LMFDB - Embedded newform 4410.2.d.a.4409.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4410,2,Mod(4409,4410)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4410, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4410.4409");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4410.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$35.2140272914$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} + \cdots + 390625 $ x^16 - 6x^15 + 21x^14 - 54x^13 + 113x^12 - 168x^11 + 186x^10 - 84x^9 - 6x^8 - 420x^7 + 4650x^6 - 21000x^5 + 70625x^4 - 168750x^3 + 328125x^2 - 468750*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4409.12
Root			$-2.11940 - 0.712845i$ of defining polynomial
Character	$\chi$	$=$	4410.4409
Dual form			4410.2.d.a.4409.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(1.67704 + 1.47903i) q^{5} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.67704 + 1.47903i) q^{5} -1.00000 q^{8} +(-1.67704 - 1.47903i) q^{10} +6.33033i q^{11} +1.05290 q^{13} +1.00000 q^{16} -4.63684i q^{17} -6.17914i q^{19} +(1.67704 + 1.47903i) q^{20} -6.33033i q^{22} -7.04472 q^{23} +(0.624933 + 4.96079i) q^{25} -1.05290 q^{26} +2.98101i q^{29} +6.31561i q^{31} -1.00000 q^{32} +4.63684i q^{34} -3.47982i q^{37} +6.17914i q^{38} +(-1.67704 - 1.47903i) q^{40} +6.97007 q^{41} +2.58650i q^{43} +6.33033i q^{44} +7.04472 q^{46} +8.15421i q^{47} +(-0.624933 - 4.96079i) q^{50} +1.05290 q^{52} +8.87365 q^{53} +(-9.36276 + 10.6162i) q^{55} -2.98101i q^{58} +0.904592 q^{59} +10.1735i q^{61} -6.31561i q^{62} +1.00000 q^{64} +(1.76575 + 1.55727i) q^{65} -9.83224i q^{67} -4.63684i q^{68} +14.4282i q^{71} -8.36666 q^{73} +3.47982i q^{74} -6.17914i q^{76} -5.46566 q^{79} +(1.67704 + 1.47903i) q^{80} -6.97007 q^{82} +14.6297i q^{83} +(6.85803 - 7.77617i) q^{85} -2.58650i q^{86} -6.33033i q^{88} +3.83964 q^{89} -7.04472 q^{92} -8.15421i q^{94} +(9.13913 - 10.3627i) q^{95} -5.87891 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8}+O(q^{10}) $ 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8	$ 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8} + 16 q^{16} - 16 q^{23} + 12 q^{25} - 16 q^{32} + 16 q^{46} - 12 q^{50} + 32 q^{53} + 16 q^{64} - 40 q^{65} - 8 q^{79} + 64 q^{85} - 16 q^{92} - 24 q^{95}+O(q^{100}) $ 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8 + 16 * q^16 - 16 * q^23 + 12 * q^25 - 16 * q^32 + 16 * q^46 - 12 * q^50 + 32 * q^53 + 16 * q^64 - 40 * q^65 - 8 * q^79 + 64 * q^85 - 16 * q^92 - 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times$.

$n$	$1081$	$2647$	$3431$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	1.67704	+	1.47903i	0.749996	+	0.661443i
$5$	1.67704	+	1.47903i	0.749996	+	0.661443i
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.67704	−	1.47903i	−0.530327	−	0.467711i
$11$			6.33033i			1.90867i	0.298743	+	0.954334i	$0.403433\pi$
$11$			6.33033i			1.90867i	−0.298743	+	0.954334i	$0.596567\pi$
$12$		0			0
$13$	1.05290			0.292021			0.146011	−	0.989283i	$-0.453357\pi$
$13$	1.05290			0.292021			0.146011	+	0.989283i	$0.453357\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$		−	4.63684i		−	1.12460i	−0.826934	−	0.562299i	$-0.809917\pi$
$17$		−	4.63684i		−	1.12460i	0.826934	−	0.562299i	$-0.190083\pi$
$18$		0			0
$19$		−	6.17914i		−	1.41759i	−0.705414	−	0.708795i	$-0.749239\pi$
$19$		−	6.17914i		−	1.41759i	0.705414	−	0.708795i	$-0.250761\pi$
$20$	1.67704	+	1.47903i	0.374998	+	0.330721i
$21$		0			0
$22$		−	6.33033i		−	1.34963i
$23$	−7.04472			−1.46893			−0.734463	−	0.678649i	$-0.762566\pi$
$23$	−7.04472			−1.46893			−0.734463	+	0.678649i	$0.762566\pi$
$24$		0			0
$25$	0.624933	+	4.96079i	0.124987	+	0.992158i
$26$	−1.05290			−0.206490
$27$		0			0
$28$		0			0
$29$			2.98101i			0.553560i	0.960933	+	0.276780i	$0.0892674\pi$
$29$			2.98101i			0.553560i	−0.960933	+	0.276780i	$0.910733\pi$
$30$		0			0
$31$			6.31561i			1.13432i	0.823608	+	0.567159i	$0.191957\pi$
$31$			6.31561i			1.13432i	−0.823608	+	0.567159i	$0.808043\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$			4.63684i			0.795211i
$35$		0			0
$36$		0			0
$37$		−	3.47982i		−	0.572078i	−0.958218	−	0.286039i	$-0.907661\pi$
$37$		−	3.47982i		−	0.572078i	0.958218	−	0.286039i	$-0.0923388\pi$
$38$			6.17914i			1.00239i
$39$		0			0
$40$	−1.67704	−	1.47903i	−0.265163	−	0.233855i
$41$	6.97007			1.08854			0.544271	−	0.838909i	$-0.316806\pi$
$41$	6.97007			1.08854			0.544271	+	0.838909i	$0.316806\pi$
$42$		0			0
$43$			2.58650i			0.394437i	0.980360	+	0.197218i	$0.0631908\pi$
$43$			2.58650i			0.394437i	−0.980360	+	0.197218i	$0.936809\pi$
$44$			6.33033i			0.954334i
$45$		0			0
$46$	7.04472			1.03869
$47$			8.15421i			1.18941i	0.803942	+	0.594707i	$0.202732\pi$
$47$			8.15421i			1.18941i	−0.803942	+	0.594707i	$0.797268\pi$
$48$		0			0
$49$		0			0
$50$	−0.624933	−	4.96079i	−0.0883789	−	0.701562i
$51$		0			0
$52$	1.05290			0.146011
$53$	8.87365			1.21889			0.609445	−	0.792829i	$-0.291392\pi$
$53$	8.87365			1.21889			0.609445	+	0.792829i	$0.291392\pi$
$54$		0			0
$55$	−9.36276	+	10.6162i	−1.26247	+	1.43149i
$56$		0			0
$57$		0			0
$58$		−	2.98101i		−	0.391426i
$59$	0.904592			0.117768			0.0588839	−	0.998265i	$-0.481246\pi$
$59$	0.904592			0.117768			0.0588839	+	0.998265i	$0.481246\pi$
$60$		0			0
$61$			10.1735i			1.30258i	0.758830	+	0.651289i	$0.225771\pi$
$61$			10.1735i			1.30258i	−0.758830	+	0.651289i	$0.774229\pi$
$62$		−	6.31561i		−	0.802084i
$63$		0			0
$64$	1.00000			0.125000
$65$	1.76575	+	1.55727i	0.219015	+	0.193155i
$66$		0			0
$67$		−	9.83224i		−	1.20120i	−0.799550	−	0.600600i	$-0.794929\pi$
$67$		−	9.83224i		−	1.20120i	0.799550	−	0.600600i	$-0.205071\pi$
$68$		−	4.63684i		−	0.562299i
$69$		0			0
$70$		0			0
$71$			14.4282i			1.71232i	0.516713	+	0.856159i	$0.327156\pi$
$71$			14.4282i			1.71232i	−0.516713	+	0.856159i	$0.672844\pi$
$72$		0			0
$73$	−8.36666			−0.979244			−0.489622	−	0.871935i	$-0.662865\pi$
