LMFDB - Embedded newform 1226.2.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1226,2,Mod(1,1226)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1226, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1226.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1226 = 2 \cdot 613 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1226.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:	$9.78965928781$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 4 x^{16} - 28 x^{15} + 120 x^{14} + 291 x^{13} - 1382 x^{12} - 1398 x^{11} + 7700 x^{10} + \cdots - 320 $ x^17 - 4x^16 - 28x^15 + 120x^14 + 291x^13 - 1382x^12 - 1398x^11 + 7700x^10 + 3456x^9 - 21974x^8 - 6336x^7 + 33062x^6 + 9753x^5 - 24446x^4 - 8368x^3 + 7000x^2 + 2384x - 320
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.961867$ of defining polynomial
Character	$\chi$	$=$	1226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.961867 q^{3} +1.00000 q^{4} +2.82340 q^{5} +0.961867 q^{6} +4.64973 q^{7} -1.00000 q^{8} -2.07481 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.961867 q^{3} +1.00000 q^{4} +2.82340 q^{5} +0.961867 q^{6} +4.64973 q^{7} -1.00000 q^{8} -2.07481 q^{9} -2.82340 q^{10} -0.906655 q^{11} -0.961867 q^{12} +2.91189 q^{13} -4.64973 q^{14} -2.71573 q^{15} +1.00000 q^{16} +5.28255 q^{17} +2.07481 q^{18} +6.29353 q^{19} +2.82340 q^{20} -4.47242 q^{21} +0.906655 q^{22} -0.269200 q^{23} +0.961867 q^{24} +2.97157 q^{25} -2.91189 q^{26} +4.88129 q^{27} +4.64973 q^{28} -5.61545 q^{29} +2.71573 q^{30} -7.89608 q^{31} -1.00000 q^{32} +0.872082 q^{33} -5.28255 q^{34} +13.1280 q^{35} -2.07481 q^{36} +2.62073 q^{37} -6.29353 q^{38} -2.80085 q^{39} -2.82340 q^{40} -2.62339 q^{41} +4.47242 q^{42} +2.17160 q^{43} -0.906655 q^{44} -5.85802 q^{45} +0.269200 q^{46} -5.10610 q^{47} -0.961867 q^{48} +14.6200 q^{49} -2.97157 q^{50} -5.08111 q^{51} +2.91189 q^{52} -11.7647 q^{53} -4.88129 q^{54} -2.55985 q^{55} -4.64973 q^{56} -6.05354 q^{57} +5.61545 q^{58} +3.29364 q^{59} -2.71573 q^{60} -13.1351 q^{61} +7.89608 q^{62} -9.64731 q^{63} +1.00000 q^{64} +8.22142 q^{65} -0.872082 q^{66} +1.90984 q^{67} +5.28255 q^{68} +0.258934 q^{69} -13.1280 q^{70} +10.2431 q^{71} +2.07481 q^{72} +4.46400 q^{73} -2.62073 q^{74} -2.85825 q^{75} +6.29353 q^{76} -4.21570 q^{77} +2.80085 q^{78} +8.05678 q^{79} +2.82340 q^{80} +1.52928 q^{81} +2.62339 q^{82} +4.11588 q^{83} -4.47242 q^{84} +14.9147 q^{85} -2.17160 q^{86} +5.40132 q^{87} +0.906655 q^{88} -11.1253 q^{89} +5.85802 q^{90} +13.5395 q^{91} -0.269200 q^{92} +7.59498 q^{93} +5.10610 q^{94} +17.7691 q^{95} +0.961867 q^{96} +15.6039 q^{97} -14.6200 q^{98} +1.88114 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 4 q^{3} + 17 q^{4} - 5 q^{5} - 4 q^{6} + 7 q^{7} - 17 q^{8} + 21 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 4 * q^3 + 17 * q^4 - 5 * q^5 - 4 * q^6 + 7 * q^7 - 17 * q^8 + 21 * q^9	\( 17 q - 17 q^{2} + 4 q^{3} + 17 q^{4} - 5 q^{5} - 4 q^{6} + 7 q^{7} - 17 q^{8} + 21 q^{9} + 5 q^{10} + 8 q^{11} + 4 q^{12} + 9 q^{13} - 7 q^{14} - 4 q^{15} + 17 q^{16} - q^{17} - 21 q^{18} + 32 q^{19} - 5 q^{20} + 6 q^{21} - 8 q^{22} - 5 q^{23} - 4 q^{24} + 30 q^{25} - 9 q^{26} + 16 q^{27} + 7 q^{28} + 3 q^{29} + 4 q^{30} + 27 q^{31} - 17 q^{32} - 14 q^{33} + q^{34} + 25 q^{35} + 21 q^{36} + 7 q^{37} - 32 q^{38} + 27 q^{39} + 5 q^{40} - 2 q^{41} - 6 q^{42} + 36 q^{43} + 8 q^{44} - q^{45} + 5 q^{46} - 3 q^{47} + 4 q^{48} + 52 q^{49} - 30 q^{50} + 40 q^{51} + 9 q^{52} - 20 q^{53} - 16 q^{54} + 48 q^{55} - 7 q^{56} + 12 q^{57} - 3 q^{58} + 34 q^{59} - 4 q^{60} + 49 q^{61} - 27 q^{62} + 27 q^{63} + 17 q^{64} - 6 q^{65} + 14 q^{66} + 36 q^{67} - q^{68} + 18 q^{69} - 25 q^{70} - q^{71} - 21 q^{72} + 24 q^{73} - 7 q^{74} + 35 q^{75} + 32 q^{76} - 6 q^{77} - 27 q^{78} + 43 q^{79} - 5 q^{80} + 37 q^{81} + 2 q^{82} + 10 q^{83} + 6 q^{84} + 16 q^{85} - 36 q^{86} + 28 q^{87} - 8 q^{88} - 12 q^{89} + q^{90} + 42 q^{91} - 5 q^{92} + 3 q^{93} + 3 q^{94} - 10 q^{95} - 4 q^{96} + 26 q^{97} - 52 q^{98} + 34 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 4 * q^3 + 17 * q^4 - 5 * q^5 - 4 * q^6 + 7 * q^7 - 17 * q^8 + 21 * q^9 + 5 * q^10 + 8 * q^11 + 4 * q^12 + 9 * q^13 - 7 * q^14 - 4 * q^15 + 17 * q^16 - q^17 - 21 * q^18 + 32 * q^19 - 5 * q^20 + 6 * q^21 - 8 * q^22 - 5 * q^23 - 4 * q^24 + 30 * q^25 - 9 * q^26 + 16 * q^27 + 7 * q^28 + 3 * q^29 + 4 * q^30 + 27 * q^31 - 17 * q^32 - 14 * q^33 + q^34 + 25 * q^35 + 21 * q^36 + 7 * q^37 - 32 * q^38 + 27 * q^39 + 5 * q^40 - 2 * q^41 - 6 * q^42 + 36 * q^43 + 8 * q^44 - q^45 + 5 * q^46 - 3 * q^47 + 4 * q^48 + 52 * q^49 - 30 * q^50 + 40 * q^51 + 9 * q^52 - 20 * q^53 - 16 * q^54 + 48 * q^55 - 7 * q^56 + 12 * q^57 - 3 * q^58 + 34 * q^59 - 4 * q^60 + 49 * q^61 - 27 * q^62 + 27 * q^63 + 17 * q^64 - 6 * q^65 + 14 * q^66 + 36 * q^67 - q^68 + 18 * q^69 - 25 * q^70 - q^71 - 21 * q^72 + 24 * q^73 - 7 * q^74 + 35 * q^75 + 32 * q^76 - 6 * q^77 - 27 * q^78 + 43 * q^79 - 5 * q^80 + 37 * q^81 + 2 * q^82 + 10 * q^83 + 6 * q^84 + 16 * q^85 - 36 * q^86 + 28 * q^87 - 8 * q^88 - 12 * q^89 + q^90 + 42 * q^91 - 5 * q^92 + 3 * q^93 + 3 * q^94 - 10 * q^95 - 4 * q^96 + 26 * q^97 - 52 * q^98 + 34 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.961867	−0.555334	−0.277667	−	0.960677i	$-0.589561\pi$
$3$	−0.961867	−0.555334	−0.277667	+	0.960677i	$0.589561\pi$
$4$	1.00000	0.500000
$5$	2.82340	1.26266	0.631331	−	0.775514i	$-0.282509\pi$
$5$	2.82340	1.26266	0.631331	+	0.775514i	$0.282509\pi$
$6$	0.961867	0.392681
$7$	4.64973	1.75743	0.878716	−	0.477345i	$-0.158401\pi$
$7$	4.64973	1.75743	0.878716	+	0.477345i	$0.158401\pi$
$8$	−1.00000	−0.353553
$9$	−2.07481	−0.691604
$10$	−2.82340	−0.892836
$11$	−0.906655	−0.273367	−0.136683	−	0.990615i	$-0.543644\pi$
$11$	−0.906655	−0.273367	−0.136683	+	0.990615i	$0.543644\pi$
$12$	−0.961867	−0.277667
$13$	2.91189	0.807613	0.403807	−	0.914844i	$-0.367687\pi$
$13$	2.91189	0.807613	0.403807	+	0.914844i	$0.367687\pi$
$14$	−4.64973	−1.24269
$15$	−2.71573	−0.701199
$16$	1.00000	0.250000
$17$	5.28255	1.28121	0.640603	−	0.767872i	$-0.278685\pi$
$17$	5.28255	1.28121	0.640603	+	0.767872i	$0.278685\pi$
$18$	2.07481	0.489038
$19$	6.29353	1.44384	0.721918	−	0.691979i	$-0.243261\pi$
$19$	6.29353	1.44384	0.721918	+	0.691979i	$0.243261\pi$
