LMFDB - Embedded newform 900.3.f.i.199.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(199,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.f (of order $2$, degree $1$, 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:	$24.5232237924$
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} - 12x^{14} + 138x^{12} - 1000x^{10} + 5291x^{8} - 17800x^{6} + 39458x^{4} - 53588x^{2} + 32761 $ x^16 - 12x^14 + 138x^12 - 1000x^10 + 5291x^8 - 17800x^6 + 39458x^4 - 53588*x^2 + 32761
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{28} $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.9
Root			$1.36646 - 0.157629i$ of defining polynomial
Character	$\chi$	$=$	900.199
Dual form			900.3.f.i.199.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36646 - 1.46040i) q^{2} +(-0.265564 - 3.99117i) q^{4} -1.87135 q^{7} +(-6.19161 - 5.06596i) q^{8} +O(q^{10})$	\(q+(1.36646 - 1.46040i) q^{2} +(-0.265564 - 3.99117i) q^{4} -1.87135 q^{7} +(-6.19161 - 5.06596i) q^{8} -15.1162i q^{11} -18.1245i q^{13} +(-2.55712 + 2.73292i) q^{14} +(-15.8590 + 2.11983i) q^{16} +12.6890i q^{17} +28.1867i q^{19} +(-22.0757 - 20.6556i) q^{22} -10.9317 q^{23} +(-26.4691 - 24.7665i) q^{26} +(0.496963 + 7.46887i) q^{28} +9.95007 q^{29} -24.4440i q^{31} +(-18.5748 + 26.0572i) q^{32} +(18.5311 + 17.3391i) q^{34} +17.8755i q^{37} +(41.1640 + 38.5161i) q^{38} -28.8444 q^{41} -56.3734 q^{43} +(-60.3312 + 4.01431i) q^{44} +(-14.9377 + 15.9647i) q^{46} -49.5329 q^{47} -45.4981 q^{49} +(-72.3381 + 4.81323i) q^{52} -60.1494i q^{53} +(11.5867 + 9.48016i) q^{56} +(13.5964 - 14.5311i) q^{58} -110.939i q^{59} +34.2490 q^{61} +(-35.6982 - 33.4018i) q^{62} +(12.6722 + 62.7329i) q^{64} -131.460 q^{67} +(50.6442 - 3.36976i) q^{68} -52.0957i q^{71} +62.2490i q^{73} +(26.1054 + 24.4262i) q^{74} +(112.498 - 7.48539i) q^{76} +28.2876i q^{77} +103.274i q^{79} +(-39.4148 + 42.1245i) q^{82} -57.2212 q^{83} +(-77.0321 + 82.3280i) q^{86} +(-76.5778 + 93.5934i) q^{88} +145.120 q^{89} +33.9173i q^{91} +(2.90307 + 43.6303i) q^{92} +(-67.6848 + 72.3381i) q^{94} -66.7471i q^{97} +(-62.1714 + 66.4456i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 28 q^{4}+O(q^{10}) $ 16 * q + 28 * q^4	$ 16 q + 28 q^{4} - 28 q^{16} + 232 q^{34} - 368 q^{46} + 304 q^{49} + 32 q^{61} + 364 q^{64} + 768 q^{76} + 336 q^{94}+O(q^{100}) $ 16 * q + 28 * q^4 - 28 * q^16 + 232 * q^34 - 368 * q^46 + 304 * q^49 + 32 * q^61 + 364 * q^64 + 768 * q^76 + 336 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.36646	−	1.46040i	0.683231	−	0.730202i
$2$	1.36646	−	1.46040i	0.683231	−	0.730202i
$3$		0			0
$3$		0			0
$4$	−0.265564	−	3.99117i	−0.0663911	−	0.997794i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.87135			−0.267335			−0.133668	−	0.991026i	$-0.542675\pi$
$7$	−1.87135			−0.267335			−0.133668	+	0.991026i	$0.542675\pi$
$8$	−6.19161	−	5.06596i	−0.773952	−	0.633245i
$9$		0			0
$10$		0			0
$11$		−	15.1162i		−	1.37420i	−0.726565	−	0.687098i	$-0.758884\pi$
$11$		−	15.1162i		−	1.37420i	0.726565	−	0.687098i	$-0.241116\pi$
$12$		0			0
$13$		−	18.1245i		−	1.39419i	−0.716977	−	0.697097i	$-0.754475\pi$
$13$		−	18.1245i		−	1.39419i	0.716977	−	0.697097i	$-0.245525\pi$
$14$	−2.55712	+	2.73292i	−0.182652	+	0.195209i
$15$		0			0
$16$	−15.8590	+	2.11983i	−0.991184	+	0.132489i
$17$			12.6890i			0.746414i	0.927748	+	0.373207i	$0.121742\pi$
$17$			12.6890i			0.746414i	−0.927748	+	0.373207i	$0.878258\pi$
$18$		0			0
$19$			28.1867i			1.48351i	0.670671	+	0.741755i	$0.266006\pi$
$19$			28.1867i			1.48351i	−0.670671	+	0.741755i	$0.733994\pi$
$20$		0			0
$21$		0			0
$22$	−22.0757	−	20.6556i	−1.00344	−	0.938893i
$23$	−10.9317			−0.475291			−0.237646	−	0.971352i	$-0.576376\pi$
$23$	−10.9317			−0.475291			−0.237646	+	0.971352i	$0.576376\pi$
$24$		0			0
$25$		0			0
$26$	−26.4691	−	24.7665i	−1.01804	−	0.952556i
$27$		0			0
$28$	0.496963	+	7.46887i	0.0177487	+	0.266745i
$29$	9.95007			0.343106			0.171553	−	0.985175i	$-0.445122\pi$
$29$	9.95007			0.343106			0.171553	+	0.985175i	$0.445122\pi$
$30$		0			0
$31$		−	24.4440i		−	0.788516i	−0.919000	−	0.394258i	$-0.871002\pi$
$31$		−	24.4440i		−	0.788516i	0.919000	−	0.394258i	$-0.128998\pi$
$32$	−18.5748	+	26.0572i	−0.580464	+	0.814286i
$33$		0			0
$34$	18.5311	+	17.3391i	0.545033	+	0.509973i
$35$		0			0
$36$		0			0
$37$			17.8755i			0.483121i	0.970386	+	0.241561i	$0.0776593\pi$
$37$			17.8755i			0.483121i	−0.970386	+	0.241561i	$0.922341\pi$
$38$	41.1640	+	38.5161i	1.08326	+	1.01358i
$39$		0			0
$40$		0			0
$41$	−28.8444			−0.703522			−0.351761	−	0.936090i	$-0.614417\pi$
$41$	−28.8444			−0.703522			−0.351761	+	0.936090i	$0.614417\pi$
$42$		0			0
$43$	−56.3734			−1.31101			−0.655505	−	0.755191i	$-0.727544\pi$
$43$	−56.3734			−1.31101			−0.655505	+	0.755191i	$0.727544\pi$
$44$	−60.3312	+	4.01431i	−1.37116	+	0.0912344i
$45$		0			0
$46$	−14.9377	+	15.9647i	−0.324734	+	0.347059i
$47$	−49.5329			−1.05389			−0.526946	−	0.849899i	$-0.676663\pi$
$47$	−49.5329			−1.05389			−0.526946	+	0.849899i	$0.676663\pi$
$48$		0			0
$49$	−45.4981			−0.928532
$50$		0			0
$51$		0			0
$52$	−72.3381	+	4.81323i	−1.39112	+	0.0925621i
$53$		−	60.1494i		−	1.13489i	−0.823410	−	0.567447i	$-0.807931\pi$
$53$		−	60.1494i		−	1.13489i	0.823410	−	0.567447i	$-0.192069\pi$
$54$		0			0
$55$		0			0
$56$	11.5867	+	9.48016i	0.206905	+	0.169289i
$57$		0			0
$58$	13.5964	−	14.5311i	0.234421	−	0.250537i
$59$		−	110.939i		−	1.88032i	−0.340739	−	0.940158i	$-0.610677\pi$
$59$		−	110.939i		−	1.88032i	0.340739	−	0.940158i	$-0.389323\pi$
$60$		0			0
$61$	34.2490			0.561460			0.280730	−	0.959787i	$-0.409424\pi$
$61$	34.2490			0.561460			0.280730	+	0.959787i	$0.409424\pi$
$62$	−35.6982	−	33.4018i	−0.575777	−	0.538739i
$63$		0			0
$64$	12.6722	+	62.7329i	0.198003	+	0.980201i
$65$		0			0
$66$		0			0
$67$	−131.460			−1.96209			−0.981047	−	0.193770i	$-0.937928\pi$
$67$	−131.460			−1.96209			−0.981047	+	0.193770i	$0.937928\pi$
$68$	50.6442	−	3.36976i	0.744767	−	0.0495552i
$69$		0			0
$70$		0			0
$71$		−	52.0957i		−	0.733742i	−0.930272	−	0.366871i	$-0.880429\pi$
$71$		−	52.0957i		−	0.733742i	0.930272	−	0.366871i	$-0.119571\pi$
$72$		0			0
