LMFDB - Embedded newform 1764.2.e.j.1079.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1079,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1764.1079");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.e (of order $2$, degree $1$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$16$
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} - 8x^{14} + 49x^{12} - 104x^{10} + 160x^{8} - 104x^{6} + 49x^{4} - 8x^{2} + 1 $ x^16 - 8x^14 + 49x^12 - 104x^10 + 160x^8 - 104x^6 + 49x^4 - 8*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1079.4
Root			$2.04058 + 1.17813i$ of defining polynomial
Character	$\chi$	$=$	1764.1079
Dual form			1764.2.e.j.1079.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39033 + 0.258819i) q^{2} +(1.86603 - 0.719687i) q^{4} +0.732051i q^{5} +(-2.40812 + 1.48356i) q^{8} +O(q^{10})$	\(q+(-1.39033 + 0.258819i) q^{2} +(1.86603 - 0.719687i) q^{4} +0.732051i q^{5} +(-2.40812 + 1.48356i) q^{8} +(-0.189469 - 1.01779i) q^{10} -2.03558 q^{11} +1.41421 q^{13} +(2.96410 - 2.68591i) q^{16} -4.19615i q^{17} +5.56131i q^{19} +(0.526847 + 1.36603i) q^{20} +(2.83013 - 0.526847i) q^{22} -2.03558 q^{23} +4.46410 q^{25} +(-1.96622 + 0.366025i) q^{26} +5.27792i q^{29} -9.63248i q^{31} +(-3.42591 + 4.50146i) q^{32} +(1.08604 + 5.83403i) q^{34} +3.46410 q^{37} +(-1.43937 - 7.73205i) q^{38} +(-1.08604 - 1.76287i) q^{40} +8.73205i q^{41} +7.86488i q^{43} +(-3.79845 + 1.46498i) q^{44} +(2.83013 - 0.526847i) q^{46} +10.7436 q^{47} +(-6.20657 + 1.15539i) q^{50} +(2.63896 - 1.01779i) q^{52} +9.14162i q^{53} -1.49015i q^{55} +(-1.36603 - 7.33804i) q^{58} -4.98614 q^{59} -9.41902 q^{61} +(2.49307 + 13.3923i) q^{62} +(3.59808 - 7.14520i) q^{64} +1.03528i q^{65} +2.87875i q^{67} +(-3.01992 - 7.83013i) q^{68} +9.08704 q^{71} +1.69161 q^{73} +(-4.81624 + 0.896575i) q^{74} +(4.00240 + 10.3776i) q^{76} +4.98614i q^{79} +(1.96622 + 2.16987i) q^{80} +(-2.26002 - 12.1404i) q^{82} -13.6224 q^{83} +3.07180 q^{85} +(-2.03558 - 10.9348i) q^{86} +(4.90192 - 3.01992i) q^{88} -8.73205i q^{89} +(-3.79845 + 1.46498i) q^{92} +(-14.9372 + 2.78066i) q^{94} -4.07116 q^{95} +15.0759 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4}+O(q^{10}) $ 16 * q + 16 * q^4	$ 16 q + 16 q^{4} - 8 q^{16} - 24 q^{22} + 16 q^{25} - 24 q^{46} - 8 q^{58} + 16 q^{64} + 160 q^{85} + 120 q^{88}+O(q^{100}) $ 16 * q + 16 * q^4 - 8 * q^16 - 24 * q^22 + 16 * q^25 - 24 * q^46 - 8 * q^58 + 16 * q^64 + 160 * q^85 + 120 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.39033	+	0.258819i	−0.983111	+	0.183013i
$2$	−1.39033	+	0.258819i	−0.983111	+	0.183013i
$3$		0			0
$3$		0			0
$4$	1.86603	−	0.719687i	0.933013	−	0.359843i
$5$			0.732051i			0.327383i	0.986512	+	0.163692i	$0.0523402\pi$
$5$			0.732051i			0.327383i	−0.986512	+	0.163692i	$0.947660\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−2.40812	+	1.48356i	−0.851399	+	0.524519i
$9$		0			0
$10$	−0.189469	−	1.01779i	−0.0599153	−	0.321854i
$11$	−2.03558			−0.613751			−0.306876	−	0.951750i	$-0.599284\pi$
$11$	−2.03558			−0.613751			−0.306876	+	0.951750i	$0.599284\pi$
$12$		0			0
$13$	1.41421			0.392232			0.196116	−	0.980581i	$-0.437167\pi$
$13$	1.41421			0.392232			0.196116	+	0.980581i	$0.437167\pi$
$14$		0			0
$15$		0			0
$16$	2.96410	−	2.68591i	0.741025	−	0.671477i
$17$		−	4.19615i		−	1.01772i	−0.860850	−	0.508858i	$-0.830068\pi$
$17$		−	4.19615i		−	1.01772i	0.860850	−	0.508858i	$-0.169932\pi$
$18$		0			0
$19$			5.56131i			1.27585i	0.770097	+	0.637926i	$0.220208\pi$
$19$			5.56131i			1.27585i	−0.770097	+	0.637926i	$0.779792\pi$
$20$	0.526847	+	1.36603i	0.117807	+	0.305453i
$21$		0			0
$22$	2.83013	−	0.526847i	0.603385	−	0.112324i
$23$	−2.03558			−0.424448			−0.212224	−	0.977221i	$-0.568071\pi$
$23$	−2.03558			−0.424448			−0.212224	+	0.977221i	$0.568071\pi$
$24$		0			0
$25$	4.46410			0.892820
$26$	−1.96622	+	0.366025i	−0.385608	+	0.0717835i
$27$		0			0
$28$		0			0
$29$			5.27792i			0.980085i	0.871699	+	0.490042i	$0.163019\pi$
$29$			5.27792i			0.980085i	−0.871699	+	0.490042i	$0.836981\pi$
$30$		0			0
$31$		−	9.63248i		−	1.73004i	−0.501734	−	0.865022i	$-0.667304\pi$
$31$		−	9.63248i		−	1.73004i	0.501734	−	0.865022i	$-0.332696\pi$
$32$	−3.42591	+	4.50146i	−0.605621	+	0.795753i
$33$		0			0
$34$	1.08604	+	5.83403i	0.186255	+	1.00053i
$35$		0			0
$36$		0			0
$37$	3.46410			0.569495			0.284747	−	0.958603i	$-0.408090\pi$
$37$	3.46410			0.569495			0.284747	+	0.958603i	$0.408090\pi$
$38$	−1.43937	−	7.73205i	−0.233497	−	1.25430i
$39$		0			0
$40$	−1.08604	−	1.76287i	−0.171719	−	0.278734i
$41$			8.73205i			1.36372i	0.731484	+	0.681859i	$0.238828\pi$
$41$			8.73205i			1.36372i	−0.731484	+	0.681859i	$0.761172\pi$
$42$		0			0
$43$			7.86488i			1.19938i	0.800231	+	0.599692i	$0.204710\pi$
$43$			7.86488i			1.19938i	−0.800231	+	0.599692i	$0.795290\pi$
$44$	−3.79845	+	1.46498i	−0.572638	+	0.220854i
$45$		0			0
$46$	2.83013	−	0.526847i	0.417279	−	0.0776794i
$47$	10.7436			1.56712			0.783560	−	0.621316i	$-0.213402\pi$
$47$	10.7436			1.56712			0.783560	+	0.621316i	$0.213402\pi$
$48$		0			0
$49$		0			0
$50$	−6.20657	+	1.15539i	−0.877741	+	0.163397i
$51$		0			0
$52$	2.63896	−	1.01779i	0.365958	−	0.141142i
$53$			9.14162i			1.25570i	0.778335	+	0.627849i	$0.216064\pi$
$53$			9.14162i			1.25570i	−0.778335	+	0.627849i	$0.783936\pi$
$54$		0			0
$55$		−	1.49015i		−	0.200932i
$56$		0			0
$57$		0			0
$58$	−1.36603	−	7.33804i	−0.179368	−	0.963531i
$59$	−4.98614			−0.649140			−0.324570	−	0.945862i	$-0.605220\pi$
$59$	−4.98614			−0.649140			−0.324570	+	0.945862i	$0.605220\pi$
$60$		0			0
$61$	−9.41902			−1.20598			−0.602991	−	0.797748i	$-0.706025\pi$
$61$	−9.41902			−1.20598			−0.602991	+	0.797748i	$0.706025\pi$
$62$	2.49307	+	13.3923i	0.316620	+	1.70082i
$63$		0			0
$64$	3.59808	−	7.14520i	0.449760	−	0.893150i
$65$			1.03528i			0.128410i
$66$		0			0
$67$			2.87875i			0.351695i	0.984417	+	0.175847i	$0.0562666\pi$
$67$			2.87875i			0.351695i	−0.984417	+	0.175847i	$0.943733\pi$
$68$	−3.01992	−	7.83013i	−0.366219	−	0.949542i
$69$		0			0
$70$		0			0
$71$	9.08704			1.07843			0.539217	−	0.842167i	$-0.318720\pi$
$71$	9.08704			1.07843			0.539217	+	0.842167i	$0.318720\pi$
$72$		0			0
