LMFDB - Embedded newform 3549.2.a.x.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.a (trivial)

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:	yes
Analytic conductor:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.64436.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 7x^{2} + 7x + 2 $ x^4 - x^3 - 7x^2 + 7x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.233455$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.233455 q^{2} -1.00000 q^{3} -1.94550 q^{4} -2.94550 q^{5} +0.233455 q^{6} -1.00000 q^{7} +0.921097 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.233455 q^{2} -1.00000 q^{3} -1.94550 q^{4} -2.94550 q^{5} +0.233455 q^{6} -1.00000 q^{7} +0.921097 q^{8} +1.00000 q^{9} +0.687642 q^{10} +3.62146 q^{11} +1.94550 q^{12} +0.233455 q^{14} +2.94550 q^{15} +3.67596 q^{16} -1.53309 q^{17} -0.233455 q^{18} -4.10005 q^{19} +5.73046 q^{20} +1.00000 q^{21} -0.845448 q^{22} -7.03387 q^{23} -0.921097 q^{24} +3.67596 q^{25} -1.00000 q^{27} +1.94550 q^{28} -3.79095 q^{29} -0.687642 q^{30} -1.79095 q^{31} -2.70037 q^{32} -3.62146 q^{33} +0.357908 q^{34} +2.94550 q^{35} -1.94550 q^{36} -7.24292 q^{37} +0.957177 q^{38} -2.71309 q^{40} +9.15455 q^{41} -0.233455 q^{42} -5.79095 q^{43} -7.04555 q^{44} -2.94550 q^{45} +1.64209 q^{46} -7.25460 q^{47} -3.67596 q^{48} +1.00000 q^{49} -0.858172 q^{50} +1.53309 q^{51} -13.3430 q^{53} +0.233455 q^{54} -10.6670 q^{55} -0.921097 q^{56} +4.10005 q^{57} +0.885016 q^{58} +4.84545 q^{59} -5.73046 q^{60} +2.77601 q^{61} +0.418106 q^{62} -1.00000 q^{63} -6.72151 q^{64} +0.845448 q^{66} +14.8248 q^{67} +2.98262 q^{68} +7.03387 q^{69} -0.687642 q^{70} +3.62146 q^{71} +0.921097 q^{72} -14.5670 q^{73} +1.69090 q^{74} -3.67596 q^{75} +7.97664 q^{76} -3.62146 q^{77} +6.56696 q^{79} -10.8275 q^{80} +1.00000 q^{81} -2.13718 q^{82} -7.25460 q^{83} -1.94550 q^{84} +4.51571 q^{85} +1.35193 q^{86} +3.79095 q^{87} +3.33572 q^{88} +0.636396 q^{89} +0.687642 q^{90} +13.6844 q^{92} +1.79095 q^{93} +1.69362 q^{94} +12.0767 q^{95} +2.70037 q^{96} -11.3240 q^{97} -0.233455 q^{98} +3.62146 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 4 q^{3} + 7 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + q^2 - 4 * q^3 + 7 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9	$ 4 q + q^{2} - 4 q^{3} + 7 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9} - 2 q^{10} + 2 q^{11} - 7 q^{12} - q^{14} - 3 q^{15} + 17 q^{16} - 10 q^{17} + q^{18} + 7 q^{19} + 40 q^{20} + 4 q^{21} - 12 q^{22} + 3 q^{23} + 3 q^{24} + 17 q^{25} - 4 q^{27} - 7 q^{28} - 9 q^{29} + 2 q^{30} - q^{31} - 5 q^{32} - 2 q^{33} - 32 q^{34} - 3 q^{35} + 7 q^{36} - 4 q^{37} - 18 q^{38} - 4 q^{40} + 28 q^{41} + q^{42} - 17 q^{43} + 10 q^{44} + 3 q^{45} + 40 q^{46} + 3 q^{47} - 17 q^{48} + 4 q^{49} - 11 q^{50} + 10 q^{51} - 5 q^{53} - q^{54} + 8 q^{55} + 3 q^{56} - 7 q^{57} + 12 q^{58} + 28 q^{59} - 40 q^{60} - 10 q^{61} + 14 q^{62} - 4 q^{63} + 9 q^{64} + 12 q^{66} + 22 q^{67} - 12 q^{68} - 3 q^{69} + 2 q^{70} + 2 q^{71} - 3 q^{72} - 31 q^{73} + 24 q^{74} - 17 q^{75} + 46 q^{76} - 2 q^{77} - q^{79} + 54 q^{80} + 4 q^{81} + 24 q^{82} + 3 q^{83} + 7 q^{84} - 2 q^{85} + 10 q^{86} + 9 q^{87} + 4 q^{88} + 5 q^{89} - 2 q^{90} + 28 q^{92} + q^{93} - 36 q^{94} + 39 q^{95} + 5 q^{96} - 43 q^{97} + q^{98} + 2 q^{99}+O(q^{100}) $ 4 * q + q^2 - 4 * q^3 + 7 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9 - 2 * q^10 + 2 * q^11 - 7 * q^12 - q^14 - 3 * q^15 + 17 * q^16 - 10 * q^17 + q^18 + 7 * q^19 + 40 * q^20 + 4 * q^21 - 12 * q^22 + 3 * q^23 + 3 * q^24 + 17 * q^25 - 4 * q^27 - 7 * q^28 - 9 * q^29 + 2 * q^30 - q^31 - 5 * q^32 - 2 * q^33 - 32 * q^34 - 3 * q^35 + 7 * q^36 - 4 * q^37 - 18 * q^38 - 4 * q^40 + 28 * q^41 + q^42 - 17 * q^43 + 10 * q^44 + 3 * q^45 + 40 * q^46 + 3 * q^47 - 17 * q^48 + 4 * q^49 - 11 * q^50 + 10 * q^51 - 5 * q^53 - q^54 + 8 * q^55 + 3 * q^56 - 7 * q^57 + 12 * q^58 + 28 * q^59 - 40 * q^60 - 10 * q^61 + 14 * q^62 - 4 * q^63 + 9 * q^64 + 12 * q^66 + 22 * q^67 - 12 * q^68 - 3 * q^69 + 2 * q^70 + 2 * q^71 - 3 * q^72 - 31 * q^73 + 24 * q^74 - 17 * q^75 + 46 * q^76 - 2 * q^77 - q^79 + 54 * q^80 + 4 * q^81 + 24 * q^82 + 3 * q^83 + 7 * q^84 - 2 * q^85 + 10 * q^86 + 9 * q^87 + 4 * q^88 + 5 * q^89 - 2 * q^90 + 28 * q^92 + q^93 - 36 * q^94 + 39 * q^95 + 5 * q^96 - 43 * q^97 + q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.233455	−0.165078	−0.0825388	−	0.996588i	$-0.526303\pi$
$2$	−0.233455	−0.165078	−0.0825388	+	0.996588i	$0.526303\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.94550	−0.972749
$5$	−2.94550	−1.31727	−0.658634	−	0.752464i	$-0.728865\pi$
$5$	−2.94550	−1.31727	−0.658634	+	0.752464i	$0.728865\pi$
$6$	0.233455	0.0953076
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.921097	0.325657
$9$	1.00000	0.333333
$10$	0.687642	0.217451
$11$	3.62146	1.09191	0.545956	−	0.837814i	$-0.316167\pi$
$11$	3.62146	1.09191	0.545956	+	0.837814i	$0.316167\pi$
$12$	1.94550	0.561617
$13$	0	0
$13$	0	0
$14$	0.233455	0.0623935
$15$	2.94550	0.760525
$16$	3.67596	0.918991
$17$	−1.53309	−0.371829	−0.185914	−	0.982566i	$-0.559525\pi$
$17$	−1.53309	−0.371829	−0.185914	+	0.982566i	$0.559525\pi$
$18$	−0.233455	−0.0550259
$19$	−4.10005	−0.940616	−0.470308	−	0.882502i	$-0.655857\pi$
$19$	−4.10005	−0.940616	−0.470308	+	0.882502i	$0.655857\pi$
$20$	5.73046	1.28137
$21$	1.00000	0.218218
$22$	−0.845448	−0.180250
$23$	−7.03387	−1.46666	−0.733332	−	0.679871i	$-0.762036\pi$
$23$	−7.03387	−1.46666	−0.733332	+	0.679871i	$0.762036\pi$
$24$	−0.921097	−0.188018
$25$	3.67596	0.735193
$26$	0	0
$27$	−1.00000	−0.192450
$28$	1.94550	0.367665
$29$	−3.79095	−0.703961	−0.351981	−	0.936007i	$-0.614492\pi$
$29$	−3.79095	−0.703961	−0.351981	+	0.936007i	$0.614492\pi$
$30$	−0.687642	−0.125546
$31$	−1.79095	−0.321664	−0.160832	−	0.986982i	$-0.551418\pi$
$31$	−1.79095	−0.321664	−0.160832	+	0.986982i	$0.551418\pi$
$32$	−2.70037	−0.477362
$33$	−3.62146	−0.630416
$34$	0.357908	0.0613806
$35$	2.94550	0.497880
$36$	−1.94550	−0.324250
$37$	−7.24292	−1.19073	−0.595365	−	0.803456i	$-0.702992\pi$
