LMFDB - Embedded newform 1134.2.d.a.1133.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(1133,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1134.1133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.d (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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1133.7
Root			$1.40917 + 1.00709i$ of defining polynomial
Character	$\chi$	$=$	1134.1133
Dual form			1134.2.d.a.1133.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +2.34936 q^{5} +(1.07781 - 2.41626i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +2.34936 q^{5} +(1.07781 - 2.41626i) q^{7} +1.00000i q^{8} -2.34936i q^{10} -5.67667i q^{11} +1.71985i q^{13} +(-2.41626 - 1.07781i) q^{14} +1.00000 q^{16} +1.76883 q^{17} -1.13932i q^{19} -2.34936 q^{20} -5.67667 q^{22} +3.67509i q^{23} +0.519482 q^{25} +1.71985 q^{26} +(-1.07781 + 2.41626i) q^{28} +4.15561i q^{29} -8.37019i q^{31} -1.00000i q^{32} -1.76883i q^{34} +(2.53215 - 5.67667i) q^{35} -9.19773 q^{37} -1.13932 q^{38} +2.34936i q^{40} +7.99419 q^{41} -3.52106 q^{43} +5.67667i q^{44} +3.67509 q^{46} +11.8099 q^{47} +(-4.67667 - 5.20853i) q^{49} -0.519482i q^{50} -1.71985i q^{52} -13.3365i q^{55} +(2.41626 + 1.07781i) q^{56} +4.15561 q^{58} +2.22966 q^{59} -8.99970i q^{61} -8.37019 q^{62} -1.00000 q^{64} +4.04054i q^{65} +10.8712 q^{67} -1.76883 q^{68} +(-5.67667 - 2.53215i) q^{70} -4.52106i q^{71} +5.34234i q^{73} +9.19773i q^{74} +1.13932i q^{76} +(-13.7163 - 6.11835i) q^{77} -13.0284 q^{79} +2.34936 q^{80} -7.99419i q^{82} -12.5460 q^{83} +4.15561 q^{85} +3.52106i q^{86} +5.67667 q^{88} +1.16106 q^{89} +(4.15561 + 1.85366i) q^{91} -3.67509i q^{92} -11.8099i q^{94} -2.67667i q^{95} +4.59035i q^{97} +(-5.20853 + 4.67667i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 4 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 - 4 * q^7	$ 16 q - 16 q^{4} - 4 q^{7} + 16 q^{16} + 16 q^{25} + 4 q^{28} - 8 q^{37} - 8 q^{43} + 24 q^{46} + 16 q^{49} + 24 q^{58} - 16 q^{64} + 56 q^{67} + 8 q^{79} + 24 q^{85} + 24 q^{91}+O(q^{100}) $ 16 * q - 16 * q^4 - 4 * q^7 + 16 * q^16 + 16 * q^25 + 4 * q^28 - 8 * q^37 - 8 * q^43 + 24 * q^46 + 16 * q^49 + 24 * q^58 - 16 * q^64 + 56 * q^67 + 8 * q^79 + 24 * q^85 + 24 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	2.34936			1.05066			0.525332	−	0.850897i	$-0.323941\pi$
$5$	2.34936			1.05066			0.525332	+	0.850897i	$0.323941\pi$
$6$		0			0
$7$	1.07781	−	2.41626i	0.407372	−	0.913262i
$7$	1.07781	−	2.41626i	0.407372	−	0.913262i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		−	2.34936i		−	0.742932i
$11$		−	5.67667i		−	1.71158i	−0.517323	−	0.855790i	$-0.673071\pi$
$11$		−	5.67667i		−	1.71158i	0.517323	−	0.855790i	$-0.326929\pi$
$12$		0			0
$13$			1.71985i			0.477000i	0.971142	+	0.238500i	$0.0766558\pi$
$13$			1.71985i			0.477000i	−0.971142	+	0.238500i	$0.923344\pi$
$14$	−2.41626	−	1.07781i	−0.645774	−	0.288056i
$15$		0			0
$16$	1.00000			0.250000
$17$	1.76883			0.429004			0.214502	−	0.976724i	$-0.431187\pi$
$17$	1.76883			0.429004			0.214502	+	0.976724i	$0.431187\pi$
$18$		0			0
$19$		−	1.13932i		−	0.261378i	−0.991423	−	0.130689i	$-0.958281\pi$
$19$		−	1.13932i		−	0.261378i	0.991423	−	0.130689i	$-0.0417189\pi$
$20$	−2.34936			−0.525332
$21$		0			0
$22$	−5.67667			−1.21027
$23$			3.67509i			0.766310i	0.923684	+	0.383155i	$0.125162\pi$
$23$			3.67509i			0.766310i	−0.923684	+	0.383155i	$0.874838\pi$
$24$		0			0
$25$	0.519482			0.103896
$26$	1.71985			0.337290
$27$		0			0
$28$	−1.07781	+	2.41626i	−0.203686	+	0.456631i
$29$			4.15561i			0.771678i	0.922566	+	0.385839i	$0.126088\pi$
$29$			4.15561i			0.771678i	−0.922566	+	0.385839i	$0.873912\pi$
$30$		0			0
$31$		−	8.37019i		−	1.50333i	−0.659545	−	0.751665i	$-0.729251\pi$
$31$		−	8.37019i		−	1.50333i	0.659545	−	0.751665i	$-0.270749\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$		−	1.76883i		−	0.303352i
$35$	2.53215	−	5.67667i	0.428012	−	0.959532i
$36$		0			0
$37$	−9.19773			−1.51210			−0.756049	−	0.654515i	$-0.772873\pi$
$37$	−9.19773			−1.51210			−0.756049	+	0.654515i	$0.772873\pi$
$38$	−1.13932			−0.184822
$39$		0			0
$40$			2.34936i			0.371466i
$41$	7.99419			1.24848			0.624241	−	0.781232i	$-0.285408\pi$
$41$	7.99419			1.24848			0.624241	+	0.781232i	$0.285408\pi$
$42$		0			0
$43$	−3.52106			−0.536956			−0.268478	−	0.963286i	$-0.586521\pi$
$43$	−3.52106			−0.536956			−0.268478	+	0.963286i	$0.586521\pi$
$44$			5.67667i			0.855790i
$45$		0			0
$46$	3.67509			0.541863
$47$	11.8099			1.72265			0.861324	−	0.508055i	$-0.169635\pi$
$47$	11.8099			1.72265			0.861324	+	0.508055i	$0.169635\pi$
$48$		0			0
$49$	−4.67667	−	5.20853i	−0.668096	−	0.744075i
$50$		−	0.519482i		−	0.0734659i
$51$		0			0
$52$		−	1.71985i		−	0.238500i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$		−	13.3365i		−	1.79830i
$56$	2.41626	+	1.07781i	0.322887	+	0.144028i
$57$		0			0
$58$	4.15561			0.545658
$59$	2.22966			0.290277			0.145139	−	0.989411i	$-0.453637\pi$
$59$	2.22966			0.290277			0.145139	+	0.989411i	$0.453637\pi$
$60$		0			0
$61$		−	8.99970i		−	1.15229i	−0.817346	−	0.576146i	$-0.804556\pi$
$61$		−	8.99970i		−	1.15229i	0.817346	−	0.576146i	$-0.195444\pi$
$62$	−8.37019			−1.06301
$63$		0			0
$64$	−1.00000			−0.125000
$65$			4.04054i			0.501167i
$66$		0			0
$67$	10.8712			1.32813			0.664067	−	0.747673i	$-0.268829\pi$
$67$	10.8712			1.32813			0.664067	+	0.747673i	$0.268829\pi$
$68$	−1.76883			−0.214502
$69$		0			0
$70$	−5.67667	−	2.53215i	−0.678492	−	0.302650i
$71$		−	4.52106i		−	0.536551i	−0.963342	−	0.268276i	$-0.913546\pi$
$71$		−	4.52106i		−	0.536551i	0.963342	−	0.268276i	$-0.0864538\pi$
$72$		0			0
$73$			5.34234i			0.625274i	0.949873	+	0.312637i	$0.101212\pi$
$73$			5.34234i			0.625274i	−0.949873	+	0.312637i	$0.898788\pi$
$74$			9.19773i			1.06921i
$75$		0			0
$76$			1.13932i			0.130689i
$77$	−13.7163	−	6.11835i	−1.56312	−	0.697250i
$78$		0			0
$79$	−13.0284			−1.46581			−0.732907	−	0.680329i	$-0.761837\pi$
$79$	−13.0284			−1.46581			−0.732907	+	0.680329i	$0.761837\pi$
$80$	2.34936			0.262666
$81$		0			0