$20$	2.82340	0.631331
$21$	−4.47242	−0.975962
$22$	0.906655	0.193300
$23$	−0.269200	−0.0561320	−0.0280660	−	0.999606i	$-0.508935\pi$
$23$	−0.269200	−0.0561320	−0.0280660	+	0.999606i	$0.508935\pi$
$24$	0.961867	0.196340
$25$	2.97157	0.594313
$26$	−2.91189	−0.571069
$27$	4.88129	0.939405
$28$	4.64973	0.878716
$29$	−5.61545	−1.04276	−0.521382	−	0.853324i	$-0.674583\pi$
$29$	−5.61545	−1.04276	−0.521382	+	0.853324i	$0.674583\pi$
$30$	2.71573	0.495822
$31$	−7.89608	−1.41818	−0.709089	−	0.705119i	$-0.750894\pi$
$31$	−7.89608	−1.41818	−0.709089	+	0.705119i	$0.750894\pi$
$32$	−1.00000	−0.176777
$33$	0.872082	0.151810
$34$	−5.28255	−0.905949
$35$	13.1280	2.21904
$36$	−2.07481	−0.345802
$37$	2.62073	0.430845	0.215423	−	0.976521i	$-0.430887\pi$
$37$	2.62073	0.430845	0.215423	+	0.976521i	$0.430887\pi$
$38$	−6.29353	−1.02095
$39$	−2.80085	−0.448495
$40$	−2.82340	−0.446418
$41$	−2.62339	−0.409705	−0.204852	−	0.978793i	$-0.565671\pi$
$41$	−2.62339	−0.409705	−0.204852	+	0.978793i	$0.565671\pi$
$42$	4.47242	0.690109
$43$	2.17160	0.331166	0.165583	−	0.986196i	$-0.447049\pi$
$43$	2.17160	0.331166	0.165583	+	0.986196i	$0.447049\pi$
$44$	−0.906655	−0.136683
$45$	−5.85802	−0.873262
$46$	0.269200	0.0396913
$47$	−5.10610	−0.744802	−0.372401	−	0.928072i	$-0.621465\pi$
$47$	−5.10610	−0.744802	−0.372401	+	0.928072i	$0.621465\pi$
$48$	−0.961867	−0.138834
$49$	14.6200	2.08857
$50$	−2.97157	−0.420243
$51$	−5.08111	−0.711497
$52$	2.91189	0.403807
$53$	−11.7647	−1.61600	−0.808000	−	0.589182i	$-0.799450\pi$
$53$	−11.7647	−1.61600	−0.808000	+	0.589182i	$0.799450\pi$
$54$	−4.88129	−0.664260
$55$	−2.55985	−0.345170
$56$	−4.64973	−0.621346
$57$	−6.05354	−0.801811
$58$	5.61545	0.737345
$59$	3.29364	0.428796	0.214398	−	0.976746i	$-0.431221\pi$
$59$	3.29364	0.428796	0.214398	+	0.976746i	$0.431221\pi$
$60$	−2.71573	−0.350599
$61$	−13.1351	−1.68177	−0.840887	−	0.541210i	$-0.817966\pi$
$61$	−13.1351	−1.68177	−0.840887	+	0.541210i	$0.817966\pi$
$62$	7.89608	1.00280
$63$	−9.64731	−1.21545
$64$	1.00000	0.125000
$65$	8.22142	1.01974
$66$	−0.872082	−0.107346
$67$	1.90984	0.233324	0.116662	−	0.993172i	$-0.462781\pi$
$67$	1.90984	0.233324	0.116662	+	0.993172i	$0.462781\pi$
$68$	5.28255	0.640603
$69$	0.258934	0.0311720
$70$	−13.1280	−1.56910
$71$	10.2431	1.21563	0.607816	−	0.794078i	$-0.292046\pi$
$71$	10.2431	1.21563	0.607816	+	0.794078i	$0.292046\pi$
$72$	2.07481	0.244519
$73$	4.46400	0.522472	0.261236	−	0.965275i	$-0.415870\pi$
$73$	4.46400	0.522472	0.261236	+	0.965275i	$0.415870\pi$
$74$	−2.62073	−0.304653
$75$	−2.85825	−0.330042
$76$	6.29353	0.721918
$77$	−4.21570	−0.480424
$78$	2.80085	0.317134
$79$	8.05678	0.906458	0.453229	−	0.891394i	$-0.350272\pi$
$79$	8.05678	0.906458	0.453229	+	0.891394i	$0.350272\pi$
$80$	2.82340	0.315665
$81$	1.52928	0.169920
$82$	2.62339	0.289705
$83$	4.11588	0.451776	0.225888	−	0.974153i	$-0.427472\pi$
$83$	4.11588	0.451776	0.225888	+	0.974153i	$0.427472\pi$
$84$	−4.47242	−0.487981
$85$	14.9147	1.61773
$86$	−2.17160	−0.234170
$87$	5.40132	0.579082
$88$	0.906655	0.0966498
$89$	−11.1253	−1.17928	−0.589642	−	0.807665i	$-0.700731\pi$
$89$	−11.1253	−1.17928	−0.589642	+	0.807665i	$0.700731\pi$
$90$	5.85802	0.617489
$91$	13.5395	1.41933
$92$	−0.269200	−0.0280660
$93$	7.59498	0.787563
$94$	5.10610	0.526654
$95$	17.7691	1.82307
$96$	0.961867	0.0981701
$97$	15.6039	1.58433	0.792166	−	0.610305i	$-0.208953\pi$
$97$	15.6039	1.58433	0.792166	+	0.610305i	$0.208953\pi$
$98$	−14.6200	−1.47684
$99$	1.88114	0.189062
$100$	2.97157	0.297157
$101$	5.78667	0.575796	0.287898	−	0.957661i	$-0.407044\pi$
$101$	5.78667	0.575796	0.287898	+	0.957661i	$0.407044\pi$
$102$	5.08111	0.503104
$103$	8.90282	0.877221	0.438611	−	0.898677i	$-0.355471\pi$
$103$	8.90282	0.877221	0.438611	+	0.898677i	$0.355471\pi$
$104$	−2.91189	−0.285534
$105$	−12.6274	−1.23231
$106$	11.7647	1.14268
$107$	−3.69090	−0.356812	−0.178406	−	0.983957i	$-0.557094\pi$
$107$	−3.69090	−0.356812	−0.178406	+	0.983957i	$0.557094\pi$
$108$	4.88129	0.469703
$109$	−9.86341	−0.944743	−0.472372	−	0.881400i	$-0.656602\pi$
$109$	−9.86341	−0.944743	−0.472372	+	0.881400i	$0.656602\pi$
$110$	2.55985	0.244072
$111$	−2.52079	−0.239263
$112$	4.64973	0.439358
$113$	18.7540	1.76423	0.882115	−	0.471034i	$-0.156119\pi$
$113$	18.7540	1.76423	0.882115	+	0.471034i	$0.156119\pi$
$114$	6.05354	0.566966
$115$	−0.760057	−0.0708757
$116$	−5.61545	−0.521382
$117$	−6.04163	−0.558549
$118$	−3.29364	−0.303204
$119$	24.5624	2.25163
$120$	2.71573	0.247911
$121$	−10.1780	−0.925271
$122$	13.1351	1.18919
$123$	2.52335	0.227523
$124$	−7.89608	−0.709089
$125$	−5.72707	−0.512245
$126$	9.64731	0.859451
$127$	−10.9278	−0.969684	−0.484842	−	0.874602i	$-0.661123\pi$
$127$	−10.9278	−0.969684	−0.484842	+	0.874602i	$0.661123\pi$
$128$	−1.00000	−0.0883883
$129$	−2.08879	−0.183908
$130$	−8.22142	−0.721067
$131$	−2.18469	−0.190877	−0.0954386	−	0.995435i	$-0.530425\pi$
$131$	−2.18469	−0.190877	−0.0954386	+	0.995435i	$0.530425\pi$
$132$	0.872082	0.0759050
$133$	29.2632	2.53744
$134$	−1.90984	−0.164985
$135$	13.7818	1.18615
$136$	−5.28255	−0.452975
$137$	−3.12678	−0.267139	−0.133569	−	0.991039i	$-0.542644\pi$
$137$	−3.12678	−0.267139	−0.133569	+	0.991039i	$0.542644\pi$
$138$	−0.258934	−0.0220419
$139$	3.56433	0.302322	0.151161	−	0.988509i	$-0.451699\pi$
$139$	3.56433	0.302322	0.151161	+	0.988509i	$0.451699\pi$
$140$	13.1280	1.10952
$141$	4.91139	0.413614
$142$	−10.2431	−0.859582
$143$	−2.64008	−0.220775
$144$	−2.07481	−0.172901
$145$	−15.8546	−1.31666
$146$	−4.46400	−0.369443
$147$	−14.0625	−1.15985
$148$	2.62073	0.215423
$149$	6.01447	0.492724	0.246362	−	0.969178i	$-0.420765\pi$
$149$	6.01447	0.492724	0.246362	+	0.969178i	$0.420765\pi$
$150$	2.85825	0.233375
$151$	−11.7778	−0.958465	−0.479233	−	0.877688i	$-0.659085\pi$
$151$	−11.7778	−0.958465	−0.479233	+	0.877688i	$0.659085\pi$
$152$	−6.29353	−0.510473
$153$	−10.9603	−0.886087
$154$	4.21570	0.339711
$155$	−22.2938	−1.79068
$156$	−2.80085	−0.224248
$157$	20.9057	1.66845	0.834227	−	0.551421i	$-0.185914\pi$
$157$	20.9057	1.66845	0.834227	+	0.551421i	$0.185914\pi$
$158$	−8.05678	−0.640963
$159$	11.3160	0.897420
$160$	−2.82340	−0.223209
$161$	−1.25170	−0.0986482
$162$	−1.52928	−0.120152
$163$	13.5410	1.06061	0.530306	−	0.847807i	$-0.322077\pi$
$163$	13.5410	1.06061	0.530306	+	0.847807i	$0.322077\pi$
