LMFDB - Embedded newform 1800.2.d.m.1549.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(1549,1800)]

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, 1]))

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

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

chi := DirichletCharacter("1800.1549");

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.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 3x^{2} + 4 $ x^4 - 3*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1549.4
Root			$1.32288 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1800.1549
Dual form			1800.2.d.m.1549.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32288 + 0.500000i) q^{2} +(1.50000 + 1.32288i) q^{4} -4.00000i q^{7} +(1.32288 + 2.50000i) q^{8} +O(q^{10})$	\(q+(1.32288 + 0.500000i) q^{2} +(1.50000 + 1.32288i) q^{4} -4.00000i q^{7} +(1.32288 + 2.50000i) q^{8} -2.64575i q^{11} +(2.00000 - 5.29150i) q^{14} +(0.500000 + 3.96863i) q^{16} -3.00000i q^{17} -2.64575i q^{19} +(1.32288 - 3.50000i) q^{22} -4.00000i q^{23} +(5.29150 - 6.00000i) q^{28} +4.00000 q^{31} +(-1.32288 + 5.50000i) q^{32} +(1.50000 - 3.96863i) q^{34} -10.5830 q^{37} +(1.32288 - 3.50000i) q^{38} +5.00000 q^{41} +5.29150 q^{43} +(3.50000 - 3.96863i) q^{44} +(2.00000 - 5.29150i) q^{46} -8.00000i q^{47} -9.00000 q^{49} +10.5830 q^{53} +(10.0000 - 5.29150i) q^{56} +5.29150i q^{59} +10.5830i q^{61} +(5.29150 + 2.00000i) q^{62} +(-4.50000 + 6.61438i) q^{64} +7.93725 q^{67} +(3.96863 - 4.50000i) q^{68} -8.00000 q^{71} -7.00000i q^{73} +(-14.0000 - 5.29150i) q^{74} +(3.50000 - 3.96863i) q^{76} -10.5830 q^{77} -4.00000 q^{79} +(6.61438 + 2.50000i) q^{82} +7.93725 q^{83} +(7.00000 + 2.64575i) q^{86} +(6.61438 - 3.50000i) q^{88} -1.00000 q^{89} +(5.29150 - 6.00000i) q^{92} +(4.00000 - 10.5830i) q^{94} +2.00000i q^{97} +(-11.9059 - 4.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{4}+O(q^{10}) $ 4 * q + 6 * q^4	$ 4 q + 6 q^{4} + 8 q^{14} + 2 q^{16} + 16 q^{31} + 6 q^{34} + 20 q^{41} + 14 q^{44} + 8 q^{46} - 36 q^{49} + 40 q^{56} - 18 q^{64} - 32 q^{71} - 56 q^{74} + 14 q^{76} - 16 q^{79} + 28 q^{86} - 4 q^{89} + 16 q^{94}+O(q^{100}) $ 4 * q + 6 * q^4 + 8 * q^14 + 2 * q^16 + 16 * q^31 + 6 * q^34 + 20 * q^41 + 14 * q^44 + 8 * q^46 - 36 * q^49 + 40 * q^56 - 18 * q^64 - 32 * q^71 - 56 * q^74 + 14 * q^76 - 16 * q^79 + 28 * q^86 - 4 * q^89 + 16 * 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 $

$2$	1.32288	+	0.500000i	0.935414	+	0.353553i
$2$	1.32288	+	0.500000i	0.935414	+	0.353553i
$3$		0			0
$3$		0			0
$4$	1.50000	+	1.32288i	0.750000	+	0.661438i
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	4.00000i		−	1.51186i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$		−	4.00000i		−	1.51186i	0.654654	−	0.755929i	$-0.272814\pi$
$8$	1.32288	+	2.50000i	0.467707	+	0.883883i
$9$		0			0
$10$		0			0
$11$		−	2.64575i		−	0.797724i	−0.917011	−	0.398862i	$-0.869405\pi$
$11$		−	2.64575i		−	0.797724i	0.917011	−	0.398862i	$-0.130595\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	2.00000	−	5.29150i	0.534522	−	1.41421i
$15$		0			0
$16$	0.500000	+	3.96863i	0.125000	+	0.992157i
$17$		−	3.00000i		−	0.727607i	−0.931476	−	0.363803i	$-0.881478\pi$
$17$		−	3.00000i		−	0.727607i	0.931476	−	0.363803i	$-0.118522\pi$
$18$		0			0
$19$		−	2.64575i		−	0.606977i	−0.952835	−	0.303488i	$-0.901849\pi$
$19$		−	2.64575i		−	0.606977i	0.952835	−	0.303488i	$-0.0981514\pi$
$20$		0			0
$21$		0			0
$22$	1.32288	−	3.50000i	0.282038	−	0.746203i
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		0			0
$28$	5.29150	−	6.00000i	1.00000	−	1.13389i
$29$		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	$0.383046\pi$
$32$	−1.32288	+	5.50000i	−0.233854	+	0.972272i
$33$		0			0
$34$	1.50000	−	3.96863i	0.257248	−	0.680614i
$35$		0			0
$36$		0			0
$37$	−10.5830			−1.73984			−0.869918	−	0.493197i	$-0.835828\pi$
$37$	−10.5830			−1.73984			−0.869918	+	0.493197i	$0.835828\pi$
$38$	1.32288	−	3.50000i	0.214599	−	0.567775i
$39$		0			0
$40$		0			0
$41$	5.00000			0.780869			0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000			0.780869			0.390434	+	0.920631i	$0.372325\pi$
$42$		0			0
$43$	5.29150			0.806947			0.403473	−	0.914991i	$-0.367803\pi$
$43$	5.29150			0.806947			0.403473	+	0.914991i	$0.367803\pi$
$44$	3.50000	−	3.96863i	0.527645	−	0.598293i
$45$		0			0
$46$	2.00000	−	5.29150i	0.294884	−	0.780189i
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$		0			0
$49$	−9.00000			−1.28571
$50$		0			0
$51$		0			0
$52$		0			0
$53$	10.5830			1.45369			0.726844	−	0.686803i	$-0.240986\pi$
$53$	10.5830			1.45369			0.726844	+	0.686803i	$0.240986\pi$
$54$		0			0
$55$		0			0
$56$	10.0000	−	5.29150i	1.33631	−	0.707107i
$57$		0			0
$58$		0			0
$59$			5.29150i			0.688895i	0.938806	+	0.344447i	$0.111934\pi$
$59$			5.29150i			0.688895i	−0.938806	+	0.344447i	$0.888066\pi$
$60$		0			0
$61$			10.5830i			1.35501i	0.735516	+	0.677507i	$0.236940\pi$
$61$			10.5830i			1.35501i	−0.735516	+	0.677507i	$0.763060\pi$
$62$	5.29150	+	2.00000i	0.672022	+	0.254000i
$63$		0			0
$64$	−4.50000	+	6.61438i	−0.562500	+	0.826797i
$65$		0			0
$66$		0			0
$67$	7.93725			0.969690			0.484845	−	0.874600i	$-0.338876\pi$
$67$	7.93725			0.969690			0.484845	+	0.874600i	$0.338876\pi$
$68$	3.96863	−	4.50000i	0.481267	−	0.545705i
$69$		0			0
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$		−	7.00000i		−	0.819288i	−0.912245	−	0.409644i	$-0.865653\pi$
$73$		−	7.00000i		−	0.819288i	0.912245	−	0.409644i	$-0.134347\pi$
$74$	−14.0000	−	5.29150i	−1.62747	−	0.615125i
$75$		0			0
$76$	3.50000	−	3.96863i	0.401478	−	0.455233i
$77$	−10.5830			−1.20605
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$		0			0
$82$	6.61438	+	2.50000i	0.730436	+	0.276079i
$83$	7.93725			0.871227			0.435613	−	0.900134i	$-0.356531\pi$
