LMFDB - Embedded newform 1764.2.e.i.1079.14

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			1079.14
Root			$1.13008 + 0.850247i$ of defining polynomial
Character	$\chi$	$=$	1764.1079
Dual form			1764.2.e.i.1079.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13008 + 0.850247i) q^{2} +(0.554161 + 1.92169i) q^{4} -3.87147i q^{5} +(-1.00767 + 2.64284i) q^{8} +O(q^{10})$	\(q+(1.13008 + 0.850247i) q^{2} +(0.554161 + 1.92169i) q^{4} -3.87147i q^{5} +(-1.00767 + 2.64284i) q^{8} +(3.29170 - 4.37507i) q^{10} +3.46960 q^{11} -0.296538 q^{13} +(-3.38581 + 2.12986i) q^{16} +1.56741i q^{17} -7.07478i q^{19} +(7.43977 - 2.14542i) q^{20} +(3.92092 + 2.95001i) q^{22} +5.43537 q^{23} -9.98827 q^{25} +(-0.335112 - 0.252130i) q^{26} -6.85309i q^{29} -2.81507i q^{31} +(-5.63714 - 0.471866i) q^{32} +(-1.33268 + 1.77129i) q^{34} +2.51318 q^{37} +(6.01531 - 7.99507i) q^{38} +(10.2317 + 3.90115i) q^{40} +3.55418i q^{41} -0.682082i q^{43} +(1.92272 + 6.66750i) q^{44} +(6.14240 + 4.62140i) q^{46} +2.36931 q^{47} +(-11.2875 - 8.49249i) q^{50} +(-0.164330 - 0.569855i) q^{52} -0.623673i q^{53} -13.4324i q^{55} +(5.82681 - 7.74454i) q^{58} +8.85541 q^{59} +2.66536 q^{61} +(2.39350 - 3.18125i) q^{62} +(-5.96922 - 5.32621i) q^{64} +1.14804i q^{65} -10.6174i q^{67} +(-3.01207 + 0.868595i) q^{68} +0.539214 q^{71} +7.39519 q^{73} +(2.84010 + 2.13683i) q^{74} +(13.5956 - 3.92057i) q^{76} -6.16578i q^{79} +(8.24567 + 13.1081i) q^{80} +(-3.02193 + 4.01651i) q^{82} -6.15982 q^{83} +6.06816 q^{85} +(0.579938 - 0.770808i) q^{86} +(-3.49620 + 9.16959i) q^{88} +11.7165i q^{89} +(3.01207 + 10.4451i) q^{92} +(2.67751 + 2.01450i) q^{94} -27.3898 q^{95} -6.84782 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.13008	+	0.850247i	0.799087	+	0.601215i
$2$	1.13008	+	0.850247i	0.799087	+	0.601215i
$3$		0			0
$3$		0			0
$4$	0.554161	+	1.92169i	0.277081	+	0.960847i
$5$		−	3.87147i		−	1.73137i	−0.500586	−	0.865687i	$-0.666882\pi$
$5$		−	3.87147i		−	1.73137i	0.500586	−	0.865687i	$-0.333118\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00767	+	2.64284i	−0.356264	+	0.934385i
$9$		0			0
$10$	3.29170	−	4.37507i	1.04093	−	1.38352i
$11$	3.46960			1.04612			0.523061	−	0.852295i	$-0.324790\pi$
$11$	3.46960			1.04612			0.523061	+	0.852295i	$0.324790\pi$
$12$		0			0
$13$	−0.296538			−0.0822448			−0.0411224	−	0.999154i	$-0.513093\pi$
$13$	−0.296538			−0.0822448			−0.0411224	+	0.999154i	$0.513093\pi$
$14$		0			0
$15$		0			0
$16$	−3.38581	+	2.12986i	−0.846453	+	0.532464i
$17$			1.56741i			0.380152i	0.981769	+	0.190076i	$0.0608734\pi$
$17$			1.56741i			0.380152i	−0.981769	+	0.190076i	$0.939127\pi$
$18$		0			0
$19$		−	7.07478i		−	1.62307i	−0.584307	−	0.811533i	$-0.698633\pi$
$19$		−	7.07478i		−	1.62307i	0.584307	−	0.811533i	$-0.301367\pi$
$20$	7.43977	−	2.14542i	1.66358	−	0.479730i
$21$		0			0
$22$	3.92092	+	2.95001i	0.835943	+	0.628945i
$23$	5.43537			1.13335			0.566676	−	0.823940i	$-0.308229\pi$
$23$	5.43537			1.13335			0.566676	+	0.823940i	$0.308229\pi$
$24$		0			0
$25$	−9.98827			−1.99765
$26$	−0.335112	−	0.252130i	−0.0657208	−	0.0494468i
$27$		0			0
$28$		0			0
$29$		−	6.85309i		−	1.27259i	−0.771447	−	0.636293i	$-0.780467\pi$
$29$		−	6.85309i		−	1.27259i	0.771447	−	0.636293i	$-0.219533\pi$
$30$		0			0
$31$		−	2.81507i		−	0.505601i	−0.967518	−	0.252800i	$-0.918648\pi$
$31$		−	2.81507i		−	0.505601i	0.967518	−	0.252800i	$-0.0813516\pi$
$32$	−5.63714	−	0.471866i	−0.996515	−	0.0834149i
$33$		0			0
$34$	−1.33268	+	1.77129i	−0.228553	+	0.303774i
$35$		0			0
$36$		0			0
$37$	2.51318			0.413165			0.206582	−	0.978429i	$-0.433766\pi$
$37$	2.51318			0.413165			0.206582	+	0.978429i	$0.433766\pi$
$38$	6.01531	−	7.99507i	0.975812	−	1.29697i
$39$		0			0
$40$	10.2317	+	3.90115i	1.61777	+	0.616826i
$41$			3.55418i			0.555069i	0.960716	+	0.277535i	$0.0895173\pi$
$41$			3.55418i			0.555069i	−0.960716	+	0.277535i	$0.910483\pi$
$42$		0			0
$43$		−	0.682082i		−	0.104017i	−0.998647	−	0.0520083i	$-0.983438\pi$
$43$		−	0.682082i		−	0.104017i	0.998647	−	0.0520083i	$-0.0165622\pi$
$44$	1.92272	+	6.66750i	0.289860	+	1.00516i
$45$		0			0
$46$	6.14240	+	4.62140i	0.905648	+	0.681389i
$47$	2.36931			0.345600			0.172800	−	0.984957i	$-0.444719\pi$
$47$	2.36931			0.345600			0.172800	+	0.984957i	$0.444719\pi$
$48$		0			0
$49$		0			0
$50$	−11.2875	−	8.49249i	−1.59630	−	1.20102i
$51$		0			0
$52$	−0.164330	−	0.569855i	−0.0227884	−	0.0790247i
$53$		−	0.623673i		−	0.0856681i	−0.999082	−	0.0428340i	$-0.986361\pi$
$53$		−	0.623673i		−	0.0856681i	0.999082	−	0.0428340i	$-0.0136387\pi$
$54$		0			0
$55$		−	13.4324i		−	1.81123i
$56$		0			0
$57$		0			0
$58$	5.82681	−	7.74454i	0.765098	−	1.01691i
$59$	8.85541			1.15288			0.576438	−	0.817141i	$-0.304442\pi$
$59$	8.85541			1.15288			0.576438	+	0.817141i	$0.304442\pi$
$60$		0			0
$61$	2.66536			0.341265			0.170632	−	0.985335i	$-0.445419\pi$
$61$	2.66536			0.341265			0.170632	+	0.985335i	$0.445419\pi$
$62$	2.39350	−	3.18125i	0.303975	−	0.404019i
$63$		0			0
$64$	−5.96922	−	5.32621i	−0.746152	−	0.665776i
$65$			1.14804i			0.142396i
$66$		0			0
$67$		−	10.6174i		−	1.29712i	−0.761165	−	0.648559i	$-0.775372\pi$
$67$		−	10.6174i		−	1.29712i	0.761165	−	0.648559i	$-0.224628\pi$
$68$	−3.01207	+	0.868595i	−0.365267	+	0.105333i
$69$		0			0
$70$		0			0
$71$	0.539214			0.0639929			0.0319964	−	0.999488i	$-0.489813\pi$
$71$	0.539214			0.0639929			0.0319964	+	0.999488i	$0.489813\pi$
$72$		0			0
$73$	7.39519			0.865542			0.432771	−	0.901504i	$-0.357536\pi$
$73$	7.39519			0.865542			0.432771	+	0.901504i	$0.357536\pi$
$74$	2.84010	+	2.13683i	0.330155	+	0.248401i
$75$		0			0
$76$	13.5956	−	3.92057i	1.55952	−	0.449720i
$77$		0			0
$78$		0			0
$79$		−	6.16578i		−	0.693705i	−0.937920	−	0.346852i	$-0.887251\pi$
$79$		−	6.16578i		−	0.693705i	0.937920	−	0.346852i	$-0.112749\pi$
$80$	8.24567	+	13.1081i	0.921894	+	1.46553i
$81$		0			0
$82$	−3.02193	+	4.01651i	−0.333716	+	0.443549i
$83$	−6.15982			−0.676128			−0.338064	−	0.941123i	$-0.609772\pi$
$83$	−6.15982			−0.676128			−0.338064	+	0.941123i	$0.609772\pi$
$84$		0			0
$85$	6.06816			0.658184
$86$	0.579938	−	0.770808i	0.0625363	−	0.0831183i