$37$	−7.24292	−1.19073	−0.595365	+	0.803456i	$0.702992\pi$
$38$	0.957177	0.155275
$39$	0	0
$40$	−2.71309	−0.428977
$41$	9.15455	1.42970	0.714850	−	0.699277i	$-0.246495\pi$
$41$	9.15455	1.42970	0.714850	+	0.699277i	$0.246495\pi$
$42$	−0.233455	−0.0360229
$43$	−5.79095	−0.883111	−0.441556	−	0.897234i	$-0.645573\pi$
$43$	−5.79095	−0.883111	−0.441556	+	0.897234i	$0.645573\pi$
$44$	−7.04555	−1.06216
$45$	−2.94550	−0.439089
$46$	1.64209	0.242113
$47$	−7.25460	−1.05819	−0.529096	−	0.848562i	$-0.677469\pi$
$47$	−7.25460	−1.05819	−0.529096	+	0.848562i	$0.677469\pi$
$48$	−3.67596	−0.530580
$49$	1.00000	0.142857
$50$	−0.858172	−0.121364
$51$	1.53309	0.214676
$52$	0	0
$53$	−13.3430	−1.83280	−0.916399	−	0.400266i	$-0.868918\pi$
$53$	−13.3430	−1.83280	−0.916399	+	0.400266i	$0.868918\pi$
$54$	0.233455	0.0317692
$55$	−10.6670	−1.43834
$56$	−0.921097	−0.123087
$57$	4.10005	0.543065
$58$	0.885016	0.116208
$59$	4.84545	0.630824	0.315412	−	0.948955i	$-0.397857\pi$
$59$	4.84545	0.630824	0.315412	+	0.948955i	$0.397857\pi$
$60$	−5.73046	−0.739800
$61$	2.77601	0.355432	0.177716	−	0.984082i	$-0.443129\pi$
$61$	2.77601	0.355432	0.177716	+	0.984082i	$0.443129\pi$
$62$	0.418106	0.0530995
$63$	−1.00000	−0.125988
$64$	−6.72151	−0.840189
$65$	0	0
$66$	0.845448	0.104068
$67$	14.8248	1.81114	0.905570	−	0.424197i	$-0.139444\pi$
$67$	14.8248	1.81114	0.905570	+	0.424197i	$0.139444\pi$
$68$	2.98262	0.361696
$69$	7.03387	0.846778
$70$	−0.687642	−0.0821889
$71$	3.62146	0.429788	0.214894	−	0.976637i	$-0.431059\pi$
$71$	3.62146	0.429788	0.214894	+	0.976637i	$0.431059\pi$
$72$	0.921097	0.108552
$73$	−14.5670	−1.70493	−0.852467	−	0.522781i	$-0.824894\pi$
$73$	−14.5670	−1.70493	−0.852467	+	0.522781i	$0.824894\pi$
$74$	1.69090	0.196563
$75$	−3.67596	−0.424464
$76$	7.97664	0.914984
$77$	−3.62146	−0.412704
$78$	0	0
$79$	6.56696	0.738841	0.369420	−	0.929262i	$-0.379556\pi$
$79$	6.56696	0.738841	0.369420	+	0.929262i	$0.379556\pi$
$80$	−10.8275	−1.21056
$81$	1.00000	0.111111
$82$	−2.13718	−0.236012
$83$	−7.25460	−0.796296	−0.398148	−	0.917321i	$-0.630347\pi$
$83$	−7.25460	−0.796296	−0.398148	+	0.917321i	$0.630347\pi$
$84$	−1.94550	−0.212271
$85$	4.51571	0.489798
$86$	1.35193	0.145782
$87$	3.79095	0.406432
$88$	3.33572	0.355588
$89$	0.636396	0.0674578	0.0337289	−	0.999431i	$-0.489262\pi$
$89$	0.636396	0.0674578	0.0337289	+	0.999431i	$0.489262\pi$
$90$	0.687642	0.0724838
$91$	0	0
$92$	13.6844	1.42670
$93$	1.79095	0.185713
$94$	1.69362	0.174684
$95$	12.0767	1.23904
$96$	2.70037	0.275605
$97$	−11.3240	−1.14978	−0.574891	−	0.818230i	$-0.694956\pi$
$97$	−11.3240	−1.14978	−0.574891	+	0.818230i	$0.694956\pi$
$98$	−0.233455	−0.0235825
$99$	3.62146	0.363971
$100$	−7.15158	−0.715158
$101$	6.04880	0.601879	0.300939	−	0.953643i	$-0.402700\pi$
$101$	6.04880	0.601879	0.300939	+	0.953643i	$0.402700\pi$
$102$	−0.357908	−0.0354381
$103$	−18.6670	−1.83932	−0.919658	−	0.392721i	$-0.871534\pi$
$103$	−18.6670	−1.83932	−0.919658	+	0.392721i	$0.871534\pi$
$104$	0	0
$105$	−2.94550	−0.287451
$106$	3.11498	0.302554
$107$	−4.82482	−0.466433	−0.233216	−	0.972425i	$-0.574925\pi$
$107$	−4.82482	−0.466433	−0.233216	+	0.972425i	$0.574925\pi$
$108$	1.94550	0.187206
$109$	4.95718	0.474811	0.237406	−	0.971411i	$-0.423703\pi$
$109$	4.95718	0.474811	0.237406	+	0.971411i	$0.423703\pi$
$110$	2.49027	0.237438
$111$	7.24292	0.687468
$112$	−3.67596	−0.347346
$113$	3.79095	0.356622	0.178311	−	0.983974i	$-0.442937\pi$
$113$	3.79095	0.356622	0.178311	+	0.983974i	$0.442937\pi$
$114$	−0.957177	−0.0896479
$115$	20.7183	1.93199
$116$	7.37528	0.684778
$117$	0	0
$118$	−1.13119	−0.104135
$119$	1.53309	0.140538
$120$	2.71309	0.247670
$121$	2.11498	0.192271
$122$	−0.648074	−0.0586739
$123$	−9.15455	−0.825438
$124$	3.48429	0.312898
$125$	3.89995	0.348822
$126$	0.233455	0.0207978
$127$	10.4903	0.930861	0.465430	−	0.885085i	$-0.345900\pi$
$127$	10.4903	0.930861	0.465430	+	0.885085i	$0.345900\pi$
$128$	6.96990	0.616058
$129$	5.79095	0.509864
$130$	0	0
$131$	5.35193	0.467600	0.233800	−	0.972285i	$-0.424884\pi$
$131$	5.35193	0.467600	0.233800	+	0.972285i	$0.424884\pi$
$132$	7.04555	0.613236
$133$	4.10005	0.355519
$134$	−3.46093	−0.298979
$135$	2.94550	0.253508
$136$	−1.41212	−0.121089
$137$	11.6936	0.999054	0.499527	−	0.866298i	$-0.333507\pi$
$137$	11.6936	0.999054	0.499527	+	0.866298i	$0.333507\pi$
$138$	−1.64209	−0.139784
$139$	−14.6670	−1.24404	−0.622020	−	0.783002i	$-0.713688\pi$
$139$	−14.6670	−1.24404	−0.622020	+	0.783002i	$0.713688\pi$
$140$	−5.73046	−0.484313
$141$	7.25460	0.610948
$142$	−0.845448	−0.0709485
$143$	0	0
$144$	3.67596	0.306330
$145$	11.1662	0.927305
$146$	3.40073	0.281446
$147$	−1.00000	−0.0824786
$148$	14.0911	1.15828
$149$	12.6274	1.03448	0.517240	−	0.855840i	$-0.326959\pi$
$149$	12.6274	1.03448	0.517240	+	0.855840i	$0.326959\pi$
$150$	0.858172	0.0700695
$151$	18.4858	1.50436	0.752178	−	0.658959i	$-0.229003\pi$
$151$	18.4858	1.50436	0.752178	+	0.658959i	$0.229003\pi$
$152$	−3.77654	−0.306318
$153$	−1.53309	−0.123943
$154$	0.845448	0.0681282
$155$	5.27523	0.423717
$156$	0	0
$157$	−1.06618	−0.0850904	−0.0425452	−	0.999095i	$-0.513547\pi$
$157$	−1.06618	−0.0850904	−0.0425452	+	0.999095i	$0.513547\pi$
$158$	−1.53309	−0.121966
$159$	13.3430	1.05817
$160$	7.95392	0.628813
$161$	7.03387	0.554347
$162$	−0.233455	−0.0183420
$163$	23.4430	1.83620	0.918100	−	0.396350i	$-0.129723\pi$
$163$	23.4430	1.83620	0.918100	+	0.396350i	$0.129723\pi$
$164$	−17.8102	−1.39074
$165$	10.6670	0.830426
$166$	1.69362	0.131451
$167$	−7.67271	−0.593732	−0.296866	−	0.954919i	$-0.595941\pi$
$167$	−7.67271	−0.593732	−0.296866	+	0.954919i	$0.595941\pi$
$168$	0.921097	0.0710641
$169$	0	0
$170$	−1.05422	−0.0808547
$171$	−4.10005	−0.313539
$172$	11.2663	0.859046
$173$	2.66701	0.202769	0.101385	−	0.994847i	$-0.467673\pi$
$173$	2.66701	0.202769	0.101385	+	0.994847i	$0.467673\pi$
$174$	−0.885016	−0.0670929
$175$	−3.67596	−0.277877
$176$	13.3124	1.00346
$177$	−4.84545	−0.364206
$178$	−0.148570	−0.0111358
$179$	11.2340	0.839666	0.419833	−	0.907601i	$-0.362089\pi$
