LMFDB - Embedded newform 2100.3.be.b.649.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,3,Mod(649,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))

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

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

chi := DirichletCharacter("2100.649");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	2100.be (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$57.2208555157$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			649.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2100.649
Dual form			2100.3.be.b.1249.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 1.50000i) q^{3} +(-2.59808 - 6.50000i) q^{7} +(-1.50000 + 2.59808i) q^{9} +(-6.00000 - 10.3923i) q^{11} -1.73205 q^{13} +(13.5000 + 7.79423i) q^{19} +(7.50000 - 9.52628i) q^{21} +(20.7846 + 12.0000i) q^{23} -5.19615 q^{27} +6.00000 q^{29} +(-18.0000 + 10.3923i) q^{31} +(10.3923 - 18.0000i) q^{33} +(6.06218 + 3.50000i) q^{37} +(-1.50000 - 2.59808i) q^{39} -41.5692i q^{41} -50.0000i q^{43} +(-15.5885 + 27.0000i) q^{47} +(-35.5000 + 33.7750i) q^{49} +(-72.7461 + 42.0000i) q^{53} +27.0000i q^{57} +(-27.0000 + 15.5885i) q^{59} +(-52.5000 - 30.3109i) q^{61} +(20.7846 + 3.00000i) q^{63} +(-97.8609 + 56.5000i) q^{67} +41.5692i q^{69} -30.0000 q^{71} +(-6.06218 - 10.5000i) q^{73} +(-51.9615 + 66.0000i) q^{77} +(47.5000 - 82.2724i) q^{79} +(-4.50000 - 7.79423i) q^{81} -10.3923 q^{83} +(5.19615 + 9.00000i) q^{87} +(-153.000 - 88.3346i) q^{89} +(4.50000 + 11.2583i) q^{91} +(-31.1769 - 18.0000i) q^{93} -112.583 q^{97} +36.0000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{9} - 24 q^{11} + 54 q^{19} + 30 q^{21} + 24 q^{29} - 72 q^{31} - 6 q^{39} - 142 q^{49} - 108 q^{59} - 210 q^{61} - 120 q^{71} + 190 q^{79} - 18 q^{81} - 612 q^{89} + 18 q^{91} + 144 q^{99}+O(q^{100}) $ 4 * q - 6 * q^9 - 24 * q^11 + 54 * q^19 + 30 * q^21 + 24 * q^29 - 72 * q^31 - 6 * q^39 - 142 * q^49 - 108 * q^59 - 210 * q^61 - 120 * q^71 + 190 * q^79 - 18 * q^81 - 612 * q^89 + 18 * q^91 + 144 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.59808	−	6.50000i	−0.371154	−	0.928571i
$7$	−2.59808	−	6.50000i	−0.371154	−	0.928571i
$8$		0			0
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$		0			0
$11$	−6.00000	−	10.3923i	−0.545455	−	0.944755i	−0.998578	−	0.0533073i	$-0.983024\pi$
$11$	−6.00000	−	10.3923i	−0.545455	−	0.944755i	0.453124	−	0.891448i	$-0.350310\pi$
$12$		0			0
$13$	−1.73205			−0.133235			−0.0666173	−	0.997779i	$-0.521221\pi$
$13$	−1.73205			−0.133235			−0.0666173	+	0.997779i	$0.521221\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	13.5000	+	7.79423i	0.710526	+	0.410223i	0.811256	−	0.584691i	$-0.198784\pi$
$19$	13.5000	+	7.79423i	0.710526	+	0.410223i	−0.100730	+	0.994914i	$0.532118\pi$
$20$		0			0
$21$	7.50000	−	9.52628i	0.357143	−	0.453632i
$22$		0			0
$23$	20.7846	+	12.0000i	0.903679	+	0.521739i	0.878392	−	0.477941i	$-0.158617\pi$
$23$	20.7846	+	12.0000i	0.903679	+	0.521739i	0.0252868	+	0.999680i	$0.491950\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.19615			−0.192450
$28$		0			0
$29$	6.00000			0.206897			0.103448	−	0.994635i	$-0.467012\pi$
$29$	6.00000			0.206897			0.103448	+	0.994635i	$0.467012\pi$
$30$		0			0
$31$	−18.0000	+	10.3923i	−0.580645	+	0.335236i	−0.761390	−	0.648294i	$-0.775483\pi$
$31$	−18.0000	+	10.3923i	−0.580645	+	0.335236i	0.180745	+	0.983530i	$0.442149\pi$
$32$		0			0
$33$	10.3923	−	18.0000i	0.314918	−	0.545455i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.06218	+	3.50000i	0.163843	+	0.0945946i	0.579679	−	0.814845i	$-0.303178\pi$
$37$	6.06218	+	3.50000i	0.163843	+	0.0945946i	−0.415837	+	0.909439i	$0.636511\pi$
$38$		0			0
$39$	−1.50000	−	2.59808i	−0.0384615	−	0.0666173i
$40$		0			0
$41$		−	41.5692i		−	1.01388i	−0.861980	−	0.506942i	$-0.830776\pi$
$41$		−	41.5692i		−	1.01388i	0.861980	−	0.506942i	$-0.169224\pi$
$42$		0			0
$43$		−	50.0000i		−	1.16279i	−0.813621	−	0.581395i	$-0.802507\pi$
$43$		−	50.0000i		−	1.16279i	0.813621	−	0.581395i	$-0.197493\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−15.5885	+	27.0000i	−0.331669	+	0.574468i	−0.982839	−	0.184464i	$-0.940945\pi$
$47$	−15.5885	+	27.0000i	−0.331669	+	0.574468i	0.651170	+	0.758932i	$0.274278\pi$
$48$		0			0
$49$	−35.5000	+	33.7750i	−0.724490	+	0.689286i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−72.7461	+	42.0000i	−1.37257	+	0.792453i	−0.991251	−	0.131991i	$-0.957863\pi$
$53$	−72.7461	+	42.0000i	−1.37257	+	0.792453i	−0.381318	+	0.924444i	$0.624530\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			27.0000i			0.473684i
$58$		0			0
$59$	−27.0000	+	15.5885i	−0.457627	+	0.264211i	−0.711046	−	0.703146i	$-0.751778\pi$
$59$	−27.0000	+	15.5885i	−0.457627	+	0.264211i	0.253419	+	0.967357i	$0.418445\pi$
$60$		0			0
$61$	−52.5000	−	30.3109i	−0.860656	−	0.496900i	0.00357609	−	0.999994i	$-0.498862\pi$
$61$	−52.5000	−	30.3109i	−0.860656	−	0.496900i	−0.864232	+	0.503094i	$0.832195\pi$
$62$		0			0
$63$	20.7846	+	3.00000i	0.329914	+	0.0476190i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−97.8609	+	56.5000i	−1.46061	+	0.843284i	−0.999039	−	0.0438199i	$-0.986047\pi$
$67$	−97.8609	+	56.5000i	−1.46061	+	0.843284i	−0.461571	+	0.887103i	$0.652714\pi$
$68$		0			0
$69$			41.5692i			0.602452i
$70$		0			0
$71$	−30.0000			−0.422535			−0.211268	−	0.977428i	$-0.567759\pi$
$71$	−30.0000			−0.422535			−0.211268	+	0.977428i	$0.567759\pi$
$72$		0			0
$73$	−6.06218	−	10.5000i	−0.0830435	−	0.143836i	0.821512	−	0.570191i	$-0.193131\pi$
$73$	−6.06218	−	10.5000i	−0.0830435	−	0.143836i	−0.904556	+	0.426355i	$0.859797\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−51.9615	+	66.0000i	−0.674825	+	0.857143i
$78$		0			0
$79$	47.5000	−	82.2724i	0.601266	−	1.04142i	−0.391364	−	0.920236i	$-0.627997\pi$
$79$	47.5000	−	82.2724i	0.601266	−	1.04142i	0.992630	−	0.121187i	$-0.0386701\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−10.3923			−0.125208			−0.0626042	−	0.998038i	$-0.519941\pi$
