LMFDB - Embedded newform 1764.2.e.g.1079.7

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:	$12$
Coefficient field:	12.0.653473922154496.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 $ x^12 - 4x^10 + 13x^8 - 28x^6 + 52x^4 - 64*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1079.7
Root			$0.892524 + 1.09700i$ of defining polynomial
Character	$\chi$	$=$	1764.1079
Dual form			1764.2.e.g.1079.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.892524 - 1.09700i) q^{2} +(-0.406803 - 1.95819i) q^{4} +2.56483i q^{5} +(-2.51121 - 1.30147i) q^{8} +O(q^{10})$	\(q+(0.892524 - 1.09700i) q^{2} +(-0.406803 - 1.95819i) q^{4} +2.56483i q^{5} +(-2.51121 - 1.30147i) q^{8} +(2.81361 + 2.28917i) q^{10} +1.15061 q^{11} +0.578337 q^{13} +(-3.66902 + 1.59320i) q^{16} +5.39325i q^{17} -6.20555i q^{19} +(5.02242 - 1.04338i) q^{20} +(1.02695 - 1.26222i) q^{22} +7.62536 q^{23} -1.57834 q^{25} +(0.516180 - 0.634434i) q^{26} +1.41421i q^{29} +5.04888i q^{31} +(-1.52696 + 5.44687i) q^{32} +(5.91638 + 4.81361i) q^{34} +9.83276 q^{37} +(-6.80747 - 5.53860i) q^{38} +(3.33804 - 6.44082i) q^{40} -6.21115i q^{41} +11.2544i q^{43} +(-0.468073 - 2.25312i) q^{44} +(6.80581 - 8.36499i) q^{46} +11.0772 q^{47} +(-1.40870 + 1.73143i) q^{50} +(-0.235269 - 1.13249i) q^{52} +4.53333i q^{53} +2.95112i q^{55} +(1.55139 + 1.26222i) q^{58} +4.83896 q^{59} -0.951124 q^{61} +(5.53860 + 4.50624i) q^{62} +(4.61235 + 6.53653i) q^{64} +1.48333i q^{65} -2.78389i q^{67} +(10.5610 - 2.19399i) q^{68} +3.68835 q^{71} -14.0383 q^{73} +(8.77597 - 10.7865i) q^{74} +(-12.1517 + 2.52444i) q^{76} -12.8816i q^{79} +(-4.08627 - 9.41041i) q^{80} +(-6.81361 - 5.54359i) q^{82} +8.77597 q^{83} -13.8328 q^{85} +(12.3461 + 10.0448i) q^{86} +(-2.88943 - 1.49749i) q^{88} +5.68395i q^{89} +(-3.10202 - 14.9319i) q^{92} +(9.88666 - 12.1517i) q^{94} +15.9162 q^{95} +12.8816 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4}+O(q^{10}) $ 12 * q + 8 * q^4	$ 12 q + 8 q^{4} + 8 q^{10} - 20 q^{16} + 20 q^{22} - 12 q^{25} + 16 q^{34} + 8 q^{37} - 8 q^{40} - 36 q^{46} + 16 q^{52} + 4 q^{58} - 56 q^{61} - 16 q^{64} - 72 q^{76} - 56 q^{82} - 56 q^{85} + 28 q^{88} + 24 q^{94}+O(q^{100}) $ 12 * q + 8 * q^4 + 8 * q^10 - 20 * q^16 + 20 * q^22 - 12 * q^25 + 16 * q^34 + 8 * q^37 - 8 * q^40 - 36 * q^46 + 16 * q^52 + 4 * q^58 - 56 * q^61 - 16 * q^64 - 72 * q^76 - 56 * q^82 - 56 * q^85 + 28 * q^88 + 24 * q^94

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 $

$2$	0.892524	−	1.09700i	0.631109	−	0.775694i
$2$	0.892524	−	1.09700i	0.631109	−	0.775694i
$3$		0			0
$3$		0			0
$4$	−0.406803	−	1.95819i	−0.203402	−	0.979095i
$5$			2.56483i			1.14703i	0.819197	+	0.573513i	$0.194420\pi$
$5$			2.56483i			1.14703i	−0.819197	+	0.573513i	$0.805580\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−2.51121	−	1.30147i	−0.887847	−	0.460139i
$9$		0			0
$10$	2.81361	+	2.28917i	0.889740	+	0.723899i
$11$	1.15061			0.346923			0.173461	−	0.984841i	$-0.444505\pi$
$11$	1.15061			0.346923			0.173461	+	0.984841i	$0.444505\pi$
$12$		0			0
$13$	0.578337			0.160402			0.0802009	−	0.996779i	$-0.474444\pi$
$13$	0.578337			0.160402			0.0802009	+	0.996779i	$0.474444\pi$
$14$		0			0
$15$		0			0
$16$	−3.66902	+	1.59320i	−0.917256	+	0.398299i
$17$			5.39325i			1.30806i	0.756470	+	0.654028i	$0.226922\pi$
$17$			5.39325i			1.30806i	−0.756470	+	0.654028i	$0.773078\pi$
$18$		0			0
$19$		−	6.20555i		−	1.42365i	−0.702356	−	0.711825i	$-0.747869\pi$
$19$		−	6.20555i		−	1.42365i	0.702356	−	0.711825i	$-0.252131\pi$
$20$	5.02242	−	1.04338i	1.12305	−	0.233307i
$21$		0			0
$22$	1.02695	−	1.26222i	0.218946	−	0.269106i
$23$	7.62536			1.59000			0.794999	−	0.606611i	$-0.207471\pi$
$23$	7.62536			1.59000			0.794999	+	0.606611i	$0.207471\pi$
$24$		0			0
$25$	−1.57834			−0.315667
$26$	0.516180	−	0.634434i	0.101231	−	0.124423i
$27$		0			0
$28$		0			0
$29$			1.41421i			0.262613i	0.991342	+	0.131306i	$0.0419172\pi$
$29$			1.41421i			0.262613i	−0.991342	+	0.131306i	$0.958083\pi$
$30$		0			0
$31$			5.04888i			0.906805i	0.891306	+	0.453402i	$0.149790\pi$
$31$			5.04888i			0.906805i	−0.891306	+	0.453402i	$0.850210\pi$
$32$	−1.52696	+	5.44687i	−0.269930	+	0.962880i
$33$		0			0
$34$	5.91638	+	4.81361i	1.01465	+	0.825527i
$35$		0			0
$36$		0			0
$37$	9.83276			1.61650			0.808248	−	0.588842i	$-0.200416\pi$
$37$	9.83276			1.61650			0.808248	+	0.588842i	$0.200416\pi$
$38$	−6.80747	−	5.53860i	−1.10432	−	0.898480i
$39$		0			0
$40$	3.33804	−	6.44082i	0.527791	−	1.01838i
$41$		−	6.21115i		−	0.970018i	−0.874509	−	0.485009i	$-0.838816\pi$
$41$		−	6.21115i		−	0.970018i	0.874509	−	0.485009i	$-0.161184\pi$
$42$		0			0
$43$			11.2544i			1.71628i	0.513413	+	0.858142i	$0.328381\pi$
$43$			11.2544i			1.71628i	−0.513413	+	0.858142i	$0.671619\pi$
$44$	−0.468073	−	2.25312i	−0.0705647	−	0.339671i
$45$		0			0
$46$	6.80581	−	8.36499i	1.00346	−	1.23335i
$47$	11.0772			1.61578			0.807888	−	0.589336i	$-0.200611\pi$
$47$	11.0772			1.61578			0.807888	+	0.589336i	$0.200611\pi$
$48$		0			0
$49$		0			0
$50$	−1.40870	+	1.73143i	−0.199221	+	0.244861i
$51$		0			0
$52$	−0.235269	−	1.13249i	−0.0326260	−	0.157049i
$53$			4.53333i			0.622701i	0.950295	+	0.311351i	$0.100781\pi$
$53$			4.53333i			0.622701i	−0.950295	+	0.311351i	$0.899219\pi$
$54$		0			0
$55$			2.95112i			0.397929i
$56$		0			0
$57$		0			0
$58$	1.55139	+	1.26222i	0.203707	+	0.165737i
$59$	4.83896			0.629979			0.314990	−	0.949095i	$-0.397999\pi$
$59$	4.83896			0.629979			0.314990	+	0.949095i	$0.397999\pi$
$60$		0			0
$61$	−0.951124			−0.121779			−0.0608895	−	0.998145i	$-0.519394\pi$
$61$	−0.951124			−0.121779			−0.0608895	+	0.998145i	$0.519394\pi$
$62$	5.53860	+	4.50624i	0.703403	+	0.572293i
$63$		0			0
$64$	4.61235	+	6.53653i	0.576544	+	0.817066i
$65$			1.48333i			0.183985i
$66$		0			0
$67$		−	2.78389i		−	0.340106i	−0.985435	−	0.170053i	$-0.945606\pi$
$67$		−	2.78389i		−	0.340106i	0.985435	−	0.170053i	$-0.0543939\pi$
$68$	10.5610	−	2.19399i	1.28071	−	0.266061i
$69$		0			0
$70$		0			0
$71$	3.68835			0.437726			0.218863	−	0.975756i	$-0.429765\pi$
$71$	3.68835			0.437726			0.218863	+	0.975756i	$0.429765\pi$
$72$		0			0
$73$	−14.0383			−1.64306			−0.821530	−	0.570165i	$-0.806879\pi$
$73$	−14.0383			−1.64306			−0.821530	+	0.570165i	$0.806879\pi$