$73$	1.69161			0.197989			0.0989943	−	0.995088i	$-0.468437\pi$
$73$	1.69161			0.197989			0.0989943	+	0.995088i	$0.468437\pi$
$74$	−4.81624	+	0.896575i	−0.559876	+	0.104225i
$75$		0			0
$76$	4.00240	+	10.3776i	0.459107	+	1.19039i
$77$		0			0
$78$		0			0
$79$			4.98614i			0.560984i	0.959856	+	0.280492i	$0.0904977\pi$
$79$			4.98614i			0.560984i	−0.959856	+	0.280492i	$0.909502\pi$
$80$	1.96622	+	2.16987i	0.219830	+	0.242599i
$81$		0			0
$82$	−2.26002	−	12.1404i	−0.249578	−	1.34068i
$83$	−13.6224			−1.49525			−0.747625	−	0.664121i	$-0.768806\pi$
$83$	−13.6224			−1.49525			−0.747625	+	0.664121i	$0.768806\pi$
$84$		0			0
$85$	3.07180			0.333183
$86$	−2.03558	−	10.9348i	−0.219502	−	1.17913i
$87$		0			0
$88$	4.90192	−	3.01992i	0.522547	−	0.321924i
$89$		−	8.73205i		−	0.925596i	−0.886464	−	0.462798i	$-0.846846\pi$
$89$		−	8.73205i		−	0.925596i	0.886464	−	0.462798i	$-0.153154\pi$
$90$		0			0
$91$		0			0
$92$	−3.79845	+	1.46498i	−0.396016	+	0.152735i
$93$		0			0
$94$	−14.9372	+	2.78066i	−1.54065	+	0.286803i
$95$	−4.07116			−0.417693
$96$		0			0
$97$	15.0759			1.53072			0.765362	−	0.643600i	$-0.222560\pi$
$97$	15.0759			1.53072			0.765362	+	0.643600i	$0.222560\pi$
$98$		0			0
$99$		0			0
$100$	8.33013	−	3.21276i	0.833013	−	0.321276i
$101$		−	5.26795i		−	0.524181i	−0.965043	−	0.262090i	$-0.915588\pi$
$101$		−	5.26795i		−	0.524181i	0.965043	−	0.262090i	$-0.0844118\pi$
$102$		0			0
$103$			16.6839i			1.64392i	0.569547	+	0.821959i	$0.307119\pi$
$103$			16.6839i			1.64392i	−0.569547	+	0.821959i	$0.692881\pi$
$104$	−3.40559	+	2.09808i	−0.333946	+	0.205733i
$105$		0			0
$106$	−2.36603	−	12.7099i	−0.229809	−	1.23449i
$107$	13.1582			1.27205			0.636026	−	0.771668i	$-0.280577\pi$
$107$	13.1582			1.27205			0.636026	+	0.771668i	$0.280577\pi$
$108$		0			0
$109$	6.00000			0.574696			0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000			0.574696			0.287348	+	0.957826i	$0.407226\pi$
$110$	0.385679	+	2.07180i	0.0367731	+	0.197538i
$111$		0			0
$112$		0			0
$113$			0.656339i			0.0617432i	0.999523	+	0.0308716i	$0.00982829\pi$
$113$			0.656339i			0.0617432i	−0.999523	+	0.0308716i	$0.990172\pi$
$114$		0			0
$115$		−	1.49015i		−	0.138957i
$116$	3.79845	+	9.84873i	0.352677	+	0.914431i
$117$		0			0
$118$	6.93237	−	1.29051i	0.638176	−	0.118801i
$119$		0			0
$120$		0			0
$121$	−6.85641			−0.623310
$122$	13.0955	−	2.43782i	1.18561	−	0.220710i
$123$		0			0
$124$	−6.93237	−	17.9744i	−0.622545	−	1.61415i
$125$			6.92820i			0.619677i
$126$		0			0
$127$			18.6085i			1.65124i	0.564227	+	0.825619i	$0.309174\pi$
$127$			18.6085i			1.65124i	−0.564227	+	0.825619i	$0.690826\pi$
$128$	−3.15319	+	10.8654i	−0.278706	+	0.960377i
$129$		0			0
$130$	−0.267949	−	1.43937i	−0.0235007	−	0.126241i
$131$	15.7298			1.37432			0.687158	−	0.726508i	$-0.258858\pi$
$131$	15.7298			1.37432			0.687158	+	0.726508i	$0.258858\pi$
$132$		0			0
$133$		0			0
$134$	−0.745075	−	4.00240i	−0.0643646	−	0.345755i
$135$		0			0
$136$	6.22526	+	10.1048i	0.533812	+	0.866482i
$137$			5.27792i			0.450923i	0.974252	+	0.225461i	$0.0723890\pi$
$137$			5.27792i			0.450923i	−0.974252	+	0.225461i	$0.927611\pi$
$138$		0			0
$139$		−	11.1226i		−	0.943409i	−0.881757	−	0.471704i	$-0.843639\pi$
$139$		−	11.1226i		−	0.943409i	0.881757	−	0.471704i	$-0.156361\pi$
$140$		0			0
$141$		0			0
$142$	−12.6340	+	2.35190i	−1.06022	+	0.197367i
$143$	−2.87875			−0.240733
$144$		0			0
$145$	−3.86370			−0.320863
$146$	−2.35190	+	0.437822i	−0.194645	+	0.0362344i
$147$		0			0
$148$	6.46410	−	2.49307i	0.531346	−	0.204929i
$149$			4.24264i			0.347571i	0.984784	+	0.173785i	$0.0555999\pi$
$149$			4.24264i			0.347571i	−0.984784	+	0.173785i	$0.944400\pi$
$150$		0			0
$151$			7.86488i			0.640035i	0.947412	+	0.320018i	$0.103689\pi$
$151$			7.86488i			0.640035i	−0.947412	+	0.320018i	$0.896311\pi$
$152$	−8.25056	−	13.3923i	−0.669209	−	1.08626i
$153$		0			0
$154$		0			0
$155$	7.05146			0.566387
$156$		0			0
$157$	−15.0759			−1.20319			−0.601593	−	0.798803i	$-0.705467\pi$
$157$	−15.0759			−1.20319			−0.601593	+	0.798803i	$0.705467\pi$
$158$	−1.29051	−	6.93237i	−0.102667	−	0.551510i
$159$		0			0
$160$	−3.29530	−	2.50794i	−0.260516	−	0.198270i
$161$		0			0
$162$		0			0
$163$			24.3660i			1.90849i	0.299021	+	0.954247i	$0.403340\pi$
$163$			24.3660i			1.90849i	−0.299021	+	0.954247i	$0.596660\pi$
$164$	6.28434	+	16.2942i	0.490725	+	1.27237i
$165$		0			0
$166$	18.9396	−	3.52573i	1.47000	−	0.273650i
$167$	−10.7436			−0.831367			−0.415684	−	0.909509i	$-0.636458\pi$
$167$	−10.7436			−0.831367			−0.415684	+	0.909509i	$0.636458\pi$
$168$		0			0
$169$	−11.0000			−0.846154
$170$	−4.27081	+	0.795040i	−0.327556	+	0.0609767i
$171$		0			0
$172$	5.66025	+	14.6761i	0.431590	+	1.11904i
$173$			9.66025i			0.734456i	0.930131	+	0.367228i	$0.119693\pi$
$173$			9.66025i			0.734456i	−0.930131	+	0.367228i	$0.880307\pi$
$174$		0			0
$175$		0			0
$176$	−6.03367	+	5.46739i	−0.454805	+	0.412120i
$177$		0			0
$178$	2.26002	+	12.1404i	0.169396	+	0.909963i
$179$	17.2294			1.28778			0.643892	−	0.765117i	$-0.277319\pi$
$179$	17.2294			1.28778			0.643892	+	0.765117i	$0.277319\pi$
$180$		0			0
$181$	−5.00052			−0.371685			−0.185843	−	0.982580i	$-0.559501\pi$
$181$	−5.00052			−0.371685			−0.185843	+	0.982580i	$0.559501\pi$
$182$		0			0
$183$		0			0
$184$	4.90192	−	3.01992i	0.361375	−	0.222631i
$185$			2.53590i			0.186443i
$186$		0			0
$187$			8.54161i			0.624625i
$188$	20.0479	−	7.73205i	1.46214	−	0.563918i
$189$		0			0
$190$	5.66025	−	1.05369i	0.410638	−	0.0764430i
$191$	13.1582			0.952095			0.476047	−	0.879420i	$-0.342069\pi$
$191$	13.1582			0.952095			0.476047	+	0.879420i	$0.342069\pi$
$192$		0			0
$193$	−9.85641			−0.709480			−0.354740	−	0.934965i	$-0.615431\pi$
$193$	−9.85641			−0.709480			−0.354740	+	0.934965i	$0.615431\pi$
$194$	−20.9604	+	3.90192i	−1.50487	+	0.280142i
$195$		0			0
$196$		0			0
$197$			15.3533i			1.09388i	0.837173	+	0.546938i	$0.184207\pi$
$197$			15.3533i			1.09388i	−0.837173	+	0.546938i	$0.815793\pi$
$198$		0			0
$199$			4.07116i			0.288597i	0.989534	+	0.144299i	$0.0460926\pi$
$199$			4.07116i			0.288597i	−0.989534	+	0.144299i	$0.953907\pi$
$200$	−10.7501	+	6.62278i	−0.760146	+	0.468301i
