LMFDB - Embedded newform 1764.2.e.g.1079.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1764.1079");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.653473922154496.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 $ x^12 - 4x^10 + 13x^8 - 28x^6 + 52x^4 - 64*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1079.10
Root			$1.16947 - 0.795191i$ of defining polynomial
Character	$\chi$	$=$	1764.1079
Dual form			1764.2.e.g.1079.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16947 + 0.795191i) q^{2} +(0.735342 + 1.85991i) q^{4} -0.665647i q^{5} +(-0.619022 + 2.75986i) q^{8} +O(q^{10})$	\(q+(1.16947 + 0.795191i) q^{2} +(0.735342 + 1.85991i) q^{4} -0.665647i q^{5} +(-0.619022 + 2.75986i) q^{8} +(0.529317 - 0.778457i) q^{10} -2.07986 q^{11} -5.55691 q^{13} +(-2.91855 + 2.73534i) q^{16} +2.16278i q^{17} +4.49828i q^{19} +(1.23804 - 0.489478i) q^{20} +(-2.43234 - 1.65389i) q^{22} -4.28167 q^{23} +4.55691 q^{25} +(-6.49867 - 4.41881i) q^{26} +1.41421i q^{29} +6.61555i q^{31} +(-5.58828 + 0.878111i) q^{32} +(-1.71982 + 2.52932i) q^{34} -5.43965 q^{37} +(-3.57699 + 5.26063i) q^{38} +(1.83709 + 0.412050i) q^{40} +5.69588i q^{41} +2.11727i q^{43} +(-1.52941 - 3.86836i) q^{44} +(-5.00730 - 3.40475i) q^{46} -10.5213 q^{47} +(5.32920 + 3.62362i) q^{50} +(-4.08623 - 10.3354i) q^{52} -10.6042i q^{53} +1.38445i q^{55} +(-1.12457 + 1.65389i) q^{58} +13.5155 q^{59} +0.615547 q^{61} +(-5.26063 + 7.73671i) q^{62} +(-7.23362 - 3.41683i) q^{64} +3.69894i q^{65} +14.0552i q^{67} +(-4.02258 + 1.59038i) q^{68} +15.5954 q^{71} +11.9379 q^{73} +(-6.36153 - 4.32556i) q^{74} +(-8.36641 + 3.30777i) q^{76} +0.824101i q^{79} +(1.82077 + 1.94272i) q^{80} +(-4.52932 + 6.66119i) q^{82} -6.36153 q^{83} +1.43965 q^{85} +(-1.68363 + 2.47609i) q^{86} +(1.28748 - 5.74012i) q^{88} -12.6840i q^{89} +(-3.14849 - 7.96353i) q^{92} +(-12.3043 - 8.36641i) q^{94} +2.99427 q^{95} -0.824101 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4}+O(q^{10}) $ 12 * q + 8 * q^4	$ 12 q + 8 q^{4} + 8 q^{10} - 20 q^{16} + 20 q^{22} - 12 q^{25} + 16 q^{34} + 8 q^{37} - 8 q^{40} - 36 q^{46} + 16 q^{52} + 4 q^{58} - 56 q^{61} - 16 q^{64} - 72 q^{76} - 56 q^{82} - 56 q^{85} + 28 q^{88} + 24 q^{94}+O(q^{100}) $ 12 * q + 8 * q^4 + 8 * q^10 - 20 * q^16 + 20 * q^22 - 12 * q^25 + 16 * q^34 + 8 * q^37 - 8 * q^40 - 36 * q^46 + 16 * q^52 + 4 * q^58 - 56 * q^61 - 16 * q^64 - 72 * q^76 - 56 * q^82 - 56 * q^85 + 28 * q^88 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.16947	+	0.795191i	0.826943	+	0.562285i
$2$	1.16947	+	0.795191i	0.826943	+	0.562285i
$3$		0			0
$3$		0			0
$4$	0.735342	+	1.85991i	0.367671	+	0.929956i
$5$		−	0.665647i		−	0.297686i	−0.988861	−	0.148843i	$-0.952445\pi$
$5$		−	0.665647i		−	0.297686i	0.988861	−	0.148843i	$-0.0475550\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−0.619022	+	2.75986i	−0.218857	+	0.975757i
$9$		0			0
$10$	0.529317	−	0.778457i	0.167385	−	0.246170i
$11$	−2.07986			−0.627102			−0.313551	−	0.949571i	$-0.601519\pi$
$11$	−2.07986			−0.627102			−0.313551	+	0.949571i	$0.601519\pi$
$12$		0			0
$13$	−5.55691			−1.54121			−0.770605	−	0.637313i	$-0.780046\pi$
$13$	−5.55691			−1.54121			−0.770605	+	0.637313i	$0.780046\pi$
$14$		0			0
$15$		0			0
$16$	−2.91855	+	2.73534i	−0.729636	+	0.683835i
$17$			2.16278i			0.524551i	0.964993	+	0.262276i	$0.0844730\pi$
$17$			2.16278i			0.524551i	−0.964993	+	0.262276i	$0.915527\pi$
$18$		0			0
$19$			4.49828i			1.03198i	0.856596	+	0.515988i	$0.172575\pi$
$19$			4.49828i			1.03198i	−0.856596	+	0.515988i	$0.827425\pi$
$20$	1.23804	−	0.489478i	0.276835	−	0.109451i
$21$		0			0
$22$	−2.43234	−	1.65389i	−0.518577	−	0.352610i
$23$	−4.28167			−0.892790			−0.446395	−	0.894836i	$-0.647292\pi$
$23$	−4.28167			−0.892790			−0.446395	+	0.894836i	$0.647292\pi$
$24$		0			0
$25$	4.55691			0.911383
$26$	−6.49867	−	4.41881i	−1.27449	−	0.866600i
$27$		0			0
$28$		0			0
$29$			1.41421i			0.262613i	0.991342	+	0.131306i	$0.0419172\pi$
$29$			1.41421i			0.262613i	−0.991342	+	0.131306i	$0.958083\pi$
$30$		0			0
$31$			6.61555i			1.18819i	0.804396	+	0.594094i	$0.202489\pi$
$31$			6.61555i			1.18819i	−0.804396	+	0.594094i	$0.797511\pi$
$32$	−5.58828	+	0.878111i	−0.987878	+	0.155230i
$33$		0			0
$34$	−1.71982	+	2.52932i	−0.294947	+	0.433774i
$35$		0			0
$36$		0			0
$37$	−5.43965			−0.894273			−0.447136	−	0.894466i	$-0.647556\pi$
$37$	−5.43965			−0.894273			−0.447136	+	0.894466i	$0.647556\pi$
$38$	−3.57699	+	5.26063i	−0.580265	+	0.853386i
$39$		0			0
$40$	1.83709	+	0.412050i	0.290469	+	0.0651509i
$41$			5.69588i			0.889548i	0.895643	+	0.444774i	$0.146716\pi$
$41$			5.69588i			0.889548i	−0.895643	+	0.444774i	$0.853284\pi$
$42$		0			0
$43$			2.11727i			0.322880i	0.986883	+	0.161440i	$0.0516138\pi$
$43$			2.11727i			0.322880i	−0.986883	+	0.161440i	$0.948386\pi$
$44$	−1.52941	−	3.86836i	−0.230567	−	0.583177i
$45$		0			0
$46$	−5.00730	−	3.40475i	−0.738287	−	0.502002i
$47$	−10.5213			−1.53468			−0.767341	−	0.641239i	$-0.778421\pi$
$47$	−10.5213			−1.53468			−0.767341	+	0.641239i	$0.778421\pi$
$48$		0			0
$49$		0			0
$50$	5.32920	+	3.62362i	0.753662	+	0.512457i
$51$		0			0
$52$	−4.08623	−	10.3354i	−0.566658	−	1.43326i
$53$		−	10.6042i		−	1.45659i	−0.685261	−	0.728297i	$-0.740312\pi$
$53$		−	10.6042i		−	1.45659i	0.685261	−	0.728297i	$-0.259688\pi$
$54$		0			0
$55$			1.38445i			0.186680i
$56$		0			0
$57$		0			0
$58$	−1.12457	+	1.65389i	−0.147663	+	0.217166i
$59$	13.5155			1.75957			0.879785	−	0.475371i	$-0.157686\pi$
$59$	13.5155			1.75957			0.879785	+	0.475371i	$0.157686\pi$
$60$		0			0
$61$	0.615547			0.0788128			0.0394064	−	0.999223i	$-0.487453\pi$
$61$	0.615547			0.0788128			0.0394064	+	0.999223i	$0.487453\pi$
$62$	−5.26063	+	7.73671i	−0.668100	+	0.982564i
$63$		0			0
$64$	−7.23362	−	3.41683i	−0.904203	−	0.427103i
$65$			3.69894i			0.458797i
$66$		0			0
$67$			14.0552i			1.71712i	0.512717	+	0.858558i	$0.328639\pi$
$67$			14.0552i			1.71712i	−0.512717	+	0.858558i	$0.671361\pi$
$68$	−4.02258	+	1.59038i	−0.487810	+	0.192862i
$69$		0			0
$70$		0			0
$71$	15.5954			1.85083			0.925415	−	0.378954i	$-0.123716\pi$
$71$	15.5954			1.85083			0.925415	+	0.378954i	$0.123716\pi$
$72$		0			0
$73$	11.9379			1.39723			0.698614	−	0.715498i	$-0.253800\pi$