$82$		−	7.99419i		−	0.882810i
$83$	−12.5460			−1.37710			−0.688549	−	0.725189i	$-0.741752\pi$
$83$	−12.5460			−1.37710			−0.688549	+	0.725189i	$0.741752\pi$
$84$		0			0
$85$	4.15561			0.450739
$86$			3.52106i			0.379686i
$87$		0			0
$88$	5.67667			0.605135
$89$	1.16106			0.123072			0.0615360	−	0.998105i	$-0.480400\pi$
$89$	1.16106			0.123072			0.0615360	+	0.998105i	$0.480400\pi$
$90$		0			0
$91$	4.15561	+	1.85366i	0.435626	+	0.194317i
$92$		−	3.67509i		−	0.383155i
$93$		0			0
$94$		−	11.8099i		−	1.21810i
$95$		−	2.67667i		−	0.274621i
$96$		0			0
$97$			4.59035i			0.466079i	0.972467	+	0.233039i	$0.0748671\pi$
$97$			4.59035i			0.466079i	−0.972467	+	0.233039i	$0.925133\pi$
$98$	−5.20853	+	4.67667i	−0.526141	+	0.472415i
$99$		0			0
$100$	−0.519482			−0.0519482
$101$	6.62310			0.659023			0.329511	−	0.944152i	$-0.393116\pi$
$101$	6.62310			0.659023			0.329511	+	0.944152i	$0.393116\pi$
$102$		0			0
$103$		−	5.85977i		−	0.577381i	−0.957423	−	0.288690i	$-0.906780\pi$
$103$		−	5.85977i		−	0.577381i	0.957423	−	0.288690i	$-0.0932198\pi$
$104$	−1.71985			−0.168645
$105$		0			0
$106$		0			0
$107$			4.71563i			0.455878i	0.973675	+	0.227939i	$0.0731986\pi$
$107$			4.71563i			0.455878i	−0.973675	+	0.227939i	$0.926801\pi$
$108$		0			0
$109$	4.23669			0.405802			0.202901	−	0.979199i	$-0.434963\pi$
$109$	4.23669			0.405802			0.202901	+	0.979199i	$0.434963\pi$
$110$	−13.3365			−1.27159
$111$		0			0
$112$	1.07781	−	2.41626i	0.101843	−	0.228316i
$113$		−	6.83228i		−	0.642727i	−0.946956	−	0.321363i	$-0.895859\pi$
$113$		−	6.83228i		−	0.642727i	0.946956	−	0.321363i	$-0.104141\pi$
$114$		0			0
$115$			8.63411i			0.805135i
$116$		−	4.15561i		−	0.385839i
$117$		0			0
$118$		−	2.22966i		−	0.205257i
$119$	1.90645	−	4.27396i	0.174764	−	0.391793i
$120$		0			0
$121$	−21.2246			−1.92951
$122$	−8.99970			−0.814794
$123$		0			0
$124$			8.37019i			0.751665i
$125$	−10.5263			−0.941504
$126$		0			0
$127$	−6.67667			−0.592459			−0.296229	−	0.955117i	$-0.595729\pi$
$127$	−6.67667			−0.592459			−0.296229	+	0.955117i	$0.595729\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	4.04054			0.354379
$131$	7.47305			0.652923			0.326462	−	0.945210i	$-0.394144\pi$
$131$	7.47305			0.652923			0.326462	+	0.945210i	$0.394144\pi$
$132$		0			0
$133$	−2.75290	−	1.22797i	−0.238707	−	0.106478i
$134$		−	10.8712i		−	0.939133i
$135$		0			0
$136$			1.76883i			0.151676i
$137$			7.98789i			0.682452i	0.939981	+	0.341226i	$0.110842\pi$
$137$			7.98789i			0.682452i	−0.939981	+	0.341226i	$0.889158\pi$
$138$		0			0
$139$			20.7606i			1.76089i	0.474147	+	0.880446i	$0.342756\pi$
$139$			20.7606i			1.76089i	−0.474147	+	0.880446i	$0.657244\pi$
$140$	−2.53215	+	5.67667i	−0.214006	+	0.479766i
$141$		0			0
$142$	−4.52106			−0.379399
$143$	9.76302			0.816425
$144$		0			0
$145$			9.76302i			0.810774i
$146$	5.34234			0.442135
$147$		0			0
$148$	9.19773			0.756049
$149$			1.19773i			0.0981218i	0.998796	+	0.0490609i	$0.0156228\pi$
$149$			1.19773i			0.0981218i	−0.998796	+	0.0490609i	$0.984377\pi$
$150$		0			0
$151$	15.2246			1.23896			0.619480	−	0.785013i	$-0.287344\pi$
$151$	15.2246			1.23896			0.619480	+	0.785013i	$0.287344\pi$
$152$	1.13932			0.0924111
$153$		0			0
$154$	−6.11835	+	13.7163i	−0.493030	+	1.10529i
$155$		−	19.6646i		−	1.57950i
$156$		0			0
$157$			10.0269i			0.800237i	0.916463	+	0.400118i	$0.131031\pi$
$157$			10.0269i			0.800237i	−0.916463	+	0.400118i	$0.868969\pi$
$158$			13.0284i			1.03649i
$159$		0			0
$160$		−	2.34936i		−	0.185733i
$161$	8.88000	+	3.96104i	0.699842	+	0.312173i
$162$		0			0
$163$	12.0032			0.940160			0.470080	−	0.882624i	$-0.344225\pi$
$163$	12.0032			0.940160			0.470080	+	0.882624i	$0.344225\pi$
$164$	−7.99419			−0.624241
$165$		0			0
$166$			12.5460i			0.973756i
$167$	17.1494			1.32706			0.663532	−	0.748148i	$-0.269057\pi$
$167$	17.1494			1.32706			0.663532	+	0.748148i	$0.269057\pi$
$168$		0			0
$169$	10.0421			0.772471
$170$		−	4.15561i		−	0.318721i
$171$		0			0
$172$	3.52106			0.268478
$173$	1.98748			0.151105			0.0755525	−	0.997142i	$-0.475928\pi$
$173$	1.98748			0.151105			0.0755525	+	0.997142i	$0.475928\pi$
$174$		0			0
$175$	0.559901	−	1.25521i	0.0423245	−	0.0948847i
$176$		−	5.67667i		−	0.427895i
$177$		0			0
$178$		−	1.16106i		−	0.0870250i
$179$			8.31122i			0.621210i	0.950539	+	0.310605i	$0.100532\pi$
$179$			8.31122i			0.621210i	−0.950539	+	0.310605i	$0.899468\pi$
$180$		0			0
$181$		−	15.4541i		−	1.14870i	−0.818611	−	0.574348i	$-0.805256\pi$
$181$		−	15.4541i		−	1.14870i	0.818611	−	0.574348i	$-0.194744\pi$
$182$	1.85366	−	4.15561i	0.137403	−	0.308034i
$183$		0			0
$184$	−3.67509			−0.270931
$185$	−21.6088			−1.58871
$186$		0			0
$187$		−	10.0411i		−	0.734275i
$188$	−11.8099			−0.861324
$189$		0			0
$190$	−2.67667			−0.194186
$191$			12.3381i			0.892752i	0.894845	+	0.446376i	$0.147286\pi$
$191$			12.3381i			0.892752i	−0.894845	+	0.446376i	$0.852714\pi$
$192$		0			0
$193$	4.39388			0.316279			0.158139	−	0.987417i	$-0.449451\pi$
$193$	4.39388			0.316279			0.158139	+	0.987417i	$0.449451\pi$
$194$	4.59035			0.329568
$195$		0			0
$196$	4.67667	+	5.20853i	0.334048	+	0.372038i
$197$			10.8865i			0.775632i	0.921737	+	0.387816i	$0.126770\pi$
$197$			10.8865i			0.775632i	−0.921737	+	0.387816i	$0.873230\pi$
$198$		0			0
$199$			27.5665i			1.95414i	0.212926	+	0.977068i	$0.431701\pi$
$199$			27.5665i			1.95414i	−0.212926	+	0.977068i	$0.568299\pi$
$200$			0.519482i			0.0367329i
$201$		0			0
$202$		−	6.62310i		−	0.465999i
$203$	10.0411	+	4.47894i	0.704744	+	0.314360i
$204$		0			0
$205$	18.7812			1.31174
$206$	−5.85977			−0.408270
$207$		0			0
$208$			1.71985i			0.119250i
$209$	−6.46754			−0.447369
$210$		0			0
$211$	−10.3112			−0.709854			−0.354927	−	0.934894i	$-0.615494\pi$
$211$	−10.3112			−0.709854			−0.354927	+	0.934894i	$0.615494\pi$
$212$		0			0
$213$		0			0
$214$	4.71563			0.322354
$215$	−8.27223			−0.564161
$216$		0			0
$217$	−20.2246	−	9.02143i	−1.37293	−	0.612415i
$218$		−	4.23669i		−	0.286945i
$219$		0			0
$220$			13.3365i			0.899149i
$221$			3.04212i			0.204635i
$222$		0			0
