LMFDB - Embedded newform 5577.2.a.x.1.2

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:	$1$
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			1.2
Root			$2.53441$ 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)

$f(q)$	$=$	$q-2.53441 q^{2} +1.00000 q^{3} +4.42325 q^{4} -3.70100 q^{5} -2.53441 q^{6} +0.957295 q^{7} -6.14151 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.53441 q^{2} +1.00000 q^{3} +4.42325 q^{4} -3.70100 q^{5} -2.53441 q^{6} +0.957295 q^{7} -6.14151 q^{8} +1.00000 q^{9} +9.37985 q^{10} -1.00000 q^{11} +4.42325 q^{12} -2.42618 q^{14} -3.70100 q^{15} +6.71863 q^{16} -2.05542 q^{17} -2.53441 q^{18} -7.67886 q^{19} -16.3704 q^{20} +0.957295 q^{21} +2.53441 q^{22} -4.20997 q^{23} -6.14151 q^{24} +8.69737 q^{25} +1.00000 q^{27} +4.23435 q^{28} +1.97786 q^{29} +9.37985 q^{30} +10.5475 q^{31} -4.74476 q^{32} -1.00000 q^{33} +5.20928 q^{34} -3.54294 q^{35} +4.42325 q^{36} +8.30741 q^{37} +19.4614 q^{38} +22.7297 q^{40} +5.23142 q^{41} -2.42618 q^{42} +5.26116 q^{43} -4.42325 q^{44} -3.70100 q^{45} +10.6698 q^{46} +1.24656 q^{47} +6.71863 q^{48} -6.08359 q^{49} -22.0427 q^{50} -2.05542 q^{51} +2.98297 q^{53} -2.53441 q^{54} +3.70100 q^{55} -5.87924 q^{56} -7.67886 q^{57} -5.01271 q^{58} +12.3548 q^{59} -16.3704 q^{60} -0.183851 q^{61} -26.7317 q^{62} +0.957295 q^{63} -1.41208 q^{64} +2.53441 q^{66} -1.40691 q^{67} -9.09163 q^{68} -4.20997 q^{69} +8.97928 q^{70} -12.1582 q^{71} -6.14151 q^{72} +3.32573 q^{73} -21.0544 q^{74} +8.69737 q^{75} -33.9655 q^{76} -0.957295 q^{77} -3.64911 q^{79} -24.8656 q^{80} +1.00000 q^{81} -13.2586 q^{82} -3.31957 q^{83} +4.23435 q^{84} +7.60710 q^{85} -13.3340 q^{86} +1.97786 q^{87} +6.14151 q^{88} -5.24302 q^{89} +9.37985 q^{90} -18.6217 q^{92} +10.5475 q^{93} -3.15929 q^{94} +28.4194 q^{95} -4.74476 q^{96} -9.82293 q^{97} +15.4183 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.53441	−1.79210	−0.896050	−	0.443953i	$-0.853576\pi$
$2$	−2.53441	−1.79210	−0.896050	+	0.443953i	$0.853576\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.42325	2.21162
$5$	−3.70100	−1.65514	−0.827568	−	0.561366i	$-0.810276\pi$
$5$	−3.70100	−1.65514	−0.827568	+	0.561366i	$0.810276\pi$
$6$	−2.53441	−1.03467
$7$	0.957295	0.361823	0.180912	−	0.983499i	$-0.442095\pi$
$7$	0.957295	0.361823	0.180912	+	0.983499i	$0.442095\pi$
$8$	−6.14151	−2.17135
$9$	1.00000	0.333333
$10$	9.37985	2.96617
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	4.42325	1.27688
$13$	0	0
$13$	0	0
$14$	−2.42618	−0.648424
$15$	−3.70100	−0.955593
$16$	6.71863	1.67966
$17$	−2.05542	−0.498512	−0.249256	−	0.968438i	$-0.580186\pi$
$17$	−2.05542	−0.498512	−0.249256	+	0.968438i	$0.580186\pi$
$18$	−2.53441	−0.597367
$19$	−7.67886	−1.76165	−0.880825	−	0.473442i	$-0.843012\pi$
$19$	−7.67886	−1.76165	−0.880825	+	0.473442i	$0.843012\pi$
$20$	−16.3704	−3.66054
$21$	0.957295	0.208899
$22$	2.53441	0.540339
$23$	−4.20997	−0.877840	−0.438920	−	0.898526i	$-0.644639\pi$
$23$	−4.20997	−0.877840	−0.438920	+	0.898526i	$0.644639\pi$
$24$	−6.14151	−1.25363
$25$	8.69737	1.73947
$26$	0	0
$27$	1.00000	0.192450
$28$	4.23435	0.800217
$29$	1.97786	0.367279	0.183640	−	0.982994i	$-0.441212\pi$
$29$	1.97786	0.367279	0.183640	+	0.982994i	$0.441212\pi$
$30$	9.37985	1.71252
$31$	10.5475	1.89439	0.947193	−	0.320664i	$-0.103906\pi$
$31$	10.5475	1.89439	0.947193	+	0.320664i	$0.103906\pi$