$179$	11.2340	0.839666	0.419833	+	0.907601i	$0.362089\pi$
$180$	5.73046	0.427124
$181$	−9.58189	−0.712217	−0.356108	−	0.934445i	$-0.615897\pi$
$181$	−9.58189	−0.712217	−0.356108	+	0.934445i	$0.615897\pi$
$182$	0	0
$183$	−2.77601	−0.205209
$184$	−6.47887	−0.477629
$185$	21.3340	1.56851
$186$	−0.418106	−0.0306570
$187$	−5.55203	−0.406004
$188$	14.1138	1.02936
$189$	1.00000	0.0727393
$190$	−2.81936	−0.204538
$191$	−7.89100	−0.570973	−0.285486	−	0.958383i	$-0.592155\pi$
$191$	−7.89100	−0.570973	−0.285486	+	0.958383i	$0.592155\pi$
$192$	6.72151	0.485083
$193$	5.89100	0.424043	0.212022	−	0.977265i	$-0.431995\pi$
$193$	5.89100	0.424043	0.212022	+	0.977265i	$0.431995\pi$
$194$	2.64365	0.189803
$195$	0	0
$196$	−1.94550	−0.138964
$197$	19.1546	1.36471	0.682353	−	0.731023i	$-0.260957\pi$
$197$	19.1546	1.36471	0.682353	+	0.731023i	$0.260957\pi$
$198$	−0.845448	−0.0600834
$199$	−8.20010	−0.581290	−0.290645	−	0.956831i	$-0.593870\pi$
$199$	−8.20010	−0.581290	−0.290645	+	0.956831i	$0.593870\pi$
$200$	3.38592	0.239420
$201$	−14.8248	−1.04566
$202$	−1.41212	−0.0993567
$203$	3.79095	0.266072
$204$	−2.98262	−0.208825
$205$	−26.9647	−1.88330
$206$	4.35791	0.303630
$207$	−7.03387	−0.488888
$208$	0	0
$209$	−14.8482	−1.02707
$210$	0.687642	0.0474518
$211$	−11.7009	−0.805522	−0.402761	−	0.915305i	$-0.631949\pi$
$211$	−11.7009	−0.805522	−0.402761	+	0.915305i	$0.631949\pi$
$212$	25.9587	1.78285
$213$	−3.62146	−0.248138
$214$	1.12638	0.0769976
$215$	17.0572	1.16329
$216$	−0.921097	−0.0626727
$217$	1.79095	0.121577
$218$	−1.15728	−0.0783808
$219$	14.5670	0.984344
$220$	20.7527	1.39914
$221$	0	0
$222$	−1.69090	−0.113486
$223$	−5.45198	−0.365091	−0.182546	−	0.983197i	$-0.558434\pi$
$223$	−5.45198	−0.365091	−0.182546	+	0.983197i	$0.558434\pi$
$224$	2.70037	0.180426
$225$	3.67596	0.245064
$226$	−0.885016	−0.0588704
$227$	27.1133	1.79957	0.899786	−	0.436331i	$-0.143722\pi$
$227$	27.1133	1.79957	0.899786	+	0.436331i	$0.143722\pi$
$228$	−7.97664	−0.528266
$229$	−17.4918	−1.15589	−0.577946	−	0.816075i	$-0.696146\pi$
$229$	−17.4918	−1.15589	−0.577946	+	0.816075i	$0.696146\pi$
$230$	−4.83678	−0.318928
$231$	3.62146	0.238275
$232$	−3.49183	−0.229250
$233$	−13.3430	−0.874127	−0.437064	−	0.899431i	$-0.643982\pi$
$233$	−13.3430	−0.874127	−0.437064	+	0.899431i	$0.643982\pi$
$234$	0	0
$235$	21.3684	1.39392
$236$	−9.42681	−0.613633
$237$	−6.56696	−0.426570
$238$	−0.357908	−0.0231997
$239$	12.7554	0.825077	0.412539	−	0.910940i	$-0.364642\pi$
$239$	12.7554	0.825077	0.412539	+	0.910940i	$0.364642\pi$
$240$	10.8275	0.698915
$241$	−9.94875	−0.640856	−0.320428	−	0.947273i	$-0.603827\pi$
$241$	−9.94875	−0.640856	−0.320428	+	0.947273i	$0.603827\pi$
$242$	−0.493754	−0.0317397
$243$	−1.00000	−0.0641500
$244$	−5.40073	−0.345746
$245$	−2.94550	−0.188181
$246$	2.13718	0.136261
$247$	0	0
$248$	−1.64964	−0.104752
$249$	7.25460	0.459742
$250$	−0.910463	−0.0575827
$251$	−24.4002	−1.54013	−0.770064	−	0.637967i	$-0.779776\pi$
$251$	−24.4002	−1.54013	−0.770064	+	0.637967i	$0.779776\pi$
$252$	1.94550	0.122555
$253$	−25.4729	−1.60147
$254$	−2.44901	−0.153664
$255$	−4.51571	−0.282785
$256$	11.8159	0.738492
$257$	28.2190	1.76026	0.880128	−	0.474737i	$-0.157457\pi$
$257$	28.2190	1.76026	0.880128	+	0.474737i	$0.157457\pi$
$258$	−1.35193	−0.0841672
$259$	7.24292	0.450053
$260$	0	0
$261$	−3.79095	−0.234654
$262$	−1.24943	−0.0771903
$263$	−11.4520	−0.706159	−0.353080	−	0.935593i	$-0.614866\pi$
$263$	−11.4520	−0.706159	−0.353080	+	0.935593i	$0.614866\pi$
$264$	−3.33572	−0.205299
$265$	39.3017	2.41428
$266$	−0.957177	−0.0586883
$267$	−0.636396	−0.0389468
$268$	−28.8417	−1.76179
$269$	19.8009	1.20728	0.603642	−	0.797255i	$-0.293716\pi$
$269$	19.8009	1.20728	0.603642	+	0.797255i	$0.293716\pi$
$270$	−0.687642	−0.0418485
$271$	12.5391	0.761694	0.380847	−	0.924638i	$-0.375632\pi$
$271$	12.5391	0.761694	0.380847	+	0.924638i	$0.375632\pi$
$272$	−5.63558	−0.341707
$273$	0	0
$274$	−2.72994	−0.164921
$275$	13.3124	0.802765
$276$	−13.6844	−0.823703
$277$	2.43902	0.146547	0.0732733	−	0.997312i	$-0.476655\pi$
$277$	2.43902	0.146547	0.0732733	+	0.997312i	$0.476655\pi$
$278$	3.42409	0.205363
$279$	−1.79095	−0.107221
$280$	2.71309	0.162138
$281$	25.9794	1.54980	0.774900	−	0.632084i	$-0.217800\pi$
$281$	25.9794	1.54980	0.774900	+	0.632084i	$0.217800\pi$
$282$	−1.69362	−0.100854
$283$	7.78199	0.462592	0.231296	−	0.972883i	$-0.425703\pi$
$283$	7.78199	0.462592	0.231296	+	0.972883i	$0.425703\pi$
$284$	−7.04555	−0.418076
$285$	−12.0767	−0.715362
$286$	0	0
$287$	−9.15455	−0.540376
$288$	−2.70037	−0.159121
$289$	−14.6496	−0.861743
$290$	−2.60681	−0.153077
$291$	11.3240	0.663827
$292$	28.3400	1.65847
$293$	7.14560	0.417450	0.208725	−	0.977974i	$-0.433069\pi$
$293$	7.14560	0.417450	0.208725	+	0.977974i	$0.433069\pi$
$294$	0.233455	0.0136154
$295$	−14.2723	−0.830963
$296$	−6.67143	−0.387769
$297$	−3.62146	−0.210139
$298$	−2.94794	−0.170770
$299$	0	0
$300$	7.15158	0.412897
$301$	5.79095	0.333785
$302$	−4.31561	−0.248336
$303$	−6.04880	−0.347495
$304$	−15.0716	−0.864417
$305$	−8.17674	−0.468199
$306$	0.357908	0.0204602
$307$	10.4092	0.594082	0.297041	−	0.954865i	$-0.404000\pi$
$307$	10.4092	0.594082	0.297041	+	0.954865i	$0.404000\pi$
$308$	7.04555	0.401457
$309$	18.6670	1.06193
$310$	−1.23153	−0.0699462
$311$	−4.51571	−0.256063	−0.128031	−	0.991770i	$-0.540866\pi$
$311$	−4.51571	−0.256063	−0.128031	+	0.991770i	$0.540866\pi$
$312$	0	0
$313$	−21.6242	−1.22227	−0.611136	−	0.791526i	$-0.709287\pi$
$313$	−21.6242	−1.22227	−0.611136	+	0.791526i	$0.709287\pi$
$314$	0.248905	0.0140465
$315$	2.94550	0.165960
$316$	−12.7760	−0.718707
$317$	−16.8275	−0.945129	−0.472565	−	0.881296i	$-0.656672\pi$
$317$	−16.8275	−0.945129	−0.472565	+	0.881296i	$0.656672\pi$
$318$	−3.11498	−0.174680
$319$	−13.7288	−0.768664
$320$	19.7982	1.10675
$321$	4.82482	0.269295
$322$	−1.64209	−0.0915102
$323$	6.28575	0.349748
$324$	−1.94550	−0.108083
$325$	0	0
$326$	−5.47289	−0.303115
$327$	−4.95718	−0.274133
$328$	8.43223	0.465592
$329$	7.25460	0.399959
$330$	−2.49027	−0.137085
$331$	−36.1355	−1.98619	−0.993093	−	0.117331i	$-0.962566\pi$