$164$	−2.62339	−0.204852
$165$	2.46223	0.191685
$166$	−4.11588	−0.319454
$167$	−21.9296	−1.69696	−0.848482	−	0.529224i	$-0.822483\pi$
$167$	−21.9296	−1.69696	−0.848482	+	0.529224i	$0.822483\pi$
$168$	4.47242	0.345055
$169$	−4.52089	−0.347760
$170$	−14.9147	−1.14391
$171$	−13.0579	−0.998562
$172$	2.17160	0.165583
$173$	−11.2770	−0.857371	−0.428686	−	0.903454i	$-0.641023\pi$
$173$	−11.2770	−0.857371	−0.428686	+	0.903454i	$0.641023\pi$
$174$	−5.40132	−0.409473
$175$	13.8170	1.04446
$176$	−0.906655	−0.0683417
$177$	−3.16805	−0.238125
$178$	11.1253	0.833879
$179$	22.1521	1.65572	0.827862	−	0.560932i	$-0.189557\pi$
$179$	22.1521	1.65572	0.827862	+	0.560932i	$0.189557\pi$
$180$	−5.85802	−0.436631
$181$	−25.6400	−1.90580	−0.952902	−	0.303277i	$-0.901919\pi$
$181$	−25.6400	−1.90580	−0.952902	+	0.303277i	$0.901919\pi$
$182$	−13.5395	−1.00361
$183$	12.6342	0.933947
$184$	0.269200	0.0198457
$185$	7.39935	0.544011
$186$	−7.59498	−0.556891
$187$	−4.78945	−0.350239
$188$	−5.10610	−0.372401
$189$	22.6967	1.65094
$190$	−17.7691	−1.28911
$191$	17.1314	1.23958	0.619791	−	0.784767i	$-0.287217\pi$
$191$	17.1314	1.23958	0.619791	+	0.784767i	$0.287217\pi$
$192$	−0.961867	−0.0694168
$193$	−7.69579	−0.553955	−0.276978	−	0.960876i	$-0.589333\pi$
$193$	−7.69579	−0.553955	−0.276978	+	0.960876i	$0.589333\pi$
$194$	−15.6039	−1.12029
$195$	−7.90792	−0.566298
$196$	14.6200	1.04428
$197$	−2.61638	−0.186409	−0.0932046	−	0.995647i	$-0.529711\pi$
$197$	−2.61638	−0.186409	−0.0932046	+	0.995647i	$0.529711\pi$
$198$	−1.88114	−0.133687
$199$	20.3449	1.44222	0.721108	−	0.692823i	$-0.243633\pi$
$199$	20.3449	1.44222	0.721108	+	0.692823i	$0.243633\pi$
$200$	−2.97157	−0.210121
$201$	−1.83701	−0.129573
$202$	−5.78667	−0.407149
$203$	−26.1103	−1.83259
$204$	−5.08111	−0.355749
$205$	−7.40687	−0.517318
$206$	−8.90282	−0.620289
$207$	0.558539	0.0388211
$208$	2.91189	0.201903
$209$	−5.70606	−0.394697
$210$	12.6274	0.871374
$211$	17.7157	1.21960	0.609800	−	0.792556i	$-0.291250\pi$
$211$	17.7157	1.21960	0.609800	+	0.792556i	$0.291250\pi$
$212$	−11.7647	−0.808000
$213$	−9.85250	−0.675082
$214$	3.69090	0.252304
$215$	6.13130	0.418151
$216$	−4.88129	−0.332130
$217$	−36.7146	−2.49235
$218$	9.86341	0.668034
$219$	−4.29377	−0.290146
$220$	−2.55985	−0.172585
$221$	15.3822	1.03472
$222$	2.52079	0.169184
$223$	−1.27940	−0.0856752	−0.0428376	−	0.999082i	$-0.513640\pi$
$223$	−1.27940	−0.0856752	−0.0428376	+	0.999082i	$0.513640\pi$
$224$	−4.64973	−0.310673
$225$	−6.16544	−0.411029
$226$	−18.7540	−1.24750
$227$	−10.9895	−0.729401	−0.364701	−	0.931125i	$-0.618829\pi$
$227$	−10.9895	−0.729401	−0.364701	+	0.931125i	$0.618829\pi$
$228$	−6.05354	−0.400905
$229$	17.2909	1.14262	0.571308	−	0.820736i	$-0.306436\pi$
$229$	17.2909	1.14262	0.571308	+	0.820736i	$0.306436\pi$
$230$	0.760057	0.0501167
$231$	4.05494	0.266796
$232$	5.61545	0.368673
$233$	0.192576	0.0126161	0.00630804	−	0.999980i	$-0.497992\pi$
$233$	0.192576	0.0126161	0.00630804	+	0.999980i	$0.497992\pi$
$234$	6.04163	0.394954
$235$	−14.4166	−0.940432
$236$	3.29364	0.214398
$237$	−7.74955	−0.503387
$238$	−24.5624	−1.59214
$239$	−13.2705	−0.858398	−0.429199	−	0.903210i	$-0.641204\pi$
$239$	−13.2705	−0.858398	−0.429199	+	0.903210i	$0.641204\pi$
$240$	−2.71573	−0.175300
$241$	−19.9563	−1.28550	−0.642750	−	0.766076i	$-0.722207\pi$
$241$	−19.9563	−1.28550	−0.642750	+	0.766076i	$0.722207\pi$
$242$	10.1780	0.654265
$243$	−16.1148	−1.03377
$244$	−13.1351	−0.840887
$245$	41.2779	2.63715
$246$	−2.52335	−0.160883
$247$	18.3261	1.16606
$248$	7.89608	0.501402
$249$	−3.95893	−0.250887
$250$	5.72707	0.362212
$251$	19.7822	1.24864	0.624321	−	0.781168i	$-0.285376\pi$
$251$	19.7822	1.24864	0.624321	+	0.781168i	$0.285376\pi$
$252$	−9.64731	−0.607723
$253$	0.244071	0.0153446
$254$	10.9278	0.685670
$255$	−14.3460	−0.898380
$256$	1.00000	0.0625000
$257$	−26.9966	−1.68400	−0.842001	−	0.539477i	$-0.818622\pi$
$257$	−26.9966	−1.68400	−0.842001	+	0.539477i	$0.818622\pi$
$258$	2.08879	0.130043
$259$	12.1857	0.757181
$260$	8.22142	0.509871
$261$	11.6510	0.721179
$262$	2.18469	0.134971
$263$	−13.2217	−0.815283	−0.407642	−	0.913142i	$-0.633649\pi$
$263$	−13.2217	−0.815283	−0.407642	+	0.913142i	$0.633649\pi$
$264$	−0.872082	−0.0536729
$265$	−33.2163	−2.04046
$266$	−29.2632	−1.79424
$267$	10.7011	0.654896
$268$	1.90984	0.116662
$269$	−14.5077	−0.884550	−0.442275	−	0.896880i	$-0.645828\pi$
$269$	−14.5077	−0.884550	−0.442275	+	0.896880i	$0.645828\pi$
$270$	−13.7818	−0.838735
$271$	8.17745	0.496744	0.248372	−	0.968665i	$-0.420104\pi$
$271$	8.17745	0.496744	0.248372	+	0.968665i	$0.420104\pi$
$272$	5.28255	0.320301
$273$	−13.0232	−0.788200
$274$	3.12678	0.188896
$275$	−2.69419	−0.162466
$276$	0.258934	0.0155860
$277$	−3.62576	−0.217851	−0.108925	−	0.994050i	$-0.534741\pi$
$277$	−3.62576	−0.217851	−0.108925	+	0.994050i	$0.534741\pi$
$278$	−3.56433	−0.213774
$279$	16.3829	0.980817
$280$	−13.1280	−0.784549
$281$	26.5399	1.58324	0.791619	−	0.611015i	$-0.209238\pi$
$281$	26.5399	1.58324	0.791619	+	0.611015i	$0.209238\pi$
$282$	−4.91139	−0.292469
$283$	1.97086	0.117155	0.0585777	−	0.998283i	$-0.481343\pi$
$283$	1.97086	0.117155	0.0585777	+	0.998283i	$0.481343\pi$
$284$	10.2431	0.607816
$285$	−17.0915	−1.01242
$286$	2.64008	0.156111
$287$	−12.1980	−0.720028
$288$	2.07481	0.122259
$289$	10.9053	0.641488
$290$	15.8546	0.931017
$291$	−15.0088	−0.879834
$292$	4.46400	0.261236
$293$	−6.95953	−0.406580	−0.203290	−	0.979119i	$-0.565163\pi$
$293$	−6.95953	−0.406580	−0.203290	+	0.979119i	$0.565163\pi$
$294$	14.0625	0.820139
$295$	9.29926	0.541424
$296$	−2.62073	−0.152327
$297$	−4.42565	−0.256802
$298$	−6.01447	−0.348409
$299$	−0.783880	−0.0453330
$300$	−2.85825	−0.165021
$301$	10.0974	0.582002
$302$	11.7778	0.677737
$303$	−5.56601	−0.319759
$304$	6.29353	0.360959
$305$	−37.0855	−2.12351
$306$	10.9603	0.626558
$307$	16.9411	0.966882	0.483441	−	0.875377i	$-0.339387\pi$
$307$	16.9411	0.966882	0.483441	+	0.875377i	$0.339387\pi$
$308$	−4.21570	−0.240212
$309$	−8.56333	−0.487151
$310$	22.2938	1.26620
$311$	−13.7875	−0.781815	−0.390907	−	0.920430i	$-0.627839\pi$
$311$	−13.7875	−0.781815	−0.390907	+	0.920430i	$0.627839\pi$
$312$	2.80085	0.158567
$313$	−24.1874	−1.36715	−0.683576	−	0.729879i	$-0.739576\pi$
