LMFDB - Embedded newform 3549.2.a.v.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.2
Root			$1.29051$ 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)

$f(q)$	$=$	$q-1.29051 q^{2} -1.00000 q^{3} -0.334573 q^{4} +1.33457 q^{5} +1.29051 q^{6} +1.00000 q^{7} +3.01280 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.29051 q^{2} -1.00000 q^{3} -0.334573 q^{4} +1.33457 q^{5} +1.29051 q^{6} +1.00000 q^{7} +3.01280 q^{8} +1.00000 q^{9} -1.72229 q^{10} +4.88434 q^{11} +0.334573 q^{12} -1.29051 q^{14} -1.33457 q^{15} -3.21892 q^{16} -4.58103 q^{17} -1.29051 q^{18} -2.96874 q^{19} -0.446512 q^{20} -1.00000 q^{21} -6.30331 q^{22} +6.13080 q^{23} -3.01280 q^{24} -3.21892 q^{25} -1.00000 q^{27} -0.334573 q^{28} -7.63789 q^{29} +1.72229 q^{30} +5.63789 q^{31} -1.87154 q^{32} -4.88434 q^{33} +5.91188 q^{34} +1.33457 q^{35} -0.334573 q^{36} -9.76869 q^{37} +3.83120 q^{38} +4.02080 q^{40} -3.69669 q^{41} +1.29051 q^{42} -9.63789 q^{43} -1.63417 q^{44} +1.33457 q^{45} -7.91188 q^{46} -5.27206 q^{47} +3.21892 q^{48} +1.00000 q^{49} +4.15406 q^{50} +4.58103 q^{51} +10.7374 q^{53} +1.29051 q^{54} +6.51851 q^{55} +3.01280 q^{56} +2.96874 q^{57} +9.85680 q^{58} -10.3033 q^{59} +0.446512 q^{60} -11.1877 q^{61} -7.27577 q^{62} +1.00000 q^{63} +8.85308 q^{64} +6.30331 q^{66} -5.50709 q^{67} +1.53269 q^{68} -6.13080 q^{69} -1.72229 q^{70} +4.88434 q^{71} +3.01280 q^{72} +4.45023 q^{73} +12.6066 q^{74} +3.21892 q^{75} +0.993260 q^{76} +4.88434 q^{77} -3.54977 q^{79} -4.29588 q^{80} +1.00000 q^{81} +4.77063 q^{82} -5.27206 q^{83} +0.334573 q^{84} -6.11372 q^{85} +12.4378 q^{86} +7.63789 q^{87} +14.7155 q^{88} -9.94120 q^{89} -1.72229 q^{90} -2.05120 q^{92} -5.63789 q^{93} +6.80366 q^{94} -3.96200 q^{95} +1.87154 q^{96} +18.2189 q^{97} -1.29051 q^{98} +4.88434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 4 q^{3} + 7 q^{4} - 3 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - q^2 - 4 * q^3 + 7 * q^4 - 3 * q^5 + q^6 + 4 * q^7 + 3 * q^8 + 4 * q^9	$ 4 q - q^{2} - 4 q^{3} + 7 q^{4} - 3 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9} - 2 q^{10} - 2 q^{11} - 7 q^{12} - q^{14} + 3 q^{15} + 17 q^{16} - 10 q^{17} - q^{18} - 7 q^{19} - 40 q^{20} - 4 q^{21} - 12 q^{22} + 3 q^{23} - 3 q^{24} + 17 q^{25} - 4 q^{27} + 7 q^{28} - 9 q^{29} + 2 q^{30} + q^{31} + 5 q^{32} + 2 q^{33} + 32 q^{34} - 3 q^{35} + 7 q^{36} + 4 q^{37} - 18 q^{38} - 4 q^{40} - 28 q^{41} + q^{42} - 17 q^{43} - 10 q^{44} - 3 q^{45} - 40 q^{46} - 3 q^{47} - 17 q^{48} + 4 q^{49} + 11 q^{50} + 10 q^{51} - 5 q^{53} + q^{54} + 8 q^{55} + 3 q^{56} + 7 q^{57} - 12 q^{58} - 28 q^{59} + 40 q^{60} - 10 q^{61} + 14 q^{62} + 4 q^{63} + 9 q^{64} + 12 q^{66} - 22 q^{67} - 12 q^{68} - 3 q^{69} - 2 q^{70} - 2 q^{71} + 3 q^{72} + 31 q^{73} + 24 q^{74} - 17 q^{75} - 46 q^{76} - 2 q^{77} - q^{79} - 54 q^{80} + 4 q^{81} + 24 q^{82} - 3 q^{83} - 7 q^{84} + 2 q^{85} - 10 q^{86} + 9 q^{87} + 4 q^{88} - 5 q^{89} - 2 q^{90} + 28 q^{92} - q^{93} - 36 q^{94} + 39 q^{95} - 5 q^{96} + 43 q^{97} - q^{98} - 2 q^{99}+O(q^{100}) $ 4 * q - q^2 - 4 * q^3 + 7 * q^4 - 3 * q^5 + q^6 + 4 * q^7 + 3 * q^8 + 4 * q^9 - 2 * q^10 - 2 * q^11 - 7 * q^12 - q^14 + 3 * q^15 + 17 * q^16 - 10 * q^17 - q^18 - 7 * q^19 - 40 * q^20 - 4 * q^21 - 12 * q^22 + 3 * q^23 - 3 * q^24 + 17 * q^25 - 4 * q^27 + 7 * q^28 - 9 * q^29 + 2 * q^30 + q^31 + 5 * q^32 + 2 * q^33 + 32 * q^34 - 3 * q^35 + 7 * q^36 + 4 * q^37 - 18 * q^38 - 4 * q^40 - 28 * q^41 + q^42 - 17 * q^43 - 10 * q^44 - 3 * q^45 - 40 * q^46 - 3 * q^47 - 17 * q^48 + 4 * q^49 + 11 * q^50 + 10 * q^51 - 5 * q^53 + q^54 + 8 * q^55 + 3 * q^56 + 7 * q^57 - 12 * q^58 - 28 * q^59 + 40 * q^60 - 10 * q^61 + 14 * q^62 + 4 * q^63 + 9 * q^64 + 12 * q^66 - 22 * q^67 - 12 * q^68 - 3 * q^69 - 2 * q^70 - 2 * q^71 + 3 * q^72 + 31 * q^73 + 24 * q^74 - 17 * q^75 - 46 * q^76 - 2 * q^77 - q^79 - 54 * q^80 + 4 * q^81 + 24 * q^82 - 3 * q^83 - 7 * q^84 + 2 * q^85 - 10 * q^86 + 9 * q^87 + 4 * q^88 - 5 * q^89 - 2 * q^90 + 28 * q^92 - q^93 - 36 * q^94 + 39 * q^95 - 5 * q^96 + 43 * q^97 - q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.29051	−0.912531	−0.456266	−	0.889844i	$-0.650813\pi$
$2$	−1.29051	−0.912531	−0.456266	+	0.889844i	$0.650813\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.334573	−0.167286
$5$	1.33457	0.596839	0.298420	−	0.954435i	$-0.403541\pi$
$5$	1.33457	0.596839	0.298420	+	0.954435i	$0.403541\pi$
$6$	1.29051	0.526850
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.01280	1.06519
$9$	1.00000	0.333333
$10$	−1.72229	−0.544634
$11$	4.88434	1.47268	0.736342	−	0.676609i	$-0.236551\pi$
$11$	4.88434	1.47268	0.736342	+	0.676609i	$0.236551\pi$
$12$	0.334573	0.0965829
$13$	0	0
$13$	0	0
$14$	−1.29051	−0.344904
$15$	−1.33457	−0.344585
$16$	−3.21892	−0.804729
$17$	−4.58103	−1.11106	−0.555531	−	0.831496i	$-0.687485\pi$
$17$	−4.58103	−1.11106	−0.555531	+	0.831496i	$0.687485\pi$
$18$	−1.29051	−0.304177
$19$	−2.96874	−0.681076	−0.340538	−	0.940231i	$-0.610609\pi$
$19$	−2.96874	−0.681076	−0.340538	+	0.940231i	$0.610609\pi$
$20$	−0.446512	−0.0998431
$21$	−1.00000	−0.218218
$22$	−6.30331	−1.34387
$23$	6.13080	1.27836	0.639180	−	0.769057i	$-0.279274\pi$
$23$	6.13080	1.27836	0.639180	+	0.769057i	$0.279274\pi$
$24$	−3.01280	−0.614985
$25$	−3.21892	−0.643783
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−0.334573	−0.0632283
$29$	−7.63789	−1.41832	−0.709160	−	0.705048i	$-0.750926\pi$
$29$	−7.63789	−1.41832	−0.709160	+	0.705048i	$0.750926\pi$
$30$	1.72229	0.314445
$31$	5.63789	1.01259	0.506297	−	0.862359i	$-0.331014\pi$
$31$	5.63789	1.01259	0.506297	+	0.862359i	$0.331014\pi$
$32$	−1.87154	−0.330845
$33$	−4.88434	−0.850255
$34$	5.91188	1.01388
$35$	1.33457	0.225584
$36$	−0.334573	−0.0557621
$37$	−9.76869	−1.60596	−0.802981	−	0.596005i	$-0.796754\pi$
$37$	−9.76869	−1.60596	−0.802981	+	0.596005i	$0.796754\pi$
$38$	3.83120	0.621503
$39$	0	0
$40$	4.02080	0.635744
$41$	−3.69669	−0.577325	−0.288663	−	0.957431i	$-0.593211\pi$
$41$	−3.69669	−0.577325	−0.288663	+	0.957431i	$0.593211\pi$
