LMFDB - Embedded newform 2880.2.u.a.719.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2880,2,Mod(719,2880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2880, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 2]))

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

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

chi := DirichletCharacter("2880.719");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2880.u (of order $4$, degree $2$, not 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:	$22.9969157821$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 720)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			719.27
Character	$\chi$	$=$	2880.719
Dual form			2880.2.u.a.2159.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.274088 + 2.21921i) q^{5} -1.32258i q^{7} +O(q^{10})$	$q+(0.274088 + 2.21921i) q^{5} -1.32258i q^{7} +(2.92489 + 2.92489i) q^{11} +(-3.33361 - 3.33361i) q^{13} -5.12112 q^{17} +(-4.23462 - 4.23462i) q^{19} +6.44702 q^{23} +(-4.84975 + 1.21651i) q^{25} +(-4.55904 - 4.55904i) q^{29} +8.07172i q^{31} +(2.93508 - 0.362503i) q^{35} +(-4.98065 + 4.98065i) q^{37} -7.34991 q^{41} +(-4.67417 - 4.67417i) q^{43} -3.25014i q^{47} +5.25078 q^{49} +(0.0429668 + 0.0429668i) q^{53} +(-5.68926 + 7.29261i) q^{55} +(-8.42676 - 8.42676i) q^{59} +(-1.80862 + 1.80862i) q^{61} +(6.48426 - 8.31166i) q^{65} +(3.23414 - 3.23414i) q^{67} +4.08803i q^{71} -1.91406 q^{73} +(3.86841 - 3.86841i) q^{77} +8.95635i q^{79} +(-1.19997 - 1.19997i) q^{83} +(-1.40364 - 11.3648i) q^{85} +12.2303 q^{89} +(-4.40896 + 4.40896i) q^{91} +(8.23684 - 10.5582i) q^{95} -13.7776i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q + 16 q^{19} - 96 q^{49} - 64 q^{55} - 32 q^{61}+O(q^{100}) $ 96 * q + 16 * q^19 - 96 * q^49 - 64 * q^55 - 32 * q^61

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$2431$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.274088	+	2.21921i	0.122576	+	0.992459i
$5$	0.274088	+	2.21921i	0.122576	+	0.992459i
$6$		0			0
$7$		−	1.32258i		−	0.499889i	−0.968260	−	0.249944i	$-0.919588\pi$
$7$		−	1.32258i		−	0.499889i	0.968260	−	0.249944i	$-0.0804123\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.92489	+	2.92489i	0.881888	+	0.881888i	0.993726	−	0.111839i	$-0.0356740\pi$
$11$	2.92489	+	2.92489i	0.881888	+	0.881888i	−0.111839	+	0.993726i	$0.535674\pi$
$12$		0			0
$13$	−3.33361	−	3.33361i	−0.924576	−	0.924576i	0.0727729	−	0.997349i	$-0.476815\pi$
$13$	−3.33361	−	3.33361i	−0.924576	−	0.924576i	−0.997349	+	0.0727729i	$0.976815\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.12112			−1.24205			−0.621027	−	0.783789i	$-0.713284\pi$
$17$	−5.12112			−1.24205			−0.621027	+	0.783789i	$0.713284\pi$
$18$		0			0
$19$	−4.23462	−	4.23462i	−0.971489	−	0.971489i	0.0281156	−	0.999605i	$-0.491049\pi$
$19$	−4.23462	−	4.23462i	−0.971489	−	0.971489i	−0.999605	+	0.0281156i	$0.991049\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.44702			1.34430			0.672148	−	0.740417i	$-0.265372\pi$
$23$	6.44702			1.34430			0.672148	+	0.740417i	$0.265372\pi$
$24$		0			0
$25$	−4.84975	+	1.21651i	−0.969950	+	0.243303i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.55904	−	4.55904i	−0.846592	−	0.846592i	0.143114	−	0.989706i	$-0.454288\pi$
$29$	−4.55904	−	4.55904i	−0.846592	−	0.846592i	−0.989706	+	0.143114i	$0.954288\pi$
$30$		0			0
$31$			8.07172i			1.44972i	0.688895	+	0.724861i	$0.258096\pi$
$31$			8.07172i			1.44972i	−0.688895	+	0.724861i	$0.741904\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.93508	−	0.362503i	0.496119	−	0.0612742i
$36$		0			0
$37$	−4.98065	+	4.98065i	−0.818813	+	0.818813i	−0.985936	−	0.167123i	$-0.946552\pi$
$37$	−4.98065	+	4.98065i	−0.818813	+	0.818813i	0.167123	+	0.985936i	$0.446552\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.34991			−1.14786			−0.573931	−	0.818903i	$-0.694582\pi$
$41$	−7.34991			−1.14786			−0.573931	+	0.818903i	$0.694582\pi$
$42$		0			0
$43$	−4.67417	−	4.67417i	−0.712804	−	0.712804i	0.254317	−	0.967121i	$-0.418149\pi$
$43$	−4.67417	−	4.67417i	−0.712804	−	0.712804i	−0.967121	+	0.254317i	$0.918149\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	3.25014i		−	0.474082i	−0.971500	−	0.237041i	$-0.923822\pi$
$47$		−	3.25014i		−	0.474082i	0.971500	−	0.237041i	$-0.0761776\pi$
$48$		0			0
$49$	5.25078			0.750111
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.0429668	+	0.0429668i	0.00590194	+	0.00590194i	0.710052	−	0.704150i	$-0.248672\pi$
$53$	0.0429668	+	0.0429668i	0.00590194	+	0.00590194i	−0.704150	+	0.710052i	$0.748672\pi$
$54$		0			0
$55$	−5.68926	+	7.29261i	−0.767139	+	0.983335i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−8.42676	−	8.42676i	−1.09707	−	1.09707i	−0.994752	−	0.102320i	$-0.967374\pi$
$59$	−8.42676	−	8.42676i	−1.09707	−	1.09707i	−0.102320	−	0.994752i	$-0.532626\pi$
$60$		0			0
$61$	−1.80862	+	1.80862i	−0.231570	+	0.231570i	−0.813348	−	0.581778i	$-0.802357\pi$
$61$	−1.80862	+	1.80862i	−0.231570	+	0.231570i	0.581778	+	0.813348i	$0.302357\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.48426	−	8.31166i	0.804273	−	1.03093i
$66$		0			0
$67$	3.23414	−	3.23414i	0.395113	−	0.395113i	−0.481392	−	0.876505i	$-0.659869\pi$
$67$	3.23414	−	3.23414i	0.395113	−	0.395113i	0.876505	+	0.481392i	$0.159869\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			4.08803i			0.485160i	0.970131	+	0.242580i	$0.0779936\pi$
$71$			4.08803i			0.485160i	−0.970131	+	0.242580i	$0.922006\pi$
$72$		0			0
$73$	−1.91406			−0.224024			−0.112012	−	0.993707i	$-0.535730\pi$
$73$	−1.91406			−0.224024			−0.112012	+	0.993707i	$0.535730\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.86841	−	3.86841i	0.440846	−	0.440846i
$78$		0			0
$79$			8.95635i			1.00767i	0.863800	+	0.503834i	$0.168078\pi$