$83$	7.93725			0.871227			0.435613	+	0.900134i	$0.356531\pi$
$84$		0			0
$85$		0			0
$86$	7.00000	+	2.64575i	0.754829	+	0.285299i
$87$		0			0
$88$	6.61438	−	3.50000i	0.705095	−	0.373101i
$89$	−1.00000			−0.106000			−0.0529999	−	0.998595i	$-0.516878\pi$
$89$	−1.00000			−0.106000			−0.0529999	+	0.998595i	$0.516878\pi$
$90$		0			0
$91$		0			0
$92$	5.29150	−	6.00000i	0.551677	−	0.625543i
$93$		0			0
$94$	4.00000	−	10.5830i	0.412568	−	1.09155i
$95$		0			0
$96$		0			0
$97$			2.00000i			0.203069i	0.994832	+	0.101535i	$0.0323753\pi$
$97$			2.00000i			0.203069i	−0.994832	+	0.101535i	$0.967625\pi$
$98$	−11.9059	−	4.50000i	−1.20268	−	0.454569i
$99$		0			0
$100$		0			0
$101$			10.5830i			1.05305i	0.850160	+	0.526524i	$0.176505\pi$
$101$			10.5830i			1.05305i	−0.850160	+	0.526524i	$0.823495\pi$
$102$		0			0
$103$			8.00000i			0.788263i	0.919054	+	0.394132i	$0.128955\pi$
$103$			8.00000i			0.788263i	−0.919054	+	0.394132i	$0.871045\pi$
$104$		0			0
$105$		0			0
$106$	14.0000	+	5.29150i	1.35980	+	0.513956i
$107$	2.64575			0.255774			0.127887	−	0.991789i	$-0.459180\pi$
$107$	2.64575			0.255774			0.127887	+	0.991789i	$0.459180\pi$
$108$		0			0
$109$		−	10.5830i		−	1.01367i	−0.862044	−	0.506834i	$-0.830816\pi$
$109$		−	10.5830i		−	1.01367i	0.862044	−	0.506834i	$-0.169184\pi$
$110$		0			0
$111$		0			0
$112$	15.8745	−	2.00000i	1.50000	−	0.188982i
$113$			15.0000i			1.41108i	0.708669	+	0.705541i	$0.249296\pi$
$113$			15.0000i			1.41108i	−0.708669	+	0.705541i	$0.750704\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−2.64575	+	7.00000i	−0.243561	+	0.644402i
$119$	−12.0000			−1.10004
$120$		0			0
$121$	4.00000			0.363636
$122$	−5.29150	+	14.0000i	−0.479070	+	1.26750i
$123$		0			0
$124$	6.00000	+	5.29150i	0.538816	+	0.475191i
$125$		0			0
$126$		0			0
$127$		−	12.0000i		−	1.06483i	−0.846484	−	0.532414i	$-0.821285\pi$
$127$		−	12.0000i		−	1.06483i	0.846484	−	0.532414i	$-0.178715\pi$
$128$	−9.26013	+	6.50000i	−0.818488	+	0.574524i
$129$		0			0
$130$		0			0
$131$			15.8745i			1.38696i	0.720475	+	0.693481i	$0.243924\pi$
$131$			15.8745i			1.38696i	−0.720475	+	0.693481i	$0.756076\pi$
$132$		0			0
$133$	−10.5830			−0.917663
$134$	10.5000	+	3.96863i	0.907062	+	0.342837i
$135$		0			0
$136$	7.50000	−	3.96863i	0.643120	−	0.340307i
$137$		−	19.0000i		−	1.62328i	−0.584158	−	0.811640i	$-0.698575\pi$
$137$		−	19.0000i		−	1.62328i	0.584158	−	0.811640i	$-0.301425\pi$
$138$		0			0
$139$			18.5203i			1.57087i	0.618945	+	0.785434i	$0.287560\pi$
$139$			18.5203i			1.57087i	−0.618945	+	0.785434i	$0.712440\pi$
$140$		0			0
$141$		0			0
$142$	−10.5830	−	4.00000i	−0.888106	−	0.335673i
$143$		0			0
$144$		0			0
$145$		0			0
$146$	3.50000	−	9.26013i	0.289662	−	0.766374i
$147$		0			0
$148$	−15.8745	−	14.0000i	−1.30488	−	1.15079i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$		0			0
$151$	4.00000			0.325515			0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000			0.325515			0.162758	+	0.986666i	$0.447961\pi$
$152$	6.61438	−	3.50000i	0.536497	−	0.283887i
$153$		0			0
$154$	−14.0000	−	5.29150i	−1.12815	−	0.426401i
$155$		0			0
$156$		0			0
$157$	10.5830			0.844616			0.422308	−	0.906452i	$-0.361220\pi$
$157$	10.5830			0.844616			0.422308	+	0.906452i	$0.361220\pi$
$158$	−5.29150	−	2.00000i	−0.420969	−	0.159111i
$159$		0			0
$160$		0			0
$161$	−16.0000			−1.26098
$162$		0			0
$163$	13.2288			1.03616			0.518078	−	0.855333i	$-0.326648\pi$
$163$	13.2288			1.03616			0.518078	+	0.855333i	$0.326648\pi$
$164$	7.50000	+	6.61438i	0.585652	+	0.516496i
$165$		0			0
$166$	10.5000	+	3.96863i	0.814958	+	0.308025i
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$		0			0
$171$		0			0
$172$	7.93725	+	7.00000i	0.605210	+	0.533745i
$173$	−21.1660			−1.60922			−0.804611	−	0.593802i	$-0.797626\pi$
$173$	−21.1660			−1.60922			−0.804611	+	0.593802i	$0.797626\pi$
$174$		0			0
$175$		0			0
$176$	10.5000	−	1.32288i	0.791467	−	0.0997155i
$177$		0			0
$178$	−1.32288	−	0.500000i	−0.0991537	−	0.0374766i
$179$			23.8118i			1.77977i	0.456180	+	0.889887i	$0.349217\pi$
$179$			23.8118i			1.77977i	−0.456180	+	0.889887i	$0.650783\pi$
$180$		0			0
$181$			10.5830i			0.786629i	0.919404	+	0.393314i	$0.128672\pi$
$181$			10.5830i			0.786629i	−0.919404	+	0.393314i	$0.871328\pi$
$182$		0			0
$183$		0			0
$184$	10.0000	−	5.29150i	0.737210	−	0.390095i
$185$		0			0
$186$		0			0
$187$	−7.93725			−0.580429
$188$	10.5830	−	12.0000i	0.771845	−	0.875190i
$189$		0			0
$190$		0			0
$191$	−4.00000			−0.289430			−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000			−0.289430			−0.144715	+	0.989473i	$0.546227\pi$
$192$		0			0
$193$			5.00000i			0.359908i	0.983675	+	0.179954i	$0.0575949\pi$
$193$			5.00000i			0.359908i	−0.983675	+	0.179954i	$0.942405\pi$
$194$	−1.00000	+	2.64575i	−0.0717958	+	0.189954i
$195$		0			0
$196$	−13.5000	−	11.9059i	−0.964286	−	0.850420i
$197$	−10.5830			−0.754008			−0.377004	−	0.926212i	$-0.623046\pi$
$197$	−10.5830			−0.754008			−0.377004	+	0.926212i	$0.623046\pi$
$198$		0			0
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$		0			0
$201$		0			0
$202$	−5.29150	+	14.0000i	−0.372309	+	0.985037i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−4.00000	+	10.5830i	−0.278693	+	0.737353i
$207$		0			0
$208$		0			0
$209$	−7.00000			−0.484200
$210$		0			0
$211$		−	7.93725i		−	0.546423i	−0.961954	−	0.273212i	$-0.911914\pi$
$211$		−	7.93725i		−	0.546423i	0.961954	−	0.273212i	$-0.0880859\pi$
$212$	15.8745	+	14.0000i	1.09027	+	0.961524i
$213$		0			0
$214$	3.50000	+	1.32288i	0.239255	+	0.0904299i
$215$		0			0
$216$		0			0
$217$		−	16.0000i		−	1.08615i
$218$	5.29150	−	14.0000i	0.358386	−	0.948200i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		−	16.0000i		−	1.07144i	−0.844396	−	0.535720i	$-0.820040\pi$
$223$		−	16.0000i		−	1.07144i	0.844396	−	0.535720i	$-0.179960\pi$
