LMFDB - Embedded newform 3549.2.a.bd.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 9x^{6} + 14x^{5} + 25x^{4} - 24x^{3} - 16x^{2} + 8x + 1 $ x^8 - 2x^7 - 9x^6 + 14x^5 + 25x^4 - 24x^3 - 16x^2 + 8*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.485989$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.485989 q^{2} +1.00000 q^{3} -1.76381 q^{4} +1.06536 q^{5} +0.485989 q^{6} +1.00000 q^{7} -1.82917 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.485989 q^{2} +1.00000 q^{3} -1.76381 q^{4} +1.06536 q^{5} +0.485989 q^{6} +1.00000 q^{7} -1.82917 q^{8} +1.00000 q^{9} +0.517753 q^{10} +5.75611 q^{11} -1.76381 q^{12} +0.485989 q^{14} +1.06536 q^{15} +2.63867 q^{16} +2.34533 q^{17} +0.485989 q^{18} -6.20049 q^{19} -1.87910 q^{20} +1.00000 q^{21} +2.79741 q^{22} +5.51348 q^{23} -1.82917 q^{24} -3.86501 q^{25} +1.00000 q^{27} -1.76381 q^{28} +5.60430 q^{29} +0.517753 q^{30} +5.46420 q^{31} +4.94071 q^{32} +5.75611 q^{33} +1.13980 q^{34} +1.06536 q^{35} -1.76381 q^{36} -4.71551 q^{37} -3.01337 q^{38} -1.94873 q^{40} -8.88127 q^{41} +0.485989 q^{42} -9.55702 q^{43} -10.1527 q^{44} +1.06536 q^{45} +2.67949 q^{46} +5.21864 q^{47} +2.63867 q^{48} +1.00000 q^{49} -1.87835 q^{50} +2.34533 q^{51} +1.52870 q^{53} +0.485989 q^{54} +6.13233 q^{55} -1.82917 q^{56} -6.20049 q^{57} +2.72363 q^{58} +10.4663 q^{59} -1.87910 q^{60} +7.64609 q^{61} +2.65554 q^{62} +1.00000 q^{63} -2.87621 q^{64} +2.79741 q^{66} -3.27680 q^{67} -4.13673 q^{68} +5.51348 q^{69} +0.517753 q^{70} +8.66905 q^{71} -1.82917 q^{72} +7.63941 q^{73} -2.29169 q^{74} -3.86501 q^{75} +10.9365 q^{76} +5.75611 q^{77} -15.6147 q^{79} +2.81113 q^{80} +1.00000 q^{81} -4.31620 q^{82} -2.63313 q^{83} -1.76381 q^{84} +2.49862 q^{85} -4.64461 q^{86} +5.60430 q^{87} -10.5289 q^{88} +12.0669 q^{89} +0.517753 q^{90} -9.72476 q^{92} +5.46420 q^{93} +2.53620 q^{94} -6.60575 q^{95} +4.94071 q^{96} +16.7611 q^{97} +0.485989 q^{98} +5.75611 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 8 q^{3} + 6 q^{4} + 2 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 8 * q^3 + 6 * q^4 + 2 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 + 8 * q^9	\( 8 q + 2 q^{2} + 8 q^{3} + 6 q^{4} + 2 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} + 8 q^{9} - 4 q^{10} + 8 q^{11} + 6 q^{12} + 2 q^{14} + 2 q^{15} + 10 q^{16} + 10 q^{17} + 2 q^{18} + 18 q^{19} + 2 q^{20} + 8 q^{21} + 2 q^{22} - 2 q^{23} + 12 q^{24} - 6 q^{25} + 8 q^{27} + 6 q^{28} - 12 q^{29} - 4 q^{30} + 16 q^{31} + 26 q^{32} + 8 q^{33} + 24 q^{34} + 2 q^{35} + 6 q^{36} + 24 q^{37} + 16 q^{38} - 30 q^{40} - 4 q^{41} + 2 q^{42} - 10 q^{43} - 20 q^{44} + 2 q^{45} + 12 q^{46} + 10 q^{47} + 10 q^{48} + 8 q^{49} - 16 q^{50} + 10 q^{51} + 6 q^{53} + 2 q^{54} - 10 q^{55} + 12 q^{56} + 18 q^{57} + 16 q^{58} + 6 q^{59} + 2 q^{60} + 6 q^{61} + 16 q^{62} + 8 q^{63} - 8 q^{64} + 2 q^{66} + 24 q^{67} + 20 q^{68} - 2 q^{69} - 4 q^{70} + 42 q^{71} + 12 q^{72} + 32 q^{73} - 18 q^{74} - 6 q^{75} + 28 q^{76} + 8 q^{77} - 2 q^{79} - 40 q^{80} + 8 q^{81} - 18 q^{82} - 2 q^{83} + 6 q^{84} + 4 q^{85} + 26 q^{86} - 12 q^{87} - 2 q^{88} + 12 q^{89} - 4 q^{90} - 10 q^{92} + 16 q^{93} - 16 q^{94} - 4 q^{95} + 26 q^{96} + 64 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 8 * q^3 + 6 * q^4 + 2 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 + 8 * q^9 - 4 * q^10 + 8 * q^11 + 6 * q^12 + 2 * q^14 + 2 * q^15 + 10 * q^16 + 10 * q^17 + 2 * q^18 + 18 * q^19 + 2 * q^20 + 8 * q^21 + 2 * q^22 - 2 * q^23 + 12 * q^24 - 6 * q^25 + 8 * q^27 + 6 * q^28 - 12 * q^29 - 4 * q^30 + 16 * q^31 + 26 * q^32 + 8 * q^33 + 24 * q^34 + 2 * q^35 + 6 * q^36 + 24 * q^37 + 16 * q^38 - 30 * q^40 - 4 * q^41 + 2 * q^42 - 10 * q^43 - 20 * q^44 + 2 * q^45 + 12 * q^46 + 10 * q^47 + 10 * q^48 + 8 * q^49 - 16 * q^50 + 10 * q^51 + 6 * q^53 + 2 * q^54 - 10 * q^55 + 12 * q^56 + 18 * q^57 + 16 * q^58 + 6 * q^59 + 2 * q^60 + 6 * q^61 + 16 * q^62 + 8 * q^63 - 8 * q^64 + 2 * q^66 + 24 * q^67 + 20 * q^68 - 2 * q^69 - 4 * q^70 + 42 * q^71 + 12 * q^72 + 32 * q^73 - 18 * q^74 - 6 * q^75 + 28 * q^76 + 8 * q^77 - 2 * q^79 - 40 * q^80 + 8 * q^81 - 18 * q^82 - 2 * q^83 + 6 * q^84 + 4 * q^85 + 26 * q^86 - 12 * q^87 - 2 * q^88 + 12 * q^89 - 4 * q^90 - 10 * q^92 + 16 * q^93 - 16 * q^94 - 4 * q^95 + 26 * q^96 + 64 * q^97 + 2 * q^98 + 8 * 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 $

$2$	0.485989	0.343646	0.171823	−	0.985128i	$-0.445034\pi$
$2$	0.485989	0.343646	0.171823	+	0.985128i	$0.445034\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.76381	−0.881907
$5$	1.06536	0.476443	0.238221	−	0.971211i	$-0.423436\pi$
$5$	1.06536	0.476443	0.238221	+	0.971211i	$0.423436\pi$
$6$	0.485989	0.198404
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.82917	−0.646710
$9$	1.00000	0.333333
$10$	0.517753	0.163728
$11$	5.75611	1.73553	0.867767	−	0.496971i	$-0.165555\pi$
$11$	5.75611	1.73553	0.867767	+	0.496971i	$0.165555\pi$
$12$	−1.76381	−0.509169
$13$	0	0
$13$	0	0
$14$	0.485989	0.129886
$15$	1.06536	0.275074
$16$	2.63867	0.659668
$17$	2.34533	0.568826	0.284413	−	0.958702i	$-0.408201\pi$
$17$	2.34533	0.568826	0.284413	+	0.958702i	$0.408201\pi$
$18$	0.485989	0.114549
$19$	−6.20049	−1.42249	−0.711246	−	0.702944i	$-0.751869\pi$
$19$	−6.20049	−1.42249	−0.711246	+	0.702944i	$0.751869\pi$
$20$	−1.87910	−0.420178
$21$	1.00000	0.218218
$22$	2.79741	0.596410
$23$	5.51348	1.14964	0.574820	−	0.818280i	$-0.305072\pi$
$23$	5.51348	1.14964	0.574820	+	0.818280i	$0.305072\pi$
$24$	−1.82917	−0.373378
$25$	−3.86501	−0.773002
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.76381	−0.333330
$29$	5.60430	1.04069	0.520346	−	0.853955i	$-0.325803\pi$
$29$	5.60430	1.04069	0.520346	+	0.853955i	$0.325803\pi$
$30$	0.517753	0.0945283
$31$	5.46420	0.981400	0.490700	−	0.871329i	$-0.336741\pi$
$31$	5.46420	0.981400	0.490700	+	0.871329i	$0.336741\pi$
$32$	4.94071	0.873403
$33$	5.75611	1.00201
$34$	1.13980	0.195475
$35$	1.06536	0.180079
$36$	−1.76381	−0.293969
$37$	−4.71551	−0.775225	−0.387612	−	0.921822i	$-0.626700\pi$