$73$	−8.36666			−0.979244			−0.489622	+	0.871935i	$0.662865\pi$
$74$			3.47982i			0.404520i
$75$		0			0
$76$		−	6.17914i		−	0.708795i
$77$		0			0
$78$		0			0
$79$	−5.46566			−0.614934			−0.307467	−	0.951559i	$-0.599481\pi$
$79$	−5.46566			−0.614934			−0.307467	+	0.951559i	$0.599481\pi$
$80$	1.67704	+	1.47903i	0.187499	+	0.165361i
$81$		0			0
$82$	−6.97007			−0.769716
$83$			14.6297i			1.60581i	0.596105	+	0.802907i	$0.296714\pi$
$83$			14.6297i			1.60581i	−0.596105	+	0.802907i	$0.703286\pi$
$84$		0			0
$85$	6.85803	−	7.77617i	0.743858	−	0.843444i
$86$		−	2.58650i		−	0.278909i
$87$		0			0
$88$		−	6.33033i		−	0.674816i
$89$	3.83964			0.407001			0.203500	−	0.979075i	$-0.434768\pi$
$89$	3.83964			0.407001			0.203500	+	0.979075i	$0.434768\pi$
$90$		0			0
$91$		0			0
$92$	−7.04472			−0.734463
$93$		0			0
$94$		−	8.15421i		−	0.841043i
$95$	9.13913	−	10.3627i	0.937655	−	1.06319i
$96$		0			0
$97$	−5.87891			−0.596913			−0.298457	−	0.954423i	$-0.596472\pi$
$97$	−5.87891			−0.596913			−0.298457	+	0.954423i	$0.596472\pi$
$98$		0			0
$99$		0			0
$100$	0.624933	+	4.96079i	0.0624933	+	0.496079i
$101$	6.70816			0.667487			0.333744	−	0.942664i	$-0.391688\pi$
$101$	6.70816			0.667487			0.333744	+	0.942664i	$0.391688\pi$
$102$		0			0
$103$	−4.97432			−0.490135			−0.245067	−	0.969506i	$-0.578810\pi$
$103$	−4.97432			−0.490135			−0.245067	+	0.969506i	$0.578810\pi$
$104$	−1.05290			−0.103245
$105$		0			0
$106$	−8.87365			−0.861885
$107$	−7.33930			−0.709517			−0.354759	−	0.934958i	$-0.615437\pi$
$107$	−7.33930			−0.709517			−0.354759	+	0.934958i	$0.615437\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	9.36276	−	10.6162i	0.892704	−	1.01222i
$111$		0			0
$112$		0			0
$113$	−0.184551			−0.0173611			−0.00868054	−	0.999962i	$-0.502763\pi$
$113$	−0.184551			−0.0173611			−0.00868054	+	0.999962i	$0.502763\pi$
$114$		0			0
$115$	−11.8143	−	10.4194i	−1.10169	−	0.971610i
$116$			2.98101i			0.276780i
$117$		0			0
$118$	−0.904592			−0.0832745
$119$		0			0
$120$		0			0
$121$	−29.0731			−2.64301
$122$		−	10.1735i		−	0.921061i
$123$		0			0
$124$			6.31561i			0.567159i
$125$	−6.28913	+	9.24375i	−0.562517	+	0.826786i
$126$		0			0
$127$		−	6.70276i		−	0.594774i	−0.954757	−	0.297387i	$-0.903885\pi$
$127$		−	6.70276i		−	0.594774i	0.954757	−	0.297387i	$-0.0961151\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−1.76575	−	1.55727i	−0.154867	−	0.136581i
$131$	−4.48232			−0.391622			−0.195811	−	0.980642i	$-0.562734\pi$
$131$	−4.48232			−0.391622			−0.195811	+	0.980642i	$0.562734\pi$
$132$		0			0
$133$		0			0
$134$			9.83224i			0.849376i
$135$		0			0
$136$			4.63684i			0.397606i
$137$	−17.5627			−1.50049			−0.750243	−	0.661162i	$-0.770064\pi$
$137$	−17.5627			−1.50049			−0.750243	+	0.661162i	$0.770064\pi$
$138$		0			0
$139$			6.02268i			0.510837i	0.966831	+	0.255418i	$0.0822132\pi$
$139$			6.02268i			0.510837i	−0.966831	+	0.255418i	$0.917787\pi$
$140$		0			0
$141$		0			0
$142$		−	14.4282i		−	1.21079i
$143$			6.66519i			0.557371i
$144$		0			0
$145$	−4.40901	+	4.99928i	−0.366149	+	0.415168i
$146$	8.36666			0.692430
$147$		0			0
$148$		−	3.47982i		−	0.286039i
$149$			7.00381i			0.573775i	0.957964	+	0.286887i	$0.0926205\pi$
$149$			7.00381i			0.573775i	−0.957964	+	0.286887i	$0.907379\pi$
$150$		0			0
$151$	12.8708			1.04741			0.523706	−	0.851899i	$-0.324549\pi$
$151$	12.8708			1.04741			0.523706	+	0.851899i	$0.324549\pi$
$152$			6.17914i			0.501194i
$153$		0			0
$154$		0			0
$155$	−9.34099	+	10.5915i	−0.750286	+	0.850733i
$156$		0			0
$157$	11.0439			0.881396			0.440698	−	0.897655i	$-0.354731\pi$
$157$	11.0439			0.881396			0.440698	+	0.897655i	$0.354731\pi$
$158$	5.46566			0.434824
$159$		0			0
$160$	−1.67704	−	1.47903i	−0.132582	−	0.116928i
$161$		0			0
$162$		0			0
$163$			7.24574i			0.567530i	0.958894	+	0.283765i	$0.0915836\pi$
$163$			7.24574i			0.567530i	−0.958894	+	0.283765i	$0.908416\pi$
$164$	6.97007			0.544271
$165$		0			0
$166$		−	14.6297i		−	1.13548i
$167$			13.8606i			1.07257i	0.844038	+	0.536283i	$0.180172\pi$
$167$			13.8606i			1.07257i	−0.844038	+	0.536283i	$0.819828\pi$
$168$		0			0
$169$	−11.8914			−0.914724
$170$	−6.85803	+	7.77617i	−0.525987	+	0.596405i
$171$		0			0
$172$			2.58650i			0.197218i
$173$		−	0.958803i		−	0.0728965i	−0.999336	−	0.0364482i	$-0.988396\pi$
$173$		−	0.958803i		−	0.0728965i	0.999336	−	0.0364482i	$-0.0116044\pi$
$174$		0			0
$175$		0			0
$176$			6.33033i			0.477167i
$177$		0			0
$178$	−3.83964			−0.287793
$179$		−	23.3862i		−	1.74797i	−0.485954	−	0.873984i	$-0.661528\pi$
$179$		−	23.3862i		−	1.74797i	0.485954	−	0.873984i	$-0.338472\pi$
$180$		0			0
$181$		−	19.2865i		−	1.43355i	−0.697303	−	0.716776i	$-0.745617\pi$
$181$		−	19.2865i		−	1.43355i	0.697303	−	0.716776i	$-0.254383\pi$
$182$		0			0
$183$		0			0
$184$	7.04472			0.519344
$185$	5.14676	−	5.83580i	0.378397	−	0.429056i
$186$		0			0
$187$	29.3527			2.14648
$188$			8.15421i			0.594707i
$189$		0			0
$190$	−9.13913	+	10.3627i	−0.663022	+	0.751787i
$191$		−	2.82843i		−	0.204658i	−0.994751	−	0.102329i	$-0.967371\pi$
$191$		−	2.82843i		−	0.204658i	0.994751	−	0.102329i	$-0.0326294\pi$
$192$		0			0
$193$			8.21725i			0.591490i	0.955267	+	0.295745i	$0.0955679\pi$
$193$			8.21725i			0.591490i	−0.955267	+	0.295745i	$0.904432\pi$
$194$	5.87891			0.422081
$195$		0			0
$196$		0			0
$197$	−3.51321			−0.250306			−0.125153	−	0.992137i	$-0.539942\pi$
$197$	−3.51321			−0.250306			−0.125153	+	0.992137i	$0.539942\pi$
$198$		0			0
$199$		−	3.46410i		−	0.245564i	−0.992434	−	0.122782i	$-0.960818\pi$
$199$		−	3.46410i		−	0.245564i	0.992434	−	0.122782i	$-0.0391815\pi$
$200$	−0.624933	−	4.96079i	−0.0441895	−	0.350781i
$201$		0			0
$202$	−6.70816			−0.471985
$203$		0			0
$204$		0			0
$205$	11.6891	+	10.3090i	0.816402	+	0.720009i
$206$	4.97432			0.346577
$207$		0			0
$208$	1.05290			0.0730053
$209$	39.1160			2.70571
$210$		0			0