$83$	−10.3923			−0.125208			−0.0626042	+	0.998038i	$0.519941\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	5.19615	+	9.00000i	0.0597259	+	0.103448i
$88$		0			0
$89$	−153.000	−	88.3346i	−1.71910	−	0.992523i	−0.920577	−	0.390560i	$-0.872281\pi$
$89$	−153.000	−	88.3346i	−1.71910	−	0.992523i	−0.798524	−	0.601963i	$-0.794385\pi$
$90$		0			0
$91$	4.50000	+	11.2583i	0.0494505	+	0.123718i
$92$		0			0
$93$	−31.1769	−	18.0000i	−0.335236	−	0.193548i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−112.583			−1.16065			−0.580326	−	0.814384i	$-0.697075\pi$
$97$	−112.583			−1.16065			−0.580326	+	0.814384i	$0.697075\pi$
$98$		0			0
$99$	36.0000			0.363636
$100$		0			0
$101$	18.0000	−	10.3923i	0.178218	−	0.102894i	−0.408237	−	0.912876i	$-0.633856\pi$
$101$	18.0000	−	10.3923i	0.178218	−	0.102894i	0.586455	+	0.809982i	$0.300523\pi$
$102$		0			0
$103$	2.59808	−	4.50000i	0.0252240	−	0.0436893i	−0.853138	−	0.521686i	$-0.825303\pi$
$103$	2.59808	−	4.50000i	0.0252240	−	0.0436893i	0.878362	+	0.477996i	$0.158637\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.3923	+	6.00000i	0.0971243	+	0.0560748i	0.547775	−	0.836625i	$-0.315475\pi$
$107$	10.3923	+	6.00000i	0.0971243	+	0.0560748i	−0.450651	+	0.892700i	$0.648808\pi$
$108$		0			0
$109$	−8.50000	−	14.7224i	−0.0779817	−	0.135068i	0.824397	−	0.566011i	$-0.191514\pi$
$109$	−8.50000	−	14.7224i	−0.0779817	−	0.135068i	−0.902379	+	0.430943i	$0.858181\pi$
$110$		0			0
$111$			12.1244i			0.109228i
$112$		0			0
$113$			54.0000i			0.477876i	0.971035	+	0.238938i	$0.0767993\pi$
$113$			54.0000i			0.477876i	−0.971035	+	0.238938i	$0.923201\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.59808	−	4.50000i	0.0222058	−	0.0384615i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−11.5000	+	19.9186i	−0.0950413	+	0.164616i
$122$		0			0
$123$	62.3538	−	36.0000i	0.506942	−	0.292683i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			109.000i			0.858268i	0.903241	+	0.429134i	$0.141181\pi$
$127$			109.000i			0.858268i	−0.903241	+	0.429134i	$0.858819\pi$
$128$		0			0
$129$	75.0000	−	43.3013i	0.581395	−	0.335669i
$130$		0			0
$131$	18.0000	+	10.3923i	0.137405	+	0.0793306i	0.567126	−	0.823631i	$-0.308055\pi$
$131$	18.0000	+	10.3923i	0.137405	+	0.0793306i	−0.429722	+	0.902961i	$0.641388\pi$
$132$		0			0
$133$	15.5885	−	108.000i	0.117206	−	0.812030i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−135.100	+	78.0000i	−0.986131	+	0.569343i	−0.904116	−	0.427288i	$-0.859469\pi$
$137$	−135.100	+	78.0000i	−0.986131	+	0.569343i	−0.0820155	+	0.996631i	$0.526136\pi$
$138$		0			0
$139$		−	15.5885i		−	0.112147i	−0.998427	−	0.0560736i	$-0.982142\pi$
$139$		−	15.5885i		−	0.112147i	0.998427	−	0.0560736i	$-0.0178581\pi$
$140$		0			0
$141$	−54.0000			−0.382979
$142$		0			0
$143$	10.3923	+	18.0000i	0.0726735	+	0.125874i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−81.4064	−	24.0000i	−0.553785	−	0.163265i
$148$		0			0
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$		0			0
$151$	−48.5000	−	84.0045i	−0.321192	−	0.556321i	0.659542	−	0.751668i	$-0.270750\pi$
$151$	−48.5000	−	84.0045i	−0.321192	−	0.556321i	−0.980734	+	0.195347i	$0.937417\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	26.8468	+	46.5000i	0.170999	+	0.296178i	0.938769	−	0.344546i	$-0.111967\pi$
$157$	26.8468	+	46.5000i	0.170999	+	0.296178i	−0.767771	+	0.640725i	$0.778634\pi$
$158$		0			0
$159$	−126.000	−	72.7461i	−0.792453	−	0.457523i
$160$		0			0
$161$	24.0000	−	166.277i	0.149068	−	1.03278i
$162$		0			0
$163$	193.124	+	111.500i	1.18481	+	0.684049i	0.957122	−	0.289686i	$-0.0935507\pi$
$163$	193.124	+	111.500i	1.18481	+	0.684049i	0.227686	+	0.973735i	$0.426884\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−166.277			−0.995670			−0.497835	−	0.867272i	$-0.665871\pi$
$167$	−166.277			−0.995670			−0.497835	+	0.867272i	$0.665871\pi$
$168$		0			0
$169$	−166.000			−0.982249
$170$		0			0
$171$	−40.5000	+	23.3827i	−0.236842	+	0.136741i
$172$		0			0
$173$	67.5500	−	117.000i	0.390462	−	0.676301i	−0.602048	−	0.798460i	$-0.705649\pi$
$173$	67.5500	−	117.000i	0.390462	−	0.676301i	0.992511	+	0.122159i	$0.0389818\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−46.7654	−	27.0000i	−0.264211	−	0.152542i
$178$		0			0
$179$	−81.0000	−	140.296i	−0.452514	−	0.783777i	0.546028	−	0.837767i	$-0.316139\pi$
$179$	−81.0000	−	140.296i	−0.452514	−	0.783777i	−0.998541	+	0.0539901i	$0.982806\pi$
$180$		0			0
$181$		−	277.128i		−	1.53109i	−0.643380	−	0.765547i	$-0.722468\pi$
$181$		−	277.128i		−	1.53109i	0.643380	−	0.765547i	$-0.277532\pi$
$182$		0			0
$183$		−	105.000i		−	0.573770i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	13.5000	+	33.7750i	0.0714286	+	0.178704i
$190$		0			0
$191$	−78.0000	+	135.100i	−0.408377	+	0.707330i	−0.994708	−	0.102742i	$-0.967238\pi$
$191$	−78.0000	+	135.100i	−0.408377	+	0.707330i	0.586331	+	0.810072i	$0.300572\pi$
$192$		0			0
$193$	112.583	−	65.0000i	0.583333	−	0.336788i	−0.179124	−	0.983827i	$-0.557326\pi$
$193$	112.583	−	65.0000i	0.583333	−	0.336788i	0.762457	+	0.647039i	$0.223993\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			150.000i			0.761421i	0.924694	+	0.380711i	$0.124321\pi$
$197$			150.000i			0.761421i	−0.924694	+	0.380711i	$0.875679\pi$
$198$		0			0
$199$	4.50000	−	2.59808i	0.0226131	−	0.0130557i	−0.488651	−	0.872479i	$-0.662511\pi$
$199$	4.50000	−	2.59808i	0.0226131	−	0.0130557i	0.511264	+	0.859424i	$0.329177\pi$
$200$		0			0
$201$	−169.500	−	97.8609i	−0.843284	−	0.486870i
$202$		0			0
$203$	−15.5885	−	39.0000i	−0.0767904	−	0.192118i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−62.3538	+	36.0000i	−0.301226	+	0.173913i
$208$		0			0
$209$		−	187.061i		−	0.895031i
$210$		0			0
$211$	−305.000			−1.44550			−0.722749	−	0.691111i	$-0.757122\pi$
$211$	−305.000			−1.44550			−0.722749	+	0.691111i	$0.757122\pi$
$212$		0			0
