123280x^8 - 273588032x^7 + 1239640536x^6 - 1407381792x^5 - 1961185792x^4 + 4297169408x^3 + 2991779296x^2 - 11217342336*x + 7375227456
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{18} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.4
Root			$8.15703 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	252.89
Dual form			252.4.t.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.41226 + 5.91021i) q^{5} +(-14.9386 - 10.9471i) q^{7} +O(q^{10})$	$q+(-3.41226 + 5.91021i) q^{5} +(-14.9386 - 10.9471i) q^{7} +(50.5303 - 29.1737i) q^{11} +38.5535i q^{13} +(-16.1260 - 27.9310i) q^{17} +(107.846 + 62.2650i) q^{19} +(174.217 + 100.584i) q^{23} +(39.2130 + 67.9188i) q^{25} -104.357i q^{29} +(-240.747 + 138.995i) q^{31} +(115.674 - 50.9356i) q^{35} +(23.8286 - 41.2724i) q^{37} +387.272 q^{41} +272.528 q^{43} +(81.5941 - 141.325i) q^{47} +(103.321 + 327.068i) q^{49} +(313.867 - 181.211i) q^{53} +398.193i q^{55} +(105.853 + 183.342i) q^{59} +(-202.919 - 117.155i) q^{61} +(-227.859 - 131.555i) q^{65} +(-262.131 - 454.024i) q^{67} +348.689i q^{71} +(465.143 - 268.550i) q^{73} +(-1074.22 - 117.348i) q^{77} +(-362.792 + 628.374i) q^{79} +392.121 q^{83} +220.104 q^{85} +(-430.015 + 744.807i) q^{89} +(422.050 - 575.934i) q^{91} +(-735.998 + 424.929i) q^{95} -978.030i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{7}+O(q^{10}) $ 16 * q - 4 * q^7	$ 16 q - 4 q^{7} - 72 q^{19} - 212 q^{25} - 708 q^{31} + 76 q^{37} + 1408 q^{43} + 400 q^{49} - 1632 q^{61} - 1528 q^{67} - 2700 q^{73} - 364 q^{79} + 7392 q^{85} + 2472 q^{91}+O(q^{100}) $ 16 * q - 4 * q^7 - 72 * q^19 - 212 * q^25 - 708 * q^31 + 76 * q^37 + 1408 * q^43 + 400 * q^49 - 1632 * q^61 - 1528 * q^67 - 2700 * q^73 - 364 * q^79 + 7392 * q^85 + 2472 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−3.41226	+	5.91021i	−0.305202	+	0.528625i	−0.977306	−	0.211831i	$-0.932057\pi$
$5$	−3.41226	+	5.91021i	−0.305202	+	0.528625i	0.672104	+	0.740456i	$0.265391\pi$
$6$		0			0
$7$	−14.9386	−	10.9471i	−0.806607	−	0.591089i
$7$	−14.9386	−	10.9471i	−0.806607	−	0.591089i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	50.5303	−	29.1737i	1.38504	−	0.799654i	0.392290	−	0.919841i	$-0.371683\pi$
$11$	50.5303	−	29.1737i	1.38504	−	0.799654i	0.992751	+	0.120187i	$0.0383495\pi$
$12$		0			0
$13$			38.5535i			0.822525i	0.911517	+	0.411262i	$0.134912\pi$
$13$			38.5535i			0.822525i	−0.911517	+	0.411262i	$0.865088\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−16.1260	−	27.9310i	−0.230066	−	0.398486i	0.727761	−	0.685830i	$-0.240561\pi$
$17$	−16.1260	−	27.9310i	−0.230066	−	0.398486i	−0.957827	+	0.287345i	$0.907227\pi$
$18$		0			0
$19$	107.846	+	62.2650i	1.30219	+	0.751819i	0.980779	−	0.195121i	$-0.0625100\pi$
$19$	107.846	+	62.2650i	1.30219	+	0.751819i	0.321410	+	0.946940i	$0.395843\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	174.217	+	100.584i	1.57942	+	0.911880i	0.994940	+	0.100475i	$0.0320362\pi$
$23$	174.217	+	100.584i	1.57942	+	0.911880i	0.584484	+	0.811405i	$0.301297\pi$
$24$		0			0
$25$	39.2130	+	67.9188i	0.313704	+	0.543351i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	104.357i		−	0.668226i	−0.942533	−	0.334113i	$-0.891563\pi$
$29$		−	104.357i		−	0.668226i	0.942533	−	0.334113i	$-0.108437\pi$
$30$		0			0
$31$	−240.747	+	138.995i	−1.39482	+	0.805299i	−0.993844	−	0.110790i	$-0.964662\pi$
$31$	−240.747	+	138.995i	−1.39482	+	0.805299i	−0.400975	+	0.916089i	$0.631329\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	115.674	−	50.9356i	0.558642	−	0.245991i
$36$		0			0
$37$	23.8286	−	41.2724i	0.105876	−	0.183382i	−0.808220	−	0.588881i	$-0.799569\pi$
$37$	23.8286	−	41.2724i	0.105876	−	0.183382i	0.914096	+	0.405499i	$0.132902\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	387.272			1.47516			0.737582	−	0.675258i	$-0.235968\pi$
$41$	387.272			1.47516			0.737582	+	0.675258i	$0.235968\pi$
$42$		0			0
$43$	272.528			0.966515			0.483257	−	0.875478i	$-0.339454\pi$
$43$	272.528			0.966515			0.483257	+	0.875478i	$0.339454\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	81.5941	−	141.325i	0.253228	−	0.438604i	−0.711185	−	0.703005i	$-0.751841\pi$
$47$	81.5941	−	141.325i	0.253228	−	0.438604i	0.964413	+	0.264401i	$0.0851743\pi$
$48$		0			0
$49$	103.321	+	327.068i	0.301229	+	0.953552i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	313.867	−	181.211i	0.813452	−	0.469646i	−0.0347015	−	0.999398i	$-0.511048\pi$
$53$	313.867	−	181.211i	0.813452	−	0.469646i	0.848153	+	0.529751i	$0.177715\pi$
$54$		0			0
$55$			398.193i			0.976224i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	105.853	+	183.342i	0.233573	+	0.404561i	0.958857	−	0.283889i	$-0.0916248\pi$
$59$	105.853	+	183.342i	0.233573	+	0.404561i	−0.725284	+	0.688450i	$0.758291\pi$
$60$		0			0
$61$	−202.919	−	117.155i	−0.425919	−	0.245905i	0.271687	−	0.962386i	$-0.412418\pi$
$61$	−202.919	−	117.155i	−0.425919	−	0.245905i	−0.697607	+	0.716481i	$0.745752\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−227.859	−	131.555i	−0.434807	−	0.251036i
$66$		0			0
$67$	−262.131	−	454.024i	−0.477976	−	0.827879i	0.521705	−	0.853126i	$-0.325296\pi$
$67$	−262.131	−	454.024i	−0.477976	−	0.827879i	−0.999681	+	0.0252470i	$0.991963\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			348.689i			0.582842i	0.956595	+	0.291421i	$0.0941280\pi$
$71$			348.689i			0.582842i	−0.956595	+	0.291421i	$0.905872\pi$
$72$		0			0
$73$	465.143	−	268.550i	0.745765	−	0.430567i	−0.0783969	−	0.996922i	$-0.524980\pi$
$73$	465.143	−	268.550i	0.745765	−	0.430567i	0.824162	+	0.566355i	$0.191647\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1074.22	−	117.348i	−1.58985	−	0.173676i
$78$		0			0
$79$	−362.792	+	628.374i	−0.516675	+	0.894907i	0.483138	+	0.875544i	$0.339497\pi$
$79$	−362.792	+	628.374i	−0.516675	+	0.894907i	−0.999813	+	0.0193623i	$0.993836\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	392.121			0.518565			0.259283	−	0.965801i	$-0.416514\pi$