$37$	−4.71551	−0.775225	−0.387612	+	0.921822i	$0.626700\pi$
$38$	−3.01337	−0.488834
$39$	0	0
$40$	−1.94873	−0.308121
$41$	−8.88127	−1.38702	−0.693511	−	0.720446i	$-0.743937\pi$
$41$	−8.88127	−1.38702	−0.693511	+	0.720446i	$0.743937\pi$
$42$	0.485989	0.0749898
$43$	−9.55702	−1.45743	−0.728716	−	0.684816i	$-0.759883\pi$
$43$	−9.55702	−1.45743	−0.728716	+	0.684816i	$0.759883\pi$
$44$	−10.1527	−1.53058
$45$	1.06536	0.158814
$46$	2.67949	0.395070
$47$	5.21864	0.761217	0.380608	−	0.924736i	$-0.375715\pi$
$47$	5.21864	0.761217	0.380608	+	0.924736i	$0.375715\pi$
$48$	2.63867	0.380859
$49$	1.00000	0.142857
$50$	−1.87835	−0.265639
$51$	2.34533	0.328412
$52$	0	0
$53$	1.52870	0.209982	0.104991	−	0.994473i	$-0.466519\pi$
$53$	1.52870	0.209982	0.104991	+	0.994473i	$0.466519\pi$
$54$	0.485989	0.0661348
$55$	6.13233	0.826883
$56$	−1.82917	−0.244434
$57$	−6.20049	−0.821276
$58$	2.72363	0.357630
$59$	10.4663	1.36259	0.681297	−	0.732007i	$-0.261416\pi$
$59$	10.4663	1.36259	0.681297	+	0.732007i	$0.261416\pi$
$60$	−1.87910	−0.242590
$61$	7.64609	0.978982	0.489491	−	0.872008i	$-0.337183\pi$
$61$	7.64609	0.978982	0.489491	+	0.872008i	$0.337183\pi$
$62$	2.65554	0.337254
$63$	1.00000	0.125988
$64$	−2.87621	−0.359526
$65$	0	0
$66$	2.79741	0.344337
$67$	−3.27680	−0.400325	−0.200162	−	0.979763i	$-0.564147\pi$
$67$	−3.27680	−0.400325	−0.200162	+	0.979763i	$0.564147\pi$
$68$	−4.13673	−0.501652
$69$	5.51348	0.663745
$70$	0.517753	0.0618833
$71$	8.66905	1.02883	0.514413	−	0.857542i	$-0.328010\pi$
$71$	8.66905	1.02883	0.514413	+	0.857542i	$0.328010\pi$
$72$	−1.82917	−0.215570
$73$	7.63941	0.894126	0.447063	−	0.894503i	$-0.352470\pi$
$73$	7.63941	0.894126	0.447063	+	0.894503i	$0.352470\pi$
$74$	−2.29169	−0.266403
$75$	−3.86501	−0.446293
$76$	10.9365	1.25451
$77$	5.75611	0.655970
$78$	0	0
$79$	−15.6147	−1.75679	−0.878397	−	0.477932i	$-0.841387\pi$
$79$	−15.6147	−1.75679	−0.878397	+	0.477932i	$0.841387\pi$
$80$	2.81113	0.314294
$81$	1.00000	0.111111
$82$	−4.31620	−0.476645
$83$	−2.63313	−0.289024	−0.144512	−	0.989503i	$-0.546161\pi$
$83$	−2.63313	−0.289024	−0.144512	+	0.989503i	$0.546161\pi$
$84$	−1.76381	−0.192448
$85$	2.49862	0.271013
$86$	−4.64461	−0.500841
$87$	5.60430	0.600844
$88$	−10.5289	−1.12239
$89$	12.0669	1.27908	0.639542	−	0.768756i	$-0.279124\pi$
$89$	12.0669	1.27908	0.639542	+	0.768756i	$0.279124\pi$
$90$	0.517753	0.0545759
$91$	0	0
$92$	−9.72476	−1.01388
$93$	5.46420	0.566612
$94$	2.53620	0.261589
$95$	−6.60575	−0.677736
$96$	4.94071	0.504259
$97$	16.7611	1.70184	0.850918	−	0.525298i	$-0.176046\pi$
$97$	16.7611	1.70184	0.850918	+	0.525298i	$0.176046\pi$
$98$	0.485989	0.0490923
$99$	5.75611	0.578511
$100$	6.81716	0.681716
$101$	−2.57631	−0.256352	−0.128176	−	0.991751i	$-0.540912\pi$
$101$	−2.57631	−0.256352	−0.128176	+	0.991751i	$0.540912\pi$
$102$	1.13980	0.112857
$103$	−10.3824	−1.02301	−0.511506	−	0.859280i	$-0.670912\pi$
$103$	−10.3824	−1.02301	−0.511506	+	0.859280i	$0.670912\pi$
$104$	0	0
$105$	1.06536	0.103968
$106$	0.742930	0.0721597
$107$	17.0355	1.64688	0.823441	−	0.567402i	$-0.192051\pi$
$107$	17.0355	1.64688	0.823441	+	0.567402i	$0.192051\pi$
$108$	−1.76381	−0.169723
$109$	1.86126	0.178276	0.0891380	−	0.996019i	$-0.471589\pi$
$109$	1.86126	0.178276	0.0891380	+	0.996019i	$0.471589\pi$
$110$	2.98024	0.284155
$111$	−4.71551	−0.447576
$112$	2.63867	0.249331
$113$	−4.76742	−0.448481	−0.224240	−	0.974534i	$-0.571990\pi$
$113$	−4.76742	−0.448481	−0.224240	+	0.974534i	$0.571990\pi$
$114$	−3.01337	−0.282228
$115$	5.87384	0.547738
$116$	−9.88495	−0.917794
$117$	0	0
$118$	5.08650	0.468250
$119$	2.34533	0.214996
$120$	−1.94873	−0.177894
$121$	22.1329	2.01208
$122$	3.71592	0.336423
$123$	−8.88127	−0.800797
$124$	−9.63784	−0.865504
$125$	−9.44442	−0.844734
$126$	0.485989	0.0432954
$127$	−1.18761	−0.105383	−0.0526916	−	0.998611i	$-0.516780\pi$
$127$	−1.18761	−0.105383	−0.0526916	+	0.998611i	$0.516780\pi$
$128$	−11.2792	−0.996953
$129$	−9.55702	−0.841449
$130$	0	0
$131$	−14.8261	−1.29537	−0.647683	−	0.761910i	$-0.724262\pi$
$131$	−14.8261	−1.29537	−0.647683	+	0.761910i	$0.724262\pi$
$132$	−10.1527	−0.883681
$133$	−6.20049	−0.537651
$134$	−1.59249	−0.137570
$135$	1.06536	0.0916915
$136$	−4.29001	−0.367866
$137$	−6.57310	−0.561578	−0.280789	−	0.959769i	$-0.590596\pi$
$137$	−6.57310	−0.561578	−0.280789	+	0.959769i	$0.590596\pi$
$138$	2.67949	0.228094
$139$	−0.734630	−0.0623105	−0.0311553	−	0.999515i	$-0.509919\pi$
$139$	−0.734630	−0.0623105	−0.0311553	+	0.999515i	$0.509919\pi$
$140$	−1.87910	−0.158813
$141$	5.21864	0.439489
$142$	4.21306	0.353552
$143$	0	0
$144$	2.63867	0.219889
$145$	5.97059	0.495831
$146$	3.71267	0.307263
$147$	1.00000	0.0824786
$148$	8.31728	0.683676
$149$	22.6396	1.85471	0.927354	−	0.374186i	$-0.122078\pi$
$149$	22.6396	1.85471	0.927354	+	0.374186i	$0.122078\pi$
$150$	−1.87835	−0.153367
$151$	7.94508	0.646561	0.323281	−	0.946303i	$-0.395214\pi$
$151$	7.94508	0.646561	0.323281	+	0.946303i	$0.395214\pi$
$152$	11.3418	0.919940
$153$	2.34533	0.189609
$154$	2.79741	0.225422
$155$	5.82134	0.467581
$156$	0	0
$157$	15.4868	1.23598	0.617991	−	0.786185i	$-0.287947\pi$
$157$	15.4868	1.23598	0.617991	+	0.786185i	$0.287947\pi$
$158$	−7.58859	−0.603716
$159$	1.52870	0.121233
$160$	5.26363	0.416127
$161$	5.51348	0.434523
$162$	0.485989	0.0381829
$163$	−5.89612	−0.461819	−0.230910	−	0.972975i	$-0.574170\pi$
$163$	−5.89612	−0.461819	−0.230910	+	0.972975i	$0.574170\pi$
$164$	15.6649	1.22322
$165$	6.13233	0.477401
$166$	−1.27967	−0.0993219
$167$	9.50892	0.735822	0.367911	−	0.929861i	$-0.380073\pi$
$167$	9.50892	0.735822	0.367911	+	0.929861i	$0.380073\pi$
$168$	−1.82917	−0.141124
$169$	0	0
$170$	1.21430	0.0931326
$171$	−6.20049	−0.474164
$172$	16.8568	1.28532
$173$	−1.62465	−0.123520	−0.0617599	−	0.998091i	$-0.519671\pi$
$173$	−1.62465	−0.123520	−0.0617599	+	0.998091i	$0.519671\pi$
$174$	2.72363	0.206478
$175$	−3.86501	−0.292167
$176$	15.1885	1.14488
$177$	10.4663	0.786694
$178$	5.86436	0.439552
$179$	19.7547	1.47654	0.738268	−	0.674508i	$-0.235644\pi$