$32$	−4.74476	−0.838763
$33$	−1.00000	−0.174078
$34$	5.20928	0.893384
$35$	−3.54294	−0.598867
$36$	4.42325	0.737208
$37$	8.30741	1.36573	0.682865	−	0.730545i	$-0.260734\pi$
$37$	8.30741	1.36573	0.682865	+	0.730545i	$0.260734\pi$
$38$	19.4614	3.15705
$39$	0	0
$40$	22.7297	3.59388
$41$	5.23142	0.817011	0.408505	−	0.912756i	$-0.366050\pi$
$41$	5.23142	0.817011	0.408505	+	0.912756i	$0.366050\pi$
$42$	−2.42618	−0.374368
$43$	5.26116	0.802320	0.401160	−	0.916008i	$-0.368607\pi$
$43$	5.26116	0.802320	0.401160	+	0.916008i	$0.368607\pi$
$44$	−4.42325	−0.666830
$45$	−3.70100	−0.551712
$46$	10.6698	1.57318
$47$	1.24656	0.181829	0.0909145	−	0.995859i	$-0.471021\pi$
$47$	1.24656	0.181829	0.0909145	+	0.995859i	$0.471021\pi$
$48$	6.71863	0.969751
$49$	−6.08359	−0.869084
$50$	−22.0427	−3.11731
$51$	−2.05542	−0.287816
$52$	0	0
$53$	2.98297	0.409743	0.204871	−	0.978789i	$-0.434322\pi$
$53$	2.98297	0.409743	0.204871	+	0.978789i	$0.434322\pi$
$54$	−2.53441	−0.344890
$55$	3.70100	0.499042
$56$	−5.87924	−0.785646
$57$	−7.67886	−1.01709
$58$	−5.01271	−0.658202
$59$	12.3548	1.60846	0.804228	−	0.594321i	$-0.202579\pi$
$59$	12.3548	1.60846	0.804228	+	0.594321i	$0.202579\pi$
$60$	−16.3704	−2.11341
$61$	−0.183851	−0.0235397	−0.0117698	−	0.999931i	$-0.503747\pi$
$61$	−0.183851	−0.0235397	−0.0117698	+	0.999931i	$0.503747\pi$
$62$	−26.7317	−3.39493
$63$	0.957295	0.120608
$64$	−1.41208	−0.176510
$65$	0	0
$66$	2.53441	0.311965
$67$	−1.40691	−0.171881	−0.0859407	−	0.996300i	$-0.527390\pi$
$67$	−1.40691	−0.171881	−0.0859407	+	0.996300i	$0.527390\pi$
$68$	−9.09163	−1.10252
$69$	−4.20997	−0.506821
$70$	8.97928	1.07323
$71$	−12.1582	−1.44291	−0.721457	−	0.692459i	$-0.756527\pi$
$71$	−12.1582	−1.44291	−0.721457	+	0.692459i	$0.756527\pi$
$72$	−6.14151	−0.723784
$73$	3.32573	0.389247	0.194624	−	0.980878i	$-0.437651\pi$
$73$	3.32573	0.389247	0.194624	+	0.980878i	$0.437651\pi$
$74$	−21.0544	−2.44752
$75$	8.69737	1.00429
$76$	−33.9655	−3.89611
$77$	−0.957295	−0.109094
$78$	0	0
$79$	−3.64911	−0.410557	−0.205279	−	0.978704i	$-0.565810\pi$
$79$	−3.64911	−0.410557	−0.205279	+	0.978704i	$0.565810\pi$
$80$	−24.8656	−2.78006
$81$	1.00000	0.111111
$82$	−13.2586	−1.46417
$83$	−3.31957	−0.364370	−0.182185	−	0.983264i	$-0.558317\pi$
$83$	−3.31957	−0.364370	−0.182185	+	0.983264i	$0.558317\pi$
$84$	4.23435	0.462006
$85$	7.60710	0.825106
$86$	−13.3340	−1.43784
$87$	1.97786	0.212049
$88$	6.14151	0.654687
$89$	−5.24302	−0.555759	−0.277879	−	0.960616i	$-0.589632\pi$
$89$	−5.24302	−0.555759	−0.277879	+	0.960616i	$0.589632\pi$
$90$	9.37985	0.988723
$91$	0	0
$92$	−18.6217	−1.94145
$93$	10.5475	1.09372
$94$	−3.15929	−0.325856
$95$	28.4194	2.91577
$96$	−4.74476	−0.484260
$97$	−9.82293	−0.997368	−0.498684	−	0.866784i	$-0.666183\pi$
$97$	−9.82293	−0.997368	−0.498684	+	0.866784i	$0.666183\pi$
$98$	15.4183	1.55749
$99$	−1.00000	−0.100504
$100$	38.4706	3.84706
$101$	−8.42338	−0.838157	−0.419079	−	0.907950i	$-0.637647\pi$
$101$	−8.42338	−0.838157	−0.419079	+	0.907950i	$0.637647\pi$
$102$	5.20928	0.515796
$103$	−13.4029	−1.32063	−0.660314	−	0.750989i	$-0.729577\pi$
$103$	−13.4029	−1.32063	−0.660314	+	0.750989i	$0.729577\pi$
$104$	0	0
$105$	−3.54294	−0.345756
$106$	−7.56008	−0.734300
$107$	−8.05792	−0.778988	−0.389494	−	0.921029i	$-0.627350\pi$
$107$	−8.05792	−0.778988	−0.389494	+	0.921029i	$0.627350\pi$
$108$	4.42325	0.425627
