LMFDB - Embedded newform 1183.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205 q^{2} -0.732051 q^{3} +1.00000 q^{4} -1.73205 q^{5} +1.26795 q^{6} +1.00000 q^{7} +1.73205 q^{8} -2.46410 q^{9} +O(q^{10})$	\(q-1.73205 q^{2} -0.732051 q^{3} +1.00000 q^{4} -1.73205 q^{5} +1.26795 q^{6} +1.00000 q^{7} +1.73205 q^{8} -2.46410 q^{9} +3.00000 q^{10} +4.73205 q^{11} -0.732051 q^{12} -1.73205 q^{14} +1.26795 q^{15} -5.00000 q^{16} -4.26795 q^{17} +4.26795 q^{18} +2.00000 q^{19} -1.73205 q^{20} -0.732051 q^{21} -8.19615 q^{22} +1.26795 q^{23} -1.26795 q^{24} -2.00000 q^{25} +4.00000 q^{27} +1.00000 q^{28} -3.00000 q^{29} -2.19615 q^{30} -6.19615 q^{31} +5.19615 q^{32} -3.46410 q^{33} +7.39230 q^{34} -1.73205 q^{35} -2.46410 q^{36} -7.00000 q^{37} -3.46410 q^{38} -3.00000 q^{40} +5.19615 q^{41} +1.26795 q^{42} +10.1962 q^{43} +4.73205 q^{44} +4.26795 q^{45} -2.19615 q^{46} -0.928203 q^{47} +3.66025 q^{48} +1.00000 q^{49} +3.46410 q^{50} +3.12436 q^{51} +3.92820 q^{53} -6.92820 q^{54} -8.19615 q^{55} +1.73205 q^{56} -1.46410 q^{57} +5.19615 q^{58} +10.7321 q^{59} +1.26795 q^{60} -15.1962 q^{61} +10.7321 q^{62} -2.46410 q^{63} +1.00000 q^{64} +6.00000 q^{66} +4.19615 q^{67} -4.26795 q^{68} -0.928203 q^{69} +3.00000 q^{70} +6.00000 q^{71} -4.26795 q^{72} +7.19615 q^{73} +12.1244 q^{74} +1.46410 q^{75} +2.00000 q^{76} +4.73205 q^{77} +5.80385 q^{79} +8.66025 q^{80} +4.46410 q^{81} -9.00000 q^{82} +8.19615 q^{83} -0.732051 q^{84} +7.39230 q^{85} -17.6603 q^{86} +2.19615 q^{87} +8.19615 q^{88} -0.928203 q^{89} -7.39230 q^{90} +1.26795 q^{92} +4.53590 q^{93} +1.60770 q^{94} -3.46410 q^{95} -3.80385 q^{96} -14.3923 q^{97} -1.73205 q^{98} -11.6603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^7 + 2 * q^9	$ 2 q + 2 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 6 q^{11} + 2 q^{12} + 6 q^{15} - 10 q^{16} - 12 q^{17} + 12 q^{18} + 4 q^{19} + 2 q^{21} - 6 q^{22} + 6 q^{23} - 6 q^{24} - 4 q^{25} + 8 q^{27} + 2 q^{28} - 6 q^{29} + 6 q^{30} - 2 q^{31} - 6 q^{34} + 2 q^{36} - 14 q^{37} - 6 q^{40} + 6 q^{42} + 10 q^{43} + 6 q^{44} + 12 q^{45} + 6 q^{46} + 12 q^{47} - 10 q^{48} + 2 q^{49} - 18 q^{51} - 6 q^{53} - 6 q^{55} + 4 q^{57} + 18 q^{59} + 6 q^{60} - 20 q^{61} + 18 q^{62} + 2 q^{63} + 2 q^{64} + 12 q^{66} - 2 q^{67} - 12 q^{68} + 12 q^{69} + 6 q^{70} + 12 q^{71} - 12 q^{72} + 4 q^{73} - 4 q^{75} + 4 q^{76} + 6 q^{77} + 22 q^{79} + 2 q^{81} - 18 q^{82} + 6 q^{83} + 2 q^{84} - 6 q^{85} - 18 q^{86} - 6 q^{87} + 6 q^{88} + 12 q^{89} + 6 q^{90} + 6 q^{92} + 16 q^{93} + 24 q^{94} - 18 q^{96} - 8 q^{97} - 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^7 + 2 * q^9 + 6 * q^10 + 6 * q^11 + 2 * q^12 + 6 * q^15 - 10 * q^16 - 12 * q^17 + 12 * q^18 + 4 * q^19 + 2 * q^21 - 6 * q^22 + 6 * q^23 - 6 * q^24 - 4 * q^25 + 8 * q^27 + 2 * q^28 - 6 * q^29 + 6 * q^30 - 2 * q^31 - 6 * q^34 + 2 * q^36 - 14 * q^37 - 6 * q^40 + 6 * q^42 + 10 * q^43 + 6 * q^44 + 12 * q^45 + 6 * q^46 + 12 * q^47 - 10 * q^48 + 2 * q^49 - 18 * q^51 - 6 * q^53 - 6 * q^55 + 4 * q^57 + 18 * q^59 + 6 * q^60 - 20 * q^61 + 18 * q^62 + 2 * q^63 + 2 * q^64 + 12 * q^66 - 2 * q^67 - 12 * q^68 + 12 * q^69 + 6 * q^70 + 12 * q^71 - 12 * q^72 + 4 * q^73 - 4 * q^75 + 4 * q^76 + 6 * q^77 + 22 * q^79 + 2 * q^81 - 18 * q^82 + 6 * q^83 + 2 * q^84 - 6 * q^85 - 18 * q^86 - 6 * q^87 + 6 * q^88 + 12 * q^89 + 6 * q^90 + 6 * q^92 + 16 * q^93 + 24 * q^94 - 18 * q^96 - 8 * q^97 - 6 * 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 $

$2$	−1.73205	−1.22474	−0.612372	−	0.790569i	$-0.709785\pi$
$2$	−1.73205	−1.22474	−0.612372	+	0.790569i	$0.709785\pi$
$3$	−0.732051	−0.422650	−0.211325	−	0.977416i	$-0.567778\pi$
$3$	−0.732051	−0.422650	−0.211325	+	0.977416i	$0.567778\pi$
$4$	1.00000	0.500000
$5$	−1.73205	−0.774597	−0.387298	−	0.921954i	$-0.626592\pi$
$5$	−1.73205	−0.774597	−0.387298	+	0.921954i	$0.626592\pi$
$6$	1.26795	0.517638
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.73205	0.612372
$9$	−2.46410	−0.821367
$10$	3.00000	0.948683
$11$	4.73205	1.42677	0.713384	−	0.700774i	$-0.247162\pi$
$11$	4.73205	1.42677	0.713384	+	0.700774i	$0.247162\pi$
$12$	−0.732051	−0.211325
$13$	0	0
$13$	0	0
$14$	−1.73205	−0.462910
$15$	1.26795	0.327383
$16$	−5.00000	−1.25000
$17$	−4.26795	−1.03513	−0.517565	−	0.855644i	$-0.673161\pi$
$17$	−4.26795	−1.03513	−0.517565	+	0.855644i	$0.673161\pi$
$18$	4.26795	1.00597
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	−1.73205	−0.387298
$21$	−0.732051	−0.159747
$22$	−8.19615	−1.74743
$23$	1.26795	0.264386	0.132193	−	0.991224i	$-0.457798\pi$
$23$	1.26795	0.264386	0.132193	+	0.991224i	$0.457798\pi$
$24$	−1.26795	−0.258819
$25$	−2.00000	−0.400000
$26$	0	0
$27$	4.00000	0.769800
$28$	1.00000	0.188982
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	−2.19615	−0.400961
$31$	−6.19615	−1.11286	−0.556431	−	0.830894i	$-0.687830\pi$
$31$	−6.19615	−1.11286	−0.556431	+	0.830894i	$0.687830\pi$
$32$	5.19615	0.918559
$33$	−3.46410	−0.603023
$34$	7.39230	1.26777
$35$	−1.73205	−0.292770
$36$	−2.46410	−0.410684
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	−3.46410	−0.561951
$39$	0	0
$40$	−3.00000	−0.474342
$41$	5.19615	0.811503	0.405751	−	0.913984i	$-0.367010\pi$
$41$	5.19615	0.811503	0.405751	+	0.913984i	$0.367010\pi$
$42$	1.26795	0.195649
$43$	10.1962	1.55490	0.777449	−	0.628946i	$-0.216513\pi$
$43$	10.1962	1.55490	0.777449	+	0.628946i	$0.216513\pi$
$44$	4.73205	0.713384
$45$	4.26795	0.636228
$46$	−2.19615	−0.323805
$47$	−0.928203	−0.135392	−0.0676962	−	0.997706i	$-0.521565\pi$
$47$	−0.928203	−0.135392	−0.0676962	+	0.997706i	$0.521565\pi$
$48$	3.66025	0.528312
$49$	1.00000	0.142857
$50$	3.46410	0.489898
$51$	3.12436	0.437497
$52$	0	0
$53$	3.92820	0.539580	0.269790	−	0.962919i	$-0.413046\pi$
$53$	3.92820	0.539580	0.269790	+	0.962919i	$0.413046\pi$
$54$	−6.92820	−0.942809
$55$	−8.19615	−1.10517
$56$	1.73205	0.231455
$57$	−1.46410	−0.193925