$179$	19.7547	1.47654	0.738268	+	0.674508i	$0.235644\pi$
$180$	−1.87910	−0.140059
$181$	0.589428	0.0438118	0.0219059	−	0.999760i	$-0.493027\pi$
$181$	0.589428	0.0438118	0.0219059	+	0.999760i	$0.493027\pi$
$182$	0	0
$183$	7.64609	0.565215
$184$	−10.0851	−0.743484
$185$	−5.02371	−0.369350
$186$	2.65554	0.194714
$187$	13.5000	0.987217
$188$	−9.20471	−0.671323
$189$	1.00000	0.0727393
$190$	−3.21032	−0.232901
$191$	9.17624	0.663970	0.331985	−	0.943285i	$-0.392282\pi$
$191$	9.17624	0.663970	0.331985	+	0.943285i	$0.392282\pi$
$192$	−2.87621	−0.207572
$193$	−3.28733	−0.236627	−0.118314	−	0.992976i	$-0.537749\pi$
$193$	−3.28733	−0.236627	−0.118314	+	0.992976i	$0.537749\pi$
$194$	8.14574	0.584830
$195$	0	0
$196$	−1.76381	−0.125987
$197$	15.3203	1.09153	0.545765	−	0.837938i	$-0.316239\pi$
$197$	15.3203	1.09153	0.545765	+	0.837938i	$0.316239\pi$
$198$	2.79741	0.198803
$199$	−14.5230	−1.02951	−0.514754	−	0.857338i	$-0.672117\pi$
$199$	−14.5230	−1.02951	−0.514754	+	0.857338i	$0.672117\pi$
$200$	7.06977	0.499909
$201$	−3.27680	−0.231128
$202$	−1.25206	−0.0880945
$203$	5.60430	0.393345
$204$	−4.13673	−0.289629
$205$	−9.46174	−0.660837
$206$	−5.04576	−0.351554
$207$	5.51348	0.383213
$208$	0	0
$209$	−35.6908	−2.46878
$210$	0.517753	0.0357283
$211$	−16.5273	−1.13778	−0.568892	−	0.822412i	$-0.692628\pi$
$211$	−16.5273	−1.13778	−0.568892	+	0.822412i	$0.692628\pi$
$212$	−2.69634	−0.185185
$213$	8.66905	0.593993
$214$	8.27906	0.565945
$215$	−10.1817	−0.694383
$216$	−1.82917	−0.124459
$217$	5.46420	0.370934
$218$	0.904550	0.0612639
$219$	7.63941	0.516224
$220$	−10.8163	−0.729234
$221$	0	0
$222$	−2.29169	−0.153808
$223$	21.6903	1.45249	0.726246	−	0.687435i	$-0.241263\pi$
$223$	21.6903	1.45249	0.726246	+	0.687435i	$0.241263\pi$
$224$	4.94071	0.330115
$225$	−3.86501	−0.257667
$226$	−2.31691	−0.154119
$227$	−5.43551	−0.360768	−0.180384	−	0.983596i	$-0.557734\pi$
$227$	−5.43551	−0.360768	−0.180384	+	0.983596i	$0.557734\pi$
$228$	10.9365	0.724289
$229$	−9.99668	−0.660599	−0.330300	−	0.943876i	$-0.607150\pi$
$229$	−9.99668	−0.660599	−0.330300	+	0.943876i	$0.607150\pi$
$230$	2.85462	0.188228
$231$	5.75611	0.378725
$232$	−10.2512	−0.673027
$233$	−1.72553	−0.113043	−0.0565217	−	0.998401i	$-0.518001\pi$
$233$	−1.72553	−0.113043	−0.0565217	+	0.998401i	$0.518001\pi$
$234$	0	0
$235$	5.55972	0.362676
$236$	−18.4606	−1.20168
$237$	−15.6147	−1.01429
$238$	1.13980	0.0738826
$239$	−5.80837	−0.375712	−0.187856	−	0.982197i	$-0.560154\pi$
$239$	−5.80837	−0.375712	−0.187856	+	0.982197i	$0.560154\pi$
$240$	2.81113	0.181458
$241$	−11.1202	−0.716316	−0.358158	−	0.933661i	$-0.616595\pi$
$241$	−11.1202	−0.716316	−0.358158	+	0.933661i	$0.616595\pi$
$242$	10.7563	0.691443
$243$	1.00000	0.0641500
$244$	−13.4863	−0.863371
$245$	1.06536	0.0680633
$246$	−4.31620	−0.275191
$247$	0	0
$248$	−9.99498	−0.634682
$249$	−2.63313	−0.166868
$250$	−4.58988	−0.290290
$251$	9.75269	0.615584	0.307792	−	0.951454i	$-0.400410\pi$
$251$	9.75269	0.615584	0.307792	+	0.951454i	$0.400410\pi$
$252$	−1.76381	−0.111110
$253$	31.7362	1.99524
$254$	−0.577165	−0.0362145
$255$	2.49862	0.156469
$256$	0.270832	0.0169270
$257$	10.3942	0.648372	0.324186	−	0.945993i	$-0.394910\pi$
$257$	10.3942	0.648372	0.324186	+	0.945993i	$0.394910\pi$
$258$	−4.64461	−0.289161
$259$	−4.71551	−0.293007
$260$	0	0
$261$	5.60430	0.346898
$262$	−7.20535	−0.445148
$263$	−24.4789	−1.50943	−0.754717	−	0.656050i	$-0.772226\pi$
$263$	−24.4789	−1.50943	−0.754717	+	0.656050i	$0.772226\pi$
$264$	−10.5289	−0.648011
$265$	1.62861	0.100045
$266$	−3.01337	−0.184762
$267$	12.0669	0.738479
$268$	5.77966	0.353049
$269$	5.05819	0.308403	0.154202	−	0.988039i	$-0.450719\pi$
$269$	5.05819	0.308403	0.154202	+	0.988039i	$0.450719\pi$
$270$	0.517753	0.0315094
$271$	13.5704	0.824340	0.412170	−	0.911107i	$-0.364771\pi$
$271$	13.5704	0.824340	0.412170	+	0.911107i	$0.364771\pi$
$272$	6.18855	0.375236
$273$	0	0
$274$	−3.19446	−0.192984
$275$	−22.2474	−1.34157
$276$	−9.72476	−0.585362
$277$	−23.5739	−1.41642	−0.708210	−	0.706002i	$-0.750497\pi$
$277$	−23.5739	−1.41642	−0.708210	+	0.706002i	$0.750497\pi$
$278$	−0.357022	−0.0214128
$279$	5.46420	0.327133
$280$	−1.94873	−0.116459
$281$	−14.8688	−0.886996	−0.443498	−	0.896275i	$-0.646263\pi$
$281$	−14.8688	−0.886996	−0.443498	+	0.896275i	$0.646263\pi$
$282$	2.53620	0.151029
$283$	−20.9896	−1.24770	−0.623852	−	0.781543i	$-0.714433\pi$
$283$	−20.9896	−1.24770	−0.623852	+	0.781543i	$0.714433\pi$
$284$	−15.2906	−0.907330
$285$	−6.60575	−0.391291
$286$	0	0
$287$	−8.88127	−0.524245
$288$	4.94071	0.291134
$289$	−11.4994	−0.676437
$290$	2.90164	0.170390
$291$	16.7611	0.982556
$292$	−13.4745	−0.788536
$293$	−7.38064	−0.431182	−0.215591	−	0.976484i	$-0.569168\pi$
$293$	−7.38064	−0.431182	−0.215591	+	0.976484i	$0.569168\pi$
$294$	0.485989	0.0283435
$295$	11.1503	0.649198
$296$	8.62548	0.501346
$297$	5.75611	0.334004
$298$	11.0026	0.637363
$299$	0	0
$300$	6.81716	0.393589
$301$	−9.55702	−0.550858
$302$	3.86122	0.222188
$303$	−2.57631	−0.148005
$304$	−16.3611	−0.938371
$305$	8.14583	0.466429
$306$	1.13980	0.0651583
$307$	26.2172	1.49629	0.748146	−	0.663534i	$-0.230944\pi$
$307$	26.2172	1.49629	0.748146	+	0.663534i	$0.230944\pi$
$308$	−10.1527	−0.578505
$309$	−10.3824	−0.590637
$310$	2.82911	0.160683
$311$	23.3730	1.32536	0.662681	−	0.748902i	$-0.269419\pi$
$311$	23.3730	1.32536	0.662681	+	0.748902i	$0.269419\pi$
$312$	0	0
$313$	−20.5337	−1.16064	−0.580318	−	0.814390i	$-0.697072\pi$
$313$	−20.5337	−1.16064	−0.580318	+	0.814390i	$0.697072\pi$
$314$	7.52642	0.424740
$315$	1.06536	0.0600262
$316$	27.5415	1.54933
$317$	−2.73722	−0.153738	−0.0768689	−	0.997041i	$-0.524492\pi$
$317$	−2.73722	−0.153738	−0.0768689	+	0.997041i	$0.524492\pi$
$318$	0.742930	0.0416614
$319$	32.2590	1.80616
$320$	−3.06419	−0.171294
$321$	17.0355	0.950828
$322$	2.67949	0.149322
$323$	−14.5422	−0.809150
$324$	−1.76381	−0.0979897
$325$	0	0
$326$	−2.86545	−0.158703
$327$	1.86126	0.102928
$328$	16.2454	0.897001
$329$	5.21864	0.287713
$330$	2.98024	0.164057