$73$			62.2490i			0.852726i	0.904552	+	0.426363i	$0.140205\pi$
$73$			62.2490i			0.852726i	−0.904552	+	0.426363i	$0.859795\pi$
$74$	26.1054	+	24.4262i	0.352776	+	0.330083i
$75$		0			0
$76$	112.498	−	7.48539i	1.48024	−	0.0984919i
$77$			28.2876i			0.367371i
$78$		0			0
$79$			103.274i			1.30726i	0.756814	+	0.653630i	$0.226755\pi$
$79$			103.274i			1.30726i	−0.756814	+	0.653630i	$0.773245\pi$
$80$		0			0
$81$		0			0
$82$	−39.4148	+	42.1245i	−0.480668	+	0.513714i
$83$	−57.2212			−0.689413			−0.344706	−	0.938711i	$-0.612021\pi$
$83$	−57.2212			−0.689413			−0.344706	+	0.938711i	$0.612021\pi$
$84$		0			0
$85$		0			0
$86$	−77.0321	+	82.3280i	−0.895722	+	0.957302i
$87$		0			0
$88$	−76.5778	+	93.5934i	−0.870202	+	1.06356i
$89$	145.120			1.63056			0.815281	−	0.579066i	$-0.196583\pi$
$89$	145.120			1.63056			0.815281	+	0.579066i	$0.196583\pi$
$90$		0			0
$91$			33.9173i			0.372717i
$92$	2.90307	+	43.6303i	0.0315551	+	0.474242i
$93$		0			0
$94$	−67.6848	+	72.3381i	−0.720051	+	0.769554i
$95$		0			0
$96$		0			0
$97$		−	66.7471i		−	0.688114i	−0.938949	−	0.344057i	$-0.888199\pi$
$97$		−	66.7471i		−	0.688114i	0.938949	−	0.344057i	$-0.111801\pi$
$98$	−62.1714	+	66.4456i	−0.634402	+	0.678016i
$99$		0			0
$100$		0			0
$101$	164.571			1.62942			0.814709	−	0.579871i	$-0.196897\pi$
$101$	164.571			1.62942			0.814709	+	0.579871i	$0.196897\pi$
$102$		0			0
$103$	43.2740			0.420136			0.210068	−	0.977687i	$-0.432631\pi$
$103$	43.2740			0.420136			0.210068	+	0.977687i	$0.432631\pi$
$104$	−91.8180	+	112.220i	−0.882865	+	1.07904i
$105$		0			0
$106$	−87.8424	−	82.1918i	−0.828702	−	0.775394i
$107$	173.025			1.61706			0.808528	−	0.588458i	$-0.200265\pi$
$107$	173.025			1.61706			0.808528	+	0.588458i	$0.200265\pi$
$108$		0			0
$109$	162.498			1.49081			0.745404	−	0.666613i	$-0.232257\pi$
$109$	162.498			1.49081			0.745404	+	0.666613i	$0.232257\pi$
$110$		0			0
$111$		0			0
$112$	29.6776	−	3.96693i	0.264979	−	0.0354190i
$113$		−	72.3895i		−	0.640615i	−0.947314	−	0.320307i	$-0.896214\pi$
$113$		−	72.3895i		−	0.640615i	0.947314	−	0.320307i	$-0.103786\pi$
$114$		0			0
$115$		0			0
$116$	−2.64238	−	39.7125i	−0.0227792	−	0.342349i
$117$		0			0
$118$	−162.015	−	151.593i	−1.37301	−	1.28469i
$119$		−	23.7456i		−	0.199543i
$120$		0			0
$121$	−107.498			−0.888414
$122$	46.8000	−	50.0174i	0.383606	−	0.409979i
$123$		0			0
$124$	−97.5603	+	6.49146i	−0.786777	+	0.0523505i
$125$		0			0
$126$		0			0
$127$	−148.535			−1.16957			−0.584785	−	0.811188i	$-0.698821\pi$
$127$	−148.535			−1.16957			−0.584785	+	0.811188i	$0.698821\pi$
$128$	108.931	+	67.2156i	0.851027	+	0.525122i
$129$		0			0
$130$		0			0
$131$			26.7284i			0.204034i	0.994783	+	0.102017i	$0.0325296\pi$
$131$			26.7284i			0.204034i	−0.994783	+	0.102017i	$0.967470\pi$
$132$		0			0
$133$		−	52.7471i		−	0.396595i
$134$	−179.635	+	191.985i	−1.34056	+	1.43273i
$135$		0			0
$136$	64.2821	−	78.5656i	0.472662	−	0.577688i
$137$		−	126.953i		−	0.926664i	−0.886185	−	0.463332i	$-0.846654\pi$
$137$		−	126.953i		−	0.926664i	0.886185	−	0.463332i	$-0.153346\pi$
$138$		0			0
$139$		−	20.7013i		−	0.148930i	−0.997224	−	0.0744652i	$-0.976275\pi$
$139$		−	20.7013i		−	0.148930i	0.997224	−	0.0744652i	$-0.0237250\pi$
$140$		0			0
$141$		0			0
$142$	−76.0808	−	71.1868i	−0.535780	−	0.501315i
$143$	−273.973			−1.91589
$144$		0			0
$145$		0			0
$146$	90.9088	+	85.0609i	0.622663	+	0.582609i
$147$		0			0
$148$	71.3442	−	4.74709i	0.482055	−	0.0320750i
$149$	167.140			1.12174			0.560871	−	0.827903i	$-0.310466\pi$
$149$	167.140			1.12174			0.560871	+	0.827903i	$0.310466\pi$
$150$		0			0
$151$			65.6136i			0.434527i	0.976113	+	0.217264i	$0.0697132\pi$
$151$			65.6136i			0.434527i	−0.976113	+	0.217264i	$0.930287\pi$
$152$	142.793	−	174.521i	0.939425	−	1.14817i
$153$		0			0
$154$	41.3113	+	38.6539i	0.268255	+	0.250999i
$155$		0			0
$156$		0			0
$157$		−	30.3735i		−	0.193462i	−0.995311	−	0.0967310i	$-0.969161\pi$
$157$		−	30.3735i		−	0.193462i	0.995311	−	0.0967310i	$-0.0308387\pi$
$158$	150.821	+	141.119i	0.954565	+	0.893161i
$159$		0			0
$160$		0			0
$161$	20.4570			0.127062
$162$		0			0
$163$	45.1453			0.276965			0.138483	−	0.990365i	$-0.455777\pi$
$163$	45.1453			0.276965			0.138483	+	0.990365i	$0.455777\pi$
$164$	7.66005	+	115.123i	0.0467076	+	0.701970i
$165$		0			0
$166$	−78.1906	+	83.5662i	−0.471028	+	0.503411i
$167$	−32.7951			−0.196378			−0.0981889	−	0.995168i	$-0.531305\pi$
$167$	−32.7951			−0.196378			−0.0981889	+	0.995168i	$0.531305\pi$
$168$		0			0
$169$	−159.498			−0.943776
$170$		0			0
$171$		0			0
$172$	14.9708	+	224.996i	0.0870394	+	1.30812i
$173$		−	316.067i		−	1.82698i	−0.406865	−	0.913488i	$-0.633378\pi$
$173$		−	316.067i		−	1.82698i	0.406865	−	0.913488i	$-0.366622\pi$
$174$		0			0
$175$		0			0
$176$	32.0436	+	239.726i	0.182066	+	1.36208i
$177$		0			0
$178$	198.301	−	211.934i	1.11405	−	1.19064i
$179$		−	258.857i		−	1.44613i	−0.690781	−	0.723064i	$-0.742733\pi$
$179$		−	258.857i		−	1.44613i	0.690781	−	0.723064i	$-0.257267\pi$
$180$		0			0
$181$	−74.4981			−0.411592			−0.205796	−	0.978595i	$-0.565978\pi$
$181$	−74.4981			−0.411592			−0.205796	+	0.978595i	$0.565978\pi$
$182$	49.5329	+	46.3466i	0.272159	+	0.254652i
$183$		0			0
$184$	67.6848	+	55.3795i	0.367852	+	0.300975i
$185$		0			0
$186$		0			0
$187$	191.809			1.02572
$188$	13.1542	+	197.695i	0.0699690	+	1.05157i
$189$		0			0
$190$		0			0
$191$			63.7080i			0.333550i	0.985995	+	0.166775i	$0.0533353\pi$
$191$			63.7080i			0.333550i	−0.985995	+	0.166775i	$0.946665\pi$
$192$		0			0
$193$		−	45.5019i		−	0.235761i	−0.993028	−	0.117881i	$-0.962390\pi$
$193$		−	45.5019i		−	0.235761i	0.993028	−	0.117881i	$-0.0376100\pi$
$194$	−97.4778	−	91.2074i	−0.502463	−	0.470141i
$195$		0			0
$196$	12.0827	+	181.591i	0.0616463	+	0.926483i
$197$			185.926i			0.943787i	0.881656	+	0.471893i	$0.156429\pi$
$197$			185.926i			0.943787i	−0.881656	+	0.471893i	$0.843571\pi$
$198$		0			0
$199$		−	155.904i		−	0.783439i	−0.920085	−	0.391719i	$-0.871880\pi$
$199$		−	155.904i		−	0.783439i	0.920085	−	0.391719i	$-0.128120\pi$
$200$		0			0
$201$		0			0
$202$	224.880	−	240.340i	1.11327	−	1.18980i
$203$	−18.6200			−0.0917243
$204$		0			0
$205$		0			0
$206$	59.1322	−	63.1975i	0.287050	−	0.306784i
