LMFDB - Embedded newform 3549.2.a.bc.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 13x^{6} + 22x^{5} + 57x^{4} - 72x^{3} - 96x^{2} + 64x + 61 $ x^8 - 2x^7 - 13x^6 + 22x^5 + 57x^4 - 72x^3 - 96x^2 + 64*x + 61
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			1.6
Root			$1.67113$ 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)

$f(q)$	$=$	$q+1.67113 q^{2} -1.00000 q^{3} +0.792659 q^{4} +2.68351 q^{5} -1.67113 q^{6} -1.00000 q^{7} -2.01762 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.67113 q^{2} -1.00000 q^{3} +0.792659 q^{4} +2.68351 q^{5} -1.67113 q^{6} -1.00000 q^{7} -2.01762 q^{8} +1.00000 q^{9} +4.48449 q^{10} +5.79279 q^{11} -0.792659 q^{12} -1.67113 q^{14} -2.68351 q^{15} -4.95701 q^{16} +1.73722 q^{17} +1.67113 q^{18} +1.65577 q^{19} +2.12711 q^{20} +1.00000 q^{21} +9.68047 q^{22} +2.34348 q^{23} +2.01762 q^{24} +2.20124 q^{25} -1.00000 q^{27} -0.792659 q^{28} +1.72160 q^{29} -4.48449 q^{30} -9.12637 q^{31} -4.24855 q^{32} -5.79279 q^{33} +2.90312 q^{34} -2.68351 q^{35} +0.792659 q^{36} +8.57811 q^{37} +2.76699 q^{38} -5.41430 q^{40} -0.441792 q^{41} +1.67113 q^{42} +11.1218 q^{43} +4.59170 q^{44} +2.68351 q^{45} +3.91625 q^{46} +3.16304 q^{47} +4.95701 q^{48} +1.00000 q^{49} +3.67855 q^{50} -1.73722 q^{51} -12.8205 q^{53} -1.67113 q^{54} +15.5450 q^{55} +2.01762 q^{56} -1.65577 q^{57} +2.87701 q^{58} +5.61039 q^{59} -2.12711 q^{60} +6.45016 q^{61} -15.2513 q^{62} -1.00000 q^{63} +2.81417 q^{64} -9.68047 q^{66} -5.29978 q^{67} +1.37703 q^{68} -2.34348 q^{69} -4.48449 q^{70} -6.80383 q^{71} -2.01762 q^{72} +0.600675 q^{73} +14.3351 q^{74} -2.20124 q^{75} +1.31246 q^{76} -5.79279 q^{77} +6.10718 q^{79} -13.3022 q^{80} +1.00000 q^{81} -0.738290 q^{82} +11.8380 q^{83} +0.792659 q^{84} +4.66187 q^{85} +18.5858 q^{86} -1.72160 q^{87} -11.6876 q^{88} -1.97273 q^{89} +4.48449 q^{90} +1.85758 q^{92} +9.12637 q^{93} +5.28583 q^{94} +4.44327 q^{95} +4.24855 q^{96} -2.68515 q^{97} +1.67113 q^{98} +5.79279 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 8 q^{3} + 14 q^{4} + 6 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 + 14 * q^4 + 6 * q^5 - 2 * q^6 - 8 * q^7 + 12 * q^8 + 8 * q^9	\( 8 q + 2 q^{2} - 8 q^{3} + 14 q^{4} + 6 q^{5} - 2 q^{6} - 8 q^{7} + 12 q^{8} + 8 q^{9} - 4 q^{10} + 16 q^{11} - 14 q^{12} - 2 q^{14} - 6 q^{15} + 10 q^{16} - 2 q^{17} + 2 q^{18} + 14 q^{19} - 10 q^{20} + 8 q^{21} + 18 q^{22} - 6 q^{23} - 12 q^{24} + 10 q^{25} - 8 q^{27} - 14 q^{28} + 12 q^{29} + 4 q^{30} + 16 q^{31} + 26 q^{32} - 16 q^{33} + 32 q^{34} - 6 q^{35} + 14 q^{36} - 8 q^{37} + 12 q^{38} - 14 q^{40} - 4 q^{41} + 2 q^{42} + 14 q^{43} + 68 q^{44} + 6 q^{45} - 28 q^{46} + 6 q^{47} - 10 q^{48} + 8 q^{49} + 32 q^{50} + 2 q^{51} + 14 q^{53} - 2 q^{54} - 2 q^{55} - 12 q^{56} - 14 q^{57} + 24 q^{58} + 50 q^{59} + 10 q^{60} - 2 q^{61} - 20 q^{62} - 8 q^{63} + 24 q^{64} - 18 q^{66} - 16 q^{67} - 36 q^{68} + 6 q^{69} + 4 q^{70} + 34 q^{71} + 12 q^{72} - 8 q^{73} - 6 q^{74} - 10 q^{75} - 4 q^{76} - 16 q^{77} + 46 q^{79} - 24 q^{80} + 8 q^{81} - 42 q^{82} + 42 q^{83} + 14 q^{84} + 20 q^{85} + 50 q^{86} - 12 q^{87} + 62 q^{88} + 28 q^{89} - 4 q^{90} - 58 q^{92} - 16 q^{93} + 24 q^{94} - 24 q^{95} - 26 q^{96} + 16 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 8 * q^3 + 14 * q^4 + 6 * q^5 - 2 * q^6 - 8 * q^7 + 12 * q^8 + 8 * q^9 - 4 * q^10 + 16 * q^11 - 14 * q^12 - 2 * q^14 - 6 * q^15 + 10 * q^16 - 2 * q^17 + 2 * q^18 + 14 * q^19 - 10 * q^20 + 8 * q^21 + 18 * q^22 - 6 * q^23 - 12 * q^24 + 10 * q^25 - 8 * q^27 - 14 * q^28 + 12 * q^29 + 4 * q^30 + 16 * q^31 + 26 * q^32 - 16 * q^33 + 32 * q^34 - 6 * q^35 + 14 * q^36 - 8 * q^37 + 12 * q^38 - 14 * q^40 - 4 * q^41 + 2 * q^42 + 14 * q^43 + 68 * q^44 + 6 * q^45 - 28 * q^46 + 6 * q^47 - 10 * q^48 + 8 * q^49 + 32 * q^50 + 2 * q^51 + 14 * q^53 - 2 * q^54 - 2 * q^55 - 12 * q^56 - 14 * q^57 + 24 * q^58 + 50 * q^59 + 10 * q^60 - 2 * q^61 - 20 * q^62 - 8 * q^63 + 24 * q^64 - 18 * q^66 - 16 * q^67 - 36 * q^68 + 6 * q^69 + 4 * q^70 + 34 * q^71 + 12 * q^72 - 8 * q^73 - 6 * q^74 - 10 * q^75 - 4 * q^76 - 16 * q^77 + 46 * q^79 - 24 * q^80 + 8 * q^81 - 42 * q^82 + 42 * q^83 + 14 * q^84 + 20 * q^85 + 50 * q^86 - 12 * q^87 + 62 * q^88 + 28 * q^89 - 4 * q^90 - 58 * q^92 - 16 * q^93 + 24 * q^94 - 24 * q^95 - 26 * q^96 + 16 * q^97 + 2 * q^98 + 16 * 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 $

$2$	1.67113	1.18166	0.590832	−	0.806795i	$-0.298800\pi$
$2$	1.67113	1.18166	0.590832	+	0.806795i	$0.298800\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.792659	0.396329
$5$	2.68351	1.20010	0.600052	−	0.799961i	$-0.295147\pi$
$5$	2.68351	1.20010	0.600052	+	0.799961i	$0.295147\pi$
$6$	−1.67113	−0.682234
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.01762	−0.713336
$9$	1.00000	0.333333
$10$	4.48449	1.41812
$11$	5.79279	1.74659	0.873295	−	0.487191i	$-0.161978\pi$
$11$	5.79279	1.74659	0.873295	+	0.487191i	$0.161978\pi$
$12$	−0.792659	−0.228821
$13$	0	0
$13$	0	0
$14$	−1.67113	−0.446627
$15$	−2.68351	−0.692880
$16$	−4.95701	−1.23925
$17$	1.73722	0.421339	0.210669	−	0.977557i	$-0.432436\pi$
$17$	1.73722	0.421339	0.210669	+	0.977557i	$0.432436\pi$
$18$	1.67113	0.393888
$19$	1.65577	0.379859	0.189929	−	0.981798i	$-0.439174\pi$
$19$	1.65577	0.379859	0.189929	+	0.981798i	$0.439174\pi$
$20$	2.12711	0.475636
$21$	1.00000	0.218218
$22$	9.68047	2.06388
$23$	2.34348	0.488649	0.244325	−	0.969693i	$-0.421434\pi$
$23$	2.34348	0.488649	0.244325	+	0.969693i	$0.421434\pi$
$24$	2.01762	0.411845
$25$	2.20124	0.440249
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−0.792659	−0.149798
$29$	1.72160	0.319694	0.159847	−	0.987142i	$-0.448900\pi$
$29$	1.72160	0.319694	0.159847	+	0.987142i	$0.448900\pi$
$30$	−4.48449	−0.818751
$31$	−9.12637	−1.63914	−0.819572	−	0.572976i	$-0.805789\pi$
$31$	−9.12637	−1.63914	−0.819572	+	0.572976i	$0.805789\pi$
$32$	−4.24855	−0.751044
$33$	−5.79279	−1.00839
$34$	2.90312	0.497881
$35$	−2.68351	−0.453597
$36$	0.792659	0.132110
$37$	8.57811	1.41023	0.705117	−	0.709091i	$-0.250895\pi$