$79$			8.95635i			1.00767i	−0.863800	+	0.503834i	$0.831922\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.19997	−	1.19997i	−0.131714	−	0.131714i	0.638176	−	0.769890i	$-0.279689\pi$
$83$	−1.19997	−	1.19997i	−0.131714	−	0.131714i	−0.769890	+	0.638176i	$0.779689\pi$
$84$		0			0
$85$	−1.40364	−	11.3648i	−0.152246	−	1.23269i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	12.2303			1.29641			0.648207	−	0.761464i	$-0.275519\pi$
$89$	12.2303			1.29641			0.648207	+	0.761464i	$0.275519\pi$
$90$		0			0
$91$	−4.40896	+	4.40896i	−0.462185	+	0.462185i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.23684	−	10.5582i	0.845082	−	1.08324i
$96$		0			0
$97$		−	13.7776i		−	1.39890i	−0.714682	−	0.699450i	$-0.753428\pi$
$97$		−	13.7776i		−	1.39890i	0.714682	−	0.699450i	$-0.246572\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.29140	+	8.29140i	−0.825025	+	0.825025i	−0.986824	−	0.161799i	$-0.948270\pi$
$101$	−8.29140	+	8.29140i	−0.825025	+	0.825025i	0.161799	+	0.986824i	$0.448270\pi$
$102$		0			0
$103$		−	12.1337i		−	1.19557i	−0.801656	−	0.597786i	$-0.796047\pi$
$103$		−	12.1337i		−	1.19557i	0.801656	−	0.597786i	$-0.203953\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.67632	−	9.67632i	0.935445	−	0.935445i	−0.0625941	−	0.998039i	$-0.519937\pi$
$107$	9.67632	−	9.67632i	0.935445	−	0.935445i	0.998039	+	0.0625941i	$0.0199373\pi$
$108$		0			0
$109$	−10.9905	+	10.9905i	−1.05270	+	1.05270i	−0.0541632	+	0.998532i	$0.517249\pi$
$109$	−10.9905	+	10.9905i	−1.05270	+	1.05270i	−0.998532	+	0.0541632i	$0.982751\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−10.2738			−0.966478			−0.483239	−	0.875489i	$-0.660540\pi$
$113$	−10.2738			−0.966478			−0.483239	+	0.875489i	$0.660540\pi$
$114$		0			0
$115$	1.76705	+	14.3073i	0.164778	+	1.33416i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			6.77310i			0.620889i
$120$		0			0
$121$			6.10997i			0.555452i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.02895	−	10.4292i	−0.360361	−	0.932813i
$126$		0			0
$127$	−5.21363			−0.462635			−0.231317	−	0.972878i	$-0.574304\pi$
$127$	−5.21363			−0.462635			−0.231317	+	0.972878i	$0.574304\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.88036	+	5.88036i	−0.513769	+	0.513769i	−0.915679	−	0.401910i	$-0.868346\pi$
$131$	−5.88036	+	5.88036i	−0.513769	+	0.513769i	0.401910	+	0.915679i	$0.368346\pi$
$132$		0			0
$133$	−5.60063	+	5.60063i	−0.485637	+	0.485637i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	10.6048i		−	0.906033i	−0.891502	−	0.453017i	$-0.850348\pi$
$137$		−	10.6048i		−	0.906033i	0.891502	−	0.453017i	$-0.149652\pi$
$138$		0			0
$139$	3.42866	−	3.42866i	0.290815	−	0.290815i	−0.546587	−	0.837402i	$-0.684073\pi$
$139$	3.42866	−	3.42866i	0.290815	−	0.290815i	0.837402	+	0.546587i	$0.184073\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	19.5009i		−	1.63074i
$144$		0			0
$145$	8.86787	−	11.3670i	0.736436	−	0.943980i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.18888	+	2.18888i	−0.179320	+	0.179320i	−0.791059	−	0.611739i	$-0.790470\pi$
$149$	−2.18888	+	2.18888i	−0.179320	+	0.179320i	0.611739	+	0.791059i	$0.290470\pi$
$150$		0			0
$151$	−11.7775			−0.958442			−0.479221	−	0.877694i	$-0.659081\pi$
$151$	−11.7775			−0.958442			−0.479221	+	0.877694i	$0.659081\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−17.9128	+	2.21236i	−1.43879	+	0.177701i
$156$		0			0
$157$	−7.66641	−	7.66641i	−0.611846	−	0.611846i	0.331581	−	0.943427i	$-0.392418\pi$
$157$	−7.66641	−	7.66641i	−0.611846	−	0.611846i	−0.943427	+	0.331581i	$0.892418\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	8.52671i		−	0.671999i
$162$		0			0
$163$	−3.03653	+	3.03653i	−0.237839	+	0.237839i	−0.815955	−	0.578116i	$-0.803788\pi$
$163$	−3.03653	+	3.03653i	−0.237839	+	0.237839i	0.578116	+	0.815955i	$0.303788\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.87465			−0.145065			−0.0725324	−	0.997366i	$-0.523108\pi$
$167$	−1.87465			−0.145065			−0.0725324	+	0.997366i	$0.523108\pi$
$168$		0			0
$169$			9.22584i			0.709680i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.687819	+	0.687819i	−0.0522939	+	0.0522939i	−0.732770	−	0.680476i	$-0.761773\pi$
$173$	−0.687819	+	0.687819i	−0.0522939	+	0.0522939i	0.680476	+	0.732770i	$0.261773\pi$
$174$		0			0
$175$	1.60894	+	6.41419i	0.121624	+	0.484867i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.74919	+	3.74919i	−0.280227	+	0.280227i	−0.833200	−	0.552972i	$-0.813494\pi$
$179$	−3.74919	+	3.74919i	−0.280227	+	0.280227i	0.552972	+	0.833200i	$0.313494\pi$
$180$		0			0
$181$	−6.33649	−	6.33649i	−0.470987	−	0.470987i	0.431247	−	0.902234i	$-0.358074\pi$
$181$	−6.33649	−	6.33649i	−0.470987	−	0.470987i	−0.902234	+	0.431247i	$0.858074\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.4182	−	9.68795i	−0.913006	−	0.712272i
$186$		0			0
$187$	−14.9787	−	14.9787i	−1.09535	−	1.09535i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.5284			0.906526			0.453263	−	0.891377i	$-0.350260\pi$
$191$	12.5284			0.906526			0.453263	+	0.891377i	$0.350260\pi$
$192$		0			0
$193$			4.46563i			0.321443i	0.987000	+	0.160721i	$0.0513821\pi$
$193$			4.46563i			0.321443i	−0.987000	+	0.160721i	$0.948618\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	15.0440	+	15.0440i	1.07184	+	1.07184i	0.997212	+	0.0746266i	$0.0237765\pi$
$197$	15.0440	+	15.0440i	1.07184	+	1.07184i	0.0746266	+	0.997212i	$0.476224\pi$
$198$		0			0
$199$	−1.16734			−0.0827506			−0.0413753	−	0.999144i	$-0.513174\pi$
$199$	−1.16734			−0.0827506			−0.0413753	+	0.999144i	$0.513174\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.02970	+	6.02970i	−0.423202	+	0.423202i
$204$		0			0
$205$	−2.01452	−	16.3110i	−0.140700	−	1.13921i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	24.7716i		−	1.71349i