$87$		0			0
$88$	−3.49620	+	9.16959i	−0.372696	+	0.977482i
$89$			11.7165i			1.24194i	0.783832	+	0.620972i	$0.213262\pi$
$89$			11.7165i			1.24194i	−0.783832	+	0.620972i	$0.786738\pi$
$90$		0			0
$91$		0			0
$92$	3.01207	+	10.4451i	0.314030	+	1.08898i
$93$		0			0
$94$	2.67751	+	2.01450i	0.276164	+	0.207780i
$95$	−27.3898			−2.81013
$96$		0			0
$97$	−6.84782			−0.695291			−0.347645	−	0.937626i	$-0.613019\pi$
$97$	−6.84782			−0.695291			−0.347645	+	0.937626i	$0.613019\pi$
$98$		0			0
$99$		0			0
$100$	−5.53511	−	19.1944i	−0.553511	−	1.91944i
$101$			3.55418i			0.353654i	0.984242	+	0.176827i	$0.0565833\pi$
$101$			3.55418i			0.353654i	−0.984242	+	0.176827i	$0.943417\pi$
$102$		0			0
$103$		−	2.09794i		−	0.206716i	−0.994644	−	0.103358i	$-0.967041\pi$
$103$		−	2.09794i		−	0.206716i	0.994644	−	0.103358i	$-0.0329588\pi$
$104$	0.298811	−	0.783703i	0.0293009	−	0.0768484i
$105$		0			0
$106$	0.530276	−	0.704801i	0.0515050	−	0.0684563i
$107$	11.0560			1.06882			0.534411	−	0.845225i	$-0.320534\pi$
$107$	11.0560			1.06882			0.534411	+	0.845225i	$0.320534\pi$
$108$		0			0
$109$	13.3190			1.27573			0.637864	−	0.770149i	$-0.279818\pi$
$109$	13.3190			1.27573			0.637864	+	0.770149i	$0.279818\pi$
$110$	11.4209	−	15.1797i	1.08894	−	1.44733i
$111$		0			0
$112$		0			0
$113$			6.75101i			0.635082i	0.948245	+	0.317541i	$0.102857\pi$
$113$			6.75101i			0.635082i	−0.948245	+	0.317541i	$0.897143\pi$
$114$		0			0
$115$		−	21.0429i		−	1.96226i
$116$	13.1695	−	3.79772i	1.22276	−	0.352609i
$117$		0			0
$118$	10.0073	+	7.52928i	0.921248	+	0.693126i
$119$		0			0
$120$		0			0
$121$	1.03810			0.0943728
$122$	3.01207	+	2.26621i	0.272700	+	0.205173i
$123$		0			0
$124$	5.40970	−	1.56000i	0.485805	−	0.140092i
$125$			19.3119i			1.72731i
$126$		0			0
$127$			20.3153i			1.80270i	0.433097	+	0.901348i	$0.357421\pi$
$127$			20.3153i			1.80270i	−0.433097	+	0.901348i	$0.642579\pi$
$128$	−2.21710	−	11.0943i	−0.195966	−	0.980611i
$129$		0			0
$130$	−0.976115	+	1.29737i	−0.0856109	+	0.113787i
$131$	−17.2489			−1.50704			−0.753520	−	0.657425i	$-0.771646\pi$
$131$	−17.2489			−1.50704			−0.753520	+	0.657425i	$0.771646\pi$
$132$		0			0
$133$		0			0
$134$	9.02738	−	11.9985i	0.779847	−	1.03651i
$135$		0			0
$136$	−4.14240	−	1.57942i	−0.355208	−	0.135434i
$137$			16.6310i			1.42088i	0.703757	+	0.710441i	$0.251504\pi$
$137$			16.6310i			1.42088i	−0.703757	+	0.710441i	$0.748496\pi$
$138$		0			0
$139$		−	16.2475i		−	1.37809i	−0.724716	−	0.689047i	$-0.758029\pi$
$139$		−	16.2475i		−	1.37809i	0.724716	−	0.689047i	$-0.241971\pi$
$140$		0			0
$141$		0			0
$142$	0.609354	+	0.458465i	0.0511359	+	0.0384735i
$143$	−1.02887			−0.0860382
$144$		0			0
$145$	−26.5315			−2.20332
$146$	8.35716	+	6.28774i	0.691643	+	0.520377i
$147$		0			0
$148$	1.39271	+	4.82957i	0.114480	+	0.396988i
$149$		−	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
$151$			3.99775i			0.325332i	0.986681	+	0.162666i	$0.0520094\pi$
$151$			3.99775i			0.325332i	−0.986681	+	0.162666i	$0.947991\pi$
$152$	18.6975	+	7.12902i	1.51657	+	0.578240i
$153$		0			0
$154$		0			0
$155$	−10.8984			−0.875384
$156$		0			0
$157$	−10.9502			−0.873918			−0.436959	−	0.899481i	$-0.643945\pi$
$157$	−10.9502			−0.873918			−0.436959	+	0.899481i	$0.643945\pi$
$158$	5.24244	−	6.96783i	0.417066	−	0.554331i
$159$		0			0
$160$	−1.82681	+	21.8240i	−0.144422	+	1.72534i
$161$		0			0
$162$		0			0
$163$			21.0429i			1.64820i	0.566441	+	0.824102i	$0.308320\pi$
$163$			21.0429i			1.64820i	−0.566441	+	0.824102i	$0.691680\pi$
$164$	−6.83004	+	1.96959i	−0.533337	+	0.153799i
$165$		0			0
$166$	−6.96109	−	5.23736i	−0.540285	−	0.406498i
$167$	8.39346			0.649505			0.324753	−	0.945799i	$-0.394719\pi$
$167$	8.39346			0.649505			0.324753	+	0.945799i	$0.394719\pi$
$168$		0			0
$169$	−12.9121			−0.993236
$170$	6.85750	+	5.15943i	0.525947	+	0.395710i
$171$		0			0
$172$	1.31075	−	0.377984i	0.0999440	−	0.0288210i
$173$			15.0211i			1.14203i	0.820939	+	0.571016i	$0.193450\pi$
$173$			15.0211i			1.14203i	−0.820939	+	0.571016i	$0.806550\pi$
$174$		0			0
$175$		0			0
$176$	−11.7474	+	7.38974i	−0.885493	+	0.557023i
$177$		0			0
$178$	−9.96190	+	13.2406i	−0.746676	+	0.992422i
$179$	−2.57640			−0.192569			−0.0962847	−	0.995354i	$-0.530696\pi$
$179$	−2.57640			−0.192569			−0.0962847	+	0.995354i	$0.530696\pi$
$180$		0			0
$181$	−22.3412			−1.66061			−0.830305	−	0.557309i	$-0.811834\pi$
$181$	−22.3412			−1.66061			−0.830305	+	0.557309i	$0.811834\pi$
$182$		0			0
$183$		0			0
$184$	−5.47704	+	14.3648i	−0.403773	+	1.05899i
$185$		−	9.72971i		−	0.715342i
$186$		0			0
$187$			5.43826i			0.397685i
$188$	1.31298	+	4.55309i	0.0957590	+	0.332068i
$189$		0			0
$190$	−30.9526	−	23.2881i	−2.24554	−	1.68949i
$191$	8.29434			0.600157			0.300079	−	0.953914i	$-0.402987\pi$
$191$	8.29434			0.600157			0.300079	+	0.953914i	$0.402987\pi$
$192$		0			0
$193$	−21.3530			−1.53702			−0.768510	−	0.639838i	$-0.779002\pi$
$193$	−21.3530			−1.53702			−0.768510	+	0.639838i	$0.779002\pi$
$194$	−7.73859	−	5.82234i	−0.555598	−	0.418019i
$195$		0			0
$196$		0			0
$197$			0.572559i			0.0407932i	0.999792	+	0.0203966i	$0.00649288\pi$
$197$			0.572559i			0.0407932i	−0.999792	+	0.0203966i	$0.993507\pi$
$198$		0			0
$199$			17.5003i			1.24056i	0.784380	+	0.620281i	$0.212981\pi$
$199$			17.5003i			1.24056i	−0.784380	+	0.620281i	$0.787019\pi$
$200$	10.0648	−	26.3974i	0.711692	−	1.86658i
$201$		0			0
$202$	−3.02193	+	4.01651i	−0.212622	+	0.282600i
$203$		0			0
$204$		0			0
$205$	13.7599			0.961032
$206$	1.78377	−	2.37084i	0.124281	−	0.165184i
$207$		0			0
$208$	1.00402	−	0.631583i	0.0696163	−	0.0437924i
$209$		−	24.5466i		−	1.69793i
$210$		0			0
$211$			7.94873i			0.547213i	0.961842	+	0.273607i	$0.0882167\pi$
$211$			7.94873i			0.547213i	−0.961842	+	0.273607i	$0.911783\pi$
$212$	1.19851	−	0.345616i	0.0823139	−	0.0237370i
$213$		0			0
$214$	12.4941	+	9.40030i	0.854081	+	0.642592i
$215$	−2.64066			−0.180092
$216$		0			0
$217$		0			0
$218$	15.0515	+	11.3244i	1.01942	+	0.766987i
$219$		0			0
$220$	25.8130	−	7.44374i	1.74031	−	0.501857i
$221$		−	0.464795i		−	0.0312655i
$222$		0			0
