LMFDB - Embedded newform 900.3.f.g.199.1

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} - x^{12} + 25x^{8} - 16x^{4} + 256 $ x^16 - x^12 + 25x^8 - 16x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.1
Root			$-0.404496 - 1.35513i$ of defining polynomial
Character	$\chi$	$=$	900.199
Dual form			900.3.f.g.199.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.75963 - 0.950636i) q^{2} +(2.19258 + 3.34553i) q^{4} -3.98982 q^{7} +(-0.677747 - 7.97124i) q^{8} +O(q^{10})$	\(q+(-1.75963 - 0.950636i) q^{2} +(2.19258 + 3.34553i) q^{4} -3.98982 q^{7} +(-0.677747 - 7.97124i) q^{8} -8.39401i q^{11} -9.77033i q^{13} +(7.02060 + 3.79287i) q^{14} +(-6.38516 + 14.6707i) q^{16} -12.1399i q^{17} +17.3719i q^{19} +(-7.97964 + 14.7703i) q^{22} -2.97203 q^{23} +(-9.28803 + 17.1921i) q^{26} +(-8.74801 - 13.3481i) q^{28} +51.6300 q^{29} +30.7541i q^{31} +(25.1820 - 19.7450i) q^{32} +(-11.5407 + 21.3618i) q^{34} +19.5407i q^{37} +(16.5144 - 30.5682i) q^{38} -42.5603 q^{41} -62.9208 q^{43} +(28.0824 - 18.4046i) q^{44} +(5.22967 + 2.82532i) q^{46} -39.5201 q^{47} -33.0813 q^{49} +(32.6869 - 21.4223i) q^{52} -21.2096i q^{53} +(2.70409 + 31.8038i) q^{56} +(-90.8496 - 49.0813i) q^{58} +50.3640i q^{59} -70.3923 q^{61} +(29.2359 - 54.1157i) q^{62} +(-63.0813 + 10.8050i) q^{64} +94.8394 q^{67} +(40.6145 - 26.6178i) q^{68} -132.376i q^{71} -77.7033i q^{73} +(18.5761 - 34.3843i) q^{74} +(-58.1184 + 38.0894i) q^{76} +33.4906i q^{77} +48.3742i q^{79} +(74.8903 + 40.4593i) q^{82} -140.248 q^{83} +(110.717 + 59.8148i) q^{86} +(-66.9106 + 5.68901i) q^{88} -18.1394 q^{89} +38.9819i q^{91} +(-6.51642 - 9.94303i) q^{92} +(69.5407 + 37.5692i) q^{94} -15.0000i q^{97} +(58.2108 + 31.4483i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4}+O(q^{10}) $ 16 * q - 8 * q^4	$ 16 q - 8 q^{4} - 16 q^{16} + 160 q^{34} + 256 q^{46} + 160 q^{49} + 80 q^{61} - 320 q^{64} - 456 q^{76} + 768 q^{94}+O(q^{100}) $ 16 * q - 8 * q^4 - 16 * q^16 + 160 * q^34 + 256 * q^46 + 160 * q^49 + 80 * q^61 - 320 * q^64 - 456 * q^76 + 768 * 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 $

$2$	−1.75963	−	0.950636i	−0.879814	−	0.475318i
$2$	−1.75963	−	0.950636i	−0.879814	−	0.475318i
$3$		0			0
$3$		0			0
$4$	2.19258	+	3.34553i	0.548146	+	0.836383i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.98982			−0.569975			−0.284987	−	0.958531i	$-0.591989\pi$
$7$	−3.98982			−0.569975			−0.284987	+	0.958531i	$0.591989\pi$
$8$	−0.677747	−	7.97124i	−0.0847184	−	0.996405i
$9$		0			0
$10$		0			0
$11$		−	8.39401i		−	0.763091i	−0.924350	−	0.381546i	$-0.875392\pi$
$11$		−	8.39401i		−	0.763091i	0.924350	−	0.381546i	$-0.124608\pi$
$12$		0			0
$13$		−	9.77033i		−	0.751564i	−0.926708	−	0.375782i	$-0.877374\pi$
$13$		−	9.77033i		−	0.751564i	0.926708	−	0.375782i	$-0.122626\pi$
$14$	7.02060	+	3.79287i	0.501472	+	0.270919i
$15$		0			0
$16$	−6.38516	+	14.6707i	−0.399073	+	0.916919i
$17$		−	12.1399i		−	0.714114i	−0.934083	−	0.357057i	$-0.883780\pi$
$17$		−	12.1399i		−	0.714114i	0.934083	−	0.357057i	$-0.116220\pi$
$18$		0			0
$19$			17.3719i			0.914313i	0.889386	+	0.457157i	$0.151132\pi$
$19$			17.3719i			0.914313i	−0.889386	+	0.457157i	$0.848868\pi$
$20$		0			0
$21$		0			0
$22$	−7.97964	+	14.7703i	−0.362711	+	0.671379i
$23$	−2.97203			−0.129219			−0.0646094	−	0.997911i	$-0.520580\pi$
$23$	−2.97203			−0.129219			−0.0646094	+	0.997911i	$0.520580\pi$
$24$		0			0
$25$		0			0
$26$	−9.28803	+	17.1921i	−0.357232	+	0.661236i
$27$		0			0
$28$	−8.74801	−	13.3481i	−0.312429	−	0.476717i
$29$	51.6300			1.78034			0.890172	−	0.455624i	$-0.150584\pi$
$29$	51.6300			1.78034			0.890172	+	0.455624i	$0.150584\pi$
$30$		0			0
$31$			30.7541i			0.992067i	0.868303	+	0.496033i	$0.165211\pi$
$31$			30.7541i			0.992067i	−0.868303	+	0.496033i	$0.834789\pi$
$32$	25.1820	−	19.7450i	0.786938	−	0.617032i
$33$		0			0
$34$	−11.5407	+	21.3618i	−0.339431	+	0.628287i
$35$		0			0
$36$		0			0
$37$			19.5407i			0.528126i	0.964505	+	0.264063i	$0.0850627\pi$
$37$			19.5407i			0.528126i	−0.964505	+	0.264063i	$0.914937\pi$
$38$	16.5144	−	30.5682i	0.434589	−	0.804426i
$39$		0			0
$40$		0			0
$41$	−42.5603			−1.03806			−0.519028	−	0.854757i	$-0.673706\pi$
$41$	−42.5603			−1.03806			−0.519028	+	0.854757i	$0.673706\pi$
$42$		0			0
$43$	−62.9208			−1.46327			−0.731637	−	0.681694i	$-0.761244\pi$
$43$	−62.9208			−1.46327			−0.731637	+	0.681694i	$0.761244\pi$
$44$	28.0824	−	18.4046i	0.638237	−	0.418285i
$45$		0			0
$46$	5.22967	+	2.82532i	0.113688	+	0.0614200i
$47$	−39.5201			−0.840853			−0.420426	−	0.907327i	$-0.638120\pi$
$47$	−39.5201			−0.840853			−0.420426	+	0.907327i	$0.638120\pi$
$48$		0			0
$49$	−33.0813			−0.675129
$50$		0			0
$51$		0			0
$52$	32.6869	−	21.4223i	0.628595	−	0.411966i
$53$		−	21.2096i		−	0.400182i	−0.979777	−	0.200091i	$-0.935876\pi$
$53$		−	21.2096i		−	0.400182i	0.979777	−	0.200091i	$-0.0641237\pi$
$54$		0			0
$55$		0			0
$56$	2.70409	+	31.8038i	0.0482873	+	0.567926i
$57$		0			0
$58$	−90.8496	−	49.0813i	−1.56637	−	0.846230i
$59$			50.3640i			0.853628i	0.904339	+	0.426814i	$0.140364\pi$
$59$			50.3640i			0.853628i	−0.904339	+	0.426814i	$0.859636\pi$
$60$		0			0
$61$	−70.3923			−1.15397			−0.576986	−	0.816754i	$-0.695771\pi$
$61$	−70.3923			−1.15397			−0.576986	+	0.816754i	$0.695771\pi$
$62$	29.2359	−	54.1157i	0.471547	−	0.872834i
$63$		0			0
$64$	−63.0813	+	10.8050i	−0.985646	+	0.168828i
$65$		0			0
$66$		0			0
$67$	94.8394			1.41551			0.707757	−	0.706456i	$-0.249707\pi$
$67$	94.8394			1.41551			0.707757	+	0.706456i	$0.249707\pi$
$68$	40.6145	−	26.6178i	0.597273	−	0.391438i
$69$		0			0
$70$		0			0
$71$		−	132.376i		−	1.86445i	−0.361874	−	0.932227i	$-0.617863\pi$
$71$		−	132.376i		−	1.86445i	0.361874	−	0.932227i	$-0.382137\pi$
$72$		0			0
$73$		−	77.7033i		−	1.06443i	−0.846610	−	0.532214i	$-0.821360\pi$
$73$		−	77.7033i		−	1.06443i	0.846610	−	0.532214i	$-0.178640\pi$
$74$	18.5761	−	34.3843i	0.251028	−	0.464653i
$75$		0			0
$76$	−58.1184	+	38.0894i	−0.764716	+	0.501177i
$77$			33.4906i			0.434943i
$78$		0			0
$79$			48.3742i			0.612331i	0.951978	+	0.306166i	$0.0990462\pi$
