LMFDB - Embedded newform 1800.2.k.m.901.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(901,1800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1800.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1800.k (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			901.3
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1800.901
Dual form			1800.2.k.m.901.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +2.44949 q^{7} -2.82843i q^{8} +O(q^{10})$	$q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +2.44949 q^{7} -2.82843i q^{8} -3.46410i q^{11} +(3.00000 - 1.73205i) q^{14} +(-2.00000 - 3.46410i) q^{16} +4.89898 q^{17} +3.46410i q^{19} +(-2.44949 - 4.24264i) q^{22} -2.44949 q^{23} +(2.44949 - 4.24264i) q^{28} +4.00000 q^{31} +(-4.89898 - 2.82843i) q^{32} +(6.00000 - 3.46410i) q^{34} -8.48528i q^{37} +(2.44949 + 4.24264i) q^{38} -4.24264i q^{43} +(-6.00000 - 3.46410i) q^{44} +(-3.00000 + 1.73205i) q^{46} -7.34847 q^{47} -1.00000 q^{49} +5.65685i q^{53} -6.92820i q^{56} +10.3923i q^{59} -3.46410i q^{61} +(4.89898 - 2.82843i) q^{62} -8.00000 q^{64} -4.24264i q^{67} +(4.89898 - 8.48528i) q^{68} +12.0000 q^{71} +4.89898 q^{73} +(-6.00000 - 10.3923i) q^{74} +(6.00000 + 3.46410i) q^{76} -8.48528i q^{77} +4.00000 q^{79} -9.89949i q^{83} +(-3.00000 - 5.19615i) q^{86} -9.79796 q^{88} +6.00000 q^{89} +(-2.44949 + 4.24264i) q^{92} +(-9.00000 + 5.19615i) q^{94} +4.89898 q^{97} +(-1.22474 + 0.707107i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4}+O(q^{10}) $ 4 * q + 4 * q^4	$ 4 q + 4 q^{4} + 12 q^{14} - 8 q^{16} + 16 q^{31} + 24 q^{34} - 24 q^{44} - 12 q^{46} - 4 q^{49} - 32 q^{64} + 48 q^{71} - 24 q^{74} + 24 q^{76} + 16 q^{79} - 12 q^{86} + 24 q^{89} - 36 q^{94}+O(q^{100}) $ 4 * q + 4 * q^4 + 12 * q^14 - 8 * q^16 + 16 * q^31 + 24 * q^34 - 24 * q^44 - 12 * q^46 - 4 * q^49 - 32 * q^64 + 48 * q^71 - 24 * q^74 + 24 * q^76 + 16 * q^79 - 12 * q^86 + 24 * q^89 - 36 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1001$	$1351$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	1.22474	−	0.707107i	0.866025	−	0.500000i
$2$	1.22474	−	0.707107i	0.866025	−	0.500000i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.44949			0.925820			0.462910	−	0.886405i	$-0.346805\pi$
$7$	2.44949			0.925820			0.462910	+	0.886405i	$0.346805\pi$
$8$		−	2.82843i		−	1.00000i
$9$		0			0
$10$		0			0
$11$		−	3.46410i		−	1.04447i	−0.852803	−	0.522233i	$-0.825099\pi$
$11$		−	3.46410i		−	1.04447i	0.852803	−	0.522233i	$-0.174901\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	3.00000	−	1.73205i	0.801784	−	0.462910i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	4.89898			1.18818			0.594089	−	0.804400i	$-0.297513\pi$
$17$	4.89898			1.18818			0.594089	+	0.804400i	$0.297513\pi$
$18$		0			0
$19$			3.46410i			0.794719i	0.917663	+	0.397360i	$0.130073\pi$
$19$			3.46410i			0.794719i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$		0			0
$22$	−2.44949	−	4.24264i	−0.522233	−	0.904534i
$23$	−2.44949			−0.510754			−0.255377	−	0.966842i	$-0.582200\pi$
$23$	−2.44949			−0.510754			−0.255377	+	0.966842i	$0.582200\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		0			0
$28$	2.44949	−	4.24264i	0.462910	−	0.801784i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−4.89898	−	2.82843i	−0.866025	−	0.500000i
$33$		0			0
$34$	6.00000	−	3.46410i	1.02899	−	0.594089i
$35$		0			0
$36$		0			0
$37$		−	8.48528i		−	1.39497i	−0.716599	−	0.697486i	$-0.754302\pi$
$37$		−	8.48528i		−	1.39497i	0.716599	−	0.697486i	$-0.245698\pi$
$38$	2.44949	+	4.24264i	0.397360	+	0.688247i
$39$		0			0
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$		−	4.24264i		−	0.646997i	−0.946229	−	0.323498i	$-0.895141\pi$
$43$		−	4.24264i		−	0.646997i	0.946229	−	0.323498i	$-0.104859\pi$
$44$	−6.00000	−	3.46410i	−0.904534	−	0.522233i
$45$		0			0
$46$	−3.00000	+	1.73205i	−0.442326	+	0.255377i
$47$	−7.34847			−1.07188			−0.535942	−	0.844255i	$-0.680044\pi$
$47$	−7.34847			−1.07188			−0.535942	+	0.844255i	$0.680044\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$		0			0
$52$		0			0
$53$			5.65685i			0.777029i	0.921443	+	0.388514i	$0.127012\pi$
$53$			5.65685i			0.777029i	−0.921443	+	0.388514i	$0.872988\pi$
$54$		0			0
$55$		0			0
$56$		−	6.92820i		−	0.925820i
$57$		0			0
$58$		0			0
$59$			10.3923i			1.35296i	0.736460	+	0.676481i	$0.236496\pi$
$59$			10.3923i			1.35296i	−0.736460	+	0.676481i	$0.763504\pi$
$60$		0			0
$61$		−	3.46410i		−	0.443533i	−0.975100	−	0.221766i	$-0.928818\pi$
$61$		−	3.46410i		−	0.443533i	0.975100	−	0.221766i	$-0.0711822\pi$
$62$	4.89898	−	2.82843i	0.622171	−	0.359211i
$63$		0			0
$64$	−8.00000			−1.00000
$65$		0			0
$66$		0			0
$67$		−	4.24264i		−	0.518321i	−0.965834	−	0.259161i	$-0.916554\pi$
$67$		−	4.24264i		−	0.518321i	0.965834	−	0.259161i	$-0.0834459\pi$
$68$	4.89898	−	8.48528i	0.594089	−	1.02899i
$69$		0			0
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	4.89898			0.573382			0.286691	−	0.958023i	$-0.407445\pi$
$73$	4.89898			0.573382			0.286691	+	0.958023i	$0.407445\pi$
$74$	−6.00000	−	10.3923i	−0.697486	−	1.20808i
$75$		0			0
$76$	6.00000	+	3.46410i	0.688247	+	0.397360i
$77$		−	8.48528i		−	0.966988i
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	9.89949i		−	1.08661i	−0.839535	−	0.543305i	$-0.817173\pi$
$83$		−	9.89949i		−	1.08661i	0.839535	−	0.543305i	$-0.182827\pi$
$84$		0			0
$85$		0			0
$86$	−3.00000	−	5.19615i	−0.323498	−	0.560316i
$87$		0			0
$88$	−9.79796			−1.04447
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$		0			0
$92$	−2.44949	+	4.24264i	−0.255377	+	0.442326i
$93$		0			0
$94$	−9.00000	+	5.19615i	−0.928279	+	0.535942i
