LMFDB - Embedded newform 2880.2.t.e.721.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2880,2,Mod(721,2880)]

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([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("2880.721");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2880.t (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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 720)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			721.14
Character	$\chi$	$=$	2880.721
Dual form			2880.2.t.e.2161.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{5} +4.30899i q^{7} +O(q^{10})$	$q+(0.707107 - 0.707107i) q^{5} +4.30899i q^{7} +(4.45672 - 4.45672i) q^{11} +(-0.918004 - 0.918004i) q^{13} +2.39233 q^{17} +(5.30651 + 5.30651i) q^{19} +2.19729i q^{23} -1.00000i q^{25} +(-4.30220 - 4.30220i) q^{29} -5.39998 q^{31} +(3.04692 + 3.04692i) q^{35} +(0.841031 - 0.841031i) q^{37} +6.87159i q^{41} +(6.63419 - 6.63419i) q^{43} +11.0019 q^{47} -11.5674 q^{49} +(0.600698 - 0.600698i) q^{53} -6.30275i q^{55} +(0.850533 - 0.850533i) q^{59} +(-7.50667 - 7.50667i) q^{61} -1.29825 q^{65} +(8.00447 + 8.00447i) q^{67} +2.29774i q^{71} -1.27895i q^{73} +(19.2040 + 19.2040i) q^{77} -8.05468 q^{79} +(-0.110826 - 0.110826i) q^{83} +(1.69164 - 1.69164i) q^{85} +5.90573i q^{89} +(3.95567 - 3.95567i) q^{91} +7.50454 q^{95} +11.0730 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{19} - 32 q^{37} - 16 q^{43} - 32 q^{49} - 16 q^{61} + 16 q^{67} + 16 q^{79} + 16 q^{85} + 80 q^{91}+O(q^{100}) $ 32 * q - 8 * q^19 - 32 * q^37 - 16 * q^43 - 32 * q^49 - 16 * q^61 + 16 * q^67 + 16 * q^79 + 16 * q^85 + 80 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$577$	$641$	$901$	$2431$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$			4.30899i			1.62865i	0.580412	+	0.814323i	$0.302892\pi$
$7$			4.30899i			1.62865i	−0.580412	+	0.814323i	$0.697108\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.45672	−	4.45672i	1.34375	−	1.34375i	0.451459	−	0.892292i	$-0.350904\pi$
$11$	4.45672	−	4.45672i	1.34375	−	1.34375i	0.892292	−	0.451459i	$-0.149096\pi$
$12$		0			0
$13$	−0.918004	−	0.918004i	−0.254609	−	0.254609i	0.568248	−	0.822857i	$-0.307621\pi$
$13$	−0.918004	−	0.918004i	−0.254609	−	0.254609i	−0.822857	+	0.568248i	$0.807621\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.39233			0.580226			0.290113	−	0.956992i	$-0.406307\pi$
$17$	2.39233			0.580226			0.290113	+	0.956992i	$0.406307\pi$
$18$		0			0
$19$	5.30651	+	5.30651i	1.21740	+	1.21740i	0.968540	+	0.248857i	$0.0800548\pi$
$19$	5.30651	+	5.30651i	1.21740	+	1.21740i	0.248857	+	0.968540i	$0.419945\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			2.19729i			0.458166i	0.973407	+	0.229083i	$0.0735728\pi$
$23$			2.19729i			0.458166i	−0.973407	+	0.229083i	$0.926427\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.30220	−	4.30220i	−0.798899	−	0.798899i	0.184023	−	0.982922i	$-0.441088\pi$
$29$	−4.30220	−	4.30220i	−0.798899	−	0.798899i	−0.982922	+	0.184023i	$0.941088\pi$
$30$		0			0
$31$	−5.39998			−0.969866			−0.484933	−	0.874551i	$-0.661156\pi$
$31$	−5.39998			−0.969866			−0.484933	+	0.874551i	$0.661156\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.04692	+	3.04692i	0.515023	+	0.515023i
$36$		0			0
$37$	0.841031	−	0.841031i	0.138265	−	0.138265i	−0.634587	−	0.772852i	$-0.718830\pi$
$37$	0.841031	−	0.841031i	0.138265	−	0.138265i	0.772852	+	0.634587i	$0.218830\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			6.87159i			1.07316i	0.843849	+	0.536581i	$0.180285\pi$
$41$			6.87159i			1.07316i	−0.843849	+	0.536581i	$0.819715\pi$
$42$		0			0
$43$	6.63419	−	6.63419i	1.01170	−	1.01170i	0.0117734	−	0.999931i	$-0.496252\pi$
$43$	6.63419	−	6.63419i	1.01170	−	1.01170i	0.999931	−	0.0117734i	$-0.00374769\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	11.0019			1.60479			0.802394	−	0.596795i	$-0.203559\pi$
$47$	11.0019			1.60479			0.802394	+	0.596795i	$0.203559\pi$
$48$		0			0
$49$	−11.5674			−1.65249
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.600698	−	0.600698i	0.0825122	−	0.0825122i	−0.664646	−	0.747158i	$-0.731418\pi$
$53$	0.600698	−	0.600698i	0.0825122	−	0.0825122i	0.747158	+	0.664646i	$0.231418\pi$
$54$		0			0
$55$		−	6.30275i		−	0.849863i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.850533	−	0.850533i	0.110730	−	0.110730i	−0.649571	−	0.760301i	$-0.725051\pi$
$59$	0.850533	−	0.850533i	0.110730	−	0.110730i	0.760301	+	0.649571i	$0.225051\pi$
$60$		0			0
$61$	−7.50667	−	7.50667i	−0.961131	−	0.961131i	0.0381411	−	0.999272i	$-0.487856\pi$
$61$	−7.50667	−	7.50667i	−0.961131	−	0.961131i	−0.999272	+	0.0381411i	$0.987856\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.29825			−0.161029
$66$		0			0
$67$	8.00447	+	8.00447i	0.977902	+	0.977902i	0.999761	−	0.0218593i	$-0.00695858\pi$
$67$	8.00447	+	8.00447i	0.977902	+	0.977902i	−0.0218593	+	0.999761i	$0.506959\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			2.29774i			0.272692i	0.990661	+	0.136346i	$0.0435358\pi$
$71$			2.29774i			0.272692i	−0.990661	+	0.136346i	$0.956464\pi$
$72$		0			0
$73$		−	1.27895i		−	0.149690i	−0.997195	−	0.0748448i	$-0.976154\pi$
$73$		−	1.27895i		−	0.149690i	0.997195	−	0.0748448i	$-0.0238461\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	19.2040	+	19.2040i	2.18849	+	2.18849i
$78$		0			0
$79$	−8.05468			−0.906223			−0.453111	−	0.891454i	$-0.649686\pi$
$79$	−8.05468			−0.906223			−0.453111	+	0.891454i	$0.649686\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.110826	−	0.110826i	−0.0121648	−	0.0121648i	0.700998	−	0.713163i	$-0.252738\pi$