$79$			48.3742i			0.612331i	−0.951978	+	0.306166i	$0.900954\pi$
$80$		0			0
$81$		0			0
$82$	74.8903	+	40.4593i	0.913296	+	0.493407i
$83$	−140.248			−1.68974			−0.844868	−	0.534974i	$-0.820321\pi$
$83$	−140.248			−1.68974			−0.844868	+	0.534974i	$0.820321\pi$
$84$		0			0
$85$		0			0
$86$	110.717	+	59.8148i	1.28741	+	0.695521i
$87$		0			0
$88$	−66.9106	+	5.68901i	−0.760348	+	0.0646479i
$89$	−18.1394			−0.203813			−0.101907	−	0.994794i	$-0.532494\pi$
$89$	−18.1394			−0.203813			−0.101907	+	0.994794i	$0.532494\pi$
$90$		0			0
$91$			38.9819i			0.428372i
$92$	−6.51642	−	9.94303i	−0.0708307	−	0.108076i
$93$		0			0
$94$	69.5407	+	37.5692i	0.739794	+	0.399673i
$95$		0			0
$96$		0			0
$97$		−	15.0000i		−	0.154639i	−0.997006	−	0.0773196i	$-0.975364\pi$
$97$		−	15.0000i		−	0.154639i	0.997006	−	0.0773196i	$-0.0246362\pi$
$98$	58.2108	+	31.4483i	0.593988	+	0.320901i
$99$		0			0
$100$		0			0
$101$	−118.611			−1.17437			−0.587184	−	0.809453i	$-0.699763\pi$
$101$	−118.611			−1.17437			−0.587184	+	0.809453i	$0.699763\pi$
$102$		0			0
$103$	−165.740			−1.60912			−0.804562	−	0.593868i	$-0.797600\pi$
$103$	−165.740			−1.60912			−0.804562	+	0.593868i	$0.797600\pi$
$104$	−77.8816	+	6.62181i	−0.748862	+	0.0636712i
$105$		0			0
$106$	−20.1626	+	37.3211i	−0.190214	+	0.352085i
$107$	−104.222			−0.974039			−0.487020	−	0.873391i	$-0.661916\pi$
$107$	−104.222			−0.974039			−0.487020	+	0.873391i	$0.661916\pi$
$108$		0			0
$109$	−60.8516			−0.558272			−0.279136	−	0.960252i	$-0.590048\pi$
$109$	−60.8516			−0.558272			−0.279136	+	0.960252i	$0.590048\pi$
$110$		0			0
$111$		0			0
$112$	25.4757	−	58.5335i	0.227461	−	0.522621i
$113$			139.821i			1.23735i	0.785646	+	0.618676i	$0.212331\pi$
$113$			139.821i			1.23735i	−0.785646	+	0.618676i	$0.787669\pi$
$114$		0			0
$115$		0			0
$116$	113.203	+	172.730i	0.975888	+	1.48905i
$117$		0			0
$118$	47.8779	−	88.6220i	0.405745	−	0.751034i
$119$			48.4362i			0.407027i
$120$		0			0
$121$	50.5407			0.417691
$122$	123.864	+	66.9175i	1.01528	+	0.548504i
$123$		0			0
$124$	−102.889	+	67.4308i	−0.829748	+	0.543797i
$125$		0			0
$126$		0			0
$127$	−63.8372			−0.502655			−0.251327	−	0.967902i	$-0.580867\pi$
$127$	−63.8372			−0.502655			−0.251327	+	0.967902i	$0.580867\pi$
$128$	121.271	+	40.9547i	0.947432	+	0.319958i
$129$		0			0
$130$		0			0
$131$		−	205.994i		−	1.57248i	−0.617923	−	0.786238i	$-0.712026\pi$
$131$		−	205.994i		−	1.57248i	0.617923	−	0.786238i	$-0.287974\pi$
$132$		0			0
$133$		−	69.3110i		−	0.521135i
$134$	−166.882	−	90.1577i	−1.24539	−	0.672819i
$135$		0			0
$136$	−96.7703	+	8.22780i	−0.711547	+	0.0604985i
$137$			243.081i			1.77431i	0.461470	+	0.887156i	$0.347322\pi$
$137$			243.081i			1.77431i	−0.461470	+	0.887156i	$0.652678\pi$
$138$		0			0
$139$			122.520i			0.881439i	0.897645	+	0.440719i	$0.145277\pi$
$139$			122.520i			0.881439i	−0.897645	+	0.440719i	$0.854723\pi$
$140$		0			0
$141$		0			0
$142$	−125.842	+	232.933i	−0.886209	+	1.64037i
$143$	−82.0122			−0.573512
$144$		0			0
$145$		0			0
$146$	−73.8676	+	136.729i	−0.505942	+	0.936499i
$147$		0			0
$148$	−65.3739	+	42.8445i	−0.441716	+	0.289490i
$149$	−121.399			−0.814761			−0.407380	−	0.913259i	$-0.633558\pi$
$149$	−121.399			−0.814761			−0.407380	+	0.913259i	$0.633558\pi$
$150$		0			0
$151$			113.376i			0.750833i	0.926856	+	0.375417i	$0.122500\pi$
$151$			113.376i			0.750833i	−0.926856	+	0.375417i	$0.877500\pi$
$152$	138.476	−	11.7738i	0.911026	−	0.0774591i
$153$		0			0
$154$	31.8374	−	58.9310i	0.206736	−	0.382669i
$155$		0			0
$156$		0			0
$157$			117.933i			0.751165i	0.926789	+	0.375583i	$0.122557\pi$
$157$			117.933i			0.751165i	−0.926789	+	0.375583i	$0.877443\pi$
$158$	45.9862	−	85.1206i	0.291052	−	0.538738i
$159$		0			0
$160$		0			0
$161$	11.8579			0.0736514
$162$		0			0
$163$	158.677			0.973476			0.486738	−	0.873548i	$-0.338187\pi$
$163$	158.677			0.973476			0.486738	+	0.873548i	$0.338187\pi$
$164$	−93.3169	−	142.387i	−0.569006	−	0.868212i
$165$		0			0
$166$	246.785	+	133.325i	1.48665	+	0.803162i
$167$	−260.736			−1.56130			−0.780648	−	0.624972i	$-0.785111\pi$
$167$	−260.736			−1.56130			−0.780648	+	0.624972i	$0.785111\pi$
$168$		0			0
$169$	73.5407			0.435152
$170$		0			0
$171$		0			0
$172$	−137.959	−	210.504i	−0.802088	−	1.22386i
$173$			294.711i			1.70353i	0.523924	+	0.851765i	$0.324468\pi$
$173$			294.711i			1.70353i	−0.523924	+	0.851765i	$0.675532\pi$
$174$		0			0
$175$		0			0
$176$	123.146	+	53.5971i	0.699693	+	0.304529i
$177$		0			0
$178$	31.9186	+	17.2440i	0.179318	+	0.0968762i
$179$			147.236i			0.822550i	0.911511	+	0.411275i	$0.134916\pi$
$179$			147.236i			0.822550i	−0.911511	+	0.411275i	$0.865084\pi$
$180$		0			0
$181$	−71.7703			−0.396521			−0.198261	−	0.980149i	$-0.563529\pi$
$181$	−71.7703			−0.396521			−0.198261	+	0.980149i	$0.563529\pi$
$182$	37.0576	−	68.5936i	0.203613	−	0.376888i
$183$		0			0
$184$	2.01428	+	23.6908i	0.0109472	+	0.128754i
$185$		0			0
$186$		0			0
$187$	−101.903			−0.544934
$188$	−86.6510	−	132.216i	−0.460910	−	0.703275i
$189$		0			0
$190$		0			0
$191$		−	333.832i		−	1.74781i	−0.486094	−	0.873907i	$-0.661579\pi$
$191$		−	333.832i		−	1.74781i	0.486094	−	0.873907i	$-0.338421\pi$
$192$		0			0
$193$			192.703i			0.998463i	0.866469	+	0.499231i	$0.166384\pi$
$193$			192.703i			0.998463i	−0.866469	+	0.499231i	$0.833616\pi$
$194$	−14.2595	+	26.3944i	−0.0735028	+	0.136054i
$195$		0			0
$196$	−72.5335	−	110.675i	−0.370069	−	0.564666i
$197$			36.5608i			0.185588i	0.995685	+	0.0927940i	$0.0295798\pi$
$197$			36.5608i			0.185588i	−0.995685	+	0.0927940i	$0.970420\pi$
$198$		0			0
$199$		−	230.742i		−	1.15951i	−0.814793	−	0.579753i	$-0.803149\pi$
$199$		−	230.742i		−	1.15951i	0.814793	−	0.579753i	$-0.196851\pi$
$200$		0			0
$201$		0			0
$202$	208.712	+	112.756i	1.03323	+	0.558198i
$203$	−205.994			−1.01475
$204$		0			0
$205$		0			0
$206$	291.640	+	157.558i	1.41573	+	0.764846i
$207$		0			0
$208$	143.338	+	62.3852i	0.689123	+	0.299929i
$209$	145.820			0.697705
$210$		0			0
$211$		−	177.957i		−	0.843400i	−0.906735	−	0.421700i	$-0.861433\pi$