$223$			7.20913i			0.482759i	0.970431	+	0.241379i	$0.0775998\pi$
$223$			7.20913i			0.482759i	−0.970431	+	0.241379i	$0.922400\pi$
$224$	−2.41626	−	1.07781i	−0.161443	−	0.0720139i
$225$		0			0
$226$	−6.83228			−0.454477
$227$	12.7560			0.846645			0.423323	−	0.905979i	$-0.360864\pi$
$227$	12.7560			0.846645			0.423323	+	0.905979i	$0.360864\pi$
$228$		0			0
$229$			4.49418i			0.296984i	0.988914	+	0.148492i	$0.0474419\pi$
$229$			4.49418i			0.296984i	−0.988914	+	0.148492i	$0.952558\pi$
$230$	8.63411			0.569316
$231$		0			0
$232$	−4.15561			−0.272829
$233$			2.15403i			0.141115i	0.997508	+	0.0705577i	$0.0224779\pi$
$233$			2.15403i			0.141115i	−0.997508	+	0.0705577i	$0.977522\pi$
$234$		0			0
$235$	27.7456			1.80993
$236$	−2.22966			−0.145139
$237$		0			0
$238$	−4.27396	−	1.90645i	−0.277040	−	0.123577i
$239$			10.1419i			0.656027i	0.944673	+	0.328013i	$0.106379\pi$
$239$			10.1419i			0.656027i	−0.944673	+	0.328013i	$0.893621\pi$
$240$		0			0
$241$		−	10.5481i		−	0.679461i	−0.940523	−	0.339731i	$-0.889664\pi$
$241$		−	10.5481i		−	0.679461i	0.940523	−	0.339731i	$-0.110336\pi$
$242$			21.2246i			1.36437i
$243$		0			0
$244$			8.99970i			0.576146i
$245$	−10.9872	−	12.2367i	−0.701945	−	0.781774i
$246$		0			0
$247$	1.95946			0.124677
$248$	8.37019			0.531507
$249$		0			0
$250$			10.5263i			0.665744i
$251$	29.3005			1.84943			0.924714	−	0.380662i	$-0.124304\pi$
$251$	29.3005			1.84943			0.924714	+	0.380662i	$0.124304\pi$
$252$		0			0
$253$	20.8623			1.31160
$254$			6.67667i			0.418932i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−7.62860			−0.475859			−0.237930	−	0.971282i	$-0.576469\pi$
$257$	−7.62860			−0.475859			−0.237930	+	0.971282i	$0.576469\pi$
$258$		0			0
$259$	−9.91336	+	22.2241i	−0.615986	+	1.38094i
$260$		−	4.04054i		−	0.250584i
$261$		0			0
$262$		−	7.47305i		−	0.461687i
$263$		−	12.1856i		−	0.751398i	−0.926742	−	0.375699i	$-0.877403\pi$
$263$		−	12.1856i		−	0.751398i	0.926742	−	0.375699i	$-0.122597\pi$
$264$		0			0
$265$		0			0
$266$	−1.22797	+	2.75290i	−0.0752914	+	0.168791i
$267$		0			0
$268$	−10.8712			−0.664067
$269$	−2.77433			−0.169154			−0.0845771	−	0.996417i	$-0.526954\pi$
$269$	−2.77433			−0.169154			−0.0845771	+	0.996417i	$0.526954\pi$
$270$		0			0
$271$		−	3.20793i		−	0.194868i	−0.995242	−	0.0974338i	$-0.968937\pi$
$271$		−	3.20793i		−	0.194868i	0.995242	−	0.0974338i	$-0.0310634\pi$
$272$	1.76883			0.107251
$273$		0			0
$274$	7.98789			0.482566
$275$		−	2.94893i		−	0.177827i
$276$		0			0
$277$	10.0811			0.605714			0.302857	−	0.953036i	$-0.402060\pi$
$277$	10.0811			0.605714			0.302857	+	0.953036i	$0.402060\pi$
$278$	20.7606			1.24514
$279$		0			0
$280$	5.67667	+	2.53215i	0.339246	+	0.151325i
$281$			4.87282i			0.290688i	0.989381	+	0.145344i	$0.0464289\pi$
$281$			4.87282i			0.290688i	−0.989381	+	0.145344i	$0.953571\pi$
$282$		0			0
$283$		−	2.81781i		−	0.167502i	−0.996487	−	0.0837508i	$-0.973310\pi$
$283$		−	2.81781i		−	0.167502i	0.996487	−	0.0837508i	$-0.0266900\pi$
$284$			4.52106i			0.268276i
$285$		0			0
$286$		−	9.76302i		−	0.577299i
$287$	8.61618	−	19.3161i	0.508597	−	1.14019i
$288$		0			0
$289$	−13.8712			−0.815956
$290$	9.76302			0.573304
$291$		0			0
$292$		−	5.34234i		−	0.312637i
$293$	−8.11389			−0.474018			−0.237009	−	0.971507i	$-0.576167\pi$
$293$	−8.11389			−0.474018			−0.237009	+	0.971507i	$0.576167\pi$
$294$		0			0
$295$	5.23827			0.304984
$296$		−	9.19773i		−	0.534607i
$297$		0			0
$298$	1.19773			0.0693826
$299$	−6.32061			−0.365530
$300$		0			0
$301$	−3.79502	+	8.50781i	−0.218741	+	0.490382i
$302$		−	15.2246i		−	0.876076i
$303$		0			0
$304$		−	1.13932i		−	0.0653445i
$305$		−	21.1435i		−	1.21067i
$306$		0			0
$307$			10.8996i			0.622074i	0.950398	+	0.311037i	$0.100676\pi$
$307$			10.8996i			0.622074i	−0.950398	+	0.311037i	$0.899324\pi$
$308$	13.7163	+	6.11835i	0.781561	+	0.348625i
$309$		0			0
$310$	−19.6646			−1.11687
$311$	8.23637			0.467042			0.233521	−	0.972352i	$-0.424975\pi$
$311$	8.23637			0.467042			0.233521	+	0.972352i	$0.424975\pi$
$312$		0			0
$313$			33.8023i			1.91062i	0.295611	+	0.955308i	$0.404477\pi$
$313$			33.8023i			1.91062i	−0.295611	+	0.955308i	$0.595523\pi$
$314$	10.0269			0.565853
$315$		0			0
$316$	13.0284			0.732907
$317$			6.73090i			0.378045i	0.981973	+	0.189022i	$0.0605319\pi$
$317$			6.73090i			0.378045i	−0.981973	+	0.189022i	$0.939468\pi$
$318$		0			0
$319$	23.5900			1.32079
$320$	−2.34936			−0.131333
$321$		0			0
$322$	3.96104	−	8.88000i	0.220740	−	0.494863i
$323$		−	2.01526i		−	0.112132i
$324$		0			0
$325$			0.893431i			0.0495586i
$326$		−	12.0032i		−	0.664793i
$327$		0			0
$328$			7.99419i			0.441405i
$329$	12.7288	−	28.5358i	0.701759	−	1.57323i
$330$		0			0
$331$	−32.0569			−1.76200			−0.881002	−	0.473112i	$-0.843131\pi$
$331$	−32.0569			−1.76200			−0.881002	+	0.473112i	$0.843131\pi$
$332$	12.5460			0.688549
$333$		0			0
$334$		−	17.1494i		−	0.938375i
$335$	25.5404			1.39542
$336$		0			0
$337$	24.2246			1.31960			0.659799	−	0.751442i	$-0.270642\pi$
$337$	24.2246			1.31960			0.659799	+	0.751442i	$0.270642\pi$
$338$		−	10.0421i		−	0.546219i
$339$		0			0
$340$	−4.15561			−0.225370
$341$	−47.5148			−2.57307
$342$		0			0
$343$	−17.6257	+	5.68629i	−0.951700	+	0.307031i
$344$		−	3.52106i		−	0.189843i
$345$		0			0
$346$		−	1.98748i		−	0.106847i
$347$		−	22.7999i		−	1.22396i	−0.790873	−	0.611981i	$-0.790373\pi$
$347$		−	22.7999i		−	1.22396i	0.790873	−	0.611981i	$-0.209627\pi$
$348$		0			0
$349$			2.84505i			0.152292i	0.997097	+	0.0761461i	$0.0242615\pi$
$349$			2.84505i			0.152292i	−0.997097	+	0.0761461i	$0.975738\pi$
$350$	−1.25521	−	0.559901i	−0.0670936	−	0.0299279i
$351$		0			0
$352$	−5.67667			−0.302568
$353$	−7.14424			−0.380249			−0.190125	−	0.981760i	$-0.560889\pi$
$353$	−7.14424			−0.380249			−0.190125	+	0.981760i	$0.560889\pi$
$354$		0			0
$355$		−	10.6216i		−	0.563735i
$356$	−1.16106			−0.0615360
$357$		0			0
$358$	8.31122			0.439262
$359$			11.6037i			0.612421i	0.951964	+	0.306210i	$0.0990611\pi$
$359$			11.6037i			0.612421i	−0.951964	+	0.306210i	$0.900939\pi$
$360$		0			0
$361$	17.7019			0.931682
$362$	−15.4541			−0.812250