$74$	8.77597	−	10.7865i	1.02019	−	1.25391i
$75$		0			0
$76$	−12.1517	+	2.52444i	−1.39389	+	0.289573i
$77$		0			0
$78$		0			0
$79$		−	12.8816i		−	1.44930i	−0.689118	−	0.724649i	$-0.742002\pi$
$79$		−	12.8816i		−	1.44930i	0.689118	−	0.724649i	$-0.257998\pi$
$80$	−4.08627	−	9.41041i	−0.456859	−	1.05212i
$81$		0			0
$82$	−6.81361	−	5.54359i	−0.752437	−	0.612188i
$83$	8.77597			0.963288			0.481644	−	0.876367i	$-0.340040\pi$
$83$	8.77597			0.963288			0.481644	+	0.876367i	$0.340040\pi$
$84$		0			0
$85$	−13.8328			−1.50037
$86$	12.3461	+	10.0448i	1.33131	+	1.08316i
$87$		0			0
$88$	−2.88943	−	1.49749i	−0.308014	−	0.159633i
$89$			5.68395i			0.602497i	0.953546	+	0.301249i	$0.0974034\pi$
$89$			5.68395i			0.602497i	−0.953546	+	0.301249i	$0.902597\pi$
$90$		0			0
$91$		0			0
$92$	−3.10202	−	14.9319i	−0.323408	−	1.55676i
$93$		0			0
$94$	9.88666	−	12.1517i	1.01973	−	1.25335i
$95$	15.9162			1.63296
$96$		0			0
$97$	12.8816			1.30793			0.653966	−	0.756524i	$-0.273104\pi$
$97$	12.8816			1.30793			0.653966	+	0.756524i	$0.273104\pi$
$98$		0			0
$99$		0			0
$100$	0.642073	+	3.09069i	0.0642073	+	0.309069i
$101$		−	3.75747i		−	0.373882i	−0.982371	−	0.186941i	$-0.940143\pi$
$101$		−	3.75747i		−	0.373882i	0.982371	−	0.186941i	$-0.0598574\pi$
$102$		0			0
$103$			1.79445i			0.176812i	0.996085	+	0.0884062i	$0.0281774\pi$
$103$			1.79445i			0.176812i	−0.996085	+	0.0884062i	$0.971823\pi$
$104$	−1.45233	−	0.752688i	−0.142412	−	0.0738071i
$105$		0			0
$106$	4.97305	+	4.04611i	0.483025	+	0.392993i
$107$	−10.1631			−0.982503			−0.491252	−	0.871018i	$-0.663460\pi$
$107$	−10.1631			−0.982503			−0.491252	+	0.871018i	$0.663460\pi$
$108$		0			0
$109$	−15.2544			−1.46111			−0.730555	−	0.682854i	$-0.760738\pi$
$109$	−15.2544			−1.46111			−0.730555	+	0.682854i	$0.760738\pi$
$110$	3.23737	+	2.63395i	0.308671	+	0.251137i
$111$		0			0
$112$		0			0
$113$			5.06053i			0.476055i	0.971258	+	0.238027i	$0.0765008\pi$
$113$			5.06053i			0.476055i	−0.971258	+	0.238027i	$0.923499\pi$
$114$		0			0
$115$			19.5577i			1.82377i
$116$	2.76930	−	0.575307i	0.257123	−	0.0534159i
$117$		0			0
$118$	4.31889	−	5.30833i	0.397586	−	0.488671i
$119$		0			0
$120$		0			0
$121$	−9.67609			−0.879644
$122$	−0.848901	+	1.04338i	−0.0768559	+	0.0944632i
$123$		0			0
$124$	9.88666	−	2.05390i	0.887848	−	0.184446i
$125$			8.77597i			0.784947i
$126$		0			0
$127$			0.470539i			0.0417536i	0.999782	+	0.0208768i	$0.00664577\pi$
$127$			0.470539i			0.0417536i	−0.999782	+	0.0208768i	$0.993354\pi$
$128$	11.2872	+	0.774269i	0.997655	+	0.0684364i
$129$		0			0
$130$	1.62721	+	1.32391i	0.142716	+	0.116115i
$131$	15.9162			1.39060			0.695301	−	0.718719i	$-0.255271\pi$
$131$	15.9162			1.39060			0.695301	+	0.718719i	$0.255271\pi$
$132$		0			0
$133$		0			0
$134$	−3.05391	−	2.48469i	−0.263818	−	0.214644i
$135$		0			0
$136$	7.01916	−	13.5436i	0.601888	−	1.16135i
$137$			8.55440i			0.730852i	0.930840	+	0.365426i	$0.119077\pi$
$137$			8.55440i			0.730852i	−0.930840	+	0.365426i	$0.880923\pi$
$138$		0			0
$139$		−	16.0000i		−	1.35710i	−0.734553	−	0.678551i	$-0.762608\pi$
$139$		−	16.0000i		−	1.35710i	0.734553	−	0.678551i	$-0.237392\pi$
$140$		0			0
$141$		0			0
$142$	3.29194	−	4.04611i	0.276253	−	0.339542i
$143$	0.665442			0.0556471
$144$		0			0
$145$	−3.62721			−0.301224
$146$	−12.5295	+	15.4000i	−1.03695	+	1.27451i
$147$		0			0
$148$	−4.00000	−	19.2544i	−0.328798	−	1.58270i
$149$		−	16.8032i		−	1.37657i	−0.725441	−	0.688285i	$-0.758364\pi$
$149$		−	16.8032i		−	1.37657i	0.725441	−	0.688285i	$-0.241636\pi$
$150$		0			0
$151$			2.09775i			0.170713i	0.996350	+	0.0853563i	$0.0272029\pi$
$151$			2.09775i			0.170713i	−0.996350	+	0.0853563i	$0.972797\pi$
$152$	−8.07634	+	15.5834i	−0.655077	+	1.26398i
$153$		0			0
$154$		0			0
$155$	−12.9495			−1.04013
$156$		0			0
$157$	−17.3622			−1.38566			−0.692828	−	0.721103i	$-0.743636\pi$
$157$	−17.3622			−1.38566			−0.692828	+	0.721103i	$0.743636\pi$
$158$	−14.1311	−	11.4972i	−1.12421	−	0.914665i
$159$		0			0
$160$	−13.9703	−	3.91638i	−1.10445	−	0.309617i
$161$		0			0
$162$		0			0
$163$		−	0.470539i		−	0.0368554i	−0.999830	−	0.0184277i	$-0.994134\pi$
$163$		−	0.470539i		−	0.0368554i	0.999830	−	0.0184277i	$-0.00586606\pi$
$164$	−12.1626	+	2.52671i	−0.949740	+	0.197303i
$165$		0			0
$166$	7.83276	−	9.62721i	0.607940	−	0.747217i
$167$	−20.7551			−1.60608			−0.803040	−	0.595925i	$-0.796785\pi$
$167$	−20.7551			−1.60608			−0.803040	+	0.595925i	$0.796785\pi$
$168$		0			0
$169$	−12.6655			−0.974271
$170$	−12.3461	+	15.1745i	−0.946900	+	1.16383i
$171$		0			0
$172$	22.0383	−	4.57834i	1.68041	−	0.349095i
$173$		−	14.1692i		−	1.07727i	−0.842540	−	0.538633i	$-0.818941\pi$
$173$		−	14.1692i		−	1.07727i	0.842540	−	0.538633i	$-0.181059\pi$
$174$		0			0
$175$		0			0
$176$	−4.22163	+	1.83315i	−0.318217	+	0.138179i
$177$		0			0
$178$	6.23527	+	5.07306i	0.467353	+	0.380242i
$179$	1.15061			0.0860009			0.0430004	−	0.999075i	$-0.486308\pi$
$179$	1.15061			0.0860009			0.0430004	+	0.999075i	$0.486308\pi$
$180$		0			0
$181$	−3.83276			−0.284887			−0.142444	−	0.989803i	$-0.545496\pi$
$181$	−3.83276			−0.284887			−0.142444	+	0.989803i	$0.545496\pi$
$182$		0			0
$183$		0			0
$184$	−19.1489	−	9.92417i	−1.41167	−	0.731620i
$185$			25.2193i			1.85416i
$186$		0			0
$187$			6.20555i			0.453795i
$188$	−4.50624	−	21.6913i	−0.328651	−	1.58200i
$189$		0			0
$190$	14.2056	−	17.4600i	1.03058	−	1.26668i
$191$	−9.92659			−0.718263			−0.359131	−	0.933287i	$-0.616927\pi$
$191$	−9.92659			−0.718263			−0.359131	+	0.933287i	$0.616927\pi$
$192$		0			0
$193$	12.6761			0.912445			0.456222	−	0.889866i	$-0.349202\pi$
$193$	12.6761			0.912445			0.456222	+	0.889866i	$0.349202\pi$
$194$	11.4972	−	14.1311i	0.825448	−	1.01455i
$195$		0			0
$196$		0			0
$197$			1.70491i			0.121469i	0.998154	+	0.0607347i	$0.0193444\pi$
$197$			1.70491i			0.121469i	−0.998154	+	0.0607347i	$0.980656\pi$
$198$		0			0
$199$			14.8433i			1.05222i	0.850418	+	0.526108i	$0.176349\pi$
$199$			14.8433i			1.05222i	−0.850418	+	0.526108i	$0.823651\pi$
$200$	3.96354	+	2.05416i	0.280264	+	0.145251i
$201$		0			0
$202$	−4.12193	−	3.35363i	−0.290018	−	0.235961i
$203$		0			0
$204$		0			0
$205$	15.9305			1.11264
$206$	1.96851	+	1.60159i	0.137152	+	0.111588i
$207$		0			0
