LMFDB - Embedded newform 1764.2.e.i.1079.15

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} + x^{12} - 10x^{10} + 4x^{8} - 40x^{6} + 16x^{4} + 256 $ x^16 + x^12 - 10x^10 + 4x^8 - 40x^6 + 16x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1079.15
Root			$1.41135 - 0.0900240i$ of defining polynomial
Character	$\chi$	$=$	1764.1079
Dual form			1764.2.e.i.1079.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41135 - 0.0900240i) q^{2} +(1.98379 - 0.254110i) q^{4} +2.48866i q^{5} +(2.77694 - 0.537226i) q^{8} +O(q^{10})$	\(q+(1.41135 - 0.0900240i) q^{2} +(1.98379 - 0.254110i) q^{4} +2.48866i q^{5} +(2.77694 - 0.537226i) q^{8} +(0.224040 + 3.51237i) q^{10} -4.60787 q^{11} +5.22221 q^{13} +(3.87086 - 1.00820i) q^{16} +5.61101i q^{17} +3.19355i q^{19} +(0.632394 + 4.93699i) q^{20} +(-6.50329 + 0.414819i) q^{22} -0.718731 q^{23} -1.19345 q^{25} +(7.37034 - 0.470124i) q^{26} -4.53656i q^{29} +1.17715i q^{31} +(5.37235 - 1.77139i) q^{32} +(0.505125 + 7.91907i) q^{34} +2.71296 q^{37} +(0.287496 + 4.50721i) q^{38} +(1.33697 + 6.91087i) q^{40} +3.83670i q^{41} +11.1773i q^{43} +(-9.14105 + 1.17091i) q^{44} +(-1.01438 + 0.0647031i) q^{46} -5.41810 q^{47} +(-1.68437 + 0.107439i) q^{50} +(10.3598 - 1.32702i) q^{52} -2.06823i q^{53} -11.4674i q^{55} +(-0.408399 - 6.40265i) q^{58} +4.11641 q^{59} -1.01025 q^{61} +(0.105972 + 1.66136i) q^{62} +(7.42278 - 2.98369i) q^{64} +12.9963i q^{65} -12.6446i q^{67} +(1.42581 + 11.1311i) q^{68} +7.31012 q^{71} +9.63787 q^{73} +(3.82892 - 0.244231i) q^{74} +(0.811513 + 6.33534i) q^{76} +8.83951i q^{79} +(2.50908 + 9.63326i) q^{80} +(0.345395 + 5.41491i) q^{82} -13.7657 q^{83} -13.9639 q^{85} +(1.00623 + 15.7751i) q^{86} +(-12.7958 + 2.47547i) q^{88} -8.52595i q^{89} +(-1.42581 + 0.182637i) q^{92} +(-7.64682 + 0.487759i) q^{94} -7.94768 q^{95} -10.7232 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 8 q^{13} - 4 q^{16} - 16 q^{22} - 24 q^{25} - 8 q^{34} - 8 q^{37} + 52 q^{40} + 24 q^{46} + 52 q^{52} + 12 q^{58} + 16 q^{61} + 60 q^{64} + 8 q^{73} + 36 q^{76} - 68 q^{82} - 16 q^{85} - 44 q^{88} - 60 q^{94} - 88 q^{97}+O(q^{100}) $ 16 * q + 8 * q^13 - 4 * q^16 - 16 * q^22 - 24 * q^25 - 8 * q^34 - 8 * q^37 + 52 * q^40 + 24 * q^46 + 52 * q^52 + 12 * q^58 + 16 * q^61 + 60 * q^64 + 8 * q^73 + 36 * q^76 - 68 * q^82 - 16 * q^85 - 44 * q^88 - 60 * q^94 - 88 * q^97

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 $

$2$	1.41135	−	0.0900240i	0.997972	−	0.0636566i
$2$	1.41135	−	0.0900240i	0.997972	−	0.0636566i
$3$		0			0
$3$		0			0
$4$	1.98379	−	0.254110i	0.991896	−	0.127055i
$5$			2.48866i			1.11296i	0.830859	+	0.556482i	$0.187849\pi$
$5$			2.48866i			1.11296i	−0.830859	+	0.556482i	$0.812151\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	2.77694	−	0.537226i	0.981796	−	0.189938i
$9$		0			0
$10$	0.224040	+	3.51237i	0.0708475	+	1.11071i
$11$	−4.60787			−1.38932			−0.694662	−	0.719336i	$-0.744446\pi$
$11$	−4.60787			−1.38932			−0.694662	+	0.719336i	$0.744446\pi$
$12$		0			0
$13$	5.22221			1.44838			0.724190	−	0.689600i	$-0.242214\pi$
$13$	5.22221			1.44838			0.724190	+	0.689600i	$0.242214\pi$
$14$		0			0
$15$		0			0
$16$	3.87086	−	1.00820i	0.967714	−	0.252051i
$17$			5.61101i			1.36087i	0.732809	+	0.680435i	$0.238209\pi$
$17$			5.61101i			1.36087i	−0.732809	+	0.680435i	$0.761791\pi$
$18$		0			0
$19$			3.19355i			0.732651i	0.930487	+	0.366326i	$0.119384\pi$
$19$			3.19355i			0.732651i	−0.930487	+	0.366326i	$0.880616\pi$
$20$	0.632394	+	4.93699i	0.141408	+	1.10394i
$21$		0			0
$22$	−6.50329	+	0.414819i	−1.38651	+	0.0884397i
$23$	−0.718731			−0.149866			−0.0749329	−	0.997189i	$-0.523874\pi$
$23$	−0.718731			−0.149866			−0.0749329	+	0.997189i	$0.523874\pi$
$24$		0			0
$25$	−1.19345			−0.238691
$26$	7.37034	−	0.470124i	1.44544	−	0.0921989i
$27$		0			0
$28$		0			0
$29$		−	4.53656i		−	0.842418i	−0.906964	−	0.421209i	$-0.861606\pi$
$29$		−	4.53656i		−	0.842418i	0.906964	−	0.421209i	$-0.138394\pi$
$30$		0			0
$31$			1.17715i			0.211422i	0.994397	+	0.105711i	$0.0337119\pi$
$31$			1.17715i			0.211422i	−0.994397	+	0.105711i	$0.966288\pi$
$32$	5.37235	−	1.77139i	0.949707	−	0.313141i
$33$		0			0
$34$	0.505125	+	7.91907i	0.0866283	+	1.35811i
$35$		0			0
$36$		0			0
$37$	2.71296			0.446007			0.223004	−	0.974818i	$-0.428414\pi$
$37$	2.71296			0.446007			0.223004	+	0.974818i	$0.428414\pi$
$38$	0.287496	+	4.50721i	0.0466381	+	0.731165i
$39$		0			0
$40$	1.33697	+	6.91087i	0.211394	+	1.09270i
$41$			3.83670i			0.599192i	0.954066	+	0.299596i	$0.0968519\pi$
$41$			3.83670i			0.599192i	−0.954066	+	0.299596i	$0.903148\pi$
$42$		0			0
$43$			11.1773i			1.70453i	0.523113	+	0.852263i	$0.324771\pi$
$43$			11.1773i			1.70453i	−0.523113	+	0.852263i	$0.675229\pi$
$44$	−9.14105	+	1.17091i	−1.37807	+	0.176521i
$45$		0			0
$46$	−1.01438	+	0.0647031i	−0.149562	+	0.00953995i
$47$	−5.41810			−0.790312			−0.395156	−	0.918614i	$-0.629309\pi$
$47$	−5.41810			−0.790312			−0.395156	+	0.918614i	$0.629309\pi$
$48$		0			0
$49$		0			0
$50$	−1.68437	+	0.107439i	−0.238206	+	0.0151942i
$51$		0			0
$52$	10.3598	−	1.32702i	1.43664	−	0.184024i
$53$		−	2.06823i		−	0.284093i	−0.989860	−	0.142046i	$-0.954632\pi$
$53$		−	2.06823i		−	0.284093i	0.989860	−	0.142046i	$-0.0453682\pi$
$54$		0			0
$55$		−	11.4674i		−	1.54627i
$56$		0			0
$57$		0			0
$58$	−0.408399	−	6.40265i	−0.0536254	−	0.840709i
$59$	4.11641			0.535912			0.267956	−	0.963431i	$-0.413652\pi$
$59$	4.11641			0.535912			0.267956	+	0.963431i	$0.413652\pi$
$60$		0			0
$61$	−1.01025			−0.129349			−0.0646747	−	0.997906i	$-0.520601\pi$
$61$	−1.01025			−0.129349			−0.0646747	+	0.997906i	$0.520601\pi$
$62$	0.105972	+	1.66136i	0.0134584	+	0.210993i
$63$		0			0
$64$	7.42278	−	2.98369i	0.927847	−	0.372961i
$65$			12.9963i			1.61200i
$66$		0			0
$67$		−	12.6446i		−	1.54478i	−0.635147	−	0.772391i	$-0.719060\pi$
$67$		−	12.6446i		−	1.54478i	0.635147	−	0.772391i	$-0.280940\pi$
$68$	1.42581	+	11.1311i	0.172905	+	1.34984i
$69$		0			0
$70$		0			0
$71$	7.31012			0.867552			0.433776	−	0.901021i	$-0.357181\pi$
$71$	7.31012			0.867552			0.433776	+	0.901021i	$0.357181\pi$
$72$		0			0
$73$	9.63787			1.12803			0.564014	−	0.825765i	$-0.309256\pi$
$73$	9.63787			1.12803			0.564014	+	0.825765i	$0.309256\pi$
$74$	3.82892	−	0.244231i	0.445103	−	0.0283913i
$75$		0			0
