LMFDB - Embedded newform 1008.3.cg.h.145.1

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			145.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1008.145
Dual form			1008.3.cg.h.577.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.24264 - 4.18154i) q^{5} +(6.74264 - 1.88064i) q^{7} +(-3.00000 - 5.19615i) q^{11} -17.8639i q^{13} +(16.2426 - 9.37769i) q^{17} +(14.7426 + 8.51167i) q^{19} +(-6.72792 + 11.6531i) q^{23} +(22.4706 + 38.9202i) q^{25} -33.9411 q^{29} +(-12.7721 + 7.37396i) q^{31} +(-56.6985 - 14.5738i) q^{35} +(-2.98528 + 5.17066i) q^{37} -35.2354i q^{41} -15.4853 q^{43} +(-28.7574 - 16.6031i) q^{47} +(41.9264 - 25.3609i) q^{49} +(-17.2721 - 29.9161i) q^{53} +50.1785i q^{55} +(23.6985 - 13.6823i) q^{59} +(-34.9706 - 20.1903i) q^{61} +(-74.6985 + 129.382i) q^{65} +(-57.1985 - 99.0707i) q^{67} +18.6030 q^{71} +(-101.353 + 58.5161i) q^{73} +(-30.0000 - 29.3939i) q^{77} +(-44.1690 + 76.5030i) q^{79} +75.7601i q^{83} -156.853 q^{85} +(18.0000 + 10.3923i) q^{89} +(-33.5955 - 120.450i) q^{91} +(-71.1838 - 123.294i) q^{95} +30.5826i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−7.24264	−	4.18154i	−1.44853	−	0.836308i	−0.450134	−	0.892961i	$-0.648624\pi$
$5$	−7.24264	−	4.18154i	−1.44853	−	0.836308i	−0.998394	+	0.0566528i	$0.981957\pi$
$6$		0			0
$7$	6.74264	−	1.88064i	0.963234	−	0.268662i
$7$	6.74264	−	1.88064i	0.963234	−	0.268662i
$8$		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
$13$		−	17.8639i		−	1.37414i	−0.726590	−	0.687072i	$-0.758896\pi$
$13$		−	17.8639i		−	1.37414i	0.726590	−	0.687072i	$-0.241104\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	16.2426	−	9.37769i	0.955449	−	0.551629i	0.0606799	−	0.998157i	$-0.480673\pi$
$17$	16.2426	−	9.37769i	0.955449	−	0.551629i	0.894770	+	0.446528i	$0.147340\pi$
$18$		0			0
$19$	14.7426	+	8.51167i	0.775928	+	0.447983i	0.834985	−	0.550272i	$-0.185476\pi$
$19$	14.7426	+	8.51167i	0.775928	+	0.447983i	−0.0590569	+	0.998255i	$0.518809\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.72792	+	11.6531i	−0.292518	+	0.506657i	−0.974405	−	0.224802i	$-0.927827\pi$
$23$	−6.72792	+	11.6531i	−0.292518	+	0.506657i	0.681886	+	0.731458i	$0.261160\pi$
$24$		0			0
$25$	22.4706	+	38.9202i	0.898823	+	1.55681i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−33.9411			−1.17038			−0.585192	−	0.810895i	$-0.698981\pi$
$29$	−33.9411			−1.17038			−0.585192	+	0.810895i	$0.698981\pi$
$30$		0			0
$31$	−12.7721	+	7.37396i	−0.412003	+	0.237870i	−0.691650	−	0.722233i	$-0.743116\pi$
$31$	−12.7721	+	7.37396i	−0.412003	+	0.237870i	0.279647	+	0.960103i	$0.409782\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−56.6985	−	14.5738i	−1.61996	−	0.416396i
$36$		0			0
$37$	−2.98528	+	5.17066i	−0.0806833	+	0.139748i	−0.903544	−	0.428496i	$-0.859044\pi$
$37$	−2.98528	+	5.17066i	−0.0806833	+	0.139748i	0.822860	+	0.568244i	$0.192377\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	35.2354i		−	0.859399i	−0.902972	−	0.429700i	$-0.858619\pi$
$41$		−	35.2354i		−	0.859399i	0.902972	−	0.429700i	$-0.141381\pi$
$42$		0			0
$43$	−15.4853			−0.360123			−0.180061	−	0.983655i	$-0.557630\pi$
$43$	−15.4853			−0.360123			−0.180061	+	0.983655i	$0.557630\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−28.7574	−	16.6031i	−0.611859	−	0.353257i	0.161834	−	0.986818i	$-0.448259\pi$
$47$	−28.7574	−	16.6031i	−0.611859	−	0.353257i	−0.773693	+	0.633561i	$0.781592\pi$
$48$		0			0
$49$	41.9264	−	25.3609i	0.855641	−	0.517570i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−17.2721	−	29.9161i	−0.325888	−	0.564455i	0.655803	−	0.754932i	$-0.272330\pi$
$53$	−17.2721	−	29.9161i	−0.325888	−	0.564455i	−0.981692	+	0.190477i	$0.938997\pi$
$54$		0			0
$55$			50.1785i			0.912336i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	23.6985	−	13.6823i	0.401669	−	0.231904i	−0.285535	−	0.958368i	$-0.592171\pi$
$59$	23.6985	−	13.6823i	0.401669	−	0.231904i	0.687204	+	0.726465i	$0.258838\pi$
$60$		0			0
$61$	−34.9706	−	20.1903i	−0.573288	−	0.330988i	0.185174	−	0.982706i	$-0.440715\pi$
$61$	−34.9706	−	20.1903i	−0.573288	−	0.330988i	−0.758461	+	0.651718i	$0.774049\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−74.6985	+	129.382i	−1.14921	+	1.99049i
$66$		0			0
$67$	−57.1985	−	99.0707i	−0.853709	−	1.47867i	−0.877838	−	0.478958i	$-0.841015\pi$
$67$	−57.1985	−	99.0707i	−0.853709	−	1.47867i	0.0241291	−	0.999709i	$-0.492319\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	18.6030			0.262015			0.131007	−	0.991381i	$-0.458179\pi$
$71$	18.6030			0.262015			0.131007	+	0.991381i	$0.458179\pi$
$72$		0			0
$73$	−101.353	+	58.5161i	−1.38839	+	0.801590i	−0.993134	−	0.116979i	$-0.962679\pi$
$73$	−101.353	+	58.5161i	−1.38839	+	0.801590i	−0.395260	+	0.918569i	$0.629346\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−30.0000	−	29.3939i	−0.389610	−	0.381739i
$78$		0			0
$79$	−44.1690	+	76.5030i	−0.559102	+	0.968393i	0.438470	+	0.898746i	$0.355521\pi$
$79$	−44.1690	+	76.5030i	−0.559102	+	0.968393i	−0.997572	+	0.0696469i	$0.977813\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			75.7601i			0.912772i	0.889782	+	0.456386i	$0.150856\pi$
$83$			75.7601i			0.912772i	−0.889782	+	0.456386i	$0.849144\pi$
$84$		0			0
$85$	−156.853			−1.84533
$86$		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
$91$	−33.5955	−	120.450i	−0.369181	−	1.32362i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−71.1838	−	123.294i	−0.749303	−	1.29783i
$96$		0			0
$97$			30.5826i			0.315284i	0.987496	+	0.157642i	$0.0503892\pi$
$97$			30.5826i			0.315284i	−0.987496	+	0.157642i	$0.949611\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−110.823	+	63.9839i	−1.09726	+	0.633504i	−0.935500	−	0.353326i	$-0.885051\pi$
$101$	−110.823	+	63.9839i	−1.09726	+	0.633504i	−0.161761	+	0.986830i	$0.551717\pi$