$223$			1.17855i			0.0789216i	0.999221	+	0.0394608i	$0.0125640\pi$
$223$			1.17855i			0.0789216i	−0.999221	+	0.0394608i	$0.987436\pi$
$224$		0			0
$225$		0			0
$226$	−5.74002	+	7.62918i	−0.381821	+	0.507486i
$227$	4.54802			0.301863			0.150931	−	0.988544i	$-0.451773\pi$
$227$	4.54802			0.301863			0.150931	+	0.988544i	$0.451773\pi$
$228$		0			0
$229$	16.1287			1.06582			0.532908	−	0.846173i	$-0.321099\pi$
$229$	16.1287			1.06582			0.532908	+	0.846173i	$0.321099\pi$
$230$	17.8916	−	23.7801i	1.17974	−	1.56801i
$231$		0			0
$232$	18.1116	+	6.90563i	1.18909	+	0.453377i
$233$			8.27821i			0.542323i	0.962534	+	0.271162i	$0.0874078\pi$
$233$			8.27821i			0.542323i	−0.962534	+	0.271162i	$0.912592\pi$
$234$		0			0
$235$		−	9.17272i		−	0.598362i
$236$	4.90732	+	17.0174i	0.319440	+	1.10774i
$237$		0			0
$238$		0			0
$239$	18.1308			1.17279			0.586393	−	0.810027i	$-0.300547\pi$
$239$	18.1308			1.17279			0.586393	+	0.810027i	$0.300547\pi$
$240$		0			0
$241$	−19.4216			−1.25105			−0.625526	−	0.780203i	$-0.715116\pi$
$241$	−19.4216			−1.25105			−0.625526	+	0.780203i	$0.715116\pi$
$242$	1.17314	+	0.882641i	0.0754121	+	0.0567383i
$243$		0			0
$244$	1.47704	+	5.12201i	0.0945578	+	0.327903i
$245$		0			0
$246$		0			0
$247$			2.09794i			0.133489i
$248$	7.43977	+	2.83665i	0.472426	+	0.180127i
$249$		0			0
$250$	−16.4199	+	21.8240i	−1.03849	+	1.38027i
$251$	−13.8654			−0.875175			−0.437587	−	0.899176i	$-0.644167\pi$
$251$	−13.8654			−0.875175			−0.437587	+	0.899176i	$0.644167\pi$
$252$		0			0
$253$	18.8585			1.18563
$254$	−17.2731	+	22.9580i	−1.08381	+	1.44051i
$255$		0			0
$256$	6.92742	−	14.4226i	0.432964	−	0.901411i
$257$		−	7.69751i		−	0.480157i	−0.970753	−	0.240079i	$-0.922827\pi$
$257$		−	7.69751i		−	0.480157i	0.970753	−	0.240079i	$-0.0771733\pi$
$258$		0			0
$259$		0			0
$260$	−2.20618	+	0.636198i	−0.136821	+	0.0394553i
$261$		0			0
$262$	−19.4926	−	14.6658i	−1.20426	−	0.906055i
$263$	10.0548			0.620006			0.310003	−	0.950736i	$-0.399670\pi$
$263$	10.0548			0.620006			0.310003	+	0.950736i	$0.399670\pi$
$264$		0			0
$265$	−2.41453			−0.148323
$266$		0			0
$267$		0			0
$268$	20.4033	−	5.88373i	1.24633	−	0.359406i
$269$			28.1088i			1.71382i	0.515463	+	0.856912i	$0.327620\pi$
$269$			28.1088i			1.71382i	−0.515463	+	0.856912i	$0.672380\pi$
$270$		0			0
$271$		−	25.3026i		−	1.53702i	−0.639837	−	0.768511i	$-0.720998\pi$
$271$		−	25.3026i		−	1.53702i	0.639837	−	0.768511i	$-0.279002\pi$
$272$	−3.33835	−	5.30694i	−0.202417	−	0.321780i
$273$		0			0
$274$	−14.1404	+	18.7944i	−0.854255	+	1.13541i
$275$	−34.6553			−2.08979
$276$		0			0
$277$	2.52861			0.151929			0.0759647	−	0.997111i	$-0.475796\pi$
$277$	2.52861			0.151929			0.0759647	+	0.997111i	$0.475796\pi$
$278$	13.8144	−	18.3610i	0.828532	−	1.10122i
$279$		0			0
$280$		0			0
$281$			8.00911i			0.477784i	0.971046	+	0.238892i	$0.0767841\pi$
$281$			8.00911i			0.477784i	−0.971046	+	0.238892i	$0.923216\pi$
$282$		0			0
$283$			7.07478i			0.420552i	0.977642	+	0.210276i	$0.0674363\pi$
$283$			7.07478i			0.420552i	−0.977642	+	0.210276i	$0.932564\pi$
$284$	0.298811	+	1.03620i	0.0177312	+	0.0614873i
$285$		0			0
$286$	−1.16270	−	0.874791i	−0.0687520	−	0.0517275i
$287$		0			0
$288$		0			0
$289$	14.5432			0.855485
$290$	−29.9827	−	22.5583i	−1.76065	−	1.32467i
$291$		0			0
$292$	4.09813	+	14.2113i	0.239825	+	0.831653i
$293$			19.9465i			1.16529i	0.812728	+	0.582643i	$0.197982\pi$
$293$			19.9465i			1.16529i	−0.812728	+	0.582643i	$0.802018\pi$
$294$		0			0
$295$		−	34.2834i		−	1.99606i
$296$	−2.53245	+	6.64194i	−0.147196	+	0.386055i
$297$		0			0
$298$	4.80972	−	6.39270i	0.278620	−	0.370319i
$299$	−1.61179			−0.0932124
$300$		0			0
$301$		0			0
$302$	−3.39908	+	4.51778i	−0.195595	+	0.259969i
$303$		0			0
$304$	15.0683	+	23.9539i	0.864224	+	1.37385i
$305$		−	10.3189i		−	0.590856i
$306$		0			0
$307$		−	10.4255i		−	0.595014i	−0.954720	−	0.297507i	$-0.903845\pi$
$307$		−	10.4255i		−	0.595014i	0.954720	−	0.297507i	$-0.0961552\pi$
$308$		0			0
$309$		0			0
$310$	−12.3161	−	9.26636i	−0.699508	−	0.526294i
$311$	−22.7061			−1.28754			−0.643772	−	0.765217i	$-0.722632\pi$
$311$	−22.7061			−1.28754			−0.643772	+	0.765217i	$0.722632\pi$
$312$		0			0
$313$	−22.3835			−1.26519			−0.632594	−	0.774484i	$-0.718010\pi$
$313$	−22.3835			−1.26519			−0.632594	+	0.774484i	$0.718010\pi$
$314$	−12.3746	−	9.31034i	−0.698337	−	0.525413i
$315$		0			0
$316$	11.8487	−	3.41684i	0.666544	−	0.192212i
$317$		−	29.1409i		−	1.63672i	−0.574707	−	0.818359i	$-0.694884\pi$
$317$		−	29.1409i		−	1.63672i	0.574707	−	0.818359i	$-0.305116\pi$
$318$		0			0
$319$		−	23.7774i		−	1.33128i
$320$	−20.6202	+	23.1096i	−1.15271	+	1.29187i
$321$		0			0
$322$		0			0
$323$	11.0890			0.617011
$324$		0			0
$325$	2.96190			0.164297
$326$	−17.8916	+	23.7801i	−0.990925	+	1.31706i
$327$		0			0
$328$	−9.39313	−	3.58143i	−0.518649	−	0.197751i
$329$		0			0
$330$		0			0
$331$		−	20.4309i		−	1.12298i	−0.827483	−	0.561491i	$-0.810228\pi$
$331$		−	20.4309i		−	1.12298i	0.827483	−	0.561491i	$-0.189772\pi$
$332$	−3.41353	−	11.8373i	−0.187342	−	0.649655i
$333$		0			0
$334$	9.48528	+	7.13651i	0.519011	+	0.390492i
$335$	−41.1048			−2.24579
$336$		0			0
$337$	−6.16681			−0.335928			−0.167964	−	0.985793i	$-0.553719\pi$
$337$	−6.16681			−0.335928			−0.167964	+	0.985793i	$0.553719\pi$
$338$	−14.5917	−	10.9784i	−0.793682	−	0.597148i
$339$		0			0
$340$	3.36274	+	11.6611i	0.182370	+	0.632414i
$341$		−	9.76715i		−	0.528921i
$342$		0			0
$343$		0			0
$344$	1.80264	+	0.687312i	0.0971916	+	0.0370574i
$345$		0			0
$346$	−12.7716	+	16.9750i	−0.686607	+	0.912583i
$347$	15.1197			0.811669			0.405834	−	0.913947i	$-0.366981\pi$
$347$	15.1197			0.811669			0.405834	+	0.913947i	$0.366981\pi$
$348$		0			0
$349$	18.8933			1.01134			0.505668	−	0.862728i	$-0.331246\pi$
$349$	18.8933			1.01134			0.505668	+	0.862728i	$0.331246\pi$
$350$		0			0
$351$		0			0
$352$	−19.5586	−	1.63718i	−1.04248	−	0.0872622i
$353$		−	10.6282i		−	0.565680i	−0.959167	−	0.282840i	$-0.908723\pi$
$353$		−	10.6282i		−	0.565680i	0.959167	−	0.282840i	$-0.0912766\pi$
$354$		0			0
$355$		−	2.08755i		−	0.110796i