$331$	−9.65148	−0.530493	−0.265247	−	0.964181i	$-0.585453\pi$
$331$	−9.65148	−0.530493	−0.265247	+	0.964181i	$0.585453\pi$
$332$	4.64435	0.254892
$333$	−4.71551	−0.258408
$334$	4.62123	0.252863
$335$	−3.49097	−0.190732
$336$	2.63867	0.143951
$337$	−11.3368	−0.617555	−0.308778	−	0.951134i	$-0.599920\pi$
$337$	−11.3368	−0.617555	−0.308778	+	0.951134i	$0.599920\pi$
$338$	0	0
$339$	−4.76742	−0.258930
$340$	−4.40710	−0.239008
$341$	31.4526	1.70325
$342$	−3.01337	−0.162945
$343$	1.00000	0.0539949
$344$	17.4814	0.942537
$345$	5.87384	0.316237
$346$	−0.789562	−0.0424471
$347$	−19.6733	−1.05612	−0.528060	−	0.849207i	$-0.677080\pi$
$347$	−19.6733	−1.05612	−0.528060	+	0.849207i	$0.677080\pi$
$348$	−9.88495	−0.529889
$349$	7.88649	0.422154	0.211077	−	0.977469i	$-0.432303\pi$
$349$	7.88649	0.422154	0.211077	+	0.977469i	$0.432303\pi$
$350$	−1.87835	−0.100402
$351$	0	0
$352$	28.4393	1.51582
$353$	−14.6821	−0.781448	−0.390724	−	0.920508i	$-0.627775\pi$
$353$	−14.6821	−0.781448	−0.390724	+	0.920508i	$0.627775\pi$
$354$	5.08650	0.270344
$355$	9.23565	0.490177
$356$	−21.2837	−1.12803
$357$	2.34533	0.124128
$358$	9.60057	0.507406
$359$	−16.7725	−0.885220	−0.442610	−	0.896714i	$-0.645947\pi$
$359$	−16.7725	−0.885220	−0.442610	+	0.896714i	$0.645947\pi$
$360$	−1.94873	−0.102707
$361$	19.4461	1.02348
$362$	0.286456	0.0150558
$363$	22.1329	1.16167
$364$	0	0
$365$	8.13871	0.426000
$366$	3.71592	0.194234
$367$	−10.9405	−0.571087	−0.285543	−	0.958366i	$-0.592174\pi$
$367$	−10.9405	−0.571087	−0.285543	+	0.958366i	$0.592174\pi$
$368$	14.5483	0.758380
$369$	−8.88127	−0.462341
$370$	−2.44147	−0.126926
$371$	1.52870	0.0793659
$372$	−9.63784	−0.499699
$373$	−7.23534	−0.374632	−0.187316	−	0.982300i	$-0.559979\pi$
$373$	−7.23534	−0.374632	−0.187316	+	0.982300i	$0.559979\pi$
$374$	6.56085	0.339253
$375$	−9.44442	−0.487708
$376$	−9.54580	−0.492287
$377$	0	0
$378$	0.485989	0.0249966
$379$	−2.63482	−0.135341	−0.0676707	−	0.997708i	$-0.521557\pi$
$379$	−2.63482	−0.135341	−0.0676707	+	0.997708i	$0.521557\pi$
$380$	11.6513	0.597700
$381$	−1.18761	−0.0608430
$382$	4.45956	0.228171
$383$	8.60864	0.439881	0.219941	−	0.975513i	$-0.429414\pi$
$383$	8.60864	0.439881	0.219941	+	0.975513i	$0.429414\pi$
$384$	−11.2792	−0.575591
$385$	6.13233	0.312532
$386$	−1.59761	−0.0813161
$387$	−9.55702	−0.485811
$388$	−29.5636	−1.50086
$389$	−19.9726	−1.01265	−0.506325	−	0.862343i	$-0.668996\pi$
$389$	−19.9726	−1.01265	−0.506325	+	0.862343i	$0.668996\pi$
$390$	0	0
$391$	12.9309	0.653945
$392$	−1.82917	−0.0923872
$393$	−14.8261	−0.747880
$394$	7.44552	0.375100
$395$	−16.6353	−0.837012
$396$	−10.1527	−0.510193
$397$	2.85916	0.143497	0.0717485	−	0.997423i	$-0.477142\pi$
$397$	2.85916	0.143497	0.0717485	+	0.997423i	$0.477142\pi$
$398$	−7.05802	−0.353787
$399$	−6.20049	−0.310413
$400$	−10.1985	−0.509924
$401$	18.0257	0.900160	0.450080	−	0.892988i	$-0.351395\pi$
$401$	18.0257	0.900160	0.450080	+	0.892988i	$0.351395\pi$
$402$	−1.59249	−0.0794261
$403$	0	0
$404$	4.54413	0.226079
$405$	1.06536	0.0529381
$406$	2.72363	0.135171
$407$	−27.1430	−1.34543
$408$	−4.29001	−0.212387
$409$	−8.75748	−0.433029	−0.216515	−	0.976279i	$-0.569469\pi$
$409$	−8.75748	−0.433029	−0.216515	+	0.976279i	$0.569469\pi$
$410$	−4.59830	−0.227094
$411$	−6.57310	−0.324227
$412$	18.3127	0.902202
$413$	10.4663	0.515012
$414$	2.67949	0.131690
$415$	−2.80523	−0.137703
$416$	0	0
$417$	−0.734630	−0.0359750
$418$	−17.3453	−0.848387
$419$	−1.72889	−0.0844619	−0.0422310	−	0.999108i	$-0.513447\pi$
$419$	−1.72889	−0.0844619	−0.0422310	+	0.999108i	$0.513447\pi$
$420$	−1.87910	−0.0916905
$421$	25.6427	1.24975	0.624874	−	0.780726i	$-0.285150\pi$
$421$	25.6427	1.24975	0.624874	+	0.780726i	$0.285150\pi$
$422$	−8.03208	−0.390995
$423$	5.21864	0.253739
$424$	−2.79625	−0.135798
$425$	−9.06472	−0.439704
$426$	4.21306	0.204124
$427$	7.64609	0.370020
$428$	−30.0474	−1.45240
$429$	0	0
$430$	−4.94818	−0.238622
$431$	−0.257465	−0.0124017	−0.00620083	−	0.999981i	$-0.501974\pi$
$431$	−0.257465	−0.0124017	−0.00620083	+	0.999981i	$0.501974\pi$
$432$	2.63867	0.126953
$433$	−24.3282	−1.16914	−0.584570	−	0.811344i	$-0.698737\pi$
$433$	−24.3282	−1.16914	−0.584570	+	0.811344i	$0.698737\pi$
$434$	2.65554	0.127470
$435$	5.97059	0.286268
$436$	−3.28291	−0.157223
$437$	−34.1863	−1.63535
$438$	3.71267	0.177398
$439$	17.0180	0.812224	0.406112	−	0.913823i	$-0.366884\pi$
$439$	17.0180	0.812224	0.406112	+	0.913823i	$0.366884\pi$
$440$	−11.2171	−0.534754
$441$	1.00000	0.0476190
$442$	0	0
$443$	38.1564	1.81287	0.906433	−	0.422349i	$-0.138794\pi$
$443$	38.1564	1.81287	0.906433	+	0.422349i	$0.138794\pi$
$444$	8.31728	0.394721
$445$	12.8555	0.609410
$446$	10.5413	0.499143
$447$	22.6396	1.07082
$448$	−2.87621	−0.135888
$449$	−41.3335	−1.95065	−0.975325	−	0.220773i	$-0.929142\pi$
$449$	−41.3335	−1.95065	−0.975325	+	0.220773i	$0.929142\pi$
$450$	−1.87835	−0.0885464
$451$	−51.1216	−2.40722
$452$	8.40884	0.395518
$453$	7.94508	0.373292
$454$	−2.64160	−0.123976
$455$	0	0
$456$	11.3418	0.531127
$457$	18.6232	0.871155	0.435578	−	0.900151i	$-0.356544\pi$
$457$	18.6232	0.871155	0.435578	+	0.900151i	$0.356544\pi$
$458$	−4.85828	−0.227012
$459$	2.34533	0.109471
$460$	−10.3604	−0.483054
$461$	−7.60929	−0.354400	−0.177200	−	0.984175i	$-0.556704\pi$
$461$	−7.60929	−0.354400	−0.177200	+	0.984175i	$0.556704\pi$
$462$	2.79741	0.130147
$463$	−25.2029	−1.17128	−0.585640	−	0.810571i	$-0.699157\pi$
$463$	−25.2029	−1.17128	−0.585640	+	0.810571i	$0.699157\pi$
$464$	14.7879	0.686511
$465$	5.82134	0.269958
$466$	−0.838591	−0.0388470
$467$	−18.6005	−0.860727	−0.430364	−	0.902656i	$-0.641615\pi$
$467$	−18.6005	−0.860727	−0.430364	+	0.902656i	$0.641615\pi$
$468$	0	0
$469$	−3.27680	−0.151308
$470$	2.70197	0.124632
$471$	15.4868	0.713594
$472$	−19.1446	−0.881203
$473$	−55.0113	−2.52942
$474$	−7.58859	−0.348555
$475$	23.9650	1.09959
$476$	−4.13673	−0.189607
$477$	1.52870	0.0699942
$478$	−2.82281	−0.129112
$479$	−24.5390	−1.12122	−0.560608	−	0.828081i	$-0.689432\pi$
$479$	−24.5390	−1.12122	−0.560608	+	0.828081i	$0.689432\pi$
$480$	5.26363	0.240251
