LMFDB - Embedded newform 1008.3.cg.h.145.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,3,Mod(145,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.145"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1008.cg (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,-12,0,10,0,0,0,-12,0,0,0,0,0,48,0,42] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$27.4660106475$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1008.145
Dual form			1008.3.cg.h.577.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24264 + 0.717439i) q^{5} +(-1.74264 - 6.77962i) q^{7} +(-3.00000 - 5.19615i) q^{11} +21.3280i q^{13} +(7.75736 - 4.47871i) q^{17} +(6.25736 + 3.61269i) q^{19} +(18.7279 - 32.4377i) q^{23} +(-11.4706 - 19.8676i) q^{25} +33.9411 q^{29} +(-38.2279 + 22.0709i) q^{31} +(2.69848 - 9.67487i) q^{35} +(13.9853 - 24.2232i) q^{37} -54.8313i q^{41} +1.48528 q^{43} +(-37.2426 - 21.5020i) q^{47} +(-42.9264 + 23.6289i) q^{49} +(-42.7279 - 74.0069i) q^{53} -8.60927i q^{55} +(-35.6985 + 20.6105i) q^{59} +(-1.02944 - 0.594346i) q^{61} +(-15.3015 + 26.5030i) q^{65} +(2.19848 + 3.80789i) q^{67} +137.397 q^{71} +(68.3528 - 39.4635i) q^{73} +(-30.0000 + 29.3939i) q^{77} +(49.1690 - 85.1633i) q^{79} -110.401i q^{83} +12.8528 q^{85} +(18.0000 + 10.3923i) q^{89} +(144.595 - 37.1670i) q^{91} +(5.18377 + 8.97855i) q^{95} +10.9867i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{5} + 10 q^{7} - 12 q^{11} + 48 q^{17} + 42 q^{19} + 24 q^{23} + 22 q^{25} - 102 q^{31} - 108 q^{35} + 22 q^{37} - 28 q^{43} - 132 q^{47} - 2 q^{49} - 120 q^{53} - 24 q^{59} - 72 q^{61} - 180 q^{65}+ \cdots - 132 q^{95}+O(q^{100}) $ 4 * q - 12 * q^5 + 10 * q^7 - 12 * q^11 + 48 * q^17 + 42 * q^19 + 24 * q^23 + 22 * q^25 - 102 * q^31 - 108 * q^35 + 22 * q^37 - 28 * q^43 - 132 * q^47 - 2 * q^49 - 120 * q^53 - 24 * q^59 - 72 * q^61 - 180 * q^65 - 110 * q^67 + 312 * q^71 - 66 * q^73 - 120 * q^77 + 10 * q^79 - 288 * q^85 + 72 * q^89 + 222 * q^91 - 132 * q^95

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
$5$	1.24264	+	0.717439i	0.248528	+	0.143488i	0.619090	−	0.785320i	$-0.287502\pi$
$5$	1.24264	+	0.717439i	0.248528	+	0.143488i	−0.370562	+	0.928808i	$0.620835\pi$
$6$		0			0
$7$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$7$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.00000	−	5.19615i	−0.272727	−	0.472377i	0.696832	−	0.717234i	$-0.254592\pi$
$11$	−3.00000	−	5.19615i	−0.272727	−	0.472377i	−0.969559	+	0.244857i	$0.921259\pi$
$12$		0			0
$13$			21.3280i			1.64061i	0.571924	+	0.820306i	$0.306197\pi$
$13$			21.3280i			1.64061i	−0.571924	+	0.820306i	$0.693803\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	7.75736	−	4.47871i	0.456315	−	0.263454i	−0.254178	−	0.967157i	$-0.581805\pi$
$17$	7.75736	−	4.47871i	0.456315	−	0.263454i	0.710494	+	0.703704i	$0.248472\pi$
$18$		0			0
$19$	6.25736	+	3.61269i	0.329335	+	0.190141i	0.655546	−	0.755156i	$-0.272439\pi$
$19$	6.25736	+	3.61269i	0.329335	+	0.190141i	−0.326211	+	0.945297i	$0.605772\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	18.7279	−	32.4377i	0.814257	−	1.41034i	−0.0956024	−	0.995420i	$-0.530478\pi$
$23$	18.7279	−	32.4377i	0.814257	−	1.41034i	0.909860	−	0.414916i	$-0.136189\pi$
$24$		0			0
$25$	−11.4706	−	19.8676i	−0.458823	−	0.794704i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	33.9411			1.17038			0.585192	−	0.810895i	$-0.301019\pi$
$29$	33.9411			1.17038			0.585192	+	0.810895i	$0.301019\pi$
$30$		0			0
$31$	−38.2279	+	22.0709i	−1.23316	+	0.711965i	−0.967687	−	0.252154i	$-0.918861\pi$
$31$	−38.2279	+	22.0709i	−1.23316	+	0.711965i	−0.265472	+	0.964119i	$0.585528\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.69848	−	9.67487i	0.0770996	−	0.276425i
$36$		0			0
$37$	13.9853	−	24.2232i	0.377981	−	0.654682i	−0.612788	−	0.790248i	$-0.709952\pi$
$37$	13.9853	−	24.2232i	0.377981	−	0.654682i	0.990768	+	0.135566i	$0.0432853\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	54.8313i		−	1.33735i	−0.743556	−	0.668674i	$-0.766862\pi$
$41$		−	54.8313i		−	1.33735i	0.743556	−	0.668674i	$-0.233138\pi$
$42$		0			0
$43$	1.48528			0.0345414			0.0172707	−	0.999851i	$-0.494502\pi$
$43$	1.48528			0.0345414			0.0172707	+	0.999851i	$0.494502\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−37.2426	−	21.5020i	−0.792397	−	0.457490i	0.0484090	−	0.998828i	$-0.484585\pi$
$47$	−37.2426	−	21.5020i	−0.792397	−	0.457490i	−0.840806	+	0.541337i	$0.817918\pi$
$48$		0			0
$49$	−42.9264	+	23.6289i	−0.876049	+	0.482222i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−42.7279	−	74.0069i	−0.806187	−	1.39636i	−0.915487	−	0.402348i	$-0.868194\pi$
$53$	−42.7279	−	74.0069i	−0.806187	−	1.39636i	0.109299	−	0.994009i	$-0.465139\pi$
$54$		0			0
$55$		−	8.60927i		−	0.156532i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−35.6985	+	20.6105i	−0.605059	+	0.349331i	−0.771029	−	0.636800i	$-0.780258\pi$
$59$	−35.6985	+	20.6105i	−0.605059	+	0.349331i	0.165970	+	0.986131i	$0.446924\pi$
$60$		0			0
$61$	−1.02944	−	0.594346i	−0.0168760	−	0.00974337i	0.491538	−	0.870856i	$-0.336435\pi$
$61$	−1.02944	−	0.594346i	−0.0168760	−	0.00974337i	−0.508414	+	0.861113i	$0.669768\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−15.3015	+	26.5030i	−0.235408	+	0.407738i
$66$		0			0
$67$	2.19848	+	3.80789i	0.0328132	+	0.0568341i	0.881966	−	0.471314i	$-0.156220\pi$
$67$	2.19848	+	3.80789i	0.0328132	+	0.0568341i	−0.849152	+	0.528148i	$0.822887\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	137.397			1.93517			0.967584	−	0.252548i	$-0.0812687\pi$
$71$	137.397			1.93517			0.967584	+	0.252548i	$0.0812687\pi$
$72$		0			0
$73$	68.3528	−	39.4635i	0.936340	−	0.540596i	0.0475288	−	0.998870i	$-0.484865\pi$
$73$	68.3528	−	39.4635i	0.936340	−	0.540596i	0.888811	+	0.458274i	$0.151532\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−30.0000	+	29.3939i	−0.389610	+	0.381739i
$78$		0			0
$79$	49.1690	−	85.1633i	0.622393	−	1.07802i	−0.366646	−	0.930361i	$-0.619494\pi$