$313$	−24.1874	−1.36715	−0.683576	+	0.729879i	$0.739576\pi$
$314$	−20.9057	−1.17978
$315$	−27.2382	−1.53470
$316$	8.05678	0.453229
$317$	−10.8318	−0.608376	−0.304188	−	0.952612i	$-0.598385\pi$
$317$	−10.8318	−0.608376	−0.304188	+	0.952612i	$0.598385\pi$
$318$	−11.3160	−0.634572
$319$	5.09128	0.285057
$320$	2.82340	0.157833
$321$	3.55015	0.198150
$322$	1.25170	0.0697548
$323$	33.2459	1.84985
$324$	1.52928	0.0849601
$325$	8.65288	0.479975
$326$	−13.5410	−0.749965
$327$	9.48729	0.524648
$328$	2.62339	0.144852
$329$	−23.7420	−1.30894
$330$	−2.46223	−0.135541
$331$	24.6099	1.35268	0.676342	−	0.736588i	$-0.263564\pi$
$331$	24.6099	1.35268	0.676342	+	0.736588i	$0.263564\pi$
$332$	4.11588	0.225888
$333$	−5.43752	−0.297974
$334$	21.9296	1.19994
$335$	5.39223	0.294609
$336$	−4.47242	−0.243990
$337$	−6.86557	−0.373991	−0.186996	−	0.982361i	$-0.559875\pi$
$337$	−6.86557	−0.373991	−0.186996	+	0.982361i	$0.559875\pi$
$338$	4.52089	0.245904
$339$	−18.0389	−0.979737
$340$	14.9147	0.808864
$341$	7.15902	0.387683
$342$	13.0579	0.706090
$343$	35.4307	1.91308
$344$	−2.17160	−0.117085
$345$	0.731074	0.0393597
$346$	11.2770	0.606253
$347$	7.91530	0.424916	0.212458	−	0.977170i	$-0.431853\pi$
$347$	7.91530	0.424916	0.212458	+	0.977170i	$0.431853\pi$
$348$	5.40132	0.289541
$349$	29.6072	1.58483	0.792417	−	0.609979i	$-0.208822\pi$
$349$	29.6072	1.58483	0.792417	+	0.609979i	$0.208822\pi$
$350$	−13.8170	−0.738548
$351$	14.2138	0.758676
$352$	0.906655	0.0483249
$353$	−30.9921	−1.64954	−0.824771	−	0.565467i	$-0.808696\pi$
$353$	−30.9921	−1.64954	−0.824771	+	0.565467i	$0.808696\pi$
$354$	3.16805	0.168380
$355$	28.9203	1.53493
$356$	−11.1253	−0.589642
$357$	−23.6258	−1.25041
$358$	−22.1521	−1.17077
$359$	−4.71006	−0.248587	−0.124294	−	0.992245i	$-0.539666\pi$
$359$	−4.71006	−0.248587	−0.124294	+	0.992245i	$0.539666\pi$
$360$	5.85802	0.308745
$361$	20.6085	1.08466
$362$	25.6400	1.34761
$363$	9.78986	0.513834
$364$	13.5395	0.709663
$365$	12.6036	0.659705
$366$	−12.6342	−0.660400
$367$	−28.5256	−1.48903	−0.744513	−	0.667608i	$-0.767318\pi$
$367$	−28.5256	−1.48903	−0.744513	+	0.667608i	$0.767318\pi$
$368$	−0.269200	−0.0140330
$369$	5.44304	0.283353
$370$	−7.39935	−0.384674
$371$	−54.7025	−2.84001
$372$	7.59498	0.393781
$373$	−7.13206	−0.369284	−0.184642	−	0.982806i	$-0.559113\pi$
$373$	−7.13206	−0.369284	−0.184642	+	0.982806i	$0.559113\pi$
$374$	4.78945	0.247657
$375$	5.50868	0.284467
$376$	5.10610	0.263327
$377$	−16.3516	−0.842150
$378$	−22.6967	−1.16739
$379$	1.05656	0.0542719	0.0271359	−	0.999632i	$-0.491361\pi$
$379$	1.05656	0.0542719	0.0271359	+	0.999632i	$0.491361\pi$
$380$	17.7691	0.911537
$381$	10.5111	0.538498
$382$	−17.1314	−0.876517
$383$	−32.0352	−1.63692	−0.818462	−	0.574560i	$-0.805173\pi$
$383$	−32.0352	−1.63692	−0.818462	+	0.574560i	$0.805173\pi$
$384$	0.961867	0.0490851
$385$	−11.9026	−0.606612
$386$	7.69579	0.391705
$387$	−4.50567	−0.229036
$388$	15.6039	0.792166
$389$	−33.7275	−1.71005	−0.855026	−	0.518585i	$-0.826459\pi$
$389$	−33.7275	−1.71005	−0.855026	+	0.518585i	$0.826459\pi$
$390$	7.90792	0.400433
$391$	−1.42206	−0.0719166
$392$	−14.6200	−0.738419
$393$	2.10138	0.106001
$394$	2.61638	0.131811
$395$	22.7475	1.14455
$396$	1.88114	0.0945308
$397$	−24.4338	−1.22630	−0.613149	−	0.789967i	$-0.710098\pi$
$397$	−24.4338	−1.22630	−0.613149	+	0.789967i	$0.710098\pi$
$398$	−20.3449	−1.01980
$399$	−28.1473	−1.40913
$400$	2.97157	0.148578
$401$	−19.3322	−0.965402	−0.482701	−	0.875785i	$-0.660344\pi$
$401$	−19.3322	−0.965402	−0.482701	+	0.875785i	$0.660344\pi$
$402$	1.83701	0.0916217
$403$	−22.9925	−1.14534
$404$	5.78667	0.287898
$405$	4.31777	0.214552
$406$	26.1103	1.29583
$407$	−2.37610	−0.117779
$408$	5.08111	0.251552
$409$	19.2997	0.954307	0.477154	−	0.878820i	$-0.341669\pi$
$409$	19.2997	0.954307	0.477154	+	0.878820i	$0.341669\pi$
$410$	7.40687	0.365799
$411$	3.00754	0.148351
$412$	8.90282	0.438611
$413$	15.3145	0.753579
$414$	−0.558539	−0.0274507
$415$	11.6208	0.570440
$416$	−2.91189	−0.142767
$417$	−3.42841	−0.167890
$418$	5.70606	0.279093
$419$	−23.3620	−1.14131	−0.570655	−	0.821190i	$-0.693311\pi$
$419$	−23.3620	−1.14131	−0.570655	+	0.821190i	$0.693311\pi$
$420$	−12.6274	−0.616154
$421$	−35.5525	−1.73272	−0.866362	−	0.499416i	$-0.833548\pi$
$421$	−35.5525	−1.73272	−0.866362	+	0.499416i	$0.833548\pi$
$422$	−17.7157	−0.862387
$423$	10.5942	0.515108
$424$	11.7647	0.571342
$425$	15.6974	0.761437
$426$	9.85250	0.477355
$427$	−61.0745	−2.95560
$428$	−3.69090	−0.178406
$429$	2.53941	0.122604
$430$	−6.13130	−0.295677
$431$	−5.64723	−0.272017	−0.136009	−	0.990708i	$-0.543428\pi$
$431$	−5.64723	−0.272017	−0.136009	+	0.990708i	$0.543428\pi$
$432$	4.88129	0.234851
$433$	−23.1291	−1.11152	−0.555758	−	0.831344i	$-0.687572\pi$
$433$	−23.1291	−1.11152	−0.555758	+	0.831344i	$0.687572\pi$
$434$	36.7146	1.76236
$435$	15.2501	0.731184
$436$	−9.86341	−0.472372
$437$	−1.69422	−0.0810454
$438$	4.29377	0.205165
$439$	−17.6728	−0.843476	−0.421738	−	0.906718i	$-0.638580\pi$
$439$	−17.6728	−0.843476	−0.421738	+	0.906718i	$0.638580\pi$
$440$	2.55985	0.122036
$441$	−30.3337	−1.44446
$442$	−15.3822	−0.731657
$443$	35.9296	1.70706	0.853532	−	0.521040i	$-0.174456\pi$
$443$	35.9296	1.70706	0.853532	+	0.521040i	$0.174456\pi$
$444$	−2.52079	−0.119631
$445$	−31.4112	−1.48903
$446$	1.27940	0.0605816
$447$	−5.78511	−0.273627
$448$	4.64973	0.219679
$449$	11.4461	0.540176	0.270088	−	0.962836i	$-0.412947\pi$
$449$	11.4461	0.540176	0.270088	+	0.962836i	$0.412947\pi$
$450$	6.16544	0.290642
$451$	2.37851	0.112000
$452$	18.7540	0.882115
$453$	11.3287	0.532269
$454$	10.9895	0.515765
$455$	38.2274	1.79213
$456$	6.05354	0.283483
$457$	−0.127962	−0.00598581	−0.00299290	−	0.999996i	$-0.500953\pi$
$457$	−0.127962	−0.00598581	−0.00299290	+	0.999996i	$0.500953\pi$
$458$	−17.2909	−0.807951
$459$	25.7857	1.20357
$460$	−0.760057	−0.0354379
$461$	12.3014	0.572935	0.286468	−	0.958090i	$-0.407519\pi$
$461$	12.3014	0.572935	0.286468	+	0.958090i	$0.407519\pi$
$462$	−4.05494	−0.188653
$463$	31.4322	1.46078	0.730390	−	0.683030i	$-0.239338\pi$
$463$	31.4322	1.46078	0.730390	+	0.683030i	$0.239338\pi$
$464$	−5.61545	−0.260691
$465$	21.4436	0.994425
$466$	−0.192576	−0.00892091
$467$	−15.2559	−0.705961	−0.352981	−	0.935631i	$-0.614832\pi$
$467$	−15.2559	−0.705961	−0.352981	+	0.935631i	$0.614832\pi$