$211$		−	177.957i		−	0.843400i	0.906735	−	0.421700i	$-0.138567\pi$
$212$	70.9575	−	46.5039i	0.334705	−	0.219358i
$213$		0			0
$214$	183.392	+	99.0774i	0.856973	+	0.462978i
$215$		0			0
$216$		0			0
$217$		−	122.703i		−	0.565453i
$218$	107.076	+	57.8478i	0.491176	+	0.265357i
$219$		0			0
$220$		0			0
$221$	−118.611			−0.536702
$222$		0			0
$223$	175.877			0.788684			0.394342	−	0.918964i	$-0.370972\pi$
$223$	175.877			0.788684			0.394342	+	0.918964i	$0.370972\pi$
$224$	−100.472	+	78.7791i	−0.448535	+	0.351693i
$225$		0			0
$226$	132.919	−	246.033i	0.588136	−	1.08864i
$227$	−76.5902			−0.337402			−0.168701	−	0.985667i	$-0.553957\pi$
$227$	−76.5902			−0.337402			−0.168701	+	0.985667i	$0.553957\pi$
$228$		0			0
$229$	77.6363			0.339023			0.169511	−	0.985528i	$-0.445781\pi$
$229$	77.6363			0.339023			0.169511	+	0.985528i	$0.445781\pi$
$230$		0			0
$231$		0			0
$232$	−34.9921	−	411.555i	−0.150828	−	1.77394i
$233$		−	133.539i		−	0.573130i	−0.958061	−	0.286565i	$-0.907487\pi$
$233$		−	133.539i		−	0.573130i	0.958061	−	0.286565i	$-0.0925134\pi$
$234$		0			0
$235$		0			0
$236$	−168.494	+	110.427i	−0.713960	+	0.467912i
$237$		0			0
$238$	46.0452	−	85.2297i	0.193467	−	0.358108i
$239$		−	14.8602i		−	0.0621764i	−0.999517	−	0.0310882i	$-0.990103\pi$
$239$		−	14.8602i		−	0.0621764i	0.999517	−	0.0310882i	$-0.00989727\pi$
$240$		0			0
$241$	125.622			0.521253			0.260627	−	0.965440i	$-0.416071\pi$
$241$	125.622			0.521253			0.260627	+	0.965440i	$0.416071\pi$
$242$	−88.9328	−	48.0458i	−0.367491	−	0.198536i
$243$		0			0
$244$	−154.341	−	235.500i	−0.632545	−	0.965163i
$245$		0			0
$246$		0			0
$247$	169.730			0.687165
$248$	245.148	−	20.8435i	0.988500	−	0.0840463i
$249$		0			0
$250$		0			0
$251$		−	164.024i		−	0.653484i	−0.945114	−	0.326742i	$-0.894049\pi$
$251$		−	164.024i		−	0.653484i	0.945114	−	0.326742i	$-0.105951\pi$
$252$		0			0
$253$			24.9473i			0.0986057i
$254$	112.330	+	60.6859i	0.442243	+	0.238921i
$255$		0			0
$256$	−174.459	−	187.350i	−0.681482	−	0.731835i
$257$		−	188.098i		−	0.731901i	−0.930634	−	0.365950i	$-0.880744\pi$
$257$		−	188.098i		−	0.731901i	0.930634	−	0.365950i	$-0.119256\pi$
$258$		0			0
$259$		−	77.9638i		−	0.301018i
$260$		0			0
$261$		0			0
$262$	−195.826	+	362.474i	−0.747426	+	1.38349i
$263$	−114.544			−0.435529			−0.217764	−	0.976001i	$-0.569876\pi$
$263$	−114.544			−0.435529			−0.217764	+	0.976001i	$0.569876\pi$
$264$		0			0
$265$		0			0
$266$	−65.8895	+	121.962i	−0.247705	+	0.458502i
$267$		0			0
$268$	207.943	+	317.288i	0.775907	+	1.18391i
$269$	221.871			0.824800			0.412400	−	0.911003i	$-0.364691\pi$
$269$	221.871			0.824800			0.412400	+	0.911003i	$0.364691\pi$
$270$		0			0
$271$		−	390.163i		−	1.43971i	−0.694122	−	0.719857i	$-0.744207\pi$
$271$		−	390.163i		−	1.43971i	0.694122	−	0.719857i	$-0.255793\pi$
$272$	178.101	+	77.5155i	0.654785	+	0.284983i
$273$		0			0
$274$	231.081	−	427.732i	0.843362	−	1.56106i
$275$		0			0
$276$		0			0
$277$		−	272.421i		−	0.983469i	−0.870745	−	0.491734i	$-0.836363\pi$
$277$		−	272.421i		−	0.983469i	0.870745	−	0.491734i	$-0.163637\pi$
$278$	116.472	−	215.590i	0.418964	−	0.775502i
$279$		0			0
$280$		0			0
$281$	−473.740			−1.68591			−0.842953	−	0.537987i	$-0.819185\pi$
$281$	−473.740			−1.68591			−0.842953	+	0.537987i	$0.819185\pi$
$282$		0			0
$283$	164.824			0.582415			0.291208	−	0.956660i	$-0.405943\pi$
$283$	164.824			0.582415			0.291208	+	0.956660i	$0.405943\pi$
$284$	442.869	−	290.246i	1.55940	−	1.02199i
$285$		0			0
$286$	144.311	+	77.9638i	0.504584	+	0.272601i
$287$	169.808			0.591665
$288$		0			0
$289$	141.622			0.490041
$290$		0			0
$291$		0			0
$292$	259.959	−	170.371i	0.890270	−	0.583462i
$293$		−	273.219i		−	0.932488i	−0.884656	−	0.466244i	$-0.845607\pi$
$293$		−	273.219i		−	0.932488i	0.884656	−	0.466244i	$-0.154393\pi$
$294$		0			0
$295$		0			0
$296$	155.763	−	13.2436i	0.526227	−	0.0447420i
$297$		0			0
$298$	213.618	+	115.407i	0.716838	+	0.387270i
$299$			29.0377i			0.0971161i
$300$		0			0
$301$	251.043			0.834029
$302$	107.779	−	199.499i	0.356885	−	0.660594i
$303$		0			0
$304$	−254.859	−	110.923i	−0.838351	−	0.364877i
$305$		0			0
$306$		0			0
$307$	−132.905			−0.432915			−0.216458	−	0.976292i	$-0.569450\pi$
$307$	−132.905			−0.432915			−0.216458	+	0.976292i	$0.569450\pi$
$308$	−112.044	+	73.4309i	−0.363779	+	0.238412i
$309$		0			0
$310$		0			0
$311$			235.032i			0.755730i	0.925861	+	0.377865i	$0.123342\pi$
$311$			235.032i			0.755730i	−0.925861	+	0.377865i	$0.876658\pi$
$312$		0			0
$313$			497.651i			1.58994i	0.606650	+	0.794969i	$0.292513\pi$
$313$			497.651i			1.58994i	−0.606650	+	0.794969i	$0.707487\pi$
$314$	112.111	−	207.518i	0.357042	−	0.660886i
$315$		0			0
$316$	−161.837	+	106.064i	−0.512144	+	0.335647i
$317$			169.959i			0.536149i	0.963398	+	0.268074i	$0.0863873\pi$
$317$			169.959i			0.536149i	−0.963398	+	0.268074i	$0.913613\pi$
$318$		0			0
$319$		−	433.382i		−	1.35857i
$320$		0			0
$321$		0			0
$322$	−20.8655	−	11.2725i	−0.0647996	−	0.0350078i
$323$	210.894			0.652924
$324$		0			0
$325$		0			0
$326$	−279.212	−	150.844i	−0.856478	−	0.462711i
$327$		0			0
$328$	28.8451	+	339.258i	0.0879424	+	1.03432i
$329$	157.678			0.479265
$330$		0			0
$331$		−	10.3086i		−	0.0311440i	−0.999879	−	0.0155720i	$-0.995043\pi$
$331$		−	10.3086i		−	0.0311440i	0.999879	−	0.0155720i	$-0.00495691\pi$
$332$	−307.506	−	469.205i	−0.926222	−	1.41327i
$333$		0			0
$334$	458.799	+	247.865i	1.37365	+	0.742112i
$335$		0			0
$336$		0			0
$337$			109.029i			0.323527i	0.986830	+	0.161763i	$0.0517182\pi$
$337$			109.029i			0.323527i	−0.986830	+	0.161763i	$0.948282\pi$
$338$	−129.404	−	69.9104i	−0.382853	−	0.206835i
$339$		0			0
$340$		0			0
$341$	258.150			0.757038
$342$		0			0
$343$	327.490			0.954781
$344$	42.6444	+	501.557i	0.123966	+	1.45801i
$345$		0			0
$346$	280.163	−	518.581i	0.809719	−	1.49879i
$347$	−173.824			−0.500934			−0.250467	−	0.968125i	$-0.580584\pi$
$347$	−173.824			−0.500934			−0.250467	+	0.968125i	$0.580584\pi$
$348$		0			0
$349$	−259.244			−0.742819			−0.371410	−	0.928469i	$-0.621125\pi$
$349$	−259.244			−0.742819			−0.371410	+	0.928469i	$0.621125\pi$