$79$	49.1690	−	85.1633i	0.622393	−	1.07802i	0.989039	−	0.147656i	$-0.0471728\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	110.401i		−	1.33013i	−0.746784	−	0.665067i	$-0.768403\pi$
$83$		−	110.401i		−	1.33013i	0.746784	−	0.665067i	$-0.231597\pi$
$84$		0			0
$85$	12.8528			0.151210
$86$		0			0
$87$		0			0
$88$		0			0
$89$	18.0000	+	10.3923i	0.202247	+	0.116767i	0.597703	−	0.801717i	$-0.296080\pi$
$89$	18.0000	+	10.3923i	0.202247	+	0.116767i	−0.395456	+	0.918485i	$0.629413\pi$
$90$		0			0
$91$	144.595	−	37.1670i	1.58896	−	0.408428i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.18377	+	8.97855i	0.0545660	+	0.0945110i
$96$		0			0
$97$			10.9867i			0.113264i	0.998395	+	0.0566322i	$0.0180362\pi$
$97$			10.9867i			0.113264i	−0.998395	+	0.0566322i	$0.981964\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	92.8234	−	53.5916i	0.919043	−	0.530610i	0.0357136	−	0.999362i	$-0.488630\pi$
$101$	92.8234	−	53.5916i	0.919043	−	0.530610i	0.883330	+	0.468752i	$0.155296\pi$
$102$		0			0
$103$	−91.1102	−	52.6025i	−0.884565	−	0.510704i	−0.0124040	−	0.999923i	$-0.503948\pi$
$103$	−91.1102	−	52.6025i	−0.884565	−	0.510704i	−0.872161	+	0.489219i	$0.837282\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−59.2721	+	102.662i	−0.553945	+	0.959460i	0.444040	+	0.896007i	$0.353545\pi$
$107$	−59.2721	+	102.662i	−0.553945	+	0.959460i	−0.997985	+	0.0634534i	$0.979789\pi$
$108$		0			0
$109$	−55.5294	−	96.1798i	−0.509444	−	0.882384i	−0.999940	−	0.0109400i	$-0.996518\pi$
$109$	−55.5294	−	96.1798i	−0.509444	−	0.882384i	0.490496	−	0.871444i	$-0.336816\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−101.397			−0.897318			−0.448659	−	0.893703i	$-0.648098\pi$
$113$	−101.397			−0.897318			−0.448659	+	0.893703i	$0.648098\pi$
$114$		0			0
$115$	46.5442	−	26.8723i	0.404732	−	0.233672i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−43.8823	−	44.7871i	−0.368758	−	0.376362i
$120$		0			0
$121$	42.5000	−	73.6122i	0.351240	−	0.608365i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	68.7897i		−	0.550317i
$126$		0			0
$127$	−82.5736			−0.650186			−0.325093	−	0.945682i	$-0.605396\pi$
$127$	−82.5736			−0.650186			−0.325093	+	0.945682i	$0.605396\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−52.4558	−	30.2854i	−0.400426	−	0.231186i	0.286242	−	0.958157i	$-0.407594\pi$
$131$	−52.4558	−	30.2854i	−0.400426	−	0.231186i	−0.686668	+	0.726971i	$0.740927\pi$
$132$		0			0
$133$	13.5883	−	48.7181i	0.102168	−	0.366302i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	33.5147	+	58.0492i	0.244633	+	0.423717i	0.962028	−	0.272949i	$-0.0879992\pi$
$137$	33.5147	+	58.0492i	0.244633	+	0.423717i	−0.717395	+	0.696666i	$0.754666\pi$
$138$		0			0
$139$			91.5525i			0.658651i	0.944216	+	0.329326i	$0.106821\pi$
$139$			91.5525i			0.658651i	−0.944216	+	0.329326i	$0.893179\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	110.823	−	63.9839i	0.774989	−	0.447440i
$144$		0			0
$145$	42.1766	+	24.3507i	0.290873	+	0.167936i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	40.5442	−	70.2245i	0.272108	−	0.471306i	−0.697293	−	0.716786i	$-0.745612\pi$
$149$	40.5442	−	70.2245i	0.272108	−	0.471306i	0.969402	+	0.245480i	$0.0789457\pi$
$150$		0			0
$151$	−25.6030	−	44.3457i	−0.169556	−	0.293680i	0.768708	−	0.639600i	$-0.220900\pi$
$151$	−25.6030	−	44.3457i	−0.169556	−	0.293680i	−0.938264	+	0.345920i	$0.887567\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−63.3381			−0.408633
$156$		0			0
$157$	162.000	−	93.5307i	1.03185	−	0.595737i	0.114334	−	0.993442i	$-0.463527\pi$
$157$	162.000	−	93.5307i	1.03185	−	0.595737i	0.917513	+	0.397705i	$0.130193\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−252.551	−	70.4409i	−1.56864	−	0.437521i
$162$		0			0
$163$	41.9706	−	72.6951i	0.257488	−	0.445982i	−0.708080	−	0.706132i	$-0.750439\pi$
$163$	41.9706	−	72.6951i	0.257488	−	0.445982i	0.965568	+	0.260149i	$0.0837718\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			127.620i			0.764190i	0.924123	+	0.382095i	$0.124797\pi$
$167$			127.620i			0.764190i	−0.924123	+	0.382095i	$0.875203\pi$
$168$		0			0
$169$	−285.882			−1.69161
$170$		0			0
$171$		0			0
$172$		0			0
$173$	123.816	+	71.4853i	0.715701	+	0.413210i	0.813168	−	0.582029i	$-0.197741\pi$
$173$	123.816	+	71.4853i	0.715701	+	0.413210i	−0.0974675	+	0.995239i	$0.531074\pi$
$174$		0			0
$175$	−114.706	+	112.388i	−0.655461	+	0.642218i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−84.6396	−	146.600i	−0.472847	−	0.818995i	0.526670	−	0.850070i	$-0.323440\pi$
$179$	−84.6396	−	146.600i	−0.472847	−	0.818995i	−0.999517	+	0.0310748i	$0.990107\pi$
$180$		0			0
$181$			209.969i			1.16005i	0.814600	+	0.580024i	$0.196957\pi$
$181$			209.969i			1.16005i	−0.814600	+	0.580024i	$0.803043\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	34.7574	−	20.0672i	0.187878	−	0.108471i
$186$		0			0
$187$	−46.5442	−	26.8723i	−0.248899	−	0.143702i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−33.3015	+	57.6799i	−0.174353	+	0.301989i	−0.939937	−	0.341347i	$-0.889117\pi$
$191$	−33.3015	+	57.6799i	−0.174353	+	0.301989i	0.765584	+	0.643336i	$0.222450\pi$
$192$		0			0
$193$	4.89697	+	8.48180i	0.0253729	+	0.0439472i	0.878433	−	0.477865i	$-0.158589\pi$
$193$	4.89697	+	8.48180i	0.0253729	+	0.0439472i	−0.853060	+	0.521813i	$0.825256\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	267.161			1.35615			0.678075	−	0.734993i	$-0.262815\pi$
$197$	267.161			1.35615			0.678075	+	0.734993i	$0.262815\pi$
$198$		0			0
$199$	113.397	−	65.4698i	0.569834	−	0.328994i	−0.187249	−	0.982312i	$-0.559957\pi$
$199$	113.397	−	65.4698i	0.569834	−	0.328994i	0.757083	+	0.653319i	$0.226624\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−59.1472	−	230.108i	−0.291365	−	1.13354i
$204$		0			0
$205$	39.3381	−	68.1356i	0.191893	−	0.332369i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	43.3523i		−	0.207427i
$210$		0			0
$211$	23.0883			0.109423			0.0547116	−	0.998502i	$-0.482576\pi$