$224$	22.0000	+	5.29150i	1.46994	+	0.353553i
$225$		0			0
$226$	−7.50000	+	19.8431i	−0.498893	+	1.31995i
$227$	−15.8745			−1.05363			−0.526814	−	0.849981i	$-0.676614\pi$
$227$	−15.8745			−1.05363			−0.526814	+	0.849981i	$0.676614\pi$
$228$		0			0
$229$		−	21.1660i		−	1.39869i	−0.714785	−	0.699345i	$-0.753475\pi$
$229$		−	21.1660i		−	1.39869i	0.714785	−	0.699345i	$-0.246525\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	6.00000i		−	0.393073i	−0.980497	−	0.196537i	$-0.937031\pi$
$233$		−	6.00000i		−	0.393073i	0.980497	−	0.196537i	$-0.0629694\pi$
$234$		0			0
$235$		0			0
$236$	−7.00000	+	7.93725i	−0.455661	+	0.516671i
$237$		0			0
$238$	−15.8745	−	6.00000i	−1.02899	−	0.388922i
$239$	−8.00000			−0.517477			−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000			−0.517477			−0.258738	+	0.965947i	$0.583307\pi$
$240$		0			0
$241$	−21.0000			−1.35273			−0.676364	−	0.736567i	$-0.736446\pi$
$241$	−21.0000			−1.35273			−0.676364	+	0.736567i	$0.736446\pi$
$242$	5.29150	+	2.00000i	0.340151	+	0.128565i
$243$		0			0
$244$	−14.0000	+	15.8745i	−0.896258	+	1.01626i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	5.29150	+	10.0000i	0.336011	+	0.635001i
$249$		0			0
$250$		0			0
$251$			7.93725i			0.500995i	0.968117	+	0.250498i	$0.0805942\pi$
$251$			7.93725i			0.500995i	−0.968117	+	0.250498i	$0.919406\pi$
$252$		0			0
$253$	−10.5830			−0.665348
$254$	6.00000	−	15.8745i	0.376473	−	0.996055i
$255$		0			0
$256$	−15.5000	+	3.96863i	−0.968750	+	0.248039i
$257$			14.0000i			0.873296i	0.899632	+	0.436648i	$0.143834\pi$
$257$			14.0000i			0.873296i	−0.899632	+	0.436648i	$0.856166\pi$
$258$		0			0
$259$			42.3320i			2.63038i
$260$		0			0
$261$		0			0
$262$	−7.93725	+	21.0000i	−0.490365	+	1.29738i
$263$		−	12.0000i		−	0.739952i	−0.929041	−	0.369976i	$-0.879366\pi$
$263$		−	12.0000i		−	0.739952i	0.929041	−	0.369976i	$-0.120634\pi$
$264$		0			0
$265$		0			0
$266$	−14.0000	−	5.29150i	−0.858395	−	0.324443i
$267$		0			0
$268$	11.9059	+	10.5000i	0.727267	+	0.641390i
$269$		−	21.1660i		−	1.29051i	−0.763965	−	0.645257i	$-0.776750\pi$
$269$		−	21.1660i		−	1.29051i	0.763965	−	0.645257i	$-0.223250\pi$
$270$		0			0
$271$	−20.0000			−1.21491			−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000			−1.21491			−0.607457	+	0.794353i	$0.707810\pi$
$272$	11.9059	−	1.50000i	0.721900	−	0.0909509i
$273$		0			0
$274$	9.50000	−	25.1346i	0.573916	−	1.51844i
$275$		0			0
$276$		0			0
$277$	−21.1660			−1.27174			−0.635871	−	0.771795i	$-0.719359\pi$
$277$	−21.1660			−1.27174			−0.635871	+	0.771795i	$0.719359\pi$
$278$	−9.26013	+	24.5000i	−0.555386	+	1.46941i
$279$		0			0
$280$		0			0
$281$	22.0000			1.31241			0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000			1.31241			0.656205	+	0.754583i	$0.272161\pi$
$282$		0			0
$283$	13.2288			0.786368			0.393184	−	0.919460i	$-0.371374\pi$
$283$	13.2288			0.786368			0.393184	+	0.919460i	$0.371374\pi$
$284$	−12.0000	−	10.5830i	−0.712069	−	0.627986i
$285$		0			0
$286$		0			0
$287$		−	20.0000i		−	1.18056i
$288$		0			0
$289$	8.00000			0.470588
$290$		0			0
$291$		0			0
$292$	9.26013	−	10.5000i	0.541908	−	0.614466i
$293$	−10.5830			−0.618266			−0.309133	−	0.951019i	$-0.600039\pi$
$293$	−10.5830			−0.618266			−0.309133	+	0.951019i	$0.600039\pi$
$294$		0			0
$295$		0			0
$296$	−14.0000	−	26.4575i	−0.813733	−	1.53781i
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		−	21.1660i		−	1.21999i
$302$	5.29150	+	2.00000i	0.304492	+	0.115087i
$303$		0			0
$304$	10.5000	−	1.32288i	0.602216	−	0.0758721i
$305$		0			0
$306$		0			0
$307$	−2.64575			−0.151001			−0.0755005	−	0.997146i	$-0.524055\pi$
$307$	−2.64575			−0.151001			−0.0755005	+	0.997146i	$0.524055\pi$
$308$	−15.8745	−	14.0000i	−0.904534	−	0.797724i
$309$		0			0
$310$		0			0
$311$	4.00000			0.226819			0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000			0.226819			0.113410	+	0.993548i	$0.463823\pi$
$312$		0			0
$313$			6.00000i			0.339140i	0.985518	+	0.169570i	$0.0542379\pi$
$313$			6.00000i			0.339140i	−0.985518	+	0.169570i	$0.945762\pi$
$314$	14.0000	+	5.29150i	0.790066	+	0.298617i
$315$		0			0
$316$	−6.00000	−	5.29150i	−0.337526	−	0.297670i
$317$		0			0			−	1.00000i	$-0.5\pi$
$317$		0			0				1.00000i	$0.5\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$	−21.1660	−	8.00000i	−1.17954	−	0.445823i
$323$	−7.93725			−0.441641
$324$		0			0
$325$		0			0
$326$	17.5000	+	6.61438i	0.969235	+	0.366337i
$327$		0			0
$328$	6.61438	+	12.5000i	0.365218	+	0.690197i
$329$	−32.0000			−1.76422
$330$		0			0
$331$			2.64575i			0.145424i	0.997353	+	0.0727118i	$0.0231653\pi$
$331$			2.64575i			0.145424i	−0.997353	+	0.0727118i	$0.976835\pi$
$332$	11.9059	+	10.5000i	0.653420	+	0.576262i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$			15.0000i			0.817102i	0.912735	+	0.408551i	$0.133966\pi$
$337$			15.0000i			0.817102i	−0.912735	+	0.408551i	$0.866034\pi$
$338$	−17.1974	−	6.50000i	−0.935414	−	0.353553i
$339$		0			0
$340$		0			0
$341$		−	10.5830i		−	0.573102i
$342$		0			0
$343$			8.00000i			0.431959i
$344$	7.00000	+	13.2288i	0.377415	+	0.713247i
$345$		0			0
$346$	−28.0000	−	10.5830i	−1.50529	−	0.568946i
$347$	2.64575			0.142031			0.0710157	−	0.997475i	$-0.477376\pi$
$347$	2.64575			0.142031			0.0710157	+	0.997475i	$0.477376\pi$
$348$		0			0
$349$			10.5830i			0.566495i	0.959047	+	0.283248i	$0.0914118\pi$
$349$			10.5830i			0.566495i	−0.959047	+	0.283248i	$0.908588\pi$
$350$		0			0
$351$		0			0
$352$	14.5516	+	3.50000i	0.775605	+	0.186551i
$353$			18.0000i			0.958043i	0.877803	+	0.479022i	$0.159008\pi$
$353$			18.0000i			0.958043i	−0.877803	+	0.479022i	$0.840992\pi$
$354$		0			0
$355$		0			0
$356$	−1.50000	−	1.32288i	−0.0794998	−	0.0701123i
$357$		0			0
$358$	−11.9059	+	31.5000i	−0.629245	+	1.66483i
$359$	36.0000			1.90001			0.950004	−	0.312239i	$-0.101079\pi$
