LMFDB - Embedded newform 2880.2.u.a.719.3

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			719.3
Character	$\chi$	$=$	2880.719
Dual form			2880.2.u.a.2159.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.21921 - 0.274088i) q^{5} +1.32258i q^{7} +O(q^{10})$	$q+(-2.21921 - 0.274088i) q^{5} +1.32258i q^{7} +(2.92489 + 2.92489i) q^{11} +(3.33361 + 3.33361i) q^{13} +5.12112 q^{17} +(-4.23462 - 4.23462i) q^{19} -6.44702 q^{23} +(4.84975 + 1.21651i) q^{25} +(-4.55904 - 4.55904i) q^{29} +8.07172i q^{31} +(0.362503 - 2.93508i) q^{35} +(4.98065 - 4.98065i) q^{37} -7.34991 q^{41} +(4.67417 + 4.67417i) q^{43} +3.25014i q^{47} +5.25078 q^{49} +(-0.0429668 - 0.0429668i) q^{53} +(-5.68926 - 7.29261i) q^{55} +(-8.42676 - 8.42676i) q^{59} +(-1.80862 + 1.80862i) q^{61} +(-6.48426 - 8.31166i) q^{65} +(-3.23414 + 3.23414i) q^{67} +4.08803i q^{71} +1.91406 q^{73} +(-3.86841 + 3.86841i) q^{77} +8.95635i q^{79} +(1.19997 + 1.19997i) q^{83} +(-11.3648 - 1.40364i) q^{85} +12.2303 q^{89} +(-4.40896 + 4.40896i) q^{91} +(8.23684 + 10.5582i) q^{95} +13.7776i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.21921	−	0.274088i	−0.992459	−	0.122576i
$5$	−2.21921	−	0.274088i	−0.992459	−	0.122576i
$6$		0			0
$7$			1.32258i			0.499889i	0.968260	+	0.249944i	$0.0804123\pi$
$7$			1.32258i			0.499889i	−0.968260	+	0.249944i	$0.919588\pi$
$8$		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	0.997349	−	0.0727729i	$-0.0231848\pi$
$13$	3.33361	+	3.33361i	0.924576	+	0.924576i	−0.0727729	+	0.997349i	$0.523185\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.12112			1.24205			0.621027	−	0.783789i	$-0.286716\pi$
$17$	5.12112			1.24205			0.621027	+	0.783789i	$0.286716\pi$
$18$		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	$-0.734628\pi$
$23$	−6.44702			−1.34430			−0.672148	+	0.740417i	$0.734628\pi$
$24$		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
$35$	0.362503	−	2.93508i	0.0612742	−	0.496119i
$36$		0			0
$37$	4.98065	−	4.98065i	0.818813	−	0.818813i	−0.167123	−	0.985936i	$-0.553448\pi$
$37$	4.98065	−	4.98065i	0.818813	−	0.818813i	0.985936	+	0.167123i	$0.0534476\pi$
$38$		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	0.967121	−	0.254317i	$-0.0818507\pi$
$43$	4.67417	+	4.67417i	0.712804	+	0.712804i	−0.254317	+	0.967121i	$0.581851\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			3.25014i			0.474082i	0.971500	+	0.237041i	$0.0761776\pi$
$47$			3.25014i			0.474082i	−0.971500	+	0.237041i	$0.923822\pi$
$48$		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	0.704150	−	0.710052i	$-0.251328\pi$
$53$	−0.0429668	−	0.0429668i	−0.00590194	−	0.00590194i	−0.710052	+	0.704150i	$0.751328\pi$
$54$		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	−0.876505	−	0.481392i	$-0.840131\pi$
$67$	−3.23414	+	3.23414i	−0.395113	+	0.395113i	0.481392	+	0.876505i	$0.340131\pi$
$68$		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	$-0.464270\pi$
$73$	1.91406			0.224024			0.112012	+	0.993707i	$0.464270\pi$
$74$		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	0.769890	−	0.638176i	$-0.220311\pi$
$83$	1.19997	+	1.19997i	0.131714	+	0.131714i	−0.638176	+	0.769890i	$0.720311\pi$
$84$		0			0
$85$	−11.3648	−	1.40364i	−1.23269	−	0.152246i
$86$		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	$0.246572\pi$