$211$	23.0883			0.109423			0.0547116	+	0.998502i	$0.482576\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.84567	+	1.06560i	0.00858452	+	0.00495627i
$216$		0			0
$217$	216.250	+	220.709i	0.996543	+	1.01709i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	95.5219	+	165.449i	0.432226	+	0.748637i
$222$		0			0
$223$			228.631i			1.02525i	0.858613	+	0.512625i	$0.171327\pi$
$223$			228.631i			1.02525i	−0.858613	+	0.512625i	$0.828673\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	56.8234	−	32.8070i	0.250323	−	0.144524i	−0.369589	−	0.929195i	$-0.620502\pi$
$227$	56.8234	−	32.8070i	0.250323	−	0.144524i	0.619912	+	0.784671i	$0.287168\pi$
$228$		0			0
$229$	80.9558	+	46.7399i	0.353519	+	0.204104i	0.666234	−	0.745743i	$-0.267905\pi$
$229$	80.9558	+	46.7399i	0.353519	+	0.204104i	−0.312715	+	0.949847i	$0.601239\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−118.757	+	205.694i	−0.509688	+	0.882806i	0.490249	+	0.871583i	$0.336906\pi$
$233$	−118.757	+	205.694i	−0.509688	+	0.882806i	−0.999937	+	0.0112234i	$0.996427\pi$
$234$		0			0
$235$	−30.8528	−	53.4386i	−0.131289	−	0.227398i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	366.853			1.53495			0.767475	−	0.641079i	$-0.221513\pi$
$239$	366.853			1.53495			0.767475	+	0.641079i	$0.221513\pi$
$240$		0			0
$241$	−364.617	+	210.512i	−1.51293	+	0.873493i	−0.513049	+	0.858359i	$0.671484\pi$
$241$	−364.617	+	210.512i	−1.51293	+	0.873493i	−0.999885	+	0.0151343i	$0.995182\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−70.2944	−	1.43488i	−0.286916	−	0.00585664i
$246$		0			0
$247$	−77.0513	+	133.457i	−0.311949	+	0.540311i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			146.621i			0.584148i	0.956396	+	0.292074i	$0.0943454\pi$
$251$			146.621i			0.584148i	−0.956396	+	0.292074i	$0.905655\pi$
$252$		0			0
$253$	−224.735			−0.888281
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−21.7279	−	12.5446i	−0.0845444	−	0.0488118i	0.457132	−	0.889399i	$-0.348877\pi$
$257$	−21.7279	−	12.5446i	−0.0845444	−	0.0488118i	−0.541676	+	0.840587i	$0.682210\pi$
$258$		0			0
$259$	−188.595	−	52.6025i	−0.728168	−	0.203098i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	45.3381	+	78.5279i	0.172388	+	0.298585i	0.939254	−	0.343222i	$-0.111518\pi$
$263$	45.3381	+	78.5279i	0.172388	+	0.298585i	−0.766866	+	0.641807i	$0.778185\pi$
$264$		0			0
$265$		−	122.619i		−	0.462712i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	59.2355	−	34.1996i	0.220206	−	0.127136i	−0.385839	−	0.922566i	$-0.626088\pi$
$269$	59.2355	−	34.1996i	0.220206	−	0.127136i	0.606046	+	0.795430i	$0.292755\pi$
$270$		0			0
$271$	106.971	+	61.7595i	0.394725	+	0.227895i	0.684206	−	0.729289i	$-0.260149\pi$
$271$	106.971	+	61.7595i	0.394725	+	0.227895i	−0.289480	+	0.957184i	$0.593482\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−68.8234	+	119.206i	−0.250267	+	0.433475i
$276$		0			0
$277$	136.441	+	236.323i	0.492567	+	0.853151i	0.999963	−	0.00856145i	$-0.00272523\pi$
$277$	136.441	+	236.323i	0.492567	+	0.853151i	−0.507396	+	0.861713i	$0.669392\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−133.103			−0.473675			−0.236837	−	0.971549i	$-0.576111\pi$
$281$	−133.103			−0.473675			−0.236837	+	0.971549i	$0.576111\pi$
$282$		0			0
$283$	111.507	−	64.3787i	0.394018	−	0.227486i	−0.289882	−	0.957063i	$-0.593616\pi$
$283$	111.507	−	64.3787i	0.394018	−	0.227486i	0.683900	+	0.729576i	$0.260283\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−371.735	+	95.5512i	−1.29524	+	0.332931i
$288$		0			0
$289$	−104.382	+	180.795i	−0.361184	+	0.625589i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	308.984i		−	1.05455i	−0.849694	−	0.527276i	$-0.823213\pi$
$293$		−	308.984i		−	1.05455i	0.849694	−	0.527276i	$-0.176787\pi$
$294$		0			0
$295$	−59.1472			−0.200499
$296$		0			0
$297$		0			0
$298$		0			0
$299$	691.831	+	399.429i	2.31381	+	1.33588i
$300$		0			0
$301$	−2.58831	−	10.0696i	−0.00859904	−	0.0334539i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.852814	−	1.47712i	−0.00279611	−	0.00484301i
$306$		0			0
$307$			606.090i			1.97423i	0.160003	+	0.987117i	$0.448850\pi$
$307$			606.090i			1.97423i	−0.160003	+	0.987117i	$0.551150\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−176.044	+	101.639i	−0.566057	+	0.326813i	−0.755573	−	0.655064i	$-0.772641\pi$
$311$	−176.044	+	101.639i	−0.566057	+	0.326813i	0.189516	+	0.981878i	$0.439308\pi$
$312$		0			0
$313$	−351.294	−	202.820i	−1.12234	−	0.647986i	−0.180346	−	0.983603i	$-0.557722\pi$
$313$	−351.294	−	202.820i	−1.12234	−	0.647986i	−0.941999	+	0.335617i	$0.891055\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.0294	+	22.5676i	−0.0411023	+	0.0711913i	−0.885845	−	0.463982i	$-0.846420\pi$
$317$	−13.0294	+	22.5676i	−0.0411023	+	0.0711913i	0.844742	+	0.535173i	$0.179754\pi$
$318$		0			0
$319$	−101.823	−	176.363i	−0.319196	−	0.552863i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	64.7208			0.200374
$324$		0			0
$325$	423.735	−	244.644i	1.30380	−	0.752750i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−80.8751	+	289.961i	−0.245821	+	0.881341i
$330$		0			0
$331$	−54.3162	+	94.0785i	−0.164097	+	0.284225i	−0.936334	−	0.351110i	$-0.885804\pi$
$331$	−54.3162	+	94.0785i	−0.164097	+	0.284225i	0.772237	+	0.635335i	$0.219138\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			6.30911i			0.0188332i
$336$		0			0
$337$	441.735			1.31079			0.655393	−	0.755288i	$-0.272503\pi$
$337$	441.735			1.31079			0.655393	+	0.755288i	$0.272503\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	229.368	+	132.425i	0.672632	+	0.388344i
$342$		0			0
$343$	235.000	+	249.848i	0.685131	+	0.728420i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.0955	−	29.6102i	−0.0492664	−	0.0853320i	0.840341	−	0.542059i	$-0.182355\pi$
$347$	−17.0955	−	29.6102i	−0.0492664	−	0.0853320i	−0.889607	+	0.456727i	$0.849022\pi$
$348$		0			0
$349$		−	221.787i		−	0.635493i	−0.948176	−	0.317746i	$-0.897074\pi$
$349$		−	221.787i		−	0.635493i	0.948176	−	0.317746i	$-0.102926\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−387.448	+	223.693i	−1.09759	+	0.633692i	−0.935586	−	0.353099i	$-0.885128\pi$
