LMFDB - Embedded newform 3549.2.a.bb.1.3

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:	$1$
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			1.3
Root			$1.10207$ 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)

$f(q)$	$=$	$q-1.10207 q^{2} +1.00000 q^{3} -0.785435 q^{4} -3.28432 q^{5} -1.10207 q^{6} -1.00000 q^{7} +3.06975 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.10207 q^{2} +1.00000 q^{3} -0.785435 q^{4} -3.28432 q^{5} -1.10207 q^{6} -1.00000 q^{7} +3.06975 q^{8} +1.00000 q^{9} +3.61956 q^{10} -1.40850 q^{11} -0.785435 q^{12} +1.10207 q^{14} -3.28432 q^{15} -1.81222 q^{16} +5.77983 q^{17} -1.10207 q^{18} -6.19600 q^{19} +2.57962 q^{20} -1.00000 q^{21} +1.55227 q^{22} +3.40145 q^{23} +3.06975 q^{24} +5.78675 q^{25} +1.00000 q^{27} +0.785435 q^{28} -8.57692 q^{29} +3.61956 q^{30} +7.64123 q^{31} -4.14230 q^{32} -1.40850 q^{33} -6.36980 q^{34} +3.28432 q^{35} -0.785435 q^{36} +5.59124 q^{37} +6.82845 q^{38} -10.0820 q^{40} +1.15399 q^{41} +1.10207 q^{42} +0.818994 q^{43} +1.10628 q^{44} -3.28432 q^{45} -3.74865 q^{46} +3.35146 q^{47} -1.81222 q^{48} +1.00000 q^{49} -6.37742 q^{50} +5.77983 q^{51} +5.54281 q^{53} -1.10207 q^{54} +4.62595 q^{55} -3.06975 q^{56} -6.19600 q^{57} +9.45240 q^{58} +4.88973 q^{59} +2.57962 q^{60} -2.97751 q^{61} -8.42119 q^{62} -1.00000 q^{63} +8.18957 q^{64} +1.55227 q^{66} -0.268759 q^{67} -4.53968 q^{68} +3.40145 q^{69} -3.61956 q^{70} -9.28104 q^{71} +3.06975 q^{72} -12.1448 q^{73} -6.16196 q^{74} +5.78675 q^{75} +4.86656 q^{76} +1.40850 q^{77} +6.00232 q^{79} +5.95192 q^{80} +1.00000 q^{81} -1.27178 q^{82} -6.02174 q^{83} +0.785435 q^{84} -18.9828 q^{85} -0.902592 q^{86} -8.57692 q^{87} -4.32374 q^{88} +16.5783 q^{89} +3.61956 q^{90} -2.67162 q^{92} +7.64123 q^{93} -3.69355 q^{94} +20.3496 q^{95} -4.14230 q^{96} -18.7352 q^{97} -1.10207 q^{98} -1.40850 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.10207	−0.779283	−0.389642	−	0.920967i	$-0.627401\pi$
$2$	−1.10207	−0.779283	−0.389642	+	0.920967i	$0.627401\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.785435	−0.392717
$5$	−3.28432	−1.46879	−0.734396	−	0.678721i	$-0.762534\pi$
$5$	−3.28432	−1.46879	−0.734396	+	0.678721i	$0.762534\pi$
$6$	−1.10207	−0.449919
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.06975	1.08532
$9$	1.00000	0.333333
$10$	3.61956	1.14460
$11$	−1.40850	−0.424678	−0.212339	−	0.977196i	$-0.568108\pi$
$11$	−1.40850	−0.424678	−0.212339	+	0.977196i	$0.568108\pi$
$12$	−0.785435	−0.226735
$13$	0	0
$13$	0	0
$14$	1.10207	0.294541
$15$	−3.28432	−0.848007
$16$	−1.81222	−0.453056
$17$	5.77983	1.40181	0.700907	−	0.713252i	$-0.252779\pi$
$17$	5.77983	1.40181	0.700907	+	0.713252i	$0.252779\pi$
$18$	−1.10207	−0.259761
$19$	−6.19600	−1.42146	−0.710730	−	0.703465i	$-0.751635\pi$
$19$	−6.19600	−1.42146	−0.710730	+	0.703465i	$0.751635\pi$
$20$	2.57962	0.576820
$21$	−1.00000	−0.218218
$22$	1.55227	0.330944
$23$	3.40145	0.709251	0.354626	−	0.935008i	$-0.384608\pi$
$23$	3.40145	0.709251	0.354626	+	0.935008i	$0.384608\pi$
$24$	3.06975	0.626611
$25$	5.78675	1.15735
$26$	0	0
$27$	1.00000	0.192450
$28$	0.785435	0.148433
$29$	−8.57692	−1.59269	−0.796347	−	0.604840i	$-0.793237\pi$
$29$	−8.57692	−1.59269	−0.796347	+	0.604840i	$0.793237\pi$
$30$	3.61956	0.660838
$31$	7.64123	1.37240	0.686202	−	0.727411i	$-0.259276\pi$
$31$	7.64123	1.37240	0.686202	+	0.727411i	$0.259276\pi$
$32$	−4.14230	−0.732263
$33$	−1.40850	−0.245188
$34$	−6.36980	−1.09241
$35$	3.28432	0.555151
$36$	−0.785435	−0.130906
$37$	5.59124	0.919195	0.459597	−	0.888127i	$-0.347994\pi$
$37$	5.59124	0.919195	0.459597	+	0.888127i	$0.347994\pi$
$38$	6.82845	1.10772
$39$	0	0
$40$	−10.0820	−1.59411
$41$	1.15399	0.180223	0.0901116	−	0.995932i	$-0.471278\pi$
$41$	1.15399	0.180223	0.0901116	+	0.995932i	$0.471278\pi$
$42$	1.10207	0.170054
$43$	0.818994	0.124895	0.0624477	−	0.998048i	$-0.480109\pi$
$43$	0.818994	0.124895	0.0624477	+	0.998048i	$0.480109\pi$
$44$	1.10628	0.166778
$45$	−3.28432	−0.489597
$46$	−3.74865	−0.552708
$47$	3.35146	0.488861	0.244430	−	0.969667i	$-0.421399\pi$
$47$	3.35146	0.488861	0.244430	+	0.969667i	$0.421399\pi$
$48$	−1.81222	−0.261572
$49$	1.00000	0.142857
$50$	−6.37742	−0.901903
$51$	5.77983	0.809338
$52$	0	0
$53$	5.54281	0.761363	0.380682	−	0.924706i	$-0.375689\pi$
$53$	5.54281	0.761363	0.380682	+	0.924706i	$0.375689\pi$
$54$	−1.10207	−0.149973
$55$	4.62595	0.623763
$56$	−3.06975	−0.410213
$57$	−6.19600	−0.820681
$58$	9.45240	1.24116
$59$	4.88973	0.636588	0.318294	−	0.947992i	$-0.396890\pi$
$59$	4.88973	0.636588	0.318294	+	0.947992i	$0.396890\pi$
$60$	2.57962	0.333027
$61$	−2.97751	−0.381231	−0.190616	−	0.981665i	$-0.561048\pi$
$61$	−2.97751	−0.381231	−0.190616	+	0.981665i	$0.561048\pi$
$62$	−8.42119	−1.06949
$63$	−1.00000	−0.125988
$64$	8.18957	1.02370
$65$	0	0
$66$	1.55227	0.191071
$67$	−0.268759	−0.0328341	−0.0164171	−	0.999865i	$-0.505226\pi$
$67$	−0.268759	−0.0328341	−0.0164171	+	0.999865i	$0.505226\pi$
$68$	−4.53968	−0.550517
$69$	3.40145	0.409486
$70$	−3.61956	−0.432620
$71$	−9.28104	−1.10146	−0.550728	−	0.834684i	$-0.685650\pi$
$71$	−9.28104	−1.10146	−0.550728	+	0.834684i	$0.685650\pi$
$72$	3.06975	0.361774
$73$	−12.1448	−1.42144	−0.710721	−	0.703474i	$-0.751631\pi$
$73$	−12.1448	−1.42144	−0.710721	+	0.703474i	$0.751631\pi$
$74$	−6.16196	−0.716313
$75$	5.78675	0.668196
$76$	4.86656	0.558232
$77$	1.40850	0.160513
$78$	0	0