$37$	8.57811	1.41023	0.705117	+	0.709091i	$0.250895\pi$
$38$	2.76699	0.448865
$39$	0	0
$40$	−5.41430	−0.856077
$41$	−0.441792	−0.0689964	−0.0344982	−	0.999405i	$-0.510983\pi$
$41$	−0.441792	−0.0689964	−0.0344982	+	0.999405i	$0.510983\pi$
$42$	1.67113	0.257860
$43$	11.1218	1.69605	0.848026	−	0.529955i	$-0.177791\pi$
$43$	11.1218	1.69605	0.848026	+	0.529955i	$0.177791\pi$
$44$	4.59170	0.692225
$45$	2.68351	0.400035
$46$	3.91625	0.577419
$47$	3.16304	0.461377	0.230688	−	0.973028i	$-0.425902\pi$
$47$	3.16304	0.461377	0.230688	+	0.973028i	$0.425902\pi$
$48$	4.95701	0.715483
$49$	1.00000	0.142857
$50$	3.67855	0.520226
$51$	−1.73722	−0.243260
$52$	0	0
$53$	−12.8205	−1.76103	−0.880514	−	0.474020i	$-0.842802\pi$
$53$	−12.8205	−1.76103	−0.880514	+	0.474020i	$0.842802\pi$
$54$	−1.67113	−0.227411
$55$	15.5450	2.09609
$56$	2.01762	0.269616
$57$	−1.65577	−0.219311
$58$	2.87701	0.377770
$59$	5.61039	0.730411	0.365205	−	0.930927i	$-0.380999\pi$
$59$	5.61039	0.730411	0.365205	+	0.930927i	$0.380999\pi$
$60$	−2.12711	−0.274609
$61$	6.45016	0.825859	0.412929	−	0.910763i	$-0.364506\pi$
$61$	6.45016	0.825859	0.412929	+	0.910763i	$0.364506\pi$
$62$	−15.2513	−1.93692
$63$	−1.00000	−0.125988
$64$	2.81417	0.351771
$65$	0	0
$66$	−9.68047	−1.19158
$67$	−5.29978	−0.647471	−0.323736	−	0.946148i	$-0.604939\pi$
$67$	−5.29978	−0.647471	−0.323736	+	0.946148i	$0.604939\pi$
$68$	1.37703	0.166989
$69$	−2.34348	−0.282122
$70$	−4.48449	−0.535999
$71$	−6.80383	−0.807466	−0.403733	−	0.914877i	$-0.632287\pi$
$71$	−6.80383	−0.807466	−0.403733	+	0.914877i	$0.632287\pi$
$72$	−2.01762	−0.237779
$73$	0.600675	0.0703037	0.0351518	−	0.999382i	$-0.488809\pi$
$73$	0.600675	0.0703037	0.0351518	+	0.999382i	$0.488809\pi$
$74$	14.3351	1.66642
$75$	−2.20124	−0.254178
$76$	1.31246	0.150549
$77$	−5.79279	−0.660149
$78$	0	0
$79$	6.10718	0.687112	0.343556	−	0.939132i	$-0.388369\pi$
$79$	6.10718	0.687112	0.343556	+	0.939132i	$0.388369\pi$
$80$	−13.3022	−1.48723
$81$	1.00000	0.111111
$82$	−0.738290	−0.0815305
$83$	11.8380	1.29939	0.649696	−	0.760194i	$-0.274896\pi$
$83$	11.8380	1.29939	0.649696	+	0.760194i	$0.274896\pi$
$84$	0.792659	0.0864862
$85$	4.66187	0.505650
$86$	18.5858	2.00416
$87$	−1.72160	−0.184575
$88$	−11.6876	−1.24591
$89$	−1.97273	−0.209109	−0.104554	−	0.994519i	$-0.533342\pi$
$89$	−1.97273	−0.209109	−0.104554	+	0.994519i	$0.533342\pi$
$90$	4.48449	0.472706
$91$	0	0
$92$	1.85758	0.193666
$93$	9.12637	0.946361
$94$	5.28583	0.545192
$95$	4.44327	0.455870
$96$	4.24855	0.433616
$97$	−2.68515	−0.272635	−0.136318	−	0.990665i	$-0.543527\pi$
$97$	−2.68515	−0.272635	−0.136318	+	0.990665i	$0.543527\pi$
$98$	1.67113	0.168809
$99$	5.79279	0.582197
$100$	1.74484	0.174484
$101$	17.4773	1.73906	0.869530	−	0.493881i	$-0.164422\pi$
$101$	17.4773	1.73906	0.869530	+	0.493881i	$0.164422\pi$
$102$	−2.90312	−0.287452
$103$	14.0766	1.38701	0.693503	−	0.720453i	$-0.256066\pi$
$103$	14.0766	1.38701	0.693503	+	0.720453i	$0.256066\pi$
$104$	0	0
$105$	2.68351	0.261884
$106$	−21.4246	−2.08094
$107$	−3.33482	−0.322390	−0.161195	−	0.986923i	$-0.551535\pi$
$107$	−3.33482	−0.322390	−0.161195	+	0.986923i	$0.551535\pi$
$108$	−0.792659	−0.0762736
$109$	−10.6928	−1.02418	−0.512092	−	0.858931i	$-0.671129\pi$
$109$	−10.6928	−1.02418	−0.512092	+	0.858931i	$0.671129\pi$
$110$	25.9777	2.47687
$111$	−8.57811	−0.814199
$112$	4.95701	0.468393
$113$	11.4384	1.07604	0.538019	−	0.842933i	$-0.319173\pi$
$113$	11.4384	1.07604	0.538019	+	0.842933i	$0.319173\pi$
$114$	−2.76699	−0.259152
$115$	6.28876	0.586430
$116$	1.36464	0.126704
$117$	0	0
$118$	9.37566	0.863100
$119$	−1.73722	−0.159251
$120$	5.41430	0.494256
$121$	22.5564	2.05058
$122$	10.7790	0.975887
$123$	0.441792	0.0398351
$124$	−7.23410	−0.649641
$125$	−7.51050	−0.671760
$126$	−1.67113	−0.148876
$127$	14.4088	1.27858	0.639289	−	0.768967i	$-0.279229\pi$
$127$	14.4088	1.27858	0.639289	+	0.768967i	$0.279229\pi$
$128$	13.1999	1.16672
$129$	−11.1218	−0.979216
$130$	0	0
$131$	−3.76222	−0.328707	−0.164353	−	0.986402i	$-0.552554\pi$
$131$	−3.76222	−0.328707	−0.164353	+	0.986402i	$0.552554\pi$
$132$	−4.59170	−0.399657
$133$	−1.65577	−0.143573
$134$	−8.85660	−0.765093
$135$	−2.68351	−0.230960
$136$	−3.50506	−0.300556
$137$	−21.5100	−1.83773	−0.918863	−	0.394576i	$-0.870892\pi$
$137$	−21.5100	−1.83773	−0.918863	+	0.394576i	$0.870892\pi$
$138$	−3.91625	−0.333373
$139$	3.99178	0.338579	0.169289	−	0.985566i	$-0.445853\pi$
$139$	3.99178	0.338579	0.169289	+	0.985566i	$0.445853\pi$
$140$	−2.12711	−0.179774
$141$	−3.16304	−0.266376
$142$	−11.3700	−0.954153
$143$	0	0
$144$	−4.95701	−0.413084
$145$	4.61994	0.383666
$146$	1.00380	0.0830753
$147$	−1.00000	−0.0824786
$148$	6.79952	0.558917
$149$	10.4795	0.858515	0.429258	−	0.903182i	$-0.358775\pi$
$149$	10.4795	0.858515	0.429258	+	0.903182i	$0.358775\pi$
$150$	−3.67855	−0.300353
$151$	17.5261	1.42625	0.713126	−	0.701035i	$-0.247279\pi$
$151$	17.5261	1.42625	0.713126	+	0.701035i	$0.247279\pi$
$152$	−3.34070	−0.270967
$153$	1.73722	0.140446
$154$	−9.68047	−0.780075
$155$	−24.4907	−1.96714
$156$	0	0
$157$	−18.5395	−1.47961	−0.739805	−	0.672822i	$-0.765082\pi$
$157$	−18.5395	−1.47961	−0.739805	+	0.672822i	$0.765082\pi$
$158$	10.2059	0.811935
$159$	12.8205	1.01673
$160$	−11.4010	−0.901331
$161$	−2.34348	−0.184692
$162$	1.67113	0.131296
$163$	17.8720	1.39984	0.699921	−	0.714220i	$-0.253218\pi$
$163$	17.8720	1.39984	0.699921	+	0.714220i	$0.253218\pi$
$164$	−0.350191	−0.0273453
$165$	−15.5450	−1.21018
$166$	19.7828	1.53544
$167$	−0.992365	−0.0767915	−0.0383958	−	0.999263i	$-0.512225\pi$
$167$	−0.992365	−0.0767915	−0.0383958	+	0.999263i	$0.512225\pi$
$168$	−2.01762	−0.155663
$169$	0	0
$170$	7.79056	0.597509
$171$	1.65577	0.126620
$172$	8.81576	0.672195
$173$	−20.6834	−1.57253	−0.786265	−	0.617890i	$-0.787988\pi$
$173$	−20.6834	−1.57253	−0.786265	+	0.617890i	$0.787988\pi$
$174$	−2.87701	−0.218106
$175$	−2.20124	−0.166398
$176$	−28.7149	−2.16447
$177$	−5.61039	−0.421703
$178$	−3.29667	−0.247096
