LMFDB - Embedded newform 900.3.c.o.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(451,900)]

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, 0]))

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

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

chi := DirichletCharacter("900.451");

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.c (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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.15012375625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{6} + 28x^{4} + 112x^{2} + 256 $ x^8 + 7x^6 + 28x^4 + 112*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			451.1
Root			$-1.46040 - 1.36646i$ of defining polynomial
Character	$\chi$	$=$	900.451
Dual form			900.3.c.o.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46040 - 1.36646i) q^{2} +(0.265564 + 3.99117i) q^{4} -1.87135i q^{7} +(5.06596 - 6.19161i) q^{8} +O(q^{10})$	\(q+(-1.46040 - 1.36646i) q^{2} +(0.265564 + 3.99117i) q^{4} -1.87135i q^{7} +(5.06596 - 6.19161i) q^{8} +15.1162i q^{11} -18.1245 q^{13} +(-2.55712 + 2.73292i) q^{14} +(-15.8590 + 2.11983i) q^{16} +12.6890 q^{17} -28.1867i q^{19} +(20.6556 - 22.0757i) q^{22} -10.9317i q^{23} +(26.4691 + 24.7665i) q^{26} +(7.46887 - 0.496963i) q^{28} +9.95007 q^{29} -24.4440i q^{31} +(26.0572 + 18.5748i) q^{32} +(-18.5311 - 17.3391i) q^{34} -17.8755 q^{37} +(-38.5161 + 41.1640i) q^{38} +28.8444 q^{41} +56.3734i q^{43} +(-60.3312 + 4.01431i) q^{44} +(-14.9377 + 15.9647i) q^{46} +49.5329i q^{47} +45.4981 q^{49} +(-4.81323 - 72.3381i) q^{52} +60.1494 q^{53} +(-11.5867 - 9.48016i) q^{56} +(-14.5311 - 13.5964i) q^{58} -110.939i q^{59} +34.2490 q^{61} +(-33.4018 + 35.6982i) q^{62} +(-12.6722 - 62.7329i) q^{64} -131.460i q^{67} +(3.36976 + 50.6442i) q^{68} +52.0957i q^{71} +62.2490 q^{73} +(26.1054 + 24.4262i) q^{74} +(112.498 - 7.48539i) q^{76} +28.2876 q^{77} -103.274i q^{79} +(-42.1245 - 39.4148i) q^{82} -57.2212i q^{83} +(77.0321 - 82.3280i) q^{86} +(93.5934 + 76.5778i) q^{88} +145.120 q^{89} +33.9173i q^{91} +(43.6303 - 2.90307i) q^{92} +(67.6848 - 72.3381i) q^{94} +66.7471 q^{97} +(-66.4456 - 62.1714i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 14 q^{4}+O(q^{10}) $ 8 * q - 14 * q^4	$ 8 q - 14 q^{4} - 16 q^{13} - 14 q^{16} + 4 q^{22} + 92 q^{28} - 116 q^{34} - 272 q^{37} - 184 q^{46} - 152 q^{49} - 232 q^{52} - 84 q^{58} + 16 q^{61} - 182 q^{64} + 240 q^{73} + 384 q^{76} - 208 q^{82} + 652 q^{88} - 168 q^{94} - 240 q^{97}+O(q^{100}) $ 8 * q - 14 * q^4 - 16 * q^13 - 14 * q^16 + 4 * q^22 + 92 * q^28 - 116 * q^34 - 272 * q^37 - 184 * q^46 - 152 * q^49 - 232 * q^52 - 84 * q^58 + 16 * q^61 - 182 * q^64 + 240 * q^73 + 384 * q^76 - 208 * q^82 + 652 * q^88 - 168 * q^94 - 240 * q^97

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 $

$2$	−1.46040	−	1.36646i	−0.730202	−	0.683231i
$2$	−1.46040	−	1.36646i	−0.730202	−	0.683231i
$3$		0			0
$3$		0			0
$4$	0.265564	+	3.99117i	0.0663911	+	0.997794i
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	1.87135i		−	0.267335i	−0.991026	−	0.133668i	$-0.957325\pi$
$7$		−	1.87135i		−	0.267335i	0.991026	−	0.133668i	$-0.0426755\pi$
$8$	5.06596	−	6.19161i	0.633245	−	0.773952i
$9$		0			0
$10$		0			0
$11$			15.1162i			1.37420i	0.726565	+	0.687098i	$0.241116\pi$
$11$			15.1162i			1.37420i	−0.726565	+	0.687098i	$0.758884\pi$
$12$		0			0
$13$	−18.1245			−1.39419			−0.697097	−	0.716977i	$-0.745525\pi$
$13$	−18.1245			−1.39419			−0.697097	+	0.716977i	$0.745525\pi$
$14$	−2.55712	+	2.73292i	−0.182652	+	0.195209i
$15$		0			0
$16$	−15.8590	+	2.11983i	−0.991184	+	0.132489i
$17$	12.6890			0.746414			0.373207	−	0.927748i	$-0.378258\pi$
$17$	12.6890			0.746414			0.373207	+	0.927748i	$0.378258\pi$
$18$		0			0
$19$		−	28.1867i		−	1.48351i	−0.670671	−	0.741755i	$-0.733994\pi$
$19$		−	28.1867i		−	1.48351i	0.670671	−	0.741755i	$-0.266006\pi$
$20$		0			0
$21$		0			0
$22$	20.6556	−	22.0757i	0.938893	−	1.00344i
$23$		−	10.9317i		−	0.475291i	−0.971352	−	0.237646i	$-0.923624\pi$
$23$		−	10.9317i		−	0.475291i	0.971352	−	0.237646i	$-0.0763757\pi$
$24$		0			0
$25$		0			0
$26$	26.4691	+	24.7665i	1.01804	+	0.952556i
$27$		0			0
$28$	7.46887	−	0.496963i	0.266745	−	0.0177487i
$29$	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	$-0.128998\pi$
$32$	26.0572	+	18.5748i	0.814286	+	0.580464i
$33$		0			0
$34$	−18.5311	−	17.3391i	−0.545033	−	0.509973i
$35$		0			0
$36$		0			0
$37$	−17.8755			−0.483121			−0.241561	−	0.970386i	$-0.577659\pi$
$37$	−17.8755			−0.483121			−0.241561	+	0.970386i	$0.577659\pi$
$38$	−38.5161	+	41.1640i	−1.01358	+	1.08326i
$39$		0			0
$40$		0			0
$41$	28.8444			0.703522			0.351761	−	0.936090i	$-0.385583\pi$
$41$	28.8444			0.703522			0.351761	+	0.936090i	$0.385583\pi$
$42$		0			0
$43$			56.3734i			1.31101i	0.755191	+	0.655505i	$0.227544\pi$
$43$			56.3734i			1.31101i	−0.755191	+	0.655505i	$0.772456\pi$
$44$	−60.3312	+	4.01431i	−1.37116	+	0.0912344i
$45$		0			0
$46$	−14.9377	+	15.9647i	−0.324734	+	0.347059i
$47$			49.5329i			1.05389i	0.849899	+	0.526946i	$0.176663\pi$
$47$			49.5329i			1.05389i	−0.849899	+	0.526946i	$0.823337\pi$
$48$		0			0
$49$	45.4981			0.928532
$50$		0			0
$51$		0			0
$52$	−4.81323	−	72.3381i	−0.0925621	−	1.39112i
$53$	60.1494			1.13489			0.567447	−	0.823410i	$-0.307931\pi$
$53$	60.1494			1.13489			0.567447	+	0.823410i	$0.307931\pi$
$54$		0			0
$55$		0			0
$56$	−11.5867	−	9.48016i	−0.206905	−	0.169289i
$57$		0			0
$58$	−14.5311	−	13.5964i	−0.250537	−	0.234421i
$59$		−	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	$0.409424\pi$
$62$	−33.4018	+	35.6982i	−0.538739	+	0.575777i
$63$		0			0
$64$	−12.6722	−	62.7329i	−0.198003	−	0.980201i