$208$	−2.12193	+	0.921405i	−0.147129	+	0.0638879i
$209$		−	7.14019i		−	0.493897i
$210$		0			0
$211$		−	1.15667i		−	0.0796287i	−0.999207	−	0.0398144i	$-0.987323\pi$
$211$		−	1.15667i		−	0.0796287i	0.999207	−	0.0398144i	$-0.0126767\pi$
$212$	8.87713	−	1.84417i	0.609684	−	0.126658i
$213$		0			0
$214$	−9.07080	+	11.1489i	−0.620067	+	0.762122i
$215$	−28.8657			−1.96862
$216$		0			0
$217$		0			0
$218$	−13.6149	+	16.7341i	−0.922120	+	1.13337i
$219$		0			0
$220$	5.77886	−	1.20053i	0.389611	−	0.0809395i
$221$			3.11912i			0.209815i
$222$		0			0
$223$		−	23.6655i		−	1.58476i	−0.610027	−	0.792380i	$-0.708842\pi$
$223$		−	23.6655i		−	1.58476i	0.610027	−	0.792380i	$-0.291158\pi$
$224$		0			0
$225$		0			0
$226$	5.55139	+	4.51664i	0.369273	+	0.300443i
$227$	9.44142			0.626649			0.313324	−	0.949646i	$-0.398557\pi$
$227$	9.44142			0.626649			0.313324	+	0.949646i	$0.398557\pi$
$228$		0			0
$229$	0.578337			0.0382176			0.0191088	−	0.999817i	$-0.493917\pi$
$229$	0.578337			0.0382176			0.0191088	+	0.999817i	$0.493917\pi$
$230$	21.4548	+	17.4557i	1.41469	+	1.15100i
$231$		0			0
$232$	1.84056	−	3.55139i	0.120838	−	0.233160i
$233$		−	0.305630i		−	0.0200225i	−0.999950	−	0.0100112i	$-0.996813\pi$
$233$		−	0.305630i		−	0.0200225i	0.999950	−	0.0100112i	$-0.00318673\pi$
$234$		0			0
$235$			28.4111i			1.85334i
$236$	−1.96851	−	9.47561i	−0.128139	−	0.616810i
$237$		0			0
$238$		0			0
$239$	9.92659			0.642098			0.321049	−	0.947063i	$-0.395965\pi$
$239$	9.92659			0.642098			0.321049	+	0.947063i	$0.395965\pi$
$240$		0			0
$241$	−9.29274			−0.598598			−0.299299	−	0.954159i	$-0.596753\pi$
$241$	−9.29274			−0.598598			−0.299299	+	0.954159i	$0.596753\pi$
$242$	−8.63614	+	10.6146i	−0.555152	+	0.682335i
$243$		0			0
$244$	0.386920	+	1.86248i	0.0247700	+	0.119233i
$245$		0			0
$246$		0			0
$247$		−	3.58890i		−	0.228356i
$248$	6.57096	−	12.6788i	0.417256	−	0.805104i
$249$		0			0
$250$	9.62721	+	7.83276i	0.608878	+	0.495387i
$251$	−3.93701			−0.248502			−0.124251	−	0.992251i	$-0.539653\pi$
$251$	−3.93701			−0.248502			−0.124251	+	0.992251i	$0.539653\pi$
$252$		0			0
$253$	8.77384			0.551607
$254$	0.516180	+	0.419967i	0.0323880	+	0.0263511i
$255$		0			0
$256$	10.9234	−	11.6909i	0.682716	−	0.730684i
$257$			15.8891i			0.991133i	0.868570	+	0.495566i	$0.165040\pi$
$257$			15.8891i			0.991133i	−0.868570	+	0.495566i	$0.834960\pi$
$258$		0			0
$259$		0			0
$260$	2.90465	−	0.603425i	0.180139	−	0.0374228i
$261$		0			0
$262$	14.2056	−	17.4600i	0.877622	−	1.07868i
$263$	1.38712			0.0855336			0.0427668	−	0.999085i	$-0.486383\pi$
$263$	1.38712			0.0855336			0.0427668	+	0.999085i	$0.486383\pi$
$264$		0			0
$265$	−11.6272			−0.714254
$266$		0			0
$267$		0			0
$268$	−5.45138	+	1.13249i	−0.332996	+	0.0691781i
$269$		−	1.60869i		−	0.0980837i	−0.998797	−	0.0490419i	$-0.984383\pi$
$269$		−	1.60869i		−	0.0980837i	0.998797	−	0.0490419i	$-0.0156168\pi$
$270$		0			0
$271$			8.30330i			0.504390i	0.967676	+	0.252195i	$0.0811524\pi$
$271$			8.30330i			0.504390i	−0.967676	+	0.252195i	$0.918848\pi$
$272$	−8.59251	−	19.7880i	−0.520998	−	1.19982i
$273$		0			0
$274$	9.38415	+	7.63501i	0.566917	+	0.461248i
$275$	−1.81606			−0.109512
$276$		0			0
$277$	−3.83276			−0.230288			−0.115144	−	0.993349i	$-0.536733\pi$
$277$	−3.83276			−0.230288			−0.115144	+	0.993349i	$0.536733\pi$
$278$	−17.5519	−	14.2804i	−1.05270	−	0.856480i
$279$		0			0
$280$		0			0
$281$			28.9348i			1.72610i	0.505115	+	0.863052i	$0.331450\pi$
$281$			28.9348i			1.72610i	−0.505115	+	0.863052i	$0.668550\pi$
$282$		0			0
$283$		−	31.0278i		−	1.84441i	−0.386703	−	0.922204i	$-0.626386\pi$
$283$		−	31.0278i		−	1.84441i	0.386703	−	0.922204i	$-0.373614\pi$
$284$	−1.50043	−	7.22249i	−0.0890343	−	0.428576i
$285$		0			0
$286$	0.593923	−	0.729988i	0.0351194	−	0.0431651i
$287$		0			0
$288$		0			0
$289$	−12.0872			−0.711011
$290$	−3.23737	+	3.97904i	−0.190105	+	0.233657i
$291$		0			0
$292$	5.71083	+	27.4897i	0.334201	+	1.60871i
$293$		−	5.01850i		−	0.293184i	−0.989197	−	0.146592i	$-0.953170\pi$
$293$		−	5.01850i		−	0.293184i	0.989197	−	0.146592i	$-0.0468305\pi$
$294$		0			0
$295$			12.4111i			0.722602i
$296$	−24.6921	−	12.7970i	−1.43520	−	0.743813i
$297$		0			0
$298$	−18.4330	−	14.9972i	−1.06780	−	0.868766i
$299$	4.41003			0.255039
$300$		0			0
$301$		0			0
$302$	2.30123	+	1.87229i	0.132421	+	0.107738i
$303$		0			0
$304$	9.88666	+	22.7683i	0.567039	+	1.30585i
$305$		−	2.43947i		−	0.139684i
$306$		0			0
$307$			15.3622i			0.876768i	0.898788	+	0.438384i	$0.144449\pi$
$307$			15.3622i			0.876768i	−0.898788	+	0.438384i	$0.855551\pi$
$308$		0			0
$309$		0			0
$310$	−11.5577	+	14.2056i	−0.656435	+	0.806821i
$311$	−4.83896			−0.274392			−0.137196	−	0.990544i	$-0.543809\pi$
$311$	−4.83896			−0.274392			−0.137196	+	0.990544i	$0.543809\pi$
$312$		0			0
$313$	−19.7633			−1.11709			−0.558543	−	0.829475i	$-0.688640\pi$
$313$	−19.7633			−1.11709			−0.558543	+	0.829475i	$0.688640\pi$
$314$	−15.4962	+	19.0463i	−0.874501	+	1.07484i
$315$		0			0
$316$	−25.2247	+	5.24029i	−1.41900	+	0.294789i
$317$			5.96248i			0.334886i	0.985882	+	0.167443i	$0.0535511\pi$
$317$			5.96248i			0.334886i	−0.985882	+	0.167443i	$0.946449\pi$
$318$		0			0
$319$			1.62721i			0.0911064i
$320$	−16.7651	+	11.8299i	−0.937195	+	0.661311i
$321$		0			0
$322$		0			0
$323$	33.4681			1.86222
$324$		0			0
$325$	−0.912811			−0.0506336
$326$	−0.516180	−	0.419967i	−0.0285885	−	0.0232598i
$327$		0			0
$328$	−8.08362	+	15.5975i	−0.446343	+	0.861228i
$329$		0			0
$330$		0			0
$331$		−	1.15667i		−	0.0635766i	−0.999495	−	0.0317883i	$-0.989880\pi$
$331$		−	1.15667i		−	0.0635766i	0.999495	−	0.0317883i	$-0.0101202\pi$
$332$	−3.57009	−	17.1850i	−0.195934	−	0.943151i
$333$		0			0
$334$	−18.5244	+	22.7683i	−1.01361	+	1.24583i
$335$	7.14019			0.390110
$336$		0			0
$337$	3.25443			0.177280			0.0886399	−	0.996064i	$-0.471748\pi$
$337$	3.25443			0.177280			0.0886399	+	0.996064i	$0.471748\pi$
$338$	−11.3043	+	13.8940i	−0.614872	+	0.755736i
$339$		0			0
$340$	5.62721	+	27.0872i	0.305178	+	1.46901i
$341$			5.80930i			0.314591i
$342$		0			0
$343$		0			0
$344$	14.6473	−	28.2622i	0.789729	−	1.52380i
$345$		0			0
$346$	−15.5436	−	12.6464i	−0.835629	−	0.679873i
$347$	−16.4013			−0.880470			−0.440235	−	0.897883i	$-0.645105\pi$
