LMFDB - Embedded newform 1728.3.o.h.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,3,Mod(127,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

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

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

chi := DirichletCharacter("1728.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1728.o (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:	$47.0845896815$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 50 x^{18} - 130 x^{17} + 203 x^{16} - 296 x^{15} + 1260 x^{14} - 3380 x^{13} + \cdots + 64 $ x^20 - 10x^19 + 50x^18 - 130x^17 + 203x^16 - 296x^15 + 1260x^14 - 3380x^13 + 4843x^12 - 2370x^11 + 8978x^10 - 23570x^9 + 32213x^8 - 6940x^7 + 11856x^6 - 30488x^5 + 41556x^4 - 6096x^3 + 288x^2 + 192*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.4
Root			$0.189070 - 0.189070i$ of defining polynomial
Character	$\chi$	$=$	1728.127
Dual form			1728.3.o.h.1279.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.966952 - 1.67481i) q^{5} +(8.96285 + 5.17470i) q^{7} +O(q^{10})$	$q+(-0.966952 - 1.67481i) q^{5} +(8.96285 + 5.17470i) q^{7} +(18.2506 + 10.5370i) q^{11} +(7.47096 + 12.9401i) q^{13} -5.89794 q^{17} +32.7678i q^{19} +(-4.30154 + 2.48349i) q^{23} +(10.6300 - 18.4117i) q^{25} +(-9.34387 + 16.1841i) q^{29} +(-8.55802 + 4.94098i) q^{31} -20.0147i q^{35} -43.5347 q^{37} +(7.82699 + 13.5567i) q^{41} +(-7.26635 - 4.19523i) q^{43} +(-43.2309 - 24.9594i) q^{47} +(29.0551 + 50.3249i) q^{49} -75.8512 q^{53} -40.7551i q^{55} +(58.8809 - 33.9949i) q^{59} +(-9.64421 + 16.7043i) q^{61} +(14.4481 - 25.0249i) q^{65} +(-32.2998 + 18.6483i) q^{67} -95.4928i q^{71} +68.3482 q^{73} +(109.052 + 188.883i) q^{77} +(-73.2208 - 42.2741i) q^{79} +(-14.0131 - 8.09049i) q^{83} +(5.70303 + 9.87793i) q^{85} -42.9444 q^{89} +154.640i q^{91} +(54.8798 - 31.6848i) q^{95} +(15.8988 - 27.5376i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 14 q^{5}+O(q^{10}) $ 20 * q + 14 * q^5	$ 20 q + 14 q^{5} - 26 q^{13} - 72 q^{17} + 36 q^{25} - 134 q^{29} - 96 q^{37} + 26 q^{41} + 348 q^{49} - 192 q^{53} - 386 q^{61} + 106 q^{65} - 168 q^{73} + 58 q^{77} - 192 q^{85} + 240 q^{89} + 374 q^{97}+O(q^{100}) $ 20 * q + 14 * q^5 - 26 * q^13 - 72 * q^17 + 36 * q^25 - 134 * q^29 - 96 * q^37 + 26 * q^41 + 348 * q^49 - 192 * q^53 - 386 * q^61 + 106 * q^65 - 168 * q^73 + 58 * q^77 - 192 * q^85 + 240 * q^89 + 374 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$5$	−0.966952	−	1.67481i	−0.193390	−	0.334962i	0.752981	−	0.658042i	$-0.228615\pi$
$5$	−0.966952	−	1.67481i	−0.193390	−	0.334962i	−0.946372	+	0.323080i	$0.895282\pi$
$6$		0			0
$7$	8.96285	+	5.17470i	1.28041	+	0.739243i	0.976923	−	0.213593i	$-0.0685168\pi$
$7$	8.96285	+	5.17470i	1.28041	+	0.739243i	0.303484	+	0.952837i	$0.401850\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	18.2506	+	10.5370i	1.65915	+	0.957910i	0.973109	+	0.230347i	$0.0739860\pi$
$11$	18.2506	+	10.5370i	1.65915	+	0.957910i	0.686040	+	0.727564i	$0.259347\pi$
$12$		0			0
$13$	7.47096	+	12.9401i	0.574690	+	0.995391i	0.996075	+	0.0885100i	$0.0282105\pi$
$13$	7.47096	+	12.9401i	0.574690	+	0.995391i	−0.421386	+	0.906881i	$0.638456\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.89794			−0.346938			−0.173469	−	0.984839i	$-0.555498\pi$
$17$	−5.89794			−0.346938			−0.173469	+	0.984839i	$0.555498\pi$
$18$		0			0
$19$			32.7678i			1.72462i	0.506382	+	0.862309i	$0.330983\pi$
$19$			32.7678i			1.72462i	−0.506382	+	0.862309i	$0.669017\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.30154	+	2.48349i	−0.187023	+	0.107978i	−0.590588	−	0.806973i	$-0.701104\pi$
$23$	−4.30154	+	2.48349i	−0.187023	+	0.107978i	0.403565	+	0.914951i	$0.367771\pi$
$24$		0			0
$25$	10.6300	−	18.4117i	0.425200	−	0.736469i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−9.34387	+	16.1841i	−0.322202	+	0.558071i	−0.980942	−	0.194300i	$-0.937756\pi$
$29$	−9.34387	+	16.1841i	−0.322202	+	0.558071i	0.658740	+	0.752371i	$0.271090\pi$
$30$		0			0
$31$	−8.55802	+	4.94098i	−0.276065	+	0.159386i	−0.631641	−	0.775261i	$-0.717618\pi$
$31$	−8.55802	+	4.94098i	−0.276065	+	0.159386i	0.355576	+	0.934648i	$0.384285\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	20.0147i		−	0.571850i
$36$		0			0
$37$	−43.5347			−1.17661			−0.588307	−	0.808638i	$-0.700205\pi$
$37$	−43.5347			−1.17661			−0.588307	+	0.808638i	$0.700205\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	7.82699	+	13.5567i	0.190902	+	0.330652i	0.945549	−	0.325478i	$-0.105525\pi$
$41$	7.82699	+	13.5567i	0.190902	+	0.330652i	−0.754647	+	0.656131i	$0.772192\pi$
$42$		0			0
$43$	−7.26635	−	4.19523i	−0.168985	−	0.0975635i	0.413122	−	0.910676i	$-0.364438\pi$
$43$	−7.26635	−	4.19523i	−0.168985	−	0.0975635i	−0.582107	+	0.813112i	$0.697772\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−43.2309	−	24.9594i	−0.919807	−	0.531051i	−0.0362337	−	0.999343i	$-0.511536\pi$
$47$	−43.2309	−	24.9594i	−0.919807	−	0.531051i	−0.883574	+	0.468292i	$0.844869\pi$
$48$		0			0
$49$	29.0551	+	50.3249i	0.592961	+	1.02704i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−75.8512			−1.43115			−0.715577	−	0.698534i	$-0.753836\pi$
$53$	−75.8512			−1.43115			−0.715577	+	0.698534i	$0.753836\pi$
$54$		0			0
$55$		−	40.7551i		−	0.741002i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	58.8809	−	33.9949i	0.997981	−	0.576185i	0.0903307	−	0.995912i	$-0.471208\pi$
$59$	58.8809	−	33.9949i	0.997981	−	0.576185i	0.907650	+	0.419727i	$0.137874\pi$
$60$		0			0
$61$	−9.64421	+	16.7043i	−0.158102	+	0.273840i	−0.934184	−	0.356791i	$-0.883871\pi$
$61$	−9.64421	+	16.7043i	−0.158102	+	0.273840i	0.776082	+	0.630632i	$0.217204\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	14.4481	−	25.0249i	0.222279	−	0.384998i
$66$		0			0
$67$	−32.2998	+	18.6483i	−0.482086	+	0.278333i	−0.721286	−	0.692638i	$-0.756448\pi$
$67$	−32.2998	+	18.6483i	−0.482086	+	0.278333i	0.239199	+	0.970971i	$0.423115\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	95.4928i		−	1.34497i	−0.740111	−	0.672485i	$-0.765227\pi$