$331$	−36.1355	−1.98619	−0.993093	+	0.117331i	$0.962566\pi$
$332$	14.1138	0.774596
$333$	−7.24292	−0.396910
$334$	1.79123	0.0980119
$335$	−43.6665	−2.38575
$336$	3.67596	0.200540
$337$	33.4595	1.82266	0.911328	−	0.411681i	$-0.135058\pi$
$337$	33.4595	1.82266	0.911328	+	0.411681i	$0.135058\pi$
$338$	0	0
$339$	−3.79095	−0.205896
$340$	−8.78532	−0.476451
$341$	−6.48585	−0.351228
$342$	0.957177	0.0517582
$343$	−1.00000	−0.0539949
$344$	−5.33402	−0.287591
$345$	−20.7183	−1.11543
$346$	−0.622627	−0.0334726
$347$	−8.72721	−0.468501	−0.234251	−	0.972176i	$-0.575264\pi$
$347$	−8.72721	−0.468501	−0.234251	+	0.972176i	$0.575264\pi$
$348$	−7.37528	−0.395357
$349$	0.852706	0.0456443	0.0228222	−	0.999740i	$-0.492735\pi$
$349$	0.852706	0.0456443	0.0228222	+	0.999740i	$0.492735\pi$
$350$	0.858172	0.0458712
$351$	0	0
$352$	−9.77927	−0.521237
$353$	−7.46365	−0.397250	−0.198625	−	0.980076i	$-0.563648\pi$
$353$	−7.46365	−0.397250	−0.198625	+	0.980076i	$0.563648\pi$
$354$	1.13119	0.0601223
$355$	−10.6670	−0.566146
$356$	−1.23811	−0.0656195
$357$	−1.53309	−0.0811397
$358$	−2.62263	−0.138610
$359$	12.4019	0.654547	0.327274	−	0.944930i	$-0.393870\pi$
$359$	12.4019	0.654547	0.327274	+	0.944930i	$0.393870\pi$
$360$	−2.71309	−0.142992
$361$	−2.18959	−0.115241
$362$	2.23694	0.117571
$363$	−2.11498	−0.111008
$364$	0	0
$365$	42.9070	2.24585
$366$	0.648074	0.0338754
$367$	−9.31508	−0.486243	−0.243122	−	0.969996i	$-0.578171\pi$
$367$	−9.31508	−0.486243	−0.243122	+	0.969996i	$0.578171\pi$
$368$	−25.8562	−1.34785
$369$	9.15455	0.476567
$370$	−4.98053	−0.258926
$371$	13.3430	0.692733
$372$	−3.48429	−0.180652
$373$	−3.73319	−0.193297	−0.0966486	−	0.995319i	$-0.530812\pi$
$373$	−3.73319	−0.193297	−0.0966486	+	0.995319i	$0.530812\pi$
$374$	1.29615	0.0670222
$375$	−3.89995	−0.201393
$376$	−6.68219	−0.344608
$377$	0	0
$378$	−0.233455	−0.0120076
$379$	12.0000	0.616399	0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$380$	−23.4952	−1.20528
$381$	−10.4903	−0.537433
$382$	1.84219	0.0942548
$383$	−8.80419	−0.449873	−0.224936	−	0.974373i	$-0.572217\pi$
$383$	−8.80419	−0.449873	−0.224936	+	0.974373i	$0.572217\pi$
$384$	−6.96990	−0.355681
$385$	10.6670	0.543641
$386$	−1.37528	−0.0700001
$387$	−5.79095	−0.294370
$388$	22.0309	1.11845
$389$	26.4978	1.34349	0.671746	−	0.740781i	$-0.265545\pi$
$389$	26.4978	1.34349	0.671746	+	0.740781i	$0.265545\pi$
$390$	0	0
$391$	10.7836	0.545348
$392$	0.921097	0.0465224
$393$	−5.35193	−0.269969
$394$	−4.47173	−0.225282
$395$	−19.3430	−0.973251
$396$	−7.04555	−0.354052
$397$	−16.0399	−0.805017	−0.402509	−	0.915416i	$-0.631862\pi$
$397$	−16.0399	−0.805017	−0.402509	+	0.915416i	$0.631862\pi$
$398$	1.91435	0.0959579
$399$	−4.10005	−0.205259
$400$	13.5127	0.675635
$401$	12.2885	0.613657	0.306829	−	0.951765i	$-0.400732\pi$
$401$	12.2885	0.613657	0.306829	+	0.951765i	$0.400732\pi$
$402$	3.46093	0.172615
$403$	0	0
$404$	−11.7679	−0.585477
$405$	−2.94550	−0.146363
$406$	−0.885016	−0.0439226
$407$	−26.2300	−1.30017
$408$	1.41212	0.0699105
$409$	24.8114	1.22685	0.613423	−	0.789754i	$-0.289792\pi$
$409$	24.8114	1.22685	0.613423	+	0.789754i	$0.289792\pi$
$410$	6.29505	0.310890
$411$	−11.6936	−0.576804
$412$	36.3166	1.78919
$413$	−4.84545	−0.238429
$414$	1.64209	0.0807044
$415$	21.3684	1.04893
$416$	0	0
$417$	14.6670	0.718247
$418$	3.46638	0.169546
$419$	21.6496	1.05765	0.528827	−	0.848730i	$-0.322632\pi$
$419$	21.6496	1.05765	0.528827	+	0.848730i	$0.322632\pi$
$420$	5.73046	0.279618
$421$	−22.4679	−1.09502	−0.547510	−	0.836799i	$-0.684424\pi$
$421$	−22.4679	−1.09502	−0.547510	+	0.836799i	$0.684424\pi$
$422$	2.73163	0.132974
$423$	−7.25460	−0.352731
$424$	−12.2902	−0.596863
$425$	−5.63558	−0.273366
$426$	0.845448	0.0409621
$427$	−2.77601	−0.134341
$428$	9.38668	0.453722
$429$	0	0
$430$	−3.98210	−0.192034
$431$	28.7787	1.38622	0.693112	−	0.720830i	$-0.256239\pi$
$431$	28.7787	1.38622	0.693112	+	0.720830i	$0.256239\pi$
$432$	−3.67596	−0.176860
$433$	29.5217	1.41872	0.709361	−	0.704845i	$-0.248984\pi$
$433$	29.5217	1.41872	0.709361	+	0.704845i	$0.248984\pi$
$434$	−0.418106	−0.0200697
$435$	−11.1662	−0.535380
$436$	−9.64418	−0.461873
$437$	28.8392	1.37957
$438$	−3.40073	−0.162493
$439$	−18.6670	−0.890928	−0.445464	−	0.895300i	$-0.646961\pi$
$439$	−18.6670	−0.890928	−0.445464	+	0.895300i	$0.646961\pi$
$440$	−9.82535	−0.468405
$441$	1.00000	0.0476190
$442$	0	0
$443$	15.2340	0.723788	0.361894	−	0.932219i	$-0.382130\pi$
$443$	15.2340	0.723788	0.361894	+	0.932219i	$0.382130\pi$
$444$	−14.0911	−0.668734
$445$	−1.87450	−0.0888599
$446$	1.27279	0.0602684
$447$	−12.6274	−0.597258
$448$	6.72151	0.317562
$449$	−11.2755	−0.532125	−0.266062	−	0.963956i	$-0.585723\pi$
$449$	−11.2755	−0.532125	−0.266062	+	0.963956i	$0.585723\pi$
$450$	−0.858172	−0.0404546
$451$	33.1529	1.56111
$452$	−7.37528	−0.346904
$453$	−18.4858	−0.868541
$454$	−6.32973	−0.297069
$455$	0	0
$456$	3.77654	0.176853
$457$	−24.0234	−1.12377	−0.561883	−	0.827217i	$-0.689923\pi$
$457$	−24.0234	−1.12377	−0.561883	+	0.827217i	$0.689923\pi$
$458$	4.08356	0.190812
$459$	1.53309	0.0715585
$460$	−40.3073	−1.87934
$461$	1.91163	0.0890334	0.0445167	−	0.999009i	$-0.485825\pi$
$461$	1.91163	0.0890334	0.0445167	+	0.999009i	$0.485825\pi$
$462$	−0.845448	−0.0393338
$463$	−15.2250	−0.707567	−0.353783	−	0.935327i	$-0.615105\pi$
$463$	−15.2250	−0.707567	−0.353783	+	0.935327i	$0.615105\pi$
$464$	−13.9354	−0.646934
$465$	−5.27523	−0.244633
$466$	3.11498	0.144299
$467$	−31.0483	−1.43674	−0.718371	−	0.695660i	$-0.755112\pi$
$467$	−31.0483	−1.43674	−0.718371	+	0.695660i	$0.755112\pi$
$468$	0	0
$469$	−14.8248	−0.684546
$470$	−4.98857	−0.230105
$471$	1.06618	0.0491270
$472$	4.46313	0.205432
$473$	−20.9717	−0.964279
$474$	1.53309	0.0704172
$475$	−15.0716	−0.691534
$476$	−2.98262	−0.136708
$477$	−13.3430	−0.610933
$478$	−2.97781	−0.136202
$479$	−39.6314	−1.81081	−0.905403	−	0.424552i	$-0.860432\pi$
$479$	−39.6314	−1.81081	−0.905403	+	0.424552i	$0.860432\pi$
$480$	−7.95392	−0.363045
$481$	0	0
$482$	2.32259	0.105791
$483$	−7.03387	−0.320052