$83$	−0.110826	−	0.110826i	−0.0121648	−	0.0121648i	−0.713163	+	0.700998i	$0.752738\pi$
$84$		0			0
$85$	1.69164	−	1.69164i	0.183484	−	0.183484i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			5.90573i			0.626006i	0.949752	+	0.313003i	$0.101335\pi$
$89$			5.90573i			0.626006i	−0.949752	+	0.313003i	$0.898665\pi$
$90$		0			0
$91$	3.95567	−	3.95567i	0.414667	−	0.414667i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.50454			0.769950
$96$		0			0
$97$	11.0730			1.12429			0.562147	−	0.827037i	$-0.309975\pi$
$97$	11.0730			1.12429			0.562147	+	0.827037i	$0.309975\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.30536	−	1.30536i	0.129888	−	0.129888i	−0.639174	−	0.769062i	$-0.720724\pi$
$101$	1.30536	−	1.30536i	0.129888	−	0.129888i	0.769062	+	0.639174i	$0.220724\pi$
$102$		0			0
$103$			7.12042i			0.701596i	0.936451	+	0.350798i	$0.114090\pi$
$103$			7.12042i			0.701596i	−0.936451	+	0.350798i	$0.885910\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−11.8678	+	11.8678i	−1.14731	+	1.14731i	−0.160227	+	0.987080i	$0.551223\pi$
$107$	−11.8678	+	11.8678i	−1.14731	+	1.14731i	−0.987080	+	0.160227i	$0.948777\pi$
$108$		0			0
$109$	11.1831	+	11.1831i	1.07114	+	1.07114i	0.997268	+	0.0738750i	$0.0235366\pi$
$109$	11.1831	+	11.1831i	1.07114	+	1.07114i	0.0738750	+	0.997268i	$0.476463\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	11.8054			1.11056			0.555281	−	0.831663i	$-0.312611\pi$
$113$	11.8054			1.11056			0.555281	+	0.831663i	$0.312611\pi$
$114$		0			0
$115$	1.55372	+	1.55372i	0.144885	+	0.144885i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			10.3085i			0.944983i
$120$		0			0
$121$		−	28.7247i		−	2.61133i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	4.26410			0.378378			0.189189	−	0.981941i	$-0.439414\pi$
$127$	4.26410			0.378378			0.189189	+	0.981941i	$0.439414\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	10.8702	+	10.8702i	0.949736	+	0.949736i	0.998796	−	0.0490600i	$-0.0156226\pi$
$131$	10.8702	+	10.8702i	0.949736	+	0.949736i	−0.0490600	+	0.998796i	$0.515623\pi$
$132$		0			0
$133$	−22.8657	+	22.8657i	−1.98271	+	1.98271i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	13.8075i		−	1.17965i	−0.807529	−	0.589827i	$-0.799196\pi$
$137$		−	13.8075i		−	1.17965i	0.807529	−	0.589827i	$-0.200804\pi$
$138$		0			0
$139$	−10.5626	+	10.5626i	−0.895908	+	0.895908i	−0.995071	−	0.0991634i	$-0.968383\pi$
$139$	−10.5626	+	10.5626i	−0.895908	+	0.895908i	0.0991634	+	0.995071i	$0.468383\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.18257			−0.684261
$144$		0			0
$145$	−6.08423			−0.505268
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.82465	−	3.82465i	0.313328	−	0.313328i	−0.532870	−	0.846197i	$-0.678886\pi$
$149$	3.82465	−	3.82465i	0.313328	−	0.313328i	0.846197	+	0.532870i	$0.178886\pi$
$150$		0			0
$151$			7.71444i			0.627793i	0.949457	+	0.313896i	$0.101634\pi$
$151$			7.71444i			0.627793i	−0.949457	+	0.313896i	$0.898366\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.81837	+	3.81837i	−0.306699	+	0.306699i
$156$		0			0
$157$	10.4546	+	10.4546i	0.834369	+	0.834369i	0.988111	−	0.153742i	$-0.0491326\pi$
$157$	10.4546	+	10.4546i	0.834369	+	0.834369i	−0.153742	+	0.988111i	$0.549133\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−9.46810			−0.746191
$162$		0			0
$163$	−3.68474	−	3.68474i	−0.288611	−	0.288611i	0.547920	−	0.836531i	$-0.315420\pi$
$163$	−3.68474	−	3.68474i	−0.288611	−	0.288611i	−0.836531	+	0.547920i	$0.815420\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	10.0866i		−	0.780526i	−0.920703	−	0.390263i	$-0.872384\pi$
$167$		−	10.0866i		−	0.780526i	0.920703	−	0.390263i	$-0.127616\pi$
$168$		0			0
$169$		−	11.3145i		−	0.870349i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.19016	+	9.19016i	0.698715	+	0.698715i	0.964133	−	0.265418i	$-0.0855101\pi$
$173$	9.19016	+	9.19016i	0.698715	+	0.698715i	−0.265418	+	0.964133i	$0.585510\pi$
$174$		0			0
$175$	4.30899			0.325729
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.28517	+	4.28517i	0.320289	+	0.320289i	0.848878	−	0.528589i	$-0.177279\pi$
$179$	4.28517	+	4.28517i	0.320289	+	0.320289i	−0.528589	+	0.848878i	$0.677279\pi$
$180$		0			0
$181$	−0.167638	+	0.167638i	−0.0124604	+	0.0124604i	−0.713310	−	0.700849i	$-0.752805\pi$
$181$	−0.167638	+	0.167638i	−0.0124604	+	0.0124604i	0.700849	+	0.713310i	$0.252805\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		−	1.18940i		−	0.0874462i
$186$		0			0
$187$	10.6620	−	10.6620i	0.779679	−	0.779679i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	14.2210			1.02900			0.514499	−	0.857491i	$-0.327978\pi$
$191$	14.2210			1.02900			0.514499	+	0.857491i	$0.327978\pi$
$192$		0			0
$193$	4.99666			0.359667			0.179834	−	0.983697i	$-0.442444\pi$
$193$	4.99666			0.359667			0.179834	+	0.983697i	$0.442444\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	11.9929	−	11.9929i	0.854457	−	0.854457i	−0.136222	−	0.990678i	$-0.543496\pi$
$197$	11.9929	−	11.9929i	0.854457	−	0.854457i	0.990678	+	0.136222i	$0.0434959\pi$
$198$		0			0
$199$		−	9.06922i		−	0.642900i	−0.946927	−	0.321450i	$-0.895830\pi$
$199$		−	9.06922i		−	0.642900i	0.946927	−	0.321450i	$-0.104170\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	18.5381	−	18.5381i	1.30112	−	1.30112i
$204$		0			0
$205$	4.85895	+	4.85895i	0.339364	+	0.339364i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	47.2992			3.27176
$210$		0			0
$211$	−2.16723	−	2.16723i	−0.149198	−	0.149198i	0.628562	−	0.777760i	$-0.283644\pi$