$102$		0			0
$103$	70.1102	+	40.4781i	0.680681	+	0.392992i	0.800112	−	0.599851i	$-0.204774\pi$
$103$	70.1102	+	40.4781i	0.680681	+	0.392992i	−0.119430	+	0.992843i	$0.538107\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−84.7279	+	146.753i	−0.791850	+	1.37152i	0.132971	+	0.991120i	$0.457548\pi$
$107$	−84.7279	+	146.753i	−0.791850	+	1.37152i	−0.924820	+	0.380404i	$0.875785\pi$
$108$		0			0
$109$	−89.4706	−	154.968i	−0.820831	−	1.42172i	−0.905064	−	0.425275i	$-0.860177\pi$
$109$	−89.4706	−	154.968i	−0.820831	−	1.42172i	0.0842335	−	0.996446i	$-0.473156\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	17.3970			0.153955			0.0769777	−	0.997033i	$-0.475473\pi$
$113$	17.3970			0.153955			0.0769777	+	0.997033i	$0.475473\pi$
$114$		0			0
$115$	97.4558	−	56.2662i	0.847442	−	0.489271i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	91.8823	−	93.7769i	0.772120	−	0.788041i
$120$		0			0
$121$	42.5000	−	73.6122i	0.351240	−	0.608365i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	166.769i		−	1.33415i
$126$		0			0
$127$	−167.426			−1.31832			−0.659159	−	0.752004i	$-0.729088\pi$
$127$	−167.426			−1.31832			−0.659159	+	0.752004i	$0.729088\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.54416	−	0.891519i	−0.0117874	−	0.00680549i	0.494095	−	0.869408i	$-0.335500\pi$
$131$	−1.54416	−	0.891519i	−0.0117874	−	0.00680549i	−0.505882	+	0.862603i	$0.668833\pi$
$132$		0			0
$133$	115.412	+	29.6656i	0.867757	+	0.223049i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	50.4853	+	87.4431i	0.368506	+	0.638271i	0.989332	−	0.145677i	$-0.0465362\pi$
$137$	50.4853	+	87.4431i	0.368506	+	0.638271i	−0.620826	+	0.783948i	$0.713203\pi$
$138$		0			0
$139$			140.542i			1.01110i	0.862799	+	0.505548i	$0.168710\pi$
$139$			140.542i			1.01110i	−0.862799	+	0.505548i	$0.831290\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−92.8234	+	53.5916i	−0.649115	+	0.374766i
$144$		0			0
$145$	245.823	+	141.926i	1.69533	+	0.978801i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	91.4558	−	158.406i	0.613798	−	1.06313i	−0.376797	−	0.926296i	$-0.622974\pi$
$149$	91.4558	−	158.406i	0.613798	−	1.06313i	0.990594	−	0.136833i	$-0.0436922\pi$
$150$		0			0
$151$	−144.397	−	250.103i	−0.956271	−	1.65631i	−0.731432	−	0.681915i	$-0.761148\pi$
$151$	−144.397	−	250.103i	−0.956271	−	1.65631i	−0.224840	−	0.974396i	$-0.572186\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	123.338			0.795730
$156$		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
$161$	−23.4487	+	91.2255i	−0.145644	+	0.566618i
$162$		0			0
$163$	8.02944	−	13.9074i	0.0492604	−	0.0853214i	−0.840344	−	0.542054i	$-0.817647\pi$
$163$	8.02944	−	13.9074i	0.0492604	−	0.0853214i	0.889604	+	0.456732i	$0.150980\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	176.117i		−	1.05459i	−0.849681	−	0.527297i	$-0.823206\pi$
$167$		−	176.117i		−	1.05459i	0.849681	−	0.527297i	$-0.176794\pi$
$168$		0			0
$169$	−150.118			−0.888271
$170$		0			0
$171$		0			0
$172$		0			0
$173$	200.184	+	115.576i	1.15713	+	0.668070i	0.950615	−	0.310373i	$-0.100454\pi$
$173$	200.184	+	115.576i	1.15713	+	0.668070i	0.206517	+	0.978443i	$0.433787\pi$
$174$		0			0
$175$	224.706	+	220.166i	1.28403	+	1.25809i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	42.6396	+	73.8540i	0.238210	+	0.412592i	0.960201	−	0.279311i	$-0.0901060\pi$
$179$	42.6396	+	73.8540i	0.238210	+	0.412592i	−0.721991	+	0.691903i	$0.756773\pi$
$180$		0			0
$181$		−	5.58655i		−	0.0308649i	−0.999881	−	0.0154325i	$-0.995087\pi$
$181$		−	5.58655i		−	0.0308649i	0.999881	−	0.0154325i	$-0.00491250\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	43.2426	−	24.9662i	0.233744	−	0.134952i
$186$		0			0
$187$	−97.4558	−	56.2662i	−0.521154	−	0.300889i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−92.6985	+	160.558i	−0.485332	+	0.840620i	−0.999858	−	0.0168547i	$-0.994635\pi$
$191$	−92.6985	+	160.558i	−0.485332	+	0.840620i	0.514526	+	0.857475i	$0.327968\pi$
$192$		0			0
$193$	−113.897	−	197.275i	−0.590140	−	1.02215i	−0.994213	−	0.107425i	$-0.965739\pi$
$193$	−113.897	−	197.275i	−0.590140	−	1.02215i	0.404073	−	0.914727i	$-0.367594\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−123.161			−0.625185			−0.312593	−	0.949887i	$-0.601197\pi$
$197$	−123.161			−0.625185			−0.312593	+	0.949887i	$0.601197\pi$
$198$		0			0
$199$	−5.39697	+	3.11594i	−0.0271205	+	0.0156580i	−0.513499	−	0.858090i	$-0.671651\pi$
$199$	−5.39697	+	3.11594i	−0.0271205	+	0.0156580i	0.486378	+	0.873748i	$0.338318\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−228.853	+	63.8309i	−1.12735	+	0.314438i
$204$		0			0
$205$	−147.338	+	255.197i	−0.718722	+	1.24486i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	102.140i		−	0.488708i
$210$		0			0
$211$	124.912			0.591999			0.295999	−	0.955188i	$-0.404347\pi$
$211$	124.912			0.591999			0.295999	+	0.955188i	$0.404347\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	112.154	+	64.7523i	0.521648	+	0.301174i
$216$		0			0
$217$	−72.2498	+	73.7396i	−0.332948	+	0.339814i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−167.522	−	290.156i	−0.758017	−	1.31292i
$222$		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
$227$	−146.823	+	84.7685i	−0.646799	+	0.373430i	−0.787229	−	0.616661i	$-0.788485\pi$
$227$	−146.823	+	84.7685i	−0.646799	+	0.373430i	0.140430	+	0.990091i	$0.455152\pi$
$228$		0			0
$229$	30.0442	+	17.3460i	0.131197	+	0.0757467i	0.564162	−	0.825664i	$-0.309199\pi$
$229$	30.0442	+	17.3460i	0.131197	+	0.0757467i	−0.432965	+	0.901411i	$0.642533\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−127.243	+	220.391i	−0.546106	+	0.945883i	0.452431	+	0.891800i	$0.350557\pi$
$233$	−127.243	+	220.391i	−0.546106	+	0.945883i	−0.998536	+	0.0540833i	$0.982776\pi$