$73$	11.9379			1.39723			0.698614	+	0.715498i	$0.253800\pi$
$74$	−6.36153	−	4.32556i	−0.739513	−	0.502836i
$75$		0			0
$76$	−8.36641	+	3.30777i	−0.959693	+	0.379428i
$77$		0			0
$78$		0			0
$79$			0.824101i			0.0927186i	0.998925	+	0.0463593i	$0.0147619\pi$
$79$			0.824101i			0.0927186i	−0.998925	+	0.0463593i	$0.985238\pi$
$80$	1.82077	+	1.94272i	0.203568	+	0.217203i
$81$		0			0
$82$	−4.52932	+	6.66119i	−0.500179	+	0.735605i
$83$	−6.36153			−0.698269			−0.349134	−	0.937073i	$-0.613524\pi$
$83$	−6.36153			−0.698269			−0.349134	+	0.937073i	$0.613524\pi$
$84$		0			0
$85$	1.43965			0.156152
$86$	−1.68363	+	2.47609i	−0.181551	+	0.267004i
$87$		0			0
$88$	1.28748	−	5.74012i	0.137246	−	0.611899i
$89$		−	12.6840i		−	1.34450i	−0.740322	−	0.672252i	$-0.765327\pi$
$89$		−	12.6840i		−	1.34450i	0.740322	−	0.672252i	$-0.234673\pi$
$90$		0			0
$91$		0			0
$92$	−3.14849	−	7.96353i	−0.328253	−	0.830255i
$93$		0			0
$94$	−12.3043	−	8.36641i	−1.26910	−	0.862929i
$95$	2.99427			0.307205
$96$		0			0
$97$	−0.824101			−0.0836747			−0.0418374	−	0.999124i	$-0.513321\pi$
$97$	−0.824101			−0.0836747			−0.0418374	+	0.999124i	$0.513321\pi$
$98$		0			0
$99$		0			0
$100$	3.35089	+	8.47546i	0.335089	+	0.847546i
$101$		−	17.8801i		−	1.77914i	−0.456802	−	0.889569i	$-0.651005\pi$
$101$		−	17.8801i		−	1.77914i	0.456802	−	0.889569i	$-0.348995\pi$
$102$		0			0
$103$			12.4983i			1.23149i	0.787945	+	0.615746i	$0.211145\pi$
$103$			12.4983i			1.23149i	−0.787945	+	0.615746i	$0.788855\pi$
$104$	3.43985	−	15.3363i	0.337305	−	1.50385i
$105$		0			0
$106$	8.43234	−	12.4013i	0.819022	−	1.20452i
$107$	−13.3936			−1.29481			−0.647403	−	0.762148i	$-0.724145\pi$
$107$	−13.3936			−1.29481			−0.647403	+	0.762148i	$0.724145\pi$
$108$		0			0
$109$	−6.11727			−0.585928			−0.292964	−	0.956123i	$-0.594642\pi$
$109$	−6.11727			−0.585928			−0.292964	+	0.956123i	$0.594642\pi$
$110$	−1.10090	+	1.61908i	−0.104967	+	0.154373i
$111$		0			0
$112$		0			0
$113$		−	3.61602i		−	0.340167i	−0.985430	−	0.170083i	$-0.945596\pi$
$113$		−	3.61602i		−	0.340167i	0.985430	−	0.170083i	$-0.0544037\pi$
$114$		0			0
$115$			2.85008i			0.265771i
$116$	−2.63031	+	1.03993i	−0.244218	+	0.0965551i
$117$		0			0
$118$	15.8061	+	10.7474i	1.45507	+	0.989380i
$119$		0			0
$120$		0			0
$121$	−6.67418			−0.606744
$122$	0.719867	+	0.489478i	0.0651737	+	0.0443152i
$123$		0			0
$124$	−12.3043	+	4.86469i	−1.10496	+	0.436862i
$125$		−	6.36153i		−	0.568993i
$126$		0			0
$127$			8.17246i			0.725189i	0.931947	+	0.362594i	$0.118109\pi$
$127$			8.17246i			0.725189i	−0.931947	+	0.362594i	$0.881891\pi$
$128$	−5.74251	−	9.74801i	−0.507571	−	0.861610i
$129$		0			0
$130$	−2.94137	+	4.32582i	−0.257975	+	0.379399i
$131$	2.99427			0.261610			0.130805	−	0.991408i	$-0.458244\pi$
$131$	2.99427			0.261610			0.130805	+	0.991408i	$0.458244\pi$
$132$		0			0
$133$		0			0
$134$	−11.1766	+	16.4372i	−0.965508	+	1.41996i
$135$		0			0
$136$	−5.96896	−	1.33881i	−0.511834	−	0.114802i
$137$			10.7700i			0.920144i	0.887882	+	0.460072i	$0.152176\pi$
$137$			10.7700i			0.920144i	−0.887882	+	0.460072i	$0.847824\pi$
$138$		0			0
$139$		−	16.0000i		−	1.35710i	−0.734553	−	0.678551i	$-0.762608\pi$
$139$		−	16.0000i		−	1.35710i	0.734553	−	0.678551i	$-0.237392\pi$
$140$		0			0
$141$		0			0
$142$	18.2384	+	12.4013i	1.53053	+	1.04069i
$143$	11.5576			0.966496
$144$		0			0
$145$	0.941367			0.0781763
$146$	13.9611	+	9.49294i	1.15543	+	0.785641i
$147$		0			0
$148$	−4.00000	−	10.1173i	−0.328798	−	0.831634i
$149$			2.57967i			0.211335i	0.994402	+	0.105667i	$0.0336979\pi$
$149$			2.57967i			0.211335i	−0.994402	+	0.105667i	$0.966302\pi$
$150$		0			0
$151$			5.23109i			0.425700i	0.977085	+	0.212850i	$0.0682746\pi$
$151$			5.23109i			0.425700i	−0.977085	+	0.212850i	$0.931725\pi$
$152$	−12.4146	−	2.78454i	−1.00696	−	0.225856i
$153$		0			0
$154$		0			0
$155$	4.40362			0.353707
$156$		0			0
$157$	5.61211			0.447895			0.223948	−	0.974601i	$-0.428106\pi$
$157$	5.61211			0.447895			0.223948	+	0.974601i	$0.428106\pi$
$158$	−0.655318	+	0.963765i	−0.0521343	+	0.0766730i
$159$		0			0
$160$	0.584512	+	3.71982i	0.0462097	+	0.294078i
$161$		0			0
$162$		0			0
$163$		−	8.17246i		−	0.640117i	−0.947398	−	0.320058i	$-0.896297\pi$
$163$		−	8.17246i		−	0.640117i	0.947398	−	0.320058i	$-0.103703\pi$
$164$	−10.5938	+	4.18842i	−0.827240	+	0.327061i
$165$		0			0
$166$	−7.43965	−	5.05863i	−0.577429	−	0.392626i
$167$	−16.5098			−1.27757			−0.638783	−	0.769387i	$-0.720562\pi$
$167$	−16.5098			−1.27757			−0.638783	+	0.769387i	$0.720562\pi$
$168$		0			0
$169$	17.8793			1.37533
$170$	1.68363	+	1.14480i	0.129129	+	0.0878018i
$171$		0			0
$172$	−3.93793	+	1.55691i	−0.300264	+	0.118714i
$173$			4.19875i			0.319225i	0.987180	+	0.159613i	$0.0510245\pi$
$173$			4.19875i			0.319225i	−0.987180	+	0.159613i	$0.948976\pi$
$174$		0			0
$175$		0			0
$176$	6.07017	−	5.68913i	0.457556	−	0.428834i
$177$		0			0
$178$	10.0862	−	14.8337i	0.755995	−	1.11183i
$179$	−2.07986			−0.155456			−0.0777280	−	0.996975i	$-0.524767\pi$
$179$	−2.07986			−0.155456			−0.0777280	+	0.996975i	$0.524767\pi$
$180$		0			0
$181$	11.4396			0.850302			0.425151	−	0.905122i	$-0.360221\pi$
$181$	11.4396			0.850302			0.425151	+	0.905122i	$0.360221\pi$
$182$		0			0
$183$		0			0
$184$	2.65045	−	11.8168i	0.195394	−	0.871146i
$185$			3.62088i			0.266213i
$186$		0			0
$187$		−	4.49828i		−	0.328947i
$188$	−7.73671	−	19.5686i	−0.564258	−	1.42719i
$189$		0			0
$190$	3.50172	+	2.38101i	0.254041	+	0.172737i
$191$	8.44139			0.610798			0.305399	−	0.952225i	$-0.401210\pi$
$191$	8.44139			0.610798			0.305399	+	0.952225i	$0.401210\pi$
$192$		0			0
$193$	9.67418			0.696363			0.348181	−	0.937427i	$-0.386799\pi$
$193$	9.67418			0.696363			0.348181	+	0.937427i	$0.386799\pi$
$194$	−0.963765	−	0.655318i	−0.0691943	−	0.0470491i
$195$		0			0
$196$		0			0
$197$		−	13.4326i		−	0.957033i	−0.878079	−	0.478516i	$-0.841175\pi$
$197$		−	13.4326i		−	0.957033i	0.878079	−	0.478516i	$-0.158825\pi$
$198$		0			0
$199$			27.1138i			1.92205i	0.276464	+	0.961024i	$0.410837\pi$
$199$			27.1138i			1.92205i	−0.276464	+	0.961024i	$0.589163\pi$
$200$	−2.82083	+	12.5764i	−0.199463	+	0.889288i
$201$		0			0
$202$	14.2181	−	20.9103i	1.00038	−	1.47125i
$203$		0			0
$204$		0			0
$205$	3.79145			0.264806