$211$	−9.96592			−0.686082			−0.343041	−	0.939320i	$-0.611457\pi$
$211$	−9.96592			−0.686082			−0.343041	+	0.939320i	$0.611457\pi$
$212$	8.87365			0.609445
$213$		0			0
$214$	7.33930			0.501705
$215$	−3.82551	+	4.33766i	−0.260897	+	0.295826i
$216$		0			0
$217$		0			0
$218$	−2.00000			−0.135457
$219$		0			0
$220$	−9.36276	+	10.6162i	−0.631237	+	0.715746i
$221$		−	4.88212i		−	0.328407i
$222$		0			0
$223$	−11.1087			−0.743894			−0.371947	−	0.928254i	$-0.621310\pi$
$223$	−11.1087			−0.743894			−0.371947	+	0.928254i	$0.621310\pi$
$224$		0			0
$225$		0			0
$226$	0.184551			0.0122761
$227$			23.5238i			1.56133i	0.624949	+	0.780665i	$0.285120\pi$
$227$			23.5238i			1.56133i	−0.624949	+	0.780665i	$0.714880\pi$
$228$		0			0
$229$			9.48678i			0.626904i	0.949604	+	0.313452i	$0.101485\pi$
$229$			9.48678i			0.626904i	−0.949604	+	0.313452i	$0.898515\pi$
$230$	11.8143	+	10.4194i	0.779011	+	0.687032i
$231$		0			0
$232$		−	2.98101i		−	0.195713i
$233$	−10.3734			−0.679583			−0.339791	−	0.940501i	$-0.610356\pi$
$233$	−10.3734			−0.679583			−0.339791	+	0.940501i	$0.610356\pi$
$234$		0			0
$235$	−12.0603	+	13.6750i	−0.786730	+	0.892056i
$236$	0.904592			0.0588839
$237$		0			0
$238$		0			0
$239$		−	12.3746i		−	0.800444i	−0.916418	−	0.400222i	$-0.868933\pi$
$239$		−	12.3746i		−	0.800444i	0.916418	−	0.400222i	$-0.131067\pi$
$240$		0			0
$241$		−	12.4947i		−	0.804858i	−0.915451	−	0.402429i	$-0.868166\pi$
$241$		−	12.4947i		−	0.804858i	0.915451	−	0.402429i	$-0.131834\pi$
$242$	29.0731			1.86889
$243$		0			0
$244$			10.1735i			0.651289i
$245$		0			0
$246$		0			0
$247$		−	6.50600i		−	0.413967i
$248$		−	6.31561i		−	0.401042i
$249$		0			0
$250$	6.28913	−	9.24375i	0.397759	−	0.584626i
$251$	−13.5304			−0.854034			−0.427017	−	0.904244i	$-0.640436\pi$
$251$	−13.5304			−0.854034			−0.427017	+	0.904244i	$0.640436\pi$
$252$		0			0
$253$		−	44.5954i		−	2.80369i
$254$			6.70276i			0.420569i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	4.41799i		−	0.275587i	−0.990461	−	0.137793i	$-0.955999\pi$
$257$		−	4.41799i		−	0.275587i	0.990461	−	0.137793i	$-0.0440010\pi$
$258$		0			0
$259$		0			0
$260$	1.76575	+	1.55727i	0.109507	+	0.0965777i
$261$		0			0
$262$	4.48232			0.276919
$263$	6.12635			0.377767			0.188884	−	0.981999i	$-0.439513\pi$
$263$	6.12635			0.377767			0.188884	+	0.981999i	$0.439513\pi$
$264$		0			0
$265$	14.8815	+	13.1244i	0.914162	+	0.806226i
$266$		0			0
$267$		0			0
$268$		−	9.83224i		−	0.600600i
$269$	4.18740			0.255310			0.127655	−	0.991819i	$-0.459255\pi$
$269$	4.18740			0.255310			0.127655	+	0.991819i	$0.459255\pi$
$270$		0			0
$271$		−	0.292938i		−	0.0177947i	−0.999960	−	0.00889737i	$-0.997168\pi$
$271$		−	0.292938i		−	0.0177947i	0.999960	−	0.00889737i	$-0.00283216\pi$
$272$		−	4.63684i		−	0.281150i
$273$		0			0
$274$	17.5627			1.06100
$275$	−31.4035	+	3.95604i	−1.89370	+	0.238558i
$276$		0			0
$277$			14.6220i			0.878550i	0.898353	+	0.439275i	$0.144765\pi$
$277$			14.6220i			0.878550i	−0.898353	+	0.439275i	$0.855235\pi$
$278$		−	6.02268i		−	0.361216i
$279$		0			0
$280$		0			0
$281$			18.1691i			1.08388i	0.840419	+	0.541938i	$0.182309\pi$
$281$			18.1691i			1.08388i	−0.840419	+	0.541938i	$0.817691\pi$
$282$		0			0
$283$	21.2133			1.26100			0.630499	−	0.776190i	$-0.282850\pi$
$283$	21.2133			1.26100			0.630499	+	0.776190i	$0.282850\pi$
$284$			14.4282i			0.856159i
$285$		0			0
$286$		−	6.66519i		−	0.394121i
$287$		0			0
$288$		0			0
$289$	−4.50027			−0.264722
$290$	4.40901	−	4.99928i	0.258906	−	0.293568i
$291$		0			0
$292$	−8.36666			−0.489622
$293$		−	7.64481i		−	0.446615i	−0.974748	−	0.223307i	$-0.928315\pi$
$293$		−	7.64481i		−	0.446615i	0.974748	−	0.223307i	$-0.0716853\pi$
$294$		0			0
$295$	1.51704	+	1.33792i	0.0883254	+	0.0778967i
$296$			3.47982i			0.202260i
$297$		0			0
$298$		−	7.00381i		−	0.405720i
$299$	−7.41737			−0.428957
$300$		0			0
$301$		0			0
$302$	−12.8708			−0.740632
$303$		0			0
$304$		−	6.17914i		−	0.354398i
$305$	−15.0469	+	17.0613i	−0.861581	+	0.976927i
$306$		0			0
$307$	−13.1561			−0.750859			−0.375429	−	0.926851i	$-0.622505\pi$
$307$	−13.1561			−0.750859			−0.375429	+	0.926851i	$0.622505\pi$
$308$		0			0
$309$		0			0
$310$	9.34099	−	10.5915i	0.530533	−	0.601559i
$311$	−6.26087			−0.355021			−0.177511	−	0.984119i	$-0.556804\pi$
$311$	−6.26087			−0.355021			−0.177511	+	0.984119i	$0.556804\pi$
$312$		0			0
$313$	−17.4813			−0.988101			−0.494051	−	0.869433i	$-0.664484\pi$
$313$	−17.4813			−0.988101			−0.494051	+	0.869433i	$0.664484\pi$
$314$	−11.0439			−0.623241
$315$		0			0
$316$	−5.46566			−0.307467
$317$	1.53381			0.0861474			0.0430737	−	0.999072i	$-0.486285\pi$
$317$	1.53381			0.0861474			0.0430737	+	0.999072i	$0.486285\pi$
$318$		0			0
$319$	−18.8708			−1.05656
$320$	1.67704	+	1.47903i	0.0937494	+	0.0826804i
$321$		0			0
$322$		0			0
$323$	−28.6516			−1.59422
$324$		0			0
$325$	0.657991	+	5.22321i	0.0364988	+	0.289731i
$326$		−	7.24574i		−	0.401305i
$327$		0			0
$328$	−6.97007			−0.384858
$329$		0			0
$330$		0			0
$331$	−1.51321			−0.0831737			−0.0415869	−	0.999135i	$-0.513241\pi$
$331$	−1.51321			−0.0831737			−0.0415869	+	0.999135i	$0.513241\pi$
$332$			14.6297i			0.802907i
$333$		0			0
$334$		−	13.8606i		−	0.758419i
$335$	14.5422	−	16.4891i	0.794525	−	0.900894i
$336$		0			0
$337$		−	3.14064i		−	0.171082i	−0.996335	−	0.0855408i	$-0.972738\pi$
$337$		−	3.14064i		−	0.171082i	0.996335	−	0.0855408i	$-0.0272618\pi$
$338$	11.8914			0.646807
$339$		0			0
$340$	6.85803	−	7.77617i	0.371929	−	0.421722i
$341$	−39.9799			−2.16504
$342$		0			0
$343$		0			0
$344$		−	2.58650i		−	0.139455i
$345$		0			0
$346$			0.958803i			0.0515456i
$347$	27.4052			1.47119			0.735593	−	0.677424i	$-0.236904\pi$
$347$	27.4052			1.47119			0.735593	+	0.677424i	$0.236904\pi$
$348$		0			0
$349$			19.5594i			1.04699i	0.852028	+	0.523496i	$0.175373\pi$
$349$			19.5594i			1.04699i	−0.852028	+	0.523496i	$0.824627\pi$
$350$		0			0
$351$		0			0