$213$	−25.9808	−	45.0000i	−0.121975	−	0.211268i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	114.315	+	90.0000i	0.526799	+	0.414747i
$218$		0			0
$219$	10.5000	−	18.1865i	0.0479452	−	0.0830435i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	22.5167			0.100972			0.0504858	−	0.998725i	$-0.483923\pi$
$223$	22.5167			0.100972			0.0504858	+	0.998725i	$0.483923\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	192.258	+	333.000i	0.846950	+	1.46696i	0.883917	+	0.467644i	$0.154897\pi$
$227$	192.258	+	333.000i	0.846950	+	1.46696i	−0.0369670	+	0.999316i	$0.511770\pi$
$228$		0			0
$229$	−205.500	−	118.645i	−0.897380	−	0.518103i	−0.0210307	−	0.999779i	$-0.506695\pi$
$229$	−205.500	−	118.645i	−0.897380	−	0.518103i	−0.876349	+	0.481676i	$0.840028\pi$
$230$		0			0
$231$	−144.000	−	20.7846i	−0.623377	−	0.0899767i
$232$		0			0
$233$	259.808	+	150.000i	1.11505	+	0.643777i	0.940134	−	0.340806i	$-0.110700\pi$
$233$	259.808	+	150.000i	1.11505	+	0.643777i	0.174920	+	0.984583i	$0.444033\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	164.545			0.694282
$238$		0			0
$239$	−240.000			−1.00418			−0.502092	−	0.864814i	$-0.667436\pi$
$239$	−240.000			−1.00418			−0.502092	+	0.864814i	$0.667436\pi$
$240$		0			0
$241$	184.500	−	106.521i	0.765560	−	0.441996i	−0.0657283	−	0.997838i	$-0.520937\pi$
$241$	184.500	−	106.521i	0.765560	−	0.441996i	0.831289	+	0.555841i	$0.187604\pi$
$242$		0			0
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−23.3827	−	13.5000i	−0.0946667	−	0.0546559i
$248$		0			0
$249$	−9.00000	−	15.5885i	−0.0361446	−	0.0626042i
$250$		0			0
$251$			114.315i			0.455440i	0.973727	+	0.227720i	$0.0731270\pi$
$251$			114.315i			0.455440i	−0.973727	+	0.227720i	$0.926873\pi$
$252$		0			0
$253$		−	288.000i		−	1.13834i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−192.258	+	333.000i	−0.748084	+	1.29572i	0.200656	+	0.979662i	$0.435693\pi$
$257$	−192.258	+	333.000i	−0.748084	+	1.29572i	−0.948740	+	0.316058i	$0.897641\pi$
$258$		0			0
$259$	7.00000	−	48.4974i	0.0270270	−	0.187249i
$260$		0			0
$261$	−9.00000	+	15.5885i	−0.0344828	+	0.0597259i
$262$		0			0
$263$	166.277	−	96.0000i	0.632231	−	0.365019i	−0.149384	−	0.988779i	$-0.547729\pi$
$263$	166.277	−	96.0000i	0.632231	−	0.365019i	0.781616	+	0.623760i	$0.214396\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	306.000i		−	1.14607i
$268$		0			0
$269$	63.0000	−	36.3731i	0.234201	−	0.135216i	−0.378308	−	0.925680i	$-0.623494\pi$
$269$	63.0000	−	36.3731i	0.234201	−	0.135216i	0.612508	+	0.790464i	$0.290161\pi$
$270$		0			0
$271$	−210.000	−	121.244i	−0.774908	−	0.447393i	0.0597148	−	0.998215i	$-0.480981\pi$
$271$	−210.000	−	121.244i	−0.774908	−	0.447393i	−0.834623	+	0.550822i	$0.814314\pi$
$272$		0			0
$273$	−12.9904	+	16.5000i	−0.0475838	+	0.0604396i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	99.5929	−	57.5000i	0.359541	−	0.207581i	−0.309338	−	0.950952i	$-0.600108\pi$
$277$	99.5929	−	57.5000i	0.359541	−	0.207581i	0.668880	+	0.743371i	$0.266774\pi$
$278$		0			0
$279$		−	62.3538i		−	0.223490i
$280$		0			0
$281$	528.000			1.87900			0.939502	−	0.342544i	$-0.111289\pi$
$281$	528.000			1.87900			0.939502	+	0.342544i	$0.111289\pi$
$282$		0			0
$283$	−99.5929	−	172.500i	−0.351918	−	0.609541i	0.634667	−	0.772786i	$-0.281137\pi$
$283$	−99.5929	−	172.500i	−0.351918	−	0.609541i	−0.986586	+	0.163245i	$0.947804\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−270.200	+	108.000i	−0.941463	+	0.376307i
$288$		0			0
$289$	144.500	−	250.281i	0.500000	−	0.866025i
$290$		0			0
$291$	−97.5000	−	168.875i	−0.335052	−	0.580326i
$292$		0			0
$293$	−197.454			−0.673904			−0.336952	−	0.941522i	$-0.609396\pi$
$293$	−197.454			−0.673904			−0.336952	+	0.941522i	$0.609396\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	31.1769	+	54.0000i	0.104973	+	0.181818i
$298$		0			0
$299$	−36.0000	−	20.7846i	−0.120401	−	0.0695137i
$300$		0			0
$301$	−325.000	+	129.904i	−1.07973	+	0.431574i
$302$		0			0
$303$	31.1769	+	18.0000i	0.102894	+	0.0594059i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−478.046			−1.55715			−0.778577	−	0.627550i	$-0.784058\pi$
$307$	−478.046			−1.55715			−0.778577	+	0.627550i	$0.784058\pi$
$308$		0			0
$309$	9.00000			0.0291262
$310$		0			0
$311$	207.000	−	119.512i	0.665595	−	0.384281i	−0.128811	−	0.991669i	$-0.541116\pi$
$311$	207.000	−	119.512i	0.665595	−	0.384281i	0.794405	+	0.607388i	$0.207783\pi$
$312$		0			0
$313$	−159.349	+	276.000i	−0.509101	+	0.881789i	0.490843	+	0.871248i	$0.336689\pi$
$313$	−159.349	+	276.000i	−0.509101	+	0.881789i	−0.999944	+	0.0105412i	$0.996645\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−57.1577	−	33.0000i	−0.180308	−	0.104101i	0.407129	−	0.913371i	$-0.366530\pi$
$317$	−57.1577	−	33.0000i	−0.180308	−	0.104101i	−0.587437	+	0.809270i	$0.699863\pi$
$318$		0			0
$319$	−36.0000	−	62.3538i	−0.112853	−	0.195467i
$320$		0			0
$321$			20.7846i			0.0647496i
$322$		0			0
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$	14.7224	−	25.5000i	0.0450227	−	0.0779817i
$328$		0			0
$329$	216.000	+	31.1769i	0.656535	+	0.0947627i
$330$		0			0
$331$	−111.500	+	193.124i	−0.336858	+	0.583455i	−0.983840	−	0.179050i	$-0.942698\pi$
$331$	−111.500	+	193.124i	−0.336858	+	0.583455i	0.646982	+	0.762505i	$0.276031\pi$
$332$		0			0
$333$	−18.1865	+	10.5000i	−0.0546142	+	0.0315315i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			158.000i			0.468843i	0.972135	+	0.234421i	$0.0753195\pi$
$337$			158.000i			0.468843i	−0.972135	+	0.234421i	$0.924680\pi$
$338$		0			0
$339$	−81.0000	+	46.7654i	−0.238938	+	0.137951i
$340$		0			0
$341$	216.000	+	124.708i	0.633431	+	0.365712i
$342$		0			0
$343$	311.769	+	143.000i	0.908948	+	0.416910i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−51.9615	+	30.0000i	−0.149745	+	0.0864553i	−0.573000	−	0.819555i	$-0.694221\pi$
$347$	−51.9615	+	30.0000i	−0.149745	+	0.0864553i	0.423255	+	0.906010i	$0.360887\pi$
$348$		0			0
