LMFDB - Embedded newform 5577.2.a.y.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5577,2,Mod(1,5577)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5577, 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("5577.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5577 = 3 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5577.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:	$44.5325692073$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 7x^{5} + 21x^{4} + 13x^{3} - 33x^{2} - 7x + 7 $ x^7 - 3x^6 - 7x^5 + 21x^4 + 13x^3 - 33x^2 - 7x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 429)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.409068$ of defining polynomial
Character	$\chi$	$=$	5577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.409068 q^{2} +1.00000 q^{3} -1.83266 q^{4} +4.13953 q^{5} +0.409068 q^{6} +5.18273 q^{7} -1.56782 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.409068 q^{2} +1.00000 q^{3} -1.83266 q^{4} +4.13953 q^{5} +0.409068 q^{6} +5.18273 q^{7} -1.56782 q^{8} +1.00000 q^{9} +1.69335 q^{10} +1.00000 q^{11} -1.83266 q^{12} +2.12009 q^{14} +4.13953 q^{15} +3.02398 q^{16} -0.488730 q^{17} +0.409068 q^{18} -0.446180 q^{19} -7.58636 q^{20} +5.18273 q^{21} +0.409068 q^{22} +5.50882 q^{23} -1.56782 q^{24} +12.1357 q^{25} +1.00000 q^{27} -9.49821 q^{28} -6.58571 q^{29} +1.69335 q^{30} +1.52580 q^{31} +4.37265 q^{32} +1.00000 q^{33} -0.199924 q^{34} +21.4541 q^{35} -1.83266 q^{36} -7.87139 q^{37} -0.182518 q^{38} -6.49004 q^{40} -8.78563 q^{41} +2.12009 q^{42} -4.57514 q^{43} -1.83266 q^{44} +4.13953 q^{45} +2.25348 q^{46} +5.42082 q^{47} +3.02398 q^{48} +19.8607 q^{49} +4.96433 q^{50} -0.488730 q^{51} +8.66677 q^{53} +0.409068 q^{54} +4.13953 q^{55} -8.12559 q^{56} -0.446180 q^{57} -2.69400 q^{58} +5.60493 q^{59} -7.58636 q^{60} -0.855775 q^{61} +0.624155 q^{62} +5.18273 q^{63} -4.25925 q^{64} +0.409068 q^{66} -3.87464 q^{67} +0.895677 q^{68} +5.50882 q^{69} +8.77618 q^{70} -8.49886 q^{71} -1.56782 q^{72} +5.95291 q^{73} -3.21993 q^{74} +12.1357 q^{75} +0.817698 q^{76} +5.18273 q^{77} -8.91459 q^{79} +12.5179 q^{80} +1.00000 q^{81} -3.59392 q^{82} +0.457495 q^{83} -9.49821 q^{84} -2.02311 q^{85} -1.87154 q^{86} -6.58571 q^{87} -1.56782 q^{88} -4.68461 q^{89} +1.69335 q^{90} -10.0958 q^{92} +1.52580 q^{93} +2.21748 q^{94} -1.84697 q^{95} +4.37265 q^{96} -2.06057 q^{97} +8.12439 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} + 7 q^{3} + 9 q^{4} + 6 q^{5} + 3 q^{6} + 6 q^{7} + 15 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 3 * q^2 + 7 * q^3 + 9 * q^4 + 6 * q^5 + 3 * q^6 + 6 * q^7 + 15 * q^8 + 7 * q^9	$ 7 q + 3 q^{2} + 7 q^{3} + 9 q^{4} + 6 q^{5} + 3 q^{6} + 6 q^{7} + 15 q^{8} + 7 q^{9} + 7 q^{11} + 9 q^{12} + 8 q^{14} + 6 q^{15} + 17 q^{16} - 2 q^{17} + 3 q^{18} + 8 q^{19} - 2 q^{20} + 6 q^{21} + 3 q^{22} + 4 q^{23} + 15 q^{24} + 13 q^{25} + 7 q^{27} + 12 q^{28} - 12 q^{29} - 10 q^{31} + 33 q^{32} + 7 q^{33} + 28 q^{34} - 4 q^{35} + 9 q^{36} + 6 q^{37} + 16 q^{38} - 10 q^{40} + 2 q^{41} + 8 q^{42} - 16 q^{43} + 9 q^{44} + 6 q^{45} - 26 q^{46} + 18 q^{47} + 17 q^{48} + 23 q^{49} + 39 q^{50} - 2 q^{51} + 10 q^{53} + 3 q^{54} + 6 q^{55} + 16 q^{56} + 8 q^{57} + 10 q^{58} + 2 q^{59} - 2 q^{60} - 10 q^{61} - 36 q^{62} + 6 q^{63} + 29 q^{64} + 3 q^{66} + 8 q^{67} - 10 q^{68} + 4 q^{69} - 20 q^{70} + 36 q^{71} + 15 q^{72} + 20 q^{73} + 13 q^{75} + 10 q^{76} + 6 q^{77} + 6 q^{79} - 20 q^{80} + 7 q^{81} - 10 q^{82} + 30 q^{83} + 12 q^{84} - 40 q^{85} + 6 q^{86} - 12 q^{87} + 15 q^{88} + 34 q^{89} - 12 q^{92} - 10 q^{93} + 32 q^{94} + 18 q^{95} + 33 q^{96} + 16 q^{97} + q^{98} + 7 q^{99}+O(q^{100}) $ 7 * q + 3 * q^2 + 7 * q^3 + 9 * q^4 + 6 * q^5 + 3 * q^6 + 6 * q^7 + 15 * q^8 + 7 * q^9 + 7 * q^11 + 9 * q^12 + 8 * q^14 + 6 * q^15 + 17 * q^16 - 2 * q^17 + 3 * q^18 + 8 * q^19 - 2 * q^20 + 6 * q^21 + 3 * q^22 + 4 * q^23 + 15 * q^24 + 13 * q^25 + 7 * q^27 + 12 * q^28 - 12 * q^29 - 10 * q^31 + 33 * q^32 + 7 * q^33 + 28 * q^34 - 4 * q^35 + 9 * q^36 + 6 * q^37 + 16 * q^38 - 10 * q^40 + 2 * q^41 + 8 * q^42 - 16 * q^43 + 9 * q^44 + 6 * q^45 - 26 * q^46 + 18 * q^47 + 17 * q^48 + 23 * q^49 + 39 * q^50 - 2 * q^51 + 10 * q^53 + 3 * q^54 + 6 * q^55 + 16 * q^56 + 8 * q^57 + 10 * q^58 + 2 * q^59 - 2 * q^60 - 10 * q^61 - 36 * q^62 + 6 * q^63 + 29 * q^64 + 3 * q^66 + 8 * q^67 - 10 * q^68 + 4 * q^69 - 20 * q^70 + 36 * q^71 + 15 * q^72 + 20 * q^73 + 13 * q^75 + 10 * q^76 + 6 * q^77 + 6 * q^79 - 20 * q^80 + 7 * q^81 - 10 * q^82 + 30 * q^83 + 12 * q^84 - 40 * q^85 + 6 * q^86 - 12 * q^87 + 15 * q^88 + 34 * q^89 - 12 * q^92 - 10 * q^93 + 32 * q^94 + 18 * q^95 + 33 * q^96 + 16 * q^97 + q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.409068	0.289255	0.144627	−	0.989486i	$-0.453802\pi$
$2$	0.409068	0.289255	0.144627	+	0.989486i	$0.453802\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.83266	−0.916332
$5$	4.13953	1.85125	0.925627	−	0.378437i	$-0.123538\pi$
$5$	4.13953	1.85125	0.925627	+	0.378437i	$0.123538\pi$
$6$	0.409068	0.167001
$7$	5.18273	1.95889	0.979445	−	0.201714i	$-0.0646510\pi$
$7$	5.18273	1.95889	0.979445	+	0.201714i	$0.0646510\pi$
$8$	−1.56782	−0.554308
$9$	1.00000	0.333333
$10$	1.69335	0.535484
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.83266	−0.529044
$13$	0	0
$13$	0	0
$14$	2.12009	0.566618
$15$	4.13953	1.06882
$16$	3.02398	0.755995
$17$	−0.488730	−0.118534	−0.0592672	−	0.998242i	$-0.518876\pi$
$17$	−0.488730	−0.118534	−0.0592672	+	0.998242i	$0.518876\pi$
$18$	0.409068	0.0964183
$19$	−0.446180	−0.102361	−0.0511803	−	0.998689i	$-0.516298\pi$
$19$	−0.446180	−0.102361	−0.0511803	+	0.998689i	$0.516298\pi$
$20$	−7.58636	−1.69636
$21$	5.18273	1.13097
$22$	0.409068	0.0872136
$23$	5.50882	1.14867	0.574334	−	0.818621i	$-0.305261\pi$
$23$	5.50882	1.14867	0.574334	+	0.818621i	$0.305261\pi$
$24$	−1.56782	−0.320030
$25$	12.1357	2.42714
$26$	0	0
$27$	1.00000	0.192450
$28$	−9.49821	−1.79499
$29$	−6.58571	−1.22294	−0.611468	−	0.791269i	$-0.709421\pi$
$29$	−6.58571	−1.22294	−0.611468	+	0.791269i	$0.709421\pi$
$30$	1.69335	0.309162