$95$		0			0
$96$		0			0
$97$	4.89898			0.497416			0.248708	−	0.968579i	$-0.419994\pi$
$97$	4.89898			0.497416			0.248708	+	0.968579i	$0.419994\pi$
$98$	−1.22474	+	0.707107i	−0.123718	+	0.0714286i
$99$		0			0
$100$		0			0
$101$			13.8564i			1.37876i	0.724398	+	0.689382i	$0.242118\pi$
$101$			13.8564i			1.37876i	−0.724398	+	0.689382i	$0.757882\pi$
$102$		0			0
$103$	−7.34847			−0.724066			−0.362033	−	0.932165i	$-0.617917\pi$
$103$	−7.34847			−0.724066			−0.362033	+	0.932165i	$0.617917\pi$
$104$		0			0
$105$		0			0
$106$	4.00000	+	6.92820i	0.388514	+	0.672927i
$107$		−	1.41421i		−	0.136717i	−0.997661	−	0.0683586i	$-0.978224\pi$
$107$		−	1.41421i		−	0.136717i	0.997661	−	0.0683586i	$-0.0217762\pi$
$108$		0			0
$109$		−	3.46410i		−	0.331801i	−0.986143	−	0.165900i	$-0.946947\pi$
$109$		−	3.46410i		−	0.331801i	0.986143	−	0.165900i	$-0.0530530\pi$
$110$		0			0
$111$		0			0
$112$	−4.89898	−	8.48528i	−0.462910	−	0.801784i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	7.34847	+	12.7279i	0.676481	+	1.17170i
$119$	12.0000			1.10004
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	−2.44949	−	4.24264i	−0.221766	−	0.384111i
$123$		0			0
$124$	4.00000	−	6.92820i	0.359211	−	0.622171i
$125$		0			0
$126$		0			0
$127$	−17.1464			−1.52150			−0.760750	−	0.649045i	$-0.775169\pi$
$127$	−17.1464			−1.52150			−0.760750	+	0.649045i	$0.775169\pi$
$128$	−9.79796	+	5.65685i	−0.866025	+	0.500000i
$129$		0			0
$130$		0			0
$131$			3.46410i			0.302660i	0.988483	+	0.151330i	$0.0483556\pi$
$131$			3.46410i			0.302660i	−0.988483	+	0.151330i	$0.951644\pi$
$132$		0			0
$133$			8.48528i			0.735767i
$134$	−3.00000	−	5.19615i	−0.259161	−	0.448879i
$135$		0			0
$136$		−	13.8564i		−	1.18818i
$137$	−9.79796			−0.837096			−0.418548	−	0.908195i	$-0.637461\pi$
$137$	−9.79796			−0.837096			−0.418548	+	0.908195i	$0.637461\pi$
$138$		0			0
$139$			10.3923i			0.881464i	0.897639	+	0.440732i	$0.145281\pi$
$139$			10.3923i			0.881464i	−0.897639	+	0.440732i	$0.854719\pi$
$140$		0			0
$141$		0			0
$142$	14.6969	−	8.48528i	1.23334	−	0.712069i
$143$		0			0
$144$		0			0
$145$		0			0
$146$	6.00000	−	3.46410i	0.496564	−	0.286691i
$147$		0			0
$148$	−14.6969	−	8.48528i	−1.20808	−	0.697486i
$149$			17.3205i			1.41895i	0.704730	+	0.709476i	$0.251068\pi$
$149$			17.3205i			1.41895i	−0.704730	+	0.709476i	$0.748932\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	9.79796			0.794719
$153$		0			0
$154$	−6.00000	−	10.3923i	−0.483494	−	0.837436i
$155$		0			0
$156$		0			0
$157$			8.48528i			0.677199i	0.940931	+	0.338600i	$0.109953\pi$
$157$			8.48528i			0.677199i	−0.940931	+	0.338600i	$0.890047\pi$
$158$	4.89898	−	2.82843i	0.389742	−	0.225018i
$159$		0			0
$160$		0			0
$161$	−6.00000			−0.472866
$162$		0			0
$163$		−	21.2132i		−	1.66155i	−0.556611	−	0.830773i	$-0.687899\pi$
$163$		−	21.2132i		−	1.66155i	0.556611	−	0.830773i	$-0.312101\pi$
$164$		0			0
$165$		0			0
$166$	−7.00000	−	12.1244i	−0.543305	−	0.941033i
$167$	12.2474			0.947736			0.473868	−	0.880596i	$-0.342857\pi$
$167$	12.2474			0.947736			0.473868	+	0.880596i	$0.342857\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$		0			0
$172$	−7.34847	−	4.24264i	−0.560316	−	0.323498i
$173$			2.82843i			0.215041i	0.994203	+	0.107521i	$0.0342912\pi$
$173$			2.82843i			0.215041i	−0.994203	+	0.107521i	$0.965709\pi$
$174$		0			0
$175$		0			0
$176$	−12.0000	+	6.92820i	−0.904534	+	0.522233i
$177$		0			0
$178$	7.34847	−	4.24264i	0.550791	−	0.317999i
$179$			3.46410i			0.258919i	0.991585	+	0.129460i	$0.0413242\pi$
$179$			3.46410i			0.258919i	−0.991585	+	0.129460i	$0.958676\pi$
$180$		0			0
$181$			13.8564i			1.02994i	0.857209	+	0.514969i	$0.172197\pi$
$181$			13.8564i			1.02994i	−0.857209	+	0.514969i	$0.827803\pi$
$182$		0			0
$183$		0			0
$184$			6.92820i			0.510754i
$185$		0			0
$186$		0			0
$187$		−	16.9706i		−	1.24101i
$188$	−7.34847	+	12.7279i	−0.535942	+	0.928279i
$189$		0			0
$190$		0			0
$191$	−24.0000			−1.73658			−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000			−1.73658			−0.868290	+	0.496058i	$0.834780\pi$
$192$		0			0
$193$	24.4949			1.76318			0.881591	−	0.472015i	$-0.156473\pi$
$193$	24.4949			1.76318			0.881591	+	0.472015i	$0.156473\pi$
$194$	6.00000	−	3.46410i	0.430775	−	0.248708i
$195$		0			0
$196$	−1.00000	+	1.73205i	−0.0714286	+	0.123718i
$197$			5.65685i			0.403034i	0.979485	+	0.201517i	$0.0645872\pi$
$197$			5.65685i			0.403034i	−0.979485	+	0.201517i	$0.935413\pi$
$198$		0			0
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$		0			0
$201$		0			0
$202$	9.79796	+	16.9706i	0.689382	+	1.19404i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−9.00000	+	5.19615i	−0.627060	+	0.362033i
$207$		0			0
$208$		0			0
$209$	12.0000			0.830057
$210$		0			0
$211$			24.2487i			1.66935i	0.550743	+	0.834675i	$0.314345\pi$
$211$			24.2487i			1.66935i	−0.550743	+	0.834675i	$0.685655\pi$
$212$	9.79796	+	5.65685i	0.672927	+	0.388514i
$213$		0			0
$214$	−1.00000	−	1.73205i	−0.0683586	−	0.118401i
$215$		0			0
$216$		0			0
$217$	9.79796			0.665129
$218$	−2.44949	−	4.24264i	−0.165900	−	0.287348i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−22.0454			−1.47627			−0.738135	−	0.674653i	$-0.764293\pi$
$223$	−22.0454			−1.47627			−0.738135	+	0.674653i	$0.764293\pi$
$224$	−12.0000	−	6.92820i	−0.801784	−	0.462910i
$225$		0			0
$226$		0			0
$227$			1.41421i			0.0938647i	0.998898	+	0.0469323i	$0.0149445\pi$
$227$			1.41421i			0.0938647i	−0.998898	+	0.0469323i	$0.985055\pi$
$228$		0			0
$229$			27.7128i			1.83131i	0.401960	+	0.915657i	$0.368329\pi$