$481$	0	0
$482$	−5.40430	−0.246159
$483$	5.51348	0.250872
$484$	−39.0382	−1.77447
$485$	17.8566	0.810828
$486$	0.485989	0.0220449
$487$	−30.7639	−1.39404	−0.697022	−	0.717049i	$-0.745492\pi$
$487$	−30.7639	−1.39404	−0.697022	+	0.717049i	$0.745492\pi$
$488$	−13.9860	−0.633118
$489$	−5.89612	−0.266632
$490$	0.517753	0.0233897
$491$	−19.2032	−0.866627	−0.433313	−	0.901243i	$-0.642656\pi$
$491$	−19.2032	−0.866627	−0.433313	+	0.901243i	$0.642656\pi$
$492$	15.6649	0.706229
$493$	13.1439	0.591973
$494$	0	0
$495$	6.13233	0.275628
$496$	14.4182	0.647398
$497$	8.66905	0.388860
$498$	−1.27967	−0.0573435
$499$	14.0592	0.629376	0.314688	−	0.949195i	$-0.398100\pi$
$499$	14.0592	0.629376	0.314688	+	0.949195i	$0.398100\pi$
$500$	16.6582	0.744977
$501$	9.50892	0.424827
$502$	4.73970	0.211543
$503$	−0.602593	−0.0268683	−0.0134341	−	0.999910i	$-0.504276\pi$
$503$	−0.602593	−0.0268683	−0.0134341	+	0.999910i	$0.504276\pi$
$504$	−1.82917	−0.0814779
$505$	−2.74469	−0.122137
$506$	15.4235	0.685657
$507$	0	0
$508$	2.09472	0.0929382
$509$	7.87345	0.348984	0.174492	−	0.984659i	$-0.444172\pi$
$509$	7.87345	0.348984	0.174492	+	0.984659i	$0.444172\pi$
$510$	1.21430	0.0537702
$511$	7.63941	0.337948
$512$	22.6901	1.00277
$513$	−6.20049	−0.273759
$514$	5.05147	0.222811
$515$	−11.0610	−0.487407
$516$	16.8568	0.742080
$517$	30.0391	1.32112
$518$	−2.29169	−0.100691
$519$	−1.62465	−0.0713142
$520$	0	0
$521$	−26.5275	−1.16219	−0.581096	−	0.813835i	$-0.697376\pi$
$521$	−26.5275	−1.16219	−0.581096	+	0.813835i	$0.697376\pi$
$522$	2.72363	0.119210
$523$	−7.55937	−0.330548	−0.165274	−	0.986248i	$-0.552851\pi$
$523$	−7.55937	−0.330548	−0.165274	+	0.986248i	$0.552851\pi$
$524$	26.1506	1.14239
$525$	−3.86501	−0.168683
$526$	−11.8965	−0.518711
$527$	12.8154	0.558246
$528$	15.1885	0.660994
$529$	7.39847	0.321673
$530$	0.791487	0.0343800
$531$	10.4663	0.454198
$532$	10.9365	0.474158
$533$	0	0
$534$	5.86436	0.253776
$535$	18.1489	0.784645
$536$	5.99383	0.258894
$537$	19.7547	0.852478
$538$	2.45823	0.105982
$539$	5.75611	0.247933
$540$	−1.87910	−0.0808634
$541$	13.8116	0.593807	0.296904	−	0.954907i	$-0.404046\pi$
$541$	13.8116	0.593807	0.296904	+	0.954907i	$0.404046\pi$
$542$	6.59504	0.283281
$543$	0.589428	0.0252948
$544$	11.5876	0.496814
$545$	1.98291	0.0849383
$546$	0	0
$547$	15.3668	0.657039	0.328519	−	0.944497i	$-0.393450\pi$
$547$	15.3668	0.657039	0.328519	+	0.944497i	$0.393450\pi$
$548$	11.5937	0.495260
$549$	7.64609	0.326327
$550$	−10.8120	−0.461026
$551$	−34.7494	−1.48038
$552$	−10.0851	−0.429251
$553$	−15.6147	−0.664006
$554$	−11.4567	−0.486747
$555$	−5.02371	−0.213245
$556$	1.29575	0.0549521
$557$	−26.0809	−1.10508	−0.552542	−	0.833485i	$-0.686342\pi$
$557$	−26.0809	−1.10508	−0.552542	+	0.833485i	$0.686342\pi$
$558$	2.65554	0.112418
$559$	0	0
$560$	2.81113	0.118792
$561$	13.5000	0.569970
$562$	−7.22606	−0.304813
$563$	−12.8706	−0.542430	−0.271215	−	0.962519i	$-0.587425\pi$
$563$	−12.8706	−0.542430	−0.271215	+	0.962519i	$0.587425\pi$
$564$	−9.20471	−0.387588
$565$	−5.07901	−0.213675
$566$	−10.2007	−0.428769
$567$	1.00000	0.0419961
$568$	−15.8572	−0.665353
$569$	−4.94976	−0.207505	−0.103752	−	0.994603i	$-0.533085\pi$
$569$	−4.94976	−0.207505	−0.103752	+	0.994603i	$0.533085\pi$
$570$	−3.21032	−0.134466
$571$	−28.2860	−1.18373	−0.591865	−	0.806037i	$-0.701608\pi$
$571$	−28.2860	−1.18373	−0.591865	+	0.806037i	$0.701608\pi$
$572$	0	0
$573$	9.17624	0.383343
$574$	−4.31620	−0.180155
$575$	−21.3097	−0.888674
$576$	−2.87621	−0.119842
$577$	30.1903	1.25684	0.628419	−	0.777875i	$-0.283702\pi$
$577$	30.1903	1.25684	0.628419	+	0.777875i	$0.283702\pi$
$578$	−5.58860	−0.232455
$579$	−3.28733	−0.136617
$580$	−10.5310	−0.437277
$581$	−2.63313	−0.109241
$582$	8.14574	0.337652
$583$	8.79935	0.364432
$584$	−13.9738	−0.578240
$585$	0	0
$586$	−3.58691	−0.148174
$587$	26.0507	1.07523	0.537614	−	0.843191i	$-0.319326\pi$
$587$	26.0507	1.07523	0.537614	+	0.843191i	$0.319326\pi$
$588$	−1.76381	−0.0727385
$589$	−33.8808	−1.39603
$590$	5.41895	0.223094
$591$	15.3203	0.630195
$592$	−12.4427	−0.511391
$593$	−10.6780	−0.438494	−0.219247	−	0.975669i	$-0.570360\pi$
$593$	−10.6780	−0.438494	−0.219247	+	0.975669i	$0.570360\pi$
$594$	2.79741	0.114779
$595$	2.49862	0.102433
$596$	−39.9320	−1.63568
$597$	−14.5230	−0.594387
$598$	0	0
$599$	−13.3791	−0.546655	−0.273327	−	0.961921i	$-0.588124\pi$
$599$	−13.3791	−0.546655	−0.273327	+	0.961921i	$0.588124\pi$
$600$	7.06977	0.288622
$601$	34.8949	1.42339	0.711697	−	0.702486i	$-0.247927\pi$
$601$	34.8949	1.42339	0.711697	+	0.702486i	$0.247927\pi$
$602$	−4.64461	−0.189300
$603$	−3.27680	−0.133442
$604$	−14.0136	−0.570207
$605$	23.5794	0.958640
$606$	−1.25206	−0.0508614
$607$	−34.8926	−1.41625	−0.708123	−	0.706089i	$-0.750458\pi$
$607$	−34.8926	−1.41625	−0.708123	+	0.706089i	$0.750458\pi$
$608$	−30.6349	−1.24241
$609$	5.60430	0.227098
$610$	3.95879	0.160287
$611$	0	0
$612$	−4.13673	−0.167217
$613$	4.05797	0.163900	0.0819500	−	0.996636i	$-0.473885\pi$
$613$	4.05797	0.163900	0.0819500	+	0.996636i	$0.473885\pi$
$614$	12.7413	0.514195
$615$	−9.46174	−0.381534
$616$	−10.5289	−0.424223
$617$	−1.53616	−0.0618435	−0.0309217	−	0.999522i	$-0.509844\pi$
$617$	−1.53616	−0.0618435	−0.0309217	+	0.999522i	$0.509844\pi$
$618$	−5.04576	−0.202970
$619$	15.0023	0.602993	0.301496	−	0.953467i	$-0.402514\pi$
$619$	15.0023	0.602993	0.301496	+	0.953467i	$0.402514\pi$
$620$	−10.2678	−0.412363
$621$	5.51348	0.221248
$622$	11.3590	0.455456
$623$	12.0669	0.483448
$624$	0	0
$625$	9.26336	0.370534
$626$	−9.97917	−0.398848
$627$	−35.6908	−1.42535
$628$	−27.3159	−1.09002
$629$	−11.0594	−0.440968
$630$	0.517753	0.0206278
$631$	9.33661	0.371685	0.185842	−	0.982580i	$-0.440499\pi$
$631$	9.33661	0.371685	0.185842	+	0.982580i	$0.440499\pi$
$632$	28.5620	1.13614
$633$	−16.5273	−0.656900
$634$	−1.33026	−0.0528314
$635$	−1.26523	−0.0502091
$636$	−2.69634	−0.106917
$637$	0	0
$638$	15.6775	0.620679
$639$	8.66905	0.342942
$640$	−12.0164	−0.474991
$641$	−13.0967	−0.517288	−0.258644	−	0.965973i	$-0.583276\pi$