$71$		−	95.4928i		−	1.34497i	0.740111	−	0.672485i	$-0.234773\pi$
$72$		0			0
$73$	68.3482			0.936277			0.468138	−	0.883655i	$-0.344925\pi$
$73$	68.3482			0.936277			0.468138	+	0.883655i	$0.344925\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	109.052	+	188.883i	1.41626	+	2.45303i
$78$		0			0
$79$	−73.2208	−	42.2741i	−0.926846	−	0.535115i	−0.0410333	−	0.999158i	$-0.513065\pi$
$79$	−73.2208	−	42.2741i	−0.926846	−	0.535115i	−0.885813	+	0.464043i	$0.846398\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−14.0131	−	8.09049i	−0.168833	−	0.0974758i	0.413202	−	0.910639i	$-0.364410\pi$
$83$	−14.0131	−	8.09049i	−0.168833	−	0.0974758i	−0.582035	+	0.813163i	$0.697744\pi$
$84$		0			0
$85$	5.70303	+	9.87793i	0.0670944	+	0.116211i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−42.9444			−0.482521			−0.241260	−	0.970460i	$-0.577561\pi$
$89$	−42.9444			−0.482521			−0.241260	+	0.970460i	$0.577561\pi$
$90$		0			0
$91$			154.640i			1.69934i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	54.8798	−	31.6848i	0.577682	−	0.333525i
$96$		0			0
$97$	15.8988	−	27.5376i	0.163905	−	0.283893i	−0.772361	−	0.635184i	$-0.780924\pi$
$97$	15.8988	−	27.5376i	0.163905	−	0.283893i	0.936266	+	0.351292i	$0.114257\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−56.1229	+	97.2077i	−0.555672	+	0.962452i	0.442179	+	0.896927i	$0.354206\pi$
$101$	−56.1229	+	97.2077i	−0.555672	+	0.962452i	−0.997851	+	0.0655252i	$0.979128\pi$
$102$		0			0
$103$	−48.3175	+	27.8961i	−0.469101	+	0.270836i	−0.715864	−	0.698240i	$-0.753967\pi$
$103$	−48.3175	+	27.8961i	−0.469101	+	0.270836i	0.246762	+	0.969076i	$0.420633\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			89.4882i			0.836338i	0.908369	+	0.418169i	$0.137328\pi$
$107$			89.4882i			0.836338i	−0.908369	+	0.418169i	$0.862672\pi$
$108$		0			0
$109$	158.842			1.45727			0.728634	−	0.684904i	$-0.240156\pi$
$109$	158.842			1.45727			0.728634	+	0.684904i	$0.240156\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	25.4171	+	44.0237i	0.224930	+	0.389591i	0.956298	−	0.292392i	$-0.0944513\pi$
$113$	25.4171	+	44.0237i	0.224930	+	0.389591i	−0.731368	+	0.681983i	$0.761118\pi$
$114$		0			0
$115$	8.31876	+	4.80284i	0.0723371	+	0.0417638i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−52.8624	−	30.5201i	−0.444222	−	0.256471i
$120$		0			0
$121$	161.557	+	279.825i	1.33518	+	2.31261i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−89.4624			−0.715699
$126$		0			0
$127$		−	20.1417i		−	0.158596i	−0.996851	−	0.0792979i	$-0.974732\pi$
$127$		−	20.1417i		−	0.158596i	0.996851	−	0.0792979i	$-0.0252678\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	55.2586	−	31.9036i	0.421821	−	0.243539i	−0.274035	−	0.961720i	$-0.588358\pi$
$131$	55.2586	−	31.9036i	0.421821	−	0.243539i	0.695856	+	0.718181i	$0.255025\pi$
$132$		0			0
$133$	−169.563	+	293.692i	−1.27491	+	2.20821i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.48134	−	9.49396i	0.0400098	−	0.0692990i	−0.845327	−	0.534249i	$-0.820594\pi$
$137$	5.48134	−	9.49396i	0.0400098	−	0.0692990i	0.885337	+	0.464950i	$0.153928\pi$
$138$		0			0
$139$	180.759	−	104.361i	1.30042	−	0.750799i	0.319945	−	0.947436i	$-0.396336\pi$
$139$	180.759	−	104.361i	1.30042	−	0.750799i	0.980476	+	0.196638i	$0.0630022\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			314.887i			2.20200i
$144$		0			0
$145$	36.1403			0.249243
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−81.2800	−	140.781i	−0.545503	−	0.944839i	−0.998575	−	0.0533652i	$-0.983005\pi$
$149$	−81.2800	−	140.781i	−0.545503	−	0.944839i	0.453072	−	0.891474i	$-0.350328\pi$
$150$		0			0
$151$	96.3636	+	55.6356i	0.638170	+	0.368447i	0.783909	−	0.620876i	$-0.213223\pi$
$151$	96.3636	+	55.6356i	0.638170	+	0.368447i	−0.145739	+	0.989323i	$0.546556\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	16.5504	+	9.55537i	0.106777	+	0.0616476i
$156$		0			0
$157$	−47.0780	−	81.5415i	−0.299860	−	0.519373i	0.676244	−	0.736678i	$-0.263607\pi$
$157$	−47.0780	−	81.5415i	−0.299860	−	0.519373i	−0.976104	+	0.217305i	$0.930273\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−51.4054			−0.319288
$162$		0			0
$163$		−	151.014i		−	0.926468i	−0.886236	−	0.463234i	$-0.846689\pi$
$163$		−	151.014i		−	0.926468i	0.886236	−	0.463234i	$-0.153311\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−72.7991	+	42.0306i	−0.435923	+	0.251680i	−0.701867	−	0.712308i	$-0.747650\pi$
$167$	−72.7991	+	42.0306i	−0.435923	+	0.251680i	0.265944	+	0.963989i	$0.414316\pi$
$168$		0			0
$169$	−27.1306	+	46.9916i	−0.160536	+	0.278057i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−131.671	+	228.060i	−0.761102	+	1.31827i	0.181180	+	0.983450i	$0.442008\pi$
$173$	−131.671	+	228.060i	−0.761102	+	1.31827i	−0.942283	+	0.334818i	$0.891325\pi$
$174$		0			0
$175$	190.550	−	110.014i	1.08886	−	0.628653i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			215.534i			1.20410i	0.798458	+	0.602050i	$0.205649\pi$
$179$			215.534i			1.20410i	−0.798458	+	0.602050i	$0.794351\pi$
$180$		0			0
$181$	332.798			1.83866			0.919332	−	0.393482i	$-0.128730\pi$
$181$	332.798			1.83866			0.919332	+	0.393482i	$0.128730\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	42.0960	+	72.9123i	0.227546	+	0.394121i
$186$		0			0
$187$	−107.641	−	62.1467i	−0.575622	−	0.332335i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−114.364	−	66.0279i	−0.598763	−	0.345696i	0.169792	−	0.985480i	$-0.445690\pi$
$191$	−114.364	−	66.0279i	−0.598763	−	0.345696i	−0.768555	+	0.639784i	$0.779024\pi$
$192$		0			0
$193$	−87.6264	−	151.773i	−0.454023	−	0.786391i	0.544609	−	0.838690i	$-0.316678\pi$
$193$	−87.6264	−	151.773i	−0.454023	−	0.786391i	−0.998631	+	0.0522997i	$0.983345\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	308.985			1.56845			0.784227	−	0.620475i	$-0.213060\pi$
$197$	308.985			1.56845			0.784227	+	0.620475i	$0.213060\pi$
$198$		0			0
$199$		−	310.934i		−	1.56248i	−0.624229	−	0.781241i	$-0.714587\pi$