$356$	−22.5155	+	6.49282i	−1.19332	+	0.344119i
$357$		0			0
$358$	−2.91154	−	2.19058i	−0.153880	−	0.115776i
$359$	−2.80941			−0.148275			−0.0741374	−	0.997248i	$-0.523620\pi$
$359$	−2.80941			−0.148275			−0.0741374	+	0.997248i	$0.523620\pi$
$360$		0			0
$361$	−31.0525			−1.63434
$362$	−25.2474	−	18.9956i	−1.32697	−	0.998384i
$363$		0			0
$364$		0			0
$365$		−	28.6302i		−	1.49858i
$366$		0			0
$367$			18.8811i			0.985585i	0.870147	+	0.492792i	$0.164024\pi$
$367$			18.8811i			0.985585i	−0.870147	+	0.492792i	$0.835976\pi$
$368$	−18.4031	+	11.5766i	−0.959329	+	0.603470i
$369$		0			0
$370$	8.27265	−	10.9953i	0.430075	−	0.571621i
$371$		0			0
$372$		0			0
$373$	−33.5884			−1.73914			−0.869570	−	0.493810i	$-0.835604\pi$
$373$	−33.5884			−1.73914			−0.869570	+	0.493810i	$0.835604\pi$
$374$	−4.62386	+	6.14567i	−0.239094	+	0.317785i
$375$		0			0
$376$	−2.38748	+	6.26172i	−0.123125	+	0.322923i
$377$			2.03220i			0.104664i
$378$		0			0
$379$			7.57538i			0.389121i	0.980890	+	0.194561i	$0.0623281\pi$
$379$			7.57538i			0.389121i	−0.980890	+	0.194561i	$0.937672\pi$
$380$	−15.1784	−	52.6348i	−0.778633	−	2.70011i
$381$		0			0
$382$	9.37326	+	7.05223i	0.479578	+	0.360824i
$383$	36.3809			1.85898			0.929488	−	0.368853i	$-0.120249\pi$
$383$	36.3809			1.85898			0.929488	+	0.368853i	$0.120249\pi$
$384$		0			0
$385$		0			0
$386$	−24.1306	−	18.1553i	−1.22821	−	0.924080i
$387$		0			0
$388$	−3.79480	−	13.1594i	−0.192652	−	0.668068i
$389$			3.41758i			0.173278i	0.996240	+	0.0866391i	$0.0276127\pi$
$389$			3.41758i			0.173278i	−0.996240	+	0.0866391i	$0.972387\pi$
$390$		0			0
$391$			8.51943i			0.430846i
$392$		0			0
$393$		0			0
$394$	−0.486817	+	0.647038i	−0.0245255	+	0.0325973i
$395$	−23.8706			−1.20106
$396$		0			0
$397$	19.7716			0.992309			0.496155	−	0.868234i	$-0.334745\pi$
$397$	19.7716			0.992309			0.496155	+	0.868234i	$0.334745\pi$
$398$	−14.8795	+	19.7767i	−0.745844	+	0.991317i
$399$		0			0
$400$	33.8184	−	21.2736i	1.69092	−	1.06368i
$401$		−	3.80960i		−	0.190242i	−0.995466	−	0.0951211i	$-0.969676\pi$
$401$		−	3.80960i		−	0.190242i	0.995466	−	0.0951211i	$-0.0303238\pi$
$402$		0			0
$403$			0.834774i			0.0415831i
$404$	−6.83004	+	1.96959i	−0.339807	+	0.0979907i
$405$		0			0
$406$		0			0
$407$	8.71973			0.432221
$408$		0			0
$409$	29.4934			1.45836			0.729178	−	0.684325i	$-0.239903\pi$
$409$	29.4934			1.45836			0.729178	+	0.684325i	$0.239903\pi$
$410$	15.5498	+	11.6993i	0.767949	+	0.577787i
$411$		0			0
$412$	4.03160	−	1.16260i	0.198623	−	0.0572771i
$413$		0			0
$414$		0			0
$415$			23.8475i			1.17063i
$416$	1.67163	+	0.139926i	0.0819582	+	0.00686044i
$417$		0			0
$418$	20.8707	−	27.7397i	1.02082	−	1.35679i
$419$	−4.99528			−0.244035			−0.122018	−	0.992528i	$-0.538936\pi$
$419$	−4.99528			−0.244035			−0.122018	+	0.992528i	$0.538936\pi$
$420$		0			0
$421$	−4.51318			−0.219959			−0.109980	−	0.993934i	$-0.535079\pi$
$421$	−4.51318			−0.219959			−0.109980	+	0.993934i	$0.535079\pi$
$422$	−6.75838	+	8.98270i	−0.328993	+	0.437271i
$423$		0			0
$424$	1.64827	+	0.628455i	0.0800470	+	0.0305205i
$425$		−	15.6557i		−	0.759411i
$426$		0			0
$427$		0			0
$428$	6.12679	+	21.2462i	0.296150	+	1.02697i
$429$		0			0
$430$	−2.98416	−	2.24521i	−0.143909	−	0.108274i
$431$	20.2872			0.977201			0.488600	−	0.872508i	$-0.337508\pi$
$431$	20.2872			0.977201			0.488600	+	0.872508i	$0.337508\pi$
$432$		0			0
$433$	8.34123			0.400854			0.200427	−	0.979709i	$-0.435767\pi$
$433$	8.34123			0.400854			0.200427	+	0.979709i	$0.435767\pi$
$434$		0			0
$435$		0			0
$436$	7.38087	+	25.5950i	0.353480	+	1.22578i
$437$		−	38.4540i		−	1.83951i
$438$		0			0
$439$			23.8683i			1.13917i	0.821931	+	0.569586i	$0.192897\pi$
$439$			23.8683i			1.13917i	−0.821931	+	0.569586i	$0.807103\pi$
$440$	35.4998	+	13.5354i	1.69239	+	0.645276i
$441$		0			0
$442$	0.395190	−	0.525256i	0.0187973	−	0.0249839i
$443$	6.00229			0.285177			0.142589	−	0.989782i	$-0.454457\pi$
$443$	6.00229			0.285177			0.142589	+	0.989782i	$0.454457\pi$
$444$		0			0
$445$	45.3600			2.15027
$446$	−1.00206	+	1.33186i	−0.0474488	+	0.0630652i
$447$		0			0
$448$		0			0
$449$			4.92296i			0.232329i	0.993230	+	0.116165i	$0.0370600\pi$
$449$			4.92296i			0.232329i	−0.993230	+	0.116165i	$0.962940\pi$
$450$		0			0
$451$			12.3316i			0.580671i
$452$	−12.9734	+	3.74115i	−0.610216	+	0.175969i
$453$		0			0
$454$	5.13963	+	3.86694i	0.241215	+	0.181485i
$455$		0			0
$456$		0			0
$457$	−26.4436			−1.23698			−0.618489	−	0.785793i	$-0.712255\pi$
$457$	−26.4436			−1.23698			−0.618489	+	0.785793i	$0.712255\pi$
$458$	18.2267	+	13.7134i	0.851679	+	0.640784i
$459$		0			0
$460$	40.4379	−	11.6611i	1.88543	−	0.543703i
$461$			8.92124i			0.415504i	0.978182	+	0.207752i	$0.0666147\pi$
$461$			8.92124i			0.415504i	−0.978182	+	0.207752i	$0.933385\pi$
$462$		0			0
$463$		−	14.3310i		−	0.666020i	−0.942923	−	0.333010i	$-0.891936\pi$
$463$		−	14.3310i		−	0.666020i	0.942923	−	0.333010i	$-0.108064\pi$
$464$	14.5961	+	23.2033i	0.677606	+	1.07718i
$465$		0			0
$466$	−7.03852	+	9.35504i	−0.326053	+	0.433364i
$467$	−21.3656			−0.988684			−0.494342	−	0.869268i	$-0.664591\pi$
$467$	−21.3656			−0.988684			−0.494342	+	0.869268i	$0.664591\pi$
$468$		0			0
$469$		0			0
$470$	7.79907	−	10.3659i	0.359744	−	0.478144i
$471$		0			0
$472$	−8.92330	+	23.4034i	−0.410728	+	1.07723i
$473$		−	2.36655i		−	0.108814i
$474$		0			0
$475$			70.6648i			3.24232i
$476$		0			0
$477$		0			0
$478$	20.4893	+	15.4157i	0.937159	+	0.705097i
$479$	−32.3851			−1.47971			−0.739856	−	0.672766i	$-0.765106\pi$
$479$	−32.3851			−1.47971			−0.739856	+	0.672766i	$0.765106\pi$
$480$		0			0
$481$	−0.745254			−0.0339807
$482$	−21.9479	−	16.5131i	−0.999700	−	0.752152i
$483$		0			0
$484$	0.575275	+	1.99491i	0.0261489	+	0.0906778i
$485$			26.5111i			1.20381i
$486$		0			0
$487$			2.88516i			0.130739i	0.997861	+	0.0653695i	$0.0208226\pi$
$487$			2.88516i			0.130739i	−0.997861	+	0.0653695i	$0.979177\pi$
$488$	−2.68580	+	7.04413i	−0.121580	+	0.318873i
$489$		0			0
$490$		0			0
$491$	16.6547			0.751617			0.375808	−	0.926697i	$-0.377365\pi$
$491$	16.6547			0.751617			0.375808	+	0.926697i	$0.377365\pi$
