LMFDB - Embedded newform 1620.3.t.e.1349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,3,Mod(269,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1620.269");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1620.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$44.1418028264$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 81 x^{14} + 4781 x^{12} - 127980 x^{10} + 2502300 x^{8} - 12798000 x^{6} + 47810000 x^{4} + \cdots + 100000000 $ x^16 - 81x^14 + 4781x^12 - 127980x^10 + 2502300x^8 - 12798000x^6 + 47810000x^4 - 81000000*x^2 + 100000000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 540)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1349.3
Root			$-1.27560 - 0.736469i$ of defining polynomial
Character	$\chi$	$=$	1620.1349
Dual form			1620.3.t.e.269.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.77776 + 4.15741i) q^{5} +(-8.02120 + 4.63104i) q^{7} +O(q^{10})$	$q+(-2.77776 + 4.15741i) q^{5} +(-8.02120 + 4.63104i) q^{7} +(-13.2457 + 7.64741i) q^{11} +(-2.59808 - 1.50000i) q^{13} +4.00858 q^{17} -27.7863 q^{19} +(18.9336 - 32.7940i) q^{23} +(-9.56808 - 23.0966i) q^{25} +(-39.7371 + 22.9422i) q^{29} +(-14.3931 + 24.9296i) q^{31} +(3.02785 - 46.2113i) q^{35} +34.3104i q^{37} +(23.6603 + 13.6603i) q^{41} +(31.4039 - 18.1310i) q^{43} +(-10.0214 - 17.3576i) q^{47} +(18.3931 - 31.8578i) q^{49} +57.9102 q^{53} +(5.00000 - 76.3104i) q^{55} +(73.8120 + 42.6154i) q^{59} +(18.8931 + 32.7239i) q^{61} +(13.4529 - 6.63462i) q^{65} +(50.4983 + 29.1552i) q^{67} -125.628i q^{71} +31.6896i q^{73} +(70.8309 - 122.683i) q^{77} +(-19.5000 - 33.7750i) q^{79} +(-32.9637 - 57.0947i) q^{83} +(-11.1349 + 16.6653i) q^{85} +85.2307i q^{89} +27.7863 q^{91} +(77.1836 - 115.519i) q^{95} +(-140.195 + 80.9415i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 72 q^{19} - 12 q^{25} - 44 q^{31} + 108 q^{49} + 80 q^{55} + 116 q^{61} - 312 q^{79} - 160 q^{85} + 72 q^{91}+O(q^{100}) $ 16 * q - 72 * q^19 - 12 * q^25 - 44 * q^31 + 108 * q^49 + 80 * q^55 + 116 * q^61 - 312 * q^79 - 160 * q^85 + 72 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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
$5$	−2.77776	+	4.15741i	−0.555552	+	0.831482i
$5$	−2.77776	+	4.15741i	−0.555552	+	0.831482i
$6$		0			0
$7$	−8.02120	+	4.63104i	−1.14589	+	0.661578i	−0.947881	−	0.318623i	$-0.896779\pi$
$7$	−8.02120	+	4.63104i	−1.14589	+	0.661578i	−0.198005	+	0.980201i	$0.563446\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−13.2457	+	7.64741i	−1.20415	+	0.695219i	−0.961476	−	0.274888i	$-0.911359\pi$
$11$	−13.2457	+	7.64741i	−1.20415	+	0.695219i	−0.242678	+	0.970107i	$0.578026\pi$
$12$		0			0
$13$	−2.59808	−	1.50000i	−0.199852	−	0.115385i	0.396734	−	0.917933i	$-0.370143\pi$
$13$	−2.59808	−	1.50000i	−0.199852	−	0.115385i	−0.596586	+	0.802549i	$0.703477\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.00858			0.235799			0.117899	−	0.993026i	$-0.462384\pi$
$17$	4.00858			0.235799			0.117899	+	0.993026i	$0.462384\pi$
$18$		0			0
$19$	−27.7863			−1.46243			−0.731217	−	0.682144i	$-0.761048\pi$
$19$	−27.7863			−1.46243			−0.731217	+	0.682144i	$0.761048\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	18.9336	−	32.7940i	0.823202	−	1.42583i	−0.0800840	−	0.996788i	$-0.525519\pi$
$23$	18.9336	−	32.7940i	0.823202	−	1.42583i	0.903286	−	0.429039i	$-0.141148\pi$
$24$		0			0
$25$	−9.56808	−	23.0966i	−0.382723	−	0.923863i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−39.7371	+	22.9422i	−1.37024	+	0.791111i	−0.990959	−	0.134168i	$-0.957164\pi$
$29$	−39.7371	+	22.9422i	−1.37024	+	0.791111i	−0.379286	+	0.925280i	$0.623830\pi$
$30$		0			0
$31$	−14.3931	+	24.9296i	−0.464295	+	0.804182i	−0.999169	−	0.0407496i	$-0.987025\pi$
$31$	−14.3931	+	24.9296i	−0.464295	+	0.804182i	0.534875	+	0.844931i	$0.320359\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.02785	−	46.2113i	0.0865101	−	1.32032i
$36$		0			0
$37$			34.3104i			0.927309i	0.886016	+	0.463655i	$0.153462\pi$
$37$			34.3104i			0.927309i	−0.886016	+	0.463655i	$0.846538\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	23.6603	+	13.6603i	0.577080	+	0.333177i	0.759972	−	0.649956i	$-0.225213\pi$
$41$	23.6603	+	13.6603i	0.577080	+	0.333177i	−0.182892	+	0.983133i	$0.558546\pi$
$42$		0			0
$43$	31.4039	−	18.1310i	0.730323	−	0.421652i	−0.0882173	−	0.996101i	$-0.528117\pi$
$43$	31.4039	−	18.1310i	0.730323	−	0.421652i	0.818540	+	0.574449i	$0.194784\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−10.0214	−	17.3576i	−0.213222	−	0.369312i	0.739499	−	0.673158i	$-0.235062\pi$
$47$	−10.0214	−	17.3576i	−0.213222	−	0.369312i	−0.952721	+	0.303846i	$0.901729\pi$
$48$		0			0
$49$	18.3931	−	31.8578i	0.375370	−	0.650160i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	57.9102			1.09264			0.546322	−	0.837575i	$-0.316027\pi$
$53$	57.9102			1.09264			0.546322	+	0.837575i	$0.316027\pi$
$54$		0			0
$55$	5.00000	−	76.3104i	0.0909091	−	1.38746i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	73.8120	+	42.6154i	1.25105	+	0.722294i	0.971318	−	0.237784i	$-0.0764210\pi$
$59$	73.8120	+	42.6154i	1.25105	+	0.722294i	0.279732	+	0.960078i	$0.409754\pi$
$60$		0			0
$61$	18.8931	+	32.7239i	0.309723	+	0.536457i	0.978302	−	0.207185i	$-0.0664302\pi$
$61$	18.8931	+	32.7239i	0.309723	+	0.536457i	−0.668578	+	0.743642i	$0.733097\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	13.4529	−	6.63462i	0.206968	−	0.102071i
$66$		0			0
$67$	50.4983	+	29.1552i	0.753706	+	0.435153i	0.827032	−	0.562156i	$-0.190028\pi$
$67$	50.4983	+	29.1552i	0.753706	+	0.435153i	−0.0733252	+	0.997308i	$0.523361\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	125.628i		−	1.76940i	−0.466158	−	0.884701i	$-0.654362\pi$
$71$		−	125.628i		−	1.76940i	0.466158	−	0.884701i	$-0.345638\pi$
$72$		0			0
$73$			31.6896i			0.434104i	0.976160	+	0.217052i	$0.0696441\pi$
$73$			31.6896i			0.434104i	−0.976160	+	0.217052i	$0.930356\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	70.8309	−	122.683i	0.919882	−	1.59328i
