LMFDB - Embedded newform 1008.4.bt.b.593.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,4,Mod(17,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1008.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1008.bt (of order $6$, degree $2$, not 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:	$59.4739252858$
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:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			593.5
Root			$5.70754 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1008.593
Dual form			1008.4.bt.b.17.5

$q$-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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	3.41226	−	5.91021i	0.305202	−	0.528625i	−0.672104	−	0.740456i	$-0.734609\pi$
$5$	3.41226	−	5.91021i	0.305202	−	0.528625i	0.977306	+	0.211831i	$0.0679427\pi$
$6$		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	0.957827	−	0.287345i	$-0.0927725\pi$
$17$	16.1260	+	27.9310i	0.230066	+	0.398486i	−0.727761	+	0.685830i	$0.759439\pi$
$18$		0			0
$19$	−107.846	−	62.2650i	−1.30219	−	0.751819i	−0.321410	−	0.946940i	$-0.604157\pi$
$19$	−107.846	−	62.2650i	−1.30219	−	0.751819i	−0.980779	+	0.195121i	$0.937490\pi$
$20$		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	$0.108437\pi$
$29$			104.357i			0.668226i	−0.942533	+	0.334113i	$0.891563\pi$
$30$		0			0
$31$	240.747	−	138.995i	1.39482	−	0.805299i	0.400975	−	0.916089i	$-0.368671\pi$
$31$	240.747	−	138.995i	1.39482	−	0.805299i	0.993844	+	0.110790i	$0.0353382\pi$
$32$		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	$-0.764032\pi$
$41$	−387.272			−1.47516			−0.737582	+	0.675258i	$0.764032\pi$
$42$		0			0
$43$	−272.528			−0.966515			−0.483257	−	0.875478i	$-0.660546\pi$
$43$	−272.528			−0.966515			−0.483257	+	0.875478i	$0.660546\pi$
$44$		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	−0.848153	−	0.529751i	$-0.822285\pi$
$53$	−313.867	+	181.211i	−0.813452	+	0.469646i	0.0347015	+	0.999398i	$0.488952\pi$
$54$		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	0.999681	−	0.0252470i	$-0.00803722\pi$
$67$	262.131	+	454.024i	0.477976	+	0.827879i	−0.521705	+	0.853126i	$0.674704\pi$
$68$		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	$-0.660503\pi$
$79$	362.792	−	628.374i	0.516675	−	0.894907i	0.999813	−	0.0193623i	$-0.00616361\pi$
$80$		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	$-0.662182\pi$
$89$	430.015	−	744.807i	0.512151	−	0.887072i	0.999901	−	0.0140882i	$-0.00448456\pi$
$90$		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	0.955060	−	0.296412i	$-0.0957902\pi$
$101$	224.150	+	388.240i	0.220830	+	0.382488i	−0.734230	+	0.678900i	$0.762457\pi$
$102$		0			0
$103$	1137.56	+	656.773i	1.08823	+	0.628289i	0.933104	−	0.359606i	$-0.117089\pi$
$103$	1137.56	+	656.773i	1.08823	+	0.628289i	0.155124	+	0.987895i	$0.450422\pi$
$104$		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	$0.392629\pi$
$113$			2267.03i			1.88729i	−0.330956	+	0.943646i	$0.607371\pi$
$114$		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	$-0.594722\pi$
$127$	−839.285			−0.586413			−0.293207	+	0.956049i	$0.594722\pi$
$128$		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	$-0.260884\pi$
$137$	2656.64	−	1533.81i	1.65673	−	0.956513i	0.974209	−	0.225647i	$-0.0724495\pi$
$138$		0			0