$179$	−3.11423	−0.232768	−0.116384	−	0.993204i	$-0.537130\pi$
$179$	−3.11423	−0.232768	−0.116384	+	0.993204i	$0.537130\pi$
$180$	2.12711	0.158545
$181$	−18.3738	−1.36572	−0.682858	−	0.730551i	$-0.739263\pi$
$181$	−18.3738	−1.36572	−0.682858	+	0.730551i	$0.739263\pi$
$182$	0	0
$183$	−6.45016	−0.476810
$184$	−4.72825	−0.348571
$185$	23.0195	1.69243
$186$	15.2513	1.11828
$187$	10.0634	0.735907
$188$	2.50721	0.182857
$189$	1.00000	0.0727393
$190$	7.42526	0.538685
$191$	4.01446	0.290476	0.145238	−	0.989397i	$-0.453605\pi$
$191$	4.01446	0.290476	0.145238	+	0.989397i	$0.453605\pi$
$192$	−2.81417	−0.203095
$193$	5.60562	0.403501	0.201751	−	0.979437i	$-0.435337\pi$
$193$	5.60562	0.403501	0.201751	+	0.979437i	$0.435337\pi$
$194$	−4.48722	−0.322163
$195$	0	0
$196$	0.792659	0.0566185
$197$	17.2583	1.22960	0.614801	−	0.788682i	$-0.289236\pi$
$197$	17.2583	1.22960	0.614801	+	0.788682i	$0.289236\pi$
$198$	9.68047	0.687961
$199$	−25.1788	−1.78488	−0.892439	−	0.451167i	$-0.851008\pi$
$199$	−25.1788	−1.78488	−0.892439	+	0.451167i	$0.851008\pi$
$200$	−4.44127	−0.314045
$201$	5.29978	0.373818
$202$	29.2068	2.05498
$203$	−1.72160	−0.120833
$204$	−1.37703	−0.0964112
$205$	−1.18556	−0.0828028
$206$	23.5237	1.63898
$207$	2.34348	0.162883
$208$	0	0
$209$	9.59149	0.663458
$210$	4.48449	0.309459
$211$	1.69338	0.116577	0.0582885	−	0.998300i	$-0.481436\pi$
$211$	1.69338	0.116577	0.0582885	+	0.998300i	$0.481436\pi$
$212$	−10.1623	−0.697947
$213$	6.80383	0.466191
$214$	−5.57291	−0.380956
$215$	29.8454	2.03544
$216$	2.01762	0.137282
$217$	9.12637	0.619538
$218$	−17.8690	−1.21024
$219$	−0.600675	−0.0405899
$220$	12.3219	0.830742
$221$	0	0
$222$	−14.3351	−0.962109
$223$	6.17175	0.413291	0.206645	−	0.978416i	$-0.433745\pi$
$223$	6.17175	0.413291	0.206645	+	0.978416i	$0.433745\pi$
$224$	4.24855	0.283868
$225$	2.20124	0.146750
$226$	19.1151	1.27152
$227$	−12.9967	−0.862618	−0.431309	−	0.902204i	$-0.641948\pi$
$227$	−12.9967	−0.862618	−0.431309	+	0.902204i	$0.641948\pi$
$228$	−1.31246	−0.0869196
$229$	−16.0448	−1.06027	−0.530136	−	0.847913i	$-0.677859\pi$
$229$	−16.0448	−1.06027	−0.530136	+	0.847913i	$0.677859\pi$
$230$	10.5093	0.692963
$231$	5.79279	0.381137
$232$	−3.47354	−0.228049
$233$	9.11345	0.597042	0.298521	−	0.954403i	$-0.403507\pi$
$233$	9.11345	0.597042	0.298521	+	0.954403i	$0.403507\pi$
$234$	0	0
$235$	8.48806	0.553700
$236$	4.44713	0.289483
$237$	−6.10718	−0.396704
$238$	−2.90312	−0.188181
$239$	20.9648	1.35610	0.678050	−	0.735016i	$-0.262825\pi$
$239$	20.9648	1.35610	0.678050	+	0.735016i	$0.262825\pi$
$240$	13.3022	0.858653
$241$	4.72484	0.304354	0.152177	−	0.988353i	$-0.451372\pi$
$241$	4.72484	0.304354	0.152177	+	0.988353i	$0.451372\pi$
$242$	37.6945	2.42310
$243$	−1.00000	−0.0641500
$244$	5.11278	0.327312
$245$	2.68351	0.171443
$246$	0.738290	0.0470717
$247$	0	0
$248$	18.4135	1.16926
$249$	−11.8380	−0.750204
$250$	−12.5510	−0.793794
$251$	−19.7338	−1.24559	−0.622793	−	0.782387i	$-0.714002\pi$
$251$	−19.7338	−1.24559	−0.622793	+	0.782387i	$0.714002\pi$
$252$	−0.792659	−0.0499328
$253$	13.5753	0.853470
$254$	24.0790	1.51085
$255$	−4.66187	−0.291937
$256$	16.4304	1.02690
$257$	−20.7204	−1.29251	−0.646253	−	0.763124i	$-0.723665\pi$
$257$	−20.7204	−1.29251	−0.646253	+	0.763124i	$0.723665\pi$
$258$	−18.5858	−1.15710
$259$	−8.57811	−0.533018
$260$	0	0
$261$	1.72160	0.106565
$262$	−6.28714	−0.388421
$263$	−23.1855	−1.42968	−0.714839	−	0.699290i	$-0.753500\pi$
$263$	−23.1855	−1.42968	−0.714839	+	0.699290i	$0.753500\pi$
$264$	11.6876	0.719324
$265$	−34.4039	−2.11342
$266$	−2.76699	−0.169655
$267$	1.97273	0.120729
$268$	−4.20092	−0.256612
$269$	−5.29407	−0.322785	−0.161393	−	0.986890i	$-0.551599\pi$
$269$	−5.29407	−0.322785	−0.161393	+	0.986890i	$0.551599\pi$
$270$	−4.48449	−0.272917
$271$	28.6500	1.74036	0.870182	−	0.492731i	$-0.164001\pi$
$271$	28.6500	1.74036	0.870182	+	0.492731i	$0.164001\pi$
$272$	−8.61144	−0.522145
$273$	0	0
$274$	−35.9460	−2.17158
$275$	12.7513	0.768934
$276$	−1.85758	−0.111813
$277$	11.5722	0.695304	0.347652	−	0.937624i	$-0.386979\pi$
$277$	11.5722	0.695304	0.347652	+	0.937624i	$0.386979\pi$
$278$	6.67077	0.400086
$279$	−9.12637	−0.546382
$280$	5.41430	0.323567
$281$	−2.83330	−0.169021	−0.0845103	−	0.996423i	$-0.526933\pi$
$281$	−2.83330	−0.169021	−0.0845103	+	0.996423i	$0.526933\pi$
$282$	−5.28583	−0.314767
$283$	8.75342	0.520337	0.260168	−	0.965563i	$-0.416222\pi$
$283$	8.75342	0.520337	0.260168	+	0.965563i	$0.416222\pi$
$284$	−5.39312	−0.320023
$285$	−4.44327	−0.263196
$286$	0	0
$287$	0.441792	0.0260782
$288$	−4.24855	−0.250348
$289$	−13.9820	−0.822474
$290$	7.72050	0.453364
$291$	2.68515	0.157406
$292$	0.476130	0.0278634
$293$	−15.0316	−0.878153	−0.439077	−	0.898450i	$-0.644694\pi$
$293$	−15.0316	−0.878153	−0.439077	+	0.898450i	$0.644694\pi$
$294$	−1.67113	−0.0974620
$295$	15.0556	0.876568
$296$	−17.3074	−1.00597
$297$	−5.79279	−0.336132
$298$	17.5126	1.01448
$299$	0	0
$300$	−1.74484	−0.100738
$301$	−11.1218	−0.641047
$302$	29.2883	1.68535
$303$	−17.4773	−1.00405
$304$	−8.20764	−0.470741
$305$	17.3091	0.991116
$306$	2.90312	0.165960
$307$	−19.6735	−1.12282	−0.561412	−	0.827536i	$-0.689742\pi$
$307$	−19.6735	−1.12282	−0.561412	+	0.827536i	$0.689742\pi$
$308$	−4.59170	−0.261637
$309$	−14.0766	−0.800789
$310$	−40.9271	−2.32450
$311$	−21.4272	−1.21503	−0.607513	−	0.794310i	$-0.707833\pi$
$311$	−21.4272	−1.21503	−0.607513	+	0.794310i	$0.707833\pi$
$312$	0	0
$313$	3.09742	0.175077	0.0875384	−	0.996161i	$-0.472100\pi$
$313$	3.09742	0.175077	0.0875384	+	0.996161i	$0.472100\pi$
$314$	−30.9817	−1.74840
$315$	−2.68351	−0.151199
$316$	4.84091	0.272323
$317$	−24.9862	−1.40337	−0.701684	−	0.712489i	$-0.747568\pi$
$317$	−24.9862	−1.40337	−0.701684	+	0.712489i	$0.747568\pi$
$318$	21.4246	1.20143
$319$	9.97288	0.558374
$320$	7.55185	0.422161
$321$	3.33482	0.186132
$322$	−3.91625	−0.218244
$323$	2.87644	0.160049
$324$	0.792659	0.0440366
$325$	0	0
$326$	29.8663	1.65414
$327$	10.6928	0.591313
$328$	0.891368	0.0492176
$329$	−3.16304	−0.174384
$330$	−25.9777	−1.43002