$58$	5.19615	0.682288
$59$	10.7321	1.39719	0.698597	−	0.715515i	$-0.253808\pi$
$59$	10.7321	1.39719	0.698597	+	0.715515i	$0.253808\pi$
$60$	1.26795	0.163692
$61$	−15.1962	−1.94567	−0.972834	−	0.231504i	$-0.925635\pi$
$61$	−15.1962	−1.94567	−0.972834	+	0.231504i	$0.925635\pi$
$62$	10.7321	1.36297
$63$	−2.46410	−0.310448
$64$	1.00000	0.125000
$65$	0	0
$66$	6.00000	0.738549
$67$	4.19615	0.512642	0.256321	−	0.966592i	$-0.417490\pi$
$67$	4.19615	0.512642	0.256321	+	0.966592i	$0.417490\pi$
$68$	−4.26795	−0.517565
$69$	−0.928203	−0.111743
$70$	3.00000	0.358569
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	−4.26795	−0.502983
$73$	7.19615	0.842246	0.421123	−	0.907004i	$-0.361636\pi$
$73$	7.19615	0.842246	0.421123	+	0.907004i	$0.361636\pi$
$74$	12.1244	1.40943
$75$	1.46410	0.169060
$76$	2.00000	0.229416
$77$	4.73205	0.539267
$78$	0	0
$79$	5.80385	0.652984	0.326492	−	0.945200i	$-0.394133\pi$
$79$	5.80385	0.652984	0.326492	+	0.945200i	$0.394133\pi$
$80$	8.66025	0.968246
$81$	4.46410	0.496011
$82$	−9.00000	−0.993884
$83$	8.19615	0.899645	0.449822	−	0.893118i	$-0.351487\pi$
$83$	8.19615	0.899645	0.449822	+	0.893118i	$0.351487\pi$
$84$	−0.732051	−0.0798733
$85$	7.39230	0.801808
$86$	−17.6603	−1.90435
$87$	2.19615	0.235452
$88$	8.19615	0.873713
$89$	−0.928203	−0.0983893	−0.0491947	−	0.998789i	$-0.515665\pi$
$89$	−0.928203	−0.0983893	−0.0491947	+	0.998789i	$0.515665\pi$
$90$	−7.39230	−0.779217
$91$	0	0
$92$	1.26795	0.132193
$93$	4.53590	0.470351
$94$	1.60770	0.165821
$95$	−3.46410	−0.355409
$96$	−3.80385	−0.388229
$97$	−14.3923	−1.46132	−0.730659	−	0.682743i	$-0.760787\pi$
$97$	−14.3923	−1.46132	−0.730659	+	0.682743i	$0.760787\pi$
$98$	−1.73205	−0.174964
$99$	−11.6603	−1.17190
$100$	−2.00000	−0.200000
$101$	−4.26795	−0.424677	−0.212338	−	0.977196i	$-0.568108\pi$
$101$	−4.26795	−0.424677	−0.212338	+	0.977196i	$0.568108\pi$
$102$	−5.41154	−0.535823
$103$	6.39230	0.629853	0.314926	−	0.949116i	$-0.398020\pi$
$103$	6.39230	0.629853	0.314926	+	0.949116i	$0.398020\pi$
$104$	0	0
$105$	1.26795	0.123739
$106$	−6.80385	−0.660848
$107$	19.8564	1.91959	0.959796	−	0.280700i	$-0.0905665\pi$
$107$	19.8564	1.91959	0.959796	+	0.280700i	$0.0905665\pi$
$108$	4.00000	0.384900
$109$	12.3923	1.18697	0.593484	−	0.804846i	$-0.297752\pi$
$109$	12.3923	1.18697	0.593484	+	0.804846i	$0.297752\pi$
$110$	14.1962	1.35355
$111$	5.12436	0.486382
$112$	−5.00000	−0.472456
$113$	−7.39230	−0.695410	−0.347705	−	0.937604i	$-0.613039\pi$
$113$	−7.39230	−0.695410	−0.347705	+	0.937604i	$0.613039\pi$
$114$	2.53590	0.237509
$115$	−2.19615	−0.204792
$116$	−3.00000	−0.278543
$117$	0	0
$118$	−18.5885	−1.71121
$119$	−4.26795	−0.391242
$120$	2.19615	0.200480
$121$	11.3923	1.03566
$122$	26.3205	2.38295
$123$	−3.80385	−0.342981
$124$	−6.19615	−0.556431
$125$	12.1244	1.08444
$126$	4.26795	0.380219
$127$	−2.39230	−0.212283	−0.106141	−	0.994351i	$-0.533850\pi$
$127$	−2.39230	−0.212283	−0.106141	+	0.994351i	$0.533850\pi$
$128$	−12.1244	−1.07165
$129$	−7.46410	−0.657178
$130$	0	0
$131$	3.46410	0.302660	0.151330	−	0.988483i	$-0.451644\pi$
$131$	3.46410	0.302660	0.151330	+	0.988483i	$0.451644\pi$
$132$	−3.46410	−0.301511
$133$	2.00000	0.173422
$134$	−7.26795	−0.627855
$135$	−6.92820	−0.596285
$136$	−7.39230	−0.633885
$137$	21.9282	1.87345	0.936726	−	0.350062i	$-0.113840\pi$
$137$	21.9282	1.87345	0.936726	+	0.350062i	$0.113840\pi$
$138$	1.60770	0.136856
$139$	20.5885	1.74629	0.873145	−	0.487460i	$-0.162077\pi$
$139$	20.5885	1.74629	0.873145	+	0.487460i	$0.162077\pi$
$140$	−1.73205	−0.146385
$141$	0.679492	0.0572235
$142$	−10.3923	−0.872103
$143$	0	0
$144$	12.3205	1.02671
$145$	5.19615	0.431517
$146$	−12.4641	−1.03154
$147$	−0.732051	−0.0603785
$148$	−7.00000	−0.575396
$149$	0.464102	0.0380207	0.0190103	−	0.999819i	$-0.493948\pi$
$149$	0.464102	0.0380207	0.0190103	+	0.999819i	$0.493948\pi$
$150$	−2.53590	−0.207055
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	3.46410	0.280976
$153$	10.5167	0.850222
$154$	−8.19615	−0.660465
$155$	10.7321	0.862019
$156$	0	0
$157$	−9.19615	−0.733933	−0.366966	−	0.930234i	$-0.619604\pi$
$157$	−9.19615	−0.733933	−0.366966	+	0.930234i	$0.619604\pi$
$158$	−10.0526	−0.799739
$159$	−2.87564	−0.228053
$160$	−9.00000	−0.711512
$161$	1.26795	0.0999284
$162$	−7.73205	−0.607487
$163$	5.80385	0.454592	0.227296	−	0.973826i	$-0.427011\pi$
$163$	5.80385	0.454592	0.227296	+	0.973826i	$0.427011\pi$
$164$	5.19615	0.405751
$165$	6.00000	0.467099
$166$	−14.1962	−1.10184
$167$	24.5885	1.90271	0.951356	−	0.308094i	$-0.0996911\pi$
$167$	24.5885	1.90271	0.951356	+	0.308094i	$0.0996911\pi$
$168$	−1.26795	−0.0978244
$169$	0	0
$170$	−12.8038	−0.982010
$171$	−4.92820	−0.376869
$172$	10.1962	0.777449
$173$	15.4641	1.17571	0.587857	−	0.808965i	$-0.299972\pi$
$173$	15.4641	1.17571	0.587857	+	0.808965i	$0.299972\pi$
$174$	−3.80385	−0.288369
$175$	−2.00000	−0.151186
$176$	−23.6603	−1.78346
$177$	−7.85641	−0.590524
$178$	1.60770	0.120502
$179$	6.92820	0.517838	0.258919	−	0.965899i	$-0.416634\pi$
$179$	6.92820	0.517838	0.258919	+	0.965899i	$0.416634\pi$
$180$	4.26795	0.318114
$181$	−25.5885	−1.90198	−0.950988	−	0.309229i	$-0.899929\pi$
$181$	−25.5885	−1.90198	−0.950988	+	0.309229i	$0.899929\pi$
$182$	0	0
$183$	11.1244	0.822336
$184$	2.19615	0.161903
$185$	12.1244	0.891400
$186$	−7.85641	−0.576060
$187$	−20.1962	−1.47689
$188$	−0.928203	−0.0676962
$189$	4.00000	0.290957
$190$	6.00000	0.435286
$191$	1.26795	0.0917456	0.0458728	−	0.998947i	$-0.485393\pi$
$191$	1.26795	0.0917456	0.0458728	+	0.998947i	$0.485393\pi$
$192$	−0.732051	−0.0528312
$193$	5.00000	0.359908	0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000	0.359908	0.179954	+	0.983675i	$0.442405\pi$
$194$	24.9282	1.78974
$195$	0	0
$196$	1.00000	0.0714286
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	20.1962	1.43528
$199$	2.00000	0.141776	0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000	0.141776	0.0708881	+	0.997484i	$0.477417\pi$