$468$	−6.04163	−0.279274
$469$	8.88022	0.410051
$470$	14.4166	0.664986
$471$	−20.1085	−0.926549
$472$	−3.29364	−0.151602
$473$	−1.96890	−0.0905299
$474$	7.74955	0.355949
$475$	18.7016	0.858090
$476$	24.5624	1.12582
$477$	24.4095	1.11763
$478$	13.2705	0.606979
$479$	1.41886	0.0648292	0.0324146	−	0.999475i	$-0.489680\pi$
$479$	1.41886	0.0648292	0.0324146	+	0.999475i	$0.489680\pi$
$480$	2.71573	0.123956
$481$	7.63128	0.347956
$482$	19.9563	0.908985
$483$	1.20397	0.0547827
$484$	−10.1780	−0.462635
$485$	44.0559	2.00048
$486$	16.1148	0.730984
$487$	32.6778	1.48077	0.740386	−	0.672182i	$-0.234643\pi$
$487$	32.6778	1.48077	0.740386	+	0.672182i	$0.234643\pi$
$488$	13.1351	0.594597
$489$	−13.0246	−0.588993
$490$	−41.2779	−1.86475
$491$	−18.0748	−0.815705	−0.407852	−	0.913048i	$-0.633722\pi$
$491$	−18.0748	−0.815705	−0.407852	+	0.913048i	$0.633722\pi$
$492$	2.52335	0.113762
$493$	−29.6639	−1.33599
$494$	−18.3261	−0.824529
$495$	5.31120	0.238721
$496$	−7.89608	−0.354544
$497$	47.6276	2.13639
$498$	3.95893	0.177404
$499$	16.3572	0.732247	0.366124	−	0.930566i	$-0.380685\pi$
$499$	16.3572	0.732247	0.366124	+	0.930566i	$0.380685\pi$
$500$	−5.72707	−0.256122
$501$	21.0934	0.942382
$502$	−19.7822	−0.882923
$503$	−12.4240	−0.553959	−0.276979	−	0.960876i	$-0.589333\pi$
$503$	−12.4240	−0.553959	−0.276979	+	0.960876i	$0.589333\pi$
$504$	9.64731	0.429725
$505$	16.3381	0.727035
$506$	−0.244071	−0.0108503
$507$	4.34849	0.193123
$508$	−10.9278	−0.484842
$509$	19.0601	0.844826	0.422413	−	0.906404i	$-0.361183\pi$
$509$	19.0601	0.844826	0.422413	+	0.906404i	$0.361183\pi$
$510$	14.3460	0.635251
$511$	20.7564	0.918208
$512$	−1.00000	−0.0441942
$513$	30.7206	1.35635
$514$	26.9966	1.19077
$515$	25.1362	1.10763
$516$	−2.08879	−0.0919540
$517$	4.62948	0.203604
$518$	−12.1857	−0.535408
$519$	10.8469	0.476128
$520$	−8.22142	−0.360533
$521$	12.2998	0.538864	0.269432	−	0.963019i	$-0.413164\pi$
$521$	12.2998	0.538864	0.269432	+	0.963019i	$0.413164\pi$
$522$	−11.6510	−0.509951
$523$	13.6607	0.597339	0.298670	−	0.954357i	$-0.403457\pi$
$523$	13.6607	0.597339	0.298670	+	0.954357i	$0.403457\pi$
$524$	−2.18469	−0.0954386
$525$	−13.2901	−0.580027
$526$	13.2217	0.576492
$527$	−41.7114	−1.81698
$528$	0.872082	0.0379525
$529$	−22.9275	−0.996849
$530$	33.2163	1.44282
$531$	−6.83369	−0.296557
$532$	29.2632	1.26872
$533$	−7.63903	−0.330883
$534$	−10.7011	−0.463081
$535$	−10.4209	−0.450533
$536$	−1.90984	−0.0824924
$537$	−21.3073	−0.919480
$538$	14.5077	0.625471
$539$	−13.2553	−0.570945
$540$	13.7818	0.593075
$541$	5.03343	0.216404	0.108202	−	0.994129i	$-0.465491\pi$
$541$	5.03343	0.216404	0.108202	+	0.994129i	$0.465491\pi$
$542$	−8.17745	−0.351251
$543$	24.6623	1.05836
$544$	−5.28255	−0.226487
$545$	−27.8483	−1.19289
$546$	13.0232	0.557341
$547$	−24.6070	−1.05212	−0.526059	−	0.850448i	$-0.676331\pi$
$547$	−24.6070	−1.05212	−0.526059	+	0.850448i	$0.676331\pi$
$548$	−3.12678	−0.133569
$549$	27.2528	1.16312
$550$	2.69419	0.114881
$551$	−35.3410	−1.50558
$552$	−0.258934	−0.0110210
$553$	37.4618	1.59304
$554$	3.62576	0.154044
$555$	−7.11719	−0.302108
$556$	3.56433	0.151161
$557$	2.28890	0.0969839	0.0484919	−	0.998824i	$-0.484558\pi$
$557$	2.28890	0.0969839	0.0484919	+	0.998824i	$0.484558\pi$
$558$	−16.3829	−0.693543
$559$	6.32347	0.267454
$560$	13.1280	0.554760
$561$	4.60681	0.194500
$562$	−26.5399	−1.11952
$563$	−24.2770	−1.02315	−0.511576	−	0.859238i	$-0.670938\pi$
$563$	−24.2770	−1.02315	−0.511576	+	0.859238i	$0.670938\pi$
$564$	4.91139	0.206807
$565$	52.9500	2.22762
$566$	−1.97086	−0.0828414
$567$	7.11074	0.298623
$568$	−10.2431	−0.429791
$569$	−24.4619	−1.02550	−0.512748	−	0.858539i	$-0.671372\pi$
$569$	−24.4619	−1.02550	−0.512748	+	0.858539i	$0.671372\pi$
$570$	17.0915	0.715886
$571$	−27.7102	−1.15964	−0.579819	−	0.814746i	$-0.696877\pi$
$571$	−27.7102	−1.15964	−0.579819	+	0.814746i	$0.696877\pi$
$572$	−2.64008	−0.110387
$573$	−16.4781	−0.688382
$574$	12.1980	0.509137
$575$	−0.799945	−0.0333600
$576$	−2.07481	−0.0864505
$577$	−11.8503	−0.493334	−0.246667	−	0.969100i	$-0.579335\pi$
$577$	−11.8503	−0.493334	−0.246667	+	0.969100i	$0.579335\pi$
$578$	−10.9053	−0.453600
$579$	7.40232	0.307630
$580$	−15.8546	−0.658328
$581$	19.1377	0.793966
$582$	15.0088	0.622137
$583$	10.6665	0.441761
$584$	−4.46400	−0.184722
$585$	−17.0579	−0.705258
$586$	6.95953	0.287496
$587$	−6.98377	−0.288251	−0.144126	−	0.989559i	$-0.546037\pi$
$587$	−6.98377	−0.288251	−0.144126	+	0.989559i	$0.546037\pi$
$588$	−14.0625	−0.579926
$589$	−49.6942	−2.04762
$590$	−9.29926	−0.382844
$591$	2.51661	0.103519
$592$	2.62073	0.107711
$593$	3.19960	0.131392	0.0656959	−	0.997840i	$-0.479073\pi$
$593$	3.19960	0.131392	0.0656959	+	0.997840i	$0.479073\pi$
$594$	4.42565	0.181587
$595$	69.3494	2.84305
$596$	6.01447	0.246362
$597$	−19.5691	−0.800911
$598$	0.783880	0.0320552
$599$	−5.39216	−0.220318	−0.110159	−	0.993914i	$-0.535136\pi$
$599$	−5.39216	−0.220318	−0.110159	+	0.993914i	$0.535136\pi$
$600$	2.85825	0.116688
$601$	46.0282	1.87753	0.938764	−	0.344560i	$-0.111972\pi$
$601$	46.0282	1.87753	0.938764	+	0.344560i	$0.111972\pi$
$602$	−10.0974	−0.411538
$603$	−3.96255	−0.161368
$604$	−11.7778	−0.479233
$605$	−28.7365	−1.16830
$606$	5.56601	0.226104
$607$	−11.6653	−0.473482	−0.236741	−	0.971573i	$-0.576079\pi$
$607$	−11.6653	−0.473482	−0.236741	+	0.971573i	$0.576079\pi$
$608$	−6.29353	−0.255236
$609$	25.1147	1.01770
$610$	37.0855	1.50155
$611$	−14.8684	−0.601512
$612$	−10.9603	−0.443043
$613$	1.00000	0.0403896
$613$	1.00000	0.0403896
$614$	−16.9411	−0.683689
$615$	7.12442	0.287284
$616$	4.21570	0.169855
$617$	4.53952	0.182754	0.0913771	−	0.995816i	$-0.470873\pi$
$617$	4.53952	0.182754	0.0913771	+	0.995816i	$0.470873\pi$
$618$	8.56333	0.344468
$619$	−3.47977	−0.139864	−0.0699320	−	0.997552i	$-0.522278\pi$
$619$	−3.47977	−0.139864	−0.0699320	+	0.997552i	$0.522278\pi$
$620$	−22.2938	−0.895339
$621$	−1.31404	−0.0527307
$622$	13.7875	0.552826
$623$	−51.7298	−2.07251
$624$	−2.80085	−0.112124
$625$	−31.0276	−1.24111
$626$	24.1874	0.966723
$627$	5.48847	0.219189
$628$	20.9057	0.834227
$629$	13.8441	0.552001
$630$	27.2382	1.08519
$631$	−46.7673	−1.86178	−0.930889	−	0.365302i	$-0.880966\pi$
$631$	−46.7673	−1.86178	−0.930889	+	0.365302i	$0.880966\pi$
