LMFDB - Embedded newform 2535.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2535,2,Mod(1,2535)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2535, 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("2535.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2535 = 3 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2535.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:	$20.2420769124$
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 195)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	2535.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.732051 q^{2} +1.00000 q^{3} -1.46410 q^{4} -1.00000 q^{5} -0.732051 q^{6} +1.73205 q^{7} +2.53590 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.732051 q^{2} +1.00000 q^{3} -1.46410 q^{4} -1.00000 q^{5} -0.732051 q^{6} +1.73205 q^{7} +2.53590 q^{8} +1.00000 q^{9} +0.732051 q^{10} +2.00000 q^{11} -1.46410 q^{12} -1.26795 q^{14} -1.00000 q^{15} +1.07180 q^{16} +0.732051 q^{17} -0.732051 q^{18} +0.535898 q^{19} +1.46410 q^{20} +1.73205 q^{21} -1.46410 q^{22} +2.00000 q^{23} +2.53590 q^{24} +1.00000 q^{25} +1.00000 q^{27} -2.53590 q^{28} -3.26795 q^{29} +0.732051 q^{30} -4.46410 q^{31} -5.85641 q^{32} +2.00000 q^{33} -0.535898 q^{34} -1.73205 q^{35} -1.46410 q^{36} +10.3923 q^{37} -0.392305 q^{38} -2.53590 q^{40} +10.7321 q^{41} -1.26795 q^{42} -9.19615 q^{43} -2.92820 q^{44} -1.00000 q^{45} -1.46410 q^{46} -0.196152 q^{47} +1.07180 q^{48} -4.00000 q^{49} -0.732051 q^{50} +0.732051 q^{51} -9.46410 q^{53} -0.732051 q^{54} -2.00000 q^{55} +4.39230 q^{56} +0.535898 q^{57} +2.39230 q^{58} +11.6603 q^{59} +1.46410 q^{60} +5.39230 q^{61} +3.26795 q^{62} +1.73205 q^{63} +2.14359 q^{64} -1.46410 q^{66} +9.19615 q^{67} -1.07180 q^{68} +2.00000 q^{69} +1.26795 q^{70} +4.73205 q^{71} +2.53590 q^{72} -1.73205 q^{73} -7.60770 q^{74} +1.00000 q^{75} -0.784610 q^{76} +3.46410 q^{77} -11.0000 q^{79} -1.07180 q^{80} +1.00000 q^{81} -7.85641 q^{82} -2.92820 q^{83} -2.53590 q^{84} -0.732051 q^{85} +6.73205 q^{86} -3.26795 q^{87} +5.07180 q^{88} -5.26795 q^{89} +0.732051 q^{90} -2.92820 q^{92} -4.46410 q^{93} +0.143594 q^{94} -0.535898 q^{95} -5.85641 q^{96} -5.19615 q^{97} +2.92820 q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{8} + 2 q^{9} - 2 q^{10} + 4 q^{11} + 4 q^{12} - 6 q^{14} - 2 q^{15} + 16 q^{16} - 2 q^{17} + 2 q^{18} + 8 q^{19} - 4 q^{20} + 4 q^{22} + 4 q^{23} + 12 q^{24} + 2 q^{25} + 2 q^{27} - 12 q^{28} - 10 q^{29} - 2 q^{30} - 2 q^{31} + 16 q^{32} + 4 q^{33} - 8 q^{34} + 4 q^{36} + 20 q^{38} - 12 q^{40} + 18 q^{41} - 6 q^{42} - 8 q^{43} + 8 q^{44} - 2 q^{45} + 4 q^{46} + 10 q^{47} + 16 q^{48} - 8 q^{49} + 2 q^{50} - 2 q^{51} - 12 q^{53} + 2 q^{54} - 4 q^{55} - 12 q^{56} + 8 q^{57} - 16 q^{58} + 6 q^{59} - 4 q^{60} - 10 q^{61} + 10 q^{62} + 32 q^{64} + 4 q^{66} + 8 q^{67} - 16 q^{68} + 4 q^{69} + 6 q^{70} + 6 q^{71} + 12 q^{72} - 36 q^{74} + 2 q^{75} + 40 q^{76} - 22 q^{79} - 16 q^{80} + 2 q^{81} + 12 q^{82} + 8 q^{83} - 12 q^{84} + 2 q^{85} + 10 q^{86} - 10 q^{87} + 24 q^{88} - 14 q^{89} - 2 q^{90} + 8 q^{92} - 2 q^{93} + 28 q^{94} - 8 q^{95} + 16 q^{96} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^8 + 2 * q^9 - 2 * q^10 + 4 * q^11 + 4 * q^12 - 6 * q^14 - 2 * q^15 + 16 * q^16 - 2 * q^17 + 2 * q^18 + 8 * q^19 - 4 * q^20 + 4 * q^22 + 4 * q^23 + 12 * q^24 + 2 * q^25 + 2 * q^27 - 12 * q^28 - 10 * q^29 - 2 * q^30 - 2 * q^31 + 16 * q^32 + 4 * q^33 - 8 * q^34 + 4 * q^36 + 20 * q^38 - 12 * q^40 + 18 * q^41 - 6 * q^42 - 8 * q^43 + 8 * q^44 - 2 * q^45 + 4 * q^46 + 10 * q^47 + 16 * q^48 - 8 * q^49 + 2 * q^50 - 2 * q^51 - 12 * q^53 + 2 * q^54 - 4 * q^55 - 12 * q^56 + 8 * q^57 - 16 * q^58 + 6 * q^59 - 4 * q^60 - 10 * q^61 + 10 * q^62 + 32 * q^64 + 4 * q^66 + 8 * q^67 - 16 * q^68 + 4 * q^69 + 6 * q^70 + 6 * q^71 + 12 * q^72 - 36 * q^74 + 2 * q^75 + 40 * q^76 - 22 * q^79 - 16 * q^80 + 2 * q^81 + 12 * q^82 + 8 * q^83 - 12 * q^84 + 2 * q^85 + 10 * q^86 - 10 * q^87 + 24 * q^88 - 14 * q^89 - 2 * q^90 + 8 * q^92 - 2 * q^93 + 28 * q^94 - 8 * q^95 + 16 * q^96 - 8 * q^98 + 4 * 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 $

$2$	−0.732051	−0.517638	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	−0.732051	−0.517638	−0.258819	+	0.965926i	$0.583333\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.46410	−0.732051
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.732051	−0.298858
$7$	1.73205	0.654654	0.327327	−	0.944911i	$-0.393852\pi$
$7$	1.73205	0.654654	0.327327	+	0.944911i	$0.393852\pi$
$8$	2.53590	0.896575
$9$	1.00000	0.333333
$10$	0.732051	0.231495
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	−1.46410	−0.422650
$13$	0	0
$13$	0	0
$14$	−1.26795	−0.338874
$15$	−1.00000	−0.258199
$16$	1.07180	0.267949
$17$	0.732051	0.177548	0.0887742	−	0.996052i	$-0.471705\pi$
$17$	0.732051	0.177548	0.0887742	+	0.996052i	$0.471705\pi$
$18$	−0.732051	−0.172546
$19$	0.535898	0.122944	0.0614718	−	0.998109i	$-0.480421\pi$
$19$	0.535898	0.122944	0.0614718	+	0.998109i	$0.480421\pi$
$20$	1.46410	0.327383
$21$	1.73205	0.377964
$22$	−1.46410	−0.312148
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	2.53590	0.517638
$25$	1.00000	0.200000
$26$	0	0
$27$	1.00000	0.192450
$28$	−2.53590	−0.479240
$29$	−3.26795	−0.606843	−0.303421	−	0.952856i	$-0.598129\pi$
$29$	−3.26795	−0.606843	−0.303421	+	0.952856i	$0.598129\pi$
$30$	0.732051	0.133654
$31$	−4.46410	−0.801776	−0.400888	−	0.916127i	$-0.631298\pi$
$31$	−4.46410	−0.801776	−0.400888	+	0.916127i	$0.631298\pi$
$32$	−5.85641	−1.03528
$33$	2.00000	0.348155
$34$	−0.535898	−0.0919058
$35$	−1.73205	−0.292770
$36$	−1.46410	−0.244017
$37$	10.3923	1.70848	0.854242	−	0.519875i	$-0.174022\pi$
$37$	10.3923	1.70848	0.854242	+	0.519875i	$0.174022\pi$
$38$	−0.392305	−0.0636402
$39$	0	0
$40$	−2.53590	−0.400961
$41$	10.7321	1.67606	0.838032	−	0.545621i	$-0.183706\pi$
$41$	10.7321	1.67606	0.838032	+	0.545621i	$0.183706\pi$
$42$	−1.26795	−0.195649
$43$	−9.19615	−1.40240	−0.701200	−	0.712965i	$-0.747352\pi$