$210$		0			0
$211$	−6.32137	−	6.32137i	−0.435181	−	0.435181i	0.455205	−	0.890386i	$-0.349566\pi$
$211$	−6.32137	−	6.32137i	−0.435181	−	0.435181i	−0.890386	+	0.455205i	$0.849566\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	9.09181	−	11.6541i	0.620056	−	0.794801i
$216$		0			0
$217$	10.6755			0.724700
$218$		0			0
$219$		0			0
$220$		0			0
$221$	17.0718	+	17.0718i	1.14837	+	1.14837i
$222$		0			0
$223$	2.46749			0.165235			0.0826177	−	0.996581i	$-0.473672\pi$
$223$	2.46749			0.165235			0.0826177	+	0.996581i	$0.473672\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.46523	+	4.46523i	0.296368	+	0.296368i	0.839589	−	0.543222i	$-0.182796\pi$
$227$	4.46523	+	4.46523i	0.296368	+	0.296368i	−0.543222	+	0.839589i	$0.682796\pi$
$228$		0			0
$229$	−0.596120	−	0.596120i	−0.0393927	−	0.0393927i	0.687136	−	0.726529i	$-0.258868\pi$
$229$	−0.596120	−	0.596120i	−0.0393927	−	0.0393927i	−0.726529	+	0.687136i	$0.758868\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	10.6506i		−	0.697743i	−0.937171	−	0.348871i	$-0.886565\pi$
$233$		−	10.6506i		−	0.697743i	0.937171	−	0.348871i	$-0.113435\pi$
$234$		0			0
$235$	7.21274	−	0.890824i	0.470507	−	0.0581110i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.57734			−0.425452			−0.212726	−	0.977112i	$-0.568234\pi$
$239$	−6.57734			−0.425452			−0.212726	+	0.977112i	$0.568234\pi$
$240$		0			0
$241$	−29.7318			−1.91519			−0.957596	−	0.288114i	$-0.906972\pi$
$241$	−29.7318			−1.91519			−0.957596	+	0.288114i	$0.906972\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.43917	+	11.6526i	0.0919454	+	0.744455i
$246$		0			0
$247$			28.2331i			1.79643i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.1656	−	12.1656i	−0.767887	−	0.767887i	0.209848	−	0.977734i	$-0.432703\pi$
$251$	−12.1656	−	12.1656i	−0.767887	−	0.767887i	−0.977734	+	0.209848i	$0.932703\pi$
$252$		0			0
$253$	18.8568	+	18.8568i	1.18552	+	1.18552i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.37446			0.397628			0.198814	−	0.980037i	$-0.436291\pi$
$257$	6.37446			0.397628			0.198814	+	0.980037i	$0.436291\pi$
$258$		0			0
$259$	6.58731	+	6.58731i	0.409316	+	0.409316i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.9280			0.797175			0.398588	−	0.917130i	$-0.369501\pi$
$263$	12.9280			0.797175			0.398588	+	0.917130i	$0.369501\pi$
$264$		0			0
$265$	−0.0835755	+	0.107129i	−0.00513400	+	0.00658087i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	16.1824	+	16.1824i	0.986659	+	0.986659i	0.999912	−	0.0132534i	$-0.00421880\pi$
$269$	16.1824	+	16.1824i	0.986659	+	0.986659i	−0.0132534	+	0.999912i	$0.504219\pi$
$270$		0			0
$271$			12.5692i			0.763523i	0.924261	+	0.381761i	$0.124682\pi$
$271$			12.5692i			0.763523i	−0.924261	+	0.381761i	$0.875318\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−17.7432	−	10.6268i	−1.06995	−	0.640821i
$276$		0			0
$277$	−16.5250	+	16.5250i	−0.992890	+	0.992890i	−0.999975	−	0.00708488i	$-0.997745\pi$
$277$	−16.5250	+	16.5250i	−0.992890	+	0.992890i	0.00708488	+	0.999975i	$0.497745\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	25.4126			1.51599			0.757994	−	0.652261i	$-0.226180\pi$
$281$	25.4126			1.51599			0.757994	+	0.652261i	$0.226180\pi$
$282$		0			0
$283$	−21.8370	−	21.8370i	−1.29807	−	1.29807i	−0.929663	−	0.368410i	$-0.879902\pi$
$283$	−21.8370	−	21.8370i	−1.29807	−	1.29807i	−0.368410	−	0.929663i	$-0.620098\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			9.72085i			0.573804i
$288$		0			0
$289$	9.22584			0.542697
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.0918390	−	0.0918390i	−0.00536529	−	0.00536529i	0.704419	−	0.709784i	$-0.251208\pi$
$293$	−0.0918390	−	0.0918390i	−0.00536529	−	0.00536529i	−0.709784	+	0.704419i	$0.751208\pi$
$294$		0			0
$295$	16.3911	−	21.0104i	0.954324	−	1.22327i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−21.4918	−	21.4918i	−1.24290	−	1.24290i
$300$		0			0
$301$	−6.18197	+	6.18197i	−0.356323	+	0.356323i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.50942	−	3.51798i	−0.258209	−	0.201439i
$306$		0			0
$307$	−13.2141	+	13.2141i	−0.754170	+	0.754170i	−0.975255	−	0.221085i	$-0.929040\pi$
$307$	−13.2141	+	13.2141i	−0.754170	+	0.754170i	0.221085	+	0.975255i	$0.429040\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			28.4185i			1.61147i	0.592279	+	0.805733i	$0.298229\pi$
$311$			28.4185i			1.61147i	−0.592279	+	0.805733i	$0.701771\pi$
$312$		0			0
$313$	−10.0449			−0.567770			−0.283885	−	0.958858i	$-0.591623\pi$
$313$	−10.0449			−0.567770			−0.283885	+	0.958858i	$0.591623\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	18.1322	−	18.1322i	1.01841	−	1.01841i	0.0185812	−	0.999827i	$-0.494085\pi$
$317$	18.1322	−	18.1322i	1.01841	−	1.01841i	0.999827	−	0.0185812i	$-0.00591494\pi$
$318$		0			0
$319$		−	26.6694i		−	1.49320i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	21.6860	+	21.6860i	1.20664	+	1.20664i
$324$		0			0
$325$	20.2225	+	12.1118i	1.12174	+	0.671841i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−4.29858			−0.236988
$330$		0			0
$331$	9.58521	−	9.58521i	0.526851	−	0.526851i	−0.392781	−	0.919632i	$-0.628487\pi$
$331$	9.58521	−	9.58521i	0.526851	−	0.526851i	0.919632	+	0.392781i	$0.128487\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	8.06366	+	6.29078i	0.440565	+	0.343702i
$336$		0			0
$337$		−	10.6389i		−	0.579540i	−0.957096	−	0.289770i	$-0.906421\pi$
$337$		−	10.6389i		−	0.579540i	0.957096	−	0.289770i	$-0.0935789\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−23.6089	+	23.6089i	−1.27849	+	1.27849i
$342$		0			0
$343$		−	16.2027i		−	0.874861i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−24.3001	+	24.3001i	−1.30450	+	1.30450i	−0.379168	+	0.925328i	$0.623790\pi$