$201$		0			0
$202$	1.36345	+	7.32418i	0.0959317	+	0.515327i
$203$		0			0
$204$		0			0
$205$	−6.39230			−0.446458
$206$	−4.31812	−	23.1962i	−0.300858	−	1.61615i
$207$		0			0
$208$	4.19187	−	3.79845i	0.290654	−	0.263375i
$209$		−	11.3205i		−	0.783056i
$210$		0			0
$211$			21.4873i			1.47924i	0.673022	+	0.739622i	$0.264996\pi$
$211$			21.4873i			1.47924i	−0.673022	+	0.739622i	$0.735004\pi$
$212$	6.57910	+	17.0585i	0.451855	+	1.17158i
$213$		0			0
$214$	−18.2942	+	3.40559i	−1.25057	+	0.232802i
$215$	−5.75749			−0.392658
$216$		0			0
$217$		0			0
$218$	−8.34197	+	1.55291i	−0.564989	+	0.105177i
$219$		0			0
$220$	−1.07244	−	2.78066i	−0.0723040	−	0.187472i
$221$		−	5.93426i		−	0.399181i
$222$		0			0
$223$		−	15.1938i		−	1.01745i	−0.860929	−	0.508726i	$-0.830117\pi$
$223$		−	15.1938i		−	1.01745i	0.860929	−	0.508726i	$-0.169883\pi$
$224$		0			0
$225$		0			0
$226$	−0.169873	−	0.912526i	−0.0112998	−	0.0607004i
$227$	10.7436			0.713080			0.356540	−	0.934280i	$-0.383956\pi$
$227$	10.7436			0.713080			0.356540	+	0.934280i	$0.383956\pi$
$228$		0			0
$229$	25.3543			1.67546			0.837730	−	0.546085i	$-0.183882\pi$
$229$	25.3543			1.67546			0.837730	+	0.546085i	$0.183882\pi$
$230$	0.385679	+	2.07180i	0.0254309	+	0.136610i
$231$		0			0
$232$	−7.83013	−	12.7099i	−0.514073	−	0.834443i
$233$			5.83272i			0.382114i	0.981579	+	0.191057i	$0.0611916\pi$
$233$			5.83272i			0.382114i	−0.981579	+	0.191057i	$0.938808\pi$
$234$		0			0
$235$			7.86488i			0.513048i
$236$	−9.30426	+	3.58846i	−0.605656	+	0.233589i
$237$		0			0
$238$		0			0
$239$	2.03558			0.131671			0.0658354	−	0.997830i	$-0.479029\pi$
$239$	2.03558			0.131671			0.0658354	+	0.997830i	$0.479029\pi$
$240$		0			0
$241$	13.0053			0.837747			0.418873	−	0.908045i	$-0.362425\pi$
$241$	13.0053			0.837747			0.418873	+	0.908045i	$0.362425\pi$
$242$	9.53266	−	1.77457i	0.612782	−	0.114074i
$243$		0			0
$244$	−17.5761	+	6.77875i	−1.12520	+	0.433965i
$245$		0			0
$246$		0			0
$247$			7.86488i			0.500431i
$248$	14.2904	+	23.1962i	0.907441	+	1.47296i
$249$		0			0
$250$	−1.79315	−	9.63248i	−0.113409	−	0.609211i
$251$	8.63624			0.545115			0.272557	−	0.962140i	$-0.412131\pi$
$251$	8.63624			0.545115			0.272557	+	0.962140i	$0.412131\pi$
$252$		0			0
$253$	4.14359			0.260505
$254$	−4.81624	−	25.8719i	−0.302198	−	1.62335i
$255$		0			0
$256$	1.57180	−	15.9226i	0.0982373	−	0.995163i
$257$			1.12436i			0.0701354i	0.999385	+	0.0350677i	$0.0111647\pi$
$257$			1.12436i			0.0701354i	−0.999385	+	0.0350677i	$0.988835\pi$
$258$		0			0
$259$		0			0
$260$	0.745075	+	1.93185i	0.0462076	+	0.119808i
$261$		0			0
$262$	−21.8695	+	4.07116i	−1.35110	+	0.251517i
$263$	2.03558			0.125519			0.0627597	−	0.998029i	$-0.480010\pi$
$263$	2.03558			0.125519			0.0627597	+	0.998029i	$0.480010\pi$
$264$		0			0
$265$	−6.69213			−0.411094
$266$		0			0
$267$		0			0
$268$	2.07180	+	5.37182i	0.126555	+	0.328136i
$269$			3.66025i			0.223170i	0.993755	+	0.111585i	$0.0355927\pi$
$269$			3.66025i			0.223170i	−0.993755	+	0.111585i	$0.964407\pi$
$270$		0			0
$271$			13.7036i			0.832437i	0.909265	+	0.416218i	$0.136645\pi$
$271$			13.7036i			0.832437i	−0.909265	+	0.416218i	$0.863355\pi$
$272$	−11.2705	−	12.4378i	−0.683373	−	0.754154i
$273$		0			0
$274$	−1.36603	−	7.33804i	−0.0825246	−	0.443307i
$275$	−9.08704			−0.547969
$276$		0			0
$277$	−7.07180			−0.424903			−0.212452	−	0.977172i	$-0.568145\pi$
$277$	−7.07180			−0.424903			−0.212452	+	0.977172i	$0.568145\pi$
$278$	2.87875	+	15.4641i	0.172656	+	0.927475i
$279$		0			0
$280$		0			0
$281$		−	23.5612i		−	1.40554i	−0.711417	−	0.702770i	$-0.751946\pi$
$281$		−	23.5612i		−	1.40554i	0.711417	−	0.702770i	$-0.248054\pi$
$282$		0			0
$283$		−	5.56131i		−	0.330586i	−0.986245	−	0.165293i	$-0.947143\pi$
$283$		−	5.56131i		−	0.330586i	0.986245	−	0.165293i	$-0.0528569\pi$
$284$	16.9567	−	6.53983i	1.00619	−	0.388067i
$285$		0			0
$286$	4.00240	−	0.745075i	0.236667	−	0.0440572i
$287$		0			0
$288$		0			0
$289$	−0.607695			−0.0357468
$290$	5.37182	−	1.00000i	0.315444	−	0.0587220i
$291$		0			0
$292$	3.15660	−	1.21743i	0.184726	−	0.0712449i
$293$		−	31.1244i		−	1.81830i	−0.416464	−	0.909152i	$-0.636731\pi$
$293$		−	31.1244i		−	1.81830i	0.416464	−	0.909152i	$-0.363269\pi$
$294$		0			0
$295$		−	3.65011i		−	0.212517i
$296$	−8.34197	+	5.13922i	−0.484867	+	0.298711i
$297$		0			0
$298$	−1.09808	−	5.89866i	−0.0636098	−	0.341700i
$299$	−2.87875			−0.166482
$300$		0			0
$301$		0			0
$302$	−2.03558	−	10.9348i	−0.117135	−	0.629225i
$303$		0			0
$304$	14.9372	+	16.4843i	0.856706	+	0.945439i
$305$		−	6.89520i		−	0.394818i
$306$		0			0
$307$		−	9.63248i		−	0.549754i	−0.961479	−	0.274877i	$-0.911363\pi$
$307$		−	9.63248i		−	0.549754i	0.961479	−	0.274877i	$-0.0886372\pi$
$308$		0			0
$309$		0			0
$310$	−9.80385	+	1.82505i	−0.556821	+	0.103656i
$311$	−20.7159			−1.17469			−0.587346	−	0.809336i	$-0.699827\pi$
$311$	−20.7159			−1.17469			−0.587346	+	0.809336i	$0.699827\pi$
$312$		0			0
$313$	−30.2533			−1.71002			−0.855008	−	0.518614i	$-0.826448\pi$
$313$	−30.2533			−1.71002			−0.855008	+	0.518614i	$0.826448\pi$
$314$	20.9604	−	3.90192i	1.18286	−	0.220198i
$315$		0			0
$316$	3.58846	+	9.30426i	0.201866	+	0.523405i
$317$			4.24264i			0.238290i	0.992877	+	0.119145i	$0.0380154\pi$
$317$			4.24264i			0.238290i	−0.992877	+	0.119145i	$0.961985\pi$
$318$		0			0
$319$		−	10.7436i		−	0.601528i
$320$	5.23065	+	2.63397i	0.292402	+	0.147244i
$321$		0			0
$322$		0			0
$323$	23.3361			1.29846
$324$		0			0
$325$	6.31319			0.350193
$326$	−6.30639	−	33.8768i	−0.349279	−	1.87626i
$327$		0			0
$328$	−12.9546	−	21.0278i	−0.715296	−	1.16107i
$329$		0			0
$330$		0			0
$331$		−	11.5150i		−	0.632921i	−0.948606	−	0.316461i	$-0.897506\pi$
$331$		−	11.5150i		−	0.632921i	0.948606	−	0.316461i	$-0.102494\pi$
$332$	−25.4197	+	9.80385i	−1.39509	+	0.538056i
$333$		0			0
$334$	14.9372	−	2.78066i	0.817326	−	0.152151i
$335$	−2.10739			−0.115139
$336$		0			0
$337$	−1.60770			−0.0875767			−0.0437884	−	0.999041i	$-0.513943\pi$
$337$	−1.60770			−0.0875767			−0.0437884	+	0.999041i	$0.513943\pi$
$338$	15.2936	−	2.84701i	0.831863	−	0.154857i
$339$		0			0
$340$	5.73205	−	2.21073i	0.310864	−	0.119894i
$341$			19.6077i			1.06182i