$65$		0			0
$66$		0			0
$67$		−	131.460i		−	1.96209i	−0.193770	−	0.981047i	$-0.562072\pi$
$67$		−	131.460i		−	1.96209i	0.193770	−	0.981047i	$-0.437928\pi$
$68$	3.36976	+	50.6442i	0.0495552	+	0.744767i
$69$		0			0
$70$		0			0
$71$			52.0957i			0.733742i	0.930272	+	0.366871i	$0.119571\pi$
$71$			52.0957i			0.733742i	−0.930272	+	0.366871i	$0.880429\pi$
$72$		0			0
$73$	62.2490			0.852726			0.426363	−	0.904552i	$-0.359795\pi$
$73$	62.2490			0.852726			0.426363	+	0.904552i	$0.359795\pi$
$74$	26.1054	+	24.4262i	0.352776	+	0.330083i
$75$		0			0
$76$	112.498	−	7.48539i	1.48024	−	0.0984919i
$77$	28.2876			0.367371
$78$		0			0
$79$		−	103.274i		−	1.30726i	−0.756814	−	0.653630i	$-0.773245\pi$
$79$		−	103.274i		−	1.30726i	0.756814	−	0.653630i	$-0.226755\pi$
$80$		0			0
$81$		0			0
$82$	−42.1245	−	39.4148i	−0.513714	−	0.480668i
$83$		−	57.2212i		−	0.689413i	−0.938711	−	0.344706i	$-0.887979\pi$
$83$		−	57.2212i		−	0.689413i	0.938711	−	0.344706i	$-0.112021\pi$
$84$		0			0
$85$		0			0
$86$	77.0321	−	82.3280i	0.895722	−	0.957302i
$87$		0			0
$88$	93.5934	+	76.5778i	1.06356	+	0.870202i
$89$	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
$92$	43.6303	−	2.90307i	0.474242	−	0.0315551i
$93$		0			0
$94$	67.6848	−	72.3381i	0.720051	−	0.769554i
$95$		0			0
$96$		0			0
$97$	66.7471			0.688114			0.344057	−	0.938949i	$-0.388199\pi$
$97$	66.7471			0.688114			0.344057	+	0.938949i	$0.388199\pi$
$98$	−66.4456	−	62.1714i	−0.678016	−	0.634402i
$99$		0			0
$100$		0			0
$101$	−164.571			−1.62942			−0.814709	−	0.579871i	$-0.803103\pi$
$101$	−164.571			−1.62942			−0.814709	+	0.579871i	$0.803103\pi$
$102$		0			0
$103$		−	43.2740i		−	0.420136i	−0.977687	−	0.210068i	$-0.932631\pi$
$103$		−	43.2740i		−	0.420136i	0.977687	−	0.210068i	$-0.0673685\pi$
$104$	−91.8180	+	112.220i	−0.882865	+	1.07904i
$105$		0			0
$106$	−87.8424	−	82.1918i	−0.828702	−	0.775394i
$107$		−	173.025i		−	1.61706i	−0.588458	−	0.808528i	$-0.700265\pi$
$107$		−	173.025i		−	1.61706i	0.588458	−	0.808528i	$-0.299735\pi$
$108$		0			0
$109$	−162.498			−1.49081			−0.745404	−	0.666613i	$-0.767743\pi$
$109$	−162.498			−1.49081			−0.745404	+	0.666613i	$0.767743\pi$
$110$		0			0
$111$		0			0
$112$	3.96693	+	29.6776i	0.0354190	+	0.264979i
$113$	72.3895			0.640615			0.320307	−	0.947314i	$-0.396214\pi$
$113$	72.3895			0.640615			0.320307	+	0.947314i	$0.396214\pi$
$114$		0			0
$115$		0			0
$116$	2.64238	+	39.7125i	0.0227792	+	0.342349i
$117$		0			0
$118$	−151.593	+	162.015i	−1.28469	+	1.37301i
$119$		−	23.7456i		−	0.199543i
$120$		0			0
$121$	−107.498			−0.888414
$122$	−50.0174	−	46.8000i	−0.409979	−	0.383606i
$123$		0			0
$124$	97.5603	−	6.49146i	0.786777	−	0.0523505i
$125$		0			0
$126$		0			0
$127$		−	148.535i		−	1.16957i	−0.811188	−	0.584785i	$-0.801179\pi$
$127$		−	148.535i		−	1.16957i	0.811188	−	0.584785i	$-0.198821\pi$
$128$	−67.2156	+	108.931i	−0.525122	+	0.851027i
$129$		0			0
$130$		0			0
$131$		−	26.7284i		−	0.204034i	−0.994783	−	0.102017i	$-0.967470\pi$
$131$		−	26.7284i		−	0.204034i	0.994783	−	0.102017i	$-0.0325296\pi$
$132$		0			0
$133$	−52.7471			−0.396595
$134$	−179.635	+	191.985i	−1.34056	+	1.43273i
$135$		0			0
$136$	64.2821	−	78.5656i	0.472662	−	0.577688i
$137$	−126.953			−0.926664			−0.463332	−	0.886185i	$-0.653346\pi$
$137$	−126.953			−0.926664			−0.463332	+	0.886185i	$0.653346\pi$
$138$		0			0
$139$			20.7013i			0.148930i	0.997224	+	0.0744652i	$0.0237250\pi$
$139$			20.7013i			0.148930i	−0.997224	+	0.0744652i	$0.976275\pi$
$140$		0			0
$141$		0			0
$142$	71.1868	−	76.0808i	0.501315	−	0.535780i
$143$		−	273.973i		−	1.91589i
$144$		0			0
$145$		0			0
$146$	−90.9088	−	85.0609i	−0.622663	−	0.582609i
$147$		0			0
$148$	−4.74709	−	71.3442i	−0.0320750	−	0.482055i
$149$	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	$0.930287\pi$
$152$	−174.521	−	142.793i	−1.14817	−	0.939425i
$153$		0			0
$154$	−41.3113	−	38.6539i	−0.268255	−	0.250999i
$155$		0			0
$156$		0			0
$157$	30.3735			0.193462			0.0967310	−	0.995311i	$-0.469161\pi$
$157$	30.3735			0.193462			0.0967310	+	0.995311i	$0.469161\pi$
$158$	−141.119	+	150.821i	−0.893161	+	0.954565i
$159$		0			0
$160$		0			0
$161$	−20.4570			−0.127062
$162$		0			0
$163$		−	45.1453i		−	0.276965i	−0.990365	−	0.138483i	$-0.955777\pi$
$163$		−	45.1453i		−	0.276965i	0.990365	−	0.138483i	$-0.0442225\pi$
$164$	7.66005	+	115.123i	0.0467076	+	0.701970i
$165$		0			0
$166$	−78.1906	+	83.5662i	−0.471028	+	0.503411i
$167$			32.7951i			0.196378i	0.995168	+	0.0981889i	$0.0313049\pi$
$167$			32.7951i			0.196378i	−0.995168	+	0.0981889i	$0.968695\pi$
$168$		0			0
$169$	159.498			0.943776
$170$		0			0
$171$		0			0
$172$	−224.996	+	14.9708i	−1.30812	+	0.0870394i
$173$	316.067			1.82698			0.913488	−	0.406865i	$-0.133378\pi$
$173$	316.067			1.82698			0.913488	+	0.406865i	$0.133378\pi$
$174$		0			0
$175$		0			0
$176$	−32.0436	−	239.726i	−0.182066	−	1.36208i
$177$		0			0
$178$	−211.934	−	198.301i	−1.19064	−	1.11405i
$179$		−	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	$0.565978\pi$
$182$	46.3466	−	49.5329i	0.254652	−	0.272159i
$183$		0			0
$184$	−67.6848	−	55.3795i	−0.367852	−	0.300975i
$185$		0			0
$186$		0			0
$187$			191.809i			1.02572i
$188$	−197.695	+	13.1542i	−1.05157	+	0.0699690i
$189$		0			0
$190$		0			0
$191$		−	63.7080i		−	0.333550i	−0.985995	−	0.166775i	$-0.946665\pi$
$191$		−	63.7080i		−	0.333550i	0.985995	−	0.166775i	$-0.0533353\pi$
$192$		0			0
$193$	−45.5019			−0.235761			−0.117881	−	0.993028i	$-0.537610\pi$
$193$	−45.5019			−0.235761			−0.117881	+	0.993028i	$0.537610\pi$
$194$	−97.4778	−	91.2074i	−0.502463	−	0.470141i
$195$		0			0
$196$	12.0827	+	181.591i	0.0616463	+	0.926483i