$229$			27.7128i			1.83131i	−0.401960	+	0.915657i	$0.631671\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	14.6969			0.962828			0.481414	−	0.876493i	$-0.340123\pi$
$233$	14.6969			0.962828			0.481414	+	0.876493i	$0.340123\pi$
$234$		0			0
$235$		0			0
$236$	18.0000	+	10.3923i	1.17170	+	0.676481i
$237$		0			0
$238$	14.6969	−	8.48528i	0.952661	−	0.550019i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	4.00000			0.257663			0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000			0.257663			0.128831	+	0.991667i	$0.458877\pi$
$242$	−1.22474	+	0.707107i	−0.0787296	+	0.0454545i
$243$		0			0
$244$	−6.00000	−	3.46410i	−0.384111	−	0.221766i
$245$		0			0
$246$		0			0
$247$		0			0
$248$		−	11.3137i		−	0.718421i
$249$		0			0
$250$		0			0
$251$			10.3923i			0.655956i	0.944685	+	0.327978i	$0.106367\pi$
$251$			10.3923i			0.655956i	−0.944685	+	0.327978i	$0.893633\pi$
$252$		0			0
$253$			8.48528i			0.533465i
$254$	−21.0000	+	12.1244i	−1.31766	+	0.760750i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	9.79796			0.611180			0.305590	−	0.952163i	$-0.401146\pi$
$257$	9.79796			0.611180			0.305590	+	0.952163i	$0.401146\pi$
$258$		0			0
$259$		−	20.7846i		−	1.29149i
$260$		0			0
$261$		0			0
$262$	2.44949	+	4.24264i	0.151330	+	0.262111i
$263$	−7.34847			−0.453126			−0.226563	−	0.973997i	$-0.572749\pi$
$263$	−7.34847			−0.453126			−0.226563	+	0.973997i	$0.572749\pi$
$264$		0			0
$265$		0			0
$266$	6.00000	+	10.3923i	0.367884	+	0.637193i
$267$		0			0
$268$	−7.34847	−	4.24264i	−0.448879	−	0.259161i
$269$			10.3923i			0.633630i	0.948487	+	0.316815i	$0.102613\pi$
$269$			10.3923i			0.633630i	−0.948487	+	0.316815i	$0.897387\pi$
$270$		0			0
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$	−9.79796	−	16.9706i	−0.594089	−	1.02899i
$273$		0			0
$274$	−12.0000	+	6.92820i	−0.724947	+	0.418548i
$275$		0			0
$276$		0			0
$277$			25.4558i			1.52949i	0.644331	+	0.764747i	$0.277136\pi$
$277$			25.4558i			1.52949i	−0.644331	+	0.764747i	$0.722864\pi$
$278$	7.34847	+	12.7279i	0.440732	+	0.763370i
$279$		0			0
$280$		0			0
$281$	12.0000			0.715860			0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$		0			0
$283$			21.2132i			1.26099i	0.776192	+	0.630497i	$0.217149\pi$
$283$			21.2132i			1.26099i	−0.776192	+	0.630497i	$0.782851\pi$
$284$	12.0000	−	20.7846i	0.712069	−	1.23334i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.00000			0.411765
$290$		0			0
$291$		0			0
$292$	4.89898	−	8.48528i	0.286691	−	0.496564i
$293$		−	19.7990i		−	1.15667i	−0.815800	−	0.578335i	$-0.803703\pi$
$293$		−	19.7990i		−	1.15667i	0.815800	−	0.578335i	$-0.196297\pi$
$294$		0			0
$295$		0			0
$296$	−24.0000			−1.39497
$297$		0			0
$298$	12.2474	+	21.2132i	0.709476	+	1.22885i
$299$		0			0
$300$		0			0
$301$		−	10.3923i		−	0.599002i
$302$	−19.5959	+	11.3137i	−1.12762	+	0.651031i
$303$		0			0
$304$	12.0000	−	6.92820i	0.688247	−	0.397360i
$305$		0			0
$306$		0			0
$307$			29.6985i			1.69498i	0.530810	+	0.847491i	$0.321888\pi$
$307$			29.6985i			1.69498i	−0.530810	+	0.847491i	$0.678112\pi$
$308$	−14.6969	−	8.48528i	−0.837436	−	0.483494i
$309$		0			0
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	9.79796			0.553813			0.276907	−	0.960897i	$-0.410691\pi$
$313$	9.79796			0.553813			0.276907	+	0.960897i	$0.410691\pi$
$314$	6.00000	+	10.3923i	0.338600	+	0.586472i
$315$		0			0
$316$	4.00000	−	6.92820i	0.225018	−	0.389742i
$317$			28.2843i			1.58860i	0.607524	+	0.794301i	$0.292163\pi$
$317$			28.2843i			1.58860i	−0.607524	+	0.794301i	$0.707837\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$	−7.34847	+	4.24264i	−0.409514	+	0.236433i
$323$			16.9706i			0.944267i
$324$		0			0
$325$		0			0
$326$	−15.0000	−	25.9808i	−0.830773	−	1.43894i
$327$		0			0
$328$		0			0
$329$	−18.0000			−0.992372
$330$		0			0
$331$		−	31.1769i		−	1.71364i	−0.515617	−	0.856819i	$-0.672437\pi$
$331$		−	31.1769i		−	1.71364i	0.515617	−	0.856819i	$-0.327563\pi$
$332$	−17.1464	−	9.89949i	−0.941033	−	0.543305i
$333$		0			0
$334$	15.0000	−	8.66025i	0.820763	−	0.473868i
$335$		0			0
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	15.9217	−	9.19239i	0.866025	−	0.500000i
$339$		0			0
$340$		0			0
$341$		−	13.8564i		−	0.750366i
$342$		0			0
$343$	−19.5959			−1.05808
$344$	−12.0000			−0.646997
$345$		0			0
$346$	2.00000	+	3.46410i	0.107521	+	0.186231i
$347$		−	15.5563i		−	0.835109i	−0.908652	−	0.417554i	$-0.862887\pi$
$347$		−	15.5563i		−	0.835109i	0.908652	−	0.417554i	$-0.137113\pi$
$348$		0			0
$349$		−	13.8564i		−	0.741716i	−0.928689	−	0.370858i	$-0.879064\pi$
$349$		−	13.8564i		−	0.741716i	0.928689	−	0.370858i	$-0.120936\pi$
$350$		0			0
$351$		0			0
$352$	−9.79796	+	16.9706i	−0.522233	+	0.904534i
$353$	29.3939			1.56448			0.782239	−	0.622978i	$-0.214078\pi$
$353$	29.3939			1.56448			0.782239	+	0.622978i	$0.214078\pi$
$354$		0			0
$355$		0			0
$356$	6.00000	−	10.3923i	0.317999	−	0.550791i
$357$		0			0
$358$	2.44949	+	4.24264i	0.129460	+	0.224231i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$		0			0
$361$	7.00000			0.368421
$362$	9.79796	+	16.9706i	0.514969	+	0.891953i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	12.2474			0.639312			0.319656	−	0.947534i	$-0.396433\pi$
$367$	12.2474			0.639312			0.319656	+	0.947534i	$0.396433\pi$
$368$	4.89898	+	8.48528i	0.255377	+	0.442326i
$369$		0			0
$370$		0			0
$371$			13.8564i			0.719389i
$372$		0			0
$373$			8.48528i			0.439351i	0.975573	+	0.219676i	$0.0704999\pi$
$373$			8.48528i			0.439351i	−0.975573	+	0.219676i	$0.929500\pi$
$374$	−12.0000	−	20.7846i	−0.620505	−	1.07475i
$375$		0			0
$376$			20.7846i			1.07188i
$377$		0			0
$378$		0			0