$97$			13.7776i			1.39890i	−0.714682	+	0.699450i	$0.753428\pi$
$98$		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	$0.203953\pi$
$103$			12.1337i			1.19557i	−0.801656	+	0.597786i	$0.796047\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.67632	+	9.67632i	−0.935445	+	0.935445i	−0.998039	−	0.0625941i	$-0.980063\pi$
$107$	−9.67632	+	9.67632i	−0.935445	+	0.935445i	0.0625941	+	0.998039i	$0.480063\pi$
$108$		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	$-0.339460\pi$
$113$	10.2738			0.966478			0.483239	+	0.875489i	$0.339460\pi$
$114$		0			0
$115$	14.3073	+	1.76705i	1.33416	+	0.164778i
$116$		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
$125$	−10.4292	−	4.02895i	−0.932813	−	0.360361i
$126$		0			0
$127$	5.21363			0.462635			0.231317	−	0.972878i	$-0.425696\pi$
$127$	5.21363			0.462635			0.231317	+	0.972878i	$0.425696\pi$
$128$		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	$0.149652\pi$
$137$			10.6048i			0.906033i	−0.891502	+	0.453017i	$0.850348\pi$
$138$		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
$155$	2.21236	−	17.9128i	0.177701	−	1.43879i
$156$		0			0
$157$	7.66641	+	7.66641i	0.611846	+	0.611846i	0.943427	−	0.331581i	$-0.107582\pi$
$157$	7.66641	+	7.66641i	0.611846	+	0.611846i	−0.331581	+	0.943427i	$0.607582\pi$
$158$		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	−0.578116	−	0.815955i	$-0.696212\pi$
$163$	3.03653	−	3.03653i	0.237839	−	0.237839i	0.815955	+	0.578116i	$0.196212\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.87465			0.145065			0.0725324	−	0.997366i	$-0.476892\pi$
$167$	1.87465			0.145065			0.0725324	+	0.997366i	$0.476892\pi$
$168$		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	−0.680476	−	0.732770i	$-0.738227\pi$
$173$	0.687819	−	0.687819i	0.0522939	−	0.0522939i	0.732770	+	0.680476i	$0.238227\pi$
$174$		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	$-0.948618\pi$
$193$		−	4.46563i		−	0.321443i	0.987000	−	0.160721i	$-0.0513821\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−15.0440	−	15.0440i	−1.07184	−	1.07184i	−0.997212	−	0.0746266i	$-0.976224\pi$
$197$	−15.0440	−	15.0440i	−1.07184	−	1.07184i	−0.0746266	−	0.997212i	$-0.523776\pi$
$198$		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
$205$	16.3110	+	2.01452i	1.13921	+	0.140700i
$206$		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	$-0.526328\pi$
$223$	−2.46749			−0.165235			−0.0826177	+	0.996581i	$0.526328\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.46523	−	4.46523i	−0.296368	−	0.296368i	0.543222	−	0.839589i	$-0.317204\pi$
$227$	−4.46523	−	4.46523i	−0.296368	−	0.296368i	−0.839589	+	0.543222i	$0.817204\pi$
$228$		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	$0.113435\pi$
$233$			10.6506i			0.697743i	−0.937171	+	0.348871i	$0.886565\pi$
$234$		0			0
$235$	0.890824	−	7.21274i	0.0581110	−	0.470507i
$236$		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
$245$	−11.6526	−	1.43917i	−0.744455	−	0.0919454i
$246$		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	$-0.563709\pi$
$257$	−6.37446			−0.397628			−0.198814	+	0.980037i	$0.563709\pi$
$258$		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	$-0.630499\pi$
$263$	−12.9280			−0.797175			−0.398588	+	0.917130i	$0.630499\pi$