$342$		0			0
$343$		0			0
$344$	−11.6681	−	18.9396i	−0.629100	−	1.02115i
$345$		0			0
$346$	−2.50026	−	13.4309i	−0.134415	−	0.722051i
$347$	−20.2097			−1.08491			−0.542456	−	0.840084i	$-0.682505\pi$
$347$	−20.2097			−1.08491			−0.542456	+	0.840084i	$0.682505\pi$
$348$		0			0
$349$	−11.4896			−0.615023			−0.307511	−	0.951544i	$-0.599496\pi$
$349$	−11.4896			−0.615023			−0.307511	+	0.951544i	$0.599496\pi$
$350$		0			0
$351$		0			0
$352$	6.97372	−	9.16309i	0.371701	−	0.488394i
$353$			28.1962i			1.50073i	0.661024	+	0.750365i	$0.270122\pi$
$353$			28.1962i			1.50073i	−0.661024	+	0.750365i	$0.729878\pi$
$354$		0			0
$355$			6.65218i			0.353061i
$356$	−6.28434	−	16.2942i	−0.333069	−	0.863592i
$357$		0			0
$358$	−23.9545	+	4.45929i	−1.26603	+	0.235681i
$359$	9.08704			0.479596			0.239798	−	0.970823i	$-0.422919\pi$
$359$	9.08704			0.479596			0.239798	+	0.970823i	$0.422919\pi$
$360$		0			0
$361$	−11.9282			−0.627800
$362$	6.95236	−	1.29423i	0.365408	−	0.0680231i
$363$		0			0
$364$		0			0
$365$			1.23835i			0.0648181i
$366$		0			0
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$	−6.03367	+	5.46739i	−0.314527	+	0.285007i
$369$		0			0
$370$	−0.656339	−	3.52573i	−0.0341214	−	0.183294i
$371$		0			0
$372$		0			0
$373$	16.9282			0.876509			0.438255	−	0.898851i	$-0.355597\pi$
$373$	16.9282			0.876509			0.438255	+	0.898851i	$0.355597\pi$
$374$	−2.21073	−	11.8756i	−0.114314	−	0.614075i
$375$		0			0
$376$	−25.8719	+	15.9389i	−1.33424	+	0.821984i
$377$			7.46410i			0.384421i
$378$		0			0
$379$		−	27.2448i		−	1.39947i	−0.714403	−	0.699735i	$-0.753302\pi$
$379$		−	27.2448i		−	1.39947i	0.714403	−	0.699735i	$-0.246698\pi$
$380$	−7.59689	+	2.92996i	−0.389712	+	0.150304i
$381$		0			0
$382$	−18.2942	+	3.40559i	−0.936014	+	0.174245i
$383$	21.4873			1.09795			0.548974	−	0.835839i	$-0.315019\pi$
$383$	21.4873			1.09795			0.548974	+	0.835839i	$0.315019\pi$
$384$		0			0
$385$		0			0
$386$	13.7036	−	2.55103i	0.697497	−	0.129844i
$387$		0			0
$388$	28.1320	−	10.8499i	1.42818	−	0.550821i
$389$		−	32.6012i		−	1.65295i	−0.562974	−	0.826474i	$-0.690343\pi$
$389$		−	32.6012i		−	1.65295i	0.562974	−	0.826474i	$-0.309657\pi$
$390$		0			0
$391$			8.54161i			0.431968i
$392$		0			0
$393$		0			0
$394$	−3.97372	−	21.3461i	−0.200193	−	1.07540i
$395$	−3.65011			−0.183657
$396$		0			0
$397$	17.3495			0.870746			0.435373	−	0.900250i	$-0.356616\pi$
$397$	17.3495			0.870746			0.435373	+	0.900250i	$0.356616\pi$
$398$	−1.05369	−	5.66025i	−0.0528169	−	0.283723i
$399$		0			0
$400$	13.2321	−	11.9902i	0.661603	−	0.599508i
$401$		−	38.2581i		−	1.91052i	−0.295770	−	0.955259i	$-0.595576\pi$
$401$		−	38.2581i		−	1.91052i	0.295770	−	0.955259i	$-0.404424\pi$
$402$		0			0
$403$		−	13.6224i		−	0.678579i
$404$	−3.79127	−	9.83013i	−0.188623	−	0.489067i
$405$		0			0
$406$		0			0
$407$	−7.05146			−0.349528
$408$		0			0
$409$	10.1769			0.503215			0.251608	−	0.967829i	$-0.419041\pi$
$409$	10.1769			0.503215			0.251608	+	0.967829i	$0.419041\pi$
$410$	8.88740	−	1.65445i	0.438918	−	0.0817075i
$411$		0			0
$412$	12.0072	+	31.1327i	0.591553	+	1.53380i
$413$		0			0
$414$		0			0
$415$		−	9.97227i		−	0.489520i
$416$	−4.84497	+	6.36603i	−0.237544	+	0.312120i
$417$		0			0
$418$	2.92996	+	15.7392i	0.143309	+	0.769831i
$419$	24.3660			1.19036			0.595179	−	0.803593i	$-0.297081\pi$
$419$	24.3660			1.19036			0.595179	+	0.803593i	$0.297081\pi$
$420$		0			0
$421$	−29.7128			−1.44811			−0.724057	−	0.689740i	$-0.757725\pi$
$421$	−29.7128			−1.44811			−0.724057	+	0.689740i	$0.757725\pi$
$422$	−5.56131	−	29.8744i	−0.270720	−	1.45426i
$423$		0			0
$424$	−13.5622	−	22.0141i	−0.658638	−	1.06910i
$425$		−	18.7321i		−	0.908638i
$426$		0			0
$427$		0			0
$428$	24.5536	−	9.46979i	1.18684	−	0.457740i
$429$		0			0
$430$	8.00481	−	1.49015i	0.386026	−	0.0718614i
$431$	32.4232			1.56177			0.780884	−	0.624676i	$-0.214769\pi$
$431$	32.4232			1.56177			0.780884	+	0.624676i	$0.214769\pi$
$432$		0			0
$433$	−14.7985			−0.711169			−0.355585	−	0.934644i	$-0.615718\pi$
$433$	−14.7985			−0.711169			−0.355585	+	0.934644i	$0.615718\pi$
$434$		0			0
$435$		0			0
$436$	11.1962	−	4.31812i	0.536198	−	0.206801i
$437$		−	11.3205i		−	0.541533i
$438$		0			0
$439$		−	27.4073i		−	1.30808i	−0.756461	−	0.654039i	$-0.773073\pi$
$439$		−	27.4073i		−	1.30808i	0.756461	−	0.654039i	$-0.226927\pi$
$440$	2.21073	+	3.58846i	0.105393	+	0.171073i
$441$		0			0
$442$	1.53590	+	8.25056i	0.0730552	+	0.392439i
$443$	−10.1779			−0.483567			−0.241784	−	0.970330i	$-0.577732\pi$
$443$	−10.1779			−0.483567			−0.241784	+	0.970330i	$0.577732\pi$
$444$		0			0
$445$	6.39230			0.303024
$446$	3.93244	+	21.1244i	0.186207	+	1.00027i
$447$		0			0
$448$		0			0
$449$		−	32.3238i		−	1.52546i	−0.646719	−	0.762728i	$-0.723859\pi$
$449$		−	32.3238i		−	1.52546i	0.646719	−	0.762728i	$-0.276141\pi$
$450$		0			0
$451$		−	17.7748i		−	0.836983i
$452$	0.472358	+	1.22474i	0.0222179	+	0.0576072i
$453$		0			0
$454$	−14.9372	+	2.78066i	−0.701036	+	0.130503i
$455$		0			0
$456$		0			0
$457$	−22.9282			−1.07254			−0.536268	−	0.844048i	$-0.680166\pi$
$457$	−22.9282			−1.07254			−0.536268	+	0.844048i	$0.680166\pi$
$458$	−35.2508	+	6.56218i	−1.64716	+	0.306630i
$459$		0			0
$460$	−1.07244	−	2.78066i	−0.0500028	−	0.129649i
$461$		−	9.26795i		−	0.431651i	−0.976432	−	0.215826i	$-0.930756\pi$
$461$		−	9.26795i		−	0.431651i	0.976432	−	0.215826i	$-0.0692443\pi$
$462$		0			0
$463$		−	7.09353i		−	0.329664i	−0.986322	−	0.164832i	$-0.947292\pi$
$463$		−	7.09353i		−	0.329664i	0.986322	−	0.164832i	$-0.0527082\pi$
$464$	14.1760	+	15.6443i	0.658104	+	0.726268i
$465$		0			0
$466$	−1.50962	−	8.10940i	−0.0699317	−	0.375660i
$467$	−12.8510			−0.594674			−0.297337	−	0.954773i	$-0.596099\pi$
$467$	−12.8510			−0.594674			−0.297337	+	0.954773i	$0.596099\pi$
$468$		0			0
$469$		0			0
$470$	−2.03558	−	10.9348i	−0.0938944	−	0.504383i
$471$		0			0
$472$	12.0072	−	7.39725i	0.552677	−	0.340486i
$473$		−	16.0096i		−	0.736123i
$474$		0			0
$475$			24.8263i			1.13911i
$476$		0			0
$477$		0			0
$478$	−2.83013	+	0.526847i	−0.129447	+	0.0240974i
$479$	12.8510			0.587178			0.293589	−	0.955932i	$-0.405150\pi$
$479$	12.8510			0.587178			0.293589	+	0.955932i	$0.405150\pi$