$42$	1.29051	0.199131
$43$	−9.63789	−1.46976	−0.734882	−	0.678195i	$-0.762762\pi$
$43$	−9.63789	−1.46976	−0.734882	+	0.678195i	$0.762762\pi$
$44$	−1.63417	−0.246360
$45$	1.33457	0.198946
$46$	−7.91188	−1.16654
$47$	−5.27206	−0.769008	−0.384504	−	0.923123i	$-0.625628\pi$
$47$	−5.27206	−0.769008	−0.384504	+	0.923123i	$0.625628\pi$
$48$	3.21892	0.464610
$49$	1.00000	0.142857
$50$	4.15406	0.587472
$51$	4.58103	0.641472
$52$	0	0
$53$	10.7374	1.47490	0.737449	−	0.675402i	$-0.236030\pi$
$53$	10.7374	1.47490	0.737449	+	0.675402i	$0.236030\pi$
$54$	1.29051	0.175617
$55$	6.51851	0.878956
$56$	3.01280	0.402602
$57$	2.96874	0.393219
$58$	9.85680	1.29426
$59$	−10.3033	−1.34138	−0.670689	−	0.741739i	$-0.734001\pi$
$59$	−10.3033	−1.34138	−0.670689	+	0.741739i	$0.734001\pi$
$60$	0.446512	0.0576444
$61$	−11.1877	−1.43243	−0.716216	−	0.697878i	$-0.754128\pi$
$61$	−11.1877	−1.43243	−0.716216	+	0.697878i	$0.754128\pi$
$62$	−7.27577	−0.924024
$63$	1.00000	0.125988
$64$	8.85308	1.10664
$65$	0	0
$66$	6.30331	0.775884
$67$	−5.50709	−0.672798	−0.336399	−	0.941720i	$-0.609209\pi$
$67$	−5.50709	−0.672798	−0.336399	+	0.941720i	$0.609209\pi$
$68$	1.53269	0.185866
$69$	−6.13080	−0.738061
$70$	−1.72229	−0.205852
$71$	4.88434	0.579665	0.289832	−	0.957077i	$-0.406400\pi$
$71$	4.88434	0.579665	0.289832	+	0.957077i	$0.406400\pi$
$72$	3.01280	0.355062
$73$	4.45023	0.520860	0.260430	−	0.965493i	$-0.416136\pi$
$73$	4.45023	0.520860	0.260430	+	0.965493i	$0.416136\pi$
$74$	12.6066	1.46549
$75$	3.21892	0.371688
$76$	0.993260	0.113935
$77$	4.88434	0.556622
$78$	0	0
$79$	−3.54977	−0.399380	−0.199690	−	0.979859i	$-0.563994\pi$
$79$	−3.54977	−0.399380	−0.199690	+	0.979859i	$0.563994\pi$
$80$	−4.29588	−0.480294
$81$	1.00000	0.111111
$82$	4.77063	0.526828
$83$	−5.27206	−0.578683	−0.289342	−	0.957226i	$-0.593436\pi$
$83$	−5.27206	−0.578683	−0.289342	+	0.957226i	$0.593436\pi$
$84$	0.334573	0.0365049
$85$	−6.11372	−0.663126
$86$	12.4378	1.34121
$87$	7.63789	0.818867
$88$	14.7155	1.56868
$89$	−9.94120	−1.05377	−0.526883	−	0.849938i	$-0.676639\pi$
$89$	−9.94120	−1.05377	−0.526883	+	0.849938i	$0.676639\pi$
$90$	−1.72229	−0.181545
$91$	0	0
$92$	−2.05120	−0.213852
$93$	−5.63789	−0.584622
$94$	6.80366	0.701744
$95$	−3.96200	−0.406493
$96$	1.87154	0.191014
$97$	18.2189	1.84985	0.924925	−	0.380149i	$-0.124127\pi$
$97$	18.2189	1.84985	0.924925	+	0.380149i	$0.124127\pi$
$98$	−1.29051	−0.130362
$99$	4.88434	0.490895
$100$	1.07696	0.107696
$101$	10.6947	1.06417	0.532083	−	0.846692i	$-0.321409\pi$
$101$	10.6947	1.06417	0.532083	+	0.846692i	$0.321409\pi$
$102$	−5.91188	−0.585364
$103$	−1.48149	−0.145975	−0.0729877	−	0.997333i	$-0.523253\pi$
$103$	−1.48149	−0.145975	−0.0729877	+	0.997333i	$0.523253\pi$
$104$	0	0
$105$	−1.33457	−0.130241
$106$	−13.8568	−1.34589
$107$	4.49291	0.434346	0.217173	−	0.976133i	$-0.430316\pi$
$107$	4.49291	0.434346	0.217173	+	0.976133i	$0.430316\pi$
$108$	0.334573	0.0321943
$109$	−7.83120	−0.750093	−0.375047	−	0.927006i	$-0.622373\pi$
$109$	−7.83120	−0.750093	−0.375047	+	0.927006i	$0.622373\pi$
$110$	−8.41223	−0.802075
$111$	9.76869	0.927203
$112$	−3.21892	−0.304159
$113$	7.63789	0.718512	0.359256	−	0.933239i	$-0.383031\pi$
$113$	7.63789	0.718512	0.359256	+	0.933239i	$0.383031\pi$
$114$	−3.83120	−0.358825
$115$	8.18200	0.762975
$116$	2.55543	0.237266
$117$	0	0
$118$	13.2966	1.22405
$119$	−4.58103	−0.419942
$120$	−4.02080	−0.367047
$121$	12.8568	1.16880
$122$	14.4378	1.30714
$123$	3.69669	0.333319
$124$	−1.88628	−0.169393
$125$	−10.9687	−0.981074
$126$	−1.29051	−0.114968
$127$	16.4122	1.45635	0.728175	−	0.685391i	$-0.240369\pi$
$127$	16.4122	1.45635	0.728175	+	0.685391i	$0.240369\pi$
$128$	−7.68195	−0.678994
$129$	9.63789	0.848569
$130$	0	0
$131$	−8.43783	−0.737217	−0.368608	−	0.929585i	$-0.620166\pi$
$131$	−8.43783	−0.737217	−0.368608	+	0.929585i	$0.620166\pi$
$132$	1.63417	0.142236
$133$	−2.96874	−0.257423
$134$	7.10698	0.613949
$135$	−1.33457	−0.114862
$136$	−13.8017	−1.18349
$137$	−16.8037	−1.43563	−0.717817	−	0.696232i	$-0.754859\pi$
$137$	−16.8037	−1.43563	−0.717817	+	0.696232i	$0.754859\pi$
$138$	7.91188	0.673504
$139$	2.51851	0.213617	0.106809	−	0.994280i	$-0.465937\pi$
$139$	2.51851	0.213617	0.106809	+	0.994280i	$0.465937\pi$
$140$	−0.446512	−0.0377371
$141$	5.27206	0.443987
$142$	−6.30331	−0.528962
$143$	0	0
$144$	−3.21892	−0.268243
$145$	−10.1933	−0.846509
$146$	−5.74309	−0.475301
$147$	−1.00000	−0.0824786
$148$	3.26834	0.268656
$149$	−11.6416	−0.953717	−0.476859	−	0.878980i	$-0.658225\pi$
$149$	−11.6416	−0.953717	−0.476859	+	0.878980i	$0.658225\pi$
$150$	−4.15406	−0.339177
$151$	15.5374	1.26441	0.632207	−	0.774800i	$-0.282149\pi$
$151$	15.5374	1.26441	0.632207	+	0.774800i	$0.282149\pi$
$152$	−8.94422	−0.725472
$153$	−4.58103	−0.370354
$154$	−6.30331	−0.507936
$155$	7.52417	0.604356
$156$	0	0
$157$	−7.16206	−0.571594	−0.285797	−	0.958290i	$-0.592258\pi$
$157$	−7.16206	−0.571594	−0.285797	+	0.958290i	$0.592258\pi$
$158$	4.58103	0.364447
$159$	−10.7374	−0.851533
$160$	−2.49771	−0.197461
$161$	6.13080	0.483175
$162$	−1.29051	−0.101392
$163$	7.70617	0.603594	0.301797	−	0.953372i	$-0.402414\pi$
$163$	7.70617	0.603594	0.301797	+	0.953372i	$0.402414\pi$
$164$	1.23681	0.0965787
$165$	−6.51851	−0.507465
$166$	6.80366	0.528067
$167$	−12.5478	−0.970980	−0.485490	−	0.874242i	$-0.661359\pi$
$167$	−12.5478	−0.970980	−0.485490	+	0.874242i	$0.661359\pi$
$168$	−3.01280	−0.232443
$169$	0	0
$170$	7.88984	0.605123
$171$	−2.96874	−0.227025
$172$	3.22458	0.245872
$173$	−14.5185	−1.10382	−0.551911	−	0.833903i	$-0.686101\pi$
$173$	−14.5185	−1.10382	−0.551911	+	0.833903i	$0.686101\pi$
$174$	−9.85680	−0.747242
$175$	−3.21892	−0.243327
$176$	−15.7223	−1.18511
$177$	10.3033	0.774444
$178$	12.8293	0.961594
$179$	−16.0683	−1.20100	−0.600500	−	0.799625i	$-0.705032\pi$
$179$	−16.0683	−1.20100	−0.600500	+	0.799625i	$0.705032\pi$
$180$	−0.446512	−0.0332810
$181$	−17.2758	−1.28410	−0.642049	−	0.766664i	$-0.721915\pi$