$79$	6.00232	0.675313	0.337657	−	0.941269i	$-0.390366\pi$
$79$	6.00232	0.675313	0.337657	+	0.941269i	$0.390366\pi$
$80$	5.95192	0.665444
$81$	1.00000	0.111111
$82$	−1.27178	−0.140445
$83$	−6.02174	−0.660972	−0.330486	−	0.943811i	$-0.607213\pi$
$83$	−6.02174	−0.660972	−0.330486	+	0.943811i	$0.607213\pi$
$84$	0.785435	0.0856980
$85$	−18.9828	−2.05897
$86$	−0.902592	−0.0973290
$87$	−8.57692	−0.919543
$88$	−4.32374	−0.460912
$89$	16.5783	1.75730	0.878650	−	0.477466i	$-0.158444\pi$
$89$	16.5783	1.75730	0.878650	+	0.477466i	$0.158444\pi$
$90$	3.61956	0.381535
$91$	0	0
$92$	−2.67162	−0.278535
$93$	7.64123	0.792358
$94$	−3.69355	−0.380961
$95$	20.3496	2.08783
$96$	−4.14230	−0.422772
$97$	−18.7352	−1.90227	−0.951134	−	0.308779i	$-0.900080\pi$
$97$	−18.7352	−1.90227	−0.951134	+	0.308779i	$0.900080\pi$
$98$	−1.10207	−0.111326
$99$	−1.40850	−0.141559
$100$	−4.54511	−0.454511
$101$	15.0516	1.49769	0.748846	−	0.662744i	$-0.230608\pi$
$101$	15.0516	1.49769	0.748846	+	0.662744i	$0.230608\pi$
$102$	−6.36980	−0.630704
$103$	−14.0763	−1.38698	−0.693488	−	0.720468i	$-0.743927\pi$
$103$	−14.0763	−1.38698	−0.693488	+	0.720468i	$0.743927\pi$
$104$	0	0
$105$	3.28432	0.320517
$106$	−6.10858	−0.593318
$107$	7.34688	0.710250	0.355125	−	0.934819i	$-0.384438\pi$
$107$	7.34688	0.710250	0.355125	+	0.934819i	$0.384438\pi$
$108$	−0.785435	−0.0755785
$109$	4.65621	0.445984	0.222992	−	0.974820i	$-0.428418\pi$
$109$	4.65621	0.445984	0.222992	+	0.974820i	$0.428418\pi$
$110$	−5.09814	−0.486089
$111$	5.59124	0.530697
$112$	1.81222	0.171239
$113$	7.17145	0.674633	0.337317	−	0.941391i	$-0.390481\pi$
$113$	7.17145	0.674633	0.337317	+	0.941391i	$0.390481\pi$
$114$	6.82845	0.639543
$115$	−11.1714	−1.04174
$116$	6.73661	0.625479
$117$	0	0
$118$	−5.38884	−0.496083
$119$	−5.77983	−0.529836
$120$	−10.0820	−0.920361
$121$	−9.01613	−0.819649
$122$	3.28143	0.297087
$123$	1.15399	0.104052
$124$	−6.00169	−0.538967
$125$	−2.58392	−0.231113
$126$	1.10207	0.0981805
$127$	−11.6599	−1.03465	−0.517326	−	0.855789i	$-0.673072\pi$
$127$	−11.6599	−1.03465	−0.517326	+	0.855789i	$0.673072\pi$
$128$	−0.740894	−0.0654864
$129$	0.818994	0.0721084
$130$	0	0
$131$	8.68221	0.758568	0.379284	−	0.925280i	$-0.376170\pi$
$131$	8.68221	0.758568	0.379284	+	0.925280i	$0.376170\pi$
$132$	1.10628	0.0962896
$133$	6.19600	0.537262
$134$	0.296192	0.0255871
$135$	−3.28432	−0.282669
$136$	17.7427	1.52142
$137$	−12.5774	−1.07456	−0.537278	−	0.843405i	$-0.680547\pi$
$137$	−12.5774	−1.07456	−0.537278	+	0.843405i	$0.680547\pi$
$138$	−3.74865	−0.319106
$139$	−10.7327	−0.910335	−0.455167	−	0.890406i	$-0.650421\pi$
$139$	−10.7327	−0.910335	−0.455167	+	0.890406i	$0.650421\pi$
$140$	−2.57962	−0.218017
$141$	3.35146	0.282244
$142$	10.2284	0.858347
$143$	0	0
$144$	−1.81222	−0.151019
$145$	28.1693	2.33934
$146$	13.3845	1.10771
$147$	1.00000	0.0824786
$148$	−4.39156	−0.360984
$149$	−11.4702	−0.939673	−0.469836	−	0.882754i	$-0.655687\pi$
$149$	−11.4702	−0.939673	−0.469836	+	0.882754i	$0.655687\pi$
$150$	−6.37742	−0.520714
$151$	9.07431	0.738457	0.369228	−	0.929339i	$-0.379622\pi$
$151$	9.07431	0.738457	0.369228	+	0.929339i	$0.379622\pi$
$152$	−19.0202	−1.54274
$153$	5.77983	0.467272
$154$	−1.55227	−0.125085
$155$	−25.0962	−2.01578
$156$	0	0
$157$	−16.8251	−1.34279	−0.671393	−	0.741101i	$-0.734304\pi$
$157$	−16.8251	−1.34279	−0.671393	+	0.741101i	$0.734304\pi$
$158$	−6.61499	−0.526260
$159$	5.54281	0.439573
$160$	13.6046	1.07554
$161$	−3.40145	−0.268072
$162$	−1.10207	−0.0865870
$163$	−20.8336	−1.63181	−0.815905	−	0.578186i	$-0.803761\pi$
$163$	−20.8336	−1.63181	−0.815905	+	0.578186i	$0.803761\pi$
$164$	−0.906385	−0.0707768
$165$	4.62595	0.360130
$166$	6.63640	0.515084
$167$	−6.20927	−0.480488	−0.240244	−	0.970713i	$-0.577227\pi$
$167$	−6.20927	−0.480488	−0.240244	+	0.970713i	$0.577227\pi$
$168$	−3.06975	−0.236837
$169$	0	0
$170$	20.9204	1.60452
$171$	−6.19600	−0.473820
$172$	−0.643267	−0.0490486
$173$	−10.5498	−0.802086	−0.401043	−	0.916059i	$-0.631352\pi$
$173$	−10.5498	−0.802086	−0.401043	+	0.916059i	$0.631352\pi$
$174$	9.45240	0.716584
$175$	−5.78675	−0.437437
$176$	2.55251	0.192403
$177$	4.88973	0.367534
$178$	−18.2705	−1.36944
$179$	−21.0058	−1.57005	−0.785025	−	0.619465i	$-0.787350\pi$
$179$	−21.0058	−1.57005	−0.785025	+	0.619465i	$0.787350\pi$
$180$	2.57962	0.192273
$181$	−14.6306	−1.08748	−0.543741	−	0.839253i	$-0.682993\pi$
$181$	−14.6306	−1.08748	−0.543741	+	0.839253i	$0.682993\pi$
$182$	0	0
$183$	−2.97751	−0.220104
$184$	10.4416	0.769766
$185$	−18.3634	−1.35011
$186$	−8.42119	−0.617472
$187$	−8.14088	−0.595320
$188$	−2.63235	−0.191984
$189$	−1.00000	−0.0727393
$190$	−22.4268	−1.62701
$191$	−5.22863	−0.378330	−0.189165	−	0.981945i	$-0.560578\pi$
$191$	−5.22863	−0.378330	−0.189165	+	0.981945i	$0.560578\pi$
$192$	8.18957	0.591031
$193$	−23.7024	−1.70614	−0.853069	−	0.521798i	$-0.825261\pi$
$193$	−23.7024	−1.70614	−0.853069	+	0.521798i	$0.825261\pi$
$194$	20.6475	1.48241
$195$	0	0
$196$	−0.785435	−0.0561025
$197$	15.6200	1.11288	0.556439	−	0.830889i	$-0.312167\pi$
$197$	15.6200	1.11288	0.556439	+	0.830889i	$0.312167\pi$
$198$	1.55227	0.110315
$199$	−20.8348	−1.47694	−0.738468	−	0.674288i	$-0.764450\pi$
$199$	−20.8348	−1.47694	−0.738468	+	0.674288i	$0.764450\pi$
$200$	17.7639	1.25610
$201$	−0.268759	−0.0189568
$202$	−16.5880	−1.16713
$203$	8.57692	0.601982
$204$	−4.53968	−0.317841
$205$	−3.79007	−0.264710
$206$	15.5131	1.08085
$207$	3.40145	0.236417
$208$	0	0
$209$	8.72705	0.603663