$200$	−3.46410	−0.244949
$201$	−3.07180	−0.216668
$202$	7.39230	0.520121
$203$	−3.00000	−0.210559
$204$	3.12436	0.218749
$205$	−9.00000	−0.628587
$206$	−11.0718	−0.771409
$207$	−3.12436	−0.217158
$208$	0	0
$209$	9.46410	0.654646
$210$	−2.19615	−0.151549
$211$	−12.1962	−0.839618	−0.419809	−	0.907613i	$-0.637903\pi$
$211$	−12.1962	−0.839618	−0.419809	+	0.907613i	$0.637903\pi$
$212$	3.92820	0.269790
$213$	−4.39230	−0.300956
$214$	−34.3923	−2.35101
$215$	−17.6603	−1.20442
$216$	6.92820	0.471405
$217$	−6.19615	−0.420622
$218$	−21.4641	−1.45373
$219$	−5.26795	−0.355975
$220$	−8.19615	−0.552584
$221$	0	0
$222$	−8.87564	−0.595694
$223$	−10.0000	−0.669650	−0.334825	−	0.942280i	$-0.608677\pi$
$223$	−10.0000	−0.669650	−0.334825	+	0.942280i	$0.608677\pi$
$224$	5.19615	0.347183
$225$	4.92820	0.328547
$226$	12.8038	0.851699
$227$	−11.6603	−0.773918	−0.386959	−	0.922097i	$-0.626475\pi$
$227$	−11.6603	−0.773918	−0.386959	+	0.922097i	$0.626475\pi$
$228$	−1.46410	−0.0969625
$229$	6.39230	0.422415	0.211208	−	0.977441i	$-0.432260\pi$
$229$	6.39230	0.422415	0.211208	+	0.977441i	$0.432260\pi$
$230$	3.80385	0.250818
$231$	−3.46410	−0.227921
$232$	−5.19615	−0.341144
$233$	25.8564	1.69391	0.846955	−	0.531665i	$-0.178433\pi$
$233$	25.8564	1.69391	0.846955	+	0.531665i	$0.178433\pi$
$234$	0	0
$235$	1.60770	0.104874
$236$	10.7321	0.698597
$237$	−4.24871	−0.275983
$238$	7.39230	0.479172
$239$	−26.1962	−1.69449	−0.847244	−	0.531204i	$-0.821740\pi$
$239$	−26.1962	−1.69449	−0.847244	+	0.531204i	$0.821740\pi$
$240$	−6.33975	−0.409229
$241$	−10.8038	−0.695937	−0.347969	−	0.937506i	$-0.613128\pi$
$241$	−10.8038	−0.695937	−0.347969	+	0.937506i	$0.613128\pi$
$242$	−19.7321	−1.26842
$243$	−15.2679	−0.979439
$244$	−15.1962	−0.972834
$245$	−1.73205	−0.110657
$246$	6.58846	0.420065
$247$	0	0
$248$	−10.7321	−0.681486
$249$	−6.00000	−0.380235
$250$	−21.0000	−1.32816
$251$	−22.3923	−1.41339	−0.706695	−	0.707518i	$-0.749815\pi$
$251$	−22.3923	−1.41339	−0.706695	+	0.707518i	$0.749815\pi$
$252$	−2.46410	−0.155224
$253$	6.00000	0.377217
$254$	4.14359	0.259992
$255$	−5.41154	−0.338884
$256$	19.0000	1.18750
$257$	−18.1244	−1.13057	−0.565283	−	0.824897i	$-0.691233\pi$
$257$	−18.1244	−1.13057	−0.565283	+	0.824897i	$0.691233\pi$
$258$	12.9282	0.804875
$259$	−7.00000	−0.434959
$260$	0	0
$261$	7.39230	0.457572
$262$	−6.00000	−0.370681
$263$	4.73205	0.291791	0.145895	−	0.989300i	$-0.453394\pi$
$263$	4.73205	0.291791	0.145895	+	0.989300i	$0.453394\pi$
$264$	−6.00000	−0.369274
$265$	−6.80385	−0.417957
$266$	−3.46410	−0.212398
$267$	0.679492	0.0415842
$268$	4.19615	0.256321
$269$	18.9282	1.15407	0.577036	−	0.816718i	$-0.304209\pi$
$269$	18.9282	1.15407	0.577036	+	0.816718i	$0.304209\pi$
$270$	12.0000	0.730297
$271$	16.1962	0.983846	0.491923	−	0.870639i	$-0.336294\pi$
$271$	16.1962	0.983846	0.491923	+	0.870639i	$0.336294\pi$
$272$	21.3397	1.29391
$273$	0	0
$274$	−37.9808	−2.29450
$275$	−9.46410	−0.570707
$276$	−0.928203	−0.0558713
$277$	17.0000	1.02143	0.510716	−	0.859750i	$-0.329381\pi$
$277$	17.0000	1.02143	0.510716	+	0.859750i	$0.329381\pi$
$278$	−35.6603	−2.13876
$279$	15.2679	0.914068
$280$	−3.00000	−0.179284
$281$	−7.39230	−0.440988	−0.220494	−	0.975388i	$-0.570767\pi$
$281$	−7.39230	−0.440988	−0.220494	+	0.975388i	$0.570767\pi$
$282$	−1.17691	−0.0700842
$283$	−0.196152	−0.0116601	−0.00583003	−	0.999983i	$-0.501856\pi$
$283$	−0.196152	−0.0116601	−0.00583003	+	0.999983i	$0.501856\pi$
$284$	6.00000	0.356034
$285$	2.53590	0.150214
$286$	0	0
$287$	5.19615	0.306719
$288$	−12.8038	−0.754474
$289$	1.21539	0.0714935
$290$	−9.00000	−0.528498
$291$	10.5359	0.617625
$292$	7.19615	0.421123
$293$	−11.1962	−0.654086	−0.327043	−	0.945009i	$-0.606052\pi$
$293$	−11.1962	−0.654086	−0.327043	+	0.945009i	$0.606052\pi$
$294$	1.26795	0.0739483
$295$	−18.5885	−1.08226
$296$	−12.1244	−0.704714
$297$	18.9282	1.09833
$298$	−0.803848	−0.0465656
$299$	0	0
$300$	1.46410	0.0845299
$301$	10.1962	0.587696
$302$	−3.46410	−0.199337
$303$	3.12436	0.179490
$304$	−10.0000	−0.573539
$305$	26.3205	1.50711
$306$	−18.2154	−1.04130
$307$	26.5885	1.51748	0.758742	−	0.651392i	$-0.225814\pi$
$307$	26.5885	1.51748	0.758742	+	0.651392i	$0.225814\pi$
$308$	4.73205	0.269634
$309$	−4.67949	−0.266207
$310$	−18.5885	−1.05575
$311$	4.73205	0.268330	0.134165	−	0.990959i	$-0.457165\pi$
$311$	4.73205	0.268330	0.134165	+	0.990959i	$0.457165\pi$
$312$	0	0
$313$	−12.7846	−0.722629	−0.361314	−	0.932444i	$-0.617672\pi$
$313$	−12.7846	−0.722629	−0.361314	+	0.932444i	$0.617672\pi$
$314$	15.9282	0.898881
$315$	4.26795	0.240472
$316$	5.80385	0.326492
$317$	0.464102	0.0260665	0.0130333	−	0.999915i	$-0.495851\pi$
$317$	0.464102	0.0260665	0.0130333	+	0.999915i	$0.495851\pi$
$318$	4.98076	0.279307
$319$	−14.1962	−0.794832
$320$	−1.73205	−0.0968246
$321$	−14.5359	−0.811315
$322$	−2.19615	−0.122387
$323$	−8.53590	−0.474950
$324$	4.46410	0.248006
$325$	0	0
$326$	−10.0526	−0.556760
$327$	−9.07180	−0.501672
$328$	9.00000	0.496942
$329$	−0.928203	−0.0511735
$330$	−10.3923	−0.572078
$331$	−26.9808	−1.48300	−0.741498	−	0.670955i	$-0.765885\pi$
$331$	−26.9808	−1.48300	−0.741498	+	0.670955i	$0.765885\pi$
$332$	8.19615	0.449822
$333$	17.2487	0.945224
$334$	−42.5885	−2.33034
$335$	−7.26795	−0.397090
$336$	3.66025	0.199683
$337$	11.0000	0.599208	0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000	0.599208	0.299604	+	0.954064i	$0.403145\pi$
$338$	0	0
$339$	5.41154	0.293915
$340$	7.39230	0.400904
$341$	−29.3205	−1.58779
$342$	8.53590	0.461569
$343$	1.00000	0.0539949
$344$	17.6603	0.952177
$345$	1.60770	0.0865554
$346$	−26.7846	−1.43995
$347$	10.7321	0.576127	0.288063	−	0.957611i	$-0.406989\pi$
$347$	10.7321	0.576127	0.288063	+	0.957611i	$0.406989\pi$
$348$	2.19615	0.117726
$349$	16.7846	0.898460	0.449230	−	0.893416i	$-0.351698\pi$
$349$	16.7846	0.898460	0.449230	+	0.893416i	$0.351698\pi$