$181$	−17.2758	−1.28410	−0.642049	+	0.766664i	$0.721915\pi$
$182$	0	0
$183$	11.1877	0.827015
$184$	18.4709	1.36169
$185$	−13.0370	−0.958501
$186$	7.27577	0.533486
$187$	−22.3753	−1.63624
$188$	1.76389	0.128645
$189$	−1.00000	−0.0727393
$190$	5.11302	0.370937
$191$	−4.66915	−0.337848	−0.168924	−	0.985629i	$-0.554029\pi$
$191$	−4.66915	−0.337848	−0.168924	+	0.985629i	$0.554029\pi$
$192$	−8.85308	−0.638916
$193$	−2.66915	−0.192129	−0.0960647	−	0.995375i	$-0.530626\pi$
$193$	−2.66915	−0.192129	−0.0960647	+	0.995375i	$0.530626\pi$
$194$	−23.5118	−1.68805
$195$	0	0
$196$	−0.334573	−0.0238981
$197$	−13.6967	−0.975848	−0.487924	−	0.872886i	$-0.662246\pi$
$197$	−13.6967	−0.975848	−0.487924	+	0.872886i	$0.662246\pi$
$198$	−6.30331	−0.447957
$199$	5.93748	0.420897	0.210448	−	0.977605i	$-0.432508\pi$
$199$	5.93748	0.420897	0.210448	+	0.977605i	$0.432508\pi$
$200$	−9.69795	−0.685748
$201$	5.50709	0.388440
$202$	−13.8017	−0.971086
$203$	−7.63789	−0.536075
$204$	−1.53269	−0.107310
$205$	−4.93350	−0.344570
$206$	1.91188	0.133207
$207$	6.13080	0.426120
$208$	0	0
$209$	−14.5003	−1.00301
$210$	1.72229	0.118849
$211$	18.6493	1.28387	0.641936	−	0.766758i	$-0.278132\pi$
$211$	18.6493	1.28387	0.641936	+	0.766758i	$0.278132\pi$
$212$	−3.59245	−0.246731
$213$	−4.88434	−0.334670
$214$	−5.79817	−0.396355
$215$	−12.8625	−0.877213
$216$	−3.01280	−0.204995
$217$	5.63789	0.382725
$218$	10.1063	0.684484
$219$	−4.45023	−0.300719
$220$	−2.18092	−0.147037
$221$	0	0
$222$	−12.6066	−0.846101
$223$	−15.4066	−1.03170	−0.515850	−	0.856679i	$-0.672524\pi$
$223$	−15.4066	−1.03170	−0.515850	+	0.856679i	$0.672524\pi$
$224$	−1.87154	−0.125048
$225$	−3.21892	−0.214594
$226$	−9.85680	−0.655665
$227$	7.89576	0.524060	0.262030	−	0.965060i	$-0.415608\pi$
$227$	7.89576	0.524060	0.262030	+	0.965060i	$0.415608\pi$
$228$	−0.993260	−0.0657803
$229$	−9.01142	−0.595492	−0.297746	−	0.954645i	$-0.596235\pi$
$229$	−9.01142	−0.595492	−0.297746	+	0.954645i	$0.596235\pi$
$230$	−10.5590	−0.696239
$231$	−4.88434	−0.321366
$232$	−23.0114	−1.51077
$233$	10.7374	0.703432	0.351716	−	0.936107i	$-0.385598\pi$
$233$	10.7374	0.703432	0.351716	+	0.936107i	$0.385598\pi$
$234$	0	0
$235$	−7.03594	−0.458974
$236$	3.44721	0.224394
$237$	3.54977	0.230582
$238$	5.91188	0.383210
$239$	15.9839	1.03391	0.516956	−	0.856012i	$-0.327065\pi$
$239$	15.9839	1.03391	0.516956	+	0.856012i	$0.327065\pi$
$240$	4.29588	0.277298
$241$	21.6635	1.39547	0.697734	−	0.716357i	$-0.254192\pi$
$241$	21.6635	1.39547	0.697734	+	0.716357i	$0.254192\pi$
$242$	−16.5919	−1.06657
$243$	−1.00000	−0.0641500
$244$	3.74309	0.239627
$245$	1.33457	0.0852627
$246$	−4.77063	−0.304164
$247$	0	0
$248$	16.9858	1.07860
$249$	5.27206	0.334103
$250$	14.1553	0.895261
$251$	3.87496	0.244586	0.122293	−	0.992494i	$-0.460975\pi$
$251$	3.87496	0.244586	0.122293	+	0.992494i	$0.460975\pi$
$252$	−0.334573	−0.0210761
$253$	29.9449	1.88262
$254$	−21.1802	−1.32897
$255$	6.11372	0.382856
$256$	−7.79251	−0.487032
$257$	−16.8938	−1.05381	−0.526904	−	0.849925i	$-0.676647\pi$
$257$	−16.8938	−1.05381	−0.526904	+	0.849925i	$0.676647\pi$
$258$	−12.4378	−0.774346
$259$	−9.76869	−0.606997
$260$	0	0
$261$	−7.63789	−0.472773
$262$	10.8891	0.672733
$263$	9.40657	0.580034	0.290017	−	0.957021i	$-0.406339\pi$
$263$	9.40657	0.580034	0.290017	+	0.957021i	$0.406339\pi$
$264$	−14.7155	−0.905679
$265$	14.3299	0.880277
$266$	3.83120	0.234906
$267$	9.94120	0.608392
$268$	1.84252	0.112550
$269$	−17.6181	−1.07419	−0.537096	−	0.843521i	$-0.680479\pi$
$269$	−17.6181	−1.07419	−0.537096	+	0.843521i	$0.680479\pi$
$270$	1.72229	0.104815
$271$	−23.1070	−1.40365	−0.701824	−	0.712350i	$-0.747631\pi$
$271$	−23.1070	−1.40365	−0.701824	+	0.712350i	$0.747631\pi$
$272$	14.7459	0.894104
$273$	0	0
$274$	21.6854	1.31006
$275$	−15.7223	−0.948089
$276$	2.05120	0.123468
$277$	20.0757	1.20623	0.603116	−	0.797653i	$-0.293925\pi$
$277$	20.0757	1.20623	0.603116	+	0.797653i	$0.293925\pi$
$278$	−3.25017	−0.194932
$279$	5.63789	0.337531
$280$	4.02080	0.240289
$281$	−11.2038	−0.668361	−0.334181	−	0.942509i	$-0.608460\pi$
$281$	−11.2038	−0.668361	−0.334181	+	0.942509i	$0.608460\pi$
$282$	−6.80366	−0.405152
$283$	1.33829	0.0795532	0.0397766	−	0.999209i	$-0.487335\pi$
$283$	1.33829	0.0795532	0.0397766	+	0.999209i	$0.487335\pi$
$284$	−1.63417	−0.0969700
$285$	3.96200	0.234689
$286$	0	0
$287$	−3.69669	−0.218208
$288$	−1.87154	−0.110282
$289$	3.98582	0.234460
$290$	13.1546	0.772466
$291$	−18.2189	−1.06801
$292$	−1.48893	−0.0871328
$293$	8.60291	0.502587	0.251294	−	0.967911i	$-0.419144\pi$
$293$	8.60291	0.502587	0.251294	+	0.967911i	$0.419144\pi$
$294$	1.29051	0.0752643
$295$	−13.7505	−0.800586
$296$	−29.4311	−1.71065
$297$	−4.88434	−0.283418
$298$	15.0237	0.870297
$299$	0	0
$300$	−1.07696	−0.0621784
$301$	−9.63789	−0.555519
$302$	−20.0512	−1.15382
$303$	−10.6947	−0.614397
$304$	9.55613	0.548081
$305$	−14.9307	−0.854932
$306$	5.91188	0.337960
$307$	7.57537	0.432349	0.216175	−	0.976355i	$-0.430642\pi$
$307$	7.57537	0.432349	0.216175	+	0.976355i	$0.430642\pi$
$308$	−1.63417	−0.0931154
$309$	1.48149	0.0842790
$310$	−9.71005	−0.551494
$311$	−6.11372	−0.346677	−0.173339	−	0.984862i	$-0.555455\pi$
$311$	−6.11372	−0.346677	−0.173339	+	0.984862i	$0.555455\pi$
$312$	0	0
$313$	−7.31269	−0.413338	−0.206669	−	0.978411i	$-0.566262\pi$
$313$	−7.31269	−0.413338	−0.206669	+	0.978411i	$0.566262\pi$
$314$	9.24274	0.521598
$315$	1.33457	0.0751947
$316$	1.18766	0.0668109
$317$	1.70412	0.0957131	0.0478565	−	0.998854i	$-0.484761\pi$
$317$	1.70412	0.0957131	0.0478565	+	0.998854i	$0.484761\pi$
$318$	13.8568	0.777051
$319$	−37.3061	−2.08874
$320$	11.8151	0.660483
$321$	−4.49291	−0.250770
$322$	−7.91188	−0.440912
$323$	13.5999	0.756718
$324$	−0.334573	−0.0185874
$325$	0	0
$326$	−9.94492	−0.550798
$327$	7.83120	0.433067
$328$	−11.1374	−0.614959
$329$	−5.27206	−0.290658
$330$	8.41223	0.463078
$331$	−16.5232	−0.908197	−0.454098	−	0.890952i	$-0.650039\pi$
$331$	−16.5232	−0.908197	−0.454098	+	0.890952i	$0.650039\pi$
$332$	1.76389	0.0968058