$78$		0			0
$79$	−19.5000	−	33.7750i	−0.246835	−	0.427532i	0.715811	−	0.698294i	$-0.246057\pi$
$79$	−19.5000	−	33.7750i	−0.246835	−	0.427532i	−0.962646	+	0.270763i	$0.912724\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−32.9637	−	57.0947i	−0.397153	−	0.687888i	0.596221	−	0.802821i	$-0.296668\pi$
$83$	−32.9637	−	57.0947i	−0.397153	−	0.687888i	−0.993373	+	0.114932i	$0.963335\pi$
$84$		0			0
$85$	−11.1349	+	16.6653i	−0.130998	+	0.196062i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			85.2307i			0.957648i	0.877911	+	0.478824i	$0.158937\pi$
$89$			85.2307i			0.957648i	−0.877911	+	0.478824i	$0.841063\pi$
$90$		0			0
$91$	27.7863			0.305344
$92$		0			0
$93$		0			0
$94$		0			0
$95$	77.1836	−	115.519i	0.812459	−	1.21599i
$96$		0			0
$97$	−140.195	+	80.9415i	−1.44531	+	0.834448i	−0.998197	−	0.0600306i	$-0.980880\pi$
$97$	−140.195	+	80.9415i	−1.44531	+	0.834448i	−0.447110	+	0.894479i	$0.647547\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	63.3974	−	36.6025i	0.627697	−	0.362401i	−0.152163	−	0.988355i	$-0.548624\pi$
$101$	63.3974	−	36.6025i	0.627697	−	0.362401i	0.779860	+	0.625955i	$0.215290\pi$
$102$		0			0
$103$	−133.637	−	77.1552i	−1.29744	−	0.749080i	−0.317482	−	0.948264i	$-0.602837\pi$
$103$	−133.637	−	77.1552i	−1.29744	−	0.749080i	−0.979962	+	0.199184i	$0.936171\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	149.679			1.39887			0.699435	−	0.714696i	$-0.253435\pi$
$107$	149.679			1.39887			0.699435	+	0.714696i	$0.253435\pi$
$108$		0			0
$109$	132.718			1.21759			0.608796	−	0.793327i	$-0.291653\pi$
$109$	132.718			1.21759			0.608796	+	0.793327i	$0.291653\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	46.9937	−	81.3954i	0.415873	−	0.720314i	−0.579646	−	0.814868i	$-0.696809\pi$
$113$	46.9937	−	81.3954i	0.415873	−	0.720314i	0.995520	+	0.0945544i	$0.0301426\pi$
$114$		0			0
$115$	83.7450	+	169.809i	0.728218	+	1.47660i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−32.1536	+	18.5639i	−0.270198	+	0.155999i
$120$		0			0
$121$	56.4657	−	97.8014i	0.466658	−	0.808276i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	122.600	+	24.3784i	0.980798	+	0.195027i
$126$		0			0
$127$			149.242i			1.17513i	0.809176	+	0.587566i	$0.199914\pi$
$127$			149.242i			1.17513i	−0.809176	+	0.587566i	$0.800086\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−106.875	−	61.7046i	−0.815843	−	0.471027i	0.0331379	−	0.999451i	$-0.489450\pi$
$131$	−106.875	−	61.7046i	−0.815843	−	0.471027i	−0.848981	+	0.528424i	$0.822783\pi$
$132$		0			0
$133$	222.879	−	128.679i	1.67578	−	0.967514i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−38.7623	−	67.1383i	−0.282937	−	0.490061i	0.689170	−	0.724600i	$-0.257975\pi$
$137$	−38.7623	−	67.1383i	−0.282937	−	0.490061i	−0.972107	+	0.234539i	$0.924642\pi$
$138$		0			0
$139$	−31.4657	+	54.5001i	−0.226372	+	0.392087i	−0.956730	−	0.290977i	$-0.906020\pi$
$139$	−31.4657	+	54.5001i	−0.226372	+	0.392087i	0.730358	+	0.683064i	$0.239353\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	45.8844			0.320870
$144$		0			0
$145$	15.0000	−	228.931i	0.103448	−	1.57884i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−233.670	−	134.910i	−1.56826	−	0.905433i	−0.996373	−	0.0850984i	$-0.972880\pi$
$149$	−233.670	−	134.910i	−1.56826	−	0.905433i	−0.571884	−	0.820335i	$-0.693787\pi$
$150$		0			0
$151$	−38.0725	−	65.9435i	−0.252136	−	0.436712i	0.711978	−	0.702202i	$-0.247800\pi$
$151$	−38.0725	−	65.9435i	−0.252136	−	0.436712i	−0.964114	+	0.265490i	$0.914466\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−63.6620	−	129.087i	−0.410722	−	0.832817i
$156$		0			0
$157$	98.4999	+	56.8690i	0.627388	+	0.362223i	0.779740	−	0.626104i	$-0.215351\pi$
$157$	98.4999	+	56.8690i	0.627388	+	0.362223i	−0.152352	+	0.988326i	$0.548685\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			350.730i			2.17845i
$162$		0			0
$163$			90.3791i			0.554473i	0.960802	+	0.277237i	$0.0894186\pi$
$163$			90.3791i			0.554473i	−0.960802	+	0.277237i	$0.910581\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	103.795	−	179.778i	0.621525	−	1.07651i	−0.367677	−	0.929953i	$-0.619847\pi$
$167$	103.795	−	179.778i	0.621525	−	1.07651i	0.989202	−	0.146559i	$-0.0468198\pi$
$168$		0			0
$169$	−80.0000	−	138.564i	−0.473373	−	0.819906i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	28.0600	+	48.6014i	0.162197	+	0.280933i	0.935656	−	0.352913i	$-0.114809\pi$
$173$	28.0600	+	48.6014i	0.162197	+	0.280933i	−0.773459	+	0.633846i	$0.781475\pi$
$174$		0			0
$175$	183.709	+	140.952i	1.04976	+	0.805441i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	70.9865i		−	0.396573i	−0.980144	−	0.198286i	$-0.936462\pi$
$179$		−	70.9865i		−	0.396573i	0.980144	−	0.198286i	$-0.0635376\pi$
$180$		0			0
$181$	−94.9313			−0.524482			−0.262241	−	0.965002i	$-0.584462\pi$
$181$	−94.9313			−0.524482			−0.262241	+	0.965002i	$0.584462\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−142.642	−	95.3062i	−0.771040	−	0.515169i
$186$		0			0
$187$	−53.0964	+	30.6552i	−0.283938	+	0.163932i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−117.290	+	67.7174i	−0.614084	+	0.354541i	−0.774562	−	0.632498i	$-0.782030\pi$
$191$	−117.290	+	67.7174i	−0.614084	+	0.354541i	0.160478	+	0.987039i	$0.448696\pi$
$192$		0			0
$193$	−171.574	−	99.0585i	−0.888986	−	0.513257i	−0.0153756	−	0.999882i	$-0.504894\pi$
$193$	−171.574	−	99.0585i	−0.888986	−	0.513257i	−0.873611	+	0.486625i	$0.838228\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	143.452			0.728183			0.364091	−	0.931363i	$-0.381380\pi$
$197$	143.452			0.728183			0.364091	+	0.931363i	$0.381380\pi$
$198$		0			0
$199$	−328.863			−1.65258			−0.826288	−	0.563248i	$-0.809552\pi$
$199$	−328.863			−1.65258			−0.826288	+	0.563248i	$0.809552\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	212.493	−	368.048i	1.04676	−	1.81305i
$204$		0			0
$205$	−122.514	+	60.4205i	−0.597629	+	0.294734i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	368.048	−	212.493i	1.76100	−	1.01671i