$353$	−387.448	+	223.693i	−1.09759	+	0.633692i	−0.162000	+	0.986791i	$0.551794\pi$
$354$		0			0
$355$	170.735	+	98.5739i	0.480944	+	0.277673i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−145.882	+	252.675i	−0.406357	+	0.703831i	−0.994478	−	0.104941i	$-0.966534\pi$
$359$	−145.882	+	252.675i	−0.406357	+	0.703831i	0.588121	+	0.808773i	$0.299868\pi$
$360$		0			0
$361$	−154.397	−	267.423i	−0.427692	−	0.740785i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	113.251			0.310276
$366$		0			0
$367$	363.169	−	209.676i	0.989561	−	0.571324i	0.0844183	−	0.996430i	$-0.473097\pi$
$367$	363.169	−	209.676i	0.989561	−	0.571324i	0.905143	+	0.425107i	$0.139763\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−427.279	+	418.646i	−1.15170	+	1.12843i
$372$		0			0
$373$	−15.6909	+	27.1775i	−0.0420668	+	0.0728618i	−0.886292	−	0.463127i	$-0.846728\pi$
$373$	−15.6909	+	27.1775i	−0.0420668	+	0.0728618i	0.844225	+	0.535988i	$0.180061\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			723.895i			1.92015i
$378$		0			0
$379$	−206.779			−0.545590			−0.272795	−	0.962072i	$-0.587948\pi$
$379$	−206.779			−0.545590			−0.272795	+	0.962072i	$0.587948\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−431.772	−	249.283i	−1.12734	−	0.650871i	−0.184076	−	0.982912i	$-0.558929\pi$
$383$	−431.772	−	249.283i	−1.12734	−	0.650871i	−0.943265	+	0.332041i	$0.892263\pi$
$384$		0			0
$385$	−58.3675	+	15.0029i	−0.151604	+	0.0389685i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−324.213	−	561.554i	−0.833453	−	1.44358i	−0.895284	−	0.445496i	$-0.853027\pi$
$389$	−324.213	−	561.554i	−0.833453	−	1.44358i	0.0618308	−	0.998087i	$-0.480306\pi$
$390$		0			0
$391$		−	335.508i		−	0.858077i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	122.199	−	70.5516i	0.309364	−	0.178612i
$396$		0			0
$397$	65.6026	+	37.8757i	0.165246	+	0.0954047i	0.580342	−	0.814373i	$-0.302919\pi$
$397$	65.6026	+	37.8757i	0.165246	+	0.0954047i	−0.415096	+	0.909777i	$0.636252\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−282.125	+	488.655i	−0.703553	+	1.21859i	0.263658	+	0.964616i	$0.415071\pi$
$401$	−282.125	+	488.655i	−0.703553	+	1.21859i	−0.967211	+	0.253974i	$0.918262\pi$
$402$		0			0
$403$	−470.727	−	815.324i	−1.16806	−	2.02314i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−167.823			−0.412342
$408$		0			0
$409$	−309.559	+	178.724i	−0.756868	+	0.436978i	−0.828170	−	0.560477i	$-0.810618\pi$
$409$	−309.559	+	178.724i	−0.756868	+	0.436978i	0.0713023	+	0.997455i	$0.477284\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	201.941	+	206.105i	0.488962	+	0.499044i
$414$		0			0
$415$	79.2061	−	137.189i	0.190858	−	0.330576i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			502.175i			1.19851i	0.800559	+	0.599254i	$0.204536\pi$
$419$			502.175i			1.19851i	−0.800559	+	0.599254i	$0.795464\pi$
$420$		0			0
$421$	33.7939			0.0802706			0.0401353	−	0.999194i	$-0.487221\pi$
$421$	33.7939			0.0802706			0.0401353	+	0.999194i	$0.487221\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−177.963	−	102.747i	−0.418735	−	0.241757i
$426$		0			0
$427$	−2.23550	+	8.01492i	−0.00523536	+	0.0187703i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−251.860	−	436.234i	−0.584362	−	1.01214i	−0.994955	−	0.100326i	$-0.968012\pi$
$431$	−251.860	−	436.234i	−0.584362	−	1.01214i	0.410593	−	0.911819i	$-0.365322\pi$
$432$		0			0
$433$			837.548i			1.93429i	0.254224	+	0.967145i	$0.418180\pi$
$433$			837.548i			1.93429i	−0.254224	+	0.967145i	$0.581820\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	234.375	−	135.316i	0.536326	−	0.309648i
$438$		0			0
$439$	164.558	+	95.0079i	0.374848	+	0.216419i	0.675575	−	0.737292i	$-0.263896\pi$
$439$	164.558	+	95.0079i	0.374848	+	0.216419i	−0.300726	+	0.953711i	$0.597229\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	84.7279	−	146.753i	0.191259	−	0.331271i	−0.754408	−	0.656405i	$-0.772076\pi$
$443$	84.7279	−	146.753i	0.191259	−	0.331271i	0.945668	+	0.325134i	$0.105409\pi$
$444$		0			0
$445$	14.9117	+	25.8278i	0.0335094	+	0.0580400i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−18.1035			−0.0403195			−0.0201598	−	0.999797i	$-0.506417\pi$
$449$	−18.1035			−0.0403195			−0.0201598	+	0.999797i	$0.506417\pi$
$450$		0			0
$451$	−284.912	+	164.494i	−0.631733	+	0.364731i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	206.345	+	57.5532i	0.453506	+	0.126491i
$456$		0			0
$457$	164.412	−	284.769i	0.359763	−	0.623128i	−0.628158	−	0.778086i	$-0.716191\pi$
$457$	164.412	−	284.769i	0.359763	−	0.623128i	0.987921	+	0.154958i	$0.0495242\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			794.331i			1.72306i	0.507706	+	0.861530i	$0.330494\pi$
$461$			794.331i			1.72306i	−0.507706	+	0.861530i	$0.669506\pi$
$462$		0			0
$463$	403.396			0.871266			0.435633	−	0.900124i	$-0.356525\pi$
$463$	403.396			0.871266			0.435633	+	0.900124i	$0.356525\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.44870	−	1.41376i	−0.00524347	−	0.00302732i	0.497376	−	0.867535i	$-0.334297\pi$
$467$	−2.44870	−	1.41376i	−0.00524347	−	0.00302732i	−0.502619	+	0.864508i	$0.667630\pi$
$468$		0			0
$469$	21.9848	−	21.5407i	0.0468760	−	0.0459289i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.45584	−	7.71775i	−0.00942039	−	0.0163166i
$474$		0			0
$475$		−	165.758i		−	0.348965i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	328.669	−	189.757i	0.686157	−	0.396153i	−0.116014	−	0.993248i	$-0.537012\pi$
$479$	328.669	−	189.757i	0.686157	−	0.396153i	0.802171	+	0.597095i	$0.203678\pi$
$480$		0			0
$481$	516.632	+	298.278i	1.07408	+	0.620120i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.88225	+	13.6525i	−0.0162521	+	0.0281494i
$486$		0			0
$487$	287.757	+	498.410i	0.590877	+	1.02343i	0.994115	+	0.108333i	$0.0345513\pi$
$487$	287.757	+	498.410i	0.590877	+	1.02343i	−0.403238	+	0.915095i	$0.632115\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	238.441			0.485623			0.242811	−	0.970074i	$-0.421930\pi$