$206$	−9.93852	+	14.6164i	−0.692450	+	1.01837i
$207$		0			0
$208$	16.2181	−	15.2001i	1.12452	−	1.05393i
$209$		−	9.35580i		−	0.647154i
$210$		0			0
$211$			11.1138i			0.765108i	0.923933	+	0.382554i	$0.124955\pi$
$211$			11.1138i			0.765108i	−0.923933	+	0.382554i	$0.875045\pi$
$212$	19.7228	−	7.79769i	1.35457	−	0.535547i
$213$		0			0
$214$	−15.6634	−	10.6504i	−1.07073	−	0.728050i
$215$	1.40935			0.0961170
$216$		0			0
$217$		0			0
$218$	−7.15399	−	4.86440i	−0.484529	−	0.329459i
$219$		0			0
$220$	−2.57496	+	1.01805i	−0.173604	+	0.0686366i
$221$		−	12.0184i		−	0.808444i
$222$		0			0
$223$			6.87930i			0.460672i	0.973111	+	0.230336i	$0.0739825\pi$
$223$			6.87930i			0.460672i	−0.973111	+	0.230336i	$0.926018\pi$
$224$		0			0
$225$		0			0
$226$	2.87543	−	4.22885i	0.191271	−	0.281299i
$227$	5.19608			0.344876			0.172438	−	0.985020i	$-0.444836\pi$
$227$	5.19608			0.344876			0.172438	+	0.985020i	$0.444836\pi$
$228$		0			0
$229$	−5.55691			−0.367211			−0.183606	−	0.983000i	$-0.558777\pi$
$229$	−5.55691			−0.367211			−0.183606	+	0.983000i	$0.558777\pi$
$230$	−2.26636	+	3.33310i	−0.149439	+	0.219778i
$231$		0			0
$232$	−3.90303	−	0.875430i	−0.256246	−	0.0574748i
$233$		−	24.1197i		−	1.58013i	−0.613021	−	0.790067i	$-0.710046\pi$
$233$		−	24.1197i		−	1.58013i	0.613021	−	0.790067i	$-0.289954\pi$
$234$		0			0
$235$			7.00344i			0.456854i
$236$	9.93852	+	25.1377i	0.646943	+	1.63632i
$237$		0			0
$238$		0			0
$239$	−8.44139			−0.546028			−0.273014	−	0.962010i	$-0.588021\pi$
$239$	−8.44139			−0.546028			−0.273014	+	0.962010i	$0.588021\pi$
$240$		0			0
$241$	25.8207			1.66326			0.831628	−	0.555334i	$-0.187409\pi$
$241$	25.8207			1.66326			0.831628	+	0.555334i	$0.187409\pi$
$242$	−7.80528	−	5.30725i	−0.501743	−	0.341163i
$243$		0			0
$244$	0.452638	+	1.14486i	0.0289772	+	0.0732924i
$245$		0			0
$246$		0			0
$247$		−	24.9966i		−	1.59049i
$248$	−18.2580	−	4.09517i	−1.15938	−	0.260044i
$249$		0			0
$250$	5.05863	−	7.43965i	0.319936	−	0.470525i
$251$	19.8770			1.25463			0.627314	−	0.778766i	$-0.284154\pi$
$251$	19.8770			1.25463			0.627314	+	0.778766i	$0.284154\pi$
$252$		0			0
$253$	8.90528			0.559870
$254$	−6.49867	+	9.55749i	−0.407763	+	0.599690i
$255$		0			0
$256$	1.03581	−	15.9664i	0.0647382	−	0.997902i
$257$			21.3352i			1.33085i	0.746465	+	0.665425i	$0.231750\pi$
$257$			21.3352i			1.33085i	−0.746465	+	0.665425i	$0.768250\pi$
$258$		0			0
$259$		0			0
$260$	−6.87971	+	2.71999i	−0.426661	+	0.168686i
$261$		0			0
$262$	3.50172	+	2.38101i	0.216337	+	0.147100i
$263$	19.7551			1.21815			0.609076	−	0.793112i	$-0.291541\pi$
$263$	19.7551			1.21815			0.609076	+	0.793112i	$0.291541\pi$
$264$		0			0
$265$	−7.05863			−0.433608
$266$		0			0
$267$		0			0
$268$	−26.1414	+	10.3354i	−1.59684	+	0.631333i
$269$		−	2.62356i		−	0.159961i	−0.996796	−	0.0799806i	$-0.974514\pi$
$269$		−	2.62356i		−	0.159961i	0.996796	−	0.0799806i	$-0.0254858\pi$
$270$		0			0
$271$			0.732814i			0.0445153i	0.999752	+	0.0222576i	$0.00708541\pi$
$271$			0.732814i			0.0445153i	−0.999752	+	0.0222576i	$0.992915\pi$
$272$	−5.91594	−	6.31217i	−0.358707	−	0.382732i
$273$		0			0
$274$	−8.56422	+	12.5953i	−0.517383	+	0.760907i
$275$	−9.47775			−0.571530
$276$		0			0
$277$	11.4396			0.687342			0.343671	−	0.939090i	$-0.388330\pi$
$277$	11.4396			0.687342			0.343671	+	0.939090i	$0.388330\pi$
$278$	12.7231	−	18.7116i	0.763078	−	1.12225i
$279$		0			0
$280$		0			0
$281$			0.875377i			0.0522206i	0.999659	+	0.0261103i	$0.00831212\pi$
$281$			0.875377i			0.0522206i	−0.999659	+	0.0261103i	$0.991688\pi$
$282$		0			0
$283$			22.4914i			1.33698i	0.743723	+	0.668488i	$0.233058\pi$
$283$			22.4914i			1.33698i	−0.743723	+	0.668488i	$0.766942\pi$
$284$	11.4679	+	29.0060i	0.680497	+	1.72119i
$285$		0			0
$286$	13.5163	+	9.19051i	0.799237	+	0.543446i
$287$		0			0
$288$		0			0
$289$	12.3224			0.724846
$290$	1.10090	+	0.748567i	0.0646473	+	0.0439573i
$291$		0			0
$292$	8.77846	+	22.2035i	0.513720	+	1.29936i
$293$			24.2416i			1.41621i	0.706106	+	0.708106i	$0.250450\pi$
$293$			24.2416i			1.41621i	−0.706106	+	0.708106i	$0.749550\pi$
$294$		0			0
$295$		−	8.99656i		−	0.523800i
$296$	3.36726	−	15.0127i	0.195718	−	0.872593i
$297$		0			0
$298$	−2.05133	+	3.01686i	−0.118830	+	0.174762i
$299$	23.7929			1.37598
$300$		0			0
$301$		0			0
$302$	−4.15972	+	6.11763i	−0.239365	+	0.352030i
$303$		0			0
$304$	−12.3043	−	13.1284i	−0.705702	−	0.752967i
$305$		−	0.409737i		−	0.0234615i
$306$		0			0
$307$		−	7.61211i		−	0.434446i	−0.976122	−	0.217223i	$-0.930300\pi$
$307$		−	7.61211i		−	0.434446i	0.976122	−	0.217223i	$-0.0696999\pi$
$308$		0			0
$309$		0			0
$310$	5.14992	+	3.50172i	0.292496	+	0.198884i
$311$	−13.5155			−0.766395			−0.383197	−	0.923666i	$-0.625177\pi$
$311$	−13.5155			−0.766395			−0.383197	+	0.923666i	$0.625177\pi$
$312$		0			0
$313$	7.64820			0.432302			0.216151	−	0.976360i	$-0.430650\pi$
$313$	7.64820			0.432302			0.216151	+	0.976360i	$0.430650\pi$
$314$	6.56322	+	4.46270i	0.370384	+	0.251845i
$315$		0			0
$316$	−1.53275	+	0.605995i	−0.0862242	+	0.0340899i
$317$			29.7765i			1.67242i	0.548411	+	0.836209i	$0.315233\pi$
$317$			29.7765i			1.67242i	−0.548411	+	0.836209i	$0.684767\pi$
$318$		0			0
$319$		−	2.94137i		−	0.164685i
$320$	−2.27440	+	4.81504i	−0.127143	+	0.269169i
$321$		0			0
$322$		0			0
$323$	−9.72879			−0.541325
$324$		0			0
$325$	−25.3224			−1.40463
$326$	6.49867	−	9.55749i	0.359928	−	0.529340i
$327$		0			0
$328$	−15.7198	−	3.52588i	−0.867982	−	0.194684i
$329$		0			0
$330$		0			0
$331$			11.1138i			0.610871i	0.952213	+	0.305436i	$0.0988021\pi$
$331$			11.1138i			0.610871i	−0.952213	+	0.305436i	$0.901198\pi$
$332$	−4.67790	−	11.8319i	−0.256733	−	0.649359i
$333$		0			0
$334$	−19.3078	−	13.1284i	−1.05647	−	0.718356i
$335$	9.35580			0.511162
$336$		0			0
$337$	−5.88273			−0.320453			−0.160226	−	0.987080i	$-0.551222\pi$
$337$	−5.88273			−0.320453			−0.160226	+	0.987080i	$0.551222\pi$
$338$	20.9094	+	14.2175i	1.13732	+	0.773328i
$339$		0			0
$340$	1.05863	+	2.67762i	0.0574124	+	0.145214i
$341$		−	13.7594i		−	0.745114i
$342$		0			0
$343$		0			0
$344$	−5.84335	−	1.31064i	−0.315052	−	0.0706647i
$345$		0			0
$346$	−3.33881	+	4.91033i	−0.179495	+	0.263981i
$347$	10.6432			0.571357			0.285678	−	0.958326i	$-0.407781\pi$