$210$	−3.61956	−0.249773
$211$	−8.96355	−0.617076	−0.308538	−	0.951212i	$-0.599840\pi$
$211$	−8.96355	−0.617076	−0.308538	+	0.951212i	$0.599840\pi$
$212$	−4.35351	−0.299001
$213$	−9.28104	−0.635926
$214$	−8.09680	−0.553486
$215$	−2.68984	−0.183445
$216$	3.06975	0.208870
$217$	−7.64123	−0.518720
$218$	−5.13149	−0.347548
$219$	−12.1448	−0.820670
$220$	−3.63339	−0.244963
$221$	0	0
$222$	−6.16196	−0.413564
$223$	−3.42664	−0.229465	−0.114732	−	0.993396i	$-0.536601\pi$
$223$	−3.42664	−0.229465	−0.114732	+	0.993396i	$0.536601\pi$
$224$	4.14230	0.276769
$225$	5.78675	0.385783
$226$	−7.90346	−0.525730
$227$	−22.6121	−1.50082	−0.750408	−	0.660975i	$-0.770143\pi$
$227$	−22.6121	−1.50082	−0.750408	+	0.660975i	$0.770143\pi$
$228$	4.86656	0.322296
$229$	14.0168	0.926253	0.463126	−	0.886292i	$-0.346728\pi$
$229$	14.0168	0.926253	0.463126	+	0.886292i	$0.346728\pi$
$230$	12.3117	0.811813
$231$	1.40850	0.0926723
$232$	−26.3290	−1.72859
$233$	12.1663	0.797043	0.398522	−	0.917159i	$-0.369523\pi$
$233$	12.1663	0.797043	0.398522	+	0.917159i	$0.369523\pi$
$234$	0	0
$235$	−11.0073	−0.718034
$236$	−3.84056	−0.249999
$237$	6.00232	0.389892
$238$	6.36980	0.412893
$239$	9.34457	0.604450	0.302225	−	0.953237i	$-0.402271\pi$
$239$	9.34457	0.604450	0.302225	+	0.953237i	$0.402271\pi$
$240$	5.95192	0.384194
$241$	21.2740	1.37038	0.685190	−	0.728364i	$-0.259719\pi$
$241$	21.2740	1.37038	0.685190	+	0.728364i	$0.259719\pi$
$242$	9.93644	0.638739
$243$	1.00000	0.0641500
$244$	2.33864	0.149716
$245$	−3.28432	−0.209827
$246$	−1.27178	−0.0810859
$247$	0	0
$248$	23.4567	1.48950
$249$	−6.02174	−0.381612
$250$	2.84767	0.180103
$251$	0.690735	0.0435988	0.0217994	−	0.999762i	$-0.493060\pi$
$251$	0.690735	0.0435988	0.0217994	+	0.999762i	$0.493060\pi$
$252$	0.785435	0.0494777
$253$	−4.79093	−0.301203
$254$	12.8501	0.806287
$255$	−18.9828	−1.18875
$256$	−15.5626	−0.972663
$257$	−23.3399	−1.45590	−0.727952	−	0.685629i	$-0.759527\pi$
$257$	−23.3399	−1.45590	−0.727952	+	0.685629i	$0.759527\pi$
$258$	−0.902592	−0.0561929
$259$	−5.59124	−0.347423
$260$	0	0
$261$	−8.57692	−0.530898
$262$	−9.56843	−0.591140
$263$	−9.11003	−0.561748	−0.280874	−	0.959745i	$-0.590624\pi$
$263$	−9.11003	−0.561748	−0.280874	+	0.959745i	$0.590624\pi$
$264$	−4.32374	−0.266108
$265$	−18.2043	−1.11828
$266$	−6.82845	−0.418679
$267$	16.5783	1.01458
$268$	0.211092	0.0128945
$269$	4.40754	0.268733	0.134366	−	0.990932i	$-0.457100\pi$
$269$	4.40754	0.268733	0.134366	+	0.990932i	$0.457100\pi$
$270$	3.61956	0.220279
$271$	13.3892	0.813339	0.406669	−	0.913575i	$-0.366690\pi$
$271$	13.3892	0.813339	0.406669	+	0.913575i	$0.366690\pi$
$272$	−10.4743	−0.635100
$273$	0	0
$274$	13.8612	0.837383
$275$	−8.15062	−0.491501
$276$	−2.67162	−0.160812
$277$	8.68968	0.522112	0.261056	−	0.965324i	$-0.415929\pi$
$277$	8.68968	0.522112	0.261056	+	0.965324i	$0.415929\pi$
$278$	11.8282	0.709409
$279$	7.64123	0.457468
$280$	10.0820	0.602517
$281$	−21.7228	−1.29587	−0.647936	−	0.761695i	$-0.724368\pi$
$281$	−21.7228	−1.29587	−0.647936	+	0.761695i	$0.724368\pi$
$282$	−3.69355	−0.219948
$283$	25.3757	1.50843	0.754215	−	0.656628i	$-0.228018\pi$
$283$	25.3757	1.50843	0.754215	+	0.656628i	$0.228018\pi$
$284$	7.28965	0.432561
$285$	20.3496	1.20541
$286$	0	0
$287$	−1.15399	−0.0681179
$288$	−4.14230	−0.244088
$289$	16.4064	0.965085
$290$	−31.0447	−1.82301
$291$	−18.7352	−1.09827
$292$	9.53896	0.558225
$293$	26.5450	1.55077	0.775387	−	0.631486i	$-0.217555\pi$
$293$	26.5450	1.55077	0.775387	+	0.631486i	$0.217555\pi$
$294$	−1.10207	−0.0642742
$295$	−16.0594	−0.935016
$296$	17.1637	0.997622
$297$	−1.40850	−0.0817293
$298$	12.6410	0.732271
$299$	0	0
$300$	−4.54511	−0.262412
$301$	−0.818994	−0.0472060
$302$	−10.0006	−0.575467
$303$	15.0516	0.864693
$304$	11.2285	0.644001
$305$	9.77909	0.559949
$306$	−6.36980	−0.364137
$307$	4.33093	0.247179	0.123590	−	0.992333i	$-0.460559\pi$
$307$	4.33093	0.247179	0.123590	+	0.992333i	$0.460559\pi$
$308$	−1.10628	−0.0630363
$309$	−14.0763	−0.800771
$310$	27.6579	1.57086
$311$	14.9481	0.847629	0.423815	−	0.905749i	$-0.360691\pi$
$311$	14.9481	0.847629	0.423815	+	0.905749i	$0.360691\pi$
$312$	0	0
$313$	−8.75971	−0.495128	−0.247564	−	0.968871i	$-0.579630\pi$
$313$	−8.75971	−0.495128	−0.247564	+	0.968871i	$0.579630\pi$
$314$	18.5424	1.04641
$315$	3.28432	0.185050
$316$	−4.71443	−0.265207
$317$	5.46319	0.306843	0.153422	−	0.988161i	$-0.450971\pi$
$317$	5.46319	0.306843	0.153422	+	0.988161i	$0.450971\pi$
$318$	−6.10858	−0.342552
$319$	12.0806	0.676382
$320$	−26.8971	−1.50360
$321$	7.34688	0.410063
$322$	3.74865	0.208904
$323$	−35.8118	−1.99262
$324$	−0.785435	−0.0436353
$325$	0	0
$326$	22.9601	1.27164
$327$	4.65621	0.257489
$328$	3.54247	0.195600
$329$	−3.35146	−0.184772
$330$	−5.09814	−0.280643
$331$	−8.61829	−0.473704	−0.236852	−	0.971546i	$-0.576116\pi$
$331$	−8.61829	−0.473704	−0.236852	+	0.971546i	$0.576116\pi$
$332$	4.72968	0.259575
$333$	5.59124	0.306398
$334$	6.84307	0.374436
$335$	0.882689	0.0482265
$336$	1.81222	0.0988648
$337$	−13.6769	−0.745029	−0.372515	−	0.928026i	$-0.621504\pi$
$337$	−13.6769	−0.745029	−0.372515	+	0.928026i	$0.621504\pi$
$338$	0	0
$339$	7.17145	0.389500
$340$	14.9098	0.808595
$341$	−10.7626	−0.582830
$342$	6.82845	0.369240
$343$	−1.00000	−0.0539949
$344$	2.51411	0.135552
$345$	−11.1714	−0.601450
$346$	11.6266	0.625053
$347$	−3.79558	−0.203758	−0.101879	−	0.994797i	$-0.532485\pi$