$210$		0			0
$211$	−96.4657	+	167.083i	−0.457183	+	0.791865i	−0.998811	−	0.0487540i	$-0.984475\pi$
$211$	−96.4657	+	167.083i	−0.457183	+	0.791865i	0.541628	+	0.840619i	$0.317808\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−11.8544	+	180.922i	−0.0551366	+	0.841500i
$216$		0			0
$217$		−	266.621i		−	1.22867i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−10.4146	−	6.01287i	−0.0471248	−	0.0272075i
$222$		0			0
$223$	79.9608	−	46.1654i	0.358569	−	0.207020i	−0.309884	−	0.950774i	$-0.600290\pi$
$223$	79.9608	−	46.1654i	0.358569	−	0.207020i	0.668453	+	0.743755i	$0.266957\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−36.9722	−	64.0378i	−0.162873	−	0.282105i	0.773025	−	0.634376i	$-0.218743\pi$
$227$	−36.9722	−	64.0378i	−0.162873	−	0.282105i	−0.935898	+	0.352271i	$0.885410\pi$
$228$		0			0
$229$	137.573	−	238.283i	0.600753	−	1.04054i	−0.391954	−	0.919985i	$-0.628201\pi$
$229$	137.573	−	238.283i	0.600753	−	1.04054i	0.992707	−	0.120550i	$-0.0384660\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	310.955			1.33457			0.667286	−	0.744801i	$-0.267456\pi$
$233$	310.955			1.33457			0.667286	+	0.744801i	$0.267456\pi$
$234$		0			0
$235$	100.000	+	6.55218i	0.425532	+	0.0278816i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	38.8272	+	22.4169i	0.162457	+	0.0937946i	0.579024	−	0.815310i	$-0.303434\pi$
$239$	38.8272	+	22.4169i	0.162457	+	0.0937946i	−0.416567	+	0.909105i	$0.636767\pi$
$240$		0			0
$241$	80.5000	+	139.430i	0.334025	+	0.578548i	0.983297	−	0.182008i	$-0.0582597\pi$
$241$	80.5000	+	139.430i	0.334025	+	0.578548i	−0.649272	+	0.760556i	$0.724926\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	81.3543	+	164.961i	0.332058	+	0.673311i
$246$		0			0
$247$	72.1908	+	41.6794i	0.292271	+	0.168742i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	69.9359i		−	0.278629i	−0.990248	−	0.139315i	$-0.955510\pi$
$251$		−	69.9359i		−	0.278629i	0.990248	−	0.139315i	$-0.0444899\pi$
$252$		0			0
$253$			579.173i			2.28922i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−61.7046	+	106.875i	−0.240096	+	0.415858i	−0.960741	−	0.277446i	$-0.910512\pi$
$257$	−61.7046	+	106.875i	−0.240096	+	0.415858i	0.720646	+	0.693303i	$0.243845\pi$
$258$		0			0
$259$	−158.893	−	275.211i	−0.613487	−	1.06259i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−211.598	−	366.498i	−0.804554	−	1.39353i	−0.916591	−	0.399825i	$-0.869071\pi$
$263$	−211.598	−	366.498i	−0.804554	−	1.39353i	0.112037	−	0.993704i	$-0.464262\pi$
$264$		0			0
$265$	−160.861	+	240.756i	−0.607021	+	0.908514i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	330.998i		−	1.23048i	−0.788341	−	0.615239i	$-0.789060\pi$
$269$		−	330.998i		−	1.23048i	0.788341	−	0.615239i	$-0.210940\pi$
$270$		0			0
$271$	142.931			0.527422			0.263711	−	0.964602i	$-0.415054\pi$
$271$	142.931			0.527422			0.263711	+	0.964602i	$0.415054\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	303.365	+	232.759i	1.10314	+	0.846397i
$276$		0			0
$277$	−14.8833	+	8.59286i	−0.0537302	+	0.0310212i	−0.526624	−	0.850098i	$-0.676543\pi$
$277$	−14.8833	+	8.59286i	−0.0537302	+	0.0310212i	0.472894	+	0.881119i	$0.343209\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	255.409	−	147.461i	0.908930	−	0.524771i	0.0288429	−	0.999584i	$-0.490818\pi$
$281$	255.409	−	147.461i	0.908930	−	0.524771i	0.880087	+	0.474813i	$0.157484\pi$
$282$		0			0
$283$	−400.809	−	231.407i	−1.41629	−	0.817693i	−0.420316	−	0.907378i	$-0.638081\pi$
$283$	−400.809	−	231.407i	−1.41629	−	0.817693i	−0.995970	+	0.0896849i	$0.971414\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−253.045			−0.881691
$288$		0			0
$289$	−272.931			−0.944399
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−98.8910	+	171.284i	−0.337512	+	0.584588i	−0.983964	−	0.178367i	$-0.942919\pi$
$293$	−98.8910	+	171.284i	−0.337512	+	0.584588i	0.646452	+	0.762955i	$0.276252\pi$
$294$		0			0
$295$	−382.201	+	188.491i	−1.29560	+	0.638953i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−98.3821	+	56.8009i	−0.329037	+	0.189970i
$300$		0			0
$301$	−167.931	+	290.866i	−0.557911	+	0.966331i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−188.527	−	12.3526i	−0.618122	−	0.0405005i
$306$		0			0
$307$		−	304.221i		−	0.990949i	−0.868622	−	0.495475i	$-0.834994\pi$
$307$		−	304.221i		−	0.990949i	0.868622	−	0.495475i	$-0.165006\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	200.607	+	115.820i	0.645038	+	0.372413i	0.786552	−	0.617523i	$-0.211864\pi$
$311$	200.607	+	115.820i	0.645038	+	0.372413i	−0.141515	+	0.989936i	$0.545197\pi$
$312$		0			0
$313$	235.290	−	135.845i	0.751725	−	0.434009i	−0.0745916	−	0.997214i	$-0.523765\pi$
$313$	235.290	−	135.845i	0.751725	−	0.434009i	0.826317	+	0.563205i	$0.190432\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	139.443	+	241.523i	0.439885	+	0.761902i	0.997680	−	0.0680759i	$-0.0216860\pi$
$317$	139.443	+	241.523i	0.439885	+	0.761902i	−0.557796	+	0.829978i	$0.688353\pi$
$318$		0			0
$319$	350.897	−	607.771i	1.09999	−	1.90524i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−111.383			−0.344840
$324$		0			0
$325$	−9.78626	+	74.3588i	−0.0301116	+	0.228796i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	160.768	+	92.8195i	0.488657	+	0.282126i
$330$		0			0
$331$	251.397	+	435.432i	0.759507	+	1.31551i	0.943102	+	0.332503i	$0.107893\pi$
$331$	251.397	+	435.432i	0.759507	+	1.31551i	−0.183595	+	0.983002i	$0.558773\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−261.482	+	128.956i	−0.780545	+	0.384943i
$336$		0			0
$337$	−62.5037	−	36.0865i	−0.185471	−	0.107082i	0.404390	−	0.914587i	$-0.367484\pi$
$337$	−62.5037	−	36.0865i	−0.185471	−	0.107082i	−0.589861	+	0.807505i	$0.700817\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	440.281i		−	1.29115i
$342$		0			0
$343$		−	113.125i		−	0.329810i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	118.505	−	205.258i	0.341514	−	0.591520i	−0.643200	−	0.765698i	$-0.722394\pi$