$197$	185.926			0.943787			0.471893	−	0.881656i	$-0.343571\pi$
$197$	185.926			0.943787			0.471893	+	0.881656i	$0.343571\pi$
$198$		0			0
$199$			155.904i			0.783439i	0.920085	+	0.391719i	$0.128120\pi$
$199$			155.904i			0.783439i	−0.920085	+	0.391719i	$0.871880\pi$
$200$		0			0
$201$		0			0
$202$	240.340	+	224.880i	1.18980	+	1.11327i
$203$		−	18.6200i		−	0.0917243i
$204$		0			0
$205$		0			0
$206$	−59.1322	+	63.1975i	−0.287050	+	0.306784i
$207$		0			0
$208$	287.436	−	38.4209i	1.38190	−	0.184716i
$209$	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	$-0.194601\pi$
$212$	15.9735	+	240.067i	0.0753468	+	1.13239i
$213$		0			0
$214$	−236.432	+	252.686i	−1.10482	+	1.18078i
$215$		0			0
$216$		0			0
$217$	−45.7432			−0.210798
$218$	237.313	+	222.047i	1.08859	+	1.01857i
$219$		0			0
$220$		0			0
$221$	−229.983			−1.04065
$222$		0			0
$223$			250.054i			1.12132i	0.828046	+	0.560660i	$0.189452\pi$
$223$			250.054i			1.12132i	−0.828046	+	0.560660i	$0.810548\pi$
$224$	34.7600	−	48.7620i	0.155178	−	0.217687i
$225$		0			0
$226$	−105.718	−	98.9174i	−0.467778	−	0.437688i
$227$			60.4646i			0.266364i	0.991092	+	0.133182i	$0.0425195\pi$
$227$			60.4646i			0.266364i	−0.991092	+	0.133182i	$0.957481\pi$
$228$		0			0
$229$	78.2490			0.341699			0.170849	−	0.985297i	$-0.445349\pi$
$229$	78.2490			0.341699			0.170849	+	0.985297i	$0.445349\pi$
$230$		0			0
$231$		0			0
$232$	50.4066	−	61.6070i	0.217270	−	0.265547i
$233$	−164.742			−0.707046			−0.353523	−	0.935426i	$-0.615016\pi$
$233$	−164.742			−0.707046			−0.353523	+	0.935426i	$0.615016\pi$
$234$		0			0
$235$		0			0
$236$	442.775	−	29.4614i	1.87617	−	0.124836i
$237$		0			0
$238$	−32.4474	+	34.6782i	−0.136334	+	0.145707i
$239$		−	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	$0.207139\pi$
$242$	156.991	+	146.892i	0.648722	+	0.606992i
$243$		0			0
$244$	9.09532	+	136.694i	0.0372759	+	0.560221i
$245$		0			0
$246$		0			0
$247$			510.870i			2.06830i
$248$	−151.348	−	123.832i	−0.610274	−	0.499324i
$249$		0			0
$250$		0			0
$251$			199.753i			0.795830i	0.917422	+	0.397915i	$0.130266\pi$
$251$			199.753i			0.795830i	−0.917422	+	0.397915i	$0.869734\pi$
$252$		0			0
$253$	165.245			0.653143
$254$	−202.968	+	216.922i	−0.799086	+	0.854023i
$255$		0			0
$256$	247.013	−	67.2365i	0.964893	−	0.262643i
$257$	−158.366			−0.616209			−0.308105	−	0.951352i	$-0.599695\pi$
$257$	−158.366			−0.616209			−0.308105	+	0.951352i	$0.599695\pi$
$258$		0			0
$259$			33.4512i			0.129155i
$260$		0			0
$261$		0			0
$262$	−36.5234	+	39.0343i	−0.139402	+	0.148986i
$263$			121.610i			0.462395i	0.972907	+	0.231197i	$0.0742643\pi$
$263$			121.610i			0.462395i	−0.972907	+	0.231197i	$0.925736\pi$
$264$		0			0
$265$		0			0
$266$	77.0321	+	72.0769i	0.289594	+	0.270966i
$267$		0			0
$268$	524.681	−	34.9112i	1.95776	−	0.130266i
$269$	−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	$0.883902\pi$
$272$	−201.235	+	26.8986i	−0.739834	+	0.0988918i
$273$		0			0
$274$	185.403	+	173.476i	0.676652	+	0.633126i
$275$		0			0
$276$		0			0
$277$	−472.615			−1.70619			−0.853095	−	0.521755i	$-0.825278\pi$
$277$	−472.615			−1.70619			−0.853095	+	0.521755i	$0.825278\pi$
$278$	28.2876	−	30.2323i	0.101754	−	0.108749i
$279$		0			0
$280$		0			0
$281$	256.815			0.913934			0.456967	−	0.889484i	$-0.348936\pi$
$281$	256.815			0.913934			0.456967	+	0.889484i	$0.348936\pi$
$282$		0			0
$283$		−	416.837i		−	1.47292i	−0.676480	−	0.736461i	$-0.736495\pi$
$283$		−	416.837i		−	1.47292i	0.676480	−	0.736461i	$-0.263505\pi$
$284$	−207.923	+	13.8348i	−0.732123	+	0.0487140i
$285$		0			0
$286$	−374.374	+	400.111i	−1.30900	+	1.39899i
$287$		−	53.9779i		−	0.188076i
$288$		0			0
$289$	−127.988			−0.442866
$290$		0			0
$291$		0			0
$292$	16.5311	+	248.447i	0.0566135	+	0.850845i
$293$	240.705			0.821520			0.410760	−	0.911744i	$-0.365263\pi$
$293$	240.705			0.821520			0.410760	+	0.911744i	$0.365263\pi$
$294$		0			0
$295$		0			0
$296$	−90.5564	+	110.678i	−0.305934	+	0.373913i
$297$		0			0
$298$	−244.091	−	228.390i	−0.819099	−	0.766409i
$299$			198.132i			0.662648i
$300$		0			0
$301$	105.494			0.350479
$302$	89.6585	−	95.8225i	0.296883	−	0.317293i
$303$		0			0
$304$	59.7510	+	447.012i	0.196549	+	1.47043i
$305$		0			0
$306$		0			0
$307$			206.547i			0.672792i	0.941721	+	0.336396i	$0.109208\pi$
$307$			206.547i			0.672792i	−0.941721	+	0.336396i	$0.890792\pi$
$308$	7.51217	+	112.901i	0.0243902	+	0.366560i
$309$		0			0
$310$		0			0
$311$			458.610i			1.47463i	0.675549	+	0.737315i	$0.263907\pi$
$311$			458.610i			1.47463i	−0.675549	+	0.737315i	$0.736093\pi$
$312$		0			0
$313$	−383.992			−1.22681			−0.613406	−	0.789768i	$-0.710201\pi$
$313$	−383.992			−1.22681			−0.613406	+	0.789768i	$0.710201\pi$
$314$	−44.3577	−	41.5043i	−0.141266	−	0.132179i
$315$		0			0
$316$	412.183	−	27.4258i	1.30438	−	0.0867905i
$317$	429.433			1.35468			0.677339	−	0.735671i	$-0.263133\pi$
$317$	429.433			1.35468			0.677339	+	0.735671i	$0.263133\pi$
$318$		0			0
$319$			150.407i			0.471495i
$320$		0			0
$321$		0			0
$322$	29.8755	+	27.9537i	0.0927810	+	0.0868127i
$323$		−	357.662i		−	1.10731i
$324$		0			0
$325$		0			0
$326$	−61.6894	+	65.9305i	−0.189231	+	0.202241i
$327$		0			0
$328$	146.125	−	178.593i	0.445502	−	0.544492i
$329$	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	$0.972014\pi$
$332$	228.380	−	15.1959i	0.687892	−	0.0457709i
$333$		0			0
$334$	44.8132	−	47.8941i	0.134171	−	0.143395i
$335$		0			0
$336$		0			0
$337$	405.751			1.20401			0.602004	−	0.798493i	$-0.294369\pi$
$337$	405.751			1.20401			0.602004	+	0.798493i	$0.294369\pi$
$338$	−232.932	−	217.948i	−0.689147	−	0.644817i
$339$		0			0
$340$		0			0