$491$	238.441			0.485623			0.242811	+	0.970074i	$0.421930\pi$
$492$		0			0
$493$	263.294	−	152.013i	0.534064	−	0.308342i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−239.434	−	931.499i	−0.481758	−	1.87424i
$498$		0			0
$499$	−143.287	+	248.180i	−0.287148	+	0.497355i	−0.973128	−	0.230266i	$-0.926040\pi$
$499$	−143.287	+	248.180i	−0.287148	+	0.497355i	0.685980	+	0.727620i	$0.259374\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			25.4374i			0.0505714i	0.999680	+	0.0252857i	$0.00804954\pi$
$503$			25.4374i			0.0505714i	−0.999680	+	0.0252857i	$0.991950\pi$
$504$		0			0
$505$	153.795			0.304544
$506$		0			0
$507$		0			0
$508$		0			0
$509$	697.889	+	402.926i	1.37110	+	0.791603i	0.991066	−	0.133370i	$-0.0425800\pi$
$509$	697.889	+	402.926i	1.37110	+	0.791603i	0.380031	+	0.924974i	$0.375913\pi$
$510$		0			0
$511$	−386.662	−	394.635i	−0.756677	−	0.772280i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−75.4781	−	130.732i	−0.146559	−	0.253848i
$516$		0			0
$517$			258.025i			0.499080i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	661.706	−	382.036i	1.27007	−	0.733274i	0.295068	−	0.955476i	$-0.404658\pi$
$521$	661.706	−	382.036i	1.27007	−	0.733274i	0.975001	+	0.222202i	$0.0713244\pi$
$522$		0			0
$523$	153.096	+	88.3900i	0.292726	+	0.169006i	0.639171	−	0.769065i	$-0.279278\pi$
$523$	153.096	+	88.3900i	0.292726	+	0.169006i	−0.346444	+	0.938071i	$0.612611\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−197.698	+	342.424i	−0.375139	+	0.649761i
$528$		0			0
$529$	−436.970	−	756.854i	−0.826030	−	1.43073i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1169.44			2.19407
$534$		0			0
$535$	−147.308	+	85.0482i	−0.275342	+	0.158969i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	251.558	+	152.166i	0.466713	+	0.282311i
$540$		0			0
$541$	−8.58831	+	14.8754i	−0.0158749	+	0.0274961i	−0.873854	−	0.486189i	$-0.838387\pi$
$541$	−8.58831	+	14.8754i	−0.0158749	+	0.0274961i	0.857979	+	0.513685i	$0.171720\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	159.356i		−	0.292396i
$546$		0			0
$547$	−212.676			−0.388805			−0.194402	−	0.980922i	$-0.562277\pi$
$547$	−212.676			−0.388805			−0.194402	+	0.980922i	$0.562277\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	212.382	+	122.619i	0.385448	+	0.222538i
$552$		0			0
$553$	−663.058	−	184.938i	−1.19902	−	0.334427i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−440.823	−	763.528i	−0.791424	−	1.37079i	−0.925085	−	0.379760i	$-0.876007\pi$
$557$	−440.823	−	763.528i	−0.791424	−	1.37079i	0.133661	−	0.991027i	$-0.457327\pi$
$558$		0			0
$559$			31.6780i			0.0566691i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	664.301	−	383.534i	1.17993	−	0.681233i	0.223932	−	0.974605i	$-0.428111\pi$
$563$	664.301	−	383.534i	1.17993	−	0.681233i	0.955998	+	0.293372i	$0.0947774\pi$
$564$		0			0
$565$	−126.000	−	72.7461i	−0.223009	−	0.128754i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.6468	+	25.3689i	−0.0257412	+	0.0445851i	−0.878609	−	0.477542i	$-0.841528\pi$
$569$	−14.6468	+	25.3689i	−0.0257412	+	0.0445851i	0.852868	+	0.522127i	$0.174861\pi$
$570$		0			0
$571$	482.521	+	835.752i	0.845046	+	1.46366i	0.885581	+	0.464485i	$0.153761\pi$
$571$	482.521	+	835.752i	0.845046	+	1.46366i	−0.0405347	+	0.999178i	$0.512906\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−859.279			−1.49440
$576$		0			0
$577$	227.883	−	131.568i	0.394944	−	0.228021i	−0.289356	−	0.957222i	$-0.593441\pi$
$577$	227.883	−	131.568i	0.394944	−	0.228021i	0.684300	+	0.729201i	$0.260108\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−748.477	+	192.389i	−1.28826	+	0.331135i
$582$		0			0
$583$	−256.368	+	444.042i	−0.439738	+	0.761649i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	436.477i		−	0.743572i	−0.928318	−	0.371786i	$-0.878746\pi$
$587$		−	436.477i		−	0.743572i	0.928318	−	0.371786i	$-0.121254\pi$
$588$		0			0
$589$	−318.941			−0.541496
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−603.603	−	348.490i	−1.01788	−	0.587673i	−0.104391	−	0.994536i	$-0.533289\pi$
$593$	−603.603	−	348.490i	−1.01788	−	0.587673i	−0.913489	+	0.406863i	$0.866623\pi$
$594$		0			0
$595$	−22.3978	−	87.1372i	−0.0376434	−	0.146449i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−199.206	−	345.035i	−0.332564	−	0.576018i	0.650450	−	0.759549i	$-0.274581\pi$
$599$	−199.206	−	345.035i	−0.332564	−	0.576018i	−0.983014	+	0.183531i	$0.941247\pi$
$600$		0			0
$601$		−	36.1691i		−	0.0601816i	−0.999547	−	0.0300908i	$-0.990420\pi$
$601$		−	36.1691i		−	0.0601816i	0.999547	−	0.0300908i	$-0.00957964\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	105.624	−	60.9823i	0.174586	−	0.100797i
$606$		0			0
$607$	−27.3457	−	15.7880i	−0.0450505	−	0.0260099i	0.477306	−	0.878737i	$-0.341613\pi$
$607$	−27.3457	−	15.7880i	−0.0450505	−	0.0260099i	−0.522356	+	0.852727i	$0.674947\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	458.595	−	794.310i	0.750565	−	1.30002i
$612$		0			0
$613$	204.632	+	354.434i	0.333821	+	0.578195i	0.983258	−	0.182220i	$-0.0583285\pi$
$613$	204.632	+	354.434i	0.333821	+	0.578195i	−0.649436	+	0.760416i	$0.724995\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1227.38			−1.98927			−0.994636	−	0.103436i	$-0.967016\pi$
$617$	−1227.38			−1.98927			−0.994636	+	0.103436i	$0.967016\pi$
$618$		0			0
$619$	−412.022	+	237.881i	−0.665625	+	0.384299i	−0.794417	−	0.607373i	$-0.792223\pi$
$619$	−412.022	+	237.881i	−0.665625	+	0.384299i	0.128792	+	0.991672i	$0.458890\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	39.0883	−	140.143i	0.0627421	−	0.224949i
$624$		0			0
$625$	−237.412	+	411.209i	−0.379859	+	0.657935i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	250.544i		−	0.398322i
$630$		0			0
$631$	54.9420			0.0870713			0.0435357	−	0.999052i	$-0.486138\pi$
$631$	54.9420			0.0870713			0.0435357	+	0.999052i	$0.486138\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−102.609	−	59.2415i	−0.161589	−	0.0932937i
$636$		0			0