$492$		0			0
$493$	10.7416			0.483776
$494$	−1.78377	+	2.37084i	−0.0802555	+	0.106669i
$495$		0			0
$496$	5.99569	+	9.53128i	0.269214	+	0.427967i
$497$		0			0
$498$		0			0
$499$			26.0610i			1.16665i	0.812239	+	0.583325i	$0.198249\pi$
$499$			26.0610i			1.16665i	−0.812239	+	0.583325i	$0.801751\pi$
$500$	−37.1116	+	10.7019i	−1.65968	+	0.478604i
$501$		0			0
$502$	−15.6690	−	11.7890i	−0.699341	−	0.526168i
$503$	28.7302			1.28102			0.640509	−	0.767951i	$-0.278723\pi$
$503$	28.7302			1.28102			0.640509	+	0.767951i	$0.278723\pi$
$504$		0			0
$505$	13.7599			0.612307
$506$	21.3117	+	16.0344i	0.947419	+	0.712816i
$507$		0			0
$508$	−39.0399	+	11.2580i	−1.73211	+	0.499492i
$509$		−	15.7921i		−	0.699973i	−0.936755	−	0.349986i	$-0.886186\pi$
$509$		−	15.7921i		−	0.699973i	0.936755	−	0.349986i	$-0.113814\pi$
$510$		0			0
$511$		0			0
$512$	20.0913	−	10.4086i	0.887918	−	0.460002i
$513$		0			0
$514$	6.54478	−	8.69880i	0.288678	−	0.383688i
$515$	−8.12211			−0.357903
$516$		0			0
$517$	8.22056			0.361540
$518$		0			0
$519$		0			0
$520$	−3.03408	−	1.15684i	−0.133053	−	0.0507307i
$521$			3.41466i			0.149599i	0.997199	+	0.0747995i	$0.0238317\pi$
$521$			3.41466i			0.149599i	−0.997199	+	0.0747995i	$0.976168\pi$
$522$		0			0
$523$			6.61336i			0.289182i	0.989492	+	0.144591i	$0.0461866\pi$
$523$			6.61336i			0.289182i	−0.989492	+	0.144591i	$0.953813\pi$
$524$	−9.55865	−	33.1470i	−0.417572	−	1.44803i
$525$		0			0
$526$	11.3627	+	8.54907i	0.495439	+	0.372757i
$527$	4.41235			0.192205
$528$		0			0
$529$	6.54324			0.284489
$530$	−2.72861	−	2.05295i	−0.118523	−	0.0891743i
$531$		0			0
$532$		0			0
$533$		−	1.05395i		−	0.0456516i
$534$		0			0
$535$		−	42.8028i		−	1.85053i
$536$	28.0600	+	10.6988i	1.21201	+	0.462116i
$537$		0			0
$538$	−23.8994	+	31.7652i	−1.03038	+	1.36949i
$539$		0			0
$540$		0			0
$541$	9.39128			0.403762			0.201881	−	0.979410i	$-0.435295\pi$
$541$	9.39128			0.403762			0.201881	+	0.979410i	$0.435295\pi$
$542$	21.5134	−	28.5939i	0.924081	−	1.22821i
$543$		0			0
$544$	0.739605	−	8.83568i	0.0317103	−	0.378827i
$545$		−	51.5640i		−	2.20876i
$546$		0			0
$547$		−	14.8029i		−	0.632924i	−0.948605	−	0.316462i	$-0.897505\pi$
$547$		−	14.8029i		−	0.632924i	0.948605	−	0.316462i	$-0.102495\pi$
$548$	−31.9597	+	9.21625i	−1.36525	+	0.393699i
$549$		0			0
$550$	−39.1632	−	29.4655i	−1.66992	−	1.25641i
$551$	−48.4841			−2.06549
$552$		0			0
$553$		0			0
$554$	2.85753	+	2.14994i	0.121405	+	0.0913422i
$555$		0			0
$556$	31.2227	−	9.00374i	1.32414	−	0.381843i
$557$		−	3.59946i		−	0.152514i	−0.997088	−	0.0762569i	$-0.975703\pi$
$557$		−	3.59946i		−	0.152514i	0.997088	−	0.0762569i	$-0.0242969\pi$
$558$		0			0
$559$			0.202263i			0.00855482i
$560$		0			0
$561$		0			0
$562$	−6.80972	+	9.05094i	−0.287251	+	0.381791i
$563$	19.1320			0.806318			0.403159	−	0.915130i	$-0.367912\pi$
$563$	19.1320			0.806318			0.403159	+	0.915130i	$0.367912\pi$
$564$		0			0
$565$	26.1363			1.09956
$566$	−6.01531	+	7.99507i	−0.252842	+	0.336058i
$567$		0			0
$568$	−0.543348	+	1.42506i	−0.0227984	+	0.0597940i
$569$			31.8810i			1.33652i	0.743928	+	0.668260i	$0.232960\pi$
$569$			31.8810i			1.33652i	−0.743928	+	0.668260i	$0.767040\pi$
$570$		0			0
$571$			22.6794i			0.949102i	0.880228	+	0.474551i	$0.157390\pi$
$571$			22.6794i			0.949102i	−0.880228	+	0.474551i	$0.842610\pi$
$572$	−0.570158	−	1.97717i	−0.0238395	−	0.0826695i
$573$		0			0
$574$		0			0
$575$	−54.2899			−2.26405
$576$		0			0
$577$	−1.38056			−0.0574734			−0.0287367	−	0.999587i	$-0.509148\pi$
$577$	−1.38056			−0.0574734			−0.0287367	+	0.999587i	$0.509148\pi$
$578$	16.4350	+	12.3653i	0.683607	+	0.514330i
$579$		0			0
$580$	−14.7027	−	50.9854i	−0.610498	−	2.11705i
$581$		0			0
$582$		0			0
$583$		−	2.16389i		−	0.0896193i
$584$	−7.45189	+	19.5443i	−0.308361	+	0.808749i
$585$		0			0
$586$	−16.9594	+	22.5411i	−0.700588	+	0.931166i
$587$	39.5737			1.63338			0.816692	−	0.577074i	$-0.195806\pi$
$587$	39.5737			1.63338			0.816692	+	0.577074i	$0.195806\pi$
$588$		0			0
$589$	−19.9160			−0.820624
$590$	29.1494	−	38.7430i	1.20006	−	1.59502i
$591$		0			0
$592$	−8.50916	+	5.35272i	−0.349724	+	0.219995i
$593$			22.7337i			0.933563i	0.884373	+	0.466781i	$0.154587\pi$
$593$			22.7337i			0.933563i	−0.884373	+	0.466781i	$0.845413\pi$
$594$		0			0
$595$		0			0
$596$	10.8707	−	3.13481i	0.445283	−	0.128407i
$597$		0			0
$598$	−1.82146	−	1.37042i	−0.0744848	−	0.0560407i
$599$	13.0276			0.532293			0.266147	−	0.963933i	$-0.414249\pi$
$599$	13.0276			0.532293			0.266147	+	0.963933i	$0.414249\pi$
$600$		0			0
$601$	−43.6907			−1.78218			−0.891091	−	0.453825i	$-0.850059\pi$
$601$	−43.6907			−1.78218			−0.891091	+	0.453825i	$0.850059\pi$
$602$		0			0
$603$		0			0
$604$	−7.68245	+	2.21540i	−0.312595	+	0.0901433i
$605$		−	4.01897i		−	0.163394i
$606$		0			0
$607$		−	9.05507i		−	0.367534i	−0.982970	−	0.183767i	$-0.941171\pi$
$607$		−	9.05507i		−	0.367534i	0.982970	−	0.183767i	$-0.0588292\pi$
$608$	−3.33835	+	39.8815i	−0.135388	+	1.61741i
$609$		0			0
$610$	8.77358	−	11.6611i	0.355232	−	0.472146i
$611$	−0.702591			−0.0284238
$612$		0			0
$613$	11.6275			0.469630			0.234815	−	0.972040i	$-0.424552\pi$
$613$	11.6275			0.469630			0.234815	+	0.972040i	$0.424552\pi$
$614$	8.86424	−	11.7816i	0.357732	−	0.475468i
$615$		0			0
$616$		0			0
$617$			18.3734i			0.739685i	0.929094	+	0.369843i	$0.120588\pi$
$617$			18.3734i			0.739685i	−0.929094	+	0.369843i	$0.879412\pi$
$618$		0			0
$619$			22.6794i			0.911561i	0.890092	+	0.455781i	$0.150640\pi$
$619$			22.6794i			0.911561i	−0.890092	+	0.455781i	$0.849360\pi$
$620$	−6.03950	−	20.9435i	−0.242552	−	0.841110i
$621$		0			0
$622$	−25.6597	−	19.3058i	−1.02886	−	0.774091i
$623$		0			0
$624$		0			0
$625$	24.8241			0.992965
$626$	−25.2951	−	19.0315i	−1.01100	−	0.760650i
$627$		0			0
$628$	−6.06816	−	21.0429i	−0.242146	−	0.839702i
$629$			3.93918i			0.157065i
$630$		0			0
$631$			27.5820i			1.09802i	0.835815	+	0.549011i	$0.184995\pi$
$631$			27.5820i			1.09802i	−0.835815	+	0.549011i	$0.815005\pi$
$632$	16.2952	+	6.21305i	0.648187	+	0.247142i
$633$		0			0
$634$	24.7770	−	32.9316i	0.984020	−	1.30788i