$484$	−4.11470	−0.187032
$485$	33.3549	1.51457
$486$	0.233455	0.0105897
$487$	5.91435	0.268005	0.134002	−	0.990981i	$-0.457217\pi$
$487$	5.91435	0.268005	0.134002	+	0.990981i	$0.457217\pi$
$488$	2.55698	0.115749
$489$	−23.4430	−1.06013
$490$	0.687642	0.0310645
$491$	40.6068	1.83256	0.916280	−	0.400539i	$-0.131177\pi$
$491$	40.6068	1.83256	0.916280	+	0.400539i	$0.131177\pi$
$492$	17.8102	0.802944
$493$	5.81186	0.261753
$494$	0	0
$495$	−10.6670	−0.479446
$496$	−6.58346	−0.295606
$497$	−3.62146	−0.162445
$498$	−1.69362	−0.0758931
$499$	27.9821	1.25265	0.626325	−	0.779562i	$-0.284558\pi$
$499$	27.9821	1.25265	0.626325	+	0.779562i	$0.284558\pi$
$500$	−7.58735	−0.339316
$501$	7.67271	0.342791
$502$	5.69635	0.254241
$503$	−26.9458	−1.20145	−0.600727	−	0.799455i	$-0.705122\pi$
$503$	−26.9458	−1.20145	−0.600727	+	0.799455i	$0.705122\pi$
$504$	−0.921097	−0.0410289
$505$	−17.8167	−0.792835
$506$	5.94677	0.264366
$507$	0	0
$508$	−20.4088	−0.905494
$509$	0.836496	0.0370770	0.0185385	−	0.999828i	$-0.494099\pi$
$509$	0.836496	0.0370770	0.0185385	+	0.999828i	$0.494099\pi$
$510$	1.05422	0.0466815
$511$	14.5670	0.644404
$512$	−16.6983	−0.737966
$513$	4.10005	0.181022
$514$	−6.58788	−0.290579
$515$	54.9837	2.42287
$516$	−11.2663	−0.495970
$517$	−26.2723	−1.15545
$518$	−1.69090	−0.0742937
$519$	−2.66701	−0.117069
$520$	0	0
$521$	22.3047	0.977186	0.488593	−	0.872512i	$-0.337510\pi$
$521$	22.3047	0.977186	0.488593	+	0.872512i	$0.337510\pi$
$522$	0.885016	0.0387361
$523$	28.0010	1.22440	0.612200	−	0.790703i	$-0.290285\pi$
$523$	28.0010	1.22440	0.612200	+	0.790703i	$0.290285\pi$
$524$	−10.4122	−0.454858
$525$	3.67596	0.160432
$526$	2.67352	0.116571
$527$	2.74568	0.119604
$528$	−13.3124	−0.579346
$529$	26.4753	1.15110
$530$	−9.17518	−0.398544
$531$	4.84545	0.210275
$532$	−7.97664	−0.345831
$533$	0	0
$534$	0.148570	0.00642924
$535$	14.2115	0.614416
$536$	13.6551	0.589810
$537$	−11.2340	−0.484782
$538$	−4.62263	−0.199296
$539$	3.62146	0.155987
$540$	−5.73046	−0.246600
$541$	−5.86764	−0.252270	−0.126135	−	0.992013i	$-0.540257\pi$
$541$	−5.86764	−0.252270	−0.126135	+	0.992013i	$0.540257\pi$
$542$	−2.92731	−0.125739
$543$	9.58189	0.411198
$544$	4.13990	0.177497
$545$	−14.6014	−0.625454
$546$	0	0
$547$	26.5068	1.13335	0.566674	−	0.823942i	$-0.308230\pi$
$547$	26.5068	1.13335	0.566674	+	0.823942i	$0.308230\pi$
$548$	−22.7499	−0.971829
$549$	2.77601	0.118477
$550$	−3.10784	−0.132519
$551$	15.5431	0.662157
$552$	6.47887	0.275759
$553$	−6.56696	−0.279256
$554$	−0.569402	−0.0241916
$555$	−21.3340	−0.905579
$556$	28.5347	1.21014
$557$	−32.5862	−1.38072	−0.690360	−	0.723466i	$-0.742548\pi$
$557$	−32.5862	−1.38072	−0.690360	+	0.723466i	$0.742548\pi$
$558$	0.418106	0.0176998
$559$	0	0
$560$	10.8275	0.457547
$561$	5.55203	0.234407
$562$	−6.06501	−0.255837
$563$	9.71425	0.409407	0.204703	−	0.978824i	$-0.434377\pi$
$563$	9.71425	0.409407	0.204703	+	0.978824i	$0.434377\pi$
$564$	−14.1138	−0.594299
$565$	−11.1662	−0.469767
$566$	−1.81675	−0.0763635
$567$	−1.00000	−0.0419961
$568$	3.33572	0.139964
$569$	−3.79095	−0.158925	−0.0794624	−	0.996838i	$-0.525320\pi$
$569$	−3.79095	−0.158925	−0.0794624	+	0.996838i	$0.525320\pi$
$570$	2.81936	0.118090
$571$	3.76550	0.157581	0.0787906	−	0.996891i	$-0.474894\pi$
$571$	3.76550	0.157581	0.0787906	+	0.996891i	$0.474894\pi$
$572$	0	0
$573$	7.89100	0.329651
$574$	2.13718	0.0892040
$575$	−25.8562	−1.07828
$576$	−6.72151	−0.280063
$577$	10.7228	0.446396	0.223198	−	0.974773i	$-0.428350\pi$
$577$	10.7228	0.446396	0.223198	+	0.974773i	$0.428350\pi$
$578$	3.42003	0.142255
$579$	−5.89100	−0.244822
$580$	−21.7239	−0.902035
$581$	7.25460	0.300972
$582$	−2.64365	−0.109583
$583$	−48.3211	−2.00125
$584$	−13.4176	−0.555223
$585$	0	0
$586$	−1.66818	−0.0689117
$587$	34.0794	1.40661	0.703304	−	0.710889i	$-0.251707\pi$
$587$	34.0794	1.40661	0.703304	+	0.710889i	$0.251707\pi$
$588$	1.94550	0.0802310
$589$	7.34297	0.302562
$590$	3.33193	0.137173
$591$	−19.1546	−0.787913
$592$	−26.6247	−1.09427
$593$	38.9600	1.59990	0.799948	−	0.600069i	$-0.204860\pi$
$593$	38.9600	1.59990	0.799948	+	0.600069i	$0.204860\pi$
$594$	0.845448	0.0346892
$595$	−4.51571	−0.185126
$596$	−24.5667	−1.00629
$597$	8.20010	0.335608
$598$	0	0
$599$	−4.90151	−0.200270	−0.100135	−	0.994974i	$-0.531928\pi$
$599$	−4.90151	−0.200270	−0.100135	+	0.994974i	$0.531928\pi$
$600$	−3.38592	−0.138229
$601$	9.73970	0.397291	0.198645	−	0.980071i	$-0.436346\pi$
$601$	9.73970	0.397291	0.198645	+	0.980071i	$0.436346\pi$
$602$	−1.35193	−0.0551004
$603$	14.8248	0.603713
$604$	−35.9642	−1.46336
$605$	−6.22968	−0.253273
$606$	1.41212	0.0573636
$607$	−17.8308	−0.723730	−0.361865	−	0.932231i	$-0.617860\pi$
$607$	−17.8308	−0.723730	−0.361865	+	0.932231i	$0.617860\pi$
$608$	11.0716	0.449014
$609$	−3.79095	−0.153617
$610$	1.90890	0.0772892
$611$	0	0
$612$	2.98262	0.120565
$613$	7.83777	0.316565	0.158282	−	0.987394i	$-0.449404\pi$
$613$	7.83777	0.316565	0.158282	+	0.987394i	$0.449404\pi$
$614$	−2.43007	−0.0980696
$615$	26.9647	1.08732
$616$	−3.33572	−0.134400
$617$	40.0471	1.61224	0.806118	−	0.591755i	$-0.201565\pi$
$617$	40.0471	1.61224	0.806118	+	0.591755i	$0.201565\pi$
$618$	−4.35791	−0.175301
$619$	9.07269	0.364662	0.182331	−	0.983237i	$-0.441636\pi$
$619$	9.07269	0.364662	0.182331	+	0.983237i	$0.441636\pi$
$620$	−10.2630	−0.412170
$621$	7.03387	0.282259
$622$	1.05422	0.0422702
$623$	−0.636396	−0.0254967
$624$	0	0
$625$	−29.8671	−1.19468
$626$	5.04828	0.201770
$627$	14.8482	0.592979
$628$	2.07425	0.0827717
$629$	11.1041	0.442748
$630$	−0.687642	−0.0273963
$631$	−9.11056	−0.362686	−0.181343	−	0.983420i	$-0.558044\pi$
$631$	−9.11056	−0.362686	−0.181343	+	0.983420i	$0.558044\pi$
$632$	6.04880	0.240609
$633$	11.7009	0.465068
$634$	3.92847	0.156020
$635$	−30.8991	−1.22619
$636$	−25.9587	−1.02933
$637$	0	0
$638$	3.20505	0.126889
$639$	3.62146	0.143263
$640$	−20.5298	−0.811513
$641$	−22.8392	−0.902095	−0.451048	−	0.892500i	$-0.648950\pi$
$641$	−22.8392	−0.902095	−0.451048	+	0.892500i	$0.648950\pi$
$642$	−1.12638	−0.0444546