$76$	0.811513	+	6.33534i	0.0930870	+	0.726714i
$77$		0			0
$78$		0			0
$79$			8.83951i			0.994522i	0.867601	+	0.497261i	$0.165661\pi$
$79$			8.83951i			0.994522i	−0.867601	+	0.497261i	$0.834339\pi$
$80$	2.50908	+	9.63326i	0.280523	+	1.07703i
$81$		0			0
$82$	0.345395	+	5.41491i	0.0381425	+	0.597977i
$83$	−13.7657			−1.51099			−0.755493	−	0.655157i	$-0.772603\pi$
$83$	−13.7657			−1.51099			−0.755493	+	0.655157i	$0.772603\pi$
$84$		0			0
$85$	−13.9639			−1.51460
$86$	1.00623	+	15.7751i	0.108504	+	1.70107i
$87$		0			0
$88$	−12.7958	+	2.47547i	−1.36403	+	0.263886i
$89$		−	8.52595i		−	0.903749i	−0.892082	−	0.451874i	$-0.850756\pi$
$89$		−	8.52595i		−	0.903749i	0.892082	−	0.451874i	$-0.149244\pi$
$90$		0			0
$91$		0			0
$92$	−1.42581	+	0.182637i	−0.148651	+	0.0190412i
$93$		0			0
$94$	−7.64682	+	0.487759i	−0.788709	+	0.0503085i
$95$	−7.94768			−0.815415
$96$		0			0
$97$	−10.7232			−1.08878			−0.544388	−	0.838833i	$-0.683238\pi$
$97$	−10.7232			−1.08878			−0.544388	+	0.838833i	$0.683238\pi$
$98$		0			0
$99$		0			0
$100$	−2.36756	+	0.303268i	−0.236756	+	0.0303268i
$101$			3.83670i			0.381766i	0.981613	+	0.190883i	$0.0611351\pi$
$101$			3.83670i			0.381766i	−0.981613	+	0.190883i	$0.938865\pi$
$102$		0			0
$103$		−	16.6774i		−	1.64327i	−0.570012	−	0.821636i	$-0.693061\pi$
$103$		−	16.6774i		−	1.64327i	0.570012	−	0.821636i	$-0.306939\pi$
$104$	14.5018	−	2.80550i	1.42201	−	0.275102i
$105$		0			0
$106$	−0.186190	−	2.91898i	−0.0180844	−	0.283517i
$107$	5.73689			0.554606			0.277303	−	0.960783i	$-0.410559\pi$
$107$	5.73689			0.554606			0.277303	+	0.960783i	$0.410559\pi$
$108$		0			0
$109$	−2.82705			−0.270782			−0.135391	−	0.990792i	$-0.543229\pi$
$109$	−2.82705			−0.270782			−0.135391	+	0.990792i	$0.543229\pi$
$110$	−1.03235	−	16.1845i	−0.0984302	−	1.54313i
$111$		0			0
$112$		0			0
$113$			5.59651i			0.526476i	0.964731	+	0.263238i	$0.0847904\pi$
$113$			5.59651i			0.526476i	−0.964731	+	0.263238i	$0.915210\pi$
$114$		0			0
$115$		−	1.78868i		−	0.166795i
$116$	−1.15278	−	8.99958i	−0.107033	−	0.835590i
$117$		0			0
$118$	5.80968	−	0.370576i	0.534825	−	0.0341143i
$119$		0			0
$120$		0			0
$121$	10.2325			0.930224
$122$	−1.42581	+	0.0909468i	−0.129087	+	0.00823394i
$123$		0			0
$124$	0.299125	+	2.33522i	0.0268622	+	0.209709i
$125$			9.47322i			0.847311i
$126$		0			0
$127$		−	15.2266i		−	1.35114i	−0.737294	−	0.675572i	$-0.763897\pi$
$127$		−	15.2266i		−	1.35114i	0.737294	−	0.675572i	$-0.236103\pi$
$128$	10.2075	−	4.87924i	0.902224	−	0.431268i
$129$		0			0
$130$	1.16998	+	18.3423i	0.102614	+	1.60873i
$131$	4.15332			0.362877			0.181438	−	0.983402i	$-0.441925\pi$
$131$	4.15332			0.362877			0.181438	+	0.983402i	$0.441925\pi$
$132$		0			0
$133$		0			0
$134$	−1.13832	−	17.8459i	−0.0983356	−	1.54165i
$135$		0			0
$136$	3.01438	+	15.5814i	0.258481	+	1.33610i
$137$		−	16.3317i		−	1.39531i	−0.716433	−	0.697656i	$-0.754226\pi$
$137$		−	16.3317i		−	1.39531i	0.716433	−	0.697656i	$-0.245774\pi$
$138$		0			0
$139$		−	10.2903i		−	0.872811i	−0.899750	−	0.436406i	$-0.856251\pi$
$139$		−	10.2903i		−	0.872811i	0.899750	−	0.436406i	$-0.143749\pi$
$140$		0			0
$141$		0			0
$142$	10.3171	−	0.658086i	0.865792	−	0.0552254i
$143$	−24.0633			−2.01227
$144$		0			0
$145$	11.2900			0.937581
$146$	13.6024	−	0.867640i	1.12574	−	0.0718064i
$147$		0			0
$148$	5.38194	−	0.689389i	0.442393	−	0.0566674i
$149$		−	5.65685i		−	0.463428i	−0.972784	−	0.231714i	$-0.925567\pi$
$149$		−	5.65685i		−	0.463428i	0.972784	−	0.231714i	$-0.0744333\pi$
$150$		0			0
$151$		−	12.1625i		−	0.989767i	−0.868959	−	0.494884i	$-0.835211\pi$
$151$		−	12.1625i		−	0.989767i	0.868959	−	0.494884i	$-0.164789\pi$
$152$	1.71566	+	8.86830i	0.139158	+	0.719314i
$153$		0			0
$154$		0			0
$155$	−2.92953			−0.235305
$156$		0			0
$157$	7.03901			0.561774			0.280887	−	0.959741i	$-0.409371\pi$
$157$	7.03901			0.561774			0.280887	+	0.959741i	$0.409371\pi$
$158$	0.795768	+	12.4756i	0.0633079	+	0.992505i
$159$		0			0
$160$	4.40840	+	13.3700i	0.348515	+	1.05699i
$161$		0			0
$162$		0			0
$163$			1.78868i			0.140100i	0.997543	+	0.0700502i	$0.0223159\pi$
$163$			1.78868i			0.140100i	−0.997543	+	0.0700502i	$0.977684\pi$
$164$	0.974943	+	7.61121i	0.0761303	+	0.594336i
$165$		0			0
$166$	−19.4282	+	1.23925i	−1.50792	+	0.0961842i
$167$	−8.26973			−0.639931			−0.319965	−	0.947429i	$-0.603671\pi$
$167$	−8.26973			−0.639931			−0.319965	+	0.947429i	$0.603671\pi$
$168$		0			0
$169$	14.2715			1.09781
$170$	−19.7079	+	1.25709i	−1.51153	+	0.0964143i
$171$		0			0
$172$	2.84027	+	22.1735i	0.216569	+	1.69071i
$173$			19.3472i			1.47094i	0.677557	+	0.735470i	$0.263039\pi$
$173$			19.3472i			1.47094i	−0.677557	+	0.735470i	$0.736961\pi$
$174$		0			0
$175$		0			0
$176$	−17.8364	+	4.64566i	−1.34447	+	0.350180i
$177$		0			0
$178$	−0.767540	−	12.0331i	−0.0575296	−	0.901916i
$179$	12.0538			0.900941			0.450470	−	0.892791i	$-0.351256\pi$
$179$	12.0538			0.900941			0.450470	+	0.892791i	$0.351256\pi$
$180$		0			0
$181$	20.7992			1.54599			0.772997	−	0.634410i	$-0.218757\pi$
$181$	20.7992			1.54599			0.772997	+	0.634410i	$0.218757\pi$
$182$		0			0
$183$		0			0
$184$	−1.99587	+	0.386121i	−0.147138	+	0.0284652i
$185$			6.75164i			0.496390i
$186$		0			0
$187$		−	25.8548i		−	1.89069i
$188$	−10.7484	+	1.37679i	−0.783907	+	0.100413i
$189$		0			0
$190$	−11.2169	+	0.715482i	−0.813761	+	0.0519065i
$191$	10.6163			0.768169			0.384084	−	0.923298i	$-0.374517\pi$
$191$	10.6163			0.768169			0.384084	+	0.923298i	$0.374517\pi$
$192$		0			0
$193$	12.9927			0.935233			0.467617	−	0.883931i	$-0.345113\pi$
$193$	12.9927			0.935233			0.467617	+	0.883931i	$0.345113\pi$
$194$	−15.1341	+	0.965346i	−1.08657	+	0.0693078i
$195$		0			0
$196$		0			0
$197$		−	3.18852i		−	0.227173i	−0.993528	−	0.113586i	$-0.963766\pi$
$197$		−	3.18852i		−	0.227173i	0.993528	−	0.113586i	$-0.0362339\pi$
$198$		0			0
$199$		−	14.0495i		−	0.995940i	−0.867194	−	0.497970i	$-0.834079\pi$
$199$		−	14.0495i		−	0.995940i	0.867194	−	0.497970i	$-0.165921\pi$
$200$	−3.31415	+	0.641153i	−0.234345	+	0.0453364i
$201$		0			0
$202$	0.345395	+	5.41491i	0.0243019	+	0.380992i
$203$		0			0
$204$		0			0
$205$	−9.54826			−0.666879
$206$	−1.50137	−	23.5376i	−0.104605	−	1.63994i
$207$		0			0
$208$	20.2144	−	5.26504i	1.40162	−	0.365065i
$209$		−	14.7155i		−	1.01789i