$635$	78.6502			3.12114
$636$		0			0
$637$		0			0
$638$	20.2167	−	26.8704i	0.800387	−	1.06381i
$639$		0			0
$640$	−42.9514	+	8.58345i	−1.69780	+	0.339290i
$641$		−	28.7971i		−	1.13742i	−0.822539	−	0.568709i	$-0.807443\pi$
$641$		−	28.7971i		−	1.13742i	0.822539	−	0.568709i	$-0.192557\pi$
$642$		0			0
$643$		−	38.1698i		−	1.50527i	−0.658438	−	0.752635i	$-0.728783\pi$
$643$		−	38.1698i		−	1.50527i	0.658438	−	0.752635i	$-0.271217\pi$
$644$		0			0
$645$		0			0
$646$	12.5315	+	9.42842i	0.493046	+	0.370956i
$647$	45.7885			1.80013			0.900066	−	0.435754i	$-0.143518\pi$
$647$	45.7885			1.80013			0.900066	+	0.435754i	$0.143518\pi$
$648$		0			0
$649$	30.7247			1.20605
$650$	3.34718	+	2.51835i	0.131287	+	0.0987776i
$651$		0			0
$652$	−40.4379	+	11.6611i	−1.58367	+	0.456685i
$653$		−	6.01957i		−	0.235564i	−0.993039	−	0.117782i	$-0.962422\pi$
$653$		−	6.01957i		−	0.235564i	0.993039	−	0.117782i	$-0.0375784\pi$
$654$		0			0
$655$			66.7784i			2.60925i
$656$	−7.56989	−	12.0338i	−0.295554	−	0.469840i
$657$		0			0
$658$		0			0
$659$	−8.45187			−0.329238			−0.164619	−	0.986357i	$-0.552639\pi$
$659$	−8.45187			−0.329238			−0.164619	+	0.986357i	$0.552639\pi$
$660$		0			0
$661$	−19.3229			−0.751574			−0.375787	−	0.926706i	$-0.622628\pi$
$661$	−19.3229			−0.751574			−0.375787	+	0.926706i	$0.622628\pi$
$662$	17.3713	−	23.0885i	0.675154	−	0.897361i
$663$		0			0
$664$	6.20704	−	16.2794i	0.240880	−	0.631764i
$665$		0			0
$666$		0			0
$667$		−	37.2491i		−	1.44229i
$668$	4.65133	+	16.1296i	0.179965	+	0.624075i
$669$		0			0
$670$	−46.4517	−	34.9492i	−1.79459	−	1.35021i
$671$	9.24773			0.357005
$672$		0			0
$673$	30.5239			1.17661			0.588305	−	0.808639i	$-0.299795\pi$
$673$	30.5239			1.17661			0.588305	+	0.808639i	$0.299795\pi$
$674$	−6.96899	−	5.24331i	−0.268435	−	0.201965i
$675$		0			0
$676$	−7.15537	−	24.8130i	−0.275206	−	0.954347i
$677$			19.9465i			0.766606i	0.923623	+	0.383303i	$0.125214\pi$
$677$			19.9465i			0.766606i	−0.923623	+	0.383303i	$0.874786\pi$
$678$		0			0
$679$		0			0
$680$	−6.11468	+	16.0372i	−0.234487	+	0.614998i
$681$		0			0
$682$	8.30448	−	11.0377i	0.317995	−	0.422654i
$683$	−27.3733			−1.04741			−0.523705	−	0.851900i	$-0.675451\pi$
$683$	−27.3733			−1.04741			−0.523705	+	0.851900i	$0.675451\pi$
$684$		0			0
$685$	64.3864			2.46008
$686$		0			0
$687$		0			0
$688$	1.45274	+	2.30940i	0.0553851	+	0.0880451i
$689$			0.184943i			0.00704576i
$690$		0			0
$691$			48.3588i			1.83965i	0.392324	+	0.919827i	$0.371671\pi$
$691$			48.3588i			1.83965i	−0.392324	+	0.919827i	$0.628329\pi$
$692$	−28.8659	+	8.32410i	−1.09732	+	0.316435i
$693$		0			0
$694$	17.0865	+	12.8555i	0.648594	+	0.487987i
$695$	−62.9017			−2.38600
$696$		0			0
$697$	−5.57084			−0.211010
$698$	21.3509	+	16.0640i	0.808145	+	0.608030i
$699$		0			0
$700$		0			0
$701$			17.0447i			0.643768i	0.946779	+	0.321884i	$0.104316\pi$
$701$			17.0447i			0.643768i	−0.946779	+	0.321884i	$0.895684\pi$
$702$		0			0
$703$		−	17.7802i		−	0.670594i
$704$	−20.7108	−	18.4798i	−0.780567	−	0.696483i
$705$		0			0
$706$	9.03656	−	12.0107i	0.340095	−	0.452028i
$707$		0			0
$708$		0			0
$709$	−26.4407			−0.993000			−0.496500	−	0.868037i	$-0.665382\pi$
$709$	−26.4407			−0.993000			−0.496500	+	0.868037i	$0.665382\pi$
$710$	1.77493	−	2.35910i	0.0666120	−	0.0885353i
$711$		0			0
$712$	−30.9648	−	11.8063i	−1.16045	−	0.442460i
$713$		−	15.3009i		−	0.573024i
$714$		0			0
$715$			3.98323i			0.148964i
$716$	−1.42774	−	4.95106i	−0.0533573	−	0.185030i
$717$		0			0
$718$	−3.17485	−	2.38869i	−0.118484	−	0.0891450i
$719$	−34.7544			−1.29612			−0.648060	−	0.761590i	$-0.724419\pi$
$719$	−34.7544			−1.29612			−0.648060	+	0.761590i	$0.724419\pi$
$720$		0			0
$721$		0			0
$722$	−35.0918	−	26.4023i	−1.30598	−	0.982592i
$723$		0			0
$724$	−12.3806	−	42.9330i	−0.460123	−	1.59559i
$725$			68.4505i			2.54219i
$726$		0			0
$727$			22.9785i			0.852226i	0.904670	+	0.426113i	$0.140117\pi$
$727$			22.9785i			0.852226i	−0.904670	+	0.426113i	$0.859883\pi$
$728$		0			0
$729$		0			0
$730$	24.3428	−	32.3545i	0.900966	−	1.19749i
$731$	1.06910			0.0395421
$732$		0			0
$733$	−20.8777			−0.771134			−0.385567	−	0.922680i	$-0.625994\pi$
$733$	−20.8777			−0.771134			−0.385567	+	0.922680i	$0.625994\pi$
$734$	−16.0536	+	21.3371i	−0.592548	+	0.787568i
$735$		0			0
$736$	−30.6399	−	2.56477i	−1.12940	−	0.0945385i
$737$		−	36.8380i		−	1.35694i
$738$		0			0
$739$			6.90369i			0.253956i	0.991906	+	0.126978i	$0.0405278\pi$
$739$			6.90369i			0.253956i	−0.991906	+	0.126978i	$0.959472\pi$
$740$	18.6975	−	5.39183i	0.687334	−	0.198208i
$741$		0			0
$742$		0			0
$743$	12.7592			0.468091			0.234046	−	0.972226i	$-0.424803\pi$
$743$	12.7592			0.468091			0.234046	+	0.972226i	$0.424803\pi$
$744$		0			0
$745$	−21.9003			−0.802366
$746$	−37.9575	−	28.5584i	−1.38972	−	1.04560i
$747$		0			0
$748$	−10.4507	+	3.01368i	−0.382114	+	0.110191i
$749$		0			0
$750$		0			0
$751$		−	51.7473i		−	1.88829i	−0.329535	−	0.944143i	$-0.606892\pi$
$751$		−	51.7473i		−	1.88829i	0.329535	−	0.944143i	$-0.393108\pi$
$752$	−8.02204	+	5.04630i	−0.292534	+	0.184019i
$753$		0			0
$754$	−1.72787	+	2.29655i	−0.0629254	+	0.0836354i
$755$	15.4772			0.563272
$756$		0			0
$757$	−24.2613			−0.881793			−0.440897	−	0.897558i	$-0.645339\pi$
$757$	−24.2613			−0.881793			−0.440897	+	0.897558i	$0.645339\pi$
$758$	−6.44094	+	8.56079i	−0.233946	+	0.310942i
$759$		0			0
$760$	27.5998	−	72.3868i	1.00115	−	2.62575i
$761$		−	48.1383i		−	1.74501i	−0.488603	−	0.872506i	$-0.662493\pi$
$761$		−	48.1383i		−	1.74501i	0.488603	−	0.872506i	$-0.337507\pi$
$762$		0			0
$763$		0			0
$764$	4.59640	+	15.9392i	0.166292	+	0.576659i
$765$		0			0
$766$	41.1133	+	30.9327i	1.48548	+	1.11764i
$767$	−2.62596			−0.0948180
$768$		0			0
$769$	32.1961			1.16102			0.580510	−	0.814253i	$-0.302853\pi$
$769$	32.1961			1.16102			0.580510	+	0.814253i	$0.302853\pi$
$770$		0			0
$771$		0			0
$772$	−11.8330	−	41.0338i	−0.425879	−	1.47684i
$773$			40.1610i			1.44449i	0.691638	+	0.722245i	$0.256890\pi$
$773$			40.1610i			1.44449i	−0.691638	+	0.722245i	$0.743110\pi$
$774$		0			0
$775$			28.1176i			1.01002i