$83$	392.121			0.518565			0.259283	+	0.965801i	$0.416514\pi$
$84$		0			0
$85$	220.104			0.280866
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−430.015	+	744.807i	−0.512151	+	0.887072i	0.487750	+	0.872984i	$0.337818\pi$
$89$	−430.015	+	744.807i	−0.512151	+	0.887072i	−0.999901	+	0.0140882i	$0.995515\pi$
$90$		0			0
$91$	422.050	−	575.934i	0.486185	−	0.663454i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−735.998	+	424.929i	−0.794861	+	0.458913i
$96$		0			0
$97$		−	978.030i		−	1.02375i	−0.859059	−	0.511876i	$-0.828951\pi$
$97$		−	978.030i		−	1.02375i	0.859059	−	0.511876i	$-0.171049\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−224.150	−	388.240i	−0.220830	−	0.382488i	0.734230	−	0.678900i	$-0.237543\pi$
$101$	−224.150	−	388.240i	−0.220830	−	0.382488i	−0.955060	+	0.296412i	$0.904210\pi$
$102$		0			0
$103$	−1137.56	−	656.773i	−1.08823	−	0.628289i	−0.155124	−	0.987895i	$-0.549578\pi$
$103$	−1137.56	−	656.773i	−1.08823	−	0.628289i	−0.933104	+	0.359606i	$0.882911\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−161.506	−	93.2455i	−0.145919	−	0.0842466i	0.425263	−	0.905070i	$-0.360182\pi$
$107$	−161.506	−	93.2455i	−0.145919	−	0.0842466i	−0.571182	+	0.820823i	$0.693515\pi$
$108$		0			0
$109$	−61.5811	−	106.662i	−0.0541137	−	0.0937277i	0.837700	−	0.546131i	$-0.183900\pi$
$109$	−61.5811	−	106.662i	−0.0541137	−	0.0937277i	−0.891813	+	0.452404i	$0.850567\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	2267.03i		−	1.88729i	−0.330956	−	0.943646i	$-0.607371\pi$
$113$		−	2267.03i		−	1.88729i	0.330956	−	0.943646i	$-0.392629\pi$
$114$		0			0
$115$	−1188.95	+	686.439i	−0.964086	+	0.556615i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−64.8649	+	593.781i	−0.0499677	+	0.457410i
$120$		0			0
$121$	1036.71	−	1795.63i	0.778894	−	1.34908i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1388.28			−0.993376
$126$		0			0
$127$	839.285			0.586413			0.293207	−	0.956049i	$-0.405278\pi$
$127$	839.285			0.586413			0.293207	+	0.956049i	$0.405278\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1185.33	+	2053.06i	−0.790559	+	1.36929i	0.135063	+	0.990837i	$0.456876\pi$
$131$	−1185.33	+	2053.06i	−0.790559	+	1.36929i	−0.925621	+	0.378451i	$0.876457\pi$
$132$		0			0
$133$	−929.444	−	2110.75i	−0.605963	−	1.37613i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2656.64	+	1533.81i	−1.65673	+	0.956513i	−0.682520	+	0.730866i	$0.739116\pi$
$137$	−2656.64	+	1533.81i	−1.65673	+	0.956513i	−0.974209	+	0.225647i	$0.927550\pi$
$138$		0			0
$139$			2191.44i			1.33723i	0.743608	+	0.668616i	$0.233113\pi$
$139$			2191.44i			1.33723i	−0.743608	+	0.668616i	$0.766887\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1124.75	+	1948.12i	0.657735	+	1.13923i
$144$		0			0
$145$	616.770	+	356.092i	0.353241	+	0.203944i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	398.867	+	230.286i	0.219305	+	0.126616i	0.605628	−	0.795748i	$-0.292922\pi$
$149$	398.867	+	230.286i	0.219305	+	0.126616i	−0.386323	+	0.922363i	$0.626255\pi$
$150$		0			0
$151$	−317.552	−	550.017i	−0.171139	−	0.296422i	0.767679	−	0.640834i	$-0.221412\pi$
$151$	−317.552	−	550.017i	−0.171139	−	0.296422i	−0.938818	+	0.344412i	$0.888078\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	1897.15i		−	0.983115i
$156$		0			0
$157$	479.721	−	276.967i	0.243859	−	0.140792i	−0.373090	−	0.927795i	$-0.621702\pi$
$157$	479.721	−	276.967i	0.243859	−	0.140792i	0.616949	+	0.787003i	$0.288368\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1501.44	−	3409.76i	−0.734971	−	1.66911i
$162$		0			0
$163$	−687.621	+	1190.99i	−0.330421	+	0.572306i	−0.982594	−	0.185764i	$-0.940524\pi$
$163$	−687.621	+	1190.99i	−0.330421	+	0.572306i	0.652173	+	0.758070i	$0.273857\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3999.79			1.85337			0.926685	−	0.375839i	$-0.122645\pi$
$167$	3999.79			1.85337			0.926685	+	0.375839i	$0.122645\pi$
$168$		0			0
$169$	710.626			0.323453
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−225.948	+	391.354i	−0.0992979	+	0.171989i	−0.911394	−	0.411534i	$-0.864993\pi$
$173$	−225.948	+	391.354i	−0.0992979	+	0.171989i	0.812096	+	0.583523i	$0.198326\pi$
$174$		0			0
$175$	157.730	−	1443.88i	0.0681329	−	0.623697i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1959.62	−	1131.39i	0.818262	−	0.472424i	−0.0315548	−	0.999502i	$-0.510046\pi$
$179$	1959.62	−	1131.39i	0.818262	−	0.472424i	0.849817	+	0.527078i	$0.176713\pi$
$180$		0			0
$181$			3035.53i			1.24657i	0.781994	+	0.623286i	$0.214203\pi$
$181$			3035.53i			1.24657i	−0.781994	+	0.623286i	$0.785797\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	162.619	+	281.664i	0.0646270	+	0.111937i
$186$		0			0
$187$	−1629.70	−	940.907i	−0.637302	−	0.367946i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1676.68	+	968.031i	0.635184	+	0.366724i	0.782757	−	0.622327i	$-0.213813\pi$
$191$	1676.68	+	968.031i	0.635184	+	0.366724i	−0.147573	+	0.989051i	$0.547146\pi$
$192$		0			0
$193$	1062.00	+	1839.43i	0.396084	+	0.686038i	0.993239	−	0.116088i	$-0.0370356\pi$
$193$	1062.00	+	1839.43i	0.396084	+	0.686038i	−0.597155	+	0.802126i	$0.703702\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	2122.77i		−	0.767720i	−0.923391	−	0.383860i	$-0.874594\pi$
$197$		−	2122.77i		−	0.767720i	0.923391	−	0.383860i	$-0.125406\pi$
$198$		0			0
$199$	1035.18	−	597.659i	0.368752	−	0.212899i	−0.304161	−	0.952621i	$-0.598376\pi$
$199$	1035.18	−	597.659i	0.368752	−	0.212899i	0.672913	+	0.739722i	$0.265043\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1142.40	+	1558.94i	−0.394981	+	0.538995i
$204$		0			0
$205$	−1321.47	+	2288.86i	−0.450223	+	0.779809i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	7265.99			2.40478
$210$		0			0
$211$	188.402			0.0614698			0.0307349	−	0.999528i	$-0.490215\pi$