$641$	−13.0967	−0.517288	−0.258644	+	0.965973i	$0.583276\pi$
$642$	8.27906	0.326748
$643$	−13.8692	−0.546947	−0.273473	−	0.961880i	$-0.588173\pi$
$643$	−13.8692	−0.546947	−0.273473	+	0.961880i	$0.588173\pi$
$644$	−9.72476	−0.383209
$645$	−10.1817	−0.400902
$646$	−7.06735	−0.278061
$647$	11.6782	0.459116	0.229558	−	0.973295i	$-0.426272\pi$
$647$	11.6782	0.459116	0.229558	+	0.973295i	$0.426272\pi$
$648$	−1.82917	−0.0718567
$649$	60.2451	2.36483
$650$	0	0
$651$	5.46420	0.214159
$652$	10.3997	0.407282
$653$	8.68615	0.339915	0.169958	−	0.985451i	$-0.445637\pi$
$653$	8.68615	0.339915	0.169958	+	0.985451i	$0.445637\pi$
$654$	0.904550	0.0353707
$655$	−15.7952	−0.617168
$656$	−23.4347	−0.914973
$657$	7.63941	0.298042
$658$	2.53620	0.0988715
$659$	−48.3963	−1.88525	−0.942626	−	0.333851i	$-0.891652\pi$
$659$	−48.3963	−1.88525	−0.942626	+	0.333851i	$0.891652\pi$
$660$	−10.8163	−0.421023
$661$	−25.4739	−0.990820	−0.495410	−	0.868659i	$-0.664982\pi$
$661$	−25.4739	−0.990820	−0.495410	+	0.868659i	$0.664982\pi$
$662$	−4.69051	−0.182302
$663$	0	0
$664$	4.81645	0.186915
$665$	−6.60575	−0.256160
$666$	−2.29169	−0.0888010
$667$	30.8992	1.19642
$668$	−16.7720	−0.648927
$669$	21.6903	0.838597
$670$	−1.69657	−0.0655443
$671$	44.0118	1.69906
$672$	4.94071	0.190592
$673$	−1.31053	−0.0505171	−0.0252585	−	0.999681i	$-0.508041\pi$
$673$	−1.31053	−0.0505171	−0.0252585	+	0.999681i	$0.508041\pi$
$674$	−5.50957	−0.212221
$675$	−3.86501	−0.148764
$676$	0	0
$677$	−47.4782	−1.82473	−0.912367	−	0.409373i	$-0.865747\pi$
$677$	−47.4782	−1.82473	−0.912367	+	0.409373i	$0.865747\pi$
$678$	−2.31691	−0.0889805
$679$	16.7611	0.643234
$680$	−4.57040	−0.175267
$681$	−5.43551	−0.208289
$682$	15.2856	0.585317
$683$	−13.2075	−0.505372	−0.252686	−	0.967548i	$-0.581314\pi$
$683$	−13.2075	−0.505372	−0.252686	+	0.967548i	$0.581314\pi$
$684$	10.9365	0.418168
$685$	−7.00271	−0.267560
$686$	0.485989	0.0185552
$687$	−9.99668	−0.381397
$688$	−25.2178	−0.961421
$689$	0	0
$690$	2.85462	0.108674
$691$	6.63757	0.252505	0.126253	−	0.991998i	$-0.459705\pi$
$691$	6.63757	0.252505	0.126253	+	0.991998i	$0.459705\pi$
$692$	2.86558	0.108933
$693$	5.75611	0.218657
$694$	−9.56103	−0.362932
$695$	−0.782645	−0.0296874
$696$	−10.2512	−0.388572
$697$	−20.8295	−0.788974
$698$	3.83275	0.145072
$699$	−1.72553	−0.0652657
$700$	6.81716	0.257664
$701$	49.2722	1.86099	0.930494	−	0.366308i	$-0.119378\pi$
$701$	49.2722	1.86099	0.930494	+	0.366308i	$0.119378\pi$
$702$	0	0
$703$	29.2385	1.10275
$704$	−16.5558	−0.623970
$705$	5.55972	0.209391
$706$	−7.13533	−0.268542
$707$	−2.57631	−0.0968921
$708$	−18.4606	−0.693791
$709$	11.5730	0.434634	0.217317	−	0.976101i	$-0.430269\pi$
$709$	11.5730	0.434634	0.217317	+	0.976101i	$0.430269\pi$
$710$	4.48842	0.168448
$711$	−15.6147	−0.585598
$712$	−22.0724	−0.827197
$713$	30.1268	1.12826
$714$	1.13980	0.0426561
$715$	0	0
$716$	−34.8436	−1.30217
$717$	−5.80837	−0.216918
$718$	−8.15126	−0.304203
$719$	−12.0513	−0.449437	−0.224718	−	0.974424i	$-0.572146\pi$
$719$	−12.0513	−0.449437	−0.224718	+	0.974424i	$0.572146\pi$
$720$	2.81113	0.104765
$721$	−10.3824	−0.386662
$722$	9.45061	0.351715
$723$	−11.1202	−0.413565
$724$	−1.03964	−0.0386380
$725$	−21.6607	−0.804458
$726$	10.7563	0.399205
$727$	35.1133	1.30228	0.651139	−	0.758958i	$-0.274291\pi$
$727$	35.1133	1.30228	0.651139	+	0.758958i	$0.274291\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	3.95533	0.146393
$731$	−22.4144	−0.829025
$732$	−13.4863	−0.498468
$733$	−4.72292	−0.174445	−0.0872225	−	0.996189i	$-0.527799\pi$
$733$	−4.72292	−0.174445	−0.0872225	+	0.996189i	$0.527799\pi$
$734$	−5.31694	−0.196252
$735$	1.06536	0.0392964
$736$	27.2405	1.00410
$737$	−18.8616	−0.694777
$738$	−4.31620	−0.158882
$739$	6.05371	0.222689	0.111345	−	0.993782i	$-0.464484\pi$
$739$	6.05371	0.222689	0.111345	+	0.993782i	$0.464484\pi$
$740$	8.86089	0.325733
$741$	0	0
$742$	0.742930	0.0272738
$743$	−23.7080	−0.869761	−0.434880	−	0.900488i	$-0.643209\pi$
$743$	−23.7080	−0.869761	−0.434880	+	0.900488i	$0.643209\pi$
$744$	−9.99498	−0.366434
$745$	24.1193	0.883662
$746$	−3.51630	−0.128741
$747$	−2.63313	−0.0963412
$748$	−23.8115	−0.870634
$749$	17.0355	0.622463
$750$	−4.58988	−0.167599
$751$	24.1103	0.879797	0.439899	−	0.898047i	$-0.355014\pi$
$751$	24.1103	0.879797	0.439899	+	0.898047i	$0.355014\pi$
$752$	13.7703	0.502150
$753$	9.75269	0.355408
$754$	0	0
$755$	8.46436	0.308050
$756$	−1.76381	−0.0641493
$757$	−36.1639	−1.31440	−0.657200	−	0.753716i	$-0.728259\pi$
$757$	−36.1639	−1.31440	−0.657200	+	0.753716i	$0.728259\pi$
$758$	−1.28049	−0.0465096
$759$	31.7362	1.15195
$760$	12.0831	0.438299
$761$	13.7043	0.496781	0.248390	−	0.968660i	$-0.420098\pi$
$761$	13.7043	0.496781	0.248390	+	0.968660i	$0.420098\pi$
$762$	−0.577165	−0.0209085
$763$	1.86126	0.0673820
$764$	−16.1852	−0.585560
$765$	2.49862	0.0903377
$766$	4.18371	0.151163
$767$	0	0
$768$	0.270832	0.00977281
$769$	−42.4002	−1.52899	−0.764494	−	0.644630i	$-0.777011\pi$
$769$	−42.4002	−1.52899	−0.764494	+	0.644630i	$0.777011\pi$
$770$	2.98024	0.107401
$771$	10.3942	0.374338
$772$	5.79825	0.208683
$773$	−4.22784	−0.152065	−0.0760325	−	0.997105i	$-0.524225\pi$
$773$	−4.22784	−0.152065	−0.0760325	+	0.997105i	$0.524225\pi$
$774$	−4.64461	−0.166947
$775$	−21.1192	−0.758624
$776$	−30.6590	−1.10060
$777$	−4.71551	−0.169168
$778$	−9.70646	−0.347993
$779$	55.0683	1.97303
$780$	0	0
$781$	49.9000	1.78556
$782$	6.28429	0.224726
$783$	5.60430	0.200281
$784$	2.63867	0.0942382
$785$	16.4990	0.588875
$786$	−7.20535	−0.257006
$787$	−15.4320	−0.550090	−0.275045	−	0.961431i	$-0.588693\pi$
$787$	−15.4320	−0.550090	−0.275045	+	0.961431i	$0.588693\pi$
$788$	−27.0223	−0.962628
$789$	−24.4789	−0.871472
$790$	−8.08457	−0.287636
$791$	−4.76742	−0.169510
$792$	−10.5289	−0.374129
$793$	0	0
$794$	1.38952	0.0493122
$795$	1.62861	0.0577608
$796$	25.6159	0.907931
$797$	20.1457	0.713598	0.356799	−	0.934181i	$-0.383868\pi$
$797$	20.1457	0.713598	0.356799	+	0.934181i	$0.383868\pi$
$798$	−3.01337	−0.106672
$799$	12.2394	0.433000
$800$	−19.0959	−0.675142