$43$	−9.19615	−1.40240	−0.701200	+	0.712965i	$0.747352\pi$
$44$	−2.92820	−0.441443
$45$	−1.00000	−0.149071
$46$	−1.46410	−0.215870
$47$	−0.196152	−0.0286118	−0.0143059	−	0.999898i	$-0.504554\pi$
$47$	−0.196152	−0.0286118	−0.0143059	+	0.999898i	$0.504554\pi$
$48$	1.07180	0.154701
$49$	−4.00000	−0.571429
$50$	−0.732051	−0.103528
$51$	0.732051	0.102508
$52$	0	0
$53$	−9.46410	−1.29999	−0.649997	−	0.759937i	$-0.725230\pi$
$53$	−9.46410	−1.29999	−0.649997	+	0.759937i	$0.725230\pi$
$54$	−0.732051	−0.0996195
$55$	−2.00000	−0.269680
$56$	4.39230	0.586946
$57$	0.535898	0.0709815
$58$	2.39230	0.314125
$59$	11.6603	1.51804	0.759018	−	0.651070i	$-0.225679\pi$
$59$	11.6603	1.51804	0.759018	+	0.651070i	$0.225679\pi$
$60$	1.46410	0.189015
$61$	5.39230	0.690414	0.345207	−	0.938527i	$-0.387809\pi$
$61$	5.39230	0.690414	0.345207	+	0.938527i	$0.387809\pi$
$62$	3.26795	0.415030
$63$	1.73205	0.218218
$64$	2.14359	0.267949
$65$	0	0
$66$	−1.46410	−0.180218
$67$	9.19615	1.12349	0.561744	−	0.827311i	$-0.310130\pi$
$67$	9.19615	1.12349	0.561744	+	0.827311i	$0.310130\pi$
$68$	−1.07180	−0.129974
$69$	2.00000	0.240772
$70$	1.26795	0.151549
$71$	4.73205	0.561591	0.280796	−	0.959768i	$-0.409402\pi$
$71$	4.73205	0.561591	0.280796	+	0.959768i	$0.409402\pi$
$72$	2.53590	0.298858
$73$	−1.73205	−0.202721	−0.101361	−	0.994850i	$-0.532320\pi$
$73$	−1.73205	−0.202721	−0.101361	+	0.994850i	$0.532320\pi$
$74$	−7.60770	−0.884377
$75$	1.00000	0.115470
$76$	−0.784610	−0.0900009
$77$	3.46410	0.394771
$78$	0	0
$79$	−11.0000	−1.23760	−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000	−1.23760	−0.618798	+	0.785550i	$0.712380\pi$
$80$	−1.07180	−0.119831
$81$	1.00000	0.111111
$82$	−7.85641	−0.867595
$83$	−2.92820	−0.321412	−0.160706	−	0.987002i	$-0.551377\pi$
$83$	−2.92820	−0.321412	−0.160706	+	0.987002i	$0.551377\pi$
$84$	−2.53590	−0.276689
$85$	−0.732051	−0.0794021
$86$	6.73205	0.725936
$87$	−3.26795	−0.350361
$88$	5.07180	0.540655
$89$	−5.26795	−0.558401	−0.279201	−	0.960233i	$-0.590069\pi$
$89$	−5.26795	−0.558401	−0.279201	+	0.960233i	$0.590069\pi$
$90$	0.732051	0.0771649
$91$	0	0
$92$	−2.92820	−0.305286
$93$	−4.46410	−0.462906
$94$	0.143594	0.0148105
$95$	−0.535898	−0.0549820
$96$	−5.85641	−0.597717
$97$	−5.19615	−0.527589	−0.263795	−	0.964579i	$-0.584974\pi$
$97$	−5.19615	−0.527589	−0.263795	+	0.964579i	$0.584974\pi$
$98$	2.92820	0.295793
$99$	2.00000	0.201008
$100$	−1.46410	−0.146410
$101$	10.3923	1.03407	0.517036	−	0.855963i	$-0.327035\pi$
$101$	10.3923	1.03407	0.517036	+	0.855963i	$0.327035\pi$
$102$	−0.535898	−0.0530618
$103$	5.73205	0.564796	0.282398	−	0.959297i	$-0.408870\pi$
$103$	5.73205	0.564796	0.282398	+	0.959297i	$0.408870\pi$
$104$	0	0
$105$	−1.73205	−0.169031
$106$	6.92820	0.672927
$107$	8.19615	0.792352	0.396176	−	0.918175i	$-0.370337\pi$
$107$	8.19615	0.792352	0.396176	+	0.918175i	$0.370337\pi$
$108$	−1.46410	−0.140883
$109$	15.3923	1.47432	0.737158	−	0.675721i	$-0.236167\pi$
$109$	15.3923	1.47432	0.737158	+	0.675721i	$0.236167\pi$
$110$	1.46410	0.139597
$111$	10.3923	0.986394
$112$	1.85641	0.175414
$113$	18.3923	1.73020	0.865101	−	0.501597i	$-0.167254\pi$
$113$	18.3923	1.73020	0.865101	+	0.501597i	$0.167254\pi$
$114$	−0.392305	−0.0367427
$115$	−2.00000	−0.186501
$116$	4.78461	0.444240
$117$	0	0
$118$	−8.53590	−0.785793
$119$	1.26795	0.116233
$120$	−2.53590	−0.231495
$121$	−7.00000	−0.636364
$122$	−3.94744	−0.357385
$123$	10.7321	0.967676
$124$	6.53590	0.586941
$125$	−1.00000	−0.0894427
$126$	−1.26795	−0.112958
$127$	−0.660254	−0.0585881	−0.0292940	−	0.999571i	$-0.509326\pi$
$127$	−0.660254	−0.0585881	−0.0292940	+	0.999571i	$0.509326\pi$
$128$	10.1436	0.896575
$129$	−9.19615	−0.809676
$130$	0	0
$131$	−2.19615	−0.191879	−0.0959394	−	0.995387i	$-0.530585\pi$
$131$	−2.19615	−0.191879	−0.0959394	+	0.995387i	$0.530585\pi$
$132$	−2.92820	−0.254867
$133$	0.928203	0.0804854
$134$	−6.73205	−0.581561
$135$	−1.00000	−0.0860663
$136$	1.85641	0.159186
$137$	11.6603	0.996203	0.498101	−	0.867119i	$-0.334031\pi$
$137$	11.6603	0.996203	0.498101	+	0.867119i	$0.334031\pi$
$138$	−1.46410	−0.124633
$139$	19.9282	1.69029	0.845144	−	0.534539i	$-0.179515\pi$
$139$	19.9282	1.69029	0.845144	+	0.534539i	$0.179515\pi$
$140$	2.53590	0.214323
$141$	−0.196152	−0.0165190
$142$	−3.46410	−0.290701
$143$	0	0
$144$	1.07180	0.0893164
$145$	3.26795	0.271388
$146$	1.26795	0.104936
$147$	−4.00000	−0.329914
$148$	−15.2154	−1.25070
$149$	5.85641	0.479776	0.239888	−	0.970801i	$-0.422889\pi$
$149$	5.85641	0.479776	0.239888	+	0.970801i	$0.422889\pi$
$150$	−0.732051	−0.0597717
$151$	0.928203	0.0755361	0.0377681	−	0.999287i	$-0.487975\pi$
$151$	0.928203	0.0755361	0.0377681	+	0.999287i	$0.487975\pi$
$152$	1.35898	0.110228
$153$	0.732051	0.0591828
$154$	−2.53590	−0.204349
$155$	4.46410	0.358565
$156$	0	0
$157$	−3.73205	−0.297850	−0.148925	−	0.988848i	$-0.547581\pi$
$157$	−3.73205	−0.297850	−0.148925	+	0.988848i	$0.547581\pi$
$158$	8.05256	0.640627
$159$	−9.46410	−0.750552
$160$	5.85641	0.462990
$161$	3.46410	0.273009
$162$	−0.732051	−0.0575153
$163$	−21.1962	−1.66021	−0.830105	−	0.557607i	$-0.811720\pi$
$163$	−21.1962	−1.66021	−0.830105	+	0.557607i	$0.811720\pi$
$164$	−15.7128	−1.22696
$165$	−2.00000	−0.155700
$166$	2.14359	0.166375
$167$	21.8564	1.69130	0.845650	−	0.533738i	$-0.179213\pi$
$167$	21.8564	1.69130	0.845650	+	0.533738i	$0.179213\pi$
$168$	4.39230	0.338874
$169$	0	0
$170$	0.535898	0.0411015
$171$	0.535898	0.0409812
$172$	13.4641	1.02663
$173$	12.1962	0.927256	0.463628	−	0.886030i	$-0.346547\pi$
$173$	12.1962	0.927256	0.463628	+	0.886030i	$0.346547\pi$
$174$	2.39230	0.181360
$175$	1.73205	0.130931
$176$	2.14359	0.161579
$177$	11.6603	0.876438
$178$	3.85641	0.289050
$179$	17.6603	1.31999	0.659995	−	0.751270i	$-0.270559\pi$
$179$	17.6603	1.31999	0.659995	+	0.751270i	$0.270559\pi$
$180$	1.46410	0.109128
$181$	8.39230	0.623795	0.311898	−	0.950116i	$-0.399035\pi$
$181$	8.39230	0.623795	0.311898	+	0.950116i	$0.399035\pi$
$182$	0	0
$183$	5.39230	0.398611
$184$	5.07180	0.373898
$185$	−10.3923	−0.764057
$186$	3.26795	0.239618