$211$	188.402			0.0614698			0.0307349	+	0.999528i	$0.490215\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−929.937	+	1610.70i	−0.294982	+	0.510924i
$216$		0			0
$217$	5118.01	+	559.093i	1.60107	+	0.174902i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1076.84	−	621.712i	0.327764	−	0.189235i
$222$		0			0
$223$			2802.67i			0.841618i	0.907149	+	0.420809i	$0.138254\pi$
$223$			2802.67i			0.841618i	−0.907149	+	0.420809i	$0.861746\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	812.590	+	1407.45i	0.237593	+	0.411522i	0.960023	−	0.279921i	$-0.0903084\pi$
$227$	812.590	+	1407.45i	0.237593	+	0.411522i	−0.722430	+	0.691444i	$0.756975\pi$
$228$		0			0
$229$	−5733.12	−	3310.02i	−1.65439	−	0.955163i	−0.975236	−	0.221167i	$-0.929013\pi$
$229$	−5733.12	−	3310.02i	−1.65439	−	0.955163i	−0.679154	−	0.733996i	$-0.737653\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1356.99	−	783.461i	−0.381543	−	0.220284i	0.296946	−	0.954894i	$-0.404032\pi$
$233$	−1356.99	−	783.461i	−0.381543	−	0.220284i	−0.678490	+	0.734610i	$0.737365\pi$
$234$		0			0
$235$	556.841	+	964.477i	0.154571	+	0.267726i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	5211.23i		−	1.41040i	−0.709006	−	0.705202i	$-0.750856\pi$
$239$		−	5211.23i		−	1.41040i	0.709006	−	0.705202i	$-0.249144\pi$
$240$		0			0
$241$	−3449.81	+	1991.75i	−0.922082	+	0.532364i	−0.884299	−	0.466922i	$-0.845363\pi$
$241$	−3449.81	+	1991.75i	−0.922082	+	0.532364i	−0.0377833	+	0.999286i	$0.512030\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2285.60	−	505.391i	−0.596007	−	0.131789i
$246$		0			0
$247$	−2400.53	+	4157.85i	−0.618390	+	1.07108i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7086.26			1.78199			0.890997	−	0.454009i	$-0.150007\pi$
$251$	7086.26			1.78199			0.890997	+	0.454009i	$0.150007\pi$
$252$		0			0
$253$	11737.6			2.91676
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1221.82	−	2116.25i	0.296556	−	0.513651i	−0.678789	−	0.734333i	$-0.737495\pi$
$257$	1221.82	−	2116.25i	0.296556	−	0.513651i	0.975346	+	0.220682i	$0.0708284\pi$
$258$		0			0
$259$	−807.779	+	355.696i	−0.193795	+	0.0853354i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2167.27	+	1251.27i	−0.508135	+	0.293372i	−0.732067	−	0.681233i	$-0.761444\pi$
$263$	−2167.27	+	1251.27i	−0.508135	+	0.293372i	0.223932	+	0.974605i	$0.428111\pi$
$264$		0			0
$265$			2473.36i			0.573348i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4160.18	+	7205.64i	0.942939	+	1.63322i	0.759825	+	0.650127i	$0.225284\pi$
$269$	4160.18	+	7205.64i	0.942939	+	1.63322i	0.183114	+	0.983092i	$0.441382\pi$
$270$		0			0
$271$	5816.51	+	3358.16i	1.30379	+	0.752745i	0.981052	−	0.193742i	$-0.0620626\pi$
$271$	5816.51	+	3358.16i	1.30379	+	0.752745i	0.322740	+	0.946488i	$0.395396\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3962.88	+	2287.97i	0.868985	+	0.501709i
$276$		0			0
$277$	−3335.48	−	5777.22i	−0.723500	−	1.25314i	−0.959589	−	0.281407i	$-0.909199\pi$
$277$	−3335.48	−	5777.22i	−0.723500	−	1.25314i	0.236089	−	0.971732i	$-0.424134\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	5065.50i		−	1.07538i	−0.843142	−	0.537692i	$-0.819296\pi$
$281$		−	5065.50i		−	1.07538i	0.843142	−	0.537692i	$-0.180704\pi$
$282$		0			0
$283$	−2227.91	+	1286.28i	−0.467969	+	0.270182i	−0.715389	−	0.698726i	$-0.753751\pi$
$283$	−2227.91	+	1286.28i	−0.467969	+	0.270182i	0.247420	+	0.968908i	$0.420417\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5785.29	−	4239.51i	−1.18988	−	0.871952i
$288$		0			0
$289$	1936.41	−	3353.96i	0.394139	−	0.682670i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5796.55			−1.15576			−0.577881	−	0.816121i	$-0.696120\pi$
$293$	−5796.55			−1.15576			−0.577881	+	0.816121i	$0.696120\pi$
$294$		0			0
$295$	−1444.79			−0.285148
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3877.87	+	6716.67i	−0.750044	+	1.29911i
$300$		0			0
$301$	−4071.18	−	2983.39i	−0.779597	−	0.571296i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1384.82	−	799.528i	0.259983	−	0.150101i
$306$		0			0
$307$			753.054i			0.139997i	0.997547	+	0.0699985i	$0.0222994\pi$
$307$			753.054i			0.139997i	−0.997547	+	0.0699985i	$0.977701\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2694.45	−	4666.93i	−0.491281	−	0.850924i	0.508668	−	0.860963i	$-0.330138\pi$
$311$	−2694.45	−	4666.93i	−0.491281	−	0.850924i	−0.999950	+	0.0100384i	$0.996805\pi$
$312$		0			0
$313$	−6116.48	−	3531.35i	−1.10455	−	0.637712i	−0.167138	−	0.985934i	$-0.553452\pi$
$313$	−6116.48	−	3531.35i	−1.10455	−	0.637712i	−0.937412	+	0.348221i	$0.886786\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2126.55	+	1227.77i	0.376780	+	0.217534i	0.676416	−	0.736520i	$-0.263532\pi$
$317$	2126.55	+	1227.77i	0.376780	+	0.217534i	−0.299636	+	0.954053i	$0.596865\pi$
$318$		0			0
$319$	−3044.47	−	5273.17i	−0.534350	−	0.925521i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	4016.33i		−	0.691872i
$324$		0			0
$325$	−2618.51	+	1511.80i	−0.446919	+	0.258029i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2766.00	+	1217.98i	−0.463510	+	0.204101i
$330$		0			0
$331$	4255.12	−	7370.09i	0.706594	−	1.22386i	−0.259519	−	0.965738i	$-0.583564\pi$
$331$	4255.12	−	7370.09i	0.706594	−	1.22386i	0.966113	−	0.258119i	$-0.0831028\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3577.84			0.583517
$336$		0			0
$337$	1803.01			0.291443			0.145722	−	0.989326i	$-0.453450\pi$
$337$	1803.01			0.291443			0.145722	+	0.989326i	$0.453450\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8110.00	+	14046.9i	−1.28792	+	2.23075i
$342$		0			0
$343$	2036.98	−	6017.00i	0.320661	−	0.947194i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7237.09	+	4178.34i	−1.11962	+	0.646412i	−0.941303	−	0.337562i	$-0.890398\pi$
$347$	−7237.09	+	4178.34i	−1.11962	+	0.646412i	−0.178314	+	0.983974i	$0.557064\pi$
$348$		0			0
$349$			4977.74i			0.763474i	0.924271	+	0.381737i	$0.124674\pi$