$211$	−2.16723	−	2.16723i	−0.149198	−	0.149198i	−0.777760	+	0.628562i	$0.783644\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	9.38216i		−	0.639858i
$216$		0			0
$217$		−	23.2685i		−	1.57957i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.19617	−	2.19617i	−0.147731	−	0.147731i
$222$		0			0
$223$	−19.4573			−1.30296			−0.651480	−	0.758666i	$-0.725852\pi$
$223$	−19.4573			−1.30296			−0.651480	+	0.758666i	$0.725852\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.57822	−	3.57822i	−0.237495	−	0.237495i	0.578317	−	0.815812i	$-0.303710\pi$
$227$	−3.57822	−	3.57822i	−0.237495	−	0.237495i	−0.815812	+	0.578317i	$0.803710\pi$
$228$		0			0
$229$	−8.98770	+	8.98770i	−0.593924	+	0.593924i	−0.938689	−	0.344765i	$-0.887959\pi$
$229$	−8.98770	+	8.98770i	−0.593924	+	0.593924i	0.344765	+	0.938689i	$0.387959\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			11.7516i			0.769871i	0.922943	+	0.384936i	$0.125776\pi$
$233$			11.7516i			0.769871i	−0.922943	+	0.384936i	$0.874224\pi$
$234$		0			0
$235$	7.77950	−	7.77950i	0.507478	−	0.507478i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.42378			0.0920965			0.0460482	−	0.998939i	$-0.485337\pi$
$239$	1.42378			0.0920965			0.0460482	+	0.998939i	$0.485337\pi$
$240$		0			0
$241$	3.59330			0.231465			0.115732	−	0.993280i	$-0.463079\pi$
$241$	3.59330			0.231465			0.115732	+	0.993280i	$0.463079\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−8.17940	+	8.17940i	−0.522563	+	0.522563i
$246$		0			0
$247$		−	9.74280i		−	0.619919i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.2978	−	12.2978i	0.776229	−	0.776229i	−0.202958	−	0.979187i	$-0.565055\pi$
$251$	12.2978	−	12.2978i	0.776229	−	0.776229i	0.979187	+	0.202958i	$0.0650555\pi$
$252$		0			0
$253$	9.79270	+	9.79270i	0.615661	+	0.615661i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.804787			−0.0502012			−0.0251006	−	0.999685i	$-0.507991\pi$
$257$	−0.804787			−0.0502012			−0.0251006	+	0.999685i	$0.507991\pi$
$258$		0			0
$259$	3.62400	+	3.62400i	0.225184	+	0.225184i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			11.9393i			0.736210i	0.929784	+	0.368105i	$0.119993\pi$
$263$			11.9393i			0.736210i	−0.929784	+	0.368105i	$0.880007\pi$
$264$		0			0
$265$		−	0.849516i		−	0.0521853i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−13.8370	−	13.8370i	−0.843659	−	0.843659i	0.145674	−	0.989333i	$-0.453465\pi$
$269$	−13.8370	−	13.8370i	−0.843659	−	0.843659i	−0.989333	+	0.145674i	$0.953465\pi$
$270$		0			0
$271$	−21.4770			−1.30464			−0.652318	−	0.757946i	$-0.726203\pi$
$271$	−21.4770			−1.30464			−0.652318	+	0.757946i	$0.726203\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.45672	−	4.45672i	−0.268750	−	0.268750i
$276$		0			0
$277$	0.810554	−	0.810554i	0.0487015	−	0.0487015i	−0.682337	−	0.731038i	$-0.739036\pi$
$277$	0.810554	−	0.810554i	0.0487015	−	0.0487015i	0.731038	+	0.682337i	$0.239036\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	26.4698i		−	1.57906i	−0.613714	−	0.789529i	$-0.710325\pi$
$281$		−	26.4698i		−	1.57906i	0.613714	−	0.789529i	$-0.289675\pi$
$282$		0			0
$283$	7.89541	−	7.89541i	0.469334	−	0.469334i	−0.432365	−	0.901699i	$-0.642321\pi$
$283$	7.89541	−	7.89541i	0.469334	−	0.469334i	0.901699	+	0.432365i	$0.142321\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−29.6096			−1.74780
$288$		0			0
$289$	−11.2767			−0.663338
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.347143	−	0.347143i	0.0202803	−	0.0202803i	−0.696894	−	0.717174i	$-0.745435\pi$
$293$	0.347143	−	0.347143i	0.0202803	−	0.0202803i	0.717174	+	0.696894i	$0.245435\pi$
$294$		0			0
$295$		−	1.20284i		−	0.0700318i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.01712	−	2.01712i	0.116653	−	0.116653i
$300$		0			0
$301$	28.5867	+	28.5867i	1.64771	+	1.64771i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−10.6160			−0.607873
$306$		0			0
$307$	6.35693	+	6.35693i	0.362809	+	0.362809i	0.864846	−	0.502037i	$-0.167416\pi$
$307$	6.35693	+	6.35693i	0.362809	+	0.362809i	−0.502037	+	0.864846i	$0.667416\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			22.5627i			1.27941i	0.768619	+	0.639707i	$0.220944\pi$
$311$			22.5627i			1.27941i	−0.768619	+	0.639707i	$0.779056\pi$
$312$		0			0
$313$			8.36078i			0.472579i	0.971683	+	0.236290i	$0.0759314\pi$
$313$			8.36078i			0.472579i	−0.971683	+	0.236290i	$0.924069\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.79986	−	6.79986i	−0.381918	−	0.381918i	0.489875	−	0.871793i	$-0.337043\pi$
$317$	−6.79986	−	6.79986i	−0.381918	−	0.381918i	−0.871793	+	0.489875i	$0.837043\pi$
$318$		0			0
$319$	−38.3474			−2.14704
$320$		0			0
$321$		0			0
$322$		0			0
$323$	12.6949	+	12.6949i	0.706366	+	0.706366i
$324$		0			0
$325$	−0.918004	+	0.918004i	−0.0509217	+	0.0509217i
$326$		0			0
$327$		0			0
$328$		0			0
$329$			47.4070i			2.61363i
$330$		0			0
$331$	−7.04453	+	7.04453i	−0.387202	+	0.387202i	−0.873688	−	0.486486i	$-0.838278\pi$
$331$	−7.04453	+	7.04453i	−0.387202	+	0.387202i	0.486486	+	0.873688i	$0.338278\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	11.3200			0.618479
$336$		0			0
$337$	22.5791			1.22996			0.614981	−	0.788542i	$-0.289164\pi$
$337$	22.5791			1.22996			0.614981	+	0.788542i	$0.289164\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−24.0662	+	24.0662i	−1.30326	+	1.30326i
$342$		0			0
$343$		−	19.6810i		−	1.06267i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.0292	+	13.0292i	−0.699444	+	0.699444i	−0.964291	−	0.264846i	$-0.914679\pi$