$379$			24.2487i			1.24557i	0.782392	+	0.622786i	$0.213999\pi$
$379$			24.2487i			1.24557i	−0.782392	+	0.622786i	$0.786001\pi$
$380$		0			0
$381$		0			0
$382$	−29.3939	+	16.9706i	−1.50392	+	0.868290i
$383$	−26.9444			−1.37679			−0.688397	−	0.725334i	$-0.741685\pi$
$383$	−26.9444			−1.37679			−0.688397	+	0.725334i	$0.741685\pi$
$384$		0			0
$385$		0			0
$386$	30.0000	−	17.3205i	1.52696	−	0.881591i
$387$		0			0
$388$	4.89898	−	8.48528i	0.248708	−	0.430775i
$389$			3.46410i			0.175637i	0.996136	+	0.0878185i	$0.0279895\pi$
$389$			3.46410i			0.175637i	−0.996136	+	0.0878185i	$0.972010\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$			2.82843i			0.142857i
$393$		0			0
$394$	4.00000	+	6.92820i	0.201517	+	0.349038i
$395$		0			0
$396$		0			0
$397$		−	16.9706i		−	0.851728i	−0.904787	−	0.425864i	$-0.859970\pi$
$397$		−	16.9706i		−	0.851728i	0.904787	−	0.425864i	$-0.140030\pi$
$398$	−4.89898	+	2.82843i	−0.245564	+	0.141776i
$399$		0			0
$400$		0			0
$401$	18.0000			0.898877			0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000			0.898877			0.449439	+	0.893311i	$0.351624\pi$
$402$		0			0
$403$		0			0
$404$	24.0000	+	13.8564i	1.19404	+	0.689382i
$405$		0			0
$406$		0			0
$407$	−29.3939			−1.45700
$408$		0			0
$409$	−32.0000			−1.58230			−0.791149	−	0.611623i	$-0.790517\pi$
$409$	−32.0000			−1.58230			−0.791149	+	0.611623i	$0.790517\pi$
$410$		0			0
$411$		0			0
$412$	−7.34847	+	12.7279i	−0.362033	+	0.627060i
$413$			25.4558i			1.25260i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$	14.6969	−	8.48528i	0.718851	−	0.415029i
$419$		−	10.3923i		−	0.507697i	−0.967244	−	0.253849i	$-0.918303\pi$
$419$		−	10.3923i		−	0.507697i	0.967244	−	0.253849i	$-0.0816965\pi$
$420$		0			0
$421$		−	24.2487i		−	1.18181i	−0.806741	−	0.590905i	$-0.798771\pi$
$421$		−	24.2487i		−	1.18181i	0.806741	−	0.590905i	$-0.201229\pi$
$422$	17.1464	+	29.6985i	0.834675	+	1.44570i
$423$		0			0
$424$	16.0000			0.777029
$425$		0			0
$426$		0			0
$427$		−	8.48528i		−	0.410632i
$428$	−2.44949	−	1.41421i	−0.118401	−	0.0683586i
$429$		0			0
$430$		0			0
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$		0			0
$433$	−4.89898			−0.235430			−0.117715	−	0.993047i	$-0.537557\pi$
$433$	−4.89898			−0.235430			−0.117715	+	0.993047i	$0.537557\pi$
$434$	12.0000	−	6.92820i	0.576018	−	0.332564i
$435$		0			0
$436$	−6.00000	−	3.46410i	−0.287348	−	0.165900i
$437$		−	8.48528i		−	0.405906i
$438$		0			0
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			1.41421i			0.0671913i	0.999436	+	0.0335957i	$0.0106958\pi$
$443$			1.41421i			0.0671913i	−0.999436	+	0.0335957i	$0.989304\pi$
$444$		0			0
$445$		0			0
$446$	−27.0000	+	15.5885i	−1.27849	+	0.738135i
$447$		0			0
$448$	−19.5959			−0.925820
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$	1.00000	+	1.73205i	0.0469323	+	0.0812892i
$455$		0			0
$456$		0			0
$457$	−19.5959			−0.916658			−0.458329	−	0.888783i	$-0.651552\pi$
$457$	−19.5959			−0.916658			−0.458329	+	0.888783i	$0.651552\pi$
$458$	19.5959	+	33.9411i	0.915657	+	1.58596i
$459$		0			0
$460$		0			0
$461$		−	13.8564i		−	0.645357i	−0.946509	−	0.322679i	$-0.895417\pi$
$461$		−	13.8564i		−	0.645357i	0.946509	−	0.322679i	$-0.104583\pi$
$462$		0			0
$463$	−17.1464			−0.796862			−0.398431	−	0.917198i	$-0.630445\pi$
$463$	−17.1464			−0.796862			−0.398431	+	0.917198i	$0.630445\pi$
$464$		0			0
$465$		0			0
$466$	18.0000	−	10.3923i	0.833834	−	0.481414i
$467$			7.07107i			0.327210i	0.986526	+	0.163605i	$0.0523123\pi$
$467$			7.07107i			0.327210i	−0.986526	+	0.163605i	$0.947688\pi$
$468$		0			0
$469$		−	10.3923i		−	0.479872i
$470$		0			0
$471$		0			0
$472$	29.3939			1.35296
$473$	−14.6969			−0.675766
$474$		0			0
$475$		0			0
$476$	12.0000	−	20.7846i	0.550019	−	0.952661i
$477$		0			0
$478$	−14.6969	+	8.48528i	−0.672222	+	0.388108i
$479$	−24.0000			−1.09659			−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000			−1.09659			−0.548294	+	0.836286i	$0.684723\pi$
$480$		0			0
$481$		0			0
$482$	4.89898	−	2.82843i	0.223142	−	0.128831i
$483$		0			0
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$		0			0
$486$		0			0
$487$	−7.34847			−0.332991			−0.166495	−	0.986042i	$-0.553245\pi$
$487$	−7.34847			−0.332991			−0.166495	+	0.986042i	$0.553245\pi$
$488$	−9.79796			−0.443533
$489$		0			0
$490$		0			0
$491$		−	24.2487i		−	1.09433i	−0.837025	−	0.547165i	$-0.815707\pi$
$491$		−	24.2487i		−	1.09433i	0.837025	−	0.547165i	$-0.184293\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−8.00000	−	13.8564i	−0.359211	−	0.622171i
$497$	29.3939			1.31850
$498$		0			0
$499$		−	17.3205i		−	0.775372i	−0.921791	−	0.387686i	$-0.873274\pi$
$499$		−	17.3205i		−	0.775372i	0.921791	−	0.387686i	$-0.126726\pi$
$500$		0			0
$501$		0			0
$502$	7.34847	+	12.7279i	0.327978	+	0.568075i
$503$	−12.2474			−0.546087			−0.273043	−	0.962002i	$-0.588030\pi$
$503$	−12.2474			−0.546087			−0.273043	+	0.962002i	$0.588030\pi$
$504$		0			0
$505$		0			0
$506$	6.00000	+	10.3923i	0.266733	+	0.461994i
$507$		0			0
$508$	−17.1464	+	29.6985i	−0.760750	+	1.31766i
$509$		−	27.7128i		−	1.22835i	−0.789170	−	0.614174i	$-0.789489\pi$
$509$		−	27.7128i		−	1.22835i	0.789170	−	0.614174i	$-0.210511\pi$
$510$		0			0
$511$	12.0000			0.530849
$512$			22.6274i			1.00000i
$513$		0			0
$514$	12.0000	−	6.92820i	0.529297	−	0.305590i
$515$		0			0
$516$		0			0
$517$			25.4558i			1.11955i
$518$	−14.6969	−	25.4558i	−0.645746	−	1.11847i
$519$		0			0
$520$		0			0
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$		0			0
$523$		−	12.7279i		−	0.556553i	−0.960501	−	0.278277i	$-0.910237\pi$
$523$		−	12.7279i		−	0.556553i	0.960501	−	0.278277i	$-0.0897632\pi$