$349$			4977.74i			0.763474i	−0.924271	+	0.381737i	$0.875326\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3820.07	−	6616.56i	−0.575983	−	0.997631i	−0.995934	−	0.0900846i	$-0.971286\pi$
$353$	−3820.07	−	6616.56i	−0.575983	−	0.997631i	0.419952	−	0.907547i	$-0.362047\pi$
$354$		0			0
$355$	−2060.82	−	1189.82i	−0.308105	−	0.177884i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3601.64	−	2079.40i	−0.529490	−	0.305701i	0.211319	−	0.977417i	$-0.432224\pi$
$359$	−3601.64	−	2079.40i	−0.529490	−	0.305701i	−0.740809	+	0.671716i	$0.765558\pi$
$360$		0			0
$361$	4324.35	+	7490.00i	0.630464	+	1.09200i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			3665.45i			0.525640i
$366$		0			0
$367$	−1885.57	+	1088.64i	−0.268191	+	0.154840i	−0.628065	−	0.778161i	$-0.716153\pi$
$367$	−1885.57	+	1088.64i	−0.268191	+	0.154840i	0.359874	+	0.933001i	$0.382820\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6672.46	−	728.902i	−0.933738	−	0.102002i
$372$		0			0
$373$	190.136	−	329.324i	0.0263937	−	0.0457152i	−0.852527	−	0.522683i	$-0.824931\pi$
$373$	190.136	−	329.324i	0.0263937	−	0.0457152i	0.878921	+	0.476968i	$0.158264\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4023.32			0.549632
$378$		0			0
$379$	6918.48			0.937673			0.468837	−	0.883285i	$-0.344673\pi$
$379$	6918.48			0.937673			0.468837	+	0.883285i	$0.344673\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−63.4117	+	109.832i	−0.00846002	+	0.0146532i	−0.870224	−	0.492656i	$-0.836026\pi$
$383$	−63.4117	+	109.832i	−0.00846002	+	0.0146532i	0.861764	+	0.507309i	$0.169360\pi$
$384$		0			0
$385$	4359.06	−	5948.43i	0.577035	−	0.787429i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1278.19	+	737.963i	−0.166598	+	0.0961856i	−0.580981	−	0.813917i	$-0.697331\pi$
$389$	−1278.19	+	737.963i	−0.166598	+	0.0961856i	0.414383	+	0.910103i	$0.363998\pi$
$390$		0			0
$391$		−	6488.06i		−	0.839170i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2475.88	−	4288.35i	−0.315380	−	0.546254i
$396$		0			0
$397$	751.551	+	433.908i	0.0950107	+	0.0548545i	0.546753	−	0.837294i	$-0.315864\pi$
$397$	751.551	+	433.908i	0.0950107	+	0.0548545i	−0.451742	+	0.892149i	$0.649197\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	603.832	+	348.623i	0.0751968	+	0.0434149i	0.537127	−	0.843501i	$-0.319510\pi$
$401$	603.832	+	348.623i	0.0751968	+	0.0434149i	−0.461930	+	0.886916i	$0.652843\pi$
$402$		0			0
$403$	−5358.75	−	9281.63i	−0.662378	−	1.14727i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	2780.68i		−	0.338656i
$408$		0			0
$409$	−5359.98	+	3094.59i	−0.648005	+	0.374126i	−0.787692	−	0.616070i	$-0.788724\pi$
$409$	−5359.98	+	3094.59i	−0.648005	+	0.374126i	0.139686	+	0.990196i	$0.455391\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	425.780	−	3897.65i	0.0507295	−	0.464384i
$414$		0			0
$415$	−1338.02	+	2317.52i	−0.158267	+	0.274127i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1443.53			−0.168308			−0.0841538	−	0.996453i	$-0.526819\pi$
$419$	−1443.53			−0.168308			−0.0841538	+	0.996453i	$0.526819\pi$
$420$		0			0
$421$	−15750.0			−1.82330			−0.911648	−	0.410971i	$-0.865190\pi$
$421$	−15750.0			−1.82330			−0.911648	+	0.410971i	$0.865190\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1264.69	−	2190.51i	0.144345	−	0.250013i
$426$		0			0
$427$	1748.80	+	3971.50i	0.198198	+	0.450104i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9792.23	+	5653.55i	−1.09437	+	0.631837i	−0.934738	−	0.355339i	$-0.884366\pi$
$431$	−9792.23	+	5653.55i	−1.09437	+	0.631837i	−0.159637	+	0.987176i	$0.551032\pi$
$432$		0			0
$433$			2318.26i			0.257295i	0.991690	+	0.128647i	$0.0410635\pi$
$433$			2318.26i			0.257295i	−0.991690	+	0.128647i	$0.958936\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12525.7	+	21695.2i	1.37114	+	2.37488i
$438$		0			0
$439$	−6678.84	−	3856.03i	−0.726113	−	0.419222i	0.0908855	−	0.995861i	$-0.471030\pi$
$439$	−6678.84	−	3856.03i	−0.726113	−	0.419222i	−0.816998	+	0.576640i	$0.804364\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−11158.1	−	6442.15i	−1.19670	−	0.690916i	−0.236883	−	0.971538i	$-0.576126\pi$
$443$	−11158.1	−	6442.15i	−1.19670	−	0.690916i	−0.959818	+	0.280623i	$0.909459\pi$
$444$		0			0
$445$	−2934.64	−	5082.95i	−0.312619	−	0.541472i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	319.989i		−	0.0336330i	−0.999859	−	0.0168165i	$-0.994647\pi$
$449$		−	319.989i		−	0.0336330i	0.999859	−	0.0168165i	$-0.00535311\pi$
$450$		0			0
$451$	19569.0	−	11298.1i	2.04316	−	1.17962i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1963.75	+	4459.64i	0.202334	+	0.459497i
$456$		0			0
$457$	−3897.48	+	6750.64i	−0.398942	+	0.690988i	−0.993596	−	0.112994i	$-0.963956\pi$
$457$	−3897.48	+	6750.64i	−0.398942	+	0.690988i	0.594653	+	0.803982i	$0.297289\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4610.97			0.465844			0.232922	−	0.972495i	$-0.425171\pi$
$461$	4610.97			0.465844			0.232922	+	0.972495i	$0.425171\pi$
$462$		0			0
$463$	15203.3			1.52604			0.763022	−	0.646373i	$-0.223715\pi$
$463$	15203.3			1.52604			0.763022	+	0.646373i	$0.223715\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8060.07	−	13960.4i	0.798663	−	1.38332i	−0.121824	−	0.992552i	$-0.538874\pi$
$467$	8060.07	−	13960.4i	0.798663	−	1.38332i	0.920487	−	0.390773i	$-0.127792\pi$
$468$		0			0
$469$	−1054.39	+	9652.05i	−0.103811	+	0.950299i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	13770.9	−	7950.65i	1.33866	−	0.772878i
$474$		0			0
$475$			9766.37i			0.943393i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3361.99	+	5823.14i	0.320696	+	0.555461i	0.980632	−	0.195861i	$-0.0627500\pi$
$479$	3361.99	+	5823.14i	0.320696	+	0.555461i	−0.659936	+	0.751322i	$0.729417\pi$
$480$		0			0
$481$	1591.20	+	918.678i	0.150836	+	0.0870854i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	5780.36	+	3337.29i	0.541181	+	0.312451i
$486$		0			0
$487$	5029.52	+	8711.38i	0.467986	+	0.810575i	0.999331	−	0.0365803i	$-0.0116465\pi$