$347$	−13.0292	+	13.0292i	−0.699444	+	0.699444i	0.264846	+	0.964291i	$0.414679\pi$
$348$		0			0
$349$	−13.1583	−	13.1583i	−0.704350	−	0.704350i	0.260991	−	0.965341i	$-0.415951\pi$
$349$	−13.1583	−	13.1583i	−0.704350	−	0.704350i	−0.965341	+	0.260991i	$0.915951\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−23.7674			−1.26501			−0.632505	−	0.774557i	$-0.717973\pi$
$353$	−23.7674			−1.26501			−0.632505	+	0.774557i	$0.717973\pi$
$354$		0			0
$355$	1.62475	+	1.62475i	0.0862326	+	0.0862326i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	23.6404i		−	1.24769i	−0.781547	−	0.623846i	$-0.785569\pi$
$359$		−	23.6404i		−	1.24769i	0.781547	−	0.623846i	$-0.214431\pi$
$360$		0			0
$361$			37.3181i			1.96411i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.904353	−	0.904353i	−0.0473360	−	0.0473360i
$366$		0			0
$367$	−3.40994			−0.177998			−0.0889988	−	0.996032i	$-0.528367\pi$
$367$	−3.40994			−0.177998			−0.0889988	+	0.996032i	$0.528367\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.58840	+	2.58840i	0.134383	+	0.134383i
$372$		0			0
$373$	10.7107	−	10.7107i	0.554579	−	0.554579i	−0.373180	−	0.927759i	$-0.621733\pi$
$373$	10.7107	−	10.7107i	0.554579	−	0.554579i	0.927759	+	0.373180i	$0.121733\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			7.89887i			0.406813i
$378$		0			0
$379$	7.02838	−	7.02838i	0.361024	−	0.361024i	−0.503166	−	0.864190i	$-0.667832\pi$
$379$	7.02838	−	7.02838i	0.361024	−	0.361024i	0.864190	+	0.503166i	$0.167832\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−9.57994			−0.489512			−0.244756	−	0.969585i	$-0.578708\pi$
$383$	−9.57994			−0.489512			−0.244756	+	0.969585i	$0.578708\pi$
$384$		0			0
$385$	27.1585			1.38413
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.90856	−	3.90856i	0.198172	−	0.198172i	−0.601044	−	0.799216i	$-0.705248\pi$
$389$	3.90856	−	3.90856i	0.198172	−	0.198172i	0.799216	+	0.601044i	$0.205248\pi$
$390$		0			0
$391$			5.25665i			0.265840i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−5.69552	+	5.69552i	−0.286573	+	0.286573i
$396$		0			0
$397$	5.78005	+	5.78005i	0.290093	+	0.290093i	0.837117	−	0.547024i	$-0.184239\pi$
$397$	5.78005	+	5.78005i	0.290093	+	0.290093i	−0.547024	+	0.837117i	$0.684239\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−24.6482			−1.23087			−0.615437	−	0.788186i	$-0.711020\pi$
$401$	−24.6482			−1.23087			−0.615437	+	0.788186i	$0.711020\pi$
$402$		0			0
$403$	4.95721	+	4.95721i	0.246936	+	0.246936i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	7.49647i		−	0.371586i
$408$		0			0
$409$			13.0189i			0.643744i	0.946783	+	0.321872i	$0.104312\pi$
$409$			13.0189i			0.643744i	−0.946783	+	0.321872i	$0.895688\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	3.66494	+	3.66494i	0.180340	+	0.180340i
$414$		0			0
$415$	−0.156732			−0.00769368
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−8.64150	−	8.64150i	−0.422165	−	0.422165i	0.463784	−	0.885948i	$-0.346491\pi$
$419$	−8.64150	−	8.64150i	−0.422165	−	0.422165i	−0.885948	+	0.463784i	$0.846491\pi$
$420$		0			0
$421$	−16.8673	+	16.8673i	−0.822062	+	0.822062i	−0.986403	−	0.164342i	$-0.947450\pi$
$421$	−16.8673	+	16.8673i	−0.822062	+	0.822062i	0.164342	+	0.986403i	$0.447450\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		−	2.39233i		−	0.116045i
$426$		0			0
$427$	32.3462	−	32.3462i	1.56534	−	1.56534i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	30.8765			1.48727			0.743633	−	0.668588i	$-0.233101\pi$
$431$	30.8765			1.48727			0.743633	+	0.668588i	$0.233101\pi$
$432$		0			0
$433$	−32.7746			−1.57504			−0.787522	−	0.616286i	$-0.788637\pi$
$433$	−32.7746			−1.57504			−0.787522	+	0.616286i	$0.788637\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−11.6599	+	11.6599i	−0.557770	+	0.557770i
$438$		0			0
$439$			21.1973i			1.01169i	0.862623	+	0.505847i	$0.168820\pi$
$439$			21.1973i			1.01169i	−0.862623	+	0.505847i	$0.831180\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.169793	−	0.169793i	0.00806712	−	0.00806712i	−0.703062	−	0.711129i	$-0.748184\pi$
$443$	0.169793	−	0.169793i	0.00806712	−	0.00806712i	0.711129	+	0.703062i	$0.248184\pi$
$444$		0			0
$445$	4.17598	+	4.17598i	0.197961	+	0.197961i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−9.68014			−0.456834			−0.228417	−	0.973563i	$-0.573355\pi$
$449$	−9.68014			−0.456834			−0.228417	+	0.973563i	$0.573355\pi$
$450$		0			0
$451$	30.6247	+	30.6247i	1.44206	+	1.44206i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		−	5.59417i		−	0.262259i
$456$		0			0
$457$		−	24.7506i		−	1.15778i	−0.815405	−	0.578892i	$-0.803485\pi$
$457$		−	24.7506i		−	1.15778i	0.815405	−	0.578892i	$-0.196515\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.02398	−	3.02398i	−0.140841	−	0.140841i	0.633171	−	0.774012i	$-0.281753\pi$
$461$	−3.02398	−	3.02398i	−0.140841	−	0.140841i	−0.774012	+	0.633171i	$0.781753\pi$
$462$		0			0
$463$	−16.3330			−0.759058			−0.379529	−	0.925180i	$-0.623914\pi$
$463$	−16.3330			−0.759058			−0.379529	+	0.925180i	$0.623914\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−14.1573	−	14.1573i	−0.655121	−	0.655121i	0.299101	−	0.954222i	$-0.403313\pi$
$467$	−14.1573	−	14.1573i	−0.655121	−	0.655121i	−0.954222	+	0.299101i	$0.903313\pi$
$468$		0			0
$469$	−34.4912	+	34.4912i	−1.59266	+	1.59266i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	59.1334i		−	2.71896i
$474$		0			0
$475$	5.30651	−	5.30651i	0.243479	−	0.243479i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−10.6878			−0.488336			−0.244168	−	0.969733i	$-0.578515\pi$