$347$	10.6432			0.571357			0.285678	+	0.958326i	$0.407781\pi$
$348$		0			0
$349$	−2.49828			−0.133730			−0.0668650	−	0.997762i	$-0.521300\pi$
$349$	−2.49828			−0.133730			−0.0668650	+	0.997762i	$0.521300\pi$
$350$		0			0
$351$		0			0
$352$	11.6229	−	1.82635i	0.619500	−	0.0973447i
$353$			0.126811i			0.00674945i	0.999994	+	0.00337472i	$0.00107421\pi$
$353$			0.126811i			0.00674945i	−0.999994	+	0.00337472i	$0.998926\pi$
$354$		0			0
$355$		−	10.3810i		−	0.550967i
$356$	23.5912	−	9.32710i	1.25033	−	0.494335i
$357$		0			0
$358$	−2.43234	−	1.65389i	−0.128553	−	0.0874106i
$359$	19.7551			1.04263			0.521317	−	0.853363i	$-0.325441\pi$
$359$	19.7551			1.04263			0.521317	+	0.853363i	$0.325441\pi$
$360$		0			0
$361$	−1.23453			−0.0649754
$362$	13.3784	+	9.09671i	0.703152	+	0.478112i
$363$		0			0
$364$		0			0
$365$		−	7.94645i		−	0.415936i
$366$		0			0
$367$		−	28.7620i		−	1.50137i	−0.660663	−	0.750683i	$-0.729725\pi$
$367$		−	28.7620i		−	1.50137i	0.660663	−	0.750683i	$-0.270275\pi$
$368$	12.4962	−	11.7118i	0.651412	−	0.610521i
$369$		0			0
$370$	−2.87930	+	4.23453i	−0.149687	+	0.220143i
$371$		0			0
$372$		0			0
$373$	−0.879296			−0.0455282			−0.0227641	−	0.999741i	$-0.507247\pi$
$373$	−0.879296			−0.0455282			−0.0227641	+	0.999741i	$0.507247\pi$
$374$	3.57699	−	5.26063i	0.184962	−	0.272020i
$375$		0			0
$376$	6.51289	−	29.0371i	0.335877	−	1.49748i
$377$		−	7.85866i		−	0.404742i
$378$		0			0
$379$			22.8793i			1.17523i	0.809140	+	0.587615i	$0.199933\pi$
$379$			22.8793i			1.17523i	−0.809140	+	0.587615i	$0.800067\pi$
$380$	2.20181	+	5.56907i	0.112950	+	0.285687i
$381$		0			0
$382$	9.87199	+	6.71252i	0.505095	+	0.343442i
$383$	32.3562			1.65333			0.826663	−	0.562698i	$-0.190237\pi$
$383$	32.3562			1.65333			0.826663	+	0.562698i	$0.190237\pi$
$384$		0			0
$385$		0			0
$386$	11.3137	+	7.69282i	0.575853	+	0.391554i
$387$		0			0
$388$	−0.605995	−	1.53275i	−0.0307648	−	0.0778138i
$389$			16.3391i			0.828424i	0.910180	+	0.414212i	$0.135943\pi$
$389$			16.3391i			0.828424i	−0.910180	+	0.414212i	$0.864057\pi$
$390$		0			0
$391$		−	9.26031i		−	0.468314i
$392$		0			0
$393$		0			0
$394$	10.6815	−	15.7091i	0.538125	−	0.791412i
$395$	0.548560			0.0276010
$396$		0			0
$397$	4.85008			0.243419			0.121709	−	0.992566i	$-0.461162\pi$
$397$	4.85008			0.243419			0.121709	+	0.992566i	$0.461162\pi$
$398$	−21.5607	+	31.7089i	−1.08074	+	1.58943i
$399$		0			0
$400$	−13.2996	+	12.4647i	−0.664978	+	0.623236i
$401$			20.8305i			1.04022i	0.854098	+	0.520112i	$0.174110\pi$
$401$			20.8305i			1.04022i	−0.854098	+	0.520112i	$0.825890\pi$
$402$		0			0
$403$		−	36.7620i		−	1.83125i
$404$	33.2554	−	13.1480i	1.65452	−	0.654137i
$405$		0			0
$406$		0			0
$407$	11.3137			0.560800
$408$		0			0
$409$	−12.9345			−0.639569			−0.319785	−	0.947490i	$-0.603611\pi$
$409$	−12.9345			−0.639569			−0.319785	+	0.947490i	$0.603611\pi$
$410$	4.43400	+	3.01493i	0.218980	+	0.148897i
$411$		0			0
$412$	−23.2457	+	9.19051i	−1.14523	+	0.452784i
$413$		0			0
$414$		0			0
$415$			4.23453i			0.207865i
$416$	31.0536	−	4.87959i	1.52253	−	0.239241i
$417$		0			0
$418$	7.43965	−	10.9414i	0.363885	−	0.535160i
$419$	−14.5519			−0.710906			−0.355453	−	0.934694i	$-0.615673\pi$
$419$	−14.5519			−0.710906			−0.355453	+	0.934694i	$0.615673\pi$
$420$		0			0
$421$	−29.9018			−1.45733			−0.728663	−	0.684872i	$-0.759858\pi$
$421$	−29.9018			−1.45733			−0.728663	+	0.684872i	$0.759858\pi$
$422$	−8.83762	+	12.9973i	−0.430209	+	0.632701i
$423$		0			0
$424$	29.2660	+	6.56422i	1.42128	+	0.318787i
$425$			9.85560i			0.478067i
$426$		0			0
$427$		0			0
$428$	−9.84885	−	24.9109i	−0.476062	−	1.20411i
$429$		0			0
$430$	1.64820	+	1.12070i	0.0794833	+	0.0540452i
$431$	−5.86658			−0.282583			−0.141292	−	0.989968i	$-0.545126\pi$
$431$	−5.86658			−0.282583			−0.141292	+	0.989968i	$0.545126\pi$
$432$		0			0
$433$	−26.1104			−1.25479			−0.627393	−	0.778703i	$-0.715878\pi$
$433$	−26.1104			−1.25479			−0.627393	+	0.778703i	$0.715878\pi$
$434$		0			0
$435$		0			0
$436$	−4.49828	−	11.3776i	−0.215429	−	0.544887i
$437$		−	19.2602i		−	0.921338i
$438$		0			0
$439$		−	25.9931i		−	1.24058i	−0.784371	−	0.620292i	$-0.787014\pi$
$439$		−	25.9931i		−	1.24058i	0.784371	−	0.620292i	$-0.212986\pi$
$440$	−3.82089	−	0.857007i	−0.182154	−	0.0408562i
$441$		0			0
$442$	9.55691	−	14.0552i	0.454576	−	0.668537i
$443$	9.23385			0.438713			0.219357	−	0.975645i	$-0.429604\pi$
$443$	9.23385			0.438713			0.219357	+	0.975645i	$0.429604\pi$
$444$		0			0
$445$	−8.44309			−0.400241
$446$	−5.47036	+	8.04516i	−0.259029	+	0.380949i
$447$		0			0
$448$		0			0
$449$			33.4755i			1.57981i	0.613232	+	0.789903i	$0.289869\pi$
$449$			33.4755i			1.57981i	−0.613232	+	0.789903i	$0.710131\pi$
$450$		0			0
$451$		−	11.8466i		−	0.557837i
$452$	6.72548	−	2.65901i	0.316340	−	0.125069i
$453$		0			0
$454$	6.07668	+	4.13187i	0.285193	+	0.193918i
$455$		0			0
$456$		0			0
$457$	−30.2277			−1.41399			−0.706995	−	0.707218i	$-0.749950\pi$
$457$	−30.2277			−1.41399			−0.706995	+	0.707218i	$0.749950\pi$
$458$	−6.49867	−	4.41881i	−0.303663	−	0.206477i
$459$		0			0
$460$	−5.30090	+	2.09578i	−0.247156	+	0.0977164i
$461$			10.4822i			0.488206i	0.969749	+	0.244103i	$0.0784935\pi$
$461$			10.4822i			0.488206i	−0.969749	+	0.244103i	$0.921507\pi$
$462$		0			0
$463$			9.82066i			0.456405i	0.973614	+	0.228202i	$0.0732848\pi$
$463$			9.82066i			0.456405i	−0.973614	+	0.228202i	$0.926715\pi$
$464$	−3.86836	−	4.12745i	−0.179584	−	0.191612i
$465$		0			0
$466$	19.1798	−	28.2074i	0.888485	−	1.30668i
$467$	−21.4620			−0.993141			−0.496571	−	0.867996i	$-0.665408\pi$
$467$	−21.4620			−0.993141			−0.496571	+	0.867996i	$0.665408\pi$
$468$		0			0
$469$		0			0
$470$	−5.56907	+	8.19034i	−0.256882	+	0.377792i
$471$		0			0
$472$	−8.36641	+	37.3009i	−0.385095	+	1.71691i
$473$		−	4.40362i		−	0.202479i
$474$		0			0
$475$			20.4983i			0.940526i
$476$		0			0
$477$		0			0
$478$	−9.87199	−	6.71252i	−0.451534	−	0.307024i
$479$	−8.56334			−0.391269			−0.195634	−	0.980677i	$-0.562677\pi$
$479$	−8.56334			−0.391269			−0.195634	+	0.980677i	$0.562677\pi$
$480$		0			0
$481$	30.2277			1.37826
$482$	30.1966	+	20.5324i	1.37542	+	0.935224i
$483$		0			0
$484$	−4.90780	−	12.4134i	−0.223082	−	0.564245i
$485$			0.548560i			0.0249088i
$486$		0			0