$637$	−503.956	−	915.533i	−0.791139	−	1.43726i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−114.551	−	198.409i	−0.178707	−	0.309530i	0.762731	−	0.646716i	$-0.223858\pi$
$641$	−114.551	−	198.409i	−0.178707	−	0.309530i	−0.941438	+	0.337186i	$0.890525\pi$
$642$		0			0
$643$		−	854.640i		−	1.32914i	−0.747224	−	0.664572i	$-0.768614\pi$
$643$		−	854.640i		−	1.32914i	0.747224	−	0.664572i	$-0.231386\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	868.632	−	501.505i	1.34255	−	0.775124i	0.355372	−	0.934725i	$-0.384354\pi$
$647$	868.632	−	501.505i	1.34255	−	0.775124i	0.987182	+	0.159601i	$0.0510207\pi$
$648$		0			0
$649$	214.191	+	123.663i	0.330032	+	0.190544i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	635.382	−	1100.51i	0.973020	−	1.68532i	0.286698	−	0.958021i	$-0.407442\pi$
$653$	635.382	−	1100.51i	0.973020	−	1.68532i	0.686321	−	0.727299i	$-0.259224\pi$
$654$		0			0
$655$	−43.4558	−	75.2677i	−0.0663448	−	0.114913i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−783.308			−1.18863			−0.594315	−	0.804232i	$-0.702577\pi$
$659$	−783.308			−1.18863			−0.594315	+	0.804232i	$0.702577\pi$
$660$		0			0
$661$	72.5589	−	41.8919i	0.109771	−	0.0633765i	−0.444109	−	0.895973i	$-0.646480\pi$
$661$	72.5589	−	41.8919i	0.109771	−	0.0633765i	0.553881	+	0.832596i	$0.313146\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	51.8377	−	50.7903i	0.0779514	−	0.0763764i
$666$		0			0
$667$	635.647	−	1100.97i	0.952994	−	1.65063i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			7.13215i			0.0106291i
$672$		0			0
$673$	415.676			0.617647			0.308823	−	0.951119i	$-0.400065\pi$
$673$	415.676			0.617647			0.308823	+	0.951119i	$0.400065\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−685.279	−	395.646i	−1.01223	−	0.584411i	−0.100386	−	0.994949i	$-0.532008\pi$
$677$	−685.279	−	395.646i	−1.01223	−	0.584411i	−0.911844	+	0.410538i	$0.865341\pi$
$678$		0			0
$679$	74.4853	−	19.1458i	0.109698	−	0.0281970i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	164.080	+	284.195i	0.240235	+	0.416099i	0.960781	−	0.277308i	$-0.0894423\pi$
$683$	164.080	+	284.195i	0.240235	+	0.416099i	−0.720546	+	0.693407i	$0.756109\pi$
$684$		0			0
$685$			96.1791i			0.140407i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1578.42	−	911.300i	2.29088	−	1.32264i
$690$		0			0
$691$	−875.182	−	505.287i	−1.26654	−	0.731240i	−0.292212	−	0.956353i	$-0.594391\pi$
$691$	−875.182	−	505.287i	−1.26654	−	0.731240i	−0.974333	+	0.225113i	$0.927725\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−65.6833	+	113.767i	−0.0945084	+	0.163693i
$696$		0			0
$697$	−245.574	−	425.346i	−0.352329	−	0.610252i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	0.103464			0.000147594			7.37972e−5	−	1.00000i	$-0.499977\pi$
$701$	0.103464			0.000147594			7.37972e−5		1.00000i	$0.499977\pi$
$702$		0			0
$703$	175.022	−	101.049i	0.248964	−	0.143740i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−525.088	−	535.916i	−0.742699	−	0.758014i
$708$		0			0
$709$	−602.588	+	1043.71i	−0.849912	+	1.47209i	0.0313734	+	0.999508i	$0.490012\pi$
$709$	−602.588	+	1043.71i	−0.849912	+	1.47209i	−0.881286	+	0.472584i	$0.843321\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			1653.37i			2.31889i
$714$		0			0
$715$	183.618			0.256809
$716$		0			0
$717$		0			0
$718$		0			0
$719$	850.925	+	491.282i	1.18348	+	0.683285i	0.956818	−	0.290688i	$-0.0938840\pi$
$719$	850.925	+	491.282i	1.18348	+	0.683285i	0.226666	+	0.973973i	$0.427217\pi$
$720$		0			0
$721$	−197.852	+	709.359i	−0.274414	+	0.983855i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−389.324	−	674.329i	−0.536998	−	0.930108i
$726$		0			0
$727$		−	630.440i		−	0.867181i	−0.901110	−	0.433590i	$-0.857247\pi$
$727$		−	630.440i		−	0.867181i	0.901110	−	0.433590i	$-0.142753\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	11.5219	−	6.65215i	0.0157618	−	0.00910007i
$732$		0			0
$733$	258.486	+	149.237i	0.352641	+	0.203597i	0.665848	−	0.746088i	$-0.268070\pi$
$733$	258.486	+	149.237i	0.352641	+	0.203597i	−0.313207	+	0.949685i	$0.601403\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	13.1909	−	22.8473i	0.0178981	−	0.0310004i
$738$		0			0
$739$	172.684	+	299.097i	0.233672	+	0.404732i	0.958886	−	0.283792i	$-0.0915924\pi$
$739$	172.684	+	299.097i	0.233672	+	0.404732i	−0.725214	+	0.688524i	$0.758259\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	683.616			0.920076			0.460038	−	0.887899i	$-0.347836\pi$
$743$	683.616			0.920076			0.460038	+	0.887899i	$0.347836\pi$
$744$		0			0
$745$	100.764	−	58.1759i	0.135253	−	0.0780885i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	799.301	+	222.939i	1.06716	+	0.297648i
$750$		0			0
$751$	−289.169	+	500.855i	−0.385045	+	0.666918i	−0.991775	−	0.127990i	$-0.959148\pi$
$751$	−289.169	+	500.855i	−0.385045	+	0.666918i	0.606730	+	0.794908i	$0.292481\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	73.4744i		−	0.0973171i
$756$		0			0
$757$	1204.82			1.59158			0.795788	−	0.605576i	$-0.207057\pi$
$757$	1204.82			1.59158			0.795788	+	0.605576i	$0.207057\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	202.669	+	117.011i	0.266319	+	0.153760i	0.627214	−	0.778847i	$-0.284195\pi$
$761$	202.669	+	117.011i	0.266319	+	0.153760i	−0.360894	+	0.932607i	$0.617529\pi$
$762$		0			0
$763$	−555.294	+	544.075i	−0.727778	+	0.713074i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−439.581	−	761.376i	−0.573117	−	0.992668i
$768$		0			0
$769$		−	1290.16i		−	1.67771i	−0.544358	−	0.838853i	$-0.683226\pi$
$769$		−	1290.16i		−	1.67771i	0.544358	−	0.838853i	$-0.316774\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−345.646	+	199.559i	−0.447149	+	0.258161i	−0.706625	−	0.707588i	$-0.749783\pi$
$773$	−345.646	+	199.559i	−0.447149	+	0.258161i	0.259477	+	0.965749i	$0.416450\pi$
$774$		0			0
$775$	876.992	+	506.331i	1.13160	+	0.653331i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	198.088	−	343.099i	0.254285	−	0.440435i
$780$		0			0