$187$	1.46410	0.107066
$188$	0.287187	0.0209453
$189$	1.73205	0.125988
$190$	0.392305	0.0284608
$191$	22.5885	1.63444	0.817222	−	0.576323i	$-0.195513\pi$
$191$	22.5885	1.63444	0.817222	+	0.576323i	$0.195513\pi$
$192$	2.14359	0.154701
$193$	19.1962	1.38177	0.690885	−	0.722965i	$-0.257221\pi$
$193$	19.1962	1.38177	0.690885	+	0.722965i	$0.257221\pi$
$194$	3.80385	0.273100
$195$	0	0
$196$	5.85641	0.418315
$197$	−16.3923	−1.16790	−0.583952	−	0.811788i	$-0.698494\pi$
$197$	−16.3923	−1.16790	−0.583952	+	0.811788i	$0.698494\pi$
$198$	−1.46410	−0.104049
$199$	−24.8564	−1.76202	−0.881012	−	0.473094i	$-0.843137\pi$
$199$	−24.8564	−1.76202	−0.881012	+	0.473094i	$0.843137\pi$
$200$	2.53590	0.179315
$201$	9.19615	0.648647
$202$	−7.60770	−0.535276
$203$	−5.66025	−0.397272
$204$	−1.07180	−0.0750408
$205$	−10.7321	−0.749559
$206$	−4.19615	−0.292360
$207$	2.00000	0.139010
$208$	0	0
$209$	1.07180	0.0741377
$210$	1.26795	0.0874968
$211$	22.3205	1.53661	0.768304	−	0.640086i	$-0.221101\pi$
$211$	22.3205	1.53661	0.768304	+	0.640086i	$0.221101\pi$
$212$	13.8564	0.951662
$213$	4.73205	0.324235
$214$	−6.00000	−0.410152
$215$	9.19615	0.627172
$216$	2.53590	0.172546
$217$	−7.73205	−0.524886
$218$	−11.2679	−0.763162
$219$	−1.73205	−0.117041
$220$	2.92820	0.197419
$221$	0	0
$222$	−7.60770	−0.510595
$223$	−1.85641	−0.124314	−0.0621571	−	0.998066i	$-0.519798\pi$
$223$	−1.85641	−0.124314	−0.0621571	+	0.998066i	$0.519798\pi$
$224$	−10.1436	−0.677747
$225$	1.00000	0.0666667
$226$	−13.4641	−0.895619
$227$	4.73205	0.314077	0.157039	−	0.987592i	$-0.449805\pi$
$227$	4.73205	0.314077	0.157039	+	0.987592i	$0.449805\pi$
$228$	−0.784610	−0.0519620
$229$	−12.7846	−0.844831	−0.422415	−	0.906402i	$-0.638818\pi$
$229$	−12.7846	−0.844831	−0.422415	+	0.906402i	$0.638818\pi$
$230$	1.46410	0.0965400
$231$	3.46410	0.227921
$232$	−8.28719	−0.544080
$233$	−28.2487	−1.85063	−0.925317	−	0.379194i	$-0.876201\pi$
$233$	−28.2487	−1.85063	−0.925317	+	0.379194i	$0.876201\pi$
$234$	0	0
$235$	0.196152	0.0127956
$236$	−17.0718	−1.11128
$237$	−11.0000	−0.714527
$238$	−0.928203	−0.0601665
$239$	13.8564	0.896296	0.448148	−	0.893959i	$-0.352084\pi$
$239$	13.8564	0.896296	0.448148	+	0.893959i	$0.352084\pi$
$240$	−1.07180	−0.0691842
$241$	−4.00000	−0.257663	−0.128831	−	0.991667i	$-0.541123\pi$
$241$	−4.00000	−0.257663	−0.128831	+	0.991667i	$0.541123\pi$
$242$	5.12436	0.329406
$243$	1.00000	0.0641500
$244$	−7.89488	−0.505418
$245$	4.00000	0.255551
$246$	−7.85641	−0.500906
$247$	0	0
$248$	−11.3205	−0.718853
$249$	−2.92820	−0.185567
$250$	0.732051	0.0462990
$251$	−6.53590	−0.412542	−0.206271	−	0.978495i	$-0.566133\pi$
$251$	−6.53590	−0.412542	−0.206271	+	0.978495i	$0.566133\pi$
$252$	−2.53590	−0.159747
$253$	4.00000	0.251478
$254$	0.483340	0.0303274
$255$	−0.732051	−0.0458428
$256$	−11.7128	−0.732051
$257$	−2.19615	−0.136992	−0.0684961	−	0.997651i	$-0.521820\pi$
$257$	−2.19615	−0.136992	−0.0684961	+	0.997651i	$0.521820\pi$
$258$	6.73205	0.419119
$259$	18.0000	1.11847
$260$	0	0
$261$	−3.26795	−0.202281
$262$	1.60770	0.0993237
$263$	2.87564	0.177320	0.0886599	−	0.996062i	$-0.471742\pi$
$263$	2.87564	0.177320	0.0886599	+	0.996062i	$0.471742\pi$
$264$	5.07180	0.312148
$265$	9.46410	0.581375
$266$	−0.679492	−0.0416623
$267$	−5.26795	−0.322393
$268$	−13.4641	−0.822451
$269$	−28.5885	−1.74307	−0.871535	−	0.490334i	$-0.836875\pi$
$269$	−28.5885	−1.74307	−0.871535	+	0.490334i	$0.836875\pi$
$270$	0.732051	0.0445512
$271$	−22.4641	−1.36460	−0.682298	−	0.731074i	$-0.739020\pi$
$271$	−22.4641	−1.36460	−0.682298	+	0.731074i	$0.739020\pi$
$272$	0.784610	0.0475740
$273$	0	0
$274$	−8.53590	−0.515672
$275$	2.00000	0.120605
$276$	−2.92820	−0.176257
$277$	−26.3923	−1.58576	−0.792880	−	0.609378i	$-0.791419\pi$
$277$	−26.3923	−1.58576	−0.792880	+	0.609378i	$0.791419\pi$
$278$	−14.5885	−0.874958
$279$	−4.46410	−0.267259
$280$	−4.39230	−0.262490
$281$	11.2679	0.672189	0.336095	−	0.941828i	$-0.390894\pi$
$281$	11.2679	0.672189	0.336095	+	0.941828i	$0.390894\pi$
$282$	0.143594	0.00855087
$283$	16.1244	0.958493	0.479247	−	0.877680i	$-0.340910\pi$
$283$	16.1244	0.958493	0.479247	+	0.877680i	$0.340910\pi$
$284$	−6.92820	−0.411113
$285$	−0.535898	−0.0317439
$286$	0	0
$287$	18.5885	1.09724
$288$	−5.85641	−0.345092
$289$	−16.4641	−0.968477
$290$	−2.39230	−0.140481
$291$	−5.19615	−0.304604
$292$	2.53590	0.148402
$293$	−8.19615	−0.478824	−0.239412	−	0.970918i	$-0.576955\pi$
$293$	−8.19615	−0.478824	−0.239412	+	0.970918i	$0.576955\pi$
$294$	2.92820	0.170776
$295$	−11.6603	−0.678886
$296$	26.3538	1.53179
$297$	2.00000	0.116052
$298$	−4.28719	−0.248350
$299$	0	0
$300$	−1.46410	−0.0845299
$301$	−15.9282	−0.918086
$302$	−0.679492	−0.0391004
$303$	10.3923	0.597022
$304$	0.574374	0.0329426
$305$	−5.39230	−0.308762
$306$	−0.535898	−0.0306353
$307$	6.66025	0.380121	0.190060	−	0.981772i	$-0.439132\pi$
$307$	6.66025	0.380121	0.190060	+	0.981772i	$0.439132\pi$
$308$	−5.07180	−0.288992
$309$	5.73205	0.326085
$310$	−3.26795	−0.185607
$311$	12.5885	0.713826	0.356913	−	0.934138i	$-0.383829\pi$
$311$	12.5885	0.713826	0.356913	+	0.934138i	$0.383829\pi$
$312$	0	0
$313$	19.1962	1.08503	0.542515	−	0.840046i	$-0.317472\pi$
$313$	19.1962	1.08503	0.542515	+	0.840046i	$0.317472\pi$
$314$	2.73205	0.154179
$315$	−1.73205	−0.0975900
$316$	16.1051	0.905984
$317$	28.3923	1.59467	0.797335	−	0.603537i	$-0.206242\pi$
$317$	28.3923	1.59467	0.797335	+	0.603537i	$0.206242\pi$
$318$	6.92820	0.388514
$319$	−6.53590	−0.365940
$320$	−2.14359	−0.119831
$321$	8.19615	0.457465
$322$	−2.53590	−0.141320
$323$	0.392305	0.0218284
$324$	−1.46410	−0.0813390
$325$	0	0
$326$	15.5167	0.859388
$327$	15.3923	0.851196
$328$	27.2154	1.50272
$329$	−0.339746	−0.0187308
$330$	1.46410	0.0805961
$331$	−23.9282	−1.31521	−0.657606	−	0.753362i	$-0.728431\pi$
$331$	−23.9282	−1.31521	−0.657606	+	0.753362i	$0.728431\pi$
$332$	4.28719	0.235290
$333$	10.3923	0.569495
$334$	−16.0000	−0.875481
$335$	−9.19615	−0.502439
$336$	1.85641	0.101275
$337$	25.5885	1.39389	0.696946	−	0.717124i	$-0.254542\pi$