$210$		0			0
$211$			9.12962i			0.628509i	0.949339	+	0.314255i	$0.101755\pi$
$211$			9.12962i			0.628509i	−0.949339	+	0.314255i	$0.898245\pi$
$212$	−0.525557	−	4.10293i	−0.0360954	−	0.281790i
$213$		0			0
$214$	8.09673	−	0.516457i	0.553481	−	0.0353043i
$215$	−27.8166			−1.89708
$216$		0			0
$217$		0			0
$218$	−3.98994	+	0.254502i	−0.270233	+	0.0172371i
$219$		0			0
$220$	−2.91399	−	22.7490i	−0.196461	−	1.53374i
$221$			29.3019i			1.97106i
$222$		0			0
$223$		−	23.8384i		−	1.59634i	−0.602434	−	0.798168i	$-0.705802\pi$
$223$		−	23.8384i		−	1.59634i	0.602434	−	0.798168i	$-0.294198\pi$
$224$		0			0
$225$		0			0
$226$	0.503820	+	7.89861i	0.0335136	+	0.525408i
$227$	10.0124			0.664544			0.332272	−	0.943184i	$-0.392185\pi$
$227$	10.0124			0.664544			0.332272	+	0.943184i	$0.392185\pi$
$228$		0			0
$229$	−5.33630			−0.352633			−0.176316	−	0.984334i	$-0.556418\pi$
$229$	−5.33630			−0.352633			−0.176316	+	0.984334i	$0.556418\pi$
$230$	−0.161024	−	2.52445i	−0.0106176	−	0.166457i
$231$		0			0
$232$	−2.43716	−	12.5977i	−0.160007	−	0.827082i
$233$		−	8.76818i		−	0.574423i	−0.957867	−	0.287211i	$-0.907272\pi$
$233$		−	8.76818i		−	0.574423i	0.957867	−	0.287211i	$-0.0927282\pi$
$234$		0			0
$235$		−	13.4838i		−	0.879589i
$236$	8.16611	−	1.04602i	0.531568	−	0.0680902i
$237$		0			0
$238$		0			0
$239$	13.1385			0.849860			0.424930	−	0.905226i	$-0.360299\pi$
$239$	13.1385			0.849860			0.424930	+	0.905226i	$0.360299\pi$
$240$		0			0
$241$	−22.0638			−1.42125			−0.710627	−	0.703569i	$-0.751588\pi$
$241$	−22.0638			−1.42125			−0.710627	+	0.703569i	$0.751588\pi$
$242$	14.4415	−	0.921167i	0.928337	−	0.0592149i
$243$		0			0
$244$	−2.00413	+	0.256715i	−0.128301	+	0.0164345i
$245$		0			0
$246$		0			0
$247$			16.6774i			1.06116i
$248$	0.632394	+	3.26887i	0.0401571	+	0.207573i
$249$		0			0
$250$	0.852817	+	13.3700i	0.0539369	+	0.845592i
$251$	−26.5149			−1.67361			−0.836804	−	0.547503i	$-0.815579\pi$
$251$	−26.5149			−1.67361			−0.836804	+	0.547503i	$0.815579\pi$
$252$		0			0
$253$	3.31182			0.208212
$254$	−1.37076	−	21.4900i	−0.0860092	−	1.34840i
$255$		0			0
$256$	13.9671	−	7.80521i	0.872941	−	0.487826i
$257$		−	16.9392i		−	1.05664i	−0.849046	−	0.528320i	$-0.822822\pi$
$257$		−	16.9392i		−	1.05664i	0.849046	−	0.528320i	$-0.177178\pi$
$258$		0			0
$259$		0			0
$260$	3.30250	+	25.7820i	0.204812	+	1.59893i
$261$		0			0
$262$	5.86176	−	0.373898i	0.362141	−	0.0230995i
$263$	−13.9594			−0.860772			−0.430386	−	0.902645i	$-0.641623\pi$
$263$	−13.9594			−0.860772			−0.430386	+	0.902645i	$0.641623\pi$
$264$		0			0
$265$	5.14712			0.316185
$266$		0			0
$267$		0			0
$268$	−3.21312	−	25.0842i	−0.196272	−	1.53226i
$269$		−	15.5402i		−	0.947500i	−0.880659	−	0.473750i	$-0.842900\pi$
$269$		−	15.5402i		−	0.947500i	0.880659	−	0.473750i	$-0.157100\pi$
$270$		0			0
$271$			0.227723i			0.0138332i	0.999976	+	0.00691658i	$0.00220163\pi$
$271$			0.227723i			0.0138332i	−0.999976	+	0.00691658i	$0.997798\pi$
$272$	5.65703	+	21.7194i	0.343008	+	1.31693i
$273$		0			0
$274$	−1.47025	−	23.0497i	−0.0888208	−	1.39248i
$275$	5.49927			0.331619
$276$		0			0
$277$	−18.1028			−1.08769			−0.543846	−	0.839185i	$-0.683032\pi$
$277$	−18.1028			−1.08769			−0.543846	+	0.839185i	$0.683032\pi$
$278$	−0.926373	−	14.5232i	−0.0555602	−	0.871041i
$279$		0			0
$280$		0			0
$281$		−	16.5594i		−	0.987854i	−0.869503	−	0.493927i	$-0.835561\pi$
$281$		−	16.5594i		−	0.987854i	0.869503	−	0.493927i	$-0.164439\pi$
$282$		0			0
$283$		−	3.19355i		−	0.189837i	−0.995485	−	0.0949185i	$-0.969741\pi$
$283$		−	3.19355i		−	0.189837i	0.995485	−	0.0949185i	$-0.0302590\pi$
$284$	14.5018	−	1.85757i	0.860521	−	0.110227i
$285$		0			0
$286$	−33.9616	+	2.16627i	−2.00819	+	0.128094i
$287$		0			0
$288$		0			0
$289$	−14.4834			−0.851966
$290$	15.9341	−	1.01637i	0.935680	−	0.0596832i
$291$		0			0
$292$	19.1195	−	2.44908i	1.11889	−	0.143321i
$293$		−	3.17751i		−	0.185632i	−0.995683	−	0.0928160i	$-0.970413\pi$
$293$		−	3.17751i		−	0.185632i	0.995683	−	0.0928160i	$-0.0295868\pi$
$294$		0			0
$295$			10.2444i			0.596451i
$296$	7.53371	−	1.45747i	0.437888	−	0.0847137i
$297$		0			0
$298$	−0.509253	−	7.98377i	−0.0295002	−	0.462488i
$299$	−3.75337			−0.217063
$300$		0			0
$301$		0			0
$302$	−1.09491	−	17.1654i	−0.0630052	−	0.987760i
$303$		0			0
$304$	3.21975	+	12.3618i	0.184665	+	0.708997i
$305$		−	2.51418i		−	0.143961i
$306$		0			0
$307$			10.8559i			0.619579i	0.950805	+	0.309790i	$0.100259\pi$
$307$			10.8559i			0.619579i	−0.950805	+	0.309790i	$0.899741\pi$
$308$		0			0
$309$		0			0
$310$	−4.13458	+	0.263728i	−0.234828	+	0.0149787i
$311$	18.6821			1.05936			0.529681	−	0.848197i	$-0.322312\pi$
$311$	18.6821			1.05936			0.529681	+	0.848197i	$0.322312\pi$
$312$		0			0
$313$	−15.8313			−0.894839			−0.447420	−	0.894324i	$-0.647657\pi$
$313$	−15.8313			−0.894839			−0.447420	+	0.894324i	$0.647657\pi$
$314$	9.93447	−	0.633680i	0.560635	−	0.0357606i
$315$		0			0
$316$	2.24621	+	17.5357i	0.126359	+	0.986462i
$317$			6.13829i			0.344761i	0.985030	+	0.172380i	$0.0551458\pi$
$317$			6.13829i			0.344761i	−0.985030	+	0.172380i	$0.944854\pi$
$318$		0			0
$319$			20.9039i			1.17039i
$320$	7.42539	+	18.4728i	0.415092	+	1.03266i
$321$		0			0
$322$		0			0
$323$	−17.9191			−0.997043
$324$		0			0
$325$	−6.23246			−0.345715
$326$	0.161024	+	2.52445i	0.00891831	+	0.139816i
$327$		0			0
$328$	2.06117	+	10.6543i	0.113809	+	0.588284i
$329$		0			0
$330$		0			0
$331$			0.388432i			0.0213501i	0.999943	+	0.0106751i	$0.00339804\pi$
$331$			0.388432i			0.0213501i	−0.999943	+	0.0106751i	$0.996602\pi$
$332$	−27.3084	+	3.49801i	−1.49874	+	0.191978i
$333$		0			0
$334$	−11.6714	+	0.744474i	−0.638633	+	0.0407358i
$335$	31.4681			1.71929
$336$		0			0
$337$	6.10384			0.332497			0.166249	−	0.986084i	$-0.446835\pi$
$337$	6.10384			0.332497			0.166249	+	0.986084i	$0.446835\pi$
$338$	20.1420	−	1.28477i	1.09558	−	0.0698825i
$339$		0			0
$340$	−27.7015	+	3.54837i	−1.50233	+	0.192437i
$341$		−	5.42415i		−	0.293734i
$342$		0			0
$343$		0			0
$344$	6.00475	+	31.0388i	0.323754	+	1.67350i
$345$		0			0
$346$	1.74171	+	27.3056i	0.0936351	+	1.46796i
$347$	−29.0268			−1.55824			−0.779120	−	0.626874i	$-0.784334\pi$
$347$	−29.0268			−1.55824			−0.779120	+	0.626874i	$0.784334\pi$
$348$		0			0
$349$	−27.2889			−1.46074			−0.730371	−	0.683050i	$-0.760653\pi$