$479$	−10.6878			−0.488336			−0.244168	+	0.969733i	$0.578515\pi$
$480$		0			0
$481$	−1.54414			−0.0704067
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.82981	−	7.82981i	0.355533	−	0.355533i
$486$		0			0
$487$		−	17.4562i		−	0.791018i	−0.918462	−	0.395509i	$-0.870568\pi$
$487$		−	17.4562i		−	0.791018i	0.918462	−	0.395509i	$-0.129432\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.69666	−	1.69666i	0.0765693	−	0.0765693i	−0.667785	−	0.744354i	$-0.732757\pi$
$491$	1.69666	−	1.69666i	0.0765693	−	0.0765693i	0.744354	+	0.667785i	$0.232757\pi$
$492$		0			0
$493$	−10.2923	−	10.2923i	−0.463542	−	0.463542i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.90094			−0.444118
$498$		0			0
$499$	−29.7768	−	29.7768i	−1.33299	−	1.33299i	−0.902678	−	0.430316i	$-0.858402\pi$
$499$	−29.7768	−	29.7768i	−1.33299	−	1.33299i	−0.430316	−	0.902678i	$-0.641598\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			31.0874i			1.38612i	0.720881	+	0.693059i	$0.243738\pi$
$503$			31.0874i			1.38612i	−0.720881	+	0.693059i	$0.756262\pi$
$504$		0			0
$505$		−	1.84605i		−	0.0821483i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.60448	−	2.60448i	−0.115442	−	0.115442i	0.647026	−	0.762468i	$-0.276012\pi$
$509$	−2.60448	−	2.60448i	−0.115442	−	0.115442i	−0.762468	+	0.647026i	$0.776012\pi$
$510$		0			0
$511$	5.51098			0.243791
$512$		0			0
$513$		0			0
$514$		0			0
$515$	5.03490	+	5.03490i	0.221864	+	0.221864i
$516$		0			0
$517$	49.0322	−	49.0322i	2.15643	−	2.15643i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			3.36865i			0.147583i	0.997274	+	0.0737917i	$0.0235100\pi$
$521$			3.36865i			0.147583i	−0.997274	+	0.0737917i	$0.976490\pi$
$522$		0			0
$523$	−23.3648	+	23.3648i	−1.02167	+	1.02167i	−0.0219111	+	0.999760i	$0.506975\pi$
$523$	−23.3648	+	23.3648i	−1.02167	+	1.02167i	−0.999760	+	0.0219111i	$0.993025\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.9186			−0.562742
$528$		0			0
$529$	18.1719			0.790084
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.30815	−	6.30815i	0.273236	−	0.273236i
$534$		0			0
$535$			16.7837i			0.725621i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−51.5527	+	51.5527i	−2.22053	+	2.22053i
$540$		0			0
$541$	−14.2656	−	14.2656i	−0.613326	−	0.613326i	0.330485	−	0.943811i	$-0.392788\pi$
$541$	−14.2656	−	14.2656i	−0.613326	−	0.613326i	−0.943811	+	0.330485i	$0.892788\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	15.8152			0.677450
$546$		0			0
$547$	−7.30692	−	7.30692i	−0.312421	−	0.312421i	0.533426	−	0.845847i	$-0.320904\pi$
$547$	−7.30692	−	7.30692i	−0.312421	−	0.312421i	−0.845847	+	0.533426i	$0.820904\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	45.6593i		−	1.94515i
$552$		0			0
$553$		−	34.7076i		−	1.47592i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.2397	+	14.2397i	0.603356	+	0.603356i	0.941201	−	0.337846i	$-0.109698\pi$
$557$	14.2397	+	14.2397i	0.603356	+	0.603356i	−0.337846	+	0.941201i	$0.609698\pi$
$558$		0			0
$559$	−12.1804			−0.515177
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−28.8070	−	28.8070i	−1.21407	−	1.21407i	−0.969675	−	0.244397i	$-0.921410\pi$
$563$	−28.8070	−	28.8070i	−1.21407	−	1.21407i	−0.244397	−	0.969675i	$-0.578590\pi$
$564$		0			0
$565$	8.34771	−	8.34771i	0.351191	−	0.351191i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	22.3228i		−	0.935820i	−0.883776	−	0.467910i	$-0.845007\pi$
$569$		−	22.3228i		−	0.935820i	0.883776	−	0.467910i	$-0.154993\pi$
$570$		0			0
$571$	−1.98028	+	1.98028i	−0.0828723	+	0.0828723i	−0.747328	−	0.664456i	$-0.768664\pi$
$571$	−1.98028	+	1.98028i	−0.0828723	+	0.0828723i	0.664456	+	0.747328i	$0.268664\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	2.19729			0.0916333
$576$		0			0
$577$	−14.5615			−0.606204			−0.303102	−	0.952958i	$-0.598022\pi$
$577$	−14.5615			−0.606204			−0.303102	+	0.952958i	$0.598022\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.477550	−	0.477550i	0.0198121	−	0.0198121i
$582$		0			0
$583$		−	5.35428i		−	0.221752i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	27.7869	−	27.7869i	1.14689	−	1.14689i	0.159729	−	0.987161i	$-0.448938\pi$
$587$	27.7869	−	27.7869i	1.14689	−	1.14689i	0.987161	−	0.159729i	$-0.0510620\pi$
$588$		0			0
$589$	−28.6551	−	28.6551i	−1.18071	−	1.18071i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−35.5250			−1.45884			−0.729418	−	0.684069i	$-0.760209\pi$
$593$	−35.5250			−1.45884			−0.729418	+	0.684069i	$0.760209\pi$
$594$		0			0
$595$	7.28924	+	7.28924i	0.298830	+	0.298830i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	44.7920i		−	1.83015i	−0.403283	−	0.915075i	$-0.632131\pi$
$599$		−	44.7920i		−	1.83015i	0.403283	−	0.915075i	$-0.367869\pi$
$600$		0			0
$601$		−	14.6320i		−	0.596851i	−0.954433	−	0.298426i	$-0.903539\pi$
$601$		−	14.6320i		−	0.596851i	0.954433	−	0.298426i	$-0.0964615\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−20.3114	−	20.3114i	−0.825776	−	0.825776i
$606$		0			0
$607$	8.08782			0.328274			0.164137	−	0.986438i	$-0.447516\pi$
$607$	8.08782			0.328274			0.164137	+	0.986438i	$0.447516\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−10.0998	−	10.0998i	−0.408593	−	0.408593i
$612$		0			0
$613$	5.41663	−	5.41663i	0.218775	−	0.218775i	−0.589207	−	0.807982i	$-0.700560\pi$
$613$	5.41663	−	5.41663i	0.218775	−	0.218775i	0.807982	+	0.589207i	$0.200560\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	4.23671i		−	0.170563i	−0.996357	−	0.0852817i	$-0.972821\pi$
$617$		−	4.23671i		−	0.170563i	0.996357	−	0.0852817i	$-0.0271790\pi$
$618$		0			0