$349$			34.6410i			0.0992579i	0.998768	+	0.0496290i	$0.0158039\pi$
$349$			34.6410i			0.0992579i	−0.998768	+	0.0496290i	$0.984196\pi$
$350$		0			0
$351$	9.00000			0.0256410
$352$		0			0
$353$	−10.3923	−	18.0000i	−0.0294400	−	0.0509915i	0.850930	−	0.525279i	$-0.176039\pi$
$353$	−10.3923	−	18.0000i	−0.0294400	−	0.0509915i	−0.880370	+	0.474288i	$0.842706\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−135.000	+	233.827i	−0.376045	+	0.651328i	−0.990483	−	0.137637i	$-0.956049\pi$
$359$	−135.000	+	233.827i	−0.376045	+	0.651328i	0.614438	+	0.788965i	$0.289383\pi$
$360$		0			0
$361$	−59.0000	−	102.191i	−0.163435	−	0.283078i
$362$		0			0
$363$	−39.8372			−0.109744
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−266.736	−	462.000i	−0.726801	−	1.25886i	−0.958229	−	0.286004i	$-0.907673\pi$
$367$	−266.736	−	462.000i	−0.726801	−	1.25886i	0.231428	−	0.972852i	$-0.425660\pi$
$368$		0			0
$369$	108.000	+	62.3538i	0.292683	+	0.168981i
$370$		0			0
$371$	462.000	+	363.731i	1.24528	+	0.980406i
$372$		0			0
$373$	−264.138	−	152.500i	−0.708144	−	0.408847i	0.102229	−	0.994761i	$-0.467402\pi$
$373$	−264.138	−	152.500i	−0.708144	−	0.408847i	−0.810373	+	0.585914i	$0.800736\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.3923			−0.0275658
$378$		0			0
$379$	−271.000			−0.715040			−0.357520	−	0.933906i	$-0.616378\pi$
$379$	−271.000			−0.715040			−0.357520	+	0.933906i	$0.616378\pi$
$380$		0			0
$381$	−163.500	+	94.3968i	−0.429134	+	0.247761i
$382$		0			0
$383$	−254.611	+	441.000i	−0.664782	+	1.15144i	0.314562	+	0.949237i	$0.398142\pi$
$383$	−254.611	+	441.000i	−0.664782	+	1.15144i	−0.979344	+	0.202199i	$0.935191\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	129.904	+	75.0000i	0.335669	+	0.193798i
$388$		0			0
$389$	−339.000	−	587.165i	−0.871465	−	1.50942i	−0.860481	−	0.509482i	$-0.829837\pi$
$389$	−339.000	−	587.165i	−0.871465	−	1.50942i	−0.0109843	−	0.999940i	$-0.503496\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$			36.0000i			0.0916031i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	239.023	−	414.000i	0.602073	−	1.04282i	−0.390434	−	0.920631i	$-0.627675\pi$
$397$	239.023	−	414.000i	0.602073	−	1.04282i	0.992507	−	0.122190i	$-0.0389918\pi$
$398$		0			0
$399$	175.500	−	70.1481i	0.439850	−	0.175810i
$400$		0			0
$401$	117.000	−	202.650i	0.291771	−	0.505361i	−0.682458	−	0.730925i	$-0.739089\pi$
$401$	117.000	−	202.650i	0.291771	−	0.505361i	0.974228	+	0.225563i	$0.0724223\pi$
$402$		0			0
$403$	31.1769	−	18.0000i	0.0773621	−	0.0446650i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	84.0000i		−	0.206388i
$408$		0			0
$409$	388.500	−	224.301i	0.949878	−	0.548412i	0.0568348	−	0.998384i	$-0.481899\pi$
$409$	388.500	−	224.301i	0.949878	−	0.548412i	0.893043	+	0.449971i	$0.148566\pi$
$410$		0			0
$411$	−234.000	−	135.100i	−0.569343	−	0.328710i
$412$		0			0
$413$	171.473	+	135.000i	0.415189	+	0.326877i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	23.3827	−	13.5000i	0.0560736	−	0.0323741i
$418$		0			0
$419$			800.207i			1.90980i	0.296923	+	0.954902i	$0.404040\pi$
$419$			800.207i			1.90980i	−0.296923	+	0.954902i	$0.595960\pi$
$420$		0			0
$421$	−151.000			−0.358670			−0.179335	−	0.983788i	$-0.557395\pi$
$421$	−151.000			−0.358670			−0.179335	+	0.983788i	$0.557395\pi$
$422$		0			0
$423$	−46.7654	−	81.0000i	−0.110556	−	0.191489i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−60.6218	+	420.000i	−0.141971	+	0.983607i
$428$		0			0
$429$	−18.0000	+	31.1769i	−0.0419580	+	0.0726735i
$430$		0			0
$431$	297.000	+	514.419i	0.689095	+	1.19355i	0.972131	+	0.234438i	$0.0753251\pi$
$431$	297.000	+	514.419i	0.689095	+	1.19355i	−0.283036	+	0.959109i	$0.591342\pi$
$432$		0			0
$433$	−311.769			−0.720021			−0.360011	−	0.932948i	$-0.617227\pi$
$433$	−311.769			−0.720021			−0.360011	+	0.932948i	$0.617227\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	187.061	+	324.000i	0.428058	+	0.741419i
$438$		0			0
$439$	484.500	+	279.726i	1.10364	+	0.637190i	0.937176	−	0.348857i	$-0.113430\pi$
$439$	484.500	+	279.726i	1.10364	+	0.637190i	0.166469	+	0.986047i	$0.446764\pi$
$440$		0			0
$441$	−34.5000	−	142.894i	−0.0782313	−	0.324023i
$442$		0			0
$443$	358.535	+	207.000i	0.809333	+	0.467269i	0.846724	−	0.532032i	$-0.178571\pi$
$443$	358.535	+	207.000i	0.809333	+	0.467269i	−0.0373912	+	0.999301i	$0.511905\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−234.000			−0.521158			−0.260579	−	0.965453i	$-0.583913\pi$
$449$	−234.000			−0.521158			−0.260579	+	0.965453i	$0.583913\pi$
$450$		0			0
$451$	−432.000	+	249.415i	−0.957871	+	0.553027i
$452$		0			0
$453$	84.0045	−	145.500i	0.185440	−	0.321192i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−71.8801	−	41.5000i	−0.157287	−	0.0908096i	0.419291	−	0.907852i	$-0.362279\pi$
$457$	−71.8801	−	41.5000i	−0.157287	−	0.0908096i	−0.576578	+	0.817042i	$0.695612\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	457.261i		−	0.991890i	−0.868354	−	0.495945i	$-0.834822\pi$
$461$		−	457.261i		−	0.991890i	0.868354	−	0.495945i	$-0.165178\pi$
$462$		0			0
$463$		−	517.000i		−	1.11663i	−0.829629	−	0.558315i	$-0.811448\pi$
$463$		−	517.000i		−	1.11663i	0.829629	−	0.558315i	$-0.188552\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−275.396	+	477.000i	−0.589713	+	1.02141i	0.404557	+	0.914513i	$0.367426\pi$
$467$	−275.396	+	477.000i	−0.589713	+	1.02141i	−0.994270	+	0.106900i	$0.965907\pi$
$468$		0			0
$469$	621.500	+	489.304i	1.32516	+	1.04329i
$470$		0			0
$471$	−46.5000	+	80.5404i	−0.0987261	+	0.170999i
$472$		0			0
$473$	−519.615	+	300.000i	−1.09855	+	0.634249i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	252.000i		−	0.528302i
$478$		0			0
$479$	−297.000	+	171.473i	−0.620042	+	0.357981i	−0.776885	−	0.629642i	$-0.783202\pi$
$479$	−297.000	+	171.473i	−0.620042	+	0.357981i	0.156844	+	0.987623i	$0.449868\pi$
$480$		0			0
$481$	−10.5000	−	6.06218i	−0.0218295	−	0.0126033i
$482$		0			0