$341$	369.499			1.08358
$342$		0			0
$343$		−	176.839i		−	0.515565i
$344$	349.042	+	285.585i	1.01466	+	0.830190i
$345$		0			0
$346$	−461.586	−	431.893i	−1.33406	−	1.24825i
$347$			324.186i			0.934255i	0.884190	+	0.467127i	$0.154711\pi$
$347$			324.186i			0.934255i	−0.884190	+	0.467127i	$0.845289\pi$
$348$		0			0
$349$	34.7471			0.0995619			0.0497809	−	0.998760i	$-0.484148\pi$
$349$	34.7471			0.0995619			0.0497809	+	0.998760i	$0.484148\pi$
$350$		0			0
$351$		0			0
$352$	−280.780	+	393.884i	−0.797671	+	1.11899i
$353$	−13.5869			−0.0384899			−0.0192449	−	0.999815i	$-0.506126\pi$
$353$	−13.5869			−0.0384899			−0.0192449	+	0.999815i	$0.506126\pi$
$354$		0			0
$355$		0			0
$356$	38.5387	+	579.199i	0.108255	+	1.62696i
$357$		0			0
$358$	−353.718	+	378.036i	−0.988039	+	1.05597i
$359$		−	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
$362$	108.797	+	101.799i	0.300545	+	0.281212i
$363$		0			0
$364$	−135.370	+	9.00722i	−0.371895	+	0.0247451i
$365$		0			0
$366$		0			0
$367$		−	1.87135i		−	0.00509904i	−0.999997	−	0.00254952i	$-0.999188\pi$
$367$		−	1.87135i		−	0.00509904i	0.999997	−	0.00254952i	$-0.000811538\pi$
$368$	23.1733	+	173.365i	0.0629710	+	0.471101i
$369$		0			0
$370$		0			0
$371$		−	112.560i		−	0.303397i
$372$		0			0
$373$	384.864			1.03181			0.515903	−	0.856647i	$-0.327456\pi$
$373$	384.864			1.03181			0.515903	+	0.856647i	$0.327456\pi$
$374$	262.100	−	280.119i	0.700803	−	0.748982i
$375$		0			0
$376$	306.689	+	250.932i	0.815661	+	0.667371i
$377$	−180.340			−0.478356
$378$		0			0
$379$			483.150i			1.27480i	0.770533	+	0.637401i	$0.219990\pi$
$379$			483.150i			1.27480i	−0.770533	+	0.637401i	$0.780010\pi$
$380$		0			0
$381$		0			0
$382$	−87.0545	+	93.0394i	−0.227891	+	0.243559i
$383$			130.500i			0.340730i	0.985381	+	0.170365i	$0.0544947\pi$
$383$			130.500i			0.340730i	−0.985381	+	0.170365i	$0.945505\pi$
$384$		0			0
$385$		0			0
$386$	66.4512	+	62.1767i	0.172153	+	0.161079i
$387$		0			0
$388$	17.7257	+	266.399i	0.0456847	+	0.686596i
$389$	−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
$392$	230.491	−	281.706i	0.587988	−	0.718639i
$393$		0			0
$394$	−271.527	−	254.061i	−0.689155	−	0.644824i
$395$		0			0
$396$		0			0
$397$	228.864			0.576483			0.288242	−	0.957558i	$-0.406929\pi$
$397$	228.864			0.576483			0.288242	+	0.957558i	$0.406929\pi$
$398$	213.037	−	227.683i	0.535269	−	0.572069i
$399$		0			0
$400$		0			0
$401$	−96.9322			−0.241726			−0.120863	−	0.992669i	$-0.538566\pi$
$401$	−96.9322			−0.241726			−0.120863	+	0.992669i	$0.538566\pi$
$402$		0			0
$403$			443.036i			1.09934i
$404$	−43.7042	−	656.832i	−0.108179	−	1.62582i
$405$		0			0
$406$	−25.4436	+	27.1928i	−0.0626689	+	0.0669773i
$407$		−	270.209i		−	0.663903i
$408$		0			0
$409$	−135.494			−0.331282			−0.165641	−	0.986186i	$-0.552969\pi$
$409$	−135.494			−0.331282			−0.165641	+	0.986186i	$0.552969\pi$
$410$		0			0
$411$		0			0
$412$	172.714	−	11.4920i	0.419209	−	0.0278933i
$413$	−207.605			−0.502675
$414$		0			0
$415$		0			0
$416$	−472.273	−	336.660i	−1.13527	−	0.809279i
$417$		0			0
$418$	−622.241	−	582.215i	−1.48862	−	1.39286i
$419$			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	$0.723212\pi$
$422$	−330.983	+	353.738i	−0.784321	+	0.838242i
$423$		0			0
$424$	304.714	−	372.422i	0.718665	−	0.878353i
$425$		0			0
$426$		0			0
$427$		−	64.0918i		−	0.150098i
$428$	690.573	−	45.9493i	1.61349	−	0.107358i
$429$		0			0
$430$		0			0
$431$		−	778.192i		−	1.80555i	−0.430113	−	0.902775i	$-0.641526\pi$
$431$		−	778.192i		−	1.80555i	0.430113	−	0.902775i	$-0.358474\pi$
$432$		0			0
$433$	5.25291			0.0121314			0.00606571	−	0.999982i	$-0.498069\pi$
$433$	5.25291			0.0121314			0.00606571	+	0.999982i	$0.498069\pi$
$434$	66.8036	+	62.5064i	0.153925	+	0.144024i
$435$		0			0
$436$	−43.1537	−	648.558i	−0.0989764	−	1.48752i
$437$	−308.128			−0.705099
$438$		0			0
$439$			208.302i			0.474492i	0.971450	+	0.237246i	$0.0762447\pi$
$439$			208.302i			0.474492i	−0.971450	+	0.237246i	$0.923755\pi$
$440$		0			0
$441$		0			0
$442$	335.868	+	314.262i	0.759882	+	0.711001i
$443$			735.826i			1.66101i	0.557013	+	0.830504i	$0.311947\pi$
$443$			735.826i			1.66101i	−0.557013	+	0.830504i	$0.688053\pi$
$444$		0			0
$445$		0			0
$446$	341.689	−	365.180i	0.766120	−	0.818790i
$447$		0			0
$448$	−117.395	+	23.7140i	−0.262042	+	0.0529331i
$449$	−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
$452$	19.2241	+	288.919i	0.0425311	+	0.639201i
$453$		0			0
$454$	82.6226	−	88.3028i	0.181988	−	0.194500i
$455$		0			0
$456$		0			0
$457$	322.747			0.706230			0.353115	−	0.935580i	$-0.385122\pi$
$457$	322.747			0.706230			0.353115	+	0.935580i	$0.385122\pi$
$458$	−114.275	−	106.924i	−0.249509	−	0.233459i
$459$		0			0
$460$		0			0
$461$	−509.034			−1.10419			−0.552097	−	0.833780i	$-0.686172\pi$
$461$	−509.034			−1.10419			−0.552097	+	0.833780i	$0.686172\pi$
$462$		0			0
$463$		−	741.978i		−	1.60254i	−0.598300	−	0.801272i	$-0.704157\pi$
$463$		−	741.978i		−	1.60254i	0.598300	−	0.801272i	$-0.295843\pi$
$464$	−157.798	+	21.0924i	−0.340081	+	0.0454578i
$465$		0			0
$466$	240.590	+	225.113i	0.516287	+	0.483075i
$467$			310.692i			0.665293i	0.943052	+	0.332647i	$0.107942\pi$
$467$			310.692i			0.665293i	−0.943052	+	0.332647i	$0.892058\pi$
$468$		0			0
$469$	−246.008			−0.524537
$470$		0			0
$471$		0			0
$472$	−686.889	−	562.010i	−1.45527	−	1.19070i
$473$	−852.149			−1.80158
$474$		0			0
$475$		0			0
$476$	94.7728	−	6.30598i	0.199102	−	0.0132479i
$477$		0			0
$478$	−333.062	+	355.960i	−0.696783	+	0.744686i
$479$			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
$482$	−560.057	−	524.030i	−1.16194	−	1.08720i
$483$		0			0