$350$		0			0
$351$		0			0
$352$	−165.740	−	211.378i	−0.470852	−	0.600506i
$353$		−	115.400i		−	0.326912i	−0.986551	−	0.163456i	$-0.947736\pi$
$353$		−	115.400i		−	0.326912i	0.986551	−	0.163456i	$-0.0522642\pi$
$354$		0			0
$355$		0			0
$356$	−39.7721	−	60.6859i	−0.111719	−	0.170466i
$357$		0			0
$358$	139.968	−	259.081i	0.390973	−	0.723691i
$359$			333.832i			0.929895i	0.885338	+	0.464948i	$0.153927\pi$
$359$			333.832i			0.929895i	−0.885338	+	0.464948i	$0.846073\pi$
$360$		0			0
$361$	59.2154			0.164032
$362$	126.289	+	68.2275i	0.348865	+	0.188474i
$363$		0			0
$364$	−130.415	+	85.4710i	−0.358283	+	0.234810i
$365$		0			0
$366$		0			0
$367$	−525.148			−1.43092			−0.715461	−	0.698653i	$-0.753783\pi$
$367$	−525.148			−1.43092			−0.715461	+	0.698653i	$0.753783\pi$
$368$	18.9769	−	43.6018i	0.0515677	−	0.118483i
$369$		0			0
$370$		0			0
$371$			84.6227i			0.228093i
$372$		0			0
$373$		−	417.014i		−	1.11800i	−0.829167	−	0.559000i	$-0.811185\pi$
$373$		−	417.014i		−	1.11800i	0.829167	−	0.559000i	$-0.188815\pi$
$374$	179.311	+	96.8724i	0.479441	+	0.259017i
$375$		0			0
$376$	26.7846	+	315.024i	0.0712357	+	0.837830i
$377$		−	504.442i		−	1.33804i
$378$		0			0
$379$			126.758i			0.334454i	0.985918	+	0.167227i	$0.0534812\pi$
$379$			126.758i			0.334454i	−0.985918	+	0.167227i	$0.946519\pi$
$380$		0			0
$381$		0			0
$382$	−317.353	+	587.421i	−0.830767	+	1.53775i
$383$	−129.404			−0.337870			−0.168935	−	0.985627i	$-0.554033\pi$
$383$	−129.404			−0.337870			−0.168935	+	0.985627i	$0.554033\pi$
$384$		0			0
$385$		0			0
$386$	183.191	−	339.086i	0.474587	−	0.878462i
$387$		0			0
$388$	50.1830	−	32.8887i	0.129338	−	0.0847648i
$389$	87.9088			0.225987			0.112993	−	0.993596i	$-0.463956\pi$
$389$	87.9088			0.225987			0.112993	+	0.993596i	$0.463956\pi$
$390$		0			0
$391$			36.0803i			0.0922769i
$392$	22.4208	+	263.699i	0.0571958	+	0.672702i
$393$		0			0
$394$	34.7560	−	64.3335i	0.0882133	−	0.163283i
$395$		0			0
$396$		0			0
$397$			239.770i			0.603955i	0.953315	+	0.301978i	$0.0976468\pi$
$397$			239.770i			0.603955i	−0.953315	+	0.301978i	$0.902353\pi$
$398$	−219.351	+	406.019i	−0.551134	+	1.02015i
$399$		0			0
$400$		0			0
$401$	383.043			0.955218			0.477609	−	0.878572i	$-0.341503\pi$
$401$	383.043			0.955218			0.477609	+	0.878572i	$0.341503\pi$
$402$		0			0
$403$	300.477			0.745602
$404$	−260.065	−	396.817i	−0.643725	−	0.982221i
$405$		0			0
$406$	362.474	+	195.826i	0.892792	+	0.482329i
$407$	164.024			0.403008
$408$		0			0
$409$	731.976			1.78967			0.894836	−	0.446395i	$-0.147292\pi$
$409$	731.976			1.78967			0.894836	+	0.446395i	$0.147292\pi$
$410$		0			0
$411$		0			0
$412$	−363.398	−	554.488i	−0.882035	−	1.34584i
$413$		−	200.944i		−	0.486546i
$414$		0			0
$415$		0			0
$416$	−192.915	−	246.037i	−0.463739	−	0.591434i
$417$		0			0
$418$	−256.589	−	138.622i	−0.613850	−	0.331632i
$419$		−	692.847i		−	1.65357i	−0.562516	−	0.826786i	$-0.690167\pi$
$419$		−	692.847i		−	1.65357i	0.562516	−	0.826786i	$-0.309833\pi$
$420$		0			0
$421$	−326.622			−0.775824			−0.387912	−	0.921696i	$-0.626804\pi$
$421$	−326.622			−0.775824			−0.387912	+	0.921696i	$0.626804\pi$
$422$	−169.173	+	313.139i	−0.400883	+	0.742035i
$423$		0			0
$424$	−169.067	+	14.3748i	−0.398743	+	0.0339027i
$425$		0			0
$426$		0			0
$427$	280.853			0.657735
$428$	−228.516	−	348.679i	−0.533915	−	0.814670i
$429$		0			0
$430$		0			0
$431$			367.408i			0.852456i	0.904616	+	0.426228i	$0.140158\pi$
$431$			367.408i			0.852456i	−0.904616	+	0.426228i	$0.859842\pi$
$432$		0			0
$433$			493.622i			1.14000i	0.821643	+	0.570002i	$0.193058\pi$
$433$			493.622i			1.14000i	−0.821643	+	0.570002i	$0.806942\pi$
$434$	−116.646	+	215.912i	−0.268770	+	0.497493i
$435$		0			0
$436$	−133.422	−	203.581i	−0.306014	−	0.466929i
$437$		−	51.6300i		−	0.118146i
$438$		0			0
$439$			658.970i			1.50107i	0.660831	+	0.750535i	$0.270204\pi$
$439$			658.970i			1.50107i	−0.660831	+	0.750535i	$0.729796\pi$
$440$		0			0
$441$		0			0
$442$	208.712	+	112.756i	0.472198	+	0.255104i
$443$	623.245			1.40687			0.703437	−	0.710758i	$-0.251648\pi$
$443$	623.245			1.40687			0.703437	+	0.710758i	$0.251648\pi$
$444$		0			0
$445$		0			0
$446$	−309.477	−	167.195i	−0.693896	−	0.374876i
$447$		0			0
$448$	251.683	−	43.1099i	0.561793	−	0.0962274i
$449$	−364.198			−0.811132			−0.405566	−	0.914066i	$-0.632925\pi$
$449$	−364.198			−0.811132			−0.405566	+	0.914066i	$0.632925\pi$
$450$		0			0
$451$			357.251i			0.792132i
$452$	−467.775	+	306.569i	−1.03490	+	0.678249i
$453$		0			0
$454$	134.770	+	72.8094i	0.296851	+	0.160373i
$455$		0			0
$456$		0			0
$457$		−	215.866i		−	0.472354i	−0.971710	−	0.236177i	$-0.924105\pi$
$457$		−	215.866i		−	0.472354i	0.971710	−	0.236177i	$-0.0758946\pi$
$458$	−136.611	−	73.8038i	−0.298277	−	0.161144i
$459$		0			0
$460$		0			0
$461$	27.9142			0.0605515			0.0302757	−	0.999542i	$-0.490361\pi$
$461$	27.9142			0.0605515			0.0302757	+	0.999542i	$0.490361\pi$
$462$		0			0
$463$	−369.545			−0.798154			−0.399077	−	0.916917i	$-0.630669\pi$
$463$	−369.545			−0.798154			−0.399077	+	0.916917i	$0.630669\pi$
$464$	−329.666	+	757.448i	−0.710487	+	1.63243i
$465$		0			0
$466$	−126.947	+	234.979i	−0.272419	+	0.504248i
$467$	741.443			1.58767			0.793837	−	0.608131i	$-0.208080\pi$
$467$	741.443			1.58767			0.793837	+	0.608131i	$0.208080\pi$
$468$		0			0
$469$	−378.392			−0.806807
$470$		0			0
$471$		0			0
$472$	401.464	−	34.1341i	0.850559	−	0.0723179i
$473$			528.158i			1.11661i
$474$		0			0
$475$		0			0
$476$	−162.045	+	106.200i	−0.340430	+	0.223110i
$477$		0			0
$478$	−14.1266	+	26.1484i	−0.0295536	+	0.0547037i
$479$		−	419.700i		−	0.876201i	−0.898926	−	0.438101i	$-0.855651\pi$
$479$		−	419.700i		−	0.876201i	0.898926	−	0.438101i	$-0.144349\pi$
$480$		0			0
$481$	190.919			0.396920
$482$	−221.048	−	119.421i	−0.458606	−	0.247761i
$483$		0			0
$484$	110.815	+	169.085i	0.228956	+	0.349350i
$485$		0			0
$486$		0			0
$487$	195.501			0.401440			0.200720	−	0.979649i	$-0.435672\pi$
$487$	195.501			0.401440			0.200720	+	0.979649i	$0.435672\pi$