$347$	118.505	−	205.258i	0.341514	−	0.591520i	0.984714	+	0.174178i	$0.0557269\pi$
$348$		0			0
$349$	−192.534	−	333.479i	−0.551674	−	0.955528i	−0.998154	−	0.0607342i	$-0.980656\pi$
$349$	−192.534	−	333.479i	−0.551674	−	0.955528i	0.446480	−	0.894794i	$-0.352678\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	273.302	+	473.374i	0.774228	+	1.34100i	0.935228	+	0.354047i	$0.115195\pi$
$353$	273.302	+	473.374i	0.774228	+	1.34100i	−0.161000	+	0.986954i	$0.551472\pi$
$354$		0			0
$355$	522.285	+	348.963i	1.47123	+	0.982996i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	110.450i		−	0.307660i	−0.988097	−	0.153830i	$-0.950839\pi$
$359$		−	110.450i		−	0.307660i	0.988097	−	0.153830i	$-0.0491609\pi$
$360$		0			0
$361$	411.076			1.13872
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−131.746	−	88.0261i	−0.360949	−	0.241167i
$366$		0			0
$367$	452.215	−	261.087i	1.23219	−	0.711407i	0.264707	−	0.964329i	$-0.414725\pi$
$367$	452.215	−	261.087i	1.23219	−	0.711407i	0.967487	+	0.252921i	$0.0813914\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−464.509	+	268.185i	−1.25205	+	0.722869i
$372$		0			0
$373$	386.505	+	223.149i	1.03621	+	0.598254i	0.918757	−	0.394824i	$-0.129195\pi$
$373$	386.505	+	223.149i	1.03621	+	0.598254i	0.117450	+	0.993079i	$0.462528\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	137.653			0.365128
$378$		0			0
$379$	488.657			1.28933			0.644666	−	0.764465i	$-0.276997\pi$
$379$	488.657			1.28933			0.644666	+	0.764465i	$0.276997\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−301.362	+	521.975i	−0.786847	+	1.36286i	0.141043	+	0.990004i	$0.454955\pi$
$383$	−301.362	+	521.975i	−0.786847	+	1.36286i	−0.927889	+	0.372855i	$0.878379\pi$
$384$		0			0
$385$	313.291	+	635.257i	0.813743	+	1.65002i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−580.081	+	334.910i	−1.49121	+	0.860951i	−0.999949	−	0.0100609i	$-0.996797\pi$
$389$	−580.081	+	334.910i	−1.49121	+	0.860951i	−0.491262	+	0.871012i	$0.663464\pi$
$390$		0			0
$391$	75.8970	−	131.457i	0.194110	−	0.336208i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	194.583	+	12.7494i	0.492615	+	0.0322770i
$396$		0			0
$397$		−	696.842i		−	1.75527i	−0.479329	−	0.877635i	$-0.659120\pi$
$397$		−	696.842i		−	1.75527i	0.479329	−	0.877635i	$-0.340880\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	190.091	+	109.749i	0.474041	+	0.273688i	0.717930	−	0.696115i	$-0.245090\pi$
$401$	190.091	+	109.749i	0.474041	+	0.273688i	−0.243889	+	0.969803i	$0.578423\pi$
$402$		0			0
$403$	74.7889	−	43.1794i	0.185580	−	0.107145i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−262.386	−	454.466i	−0.644683	−	1.11662i
$408$		0			0
$409$	−92.3626	+	159.977i	−0.225825	+	0.391141i	−0.956567	−	0.291513i	$-0.905841\pi$
$409$	−92.3626	+	159.977i	−0.225825	+	0.391141i	0.730741	+	0.682654i	$0.239175\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−789.414			−1.91141
$414$		0			0
$415$	328.931	+	21.5522i	0.792606	+	0.0519330i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	116.380	+	67.1921i	0.277757	+	0.160363i	0.632408	−	0.774636i	$-0.282067\pi$
$419$	116.380	+	67.1921i	0.277757	+	0.160363i	−0.354651	+	0.934999i	$0.615400\pi$
$420$		0			0
$421$	63.5343	+	110.045i	0.150913	+	0.261389i	0.931563	−	0.363579i	$-0.118445\pi$
$421$	63.5343	+	110.045i	0.150913	+	0.261389i	−0.780650	+	0.624968i	$0.785112\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−38.3544	−	92.5844i	−0.0902456	−	0.217846i
$426$		0			0
$427$	−303.091	−	174.990i	−0.709816	−	0.409812i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	31.7575i		−	0.0736833i	−0.999321	−	0.0368417i	$-0.988270\pi$
$431$		−	31.7575i		−	0.0736833i	0.999321	−	0.0368417i	$-0.0117297\pi$
$432$		0			0
$433$			708.056i			1.63523i	0.575763	+	0.817617i	$0.304705\pi$
$433$			708.056i			1.63523i	−0.575763	+	0.817617i	$0.695295\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−526.095	+	911.224i	−1.20388	+	2.08518i
$438$		0			0
$439$	−386.359	−	669.193i	−0.880088	−	1.52436i	−0.851242	−	0.524774i	$-0.824150\pi$
$439$	−386.359	−	669.193i	−0.880088	−	1.52436i	−0.0288467	−	0.999584i	$-0.509183\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	183.538	+	317.897i	0.414306	+	0.717600i	0.995355	−	0.0962688i	$-0.0306908\pi$
$443$	183.538	+	317.897i	0.414306	+	0.717600i	−0.581049	+	0.813869i	$0.697358\pi$
$444$		0			0
$445$	−354.339	−	236.751i	−0.796267	−	0.532024i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			526.562i			1.17274i	0.810042	+	0.586372i	$0.199444\pi$
$449$			526.562i			1.17274i	−0.810042	+	0.586372i	$0.800556\pi$
$450$		0			0
$451$	−417.863			−0.926525
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−77.1836	+	115.519i	−0.169634	+	0.253888i
$456$		0			0
$457$	−397.177	+	229.310i	−0.869097	+	0.501773i	−0.867048	−	0.498225i	$-0.833986\pi$
$457$	−397.177	+	229.310i	−0.869097	+	0.501773i	−0.00204894	+	0.999998i	$0.500652\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−304.753	+	175.949i	−0.661069	+	0.381668i	−0.792684	−	0.609633i	$-0.791317\pi$
$461$	−304.753	+	175.949i	−0.661069	+	0.381668i	0.131615	+	0.991301i	$0.457984\pi$
$462$		0			0
$463$	−383.352	−	221.328i	−0.827974	−	0.478031i	0.0251847	−	0.999683i	$-0.491983\pi$
$463$	−383.352	−	221.328i	−0.827974	−	0.478031i	−0.853158	+	0.521652i	$0.825316\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−646.819			−1.38505			−0.692526	−	0.721393i	$-0.743502\pi$
$467$	−646.819			−1.38505			−0.692526	+	0.721393i	$0.743502\pi$
$468$		0			0
$469$	−540.076			−1.15155
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−277.311	+	480.317i	−0.586281	+	1.01547i
$474$		0			0
$475$	265.861	+	641.768i	0.559708	+	1.35109i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−169.261	+	97.7231i	−0.353364	+	0.204015i	−0.666166	−	0.745804i	$-0.732066\pi$
$479$	−169.261	+	97.7231i	−0.353364	+	0.204015i	0.312802	+	0.949818i	$0.398732\pi$
$480$		0			0
$481$	51.4657	−	89.1411i	0.106997	−	0.185325i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	52.9209	−	807.683i	0.109115	−	1.66533i