$333$	−9.76869	−0.535321
$334$	16.1932	0.886050
$335$	−7.34961	−0.401552
$336$	3.21892	0.175606
$337$	−12.3043	−0.670257	−0.335128	−	0.942172i	$-0.608780\pi$
$337$	−12.3043	−0.670257	−0.335128	+	0.942172i	$0.608780\pi$
$338$	0	0
$339$	−7.63789	−0.414833
$340$	2.04548	0.110932
$341$	27.5374	1.49123
$342$	3.83120	0.207168
$343$	1.00000	0.0539949
$344$	−29.0370	−1.56557
$345$	−8.18200	−0.440504
$346$	18.7363	1.00727
$347$	9.88240	0.530515	0.265258	−	0.964178i	$-0.414543\pi$
$347$	9.88240	0.530515	0.265258	+	0.964178i	$0.414543\pi$
$348$	−2.55543	−0.136985
$349$	29.1497	1.56035	0.780173	−	0.625564i	$-0.215131\pi$
$349$	29.1497	1.56035	0.780173	+	0.625564i	$0.215131\pi$
$350$	4.15406	0.222044
$351$	0	0
$352$	−9.14126	−0.487231
$353$	−8.90994	−0.474228	−0.237114	−	0.971482i	$-0.576202\pi$
$353$	−8.90994	−0.474228	−0.237114	+	0.971482i	$0.576202\pi$
$354$	−13.2966	−0.706705
$355$	6.51851	0.345967
$356$	3.32606	0.176281
$357$	4.58103	0.242454
$358$	20.7363	1.09595
$359$	−29.8776	−1.57688	−0.788440	−	0.615112i	$-0.789111\pi$
$359$	−29.8776	−1.57688	−0.788440	+	0.615112i	$0.789111\pi$
$360$	4.02080	0.211915
$361$	−10.1866	−0.536136
$362$	22.2946	1.17178
$363$	−12.8568	−0.674807
$364$	0	0
$365$	5.93916	0.310870
$366$	−14.4378	−0.754678
$367$	−5.91932	−0.308986	−0.154493	−	0.987994i	$-0.549374\pi$
$367$	−5.91932	−0.308986	−0.154493	+	0.987994i	$0.549374\pi$
$368$	−19.7345	−1.02873
$369$	−3.69669	−0.192442
$370$	16.8245	0.874662
$371$	10.7374	0.557459
$372$	1.88628	0.0977993
$373$	7.35645	0.380903	0.190451	−	0.981697i	$-0.439005\pi$
$373$	7.35645	0.380903	0.190451	+	0.981697i	$0.439005\pi$
$374$	28.8757	1.49312
$375$	10.9687	0.566423
$376$	−15.8836	−0.819136
$377$	0	0
$378$	1.29051	0.0663769
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	1.32558	0.0680007
$381$	−16.4122	−0.840824
$382$	6.02560	0.308296
$383$	−15.2891	−0.781238	−0.390619	−	0.920552i	$-0.627739\pi$
$383$	−15.2891	−0.781238	−0.390619	+	0.920552i	$0.627739\pi$
$384$	7.68195	0.392018
$385$	6.51851	0.332214
$386$	3.44457	0.175324
$387$	−9.63789	−0.489921
$388$	−6.09555	−0.309455
$389$	7.51453	0.381002	0.190501	−	0.981687i	$-0.438989\pi$
$389$	7.51453	0.381002	0.190501	+	0.981687i	$0.438989\pi$
$390$	0	0
$391$	−28.0854	−1.42034
$392$	3.01280	0.152169
$393$	8.43783	0.425632
$394$	17.6758	0.890492
$395$	−4.73743	−0.238366
$396$	−1.63417	−0.0821200
$397$	10.3951	0.521718	0.260859	−	0.965377i	$-0.415994\pi$
$397$	10.3951	0.521718	0.260859	+	0.965377i	$0.415994\pi$
$398$	−7.66241	−0.384082
$399$	2.96874	0.148623
$400$	10.3614	0.518071
$401$	13.4029	0.669307	0.334653	−	0.942341i	$-0.391381\pi$
$401$	13.4029	0.669307	0.334653	+	0.942341i	$0.391381\pi$
$402$	−7.10698	−0.354464
$403$	0	0
$404$	−3.57817	−0.178021
$405$	1.33457	0.0663155
$406$	9.85680	0.489185
$407$	−47.7136	−2.36508
$408$	13.8017	0.683287
$409$	34.7421	1.71789	0.858943	−	0.512071i	$-0.171121\pi$
$409$	34.7421	1.71789	0.858943	+	0.512071i	$0.171121\pi$
$410$	6.36675	0.314431
$411$	16.8037	0.828864
$412$	0.495666	0.0244197
$413$	−10.3033	−0.506993
$414$	−7.91188	−0.388848
$415$	−7.03594	−0.345381
$416$	0	0
$417$	−2.51851	−0.123332
$418$	18.7129	0.915278
$419$	3.01418	0.147252	0.0736261	−	0.997286i	$-0.476543\pi$
$419$	3.01418	0.147252	0.0736261	+	0.997286i	$0.476543\pi$
$420$	0.446512	0.0217875
$421$	−32.1366	−1.56624	−0.783120	−	0.621871i	$-0.786373\pi$
$421$	−32.1366	−1.56624	−0.783120	+	0.621871i	$0.786373\pi$
$422$	−24.0672	−1.17157
$423$	−5.27206	−0.256336
$424$	32.3497	1.57104
$425$	14.7459	0.715283
$426$	6.30331	0.305397
$427$	−11.1877	−0.541409
$428$	−1.50321	−0.0726602
$429$	0	0
$430$	16.5992	0.800484
$431$	−9.00938	−0.433966	−0.216983	−	0.976175i	$-0.569622\pi$
$431$	−9.00938	−0.433966	−0.216983	+	0.976175i	$0.569622\pi$
$432$	3.21892	0.154870
$433$	38.6397	1.85690	0.928452	−	0.371453i	$-0.121140\pi$
$433$	38.6397	1.85690	0.928452	+	0.371453i	$0.121140\pi$
$434$	−7.27577	−0.349248
$435$	10.1933	0.488732
$436$	2.62011	0.125480
$437$	−18.2008	−0.870660
$438$	5.74309	0.274415
$439$	−1.48149	−0.0707076	−0.0353538	−	0.999375i	$-0.511256\pi$
$439$	−1.48149	−0.0707076	−0.0353538	+	0.999375i	$0.511256\pi$
$440$	19.6390	0.936251
$441$	1.00000	0.0476190
$442$	0	0
$443$	−12.0683	−0.573381	−0.286691	−	0.958023i	$-0.592555\pi$
$443$	−12.0683	−0.573381	−0.286691	+	0.958023i	$0.592555\pi$
$444$	−3.26834	−0.155108
$445$	−13.2673	−0.628928
$446$	19.8824	0.941459
$447$	11.6416	0.550629
$448$	8.85308	0.418269
$449$	24.0794	1.13638	0.568189	−	0.822898i	$-0.307644\pi$
$449$	24.0794	1.13638	0.568189	+	0.822898i	$0.307644\pi$
$450$	4.15406	0.195824
$451$	−18.0559	−0.850218
$452$	−2.55543	−0.120197
$453$	−15.5374	−0.730009
$454$	−10.1896	−0.478222
$455$	0	0
$456$	8.94422	0.418852
$457$	32.9933	1.54336	0.771680	−	0.636011i	$-0.219417\pi$
$457$	32.9933	1.54336	0.771680	+	0.636011i	$0.219417\pi$
$458$	11.6294	0.543405
$459$	4.58103	0.213824
$460$	−2.73747	−0.127635
$461$	−13.4654	−0.627145	−0.313572	−	0.949564i	$-0.601526\pi$
$461$	−13.4654	−0.627145	−0.313572	+	0.949564i	$0.601526\pi$
$462$	6.30331	0.293257
$463$	−22.3679	−1.03952	−0.519762	−	0.854311i	$-0.673979\pi$
$463$	−22.3679	−1.03952	−0.519762	+	0.854311i	$0.673979\pi$
$464$	24.5857	1.14136
$465$	−7.52417	−0.348925
$466$	−13.8568	−0.641904
$467$	−16.5629	−0.766438	−0.383219	−	0.923658i	$-0.625185\pi$
$467$	−16.5629	−0.766438	−0.383219	+	0.923658i	$0.625185\pi$
$468$	0	0
$469$	−5.50709	−0.254294
$470$	9.07998	0.418828
$471$	7.16206	0.330010
$472$	−31.0418	−1.42882
$473$	−47.0747	−2.16450
$474$	−4.58103	−0.210414
$475$	9.55613	0.438465
$476$	1.53269	0.0702506
$477$	10.7374	0.491633
$478$	−20.6274	−0.943477
$479$	−10.1403	−0.463321	−0.231661	−	0.972797i	$-0.574416\pi$
$479$	−10.1403	−0.463321	−0.231661	+	0.972797i	$0.574416\pi$
$480$	2.49771	0.114004
$481$	0	0
$482$	−27.9570	−1.27341
$483$	−6.13080	−0.278961
$484$	−4.30154	−0.195524
$485$	24.3145	1.10406
$486$	1.29051	0.0585389
$487$	−11.6624	−0.528474	−0.264237	−	0.964458i	$-0.585120\pi$