$483$	270.200	−	108.000i	0.559420	−	0.223602i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	614.878	−	355.000i	1.26258	−	0.728953i	0.289010	−	0.957326i	$-0.406674\pi$
$487$	614.878	−	355.000i	1.26258	−	0.728953i	0.973574	+	0.228373i	$0.0733407\pi$
$488$		0			0
$489$			386.247i			0.789872i
$490$		0			0
$491$	498.000			1.01426			0.507128	−	0.861871i	$-0.330707\pi$
$491$	498.000			1.01426			0.507128	+	0.861871i	$0.330707\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	77.9423	+	195.000i	0.156826	+	0.392354i
$498$		0			0
$499$	−434.500	+	752.576i	−0.870741	+	1.50817i	−0.00951049	+	0.999955i	$0.503027\pi$
$499$	−434.500	+	752.576i	−0.870741	+	1.50817i	−0.861231	+	0.508214i	$0.830306\pi$
$500$		0			0
$501$	−144.000	−	249.415i	−0.287425	−	0.497835i
$502$		0			0
$503$	−550.792			−1.09501			−0.547507	−	0.836801i	$-0.684423\pi$
$503$	−550.792			−1.09501			−0.547507	+	0.836801i	$0.684423\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−143.760	−	249.000i	−0.283551	−	0.491124i
$508$		0			0
$509$	−315.000	−	181.865i	−0.618861	−	0.357299i	0.157565	−	0.987509i	$-0.449636\pi$
$509$	−315.000	−	181.865i	−0.618861	−	0.357299i	−0.776425	+	0.630209i	$0.782969\pi$
$510$		0			0
$511$	−52.5000	+	66.6840i	−0.102740	+	0.130497i
$512$		0			0
$513$	−70.1481	−	40.5000i	−0.136741	−	0.0789474i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	374.123			0.723642
$518$		0			0
$519$	234.000			0.450867
$520$		0			0
$521$	270.000	−	155.885i	0.518234	−	0.299203i	−0.217978	−	0.975954i	$-0.569946\pi$
$521$	270.000	−	155.885i	0.518234	−	0.299203i	0.736212	+	0.676751i	$0.236613\pi$
$522$		0			0
$523$	173.205	−	300.000i	0.331176	−	0.573614i	−0.651567	−	0.758591i	$-0.725888\pi$
$523$	173.205	−	300.000i	0.331176	−	0.573614i	0.982743	+	0.184978i	$0.0592213\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	23.5000	+	40.7032i	0.0444234	+	0.0769437i
$530$		0			0
$531$		−	93.5307i		−	0.176141i
$532$		0			0
$533$			72.0000i			0.135084i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	140.296	−	243.000i	0.261259	−	0.452514i
$538$		0			0
$539$	564.000	+	166.277i	1.04638	+	0.308491i
$540$		0			0
$541$	−68.5000	+	118.645i	−0.126617	+	0.219308i	−0.922364	−	0.386322i	$-0.873745\pi$
$541$	−68.5000	+	118.645i	−0.126617	+	0.219308i	0.795747	+	0.605630i	$0.207079\pi$
$542$		0			0
$543$	415.692	−	240.000i	0.765547	−	0.441989i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	758.000i		−	1.38574i	−0.721062	−	0.692870i	$-0.756346\pi$
$547$		−	758.000i		−	1.38574i	0.721062	−	0.692870i	$-0.243654\pi$
$548$		0			0
$549$	157.500	−	90.9327i	0.286885	−	0.165633i
$550$		0			0
$551$	81.0000	+	46.7654i	0.147005	+	0.0848736i
$552$		0			0
$553$	−658.179	−	95.0000i	−1.19020	−	0.171790i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	576.773	−	333.000i	1.03550	−	0.597846i	0.116944	−	0.993139i	$-0.462690\pi$
$557$	576.773	−	333.000i	1.03550	−	0.597846i	0.918555	+	0.395293i	$0.129357\pi$
$558$		0			0
$559$			86.6025i			0.154924i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	161.081	+	279.000i	0.286111	+	0.495560i	0.972878	−	0.231318i	$-0.0743039\pi$
$563$	161.081	+	279.000i	0.286111	+	0.495560i	−0.686767	+	0.726878i	$0.740971\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−38.9711	+	49.5000i	−0.0687322	+	0.0873016i
$568$		0			0
$569$	342.000	−	592.361i	0.601054	−	1.04106i	−0.391607	−	0.920132i	$-0.628081\pi$
$569$	342.000	−	592.361i	0.601054	−	1.04106i	0.992662	−	0.120924i	$-0.0385859\pi$
$570$		0			0
$571$	27.5000	+	47.6314i	0.0481611	+	0.0834175i	0.889101	−	0.457711i	$-0.151331\pi$
$571$	27.5000	+	47.6314i	0.0481611	+	0.0834175i	−0.840940	+	0.541129i	$0.817997\pi$
$572$		0			0
$573$	−270.200			−0.471553
$574$		0			0
$575$		0			0
$576$		0			0
$577$	79.6743	+	138.000i	0.138084	+	0.239168i	0.926771	−	0.375626i	$-0.122572\pi$
$577$	79.6743	+	138.000i	0.138084	+	0.239168i	−0.788687	+	0.614794i	$0.789239\pi$
$578$		0			0
$579$	195.000	+	112.583i	0.336788	+	0.194444i
$580$		0			0
$581$	27.0000	+	67.5500i	0.0464716	+	0.116265i
$582$		0			0
$583$	872.954	+	504.000i	1.49735	+	0.864494i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	249.415			0.424898			0.212449	−	0.977172i	$-0.431856\pi$
$587$	249.415			0.424898			0.212449	+	0.977172i	$0.431856\pi$
$588$		0			0
$589$	−324.000			−0.550085
$590$		0			0
$591$	−225.000	+	129.904i	−0.380711	+	0.219803i
$592$		0			0
$593$	−555.988	+	963.000i	−0.937586	+	1.62395i	−0.167629	+	0.985850i	$0.553611\pi$
$593$	−555.988	+	963.000i	−0.937586	+	1.62395i	−0.769957	+	0.638096i	$0.779722\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	7.79423	+	4.50000i	0.0130557	+	0.00753769i
$598$		0			0
$599$	432.000	+	748.246i	0.721202	+	1.24916i	0.960518	+	0.278217i	$0.0897434\pi$
$599$	432.000	+	748.246i	0.721202	+	1.24916i	−0.239316	+	0.970942i	$0.576923\pi$
$600$		0			0
$601$		−	829.652i		−	1.38045i	−0.723593	−	0.690227i	$-0.757511\pi$
$601$		−	829.652i		−	1.38045i	0.723593	−	0.690227i	$-0.242489\pi$
$602$		0			0
$603$		−	339.000i		−	0.562189i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	440.807	−	763.500i	0.726206	−	1.25783i	−0.232270	−	0.972651i	$-0.574615\pi$
$607$	440.807	−	763.500i	0.726206	−	1.25783i	0.958476	−	0.285174i	$-0.0920514\pi$
$608$		0			0
$609$	45.0000	−	57.1577i	0.0738916	−	0.0938550i
$610$		0			0
$611$	27.0000	−	46.7654i	0.0441899	−	0.0765391i
$612$		0			0
$613$	−39.8372	+	23.0000i	−0.0649872	+	0.0375204i	−0.532142	−	0.846655i	$-0.678613\pi$
$613$	−39.8372	+	23.0000i	−0.0649872	+	0.0375204i	0.467154	+	0.884176i	$0.345279\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	174.000i		−	0.282010i	−0.990009	−	0.141005i	$-0.954967\pi$
$617$		−	174.000i		−	0.282010i	0.990009	−	0.141005i	$-0.0450333\pi$
$618$		0			0
$619$	762.000	−	439.941i	1.23102	−	0.710728i	0.263776	−	0.964584i	$-0.415032\pi$
$619$	762.000	−	439.941i	1.23102	−	0.710728i	0.967242	+	0.253856i	$0.0816988\pi$
$620$		0			0
$621$	−108.000	−	62.3538i	−0.173913	−	0.100409i