$349$	−27.2889			−1.46074			−0.730371	+	0.683050i	$0.760653\pi$
$350$		0			0
$351$		0			0
$352$	−24.7551	+	8.16234i	−1.31945	+	0.435054i
$353$		−	30.2811i		−	1.61170i	−0.592118	−	0.805851i	$-0.701708\pi$
$353$		−	30.2811i		−	1.61170i	0.592118	−	0.805851i	$-0.298292\pi$
$354$		0			0
$355$			18.1924i			0.965554i
$356$	−2.16653	−	16.9137i	−0.114826	−	0.896424i
$357$		0			0
$358$	17.0120	−	1.08513i	0.899113	−	0.0573508i
$359$	−20.7780			−1.09662			−0.548312	−	0.836274i	$-0.684729\pi$
$359$	−20.7780			−1.09662			−0.548312	+	0.836274i	$0.684729\pi$
$360$		0			0
$361$	8.80122			0.463222
$362$	29.3549	−	1.87243i	1.54286	−	0.0984127i
$363$		0			0
$364$		0			0
$365$			23.9854i			1.25545i
$366$		0			0
$367$			20.4825i			1.06918i	0.845112	+	0.534589i	$0.179533\pi$
$367$			20.4825i			1.06918i	−0.845112	+	0.534589i	$0.820467\pi$
$368$	−2.78211	+	0.724626i	−0.145027	+	0.0377738i
$369$		0			0
$370$	0.607810	+	9.52889i	0.0315985	+	0.495384i
$371$		0			0
$372$		0			0
$373$	−23.9599			−1.24060			−0.620299	−	0.784365i	$-0.712989\pi$
$373$	−23.9599			−1.24060			−0.620299	+	0.784365i	$0.712989\pi$
$374$	−2.32755	−	36.4900i	−0.120355	−	1.88686i
$375$		0			0
$376$	−15.0457	+	2.91074i	−0.775925	+	0.150110i
$377$		−	23.6909i		−	1.22014i
$378$		0			0
$379$		−	3.00154i		−	0.154179i	−0.997024	−	0.0770894i	$-0.975437\pi$
$379$		−	3.00154i		−	0.154179i	0.997024	−	0.0770894i	$-0.0245627\pi$
$380$	−15.7665	+	2.01958i	−0.808807	+	0.103603i
$381$		0			0
$382$	14.9833	−	0.955722i	0.766611	−	0.0488990i
$383$	28.6815			1.46555			0.732777	−	0.680469i	$-0.238224\pi$
$383$	28.6815			1.46555			0.732777	+	0.680469i	$0.238224\pi$
$384$		0			0
$385$		0			0
$386$	18.3372	−	1.16965i	0.933337	−	0.0595338i
$387$		0			0
$388$	−21.2726	+	2.72487i	−1.07995	+	0.138334i
$389$			12.0942i			0.613202i	0.951838	+	0.306601i	$0.0991918\pi$
$389$			12.0942i			0.613202i	−0.951838	+	0.306601i	$0.900808\pi$
$390$		0			0
$391$		−	4.03281i		−	0.203948i
$392$		0			0
$393$		0			0
$394$	−0.287044	−	4.50011i	−0.0144610	−	0.226712i
$395$	−21.9986			−1.10687
$396$		0			0
$397$	5.25829			0.263906			0.131953	−	0.991256i	$-0.457875\pi$
$397$	5.25829			0.263906			0.131953	+	0.991256i	$0.457875\pi$
$398$	−1.26479	−	19.8286i	−0.0633981	−	0.993920i
$399$		0			0
$400$	−4.61968	+	1.20324i	−0.230984	+	0.0601621i
$401$		−	18.5470i		−	0.926193i	−0.886308	−	0.463096i	$-0.846738\pi$
$401$		−	18.5470i		−	0.926193i	0.886308	−	0.463096i	$-0.153262\pi$
$402$		0			0
$403$			6.14732i			0.306220i
$404$	0.974943	+	7.61121i	0.0485052	+	0.378672i
$405$		0			0
$406$		0			0
$407$	−12.5009			−0.619649
$408$		0			0
$409$	−17.5224			−0.866429			−0.433214	−	0.901291i	$-0.642621\pi$
$409$	−17.5224			−0.866429			−0.433214	+	0.901291i	$0.642621\pi$
$410$	−13.4759	+	0.859573i	−0.665527	+	0.0424513i
$411$		0			0
$412$	−4.23789	−	33.0845i	−0.208786	−	1.62996i
$413$		0			0
$414$		0			0
$415$		−	34.2583i		−	1.68167i
$416$	28.0555	−	9.25058i	1.37554	−	0.453547i
$417$		0			0
$418$	−1.32475	−	20.7686i	−0.0647954	−	1.01583i
$419$	26.9149			1.31488			0.657439	−	0.753508i	$-0.271640\pi$
$419$	26.9149			1.31488			0.657439	+	0.753508i	$0.271640\pi$
$420$		0			0
$421$	−4.71296			−0.229695			−0.114848	−	0.993383i	$-0.536638\pi$
$421$	−4.71296			−0.229695			−0.114848	+	0.993383i	$0.536638\pi$
$422$	0.821885	+	12.8850i	0.0400087	+	0.627234i
$423$		0			0
$424$	−1.11110	−	5.74334i	−0.0539600	−	0.278921i
$425$		−	6.69647i		−	0.324827i
$426$		0			0
$427$		0			0
$428$	11.3808	−	1.45780i	0.550111	−	0.0704654i
$429$		0			0
$430$	−39.2589	+	2.50416i	−1.89323	+	0.120761i
$431$	−3.82093			−0.184048			−0.0920239	−	0.995757i	$-0.529334\pi$
$431$	−3.82093			−0.184048			−0.0920239	+	0.995757i	$0.529334\pi$
$432$		0			0
$433$	−34.7992			−1.67234			−0.836172	−	0.548467i	$-0.815212\pi$
$433$	−34.7992			−1.67234			−0.836172	+	0.548467i	$0.815212\pi$
$434$		0			0
$435$		0			0
$436$	−5.60828	+	0.718381i	−0.268588	+	0.0344042i
$437$		−	2.29531i		−	0.109799i
$438$		0			0
$439$			35.4814i			1.69343i	0.532044	+	0.846717i	$0.321424\pi$
$439$			35.4814i			1.69343i	−0.532044	+	0.846717i	$0.678576\pi$
$440$	−6.16060	−	31.8444i	−0.293695	−	1.51812i
$441$		0			0
$442$	2.63787	+	41.3550i	0.125471	+	1.96706i
$443$	10.9584			0.520648			0.260324	−	0.965521i	$-0.416171\pi$
$443$	10.9584			0.520648			0.260324	+	0.965521i	$0.416171\pi$
$444$		0			0
$445$	21.2182			1.00584
$446$	−2.14603	−	33.6442i	−0.101617	−	1.59310i
$447$		0			0
$448$		0			0
$449$			27.1675i			1.28211i	0.767494	+	0.641056i	$0.221503\pi$
$449$			27.1675i			1.28211i	−0.767494	+	0.641056i	$0.778497\pi$
$450$		0			0
$451$		−	17.6790i		−	0.832472i
$452$	1.42213	+	11.1023i	0.0668913	+	0.522209i
$453$		0			0
$454$	14.1309	−	0.901354i	0.663197	−	0.0423026i
$455$		0			0
$456$		0			0
$457$	38.5614			1.80383			0.901914	−	0.431916i	$-0.142162\pi$
$457$	38.5614			1.80383			0.901914	+	0.431916i	$0.142162\pi$
$458$	−7.53136	+	0.480395i	−0.351918	+	0.0224474i
$459$		0			0
$460$	−0.454522	−	3.54837i	−0.0211922	−	0.165444i
$461$			13.5543i			0.631287i	0.948878	+	0.315643i	$0.102220\pi$
$461$			13.5543i			0.631287i	−0.948878	+	0.315643i	$0.897780\pi$
$462$		0			0
$463$			17.7564i			0.825212i	0.910910	+	0.412606i	$0.135381\pi$
$463$			17.7564i			0.825212i	−0.910910	+	0.412606i	$0.864619\pi$
$464$	−4.57377	−	17.5604i	−0.212332	−	0.815219i
$465$		0			0
$466$	−0.789347	−	12.3749i	−0.0365658	−	0.573258i
$467$	−10.7993			−0.499732			−0.249866	−	0.968280i	$-0.580387\pi$
$467$	−10.7993			−0.499732			−0.249866	+	0.968280i	$0.580387\pi$
$468$		0			0
$469$		0			0
$470$	−1.21387	−	19.0304i	−0.0559916	−	0.877805i
$471$		0			0
$472$	11.4310	−	2.21144i	0.526156	−	0.101790i
$473$		−	51.5037i		−	2.36814i
$474$		0			0
$475$		−	3.81135i		−	0.174877i
$476$		0			0
$477$		0			0
$478$	18.5430	−	1.18278i	0.848136	−	0.0540992i
$479$	18.9672			0.866634			0.433317	−	0.901242i	$-0.357343\pi$
$479$	18.9672			0.866634			0.433317	+	0.901242i	$0.357343\pi$
$480$		0			0
$481$	14.1676			0.645988
$482$	−31.1396	+	1.98627i	−1.41837	+	0.0904721i
$483$		0			0
$484$	20.2991	−	2.60017i	0.922685	−	0.118190i
$485$		−	26.6865i		−	1.21177i
$486$		0			0
$487$		−	14.5316i		−	0.658489i	−0.944245	−	0.329245i	$-0.893206\pi$
$487$		−	14.5316i		−	0.658489i	0.944245	−	0.329245i	$-0.106794\pi$