$484$	−28.5477	−	429.044i	−0.0589828	−	0.886454i
$485$		0			0
$486$		0			0
$487$		−	572.858i		−	1.17630i	−0.808752	−	0.588150i	$-0.799857\pi$
$487$		−	572.858i		−	1.17630i	0.808752	−	0.588150i	$-0.200143\pi$
$488$	173.504	−	212.057i	0.355541	−	0.434543i
$489$		0			0
$490$		0			0
$491$			0.260515i			0.000530580i	1.00000		0.000265290i	$8.44445e-5\pi$
$491$			0.260515i			0.000530580i	−1.00000		0.000265290i	$0.999916\pi$
$492$		0			0
$493$	126.257			0.256099
$494$	698.085	−	746.078i	1.41313	−	1.51028i
$495$		0			0
$496$	51.8171	+	387.656i	0.104470	+	0.781565i
$497$	97.4891			0.196155
$498$		0			0
$499$		−	467.713i		−	0.937300i	−0.883384	−	0.468650i	$-0.844740\pi$
$499$		−	467.713i		−	0.937300i	0.883384	−	0.468650i	$-0.155260\pi$
$500$		0			0
$501$		0			0
$502$	272.955	−	291.721i	0.543736	−	0.581117i
$503$			728.659i			1.44863i	0.689471	+	0.724313i	$0.257843\pi$
$503$			728.659i			1.44863i	−0.689471	+	0.724313i	$0.742157\pi$
$504$		0			0
$505$		0			0
$506$	−241.325	−	225.801i	−0.476927	−	0.446247i
$507$		0			0
$508$	592.831	−	39.4457i	1.16699	−	0.0776491i
$509$	−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
$512$	−452.615	−	239.341i	−0.884013	−	0.467463i
$513$		0			0
$514$	231.278	+	216.401i	0.449958	+	0.421013i
$515$		0			0
$516$		0			0
$517$	−748.747			−1.44825
$518$	45.7098	−	48.8523i	0.0882429	−	0.0943095i
$519$		0			0
$520$		0			0
$521$	624.519			1.19869			0.599346	−	0.800490i	$-0.295427\pi$
$521$	624.519			1.19869			0.599346	+	0.800490i	$0.295427\pi$
$522$		0			0
$523$			319.527i			0.610950i	0.952200	+	0.305475i	$0.0988153\pi$
$523$			319.527i			0.610950i	−0.952200	+	0.305475i	$0.901185\pi$
$524$	106.678	−	7.09812i	0.203584	−	0.0135460i
$525$		0			0
$526$	166.175	−	177.600i	0.315922	−	0.337642i
$527$		−	310.171i		−	0.588560i
$528$		0			0
$529$	409.498			0.774098
$530$		0			0
$531$		0			0
$532$	−14.0078	−	210.523i	−0.0263304	−	0.395720i
$533$	−522.791			−0.980846
$534$		0			0
$535$		0			0
$536$	−813.951	−	665.972i	−1.51857	−	1.24249i
$537$		0			0
$538$	605.586	+	566.630i	1.12562	+	1.05322i
$539$			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	$0.363473\pi$
$542$	264.180	−	282.342i	0.487416	−	0.520926i
$543$		0			0
$544$	330.640	+	235.697i	0.607794	+	0.433266i
$545$		0			0
$546$		0			0
$547$		−	650.049i		−	1.18839i	−0.804321	−	0.594195i	$-0.797471\pi$
$547$		−	650.049i		−	1.18839i	0.804321	−	0.594195i	$-0.202529\pi$
$548$	−33.7142	−	506.692i	−0.0615223	−	0.924620i
$549$		0			0
$550$		0			0
$551$		−	280.460i		−	0.509001i
$552$		0			0
$553$	−193.261			−0.349477
$554$	690.209	+	645.810i	1.24586	+	1.16572i
$555$		0			0
$556$	−82.6226	+	5.49753i	−0.148602	+	0.00988765i
$557$	−127.555			−0.229004			−0.114502	−	0.993423i	$-0.536527\pi$
$557$	−127.555			−0.229004			−0.114502	+	0.993423i	$0.536527\pi$
$558$		0			0
$559$		−	1021.74i		−	1.82780i
$560$		0			0
$561$		0			0
$562$	−375.055	−	350.928i	−0.667357	−	0.624428i
$563$		−	474.827i		−	0.843387i	−0.906738	−	0.421694i	$-0.861436\pi$
$563$		−	474.827i		−	0.843387i	0.906738	−	0.421694i	$-0.138564\pi$
$564$		0			0
$565$		0			0
$566$	−569.592	+	608.751i	−1.00635	+	1.07553i
$567$		0			0
$568$	322.556	+	263.914i	0.567881	+	0.464638i
$569$	−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	$-0.0532874\pi$
$572$	1093.47	−	72.7575i	1.91167	−	0.127198i
$573$		0			0
$574$	−73.7587	+	78.8296i	−0.128500	+	0.137334i
$575$		0			0
$576$		0			0
$577$	492.739			0.853968			0.426984	−	0.904259i	$-0.359576\pi$
$577$	492.739			0.853968			0.426984	+	0.904259i	$0.359576\pi$
$578$	186.915	+	174.891i	0.323382	+	0.302580i
$579$		0			0
$580$		0			0
$581$	−107.081			−0.184304
$582$		0			0
$583$			909.227i			1.55957i
$584$	315.351	−	385.422i	0.539984	−	0.659969i
$585$		0			0
$586$	−351.527	−	328.915i	−0.599876	−	0.561288i
$587$		−	293.954i		−	0.500774i	−0.968146	−	0.250387i	$-0.919442\pi$
$587$		−	293.954i		−	0.500774i	0.968146	−	0.250387i	$-0.0805578\pi$
$588$		0			0
$589$	−688.996			−1.16977
$590$		0			0
$591$		0			0
$592$	283.486	−	37.8930i	0.478862	−	0.0640084i
$593$	434.184			0.732181			0.366091	−	0.930579i	$-0.380696\pi$
$593$	434.184			0.732181			0.366091	+	0.930579i	$0.380696\pi$
$594$		0			0
$595$		0			0
$596$	44.3863	+	667.083i	0.0744737	+	1.11927i
$597$		0			0
$598$	270.739	−	289.352i	0.452741	−	0.483867i
$599$			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	$0.421482\pi$
$602$	−154.064	−	144.154i	−0.255921	−	0.239458i
$603$		0			0
$604$	−261.875	+	17.4246i	−0.433569	+	0.0288488i
$605$		0			0
$606$		0			0
$607$		−	35.0896i		−	0.0578082i	−0.999582	−	0.0289041i	$-0.990798\pi$
$607$		−	35.0896i		−	0.0578082i	0.999582	−	0.0289041i	$-0.00920174\pi$
$608$	523.564	−	734.465i	0.861124	−	1.20800i
$609$		0			0
$610$		0			0
$611$		−	897.760i		−	1.46933i
$612$		0			0
$613$	−49.6109			−0.0809314			−0.0404657	−	0.999181i	$-0.512884\pi$
$613$	−49.6109			−0.0809314			−0.0404657	+	0.999181i	$0.512884\pi$
$614$	282.239	−	301.642i	0.459672	−	0.491274i
$615$		0			0
$616$	143.304	−	175.146i	0.232636	−	0.284327i
$617$	−427.251			−0.692465			−0.346232	−	0.938149i	$-0.612539\pi$
$617$	−427.251			−0.692465			−0.346232	+	0.938149i	$0.612539\pi$
$618$		0			0
$619$		−	903.263i		−	1.45923i	−0.683858	−	0.729615i	$-0.739699\pi$
$619$		−	903.263i		−	1.45923i	0.683858	−	0.729615i	$-0.260301\pi$
$620$		0			0
$621$		0			0
$622$	626.673	−	669.756i	1.00751	−	1.07678i
$623$		−	271.570i		−	0.435906i
$624$		0			0
$625$		0			0
$626$	560.784	+	524.711i	0.895821	+	0.838196i
$627$		0			0
$628$	8.06613	+	121.226i	0.0128442	+	0.193035i
$629$	−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	$-0.181585\pi$
$632$	−639.430	−	523.179i	−1.01176	−	0.827816i
$633$		0			0