$352$		−	6.33033i		−	0.337408i
$353$		−	14.8103i		−	0.788272i	−0.919052	−	0.394136i	$-0.871044\pi$
$353$		−	14.8103i		−	0.788272i	0.919052	−	0.394136i	$-0.128956\pi$
$354$		0			0
$355$	−21.3398	+	24.1968i	−1.13260	+	1.28423i
$356$	3.83964			0.203500
$357$		0			0
$358$			23.3862i			1.23600i
$359$		−	16.5690i		−	0.874479i	−0.899345	−	0.437239i	$-0.855956\pi$
$359$		−	16.5690i		−	0.874479i	0.899345	−	0.437239i	$-0.144044\pi$
$360$		0			0
$361$	−19.1817			−1.00956
$362$			19.2865i			1.01367i
$363$		0			0
$364$		0			0
$365$	−14.0312	−	12.3746i	−0.734429	−	0.647714i
$366$		0			0
$367$	−14.0131			−0.731478			−0.365739	−	0.930717i	$-0.619184\pi$
$367$	−14.0131			−0.731478			−0.365739	+	0.930717i	$0.619184\pi$
$368$	−7.04472			−0.367231
$369$		0			0
$370$	−5.14676	+	5.83580i	−0.267567	+	0.303389i
$371$		0			0
$372$		0			0
$373$		−	14.6220i		−	0.757098i	−0.925581	−	0.378549i	$-0.876423\pi$
$373$		−	14.6220i		−	0.757098i	0.925581	−	0.378549i	$-0.123577\pi$
$374$	−29.3527			−1.51779
$375$		0			0
$376$		−	8.15421i		−	0.420522i
$377$			3.13870i			0.161651i
$378$		0			0
$379$	−4.68145			−0.240470			−0.120235	−	0.992745i	$-0.538365\pi$
$379$	−4.68145			−0.240470			−0.120235	+	0.992745i	$0.538365\pi$
$380$	9.13913	−	10.3627i	0.468828	−	0.531593i
$381$		0			0
$382$			2.82843i			0.144715i
$383$			11.6724i			0.596433i	0.954498	+	0.298216i	$0.0963917\pi$
$383$			11.6724i			0.596433i	−0.954498	+	0.298216i	$0.903608\pi$
$384$		0			0
$385$		0			0
$386$		−	8.21725i		−	0.418247i
$387$		0			0
$388$	−5.87891			−0.298457
$389$		−	13.1004i		−	0.664214i	−0.943242	−	0.332107i	$-0.892240\pi$
$389$		−	13.1004i		−	0.664214i	0.943242	−	0.332107i	$-0.107760\pi$
$390$		0			0
$391$			32.6652i			1.65195i
$392$		0			0
$393$		0			0
$394$	3.51321			0.176993
$395$	−9.16613	−	8.08388i	−0.461198	−	0.406744i
$396$		0			0
$397$	30.6804			1.53981			0.769903	−	0.638161i	$-0.220304\pi$
$397$	30.6804			1.53981			0.769903	+	0.638161i	$0.220304\pi$
$398$			3.46410i			0.173640i
$399$		0			0
$400$	0.624933	+	4.96079i	0.0312467	+	0.248040i
$401$			7.94533i			0.396771i	0.980124	+	0.198385i	$0.0635697\pi$
$401$			7.94533i			0.396771i	−0.980124	+	0.198385i	$0.936430\pi$
$402$		0			0
$403$			6.64969i			0.331245i
$404$	6.70816			0.333744
$405$		0			0
$406$		0			0
$407$	22.0284			1.09191
$408$		0			0
$409$			39.8323i			1.96958i	0.173754	+	0.984789i	$0.444410\pi$
$409$			39.8323i			1.96958i	−0.173754	+	0.984789i	$0.555590\pi$
$410$	−11.6891	−	10.3090i	−0.577283	−	0.509123i
$411$		0			0
$412$	−4.97432			−0.245067
$413$		0			0
$414$		0			0
$415$	−21.6377	+	24.5345i	−1.06215	+	1.20435i
$416$	−1.05290			−0.0516226
$417$		0			0
$418$	−39.1160			−1.91323
$419$	−11.0357			−0.539131			−0.269566	−	0.962982i	$-0.586880\pi$
$419$	−11.0357			−0.539131			−0.269566	+	0.962982i	$0.586880\pi$
$420$		0			0
$421$	−7.78421			−0.379379			−0.189690	−	0.981844i	$-0.560748\pi$
$421$	−7.78421			−0.379379			−0.189690	+	0.981844i	$0.560748\pi$
$422$	9.96592			0.485134
$423$		0			0
$424$	−8.87365			−0.430942
$425$	23.0024	−	2.89772i	1.11578	−	0.140560i
$426$		0			0
$427$		0			0
$428$	−7.33930			−0.354759
$429$		0			0
$430$	3.82551	−	4.33766i	0.184482	−	0.209181i
$431$			10.2338i			0.492945i	0.969150	+	0.246472i	$0.0792714\pi$
$431$			10.2338i			0.492945i	−0.969150	+	0.246472i	$0.920729\pi$
$432$		0			0
$433$	40.3902			1.94103			0.970513	−	0.241047i	$-0.0774909\pi$
$433$	40.3902			1.94103			0.970513	+	0.241047i	$0.0774909\pi$
$434$		0			0
$435$		0			0
$436$	2.00000			0.0957826
$437$			43.5303i			2.08234i
$438$		0			0
$439$			12.9709i			0.619065i	0.950889	+	0.309533i	$0.100173\pi$
$439$			12.9709i			0.619065i	−0.950889	+	0.309533i	$0.899827\pi$
$440$	9.36276	−	10.6162i	0.446352	−	0.506109i
$441$		0			0
$442$			4.88212i			0.232219i
$443$	8.65502			0.411212			0.205606	−	0.978635i	$-0.434083\pi$
$443$	8.65502			0.411212			0.205606	+	0.978635i	$0.434083\pi$
$444$		0			0
$445$	6.43923	+	5.67894i	0.305249	+	0.269208i
$446$	11.1087			0.526012
$447$		0			0
$448$		0			0
$449$			25.4407i			1.20062i	0.799768	+	0.600310i	$0.204956\pi$
$449$			25.4407i			1.20062i	−0.799768	+	0.600310i	$0.795044\pi$
$450$		0			0
$451$			44.1229i			2.07767i
$452$	−0.184551			−0.00868054
$453$		0			0
$454$		−	23.5238i		−	1.10403i
$455$		0			0
$456$		0			0
$457$		−	30.5395i		−	1.42858i	−0.699851	−	0.714289i	$-0.746750\pi$
$457$		−	30.5395i		−	1.42858i	0.699851	−	0.714289i	$-0.253250\pi$
$458$		−	9.48678i		−	0.443288i
$459$		0			0
$460$	−11.8143	−	10.4194i	−0.550844	−	0.485805i
$461$	−15.6680			−0.729734			−0.364867	−	0.931060i	$-0.618886\pi$
$461$	−15.6680			−0.729734			−0.364867	+	0.931060i	$0.618886\pi$
$462$		0			0
$463$			32.0462i			1.48931i	0.667448	+	0.744656i	$0.267387\pi$
$463$			32.0462i			1.48931i	−0.667448	+	0.744656i	$0.732613\pi$
$464$			2.98101i			0.138390i
$465$		0			0
$466$	10.3734			0.480538
$467$			0.699158i			0.0323532i	0.999869	+	0.0161766i	$0.00514940\pi$
$467$			0.699158i			0.0323532i	−0.999869	+	0.0161766i	$0.994851\pi$
$468$		0			0
$469$		0			0
$470$	12.0603	−	13.6750i	0.556302	−	0.630779i
$471$		0			0
$472$	−0.904592			−0.0416372
$473$	−16.3734			−0.752849
$474$		0			0
$475$	30.6534	−	3.86155i	1.40647	−	0.177180i
$476$		0			0
$477$		0			0
$478$			12.3746i			0.565999i
$479$	8.54561			0.390459			0.195229	−	0.980758i	$-0.437455\pi$
$479$	8.54561			0.390459			0.195229	+	0.980758i	$0.437455\pi$
$480$		0			0
$481$		−	3.66389i		−	0.167059i
$482$			12.4947i			0.569120i
$483$		0			0
$484$	−29.0731			−1.32151
$485$	−9.85918	−	8.69510i	−0.447682	−	0.394824i
$486$		0			0
$487$			23.8178i			1.07929i	0.841894	+	0.539643i	$0.181441\pi$
$487$			23.8178i			1.07929i	−0.841894	+	0.539643i	$0.818559\pi$
$488$		−	10.1735i		−	0.460531i
$489$		0			0
$490$		0			0
$491$			12.9104i			0.582638i	0.956626	+	0.291319i	$0.0940941\pi$
$491$			12.9104i			0.582638i	−0.956626	+	0.291319i	$0.905906\pi$
$492$		0			0