$486$		0			0
$487$			179.069i			0.367698i	0.982955	+	0.183849i	$0.0588557\pi$
$487$			179.069i			0.367698i	−0.982955	+	0.183849i	$0.941144\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−493.023	−	284.647i	−1.00412	−	0.579730i	−0.0946561	−	0.995510i	$-0.530175\pi$
$491$	−493.023	−	284.647i	−1.00412	−	0.579730i	−0.909465	+	0.415780i	$0.863508\pi$
$492$		0			0
$493$	−159.289	+	91.9657i	−0.323102	+	0.186543i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	581.787	+	1007.68i	1.17060	+	2.02753i
$498$		0			0
$499$	14.7099	−	25.4783i	0.0294788	−	0.0510587i	−0.850910	−	0.525312i	$-0.823949\pi$
$499$	14.7099	−	25.4783i	0.0294788	−	0.0510587i	0.880388	+	0.474253i	$0.157282\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−465.500			−0.925447			−0.462724	−	0.886503i	$-0.653128\pi$
$503$	−465.500			−0.925447			−0.462724	+	0.886503i	$0.653128\pi$
$504$		0			0
$505$	−23.9313	+	365.242i	−0.0473887	+	0.723251i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	291.304	+	168.184i	0.572306	+	0.330421i	0.758070	−	0.652173i	$-0.226143\pi$
$509$	291.304	+	168.184i	0.572306	+	0.330421i	−0.185764	+	0.982594i	$0.559476\pi$
$510$		0			0
$511$	−146.756	−	254.188i	−0.287193	−	0.497433i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	691.977	−	341.264i	1.34364	−	0.662648i
$516$		0			0
$517$	265.482	+	153.276i	0.513505	+	0.296472i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			433.625i			0.832294i	0.909297	+	0.416147i	$0.136620\pi$
$521$			433.625i			0.832294i	−0.909297	+	0.416147i	$0.863380\pi$
$522$		0			0
$523$		−	185.331i		−	0.354361i	−0.984178	−	0.177180i	$-0.943302\pi$
$523$		−	185.331i		−	0.354361i	0.984178	−	0.177180i	$-0.0566976\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−57.6960	+	99.9324i	−0.109480	+	0.189625i
$528$		0			0
$529$	−452.466	−	783.694i	−0.855323	−	1.48146i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−40.9808	−	70.9809i	−0.0768871	−	0.133172i
$534$		0			0
$535$	−415.773	+	622.277i	−0.777145	+	1.16313i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			562.639i			1.04386i
$540$		0			0
$541$	124.351			0.229854			0.114927	−	0.993374i	$-0.463337\pi$
$541$	124.351			0.229854			0.114927	+	0.993374i	$0.463337\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−368.658	+	551.761i	−0.676436	+	1.01241i
$546$		0			0
$547$	526.753	−	304.121i	0.962985	−	0.555980i	0.0658946	−	0.997827i	$-0.479010\pi$
$547$	526.753	−	304.121i	0.962985	−	0.555980i	0.897090	+	0.441847i	$0.145677\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1104.15	−	637.479i	2.00389	−	1.15695i
$552$		0			0
$553$	312.827	+	180.611i	0.565691	+	0.326602i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−87.3319			−0.156790			−0.0783949	−	0.996922i	$-0.524980\pi$
$557$	−87.3319			−0.156790			−0.0783949	+	0.996922i	$0.524980\pi$
$558$		0			0
$559$	−108.786			−0.194609
$560$		0			0
$561$		0			0
$562$		0			0
$563$	52.1115	−	90.2598i	0.0925604	−	0.160319i	−0.816027	−	0.578013i	$-0.803828\pi$
$563$	52.1115	−	90.2598i	0.0925604	−	0.160319i	0.908588	+	0.417694i	$0.137162\pi$
$564$		0			0
$565$	207.857	+	421.469i	0.367888	+	0.745963i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	563.801	−	325.511i	0.990863	−	0.572075i	0.0853310	−	0.996353i	$-0.472805\pi$
$569$	563.801	−	325.511i	0.990863	−	0.572075i	0.905532	+	0.424278i	$0.139472\pi$
$570$		0			0
$571$	57.8244	−	100.155i	0.101269	−	0.175403i	−0.810939	−	0.585131i	$-0.801043\pi$
$571$	57.8244	−	100.155i	0.101269	−	0.175403i	0.912208	+	0.409728i	$0.134376\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−938.588	−	123.526i	−1.63233	−	0.214829i
$576$		0			0
$577$		−	121.399i		−	0.210398i	−0.994451	−	0.105199i	$-0.966452\pi$
$577$		−	121.399i		−	0.210398i	0.994451	−	0.105199i	$-0.0335479\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	528.816	+	305.312i	0.910183	+	0.525495i
$582$		0			0
$583$	−767.061	+	442.863i	−1.31571	+	0.759627i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−345.709	−	598.786i	−0.588942	−	1.02008i	−0.994371	−	0.105952i	$-0.966211\pi$
$587$	−345.709	−	598.786i	−0.588942	−	1.02008i	0.405429	−	0.914127i	$-0.367122\pi$
$588$		0			0
$589$	399.931	−	692.701i	0.679001	−	1.17606i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	747.110			1.25988			0.629941	−	0.776643i	$-0.283079\pi$
$593$	747.110			1.25988			0.629941	+	0.776643i	$0.283079\pi$
$594$		0			0
$595$	12.1374	−	185.242i	0.0203990	−	0.311331i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−396.563	−	228.956i	−0.662041	−	0.382230i	0.131013	−	0.991381i	$-0.458177\pi$
$599$	−396.563	−	228.956i	−0.662041	−	0.382230i	−0.793054	+	0.609151i	$0.791510\pi$
$600$		0			0
$601$	81.6756	+	141.466i	0.135899	+	0.235385i	0.925941	−	0.377669i	$-0.123274\pi$
$601$	81.6756	+	141.466i	0.135899	+	0.235385i	−0.790041	+	0.613054i	$0.789941\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	249.752	+	506.420i	0.412813	+	0.837057i
$606$		0			0
$607$	−124.558	−	71.9135i	−0.205202	−	0.118474i	0.393877	−	0.919163i	$-0.371133\pi$
$607$	−124.558	−	71.9135i	−0.205202	−	0.118474i	−0.599080	+	0.800689i	$0.704467\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			60.1287i			0.0984102i
$612$		0			0
$613$		−	970.104i		−	1.58255i	−0.611459	−	0.791276i	$-0.709417\pi$
$613$		−	970.104i		−	1.58255i	0.611459	−	0.791276i	$-0.290583\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−325.881	+	564.442i	−0.528169	+	0.914816i	0.471291	+	0.881978i	$0.343788\pi$
$617$	−325.881	+	564.442i	−0.528169	+	0.914816i	−0.999461	+	0.0328386i	$0.989545\pi$
$618$		0			0
$619$	−257.176	−	445.441i	−0.415469	−	0.719614i	0.580008	−	0.814611i	$-0.303049\pi$
$619$	−257.176	−	445.441i	−0.415469	−	0.719614i	−0.995478	+	0.0949965i	$0.969716\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−394.707	−	683.653i	−0.633559	−	1.09736i
$624$		0			0
$625$	−441.904	+	441.980i	−0.707046	+	0.707168i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			137.536i			0.218658i