$487$	5029.52	+	8711.38i	0.467986	+	0.810575i	−0.531345	+	0.847156i	$0.678313\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	18097.6i		−	1.66340i	−0.555222	−	0.831702i	$-0.687367\pi$
$491$		−	18097.6i		−	1.66340i	0.555222	−	0.831702i	$-0.312633\pi$
$492$		0			0
$493$	−2914.78	+	1682.85i	−0.266278	+	0.153736i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3817.14	−	5208.91i	0.344511	−	0.470124i
$498$		0			0
$499$	−5594.25	+	9689.53i	−0.501870	+	0.869264i	0.498128	+	0.867104i	$0.334021\pi$
$499$	−5594.25	+	9689.53i	−0.501870	+	0.869264i	−0.999998	+	0.00216055i	$0.999312\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	2912.13			0.258142			0.129071	−	0.991635i	$-0.458800\pi$
$503$	2912.13			0.258142			0.129071	+	0.991635i	$0.458800\pi$
$504$		0			0
$505$	3059.44			0.269591
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2400.48	+	4157.75i	−0.209036	+	0.362061i	−0.951411	−	0.307924i	$-0.900366\pi$
$509$	−2400.48	+	4157.75i	−0.209036	+	0.362061i	0.742375	+	0.669984i	$0.233699\pi$
$510$		0			0
$511$	−9888.41	−	1080.21i	−0.856042	−	0.0935144i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7763.33	−	4482.16i	0.664258	−	0.383510i
$516$		0			0
$517$		−	9521.61i		−	0.809980i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−3256.63	−	5640.65i	−0.273849	−	0.474321i	0.695995	−	0.718047i	$-0.254964\pi$
$521$	−3256.63	−	5640.65i	−0.273849	−	0.474321i	−0.969844	+	0.243726i	$0.921630\pi$
$522$		0			0
$523$	−3856.61	−	2226.62i	−0.322443	−	0.186163i	0.330038	−	0.943968i	$-0.392939\pi$
$523$	−3856.61	−	2226.62i	−0.322443	−	0.186163i	−0.652481	+	0.757805i	$0.726272\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7764.54	+	4482.86i	0.641800	+	0.370543i
$528$		0			0
$529$	14150.9	+	24510.0i	1.16305	+	2.01447i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			14930.7i			1.21336i
$534$		0			0
$535$	1102.20	−	636.356i	0.0890697	−	0.0514244i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	14762.7	+	13512.6i	1.17973	+	1.07983i
$540$		0			0
$541$	−3885.32	+	6729.58i	−0.308767	+	0.534800i	−0.978093	−	0.208169i	$-0.933250\pi$
$541$	−3885.32	+	6729.58i	−0.308767	+	0.534800i	0.669326	+	0.742969i	$0.266583\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	840.523			0.0660624
$546$		0			0
$547$	−4095.62			−0.320139			−0.160069	−	0.987106i	$-0.551172\pi$
$547$	−4095.62			−0.320139			−0.160069	+	0.987106i	$0.551172\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6497.77	−	11254.5i	0.502385	−	0.870156i
$552$		0			0
$553$	12298.5	−	5415.48i	0.945722	−	0.416437i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	219.268	−	126.594i	0.0166799	−	0.00963012i	−0.491637	−	0.870800i	$-0.663601\pi$
$557$	219.268	−	126.594i	0.0166799	−	0.00963012i	0.508317	+	0.861170i	$0.330268\pi$
$558$		0			0
$559$			10506.9i			0.794982i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−10252.3	−	17757.6i	−0.767469	−	1.32929i	−0.938931	−	0.344104i	$-0.888183\pi$
$563$	−10252.3	−	17757.6i	−0.767469	−	1.32929i	0.171463	−	0.985191i	$-0.445151\pi$
$564$		0			0
$565$	13398.6	+	7735.69i	0.997670	+	0.576005i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	11746.8	+	6782.03i	0.865470	+	0.499679i	0.865840	−	0.500321i	$-0.166785\pi$
$569$	11746.8	+	6782.03i	0.865470	+	0.499679i	−0.000370481		1.00000i	$0.500118\pi$
$570$		0			0
$571$	2350.96	+	4071.98i	0.172302	+	0.298436i	0.939224	−	0.343304i	$-0.111546\pi$
$571$	2350.96	+	4071.98i	0.172302	+	0.298436i	−0.766922	+	0.641740i	$0.778213\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			15776.8i			1.14424i
$576$		0			0
$577$	−3418.50	+	1973.67i	−0.246644	+	0.142400i	−0.618227	−	0.786000i	$-0.712149\pi$
$577$	−3418.50	+	1973.67i	−0.246644	+	0.142400i	0.371582	+	0.928400i	$0.378815\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−5857.73	−	4292.60i	−0.418278	−	0.306518i
$582$		0			0
$583$	10573.2	−	18313.3i	0.751110	−	1.30096i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12531.1			−0.881116			−0.440558	−	0.897724i	$-0.645219\pi$
$587$	−12531.1			−0.881116			−0.440558	+	0.897724i	$0.645219\pi$
$588$		0			0
$589$	−34618.1			−2.42176
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6475.41	−	11215.7i	0.448420	−	0.776686i	−0.549863	−	0.835255i	$-0.685320\pi$
$593$	6475.41	−	11215.7i	0.448420	−	0.776686i	0.998283	+	0.0585683i	$0.0186535\pi$
$594$		0			0
$595$	−3288.04	−	2409.50i	−0.226548	−	0.166017i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−121.786	+	70.3130i	−0.00830722	+	0.00479618i	−0.504148	−	0.863617i	$-0.668193\pi$
$599$	−121.786	+	70.3130i	−0.00830722	+	0.00479618i	0.495841	+	0.868414i	$0.334860\pi$
$600$		0			0
$601$		−	19220.3i		−	1.30451i	−0.758000	−	0.652255i	$-0.773823\pi$
$601$		−	19220.3i		−	1.30451i	0.758000	−	0.652255i	$-0.226177\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7075.03	+	12254.3i	0.475440	+	0.823486i
$606$		0			0
$607$	14750.7	+	8516.30i	0.986344	+	0.569466i	0.904180	−	0.427152i	$-0.140483\pi$
$607$	14750.7	+	8516.30i	0.986344	+	0.569466i	0.0821649	+	0.996619i	$0.473817\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5448.58	+	3145.74i	0.360763	+	0.208287i
$612$		0			0
$613$	−3246.99	−	5623.95i	−0.213939	−	0.370553i	0.739005	−	0.673700i	$-0.235296\pi$
$613$	−3246.99	−	5623.95i	−0.213939	−	0.370553i	−0.952944	+	0.303147i	$0.901963\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	12338.5i		−	0.805074i	−0.915404	−	0.402537i	$-0.868129\pi$
$617$		−	12338.5i		−	0.805074i	0.915404	−	0.402537i	$-0.131871\pi$
$618$		0			0
$619$	−8967.52	+	5177.40i	−0.582286	+	0.336183i	−0.762041	−	0.647528i	$-0.775803\pi$
$619$	−8967.52	+	5177.40i	−0.582286	+	0.336183i	0.179755	+	0.983711i	$0.442469\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	14577.3	−	6418.93i	0.937442	−	0.412791i
$624$		0			0
$625$	−164.430	+	284.802i	−0.0105235	+	0.0182273i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1537.04			−0.0974336