$350$	3.46410	0.185164
$351$	0	0
$352$	24.5885	1.31057
$353$	3.33975	0.177757	0.0888784	−	0.996042i	$-0.471672\pi$
$353$	3.33975	0.177757	0.0888784	+	0.996042i	$0.471672\pi$
$354$	13.6077	0.723241
$355$	−10.3923	−0.551566
$356$	−0.928203	−0.0491947
$357$	3.12436	0.165358
$358$	−12.0000	−0.634220
$359$	5.07180	0.267679	0.133840	−	0.991003i	$-0.457269\pi$
$359$	5.07180	0.267679	0.133840	+	0.991003i	$0.457269\pi$
$360$	7.39230	0.389609
$361$	−15.0000	−0.789474
$362$	44.3205	2.32943
$363$	−8.33975	−0.437723
$364$	0	0
$365$	−12.4641	−0.652401
$366$	−19.2679	−1.00715
$367$	−6.19615	−0.323437	−0.161718	−	0.986837i	$-0.551704\pi$
$367$	−6.19615	−0.323437	−0.161718	+	0.986837i	$0.551704\pi$
$368$	−6.33975	−0.330482
$369$	−12.8038	−0.666542
$370$	−21.0000	−1.09174
$371$	3.92820	0.203942
$372$	4.53590	0.235175
$373$	9.39230	0.486315	0.243158	−	0.969987i	$-0.421817\pi$
$373$	9.39230	0.486315	0.243158	+	0.969987i	$0.421817\pi$
$374$	34.9808	1.80881
$375$	−8.87564	−0.458336
$376$	−1.60770	−0.0829105
$377$	0	0
$378$	−6.92820	−0.356348
$379$	−4.58846	−0.235693	−0.117847	−	0.993032i	$-0.537599\pi$
$379$	−4.58846	−0.235693	−0.117847	+	0.993032i	$0.537599\pi$
$380$	−3.46410	−0.177705
$381$	1.75129	0.0897212
$382$	−2.19615	−0.112365
$383$	5.66025	0.289225	0.144613	−	0.989488i	$-0.453806\pi$
$383$	5.66025	0.289225	0.144613	+	0.989488i	$0.453806\pi$
$384$	8.87564	0.452933
$385$	−8.19615	−0.417715
$386$	−8.66025	−0.440795
$387$	−25.1244	−1.27714
$388$	−14.3923	−0.730659
$389$	−30.4641	−1.54459	−0.772296	−	0.635263i	$-0.780892\pi$
$389$	−30.4641	−1.54459	−0.772296	+	0.635263i	$0.780892\pi$
$390$	0	0
$391$	−5.41154	−0.273673
$392$	1.73205	0.0874818
$393$	−2.53590	−0.127919
$394$	−20.7846	−1.04711
$395$	−10.0526	−0.505799
$396$	−11.6603	−0.585950
$397$	22.7846	1.14353	0.571763	−	0.820419i	$-0.306260\pi$
$397$	22.7846	1.14353	0.571763	+	0.820419i	$0.306260\pi$
$398$	−3.46410	−0.173640
$399$	−1.46410	−0.0732968
$400$	10.0000	0.500000
$401$	16.8564	0.841769	0.420884	−	0.907114i	$-0.361720\pi$
$401$	16.8564	0.841769	0.420884	+	0.907114i	$0.361720\pi$
$402$	5.32051	0.265363
$403$	0	0
$404$	−4.26795	−0.212338
$405$	−7.73205	−0.384209
$406$	5.19615	0.257881
$407$	−33.1244	−1.64191
$408$	5.41154	0.267911
$409$	−27.1962	−1.34476	−0.672382	−	0.740205i	$-0.734729\pi$
$409$	−27.1962	−1.34476	−0.672382	+	0.740205i	$0.734729\pi$
$410$	15.5885	0.769859
$411$	−16.0526	−0.791814
$412$	6.39230	0.314926
$413$	10.7321	0.528090
$414$	5.41154	0.265963
$415$	−14.1962	−0.696862
$416$	0	0
$417$	−15.0718	−0.738069
$418$	−16.3923	−0.801774
$419$	−21.8038	−1.06519	−0.532594	−	0.846371i	$-0.678783\pi$
$419$	−21.8038	−1.06519	−0.532594	+	0.846371i	$0.678783\pi$
$420$	1.26795	0.0618696
$421$	30.1769	1.47073	0.735366	−	0.677670i	$-0.237010\pi$
$421$	30.1769	1.47073	0.735366	+	0.677670i	$0.237010\pi$
$422$	21.1244	1.02832
$423$	2.28719	0.111207
$424$	6.80385	0.330424
$425$	8.53590	0.414052
$426$	7.60770	0.368594
$427$	−15.1962	−0.735393
$428$	19.8564	0.959796
$429$	0	0
$430$	30.5885	1.47511
$431$	35.3205	1.70133	0.850665	−	0.525709i	$-0.176200\pi$
$431$	35.3205	1.70133	0.850665	+	0.525709i	$0.176200\pi$
$432$	−20.0000	−0.962250
$433$	17.5885	0.845247	0.422624	−	0.906305i	$-0.361109\pi$
$433$	17.5885	0.845247	0.422624	+	0.906305i	$0.361109\pi$
$434$	10.7321	0.515155
$435$	−3.80385	−0.182381
$436$	12.3923	0.593484
$437$	2.53590	0.121308
$438$	9.12436	0.435979
$439$	−16.5885	−0.791724	−0.395862	−	0.918310i	$-0.629554\pi$
$439$	−16.5885	−0.791724	−0.395862	+	0.918310i	$0.629554\pi$
$440$	−14.1962	−0.676775
$441$	−2.46410	−0.117338
$442$	0	0
$443$	−11.3205	−0.537854	−0.268927	−	0.963161i	$-0.586669\pi$
$443$	−11.3205	−0.537854	−0.268927	+	0.963161i	$0.586669\pi$
$444$	5.12436	0.243191
$445$	1.60770	0.0762121
$446$	17.3205	0.820150
$447$	−0.339746	−0.0160694
$448$	1.00000	0.0472456
$449$	−12.0000	−0.566315	−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000	−0.566315	−0.283158	+	0.959073i	$0.591382\pi$
$450$	−8.53590	−0.402386
$451$	24.5885	1.15783
$452$	−7.39230	−0.347705
$453$	−1.46410	−0.0687895
$454$	20.1962	0.947852
$455$	0	0
$456$	−2.53590	−0.118754
$457$	11.0000	0.514558	0.257279	−	0.966337i	$-0.417174\pi$
$457$	11.0000	0.514558	0.257279	+	0.966337i	$0.417174\pi$
$458$	−11.0718	−0.517351
$459$	−17.0718	−0.796843
$460$	−2.19615	−0.102396
$461$	15.5885	0.726027	0.363013	−	0.931784i	$-0.381748\pi$
$461$	15.5885	0.726027	0.363013	+	0.931784i	$0.381748\pi$
$462$	6.00000	0.279145
$463$	26.5885	1.23567	0.617835	−	0.786308i	$-0.288010\pi$
$463$	26.5885	1.23567	0.617835	+	0.786308i	$0.288010\pi$
$464$	15.0000	0.696358
$465$	−7.85641	−0.364332
$466$	−44.7846	−2.07461
$467$	−19.5167	−0.903123	−0.451562	−	0.892240i	$-0.649133\pi$
$467$	−19.5167	−0.903123	−0.451562	+	0.892240i	$0.649133\pi$
$468$	0	0
$469$	4.19615	0.193760
$470$	−2.78461	−0.128444
$471$	6.73205	0.310197
$472$	18.5885	0.855603
$473$	48.2487	2.21848
$474$	7.35898	0.338009
$475$	−4.00000	−0.183533
$476$	−4.26795	−0.195621
$477$	−9.67949	−0.443193
$478$	45.3731	2.07532
$479$	4.73205	0.216213	0.108106	−	0.994139i	$-0.465521\pi$
$479$	4.73205	0.216213	0.108106	+	0.994139i	$0.465521\pi$
$480$	6.58846	0.300721
$481$	0	0
$482$	18.7128	0.852345
$483$	−0.928203	−0.0422347
$484$	11.3923	0.517832
$485$	24.9282	1.13193
$486$	26.4449	1.19956
$487$	−0.784610	−0.0355541	−0.0177770	−	0.999842i	$-0.505659\pi$
$487$	−0.784610	−0.0355541	−0.0177770	+	0.999842i	$0.505659\pi$
$488$	−26.3205	−1.19147
$489$	−4.24871	−0.192133
$490$	3.00000	0.135526
$491$	28.3923	1.28133	0.640663	−	0.767822i	$-0.278659\pi$
$491$	28.3923	1.28133	0.640663	+	0.767822i	$0.278659\pi$
$492$	−3.80385	−0.171491
$493$	12.8038	0.576656
$494$	0	0
$495$	20.1962	0.907750
$496$	30.9808	1.39108
$497$	6.00000	0.269137
$498$	10.3923	0.465690
$499$	12.9808	0.581099	0.290549	−	0.956860i	$-0.406162\pi$
$499$	12.9808	0.581099	0.290549	+	0.956860i	$0.406162\pi$