$359$	36.0000			1.90001			0.950004	+	0.312239i	$0.101079\pi$
$360$		0			0
$361$	12.0000			0.631579
$362$	−5.29150	+	14.0000i	−0.278115	+	0.735824i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$	15.8745	−	2.00000i	0.827516	−	0.104257i
$369$		0			0
$370$		0			0
$371$		−	42.3320i		−	2.19777i
$372$		0			0
$373$	−10.5830			−0.547967			−0.273984	−	0.961734i	$-0.588341\pi$
$373$	−10.5830			−0.547967			−0.273984	+	0.961734i	$0.588341\pi$
$374$	−10.5000	−	3.96863i	−0.542942	−	0.205213i
$375$		0			0
$376$	20.0000	−	10.5830i	1.03142	−	0.545777i
$377$		0			0
$378$		0			0
$379$			7.93725i			0.407709i	0.979001	+	0.203855i	$0.0653470\pi$
$379$			7.93725i			0.407709i	−0.979001	+	0.203855i	$0.934653\pi$
$380$		0			0
$381$		0			0
$382$	−5.29150	−	2.00000i	−0.270737	−	0.102329i
$383$			36.0000i			1.83951i	0.392488	+	0.919757i	$0.371614\pi$
$383$			36.0000i			1.83951i	−0.392488	+	0.919757i	$0.628386\pi$
$384$		0			0
$385$		0			0
$386$	−2.50000	+	6.61438i	−0.127247	+	0.336663i
$387$		0			0
$388$	−2.64575	+	3.00000i	−0.134318	+	0.152302i
$389$			10.5830i			0.536580i	0.963338	+	0.268290i	$0.0864585\pi$
$389$			10.5830i			0.536580i	−0.963338	+	0.268290i	$0.913542\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$	−11.9059	−	22.5000i	−0.601338	−	1.13642i
$393$		0			0
$394$	−14.0000	−	5.29150i	−0.705310	−	0.266582i
$395$		0			0
$396$		0			0
$397$	−21.1660			−1.06229			−0.531146	−	0.847280i	$-0.678238\pi$
$397$	−21.1660			−1.06229			−0.531146	+	0.847280i	$0.678238\pi$
$398$	31.7490	+	12.0000i	1.59143	+	0.601506i
$399$		0			0
$400$		0			0
$401$	−27.0000			−1.34832			−0.674158	−	0.738587i	$-0.735493\pi$
$401$	−27.0000			−1.34832			−0.674158	+	0.738587i	$0.735493\pi$
$402$		0			0
$403$		0			0
$404$	−14.0000	+	15.8745i	−0.696526	+	0.789786i
$405$		0			0
$406$		0			0
$407$			28.0000i			1.38791i
$408$		0			0
$409$	−3.00000			−0.148340			−0.0741702	−	0.997246i	$-0.523631\pi$
$409$	−3.00000			−0.148340			−0.0741702	+	0.997246i	$0.523631\pi$
$410$		0			0
$411$		0			0
$412$	−10.5830	+	12.0000i	−0.521387	+	0.591198i
$413$	21.1660			1.04151
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$	−9.26013	−	3.50000i	−0.452928	−	0.171191i
$419$		−	18.5203i		−	0.904774i	−0.891822	−	0.452387i	$-0.850573\pi$
$419$		−	18.5203i		−	0.904774i	0.891822	−	0.452387i	$-0.149427\pi$
$420$		0			0
$421$			21.1660i			1.03157i	0.856719	+	0.515784i	$0.172499\pi$
$421$			21.1660i			1.03157i	−0.856719	+	0.515784i	$0.827501\pi$
$422$	3.96863	−	10.5000i	0.193190	−	0.511132i
$423$		0			0
$424$	14.0000	+	26.4575i	0.679900	+	1.28489i
$425$		0			0
$426$		0			0
$427$	42.3320			2.04859
$428$	3.96863	+	3.50000i	0.191831	+	0.169179i
$429$		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
$433$			37.0000i			1.77811i	0.457804	+	0.889053i	$0.348636\pi$
$433$			37.0000i			1.77811i	−0.457804	+	0.889053i	$0.651364\pi$
$434$	8.00000	−	21.1660i	0.384012	−	1.01600i
$435$		0			0
$436$	14.0000	−	15.8745i	0.670478	−	0.760251i
$437$	−10.5830			−0.506254
$438$		0			0
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	29.1033			1.38274			0.691369	−	0.722502i	$-0.257008\pi$
$443$	29.1033			1.38274			0.691369	+	0.722502i	$0.257008\pi$
$444$		0			0
$445$		0			0
$446$	8.00000	−	21.1660i	0.378811	−	1.00224i
$447$		0			0
$448$	26.4575	+	18.0000i	1.25000	+	0.850420i
$449$	27.0000			1.27421			0.637104	−	0.770778i	$-0.280132\pi$
$449$	27.0000			1.27421			0.637104	+	0.770778i	$0.280132\pi$
$450$		0			0
$451$		−	13.2288i		−	0.622918i
$452$	−19.8431	+	22.5000i	−0.933343	+	1.05831i
$453$		0			0
$454$	−21.0000	−	7.93725i	−0.985579	−	0.372514i
$455$		0			0
$456$		0			0
$457$			27.0000i			1.26301i	0.775373	+	0.631503i	$0.217562\pi$
$457$			27.0000i			1.26301i	−0.775373	+	0.631503i	$0.782438\pi$
$458$	10.5830	−	28.0000i	0.494511	−	1.30835i
$459$		0			0
$460$		0			0
$461$			42.3320i			1.97160i	0.167927	+	0.985799i	$0.446293\pi$
$461$			42.3320i			1.97160i	−0.167927	+	0.985799i	$0.553707\pi$
$462$		0			0
$463$		−	8.00000i		−	0.371792i	−0.982569	−	0.185896i	$-0.940481\pi$
$463$		−	8.00000i		−	0.371792i	0.982569	−	0.185896i	$-0.0595187\pi$
$464$		0			0
$465$		0			0
$466$	3.00000	−	7.93725i	0.138972	−	0.367686i
$467$	26.4575			1.22431			0.612154	−	0.790739i	$-0.290303\pi$
$467$	26.4575			1.22431			0.612154	+	0.790739i	$0.290303\pi$
$468$		0			0
$469$		−	31.7490i		−	1.46603i
$470$		0			0
$471$		0			0
$472$	−13.2288	+	7.00000i	−0.608903	+	0.322201i
$473$		−	14.0000i		−	0.643721i
$474$		0			0
$475$		0			0
$476$	−18.0000	−	15.8745i	−0.825029	−	0.727607i
$477$		0			0
$478$	−10.5830	−	4.00000i	−0.484055	−	0.182956i
$479$	4.00000			0.182765			0.0913823	−	0.995816i	$-0.470871\pi$
$479$	4.00000			0.182765			0.0913823	+	0.995816i	$0.470871\pi$
$480$		0			0
$481$		0			0
$482$	−27.7804	−	10.5000i	−1.26536	−	0.478262i
$483$		0			0
$484$	6.00000	+	5.29150i	0.272727	+	0.240523i
$485$		0			0
$486$		0			0
$487$			12.0000i			0.543772i	0.962329	+	0.271886i	$0.0876473\pi$
$487$			12.0000i			0.543772i	−0.962329	+	0.271886i	$0.912353\pi$
$488$	−26.4575	+	14.0000i	−1.19768	+	0.633750i
$489$		0			0
$490$		0			0
$491$		−	5.29150i		−	0.238802i	−0.992846	−	0.119401i	$-0.961903\pi$
$491$		−	5.29150i		−	0.238802i	0.992846	−	0.119401i	$-0.0380974\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	2.00000	+	15.8745i	0.0898027	+	0.712786i
$497$			32.0000i			1.43540i
$498$		0			0
$499$		−	26.4575i		−	1.18440i	−0.805791	−	0.592200i	$-0.798259\pi$
$499$		−	26.4575i		−	1.18440i	0.805791	−	0.592200i	$-0.201741\pi$
$500$		0			0
$501$		0			0
$502$	−3.96863	+	10.5000i	−0.177128	+	0.468638i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$	−14.0000	−	5.29150i	−0.622376	−	0.235236i
$507$		0			0
$508$	15.8745	−	18.0000i	0.704317	−	0.798621i
$509$		−	31.7490i		−	1.40725i	−0.710571	−	0.703625i	$-0.751563\pi$
$509$		−	31.7490i		−	1.40725i	0.710571	−	0.703625i	$-0.248437\pi$