$524$	6.00000	+	3.46410i	0.262111	+	0.151330i
$525$		0			0
$526$	−9.00000	+	5.19615i	−0.392419	+	0.226563i
$527$	19.5959			0.853612
$528$		0			0
$529$	−17.0000			−0.739130
$530$		0			0
$531$		0			0
$532$	14.6969	+	8.48528i	0.637193	+	0.367884i
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−12.0000			−0.518321
$537$		0			0
$538$	7.34847	+	12.7279i	0.316815	+	0.548740i
$539$			3.46410i			0.149209i
$540$		0			0
$541$			41.5692i			1.78720i	0.448864	+	0.893600i	$0.351829\pi$
$541$			41.5692i			1.78720i	−0.448864	+	0.893600i	$0.648171\pi$
$542$	24.4949	−	14.1421i	1.05215	−	0.607457i
$543$		0			0
$544$	−24.0000	−	13.8564i	−1.02899	−	0.594089i
$545$		0			0
$546$		0			0
$547$			4.24264i			0.181402i	0.995878	+	0.0907011i	$0.0289108\pi$
$547$			4.24264i			0.181402i	−0.995878	+	0.0907011i	$0.971089\pi$
$548$	−9.79796	+	16.9706i	−0.418548	+	0.724947i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	9.79796			0.416652
$554$	18.0000	+	31.1769i	0.764747	+	1.32458i
$555$		0			0
$556$	18.0000	+	10.3923i	0.763370	+	0.440732i
$557$			14.1421i			0.599222i	0.954062	+	0.299611i	$0.0968568\pi$
$557$			14.1421i			0.599222i	−0.954062	+	0.299611i	$0.903143\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	14.6969	−	8.48528i	0.619953	−	0.357930i
$563$		−	41.0122i		−	1.72846i	−0.503099	−	0.864229i	$-0.667807\pi$
$563$		−	41.0122i		−	1.72846i	0.503099	−	0.864229i	$-0.332193\pi$
$564$		0			0
$565$		0			0
$566$	15.0000	+	25.9808i	0.630497	+	1.09205i
$567$		0			0
$568$		−	33.9411i		−	1.42414i
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$		0			0
$571$			3.46410i			0.144968i	0.997370	+	0.0724841i	$0.0230926\pi$
$571$			3.46410i			0.144968i	−0.997370	+	0.0724841i	$0.976907\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	29.3939			1.22368			0.611842	−	0.790980i	$-0.290429\pi$
$577$	29.3939			1.22368			0.611842	+	0.790980i	$0.290429\pi$
$578$	8.57321	−	4.94975i	0.356599	−	0.205882i
$579$		0			0
$580$		0			0
$581$		−	24.2487i		−	1.00601i
$582$		0			0
$583$	19.5959			0.811580
$584$		−	13.8564i		−	0.573382i
$585$		0			0
$586$	−14.0000	−	24.2487i	−0.578335	−	1.00171i
$587$		−	9.89949i		−	0.408596i	−0.978909	−	0.204298i	$-0.934509\pi$
$587$		−	9.89949i		−	0.408596i	0.978909	−	0.204298i	$-0.0654911\pi$
$588$		0			0
$589$			13.8564i			0.570943i
$590$		0			0
$591$		0			0
$592$	−29.3939	+	16.9706i	−1.20808	+	0.697486i
$593$	−9.79796			−0.402354			−0.201177	−	0.979555i	$-0.564477\pi$
$593$	−9.79796			−0.402354			−0.201177	+	0.979555i	$0.564477\pi$
$594$		0			0
$595$		0			0
$596$	30.0000	+	17.3205i	1.22885	+	0.709476i
$597$		0			0
$598$		0			0
$599$	12.0000			0.490307			0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000			0.490307			0.245153	+	0.969484i	$0.421162\pi$
$600$		0			0
$601$	−28.0000			−1.14214			−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000			−1.14214			−0.571072	+	0.820900i	$0.693472\pi$
$602$	−7.34847	−	12.7279i	−0.299501	−	0.518751i
$603$		0			0
$604$	−16.0000	+	27.7128i	−0.651031	+	1.12762i
$605$		0			0
$606$		0			0
$607$	7.34847			0.298265			0.149133	−	0.988817i	$-0.452352\pi$
$607$	7.34847			0.298265			0.149133	+	0.988817i	$0.452352\pi$
$608$	9.79796	−	16.9706i	0.397360	−	0.688247i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$			33.9411i			1.37087i	0.728134	+	0.685435i	$0.240388\pi$
$613$			33.9411i			1.37087i	−0.728134	+	0.685435i	$0.759612\pi$
$614$	21.0000	+	36.3731i	0.847491	+	1.46790i
$615$		0			0
$616$	−24.0000			−0.966988
$617$	−34.2929			−1.38058			−0.690289	−	0.723534i	$-0.742517\pi$
$617$	−34.2929			−1.38058			−0.690289	+	0.723534i	$0.742517\pi$
$618$		0			0
$619$		−	10.3923i		−	0.417702i	−0.977947	−	0.208851i	$-0.933028\pi$
$619$		−	10.3923i		−	0.417702i	0.977947	−	0.208851i	$-0.0669724\pi$
$620$		0			0
$621$		0			0
$622$	29.3939	−	16.9706i	1.17859	−	0.680458i
$623$	14.6969			0.588820
$624$		0			0
$625$		0			0
$626$	12.0000	−	6.92820i	0.479616	−	0.276907i
$627$		0			0
$628$	14.6969	+	8.48528i	0.586472	+	0.338600i
$629$		−	41.5692i		−	1.65747i
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$		−	11.3137i		−	0.450035i
$633$		0			0
$634$	20.0000	+	34.6410i	0.794301	+	1.37577i
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−12.0000			−0.473972			−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000			−0.473972			−0.236986	+	0.971513i	$0.576159\pi$
$642$		0			0
$643$		−	29.6985i		−	1.17119i	−0.810602	−	0.585597i	$-0.800860\pi$
$643$		−	29.6985i		−	1.17119i	0.810602	−	0.585597i	$-0.199140\pi$
$644$	−6.00000	+	10.3923i	−0.236433	+	0.409514i
$645$		0			0
$646$	12.0000	+	20.7846i	0.472134	+	0.817760i
$647$	−12.2474			−0.481497			−0.240748	−	0.970588i	$-0.577393\pi$
$647$	−12.2474			−0.481497			−0.240748	+	0.970588i	$0.577393\pi$
$648$		0			0
$649$	36.0000			1.41312
$650$		0			0
$651$		0			0
$652$	−36.7423	−	21.2132i	−1.43894	−	0.830773i
$653$			11.3137i			0.442740i	0.975190	+	0.221370i	$0.0710528\pi$
$653$			11.3137i			0.442740i	−0.975190	+	0.221370i	$0.928947\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	−22.0454	+	12.7279i	−0.859419	+	0.496186i
$659$		−	24.2487i		−	0.944596i	−0.881439	−	0.472298i	$-0.843425\pi$
$659$		−	24.2487i		−	0.944596i	0.881439	−	0.472298i	$-0.156575\pi$
$660$		0			0
$661$			10.3923i			0.404214i	0.979363	+	0.202107i	$0.0647788\pi$
$661$			10.3923i			0.404214i	−0.979363	+	0.202107i	$0.935221\pi$
$662$	−22.0454	−	38.1838i	−0.856819	−	1.48405i
$663$		0			0
$664$	−28.0000			−1.08661
$665$		0			0
$666$		0			0
$667$		0			0
$668$	12.2474	−	21.2132i	0.473868	−	0.820763i
$669$		0			0
$670$		0			0
$671$	−12.0000			−0.463255
$672$		0			0