$500$	12.1244	0.542218
$501$	−18.0000	−0.804181
$502$	38.7846	1.73104
$503$	12.5885	0.561292	0.280646	−	0.959811i	$-0.409451\pi$
$503$	12.5885	0.561292	0.280646	+	0.959811i	$0.409451\pi$
$504$	−4.26795	−0.190110
$505$	7.39230	0.328953
$506$	−10.3923	−0.461994
$507$	0	0
$508$	−2.39230	−0.106141
$509$	10.2679	0.455119	0.227559	−	0.973764i	$-0.426925\pi$
$509$	10.2679	0.455119	0.227559	+	0.973764i	$0.426925\pi$
$510$	9.37307	0.415046
$511$	7.19615	0.318339
$512$	−8.66025	−0.382733
$513$	8.00000	0.353209
$514$	31.3923	1.38466
$515$	−11.0718	−0.487882
$516$	−7.46410	−0.328589
$517$	−4.39230	−0.193173
$518$	12.1244	0.532714
$519$	−11.3205	−0.496915
$520$	0	0
$521$	0.124356	0.00544812	0.00272406	−	0.999996i	$-0.499133\pi$
$521$	0.124356	0.00544812	0.00272406	+	0.999996i	$0.499133\pi$
$522$	−12.8038	−0.560409
$523$	33.1769	1.45073	0.725363	−	0.688367i	$-0.241672\pi$
$523$	33.1769	1.45073	0.725363	+	0.688367i	$0.241672\pi$
$524$	3.46410	0.151330
$525$	1.46410	0.0638986
$526$	−8.19615	−0.357369
$527$	26.4449	1.15196
$528$	17.3205	0.753778
$529$	−21.3923	−0.930100
$530$	11.7846	0.511891
$531$	−26.4449	−1.14761
$532$	2.00000	0.0867110
$533$	0	0
$534$	−1.17691	−0.0509301
$535$	−34.3923	−1.48691
$536$	7.26795	0.313928
$537$	−5.07180	−0.218864
$538$	−32.7846	−1.41344
$539$	4.73205	0.203824
$540$	−6.92820	−0.298142
$541$	−35.3923	−1.52163	−0.760817	−	0.648966i	$-0.775202\pi$
$541$	−35.3923	−1.52163	−0.760817	+	0.648966i	$0.775202\pi$
$542$	−28.0526	−1.20496
$543$	18.7321	0.803869
$544$	−22.1769	−0.950827
$545$	−21.4641	−0.919421
$546$	0	0
$547$	28.1962	1.20558	0.602790	−	0.797900i	$-0.294056\pi$
$547$	28.1962	1.20558	0.602790	+	0.797900i	$0.294056\pi$
$548$	21.9282	0.936726
$549$	37.4449	1.59811
$550$	16.3923	0.698970
$551$	−6.00000	−0.255609
$552$	−1.60770	−0.0684280
$553$	5.80385	0.246805
$554$	−29.4449	−1.25099
$555$	−8.87564	−0.376750
$556$	20.5885	0.873145
$557$	−25.6410	−1.08644	−0.543222	−	0.839589i	$-0.682796\pi$
$557$	−25.6410	−1.08644	−0.543222	+	0.839589i	$0.682796\pi$
$558$	−26.4449	−1.11950
$559$	0	0
$560$	8.66025	0.365963
$561$	14.7846	0.624207
$562$	12.8038	0.540098
$563$	−10.0526	−0.423665	−0.211832	−	0.977306i	$-0.567943\pi$
$563$	−10.0526	−0.423665	−0.211832	+	0.977306i	$0.567943\pi$
$564$	0.679492	0.0286118
$565$	12.8038	0.538662
$566$	0.339746	0.0142806
$567$	4.46410	0.187475
$568$	10.3923	0.436051
$569$	29.0718	1.21875	0.609377	−	0.792881i	$-0.291420\pi$
$569$	29.0718	1.21875	0.609377	+	0.792881i	$0.291420\pi$
$570$	−4.39230	−0.183973
$571$	−24.7846	−1.03720	−0.518602	−	0.855016i	$-0.673547\pi$
$571$	−24.7846	−1.03720	−0.518602	+	0.855016i	$0.673547\pi$
$572$	0	0
$573$	−0.928203	−0.0387762
$574$	−9.00000	−0.375653
$575$	−2.53590	−0.105754
$576$	−2.46410	−0.102671
$577$	32.8038	1.36564	0.682821	−	0.730586i	$-0.260753\pi$
$577$	32.8038	1.36564	0.682821	+	0.730586i	$0.260753\pi$
$578$	−2.10512	−0.0875614
$579$	−3.66025	−0.152115
$580$	5.19615	0.215758
$581$	8.19615	0.340034
$582$	−18.2487	−0.756433
$583$	18.5885	0.769855
$584$	12.4641	0.515768
$585$	0	0
$586$	19.3923	0.801089
$587$	−4.39230	−0.181290	−0.0906449	−	0.995883i	$-0.528893\pi$
$587$	−4.39230	−0.181290	−0.0906449	+	0.995883i	$0.528893\pi$
$588$	−0.732051	−0.0301893
$589$	−12.3923	−0.510616
$590$	32.1962	1.32549
$591$	−8.78461	−0.361351
$592$	35.0000	1.43849
$593$	41.4449	1.70194	0.850968	−	0.525217i	$-0.176016\pi$
$593$	41.4449	1.70194	0.850968	+	0.525217i	$0.176016\pi$
$594$	−32.7846	−1.34517
$595$	7.39230	0.303055
$596$	0.464102	0.0190103
$597$	−1.46410	−0.0599217
$598$	0	0
$599$	16.1436	0.659609	0.329805	−	0.944049i	$-0.393017\pi$
$599$	16.1436	0.659609	0.329805	+	0.944049i	$0.393017\pi$
$600$	2.53590	0.103528
$601$	21.9808	0.896614	0.448307	−	0.893880i	$-0.352027\pi$
$601$	21.9808	0.896614	0.448307	+	0.893880i	$0.352027\pi$
$602$	−17.6603	−0.719778
$603$	−10.3397	−0.421067
$604$	2.00000	0.0813788
$605$	−19.7321	−0.802222
$606$	−5.41154	−0.219829
$607$	6.39230	0.259456	0.129728	−	0.991550i	$-0.458590\pi$
$607$	6.39230	0.259456	0.129728	+	0.991550i	$0.458590\pi$
$608$	10.3923	0.421464
$609$	2.19615	0.0889926
$610$	−45.5885	−1.84582
$611$	0	0
$612$	10.5167	0.425111
$613$	−17.3923	−0.702469	−0.351234	−	0.936288i	$-0.614238\pi$
$613$	−17.3923	−0.702469	−0.351234	+	0.936288i	$0.614238\pi$
$614$	−46.0526	−1.85853
$615$	6.58846	0.265672
$616$	8.19615	0.330232
$617$	28.6077	1.15170	0.575851	−	0.817555i	$-0.304671\pi$
$617$	28.6077	1.15170	0.575851	+	0.817555i	$0.304671\pi$
$618$	8.10512	0.326036
$619$	−37.3731	−1.50215	−0.751075	−	0.660217i	$-0.770464\pi$
$619$	−37.3731	−1.50215	−0.751075	+	0.660217i	$0.770464\pi$
$620$	10.7321	0.431010
$621$	5.07180	0.203524
$622$	−8.19615	−0.328636
$623$	−0.928203	−0.0371877
$624$	0	0
$625$	−11.0000	−0.440000
$626$	22.1436	0.885036
$627$	−6.92820	−0.276686
$628$	−9.19615	−0.366966
$629$	29.8756	1.19122
$630$	−7.39230	−0.294516
$631$	28.7846	1.14590	0.572949	−	0.819591i	$-0.305799\pi$
$631$	28.7846	1.14590	0.572949	+	0.819591i	$0.305799\pi$
$632$	10.0526	0.399869
$633$	8.92820	0.354864
$634$	−0.803848	−0.0319249
$635$	4.14359	0.164433
$636$	−2.87564	−0.114027
$637$	0	0
$638$	24.5885	0.973466
$639$	−14.7846	−0.584870
$640$	21.0000	0.830098
$641$	1.14359	0.0451692	0.0225846	−	0.999745i	$-0.492810\pi$
$641$	1.14359	0.0451692	0.0225846	+	0.999745i	$0.492810\pi$
$642$	25.1769	0.993654
$643$	40.7846	1.60839	0.804194	−	0.594367i	$-0.202597\pi$
$643$	40.7846	1.60839	0.804194	+	0.594367i	$0.202597\pi$
$644$	1.26795	0.0499642
$645$	12.9282	0.509048
$646$	14.7846	0.581693
$647$	−45.0333	−1.77044	−0.885221	−	0.465170i	$-0.845993\pi$
$647$	−45.0333	−1.77044	−0.885221	+	0.465170i	$0.845993\pi$
$648$	7.73205	0.303744
$649$	50.7846	1.99347
$650$	0	0
$651$	4.53590	0.177776
$652$	5.80385	0.227296
$653$	−10.1436	−0.396949	−0.198475	−	0.980106i	$-0.563599\pi$
$653$	−10.1436	−0.396949	−0.198475	+	0.980106i	$0.563599\pi$
$654$	15.7128	0.614420