$363$		0			0
$364$	−4.15561	−	1.85366i	−0.217813	−	0.0971583i
$365$			12.5511i			0.656953i
$366$		0			0
$367$		−	7.83493i		−	0.408980i	−0.978869	−	0.204490i	$-0.934446\pi$
$367$		−	7.83493i		−	0.408980i	0.978869	−	0.204490i	$-0.0655536\pi$
$368$			3.67509i			0.191577i
$369$		0			0
$370$			21.6088i			1.12339i
$371$		0			0
$372$		0			0
$373$	25.6677			1.32902			0.664512	−	0.747278i	$-0.268639\pi$
$373$	25.6677			1.32902			0.664512	+	0.747278i	$0.268639\pi$
$374$	−10.0411			−0.519211
$375$		0			0
$376$			11.8099i			0.609048i
$377$	−7.14702			−0.368091
$378$		0			0
$379$	−15.1045			−0.775868			−0.387934	−	0.921687i	$-0.626811\pi$
$379$	−15.1045			−0.775868			−0.387934	+	0.921687i	$0.626811\pi$
$380$			2.67667i			0.137310i
$381$		0			0
$382$	12.3381			0.631271
$383$	1.52664			0.0780079			0.0390040	−	0.999239i	$-0.487582\pi$
$383$	1.52664			0.0780079			0.0390040	+	0.999239i	$0.487582\pi$
$384$		0			0
$385$	−32.2246	−	14.3742i	−1.64232	−	0.732576i
$386$		−	4.39388i		−	0.223643i
$387$		0			0
$388$		−	4.59035i		−	0.233039i
$389$			14.8897i			0.754936i	0.926023	+	0.377468i	$0.123205\pi$
$389$			14.8897i			0.754936i	−0.926023	+	0.377468i	$0.876795\pi$
$390$		0			0
$391$			6.50061i			0.328750i
$392$	5.20853	−	4.67667i	0.263070	−	0.236208i
$393$		0			0
$394$	10.8865			0.548454
$395$	−30.6085			−1.54008
$396$		0			0
$397$			28.7869i			1.44478i	0.691488	+	0.722388i	$0.256955\pi$
$397$			28.7869i			1.44478i	−0.691488	+	0.722388i	$0.743045\pi$
$398$	27.5665			1.38178
$399$		0			0
$400$	0.519482			0.0259741
$401$			38.1735i			1.90629i	0.302507	+	0.953147i	$0.402176\pi$
$401$			38.1735i			1.90629i	−0.302507	+	0.953147i	$0.597824\pi$
$402$		0			0
$403$	14.3955			0.717089
$404$	−6.62310			−0.329511
$405$		0			0
$406$	4.47894	−	10.0411i	0.222286	−	0.498329i
$407$			52.2125i			2.58808i
$408$		0			0
$409$			6.96694i			0.344493i	0.985054	+	0.172247i	$0.0551026\pi$
$409$			6.96694i			0.344493i	−0.985054	+	0.172247i	$0.944897\pi$
$410$		−	18.7812i		−	0.927538i
$411$		0			0
$412$			5.85977i			0.288690i
$413$	2.40314	−	5.38745i	0.118251	−	0.265099i
$414$		0			0
$415$	−29.4750			−1.44687
$416$	1.71985			0.0843225
$417$		0			0
$418$			6.46754i			0.316338i
$419$	−34.8463			−1.70235			−0.851177	−	0.524878i	$-0.824111\pi$
$419$	−34.8463			−1.70235			−0.851177	+	0.524878i	$0.824111\pi$
$420$		0			0
$421$	−5.69193			−0.277408			−0.138704	−	0.990334i	$-0.544294\pi$
$421$	−5.69193			−0.277408			−0.138704	+	0.990334i	$0.544294\pi$
$422$			10.3112i			0.501942i
$423$		0			0
$424$		0			0
$425$	0.918875			0.0445720
$426$		0			0
$427$	−21.7456	−	9.69992i	−1.05235	−	0.469412i
$428$		−	4.71563i		−	0.227939i
$429$		0			0
$430$			8.27223i			0.398922i
$431$		−	30.2936i		−	1.45919i	−0.683880	−	0.729595i	$-0.739709\pi$
$431$		−	30.2936i		−	1.45919i	0.683880	−	0.729595i	$-0.260291\pi$
$432$		0			0
$433$			23.6094i			1.13459i	0.823513	+	0.567297i	$0.192011\pi$
$433$			23.6094i			1.13459i	−0.823513	+	0.567297i	$0.807989\pi$
$434$	−9.02143	+	20.2246i	−0.433043	+	0.970811i
$435$		0			0
$436$	−4.23669			−0.202901
$437$	4.18711			0.200297
$438$		0			0
$439$		−	25.0202i		−	1.19415i	−0.802185	−	0.597075i	$-0.796329\pi$
$439$		−	25.0202i		−	1.19415i	0.802185	−	0.597075i	$-0.203671\pi$
$440$	13.3365			0.635794
$441$		0			0
$442$	3.04212			0.144699
$443$		−	23.0300i		−	1.09419i	−0.837071	−	0.547094i	$-0.815734\pi$
$443$		−	23.0300i		−	1.09419i	0.837071	−	0.547094i	$-0.184266\pi$
$444$		0			0
$445$	2.72774			0.129307
$446$	7.20913			0.341362
$447$		0			0
$448$	−1.07781	+	2.41626i	−0.0509215	+	0.114158i
$449$			15.9028i			0.750501i	0.926923	+	0.375251i	$0.122443\pi$
$449$			15.9028i			0.750501i	−0.926923	+	0.375251i	$0.877557\pi$
$450$		0			0
$451$		−	45.3804i		−	2.13688i
$452$			6.83228i			0.321363i
$453$		0			0
$454$		−	12.7560i		−	0.598669i
$455$	9.76302	+	4.35492i	0.457697	+	0.204162i
$456$		0			0
$457$	−5.66614			−0.265051			−0.132525	−	0.991180i	$-0.542309\pi$
$457$	−5.66614			−0.265051			−0.132525	+	0.991180i	$0.542309\pi$
$458$	4.49418			0.209999
$459$		0			0
$460$		−	8.63411i		−	0.402567i
$461$	−31.4584			−1.46516			−0.732582	−	0.680679i	$-0.761685\pi$
$461$	−31.4584			−1.46516			−0.732582	+	0.680679i	$0.761685\pi$
$462$		0			0
$463$	−9.10296			−0.423051			−0.211525	−	0.977373i	$-0.567843\pi$
$463$	−9.10296			−0.423051			−0.211525	+	0.977373i	$0.567843\pi$
$464$			4.15561i			0.192919i
$465$		0			0
$466$	2.15403			0.0997837
$467$	30.3032			1.40226			0.701132	−	0.713032i	$-0.252678\pi$
$467$	30.3032			1.40226			0.701132	+	0.713032i	$0.252678\pi$
$468$		0			0
$469$	11.7171	−	26.2678i	0.541045	−	1.21293i
$470$		−	27.7456i		−	1.27981i
$471$		0			0
$472$			2.22966i			0.102628i
$473$			19.9879i			0.919044i
$474$		0			0
$475$		−	0.591856i		−	0.0271562i
$476$	−1.90645	+	4.27396i	−0.0873821	+	0.195897i
$477$		0			0
$478$	10.1419			0.463881
$479$	−4.66286			−0.213052			−0.106526	−	0.994310i	$-0.533973\pi$
$479$	−4.66286			−0.213052			−0.106526	+	0.994310i	$0.533973\pi$
$480$		0			0
$481$		−	15.8187i		−	0.721271i
$482$	−10.5481			−0.480452
$483$		0			0
$484$	21.2246			0.964754
$485$			10.7844i			0.489693i
$486$		0			0
$487$	−19.4821			−0.882818			−0.441409	−	0.897306i	$-0.645521\pi$
$487$	−19.4821			−0.882818			−0.441409	+	0.897306i	$0.645521\pi$
$488$	8.99970			0.407397
$489$		0			0
$490$	−12.2367	+	10.9872i	−0.552797	+	0.496350i
$491$			20.4886i			0.924640i	0.886713	+	0.462320i	$0.152983\pi$
$491$			20.4886i			0.924640i	−0.886713	+	0.462320i	$0.847017\pi$
$492$		0			0
$493$			7.35056i			0.331053i
$494$		−	1.95946i		−	0.0881602i
$495$		0			0
$496$		−	8.37019i		−	0.375832i
$497$	−10.9241	−	4.87282i	−0.490012	−	0.218576i
$498$		0			0
$499$	−10.2520			−0.458941			−0.229470	−	0.973316i	$-0.573699\pi$
$499$	−10.2520			−0.458941			−0.229470	+	0.973316i	$0.573699\pi$
$500$	10.5263			0.470752
$501$		0			0
$502$		−	29.3005i		−	1.30774i
$503$	14.5521			0.648845			0.324422	−	0.945912i	$-0.394830\pi$
$503$	14.5521			0.648845			0.324422	+	0.945912i	$0.394830\pi$
$504$		0			0
$505$	15.5600			0.692412
$506$		−	20.8623i		−	0.927442i