$347$	−3.79558	−0.203758	−0.101879	+	0.994797i	$0.532485\pi$
$348$	6.73661	0.361120
$349$	−11.3725	−0.608758	−0.304379	−	0.952551i	$-0.598449\pi$
$349$	−11.3725	−0.608758	−0.304379	+	0.952551i	$0.598449\pi$
$350$	6.37742	0.340887
$351$	0	0
$352$	5.83442	0.310976
$353$	17.5694	0.935126	0.467563	−	0.883960i	$-0.345132\pi$
$353$	17.5694	0.935126	0.467563	+	0.883960i	$0.345132\pi$
$354$	−5.38884	−0.286414
$355$	30.4819	1.61781
$356$	−13.0212	−0.690123
$357$	−5.77983	−0.305901
$358$	23.1500	1.22351
$359$	−5.89389	−0.311068	−0.155534	−	0.987831i	$-0.549710\pi$
$359$	−5.89389	−0.311068	−0.155534	+	0.987831i	$0.549710\pi$
$360$	−10.0820	−0.531370
$361$	19.3905	1.02055
$362$	16.1240	0.847457
$363$	−9.01613	−0.473224
$364$	0	0
$365$	39.8874	2.08780
$366$	3.28143	0.171523
$367$	16.1849	0.844846	0.422423	−	0.906399i	$-0.361180\pi$
$367$	16.1849	0.844846	0.422423	+	0.906399i	$0.361180\pi$
$368$	−6.16418	−0.321330
$369$	1.15399	0.0600744
$370$	20.2378	1.05211
$371$	−5.54281	−0.287768
$372$	−6.00169	−0.311173
$373$	−20.2446	−1.04823	−0.524113	−	0.851649i	$-0.675603\pi$
$373$	−20.2446	−1.04823	−0.524113	+	0.851649i	$0.675603\pi$
$374$	8.97184	0.463923
$375$	−2.58392	−0.133433
$376$	10.2882	0.530571
$377$	0	0
$378$	1.10207	0.0566845
$379$	−16.3848	−0.841629	−0.420815	−	0.907147i	$-0.638256\pi$
$379$	−16.3848	−0.841629	−0.420815	+	0.907147i	$0.638256\pi$
$380$	−15.9833	−0.819927
$381$	−11.6599	−0.597356
$382$	5.76233	0.294827
$383$	13.2965	0.679417	0.339708	−	0.940531i	$-0.389672\pi$
$383$	13.2965	0.679417	0.339708	+	0.940531i	$0.389672\pi$
$384$	−0.740894	−0.0378086
$385$	−4.62595	−0.235760
$386$	26.1218	1.32956
$387$	0.818994	0.0416318
$388$	14.7152	0.747054
$389$	−30.4724	−1.54501	−0.772506	−	0.635007i	$-0.780997\pi$
$389$	−30.4724	−1.54501	−0.772506	+	0.635007i	$0.780997\pi$
$390$	0	0
$391$	19.6598	0.994239
$392$	3.06975	0.155046
$393$	8.68221	0.437960
$394$	−17.2144	−0.867247
$395$	−19.7135	−0.991894
$396$	1.10628	0.0555928
$397$	−10.7849	−0.541279	−0.270640	−	0.962681i	$-0.587235\pi$
$397$	−10.7849	−0.541279	−0.270640	+	0.962681i	$0.587235\pi$
$398$	22.9614	1.15095
$399$	6.19600	0.310188
$400$	−10.4869	−0.524344
$401$	16.4052	0.819236	0.409618	−	0.912257i	$-0.365662\pi$
$401$	16.4052	0.819236	0.409618	+	0.912257i	$0.365662\pi$
$402$	0.296192	0.0147727
$403$	0	0
$404$	−11.8221	−0.588170
$405$	−3.28432	−0.163199
$406$	−9.45240	−0.469115
$407$	−7.87525	−0.390362
$408$	17.7427	0.878392
$409$	23.8898	1.18127	0.590636	−	0.806938i	$-0.298877\pi$
$409$	23.8898	1.18127	0.590636	+	0.806938i	$0.298877\pi$
$410$	4.17694	0.206284
$411$	−12.5774	−0.620395
$412$	11.0560	0.544689
$413$	−4.88973	−0.240608
$414$	−3.74865	−0.184236
$415$	19.7773	0.970830
$416$	0	0
$417$	−10.7327	−0.525582
$418$	−9.61785	−0.470425
$419$	−28.8315	−1.40851	−0.704256	−	0.709946i	$-0.748719\pi$
$419$	−28.8315	−1.40851	−0.704256	+	0.709946i	$0.748719\pi$
$420$	−2.57962	−0.125872
$421$	−13.5391	−0.659857	−0.329929	−	0.944006i	$-0.607025\pi$
$421$	−13.5391	−0.659857	−0.329929	+	0.944006i	$0.607025\pi$
$422$	9.87848	0.480877
$423$	3.35146	0.162954
$424$	17.0150	0.826324
$425$	33.4464	1.62239
$426$	10.2284	0.495567
$427$	2.97751	0.144092
$428$	−5.77050	−0.278927
$429$	0	0
$430$	2.96440	0.142956
$431$	22.3092	1.07460	0.537299	−	0.843392i	$-0.319445\pi$
$431$	22.3092	1.07460	0.537299	+	0.843392i	$0.319445\pi$
$432$	−1.81222	−0.0871906
$433$	−10.1459	−0.487582	−0.243791	−	0.969828i	$-0.578391\pi$
$433$	−10.1459	−0.487582	−0.243791	+	0.969828i	$0.578391\pi$
$434$	8.42119	0.404230
$435$	28.1693	1.35062
$436$	−3.65715	−0.175146
$437$	−21.0754	−1.00817
$438$	13.3845	0.639535
$439$	−35.5140	−1.69499	−0.847494	−	0.530805i	$-0.821890\pi$
$439$	−35.5140	−1.69499	−0.847494	+	0.530805i	$0.821890\pi$
$440$	14.2005	0.676984
$441$	1.00000	0.0476190
$442$	0	0
$443$	−25.6235	−1.21741	−0.608705	−	0.793396i	$-0.708311\pi$
$443$	−25.6235	−1.21741	−0.608705	+	0.793396i	$0.708311\pi$
$444$	−4.39156	−0.208414
$445$	−54.4486	−2.58111
$446$	3.77640	0.178818
$447$	−11.4702	−0.542520
$448$	−8.18957	−0.386921
$449$	1.37936	0.0650961	0.0325481	−	0.999470i	$-0.489638\pi$
$449$	1.37936	0.0650961	0.0325481	+	0.999470i	$0.489638\pi$
$450$	−6.37742	−0.300634
$451$	−1.62539	−0.0765368
$452$	−5.63271	−0.264940
$453$	9.07431	0.426348
$454$	24.9202	1.16956
$455$	0	0
$456$	−19.0202	−0.890702
$457$	−12.7945	−0.598502	−0.299251	−	0.954174i	$-0.596737\pi$
$457$	−12.7945	−0.598502	−0.299251	+	0.954174i	$0.596737\pi$
$458$	−15.4475	−0.721814
$459$	5.77983	0.269779
$460$	8.77444	0.409110
$461$	−4.27008	−0.198877	−0.0994386	−	0.995044i	$-0.531705\pi$
$461$	−4.27008	−0.198877	−0.0994386	+	0.995044i	$0.531705\pi$
$462$	−1.55227	−0.0722180
$463$	−0.637577	−0.0296307	−0.0148154	−	0.999890i	$-0.504716\pi$
$463$	−0.637577	−0.0296307	−0.0148154	+	0.999890i	$0.504716\pi$
$464$	15.5433	0.721579
$465$	−25.0962	−1.16381
$466$	−13.4082	−0.621123
$467$	10.3676	0.479754	0.239877	−	0.970803i	$-0.422893\pi$
$467$	10.3676	0.479754	0.239877	+	0.970803i	$0.422893\pi$
$468$	0	0
$469$	0.268759	0.0124101
$470$	12.1308	0.559552
$471$	−16.8251	−0.775258
$472$	15.0103	0.690903
$473$	−1.15355	−0.0530404
$474$	−6.61499	−0.303837
$475$	−35.8547	−1.64513
$476$	4.53968	0.208076
$477$	5.54281	0.253788
$478$	−10.2984	−0.471038
$479$	−25.5435	−1.16711	−0.583555	−	0.812073i	$-0.698339\pi$
$479$	−25.5435	−1.16711	−0.583555	+	0.812073i	$0.698339\pi$
$480$	13.6046	0.620964
$481$	0	0
$482$	−23.4455	−1.06792
$483$	−3.40145	−0.154771