$655$	−6.00000	−0.234439
$656$	−25.9808	−1.01438
$657$	−17.7321	−0.691793
$658$	1.60770	0.0626745
$659$	7.60770	0.296354	0.148177	−	0.988961i	$-0.452660\pi$
$659$	7.60770	0.296354	0.148177	+	0.988961i	$0.452660\pi$
$660$	6.00000	0.233550
$661$	−22.8038	−0.886967	−0.443483	−	0.896283i	$-0.646258\pi$
$661$	−22.8038	−0.886967	−0.443483	+	0.896283i	$0.646258\pi$
$662$	46.7321	1.81629
$663$	0	0
$664$	14.1962	0.550918
$665$	−3.46410	−0.134332
$666$	−29.8756	−1.15766
$667$	−3.80385	−0.147286
$668$	24.5885	0.951356
$669$	7.32051	0.283027
$670$	12.5885	0.486335
$671$	−71.9090	−2.77601
$672$	−3.80385	−0.146737
$673$	18.1769	0.700669	0.350334	−	0.936625i	$-0.386068\pi$
$673$	18.1769	0.700669	0.350334	+	0.936625i	$0.386068\pi$
$674$	−19.0526	−0.733877
$675$	−8.00000	−0.307920
$676$	0	0
$677$	−36.9282	−1.41927	−0.709633	−	0.704571i	$-0.751139\pi$
$677$	−36.9282	−1.41927	−0.709633	+	0.704571i	$0.751139\pi$
$678$	−9.37307	−0.359970
$679$	−14.3923	−0.552326
$680$	12.8038	0.491005
$681$	8.53590	0.327096
$682$	50.7846	1.94464
$683$	8.53590	0.326617	0.163309	−	0.986575i	$-0.447783\pi$
$683$	8.53590	0.326617	0.163309	+	0.986575i	$0.447783\pi$
$684$	−4.92820	−0.188435
$685$	−37.9808	−1.45117
$686$	−1.73205	−0.0661300
$687$	−4.67949	−0.178534
$688$	−50.9808	−1.94362
$689$	0	0
$690$	−2.78461	−0.106008
$691$	−20.3923	−0.775760	−0.387880	−	0.921710i	$-0.626792\pi$
$691$	−20.3923	−0.775760	−0.387880	+	0.921710i	$0.626792\pi$
$692$	15.4641	0.587857
$693$	−11.6603	−0.442936
$694$	−18.5885	−0.705608
$695$	−35.6603	−1.35267
$696$	3.80385	0.144184
$697$	−22.1769	−0.840011
$698$	−29.0718	−1.10038
$699$	−18.9282	−0.715930
$700$	−2.00000	−0.0755929
$701$	−20.7846	−0.785024	−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846	−0.785024	−0.392512	+	0.919747i	$0.628394\pi$
$702$	0	0
$703$	−14.0000	−0.528020
$704$	4.73205	0.178346
$705$	−1.17691	−0.0443252
$706$	−5.78461	−0.217707
$707$	−4.26795	−0.160513
$708$	−7.85641	−0.295262
$709$	−32.1769	−1.20843	−0.604215	−	0.796822i	$-0.706513\pi$
$709$	−32.1769	−1.20843	−0.604215	+	0.796822i	$0.706513\pi$
$710$	18.0000	0.675528
$711$	−14.3013	−0.536340
$712$	−1.60770	−0.0602509
$713$	−7.85641	−0.294225
$714$	−5.41154	−0.202522
$715$	0	0
$716$	6.92820	0.258919
$717$	19.1769	0.716175
$718$	−8.78461	−0.327839
$719$	−10.7321	−0.400238	−0.200119	−	0.979772i	$-0.564133\pi$
$719$	−10.7321	−0.400238	−0.200119	+	0.979772i	$0.564133\pi$
$720$	−21.3397	−0.795285
$721$	6.39230	0.238062
$722$	25.9808	0.966904
$723$	7.90897	0.294138
$724$	−25.5885	−0.950988
$725$	6.00000	0.222834
$726$	14.4449	0.536099
$727$	21.1769	0.785408	0.392704	−	0.919665i	$-0.371540\pi$
$727$	21.1769	0.785408	0.392704	+	0.919665i	$0.371540\pi$
$728$	0	0
$729$	−2.21539	−0.0820515
$730$	21.5885	0.799025
$731$	−43.5167	−1.60952
$732$	11.1244	0.411168
$733$	−7.58846	−0.280286	−0.140143	−	0.990131i	$-0.544756\pi$
$733$	−7.58846	−0.280286	−0.140143	+	0.990131i	$0.544756\pi$
$734$	10.7321	0.396127
$735$	1.26795	0.0467690
$736$	6.58846	0.242854
$737$	19.8564	0.731420
$738$	22.1769	0.816344
$739$	−0.784610	−0.0288623	−0.0144312	−	0.999896i	$-0.504594\pi$
$739$	−0.784610	−0.0288623	−0.0144312	+	0.999896i	$0.504594\pi$
$740$	12.1244	0.445700
$741$	0	0
$742$	−6.80385	−0.249777
$743$	−28.3923	−1.04161	−0.520806	−	0.853675i	$-0.674369\pi$
$743$	−28.3923	−1.04161	−0.520806	+	0.853675i	$0.674369\pi$
$744$	7.85641	0.288030
$745$	−0.803848	−0.0294507
$746$	−16.2679	−0.595612
$747$	−20.1962	−0.738939
$748$	−20.1962	−0.738444
$749$	19.8564	0.725537
$750$	15.3731	0.561345
$751$	46.1962	1.68572	0.842861	−	0.538132i	$-0.180870\pi$
$751$	46.1962	1.68572	0.842861	+	0.538132i	$0.180870\pi$
$752$	4.64102	0.169240
$753$	16.3923	0.597369
$754$	0	0
$755$	−3.46410	−0.126072
$756$	4.00000	0.145479
$757$	−16.0000	−0.581530	−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000	−0.581530	−0.290765	+	0.956795i	$0.593910\pi$
$758$	7.94744	0.288664
$759$	−4.39230	−0.159431
$760$	−6.00000	−0.217643
$761$	6.67949	0.242131	0.121066	−	0.992644i	$-0.461369\pi$
$761$	6.67949	0.242131	0.121066	+	0.992644i	$0.461369\pi$
$762$	−3.03332	−0.109886
$763$	12.3923	0.448632
$764$	1.26795	0.0458728
$765$	−18.2154	−0.658579
$766$	−9.80385	−0.354227
$767$	0	0
$768$	−13.9090	−0.501897
$769$	−47.1769	−1.70124	−0.850622	−	0.525778i	$-0.823774\pi$
$769$	−47.1769	−1.70124	−0.850622	+	0.525778i	$0.823774\pi$
$770$	14.1962	0.511594
$771$	13.2679	0.477834
$772$	5.00000	0.179954
$773$	0.928203	0.0333851	0.0166926	−	0.999861i	$-0.494686\pi$
$773$	0.928203	0.0333851	0.0166926	+	0.999861i	$0.494686\pi$
$774$	43.5167	1.56417
$775$	12.3923	0.445145
$776$	−24.9282	−0.894870
$777$	5.12436	0.183835
$778$	52.7654	1.89173
$779$	10.3923	0.372343
$780$	0	0
$781$	28.3923	1.01596
$782$	9.37307	0.335180
$783$	−12.0000	−0.428845
$784$	−5.00000	−0.178571
$785$	15.9282	0.568502
$786$	4.39230	0.156668
$787$	−38.9808	−1.38951	−0.694757	−	0.719244i	$-0.744488\pi$
$787$	−38.9808	−1.38951	−0.694757	+	0.719244i	$0.744488\pi$
$788$	12.0000	0.427482
$789$	−3.46410	−0.123325
$790$	17.4115	0.619475
$791$	−7.39230	−0.262840
$792$	−20.1962	−0.717639
$793$	0	0
$794$	−39.4641	−1.40053
$795$	4.98076	0.176649
$796$	2.00000	0.0708881
$797$	−13.6077	−0.482009	−0.241005	−	0.970524i	$-0.577477\pi$
$797$	−13.6077	−0.482009	−0.241005	+	0.970524i	$0.577477\pi$
$798$	2.53590	0.0897698
$799$	3.96152	0.140149
$800$	−10.3923	−0.367423
$801$	2.28719	0.0808138
$802$	−29.1962	−1.03095
$803$	34.0526	1.20169
$804$	−3.07180	−0.108334
$805$	−2.19615	−0.0774042
$806$	0	0
$807$	−13.8564	−0.487769
$808$	−7.39230	−0.260060
$809$	15.9282	0.560006	0.280003	−	0.959999i	$-0.409665\pi$
$809$	15.9282	0.560006	0.280003	+	0.959999i	$0.409665\pi$
$810$	13.3923	0.470558
$811$	14.5885	0.512270	0.256135	−	0.966641i	$-0.417551\pi$
$811$	14.5885	0.512270	0.256135	+	0.966641i	$0.417551\pi$
$812$	−3.00000	−0.105279
$813$	−11.8564	−0.415822
$814$	57.3731	2.01092