$264$		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
$275$	10.6268	+	17.7432i	0.640821	+	1.06995i
$276$		0			0
$277$	16.5250	−	16.5250i	0.992890	−	0.992890i	−0.00708488	−	0.999975i	$-0.502255\pi$
$277$	16.5250	−	16.5250i	0.992890	−	0.992890i	0.999975	+	0.00708488i	$0.00225521\pi$
$278$		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	$0.120098\pi$
$283$	21.8370	+	21.8370i	1.29807	+	1.29807i	0.368410	+	0.929663i	$0.379902\pi$
$284$		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	0.709784	−	0.704419i	$-0.248792\pi$
$293$	0.0918390	+	0.0918390i	0.00536529	+	0.00536529i	−0.704419	+	0.709784i	$0.748792\pi$
$294$		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	−0.221085	−	0.975255i	$-0.570960\pi$
$307$	13.2141	−	13.2141i	0.754170	−	0.754170i	0.975255	+	0.221085i	$0.0709598\pi$
$308$		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	$-0.408377\pi$
$313$	10.0449			0.567770			0.283885	+	0.958858i	$0.408377\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−18.1322	+	18.1322i	−1.01841	+	1.01841i	−0.0185812	+	0.999827i	$0.505915\pi$
$317$	−18.1322	+	18.1322i	−1.01841	+	1.01841i	−0.999827	+	0.0185812i	$0.994085\pi$
$318$		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
$325$	12.1118	+	20.2225i	0.671841	+	1.12174i
$326$		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	$0.0935789\pi$
$337$			10.6389i			0.579540i	−0.957096	+	0.289770i	$0.906421\pi$
$338$		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	$-0.376210\pi$
$347$	24.3001	−	24.3001i	1.30450	−	1.30450i	0.925328	−	0.379168i	$-0.123790\pi$
$348$		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	$-0.333620\pi$
$353$	18.7589			0.998437			0.499219	+	0.866476i	$0.333620\pi$
$354$		0			0
$355$	1.12048	−	9.07218i	0.0594688	−	0.481501i
$356$		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
$365$	−4.24770	−	0.524621i	−0.222335	−	0.0274599i
$366$		0			0
$367$	−27.9727			−1.46016			−0.730081	−	0.683360i	$-0.760518\pi$
$367$	−27.9727			−1.46016			−0.730081	+	0.683360i	$0.760518\pi$
$368$		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	−0.468273	−	0.883584i	$-0.655124\pi$
$373$	8.02099	−	8.02099i	0.415311	−	0.415311i	0.883584	+	0.468273i	$0.155124\pi$
$374$		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	$-0.872771\pi$
$383$		−	15.2314i		−	0.778287i	0.921177	−	0.389143i	$-0.127229\pi$
$384$		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
$395$	2.45483	−	19.8760i	0.123516	−	1.00007i
$396$		0			0
$397$	4.46660	+	4.46660i	0.224172	+	0.224172i	0.810253	−	0.586081i	$-0.199330\pi$
$397$	4.46660	+	4.46660i	0.224172	+	0.224172i	−0.586081	+	0.810253i	$0.699330\pi$
$398$		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	$-0.851181\pi$
$433$		−	18.7561i		−	0.901361i	0.892685	−	0.450681i	$-0.148819\pi$
$434$		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	−0.919880	−	0.392200i	$-0.871714\pi$
$443$	−11.1064	+	11.1064i	−0.527680	+	0.527680i	0.392200	+	0.919880i	$0.371714\pi$
$444$		0			0
$445$	−27.1417	−	3.35219i	−1.28664	−	0.158909i
$446$		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	$-0.829431\pi$
$457$	−36.7622			−1.71966			−0.859831	+	0.510578i	$0.829431\pi$
$458$		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	$-0.396343\pi$