$781$	−412.191	−	713.936i	−0.527773	−	0.914130i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	268.410			0.341924
$786$		0			0
$787$	1348.16	−	778.361i	1.71304	−	0.989023i	0.782637	−	0.622478i	$-0.213874\pi$
$787$	1348.16	−	778.361i	1.71304	−	0.989023i	0.930401	−	0.366544i	$-0.119459\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	176.698	+	687.433i	0.223386	+	0.869068i
$792$		0			0
$793$	12.6762	−	21.9558i	0.0159851	−	0.0276870i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			600.232i			0.753114i	0.926393	+	0.376557i	$0.122892\pi$
$797$			600.232i			0.753114i	−0.926393	+	0.376557i	$0.877108\pi$
$798$		0			0
$799$	−385.206			−0.482110
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−410.117	−	236.781i	−0.510731	−	0.294871i
$804$		0			0
$805$	−263.294	−	268.723i	−0.327073	−	0.333817i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−114.640	−	198.562i	−0.141705	−	0.245441i	0.786434	−	0.617675i	$-0.211925\pi$
$809$	−114.640	−	198.562i	−0.141705	−	0.245441i	−0.928139	+	0.372234i	$0.878592\pi$
$810$		0			0
$811$			529.955i			0.653459i	0.945118	+	0.326729i	$0.105947\pi$
$811$			529.955i			0.653459i	−0.945118	+	0.326729i	$0.894053\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	104.309	−	60.2226i	0.127986	−	0.0738928i
$816$		0			0
$817$	9.29394	+	5.36586i	0.0113757	+	0.00656776i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−151.669	+	262.698i	−0.184737	+	0.319974i	−0.943488	−	0.331407i	$-0.892477\pi$
$821$	−151.669	+	262.698i	−0.184737	+	0.319974i	0.758751	+	0.651381i	$0.225810\pi$
$822$		0			0
$823$	−564.955	−	978.531i	−0.686459	−	1.18898i	−0.972976	−	0.230906i	$-0.925831\pi$
$823$	−564.955	−	978.531i	−0.686459	−	1.18898i	0.286517	−	0.958075i	$-0.407502\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−161.604			−0.195410			−0.0977049	−	0.995215i	$-0.531150\pi$
$827$	−161.604			−0.195410			−0.0977049	+	0.995215i	$0.531150\pi$
$828$		0			0
$829$	1325.32	−	765.175i	1.59870	−	0.923010i	0.606962	−	0.794731i	$-0.292388\pi$
$829$	1325.32	−	765.175i	1.59870	−	0.923010i	0.991738	−	0.128279i	$-0.0409454\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−227.169	+	375.553i	−0.272711	+	0.450844i
$834$		0			0
$835$	−91.5593	+	158.585i	−0.109652	+	0.189923i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			218.629i			0.260583i	0.991476	+	0.130291i	$0.0415913\pi$
$839$			218.629i			0.260583i	−0.991476	+	0.130291i	$0.958409\pi$
$840$		0			0
$841$	311.000			0.369798
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−355.249	−	205.103i	−0.420413	−	0.242726i
$846$		0			0
$847$	−573.124	−	159.854i	−0.676652	−	0.188730i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−523.831	−	907.301i	−0.615547	−	1.06616i
$852$		0			0
$853$		−	762.730i		−	0.894174i	−0.894491	−	0.447087i	$-0.852461\pi$
$853$		−	762.730i		−	0.894174i	0.894491	−	0.447087i	$-0.147539\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	795.015	−	459.002i	0.927672	−	0.535592i	0.0415977	−	0.999134i	$-0.486755\pi$
$857$	795.015	−	459.002i	0.927672	−	0.535592i	0.886075	+	0.463543i	$0.153422\pi$
$858$		0			0
$859$	761.367	+	439.575i	0.886341	+	0.511729i	0.872744	−	0.488179i	$-0.162339\pi$
$859$	761.367	+	439.575i	0.886341	+	0.511729i	0.0135969	+	0.999908i	$0.495672\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−175.294	+	303.619i	−0.203122	+	0.351818i	−0.949533	−	0.313668i	$-0.898442\pi$
$863$	−175.294	+	303.619i	−0.203122	+	0.351818i	0.746411	+	0.665486i	$0.231776\pi$
$864$		0			0
$865$	102.573	+	177.661i	0.118581	+	0.205389i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−590.029			−0.678974
$870$		0			0
$871$	−81.2145	+	46.8892i	−0.0932428	+	0.0538338i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−466.368	+	119.876i	−0.532991	+	0.137001i
$876$		0			0
$877$	−1.77965	+	3.08245i	−0.00202925	+	0.00351477i	−0.867038	−	0.498242i	$-0.833979\pi$
$877$	−1.77965	+	3.08245i	−0.00202925	+	0.00351477i	0.865009	+	0.501756i	$0.167313\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	488.565i		−	0.554557i	−0.960790	−	0.277279i	$-0.910567\pi$
$881$		−	488.565i		−	0.554557i	0.960790	−	0.277279i	$-0.0894325\pi$
$882$		0			0
$883$	1162.16			1.31615			0.658075	−	0.752953i	$-0.271371\pi$
$883$	1162.16			1.31615			0.658075	+	0.752953i	$0.271371\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	75.2801	+	43.4630i	0.0848704	+	0.0490000i	0.541835	−	0.840485i	$-0.317730\pi$
$887$	75.2801	+	43.4630i	0.0848704	+	0.0490000i	−0.456964	+	0.889485i	$0.651063\pi$
$888$		0			0
$889$	143.896	+	559.817i	0.161863	+	0.629716i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−155.360	−	269.092i	−0.173976	−	0.301335i
$894$		0			0
$895$		−	242.895i		−	0.271391i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1297.50	+	749.111i	−1.44327	+	0.833272i
$900$		0			0
$901$	−662.912	−	382.732i	−0.735751	−	0.424786i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−150.640	+	260.915i	−0.166453	+	0.288304i
$906$		0			0
$907$	−230.448	−	399.148i	−0.254077	−	0.440075i	0.710567	−	0.703629i	$-0.248438\pi$
$907$	−230.448	−	399.148i	−0.254077	−	0.440075i	−0.964645	+	0.263554i	$0.915105\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1184.28			−1.29998			−0.649988	−	0.759944i	$-0.725226\pi$
$911$	−1184.28			−1.29998			−0.649988	+	0.759944i	$0.725226\pi$
$912$		0			0
$913$	−573.661	+	331.203i	−0.628325	+	0.362764i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−113.912	+	408.407i	−0.124222	+	0.445373i
$918$		0			0
$919$	−270.919	+	469.246i	−0.294798	+	0.510605i	−0.974938	−	0.222477i	$-0.928586\pi$
$919$	−270.919	+	469.246i	−0.294798	+	0.510605i	0.680140	+	0.733082i	$0.261919\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			2930.40i			3.17486i
$924$		0			0
$925$	−641.676			−0.693704
$926$		0			0
$927$		0			0
$928$		0			0
$929$	779.610	+	450.108i	0.839193	+	0.484508i	0.856990	−	0.515333i	$-0.172332\pi$
$929$	779.610	+	450.108i	0.839193	+	0.484508i	−0.0177969	+	0.999842i	$0.505665\pi$
$930$		0			0