$31$	1.52580	0.274041	0.137021	−	0.990568i	$-0.456247\pi$
$31$	1.52580	0.274041	0.137021	+	0.990568i	$0.456247\pi$
$32$	4.37265	0.772983
$33$	1.00000	0.174078
$34$	−0.199924	−0.0342866
$35$	21.4541	3.62640
$36$	−1.83266	−0.305444
$37$	−7.87139	−1.29405	−0.647024	−	0.762470i	$-0.723987\pi$
$37$	−7.87139	−1.29405	−0.647024	+	0.762470i	$0.723987\pi$
$38$	−0.182518	−0.0296083
$39$	0	0
$40$	−6.49004	−1.02617
$41$	−8.78563	−1.37209	−0.686043	−	0.727561i	$-0.740654\pi$
$41$	−8.78563	−1.37209	−0.686043	+	0.727561i	$0.740654\pi$
$42$	2.12009	0.327137
$43$	−4.57514	−0.697702	−0.348851	−	0.937178i	$-0.613428\pi$
$43$	−4.57514	−0.697702	−0.348851	+	0.937178i	$0.613428\pi$
$44$	−1.83266	−0.276284
$45$	4.13953	0.617085
$46$	2.25348	0.332258
$47$	5.42082	0.790708	0.395354	−	0.918529i	$-0.370622\pi$
$47$	5.42082	0.790708	0.395354	+	0.918529i	$0.370622\pi$
$48$	3.02398	0.436474
$49$	19.8607	2.83725
$50$	4.96433	0.702062
$51$	−0.488730	−0.0684359
$52$	0	0
$53$	8.66677	1.19047	0.595236	−	0.803551i	$-0.297059\pi$
$53$	8.66677	1.19047	0.595236	+	0.803551i	$0.297059\pi$
$54$	0.409068	0.0556671
$55$	4.13953	0.558174
$56$	−8.12559	−1.08583
$57$	−0.446180	−0.0590980
$58$	−2.69400	−0.353740
$59$	5.60493	0.729700	0.364850	−	0.931066i	$-0.381120\pi$
$59$	5.60493	0.729700	0.364850	+	0.931066i	$0.381120\pi$
$60$	−7.58636	−0.979395
$61$	−0.855775	−0.109571	−0.0547854	−	0.998498i	$-0.517447\pi$
$61$	−0.855775	−0.109571	−0.0547854	+	0.998498i	$0.517447\pi$
$62$	0.624155	0.0792678
$63$	5.18273	0.652963
$64$	−4.25925	−0.532406
$65$	0	0
$66$	0.409068	0.0503528
$67$	−3.87464	−0.473363	−0.236681	−	0.971587i	$-0.576060\pi$
$67$	−3.87464	−0.473363	−0.236681	+	0.971587i	$0.576060\pi$
$68$	0.895677	0.108617
$69$	5.50882	0.663184
$70$	8.77618	1.04895
$71$	−8.49886	−1.00863	−0.504315	−	0.863520i	$-0.668255\pi$
$71$	−8.49886	−1.00863	−0.504315	+	0.863520i	$0.668255\pi$
$72$	−1.56782	−0.184769
$73$	5.95291	0.696735	0.348368	−	0.937358i	$-0.386736\pi$
$73$	5.95291	0.696735	0.348368	+	0.937358i	$0.386736\pi$
$74$	−3.21993	−0.374310
$75$	12.1357	1.40131
$76$	0.817698	0.0937963
$77$	5.18273	0.590627
$78$	0	0
$79$	−8.91459	−1.00297	−0.501485	−	0.865166i	$-0.667213\pi$
$79$	−8.91459	−1.00297	−0.501485	+	0.865166i	$0.667213\pi$
$80$	12.5179	1.39954
$81$	1.00000	0.111111
$82$	−3.59392	−0.396882
$83$	0.457495	0.0502166	0.0251083	−	0.999685i	$-0.492007\pi$
$83$	0.457495	0.0502166	0.0251083	+	0.999685i	$0.492007\pi$
$84$	−9.49821	−1.03634
$85$	−2.02311	−0.219437
$86$	−1.87154	−0.201814
$87$	−6.58571	−0.706062
$88$	−1.56782	−0.167130
$89$	−4.68461	−0.496568	−0.248284	−	0.968687i	$-0.579867\pi$
$89$	−4.68461	−0.496568	−0.248284	+	0.968687i	$0.579867\pi$
$90$	1.69335	0.178495
$91$	0	0
$92$	−10.0958	−1.05256
$93$	1.52580	0.158218
$94$	2.21748	0.228716
$95$	−1.84697	−0.189496
$96$	4.37265	0.446282
$97$	−2.06057	−0.209219	−0.104609	−	0.994513i	$-0.533359\pi$
$97$	−2.06057	−0.209219	−0.104609	+	0.994513i	$0.533359\pi$
$98$	8.12439	0.820687
$99$	1.00000	0.100504
$100$	−22.2407	−2.22407
$101$	3.86561	0.384642	0.192321	−	0.981332i	$-0.438398\pi$
$101$	3.86561	0.384642	0.192321	+	0.981332i	$0.438398\pi$
$102$	−0.199924	−0.0197954
$103$	0.350877	0.0345730	0.0172865	−	0.999851i	$-0.494497\pi$
$103$	0.350877	0.0345730	0.0172865	+	0.999851i	$0.494497\pi$
$104$	0	0
$105$	21.4541	2.09370
$106$	3.54530	0.344350
$107$	−12.5796	−1.21612	−0.608060	−	0.793891i	$-0.708052\pi$
$107$	−12.5796	−1.21612	−0.608060	+	0.793891i	$0.708052\pi$
$108$	−1.83266	−0.176348
$109$	−4.61460	−0.441999	−0.220999	−	0.975274i	$-0.570932\pi$
$109$	−4.61460	−0.441999	−0.220999	+	0.975274i	$0.570932\pi$
$110$	1.69335	0.161455
$111$	−7.87139	−0.747119
$112$	15.6725	1.48091
$113$	2.22602	0.209407	0.104703	−	0.994504i	$-0.466611\pi$
$113$	2.22602	0.209407	0.104703	+	0.994504i	$0.466611\pi$
$114$	−0.182518	−0.0170944
$115$	22.8039	2.12648
$116$	12.0694	1.12061
$117$	0	0
$118$	2.29280	0.211069
$119$	−2.53296	−0.232196
$120$	−6.49004	−0.592457
$121$	1.00000	0.0909091
$122$	−0.350070	−0.0316939
$123$	−8.78563	−0.792174
$124$	−2.79627	−0.251113
$125$	29.5385	2.64200
$126$	2.12009	0.188873
$127$	−18.2528	−1.61967	−0.809836	−	0.586656i	$-0.800444\pi$
$127$	−18.2528	−1.61967	−0.809836	+	0.586656i	$0.800444\pi$
$128$	−10.4876	−0.926985
$129$	−4.57514	−0.402818
$130$	0	0
$131$	3.18466	0.278245	0.139122	−	0.990275i	$-0.455572\pi$
$131$	3.18466	0.278245	0.139122	+	0.990275i	$0.455572\pi$
$132$	−1.83266	−0.159513
$133$	−2.31243	−0.200513
$134$	−1.58499	−0.136922
$135$	4.13953	0.356274
$136$	0.766241	0.0657046
$137$	−5.11813	−0.437271	−0.218635	−	0.975807i	$-0.570161\pi$
$137$	−5.11813	−0.437271	−0.218635	+	0.975807i	$0.570161\pi$
$138$	2.25348	0.191829
$139$	−10.7714	−0.913617	−0.456809	−	0.889565i	$-0.651008\pi$
$139$	−10.7714	−0.913617	−0.456809	+	0.889565i	$0.651008\pi$
$140$	−39.3181	−3.32299
$141$	5.42082	0.456515
$142$	−3.47661	−0.291751
$143$	0	0
$144$	3.02398	0.251998
$145$	−27.2617	−2.26396
$146$	2.43514	0.201534
$147$	19.8607	1.63809
$148$	14.4256	1.18578
$149$	4.42220	0.362281	0.181140	−	0.983457i	$-0.442021\pi$
$149$	4.42220	0.362281	0.181140	+	0.983457i	$0.442021\pi$
$150$	4.96433	0.405336
$151$	−4.64014	−0.377609	−0.188805	−	0.982015i	$-0.560461\pi$
$151$	−4.64014	−0.377609	−0.188805	+	0.982015i	$0.560461\pi$
$152$	0.699530	0.0567394
$153$	−0.488730	−0.0395115
$154$	2.12009	0.170842
$155$	6.31608	0.507320
$156$	0	0
$157$	10.8227	0.863745	0.431873	−	0.901935i	$-0.357853\pi$
$157$	10.8227	0.863745	0.431873	+	0.901935i	$0.357853\pi$
$158$	−3.64667	−0.290114
$159$	8.66677	0.687319
$160$	18.1007	1.43099
$161$	28.5508	2.25011
$162$	0.409068	0.0321394
$163$	−24.4714	−1.91675	−0.958373	−	0.285519i	$-0.907834\pi$
$163$	−24.4714	−1.91675	−0.958373	+	0.285519i	$0.907834\pi$
$164$	16.1011	1.25729
$165$	4.13953	0.322262
$166$	0.187147	0.0145254
$167$	−1.26722	−0.0980603	−0.0490302	−	0.998797i	$-0.515613\pi$
$167$	−1.26722	−0.0980603	−0.0490302	+	0.998797i	$0.515613\pi$
$168$	−8.12559	−0.626903
$169$	0	0
$170$	−0.827590	−0.0634733
$171$	−0.446180	−0.0341202
$172$	8.38469	0.639326