$488$	−2.80541	+	0.542733i	−0.126995	+	0.0245684i
$489$		0			0
$490$		0			0
$491$	26.0025			1.17348			0.586738	−	0.809777i	$-0.300412\pi$
$491$	26.0025			1.17348			0.586738	+	0.809777i	$0.300412\pi$
$492$		0			0
$493$	25.4547			1.14642
$494$	1.50137	+	23.5376i	0.0675497	+	1.05901i
$495$		0			0
$496$	1.18680	+	4.55657i	0.0532891	+	0.204596i
$497$		0			0
$498$		0			0
$499$		−	2.74273i		−	0.122781i	−0.998114	−	0.0613907i	$-0.980446\pi$
$499$		−	2.74273i		−	0.122781i	0.998114	−	0.0613907i	$-0.0195536\pi$
$500$	2.40724	+	18.7929i	0.107655	+	0.840444i
$501$		0			0
$502$	−37.4217	+	2.38698i	−1.67021	+	0.106536i
$503$	−21.5337			−0.960139			−0.480070	−	0.877230i	$-0.659389\pi$
$503$	−21.5337			−0.960139			−0.480070	+	0.877230i	$0.659389\pi$
$504$		0			0
$505$	−9.54826			−0.424892
$506$	4.67412	−	0.298143i	0.207790	−	0.0132541i
$507$		0			0
$508$	−3.86923	−	30.2064i	−0.171669	−	1.34019i
$509$			13.1345i			0.582177i	0.956696	+	0.291089i	$0.0940175\pi$
$509$			13.1345i			0.582177i	−0.956696	+	0.291089i	$0.905983\pi$
$510$		0			0
$511$		0			0
$512$	19.0097	−	12.2732i	0.840117	−	0.542405i
$513$		0			0
$514$	−1.52494	−	23.9071i	−0.0672620	−	1.05450i
$515$	41.5045			1.82890
$516$		0			0
$517$	24.9659			1.09800
$518$		0			0
$519$		0			0
$520$	6.98196	+	36.0900i	0.306179	+	1.58265i
$521$		−	7.27913i		−	0.318905i	−0.987206	−	0.159452i	$-0.949027\pi$
$521$		−	7.27913i		−	0.318905i	0.987206	−	0.159452i	$-0.0509728\pi$
$522$		0			0
$523$			2.79029i			0.122011i	0.998137	+	0.0610055i	$0.0194307\pi$
$523$			2.79029i			0.122011i	−0.998137	+	0.0610055i	$0.980569\pi$
$524$	8.23931	−	1.05540i	0.359936	−	0.0461053i
$525$		0			0
$526$	−19.7015	+	1.25668i	−0.859027	+	0.0547938i
$527$	−6.60499			−0.287718
$528$		0			0
$529$	−22.4834			−0.977540
$530$	7.26437	−	0.463365i	0.315544	−	0.0201273i
$531$		0			0
$532$		0			0
$533$			20.0360i			0.867858i
$534$		0			0
$535$			14.2772i			0.617257i
$536$	−6.79300	−	35.1133i	−0.293413	−	1.51666i
$537$		0			0
$538$	−1.39899	−	21.9325i	−0.0603146	−	0.945578i
$539$		0			0
$540$		0			0
$541$	0.607118			0.0261020			0.0130510	−	0.999915i	$-0.495846\pi$
$541$	0.607118			0.0261020			0.0130510	+	0.999915i	$0.495846\pi$
$542$	0.0205005	+	0.321395i	0.000880572	+	0.0138051i
$543$		0			0
$544$	9.93929	+	30.1443i	0.426144	+	1.29243i
$545$		−	7.03558i		−	0.301371i
$546$		0			0
$547$		−	11.1295i		−	0.475865i	−0.971282	−	0.237933i	$-0.923530\pi$
$547$		−	11.1295i		−	0.475865i	0.971282	−	0.237933i	$-0.0764697\pi$
$548$	−4.15005	−	32.3987i	−0.177281	−	1.38400i
$549$		0			0
$550$	7.76138	−	0.495067i	0.330946	−	0.0211097i
$551$	14.4877			0.617198
$552$		0			0
$553$		0			0
$554$	−25.5493	+	1.62969i	−1.08549	+	0.0692387i
$555$		0			0
$556$	−2.61487	−	20.4138i	−0.110895	−	0.865738i
$557$			29.6533i			1.25645i	0.778031	+	0.628225i	$0.216218\pi$
$557$			29.6533i			1.25645i	−0.778031	+	0.628225i	$0.783782\pi$
$558$		0			0
$559$			58.3703i			2.46880i
$560$		0			0
$561$		0			0
$562$	−1.49075	−	23.3711i	−0.0628834	−	0.985850i
$563$	32.8348			1.38382			0.691910	−	0.721983i	$-0.256769\pi$
$563$	32.8348			1.38382			0.691910	+	0.721983i	$0.256769\pi$
$564$		0			0
$565$	−13.9278			−0.585949
$566$	−0.287496	−	4.50721i	−0.0120844	−	0.189452i
$567$		0			0
$568$	20.2998	−	3.92718i	0.851759	−	0.164781i
$569$		−	9.16895i		−	0.384382i	−0.981358	−	0.192191i	$-0.938441\pi$
$569$		−	9.16895i		−	0.384382i	0.981358	−	0.192191i	$-0.0615594\pi$
$570$		0			0
$571$			24.4499i			1.02320i	0.859224	+	0.511599i	$0.170947\pi$
$571$			24.4499i			1.02320i	−0.859224	+	0.511599i	$0.829053\pi$
$572$	−47.7365	+	6.11471i	−1.99596	+	0.255669i
$573$		0			0
$574$		0			0
$575$	0.857772			0.0357716
$576$		0			0
$577$	−12.0185			−0.500337			−0.250168	−	0.968202i	$-0.580486\pi$
$577$	−12.0185			−0.500337			−0.250168	+	0.968202i	$0.580486\pi$
$578$	−20.4411	+	1.30386i	−0.850238	+	0.0542333i
$579$		0			0
$580$	22.3969	−	2.86889i	0.929983	−	0.119124i
$581$		0			0
$582$		0			0
$583$			9.53012i			0.394697i
$584$	26.7638	−	5.17771i	1.10749	−	0.214255i
$585$		0			0
$586$	−0.286052	−	4.48456i	−0.0118167	−	0.185256i
$587$	18.8618			0.778510			0.389255	−	0.921130i	$-0.372733\pi$
$587$	18.8618			0.778510			0.389255	+	0.921130i	$0.372733\pi$
$588$		0			0
$589$	−3.75929			−0.154899
$590$	0.922240	+	14.4584i	0.0379680	+	0.595241i
$591$		0			0
$592$	10.5015	−	2.73521i	0.431608	−	0.112416i
$593$			8.83457i			0.362792i	0.983410	+	0.181396i	$0.0580616\pi$
$593$			8.83457i			0.362792i	−0.983410	+	0.181396i	$0.941938\pi$
$594$		0			0
$595$		0			0
$596$	−1.43746	−	11.2220i	−0.0588808	−	0.459672i
$597$		0			0
$598$	−5.29729	+	0.337893i	−0.216622	+	0.0138175i
$599$	27.8030			1.13600			0.568000	−	0.823028i	$-0.307717\pi$
$599$	27.8030			1.13600			0.568000	+	0.823028i	$0.307717\pi$
$600$		0			0
$601$	−12.1977			−0.497556			−0.248778	−	0.968561i	$-0.580029\pi$
$601$	−12.1977			−0.497556			−0.248778	+	0.968561i	$0.580029\pi$
$602$		0			0
$603$		0			0
$604$	−3.09060	−	24.1278i	−0.125755	−	0.981746i
$605$			25.4652i			1.03531i
$606$		0			0
$607$			10.5180i			0.426913i	0.976953	+	0.213457i	$0.0684722\pi$
$607$			10.5180i			0.426913i	−0.976953	+	0.213457i	$0.931528\pi$
$608$	5.65703	+	17.1569i	0.229423	+	0.695804i
$609$		0			0
$610$	−0.226336	−	3.54837i	−0.00916408	−	0.143669i
$611$	−28.2945			−1.14467
$612$		0			0
$613$	39.4103			1.59177			0.795884	−	0.605449i	$-0.207006\pi$
$613$	39.4103			1.59177			0.795884	+	0.605449i	$0.207006\pi$
$614$	0.977292	+	15.3214i	0.0394403	+	0.618323i
$615$		0			0
$616$		0			0
$617$		−	35.9618i		−	1.44777i	−0.689922	−	0.723884i	$-0.742355\pi$
$617$		−	35.9618i		−	1.44777i	0.689922	−	0.723884i	$-0.257645\pi$
$618$		0			0
$619$			24.4499i			0.982726i	0.870955	+	0.491363i	$0.163501\pi$
$619$			24.4499i			0.982726i	−0.870955	+	0.491363i	$0.836499\pi$
$620$	−5.81157	+	0.744422i	−0.233398	+	0.0298967i
$621$		0			0
$622$	26.3668	−	1.68183i	1.05721	−	0.0674354i
$623$		0			0
$624$		0			0
$625$	−29.5429			−1.18172
$626$	−22.3435	+	1.42520i	−0.893024	+	0.0569624i
$627$		0			0
$628$	13.9639	−	1.78868i	0.557221	−	0.0713762i
$629$			15.2224i			0.606958i
$630$		0			0
$631$			5.08034i			0.202245i	0.994874	+	0.101123i	$0.0322434\pi$
$631$			5.08034i			0.202245i	−0.994874	+	0.101123i	$0.967757\pi$
$632$	4.74881	+	24.5468i	0.188897	+	0.976418i
$633$		0			0