$139$		−	2191.44i		−	1.33723i	−0.743608	−	0.668616i	$-0.766887\pi$
$139$		−	2191.44i		−	1.33723i	0.743608	−	0.668616i	$-0.233113\pi$
$140$		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	0.386323	−	0.922363i	$-0.373745\pi$
$149$	−398.867	−	230.286i	−0.219305	−	0.126616i	−0.605628	+	0.795748i	$0.707078\pi$
$150$		0			0
$151$	317.552	+	550.017i	0.171139	+	0.296422i	0.938818	−	0.344412i	$-0.111922\pi$
$151$	317.552	+	550.017i	0.171139	+	0.296422i	−0.767679	+	0.640834i	$0.778588\pi$
$152$		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	−0.652173	−	0.758070i	$-0.726143\pi$
$163$	687.621	−	1190.99i	0.330421	−	0.572306i	0.982594	+	0.185764i	$0.0594759\pi$
$164$		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	−0.812096	−	0.583523i	$-0.801674\pi$
$173$	225.948	−	391.354i	0.0992979	−	0.171989i	0.911394	+	0.411534i	$0.135007\pi$
$174$		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	$0.125406\pi$
$197$			2122.77i			0.767720i	−0.923391	+	0.383860i	$0.874594\pi$
$198$		0			0
$199$	−1035.18	+	597.659i	−0.368752	+	0.212899i	−0.672913	−	0.739722i	$-0.734957\pi$
$199$	−1035.18	+	597.659i	−0.368752	+	0.212899i	0.304161	+	0.952621i	$0.401624\pi$
$200$		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	$-0.509785\pi$
$211$	−188.402			−0.0614698			−0.0307349	+	0.999528i	$0.509785\pi$
$212$		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	$-0.861746\pi$
$223$		−	2802.67i		−	0.841618i	0.907149	−	0.420809i	$-0.138254\pi$
$224$		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	0.678490	−	0.734610i	$-0.262635\pi$
$233$	1356.99	+	783.461i	0.381543	+	0.220284i	−0.296946	+	0.954894i	$0.595968\pi$
$234$		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	−0.975346	−	0.220682i	$-0.929172\pi$
$257$	−1221.82	+	2116.25i	−0.296556	+	0.513651i	0.678789	+	0.734333i	$0.262505\pi$
$258$		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	$-0.774716\pi$
$269$	−4160.18	−	7205.64i	−0.942939	−	1.63322i	−0.183114	−	0.983092i	$-0.558618\pi$
$270$		0			0
$271$	−5816.51	−	3358.16i	−1.30379	−	0.752745i	−0.322740	−	0.946488i	$-0.604604\pi$
$271$	−5816.51	−	3358.16i	−1.30379	−	0.752745i	−0.981052	+	0.193742i	$0.937937\pi$
$272$		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	$0.180704\pi$
$281$			5065.50i			1.07538i	−0.843142	+	0.537692i	$0.819296\pi$
$282$		0			0
$283$	2227.91	−	1286.28i	0.467969	−	0.270182i	−0.247420	−	0.968908i	$-0.579583\pi$
$283$	2227.91	−	1286.28i	0.467969	−	0.270182i	0.715389	+	0.698726i	$0.246249\pi$
$284$		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	$-0.303880\pi$
$293$	5796.55			1.15576			0.577881	+	0.816121i	$0.303880\pi$
$294$		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	$-0.977701\pi$
$307$		−	753.054i		−	0.139997i	0.997547	−	0.0699985i	$-0.0222994\pi$
$308$		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	0.299636	−	0.954053i	$-0.403135\pi$
$317$	−2126.55	−	1227.77i	−0.376780	−	0.217534i	−0.676416	+	0.736520i	$0.736468\pi$
$318$		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	$0.416436\pi$
$331$	−4255.12	+	7370.09i	−0.706594	+	1.22386i	−0.966113	+	0.258119i	$0.916897\pi$
$332$		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	$0.0287137\pi$
$353$	3820.07	+	6616.56i	0.575983	+	0.997631i	−0.419952	+	0.907547i	$0.637953\pi$