$109$	14.3600	1.37544	0.687720	−	0.725976i	$-0.258612\pi$
$109$	14.3600	1.37544	0.687720	+	0.725976i	$0.258612\pi$
$110$	−9.37985	−0.894334
$111$	8.30741	0.788504
$112$	6.43171	0.607739
$113$	18.6675	1.75609	0.878046	−	0.478577i	$-0.158847\pi$
$113$	18.6675	1.75609	0.878046	+	0.478577i	$0.158847\pi$
$114$	19.4614	1.82273
$115$	15.5811	1.45294
$116$	8.74857	0.812284
$117$	0	0
$118$	−31.3121	−2.88251
$119$	−1.96764	−0.180373
$120$	22.7297	2.07493
$121$	1.00000	0.0909091
$122$	0.465954	0.0421855
$123$	5.23142	0.471701
$124$	46.6542	4.18967
$125$	−13.6840	−1.22393
$126$	−2.42618	−0.216141
$127$	6.60130	0.585770	0.292885	−	0.956148i	$-0.405385\pi$
$127$	6.60130	0.585770	0.292885	+	0.956148i	$0.405385\pi$
$128$	13.0683	1.15509
$129$	5.26116	0.463220
$130$	0	0
$131$	5.81083	0.507694	0.253847	−	0.967244i	$-0.418304\pi$
$131$	5.81083	0.507694	0.253847	+	0.967244i	$0.418304\pi$
$132$	−4.42325	−0.384994
$133$	−7.35093	−0.637406
$134$	3.56569	0.308029
$135$	−3.70100	−0.318531
$136$	12.6234	1.08245
$137$	−5.64208	−0.482035	−0.241018	−	0.970521i	$-0.577481\pi$
$137$	−5.64208	−0.482035	−0.241018	+	0.970521i	$0.577481\pi$
$138$	10.6698	0.908274
$139$	−4.46820	−0.378987	−0.189494	−	0.981882i	$-0.560685\pi$
$139$	−4.46820	−0.378987	−0.189494	+	0.981882i	$0.560685\pi$
$140$	−15.6713	−1.32447
$141$	1.24656	0.104979
$142$	30.8139	2.58585
$143$	0	0
$144$	6.71863	0.559886
$145$	−7.32005	−0.607897
$146$	−8.42877	−0.697570
$147$	−6.08359	−0.501766
$148$	36.7457	3.02048
$149$	7.39749	0.606026	0.303013	−	0.952986i	$-0.402007\pi$
$149$	7.39749	0.606026	0.303013	+	0.952986i	$0.402007\pi$
$150$	−22.0427	−1.79978
$151$	−23.7454	−1.93237	−0.966187	−	0.257841i	$-0.916989\pi$
$151$	−23.7454	−1.93237	−0.966187	+	0.257841i	$0.916989\pi$
$152$	47.1598	3.82516
$153$	−2.05542	−0.166171
$154$	2.42618	0.195507
$155$	−39.0362	−3.13547
$156$	0	0
$157$	12.9704	1.03515	0.517576	−	0.855637i	$-0.326834\pi$
$157$	12.9704	1.03515	0.517576	+	0.855637i	$0.326834\pi$
$158$	9.24836	0.735760
$159$	2.98297	0.236565
$160$	17.5603	1.38827
$161$	−4.03018	−0.317623
$162$	−2.53441	−0.199122
$163$	−18.6880	−1.46376	−0.731878	−	0.681436i	$-0.761356\pi$
$163$	−18.6880	−1.46376	−0.731878	+	0.681436i	$0.761356\pi$
$164$	23.1399	1.80692
$165$	3.70100	0.288122
$166$	8.41316	0.652988
$167$	−25.0420	−1.93781	−0.968904	−	0.247437i	$-0.920412\pi$
$167$	−25.0420	−1.93781	−0.968904	+	0.247437i	$0.920412\pi$
$168$	−5.87924	−0.453593
$169$	0	0
$170$	−19.2795	−1.47867
$171$	−7.67886	−0.587217
$172$	23.2714	1.77443
$173$	−3.16333	−0.240503	−0.120252	−	0.992743i	$-0.538370\pi$
$173$	−3.16333	−0.240503	−0.120252	+	0.992743i	$0.538370\pi$
$174$	−5.01271	−0.380013
$175$	8.32595	0.629383
$176$	−6.71863	−0.506436
$177$	12.3548	0.928642
$178$	13.2880	0.995976
$179$	1.24977	0.0934123	0.0467062	−	0.998909i	$-0.485128\pi$
$179$	1.24977	0.0934123	0.0467062	+	0.998909i	$0.485128\pi$
$180$	−16.3704	−1.22018
$181$	16.0712	1.19456	0.597281	−	0.802032i	$-0.296248\pi$
$181$	16.0712	1.19456	0.597281	+	0.802032i	$0.296248\pi$
$182$	0	0
$183$	−0.183851	−0.0135906
$184$	25.8556	1.90610
$185$	−30.7457	−2.26047
$186$	−26.7317	−1.96006
$187$	2.05542	0.150307
$188$	5.51383	0.402137
$189$	0.957295	0.0696329
$190$	−72.0265	−5.22535
$191$	15.2909	1.10641	0.553207	−	0.833044i	$-0.313404\pi$
$191$	15.2909	1.10641	0.553207	+	0.833044i	$0.313404\pi$
$192$	−1.41208	−0.101908