$622$		0			0
$623$	−176.669	+	1224.00i	−0.283578	+	1.96469i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	280.592	−	162.000i	0.447516	−	0.258373i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	875.000			1.38669			0.693344	−	0.720607i	$-0.256137\pi$
$631$	875.000			1.38669			0.693344	+	0.720607i	$0.256137\pi$
$632$		0			0
$633$	−264.138	−	457.500i	−0.417279	−	0.722749i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	61.4878	−	58.5000i	0.0965272	−	0.0918367i
$638$		0			0
$639$	45.0000	−	77.9423i	0.0704225	−	0.121975i
$640$		0			0
$641$	486.000	+	841.777i	0.758190	+	1.31322i	0.943773	+	0.330595i	$0.107250\pi$
$641$	486.000	+	841.777i	0.758190	+	1.31322i	−0.185582	+	0.982629i	$0.559417\pi$
$642$		0			0
$643$	195.722			0.304388			0.152194	−	0.988351i	$-0.451366\pi$
$643$	195.722			0.304388			0.152194	+	0.988351i	$0.451366\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−109.119	−	189.000i	−0.168654	−	0.292117i	0.769293	−	0.638896i	$-0.220609\pi$
$647$	−109.119	−	189.000i	−0.168654	−	0.292117i	−0.937947	+	0.346779i	$0.887275\pi$
$648$		0			0
$649$	324.000	+	187.061i	0.499230	+	0.288230i
$650$		0			0
$651$	−36.0000	+	249.415i	−0.0552995	+	0.383126i
$652$		0			0
$653$	−259.808	−	150.000i	−0.397868	−	0.229709i	0.287696	−	0.957722i	$-0.407111\pi$
$653$	−259.808	−	150.000i	−0.397868	−	0.229709i	−0.685564	+	0.728013i	$0.740444\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	36.3731			0.0553624
$658$		0			0
$659$	−678.000			−1.02883			−0.514416	−	0.857541i	$-0.671991\pi$
$659$	−678.000			−1.02883			−0.514416	+	0.857541i	$0.671991\pi$
$660$		0			0
$661$	109.500	−	63.2199i	0.165658	−	0.0956427i	−0.414879	−	0.909877i	$-0.636176\pi$
$661$	109.500	−	63.2199i	0.165658	−	0.0956427i	0.580537	+	0.814234i	$0.302843\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	124.708	+	72.0000i	0.186968	+	0.107946i
$668$		0			0
$669$	19.5000	+	33.7750i	0.0291480	+	0.0504858i
$670$		0			0
$671$			727.461i			1.08415i
$672$		0			0
$673$		−	407.000i		−	0.604755i	−0.953188	−	0.302377i	$-0.902220\pi$
$673$		−	407.000i		−	0.604755i	0.953188	−	0.302377i	$-0.0977803\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	550.792	−	954.000i	0.813578	−	1.40916i	−0.0967669	−	0.995307i	$-0.530850\pi$
$677$	550.792	−	954.000i	0.813578	−	1.40916i	0.910345	−	0.413851i	$-0.135817\pi$
$678$		0			0
$679$	292.500	+	731.791i	0.430781	+	1.07775i
$680$		0			0
$681$	−333.000	+	576.773i	−0.488987	+	0.846950i
$682$		0			0
$683$	36.3731	−	21.0000i	0.0532549	−	0.0307467i	−0.473136	−	0.880989i	$-0.656878\pi$
$683$	36.3731	−	21.0000i	0.0532549	−	0.0307467i	0.526391	+	0.850243i	$0.323545\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	411.000i		−	0.598253i
$688$		0			0
$689$	126.000	−	72.7461i	0.182874	−	0.105582i
$690$		0			0
$691$	295.500	+	170.607i	0.427641	+	0.246899i	0.698341	−	0.715765i	$-0.253922\pi$
$691$	295.500	+	170.607i	0.427641	+	0.246899i	−0.270700	+	0.962664i	$0.587255\pi$
$692$		0			0
$693$	−93.5307	−	234.000i	−0.134965	−	0.337662i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$			519.615i			0.743369i
$700$		0			0
$701$	1182.00			1.68616			0.843081	−	0.537786i	$-0.180739\pi$
$701$	1182.00			1.68616			0.843081	+	0.537786i	$0.180739\pi$
$702$		0			0
$703$	54.5596	+	94.5000i	0.0776097	+	0.134424i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−114.315	−	90.0000i	−0.161691	−	0.127298i
$708$		0			0
$709$	291.500	−	504.893i	0.411142	−	0.712120i	−0.583873	−	0.811845i	$-0.698463\pi$
$709$	291.500	−	504.893i	0.411142	−	0.712120i	0.995015	+	0.0997257i	$0.0317965\pi$
$710$		0			0
$711$	142.500	+	246.817i	0.200422	+	0.347141i
$712$		0			0
$713$	−498.831			−0.699622
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−207.846	−	360.000i	−0.289883	−	0.502092i
$718$		0			0
$719$	−522.000	−	301.377i	−0.726008	−	0.419161i	0.0909518	−	0.995855i	$-0.471009\pi$
$719$	−522.000	−	301.377i	−0.726008	−	0.419161i	−0.816960	+	0.576694i	$0.804342\pi$
$720$		0			0
$721$	−36.0000	−	5.19615i	−0.0499307	−	0.00720687i
$722$		0			0
$723$	319.563	+	184.500i	0.441996	+	0.255187i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−84.8705			−0.116741			−0.0583704	−	0.998295i	$-0.518590\pi$
$727$	−84.8705			−0.116741			−0.0583704	+	0.998295i	$0.518590\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−108.253	+	187.500i	−0.147685	+	0.255798i	−0.930371	−	0.366618i	$-0.880516\pi$
$733$	−108.253	+	187.500i	−0.147685	+	0.255798i	0.782686	+	0.622416i	$0.213849\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1174.33	+	678.000i	1.59339	+	0.919946i
$738$		0			0
$739$	−243.500	−	421.754i	−0.329499	−	0.570710i	0.652913	−	0.757433i	$-0.273547\pi$
$739$	−243.500	−	421.754i	−0.329499	−	0.570710i	−0.982413	+	0.186723i	$0.940213\pi$
$740$		0			0
$741$		−	46.7654i		−	0.0631112i
$742$		0			0
$743$			480.000i			0.646030i	0.946394	+	0.323015i	$0.104696\pi$
$743$			480.000i			0.646030i	−0.946394	+	0.323015i	$0.895304\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	15.5885	−	27.0000i	0.0208681	−	0.0361446i
$748$		0			0
$749$	12.0000	−	83.1384i	0.0160214	−	0.110999i
$750$		0			0
$751$	−150.500	+	260.674i	−0.200399	+	0.347102i	−0.948657	−	0.316306i	$-0.897557\pi$
$751$	−150.500	+	260.674i	−0.200399	+	0.347102i	0.748258	+	0.663408i	$0.230891\pi$
$752$		0			0
$753$	−171.473	+	99.0000i	−0.227720	+	0.131474i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	811.000i		−	1.07133i	−0.844429	−	0.535667i	$-0.820060\pi$
$757$		−	811.000i		−	1.07133i	0.844429	−	0.535667i	$-0.179940\pi$
$758$		0			0
$759$	432.000	−	249.415i	0.569170	−	0.328610i
$760$		0			0
$761$	828.000	+	478.046i	1.08804	+	0.628181i	0.933054	−	0.359735i	$-0.117133\pi$
$761$	828.000	+	478.046i	1.08804	+	0.628181i	0.154988	+	0.987916i	$0.450466\pi$
$762$		0			0
$763$	−73.6122	+	93.5000i	−0.0964773	+	0.122543i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	46.7654	−	27.0000i	0.0609718	−	0.0352021i