$634$	−627.146	−	586.804i	−0.989189	−	0.925558i
$635$		0			0
$636$		0			0
$637$	−824.630			−1.29455
$638$	205.525	−	219.655i	0.322140	−	0.344286i
$639$		0			0
$640$		0			0
$641$	−252.576			−0.394035			−0.197018	−	0.980400i	$-0.563126\pi$
$641$	−252.576			−0.394035			−0.197018	+	0.980400i	$0.563126\pi$
$642$		0			0
$643$			15.2038i			0.0236451i	0.999930	+	0.0118225i	$0.00376332\pi$
$643$			15.2038i			0.0236451i	−0.999930	+	0.0118225i	$0.996237\pi$
$644$	−5.43265	−	81.6474i	−0.00843579	−	0.126782i
$645$		0			0
$646$	−488.732	+	522.331i	−0.756550	+	0.808563i
$647$		−	463.576i		−	0.716501i	−0.933626	−	0.358250i	$-0.883373\pi$
$647$		−	463.576i		−	0.716501i	0.933626	−	0.358250i	$-0.116627\pi$
$648$		0			0
$649$	1676.97			2.58392
$650$		0			0
$651$		0			0
$652$	180.183	−	11.9890i	0.276354	−	0.0183880i
$653$	−351.503			−0.538289			−0.269145	−	0.963100i	$-0.586741\pi$
$653$	−351.503			−0.538289			−0.269145	+	0.963100i	$0.586741\pi$
$654$		0			0
$655$		0			0
$656$	−457.442	+	61.1452i	−0.697320	+	0.0932091i
$657$		0			0
$658$	−135.370	−	126.662i	−0.205729	−	0.192495i
$659$			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	$0.459989\pi$
$662$	79.4300	−	84.8908i	0.119985	−	0.128234i
$663$		0			0
$664$	−354.292	−	289.880i	−0.533572	−	0.436567i
$665$		0			0
$666$		0			0
$667$		−	108.771i		−	0.163075i
$668$	−130.891	+	8.70921i	−0.195944	+	0.0130377i
$669$		0			0
$670$		0			0
$671$			517.714i			0.771555i
$672$		0			0
$673$	−3.74322			−0.00556199			−0.00278099	−	0.999996i	$-0.500885\pi$
$673$	−3.74322			−0.00556199			−0.00278099	+	0.999996i	$0.500885\pi$
$674$	−592.561	−	554.443i	−0.879170	−	0.822616i
$675$		0			0
$676$	42.3570	+	636.585i	0.0626583	+	0.941693i
$677$	−969.987			−1.43277			−0.716386	−	0.697704i	$-0.754205\pi$
$677$	−969.987			−1.43277			−0.716386	+	0.697704i	$0.754205\pi$
$678$		0			0
$679$		−	124.907i		−	0.183957i
$680$		0			0
$681$		0			0
$682$	−539.619	−	504.907i	−0.791230	−	0.740333i
$683$			808.424i			1.18364i	0.806071	+	0.591819i	$0.201590\pi$
$683$			808.424i			1.18364i	−0.806071	+	0.591819i	$0.798410\pi$
$684$		0			0
$685$		0			0
$686$	−241.643	+	258.256i	−0.352250	+	0.376466i
$687$		0			0
$688$	−119.502	−	894.023i	−0.173695	−	1.29945i
$689$	−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	$0.907518\pi$
$692$	83.9361	+	1261.48i	0.121295	+	1.82295i
$693$		0			0
$694$	442.988	−	473.443i	0.638312	−	0.682195i
$695$		0			0
$696$		0			0
$697$	366.008			0.525119
$698$	−50.7448	−	47.4806i	−0.0727003	−	0.0680237i
$699$		0			0
$700$		0			0
$701$	961.043			1.37096			0.685480	−	0.728091i	$-0.259592\pi$
$701$	961.043			1.37096			0.685480	+	0.728091i	$0.259592\pi$
$702$		0			0
$703$			503.851i			0.716716i
$704$	948.280	−	191.555i	1.34699	−	0.272095i
$705$		0			0
$706$	19.8424	+	18.5660i	0.0281054	+	0.0262975i
$707$			307.970i			0.435601i
$708$		0			0
$709$	−817.751			−1.15339			−0.576693	−	0.816961i	$-0.695657\pi$
$709$	−817.751			−1.15339			−0.576693	+	0.816961i	$0.695657\pi$
$710$		0			0
$711$		0			0
$712$	735.171	−	898.527i	1.03254	−	1.26198i
$713$	−267.214			−0.374775
$714$		0			0
$715$		0			0
$716$	1033.14	−	68.7432i	1.44294	−	0.0960100i
$717$		0			0
$718$	−189.977	+	203.037i	−0.264592	+	0.282782i
$719$			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
$722$	633.071	+	592.348i	0.876830	+	0.820427i
$723$		0			0
$724$	−19.7840	−	297.335i	−0.0273260	−	0.410683i
$725$		0			0
$726$		0			0
$727$		−	662.682i		−	0.911530i	−0.890100	−	0.455765i	$-0.849366\pi$
$727$		−	662.682i		−	0.911530i	0.890100	−	0.455765i	$-0.150634\pi$
$728$	210.003	+	171.823i	0.288465	+	0.236021i
$729$		0			0
$730$		0			0
$731$			715.324i			0.978556i
$732$		0			0
$733$	−430.623			−0.587480			−0.293740	−	0.955885i	$-0.594900\pi$
$733$	−430.623			−0.587480			−0.293740	+	0.955885i	$0.594900\pi$
$734$	−2.55712	+	2.73292i	−0.00348382	+	0.00372333i
$735$		0			0
$736$	203.055	−	284.849i	0.275889	−	0.387023i
$737$	1987.17			2.69630
$738$		0			0
$739$			523.620i			0.708552i	0.935141	+	0.354276i	$0.115273\pi$
$739$			523.620i			0.708552i	−0.935141	+	0.354276i	$0.884727\pi$
$740$		0			0
$741$		0			0
$742$	−153.809	+	164.384i	−0.207290	+	0.221541i
$743$			880.661i			1.18528i	0.805469	+	0.592638i	$0.201914\pi$
$743$			880.661i			1.18528i	−0.805469	+	0.592638i	$0.798086\pi$
$744$		0			0
$745$		0			0
$746$	−562.057	−	525.902i	−0.753428	−	0.704962i
$747$		0			0
$748$	−765.545	+	50.9378i	−1.02346	+	0.0680986i
$749$	−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	$-0.131425\pi$
$752$	−105.001	−	785.540i	−0.139629	−	1.04460i
$753$		0			0
$754$	263.370	+	246.428i	0.349297	+	0.326828i
$755$		0			0
$756$		0			0
$757$	−427.136			−0.564249			−0.282124	−	0.959378i	$-0.591039\pi$
$757$	−427.136			−0.564249			−0.282124	+	0.959378i	$0.591039\pi$
$758$	660.206	−	705.594i	0.870984	−	0.930863i
$759$		0			0
$760$		0			0
$761$	−239.700			−0.314980			−0.157490	−	0.987521i	$-0.550340\pi$
$761$	−239.700			−0.314980			−0.157490	+	0.987521i	$0.550340\pi$
$762$		0			0
$763$			304.090i			0.398545i
$764$	254.270	−	16.9186i	0.332814	−	0.0221447i
$765$		0			0
$766$	178.323	−	190.582i	0.232798	−	0.248802i
$767$			2010.71i			2.62152i
$768$		0			0
$769$	937.486			1.21910			0.609549	−	0.792748i	$-0.291351\pi$
$769$	937.486			1.21910			0.609549	+	0.792748i	$0.291351\pi$
$770$		0			0
$771$		0			0
$772$	−12.0837	−	181.606i	−0.0156525	−	0.235241i
$773$	−1468.30			−1.89948			−0.949740	−	0.313040i	$-0.898653\pi$
$773$	−1468.30			−1.89948			−0.949740	+	0.313040i	$0.898653\pi$
$774$		0			0
$775$		0			0
$776$	338.138	−	413.272i	0.435745	−	0.532567i
$777$		0			0
$778$	15.0292	+	14.0624i	0.0193177	+	0.0180751i
$779$		−	813.029i		−	1.04368i