$347$	−16.4013			−0.880470			−0.440235	+	0.897883i	$0.645105\pi$
$348$		0			0
$349$	8.20555			0.439233			0.219617	−	0.975586i	$-0.429519\pi$
$349$	8.20555			0.439233			0.219617	+	0.975586i	$0.429519\pi$
$350$		0			0
$351$		0			0
$352$	−1.75694	+	6.26724i	−0.0936451	+	0.334045i
$353$			24.9557i			1.32826i	0.747617	+	0.664130i	$0.231198\pi$
$353$			24.9557i			1.32826i	−0.747617	+	0.664130i	$0.768802\pi$
$354$		0			0
$355$			9.45998i			0.502083i
$356$	11.1303	−	2.31225i	0.589902	−	0.122549i
$357$		0			0
$358$	1.02695	−	1.26222i	0.0542760	−	0.0667103i
$359$	1.38712			0.0732095			0.0366048	−	0.999330i	$-0.488346\pi$
$359$	1.38712			0.0732095			0.0366048	+	0.999330i	$0.488346\pi$
$360$		0			0
$361$	−19.5089			−1.02678
$362$	−3.42083	+	4.20453i	−0.179795	+	0.220985i
$363$		0			0
$364$		0			0
$365$		−	36.0058i		−	1.88463i
$366$		0			0
$367$			10.9200i			0.570017i	0.958525	+	0.285008i	$0.0919964\pi$
$367$			10.9200i			0.570017i	−0.958525	+	0.285008i	$0.908004\pi$
$368$	−27.9776	+	12.1487i	−1.45843	+	0.633295i
$369$		0			0
$370$	27.6655	+	22.5089i	1.43826	+	1.17018i
$371$		0			0
$372$		0			0
$373$	29.6655			1.53602			0.768011	−	0.640436i	$-0.221246\pi$
$373$	29.6655			1.53602			0.768011	+	0.640436i	$0.221246\pi$
$374$	6.80747	+	5.53860i	0.352006	+	0.286394i
$375$		0			0
$376$	−27.8172	−	14.4166i	−1.43456	−	0.743481i
$377$			0.817892i			0.0421236i
$378$		0			0
$379$		−	7.66553i		−	0.393752i	−0.980428	−	0.196876i	$-0.936920\pi$
$379$		−	7.66553i		−	0.393752i	0.980428	−	0.196876i	$-0.0630796\pi$
$380$	−6.47475	−	31.1669i	−0.332147	−	1.59883i
$381$		0			0
$382$	−8.85971	+	10.8894i	−0.453302	+	0.557152i
$383$	−10.8407			−0.553933			−0.276967	−	0.960880i	$-0.589329\pi$
$383$	−10.8407			−0.553933			−0.276967	+	0.960880i	$0.589329\pi$
$384$		0			0
$385$		0			0
$386$	11.3137	−	13.9056i	0.575853	−	0.707778i
$387$		0			0
$388$	−5.24029	−	25.2247i	−0.266036	−	1.28059i
$389$		−	22.6125i		−	1.14650i	−0.819381	−	0.573249i	$-0.805683\pi$
$389$		−	22.6125i		−	1.14650i	0.819381	−	0.573249i	$-0.194317\pi$
$390$		0			0
$391$			41.1255i			2.07981i
$392$		0			0
$393$		0			0
$394$	1.87028	+	1.52167i	0.0942231	+	0.0766605i
$395$	33.0392			1.66238
$396$		0			0
$397$	21.5577			1.08195			0.540976	−	0.841038i	$-0.318055\pi$
$397$	21.5577			1.08195			0.540976	+	0.841038i	$0.318055\pi$
$398$	16.2831	+	13.2480i	0.816197	+	0.664063i
$399$		0			0
$400$	5.79095	−	2.51460i	0.289548	−	0.125730i
$401$			1.26176i			0.0630095i	0.999504	+	0.0315047i	$0.0100299\pi$
$401$			1.26176i			0.0630095i	−0.999504	+	0.0315047i	$0.989970\pi$
$402$		0			0
$403$			2.91995i			0.145453i
$404$	−7.35784	+	1.52855i	−0.366066	+	0.0760482i
$405$		0			0
$406$		0			0
$407$	11.3137			0.560800
$408$		0			0
$409$	34.4494			1.70341			0.851707	−	0.524018i	$-0.175568\pi$
$409$	34.4494			1.70341			0.851707	+	0.524018i	$0.175568\pi$
$410$	14.2184	−	17.4757i	0.702195	−	0.863064i
$411$		0			0
$412$	3.51388	−	0.729988i	0.173116	−	0.0359639i
$413$		0			0
$414$		0			0
$415$			22.5089i			1.10492i
$416$	−0.883096	+	3.15013i	−0.0432974	+	0.154448i
$417$		0			0
$418$	−7.83276	−	6.37279i	−0.383113	−	0.311703i
$419$	−16.5816			−0.810064			−0.405032	−	0.914302i	$-0.632740\pi$
$419$	−16.5816			−0.810064			−0.405032	+	0.914302i	$0.632740\pi$
$420$		0			0
$421$	−8.36274			−0.407575			−0.203788	−	0.979015i	$-0.565325\pi$
$421$	−8.36274			−0.407575			−0.203788	+	0.979015i	$0.565325\pi$
$422$	−1.26887	−	1.03236i	−0.0617675	−	0.0502545i
$423$		0			0
$424$	5.89999	−	11.3842i	0.286529	−	0.552863i
$425$		−	8.51237i		−	0.412911i
$426$		0			0
$427$		0			0
$428$	4.13438	+	19.9013i	0.199843	+	0.961965i
$429$		0			0
$430$	−25.7633	+	31.6655i	−1.24242	+	1.52705i
$431$	−37.1565			−1.78976			−0.894882	−	0.446303i	$-0.852740\pi$
$431$	−37.1565			−1.78976			−0.894882	+	0.446303i	$0.852740\pi$
$432$		0			0
$433$	7.56777			0.363684			0.181842	−	0.983328i	$-0.441794\pi$
$433$	7.56777			0.363684			0.181842	+	0.983328i	$0.441794\pi$
$434$		0			0
$435$		0			0
$436$	6.20555	+	29.8711i	0.297192	+	1.43057i
$437$		−	47.3196i		−	2.26360i
$438$		0			0
$439$			16.8222i			0.802880i	0.915885	+	0.401440i	$0.131490\pi$
$439$			16.8222i			0.802880i	−0.915885	+	0.401440i	$0.868510\pi$
$440$	3.84080	−	7.41089i	0.183103	−	0.353300i
$441$		0			0
$442$	3.42166	+	2.78389i	0.162752	+	0.132416i
$443$	12.4643			0.592198			0.296099	−	0.955157i	$-0.404314\pi$
$443$	12.4643			0.592198			0.296099	+	0.955157i	$0.404314\pi$
$444$		0			0
$445$	−14.5783			−0.691079
$446$	−25.9610	−	21.1220i	−1.22929	−	1.00016i
$447$		0			0
$448$		0			0
$449$			7.44582i			0.351390i	0.984445	+	0.175695i	$0.0562172\pi$
$449$			7.44582i			0.351390i	−0.984445	+	0.175695i	$0.943783\pi$
$450$		0			0
$451$		−	7.14663i		−	0.336522i
$452$	9.90949	−	2.05864i	0.466103	−	0.0968303i
$453$		0			0
$454$	8.42669	−	10.3572i	0.395484	−	0.486088i
$455$		0			0
$456$		0			0
$457$	−5.68665			−0.266010			−0.133005	−	0.991115i	$-0.542463\pi$
$457$	−5.68665			−0.266010			−0.133005	+	0.991115i	$0.542463\pi$
$458$	0.516180	−	0.634434i	0.0241195	−	0.0296451i
$459$		0			0
$460$	38.2978	−	7.95615i	1.78564	−	0.370957i
$461$			0.790801i			0.0368313i	0.999830	+	0.0184156i	$0.00586221\pi$
$461$			0.790801i			0.0368313i	−0.999830	+	0.0184156i	$0.994138\pi$
$462$		0			0
$463$		−	25.2927i		−	1.17545i	−0.809060	−	0.587727i	$-0.800023\pi$
$463$		−	25.2927i		−	1.17545i	0.809060	−	0.587727i	$-0.199977\pi$
$464$	−2.25312	−	5.18878i	−0.104598	−	0.240883i
$465$		0			0
$466$	−0.335275	−	0.272782i	−0.0155313	−	0.0126364i
$467$	−40.8448			−1.89007			−0.945036	−	0.326966i	$-0.893974\pi$
$467$	−40.8448			−1.89007			−0.945036	+	0.326966i	$0.893974\pi$
$468$		0			0
$469$		0			0
$470$	31.1669	+	25.3576i	1.43762	+	1.16966i
$471$		0			0
$472$	−12.1517	−	6.29776i	−0.559325	−	0.289878i
$473$			12.9495i			0.595418i
$474$		0			0
$475$			9.79445i			0.449400i
$476$		0			0
$477$		0			0
$478$	8.85971	−	10.8894i	0.405234	−	0.498071i
$479$	15.2507			0.696823			0.348412	−	0.937342i	$-0.386721\pi$
$479$	15.2507			0.696823			0.348412	+	0.937342i	$0.386721\pi$
$480$		0			0
$481$	5.68665			0.259289
$482$	−8.29399	+	10.1941i	−0.377781	+	0.464329i
$483$		0			0
$484$	3.93626	+	18.9476i	0.178921	+	0.861256i
$485$			33.0392i			1.50023i
$486$		0			0
$487$		−	24.6066i		−	1.11503i	−0.830166	−	0.557516i	$-0.811755\pi$