$234$		0			0
$235$	138.853	+	240.500i	0.590863	+	1.02340i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	197.147			0.824884			0.412442	−	0.910984i	$-0.364676\pi$
$239$	197.147			0.824884			0.412442	+	0.910984i	$0.364676\pi$
$240$		0			0
$241$	76.6173	−	44.2350i	0.317914	−	0.183548i	−0.332548	−	0.943086i	$-0.607908\pi$
$241$	76.6173	−	44.2350i	0.317914	−	0.183548i	0.650462	+	0.759538i	$0.274575\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−409.706	+	8.36308i	−1.67227	+	0.0341350i
$246$		0			0
$247$	152.051	−	263.361i	0.615592	−	1.06624i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	215.903i		−	0.860172i	−0.902788	−	0.430086i	$-0.858483\pi$
$251$		−	215.903i		−	0.860172i	0.902788	−	0.430086i	$-0.141517\pi$
$252$		0			0
$253$	80.7351			0.319111
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.72792	+	2.15232i	0.0145055	+	0.00837477i	0.507235	−	0.861808i	$-0.330668\pi$
$257$	3.72792	+	2.15232i	0.0145055	+	0.00837477i	−0.492730	+	0.870182i	$0.664001\pi$
$258$		0			0
$259$	−10.4045	+	40.4781i	−0.0401720	+	0.156286i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−141.338	−	244.805i	−0.537407	−	0.930817i	−0.999043	−	0.0437468i	$-0.986071\pi$
$263$	−141.338	−	244.805i	−0.537407	−	0.930817i	0.461635	−	0.887070i	$-0.347263\pi$
$264$		0			0
$265$			288.896i			1.09017i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	330.765	−	190.967i	1.22961	−	0.709914i	0.262660	−	0.964888i	$-0.415400\pi$
$269$	330.765	−	190.967i	1.22961	−	0.709914i	0.966948	+	0.254974i	$0.0820669\pi$
$270$		0			0
$271$	73.0294	+	42.1636i	0.269481	+	0.155585i	0.628652	−	0.777687i	$-0.283607\pi$
$271$	73.0294	+	42.1636i	0.269481	+	0.155585i	−0.359171	+	0.933272i	$0.616940\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	134.823	−	233.521i	0.490267	−	0.849167i
$276$		0			0
$277$	68.5589	+	118.747i	0.247505	+	0.428691i	0.962833	−	0.270098i	$-0.0870560\pi$
$277$	68.5589	+	118.747i	0.247505	+	0.428691i	−0.715328	+	0.698789i	$0.753723\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	325.103			1.15695			0.578474	−	0.815701i	$-0.303648\pi$
$281$	325.103			1.15695			0.578474	+	0.815701i	$0.303648\pi$
$282$		0			0
$283$	−168.507	+	97.2876i	−0.595432	+	0.343773i	−0.767242	−	0.641357i	$-0.778372\pi$
$283$	−168.507	+	97.2876i	−0.595432	+	0.343773i	0.171811	+	0.985130i	$0.445038\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−66.2649	−	237.579i	−0.230888	−	0.827803i
$288$		0			0
$289$	31.3823	−	54.3557i	0.108589	−	0.188082i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			239.702i			0.818095i	0.912513	+	0.409048i	$0.134139\pi$
$293$			239.702i			0.818095i	−0.912513	+	0.409048i	$0.865861\pi$
$294$		0			0
$295$	−228.853			−0.775772
$296$		0			0
$297$		0			0
$298$		0			0
$299$	208.169	+	120.187i	0.696219	+	0.401962i
$300$		0			0
$301$	−104.412	+	29.1222i	−0.346883	+	0.0967515i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	168.853	+	292.462i	0.553616	+	0.958891i
$306$		0			0
$307$		−	540.272i		−	1.75984i	−0.475120	−	0.879921i	$-0.657595\pi$
$307$		−	540.272i		−	1.75984i	0.475120	−	0.879921i	$-0.342405\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	350.044	−	202.098i	1.12554	−	0.649832i	0.182732	−	0.983163i	$-0.441506\pi$
$311$	350.044	−	202.098i	1.12554	−	0.649832i	0.942810	+	0.333330i	$0.108172\pi$
$312$		0			0
$313$	−113.706	−	65.6482i	−0.363278	−	0.209739i	0.307240	−	0.951632i	$-0.400595\pi$
$313$	−113.706	−	65.6482i	−0.363278	−	0.209739i	−0.670518	+	0.741893i	$0.733928\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−46.9706	+	81.3554i	−0.148172	+	0.256642i	−0.930552	−	0.366160i	$-0.880672\pi$
$317$	−46.9706	+	81.3554i	−0.148172	+	0.256642i	0.782380	+	0.622802i	$0.214006\pi$
$318$		0			0
$319$	101.823	+	176.363i	0.319196	+	0.552863i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	319.279			0.988481
$324$		0			0
$325$	695.265	−	401.411i	2.13928	−	1.23511i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−225.125	−	57.8664i	−0.684270	−	0.175886i
$330$		0			0
$331$	−130.684	+	226.351i	−0.394815	+	0.683840i	−0.993078	−	0.117460i	$-0.962525\pi$
$331$	−130.684	+	226.351i	−0.394815	+	0.683840i	0.598263	+	0.801300i	$0.295858\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			956.711i			2.85585i
$336$		0			0
$337$	136.265			0.404347			0.202173	−	0.979350i	$-0.435200\pi$
$337$	136.265			0.404347			0.202173	+	0.979350i	$0.435200\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	76.6325	+	44.2438i	0.224729	+	0.129747i
$342$		0			0
$343$	235.000	−	249.848i	0.685131	−	0.728420i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	161.095	+	279.026i	0.464252	+	0.804108i	0.999167	−	0.0407975i	$-0.0129899\pi$
$347$	161.095	+	279.026i	0.464252	+	0.804108i	−0.534915	+	0.844906i	$0.679657\pi$
$348$		0			0
$349$			346.495i			0.992821i	0.868088	+	0.496411i	$0.165349\pi$
$349$			346.495i			0.992821i	−0.868088	+	0.496411i	$0.834651\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	537.448	−	310.296i	1.52252	−	0.879025i	0.522869	−	0.852413i	$-0.324862\pi$
$353$	537.448	−	310.296i	1.52252	−	0.879025i	0.999646	−	0.0266116i	$-0.00847174\pi$
$354$		0			0
$355$	−134.735	−	77.7893i	−0.379535	−	0.219125i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−10.1177	+	17.5245i	−0.0281831	+	0.0488146i	−0.879773	−	0.475394i	$-0.842305\pi$
$359$	−10.1177	+	17.5245i	−0.0281831	+	0.0488146i	0.851590	+	0.524209i	$0.175639\pi$
$360$		0			0
$361$	−35.6030	−	61.6663i	−0.0986234	−	0.170821i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	978.749			2.68151
$366$		0			0
$367$	269.831	−	155.787i	0.735234	−	0.424488i	−0.0850998	−	0.996372i	$-0.527121\pi$
$367$	269.831	−	155.787i	0.735234	−	0.424488i	0.820334	+	0.571885i	$0.193788\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−172.721	−	169.231i	−0.465555	−	0.456149i