$488$	47.7082	+	561.114i	0.0977626	+	1.14982i
$489$		0			0
$490$		0			0
$491$			676.741i			1.37829i	0.724623	+	0.689146i	$0.242014\pi$
$491$			676.741i			1.37829i	−0.724623	+	0.689146i	$0.757986\pi$
$492$		0			0
$493$		−	626.785i		−	1.27137i
$494$	−298.661	−	161.351i	−0.604577	−	0.326622i
$495$		0			0
$496$	−451.184	−	196.370i	−0.909645	−	0.395907i
$497$			528.158i			1.06269i
$498$		0			0
$499$		−	628.139i		−	1.25880i	−0.777083	−	0.629398i	$-0.783302\pi$
$499$		−	628.139i		−	1.25880i	0.777083	−	0.629398i	$-0.216698\pi$
$500$		0			0
$501$		0			0
$502$	−155.928	+	288.622i	−0.310613	+	0.574944i
$503$	514.645			1.02315			0.511575	−	0.859238i	$-0.329062\pi$
$503$	514.645			1.02315			0.511575	+	0.859238i	$0.329062\pi$
$504$		0			0
$505$		0			0
$506$	23.7158	−	43.8979i	0.0468691	−	0.0867547i
$507$		0			0
$508$	−139.968	−	213.569i	−0.275528	−	0.420412i
$509$	−802.364			−1.57635			−0.788177	−	0.615449i	$-0.788975\pi$
$509$	−802.364			−1.57635			−0.788177	+	0.615449i	$0.788975\pi$
$510$		0			0
$511$			310.022i			0.606697i
$512$	128.882	+	495.513i	0.251723	+	0.967799i
$513$		0			0
$514$	−178.813	+	330.983i	−0.347886	+	0.643937i
$515$		0			0
$516$		0			0
$517$			331.732i			0.641648i
$518$	−74.1152	+	137.187i	−0.143079	+	0.264840i
$519$		0			0
$520$		0			0
$521$	917.482			1.76100			0.880501	−	0.474045i	$-0.157207\pi$
$521$	917.482			1.76100			0.880501	+	0.474045i	$0.157207\pi$
$522$		0			0
$523$	−957.290			−1.83038			−0.915191	−	0.403020i	$-0.867960\pi$
$523$	−957.290			−1.83038			−0.915191	+	0.403020i	$0.867960\pi$
$524$	689.161	−	451.660i	1.31519	−	0.861946i
$525$		0			0
$526$	201.555	+	108.890i	0.383184	+	0.207015i
$527$	373.352			0.708449
$528$		0			0
$529$	−520.167			−0.983303
$530$		0			0
$531$		0			0
$532$	231.882	−	151.970i	0.435869	−	0.285658i
$533$			415.828i			0.780165i
$534$		0			0
$535$		0			0
$536$	−64.2771	−	755.987i	−0.119920	−	1.41042i
$537$		0			0
$538$	−390.411	−	210.919i	−0.725670	−	0.392042i
$539$			277.685i			0.515185i
$540$		0			0
$541$	−329.014			−0.608159			−0.304080	−	0.952647i	$-0.598349\pi$
$541$	−329.014			−0.608159			−0.304080	+	0.952647i	$0.598349\pi$
$542$	−370.903	+	686.541i	−0.684322	+	1.26668i
$543$		0			0
$544$	−239.703	−	305.708i	−0.440631	−	0.561963i
$545$		0			0
$546$		0			0
$547$	25.7716			0.0471145			0.0235572	−	0.999722i	$-0.492501\pi$
$547$	25.7716			0.0471145			0.0235572	+	0.999722i	$0.492501\pi$
$548$	−813.234	+	532.975i	−1.48400	+	0.972581i
$549$		0			0
$550$		0			0
$551$			896.913i			1.62779i
$552$		0			0
$553$		−	193.004i		−	0.349013i
$554$	−258.973	+	479.359i	−0.467460	+	0.865270i
$555$		0			0
$556$	−409.895	+	268.635i	−0.737220	+	0.483157i
$557$		−	632.405i		−	1.13538i	−0.823244	−	0.567688i	$-0.807838\pi$
$557$		−	632.405i		−	1.13538i	0.823244	−	0.567688i	$-0.192162\pi$
$558$		0			0
$559$			614.757i			1.09974i
$560$		0			0
$561$		0			0
$562$	833.605	+	450.354i	1.48328	+	0.801341i
$563$	156.675			0.278285			0.139143	−	0.990272i	$-0.455565\pi$
$563$	156.675			0.278285			0.139143	+	0.990272i	$0.455565\pi$
$564$		0			0
$565$		0			0
$566$	−290.028	−	156.687i	−0.512417	−	0.276832i
$567$		0			0
$568$	−1055.20	+	89.7176i	−1.85775	+	0.157953i
$569$	−522.581			−0.918421			−0.459210	−	0.888328i	$-0.651868\pi$
$569$	−522.581			−0.918421			−0.459210	+	0.888328i	$0.651868\pi$
$570$		0			0
$571$		−	855.387i		−	1.49805i	−0.662541	−	0.749026i	$-0.730522\pi$
$571$		−	855.387i		−	1.49805i	0.662541	−	0.749026i	$-0.269478\pi$
$572$	−179.819	−	274.374i	−0.314368	−	0.479676i
$573$		0			0
$574$	−298.799	−	161.426i	−0.520556	−	0.281229i
$575$		0			0
$576$		0			0
$577$		−	484.081i		−	0.838962i	−0.907764	−	0.419481i	$-0.862212\pi$
$577$		−	484.081i		−	0.838962i	0.907764	−	0.419481i	$-0.137788\pi$
$578$	−249.202	−	134.631i	−0.431145	−	0.232926i
$579$		0			0
$580$		0			0
$581$	559.565			0.963107
$582$		0			0
$583$	−178.034			−0.305375
$584$	−619.392	+	52.6632i	−1.06060	+	0.0901766i
$585$		0			0
$586$	−259.732	+	480.764i	−0.443228	+	0.820416i
$587$	−134.666			−0.229413			−0.114707	−	0.993399i	$-0.536593\pi$
$587$	−134.666			−0.229413			−0.114707	+	0.993399i	$0.536593\pi$
$588$		0			0
$589$	−534.258			−0.907060
$590$		0			0
$591$		0			0
$592$	−286.675	−	124.770i	−0.484249	−	0.210761i
$593$		−	960.465i		−	1.61967i	−0.586657	−	0.809836i	$-0.699556\pi$
$593$		−	960.465i		−	1.61967i	0.586657	−	0.809836i	$-0.300444\pi$
$594$		0			0
$595$		0			0
$596$	−266.178	−	406.145i	−0.446608	−	0.681452i
$597$		0			0
$598$	27.6043	−	51.0956i	0.0461611	−	0.0854442i
$599$		−	492.073i		−	0.821491i	−0.911750	−	0.410746i	$-0.865268\pi$
$599$		−	492.073i		−	0.821491i	0.911750	−	0.410746i	$-0.134732\pi$
$600$		0			0
$601$	152.187			0.253223			0.126611	−	0.991952i	$-0.459590\pi$
$601$	152.187			0.253223			0.126611	+	0.991952i	$0.459590\pi$
$602$	−441.742	−	238.650i	−0.733791	−	0.396429i
$603$		0			0
$604$	−379.302	+	248.586i	−0.627984	+	0.411566i
$605$		0			0
$606$		0			0
$607$	1032.50			1.70100			0.850498	−	0.525978i	$-0.176301\pi$
$607$	1032.50			1.70100			0.850498	+	0.525978i	$0.176301\pi$
$608$	343.010	+	437.461i	0.564160	+	0.719508i
$609$		0			0
$610$		0			0
$611$			386.124i			0.631955i
$612$		0			0
$613$		−	774.029i		−	1.26269i	−0.775502	−	0.631345i	$-0.782503\pi$
$613$		−	774.029i		−	1.26269i	0.775502	−	0.631345i	$-0.217497\pi$
$614$	233.863	+	126.344i	0.380885	+	0.205772i
$615$		0			0
$616$	266.962	−	22.6981i	0.433379	−	0.0368476i
$617$			594.857i			0.964112i	0.876141	+	0.482056i	$0.160110\pi$
$617$			594.857i			0.964112i	−0.876141	+	0.482056i	$0.839890\pi$
$618$		0			0
$619$			158.333i			0.255788i	0.991788	+	0.127894i	$0.0408217\pi$
$619$			158.333i			0.255788i	−0.991788	+	0.127894i	$0.959178\pi$
$620$		0			0
$621$		0			0
$622$	223.430	−	413.569i	0.359212	−	0.664902i
$623$	72.3729			0.116168
$624$		0			0
$625$		0			0
$626$	473.085	−	875.680i	0.755726	−	1.39885i
$627$		0			0
$628$	−394.548	+	258.578i	−0.628262	+	0.411748i
$629$	237.222			0.377142
$630$		0			0
$631$			832.689i			1.31963i	0.751426	+	0.659817i	$0.229366\pi$
$631$			832.689i			1.31963i	−0.751426	+	0.659817i	$0.770634\pi$