$487$		−	24.6066i		−	1.11503i	0.830166	−	0.557516i	$-0.188245\pi$
$488$	2.38847	+	1.23786i	0.108121	+	0.0560353i
$489$		0			0
$490$		0			0
$491$	−31.3472			−1.41468			−0.707339	−	0.706875i	$-0.750104\pi$
$491$	−31.3472			−1.41468			−0.707339	+	0.706875i	$0.750104\pi$
$492$		0			0
$493$	−7.62721			−0.343512
$494$	−3.93701	−	3.20318i	−0.177135	−	0.144118i
$495$		0			0
$496$	−8.04385	−	18.5244i	−0.361180	−	0.831772i
$497$		0			0
$498$		0			0
$499$			11.2544i			0.503817i	0.967751	+	0.251909i	$0.0810583\pi$
$499$			11.2544i			0.503817i	−0.967751	+	0.251909i	$0.918942\pi$
$500$	17.1850	−	3.57009i	0.768538	−	0.159659i
$501$		0			0
$502$	−3.51388	+	4.31889i	−0.156832	+	0.192761i
$503$	27.6588			1.23325			0.616623	−	0.787259i	$-0.288500\pi$
$503$	27.6588			1.23325			0.616623	+	0.787259i	$0.288500\pi$
$504$		0			0
$505$	9.63726			0.428852
$506$	7.83086	−	9.62487i	0.348124	−	0.427878i
$507$		0			0
$508$	0.921405	−	0.191417i	0.0408807	−	0.00849274i
$509$		−	29.7947i		−	1.32063i	−0.750990	−	0.660313i	$-0.770423\pi$
$509$		−	29.7947i		−	1.32063i	0.750990	−	0.660313i	$-0.229577\pi$
$510$		0			0
$511$		0			0
$512$	−3.07550	−	22.4174i	−0.135919	−	0.990720i
$513$		0			0
$514$	17.4303	+	14.1814i	0.768816	+	0.625513i
$515$	−4.60245			−0.202808
$516$		0			0
$517$	12.7456			0.560550
$518$		0			0
$519$		0			0
$520$	1.93051	−	3.72496i	0.0846587	−	0.163351i
$521$			1.84520i			0.0808397i	0.999183	+	0.0404199i	$0.0128696\pi$
$521$			1.84520i			0.0808397i	−0.999183	+	0.0404199i	$0.987130\pi$
$522$		0			0
$523$		−	16.0000i		−	0.699631i	−0.936819	−	0.349816i	$-0.886244\pi$
$523$		−	16.0000i		−	0.699631i	0.936819	−	0.349816i	$-0.113756\pi$
$524$	−6.47475	−	31.1669i	−0.282851	−	1.36153i
$525$		0			0
$526$	1.23804	−	1.52167i	0.0539811	−	0.0663479i
$527$	−27.2299			−1.18615
$528$		0			0
$529$	35.1461			1.52809
$530$	−10.3776	+	12.7550i	−0.450772	+	0.554042i
$531$		0			0
$532$		0			0
$533$		−	3.59214i		−	0.155593i
$534$		0			0
$535$		−	26.0666i		−	1.12696i
$536$	−3.62314	+	6.99093i	−0.156496	+	0.301962i
$537$		0			0
$538$	−1.76473	−	1.43580i	−0.0760829	−	0.0619016i
$539$		0			0
$540$		0			0
$541$	−26.3416			−1.13251			−0.566257	−	0.824229i	$-0.691609\pi$
$541$	−26.3416			−1.13251			−0.566257	+	0.824229i	$0.691609\pi$
$542$	9.10869	+	7.41089i	0.391252	+	0.318325i
$543$		0			0
$544$	−29.3764	−	8.23527i	−1.25950	−	0.353084i
$545$		−	39.1250i		−	1.67593i
$546$		0			0
$547$		−	0.805013i		−	0.0344199i	−0.999852	−	0.0172099i	$-0.994522\pi$
$547$		−	0.805013i		−	0.0344199i	0.999852	−	0.0172099i	$-0.00547836\pi$
$548$	16.7512	−	3.47996i	0.715574	−	0.148656i
$549$		0			0
$550$	−1.62087	+	1.99221i	−0.0691142	+	0.0849480i
$551$	8.77597			0.373869
$552$		0			0
$553$		0			0
$554$	−3.42083	+	4.20453i	−0.145337	+	0.178633i
$555$		0			0
$556$	−31.3311	+	6.50885i	−1.32873	+	0.276037i
$557$		−	14.8909i		−	0.630948i	−0.948934	−	0.315474i	$-0.897836\pi$
$557$		−	14.8909i		−	0.630948i	0.948934	−	0.315474i	$-0.102164\pi$
$558$		0			0
$559$			6.50885i			0.275295i
$560$		0			0
$561$		0			0
$562$	31.7414	+	25.8250i	1.33893	+	1.08936i
$563$	−43.3825			−1.82836			−0.914178	−	0.405313i	$-0.867163\pi$
$563$	−43.3825			−1.82836			−0.914178	+	0.405313i	$0.867163\pi$
$564$		0			0
$565$	−12.9794			−0.546047
$566$	−34.0373	−	27.6930i	−1.43070	−	1.16402i
$567$		0			0
$568$	−9.26222	−	4.80027i	−0.388634	−	0.201415i
$569$		−	21.8786i		−	0.917201i	−0.888643	−	0.458600i	$-0.848351\pi$
$569$		−	21.8786i		−	0.917201i	0.888643	−	0.458600i	$-0.151649\pi$
$570$		0			0
$571$		−	37.7038i		−	1.57786i	−0.614485	−	0.788928i	$-0.710636\pi$
$571$		−	37.7038i		−	1.57786i	0.614485	−	0.788928i	$-0.289364\pi$
$572$	−0.270704	−	1.30306i	−0.0113187	−	0.0544838i
$573$		0			0
$574$		0			0
$575$	−12.0354			−0.501910
$576$		0			0
$577$	26.4111			1.09951			0.549754	−	0.835326i	$-0.314721\pi$
$577$	26.4111			1.09951			0.549754	+	0.835326i	$0.314721\pi$
$578$	−10.7881	+	13.2596i	−0.448726	+	0.551527i
$579$		0			0
$580$	1.47556	+	7.10278i	0.0612694	+	0.294927i
$581$		0			0
$582$		0			0
$583$			5.21611i			0.216029i
$584$	35.2532	+	18.2704i	1.45879	+	0.756036i
$585$		0			0
$586$	−5.50528	−	4.47913i	−0.227421	−	0.185031i
$587$	16.1527			0.666692			0.333346	−	0.942805i	$-0.391822\pi$
$587$	16.1527			0.666692			0.333346	+	0.942805i	$0.391822\pi$
$588$		0			0
$589$	31.3311			1.29097
$590$	13.6149	+	11.0772i	0.560518	+	0.456041i
$591$		0			0
$592$	−36.0766	+	15.6655i	−1.48274	+	0.643849i
$593$			6.44765i			0.264773i	0.991198	+	0.132387i	$0.0422641\pi$
$593$			6.44765i			0.264773i	−0.991198	+	0.132387i	$0.957736\pi$
$594$		0			0
$595$		0			0
$596$	−32.9038	+	6.83559i	−1.34779	+	0.279997i
$597$		0			0
$598$	3.93605	−	4.83779i	0.160957	−	0.197832i
$599$	18.9391			0.773829			0.386915	−	0.922116i	$-0.373541\pi$
$599$	18.9391			0.773829			0.386915	+	0.922116i	$0.373541\pi$
$600$		0			0
$601$	−18.4111			−0.751004			−0.375502	−	0.926821i	$-0.622530\pi$
$601$	−18.4111			−0.751004			−0.375502	+	0.926821i	$0.622530\pi$
$602$		0			0
$603$		0			0
$604$	4.10780	−	0.853372i	0.167144	−	0.0347232i
$605$		−	24.8175i		−	1.00897i
$606$		0			0
$607$		−	24.6066i		−	0.998751i	−0.866386	−	0.499376i	$-0.833563\pi$
$607$		−	24.6066i		−	0.998751i	0.866386	−	0.499376i	$-0.166437\pi$
$608$	33.8008	+	9.47561i	1.37080	+	0.384287i
$609$		0			0
$610$	−2.67609	−	2.17728i	−0.108352	−	0.0881556i
$611$	6.40636			0.259173
$612$		0			0
$613$	8.09775			0.327065			0.163533	−	0.986538i	$-0.447711\pi$
$613$	8.09775			0.327065			0.163533	+	0.986538i	$0.447711\pi$
$614$	16.8523	+	13.7111i	0.680104	+	0.553337i
$615$		0			0
$616$		0			0
$617$			5.14459i			0.207113i	0.994624	+	0.103557i	$0.0330223\pi$
$617$			5.14459i			0.207113i	−0.994624	+	0.103557i	$0.966978\pi$
$618$		0			0
$619$			36.2922i			1.45871i	0.684137	+	0.729354i	$0.260179\pi$
$619$			36.2922i			1.45871i	−0.684137	+	0.729354i	$0.739821\pi$
$620$	5.26790	+	25.3576i	0.211564	+	1.01838i
$621$		0			0
$622$	−4.31889	+	5.30833i	−0.173172	+	0.212844i
$623$		0			0
$624$		0			0
$625$	−30.4005			−1.21602
$626$	−17.6392	+	21.6802i	−0.705004	+	0.866517i
$627$		0			0
$628$	7.06301	+	33.9985i	0.281845	+	1.35669i
$629$			53.0306i			2.11447i
$630$		0			0
$631$		−	19.7250i		−	0.785238i	−0.919701	−	0.392619i	$-0.871569\pi$