$630$		0			0
$631$	−4917.41			−0.310236			−0.155118	−	0.987896i	$-0.549576\pi$
$631$	−4917.41			−0.310236			−0.155118	+	0.987896i	$0.549576\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2863.86	+	4960.35i	−0.178974	+	0.309993i
$636$		0			0
$637$	−12609.6	+	3983.40i	−0.784320	+	0.247768i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	14808.6	−	8549.73i	0.912486	−	0.526824i	0.0312556	−	0.999511i	$-0.490049\pi$
$641$	14808.6	−	8549.73i	0.912486	−	0.526824i	0.881230	+	0.472688i	$0.156716\pi$
$642$		0			0
$643$			14631.4i			0.897365i	0.893691	+	0.448683i	$0.148107\pi$
$643$			14631.4i			0.897365i	−0.893691	+	0.448683i	$0.851893\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−14808.8	−	25649.5i	−0.899833	−	1.55856i	−0.827706	−	0.561161i	$-0.810355\pi$
$647$	−14808.8	−	25649.5i	−0.899833	−	1.55856i	−0.0721269	−	0.997395i	$-0.522979\pi$
$648$		0			0
$649$	10697.5	+	6176.22i	0.647018	+	0.373556i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−24397.1	−	14085.7i	−1.46207	−	0.844127i	−0.462963	−	0.886378i	$-0.653214\pi$
$653$	−24397.1	−	14085.7i	−1.46207	−	0.844127i	−0.999107	+	0.0422510i	$0.986547\pi$
$654$		0			0
$655$	−8089.34	−	14011.2i	−0.482560	−	0.835818i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			25287.9i			1.49480i	0.664372	+	0.747402i	$0.268699\pi$
$659$			25287.9i			1.49480i	−0.664372	+	0.747402i	$0.731301\pi$
$660$		0			0
$661$	8541.36	−	4931.35i	0.502603	−	0.290178i	−0.227185	−	0.973852i	$-0.572952\pi$
$661$	8541.36	−	4931.35i	0.502603	−	0.290178i	0.729788	+	0.683674i	$0.239619\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	15646.5	+	1709.23i	0.912399	+	0.0996708i
$666$		0			0
$667$	10496.6	−	18180.7i	0.609342	−	1.05541i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−13671.4			−0.786555
$672$		0			0
$673$	21145.6			1.21115			0.605574	−	0.795789i	$-0.292943\pi$
$673$	21145.6			1.21115			0.605574	+	0.795789i	$0.292943\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12062.4	+	20892.7i	−0.684779	+	1.18607i	0.288727	+	0.957412i	$0.406768\pi$
$677$	−12062.4	+	20892.7i	−0.684779	+	1.18607i	−0.973506	+	0.228661i	$0.926565\pi$
$678$		0			0
$679$	−10706.6	+	14610.4i	−0.605128	+	0.825765i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−26779.8	+	15461.4i	−1.50030	+	0.866197i	−0.500296	+	0.865854i	$0.666776\pi$
$683$	−26779.8	+	15461.4i	−1.50030	+	0.866197i	−1.00000		0.000342338i	$0.999891\pi$
$684$		0			0
$685$		−	20935.1i		−	1.16772i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6986.33	+	12100.7i	0.386296	+	0.669084i
$690$		0			0
$691$	10946.4	+	6319.92i	0.602636	+	0.347932i	0.770078	−	0.637950i	$-0.220217\pi$
$691$	10946.4	+	6319.92i	0.602636	+	0.347932i	−0.167442	+	0.985882i	$0.553551\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−12951.9	−	7477.76i	−0.706895	−	0.408126i
$696$		0			0
$697$	−6245.13	−	10816.9i	−0.339385	−	0.587832i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			24051.5i			1.29588i	0.761690	+	0.647942i	$0.224370\pi$
$701$			24051.5i			1.29588i	−0.761690	+	0.647942i	$0.775630\pi$
$702$		0			0
$703$	5139.65	−	2967.38i	0.275741	−	0.159199i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−901.621	+	8253.55i	−0.0479617	+	0.439048i
$708$		0			0
$709$	5438.14	−	9419.14i	0.288059	−	0.498932i	−0.685288	−	0.728273i	$-0.740323\pi$
$709$	5438.14	−	9419.14i	0.288059	−	0.498932i	0.973346	+	0.229340i	$0.0736568\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−55922.8			−2.93735
$714$		0			0
$715$	−15351.7			−0.802968
$716$		0			0
$717$		0			0
$718$		0			0
$719$	10456.8	−	18111.7i	0.542381	−	0.939431i	−0.456386	−	0.889782i	$-0.650856\pi$
$719$	10456.8	−	18111.7i	0.542381	−	0.939431i	0.998767	−	0.0496490i	$-0.0158103\pi$
$720$		0			0
$721$	9803.80	+	22264.3i	0.506398	+	1.15002i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	7087.78	−	4092.13i	0.363081	−	0.209625i
$726$		0			0
$727$		−	22897.9i		−	1.16814i	−0.811704	−	0.584068i	$-0.801460\pi$
$727$		−	22897.9i		−	1.16814i	0.811704	−	0.584068i	$-0.198540\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4394.77	−	7611.97i	−0.222362	−	0.385142i
$732$		0			0
$733$	−26899.9	−	15530.7i	−1.35549	−	0.782590i	−0.366474	−	0.930428i	$-0.619435\pi$
$733$	−26899.9	−	15530.7i	−1.35549	−	0.782590i	−0.989012	+	0.147838i	$0.952769\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−26491.1	−	15294.7i	−1.32403	−	0.764431i
$738$		0			0
$739$	−10170.9	−	17616.5i	−0.506281	−	0.876904i	−0.999974	−	0.00726747i	$-0.997687\pi$
$739$	−10170.9	−	17616.5i	−0.506281	−	0.876904i	0.493693	−	0.869636i	$-0.335647\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			31458.9i			1.55332i	0.629921	+	0.776660i	$0.283087\pi$
$743$			31458.9i			1.55332i	−0.629921	+	0.776660i	$0.716913\pi$
$744$		0			0
$745$	−2722.08	+	1571.59i	−0.133865	+	0.0772868i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1391.90	+	3160.98i	0.0679023	+	0.154205i
$750$		0			0
$751$	−9653.81	+	16720.9i	−0.469071	+	0.812456i	−0.999375	−	0.0353523i	$-0.988745\pi$
$751$	−9653.81	+	16720.9i	−0.469071	+	0.812456i	0.530303	+	0.847808i	$0.322078\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	4334.29			0.208928
$756$		0			0
$757$	−18791.2			−0.902216			−0.451108	−	0.892469i	$-0.648971\pi$
$757$	−18791.2			−0.902216			−0.451108	+	0.892469i	$0.648971\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13249.7	−	22949.2i	0.631145	−	1.09318i	−0.356172	−	0.934420i	$-0.615918\pi$
$761$	13249.7	−	22949.2i	0.631145	−	1.09318i	0.987318	−	0.158756i	$-0.0507482\pi$
$762$		0			0
$763$	−247.703	+	2267.50i	−0.0117529	+	0.107587i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7068.48	+	4080.99i	−0.332761	+	0.192120i
$768$		0			0
$769$		−	29077.1i		−	1.36352i	−0.731575	−	0.681761i	$-0.761215\pi$