$354$		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	−0.359874	−	0.933001i	$-0.617180\pi$
$367$	1885.57	−	1088.64i	0.268191	−	0.154840i	0.628065	+	0.778161i	$0.283847\pi$
$368$		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	$-0.655327\pi$
$379$	−6918.48			−0.937673			−0.468837	+	0.883285i	$0.655327\pi$
$380$		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	−0.414383	−	0.910103i	$-0.636002\pi$
$389$	1278.19	−	737.963i	0.166598	−	0.0961856i	0.580981	+	0.813917i	$0.302669\pi$
$390$		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	0.461930	−	0.886916i	$-0.347157\pi$
$401$	−603.832	−	348.623i	−0.0751968	−	0.0434149i	−0.537127	+	0.843501i	$0.680490\pi$
$402$		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	0.816998	−	0.576640i	$-0.195636\pi$
$439$	6678.84	+	3856.03i	0.726113	+	0.419222i	−0.0908855	+	0.995861i	$0.528970\pi$
$440$		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	$0.00535311\pi$
$449$			319.989i			0.0336330i	−0.999859	+	0.0168165i	$0.994647\pi$
$450$		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	$-0.574829\pi$
$461$	−4610.97			−0.465844			−0.232922	+	0.972495i	$0.574829\pi$
$462$		0			0
$463$	−15203.3			−1.52604			−0.763022	−	0.646373i	$-0.776285\pi$
$463$	−15203.3			−1.52604			−0.763022	+	0.646373i	$0.776285\pi$
$464$		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	0.531345	−	0.847156i	$-0.321687\pi$
$487$	−5029.52	−	8711.38i	−0.467986	−	0.810575i	−0.999331	+	0.0365803i	$0.988354\pi$
$488$		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	$-0.665979\pi$
$499$	5594.25	−	9689.53i	0.501870	−	0.869264i	0.999998	−	0.00216055i	$-0.000687726\pi$
$500$		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	−0.742375	−	0.669984i	$-0.766301\pi$
$509$	2400.48	−	4157.75i	0.209036	−	0.362061i	0.951411	+	0.307924i	$0.0996341\pi$
$510$		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	0.969844	−	0.243726i	$-0.0783697\pi$
$521$	3256.63	+	5640.65i	0.273849	+	0.474321i	−0.695995	+	0.718047i	$0.745036\pi$
$522$		0			0
$523$	3856.61	+	2226.62i	0.322443	+	0.186163i	0.652481	−	0.757805i	$-0.273728\pi$
$523$	3856.61	+	2226.62i	0.322443	+	0.186163i	−0.330038	+	0.943968i	$0.607061\pi$
$524$		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	$-0.448828\pi$
$547$	4095.62			0.320139			0.160069	+	0.987106i	$0.448828\pi$
$548$		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	−0.508317	−	0.861170i	$-0.669732\pi$
$557$	−219.268	+	126.594i	−0.0166799	+	0.00963012i	0.491637	+	0.870800i	$0.336399\pi$
$558$		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	0.000370481	−	1.00000i	$-0.499882\pi$
$569$	−11746.8	−	6782.03i	−0.865470	−	0.499679i	−0.865840	+	0.500321i	$0.833215\pi$
$570$		0			0
$571$	−2350.96	−	4071.98i	−0.172302	−	0.298436i	0.766922	−	0.641740i	$-0.221787\pi$
$571$	−2350.96	−	4071.98i	−0.172302	−	0.298436i	−0.939224	+	0.343304i	$0.888454\pi$
$572$		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	−0.998283	−	0.0585683i	$-0.981346\pi$
$593$	−6475.41	+	11215.7i	−0.448420	+	0.776686i	0.549863	+	0.835255i	$0.314680\pi$
$594$		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	−0.0821649	−	0.996619i	$-0.526183\pi$
$607$	−14750.7	−	8516.30i	−0.986344	−	0.569466i	−0.904180	+	0.427152i	$0.859517\pi$
$608$		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	$0.131871\pi$