$801$	12.0669	0.426361
$802$	8.76029	0.309337
$803$	43.9733	1.55179
$804$	5.77966	0.203833
$805$	5.87384	0.207026
$806$	0	0
$807$	5.05819	0.178057
$808$	4.71252	0.165786
$809$	34.0215	1.19613	0.598067	−	0.801446i	$-0.295936\pi$
$809$	34.0215	1.19613	0.598067	+	0.801446i	$0.295936\pi$
$810$	0.517753	0.0181920
$811$	30.0516	1.05525	0.527626	−	0.849477i	$-0.323082\pi$
$811$	30.0516	1.05525	0.527626	+	0.849477i	$0.323082\pi$
$812$	−9.88495	−0.346894
$813$	13.5704	0.475933
$814$	−13.1912	−0.462352
$815$	−6.28148	−0.220031
$816$	6.18855	0.216643
$817$	59.2583	2.07318
$818$	−4.25604	−0.148809
$819$	0	0
$820$	16.6888	0.582797
$821$	−13.6105	−0.475010	−0.237505	−	0.971386i	$-0.576330\pi$
$821$	−13.6105	−0.475010	−0.237505	+	0.971386i	$0.576330\pi$
$822$	−3.19446	−0.111420
$823$	40.2600	1.40338	0.701688	−	0.712484i	$-0.252430\pi$
$823$	40.2600	1.40338	0.701688	+	0.712484i	$0.252430\pi$
$824$	18.9913	0.661593
$825$	−22.2474	−0.774557
$826$	5.08650	0.176982
$827$	−16.6662	−0.579541	−0.289771	−	0.957096i	$-0.593579\pi$
$827$	−16.6662	−0.579541	−0.289771	+	0.957096i	$0.593579\pi$
$828$	−9.72476	−0.337959
$829$	12.2378	0.425037	0.212518	−	0.977157i	$-0.431833\pi$
$829$	12.2378	0.425037	0.212518	+	0.977157i	$0.431833\pi$
$830$	−1.36331	−0.0473212
$831$	−23.5739	−0.817770
$832$	0	0
$833$	2.34533	0.0812608
$834$	−0.357022	−0.0123627
$835$	10.1304	0.350577
$836$	62.9519	2.17724
$837$	5.46420	0.188871
$838$	−0.840223	−0.0290250
$839$	−46.7656	−1.61453	−0.807265	−	0.590190i	$-0.799053\pi$
$839$	−46.7656	−1.61453	−0.807265	+	0.590190i	$0.799053\pi$
$840$	−1.94873	−0.0672374
$841$	2.40819	0.0830411
$842$	12.4621	0.429471
$843$	−14.8688	−0.512108
$844$	29.1511	1.00342
$845$	0	0
$846$	2.53620	0.0871965
$847$	22.1329	0.760494
$848$	4.03372	0.138519
$849$	−20.9896	−0.720362
$850$	−4.40536	−0.151103
$851$	−25.9989	−0.891230
$852$	−15.2906	−0.523847
$853$	4.23317	0.144941	0.0724704	−	0.997371i	$-0.476912\pi$
$853$	4.23317	0.144941	0.0724704	+	0.997371i	$0.476912\pi$
$854$	3.71592	0.127156
$855$	−6.60575	−0.225912
$856$	−31.1609	−1.06506
$857$	−12.7087	−0.434122	−0.217061	−	0.976158i	$-0.569647\pi$
$857$	−12.7087	−0.434122	−0.217061	+	0.976158i	$0.569647\pi$
$858$	0	0
$859$	12.6692	0.432266	0.216133	−	0.976364i	$-0.430655\pi$
$859$	12.6692	0.432266	0.216133	+	0.976364i	$0.430655\pi$
$860$	17.9586	0.612382
$861$	−8.88127	−0.302673
$862$	−0.125125	−0.00426178
$863$	−27.6136	−0.939979	−0.469989	−	0.882672i	$-0.655742\pi$
$863$	−27.6136	−0.939979	−0.469989	+	0.882672i	$0.655742\pi$
$864$	4.94071	0.168086
$865$	−1.73083	−0.0588501
$866$	−11.8232	−0.401770
$867$	−11.4994	−0.390541
$868$	−9.63784	−0.327130
$869$	−89.8802	−3.04898
$870$	2.90164	0.0983749
$871$	0	0
$872$	−3.40456	−0.115293
$873$	16.7611	0.567279
$874$	−16.6142	−0.561983
$875$	−9.44442	−0.319280
$876$	−13.4745	−0.455261
$877$	−2.58612	−0.0873272	−0.0436636	−	0.999046i	$-0.513903\pi$
$877$	−2.58612	−0.0873272	−0.0436636	+	0.999046i	$0.513903\pi$
$878$	8.27056	0.279118
$879$	−7.38064	−0.248943
$880$	16.1812	0.545468
$881$	15.2497	0.513776	0.256888	−	0.966441i	$-0.417303\pi$
$881$	15.2497	0.513776	0.256888	+	0.966441i	$0.417303\pi$
$882$	0.485989	0.0163641
$883$	−20.9880	−0.706304	−0.353152	−	0.935566i	$-0.614890\pi$
$883$	−20.9880	−0.706304	−0.353152	+	0.935566i	$0.614890\pi$
$884$	0	0
$885$	11.1503	0.374815
$886$	18.5436	0.622985
$887$	1.36914	0.0459712	0.0229856	−	0.999736i	$-0.492683\pi$
$887$	1.36914	0.0459712	0.0229856	+	0.999736i	$0.492683\pi$
$888$	8.62548	0.289452
$889$	−1.18761	−0.0398311
$890$	6.24765	0.209422
$891$	5.75611	0.192837
$892$	−38.2577	−1.28096
$893$	−32.3582	−1.08282
$894$	11.0026	0.367982
$895$	21.0458	0.703485
$896$	−11.2792	−0.376813
$897$	0	0
$898$	−20.0877	−0.670334
$899$	30.6230	1.02134
$900$	6.81716	0.227239
$901$	3.58529	0.119443
$902$	−24.8446	−0.827233
$903$	−9.55702	−0.318038
$904$	8.72043	0.290037
$905$	0.627952	0.0208738
$906$	3.86122	0.128281
$907$	−28.6699	−0.951968	−0.475984	−	0.879454i	$-0.657908\pi$
$907$	−28.6699	−0.951968	−0.475984	+	0.879454i	$0.657908\pi$
$908$	9.58723	0.318164
$909$	−2.57631	−0.0854508
$910$	0	0
$911$	11.9761	0.396784	0.198392	−	0.980123i	$-0.436428\pi$
$911$	11.9761	0.396784	0.198392	+	0.980123i	$0.436428\pi$
$912$	−16.3611	−0.541769
$913$	−15.1566	−0.501610
$914$	9.05066	0.299369
$915$	8.14583	0.269293
$916$	17.6323	0.582587
$917$	−14.8261	−0.489602
$918$	1.13980	0.0376192
$919$	26.0095	0.857976	0.428988	−	0.903310i	$-0.358870\pi$
$919$	26.0095	0.857976	0.428988	+	0.903310i	$0.358870\pi$
$920$	−10.7443	−0.354228
$921$	26.2172	0.863885
$922$	−3.69803	−0.121788
$923$	0	0
$924$	−10.1527	−0.334000
$925$	18.2255	0.599250
$926$	−12.2484	−0.402506
$927$	−10.3824	−0.341004
$928$	27.6892	0.908944
$929$	−28.6198	−0.938985	−0.469492	−	0.882937i	$-0.655563\pi$
$929$	−28.6198	−0.938985	−0.469492	+	0.882937i	$0.655563\pi$
$930$	2.82911	0.0927701
$931$	−6.20049	−0.203213
$932$	3.04352	0.0996938
$933$	23.3730	0.765198
$934$	−9.03963	−0.295786
$935$	14.3823	0.470352
$936$	0	0
$937$	−45.1573	−1.47522	−0.737612	−	0.675225i	$-0.764047\pi$
$937$	−45.1573	−1.47522	−0.737612	+	0.675225i	$0.764047\pi$
$938$	−1.59249	−0.0519966
$939$	−20.5337	−0.670093
$940$	−9.80632	−0.319847
$941$	−33.5054	−1.09224	−0.546122	−	0.837705i	$-0.683897\pi$
$941$	−33.5054	−1.09224	−0.546122	+	0.837705i	$0.683897\pi$
$942$	7.52642	0.245224
$943$	−48.9667	−1.59458
$944$	27.6171	0.898859
$945$	1.06536	0.0346561
$946$	−26.7349	−0.869227
$947$	40.9586	1.33098	0.665488	−	0.746409i	$-0.268224\pi$
$947$	40.9586	1.33098	0.665488	+	0.746409i	$0.268224\pi$
$948$	27.5415	0.894506
$949$	0	0
$950$	11.6467	0.377870
$951$	−2.73722	−0.0887606
$952$	−4.29001	−0.139040
$953$	−27.0812	−0.877245	−0.438622	−	0.898672i	$-0.644533\pi$
$953$	−27.0812	−0.877245	−0.438622	+	0.898672i	$0.644533\pi$
$954$	0.742930	0.0240532
$955$	9.77599	0.316344
$956$	10.2449	0.331343
$957$	32.2590	1.04279
$958$	−11.9257	−0.385302
$959$	−6.57310	−0.212257
$960$	−3.06419	−0.0988964
$961$	−1.14247	−0.0368538
$962$	0	0