$510$		0			0
$511$	−28.0000			−1.23865
$512$	−22.4889	−	2.50000i	−0.993878	−	0.110485i
$513$		0			0
$514$	−7.00000	+	18.5203i	−0.308757	+	0.816894i
$515$		0			0
$516$		0			0
$517$	−21.1660			−0.930880
$518$	−21.1660	+	56.0000i	−0.929981	+	2.46050i
$519$		0			0
$520$		0			0
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$		0			0
$523$	2.64575			0.115691			0.0578453	−	0.998326i	$-0.481577\pi$
$523$	2.64575			0.115691			0.0578453	+	0.998326i	$0.481577\pi$
$524$	−21.0000	+	23.8118i	−0.917389	+	1.04022i
$525$		0			0
$526$	6.00000	−	15.8745i	0.261612	−	0.692161i
$527$		−	12.0000i		−	0.522728i
$528$		0			0
$529$	7.00000			0.304348
$530$		0			0
$531$		0			0
$532$	−15.8745	−	14.0000i	−0.688247	−	0.606977i
$533$		0			0
$534$		0			0
$535$		0			0
$536$	10.5000	+	19.8431i	0.453531	+	0.857093i
$537$		0			0
$538$	10.5830	−	28.0000i	0.456266	−	1.20717i
$539$			23.8118i			1.02565i
$540$		0			0
$541$		−	21.1660i		−	0.909998i	−0.890492	−	0.454999i	$-0.849640\pi$
$541$		−	21.1660i		−	0.909998i	0.890492	−	0.454999i	$-0.150360\pi$
$542$	−26.4575	−	10.0000i	−1.13645	−	0.429537i
$543$		0			0
$544$	16.5000	+	3.96863i	0.707432	+	0.170153i
$545$		0			0
$546$		0			0
$547$	18.5203			0.791869			0.395935	−	0.918279i	$-0.370421\pi$
$547$	18.5203			0.791869			0.395935	+	0.918279i	$0.370421\pi$
$548$	25.1346	−	28.5000i	1.07370	−	1.21746i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$			16.0000i			0.680389i
$554$	−28.0000	−	10.5830i	−1.18961	−	0.449629i
$555$		0			0
$556$	−24.5000	+	27.7804i	−1.03903	+	1.17815i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	29.1033	+	11.0000i	1.22765	+	0.464007i
$563$	15.8745			0.669031			0.334515	−	0.942390i	$-0.391427\pi$
$563$	15.8745			0.669031			0.334515	+	0.942390i	$0.391427\pi$
$564$		0			0
$565$		0			0
$566$	17.5000	+	6.61438i	0.735580	+	0.278023i
$567$		0			0
$568$	−10.5830	−	20.0000i	−0.444053	−	0.839181i
$569$	11.0000			0.461144			0.230572	−	0.973055i	$-0.425940\pi$
$569$	11.0000			0.461144			0.230572	+	0.973055i	$0.425940\pi$
$570$		0			0
$571$		−	37.0405i		−	1.55010i	−0.631901	−	0.775049i	$-0.717725\pi$
$571$		−	37.0405i		−	1.55010i	0.631901	−	0.775049i	$-0.282275\pi$
$572$		0			0
$573$		0			0
$574$	10.0000	−	26.4575i	0.417392	−	1.10432i
$575$		0			0
$576$		0			0
$577$			7.00000i			0.291414i	0.989328	+	0.145707i	$0.0465456\pi$
$577$			7.00000i			0.291414i	−0.989328	+	0.145707i	$0.953454\pi$
$578$	10.5830	+	4.00000i	0.440195	+	0.166378i
$579$		0			0
$580$		0			0
$581$		−	31.7490i		−	1.31717i
$582$		0			0
$583$		−	28.0000i		−	1.15964i
$584$	17.5000	−	9.26013i	0.724155	−	0.383187i
$585$		0			0
$586$	−14.0000	−	5.29150i	−0.578335	−	0.218590i
$587$	−7.93725			−0.327606			−0.163803	−	0.986493i	$-0.552376\pi$
$587$	−7.93725			−0.327606			−0.163803	+	0.986493i	$0.552376\pi$
$588$		0			0
$589$		−	10.5830i		−	0.436065i
$590$		0			0
$591$		0			0
$592$	−5.29150	−	42.0000i	−0.217479	−	1.72619i
$593$		−	41.0000i		−	1.68367i	−0.539736	−	0.841834i	$-0.681476\pi$
$593$		−	41.0000i		−	1.68367i	0.539736	−	0.841834i	$-0.318524\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$		0			0
$601$	7.00000			0.285536			0.142768	−	0.989756i	$-0.454400\pi$
$601$	7.00000			0.285536			0.142768	+	0.989756i	$0.454400\pi$
$602$	10.5830	−	28.0000i	0.431331	−	1.14119i
$603$		0			0
$604$	6.00000	+	5.29150i	0.244137	+	0.215308i
$605$		0			0
$606$		0			0
$607$			8.00000i			0.324710i	0.986732	+	0.162355i	$0.0519090\pi$
$607$			8.00000i			0.324710i	−0.986732	+	0.162355i	$0.948091\pi$
$608$	14.5516	+	3.50000i	0.590147	+	0.141944i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	10.5830			0.427444			0.213722	−	0.976895i	$-0.431441\pi$
$613$	10.5830			0.427444			0.213722	+	0.976895i	$0.431441\pi$
$614$	−3.50000	−	1.32288i	−0.141249	−	0.0533869i
$615$		0			0
$616$	−14.0000	−	26.4575i	−0.564076	−	1.06600i
$617$			6.00000i			0.241551i	0.992680	+	0.120775i	$0.0385381\pi$
$617$			6.00000i			0.241551i	−0.992680	+	0.120775i	$0.961462\pi$
$618$		0			0
$619$		−	5.29150i		−	0.212683i	−0.994330	−	0.106342i	$-0.966086\pi$
$619$		−	5.29150i		−	0.212683i	0.994330	−	0.106342i	$-0.0339137\pi$
$620$		0			0
$621$		0			0
$622$	5.29150	+	2.00000i	0.212170	+	0.0801927i
$623$			4.00000i			0.160257i
$624$		0			0
$625$		0			0
$626$	−3.00000	+	7.93725i	−0.119904	+	0.317236i
$627$		0			0
$628$	15.8745	+	14.0000i	0.633462	+	0.558661i
$629$			31.7490i			1.26592i
$630$		0			0
$631$	36.0000			1.43314			0.716569	−	0.697517i	$-0.245712\pi$
$631$	36.0000			1.43314			0.716569	+	0.697517i	$0.245712\pi$
$632$	−5.29150	−	10.0000i	−0.210485	−	0.397779i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−2.00000			−0.0789953			−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000			−0.0789953			−0.0394976	+	0.999220i	$0.512576\pi$
$642$		0			0
$643$	−15.8745			−0.626029			−0.313015	−	0.949748i	$-0.601339\pi$
$643$	−15.8745			−0.626029			−0.313015	+	0.949748i	$0.601339\pi$
$644$	−24.0000	−	21.1660i	−0.945732	−	0.834058i
$645$		0			0
$646$	−10.5000	−	3.96863i	−0.413117	−	0.156144i
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$		0			0
$649$	14.0000			0.549548
$650$		0			0
$651$		0			0
$652$	19.8431	+	17.5000i	0.777117	+	0.685353i
$653$	−31.7490			−1.24243			−0.621217	−	0.783638i	$-0.713362\pi$
$653$	−31.7490			−1.24243			−0.621217	+	0.783638i	$0.713362\pi$
$654$		0			0
$655$		0			0
$656$	2.50000	+	19.8431i	0.0976086	+	0.774744i
$657$		0			0
$658$	−42.3320	−	16.0000i	−1.65027	−	0.623745i
$659$		−	7.93725i		−	0.309192i	−0.987978	−	0.154596i	$-0.950592\pi$
$659$		−	7.93725i		−	0.309192i	0.987978	−	0.154596i	$-0.0494075\pi$
$660$		0			0
$661$			21.1660i			0.823262i	0.911351	+	0.411631i	$0.135041\pi$
$661$			21.1660i			0.823262i	−0.911351	+	0.411631i	$0.864959\pi$
$662$	−1.32288	+	3.50000i	−0.0514150	+	0.136031i
$663$		0			0