$480$		0			0
$481$	4.89898			0.223374
$482$	−18.0817	+	3.36603i	−0.823597	+	0.153318i
$483$		0			0
$484$	−12.7942	+	4.93447i	−0.581556	+	0.224294i
$485$			11.0363i			0.501133i
$486$		0			0
$487$		−	13.6224i		−	0.617289i	−0.951177	−	0.308644i	$-0.900125\pi$
$487$		−	13.6224i		−	0.617289i	0.951177	−	0.308644i	$-0.0998753\pi$
$488$	22.6821	−	13.9737i	1.02677	−	0.632561i
$489$		0			0
$490$		0			0
$491$	−13.1582			−0.593822			−0.296911	−	0.954905i	$-0.595956\pi$
$491$	−13.1582			−0.593822			−0.296911	+	0.954905i	$0.595956\pi$
$492$		0			0
$493$	22.1469			0.997448
$494$	−2.03558	−	10.9348i	−0.0915852	−	0.491979i
$495$		0			0
$496$	−25.8719	−	28.5516i	−1.16168	−	1.28201i
$497$		0			0
$498$		0			0
$499$		−	29.3521i		−	1.31398i	−0.753898	−	0.656991i	$-0.771829\pi$
$499$		−	29.3521i		−	1.31398i	0.753898	−	0.656991i	$-0.228171\pi$
$500$	4.98614	+	12.9282i	0.222987	+	0.578167i
$501$		0			0
$502$	−12.0072	+	2.23522i	−0.535908	+	0.0997629i
$503$	19.3799			0.864106			0.432053	−	0.901848i	$-0.357789\pi$
$503$	19.3799			0.864106			0.432053	+	0.901848i	$0.357789\pi$
$504$		0			0
$505$	3.85641			0.171608
$506$	−5.76096	+	1.07244i	−0.256106	+	0.0476758i
$507$		0			0
$508$	13.3923	+	34.7240i	0.594187	+	1.54063i
$509$			27.6603i			1.22602i	0.790075	+	0.613010i	$0.210041\pi$
$509$			27.6603i			1.22602i	−0.790075	+	0.613010i	$0.789959\pi$
$510$		0			0
$511$		0			0
$512$	1.93576	+	22.5445i	0.0855493	+	0.996334i
$513$		0			0
$514$	−0.291005	−	1.56322i	−0.0128357	−	0.0689508i
$515$	−12.2135			−0.538191
$516$		0			0
$517$	−21.8695			−0.961821
$518$		0			0
$519$		0			0
$520$	−1.53590	−	2.49307i	−0.0673536	−	0.109328i
$521$		−	9.66025i		−	0.423223i	−0.977354	−	0.211612i	$-0.932129\pi$
$521$		−	9.66025i		−	0.423223i	0.977354	−	0.211612i	$-0.0678712\pi$
$522$		0			0
$523$		−	2.98030i		−	0.130319i	−0.997875	−	0.0651597i	$-0.979244\pi$
$523$		−	2.98030i		−	0.130319i	0.997875	−	0.0651597i	$-0.0207557\pi$
$524$	29.3521	−	11.3205i	1.28225	−	0.494539i
$525$		0			0
$526$	−2.83013	+	0.526847i	−0.123399	+	0.0229716i
$527$	−40.4193			−1.76069
$528$		0			0
$529$	−18.8564			−0.819844
$530$	9.30426	−	1.73205i	0.404151	−	0.0752355i
$531$		0			0
$532$		0			0
$533$			12.3490i			0.534894i
$534$		0			0
$535$			9.63248i			0.416448i
$536$	−4.27081	−	6.93237i	−0.184471	−	0.299433i
$537$		0			0
$538$	−0.947343	−	5.08895i	−0.0408429	−	0.219400i
$539$		0			0
$540$		0			0
$541$	15.8564			0.681720			0.340860	−	0.940114i	$-0.389282\pi$
$541$	15.8564			0.681720			0.340860	+	0.940114i	$0.389282\pi$
$542$	−3.54676	−	19.0526i	−0.152347	−	0.818377i
$543$		0			0
$544$	18.8888	+	14.3756i	0.809851	+	0.616351i
$545$			4.39230i			0.188146i
$546$		0			0
$547$		−	26.4734i		−	1.13192i	−0.824432	−	0.565960i	$-0.808505\pi$
$547$		−	26.4734i		−	1.13192i	0.824432	−	0.565960i	$-0.191495\pi$
$548$	3.79845	+	9.84873i	0.162262	+	0.420717i
$549$		0			0
$550$	12.6340	−	2.35190i	0.538714	−	0.100285i
$551$	−29.3521			−1.25044
$552$		0			0
$553$		0			0
$554$	9.83212	−	1.83032i	0.417727	−	0.0777627i
$555$		0			0
$556$	−8.00481	−	20.7551i	−0.339479	−	0.880212i
$557$			18.9396i			0.802496i	0.915970	+	0.401248i	$0.131423\pi$
$557$			18.9396i			0.802496i	−0.915970	+	0.401248i	$0.868577\pi$
$558$		0			0
$559$			11.1226i			0.470437i
$560$		0			0
$561$		0			0
$562$	6.09808	+	32.7577i	0.257232	+	1.38180i
$563$	−37.9884			−1.60102			−0.800510	−	0.599320i	$-0.795438\pi$
$563$	−37.9884			−1.60102			−0.800510	+	0.599320i	$0.795438\pi$
$564$		0			0
$565$	−0.480473			−0.0202137
$566$	1.43937	+	7.73205i	0.0605014	+	0.325002i
$567$		0			0
$568$	−21.8827	+	13.4812i	−0.918177	+	0.565659i
$569$		−	16.5916i		−	0.695557i	−0.937577	−	0.347779i	$-0.886936\pi$
$569$		−	16.5916i		−	0.695557i	0.937577	−	0.347779i	$-0.113064\pi$
$570$		0			0
$571$		−	0.771358i		−	0.0322803i	−0.999870	−	0.0161402i	$-0.994862\pi$
$571$		−	0.771358i		−	0.0322803i	0.999870	−	0.0161402i	$-0.00513780\pi$
$572$	−5.37182	+	2.07180i	−0.224607	+	0.0866262i
$573$		0			0
$574$		0			0
$575$	−9.08704			−0.378956
$576$		0			0
$577$	−7.62587			−0.317469			−0.158735	−	0.987321i	$-0.550741\pi$
$577$	−7.62587			−0.317469			−0.158735	+	0.987321i	$0.550741\pi$
$578$	0.844896	−	0.157283i	0.0351430	−	0.00654211i
$579$		0			0
$580$	−7.20977	+	2.78066i	−0.299369	+	0.115460i
$581$		0			0
$582$		0			0
$583$		−	18.6085i		−	0.770686i
$584$	−4.07361	+	2.50962i	−0.168567	+	0.103849i
$585$		0			0
$586$	8.05558	+	43.2731i	0.332773	+	1.78759i
$587$	−16.5011			−0.681074			−0.340537	−	0.940231i	$-0.610609\pi$
$587$	−16.5011			−0.681074			−0.340537	+	0.940231i	$0.610609\pi$
$588$		0			0
$589$	53.5692			2.20728
$590$	0.944717	+	5.07484i	0.0388934	+	0.208928i
$591$		0			0
$592$	10.2679	−	9.30426i	0.422010	−	0.382403i
$593$		−	28.1962i		−	1.15788i	−0.815371	−	0.578939i	$-0.803467\pi$
$593$		−	28.1962i		−	1.15788i	0.815371	−	0.578939i	$-0.196533\pi$
$594$		0			0
$595$		0			0
$596$	3.05337	+	7.91688i	0.125071	+	0.324288i
$597$		0			0
$598$	4.00240	−	0.745075i	0.163670	−	0.0304684i
$599$	−31.3323			−1.28020			−0.640101	−	0.768290i	$-0.721108\pi$
$599$	−31.3323			−1.28020			−0.640101	+	0.768290i	$0.721108\pi$
$600$		0			0
$601$	30.4564			1.24234			0.621170	−	0.783676i	$-0.286657\pi$
$601$	30.4564			1.24234			0.621170	+	0.783676i	$0.286657\pi$
$602$		0			0
$603$		0			0
$604$	5.66025	+	14.6761i	0.230312	+	0.597161i
$605$		−	5.01924i		−	0.204061i
$606$		0			0
$607$		−	14.1029i		−	0.572420i	−0.958167	−	0.286210i	$-0.907604\pi$
$607$		−	14.1029i		−	0.572420i	0.958167	−	0.286210i	$-0.0923955\pi$
$608$	−25.0340	−	19.0526i	−1.01526	−	0.772683i
$609$		0			0
$610$	1.78461	+	9.58659i	0.0722567	+	0.388150i
$611$	15.1938			0.614675
$612$		0			0
$613$	16.3923			0.662079			0.331039	−	0.943617i	$-0.392601\pi$
$613$	16.3923			0.662079			0.331039	+	0.943617i	$0.392601\pi$
$614$	2.49307	+	13.3923i	0.100612	+	0.540469i
$615$		0			0
$616$		0			0
$617$		−	10.3800i		−	0.417882i	−0.977928	−	0.208941i	$-0.932998\pi$
$617$		−	10.3800i		−	0.417882i	0.977928	−	0.208941i	$-0.0670016\pi$
$618$		0			0
$619$			26.3164i			1.05775i	0.848701	+	0.528873i	$0.177385\pi$
$619$			26.3164i			1.05775i	−0.848701	+	0.528873i	$0.822615\pi$
$620$	13.1582	−	5.07484i	0.528446	−	0.203811i