$493$	13.8225			0.622533
$494$			6.50600i			0.292719i
$495$		0			0
$496$			6.31561i			0.283579i
$497$		0			0
$498$		0			0
$499$	−16.3365			−0.731321			−0.365660	−	0.930748i	$-0.619157\pi$
$499$	−16.3365			−0.731321			−0.365660	+	0.930748i	$0.619157\pi$
$500$	−6.28913	+	9.24375i	−0.281258	+	0.413393i
$501$		0			0
$502$	13.5304			0.603893
$503$			28.3413i			1.26368i	0.775100	+	0.631838i	$0.217699\pi$
$503$			28.3413i			1.26368i	−0.775100	+	0.631838i	$0.782301\pi$
$504$		0			0
$505$	11.2499	+	9.92158i	0.500613	+	0.441505i
$506$			44.5954i			1.98251i
$507$		0			0
$508$		−	6.70276i		−	0.297387i
$509$	2.37821			0.105412			0.0527062	−	0.998610i	$-0.483215\pi$
$509$	2.37821			0.105412			0.0527062	+	0.998610i	$0.483215\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$			4.41799i			0.194869i
$515$	−8.34214	−	7.35718i	−0.367599	−	0.324196i
$516$		0			0
$517$	−51.6189			−2.27020
$518$		0			0
$519$		0			0
$520$	−1.76575	−	1.55727i	−0.0774334	−	0.0682907i
$521$	−8.28370			−0.362915			−0.181458	−	0.983399i	$-0.558082\pi$
$521$	−8.28370			−0.362915			−0.181458	+	0.983399i	$0.558082\pi$
$522$		0			0
$523$	41.8616			1.83048			0.915239	−	0.402910i	$-0.132001\pi$
$523$	41.8616			1.83048			0.915239	+	0.402910i	$0.132001\pi$
$524$	−4.48232			−0.195811
$525$		0			0
$526$	−6.12635			−0.267122
$527$	29.2845			1.27565
$528$		0			0
$529$	26.6281			1.15774
$530$	−14.8815	−	13.1244i	−0.646410	−	0.570088i
$531$		0			0
$532$		0			0
$533$	7.33877			0.317877
$534$		0			0
$535$	−12.3083	−	10.8551i	−0.532135	−	0.469305i
$536$			9.83224i			0.424688i
$537$		0			0
$538$	−4.18740			−0.180531
$539$		0			0
$540$		0			0
$541$	45.9304			1.97470			0.987352	−	0.158543i	$-0.0506796\pi$
$541$	45.9304			1.97470			0.987352	+	0.158543i	$0.0506796\pi$
$542$			0.292938i			0.0125828i
$543$		0			0
$544$			4.63684i			0.198803i
$545$	3.35408	+	2.95806i	0.143673	+	0.126709i
$546$		0			0
$547$		−	4.88688i		−	0.208948i	−0.994528	−	0.104474i	$-0.966684\pi$
$547$		−	4.88688i		−	0.208948i	0.994528	−	0.104474i	$-0.0333159\pi$
$548$	−17.5627			−0.750243
$549$		0			0
$550$	31.4035	−	3.95604i	1.33905	−	0.168686i
$551$	18.4201			0.784722
$552$		0			0
$553$		0			0
$554$		−	14.6220i		−	0.621229i
$555$		0			0
$556$			6.02268i			0.255418i
$557$	−29.3677			−1.24435			−0.622175	−	0.782878i	$-0.713751\pi$
$557$	−29.3677			−1.24435			−0.622175	+	0.782878i	$0.713751\pi$
$558$		0			0
$559$			2.72332i			0.115184i
$560$		0			0
$561$		0			0
$562$		−	18.1691i		−	0.766415i
$563$			2.73921i			0.115444i	0.998333	+	0.0577220i	$0.0183837\pi$
$563$			2.73921i			0.115444i	−0.998333	+	0.0577220i	$0.981616\pi$
$564$		0			0
$565$	−0.309499	−	0.272956i	−0.0130207	−	0.0114834i
$566$	−21.2133			−0.891660
$567$		0			0
$568$		−	14.4282i		−	0.605396i
$569$		−	0.922450i		−	0.0386711i	−0.999813	−	0.0193356i	$-0.993845\pi$
$569$		−	0.922450i		−	0.0386711i	0.999813	−	0.0193356i	$-0.00615508\pi$
$570$		0			0
$571$	−24.5523			−1.02748			−0.513740	−	0.857946i	$-0.671740\pi$
$571$	−24.5523			−1.02748			−0.513740	+	0.857946i	$0.671740\pi$
$572$			6.66519i			0.278686i
$573$		0			0
$574$		0			0
$575$	−4.40248	−	34.9474i	−0.183596	−	1.45741i
$576$		0			0
$577$	27.1333			1.12958			0.564788	−	0.825236i	$-0.308958\pi$
$577$	27.1333			1.12958			0.564788	+	0.825236i	$0.308958\pi$
$578$	4.50027			0.187186
$579$		0			0
$580$	−4.40901	+	4.99928i	−0.183074	+	0.207584i
$581$		0			0
$582$		0			0
$583$			56.1731i			2.32645i
$584$	8.36666			0.346215
$585$		0			0
$586$			7.64481i			0.315804i
$587$		−	8.71353i		−	0.359646i	−0.983699	−	0.179823i	$-0.942448\pi$
$587$		−	8.71353i		−	0.359646i	0.983699	−	0.179823i	$-0.0575525\pi$
$588$		0			0
$589$	39.0250			1.60800
$590$	−1.51704	−	1.33792i	−0.0624555	−	0.0550813i
$591$		0			0
$592$		−	3.47982i		−	0.143020i
$593$			18.2686i			0.750203i	0.926984	+	0.375102i	$0.122392\pi$
$593$			18.2686i			0.750203i	−0.926984	+	0.375102i	$0.877608\pi$
$594$		0			0
$595$		0			0
$596$			7.00381i			0.286887i
$597$		0			0
$598$	7.41737			0.303319
$599$			11.4844i			0.469239i	0.972087	+	0.234619i	$0.0753844\pi$
$599$			11.4844i			0.469239i	−0.972087	+	0.234619i	$0.924616\pi$
$600$		0			0
$601$		−	34.4022i		−	1.40329i	−0.712525	−	0.701647i	$-0.752448\pi$
$601$		−	34.4022i		−	1.40329i	0.712525	−	0.701647i	$-0.247552\pi$
$602$		0			0
$603$		0			0
$604$	12.8708			0.523706
$605$	−48.7568	−	43.0001i	−1.98225	−	1.74820i
$606$		0			0
$607$	45.5128			1.84731			0.923653	−	0.383229i	$-0.125188\pi$
$607$	45.5128			1.84731			0.923653	+	0.383229i	$0.125188\pi$
$608$			6.17914i			0.250597i
$609$		0			0
$610$	15.0469	−	17.0613i	0.609229	−	0.690792i
$611$			8.58555i			0.347334i
$612$		0			0
$613$		−	11.7041i		−	0.472724i	−0.971665	−	0.236362i	$-0.924045\pi$
$613$		−	11.7041i		−	0.472724i	0.971665	−	0.236362i	$-0.0759552\pi$
$614$	13.1561			0.530937
$615$		0			0
$616$		0			0
$617$	24.0582			0.968547			0.484273	−	0.874917i	$-0.339084\pi$
$617$	24.0582			0.968547			0.484273	+	0.874917i	$0.339084\pi$
$618$		0			0
$619$			3.84278i			0.154454i	0.997014	+	0.0772271i	$0.0246067\pi$
$619$			3.84278i			0.154454i	−0.997014	+	0.0772271i	$0.975393\pi$
$620$	−9.34099	+	10.5915i	−0.375143	+	0.425367i
$621$		0			0
$622$	6.26087			0.251038
$623$		0			0
$624$		0			0
$625$	−24.2189	+	6.20033i	−0.968757	+	0.248013i
$626$	17.4813			0.698693
$627$		0			0
$628$	11.0439			0.440698
$629$	−16.1353			−0.643358
$630$		0			0
$631$	−25.4387			−1.01270			−0.506349	−	0.862328i	$-0.669005\pi$
$631$	−25.4387			−1.01270			−0.506349	+	0.862328i	$0.669005\pi$
$632$	5.46566			0.217412
$633$		0			0
$634$	−1.53381			−0.0609154
$635$	9.91359	−	11.2408i	0.393409	−	0.446078i
$636$		0			0
$637$		0			0
$638$	18.8708			0.747102
$639$		0			0
$640$	−1.67704	−	1.47903i	−0.0662909	−	0.0584638i
$641$		−	39.5346i		−	1.56152i	−0.624829	−	0.780762i	$-0.714831\pi$
$641$		−	39.5346i		−	1.56152i	0.624829	−	0.780762i	$-0.285169\pi$
$642$		0			0