$631$		−	19.7250i		−	0.785238i	0.919701	−	0.392619i	$-0.128431\pi$
$632$	−16.7651	+	32.3485i	−0.666878	+	1.28675i
$633$		0			0
$634$	6.54082	+	5.32166i	0.259769	+	0.211350i
$635$	−1.20685			−0.0478924
$636$		0			0
$637$		0			0
$638$	1.78505	+	1.45233i	0.0706707	+	0.0574981i
$639$		0			0
$640$	−1.98587	+	28.9497i	−0.0784983	+	1.14434i
$641$			20.6860i			0.817048i	0.912748	+	0.408524i	$0.133956\pi$
$641$			20.6860i			0.817048i	−0.912748	+	0.408524i	$0.866044\pi$
$642$		0			0
$643$		−	15.0278i		−	0.592637i	−0.955089	−	0.296318i	$-0.904241\pi$
$643$		−	15.0278i		−	0.592637i	0.955089	−	0.296318i	$-0.0957589\pi$
$644$		0			0
$645$		0			0
$646$	29.8711	−	36.7144i	1.17526	−	1.44451i
$647$	−22.3909			−0.880277			−0.440139	−	0.897930i	$-0.645071\pi$
$647$	−22.3909			−0.880277			−0.440139	+	0.897930i	$0.645071\pi$
$648$		0			0
$649$	5.56777			0.218554
$650$	−0.814705	+	1.00135i	−0.0319554	+	0.0392762i
$651$		0			0
$652$	−0.921405	+	0.191417i	−0.0360850	+	0.00749646i
$653$		−	31.0978i		−	1.21695i	−0.793573	−	0.608475i	$-0.791782\pi$
$653$		−	31.0978i		−	1.21695i	0.793573	−	0.608475i	$-0.208218\pi$
$654$		0			0
$655$			40.8222i			1.59506i
$656$	9.89558	+	22.7888i	0.386357	+	0.889754i
$657$		0			0
$658$		0			0
$659$	10.1631			0.395898			0.197949	−	0.980212i	$-0.436572\pi$
$659$	10.1631			0.395898			0.197949	+	0.980212i	$0.436572\pi$
$660$		0			0
$661$	15.1255			0.588314			0.294157	−	0.955757i	$-0.404961\pi$
$661$	15.1255			0.588314			0.294157	+	0.955757i	$0.404961\pi$
$662$	−1.26887	−	1.03236i	−0.0493159	−	0.0401238i
$663$		0			0
$664$	−22.0383	−	11.4217i	−0.855252	−	0.443246i
$665$		0			0
$666$		0			0
$667$			10.7839i			0.417554i
$668$	8.44325	+	40.6425i	0.326679	+	1.57251i
$669$		0			0
$670$	6.37279	−	7.83276i	0.246202	−	0.302606i
$671$	−1.09438			−0.0422479
$672$		0			0
$673$	36.8716			1.42130			0.710648	−	0.703548i	$-0.248402\pi$
$673$	36.8716			1.42130			0.710648	+	0.703548i	$0.248402\pi$
$674$	2.90465	−	3.57009i	0.111883	−	0.137515i
$675$		0			0
$676$	5.15238	+	24.8015i	0.198168	+	0.953904i
$677$			10.3705i			0.398569i	0.979942	+	0.199285i	$0.0638618\pi$
$677$			10.3705i			0.398569i	−0.979942	+	0.199285i	$0.936138\pi$
$678$		0			0
$679$		0			0
$680$	34.7370	+	18.0029i	1.33210	+	0.690381i
$681$		0			0
$682$	6.37279	+	5.18494i	0.244027	+	0.198542i
$683$	−9.19275			−0.351751			−0.175875	−	0.984412i	$-0.556276\pi$
$683$	−9.19275			−0.351751			−0.175875	+	0.984412i	$0.556276\pi$
$684$		0			0
$685$	−21.9406			−0.838306
$686$		0			0
$687$		0			0
$688$	−17.9305	−	41.2927i	−0.683594	−	1.57427i
$689$			2.62179i			0.0998824i
$690$		0			0
$691$			22.8433i			0.869001i	0.900672	+	0.434501i	$0.143075\pi$
$691$			22.8433i			0.869001i	−0.900672	+	0.434501i	$0.856925\pi$
$692$	−27.7460	+	5.76409i	−1.05475	+	0.219118i
$693$		0			0
$694$	−14.6386	+	17.9922i	−0.555673	+	0.682975i
$695$	41.0372			1.55663
$696$		0			0
$697$	33.4983			1.26884
$698$	7.32365	−	9.00146i	0.277204	−	0.340710i
$699$		0			0
$700$		0			0
$701$		−	19.1044i		−	0.721563i	−0.932650	−	0.360782i	$-0.882510\pi$
$701$		−	19.1044i		−	0.721563i	0.932650	−	0.360782i	$-0.117490\pi$
$702$		0			0
$703$		−	61.0177i		−	2.30133i
$704$	5.30704	+	7.52102i	0.200016	+	0.283459i
$705$		0			0
$706$	27.3764	+	22.2736i	1.03032	+	0.838277i
$707$		0			0
$708$		0			0
$709$	−9.56777			−0.359325			−0.179663	−	0.983728i	$-0.557501\pi$
$709$	−9.56777			−0.359325			−0.179663	+	0.983728i	$0.557501\pi$
$710$	10.3776	+	8.44325i	0.389463	+	0.316870i
$711$		0			0
$712$	7.39748	−	14.2736i	0.277232	−	0.534925i
$713$			38.4995i			1.44182i
$714$		0			0
$715$			1.70674i			0.0638286i
$716$	−0.468073	−	2.25312i	−0.0174927	−	0.0842031i
$717$		0			0
$718$	1.23804	−	1.52167i	0.0462032	−	0.0567882i
$719$	30.5014			1.13751			0.568756	−	0.822506i	$-0.307425\pi$
$719$	30.5014			1.13751			0.568756	+	0.822506i	$0.307425\pi$
$720$		0			0
$721$		0			0
$722$	−17.4121	+	21.4011i	−0.648012	+	0.796468i
$723$		0			0
$724$	1.55918	+	7.50528i	0.0579465	+	0.278932i
$725$		−	2.23211i		−	0.0828983i
$726$		0			0
$727$		−	32.5189i		−	1.20606i	−0.797719	−	0.603030i	$-0.793960\pi$
$727$		−	32.5189i		−	1.20606i	0.797719	−	0.603030i	$-0.206040\pi$
$728$		0			0
$729$		0			0
$730$	−39.4983	−	32.1361i	−1.46190	−	1.18941i
$731$	−60.6980			−2.24500
$732$		0			0
$733$	−19.0106			−0.702171			−0.351086	−	0.936343i	$-0.614187\pi$
$733$	−19.0106			−0.702171			−0.351086	+	0.936343i	$0.614187\pi$
$734$	11.9792	+	9.74632i	0.442159	+	0.359743i
$735$		0			0
$736$	−11.6436	+	41.5343i	−0.429189	+	1.53098i
$737$		−	3.20318i		−	0.117991i
$738$		0			0
$739$		−	19.7250i		−	0.725595i	−0.931868	−	0.362797i	$-0.881822\pi$
$739$		−	19.7250i		−	0.725595i	0.931868	−	0.362797i	$-0.118178\pi$
$740$	49.3843	−	10.2593i	1.81540	−	0.377140i
$741$		0			0
$742$		0			0
$743$	−33.8849			−1.24312			−0.621558	−	0.783368i	$-0.713500\pi$
$743$	−33.8849			−1.24312			−0.621558	+	0.783368i	$0.713500\pi$
$744$		0			0
$745$	43.0972			1.57896
$746$	26.4772	−	32.5430i	0.969399	−	1.19148i
$747$		0			0
$748$	12.1517	−	2.52444i	0.444308	−	0.0923026i
$749$		0			0
$750$		0			0
$751$			30.5089i			1.11328i	0.830753	+	0.556642i	$0.187910\pi$
$751$			30.5089i			1.11328i	−0.830753	+	0.556642i	$0.812090\pi$
$752$	−40.6425	+	17.6482i	−1.48208	+	0.643562i
$753$		0			0
$754$	0.897225	+	0.729988i	0.0326750	+	0.0265846i
$755$	−5.38037			−0.195812
$756$		0			0
$757$	−48.0766			−1.74737			−0.873687	−	0.486488i	$-0.838278\pi$
$757$	−48.0766			−1.74737			−0.873687	+	0.486488i	$0.838278\pi$
$758$	−8.40906	−	6.84166i	−0.305431	−	0.248500i
$759$		0			0
$760$	−39.9688	−	20.7144i	−1.44982	−	0.751390i
$761$			13.4055i			0.485950i	0.970033	+	0.242975i	$0.0781232\pi$
$761$			13.4055i			0.485950i	−0.970033	+	0.242975i	$0.921877\pi$
$762$		0			0
$763$		0			0
$764$	4.03817	+	19.4382i	0.146096	+	0.703248i
$765$		0			0
$766$	−9.67557	+	11.8922i	−0.349593	+	0.429683i
$767$	2.79855			0.101050
$768$		0			0
$769$	−13.4700			−0.485741			−0.242871	−	0.970059i	$-0.578089\pi$
$769$	−13.4700			−0.485741			−0.242871	+	0.970059i	$0.578089\pi$
$770$		0			0
$771$		0			0
$772$	−5.15667	−	24.8222i	−0.185593	−	0.893371i
$773$		−	28.5479i		−	1.02680i	−0.858151	−	0.513398i	$-0.828387\pi$
$773$		−	28.5479i		−	1.02680i	0.858151	−	0.513398i	$-0.171613\pi$