$199$		−	310.934i		−	1.56248i	0.624229	−	0.781241i	$-0.285413\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−167.495	+	96.7035i	−0.825100	+	0.476372i
$204$		0			0
$205$	15.1366	−	26.2174i	0.0738373	−	0.127890i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−345.274	+	598.032i	−1.65203	+	2.86140i
$210$		0			0
$211$	8.05601	−	4.65114i	0.0381802	−	0.0220433i	−0.480788	−	0.876837i	$-0.659649\pi$
$211$	8.05601	−	4.65114i	0.0381802	−	0.0220433i	0.518969	+	0.854793i	$0.326316\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			16.2263i			0.0754714i
$216$		0			0
$217$	−102.272			−0.471301
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−44.0633	−	76.3199i	−0.199382	−	0.345339i
$222$		0			0
$223$	360.713	+	208.258i	1.61755	+	0.933891i	0.987552	+	0.157292i	$0.0502764\pi$
$223$	360.713	+	208.258i	1.61755	+	0.933891i	0.629995	+	0.776599i	$0.283057\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−308.860	−	178.321i	−1.36062	−	0.785553i	−0.370912	−	0.928668i	$-0.620955\pi$
$227$	−308.860	−	178.321i	−1.36062	−	0.785553i	−0.989706	+	0.143114i	$0.954288\pi$
$228$		0			0
$229$	164.486	+	284.898i	0.718280	+	1.24410i	0.961681	+	0.274172i	$0.0884036\pi$
$229$	164.486	+	284.898i	0.718280	+	1.24410i	−0.243401	+	0.969926i	$0.578263\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	65.3289			0.280382			0.140191	−	0.990124i	$-0.455228\pi$
$233$	65.3289			0.280382			0.140191	+	0.990124i	$0.455228\pi$
$234$		0			0
$235$			96.5381i			0.410801i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	81.9440	−	47.3104i	0.342862	−	0.197951i	−0.318675	−	0.947864i	$-0.603238\pi$
$239$	81.9440	−	47.3104i	0.342862	−	0.197951i	0.661537	+	0.749913i	$0.269905\pi$
$240$		0			0
$241$	42.2962	−	73.2591i	0.175503	−	0.303980i	−0.764832	−	0.644229i	$-0.777178\pi$
$241$	42.2962	−	73.2591i	0.175503	−	0.303980i	0.940335	+	0.340250i	$0.110512\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	56.1897	−	97.3235i	0.229346	−	0.397239i
$246$		0			0
$247$	−424.018	+	244.807i	−1.71667	+	0.991120i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	1.43066i		−	0.00569986i	−0.999996	−	0.00284993i	$-0.999093\pi$
$251$		−	1.43066i		−	0.00569986i	0.999996	−	0.00284993i	$-0.000907162\pi$
$252$		0			0
$253$	−104.674			−0.413733
$254$		0			0
$255$		0			0
$256$		0			0
$257$	69.7372	+	120.788i	0.271351	+	0.469994i	0.969208	−	0.246243i	$-0.0791962\pi$
$257$	69.7372	+	120.788i	0.271351	+	0.469994i	−0.697857	+	0.716237i	$0.745863\pi$
$258$		0			0
$259$	−390.195	−	225.279i	−1.50654	−	0.869804i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	234.380	+	135.319i	0.891178	+	0.514522i	0.874327	−	0.485336i	$-0.161303\pi$
$263$	234.380	+	135.319i	0.891178	+	0.514522i	0.0168501	+	0.999858i	$0.494636\pi$
$264$		0			0
$265$	73.3444	+	127.036i	0.276771	+	0.479382i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−176.888			−0.657577			−0.328788	−	0.944404i	$-0.606640\pi$
$269$	−176.888			−0.657577			−0.328788	+	0.944404i	$0.606640\pi$
$270$		0			0
$271$			205.187i			0.757147i	0.925571	+	0.378574i	$0.123585\pi$
$271$			205.187i			0.757147i	−0.925571	+	0.378574i	$0.876415\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	388.009	−	224.017i	1.41094	−	0.814607i
$276$		0			0
$277$	120.995	−	209.569i	0.436805	−	0.756568i	−0.560636	−	0.828062i	$-0.689443\pi$
$277$	120.995	−	209.569i	0.436805	−	0.756568i	0.997441	+	0.0714943i	$0.0227768\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−21.4562	+	37.1632i	−0.0763566	+	0.132253i	−0.901675	−	0.432414i	$-0.857662\pi$
$281$	−21.4562	+	37.1632i	−0.0763566	+	0.132253i	0.825319	+	0.564667i	$0.190995\pi$
$282$		0			0
$283$	328.185	−	189.478i	1.15966	−	0.669533i	0.208441	−	0.978035i	$-0.433161\pi$
$283$	328.185	−	189.478i	1.15966	−	0.669533i	0.951224	+	0.308502i	$0.0998277\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			162.009i			0.564492i
$288$		0			0
$289$	−254.214			−0.879634
$290$		0			0
$291$		0			0
$292$		0			0
$293$	56.2663	+	97.4561i	0.192035	+	0.332615i	0.945925	−	0.324387i	$-0.105158\pi$
$293$	56.2663	+	97.4561i	0.192035	+	0.332615i	−0.753889	+	0.657001i	$0.771825\pi$
$294$		0			0
$295$	−113.870	−	65.7428i	−0.386000	−	0.222857i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−64.2733	−	37.1082i	−0.214961	−	0.124108i
$300$		0			0
$301$	−43.4181	−	75.2024i	−0.144246	−	0.249842i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	37.3020			0.122301
$306$		0			0
$307$		−	109.964i		−	0.358189i	−0.983832	−	0.179094i	$-0.942683\pi$
$307$		−	109.964i		−	0.358189i	0.983832	−	0.179094i	$-0.0573167\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	462.400	−	266.967i	1.48682	−	0.858413i	0.486929	−	0.873442i	$-0.338117\pi$
$311$	462.400	−	266.967i	1.48682	−	0.858413i	0.999887	+	0.0150284i	$0.00478386\pi$
$312$		0			0
$313$	−78.8728	+	136.612i	−0.251990	+	0.436459i	−0.964074	−	0.265635i	$-0.914418\pi$
$313$	−78.8728	+	136.612i	−0.251990	+	0.436459i	0.712084	+	0.702095i	$0.247752\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	111.823	−	193.683i	0.352753	−	0.610987i	−0.633977	−	0.773352i	$-0.718579\pi$
$317$	111.823	−	193.683i	0.352753	−	0.610987i	0.986731	+	0.162365i	$0.0519121\pi$
$318$		0			0
$319$	−341.063	+	196.913i	−1.06916	+	0.617282i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	193.262i		−	0.598336i
$324$		0			0
$325$	317.666			0.977433
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−258.315	−	447.414i	−0.785152	−	1.35992i
$330$		0			0
$331$	177.292	+	102.360i	0.535625	+	0.309243i	0.743304	−	0.668954i	$-0.233258\pi$
$331$	177.292	+	102.360i	0.535625	+	0.309243i	−0.207679	+	0.978197i	$0.566591\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	62.4647	+	36.0640i	0.186462	+	0.107654i
$336$		0			0
$337$	251.883	+	436.275i	0.747428	+	1.29458i	0.949052	+	0.315120i	$0.102045\pi$
$337$	251.883	+	436.275i	0.747428	+	1.29458i	−0.201624	+	0.979463i	$0.564622\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−208.252			−0.610711