$487$		−	9.46563i		−	0.428929i	−0.976732	−	0.214464i	$-0.931199\pi$
$487$		−	9.46563i		−	0.428929i	0.976732	−	0.214464i	$-0.0688005\pi$
$488$	−0.381038	+	1.69882i	−0.0172488	+	0.0769021i
$489$		0			0
$490$		0			0
$491$	−19.6260			−0.885709			−0.442854	−	0.896593i	$-0.646034\pi$
$491$	−19.6260			−0.885709			−0.442854	+	0.896593i	$0.646034\pi$
$492$		0			0
$493$	−3.05863			−0.137754
$494$	19.8770	−	29.2328i	0.894311	−	1.31525i
$495$		0			0
$496$	−18.0958	−	19.3078i	−0.812525	−	0.866945i
$497$		0			0
$498$		0			0
$499$			2.11727i			0.0947819i	0.998876	+	0.0473909i	$0.0150907\pi$
$499$			2.11727i			0.0947819i	−0.998876	+	0.0473909i	$0.984909\pi$
$500$	11.8319	−	4.67790i	0.529138	−	0.209202i
$501$		0			0
$502$	23.2457	+	15.8061i	1.03751	+	0.705459i
$503$	4.03062			0.179717			0.0898583	−	0.995955i	$-0.471359\pi$
$503$	4.03062			0.179717			0.0898583	+	0.995955i	$0.471359\pi$
$504$		0			0
$505$	−11.9018			−0.529625
$506$	10.4145	+	7.08140i	0.462981	+	0.314807i
$507$		0			0
$508$	−15.2001	+	6.00955i	−0.674394	+	0.266631i
$509$		−	13.6423i		−	0.604686i	−0.953199	−	0.302343i	$-0.902231\pi$
$509$		−	13.6423i		−	0.604686i	0.953199	−	0.302343i	$-0.0977687\pi$
$510$		0			0
$511$		0			0
$512$	13.9077	−	17.8487i	0.614640	−	0.788807i
$513$		0			0
$514$	−16.9655	+	24.9509i	−0.748317	+	1.10054i
$515$	8.31944			0.366598
$516$		0			0
$517$	21.8827			0.962402
$518$		0			0
$519$		0			0
$520$	−10.2086	−	2.28973i	−0.447675	−	0.100411i
$521$			24.4585i			1.07155i	0.844362	+	0.535774i	$0.179980\pi$
$521$			24.4585i			1.07155i	−0.844362	+	0.535774i	$0.820020\pi$
$522$		0			0
$523$		−	16.0000i		−	0.699631i	−0.936819	−	0.349816i	$-0.886244\pi$
$523$		−	16.0000i		−	0.699631i	0.936819	−	0.349816i	$-0.113756\pi$
$524$	2.20181	+	5.56907i	0.0961865	+	0.243286i
$525$		0			0
$526$	23.1031	+	15.7091i	1.00734	+	0.684949i
$527$	−14.3080			−0.623265
$528$		0			0
$529$	−4.66730			−0.202926
$530$	−8.25489	−	5.61296i	−0.358570	−	0.243812i
$531$		0			0
$532$		0			0
$533$		−	31.6515i		−	1.37098i
$534$		0			0
$535$			8.91539i			0.385446i
$536$	−38.7903	−	8.70048i	−1.67549	−	0.375803i
$537$		0			0
$538$	2.08623	−	3.06819i	0.0899438	−	0.132279i
$539$		0			0
$540$		0			0
$541$	7.20512			0.309772			0.154886	−	0.987932i	$-0.450499\pi$
$541$	7.20512			0.309772			0.154886	+	0.987932i	$0.450499\pi$
$542$	−0.582727	+	0.857007i	−0.0250303	+	0.0368116i
$543$		0			0
$544$	−1.89916	−	12.0862i	−0.0814259	−	0.518193i
$545$			4.07194i			0.174423i
$546$		0			0
$547$		−	39.0518i		−	1.66973i	−0.550453	−	0.834866i	$-0.685545\pi$
$547$		−	39.0518i		−	1.66973i	0.550453	−	0.834866i	$-0.314455\pi$
$548$	−20.0313	+	7.91964i	−0.855694	+	0.338310i
$549$		0			0
$550$	−11.0840	−	7.53662i	−0.472623	−	0.321363i
$551$	−6.36153			−0.271010
$552$		0			0
$553$		0			0
$554$	13.3784	+	9.09671i	0.568393	+	0.386482i
$555$		0			0
$556$	29.7586	−	11.7655i	1.26205	−	0.498967i
$557$		−	3.99874i		−	0.169432i	−0.996405	−	0.0847161i	$-0.973002\pi$
$557$		−	3.99874i		−	0.169432i	0.996405	−	0.0847161i	$-0.0269983\pi$
$558$		0			0
$559$		−	11.7655i		−	0.497626i
$560$		0			0
$561$		0			0
$562$	−0.696092	+	1.02373i	−0.0293629	+	0.0431835i
$563$	−39.1372			−1.64944			−0.824718	−	0.565544i	$-0.808666\pi$
$563$	−39.1372			−1.64944			−0.824718	+	0.565544i	$0.808666\pi$
$564$		0			0
$565$	−2.40699			−0.101263
$566$	−17.8850	+	26.3031i	−0.751761	+	1.10560i
$567$		0			0
$568$	−9.65389	+	43.0410i	−0.405068	+	1.80596i
$569$		−	32.7708i		−	1.37382i	−0.726741	−	0.686912i	$-0.758966\pi$
$569$		−	32.7708i		−	1.37382i	0.726741	−	0.686912i	$-0.241034\pi$
$570$		0			0
$571$			18.8172i			0.787476i	0.919223	+	0.393738i	$0.128818\pi$
$571$			18.8172i			0.787476i	−0.919223	+	0.393738i	$0.871182\pi$
$572$	8.49879	+	21.4961i	0.355352	+	0.898798i
$573$		0			0
$574$		0			0
$575$	−19.5112			−0.813673
$576$		0			0
$577$	5.00344			0.208296			0.104148	−	0.994562i	$-0.466788\pi$
$577$	5.00344			0.208296			0.104148	+	0.994562i	$0.466788\pi$
$578$	14.4107	+	9.79865i	0.599407	+	0.407570i
$579$		0			0
$580$	0.692226	+	1.75086i	0.0287431	+	0.0727005i
$581$		0			0
$582$		0			0
$583$			22.0552i			0.913433i
$584$	−7.38984	+	32.9470i	−0.305794	+	1.36336i
$585$		0			0
$586$	−19.2767	+	28.3500i	−0.796315	+	1.17113i
$587$	24.8292			1.02481			0.512406	−	0.858743i	$-0.328754\pi$
$587$	24.8292			1.02481			0.512406	+	0.858743i	$0.328754\pi$
$588$		0			0
$589$	−29.7586			−1.22618
$590$	7.15399	−	10.5213i	0.294525	−	0.433153i
$591$		0			0
$592$	15.8759	−	14.8793i	0.652494	−	0.611535i
$593$			16.1391i			0.662752i	0.943499	+	0.331376i	$0.107513\pi$
$593$			16.1391i			0.662752i	−0.943499	+	0.331376i	$0.892487\pi$
$594$		0			0
$595$		0			0
$596$	−4.79795	+	1.89694i	−0.196532	+	0.0777016i
$597$		0			0
$598$	27.8252	+	18.9199i	1.13786	+	0.773692i
$599$	7.03204			0.287321			0.143661	−	0.989627i	$-0.454113\pi$
$599$	7.03204			0.287321			0.143661	+	0.989627i	$0.454113\pi$
$600$		0			0
$601$	2.99656			0.122232			0.0611162	−	0.998131i	$-0.480534\pi$
$601$	2.99656			0.122232			0.0611162	+	0.998131i	$0.480534\pi$
$602$		0			0
$603$		0			0
$604$	−9.72938	+	3.84664i	−0.395883	+	0.156518i
$605$			4.44265i			0.180619i
$606$		0			0
$607$		−	9.46563i		−	0.384198i	−0.981376	−	0.192099i	$-0.938471\pi$
$607$		−	9.46563i		−	0.384198i	0.981376	−	0.192099i	$-0.0615295\pi$
$608$	−3.94999	−	25.1377i	−0.160193	−	1.01947i
$609$		0			0
$610$	0.325819	−	0.479177i	0.0131920	−	0.0194013i
$611$	58.4657			2.36527
$612$		0			0
$613$	11.2311			0.453620			0.226810	−	0.973939i	$-0.427170\pi$
$613$	11.2311			0.453620			0.226810	+	0.973939i	$0.427170\pi$
$614$	6.05308	−	8.90217i	0.244283	−	0.359262i
$615$		0			0
$616$		0			0
$617$			37.6352i			1.51514i	0.652756	+	0.757568i	$0.273613\pi$
$617$			37.6352i			1.51514i	−0.652756	+	0.757568i	$0.726387\pi$
$618$		0			0
$619$		−	43.3346i		−	1.74177i	−0.491491	−	0.870883i	$-0.663548\pi$
$619$		−	43.3346i		−	1.74177i	0.491491	−	0.870883i	$-0.336452\pi$
$620$	3.23816	+	8.19034i	0.130048	+	0.328932i
$621$		0			0
$622$	−15.8061	−	10.7474i	−0.633765	−	0.430932i
$623$		0			0
$624$		0			0
$625$	18.5500			0.742002
$626$	8.94438	+	6.08178i	0.357489	+	0.243077i
$627$		0			0
$628$	4.12682	+	10.4380i	0.164678	+	0.416523i
$629$		−	11.7648i		−	0.469092i
$630$		0			0