$630$		0			0
$631$	−552.794			−0.876060			−0.438030	−	0.898960i	$-0.644324\pi$
$631$	−552.794			−0.876060			−0.438030	+	0.898960i	$0.644324\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−620.459	−	414.558i	−0.977100	−	0.652847i
$636$		0			0
$637$	−95.5735	+	55.1794i	−0.150037	+	0.0866239i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	126.795	−	73.2050i	0.197808	−	0.114204i	−0.397825	−	0.917461i	$-0.630235\pi$
$641$	126.795	−	73.2050i	0.197808	−	0.114204i	0.595633	+	0.803257i	$0.296901\pi$
$642$		0			0
$643$	768.852	+	443.897i	1.19573	+	0.690353i	0.959600	−	0.281369i	$-0.0907886\pi$
$643$	768.852	+	443.897i	1.19573	+	0.690353i	0.236127	+	0.971722i	$0.424122\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−250.322			−0.386896			−0.193448	−	0.981111i	$-0.561967\pi$
$647$	−250.322			−0.386896			−0.193448	+	0.981111i	$0.561967\pi$
$648$		0			0
$649$	−1303.59			−2.00861
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−479.316	+	830.199i	−0.734021	+	1.27136i	0.221131	+	0.975244i	$0.429025\pi$
$653$	−479.316	+	830.199i	−0.734021	+	1.27136i	−0.955152	+	0.296117i	$0.904308\pi$
$654$		0			0
$655$	553.405	−	272.924i	0.844894	−	0.416678i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	720.930	−	416.229i	1.09398	−	0.631607i	0.159343	−	0.987223i	$-0.449062\pi$
$659$	720.930	−	416.229i	1.09398	−	0.631607i	0.934632	+	0.355616i	$0.115729\pi$
$660$		0			0
$661$	−643.260	+	1114.16i	−0.973161	+	1.68556i	−0.287287	+	0.957845i	$0.592753\pi$
$661$	−643.260	+	1114.16i	−0.973161	+	1.68556i	−0.685874	+	0.727720i	$0.740580\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−84.1327	+	1284.04i	−0.126515	+	1.93089i
$666$		0			0
$667$			1737.52i			2.60498i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−500.505	−	288.967i	−0.745910	−	0.430651i
$672$		0			0
$673$	890.605	−	514.191i	1.32334	−	0.764028i	0.339076	−	0.940759i	$-0.389886\pi$
$673$	890.605	−	514.191i	1.32334	−	0.764028i	0.984259	+	0.176731i	$0.0565522\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	450.827	+	780.856i	0.665919	+	1.15341i	0.979035	+	0.203691i	$0.0652938\pi$
$677$	450.827	+	780.856i	0.665919	+	1.15341i	−0.313116	+	0.949715i	$0.601373\pi$
$678$		0			0
$679$	749.687	−	1298.50i	1.10410	−	1.91237i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−218.253			−0.319551			−0.159775	−	0.987153i	$-0.551077\pi$
$683$	−218.253			−0.319551			−0.159775	+	0.987153i	$0.551077\pi$
$684$		0			0
$685$	386.794	+	25.3434i	0.564663	+	0.0369977i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−150.455	−	86.8653i	−0.218367	−	0.126074i
$690$		0			0
$691$	251.863	+	436.239i	0.364490	+	0.631315i	0.988694	−	0.149946i	$-0.0479100\pi$
$691$	251.863	+	436.239i	0.364490	+	0.631315i	−0.624204	+	0.781261i	$0.714577\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−139.175	−	282.204i	−0.200252	−	0.406049i
$696$		0			0
$697$	94.8441	+	54.7583i	0.136075	+	0.0785628i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	377.933i		−	0.539135i	−0.962982	−	0.269567i	$-0.913119\pi$
$701$		−	377.933i		−	0.539135i	0.962982	−	0.269567i	$-0.0868807\pi$
$702$		0			0
$703$		−	953.359i		−	1.35613i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−339.015	+	587.192i	−0.479513	+	0.830540i
$708$		0			0
$709$	−605.038	−	1047.96i	−0.853368	−	1.47808i	−0.878150	−	0.478385i	$-0.841223\pi$
$709$	−605.038	−	1047.96i	−0.853368	−	1.47808i	0.0247821	−	0.999693i	$-0.492111\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	545.029	+	944.018i	0.764416	+	1.32401i
$714$		0			0
$715$	−127.456	+	190.760i	−0.178260	+	0.266798i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			462.113i			0.642717i	0.946958	+	0.321358i	$0.104139\pi$
$719$			462.113i			0.642717i	−0.946958	+	0.321358i	$0.895861\pi$
$720$		0			0
$721$	1429.24			1.98230
$722$		0			0
$723$		0			0
$724$		0			0
$725$	910.094	+	698.278i	1.25530	+	0.963142i
$726$		0			0
$727$	−462.352	+	266.939i	−0.635972	+	0.367179i	−0.783061	−	0.621944i	$-0.786343\pi$
$727$	−462.352	+	266.939i	−0.635972	+	0.367179i	0.147089	+	0.989123i	$0.453010\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	125.885	−	72.6797i	0.172209	−	0.0994250i
$732$		0			0
$733$	−461.444	−	266.415i	−0.629528	−	0.363458i	0.151041	−	0.988527i	$-0.451737\pi$
$733$	−461.444	−	266.415i	−0.629528	−	0.363458i	−0.780569	+	0.625069i	$0.785071\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−891.847			−1.21010
$738$		0			0
$739$	39.8626			0.0539413			0.0269706	−	0.999636i	$-0.491414\pi$
$739$	39.8626			0.0539413			0.0269706	+	0.999636i	$0.491414\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	457.268	−	792.012i	0.615435	−	1.06597i	−0.374873	−	0.927076i	$-0.622314\pi$
$743$	457.268	−	792.012i	0.615435	−	1.06597i	0.990308	−	0.138889i	$-0.0443531\pi$
$744$		0			0
$745$	1209.95	−	596.716i	1.62410	−	0.800961i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1200.61	+	693.170i	−1.60295	+	0.925461i
$750$		0			0
$751$	−427.363	+	740.214i	−0.569058	+	0.985638i	0.427601	+	0.903967i	$0.359359\pi$
$751$	−427.363	+	740.214i	−0.569058	+	0.985638i	−0.996659	+	0.0816701i	$0.973975\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	379.911	+	24.8924i	0.503193	+	0.0329701i
$756$		0			0
$757$			152.532i			0.201495i	0.994912	+	0.100748i	$0.0321235\pi$
$757$			152.532i			0.201495i	−0.994912	+	0.100748i	$0.967877\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1091.00	−	629.890i	−1.43364	−	0.827713i	−0.436245	−	0.899828i	$-0.643692\pi$
$761$	−1091.00	−	629.890i	−1.43364	−	0.827713i	−0.997396	+	0.0721147i	$0.977025\pi$
$762$		0			0
$763$	−1064.55	+	614.621i	−1.39522	+	0.805532i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−127.846	−	221.436i	−0.166683	−	0.288704i
$768$		0			0
$769$	588.363	−	1019.07i	0.765101	−	1.32519i	−0.175092	−	0.984552i	$-0.556022\pi$
$769$	588.363	−	1019.07i	0.765101	−	1.32519i	0.940193	−	0.340642i	$-0.110644\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−112.317			−0.145300			−0.0726499	−	0.997358i	$-0.523146\pi$