$780$		0			0
$781$	−787.486			−1.00831
$782$	−189.546	+	202.577i	−0.242386	+	0.259049i
$783$		0			0
$784$	−721.552	+	96.4481i	−0.920346	+	0.123020i
$785$		0			0
$786$		0			0
$787$			408.886i			0.519550i	0.965669	+	0.259775i	$0.0836483\pi$
$787$			408.886i			0.519550i	−0.965669	+	0.259775i	$0.916352\pi$
$788$	49.3753	+	742.063i	0.0626591	+	0.941705i
$789$		0			0
$790$		0			0
$791$		−	135.466i		−	0.171259i
$792$		0			0
$793$	−620.747			−0.782783
$794$	−334.234	−	312.734i	−0.420949	−	0.393871i
$795$		0			0
$796$	−622.241	+	41.4026i	−0.781710	+	0.0520134i
$797$	400.122			0.502035			0.251018	−	0.967982i	$-0.419235\pi$
$797$	400.122			0.502035			0.251018	+	0.967982i	$0.419235\pi$
$798$		0			0
$799$			628.525i			0.786639i
$800$		0			0
$801$		0			0
$802$	141.560	+	132.454i	0.176509	+	0.165155i
$803$			940.966i			1.17181i
$804$		0			0
$805$		0			0
$806$	605.392	−	647.012i	0.751106	−	0.802744i
$807$		0			0
$808$	−833.710	+	1018.96i	−1.03182	+	1.26109i
$809$	−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	$-0.0583259\pi$
$812$	74.3158	−	4.94482i	0.0915219	−	0.00608968i
$813$		0			0
$814$	−369.230	+	394.614i	−0.453599	+	0.484784i
$815$		0			0
$816$		0			0
$817$	1588.98			1.94490
$818$	197.876	+	185.148i	0.241903	+	0.226342i
$819$		0			0
$820$		0			0
$821$	1227.23			1.49480			0.747402	−	0.664372i	$-0.231301\pi$
$821$	1227.23			1.49480			0.747402	+	0.664372i	$0.231301\pi$
$822$		0			0
$823$		−	881.623i		−	1.07123i	−0.844462	−	0.535615i	$-0.820080\pi$
$823$		−	881.623i		−	1.07123i	0.844462	−	0.535615i	$-0.179920\pi$
$824$	−267.936	−	219.224i	−0.325165	−	0.266049i
$825$		0			0
$826$	303.187	+	283.684i	0.367054	+	0.343443i
$827$		−	850.269i		−	1.02814i	−0.857749	−	0.514068i	$-0.828138\pi$
$827$		−	850.269i		−	1.02814i	0.857749	−	0.514068i	$-0.171862\pi$
$828$		0			0
$829$	−1328.47			−1.60250			−0.801251	−	0.598328i	$-0.795832\pi$
$829$	−1328.47			−1.60250			−0.801251	+	0.598328i	$0.795832\pi$
$830$		0			0
$831$		0			0
$832$	229.677	+	1137.00i	0.276054	+	1.36659i
$833$	577.327			0.693069
$834$		0			0
$835$		0			0
$836$	113.150	+	1700.54i	0.135347	+	2.03414i
$837$		0			0
$838$	525.967	−	562.127i	0.627646	−	0.670796i
$839$			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
$842$	793.335	+	742.303i	0.942203	+	0.881594i
$843$		0			0
$844$	966.739	−	64.3248i	1.14543	−	0.0762142i
$845$		0			0
$846$		0			0
$847$			201.166i			0.237504i
$848$	−953.906	+	127.506i	−1.12489	+	0.150361i
$849$		0			0
$850$		0			0
$851$			195.409i			0.229623i
$852$		0			0
$853$	742.887			0.870911			0.435456	−	0.900210i	$-0.356587\pi$
$853$	742.887			0.870911			0.435456	+	0.900210i	$0.356587\pi$
$854$	−87.5790	+	93.6000i	−0.102552	+	0.109602i
$855$		0			0
$856$	−1071.30	−	876.537i	−1.25152	−	1.02399i
$857$	−679.145			−0.792468			−0.396234	−	0.918150i	$-0.629683\pi$
$857$	−679.145			−0.792468			−0.396234	+	0.918150i	$0.629683\pi$
$858$		0			0
$859$		−	756.133i		−	0.880248i	−0.897937	−	0.440124i	$-0.854934\pi$
$859$		−	756.133i		−	0.880248i	0.897937	−	0.440124i	$-0.145066\pi$
$860$		0			0
$861$		0			0
$862$	−1063.37	+	1136.48i	−1.23361	+	1.31842i
$863$		−	1130.05i		−	1.30944i	−0.755871	−	0.654721i	$-0.772786\pi$
$863$		−	1130.05i		−	1.30944i	0.755871	−	0.654721i	$-0.227214\pi$
$864$		0			0
$865$		0			0
$866$	−7.67137	−	7.17790i	−0.00885840	−	0.00828856i
$867$		0			0
$868$	−12.1478	−	182.569i	−0.0139951	−	0.210333i
$869$	1561.10			1.79643
$870$		0			0
$871$			2382.65i			2.73554i
$872$	−823.208	+	1006.13i	−0.944046	+	1.15381i
$873$		0			0
$874$	449.992	+	421.046i	0.514865	+	0.481746i
$875$		0			0
$876$		0			0
$877$	−910.607			−1.03832			−0.519160	−	0.854677i	$-0.673755\pi$
$877$	−910.607			−1.03832			−0.519160	+	0.854677i	$0.673755\pi$
$878$	284.637	−	304.205i	0.324188	−	0.346475i
$879$		0			0
$880$		0			0
$881$	−405.402			−0.460161			−0.230080	−	0.973172i	$-0.573899\pi$
$881$	−405.402			−0.460161			−0.230080	+	0.973172i	$0.573899\pi$
$882$		0			0
$883$		−	819.868i		−	0.928503i	−0.885703	−	0.464252i	$-0.846323\pi$
$883$		−	819.868i		−	0.928503i	0.885703	−	0.464252i	$-0.153677\pi$
$884$	−61.0752	−	917.901i	−0.0690896	−	1.03835i
$885$		0			0
$886$	1005.48	−	1074.60i	1.13485	−	1.21287i
$887$			1003.99i			1.13190i	0.824440	+	0.565949i	$0.191490\pi$
$887$			1003.99i			1.13190i	−0.824440	+	0.565949i	$0.808510\pi$
$888$		0			0
$889$	−277.961			−0.312667
$890$		0			0
$891$		0			0
$892$	−998.010	+	66.4055i	−1.11885	+	0.0744456i
$893$	1396.17			1.56346
$894$		0			0
$895$		0			0
$896$	203.849	+	125.784i	0.227510	+	0.140384i
$897$		0			0
$898$	901.296	+	843.318i	1.00367	+	0.939107i
$899$		−	243.220i		−	0.270545i
$900$		0			0
$901$	763.237			0.847100
$902$	595.800	−	636.761i	0.660532	−	0.705943i
$903$		0			0
$904$	366.722	−	448.208i	0.405666	−	0.495805i
$905$		0			0
$906$		0			0
$907$		−	361.629i		−	0.398709i	−0.979927	−	0.199354i	$-0.936116\pi$
$907$		−	361.629i		−	0.398709i	0.979927	−	0.199354i	$-0.0638845\pi$
$908$	−241.325	+	16.0572i	−0.265776	+	0.0176842i
$909$		0			0
$910$		0			0
$911$			294.475i			0.323244i	0.986853	+	0.161622i	$0.0516725\pi$
$911$			294.475i			0.323244i	−0.986853	+	0.161622i	$0.948327\pi$
$912$		0			0
$913$	864.965			0.947388
$914$	−471.341	−	441.022i	−0.515691	−	0.482518i
$915$		0			0
$916$	20.7802	+	312.306i	0.0226858	+	0.340945i
$917$	−50.0182			−0.0545454
$918$		0			0
$919$		−	17.4246i		−	0.0189604i	−0.999955	−	0.00948022i	$-0.996982\pi$
$919$		−	17.4246i		−	0.0189604i	0.999955	−	0.00948022i	$-0.00301769\pi$
$920$		0			0
$921$		0			0
$922$	743.395	+	695.575i	0.806285	+	0.754420i
$923$		−	944.209i		−	1.02298i
$924$		0			0
$925$		0			0
$926$	−1013.88	+	1083.59i	−1.09491	+	1.17018i