$173$	3.24638	0.246818	0.123409	−	0.992356i	$-0.460617\pi$
$173$	3.24638	0.246818	0.123409	+	0.992356i	$0.460617\pi$
$174$	−2.69400	−0.204232
$175$	62.8961	4.75450
$176$	3.02398	0.227941
$177$	5.60493	0.421292
$178$	−1.91633	−0.143635
$179$	−16.5303	−1.23553	−0.617765	−	0.786363i	$-0.711962\pi$
$179$	−16.5303	−1.23553	−0.617765	+	0.786363i	$0.711962\pi$
$180$	−7.58636	−0.565454
$181$	12.2065	0.907303	0.453651	−	0.891179i	$-0.350121\pi$
$181$	12.2065	0.907303	0.453651	+	0.891179i	$0.350121\pi$
$182$	0	0
$183$	−0.855775	−0.0632607
$184$	−8.63684	−0.636717
$185$	−32.5838	−2.39561
$186$	0.624155	0.0457653
$187$	−0.488730	−0.0357395
$188$	−9.93454	−0.724551
$189$	5.18273	0.376988
$190$	−0.755539	−0.0548125
$191$	−17.4410	−1.26199	−0.630995	−	0.775787i	$-0.717353\pi$
$191$	−17.4410	−1.26199	−0.630995	+	0.775787i	$0.717353\pi$
$192$	−4.25925	−0.307385
$193$	−0.941498	−0.0677705	−0.0338852	−	0.999426i	$-0.510788\pi$
$193$	−0.941498	−0.0677705	−0.0338852	+	0.999426i	$0.510788\pi$
$194$	−0.842912	−0.0605175
$195$	0	0
$196$	−36.3980	−2.59986
$197$	16.7419	1.19281	0.596404	−	0.802684i	$-0.296596\pi$
$197$	16.7419	1.19281	0.596404	+	0.802684i	$0.296596\pi$
$198$	0.409068	0.0290712
$199$	13.1573	0.932693	0.466347	−	0.884602i	$-0.345570\pi$
$199$	13.1573	0.932693	0.466347	+	0.884602i	$0.345570\pi$
$200$	−19.0266	−1.34538
$201$	−3.87464	−0.273296
$202$	1.58130	0.111260
$203$	−34.1320	−2.39560
$204$	0.895677	0.0627100
$205$	−36.3684	−2.54008
$206$	0.143533	0.0100004
$207$	5.50882	0.382890
$208$	0	0
$209$	−0.446180	−0.0308629
$210$	8.77618	0.605614
$211$	13.5657	0.933898	0.466949	−	0.884284i	$-0.345353\pi$
$211$	13.5657	0.933898	0.466949	+	0.884284i	$0.345353\pi$
$212$	−15.8833	−1.09087
$213$	−8.49886	−0.582332
$214$	−5.14593	−0.351768
$215$	−18.9389	−1.29162
$216$	−1.56782	−0.106677
$217$	7.90780	0.536816
$218$	−1.88769	−0.127850
$219$	5.95291	0.402260
$220$	−7.58636	−0.511473
$221$	0	0
$222$	−3.21993	−0.216108
$223$	11.8725	0.795044	0.397522	−	0.917593i	$-0.369870\pi$
$223$	11.8725	0.795044	0.397522	+	0.917593i	$0.369870\pi$
$224$	22.6623	1.51419
$225$	12.1357	0.809047
$226$	0.910595	0.0605719
$227$	−13.0255	−0.864532	−0.432266	−	0.901746i	$-0.642286\pi$
$227$	−13.0255	−0.864532	−0.432266	+	0.901746i	$0.642286\pi$
$228$	0.817698	0.0541533
$229$	6.45867	0.426801	0.213401	−	0.976965i	$-0.431546\pi$
$229$	6.45867	0.426801	0.213401	+	0.976965i	$0.431546\pi$
$230$	9.32836	0.615094
$231$	5.18273	0.340999
$232$	10.3252	0.677883
$233$	−13.2616	−0.868795	−0.434397	−	0.900721i	$-0.643039\pi$
$233$	−13.2616	−0.868795	−0.434397	+	0.900721i	$0.643039\pi$
$234$	0	0
$235$	22.4396	1.46380
$236$	−10.2720	−0.668647
$237$	−8.91459	−0.579065
$238$	−1.03615	−0.0671637
$239$	0.426040	0.0275583	0.0137791	−	0.999905i	$-0.495614\pi$
$239$	0.426040	0.0275583	0.0137791	+	0.999905i	$0.495614\pi$
$240$	12.5179	0.808024
$241$	12.9860	0.836503	0.418251	−	0.908331i	$-0.362643\pi$
$241$	12.9860	0.836503	0.418251	+	0.908331i	$0.362643\pi$
$242$	0.409068	0.0262959
$243$	1.00000	0.0641500
$244$	1.56835	0.100403
$245$	82.2141	5.25246
$246$	−3.59392	−0.229140
$247$	0	0
$248$	−2.39218	−0.151903
$249$	0.457495	0.0289926
$250$	12.0832	0.764211
$251$	4.37202	0.275959	0.137980	−	0.990435i	$-0.455939\pi$
$251$	4.37202	0.275959	0.137980	+	0.990435i	$0.455939\pi$
$252$	−9.49821	−0.598331
$253$	5.50882	0.346337
$254$	−7.46663	−0.468498
$255$	−2.02311	−0.126692
$256$	4.22834	0.264271
$257$	−11.2798	−0.703614	−0.351807	−	0.936073i	$-0.614433\pi$
$257$	−11.2798	−0.703614	−0.351807	+	0.936073i	$0.614433\pi$
$258$	−1.87154	−0.116517
$259$	−40.7953	−2.53490
$260$	0	0
$261$	−6.58571	−0.407645
$262$	1.30274	0.0804836
$263$	−0.914614	−0.0563975	−0.0281988	−	0.999602i	$-0.508977\pi$
$263$	−0.914614	−0.0563975	−0.0281988	+	0.999602i	$0.508977\pi$
$264$	−1.56782	−0.0964927
$265$	35.8763	2.20387
$266$	−0.945942	−0.0579994
$267$	−4.68461	−0.286694
$268$	7.10091	0.433757
$269$	13.1384	0.801064	0.400532	−	0.916283i	$-0.368825\pi$
$269$	13.1384	0.801064	0.400532	+	0.916283i	$0.368825\pi$
$270$	1.69335	0.103054
$271$	−12.3173	−0.748224	−0.374112	−	0.927384i	$-0.622052\pi$
$271$	−12.3173	−0.748224	−0.374112	+	0.927384i	$0.622052\pi$
$272$	−1.47791	−0.0896115
$273$	0	0
$274$	−2.09366	−0.126483
$275$	12.1357	0.731810
$276$	−10.0958	−0.607697
$277$	−20.1395	−1.21006	−0.605031	−	0.796202i	$-0.706839\pi$
$277$	−20.1395	−1.21006	−0.605031	+	0.796202i	$0.706839\pi$
$278$	−4.40623	−0.264268
$279$	1.52580	0.0913471
$280$	−33.6361	−2.01014
$281$	−6.66666	−0.397699	−0.198850	−	0.980030i	$-0.563721\pi$
$281$	−6.66666	−0.397699	−0.198850	+	0.980030i	$0.563721\pi$
$282$	2.21748	0.132049
$283$	27.5589	1.63820	0.819102	−	0.573647i	$-0.194472\pi$
$283$	27.5589	1.63820	0.819102	+	0.573647i	$0.194472\pi$
$284$	15.5755	0.924239
$285$	−1.84697	−0.109405
$286$	0	0
$287$	−45.5336	−2.68776
$288$	4.37265	0.257661
$289$	−16.7611	−0.985950
$290$	−11.1519	−0.654863
$291$	−2.06057	−0.120793
$292$	−10.9097	−0.638440
$293$	−13.8127	−0.806945	−0.403472	−	0.914992i	$-0.632197\pi$
$293$	−13.8127	−0.806945	−0.403472	+	0.914992i	$0.632197\pi$
$294$	8.12439	0.473824
$295$	23.2018	1.35086
$296$	12.3409	0.717301
$297$	1.00000	0.0580259
$298$	1.80898	0.104791
$299$	0	0
$300$	−22.2407	−1.28406
$301$	−23.7117	−1.36672
$302$	−1.89813	−0.109225
$303$	3.86561	0.222073
$304$	−1.34924	−0.0773842
$305$	−3.54251	−0.202843
$306$	−0.199924	−0.0114289
$307$	21.0868	1.20349	0.601743	−	0.798690i	$-0.294473\pi$
$307$	21.0868	1.20349	0.601743	+	0.798690i	$0.294473\pi$
$308$	−9.49821	−0.541210
$309$	0.350877	0.0199607
$310$	2.58371	0.146745
$311$	−29.7858	−1.68900	−0.844498	−	0.535558i	$-0.820101\pi$
$311$	−29.7858	−1.68900	−0.844498	+	0.535558i	$0.820101\pi$
$312$	0	0
$313$	26.3709	1.49057	0.745287	−	0.666744i	$-0.232312\pi$
$313$	26.3709	1.49057	0.745287	+	0.666744i	$0.232312\pi$
$314$	4.42722	0.249842
$315$	21.4541	1.20880
$316$	16.3374	0.919053
$317$	24.5073	1.37647	0.688233	−	0.725490i	$-0.258387\pi$
$317$	24.5073	1.37647	0.688233	+	0.725490i	$0.258387\pi$
$318$	3.54530	0.198810
$319$	−6.58571	−0.368729
$320$	−17.6313	−0.985619