$632$	−8.05678	−0.320481
$633$	−17.0401	−0.677285
$634$	10.8318	0.430187
$635$	−30.8535	−1.22438
$636$	11.3160	0.448710
$637$	42.5717	1.68675
$638$	−5.09128	−0.201566
$639$	−21.2525	−0.840736
$640$	−2.82340	−0.111605
$641$	0.555692	0.0219485	0.0109743	−	0.999940i	$-0.496507\pi$
$641$	0.555692	0.0219485	0.0109743	+	0.999940i	$0.496507\pi$
$642$	−3.55015	−0.140113
$643$	2.74214	0.108139	0.0540697	−	0.998537i	$-0.482781\pi$
$643$	2.74214	0.108139	0.0540697	+	0.998537i	$0.482781\pi$
$644$	−1.25170	−0.0493241
$645$	−5.89749	−0.232213
$646$	−33.2459	−1.30804
$647$	11.8329	0.465200	0.232600	−	0.972572i	$-0.425277\pi$
$647$	11.8329	0.465200	0.232600	+	0.972572i	$0.425277\pi$
$648$	−1.52928	−0.0600758
$649$	−2.98620	−0.117219
$650$	−8.65288	−0.339394
$651$	35.3146	1.38409
$652$	13.5410	0.530306
$653$	29.5168	1.15508	0.577542	−	0.816361i	$-0.304012\pi$
$653$	29.5168	1.15508	0.577542	+	0.816361i	$0.304012\pi$
$654$	−9.48729	−0.370982
$655$	−6.16825	−0.241013
$656$	−2.62339	−0.102426
$657$	−9.26196	−0.361344
$658$	23.7420	0.925559
$659$	1.52311	0.0593319	0.0296659	−	0.999560i	$-0.490556\pi$
$659$	1.52311	0.0593319	0.0296659	+	0.999560i	$0.490556\pi$
$660$	2.46223	0.0958423
$661$	−16.5354	−0.643152	−0.321576	−	0.946884i	$-0.604213\pi$
$661$	−16.5354	−0.643152	−0.321576	+	0.946884i	$0.604213\pi$
$662$	−24.6099	−0.956492
$663$	−14.7956	−0.574615
$664$	−4.11588	−0.159727
$665$	82.6216	3.20393
$666$	5.43752	0.210700
$667$	1.51168	0.0585324
$668$	−21.9296	−0.848482
$669$	1.23062	0.0475784
$670$	−5.39223	−0.208320
$671$	11.9090	0.459742
$672$	4.47242	0.172527
$673$	33.7964	1.30275	0.651377	−	0.758754i	$-0.274191\pi$
$673$	33.7964	1.30275	0.651377	+	0.758754i	$0.274191\pi$
$674$	6.86557	0.264452
$675$	14.5051	0.558301
$676$	−4.52089	−0.173880
$677$	−5.80086	−0.222945	−0.111473	−	0.993768i	$-0.535557\pi$
$677$	−5.80086	−0.222945	−0.111473	+	0.993768i	$0.535557\pi$
$678$	18.0389	0.692779
$679$	72.5537	2.78436
$680$	−14.9147	−0.571953
$681$	10.5705	0.405061
$682$	−7.15902	−0.274133
$683$	−28.1824	−1.07837	−0.539185	−	0.842187i	$-0.681268\pi$
$683$	−28.1824	−1.07837	−0.539185	+	0.842187i	$0.681268\pi$
$684$	−13.0579	−0.499281
$685$	−8.82813	−0.337306
$686$	−35.4307	−1.35275
$687$	−16.6316	−0.634533
$688$	2.17160	0.0827916
$689$	−34.2574	−1.30510
$690$	−0.731074	−0.0278315
$691$	28.7440	1.09347	0.546737	−	0.837304i	$-0.315870\pi$
$691$	28.7440	1.09347	0.546737	+	0.837304i	$0.315870\pi$
$692$	−11.2770	−0.428686
$693$	8.74679	0.332263
$694$	−7.91530	−0.300461
$695$	10.0635	0.381731
$696$	−5.40132	−0.204736
$697$	−13.8582	−0.524916
$698$	−29.6072	−1.12065
$699$	−0.185233	−0.00700614
$700$	13.8170	0.522232
$701$	46.1489	1.74302	0.871511	−	0.490376i	$-0.163141\pi$
$701$	46.1489	1.74302	0.871511	+	0.490376i	$0.163141\pi$
$702$	−14.2138	−0.536465
$703$	16.4936	0.622069
$704$	−0.906655	−0.0341709
$705$	13.8668	0.522254
$706$	30.9921	1.16640
$707$	26.9064	1.01192
$708$	−3.16805	−0.119062
$709$	−42.8837	−1.61053	−0.805266	−	0.592913i	$-0.797978\pi$
$709$	−42.8837	−1.61053	−0.805266	+	0.592913i	$0.797978\pi$
$710$	−28.9203	−1.08536
$711$	−16.7163	−0.626910
$712$	11.1253	0.416940
$713$	2.12562	0.0796052
$714$	23.6258	0.884172
$715$	−7.45400	−0.278764
$716$	22.1521	0.827862
$717$	12.7645	0.476698
$718$	4.71006	0.175778
$719$	11.7460	0.438051	0.219025	−	0.975719i	$-0.429712\pi$
$719$	11.7460	0.438051	0.219025	+	0.975719i	$0.429712\pi$
$720$	−5.85802	−0.218315
$721$	41.3957	1.54166
$722$	−20.6085	−0.766970
$723$	19.1953	0.713882
$724$	−25.6400	−0.952902
$725$	−16.6867	−0.619728
$726$	−9.78986	−0.363336
$727$	−31.2499	−1.15900	−0.579498	−	0.814974i	$-0.696751\pi$
$727$	−31.2499	−1.15900	−0.579498	+	0.814974i	$0.696751\pi$
$728$	−13.5395	−0.501807
$729$	10.9125	0.404166
$730$	−12.6036	−0.466482
$731$	11.4716	0.424292
$732$	12.6342	0.466973
$733$	20.8446	0.769911	0.384956	−	0.922935i	$-0.374217\pi$
$733$	20.8446	0.769911	0.384956	+	0.922935i	$0.374217\pi$
$734$	28.5256	1.05290
$735$	−39.7039	−1.46450
$736$	0.269200	0.00992283
$737$	−1.73157	−0.0637830
$738$	−5.44304	−0.200361
$739$	−16.0540	−0.590557	−0.295279	−	0.955411i	$-0.595412\pi$
$739$	−16.0540	−0.590557	−0.295279	+	0.955411i	$0.595412\pi$
$740$	7.39935	0.272006
$741$	−17.6273	−0.647553
$742$	54.7025	2.00819
$743$	−7.07828	−0.259677	−0.129838	−	0.991535i	$-0.541446\pi$
$743$	−7.07828	−0.259677	−0.129838	+	0.991535i	$0.541446\pi$
$744$	−7.59498	−0.278445
$745$	16.9812	0.622144
$746$	7.13206	0.261123
$747$	−8.53967	−0.312450
$748$	−4.78945	−0.175120
$749$	−17.1617	−0.627073
$750$	−5.50868	−0.201149
$751$	36.8762	1.34563	0.672816	−	0.739810i	$-0.265084\pi$
$751$	36.8762	1.34563	0.672816	+	0.739810i	$0.265084\pi$
$752$	−5.10610	−0.186200
$753$	−19.0279	−0.693414
$754$	16.3516	0.595490
$755$	−33.2535	−1.21022
$756$	22.6967	0.825470
$757$	8.97415	0.326171	0.163086	−	0.986612i	$-0.447855\pi$
$757$	8.97415	0.326171	0.163086	+	0.986612i	$0.447855\pi$
$758$	−1.05656	−0.0383760
$759$	−0.234764	−0.00852140
$760$	−17.7691	−0.644554
$761$	−6.55464	−0.237606	−0.118803	−	0.992918i	$-0.537906\pi$
$761$	−6.55464	−0.237606	−0.118803	+	0.992918i	$0.537906\pi$
$762$	−10.5111	−0.380776
$763$	−45.8622	−1.66032
$764$	17.1314	0.619791
$765$	−30.9452	−1.11883
$766$	32.0352	1.15748
$767$	9.59073	0.346301
$768$	−0.961867	−0.0347084
$769$	51.9332	1.87276	0.936380	−	0.350988i	$-0.114154\pi$
$769$	51.9332	1.87276	0.936380	+	0.350988i	$0.114154\pi$
$770$	11.9026	0.428940
$771$	25.9671	0.935183
$772$	−7.69579	−0.276978
$773$	36.3577	1.30770	0.653848	−	0.756626i	$-0.273154\pi$
$773$	36.3577	1.30770	0.653848	+	0.756626i	$0.273154\pi$
$774$	4.50567	0.161953
$775$	−23.4637	−0.842842
$776$	−15.6039	−0.560146
$777$	−11.7210	−0.420488
$778$	33.7275	1.20919
$779$	−16.5104	−0.591546
$780$	−7.90792	−0.283149
$781$	−9.28696	−0.332314
$782$	1.42206	0.0508527
$783$	−27.4107	−0.979578
$784$	14.6200	0.522141
$785$	59.0250	2.10669
$786$	−2.10138	−0.0749538
$787$	37.2863	1.32911	0.664557	−	0.747238i	$-0.268620\pi$
$787$	37.2863	1.32911	0.664557	+	0.747238i	$0.268620\pi$
$788$	−2.61638	−0.0932046
$789$	12.7175	0.452755
$790$	−22.7475	−0.809319
$791$	87.2011	3.10051
$792$	−1.88114	−0.0668434
$793$	−38.2479	−1.35822
$794$	24.4338	0.867124
$795$	31.9497	1.13314
$796$	20.3449	0.721108
$797$	−8.76334	−0.310414	−0.155207	−	0.987882i	$-0.549604\pi$