$342$		0			0
$343$			94.2847i			0.274883i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−256.064	+	147.839i	−0.737938	+	0.426049i	−0.821319	−	0.570469i	$-0.806761\pi$
$347$	−256.064	+	147.839i	−0.737938	+	0.426049i	0.0833813	+	0.996518i	$0.473428\pi$
$348$		0			0
$349$	29.0465	−	50.3101i	0.0832279	−	0.144155i	−0.821407	−	0.570343i	$-0.806810\pi$
$349$	29.0465	−	50.3101i	0.0832279	−	0.144155i	0.904635	+	0.426188i	$0.140144\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	250.158	−	433.286i	0.708662	−	1.22744i	−0.256692	−	0.966493i	$-0.582633\pi$
$353$	250.158	−	433.286i	0.708662	−	1.22744i	0.965354	−	0.260945i	$-0.0840341\pi$
$354$		0			0
$355$	−159.932	+	92.3370i	−0.450514	+	0.260104i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	204.499i		−	0.569636i	−0.958582	−	0.284818i	$-0.908067\pi$
$359$		−	204.499i		−	0.569636i	0.958582	−	0.284818i	$-0.0919332\pi$
$360$		0			0
$361$	−712.726			−1.97431
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−66.0894	−	114.470i	−0.181067	−	0.313617i
$366$		0			0
$367$	152.383	+	87.9782i	0.415212	+	0.239723i	0.693027	−	0.720912i	$-0.256277\pi$
$367$	152.383	+	87.9782i	0.415212	+	0.239723i	−0.277815	+	0.960635i	$0.589610\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−679.842	−	392.507i	−1.83246	−	1.05797i
$372$		0			0
$373$	−175.334	−	303.688i	−0.470065	−	0.814177i	0.529349	−	0.848404i	$-0.322436\pi$
$373$	−175.334	−	303.688i	−0.470065	−	0.814177i	−0.999414	+	0.0342271i	$0.989103\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−279.231			−0.740665
$378$		0			0
$379$			79.8445i			0.210672i	0.994437	+	0.105336i	$0.0335917\pi$
$379$			79.8445i			0.210672i	−0.994437	+	0.105336i	$0.966408\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	256.795	−	148.261i	0.670482	−	0.387103i	−0.125777	−	0.992059i	$-0.540142\pi$
$383$	256.795	−	148.261i	0.670482	−	0.387103i	0.796259	+	0.604955i	$0.206809\pi$
$384$		0			0
$385$	210.896	−	365.282i	0.547781	−	0.948784i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	63.0249	−	109.162i	0.162018	−	0.280623i	−0.773574	−	0.633705i	$-0.781533\pi$
$389$	63.0249	−	109.162i	0.162018	−	0.280623i	0.935592	+	0.353082i	$0.114866\pi$
$390$		0			0
$391$	25.3702	−	14.6475i	0.0648855	−	0.0374617i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			163.508i			0.413944i
$396$		0			0
$397$	1.66640			0.00419748			0.00209874	−	0.999998i	$-0.499332\pi$
$397$	1.66640			0.00419748			0.00209874	+	0.999998i	$0.499332\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	279.021	+	483.278i	0.695813	+	1.20518i	0.969906	+	0.243480i	$0.0782890\pi$
$401$	279.021	+	483.278i	0.695813	+	1.20518i	−0.274093	+	0.961703i	$0.588378\pi$
$402$		0			0
$403$	−127.873	−	73.8277i	−0.317304	−	0.183195i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−794.536	−	458.726i	−1.95218	−	1.12709i
$408$		0			0
$409$	−99.7341	−	172.744i	−0.243849	−	0.422358i	0.717959	−	0.696086i	$-0.245077\pi$
$409$	−99.7341	−	172.744i	−0.243849	−	0.422358i	−0.961807	+	0.273728i	$0.911743\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	703.654			1.70376
$414$		0			0
$415$			31.2925i			0.0754035i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	299.782	−	173.079i	0.715469	−	0.413076i	−0.0976136	−	0.995224i	$-0.531121\pi$
$419$	299.782	−	173.079i	0.715469	−	0.413076i	0.813083	+	0.582148i	$0.197788\pi$
$420$		0			0
$421$	−160.593	+	278.155i	−0.381456	+	0.660702i	−0.991271	−	0.131842i	$-0.957911\pi$
$421$	−160.593	+	278.155i	−0.381456	+	0.660702i	0.609814	+	0.792544i	$0.291244\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−62.6952	+	108.591i	−0.147518	+	0.255509i
$426$		0			0
$427$	−172.879	+	99.8118i	−0.404869	+	0.233751i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			734.565i			1.70433i	0.523276	+	0.852163i	$0.324710\pi$
$431$			734.565i			1.70433i	−0.523276	+	0.852163i	$0.675290\pi$
$432$		0			0
$433$	400.407			0.924729			0.462364	−	0.886690i	$-0.347001\pi$
$433$	400.407			0.924729			0.462364	+	0.886690i	$0.347001\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−81.3785	−	140.952i	−0.186221	−	0.322544i
$438$		0			0
$439$	−143.545	−	82.8758i	−0.326982	−	0.188783i	0.327518	−	0.944845i	$-0.393788\pi$
$439$	−143.545	−	82.8758i	−0.326982	−	0.188783i	−0.654500	+	0.756062i	$0.727121\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	492.357	+	284.262i	1.11141	+	0.641675i	0.939195	−	0.343383i	$-0.111573\pi$
$443$	492.357	+	284.262i	1.11141	+	0.641675i	0.172219	+	0.985059i	$0.444906\pi$
$444$		0			0
$445$	41.5251	+	71.9236i	0.0933149	+	0.161626i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	183.191			0.407999			0.203999	−	0.978971i	$-0.434606\pi$
$449$	183.191			0.407999			0.203999	+	0.978971i	$0.434606\pi$
$450$		0			0
$451$			329.892i			0.731468i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	258.993	−	149.529i	0.569215	−	0.328636i
$456$		0			0
$457$	194.840	−	337.473i	0.426346	−	0.738453i	−0.570199	−	0.821507i	$-0.693134\pi$
$457$	194.840	−	337.473i	0.426346	−	0.738453i	0.996545	+	0.0830536i	$0.0264673\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	234.336	−	405.883i	0.508322	−	0.880439i	−0.491632	−	0.870803i	$-0.663599\pi$
$461$	234.336	−	405.883i	0.508322	−	0.880439i	0.999954	−	0.00963620i	$-0.00306735\pi$
$462$		0			0
$463$	381.289	−	220.137i	0.823518	−	0.475458i	−0.0281101	−	0.999605i	$-0.508949\pi$
$463$	381.289	−	220.137i	0.823518	−	0.475458i	0.851628	+	0.524146i	$0.175616\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			232.287i			0.497403i	0.968580	+	0.248701i	$0.0800038\pi$
$467$			232.287i			0.497403i	−0.968580	+	0.248701i	$0.919996\pi$
$468$		0			0
$469$	−385.997			−0.823022
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−88.4104	−	153.131i	−0.186914	−	0.323745i
$474$		0			0
$475$	603.311	+	348.322i	1.27013	+	0.733308i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	54.7737	+	31.6236i	0.114350	+	0.0660200i	0.556084	−	0.831126i	$-0.312303\pi$
$479$	54.7737	+	31.6236i	0.114350	+	0.0660200i	−0.441734	+	0.897146i	$0.645637\pi$