$207$		0			0
$208$	38.4209	+	287.436i	0.184716	+	1.38190i
$209$	426.075			2.03863
$210$		0			0
$211$		−	242.219i		−	1.14796i	−0.818870	−	0.573979i	$-0.805399\pi$
$211$		−	242.219i		−	1.14796i	0.818870	−	0.573979i	$-0.194601\pi$
$212$	−240.067	+	15.9735i	−1.13239	+	0.0753468i
$213$		0			0
$214$	236.432	−	252.686i	1.10482	−	1.18078i
$215$		0			0
$216$		0			0
$217$			45.7432i			0.210798i
$218$	222.047	−	237.313i	1.01857	−	1.08859i
$219$		0			0
$220$		0			0
$221$	229.983			1.04065
$222$		0			0
$223$	−250.054			−1.12132			−0.560660	−	0.828046i	$-0.689452\pi$
$223$	−250.054			−1.12132			−0.560660	+	0.828046i	$0.689452\pi$
$224$	34.7600	−	48.7620i	0.155178	−	0.217687i
$225$		0			0
$226$	−105.718	−	98.9174i	−0.467778	−	0.437688i
$227$	−60.4646			−0.266364			−0.133182	−	0.991092i	$-0.542519\pi$
$227$	−60.4646			−0.266364			−0.133182	+	0.991092i	$0.542519\pi$
$228$		0			0
$229$	−78.2490			−0.341699			−0.170849	−	0.985297i	$-0.554651\pi$
$229$	−78.2490			−0.341699			−0.170849	+	0.985297i	$0.554651\pi$
$230$		0			0
$231$		0			0
$232$	−61.6070	−	50.4066i	−0.265547	−	0.217270i
$233$			164.742i			0.707046i	0.935426	+	0.353523i	$0.115016\pi$
$233$			164.742i			0.707046i	−0.935426	+	0.353523i	$0.884984\pi$
$234$		0			0
$235$		0			0
$236$	−442.775	+	29.4614i	−1.87617	+	0.124836i
$237$		0			0
$238$	−34.6782	−	32.4474i	−0.145707	−	0.136334i
$239$		−	243.741i		−	1.01984i	−0.860223	−	0.509918i	$-0.829676\pi$
$239$		−	243.741i		−	1.01984i	0.860223	−	0.509918i	$-0.170324\pi$
$240$		0			0
$241$	383.494			1.59126			0.795631	−	0.605781i	$-0.207139\pi$
$241$	383.494			1.59126			0.795631	+	0.605781i	$0.207139\pi$
$242$	−146.892	+	156.991i	−0.606992	+	0.648722i
$243$		0			0
$244$	−9.09532	−	136.694i	−0.0372759	−	0.560221i
$245$		0			0
$246$		0			0
$247$	510.870			2.06830
$248$	−123.832	+	151.348i	−0.499324	+	0.610274i
$249$		0			0
$250$		0			0
$251$		−	199.753i		−	0.795830i	−0.917422	−	0.397915i	$-0.869734\pi$
$251$		−	199.753i		−	0.795830i	0.917422	−	0.397915i	$-0.130266\pi$
$252$		0			0
$253$			165.245i			0.653143i
$254$	−202.968	+	216.922i	−0.799086	+	0.854023i
$255$		0			0
$256$	247.013	−	67.2365i	0.964893	−	0.262643i
$257$		−	158.366i		−	0.616209i	−0.951352	−	0.308105i	$-0.900305\pi$
$257$		−	158.366i		−	0.616209i	0.951352	−	0.308105i	$-0.0996947\pi$
$258$		0			0
$259$		−	33.4512i		−	0.129155i
$260$		0			0
$261$		0			0
$262$	39.0343	+	36.5234i	0.148986	+	0.139402i
$263$	121.610			0.462395			0.231197	−	0.972907i	$-0.425736\pi$
$263$	121.610			0.462395			0.231197	+	0.972907i	$0.425736\pi$
$264$		0			0
$265$		0			0
$266$	−77.0321	−	72.0769i	−0.289594	−	0.270966i
$267$		0			0
$268$	34.9112	+	524.681i	0.130266	+	1.95776i
$269$	−414.670			−1.54152			−0.770762	−	0.637124i	$-0.780124\pi$
$269$	−414.670			−1.54152			−0.770762	+	0.637124i	$0.780124\pi$
$270$		0			0
$271$			193.331i			0.713399i	0.934219	+	0.356700i	$0.116098\pi$
$271$			193.331i			0.713399i	−0.934219	+	0.356700i	$0.883902\pi$
$272$	−26.8986	−	201.235i	−0.0988918	−	0.739834i
$273$		0			0
$274$	−185.403	−	173.476i	−0.676652	−	0.633126i
$275$		0			0
$276$		0			0
$277$			472.615i			1.70619i	0.521755	+	0.853095i	$0.325278\pi$
$277$			472.615i			1.70619i	−0.521755	+	0.853095i	$0.674722\pi$
$278$	−30.2323	−	28.2876i	−0.108749	−	0.101754i
$279$		0			0
$280$		0			0
$281$	−256.815			−0.913934			−0.456967	−	0.889484i	$-0.651064\pi$
$281$	−256.815			−0.913934			−0.456967	+	0.889484i	$0.651064\pi$
$282$		0			0
$283$	416.837			1.47292			0.736461	−	0.676480i	$-0.236495\pi$
$283$	416.837			1.47292			0.736461	+	0.676480i	$0.236495\pi$
$284$	−207.923	+	13.8348i	−0.732123	+	0.0487140i
$285$		0			0
$286$	−374.374	+	400.111i	−1.30900	+	1.39899i
$287$	53.9779			0.188076
$288$		0			0
$289$	127.988			0.442866
$290$		0			0
$291$		0			0
$292$	248.447	−	16.5311i	0.850845	−	0.0566135i
$293$		−	240.705i		−	0.821520i	−0.911744	−	0.410760i	$-0.865263\pi$
$293$		−	240.705i		−	0.821520i	0.911744	−	0.410760i	$-0.134737\pi$
$294$		0			0
$295$		0			0
$296$	90.5564	−	110.678i	0.305934	−	0.373913i
$297$		0			0
$298$	228.390	−	244.091i	0.766409	−	0.819099i
$299$			198.132i			0.662648i
$300$		0			0
$301$	105.494			0.350479
$302$	95.8225	+	89.6585i	0.317293	+	0.296883i
$303$		0			0
$304$	−59.7510	−	447.012i	−0.196549	−	1.47043i
$305$		0			0
$306$		0			0
$307$	206.547			0.672792			0.336396	−	0.941721i	$-0.390792\pi$
$307$	206.547			0.672792			0.336396	+	0.941721i	$0.390792\pi$
$308$	112.901	−	7.51217i	0.366560	−	0.0243902i
$309$		0			0
$310$		0			0
$311$		−	458.610i		−	1.47463i	−0.675549	−	0.737315i	$-0.736093\pi$
$311$		−	458.610i		−	1.47463i	0.675549	−	0.737315i	$-0.263907\pi$
$312$		0			0
$313$		−	383.992i		−	1.22681i	−0.789768	−	0.613406i	$-0.789799\pi$
$313$		−	383.992i		−	1.22681i	0.789768	−	0.613406i	$-0.210201\pi$
$314$	−44.3577	−	41.5043i	−0.141266	−	0.132179i
$315$		0			0
$316$	412.183	−	27.4258i	1.30438	−	0.0867905i
$317$			429.433i			1.35468i	0.735671	+	0.677339i	$0.236867\pi$
$317$			429.433i			1.35468i	−0.735671	+	0.677339i	$0.763133\pi$
$318$		0			0
$319$		−	150.407i		−	0.471495i
$320$		0			0
$321$		0			0
$322$	27.9537	−	29.8755i	0.0868127	−	0.0927810i
$323$	−357.662			−1.10731
$324$		0			0
$325$		0			0
$326$	61.6894	−	65.9305i	0.189231	−	0.202241i
$327$		0			0
$328$	178.593	+	146.125i	0.544492	+	0.445502i
$329$	92.6933			0.281742
$330$		0			0
$331$			58.1282i			0.175614i	0.996138	+	0.0878070i	$0.0279859\pi$
$331$			58.1282i			0.175614i	−0.996138	+	0.0878070i	$0.972014\pi$
$332$	15.1959	+	228.380i	0.0457709	+	0.687892i
$333$		0			0
$334$	−44.8132	+	47.8941i	−0.134171	+	0.143395i
$335$		0			0
$336$		0			0
$337$		−	405.751i		−	1.20401i	−0.798493	−	0.602004i	$-0.794369\pi$
$337$		−	405.751i		−	1.20401i	0.798493	−	0.602004i	$-0.205631\pi$
$338$	−217.948	+	232.932i	−0.644817	+	0.689147i
$339$		0			0
$340$		0			0
$341$	−369.499			−1.08358
$342$		0			0
$343$	176.839			0.515565
$344$	349.042	+	285.585i	1.01466	+	0.830190i
$345$		0			0
$346$	−461.586	−	431.893i	−1.33406	−	1.24825i
$347$	−324.186			−0.934255			−0.467127	−	0.884190i	$-0.654711\pi$
$347$	−324.186			−0.934255			−0.467127	+	0.884190i	$0.654711\pi$
$348$		0			0