$507$		0			0
$508$	6.67667			0.296229
$509$	−33.3234			−1.47703			−0.738517	−	0.674235i	$-0.764473\pi$
$509$	−33.3234			−1.47703			−0.738517	+	0.674235i	$0.764473\pi$
$510$		0			0
$511$	12.9085	+	5.75800i	0.571039	+	0.254719i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$			7.62860i			0.336483i
$515$		−	13.7667i		−	0.606634i
$516$		0			0
$517$		−	67.0408i		−	2.94845i
$518$	22.2241	+	9.91336i	0.976473	+	0.435568i
$519$		0			0
$520$	−4.04054			−0.177189
$521$	6.53925			0.286490			0.143245	−	0.989687i	$-0.454246\pi$
$521$	6.53925			0.286490			0.143245	+	0.989687i	$0.454246\pi$
$522$		0			0
$523$		−	0.786858i		−	0.0344069i	−0.999852	−	0.0172034i	$-0.994524\pi$
$523$		−	0.786858i		−	0.0344069i	0.999852	−	0.0172034i	$-0.00547630\pi$
$524$	−7.47305			−0.326462
$525$		0			0
$526$	−12.1856			−0.531318
$527$		−	14.8054i		−	0.644934i
$528$		0			0
$529$	9.49369			0.412769
$530$		0			0
$531$		0			0
$532$	2.75290	+	1.22797i	0.119353	+	0.0532391i
$533$			13.7488i			0.595527i
$534$		0			0
$535$			11.0787i			0.478975i
$536$			10.8712i			0.469566i
$537$		0			0
$538$			2.77433i			0.119610i
$539$	−29.5671	+	26.5479i	−1.27354	+	1.14350i
$540$		0			0
$541$	5.60454			0.240958			0.120479	−	0.992716i	$-0.461557\pi$
$541$	5.60454			0.240958			0.120479	+	0.992716i	$0.461557\pi$
$542$	−3.20793			−0.137792
$543$		0			0
$544$		−	1.76883i		−	0.0758379i
$545$	9.95351			0.426362
$546$		0			0
$547$	13.8291			0.591291			0.295645	−	0.955298i	$-0.404465\pi$
$547$	13.8291			0.591291			0.295645	+	0.955298i	$0.404465\pi$
$548$		−	7.98789i		−	0.341226i
$549$		0			0
$550$	−2.94893			−0.125743
$551$	4.73457			0.201700
$552$		0			0
$553$	−14.0421	+	31.4801i	−0.597132	+	1.33867i
$554$		−	10.0811i		−	0.428304i
$555$		0			0
$556$		−	20.7606i		−	0.880446i
$557$			27.8233i			1.17891i	0.807800	+	0.589456i	$0.200658\pi$
$557$			27.8233i			1.17891i	−0.807800	+	0.589456i	$0.799342\pi$
$558$		0			0
$559$		−	6.05569i		−	0.256128i
$560$	2.53215	−	5.67667i	0.107003	−	0.239883i
$561$		0			0
$562$	4.87282			0.205548
$563$	24.5300			1.03382			0.516909	−	0.856040i	$-0.327083\pi$
$563$	24.5300			1.03382			0.516909	+	0.856040i	$0.327083\pi$
$564$		0			0
$565$		−	16.0515i		−	0.675291i
$566$	−2.81781			−0.118441
$567$		0			0
$568$	4.52106			0.189699
$569$		−	27.1079i		−	1.13642i	−0.822882	−	0.568212i	$-0.807635\pi$
$569$		−	27.1079i		−	1.13642i	0.822882	−	0.568212i	$-0.192365\pi$
$570$		0			0
$571$	−29.8354			−1.24857			−0.624287	−	0.781195i	$-0.714610\pi$
$571$	−29.8354			−1.24857			−0.624287	+	0.781195i	$0.714610\pi$
$572$	−9.76302			−0.408212
$573$		0			0
$574$	−19.3161	−	8.61618i	−0.806237	−	0.359632i
$575$			1.90915i			0.0796169i
$576$		0			0
$577$		−	28.1666i		−	1.17259i	−0.810097	−	0.586296i	$-0.800585\pi$
$577$		−	28.1666i		−	1.17259i	0.810097	−	0.586296i	$-0.199415\pi$
$578$			13.8712i			0.576968i
$579$		0			0
$580$		−	9.76302i		−	0.405387i
$581$	−13.5221	+	30.3144i	−0.560992	+	1.25765i
$582$		0			0
$583$		0			0
$584$	−5.34234			−0.221068
$585$		0			0
$586$			8.11389i			0.335182i
$587$	9.91857			0.409383			0.204692	−	0.978827i	$-0.434381\pi$
$587$	9.91857			0.409383			0.204692	+	0.978827i	$0.434381\pi$
$588$		0			0
$589$	−9.53632			−0.392937
$590$		−	5.23827i		−	0.215656i
$591$		0			0
$592$	−9.19773			−0.378024
$593$	4.69872			0.192953			0.0964766	−	0.995335i	$-0.469243\pi$
$593$	4.69872			0.192953			0.0964766	+	0.995335i	$0.469243\pi$
$594$		0			0
$595$	4.47894	−	10.0411i	0.183619	−	0.411643i
$596$		−	1.19773i		−	0.0490609i
$597$		0			0
$598$			6.32061i			0.258469i
$599$		−	14.7004i		−	0.600641i	−0.953838	−	0.300320i	$-0.902906\pi$
$599$		−	14.7004i		−	0.600641i	0.953838	−	0.300320i	$-0.0970936\pi$
$600$		0			0
$601$		−	18.8127i		−	0.767385i	−0.923461	−	0.383693i	$-0.874652\pi$
$601$		−	18.8127i		−	0.767385i	0.923461	−	0.383693i	$-0.125348\pi$
$602$	8.50781	+	3.79502i	0.346752	+	0.154673i
$603$		0			0
$604$	−15.2246			−0.619480
$605$	−49.8641			−2.02727
$606$		0			0
$607$			12.5922i			0.511100i	0.966796	+	0.255550i	$0.0822565\pi$
$607$			12.5922i			0.511100i	−0.966796	+	0.255550i	$0.917743\pi$
$608$	−1.13932			−0.0462055
$609$		0			0
$610$	−21.1435			−0.856075
$611$			20.3112i			0.821704i
$612$		0			0
$613$	−9.82017			−0.396633			−0.198317	−	0.980138i	$-0.563547\pi$
$613$	−9.82017			−0.396633			−0.198317	+	0.980138i	$0.563547\pi$
$614$	10.8996			0.439873
$615$		0			0
$616$	6.11835	−	13.7163i	0.246515	−	0.552647i
$617$			3.75460i			0.151154i	0.997140	+	0.0755772i	$0.0240799\pi$
$617$			3.75460i			0.151154i	−0.997140	+	0.0755772i	$0.975920\pi$
$618$		0			0
$619$		−	11.0494i		−	0.444111i	−0.975034	−	0.222055i	$-0.928723\pi$
$619$		−	11.0494i		−	0.444111i	0.975034	−	0.222055i	$-0.0712766\pi$
$620$			19.6646i			0.789748i
$621$		0			0
$622$		−	8.23637i		−	0.330248i
$623$	1.25140	−	2.80542i	0.0501361	−	0.112397i
$624$		0			0
$625$	−27.3275			−1.09310
$626$	33.8023			1.35101
$627$		0			0
$628$		−	10.0269i		−	0.400118i
$629$	−16.2692			−0.648696
$630$		0			0
$631$	19.4921			0.775969			0.387984	−	0.921666i	$-0.373171\pi$
$631$	19.4921			0.775969			0.387984	+	0.921666i	$0.373171\pi$
$632$		−	13.0284i		−	0.518243i
$633$		0			0
$634$	6.73090			0.267318
$635$	−15.6859			−0.622475
$636$		0			0
$637$	8.95788	−	8.04317i	0.354924	−	0.318682i
$638$		−	23.5900i		−	0.933938i
$639$		0			0
$640$			2.34936i			0.0928665i
$641$		−	26.1735i		−	1.03379i	−0.856048	−	0.516896i	$-0.827087\pi$
$641$		−	26.1735i		−	1.03379i	0.856048	−	0.516896i	$-0.172913\pi$
$642$		0			0
$643$			10.9807i			0.433036i	0.976279	+	0.216518i	$0.0694699\pi$
$643$			10.9807i			0.433036i	−0.976279	+	0.216518i	$0.930530\pi$
$644$	−8.88000	−	3.96104i	−0.349921	−	0.156087i
$645$		0			0
$646$	−2.01526			−0.0792894
$647$	−32.0126			−1.25855			−0.629273	−	0.777185i	$-0.716647\pi$
$647$	−32.0126			−1.25855			−0.629273	+	0.777185i	$0.716647\pi$
$648$		0			0
$649$		−	12.6570i		−	0.496833i
$650$	0.893431			0.0350432
$651$		0			0
$652$	−12.0032			−0.470080
$653$		−	22.3649i		−	0.875208i	−0.899168	−	0.437604i	$-0.855827\pi$
$653$		−	22.3649i		−	0.875208i	0.899168	−	0.437604i	$-0.144173\pi$