$480$		0			0
$481$	−325.246	−	563.343i	−0.676188	−	1.17119i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−61.4936			−0.126791
$486$		0			0
$487$			65.1317i			0.133741i	0.997762	+	0.0668704i	$0.0213014\pi$
$487$			65.1317i			0.133741i	−0.997762	+	0.0668704i	$0.978699\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	593.177	−	342.471i	1.20810	−	0.697496i	0.245755	−	0.969332i	$-0.420964\pi$
$491$	593.177	−	342.471i	1.20810	−	0.697496i	0.962344	+	0.271835i	$0.0876306\pi$
$492$		0			0
$493$	55.1096	−	95.4526i	0.111784	−	0.193616i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	494.147	−	855.888i	0.994259	−	1.72211i
$498$		0			0
$499$	−233.586	+	134.861i	−0.468108	+	0.270262i	−0.715447	−	0.698667i	$-0.753777\pi$
$499$	−233.586	+	134.861i	−0.468108	+	0.270262i	0.247340	+	0.968929i	$0.420444\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			182.143i			0.362114i	0.983473	+	0.181057i	$0.0579518\pi$
$503$			182.143i			0.362114i	−0.983473	+	0.181057i	$0.942048\pi$
$504$		0			0
$505$	217.072			0.429846
$506$		0			0
$507$		0			0
$508$		0			0
$509$	121.872	+	211.088i	0.239433	+	0.414711i	0.960552	−	0.278101i	$-0.0897050\pi$
$509$	121.872	+	211.088i	0.239433	+	0.414711i	−0.721119	+	0.692812i	$0.756372\pi$
$510$		0			0
$511$	612.595	+	353.682i	1.19882	+	0.692136i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	93.4413	+	53.9484i	0.181439	+	0.104754i
$516$		0			0
$517$	−525.995	−	911.050i	−1.01740	−	1.76219i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	698.539			1.34077			0.670383	−	0.742016i	$-0.266130\pi$
$521$	698.539			1.34077			0.670383	+	0.742016i	$0.266130\pi$
$522$		0			0
$523$		−	76.4187i		−	0.146116i	−0.997328	−	0.0730580i	$-0.976724\pi$
$523$		−	76.4187i		−	0.146116i	0.997328	−	0.0730580i	$-0.0232758\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	50.4747	−	29.1416i	0.0957775	−	0.0552972i
$528$		0			0
$529$	−252.165	+	436.762i	−0.476681	+	0.825637i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−116.950	+	202.564i	−0.219419	+	0.380045i
$534$		0			0
$535$	149.876	−	86.5308i	0.280142	−	0.161740i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			1224.61i			2.27201i
$540$		0			0
$541$	−319.631			−0.590816			−0.295408	−	0.955371i	$-0.595456\pi$
$541$	−319.631			−0.590816			−0.295408	+	0.955371i	$0.595456\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−153.593	−	266.030i	−0.281821	−	0.488129i
$546$		0			0
$547$	−21.7181	−	12.5389i	−0.0397040	−	0.0229231i	0.480017	−	0.877259i	$-0.340631\pi$
$547$	−21.7181	−	12.5389i	−0.0397040	−	0.0229231i	−0.519721	+	0.854336i	$0.673964\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−530.315	−	306.178i	−0.962459	−	0.555676i
$552$		0			0
$553$	−437.511	−	757.792i	−0.791160	−	1.37033i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−993.726			−1.78407			−0.892035	−	0.451967i	$-0.850722\pi$
$557$	−993.726			−1.78407			−0.892035	+	0.451967i	$0.850722\pi$
$558$		0			0
$559$		−	125.370i		−	0.224275i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	792.494	−	457.546i	1.40763	−	0.812693i	0.412467	−	0.910972i	$-0.364667\pi$
$563$	792.494	−	457.546i	1.40763	−	0.812693i	0.995159	+	0.0982790i	$0.0313338\pi$
$564$		0			0
$565$	49.1542	−	85.1377i	0.0869987	−	0.150686i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	86.7437	−	150.245i	0.152449	−	0.264050i	−0.779678	−	0.626181i	$-0.784617\pi$
$569$	86.7437	−	150.245i	0.152449	−	0.264050i	0.932127	+	0.362131i	$0.117951\pi$
$570$		0			0
$571$	−516.243	+	298.053i	−0.904103	+	0.521984i	−0.878529	−	0.477689i	$-0.841475\pi$
$571$	−516.243	+	298.053i	−0.904103	+	0.521984i	−0.0255737	+	0.999673i	$0.508141\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			105.598i			0.183649i
$576$		0			0
$577$	−121.875			−0.211222			−0.105611	−	0.994408i	$-0.533680\pi$
$577$	−121.875			−0.211222			−0.105611	+	0.994408i	$0.533680\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−83.7317	−	145.028i	−0.144117	−	0.249617i
$582$		0			0
$583$	−1384.33	−	799.245i	−2.37450	−	1.37092i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−281.323	−	162.422i	−0.479256	−	0.276698i	0.240851	−	0.970562i	$-0.422574\pi$
$587$	−281.323	−	162.422i	−0.479256	−	0.276698i	−0.720106	+	0.693864i	$0.755907\pi$
$588$		0			0
$589$	−161.905	−	280.427i	−0.274881	−	0.476107i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−785.829			−1.32518			−0.662588	−	0.748984i	$-0.730542\pi$
$593$	−785.829			−1.32518			−0.662588	+	0.748984i	$0.730542\pi$
$594$		0			0
$595$			118.046i			0.198396i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−623.633	+	360.054i	−1.04112	+	0.601093i	−0.920151	−	0.391563i	$-0.871934\pi$
$599$	−623.633	+	360.054i	−1.04112	+	0.601093i	−0.120972	+	0.992656i	$0.538601\pi$
$600$		0			0
$601$	283.454	−	490.956i	0.471637	−	0.816899i	−0.527837	−	0.849346i	$-0.676997\pi$
$601$	283.454	−	490.956i	0.471637	−	0.816899i	0.999473	+	0.0324471i	$0.0103300\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	312.436	−	541.155i	0.516423	−	0.894471i
$606$		0			0
$607$	68.5352	−	39.5688i	0.112908	−	0.0651875i	−0.442483	−	0.896777i	$-0.645902\pi$
$607$	68.5352	−	39.5688i	0.112908	−	0.0651875i	0.555391	+	0.831590i	$0.312569\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	745.883i		−	1.22076i
$612$		0			0
$613$	−951.491			−1.55219			−0.776094	−	0.630617i	$-0.782802\pi$
$613$	−951.491			−1.55219			−0.776094	+	0.630617i	$0.782802\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−152.435	−	264.025i	−0.247059	−	0.427918i	0.715650	−	0.698459i	$-0.246131\pi$
$617$	−152.435	−	264.025i	−0.247059	−	0.427918i	−0.962708	+	0.270541i	$0.912797\pi$
$618$		0			0
$619$	−44.3755	−	25.6202i	−0.0716891	−	0.0413897i	0.463727	−	0.885978i	$-0.346512\pi$
$619$	−44.3755	−	25.6202i	−0.0716891	−	0.0413897i	−0.535416	+	0.844588i	$0.679845\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−384.904	−	222.224i	−0.617823	−	0.356700i
$624$		0			0