$487$	−11.6624	−0.528474	−0.264237	+	0.964458i	$0.585120\pi$
$488$	−33.7062	−1.52581
$489$	−7.70617	−0.348485
$490$	−1.72229	−0.0778049
$491$	24.8454	1.12126	0.560628	−	0.828068i	$-0.310560\pi$
$491$	24.8454	1.12126	0.560628	+	0.828068i	$0.310560\pi$
$492$	−1.23681	−0.0557597
$493$	34.9894	1.57584
$494$	0	0
$495$	6.51851	0.292985
$496$	−18.1479	−0.814864
$497$	4.88434	0.219093
$498$	−6.80366	−0.304879
$499$	−7.40081	−0.331306	−0.165653	−	0.986184i	$-0.552973\pi$
$499$	−7.40081	−0.331306	−0.165653	+	0.986184i	$0.552973\pi$
$500$	3.66984	0.164120
$501$	12.5478	0.560596
$502$	−5.00070	−0.223192
$503$	−35.8898	−1.60025	−0.800124	−	0.599834i	$-0.795233\pi$
$503$	−35.8898	−1.60025	−0.800124	+	0.599834i	$0.795233\pi$
$504$	3.01280	0.134201
$505$	14.2729	0.635136
$506$	−38.6443	−1.71795
$507$	0	0
$508$	−5.49109	−0.243628
$509$	3.99628	0.177132	0.0885660	−	0.996070i	$-0.471772\pi$
$509$	3.99628	0.177132	0.0885660	+	0.996070i	$0.471772\pi$
$510$	−7.88984	−0.349368
$511$	4.45023	0.196867
$512$	25.4202	1.12343
$513$	2.96874	0.131073
$514$	21.8017	0.961633
$515$	−1.97716	−0.0871239
$516$	−3.22458	−0.141954
$517$	−25.7505	−1.13251
$518$	12.6066	0.553903
$519$	14.5185	0.637292
$520$	0	0
$521$	−28.5562	−1.25107	−0.625536	−	0.780196i	$-0.715119\pi$
$521$	−28.5562	−1.25107	−0.625536	+	0.780196i	$0.715119\pi$
$522$	9.85680	0.431421
$523$	−23.5555	−1.03001	−0.515006	−	0.857187i	$-0.672210\pi$
$523$	−23.5555	−1.03001	−0.515006	+	0.857187i	$0.672210\pi$
$524$	2.82307	0.123326
$525$	3.21892	0.140485
$526$	−12.1393	−0.529299
$527$	−25.8273	−1.12506
$528$	15.7223	0.684225
$529$	14.5867	0.634204
$530$	−18.4929	−0.803281
$531$	−10.3033	−0.447126
$532$	0.993260	0.0430633
$533$	0	0
$534$	−12.8293	−0.555176
$535$	5.99612	0.259235
$536$	−16.5918	−0.716655
$537$	16.0683	0.693397
$538$	22.7363	0.980233
$539$	4.88434	0.210384
$540$	0.446512	0.0192148
$541$	−6.32411	−0.271895	−0.135947	−	0.990716i	$-0.543408\pi$
$541$	−6.32411	−0.271895	−0.135947	+	0.990716i	$0.543408\pi$
$542$	29.8199	1.28087
$543$	17.2758	0.741374
$544$	8.57359	0.367590
$545$	−10.4513	−0.447685
$546$	0	0
$547$	17.8141	0.761677	0.380838	−	0.924642i	$-0.375635\pi$
$547$	17.8141	0.761677	0.380838	+	0.924642i	$0.375635\pi$
$548$	5.62205	0.240162
$549$	−11.1877	−0.477478
$550$	20.2898	0.865161
$551$	22.6749	0.965984
$552$	−18.4709	−0.786172
$553$	−3.54977	−0.150952
$554$	−25.9080	−1.10073
$555$	13.0370	0.553391
$556$	−0.842625	−0.0357353
$557$	2.04915	0.0868255	0.0434127	−	0.999057i	$-0.486177\pi$
$557$	2.04915	0.0868255	0.0434127	+	0.999057i	$0.486177\pi$
$558$	−7.27577	−0.308008
$559$	0	0
$560$	−4.29588	−0.181534
$561$	22.3753	0.944686
$562$	14.4586	0.609901
$563$	29.5999	1.24749	0.623743	−	0.781629i	$-0.285611\pi$
$563$	29.5999	1.24749	0.623743	+	0.781629i	$0.285611\pi$
$564$	−1.76389	−0.0742730
$565$	10.1933	0.428836
$566$	−1.72708	−0.0725948
$567$	1.00000	0.0419961
$568$	14.7155	0.617451
$569$	−7.63789	−0.320197	−0.160098	−	0.987101i	$-0.551181\pi$
$569$	−7.63789	−0.320197	−0.160098	+	0.987101i	$0.551181\pi$
$570$	−5.11302	−0.214161
$571$	11.9364	0.499523	0.249761	−	0.968307i	$-0.419648\pi$
$571$	11.9364	0.499523	0.249761	+	0.968307i	$0.419648\pi$
$572$	0	0
$573$	4.66915	0.195056
$574$	4.77063	0.199122
$575$	−19.7345	−0.822986
$576$	8.85308	0.368878
$577$	47.8320	1.99127	0.995636	−	0.0933200i	$-0.0297479\pi$
$577$	47.8320	1.99127	0.995636	+	0.0933200i	$0.0297479\pi$
$578$	−5.14376	−0.213952
$579$	2.66915	0.110926
$580$	3.41041	0.141609
$581$	−5.27206	−0.218722
$582$	23.5118	0.974594
$583$	52.4453	2.17206
$584$	13.4077	0.554813
$585$	0	0
$586$	−11.1022	−0.458627
$587$	−12.2350	−0.504994	−0.252497	−	0.967598i	$-0.581252\pi$
$587$	−12.2350	−0.504994	−0.252497	+	0.967598i	$0.581252\pi$
$588$	0.334573	0.0137976
$589$	−16.7374	−0.689654
$590$	17.7452	0.730560
$591$	13.6967	0.563406
$592$	31.4446	1.29236
$593$	33.5714	1.37861	0.689305	−	0.724471i	$-0.257916\pi$
$593$	33.5714	1.37861	0.689305	+	0.724471i	$0.257916\pi$
$594$	6.30331	0.258628
$595$	−6.11372	−0.250638
$596$	3.89496	0.159544
$597$	−5.93748	−0.243005
$598$	0	0
$599$	20.4549	0.835765	0.417883	−	0.908501i	$-0.362772\pi$
$599$	20.4549	0.835765	0.417883	+	0.908501i	$0.362772\pi$
$600$	9.69795	0.395917
$601$	25.3014	1.03206	0.516032	−	0.856569i	$-0.327408\pi$
$601$	25.3014	1.03206	0.516032	+	0.856569i	$0.327408\pi$
$602$	12.4378	0.506928
$603$	−5.50709	−0.224266
$604$	−5.19838	−0.211519
$605$	17.1583	0.697586
$606$	13.8017	0.560657
$607$	−16.0330	−0.650761	−0.325380	−	0.945583i	$-0.605492\pi$
$607$	−16.0330	−0.650761	−0.325380	+	0.945583i	$0.605492\pi$
$608$	5.55613	0.225331
$609$	7.63789	0.309503
$610$	19.2683	0.780152
$611$	0	0
$612$	1.53269	0.0619552
$613$	39.9752	1.61458	0.807292	−	0.590153i	$-0.200933\pi$
$613$	39.9752	1.61458	0.807292	+	0.590153i	$0.200933\pi$
$614$	−9.77612	−0.394532
$615$	4.93350	0.198938
$616$	14.7155	0.592906
$617$	1.05782	0.0425863	0.0212932	−	0.999773i	$-0.493222\pi$
$617$	1.05782	0.0425863	0.0212932	+	0.999773i	$0.493222\pi$
$618$	−1.91188	−0.0769072
$619$	−41.8199	−1.68088	−0.840442	−	0.541902i	$-0.817704\pi$
$619$	−41.8199	−1.68088	−0.840442	+	0.541902i	$0.817704\pi$
$620$	−2.51738	−0.101101
$621$	−6.13080	−0.246020
$622$	7.88984	0.316354
$623$	−9.94120	−0.398286
$624$	0	0
$625$	1.45599	0.0582397
$626$	9.43713	0.377184
$627$	14.5003	0.579088
$628$	2.39623	0.0956200
$629$	44.7506	1.78432
$630$	−1.72229	−0.0686175
$631$	−20.0928	−0.799882	−0.399941	−	0.916541i	$-0.630969\pi$
$631$	−20.0928	−0.799882	−0.399941	+	0.916541i	$0.630969\pi$
$632$	−10.6947	−0.425414
$633$	−18.6493	−0.741243
$634$	−2.19920	−0.0873412
$635$	21.9033	0.869207
$636$	3.59245	0.142450
$637$	0	0
$638$	48.1440	1.90604
$639$	4.88434	0.193222
$640$	−10.2521	−0.405250
$641$	−12.2008	−0.481901	−0.240950	−	0.970537i	$-0.577459\pi$
$641$	−12.2008	−0.481901	−0.240950	+	0.970537i	$0.577459\pi$
$642$	5.79817	0.228835
$643$	−0.0511985	−0.00201907	−0.00100954	−	0.999999i	$-0.500321\pi$
$643$	−0.0511985	−0.00201907	−0.00100954	+	0.999999i	$0.500321\pi$