$321$	−12.5796	−0.702127
$322$	11.6792	0.650857
$323$	0.218061	0.0121333
$324$	−1.83266	−0.101815
$325$	0	0
$326$	−10.0105	−0.554428
$327$	−4.61460	−0.255188
$328$	13.7743	0.760558
$329$	28.0947	1.54891
$330$	1.69335	0.0932158
$331$	10.4965	0.576939	0.288469	−	0.957489i	$-0.406854\pi$
$331$	10.4965	0.576939	0.288469	+	0.957489i	$0.406854\pi$
$332$	−0.838434	−0.0460150
$333$	−7.87139	−0.431349
$334$	−0.518379	−0.0283644
$335$	−16.0392	−0.876315
$336$	15.6725	0.855004
$337$	21.9103	1.19353	0.596765	−	0.802416i	$-0.296453\pi$
$337$	21.9103	1.19353	0.596765	+	0.802416i	$0.296453\pi$
$338$	0	0
$339$	2.22602	0.120901
$340$	3.70768	0.201077
$341$	1.52580	0.0826266
$342$	−0.182518	−0.00986944
$343$	66.6537	3.59896
$344$	7.17299	0.386742
$345$	22.8039	1.22772
$346$	1.32799	0.0713933
$347$	−16.4119	−0.881036	−0.440518	−	0.897744i	$-0.645205\pi$
$347$	−16.4119	−0.881036	−0.440518	+	0.897744i	$0.645205\pi$
$348$	12.0694	0.646987
$349$	−25.0915	−1.34312	−0.671559	−	0.740951i	$-0.734375\pi$
$349$	−25.0915	−1.34312	−0.671559	+	0.740951i	$0.734375\pi$
$350$	25.7288	1.37526
$351$	0	0
$352$	4.37265	0.233063
$353$	9.19662	0.489486	0.244743	−	0.969588i	$-0.421296\pi$
$353$	9.19662	0.489486	0.244743	+	0.969588i	$0.421296\pi$
$354$	2.29280	0.121861
$355$	−35.1813	−1.86723
$356$	8.58532	0.455021
$357$	−2.53296	−0.134058
$358$	−6.76200	−0.357383
$359$	22.6236	1.19403	0.597013	−	0.802231i	$-0.296354\pi$
$359$	22.6236	1.19403	0.597013	+	0.802231i	$0.296354\pi$
$360$	−6.49004	−0.342055
$361$	−18.8009	−0.989522
$362$	4.99329	0.262442
$363$	1.00000	0.0524864
$364$	0	0
$365$	24.6422	1.28983
$366$	−0.350070	−0.0182985
$367$	−13.9344	−0.727371	−0.363685	−	0.931522i	$-0.618482\pi$
$367$	−13.9344	−0.727371	−0.363685	+	0.931522i	$0.618482\pi$
$368$	16.6586	0.868388
$369$	−8.78563	−0.457362
$370$	−13.3290	−0.692942
$371$	44.9175	2.33200
$372$	−2.79627	−0.144980
$373$	20.5104	1.06199	0.530995	−	0.847375i	$-0.321818\pi$
$373$	20.5104	1.06199	0.530995	+	0.847375i	$0.321818\pi$
$374$	−0.199924	−0.0103378
$375$	29.5385	1.52536
$376$	−8.49887	−0.438296
$377$	0	0
$378$	2.12009	0.109046
$379$	−2.32811	−0.119587	−0.0597934	−	0.998211i	$-0.519044\pi$
$379$	−2.32811	−0.119587	−0.0597934	+	0.998211i	$0.519044\pi$
$380$	3.38488	0.173641
$381$	−18.2528	−0.935118
$382$	−7.13457	−0.365037
$383$	27.2203	1.39089	0.695447	−	0.718578i	$-0.255207\pi$
$383$	27.2203	1.39089	0.695447	+	0.718578i	$0.255207\pi$
$384$	−10.4876	−0.535195
$385$	21.4541	1.09340
$386$	−0.385137	−0.0196029
$387$	−4.57514	−0.232567
$388$	3.77632	0.191714
$389$	−24.9318	−1.26409	−0.632047	−	0.774930i	$-0.717785\pi$
$389$	−24.9318	−1.26409	−0.632047	+	0.774930i	$0.717785\pi$
$390$	0	0
$391$	−2.69233	−0.136157
$392$	−31.1381	−1.57271
$393$	3.18466	0.160645
$394$	6.84856	0.345026
$395$	−36.9022	−1.85675
$396$	−1.83266	−0.0920948
$397$	−31.3269	−1.57225	−0.786126	−	0.618066i	$-0.787916\pi$
$397$	−31.3269	−1.57225	−0.786126	+	0.618066i	$0.787916\pi$
$398$	5.38222	0.269786
$399$	−2.31243	−0.115766
$400$	36.6981	1.83491
$401$	8.94790	0.446837	0.223418	−	0.974723i	$-0.428278\pi$
$401$	8.94790	0.446837	0.223418	+	0.974723i	$0.428278\pi$
$402$	−1.58499	−0.0790522
$403$	0	0
$404$	−7.08435	−0.352460
$405$	4.13953	0.205695
$406$	−13.9623	−0.692937
$407$	−7.87139	−0.390170
$408$	0.766241	0.0379346
$409$	−30.0934	−1.48802	−0.744012	−	0.668166i	$-0.767079\pi$
$409$	−30.0934	−1.48802	−0.744012	+	0.668166i	$0.767079\pi$
$410$	−14.8771	−0.734730
$411$	−5.11813	−0.252459
$412$	−0.643040	−0.0316803
$413$	29.0489	1.42940
$414$	2.25348	0.110753
$415$	1.89381	0.0929636
$416$	0	0
$417$	−10.7714	−0.527477
$418$	−0.182518	−0.00892725
$419$	32.6525	1.59518	0.797588	−	0.603202i	$-0.206109\pi$
$419$	32.6525	1.59518	0.797588	+	0.603202i	$0.206109\pi$
$420$	−39.3181	−1.91853
$421$	−28.3956	−1.38392	−0.691958	−	0.721938i	$-0.743252\pi$
$421$	−28.3956	−1.38392	−0.691958	+	0.721938i	$0.743252\pi$
$422$	5.54928	0.270135
$423$	5.42082	0.263569
$424$	−13.5879	−0.659888
$425$	−5.93108	−0.287700
$426$	−3.47661	−0.168442
$427$	−4.43525	−0.214637
$428$	23.0542	1.11437
$429$	0	0
$430$	−7.74731	−0.373608
$431$	14.1585	0.681992	0.340996	−	0.940065i	$-0.389236\pi$
$431$	14.1585	0.681992	0.340996	+	0.940065i	$0.389236\pi$
$432$	3.02398	0.145491
$433$	15.5980	0.749590	0.374795	−	0.927108i	$-0.377713\pi$
$433$	15.5980	0.749590	0.374795	+	0.927108i	$0.377713\pi$
$434$	3.23483	0.155277
$435$	−27.2617	−1.30710
$436$	8.45701	0.405017
$437$	−2.45793	−0.117579
$438$	2.43514	0.116356
$439$	16.0616	0.766579	0.383289	−	0.923628i	$-0.374791\pi$
$439$	16.0616	0.766579	0.383289	+	0.923628i	$0.374791\pi$
$440$	−6.49004	−0.309400
$441$	19.8607	0.945749
$442$	0	0
$443$	−8.20834	−0.389990	−0.194995	−	0.980804i	$-0.562469\pi$
$443$	−8.20834	−0.389990	−0.194995	+	0.980804i	$0.562469\pi$
$444$	14.4256	0.684609
$445$	−19.3921	−0.919273
$446$	4.85668	0.229970
$447$	4.42220	0.209163
$448$	−22.0746	−1.04292
$449$	10.4304	0.492242	0.246121	−	0.969239i	$-0.420844\pi$
$449$	10.4304	0.492242	0.246121	+	0.969239i	$0.420844\pi$
$450$	4.96433	0.234021
$451$	−8.78563	−0.413699
$452$	−4.07955	−0.191886
$453$	−4.64014	−0.218013
$454$	−5.32831	−0.250070
$455$	0	0
$456$	0.699530	0.0327585
$457$	−18.1240	−0.847807	−0.423904	−	0.905707i	$-0.639340\pi$
$457$	−18.1240	−0.847807	−0.423904	+	0.905707i	$0.639340\pi$
$458$	2.64204	0.123454
$459$	−0.488730	−0.0228120
$460$	−41.7919	−1.94856
$461$	28.6242	1.33316	0.666581	−	0.745432i	$-0.267757\pi$
$461$	28.6242	1.33316	0.666581	+	0.745432i	$0.267757\pi$
$462$	2.12009	0.0986356
$463$	−9.44955	−0.439158	−0.219579	−	0.975595i	$-0.570468\pi$
$463$	−9.44955	−0.439158	−0.219579	+	0.975595i	$0.570468\pi$
$464$	−19.9151	−0.924534
$465$	6.31608	0.292901
$466$	−5.42489	−0.251303
$467$	19.1423	0.885800	0.442900	−	0.896571i	$-0.353950\pi$
$467$	19.1423	0.885800	0.442900	+	0.896571i	$0.353950\pi$
$468$	0	0
$469$	−20.0812	−0.927265
$470$	9.17934	0.423412
$471$	10.8227	0.498683
$472$	−8.78753	−0.404479
$473$	−4.57514	−0.210365
$474$	−3.64667	−0.167497
$475$	−5.41471	−0.248444
$476$	4.64206	0.212768
$477$	8.66677	0.396824