$193$	−6.76152	−0.486705	−0.243353	−	0.969938i	$-0.578247\pi$
$193$	−6.76152	−0.486705	−0.243353	+	0.969938i	$0.578247\pi$
$194$	24.8954	1.78738
$195$	0	0
$196$	−26.9092	−1.92209
$197$	11.3320	0.807374	0.403687	−	0.914897i	$-0.367728\pi$
$197$	11.3320	0.807374	0.403687	+	0.914897i	$0.367728\pi$
$198$	2.53441	0.180113
$199$	21.5642	1.52864	0.764321	−	0.644836i	$-0.223074\pi$
$199$	21.5642	1.52864	0.764321	+	0.644836i	$0.223074\pi$
$200$	−53.4150	−3.77701
$201$	−1.40691	−0.0992358
$202$	21.3483	1.50206
$203$	1.89339	0.132890
$204$	−9.09163	−0.636541
$205$	−19.3615	−1.35226
$206$	33.9685	2.36670
$207$	−4.20997	−0.292613
$208$	0	0
$209$	7.67886	0.531158
$210$	8.97928	0.619629
$211$	−23.5992	−1.62463	−0.812317	−	0.583217i	$-0.801794\pi$
$211$	−23.5992	−1.62463	−0.812317	+	0.583217i	$0.801794\pi$
$212$	13.1944	0.906197
$213$	−12.1582	−0.833067
$214$	20.4221	1.39603
$215$	−19.4715	−1.32795
$216$	−6.14151	−0.417877
$217$	10.0971	0.685433
$218$	−36.3942	−2.46493
$219$	3.32573	0.224732
$220$	16.3704	1.10369
$221$	0	0
$222$	−21.0544	−1.41308
$223$	14.7201	0.985730	0.492865	−	0.870106i	$-0.335950\pi$
$223$	14.7201	0.985730	0.492865	+	0.870106i	$0.335950\pi$
$224$	−4.54213	−0.303484
$225$	8.69737	0.579825
$226$	−47.3112	−3.14709
$227$	−0.0358913	−0.00238219	−0.00119109	−	0.999999i	$-0.500379\pi$
$227$	−0.0358913	−0.00238219	−0.00119109	+	0.999999i	$0.500379\pi$
$228$	−33.9655	−2.24942
$229$	−8.37257	−0.553275	−0.276637	−	0.960974i	$-0.589220\pi$
$229$	−8.37257	−0.553275	−0.276637	+	0.960974i	$0.589220\pi$
$230$	−39.4889	−2.60382
$231$	−0.957295	−0.0629854
$232$	−12.1471	−0.797493
$233$	−18.0020	−1.17935	−0.589674	−	0.807641i	$-0.700744\pi$
$233$	−18.0020	−1.17935	−0.589674	+	0.807641i	$0.700744\pi$
$234$	0	0
$235$	−4.61350	−0.300952
$236$	54.6483	3.55730
$237$	−3.64911	−0.237035
$238$	4.98682	0.323247
$239$	5.74497	0.371611	0.185806	−	0.982587i	$-0.440511\pi$
$239$	5.74497	0.371611	0.185806	+	0.982587i	$0.440511\pi$
$240$	−24.8656	−1.60507
$241$	16.1458	1.04004	0.520022	−	0.854153i	$-0.325924\pi$
$241$	16.1458	1.04004	0.520022	+	0.854153i	$0.325924\pi$
$242$	−2.53441	−0.162918
$243$	1.00000	0.0641500
$244$	−0.813218	−0.0520609
$245$	22.5153	1.43845
$246$	−13.2586	−0.845336
$247$	0	0
$248$	−64.7776	−4.11338
$249$	−3.31957	−0.210369
$250$	34.6808	2.19341
$251$	−6.83631	−0.431504	−0.215752	−	0.976448i	$-0.569220\pi$
$251$	−6.83631	−0.431504	−0.215752	+	0.976448i	$0.569220\pi$
$252$	4.23435	0.266739
$253$	4.20997	0.264679
$254$	−16.7304	−1.04976
$255$	7.60710	0.476375
$256$	−30.2963	−1.89352
$257$	−26.8038	−1.67197	−0.835987	−	0.548749i	$-0.815104\pi$
$257$	−26.8038	−1.67197	−0.835987	+	0.548749i	$0.815104\pi$
$258$	−13.3340	−0.830136
$259$	7.95264	0.494153
$260$	0	0
$261$	1.97786	0.122426
$262$	−14.7270	−0.909839
$263$	−11.9518	−0.736980	−0.368490	−	0.929632i	$-0.620125\pi$
$263$	−11.9518	−0.736980	−0.368490	+	0.929632i	$0.620125\pi$
$264$	6.14151	0.377984
$265$	−11.0400	−0.678180
$266$	18.6303	1.14230
$267$	−5.24302	−0.320868
$268$	−6.22311	−0.380137
$269$	4.59663	0.280261	0.140131	−	0.990133i	$-0.455248\pi$
$269$	4.59663	0.280261	0.140131	+	0.990133i	$0.455248\pi$
$270$	9.37985	0.570840
$271$	−19.8969	−1.20865	−0.604326	−	0.796738i	$-0.706557\pi$
$271$	−19.8969	−1.20865	−0.604326	+	0.796738i	$0.706557\pi$
$272$	−13.8096	−0.837330
$273$	0	0
$274$	14.2994	0.863856
$275$	−8.69737	−0.524471