$631$		−	18.2897i		−	0.728103i	−0.931379	−	0.364051i	$-0.881393\pi$
$631$		−	18.2897i		−	0.728103i	0.931379	−	0.364051i	$-0.118607\pi$
$632$	−2.27440	−	0.510137i	−0.0904708	−	0.0202921i
$633$		0			0
$634$	−23.6780	+	34.8229i	−0.940375	+	1.38299i
$635$	5.43997			0.215879
$636$		0			0
$637$		0			0
$638$	2.33895	−	3.43985i	0.0925999	−	0.136185i
$639$		0			0
$640$	−6.48873	+	3.82248i	−0.256490	+	0.151097i
$641$			14.2251i			0.561856i	0.959729	+	0.280928i	$0.0906422\pi$
$641$			14.2251i			0.561856i	−0.959729	+	0.280928i	$0.909358\pi$
$642$		0			0
$643$			38.4914i			1.51795i	0.651118	+	0.758976i	$0.274300\pi$
$643$			38.4914i			1.51795i	−0.651118	+	0.758976i	$0.725700\pi$
$644$		0			0
$645$		0			0
$646$	−11.3776	−	7.73625i	−0.447645	−	0.304379i
$647$	−0.792458			−0.0311547			−0.0155774	−	0.999879i	$-0.504959\pi$
$647$	−0.792458			−0.0311547			−0.0155774	+	0.999879i	$0.504959\pi$
$648$		0			0
$649$	−28.1104			−1.10343
$650$	−29.6139	−	20.1361i	−1.16155	−	0.789804i
$651$		0			0
$652$	15.2001	−	6.00955i	0.595280	−	0.235352i
$653$			7.85380i			0.307343i	0.988122	+	0.153672i	$0.0491098\pi$
$653$			7.85380i			0.307343i	−0.988122	+	0.153672i	$0.950890\pi$
$654$		0			0
$655$		−	1.99312i		−	0.0778778i
$656$	−15.5802	−	16.6237i	−0.608304	−	0.649046i
$657$		0			0
$658$		0			0
$659$	13.3936			0.521739			0.260870	−	0.965374i	$-0.415991\pi$
$659$	13.3936			0.521739			0.260870	+	0.965374i	$0.415991\pi$
$660$		0			0
$661$	−35.2603			−1.37147			−0.685734	−	0.727853i	$-0.740518\pi$
$661$	−35.2603			−1.37147			−0.685734	+	0.727853i	$0.740518\pi$
$662$	−8.83762	+	12.9973i	−0.343484	+	0.505156i
$663$		0			0
$664$	3.93793	−	17.5569i	0.152821	−	0.681340i
$665$		0			0
$666$		0			0
$667$		−	6.05520i		−	0.234458i
$668$	−12.1403	−	30.7067i	−0.469724	−	1.18808i
$669$		0			0
$670$	10.9414	+	7.43965i	0.422702	+	0.287419i
$671$	−1.28025			−0.0494236
$672$		0			0
$673$	40.1364			1.54714			0.773572	−	0.633709i	$-0.218468\pi$
$673$	40.1364			1.54714			0.773572	+	0.633709i	$0.218468\pi$
$674$	−6.87971	−	4.67790i	−0.264996	−	0.180186i
$675$		0			0
$676$	13.1474	+	33.2539i	0.505669	+	1.27900i
$677$			20.2478i			0.778184i	0.921199	+	0.389092i	$0.127211\pi$
$677$			20.2478i			0.778184i	−0.921199	+	0.389092i	$0.872789\pi$
$678$		0			0
$679$		0			0
$680$	−0.891174	+	3.97322i	−0.0341750	+	0.152366i
$681$		0			0
$682$	10.9414	−	16.0913i	0.418967	−	0.616167i
$683$	−40.6685			−1.55614			−0.778068	−	0.628179i	$-0.783800\pi$
$683$	−40.6685			−1.55614			−0.778068	+	0.628179i	$0.783800\pi$
$684$		0			0
$685$	7.16902			0.273914
$686$		0			0
$687$		0			0
$688$	−5.79145	−	6.17934i	−0.220797	−	0.235585i
$689$			58.9265i			2.24492i
$690$		0			0
$691$			35.1138i			1.33579i	0.744254	+	0.667896i	$0.232805\pi$
$691$			35.1138i			1.33579i	−0.744254	+	0.667896i	$0.767195\pi$
$692$	−7.80931	+	3.08752i	−0.296865	+	0.117370i
$693$		0			0
$694$	12.4470	+	8.46338i	0.472480	+	0.321265i
$695$	−10.6504			−0.403991
$696$		0			0
$697$	−12.3189			−0.466613
$698$	−2.92168	−	1.98661i	−0.110587	−	0.0751943i
$699$		0			0
$700$		0			0
$701$			6.73939i			0.254543i	0.991868	+	0.127272i	$0.0406220\pi$
$701$			6.73939i			0.254543i	−0.991868	+	0.127272i	$0.959378\pi$
$702$		0			0
$703$		−	24.4691i		−	0.922868i
$704$	15.0449	+	7.10652i	0.567027	+	0.267837i
$705$		0			0
$706$	−0.100839	+	0.148302i	−0.00379512	+	0.00558141i
$707$		0			0
$708$		0			0
$709$	24.1104			0.905485			0.452742	−	0.891641i	$-0.350446\pi$
$709$	24.1104			0.905485			0.452742	+	0.891641i	$0.350446\pi$
$710$	8.25489	−	12.1403i	0.309801	−	0.455619i
$711$		0			0
$712$	35.0061	+	7.85170i	1.31191	+	0.294255i
$713$		−	28.3256i		−	1.06080i
$714$		0			0
$715$		−	7.69328i		−	0.287713i
$716$	−1.52941	−	3.86836i	−0.0571567	−	0.144567i
$717$		0			0
$718$	23.1031	+	15.7091i	0.862200	+	0.586258i
$719$	−17.1267			−0.638717			−0.319359	−	0.947634i	$-0.603467\pi$
$719$	−17.1267			−0.638717			−0.319359	+	0.947634i	$0.603467\pi$
$720$		0			0
$721$		0			0
$722$	−1.44375	−	0.981690i	−0.0537310	−	0.0365347i
$723$		0			0
$724$	8.41205	+	21.2767i	0.312631	+	0.790744i
$725$			6.44445i			0.239341i
$726$		0			0
$727$			2.72594i			0.101099i	0.998722	+	0.0505497i	$0.0160973\pi$
$727$			2.72594i			0.101099i	−0.998722	+	0.0505497i	$0.983903\pi$
$728$		0			0
$729$		0			0
$730$	6.31894	−	9.29317i	0.233875	−	0.343955i
$731$	−4.57918			−0.169367
$732$		0			0
$733$	−46.5535			−1.71949			−0.859746	−	0.510722i	$-0.829378\pi$
$733$	−46.5535			−1.71949			−0.859746	+	0.510722i	$0.829378\pi$
$734$	22.8713	−	33.6365i	0.844196	−	1.24154i
$735$		0			0
$736$	23.9272	−	3.75978i	0.881968	−	0.138587i
$737$		−	29.2328i		−	1.07681i
$738$		0			0
$739$		−	18.2897i		−	0.672799i	−0.941719	−	0.336399i	$-0.890791\pi$
$739$		−	18.2897i		−	0.672799i	0.941719	−	0.336399i	$-0.109209\pi$
$740$	−6.73453	+	2.66259i	−0.247566	+	0.0978787i
$741$		0			0
$742$		0			0
$743$	−37.3012			−1.36845			−0.684225	−	0.729271i	$-0.739859\pi$
$743$	−37.3012			−1.36845			−0.684225	+	0.729271i	$0.739859\pi$
$744$		0			0
$745$	1.71715			0.0629114
$746$	−1.02831	−	0.699208i	−0.0376493	−	0.0255998i
$747$		0			0
$748$	8.36641	−	3.30777i	0.305906	−	0.120944i
$749$		0			0
$750$		0			0
$751$			12.2345i			0.446444i	0.974768	+	0.223222i	$0.0716576\pi$
$751$			12.2345i			0.446444i	−0.974768	+	0.223222i	$0.928342\pi$
$752$	30.7067	−	28.7792i	1.11976	−	1.04947i
$753$		0			0
$754$	6.24914	−	9.19051i	0.227580	−	0.334699i
$755$	3.48206			0.126725
$756$		0			0
$757$	3.87586			0.140870			0.0704352	−	0.997516i	$-0.477561\pi$
$757$	3.87586			0.140870			0.0704352	+	0.997516i	$0.477561\pi$
$758$	−18.1934	+	26.7568i	−0.660815	+	0.971849i
$759$		0			0
$760$	−1.85352	+	8.26375i	−0.0672342	+	0.299758i
$761$		−	33.0219i		−	1.19704i	−0.801107	−	0.598521i	$-0.795755\pi$
$761$		−	33.0219i		−	1.19704i	0.801107	−	0.598521i	$-0.204245\pi$
$762$		0			0
$763$		0			0
$764$	6.20731	+	15.7002i	0.224572	+	0.568015i
$765$		0			0
$766$	37.8398	+	25.7294i	1.36721	+	0.929640i
$767$	−75.1046			−2.71187
$768$		0			0
$769$	23.3415			0.841715			0.420858	−	0.907127i	$-0.361729\pi$
$769$	23.3415			0.841715			0.420858	+	0.907127i	$0.361729\pi$
$770$		0			0
$771$		0			0
$772$	7.11383	+	17.9931i	0.256032	+	0.647587i
$773$		−	31.7783i		−	1.14299i	−0.820606	−	0.571494i	$-0.806364\pi$