$774$		0			0
$775$		−	7.96883i		−	0.286249i
$776$	−32.3485	−	16.7651i	−1.16124	−	0.601831i
$777$		0			0
$778$	−24.8058	−	20.1822i	−0.889332	−	0.723566i
$779$	−38.5436			−1.38097
$780$		0			0
$781$	4.24386			0.151857
$782$	45.1145	+	36.7055i	1.61329	+	1.31259i
$783$		0			0
$784$		0			0
$785$		−	44.5311i		−	1.58938i
$786$		0			0
$787$		−	25.7633i		−	0.918362i	−0.888343	−	0.459181i	$-0.848143\pi$
$787$		−	25.7633i		−	0.918362i	0.888343	−	0.459181i	$-0.151857\pi$
$788$	3.33853	−	0.693561i	0.118930	−	0.0247071i
$789$		0			0
$790$	29.4882	−	36.2439i	1.04914	−	1.28950i
$791$		0			0
$792$		0			0
$793$	−0.550070			−0.0195336
$794$	19.2408	−	23.6488i	0.682830	−	0.839263i
$795$		0			0
$796$	29.0661	−	6.03831i	1.03022	−	0.214022i
$797$		−	23.3741i		−	0.827954i	−0.910287	−	0.413977i	$-0.864139\pi$
$797$		−	23.3741i		−	0.827954i	0.910287	−	0.413977i	$-0.135861\pi$
$798$		0			0
$799$			59.7422i			2.11353i
$800$	2.41005	−	8.59700i	0.0852083	−	0.303950i
$801$		0			0
$802$	1.38415	+	1.12615i	0.0488761	+	0.0397659i
$803$	−16.1527			−0.570015
$804$		0			0
$805$		0			0
$806$	3.20318	+	2.60613i	0.112827	+	0.0917969i
$807$		0			0
$808$	−4.89023	+	9.43580i	−0.172038	+	0.331950i
$809$		−	20.6019i		−	0.724326i	−0.932115	−	0.362163i	$-0.882038\pi$
$809$		−	20.6019i		−	0.724326i	0.932115	−	0.362163i	$-0.117962\pi$
$810$		0			0
$811$		−	2.64782i		−	0.0929776i	−0.998919	−	0.0464888i	$-0.985197\pi$
$811$		−	2.64782i		−	0.0929776i	0.998919	−	0.0464888i	$-0.0148032\pi$
$812$		0			0
$813$		0			0
$814$	10.0978	−	12.4111i	0.353926	−	0.435009i
$815$	1.20685			0.0422741
$816$		0			0
$817$	69.8399			2.44339
$818$	30.7469	−	37.7909i	1.07504	−	1.32133i
$819$		0			0
$820$	−6.48059	−	31.1950i	−0.226312	−	1.08938i
$821$			43.5201i			1.51886i	0.650589	+	0.759430i	$0.274522\pi$
$821$			43.5201i			1.51886i	−0.650589	+	0.759430i	$0.725478\pi$
$822$		0			0
$823$		−	10.5683i		−	0.368387i	−0.982890	−	0.184194i	$-0.941033\pi$
$823$		−	10.5683i		−	0.368387i	0.982890	−	0.184194i	$-0.0589674\pi$
$824$	2.33542	−	4.50624i	0.0813583	−	0.156982i
$825$		0			0
$826$		0			0
$827$	3.92486			0.136481			0.0682403	−	0.997669i	$-0.478262\pi$
$827$	3.92486			0.136481			0.0682403	+	0.997669i	$0.478262\pi$
$828$		0			0
$829$	−15.2061			−0.528129			−0.264064	−	0.964505i	$-0.585063\pi$
$829$	−15.2061			−0.528129			−0.264064	+	0.964505i	$0.585063\pi$
$830$	24.6921	+	20.0897i	0.857077	+	0.697323i
$831$		0			0
$832$	2.66750	+	3.78032i	0.0924788	+	0.131059i
$833$		0			0
$834$		0			0
$835$		−	53.2333i		−	1.84221i
$836$	−13.9819	+	2.90465i	−0.483572	+	0.100459i
$837$		0			0
$838$	−14.7995	+	18.1900i	−0.511239	+	0.628362i
$839$	−12.2841			−0.424093			−0.212046	−	0.977260i	$-0.568013\pi$
$839$	−12.2841			−0.424093			−0.212046	+	0.977260i	$0.568013\pi$
$840$		0			0
$841$	27.0000			0.931034
$842$	−7.46394	+	9.17390i	−0.257224	+	0.316153i
$843$		0			0
$844$	−2.26499	+	0.470539i	−0.0779641	+	0.0161966i
$845$		−	32.4849i		−	1.11751i
$846$		0			0
$847$		0			0
$848$	−7.22249	−	16.6329i	−0.248021	−	0.571176i
$849$		0			0
$850$	−9.33804	−	7.59749i	−0.320292	−	0.260592i
$851$	74.9784			2.57022
$852$		0			0
$853$	−16.2056			−0.554867			−0.277434	−	0.960745i	$-0.589484\pi$
$853$	−16.2056			−0.554867			−0.277434	+	0.960745i	$0.589484\pi$
$854$		0			0
$855$		0			0
$856$	25.5217	+	13.2270i	0.872313	+	0.452088i
$857$			15.9873i			0.546117i	0.961997	+	0.273059i	$0.0880353\pi$
$857$			15.9873i			0.546117i	−0.961997	+	0.273059i	$0.911965\pi$
$858$		0			0
$859$		−	31.9688i		−	1.09076i	−0.838188	−	0.545381i	$-0.816385\pi$
$859$		−	31.9688i		−	1.09076i	0.838188	−	0.545381i	$-0.183615\pi$
$860$	11.7426	+	56.5245i	0.400421	+	1.92747i
$861$		0			0
$862$	−33.1630	+	40.7605i	−1.12954	+	1.38831i
$863$	38.9847			1.32705			0.663527	−	0.748153i	$-0.269059\pi$
$863$	38.9847			1.32705			0.663527	+	0.748153i	$0.269059\pi$
$864$		0			0
$865$	36.3416			1.23565
$866$	6.75442	−	8.30182i	0.229524	−	0.282107i
$867$		0			0
$868$		0			0
$869$		−	14.8218i		−	0.502795i
$870$		0			0
$871$		−	1.61003i		−	0.0545536i
$872$	38.3071	+	19.8532i	1.29724	+	0.672313i
$873$		0			0
$874$	−51.9094	−	42.2338i	−1.75586	−	1.42858i
$875$		0			0
$876$		0			0
$877$	−6.07663			−0.205193			−0.102597	−	0.994723i	$-0.532715\pi$
$877$	−6.07663			−0.205193			−0.102597	+	0.994723i	$0.532715\pi$
$878$	18.4539	+	15.0142i	0.622789	+	0.506705i
$879$		0			0
$880$	−4.70172	−	10.8277i	−0.158495	−	0.365003i
$881$			15.9575i			0.537621i	0.963193	+	0.268810i	$0.0866305\pi$
$881$			15.9575i			0.537621i	−0.963193	+	0.268810i	$0.913370\pi$
$882$		0			0
$883$		−	43.2544i		−	1.45563i	−0.685775	−	0.727814i	$-0.740537\pi$
$883$		−	43.2544i		−	1.45563i	0.685775	−	0.727814i	$-0.259463\pi$
$884$	6.10783	−	1.26887i	0.205429	−	0.0426766i
$885$		0			0
$886$	11.1247	−	13.6733i	0.373742	−	0.459364i
$887$	46.1811			1.55061			0.775305	−	0.631587i	$-0.217596\pi$
$887$	46.1811			1.55061			0.775305	+	0.631587i	$0.217596\pi$
$888$		0			0
$889$		0			0
$890$	−13.0115	+	15.9924i	−0.436147	+	0.536066i
$891$		0			0
$892$	−46.3416	+	9.62721i	−1.55163	+	0.322343i
$893$		−	68.7401i		−	2.30030i
$894$		0			0
$895$			2.95112i			0.0986452i
$896$		0			0
$897$		0			0
$898$	8.16804	+	6.64557i	0.272571	+	0.221765i
$899$	−7.14019			−0.238139
$900$		0			0
$901$	−24.4494			−0.814528
$902$	−7.83983	−	6.37853i	−0.261038	−	0.212382i
$903$		0			0
$904$	6.58613	−	12.7081i	0.219051	−	0.422664i
$905$		−	9.83037i		−	0.326773i
$906$		0			0
$907$		−	8.94108i		−	0.296884i	−0.988921	−	0.148442i	$-0.952574\pi$
$907$		−	8.94108i		−	0.296884i	0.988921	−	0.148442i	$-0.0474258\pi$
$908$	−3.84080	−	18.4881i	−0.127461	−	0.613549i
$909$		0			0
$910$		0			0
$911$	−37.8219			−1.25310			−0.626548	−	0.779383i	$-0.715533\pi$
$911$	−37.8219			−1.25310			−0.626548	+	0.779383i	$0.715533\pi$
$912$		0			0
$913$	10.0978			0.334187
$914$	−5.07547	+	6.23824i	−0.167882	+	0.206343i
$915$		0			0
$916$	−0.235269	−	1.13249i	−0.00777352	−	0.0374187i
$917$		0			0
$918$		0			0
$919$		−	38.7244i		−	1.27740i	−0.769455	−	0.638701i	$-0.779472\pi$
$919$		−	38.7244i		−	1.27740i	0.769455	−	0.638701i	$-0.220528\pi$
$920$	25.4538	−	49.1136i	0.839187	−	1.61923i
$921$		0			0
$922$	0.867506	+	0.705808i	0.0285698	+	0.0232446i
$923$	2.13311			0.0702121
$924$		0			0
$925$	−15.5194			−0.510275