$276$	−18.6217	−1.12090
$277$	−11.2319	−0.674857	−0.337428	−	0.941351i	$-0.609557\pi$
$277$	−11.2319	−0.674857	−0.337428	+	0.941351i	$0.609557\pi$
$278$	11.3243	0.679183
$279$	10.5475	0.631462
$280$	21.7590	1.30035
$281$	30.2946	1.80722	0.903612	−	0.428352i	$-0.140906\pi$
$281$	30.2946	1.80722	0.903612	+	0.428352i	$0.140906\pi$
$282$	−3.15929	−0.188133
$283$	−15.3889	−0.914777	−0.457389	−	0.889267i	$-0.651215\pi$
$283$	−15.3889	−0.914777	−0.457389	+	0.889267i	$0.651215\pi$
$284$	−53.7788	−3.19118
$285$	28.4194	1.68342
$286$	0	0
$287$	5.00801	0.295614
$288$	−4.74476	−0.279588
$289$	−12.7753	−0.751485
$290$	18.5520	1.08941
$291$	−9.82293	−0.575831
$292$	14.7105	0.860869
$293$	−6.95822	−0.406503	−0.203252	−	0.979127i	$-0.565151\pi$
$293$	−6.95822	−0.406503	−0.203252	+	0.979127i	$0.565151\pi$
$294$	15.4183	0.899215
$295$	−45.7250	−2.66221
$296$	−51.0200	−2.96548
$297$	−1.00000	−0.0580259
$298$	−18.7483	−1.08606
$299$	0	0
$300$	38.4706	2.22110
$301$	5.03648	0.290298
$302$	60.1807	3.46301
$303$	−8.42338	−0.483910
$304$	−51.5914	−2.95897
$305$	0.680431	0.0389614
$306$	5.20928	0.297795
$307$	12.6233	0.720447	0.360224	−	0.932866i	$-0.382700\pi$
$307$	12.6233	0.720447	0.360224	+	0.932866i	$0.382700\pi$
$308$	−4.23435	−0.241275
$309$	−13.4029	−0.762465
$310$	98.9339	5.61907
$311$	2.12116	0.120280	0.0601399	−	0.998190i	$-0.480845\pi$
$311$	2.12116	0.120280	0.0601399	+	0.998190i	$0.480845\pi$
$312$	0	0
$313$	21.5919	1.22045	0.610224	−	0.792229i	$-0.291079\pi$
$313$	21.5919	1.22045	0.610224	+	0.792229i	$0.291079\pi$
$314$	−32.8724	−1.85510
$315$	−3.54294	−0.199622
$316$	−16.1409	−0.907999
$317$	−15.7684	−0.885640	−0.442820	−	0.896611i	$-0.646022\pi$
$317$	−15.7684	−0.885640	−0.442820	+	0.896611i	$0.646022\pi$
$318$	−7.56008	−0.423948
$319$	−1.97786	−0.110739
$320$	5.22612	0.292149
$321$	−8.05792	−0.449749
$322$	10.2141	0.569212
$323$	15.7833	0.878205
$324$	4.42325	0.245736
$325$	0	0
$326$	47.3631	2.62320
$327$	14.3600	0.794111
$328$	−32.1288	−1.77402
$329$	1.19332	0.0657900
$330$	−9.37985	−0.516344
$331$	−11.6602	−0.640902	−0.320451	−	0.947265i	$-0.603834\pi$
$331$	−11.6602	−0.640902	−0.320451	+	0.947265i	$0.603834\pi$
$332$	−14.6833	−0.805850
$333$	8.30741	0.455243
$334$	63.4668	3.47275
$335$	5.20697	0.284487
$336$	6.43171	0.350879
$337$	−7.63508	−0.415909	−0.207955	−	0.978138i	$-0.566681\pi$
$337$	−7.63508	−0.415909	−0.207955	+	0.978138i	$0.566681\pi$
$338$	0	0
$339$	18.6675	1.01388
$340$	33.6481	1.82482
$341$	−10.5475	−0.571179
$342$	19.4614	1.05235
$343$	−12.5248	−0.676278
$344$	−32.3115	−1.74212
$345$	15.5811	0.838858
$346$	8.01717	0.431006
$347$	−17.7823	−0.954606	−0.477303	−	0.878739i	$-0.658386\pi$
$347$	−17.7823	−0.954606	−0.477303	+	0.878739i	$0.658386\pi$
$348$	8.74857	0.468972
$349$	−12.1663	−0.651245	−0.325622	−	0.945500i	$-0.605574\pi$
$349$	−12.1663	−0.651245	−0.325622	+	0.945500i	$0.605574\pi$
$350$	−21.1014	−1.12792
$351$	0	0
$352$	4.74476	0.252896
$353$	32.9025	1.75122	0.875612	−	0.483014i	$-0.160458\pi$
$353$	32.9025	1.75122	0.875612	+	0.483014i	$0.160458\pi$
$354$	−31.3121	−1.66422
$355$	44.9975	2.38822
$356$	−23.1912	−1.22913
$357$	−1.96764	−0.104139
$358$	−3.16744	−0.167404
$359$	−7.29760	−0.385153	−0.192576	−	0.981282i	$-0.561684\pi$
$359$	−7.29760	−0.385153	−0.192576	+	0.981282i	$0.561684\pi$
$360$	22.7297	1.19796
$361$	39.9648	2.10341
$362$	−40.7310	−2.14078