$632$	385.602	−	32.7854i	0.610130	−	0.0518757i
$633$		0			0
$634$	161.569	−	299.065i	0.254841	−	0.471711i
$635$		0			0
$636$		0			0
$637$			323.215i			0.507402i
$638$	−411.989	+	762.592i	−0.645751	+	1.19529i
$639$		0			0
$640$		0			0
$641$	−23.7158			−0.0369981			−0.0184990	−	0.999829i	$-0.505889\pi$
$641$	−23.7158			−0.0369981			−0.0184990	+	0.999829i	$0.505889\pi$
$642$		0			0
$643$	−637.188			−0.990961			−0.495480	−	0.868619i	$-0.665008\pi$
$643$	−637.188			−0.990961			−0.495480	+	0.868619i	$0.665008\pi$
$644$	25.9994	+	39.6709i	0.0403717	+	0.0616008i
$645$		0			0
$646$	−371.096	−	200.484i	−0.574451	−	0.310346i
$647$	462.353			0.714610			0.357305	−	0.933988i	$-0.383696\pi$
$647$	462.353			0.714610			0.357305	+	0.933988i	$0.383696\pi$
$648$		0			0
$649$	422.756			0.651396
$650$		0			0
$651$		0			0
$652$	347.911	+	530.857i	0.533606	+	0.814198i
$653$		−	661.697i		−	1.01332i	−0.862146	−	0.506659i	$-0.830880\pi$
$653$		−	661.697i		−	1.01332i	0.862146	−	0.506659i	$-0.169120\pi$
$654$		0			0
$655$		0			0
$656$	271.754	−	624.390i	0.414260	−	0.951813i
$657$		0			0
$658$	−277.455	−	149.895i	−0.421664	−	0.227803i
$659$		−	248.647i		−	0.377310i	−0.982043	−	0.188655i	$-0.939587\pi$
$659$		−	248.647i		−	0.377310i	0.982043	−	0.188655i	$-0.0604127\pi$
$660$		0			0
$661$	−1022.35			−1.54668			−0.773339	−	0.633993i	$-0.781415\pi$
$661$	−1022.35			−1.54668			−0.773339	+	0.633993i	$0.781415\pi$
$662$	−9.79977	+	18.1394i	−0.0148033	+	0.0274009i
$663$		0			0
$664$	95.0527	+	1117.95i	0.143152	+	1.68366i
$665$		0			0
$666$		0			0
$667$	−153.446			−0.230054
$668$	−571.686	−	872.301i	−0.855817	−	1.30584i
$669$		0			0
$670$		0			0
$671$			590.873i			0.880586i
$672$		0			0
$673$			683.215i			1.01518i	0.861599	+	0.507589i	$0.169463\pi$
$673$			683.215i			1.01518i	−0.861599	+	0.507589i	$0.830537\pi$
$674$	103.646	−	191.850i	0.153778	−	0.284644i
$675$		0			0
$676$	161.244	+	246.033i	0.238527	+	0.363954i
$677$		−	707.751i		−	1.04542i	−0.852510	−	0.522711i	$-0.824921\pi$
$677$		−	707.751i		−	1.04542i	0.852510	−	0.522711i	$-0.175079\pi$
$678$		0			0
$679$			59.8473i			0.0881404i
$680$		0			0
$681$		0			0
$682$	−454.248	−	245.407i	−0.666053	−	0.359834i
$683$	597.701			0.875112			0.437556	−	0.899191i	$-0.355844\pi$
$683$	597.701			0.875112			0.437556	+	0.899191i	$0.355844\pi$
$684$		0			0
$685$		0			0
$686$	−576.260	−	311.324i	−0.840030	−	0.453825i
$687$		0			0
$688$	401.760	−	923.093i	0.583953	−	1.34170i
$689$	−207.225			−0.300762
$690$		0			0
$691$			1280.71i			1.85342i	0.375777	+	0.926710i	$0.377376\pi$
$691$			1280.71i			1.85342i	−0.375777	+	0.926710i	$0.622624\pi$
$692$	−985.964	+	646.178i	−1.42480	+	0.933783i
$693$		0			0
$694$	305.866	+	165.244i	0.440729	+	0.238103i
$695$		0			0
$696$		0			0
$697$			516.679i			0.741290i
$698$	456.173	+	246.447i	0.653543	+	0.353075i
$699$		0			0
$700$		0			0
$701$	−312.568			−0.445889			−0.222944	−	0.974831i	$-0.571567\pi$
$701$	−312.568			−0.445889			−0.222944	+	0.974831i	$0.571567\pi$
$702$		0			0
$703$	−339.459			−0.482872
$704$	90.6969	+	529.505i	0.128831	+	0.752138i
$705$		0			0
$706$	−109.703	+	203.061i	−0.155387	+	0.287622i
$707$	473.237			0.669360
$708$		0			0
$709$	−265.120			−0.373935			−0.186967	−	0.982366i	$-0.559866\pi$
$709$	−265.120			−0.373935			−0.186967	+	0.982366i	$0.559866\pi$
$710$		0			0
$711$		0			0
$712$	12.2939	+	144.593i	0.0172667	+	0.203081i
$713$		−	91.4021i		−	0.128194i
$714$		0			0
$715$		0			0
$716$	−492.584	+	322.828i	−0.687967	+	0.450877i
$717$		0			0
$718$	317.353	−	587.421i	0.441996	−	0.818135i
$719$			430.705i			0.599033i	0.954091	+	0.299517i	$0.0968254\pi$
$719$			430.705i			0.599033i	−0.954091	+	0.299517i	$0.903175\pi$
$720$		0			0
$721$	661.273			0.917160
$722$	−104.197	−	56.2923i	−0.144317	−	0.0779671i
$723$		0			0
$724$	−157.362	−	240.110i	−0.217351	−	0.331644i
$725$		0			0
$726$		0			0
$727$	−679.243			−0.934310			−0.467155	−	0.884176i	$-0.654721\pi$
$727$	−679.243			−0.934310			−0.467155	+	0.884176i	$0.654721\pi$
$728$	310.734	−	26.4198i	0.426832	−	0.0362910i
$729$		0			0
$730$		0			0
$731$			763.855i			1.04494i
$732$		0			0
$733$		−	1045.41i		−	1.42620i	−0.701061	−	0.713101i	$-0.747290\pi$
$733$		−	1045.41i		−	1.42620i	0.701061	−	0.713101i	$-0.252710\pi$
$734$	924.066	+	499.225i	1.25895	+	0.680143i
$735$		0			0
$736$	−74.8418	+	58.6828i	−0.101687	+	0.0797321i
$737$		−	796.082i		−	1.08017i
$738$		0			0
$739$			846.147i			1.14499i	0.819908	+	0.572495i	$0.194024\pi$
$739$			846.147i			1.14499i	−0.819908	+	0.572495i	$0.805976\pi$
$740$		0			0
$741$		0			0
$742$	80.4453	−	148.904i	0.108417	−	0.200680i
$743$	322.828			0.434493			0.217246	−	0.976117i	$-0.430293\pi$
$743$	322.828			0.434493			0.217246	+	0.976117i	$0.430293\pi$
$744$		0			0
$745$		0			0
$746$	−396.429	+	733.790i	−0.531406	+	0.983633i
$747$		0			0
$748$	−223.430	−	340.919i	−0.298703	−	0.455774i
$749$	415.828			0.555178
$750$		0			0
$751$		−	716.488i		−	0.954045i	−0.878891	−	0.477023i	$-0.841716\pi$
$751$		−	716.488i		−	0.954045i	0.878891	−	0.477023i	$-0.158284\pi$
$752$	252.342	−	579.788i	0.335562	−	0.770994i
$753$		0			0
$754$	−479.541	+	887.630i	−0.635996	+	1.17723i
$755$		0			0
$756$		0			0
$757$			375.636i			0.496217i	0.968732	+	0.248108i	$0.0798089\pi$
$757$			375.636i			0.496217i	−0.968732	+	0.248108i	$0.920191\pi$
$758$	120.501	−	223.047i	0.158972	−	0.294257i
$759$		0			0
$760$		0			0
$761$	97.6836			0.128362			0.0641811	−	0.997938i	$-0.479556\pi$
$761$	97.6836			0.128362			0.0641811	+	0.997938i	$0.479556\pi$
$762$		0			0
$763$	242.787			0.318201
$764$	1116.85	−	731.955i	1.46184	−	0.958056i
$765$		0			0
$766$	227.703	+	123.016i	0.297263	+	0.160596i
$767$	492.073			0.641556
$768$		0			0
$769$	665.651			0.865605			0.432803	−	0.901489i	$-0.357525\pi$
$769$	665.651			0.865605			0.432803	+	0.901489i	$0.357525\pi$
$770$		0			0
$771$		0			0
$772$	−644.695	+	422.518i	−0.835097	+	0.547303i
$773$		−	167.735i		−	0.216992i	−0.994097	−	0.108496i	$-0.965396\pi$
$773$		−	167.735i		−	0.216992i	0.994097	−	0.108496i	$-0.0346035\pi$
$774$		0			0
$775$		0			0