$776$	6.90032	−	18.0977i	0.247707	−	0.649670i
$777$		0			0
$778$	−2.90579	+	3.86214i	−0.104177	+	0.138464i
$779$	25.1450			0.900914
$780$		0			0
$781$	1.87085			0.0669444
$782$	−7.24361	+	9.62763i	−0.259031	+	0.344283i
$783$		0			0
$784$		0			0
$785$			42.3932i			1.51308i
$786$		0			0
$787$			35.1924i			1.25447i	0.778828	+	0.627237i	$0.215814\pi$
$787$			35.1924i			1.25447i	−0.778828	+	0.627237i	$0.784186\pi$
$788$	−1.10028	+	0.317290i	−0.0391960	+	0.0113030i
$789$		0			0
$790$	−26.9757	−	20.2959i	−0.959753	−	0.722096i
$791$		0			0
$792$		0			0
$793$	−0.790381			−0.0280672
$794$	22.3435	+	16.8108i	0.792942	+	0.596591i
$795$		0			0
$796$	−33.6302	+	9.69798i	−1.19199	+	0.343736i
$797$		−	18.8026i		−	0.666021i	−0.942923	−	0.333010i	$-0.891936\pi$
$797$		−	18.8026i		−	0.666021i	0.942923	−	0.333010i	$-0.108064\pi$
$798$		0			0
$799$			3.71367i			0.131380i
$800$	56.3053	+	4.71312i	1.99069	+	0.166634i
$801$		0			0
$802$	3.23910	−	4.30515i	0.114376	−	0.152020i
$803$	25.6583			0.905463
$804$		0			0
$805$		0			0
$806$	−0.709764	+	0.943361i	−0.0250004	+	0.0332285i
$807$		0			0
$808$	−9.39313	−	3.58143i	−0.330449	−	0.125994i
$809$		−	54.3925i		−	1.91234i	−0.292816	−	0.956169i	$-0.594592\pi$
$809$		−	54.3925i		−	1.91234i	0.292816	−	0.956169i	$-0.405408\pi$
$810$		0			0
$811$		−	1.91646i		−	0.0672961i	−0.999434	−	0.0336480i	$-0.989287\pi$
$811$		−	1.91646i		−	0.0672961i	0.999434	−	0.0336480i	$-0.0107125\pi$
$812$		0			0
$813$		0			0
$814$	9.85399	+	7.41392i	0.345382	+	0.259858i
$815$	81.4668			2.85366
$816$		0			0
$817$	−4.82558			−0.168826
$818$	33.3299	+	25.0767i	1.16535	+	0.876785i
$819$		0			0
$820$	7.62520	+	26.4423i	0.266283	+	0.923405i
$821$		−	25.3538i		−	0.884853i	−0.896805	−	0.442426i	$-0.854118\pi$
$821$		−	25.3538i		−	0.884853i	0.896805	−	0.442426i	$-0.145882\pi$
$822$		0			0
$823$		−	5.26718i		−	0.183602i	−0.995777	−	0.0918011i	$-0.970738\pi$
$823$		−	5.26718i		−	0.183602i	0.995777	−	0.0918011i	$-0.0292624\pi$
$824$	5.54452	+	2.11402i	0.193153	+	0.0736455i
$825$		0			0
$826$		0			0
$827$	−43.4115			−1.50957			−0.754784	−	0.655974i	$-0.772258\pi$
$827$	−43.4115			−1.50957			−0.754784	+	0.655974i	$0.772258\pi$
$828$		0			0
$829$	8.96581			0.311396			0.155698	−	0.987805i	$-0.450237\pi$
$829$	8.96581			0.311396			0.155698	+	0.987805i	$0.450237\pi$
$830$	−20.2763	+	26.9496i	−0.703800	+	0.935435i
$831$		0			0
$832$	1.77010	+	1.57942i	0.0613671	+	0.0547566i
$833$		0			0
$834$		0			0
$835$		−	32.4950i		−	1.12454i
$836$	47.1711	−	13.6028i	1.63145	−	0.470462i
$837$		0			0
$838$	−5.64506	−	4.24722i	−0.195005	−	0.146718i
$839$	36.4358			1.25790			0.628952	−	0.777444i	$-0.283484\pi$
$839$	36.4358			1.25790			0.628952	+	0.777444i	$0.283484\pi$
$840$		0			0
$841$	−17.9648			−0.619476
$842$	−5.10026	−	3.83732i	−0.175766	−	0.132243i
$843$		0			0
$844$	−15.2750	+	4.40488i	−0.525788	+	0.151622i
$845$			49.9887i			1.71966i
$846$		0			0
$847$		0			0
$848$	1.32833	+	2.11164i	0.0456152	+	0.0725140i
$849$		0			0
$850$	13.3112	−	17.6921i	0.456569	−	0.606836i
$851$	13.6601			0.468262
$852$		0			0
$853$	4.08381			0.139827			0.0699135	−	0.997553i	$-0.477728\pi$
$853$	4.08381			0.139827			0.0699135	+	0.997553i	$0.477728\pi$
$854$		0			0
$855$		0			0
$856$	−11.1407	+	29.2192i	−0.380782	+	0.998691i
$857$			11.7762i			0.402267i	0.979564	+	0.201134i	$0.0644626\pi$
$857$			11.7762i			0.402267i	−0.979564	+	0.201134i	$0.935537\pi$
$858$		0			0
$859$		−	33.3744i		−	1.13872i	−0.822088	−	0.569360i	$-0.807191\pi$
$859$		−	33.3744i		−	1.13872i	0.822088	−	0.569360i	$-0.192809\pi$
$860$	−1.46335	−	5.07454i	−0.0498999	−	0.173040i
$861$		0			0
$862$	22.9262	+	17.2491i	0.780869	+	0.587508i
$863$	24.8629			0.846344			0.423172	−	0.906049i	$-0.360917\pi$
$863$	24.8629			0.846344			0.423172	+	0.906049i	$0.360917\pi$
$864$		0			0
$865$	58.1536			1.97728
$866$	9.42626	+	7.09210i	0.320317	+	0.240999i
$867$		0			0
$868$		0			0
$869$		−	21.3928i		−	0.725700i
$870$		0			0
$871$			3.14845i			0.106681i
$872$	−13.4211	+	35.2000i	−0.454496	+	1.19202i
$873$		0			0
$874$	32.6954	−	43.4561i	1.10594	−	1.46993i
$875$		0			0
$876$		0			0
$877$	46.0935			1.55647			0.778234	−	0.627975i	$-0.216116\pi$
$877$	46.0935			1.55647			0.778234	+	0.627975i	$0.216116\pi$
$878$	−20.2940	+	26.9731i	−0.684888	+	0.910298i
$879$		0			0
$880$	28.6092	+	45.4797i	0.964414	+	1.53312i
$881$		−	15.9952i		−	0.538893i	−0.963015	−	0.269446i	$-0.913159\pi$
$881$		−	15.9952i		−	0.538893i	0.963015	−	0.269446i	$-0.0868407\pi$
$882$		0			0
$883$		−	42.9597i		−	1.44571i	−0.691001	−	0.722854i	$-0.742830\pi$
$883$		−	42.9597i		−	1.44571i	0.691001	−	0.722854i	$-0.257170\pi$
$884$	0.893193	−	0.257571i	0.0300413	−	0.00866306i
$885$		0			0
$886$	6.78306	+	5.10342i	0.227882	+	0.171453i
$887$	19.5243			0.655563			0.327781	−	0.944754i	$-0.393699\pi$
$887$	19.5243			0.655563			0.327781	+	0.944754i	$0.393699\pi$
$888$		0			0
$889$		0			0
$890$	51.2604	+	38.5672i	1.71825	+	1.29277i
$891$		0			0
$892$	−2.26481	+	0.653107i	−0.0758315	+	0.0218676i
$893$		−	16.7624i		−	0.560931i
$894$		0			0
$895$			9.97446i			0.333410i
$896$		0			0
$897$		0			0
$898$	−4.18573	+	5.56334i	−0.139680	+	0.185651i
$899$	−19.2919			−0.643421
$900$		0			0
$901$	0.977548			0.0325669
$902$	−10.4849	+	13.9357i	−0.349108	+	0.464006i
$903$		0			0
$904$	−17.8418	−	6.80277i	−0.593411	−	0.226257i
$905$			86.4934i			2.87514i
$906$		0			0
$907$			30.2961i			1.00596i	0.864297	+	0.502982i	$0.167764\pi$
$907$			30.2961i			1.00596i	−0.864297	+	0.502982i	$0.832236\pi$
$908$	2.52034	+	8.73991i	0.0836404	+	0.290044i
$909$		0			0
$910$		0			0
$911$	−25.1485			−0.833207			−0.416604	−	0.909088i	$-0.636780\pi$
$911$	−25.1485			−0.833207			−0.416604	+	0.909088i	$0.636780\pi$
$912$		0			0
$913$	−21.3721			−0.707313
$914$	−29.8834	−	22.4836i	−0.988453	−	0.743690i
$915$		0			0
$916$	8.93791	+	30.9944i	0.295317	+	1.02408i
$917$		0			0
$918$		0			0
$919$			4.15458i			0.137047i	0.997650	+	0.0685235i	$0.0218288\pi$
$919$			4.15458i			0.137047i	−0.997650	+	0.0685235i	$0.978171\pi$
$920$	55.6129	+	21.2042i	1.83350	+	0.699081i
$921$		0			0
$922$	−7.58526	+	10.0817i	−0.249807	+	0.332024i