$654$		0			0
$655$	17.5569			0.686004
$656$	7.99419			0.312121
$657$		0			0
$658$	−28.5358	−	12.7288i	−1.11244	−	0.496219i
$659$		−	22.2333i		−	0.866086i	−0.901373	−	0.433043i	$-0.857440\pi$
$659$		−	22.2333i		−	0.866086i	0.901373	−	0.433043i	$-0.142560\pi$
$660$		0			0
$661$		−	10.5499i		−	0.410343i	−0.978726	−	0.205171i	$-0.934225\pi$
$661$		−	10.5499i		−	0.410343i	0.978726	−	0.205171i	$-0.0657751\pi$
$662$			32.0569i			1.24593i
$663$		0			0
$664$		−	12.5460i		−	0.486878i
$665$	−6.46754	−	2.88493i	−0.250801	−	0.111873i
$666$		0			0
$667$	−15.2723			−0.591344
$668$	−17.1494			−0.663532
$669$		0			0
$670$		−	25.5404i		−	0.986713i
$671$	−51.0883			−1.97224
$672$		0			0
$673$	−19.8712			−0.765980			−0.382990	−	0.923752i	$-0.625106\pi$
$673$	−19.8712			−0.765980			−0.382990	+	0.923752i	$0.625106\pi$
$674$		−	24.2246i		−	0.933096i
$675$		0			0
$676$	−10.0421			−0.386235
$677$	−15.9290			−0.612201			−0.306100	−	0.951999i	$-0.599024\pi$
$677$	−15.9290			−0.612201			−0.306100	+	0.951999i	$0.599024\pi$
$678$		0			0
$679$	11.0915	+	4.94750i	0.425652	+	0.189868i
$680$			4.15561i			0.159360i
$681$		0			0
$682$			47.5148i			1.81944i
$683$		−	19.0269i		−	0.728042i	−0.931391	−	0.364021i	$-0.881404\pi$
$683$		−	19.0269i		−	0.728042i	0.931391	−	0.364021i	$-0.118596\pi$
$684$		0			0
$685$			18.7664i			0.717028i
$686$	5.68629	+	17.6257i	0.217104	+	0.672953i
$687$		0			0
$688$	−3.52106			−0.134239
$689$		0			0
$690$		0			0
$691$		−	0.161055i		−	0.00612681i	−0.999995	−	0.00306340i	$-0.999025\pi$
$691$		−	0.161055i		−	0.00612681i	0.999995	−	0.00306340i	$-0.000975113\pi$
$692$	−1.98748			−0.0755525
$693$		0			0
$694$	−22.7999			−0.865471
$695$			48.7741i			1.85011i
$696$		0			0
$697$	14.1403			0.535604
$698$	2.84505			0.107687
$699$		0			0
$700$	−0.559901	+	1.25521i	−0.0211623	+	0.0474423i
$701$			9.98234i			0.377028i	0.982071	+	0.188514i	$0.0603670\pi$
$701$			9.98234i			0.377028i	−0.982071	+	0.188514i	$0.939633\pi$
$702$		0			0
$703$			10.4792i			0.395229i
$704$			5.67667i			0.213948i
$705$		0			0
$706$			7.14424i			0.268877i
$707$	7.13841	−	16.0032i	0.268468	−	0.601861i
$708$		0			0
$709$	−24.3923			−0.916072			−0.458036	−	0.888934i	$-0.651447\pi$
$709$	−24.3923			−0.916072			−0.458036	+	0.888934i	$0.651447\pi$
$710$	−10.6216			−0.398621
$711$		0			0
$712$			1.16106i			0.0435125i
$713$	30.7612			1.15202
$714$		0			0
$715$	22.9368			0.857788
$716$		−	8.31122i		−	0.310605i
$717$		0			0
$718$	11.6037			0.433047
$719$	16.2692			0.606739			0.303370	−	0.952873i	$-0.401888\pi$
$719$	16.2692			0.606739			0.303370	+	0.952873i	$0.401888\pi$
$720$		0			0
$721$	−14.1588	−	6.31570i	−0.527300	−	0.235209i
$722$		−	17.7019i		−	0.658798i
$723$		0			0
$724$			15.4541i			0.574348i
$725$			2.15877i			0.0801745i
$726$		0			0
$727$		−	23.8592i		−	0.884887i	−0.896796	−	0.442444i	$-0.854112\pi$
$727$		−	23.8592i		−	0.884887i	0.896796	−	0.442444i	$-0.145888\pi$
$728$	−1.85366	+	4.15561i	−0.0687013	+	0.154017i
$729$		0			0
$730$	12.5511			0.464536
$731$	−6.22815			−0.230356
$732$		0			0
$733$			12.2697i			0.453193i	0.973989	+	0.226596i	$0.0727598\pi$
$733$			12.2697i			0.453193i	−0.973989	+	0.226596i	$0.927240\pi$
$734$	−7.83493			−0.289193
$735$		0			0
$736$	3.67509			0.135466
$737$		−	61.7125i		−	2.27321i
$738$		0			0
$739$	41.8891			1.54092			0.770459	−	0.637490i	$-0.220027\pi$
$739$	41.8891			1.54092			0.770459	+	0.637490i	$0.220027\pi$
$740$	21.6088			0.794354
$741$		0			0
$742$		0			0
$743$		−	50.7098i		−	1.86036i	−0.367099	−	0.930182i	$-0.619649\pi$
$743$		−	50.7098i		−	1.86036i	0.367099	−	0.930182i	$-0.380351\pi$
$744$		0			0
$745$			2.81390i			0.103093i
$746$		−	25.6677i		−	0.939762i
$747$		0			0
$748$			10.0411i			0.367137i
$749$	11.3942	+	5.08254i	0.416336	+	0.185712i
$750$		0			0
$751$	−32.7367			−1.19458			−0.597289	−	0.802026i	$-0.703756\pi$
$751$	−32.7367			−1.19458			−0.597289	+	0.802026i	$0.703756\pi$
$752$	11.8099			0.430662
$753$		0			0
$754$			7.14702i			0.260279i
$755$	35.7680			1.30173
$756$		0			0
$757$	−17.9255			−0.651512			−0.325756	−	0.945454i	$-0.605619\pi$
$757$	−17.9255			−0.651512			−0.325756	+	0.945454i	$0.605619\pi$
$758$			15.1045i			0.548622i
$759$		0			0
$760$	2.67667			0.0970930
$761$	43.7019			1.58419			0.792096	−	0.610397i	$-0.208990\pi$
$761$	43.7019			1.58419			0.792096	+	0.610397i	$0.208990\pi$
$762$		0			0
$763$	4.56633	−	10.2370i	0.165312	−	0.370603i
$764$		−	12.3381i		−	0.446376i
$765$		0			0
$766$		−	1.52664i		−	0.0551599i
$767$			3.83468i			0.138462i
$768$		0			0
$769$		−	42.8237i		−	1.54426i	−0.635463	−	0.772131i	$-0.719191\pi$
$769$		−	42.8237i		−	1.54426i	0.635463	−	0.772131i	$-0.280809\pi$
$770$	−14.3742	+	32.2246i	−0.518010	+	1.16129i
$771$		0			0
$772$	−4.39388			−0.158139
$773$	21.6051			0.777080			0.388540	−	0.921432i	$-0.372980\pi$
$773$	21.6051			0.777080			0.388540	+	0.921432i	$0.372980\pi$
$774$		0			0
$775$		−	4.34816i		−	0.156191i
$776$	−4.59035			−0.164784
$777$		0			0
$778$	14.8897			0.533820
$779$		−	9.10794i		−	0.326326i
$780$		0			0
$781$	−25.6646			−0.918350
$782$	6.50061			0.232461
$783$		0			0
$784$	−4.67667	−	5.20853i	−0.167024	−	0.186019i
$785$			23.5569i			0.840781i
$786$		0			0
$787$		−	51.3042i		−	1.82880i	−0.404817	−	0.914398i	$-0.632665\pi$
$787$		−	51.3042i		−	1.82880i	0.404817	−	0.914398i	$-0.367335\pi$
$788$		−	10.8865i		−	0.387816i
$789$		0			0
$790$			30.6085i			1.08900i
$791$	−16.5086	−	7.36387i	−0.586978	−	0.261829i
$792$		0			0
$793$	15.4781			0.549644
$794$	28.7869			1.02161
$795$		0			0
$796$		−	27.5665i		−	0.977068i
$797$	−1.79819			−0.0636951			−0.0318476	−	0.999493i	$-0.510139\pi$
$797$	−1.79819			−0.0636951			−0.0318476	+	0.999493i	$0.510139\pi$
$798$		0			0
$799$	20.8897			0.739023
$800$		−	0.519482i		−	0.0183665i
$801$		0			0
$802$	38.1735			1.34795
$803$	30.3267			1.07021
$804$		0			0
$805$	20.8623	+	9.30589i	0.735299	+	0.327990i
$806$		−	14.3955i		−	0.507058i
$807$		0			0
$808$			6.62310i			0.233000i
$809$			40.6883i			1.43052i	0.698857	+	0.715262i	$0.253692\pi$
$809$			40.6883i			1.43052i	−0.698857	+	0.715262i	$0.746308\pi$