$363$	1.00000	0.0524864
$364$	0	0
$365$	−12.3085	−0.644257
$366$	0.465954	0.0243558
$367$	−8.94917	−0.467143	−0.233571	−	0.972340i	$-0.575041\pi$
$367$	−8.94917	−0.467143	−0.233571	+	0.972340i	$0.575041\pi$
$368$	−28.2852	−1.47447
$369$	5.23142	0.272337
$370$	77.9222	4.05098
$371$	2.85558	0.148254
$372$	46.6542	2.41891
$373$	−18.1913	−0.941908	−0.470954	−	0.882158i	$-0.656090\pi$
$373$	−18.1913	−0.941908	−0.470954	+	0.882158i	$0.656090\pi$
$374$	−5.20928	−0.269366
$375$	−13.6840	−0.706637
$376$	−7.65574	−0.394815
$377$	0	0
$378$	−2.42618	−0.124789
$379$	−20.1063	−1.03279	−0.516396	−	0.856350i	$-0.672727\pi$
$379$	−20.1063	−1.03279	−0.516396	+	0.856350i	$0.672727\pi$
$380$	125.706	6.44859
$381$	6.60130	0.338195
$382$	−38.7536	−1.98281
$383$	7.99092	0.408317	0.204158	−	0.978938i	$-0.434554\pi$
$383$	7.99092	0.408317	0.204158	+	0.978938i	$0.434554\pi$
$384$	13.0683	0.666890
$385$	3.54294	0.180565
$386$	17.1365	0.872224
$387$	5.26116	0.267440
$388$	−43.4493	−2.20580
$389$	4.31617	0.218839	0.109419	−	0.993996i	$-0.465101\pi$
$389$	4.31617	0.218839	0.109419	+	0.993996i	$0.465101\pi$
$390$	0	0
$391$	8.65326	0.437614
$392$	37.3624	1.88709
$393$	5.81083	0.293117
$394$	−28.7201	−1.44690
$395$	13.5054	0.679528
$396$	−4.42325	−0.222277
$397$	−23.4560	−1.17722	−0.588612	−	0.808416i	$-0.700325\pi$
$397$	−23.4560	−1.17722	−0.588612	+	0.808416i	$0.700325\pi$
$398$	−54.6525	−2.73948
$399$	−7.35093	−0.368007
$400$	58.4344	2.92172
$401$	2.38235	0.118969	0.0594844	−	0.998229i	$-0.481054\pi$
$401$	2.38235	0.118969	0.0594844	+	0.998229i	$0.481054\pi$
$402$	3.56569	0.177841
$403$	0	0
$404$	−37.2587	−1.85369
$405$	−3.70100	−0.183904
$406$	−4.79864	−0.238153
$407$	−8.30741	−0.411783
$408$	12.6234	0.624951
$409$	10.3945	0.513973	0.256987	−	0.966415i	$-0.417270\pi$
$409$	10.3945	0.513973	0.256987	+	0.966415i	$0.417270\pi$
$410$	49.0700	2.42339
$411$	−5.64208	−0.278303
$412$	−59.2844	−2.92073
$413$	11.8272	0.581977
$414$	10.6698	0.524392
$415$	12.2857	0.603082
$416$	0	0
$417$	−4.46820	−0.218808
$418$	−19.4614	−0.951888
$419$	13.6447	0.666586	0.333293	−	0.942823i	$-0.391840\pi$
$419$	13.6447	0.666586	0.333293	+	0.942823i	$0.391840\pi$
$420$	−15.6713	−0.764682
$421$	−6.41040	−0.312424	−0.156212	−	0.987724i	$-0.549928\pi$
$421$	−6.41040	−0.312424	−0.156212	+	0.987724i	$0.549928\pi$
$422$	59.8100	2.91151
$423$	1.24656	0.0606097
$424$	−18.3200	−0.889696
$425$	−17.8768	−0.867150
$426$	30.8139	1.49294
$427$	−0.175999	−0.00851721
$428$	−35.6422	−1.72283
$429$	0	0
$430$	49.3489	2.37982
$431$	−15.8350	−0.762747	−0.381374	−	0.924421i	$-0.624549\pi$
$431$	−15.8350	−0.762747	−0.381374	+	0.924421i	$0.624549\pi$
$432$	6.71863	0.323250
$433$	−10.6273	−0.510716	−0.255358	−	0.966847i	$-0.582193\pi$
$433$	−10.6273	−0.510716	−0.255358	+	0.966847i	$0.582193\pi$
$434$	−25.5901	−1.22836
$435$	−7.32005	−0.350970
$436$	63.5179	3.04196
$437$	32.3278	1.54645
$438$	−8.42877	−0.402742
$439$	−17.2195	−0.821841	−0.410920	−	0.911671i	$-0.634793\pi$
$439$	−17.2195	−0.821841	−0.410920	+	0.911671i	$0.634793\pi$
$440$	−22.7297	−1.08360
$441$	−6.08359	−0.289695
$442$	0	0
$443$	−25.1359	−1.19424	−0.597120	−	0.802152i	$-0.703689\pi$
$443$	−25.1359	−1.19424	−0.597120	+	0.802152i	$0.703689\pi$
$444$	36.7457	1.74387
$445$	19.4044	0.919857
$446$	−37.3068	−1.76653
$447$	7.39749	0.349889
$448$	−1.35178	−0.0638656
$449$	2.01596	0.0951392	0.0475696	−	0.998868i	$-0.484852\pi$