$963$	17.0355	0.548961
$964$	19.6140	0.631724
$965$	−3.50219	−0.112739
$966$	2.67949	0.0862113
$967$	−57.7720	−1.85782	−0.928912	−	0.370301i	$-0.879254\pi$
$967$	−57.7720	−1.85782	−0.928912	+	0.370301i	$0.879254\pi$
$968$	−40.4848	−1.30123
$969$	−14.5422	−0.467163
$970$	8.67813	0.278638
$971$	55.7685	1.78970	0.894849	−	0.446370i	$-0.147283\pi$
$971$	55.7685	1.78970	0.894849	+	0.446370i	$0.147283\pi$
$972$	−1.76381	−0.0565744
$973$	−0.734630	−0.0235512
$974$	−14.9509	−0.479058
$975$	0	0
$976$	20.1755	0.645803
$977$	29.4083	0.940855	0.470427	−	0.882439i	$-0.344100\pi$
$977$	29.4083	0.940855	0.470427	+	0.882439i	$0.344100\pi$
$978$	−2.86545	−0.0916270
$979$	69.4582	2.21989
$980$	−1.87910	−0.0600255
$981$	1.86126	0.0594253
$982$	−9.33253	−0.297813
$983$	−43.0253	−1.37229	−0.686146	−	0.727464i	$-0.740699\pi$
$983$	−43.0253	−1.37229	−0.686146	+	0.727464i	$0.740699\pi$
$984$	16.2454	0.517884
$985$	16.3217	0.520052
$986$	6.38781	0.203429
$987$	5.21864	0.166111
$988$	0	0
$989$	−52.6925	−1.67552
$990$	2.98024	0.0947184
$991$	−51.9229	−1.64939	−0.824693	−	0.565581i	$-0.808652\pi$
$991$	−51.9229	−1.64939	−0.824693	+	0.565581i	$0.808652\pi$
$992$	26.9971	0.857158
$993$	−9.65148	−0.306280
$994$	4.21306	0.133630
$995$	−15.4722	−0.490502
$996$	4.64435	0.147162
$997$	−8.10714	−0.256756	−0.128378	−	0.991725i	$-0.540977\pi$
$997$	−8.10714	−0.256756	−0.128378	+	0.991725i	$0.540977\pi$
$998$	6.83262	0.216283
$999$	−4.71551	−0.149192

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bd.1.5		8
13.6	odd	12		273.2.bd.a.127.4	yes	16
13.11	odd	12		273.2.bd.a.43.4	✓	16
13.12	even	2		3549.2.a.bb.1.4		8
39.11	even	12		819.2.ct.b.316.5		16
39.32	even	12		819.2.ct.b.127.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.a.43.4	✓	16	13.11	odd	12
273.2.bd.a.127.4	yes	16	13.6	odd	12
819.2.ct.b.127.5		16	39.32	even	12
819.2.ct.b.316.5		16	39.11	even	12
3549.2.a.bb.1.4		8	13.12	even	2
3549.2.a.bd.1.5		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.485989 q^{2} +1.00000 q^{3} -1.76381 q^{4} +1.06536 q^{5} +0.485989 q^{6} +1.00000 q^{7} -1.82917 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.485989 q^{2} +1.00000 q^{3} -1.76381 q^{4} +1.06536 q^{5} +0.485989 q^{6} +1.00000 q^{7} -1.82917 q^{8} +1.00000 q^{9} +0.517753 q^{10} +5.75611 q^{11} -1.76381 q^{12} +0.485989 q^{14} +1.06536 q^{15} +2.63867 q^{16} +2.34533 q^{17} +0.485989 q^{18} -6.20049 q^{19} -1.87910 q^{20} +1.00000 q^{21} +2.79741 q^{22} +5.51348 q^{23} -1.82917 q^{24} -3.86501 q^{25} +1.00000 q^{27} -1.76381 q^{28} +5.60430 q^{29} +0.517753 q^{30} +5.46420 q^{31} +4.94071 q^{32} +5.75611 q^{33} +1.13980 q^{34} +1.06536 q^{35} -1.76381 q^{36} -4.71551 q^{37} -3.01337 q^{38} -1.94873 q^{40} -8.88127 q^{41} +0.485989 q^{42} -9.55702 q^{43} -10.1527 q^{44} +1.06536 q^{45} +2.67949 q^{46} +5.21864 q^{47} +2.63867 q^{48} +1.00000 q^{49} -1.87835 q^{50} +2.34533 q^{51} +1.52870 q^{53} +0.485989 q^{54} +6.13233 q^{55} -1.82917 q^{56} -6.20049 q^{57} +2.72363 q^{58} +10.4663 q^{59} -1.87910 q^{60} +7.64609 q^{61} +2.65554 q^{62} +1.00000 q^{63} -2.87621 q^{64} +2.79741 q^{66} -3.27680 q^{67} -4.13673 q^{68} +5.51348 q^{69} +0.517753 q^{70} +8.66905 q^{71} -1.82917 q^{72} +7.63941 q^{73} -2.29169 q^{74} -3.86501 q^{75} +10.9365 q^{76} +5.75611 q^{77} -15.6147 q^{79} +2.81113 q^{80} +1.00000 q^{81} -4.31620 q^{82} -2.63313 q^{83} -1.76381 q^{84} +2.49862 q^{85} -4.64461 q^{86} +5.60430 q^{87} -10.5289 q^{88} +12.0669 q^{89} +0.517753 q^{90} -9.72476 q^{92} +5.46420 q^{93} +2.53620 q^{94} -6.60575 q^{95} +4.94071 q^{96} +16.7611 q^{97} +0.485989 q^{98} +5.75611 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 8 q^{3} + 6 q^{4} + 2 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 8 * q^3 + 6 * q^4 + 2 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 + 8 * q^9	\( 8 q + 2 q^{2} + 8 q^{3} + 6 q^{4} + 2 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} + 8 q^{9} - 4 q^{10} + 8 q^{11} + 6 q^{12} + 2 q^{14} + 2 q^{15} + 10 q^{16} + 10 q^{17} + 2 q^{18} + 18 q^{19} + 2 q^{20} + 8 q^{21} + 2 q^{22} - 2 q^{23} + 12 q^{24} - 6 q^{25} + 8 q^{27} + 6 q^{28} - 12 q^{29} - 4 q^{30} + 16 q^{31} + 26 q^{32} + 8 q^{33} + 24 q^{34} + 2 q^{35} + 6 q^{36} + 24 q^{37} + 16 q^{38} - 30 q^{40} - 4 q^{41} + 2 q^{42} - 10 q^{43} - 20 q^{44} + 2 q^{45} + 12 q^{46} + 10 q^{47} + 10 q^{48} + 8 q^{49} - 16 q^{50} + 10 q^{51} + 6 q^{53} + 2 q^{54} - 10 q^{55} + 12 q^{56} + 18 q^{57} + 16 q^{58} + 6 q^{59} + 2 q^{60} + 6 q^{61} + 16 q^{62} + 8 q^{63} - 8 q^{64} + 2 q^{66} + 24 q^{67} + 20 q^{68} - 2 q^{69} - 4 q^{70} + 42 q^{71} + 12 q^{72} + 32 q^{73} - 18 q^{74} - 6 q^{75} + 28 q^{76} + 8 q^{77} - 2 q^{79} - 40 q^{80} + 8 q^{81} - 18 q^{82} - 2 q^{83} + 6 q^{84} + 4 q^{85} + 26 q^{86} - 12 q^{87} - 2 q^{88} + 12 q^{89} - 4 q^{90} - 10 q^{92} + 16 q^{93} - 16 q^{94} - 4 q^{95} + 26 q^{96} + 64 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 8 * q^3 + 6 * q^4 + 2 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 + 8 * q^9 - 4 * q^10 + 8 * q^11 + 6 * q^12 + 2 * q^14 + 2 * q^15 + 10 * q^16 + 10 * q^17 + 2 * q^18 + 18 * q^19 + 2 * q^20 + 8 * q^21 + 2 * q^22 - 2 * q^23 + 12 * q^24 - 6 * q^25 + 8 * q^27 + 6 * q^28 - 12 * q^29 - 4 * q^30 + 16 * q^31 + 26 * q^32 + 8 * q^33 + 24 * q^34 + 2 * q^35 + 6 * q^36 + 24 * q^37 + 16 * q^38 - 30 * q^40 - 4 * q^41 + 2 * q^42 - 10 * q^43 - 20 * q^44 + 2 * q^45 + 12 * q^46 + 10 * q^47 + 10 * q^48 + 8 * q^49 - 16 * q^50 + 10 * q^51 + 6 * q^53 + 2 * q^54 - 10 * q^55 + 12 * q^56 + 18 * q^57 + 16 * q^58 + 6 * q^59 + 2 * q^60 + 6 * q^61 + 16 * q^62 + 8 * q^63 - 8 * q^64 + 2 * q^66 + 24 * q^67 + 20 * q^68 - 2 * q^69 - 4 * q^70 + 42 * q^71 + 12 * q^72 + 32 * q^73 - 18 * q^74 - 6 * q^75 + 28 * q^76 + 8 * q^77 - 2 * q^79 - 40 * q^80 + 8 * q^81 - 18 * q^82 - 2 * q^83 + 6 * q^84 + 4 * q^85 + 26 * q^86 - 12 * q^87 - 2 * q^88 + 12 * q^89 - 4 * q^90 - 10 * q^92 + 16 * q^93 - 16 * q^94 - 4 * q^95 + 26 * q^96 + 64 * q^97 + 2 * q^98 + 8 * q^99

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