$625$	−179.244	−	310.460i	−0.286791	−	0.496737i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	256.765			0.408212
$630$		0			0
$631$		−	316.484i		−	0.501560i	−0.968044	−	0.250780i	$-0.919313\pi$
$631$		−	316.484i		−	0.501560i	0.968044	−	0.250780i	$-0.0806871\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−33.7335	+	19.4760i	−0.0531236	+	0.0306709i
$636$		0			0
$637$	−434.139	+	751.951i	−0.681537	+	1.18046i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	608.032	−	1053.14i	0.948568	−	1.64297i	0.200124	−	0.979770i	$-0.435865\pi$
$641$	608.032	−	1053.14i	0.948568	−	1.64297i	0.748444	−	0.663198i	$-0.230801\pi$
$642$		0			0
$643$	696.018	−	401.846i	1.08245	−	0.624955i	0.150896	−	0.988550i	$-0.451784\pi$
$643$	696.018	−	401.846i	1.08245	−	0.624955i	0.931557	+	0.363595i	$0.118451\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	1091.43i		−	1.68690i	−0.537205	−	0.843452i	$-0.680520\pi$
$647$		−	1091.43i		−	1.68690i	0.537205	−	0.843452i	$-0.319480\pi$
$648$		0			0
$649$	1432.82			2.20773
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−25.8433	−	44.7619i	−0.0395762	−	0.0685480i	0.845559	−	0.533882i	$-0.179267\pi$
$653$	−25.8433	−	44.7619i	−0.0395762	−	0.0685480i	−0.885135	+	0.465334i	$0.845934\pi$
$654$		0			0
$655$	−106.865	−	61.6984i	−0.163152	−	0.0941961i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−440.684	−	254.429i	−0.668716	−	0.386083i	0.126874	−	0.991919i	$-0.459506\pi$
$659$	−440.684	−	254.429i	−0.668716	−	0.386083i	−0.795590	+	0.605836i	$0.792839\pi$
$660$		0			0
$661$	163.945	+	283.961i	0.248026	+	0.429593i	0.962978	−	0.269580i	$-0.0868849\pi$
$661$	163.945	+	283.961i	0.248026	+	0.429593i	−0.714952	+	0.699173i	$0.753552\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	655.838			0.986223
$666$		0			0
$667$		−	92.8218i		−	0.139163i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−352.026	+	203.242i	−0.524629	+	0.302895i
$672$		0			0
$673$	−341.446	+	591.401i	−0.507349	+	0.878754i	0.492615	+	0.870247i	$0.336041\pi$
$673$	−341.446	+	591.401i	−0.507349	+	0.878754i	−0.999964	+	0.00850630i	$0.997292\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	178.474	−	309.125i	0.263624	−	0.456611i	−0.703578	−	0.710618i	$-0.748415\pi$
$677$	178.474	−	309.125i	0.263624	−	0.456611i	0.967202	+	0.254007i	$0.0817488\pi$
$678$		0			0
$679$	284.998	−	164.543i	0.419731	−	0.242332i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			1099.06i			1.60917i	0.593839	+	0.804584i	$0.297612\pi$
$683$			1099.06i			1.60917i	−0.593839	+	0.804584i	$0.702388\pi$
$684$		0			0
$685$	−21.2008			−0.0309500
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−566.681	−	981.521i	−0.822469	−	1.42456i
$690$		0			0
$691$	−823.701	−	475.564i	−1.19204	−	0.688226i	−0.233273	−	0.972411i	$-0.574944\pi$
$691$	−823.701	−	475.564i	−1.19204	−	0.688226i	−0.958769	+	0.284186i	$0.908277\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−349.570	−	201.824i	−0.502978	−	0.290394i
$696$		0			0
$697$	−46.1631	−	79.9569i	−0.0662312	−	0.114716i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	99.5247			0.141975			0.0709876	−	0.997477i	$-0.477385\pi$
$701$	99.5247			0.141975			0.0709876	+	0.997477i	$0.477385\pi$
$702$		0			0
$703$		−	1426.53i		−	2.02921i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1006.04	+	580.838i	−1.42297	+	0.821553i
$708$		0			0
$709$	631.369	−	1093.56i	0.890506	−	1.54240i	0.0512359	−	0.998687i	$-0.483684\pi$
$709$	631.369	−	1093.56i	0.890506	−	1.54240i	0.839270	−	0.543715i	$-0.182983\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	24.5418	−	42.5076i	0.0344204	−	0.0596180i
$714$		0			0
$715$	527.375	−	304.480i	0.737587	−	0.425846i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			875.064i			1.21706i	0.793532	+	0.608528i	$0.208240\pi$
$719$			875.064i			1.21706i	−0.793532	+	0.608528i	$0.791760\pi$
$720$		0			0
$721$	−577.416			−0.800854
$722$		0			0
$723$		0			0
$724$		0			0
$725$	198.651	+	344.073i	0.274001	+	0.474584i
$726$		0			0
$727$	−129.425	−	74.7236i	−0.178026	−	0.102784i	0.408339	−	0.912830i	$-0.366108\pi$
$727$	−129.425	−	74.7236i	−0.178026	−	0.102784i	−0.586365	+	0.810047i	$0.699442\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	42.8565	+	24.7432i	0.0586273	+	0.0338485i
$732$		0			0
$733$	114.030	+	197.506i	0.155566	+	0.269449i	0.933265	−	0.359188i	$-0.116946\pi$
$733$	114.030	+	197.506i	0.155566	+	0.269449i	−0.777699	+	0.628637i	$0.783613\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−785.989			−1.06647
$738$		0			0
$739$		−	283.397i		−	0.383487i	−0.981445	−	0.191744i	$-0.938586\pi$
$739$		−	283.397i		−	0.383487i	0.981445	−	0.191744i	$-0.0614142\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	755.841	−	436.385i	1.01728	−	0.587328i	0.103967	−	0.994581i	$-0.466846\pi$
$743$	755.841	−	436.385i	1.01728	−	0.587328i	0.913316	+	0.407253i	$0.133513\pi$
$744$		0			0
$745$	−157.188	+	272.257i	−0.210990	+	0.365446i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−463.075	+	802.069i	−0.618257	+	1.07085i
$750$		0			0
$751$	699.693	−	403.968i	0.931682	−	0.537907i	0.0443390	−	0.999017i	$-0.485882\pi$
$751$	699.693	−	403.968i	0.931682	−	0.537907i	0.887343	+	0.461110i	$0.152549\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	215.188i		−	0.285017i
$756$		0			0
$757$	−447.804			−0.591551			−0.295775	−	0.955258i	$-0.595578\pi$
$757$	−447.804			−0.591551			−0.295775	+	0.955258i	$0.595578\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	650.854	+	1127.31i	0.855261	+	1.48136i	0.876403	+	0.481579i	$0.159937\pi$
$761$	650.854	+	1127.31i	0.855261	+	1.48136i	−0.0211418	+	0.999776i	$0.506730\pi$
$762$		0			0
$763$	1423.68	+	821.961i	1.86589	+	1.07727i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	879.794	+	507.949i	1.14706	+	0.662255i
$768$		0			0
$769$	58.7699	+	101.792i	0.0764238	+	0.132370i	0.901705	−	0.432353i	$-0.142316\pi$
$769$	58.7699	+	101.792i	0.0764238	+	0.132370i	−0.825281	+	0.564723i	$0.808983\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	748.233			0.967960			0.483980	−	0.875079i	$-0.339191\pi$