$634$	0.552594	+	8.66325i	0.0219463	+	0.344062i
$635$	37.8939			1.50377
$636$		0			0
$637$		0			0
$638$	1.88185	+	29.5026i	0.0745031	+	1.16802i
$639$		0			0
$640$	12.1428	+	25.4030i	0.479986	+	1.00414i
$641$			26.7077i			1.05489i	0.849589	+	0.527445i	$0.176850\pi$
$641$			26.7077i			1.05489i	−0.849589	+	0.527445i	$0.823150\pi$
$642$		0			0
$643$			24.3919i			0.961924i	0.876741	+	0.480962i	$0.159713\pi$
$643$			24.3919i			0.961924i	−0.876741	+	0.480962i	$0.840287\pi$
$644$		0			0
$645$		0			0
$646$	−25.2900	+	1.61314i	−0.995021	+	0.0634683i
$647$	−4.83841			−0.190218			−0.0951088	−	0.995467i	$-0.530320\pi$
$647$	−4.83841			−0.190218			−0.0951088	+	0.995467i	$0.530320\pi$
$648$		0			0
$649$	−18.9679			−0.744555
$650$	−8.79615	+	0.561071i	−0.345014	+	0.0220070i
$651$		0			0
$652$	0.454522	+	3.54837i	0.0178004	+	0.138965i
$653$			22.5851i			0.883821i	0.897059	+	0.441911i	$0.145699\pi$
$653$			22.5851i			0.883821i	−0.897059	+	0.441911i	$0.854301\pi$
$654$		0			0
$655$			10.3362i			0.403869i
$656$	3.86817	+	14.8513i	0.151027	+	0.579846i
$657$		0			0
$658$		0			0
$659$	−13.4237			−0.522911			−0.261456	−	0.965215i	$-0.584203\pi$
$659$	−13.4237			−0.522911			−0.261456	+	0.965215i	$0.584203\pi$
$660$		0			0
$661$	−14.2037			−0.552460			−0.276230	−	0.961092i	$-0.589085\pi$
$661$	−14.2037			−0.552460			−0.276230	+	0.961092i	$0.589085\pi$
$662$	0.0349682	+	0.548211i	0.00135908	+	0.0213068i
$663$		0			0
$664$	−38.2266	+	7.39531i	−1.48348	+	0.286994i
$665$		0			0
$666$		0			0
$667$			3.26057i			0.126250i
$668$	−16.4054	+	2.10142i	−0.634745	+	0.0813064i
$669$		0			0
$670$	44.4124	−	2.83289i	1.71580	−	0.109444i
$671$	4.65510			0.179708
$672$		0			0
$673$	11.3016			0.435643			0.217822	−	0.975989i	$-0.430105\pi$
$673$	11.3016			0.435643			0.217822	+	0.975989i	$0.430105\pi$
$674$	8.61463	−	0.549492i	0.331823	−	0.0211657i
$675$		0			0
$676$	28.3116	−	3.62652i	1.08891	−	0.139482i
$677$		−	3.17751i		−	0.122122i	−0.998134	−	0.0610608i	$-0.980552\pi$
$677$		−	3.17751i		−	0.122122i	0.998134	−	0.0610608i	$-0.0194484\pi$
$678$		0			0
$679$		0			0
$680$	−38.7770	+	7.50178i	−1.48703	+	0.287680i
$681$		0			0
$682$	−0.488303	−	7.65534i	−0.0186981	−	0.293138i
$683$	6.26524			0.239733			0.119866	−	0.992790i	$-0.461753\pi$
$683$	6.26524			0.239733			0.119866	+	0.992790i	$0.461753\pi$
$684$		0			0
$685$	40.6441			1.55293
$686$		0			0
$687$		0			0
$688$	11.2690	+	43.2658i	0.429627	+	1.64949i
$689$		−	10.8007i		−	0.411474i
$690$		0			0
$691$		−	16.1301i		−	0.613619i	−0.951771	−	0.306809i	$-0.900739\pi$
$691$		−	16.1301i		−	0.613619i	0.951771	−	0.306809i	$-0.0992614\pi$
$692$	4.91632	+	38.3808i	0.186890	+	1.45902i
$693$		0			0
$694$	−40.9669	+	2.61311i	−1.55508	+	0.0991923i
$695$	25.6091			0.971408
$696$		0			0
$697$	−21.5278			−0.815422
$698$	−38.5141	+	2.45666i	−1.45778	+	0.0929859i
$699$		0			0
$700$		0			0
$701$		−	50.8903i		−	1.92210i	−0.276373	−	0.961050i	$-0.589133\pi$
$701$		−	50.8903i		−	1.92210i	0.276373	−	0.961050i	$-0.410867\pi$
$702$		0			0
$703$			8.66397i			0.326768i
$704$	−34.2032	+	13.7484i	−1.28908	+	0.518164i
$705$		0			0
$706$	−2.72603	−	42.7371i	−0.102595	−	1.60843i
$707$		0			0
$708$		0			0
$709$	21.3743			0.802727			0.401364	−	0.915919i	$-0.368536\pi$
$709$	21.3743			0.802727			0.401364	+	0.915919i	$0.368536\pi$
$710$	1.63776	+	25.6758i	0.0614639	+	0.963596i
$711$		0			0
$712$	−4.58036	−	23.6760i	−0.171656	−	0.887297i
$713$		−	0.846054i		−	0.0316850i
$714$		0			0
$715$		−	59.8854i		−	2.23959i
$716$	23.9122	−	3.06298i	0.893639	−	0.114469i
$717$		0			0
$718$	−29.3250	+	1.87052i	−1.09440	+	0.0698073i
$719$	24.3853			0.909418			0.454709	−	0.890640i	$-0.349743\pi$
$719$	24.3853			0.909418			0.454709	+	0.890640i	$0.349743\pi$
$720$		0			0
$721$		0			0
$722$	12.4216	−	0.792321i	0.462283	−	0.0294871i
$723$		0			0
$724$	41.2613	−	5.28529i	1.53346	−	0.196426i
$725$			5.41417i			0.201077i
$726$		0			0
$727$			37.0825i			1.37531i	0.726037	+	0.687656i	$0.241360\pi$
$727$			37.0825i			1.37531i	−0.726037	+	0.687656i	$0.758640\pi$
$728$		0			0
$729$		0			0
$730$	2.15926	+	33.8517i	0.0799180	+	1.25291i
$731$	−62.7161			−2.31964
$732$		0			0
$733$	45.1262			1.66678			0.833388	−	0.552689i	$-0.186398\pi$
$733$	45.1262			1.66678			0.833388	+	0.552689i	$0.186398\pi$
$734$	1.84392	+	28.9079i	0.0680602	+	1.06701i
$735$		0			0
$736$	−3.86128	+	1.27315i	−0.142329	+	0.0469291i
$737$			58.2646i			2.14621i
$738$		0			0
$739$			43.0456i			1.58346i	0.610872	+	0.791729i	$0.290819\pi$
$739$			43.0456i			1.58346i	−0.610872	+	0.791729i	$0.709181\pi$
$740$	1.71566	+	13.3938i	0.0630689	+	0.492367i
$741$		0			0
$742$		0			0
$743$	7.52770			0.276165			0.138082	−	0.990421i	$-0.455906\pi$
$743$	7.52770			0.276165			0.138082	+	0.990421i	$0.455906\pi$
$744$		0			0
$745$	14.0780			0.515779
$746$	−33.8158	+	2.15697i	−1.23808	+	0.0789723i
$747$		0			0
$748$	−6.56996	−	51.2905i	−0.240222	−	1.87537i
$749$		0			0
$750$		0			0
$751$		−	44.0306i		−	1.60670i	−0.595509	−	0.803349i	$-0.703050\pi$
$751$		−	44.0306i		−	1.60670i	0.595509	−	0.803349i	$-0.296950\pi$
$752$	−20.9727	+	5.46254i	−0.764796	+	0.199198i
$753$		0			0
$754$	−2.13275	−	33.4360i	−0.0776700	−	1.21767i
$755$	30.2683			1.10158
$756$		0			0
$757$	7.64185			0.277748			0.138874	−	0.990310i	$-0.455652\pi$
$757$	7.64185			0.277748			0.138874	+	0.990310i	$0.455652\pi$
$758$	−0.270211	−	4.23621i	−0.00981449	−	0.153866i
$759$		0			0
$760$	−22.0702	+	4.26970i	−0.800571	+	0.154878i
$761$		−	17.4602i		−	0.632932i	−0.948604	−	0.316466i	$-0.897504\pi$
$761$		−	17.4602i		−	0.632932i	0.948604	−	0.316466i	$-0.102496\pi$
$762$		0			0
$763$		0			0
$764$	21.0605	−	2.69771i	0.761943	−	0.0975996i
$765$		0			0
$766$	40.4794	−	2.58202i	1.46258	−	0.0932922i
$767$	21.4968			0.776204
$768$		0			0
$769$	3.13489			0.113047			0.0565235	−	0.998401i	$-0.481998\pi$
$769$	3.13489			0.113047			0.0565235	+	0.998401i	$0.481998\pi$
$770$		0			0
$771$		0			0
$772$	25.7748	−	3.30157i	0.927654	−	0.118826i
$773$			19.0221i			0.684179i	0.939667	+	0.342090i	$0.111135\pi$
$773$			19.0221i			0.684179i	−0.939667	+	0.342090i	$0.888865\pi$
$774$		0			0
$775$		−	1.40487i		−	0.0504645i
$776$	−29.7777	+	5.76078i	−1.06896	+	0.206800i
$777$		0			0
$778$	1.08877	+	17.0692i	0.0390344	+	0.611959i
$779$	−12.2527			−0.438999
$780$		0			0