$349$	−34.7471			−0.0995619			−0.0497809	−	0.998760i	$-0.515852\pi$
$349$	−34.7471			−0.0995619			−0.0497809	+	0.998760i	$0.515852\pi$
$350$		0			0
$351$		0			0
$352$	393.884	+	280.780i	1.11899	+	0.797671i
$353$			13.5869i			0.0384899i	0.999815	+	0.0192449i	$0.00612623\pi$
$353$			13.5869i			0.0384899i	−0.999815	+	0.0192449i	$0.993874\pi$
$354$		0			0
$355$		0			0
$356$	−38.5387	−	579.199i	−0.108255	−	1.62696i
$357$		0			0
$358$	−378.036	−	353.718i	−1.05597	−	0.988039i
$359$		−	139.028i		−	0.387265i	−0.981074	−	0.193633i	$-0.937973\pi$
$359$		−	139.028i		−	0.387265i	0.981074	−	0.193633i	$-0.0620270\pi$
$360$		0			0
$361$	−433.490			−1.20080
$362$	−101.799	+	108.797i	−0.281212	+	0.300545i
$363$		0			0
$364$	135.370	−	9.00722i	0.371895	−	0.0247451i
$365$		0			0
$366$		0			0
$367$	−1.87135			−0.00509904			−0.00254952	−	0.999997i	$-0.500812\pi$
$367$	−1.87135			−0.00509904			−0.00254952	+	0.999997i	$0.500812\pi$
$368$	173.365	−	23.1733i	0.471101	−	0.0629710i
$369$		0			0
$370$		0			0
$371$			112.560i			0.303397i
$372$		0			0
$373$			384.864i			1.03181i	0.856647	+	0.515903i	$0.172544\pi$
$373$			384.864i			1.03181i	−0.856647	+	0.515903i	$0.827456\pi$
$374$	262.100	−	280.119i	0.700803	−	0.748982i
$375$		0			0
$376$	306.689	+	250.932i	0.815661	+	0.667371i
$377$		−	180.340i		−	0.478356i
$378$		0			0
$379$		−	483.150i		−	1.27480i	−0.770533	−	0.637401i	$-0.780010\pi$
$379$		−	483.150i		−	1.27480i	0.770533	−	0.637401i	$-0.219990\pi$
$380$		0			0
$381$		0			0
$382$	93.0394	+	87.0545i	0.243559	+	0.227891i
$383$	130.500			0.340730			0.170365	−	0.985381i	$-0.445505\pi$
$383$	130.500			0.340730			0.170365	+	0.985381i	$0.445505\pi$
$384$		0			0
$385$		0			0
$386$	−66.4512	−	62.1767i	−0.172153	−	0.161079i
$387$		0			0
$388$	−266.399	+	17.7257i	−0.686596	+	0.0456847i
$389$	−10.2911			−0.0264553			−0.0132277	−	0.999913i	$-0.504211\pi$
$389$	−10.2911			−0.0264553			−0.0132277	+	0.999913i	$0.504211\pi$
$390$		0			0
$391$		−	138.713i		−	0.354764i
$392$	281.706	+	230.491i	0.718639	+	0.587988i
$393$		0			0
$394$	271.527	+	254.061i	0.689155	+	0.644824i
$395$		0			0
$396$		0			0
$397$		−	228.864i		−	0.576483i	−0.957558	−	0.288242i	$-0.906929\pi$
$397$		−	228.864i		−	0.576483i	0.957558	−	0.288242i	$-0.0930706\pi$
$398$	−227.683	−	213.037i	−0.572069	−	0.535269i
$399$		0			0
$400$		0			0
$401$	96.9322			0.241726			0.120863	−	0.992669i	$-0.461434\pi$
$401$	96.9322			0.241726			0.120863	+	0.992669i	$0.461434\pi$
$402$		0			0
$403$	−443.036			−1.09934
$404$	−43.7042	−	656.832i	−0.108179	−	1.62582i
$405$		0			0
$406$	−25.4436	+	27.1928i	−0.0626689	+	0.0669773i
$407$	270.209			0.663903
$408$		0			0
$409$	135.494			0.331282			0.165641	−	0.986186i	$-0.447031\pi$
$409$	135.494			0.331282			0.165641	+	0.986186i	$0.447031\pi$
$410$		0			0
$411$		0			0
$412$	−11.4920	−	172.714i	−0.0278933	−	0.419209i
$413$			207.605i			0.502675i
$414$		0			0
$415$		0			0
$416$	472.273	+	336.660i	1.13527	+	0.809279i
$417$		0			0
$418$	582.215	−	622.241i	1.39286	−	1.48862i
$419$			384.912i			0.918643i	0.888270	+	0.459322i	$0.151907\pi$
$419$			384.912i			0.918643i	−0.888270	+	0.459322i	$0.848093\pi$
$420$		0			0
$421$	−543.230			−1.29033			−0.645166	−	0.764043i	$-0.723212\pi$
$421$	−543.230			−1.29033			−0.645166	+	0.764043i	$0.723212\pi$
$422$	−353.738	−	330.983i	−0.838242	−	0.784321i
$423$		0			0
$424$	−304.714	+	372.422i	−0.718665	+	0.878353i
$425$		0			0
$426$		0			0
$427$	−64.0918			−0.150098
$428$	−45.9493	−	690.573i	−0.107358	−	1.61349i
$429$		0			0
$430$		0			0
$431$			778.192i			1.80555i	0.430113	+	0.902775i	$0.358474\pi$
$431$			778.192i			1.80555i	−0.430113	+	0.902775i	$0.641526\pi$
$432$		0			0
$433$			5.25291i			0.0121314i	0.999982	+	0.00606571i	$0.00193079\pi$
$433$			5.25291i			0.0121314i	−0.999982	+	0.00606571i	$0.998069\pi$
$434$	66.8036	+	62.5064i	0.153925	+	0.144024i
$435$		0			0
$436$	−43.1537	−	648.558i	−0.0989764	−	1.48752i
$437$		−	308.128i		−	0.705099i
$438$		0			0
$439$		−	208.302i		−	0.474492i	−0.971450	−	0.237246i	$-0.923755\pi$
$439$		−	208.302i		−	0.474492i	0.971450	−	0.237246i	$-0.0762447\pi$
$440$		0			0
$441$		0			0
$442$	314.262	−	335.868i	0.711001	−	0.759882i
$443$	735.826			1.66101			0.830504	−	0.557013i	$-0.188053\pi$
$443$	735.826			1.66101			0.830504	+	0.557013i	$0.188053\pi$
$444$		0			0
$445$		0			0
$446$	−341.689	+	365.180i	−0.766120	+	0.818790i
$447$		0			0
$448$	−23.7140	−	117.395i	−0.0529331	−	0.262042i
$449$	−617.155			−1.37451			−0.687255	−	0.726416i	$-0.741184\pi$
$449$	−617.155			−1.37451			−0.687255	+	0.726416i	$0.741184\pi$
$450$		0			0
$451$			436.016i			0.966777i
$452$	−288.919	+	19.2241i	−0.639201	+	0.0425311i
$453$		0			0
$454$	−82.6226	+	88.3028i	−0.181988	+	0.194500i
$455$		0			0
$456$		0			0
$457$		−	322.747i		−	0.706230i	−0.935580	−	0.353115i	$-0.885122\pi$
$457$		−	322.747i		−	0.706230i	0.935580	−	0.353115i	$-0.114878\pi$
$458$	−106.924	+	114.275i	−0.233459	+	0.249509i
$459$		0			0
$460$		0			0
$461$	509.034			1.10419			0.552097	−	0.833780i	$-0.313828\pi$
$461$	509.034			1.10419			0.552097	+	0.833780i	$0.313828\pi$
$462$		0			0
$463$	741.978			1.60254			0.801272	−	0.598300i	$-0.204157\pi$
$463$	741.978			1.60254			0.801272	+	0.598300i	$0.204157\pi$
$464$	−157.798	+	21.0924i	−0.340081	+	0.0454578i
$465$		0			0
$466$	240.590	+	225.113i	0.516287	+	0.483075i
$467$	−310.692			−0.665293			−0.332647	−	0.943052i	$-0.607942\pi$
$467$	−310.692			−0.665293			−0.332647	+	0.943052i	$0.607942\pi$
$468$		0			0
$469$	246.008			0.524537
$470$		0			0
$471$		0			0
$472$	−562.010	+	686.889i	−1.19070	+	1.45527i
$473$			852.149i			1.80158i
$474$		0			0
$475$		0			0
$476$	−94.7728	+	6.30598i	−0.199102	+	0.0132479i
$477$		0			0
$478$	−355.960	−	333.062i	−0.744686	−	0.696783i
$479$			479.112i			1.00023i	0.865958	+	0.500117i	$0.166710\pi$
$479$			479.112i			1.00023i	−0.865958	+	0.500117i	$0.833290\pi$
$480$		0			0
$481$	323.984			0.673564
$482$	524.030	−	560.057i	1.08720	−	1.16194i
$483$		0			0
$484$	28.5477	+	429.044i	0.0589828	+	0.886454i
$485$		0			0
$486$		0			0
$487$	−572.858			−1.17630			−0.588150	−	0.808752i	$-0.700143\pi$
$487$	−572.858			−1.17630			−0.588150	+	0.808752i	$0.700143\pi$