$621$		0			0
$622$	28.8019	−	5.36167i	1.15485	−	0.214983i
$623$		0			0
$624$		0			0
$625$	17.2487			0.689948
$626$	42.0620	−	7.83013i	1.68114	−	0.312955i
$627$		0			0
$628$	−28.1320	+	10.8499i	−1.12259	+	0.432959i
$629$		−	14.5359i		−	0.579584i
$630$		0			0
$631$		−	7.09353i		−	0.282389i	−0.989982	−	0.141194i	$-0.954906\pi$
$631$		−	7.09353i		−	0.282389i	0.989982	−	0.141194i	$-0.0450943\pi$
$632$	−7.39725	−	12.0072i	−0.294247	−	0.477621i
$633$		0			0
$634$	−1.09808	−	5.89866i	−0.0436102	−	0.234266i
$635$	−13.6224			−0.540588
$636$		0			0
$637$		0			0
$638$	2.78066	+	14.9372i	0.110087	+	0.591368i
$639$		0			0
$640$	−7.95404	−	2.30830i	−0.314411	−	0.0912435i
$641$		−	3.96524i		−	0.156618i	−0.996929	−	0.0783088i	$-0.975048\pi$
$641$		−	3.96524i		−	0.156618i	0.996929	−	0.0783088i	$-0.0249520\pi$
$642$		0			0
$643$		−	2.58101i		−	0.101785i	−0.998704	−	0.0508926i	$-0.983793\pi$
$643$		−	2.58101i		−	0.101785i	0.998704	−	0.0508926i	$-0.0162066\pi$
$644$		0			0
$645$		0			0
$646$	−32.4449	+	6.03983i	−1.27653	+	0.237634i
$647$	47.9607			1.88553			0.942764	−	0.333460i	$-0.108216\pi$
$647$	47.9607			1.88553			0.942764	+	0.333460i	$0.108216\pi$
$648$		0			0
$649$	10.1497			0.398410
$650$	−8.77741	+	1.63397i	−0.344278	+	0.0640898i
$651$		0			0
$652$	17.5359	+	45.4676i	0.686759	+	1.78065i
$653$			39.2190i			1.53476i	0.641193	+	0.767380i	$0.278440\pi$
$653$			39.2190i			1.53476i	−0.641193	+	0.767380i	$0.721560\pi$
$654$		0			0
$655$			11.5150i			0.449928i
$656$	23.4535	+	25.8827i	0.915705	+	1.01055i
$657$		0			0
$658$		0			0
$659$	−47.6170			−1.85489			−0.927447	−	0.373956i	$-0.878001\pi$
$659$	−47.6170			−1.85489			−0.927447	+	0.373956i	$0.878001\pi$
$660$		0			0
$661$	−30.7338			−1.19540			−0.597702	−	0.801718i	$-0.703920\pi$
$661$	−30.7338			−1.19540			−0.597702	+	0.801718i	$0.703920\pi$
$662$	2.98030	+	16.0096i	0.115833	+	0.622231i
$663$		0			0
$664$	32.8043	−	20.2097i	1.27305	−	0.784287i
$665$		0			0
$666$		0			0
$667$		−	10.7436i		−	0.415995i
$668$	−20.0479	+	7.73205i	−0.775676	+	0.299162i
$669$		0			0
$670$	2.92996	−	0.545433i	0.113194	−	0.0210719i
$671$	19.1732			0.740173
$672$		0			0
$673$	−42.0000			−1.61898			−0.809491	−	0.587133i	$-0.800257\pi$
$673$	−42.0000			−1.61898			−0.809491	+	0.587133i	$0.800257\pi$
$674$	2.23522	−	0.416102i	0.0860976	−	0.0160277i
$675$		0			0
$676$	−20.5263	+	7.91656i	−0.789472	+	0.304483i
$677$			24.8756i			0.956049i	0.878347	+	0.478024i	$0.158647\pi$
$677$			24.8756i			0.956049i	−0.878347	+	0.478024i	$0.841353\pi$
$678$		0			0
$679$		0			0
$680$	−7.39725	+	4.55721i	−0.283672	+	0.174761i
$681$		0			0
$682$	−5.07484	−	27.2611i	−0.194326	−	1.04388i
$683$	24.2808			0.929080			0.464540	−	0.885552i	$-0.346220\pi$
$683$	24.2808			0.929080			0.464540	+	0.885552i	$0.346220\pi$
$684$		0			0
$685$	−3.86370			−0.147625
$686$		0			0
$687$		0			0
$688$	21.1244	+	23.3123i	0.805359	+	0.888774i
$689$			12.9282i			0.492525i
$690$		0			0
$691$		−	37.4390i		−	1.42425i	−0.702054	−	0.712124i	$-0.747733\pi$
$691$		−	37.4390i		−	1.42425i	0.702054	−	0.712124i	$-0.252267\pi$
$692$	6.95236	+	18.0263i	0.264289	+	0.685256i
$693$		0			0
$694$	28.0981	−	5.23065i	1.06659	−	0.198553i
$695$	8.14233			0.308856
$696$		0			0
$697$	36.6410			1.38788
$698$	15.9743	−	2.97372i	0.604635	−	0.112557i
$699$		0			0
$700$		0			0
$701$			48.2591i			1.82272i	0.411608	+	0.911361i	$0.364967\pi$
$701$			48.2591i			1.82272i	−0.411608	+	0.911361i	$0.635033\pi$
$702$		0			0
$703$			19.2650i			0.726591i
$704$	−7.32418	+	14.5446i	−0.276040	+	0.548172i
$705$		0			0
$706$	−7.29770	−	39.2019i	−0.274653	−	1.47538i
$707$		0			0
$708$		0			0
$709$	−0.928203			−0.0348594			−0.0174297	−	0.999848i	$-0.505548\pi$
$709$	−0.928203			−0.0348594			−0.0174297	+	0.999848i	$0.505548\pi$
$710$	−1.72171	−	9.24871i	−0.0646146	−	0.347098i
$711$		0			0
$712$	12.9546	+	21.0278i	0.485492	+	0.788051i
$713$			19.6077i			0.734314i
$714$		0			0
$715$		−	2.10739i		−	0.0788119i
$716$	32.1504	−	12.3998i	1.20152	−	0.463401i
$717$		0			0
$718$	−12.6340	+	2.35190i	−0.471496	+	0.0877721i
$719$	−52.9468			−1.97458			−0.987291	−	0.158921i	$-0.949198\pi$
$719$	−52.9468			−1.97458			−0.987291	+	0.158921i	$0.949198\pi$
$720$		0			0
$721$		0			0
$722$	16.5841	−	3.08725i	0.617197	−	0.114895i
$723$		0			0
$724$	−9.33109	+	3.59881i	−0.346787	+	0.133749i
$725$			23.5612i			0.875039i
$726$		0			0
$727$			10.7233i			0.397707i	0.980029	+	0.198853i	$0.0637218\pi$
$727$			10.7233i			0.397707i	−0.980029	+	0.198853i	$0.936278\pi$
$728$		0			0
$729$		0			0
$730$	−0.320508	−	1.72171i	−0.0118625	−	0.0637234i
$731$	33.0023			1.22063
$732$		0			0
$733$	19.1427			0.707050			0.353525	−	0.935425i	$-0.384983\pi$
$733$	19.1427			0.707050			0.353525	+	0.935425i	$0.384983\pi$
$734$		0			0
$735$		0			0
$736$	6.97372	−	9.16309i	0.257055	−	0.337756i
$737$		−	5.85993i		−	0.215853i
$738$		0			0
$739$		−	12.8510i		−	0.472732i	−0.971664	−	0.236366i	$-0.924043\pi$
$739$		−	12.8510i		−	0.472732i	0.971664	−	0.236366i	$-0.0759565\pi$
$740$	1.82505	+	4.73205i	0.0670903	+	0.173954i
$741$		0			0
$742$		0			0
$743$	−25.3717			−0.930797			−0.465399	−	0.885101i	$-0.654089\pi$
$743$	−25.3717			−0.930797			−0.465399	+	0.885101i	$0.654089\pi$
$744$		0			0
$745$	−3.10583			−0.113789
$746$	−23.5358	+	4.38134i	−0.861705	+	0.160412i
$747$		0			0
$748$	6.14729	+	15.9389i	0.224767	+	0.582783i
$749$		0			0
$750$		0			0
$751$			33.0023i			1.20427i	0.798395	+	0.602135i	$0.205683\pi$
$751$			33.0023i			1.20427i	−0.798395	+	0.602135i	$0.794317\pi$
$752$	31.8452	−	28.8564i	1.16128	−	1.05228i
$753$		0			0
$754$	−1.93185	−	10.3776i	−0.0703539	−	0.377928i
$755$	−5.75749			−0.209537
$756$		0			0
$757$	40.6410			1.47712			0.738561	−	0.674186i	$-0.235505\pi$
$757$	40.6410			1.47712			0.738561	+	0.674186i	$0.235505\pi$
$758$	7.05146	+	37.8792i	0.256121	+	1.37583i
$759$		0			0
$760$	9.80385	−	6.03983i	0.355623	−	0.219088i
$761$		−	37.1244i		−	1.34576i	−0.739753	−	0.672878i	$-0.765058\pi$
$761$		−	37.1244i		−	1.34576i	0.739753	−	0.672878i	$-0.234942\pi$
$762$		0			0
$763$		0			0
$764$	24.5536	−	9.46979i	0.888316	−	0.342605i
$765$		0			0
$766$	−29.8744	+	5.56131i	−1.07940	+	0.200938i
$767$	−7.05146			−0.254614