$478$	0.174280	0.00797136
$479$	11.5433	0.527428	0.263714	−	0.964601i	$-0.415052\pi$
$479$	11.5433	0.527428	0.263714	+	0.964601i	$0.415052\pi$
$480$	18.1007	0.826182
$481$	0	0
$482$	5.31216	0.241962
$483$	28.5508	1.29910
$484$	−1.83266	−0.0833029
$485$	−8.52977	−0.387317
$486$	0.409068	0.0185557
$487$	34.7318	1.57385	0.786923	−	0.617051i	$-0.211673\pi$
$487$	34.7318	1.57385	0.786923	+	0.617051i	$0.211673\pi$
$488$	1.34170	0.0607360
$489$	−24.4714	−1.10663
$490$	33.6311	1.51930
$491$	19.9935	0.902295	0.451148	−	0.892449i	$-0.351015\pi$
$491$	19.9935	0.902295	0.451148	+	0.892449i	$0.351015\pi$
$492$	16.1011	0.725894
$493$	3.21863	0.144960
$494$	0	0
$495$	4.13953	0.186058
$496$	4.61398	0.207174
$497$	−44.0473	−1.97579
$498$	0.187147	0.00838624
$499$	−10.3565	−0.463623	−0.231811	−	0.972761i	$-0.574465\pi$
$499$	−10.3565	−0.463623	−0.231811	+	0.972761i	$0.574465\pi$
$500$	−54.1340	−2.42095
$501$	−1.26722	−0.0566151
$502$	1.78845	0.0798226
$503$	41.2438	1.83897	0.919486	−	0.393124i	$-0.128606\pi$
$503$	41.2438	1.83897	0.919486	+	0.393124i	$0.128606\pi$
$504$	−8.12559	−0.361943
$505$	16.0018	0.712070
$506$	2.25348	0.100180
$507$	0	0
$508$	33.4512	1.48416
$509$	9.47338	0.419900	0.209950	−	0.977712i	$-0.432670\pi$
$509$	9.47338	0.419900	0.209950	+	0.977712i	$0.432670\pi$
$510$	−0.827590	−0.0366463
$511$	30.8523	1.36483
$512$	22.7049	1.00343
$513$	−0.446180	−0.0196993
$514$	−4.61420	−0.203524
$515$	1.45247	0.0640033
$516$	8.38469	0.369115
$517$	5.42082	0.238407
$518$	−16.6881	−0.733231
$519$	3.24638	0.142500
$520$	0	0
$521$	−6.47023	−0.283466	−0.141733	−	0.989905i	$-0.545267\pi$
$521$	−6.47023	−0.283466	−0.141733	+	0.989905i	$0.545267\pi$
$522$	−2.69400	−0.117913
$523$	16.1999	0.708372	0.354186	−	0.935175i	$-0.384758\pi$
$523$	16.1999	0.708372	0.354186	+	0.935175i	$0.384758\pi$
$524$	−5.83640	−0.254964
$525$	62.8961	2.74501
$526$	−0.374140	−0.0163133
$527$	−0.745703	−0.0324833
$528$	3.02398	0.131602
$529$	7.34712	0.319440
$530$	14.6759	0.637479
$531$	5.60493	0.243233
$532$	4.23791	0.183737
$533$	0	0
$534$	−1.91633	−0.0829275
$535$	−52.0738	−2.25135
$536$	6.07474	0.262389
$537$	−16.5303	−0.713334
$538$	5.37451	0.231712
$539$	19.8607	0.855462
$540$	−7.58636	−0.326465
$541$	−6.65767	−0.286236	−0.143118	−	0.989706i	$-0.545713\pi$
$541$	−6.65767	−0.286236	−0.143118	+	0.989706i	$0.545713\pi$
$542$	−5.03862	−0.216427
$543$	12.2065	0.523832
$544$	−2.13705	−0.0916251
$545$	−19.1023	−0.818252
$546$	0	0
$547$	2.06963	0.0884912	0.0442456	−	0.999021i	$-0.485912\pi$
$547$	2.06963	0.0884912	0.0442456	+	0.999021i	$0.485912\pi$
$548$	9.37980	0.400685
$549$	−0.855775	−0.0365236
$550$	4.96433	0.211680
$551$	2.93841	0.125181
$552$	−8.63684	−0.367608
$553$	−46.2020	−1.96471
$554$	−8.23841	−0.350016
$555$	−32.5838	−1.38311
$556$	19.7403	0.837176
$557$	12.3459	0.523111	0.261556	−	0.965188i	$-0.415764\pi$
$557$	12.3459	0.523111	0.261556	+	0.965188i	$0.415764\pi$
$558$	0.624155	0.0264226
$559$	0	0
$560$	64.8767	2.74154
$561$	−0.488730	−0.0206342
$562$	−2.72712	−0.115037
$563$	−3.72355	−0.156929	−0.0784645	−	0.996917i	$-0.525002\pi$
$563$	−3.72355	−0.156929	−0.0784645	+	0.996917i	$0.525002\pi$
$564$	−9.93454	−0.418320
$565$	9.21469	0.387665
$566$	11.2735	0.473859
$567$	5.18273	0.217654
$568$	13.3247	0.559091
$569$	27.2092	1.14067	0.570334	−	0.821413i	$-0.306814\pi$
$569$	27.2092	1.14067	0.570334	+	0.821413i	$0.306814\pi$
$570$	−0.755539	−0.0316460
$571$	31.1102	1.30192	0.650961	−	0.759112i	$-0.274366\pi$
$571$	31.1102	1.30192	0.650961	+	0.759112i	$0.274366\pi$
$572$	0	0
$573$	−17.4410	−0.728610
$574$	−18.6263	−0.777448
$575$	66.8534	2.78798
$576$	−4.25925	−0.177469
$577$	−5.53948	−0.230611	−0.115306	−	0.993330i	$-0.536785\pi$
$577$	−5.53948	−0.230611	−0.115306	+	0.993330i	$0.536785\pi$
$578$	−6.85645	−0.285191
$579$	−0.941498	−0.0391273
$580$	49.9616	2.07454
$581$	2.37107	0.0983687
$582$	−0.842912	−0.0349398
$583$	8.66677	0.358941
$584$	−9.33309	−0.386206
$585$	0	0
$586$	−5.65032	−0.233413
$587$	−27.8516	−1.14956	−0.574780	−	0.818308i	$-0.694912\pi$
$587$	−27.8516	−1.14956	−0.574780	+	0.818308i	$0.694912\pi$
$588$	−36.3980	−1.50103
$589$	−0.680780	−0.0280511
$590$	9.49111	0.390743
$591$	16.7419	0.688668
$592$	−23.8029	−0.978294
$593$	−0.298235	−0.0122470	−0.00612351	−	0.999981i	$-0.501949\pi$
$593$	−0.298235	−0.0122470	−0.00612351	+	0.999981i	$0.501949\pi$
$594$	0.409068	0.0167843
$595$	−10.4852	−0.429853
$596$	−8.10440	−0.331969
$597$	13.1573	0.538491
$598$	0	0
$599$	22.8194	0.932375	0.466188	−	0.884686i	$-0.345627\pi$
$599$	22.8194	0.932375	0.466188	+	0.884686i	$0.345627\pi$
$600$	−19.0266	−0.776758
$601$	−2.27297	−0.0927164	−0.0463582	−	0.998925i	$-0.514762\pi$
$601$	−2.27297	−0.0927164	−0.0463582	+	0.998925i	$0.514762\pi$
$602$	−9.69971	−0.395331
$603$	−3.87464	−0.157788
$604$	8.50381	0.346015
$605$	4.13953	0.168296
$606$	1.58130	0.0642358
$607$	−4.31576	−0.175171	−0.0875857	−	0.996157i	$-0.527915\pi$
$607$	−4.31576	−0.175171	−0.0875857	+	0.996157i	$0.527915\pi$
$608$	−1.95099	−0.0791231
$609$	−34.1320	−1.38310
$610$	−1.44913	−0.0586734
$611$	0	0
$612$	0.895677	0.0362056
$613$	11.3555	0.458646	0.229323	−	0.973350i	$-0.426349\pi$
$613$	11.3555	0.458646	0.229323	+	0.973350i	$0.426349\pi$
$614$	8.62593	0.348114
$615$	−36.3684	−1.46651
$616$	−8.12559	−0.327390
$617$	−23.6846	−0.953507	−0.476753	−	0.879037i	$-0.658186\pi$
$617$	−23.6846	−0.953507	−0.476753	+	0.879037i	$0.658186\pi$
$618$	0.143533	0.00577373
$619$	−27.4080	−1.10162	−0.550810	−	0.834631i	$-0.685681\pi$
$619$	−27.4080	−1.10162	−0.550810	+	0.834631i	$0.685681\pi$
$620$	−11.5753	−0.464873
$621$	5.50882	0.221061
$622$	−12.1844	−0.488550
$623$	−24.2791	−0.972721
$624$	0	0
$625$	61.5968	2.46387
$626$	10.7875	0.431156
$627$	−0.446180	−0.0178187
$628$	−19.8344	−0.791477
$629$	3.84698	0.153389
$630$	8.77618	0.349651
$631$	42.3930	1.68764	0.843819	−	0.536627i	$-0.180302\pi$
$631$	42.3930	1.68764	0.843819	+	0.536627i	$0.180302\pi$
$632$	13.9765	0.555954
$633$	13.5657	0.539186
$634$	10.0251	0.398149
$635$	−75.5579	−2.99842
$636$	−15.8833	−0.629812
$637$	0	0