$931$	−353.970	−	7.22538i	−0.380204	−	0.00776088i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−38.5584	−	66.7852i	−0.0412390	−	0.0714280i
$936$		0			0
$937$		−	233.964i		−	0.249695i	−0.992176	−	0.124847i	$-0.960156\pi$
$937$		−	233.964i		−	0.249695i	0.992176	−	0.124847i	$-0.0398441\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1132.49	+	653.845i	−1.20350	+	0.694840i	−0.961331	−	0.275394i	$-0.911192\pi$
$941$	−1132.49	+	653.845i	−1.20350	+	0.694840i	−0.242167	+	0.970234i	$0.577858\pi$
$942$		0			0
$943$	−1778.60	−	1026.88i	−1.88611	−	1.08895i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	563.881	−	976.671i	0.595440	−	1.03133i	−0.398045	−	0.917366i	$-0.630311\pi$
$947$	563.881	−	976.671i	0.595440	−	1.03133i	0.993485	−	0.113966i	$-0.0363555\pi$
$948$		0			0
$949$	841.677	+	1457.83i	0.886909	+	1.53617i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	91.4255			0.0959345			0.0479672	−	0.998849i	$-0.484726\pi$
$953$	91.4255			0.0959345			0.0479672	+	0.998849i	$0.484726\pi$
$954$		0			0
$955$	−82.7636	+	47.7836i	−0.0866635	+	0.0500352i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	335.147	−	328.376i	0.349476	−	0.342415i
$960$		0			0
$961$	493.749	−	855.199i	0.513787	−	0.889905i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			14.0531i			0.0145628i
$966$		0			0
$967$	1098.19			1.13567			0.567834	−	0.823143i	$-0.307782\pi$
$967$	1098.19			1.13567			0.567834	+	0.823143i	$0.307782\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	114.405	+	66.0517i	0.117822	+	0.0680245i	0.557753	−	0.830007i	$-0.311664\pi$
$971$	114.405	+	66.0517i	0.117822	+	0.0680245i	−0.439931	+	0.898032i	$0.644997\pi$
$972$		0			0
$973$	620.691	−	159.543i	0.637915	−	0.163970i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	224.117	+	388.182i	0.229393	+	0.397320i	0.957628	−	0.288007i	$-0.0929926\pi$
$977$	224.117	+	388.182i	0.229393	+	0.397320i	−0.728235	+	0.685327i	$0.759659\pi$
$978$		0			0
$979$		−	124.708i		−	0.127383i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1426.14	−	823.382i	1.45080	−	0.837621i	0.452276	−	0.891878i	$-0.350612\pi$
$983$	1426.14	−	823.382i	1.45080	−	0.837621i	0.998527	+	0.0542567i	$0.0172789\pi$
$984$		0			0
$985$	331.986	+	191.672i	0.337041	+	0.194591i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	27.8162	−	48.1791i	0.0281256	−	0.0487150i
$990$		0			0
$991$	−314.448	−	544.640i	−0.317304	−	0.549587i	0.662621	−	0.748955i	$-0.269444\pi$
$991$	−314.448	−	544.640i	−0.317304	−	0.549587i	−0.979925	+	0.199369i	$0.936111\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	187.882			0.188826
$996$		0			0
$997$	−869.645	+	502.090i	−0.872262	+	0.503601i	−0.868099	−	0.496390i	$-0.834658\pi$
$997$	−869.645	+	502.090i	−0.872262	+	0.503601i	−0.00416289	+	0.999991i	$0.501325\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.3.cg.h.145.2		4
3.2	odd	2		336.3.bh.e.145.1		4
4.3	odd	2		126.3.n.a.19.1		4
7.3	odd	6	inner	1008.3.cg.h.577.2		4
12.11	even	2		42.3.g.a.19.2	✓	4
21.2	odd	6		2352.3.f.e.97.2		4
21.5	even	6		2352.3.f.e.97.3		4
21.17	even	6		336.3.bh.e.241.1		4
28.3	even	6		126.3.n.a.73.1		4
28.11	odd	6		882.3.n.e.325.1		4
28.19	even	6		882.3.c.b.685.4		4
28.23	odd	6		882.3.c.b.685.3		4
28.27	even	2		882.3.n.e.19.1		4
60.23	odd	4		1050.3.q.a.649.2		8
60.47	odd	4		1050.3.q.a.649.3		8
60.59	even	2		1050.3.p.a.901.1		4
84.11	even	6		294.3.g.a.31.2		4
84.23	even	6		294.3.c.a.97.2		4
84.47	odd	6		294.3.c.a.97.1		4
84.59	odd	6		42.3.g.a.31.2	yes	4
84.83	odd	2		294.3.g.a.19.2		4
420.59	odd	6		1050.3.p.a.451.1		4
420.143	even	12		1050.3.q.a.199.3		8
420.227	even	12		1050.3.q.a.199.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.g.a.19.2	✓	4	12.11	even	2
42.3.g.a.31.2	yes	4	84.59	odd	6
126.3.n.a.19.1		4	4.3	odd	2
126.3.n.a.73.1		4	28.3	even	6
294.3.c.a.97.1		4	84.47	odd	6
294.3.c.a.97.2		4	84.23	even	6
294.3.g.a.19.2		4	84.83	odd	2
294.3.g.a.31.2		4	84.11	even	6
336.3.bh.e.145.1		4	3.2	odd	2
336.3.bh.e.241.1		4	21.17	even	6
882.3.c.b.685.3		4	28.23	odd	6
882.3.c.b.685.4		4	28.19	even	6
882.3.n.e.19.1		4	28.27	even	2
882.3.n.e.325.1		4	28.11	odd	6
1008.3.cg.h.145.2		4	1.1	even	1	trivial
1008.3.cg.h.577.2		4	7.3	odd	6	inner
1050.3.p.a.451.1		4	420.59	odd	6
1050.3.p.a.901.1		4	60.59	even	2
1050.3.q.a.199.2		8	420.227	even	12
1050.3.q.a.199.3		8	420.143	even	12
1050.3.q.a.649.2		8	60.23	odd	4
1050.3.q.a.649.3		8	60.47	odd	4
2352.3.f.e.97.2		4	21.2	odd	6
2352.3.f.e.97.3		4	21.5	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cg (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.24264 + 0.717439i) q^{5} +(-1.74264 - 6.77962i) q^{7} +(-3.00000 - 5.19615i) q^{11} +21.3280i q^{13} +(7.75736 - 4.47871i) q^{17} +(6.25736 + 3.61269i) q^{19} +(18.7279 - 32.4377i) q^{23} +(-11.4706 - 19.8676i) q^{25} +33.9411 q^{29} +(-38.2279 + 22.0709i) q^{31} +(2.69848 - 9.67487i) q^{35} +(13.9853 - 24.2232i) q^{37} -54.8313i q^{41} +1.48528 q^{43} +(-37.2426 - 21.5020i) q^{47} +(-42.9264 + 23.6289i) q^{49} +(-42.7279 - 74.0069i) q^{53} -8.60927i q^{55} +(-35.6985 + 20.6105i) q^{59} +(-1.02944 - 0.594346i) q^{61} +(-15.3015 + 26.5030i) q^{65} +(2.19848 + 3.80789i) q^{67} +137.397 q^{71} +(68.3528 - 39.4635i) q^{73} +(-30.0000 + 29.3939i) q^{77} +(49.1690 - 85.1633i) q^{79} -110.401i q^{83} +12.8528 q^{85} +(18.0000 + 10.3923i) q^{89} +(144.595 - 37.1670i) q^{91} +(5.18377 + 8.97855i) q^{95} +10.9867i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{5} + 10 q^{7} - 12 q^{11} + 48 q^{17} + 42 q^{19} + 24 q^{23} + 22 q^{25} - 102 q^{31} - 108 q^{35} + 22 q^{37} - 28 q^{43} - 132 q^{47} - 2 q^{49} - 120 q^{53} - 24 q^{59} - 72 q^{61} - 180 q^{65}+ \cdots - 132 q^{95}+O(q^{100}) \) 4 * q - 12 * q^5 + 10 * q^7 - 12 * q^11 + 48 * q^17 + 42 * q^19 + 24 * q^23 + 22 * q^25 - 102 * q^31 - 108 * q^35 + 22 * q^37 - 28 * q^43 - 132 * q^47 - 2 * q^49 - 120 * q^53 - 24 * q^59 - 72 * q^61 - 180 * q^65 - 110 * q^67 + 312 * q^71 - 66 * q^73 - 120 * q^77 + 10 * q^79 - 288 * q^85 + 72 * q^89 + 222 * q^91 - 132 * q^95

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