$673$	34.2929			1.32189			0.660946	−	0.750433i	$-0.270155\pi$
$673$	34.2929			1.32189			0.660946	+	0.750433i	$0.270155\pi$
$674$		0			0
$675$		0			0
$676$	13.0000	−	22.5167i	0.500000	−	0.866025i
$677$		−	22.6274i		−	0.869642i	−0.900517	−	0.434821i	$-0.856812\pi$
$677$		−	22.6274i		−	0.869642i	0.900517	−	0.434821i	$-0.143188\pi$
$678$		0			0
$679$	12.0000			0.460518
$680$		0			0
$681$		0			0
$682$	−9.79796	−	16.9706i	−0.375183	−	0.649836i
$683$			15.5563i			0.595247i	0.954683	+	0.297624i	$0.0961940\pi$
$683$			15.5563i			0.595247i	−0.954683	+	0.297624i	$0.903806\pi$
$684$		0			0
$685$		0			0
$686$	−24.0000	+	13.8564i	−0.916324	+	0.529040i
$687$		0			0
$688$	−14.6969	+	8.48528i	−0.560316	+	0.323498i
$689$		0			0
$690$		0			0
$691$		−	3.46410i		−	0.131781i	−0.997827	−	0.0658903i	$-0.979011\pi$
$691$		−	3.46410i		−	0.131781i	0.997827	−	0.0658903i	$-0.0209887\pi$
$692$	4.89898	+	2.82843i	0.186231	+	0.107521i
$693$		0			0
$694$	−11.0000	−	19.0526i	−0.417554	−	0.723225i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−9.79796	−	16.9706i	−0.370858	−	0.642345i
$699$		0			0
$700$		0			0
$701$			24.2487i			0.915861i	0.888988	+	0.457931i	$0.151409\pi$
$701$			24.2487i			0.915861i	−0.888988	+	0.457931i	$0.848591\pi$
$702$		0			0
$703$	29.3939			1.10861
$704$			27.7128i			1.04447i
$705$		0			0
$706$	36.0000	−	20.7846i	1.35488	−	0.782239i
$707$			33.9411i			1.27649i
$708$		0			0
$709$		−	41.5692i		−	1.56116i	−0.625053	−	0.780582i	$-0.714923\pi$
$709$		−	41.5692i		−	1.56116i	0.625053	−	0.780582i	$-0.285077\pi$
$710$		0			0
$711$		0			0
$712$		−	16.9706i		−	0.635999i
$713$	−9.79796			−0.366936
$714$		0			0
$715$		0			0
$716$	6.00000	+	3.46410i	0.224231	+	0.129460i
$717$		0			0
$718$	29.3939	−	16.9706i	1.09697	−	0.633336i
$719$	−36.0000			−1.34257			−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000			−1.34257			−0.671287	+	0.741198i	$0.734258\pi$
$720$		0			0
$721$	−18.0000			−0.670355
$722$	8.57321	−	4.94975i	0.319062	−	0.184211i
$723$		0			0
$724$	24.0000	+	13.8564i	0.891953	+	0.514969i
$725$		0			0
$726$		0			0
$727$	−46.5403			−1.72608			−0.863042	−	0.505132i	$-0.831444\pi$
$727$	−46.5403			−1.72608			−0.863042	+	0.505132i	$0.831444\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		−	20.7846i		−	0.768747i
$732$		0			0
$733$		−	42.4264i		−	1.56706i	−0.621357	−	0.783528i	$-0.713418\pi$
$733$		−	42.4264i		−	1.56706i	0.621357	−	0.783528i	$-0.286582\pi$
$734$	15.0000	−	8.66025i	0.553660	−	0.319656i
$735$		0			0
$736$	12.0000	+	6.92820i	0.442326	+	0.255377i
$737$	−14.6969			−0.541369
$738$		0			0
$739$		−	3.46410i		−	0.127429i	−0.997968	−	0.0637145i	$-0.979705\pi$
$739$		−	3.46410i		−	0.127429i	0.997968	−	0.0637145i	$-0.0202947\pi$
$740$		0			0
$741$		0			0
$742$	9.79796	+	16.9706i	0.359694	+	0.623009i
$743$	51.4393			1.88712			0.943562	−	0.331195i	$-0.107452\pi$
$743$	51.4393			1.88712			0.943562	+	0.331195i	$0.107452\pi$
$744$		0			0
$745$		0			0
$746$	6.00000	+	10.3923i	0.219676	+	0.380489i
$747$		0			0
$748$	−29.3939	−	16.9706i	−1.07475	−	0.620505i
$749$		−	3.46410i		−	0.126576i
$750$		0			0
$751$	−32.0000			−1.16770			−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000			−1.16770			−0.583848	+	0.811863i	$0.698454\pi$
$752$	14.6969	+	25.4558i	0.535942	+	0.928279i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	25.4558i		−	0.925208i	−0.886565	−	0.462604i	$-0.846915\pi$
$757$		−	25.4558i		−	0.925208i	0.886565	−	0.462604i	$-0.153085\pi$
$758$	17.1464	+	29.6985i	0.622786	+	1.07870i
$759$		0			0
$760$		0			0
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$		0			0
$763$		−	8.48528i		−	0.307188i
$764$	−24.0000	+	41.5692i	−0.868290	+	1.50392i
$765$		0			0
$766$	−33.0000	+	19.0526i	−1.19234	+	0.688397i
$767$		0			0
$768$		0			0
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$		0			0
$772$	24.4949	−	42.4264i	0.881591	−	1.52696i
$773$			28.2843i			1.01731i	0.860969	+	0.508657i	$0.169858\pi$
$773$			28.2843i			1.01731i	−0.860969	+	0.508657i	$0.830142\pi$
$774$		0			0
$775$		0			0
$776$		−	13.8564i		−	0.497416i
$777$		0			0
$778$	2.44949	+	4.24264i	0.0878185	+	0.152106i
$779$		0			0
$780$		0			0
$781$		−	41.5692i		−	1.48746i
$782$	−14.6969	+	8.48528i	−0.525561	+	0.303433i
$783$		0			0
$784$	2.00000	+	3.46410i	0.0714286	+	0.123718i
$785$		0			0
$786$		0			0
$787$		−	21.2132i		−	0.756169i	−0.925771	−	0.378085i	$-0.876583\pi$
$787$		−	21.2132i		−	0.756169i	0.925771	−	0.378085i	$-0.123417\pi$
$788$	9.79796	+	5.65685i	0.349038	+	0.201517i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−12.0000	−	20.7846i	−0.425864	−	0.737618i
$795$		0			0
$796$	−4.00000	+	6.92820i	−0.141776	+	0.245564i
$797$		−	39.5980i		−	1.40263i	−0.712850	−	0.701316i	$-0.752596\pi$
$797$		−	39.5980i		−	1.40263i	0.712850	−	0.701316i	$-0.247404\pi$
$798$		0			0
$799$	−36.0000			−1.27359
$800$		0			0
$801$		0			0
$802$	22.0454	−	12.7279i	0.778450	−	0.449439i
$803$		−	16.9706i		−	0.598878i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	39.1918			1.37876
$809$	−30.0000			−1.05474			−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000			−1.05474			−0.527372	+	0.849635i	$0.676823\pi$
$810$		0			0
$811$		−	10.3923i		−	0.364923i	−0.983213	−	0.182462i	$-0.941593\pi$
$811$		−	10.3923i		−	0.364923i	0.983213	−	0.182462i	$-0.0584065\pi$
$812$		0			0
$813$		0			0
$814$	−36.0000	+	20.7846i	−1.26180	+	0.728500i
$815$		0			0
$816$		0			0
$817$	14.6969			0.514181
$818$	−39.1918	+	22.6274i	−1.37031	+	0.791149i
$819$		0			0
$820$		0			0
$821$			31.1769i			1.08808i	0.839059	+	0.544041i	$0.183106\pi$
$821$			31.1769i			1.08808i	−0.839059	+	0.544041i	$0.816894\pi$