$768$		0			0
$769$			1344.07i			1.74782i	0.486090	+	0.873909i	$0.338423\pi$
$769$			1344.07i			1.74782i	−0.486090	+	0.873909i	$0.661577\pi$
$770$		0			0
$771$	−666.000			−0.863813
$772$		0			0
$773$	−363.731	−	630.000i	−0.470544	−	0.815006i	0.528888	−	0.848691i	$-0.322609\pi$
$773$	−363.731	−	630.000i	−0.470544	−	0.815006i	−0.999433	+	0.0336850i	$0.989276\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	78.8083	−	31.5000i	0.101426	−	0.0405405i
$778$		0			0
$779$	324.000	−	561.184i	0.415918	−	0.720391i
$780$		0			0
$781$	180.000	+	311.769i	0.230474	+	0.399192i
$782$		0			0
$783$	−31.1769			−0.0398173
$784$		0			0
$785$		0			0
$786$		0			0
$787$	446.003	+	772.500i	0.566713	+	0.981576i	0.996888	+	0.0788301i	$0.0251185\pi$
$787$	446.003	+	772.500i	0.566713	+	0.981576i	−0.430175	+	0.902745i	$0.641548\pi$
$788$		0			0
$789$	288.000	+	166.277i	0.365019	+	0.210744i
$790$		0			0
$791$	351.000	−	140.296i	0.443742	−	0.177366i
$792$		0			0
$793$	90.9327	+	52.5000i	0.114669	+	0.0662043i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1351.00			−1.69511			−0.847553	−	0.530711i	$-0.821925\pi$
$797$	−1351.00			−1.69511			−0.847553	+	0.530711i	$0.821925\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	459.000	−	265.004i	0.573034	−	0.330841i
$802$		0			0
$803$	−72.7461	+	126.000i	−0.0905929	+	0.156912i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	109.119	+	63.0000i	0.135216	+	0.0780669i
$808$		0			0
$809$	−96.0000	−	166.277i	−0.118665	−	0.205534i	0.800574	−	0.599234i	$-0.204528\pi$
$809$	−96.0000	−	166.277i	−0.118665	−	0.205534i	−0.919239	+	0.393700i	$0.871195\pi$
$810$		0			0
$811$			1234.95i			1.52275i	0.648310	+	0.761376i	$0.275476\pi$
$811$			1234.95i			1.52275i	−0.648310	+	0.761376i	$0.724524\pi$
$812$		0			0
$813$		−	420.000i		−	0.516605i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	389.711	−	675.000i	0.477003	−	0.826193i
$818$		0			0
$819$	−36.0000	−	5.19615i	−0.0439560	−	0.00634451i
$820$		0			0
$821$	−498.000	+	862.561i	−0.606577	+	1.05062i	0.385223	+	0.922824i	$0.374125\pi$
$821$	−498.000	+	862.561i	−0.606577	+	1.05062i	−0.991800	+	0.127799i	$0.959209\pi$
$822$		0			0
$823$	809.734	−	467.500i	0.983881	−	0.568044i	0.0804411	−	0.996759i	$-0.474367\pi$
$823$	809.734	−	467.500i	0.983881	−	0.568044i	0.903439	+	0.428716i	$0.141034\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	228.000i		−	0.275695i	−0.990453	−	0.137848i	$-0.955982\pi$
$827$		−	228.000i		−	0.275695i	0.990453	−	0.137848i	$-0.0440184\pi$
$828$		0			0
$829$	304.500	−	175.803i	0.367310	−	0.212067i	−0.304973	−	0.952361i	$-0.598647\pi$
$829$	304.500	−	175.803i	0.367310	−	0.212067i	0.672283	+	0.740295i	$0.265314\pi$
$830$		0			0
$831$	172.500	+	99.5929i	0.207581	+	0.119847i
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	93.5307	−	54.0000i	0.111745	−	0.0645161i
$838$		0			0
$839$			852.169i			1.01570i	0.861447	+	0.507848i	$0.169559\pi$
$839$			852.169i			1.01570i	−0.861447	+	0.507848i	$0.830441\pi$
$840$		0			0
$841$	−805.000			−0.957194
$842$		0			0
$843$	457.261	+	792.000i	0.542422	+	0.939502i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	159.349	+	23.0000i	0.188133	+	0.0271547i
$848$		0			0
$849$	172.500	−	298.779i	0.203180	−	0.351918i
$850$		0			0
$851$	84.0000	+	145.492i	0.0987074	+	0.170966i
$852$		0			0
$853$	−1344.07			−1.57570			−0.787850	−	0.615868i	$-0.788806\pi$
$853$	−1344.07			−1.57570			−0.787850	+	0.615868i	$0.788806\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	493.634	+	855.000i	0.576003	+	0.997666i	0.995932	+	0.0901093i	$0.0287216\pi$
$857$	493.634	+	855.000i	0.576003	+	0.997666i	−0.419929	+	0.907557i	$0.637945\pi$
$858$		0			0
$859$	−1194.00	−	689.356i	−1.38999	−	0.802510i	−0.396675	−	0.917959i	$-0.629836\pi$
$859$	−1194.00	−	689.356i	−1.38999	−	0.802510i	−0.993313	+	0.115449i	$0.963169\pi$
$860$		0			0
$861$	−396.000	−	311.769i	−0.459930	−	0.362101i
$862$		0			0
$863$	1299.04	+	750.000i	1.50526	+	0.869061i	0.999981	+	0.00610429i	$0.00194307\pi$
$863$	1299.04	+	750.000i	1.50526	+	0.869061i	0.505277	+	0.862957i	$0.331390\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	500.563			0.577350
$868$		0			0
$869$	−1140.00			−1.31185
$870$		0			0
$871$	169.500	−	97.8609i	0.194604	−	0.112355i
$872$		0			0
$873$	168.875	−	292.500i	0.193442	−	0.335052i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	627.868	+	362.500i	0.715928	+	0.413341i	0.813252	−	0.581912i	$-0.197695\pi$
$877$	627.868	+	362.500i	0.715928	+	0.413341i	−0.0973244	+	0.995253i	$0.531028\pi$
$878$		0			0
$879$	−171.000	−	296.181i	−0.194539	−	0.336952i
$880$		0			0
$881$		−	280.592i		−	0.318493i	−0.987239	−	0.159246i	$-0.949094\pi$
$881$		−	280.592i		−	0.318493i	0.987239	−	0.159246i	$-0.0509064\pi$
$882$		0			0
$883$			691.000i			0.782559i	0.920272	+	0.391280i	$0.127968\pi$
$883$			691.000i			0.782559i	−0.920272	+	0.391280i	$0.872032\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−161.081	+	279.000i	−0.181602	+	0.314543i	−0.942426	−	0.334414i	$-0.891461\pi$
$887$	−161.081	+	279.000i	−0.181602	+	0.314543i	0.760824	+	0.648958i	$0.224795\pi$
$888$		0			0
$889$	708.500	−	283.190i	0.796963	−	0.318549i
$890$		0			0
$891$	−54.0000	+	93.5307i	−0.0606061	+	0.104973i
$892$		0			0
$893$	−420.888	+	243.000i	−0.471320	+	0.272116i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	72.0000i		−	0.0802676i
$898$		0			0
$899$	−108.000	+	62.3538i	−0.120133	+	0.0693591i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−476.314	−	375.000i	−0.527479	−	0.415282i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	814.930	−	470.500i	0.898489	−	0.518743i	0.0217796	−	0.999763i	$-0.493067\pi$
$907$	814.930	−	470.500i	0.898489	−	0.518743i	0.876710	+	0.481020i	$0.159733\pi$
$908$		0			0
$909$			62.3538i			0.0685961i
$910$		0			0
$911$	780.000			0.856202			0.428101	−	0.903731i	$-0.359183\pi$
$911$	780.000			0.856202			0.428101	+	0.903731i	$0.359183\pi$
$912$		0			0