$488$	−212.057	−	173.504i	−0.434543	−	0.355541i
$489$		0			0
$490$		0			0
$491$		−	0.260515i		−	0.000530580i	−1.00000		0.000265290i	$-0.999916\pi$
$491$		−	0.260515i		−	0.000530580i	1.00000		0.000265290i	$-8.44445e-5\pi$
$492$		0			0
$493$			126.257i			0.256099i
$494$	698.085	−	746.078i	1.41313	−	1.51028i
$495$		0			0
$496$	51.8171	+	387.656i	0.104470	+	0.781565i
$497$			97.4891i			0.196155i
$498$		0			0
$499$			467.713i			0.937300i	0.883384	+	0.468650i	$0.155260\pi$
$499$			467.713i			0.937300i	−0.883384	+	0.468650i	$0.844740\pi$
$500$		0			0
$501$		0			0
$502$	−291.721	−	272.955i	−0.581117	−	0.543736i
$503$	728.659			1.44863			0.724313	−	0.689471i	$-0.242157\pi$
$503$	728.659			1.44863			0.724313	+	0.689471i	$0.242157\pi$
$504$		0			0
$505$		0			0
$506$	241.325	+	225.801i	0.476927	+	0.446247i
$507$		0			0
$508$	39.4457	+	592.831i	0.0776491	+	1.16699i
$509$	−453.697			−0.891350			−0.445675	−	0.895195i	$-0.647036\pi$
$509$	−453.697			−0.891350			−0.445675	+	0.895195i	$0.647036\pi$
$510$		0			0
$511$		−	116.490i		−	0.227964i
$512$	239.341	−	452.615i	0.467463	−	0.884013i
$513$		0			0
$514$	−231.278	−	216.401i	−0.449958	−	0.421013i
$515$		0			0
$516$		0			0
$517$			748.747i			1.44825i
$518$	−48.8523	−	45.7098i	−0.0943095	−	0.0882429i
$519$		0			0
$520$		0			0
$521$	−624.519			−1.19869			−0.599346	−	0.800490i	$-0.704573\pi$
$521$	−624.519			−1.19869			−0.599346	+	0.800490i	$0.704573\pi$
$522$		0			0
$523$	−319.527			−0.610950			−0.305475	−	0.952200i	$-0.598815\pi$
$523$	−319.527			−0.610950			−0.305475	+	0.952200i	$0.598815\pi$
$524$	106.678	−	7.09812i	0.203584	−	0.0135460i
$525$		0			0
$526$	166.175	−	177.600i	0.315922	−	0.337642i
$527$	310.171			0.588560
$528$		0			0
$529$	−409.498			−0.774098
$530$		0			0
$531$		0			0
$532$	−210.523	+	14.0078i	−0.395720	+	0.0263304i
$533$			522.791i			0.980846i
$534$		0			0
$535$		0			0
$536$	813.951	+	665.972i	1.51857	+	1.24249i
$537$		0			0
$538$	−566.630	+	605.586i	−1.05322	+	1.12562i
$539$			687.756i			1.27598i
$540$		0			0
$541$	449.984			0.831764			0.415882	−	0.909419i	$-0.363473\pi$
$541$	449.984			0.831764			0.415882	+	0.909419i	$0.363473\pi$
$542$	282.342	+	264.180i	0.520926	+	0.487416i
$543$		0			0
$544$	−330.640	−	235.697i	−0.607794	−	0.433266i
$545$		0			0
$546$		0			0
$547$	−650.049			−1.18839			−0.594195	−	0.804321i	$-0.702529\pi$
$547$	−650.049			−1.18839			−0.594195	+	0.804321i	$0.702529\pi$
$548$	−506.692	+	33.7142i	−0.924620	+	0.0615223i
$549$		0			0
$550$		0			0
$551$			280.460i			0.509001i
$552$		0			0
$553$		−	193.261i		−	0.349477i
$554$	690.209	+	645.810i	1.24586	+	1.16572i
$555$		0			0
$556$	−82.6226	+	5.49753i	−0.148602	+	0.00988765i
$557$		−	127.555i		−	0.229004i	−0.993423	−	0.114502i	$-0.963473\pi$
$557$		−	127.555i		−	0.229004i	0.993423	−	0.114502i	$-0.0365272\pi$
$558$		0			0
$559$			1021.74i			1.82780i
$560$		0			0
$561$		0			0
$562$	−350.928	+	375.055i	−0.624428	+	0.667357i
$563$	−474.827			−0.843387			−0.421694	−	0.906738i	$-0.638564\pi$
$563$	−474.827			−0.843387			−0.421694	+	0.906738i	$0.638564\pi$
$564$		0			0
$565$		0			0
$566$	569.592	−	608.751i	1.00635	−	1.07553i
$567$		0			0
$568$	−263.914	+	322.556i	−0.464638	+	0.567881i
$569$	−125.095			−0.219850			−0.109925	−	0.993940i	$-0.535061\pi$
$569$	−125.095			−0.219850			−0.109925	+	0.993940i	$0.535061\pi$
$570$		0			0
$571$		−	190.288i		−	0.333253i	−0.986020	−	0.166627i	$-0.946713\pi$
$571$		−	190.288i		−	0.333253i	0.986020	−	0.166627i	$-0.0532874\pi$
$572$	72.7575	+	1093.47i	0.127198	+	1.91167i
$573$		0			0
$574$	73.7587	−	78.8296i	0.128500	−	0.137334i
$575$		0			0
$576$		0			0
$577$		−	492.739i		−	0.853968i	−0.904259	−	0.426984i	$-0.859576\pi$
$577$		−	492.739i		−	0.853968i	0.904259	−	0.426984i	$-0.140424\pi$
$578$	174.891	−	186.915i	0.302580	−	0.323382i
$579$		0			0
$580$		0			0
$581$	107.081			0.184304
$582$		0			0
$583$	−909.227			−1.55957
$584$	315.351	−	385.422i	0.539984	−	0.659969i
$585$		0			0
$586$	−351.527	−	328.915i	−0.599876	−	0.561288i
$587$	293.954			0.500774			0.250387	−	0.968146i	$-0.419442\pi$
$587$	293.954			0.500774			0.250387	+	0.968146i	$0.419442\pi$
$588$		0			0
$589$	688.996			1.16977
$590$		0			0
$591$		0			0
$592$	−37.8930	−	283.486i	−0.0640084	−	0.478862i
$593$		−	434.184i		−	0.732181i	−0.930579	−	0.366091i	$-0.880696\pi$
$593$		−	434.184i		−	0.732181i	0.930579	−	0.366091i	$-0.119304\pi$
$594$		0			0
$595$		0			0
$596$	−44.3863	−	667.083i	−0.0744737	−	1.11927i
$597$		0			0
$598$	289.352	+	270.739i	0.483867	+	0.452741i
$599$			509.345i			0.850325i	0.905117	+	0.425162i	$0.139783\pi$
$599$			509.345i			0.850325i	−0.905117	+	0.425162i	$0.860217\pi$
$600$		0			0
$601$	293.502			0.488356			0.244178	−	0.969730i	$-0.421482\pi$
$601$	293.502			0.488356			0.244178	+	0.969730i	$0.421482\pi$
$602$	144.154	−	154.064i	0.239458	−	0.255921i
$603$		0			0
$604$	261.875	−	17.4246i	0.433569	−	0.0288488i
$605$		0			0
$606$		0			0
$607$	−35.0896			−0.0578082			−0.0289041	−	0.999582i	$-0.509202\pi$
$607$	−35.0896			−0.0578082			−0.0289041	+	0.999582i	$0.509202\pi$
$608$	−734.465	−	523.564i	−1.20800	−	0.861124i
$609$		0			0
$610$		0			0
$611$			897.760i			1.46933i
$612$		0			0
$613$		−	49.6109i		−	0.0809314i	−0.999181	−	0.0404657i	$-0.987116\pi$
$613$		−	49.6109i		−	0.0809314i	0.999181	−	0.0404657i	$-0.0128842\pi$
$614$	282.239	−	301.642i	0.459672	−	0.491274i
$615$		0			0
$616$	143.304	−	175.146i	0.232636	−	0.284327i
$617$		−	427.251i		−	0.692465i	−0.938149	−	0.346232i	$-0.887461\pi$
$617$		−	427.251i		−	0.692465i	0.938149	−	0.346232i	$-0.112539\pi$
$618$		0			0
$619$			903.263i			1.45923i	0.683858	+	0.729615i	$0.260301\pi$
$619$			903.263i			1.45923i	−0.683858	+	0.729615i	$0.739699\pi$
$620$		0			0
$621$		0			0
$622$	−669.756	−	626.673i	−1.07678	−	1.00751i
$623$	−271.570			−0.435906
$624$		0			0
$625$		0			0
$626$	−560.784	−	524.711i	−0.895821	−	0.838196i
$627$		0			0
$628$	−121.226	+	8.06613i	−0.193035	+	0.0128442i
$629$	−226.823			−0.360608
$630$		0			0
$631$		−	681.512i		−	1.08005i	−0.841649	−	0.540026i	$-0.818415\pi$
$631$		−	681.512i		−	1.08005i	0.841649	−	0.540026i	$-0.181585\pi$
$632$	523.179	−	639.430i	0.827816	−	1.01176i