$643$	12.2816			0.484341			0.242170	−	0.970234i	$-0.422141\pi$
$643$	12.2816			0.484341			0.242170	+	0.970234i	$0.422141\pi$
$644$		0			0
$645$		0			0
$646$	28.6516			1.12728
$647$			13.3894i			0.526392i	0.964742	+	0.263196i	$0.0847766\pi$
$647$			13.3894i			0.526392i	−0.964742	+	0.263196i	$0.915223\pi$
$648$		0			0
$649$			5.72637i			0.224780i
$650$	−0.657991	−	5.22321i	−0.0258085	−	0.204871i
$651$		0			0
$652$			7.24574i			0.283765i
$653$	−49.5777			−1.94012			−0.970062	−	0.242857i	$-0.921915\pi$
$653$	−49.5777			−1.94012			−0.970062	+	0.242857i	$0.921915\pi$
$654$		0			0
$655$	−7.51704	−	6.62949i	−0.293715	−	0.259036i
$656$	6.97007			0.272136
$657$		0			0
$658$		0			0
$659$		−	40.7622i		−	1.58787i	−0.608002	−	0.793936i	$-0.708029\pi$
$659$		−	40.7622i		−	1.58787i	0.608002	−	0.793936i	$-0.291971\pi$
$660$		0			0
$661$		−	35.7556i		−	1.39073i	−0.718657	−	0.695365i	$-0.755243\pi$
$661$		−	35.7556i		−	1.39073i	0.718657	−	0.695365i	$-0.244757\pi$
$662$	1.51321			0.0588127
$663$		0			0
$664$		−	14.6297i		−	0.567741i
$665$		0			0
$666$		0			0
$667$		−	21.0004i		−	0.813139i
$668$			13.8606i			0.536283i
$669$		0			0
$670$	−14.5422	+	16.4891i	−0.561814	+	0.637028i
$671$	−64.4014			−2.48619
$672$		0			0
$673$			35.1987i			1.35681i	0.734687	+	0.678406i	$0.237329\pi$
$673$			35.1987i			1.35681i	−0.734687	+	0.678406i	$0.762671\pi$
$674$			3.14064i			0.120973i
$675$		0			0
$676$	−11.8914			−0.457362
$677$			38.4422i			1.47745i	0.674005	+	0.738727i	$0.264573\pi$
$677$			38.4422i			1.47745i	−0.674005	+	0.738727i	$0.735427\pi$
$678$		0			0
$679$		0			0
$680$	−6.85803	+	7.77617i	−0.262993	+	0.298202i
$681$		0			0
$682$	39.9799			1.53091
$683$	−38.4023			−1.46942			−0.734712	−	0.678379i	$-0.762683\pi$
$683$	−38.4023			−1.46942			−0.734712	+	0.678379i	$0.762683\pi$
$684$		0			0
$685$	−29.4534	−	25.9758i	−1.12536	−	0.992486i
$686$		0			0
$687$		0			0
$688$			2.58650i			0.0986092i
$689$	9.34304			0.355942
$690$		0			0
$691$		−	20.3469i		−	0.774033i	−0.922073	−	0.387016i	$-0.873506\pi$
$691$		−	20.3469i		−	0.774033i	0.922073	−	0.387016i	$-0.126494\pi$
$692$		−	0.958803i		−	0.0364482i
$693$		0			0
$694$	−27.4052			−1.04029
$695$	−8.90772	+	10.1003i	−0.337889	+	0.383125i
$696$		0			0
$697$		−	32.3191i		−	1.22417i
$698$		−	19.5594i		−	0.740335i
$699$		0			0
$700$		0			0
$701$			6.98574i			0.263848i	0.991260	+	0.131924i	$0.0421154\pi$
$701$			6.98574i			0.263848i	−0.991260	+	0.131924i	$0.957885\pi$
$702$		0			0
$703$	−21.5023			−0.810973
$704$			6.33033i			0.238583i
$705$		0			0
$706$			14.8103i			0.557393i
$707$		0			0
$708$		0			0
$709$	12.0270			0.451682			0.225841	−	0.974164i	$-0.427487\pi$
$709$	12.0270			0.451682			0.225841	+	0.974164i	$0.427487\pi$
$710$	21.3398	−	24.1968i	0.800869	−	0.908088i
$711$		0			0
$712$	−3.83964			−0.143896
$713$		−	44.4917i		−	1.66623i
$714$		0			0
$715$	−9.85803	+	11.1778i	−0.368669	+	0.418026i
$716$		−	23.3862i		−	0.873984i
$717$		0			0
$718$			16.5690i			0.618350i
$719$	−1.67139			−0.0623323			−0.0311661	−	0.999514i	$-0.509922\pi$
$719$	−1.67139			−0.0623323			−0.0311661	+	0.999514i	$0.509922\pi$
$720$		0			0
$721$		0			0
$722$	19.1817			0.713869
$723$		0			0
$724$		−	19.2865i		−	0.716776i
$725$	−14.7882	+	1.86294i	−0.549220	+	0.0691877i
$726$		0			0
$727$	42.5043			1.57640			0.788198	−	0.615422i	$-0.211014\pi$
$727$	42.5043			1.57640			0.788198	+	0.615422i	$0.211014\pi$
$728$		0			0
$729$		0			0
$730$	14.0312	+	12.3746i	0.519319	+	0.458003i
$731$	11.9932			0.443583
$732$		0			0
$733$	−31.8759			−1.17736			−0.588681	−	0.808365i	$-0.700353\pi$
$733$	−31.8759			−1.17736			−0.588681	+	0.808365i	$0.700353\pi$
$734$	14.0131			0.517233
$735$		0			0
$736$	7.04472			0.259672
$737$	62.2414			2.29269
$738$		0			0
$739$	16.4186			0.603969			0.301985	−	0.953313i	$-0.402351\pi$
$739$	16.4186			0.603969			0.301985	+	0.953313i	$0.402351\pi$
$740$	5.14676	−	5.83580i	0.189199	−	0.214528i
$741$		0			0
$742$		0			0
$743$	4.52385			0.165964			0.0829821	−	0.996551i	$-0.473556\pi$
$743$	4.52385			0.165964			0.0829821	+	0.996551i	$0.473556\pi$
$744$		0			0
$745$	−10.3589	+	11.7457i	−0.379519	+	0.430328i
$746$			14.6220i			0.535349i
$747$		0			0
$748$	29.3527			1.07324
$749$		0			0
$750$		0			0
$751$	−17.3975			−0.634844			−0.317422	−	0.948284i	$-0.602817\pi$
$751$	−17.3975			−0.634844			−0.317422	+	0.948284i	$0.602817\pi$
$752$			8.15421i			0.297354i
$753$		0			0
$754$		−	3.13870i		−	0.114305i
$755$	21.5849	+	19.0363i	0.785554	+	0.692803i
$756$		0			0
$757$		−	5.25454i		−	0.190980i	−0.995430	−	0.0954898i	$-0.969558\pi$
$757$		−	5.25454i		−	0.190980i	0.995430	−	0.0954898i	$-0.0304417\pi$
$758$	4.68145			0.170038
$759$		0			0
$760$	−9.13913	+	10.3627i	−0.331511	+	0.375893i
$761$	−14.6280			−0.530266			−0.265133	−	0.964212i	$-0.585416\pi$
$761$	−14.6280			−0.530266			−0.265133	+	0.964212i	$0.585416\pi$
$762$		0			0
$763$		0			0
$764$		−	2.82843i		−	0.102329i
$765$		0			0
$766$		−	11.6724i		−	0.421742i
$767$	0.952443			0.0343907
$768$		0			0
$769$		−	12.4548i		−	0.449131i	−0.974459	−	0.224566i	$-0.927904\pi$
$769$		−	12.4548i		−	0.449131i	0.974459	−	0.224566i	$-0.0720963\pi$
$770$		0			0
$771$		0			0
$772$			8.21725i			0.295745i
$773$			8.30576i			0.298737i	0.988782	+	0.149369i	$0.0477241\pi$
$773$			8.30576i			0.298737i	−0.988782	+	0.149369i	$0.952276\pi$
$774$		0			0
$775$	−31.3304	+	3.94684i	−1.12542	+	0.141775i
$776$	5.87891			0.211041
$777$		0			0
$778$			13.1004i			0.469670i
$779$		−	43.0690i		−	1.54311i
$780$		0			0
$781$	−91.3356			−3.26824
$782$		−	32.6652i		−	1.16811i
$783$		0			0
$784$		0			0
$785$	18.5210	+	16.3342i	0.661043	+	0.582993i
$786$		0			0
$787$	50.6071			1.80395			0.901975	−	0.431788i	$-0.142117\pi$
$787$	50.6071			1.80395			0.901975	+	0.431788i	$0.142117\pi$
$788$	−3.51321			−0.125153
$789$		0			0
$790$	9.16613	+	8.08388i	0.326116	+	0.287611i
$791$		0			0
$792$		0			0
$793$			10.7116i			0.380380i