$644$	−2.05120	−0.0808285
$645$	12.8625	0.506459
$646$	−17.5508	−0.690529
$647$	−6.63691	−0.260924	−0.130462	−	0.991453i	$-0.541646\pi$
$647$	−6.63691	−0.260924	−0.130462	+	0.991453i	$0.541646\pi$
$648$	3.01280	0.118354
$649$	−50.3249	−1.97543
$650$	0	0
$651$	−5.63789	−0.220966
$652$	−2.57827	−0.100973
$653$	14.1250	0.552755	0.276378	−	0.961049i	$-0.410866\pi$
$653$	14.1250	0.552755	0.276378	+	0.961049i	$0.410866\pi$
$654$	−10.1063	−0.395187
$655$	−11.2609	−0.440000
$656$	11.8993	0.464590
$657$	4.45023	0.173620
$658$	6.80366	0.265234
$659$	−9.95456	−0.387775	−0.193887	−	0.981024i	$-0.562110\pi$
$659$	−9.95456	−0.387775	−0.193887	+	0.981024i	$0.562110\pi$
$660$	2.18092	0.0848921
$661$	−11.0359	−0.429248	−0.214624	−	0.976697i	$-0.568853\pi$
$661$	−11.0359	−0.429248	−0.214624	+	0.976697i	$0.568853\pi$
$662$	21.3234	0.828758
$663$	0	0
$664$	−15.8836	−0.616405
$665$	−3.96200	−0.153640
$666$	12.6066	0.488497
$667$	−46.8263	−1.81312
$668$	4.19816	0.162432
$669$	15.4066	0.595652
$670$	9.48478	0.366429
$671$	−54.6443	−2.10952
$672$	1.87154	0.0721963
$673$	9.64921	0.371950	0.185975	−	0.982555i	$-0.440456\pi$
$673$	9.64921	0.371950	0.185975	+	0.982555i	$0.440456\pi$
$674$	15.8788	0.611630
$675$	3.21892	0.123896
$676$	0	0
$677$	27.8320	1.06967	0.534835	−	0.844956i	$-0.320374\pi$
$677$	27.8320	1.06967	0.534835	+	0.844956i	$0.320374\pi$
$678$	9.85680	0.378548
$679$	18.2189	0.699178
$680$	−18.4194	−0.706352
$681$	−7.89576	−0.302566
$682$	−35.5374	−1.36080
$683$	−43.8151	−1.67654	−0.838269	−	0.545257i	$-0.816432\pi$
$683$	−43.8151	−1.67654	−0.838269	+	0.545257i	$0.816432\pi$
$684$	0.993260	0.0379782
$685$	−22.4257	−0.856842
$686$	−1.29051	−0.0492721
$687$	9.01142	0.343807
$688$	31.0235	1.18276
$689$	0	0
$690$	10.5590	0.401974
$691$	−41.6057	−1.58275	−0.791377	−	0.611329i	$-0.790635\pi$
$691$	−41.6057	−1.58275	−0.791377	+	0.611329i	$0.790635\pi$
$692$	4.85750	0.184654
$693$	4.88434	0.185541
$694$	−12.7534	−0.484112
$695$	3.36114	0.127495
$696$	23.0114	0.872246
$697$	16.9346	0.641445
$698$	−37.6181	−1.42386
$699$	−10.7374	−0.406127
$700$	1.07696	0.0407053
$701$	35.4765	1.33993	0.669965	−	0.742393i	$-0.266309\pi$
$701$	35.4765	1.33993	0.669965	+	0.742393i	$0.266309\pi$
$702$	0	0
$703$	29.0007	1.09378
$704$	43.2415	1.62973
$705$	7.03594	0.264989
$706$	11.4984	0.432748
$707$	10.6947	0.402217
$708$	−3.44721	−0.129554
$709$	17.8937	0.672013	0.336006	−	0.941860i	$-0.390924\pi$
$709$	17.8937	0.672013	0.336006	+	0.941860i	$0.390924\pi$
$710$	−8.41223	−0.315705
$711$	−3.54977	−0.133127
$712$	−29.9508	−1.12246
$713$	34.5647	1.29446
$714$	−5.91188	−0.221247
$715$	0	0
$716$	5.37601	0.200911
$717$	−15.9839	−0.596929
$718$	38.5575	1.43895
$719$	34.1137	1.27223	0.636113	−	0.771596i	$-0.280541\pi$
$719$	34.1137	1.27223	0.636113	+	0.771596i	$0.280541\pi$
$720$	−4.29588	−0.160098
$721$	−1.48149	−0.0551735
$722$	13.1459	0.489241
$723$	−21.6635	−0.805674
$724$	5.78000	0.214812
$725$	24.5857	0.913090
$726$	16.5919	0.615783
$727$	0.599191	0.0222228	0.0111114	−	0.999938i	$-0.496463\pi$
$727$	0.599191	0.0222228	0.0111114	+	0.999938i	$0.496463\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−7.66457	−0.283678
$731$	44.1514	1.63300
$732$	−3.74309	−0.138348
$733$	−41.7125	−1.54069	−0.770344	−	0.637629i	$-0.779915\pi$
$733$	−41.7125	−1.54069	−0.770344	+	0.637629i	$0.779915\pi$
$734$	7.63897	0.281959
$735$	−1.33457	−0.0492265
$736$	−11.4741	−0.422939
$737$	−26.8985	−0.990819
$738$	4.77063	0.175609
$739$	−19.4446	−0.715280	−0.357640	−	0.933860i	$-0.616419\pi$
$739$	−19.4446	−0.715280	−0.357640	+	0.933860i	$0.616419\pi$
$740$	4.36183	0.160344
$741$	0	0
$742$	−13.8568	−0.508699
$743$	9.44721	0.346584	0.173292	−	0.984870i	$-0.444559\pi$
$743$	9.44721	0.346584	0.173292	+	0.984870i	$0.444559\pi$
$744$	−16.9858	−0.622730
$745$	−15.5366	−0.569216
$746$	−9.49361	−0.347586
$747$	−5.27206	−0.192894
$748$	7.48617	0.273722
$749$	4.49291	0.164167
$750$	−14.1553	−0.516879
$751$	8.91366	0.325264	0.162632	−	0.986687i	$-0.448002\pi$
$751$	8.91366	0.325264	0.162632	+	0.986687i	$0.448002\pi$
$752$	16.9703	0.618843
$753$	−3.87496	−0.141212
$754$	0	0
$755$	20.7358	0.754651
$756$	0.334573	0.0121683
$757$	−43.8416	−1.59345	−0.796726	−	0.604341i	$-0.793437\pi$
$757$	−43.8416	−1.59345	−0.796726	+	0.604341i	$0.793437\pi$
$758$	15.4862	0.562483
$759$	−29.9449	−1.08693
$760$	−11.9367	−0.432990
$761$	11.2283	0.407025	0.203513	−	0.979072i	$-0.434764\pi$
$761$	11.2283	0.407025	0.203513	+	0.979072i	$0.434764\pi$
$762$	21.1802	0.767278
$763$	−7.83120	−0.283509
$764$	1.56217	0.0565173
$765$	−6.11372	−0.221042
$766$	19.7309	0.712905
$767$	0	0
$768$	7.79251	0.281188
$769$	−13.1860	−0.475499	−0.237749	−	0.971327i	$-0.576410\pi$
$769$	−13.1860	−0.475499	−0.237749	+	0.971327i	$0.576410\pi$
$770$	−8.41223	−0.303156
$771$	16.8938	0.608416
$772$	0.893024	0.0321406
$773$	−25.6094	−0.921105	−0.460552	−	0.887632i	$-0.652349\pi$
$773$	−25.6094	−0.921105	−0.460552	+	0.887632i	$0.652349\pi$
$774$	12.4378	0.447069
$775$	−18.1479	−0.651891
$776$	54.8899	1.97043
$777$	9.76869	0.350450
$778$	−9.69760	−0.347676
$779$	10.9745	0.393202
$780$	0	0
$781$	23.8568	0.853663
$782$	36.2446	1.29610
$783$	7.63789	0.272956
$784$	−3.21892	−0.114961
$785$	−9.55829	−0.341150
$786$	−10.8891	−0.388403
$787$	47.8047	1.70405	0.852027	−	0.523497i	$-0.175373\pi$
$787$	47.8047	1.70405	0.852027	+	0.523497i	$0.175373\pi$
$788$	4.58254	0.163246
$789$	−9.40657	−0.334883
$790$	6.11372	0.217516
$791$	7.63789	0.271572
$792$	14.7155	0.522894
$793$	0	0
$794$	−13.4151	−0.476084
$795$	−14.3299	−0.508228
$796$	−1.98652	−0.0704103
$797$	−23.1326	−0.819398	−0.409699	−	0.912221i	$-0.634366\pi$
$797$	−23.1326	−0.819398	−0.409699	+	0.912221i	$0.634366\pi$
$798$	−3.83120	−0.135623
$799$	24.1514	0.854416
$800$	6.02434	0.212993
$801$	−9.94120	−0.351255
$802$	−17.2966	−0.610763
$803$	21.7364	0.767063
$804$	−1.84252	−0.0649807
$805$	8.18200	0.288377
$806$	0	0
$807$	17.6181	0.620185
$808$	32.2211	1.13354