$331$	12.4206	0.682698	0.341349	−	0.939937i	$-0.389116\pi$
$331$	12.4206	0.682698	0.341349	+	0.939937i	$0.389116\pi$
$332$	9.38351	0.514987
$333$	8.57811	0.470078
$334$	−1.65837	−0.0907418
$335$	−14.2220	−0.777033
$336$	−4.95701	−0.270427
$337$	−1.91449	−0.104289	−0.0521444	−	0.998640i	$-0.516606\pi$
$337$	−1.91449	−0.104289	−0.0521444	+	0.998640i	$0.516606\pi$
$338$	0	0
$339$	−11.4384	−0.621251
$340$	3.69527	0.200404
$341$	−52.8671	−2.86291
$342$	2.76699	0.149622
$343$	−1.00000	−0.0539949
$344$	−22.4395	−1.20985
$345$	−6.28876	−0.338575
$346$	−34.5645	−1.85820
$347$	−10.8041	−0.579992	−0.289996	−	0.957028i	$-0.593654\pi$
$347$	−10.8041	−0.579992	−0.289996	+	0.957028i	$0.593654\pi$
$348$	−1.36464	−0.0731526
$349$	2.51066	0.134393	0.0671963	−	0.997740i	$-0.478595\pi$
$349$	2.51066	0.134393	0.0671963	+	0.997740i	$0.478595\pi$
$350$	−3.67855	−0.196627
$351$	0	0
$352$	−24.6109	−1.31177
$353$	17.7305	0.943701	0.471850	−	0.881679i	$-0.343586\pi$
$353$	17.7305	0.943701	0.471850	+	0.881679i	$0.343586\pi$
$354$	−9.37566	−0.498311
$355$	−18.2582	−0.969043
$356$	−1.56370	−0.0828759
$357$	1.73722	0.0919437
$358$	−5.20426	−0.275054
$359$	−8.10815	−0.427932	−0.213966	−	0.976841i	$-0.568638\pi$
$359$	−8.10815	−0.427932	−0.213966	+	0.976841i	$0.568638\pi$
$360$	−5.41430	−0.285359
$361$	−16.2584	−0.855707
$362$	−30.7050	−1.61382
$363$	−22.5564	−1.18390
$364$	0	0
$365$	1.61192	0.0843717
$366$	−10.7790	−0.563429
$367$	−7.46496	−0.389668	−0.194834	−	0.980836i	$-0.562417\pi$
$367$	−7.46496	−0.389668	−0.194834	+	0.980836i	$0.562417\pi$
$368$	−11.6167	−0.605560
$369$	−0.441792	−0.0229988
$370$	38.4684	1.99988
$371$	12.8205	0.665606
$372$	7.23410	0.375071
$373$	−9.98016	−0.516753	−0.258376	−	0.966044i	$-0.583187\pi$
$373$	−9.98016	−0.516753	−0.258376	+	0.966044i	$0.583187\pi$
$374$	16.8172	0.869594
$375$	7.51050	0.387841
$376$	−6.38180	−0.329116
$377$	0	0
$378$	1.67113	0.0859534
$379$	−13.1742	−0.676713	−0.338356	−	0.941018i	$-0.609871\pi$
$379$	−13.1742	−0.676713	−0.338356	+	0.941018i	$0.609871\pi$
$380$	3.52200	0.180675
$381$	−14.4088	−0.738187
$382$	6.70866	0.343245
$383$	−23.9371	−1.22313	−0.611563	−	0.791195i	$-0.709459\pi$
$383$	−23.9371	−1.22313	−0.611563	+	0.791195i	$0.709459\pi$
$384$	−13.1999	−0.673605
$385$	−15.5450	−0.792248
$386$	9.36769	0.476803
$387$	11.1218	0.565351
$388$	−2.12841	−0.108053
$389$	31.9544	1.62015	0.810076	−	0.586325i	$-0.199426\pi$
$389$	31.9544	1.62015	0.810076	+	0.586325i	$0.199426\pi$
$390$	0	0
$391$	4.07115	0.205887
$392$	−2.01762	−0.101905
$393$	3.76222	0.189779
$394$	28.8408	1.45298
$395$	16.3887	0.824605
$396$	4.59170	0.230742
$397$	8.42333	0.422755	0.211377	−	0.977405i	$-0.432205\pi$
$397$	8.42333	0.422755	0.211377	+	0.977405i	$0.432205\pi$
$398$	−42.0769	−2.10913
$399$	1.65577	0.0828919
$400$	−10.9116	−0.545579
$401$	6.41705	0.320452	0.160226	−	0.987080i	$-0.448778\pi$
$401$	6.41705	0.320452	0.160226	+	0.987080i	$0.448778\pi$
$402$	8.85660	0.441727
$403$	0	0
$404$	13.8536	0.689240
$405$	2.68351	0.133345
$406$	−2.87701	−0.142784
$407$	49.6912	2.46310
$408$	3.50506	0.173526
$409$	5.38327	0.266186	0.133093	−	0.991104i	$-0.457509\pi$
$409$	5.38327	0.266186	0.133093	+	0.991104i	$0.457509\pi$
$410$	−1.98121	−0.0978451
$411$	21.5100	1.06101
$412$	11.1579	0.549712
$413$	−5.61039	−0.276069
$414$	3.91625	0.192473
$415$	31.7675	1.55940
$416$	0	0
$417$	−3.99178	−0.195478
$418$	16.0286	0.783984
$419$	−14.2163	−0.694512	−0.347256	−	0.937770i	$-0.612887\pi$
$419$	−14.2163	−0.694512	−0.347256	+	0.937770i	$0.612887\pi$
$420$	2.12711	0.103792
$421$	−26.7633	−1.30436	−0.652182	−	0.758063i	$-0.726146\pi$
$421$	−26.7633	−1.30436	−0.652182	+	0.758063i	$0.726146\pi$
$422$	2.82985	0.137755
$423$	3.16304	0.153792
$424$	25.8668	1.25620
$425$	3.82406	0.185494
$426$	11.3700	0.550881
$427$	−6.45016	−0.312145
$428$	−2.64338	−0.127772
$429$	0	0
$430$	49.8754	2.40520
$431$	12.9763	0.625047	0.312524	−	0.949910i	$-0.398826\pi$
$431$	12.9763	0.625047	0.312524	+	0.949910i	$0.398826\pi$
$432$	4.95701	0.238494
$433$	−12.4224	−0.596983	−0.298491	−	0.954412i	$-0.596483\pi$
$433$	−12.4224	−0.596983	−0.298491	+	0.954412i	$0.596483\pi$
$434$	15.2513	0.732086
$435$	−4.61994	−0.221509
$436$	−8.47574	−0.405914
$437$	3.88025	0.185618
$438$	−1.00380	−0.0479636
$439$	−20.5571	−0.981135	−0.490567	−	0.871403i	$-0.663210\pi$
$439$	−20.5571	−0.981135	−0.490567	+	0.871403i	$0.663210\pi$
$440$	−31.3639	−1.49522
$441$	1.00000	0.0476190
$442$	0	0
$443$	24.1703	1.14836	0.574182	−	0.818728i	$-0.305320\pi$
$443$	24.1703	1.14836	0.574182	+	0.818728i	$0.305320\pi$
$444$	−6.79952	−0.322691
$445$	−5.29384	−0.250952
$446$	10.3138	0.488371
$447$	−10.4795	−0.495664
$448$	−2.81417	−0.132957
$449$	22.0663	1.04137	0.520685	−	0.853749i	$-0.325676\pi$
$449$	22.0663	1.04137	0.520685	+	0.853749i	$0.325676\pi$
$450$	3.67855	0.173409
$451$	−2.55921	−0.120508
$452$	9.06678	0.426466
$453$	−17.5261	−0.823447
$454$	−21.7190	−1.01933
$455$	0	0
$456$	3.34070	0.156443
$457$	12.9498	0.605768	0.302884	−	0.953027i	$-0.402050\pi$
$457$	12.9498	0.605768	0.302884	+	0.953027i	$0.402050\pi$
$458$	−26.8129	−1.25288
$459$	−1.73722	−0.0810867
$460$	4.98484	0.232419
$461$	−0.717937	−0.0334376	−0.0167188	−	0.999860i	$-0.505322\pi$
$461$	−0.717937	−0.0334376	−0.0167188	+	0.999860i	$0.505322\pi$
$462$	9.68047	0.450376
$463$	−30.2503	−1.40585	−0.702926	−	0.711263i	$-0.748124\pi$
$463$	−30.2503	−1.40585	−0.702926	+	0.711263i	$0.748124\pi$
$464$	−8.53400	−0.396181
$465$	24.4907	1.13573
$466$	15.2297	0.705503
$467$	−21.6830	−1.00337	−0.501684	−	0.865051i	$-0.667286\pi$
$467$	−21.6830	−1.00337	−0.501684	+	0.865051i	$0.667286\pi$
$468$	0	0
$469$	5.29978	0.244721
$470$	14.1846	0.654287
$471$	18.5395	0.854253
$472$	−11.3196	−0.521028
$473$	64.4260	2.96231
$474$	−10.2059	−0.468771
$475$	3.64474	0.167232
$476$	−1.37703	−0.0631159
$477$	−12.8205	−0.587009
$478$	35.0348	1.60245
$479$	19.2790	0.880881	0.440441	−	0.897782i	$-0.354822\pi$
$479$	19.2790	0.880881	0.440441	+	0.897782i	$0.354822\pi$
$480$	11.4010	0.520384