$776$	−119.569	+	10.1662i	−0.154083	+	0.0131008i
$777$		0			0
$778$	−154.687	−	83.5692i	−0.198826	−	0.107415i
$779$		−	739.355i		−	0.949108i
$780$		0			0
$781$	−1111.17			−1.42275
$782$	34.2992	−	63.4879i	0.0438609	−	0.0811865i
$783$		0			0
$784$	211.230	−	485.326i	0.269426	−	0.619039i
$785$		0			0
$786$		0			0
$787$	185.097			0.235193			0.117597	−	0.993061i	$-0.462481\pi$
$787$	185.097			0.235193			0.117597	+	0.993061i	$0.462481\pi$
$788$	−122.315	+	80.1626i	−0.155223	+	0.101729i
$789$		0			0
$790$		0			0
$791$		−	557.860i		−	0.705259i
$792$		0			0
$793$			687.756i			0.867284i
$794$	227.934	−	421.907i	0.287071	−	0.531369i
$795$		0			0
$796$	771.953	−	505.920i	0.969790	−	0.635578i
$797$			529.145i			0.663921i	0.943293	+	0.331960i	$0.107710\pi$
$797$			529.145i			0.663921i	−0.943293	+	0.331960i	$0.892290\pi$
$798$		0			0
$799$			479.771i			0.600465i
$800$		0			0
$801$		0			0
$802$	−674.013	−	364.134i	−0.840415	−	0.454033i
$803$	−652.242			−0.812256
$804$		0			0
$805$		0			0
$806$	−528.729	−	285.645i	−0.655991	−	0.354398i
$807$		0			0
$808$	80.3883	+	945.478i	0.0994905	+	1.17015i
$809$	1306.81			1.61533			0.807667	−	0.589638i	$-0.200730\pi$
$809$	1306.81			1.61533			0.807667	+	0.589638i	$0.200730\pi$
$810$		0			0
$811$			582.743i			0.718549i	0.933232	+	0.359274i	$0.116976\pi$
$811$			582.743i			0.718549i	−0.933232	+	0.359274i	$0.883024\pi$
$812$	−451.660	−	689.161i	−0.556231	−	0.848720i
$813$		0			0
$814$	−288.622	−	155.928i	−0.354572	−	0.191557i
$815$		0			0
$816$		0			0
$817$		−	1093.06i		−	1.33789i
$818$	−1288.01	−	695.843i	−1.57458	−	0.850663i
$819$		0			0
$820$		0			0
$821$	224.659			0.273641			0.136821	−	0.990596i	$-0.456312\pi$
$821$	224.659			0.273641			0.136821	+	0.990596i	$0.456312\pi$
$822$		0			0
$823$	680.427			0.826764			0.413382	−	0.910558i	$-0.364347\pi$
$823$	680.427			0.826764			0.413382	+	0.910558i	$0.364347\pi$
$824$	112.330	+	1321.15i	0.136322	+	1.60334i
$825$		0			0
$826$	−191.024	+	353.586i	−0.231264	+	0.428070i
$827$	594.207			0.718509			0.359255	−	0.933240i	$-0.383031\pi$
$827$	594.207			0.718509			0.359255	+	0.933240i	$0.383031\pi$
$828$		0			0
$829$	−546.029			−0.658659			−0.329330	−	0.944215i	$-0.606823\pi$
$829$	−546.029			−0.658659			−0.329330	+	0.944215i	$0.606823\pi$
$830$		0			0
$831$		0			0
$832$	105.568	+	616.325i	0.126885	+	0.740776i
$833$			401.605i			0.482119i
$834$		0			0
$835$		0			0
$836$	319.723	+	487.846i	0.382444	+	0.583548i
$837$		0			0
$838$	−658.645	+	1219.15i	−0.785973	+	1.45484i
$839$		−	279.613i		−	0.333269i	−0.986019	−	0.166634i	$-0.946710\pi$
$839$		−	279.613i		−	0.333269i	0.986019	−	0.166634i	$-0.0532900\pi$
$840$		0			0
$841$	1824.65			2.16963
$842$	574.733	+	310.499i	0.682581	+	0.368763i
$843$		0			0
$844$	595.362	−	390.186i	0.705406	−	0.462306i
$845$		0			0
$846$		0			0
$847$	−201.648			−0.238073
$848$	311.160	+	135.427i	0.366934	+	0.159702i
$849$		0			0
$850$		0			0
$851$		−	58.0755i		−	0.0682438i
$852$		0			0
$853$		−	422.173i		−	0.494927i	−0.968897	−	0.247463i	$-0.920403\pi$
$853$		−	422.173i		−	0.494927i	0.968897	−	0.247463i	$-0.0795970\pi$
$854$	−494.196	−	266.989i	−0.578684	−	0.312633i
$855$		0			0
$856$	70.6363	+	830.780i	0.0825190	+	0.970537i
$857$		−	1609.18i		−	1.87768i	−0.344347	−	0.938842i	$-0.611900\pi$
$857$		−	1609.18i		−	1.87768i	0.344347	−	0.938842i	$-0.388100\pi$
$858$		0			0
$859$		−	1146.70i		−	1.33493i	−0.744643	−	0.667463i	$-0.767380\pi$
$859$		−	1146.70i		−	1.33493i	0.744643	−	0.667463i	$-0.232620\pi$
$860$		0			0
$861$		0			0
$862$	349.272	−	646.502i	0.405188	−	0.750003i
$863$	1318.54			1.52786			0.763929	−	0.645300i	$-0.223268\pi$
$863$	1318.54			1.52786			0.763929	+	0.645300i	$0.223268\pi$
$864$		0			0
$865$		0			0
$866$	469.255	−	868.591i	0.541865	−	1.00299i
$867$		0			0
$868$	410.508	−	269.037i	0.472935	−	0.309951i
$869$	406.053			0.467265
$870$		0			0
$871$		−	926.612i		−	1.06385i
$872$	41.2420	+	485.063i	0.0472959	+	0.556265i
$873$		0			0
$874$	−49.0813	+	90.8496i	−0.0561571	+	0.103947i
$875$		0			0
$876$		0			0
$877$			1194.61i			1.36216i	0.732210	+	0.681079i	$0.238489\pi$
$877$			1194.61i			1.36216i	−0.732210	+	0.681079i	$0.761511\pi$
$878$	626.440	−	1159.54i	0.713485	−	1.32066i
$879$		0			0
$880$		0			0
$881$	−1008.88			−1.14516			−0.572579	−	0.819850i	$-0.694057\pi$
$881$	−1008.88			−1.14516			−0.572579	+	0.819850i	$0.694057\pi$
$882$		0			0
$883$	210.869			0.238809			0.119405	−	0.992846i	$-0.461901\pi$
$883$	210.869			0.238809			0.119405	+	0.992846i	$0.461901\pi$
$884$	−260.065	−	396.817i	−0.294191	−	0.448888i
$885$		0			0
$886$	−1096.68	−	592.479i	−1.23779	−	0.668712i
$887$	−1682.25			−1.89657			−0.948283	−	0.317425i	$-0.897182\pi$
$887$	−1682.25			−1.89657			−0.948283	+	0.317425i	$0.897182\pi$
$888$		0			0
$889$	254.699			0.286500
$890$		0			0
$891$		0			0
$892$	385.624	+	588.401i	0.432314	+	0.659642i
$893$		−	686.541i		−	0.768803i
$894$		0			0
$895$		0			0
$896$	−483.851	−	163.402i	−0.540012	−	0.182368i
$897$		0			0
$898$	640.853	+	346.220i	0.713645	+	0.385545i
$899$			1587.83i			1.76622i
$900$		0			0
$901$	−257.484			−0.285775
$902$	339.616	−	628.629i	0.376514	−	0.696928i
$903$		0			0
$904$	1114.55	−	94.7631i	1.23290	−	0.104826i
$905$		0			0
$906$		0			0
$907$	−1198.24			−1.32111			−0.660554	−	0.750779i	$-0.729678\pi$
$907$	−1198.24			−1.32111			−0.660554	+	0.750779i	$0.729678\pi$
$908$	−167.930	−	256.235i	−0.184945	−	0.282197i
$909$		0			0
$910$		0			0
$911$		−	647.021i		−	0.710232i	−0.934822	−	0.355116i	$-0.884441\pi$
$911$		−	647.021i		−	0.710232i	0.934822	−	0.355116i	$-0.115559\pi$
$912$		0			0
$913$			1177.24i			1.28942i
$914$	−205.210	+	379.844i	−0.224519	+	0.415584i
$915$		0			0
$916$	170.224	+	259.735i	0.185834	+	0.283553i
$917$			821.881i			0.896272i
$918$		0			0
$919$		−	1316.77i		−	1.43283i	−0.697672	−	0.716417i	$-0.745781\pi$
$919$		−	1316.77i		−	1.43283i	0.697672	−	0.716417i	$-0.254219\pi$
$920$		0			0
$921$		0			0
$922$	−49.1187	−	26.5363i	−0.0532740	−	0.0287812i
$923$	−1293.36			−1.40126
$924$		0			0
$925$		0			0
$926$	650.262	+	351.303i	0.702227	+	0.379377i
$927$		0			0