$927$		0			0
$928$	259.270	+	184.821i	0.279386	+	0.199161i
$929$	−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
$932$	−43.7495	−	657.513i	−0.0469416	−	0.705486i
$933$		0			0
$934$	424.549	−	453.736i	0.454549	−	0.485799i
$935$		0			0
$936$		0			0
$937$	802.514			0.856471			0.428236	−	0.903667i	$-0.359135\pi$
$937$	802.514			0.856471			0.428236	+	0.903667i	$0.359135\pi$
$938$	359.271	+	336.160i	0.383018	+	0.358380i
$939$		0			0
$940$		0			0
$941$	−730.288			−0.776076			−0.388038	−	0.921643i	$-0.626847\pi$
$941$	−730.288			−0.776076			−0.388038	+	0.921643i	$0.626847\pi$
$942$		0			0
$943$		−	315.318i		−	0.334378i
$944$	235.171	+	1759.37i	0.249122	+	1.86374i
$945$		0			0
$946$	1244.48	+	1164.43i	1.31552	+	1.23090i
$947$		−	882.383i		−	0.931767i	−0.884846	−	0.465884i	$-0.845737\pi$
$947$		−	882.383i		−	0.931767i	0.884846	−	0.465884i	$-0.154263\pi$
$948$		0			0
$949$	−1128.23			−1.18887
$950$		0			0
$951$		0			0
$952$	−147.023	−	120.294i	−0.154436	−	0.126359i
$953$	1047.62			1.09929			0.549644	−	0.835399i	$-0.314763\pi$
$953$	1047.62			1.09929			0.549644	+	0.835399i	$0.314763\pi$
$954$		0			0
$955$		0			0
$956$	972.811	−	64.7288i	1.01759	−	0.0677080i
$957$		0			0
$958$	654.689	−	699.698i	0.683391	−	0.730374i
$959$			237.573i			0.247730i
$960$		0			0
$961$	363.490			0.378242
$962$	−473.149	−	442.712i	−0.491838	−	0.460200i
$963$		0			0
$964$	101.842	+	1530.59i	0.105646	+	1.58775i
$965$		0			0
$966$		0			0
$967$			519.528i			0.537258i	0.963244	+	0.268629i	$0.0865705\pi$
$967$			519.528i			0.537258i	−0.963244	+	0.268629i	$0.913430\pi$
$968$	−544.580	+	665.587i	−0.562583	+	0.687589i
$969$		0			0
$970$		0			0
$971$		−	398.406i		−	0.410305i	−0.978730	−	0.205152i	$-0.934231\pi$
$971$		−	398.406i		−	0.410305i	0.978730	−	0.205152i	$-0.0657690\pi$
$972$		0			0
$973$	38.7393			0.0398143
$974$	−782.788	+	836.604i	−0.803684	+	0.858937i
$975$		0			0
$976$	−543.154	+	72.6021i	−0.556510	+	0.0743874i
$977$	−367.857			−0.376517			−0.188258	−	0.982120i	$-0.560284\pi$
$977$	−367.857			−0.376517			−0.188258	+	0.982120i	$0.560284\pi$
$978$		0			0
$979$			2193.66i			2.24071i
$980$		0			0
$981$		0			0
$982$	0.355984	−	0.380457i	0.000362509	−	0.000387431i
$983$		−	1473.69i		−	1.49918i	−0.661902	−	0.749590i	$-0.730251\pi$
$983$		−	1473.69i		−	1.49918i	0.661902	−	0.749590i	$-0.269749\pi$
$984$		0			0
$985$		0			0
$986$	−184.386	−	172.525i	−0.187004	−	0.174975i
$987$		0			0
$988$	−2038.97	+	135.669i	−2.06374	+	0.137317i
$989$	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	$0.875936\pi$
$992$	454.044	−	636.941i	0.457705	−	0.642078i
$993$		0			0
$994$	−142.374	−	133.215i	−0.143233	−	0.134019i
$995$		0			0
$996$		0			0
$997$	−767.370			−0.769679			−0.384839	−	0.922984i	$-0.625743\pi$
$997$	−767.370			−0.769679			−0.384839	+	0.922984i	$0.625743\pi$
$998$	−639.112	+	683.050i	−0.640393	+	0.684419i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.c.c.91.1	✓	8	15.14	odd	2
180.3.c.c.91.2	yes	8	60.59	even	2
180.3.c.c.91.7	yes	8	20.19	odd	2
180.3.c.c.91.8	yes	8	5.4	even	2
900.3.c.o.451.1		8	1.1	even	1	trivial
900.3.c.o.451.2		8	4.3	odd	2	inner
900.3.c.o.451.7		8	12.11	even	2	inner
900.3.c.o.451.8		8	3.2	odd	2	inner
900.3.f.i.199.5		16	20.7	even	4
900.3.f.i.199.6		16	60.23	odd	4
900.3.f.i.199.7		16	5.3	odd	4
900.3.f.i.199.8		16	15.2	even	4
900.3.f.i.199.9		16	15.8	even	4
900.3.f.i.199.10		16	5.2	odd	4
900.3.f.i.199.11		16	60.47	odd	4
900.3.f.i.199.12		16	20.3	even	4
2880.3.e.i.2431.2		8	40.19	odd	2
2880.3.e.i.2431.3		8	40.29	even	2
2880.3.e.i.2431.6		8	120.59	even	2
2880.3.e.i.2431.7		8	120.29	odd	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46040 - 1.36646i) q^{2} +(0.265564 + 3.99117i) q^{4} -1.87135i q^{7} +(5.06596 - 6.19161i) q^{8} +O(q^{10})\)	\(q+(-1.46040 - 1.36646i) q^{2} +(0.265564 + 3.99117i) q^{4} -1.87135i q^{7} +(5.06596 - 6.19161i) q^{8} +15.1162i q^{11} -18.1245 q^{13} +(-2.55712 + 2.73292i) q^{14} +(-15.8590 + 2.11983i) q^{16} +12.6890 q^{17} -28.1867i q^{19} +(20.6556 - 22.0757i) q^{22} -10.9317i q^{23} +(26.4691 + 24.7665i) q^{26} +(7.46887 - 0.496963i) q^{28} +9.95007 q^{29} -24.4440i q^{31} +(26.0572 + 18.5748i) q^{32} +(-18.5311 - 17.3391i) q^{34} -17.8755 q^{37} +(-38.5161 + 41.1640i) q^{38} +28.8444 q^{41} +56.3734i q^{43} +(-60.3312 + 4.01431i) q^{44} +(-14.9377 + 15.9647i) q^{46} +49.5329i q^{47} +45.4981 q^{49} +(-4.81323 - 72.3381i) q^{52} +60.1494 q^{53} +(-11.5867 - 9.48016i) q^{56} +(-14.5311 - 13.5964i) q^{58} -110.939i q^{59} +34.2490 q^{61} +(-33.4018 + 35.6982i) q^{62} +(-12.6722 - 62.7329i) q^{64} -131.460i q^{67} +(3.36976 + 50.6442i) q^{68} +52.0957i q^{71} +62.2490 q^{73} +(26.1054 + 24.4262i) q^{74} +(112.498 - 7.48539i) q^{76} +28.2876 q^{77} -103.274i q^{79} +(-42.1245 - 39.4148i) q^{82} -57.2212i q^{83} +(77.0321 - 82.3280i) q^{86} +(93.5934 + 76.5778i) q^{88} +145.120 q^{89} +33.9173i q^{91} +(43.6303 - 2.90307i) q^{92} +(67.6848 - 72.3381i) q^{94} +66.7471 q^{97} +(-66.4456 - 62.1714i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 14 q^{4}+O(q^{10}) \) 8 * q - 14 * q^4	\( 8 q - 14 q^{4} - 16 q^{13} - 14 q^{16} + 4 q^{22} + 92 q^{28} - 116 q^{34} - 272 q^{37} - 184 q^{46} - 152 q^{49} - 232 q^{52} - 84 q^{58} + 16 q^{61} - 182 q^{64} + 240 q^{73} + 384 q^{76} - 208 q^{82} + 652 q^{88} - 168 q^{94} - 240 q^{97}+O(q^{100}) \) 8 * q - 14 * q^4 - 16 * q^13 - 14 * q^16 + 4 * q^22 + 92 * q^28 - 116 * q^34 - 272 * q^37 - 184 * q^46 - 152 * q^49 - 232 * q^52 - 84 * q^58 + 16 * q^61 - 182 * q^64 + 240 * q^73 + 384 * q^76 - 208 * q^82 + 652 * q^88 - 168 * q^94 - 240 * q^97

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