$484$	7.08159	0.321890
$485$	61.5322	2.79403
$486$	−1.10207	−0.0499911
$487$	12.8011	0.580074	0.290037	−	0.957015i	$-0.406332\pi$
$487$	12.8011	0.580074	0.290037	+	0.957015i	$0.406332\pi$
$488$	−9.14022	−0.413758
$489$	−20.8336	−0.942126
$490$	3.61956	0.163515
$491$	−6.83325	−0.308380	−0.154190	−	0.988041i	$-0.549277\pi$
$491$	−6.83325	−0.308380	−0.154190	+	0.988041i	$0.549277\pi$
$492$	−0.906385	−0.0408630
$493$	−49.5732	−2.23266
$494$	0	0
$495$	4.62595	0.207921
$496$	−13.8476	−0.621776
$497$	9.28104	0.416312
$498$	6.63640	0.297384
$499$	−29.8319	−1.33546	−0.667729	−	0.744405i	$-0.732733\pi$
$499$	−29.8319	−1.33546	−0.667729	+	0.744405i	$0.732733\pi$
$500$	2.02950	0.0907621
$501$	−6.20927	−0.277410
$502$	−0.761241	−0.0339758
$503$	19.5429	0.871376	0.435688	−	0.900098i	$-0.356505\pi$
$503$	19.5429	0.871376	0.435688	+	0.900098i	$0.356505\pi$
$504$	−3.06975	−0.136738
$505$	−49.4343	−2.19980
$506$	5.27996	0.234723
$507$	0	0
$508$	9.15811	0.406326
$509$	2.35518	0.104392	0.0521958	−	0.998637i	$-0.483378\pi$
$509$	2.35518	0.104392	0.0521958	+	0.998637i	$0.483378\pi$
$510$	20.9204	0.926372
$511$	12.1448	0.537255
$512$	18.6329	0.823467
$513$	−6.19600	−0.273560
$514$	25.7223	1.13456
$515$	46.2309	2.03718
$516$	−0.643267	−0.0283182
$517$	−4.72052	−0.207608
$518$	6.16196	0.270741
$519$	−10.5498	−0.463085
$520$	0	0
$521$	27.5527	1.20711	0.603553	−	0.797323i	$-0.293751\pi$
$521$	27.5527	1.20711	0.603553	+	0.797323i	$0.293751\pi$
$522$	9.45240	0.413720
$523$	26.0767	1.14025	0.570127	−	0.821557i	$-0.306894\pi$
$523$	26.0767	1.14025	0.570127	+	0.821557i	$0.306894\pi$
$524$	−6.81931	−0.297903
$525$	−5.78675	−0.252554
$526$	10.0399	0.437761
$527$	44.1650	1.92386
$528$	2.55251	0.111084
$529$	−11.4301	−0.496963
$530$	20.0625	0.871460
$531$	4.88973	0.212196
$532$	−4.86656	−0.210992
$533$	0	0
$534$	−18.2705	−0.790644
$535$	−24.1295	−1.04321
$536$	−0.825023	−0.0356356
$537$	−21.0058	−0.906468
$538$	−4.85744	−0.209419
$539$	−1.40850	−0.0606683
$540$	2.57962	0.111009
$541$	8.83112	0.379679	0.189840	−	0.981815i	$-0.439203\pi$
$541$	8.83112	0.379679	0.189840	+	0.981815i	$0.439203\pi$
$542$	−14.7559	−0.633821
$543$	−14.6306	−0.627858
$544$	−23.9418	−1.02650
$545$	−15.2925	−0.655058
$546$	0	0
$547$	9.61127	0.410948	0.205474	−	0.978663i	$-0.434126\pi$
$547$	9.61127	0.410948	0.205474	+	0.978663i	$0.434126\pi$
$548$	9.87869	0.421997
$549$	−2.97751	−0.127077
$550$	8.98258	0.383018
$551$	53.1426	2.26395
$552$	10.4416	0.444424
$553$	−6.00232	−0.255244
$554$	−9.57666	−0.406873
$555$	−18.3634	−0.779484
$556$	8.42982	0.357504
$557$	29.2549	1.23957	0.619786	−	0.784771i	$-0.287220\pi$
$557$	29.2549	1.23957	0.619786	+	0.784771i	$0.287220\pi$
$558$	−8.42119	−0.356497
$559$	0	0
$560$	−5.95192	−0.251514
$561$	−8.14088	−0.343708
$562$	23.9401	1.00985
$563$	−4.57916	−0.192989	−0.0964943	−	0.995334i	$-0.530763\pi$
$563$	−4.57916	−0.192989	−0.0964943	+	0.995334i	$0.530763\pi$
$564$	−2.63235	−0.110842
$565$	−23.5533	−0.990896
$566$	−27.9659	−1.17549
$567$	−1.00000	−0.0419961
$568$	−28.4905	−1.19543
$569$	−40.8223	−1.71136	−0.855681	−	0.517504i	$-0.826861\pi$
$569$	−40.8223	−1.71136	−0.855681	+	0.517504i	$0.826861\pi$
$570$	−22.4268	−0.939355
$571$	19.6348	0.821692	0.410846	−	0.911705i	$-0.365233\pi$
$571$	19.6348	0.821692	0.410846	+	0.911705i	$0.365233\pi$
$572$	0	0
$573$	−5.22863	−0.218429
$574$	1.27178	0.0530832
$575$	19.6833	0.820851
$576$	8.18957	0.341232
$577$	35.5481	1.47989	0.739944	−	0.672669i	$-0.234852\pi$
$577$	35.5481	1.47989	0.739944	+	0.672669i	$0.234852\pi$
$578$	−18.0811	−0.752074
$579$	−23.7024	−0.985039
$580$	−22.1252	−0.918698
$581$	6.02174	0.249824
$582$	20.6475	0.855867
$583$	−7.80703	−0.323334
$584$	−37.2816	−1.54272
$585$	0	0
$586$	−29.2545	−1.20849
$587$	−38.0391	−1.57004	−0.785020	−	0.619470i	$-0.787347\pi$
$587$	−38.0391	−1.57004	−0.785020	+	0.619470i	$0.787347\pi$
$588$	−0.785435	−0.0323908
$589$	−47.3451	−1.95082
$590$	17.6987	0.728642
$591$	15.6200	0.642520
$592$	−10.1326	−0.416446
$593$	26.2586	1.07831	0.539155	−	0.842207i	$-0.318744\pi$
$593$	26.2586	1.07831	0.539155	+	0.842207i	$0.318744\pi$
$594$	1.55227	0.0636903
$595$	18.9828	0.778219
$596$	9.00907	0.369026
$597$	−20.8348	−0.852710
$598$	0	0
$599$	−12.4404	−0.508299	−0.254150	−	0.967165i	$-0.581796\pi$
$599$	−12.4404	−0.508299	−0.254150	+	0.967165i	$0.581796\pi$
$600$	17.7639	0.725207
$601$	19.9741	0.814762	0.407381	−	0.913258i	$-0.366442\pi$
$601$	19.9741	0.814762	0.407381	+	0.913258i	$0.366442\pi$
$602$	0.902592	0.0367869
$603$	−0.268759	−0.0109447
$604$	−7.12728	−0.290005
$605$	29.6119	1.20389
$606$	−16.5880	−0.673841
$607$	27.3862	1.11157	0.555785	−	0.831326i	$-0.312418\pi$
$607$	27.3862	1.11157	0.555785	+	0.831326i	$0.312418\pi$
$608$	25.6657	1.04088
$609$	8.57692	0.347554
$610$	−10.7773	−0.436359
$611$	0	0
$612$	−4.53968	−0.183506
$613$	2.87689	0.116197	0.0580983	−	0.998311i	$-0.481496\pi$
$613$	2.87689	0.116197	0.0580983	+	0.998311i	$0.481496\pi$
$614$	−4.77300	−0.192623
$615$	−3.79007	−0.152831
$616$	4.32374	0.174208
$617$	29.9248	1.20473	0.602364	−	0.798222i	$-0.294226\pi$
$617$	29.9248	1.20473	0.602364	+	0.798222i	$0.294226\pi$
$618$	15.5131	0.624027
$619$	33.5695	1.34927	0.674637	−	0.738150i	$-0.264300\pi$
$619$	33.5695	1.34927	0.674637	+	0.738150i	$0.264300\pi$
$620$	19.7114	0.791631
$621$	3.40145	0.136495
$622$	−16.4739	−0.660543
$623$	−16.5783	−0.664197
$624$	0	0
$625$	−20.4473	−0.817892