$773$	−112.317			−0.145300			−0.0726499	+	0.997358i	$0.523146\pi$
$774$		0			0
$775$	713.504	+	93.9033i	0.920650	+	0.121166i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−657.431	−	379.568i	−0.843942	−	0.487250i
$780$		0			0
$781$	960.725	+	1664.02i	1.23012	+	2.13063i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−510.037	+	251.536i	−0.649728	+	0.320428i
$786$		0			0
$787$	−423.438	−	244.472i	−0.538041	−	0.310638i	0.206244	−	0.978501i	$-0.433876\pi$
$787$	−423.438	−	244.472i	−0.538041	−	0.310638i	−0.744284	+	0.667863i	$0.767209\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			870.519i			1.10053i
$792$		0			0
$793$		−	113.359i		−	0.142949i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	617.902	−	1070.24i	0.775285	−	1.34283i	−0.159349	−	0.987222i	$-0.550939\pi$
$797$	617.902	−	1070.24i	0.775285	−	1.34283i	0.934634	−	0.355611i	$-0.115727\pi$
$798$		0			0
$799$	−40.1717	−	69.5795i	−0.0502775	−	0.0870832i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−242.343	−	419.750i	−0.301797	−	0.522728i
$804$		0			0
$805$	−1458.13	−	974.245i	−1.81134	−	1.21024i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	1251.84i		−	1.54739i	−0.633558	−	0.773695i	$-0.718406\pi$
$809$		−	1251.84i		−	1.54739i	0.633558	−	0.773695i	$-0.281594\pi$
$810$		0			0
$811$	340.580			0.419951			0.209975	−	0.977707i	$-0.432662\pi$
$811$	340.580			0.419951			0.209975	+	0.977707i	$0.432662\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−375.743	−	251.052i	−0.461034	−	0.308039i
$816$		0			0
$817$	−872.597	+	503.794i	−1.06805	+	0.616639i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−853.590	+	492.820i	−1.03970	+	0.600268i	−0.919747	−	0.392512i	$-0.871606\pi$
$821$	−853.590	+	492.820i	−1.03970	+	0.600268i	−0.119948	+	0.992780i	$0.538273\pi$
$822$		0			0
$823$	780.229	+	450.466i	0.948031	+	0.547346i	0.892469	−	0.451109i	$-0.148972\pi$
$823$	780.229	+	450.466i	0.948031	+	0.547346i	0.0555622	+	0.998455i	$0.482305\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1571.67			1.90045			0.950223	−	0.311572i	$-0.100855\pi$
$827$	1571.67			1.90045			0.950223	+	0.311572i	$0.100855\pi$
$828$		0			0
$829$	486.519			0.586875			0.293437	−	0.955978i	$-0.405201\pi$
$829$	486.519			0.586875			0.293437	+	0.955978i	$0.405201\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	73.7303	−	127.705i	0.0885117	−	0.153307i
$834$		0			0
$835$	459.092	+	930.896i	0.549811	+	1.11485i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	590.496	−	340.923i	0.703809	−	0.406344i	−0.104956	−	0.994477i	$-0.533470\pi$
$839$	590.496	−	340.923i	0.703809	−	0.406344i	0.808764	+	0.588133i	$0.200137\pi$
$840$		0			0
$841$	632.191	−	1094.99i	0.751713	−	1.30201i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	798.288	+	52.3053i	0.944720	+	0.0618998i
$846$		0			0
$847$			1045.98i			1.23492i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1125.18	+	649.622i	1.32218	+	0.763363i
$852$		0			0
$853$	−1364.29	+	787.673i	−1.59940	+	0.923415i	−0.607800	+	0.794091i	$0.707948\pi$
$853$	−1364.29	+	787.673i	−1.59940	+	0.923415i	−0.991602	+	0.129325i	$0.958719\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−787.158	−	1363.40i	−0.918504	−	1.59089i	−0.801689	−	0.597741i	$-0.796065\pi$
$857$	−787.158	−	1363.40i	−0.918504	−	1.59089i	−0.116814	−	0.993154i	$-0.537268\pi$
$858$		0			0
$859$	−387.191	+	670.634i	−0.450746	+	0.780715i	−0.998433	−	0.0559685i	$-0.982175\pi$
$859$	−387.191	+	670.634i	−0.450746	+	0.780715i	0.547686	+	0.836684i	$0.315509\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−505.662			−0.585935			−0.292968	−	0.956122i	$-0.594643\pi$
$863$	−505.662			−0.585935			−0.292968	+	0.956122i	$0.594643\pi$
$864$		0			0
$865$	−280.000	−	18.3461i	−0.323699	−	0.0212094i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	516.582	+	298.249i	0.594456	+	0.343209i
$870$		0			0
$871$	−87.4657	−	151.495i	−0.100420	−	0.173932i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1096.29	+	372.221i	−1.25291	+	0.425395i
$876$		0			0
$877$	799.928	+	461.838i	0.912118	+	0.526612i	0.881112	−	0.472908i	$-0.156796\pi$
$877$	799.928	+	461.838i	0.912118	+	0.526612i	0.0310061	+	0.999519i	$0.490129\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	599.650i		−	0.680646i	−0.940309	−	0.340323i	$-0.889464\pi$
$881$		−	599.650i		−	0.680646i	0.940309	−	0.340323i	$-0.110536\pi$
$882$		0			0
$883$		−	1628.09i		−	1.84382i	−0.387406	−	0.921909i	$-0.626629\pi$
$883$		−	1628.09i		−	1.84382i	0.387406	−	0.921909i	$-0.373371\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	365.500	−	633.064i	0.412063	−	0.713714i	−0.583052	−	0.812435i	$-0.698142\pi$
$887$	365.500	−	633.064i	0.412063	−	0.713714i	0.995115	+	0.0987210i	$0.0314751\pi$
$888$		0			0
$889$	−691.145	−	1197.10i	−0.777441	−	1.34657i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	278.458	+	482.304i	0.311824	+	0.540094i
$894$		0			0
$895$	295.120	+	197.184i	0.329743	+	0.220317i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	1320.84i		−	1.46923i
$900$		0			0
$901$	232.137			0.257644
$902$		0			0
$903$		0			0
$904$		0			0
$905$	263.697	−	394.668i	0.291377	−	0.436097i
$906$		0			0
$907$	925.543	−	534.363i	1.02044	−	0.589154i	0.106212	−	0.994344i	$-0.466128\pi$
$907$	925.543	−	534.363i	1.02044	−	0.589154i	0.914233	+	0.405190i	$0.132794\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−917.491	+	529.714i	−1.00713	+	0.581464i	−0.910349	−	0.413842i	$-0.864187\pi$
$911$	−917.491	+	529.714i	−1.00713	+	0.581464i	−0.0967764	+	0.995306i	$0.530853\pi$
$912$		0			0
$913$	873.253	+	504.173i	0.956466	+	0.552216i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1143.03			1.24648
$918$		0			0
$919$	−874.802			−0.951906			−0.475953	−	0.879471i	$-0.657897\pi$
$919$	−874.802			−0.951906			−0.475953	+	0.879471i	$0.657897\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−188.441	+	326.390i	−0.204162	+	0.353619i