$638$	−2.69400	−0.106657
$639$	−8.49886	−0.336210
$640$	−43.4139	−1.71608
$641$	18.4040	0.726916	0.363458	−	0.931611i	$-0.381596\pi$
$641$	18.4040	0.726916	0.363458	+	0.931611i	$0.381596\pi$
$642$	−5.14593	−0.203094
$643$	0.572048	0.0225594	0.0112797	−	0.999936i	$-0.496409\pi$
$643$	0.572048	0.0225594	0.0112797	+	0.999936i	$0.496409\pi$
$644$	−52.3239	−2.06185
$645$	−18.9389	−0.745719
$646$	0.0892020	0.00350961
$647$	16.2324	0.638163	0.319082	−	0.947727i	$-0.396626\pi$
$647$	16.2324	0.638163	0.319082	+	0.947727i	$0.396626\pi$
$648$	−1.56782	−0.0615898
$649$	5.60493	0.220013
$650$	0	0
$651$	7.90780	0.309931
$652$	44.8478	1.75638
$653$	−2.56096	−0.100218	−0.0501090	−	0.998744i	$-0.515957\pi$
$653$	−2.56096	−0.100218	−0.0501090	+	0.998744i	$0.515957\pi$
$654$	−1.88769	−0.0738144
$655$	13.1830	0.515102
$656$	−26.5676	−1.03729
$657$	5.95291	0.232245
$658$	11.4926	0.448029
$659$	−37.8432	−1.47416	−0.737082	−	0.675804i	$-0.763797\pi$
$659$	−37.8432	−1.47416	−0.737082	+	0.675804i	$0.763797\pi$
$660$	−7.58636	−0.295299
$661$	33.9955	1.32227	0.661135	−	0.750267i	$-0.270075\pi$
$661$	33.9955	1.32227	0.661135	+	0.750267i	$0.270075\pi$
$662$	4.29378	0.166882
$663$	0	0
$664$	−0.717270	−0.0278355
$665$	−9.57238	−0.371201
$666$	−3.21993	−0.124770
$667$	−36.2795	−1.40475
$668$	2.32238	0.0898558
$669$	11.8725	0.459019
$670$	−6.56112	−0.253478
$671$	−0.855775	−0.0330368
$672$	22.6623	0.874217
$673$	−34.7689	−1.34024	−0.670122	−	0.742251i	$-0.733758\pi$
$673$	−34.7689	−1.34024	−0.670122	+	0.742251i	$0.733758\pi$
$674$	8.96280	0.345234
$675$	12.1357	0.467103
$676$	0	0
$677$	−31.6215	−1.21531	−0.607656	−	0.794201i	$-0.707890\pi$
$677$	−31.6215	−1.21531	−0.607656	+	0.794201i	$0.707890\pi$
$678$	0.910595	0.0349712
$679$	−10.6794	−0.409836
$680$	3.17188	0.121636
$681$	−13.0255	−0.499138
$682$	0.624155	0.0239001
$683$	29.1127	1.11397	0.556984	−	0.830523i	$-0.311959\pi$
$683$	29.1127	1.11397	0.556984	+	0.830523i	$0.311959\pi$
$684$	0.817698	0.0312654
$685$	−21.1866	−0.809500
$686$	27.2659	1.04102
$687$	6.45867	0.246414
$688$	−13.8351	−0.527459
$689$	0	0
$690$	9.32836	0.355125
$691$	−6.72289	−0.255751	−0.127875	−	0.991790i	$-0.540816\pi$
$691$	−6.72289	−0.255751	−0.127875	+	0.991790i	$0.540816\pi$
$692$	−5.94953	−0.226167
$693$	5.18273	0.196876
$694$	−6.71357	−0.254844
$695$	−44.5885	−1.69134
$696$	10.3252	0.391376
$697$	4.29380	0.162639
$698$	−10.2641	−0.388503
$699$	−13.2616	−0.501599
$700$	−115.267	−4.35670
$701$	−33.5332	−1.26653	−0.633265	−	0.773935i	$-0.718286\pi$
$701$	−33.5332	−1.26653	−0.633265	+	0.773935i	$0.718286\pi$
$702$	0	0
$703$	3.51205	0.132460
$704$	−4.25925	−0.160526
$705$	22.4396	0.845126
$706$	3.76204	0.141586
$707$	20.0344	0.753471
$708$	−10.2720	−0.386044
$709$	−40.1123	−1.50645	−0.753224	−	0.657764i	$-0.771502\pi$
$709$	−40.1123	−1.50645	−0.753224	+	0.657764i	$0.771502\pi$
$710$	−14.3915	−0.540105
$711$	−8.91459	−0.334323
$712$	7.34463	0.275252
$713$	8.40535	0.314783
$714$	−1.03615	−0.0387770
$715$	0	0
$716$	30.2944	1.13216
$717$	0.426040	0.0159108
$718$	9.25458	0.345378
$719$	7.15141	0.266703	0.133351	−	0.991069i	$-0.457426\pi$
$719$	7.15141	0.266703	0.133351	+	0.991069i	$0.457426\pi$
$720$	12.5179	0.466513
$721$	1.81850	0.0677246
$722$	−7.69086	−0.286224
$723$	12.9860	0.482955
$724$	−22.3704	−0.831390
$725$	−79.9222	−2.96824
$726$	0.409068	0.0151819
$727$	−38.2917	−1.42016	−0.710081	−	0.704120i	$-0.751342\pi$
$727$	−38.2917	−1.42016	−0.710081	+	0.704120i	$0.751342\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	10.0804	0.373091
$731$	2.23601	0.0827017
$732$	1.56835	0.0579678
$733$	−35.4025	−1.30762	−0.653811	−	0.756658i	$-0.726831\pi$
$733$	−35.4025	−1.30762	−0.653811	+	0.756658i	$0.726831\pi$
$734$	−5.70013	−0.210395
$735$	82.2141	3.03251
$736$	24.0882	0.887902
$737$	−3.87464	−0.142724
$738$	−3.59392	−0.132294
$739$	2.87016	0.105580	0.0527902	−	0.998606i	$-0.483189\pi$
$739$	2.87016	0.105580	0.0527902	+	0.998606i	$0.483189\pi$
$740$	59.7152	2.19517
$741$	0	0
$742$	18.3743	0.674543
$743$	23.1129	0.847930	0.423965	−	0.905679i	$-0.360638\pi$
$743$	23.1129	0.847930	0.423965	+	0.905679i	$0.360638\pi$
$744$	−2.39218	−0.0877014
$745$	18.3058	0.670673
$746$	8.39016	0.307185
$747$	0.457495	0.0167389
$748$	0.895677	0.0327492
$749$	−65.1969	−2.38224
$750$	12.0832	0.441218
$751$	−37.5587	−1.37054	−0.685268	−	0.728291i	$-0.740315\pi$
$751$	−37.5587	−1.37054	−0.685268	+	0.728291i	$0.740315\pi$
$752$	16.3925	0.597771
$753$	4.37202	0.159325
$754$	0	0
$755$	−19.2080	−0.699050
$756$	−9.49821	−0.345446
$757$	−47.4259	−1.72372	−0.861862	−	0.507143i	$-0.830702\pi$
$757$	−47.4259	−1.72372	−0.861862	+	0.507143i	$0.830702\pi$
$758$	−0.952354	−0.0345910
$759$	5.50882	0.199958
$760$	2.89572	0.105039
$761$	23.0592	0.835895	0.417947	−	0.908471i	$-0.362750\pi$
$761$	23.0592	0.835895	0.417947	+	0.908471i	$0.362750\pi$
$762$	−7.46663	−0.270487
$763$	−23.9163	−0.865826
$764$	31.9636	1.15640
$765$	−2.02311	−0.0731458
$766$	11.1350	0.402323
$767$	0	0
$768$	4.22834	0.152577
$769$	−40.2536	−1.45158	−0.725792	−	0.687915i	$-0.758526\pi$
$769$	−40.2536	−1.45158	−0.725792	+	0.687915i	$0.758526\pi$
$770$	8.77618	0.316272
$771$	−11.2798	−0.406232
$772$	1.72545	0.0621003
$773$	25.6183	0.921426	0.460713	−	0.887549i	$-0.347594\pi$
$773$	25.6183	0.921426	0.460713	+	0.887549i	$0.347594\pi$
$774$	−1.87154	−0.0672712
$775$	18.5166	0.665137
$776$	3.23060	0.115972
$777$	−40.7953	−1.46352
$778$	−10.1988	−0.365645
$779$	3.91997	0.140448
$780$	0	0
$781$	−8.49886	−0.304113
$782$	−1.10134	−0.0393840
$783$	−6.58571	−0.235354
$784$	60.0585	2.14495
$785$	44.8009	1.59901
$786$	1.30274	0.0464673
$787$	23.3425	0.832070	0.416035	−	0.909349i	$-0.363419\pi$
$787$	23.3425	0.832070	0.416035	+	0.909349i	$0.363419\pi$
$788$	−30.6822	−1.09301
$789$	−0.914614	−0.0325611
$790$	−15.0955	−0.537074
$791$	11.5369	0.410204
$792$	−1.56782	−0.0557101
$793$	0	0
$794$	−12.8148	−0.454781
$795$	35.8763	1.27240
$796$	−24.1128	−0.854656
$797$	−49.4116	−1.75025	−0.875125	−	0.483897i	$-0.839221\pi$
$797$	−49.4116	−1.75025	−0.875125	+	0.483897i	$0.839221\pi$