$643$	−15.6844	−0.618532	−0.309266	−	0.950976i	$-0.600083\pi$
$643$	−15.6844	−0.618532	−0.309266	+	0.950976i	$0.600083\pi$
$644$	−13.6844	−0.539240
$645$	−17.0572	−0.671628
$646$	−1.46744	−0.0577356
$647$	47.6198	1.87213	0.936063	−	0.351832i	$-0.114441\pi$
$647$	47.6198	1.87213	0.936063	+	0.351832i	$0.114441\pi$
$648$	0.921097	0.0361841
$649$	17.5476	0.688804
$650$	0	0
$651$	−1.79095	−0.0701928
$652$	−45.6084	−1.78616
$653$	42.4002	1.65925	0.829624	−	0.558322i	$-0.188555\pi$
$653$	42.4002	1.65925	0.829624	+	0.558322i	$0.188555\pi$
$654$	1.15728	0.0452532
$655$	−15.7641	−0.615954
$656$	33.6518	1.31388
$657$	−14.5670	−0.568311
$658$	−1.69362	−0.0660243
$659$	15.7497	0.613521	0.306760	−	0.951787i	$-0.400755\pi$
$659$	15.7497	0.613521	0.306760	+	0.951787i	$0.400755\pi$
$660$	−20.7527	−0.807796
$661$	−17.3684	−0.675553	−0.337777	−	0.941226i	$-0.609675\pi$
$661$	−17.3684	−0.675553	−0.337777	+	0.941226i	$0.609675\pi$
$662$	8.43601	0.327875
$663$	0	0
$664$	−6.68219	−0.259319
$665$	−12.0767	−0.468314
$666$	1.69090	0.0655209
$667$	26.6650	1.03247
$668$	14.9272	0.577552
$669$	5.45198	0.210786
$670$	10.1942	0.393835
$671$	10.0532	0.388100
$672$	−2.70037	−0.104169
$673$	35.6754	1.37519	0.687593	−	0.726096i	$-0.258667\pi$
$673$	35.6754	1.37519	0.687593	+	0.726096i	$0.258667\pi$
$674$	−7.81129	−0.300880
$675$	−3.67596	−0.141488
$676$	0	0
$677$	−30.7228	−1.18077	−0.590386	−	0.807121i	$-0.701025\pi$
$677$	−30.7228	−1.18077	−0.590386	+	0.807121i	$0.701025\pi$
$678$	0.885016	0.0339888
$679$	11.3240	0.434577
$680$	4.15941	0.159506
$681$	−27.1133	−1.03898
$682$	1.51415	0.0579799
$683$	12.2018	0.466889	0.233444	−	0.972370i	$-0.425000\pi$
$683$	12.2018	0.466889	0.233444	+	0.972370i	$0.425000\pi$
$684$	7.97664	0.304995
$685$	−34.4436	−1.31602
$686$	0.233455	0.00891335
$687$	17.4918	0.667355
$688$	−21.2873	−0.811571
$689$	0	0
$690$	4.83678	0.184133
$691$	−19.7198	−0.750177	−0.375089	−	0.926989i	$-0.622388\pi$
$691$	−19.7198	−0.750177	−0.375089	+	0.926989i	$0.622388\pi$
$692$	−5.18867	−0.197243
$693$	−3.62146	−0.137568
$694$	2.03741	0.0773391
$695$	43.2017	1.63873
$696$	3.49183	0.132357
$697$	−14.0348	−0.531604
$698$	−0.199069	−0.00753486
$699$	13.3430	0.504678
$700$	7.15158	0.270304
$701$	38.4211	1.45115	0.725573	−	0.688145i	$-0.241575\pi$
$701$	38.4211	1.45115	0.725573	+	0.688145i	$0.241575\pi$
$702$	0	0
$703$	29.6963	1.12002
$704$	−24.3417	−0.917412
$705$	−21.3684	−0.804781
$706$	1.74243	0.0655771
$707$	−6.04880	−0.227489
$708$	9.42681	0.354281
$709$	−29.1573	−1.09502	−0.547512	−	0.836798i	$-0.684425\pi$
$709$	−29.1573	−1.09502	−0.547512	+	0.836798i	$0.684425\pi$
$710$	2.49027	0.0934581
$711$	6.56696	0.246280
$712$	0.586182	0.0219681
$713$	12.5973	0.471772
$714$	0.357908	0.0133944
$715$	0	0
$716$	−21.8557	−0.816785
$717$	−12.7554	−0.476358
$718$	−2.89528	−0.108051
$719$	32.5157	1.21263	0.606316	−	0.795224i	$-0.292647\pi$
$719$	32.5157	1.21263	0.606316	+	0.795224i	$0.292647\pi$
$720$	−10.8275	−0.403519
$721$	18.6670	0.695196
$722$	0.511170	0.0190238
$723$	9.94875	0.369998
$724$	18.6416	0.692808
$725$	−13.9354	−0.517547
$726$	0.493754	0.0183249
$727$	−19.9821	−0.741095	−0.370547	−	0.928814i	$-0.620830\pi$
$727$	−19.9821	−0.741095	−0.370547	+	0.928814i	$0.620830\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−10.0168	−0.370740
$731$	8.87804	0.328366
$732$	5.40073	0.199617
$733$	26.1956	0.967555	0.483778	−	0.875191i	$-0.339264\pi$
$733$	26.1956	0.967555	0.483778	+	0.875191i	$0.339264\pi$
$734$	2.17465	0.0802679
$735$	2.94550	0.108646
$736$	18.9940	0.700129
$737$	53.6875	1.97760
$738$	−2.13718	−0.0786705
$739$	14.6247	0.537979	0.268989	−	0.963143i	$-0.413310\pi$
$739$	14.6247	0.537979	0.268989	+	0.963143i	$0.413310\pi$
$740$	−41.5053	−1.52577
$741$	0	0
$742$	−3.11498	−0.114355
$743$	−15.4268	−0.565955	−0.282977	−	0.959127i	$-0.591322\pi$
$743$	−15.4268	−0.565955	−0.282977	+	0.959127i	$0.591322\pi$
$744$	1.64964	0.0604786
$745$	−37.1941	−1.36269
$746$	0.871532	0.0319091
$747$	−7.25460	−0.265432
$748$	10.8015	0.394941
$749$	4.82482	0.176295
$750$	0.910463	0.0332454
$751$	−2.62716	−0.0958664	−0.0479332	−	0.998851i	$-0.515263\pi$
$751$	−2.62716	−0.0958664	−0.0479332	+	0.998851i	$0.515263\pi$
$752$	−26.6676	−0.972469
$753$	24.4002	0.889193
$754$	0	0
$755$	−54.4500	−1.98164
$756$	−1.94550	−0.0707571
$757$	35.9454	1.30646	0.653228	−	0.757161i	$-0.273414\pi$
$757$	35.9454	1.30646	0.653228	+	0.757161i	$0.273414\pi$
$758$	−2.80146	−0.101754
$759$	25.4729	0.924607
$760$	11.1238	0.403503
$761$	−24.1028	−0.873725	−0.436862	−	0.899528i	$-0.643910\pi$
$761$	−24.1028	−0.873725	−0.436862	+	0.899528i	$0.643910\pi$
$762$	2.44901	0.0887181
$763$	−4.95718	−0.179462
$764$	15.3519	0.555413
$765$	4.51571	0.163266
$766$	2.05538	0.0742640
$767$	0	0
$768$	−11.8159	−0.426368
$769$	−51.8831	−1.87095	−0.935476	−	0.353391i	$-0.885029\pi$
$769$	−51.8831	−1.87095	−0.935476	+	0.353391i	$0.885029\pi$
$770$	−2.49027	−0.0897430
$771$	−28.2190	−1.01628
$772$	−11.4609	−0.412488
$773$	−30.8833	−1.11080	−0.555398	−	0.831585i	$-0.687434\pi$
$773$	−30.8833	−1.11080	−0.555398	+	0.831585i	$0.687434\pi$
$774$	1.35193	0.0485940
$775$	−6.58346	−0.236485
$776$	−10.4305	−0.374434
$777$	−7.24292	−0.259838
$778$	−6.18605	−0.221781
$779$	−37.5341	−1.34480
$780$	0	0
$781$	13.1150	0.469291
$782$	−2.51748	−0.0900247
$783$	3.79095	0.135477
$784$	3.67596	0.131284
$785$	3.14043	0.112087
$786$	1.24943	0.0445658
$787$	53.9877	1.92445	0.962226	−	0.272252i	$-0.0877683\pi$
$787$	53.9877	1.92445	0.962226	+	0.272252i	$0.0877683\pi$
$788$	−37.2652	−1.32752
$789$	11.4520	0.407701
$790$	4.51571	0.160662
$791$	−3.79095	−0.134791
$792$	3.33572	0.118529
$793$	0	0
$794$	3.74458	0.132890
$795$	−39.3017	−1.39389
$796$	15.9533	0.565449
$797$	−4.69688	−0.166372	−0.0831860	−	0.996534i	$-0.526510\pi$
$797$	−4.69688	−0.166372	−0.0831860	+	0.996534i	$0.526510\pi$
$798$	0.957177	0.0338837
$799$	11.1220	0.393467
$800$	−9.92644	−0.350953
$801$	0.636396	0.0224859
$802$	−2.86881	−0.101301
$803$	−52.7537	−1.86164
$804$	28.8417	1.01717
$805$	−20.7183	−0.730223
$806$	0	0