$626$	9.65385	0.385845
$627$	8.72705	0.348525
$628$	13.2150	0.527335
$629$	32.3164	1.28854
$630$	−3.61956	−0.144207
$631$	26.4413	1.05261	0.526306	−	0.850295i	$-0.323577\pi$
$631$	26.4413	1.05261	0.526306	+	0.850295i	$0.323577\pi$
$632$	18.4256	0.732932
$633$	−8.96355	−0.356269
$634$	−6.02083	−0.239118
$635$	38.2949	1.51969
$636$	−4.35351	−0.172628
$637$	0	0
$638$	−13.3137	−0.527094
$639$	−9.28104	−0.367152
$640$	2.43333	0.0961859
$641$	−24.8891	−0.983059	−0.491530	−	0.870861i	$-0.663562\pi$
$641$	−24.8891	−0.983059	−0.491530	+	0.870861i	$0.663562\pi$
$642$	−8.09680	−0.319555
$643$	−39.2941	−1.54961	−0.774804	−	0.632201i	$-0.782152\pi$
$643$	−39.2941	−1.54961	−0.774804	+	0.632201i	$0.782152\pi$
$644$	2.67162	0.105276
$645$	−2.68984	−0.105912
$646$	39.4673	1.55282
$647$	−29.1771	−1.14707	−0.573534	−	0.819182i	$-0.694428\pi$
$647$	−29.1771	−1.14707	−0.573534	+	0.819182i	$0.694428\pi$
$648$	3.06975	0.120591
$649$	−6.88717	−0.270345
$650$	0	0
$651$	−7.64123	−0.299483
$652$	16.3634	0.640840
$653$	−8.06661	−0.315671	−0.157835	−	0.987465i	$-0.550452\pi$
$653$	−8.06661	−0.315671	−0.157835	+	0.987465i	$0.550452\pi$
$654$	−5.13149	−0.200657
$655$	−28.5151	−1.11418
$656$	−2.09129	−0.0816511
$657$	−12.1448	−0.473814
$658$	3.69355	0.143990
$659$	−39.1879	−1.52654	−0.763271	−	0.646078i	$-0.776408\pi$
$659$	−39.1879	−1.52654	−0.763271	+	0.646078i	$0.776408\pi$
$660$	−3.63339	−0.141429
$661$	−24.7993	−0.964583	−0.482291	−	0.876011i	$-0.660195\pi$
$661$	−24.7993	−0.964583	−0.482291	+	0.876011i	$0.660195\pi$
$662$	9.49798	0.369150
$663$	0	0
$664$	−18.4853	−0.717367
$665$	−20.3496	−0.789125
$666$	−6.16196	−0.238771
$667$	−29.1740	−1.12962
$668$	4.87698	0.188696
$669$	−3.42664	−0.132481
$670$	−0.972788	−0.0375821
$671$	4.19382	0.161900
$672$	4.14230	0.159793
$673$	−28.0542	−1.08141	−0.540706	−	0.841212i	$-0.681843\pi$
$673$	−28.0542	−1.08141	−0.540706	+	0.841212i	$0.681843\pi$
$674$	15.0730	0.580589
$675$	5.78675	0.222732
$676$	0	0
$677$	−17.7868	−0.683602	−0.341801	−	0.939772i	$-0.611037\pi$
$677$	−17.7868	−0.683602	−0.341801	+	0.939772i	$0.611037\pi$
$678$	−7.90346	−0.303531
$679$	18.7352	0.718990
$680$	−58.2725	−2.23465
$681$	−22.6121	−0.866497
$682$	11.8612	0.454190
$683$	−7.53488	−0.288314	−0.144157	−	0.989555i	$-0.546047\pi$
$683$	−7.53488	−0.288314	−0.144157	+	0.989555i	$0.546047\pi$
$684$	4.86656	0.186077
$685$	41.3080	1.57830
$686$	1.10207	0.0420773
$687$	14.0168	0.534772
$688$	−1.48420	−0.0565846
$689$	0	0
$690$	12.3117	0.468700
$691$	−47.2784	−1.79856	−0.899278	−	0.437377i	$-0.855907\pi$
$691$	−47.2784	−1.79856	−0.899278	+	0.437377i	$0.855907\pi$
$692$	8.28618	0.314993
$693$	1.40850	0.0535044
$694$	4.18301	0.158785
$695$	35.2496	1.33709
$696$	−26.3290	−0.997999
$697$	6.66987	0.252639
$698$	12.5334	0.474395
$699$	12.1663	0.460173
$700$	4.54511	0.171789
$701$	−5.95873	−0.225058	−0.112529	−	0.993648i	$-0.535895\pi$
$701$	−5.95873	−0.225058	−0.112529	+	0.993648i	$0.535895\pi$
$702$	0	0
$703$	−34.6434	−1.30660
$704$	−11.5350	−0.434741
$705$	−11.0073	−0.414557
$706$	−19.3628	−0.728728
$707$	−15.0516	−0.566074
$708$	−3.84056	−0.144337
$709$	−46.4175	−1.74325	−0.871623	−	0.490176i	$-0.836932\pi$
$709$	−46.4175	−1.74325	−0.871623	+	0.490176i	$0.836932\pi$
$710$	−33.5933	−1.26073
$711$	6.00232	0.225104
$712$	50.8914	1.90724
$713$	25.9912	0.973380
$714$	6.36980	0.238384
$715$	0	0
$716$	16.4987	0.616586
$717$	9.34457	0.348979
$718$	6.49550	0.242410
$719$	14.1409	0.527366	0.263683	−	0.964609i	$-0.415063\pi$
$719$	14.1409	0.527366	0.263683	+	0.964609i	$0.415063\pi$
$720$	5.95192	0.221815
$721$	14.0763	0.524228
$722$	−21.3697	−0.795298
$723$	21.2740	0.791190
$724$	11.4914	0.427073
$725$	−49.6325	−1.84330
$726$	9.93644	0.368776
$727$	25.8145	0.957405	0.478703	−	0.877977i	$-0.341107\pi$
$727$	25.8145	0.957405	0.478703	+	0.877977i	$0.341107\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−43.9589	−1.62699
$731$	4.73365	0.175080
$732$	2.33864	0.0864386
$733$	35.3926	1.30725	0.653627	−	0.756817i	$-0.273247\pi$
$733$	35.3926	1.30725	0.653627	+	0.756817i	$0.273247\pi$
$734$	−17.8370	−0.658375
$735$	−3.28432	−0.121144
$736$	−14.0898	−0.519358
$737$	0.378546	0.0139439
$738$	−1.27178	−0.0468150
$739$	45.9352	1.68975	0.844877	−	0.534961i	$-0.179674\pi$
$739$	45.9352	1.68975	0.844877	+	0.534961i	$0.179674\pi$
$740$	14.4233	0.530210
$741$	0	0
$742$	6.10858	0.224253
$743$	29.8763	1.09605	0.548027	−	0.836461i	$-0.315379\pi$
$743$	29.8763	1.09605	0.548027	+	0.836461i	$0.315379\pi$
$744$	23.4567	0.859964
$745$	37.6717	1.38018
$746$	22.3110	0.816865
$747$	−6.02174	−0.220324
$748$	6.39413	0.233792
$749$	−7.34688	−0.268449
$750$	2.84767	0.103982
$751$	35.8225	1.30718	0.653591	−	0.756848i	$-0.273262\pi$
$751$	35.8225	1.30718	0.653591	+	0.756848i	$0.273262\pi$
$752$	−6.07359	−0.221481
$753$	0.690735	0.0251718
$754$	0	0
$755$	−29.8029	−1.08464
$756$	0.785435	0.0285660
$757$	−30.6066	−1.11242	−0.556208	−	0.831043i	$-0.687744\pi$
$757$	−30.6066	−1.11242	−0.556208	+	0.831043i	$0.687744\pi$
$758$	18.0572	0.655868
$759$	−4.79093	−0.173900
$760$	62.4684	2.26597
$761$	8.73930	0.316799	0.158400	−	0.987375i	$-0.449367\pi$
$761$	8.73930	0.316799	0.158400	+	0.987375i	$0.449367\pi$
$762$	12.8501	0.465510
$763$	−4.65621	−0.168566
$764$	4.10675	0.148577
$765$	−18.9828	−0.686325
$766$	−14.6537	−0.529458
$767$	0	0
$768$	−15.5626	−0.561567
$769$	−27.4420	−0.989584	−0.494792	−	0.869011i	$-0.664756\pi$