$768$		0			0
$769$	−2.72689			−0.0983342			−0.0491671	−	0.998791i	$-0.515657\pi$
$769$	−2.72689			−0.0983342			−0.0491671	+	0.998791i	$0.515657\pi$
$770$		0			0
$771$		0			0
$772$	−18.3923	+	7.09353i	−0.661954	+	0.255302i
$773$			11.5167i			0.414225i	0.978317	+	0.207113i	$0.0664067\pi$
$773$			11.5167i			0.414225i	−0.978317	+	0.207113i	$0.933593\pi$
$774$		0			0
$775$		−	43.0004i		−	1.54462i
$776$	−36.3045	+	22.3660i	−1.30326	+	0.802894i
$777$		0			0
$778$	8.43782	+	45.3264i	0.302511	+	1.62503i
$779$	−48.5617			−1.73990
$780$		0			0
$781$	−18.4974			−0.661890
$782$	−2.21073	−	11.8756i	−0.0790556	−	0.424672i
$783$		0			0
$784$		0			0
$785$		−	11.0363i		−	0.393903i
$786$		0			0
$787$			29.2967i			1.04432i	0.852849	+	0.522158i	$0.174873\pi$
$787$			29.2967i			1.04432i	−0.852849	+	0.522158i	$0.825127\pi$
$788$	11.0496	+	28.6496i	0.393624	+	1.02060i
$789$		0			0
$790$	5.07484	−	0.944717i	0.180555	−	0.0336115i
$791$		0			0
$792$		0			0
$793$	−13.3205			−0.473025
$794$	−24.1215	+	4.49038i	−0.856040	+	0.159358i
$795$		0			0
$796$	2.92996	+	7.59689i	0.103850	+	0.269265i
$797$			30.0526i			1.06452i	0.846582	+	0.532258i	$0.178656\pi$
$797$			30.0526i			1.06452i	−0.846582	+	0.532258i	$0.821344\pi$
$798$		0			0
$799$		−	45.0819i		−	1.59488i
$800$	−15.2936	+	20.0950i	−0.540711	+	0.710465i
$801$		0			0
$802$	9.90192	+	53.1913i	0.349649	+	1.87825i
$803$	−3.44342			−0.121516
$804$		0			0
$805$		0			0
$806$	3.52573	+	18.9396i	0.124189	+	0.667118i
$807$		0			0
$808$	7.81534	+	12.6858i	0.274943	+	0.446287i
$809$			24.7995i			0.871904i	0.899970	+	0.435952i	$0.143588\pi$
$809$			24.7995i			0.871904i	−0.899970	+	0.435952i	$0.856412\pi$
$810$		0			0
$811$			37.4390i			1.31466i	0.753602	+	0.657331i	$0.228315\pi$
$811$			37.4390i			1.31466i	−0.753602	+	0.657331i	$0.771685\pi$
$812$		0			0
$813$		0			0
$814$	9.80385	−	1.82505i	0.343625	−	0.0639681i
$815$	−17.8372			−0.624808
$816$		0			0
$817$	−43.7391			−1.53024
$818$	−14.1492	+	2.63397i	−0.494716	+	0.0920948i
$819$		0			0
$820$	−11.9282	+	4.60046i	−0.416551	+	0.160655i
$821$			5.55532i			0.193882i	0.995290	+	0.0969410i	$0.0309058\pi$
$821$			5.55532i			0.193882i	−0.995290	+	0.0969410i	$0.969094\pi$
$822$		0			0
$823$			28.0161i			0.976580i	0.872681	+	0.488290i	$0.162379\pi$
$823$			28.0161i			0.976580i	−0.872681	+	0.488290i	$0.837621\pi$
$824$	−24.7517	−	40.1769i	−0.862266	−	1.39963i
$825$		0			0
$826$		0			0
$827$	−24.2808			−0.844327			−0.422164	−	0.906520i	$-0.638729\pi$
$827$	−24.2808			−0.844327			−0.422164	+	0.906520i	$0.638729\pi$
$828$		0			0
$829$	−51.1619			−1.77693			−0.888463	−	0.458949i	$-0.848226\pi$
$829$	−51.1619			−1.77693			−0.888463	+	0.458949i	$0.848226\pi$
$830$	2.58101	+	13.8647i	0.0895883	+	0.481252i
$831$		0			0
$832$	5.08845	−	10.1048i	0.176410	−	0.350322i
$833$		0			0
$834$		0			0
$835$		−	7.86488i		−	0.272176i
$836$	−8.14722	−	21.1244i	−0.281778	−	0.730601i
$837$		0			0
$838$	−33.8768	+	6.30639i	−1.17025	+	0.217851i
$839$	−2.87875			−0.0993854			−0.0496927	−	0.998765i	$-0.515824\pi$
$839$	−2.87875			−0.0993854			−0.0496927	+	0.998765i	$0.515824\pi$
$840$		0			0
$841$	1.14359			0.0394343
$842$	41.3106	−	7.69024i	1.42366	−	0.265023i
$843$		0			0
$844$	15.4641	+	40.0958i	0.532296	+	1.38015i
$845$		−	8.05256i		−	0.277016i
$846$		0			0
$847$		0			0
$848$	24.5536	+	27.0967i	0.843172	+	0.930504i
$849$		0			0
$850$	4.84821	+	26.0437i	0.166292	+	0.893292i
$851$	−7.05146			−0.241721
$852$		0			0
$853$	15.6307			0.535184			0.267592	−	0.963532i	$-0.413772\pi$
$853$	15.6307			0.535184			0.267592	+	0.963532i	$0.413772\pi$
$854$		0			0
$855$		0			0
$856$	−31.6865	+	19.5210i	−1.08302	+	0.667216i
$857$		−	11.2679i		−	0.384906i	−0.981306	−	0.192453i	$-0.938356\pi$
$857$		−	11.2679i		−	0.384906i	0.981306	−	0.192453i	$-0.0616443\pi$
$858$		0			0
$859$		−	51.1427i		−	1.74497i	−0.488645	−	0.872483i	$-0.662509\pi$
$859$		−	51.1427i		−	1.74497i	0.488645	−	0.872483i	$-0.337491\pi$
$860$	−10.7436	+	4.14359i	−0.366355	+	0.141295i
$861$		0			0
$862$	−45.0788	+	8.39173i	−1.53539	+	0.285824i
$863$	31.3323			1.06656			0.533282	−	0.845938i	$-0.320959\pi$
$863$	31.3323			1.06656			0.533282	+	0.845938i	$0.320959\pi$
$864$		0			0
$865$	−7.07180			−0.240448
$866$	20.5747	−	3.83013i	0.699158	−	0.130153i
$867$		0			0
$868$		0			0
$869$		−	10.1497i		−	0.344305i
$870$		0			0
$871$			4.07116i			0.137946i
$872$	−14.4487	+	8.90138i	−0.489295	+	0.301439i
$873$		0			0
$874$	2.92996	+	15.7392i	0.0991075	+	0.532387i
$875$		0			0
$876$		0			0
$877$	23.3205			0.787478			0.393739	−	0.919222i	$-0.371181\pi$
$877$	23.3205			0.787478			0.393739	+	0.919222i	$0.371181\pi$
$878$	7.09353	+	38.1051i	0.239395	+	1.28599i
$879$		0			0
$880$	−4.00240	−	4.41695i	−0.134921	−	0.148895i
$881$			42.4449i			1.43000i	0.699123	+	0.715002i	$0.253574\pi$
$881$			42.4449i			1.43000i	−0.699123	+	0.715002i	$0.746426\pi$
$882$		0			0
$883$			9.40760i			0.316591i	0.987392	+	0.158295i	$0.0505999\pi$
$883$			9.40760i			0.316591i	−0.987392	+	0.158295i	$0.949400\pi$
$884$	−4.27081	−	11.0735i	−0.143643	−	0.372441i
$885$		0			0
$886$	14.1506	−	2.63424i	0.475400	−	0.0884989i
$887$	26.4734			0.888890			0.444445	−	0.895806i	$-0.353401\pi$
$887$	26.4734			0.888890			0.444445	+	0.895806i	$0.353401\pi$
$888$		0			0
$889$		0			0
$890$	−8.88740	+	1.65445i	−0.297906	+	0.0554573i
$891$		0			0
$892$	−10.9348	−	28.3520i	−0.366123	−	0.949295i
$893$			59.7487i			1.99941i
$894$		0			0
$895$			12.6128i			0.421599i
$896$		0			0
$897$		0			0
$898$	8.36603	+	44.9407i	0.279178	+	1.49969i
$899$	50.8394			1.69559
$900$		0			0
$901$	38.3596			1.27794
$902$	4.60046	+	24.7128i	0.153178	+	0.822847i
$903$		0			0
$904$	−0.973721	−	1.58054i	−0.0323855	−	0.0525680i
$905$		−	3.66063i		−	0.121684i
$906$		0			0
$907$		−	17.8372i		−	0.592273i	−0.955146	−	0.296137i	$-0.904302\pi$
$907$		−	17.8372i		−	0.592273i	0.955146	−	0.296137i	$-0.0956983\pi$
$908$	20.0479	−	7.73205i	0.665313	−	0.256597i
$909$		0			0
$910$		0			0
$911$	36.4943			1.20911			0.604555	−	0.796563i	$-0.293351\pi$
$911$	36.4943			1.20911			0.604555	+	0.796563i	$0.293351\pi$
$912$		0			0
$913$	27.7295			0.917711
$914$	31.8777	−	5.93426i	1.05442	−	0.196288i