$463$	13.7679			0.639848			0.319924	+	0.947443i	$0.396343\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.48388	+	2.48388i	0.114940	+	0.114940i	0.762238	−	0.647297i	$-0.224101\pi$
$467$	2.48388	+	2.48388i	0.114940	+	0.114940i	−0.647297	+	0.762238i	$0.724101\pi$
$468$		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
$475$	−15.3854	−	25.6883i	−0.705930	−	1.17866i
$476$		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
$485$	3.77626	−	30.5753i	0.171471	−	1.38835i
$486$		0			0
$487$		−	26.4735i		−	1.19963i	−0.800139	−	0.599815i	$-0.795241\pi$
$487$		−	26.4735i		−	1.19963i	0.800139	−	0.599815i	$-0.204759\pi$
$488$		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	$-0.747333\pi$
$503$	−31.4506			−1.40232			−0.701158	+	0.713006i	$0.747333\pi$
$504$		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
$515$	3.32571	−	26.9272i	0.146548	−	1.18656i
$516$		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	$-0.893106\pi$
$523$	−29.1281	−	29.1281i	−1.27368	−	1.27368i	−0.329542	−	0.944141i	$-0.606894\pi$
$524$		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	−0.999421	−	0.0340143i	$-0.989171\pi$
$547$	−22.5790	+	22.5790i	−0.965407	+	0.965407i	0.0340143	+	0.999421i	$0.489171\pi$
$548$		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	−0.454070	−	0.890966i	$-0.650028\pi$
$557$	10.3111	−	10.3111i	0.436897	−	0.436897i	0.890966	+	0.454070i	$0.150028\pi$
$558$		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	0.987708	−	0.156308i	$-0.0499592\pi$
$563$	19.7272	+	19.7272i	0.831400	+	0.831400i	−0.156308	+	0.987708i	$0.549959\pi$
$564$		0			0
$565$	−22.7997	−	2.81592i	−0.959190	−	0.118467i
$566$		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	$0.107866\pi$
$577$			15.9701i			0.664845i	−0.943131	+	0.332423i	$0.892134\pi$
$578$		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	−0.796196	−	0.605039i	$-0.793158\pi$
$587$	−4.63137	+	4.63137i	−0.191157	+	0.191157i	0.605039	+	0.796196i	$0.293158\pi$
$588$		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	$-0.488698\pi$
$593$	1.72897			0.0710002			0.0355001	+	0.999370i	$0.488698\pi$
$594$		0			0
$595$	1.85642	−	15.0309i	0.0761059	−	0.616207i
$596$		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
$605$	1.67467	−	13.5593i	0.0680849	−	0.551263i
$606$		0			0
$607$	−18.8893			−0.766694			−0.383347	−	0.923604i	$-0.625229\pi$
$607$	−18.8893			−0.766694			−0.383347	+	0.923604i	$0.625229\pi$
$608$		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	−0.812025	−	0.583623i	$-0.801635\pi$
$613$	−5.65497	+	5.65497i	−0.228402	+	0.228402i	0.583623	+	0.812025i	$0.301635\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	26.8434i		−	1.08068i	−0.841448	−	0.540338i	$-0.818297\pi$
$617$		−	26.8434i		−	1.08068i	0.841448	−	0.540338i	$-0.181703\pi$
$618$		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
$635$	−11.5701	−	1.42899i	−0.459146	−	0.0567078i
$636$		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	−0.0813247	−	0.996688i	$-0.525915\pi$
$643$	23.2113	−	23.2113i	0.915363	−	0.915363i	0.996688	+	0.0813247i	$0.0259151\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	3.32710			0.130802			0.0654009	−	0.997859i	$-0.479167\pi$
$647$	3.32710			0.130802			0.0654009	+	0.997859i	$0.479167\pi$