$372$		0			0
$373$	340.691	−	590.094i	0.913380	−	1.58202i	0.104125	−	0.994564i	$-0.466796\pi$
$373$	340.691	−	590.094i	0.913380	−	1.58202i	0.809255	−	0.587457i	$-0.199871\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			606.320i			1.60828i
$378$		0			0
$379$	624.779			1.64849			0.824246	−	0.566231i	$-0.191599\pi$
$379$	624.779			1.64849			0.824246	+	0.566231i	$0.191599\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	119.772	+	69.1502i	0.312720	+	0.180549i	0.648143	−	0.761519i	$-0.275546\pi$
$383$	119.772	+	69.1502i	0.312720	+	0.180549i	−0.335423	+	0.942068i	$0.608879\pi$
$384$		0			0
$385$	94.3675	+	338.336i	0.245110	+	0.878794i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−281.787	−	488.069i	−0.724388	−	1.25468i	−0.959226	−	0.282642i	$-0.908789\pi$
$389$	−281.787	−	488.069i	−0.724388	−	1.25468i	0.234838	−	0.972035i	$-0.424544\pi$
$390$		0			0
$391$			252.370i			0.645446i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	639.801	−	369.389i	1.61975	−	0.935163i
$396$		0			0
$397$	−392.603	−	226.669i	−0.988923	−	0.570955i	−0.0839711	−	0.996468i	$-0.526760\pi$
$397$	−392.603	−	226.669i	−0.988923	−	0.570955i	−0.904952	+	0.425513i	$0.860094\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−137.875	+	238.807i	−0.343828	+	0.595528i	−0.985140	−	0.171752i	$-0.945057\pi$
$401$	−137.875	+	238.807i	−0.343828	+	0.595528i	0.641312	+	0.767280i	$0.278390\pi$
$402$		0			0
$403$	131.727	+	228.159i	0.326867	+	0.566151i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	35.8234			0.0880181
$408$		0			0
$409$	−377.441	+	217.916i	−0.922839	+	0.532801i	−0.884540	−	0.466465i	$-0.845527\pi$
$409$	−377.441	+	217.916i	−0.922839	+	0.532801i	−0.0382993	+	0.999266i	$0.512194\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	134.059	−	136.823i	0.324598	−	0.331291i
$414$		0			0
$415$	316.794	−	548.703i	0.763359	−	1.32218i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	301.257i		−	0.718991i	−0.933147	−	0.359496i	$-0.882949\pi$
$419$		−	301.257i		−	0.718991i	0.933147	−	0.359496i	$-0.117051\pi$
$420$		0			0
$421$	−203.794			−0.484071			−0.242036	−	0.970267i	$-0.577815\pi$
$421$	−203.794			−0.484071			−0.242036	+	0.970267i	$0.577815\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	729.963	+	421.444i	1.71756	+	0.991633i
$426$		0			0
$427$	−273.765	−	70.3688i	−0.641135	−	0.164798i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	197.860	+	342.703i	0.459072	+	0.795136i	0.998912	−	0.0466317i	$-0.0148487\pi$
$431$	197.860	+	342.703i	0.459072	+	0.795136i	−0.539840	+	0.841767i	$0.681515\pi$
$432$		0			0
$433$		−	44.2685i		−	0.102237i	−0.998693	−	0.0511184i	$-0.983721\pi$
$433$		−	44.2685i		−	0.102237i	0.998693	−	0.0511184i	$-0.0162786\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−198.375	+	114.532i	−0.453947	+	0.262086i
$438$		0			0
$439$	−344.558	−	198.931i	−0.784871	−	0.453146i	0.0532827	−	0.998579i	$-0.483032\pi$
$439$	−344.558	−	198.931i	−0.784871	−	0.453146i	−0.838154	+	0.545434i	$0.816365\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	59.2721	−	102.662i	0.133797	−	0.231743i	−0.791340	−	0.611376i	$-0.790616\pi$
$443$	59.2721	−	102.662i	0.133797	−	0.231743i	0.925137	+	0.379633i	$0.123950\pi$
$444$		0			0
$445$	−86.9117	−	150.535i	−0.195307	−	0.338282i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−713.897			−1.58997			−0.794985	−	0.606629i	$-0.792521\pi$
$449$	−713.897			−1.58997			−0.794985	+	0.606629i	$0.792521\pi$
$450$		0			0
$451$	−183.088	+	105.706i	−0.405961	+	0.234382i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−260.345	+	1012.85i	−0.572187	+	2.22605i
$456$		0			0
$457$	62.5883	−	108.406i	0.136955	−	0.237213i	−0.789388	−	0.613895i	$-0.789602\pi$
$457$	62.5883	−	108.406i	0.136955	−	0.237213i	0.926342	+	0.376682i	$0.122935\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	655.767i		−	1.42249i	−0.702945	−	0.711244i	$-0.748132\pi$
$461$		−	655.767i		−	1.42249i	0.702945	−	0.711244i	$-0.251868\pi$
$462$		0			0
$463$	−869.396			−1.87775			−0.938873	−	0.344265i	$-0.888128\pi$
$463$	−869.396			−1.87775			−0.938873	+	0.344265i	$0.888128\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−231.551	−	133.686i	−0.495827	−	0.286266i	0.231162	−	0.972915i	$-0.425747\pi$
$467$	−231.551	−	133.686i	−0.495827	−	0.286266i	−0.726989	+	0.686649i	$0.759081\pi$
$468$		0			0
$469$	−571.985	−	560.428i	−1.21958	−	1.19494i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	46.4558	+	80.4639i	0.0982153	+	0.170114i
$474$		0			0
$475$			765.048i			1.61063i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	235.331	−	135.868i	0.491296	−	0.283650i	−0.233816	−	0.972281i	$-0.575121\pi$
$479$	235.331	−	135.868i	0.491296	−	0.283650i	0.725112	+	0.688631i	$0.241788\pi$
$480$		0			0
$481$	92.3680	+	53.3287i	0.192033	+	0.110870i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	127.882	−	221.499i	0.263675	−	0.456698i
$486$		0			0
$487$	−280.757	−	486.285i	−0.576503	−	0.998532i	−0.995877	−	0.0907186i	$-0.971084\pi$
$487$	−280.757	−	486.285i	−0.576503	−	0.998532i	0.419374	−	0.907814i	$-0.362250\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−406.441			−0.827781			−0.413891	−	0.910327i	$-0.635830\pi$
$491$	−406.441			−0.827781			−0.413891	+	0.910327i	$0.635830\pi$
$492$		0			0
$493$	−551.294	+	318.289i	−1.11824	+	0.645618i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	125.434	−	34.9856i	0.252381	−	0.0703935i
$498$		0			0
$499$	−185.713	+	321.665i	−0.372171	+	0.644619i	−0.989899	−	0.141773i	$-0.954720\pi$
$499$	−185.713	+	321.665i	−0.372171	+	0.644619i	0.617728	+	0.786391i	$0.288053\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			64.6292i			0.128488i	0.997934	+	0.0642438i	$0.0204635\pi$