$769$	−27.4420	−0.989584	−0.494792	+	0.869011i	$0.664756\pi$
$770$	5.09814	0.183724
$771$	−23.3399	−0.840566
$772$	18.6167	0.670030
$773$	−13.1167	−0.471776	−0.235888	−	0.971780i	$-0.575800\pi$
$773$	−13.1167	−0.471776	−0.235888	+	0.971780i	$0.575800\pi$
$774$	−0.902592	−0.0324430
$775$	44.2178	1.58835
$776$	−57.5123	−2.06457
$777$	−5.59124	−0.200585
$778$	33.5828	1.20400
$779$	−7.15013	−0.256180
$780$	0	0
$781$	13.0723	0.467764
$782$	−21.6665	−0.774794
$783$	−8.57692	−0.306514
$784$	−1.81222	−0.0647222
$785$	55.2589	1.97227
$786$	−9.56843	−0.341295
$787$	−26.5973	−0.948091	−0.474046	−	0.880500i	$-0.657207\pi$
$787$	−26.5973	−0.948091	−0.474046	+	0.880500i	$0.657207\pi$
$788$	−12.2685	−0.437046
$789$	−9.11003	−0.324326
$790$	21.7257	0.772967
$791$	−7.17145	−0.254987
$792$	−4.32374	−0.153637
$793$	0	0
$794$	11.8858	0.421810
$795$	−18.2043	−0.645642
$796$	16.3643	0.580019
$797$	5.10413	0.180798	0.0903988	−	0.995906i	$-0.471186\pi$
$797$	5.10413	0.180798	0.0903988	+	0.995906i	$0.471186\pi$
$798$	−6.82845	−0.241724
$799$	19.3709	0.685292
$800$	−23.9705	−0.847484
$801$	16.5783	0.585767
$802$	−18.0797	−0.638417
$803$	17.1059	0.603655
$804$	0.211092	0.00744466
$805$	11.1714	0.393742
$806$	0	0
$807$	4.40754	0.155153
$808$	46.2048	1.62548
$809$	1.42220	0.0500019	0.0250010	−	0.999687i	$-0.492041\pi$
$809$	1.42220	0.0500019	0.0250010	+	0.999687i	$0.492041\pi$
$810$	3.61956	0.127178
$811$	4.11149	0.144374	0.0721870	−	0.997391i	$-0.477002\pi$
$811$	4.11149	0.144374	0.0721870	+	0.997391i	$0.477002\pi$
$812$	−6.73661	−0.236409
$813$	13.3892	0.469581
$814$	8.67910	0.304202
$815$	68.4240	2.39679
$816$	−10.4743	−0.366675
$817$	−5.07449	−0.177534
$818$	−26.3283	−0.920546
$819$	0	0
$820$	2.97686	0.103956
$821$	10.9773	0.383110	0.191555	−	0.981482i	$-0.438647\pi$
$821$	10.9773	0.383110	0.191555	+	0.981482i	$0.438647\pi$
$822$	13.8612	0.483464
$823$	39.3152	1.37044	0.685221	−	0.728335i	$-0.259706\pi$
$823$	39.3152	1.37044	0.685221	+	0.728335i	$0.259706\pi$
$824$	−43.2107	−1.50531
$825$	−8.15062	−0.283768
$826$	5.38884	0.187502
$827$	20.7986	0.723238	0.361619	−	0.932326i	$-0.382224\pi$
$827$	20.7986	0.723238	0.361619	+	0.932326i	$0.382224\pi$
$828$	−2.67162	−0.0928451
$829$	−20.8735	−0.724968	−0.362484	−	0.931990i	$-0.618071\pi$
$829$	−20.8735	−0.724968	−0.362484	+	0.931990i	$0.618071\pi$
$830$	−21.7960	−0.756552
$831$	8.68968	0.301442
$832$	0	0
$833$	5.77983	0.200259
$834$	11.8282	0.409577
$835$	20.3932	0.705736
$836$	−6.85453	−0.237069
$837$	7.64123	0.264119
$838$	31.7744	1.09763
$839$	7.27089	0.251019	0.125509	−	0.992092i	$-0.459943\pi$
$839$	7.27089	0.251019	0.125509	+	0.992092i	$0.459943\pi$
$840$	10.0820	0.347864
$841$	44.5636	1.53668
$842$	14.9211	0.514216
$843$	−21.7228	−0.748172
$844$	7.04028	0.242336
$845$	0	0
$846$	−3.69355	−0.126987
$847$	9.01613	0.309798
$848$	−10.0448	−0.344940
$849$	25.3757	0.870892
$850$	−36.8604	−1.26430
$851$	19.0183	0.651940
$852$	7.28965	0.249739
$853$	−25.1125	−0.859835	−0.429917	−	0.902868i	$-0.641457\pi$
$853$	−25.1125	−0.859835	−0.429917	+	0.902868i	$0.641457\pi$
$854$	−3.28143	−0.112288
$855$	20.3496	0.695943
$856$	22.5531	0.770849
$857$	−16.3023	−0.556875	−0.278438	−	0.960454i	$-0.589817\pi$
$857$	−16.3023	−0.556875	−0.278438	+	0.960454i	$0.589817\pi$
$858$	0	0
$859$	−23.6024	−0.805303	−0.402652	−	0.915353i	$-0.631911\pi$
$859$	−23.6024	−0.805303	−0.402652	+	0.915353i	$0.631911\pi$
$860$	2.11269	0.0720422
$861$	−1.15399	−0.0393279
$862$	−24.5864	−0.837417
$863$	−6.17526	−0.210208	−0.105104	−	0.994461i	$-0.533518\pi$
$863$	−6.17526	−0.210208	−0.105104	+	0.994461i	$0.533518\pi$
$864$	−4.14230	−0.140924
$865$	34.6489	1.17810
$866$	11.1816	0.379965
$867$	16.4064	0.557192
$868$	6.00169	0.203710
$869$	−8.45425	−0.286791
$870$	−31.0447	−1.05251
$871$	0	0
$872$	14.2934	0.484036
$873$	−18.7352	−0.634089
$874$	23.2266	0.785652
$875$	2.58392	0.0873525
$876$	9.53896	0.322292
$877$	−6.53888	−0.220802	−0.110401	−	0.993887i	$-0.535214\pi$
$877$	−6.53888	−0.220802	−0.110401	+	0.993887i	$0.535214\pi$
$878$	39.1390	1.32088
$879$	26.5450	0.895340
$880$	−8.38326	−0.282600
$881$	−11.7551	−0.396039	−0.198019	−	0.980198i	$-0.563451\pi$
$881$	−11.7551	−0.396039	−0.198019	+	0.980198i	$0.563451\pi$
$882$	−1.10207	−0.0371087
$883$	−33.9878	−1.14378	−0.571890	−	0.820330i	$-0.693790\pi$
$883$	−33.9878	−1.14378	−0.571890	+	0.820330i	$0.693790\pi$
$884$	0	0
$885$	−16.0594	−0.539832
$886$	28.2390	0.948708
$887$	11.4537	0.384577	0.192289	−	0.981338i	$-0.438409\pi$
$887$	11.4537	0.384577	0.192289	+	0.981338i	$0.438409\pi$
$888$	17.1637	0.575977
$889$	11.6599	0.391061
$890$	60.0063	2.01142
$891$	−1.40850	−0.0471864
$892$	2.69140	0.0901147
$893$	−20.7657	−0.694896
$894$	12.6410	0.422777
$895$	68.9898	2.30608
$896$	0.740894	0.0247515
$897$	0	0
$898$	−1.52016	−0.0507283
$899$	−65.5382	−2.18582
$900$	−4.54511	−0.151504
$901$	32.0365	1.06729
$902$	1.79130	0.0596439
$903$	−0.818994	−0.0272544
$904$	22.0146	0.732194
$905$	48.0515	1.59728
$906$	−10.0006	−0.332246
$907$	31.8705	1.05824	0.529121	−	0.848547i	$-0.322522\pi$
$907$	31.8705	1.05824	0.529121	+	0.848547i	$0.322522\pi$
$908$	17.7603	0.589397
$909$	15.0516	0.499231
$910$	0	0
$911$	19.2082	0.636395	0.318197	−	0.948024i	$-0.396923\pi$
$911$	19.2082	0.636395	0.318197	+	0.948024i	$0.396923\pi$
$912$	11.2285	0.371814
$913$	8.48161	0.280700
$914$	14.1005	0.466403
$915$	9.77909	0.323287
$916$	−11.0092	−0.363756
$917$	−8.68221	−0.286712