$815$	−10.0526	−0.352126
$816$	−15.6218	−0.546872
$817$	20.3923	0.713436
$818$	47.1051	1.64699
$819$	0	0
$820$	−9.00000	−0.314294
$821$	31.8564	1.11180	0.555898	−	0.831250i	$-0.312374\pi$
$821$	31.8564	1.11180	0.555898	+	0.831250i	$0.312374\pi$
$822$	27.8038	0.969771
$823$	21.1769	0.738181	0.369090	−	0.929393i	$-0.379669\pi$
$823$	21.1769	0.738181	0.369090	+	0.929393i	$0.379669\pi$
$824$	11.0718	0.385704
$825$	6.92820	0.241209
$826$	−18.5885	−0.646775
$827$	34.9808	1.21640	0.608200	−	0.793784i	$-0.291892\pi$
$827$	34.9808	1.21640	0.608200	+	0.793784i	$0.291892\pi$
$828$	−3.12436	−0.108579
$829$	−31.5885	−1.09711	−0.548556	−	0.836114i	$-0.684822\pi$
$829$	−31.5885	−1.09711	−0.548556	+	0.836114i	$0.684822\pi$
$830$	24.5885	0.853478
$831$	−12.4449	−0.431708
$832$	0	0
$833$	−4.26795	−0.147876
$834$	26.1051	0.903946
$835$	−42.5885	−1.47383
$836$	9.46410	0.327323
$837$	−24.7846	−0.856681
$838$	37.7654	1.30458
$839$	−18.0000	−0.621429	−0.310715	−	0.950503i	$-0.600568\pi$
$839$	−18.0000	−0.621429	−0.310715	+	0.950503i	$0.600568\pi$
$840$	2.19615	0.0757745
$841$	−20.0000	−0.689655
$842$	−52.2679	−1.80127
$843$	5.41154	0.186383
$844$	−12.1962	−0.419809
$845$	0	0
$846$	−3.96152	−0.136200
$847$	11.3923	0.391444
$848$	−19.6410	−0.674475
$849$	0.143594	0.00492812
$850$	−14.7846	−0.507108
$851$	−8.87564	−0.304253
$852$	−4.39230	−0.150478
$853$	−25.5885	−0.876132	−0.438066	−	0.898943i	$-0.644336\pi$
$853$	−25.5885	−0.876132	−0.438066	+	0.898943i	$0.644336\pi$
$854$	26.3205	0.900669
$855$	8.53590	0.291922
$856$	34.3923	1.17550
$857$	−5.87564	−0.200708	−0.100354	−	0.994952i	$-0.531998\pi$
$857$	−5.87564	−0.200708	−0.100354	+	0.994952i	$0.531998\pi$
$858$	0	0
$859$	−18.1962	−0.620845	−0.310422	−	0.950599i	$-0.600470\pi$
$859$	−18.1962	−0.620845	−0.310422	+	0.950599i	$0.600470\pi$
$860$	−17.6603	−0.602210
$861$	−3.80385	−0.129635
$862$	−61.1769	−2.08369
$863$	−37.5167	−1.27708	−0.638541	−	0.769588i	$-0.720462\pi$
$863$	−37.5167	−1.27708	−0.638541	+	0.769588i	$0.720462\pi$
$864$	20.7846	0.707107
$865$	−26.7846	−0.910704
$866$	−30.4641	−1.03521
$867$	−0.889727	−0.0302167
$868$	−6.19615	−0.210311
$869$	27.4641	0.931656
$870$	6.58846	0.223370
$871$	0	0
$872$	21.4641	0.726866
$873$	35.4641	1.20028
$874$	−4.39230	−0.148572
$875$	12.1244	0.409878
$876$	−5.26795	−0.177988
$877$	−21.7846	−0.735614	−0.367807	−	0.929902i	$-0.619891\pi$
$877$	−21.7846	−0.735614	−0.367807	+	0.929902i	$0.619891\pi$
$878$	28.7321	0.969660
$879$	8.19615	0.276449
$880$	40.9808	1.38146
$881$	−39.5885	−1.33377	−0.666885	−	0.745161i	$-0.732373\pi$
$881$	−39.5885	−1.33377	−0.666885	+	0.745161i	$0.732373\pi$
$882$	4.26795	0.143709
$883$	45.7654	1.54013	0.770064	−	0.637967i	$-0.220224\pi$
$883$	45.7654	1.54013	0.770064	+	0.637967i	$0.220224\pi$
$884$	0	0
$885$	13.6077	0.457418
$886$	19.6077	0.658733
$887$	−23.3205	−0.783026	−0.391513	−	0.920173i	$-0.628048\pi$
$887$	−23.3205	−0.783026	−0.391513	+	0.920173i	$0.628048\pi$
$888$	8.87564	0.297847
$889$	−2.39230	−0.0802353
$890$	−2.78461	−0.0933403
$891$	21.1244	0.707693
$892$	−10.0000	−0.334825
$893$	−1.85641	−0.0621223
$894$	0.588457	0.0196810
$895$	−12.0000	−0.401116
$896$	−12.1244	−0.405046
$897$	0	0
$898$	20.7846	0.693591
$899$	18.5885	0.619960
$900$	4.92820	0.164273
$901$	−16.7654	−0.558536
$902$	−42.5885	−1.41804
$903$	−7.46410	−0.248390
$904$	−12.8038	−0.425850
$905$	44.3205	1.47326
$906$	2.53590	0.0842496
$907$	14.5885	0.484402	0.242201	−	0.970226i	$-0.422131\pi$
$907$	14.5885	0.484402	0.242201	+	0.970226i	$0.422131\pi$
$908$	−11.6603	−0.386959
$909$	10.5167	0.348816
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	7.32051	0.242406
$913$	38.7846	1.28358
$914$	−19.0526	−0.630203
$915$	−19.2679	−0.636979
$916$	6.39230	0.211208
$917$	3.46410	0.114395
$918$	29.5692	0.975930
$919$	43.5692	1.43722	0.718608	−	0.695415i	$-0.244780\pi$
$919$	43.5692	1.43722	0.718608	+	0.695415i	$0.244780\pi$
$920$	−3.80385	−0.125409
$921$	−19.4641	−0.641364
$922$	−27.0000	−0.889198
$923$	0	0
$924$	−3.46410	−0.113961
$925$	14.0000	0.460317
$926$	−46.0526	−1.51338
$927$	−15.7513	−0.517340
$928$	−15.5885	−0.511716
$929$	7.48334	0.245520	0.122760	−	0.992436i	$-0.460825\pi$
$929$	7.48334	0.245520	0.122760	+	0.992436i	$0.460825\pi$
$930$	13.6077	0.446214
$931$	2.00000	0.0655474
$932$	25.8564	0.846955
$933$	−3.46410	−0.113410
$934$	33.8038	1.10610
$935$	34.9808	1.14399
$936$	0	0
$937$	−40.8038	−1.33300	−0.666502	−	0.745503i	$-0.732209\pi$
$937$	−40.8038	−1.33300	−0.666502	+	0.745503i	$0.732209\pi$
$938$	−7.26795	−0.237307
$939$	9.35898	0.305419
$940$	1.60770	0.0524372
$941$	−55.8564	−1.82087	−0.910433	−	0.413656i	$-0.864252\pi$
$941$	−55.8564	−1.82087	−0.910433	+	0.413656i	$0.864252\pi$
$942$	−11.6603	−0.379912
$943$	6.58846	0.214550
$944$	−53.6603	−1.74649
$945$	−6.92820	−0.225374
$946$	−83.5692	−2.71707
$947$	−10.7321	−0.348745	−0.174372	−	0.984680i	$-0.555790\pi$
$947$	−10.7321	−0.348745	−0.174372	+	0.984680i	$0.555790\pi$
$948$	−4.24871	−0.137992
$949$	0	0
$950$	6.92820	0.224781
$951$	−0.339746	−0.0110170
$952$	−7.39230	−0.239586
$953$	37.1769	1.20428	0.602139	−	0.798391i	$-0.294315\pi$
$953$	37.1769	1.20428	0.602139	+	0.798391i	$0.294315\pi$
$954$	16.7654	0.542799
$955$	−2.19615	−0.0710658
$956$	−26.1962	−0.847244
$957$	10.3923	0.335936
$958$	−8.19615	−0.264806
$959$	21.9282	0.708099
$960$	1.26795	0.0409229
$961$	7.39230	0.238461
$962$	0	0
$963$	−48.9282	−1.57669
$964$	−10.8038	−0.347969
$965$	−8.66025	−0.278783
$966$	1.60770	0.0517267
$967$	3.01924	0.0970921	0.0485461	−	0.998821i	$-0.484541\pi$
$967$	3.01924	0.0970921	0.0485461	+	0.998821i	$0.484541\pi$
$968$	19.7321	0.634212
$969$	6.24871	0.200738
$970$	−43.1769	−1.38633
$971$	16.6410	0.534036	0.267018	−	0.963692i	$-0.413962\pi$
$971$	16.6410	0.534036	0.267018	+	0.963692i	$0.413962\pi$
$972$	−15.2679	−0.489720
$973$	20.5885	0.660036
$974$	1.35898	0.0435447
$975$	0	0
$976$	75.9808	2.43208