$809$	−40.0757	−1.40899	−0.704494	−	0.709710i	$-0.748826\pi$
$809$	−40.0757	−1.40899	−0.704494	+	0.709710i	$0.748826\pi$
$810$	−1.72229	−0.0605149
$811$	−23.5374	−0.826509	−0.413254	−	0.910616i	$-0.635608\pi$
$811$	−23.5374	−0.826509	−0.413254	+	0.910616i	$0.635608\pi$
$812$	2.55543	0.0896780
$813$	23.1070	0.810397
$814$	61.5751	2.15821
$815$	10.2844	0.360248
$816$	−14.7459	−0.516211
$817$	28.6124	1.00102
$818$	−44.8352	−1.56763
$819$	0	0
$820$	1.65061	0.0576419
$821$	−3.71760	−0.129745	−0.0648726	−	0.997894i	$-0.520664\pi$
$821$	−3.71760	−0.129745	−0.0648726	+	0.997894i	$0.520664\pi$
$822$	−21.6854	−0.756364
$823$	−39.0747	−1.36206	−0.681030	−	0.732256i	$-0.738468\pi$
$823$	−39.0747	−1.36206	−0.681030	+	0.732256i	$0.738468\pi$
$824$	−4.46343	−0.155491
$825$	15.7223	0.547380
$826$	13.2966	0.462647
$827$	−3.55349	−0.123567	−0.0617834	−	0.998090i	$-0.519679\pi$
$827$	−3.55349	−0.123567	−0.0617834	+	0.998090i	$0.519679\pi$
$828$	−2.05120	−0.0712841
$829$	53.3107	1.85156	0.925779	−	0.378065i	$-0.123410\pi$
$829$	53.3107	1.85156	0.925779	+	0.378065i	$0.123410\pi$
$830$	9.07998	0.315171
$831$	−20.0757	−0.696419
$832$	0	0
$833$	−4.58103	−0.158723
$834$	3.25017	0.112544
$835$	−16.7460	−0.579519
$836$	4.85142	0.167790
$837$	−5.63789	−0.194874
$838$	−3.88984	−0.134372
$839$	19.7344	0.681307	0.340654	−	0.940189i	$-0.389352\pi$
$839$	19.7344	0.681307	0.340654	+	0.940189i	$0.389352\pi$
$840$	−4.02080	−0.138731
$841$	29.3373	1.01163
$842$	41.4727	1.42924
$843$	11.2038	0.385878
$844$	−6.23955	−0.214774
$845$	0	0
$846$	6.80366	0.233915
$847$	12.8568	0.441765
$848$	−34.5629	−1.18689
$849$	−1.33829	−0.0459300
$850$	−19.0299	−0.652719
$851$	−59.8898	−2.05300
$852$	1.63417	0.0559857
$853$	11.8188	0.404668	0.202334	−	0.979317i	$-0.435147\pi$
$853$	11.8188	0.404668	0.202334	+	0.979317i	$0.435147\pi$
$854$	14.4378	0.494052
$855$	−3.96200	−0.135498
$856$	13.5362	0.462659
$857$	6.76858	0.231210	0.115605	−	0.993295i	$-0.463119\pi$
$857$	6.76858	0.231210	0.115605	+	0.993295i	$0.463119\pi$
$858$	0	0
$859$	−54.6881	−1.86593	−0.932967	−	0.359962i	$-0.882790\pi$
$859$	−54.6881	−1.86593	−0.932967	+	0.359962i	$0.882790\pi$
$860$	4.30343	0.146746
$861$	3.69669	0.125983
$862$	11.6267	0.396008
$863$	−6.17144	−0.210078	−0.105039	−	0.994468i	$-0.533497\pi$
$863$	−6.17144	−0.210078	−0.105039	+	0.994468i	$0.533497\pi$
$864$	1.87154	0.0636712
$865$	−19.3760	−0.658804
$866$	−49.8650	−1.69448
$867$	−3.98582	−0.135366
$868$	−1.88628	−0.0640246
$869$	−17.3383	−0.588161
$870$	−13.1546	−0.445983
$871$	0	0
$872$	−23.5938	−0.798988
$873$	18.2189	0.616617
$874$	23.4883	0.794505
$875$	−10.9687	−0.370811
$876$	1.48893	0.0503062
$877$	6.22388	0.210165	0.105083	−	0.994463i	$-0.466489\pi$
$877$	6.22388	0.210165	0.105083	+	0.994463i	$0.466489\pi$
$878$	1.91188	0.0645229
$879$	−8.60291	−0.290169
$880$	−20.9825	−0.707321
$881$	−28.5810	−0.962919	−0.481460	−	0.876468i	$-0.659893\pi$
$881$	−28.5810	−0.962919	−0.481460	+	0.876468i	$0.659893\pi$
$882$	−1.29051	−0.0434539
$883$	49.3391	1.66039	0.830196	−	0.557471i	$-0.188228\pi$
$883$	49.3391	1.66039	0.830196	+	0.557471i	$0.188228\pi$
$884$	0	0
$885$	13.7505	0.462219
$886$	15.5743	0.523228
$887$	4.90046	0.164541	0.0822707	−	0.996610i	$-0.473783\pi$
$887$	4.90046	0.164541	0.0822707	+	0.996610i	$0.473783\pi$
$888$	29.4311	0.987643
$889$	16.4122	0.550449
$890$	17.1216	0.573917
$891$	4.88434	0.163632
$892$	5.15462	0.172589
$893$	15.6514	0.523753
$894$	−15.0237	−0.502466
$895$	−21.4443	−0.716804
$896$	−7.68195	−0.256636
$897$	0	0
$898$	−31.0749	−1.03698
$899$	−43.0615	−1.43618
$900$	1.07696	0.0358987
$901$	−49.1885	−1.63871
$902$	23.3014	0.775851
$903$	9.63789	0.320729
$904$	23.0114	0.765349
$905$	−23.0558	−0.766400
$906$	20.0512	0.666156
$907$	25.5021	0.846784	0.423392	−	0.905947i	$-0.360839\pi$
$907$	25.5021	0.846784	0.423392	+	0.905947i	$0.360839\pi$
$908$	−2.64171	−0.0876682
$909$	10.6947	0.354722
$910$	0	0
$911$	37.2452	1.23399	0.616994	−	0.786967i	$-0.288350\pi$
$911$	37.2452	1.23399	0.616994	+	0.786967i	$0.288350\pi$
$912$	−9.55613	−0.316435
$913$	−25.7505	−0.852218
$914$	−42.5783	−1.40836
$915$	14.9307	0.493595
$916$	3.01498	0.0996176
$917$	−8.43783	−0.278642
$918$	−5.91188	−0.195121
$919$	23.0739	0.761139	0.380570	−	0.924752i	$-0.375728\pi$
$919$	23.0739	0.761139	0.380570	+	0.924752i	$0.375728\pi$
$920$	24.6507	0.812710
$921$	−7.57537	−0.249617
$922$	17.3773	0.572289
$923$	0	0
$924$	1.63417	0.0537602
$925$	31.4446	1.03389
$926$	28.8661	0.948598
$927$	−1.48149	−0.0486585
$928$	14.2946	0.469244
$929$	−41.0085	−1.34545	−0.672723	−	0.739895i	$-0.734875\pi$
$929$	−41.0085	−1.34545	−0.672723	+	0.739895i	$0.734875\pi$
$930$	9.71005	0.318405
$931$	−2.96874	−0.0972966
$932$	−3.59245	−0.117675
$933$	6.11372	0.200154
$934$	21.3746	0.699399
$935$	−29.8615	−0.976575
$936$	0	0
$937$	8.17348	0.267016	0.133508	−	0.991048i	$-0.457376\pi$
$937$	8.17348	0.267016	0.133508	+	0.991048i	$0.457376\pi$
$938$	7.10698	0.232051
$939$	7.31269	0.238641
$940$	2.35403	0.0767801
$941$	−33.1732	−1.08142	−0.540708	−	0.841210i	$-0.681844\pi$
$941$	−33.1732	−1.08142	−0.540708	+	0.841210i	$0.681844\pi$
$942$	−9.24274	−0.301145
$943$	−22.6636	−0.738030
$944$	33.1655	1.07944
$945$	−1.33457	−0.0434137
$946$	60.7506	1.97517
$947$	−8.32148	−0.270412	−0.135206	−	0.990818i	$-0.543170\pi$
$947$	−8.32148	−0.270412	−0.135206	+	0.990818i	$0.543170\pi$
$948$	−1.18766	−0.0385733
$949$	0	0
$950$	−12.3323	−0.400113
$951$	−1.70412	−0.0552600
$952$	−13.8017	−0.447316
$953$	−6.39047	−0.207008	−0.103504	−	0.994629i	$-0.533005\pi$
$953$	−6.39047	−0.207008	−0.103504	+	0.994629i	$0.533005\pi$
$954$	−13.8568	−0.448631
$955$	−6.23131	−0.201641
$956$	−5.34777	−0.172959
$957$	37.3061	1.20593
$958$	13.0862	0.422795
$959$	−16.8037	−0.542619
$960$	−11.8151	−0.381330
$961$	0.785767	0.0253473
$962$	0	0
$963$	4.49291	0.144782
$964$	−7.24801	−0.233443
$965$	−3.56217	−0.114670
$966$	7.91188	0.254561
$967$	12.4304	0.399735	0.199867	−	0.979823i	$-0.435949\pi$
$967$	12.4304	0.399735	0.199867	+	0.979823i	$0.435949\pi$