$918$	−6.36980	−0.210235
$919$	54.3884	1.79411	0.897053	−	0.441922i	$-0.145703\pi$
$919$	54.3884	1.79411	0.897053	+	0.441922i	$0.145703\pi$
$920$	−34.2936	−1.13063
$921$	4.33093	0.142709
$922$	4.70594	0.154982
$923$	0	0
$924$	−1.10628	−0.0363940
$925$	32.3551	1.06383
$926$	0.702656	0.0230907
$927$	−14.0763	−0.462325
$928$	35.5282	1.16627
$929$	−46.5083	−1.52589	−0.762944	−	0.646465i	$-0.776247\pi$
$929$	−46.5083	−1.52589	−0.762944	+	0.646465i	$0.776247\pi$
$930$	27.6579	0.906937
$931$	−6.19600	−0.203066
$932$	−9.55587	−0.313013
$933$	14.9481	0.489379
$934$	−11.4258	−0.373864
$935$	26.7372	0.874401
$936$	0	0
$937$	34.6775	1.13286	0.566432	−	0.824108i	$-0.308323\pi$
$937$	34.6775	1.13286	0.566432	+	0.824108i	$0.308323\pi$
$938$	−0.296192	−0.00967101
$939$	−8.75971	−0.285862
$940$	8.64549	0.281985
$941$	−39.8173	−1.29801	−0.649004	−	0.760785i	$-0.724814\pi$
$941$	−39.8173	−1.29801	−0.649004	+	0.760785i	$0.724814\pi$
$942$	18.5424	0.604146
$943$	3.92524	0.127824
$944$	−8.86128	−0.288410
$945$	3.28432	0.106839
$946$	1.27130	0.0413335
$947$	−30.3825	−0.987300	−0.493650	−	0.869661i	$-0.664338\pi$
$947$	−30.3825	−0.987300	−0.493650	+	0.869661i	$0.664338\pi$
$948$	−4.71443	−0.153117
$949$	0	0
$950$	39.5145	1.28202
$951$	5.46319	0.177156
$952$	−17.7427	−0.575043
$953$	−2.44213	−0.0791084	−0.0395542	−	0.999217i	$-0.512594\pi$
$953$	−2.44213	−0.0791084	−0.0395542	+	0.999217i	$0.512594\pi$
$954$	−6.10858	−0.197773
$955$	17.1725	0.555688
$956$	−7.33955	−0.237378
$957$	12.0806	0.390510
$958$	28.1508	0.909510
$959$	12.5774	0.406144
$960$	−26.8971	−0.868102
$961$	27.3884	0.883495
$962$	0	0
$963$	7.34688	0.236750
$964$	−16.7094	−0.538172
$965$	77.8463	2.50596
$966$	3.74865	0.120611
$967$	−45.3725	−1.45908	−0.729541	−	0.683938i	$-0.760266\pi$
$967$	−45.3725	−1.45908	−0.729541	+	0.683938i	$0.760266\pi$
$968$	−27.6773	−0.889582
$969$	−35.8118	−1.15044
$970$	−67.8130	−2.17734
$971$	31.9137	1.02416	0.512079	−	0.858938i	$-0.328875\pi$
$971$	31.9137	1.02416	0.512079	+	0.858938i	$0.328875\pi$
$972$	−0.785435	−0.0251928
$973$	10.7327	0.344074
$974$	−14.1078	−0.452042
$975$	0	0
$976$	5.39591	0.172719
$977$	4.99280	0.159734	0.0798669	−	0.996806i	$-0.474550\pi$
$977$	4.99280	0.159734	0.0798669	+	0.996806i	$0.474550\pi$
$978$	22.9601	0.734183
$979$	−23.3506	−0.746287
$980$	2.57962	0.0824029
$981$	4.65621	0.148661
$982$	7.53074	0.240316
$983$	18.7912	0.599345	0.299672	−	0.954042i	$-0.403123\pi$
$983$	18.7912	0.599345	0.299672	+	0.954042i	$0.403123\pi$
$984$	3.54247	0.112930
$985$	−51.3010	−1.63458
$986$	54.6332	1.73988
$987$	−3.35146	−0.106678
$988$	0	0
$989$	2.78577	0.0885823
$990$	−5.09814	−0.162030
$991$	41.3604	1.31386	0.656929	−	0.753953i	$-0.271855\pi$
$991$	41.3604	1.31386	0.656929	+	0.753953i	$0.271855\pi$
$992$	−31.6523	−1.00496
$993$	−8.61829	−0.273493
$994$	−10.2284	−0.324425
$995$	68.4279	2.16931
$996$	4.72968	0.149866
$997$	12.2118	0.386753	0.193376	−	0.981125i	$-0.438056\pi$
$997$	12.2118	0.386753	0.193376	+	0.981125i	$0.438056\pi$
$998$	32.8769	1.04070
$999$	5.59124	0.176899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bb.1.3		8
13.6	odd	12		273.2.bd.a.127.6	yes	16
13.11	odd	12		273.2.bd.a.43.6	✓	16
13.12	even	2		3549.2.a.bd.1.6		8
39.11	even	12		819.2.ct.b.316.3		16
39.32	even	12		819.2.ct.b.127.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.a.43.6	✓	16	13.11	odd	12
273.2.bd.a.127.6	yes	16	13.6	odd	12
819.2.ct.b.127.3		16	39.32	even	12
819.2.ct.b.316.3		16	39.11	even	12
3549.2.a.bb.1.3		8	1.1	even	1	trivial
3549.2.a.bd.1.6		8	13.12	even	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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q-1.10207 q^{2} +1.00000 q^{3} -0.785435 q^{4} -3.28432 q^{5} -1.10207 q^{6} -1.00000 q^{7} +3.06975 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.10207 q^{2} +1.00000 q^{3} -0.785435 q^{4} -3.28432 q^{5} -1.10207 q^{6} -1.00000 q^{7} +3.06975 q^{8} +1.00000 q^{9} +3.61956 q^{10} -1.40850 q^{11} -0.785435 q^{12} +1.10207 q^{14} -3.28432 q^{15} -1.81222 q^{16} +5.77983 q^{17} -1.10207 q^{18} -6.19600 q^{19} +2.57962 q^{20} -1.00000 q^{21} +1.55227 q^{22} +3.40145 q^{23} +3.06975 q^{24} +5.78675 q^{25} +1.00000 q^{27} +0.785435 q^{28} -8.57692 q^{29} +3.61956 q^{30} +7.64123 q^{31} -4.14230 q^{32} -1.40850 q^{33} -6.36980 q^{34} +3.28432 q^{35} -0.785435 q^{36} +5.59124 q^{37} +6.82845 q^{38} -10.0820 q^{40} +1.15399 q^{41} +1.10207 q^{42} +0.818994 q^{43} +1.10628 q^{44} -3.28432 q^{45} -3.74865 q^{46} +3.35146 q^{47} -1.81222 q^{48} +1.00000 q^{49} -6.37742 q^{50} +5.77983 q^{51} +5.54281 q^{53} -1.10207 q^{54} +4.62595 q^{55} -3.06975 q^{56} -6.19600 q^{57} +9.45240 q^{58} +4.88973 q^{59} +2.57962 q^{60} -2.97751 q^{61} -8.42119 q^{62} -1.00000 q^{63} +8.18957 q^{64} +1.55227 q^{66} -0.268759 q^{67} -4.53968 q^{68} +3.40145 q^{69} -3.61956 q^{70} -9.28104 q^{71} +3.06975 q^{72} -12.1448 q^{73} -6.16196 q^{74} +5.78675 q^{75} +4.86656 q^{76} +1.40850 q^{77} +6.00232 q^{79} +5.95192 q^{80} +1.00000 q^{81} -1.27178 q^{82} -6.02174 q^{83} +0.785435 q^{84} -18.9828 q^{85} -0.902592 q^{86} -8.57692 q^{87} -4.32374 q^{88} +16.5783 q^{89} +3.61956 q^{90} -2.67162 q^{92} +7.64123 q^{93} -3.69355 q^{94} +20.3496 q^{95} -4.14230 q^{96} -18.7352 q^{97} -1.10207 q^{98} -1.40850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 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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