$347$	−24.3001	+	24.3001i	−1.30450	+	1.30450i	−0.925328	+	0.379168i	$0.876210\pi$
$348$		0			0
$349$	7.04357	−	7.04357i	0.377034	−	0.377034i	−0.492997	−	0.870031i	$-0.664099\pi$
$349$	7.04357	−	7.04357i	0.377034	−	0.377034i	0.870031	+	0.492997i	$0.164099\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−18.7589			−0.998437			−0.499219	−	0.866476i	$-0.666380\pi$
$353$	−18.7589			−0.998437			−0.499219	+	0.866476i	$0.666380\pi$
$354$		0			0
$355$	−9.07218	+	1.12048i	−0.481501	+	0.0594688i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	24.3658i		−	1.28598i	−0.765877	−	0.642988i	$-0.777695\pi$
$359$		−	24.3658i		−	1.28598i	0.765877	−	0.642988i	$-0.222305\pi$
$360$		0			0
$361$			16.8641i			0.887582i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.524621	−	4.24770i	−0.0274599	−	0.222335i
$366$		0			0
$367$	27.9727			1.46016			0.730081	−	0.683360i	$-0.239482\pi$
$367$	27.9727			1.46016			0.730081	+	0.683360i	$0.239482\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.0568271	−	0.0568271i	0.00295032	−	0.00295032i
$372$		0			0
$373$	−8.02099	+	8.02099i	−0.415311	+	0.415311i	−0.883584	−	0.468273i	$-0.844876\pi$
$373$	−8.02099	+	8.02099i	−0.415311	+	0.415311i	0.468273	+	0.883584i	$0.344876\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			30.3961i			1.56548i
$378$		0			0
$379$	15.0759	−	15.0759i	0.774397	−	0.774397i	−0.204475	−	0.978872i	$-0.565549\pi$
$379$	15.0759	−	15.0759i	0.774397	−	0.774397i	0.978872	+	0.204475i	$0.0655487\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$			15.2314i			0.778287i	0.921177	+	0.389143i	$0.127229\pi$
$383$			15.2314i			0.778287i	−0.921177	+	0.389143i	$0.872771\pi$
$384$		0			0
$385$	9.64507	+	7.52451i	0.491558	+	0.383484i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.98674	+	7.98674i	−0.404944	+	0.404944i	−0.879971	−	0.475027i	$-0.842438\pi$
$389$	−7.98674	+	7.98674i	−0.404944	+	0.404944i	0.475027	+	0.879971i	$0.342438\pi$
$390$		0			0
$391$	−33.0159			−1.66969
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−19.8760	+	2.45483i	−1.00007	+	0.123516i
$396$		0			0
$397$	−4.46660	−	4.46660i	−0.224172	−	0.224172i	0.586081	−	0.810253i	$-0.300670\pi$
$397$	−4.46660	−	4.46660i	−0.224172	−	0.224172i	−0.810253	+	0.586081i	$0.800670\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			23.0409i			1.15061i	0.817939	+	0.575304i	$0.195116\pi$
$401$			23.0409i			1.15061i	−0.817939	+	0.575304i	$0.804884\pi$
$402$		0			0
$403$	26.9079	−	26.9079i	1.34038	−	1.34038i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−29.1357			−1.44420
$408$		0			0
$409$			15.7543i			0.778999i	0.921027	+	0.389500i	$0.127352\pi$
$409$			15.7543i			0.778999i	−0.921027	+	0.389500i	$0.872648\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−11.1451	+	11.1451i	−0.548414	+	0.548414i
$414$		0			0
$415$	2.33408	−	2.99188i	0.114576	−	0.146865i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.26899	+	6.26899i	−0.306260	+	0.306260i	−0.843457	−	0.537197i	$-0.819483\pi$
$419$	−6.26899	+	6.26899i	−0.306260	+	0.306260i	0.537197	+	0.843457i	$0.319483\pi$
$420$		0			0
$421$	−26.4935	−	26.4935i	−1.29121	−	1.29121i	−0.934036	−	0.357178i	$-0.883739\pi$
$421$	−26.4935	−	26.4935i	−1.29121	−	1.29121i	−0.357178	−	0.934036i	$-0.616261\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	24.8361	−	6.22991i	1.20473	−	0.302195i
$426$		0			0
$427$	2.39205	+	2.39205i	0.115759	+	0.115759i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	17.3701			0.836686			0.418343	−	0.908289i	$-0.362611\pi$
$431$	17.3701			0.836686			0.418343	+	0.908289i	$0.362611\pi$
$432$		0			0
$433$			18.7561i			0.901361i	0.892685	+	0.450681i	$0.148819\pi$
$433$			18.7561i			0.901361i	−0.892685	+	0.450681i	$0.851181\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−27.3007	−	27.3007i	−1.30597	−	1.30597i
$438$		0			0
$439$	6.87959			0.328345			0.164173	−	0.986432i	$-0.447505\pi$
$439$	6.87959			0.328345			0.164173	+	0.986432i	$0.447505\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.1064	−	11.1064i	0.527680	−	0.527680i	−0.392200	−	0.919880i	$-0.628286\pi$
$443$	11.1064	−	11.1064i	0.527680	−	0.527680i	0.919880	+	0.392200i	$0.128286\pi$
$444$		0			0
$445$	3.35219	+	27.1417i	0.158909	+	1.28664i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	0.0943911i		−	0.00445459i	−0.999998	−	0.00222730i	$-0.999291\pi$
$449$		−	0.0943911i		−	0.00445459i	0.999998	−	0.00222730i	$-0.000708971\pi$
$450$		0			0
$451$	−21.4977	−	21.4977i	−1.01229	−	1.01229i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−10.9928	−	8.57596i	−0.515352	−	0.402047i
$456$		0			0
$457$	36.7622			1.71966			0.859831	−	0.510578i	$-0.170569\pi$
$457$	36.7622			1.71966			0.859831	+	0.510578i	$0.170569\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.442141	−	0.442141i	−0.0205926	−	0.0205926i	0.696736	−	0.717328i	$-0.254635\pi$
$461$	−0.442141	−	0.442141i	−0.0205926	−	0.0205926i	−0.717328	+	0.696736i	$0.754635\pi$
$462$		0			0
$463$	−13.7679			−0.639848			−0.319924	−	0.947443i	$-0.603657\pi$
$463$	−13.7679			−0.639848			−0.319924	+	0.947443i	$0.603657\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.48388	−	2.48388i	−0.114940	−	0.114940i	0.647297	−	0.762238i	$-0.275899\pi$
$467$	−2.48388	−	2.48388i	−0.114940	−	0.114940i	−0.762238	+	0.647297i	$0.775899\pi$
$468$		0			0
$469$	−4.27741	−	4.27741i	−0.197513	−	0.197513i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	27.3429i		−	1.25723i
$474$		0			0
$475$	25.6883	+	15.3854i	1.17866	+	0.705930i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	24.0177			1.09739			0.548697	−	0.836021i	$-0.315124\pi$
$479$	24.0177			1.09739			0.548697	+	0.836021i	$0.315124\pi$
$480$		0			0
$481$	33.2070			1.51411
$482$		0			0
$483$		0			0
$484$		0			0