$798$	−0.945942	−0.0334860
$799$	−2.64932	−0.0937261
$800$	53.0652	1.87614
$801$	−4.68461	−0.165523
$802$	3.66030	0.129250
$803$	5.95291	0.210074
$804$	7.10091	0.250430
$805$	118.187	4.16553
$806$	0	0
$807$	13.1384	0.462495
$808$	−6.06058	−0.213210
$809$	22.7489	0.799810	0.399905	−	0.916556i	$-0.369043\pi$
$809$	22.7489	0.799810	0.399905	+	0.916556i	$0.369043\pi$
$810$	1.69335	0.0594982
$811$	−23.4289	−0.822701	−0.411350	−	0.911477i	$-0.634943\pi$
$811$	−23.4289	−0.822701	−0.411350	+	0.911477i	$0.634943\pi$
$812$	62.5524	2.19516
$813$	−12.3173	−0.431987
$814$	−3.21993	−0.112859
$815$	−101.300	−3.54838
$816$	−1.47791	−0.0517372
$817$	2.04133	0.0714173
$818$	−12.3103	−0.430418
$819$	0	0
$820$	66.6510	2.32755
$821$	−6.75303	−0.235682	−0.117841	−	0.993032i	$-0.537597\pi$
$821$	−6.75303	−0.235682	−0.117841	+	0.993032i	$0.537597\pi$
$822$	−2.09366	−0.0730248
$823$	−36.4194	−1.26950	−0.634751	−	0.772717i	$-0.718897\pi$
$823$	−36.4194	−1.26950	−0.634751	+	0.772717i	$0.718897\pi$
$824$	−0.550113	−0.0191641
$825$	12.1357	0.422511
$826$	11.8830	0.413461
$827$	−49.2124	−1.71128	−0.855642	−	0.517569i	$-0.826837\pi$
$827$	−49.2124	−1.71128	−0.855642	+	0.517569i	$0.826837\pi$
$828$	−10.0958	−0.350854
$829$	2.84332	0.0987525	0.0493762	−	0.998780i	$-0.484277\pi$
$829$	2.84332	0.0987525	0.0493762	+	0.998780i	$0.484277\pi$
$830$	0.774699	0.0268902
$831$	−20.1395	−0.698630
$832$	0	0
$833$	−9.70653	−0.336311
$834$	−4.40623	−0.152575
$835$	−5.24569	−0.181535
$836$	0.817698	0.0282807
$837$	1.52580	0.0527393
$838$	13.3571	0.461413
$839$	8.15579	0.281569	0.140785	−	0.990040i	$-0.455038\pi$
$839$	8.15579	0.281569	0.140785	+	0.990040i	$0.455038\pi$
$840$	−33.6361	−1.16056
$841$	14.3716	0.495571
$842$	−11.6157	−0.400304
$843$	−6.66666	−0.229612
$844$	−24.8613	−0.855761
$845$	0	0
$846$	2.21748	0.0762387
$847$	5.18273	0.178081
$848$	26.2081	0.899991
$849$	27.5589	0.945818
$850$	−2.42622	−0.0832185
$851$	−43.3621	−1.48643
$852$	15.5755	0.533609
$853$	12.7020	0.434910	0.217455	−	0.976070i	$-0.430225\pi$
$853$	12.7020	0.434910	0.217455	+	0.976070i	$0.430225\pi$
$854$	−1.81432	−0.0620848
$855$	−1.84697	−0.0631652
$856$	19.7226	0.674105
$857$	−50.4563	−1.72355	−0.861777	−	0.507287i	$-0.830648\pi$
$857$	−50.4563	−1.72355	−0.861777	+	0.507287i	$0.830648\pi$
$858$	0	0
$859$	−8.22512	−0.280637	−0.140319	−	0.990106i	$-0.544813\pi$
$859$	−8.22512	−0.280637	−0.140319	+	0.990106i	$0.544813\pi$
$860$	34.7087	1.18356
$861$	−45.5336	−1.55178
$862$	5.79180	0.197269
$863$	−15.2200	−0.518094	−0.259047	−	0.965865i	$-0.583408\pi$
$863$	−15.2200	−0.518094	−0.259047	+	0.965865i	$0.583408\pi$
$864$	4.37265	0.148761
$865$	13.4385	0.456923
$866$	6.38063	0.216823
$867$	−16.7611	−0.569238
$868$	−14.4923	−0.491902
$869$	−8.91459	−0.302407
$870$	−11.1519	−0.378085
$871$	0	0
$872$	7.23487	0.245003
$873$	−2.06057	−0.0697396
$874$	−1.00546	−0.0340102
$875$	153.090	5.17538
$876$	−10.9097	−0.368604
$877$	−16.0542	−0.542113	−0.271057	−	0.962563i	$-0.587373\pi$
$877$	−16.0542	−0.542113	−0.271057	+	0.962563i	$0.587373\pi$
$878$	6.57029	0.221737
$879$	−13.8127	−0.465890
$880$	12.5179	0.421977
$881$	51.9810	1.75128	0.875642	−	0.482961i	$-0.160439\pi$
$881$	51.9810	1.75128	0.875642	+	0.482961i	$0.160439\pi$
$882$	8.12439	0.273562
$883$	−21.5188	−0.724164	−0.362082	−	0.932146i	$-0.617934\pi$
$883$	−21.5188	−0.724164	−0.362082	+	0.932146i	$0.617934\pi$
$884$	0	0
$885$	23.2018	0.779919
$886$	−3.35777	−0.112806
$887$	−18.2083	−0.611376	−0.305688	−	0.952132i	$-0.598887\pi$
$887$	−18.2083	−0.611376	−0.305688	+	0.952132i	$0.598887\pi$
$888$	12.3409	0.414134
$889$	−94.5993	−3.17276
$890$	−7.93269	−0.265904
$891$	1.00000	0.0335013
$892$	−21.7584	−0.728524
$893$	−2.41866	−0.0809374
$894$	1.80898	0.0605014
$895$	−68.4275	−2.28728
$896$	−54.3546	−1.81586
$897$	0	0
$898$	4.26676	0.142384
$899$	−10.0485	−0.335135
$900$	−22.2407	−0.741355
$901$	−4.23571	−0.141112
$902$	−3.59392	−0.119665
$903$	−23.7117	−0.789077
$904$	−3.49000	−0.116076
$905$	50.5292	1.67965
$906$	−1.89813	−0.0630612
$907$	−6.58414	−0.218623	−0.109311	−	0.994008i	$-0.534865\pi$
$907$	−6.58414	−0.218623	−0.109311	+	0.994008i	$0.534865\pi$
$908$	23.8713	0.792198
$909$	3.86561	0.128214
$910$	0	0
$911$	−51.4764	−1.70549	−0.852745	−	0.522328i	$-0.825064\pi$
$911$	−51.4764	−1.70549	−0.852745	+	0.522328i	$0.825064\pi$
$912$	−1.34924	−0.0446778
$913$	0.457495	0.0151409
$914$	−7.41397	−0.245232
$915$	−3.54251	−0.117112
$916$	−11.8366	−0.391091
$917$	16.5052	0.545051
$918$	−0.199924	−0.00659847
$919$	−31.1301	−1.02689	−0.513443	−	0.858123i	$-0.671630\pi$
$919$	−31.1301	−1.02689	−0.513443	+	0.858123i	$0.671630\pi$
$920$	−35.7525	−1.17872
$921$	21.0868	0.694833
$922$	11.7093	0.385624
$923$	0	0
$924$	−9.49821	−0.312468
$925$	−95.5248	−3.14084
$926$	−3.86551	−0.127029
$927$	0.350877	0.0115243
$928$	−28.7970	−0.945309
$929$	54.5430	1.78950	0.894749	−	0.446569i	$-0.147354\pi$
$929$	54.5430	1.78950	0.894749	+	0.446569i	$0.147354\pi$
$930$	2.58371	0.0847231
$931$	−8.86146	−0.290423
$932$	24.3040	0.796104
$933$	−29.7858	−0.975142
$934$	7.83051	0.256222
$935$	−2.02311	−0.0661628
$936$	0	0
$937$	−36.4863	−1.19195	−0.595977	−	0.803001i	$-0.703235\pi$
$937$	−36.4863	−1.19195	−0.595977	+	0.803001i	$0.703235\pi$
$938$	−8.21459	−0.268216
$939$	26.3709	0.860583
$940$	−41.1243	−1.34133
$941$	6.77293	0.220791	0.110396	−	0.993888i	$-0.464788\pi$
$941$	6.77293	0.220791	0.110396	+	0.993888i	$0.464788\pi$
$942$	4.42722	0.144247
$943$	−48.3985	−1.57607
$944$	16.9492	0.551650
$945$	21.4541	0.697901
$946$	−1.87154	−0.0608491
$947$	−4.44833	−0.144551	−0.0722756	−	0.997385i	$-0.523026\pi$
$947$	−4.44833	−0.144551	−0.0722756	+	0.997385i	$0.523026\pi$
$948$	16.3374	0.530616
$949$	0	0
$950$	−2.21498	−0.0718636
$951$	24.5073	0.794703
$952$	3.97122	0.128708
$953$	−52.2252	−1.69174	−0.845870	−	0.533389i	$-0.820918\pi$
$953$	−52.2252	−1.69174	−0.845870	+	0.533389i	$0.820918\pi$
$954$	3.54530	0.114783
$955$	−72.1977	−2.33626
$956$	−0.780789	−0.0252525
$957$	−6.58571	−0.212886
$958$	4.72201	0.152561
$959$	−26.5259	−0.856565
$960$	−17.6313	−0.569047