$664$	10.5000	+	19.8431i	0.407479	+	0.770063i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$	28.0000			1.08093
$672$		0			0
$673$		−	34.0000i		−	1.31060i	−0.755367	−	0.655302i	$-0.772541\pi$
$673$		−	34.0000i		−	1.31060i	0.755367	−	0.655302i	$-0.227459\pi$
$674$	−7.50000	+	19.8431i	−0.288889	+	0.764329i
$675$		0			0
$676$	−19.5000	−	17.1974i	−0.750000	−	0.661438i
$677$	42.3320			1.62695			0.813476	−	0.581599i	$-0.197573\pi$
$677$	42.3320			1.62695			0.813476	+	0.581599i	$0.197573\pi$
$678$		0			0
$679$	8.00000			0.307012
$680$		0			0
$681$		0			0
$682$	5.29150	−	14.0000i	0.202622	−	0.536088i
$683$	−23.8118			−0.911132			−0.455566	−	0.890202i	$-0.650563\pi$
$683$	−23.8118			−0.911132			−0.455566	+	0.890202i	$0.650563\pi$
$684$		0			0
$685$		0			0
$686$	−4.00000	+	10.5830i	−0.152721	+	0.404061i
$687$		0			0
$688$	2.64575	+	21.0000i	0.100868	+	0.800617i
$689$		0			0
$690$		0			0
$691$			23.8118i			0.905842i	0.891551	+	0.452921i	$0.149618\pi$
$691$			23.8118i			0.905842i	−0.891551	+	0.452921i	$0.850382\pi$
$692$	−31.7490	−	28.0000i	−1.20692	−	1.06440i
$693$		0			0
$694$	3.50000	+	1.32288i	0.132858	+	0.0502157i
$695$		0			0
$696$		0			0
$697$		−	15.0000i		−	0.568166i
$698$	−5.29150	+	14.0000i	−0.200286	+	0.529908i
$699$		0			0
$700$		0			0
$701$		−	21.1660i		−	0.799429i	−0.916640	−	0.399715i	$-0.869109\pi$
$701$		−	21.1660i		−	0.799429i	0.916640	−	0.399715i	$-0.130891\pi$
$702$		0			0
$703$			28.0000i			1.05604i
$704$	17.5000	+	11.9059i	0.659556	+	0.448720i
$705$		0			0
$706$	−9.00000	+	23.8118i	−0.338719	+	0.896167i
$707$	42.3320			1.59206
$708$		0			0
$709$		−	21.1660i		−	0.794906i	−0.917622	−	0.397453i	$-0.869894\pi$
$709$		−	21.1660i		−	0.794906i	0.917622	−	0.397453i	$-0.130106\pi$
$710$		0			0
$711$		0			0
$712$	−1.32288	−	2.50000i	−0.0495769	−	0.0936915i
$713$		−	16.0000i		−	0.599205i
$714$		0			0
$715$		0			0
$716$	−31.5000	+	35.7176i	−1.17721	+	1.33483i
$717$		0			0
$718$	47.6235	+	18.0000i	1.77729	+	0.671754i
$719$	36.0000			1.34257			0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000			1.34257			0.671287	+	0.741198i	$0.265742\pi$
$720$		0			0
$721$	32.0000			1.19174
$722$	15.8745	+	6.00000i	0.590788	+	0.223297i
$723$		0			0
$724$	−14.0000	+	15.8745i	−0.520306	+	0.589971i
$725$		0			0
$726$		0			0
$727$			16.0000i			0.593407i	0.954970	+	0.296704i	$0.0958873\pi$
$727$			16.0000i			0.593407i	−0.954970	+	0.296704i	$0.904113\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		−	15.8745i		−	0.587140i
$732$		0			0
$733$		0			0			−	1.00000i	$-0.5\pi$
$733$		0			0				1.00000i	$0.5\pi$
$734$		0			0
$735$		0			0
$736$	22.0000	+	5.29150i	0.810931	+	0.195047i
$737$		−	21.0000i		−	0.773545i
$738$		0			0
$739$			15.8745i			0.583953i	0.956425	+	0.291977i	$0.0943129\pi$
$739$			15.8745i			0.583953i	−0.956425	+	0.291977i	$0.905687\pi$
$740$		0			0
$741$		0			0
$742$	21.1660	−	56.0000i	0.777029	−	2.05582i
$743$		−	36.0000i		−	1.32071i	−0.750953	−	0.660356i	$-0.770405\pi$
$743$		−	36.0000i		−	1.32071i	0.750953	−	0.660356i	$-0.229595\pi$
$744$		0			0
$745$		0			0
$746$	−14.0000	−	5.29150i	−0.512576	−	0.193736i
$747$		0			0
$748$	−11.9059	−	10.5000i	−0.435322	−	0.383918i
$749$		−	10.5830i		−	0.386695i
$750$		0			0
$751$	8.00000			0.291924			0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000			0.291924			0.145962	+	0.989290i	$0.453372\pi$
$752$	31.7490	−	4.00000i	1.15777	−	0.145865i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	21.1660			0.769292			0.384646	−	0.923064i	$-0.374324\pi$
$757$	21.1660			0.769292			0.384646	+	0.923064i	$0.374324\pi$
$758$	−3.96863	+	10.5000i	−0.144147	+	0.381377i
$759$		0			0
$760$		0			0
$761$	29.0000			1.05125			0.525625	−	0.850717i	$-0.323832\pi$
$761$	29.0000			1.05125			0.525625	+	0.850717i	$0.323832\pi$
$762$		0			0
$763$	−42.3320			−1.53252
$764$	−6.00000	−	5.29150i	−0.217072	−	0.191440i
$765$		0			0
$766$	−18.0000	+	47.6235i	−0.650366	+	1.72071i
$767$		0			0
$768$		0			0
$769$	21.0000			0.757279			0.378640	−	0.925544i	$-0.376392\pi$
$769$	21.0000			0.757279			0.378640	+	0.925544i	$0.376392\pi$
$770$		0			0
$771$		0			0
$772$	−6.61438	+	7.50000i	−0.238057	+	0.269931i
$773$		0			0			−	1.00000i	$-0.5\pi$
$773$		0			0				1.00000i	$0.5\pi$
$774$		0			0
$775$		0			0
$776$	−5.00000	+	2.64575i	−0.179490	+	0.0949769i
$777$		0			0
$778$	−5.29150	+	14.0000i	−0.189710	+	0.501924i
$779$		−	13.2288i		−	0.473969i
$780$		0			0
$781$			21.1660i			0.757379i
$782$	−15.8745	−	6.00000i	−0.567671	−	0.214560i
$783$		0			0
$784$	−4.50000	−	35.7176i	−0.160714	−	1.27563i
$785$		0			0
$786$		0			0
$787$	−26.4575			−0.943108			−0.471554	−	0.881837i	$-0.656307\pi$
$787$	−26.4575			−0.943108			−0.471554	+	0.881837i	$0.656307\pi$
$788$	−15.8745	−	14.0000i	−0.565506	−	0.498729i
$789$		0			0
$790$		0			0
$791$	60.0000			2.13335
$792$		0			0
$793$		0			0
$794$	−28.0000	−	10.5830i	−0.993683	−	0.375577i
$795$		0			0
$796$	36.0000	+	31.7490i	1.27599	+	1.12531i
$797$	−31.7490			−1.12461			−0.562304	−	0.826931i	$-0.690085\pi$
$797$	−31.7490			−1.12461			−0.562304	+	0.826931i	$0.690085\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$		0			0
$801$		0			0
$802$	−35.7176	−	13.5000i	−1.26123	−	0.476702i
$803$	−18.5203			−0.653566
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−26.4575	+	14.0000i	−0.930772	+	0.492518i
$809$	10.0000			0.351581			0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000			0.351581			0.175791	+	0.984428i	$0.443752\pi$
$810$		0			0
$811$			5.29150i			0.185810i	0.995675	+	0.0929049i	$0.0296153\pi$
$811$			5.29150i			0.185810i	−0.995675	+	0.0929049i	$0.970385\pi$
$812$		0			0
$813$		0			0
$814$	−14.0000	+	37.0405i	−0.490700	+	1.29827i
$815$		0			0
$816$		0			0
$817$		−	14.0000i		−	0.489798i
$818$	−3.96863	−	1.50000i	−0.138760	−	0.0524463i
$819$		0			0
$820$		0			0