$773$	748.233			0.967960			0.483980	+	0.875079i	$0.339191\pi$
$774$		0			0
$775$			210.090i			0.271084i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−444.224	+	256.473i	−0.570249	+	0.329233i
$780$		0			0
$781$	1006.21	−	1742.81i	1.28836	−	2.23150i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−91.0444	+	157.694i	−0.115980	+	0.200883i
$786$		0			0
$787$	−552.393	+	318.924i	−0.701897	+	0.405240i	−0.808054	−	0.589109i	$-0.799479\pi$
$787$	−552.393	+	318.924i	−0.701897	+	0.405240i	0.106157	+	0.994349i	$0.466145\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			526.104i			0.665112i
$792$		0			0
$793$	−288.206			−0.363438
$794$		0			0
$795$		0			0
$796$		0			0
$797$	85.2936	+	147.733i	0.107018	+	0.185361i	0.914561	−	0.404448i	$-0.132536\pi$
$797$	85.2936	+	147.733i	0.107018	+	0.185361i	−0.807543	+	0.589809i	$0.799203\pi$
$798$		0			0
$799$	254.974	+	147.209i	0.319116	+	0.184242i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1247.40	+	720.186i	1.55342	+	0.896869i
$804$		0			0
$805$	49.7065	+	86.0942i	0.0617472	+	0.106949i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	969.433			1.19831			0.599155	−	0.800633i	$-0.295503\pi$
$809$	969.433			1.19831			0.599155	+	0.800633i	$0.295503\pi$
$810$		0			0
$811$		−	230.645i		−	0.284396i	−0.989838	−	0.142198i	$-0.954583\pi$
$811$		−	230.645i		−	0.284396i	0.989838	−	0.142198i	$-0.0454170\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−252.920	+	146.024i	−0.310332	+	0.179170i
$816$		0			0
$817$	137.468	−	238.102i	0.168260	−	0.291435i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−627.592	+	1087.02i	−0.764424	+	1.32402i	0.176126	+	0.984368i	$0.443643\pi$
$821$	−627.592	+	1087.02i	−0.764424	+	1.32402i	−0.940551	+	0.339654i	$0.889690\pi$
$822$		0			0
$823$	−344.755	+	199.044i	−0.418900	+	0.241852i	−0.694606	−	0.719390i	$-0.744421\pi$
$823$	−344.755	+	199.044i	−0.418900	+	0.241852i	0.275707	+	0.961242i	$0.411088\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	406.686i		−	0.491760i	−0.969300	−	0.245880i	$-0.920923\pi$
$827$		−	406.686i		−	0.491760i	0.969300	−	0.245880i	$-0.0790770\pi$
$828$		0			0
$829$	−1333.85			−1.60899			−0.804494	−	0.593961i	$-0.797563\pi$
$829$	−1333.85			−1.60899			−0.804494	+	0.593961i	$0.797563\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−171.365	−	296.813i	−0.205721	−	0.356318i
$834$		0			0
$835$	140.786	+	81.2831i	0.168607	+	0.0973450i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	285.181	+	164.649i	0.339905	+	0.196244i	0.660230	−	0.751063i	$-0.270459\pi$
$839$	285.181	+	164.649i	0.339905	+	0.196244i	−0.320325	+	0.947308i	$0.603792\pi$
$840$		0			0
$841$	245.884	+	425.884i	0.292371	+	0.506402i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	104.936			0.124185
$846$		0			0
$847$			3344.04i			3.94810i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	187.266	−	108.118i	0.220054	−	0.127048i
$852$		0			0
$853$	−245.911	+	425.931i	−0.288290	+	0.499332i	−0.973402	−	0.229105i	$-0.926420\pi$
$853$	−245.911	+	425.931i	−0.288290	+	0.499332i	0.685112	+	0.728438i	$0.259753\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−293.484	+	508.329i	−0.342455	+	0.593149i	−0.984888	−	0.173192i	$-0.944592\pi$
$857$	−293.484	+	508.329i	−0.342455	+	0.593149i	0.642433	+	0.766342i	$0.277925\pi$
$858$		0			0
$859$	221.512	−	127.890i	0.257872	−	0.148883i	−0.365491	−	0.930815i	$-0.619099\pi$
$859$	221.512	−	127.890i	0.257872	−	0.148883i	0.623364	+	0.781932i	$0.285766\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			1123.57i			1.30193i	0.759107	+	0.650966i	$0.225636\pi$
$863$			1123.57i			1.30193i	−0.759107	+	0.650966i	$0.774364\pi$
$864$		0			0
$865$	509.277			0.588760
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−890.885	−	1543.06i	−1.02518	−	1.77567i
$870$		0			0
$871$	−482.621	−	278.641i	−0.554100	−	0.319910i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−801.838	−	462.941i	−0.916386	−	0.529076i
$876$		0			0
$877$	498.332	+	863.136i	0.568223	+	0.984192i	0.996742	+	0.0806586i	$0.0257024\pi$
$877$	498.332	+	863.136i	0.568223	+	0.984192i	−0.428518	+	0.903533i	$0.640964\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	804.052			0.912659			0.456329	−	0.889811i	$-0.349164\pi$
$881$	804.052			0.912659			0.456329	+	0.889811i	$0.349164\pi$
$882$		0			0
$883$		−	852.030i		−	0.964926i	−0.875916	−	0.482463i	$-0.839742\pi$
$883$		−	852.030i		−	0.964926i	0.875916	−	0.482463i	$-0.160258\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	588.730	−	339.904i	0.663732	−	0.383206i	−0.129965	−	0.991519i	$-0.541487\pi$
$887$	588.730	−	339.904i	0.663732	−	0.383206i	0.793697	+	0.608313i	$0.208153\pi$
$888$		0			0
$889$	104.227	−	180.527i	0.117241	−	0.203067i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	817.863	−	1416.58i	0.915860	−	1.58632i
$894$		0			0
$895$	360.978	−	208.411i	0.403328	−	0.232861i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	184.671i		−	0.205419i
$900$		0			0
$901$	447.366			0.496522
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−321.800	−	557.374i	−0.355580	−	0.615883i
$906$		0			0
$907$	1033.20	+	596.521i	1.13914	+	0.657685i	0.946219	−	0.323528i	$-0.104869\pi$
$907$	1033.20	+	596.521i	1.13914	+	0.657685i	0.192926	+	0.981213i	$0.438202\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−466.555	−	269.365i	−0.512135	−	0.295681i	0.221576	−	0.975143i	$-0.428880\pi$
$911$	−466.555	−	269.365i	−0.512135	−	0.295681i	−0.733711	+	0.679462i	$0.762213\pi$
$912$		0			0
$913$	−170.499	−	295.313i	−0.186746	−	0.323454i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	660.366			0.720137
$918$		0			0
$919$			1195.64i			1.30102i	0.759498	+	0.650509i	$0.225445\pi$
$919$			1195.64i			1.30102i	−0.759498	+	0.650509i	$0.774555\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1235.69	−	713.424i	1.33877	−	0.772940i
$924$		0			0