$485$	30.5753	−	3.77626i	1.38835	−	0.171471i
$486$		0			0
$487$			26.4735i			1.19963i	0.800139	+	0.599815i	$0.204759\pi$
$487$			26.4735i			1.19963i	−0.800139	+	0.599815i	$0.795241\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	24.5287	+	24.5287i	1.10697	+	1.10697i	0.993547	+	0.113419i	$0.0361804\pi$
$491$	24.5287	+	24.5287i	1.10697	+	1.10697i	0.113419	+	0.993547i	$0.463820\pi$
$492$		0			0
$493$	23.3474	+	23.3474i	1.05151	+	1.05151i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	5.40675			0.242526
$498$		0			0
$499$	9.49544	+	9.49544i	0.425074	+	0.425074i	0.886946	−	0.461872i	$-0.152822\pi$
$499$	9.49544	+	9.49544i	0.425074	+	0.425074i	−0.461872	+	0.886946i	$0.652822\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	31.4506			1.40232			0.701158	−	0.713006i	$-0.252667\pi$
$503$	31.4506			1.40232			0.701158	+	0.713006i	$0.252667\pi$
$504$		0			0
$505$	−20.6729	−	16.1278i	−0.919932	−	0.717676i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.7518	−	13.7518i	−0.609539	−	0.609539i	0.333286	−	0.942826i	$-0.391842\pi$
$509$	−13.7518	−	13.7518i	−0.609539	−	0.609539i	−0.942826	+	0.333286i	$0.891842\pi$
$510$		0			0
$511$			2.53150i			0.111987i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	26.9272	−	3.32571i	1.18656	−	0.146548i
$516$		0			0
$517$	9.50631	−	9.50631i	0.418087	−	0.418087i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	11.9557			0.523790			0.261895	−	0.965096i	$-0.415653\pi$
$521$	11.9557			0.523790			0.261895	+	0.965096i	$0.415653\pi$
$522$		0			0
$523$	29.1281	+	29.1281i	1.27368	+	1.27368i	0.944141	+	0.329542i	$0.106894\pi$
$523$	29.1281	+	29.1281i	1.27368	+	1.27368i	0.329542	+	0.944141i	$0.393106\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	41.3362i		−	1.80063i
$528$		0			0
$529$	18.5641			0.807133
$530$		0			0
$531$		0			0
$532$		0			0
$533$	24.5017	+	24.5017i	1.06129	+	1.06129i
$534$		0			0
$535$	24.1259	+	18.8216i	1.04305	+	0.813728i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	15.3580	+	15.3580i	0.661514	+	0.661514i
$540$		0			0
$541$	−13.9033	+	13.9033i	−0.597751	+	0.597751i	−0.939713	−	0.341963i	$-0.888908\pi$
$541$	−13.9033	+	13.9033i	−0.597751	+	0.597751i	0.341963	+	0.939713i	$0.388908\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−27.4024	−	21.3777i	−1.17379	−	0.915722i
$546$		0			0
$547$	22.5790	−	22.5790i	0.965407	−	0.965407i	−0.0340143	−	0.999421i	$-0.510829\pi$
$547$	22.5790	−	22.5790i	0.965407	−	0.965407i	0.999421	+	0.0340143i	$0.0108292\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			38.6116i			1.64491i
$552$		0			0
$553$	11.8455			0.503722
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−10.3111	+	10.3111i	−0.436897	+	0.436897i	−0.890966	−	0.454070i	$-0.849972\pi$
$557$	−10.3111	+	10.3111i	−0.436897	+	0.436897i	0.454070	+	0.890966i	$0.349972\pi$
$558$		0			0
$559$			31.1637i			1.31808i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−19.7272	−	19.7272i	−0.831400	−	0.831400i	0.156308	−	0.987708i	$-0.450041\pi$
$563$	−19.7272	−	19.7272i	−0.831400	−	0.831400i	−0.987708	+	0.156308i	$0.950041\pi$
$564$		0			0
$565$	−2.81592	−	22.7997i	−0.118467	−	0.959190i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−7.99659			−0.335234			−0.167617	−	0.985852i	$-0.553607\pi$
$569$	−7.99659			−0.335234			−0.167617	+	0.985852i	$0.553607\pi$
$570$		0			0
$571$	−9.69845	+	9.69845i	−0.405868	+	0.405868i	−0.880295	−	0.474427i	$-0.842655\pi$
$571$	−9.69845	+	9.69845i	−0.405868	+	0.405868i	0.474427	+	0.880295i	$0.342655\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−31.2664	+	7.84289i	−1.30390	+	0.327071i
$576$		0			0
$577$		−	15.9701i		−	0.664845i	−0.943131	−	0.332423i	$-0.892134\pi$
$577$		−	15.9701i		−	0.664845i	0.943131	−	0.332423i	$-0.107866\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.58706	+	1.58706i	−0.0658422	+	0.0658422i
$582$		0			0
$583$			0.251346i			0.0104097i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.63137	−	4.63137i	0.191157	−	0.191157i	−0.605039	−	0.796196i	$-0.706842\pi$
$587$	4.63137	−	4.63137i	0.191157	−	0.191157i	0.796196	+	0.605039i	$0.206842\pi$
$588$		0			0
$589$	34.1807	−	34.1807i	1.40839	−	1.40839i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.72897			−0.0710002			−0.0355001	−	0.999370i	$-0.511302\pi$
$593$	−1.72897			−0.0710002			−0.0355001	+	0.999370i	$0.511302\pi$
$594$		0			0
$595$	−15.0309	+	1.85642i	−0.616207	+	0.0761059i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			1.82848i			0.0747098i	0.999302	+	0.0373549i	$0.0118932\pi$
$599$			1.82848i			0.0747098i	−0.999302	+	0.0373549i	$0.988107\pi$
$600$		0			0
$601$		−	34.0274i		−	1.38801i	−0.719972	−	0.694003i	$-0.755846\pi$
$601$		−	34.0274i		−	1.38801i	0.719972	−	0.694003i	$-0.244154\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−13.5593	+	1.67467i	−0.551263	+	0.0680849i
$606$		0			0
$607$	18.8893			0.766694			0.383347	−	0.923604i	$-0.374771\pi$
$607$	18.8893			0.766694			0.383347	+	0.923604i	$0.374771\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−10.8347	+	10.8347i	−0.438325	+	0.438325i
$612$		0			0
$613$	5.65497	−	5.65497i	0.228402	−	0.228402i	−0.583623	−	0.812025i	$-0.698365\pi$
$613$	5.65497	−	5.65497i	0.228402	−	0.228402i	0.812025	+	0.583623i	$0.198365\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			26.8434i			1.08068i	0.841448	+	0.540338i	$0.181703\pi$
$617$			26.8434i			1.08068i	−0.841448	+	0.540338i	$0.818297\pi$
$618$		0			0
$619$	7.64371	−	7.64371i	0.307227	−	0.307227i	−0.536606	−	0.843833i	$-0.680294\pi$
$619$	7.64371	−	7.64371i	0.307227	−	0.307227i	0.843833	+	0.536606i	$0.180294\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	16.1756i		−	0.648063i
$624$		0			0