$617$			12338.5i			0.805074i	−0.915404	+	0.402537i	$0.868129\pi$
$618$		0			0
$619$	8967.52	−	5177.40i	0.582286	−	0.336183i	−0.179755	−	0.983711i	$-0.557531\pi$
$619$	8967.52	−	5177.40i	0.582286	−	0.336183i	0.762041	+	0.647528i	$0.224197\pi$
$620$		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	$-0.450424\pi$
$631$	4917.41			0.310236			0.155118	+	0.987896i	$0.450424\pi$
$632$		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	−0.881230	−	0.472688i	$-0.843284\pi$
$641$	−14808.6	+	8549.73i	−0.912486	+	0.526824i	−0.0312556	+	0.999511i	$0.509951\pi$
$642$		0			0
$643$		−	14631.4i		−	0.897365i	−0.893691	−	0.448683i	$-0.851893\pi$
$643$		−	14631.4i		−	0.897365i	0.893691	−	0.448683i	$-0.148107\pi$
$644$		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	0.999107	−	0.0422510i	$-0.0134529\pi$
$653$	24397.1	+	14085.7i	1.46207	+	0.844127i	0.462963	+	0.886378i	$0.346786\pi$
$654$		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	$-0.593232\pi$
$677$	12062.4	−	20892.7i	0.684779	−	1.18607i	0.973506	−	0.228661i	$-0.0734348\pi$
$678$		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	0.167442	−	0.985882i	$-0.446449\pi$
$691$	−10946.4	−	6319.92i	−0.602636	−	0.347932i	−0.770078	+	0.637950i	$0.779783\pi$
$692$		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	$-0.775630\pi$
$701$		−	24051.5i		−	1.29588i	0.761690	−	0.647942i	$-0.224370\pi$
$702$		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	$0.198540\pi$
$727$			22897.9i			1.16814i	−0.811704	+	0.584068i	$0.801460\pi$
$728$		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	$0.00231333\pi$
$739$	10170.9	+	17616.5i	0.506281	+	0.876904i	−0.493693	+	0.869636i	$0.664353\pi$
$740$		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	−0.530303	−	0.847808i	$-0.677922\pi$
$751$	9653.81	−	16720.9i	0.469071	−	0.812456i	0.999375	+	0.0353523i	$0.0112553\pi$
$752$		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	$0.384082\pi$
$761$	−13249.7	+	22949.2i	−0.631145	+	1.09318i	−0.987318	+	0.158756i	$0.949252\pi$
$762$		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	$0.0711721\pi$
$773$	14605.3	+	25297.2i	0.679582	+	1.17707i	−0.295525	+	0.955335i	$0.595495\pi$
$774$		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	−0.988766	−	0.149471i	$-0.952243\pi$
$787$	−29887.2	+	17255.4i	−1.35370	+	0.781561i	−0.364937	+	0.931032i	$0.618910\pi$
$788$		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	$-0.149536\pi$
$797$	40125.5			1.78333			0.891667	+	0.452692i	$0.149536\pi$
$798$		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	−0.896210	−	0.443630i	$-0.853691\pi$
$809$	−22092.7	+	12755.2i	−0.960121	+	0.554326i	−0.0639107	+	0.997956i	$0.520357\pi$
$810$		0			0
$811$			34785.8i			1.50616i	0.657930	+	0.753079i	$0.271432\pi$
$811$			34785.8i			1.50616i	−0.657930	+	0.753079i	$0.728568\pi$
$812$		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	0.854574	−	0.519330i	$-0.173818\pi$
$821$	19574.7	+	11301.4i	0.832108	+	0.480418i	−0.0224658	+	0.999748i	$0.507152\pi$
$822$		0			0
$823$	−9554.31	−	16548.6i	−0.404669	−	0.700907i	0.589614	−	0.807685i	$-0.299280\pi$
$823$	−9554.31	−	16548.6i	−0.404669	−	0.700907i	−0.994283	+	0.106778i	$0.965947\pi$
$824$		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	0.913278	−	0.407337i	$-0.133543\pi$