$807$	−19.8009	−0.697026
$808$	5.57153	0.196006
$809$	−22.4390	−0.788914	−0.394457	−	0.918914i	$-0.629067\pi$
$809$	−22.4390	−0.788914	−0.394457	+	0.918914i	$0.629067\pi$
$810$	0.687642	0.0241613
$811$	−10.4858	−0.368208	−0.184104	−	0.982907i	$-0.558938\pi$
$811$	−10.4858	−0.368208	−0.184104	+	0.982907i	$0.558938\pi$
$812$	−7.37528	−0.258822
$813$	−12.5391	−0.439764
$814$	6.12352	0.214629
$815$	−69.0514	−2.41876
$816$	5.63558	0.197285
$817$	23.7432	0.830669
$818$	−5.79236	−0.202525
$819$	0	0
$820$	52.4598	1.83198
$821$	36.7808	1.28366	0.641830	−	0.766847i	$-0.278176\pi$
$821$	36.7808	1.28366	0.641830	+	0.766847i	$0.278176\pi$
$822$	2.72994	0.0952174
$823$	28.9717	1.00989	0.504945	−	0.863152i	$-0.331513\pi$
$823$	28.9717	1.00989	0.504945	+	0.863152i	$0.331513\pi$
$824$	−17.1941	−0.598986
$825$	−13.3124	−0.463477
$826$	1.13119	0.0393593
$827$	−1.73046	−0.0601741	−0.0300871	−	0.999547i	$-0.509578\pi$
$827$	−1.73046	−0.0601741	−0.0300871	+	0.999547i	$0.509578\pi$
$828$	13.6844	0.475565
$829$	−33.1972	−1.15299	−0.576494	−	0.817101i	$-0.695580\pi$
$829$	−33.1972	−1.15299	−0.576494	+	0.817101i	$0.695580\pi$
$830$	−4.98857	−0.173156
$831$	−2.43902	−0.0846087
$832$	0	0
$833$	−1.53309	−0.0531184
$834$	−3.42409	−0.118566
$835$	22.6000	0.782104
$836$	28.8871	0.999081
$837$	1.79095	0.0619042
$838$	−5.05422	−0.174595
$839$	8.48312	0.292870	0.146435	−	0.989220i	$-0.453220\pi$
$839$	8.48312	0.292870	0.146435	+	0.989220i	$0.453220\pi$
$840$	−2.71309	−0.0936105
$841$	−14.6287	−0.504439
$842$	5.24525	0.180763
$843$	−25.9794	−0.894777
$844$	22.7640	0.783571
$845$	0	0
$846$	1.69362	0.0582280
$847$	−2.11498	−0.0726717
$848$	−49.0483	−1.68432
$849$	−7.78199	−0.267077
$850$	1.31565	0.0451266
$851$	50.9458	1.74640
$852$	7.04555	0.241377
$853$	14.9617	0.512279	0.256140	−	0.966640i	$-0.417549\pi$
$853$	14.9617	0.512279	0.256140	+	0.966640i	$0.417549\pi$
$854$	0.648074	0.0221766
$855$	12.0767	0.413014
$856$	−4.44412	−0.151897
$857$	46.1334	1.57589	0.787943	−	0.615748i	$-0.211146\pi$
$857$	46.1334	1.57589	0.787943	+	0.615748i	$0.211146\pi$
$858$	0	0
$859$	15.3042	0.522171	0.261085	−	0.965316i	$-0.415920\pi$
$859$	15.3042	0.522171	0.261085	+	0.965316i	$0.415920\pi$
$860$	−33.1848	−1.13159
$861$	9.15455	0.311986
$862$	−6.71854	−0.228834
$863$	19.8449	0.675529	0.337764	−	0.941231i	$-0.390329\pi$
$863$	19.8449	0.675529	0.337764	+	0.941231i	$0.390329\pi$
$864$	2.70037	0.0918683
$865$	−7.85568	−0.267101
$866$	−6.89199	−0.234199
$867$	14.6496	0.497528
$868$	−3.48429	−0.118264
$869$	23.7820	0.806749
$870$	2.60681	0.0883792
$871$	0	0
$872$	4.56604	0.154626
$873$	−11.3240	−0.383261
$874$	−6.73266	−0.227736
$875$	−3.89995	−0.131842
$876$	−28.3400	−0.957520
$877$	−13.5699	−0.458224	−0.229112	−	0.973400i	$-0.573582\pi$
$877$	−13.5699	−0.458224	−0.229112	+	0.973400i	$0.573582\pi$
$878$	4.35791	0.147072
$879$	−7.14560	−0.241015
$880$	−39.2115	−1.32182
$881$	−25.5331	−0.860232	−0.430116	−	0.902774i	$-0.641527\pi$
$881$	−25.5331	−0.860232	−0.430116	+	0.902774i	$0.641527\pi$
$882$	−0.233455	−0.00786084
$883$	0.102030	0.00343357	0.00171679	−	0.999999i	$-0.499454\pi$
$883$	0.102030	0.00343357	0.00171679	+	0.999999i	$0.499454\pi$
$884$	0	0
$885$	14.2723	0.479757
$886$	−3.55645	−0.119481
$887$	25.1339	0.843914	0.421957	−	0.906616i	$-0.361343\pi$
$887$	25.1339	0.843914	0.421957	+	0.906616i	$0.361343\pi$
$888$	6.67143	0.223879
$889$	−10.4903	−0.351832
$890$	0.437612	0.0146688
$891$	3.62146	0.121324
$892$	10.6068	0.355142
$893$	29.7442	0.995353
$894$	2.94794	0.0985939
$895$	−33.0896	−1.10606
$896$	−6.96990	−0.232848
$897$	0	0
$898$	2.63233	0.0878419
$899$	6.78939	0.226439
$900$	−7.15158	−0.238386
$901$	20.4560	0.681487
$902$	−7.73970	−0.257704
$903$	−5.79095	−0.192711
$904$	3.49183	0.116136
$905$	28.2235	0.938179
$906$	4.31561	0.143377
$907$	20.5789	0.683312	0.341656	−	0.939825i	$-0.389012\pi$
$907$	20.5789	0.683312	0.341656	+	0.939825i	$0.389012\pi$
$908$	−52.7489	−1.75053
$909$	6.04880	0.200626
$910$	0	0
$911$	23.1782	0.767928	0.383964	−	0.923348i	$-0.374559\pi$
$911$	23.1782	0.767928	0.383964	+	0.923348i	$0.374559\pi$
$912$	15.0716	0.499072
$913$	−26.2723	−0.869485
$914$	5.60837	0.185509
$915$	8.17674	0.270315
$916$	34.0303	1.12439
$917$	−5.35193	−0.176736
$918$	−0.357908	−0.0118127
$919$	10.7083	0.353233	0.176617	−	0.984280i	$-0.443485\pi$
$919$	10.7083	0.353233	0.176617	+	0.984280i	$0.443485\pi$
$920$	19.0835	0.629165
$921$	−10.4092	−0.342993
$922$	−0.446279	−0.0146974
$923$	0	0
$924$	−7.04555	−0.231782
$925$	−26.6247	−0.875415
$926$	3.55436	0.116803
$927$	−18.6670	−0.613105
$928$	10.2369	0.336044
$929$	−46.0083	−1.50948	−0.754742	−	0.656022i	$-0.772238\pi$
$929$	−46.0083	−1.50948	−0.754742	+	0.656022i	$0.772238\pi$
$930$	1.23153	0.0403834
$931$	−4.10005	−0.134374
$932$	25.9587	0.850307
$933$	4.51571	0.147838
$934$	7.24838	0.237174
$935$	16.3535	0.534816
$936$	0	0
$937$	−24.4256	−0.797951	−0.398976	−	0.916962i	$-0.630634\pi$
$937$	−24.4256	−0.797951	−0.398976	+	0.916962i	$0.630634\pi$
$938$	3.46093	0.113003
$939$	21.6242	0.705679
$940$	−41.5722	−1.35594
$941$	41.5757	1.35533	0.677664	−	0.735372i	$-0.262992\pi$
$941$	41.5757	1.35533	0.677664	+	0.735372i	$0.262992\pi$
$942$	−0.248905	−0.00810976
$943$	−64.3919	−2.09689
$944$	17.8117	0.579721
$945$	−2.94550	−0.0958171
$946$	4.89595	0.159181
$947$	−14.6697	−0.476702	−0.238351	−	0.971179i	$-0.576607\pi$
$947$	−14.6697	−0.476702	−0.238351	+	0.971179i	$0.576607\pi$
$948$	12.7760	0.414946
$949$	0	0
$950$	3.51855	0.114157
$951$	16.8275	0.545671
$952$	1.41212	0.0457672
$953$	−47.5083	−1.53895	−0.769473	−	0.638680i	$-0.779481\pi$
$953$	−47.5083	−1.53895	−0.769473	+	0.638680i	$0.779481\pi$
$954$	3.11498	0.100851
$955$	23.2429	0.752123
$956$	−24.8156	−0.802593
$957$	13.7288	0.443788
$958$	9.25216	0.298924
$959$	−11.6936	−0.377607
$960$	−19.7982	−0.638984
$961$	−27.7925	−0.896533
$962$	0	0
$963$	−4.82482	−0.155478
$964$	19.3553	0.623392
$965$	−17.3519	−0.558578
$966$	1.64209	0.0528335
$967$	11.0249	0.354537	0.177269	−	0.984162i	$-0.443274\pi$
$967$	11.0249	0.354537	0.177269	+	0.984162i	$0.443274\pi$