$926$	−27.7460	−	22.5744i	−0.911792	−	0.741840i
$927$		0			0
$928$	−7.70304	−	2.15944i	−0.252865	−	0.0708872i
$929$		−	11.9222i		−	0.391154i	−0.980688	−	0.195577i	$-0.937342\pi$
$929$		−	11.9222i		−	0.391154i	0.980688	−	0.195577i	$-0.0626580\pi$
$930$		0			0
$931$		0			0
$932$	−0.598481	+	0.124331i	−0.0196039	+	0.00407260i
$933$		0			0
$934$	−36.4550	+	44.8066i	−1.19284	+	1.46612i
$935$	−15.9162			−0.520514
$936$		0			0
$937$	−28.1744			−0.920417			−0.460208	−	0.887811i	$-0.652225\pi$
$937$	−28.1744			−0.920417			−0.460208	+	0.887811i	$0.652225\pi$
$938$		0			0
$939$		0			0
$940$	55.6344	−	11.5577i	1.81459	−	0.376972i
$941$		−	53.9054i		−	1.75727i	−0.477496	−	0.878634i	$-0.658456\pi$
$941$		−	53.9054i		−	1.75727i	0.477496	−	0.878634i	$-0.341544\pi$
$942$		0			0
$943$		−	47.3622i		−	1.54233i
$944$	−17.7543	+	7.70942i	−0.577852	+	0.250920i
$945$		0			0
$946$	14.2056	+	11.5577i	0.461862	+	0.375774i
$947$	36.7275			1.19348			0.596742	−	0.802433i	$-0.296462\pi$
$947$	36.7275			1.19348			0.596742	+	0.802433i	$0.296462\pi$
$948$		0			0
$949$	−8.11888			−0.263550
$950$	10.7445	+	8.74178i	0.348597	+	0.283621i
$951$		0			0
$952$		0			0
$953$			58.9090i			1.90825i	0.299408	+	0.954125i	$0.403211\pi$
$953$			58.9090i			1.90825i	−0.299408	+	0.954125i	$0.596789\pi$
$954$		0			0
$955$		−	25.4600i		−	0.823865i
$956$	−4.03817	−	19.4382i	−0.130604	−	0.628675i
$957$		0			0
$958$	13.6116	−	16.7300i	0.439772	−	0.540521i
$959$		0			0
$960$		0			0
$961$	5.50885			0.177705
$962$	5.07547	−	6.23824i	0.163640	−	0.201129i
$963$		0			0
$964$	3.78032	+	18.1970i	0.121756	+	0.586084i
$965$			32.5120i			1.04660i
$966$		0			0
$967$		−	43.6061i		−	1.40228i	−0.713025	−	0.701139i	$-0.752675\pi$
$967$		−	43.6061i		−	1.40228i	0.713025	−	0.701139i	$-0.247325\pi$
$968$	24.2987	+	12.5931i	0.780990	+	0.404759i
$969$		0			0
$970$	36.2439	+	29.4882i	1.16372	+	0.946810i
$971$	59.7960			1.91895			0.959473	−	0.281801i	$-0.0909317\pi$
$971$	59.7960			1.91895			0.959473	+	0.281801i	$0.0909317\pi$
$972$		0			0
$973$		0			0
$974$	−26.9934	−	21.9620i	−0.864923	−	0.703707i
$975$		0			0
$976$	3.48970	−	1.51533i	0.111702	−	0.0485045i
$977$			41.5794i			1.33024i	0.746736	+	0.665121i	$0.231620\pi$
$977$			41.5794i			1.33024i	−0.746736	+	0.665121i	$0.768380\pi$
$978$		0			0
$979$			6.54002i			0.209020i
$980$		0			0
$981$		0			0
$982$	−27.9781	+	34.3877i	−0.892816	+	1.09736i
$983$	−0.428934			−0.0136809			−0.00684043	−	0.999977i	$-0.502177\pi$
$983$	−0.428934			−0.0136809			−0.00684043	+	0.999977i	$0.502177\pi$
$984$		0			0
$985$	−4.37279			−0.139329
$986$	−6.80747	+	8.36703i	−0.216794	+	0.266460i
$987$		0			0
$988$	−7.02775	+	1.45998i	−0.223583	+	0.0464480i
$989$			85.8190i			2.72889i
$990$		0			0
$991$		−	31.5466i		−	1.00211i	−0.865415	−	0.501056i	$-0.832945\pi$
$991$		−	31.5466i		−	1.00211i	0.865415	−	0.501056i	$-0.167055\pi$
$992$	−27.5006	−	7.70942i	−0.873144	−	0.244774i
$993$		0			0
$994$		0			0
$995$	−38.0706			−1.20692
$996$		0			0
$997$	−34.7144			−1.09942			−0.549708	−	0.835357i	$-0.685261\pi$
$997$	−34.7144			−1.09942			−0.549708	+	0.835357i	$0.685261\pi$
$998$	12.3461	+	10.0448i	0.390808	+	0.317964i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.e.g.1079.7		12
3.2	odd	2	inner	1764.2.e.g.1079.6		12
4.3	odd	2	inner	1764.2.e.g.1079.5		12
7.6	odd	2		252.2.e.a.71.7	yes	12
12.11	even	2	inner	1764.2.e.g.1079.8		12
21.20	even	2		252.2.e.a.71.6	yes	12
28.27	even	2		252.2.e.a.71.5	✓	12
56.13	odd	2		4032.2.h.h.575.10		12
56.27	even	2		4032.2.h.h.575.9		12
84.83	odd	2		252.2.e.a.71.8	yes	12
168.83	odd	2		4032.2.h.h.575.3		12
168.125	even	2		4032.2.h.h.575.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.e.a.71.5	✓	12	28.27	even	2
252.2.e.a.71.6	yes	12	21.20	even	2
252.2.e.a.71.7	yes	12	7.6	odd	2
252.2.e.a.71.8	yes	12	84.83	odd	2
1764.2.e.g.1079.5		12	4.3	odd	2	inner
1764.2.e.g.1079.6		12	3.2	odd	2	inner
1764.2.e.g.1079.7		12	1.1	even	1	trivial
1764.2.e.g.1079.8		12	12.11	even	2	inner
4032.2.h.h.575.3		12	168.83	odd	2
4032.2.h.h.575.4		12	168.125	even	2
4032.2.h.h.575.9		12	56.27	even	2
4032.2.h.h.575.10		12	56.13	odd	2

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)

\(f(q)\)	\(=\)	\(q+(0.892524 - 1.09700i) q^{2} +(-0.406803 - 1.95819i) q^{4} +2.56483i q^{5} +(-2.51121 - 1.30147i) q^{8} +O(q^{10})\)	\(q+(0.892524 - 1.09700i) q^{2} +(-0.406803 - 1.95819i) q^{4} +2.56483i q^{5} +(-2.51121 - 1.30147i) q^{8} +(2.81361 + 2.28917i) q^{10} +1.15061 q^{11} +0.578337 q^{13} +(-3.66902 + 1.59320i) q^{16} +5.39325i q^{17} -6.20555i q^{19} +(5.02242 - 1.04338i) q^{20} +(1.02695 - 1.26222i) q^{22} +7.62536 q^{23} -1.57834 q^{25} +(0.516180 - 0.634434i) q^{26} +1.41421i q^{29} +5.04888i q^{31} +(-1.52696 + 5.44687i) q^{32} +(5.91638 + 4.81361i) q^{34} +9.83276 q^{37} +(-6.80747 - 5.53860i) q^{38} +(3.33804 - 6.44082i) q^{40} -6.21115i q^{41} +11.2544i q^{43} +(-0.468073 - 2.25312i) q^{44} +(6.80581 - 8.36499i) q^{46} +11.0772 q^{47} +(-1.40870 + 1.73143i) q^{50} +(-0.235269 - 1.13249i) q^{52} +4.53333i q^{53} +2.95112i q^{55} +(1.55139 + 1.26222i) q^{58} +4.83896 q^{59} -0.951124 q^{61} +(5.53860 + 4.50624i) q^{62} +(4.61235 + 6.53653i) q^{64} +1.48333i q^{65} -2.78389i q^{67} +(10.5610 - 2.19399i) q^{68} +3.68835 q^{71} -14.0383 q^{73} +(8.77597 - 10.7865i) q^{74} +(-12.1517 + 2.52444i) q^{76} -12.8816i q^{79} +(-4.08627 - 9.41041i) q^{80} +(-6.81361 - 5.54359i) q^{82} +8.77597 q^{83} -13.8328 q^{85} +(12.3461 + 10.0448i) q^{86} +(-2.88943 - 1.49749i) q^{88} +5.68395i q^{89} +(-3.10202 - 14.9319i) q^{92} +(9.88666 - 12.1517i) q^{94} +15.9162 q^{95} +12.8816 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4}+O(q^{10}) \) 12 * q + 8 * q^4	\( 12 q + 8 q^{4} + 8 q^{10} - 20 q^{16} + 20 q^{22} - 12 q^{25} + 16 q^{34} + 8 q^{37} - 8 q^{40} - 36 q^{46} + 16 q^{52} + 4 q^{58} - 56 q^{61} - 16 q^{64} - 72 q^{76} - 56 q^{82} - 56 q^{85} + 28 q^{88} + 24 q^{94}+O(q^{100}) \) 12 * q + 8 * q^4 + 8 * q^10 - 20 * q^16 + 20 * q^22 - 12 * q^25 + 16 * q^34 + 8 * q^37 - 8 * q^40 - 36 * q^46 + 16 * q^52 + 4 * q^58 - 56 * q^61 - 16 * q^64 - 72 * q^76 - 56 * q^82 - 56 * q^85 + 28 * q^88 + 24 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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