$923$	−0.159897			−0.00526308
$924$		0			0
$925$	−25.1023			−0.825360
$926$	12.1849	−	16.1952i	0.400421	−	0.532208i
$927$		0			0
$928$	−3.23374	+	38.6318i	−0.106153	+	1.26815i
$929$		−	43.3371i		−	1.42184i	−0.703271	−	0.710922i	$-0.748278\pi$
$929$		−	43.3371i		−	1.42184i	0.703271	−	0.710922i	$-0.251722\pi$
$930$		0			0
$931$		0			0
$932$	−15.9082	+	4.58746i	−0.521090	+	0.150267i
$933$		0			0
$934$	−24.1449	−	18.1661i	−0.790045	−	0.594412i
$935$	21.0541			0.688541
$936$		0			0
$937$	−28.6116			−0.934701			−0.467350	−	0.884072i	$-0.654791\pi$
$937$	−28.6116			−0.934701			−0.467350	+	0.884072i	$0.654791\pi$
$938$		0			0
$939$		0			0
$940$	17.6272	−	5.08317i	0.574934	−	0.165795i
$941$			23.2511i			0.757964i	0.925404	+	0.378982i	$0.123726\pi$
$941$			23.2511i			0.757964i	−0.925404	+	0.378982i	$0.876274\pi$
$942$		0			0
$943$			19.3183i			0.629089i
$944$	−29.9827	+	18.8607i	−0.975855	+	0.613865i
$945$		0			0
$946$	2.01215	−	2.67439i	0.0654207	−	0.0869520i
$947$	49.6558			1.61360			0.806798	−	0.590827i	$-0.201199\pi$
$947$	49.6558			1.61360			0.806798	+	0.590827i	$0.201199\pi$
$948$		0			0
$949$	−2.19295			−0.0711863
$950$	−60.0825	+	79.8569i	−1.94933	+	2.59090i
$951$		0			0
$952$		0			0
$953$		−	44.7824i		−	1.45065i	−0.688409	−	0.725323i	$-0.741690\pi$
$953$		−	44.7824i		−	1.45065i	0.688409	−	0.725323i	$-0.258310\pi$
$954$		0			0
$955$		−	32.1113i		−	1.03910i
$956$	10.0474	+	34.8419i	0.324956	+	1.12687i
$957$		0			0
$958$	−36.5977	−	27.5353i	−1.18242	−	0.889625i
$959$		0			0
$960$		0			0
$961$	23.0754			0.744368
$962$	−0.842197	−	0.633650i	−0.0271535	−	0.0204297i
$963$		0			0
$964$	−10.7627	−	37.3223i	−0.346642	−	1.20207i
$965$			82.6673i			2.66116i
$966$		0			0
$967$			13.2510i			0.426122i	0.977039	+	0.213061i	$0.0683433\pi$
$967$			13.2510i			0.426122i	−0.977039	+	0.213061i	$0.931657\pi$
$968$	−1.04606	+	2.74353i	−0.0336216	+	0.0881805i
$969$		0			0
$970$	−22.5410	+	29.9597i	−0.723748	+	0.961948i
$971$	−4.38813			−0.140822			−0.0704108	−	0.997518i	$-0.522431\pi$
$971$	−4.38813			−0.140822			−0.0704108	+	0.997518i	$0.522431\pi$
$972$		0			0
$973$		0			0
$974$	−2.45309	+	3.26046i	−0.0786022	+	0.104472i
$975$		0			0
$976$	−9.02441	+	5.67684i	−0.288864	+	0.181711i
$977$		−	35.5266i		−	1.13660i	−0.822823	−	0.568298i	$-0.807602\pi$
$977$		−	35.5266i		−	1.13660i	0.822823	−	0.568298i	$-0.192398\pi$
$978$		0			0
$979$			40.6515i			1.29923i
$980$		0			0
$981$		0			0
$982$	18.8212	+	14.1606i	0.600608	+	0.451884i
$983$	12.2843			0.391808			0.195904	−	0.980623i	$-0.437236\pi$
$983$	12.2843			0.391808			0.195904	+	0.980623i	$0.437236\pi$
$984$		0			0
$985$	2.21665			0.0706282
$986$	12.1388	+	9.13298i	0.386579	+	0.290853i
$987$		0			0
$988$	−4.03160	+	1.16260i	−0.128262	+	0.0369872i
$989$		−	3.70737i		−	0.117887i
$990$		0			0
$991$		−	30.4376i		−	0.966881i	−0.875377	−	0.483441i	$-0.839387\pi$
$991$		−	30.4376i		−	0.966881i	0.875377	−	0.483441i	$-0.160613\pi$
$992$	−1.32833	+	15.8689i	−0.0421747	+	0.503839i
$993$		0			0
$994$		0			0
$995$	67.7518			2.14788
$996$		0			0
$997$	51.4846			1.63053			0.815266	−	0.579086i	$-0.196591\pi$
$997$	51.4846			1.63053			0.815266	+	0.579086i	$0.196591\pi$
$998$	−22.1583	+	29.4510i	−0.701408	+	0.932256i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.e.i.1079.14		16
3.2	odd	2	inner	1764.2.e.i.1079.3		16
4.3	odd	2	inner	1764.2.e.i.1079.4		16
7.2	even	3		252.2.be.a.179.9	yes	32
7.4	even	3		252.2.be.a.107.3	✓	32
7.6	odd	2		1764.2.e.h.1079.14		16
12.11	even	2	inner	1764.2.e.i.1079.13		16
21.2	odd	6		252.2.be.a.179.8	yes	32
21.11	odd	6		252.2.be.a.107.14	yes	32
21.20	even	2		1764.2.e.h.1079.3		16
28.11	odd	6		252.2.be.a.107.8	yes	32
28.23	odd	6		252.2.be.a.179.14	yes	32
28.27	even	2		1764.2.e.h.1079.4		16
84.11	even	6		252.2.be.a.107.9	yes	32
84.23	even	6		252.2.be.a.179.3	yes	32
84.83	odd	2		1764.2.e.h.1079.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.be.a.107.3	✓	32	7.4	even	3
252.2.be.a.107.8	yes	32	28.11	odd	6
252.2.be.a.107.9	yes	32	84.11	even	6
252.2.be.a.107.14	yes	32	21.11	odd	6
252.2.be.a.179.3	yes	32	84.23	even	6
252.2.be.a.179.8	yes	32	21.2	odd	6
252.2.be.a.179.9	yes	32	7.2	even	3
252.2.be.a.179.14	yes	32	28.23	odd	6
1764.2.e.h.1079.3		16	21.20	even	2
1764.2.e.h.1079.4		16	28.27	even	2
1764.2.e.h.1079.13		16	84.83	odd	2
1764.2.e.h.1079.14		16	7.6	odd	2
1764.2.e.i.1079.3		16	3.2	odd	2	inner
1764.2.e.i.1079.4		16	4.3	odd	2	inner
1764.2.e.i.1079.13		16	12.11	even	2	inner
1764.2.e.i.1079.14		16	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.13008 + 0.850247i) q^{2} +(0.554161 + 1.92169i) q^{4} -3.87147i q^{5} +(-1.00767 + 2.64284i) q^{8} +O(q^{10})\)	\(q+(1.13008 + 0.850247i) q^{2} +(0.554161 + 1.92169i) q^{4} -3.87147i q^{5} +(-1.00767 + 2.64284i) q^{8} +(3.29170 - 4.37507i) q^{10} +3.46960 q^{11} -0.296538 q^{13} +(-3.38581 + 2.12986i) q^{16} +1.56741i q^{17} -7.07478i q^{19} +(7.43977 - 2.14542i) q^{20} +(3.92092 + 2.95001i) q^{22} +5.43537 q^{23} -9.98827 q^{25} +(-0.335112 - 0.252130i) q^{26} -6.85309i q^{29} -2.81507i q^{31} +(-5.63714 - 0.471866i) q^{32} +(-1.33268 + 1.77129i) q^{34} +2.51318 q^{37} +(6.01531 - 7.99507i) q^{38} +(10.2317 + 3.90115i) q^{40} +3.55418i q^{41} -0.682082i q^{43} +(1.92272 + 6.66750i) q^{44} +(6.14240 + 4.62140i) q^{46} +2.36931 q^{47} +(-11.2875 - 8.49249i) q^{50} +(-0.164330 - 0.569855i) q^{52} -0.623673i q^{53} -13.4324i q^{55} +(5.82681 - 7.74454i) q^{58} +8.85541 q^{59} +2.66536 q^{61} +(2.39350 - 3.18125i) q^{62} +(-5.96922 - 5.32621i) q^{64} +1.14804i q^{65} -10.6174i q^{67} +(-3.01207 + 0.868595i) q^{68} +0.539214 q^{71} +7.39519 q^{73} +(2.84010 + 2.13683i) q^{74} +(13.5956 - 3.92057i) q^{76} -6.16578i q^{79} +(8.24567 + 13.1081i) q^{80} +(-3.02193 + 4.01651i) q^{82} -6.15982 q^{83} +6.06816 q^{85} +(0.579938 - 0.770808i) q^{86} +(-3.49620 + 9.16959i) q^{88} +11.7165i q^{89} +(3.01207 + 10.4451i) q^{92} +(2.67751 + 2.01450i) q^{94} -27.3898 q^{95} -6.84782 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 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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