$810$		0			0
$811$		−	0.378710i		−	0.0132983i	−0.999978	−	0.00664916i	$-0.997883\pi$
$811$		−	0.378710i		−	0.0132983i	0.999978	−	0.00664916i	$-0.00211651\pi$
$812$	−10.0411	−	4.47894i	−0.352372	−	0.157180i
$813$		0			0
$814$	52.2125			1.83005
$815$	28.1997			0.987793
$816$		0			0
$817$			4.01161i			0.140349i
$818$	6.96694			0.243593
$819$		0			0
$820$	−18.7812			−0.655868
$821$			13.2754i			0.463315i	0.972797	+	0.231658i	$0.0744149\pi$
$821$			13.2754i			0.463315i	−0.972797	+	0.231658i	$0.925585\pi$
$822$		0			0
$823$	27.7422			0.967034			0.483517	−	0.875335i	$-0.339359\pi$
$823$	27.7422			0.967034			0.483517	+	0.875335i	$0.339359\pi$
$824$	5.85977			0.204135
$825$		0			0
$826$	−5.38745	−	2.40314i	−0.187453	−	0.0836160i
$827$			27.7183i			0.963859i	0.876210	+	0.481929i	$0.160064\pi$
$827$			27.7183i			0.963859i	−0.876210	+	0.481929i	$0.839936\pi$
$828$		0			0
$829$		−	42.7361i		−	1.48429i	−0.670242	−	0.742143i	$-0.733810\pi$
$829$		−	42.7361i		−	1.48429i	0.670242	−	0.742143i	$-0.266190\pi$
$830$			29.4750i			1.02309i
$831$		0			0
$832$		−	1.71985i		−	0.0596250i
$833$	−8.27223	−	9.21299i	−0.286616	−	0.319211i
$834$		0			0
$835$	40.2902			1.39430
$836$	6.46754			0.223685
$837$		0			0
$838$			34.8463i			1.20375i
$839$	−3.84876			−0.132874			−0.0664370	−	0.997791i	$-0.521163\pi$
$839$	−3.84876			−0.132874			−0.0664370	+	0.997791i	$0.521163\pi$
$840$		0			0
$841$	11.7309			0.404514
$842$			5.69193i			0.196157i
$843$		0			0
$844$	10.3112			0.354927
$845$	23.5925			0.811608
$846$		0			0
$847$	−22.8760	+	51.2842i	−0.786028	+	1.76215i
$848$		0			0
$849$		0			0
$850$		−	0.918875i		−	0.0315171i
$851$		−	33.8025i		−	1.15874i
$852$		0			0
$853$			30.4229i			1.04166i	0.853661	+	0.520830i	$0.174377\pi$
$853$			30.4229i			1.04166i	−0.853661	+	0.520830i	$0.825623\pi$
$854$	−9.69992	+	21.7456i	−0.331924	+	0.744121i
$855$		0			0
$856$	−4.71563			−0.161177
$857$	38.9315			1.32987			0.664937	−	0.746900i	$-0.268459\pi$
$857$	38.9315			1.32987			0.664937	+	0.746900i	$0.268459\pi$
$858$		0			0
$859$			13.3855i			0.456708i	0.973578	+	0.228354i	$0.0733343\pi$
$859$			13.3855i			0.456708i	−0.973578	+	0.228354i	$0.926666\pi$
$860$	8.27223			0.282081
$861$		0			0
$862$	−30.2936			−1.03180
$863$		−	21.7219i		−	0.739424i	−0.929146	−	0.369712i	$-0.879456\pi$
$863$		−	21.7219i		−	0.739424i	0.929146	−	0.369712i	$-0.120544\pi$
$864$		0			0
$865$	4.66929			0.158761
$866$	23.6094			0.802279
$867$		0			0
$868$	20.2246	+	9.02143i	0.686467	+	0.306207i
$869$			73.9581i			2.50886i
$870$		0			0
$871$			18.6969i			0.633520i
$872$			4.23669i			0.143473i
$873$		0			0
$874$		−	4.18711i		−	0.141631i
$875$	−11.3453	+	25.4344i	−0.383543	+	0.859840i
$876$		0			0
$877$	0.392305			0.0132472			0.00662360	−	0.999978i	$-0.497892\pi$
$877$	0.392305			0.0132472			0.00662360	+	0.999978i	$0.497892\pi$
$878$	−25.0202			−0.844392
$879$		0			0
$880$		−	13.3365i		−	0.449574i
$881$	−43.3363			−1.46004			−0.730018	−	0.683427i	$-0.760489\pi$
$881$	−43.3363			−1.46004			−0.730018	+	0.683427i	$0.760489\pi$
$882$		0			0
$883$	2.17403			0.0731618			0.0365809	−	0.999331i	$-0.488353\pi$
$883$	2.17403			0.0731618			0.0365809	+	0.999331i	$0.488353\pi$
$884$		−	3.04212i		−	0.102318i
$885$		0			0
$886$	−23.0300			−0.773708
$887$	−11.4443			−0.384262			−0.192131	−	0.981369i	$-0.561540\pi$
$887$	−11.4443			−0.384262			−0.192131	+	0.981369i	$0.561540\pi$
$888$		0			0
$889$	−7.19615	+	16.1326i	−0.241351	+	0.541070i
$890$		−	2.72774i		−	0.0914341i
$891$		0			0
$892$		−	7.20913i		−	0.241379i
$893$		−	13.4552i		−	0.450262i
$894$		0			0
$895$			19.5260i			0.652683i
$896$	2.41626	+	1.07781i	0.0807217	+	0.0360070i
$897$		0			0
$898$	15.9028			0.530684
$899$	34.7832			1.16009
$900$		0			0
$901$		0			0
$902$	−45.3804			−1.51100
$903$		0			0
$904$	6.83228			0.227238
$905$		−	36.3072i		−	1.20689i
$906$		0			0
$907$	−53.8891			−1.78936			−0.894680	−	0.446708i	$-0.852596\pi$
$907$	−53.8891			−1.78936			−0.894680	+	0.446708i	$0.852596\pi$
$908$	−12.7560			−0.423323
$909$		0			0
$910$	4.35492	−	9.76302i	0.144364	−	0.323641i
$911$		−	8.08821i		−	0.267974i	−0.990983	−	0.133987i	$-0.957222\pi$
$911$		−	8.08821i		−	0.267974i	0.990983	−	0.133987i	$-0.0427781\pi$
$912$		0			0
$913$			71.2193i			2.35702i
$914$			5.66614i			0.187419i
$915$		0			0
$916$		−	4.49418i		−	0.148492i
$917$	8.05450	−	18.0569i	0.265983	−	0.596290i
$918$		0			0
$919$	25.6751			0.846943			0.423472	−	0.905909i	$-0.360811\pi$
$919$	25.6751			0.846943			0.423472	+	0.905909i	$0.360811\pi$
$920$	−8.63411			−0.284658
$921$		0			0
$922$			31.4584i			1.03603i
$923$	7.77554			0.255935
$924$		0			0
$925$	−4.77806			−0.157101
$926$			9.10296i			0.299142i
$927$		0			0
$928$	4.15561			0.136415
$929$	10.8524			0.356055			0.178027	−	0.984026i	$-0.443028\pi$
$929$	10.8524			0.356055			0.178027	+	0.984026i	$0.443028\pi$
$930$		0			0
$931$	−5.93418	+	5.32822i	−0.194485	+	0.174625i
$932$		−	2.15403i		−	0.0705577i
$933$		0			0
$934$		−	30.3032i		−	0.991550i
$935$		−	23.5900i		−	0.771477i
$936$		0			0
$937$		−	0.458120i		−	0.0149661i	−0.999972	−	0.00748306i	$-0.997618\pi$
$937$		−	0.458120i		−	0.0149661i	0.999972	−	0.00748306i	$-0.00238195\pi$
$938$	−26.2678	−	11.7171i	−0.857674	−	0.382577i
$939$		0			0
$940$	−27.7456			−0.904963
$941$	−7.37780			−0.240510			−0.120255	−	0.992743i	$-0.538371\pi$
$941$	−7.37780			−0.240510			−0.120255	+	0.992743i	$0.538371\pi$
$942$		0			0
$943$			29.3794i			0.956725i
$944$	2.22966			0.0725693
$945$		0			0
$946$	19.9879			0.649862
$947$		−	11.9910i		−	0.389657i	−0.980837	−	0.194828i	$-0.937585\pi$
$947$		−	11.9910i		−	0.389657i	0.980837	−	0.194828i	$-0.0624150\pi$
$948$		0			0
$949$	−9.18802			−0.298256
$950$	−0.591856			−0.0192024
$951$		0			0
$952$	4.27396	+	1.90645i	0.138520	+	0.0617885i
$953$			58.6883i			1.90110i	0.310572	+	0.950550i	$0.399479\pi$
$953$			58.6883i			1.90110i	−0.310572	+	0.950550i	$0.600521\pi$
$954$		0			0
$955$			28.9866i			0.937983i
$956$		−	10.1419i		−	0.328013i
$957$		0			0
$958$			4.66286i			0.150650i
$959$	19.3009	+	8.60940i	0.623257	+	0.278012i