$449$	2.01596	0.0951392	0.0475696	+	0.998868i	$0.484852\pi$
$450$	−22.0427	−1.03910
$451$	−5.23142	−0.246338
$452$	82.5710	3.88382
$453$	−23.7454	−1.11566
$454$	0.0909634	0.00426912
$455$	0	0
$456$	47.1598	2.20846
$457$	−33.7659	−1.57950	−0.789752	−	0.613426i	$-0.789791\pi$
$457$	−33.7659	−1.57950	−0.789752	+	0.613426i	$0.789791\pi$
$458$	21.2195	0.991524
$459$	−2.05542	−0.0959388
$460$	68.9190	3.21337
$461$	−16.7600	−0.780589	−0.390294	−	0.920690i	$-0.627627\pi$
$461$	−16.7600	−0.780589	−0.390294	+	0.920690i	$0.627627\pi$
$462$	2.42618	0.112876
$463$	−27.5446	−1.28011	−0.640054	−	0.768330i	$-0.721088\pi$
$463$	−27.5446	−1.28011	−0.640054	+	0.768330i	$0.721088\pi$
$464$	13.2885	0.616904
$465$	−39.0362	−1.81026
$466$	45.6244	2.11351
$467$	22.9318	1.06116	0.530578	−	0.847636i	$-0.321975\pi$
$467$	22.9318	1.06116	0.530578	+	0.847636i	$0.321975\pi$
$468$	0	0
$469$	−1.34683	−0.0621907
$470$	11.6925	0.539336
$471$	12.9704	0.597646
$472$	−75.8770	−3.49252
$473$	−5.26116	−0.241909
$474$	9.24836	0.424791
$475$	−66.7859	−3.06435
$476$	−8.70337	−0.398918
$477$	2.98297	0.136581
$478$	−14.5601	−0.665965
$479$	5.71495	0.261123	0.130561	−	0.991440i	$-0.458322\pi$
$479$	5.71495	0.261123	0.130561	+	0.991440i	$0.458322\pi$
$480$	17.5603	0.801516
$481$	0	0
$482$	−40.9202	−1.86386
$483$	−4.03018	−0.183380
$484$	4.42325	0.201057
$485$	36.3546	1.65078
$486$	−2.53441	−0.114963
$487$	−10.4987	−0.475742	−0.237871	−	0.971297i	$-0.576450\pi$
$487$	−10.4987	−0.475742	−0.237871	+	0.971297i	$0.576450\pi$
$488$	1.12912	0.0511129
$489$	−18.6880	−0.845100
$490$	−57.0631	−2.57785
$491$	13.0458	0.588747	0.294373	−	0.955691i	$-0.404889\pi$
$491$	13.0458	0.588747	0.294373	+	0.955691i	$0.404889\pi$
$492$	23.1399	1.04323
$493$	−4.06533	−0.183093
$494$	0	0
$495$	3.70100	0.166347
$496$	70.8647	3.18192
$497$	−11.6390	−0.522080
$498$	8.41316	0.377003
$499$	38.6395	1.72974	0.864870	−	0.501995i	$-0.167400\pi$
$499$	38.6395	1.72974	0.864870	+	0.501995i	$0.167400\pi$
$500$	−60.5276	−2.70688
$501$	−25.0420	−1.11879
$502$	17.3260	0.773298
$503$	0.330867	0.0147526	0.00737631	−	0.999973i	$-0.497652\pi$
$503$	0.330867	0.0147526	0.00737631	+	0.999973i	$0.497652\pi$
$504$	−5.87924	−0.261882
$505$	31.1749	1.38726
$506$	−10.6698	−0.474331
$507$	0	0
$508$	29.1992	1.29550
$509$	−44.2090	−1.95953	−0.979764	−	0.200157i	$-0.935855\pi$
$509$	−44.2090	−1.95953	−0.979764	+	0.200157i	$0.935855\pi$
$510$	−19.2795	−0.853712
$511$	3.18370	0.140839
$512$	50.6468	2.23829
$513$	−7.67886	−0.339030
$514$	67.9318	2.99635
$515$	49.6041	2.18582
$516$	23.2714	1.02447
$517$	−1.24656	−0.0548235
$518$	−20.1553	−0.885571
$519$	−3.16333	−0.138855
$520$	0	0
$521$	9.66049	0.423234	0.211617	−	0.977353i	$-0.432127\pi$
$521$	9.66049	0.423234	0.211617	+	0.977353i	$0.432127\pi$
$522$	−5.01271	−0.219401
$523$	21.7358	0.950440	0.475220	−	0.879867i	$-0.342368\pi$
$523$	21.7358	0.950440	0.475220	+	0.879867i	$0.342368\pi$
$524$	25.7027	1.12283
$525$	8.32595	0.363374
$526$	30.2908	1.32074
$527$	−21.6795	−0.944375
$528$	−6.71863	−0.292391
$529$	−5.27614	−0.229398
$530$	27.9798	1.21537
$531$	12.3548	0.536152
$532$	−32.5150	−1.40970
$533$	0	0
$534$	13.2880	0.575027
$535$	29.8223	1.28933
$536$	8.64056	0.373215
$537$	1.24977	0.0539316
$538$	−11.6497	−0.502256
$539$	6.08359	0.262039
$540$	−16.3704	−0.704471
$541$	−18.0139	−0.774478	−0.387239	−	0.921979i	$-0.626571\pi$