$977$	−37.6410	−1.20424	−0.602121	−	0.798405i	$-0.705678\pi$
$977$	−37.6410	−1.20424	−0.602121	+	0.798405i	$0.705678\pi$
$978$	7.35898	0.235314
$979$	−4.39230	−0.140379
$980$	−1.73205	−0.0553283
$981$	−30.5359	−0.974936
$982$	−49.1769	−1.56930
$983$	17.3205	0.552438	0.276219	−	0.961095i	$-0.410918\pi$
$983$	17.3205	0.552438	0.276219	+	0.961095i	$0.410918\pi$
$984$	−6.58846	−0.210032
$985$	−20.7846	−0.662253
$986$	−22.1769	−0.706257
$987$	0.679492	0.0216285
$988$	0	0
$989$	12.9282	0.411093
$990$	−34.9808	−1.11176
$991$	−32.9808	−1.04767	−0.523834	−	0.851820i	$-0.675499\pi$
$991$	−32.9808	−1.04767	−0.523834	+	0.851820i	$0.675499\pi$
$992$	−32.1962	−1.02223
$993$	19.7513	0.626788
$994$	−10.3923	−0.329624
$995$	−3.46410	−0.109819
$996$	−6.00000	−0.190117
$997$	−15.1962	−0.481267	−0.240633	−	0.970616i	$-0.577355\pi$
$997$	−15.1962	−0.481267	−0.240633	+	0.970616i	$0.577355\pi$
$998$	−22.4833	−0.711698
$999$	−28.0000	−0.885881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.f.1.1		2
7.6	odd	2		8281.2.a.r.1.1		2
13.3	even	3		91.2.f.b.22.2	✓	4
13.5	odd	4		1183.2.c.e.337.3		4
13.8	odd	4		1183.2.c.e.337.1		4
13.9	even	3		91.2.f.b.29.2	yes	4
13.12	even	2		1183.2.a.e.1.2		2
39.29	odd	6		819.2.o.b.568.1		4
39.35	odd	6		819.2.o.b.757.1		4
52.3	odd	6		1456.2.s.o.113.1		4
52.35	odd	6		1456.2.s.o.1121.1		4
91.3	odd	6		637.2.g.d.373.2		4
91.9	even	3		637.2.g.e.263.2		4
91.16	even	3		637.2.h.d.165.1		4
91.48	odd	6		637.2.f.d.393.2		4
91.55	odd	6		637.2.f.d.295.2		4
91.61	odd	6		637.2.g.d.263.2		4
91.68	odd	6		637.2.h.e.165.1		4
91.74	even	3		637.2.h.d.471.1		4
91.81	even	3		637.2.g.e.373.2		4
91.87	odd	6		637.2.h.e.471.1		4
91.90	odd	2		8281.2.a.t.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.b.22.2	✓	4	13.3	even	3
91.2.f.b.29.2	yes	4	13.9	even	3
637.2.f.d.295.2		4	91.55	odd	6
637.2.f.d.393.2		4	91.48	odd	6
637.2.g.d.263.2		4	91.61	odd	6
637.2.g.d.373.2		4	91.3	odd	6
637.2.g.e.263.2		4	91.9	even	3
637.2.g.e.373.2		4	91.81	even	3
637.2.h.d.165.1		4	91.16	even	3
637.2.h.d.471.1		4	91.74	even	3
637.2.h.e.165.1		4	91.68	odd	6
637.2.h.e.471.1		4	91.87	odd	6
819.2.o.b.568.1		4	39.29	odd	6
819.2.o.b.757.1		4	39.35	odd	6
1183.2.a.e.1.2		2	13.12	even	2
1183.2.a.f.1.1		2	1.1	even	1	trivial
1183.2.c.e.337.1		4	13.8	odd	4
1183.2.c.e.337.3		4	13.5	odd	4
1456.2.s.o.113.1		4	52.3	odd	6
1456.2.s.o.1121.1		4	52.35	odd	6
8281.2.a.r.1.1		2	7.6	odd	2
8281.2.a.t.1.2		2	91.90	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q-1.73205 q^{2} -0.732051 q^{3} +1.00000 q^{4} -1.73205 q^{5} +1.26795 q^{6} +1.00000 q^{7} +1.73205 q^{8} -2.46410 q^{9} +O(q^{10})\)	\(q-1.73205 q^{2} -0.732051 q^{3} +1.00000 q^{4} -1.73205 q^{5} +1.26795 q^{6} +1.00000 q^{7} +1.73205 q^{8} -2.46410 q^{9} +3.00000 q^{10} +4.73205 q^{11} -0.732051 q^{12} -1.73205 q^{14} +1.26795 q^{15} -5.00000 q^{16} -4.26795 q^{17} +4.26795 q^{18} +2.00000 q^{19} -1.73205 q^{20} -0.732051 q^{21} -8.19615 q^{22} +1.26795 q^{23} -1.26795 q^{24} -2.00000 q^{25} +4.00000 q^{27} +1.00000 q^{28} -3.00000 q^{29} -2.19615 q^{30} -6.19615 q^{31} +5.19615 q^{32} -3.46410 q^{33} +7.39230 q^{34} -1.73205 q^{35} -2.46410 q^{36} -7.00000 q^{37} -3.46410 q^{38} -3.00000 q^{40} +5.19615 q^{41} +1.26795 q^{42} +10.1962 q^{43} +4.73205 q^{44} +4.26795 q^{45} -2.19615 q^{46} -0.928203 q^{47} +3.66025 q^{48} +1.00000 q^{49} +3.46410 q^{50} +3.12436 q^{51} +3.92820 q^{53} -6.92820 q^{54} -8.19615 q^{55} +1.73205 q^{56} -1.46410 q^{57} +5.19615 q^{58} +10.7321 q^{59} +1.26795 q^{60} -15.1962 q^{61} +10.7321 q^{62} -2.46410 q^{63} +1.00000 q^{64} +6.00000 q^{66} +4.19615 q^{67} -4.26795 q^{68} -0.928203 q^{69} +3.00000 q^{70} +6.00000 q^{71} -4.26795 q^{72} +7.19615 q^{73} +12.1244 q^{74} +1.46410 q^{75} +2.00000 q^{76} +4.73205 q^{77} +5.80385 q^{79} +8.66025 q^{80} +4.46410 q^{81} -9.00000 q^{82} +8.19615 q^{83} -0.732051 q^{84} +7.39230 q^{85} -17.6603 q^{86} +2.19615 q^{87} +8.19615 q^{88} -0.928203 q^{89} -7.39230 q^{90} +1.26795 q^{92} +4.53590 q^{93} +1.60770 q^{94} -3.46410 q^{95} -3.80385 q^{96} -14.3923 q^{97} -1.73205 q^{98} -11.6603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^7 + 2 * q^9	\( 2 q + 2 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 6 q^{11} + 2 q^{12} + 6 q^{15} - 10 q^{16} - 12 q^{17} + 12 q^{18} + 4 q^{19} + 2 q^{21} - 6 q^{22} + 6 q^{23} - 6 q^{24} - 4 q^{25} + 8 q^{27} + 2 q^{28} - 6 q^{29} + 6 q^{30} - 2 q^{31} - 6 q^{34} + 2 q^{36} - 14 q^{37} - 6 q^{40} + 6 q^{42} + 10 q^{43} + 6 q^{44} + 12 q^{45} + 6 q^{46} + 12 q^{47} - 10 q^{48} + 2 q^{49} - 18 q^{51} - 6 q^{53} - 6 q^{55} + 4 q^{57} + 18 q^{59} + 6 q^{60} - 20 q^{61} + 18 q^{62} + 2 q^{63} + 2 q^{64} + 12 q^{66} - 2 q^{67} - 12 q^{68} + 12 q^{69} + 6 q^{70} + 12 q^{71} - 12 q^{72} + 4 q^{73} - 4 q^{75} + 4 q^{76} + 6 q^{77} + 22 q^{79} + 2 q^{81} - 18 q^{82} + 6 q^{83} + 2 q^{84} - 6 q^{85} - 18 q^{86} - 6 q^{87} + 6 q^{88} + 12 q^{89} + 6 q^{90} + 6 q^{92} + 16 q^{93} + 24 q^{94} - 18 q^{96} - 8 q^{97} - 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^7 + 2 * q^9 + 6 * q^10 + 6 * q^11 + 2 * q^12 + 6 * q^15 - 10 * q^16 - 12 * q^17 + 12 * q^18 + 4 * q^19 + 2 * q^21 - 6 * q^22 + 6 * q^23 - 6 * q^24 - 4 * q^25 + 8 * q^27 + 2 * q^28 - 6 * q^29 + 6 * q^30 - 2 * q^31 - 6 * q^34 + 2 * q^36 - 14 * q^37 - 6 * q^40 + 6 * q^42 + 10 * q^43 + 6 * q^44 + 12 * q^45 + 6 * q^46 + 12 * q^47 - 10 * q^48 + 2 * q^49 - 18 * q^51 - 6 * q^53 - 6 * q^55 + 4 * q^57 + 18 * q^59 + 6 * q^60 - 20 * q^61 + 18 * q^62 + 2 * q^63 + 2 * q^64 + 12 * q^66 - 2 * q^67 - 12 * q^68 + 12 * q^69 + 6 * q^70 + 12 * q^71 - 12 * q^72 + 4 * q^73 - 4 * q^75 + 4 * q^76 + 6 * q^77 + 22 * q^79 + 2 * q^81 - 18 * q^82 + 6 * q^83 + 2 * q^84 - 6 * q^85 - 18 * q^86 - 6 * q^87 + 6 * q^88 + 12 * q^89 + 6 * q^90 + 6 * q^92 + 16 * q^93 + 24 * q^94 - 18 * q^96 - 8 * q^97 - 6 * q^99

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