$960$		0			0
$961$	−39.0600			−1.26000
$962$	−15.8187			−0.510016
$963$		0			0
$964$			10.5481i			0.339731i
$965$	10.3228			0.332303
$966$		0			0
$967$	6.75120			0.217104			0.108552	−	0.994091i	$-0.465379\pi$
$967$	6.75120			0.217104			0.108552	+	0.994091i	$0.465379\pi$
$968$		−	21.2246i		−	0.682184i
$969$		0			0
$970$	10.7844			0.346265
$971$	6.40724			0.205618			0.102809	−	0.994701i	$-0.467217\pi$
$971$	6.40724			0.205618			0.102809	+	0.994701i	$0.467217\pi$
$972$		0			0
$973$	50.1631	+	22.3759i	1.60816	+	0.717338i
$974$			19.4821i			0.624247i
$975$		0			0
$976$		−	8.99970i		−	0.288073i
$977$		−	13.5987i		−	0.435062i	−0.976053	−	0.217531i	$-0.930200\pi$
$977$		−	13.5987i		−	0.435062i	0.976053	−	0.217531i	$-0.0698004\pi$
$978$		0			0
$979$		−	6.59095i		−	0.210648i
$980$	10.9872	+	12.2367i	0.350972	+	0.390887i
$981$		0			0
$982$	20.4886			0.653819
$983$	22.7698			0.726244			0.363122	−	0.931742i	$-0.381711\pi$
$983$	22.7698			0.726244			0.363122	+	0.931742i	$0.381711\pi$
$984$		0			0
$985$			25.5763i			0.814929i
$986$	7.35056			0.234090
$987$		0			0
$988$	−1.95946			−0.0623387
$989$		−	12.9402i		−	0.411475i
$990$		0			0
$991$	−26.9905			−0.857383			−0.428691	−	0.903451i	$-0.641025\pi$
$991$	−26.9905			−0.857383			−0.428691	+	0.903451i	$0.641025\pi$
$992$	−8.37019			−0.265754
$993$		0			0
$994$	−4.87282	+	10.9241i	−0.154557	+	0.346491i
$995$			64.7635i			2.05314i
$996$		0			0
$997$			19.3139i			0.611677i	0.952083	+	0.305838i	$0.0989367\pi$
$997$			19.3139i			0.611677i	−0.952083	+	0.305838i	$0.901063\pi$
$998$			10.2520i			0.324520i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.d.a.1133.7		16
3.2	odd	2	inner	1134.2.d.a.1133.10		16
7.6	odd	2	inner	1134.2.d.a.1133.2		16
9.2	odd	6		378.2.m.a.125.7		16
9.4	even	3		378.2.m.a.251.6		16
9.5	odd	6		126.2.m.a.83.3	yes	16
9.7	even	3		126.2.m.a.41.2	✓	16
21.20	even	2	inner	1134.2.d.a.1133.15		16
36.7	odd	6		1008.2.cc.b.545.6		16
36.11	even	6		3024.2.cc.b.881.7		16
36.23	even	6		1008.2.cc.b.209.3		16
36.31	odd	6		3024.2.cc.b.2897.2		16
63.2	odd	6		2646.2.t.a.2285.2		16
63.4	even	3		2646.2.t.a.1979.3		16
63.5	even	6		882.2.l.a.227.6		16
63.11	odd	6		2646.2.l.b.1097.7		16
63.13	odd	6		378.2.m.a.251.7		16
63.16	even	3		882.2.t.b.815.8		16
63.20	even	6		378.2.m.a.125.6		16
63.23	odd	6		882.2.l.a.227.7		16
63.25	even	3		882.2.l.a.509.2		16
63.31	odd	6		2646.2.t.a.1979.2		16
63.32	odd	6		882.2.t.b.803.5		16
63.34	odd	6		126.2.m.a.41.3	yes	16
63.38	even	6		2646.2.l.b.1097.6		16
63.40	odd	6		2646.2.l.b.521.3		16
63.41	even	6		126.2.m.a.83.2	yes	16
63.47	even	6		2646.2.t.a.2285.3		16
63.52	odd	6		882.2.l.a.509.3		16
63.58	even	3		2646.2.l.b.521.2		16
63.59	even	6		882.2.t.b.803.8		16
63.61	odd	6		882.2.t.b.815.5		16
252.83	odd	6		3024.2.cc.b.881.2		16
252.139	even	6		3024.2.cc.b.2897.7		16
252.167	odd	6		1008.2.cc.b.209.6		16
252.223	even	6		1008.2.cc.b.545.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.2	✓	16	9.7	even	3
126.2.m.a.41.3	yes	16	63.34	odd	6
126.2.m.a.83.2	yes	16	63.41	even	6
126.2.m.a.83.3	yes	16	9.5	odd	6
378.2.m.a.125.6		16	63.20	even	6
378.2.m.a.125.7		16	9.2	odd	6
378.2.m.a.251.6		16	9.4	even	3
378.2.m.a.251.7		16	63.13	odd	6
882.2.l.a.227.6		16	63.5	even	6
882.2.l.a.227.7		16	63.23	odd	6
882.2.l.a.509.2		16	63.25	even	3
882.2.l.a.509.3		16	63.52	odd	6
882.2.t.b.803.5		16	63.32	odd	6
882.2.t.b.803.8		16	63.59	even	6
882.2.t.b.815.5		16	63.61	odd	6
882.2.t.b.815.8		16	63.16	even	3
1008.2.cc.b.209.3		16	36.23	even	6
1008.2.cc.b.209.6		16	252.167	odd	6
1008.2.cc.b.545.3		16	252.223	even	6
1008.2.cc.b.545.6		16	36.7	odd	6
1134.2.d.a.1133.2		16	7.6	odd	2	inner
1134.2.d.a.1133.7		16	1.1	even	1	trivial
1134.2.d.a.1133.10		16	3.2	odd	2	inner
1134.2.d.a.1133.15		16	21.20	even	2	inner
2646.2.l.b.521.2		16	63.58	even	3
2646.2.l.b.521.3		16	63.40	odd	6
2646.2.l.b.1097.6		16	63.38	even	6
2646.2.l.b.1097.7		16	63.11	odd	6
2646.2.t.a.1979.2		16	63.31	odd	6
2646.2.t.a.1979.3		16	63.4	even	3
2646.2.t.a.2285.2		16	63.2	odd	6
2646.2.t.a.2285.3		16	63.47	even	6
3024.2.cc.b.881.2		16	252.83	odd	6
3024.2.cc.b.881.7		16	36.11	even	6
3024.2.cc.b.2897.2		16	36.31	odd	6
3024.2.cc.b.2897.7		16	252.139	even	6

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +2.34936 q^{5} +(1.07781 - 2.41626i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +2.34936 q^{5} +(1.07781 - 2.41626i) q^{7} +1.00000i q^{8} -2.34936i q^{10} -5.67667i q^{11} +1.71985i q^{13} +(-2.41626 - 1.07781i) q^{14} +1.00000 q^{16} +1.76883 q^{17} -1.13932i q^{19} -2.34936 q^{20} -5.67667 q^{22} +3.67509i q^{23} +0.519482 q^{25} +1.71985 q^{26} +(-1.07781 + 2.41626i) q^{28} +4.15561i q^{29} -8.37019i q^{31} -1.00000i q^{32} -1.76883i q^{34} +(2.53215 - 5.67667i) q^{35} -9.19773 q^{37} -1.13932 q^{38} +2.34936i q^{40} +7.99419 q^{41} -3.52106 q^{43} +5.67667i q^{44} +3.67509 q^{46} +11.8099 q^{47} +(-4.67667 - 5.20853i) q^{49} -0.519482i q^{50} -1.71985i q^{52} -13.3365i q^{55} +(2.41626 + 1.07781i) q^{56} +4.15561 q^{58} +2.22966 q^{59} -8.99970i q^{61} -8.37019 q^{62} -1.00000 q^{64} +4.04054i q^{65} +10.8712 q^{67} -1.76883 q^{68} +(-5.67667 - 2.53215i) q^{70} -4.52106i q^{71} +5.34234i q^{73} +9.19773i q^{74} +1.13932i q^{76} +(-13.7163 - 6.11835i) q^{77} -13.0284 q^{79} +2.34936 q^{80} -7.99419i q^{82} -12.5460 q^{83} +4.15561 q^{85} +3.52106i q^{86} +5.67667 q^{88} +1.16106 q^{89} +(4.15561 + 1.85366i) q^{91} -3.67509i q^{92} -11.8099i q^{94} -2.67667i q^{95} +4.59035i q^{97} +(-5.20853 + 4.67667i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 4 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 - 4 * q^7	\( 16 q - 16 q^{4} - 4 q^{7} + 16 q^{16} + 16 q^{25} + 4 q^{28} - 8 q^{37} - 8 q^{43} + 24 q^{46} + 16 q^{49} + 24 q^{58} - 16 q^{64} + 56 q^{67} + 8 q^{79} + 24 q^{85} + 24 q^{91}+O(q^{100}) \) 16 * q - 16 * q^4 - 4 * q^7 + 16 * q^16 + 16 * q^25 + 4 * q^28 - 8 * q^37 - 8 * q^43 + 24 * q^46 + 16 * q^49 + 24 * q^58 - 16 * q^64 + 56 * q^67 + 8 * q^79 + 24 * q^85 + 24 * q^91

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