$503$			64.6292i			0.128488i	−0.997934	+	0.0642438i	$0.979536\pi$
$504$		0			0
$505$	1070.21			2.11922
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−871.889	−	503.385i	−1.71294	−	0.988969i	−0.930534	−	0.366205i	$-0.880657\pi$
$509$	−871.889	−	503.385i	−1.71294	−	0.988969i	−0.782410	−	0.622764i	$-0.786010\pi$
$510$		0			0
$511$	−573.338	+	585.161i	−1.12199	+	1.14513i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−338.522	−	586.337i	−0.657324	−	1.13852i
$516$		0			0
$517$			199.237i			0.385371i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	322.294	−	186.077i	0.618607	−	0.357153i	−0.157719	−	0.987484i	$-0.550414\pi$
$521$	322.294	−	186.077i	0.618607	−	0.357153i	0.776327	+	0.630331i	$0.217081\pi$
$522$		0			0
$523$	551.904	+	318.642i	1.05527	+	0.609258i	0.924119	−	0.382105i	$-0.124801\pi$
$523$	551.904	+	318.642i	1.05527	+	0.609258i	0.131147	+	0.991363i	$0.458134\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−138.302	+	239.545i	−0.262432	+	0.454545i
$528$		0			0
$529$	173.970	+	301.325i	0.328866	+	0.569613i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−629.440			−1.18094
$534$		0			0
$535$	1227.31	−	708.586i	2.29403	−	1.32446i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−257.558	−	141.773i	−0.477845	−	0.263030i
$540$		0			0
$541$	−110.412	+	191.239i	−0.204088	+	0.353491i	−0.949842	−	0.312731i	$-0.898756\pi$
$541$	−110.412	+	191.239i	−0.204088	+	0.353491i	0.745754	+	0.666222i	$0.232090\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			1496.50i			2.74587i
$546$		0			0
$547$	160.676			0.293741			0.146870	−	0.989156i	$-0.453080\pi$
$547$	160.676			0.293741			0.146870	+	0.989156i	$0.453080\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−500.382	−	288.896i	−0.908134	−	0.524311i
$552$		0			0
$553$	−153.942	+	598.898i	−0.278375	+	1.08300i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−237.177	−	410.802i	−0.425811	−	0.737526i	0.570685	−	0.821169i	$-0.306678\pi$
$557$	−237.177	−	410.802i	−0.425811	−	0.737526i	−0.996496	+	0.0836431i	$0.973344\pi$
$558$		0			0
$559$			276.627i			0.494860i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−430.301	+	248.434i	−0.764300	+	0.441269i	−0.830837	−	0.556515i	$-0.812138\pi$
$563$	−430.301	+	248.434i	−0.764300	+	0.441269i	0.0665378	+	0.997784i	$0.478805\pi$
$564$		0			0
$565$	−126.000	−	72.7461i	−0.223009	−	0.128754i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	392.647	−	680.084i	0.690065	−	1.19523i	−0.281752	−	0.959487i	$-0.590915\pi$
$569$	392.647	−	680.084i	0.690065	−	1.19523i	0.971816	−	0.235740i	$-0.0757512\pi$
$570$		0			0
$571$	−357.521	−	619.245i	−0.626132	−	1.08449i	−0.988321	−	0.152388i	$-0.951304\pi$
$571$	−357.521	−	619.245i	−0.626132	−	1.08449i	0.362189	−	0.932105i	$-0.382030\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−604.721			−1.05169
$576$		0			0
$577$	669.117	−	386.315i	1.15965	−	0.669524i	0.208429	−	0.978038i	$-0.433165\pi$
$577$	669.117	−	386.315i	1.15965	−	0.669524i	0.951220	+	0.308514i	$0.0998317\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	142.477	+	510.823i	0.245228	+	0.879214i
$582$		0			0
$583$	−103.632	+	179.497i	−0.177757	+	0.307885i
$584$		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
$589$	−251.059			−0.426246
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−722.397	−	417.076i	−1.21821	−	0.703332i	−0.253673	−	0.967290i	$-0.581639\pi$
$593$	−722.397	−	417.076i	−1.21821	−	0.703332i	−0.964534	+	0.263958i	$0.914972\pi$
$594$		0			0
$595$	−1057.60	+	294.983i	−1.77748	+	0.495770i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−436.794	−	756.549i	−0.729205	−	1.26302i	−0.957220	−	0.289363i	$-0.906557\pi$
$599$	−436.794	−	756.549i	−0.729205	−	1.26302i	0.228014	−	0.973658i	$-0.426777\pi$
$600$		0			0
$601$			198.982i			0.331085i	0.986203	+	0.165542i	$0.0529375\pi$
$601$			198.982i			0.331085i	−0.986203	+	0.165542i	$0.947063\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−615.624	+	355.431i	−1.01756	+	0.587489i
$606$		0			0
$607$	−137.654	−	79.4748i	−0.226778	−	0.130930i	0.382307	−	0.924035i	$-0.375130\pi$
$607$	−137.654	−	79.4748i	−0.226778	−	0.130930i	−0.609085	+	0.793105i	$0.708463\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−296.595	+	513.718i	−0.485426	+	0.840782i
$612$		0			0
$613$	357.368	+	618.979i	0.582981	+	1.00975i	0.995124	+	0.0986338i	$0.0314473\pi$
$613$	357.368	+	618.979i	0.582981	+	1.00975i	−0.412143	+	0.911119i	$0.635219\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	639.381			1.03627			0.518137	−	0.855298i	$-0.326626\pi$
$617$	639.381			1.03627			0.518137	+	0.855298i	$0.326626\pi$
$618$		0			0
$619$	−148.978	+	86.0126i	−0.240676	+	0.138954i	−0.615487	−	0.788147i	$-0.711041\pi$
$619$	−148.978	+	86.0126i	−0.240676	+	0.138954i	0.374812	+	0.927101i	$0.377707\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	140.912	+	36.2201i	0.226182	+	0.0581382i
$624$		0			0
$625$	−135.588	+	234.846i	−0.216941	+	0.375753i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			111.980i			0.178029i
$630$		0			0
$631$	1141.06			1.80833			0.904166	−	0.427180i	$-0.140493\pi$
$631$	1141.06			1.80833			0.904166	+	0.427180i	$0.140493\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1212.61	+	700.100i	1.90962	+	1.10252i
$636$		0			0
$637$	−453.044	−	748.968i	−0.711215	−	1.17577i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	114.551	+	198.409i	0.178707	+	0.309530i	0.941438	−	0.337186i	$-0.109475\pi$
$641$	114.551	+	198.409i	0.178707	+	0.309530i	−0.762731	+	0.646716i	$0.776142\pi$
$642$		0			0
$643$		−	707.670i		−	1.10058i	−0.834975	−	0.550288i	$-0.814518\pi$