$481$	0	0
$482$	7.89580	0.359644
$483$	2.34348	0.106632
$484$	17.8795	0.812705
$485$	−7.20563	−0.327191
$486$	−1.67113	−0.0758038
$487$	23.5086	1.06527	0.532637	−	0.846344i	$-0.321201\pi$
$487$	23.5086	1.06527	0.532637	+	0.846344i	$0.321201\pi$
$488$	−13.0140	−0.589114
$489$	−17.8720	−0.808200
$490$	4.48449	0.202588
$491$	26.3370	1.18857	0.594285	−	0.804254i	$-0.297435\pi$
$491$	26.3370	1.18857	0.594285	+	0.804254i	$0.297435\pi$
$492$	0.350191	0.0157878
$493$	2.99081	0.134699
$494$	0	0
$495$	15.5450	0.698697
$496$	45.2395	2.03131
$497$	6.80383	0.305193
$498$	−19.7828	−0.886489
$499$	−12.8363	−0.574634	−0.287317	−	0.957836i	$-0.592763\pi$
$499$	−12.8363	−0.574634	−0.287317	+	0.957836i	$0.592763\pi$
$500$	−5.95326	−0.266238
$501$	0.992365	0.0443356
$502$	−32.9776	−1.47186
$503$	−20.3127	−0.905697	−0.452849	−	0.891587i	$-0.649592\pi$
$503$	−20.3127	−0.905697	−0.452849	+	0.891587i	$0.649592\pi$
$504$	2.01762	0.0898718
$505$	46.9006	2.08705
$506$	22.6860	1.00852
$507$	0	0
$508$	11.4213	0.506738
$509$	19.3090	0.855857	0.427929	−	0.903812i	$-0.359243\pi$
$509$	19.3090	0.855857	0.427929	+	0.903812i	$0.359243\pi$
$510$	−7.79056	−0.344972
$511$	−0.600675	−0.0265723
$512$	1.05739	0.0467304
$513$	−1.65577	−0.0731038
$514$	−34.6264	−1.52731
$515$	37.7747	1.66455
$516$	−8.81576	−0.388092
$517$	18.3228	0.805836
$518$	−14.3351	−0.629848
$519$	20.6834	0.907900
$520$	0	0
$521$	−12.5091	−0.548034	−0.274017	−	0.961725i	$-0.588353\pi$
$521$	−12.5091	−0.548034	−0.274017	+	0.961725i	$0.588353\pi$
$522$	2.87701	0.125923
$523$	−34.3007	−1.49987	−0.749933	−	0.661514i	$-0.769914\pi$
$523$	−34.3007	−1.49987	−0.749933	+	0.661514i	$0.769914\pi$
$524$	−2.98216	−0.130276
$525$	2.20124	0.0960702
$526$	−38.7458	−1.68940
$527$	−15.8546	−0.690635
$528$	28.7149	1.24966
$529$	−17.5081	−0.761222
$530$	−57.4933	−2.49735
$531$	5.61039	0.243470
$532$	−1.31246	−0.0569022
$533$	0	0
$534$	3.29667	0.142661
$535$	−8.94904	−0.386901
$536$	10.6929	0.461864
$537$	3.11423	0.134389
$538$	−8.84705	−0.381423
$539$	5.79279	0.249513
$540$	−2.12711	−0.0915363
$541$	−25.1013	−1.07919	−0.539596	−	0.841924i	$-0.681423\pi$
$541$	−25.1013	−1.07919	−0.539596	+	0.841924i	$0.681423\pi$
$542$	47.8777	2.05652
$543$	18.3738	0.788496
$544$	−7.38068	−0.316444
$545$	−28.6943	−1.22913
$546$	0	0
$547$	−15.0430	−0.643192	−0.321596	−	0.946877i	$-0.604219\pi$
$547$	−15.0430	−0.643192	−0.321596	+	0.946877i	$0.604219\pi$
$548$	−17.0501	−0.728345
$549$	6.45016	0.275286
$550$	21.3091	0.908622
$551$	2.85057	0.121438
$552$	4.72825	0.201248
$553$	−6.10718	−0.259704
$554$	19.3385	0.821616
$555$	−23.0195	−0.977123
$556$	3.16412	0.134189
$557$	−21.3674	−0.905368	−0.452684	−	0.891671i	$-0.649533\pi$
$557$	−21.3674	−0.905368	−0.452684	+	0.891671i	$0.649533\pi$
$558$	−15.2513	−0.645639
$559$	0	0
$560$	13.3022	0.562121
$561$	−10.0634	−0.424876
$562$	−4.73480	−0.199726
$563$	2.34808	0.0989597	0.0494799	−	0.998775i	$-0.484244\pi$
$563$	2.34808	0.0989597	0.0494799	+	0.998775i	$0.484244\pi$
$564$	−2.50721	−0.105573
$565$	30.6952	1.29136
$566$	14.6281	0.614863
$567$	−1.00000	−0.0419961
$568$	13.7275	0.575994
$569$	10.1151	0.424048	0.212024	−	0.977264i	$-0.431995\pi$
$569$	10.1151	0.424048	0.212024	+	0.977264i	$0.431995\pi$
$570$	−7.42526	−0.311010
$571$	28.1994	1.18011	0.590053	−	0.807364i	$-0.299107\pi$
$571$	28.1994	1.18011	0.590053	+	0.807364i	$0.299107\pi$
$572$	0	0
$573$	−4.01446	−0.167706
$574$	0.738290	0.0308156
$575$	5.15857	0.215127
$576$	2.81417	0.117257
$577$	−22.7245	−0.946034	−0.473017	−	0.881053i	$-0.656835\pi$
$577$	−22.7245	−0.946034	−0.473017	+	0.881053i	$0.656835\pi$
$578$	−23.3658	−0.971887
$579$	−5.60562	−0.232961
$580$	3.66204	0.152058
$581$	−11.8380	−0.491124
$582$	4.48722	0.186001
$583$	−74.2663	−3.07580
$584$	−1.21193	−0.0501501
$585$	0	0
$586$	−25.1196	−1.03768
$587$	−34.8951	−1.44028	−0.720138	−	0.693831i	$-0.755921\pi$
$587$	−34.8951	−1.44028	−0.720138	+	0.693831i	$0.755921\pi$
$588$	−0.792659	−0.0326887
$589$	−15.1111	−0.622643
$590$	25.1597	1.03581
$591$	−17.2583	−0.709911
$592$	−42.5218	−1.74764
$593$	17.0082	0.698443	0.349222	−	0.937040i	$-0.386446\pi$
$593$	17.0082	0.698443	0.349222	+	0.937040i	$0.386446\pi$
$594$	−9.68047	−0.397195
$595$	−4.66187	−0.191118
$596$	8.30668	0.340255
$597$	25.1788	1.03050
$598$	0	0
$599$	−15.0841	−0.616318	−0.308159	−	0.951335i	$-0.599713\pi$
$599$	−15.0841	−0.616318	−0.308159	+	0.951335i	$0.599713\pi$
$600$	4.44127	0.181314
$601$	−14.2374	−0.580754	−0.290377	−	0.956912i	$-0.593781\pi$
$601$	−14.2374	−0.580754	−0.290377	+	0.956912i	$0.593781\pi$
$602$	−18.5858	−0.757503
$603$	−5.29978	−0.215824
$604$	13.8922	0.565266
$605$	60.5303	2.46091
$606$	−29.2068	−1.18645
$607$	−41.0169	−1.66482	−0.832412	−	0.554158i	$-0.813040\pi$
$607$	−41.0169	−1.66482	−0.832412	+	0.554158i	$0.813040\pi$
$608$	−7.03460	−0.285291
$609$	1.72160	0.0697629
$610$	28.9257	1.17117
$611$	0	0
$612$	1.37703	0.0556630
$613$	−24.4359	−0.986956	−0.493478	−	0.869758i	$-0.664275\pi$
$613$	−24.4359	−0.986956	−0.493478	+	0.869758i	$0.664275\pi$
$614$	−32.8769	−1.32680
$615$	1.18556	0.0478062
$616$	11.6876	0.470908
$617$	−35.6040	−1.43336	−0.716681	−	0.697401i	$-0.754340\pi$
$617$	−35.6040	−1.43336	−0.716681	+	0.697401i	$0.754340\pi$
$618$	−23.5237	−0.946263
$619$	38.0783	1.53050	0.765249	−	0.643735i	$-0.222616\pi$
$619$	38.0783	1.53050	0.765249	+	0.643735i	$0.222616\pi$
$620$	−19.4128	−0.779637
$621$	−2.34348	−0.0940406
$622$	−35.8076	−1.43575
$623$	1.97273	0.0790356
$624$	0	0
$625$	−31.1607	−1.24643
$626$	5.17618	0.206882
$627$	−9.59149	−0.383047
$628$	−14.6955	−0.586413
$629$	14.9021	0.594186
$630$	−4.48449	−0.178666
$631$	26.4944	1.05472	0.527362	−	0.849640i	$-0.323181\pi$
$631$	26.4944	1.05472	0.527362	+	0.849640i	$0.323181\pi$
$632$	−12.3220	−0.490141
$633$	−1.69338	−0.0673058
$634$	−41.7551	−1.65831
$635$	38.6663	1.53443
$636$	10.1623	0.402960
$637$	0	0
$638$	16.6659	0.659810
$639$	−6.80383	−0.269155
$640$	35.4222	1.40018
$641$	27.1629	1.07287	0.536436	−	0.843941i	$-0.319770\pi$