$781$	−33.6841			−1.20531
$782$	−0.363050	−	5.69169i	−0.0129826	−	0.203534i
$783$		0			0
$784$		0			0
$785$			17.5177i			0.625235i
$786$		0			0
$787$		−	4.59842i		−	0.163916i	−0.996636	−	0.0819581i	$-0.973883\pi$
$787$		−	4.59842i		−	0.163916i	0.996636	−	0.0819581i	$-0.0261174\pi$
$788$	−0.810235	−	6.32536i	−0.0288634	−	0.225332i
$789$		0			0
$790$	−31.0476	+	1.98040i	−1.10462	+	0.0704594i
$791$		0			0
$792$		0			0
$793$	−5.27574			−0.187347
$794$	7.42126	−	0.473372i	0.263371	−	0.0167993i
$795$		0			0
$796$	−3.57011	−	27.8712i	−0.126539	−	0.987869i
$797$			40.4802i			1.43388i	0.697134	+	0.716941i	$0.254458\pi$
$797$			40.4802i			1.43388i	−0.697134	+	0.716941i	$0.745542\pi$
$798$		0			0
$799$		−	30.4010i		−	1.07551i
$800$	−6.41165	+	2.11407i	−0.226686	+	0.0747437i
$801$		0			0
$802$	−1.66967	−	26.1762i	−0.0589583	−	0.924314i
$803$	−44.4100			−1.56720
$804$		0			0
$805$		0			0
$806$	0.553406	+	8.67599i	0.0194929	+	0.305599i
$807$		0			0
$808$	2.06117	+	10.6543i	0.0725118	+	0.374816i
$809$		−	9.86400i		−	0.346800i	−0.984851	−	0.173400i	$-0.944525\pi$
$809$		−	9.86400i		−	0.346800i	0.984851	−	0.173400i	$-0.0554753\pi$
$810$		0			0
$811$		−	28.0467i		−	0.984854i	−0.870354	−	0.492427i	$-0.836110\pi$
$811$		−	28.0467i		−	0.984854i	0.870354	−	0.492427i	$-0.163890\pi$
$812$		0			0
$813$		0			0
$814$	−17.6432	+	1.12539i	−0.618392	+	0.0394447i
$815$	−4.45143			−0.155927
$816$		0			0
$817$	−35.6954			−1.24882
$818$	−24.7302	+	1.57744i	−0.864671	+	0.0551539i
$819$		0			0
$820$	−18.9418	+	2.42631i	−0.661475	+	0.0847303i
$821$		−	26.5158i		−	0.925408i	−0.886513	−	0.462704i	$-0.846879\pi$
$821$		−	26.5158i		−	0.925408i	0.886513	−	0.462704i	$-0.153121\pi$
$822$		0			0
$823$		−	20.3844i		−	0.710555i	−0.934761	−	0.355277i	$-0.884386\pi$
$823$		−	20.3844i		−	0.710555i	0.934761	−	0.355277i	$-0.115614\pi$
$824$	−8.95953	−	46.3121i	−0.312120	−	1.61336i
$825$		0			0
$826$		0			0
$827$	−17.5032			−0.608645			−0.304322	−	0.952569i	$-0.598430\pi$
$827$	−17.5032			−0.608645			−0.304322	+	0.952569i	$0.598430\pi$
$828$		0			0
$829$	10.7983			0.375040			0.187520	−	0.982261i	$-0.439955\pi$
$829$	10.7983			0.375040			0.187520	+	0.982261i	$0.439955\pi$
$830$	−3.08407	−	48.3503i	−0.107050	−	1.67826i
$831$		0			0
$832$	38.7633	−	15.5814i	1.34388	−	0.540189i
$833$		0			0
$834$		0			0
$835$		−	20.5806i		−	0.712221i
$836$	−3.73935	−	29.1924i	−0.129328	−	1.00964i
$837$		0			0
$838$	37.9862	−	2.42299i	1.31221	−	0.0837006i
$839$	−8.78448			−0.303274			−0.151637	−	0.988436i	$-0.548454\pi$
$839$	−8.78448			−0.303274			−0.151637	+	0.988436i	$0.548454\pi$
$840$		0			0
$841$	8.41964			0.290332
$842$	−6.65161	+	0.424279i	−0.229230	+	0.0146216i
$843$		0			0
$844$	2.31993	+	18.1113i	0.0798552	+	0.623415i
$845$			35.5169i			1.22182i
$846$		0			0
$847$		0			0
$848$	−2.08519	−	8.00581i	−0.0716057	−	0.274921i
$849$		0			0
$850$	−0.602843	−	9.45104i	−0.0206774	−	0.324168i
$851$	−1.94989			−0.0668413
$852$		0			0
$853$	3.87338			0.132622			0.0663110	−	0.997799i	$-0.478877\pi$
$853$	3.87338			0.132622			0.0663110	+	0.997799i	$0.478877\pi$
$854$		0			0
$855$		0			0
$856$	15.9310	−	3.08200i	0.544510	−	0.105341i
$857$			43.2775i			1.47833i	0.673524	+	0.739165i	$0.264780\pi$
$857$			43.2775i			1.47833i	−0.673524	+	0.739165i	$0.735220\pi$
$858$		0			0
$859$			15.8903i			0.542171i	0.962555	+	0.271086i	$0.0873826\pi$
$859$			15.8903i			0.542171i	−0.962555	+	0.271086i	$0.912617\pi$
$860$	−55.1824	+	7.06848i	−1.88170	+	0.241033i
$861$		0			0
$862$	−5.39266	+	0.343976i	−0.183675	+	0.0117159i
$863$	10.5584			0.359413			0.179707	−	0.983720i	$-0.442485\pi$
$863$	10.5584			0.359413			0.179707	+	0.983720i	$0.442485\pi$
$864$		0			0
$865$	−48.1487			−1.63711
$866$	−49.1137	+	3.13277i	−1.66895	+	0.106456i
$867$		0			0
$868$		0			0
$869$		−	40.7313i		−	1.38171i
$870$		0			0
$871$		−	66.0327i		−	2.23743i
$872$	−7.85054	+	1.51876i	−0.265853	+	0.0514318i
$873$		0			0
$874$	−0.206633	−	3.23947i	−0.00698945	−	0.109577i
$875$		0			0
$876$		0			0
$877$	−1.75594			−0.0592940			−0.0296470	−	0.999560i	$-0.509438\pi$
$877$	−1.75594			−0.0592940			−0.0296470	+	0.999560i	$0.509438\pi$
$878$	3.19418	+	50.0765i	0.107798	+	1.69000i
$879$		0			0
$880$	−11.5615	−	44.3888i	−0.389738	−	1.49635i
$881$		−	39.9987i		−	1.34759i	−0.738917	−	0.673796i	$-0.764663\pi$
$881$		−	39.9987i		−	1.34759i	0.738917	−	0.673796i	$-0.235337\pi$
$882$		0			0
$883$		−	15.9005i		−	0.535096i	−0.963545	−	0.267548i	$-0.913787\pi$
$883$		−	15.9005i		−	0.535096i	0.963545	−	0.267548i	$-0.0862133\pi$
$884$	7.44589	+	58.1288i	0.250433	+	1.95508i
$885$		0			0
$886$	15.4661	−	0.986517i	0.519592	−	0.0331427i
$887$	33.3735			1.12057			0.560286	−	0.828299i	$-0.310691\pi$
$887$	33.3735			1.12057			0.560286	+	0.828299i	$0.310691\pi$
$888$		0			0
$889$		0			0
$890$	29.9462	−	1.91015i	1.00380	−	0.0640284i
$891$		0			0
$892$	−6.05757	−	47.2904i	−0.202823	−	1.58340i
$893$		−	17.3030i		−	0.579023i
$894$		0			0
$895$			29.9978i			1.00272i
$896$		0			0
$897$		0			0
$898$	2.44572	+	38.3427i	0.0816148	+	1.27951i
$899$	5.34020			0.178106
$900$		0			0
$901$	11.6048			0.386613
$902$	−1.59154	−	24.9512i	−0.0529923	−	0.830784i
$903$		0			0
$904$	3.00659	+	15.5412i	0.0999977	+	0.516892i
$905$			51.7623i			1.72064i
$906$		0			0
$907$			36.7879i			1.22152i	0.791815	+	0.610762i	$0.209137\pi$
$907$			36.7879i			1.22152i	−0.791815	+	0.610762i	$0.790863\pi$
$908$	19.8625	−	2.54424i	0.659159	−	0.0844337i
$909$		0			0
$910$		0			0
$911$	−46.9066			−1.55409			−0.777043	−	0.629448i	$-0.783281\pi$
$911$	−46.9066			−1.55409			−0.777043	+	0.629448i	$0.783281\pi$
$912$		0			0
$913$	63.4307			2.09925
$914$	54.4235	−	3.47145i	1.80017	−	0.114826i
$915$		0			0
$916$	−10.5861	+	1.35601i	−0.349775	+	0.0448037i
$917$		0			0
$918$		0			0
$919$			18.0153i			0.594268i	0.954836	+	0.297134i	$0.0960309\pi$
$919$			18.0153i			0.594268i	−0.954836	+	0.297134i	$0.903969\pi$
$920$	−0.960926	−	4.96706i	−0.0316808	−	0.163759i
$921$		0			0
$922$	1.22021	+	19.1298i	0.0401856	+	0.630006i
$923$	38.1750			1.25654
$924$		0			0
$925$	−3.23779			−0.106458
$926$	1.59851	+	25.0605i	0.0525302	+	0.823538i
$927$		0			0
$928$	−8.03602	−	24.3720i	−0.263795	−	0.800050i
$929$		−	32.6340i		−	1.07069i	−0.844635	−	0.535343i	$-0.820182\pi$
$929$		−	32.6340i		−	1.07069i	0.844635	−	0.535343i	$-0.179818\pi$