$625$	22.0402	−	11.7996i	0.881607	−	0.471983i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	25.5065	−	25.5065i	1.01701	−	1.01701i
$630$		0			0
$631$	36.7657			1.46362			0.731810	−	0.681509i	$-0.238676\pi$
$631$	36.7657			1.46362			0.731810	+	0.681509i	$0.238676\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.42899	−	11.5701i	−0.0567078	−	0.459146i
$636$		0			0
$637$	−17.5040	−	17.5040i	−0.693535	−	0.693535i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			42.4609i			1.67710i	0.544823	+	0.838551i	$0.316597\pi$
$641$			42.4609i			1.67710i	−0.544823	+	0.838551i	$0.683403\pi$
$642$		0			0
$643$	−23.2113	+	23.2113i	−0.915363	+	0.915363i	−0.996688	−	0.0813247i	$-0.974085\pi$
$643$	−23.2113	+	23.2113i	−0.915363	+	0.915363i	0.0813247	+	0.996688i	$0.474085\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−3.32710			−0.130802			−0.0654009	−	0.997859i	$-0.520833\pi$
$647$	−3.32710			−0.130802			−0.0654009	+	0.997859i	$0.520833\pi$
$648$		0			0
$649$		−	49.2947i		−	1.93499i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.27095	+	4.27095i	−0.167135	+	0.167135i	−0.785719	−	0.618584i	$-0.787707\pi$
$653$	−4.27095	+	4.27095i	−0.167135	+	0.167135i	0.618584	+	0.785719i	$0.287707\pi$
$654$		0			0
$655$	−14.6615	−	11.4380i	−0.572870	−	0.446919i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	14.6143	−	14.6143i	0.569290	−	0.569290i	−0.362639	−	0.931930i	$-0.618124\pi$
$659$	14.6143	−	14.6143i	0.569290	−	0.569290i	0.931930	+	0.362639i	$0.118124\pi$
$660$		0			0
$661$	22.1543	+	22.1543i	0.861702	+	0.861702i	0.991536	−	0.129834i	$-0.0414443\pi$
$661$	22.1543	+	22.1543i	0.861702	+	0.861702i	−0.129834	+	0.991536i	$0.541444\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−13.9640	−	10.8939i	−0.541502	−	0.422447i
$666$		0			0
$667$	−29.3922	−	29.3922i	−1.13807	−	1.13807i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−10.5800			−0.408438
$672$		0			0
$673$			21.7529i			0.838514i	0.907868	+	0.419257i	$0.137709\pi$
$673$			21.7529i			0.838514i	−0.907868	+	0.419257i	$0.862291\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−24.9075	−	24.9075i	−0.957273	−	0.957273i	0.0418508	−	0.999124i	$-0.486675\pi$
$677$	−24.9075	−	24.9075i	−0.957273	−	0.957273i	−0.999124	+	0.0418508i	$0.986675\pi$
$678$		0			0
$679$	−18.2220			−0.699294
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−23.0233	+	23.0233i	−0.880962	+	0.880962i	−0.993632	−	0.112671i	$-0.964059\pi$
$683$	−23.0233	+	23.0233i	−0.880962	+	0.880962i	0.112671	+	0.993632i	$0.464059\pi$
$684$		0			0
$685$	23.5343	−	2.90666i	0.899201	−	0.111058i
$686$		0			0
$687$		0			0
$688$		0			0
$689$		−	0.286469i		−	0.0109136i
$690$		0			0
$691$	25.0683	+	25.0683i	0.953642	+	0.953642i	0.998972	−	0.0453303i	$-0.0144340\pi$
$691$	25.0683	+	25.0683i	0.953642	+	0.953642i	−0.0453303	+	0.998972i	$0.514434\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	8.54864	+	6.66914i	0.324269	+	0.252975i
$696$		0			0
$697$	37.6397			1.42571
$698$		0			0
$699$		0			0
$700$		0			0
$701$	29.3580	+	29.3580i	1.10884	+	1.10884i	0.993304	+	0.115531i	$0.0368571\pi$
$701$	29.3580	+	29.3580i	1.10884	+	1.10884i	0.115531	+	0.993304i	$0.463143\pi$
$702$		0			0
$703$	42.1823			1.59094
$704$		0			0
$705$		0			0
$706$		0			0
$707$	10.9661	+	10.9661i	0.412421	+	0.412421i
$708$		0			0
$709$	−6.79674	−	6.79674i	−0.255257	−	0.255257i	0.567865	−	0.823122i	$-0.307770\pi$
$709$	−6.79674	−	6.79674i	−0.255257	−	0.255257i	−0.823122	+	0.567865i	$0.807770\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			52.0385i			1.94886i
$714$		0			0
$715$	43.2764	−	5.34495i	1.61845	−	0.199890i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	27.6311			1.03047			0.515233	−	0.857050i	$-0.327705\pi$
$719$	27.6311			1.03047			0.515233	+	0.857050i	$0.327705\pi$
$720$		0			0
$721$	−16.0478			−0.597653
$722$		0			0
$723$		0			0
$724$		0			0
$725$	27.6563	+	16.5641i	1.02713	+	0.615174i
$726$		0			0
$727$			45.4745i			1.68656i	0.537478	+	0.843278i	$0.319377\pi$
$727$			45.4745i			1.68656i	−0.537478	+	0.843278i	$0.680623\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	23.9370	+	23.9370i	0.885340	+	0.885340i
$732$		0			0
$733$	−19.3242	−	19.3242i	−0.713757	−	0.713757i	0.253562	−	0.967319i	$-0.418398\pi$
$733$	−19.3242	−	19.3242i	−0.713757	−	0.713757i	−0.967319	+	0.253562i	$0.918398\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	18.9190			0.696890
$738$		0			0
$739$	−20.6097	−	20.6097i	−0.758140	−	0.758140i	0.217844	−	0.975984i	$-0.430098\pi$
$739$	−20.6097	−	20.6097i	−0.758140	−	0.758140i	−0.975984	+	0.217844i	$0.930098\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−24.9720			−0.916134			−0.458067	−	0.888918i	$-0.651458\pi$
$743$	−24.9720			−0.916134			−0.458067	+	0.888918i	$0.651458\pi$
$744$		0			0
$745$	−5.45752	−	4.25763i	−0.199948	−	0.155987i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−12.7977	−	12.7977i	−0.467618	−	0.467618i
$750$		0			0
$751$		−	17.1846i		−	0.627077i	−0.949576	−	0.313538i	$-0.898486\pi$
$751$		−	17.1846i		−	0.627077i	0.949576	−	0.313538i	$-0.101514\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−3.22808	−	26.1368i	−0.117482	−	0.951215i
$756$		0			0
$757$	−11.4284	+	11.4284i	−0.415373	+	0.415373i	−0.883605	−	0.468233i	$-0.844891\pi$
$757$	−11.4284	+	11.4284i	−0.415373	+	0.415373i	0.468233	+	0.883605i	$0.344891\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.21731			−0.334127			−0.167064	−	0.985946i	$-0.553428\pi$
$761$	−9.21731			−0.334127			−0.167064	+	0.985946i	$0.553428\pi$
$762$		0			0
$763$	14.5358	+	14.5358i	0.526231	+	0.526231i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			56.1830i			2.02865i
$768$		0			0
$769$	−37.2893			−1.34469			−0.672343	−	0.740239i	$-0.734712\pi$