$821$			10.5830i			0.369349i	0.982800	+	0.184675i	$0.0591232\pi$
$821$			10.5830i			0.369349i	−0.982800	+	0.184675i	$0.940877\pi$
$822$		0			0
$823$		−	24.0000i		−	0.836587i	−0.908312	−	0.418294i	$-0.862628\pi$
$823$		−	24.0000i		−	0.836587i	0.908312	−	0.418294i	$-0.137372\pi$
$824$	−20.0000	+	10.5830i	−0.696733	+	0.368676i
$825$		0			0
$826$	28.0000	+	10.5830i	0.974245	+	0.368230i
$827$	13.2288			0.460009			0.230004	−	0.973190i	$-0.426126\pi$
$827$	13.2288			0.460009			0.230004	+	0.973190i	$0.426126\pi$
$828$		0			0
$829$			21.1660i			0.735126i	0.929999	+	0.367563i	$0.119808\pi$
$829$			21.1660i			0.735126i	−0.929999	+	0.367563i	$0.880192\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$			27.0000i			0.935495i
$834$		0			0
$835$		0			0
$836$	−10.5000	−	9.26013i	−0.363150	−	0.320268i
$837$		0			0
$838$	9.26013	−	24.5000i	0.319886	−	0.846338i
$839$	40.0000			1.38095			0.690477	−	0.723355i	$-0.257401\pi$
$839$	40.0000			1.38095			0.690477	+	0.723355i	$0.257401\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$	−10.5830	+	28.0000i	−0.364714	+	0.964944i
$843$		0			0
$844$	10.5000	−	11.9059i	0.361425	−	0.409817i
$845$		0			0
$846$		0			0
$847$		−	16.0000i		−	0.549767i
$848$	5.29150	+	42.0000i	0.181711	+	1.44229i
$849$		0			0
$850$		0			0
$851$			42.3320i			1.45112i
$852$		0			0
$853$	−52.9150			−1.81178			−0.905888	−	0.423517i	$-0.860795\pi$
$853$	−52.9150			−1.81178			−0.905888	+	0.423517i	$0.860795\pi$
$854$	56.0000	+	21.1660i	1.91628	+	0.724286i
$855$		0			0
$856$	3.50000	+	6.61438i	0.119628	+	0.226075i
$857$			21.0000i			0.717346i	0.933463	+	0.358673i	$0.116771\pi$
$857$			21.0000i			0.717346i	−0.933463	+	0.358673i	$0.883229\pi$
$858$		0			0
$859$		−	2.64575i		−	0.0902719i	−0.998981	−	0.0451359i	$-0.985628\pi$
$859$		−	2.64575i		−	0.0902719i	0.998981	−	0.0451359i	$-0.0143721\pi$
$860$		0			0
$861$		0			0
$862$	−15.8745	−	6.00000i	−0.540688	−	0.204361i
$863$		−	24.0000i		−	0.816970i	−0.912765	−	0.408485i	$-0.866057\pi$
$863$		−	24.0000i		−	0.816970i	0.912765	−	0.408485i	$-0.133943\pi$
$864$		0			0
$865$		0			0
$866$	−18.5000	+	48.9464i	−0.628656	+	1.66327i
$867$		0			0
$868$	21.1660	−	24.0000i	0.718421	−	0.814613i
$869$			10.5830i			0.359004i
$870$		0			0
$871$		0			0
$872$	26.4575	−	14.0000i	0.895964	−	0.474100i
$873$		0			0
$874$	−14.0000	−	5.29150i	−0.473557	−	0.178988i
$875$		0			0
$876$		0			0
$877$	42.3320			1.42945			0.714725	−	0.699405i	$-0.246552\pi$
$877$	42.3320			1.42945			0.714725	+	0.699405i	$0.246552\pi$
$878$	−10.5830	−	4.00000i	−0.357159	−	0.134993i
$879$		0			0
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	44.9778			1.51362			0.756811	−	0.653633i	$-0.226756\pi$
$883$	44.9778			1.51362			0.756811	+	0.653633i	$0.226756\pi$
$884$		0			0
$885$		0			0
$886$	38.5000	+	14.5516i	1.29343	+	0.488872i
$887$			56.0000i			1.88030i	0.340766	+	0.940148i	$0.389313\pi$
$887$			56.0000i			1.88030i	−0.340766	+	0.940148i	$0.610687\pi$
$888$		0			0
$889$	−48.0000			−1.60987
$890$		0			0
$891$		0			0
$892$	21.1660	−	24.0000i	0.708690	−	0.803579i
$893$	−21.1660			−0.708294
$894$		0			0
$895$		0			0
$896$	26.0000	+	37.0405i	0.868599	+	1.23744i
$897$		0			0
$898$	35.7176	+	13.5000i	1.19191	+	0.450501i
$899$		0			0
$900$		0			0
$901$		−	31.7490i		−	1.05771i
$902$	6.61438	−	17.5000i	0.220235	−	0.582686i
$903$		0			0
$904$	−37.5000	+	19.8431i	−1.24723	+	0.659973i
$905$		0			0
$906$		0			0
$907$	−5.29150			−0.175701			−0.0878507	−	0.996134i	$-0.528000\pi$
$907$	−5.29150			−0.175701			−0.0878507	+	0.996134i	$0.528000\pi$
$908$	−23.8118	−	21.0000i	−0.790221	−	0.696909i
$909$		0			0
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$		−	21.0000i		−	0.694999i
$914$	−13.5000	+	35.7176i	−0.446540	+	1.18143i
$915$		0			0
$916$	28.0000	−	31.7490i	0.925146	−	1.04902i
$917$	63.4980			2.09689
$918$		0			0
$919$	−4.00000			−0.131948			−0.0659739	−	0.997821i	$-0.521015\pi$
$919$	−4.00000			−0.131948			−0.0659739	+	0.997821i	$0.521015\pi$
$920$		0			0
$921$		0			0
$922$	−21.1660	+	56.0000i	−0.697065	+	1.84426i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	4.00000	−	10.5830i	0.131448	−	0.347779i
$927$		0			0
$928$		0			0
$929$	−14.0000			−0.459325			−0.229663	−	0.973270i	$-0.573762\pi$
$929$	−14.0000			−0.459325			−0.229663	+	0.973270i	$0.573762\pi$
$930$		0			0
$931$			23.8118i			0.780399i
$932$	7.93725	−	9.00000i	0.259993	−	0.294805i
$933$		0			0
$934$	35.0000	+	13.2288i	1.14523	+	0.432858i
$935$		0			0
$936$		0			0
$937$			7.00000i			0.228680i	0.993442	+	0.114340i	$0.0364753\pi$
$937$			7.00000i			0.228680i	−0.993442	+	0.114340i	$0.963525\pi$
$938$	15.8745	−	42.0000i	0.518321	−	1.37135i
$939$		0			0
$940$		0			0
$941$		−	42.3320i		−	1.37998i	−0.723817	−	0.689992i	$-0.757614\pi$
$941$		−	42.3320i		−	1.37998i	0.723817	−	0.689992i	$-0.242386\pi$
$942$		0			0
$943$		−	20.0000i		−	0.651290i
$944$	−21.0000	+	2.64575i	−0.683492	+	0.0861119i
$945$		0			0
$946$	7.00000	−	18.5203i	0.227590	−	0.602146i
$947$	−15.8745			−0.515852			−0.257926	−	0.966165i	$-0.583039\pi$
$947$	−15.8745			−0.515852			−0.257926	+	0.966165i	$0.583039\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$	−15.8745	−	30.0000i	−0.514496	−	0.972306i
$953$		−	5.00000i		−	0.161966i	−0.996715	−	0.0809829i	$-0.974194\pi$
$953$		−	5.00000i		−	0.161966i	0.996715	−	0.0809829i	$-0.0258059\pi$
$954$		0			0
$955$		0			0
$956$	−12.0000	−	10.5830i	−0.388108	−	0.342279i
$957$		0			0
$958$	5.29150	+	2.00000i	0.170961	+	0.0646171i
$959$	−76.0000			−2.45417
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$		0			0
$964$	−31.5000	−	27.7804i	−1.01455	−	0.894746i
$965$		0			0
$966$		0			0
$967$		−	8.00000i		−	0.257263i	−0.991692	−	0.128631i	$-0.958942\pi$
$967$		−	8.00000i		−	0.257263i	0.991692	−	0.128631i	$-0.0410584\pi$
$968$	5.29150	+	10.0000i	0.170075	+	0.321412i