$924$		0			0
$925$	792.454	−	328.285i	0.856707	−	0.354903i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	875.024	−	505.195i	0.941899	−	0.543806i	0.0513440	−	0.998681i	$-0.483650\pi$
$929$	875.024	−	505.195i	0.941899	−	0.543806i	0.890555	+	0.454875i	$0.150316\pi$
$930$		0			0
$931$	−511.076	+	885.210i	−0.548954	+	0.950817i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	20.0429	−	305.896i	0.0214362	−	0.327162i
$936$		0			0
$937$			611.705i			0.652833i	0.945226	+	0.326417i	$0.105841\pi$
$937$			611.705i			0.652833i	−0.945226	+	0.326417i	$0.894159\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1237.72	+	714.595i	1.31532	+	0.759400i	0.982972	−	0.183757i	$-0.0588260\pi$
$941$	1237.72	+	714.595i	1.31532	+	0.759400i	0.332347	+	0.943157i	$0.392159\pi$
$942$		0			0
$943$	895.951	−	517.277i	0.950107	−	0.548544i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	474.022	+	821.030i	0.500551	+	0.866980i	1.00000		0.000636505i	$0.000202606\pi$
$947$	474.022	+	821.030i	0.500551	+	0.866980i	−0.499449	+	0.866343i	$0.666464\pi$
$948$		0			0
$949$	47.5343	−	82.3319i	0.0500889	−	0.0867565i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−435.221			−0.456686			−0.228343	−	0.973581i	$-0.573331\pi$
$953$	−435.221			−0.456686			−0.228343	+	0.973581i	$0.573331\pi$
$954$		0			0
$955$	44.2748	−	675.725i	0.0463610	−	0.707566i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	621.841	+	359.020i	0.648427	+	0.374369i
$960$		0			0
$961$	66.1756	+	114.619i	0.0688611	+	0.119271i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	888.419	−	438.144i	0.920642	−	0.454035i
$966$		0			0
$967$	−1099.46	−	634.776i	−1.13698	−	0.656439i	−0.191303	−	0.981531i	$-0.561271\pi$
$967$	−1099.46	−	634.776i	−1.13698	−	0.656439i	−0.945682	+	0.325093i	$0.894605\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			763.925i			0.786740i	0.919380	+	0.393370i	$0.128691\pi$
$971$			763.925i			0.786740i	−0.919380	+	0.393370i	$0.871309\pi$
$972$		0			0
$973$		−	582.875i		−	0.599050i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	66.6082	−	115.369i	0.0681762	−	0.118085i	−0.829922	−	0.557879i	$-0.811615\pi$
$977$	66.6082	−	115.369i	0.0681762	−	0.118085i	0.898099	+	0.439794i	$0.144949\pi$
$978$		0			0
$979$	−651.794	−	1128.94i	−0.665775	−	1.15316i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−69.2551	−	119.953i	−0.0704527	−	0.122028i	0.828647	−	0.559771i	$-0.189111\pi$
$983$	−69.2551	−	119.953i	−0.0704527	−	0.122028i	−0.899100	+	0.437744i	$0.855778\pi$
$984$		0			0
$985$	−398.475	+	596.388i	−0.404544	+	0.605470i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	1373.15i		−	1.38842i
$990$		0			0
$991$	−1011.72			−1.02091			−0.510453	−	0.859906i	$-0.670522\pi$
$991$	−1011.72			−1.02091			−0.510453	+	0.859906i	$0.670522\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	913.502	−	1367.22i	0.918092	−	1.37409i
$996$		0			0
$997$	720.117	−	415.760i	0.722284	−	0.417011i	−0.0933090	−	0.995637i	$-0.529744\pi$
$997$	720.117	−	415.760i	0.722284	−	0.417011i	0.815593	+	0.578627i	$0.196411\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.3.t.e.1349.3		16
3.2	odd	2	inner	1620.3.t.e.1349.6		16
5.4	even	2	inner	1620.3.t.e.1349.5		16
9.2	odd	6	inner	1620.3.t.e.269.5		16
9.4	even	3		540.3.b.c.269.8	yes	8
9.5	odd	6		540.3.b.c.269.1	✓	8
9.7	even	3	inner	1620.3.t.e.269.4		16
15.14	odd	2	inner	1620.3.t.e.1349.4		16
36.23	even	6		2160.3.c.n.1889.1		8
36.31	odd	6		2160.3.c.n.1889.8		8
45.4	even	6		540.3.b.c.269.2	yes	8
45.13	odd	12		2700.3.g.o.701.1		4
45.14	odd	6		540.3.b.c.269.7	yes	8
45.22	odd	12		2700.3.g.p.701.3		4
45.23	even	12		2700.3.g.o.701.2		4
45.29	odd	6	inner	1620.3.t.e.269.3		16
45.32	even	12		2700.3.g.p.701.4		4
45.34	even	6	inner	1620.3.t.e.269.6		16
180.59	even	6		2160.3.c.n.1889.7		8
180.139	odd	6		2160.3.c.n.1889.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.3.b.c.269.1	✓	8	9.5	odd	6
540.3.b.c.269.2	yes	8	45.4	even	6
540.3.b.c.269.7	yes	8	45.14	odd	6
540.3.b.c.269.8	yes	8	9.4	even	3
1620.3.t.e.269.3		16	45.29	odd	6	inner
1620.3.t.e.269.4		16	9.7	even	3	inner
1620.3.t.e.269.5		16	9.2	odd	6	inner
1620.3.t.e.269.6		16	45.34	even	6	inner
1620.3.t.e.1349.3		16	1.1	even	1	trivial
1620.3.t.e.1349.4		16	15.14	odd	2	inner
1620.3.t.e.1349.5		16	5.4	even	2	inner
1620.3.t.e.1349.6		16	3.2	odd	2	inner
2160.3.c.n.1889.1		8	36.23	even	6
2160.3.c.n.1889.2		8	180.139	odd	6
2160.3.c.n.1889.7		8	180.59	even	6
2160.3.c.n.1889.8		8	36.31	odd	6
2700.3.g.o.701.1		4	45.13	odd	12
2700.3.g.o.701.2		4	45.23	even	12
2700.3.g.p.701.3		4	45.22	odd	12
2700.3.g.p.701.4		4	45.32	even	12

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1620.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.77776 + 4.15741i) q^{5} +(-8.02120 + 4.63104i) q^{7} +O(q^{10})\)	\(q+(-2.77776 + 4.15741i) q^{5} +(-8.02120 + 4.63104i) q^{7} +(-13.2457 + 7.64741i) q^{11} +(-2.59808 - 1.50000i) q^{13} +4.00858 q^{17} -27.7863 q^{19} +(18.9336 - 32.7940i) q^{23} +(-9.56808 - 23.0966i) q^{25} +(-39.7371 + 22.9422i) q^{29} +(-14.3931 + 24.9296i) q^{31} +(3.02785 - 46.2113i) q^{35} +34.3104i q^{37} +(23.6603 + 13.6603i) q^{41} +(31.4039 - 18.1310i) q^{43} +(-10.0214 - 17.3576i) q^{47} +(18.3931 - 31.8578i) q^{49} +57.9102 q^{53} +(5.00000 - 76.3104i) q^{55} +(73.8120 + 42.6154i) q^{59} +(18.8931 + 32.7239i) q^{61} +(13.4529 - 6.63462i) q^{65} +(50.4983 + 29.1552i) q^{67} -125.628i q^{71} +31.6896i q^{73} +(70.8309 - 122.683i) q^{77} +(-19.5000 - 33.7750i) q^{79} +(-32.9637 - 57.0947i) q^{83} +(-11.1349 + 16.6653i) q^{85} +85.2307i q^{89} +27.7863 q^{91} +(77.1836 - 115.519i) q^{95} +(-140.195 + 80.9415i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 72 q^{19} - 12 q^{25} - 44 q^{31} + 108 q^{49} + 80 q^{55} + 116 q^{61} - 312 q^{79} - 160 q^{85} + 72 q^{91}+O(q^{100}) \) 16 * q - 72 * q^19 - 12 * q^25 - 44 * q^31 + 108 * q^49 + 80 * q^55 + 116 * q^61 - 312 * q^79 - 160 * q^85 + 72 * q^91

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