$337$	25.5885	1.39389	0.696946	+	0.717124i	$0.254542\pi$
$338$	0	0
$339$	18.3923	0.998933
$340$	1.07180	0.0581263
$341$	−8.92820	−0.483489
$342$	−0.392305	−0.0212134
$343$	−19.0526	−1.02874
$344$	−23.3205	−1.25736
$345$	−2.00000	−0.107676
$346$	−8.92820	−0.479983
$347$	−1.46410	−0.0785971	−0.0392985	−	0.999228i	$-0.512512\pi$
$347$	−1.46410	−0.0785971	−0.0392985	+	0.999228i	$0.512512\pi$
$348$	4.78461	0.256482
$349$	−30.8564	−1.65171	−0.825853	−	0.563886i	$-0.809306\pi$
$349$	−30.8564	−1.65171	−0.825853	+	0.563886i	$0.809306\pi$
$350$	−1.26795	−0.0677747
$351$	0	0
$352$	−11.7128	−0.624295
$353$	9.60770	0.511366	0.255683	−	0.966761i	$-0.417700\pi$
$353$	9.60770	0.511366	0.255683	+	0.966761i	$0.417700\pi$
$354$	−8.53590	−0.453678
$355$	−4.73205	−0.251151
$356$	7.71281	0.408778
$357$	1.26795	0.0671070
$358$	−12.9282	−0.683277
$359$	−0.196152	−0.0103525	−0.00517626	−	0.999987i	$-0.501648\pi$
$359$	−0.196152	−0.0103525	−0.00517626	+	0.999987i	$0.501648\pi$
$360$	−2.53590	−0.133654
$361$	−18.7128	−0.984885
$362$	−6.14359	−0.322900
$363$	−7.00000	−0.367405
$364$	0	0
$365$	1.73205	0.0906597
$366$	−3.94744	−0.206336
$367$	15.0526	0.785737	0.392869	−	0.919595i	$-0.371483\pi$
$367$	15.0526	0.785737	0.392869	+	0.919595i	$0.371483\pi$
$368$	2.14359	0.111743
$369$	10.7321	0.558688
$370$	7.60770	0.395505
$371$	−16.3923	−0.851046
$372$	6.53590	0.338871
$373$	7.33975	0.380038	0.190019	−	0.981780i	$-0.439145\pi$
$373$	7.33975	0.380038	0.190019	+	0.981780i	$0.439145\pi$
$374$	−1.07180	−0.0554213
$375$	−1.00000	−0.0516398
$376$	−0.497423	−0.0256526
$377$	0	0
$378$	−1.26795	−0.0652163
$379$	−6.46410	−0.332039	−0.166019	−	0.986123i	$-0.553091\pi$
$379$	−6.46410	−0.332039	−0.166019	+	0.986123i	$0.553091\pi$
$380$	0.784610	0.0402496
$381$	−0.660254	−0.0338258
$382$	−16.5359	−0.846050
$383$	19.2679	0.984546	0.492273	−	0.870441i	$-0.336166\pi$
$383$	19.2679	0.984546	0.492273	+	0.870441i	$0.336166\pi$
$384$	10.1436	0.517638
$385$	−3.46410	−0.176547
$386$	−14.0526	−0.715256
$387$	−9.19615	−0.467467
$388$	7.60770	0.386222
$389$	−14.5359	−0.736999	−0.368500	−	0.929628i	$-0.620128\pi$
$389$	−14.5359	−0.736999	−0.368500	+	0.929628i	$0.620128\pi$
$390$	0	0
$391$	1.46410	0.0740428
$392$	−10.1436	−0.512329
$393$	−2.19615	−0.110781
$394$	12.0000	0.604551
$395$	11.0000	0.553470
$396$	−2.92820	−0.147148
$397$	−9.73205	−0.488438	−0.244219	−	0.969720i	$-0.578532\pi$
$397$	−9.73205	−0.488438	−0.244219	+	0.969720i	$0.578532\pi$
$398$	18.1962	0.912091
$399$	0.928203	0.0464683
$400$	1.07180	0.0535898
$401$	30.2487	1.51055	0.755274	−	0.655409i	$-0.227504\pi$
$401$	30.2487	1.51055	0.755274	+	0.655409i	$0.227504\pi$
$402$	−6.73205	−0.335764
$403$	0	0
$404$	−15.2154	−0.756994
$405$	−1.00000	−0.0496904
$406$	4.14359	0.205643
$407$	20.7846	1.03025
$408$	1.85641	0.0919058
$409$	−6.32051	−0.312529	−0.156265	−	0.987715i	$-0.549945\pi$
$409$	−6.32051	−0.312529	−0.156265	+	0.987715i	$0.549945\pi$
$410$	7.85641	0.388000
$411$	11.6603	0.575158
$412$	−8.39230	−0.413459
$413$	20.1962	0.993788
$414$	−1.46410	−0.0719567
$415$	2.92820	0.143740
$416$	0	0
$417$	19.9282	0.975888
$418$	−0.784610	−0.0383765
$419$	−39.9090	−1.94968	−0.974840	−	0.222905i	$-0.928446\pi$
$419$	−39.9090	−1.94968	−0.974840	+	0.222905i	$0.928446\pi$
$420$	2.53590	0.123739
$421$	−12.8564	−0.626583	−0.313291	−	0.949657i	$-0.601432\pi$
$421$	−12.8564	−0.626583	−0.313291	+	0.949657i	$0.601432\pi$
$422$	−16.3397	−0.795406
$423$	−0.196152	−0.00953726
$424$	−24.0000	−1.16554
$425$	0.732051	0.0355097
$426$	−3.46410	−0.167836
$427$	9.33975	0.451982
$428$	−12.0000	−0.580042
$429$	0	0
$430$	−6.73205	−0.324648
$431$	21.0718	1.01499	0.507496	−	0.861654i	$-0.330571\pi$
$431$	21.0718	1.01499	0.507496	+	0.861654i	$0.330571\pi$
$432$	1.07180	0.0515668
$433$	19.0526	0.915608	0.457804	−	0.889053i	$-0.348636\pi$
$433$	19.0526	0.915608	0.457804	+	0.889053i	$0.348636\pi$
$434$	5.66025	0.271701
$435$	3.26795	0.156686
$436$	−22.5359	−1.07927
$437$	1.07180	0.0512710
$438$	1.26795	0.0605850
$439$	−19.3923	−0.925544	−0.462772	−	0.886477i	$-0.653145\pi$
$439$	−19.3923	−0.925544	−0.462772	+	0.886477i	$0.653145\pi$
$440$	−5.07180	−0.241788
$441$	−4.00000	−0.190476
$442$	0	0
$443$	29.1244	1.38374	0.691870	−	0.722022i	$-0.256787\pi$
$443$	29.1244	1.38374	0.691870	+	0.722022i	$0.256787\pi$
$444$	−15.2154	−0.722090
$445$	5.26795	0.249725
$446$	1.35898	0.0643498
$447$	5.85641	0.276999
$448$	3.71281	0.175414
$449$	−15.4641	−0.729796	−0.364898	−	0.931047i	$-0.618896\pi$
$449$	−15.4641	−0.729796	−0.364898	+	0.931047i	$0.618896\pi$
$450$	−0.732051	−0.0345092
$451$	21.4641	1.01071
$452$	−26.9282	−1.26660
$453$	0.928203	0.0436108
$454$	−3.46410	−0.162578
$455$	0	0
$456$	1.35898	0.0636402
$457$	14.5167	0.679061	0.339530	−	0.940595i	$-0.389732\pi$
$457$	14.5167	0.679061	0.339530	+	0.940595i	$0.389732\pi$
$458$	9.35898	0.437317
$459$	0.732051	0.0341692
$460$	2.92820	0.136528
$461$	10.0526	0.468194	0.234097	−	0.972213i	$-0.424787\pi$
$461$	10.0526	0.468194	0.234097	+	0.972213i	$0.424787\pi$
$462$	−2.53590	−0.117981
$463$	1.33975	0.0622633	0.0311316	−	0.999515i	$-0.490089\pi$
$463$	1.33975	0.0622633	0.0311316	+	0.999515i	$0.490089\pi$
$464$	−3.50258	−0.162603
$465$	4.46410	0.207018
$466$	20.6795	0.957959
$467$	10.3397	0.478466	0.239233	−	0.970962i	$-0.423104\pi$
$467$	10.3397	0.478466	0.239233	+	0.970962i	$0.423104\pi$
$468$	0	0
$469$	15.9282	0.735496
$470$	−0.143594	−0.00662348
$471$	−3.73205	−0.171964
$472$	29.5692	1.36103
$473$	−18.3923	−0.845679
$474$	8.05256	0.369866
$475$	0.535898	0.0245887
$476$	−1.85641	−0.0850883
$477$	−9.46410	−0.433331
$478$	−10.1436	−0.463957
$479$	−38.8372	−1.77452	−0.887258	−	0.461274i	$-0.847393\pi$
$479$	−38.8372	−1.77452	−0.887258	+	0.461274i	$0.847393\pi$
$480$	5.85641	0.267307
$481$	0	0
$482$	2.92820	0.133376
$483$	3.46410	0.157622
$484$	10.2487	0.465851
$485$	5.19615	0.235945
$486$	−0.732051	−0.0332065
$487$	−5.60770	−0.254109	−0.127054	−	0.991896i	$-0.540552\pi$
$487$	−5.60770	−0.254109	−0.127054	+	0.991896i	$0.540552\pi$