$648$		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	−0.618584	−	0.785719i	$-0.712293\pi$
$653$	4.27095	−	4.27095i	0.167135	−	0.167135i	0.785719	+	0.618584i	$0.212293\pi$
$654$		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	$-0.862291\pi$
$673$		−	21.7529i		−	0.838514i	0.907868	−	0.419257i	$-0.137709\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	24.9075	+	24.9075i	0.957273	+	0.957273i	0.999124	−	0.0418508i	$-0.0133254\pi$
$677$	24.9075	+	24.9075i	0.957273	+	0.957273i	−0.0418508	+	0.999124i	$0.513325\pi$
$678$		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	−0.112671	−	0.993632i	$-0.535941\pi$
$683$	23.0233	−	23.0233i	0.880962	−	0.880962i	0.993632	+	0.112671i	$0.0359405\pi$
$684$		0			0
$685$	2.90666	−	23.5343i	0.111058	−	0.899201i
$686$		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
$715$	5.34495	−	43.2764i	0.199890	−	1.61845i
$716$		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
$725$	−16.5641	−	27.6563i	−0.615174	−	1.02713i
$726$		0			0
$727$		−	45.4745i		−	1.68656i	−0.537478	−	0.843278i	$-0.680623\pi$
$727$		−	45.4745i		−	1.68656i	0.537478	−	0.843278i	$-0.319377\pi$
$728$		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	0.967319	−	0.253562i	$-0.0816021\pi$
$733$	19.3242	+	19.3242i	0.713757	+	0.713757i	−0.253562	+	0.967319i	$0.581602\pi$
$734$		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	$-0.348542\pi$
$743$	24.9720			0.916134			0.458067	+	0.888918i	$0.348542\pi$
$744$		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
$755$	26.1368	+	3.22808i	0.951215	+	0.117482i
$756$		0			0
$757$	11.4284	−	11.4284i	0.415373	−	0.415373i	−0.468233	−	0.883605i	$-0.655109\pi$
$757$	11.4284	−	11.4284i	0.415373	−	0.415373i	0.883605	+	0.468233i	$0.155109\pi$
$758$		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	0.818211	−	0.574917i	$-0.194966\pi$
$773$	6.76428	+	6.76428i	0.243294	+	0.243294i	−0.574917	+	0.818211i	$0.694966\pi$
$774$		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	−0.871842	−	0.489788i	$-0.837074\pi$
$787$	−10.7179	+	10.7179i	−0.382054	+	0.382054i	0.489788	+	0.871842i	$0.337074\pi$
$788$		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	−0.348497	−	0.937310i	$-0.613308\pi$
$797$	16.6229	−	16.6229i	0.588813	−	0.588813i	0.937310	+	0.348497i	$0.113308\pi$
$798$		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
$805$	−2.33707	+	18.9225i	−0.0823708	+	0.666931i
$806$		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	$0.0477018\pi$
$823$			8.56619i			0.298599i	−0.988792	+	0.149299i	$0.952298\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−35.0881	+	35.0881i	−1.22013	+	1.22013i	−0.252549	+	0.967584i	$0.581269\pi$
$827$	−35.0881	+	35.0881i	−1.22013	+	1.22013i	−0.967584	+	0.252549i	$0.918731\pi$
$828$		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
$835$	−4.16023	−	0.513818i	−0.143971	−	0.0177814i
$836$		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
$845$	2.52869	−	20.4741i	0.0869896	−	0.704329i
$846$		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	−0.879924	−	0.475114i	$-0.842407\pi$
$853$	−11.8229	+	11.8229i	−0.404810	+	0.404810i	0.475114	+	0.879924i	$0.342407\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	17.3781i		−	0.593626i	−0.954936	−	0.296813i	$-0.904076\pi$