$969$		0			0
$970$		0			0
$971$		−	23.8118i		−	0.764156i	−0.924130	−	0.382078i	$-0.875209\pi$
$971$		−	23.8118i		−	0.764156i	0.924130	−	0.382078i	$-0.124791\pi$
$972$		0			0
$973$	74.0810			2.37493
$974$	−6.00000	+	15.8745i	−0.192252	+	0.508652i
$975$		0			0
$976$	−42.0000	+	5.29150i	−1.34439	+	0.169377i
$977$			37.0000i			1.18373i	0.806035	+	0.591867i	$0.201609\pi$
$977$			37.0000i			1.18373i	−0.806035	+	0.591867i	$0.798391\pi$
$978$		0			0
$979$			2.64575i			0.0845586i
$980$		0			0
$981$		0			0
$982$	2.64575	−	7.00000i	0.0844293	−	0.223379i
$983$			28.0000i			0.893061i	0.894768	+	0.446531i	$0.147341\pi$
$983$			28.0000i			0.893061i	−0.894768	+	0.446531i	$0.852659\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	21.1660i		−	0.673040i
$990$		0			0
$991$	44.0000			1.39771			0.698853	−	0.715265i	$-0.253694\pi$
$991$	44.0000			1.39771			0.698853	+	0.715265i	$0.253694\pi$
$992$	−5.29150	+	22.0000i	−0.168005	+	0.698501i
$993$		0			0
$994$	−16.0000	+	42.3320i	−0.507489	+	1.34269i
$995$		0			0
$996$		0			0
$997$	42.3320			1.34067			0.670334	−	0.742059i	$-0.266151\pi$
$997$	42.3320			1.34067			0.670334	+	0.742059i	$0.266151\pi$
$998$	13.2288	−	35.0000i	0.418749	−	1.10791i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.d.m.1549.4		4
3.2	odd	2		200.2.f.d.149.1		4
4.3	odd	2		7200.2.d.m.2449.4		4
5.2	odd	4		1800.2.k.d.901.2		2
5.3	odd	4		1800.2.k.f.901.1		2
5.4	even	2	inner	1800.2.d.m.1549.1		4
8.3	odd	2		7200.2.d.m.2449.3		4
8.5	even	2	inner	1800.2.d.m.1549.2		4
12.11	even	2		800.2.f.d.49.2		4
15.2	even	4		200.2.d.c.101.1	yes	2
15.8	even	4		200.2.d.b.101.2	yes	2
15.14	odd	2		200.2.f.d.149.4		4
20.3	even	4		7200.2.k.i.3601.2		2
20.7	even	4		7200.2.k.b.3601.2		2
20.19	odd	2		7200.2.d.m.2449.2		4
24.5	odd	2		200.2.f.d.149.3		4
24.11	even	2		800.2.f.d.49.4		4
40.3	even	4		7200.2.k.i.3601.1		2
40.13	odd	4		1800.2.k.f.901.2		2
40.19	odd	2		7200.2.d.m.2449.1		4
40.27	even	4		7200.2.k.b.3601.1		2
40.29	even	2	inner	1800.2.d.m.1549.3		4
40.37	odd	4		1800.2.k.d.901.1		2
60.23	odd	4		800.2.d.d.401.1		2
60.47	odd	4		800.2.d.a.401.2		2
60.59	even	2		800.2.f.d.49.3		4
120.29	odd	2		200.2.f.d.149.2		4
120.53	even	4		200.2.d.b.101.1	✓	2
120.59	even	2		800.2.f.d.49.1		4
120.77	even	4		200.2.d.c.101.2	yes	2
120.83	odd	4		800.2.d.d.401.2		2
120.107	odd	4		800.2.d.a.401.1		2
240.53	even	4		6400.2.a.cc.1.2		2
240.77	even	4		6400.2.a.bg.1.2		2
240.83	odd	4		6400.2.a.bh.1.2		2
240.107	odd	4		6400.2.a.cb.1.2		2
240.173	even	4		6400.2.a.cc.1.1		2
240.197	even	4		6400.2.a.bg.1.1		2
240.203	odd	4		6400.2.a.bh.1.1		2
240.227	odd	4		6400.2.a.cb.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.d.b.101.1	✓	2	120.53	even	4
200.2.d.b.101.2	yes	2	15.8	even	4
200.2.d.c.101.1	yes	2	15.2	even	4
200.2.d.c.101.2	yes	2	120.77	even	4
200.2.f.d.149.1		4	3.2	odd	2
200.2.f.d.149.2		4	120.29	odd	2
200.2.f.d.149.3		4	24.5	odd	2
200.2.f.d.149.4		4	15.14	odd	2
800.2.d.a.401.1		2	120.107	odd	4
800.2.d.a.401.2		2	60.47	odd	4
800.2.d.d.401.1		2	60.23	odd	4
800.2.d.d.401.2		2	120.83	odd	4
800.2.f.d.49.1		4	120.59	even	2
800.2.f.d.49.2		4	12.11	even	2
800.2.f.d.49.3		4	60.59	even	2
800.2.f.d.49.4		4	24.11	even	2
1800.2.d.m.1549.1		4	5.4	even	2	inner
1800.2.d.m.1549.2		4	8.5	even	2	inner
1800.2.d.m.1549.3		4	40.29	even	2	inner
1800.2.d.m.1549.4		4	1.1	even	1	trivial
1800.2.k.d.901.1		2	40.37	odd	4
1800.2.k.d.901.2		2	5.2	odd	4
1800.2.k.f.901.1		2	5.3	odd	4
1800.2.k.f.901.2		2	40.13	odd	4
6400.2.a.bg.1.1		2	240.197	even	4
6400.2.a.bg.1.2		2	240.77	even	4
6400.2.a.bh.1.1		2	240.203	odd	4
6400.2.a.bh.1.2		2	240.83	odd	4
6400.2.a.cb.1.1		2	240.227	odd	4
6400.2.a.cb.1.2		2	240.107	odd	4
6400.2.a.cc.1.1		2	240.173	even	4
6400.2.a.cc.1.2		2	240.53	even	4
7200.2.d.m.2449.1		4	40.19	odd	2
7200.2.d.m.2449.2		4	20.19	odd	2
7200.2.d.m.2449.3		4	8.3	odd	2
7200.2.d.m.2449.4		4	4.3	odd	2
7200.2.k.b.3601.1		2	40.27	even	4
7200.2.k.b.3601.2		2	20.7	even	4
7200.2.k.i.3601.1		2	40.3	even	4
7200.2.k.i.3601.2		2	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.32288 + 0.500000i) q^{2} +(1.50000 + 1.32288i) q^{4} -4.00000i q^{7} +(1.32288 + 2.50000i) q^{8} +O(q^{10})\)	\(q+(1.32288 + 0.500000i) q^{2} +(1.50000 + 1.32288i) q^{4} -4.00000i q^{7} +(1.32288 + 2.50000i) q^{8} -2.64575i q^{11} +(2.00000 - 5.29150i) q^{14} +(0.500000 + 3.96863i) q^{16} -3.00000i q^{17} -2.64575i q^{19} +(1.32288 - 3.50000i) q^{22} -4.00000i q^{23} +(5.29150 - 6.00000i) q^{28} +4.00000 q^{31} +(-1.32288 + 5.50000i) q^{32} +(1.50000 - 3.96863i) q^{34} -10.5830 q^{37} +(1.32288 - 3.50000i) q^{38} +5.00000 q^{41} +5.29150 q^{43} +(3.50000 - 3.96863i) q^{44} +(2.00000 - 5.29150i) q^{46} -8.00000i q^{47} -9.00000 q^{49} +10.5830 q^{53} +(10.0000 - 5.29150i) q^{56} +5.29150i q^{59} +10.5830i q^{61} +(5.29150 + 2.00000i) q^{62} +(-4.50000 + 6.61438i) q^{64} +7.93725 q^{67} +(3.96863 - 4.50000i) q^{68} -8.00000 q^{71} -7.00000i q^{73} +(-14.0000 - 5.29150i) q^{74} +(3.50000 - 3.96863i) q^{76} -10.5830 q^{77} -4.00000 q^{79} +(6.61438 + 2.50000i) q^{82} +7.93725 q^{83} +(7.00000 + 2.64575i) q^{86} +(6.61438 - 3.50000i) q^{88} -1.00000 q^{89} +(5.29150 - 6.00000i) q^{92} +(4.00000 - 10.5830i) q^{94} +2.00000i q^{97} +(-11.9059 - 4.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{4}+O(q^{10}) \) 4 * q + 6 * q^4	\( 4 q + 6 q^{4} + 8 q^{14} + 2 q^{16} + 16 q^{31} + 6 q^{34} + 20 q^{41} + 14 q^{44} + 8 q^{46} - 36 q^{49} + 40 q^{56} - 18 q^{64} - 32 q^{71} - 56 q^{74} + 14 q^{76} - 16 q^{79} + 28 q^{86} - 4 q^{89} + 16 q^{94}+O(q^{100}) \) 4 * q + 6 * q^4 + 8 * q^14 + 2 * q^16 + 16 * q^31 + 6 * q^34 + 20 * q^41 + 14 * q^44 + 8 * q^46 - 36 * q^49 + 40 * q^56 - 18 * q^64 - 32 * q^71 - 56 * q^74 + 14 * q^76 - 16 * q^79 + 28 * q^86 - 4 * q^89 + 16 * q^94

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