$619$	−1.40756	+	1.40756i	−0.0565744	+	0.0565744i	−0.734828	−	0.678254i	$-0.762737\pi$
$619$	−1.40756	+	1.40756i	−0.0565744	+	0.0565744i	0.678254	+	0.734828i	$0.262737\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−25.4478			−1.01954
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.01203	−	2.01203i	0.0802247	−	0.0802247i
$630$		0			0
$631$		−	18.4821i		−	0.735759i	−0.929873	−	0.367880i	$-0.880084\pi$
$631$		−	18.4821i		−	0.735759i	0.929873	−	0.367880i	$-0.119916\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.01518	−	3.01518i	0.119654	−	0.119654i
$636$		0			0
$637$	10.6189	+	10.6189i	0.420737	+	0.420737i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−29.8385			−1.17855			−0.589275	−	0.807933i	$-0.700586\pi$
$641$	−29.8385			−1.17855			−0.589275	+	0.807933i	$0.700586\pi$
$642$		0			0
$643$	24.6679	+	24.6679i	0.972806	+	0.972806i	0.999640	−	0.0268338i	$-0.00854250\pi$
$643$	24.6679	+	24.6679i	0.972806	+	0.972806i	−0.0268338	+	0.999640i	$0.508543\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			27.2647i			1.07189i	0.844254	+	0.535944i	$0.180044\pi$
$647$			27.2647i			1.07189i	−0.844254	+	0.535944i	$0.819956\pi$
$648$		0			0
$649$		−	7.58117i		−	0.297587i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.27290	+	4.27290i	0.167211	+	0.167211i	0.785752	−	0.618541i	$-0.212276\pi$
$653$	4.27290	+	4.27290i	0.167211	+	0.167211i	−0.618541	+	0.785752i	$0.712276\pi$
$654$		0			0
$655$	15.3728			0.600666
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−31.6320	−	31.6320i	−1.23221	−	1.23221i	−0.963114	−	0.269095i	$-0.913275\pi$
$659$	−31.6320	−	31.6320i	−1.23221	−	1.23221i	−0.269095	−	0.963114i	$-0.586725\pi$
$660$		0			0
$661$	4.07450	−	4.07450i	0.158480	−	0.158480i	−0.623413	−	0.781893i	$-0.714254\pi$
$661$	4.07450	−	4.07450i	0.158480	−	0.158480i	0.781893	+	0.623413i	$0.214254\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			32.3370i			1.25398i
$666$		0			0
$667$	9.45318	−	9.45318i	0.366028	−	0.366028i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−66.9103			−2.58304
$672$		0			0
$673$	−16.9851			−0.654726			−0.327363	−	0.944899i	$-0.606160\pi$
$673$	−16.9851			−0.654726			−0.327363	+	0.944899i	$0.606160\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	28.6084	−	28.6084i	1.09951	−	1.09951i	0.105042	−	0.994468i	$-0.466502\pi$
$677$	28.6084	−	28.6084i	1.09951	−	1.09951i	0.994468	−	0.105042i	$-0.0334976\pi$
$678$		0			0
$679$			47.7136i			1.83108i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	14.2208	−	14.2208i	0.544143	−	0.544143i	−0.380598	−	0.924741i	$-0.624282\pi$
$683$	14.2208	−	14.2208i	0.544143	−	0.544143i	0.924741	+	0.380598i	$0.124282\pi$
$684$		0			0
$685$	−9.76338	−	9.76338i	−0.373040	−	0.373040i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.10289			−0.0420166
$690$		0			0
$691$	−3.08885	−	3.08885i	−0.117506	−	0.117506i	0.645909	−	0.763414i	$-0.276479\pi$
$691$	−3.08885	−	3.08885i	−0.117506	−	0.117506i	−0.763414	+	0.645909i	$0.776479\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			14.9378i			0.566622i
$696$		0			0
$697$			16.4391i			0.622677i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−6.44414	−	6.44414i	−0.243392	−	0.243392i	0.574860	−	0.818252i	$-0.305057\pi$
$701$	−6.44414	−	6.44414i	−0.243392	−	0.243392i	−0.818252	+	0.574860i	$0.805057\pi$
$702$		0			0
$703$	8.92588			0.336646
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.62477	+	5.62477i	0.211541	+	0.211541i
$708$		0			0
$709$	−8.11359	+	8.11359i	−0.304712	+	0.304712i	−0.842854	−	0.538142i	$-0.819126\pi$
$709$	−8.11359	+	8.11359i	−0.304712	+	0.304712i	0.538142	+	0.842854i	$0.319126\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	11.8653i		−	0.444360i
$714$		0			0
$715$	−5.78595	+	5.78595i	−0.216382	+	0.216382i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	44.6354			1.66462			0.832309	−	0.554312i	$-0.187018\pi$
$719$	44.6354			1.66462			0.832309	+	0.554312i	$0.187018\pi$
$720$		0			0
$721$	−30.6818			−1.14265
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.30220	+	4.30220i	−0.159780	+	0.159780i
$726$		0			0
$727$		−	31.1523i		−	1.15537i	−0.816258	−	0.577687i	$-0.803955\pi$
$727$		−	31.1523i		−	1.15537i	0.816258	−	0.577687i	$-0.196045\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	15.8712	−	15.8712i	0.587017	−	0.587017i
$732$		0			0
$733$	25.4491	+	25.4491i	0.939984	+	0.939984i	0.998298	−	0.0583147i	$-0.0185727\pi$
$733$	25.4491	+	25.4491i	0.939984	+	0.939984i	−0.0583147	+	0.998298i	$0.518573\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	71.3473			2.62811
$738$		0			0
$739$	−13.7239	−	13.7239i	−0.504840	−	0.504840i	0.408098	−	0.912938i	$-0.366192\pi$
$739$	−13.7239	−	13.7239i	−0.504840	−	0.504840i	−0.912938	+	0.408098i	$0.866192\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			4.03988i			0.148209i	0.997250	+	0.0741045i	$0.0236098\pi$
$743$			4.03988i			0.148209i	−0.997250	+	0.0741045i	$0.976390\pi$
$744$		0			0
$745$		−	5.40887i		−	0.198166i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−51.1384	−	51.1384i	−1.86856	−	1.86856i
$750$		0			0
$751$	39.8481			1.45408			0.727039	−	0.686597i	$-0.240896\pi$
$751$	39.8481			1.45408			0.727039	+	0.686597i	$0.240896\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	5.45494	+	5.45494i	0.198525	+	0.198525i
$756$		0			0
$757$	−33.3203	+	33.3203i	−1.21105	+	1.21105i	−0.240364	+	0.970683i	$0.577267\pi$
$757$	−33.3203	+	33.3203i	−1.21105	+	1.21105i	−0.970683	+	0.240364i	$0.922733\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			12.0619i			0.437242i	0.975810	+	0.218621i	$0.0701558\pi$