$913$	62.3538	+	108.000i	0.0682955	+	0.118291i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	20.7846	−	144.000i	0.0226659	−	0.157034i
$918$		0			0
$919$	809.000	−	1401.23i	0.880305	−	1.52473i	0.0293023	−	0.999571i	$-0.490671\pi$
$919$	809.000	−	1401.23i	0.880305	−	1.52473i	0.851002	−	0.525162i	$-0.175995\pi$
$920$		0			0
$921$	−414.000	−	717.069i	−0.449511	−	0.778577i
$922$		0			0
$923$	51.9615			0.0562963
$924$		0			0
$925$		0			0
$926$		0			0
$927$	7.79423	+	13.5000i	0.00840801	+	0.0145631i
$928$		0			0
$929$	−225.000	−	129.904i	−0.242196	−	0.139832i	0.373990	−	0.927433i	$-0.377990\pi$
$929$	−225.000	−	129.904i	−0.242196	−	0.139832i	−0.616186	+	0.787601i	$0.711323\pi$
$930$		0			0
$931$	−742.500	+	179.267i	−0.797530	+	0.192553i
$932$		0			0
$933$	358.535	+	207.000i	0.384281	+	0.221865i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	6.92820			0.00739403			0.00369701	−	0.999993i	$-0.498823\pi$
$937$	6.92820			0.00739403			0.00369701	+	0.999993i	$0.498823\pi$
$938$		0			0
$939$	−552.000			−0.587859
$940$		0			0
$941$	621.000	−	358.535i	0.659936	−	0.381014i	−0.132316	−	0.991208i	$-0.542242\pi$
$941$	621.000	−	358.535i	0.659936	−	0.381014i	0.792253	+	0.610193i	$0.208908\pi$
$942$		0			0
$943$	498.831	−	864.000i	0.528983	−	0.916225i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	233.827	+	135.000i	0.246913	+	0.142555i	0.618350	−	0.785903i	$-0.287801\pi$
$947$	233.827	+	135.000i	0.246913	+	0.142555i	−0.371437	+	0.928458i	$0.621135\pi$
$948$		0			0
$949$	10.5000	+	18.1865i	0.0110643	+	0.0191639i
$950$		0			0
$951$		−	114.315i		−	0.120205i
$952$		0			0
$953$		−	1266.00i		−	1.32844i	−0.747539	−	0.664218i	$-0.768765\pi$
$953$		−	1266.00i		−	1.32844i	0.747539	−	0.664218i	$-0.231235\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	62.3538	−	108.000i	0.0651555	−	0.112853i
$958$		0			0
$959$	858.000	+	675.500i	0.894682	+	0.704379i
$960$		0			0
$961$	−264.500	+	458.127i	−0.275234	+	0.476719i
$962$		0			0
$963$	−31.1769	+	18.0000i	−0.0323748	+	0.0186916i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	1151.00i		−	1.19028i	−0.803622	−	0.595140i	$-0.797097\pi$
$967$		−	1151.00i		−	1.19028i	0.803622	−	0.595140i	$-0.202903\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	441.000	+	254.611i	0.454171	+	0.262216i	0.709590	−	0.704615i	$-0.248880\pi$
$971$	441.000	+	254.611i	0.454171	+	0.262216i	−0.255419	+	0.966830i	$0.582213\pi$
$972$		0			0
$973$	−101.325	+	40.5000i	−0.104137	+	0.0416238i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1179.53	−	681.000i	1.20729	−	0.697032i	0.245127	−	0.969491i	$-0.421170\pi$
$977$	1179.53	−	681.000i	1.20729	−	0.697032i	0.962167	+	0.272459i	$0.0878370\pi$
$978$		0			0
$979$			2120.03i			2.16551i
$980$		0			0
$981$	51.0000			0.0519878
$982$		0			0
$983$	498.831	+	864.000i	0.507457	+	0.878942i	0.999963	+	0.00863259i	$0.00274787\pi$
$983$	498.831	+	864.000i	0.507457	+	0.878942i	−0.492505	+	0.870309i	$0.663919\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	140.296	+	351.000i	0.142144	+	0.355623i
$988$		0			0
$989$	600.000	−	1039.23i	0.606673	−	1.05079i
$990$		0			0
$991$	−581.000	−	1006.32i	−0.586276	−	1.01546i	−0.994715	−	0.102675i	$-0.967260\pi$
$991$	−581.000	−	1006.32i	−0.586276	−	1.01546i	0.408438	−	0.912786i	$-0.366073\pi$
$992$		0			0
$993$	−386.247			−0.388970
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−754.308	−	1306.50i	−0.756578	−	1.31043i	−0.944586	−	0.328264i	$-0.893536\pi$
$997$	−754.308	−	1306.50i	−0.756578	−	1.31043i	0.188008	−	0.982167i	$-0.439797\pi$
$998$		0			0
$999$	−31.5000	−	18.1865i	−0.0315315	−	0.0182047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.3.be.b.649.2		4
5.2	odd	4		2100.3.bd.e.901.1	yes	2
5.3	odd	4		2100.3.bd.a.901.1	✓	2
5.4	even	2	inner	2100.3.be.b.649.1		4
7.3	odd	6	inner	2100.3.be.b.1249.1		4
35.3	even	12		2100.3.bd.a.1501.1	yes	2
35.17	even	12		2100.3.bd.e.1501.1	yes	2
35.24	odd	6	inner	2100.3.be.b.1249.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.3.bd.a.901.1	✓	2	5.3	odd	4
2100.3.bd.a.1501.1	yes	2	35.3	even	12
2100.3.bd.e.901.1	yes	2	5.2	odd	4
2100.3.bd.e.1501.1	yes	2	35.17	even	12
2100.3.be.b.649.1		4	5.4	even	2	inner
2100.3.be.b.649.2		4	1.1	even	1	trivial
2100.3.be.b.1249.1		4	7.3	odd	6	inner
2100.3.be.b.1249.2		4	35.24	odd	6	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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2100.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.50000i) q^{3} +(-2.59808 - 6.50000i) q^{7} +(-1.50000 + 2.59808i) q^{9} +(-6.00000 - 10.3923i) q^{11} -1.73205 q^{13} +(13.5000 + 7.79423i) q^{19} +(7.50000 - 9.52628i) q^{21} +(20.7846 + 12.0000i) q^{23} -5.19615 q^{27} +6.00000 q^{29} +(-18.0000 + 10.3923i) q^{31} +(10.3923 - 18.0000i) q^{33} +(6.06218 + 3.50000i) q^{37} +(-1.50000 - 2.59808i) q^{39} -41.5692i q^{41} -50.0000i q^{43} +(-15.5885 + 27.0000i) q^{47} +(-35.5000 + 33.7750i) q^{49} +(-72.7461 + 42.0000i) q^{53} +27.0000i q^{57} +(-27.0000 + 15.5885i) q^{59} +(-52.5000 - 30.3109i) q^{61} +(20.7846 + 3.00000i) q^{63} +(-97.8609 + 56.5000i) q^{67} +41.5692i q^{69} -30.0000 q^{71} +(-6.06218 - 10.5000i) q^{73} +(-51.9615 + 66.0000i) q^{77} +(47.5000 - 82.2724i) q^{79} +(-4.50000 - 7.79423i) q^{81} -10.3923 q^{83} +(5.19615 + 9.00000i) q^{87} +(-153.000 - 88.3346i) q^{89} +(4.50000 + 11.2583i) q^{91} +(-31.1769 - 18.0000i) q^{93} -112.583 q^{97} +36.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{9} - 24 q^{11} + 54 q^{19} + 30 q^{21} + 24 q^{29} - 72 q^{31} - 6 q^{39} - 142 q^{49} - 108 q^{59} - 210 q^{61} - 120 q^{71} + 190 q^{79} - 18 q^{81} - 612 q^{89} + 18 q^{91} + 144 q^{99}+O(q^{100}) \) 4 * q - 6 * q^9 - 24 * q^11 + 54 * q^19 + 30 * q^21 + 24 * q^29 - 72 * q^31 - 6 * q^39 - 142 * q^49 - 108 * q^59 - 210 * q^61 - 120 * q^71 + 190 * q^79 - 18 * q^81 - 612 * q^89 + 18 * q^91 + 144 * q^99

Introduction

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