$769$		−	29077.1i		−	1.36352i	0.731575	−	0.681761i	$-0.238785\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−14605.3	−	25297.2i	−0.679582	−	1.17707i	−0.975107	−	0.221735i	$-0.928828\pi$
$773$	−14605.3	−	25297.2i	−0.679582	−	1.17707i	0.295525	−	0.955335i	$-0.404505\pi$
$774$		0			0
$775$	−18880.8	−	10900.8i	−0.875119	−	0.505250i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	41765.8	+	24113.5i	1.92094	+	1.10906i
$780$		0			0
$781$	10172.5	+	17619.4i	0.466072	+	0.807260i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			3780.33i			0.171880i
$786$		0			0
$787$	29887.2	−	17255.4i	1.35370	−	0.781561i	0.364937	−	0.931032i	$-0.381090\pi$
$787$	29887.2	−	17255.4i	1.35370	−	0.781561i	0.988766	+	0.149471i	$0.0477571\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−24817.4	+	33866.1i	−1.11556	+	1.52230i
$792$		0			0
$793$	4516.74	−	7823.23i	0.202263	−	0.350329i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−40125.5			−1.78333			−0.891667	−	0.452692i	$-0.850464\pi$
$797$	−40125.5			−1.78333			−0.891667	+	0.452692i	$0.850464\pi$
$798$		0			0
$799$	−5263.13			−0.233037
$800$		0			0
$801$		0			0
$802$		0			0
$803$	15669.2	−	27139.8i	0.688610	−	1.19271i
$804$		0			0
$805$	25275.7	+	2761.13i	1.10665	+	0.120891i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	22092.7	−	12755.2i	0.960121	−	0.554326i	0.0639107	−	0.997956i	$-0.479643\pi$
$809$	22092.7	−	12755.2i	0.960121	−	0.554326i	0.896210	+	0.443630i	$0.146309\pi$
$810$		0			0
$811$		−	34785.8i		−	1.50616i	−0.657930	−	0.753079i	$-0.728568\pi$
$811$		−	34785.8i		−	1.50616i	0.657930	−	0.753079i	$-0.271432\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4692.68	−	8127.97i	−0.201690	−	0.349338i
$816$		0			0
$817$	29391.1	+	16968.9i	1.25858	+	0.726644i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−19574.7	−	11301.4i	−0.832108	−	0.480418i	0.0224658	−	0.999748i	$-0.492848\pi$
$821$	−19574.7	−	11301.4i	−0.832108	−	0.480418i	−0.854574	+	0.519330i	$0.826182\pi$
$822$		0			0
$823$	9554.31	+	16548.6i	0.404669	+	0.700907i	0.994283	−	0.106778i	$-0.0340535\pi$
$823$	9554.31	+	16548.6i	0.404669	+	0.700907i	−0.589614	+	0.807685i	$0.700720\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			7545.77i			0.317282i	0.987336	+	0.158641i	$0.0507112\pi$
$827$			7545.77i			0.317282i	−0.987336	+	0.158641i	$0.949289\pi$
$828$		0			0
$829$	−27729.7	+	16009.8i	−1.16175	+	0.670738i	−0.951723	−	0.306957i	$-0.900689\pi$
$829$	−27729.7	+	16009.8i	−1.16175	+	0.670738i	−0.210029	+	0.977695i	$0.567356\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	7469.18	−	8160.16i	0.310674	−	0.339415i
$834$		0			0
$835$	−13648.3	+	23639.6i	−0.565652	+	0.979738i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	33582.9			1.38190			0.690948	−	0.722905i	$-0.257194\pi$
$839$	33582.9			1.38190			0.690948	+	0.722905i	$0.257194\pi$
$840$		0			0
$841$	13498.7			0.553474
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2424.84	+	4199.95i	−0.0987185	+	0.170985i
$846$		0			0
$847$	−35143.9	+	15475.2i	−1.42569	+	0.627785i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	8302.70	−	4793.57i	0.334445	−	0.193092i
$852$		0			0
$853$		−	119.927i		−	0.00481387i	−0.999997	−	0.00240693i	$-0.999234\pi$
$853$		−	119.927i		−	0.00481387i	0.999997	−	0.00240693i	$-0.000766151\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2606.04	−	4513.80i	−0.103875	−	0.179917i	0.809403	−	0.587253i	$-0.199791\pi$
$857$	−2606.04	−	4513.80i	−0.103875	−	0.179917i	−0.913278	+	0.407337i	$0.866457\pi$
$858$		0			0
$859$	16503.5	+	9528.29i	0.655520	+	0.378464i	0.790568	−	0.612375i	$-0.209786\pi$
$859$	16503.5	+	9528.29i	0.655520	+	0.378464i	−0.135048	+	0.990839i	$0.543119\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−3451.41	−	1992.67i	−0.136138	−	0.0785994i	0.430384	−	0.902646i	$-0.358378\pi$
$863$	−3451.41	−	1992.67i	−0.136138	−	0.0785994i	−0.566522	+	0.824046i	$0.691711\pi$
$864$		0			0
$865$	−1541.99	−	2670.81i	−0.0606118	−	0.104983i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			42335.9i			1.65264i
$870$		0			0
$871$	17504.2	−	10106.1i	0.680951	−	0.393147i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	20739.0	+	15197.7i	0.801263	+	0.587173i
$876$		0			0
$877$	15501.1	−	26848.8i	0.596848	−	1.03377i	−0.396435	−	0.918063i	$-0.629753\pi$
$877$	15501.1	−	26848.8i	0.596848	−	1.03377i	0.993283	−	0.115709i	$-0.0369140\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−29240.6			−1.11821			−0.559103	−	0.829098i	$-0.688854\pi$
$881$	−29240.6			−1.11821			−0.559103	+	0.829098i	$0.688854\pi$
$882$		0			0
$883$	−42056.9			−1.60286			−0.801431	−	0.598088i	$-0.795927\pi$
$883$	−42056.9			−1.60286			−0.801431	+	0.598088i	$0.795927\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1216.16	−	2106.45i	0.0460367	−	0.0797379i	−0.842089	−	0.539339i	$-0.818674\pi$
$887$	1216.16	−	2106.45i	0.0460367	−	0.0797379i	0.888126	+	0.459601i	$0.152008\pi$
$888$		0			0
$889$	−12537.7	−	9187.75i	−0.473005	−	0.346622i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	17599.2	−	10160.9i	0.659502	−	0.380764i
$894$		0			0
$895$			15442.4i			0.576738i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	14505.1	+	25123.5i	0.538122	+	0.932054i
$900$		0			0
$901$	−10122.8	−	5844.41i	−0.374295	−	0.216099i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−17940.6	−	10358.0i	−0.658969	−	0.380456i
$906$		0			0
$907$	3376.70	+	5848.61i	0.123618	+	0.214112i	0.921192	−	0.389109i	$-0.127217\pi$
$907$	3376.70	+	5848.61i	0.123618	+	0.214112i	−0.797574	+	0.603221i	$0.793884\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	13545.2i		−	0.492615i	−0.969192	−	0.246308i	$-0.920783\pi$
$911$		−	13545.2i		−	0.492615i	0.969192	−	0.246308i	$-0.0792174\pi$
$912$		0			0
$913$	19814.0	−	11439.6i	0.718234	−	0.414673i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	40182.3	−	17693.8i	1.44704	−	0.637186i
$918$		0			0
$919$	−19698.8	+	34119.3i	−0.707077	+	1.22469i	0.258860	+	0.965915i	$0.416653\pi$