$761$			12.0619i			0.437242i	−0.975810	+	0.218621i	$0.929844\pi$
$762$		0			0
$763$	−48.1877	+	48.1877i	−1.74451	+	1.74451i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.56159			−0.0563856
$768$		0			0
$769$	−46.5853			−1.67991			−0.839954	−	0.542657i	$-0.817418\pi$
$769$	−46.5853			−1.67991			−0.839954	+	0.542657i	$0.817418\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−11.8770	+	11.8770i	−0.427186	+	0.427186i	−0.887669	−	0.460483i	$-0.847676\pi$
$773$	−11.8770	+	11.8770i	−0.427186	+	0.427186i	0.460483	+	0.887669i	$0.347676\pi$
$774$		0			0
$775$			5.39998i			0.193973i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−36.4642	+	36.4642i	−1.30646	+	1.30646i
$780$		0			0
$781$	10.2404	+	10.2404i	0.366429	+	0.366429i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	14.7850			0.527701
$786$		0			0
$787$	20.7527	+	20.7527i	0.739753	+	0.739753i	0.972530	−	0.232777i	$-0.0747812\pi$
$787$	20.7527	+	20.7527i	0.739753	+	0.739753i	−0.232777	+	0.972530i	$0.574781\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			50.8695i			1.80871i
$792$		0			0
$793$			13.7823i			0.489424i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−31.4504	−	31.4504i	−1.11403	−	1.11403i	−0.992600	−	0.121430i	$-0.961252\pi$
$797$	−31.4504	−	31.4504i	−1.11403	−	1.11403i	−0.121430	−	0.992600i	$-0.538748\pi$
$798$		0			0
$799$	26.3201			0.931139
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.69991	−	5.69991i	−0.201145	−	0.201145i
$804$		0			0
$805$	−6.69496	+	6.69496i	−0.235966	+	0.235966i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	6.02407i		−	0.211795i	−0.994377	−	0.105898i	$-0.966228\pi$
$809$		−	6.02407i		−	0.211795i	0.994377	−	0.105898i	$-0.0337716\pi$
$810$		0			0
$811$	16.1703	−	16.1703i	0.567815	−	0.567815i	−0.363701	−	0.931516i	$-0.618487\pi$
$811$	16.1703	−	16.1703i	0.567815	−	0.567815i	0.931516	+	0.363701i	$0.118487\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.21101			−0.182534
$816$		0			0
$817$	70.4088			2.46329
$818$		0			0
$819$		0			0
$820$		0			0
$821$	32.1893	−	32.1893i	1.12341	−	1.12341i	0.132190	−	0.991224i	$-0.457799\pi$
$821$	32.1893	−	32.1893i	1.12341	−	1.12341i	0.991224	−	0.132190i	$-0.0422008\pi$
$822$		0			0
$823$			46.8054i			1.63154i	0.578380	+	0.815768i	$0.303685\pi$
$823$			46.8054i			1.63154i	−0.578380	+	0.815768i	$0.696315\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−3.88598	+	3.88598i	−0.135129	+	0.135129i	−0.771436	−	0.636307i	$-0.780461\pi$
$827$	−3.88598	+	3.88598i	−0.135129	+	0.135129i	0.636307	+	0.771436i	$0.280461\pi$
$828$		0			0
$829$	11.3255	+	11.3255i	0.393350	+	0.393350i	0.875880	−	0.482530i	$-0.160282\pi$
$829$	11.3255	+	11.3255i	0.393350	+	0.393350i	−0.482530	+	0.875880i	$0.660282\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−27.6731			−0.958817
$834$		0			0
$835$	−7.13232	−	7.13232i	−0.246824	−	0.246824i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	29.1290i		−	1.00564i	−0.864390	−	0.502822i	$-0.832295\pi$
$839$		−	29.1290i		−	1.00564i	0.864390	−	0.502822i	$-0.167705\pi$
$840$		0			0
$841$			8.01785i			0.276478i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−8.00059	−	8.00059i	−0.275229	−	0.275229i
$846$		0			0
$847$	123.774			4.25294
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.84799	+	1.84799i	0.0633482	+	0.0633482i
$852$		0			0
$853$	2.72586	−	2.72586i	0.0933317	−	0.0933317i	−0.658899	−	0.752231i	$-0.728978\pi$
$853$	2.72586	−	2.72586i	0.0933317	−	0.0933317i	0.752231	+	0.658899i	$0.228978\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			33.4996i			1.14433i	0.820140	+	0.572163i	$0.193896\pi$
$857$			33.4996i			1.14433i	−0.820140	+	0.572163i	$0.806104\pi$
$858$		0			0
$859$	−19.9283	+	19.9283i	−0.679944	+	0.679944i	−0.959987	−	0.280043i	$-0.909651\pi$
$859$	−19.9283	+	19.9283i	−0.679944	+	0.679944i	0.280043	+	0.959987i	$0.409651\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−54.9834			−1.87166			−0.935829	−	0.352454i	$-0.885347\pi$
$863$	−54.9834			−1.87166			−0.935829	+	0.352454i	$0.885347\pi$
$864$		0			0
$865$	12.9968			0.441906
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−35.8974	+	35.8974i	−1.21774	+	1.21774i
$870$		0			0
$871$		−	14.6963i		−	0.497964i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	3.04692	−	3.04692i	0.103005	−	0.103005i
$876$		0			0
$877$	−26.6186	−	26.6186i	−0.898845	−	0.898845i	0.0964890	−	0.995334i	$-0.469239\pi$
$877$	−26.6186	−	26.6186i	−0.898845	−	0.898845i	−0.995334	+	0.0964890i	$0.969239\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	5.44957			0.183601			0.0918004	−	0.995777i	$-0.470738\pi$
$881$	5.44957			0.183601			0.0918004	+	0.995777i	$0.470738\pi$
$882$		0			0
$883$	−27.7411	−	27.7411i	−0.933563	−	0.933563i	0.0643632	−	0.997927i	$-0.479498\pi$
$883$	−27.7411	−	27.7411i	−0.933563	−	0.933563i	−0.997927	+	0.0643632i	$0.979498\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$			37.1392i			1.24701i	0.781818	+	0.623507i	$0.214293\pi$
$887$			37.1392i			1.24701i	−0.781818	+	0.623507i	$0.785707\pi$
$888$		0			0
$889$			18.3740i			0.616244i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	58.3815	+	58.3815i	1.95366	+	1.95366i
$894$		0			0
$895$	6.06015			0.202568
$896$		0			0
$897$		0			0
$898$		0			0
$899$	23.2318	+	23.2318i	0.774824	+	0.774824i
$900$		0			0
$901$	1.43707	−	1.43707i	0.0478758	−	0.0478758i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			0.237076i			0.00788067i
$906$		0			0