$641$	27.1629	1.07287	0.536436	+	0.843941i	$0.319770\pi$
$642$	5.57291	0.219945
$643$	−7.32165	−0.288738	−0.144369	−	0.989524i	$-0.546115\pi$
$643$	−7.32165	−0.288738	−0.144369	+	0.989524i	$0.546115\pi$
$644$	−1.85758	−0.0731989
$645$	−29.8454	−1.17516
$646$	4.80688	0.189124
$647$	10.3203	0.405735	0.202867	−	0.979206i	$-0.434974\pi$
$647$	10.3203	0.405735	0.202867	+	0.979206i	$0.434974\pi$
$648$	−2.01762	−0.0792595
$649$	32.4998	1.27573
$650$	0	0
$651$	−9.12637	−0.357691
$652$	14.1664	0.554799
$653$	−12.8779	−0.503949	−0.251975	−	0.967734i	$-0.581080\pi$
$653$	−12.8779	−0.503949	−0.251975	+	0.967734i	$0.581080\pi$
$654$	17.8690	0.698733
$655$	−10.0960	−0.394482
$656$	2.18997	0.0855039
$657$	0.600675	0.0234346
$658$	−5.28583	−0.206063
$659$	−27.7895	−1.08252	−0.541262	−	0.840854i	$-0.682053\pi$
$659$	−27.7895	−1.08252	−0.541262	+	0.840854i	$0.682053\pi$
$660$	−12.3219	−0.479629
$661$	7.27008	0.282773	0.141387	−	0.989954i	$-0.454844\pi$
$661$	7.27008	0.282773	0.141387	+	0.989954i	$0.454844\pi$
$662$	20.7564	0.806720
$663$	0	0
$664$	−23.8846	−0.926902
$665$	−4.44327	−0.172303
$666$	14.3351	0.555474
$667$	4.03454	0.156218
$668$	−0.786607	−0.0304347
$669$	−6.17175	−0.238613
$670$	−23.7668	−0.918191
$671$	37.3644	1.44244
$672$	−4.24855	−0.163891
$673$	26.9789	1.03996	0.519979	−	0.854179i	$-0.325940\pi$
$673$	26.9789	1.03996	0.519979	+	0.854179i	$0.325940\pi$
$674$	−3.19935	−0.123234
$675$	−2.20124	−0.0847259
$676$	0	0
$677$	−11.5807	−0.445084	−0.222542	−	0.974923i	$-0.571435\pi$
$677$	−11.5807	−0.445084	−0.222542	+	0.974923i	$0.571435\pi$
$678$	−19.1151	−0.734110
$679$	2.68515	0.103047
$680$	−9.40586	−0.360698
$681$	12.9967	0.498033
$682$	−88.3476	−3.38300
$683$	−15.9751	−0.611271	−0.305635	−	0.952149i	$-0.598869\pi$
$683$	−15.9751	−0.611271	−0.305635	+	0.952149i	$0.598869\pi$
$684$	1.31246	0.0501831
$685$	−57.7225	−2.20546
$686$	−1.67113	−0.0638039
$687$	16.0448	0.612148
$688$	−55.1307	−2.10184
$689$	0	0
$690$	−10.5093	−0.400082
$691$	13.9788	0.531777	0.265888	−	0.964004i	$-0.414335\pi$
$691$	13.9788	0.531777	0.265888	+	0.964004i	$0.414335\pi$
$692$	−16.3949	−0.623240
$693$	−5.79279	−0.220050
$694$	−18.0549	−0.685356
$695$	10.7120	0.406329
$696$	3.47354	0.131664
$697$	−0.767492	−0.0290709
$698$	4.19563	0.158807
$699$	−9.11345	−0.344702
$700$	−1.74484	−0.0659486
$701$	−17.3224	−0.654259	−0.327129	−	0.944980i	$-0.606081\pi$
$701$	−17.3224	−0.654259	−0.327129	+	0.944980i	$0.606081\pi$
$702$	0	0
$703$	14.2033	0.535689
$704$	16.3019	0.614399
$705$	−8.48806	−0.319679
$706$	29.6299	1.11514
$707$	−17.4773	−0.657303
$708$	−4.44713	−0.167133
$709$	−18.7995	−0.706028	−0.353014	−	0.935618i	$-0.614843\pi$
$709$	−18.7995	−0.706028	−0.353014	+	0.935618i	$0.614843\pi$
$710$	−30.5117	−1.14508
$711$	6.10718	0.229037
$712$	3.98021	0.149165
$713$	−21.3875	−0.800967
$714$	2.90312	0.108647
$715$	0	0
$716$	−2.46852	−0.0922529
$717$	−20.9648	−0.782945
$718$	−13.5497	−0.505671
$719$	15.5507	0.579943	0.289971	−	0.957035i	$-0.406354\pi$
$719$	15.5507	0.579943	0.289971	+	0.957035i	$0.406354\pi$
$720$	−13.3022	−0.495744
$721$	−14.0766	−0.524239
$722$	−27.1699	−1.01116
$723$	−4.72484	−0.175719
$724$	−14.5642	−0.541273
$725$	3.78967	0.140745
$726$	−37.6945	−1.39897
$727$	−13.4907	−0.500343	−0.250171	−	0.968202i	$-0.580487\pi$
$727$	−13.4907	−0.500343	−0.250171	+	0.968202i	$0.580487\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.69372	0.0996990
$731$	19.3210	0.714613
$732$	−5.11278	−0.188974
$733$	18.7477	0.692463	0.346231	−	0.938149i	$-0.387461\pi$
$733$	18.7477	0.692463	0.346231	+	0.938149i	$0.387461\pi$
$734$	−12.4749	−0.460456
$735$	−2.68351	−0.0989829
$736$	−9.95639	−0.366997
$737$	−30.7005	−1.13087
$738$	−0.738290	−0.0271768
$739$	−0.796651	−0.0293053	−0.0146526	−	0.999893i	$-0.504664\pi$
$739$	−0.796651	−0.0293053	−0.0146526	+	0.999893i	$0.504664\pi$
$740$	18.2466	0.670758
$741$	0	0
$742$	21.4246	0.786523
$743$	−5.90878	−0.216772	−0.108386	−	0.994109i	$-0.534568\pi$
$743$	−5.90878	−0.216772	−0.108386	+	0.994109i	$0.534568\pi$
$744$	−18.4135	−0.675073
$745$	28.1219	1.03031
$746$	−16.6781	−0.610628
$747$	11.8380	0.433131
$748$	7.97682	0.291662
$749$	3.33482	0.121852
$750$	12.5510	0.458297
$751$	−27.5264	−1.00445	−0.502227	−	0.864736i	$-0.667486\pi$
$751$	−27.5264	−1.00445	−0.502227	+	0.864736i	$0.667486\pi$
$752$	−15.6792	−0.571762
$753$	19.7338	0.719139
$754$	0	0
$755$	47.0315	1.71165
$756$	0.792659	0.0288287
$757$	−2.64691	−0.0962036	−0.0481018	−	0.998842i	$-0.515317\pi$
$757$	−2.64691	−0.0962036	−0.0481018	+	0.998842i	$0.515317\pi$
$758$	−22.0157	−0.799647
$759$	−13.5753	−0.492751
$760$	−8.96482	−0.325188
$761$	−32.9977	−1.19617	−0.598083	−	0.801434i	$-0.704071\pi$
$761$	−32.9977	−1.19617	−0.598083	+	0.801434i	$0.704071\pi$
$762$	−24.0790	−0.872289
$763$	10.6928	0.387105
$764$	3.18209	0.115124
$765$	4.66187	0.168550
$766$	−40.0018	−1.44532
$767$	0	0
$768$	−16.4304	−0.592880
$769$	−10.9286	−0.394095	−0.197048	−	0.980394i	$-0.563135\pi$
$769$	−10.9286	−0.394095	−0.197048	+	0.980394i	$0.563135\pi$
$770$	−25.9777	−0.936170
$771$	20.7204	0.746228
$772$	4.44334	0.159919
$773$	1.49151	0.0536460	0.0268230	−	0.999640i	$-0.491461\pi$
$773$	1.49151	0.0536460	0.0268230	+	0.999640i	$0.491461\pi$
$774$	18.5858	0.668054
$775$	−20.0894	−0.721631
$776$	5.41760	0.194481
$777$	8.57811	0.307738
$778$	53.3998	1.91447
$779$	−0.731504	−0.0262089
$780$	0	0
$781$	−39.4131	−1.41031
$782$	6.80340	0.243289
$783$	−1.72160	−0.0615251
$784$	−4.95701	−0.177036
$785$	−49.7509	−1.77568
$786$	6.28714	0.224255
$787$	−18.7110	−0.666977	−0.333488	−	0.942754i	$-0.608226\pi$
$787$	−18.7110	−0.666977	−0.333488	+	0.942754i	$0.608226\pi$
$788$	13.6799	0.487328
$789$	23.1855	0.825424
$790$	27.3876	0.974406
$791$	−11.4384	−0.406704
$792$	−11.6876	−0.415302
$793$	0	0
$794$	14.0764	0.499554
$795$	34.4039	1.22018
$796$	−19.9582	−0.707400
$797$	−19.3878	−0.686751	−0.343376	−	0.939198i	$-0.611570\pi$
$797$	−19.3878	−0.686751	−0.343376	+	0.939198i	$0.611570\pi$
$798$	2.76699	0.0979504
$799$	5.49491	0.194396