$794$	−30.6804			−1.08881
$795$		0			0
$796$		−	3.46410i		−	0.122782i
$797$		−	36.6354i		−	1.29769i	−0.760920	−	0.648846i	$-0.775252\pi$
$797$		−	36.6354i		−	1.29769i	0.760920	−	0.648846i	$-0.224748\pi$
$798$		0			0
$799$	37.8098			1.33761
$800$	−0.624933	−	4.96079i	−0.0220947	−	0.175390i
$801$		0			0
$802$		−	7.94533i		−	0.280559i
$803$		−	52.9638i		−	1.86905i
$804$		0			0
$805$		0			0
$806$		−	6.64969i		−	0.234225i
$807$		0			0
$808$	−6.70816			−0.235992
$809$		−	43.5386i		−	1.53074i	−0.643593	−	0.765368i	$-0.722557\pi$
$809$		−	43.5386i		−	1.53074i	0.643593	−	0.765368i	$-0.277443\pi$
$810$		0			0
$811$			13.8915i			0.487795i	0.969801	+	0.243897i	$0.0784260\pi$
$811$			13.8915i			0.487795i	−0.969801	+	0.243897i	$0.921574\pi$
$812$		0			0
$813$		0			0
$814$	−22.0284			−0.772095
$815$	−10.7167	+	12.1514i	−0.375389	+	0.425645i
$816$		0			0
$817$	15.9823			0.559150
$818$		−	39.8323i		−	1.39270i
$819$		0			0
$820$	11.6891	+	10.3090i	0.408201	+	0.360004i
$821$		−	9.54514i		−	0.333128i	−0.986031	−	0.166564i	$-0.946733\pi$
$821$		−	9.54514i		−	0.333128i	0.986031	−	0.166564i	$-0.0532672\pi$
$822$		0			0
$823$		−	10.7960i		−	0.376323i	−0.982138	−	0.188162i	$-0.939747\pi$
$823$		−	10.7960i		−	0.376323i	0.982138	−	0.188162i	$-0.0602529\pi$
$824$	4.97432			0.173289
$825$		0			0
$826$		0			0
$827$	−10.5599			−0.367204			−0.183602	−	0.983001i	$-0.558776\pi$
$827$	−10.5599			−0.367204			−0.183602	+	0.983001i	$0.558776\pi$
$828$		0			0
$829$		−	35.4826i		−	1.23236i	−0.787605	−	0.616181i	$-0.788679\pi$
$829$		−	35.4826i		−	1.23236i	0.787605	−	0.616181i	$-0.211321\pi$
$830$	21.6377	−	24.5345i	0.751056	−	0.851606i
$831$		0			0
$832$	1.05290			0.0365027
$833$		0			0
$834$		0			0
$835$	−20.5003	+	23.2448i	−0.709441	+	0.804420i
$836$	39.1160			1.35285
$837$		0			0
$838$	11.0357			0.381223
$839$	32.5932			1.12524			0.562621	−	0.826715i	$-0.309793\pi$
$839$	32.5932			1.12524			0.562621	+	0.826715i	$0.309793\pi$
$840$		0			0
$841$	20.1136			0.693571
$842$	7.78421			0.268262
$843$		0			0
$844$	−9.96592			−0.343041
$845$	−19.9424	−	17.5878i	−0.686039	−	0.605037i
$846$		0			0
$847$		0			0
$848$	8.87365			0.304722
$849$		0			0
$850$	−23.0024	+	2.89772i	−0.788975	+	0.0993908i
$851$			24.5143i			0.840340i
$852$		0			0
$853$	−20.2310			−0.692695			−0.346347	−	0.938106i	$-0.612578\pi$
$853$	−20.2310			−0.692695			−0.346347	+	0.938106i	$0.612578\pi$
$854$		0			0
$855$		0			0
$856$	7.33930			0.250852
$857$		−	44.9710i		−	1.53618i	−0.640341	−	0.768091i	$-0.721207\pi$
$857$		−	44.9710i		−	1.53618i	0.640341	−	0.768091i	$-0.278793\pi$
$858$		0			0
$859$			43.7042i			1.49117i	0.666411	+	0.745585i	$0.267830\pi$
$859$			43.7042i			1.49117i	−0.666411	+	0.745585i	$0.732170\pi$
$860$	−3.82551	+	4.33766i	−0.130449	+	0.147913i
$861$		0			0
$862$		−	10.2338i		−	0.348565i
$863$	35.6382			1.21314			0.606569	−	0.795031i	$-0.292546\pi$
$863$	35.6382			1.21314			0.606569	+	0.795031i	$0.292546\pi$
$864$		0			0
$865$	1.41810	−	1.60795i	0.0482168	−	0.0546720i
$866$	−40.3902			−1.37251
$867$		0			0
$868$		0			0
$869$		−	34.5994i		−	1.17371i
$870$		0			0
$871$		−	10.3523i		−	0.350776i
$872$	−2.00000			−0.0677285
$873$		0			0
$874$		−	43.5303i		−	1.47243i
$875$		0			0
$876$		0			0
$877$		−	36.4906i		−	1.23220i	−0.787668	−	0.616100i	$-0.788712\pi$
$877$		−	36.4906i		−	1.23220i	0.787668	−	0.616100i	$-0.211288\pi$
$878$		−	12.9709i		−	0.437745i
$879$		0			0
$880$	−9.36276	+	10.6162i	−0.315619	+	0.357873i
$881$	−0.487935			−0.0164390			−0.00821948	−	0.999966i	$-0.502616\pi$
$881$	−0.487935			−0.0164390			−0.00821948	+	0.999966i	$0.502616\pi$
$882$		0			0
$883$			6.26720i			0.210908i	0.994424	+	0.105454i	$0.0336296\pi$
$883$			6.26720i			0.210908i	−0.994424	+	0.105454i	$0.966370\pi$
$884$		−	4.88212i		−	0.164203i
$885$		0			0
$886$	−8.65502			−0.290771
$887$			56.9197i			1.91118i	0.294706	+	0.955588i	$0.404778\pi$
$887$			56.9197i			1.91118i	−0.294706	+	0.955588i	$0.595222\pi$
$888$		0			0
$889$		0			0
$890$	−6.43923	−	5.67894i	−0.215843	−	0.190359i
$891$		0			0
$892$	−11.1087			−0.371947
$893$	50.3860			1.68610
$894$		0			0
$895$	34.5890	−	39.2197i	1.15618	−	1.31097i
$896$		0			0
$897$		0			0
$898$		−	25.4407i		−	0.848966i
$899$	−18.8269			−0.627913
$900$		0			0
$901$		−	41.1457i		−	1.37076i
$902$		−	44.1229i		−	1.46913i
$903$		0			0
$904$	0.184551			0.00613807
$905$	28.5253	−	32.3442i	0.948213	−	1.07516i
$906$		0			0
$907$		−	16.6606i		−	0.553207i	−0.960984	−	0.276603i	$-0.910791\pi$
$907$		−	16.6606i		−	0.553207i	0.960984	−	0.276603i	$-0.0892088\pi$
$908$			23.5238i			0.780665i
$909$		0			0
$910$		0			0
$911$		−	8.02653i		−	0.265931i	−0.991121	−	0.132965i	$-0.957550\pi$
$911$		−	8.02653i		−	0.265931i	0.991121	−	0.132965i	$-0.0424499\pi$
$912$		0			0
$913$	−92.6106			−3.06496
$914$			30.5395i			1.01016i
$915$		0			0
$916$			9.48678i			0.313452i
$917$		0			0
$918$		0			0
$919$	13.7147			0.452405			0.226202	−	0.974080i	$-0.427369\pi$
$919$	13.7147			0.452405			0.226202	+	0.974080i	$0.427369\pi$
$920$	11.8143	+	10.4194i	0.389505	+	0.343516i
$921$		0			0
$922$	15.6680			0.516000
$923$			15.1915i			0.500033i
$924$		0			0
$925$	17.2626	−	2.17465i	0.567592	−	0.0715022i
$926$		−	32.0462i		−	1.05310i
$927$		0			0
$928$		−	2.98101i		−	0.0978566i
$929$	−45.8959			−1.50580			−0.752898	−	0.658137i	$-0.771345\pi$
$929$	−45.8959			−1.50580			−0.752898	+	0.658137i	$0.771345\pi$
$930$		0			0
$931$		0			0
$932$	−10.3734			−0.339791
$933$		0			0
$934$		−	0.699158i		−	0.0228772i
$935$	49.2257	+	43.4136i	1.60985	+	1.41978i
$936$		0			0
$937$	6.17552			0.201746			0.100873	−	0.994899i	$-0.467836\pi$
$937$	6.17552			0.201746			0.100873	+	0.994899i	$0.467836\pi$
$938$		0			0
$939$		0			0
$940$	−12.0603	+	13.6750i	−0.393365	+	0.446028i
$941$	33.4096			1.08912			0.544560	−	0.838722i	$-0.316696\pi$
$941$	33.4096			1.08912			0.544560	+	0.838722i	$0.316696\pi$
$942$		0			0