$961$	−28.6719	−0.924901
$962$	0	0
$963$	−12.5796	−0.405373
$964$	−23.7990	−0.766514
$965$	−3.89736	−0.125460
$966$	11.6792	0.375772
$967$	24.6459	0.792559	0.396279	−	0.918130i	$-0.370301\pi$
$967$	24.6459	0.792559	0.396279	+	0.918130i	$0.370301\pi$
$968$	−1.56782	−0.0503917
$969$	0.218061	0.00700514
$970$	−3.48926	−0.112033
$971$	16.6242	0.533495	0.266748	−	0.963766i	$-0.414051\pi$
$971$	16.6242	0.533495	0.266748	+	0.963766i	$0.414051\pi$
$972$	−1.83266	−0.0587827
$973$	−55.8252	−1.78967
$974$	14.2077	0.455243
$975$	0	0
$976$	−2.58785	−0.0828350
$977$	−11.6096	−0.371425	−0.185712	−	0.982604i	$-0.559459\pi$
$977$	−11.6096	−0.371425	−0.185712	+	0.982604i	$0.559459\pi$
$978$	−10.0105	−0.320099
$979$	−4.68461	−0.149721
$980$	−150.671	−4.81300
$981$	−4.61460	−0.147333
$982$	8.17871	0.260993
$983$	58.4986	1.86582	0.932908	−	0.360114i	$-0.117262\pi$
$983$	58.4986	1.86582	0.932908	+	0.360114i	$0.117262\pi$
$984$	13.7743	0.439108
$985$	69.3034	2.20819
$986$	1.31664	0.0419304
$987$	28.0947	0.894263
$988$	0	0
$989$	−25.2036	−0.801429
$990$	1.69335	0.0538182
$991$	24.4396	0.776350	0.388175	−	0.921586i	$-0.373106\pi$
$991$	24.4396	0.776350	0.388175	+	0.921586i	$0.373106\pi$
$992$	6.67178	0.211829
$993$	10.4965	0.333096
$994$	−18.0184	−0.571508
$995$	54.4649	1.72665
$996$	−0.838434	−0.0265668
$997$	−36.4681	−1.15496	−0.577478	−	0.816406i	$-0.695963\pi$
$997$	−36.4681	−1.15496	−0.577478	+	0.816406i	$0.695963\pi$
$998$	−4.23653	−0.134105
$999$	−7.87139	−0.249040

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.y.1.4		7
13.5	odd	4		429.2.b.b.298.7	✓	14
13.8	odd	4		429.2.b.b.298.8	yes	14
13.12	even	2		5577.2.a.x.1.4		7
39.5	even	4		1287.2.b.c.298.8		14
39.8	even	4		1287.2.b.c.298.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.b.b.298.7	✓	14	13.5	odd	4
429.2.b.b.298.8	yes	14	13.8	odd	4
1287.2.b.c.298.7		14	39.8	even	4
1287.2.b.c.298.8		14	39.5	even	4
5577.2.a.x.1.4		7	13.12	even	2
5577.2.a.y.1.4		7	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:	\( N \)	\(=\)	\( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5577.a (trivial)

\(f(q)\)	\(=\)	\(q+0.409068 q^{2} +1.00000 q^{3} -1.83266 q^{4} +4.13953 q^{5} +0.409068 q^{6} +5.18273 q^{7} -1.56782 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.409068 q^{2} +1.00000 q^{3} -1.83266 q^{4} +4.13953 q^{5} +0.409068 q^{6} +5.18273 q^{7} -1.56782 q^{8} +1.00000 q^{9} +1.69335 q^{10} +1.00000 q^{11} -1.83266 q^{12} +2.12009 q^{14} +4.13953 q^{15} +3.02398 q^{16} -0.488730 q^{17} +0.409068 q^{18} -0.446180 q^{19} -7.58636 q^{20} +5.18273 q^{21} +0.409068 q^{22} +5.50882 q^{23} -1.56782 q^{24} +12.1357 q^{25} +1.00000 q^{27} -9.49821 q^{28} -6.58571 q^{29} +1.69335 q^{30} +1.52580 q^{31} +4.37265 q^{32} +1.00000 q^{33} -0.199924 q^{34} +21.4541 q^{35} -1.83266 q^{36} -7.87139 q^{37} -0.182518 q^{38} -6.49004 q^{40} -8.78563 q^{41} +2.12009 q^{42} -4.57514 q^{43} -1.83266 q^{44} +4.13953 q^{45} +2.25348 q^{46} +5.42082 q^{47} +3.02398 q^{48} +19.8607 q^{49} +4.96433 q^{50} -0.488730 q^{51} +8.66677 q^{53} +0.409068 q^{54} +4.13953 q^{55} -8.12559 q^{56} -0.446180 q^{57} -2.69400 q^{58} +5.60493 q^{59} -7.58636 q^{60} -0.855775 q^{61} +0.624155 q^{62} +5.18273 q^{63} -4.25925 q^{64} +0.409068 q^{66} -3.87464 q^{67} +0.895677 q^{68} +5.50882 q^{69} +8.77618 q^{70} -8.49886 q^{71} -1.56782 q^{72} +5.95291 q^{73} -3.21993 q^{74} +12.1357 q^{75} +0.817698 q^{76} +5.18273 q^{77} -8.91459 q^{79} +12.5179 q^{80} +1.00000 q^{81} -3.59392 q^{82} +0.457495 q^{83} -9.49821 q^{84} -2.02311 q^{85} -1.87154 q^{86} -6.58571 q^{87} -1.56782 q^{88} -4.68461 q^{89} +1.69335 q^{90} -10.0958 q^{92} +1.52580 q^{93} +2.21748 q^{94} -1.84697 q^{95} +4.37265 q^{96} -2.06057 q^{97} +8.12439 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} + 7 q^{3} + 9 q^{4} + 6 q^{5} + 3 q^{6} + 6 q^{7} + 15 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 3 * q^2 + 7 * q^3 + 9 * q^4 + 6 * q^5 + 3 * q^6 + 6 * q^7 + 15 * q^8 + 7 * q^9	\( 7 q + 3 q^{2} + 7 q^{3} + 9 q^{4} + 6 q^{5} + 3 q^{6} + 6 q^{7} + 15 q^{8} + 7 q^{9} + 7 q^{11} + 9 q^{12} + 8 q^{14} + 6 q^{15} + 17 q^{16} - 2 q^{17} + 3 q^{18} + 8 q^{19} - 2 q^{20} + 6 q^{21} + 3 q^{22} + 4 q^{23} + 15 q^{24} + 13 q^{25} + 7 q^{27} + 12 q^{28} - 12 q^{29} - 10 q^{31} + 33 q^{32} + 7 q^{33} + 28 q^{34} - 4 q^{35} + 9 q^{36} + 6 q^{37} + 16 q^{38} - 10 q^{40} + 2 q^{41} + 8 q^{42} - 16 q^{43} + 9 q^{44} + 6 q^{45} - 26 q^{46} + 18 q^{47} + 17 q^{48} + 23 q^{49} + 39 q^{50} - 2 q^{51} + 10 q^{53} + 3 q^{54} + 6 q^{55} + 16 q^{56} + 8 q^{57} + 10 q^{58} + 2 q^{59} - 2 q^{60} - 10 q^{61} - 36 q^{62} + 6 q^{63} + 29 q^{64} + 3 q^{66} + 8 q^{67} - 10 q^{68} + 4 q^{69} - 20 q^{70} + 36 q^{71} + 15 q^{72} + 20 q^{73} + 13 q^{75} + 10 q^{76} + 6 q^{77} + 6 q^{79} - 20 q^{80} + 7 q^{81} - 10 q^{82} + 30 q^{83} + 12 q^{84} - 40 q^{85} + 6 q^{86} - 12 q^{87} + 15 q^{88} + 34 q^{89} - 12 q^{92} - 10 q^{93} + 32 q^{94} + 18 q^{95} + 33 q^{96} + 16 q^{97} + q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 + 7 * q^3 + 9 * q^4 + 6 * q^5 + 3 * q^6 + 6 * q^7 + 15 * q^8 + 7 * q^9 + 7 * q^11 + 9 * q^12 + 8 * q^14 + 6 * q^15 + 17 * q^16 - 2 * q^17 + 3 * q^18 + 8 * q^19 - 2 * q^20 + 6 * q^21 + 3 * q^22 + 4 * q^23 + 15 * q^24 + 13 * q^25 + 7 * q^27 + 12 * q^28 - 12 * q^29 - 10 * q^31 + 33 * q^32 + 7 * q^33 + 28 * q^34 - 4 * q^35 + 9 * q^36 + 6 * q^37 + 16 * q^38 - 10 * q^40 + 2 * q^41 + 8 * q^42 - 16 * q^43 + 9 * q^44 + 6 * q^45 - 26 * q^46 + 18 * q^47 + 17 * q^48 + 23 * q^49 + 39 * q^50 - 2 * q^51 + 10 * q^53 + 3 * q^54 + 6 * q^55 + 16 * q^56 + 8 * q^57 + 10 * q^58 + 2 * q^59 - 2 * q^60 - 10 * q^61 - 36 * q^62 + 6 * q^63 + 29 * q^64 + 3 * q^66 + 8 * q^67 - 10 * q^68 + 4 * q^69 - 20 * q^70 + 36 * q^71 + 15 * q^72 + 20 * q^73 + 13 * q^75 + 10 * q^76 + 6 * q^77 + 6 * q^79 - 20 * q^80 + 7 * q^81 - 10 * q^82 + 30 * q^83 + 12 * q^84 - 40 * q^85 + 6 * q^86 - 12 * q^87 + 15 * q^88 + 34 * q^89 - 12 * q^92 - 10 * q^93 + 32 * q^94 + 18 * q^95 + 33 * q^96 + 16 * q^97 + q^98 + 7 * q^99

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