$925$	−462.774	+	801.549i	−0.500297	+	0.866539i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−706.854	+	1224.31i	−0.760876	+	1.31788i	0.181523	+	0.983387i	$0.441897\pi$
$929$	−706.854	+	1224.31i	−0.760876	+	1.31788i	−0.942400	+	0.334489i	$0.891436\pi$
$930$		0			0
$931$	−1649.03	+	952.070i	−1.77125	+	1.02263i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			240.371i			0.257082i
$936$		0			0
$937$	−1275.33			−1.36108			−0.680541	−	0.732710i	$-0.738255\pi$
$937$	−1275.33			−1.36108			−0.680541	+	0.732710i	$0.738255\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−275.421	−	477.043i	−0.292690	−	0.506954i	0.681755	−	0.731580i	$-0.261217\pi$
$941$	−275.421	−	477.043i	−0.292690	−	0.506954i	−0.974445	+	0.224627i	$0.927884\pi$
$942$		0			0
$943$	−67.3362	−	38.8766i	−0.0714064	−	0.0412265i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−696.651	−	402.212i	−0.735640	−	0.424722i	0.0848419	−	0.996394i	$-0.472961\pi$
$947$	−696.651	−	402.212i	−0.735640	−	0.424722i	−0.820482	+	0.571672i	$0.806295\pi$
$948$		0			0
$949$	510.627	+	884.432i	0.538069	+	0.931962i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−721.612			−0.757200			−0.378600	−	0.925560i	$-0.623594\pi$
$953$	−721.612			−0.757200			−0.378600	+	0.925560i	$0.623594\pi$
$954$		0			0
$955$			255.383i			0.267417i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	98.2568	−	56.7286i	0.102458	−	0.0591539i
$960$		0			0
$961$	−431.674	+	747.680i	−0.449192	+	0.778023i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−169.461	+	293.515i	−0.175607	+	0.304161i
$966$		0			0
$967$	1030.73	−	595.091i	1.06590	−	0.615400i	0.138844	−	0.990314i	$-0.455661\pi$
$967$	1030.73	−	595.091i	1.06590	−	0.615400i	0.927059	+	0.374915i	$0.122328\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			1024.09i			1.05467i	0.849657	+	0.527335i	$0.176809\pi$
$971$			1024.09i			1.05467i	−0.849657	+	0.527335i	$0.823191\pi$
$972$		0			0
$973$	2160.15			2.22009
$974$		0			0
$975$		0			0
$976$		0			0
$977$	641.906	+	1111.81i	0.657018	+	1.13799i	0.981384	+	0.192056i	$0.0615156\pi$
$977$	641.906	+	1111.81i	0.657018	+	1.13799i	−0.324366	+	0.945932i	$0.605151\pi$
$978$		0			0
$979$	−783.762	−	452.505i	−0.800574	−	0.462212i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	103.885	+	59.9782i	0.105682	+	0.0610154i	0.551909	−	0.833904i	$-0.313899\pi$
$983$	103.885	+	59.9782i	0.105682	+	0.0610154i	−0.446227	+	0.894920i	$0.647233\pi$
$984$		0			0
$985$	−298.774	−	517.492i	−0.303324	−	0.525372i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	41.6753			0.0421389
$990$		0			0
$991$		−	549.882i		−	0.554876i	−0.960744	−	0.277438i	$-0.910515\pi$
$991$		−	549.882i		−	0.554876i	0.960744	−	0.277438i	$-0.0894853\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−520.755	+	300.658i	−0.523372	+	0.302169i
$996$		0			0
$997$	20.2764	−	35.1198i	0.0203374	−	0.0352254i	−0.855678	−	0.517509i	$-0.826859\pi$
$997$	20.2764	−	35.1198i	0.0203374	−	0.0352254i	0.876015	+	0.482284i	$0.160193\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.3.o.h.127.4		20
3.2	odd	2		576.3.o.h.511.7		20
4.3	odd	2	inner	1728.3.o.h.127.3		20
8.3	odd	2		864.3.o.b.127.7		20
8.5	even	2		864.3.o.b.127.8		20
9.4	even	3	inner	1728.3.o.h.1279.3		20
9.5	odd	6		576.3.o.h.319.4		20
12.11	even	2		576.3.o.h.511.4		20
24.5	odd	2		288.3.o.b.223.4	yes	20
24.11	even	2		288.3.o.b.223.7	yes	20
36.23	even	6		576.3.o.h.319.7		20
36.31	odd	6	inner	1728.3.o.h.1279.4		20
72.5	odd	6		288.3.o.b.31.7	yes	20
72.11	even	6		2592.3.g.g.2431.8		10
72.13	even	6		864.3.o.b.415.7		20
72.29	odd	6		2592.3.g.g.2431.7		10
72.43	odd	6		2592.3.g.h.2431.4		10
72.59	even	6		288.3.o.b.31.4	✓	20
72.61	even	6		2592.3.g.h.2431.3		10
72.67	odd	6		864.3.o.b.415.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.3.o.b.31.4	✓	20	72.59	even	6
288.3.o.b.31.7	yes	20	72.5	odd	6
288.3.o.b.223.4	yes	20	24.5	odd	2
288.3.o.b.223.7	yes	20	24.11	even	2
576.3.o.h.319.4		20	9.5	odd	6
576.3.o.h.319.7		20	36.23	even	6
576.3.o.h.511.4		20	12.11	even	2
576.3.o.h.511.7		20	3.2	odd	2
864.3.o.b.127.7		20	8.3	odd	2
864.3.o.b.127.8		20	8.5	even	2
864.3.o.b.415.7		20	72.13	even	6
864.3.o.b.415.8		20	72.67	odd	6
1728.3.o.h.127.3		20	4.3	odd	2	inner
1728.3.o.h.127.4		20	1.1	even	1	trivial
1728.3.o.h.1279.3		20	9.4	even	3	inner
1728.3.o.h.1279.4		20	36.31	odd	6	inner
2592.3.g.g.2431.7		10	72.29	odd	6
2592.3.g.g.2431.8		10	72.11	even	6
2592.3.g.h.2431.3		10	72.61	even	6
2592.3.g.h.2431.4		10	72.43	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1728.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.966952 - 1.67481i) q^{5} +(8.96285 + 5.17470i) q^{7} +O(q^{10})\)	\(q+(-0.966952 - 1.67481i) q^{5} +(8.96285 + 5.17470i) q^{7} +(18.2506 + 10.5370i) q^{11} +(7.47096 + 12.9401i) q^{13} -5.89794 q^{17} +32.7678i q^{19} +(-4.30154 + 2.48349i) q^{23} +(10.6300 - 18.4117i) q^{25} +(-9.34387 + 16.1841i) q^{29} +(-8.55802 + 4.94098i) q^{31} -20.0147i q^{35} -43.5347 q^{37} +(7.82699 + 13.5567i) q^{41} +(-7.26635 - 4.19523i) q^{43} +(-43.2309 - 24.9594i) q^{47} +(29.0551 + 50.3249i) q^{49} -75.8512 q^{53} -40.7551i q^{55} +(58.8809 - 33.9949i) q^{59} +(-9.64421 + 16.7043i) q^{61} +(14.4481 - 25.0249i) q^{65} +(-32.2998 + 18.6483i) q^{67} -95.4928i q^{71} +68.3482 q^{73} +(109.052 + 188.883i) q^{77} +(-73.2208 - 42.2741i) q^{79} +(-14.0131 - 8.09049i) q^{83} +(5.70303 + 9.87793i) q^{85} -42.9444 q^{89} +154.640i q^{91} +(54.8798 - 31.6848i) q^{95} +(15.8988 - 27.5376i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 14 q^{5}+O(q^{10}) \) 20 * q + 14 * q^5	\( 20 q + 14 q^{5} - 26 q^{13} - 72 q^{17} + 36 q^{25} - 134 q^{29} - 96 q^{37} + 26 q^{41} + 348 q^{49} - 192 q^{53} - 386 q^{61} + 106 q^{65} - 168 q^{73} + 58 q^{77} - 192 q^{85} + 240 q^{89} + 374 q^{97}+O(q^{100}) \) 20 * q + 14 * q^5 - 26 * q^13 - 72 * q^17 + 36 * q^25 - 134 * q^29 - 96 * q^37 + 26 * q^41 + 348 * q^49 - 192 * q^53 - 386 * q^61 + 106 * q^65 - 168 * q^73 + 58 * q^77 - 192 * q^85 + 240 * q^89 + 374 * q^97

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