$857$	2606.04	+	4513.80i	0.103875	+	0.179917i	−0.809403	+	0.587253i	$0.800209\pi$
$858$		0			0
$859$	−16503.5	−	9528.29i	−0.655520	−	0.378464i	0.135048	−	0.990839i	$-0.456881\pi$
$859$	−16503.5	−	9528.29i	−0.655520	−	0.378464i	−0.790568	+	0.612375i	$0.790214\pi$
$860$		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	$-0.311146\pi$
$881$	29240.6			1.11821			0.559103	+	0.829098i	$0.311146\pi$
$882$		0			0
$883$	42056.9			1.60286			0.801431	−	0.598088i	$-0.204073\pi$
$883$	42056.9			1.60286			0.801431	+	0.598088i	$0.204073\pi$
$884$		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	0.797574	−	0.603221i	$-0.206116\pi$
$907$	−3376.70	−	5848.61i	−0.123618	−	0.214112i	−0.921192	+	0.389109i	$0.872783\pi$
$908$		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	$-0.583347\pi$
$919$	19698.8	−	34119.3i	0.707077	−	1.22469i	0.965937	−	0.258778i	$-0.0833198\pi$
$920$		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	−0.947508	−	0.319733i	$-0.896407\pi$
$929$	−5574.09	+	9654.60i	−0.196857	+	0.340966i	0.750651	+	0.660699i	$0.229740\pi$
$930$		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	0.910805	−	0.412836i	$-0.135462\pi$
$941$	2825.28	+	4893.52i	0.0978761	+	0.169526i	−0.812929	+	0.582362i	$0.802128\pi$
$942$		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	$0.134560\pi$
$953$			24139.2i			0.820511i	−0.911971	+	0.410255i	$0.865440\pi$
$954$		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	$-0.561110\pi$
$967$	−11475.1			−0.381609			−0.190804	+	0.981628i	$0.561110\pi$
$968$		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	−0.677544	−	0.735482i	$-0.736956\pi$
$977$	−11585.2	+	6688.74i	−0.379370	+	0.219029i	0.298174	+	0.954512i	$0.403622\pi$
$978$		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	0.980796	−	0.195035i	$-0.0624820\pi$
$991$	10029.6	+	17371.7i	0.321493	+	0.556842i	−0.659303	+	0.751877i	$0.729149\pi$
$992$		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	1008.4.bt.b.593.5		16
3.2	odd	2	inner	1008.4.bt.b.593.4		16
4.3	odd	2		252.4.t.a.89.5	yes	16
7.3	odd	6	inner	1008.4.bt.b.17.4		16
12.11	even	2		252.4.t.a.89.4	yes	16
21.17	even	6	inner	1008.4.bt.b.17.5		16
28.3	even	6		252.4.t.a.17.4	✓	16
28.11	odd	6		1764.4.t.b.521.5		16
28.19	even	6		1764.4.f.a.881.9		16
28.23	odd	6		1764.4.f.a.881.7		16
28.27	even	2		1764.4.t.b.1097.4		16
84.11	even	6		1764.4.t.b.521.4		16
84.23	even	6		1764.4.f.a.881.10		16
84.47	odd	6		1764.4.f.a.881.8		16
84.59	odd	6		252.4.t.a.17.5	yes	16
84.83	odd	2		1764.4.t.b.1097.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.t.a.17.4	✓	16	28.3	even	6
252.4.t.a.17.5	yes	16	84.59	odd	6
252.4.t.a.89.4	yes	16	12.11	even	2
252.4.t.a.89.5	yes	16	4.3	odd	2
1008.4.bt.b.17.4		16	7.3	odd	6	inner
1008.4.bt.b.17.5		16	21.17	even	6	inner
1008.4.bt.b.593.4		16	3.2	odd	2	inner
1008.4.bt.b.593.5		16	1.1	even	1	trivial
1764.4.f.a.881.7		16	28.23	odd	6
1764.4.f.a.881.8		16	84.47	odd	6
1764.4.f.a.881.9		16	28.19	even	6
1764.4.f.a.881.10		16	84.23	even	6
1764.4.t.b.521.4		16	84.11	even	6
1764.4.t.b.521.5		16	28.11	odd	6
1764.4.t.b.1097.4		16	28.27	even	2
1764.4.t.b.1097.5		16	84.83	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1008.bt (of order \(6\), degree \(2\), not 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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