$907$	−10.8291	+	10.8291i	−0.359573	+	0.359573i	−0.863655	−	0.504083i	$-0.831831\pi$
$907$	−10.8291	+	10.8291i	−0.359573	+	0.359573i	0.504083	+	0.863655i	$0.331831\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−43.3251			−1.43542			−0.717712	−	0.696340i	$-0.754811\pi$
$911$	−43.3251			−1.43542			−0.717712	+	0.696340i	$0.754811\pi$
$912$		0			0
$913$	−0.987844			−0.0326929
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−46.8397	+	46.8397i	−1.54678	+	1.54678i
$918$		0			0
$919$			2.17974i			0.0719031i	0.999354	+	0.0359515i	$0.0114462\pi$
$919$			2.17974i			0.0719031i	−0.999354	+	0.0359515i	$0.988554\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.10933	−	2.10933i	0.0694296	−	0.0694296i
$924$		0			0
$925$	−0.841031	−	0.841031i	−0.0276529	−	0.0276529i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−16.3996			−0.538054			−0.269027	−	0.963133i	$-0.586702\pi$
$929$	−16.3996			−0.538054			−0.269027	+	0.963133i	$0.586702\pi$
$930$		0			0
$931$	−61.3826	−	61.3826i	−2.01173	−	2.01173i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	15.0783i		−	0.493113i
$936$		0			0
$937$		−	4.68417i		−	0.153025i	−0.997069	−	0.0765126i	$-0.975621\pi$
$937$		−	4.68417i		−	0.153025i	0.997069	−	0.0765126i	$-0.0243785\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	14.0693	+	14.0693i	0.458647	+	0.458647i	0.898211	−	0.439564i	$-0.144867\pi$
$941$	14.0693	+	14.0693i	0.458647	+	0.458647i	−0.439564	+	0.898211i	$0.644867\pi$
$942$		0			0
$943$	−15.0989			−0.491687
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.57105	−	8.57105i	−0.278522	−	0.278522i	0.553997	−	0.832519i	$-0.313102\pi$
$947$	−8.57105	−	8.57105i	−0.278522	−	0.278522i	−0.832519	+	0.553997i	$0.813102\pi$
$948$		0			0
$949$	−1.17408	+	1.17408i	−0.0381122	+	0.0381122i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			18.8256i			0.609822i	0.952381	+	0.304911i	$0.0986267\pi$
$953$			18.8256i			0.609822i	−0.952381	+	0.304911i	$0.901373\pi$
$954$		0			0
$955$	10.0558	−	10.0558i	0.325398	−	0.325398i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	59.4964			1.92124
$960$		0			0
$961$	−1.84016			−0.0593601
$962$		0			0
$963$		0			0
$964$		0			0
$965$	3.53317	−	3.53317i	0.113737	−	0.113737i
$966$		0			0
$967$			37.5894i			1.20879i	0.796684	+	0.604397i	$0.206586\pi$
$967$			37.5894i			1.20879i	−0.796684	+	0.604397i	$0.793414\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	10.8536	−	10.8536i	0.348310	−	0.348310i	−0.511170	−	0.859480i	$-0.670788\pi$
$971$	10.8536	−	10.8536i	0.348310	−	0.348310i	0.859480	+	0.511170i	$0.170788\pi$
$972$		0			0
$973$	−45.5141	−	45.5141i	−1.45912	−	1.45912i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−52.8951			−1.69227			−0.846133	−	0.532972i	$-0.821075\pi$
$977$	−52.8951			−1.69227			−0.846133	+	0.532972i	$0.821075\pi$
$978$		0			0
$979$	26.3202	+	26.3202i	0.841197	+	0.841197i
$980$		0			0
$981$		0			0
$982$		0			0
$983$		−	48.5114i		−	1.54727i	−0.633630	−	0.773636i	$-0.718436\pi$
$983$		−	48.5114i		−	1.54727i	0.633630	−	0.773636i	$-0.281564\pi$
$984$		0			0
$985$		−	16.9605i		−	0.540406i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	14.5772	+	14.5772i	0.463529	+	0.463529i
$990$		0			0
$991$	−19.9741			−0.634499			−0.317250	−	0.948342i	$-0.602759\pi$
$991$	−19.9741			−0.634499			−0.317250	+	0.948342i	$0.602759\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−6.41290	−	6.41290i	−0.203303	−	0.203303i
$996$		0			0
$997$	26.0697	−	26.0697i	0.825636	−	0.825636i	−0.161274	−	0.986910i	$-0.551560\pi$
$997$	26.0697	−	26.0697i	0.825636	−	0.825636i	0.986910	+	0.161274i	$0.0515602\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2880.2.t.e.721.14		32
3.2	odd	2	inner	2880.2.t.e.721.1		32
4.3	odd	2		720.2.t.e.541.6	yes	32
12.11	even	2		720.2.t.e.541.11	yes	32
16.5	even	4	inner	2880.2.t.e.2161.14		32
16.11	odd	4		720.2.t.e.181.6	✓	32
48.5	odd	4	inner	2880.2.t.e.2161.1		32
48.11	even	4		720.2.t.e.181.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.t.e.181.6	✓	32	16.11	odd	4
720.2.t.e.181.11	yes	32	48.11	even	4
720.2.t.e.541.6	yes	32	4.3	odd	2
720.2.t.e.541.11	yes	32	12.11	even	2
2880.2.t.e.721.1		32	3.2	odd	2	inner
2880.2.t.e.721.14		32	1.1	even	1	trivial
2880.2.t.e.2161.1		32	48.5	odd	4	inner
2880.2.t.e.2161.14		32	16.5	even	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.t (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{5} +4.30899i q^{7} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{5} +4.30899i q^{7} +(4.45672 - 4.45672i) q^{11} +(-0.918004 - 0.918004i) q^{13} +2.39233 q^{17} +(5.30651 + 5.30651i) q^{19} +2.19729i q^{23} -1.00000i q^{25} +(-4.30220 - 4.30220i) q^{29} -5.39998 q^{31} +(3.04692 + 3.04692i) q^{35} +(0.841031 - 0.841031i) q^{37} +6.87159i q^{41} +(6.63419 - 6.63419i) q^{43} +11.0019 q^{47} -11.5674 q^{49} +(0.600698 - 0.600698i) q^{53} -6.30275i q^{55} +(0.850533 - 0.850533i) q^{59} +(-7.50667 - 7.50667i) q^{61} -1.29825 q^{65} +(8.00447 + 8.00447i) q^{67} +2.29774i q^{71} -1.27895i q^{73} +(19.2040 + 19.2040i) q^{77} -8.05468 q^{79} +(-0.110826 - 0.110826i) q^{83} +(1.69164 - 1.69164i) q^{85} +5.90573i q^{89} +(3.95567 - 3.95567i) q^{91} +7.50454 q^{95} +11.0730 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{19} - 32 q^{37} - 16 q^{43} - 32 q^{49} - 16 q^{61} + 16 q^{67} + 16 q^{79} + 16 q^{85} + 80 q^{91}+O(q^{100}) \) 32 * q - 8 * q^19 - 32 * q^37 - 16 * q^43 - 32 * q^49 - 16 * q^61 + 16 * q^67 + 16 * q^79 + 16 * q^85 + 80 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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