$488$	13.6743	0.619008
$489$	−21.1962	−0.958523
$490$	−2.92820	−0.132283
$491$	−18.9808	−0.856590	−0.428295	−	0.903639i	$-0.640886\pi$
$491$	−18.9808	−0.856590	−0.428295	+	0.903639i	$0.640886\pi$
$492$	−15.7128	−0.708388
$493$	−2.39230	−0.107744
$494$	0	0
$495$	−2.00000	−0.0898933
$496$	−4.78461	−0.214835
$497$	8.19615	0.367648
$498$	2.14359	0.0960567
$499$	25.3205	1.13350	0.566751	−	0.823889i	$-0.308200\pi$
$499$	25.3205	1.13350	0.566751	+	0.823889i	$0.308200\pi$
$500$	1.46410	0.0654766
$501$	21.8564	0.976472
$502$	4.78461	0.213548
$503$	−12.9282	−0.576440	−0.288220	−	0.957564i	$-0.593063\pi$
$503$	−12.9282	−0.576440	−0.288220	+	0.957564i	$0.593063\pi$
$504$	4.39230	0.195649
$505$	−10.3923	−0.462451
$506$	−2.92820	−0.130175
$507$	0	0
$508$	0.966679	0.0428894
$509$	18.0000	0.797836	0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000	0.797836	0.398918	+	0.916987i	$0.369386\pi$
$510$	0.535898	0.0237300
$511$	−3.00000	−0.132712
$512$	−11.7128	−0.517638
$513$	0.535898	0.0236605
$514$	1.60770	0.0709124
$515$	−5.73205	−0.252584
$516$	13.4641	0.592724
$517$	−0.392305	−0.0172535
$518$	−13.1769	−0.578960
$519$	12.1962	0.535352
$520$	0	0
$521$	23.8038	1.04287	0.521433	−	0.853292i	$-0.325398\pi$
$521$	23.8038	1.04287	0.521433	+	0.853292i	$0.325398\pi$
$522$	2.39230	0.104708
$523$	29.1769	1.27582	0.637909	−	0.770112i	$-0.279800\pi$
$523$	29.1769	1.27582	0.637909	+	0.770112i	$0.279800\pi$
$524$	3.21539	0.140465
$525$	1.73205	0.0755929
$526$	−2.10512	−0.0917875
$527$	−3.26795	−0.142354
$528$	2.14359	0.0932879
$529$	−19.0000	−0.826087
$530$	−6.92820	−0.300942
$531$	11.6603	0.506012
$532$	−1.35898	−0.0589194
$533$	0	0
$534$	3.85641	0.166883
$535$	−8.19615	−0.354351
$536$	23.3205	1.00729
$537$	17.6603	0.762096
$538$	20.9282	0.902279
$539$	−8.00000	−0.344584
$540$	1.46410	0.0630049
$541$	−11.2487	−0.483620	−0.241810	−	0.970324i	$-0.577741\pi$
$541$	−11.2487	−0.483620	−0.241810	+	0.970324i	$0.577741\pi$
$542$	16.4449	0.706367
$543$	8.39230	0.360148
$544$	−4.28719	−0.183812
$545$	−15.3923	−0.659334
$546$	0	0
$547$	−31.9808	−1.36740	−0.683699	−	0.729764i	$-0.739630\pi$
$547$	−31.9808	−1.36740	−0.683699	+	0.729764i	$0.739630\pi$
$548$	−17.0718	−0.729271
$549$	5.39230	0.230138
$550$	−1.46410	−0.0624295
$551$	−1.75129	−0.0746074
$552$	5.07180	0.215870
$553$	−19.0526	−0.810197
$554$	19.3205	0.820850
$555$	−10.3923	−0.441129
$556$	−29.1769	−1.23738
$557$	−9.46410	−0.401007	−0.200503	−	0.979693i	$-0.564258\pi$
$557$	−9.46410	−0.401007	−0.200503	+	0.979693i	$0.564258\pi$
$558$	3.26795	0.138343
$559$	0	0
$560$	−1.85641	−0.0784475
$561$	1.46410	0.0618144
$562$	−8.24871	−0.347951
$563$	−34.7846	−1.46600	−0.732998	−	0.680231i	$-0.761880\pi$
$563$	−34.7846	−1.46600	−0.732998	+	0.680231i	$0.761880\pi$
$564$	0.287187	0.0120928
$565$	−18.3923	−0.773770
$566$	−11.8038	−0.496153
$567$	1.73205	0.0727393
$568$	12.0000	0.503509
$569$	−18.9808	−0.795715	−0.397857	−	0.917447i	$-0.630246\pi$
$569$	−18.9808	−0.795715	−0.397857	+	0.917447i	$0.630246\pi$
$570$	0.392305	0.0164318
$571$	−42.7846	−1.79048	−0.895240	−	0.445584i	$-0.852996\pi$
$571$	−42.7846	−1.79048	−0.895240	+	0.445584i	$0.852996\pi$
$572$	0	0
$573$	22.5885	0.943646
$574$	−13.6077	−0.567974
$575$	2.00000	0.0834058
$576$	2.14359	0.0893164
$577$	8.53590	0.355354	0.177677	−	0.984089i	$-0.443142\pi$
$577$	8.53590	0.355354	0.177677	+	0.984089i	$0.443142\pi$
$578$	12.0526	0.501320
$579$	19.1962	0.797765
$580$	−4.78461	−0.198670
$581$	−5.07180	−0.210414
$582$	3.80385	0.157675
$583$	−18.9282	−0.783926
$584$	−4.39230	−0.181755
$585$	0	0
$586$	6.00000	0.247858
$587$	−28.9808	−1.19616	−0.598082	−	0.801435i	$-0.704070\pi$
$587$	−28.9808	−1.19616	−0.598082	+	0.801435i	$0.704070\pi$
$588$	5.85641	0.241514
$589$	−2.39230	−0.0985732
$590$	8.53590	0.351417
$591$	−16.3923	−0.674289
$592$	11.1384	0.457787
$593$	15.4641	0.635035	0.317517	−	0.948252i	$-0.397151\pi$
$593$	15.4641	0.635035	0.317517	+	0.948252i	$0.397151\pi$
$594$	−1.46410	−0.0600728
$595$	−1.26795	−0.0519808
$596$	−8.57437	−0.351220
$597$	−24.8564	−1.01730
$598$	0	0
$599$	−18.9808	−0.775533	−0.387766	−	0.921758i	$-0.626753\pi$
$599$	−18.9808	−0.775533	−0.387766	+	0.921758i	$0.626753\pi$
$600$	2.53590	0.103528
$601$	−10.5359	−0.429768	−0.214884	−	0.976640i	$-0.568937\pi$
$601$	−10.5359	−0.429768	−0.214884	+	0.976640i	$0.568937\pi$
$602$	11.6603	0.475236
$603$	9.19615	0.374496
$604$	−1.35898	−0.0552963
$605$	7.00000	0.284590
$606$	−7.60770	−0.309041
$607$	18.3923	0.746521	0.373260	−	0.927727i	$-0.378240\pi$
$607$	18.3923	0.746521	0.373260	+	0.927727i	$0.378240\pi$
$608$	−3.13844	−0.127280
$609$	−5.66025	−0.229365
$610$	3.94744	0.159827
$611$	0	0
$612$	−1.07180	−0.0433248
$613$	−28.2679	−1.14173	−0.570866	−	0.821043i	$-0.693392\pi$
$613$	−28.2679	−1.14173	−0.570866	+	0.821043i	$0.693392\pi$
$614$	−4.87564	−0.196765
$615$	−10.7321	−0.432758
$616$	8.78461	0.353942
$617$	34.1051	1.37302	0.686510	−	0.727120i	$-0.259142\pi$
$617$	34.1051	1.37302	0.686510	+	0.727120i	$0.259142\pi$
$618$	−4.19615	−0.168794
$619$	−31.9282	−1.28330	−0.641651	−	0.766996i	$-0.721750\pi$
$619$	−31.9282	−1.28330	−0.641651	+	0.766996i	$0.721750\pi$
$620$	−6.53590	−0.262488
$621$	2.00000	0.0802572
$622$	−9.21539	−0.369503
$623$	−9.12436	−0.365560
$624$	0	0
$625$	1.00000	0.0400000
$626$	−14.0526	−0.561653
$627$	1.07180	0.0428034
$628$	5.46410	0.218041
$629$	7.60770	0.303339
$630$	1.26795	0.0505163
$631$	−25.3923	−1.01085	−0.505426	−	0.862870i	$-0.668665\pi$
$631$	−25.3923	−1.01085	−0.505426	+	0.862870i	$0.668665\pi$
$632$	−27.8949	−1.10960
$633$	22.3205	0.887161
$634$	−20.7846	−0.825462
$635$	0.660254	0.0262014
$636$	13.8564	0.549442
$637$	0	0
$638$	4.78461	0.189425
$639$	4.73205	0.187197
$640$	−10.1436	−0.400961
$641$	−3.46410	−0.136824	−0.0684119	−	0.997657i	$-0.521793\pi$
$641$	−3.46410	−0.136824	−0.0684119	+	0.997657i	$0.521793\pi$
$642$	−6.00000	−0.236801
$643$	−13.5885	−0.535876	−0.267938	−	0.963436i	$-0.586342\pi$
$643$	−13.5885	−0.535876	−0.267938	+	0.963436i	$0.586342\pi$
$644$	−5.07180	−0.199857