$800$	−9.35209	−0.330646
$801$	−1.97273	−0.0697029
$802$	10.7237	0.378667
$803$	3.47958	0.122792
$804$	4.20092	0.148155
$805$	−6.28876	−0.221650
$806$	0	0
$807$	5.29407	0.186360
$808$	−35.2626	−1.24053
$809$	−3.13195	−0.110114	−0.0550568	−	0.998483i	$-0.517534\pi$
$809$	−3.13195	−0.110114	−0.0550568	+	0.998483i	$0.517534\pi$
$810$	4.48449	0.157569
$811$	51.1164	1.79494	0.897469	−	0.441077i	$-0.145403\pi$
$811$	51.1164	1.79494	0.897469	+	0.441077i	$0.145403\pi$
$812$	−1.36464	−0.0478896
$813$	−28.6500	−1.00480
$814$	83.0402	2.91056
$815$	47.9597	1.67996
$816$	8.61144	0.301461
$817$	18.4150	0.644260
$818$	8.99612	0.314542
$819$	0	0
$820$	−0.939741	−0.0328172
$821$	6.56042	0.228960	0.114480	−	0.993426i	$-0.463480\pi$
$821$	6.56042	0.228960	0.114480	+	0.993426i	$0.463480\pi$
$822$	35.9460	1.25376
$823$	−23.9753	−0.835727	−0.417863	−	0.908510i	$-0.637221\pi$
$823$	−23.9753	−0.835727	−0.417863	+	0.908510i	$0.637221\pi$
$824$	−28.4012	−0.989401
$825$	−12.7513	−0.443944
$826$	−9.37566	−0.326221
$827$	32.8611	1.14269	0.571346	−	0.820709i	$-0.306422\pi$
$827$	32.8611	1.14269	0.571346	+	0.820709i	$0.306422\pi$
$828$	1.85758	0.0645554
$829$	−54.1186	−1.87962	−0.939808	−	0.341704i	$-0.888996\pi$
$829$	−54.1186	−1.87962	−0.939808	+	0.341704i	$0.888996\pi$
$830$	53.0874	1.84269
$831$	−11.5722	−0.401434
$832$	0	0
$833$	1.73722	0.0601913
$834$	−6.67077	−0.230990
$835$	−2.66303	−0.0921578
$836$	7.60278	0.262948
$837$	9.12637	0.315454
$838$	−23.7572	−0.820680
$839$	20.9038	0.721681	0.360840	−	0.932628i	$-0.382490\pi$
$839$	20.9038	0.721681	0.360840	+	0.932628i	$0.382490\pi$
$840$	−5.41430	−0.186811
$841$	−26.0361	−0.897796
$842$	−44.7248	−1.54132
$843$	2.83330	0.0975841
$844$	1.34227	0.0462029
$845$	0	0
$846$	5.28583	0.181731
$847$	−22.5564	−0.775046
$848$	63.5512	2.18236
$849$	−8.75342	−0.300417
$850$	6.39047	0.219191
$851$	20.1026	0.689110
$852$	5.39312	0.184765
$853$	−34.8912	−1.19465	−0.597327	−	0.801998i	$-0.703770\pi$
$853$	−34.8912	−1.19465	−0.597327	+	0.801998i	$0.703770\pi$
$854$	−10.7790	−0.368851
$855$	4.44327	0.151957
$856$	6.72840	0.229972
$857$	15.9673	0.545431	0.272716	−	0.962095i	$-0.412078\pi$
$857$	15.9673	0.545431	0.272716	+	0.962095i	$0.412078\pi$
$858$	0	0
$859$	43.0509	1.46888	0.734438	−	0.678676i	$-0.237446\pi$
$859$	43.0509	1.46888	0.734438	+	0.678676i	$0.237446\pi$
$860$	23.6572	0.806704
$861$	−0.441792	−0.0150562
$862$	21.6851	0.738596
$863$	−34.7890	−1.18423	−0.592116	−	0.805853i	$-0.701707\pi$
$863$	−34.7890	−1.18423	−0.592116	+	0.805853i	$0.701707\pi$
$864$	4.24855	0.144539
$865$	−55.5042	−1.88720
$866$	−20.7594	−0.705433
$867$	13.9820	0.474855
$868$	7.23410	0.245541
$869$	35.3776	1.20010
$870$	−7.72050	−0.261750
$871$	0	0
$872$	21.5740	0.730587
$873$	−2.68515	−0.0908785
$874$	6.48439	0.219338
$875$	7.51050	0.253901
$876$	−0.476130	−0.0160870
$877$	−43.6768	−1.47486	−0.737431	−	0.675423i	$-0.763961\pi$
$877$	−43.6768	−1.47486	−0.737431	+	0.675423i	$0.763961\pi$
$878$	−34.3534	−1.15937
$879$	15.0316	0.507002
$880$	−77.0568	−2.59758
$881$	50.5044	1.70154	0.850768	−	0.525541i	$-0.176137\pi$
$881$	50.5044	1.70154	0.850768	+	0.525541i	$0.176137\pi$
$882$	1.67113	0.0562697
$883$	−5.36093	−0.180409	−0.0902047	−	0.995923i	$-0.528752\pi$
$883$	−5.36093	−0.180409	−0.0902047	+	0.995923i	$0.528752\pi$
$884$	0	0
$885$	−15.0556	−0.506087
$886$	40.3915	1.35698
$887$	38.7877	1.30236	0.651182	−	0.758922i	$-0.274274\pi$
$887$	38.7877	1.30236	0.651182	+	0.758922i	$0.274274\pi$
$888$	17.3074	0.580797
$889$	−14.4088	−0.483257
$890$	−8.84667	−0.296541
$891$	5.79279	0.194066
$892$	4.89209	0.163799
$893$	5.23725	0.175258
$894$	−17.5126	−0.585708
$895$	−8.35707	−0.279346
$896$	−13.1999	−0.440978
$897$	0	0
$898$	36.8755	1.23055
$899$	−15.7120	−0.524024
$900$	1.74484	0.0581612
$901$	−22.2721	−0.741990
$902$	−4.27676	−0.142400
$903$	11.1218	0.370109
$904$	−23.0784	−0.767576
$905$	−49.3064	−1.63900
$906$	−29.2883	−0.973038
$907$	21.1043	0.700757	0.350378	−	0.936608i	$-0.386053\pi$
$907$	21.1043	0.700757	0.350378	+	0.936608i	$0.386053\pi$
$908$	−10.3019	−0.341881
$909$	17.4773	0.579686
$910$	0	0
$911$	0.531159	0.0175981	0.00879903	−	0.999961i	$-0.497199\pi$
$911$	0.531159	0.0175981	0.00879903	+	0.999961i	$0.497199\pi$
$912$	8.20764	0.271782
$913$	68.5751	2.26951
$914$	21.6408	0.715814
$915$	−17.3091	−0.572221
$916$	−12.7181	−0.420217
$917$	3.76222	0.124239
$918$	−2.90312	−0.0958172
$919$	−3.57103	−0.117797	−0.0588987	−	0.998264i	$-0.518759\pi$
$919$	−3.57103	−0.117797	−0.0588987	+	0.998264i	$0.518759\pi$
$920$	−12.6883	−0.418321
$921$	19.6735	0.648263
$922$	−1.19976	−0.0395120
$923$	0	0
$924$	4.59170	0.151056
$925$	18.8825	0.620853
$926$	−50.5521	−1.66125
$927$	14.0766	0.462336
$928$	−7.31431	−0.240104
$929$	−3.48785	−0.114433	−0.0572164	−	0.998362i	$-0.518222\pi$
$929$	−3.48785	−0.114433	−0.0572164	+	0.998362i	$0.518222\pi$
$930$	40.9271	1.34205
$931$	1.65577	0.0542655
$932$	7.22386	0.236625
$933$	21.4272	0.701496
$934$	−36.2350	−1.18564
$935$	27.0052	0.883164
$936$	0	0
$937$	−58.4186	−1.90845	−0.954226	−	0.299085i	$-0.903319\pi$
$937$	−58.4186	−1.90845	−0.954226	+	0.299085i	$0.903319\pi$
$938$	8.85660	0.289178
$939$	−3.09742	−0.101081
$940$	6.72813	0.219448
$941$	−29.3083	−0.955422	−0.477711	−	0.878517i	$-0.658533\pi$
$941$	−29.3083	−0.955422	−0.477711	+	0.878517i	$0.658533\pi$
$942$	30.9817	1.00944
$943$	−1.03533	−0.0337150
$944$	−27.8108	−0.905163
$945$	2.68351	0.0872947
$946$	107.664	3.50045
$947$	27.5962	0.896757	0.448379	−	0.893844i	$-0.352002\pi$
$947$	27.5962	0.896757	0.448379	+	0.893844i	$0.352002\pi$
$948$	−4.84091	−0.157226
$949$	0	0
$950$	6.09082	0.197612
$951$	24.9862	0.810235
$952$	3.50506	0.113600
$953$	−18.4512	−0.597695	−0.298847	−	0.954301i	$-0.596602\pi$
$953$	−18.4512	−0.597695	−0.298847	+	0.954301i	$0.596602\pi$
$954$	−21.4246	−0.693648
$955$	10.7728	0.348601
$956$	16.6179	0.537462
$957$	−9.97288	−0.322377
$958$	32.2177	1.04091
$959$	21.5100	0.694595
$960$	−7.55185	−0.243735
$961$	52.2906	1.68679
$962$	0	0