$633$		0			0
$634$	627.146	+	586.804i	0.989189	+	0.925558i
$635$		0			0
$636$		0			0
$637$			824.630i			1.29455i
$638$	−219.655	−	205.525i	−0.344286	−	0.322140i
$639$		0			0
$640$		0			0
$641$	252.576			0.394035			0.197018	−	0.980400i	$-0.436874\pi$
$641$	252.576			0.394035			0.197018	+	0.980400i	$0.436874\pi$
$642$		0			0
$643$	−15.2038			−0.0236451			−0.0118225	−	0.999930i	$-0.503763\pi$
$643$	−15.2038			−0.0236451			−0.0118225	+	0.999930i	$0.503763\pi$
$644$	−5.43265	−	81.6474i	−0.00843579	−	0.126782i
$645$		0			0
$646$	−488.732	+	522.331i	−0.756550	+	0.808563i
$647$	463.576			0.716501			0.358250	−	0.933626i	$-0.383373\pi$
$647$	463.576			0.716501			0.358250	+	0.933626i	$0.383373\pi$
$648$		0			0
$649$	−1676.97			−2.58392
$650$		0			0
$651$		0			0
$652$	−11.9890	−	180.183i	−0.0183880	−	0.276354i
$653$			351.503i			0.538289i	0.963100	+	0.269145i	$0.0867410\pi$
$653$			351.503i			0.538289i	−0.963100	+	0.269145i	$0.913259\pi$
$654$		0			0
$655$		0			0
$656$	457.442	−	61.1452i	0.697320	−	0.0932091i
$657$		0			0
$658$	126.662	−	135.370i	0.192495	−	0.205729i
$659$			494.229i			0.749967i	0.927031	+	0.374984i	$0.122352\pi$
$659$			494.229i			0.749967i	−0.927031	+	0.374984i	$0.877648\pi$
$660$		0			0
$661$	165.735			0.250734			0.125367	−	0.992110i	$-0.459989\pi$
$661$	165.735			0.250734			0.125367	+	0.992110i	$0.459989\pi$
$662$	84.8908	+	79.4300i	0.128234	+	0.119985i
$663$		0			0
$664$	354.292	+	289.880i	0.533572	+	0.436567i
$665$		0			0
$666$		0			0
$667$	−108.771			−0.163075
$668$	8.70921	+	130.891i	0.0130377	+	0.195944i
$669$		0			0
$670$		0			0
$671$		−	517.714i		−	0.771555i
$672$		0			0
$673$		−	3.74322i		−	0.00556199i	−0.999996	−	0.00278099i	$-0.999115\pi$
$673$		−	3.74322i		−	0.00556199i	0.999996	−	0.00278099i	$-0.000885219\pi$
$674$	−592.561	−	554.443i	−0.879170	−	0.822616i
$675$		0			0
$676$	42.3570	+	636.585i	0.0626583	+	0.941693i
$677$		−	969.987i		−	1.43277i	−0.697704	−	0.716386i	$-0.745795\pi$
$677$		−	969.987i		−	1.43277i	0.697704	−	0.716386i	$-0.254205\pi$
$678$		0			0
$679$			124.907i			0.183957i
$680$		0			0
$681$		0			0
$682$	−504.907	+	539.619i	−0.740333	+	0.791230i
$683$	808.424			1.18364			0.591819	−	0.806071i	$-0.298410\pi$
$683$	808.424			1.18364			0.591819	+	0.806071i	$0.298410\pi$
$684$		0			0
$685$		0			0
$686$	241.643	−	258.256i	0.352250	−	0.376466i
$687$		0			0
$688$	894.023	−	119.502i	1.29945	−	0.173695i
$689$	−1090.18			−1.58226
$690$		0			0
$691$			395.903i			0.572942i	0.958089	+	0.286471i	$0.0924821\pi$
$691$			395.903i			0.572942i	−0.958089	+	0.286471i	$0.907518\pi$
$692$	−1261.48	+	83.9361i	−1.82295	+	0.121295i
$693$		0			0
$694$	−442.988	+	473.443i	−0.638312	+	0.682195i
$695$		0			0
$696$		0			0
$697$		−	366.008i		−	0.525119i
$698$	−47.4806	+	50.7448i	−0.0680237	+	0.0727003i
$699$		0			0
$700$		0			0
$701$	−961.043			−1.37096			−0.685480	−	0.728091i	$-0.740408\pi$
$701$	−961.043			−1.37096			−0.685480	+	0.728091i	$0.740408\pi$
$702$		0			0
$703$	−503.851			−0.716716
$704$	948.280	−	191.555i	1.34699	−	0.272095i
$705$		0			0
$706$	19.8424	+	18.5660i	0.0281054	+	0.0262975i
$707$	−307.970			−0.435601
$708$		0			0
$709$	817.751			1.15339			0.576693	−	0.816961i	$-0.304343\pi$
$709$	817.751			1.15339			0.576693	+	0.816961i	$0.304343\pi$
$710$		0			0
$711$		0			0
$712$	−898.527	−	735.171i	−1.26198	−	1.03254i
$713$			267.214i			0.374775i
$714$		0			0
$715$		0			0
$716$	−1033.14	+	68.7432i	−1.44294	+	0.0960100i
$717$		0			0
$718$	−203.037	−	189.977i	−0.282782	−	0.264592i
$719$			91.2179i			0.126868i	0.997986	+	0.0634339i	$0.0202052\pi$
$719$			91.2179i			0.126868i	−0.997986	+	0.0634339i	$0.979795\pi$
$720$		0			0
$721$	−80.9806			−0.112317
$722$	−592.348	+	633.071i	−0.820427	+	0.876830i
$723$		0			0
$724$	19.7840	+	297.335i	0.0273260	+	0.410683i
$725$		0			0
$726$		0			0
$727$	−662.682			−0.911530			−0.455765	−	0.890100i	$-0.650634\pi$
$727$	−662.682			−0.911530			−0.455765	+	0.890100i	$0.650634\pi$
$728$	171.823	−	210.003i	0.236021	−	0.288465i
$729$		0			0
$730$		0			0
$731$		−	715.324i		−	0.978556i
$732$		0			0
$733$		−	430.623i		−	0.587480i	−0.955885	−	0.293740i	$-0.905100\pi$
$733$		−	430.623i		−	0.587480i	0.955885	−	0.293740i	$-0.0948999\pi$
$734$	−2.55712	+	2.73292i	−0.00348382	+	0.00372333i
$735$		0			0
$736$	203.055	−	284.849i	0.275889	−	0.387023i
$737$			1987.17i			2.69630i
$738$		0			0
$739$		−	523.620i		−	0.708552i	−0.935141	−	0.354276i	$-0.884727\pi$
$739$		−	523.620i		−	0.708552i	0.935141	−	0.354276i	$-0.115273\pi$
$740$		0			0
$741$		0			0
$742$	164.384	+	153.809i	0.221541	+	0.207290i
$743$	880.661			1.18528			0.592638	−	0.805469i	$-0.298086\pi$
$743$	880.661			1.18528			0.592638	+	0.805469i	$0.298086\pi$
$744$		0			0
$745$		0			0
$746$	562.057	+	525.902i	0.753428	+	0.704962i
$747$		0			0
$748$	−50.9378	−	765.545i	−0.0680986	−	1.02346i
$749$	−323.790			−0.432296
$750$		0			0
$751$		−	602.683i		−	0.802507i	−0.915967	−	0.401254i	$-0.868575\pi$
$751$		−	602.683i		−	0.802507i	0.915967	−	0.401254i	$-0.131425\pi$
$752$	785.540	−	105.001i	1.04460	−	0.139629i
$753$		0			0
$754$	−263.370	−	246.428i	−0.349297	−	0.326828i
$755$		0			0
$756$		0			0
$757$			427.136i			0.564249i	0.959378	+	0.282124i	$0.0910390\pi$
$757$			427.136i			0.564249i	−0.959378	+	0.282124i	$0.908961\pi$
$758$	−705.594	−	660.206i	−0.930863	−	0.870984i
$759$		0			0
$760$		0			0
$761$	239.700			0.314980			0.157490	−	0.987521i	$-0.449660\pi$
$761$	239.700			0.314980			0.157490	+	0.987521i	$0.449660\pi$
$762$		0			0
$763$	−304.090			−0.398545
$764$	254.270	−	16.9186i	0.332814	−	0.0221447i
$765$		0			0
$766$	178.323	−	190.582i	0.232798	−	0.248802i
$767$	−2010.71			−2.62152
$768$		0			0
$769$	−937.486			−1.21910			−0.609549	−	0.792748i	$-0.708649\pi$
$769$	−937.486			−1.21910			−0.609549	+	0.792748i	$0.708649\pi$
$770$		0			0
$771$		0			0
$772$	−181.606	+	12.0837i	−0.235241	+	0.0156525i
$773$			1468.30i			1.89948i	0.313040	+	0.949740i	$0.398653\pi$
$773$			1468.30i			1.89948i	−0.313040	+	0.949740i	$0.601347\pi$
$774$		0			0
$775$		0			0
$776$	−338.138	+	413.272i	−0.435745	+	0.532567i
$777$		0			0
$778$	−14.0624	+	15.0292i	−0.0180751	+	0.0193177i