$643$		−	707.670i		−	1.10058i	0.834975	−	0.550288i	$-0.185482\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1021.37	−	589.687i	1.57862	−	0.911417i	0.583568	−	0.812064i	$-0.301656\pi$
$647$	1021.37	−	589.687i	1.57862	−	0.911417i	0.995052	−	0.0993530i	$-0.0316773\pi$
$648$		0			0
$649$	−142.191	−	82.0940i	−0.219092	−	0.126493i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−77.3818	+	134.029i	−0.118502	+	0.205252i	−0.919174	−	0.393851i	$-0.871143\pi$
$653$	−77.3818	+	134.029i	−0.118502	+	0.205252i	0.800672	+	0.599103i	$0.204476\pi$
$654$		0			0
$655$	7.45584	+	12.9139i	0.0113830	+	0.0197159i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	591.308			0.897280			0.448640	−	0.893712i	$-0.351908\pi$
$659$	591.308			0.897280			0.448640	+	0.893712i	$0.351908\pi$
$660$		0			0
$661$	140.441	−	81.0837i	0.212468	−	0.122668i	−0.389990	−	0.920819i	$-0.627522\pi$
$661$	140.441	−	81.0837i	0.212468	−	0.122668i	0.602458	+	0.798151i	$0.294188\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−711.838	−	697.456i	−1.07043	−	1.04881i
$666$		0			0
$667$	228.353	−	395.519i	0.342359	−	0.592983i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			242.283i			0.361078i
$672$		0			0
$673$	42.3238			0.0628883			0.0314441	−	0.999506i	$-0.489989\pi$
$673$	42.3238			0.0628883			0.0314441	+	0.999506i	$0.489989\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−430.721	−	248.677i	−0.636220	−	0.367322i	0.146937	−	0.989146i	$-0.453059\pi$
$677$	−430.721	−	248.677i	−0.636220	−	0.367322i	−0.783157	+	0.621824i	$0.786392\pi$
$678$		0			0
$679$	57.5147	+	206.207i	0.0847050	+	0.303693i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−608.080	−	1053.23i	−0.890308	−	1.54206i	−0.839506	−	0.543350i	$-0.817156\pi$
$683$	−608.080	−	1053.23i	−0.890308	−	1.54206i	−0.0508015	−	0.998709i	$-0.516178\pi$
$684$		0			0
$685$		−	844.425i		−	1.23274i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−534.418	+	308.546i	−0.775642	+	0.447817i
$690$		0			0
$691$	932.182	+	538.196i	1.34903	+	0.778865i	0.988113	−	0.153731i	$-0.0491290\pi$
$691$	932.182	+	538.196i	1.34903	+	0.778865i	0.360921	+	0.932596i	$0.382462\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	587.683	−	1017.90i	0.845588	−	1.46460i
$696$		0			0
$697$	−330.426	−	572.315i	−0.474069	−	0.821112i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	695.897			0.992720			0.496360	−	0.868117i	$-0.334670\pi$
$701$	695.897			0.992720			0.496360	+	0.868117i	$0.334670\pi$
$702$		0			0
$703$	−88.0219	+	50.8194i	−0.125209	+	0.0722894i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−626.912	+	639.839i	−0.886721	+	0.905006i
$708$		0			0
$709$	−127.412	+	220.684i	−0.179707	+	0.311261i	−0.941780	−	0.336229i	$-0.890848\pi$
$709$	−127.412	+	220.684i	−0.179707	+	0.311261i	0.762073	+	0.647491i	$0.224182\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	198.446i		−	0.278325i
$714$		0			0
$715$	896.382			1.25368
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−964.925	−	557.100i	−1.34204	−	0.774826i	−0.354931	−	0.934892i	$-0.615496\pi$
$719$	−964.925	−	557.100i	−1.34204	−	0.774826i	−0.987106	+	0.160066i	$0.948829\pi$
$720$		0			0
$721$	548.852	+	141.078i	0.761238	+	0.195669i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−762.676	−	1320.99i	−1.05197	−	1.82206i
$726$		0			0
$727$			398.345i			0.547930i	0.961740	+	0.273965i	$0.0883353\pi$
$727$			398.345i			0.547930i	−0.961740	+	0.273965i	$0.911665\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−251.522	+	145.216i	−0.344079	+	0.198654i
$732$		0			0
$733$	818.514	+	472.569i	1.11666	+	0.644706i	0.940547	−	0.339663i	$-0.110313\pi$
$733$	818.514	+	472.569i	1.11666	+	0.644706i	0.176116	+	0.984369i	$0.443646\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−343.191	+	594.424i	−0.465659	+	0.806546i
$738$		0			0
$739$	96.3162	+	166.825i	0.130333	+	0.225744i	0.923805	−	0.382863i	$-0.125062\pi$
$739$	96.3162	+	166.825i	0.130333	+	0.225744i	−0.793472	+	0.608607i	$0.791729\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−911.616			−1.22694			−0.613470	−	0.789718i	$-0.710227\pi$
$743$	−911.616			−1.22694			−0.613470	+	0.789718i	$0.710227\pi$
$744$		0			0
$745$	−1324.76	+	764.853i	−1.77821	+	1.02665i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−295.301	+	1148.85i	−0.394260	+	1.53384i
$750$		0			0
$751$	−195.831	+	339.189i	−0.260760	+	0.451650i	−0.966444	−	0.256877i	$-0.917307\pi$
$751$	−195.831	+	339.189i	−0.260760	+	0.451650i	0.705684	+	0.708527i	$0.250640\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			2415.21i			3.19895i
$756$		0			0
$757$	−152.823			−0.201879			−0.100940	−	0.994893i	$-0.532185\pi$
$757$	−152.823			−0.201879			−0.100940	+	0.994893i	$0.532185\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	109.331	+	63.1223i	0.143667	+	0.0829465i	0.570111	−	0.821568i	$-0.306900\pi$
$761$	109.331	+	63.1223i	0.143667	+	0.0829465i	−0.426443	+	0.904514i	$0.640234\pi$
$762$		0			0
$763$	−894.706	−	876.629i	−1.17262	−	1.14892i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−244.419	−	423.347i	−0.318669	−	0.551951i
$768$		0			0
$769$		−	369.148i		−	0.480037i	−0.970768	−	0.240018i	$-0.922847\pi$
$769$		−	369.148i		−	0.480037i	0.970768	−	0.240018i	$-0.0771535\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1215.65	−	701.853i	1.57263	−	0.907961i	0.576789	−	0.816893i	$-0.304305\pi$
$773$	1215.65	−	701.853i	1.57263	−	0.907961i	0.995845	−	0.0910674i	$-0.0290279\pi$
$774$		0			0
$775$	−573.992	−	331.394i	−0.740634	−	0.427605i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	299.912	−	519.462i	0.384996	−	0.666832i
$780$		0			0
$781$	−55.8091	−	96.6642i	−0.0714585	−	0.123770i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1564.41			−1.99288
$786$		0			0
$787$	−196.161	+	113.253i	−0.249251	+	0.143905i	−0.619421	−	0.785059i	$-0.712633\pi$