$645$	9.19615	0.362098
$646$	−0.287187	−0.0112992
$647$	−4.14359	−0.162901	−0.0814507	−	0.996677i	$-0.525955\pi$
$647$	−4.14359	−0.162901	−0.0814507	+	0.996677i	$0.525955\pi$
$648$	2.53590	0.0996195
$649$	23.3205	0.915410
$650$	0	0
$651$	−7.73205	−0.303043
$652$	31.0333	1.21536
$653$	13.5167	0.528948	0.264474	−	0.964393i	$-0.414802\pi$
$653$	13.5167	0.528948	0.264474	+	0.964393i	$0.414802\pi$
$654$	−11.2679	−0.440612
$655$	2.19615	0.0858108
$656$	11.5026	0.449100
$657$	−1.73205	−0.0675737
$658$	0.248711	0.00969578
$659$	−18.2487	−0.710869	−0.355434	−	0.934701i	$-0.615667\pi$
$659$	−18.2487	−0.710869	−0.355434	+	0.934701i	$0.615667\pi$
$660$	2.92820	0.113980
$661$	−36.1769	−1.40712	−0.703559	−	0.710636i	$-0.748407\pi$
$661$	−36.1769	−1.40712	−0.703559	+	0.710636i	$0.748407\pi$
$662$	17.5167	0.680804
$663$	0	0
$664$	−7.42563	−0.288170
$665$	−0.928203	−0.0359942
$666$	−7.60770	−0.294792
$667$	−6.53590	−0.253071
$668$	−32.0000	−1.23812
$669$	−1.85641	−0.0717728
$670$	6.73205	0.260082
$671$	10.7846	0.416335
$672$	−10.1436	−0.391298
$673$	−12.9474	−0.499087	−0.249544	−	0.968364i	$-0.580281\pi$
$673$	−12.9474	−0.499087	−0.249544	+	0.968364i	$0.580281\pi$
$674$	−18.7321	−0.721532
$675$	1.00000	0.0384900
$676$	0	0
$677$	50.9282	1.95733	0.978665	−	0.205463i	$-0.0658700\pi$
$677$	50.9282	1.95733	0.978665	+	0.205463i	$0.0658700\pi$
$678$	−13.4641	−0.517086
$679$	−9.00000	−0.345388
$680$	−1.85641	−0.0711899
$681$	4.73205	0.181333
$682$	6.53590	0.250272
$683$	−16.5885	−0.634740	−0.317370	−	0.948302i	$-0.602800\pi$
$683$	−16.5885	−0.634740	−0.317370	+	0.948302i	$0.602800\pi$
$684$	−0.784610	−0.0300003
$685$	−11.6603	−0.445515
$686$	13.9474	0.532516
$687$	−12.7846	−0.487763
$688$	−9.85641	−0.375772
$689$	0	0
$690$	1.46410	0.0557374
$691$	27.9282	1.06244	0.531219	−	0.847234i	$-0.321734\pi$
$691$	27.9282	1.06244	0.531219	+	0.847234i	$0.321734\pi$
$692$	−17.8564	−0.678799
$693$	3.46410	0.131590
$694$	1.07180	0.0406848
$695$	−19.9282	−0.755920
$696$	−8.28719	−0.314125
$697$	7.85641	0.297583
$698$	22.5885	0.854986
$699$	−28.2487	−1.06846
$700$	−2.53590	−0.0958479
$701$	−37.4641	−1.41500	−0.707500	−	0.706714i	$-0.750177\pi$
$701$	−37.4641	−1.41500	−0.707500	+	0.706714i	$0.750177\pi$
$702$	0	0
$703$	5.56922	0.210047
$704$	4.28719	0.161579
$705$	0.196152	0.00738753
$706$	−7.03332	−0.264703
$707$	18.0000	0.676960
$708$	−17.0718	−0.641597
$709$	37.2487	1.39890	0.699452	−	0.714679i	$-0.253427\pi$
$709$	37.2487	1.39890	0.699452	+	0.714679i	$0.253427\pi$
$710$	3.46410	0.130005
$711$	−11.0000	−0.412532
$712$	−13.3590	−0.500649
$713$	−8.92820	−0.334364
$714$	−0.928203	−0.0347371
$715$	0	0
$716$	−25.8564	−0.966299
$717$	13.8564	0.517477
$718$	0.143594	0.00535886
$719$	23.6603	0.882379	0.441189	−	0.897414i	$-0.354557\pi$
$719$	23.6603	0.882379	0.441189	+	0.897414i	$0.354557\pi$
$720$	−1.07180	−0.0399435
$721$	9.92820	0.369746
$722$	13.6987	0.509814
$723$	−4.00000	−0.148762
$724$	−12.2872	−0.456650
$725$	−3.26795	−0.121369
$726$	5.12436	0.190183
$727$	−2.66025	−0.0986634	−0.0493317	−	0.998782i	$-0.515709\pi$
$727$	−2.66025	−0.0986634	−0.0493317	+	0.998782i	$0.515709\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.26795	−0.0469289
$731$	−6.73205	−0.248994
$732$	−7.89488	−0.291803
$733$	−13.9808	−0.516391	−0.258196	−	0.966093i	$-0.583128\pi$
$733$	−13.9808	−0.516391	−0.258196	+	0.966093i	$0.583128\pi$
$734$	−11.0192	−0.406727
$735$	4.00000	0.147542
$736$	−11.7128	−0.431740
$737$	18.3923	0.677489
$738$	−7.85641	−0.289198
$739$	−1.07180	−0.0394267	−0.0197133	−	0.999806i	$-0.506275\pi$
$739$	−1.07180	−0.0394267	−0.0197133	+	0.999806i	$0.506275\pi$
$740$	15.2154	0.559329
$741$	0	0
$742$	12.0000	0.440534
$743$	35.9090	1.31737	0.658686	−	0.752418i	$-0.271113\pi$
$743$	35.9090	1.31737	0.658686	+	0.752418i	$0.271113\pi$
$744$	−11.3205	−0.415030
$745$	−5.85641	−0.214562
$746$	−5.37307	−0.196722
$747$	−2.92820	−0.107137
$748$	−2.14359	−0.0783775
$749$	14.1962	0.518716
$750$	0.732051	0.0267307
$751$	10.3923	0.379221	0.189610	−	0.981859i	$-0.439278\pi$
$751$	10.3923	0.379221	0.189610	+	0.981859i	$0.439278\pi$
$752$	−0.210236	−0.00766650
$753$	−6.53590	−0.238181
$754$	0	0
$755$	−0.928203	−0.0337808
$756$	−2.53590	−0.0922297
$757$	−18.9282	−0.687957	−0.343979	−	0.938977i	$-0.611775\pi$
$757$	−18.9282	−0.687957	−0.343979	+	0.938977i	$0.611775\pi$
$758$	4.73205	0.171876
$759$	4.00000	0.145191
$760$	−1.35898	−0.0492955
$761$	25.0718	0.908852	0.454426	−	0.890785i	$-0.349844\pi$
$761$	25.0718	0.908852	0.454426	+	0.890785i	$0.349844\pi$
$762$	0.483340	0.0175095
$763$	26.6603	0.965166
$764$	−33.0718	−1.19650
$765$	−0.732051	−0.0264674
$766$	−14.1051	−0.509639
$767$	0	0
$768$	−11.7128	−0.422650
$769$	8.78461	0.316781	0.158391	−	0.987377i	$-0.449369\pi$
$769$	8.78461	0.316781	0.158391	+	0.987377i	$0.449369\pi$
$770$	2.53590	0.0913874
$771$	−2.19615	−0.0790925
$772$	−28.1051	−1.01153
$773$	−22.3923	−0.805395	−0.402698	−	0.915333i	$-0.631927\pi$
$773$	−22.3923	−0.805395	−0.402698	+	0.915333i	$0.631927\pi$
$774$	6.73205	0.241979
$775$	−4.46410	−0.160355
$776$	−13.1769	−0.473024
$777$	18.0000	0.645746
$778$	10.6410	0.381499
$779$	5.75129	0.206061
$780$	0	0
$781$	9.46410	0.338652
$782$	−1.07180	−0.0383274
$783$	−3.26795	−0.116787
$784$	−4.28719	−0.153114
$785$	3.73205	0.133203
$786$	1.60770	0.0573446
$787$	−44.1244	−1.57286	−0.786432	−	0.617677i	$-0.788074\pi$
$787$	−44.1244	−1.57286	−0.786432	+	0.617677i	$0.788074\pi$
$788$	24.0000	0.854965
$789$	2.87564	0.102376
$790$	−8.05256	−0.286497
$791$	31.8564	1.13268
$792$	5.07180	0.180218
$793$	0	0
$794$	7.12436	0.252834
$795$	9.46410	0.335657
$796$	36.3923	1.28989
$797$	−7.66025	−0.271340	−0.135670	−	0.990754i	$-0.543319\pi$
$797$	−7.66025	−0.271340	−0.135670	+	0.990754i	$0.543319\pi$
$798$	−0.679492	−0.0240538
$799$	−0.143594	−0.00507997
$800$	−5.85641	−0.207055
$801$	−5.26795	−0.186134
$802$	−22.1436	−0.781917
$803$	−3.46410	−0.122245
$804$	−13.4641	−0.474842
$805$	−3.46410	−0.122094
$806$	0	0
$807$	−28.5885	−1.00636
$808$	26.3538	0.927124