$769$	−37.2893			−1.34469			−0.672343	+	0.740239i	$0.734712\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6.76428	−	6.76428i	−0.243294	−	0.243294i	0.574917	−	0.818211i	$-0.305034\pi$
$773$	−6.76428	−	6.76428i	−0.243294	−	0.243294i	−0.818211	+	0.574917i	$0.805034\pi$
$774$		0			0
$775$	−9.81936	−	39.1458i	−0.352722	−	1.40616i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	31.1241	+	31.1241i	1.11514	+	1.11514i
$780$		0			0
$781$	−11.9570	+	11.9570i	−0.427856	+	0.427856i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	14.9121	−	19.1146i	0.532235	−	0.682229i
$786$		0			0
$787$	10.7179	−	10.7179i	0.382054	−	0.382054i	−0.489788	−	0.871842i	$-0.662926\pi$
$787$	10.7179	−	10.7179i	0.382054	−	0.382054i	0.871842	+	0.489788i	$0.162926\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			13.5879i			0.483131i
$792$		0			0
$793$	12.0584			0.428208
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−16.6229	+	16.6229i	−0.588813	+	0.588813i	−0.937310	−	0.348497i	$-0.886692\pi$
$797$	−16.6229	+	16.6229i	−0.588813	+	0.588813i	0.348497	+	0.937310i	$0.386692\pi$
$798$		0			0
$799$			16.6444i			0.588835i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.59842	−	5.59842i	−0.197564	−	0.197564i
$804$		0			0
$805$	18.9225	−	2.33707i	0.666931	−	0.0823708i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−16.6458			−0.585235			−0.292618	−	0.956230i	$-0.594526\pi$
$809$	−16.6458			−0.585235			−0.292618	+	0.956230i	$0.594526\pi$
$810$		0			0
$811$	−23.0710	+	23.0710i	−0.810133	+	0.810133i	−0.984653	−	0.174521i	$-0.944162\pi$
$811$	−23.0710	+	23.0710i	−0.810133	+	0.810133i	0.174521	+	0.984653i	$0.444162\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−7.57095	−	5.90641i	−0.265199	−	0.206892i
$816$		0			0
$817$			39.5867i			1.38496i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	11.6527	−	11.6527i	0.406681	−	0.406681i	−0.473898	−	0.880580i	$-0.657154\pi$
$821$	11.6527	−	11.6527i	0.406681	−	0.406681i	0.880580	+	0.473898i	$0.157154\pi$
$822$		0			0
$823$		−	8.56619i		−	0.298599i	−0.988792	−	0.149299i	$-0.952298\pi$
$823$		−	8.56619i		−	0.298599i	0.988792	−	0.149299i	$-0.0477018\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	35.0881	−	35.0881i	1.22013	−	1.22013i	0.252549	−	0.967584i	$-0.418731\pi$
$827$	35.0881	−	35.0881i	1.22013	−	1.22013i	0.967584	−	0.252549i	$-0.0812690\pi$
$828$		0			0
$829$	4.58609	−	4.58609i	0.159282	−	0.159282i	−0.622967	−	0.782248i	$-0.714073\pi$
$829$	4.58609	−	4.58609i	0.159282	−	0.159282i	0.782248	+	0.622967i	$0.214073\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−26.8899			−0.931678
$834$		0			0
$835$	−0.513818	−	4.16023i	−0.0177814	−	0.143971i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			1.91127i			0.0659844i	0.999456	+	0.0329922i	$0.0105036\pi$
$839$			1.91127i			0.0659844i	−0.999456	+	0.0329922i	$0.989496\pi$
$840$		0			0
$841$			12.5697i			0.433436i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−20.4741	+	2.52869i	−0.704329	+	0.0869896i
$846$		0			0
$847$	8.08093			0.277664
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−32.1103	+	32.1103i	−1.10073	+	1.10073i
$852$		0			0
$853$	11.8229	−	11.8229i	0.404810	−	0.404810i	−0.475114	−	0.879924i	$-0.657593\pi$
$853$	11.8229	−	11.8229i	0.404810	−	0.404810i	0.879924	+	0.475114i	$0.157593\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			17.3781i			0.593626i	0.954936	+	0.296813i	$0.0959238\pi$
$857$			17.3781i			0.593626i	−0.954936	+	0.296813i	$0.904076\pi$
$858$		0			0
$859$	−17.1261	+	17.1261i	−0.584335	+	0.584335i	−0.936091	−	0.351757i	$-0.885584\pi$
$859$	−17.1261	+	17.1261i	−0.584335	+	0.584335i	0.351757	+	0.936091i	$0.385584\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			38.5030i			1.31066i	0.755343	+	0.655329i	$0.227470\pi$
$863$			38.5030i			1.31066i	−0.755343	+	0.655329i	$0.772530\pi$
$864$		0			0
$865$	−1.71494	−	1.33789i	−0.0583096	−	0.0454896i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−26.1963	+	26.1963i	−0.888650	+	0.888650i
$870$		0			0
$871$	−21.5627			−0.730624
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−13.7934	+	5.32862i	−0.466303	+	0.180140i
$876$		0			0
$877$	11.7948	+	11.7948i	0.398281	+	0.398281i	0.877626	−	0.479345i	$-0.159126\pi$
$877$	11.7948	+	11.7948i	0.398281	+	0.398281i	−0.479345	+	0.877626i	$0.659126\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			5.24104i			0.176575i	0.996095	+	0.0882876i	$0.0281394\pi$
$881$			5.24104i			0.176575i	−0.996095	+	0.0882876i	$0.971861\pi$
$882$		0			0
$883$	−33.9641	+	33.9641i	−1.14298	+	1.14298i	−0.155081	+	0.987902i	$0.549564\pi$
$883$	−33.9641	+	33.9641i	−1.14298	+	1.14298i	−0.987902	+	0.155081i	$0.950436\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−47.5764			−1.59746			−0.798730	−	0.601690i	$-0.794494\pi$
$887$	−47.5764			−1.59746			−0.798730	+	0.601690i	$0.794494\pi$
$888$		0			0
$889$			6.89545i			0.231266i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−13.7631	+	13.7631i	−0.460566	+	0.460566i
$894$		0			0
$895$	−9.34783	−	7.29261i	−0.312463	−	0.243765i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	36.7993	−	36.7993i	1.22732	−	1.22732i
$900$		0			0
$901$	−0.220038	−	0.220038i	−0.00733053	−	0.00733053i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	12.3252	−	15.7987i	0.409704	−	0.525167i
$906$		0			0
$907$	−0.839751	−	0.839751i	−0.0278835	−	0.0278835i	0.693028	−	0.720911i	$-0.256276\pi$
$907$	−0.839751	−	0.839751i	−0.0278835	−	0.0278835i	−0.720911	+	0.693028i	$0.756276\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−34.6744			−1.14882			−0.574408	−	0.818569i	$-0.694768\pi$
$911$	−34.6744			−1.14882			−0.574408	+	0.818569i	$0.694768\pi$
$912$		0			0
$913$		−	7.01956i		−	0.232314i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.77725	+	7.77725i	0.256827	+	0.256827i