$787$	−196.161	+	113.253i	−0.249251	+	0.143905i	0.370170	+	0.928964i	$0.379299\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	117.302	−	32.7174i	0.148295	−	0.0413621i
$792$		0			0
$793$	−360.676	+	624.709i	−0.454825	+	0.787780i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			688.414i			0.863756i	0.901932	+	0.431878i	$0.142149\pi$
$797$			688.414i			0.863756i	−0.901932	+	0.431878i	$0.857851\pi$
$798$		0			0
$799$	−622.794			−0.779467
$800$		0			0
$801$		0			0
$802$		0			0
$803$	608.117	+	351.096i	0.757306	+	0.437231i
$804$		0			0
$805$	551.294	−	562.662i	0.684837	−	0.698958i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	12.6396	+	21.8924i	0.0156237	+	0.0270611i	0.873732	−	0.486408i	$-0.161693\pi$
$809$	12.6396	+	21.8924i	0.0156237	+	0.0270611i	−0.858108	+	0.513470i	$0.828360\pi$
$810$		0			0
$811$		−	1527.62i		−	1.88362i	−0.336145	−	0.941810i	$-0.609123\pi$
$811$		−	1527.62i		−	1.88362i	0.336145	−	0.941810i	$-0.390877\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−116.309	+	67.1508i	−0.142710	+	0.0823937i
$816$		0			0
$817$	−228.294	−	131.806i	−0.279430	−	0.161329i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−58.3310	+	101.032i	−0.0710487	+	0.123060i	−0.899361	−	0.437206i	$-0.855968\pi$
$821$	−58.3310	+	101.032i	−0.0710487	+	0.123060i	0.828312	+	0.560266i	$0.189301\pi$
$822$		0			0
$823$	62.9554	+	109.042i	0.0764950	+	0.132493i	0.901735	−	0.432288i	$-0.142294\pi$
$823$	62.9554	+	109.042i	0.0764950	+	0.132493i	−0.825240	+	0.564782i	$0.808960\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1434.40			−1.73446			−0.867229	−	0.497910i	$-0.834101\pi$
$827$	−1434.40			−1.73446			−0.867229	+	0.497910i	$0.834101\pi$
$828$		0			0
$829$	−32.3225	+	18.6614i	−0.0389898	+	0.0225107i	−0.519368	−	0.854551i	$-0.673833\pi$
$829$	−32.3225	+	18.6614i	−0.0389898	+	0.0225107i	0.480378	+	0.877061i	$0.340499\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	443.169	−	805.101i	0.532015	−	0.966508i
$834$		0			0
$835$	−736.441	+	1275.55i	−0.881965	+	1.52761i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			3.07370i			0.00366353i	0.999998	+	0.00183177i	$0.000583069\pi$
$839$			3.07370i			0.00366353i	−0.999998	+	0.00183177i	$0.999417\pi$
$840$		0			0
$841$	311.000			0.369798
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1087.25	+	627.723i	1.28669	+	0.742868i
$846$		0			0
$847$	148.124	−	576.267i	0.174881	−	0.680363i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−40.1695	−	69.5756i	−0.0472027	−	0.0817574i
$852$		0			0
$853$		−	155.257i		−	0.182013i	−0.995850	−	0.0910063i	$-0.970992\pi$
$853$		−	155.257i		−	0.182013i	0.995850	−	0.0910063i	$-0.0290083\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1388.98	−	801.931i	1.62075	−	0.935742i	0.634033	−	0.773306i	$-0.281398\pi$
$857$	1388.98	−	801.931i	1.62075	−	0.935742i	0.986719	−	0.162436i	$-0.0519352\pi$
$858$		0			0
$859$	−545.367	−	314.868i	−0.634886	−	0.366551i	0.147756	−	0.989024i	$-0.452795\pi$
$859$	−545.367	−	314.868i	−0.634886	−	0.366551i	−0.782642	+	0.622472i	$0.786128\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−514.706	+	891.496i	−0.596414	+	1.03302i	0.396931	+	0.917848i	$0.370075\pi$
$863$	−514.706	+	891.496i	−0.596414	+	1.03302i	−0.993346	+	0.115172i	$0.963258\pi$
$864$		0			0
$865$	−966.573	−	1674.15i	−1.11743	−	1.93544i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	530.029			0.609929
$870$		0			0
$871$	−1769.79	+	1021.79i	−2.03190	+	1.17312i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−313.632	−	1124.47i	−0.358437	−	1.28510i
$876$		0			0
$877$	−324.220	+	561.566i	−0.369693	+	0.640326i	−0.989517	−	0.144414i	$-0.953870\pi$
$877$	−324.220	+	561.566i	−0.369693	+	0.640326i	0.619825	+	0.784740i	$0.287204\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			363.857i			0.413005i	0.978446	+	0.206502i	$0.0662082\pi$
$881$			363.857i			0.413005i	−0.978446	+	0.206502i	$0.933792\pi$
$882$		0			0
$883$	−1536.16			−1.73971			−0.869853	−	0.493312i	$-0.835786\pi$
$883$	−1536.16			−1.73971			−0.869853	+	0.493312i	$0.835786\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	974.720	+	562.755i	1.09890	+	0.634447i	0.935931	−	0.352185i	$-0.114561\pi$
$887$	974.720	+	562.755i	1.09890	+	0.634447i	0.162964	+	0.986632i	$0.447894\pi$
$888$		0			0
$889$	−1128.90	+	314.868i	−1.26985	+	0.354183i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−282.640	−	489.546i	−0.316506	−	0.548204i
$894$		0			0
$895$		−	713.197i		−	0.796868i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	433.499	−	250.281i	0.482201	−	0.278399i
$900$		0			0
$901$	−561.088	−	323.944i	−0.622740	−	0.359539i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−23.3604	+	40.4614i	−0.0258126	+	0.0447087i
$906$		0			0
$907$	117.448	+	203.426i	0.129491	+	0.224285i	0.923479	−	0.383648i	$-0.125332\pi$
$907$	117.448	+	203.426i	0.129491	+	0.224285i	−0.793989	+	0.607933i	$0.791999\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	224.278			0.246189			0.123095	−	0.992395i	$-0.460718\pi$
$911$	224.278			0.246189			0.123095	+	0.992395i	$0.460718\pi$
$912$		0			0
$913$	393.661	−	227.280i	0.431173	−	0.248938i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−12.0883	−	3.10719i	−0.0131825	−	0.00338843i
$918$		0			0
$919$	−466.081	+	807.276i	−0.507161	+	0.878428i	0.492805	+	0.870140i	$0.335972\pi$
$919$	−466.081	+	807.276i	−0.507161	+	0.878428i	−0.999966	+	0.00828836i	$0.997362\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	332.322i		−	0.360046i
$924$		0			0
$925$	−268.324			−0.290080
$926$		0			0
$927$		0			0
$928$		0			0
$929$	618.390	+	357.028i	0.665651	+	0.384314i	0.794427	−	0.607360i	$-0.207771\pi$
$929$	618.390	+	357.028i	0.665651	+	0.384314i	−0.128776	+	0.991674i	$0.541105\pi$