$809$	−44.1051	−1.55065	−0.775327	−	0.631560i	$-0.782415\pi$
$809$	−44.1051	−1.55065	−0.775327	+	0.631560i	$0.782415\pi$
$810$	0.732051	0.0257216
$811$	17.6410	0.619460	0.309730	−	0.950825i	$-0.399761\pi$
$811$	17.6410	0.619460	0.309730	+	0.950825i	$0.399761\pi$
$812$	8.28719	0.290823
$813$	−22.4641	−0.787850
$814$	−15.2154	−0.533299
$815$	21.1962	0.742469
$816$	0.784610	0.0274668
$817$	−4.92820	−0.172416
$818$	4.62693	0.161777
$819$	0	0
$820$	15.7128	0.548715
$821$	−34.0000	−1.18661	−0.593304	−	0.804978i	$-0.702177\pi$
$821$	−34.0000	−1.18661	−0.593304	+	0.804978i	$0.702177\pi$
$822$	−8.53590	−0.297724
$823$	−12.6795	−0.441979	−0.220990	−	0.975276i	$-0.570929\pi$
$823$	−12.6795	−0.441979	−0.220990	+	0.975276i	$0.570929\pi$
$824$	14.5359	0.506382
$825$	2.00000	0.0696311
$826$	−14.7846	−0.514422
$827$	−11.6603	−0.405467	−0.202733	−	0.979234i	$-0.564982\pi$
$827$	−11.6603	−0.405467	−0.202733	+	0.979234i	$0.564982\pi$
$828$	−2.92820	−0.101762
$829$	46.3205	1.60878	0.804389	−	0.594103i	$-0.202493\pi$
$829$	46.3205	1.60878	0.804389	+	0.594103i	$0.202493\pi$
$830$	−2.14359	−0.0744052
$831$	−26.3923	−0.915539
$832$	0	0
$833$	−2.92820	−0.101456
$834$	−14.5885	−0.505157
$835$	−21.8564	−0.756372
$836$	−1.56922	−0.0542726
$837$	−4.46410	−0.154302
$838$	29.2154	1.00923
$839$	−38.3923	−1.32545	−0.662725	−	0.748863i	$-0.730600\pi$
$839$	−38.3923	−1.32545	−0.662725	+	0.748863i	$0.730600\pi$
$840$	−4.39230	−0.151549
$841$	−18.3205	−0.631742
$842$	9.41154	0.324343
$843$	11.2679	0.388089
$844$	−32.6795	−1.12487
$845$	0	0
$846$	0.143594	0.00493685
$847$	−12.1244	−0.416598
$848$	−10.1436	−0.348332
$849$	16.1244	0.553386
$850$	−0.535898	−0.0183812
$851$	20.7846	0.712487
$852$	−6.92820	−0.237356
$853$	32.6603	1.11827	0.559133	−	0.829078i	$-0.311134\pi$
$853$	32.6603	1.11827	0.559133	+	0.829078i	$0.311134\pi$
$854$	−6.83717	−0.233963
$855$	−0.535898	−0.0183273
$856$	20.7846	0.710403
$857$	−47.8038	−1.63295	−0.816474	−	0.577382i	$-0.804074\pi$
$857$	−47.8038	−1.63295	−0.816474	+	0.577382i	$0.804074\pi$
$858$	0	0
$859$	11.9282	0.406985	0.203493	−	0.979077i	$-0.434771\pi$
$859$	11.9282	0.406985	0.203493	+	0.979077i	$0.434771\pi$
$860$	−13.4641	−0.459122
$861$	18.5885	0.633493
$862$	−15.4256	−0.525399
$863$	−47.9615	−1.63263	−0.816315	−	0.577607i	$-0.803986\pi$
$863$	−47.9615	−1.63263	−0.816315	+	0.577607i	$0.803986\pi$
$864$	−5.85641	−0.199239
$865$	−12.1962	−0.414682
$866$	−13.9474	−0.473953
$867$	−16.4641	−0.559150
$868$	11.3205	0.384243
$869$	−22.0000	−0.746299
$870$	−2.39230	−0.0811067
$871$	0	0
$872$	39.0333	1.32184
$873$	−5.19615	−0.175863
$874$	−0.784610	−0.0265398
$875$	−1.73205	−0.0585540
$876$	2.53590	0.0856801
$877$	−5.60770	−0.189358	−0.0946792	−	0.995508i	$-0.530183\pi$
$877$	−5.60770	−0.189358	−0.0946792	+	0.995508i	$0.530183\pi$
$878$	14.1962	0.479097
$879$	−8.19615	−0.276449
$880$	−2.14359	−0.0722605
$881$	−15.6077	−0.525837	−0.262918	−	0.964818i	$-0.584685\pi$
$881$	−15.6077	−0.525837	−0.262918	+	0.964818i	$0.584685\pi$
$882$	2.92820	0.0985977
$883$	31.7321	1.06787	0.533934	−	0.845526i	$-0.320713\pi$
$883$	31.7321	1.06787	0.533934	+	0.845526i	$0.320713\pi$
$884$	0	0
$885$	−11.6603	−0.391955
$886$	−21.3205	−0.716276
$887$	37.2679	1.25134	0.625668	−	0.780090i	$-0.284827\pi$
$887$	37.2679	1.25134	0.625668	+	0.780090i	$0.284827\pi$
$888$	26.3538	0.884377
$889$	−1.14359	−0.0383549
$890$	−3.85641	−0.129267
$891$	2.00000	0.0670025
$892$	2.71797	0.0910043
$893$	−0.105118	−0.00351763
$894$	−4.28719	−0.143385
$895$	−17.6603	−0.590317
$896$	17.5692	0.586946
$897$	0	0
$898$	11.3205	0.377770
$899$	14.5885	0.486552
$900$	−1.46410	−0.0488034
$901$	−6.92820	−0.230812
$902$	−15.7128	−0.523179
$903$	−15.9282	−0.530057
$904$	46.6410	1.55126
$905$	−8.39230	−0.278970
$906$	−0.679492	−0.0225746
$907$	56.2487	1.86771	0.933854	−	0.357655i	$-0.116424\pi$
$907$	56.2487	1.86771	0.933854	+	0.357655i	$0.116424\pi$
$908$	−6.92820	−0.229920
$909$	10.3923	0.344691
$910$	0	0
$911$	−43.0333	−1.42576	−0.712879	−	0.701287i	$-0.752609\pi$
$911$	−43.0333	−1.42576	−0.712879	+	0.701287i	$0.752609\pi$
$912$	0.574374	0.0190194
$913$	−5.85641	−0.193819
$914$	−10.6269	−0.351508
$915$	−5.39230	−0.178264
$916$	18.7180	0.618459
$917$	−3.80385	−0.125614
$918$	−0.535898	−0.0176873
$919$	3.85641	0.127211	0.0636056	−	0.997975i	$-0.479740\pi$
$919$	3.85641	0.127211	0.0636056	+	0.997975i	$0.479740\pi$
$920$	−5.07180	−0.167212
$921$	6.66025	0.219463
$922$	−7.35898	−0.242355
$923$	0	0
$924$	−5.07180	−0.166850
$925$	10.3923	0.341697
$926$	−0.980762	−0.0322298
$927$	5.73205	0.188265
$928$	19.1384	0.628250
$929$	41.0718	1.34752	0.673761	−	0.738949i	$-0.264678\pi$
$929$	41.0718	1.34752	0.673761	+	0.738949i	$0.264678\pi$
$930$	−3.26795	−0.107160
$931$	−2.14359	−0.0702534
$932$	41.3590	1.35476
$933$	12.5885	0.412128
$934$	−7.56922	−0.247672
$935$	−1.46410	−0.0478812
$936$	0	0
$937$	−12.5359	−0.409530	−0.204765	−	0.978811i	$-0.565643\pi$
$937$	−12.5359	−0.409530	−0.204765	+	0.978811i	$0.565643\pi$
$938$	−11.6603	−0.380721
$939$	19.1962	0.626443
$940$	−0.287187	−0.00936701
$941$	−41.5167	−1.35340	−0.676702	−	0.736257i	$-0.736592\pi$
$941$	−41.5167	−1.35340	−0.676702	+	0.736257i	$0.736592\pi$
$942$	2.73205	0.0890150
$943$	21.4641	0.698967
$944$	12.4974	0.406756
$945$	−1.73205	−0.0563436
$946$	13.4641	0.437756
$947$	12.3397	0.400988	0.200494	−	0.979695i	$-0.435745\pi$
$947$	12.3397	0.400988	0.200494	+	0.979695i	$0.435745\pi$
$948$	16.1051	0.523070
$949$	0	0
$950$	−0.392305	−0.0127280
$951$	28.3923	0.920684
$952$	3.21539	0.104211
$953$	19.4641	0.630504	0.315252	−	0.949008i	$-0.397911\pi$
$953$	19.4641	0.630504	0.315252	+	0.949008i	$0.397911\pi$
$954$	6.92820	0.224309
$955$	−22.5885	−0.730945
$956$	−20.2872	−0.656135
$957$	−6.53590	−0.211276
$958$	28.4308	0.918557
$959$	20.1962	0.652168
$960$	−2.14359	−0.0691842
$961$	−11.0718	−0.357155
$962$	0	0
$963$	8.19615	0.264117
$964$	5.85641	0.188622
$965$	−19.1962	−0.617946
$966$	−2.53590	−0.0815912
$967$	−28.1051	−0.903800	−0.451900	−	0.892069i	$-0.649254\pi$