$963$	−3.33482	−0.107463
$964$	3.74519	0.120624
$965$	15.0427	0.484243
$966$	3.91625	0.126003
$967$	22.7001	0.729986	0.364993	−	0.931010i	$-0.381071\pi$
$967$	22.7001	0.729986	0.364993	+	0.931010i	$0.381071\pi$
$968$	−45.5101	−1.46275
$969$	−2.87644	−0.0924045
$970$	−12.0415	−0.386630
$971$	49.0236	1.57324	0.786621	−	0.617437i	$-0.211829\pi$
$971$	49.0236	1.57324	0.786621	+	0.617437i	$0.211829\pi$
$972$	−0.792659	−0.0254245
$973$	−3.99178	−0.127971
$974$	39.2858	1.25880
$975$	0	0
$976$	−31.9735	−1.02345
$977$	27.5404	0.881097	0.440548	−	0.897729i	$-0.354784\pi$
$977$	27.5404	0.881097	0.440548	+	0.897729i	$0.354784\pi$
$978$	−29.8663	−0.955020
$979$	−11.4276	−0.365227
$980$	2.12711	0.0679481
$981$	−10.6928	−0.341395
$982$	44.0124	1.40449
$983$	−45.2301	−1.44262	−0.721309	−	0.692614i	$-0.756459\pi$
$983$	−45.2301	−1.44262	−0.721309	+	0.692614i	$0.756459\pi$
$984$	−0.891368	−0.0284158
$985$	46.3128	1.47565
$986$	4.99802	0.159169
$987$	3.16304	0.100681
$988$	0	0
$989$	26.0636	0.828775
$990$	25.9777	0.825625
$991$	50.8266	1.61456	0.807280	−	0.590169i	$-0.200939\pi$
$991$	50.8266	1.61456	0.807280	+	0.590169i	$0.200939\pi$
$992$	38.7738	1.23107
$993$	−12.4206	−0.394156
$994$	11.3700	0.360636
$995$	−67.5677	−2.14204
$996$	−9.38351	−0.297328
$997$	−53.5494	−1.69593	−0.847963	−	0.530056i	$-0.822171\pi$
$997$	−53.5494	−1.69593	−0.847963	+	0.530056i	$0.822171\pi$
$998$	−21.4511	−0.679024
$999$	−8.57811	−0.271400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bc.1.6		8
13.6	odd	12		273.2.bd.b.127.3	yes	16
13.11	odd	12		273.2.bd.b.43.3	✓	16
13.12	even	2		3549.2.a.ba.1.3		8
39.11	even	12		819.2.ct.c.316.6		16
39.32	even	12		819.2.ct.c.127.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.b.43.3	✓	16	13.11	odd	12
273.2.bd.b.127.3	yes	16	13.6	odd	12
819.2.ct.c.127.6		16	39.32	even	12
819.2.ct.c.316.6		16	39.11	even	12
3549.2.a.ba.1.3		8	13.12	even	2
3549.2.a.bc.1.6		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.67113 q^{2} -1.00000 q^{3} +0.792659 q^{4} +2.68351 q^{5} -1.67113 q^{6} -1.00000 q^{7} -2.01762 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.67113 q^{2} -1.00000 q^{3} +0.792659 q^{4} +2.68351 q^{5} -1.67113 q^{6} -1.00000 q^{7} -2.01762 q^{8} +1.00000 q^{9} +4.48449 q^{10} +5.79279 q^{11} -0.792659 q^{12} -1.67113 q^{14} -2.68351 q^{15} -4.95701 q^{16} +1.73722 q^{17} +1.67113 q^{18} +1.65577 q^{19} +2.12711 q^{20} +1.00000 q^{21} +9.68047 q^{22} +2.34348 q^{23} +2.01762 q^{24} +2.20124 q^{25} -1.00000 q^{27} -0.792659 q^{28} +1.72160 q^{29} -4.48449 q^{30} -9.12637 q^{31} -4.24855 q^{32} -5.79279 q^{33} +2.90312 q^{34} -2.68351 q^{35} +0.792659 q^{36} +8.57811 q^{37} +2.76699 q^{38} -5.41430 q^{40} -0.441792 q^{41} +1.67113 q^{42} +11.1218 q^{43} +4.59170 q^{44} +2.68351 q^{45} +3.91625 q^{46} +3.16304 q^{47} +4.95701 q^{48} +1.00000 q^{49} +3.67855 q^{50} -1.73722 q^{51} -12.8205 q^{53} -1.67113 q^{54} +15.5450 q^{55} +2.01762 q^{56} -1.65577 q^{57} +2.87701 q^{58} +5.61039 q^{59} -2.12711 q^{60} +6.45016 q^{61} -15.2513 q^{62} -1.00000 q^{63} +2.81417 q^{64} -9.68047 q^{66} -5.29978 q^{67} +1.37703 q^{68} -2.34348 q^{69} -4.48449 q^{70} -6.80383 q^{71} -2.01762 q^{72} +0.600675 q^{73} +14.3351 q^{74} -2.20124 q^{75} +1.31246 q^{76} -5.79279 q^{77} +6.10718 q^{79} -13.3022 q^{80} +1.00000 q^{81} -0.738290 q^{82} +11.8380 q^{83} +0.792659 q^{84} +4.66187 q^{85} +18.5858 q^{86} -1.72160 q^{87} -11.6876 q^{88} -1.97273 q^{89} +4.48449 q^{90} +1.85758 q^{92} +9.12637 q^{93} +5.28583 q^{94} +4.44327 q^{95} +4.24855 q^{96} -2.68515 q^{97} +1.67113 q^{98} +5.79279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 8 q^{3} + 14 q^{4} + 6 q^{5} - 2 q^{6} - 8 q^{7} + 12 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 8 * q^3 + 14 * q^4 + 6 * q^5 - 2 * q^6 - 8 * q^7 + 12 * q^8 + 8 * q^9	\( 8 q + 2 q^{2} - 8 q^{3} + 14 q^{4} + 6 q^{5} - 2 q^{6} - 8 q^{7} + 12 q^{8} + 8 q^{9} - 4 q^{10} + 16 q^{11} - 14 q^{12} - 2 q^{14} - 6 q^{15} + 10 q^{16} - 2 q^{17} + 2 q^{18} + 14 q^{19} - 10 q^{20} + 8 q^{21} + 18 q^{22} - 6 q^{23} - 12 q^{24} + 10 q^{25} - 8 q^{27} - 14 q^{28} + 12 q^{29} + 4 q^{30} + 16 q^{31} + 26 q^{32} - 16 q^{33} + 32 q^{34} - 6 q^{35} + 14 q^{36} - 8 q^{37} + 12 q^{38} - 14 q^{40} - 4 q^{41} + 2 q^{42} + 14 q^{43} + 68 q^{44} + 6 q^{45} - 28 q^{46} + 6 q^{47} - 10 q^{48} + 8 q^{49} + 32 q^{50} + 2 q^{51} + 14 q^{53} - 2 q^{54} - 2 q^{55} - 12 q^{56} - 14 q^{57} + 24 q^{58} + 50 q^{59} + 10 q^{60} - 2 q^{61} - 20 q^{62} - 8 q^{63} + 24 q^{64} - 18 q^{66} - 16 q^{67} - 36 q^{68} + 6 q^{69} + 4 q^{70} + 34 q^{71} + 12 q^{72} - 8 q^{73} - 6 q^{74} - 10 q^{75} - 4 q^{76} - 16 q^{77} + 46 q^{79} - 24 q^{80} + 8 q^{81} - 42 q^{82} + 42 q^{83} + 14 q^{84} + 20 q^{85} + 50 q^{86} - 12 q^{87} + 62 q^{88} + 28 q^{89} - 4 q^{90} - 58 q^{92} - 16 q^{93} + 24 q^{94} - 24 q^{95} - 26 q^{96} + 16 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 8 * q^3 + 14 * q^4 + 6 * q^5 - 2 * q^6 - 8 * q^7 + 12 * q^8 + 8 * q^9 - 4 * q^10 + 16 * q^11 - 14 * q^12 - 2 * q^14 - 6 * q^15 + 10 * q^16 - 2 * q^17 + 2 * q^18 + 14 * q^19 - 10 * q^20 + 8 * q^21 + 18 * q^22 - 6 * q^23 - 12 * q^24 + 10 * q^25 - 8 * q^27 - 14 * q^28 + 12 * q^29 + 4 * q^30 + 16 * q^31 + 26 * q^32 - 16 * q^33 + 32 * q^34 - 6 * q^35 + 14 * q^36 - 8 * q^37 + 12 * q^38 - 14 * q^40 - 4 * q^41 + 2 * q^42 + 14 * q^43 + 68 * q^44 + 6 * q^45 - 28 * q^46 + 6 * q^47 - 10 * q^48 + 8 * q^49 + 32 * q^50 + 2 * q^51 + 14 * q^53 - 2 * q^54 - 2 * q^55 - 12 * q^56 - 14 * q^57 + 24 * q^58 + 50 * q^59 + 10 * q^60 - 2 * q^61 - 20 * q^62 - 8 * q^63 + 24 * q^64 - 18 * q^66 - 16 * q^67 - 36 * q^68 + 6 * q^69 + 4 * q^70 + 34 * q^71 + 12 * q^72 - 8 * q^73 - 6 * q^74 - 10 * q^75 - 4 * q^76 - 16 * q^77 + 46 * q^79 - 24 * q^80 + 8 * q^81 - 42 * q^82 + 42 * q^83 + 14 * q^84 + 20 * q^85 + 50 * q^86 - 12 * q^87 + 62 * q^88 + 28 * q^89 - 4 * q^90 - 58 * q^92 - 16 * q^93 + 24 * q^94 - 24 * q^95 - 26 * q^96 + 16 * q^97 + 2 * q^98 + 16 * q^99

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