$779$		−	813.029i		−	1.04368i
$780$		0			0
$781$	−787.486			−1.00831
$782$	−202.577	−	189.546i	−0.259049	−	0.242386i
$783$		0			0
$784$	721.552	−	96.4481i	0.920346	−	0.123020i
$785$		0			0
$786$		0			0
$787$	408.886			0.519550			0.259775	−	0.965669i	$-0.416352\pi$
$787$	408.886			0.519550			0.259775	+	0.965669i	$0.416352\pi$
$788$	742.063	−	49.3753i	0.941705	−	0.0626591i
$789$		0			0
$790$		0			0
$791$			135.466i			0.171259i
$792$		0			0
$793$		−	620.747i		−	0.782783i
$794$	−334.234	−	312.734i	−0.420949	−	0.393871i
$795$		0			0
$796$	−622.241	+	41.4026i	−0.781710	+	0.0520134i
$797$			400.122i			0.502035i	0.967982	+	0.251018i	$0.0807652\pi$
$797$			400.122i			0.502035i	−0.967982	+	0.251018i	$0.919235\pi$
$798$		0			0
$799$		−	628.525i		−	0.786639i
$800$		0			0
$801$		0			0
$802$	132.454	−	141.560i	0.165155	−	0.176509i
$803$	940.966			1.17181
$804$		0			0
$805$		0			0
$806$	−605.392	+	647.012i	−0.751106	+	0.802744i
$807$		0			0
$808$	−1018.96	−	833.710i	−1.26109	−	1.03182i
$809$	−255.486			−0.315805			−0.157902	−	0.987455i	$-0.550473\pi$
$809$	−255.486			−0.315805			−0.157902	+	0.987455i	$0.550473\pi$
$810$		0			0
$811$		−	295.549i		−	0.364425i	−0.983259	−	0.182213i	$-0.941674\pi$
$811$		−	295.549i		−	0.364425i	0.983259	−	0.182213i	$-0.0583259\pi$
$812$	4.94482	+	74.3158i	0.00608968	+	0.0915219i
$813$		0			0
$814$	369.230	−	394.614i	0.453599	−	0.484784i
$815$		0			0
$816$		0			0
$817$		−	1588.98i		−	1.94490i
$818$	185.148	−	197.876i	0.226342	−	0.241903i
$819$		0			0
$820$		0			0
$821$	−1227.23			−1.49480			−0.747402	−	0.664372i	$-0.768699\pi$
$821$	−1227.23			−1.49480			−0.747402	+	0.664372i	$0.768699\pi$
$822$		0			0
$823$	881.623			1.07123			0.535615	−	0.844462i	$-0.320080\pi$
$823$	881.623			1.07123			0.535615	+	0.844462i	$0.320080\pi$
$824$	−267.936	−	219.224i	−0.325165	−	0.266049i
$825$		0			0
$826$	303.187	+	283.684i	0.367054	+	0.343443i
$827$	850.269			1.02814			0.514068	−	0.857749i	$-0.328138\pi$
$827$	850.269			1.02814			0.514068	+	0.857749i	$0.328138\pi$
$828$		0			0
$829$	1328.47			1.60250			0.801251	−	0.598328i	$-0.204168\pi$
$829$	1328.47			1.60250			0.801251	+	0.598328i	$0.204168\pi$
$830$		0			0
$831$		0			0
$832$	1137.00	−	229.677i	1.36659	−	0.276054i
$833$		−	577.327i		−	0.693069i
$834$		0			0
$835$		0			0
$836$	−113.150	−	1700.54i	−0.135347	−	2.03414i
$837$		0			0
$838$	562.127	+	525.967i	0.670796	+	0.627646i
$839$			55.3391i			0.0659583i	0.999456	+	0.0329792i	$0.0104995\pi$
$839$			55.3391i			0.0659583i	−0.999456	+	0.0329792i	$0.989500\pi$
$840$		0			0
$841$	−741.996			−0.882278
$842$	−742.303	+	793.335i	−0.881594	+	0.942203i
$843$		0			0
$844$	−966.739	+	64.3248i	−1.14543	+	0.0762142i
$845$		0			0
$846$		0			0
$847$	201.166			0.237504
$848$	127.506	+	953.906i	0.150361	+	1.12489i
$849$		0			0
$850$		0			0
$851$		−	195.409i		−	0.229623i
$852$		0			0
$853$			742.887i			0.870911i	0.900210	+	0.435456i	$0.143413\pi$
$853$			742.887i			0.870911i	−0.900210	+	0.435456i	$0.856587\pi$
$854$	−87.5790	+	93.6000i	−0.102552	+	0.109602i
$855$		0			0
$856$	−1071.30	−	876.537i	−1.25152	−	1.02399i
$857$		−	679.145i		−	0.792468i	−0.918150	−	0.396234i	$-0.870317\pi$
$857$		−	679.145i		−	0.792468i	0.918150	−	0.396234i	$-0.129683\pi$
$858$		0			0
$859$			756.133i			0.880248i	0.897937	+	0.440124i	$0.145066\pi$
$859$			756.133i			0.880248i	−0.897937	+	0.440124i	$0.854934\pi$
$860$		0			0
$861$		0			0
$862$	1136.48	+	1063.37i	1.31842	+	1.23361i
$863$	−1130.05			−1.30944			−0.654721	−	0.755871i	$-0.727214\pi$
$863$	−1130.05			−1.30944			−0.654721	+	0.755871i	$0.727214\pi$
$864$		0			0
$865$		0			0
$866$	7.67137	+	7.17790i	0.00885840	+	0.00828856i
$867$		0			0
$868$	182.569	−	12.1478i	0.210333	−	0.0139951i
$869$	1561.10			1.79643
$870$		0			0
$871$			2382.65i			2.73554i
$872$	−1006.13	−	823.208i	−1.15381	−	0.944046i
$873$		0			0
$874$	−449.992	−	421.046i	−0.514865	−	0.481746i
$875$		0			0
$876$		0			0
$877$			910.607i			1.03832i	0.854677	+	0.519160i	$0.173755\pi$
$877$			910.607i			1.03832i	−0.854677	+	0.519160i	$0.826245\pi$
$878$	−304.205	−	284.637i	−0.346475	−	0.324188i
$879$		0			0
$880$		0			0
$881$	405.402			0.460161			0.230080	−	0.973172i	$-0.426101\pi$
$881$	405.402			0.460161			0.230080	+	0.973172i	$0.426101\pi$
$882$		0			0
$883$	819.868			0.928503			0.464252	−	0.885703i	$-0.346323\pi$
$883$	819.868			0.928503			0.464252	+	0.885703i	$0.346323\pi$
$884$	−61.0752	−	917.901i	−0.0690896	−	1.03835i
$885$		0			0
$886$	1005.48	−	1074.60i	1.13485	−	1.21287i
$887$	−1003.99			−1.13190			−0.565949	−	0.824440i	$-0.691490\pi$
$887$	−1003.99			−1.13190			−0.565949	+	0.824440i	$0.691490\pi$
$888$		0			0
$889$	277.961			0.312667
$890$		0			0
$891$		0			0
$892$	66.4055	+	998.010i	0.0744456	+	1.11885i
$893$		−	1396.17i		−	1.56346i
$894$		0			0
$895$		0			0
$896$	−203.849	−	125.784i	−0.227510	−	0.140384i
$897$		0			0
$898$	−843.318	+	901.296i	−0.939107	+	1.00367i
$899$		−	243.220i		−	0.270545i
$900$		0			0
$901$	763.237			0.847100
$902$	636.761	+	595.800i	0.705943	+	0.660532i
$903$		0			0
$904$	−366.722	+	448.208i	−0.405666	+	0.495805i
$905$		0			0
$906$		0			0
$907$	−361.629			−0.398709			−0.199354	−	0.979927i	$-0.563884\pi$
$907$	−361.629			−0.398709			−0.199354	+	0.979927i	$0.563884\pi$
$908$	16.0572	+	241.325i	0.0176842	+	0.265776i
$909$		0			0
$910$		0			0
$911$		−	294.475i		−	0.323244i	−0.986853	−	0.161622i	$-0.948327\pi$
$911$		−	294.475i		−	0.323244i	0.986853	−	0.161622i	$-0.0516725\pi$
$912$		0			0
$913$			864.965i			0.947388i
$914$	−471.341	−	441.022i	−0.515691	−	0.482518i
$915$		0			0
$916$	20.7802	+	312.306i	0.0226858	+	0.340945i
$917$		−	50.0182i		−	0.0545454i
$918$		0			0
$919$			17.4246i			0.0189604i	0.999955	+	0.00948022i	$0.00301769\pi$
$919$			17.4246i			0.0189604i	−0.999955	+	0.00948022i	$0.996982\pi$
$920$		0			0
$921$		0			0
$922$	695.575	−	743.395i	0.754420	−	0.806285i
$923$	−944.209			−1.02298
$924$		0			0
$925$		0			0
$926$	1013.88	−	1083.59i	1.09491	−	1.17018i
$927$		0			0
$928$	−184.821	+	259.270i	−0.199161	+	0.279386i
$929$	−743.488			−0.800310			−0.400155	−	0.916447i	$-0.631044\pi$
$929$	−743.488			−0.800310			−0.400155	+	0.916447i	$0.631044\pi$