$967$	−28.1051	−0.903800	−0.451900	+	0.892069i	$0.649254\pi$
$968$	−17.7513	−0.570548
$969$	0.392305	0.0126026
$970$	−3.80385	−0.122134
$971$	−7.60770	−0.244143	−0.122071	−	0.992521i	$-0.538954\pi$
$971$	−7.60770	−0.244143	−0.122071	+	0.992521i	$0.538954\pi$
$972$	−1.46410	−0.0469611
$973$	34.5167	1.10655
$974$	4.10512	0.131536
$975$	0	0
$976$	5.77945	0.184996
$977$	−45.4641	−1.45453	−0.727263	−	0.686359i	$-0.759208\pi$
$977$	−45.4641	−1.45453	−0.727263	+	0.686359i	$0.759208\pi$
$978$	15.5167	0.496168
$979$	−10.5359	−0.336729
$980$	−5.85641	−0.187076
$981$	15.3923	0.491438
$982$	13.8949	0.443404
$983$	−13.6077	−0.434018	−0.217009	−	0.976170i	$-0.569630\pi$
$983$	−13.6077	−0.434018	−0.217009	+	0.976170i	$0.569630\pi$
$984$	27.2154	0.867595
$985$	16.3923	0.522302
$986$	1.75129	0.0557724
$987$	−0.339746	−0.0108142
$988$	0	0
$989$	−18.3923	−0.584841
$990$	1.46410	0.0465322
$991$	0.928203	0.0294853	0.0147427	−	0.999891i	$-0.495307\pi$
$991$	0.928203	0.0294853	0.0147427	+	0.999891i	$0.495307\pi$
$992$	26.1436	0.830060
$993$	−23.9282	−0.759339
$994$	−6.00000	−0.190308
$995$	24.8564	0.788001
$996$	4.28719	0.135845
$997$	1.19615	0.0378825	0.0189413	−	0.999821i	$-0.493970\pi$
$997$	1.19615	0.0378825	0.0189413	+	0.999821i	$0.493970\pi$
$998$	−18.5359	−0.586744
$999$	10.3923	0.328798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2535.2.a.r.1.1		2
3.2	odd	2		7605.2.a.z.1.2		2
13.4	even	6		195.2.i.c.16.1	✓	4
13.10	even	6		195.2.i.c.61.1	yes	4
13.12	even	2		2535.2.a.o.1.2		2
39.17	odd	6		585.2.j.c.406.2		4
39.23	odd	6		585.2.j.c.451.2		4
39.38	odd	2		7605.2.a.bj.1.1		2
65.4	even	6		975.2.i.j.601.2		4
65.17	odd	12		975.2.bb.h.874.1		4
65.23	odd	12		975.2.bb.h.724.1		4
65.43	odd	12		975.2.bb.a.874.2		4
65.49	even	6		975.2.i.j.451.2		4
65.62	odd	12		975.2.bb.a.724.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.c.16.1	✓	4	13.4	even	6
195.2.i.c.61.1	yes	4	13.10	even	6
585.2.j.c.406.2		4	39.17	odd	6
585.2.j.c.451.2		4	39.23	odd	6
975.2.i.j.451.2		4	65.49	even	6
975.2.i.j.601.2		4	65.4	even	6
975.2.bb.a.724.2		4	65.62	odd	12
975.2.bb.a.874.2		4	65.43	odd	12
975.2.bb.h.724.1		4	65.23	odd	12
975.2.bb.h.874.1		4	65.17	odd	12
2535.2.a.o.1.2		2	13.12	even	2
2535.2.a.r.1.1		2	1.1	even	1	trivial
7605.2.a.z.1.2		2	3.2	odd	2
7605.2.a.bj.1.1		2	39.38	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:	\( N \)	\(=\)	\( 2535 = 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2535.a (trivial)

\(f(q)\)	\(=\)	\(q-0.732051 q^{2} +1.00000 q^{3} -1.46410 q^{4} -1.00000 q^{5} -0.732051 q^{6} +1.73205 q^{7} +2.53590 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.732051 q^{2} +1.00000 q^{3} -1.46410 q^{4} -1.00000 q^{5} -0.732051 q^{6} +1.73205 q^{7} +2.53590 q^{8} +1.00000 q^{9} +0.732051 q^{10} +2.00000 q^{11} -1.46410 q^{12} -1.26795 q^{14} -1.00000 q^{15} +1.07180 q^{16} +0.732051 q^{17} -0.732051 q^{18} +0.535898 q^{19} +1.46410 q^{20} +1.73205 q^{21} -1.46410 q^{22} +2.00000 q^{23} +2.53590 q^{24} +1.00000 q^{25} +1.00000 q^{27} -2.53590 q^{28} -3.26795 q^{29} +0.732051 q^{30} -4.46410 q^{31} -5.85641 q^{32} +2.00000 q^{33} -0.535898 q^{34} -1.73205 q^{35} -1.46410 q^{36} +10.3923 q^{37} -0.392305 q^{38} -2.53590 q^{40} +10.7321 q^{41} -1.26795 q^{42} -9.19615 q^{43} -2.92820 q^{44} -1.00000 q^{45} -1.46410 q^{46} -0.196152 q^{47} +1.07180 q^{48} -4.00000 q^{49} -0.732051 q^{50} +0.732051 q^{51} -9.46410 q^{53} -0.732051 q^{54} -2.00000 q^{55} +4.39230 q^{56} +0.535898 q^{57} +2.39230 q^{58} +11.6603 q^{59} +1.46410 q^{60} +5.39230 q^{61} +3.26795 q^{62} +1.73205 q^{63} +2.14359 q^{64} -1.46410 q^{66} +9.19615 q^{67} -1.07180 q^{68} +2.00000 q^{69} +1.26795 q^{70} +4.73205 q^{71} +2.53590 q^{72} -1.73205 q^{73} -7.60770 q^{74} +1.00000 q^{75} -0.784610 q^{76} +3.46410 q^{77} -11.0000 q^{79} -1.07180 q^{80} +1.00000 q^{81} -7.85641 q^{82} -2.92820 q^{83} -2.53590 q^{84} -0.732051 q^{85} +6.73205 q^{86} -3.26795 q^{87} +5.07180 q^{88} -5.26795 q^{89} +0.732051 q^{90} -2.92820 q^{92} -4.46410 q^{93} +0.143594 q^{94} -0.535898 q^{95} -5.85641 q^{96} -5.19615 q^{97} +2.92820 q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{8} + 2 q^{9} - 2 q^{10} + 4 q^{11} + 4 q^{12} - 6 q^{14} - 2 q^{15} + 16 q^{16} - 2 q^{17} + 2 q^{18} + 8 q^{19} - 4 q^{20} + 4 q^{22} + 4 q^{23} + 12 q^{24} + 2 q^{25} + 2 q^{27} - 12 q^{28} - 10 q^{29} - 2 q^{30} - 2 q^{31} + 16 q^{32} + 4 q^{33} - 8 q^{34} + 4 q^{36} + 20 q^{38} - 12 q^{40} + 18 q^{41} - 6 q^{42} - 8 q^{43} + 8 q^{44} - 2 q^{45} + 4 q^{46} + 10 q^{47} + 16 q^{48} - 8 q^{49} + 2 q^{50} - 2 q^{51} - 12 q^{53} + 2 q^{54} - 4 q^{55} - 12 q^{56} + 8 q^{57} - 16 q^{58} + 6 q^{59} - 4 q^{60} - 10 q^{61} + 10 q^{62} + 32 q^{64} + 4 q^{66} + 8 q^{67} - 16 q^{68} + 4 q^{69} + 6 q^{70} + 6 q^{71} + 12 q^{72} - 36 q^{74} + 2 q^{75} + 40 q^{76} - 22 q^{79} - 16 q^{80} + 2 q^{81} + 12 q^{82} + 8 q^{83} - 12 q^{84} + 2 q^{85} + 10 q^{86} - 10 q^{87} + 24 q^{88} - 14 q^{89} - 2 q^{90} + 8 q^{92} - 2 q^{93} + 28 q^{94} - 8 q^{95} + 16 q^{96} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^8 + 2 * q^9 - 2 * q^10 + 4 * q^11 + 4 * q^12 - 6 * q^14 - 2 * q^15 + 16 * q^16 - 2 * q^17 + 2 * q^18 + 8 * q^19 - 4 * q^20 + 4 * q^22 + 4 * q^23 + 12 * q^24 + 2 * q^25 + 2 * q^27 - 12 * q^28 - 10 * q^29 - 2 * q^30 - 2 * q^31 + 16 * q^32 + 4 * q^33 - 8 * q^34 + 4 * q^36 + 20 * q^38 - 12 * q^40 + 18 * q^41 - 6 * q^42 - 8 * q^43 + 8 * q^44 - 2 * q^45 + 4 * q^46 + 10 * q^47 + 16 * q^48 - 8 * q^49 + 2 * q^50 - 2 * q^51 - 12 * q^53 + 2 * q^54 - 4 * q^55 - 12 * q^56 + 8 * q^57 - 16 * q^58 + 6 * q^59 - 4 * q^60 - 10 * q^61 + 10 * q^62 + 32 * q^64 + 4 * q^66 + 8 * q^67 - 16 * q^68 + 4 * q^69 + 6 * q^70 + 6 * q^71 + 12 * q^72 - 36 * q^74 + 2 * q^75 + 40 * q^76 - 22 * q^79 - 16 * q^80 + 2 * q^81 + 12 * q^82 + 8 * q^83 - 12 * q^84 + 2 * q^85 + 10 * q^86 - 10 * q^87 + 24 * q^88 - 14 * q^89 - 2 * q^90 + 8 * q^92 - 2 * q^93 + 28 * q^94 - 8 * q^95 + 16 * q^96 - 8 * q^98 + 4 * q^99

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