$797$	−8.76334	−0.310414	−0.155207	+	0.987882i	$0.549604\pi$
$798$	28.1473	0.996404
$799$	−26.9732	−0.954244
$800$	−2.97157	−0.105061
$801$	23.0830	0.815597
$802$	19.3322	0.682643
$803$	−4.04731	−0.142827
$804$	−1.83701	−0.0647863
$805$	−3.53406	−0.124559
$806$	22.9925	0.809877
$807$	13.9545	0.491221
$808$	−5.78667	−0.203574
$809$	−30.7891	−1.08249	−0.541243	−	0.840866i	$-0.682046\pi$
$809$	−30.7891	−1.08249	−0.541243	+	0.840866i	$0.682046\pi$
$810$	−4.31777	−0.151711
$811$	−38.2392	−1.34276	−0.671380	−	0.741113i	$-0.734298\pi$
$811$	−38.2392	−1.34276	−0.671380	+	0.741113i	$0.734298\pi$
$812$	−26.1103	−0.916293
$813$	−7.86561	−0.275859
$814$	2.37610	0.0832822
$815$	38.2315	1.33919
$816$	−5.08111	−0.177874
$817$	13.6671	0.478150
$818$	−19.2997	−0.674797
$819$	−28.0919	−0.981611
$820$	−7.40687	−0.258659
$821$	36.4363	1.27164	0.635818	−	0.771839i	$-0.280663\pi$
$821$	36.4363	1.27164	0.635818	+	0.771839i	$0.280663\pi$
$822$	−3.00754	−0.104900
$823$	−52.8491	−1.84220	−0.921101	−	0.389323i	$-0.872709\pi$
$823$	−52.8491	−1.84220	−0.921101	+	0.389323i	$0.872709\pi$
$824$	−8.90282	−0.310145
$825$	2.59145	0.0902227
$826$	−15.3145	−0.532861
$827$	26.9295	0.936431	0.468216	−	0.883614i	$-0.344897\pi$
$827$	26.9295	0.936431	0.468216	+	0.883614i	$0.344897\pi$
$828$	0.558539	0.0194106
$829$	3.80522	0.132161	0.0660804	−	0.997814i	$-0.478951\pi$
$829$	3.80522	0.132161	0.0660804	+	0.997814i	$0.478951\pi$
$830$	−11.6208	−0.403362
$831$	3.48750	0.120980
$832$	2.91189	0.100952
$833$	77.2306	2.67588
$834$	3.42841	0.118716
$835$	−61.9160	−2.14269
$836$	−5.70606	−0.197348
$837$	−38.5431	−1.33224
$838$	23.3620	0.807028
$839$	−25.2290	−0.871002	−0.435501	−	0.900188i	$-0.643429\pi$
$839$	−25.2290	−0.871002	−0.435501	+	0.900188i	$0.643429\pi$
$840$	12.6274	0.435687
$841$	2.53331	0.0873555
$842$	35.5525	1.22522
$843$	−25.5279	−0.879226
$844$	17.7157	0.609800
$845$	−12.7643	−0.439104
$846$	−10.5942	−0.364236
$847$	−47.3248	−1.62610
$848$	−11.7647	−0.404000
$849$	−1.89570	−0.0650604
$850$	−15.6974	−0.538418
$851$	−0.705499	−0.0241842
$852$	−9.85250	−0.337541
$853$	−9.33371	−0.319580	−0.159790	−	0.987151i	$-0.551082\pi$
$853$	−9.33371	−0.319580	−0.159790	+	0.987151i	$0.551082\pi$
$854$	61.0745	2.08993
$855$	−36.8676	−1.26085
$856$	3.69090	0.126152
$857$	−10.1861	−0.347951	−0.173976	−	0.984750i	$-0.555661\pi$
$857$	−10.1861	−0.347951	−0.173976	+	0.984750i	$0.555661\pi$
$858$	−2.53941	−0.0866940
$859$	37.2579	1.27122	0.635612	−	0.772008i	$-0.280748\pi$
$859$	37.2579	1.27122	0.635612	+	0.772008i	$0.280748\pi$
$860$	6.13130	0.209075
$861$	11.7329	0.399856
$862$	5.64723	0.192345
$863$	−14.6118	−0.497391	−0.248696	−	0.968582i	$-0.580002\pi$
$863$	−14.6118	−0.497391	−0.248696	+	0.968582i	$0.580002\pi$
$864$	−4.88129	−0.166065
$865$	−31.8393	−1.08257
$866$	23.1291	0.785960
$867$	−10.4894	−0.356240
$868$	−36.7146	−1.24618
$869$	−7.30472	−0.247796
$870$	−15.2501	−0.517025
$871$	5.56124	0.188435
$872$	9.86341	0.334017
$873$	−32.3751	−1.09573
$874$	1.69422	0.0573077
$875$	−26.6293	−0.900235
$876$	−4.29377	−0.145073
$877$	21.9366	0.740747	0.370373	−	0.928883i	$-0.379230\pi$
$877$	21.9366	0.740747	0.370373	+	0.928883i	$0.379230\pi$
$878$	17.6728	0.596427
$879$	6.69414	0.225788
$880$	−2.55985	−0.0862924
$881$	−22.7508	−0.766493	−0.383247	−	0.923646i	$-0.625194\pi$
$881$	−22.7508	−0.766493	−0.383247	+	0.923646i	$0.625194\pi$
$882$	30.3337	1.02139
$883$	48.8566	1.64415	0.822077	−	0.569376i	$-0.192815\pi$
$883$	48.8566	1.64415	0.822077	+	0.569376i	$0.192815\pi$
$884$	15.3822	0.517359
$885$	−8.94465	−0.300671
$886$	−35.9296	−1.20708
$887$	−4.82569	−0.162031	−0.0810153	−	0.996713i	$-0.525816\pi$
$887$	−4.82569	−0.162031	−0.0810153	+	0.996713i	$0.525816\pi$
$888$	2.52079	0.0845922
$889$	−50.8112	−1.70415
$890$	31.4112	1.05291
$891$	−1.38653	−0.0464505
$892$	−1.27940	−0.0428376
$893$	−32.1354	−1.07537
$894$	5.78511	0.193483
$895$	62.5441	2.09062
$896$	−4.64973	−0.155336
$897$	0.753989	0.0251749
$898$	−11.4461	−0.381962
$899$	44.3401	1.47882
$900$	−6.16544	−0.205515
$901$	−62.1474	−2.07043
$902$	−2.37851	−0.0791958
$903$	−9.71232	−0.323206
$904$	−18.7540	−0.623749
$905$	−72.3918	−2.40639
$906$	−11.3287	−0.376371
$907$	−32.6051	−1.08264	−0.541318	−	0.840818i	$-0.682074\pi$
$907$	−32.6051	−1.08264	−0.541318	+	0.840818i	$0.682074\pi$
$908$	−10.9895	−0.364701
$909$	−12.0063	−0.398222
$910$	−38.2274	−1.26723
$911$	−15.6403	−0.518185	−0.259092	−	0.965853i	$-0.583423\pi$
$911$	−15.6403	−0.518185	−0.259092	+	0.965853i	$0.583423\pi$
$912$	−6.05354	−0.200453
$913$	−3.73168	−0.123501
$914$	0.127962	0.00423261
$915$	35.6713	1.17926
$916$	17.2909	0.571308
$917$	−10.1582	−0.335454
$918$	−25.7857	−0.851054
$919$	16.6103	0.547924	0.273962	−	0.961740i	$-0.411666\pi$
$919$	16.6103	0.547924	0.273962	+	0.961740i	$0.411666\pi$
$920$	0.760057	0.0250583
$921$	−16.2951	−0.536942
$922$	−12.3014	−0.405126
$923$	29.8268	0.981761
$924$	4.05494	0.133398
$925$	7.78767	0.256057
$926$	−31.4322	−1.03293
$927$	−18.4717	−0.606690
$928$	5.61545	0.184336
$929$	35.2642	1.15698	0.578490	−	0.815689i	$-0.303642\pi$
$929$	35.2642	1.15698	0.578490	+	0.815689i	$0.303642\pi$
$930$	−21.4436	−0.703164
$931$	92.0112	3.01554
$932$	0.192576	0.00630804
$933$	13.2617	0.434168
$934$	15.2559	0.499190
$935$	−13.5225	−0.442233
$936$	6.04163	0.197477
$937$	56.7441	1.85375	0.926875	−	0.375371i	$-0.122485\pi$
$937$	56.7441	1.85375	0.926875	+	0.375371i	$0.122485\pi$
$938$	−8.88022	−0.289950
$939$	23.2651	0.759226
$940$	−14.4166	−0.470216
$941$	43.0657	1.40390	0.701951	−	0.712226i	$-0.252313\pi$
$941$	43.0657	1.40390	0.701951	+	0.712226i	$0.252313\pi$
$942$	20.1085	0.655169
$943$	0.706216	0.0229975
$944$	3.29364	0.107199
$945$	64.0817	2.08458
$946$	1.96890	0.0640143
$947$	34.8969	1.13400	0.566998	−	0.823719i	$-0.308105\pi$
$947$	34.8969	1.13400	0.566998	+	0.823719i	$0.308105\pi$
$948$	−7.74955	−0.251694
$949$	12.9987	0.421955
$950$	−18.7016	−0.606762
$951$	10.4188	0.337852
$952$	−24.5624	−0.796072
$953$	−2.54371	−0.0823987	−0.0411994	−	0.999151i	$-0.513118\pi$
$953$	−2.54371	−0.0823987	−0.0411994	+	0.999151i	$0.513118\pi$
$954$	−24.4095	−0.790285
$955$	48.3686	1.56517
$956$	−13.2705	−0.429199
$957$	−4.89713	−0.158302
$958$	−1.41886	−0.0458412
$959$	−14.5387	−0.469478