$928$	1300.15	−	1019.44i	1.40102	−	1.09853i
$929$	29.9973			0.0322898			0.0161449	−	0.999870i	$-0.494861\pi$
$929$	29.9973			0.0322898			0.0161449	+	0.999870i	$0.494861\pi$
$930$		0			0
$931$		−	574.687i		−	0.617279i
$932$	446.760	−	292.796i	0.479356	−	0.314159i
$933$		0			0
$934$	−1304.66	−	704.843i	−1.39686	−	0.754650i
$935$		0			0
$936$		0			0
$937$		−	1023.87i		−	1.09271i	−0.837553	−	0.546356i	$-0.816015\pi$
$937$		−	1023.87i		−	1.09271i	0.837553	−	0.546356i	$-0.183985\pi$
$938$	665.830	+	359.713i	0.709840	+	0.383490i
$939$		0			0
$940$		0			0
$941$	746.535			0.793343			0.396671	−	0.917961i	$-0.370165\pi$
$941$	746.535			0.793343			0.396671	+	0.917961i	$0.370165\pi$
$942$		0			0
$943$	126.491			0.134136
$944$	−738.876	−	321.583i	−0.782708	−	0.340660i
$945$		0			0
$946$	502.086	−	929.361i	0.530746	−	0.982411i
$947$	−1070.22			−1.13011			−0.565056	−	0.825053i	$-0.691145\pi$
$947$	−1070.22			−1.13011			−0.565056	+	0.825053i	$0.691145\pi$
$948$		0			0
$949$	−759.187			−0.799986
$950$		0			0
$951$		0			0
$952$	386.096	−	32.8275i	0.405563	−	0.0344826i
$953$		−	121.117i		−	0.127091i	−0.997979	−	0.0635453i	$-0.979759\pi$
$953$		−	121.117i		−	0.127091i	0.997979	−	0.0635453i	$-0.0202407\pi$
$954$		0			0
$955$		0			0
$956$	49.7151	−	32.5821i	0.0520033	−	0.0340817i
$957$		0			0
$958$	−398.982	+	738.516i	−0.416474	+	0.770894i
$959$		−	969.849i		−	1.01131i
$960$		0			0
$961$	15.1868			0.0158031
$962$	−335.946	−	181.494i	−0.349216	−	0.188663i
$963$		0			0
$964$	275.437	+	420.272i	0.285723	+	0.435967i
$965$		0			0
$966$		0			0
$967$	1543.20			1.59587			0.797933	−	0.602747i	$-0.205927\pi$
$967$	1543.20			1.59587			0.797933	+	0.602747i	$0.205927\pi$
$968$	−34.2538	−	402.872i	−0.0353861	−	0.416190i
$969$		0			0
$970$		0			0
$971$		−	945.350i		−	0.973584i	−0.873518	−	0.486792i	$-0.838167\pi$
$971$		−	945.350i		−	0.973584i	0.873518	−	0.486792i	$-0.161833\pi$
$972$		0			0
$973$		−	488.833i		−	0.502398i
$974$	−344.010	−	185.851i	−0.353193	−	0.190812i
$975$		0			0
$976$	449.466	−	1032.70i	0.460519	−	1.05810i
$977$			419.744i			0.429626i	0.976655	+	0.214813i	$0.0689142\pi$
$977$			419.744i			0.429626i	−0.976655	+	0.214813i	$0.931086\pi$
$978$		0			0
$979$			152.262i			0.155528i
$980$		0			0
$981$		0			0
$982$	643.335	−	1190.81i	0.655127	−	1.21264i
$983$	−645.254			−0.656413			−0.328206	−	0.944606i	$-0.606444\pi$
$983$	−645.254			−0.656413			−0.328206	+	0.944606i	$0.606444\pi$
$984$		0			0
$985$		0			0
$986$	−595.844	+	1102.91i	−0.604304	+	1.11857i
$987$		0			0
$988$	372.146	+	567.836i	0.376666	+	0.574733i
$989$	187.003			0.189083
$990$		0			0
$991$		−	994.611i		−	1.00364i	−0.864971	−	0.501822i	$-0.832663\pi$
$991$		−	994.611i		−	1.00364i	0.864971	−	0.501822i	$-0.167337\pi$
$992$	607.240	+	774.450i	0.612137	+	0.780695i
$993$		0			0
$994$	502.086	−	929.361i	0.505116	−	0.934971i
$995$		0			0
$996$		0			0
$997$		−	1027.03i		−	1.03012i	−0.857153	−	0.515062i	$-0.827769\pi$
$997$		−	1027.03i		−	1.03012i	0.857153	−	0.515062i	$-0.172231\pi$
$998$	−597.132	+	1105.29i	−0.598328	+	1.10751i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.f.g.199.1		16
3.2	odd	2	inner	900.3.f.g.199.15		16
4.3	odd	2	inner	900.3.f.g.199.14		16
5.2	odd	4		900.3.c.q.451.5	yes	8
5.3	odd	4		900.3.c.p.451.4	yes	8
5.4	even	2	inner	900.3.f.g.199.16		16
12.11	even	2	inner	900.3.f.g.199.4		16
15.2	even	4		900.3.c.q.451.4	yes	8
15.8	even	4		900.3.c.p.451.5	yes	8
15.14	odd	2	inner	900.3.f.g.199.2		16
20.3	even	4		900.3.c.p.451.3	✓	8
20.7	even	4		900.3.c.q.451.6	yes	8
20.19	odd	2	inner	900.3.f.g.199.3		16
60.23	odd	4		900.3.c.p.451.6	yes	8
60.47	odd	4		900.3.c.q.451.3	yes	8
60.59	even	2	inner	900.3.f.g.199.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.c.p.451.3	✓	8	20.3	even	4
900.3.c.p.451.4	yes	8	5.3	odd	4
900.3.c.p.451.5	yes	8	15.8	even	4
900.3.c.p.451.6	yes	8	60.23	odd	4
900.3.c.q.451.3	yes	8	60.47	odd	4
900.3.c.q.451.4	yes	8	15.2	even	4
900.3.c.q.451.5	yes	8	5.2	odd	4
900.3.c.q.451.6	yes	8	20.7	even	4
900.3.f.g.199.1		16	1.1	even	1	trivial
900.3.f.g.199.2		16	15.14	odd	2	inner
900.3.f.g.199.3		16	20.19	odd	2	inner
900.3.f.g.199.4		16	12.11	even	2	inner
900.3.f.g.199.13		16	60.59	even	2	inner
900.3.f.g.199.14		16	4.3	odd	2	inner
900.3.f.g.199.15		16	3.2	odd	2	inner
900.3.f.g.199.16		16	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.75963 - 0.950636i) q^{2} +(2.19258 + 3.34553i) q^{4} -3.98982 q^{7} +(-0.677747 - 7.97124i) q^{8} +O(q^{10})\)	\(q+(-1.75963 - 0.950636i) q^{2} +(2.19258 + 3.34553i) q^{4} -3.98982 q^{7} +(-0.677747 - 7.97124i) q^{8} -8.39401i q^{11} -9.77033i q^{13} +(7.02060 + 3.79287i) q^{14} +(-6.38516 + 14.6707i) q^{16} -12.1399i q^{17} +17.3719i q^{19} +(-7.97964 + 14.7703i) q^{22} -2.97203 q^{23} +(-9.28803 + 17.1921i) q^{26} +(-8.74801 - 13.3481i) q^{28} +51.6300 q^{29} +30.7541i q^{31} +(25.1820 - 19.7450i) q^{32} +(-11.5407 + 21.3618i) q^{34} +19.5407i q^{37} +(16.5144 - 30.5682i) q^{38} -42.5603 q^{41} -62.9208 q^{43} +(28.0824 - 18.4046i) q^{44} +(5.22967 + 2.82532i) q^{46} -39.5201 q^{47} -33.0813 q^{49} +(32.6869 - 21.4223i) q^{52} -21.2096i q^{53} +(2.70409 + 31.8038i) q^{56} +(-90.8496 - 49.0813i) q^{58} +50.3640i q^{59} -70.3923 q^{61} +(29.2359 - 54.1157i) q^{62} +(-63.0813 + 10.8050i) q^{64} +94.8394 q^{67} +(40.6145 - 26.6178i) q^{68} -132.376i q^{71} -77.7033i q^{73} +(18.5761 - 34.3843i) q^{74} +(-58.1184 + 38.0894i) q^{76} +33.4906i q^{77} +48.3742i q^{79} +(74.8903 + 40.4593i) q^{82} -140.248 q^{83} +(110.717 + 59.8148i) q^{86} +(-66.9106 + 5.68901i) q^{88} -18.1394 q^{89} +38.9819i q^{91} +(-6.51642 - 9.94303i) q^{92} +(69.5407 + 37.5692i) q^{94} -15.0000i q^{97} +(58.2108 + 31.4483i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4}+O(q^{10}) \) 16 * q - 8 * q^4	\( 16 q - 8 q^{4} - 16 q^{16} + 160 q^{34} + 256 q^{46} + 160 q^{49} + 80 q^{61} - 320 q^{64} - 456 q^{76} + 768 q^{94}+O(q^{100}) \) 16 * q - 8 * q^4 - 16 * q^16 + 160 * q^34 + 256 * q^46 + 160 * q^49 + 80 * q^61 - 320 * q^64 - 456 * q^76 + 768 * q^94

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