$822$		0			0
$823$	−26.9444			−0.939222			−0.469611	−	0.882873i	$-0.655606\pi$
$823$	−26.9444			−0.939222			−0.469611	+	0.882873i	$0.655606\pi$
$824$			20.7846i			0.724066i
$825$		0			0
$826$	18.0000	+	31.1769i	0.626300	+	1.08478i
$827$			35.3553i			1.22943i	0.788751	+	0.614713i	$0.210728\pi$
$827$			35.3553i			1.22943i	−0.788751	+	0.614713i	$0.789272\pi$
$828$		0			0
$829$		−	10.3923i		−	0.360940i	−0.983581	−	0.180470i	$-0.942238\pi$
$829$		−	10.3923i		−	0.360940i	0.983581	−	0.180470i	$-0.0577618\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.89898			−0.169740
$834$		0			0
$835$		0			0
$836$	12.0000	−	20.7846i	0.415029	−	0.718851i
$837$		0			0
$838$	−7.34847	−	12.7279i	−0.253849	−	0.439679i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$	−17.1464	−	29.6985i	−0.590905	−	1.02348i
$843$		0			0
$844$	42.0000	+	24.2487i	1.44570	+	0.834675i
$845$		0			0
$846$		0			0
$847$	−2.44949			−0.0841655
$848$	19.5959	−	11.3137i	0.672927	−	0.388514i
$849$		0			0
$850$		0			0
$851$			20.7846i			0.712487i
$852$		0			0
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$	−6.00000	−	10.3923i	−0.205316	−	0.355617i
$855$		0			0
$856$	−4.00000			−0.136717
$857$	39.1918			1.33877			0.669384	−	0.742917i	$-0.266558\pi$
$857$	39.1918			1.33877			0.669384	+	0.742917i	$0.266558\pi$
$858$		0			0
$859$			3.46410i			0.118194i	0.998252	+	0.0590968i	$0.0188221\pi$
$859$			3.46410i			0.118194i	−0.998252	+	0.0590968i	$0.981178\pi$
$860$		0			0
$861$		0			0
$862$	−14.6969	+	8.48528i	−0.500580	+	0.289010i
$863$	−2.44949			−0.0833816			−0.0416908	−	0.999131i	$-0.513274\pi$
$863$	−2.44949			−0.0833816			−0.0416908	+	0.999131i	$0.513274\pi$
$864$		0			0
$865$		0			0
$866$	−6.00000	+	3.46410i	−0.203888	+	0.117715i
$867$		0			0
$868$	9.79796	−	16.9706i	0.332564	−	0.576018i
$869$		−	13.8564i		−	0.470046i
$870$		0			0
$871$		0			0
$872$	−9.79796			−0.331801
$873$		0			0
$874$	−6.00000	−	10.3923i	−0.202953	−	0.351525i
$875$		0			0
$876$		0			0
$877$		−	8.48528i		−	0.286528i	−0.989685	−	0.143264i	$-0.954240\pi$
$877$		−	8.48528i		−	0.286528i	0.989685	−	0.143264i	$-0.0457597\pi$
$878$	9.79796	−	5.65685i	0.330665	−	0.190910i
$879$		0			0
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$		−	4.24264i		−	0.142776i	−0.997449	−	0.0713881i	$-0.977257\pi$
$883$		−	4.24264i		−	0.142776i	0.997449	−	0.0713881i	$-0.0227429\pi$
$884$		0			0
$885$		0			0
$886$	1.00000	+	1.73205i	0.0335957	+	0.0581894i
$887$	26.9444			0.904704			0.452352	−	0.891839i	$-0.350585\pi$
$887$	26.9444			0.904704			0.452352	+	0.891839i	$0.350585\pi$
$888$		0			0
$889$	−42.0000			−1.40863
$890$		0			0
$891$		0			0
$892$	−22.0454	+	38.1838i	−0.738135	+	1.27849i
$893$		−	25.4558i		−	0.851847i
$894$		0			0
$895$		0			0
$896$	−24.0000	+	13.8564i	−0.801784	+	0.462910i
$897$		0			0
$898$	−14.6969	+	8.48528i	−0.490443	+	0.283158i
$899$		0			0
$900$		0			0
$901$			27.7128i			0.923248i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	4.24264i		−	0.140875i	−0.997516	−	0.0704373i	$-0.977561\pi$
$907$		−	4.24264i		−	0.140875i	0.997516	−	0.0704373i	$-0.0224395\pi$
$908$	2.44949	+	1.41421i	0.0812892	+	0.0469323i
$909$		0			0
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$	−34.2929			−1.13493
$914$	−24.0000	+	13.8564i	−0.793849	+	0.458329i
$915$		0			0
$916$	48.0000	+	27.7128i	1.58596	+	0.915657i
$917$			8.48528i			0.280209i
$918$		0			0
$919$	4.00000			0.131948			0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000			0.131948			0.0659739	+	0.997821i	$0.478985\pi$
$920$		0			0
$921$		0			0
$922$	−9.79796	−	16.9706i	−0.322679	−	0.558896i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−21.0000	+	12.1244i	−0.690103	+	0.398431i
$927$		0			0
$928$		0			0
$929$	−36.0000			−1.18112			−0.590561	−	0.806993i	$-0.701093\pi$
$929$	−36.0000			−1.18112			−0.590561	+	0.806993i	$0.701093\pi$
$930$		0			0
$931$		−	3.46410i		−	0.113531i
$932$	14.6969	−	25.4558i	0.481414	−	0.833834i
$933$		0			0
$934$	5.00000	+	8.66025i	0.163605	+	0.283372i
$935$		0			0
$936$		0			0
$937$	4.89898			0.160043			0.0800213	−	0.996793i	$-0.474501\pi$
$937$	4.89898			0.160043			0.0800213	+	0.996793i	$0.474501\pi$
$938$	−7.34847	−	12.7279i	−0.239936	−	0.415581i
$939$		0			0
$940$		0			0
$941$			13.8564i			0.451706i	0.974161	+	0.225853i	$0.0725169\pi$
$941$			13.8564i			0.451706i	−0.974161	+	0.225853i	$0.927483\pi$
$942$		0			0
$943$		0			0
$944$	36.0000	−	20.7846i	1.17170	−	0.676481i
$945$		0			0
$946$	−18.0000	+	10.3923i	−0.585230	+	0.337883i
$947$		−	41.0122i		−	1.33272i	−0.745631	−	0.666359i	$-0.767852\pi$
$947$		−	41.0122i		−	1.33272i	0.745631	−	0.666359i	$-0.232148\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		−	33.9411i		−	1.10004i
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$		0			0
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$		0			0
$958$	−29.3939	+	16.9706i	−0.949673	+	0.548294i
$959$	−24.0000			−0.775000
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$		0			0
$964$	4.00000	−	6.92820i	0.128831	−	0.223142i
$965$		0			0
$966$		0			0
$967$	17.1464			0.551392			0.275696	−	0.961245i	$-0.411092\pi$
$967$	17.1464			0.551392			0.275696	+	0.961245i	$0.411092\pi$
$968$			2.82843i			0.0909091i
$969$		0			0
$970$		0			0
$971$			3.46410i			0.111168i	0.998454	+	0.0555842i	$0.0177021\pi$
$971$			3.46410i			0.111168i	−0.998454	+	0.0555842i	$0.982298\pi$
$972$		0			0
$973$			25.4558i			0.816077i
$974$	−9.00000	+	5.19615i	−0.288379	+	0.166495i
$975$		0			0
$976$	−12.0000	+	6.92820i	−0.384111	+	0.221766i
$977$	−44.0908			−1.41059			−0.705295	−	0.708914i	$-0.749185\pi$