$915$		0			0
$916$	47.3118	−	18.2472i	1.56323	−	0.602903i
$917$		0			0
$918$		0			0
$919$		−	29.3521i		−	0.968238i	−0.875002	−	0.484119i	$-0.839140\pi$
$919$		−	29.3521i		−	0.968238i	0.875002	−	0.484119i	$-0.160860\pi$
$920$	2.21073	+	3.58846i	0.0728857	+	0.118308i
$921$		0			0
$922$	2.39872	+	12.8855i	0.0789977	+	0.424361i
$923$	12.8510			0.422997
$924$		0			0
$925$	15.4641			0.508457
$926$	1.83594	+	9.86233i	0.0603327	+	0.324096i
$927$		0			0
$928$	−23.7583	−	18.0817i	−0.779905	−	0.593560i
$929$		−	45.9090i		−	1.50622i	−0.657892	−	0.753112i	$-0.728552\pi$
$929$		−	45.9090i		−	1.50622i	0.657892	−	0.753112i	$-0.271448\pi$
$930$		0			0
$931$		0			0
$932$	4.19773	+	10.8840i	0.137501	+	0.356517i
$933$		0			0
$934$	17.8671	−	3.32609i	0.584631	−	0.108833i
$935$	−6.25289			−0.204491
$936$		0			0
$937$	54.9513			1.79518			0.897590	−	0.440832i	$-0.145317\pi$
$937$	54.9513			1.79518			0.897590	+	0.440832i	$0.145317\pi$
$938$		0			0
$939$		0			0
$940$	5.66025	+	14.6761i	0.184617	+	0.478681i
$941$		−	61.2295i		−	1.99602i	−0.0630259	−	0.998012i	$-0.520075\pi$
$941$		−	61.2295i		−	1.99602i	0.0630259	−	0.998012i	$-0.479925\pi$
$942$		0			0
$943$		−	17.7748i		−	0.578827i
$944$	−14.7794	+	13.3923i	−0.481029	+	0.435882i
$945$		0			0
$946$	4.14359	+	22.2586i	0.134720	+	0.723690i
$947$	24.2808			0.789021			0.394511	−	0.918891i	$-0.370914\pi$
$947$	24.2808			0.789021			0.394511	+	0.918891i	$0.370914\pi$
$948$		0			0
$949$	2.39230			0.0776575
$950$	−6.42551	−	34.5167i	−0.208471	−	1.11987i
$951$		0			0
$952$		0			0
$953$			0.656339i			0.0212609i	0.999943	+	0.0106304i	$0.00338384\pi$
$953$			0.656339i			0.0212609i	−0.999943	+	0.0106304i	$0.996616\pi$
$954$		0			0
$955$			9.63248i			0.311700i
$956$	3.79845	−	1.46498i	0.122851	−	0.0473809i
$957$		0			0
$958$	−17.8671	+	3.32609i	−0.577261	+	0.107461i
$959$		0			0
$960$		0			0
$961$	−61.7846			−1.99305
$962$	−6.81119	+	1.26795i	−0.219602	+	0.0408803i
$963$		0			0
$964$	24.2683	−	9.35976i	0.781628	−	0.301458i
$965$		−	7.21539i		−	0.232272i
$966$		0			0
$967$		−	34.3383i		−	1.10424i	−0.833763	−	0.552122i	$-0.813818\pi$
$967$		−	34.3383i		−	1.10424i	0.833763	−	0.552122i	$-0.186182\pi$
$968$	16.5110	−	10.1719i	0.530685	−	0.326938i
$969$		0			0
$970$	−2.85641	−	15.3441i	−0.0917137	−	0.492669i
$971$	−23.5947			−0.757188			−0.378594	−	0.925563i	$-0.623592\pi$
$971$	−23.5947			−0.757188			−0.378594	+	0.925563i	$0.623592\pi$
$972$		0			0
$973$		0			0
$974$	3.52573	+	18.9396i	0.112972	+	0.606863i
$975$		0			0
$976$	−27.9189	+	25.2986i	−0.893663	+	0.809789i
$977$		−	26.3896i		−	0.844278i	−0.906531	−	0.422139i	$-0.861279\pi$
$977$		−	26.3896i		−	0.844278i	0.906531	−	0.422139i	$-0.138721\pi$
$978$		0			0
$979$			17.7748i			0.568085i
$980$		0			0
$981$		0			0
$982$	18.2942	−	3.40559i	0.583792	−	0.108677i
$983$	12.0797			0.385281			0.192641	−	0.981269i	$-0.438295\pi$
$983$	12.0797			0.385281			0.192641	+	0.981269i	$0.438295\pi$
$984$		0			0
$985$	−11.2394			−0.358116
$986$	−30.7915	+	5.73205i	−0.980602	+	0.182546i
$987$		0			0
$988$	5.66025	+	14.6761i	0.180077	+	0.466908i
$989$		−	16.0096i		−	0.509076i
$990$		0			0
$991$			23.5947i			0.749509i	0.927124	+	0.374754i	$0.122273\pi$
$991$			23.5947i			0.749509i	−0.927124	+	0.374754i	$0.877727\pi$
$992$	43.3602	+	33.0000i	1.37669	+	1.04775i
$993$		0			0
$994$		0			0
$995$	−2.98030			−0.0944818
$996$		0			0
$997$	−5.27792			−0.167153			−0.0835767	−	0.996501i	$-0.526634\pi$
$997$	−5.27792			−0.167153			−0.0835767	+	0.996501i	$0.526634\pi$
$998$	7.59689	+	40.8091i	0.240476	+	1.29179i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.e.j.1079.4	yes	16
3.2	odd	2	inner	1764.2.e.j.1079.13	yes	16
4.3	odd	2	inner	1764.2.e.j.1079.16	yes	16
7.6	odd	2	inner	1764.2.e.j.1079.3	yes	16
12.11	even	2	inner	1764.2.e.j.1079.1	✓	16
21.20	even	2	inner	1764.2.e.j.1079.14	yes	16
28.27	even	2	inner	1764.2.e.j.1079.15	yes	16
84.83	odd	2	inner	1764.2.e.j.1079.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.e.j.1079.1	✓	16	12.11	even	2	inner
1764.2.e.j.1079.2	yes	16	84.83	odd	2	inner
1764.2.e.j.1079.3	yes	16	7.6	odd	2	inner
1764.2.e.j.1079.4	yes	16	1.1	even	1	trivial
1764.2.e.j.1079.13	yes	16	3.2	odd	2	inner
1764.2.e.j.1079.14	yes	16	21.20	even	2	inner
1764.2.e.j.1079.15	yes	16	28.27	even	2	inner
1764.2.e.j.1079.16	yes	16	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39033 + 0.258819i) q^{2} +(1.86603 - 0.719687i) q^{4} +0.732051i q^{5} +(-2.40812 + 1.48356i) q^{8} +O(q^{10})\)	\(q+(-1.39033 + 0.258819i) q^{2} +(1.86603 - 0.719687i) q^{4} +0.732051i q^{5} +(-2.40812 + 1.48356i) q^{8} +(-0.189469 - 1.01779i) q^{10} -2.03558 q^{11} +1.41421 q^{13} +(2.96410 - 2.68591i) q^{16} -4.19615i q^{17} +5.56131i q^{19} +(0.526847 + 1.36603i) q^{20} +(2.83013 - 0.526847i) q^{22} -2.03558 q^{23} +4.46410 q^{25} +(-1.96622 + 0.366025i) q^{26} +5.27792i q^{29} -9.63248i q^{31} +(-3.42591 + 4.50146i) q^{32} +(1.08604 + 5.83403i) q^{34} +3.46410 q^{37} +(-1.43937 - 7.73205i) q^{38} +(-1.08604 - 1.76287i) q^{40} +8.73205i q^{41} +7.86488i q^{43} +(-3.79845 + 1.46498i) q^{44} +(2.83013 - 0.526847i) q^{46} +10.7436 q^{47} +(-6.20657 + 1.15539i) q^{50} +(2.63896 - 1.01779i) q^{52} +9.14162i q^{53} -1.49015i q^{55} +(-1.36603 - 7.33804i) q^{58} -4.98614 q^{59} -9.41902 q^{61} +(2.49307 + 13.3923i) q^{62} +(3.59808 - 7.14520i) q^{64} +1.03528i q^{65} +2.87875i q^{67} +(-3.01992 - 7.83013i) q^{68} +9.08704 q^{71} +1.69161 q^{73} +(-4.81624 + 0.896575i) q^{74} +(4.00240 + 10.3776i) q^{76} +4.98614i q^{79} +(1.96622 + 2.16987i) q^{80} +(-2.26002 - 12.1404i) q^{82} -13.6224 q^{83} +3.07180 q^{85} +(-2.03558 - 10.9348i) q^{86} +(4.90192 - 3.01992i) q^{88} -8.73205i q^{89} +(-3.79845 + 1.46498i) q^{92} +(-14.9372 + 2.78066i) q^{94} -4.07116 q^{95} +15.0759 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4}+O(q^{10}) \) 16 * q + 16 * q^4	\( 16 q + 16 q^{4} - 8 q^{16} - 24 q^{22} + 16 q^{25} - 24 q^{46} - 8 q^{58} + 16 q^{64} + 160 q^{85} + 120 q^{88}+O(q^{100}) \) 16 * q + 16 * q^4 - 8 * q^16 - 24 * q^22 + 16 * q^25 - 24 * q^46 - 8 * q^58 + 16 * q^64 + 160 * q^85 + 120 * q^88

Introduction

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