$930$		0			0
$931$	833.970	−	17.0233i	0.895778	−	0.0182850i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	470.558	+	815.031i	0.503271	+	0.871691i
$936$		0			0
$937$		−	1723.25i		−	1.83912i	−0.392952	−	0.919559i	$-0.628546\pi$
$937$		−	1723.25i		−	1.83912i	0.392952	−	0.919559i	$-0.371454\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−835.508	+	482.381i	−0.887893	+	0.512625i	−0.873253	−	0.487267i	$-0.837994\pi$
$941$	−835.508	+	482.381i	−0.887893	+	0.512625i	−0.0146405	+	0.999893i	$0.504660\pi$
$942$		0			0
$943$	410.601	+	237.061i	0.435420	+	0.251390i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−725.881	+	1257.26i	−0.766506	+	1.32763i	0.172940	+	0.984932i	$0.444673\pi$
$947$	−725.881	+	1257.26i	−0.766506	+	1.32763i	−0.939447	+	0.342695i	$0.888660\pi$
$948$		0			0
$949$	1045.32	+	1810.55i	1.10150	+	1.90785i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1147.43			−1.20401			−0.602007	−	0.798491i	$-0.705632\pi$
$953$	−1147.43			−1.20401			−0.602007	+	0.798491i	$0.705632\pi$
$954$		0			0
$955$	1342.76	−	775.245i	1.40604	−	0.811775i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	504.853	+	494.653i	0.526437	+	0.515801i
$960$		0			0
$961$	−371.749	+	643.889i	−0.386836	+	0.670020i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			1905.06i			1.97415i
$966$		0			0
$967$	−412.190			−0.426257			−0.213128	−	0.977024i	$-0.568365\pi$
$967$	−412.190			−0.426257			−0.213128	+	0.977024i	$0.568365\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	869.595	+	502.061i	0.895566	+	0.517056i	0.875759	−	0.482748i	$-0.160361\pi$
$971$	869.595	+	502.061i	0.895566	+	0.517056i	0.0198073	+	0.999804i	$0.493695\pi$
$972$		0			0
$973$	264.309	+	947.626i	0.271643	+	0.973922i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−794.117	−	1375.45i	−0.812812	−	1.40783i	−0.910889	−	0.412652i	$-0.864603\pi$
$977$	−794.117	−	1375.45i	−0.812812	−	1.40783i	0.0980772	−	0.995179i	$-0.468731\pi$
$978$		0			0
$979$		−	124.708i		−	0.127383i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	721.861	−	416.767i	0.734345	−	0.423974i	−0.0856648	−	0.996324i	$-0.527301\pi$
$983$	721.861	−	416.767i	0.734345	−	0.423974i	0.820009	+	0.572350i	$0.193968\pi$
$984$		0			0
$985$	892.014	+	515.005i	0.905598	+	0.522847i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	104.184	−	180.452i	0.105343	−	0.182459i
$990$		0			0
$991$	33.4483	+	57.9341i	0.0337520	+	0.0584602i	0.882408	−	0.470485i	$-0.155921\pi$
$991$	33.4483	+	57.9341i	0.0337520	+	0.0584602i	−0.848656	+	0.528945i	$0.822588\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	52.1177			0.0523796
$996$		0			0
$997$	1268.65	−	732.453i	1.27246	−	0.734657i	0.297012	−	0.954874i	$-0.404010\pi$
$997$	1268.65	−	732.453i	1.27246	−	0.734657i	0.975451	+	0.220217i	$0.0706765\pi$
$998$		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.145.1		4
3.2	odd	2		336.3.bh.e.145.2		4
4.3	odd	2		126.3.n.a.19.2		4
7.3	odd	6	inner	1008.3.cg.h.577.1		4
12.11	even	2		42.3.g.a.19.1	✓	4
21.2	odd	6		2352.3.f.e.97.1		4
21.5	even	6		2352.3.f.e.97.4		4
21.17	even	6		336.3.bh.e.241.2		4
28.3	even	6		126.3.n.a.73.2		4
28.11	odd	6		882.3.n.e.325.2		4
28.19	even	6		882.3.c.b.685.1		4
28.23	odd	6		882.3.c.b.685.2		4
28.27	even	2		882.3.n.e.19.2		4
60.23	odd	4		1050.3.q.a.649.4		8
60.47	odd	4		1050.3.q.a.649.1		8
60.59	even	2		1050.3.p.a.901.2		4
84.11	even	6		294.3.g.a.31.1		4
84.23	even	6		294.3.c.a.97.4		4
84.47	odd	6		294.3.c.a.97.3		4
84.59	odd	6		42.3.g.a.31.1	yes	4
84.83	odd	2		294.3.g.a.19.1		4
420.59	odd	6		1050.3.p.a.451.2		4
420.143	even	12		1050.3.q.a.199.1		8
420.227	even	12		1050.3.q.a.199.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.g.a.19.1	✓	4	12.11	even	2
42.3.g.a.31.1	yes	4	84.59	odd	6
126.3.n.a.19.2		4	4.3	odd	2
126.3.n.a.73.2		4	28.3	even	6
294.3.c.a.97.3		4	84.47	odd	6
294.3.c.a.97.4		4	84.23	even	6
294.3.g.a.19.1		4	84.83	odd	2
294.3.g.a.31.1		4	84.11	even	6
336.3.bh.e.145.2		4	3.2	odd	2
336.3.bh.e.241.2		4	21.17	even	6
882.3.c.b.685.1		4	28.19	even	6
882.3.c.b.685.2		4	28.23	odd	6
882.3.n.e.19.2		4	28.27	even	2
882.3.n.e.325.2		4	28.11	odd	6
1008.3.cg.h.145.1		4	1.1	even	1	trivial
1008.3.cg.h.577.1		4	7.3	odd	6	inner
1050.3.p.a.451.2		4	420.59	odd	6
1050.3.p.a.901.2		4	60.59	even	2
1050.3.q.a.199.1		8	420.143	even	12
1050.3.q.a.199.4		8	420.227	even	12
1050.3.q.a.649.1		8	60.47	odd	4
1050.3.q.a.649.4		8	60.23	odd	4
2352.3.f.e.97.1		4	21.2	odd	6
2352.3.f.e.97.4		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)

\(f(q)\)	\(=\)	\(q+(-7.24264 - 4.18154i) q^{5} +(6.74264 - 1.88064i) q^{7} +(-3.00000 - 5.19615i) q^{11} -17.8639i q^{13} +(16.2426 - 9.37769i) q^{17} +(14.7426 + 8.51167i) q^{19} +(-6.72792 + 11.6531i) q^{23} +(22.4706 + 38.9202i) q^{25} -33.9411 q^{29} +(-12.7721 + 7.37396i) q^{31} +(-56.6985 - 14.5738i) q^{35} +(-2.98528 + 5.17066i) q^{37} -35.2354i q^{41} -15.4853 q^{43} +(-28.7574 - 16.6031i) q^{47} +(41.9264 - 25.3609i) q^{49} +(-17.2721 - 29.9161i) q^{53} +50.1785i q^{55} +(23.6985 - 13.6823i) q^{59} +(-34.9706 - 20.1903i) q^{61} +(-74.6985 + 129.382i) q^{65} +(-57.1985 - 99.0707i) q^{67} +18.6030 q^{71} +(-101.353 + 58.5161i) q^{73} +(-30.0000 - 29.3939i) q^{77} +(-44.1690 + 76.5030i) q^{79} +75.7601i q^{83} -156.853 q^{85} +(18.0000 + 10.3923i) q^{89} +(-33.5955 - 120.450i) q^{91} +(-71.1838 - 123.294i) q^{95} +30.5826i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{5} + 10 q^{7} - 12 q^{11} + 48 q^{17} + 42 q^{19} + 24 q^{23} + 22 q^{25} - 102 q^{31} - 108 q^{35} + 22 q^{37} - 28 q^{43} - 132 q^{47} - 2 q^{49} - 120 q^{53} - 24 q^{59} - 72 q^{61} - 180 q^{65}+ \cdots - 132 q^{95}+O(q^{100}) \) 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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