$930$		0			0
$931$		0			0
$932$	−2.22808	−	17.3942i	−0.0729833	−	0.569768i
$933$		0			0
$934$	−15.2416	+	0.972197i	−0.498719	+	0.0318113i
$935$	64.3439			2.10427
$936$		0			0
$937$	4.08001			0.133288			0.0666441	−	0.997777i	$-0.478771\pi$
$937$	4.08001			0.133288			0.0666441	+	0.997777i	$0.478771\pi$
$938$		0			0
$939$		0			0
$940$	−3.42638	−	26.7491i	−0.111756	−	0.872461i
$941$			24.6956i			0.805055i	0.915408	+	0.402527i	$0.131868\pi$
$941$			24.6956i			0.805055i	−0.915408	+	0.402527i	$0.868132\pi$
$942$		0			0
$943$		−	2.75756i		−	0.0897984i
$944$	15.9341	−	4.15018i	0.518609	−	0.135077i
$945$		0			0
$946$	−4.63657	−	72.6895i	−0.150748	−	2.36334i
$947$	−36.9305			−1.20008			−0.600040	−	0.799970i	$-0.704849\pi$
$947$	−36.9305			−1.20008			−0.600040	+	0.799970i	$0.704849\pi$
$948$		0			0
$949$	50.3310			1.63381
$950$	−0.343113	−	5.37914i	−0.0111321	−	0.174522i
$951$		0			0
$952$		0			0
$953$			61.5883i			1.99504i	0.0703720	+	0.997521i	$0.477581\pi$
$953$			61.5883i			1.99504i	−0.0703720	+	0.997521i	$0.522419\pi$
$954$		0			0
$955$			26.4204i			0.854945i
$956$	26.0641	−	3.33863i	0.842972	−	0.107979i
$957$		0			0
$958$	26.7693	−	1.70750i	0.864876	−	0.0551669i
$959$		0			0
$960$		0			0
$961$	29.6143			0.955301
$962$	19.9954	−	1.27543i	0.644678	−	0.0411214i
$963$		0			0
$964$	−43.7699	+	5.60663i	−1.40973	+	0.180577i
$965$			32.3344i			1.04088i
$966$		0			0
$967$			22.8368i			0.734381i	0.930146	+	0.367191i	$0.119680\pi$
$967$			22.8368i			0.734381i	−0.930146	+	0.367191i	$0.880320\pi$
$968$	28.4149	−	5.49714i	0.913290	−	0.176685i
$969$		0			0
$970$	−2.40242	−	37.6638i	−0.0771371	−	1.20931i
$971$	−48.1874			−1.54641			−0.773203	−	0.634159i	$-0.781347\pi$
$971$	−48.1874			−1.54641			−0.773203	+	0.634159i	$0.781347\pi$
$972$		0			0
$973$		0			0
$974$	−1.30819	−	20.5091i	−0.0419172	−	0.657154i
$975$		0			0
$976$	−3.91054	+	1.01854i	−0.125173	+	0.0326026i
$977$		−	31.4737i		−	1.00693i	−0.864015	−	0.503466i	$-0.832058\pi$
$977$		−	31.4737i		−	1.00693i	0.864015	−	0.503466i	$-0.167942\pi$
$978$		0			0
$979$			39.2865i			1.25560i
$980$		0			0
$981$		0			0
$982$	36.6985	−	2.34085i	1.17110	−	0.0746995i
$983$	40.0880			1.27861			0.639304	−	0.768954i	$-0.279223\pi$
$983$	40.0880			1.27861			0.639304	+	0.768954i	$0.279223\pi$
$984$		0			0
$985$	7.93517			0.252835
$986$	35.9253	−	2.29153i	1.14410	−	0.0729772i
$987$		0			0
$988$	4.23789	+	33.0845i	0.134825	+	1.05256i
$989$		−	8.03350i		−	0.255450i
$990$		0			0
$991$			51.5681i			1.63812i	0.573711	+	0.819058i	$0.305503\pi$
$991$			51.5681i			1.63812i	−0.573711	+	0.819058i	$0.694497\pi$
$992$	2.08519	+	6.32406i	0.0662049	+	0.200789i
$993$		0			0
$994$		0			0
$995$	34.9644			1.10845
$996$		0			0
$997$	−21.5162			−0.681424			−0.340712	−	0.940168i	$-0.610668\pi$
$997$	−21.5162			−0.681424			−0.340712	+	0.940168i	$0.610668\pi$
$998$	−0.246911	−	3.87094i	−0.00781584	−	0.122532i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.e.i.1079.15		16
3.2	odd	2	inner	1764.2.e.i.1079.2		16
4.3	odd	2	inner	1764.2.e.i.1079.1		16
7.2	even	3		252.2.be.a.179.5	yes	32
7.4	even	3		252.2.be.a.107.7	yes	32
7.6	odd	2		1764.2.e.h.1079.15		16
12.11	even	2	inner	1764.2.e.i.1079.16		16
21.2	odd	6		252.2.be.a.179.12	yes	32
21.11	odd	6		252.2.be.a.107.10	yes	32
21.20	even	2		1764.2.e.h.1079.2		16
28.11	odd	6		252.2.be.a.107.12	yes	32
28.23	odd	6		252.2.be.a.179.10	yes	32
28.27	even	2		1764.2.e.h.1079.1		16
84.11	even	6		252.2.be.a.107.5	✓	32
84.23	even	6		252.2.be.a.179.7	yes	32
84.83	odd	2		1764.2.e.h.1079.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.be.a.107.5	✓	32	84.11	even	6
252.2.be.a.107.7	yes	32	7.4	even	3
252.2.be.a.107.10	yes	32	21.11	odd	6
252.2.be.a.107.12	yes	32	28.11	odd	6
252.2.be.a.179.5	yes	32	7.2	even	3
252.2.be.a.179.7	yes	32	84.23	even	6
252.2.be.a.179.10	yes	32	28.23	odd	6
252.2.be.a.179.12	yes	32	21.2	odd	6
1764.2.e.h.1079.1		16	28.27	even	2
1764.2.e.h.1079.2		16	21.20	even	2
1764.2.e.h.1079.15		16	7.6	odd	2
1764.2.e.h.1079.16		16	84.83	odd	2
1764.2.e.i.1079.1		16	4.3	odd	2	inner
1764.2.e.i.1079.2		16	3.2	odd	2	inner
1764.2.e.i.1079.15		16	1.1	even	1	trivial
1764.2.e.i.1079.16		16	12.11	even	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)

\(f(q)\)	\(=\)	\(q+(1.41135 - 0.0900240i) q^{2} +(1.98379 - 0.254110i) q^{4} +2.48866i q^{5} +(2.77694 - 0.537226i) q^{8} +O(q^{10})\)	\(q+(1.41135 - 0.0900240i) q^{2} +(1.98379 - 0.254110i) q^{4} +2.48866i q^{5} +(2.77694 - 0.537226i) q^{8} +(0.224040 + 3.51237i) q^{10} -4.60787 q^{11} +5.22221 q^{13} +(3.87086 - 1.00820i) q^{16} +5.61101i q^{17} +3.19355i q^{19} +(0.632394 + 4.93699i) q^{20} +(-6.50329 + 0.414819i) q^{22} -0.718731 q^{23} -1.19345 q^{25} +(7.37034 - 0.470124i) q^{26} -4.53656i q^{29} +1.17715i q^{31} +(5.37235 - 1.77139i) q^{32} +(0.505125 + 7.91907i) q^{34} +2.71296 q^{37} +(0.287496 + 4.50721i) q^{38} +(1.33697 + 6.91087i) q^{40} +3.83670i q^{41} +11.1773i q^{43} +(-9.14105 + 1.17091i) q^{44} +(-1.01438 + 0.0647031i) q^{46} -5.41810 q^{47} +(-1.68437 + 0.107439i) q^{50} +(10.3598 - 1.32702i) q^{52} -2.06823i q^{53} -11.4674i q^{55} +(-0.408399 - 6.40265i) q^{58} +4.11641 q^{59} -1.01025 q^{61} +(0.105972 + 1.66136i) q^{62} +(7.42278 - 2.98369i) q^{64} +12.9963i q^{65} -12.6446i q^{67} +(1.42581 + 11.1311i) q^{68} +7.31012 q^{71} +9.63787 q^{73} +(3.82892 - 0.244231i) q^{74} +(0.811513 + 6.33534i) q^{76} +8.83951i q^{79} +(2.50908 + 9.63326i) q^{80} +(0.345395 + 5.41491i) q^{82} -13.7657 q^{83} -13.9639 q^{85} +(1.00623 + 15.7751i) q^{86} +(-12.7958 + 2.47547i) q^{88} -8.52595i q^{89} +(-1.42581 + 0.182637i) q^{92} +(-7.64682 + 0.487759i) q^{94} -7.94768 q^{95} -10.7232 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 8 q^{13} - 4 q^{16} - 16 q^{22} - 24 q^{25} - 8 q^{34} - 8 q^{37} + 52 q^{40} + 24 q^{46} + 52 q^{52} + 12 q^{58} + 16 q^{61} + 60 q^{64} + 8 q^{73} + 36 q^{76} - 68 q^{82} - 16 q^{85} - 44 q^{88} - 60 q^{94} - 88 q^{97}+O(q^{100}) \) 16 * q + 8 * q^13 - 4 * q^16 - 16 * q^22 - 24 * q^25 - 8 * q^34 - 8 * q^37 + 52 * q^40 + 24 * q^46 + 52 * q^52 + 12 * q^58 + 16 * q^61 + 60 * q^64 + 8 * q^73 + 36 * q^76 - 68 * q^82 - 16 * q^85 - 44 * q^88 - 60 * q^94 - 88 * q^97

Introduction

L-functions

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