$968$	1.94810	0.0626145
$969$	−6.28575	−0.201927
$970$	−7.78688	−0.250022
$971$	34.4858	1.10670	0.553352	−	0.832948i	$-0.313349\pi$
$971$	34.4858	1.10670	0.553352	+	0.832948i	$0.313349\pi$
$972$	1.94550	0.0624019
$973$	14.6670	0.470203
$974$	−1.38074	−0.0442416
$975$	0	0
$976$	10.2045	0.326639
$977$	−46.5797	−1.49022	−0.745108	−	0.666944i	$-0.767602\pi$
$977$	−46.5797	−1.49022	−0.745108	+	0.666944i	$0.767602\pi$
$978$	5.47289	0.175004
$979$	2.30468	0.0736580
$980$	5.73046	0.183053
$981$	4.95718	0.158270
$982$	−9.47986	−0.302515
$983$	47.9704	1.53002	0.765009	−	0.644019i	$-0.222734\pi$
$983$	47.9704	1.53002	0.765009	+	0.644019i	$0.222734\pi$
$984$	−8.43223	−0.268810
$985$	−56.4197	−1.79768
$986$	−1.35681	−0.0432096
$987$	−7.25460	−0.230917
$988$	0	0
$989$	40.7328	1.29523
$990$	2.49027	0.0791459
$991$	−53.1160	−1.68729	−0.843643	−	0.536905i	$-0.819593\pi$
$991$	−53.1160	−1.68729	−0.843643	+	0.536905i	$0.819593\pi$
$992$	4.83621	0.153550
$993$	36.1355	1.14672
$994$	0.845448	0.0268160
$995$	24.1534	0.765714
$996$	−14.1138	−0.447213
$997$	−56.7238	−1.79646	−0.898231	−	0.439524i	$-0.855147\pi$
$997$	−56.7238	−1.79646	−0.898231	+	0.439524i	$0.855147\pi$
$998$	−6.53256	−0.206785
$999$	7.24292	0.229156

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.x.1.2		4
13.5	odd	4		273.2.c.c.64.5	yes	8
13.8	odd	4		273.2.c.c.64.4	✓	8
13.12	even	2		3549.2.a.v.1.3		4
39.5	even	4		819.2.c.d.64.4		8
39.8	even	4		819.2.c.d.64.5		8
52.31	even	4		4368.2.h.q.337.6		8
52.47	even	4		4368.2.h.q.337.3		8
91.34	even	4		1911.2.c.l.883.4		8
91.83	even	4		1911.2.c.l.883.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.c.c.64.4	✓	8	13.8	odd	4
273.2.c.c.64.5	yes	8	13.5	odd	4
819.2.c.d.64.4		8	39.5	even	4
819.2.c.d.64.5		8	39.8	even	4
1911.2.c.l.883.4		8	91.34	even	4
1911.2.c.l.883.5		8	91.83	even	4
3549.2.a.v.1.3		4	13.12	even	2
3549.2.a.x.1.2		4	1.1	even	1	trivial
4368.2.h.q.337.3		8	52.47	even	4
4368.2.h.q.337.6		8	52.31	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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q-0.233455 q^{2} -1.00000 q^{3} -1.94550 q^{4} -2.94550 q^{5} +0.233455 q^{6} -1.00000 q^{7} +0.921097 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.233455 q^{2} -1.00000 q^{3} -1.94550 q^{4} -2.94550 q^{5} +0.233455 q^{6} -1.00000 q^{7} +0.921097 q^{8} +1.00000 q^{9} +0.687642 q^{10} +3.62146 q^{11} +1.94550 q^{12} +0.233455 q^{14} +2.94550 q^{15} +3.67596 q^{16} -1.53309 q^{17} -0.233455 q^{18} -4.10005 q^{19} +5.73046 q^{20} +1.00000 q^{21} -0.845448 q^{22} -7.03387 q^{23} -0.921097 q^{24} +3.67596 q^{25} -1.00000 q^{27} +1.94550 q^{28} -3.79095 q^{29} -0.687642 q^{30} -1.79095 q^{31} -2.70037 q^{32} -3.62146 q^{33} +0.357908 q^{34} +2.94550 q^{35} -1.94550 q^{36} -7.24292 q^{37} +0.957177 q^{38} -2.71309 q^{40} +9.15455 q^{41} -0.233455 q^{42} -5.79095 q^{43} -7.04555 q^{44} -2.94550 q^{45} +1.64209 q^{46} -7.25460 q^{47} -3.67596 q^{48} +1.00000 q^{49} -0.858172 q^{50} +1.53309 q^{51} -13.3430 q^{53} +0.233455 q^{54} -10.6670 q^{55} -0.921097 q^{56} +4.10005 q^{57} +0.885016 q^{58} +4.84545 q^{59} -5.73046 q^{60} +2.77601 q^{61} +0.418106 q^{62} -1.00000 q^{63} -6.72151 q^{64} +0.845448 q^{66} +14.8248 q^{67} +2.98262 q^{68} +7.03387 q^{69} -0.687642 q^{70} +3.62146 q^{71} +0.921097 q^{72} -14.5670 q^{73} +1.69090 q^{74} -3.67596 q^{75} +7.97664 q^{76} -3.62146 q^{77} +6.56696 q^{79} -10.8275 q^{80} +1.00000 q^{81} -2.13718 q^{82} -7.25460 q^{83} -1.94550 q^{84} +4.51571 q^{85} +1.35193 q^{86} +3.79095 q^{87} +3.33572 q^{88} +0.636396 q^{89} +0.687642 q^{90} +13.6844 q^{92} +1.79095 q^{93} +1.69362 q^{94} +12.0767 q^{95} +2.70037 q^{96} -11.3240 q^{97} -0.233455 q^{98} +3.62146 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 4 q^{3} + 7 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + q^2 - 4 * q^3 + 7 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9	\( 4 q + q^{2} - 4 q^{3} + 7 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9} - 2 q^{10} + 2 q^{11} - 7 q^{12} - q^{14} - 3 q^{15} + 17 q^{16} - 10 q^{17} + q^{18} + 7 q^{19} + 40 q^{20} + 4 q^{21} - 12 q^{22} + 3 q^{23} + 3 q^{24} + 17 q^{25} - 4 q^{27} - 7 q^{28} - 9 q^{29} + 2 q^{30} - q^{31} - 5 q^{32} - 2 q^{33} - 32 q^{34} - 3 q^{35} + 7 q^{36} - 4 q^{37} - 18 q^{38} - 4 q^{40} + 28 q^{41} + q^{42} - 17 q^{43} + 10 q^{44} + 3 q^{45} + 40 q^{46} + 3 q^{47} - 17 q^{48} + 4 q^{49} - 11 q^{50} + 10 q^{51} - 5 q^{53} - q^{54} + 8 q^{55} + 3 q^{56} - 7 q^{57} + 12 q^{58} + 28 q^{59} - 40 q^{60} - 10 q^{61} + 14 q^{62} - 4 q^{63} + 9 q^{64} + 12 q^{66} + 22 q^{67} - 12 q^{68} - 3 q^{69} + 2 q^{70} + 2 q^{71} - 3 q^{72} - 31 q^{73} + 24 q^{74} - 17 q^{75} + 46 q^{76} - 2 q^{77} - q^{79} + 54 q^{80} + 4 q^{81} + 24 q^{82} + 3 q^{83} + 7 q^{84} - 2 q^{85} + 10 q^{86} + 9 q^{87} + 4 q^{88} + 5 q^{89} - 2 q^{90} + 28 q^{92} + q^{93} - 36 q^{94} + 39 q^{95} + 5 q^{96} - 43 q^{97} + q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q + q^2 - 4 * q^3 + 7 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9 - 2 * q^10 + 2 * q^11 - 7 * q^12 - q^14 - 3 * q^15 + 17 * q^16 - 10 * q^17 + q^18 + 7 * q^19 + 40 * q^20 + 4 * q^21 - 12 * q^22 + 3 * q^23 + 3 * q^24 + 17 * q^25 - 4 * q^27 - 7 * q^28 - 9 * q^29 + 2 * q^30 - q^31 - 5 * q^32 - 2 * q^33 - 32 * q^34 - 3 * q^35 + 7 * q^36 - 4 * q^37 - 18 * q^38 - 4 * q^40 + 28 * q^41 + q^42 - 17 * q^43 + 10 * q^44 + 3 * q^45 + 40 * q^46 + 3 * q^47 - 17 * q^48 + 4 * q^49 - 11 * q^50 + 10 * q^51 - 5 * q^53 - q^54 + 8 * q^55 + 3 * q^56 - 7 * q^57 + 12 * q^58 + 28 * q^59 - 40 * q^60 - 10 * q^61 + 14 * q^62 - 4 * q^63 + 9 * q^64 + 12 * q^66 + 22 * q^67 - 12 * q^68 - 3 * q^69 + 2 * q^70 + 2 * q^71 - 3 * q^72 - 31 * q^73 + 24 * q^74 - 17 * q^75 + 46 * q^76 - 2 * q^77 - q^79 + 54 * q^80 + 4 * q^81 + 24 * q^82 + 3 * q^83 + 7 * q^84 - 2 * q^85 + 10 * q^86 + 9 * q^87 + 4 * q^88 + 5 * q^89 - 2 * q^90 + 28 * q^92 + q^93 - 36 * q^94 + 39 * q^95 + 5 * q^96 - 43 * q^97 + q^98 + 2 * q^99

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