$918$		0			0
$919$	46.8748			1.54626			0.773129	−	0.634249i	$-0.218691\pi$
$919$	46.8748			1.54626			0.773129	+	0.634249i	$0.218691\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	13.6279	−	13.6279i	0.448567	−	0.448567i
$924$		0			0
$925$	18.0959	−	30.2139i	0.594989	−	0.993428i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	0.245775i		−	0.00806362i	−0.999992	−	0.00403181i	$-0.998717\pi$
$929$		−	0.245775i		−	0.00806362i	0.999992	−	0.00403181i	$-0.00128337\pi$
$930$		0			0
$931$	−22.2351	−	22.2351i	−0.728725	−	0.728725i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	29.1354	−	37.3463i	0.952828	−	1.22136i
$936$		0			0
$937$	−32.2193			−1.05256			−0.526279	−	0.850312i	$-0.676413\pi$
$937$	−32.2193			−1.05256			−0.526279	+	0.850312i	$0.676413\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.05423	+	2.05423i	0.0669660	+	0.0669660i	0.739797	−	0.672831i	$-0.234922\pi$
$941$	2.05423	+	2.05423i	0.0669660	+	0.0669660i	−0.672831	+	0.739797i	$0.734922\pi$
$942$		0			0
$943$	−47.3850			−1.54307
$944$		0			0
$945$		0			0
$946$		0			0
$947$	31.9491	+	31.9491i	1.03820	+	1.03820i	0.999241	+	0.0389644i	$0.0124059\pi$
$947$	31.9491	+	31.9491i	1.03820	+	1.03820i	0.0389644	+	0.999241i	$0.487594\pi$
$948$		0			0
$949$	6.38073	+	6.38073i	0.207127	+	0.207127i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	0.615266i		−	0.0199304i	−0.999950	−	0.00996521i	$-0.996828\pi$
$953$		−	0.615266i		−	0.0199304i	0.999950	−	0.00996521i	$-0.00317208\pi$
$954$		0			0
$955$	3.43389	+	27.8032i	0.111118	+	0.899690i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−14.0258			−0.452916
$960$		0			0
$961$	−34.1526			−1.10170
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−9.91014	+	1.22397i	−0.319019	+	0.0394011i
$966$		0			0
$967$			20.2322i			0.650625i	0.945607	+	0.325312i	$0.105469\pi$
$967$			20.2322i			0.650625i	−0.945607	+	0.325312i	$0.894531\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	19.5255	+	19.5255i	0.626603	+	0.626603i	0.947212	−	0.320609i	$-0.103887\pi$
$971$	19.5255	+	19.5255i	0.626603	+	0.626603i	−0.320609	+	0.947212i	$0.603887\pi$
$972$		0			0
$973$	−4.53468	−	4.53468i	−0.145375	−	0.145375i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.86357			−0.251578			−0.125789	−	0.992057i	$-0.540146\pi$
$977$	−7.86357			−0.251578			−0.125789	+	0.992057i	$0.540146\pi$
$978$		0			0
$979$	35.7724	+	35.7724i	1.14329	+	1.14329i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−4.22528			−0.134765			−0.0673827	−	0.997727i	$-0.521465\pi$
$983$	−4.22528			−0.134765			−0.0673827	+	0.997727i	$0.521465\pi$
$984$		0			0
$985$	−29.2623	+	37.5090i	−0.932374	+	1.19514i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−30.1345	−	30.1345i	−0.958220	−	0.958220i
$990$		0			0
$991$		−	46.9958i		−	1.49287i	−0.665457	−	0.746436i	$-0.731763\pi$
$991$		−	46.9958i		−	1.49287i	0.665457	−	0.746436i	$-0.268237\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.319954	−	2.59057i	−0.0101432	−	0.0821266i
$996$		0			0
$997$	−42.2361	+	42.2361i	−1.33763	+	1.33763i	−0.439281	+	0.898349i	$0.644767\pi$
$997$	−42.2361	+	42.2361i	−1.33763	+	1.33763i	−0.898349	+	0.439281i	$0.855233\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2880.2.u.a.719.27		96
3.2	odd	2	inner	2880.2.u.a.719.22		96
4.3	odd	2		720.2.u.a.539.23	yes	96
5.4	even	2	inner	2880.2.u.a.719.3		96
12.11	even	2		720.2.u.a.539.26	yes	96
15.14	odd	2	inner	2880.2.u.a.719.46		96
16.3	odd	4	inner	2880.2.u.a.2159.46		96
16.13	even	4		720.2.u.a.179.24	yes	96
20.19	odd	2		720.2.u.a.539.25	yes	96
48.29	odd	4		720.2.u.a.179.25	yes	96
48.35	even	4	inner	2880.2.u.a.2159.3		96
60.59	even	2		720.2.u.a.539.24	yes	96
80.19	odd	4	inner	2880.2.u.a.2159.22		96
80.29	even	4		720.2.u.a.179.26	yes	96
240.29	odd	4		720.2.u.a.179.23	✓	96
240.179	even	4	inner	2880.2.u.a.2159.27		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.23	✓	96	240.29	odd	4
720.2.u.a.179.24	yes	96	16.13	even	4
720.2.u.a.179.25	yes	96	48.29	odd	4
720.2.u.a.179.26	yes	96	80.29	even	4
720.2.u.a.539.23	yes	96	4.3	odd	2
720.2.u.a.539.24	yes	96	60.59	even	2
720.2.u.a.539.25	yes	96	20.19	odd	2
720.2.u.a.539.26	yes	96	12.11	even	2
2880.2.u.a.719.3		96	5.4	even	2	inner
2880.2.u.a.719.22		96	3.2	odd	2	inner
2880.2.u.a.719.27		96	1.1	even	1	trivial
2880.2.u.a.719.46		96	15.14	odd	2	inner
2880.2.u.a.2159.3		96	48.35	even	4	inner
2880.2.u.a.2159.22		96	80.19	odd	4	inner
2880.2.u.a.2159.27		96	240.179	even	4	inner
2880.2.u.a.2159.46		96	16.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.u (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.274088 + 2.21921i) q^{5} -1.32258i q^{7} +O(q^{10})\)	\(q+(0.274088 + 2.21921i) q^{5} -1.32258i q^{7} +(2.92489 + 2.92489i) q^{11} +(-3.33361 - 3.33361i) q^{13} -5.12112 q^{17} +(-4.23462 - 4.23462i) q^{19} +6.44702 q^{23} +(-4.84975 + 1.21651i) q^{25} +(-4.55904 - 4.55904i) q^{29} +8.07172i q^{31} +(2.93508 - 0.362503i) q^{35} +(-4.98065 + 4.98065i) q^{37} -7.34991 q^{41} +(-4.67417 - 4.67417i) q^{43} -3.25014i q^{47} +5.25078 q^{49} +(0.0429668 + 0.0429668i) q^{53} +(-5.68926 + 7.29261i) q^{55} +(-8.42676 - 8.42676i) q^{59} +(-1.80862 + 1.80862i) q^{61} +(6.48426 - 8.31166i) q^{65} +(3.23414 - 3.23414i) q^{67} +4.08803i q^{71} -1.91406 q^{73} +(3.86841 - 3.86841i) q^{77} +8.95635i q^{79} +(-1.19997 - 1.19997i) q^{83} +(-1.40364 - 11.3648i) q^{85} +12.2303 q^{89} +(-4.40896 + 4.40896i) q^{91} +(8.23684 - 10.5582i) q^{95} -13.7776i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q + 16 q^{19} - 96 q^{49} - 64 q^{55} - 32 q^{61}+O(q^{100}) \) 96 * q + 16 * q^19 - 96 * q^49 - 64 * q^55 - 32 * q^61

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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