$977$	−44.0908			−1.41059			−0.705295	+	0.708914i	$0.749185\pi$
$978$		0			0
$979$		−	20.7846i		−	0.664279i
$980$		0			0
$981$		0			0
$982$	−17.1464	−	29.6985i	−0.547165	−	0.947717i
$983$	−56.3383			−1.79691			−0.898456	−	0.439064i	$-0.855310\pi$
$983$	−56.3383			−1.79691			−0.898456	+	0.439064i	$0.855310\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$			10.3923i			0.330456i
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	−19.5959	−	11.3137i	−0.622171	−	0.359211i
$993$		0			0
$994$	36.0000	−	20.7846i	1.14185	−	0.659248i
$995$		0			0
$996$		0			0
$997$		−	50.9117i		−	1.61239i	−0.591650	−	0.806195i	$-0.701523\pi$
$997$		−	50.9117i		−	1.61239i	0.591650	−	0.806195i	$-0.298477\pi$
$998$	−12.2474	−	21.2132i	−0.387686	−	0.671492i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.k.m.901.3		4
3.2	odd	2		200.2.d.e.101.2		4
4.3	odd	2		7200.2.k.l.3601.2		4
5.2	odd	4		360.2.d.b.109.4		4
5.3	odd	4		360.2.d.b.109.1		4
5.4	even	2	inner	1800.2.k.m.901.2		4
8.3	odd	2		7200.2.k.l.3601.1		4
8.5	even	2	inner	1800.2.k.m.901.4		4
12.11	even	2		800.2.d.f.401.1		4
15.2	even	4		40.2.f.a.29.1	✓	4
15.8	even	4		40.2.f.a.29.4	yes	4
15.14	odd	2		200.2.d.e.101.3		4
20.3	even	4		1440.2.d.c.1009.2		4
20.7	even	4		1440.2.d.c.1009.4		4
20.19	odd	2		7200.2.k.l.3601.4		4
24.5	odd	2		200.2.d.e.101.1		4
24.11	even	2		800.2.d.f.401.3		4
40.3	even	4		1440.2.d.c.1009.3		4
40.13	odd	4		360.2.d.b.109.3		4
40.19	odd	2		7200.2.k.l.3601.3		4
40.27	even	4		1440.2.d.c.1009.1		4
40.29	even	2	inner	1800.2.k.m.901.1		4
40.37	odd	4		360.2.d.b.109.2		4
48.5	odd	4		6400.2.a.co.1.3		4
48.11	even	4		6400.2.a.cm.1.2		4
48.29	odd	4		6400.2.a.co.1.1		4
48.35	even	4		6400.2.a.cm.1.4		4
60.23	odd	4		160.2.f.a.49.3		4
60.47	odd	4		160.2.f.a.49.1		4
60.59	even	2		800.2.d.f.401.4		4
120.29	odd	2		200.2.d.e.101.4		4
120.53	even	4		40.2.f.a.29.2	yes	4
120.59	even	2		800.2.d.f.401.2		4
120.77	even	4		40.2.f.a.29.3	yes	4
120.83	odd	4		160.2.f.a.49.2		4
120.107	odd	4		160.2.f.a.49.4		4
240.29	odd	4		6400.2.a.co.1.4		4
240.53	even	4		1280.2.c.i.769.4		4
240.59	even	4		6400.2.a.cm.1.3		4
240.77	even	4		1280.2.c.i.769.3		4
240.83	odd	4		1280.2.c.k.769.3		4
240.107	odd	4		1280.2.c.k.769.4		4
240.149	odd	4		6400.2.a.co.1.2		4
240.173	even	4		1280.2.c.i.769.1		4
240.179	even	4		6400.2.a.cm.1.1		4
240.197	even	4		1280.2.c.i.769.2		4
240.203	odd	4		1280.2.c.k.769.2		4
240.227	odd	4		1280.2.c.k.769.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.f.a.29.1	✓	4	15.2	even	4
40.2.f.a.29.2	yes	4	120.53	even	4
40.2.f.a.29.3	yes	4	120.77	even	4
40.2.f.a.29.4	yes	4	15.8	even	4
160.2.f.a.49.1		4	60.47	odd	4
160.2.f.a.49.2		4	120.83	odd	4
160.2.f.a.49.3		4	60.23	odd	4
160.2.f.a.49.4		4	120.107	odd	4
200.2.d.e.101.1		4	24.5	odd	2
200.2.d.e.101.2		4	3.2	odd	2
200.2.d.e.101.3		4	15.14	odd	2
200.2.d.e.101.4		4	120.29	odd	2
360.2.d.b.109.1		4	5.3	odd	4
360.2.d.b.109.2		4	40.37	odd	4
360.2.d.b.109.3		4	40.13	odd	4
360.2.d.b.109.4		4	5.2	odd	4
800.2.d.f.401.1		4	12.11	even	2
800.2.d.f.401.2		4	120.59	even	2
800.2.d.f.401.3		4	24.11	even	2
800.2.d.f.401.4		4	60.59	even	2
1280.2.c.i.769.1		4	240.173	even	4
1280.2.c.i.769.2		4	240.197	even	4
1280.2.c.i.769.3		4	240.77	even	4
1280.2.c.i.769.4		4	240.53	even	4
1280.2.c.k.769.1		4	240.227	odd	4
1280.2.c.k.769.2		4	240.203	odd	4
1280.2.c.k.769.3		4	240.83	odd	4
1280.2.c.k.769.4		4	240.107	odd	4
1440.2.d.c.1009.1		4	40.27	even	4
1440.2.d.c.1009.2		4	20.3	even	4
1440.2.d.c.1009.3		4	40.3	even	4
1440.2.d.c.1009.4		4	20.7	even	4
1800.2.k.m.901.1		4	40.29	even	2	inner
1800.2.k.m.901.2		4	5.4	even	2	inner
1800.2.k.m.901.3		4	1.1	even	1	trivial
1800.2.k.m.901.4		4	8.5	even	2	inner
6400.2.a.cm.1.1		4	240.179	even	4
6400.2.a.cm.1.2		4	48.11	even	4
6400.2.a.cm.1.3		4	240.59	even	4
6400.2.a.cm.1.4		4	48.35	even	4
6400.2.a.co.1.1		4	48.29	odd	4
6400.2.a.co.1.2		4	240.149	odd	4
6400.2.a.co.1.3		4	48.5	odd	4
6400.2.a.co.1.4		4	240.29	odd	4
7200.2.k.l.3601.1		4	8.3	odd	2
7200.2.k.l.3601.2		4	4.3	odd	2
7200.2.k.l.3601.3		4	40.19	odd	2
7200.2.k.l.3601.4		4	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +2.44949 q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +2.44949 q^{7} -2.82843i q^{8} -3.46410i q^{11} +(3.00000 - 1.73205i) q^{14} +(-2.00000 - 3.46410i) q^{16} +4.89898 q^{17} +3.46410i q^{19} +(-2.44949 - 4.24264i) q^{22} -2.44949 q^{23} +(2.44949 - 4.24264i) q^{28} +4.00000 q^{31} +(-4.89898 - 2.82843i) q^{32} +(6.00000 - 3.46410i) q^{34} -8.48528i q^{37} +(2.44949 + 4.24264i) q^{38} -4.24264i q^{43} +(-6.00000 - 3.46410i) q^{44} +(-3.00000 + 1.73205i) q^{46} -7.34847 q^{47} -1.00000 q^{49} +5.65685i q^{53} -6.92820i q^{56} +10.3923i q^{59} -3.46410i q^{61} +(4.89898 - 2.82843i) q^{62} -8.00000 q^{64} -4.24264i q^{67} +(4.89898 - 8.48528i) q^{68} +12.0000 q^{71} +4.89898 q^{73} +(-6.00000 - 10.3923i) q^{74} +(6.00000 + 3.46410i) q^{76} -8.48528i q^{77} +4.00000 q^{79} -9.89949i q^{83} +(-3.00000 - 5.19615i) q^{86} -9.79796 q^{88} +6.00000 q^{89} +(-2.44949 + 4.24264i) q^{92} +(-9.00000 + 5.19615i) q^{94} +4.89898 q^{97} +(-1.22474 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4}+O(q^{10}) \) 4 * q + 4 * q^4	\( 4 q + 4 q^{4} + 12 q^{14} - 8 q^{16} + 16 q^{31} + 24 q^{34} - 24 q^{44} - 12 q^{46} - 4 q^{49} - 32 q^{64} + 48 q^{71} - 24 q^{74} + 24 q^{76} + 16 q^{79} - 12 q^{86} + 24 q^{89} - 36 q^{94}+O(q^{100}) \) 4 * q + 4 * q^4 + 12 * q^14 - 8 * q^16 + 16 * q^31 + 24 * q^34 - 24 * q^44 - 12 * q^46 - 4 * q^49 - 32 * q^64 + 48 * q^71 - 24 * q^74 + 24 * q^76 + 16 * q^79 - 12 * q^86 + 24 * q^89 - 36 * q^94

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