$968$	38.7350	1.24499
$969$	−13.5999	−0.436891
$970$	−31.3782	−1.00749
$971$	0.462630	0.0148465	0.00742325	−	0.999972i	$-0.497637\pi$
$971$	0.462630	0.0148465	0.00742325	+	0.999972i	$0.497637\pi$
$972$	0.334573	0.0107314
$973$	2.51851	0.0807398
$974$	15.0505	0.482249
$975$	0	0
$976$	36.0121	1.15272
$977$	−10.6087	−0.339401	−0.169701	−	0.985496i	$-0.554280\pi$
$977$	−10.6087	−0.339401	−0.169701	+	0.985496i	$0.554280\pi$
$978$	9.94492	0.318003
$979$	−48.5562	−1.55186
$980$	−0.446512	−0.0142633
$981$	−7.83120	−0.250031
$982$	−32.0633	−1.02318
$983$	−22.9042	−0.730530	−0.365265	−	0.930904i	$-0.619022\pi$
$983$	−22.9042	−0.730530	−0.365265	+	0.930904i	$0.619022\pi$
$984$	11.1374	0.355047
$985$	−18.2792	−0.582425
$986$	−45.1543	−1.43801
$987$	5.27206	0.167811
$988$	0	0
$989$	−59.0879	−1.87889
$990$	−8.41223	−0.267358
$991$	−12.3013	−0.390763	−0.195381	−	0.980727i	$-0.562594\pi$
$991$	−12.3013	−0.390763	−0.195381	+	0.980727i	$0.562594\pi$
$992$	−10.5515	−0.335012
$993$	16.5232	0.524348
$994$	−6.30331	−0.199929
$995$	7.92400	0.251208
$996$	−1.76389	−0.0558909
$997$	53.3875	1.69080	0.845400	−	0.534134i	$-0.179362\pi$
$997$	53.3875	1.69080	0.845400	+	0.534134i	$0.179362\pi$
$998$	9.55085	0.302327
$999$	9.76869	0.309068

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.v.1.2		4
13.5	odd	4		273.2.c.c.64.6	yes	8
13.8	odd	4		273.2.c.c.64.3	✓	8
13.12	even	2		3549.2.a.x.1.3		4
39.5	even	4		819.2.c.d.64.3		8
39.8	even	4		819.2.c.d.64.6		8
52.31	even	4		4368.2.h.q.337.4		8
52.47	even	4		4368.2.h.q.337.5		8
91.34	even	4		1911.2.c.l.883.3		8
91.83	even	4		1911.2.c.l.883.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.c.c.64.3	✓	8	13.8	odd	4
273.2.c.c.64.6	yes	8	13.5	odd	4
819.2.c.d.64.3		8	39.5	even	4
819.2.c.d.64.6		8	39.8	even	4
1911.2.c.l.883.3		8	91.34	even	4
1911.2.c.l.883.6		8	91.83	even	4
3549.2.a.v.1.2		4	1.1	even	1	trivial
3549.2.a.x.1.3		4	13.12	even	2
4368.2.h.q.337.4		8	52.31	even	4
4368.2.h.q.337.5		8	52.47	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.29051 q^{2} -1.00000 q^{3} -0.334573 q^{4} +1.33457 q^{5} +1.29051 q^{6} +1.00000 q^{7} +3.01280 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.29051 q^{2} -1.00000 q^{3} -0.334573 q^{4} +1.33457 q^{5} +1.29051 q^{6} +1.00000 q^{7} +3.01280 q^{8} +1.00000 q^{9} -1.72229 q^{10} +4.88434 q^{11} +0.334573 q^{12} -1.29051 q^{14} -1.33457 q^{15} -3.21892 q^{16} -4.58103 q^{17} -1.29051 q^{18} -2.96874 q^{19} -0.446512 q^{20} -1.00000 q^{21} -6.30331 q^{22} +6.13080 q^{23} -3.01280 q^{24} -3.21892 q^{25} -1.00000 q^{27} -0.334573 q^{28} -7.63789 q^{29} +1.72229 q^{30} +5.63789 q^{31} -1.87154 q^{32} -4.88434 q^{33} +5.91188 q^{34} +1.33457 q^{35} -0.334573 q^{36} -9.76869 q^{37} +3.83120 q^{38} +4.02080 q^{40} -3.69669 q^{41} +1.29051 q^{42} -9.63789 q^{43} -1.63417 q^{44} +1.33457 q^{45} -7.91188 q^{46} -5.27206 q^{47} +3.21892 q^{48} +1.00000 q^{49} +4.15406 q^{50} +4.58103 q^{51} +10.7374 q^{53} +1.29051 q^{54} +6.51851 q^{55} +3.01280 q^{56} +2.96874 q^{57} +9.85680 q^{58} -10.3033 q^{59} +0.446512 q^{60} -11.1877 q^{61} -7.27577 q^{62} +1.00000 q^{63} +8.85308 q^{64} +6.30331 q^{66} -5.50709 q^{67} +1.53269 q^{68} -6.13080 q^{69} -1.72229 q^{70} +4.88434 q^{71} +3.01280 q^{72} +4.45023 q^{73} +12.6066 q^{74} +3.21892 q^{75} +0.993260 q^{76} +4.88434 q^{77} -3.54977 q^{79} -4.29588 q^{80} +1.00000 q^{81} +4.77063 q^{82} -5.27206 q^{83} +0.334573 q^{84} -6.11372 q^{85} +12.4378 q^{86} +7.63789 q^{87} +14.7155 q^{88} -9.94120 q^{89} -1.72229 q^{90} -2.05120 q^{92} -5.63789 q^{93} +6.80366 q^{94} -3.96200 q^{95} +1.87154 q^{96} +18.2189 q^{97} -1.29051 q^{98} +4.88434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 4 q^{3} + 7 q^{4} - 3 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - q^2 - 4 * q^3 + 7 * q^4 - 3 * q^5 + q^6 + 4 * q^7 + 3 * q^8 + 4 * q^9	\( 4 q - q^{2} - 4 q^{3} + 7 q^{4} - 3 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9} - 2 q^{10} - 2 q^{11} - 7 q^{12} - q^{14} + 3 q^{15} + 17 q^{16} - 10 q^{17} - q^{18} - 7 q^{19} - 40 q^{20} - 4 q^{21} - 12 q^{22} + 3 q^{23} - 3 q^{24} + 17 q^{25} - 4 q^{27} + 7 q^{28} - 9 q^{29} + 2 q^{30} + q^{31} + 5 q^{32} + 2 q^{33} + 32 q^{34} - 3 q^{35} + 7 q^{36} + 4 q^{37} - 18 q^{38} - 4 q^{40} - 28 q^{41} + q^{42} - 17 q^{43} - 10 q^{44} - 3 q^{45} - 40 q^{46} - 3 q^{47} - 17 q^{48} + 4 q^{49} + 11 q^{50} + 10 q^{51} - 5 q^{53} + q^{54} + 8 q^{55} + 3 q^{56} + 7 q^{57} - 12 q^{58} - 28 q^{59} + 40 q^{60} - 10 q^{61} + 14 q^{62} + 4 q^{63} + 9 q^{64} + 12 q^{66} - 22 q^{67} - 12 q^{68} - 3 q^{69} - 2 q^{70} - 2 q^{71} + 3 q^{72} + 31 q^{73} + 24 q^{74} - 17 q^{75} - 46 q^{76} - 2 q^{77} - q^{79} - 54 q^{80} + 4 q^{81} + 24 q^{82} - 3 q^{83} - 7 q^{84} + 2 q^{85} - 10 q^{86} + 9 q^{87} + 4 q^{88} - 5 q^{89} - 2 q^{90} + 28 q^{92} - q^{93} - 36 q^{94} + 39 q^{95} - 5 q^{96} + 43 q^{97} - q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q - q^2 - 4 * q^3 + 7 * q^4 - 3 * q^5 + q^6 + 4 * q^7 + 3 * q^8 + 4 * q^9 - 2 * q^10 - 2 * q^11 - 7 * q^12 - q^14 + 3 * q^15 + 17 * q^16 - 10 * q^17 - q^18 - 7 * q^19 - 40 * q^20 - 4 * q^21 - 12 * q^22 + 3 * q^23 - 3 * q^24 + 17 * q^25 - 4 * q^27 + 7 * q^28 - 9 * q^29 + 2 * q^30 + q^31 + 5 * q^32 + 2 * q^33 + 32 * q^34 - 3 * q^35 + 7 * q^36 + 4 * q^37 - 18 * q^38 - 4 * q^40 - 28 * q^41 + q^42 - 17 * q^43 - 10 * q^44 - 3 * q^45 - 40 * q^46 - 3 * q^47 - 17 * q^48 + 4 * q^49 + 11 * q^50 + 10 * q^51 - 5 * q^53 + q^54 + 8 * q^55 + 3 * q^56 + 7 * q^57 - 12 * q^58 - 28 * q^59 + 40 * q^60 - 10 * q^61 + 14 * q^62 + 4 * q^63 + 9 * q^64 + 12 * q^66 - 22 * q^67 - 12 * q^68 - 3 * q^69 - 2 * q^70 - 2 * q^71 + 3 * q^72 + 31 * q^73 + 24 * q^74 - 17 * q^75 - 46 * q^76 - 2 * q^77 - q^79 - 54 * q^80 + 4 * q^81 + 24 * q^82 - 3 * q^83 - 7 * q^84 + 2 * q^85 - 10 * q^86 + 9 * q^87 + 4 * q^88 - 5 * q^89 - 2 * q^90 + 28 * q^92 - q^93 - 36 * q^94 + 39 * q^95 - 5 * q^96 + 43 * q^97 - q^98 - 2 * q^99

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