$919$	−19698.8	+	34119.3i	−0.707077	+	1.22469i	−0.965937	+	0.258778i	$0.916680\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−13443.2			−0.479402
$924$		0			0
$925$	3737.56			0.132854
$926$		0			0
$927$		0			0
$928$		0			0
$929$	5574.09	−	9654.60i	0.196857	−	0.340966i	−0.750651	−	0.660699i	$-0.770260\pi$
$929$	5574.09	−	9654.60i	0.196857	−	0.340966i	0.947508	+	0.319733i	$0.103593\pi$
$930$		0			0
$931$	−9222.09	+	41706.3i	−0.324642	+	1.46817i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	11121.9	−	6421.24i	0.389011	−	0.224596i
$936$		0			0
$937$			22882.5i			0.797800i	0.916994	+	0.398900i	$0.130608\pi$
$937$			22882.5i			0.797800i	−0.916994	+	0.398900i	$0.869392\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−2825.28	−	4893.52i	−0.0978761	−	0.169526i	0.812929	−	0.582362i	$-0.197872\pi$
$941$	−2825.28	−	4893.52i	−0.0978761	−	0.169526i	−0.910805	+	0.412836i	$0.864538\pi$
$942$		0			0
$943$	67469.3	+	38953.4i	2.32991	+	1.34517i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	26394.5	+	15238.9i	0.905709	+	0.522911i	0.879048	−	0.476733i	$-0.158179\pi$
$947$	26394.5	+	15238.9i	0.905709	+	0.522911i	0.0266611	+	0.999645i	$0.491513\pi$
$948$		0			0
$949$	10353.6	+	17932.9i	0.354152	+	0.613410i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	24139.2i		−	0.820511i	−0.911971	−	0.410255i	$-0.865440\pi$
$953$		−	24139.2i		−	0.820511i	0.911971	−	0.410255i	$-0.134560\pi$
$954$		0			0
$955$	−11442.5	+	6606.35i	−0.387719	+	0.223850i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	56477.2	+	6169.59i	1.90171	+	0.207744i
$960$		0			0
$961$	23743.8	−	41125.5i	0.797013	−	1.38047i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−14495.2			−0.483542
$966$		0			0
$967$	11475.1			0.381609			0.190804	−	0.981628i	$-0.438890\pi$
$967$	11475.1			0.381609			0.190804	+	0.981628i	$0.438890\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	2519.42	−	4363.76i	0.0832667	−	0.144222i	−0.821385	−	0.570375i	$-0.806798\pi$
$971$	2519.42	−	4363.76i	0.0832667	−	0.144222i	0.904651	+	0.426153i	$0.140131\pi$
$972$		0			0
$973$	23989.9	−	32736.9i	0.790423	−	1.07862i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11585.2	−	6688.74i	0.379370	−	0.219029i	−0.298174	−	0.954512i	$-0.596378\pi$
$977$	11585.2	−	6688.74i	0.379370	−	0.219029i	0.677544	+	0.735482i	$0.263044\pi$
$978$		0			0
$979$			50180.4i			1.63818i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5785.08	−	10020.1i	−0.187707	−	0.325117i	0.756779	−	0.653671i	$-0.226772\pi$
$983$	−5785.08	−	10020.1i	−0.187707	−	0.325117i	−0.944485	+	0.328554i	$0.893439\pi$
$984$		0			0
$985$	12546.0	+	7243.43i	0.405836	+	0.234310i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	47479.0	+	27412.0i	1.52654	+	0.881346i
$990$		0			0
$991$	−10029.6	−	17371.7i	−0.321493	−	0.556842i	0.659303	−	0.751877i	$-0.270851\pi$
$991$	−10029.6	−	17371.7i	−0.321493	−	0.556842i	−0.980796	+	0.195035i	$0.937518\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			8157.47i			0.259909i
$996$		0			0
$997$	−29515.9	+	17041.0i	−0.937592	+	0.541319i	−0.889205	−	0.457510i	$-0.848741\pi$
$997$	−29515.9	+	17041.0i	−0.937592	+	0.541319i	−0.0483872	+	0.998829i	$0.515408\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.t.a.89.4	yes	16
3.2	odd	2	inner	252.4.t.a.89.5	yes	16
4.3	odd	2		1008.4.bt.b.593.4		16
7.2	even	3		1764.4.f.a.881.10		16
7.3	odd	6	inner	252.4.t.a.17.5	yes	16
7.4	even	3		1764.4.t.b.521.4		16
7.5	odd	6		1764.4.f.a.881.8		16
7.6	odd	2		1764.4.t.b.1097.5		16
12.11	even	2		1008.4.bt.b.593.5		16
21.2	odd	6		1764.4.f.a.881.7		16
21.5	even	6		1764.4.f.a.881.9		16
21.11	odd	6		1764.4.t.b.521.5		16
21.17	even	6	inner	252.4.t.a.17.4	✓	16
21.20	even	2		1764.4.t.b.1097.4		16
28.3	even	6		1008.4.bt.b.17.5		16
84.59	odd	6		1008.4.bt.b.17.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.t.a.17.4	✓	16	21.17	even	6	inner
252.4.t.a.17.5	yes	16	7.3	odd	6	inner
252.4.t.a.89.4	yes	16	1.1	even	1	trivial
252.4.t.a.89.5	yes	16	3.2	odd	2	inner
1008.4.bt.b.17.4		16	84.59	odd	6
1008.4.bt.b.17.5		16	28.3	even	6
1008.4.bt.b.593.4		16	4.3	odd	2
1008.4.bt.b.593.5		16	12.11	even	2
1764.4.f.a.881.7		16	21.2	odd	6
1764.4.f.a.881.8		16	7.5	odd	6
1764.4.f.a.881.9		16	21.5	even	6
1764.4.f.a.881.10		16	7.2	even	3
1764.4.t.b.521.4		16	7.4	even	3
1764.4.t.b.521.5		16	21.11	odd	6
1764.4.t.b.1097.4		16	21.20	even	2
1764.4.t.b.1097.5		16	7.6	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.41226 + 5.91021i) q^{5} +(-14.9386 - 10.9471i) q^{7} +O(q^{10})\)	\(q+(-3.41226 + 5.91021i) q^{5} +(-14.9386 - 10.9471i) q^{7} +(50.5303 - 29.1737i) q^{11} +38.5535i q^{13} +(-16.1260 - 27.9310i) q^{17} +(107.846 + 62.2650i) q^{19} +(174.217 + 100.584i) q^{23} +(39.2130 + 67.9188i) q^{25} -104.357i q^{29} +(-240.747 + 138.995i) q^{31} +(115.674 - 50.9356i) q^{35} +(23.8286 - 41.2724i) q^{37} +387.272 q^{41} +272.528 q^{43} +(81.5941 - 141.325i) q^{47} +(103.321 + 327.068i) q^{49} +(313.867 - 181.211i) q^{53} +398.193i q^{55} +(105.853 + 183.342i) q^{59} +(-202.919 - 117.155i) q^{61} +(-227.859 - 131.555i) q^{65} +(-262.131 - 454.024i) q^{67} +348.689i q^{71} +(465.143 - 268.550i) q^{73} +(-1074.22 - 117.348i) q^{77} +(-362.792 + 628.374i) q^{79} +392.121 q^{83} +220.104 q^{85} +(-430.015 + 744.807i) q^{89} +(422.050 - 575.934i) q^{91} +(-735.998 + 424.929i) q^{95} -978.030i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{7}+O(q^{10}) \) 16 * q - 4 * q^7	\( 16 q - 4 q^{7} - 72 q^{19} - 212 q^{25} - 708 q^{31} + 76 q^{37} + 1408 q^{43} + 400 q^{49} - 1632 q^{61} - 1528 q^{67} - 2700 q^{73} - 364 q^{79} + 7392 q^{85} + 2472 q^{91}+O(q^{100}) \) 16 * q - 4 * q^7 - 72 * q^19 - 212 * q^25 - 708 * q^31 + 76 * q^37 + 1408 * q^43 + 400 * q^49 - 1632 * q^61 - 1528 * q^67 - 2700 * q^73 - 364 * q^79 + 7392 * q^85 + 2472 * q^91

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