$773$		−	31.7783i		−	1.14299i	0.820606	−	0.571494i	$-0.193636\pi$
$774$		0			0
$775$			30.1465i			1.08289i
$776$	0.510137	−	2.27440i	0.0183128	−	0.0816462i
$777$		0			0
$778$	−12.9927	+	19.1081i	−0.465811	+	0.685060i
$779$	−25.6217			−0.917992
$780$		0			0
$781$	−32.4362			−1.16066
$782$	7.36372	−	10.8297i	0.263326	−	0.387269i
$783$		0			0
$784$		0			0
$785$		−	3.73568i		−	0.133332i
$786$		0			0
$787$			1.64820i			0.0587520i	0.999568	+	0.0293760i	$0.00935202\pi$
$787$			1.64820i			0.0587520i	−0.999568	+	0.0293760i	$0.990648\pi$
$788$	24.9834	−	9.87755i	0.889999	−	0.351873i
$789$		0			0
$790$	0.641527	+	0.436210i	0.0228245	+	0.0155197i
$791$		0			0
$792$		0			0
$793$	−3.42054			−0.121467
$794$	5.67205	+	3.85674i	0.201293	+	0.136871i
$795$		0			0
$796$	−50.4293	+	19.9379i	−1.78742	+	0.706681i
$797$			20.8376i			0.738107i	0.929408	+	0.369053i	$0.120318\pi$
$797$			20.8376i			0.738107i	−0.929408	+	0.369053i	$0.879682\pi$
$798$		0			0
$799$		−	22.7552i		−	0.805019i
$800$	−25.4653	+	4.00148i	−0.900335	+	0.141474i
$801$		0			0
$802$	−16.5642	+	24.3607i	−0.584903	+	0.860207i
$803$	−24.8292			−0.876204
$804$		0			0
$805$		0			0
$806$	29.2328	−	42.9923i	1.02968	−	1.51434i
$807$		0			0
$808$	49.3465	+	11.0682i	1.73601	+	0.389377i
$809$			27.0262i			0.950190i	0.879935	+	0.475095i	$0.157586\pi$
$809$			27.0262i			0.950190i	−0.879935	+	0.475095i	$0.842414\pi$
$810$		0			0
$811$		−	8.65164i		−	0.303800i	−0.988396	−	0.151900i	$-0.951461\pi$
$811$		−	8.65164i		−	0.303800i	0.988396	−	0.151900i	$-0.0485392\pi$
$812$		0			0
$813$		0			0
$814$	13.2311	+	8.99656i	0.463750	+	0.315329i
$815$	−5.43997			−0.190554
$816$		0			0
$817$	−9.52406			−0.333205
$818$	−15.1266	−	10.2854i	−0.528888	−	0.359620i
$819$		0			0
$820$	2.78801	+	7.05176i	0.0973615	+	0.246258i
$821$		−	19.2456i		−	0.671675i	−0.941920	−	0.335837i	$-0.890981\pi$
$821$		−	19.2456i		−	0.671675i	0.941920	−	0.335837i	$-0.109019\pi$
$822$		0			0
$823$		−	21.4036i		−	0.746081i	−0.927815	−	0.373041i	$-0.878315\pi$
$823$		−	21.4036i		−	0.746081i	0.927815	−	0.373041i	$-0.121685\pi$
$824$	−34.4935	−	7.73671i	−1.20164	−	0.269521i
$825$		0			0
$826$		0			0
$827$	37.4303			1.30158			0.650790	−	0.759258i	$-0.274438\pi$
$827$	37.4303			1.30158			0.650790	+	0.759258i	$0.274438\pi$
$828$		0			0
$829$	−49.0157			−1.70238			−0.851192	−	0.524854i	$-0.824120\pi$
$829$	−49.0157			−1.70238			−0.851192	+	0.524854i	$0.824120\pi$
$830$	−3.36726	+	4.95218i	−0.116879	+	0.171893i
$831$		0			0
$832$	40.1966	+	18.9870i	1.39357	+	0.658256i
$833$		0			0
$834$		0			0
$835$			10.9897i			0.380314i
$836$	17.4010	−	6.87971i	0.601825	−	0.237940i
$837$		0			0
$838$	−17.0180	−	11.5715i	−0.587879	−	0.399732i
$839$	15.9612			0.551043			0.275521	−	0.961295i	$-0.411150\pi$
$839$	15.9612			0.551043			0.275521	+	0.961295i	$0.411150\pi$
$840$		0			0
$841$	27.0000			0.931034
$842$	−34.9694	−	23.7777i	−1.20513	−	0.819433i
$843$		0			0
$844$	−20.6707	+	8.17246i	−0.711516	+	0.281308i
$845$		−	11.9013i		−	0.409417i
$846$		0			0
$847$		0			0
$848$	29.0060	+	30.9488i	0.996071	+	1.06278i
$849$		0			0
$850$	−7.83709	+	11.5259i	−0.268810	+	0.395334i
$851$	23.2908			0.798398
$852$		0			0
$853$	−5.50172			−0.188375			−0.0941876	−	0.995554i	$-0.530025\pi$
$853$	−5.50172			−0.188375			−0.0941876	+	0.995554i	$0.530025\pi$
$854$		0			0
$855$		0			0
$856$	8.29092	−	36.9643i	0.283378	−	1.26342i
$857$			38.6007i			1.31857i	0.751892	+	0.659287i	$0.229142\pi$
$857$			38.6007i			1.31857i	−0.751892	+	0.659287i	$0.770858\pi$
$858$		0			0
$859$			6.14648i			0.209715i	0.994487	+	0.104858i	$0.0334387\pi$
$859$			6.14648i			0.209715i	−0.994487	+	0.104858i	$0.966561\pi$
$860$	1.03636	+	2.62127i	0.0353394	+	0.0893846i
$861$		0			0
$862$	−6.86082	−	4.66506i	−0.233681	−	0.158892i
$863$	−41.9631			−1.42844			−0.714220	−	0.699922i	$-0.753218\pi$
$863$	−41.9631			−1.42844			−0.714220	+	0.699922i	$0.753218\pi$
$864$		0			0
$865$	2.79488			0.0950289
$866$	−30.5354	−	20.7628i	−1.03764	−	0.705547i
$867$		0			0
$868$		0			0
$869$		−	1.71401i		−	0.0581439i
$870$		0			0
$871$		−	78.1035i		−	2.64644i
$872$	3.78672	−	16.8828i	0.128235	−	0.571723i
$873$		0			0
$874$	15.3155	−	22.5243i	0.518055	−	0.761894i
$875$		0			0
$876$		0			0
$877$	45.8759			1.54912			0.774559	−	0.632502i	$-0.217972\pi$
$877$	45.8759			1.54912			0.774559	+	0.632502i	$0.217972\pi$
$878$	20.6695	−	30.3983i	0.697562	−	1.02589i
$879$		0			0
$880$	−3.78695	−	4.04059i	−0.127658	−	0.136208i
$881$		−	39.3323i		−	1.32514i	−0.749000	−	0.662570i	$-0.769466\pi$
$881$		−	39.3323i		−	1.32514i	0.749000	−	0.662570i	$-0.230534\pi$
$882$		0			0
$883$		−	34.1173i		−	1.14814i	−0.818807	−	0.574069i	$-0.805364\pi$
$883$		−	34.1173i		−	1.14814i	0.818807	−	0.574069i	$-0.194636\pi$
$884$	22.3531	−	8.83762i	0.751817	−	0.297241i
$885$		0			0
$886$	10.7988	+	7.34268i	0.362791	+	0.246682i
$887$	−35.9674			−1.20767			−0.603833	−	0.797111i	$-0.706361\pi$
$887$	−35.9674			−1.20767			−0.603833	+	0.797111i	$0.706361\pi$
$888$		0			0
$889$		0			0
$890$	−9.87397	−	6.71387i	−0.330976	−	0.225049i
$891$		0			0
$892$	−12.7949	+	5.05863i	−0.428404	+	0.169376i
$893$		−	47.3275i		−	1.58376i
$894$		0			0
$895$			1.38445i			0.0462771i
$896$		0			0
$897$		0			0
$898$	−26.6194	+	39.1487i	−0.888301	+	1.30641i
$899$	−9.35580			−0.312033
$900$		0			0
$901$	22.9345			0.764059
$902$	9.42035	−	13.8543i	0.313663	−	0.461299i
$903$		0			0
$904$	9.97971	+	2.23840i	0.331920	+	0.0744480i
$905$		−	7.61477i		−	0.253123i
$906$		0			0
$907$		−	24.3449i		−	0.808360i	−0.914679	−	0.404180i	$-0.867557\pi$
$907$		−	24.3449i		−	0.808360i	0.914679	−	0.404180i	$-0.132443\pi$
$908$	3.82089	+	9.66424i	0.126801	+	0.320719i
$909$		0			0
$910$		0			0
$911$	−17.4242			−0.577289			−0.288645	−	0.957436i	$-0.593205\pi$
$911$	−17.4242			−0.577289			−0.288645	+	0.957436i	$0.593205\pi$
$912$		0			0
$913$	13.2311			0.437885
$914$	−35.3505	−	24.0368i	−1.16929	−	0.795066i
$915$		0			0
$916$	−4.08623	−	10.3354i	−0.135013	−	0.341490i
$917$		0			0
$918$		0			0
$919$			7.22422i			0.238305i	0.992876	+	0.119152i	$0.0380177\pi$
$919$			7.22422i			0.238305i	−0.992876	+	0.119152i	$0.961982\pi$
$920$	−7.86581	−	1.76426i	−0.259328	−	0.0581660i
$921$		0			0
$922$	−8.33537	+	12.2587i	−0.274511	+	0.403719i
$923$	−86.6622			−2.85252
$924$		0			0