$960$	−2.71573	−0.0876499
$961$	31.3481	1.01123
$962$	−7.63128	−0.246042
$963$	7.65791	0.246773
$964$	−19.9563	−0.642750
$965$	−21.7283	−0.699458
$966$	−1.20397	−0.0387372
$967$	−40.7115	−1.30919	−0.654597	−	0.755978i	$-0.727162\pi$
$967$	−40.7115	−1.30919	−0.654597	+	0.755978i	$0.727162\pi$
$968$	10.1780	0.327133
$969$	−31.9781	−1.02728
$970$	−44.0559	−1.41455
$971$	23.7310	0.761563	0.380781	−	0.924665i	$-0.375655\pi$
$971$	23.7310	0.761563	0.380781	+	0.924665i	$0.375655\pi$
$972$	−16.1148	−0.516884
$973$	16.5732	0.531311
$974$	−32.6778	−1.04706
$975$	−8.32292	−0.266547
$976$	−13.1351	−0.420444
$977$	−13.9330	−0.445758	−0.222879	−	0.974846i	$-0.571545\pi$
$977$	−13.9330	−0.445758	−0.222879	+	0.974846i	$0.571545\pi$
$978$	13.0246	0.416481
$979$	10.0868	0.322377
$980$	41.2779	1.31858
$981$	20.4647	0.653388
$982$	18.0748	0.576790
$983$	30.2318	0.964244	0.482122	−	0.876104i	$-0.339866\pi$
$983$	30.2318	0.964244	0.482122	+	0.876104i	$0.339866\pi$
$984$	−2.52335	−0.0804415
$985$	−7.38707	−0.235372
$986$	29.6639	0.944691
$987$	22.8366	0.726898
$988$	18.3261	0.583030
$989$	−0.584595	−0.0185890
$990$	−5.31120	−0.168801
$991$	−25.7268	−0.817238	−0.408619	−	0.912705i	$-0.633990\pi$
$991$	−25.7268	−0.817238	−0.408619	+	0.912705i	$0.633990\pi$
$992$	7.89608	0.250701
$993$	−23.6715	−0.751192
$994$	−47.6276	−1.51066
$995$	57.4419	1.82103
$996$	−3.95893	−0.125443
$997$	−28.9694	−0.917469	−0.458735	−	0.888573i	$-0.651697\pi$
$997$	−28.9694	−0.917469	−0.458735	+	0.888573i	$0.651697\pi$
$998$	−16.3572	−0.517777
$999$	12.7925	0.404738

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1226.2.a.e.1.6	✓	17
4.3	odd	2		9808.2.a.f.1.12		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1226.2.a.e.1.6	✓	17	1.1	even	1	trivial
9808.2.a.f.1.12		17	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1226 = 2 \cdot 613 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1226.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.961867 q^{3} +1.00000 q^{4} +2.82340 q^{5} +0.961867 q^{6} +4.64973 q^{7} -1.00000 q^{8} -2.07481 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.961867 q^{3} +1.00000 q^{4} +2.82340 q^{5} +0.961867 q^{6} +4.64973 q^{7} -1.00000 q^{8} -2.07481 q^{9} -2.82340 q^{10} -0.906655 q^{11} -0.961867 q^{12} +2.91189 q^{13} -4.64973 q^{14} -2.71573 q^{15} +1.00000 q^{16} +5.28255 q^{17} +2.07481 q^{18} +6.29353 q^{19} +2.82340 q^{20} -4.47242 q^{21} +0.906655 q^{22} -0.269200 q^{23} +0.961867 q^{24} +2.97157 q^{25} -2.91189 q^{26} +4.88129 q^{27} +4.64973 q^{28} -5.61545 q^{29} +2.71573 q^{30} -7.89608 q^{31} -1.00000 q^{32} +0.872082 q^{33} -5.28255 q^{34} +13.1280 q^{35} -2.07481 q^{36} +2.62073 q^{37} -6.29353 q^{38} -2.80085 q^{39} -2.82340 q^{40} -2.62339 q^{41} +4.47242 q^{42} +2.17160 q^{43} -0.906655 q^{44} -5.85802 q^{45} +0.269200 q^{46} -5.10610 q^{47} -0.961867 q^{48} +14.6200 q^{49} -2.97157 q^{50} -5.08111 q^{51} +2.91189 q^{52} -11.7647 q^{53} -4.88129 q^{54} -2.55985 q^{55} -4.64973 q^{56} -6.05354 q^{57} +5.61545 q^{58} +3.29364 q^{59} -2.71573 q^{60} -13.1351 q^{61} +7.89608 q^{62} -9.64731 q^{63} +1.00000 q^{64} +8.22142 q^{65} -0.872082 q^{66} +1.90984 q^{67} +5.28255 q^{68} +0.258934 q^{69} -13.1280 q^{70} +10.2431 q^{71} +2.07481 q^{72} +4.46400 q^{73} -2.62073 q^{74} -2.85825 q^{75} +6.29353 q^{76} -4.21570 q^{77} +2.80085 q^{78} +8.05678 q^{79} +2.82340 q^{80} +1.52928 q^{81} +2.62339 q^{82} +4.11588 q^{83} -4.47242 q^{84} +14.9147 q^{85} -2.17160 q^{86} +5.40132 q^{87} +0.906655 q^{88} -11.1253 q^{89} +5.85802 q^{90} +13.5395 q^{91} -0.269200 q^{92} +7.59498 q^{93} +5.10610 q^{94} +17.7691 q^{95} +0.961867 q^{96} +15.6039 q^{97} -14.6200 q^{98} +1.88114 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 4 q^{3} + 17 q^{4} - 5 q^{5} - 4 q^{6} + 7 q^{7} - 17 q^{8} + 21 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 4 * q^3 + 17 * q^4 - 5 * q^5 - 4 * q^6 + 7 * q^7 - 17 * q^8 + 21 * q^9	\( 17 q - 17 q^{2} + 4 q^{3} + 17 q^{4} - 5 q^{5} - 4 q^{6} + 7 q^{7} - 17 q^{8} + 21 q^{9} + 5 q^{10} + 8 q^{11} + 4 q^{12} + 9 q^{13} - 7 q^{14} - 4 q^{15} + 17 q^{16} - q^{17} - 21 q^{18} + 32 q^{19} - 5 q^{20} + 6 q^{21} - 8 q^{22} - 5 q^{23} - 4 q^{24} + 30 q^{25} - 9 q^{26} + 16 q^{27} + 7 q^{28} + 3 q^{29} + 4 q^{30} + 27 q^{31} - 17 q^{32} - 14 q^{33} + q^{34} + 25 q^{35} + 21 q^{36} + 7 q^{37} - 32 q^{38} + 27 q^{39} + 5 q^{40} - 2 q^{41} - 6 q^{42} + 36 q^{43} + 8 q^{44} - q^{45} + 5 q^{46} - 3 q^{47} + 4 q^{48} + 52 q^{49} - 30 q^{50} + 40 q^{51} + 9 q^{52} - 20 q^{53} - 16 q^{54} + 48 q^{55} - 7 q^{56} + 12 q^{57} - 3 q^{58} + 34 q^{59} - 4 q^{60} + 49 q^{61} - 27 q^{62} + 27 q^{63} + 17 q^{64} - 6 q^{65} + 14 q^{66} + 36 q^{67} - q^{68} + 18 q^{69} - 25 q^{70} - q^{71} - 21 q^{72} + 24 q^{73} - 7 q^{74} + 35 q^{75} + 32 q^{76} - 6 q^{77} - 27 q^{78} + 43 q^{79} - 5 q^{80} + 37 q^{81} + 2 q^{82} + 10 q^{83} + 6 q^{84} + 16 q^{85} - 36 q^{86} + 28 q^{87} - 8 q^{88} - 12 q^{89} + q^{90} + 42 q^{91} - 5 q^{92} + 3 q^{93} + 3 q^{94} - 10 q^{95} - 4 q^{96} + 26 q^{97} - 52 q^{98} + 34 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 4 * q^3 + 17 * q^4 - 5 * q^5 - 4 * q^6 + 7 * q^7 - 17 * q^8 + 21 * q^9 + 5 * q^10 + 8 * q^11 + 4 * q^12 + 9 * q^13 - 7 * q^14 - 4 * q^15 + 17 * q^16 - q^17 - 21 * q^18 + 32 * q^19 - 5 * q^20 + 6 * q^21 - 8 * q^22 - 5 * q^23 - 4 * q^24 + 30 * q^25 - 9 * q^26 + 16 * q^27 + 7 * q^28 + 3 * q^29 + 4 * q^30 + 27 * q^31 - 17 * q^32 - 14 * q^33 + q^34 + 25 * q^35 + 21 * q^36 + 7 * q^37 - 32 * q^38 + 27 * q^39 + 5 * q^40 - 2 * q^41 - 6 * q^42 + 36 * q^43 + 8 * q^44 - q^45 + 5 * q^46 - 3 * q^47 + 4 * q^48 + 52 * q^49 - 30 * q^50 + 40 * q^51 + 9 * q^52 - 20 * q^53 - 16 * q^54 + 48 * q^55 - 7 * q^56 + 12 * q^57 - 3 * q^58 + 34 * q^59 - 4 * q^60 + 49 * q^61 - 27 * q^62 + 27 * q^63 + 17 * q^64 - 6 * q^65 + 14 * q^66 + 36 * q^67 - q^68 + 18 * q^69 - 25 * q^70 - q^71 - 21 * q^72 + 24 * q^73 - 7 * q^74 + 35 * q^75 + 32 * q^76 - 6 * q^77 - 27 * q^78 + 43 * q^79 - 5 * q^80 + 37 * q^81 + 2 * q^82 + 10 * q^83 + 6 * q^84 + 16 * q^85 - 36 * q^86 + 28 * q^87 - 8 * q^88 - 12 * q^89 + q^90 + 42 * q^91 - 5 * q^92 + 3 * q^93 + 3 * q^94 - 10 * q^95 - 4 * q^96 + 26 * q^97 - 52 * q^98 + 34 * q^99

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