$943$	−49.1022			−1.59899
$944$	0.904592			0.0294420
$945$		0			0
$946$	16.3734			0.532345
$947$	6.55365			0.212965			0.106483	−	0.994315i	$-0.466041\pi$
$947$	6.55365			0.212965			0.106483	+	0.994315i	$0.466041\pi$
$948$		0			0
$949$	−8.80924			−0.285960
$950$	−30.6534	+	3.86155i	−0.994528	+	0.125285i
$951$		0			0
$952$		0			0
$953$	46.5253			1.50710			0.753551	−	0.657389i	$-0.228339\pi$
$953$	46.5253			1.50710			0.753551	+	0.657389i	$0.228339\pi$
$954$		0			0
$955$	4.18333	−	4.74339i	0.135369	−	0.153492i
$956$		−	12.3746i		−	0.400222i
$957$		0			0
$958$	−8.54561			−0.276096
$959$		0			0
$960$		0			0
$961$	−8.88697			−0.286677
$962$			3.66389i			0.118129i
$963$		0			0
$964$		−	12.4947i		−	0.402429i
$965$	−12.1536	+	13.7807i	−0.391237	+	0.443615i
$966$		0			0
$967$		−	5.93169i		−	0.190750i	−0.995441	−	0.0953752i	$-0.969595\pi$
$967$		−	5.93169i		−	0.190750i	0.995441	−	0.0953752i	$-0.0304051\pi$
$968$	29.0731			0.934445
$969$		0			0
$970$	9.85918	+	8.69510i	0.316559	+	0.279183i
$971$	0.340138			0.0109155			0.00545777	−	0.999985i	$-0.498263\pi$
$971$	0.340138			0.0109155			0.00545777	+	0.999985i	$0.498263\pi$
$972$		0			0
$973$		0			0
$974$		−	23.8178i		−	0.763171i
$975$		0			0
$976$			10.1735i			0.325644i
$977$	20.6886			0.661886			0.330943	−	0.943651i	$-0.392633\pi$
$977$	20.6886			0.661886			0.330943	+	0.943651i	$0.392633\pi$
$978$		0			0
$979$			24.3062i			0.776829i
$980$		0			0
$981$		0			0
$982$		−	12.9104i		−	0.411987i
$983$		−	21.2258i		−	0.676997i	−0.940967	−	0.338499i	$-0.890081\pi$
$983$		−	21.2258i		−	0.676997i	0.940967	−	0.338499i	$-0.109919\pi$
$984$		0			0
$985$	−5.89180	−	5.19615i	−0.187728	−	0.165563i
$986$	−13.8225			−0.440197
$987$		0			0
$988$		−	6.50600i		−	0.206983i
$989$		−	18.2211i		−	0.579398i
$990$		0			0
$991$	58.2067			1.84900			0.924499	−	0.381184i	$-0.124484\pi$
$991$	58.2067			1.84900			0.924499	+	0.381184i	$0.124484\pi$
$992$		−	6.31561i		−	0.200521i
$993$		0			0
$994$		0			0
$995$	5.12351	−	5.80944i	0.162426	−	0.184172i
$996$		0			0
$997$	38.2832			1.21244			0.606220	−	0.795297i	$-0.292685\pi$
$997$	38.2832			1.21244			0.606220	+	0.795297i	$0.292685\pi$
$998$	16.3365			0.517122
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4410.2.d.a.4409.12		16
3.2	odd	2		4410.2.d.b.4409.5		16
5.4	even	2		4410.2.d.b.4409.11		16
7.4	even	3		630.2.bo.b.89.1	yes	16
7.5	odd	6		630.2.bo.b.269.3	yes	16
7.6	odd	2	inner	4410.2.d.a.4409.5		16
15.14	odd	2	inner	4410.2.d.a.4409.6		16
21.5	even	6		630.2.bo.a.269.6	yes	16
21.11	odd	6		630.2.bo.a.89.8	yes	16
21.20	even	2		4410.2.d.b.4409.12		16
35.4	even	6		630.2.bo.a.89.6	✓	16
35.12	even	12		3150.2.bf.f.1151.3		32
35.18	odd	12		3150.2.bf.f.1601.4		32
35.19	odd	6		630.2.bo.a.269.8	yes	16
35.32	odd	12		3150.2.bf.f.1601.15		32
35.33	even	12		3150.2.bf.f.1151.14		32
35.34	odd	2		4410.2.d.b.4409.6		16
105.32	even	12		3150.2.bf.f.1601.3		32
105.47	odd	12		3150.2.bf.f.1151.13		32
105.53	even	12		3150.2.bf.f.1601.16		32
105.68	odd	12		3150.2.bf.f.1151.4		32
105.74	odd	6		630.2.bo.b.89.3	yes	16
105.89	even	6		630.2.bo.b.269.1	yes	16
105.104	even	2	inner	4410.2.d.a.4409.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bo.a.89.6	✓	16	35.4	even	6
630.2.bo.a.89.8	yes	16	21.11	odd	6
630.2.bo.a.269.6	yes	16	21.5	even	6
630.2.bo.a.269.8	yes	16	35.19	odd	6
630.2.bo.b.89.1	yes	16	7.4	even	3
630.2.bo.b.89.3	yes	16	105.74	odd	6
630.2.bo.b.269.1	yes	16	105.89	even	6
630.2.bo.b.269.3	yes	16	7.5	odd	6
3150.2.bf.f.1151.3		32	35.12	even	12
3150.2.bf.f.1151.4		32	105.68	odd	12
3150.2.bf.f.1151.13		32	105.47	odd	12
3150.2.bf.f.1151.14		32	35.33	even	12
3150.2.bf.f.1601.3		32	105.32	even	12
3150.2.bf.f.1601.4		32	35.18	odd	12
3150.2.bf.f.1601.15		32	35.32	odd	12
3150.2.bf.f.1601.16		32	105.53	even	12
4410.2.d.a.4409.5		16	7.6	odd	2	inner
4410.2.d.a.4409.6		16	15.14	odd	2	inner
4410.2.d.a.4409.11		16	105.104	even	2	inner
4410.2.d.a.4409.12		16	1.1	even	1	trivial
4410.2.d.b.4409.5		16	3.2	odd	2
4410.2.d.b.4409.6		16	35.34	odd	2
4410.2.d.b.4409.11		16	5.4	even	2
4410.2.d.b.4409.12		16	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4410.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.67704 + 1.47903i) q^{5} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.67704 + 1.47903i) q^{5} -1.00000 q^{8} +(-1.67704 - 1.47903i) q^{10} +6.33033i q^{11} +1.05290 q^{13} +1.00000 q^{16} -4.63684i q^{17} -6.17914i q^{19} +(1.67704 + 1.47903i) q^{20} -6.33033i q^{22} -7.04472 q^{23} +(0.624933 + 4.96079i) q^{25} -1.05290 q^{26} +2.98101i q^{29} +6.31561i q^{31} -1.00000 q^{32} +4.63684i q^{34} -3.47982i q^{37} +6.17914i q^{38} +(-1.67704 - 1.47903i) q^{40} +6.97007 q^{41} +2.58650i q^{43} +6.33033i q^{44} +7.04472 q^{46} +8.15421i q^{47} +(-0.624933 - 4.96079i) q^{50} +1.05290 q^{52} +8.87365 q^{53} +(-9.36276 + 10.6162i) q^{55} -2.98101i q^{58} +0.904592 q^{59} +10.1735i q^{61} -6.31561i q^{62} +1.00000 q^{64} +(1.76575 + 1.55727i) q^{65} -9.83224i q^{67} -4.63684i q^{68} +14.4282i q^{71} -8.36666 q^{73} +3.47982i q^{74} -6.17914i q^{76} -5.46566 q^{79} +(1.67704 + 1.47903i) q^{80} -6.97007 q^{82} +14.6297i q^{83} +(6.85803 - 7.77617i) q^{85} -2.58650i q^{86} -6.33033i q^{88} +3.83964 q^{89} -7.04472 q^{92} -8.15421i q^{94} +(9.13913 - 10.3627i) q^{95} -5.87891 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8}+O(q^{10}) \) 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8	\( 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8} + 16 q^{16} - 16 q^{23} + 12 q^{25} - 16 q^{32} + 16 q^{46} - 12 q^{50} + 32 q^{53} + 16 q^{64} - 40 q^{65} - 8 q^{79} + 64 q^{85} - 16 q^{92} - 24 q^{95}+O(q^{100}) \) 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8 + 16 * q^16 - 16 * q^23 + 12 * q^25 - 16 * q^32 + 16 * q^46 - 12 * q^50 + 32 * q^53 + 16 * q^64 - 40 * q^65 - 8 * q^79 + 64 * q^85 - 16 * q^92 - 24 * q^95

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