$925$	−24.7880			−0.815025
$926$	−7.80931	+	11.4850i	−0.256630	+	0.377421i
$927$		0			0
$928$	−1.24184	−	7.90303i	−0.0407653	−	0.259430i
$929$			36.7208i			1.20477i	0.798206	+	0.602385i	$0.205783\pi$
$929$			36.7208i			1.20477i	−0.798206	+	0.602385i	$0.794217\pi$
$930$		0			0
$931$		0			0
$932$	44.8605	−	17.7362i	1.46945	−	0.580969i
$933$		0			0
$934$	−25.0992	−	17.0664i	−0.821272	−	0.558429i
$935$	−2.99427			−0.0979230
$936$		0			0
$937$	20.6448			0.674435			0.337218	−	0.941427i	$-0.390514\pi$
$937$	20.6448			0.674435			0.337218	+	0.941427i	$0.390514\pi$
$938$		0			0
$939$		0			0
$940$	−13.0258	+	5.14992i	−0.424854	+	0.167972i
$941$		−	39.9687i		−	1.30294i	−0.758674	−	0.651471i	$-0.774152\pi$
$941$		−	39.9687i		−	1.30294i	0.758674	−	0.651471i	$-0.225848\pi$
$942$		0			0
$943$		−	24.3879i		−	0.794179i
$944$	−39.4456	+	36.9696i	−1.28385	+	1.20326i
$945$		0			0
$946$	3.50172	−	5.14992i	0.113851	−	0.167438i
$947$	16.1439			0.524607			0.262304	−	0.964985i	$-0.415518\pi$
$947$	16.1439			0.524607			0.262304	+	0.964985i	$0.415518\pi$
$948$		0			0
$949$	−66.3380			−2.15342
$950$	−16.3001	+	23.9722i	−0.528844	+	0.777761i
$951$		0			0
$952$		0			0
$953$		−	23.2394i		−	0.752800i	−0.926457	−	0.376400i	$-0.877162\pi$
$953$		−	23.2394i		−	0.752800i	0.926457	−	0.376400i	$-0.122838\pi$
$954$		0			0
$955$		−	5.61899i		−	0.181826i
$956$	−6.20731	−	15.7002i	−0.200759	−	0.507782i
$957$		0			0
$958$	−10.0146	−	6.80949i	−0.323557	−	0.220005i
$959$		0			0
$960$		0			0
$961$	−12.7655			−0.411789
$962$	35.3505	+	24.0368i	1.13975	+	0.774977i
$963$		0			0
$964$	18.9870	+	48.0242i	0.611530	+	1.54675i
$965$		−	6.43959i		−	0.207298i
$966$		0			0
$967$			16.0483i			0.516079i	0.966134	+	0.258040i	$0.0830765\pi$
$967$			16.0483i			0.516079i	−0.966134	+	0.258040i	$0.916924\pi$
$968$	4.13147	−	18.4198i	0.132790	−	0.592034i
$969$		0			0
$970$	−0.436210	+	0.641527i	−0.0140059	+	0.0205982i
$971$	−28.8134			−0.924665			−0.462333	−	0.886707i	$-0.652987\pi$
$971$	−28.8134			−0.924665			−0.462333	+	0.886707i	$0.652987\pi$
$972$		0			0
$973$		0			0
$974$	7.52698	−	11.0698i	0.241180	−	0.354700i
$975$		0			0
$976$	−1.79650	+	1.68373i	−0.0575047	+	0.0538950i
$977$			35.3043i			1.12948i	0.825267	+	0.564742i	$0.191024\pi$
$977$			35.3043i			1.12948i	−0.825267	+	0.564742i	$0.808976\pi$
$978$		0			0
$979$			26.3810i			0.843141i
$980$		0			0
$981$		0			0
$982$	−22.9521	−	15.6064i	−0.732431	−	0.498021i
$983$	10.2774			0.327797			0.163898	−	0.986477i	$-0.447593\pi$
$983$	10.2774			0.327797			0.163898	+	0.986477i	$0.447593\pi$
$984$		0			0
$985$	−8.94137			−0.284896
$986$	−3.57699	−	2.43220i	−0.113915	−	0.0774570i
$987$		0			0
$988$	46.4914	−	18.3810i	1.47909	−	0.584778i
$989$		−	9.06543i		−	0.288264i
$990$		0			0
$991$			57.2173i			1.81757i	0.417266	+	0.908784i	$0.362988\pi$
$991$			57.2173i			1.81757i	−0.417266	+	0.908784i	$0.637012\pi$
$992$	−5.80919	−	36.9696i	−0.184442	−	1.17378i
$993$		0			0
$994$		0			0
$995$	18.0482			0.572168
$996$		0			0
$997$	−5.73625			−0.181669			−0.0908345	−	0.995866i	$-0.528953\pi$
$997$	−5.73625			−0.181669			−0.0908345	+	0.995866i	$0.528953\pi$
$998$	−1.68363	+	2.47609i	−0.0532944	+	0.0783792i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.e.g.1079.10		12
3.2	odd	2	inner	1764.2.e.g.1079.3		12
4.3	odd	2	inner	1764.2.e.g.1079.4		12
7.6	odd	2		252.2.e.a.71.10	yes	12
12.11	even	2	inner	1764.2.e.g.1079.9		12
21.20	even	2		252.2.e.a.71.3	✓	12
28.27	even	2		252.2.e.a.71.4	yes	12
56.13	odd	2		4032.2.h.h.575.6		12
56.27	even	2		4032.2.h.h.575.5		12
84.83	odd	2		252.2.e.a.71.9	yes	12
168.83	odd	2		4032.2.h.h.575.7		12
168.125	even	2		4032.2.h.h.575.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.e.a.71.3	✓	12	21.20	even	2
252.2.e.a.71.4	yes	12	28.27	even	2
252.2.e.a.71.9	yes	12	84.83	odd	2
252.2.e.a.71.10	yes	12	7.6	odd	2
1764.2.e.g.1079.3		12	3.2	odd	2	inner
1764.2.e.g.1079.4		12	4.3	odd	2	inner
1764.2.e.g.1079.9		12	12.11	even	2	inner
1764.2.e.g.1079.10		12	1.1	even	1	trivial
4032.2.h.h.575.5		12	56.27	even	2
4032.2.h.h.575.6		12	56.13	odd	2
4032.2.h.h.575.7		12	168.83	odd	2
4032.2.h.h.575.8		12	168.125	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.16947 + 0.795191i) q^{2} +(0.735342 + 1.85991i) q^{4} -0.665647i q^{5} +(-0.619022 + 2.75986i) q^{8} +O(q^{10})\)	\(q+(1.16947 + 0.795191i) q^{2} +(0.735342 + 1.85991i) q^{4} -0.665647i q^{5} +(-0.619022 + 2.75986i) q^{8} +(0.529317 - 0.778457i) q^{10} -2.07986 q^{11} -5.55691 q^{13} +(-2.91855 + 2.73534i) q^{16} +2.16278i q^{17} +4.49828i q^{19} +(1.23804 - 0.489478i) q^{20} +(-2.43234 - 1.65389i) q^{22} -4.28167 q^{23} +4.55691 q^{25} +(-6.49867 - 4.41881i) q^{26} +1.41421i q^{29} +6.61555i q^{31} +(-5.58828 + 0.878111i) q^{32} +(-1.71982 + 2.52932i) q^{34} -5.43965 q^{37} +(-3.57699 + 5.26063i) q^{38} +(1.83709 + 0.412050i) q^{40} +5.69588i q^{41} +2.11727i q^{43} +(-1.52941 - 3.86836i) q^{44} +(-5.00730 - 3.40475i) q^{46} -10.5213 q^{47} +(5.32920 + 3.62362i) q^{50} +(-4.08623 - 10.3354i) q^{52} -10.6042i q^{53} +1.38445i q^{55} +(-1.12457 + 1.65389i) q^{58} +13.5155 q^{59} +0.615547 q^{61} +(-5.26063 + 7.73671i) q^{62} +(-7.23362 - 3.41683i) q^{64} +3.69894i q^{65} +14.0552i q^{67} +(-4.02258 + 1.59038i) q^{68} +15.5954 q^{71} +11.9379 q^{73} +(-6.36153 - 4.32556i) q^{74} +(-8.36641 + 3.30777i) q^{76} +0.824101i q^{79} +(1.82077 + 1.94272i) q^{80} +(-4.52932 + 6.66119i) q^{82} -6.36153 q^{83} +1.43965 q^{85} +(-1.68363 + 2.47609i) q^{86} +(1.28748 - 5.74012i) q^{88} -12.6840i q^{89} +(-3.14849 - 7.96353i) q^{92} +(-12.3043 - 8.36641i) q^{94} +2.99427 q^{95} -0.824101 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4}+O(q^{10}) \) 12 * q + 8 * q^4	\( 12 q + 8 q^{4} + 8 q^{10} - 20 q^{16} + 20 q^{22} - 12 q^{25} + 16 q^{34} + 8 q^{37} - 8 q^{40} - 36 q^{46} + 16 q^{52} + 4 q^{58} - 56 q^{61} - 16 q^{64} - 72 q^{76} - 56 q^{82} - 56 q^{85} + 28 q^{88} + 24 q^{94}+O(q^{100}) \) 12 * q + 8 * q^4 + 8 * q^10 - 20 * q^16 + 20 * q^22 - 12 * q^25 + 16 * q^34 + 8 * q^37 - 8 * q^40 - 36 * q^46 + 16 * q^52 + 4 * q^58 - 56 * q^61 - 16 * q^64 - 72 * q^76 - 56 * q^82 - 56 * q^85 + 28 * q^88 + 24 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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