$857$		−	17.3781i		−	0.593626i	0.954936	−	0.296813i	$-0.0959238\pi$
$858$		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	$-0.772530\pi$
$863$		−	38.5030i		−	1.31066i	0.755343	−	0.655329i	$-0.227470\pi$
$864$		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
$875$	5.32862	−	13.7934i	0.180140	−	0.466303i
$876$		0			0
$877$	−11.7948	−	11.7948i	−0.398281	−	0.398281i	0.479345	−	0.877626i	$-0.340874\pi$
$877$	−11.7948	−	11.7948i	−0.398281	−	0.398281i	−0.877626	+	0.479345i	$0.840874\pi$
$878$		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	$-0.450436\pi$
$883$	33.9641	−	33.9641i	1.14298	−	1.14298i	0.987902	−	0.155081i	$-0.0495639\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	47.5764			1.59746			0.798730	−	0.601690i	$-0.205506\pi$
$887$	47.5764			1.59746			0.798730	+	0.601690i	$0.205506\pi$
$888$		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	0.720911	−	0.693028i	$-0.243724\pi$
$907$	0.839751	+	0.839751i	0.0278835	+	0.0278835i	−0.693028	+	0.720911i	$0.743724\pi$
$908$		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
$925$	30.2139	−	18.0959i	0.993428	−	0.594989i
$926$		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	$-0.323587\pi$
$937$	32.2193			1.05256			0.526279	+	0.850312i	$0.323587\pi$
$938$		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	$-0.987594\pi$
$947$	−31.9491	−	31.9491i	−1.03820	−	1.03820i	−0.0389644	−	0.999241i	$-0.512406\pi$
$948$		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	$0.00317208\pi$
$953$			0.615266i			0.0199304i	−0.999950	+	0.00996521i	$0.996828\pi$
$954$		0			0
$955$	−27.8032	−	3.43389i	−0.899690	−	0.111118i
$956$		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
$965$	−1.22397	+	9.91014i	−0.0394011	+	0.319019i
$966$		0			0
$967$		−	20.2322i		−	0.650625i	−0.945607	−	0.325312i	$-0.894531\pi$
$967$		−	20.2322i		−	0.650625i	0.945607	−	0.325312i	$-0.105469\pi$
$968$		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	$-0.459854\pi$
$977$	7.86357			0.251578			0.125789	+	0.992057i	$0.459854\pi$
$978$		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	$-0.478535\pi$
$983$	4.22528			0.134765			0.0673827	+	0.997727i	$0.478535\pi$
$984$		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
$995$	2.59057	+	0.319954i	0.0821266	+	0.0101432i
$996$		0			0
$997$	42.2361	−	42.2361i	1.33763	−	1.33763i	0.439281	−	0.898349i	$-0.355233\pi$
$997$	42.2361	−	42.2361i	1.33763	−	1.33763i	0.898349	−	0.439281i	$-0.144767\pi$
$998$		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.719.3		96
3.2	odd	2	inner	2880.2.u.a.719.46		96
4.3	odd	2		720.2.u.a.539.25	yes	96
5.4	even	2	inner	2880.2.u.a.719.27		96
12.11	even	2		720.2.u.a.539.24	yes	96
15.14	odd	2	inner	2880.2.u.a.719.22		96
16.3	odd	4	inner	2880.2.u.a.2159.22		96
16.13	even	4		720.2.u.a.179.26	yes	96
20.19	odd	2		720.2.u.a.539.23	yes	96
48.29	odd	4		720.2.u.a.179.23	✓	96
48.35	even	4	inner	2880.2.u.a.2159.27		96
60.59	even	2		720.2.u.a.539.26	yes	96
80.19	odd	4	inner	2880.2.u.a.2159.46		96
80.29	even	4		720.2.u.a.179.24	yes	96
240.29	odd	4		720.2.u.a.179.25	yes	96
240.179	even	4	inner	2880.2.u.a.2159.3		96

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

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