$930$		0			0
$931$		−	1282.44i		−	1.37749i
$932$	657.513	−	43.7495i	0.705486	−	0.0469416i
$933$		0			0
$934$	−424.549	+	453.736i	−0.454549	+	0.485799i
$935$		0			0
$936$		0			0
$937$		−	802.514i		−	0.856471i	−0.903667	−	0.428236i	$-0.859135\pi$
$937$		−	802.514i		−	0.856471i	0.903667	−	0.428236i	$-0.140865\pi$
$938$	336.160	−	359.271i	0.358380	−	0.383018i
$939$		0			0
$940$		0			0
$941$	730.288			0.776076			0.388038	−	0.921643i	$-0.373153\pi$
$941$	730.288			0.776076			0.388038	+	0.921643i	$0.373153\pi$
$942$		0			0
$943$	315.318			0.334378
$944$	235.171	+	1759.37i	0.249122	+	1.86374i
$945$		0			0
$946$	1244.48	+	1164.43i	1.31552	+	1.23090i
$947$	882.383			0.931767			0.465884	−	0.884846i	$-0.345737\pi$
$947$	882.383			0.931767			0.465884	+	0.884846i	$0.345737\pi$
$948$		0			0
$949$	1128.23			1.18887
$950$		0			0
$951$		0			0
$952$	−120.294	+	147.023i	−0.126359	+	0.154436i
$953$		−	1047.62i		−	1.09929i	−0.835399	−	0.549644i	$-0.814763\pi$
$953$		−	1047.62i		−	1.09929i	0.835399	−	0.549644i	$-0.185237\pi$
$954$		0			0
$955$		0			0
$956$	−972.811	+	64.7288i	−1.01759	+	0.0677080i
$957$		0			0
$958$	699.698	+	654.689i	0.730374	+	0.683391i
$959$			237.573i			0.247730i
$960$		0			0
$961$	363.490			0.378242
$962$	442.712	−	473.149i	0.460200	−	0.491838i
$963$		0			0
$964$	−101.842	−	1530.59i	−0.105646	−	1.58775i
$965$		0			0
$966$		0			0
$967$	519.528			0.537258			0.268629	−	0.963244i	$-0.413430\pi$
$967$	519.528			0.537258			0.268629	+	0.963244i	$0.413430\pi$
$968$	665.587	+	544.580i	0.687589	+	0.562583i
$969$		0			0
$970$		0			0
$971$			398.406i			0.410305i	0.978730	+	0.205152i	$0.0657690\pi$
$971$			398.406i			0.410305i	−0.978730	+	0.205152i	$0.934231\pi$
$972$		0			0
$973$			38.7393i			0.0398143i
$974$	−782.788	+	836.604i	−0.803684	+	0.858937i
$975$		0			0
$976$	−543.154	+	72.6021i	−0.556510	+	0.0743874i
$977$		−	367.857i		−	0.376517i	−0.982120	−	0.188258i	$-0.939716\pi$
$977$		−	367.857i		−	0.376517i	0.982120	−	0.188258i	$-0.0602842\pi$
$978$		0			0
$979$		−	2193.66i		−	2.24071i
$980$		0			0
$981$		0			0
$982$	−0.380457	−	0.355984i	−0.000387431	−	0.000362509i
$983$	−1473.69			−1.49918			−0.749590	−	0.661902i	$-0.769749\pi$
$983$	−1473.69			−1.49918			−0.749590	+	0.661902i	$0.769749\pi$
$984$		0			0
$985$		0			0
$986$	184.386	+	172.525i	0.187004	+	0.174975i
$987$		0			0
$988$	−135.669	−	2038.97i	−0.137317	−	2.06374i
$989$	616.257			0.623111
$990$		0			0
$991$			753.090i			0.759929i	0.925001	+	0.379964i	$0.124064\pi$
$991$			753.090i			0.759929i	−0.925001	+	0.379964i	$0.875936\pi$
$992$	636.941	+	454.044i	0.642078	+	0.457705i
$993$		0			0
$994$	142.374	+	133.215i	0.143233	+	0.134019i
$995$		0			0
$996$		0			0
$997$			767.370i			0.769679i	0.922984	+	0.384839i	$0.125743\pi$
$997$			767.370i			0.769679i	−0.922984	+	0.384839i	$0.874257\pi$
$998$	683.050	+	639.112i	0.684419	+	0.640393i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.f.i.199.9		16
3.2	odd	2	inner	900.3.f.i.199.7		16
4.3	odd	2	inner	900.3.f.i.199.6		16
5.2	odd	4		900.3.c.o.451.8		8
5.3	odd	4		180.3.c.c.91.1	✓	8
5.4	even	2	inner	900.3.f.i.199.8		16
12.11	even	2	inner	900.3.f.i.199.12		16
15.2	even	4		900.3.c.o.451.1		8
15.8	even	4		180.3.c.c.91.8	yes	8
15.14	odd	2	inner	900.3.f.i.199.10		16
20.3	even	4		180.3.c.c.91.2	yes	8
20.7	even	4		900.3.c.o.451.7		8
20.19	odd	2	inner	900.3.f.i.199.11		16
40.3	even	4		2880.3.e.i.2431.6		8
40.13	odd	4		2880.3.e.i.2431.7		8
60.23	odd	4		180.3.c.c.91.7	yes	8
60.47	odd	4		900.3.c.o.451.2		8
60.59	even	2	inner	900.3.f.i.199.5		16
120.53	even	4		2880.3.e.i.2431.3		8
120.83	odd	4		2880.3.e.i.2431.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.c.c.91.1	✓	8	5.3	odd	4
180.3.c.c.91.2	yes	8	20.3	even	4
180.3.c.c.91.7	yes	8	60.23	odd	4
180.3.c.c.91.8	yes	8	15.8	even	4
900.3.c.o.451.1		8	15.2	even	4
900.3.c.o.451.2		8	60.47	odd	4
900.3.c.o.451.7		8	20.7	even	4
900.3.c.o.451.8		8	5.2	odd	4
900.3.f.i.199.5		16	60.59	even	2	inner
900.3.f.i.199.6		16	4.3	odd	2	inner
900.3.f.i.199.7		16	3.2	odd	2	inner
900.3.f.i.199.8		16	5.4	even	2	inner
900.3.f.i.199.9		16	1.1	even	1	trivial
900.3.f.i.199.10		16	15.14	odd	2	inner
900.3.f.i.199.11		16	20.19	odd	2	inner
900.3.f.i.199.12		16	12.11	even	2	inner
2880.3.e.i.2431.2		8	120.83	odd	4
2880.3.e.i.2431.3		8	120.53	even	4
2880.3.e.i.2431.6		8	40.3	even	4
2880.3.e.i.2431.7		8	40.13	odd	4

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36646 - 1.46040i) q^{2} +(-0.265564 - 3.99117i) q^{4} -1.87135 q^{7} +(-6.19161 - 5.06596i) q^{8} +O(q^{10})\)	\(q+(1.36646 - 1.46040i) q^{2} +(-0.265564 - 3.99117i) q^{4} -1.87135 q^{7} +(-6.19161 - 5.06596i) q^{8} -15.1162i q^{11} -18.1245i q^{13} +(-2.55712 + 2.73292i) q^{14} +(-15.8590 + 2.11983i) q^{16} +12.6890i q^{17} +28.1867i q^{19} +(-22.0757 - 20.6556i) q^{22} -10.9317 q^{23} +(-26.4691 - 24.7665i) q^{26} +(0.496963 + 7.46887i) q^{28} +9.95007 q^{29} -24.4440i q^{31} +(-18.5748 + 26.0572i) q^{32} +(18.5311 + 17.3391i) q^{34} +17.8755i q^{37} +(41.1640 + 38.5161i) q^{38} -28.8444 q^{41} -56.3734 q^{43} +(-60.3312 + 4.01431i) q^{44} +(-14.9377 + 15.9647i) q^{46} -49.5329 q^{47} -45.4981 q^{49} +(-72.3381 + 4.81323i) q^{52} -60.1494i q^{53} +(11.5867 + 9.48016i) q^{56} +(13.5964 - 14.5311i) q^{58} -110.939i q^{59} +34.2490 q^{61} +(-35.6982 - 33.4018i) q^{62} +(12.6722 + 62.7329i) q^{64} -131.460 q^{67} +(50.6442 - 3.36976i) q^{68} -52.0957i q^{71} +62.2490i q^{73} +(26.1054 + 24.4262i) q^{74} +(112.498 - 7.48539i) q^{76} +28.2876i q^{77} +103.274i q^{79} +(-39.4148 + 42.1245i) q^{82} -57.2212 q^{83} +(-77.0321 + 82.3280i) q^{86} +(-76.5778 + 93.5934i) q^{88} +145.120 q^{89} +33.9173i q^{91} +(2.90307 + 43.6303i) q^{92} +(-67.6848 + 72.3381i) q^{94} -66.7471i q^{97} +(-62.1714 + 66.4456i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 28 q^{4}+O(q^{10}) \) 16 * q + 28 * q^4	\( 16 q + 28 q^{4} - 28 q^{16} + 232 q^{34} - 368 q^{46} + 304 q^{49} + 32 q^{61} + 364 q^{64} + 768 q^{76} + 336 q^{94}+O(q^{100}) \) 16 * q + 28 * q^4 - 28 * q^16 + 232 * q^34 - 368 * q^46 + 304 * q^49 + 32 * q^61 + 364 * q^64 + 768 * q^76 + 336 * q^94

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