$541$	−18.0139	−0.774478	−0.387239	+	0.921979i	$0.626571\pi$
$542$	50.4270	2.16602
$543$	16.0712	0.689681
$544$	9.75247	0.418134
$545$	−53.1464	−2.27654
$546$	0	0
$547$	23.2740	0.995125	0.497563	−	0.867428i	$-0.334228\pi$
$547$	23.2740	0.995125	0.497563	+	0.867428i	$0.334228\pi$
$548$	−24.9563	−1.06608
$549$	−0.183851	−0.00784656
$550$	22.0427	0.939906
$551$	−15.1877	−0.647018
$552$	25.8556	1.10049
$553$	−3.49328	−0.148549
$554$	28.4662	1.20941
$555$	−30.7457	−1.30508
$556$	−19.7639	−0.838178
$557$	−11.5996	−0.491491	−0.245745	−	0.969334i	$-0.579033\pi$
$557$	−11.5996	−0.491491	−0.245745	+	0.969334i	$0.579033\pi$
$558$	−26.7317	−1.13164
$559$	0	0
$560$	−23.8037	−1.00589
$561$	2.05542	0.0867799
$562$	−76.7790	−3.23873
$563$	26.5695	1.11977	0.559885	−	0.828570i	$-0.310845\pi$
$563$	26.5695	1.11977	0.559885	+	0.828570i	$0.310845\pi$
$564$	5.51383	0.232174
$565$	−69.0884	−2.90657
$566$	39.0019	1.63937
$567$	0.957295	0.0402026
$568$	74.6698	3.13308
$569$	−22.7470	−0.953603	−0.476802	−	0.879011i	$-0.658204\pi$
$569$	−22.7470	−0.953603	−0.476802	+	0.879011i	$0.658204\pi$
$570$	−72.0265	−3.01686
$571$	−29.4622	−1.23296	−0.616478	−	0.787372i	$-0.711441\pi$
$571$	−29.4622	−1.23296	−0.616478	+	0.787372i	$0.711441\pi$
$572$	0	0
$573$	15.2909	0.638788
$574$	−12.6924	−0.529769
$575$	−36.6157	−1.52698
$576$	−1.41208	−0.0588368
$577$	26.6537	1.10961	0.554803	−	0.831981i	$-0.312793\pi$
$577$	26.6537	1.10961	0.554803	+	0.831981i	$0.312793\pi$
$578$	32.3778	1.34674
$579$	−6.76152	−0.280999
$580$	−32.3784	−1.34444
$581$	−3.17781	−0.131838
$582$	24.8954	1.03195
$583$	−2.98297	−0.123542
$584$	−20.4250	−0.845193
$585$	0	0
$586$	17.6350	0.728495
$587$	−10.9203	−0.450729	−0.225364	−	0.974275i	$-0.572357\pi$
$587$	−10.9203	−0.450729	−0.225364	+	0.974275i	$0.572357\pi$
$588$	−26.9092	−1.10972
$589$	−80.9927	−3.33725
$590$	115.886	4.77095
$591$	11.3320	0.466138
$592$	55.8144	2.29396
$593$	−19.3064	−0.792820	−0.396410	−	0.918074i	$-0.629744\pi$
$593$	−19.3064	−0.792820	−0.396410	+	0.918074i	$0.629744\pi$
$594$	2.53441	0.103988
$595$	7.28224	0.298543
$596$	32.7209	1.34030
$597$	21.5642	0.882562
$598$	0	0
$599$	2.01132	0.0821802	0.0410901	−	0.999155i	$-0.486917\pi$
$599$	2.01132	0.0821802	0.0410901	+	0.999155i	$0.486917\pi$
$600$	−53.4150	−2.18066
$601$	−40.1233	−1.63667	−0.818333	−	0.574745i	$-0.805101\pi$
$601$	−40.1233	−1.63667	−0.818333	+	0.574745i	$0.805101\pi$
$602$	−12.7645	−0.520243
$603$	−1.40691	−0.0572938
$604$	−105.032	−4.27369
$605$	−3.70100	−0.150467
$606$	21.3483	0.867216
$607$	−35.4310	−1.43810	−0.719049	−	0.694959i	$-0.755422\pi$
$607$	−35.4310	−1.43810	−0.719049	+	0.694959i	$0.755422\pi$
$608$	36.4343	1.47761
$609$	1.89339	0.0767242
$610$	−1.72449	−0.0698227
$611$	0	0
$612$	−9.09163	−0.367507
$613$	−0.644081	−0.0260142	−0.0130071	−	0.999915i	$-0.504140\pi$
$613$	−0.644081	−0.0260142	−0.0130071	+	0.999915i	$0.504140\pi$
$614$	−31.9925	−1.29111
$615$	−19.3615	−0.780730
$616$	5.87924	0.236881
$617$	−23.5775	−0.949194	−0.474597	−	0.880203i	$-0.657406\pi$
$617$	−23.5775	−0.949194	−0.474597	+	0.880203i	$0.657406\pi$
$618$	33.9685	1.36641
$619$	5.86810	0.235859	0.117929	−	0.993022i	$-0.462374\pi$
$619$	5.86810	0.235859	0.117929	+	0.993022i	$0.462374\pi$
$620$	−172.667	−6.93447
$621$	−4.20997	−0.168940
$622$	−5.37589	−0.215553
$623$	−5.01911	−0.201087
$624$	0	0
$625$	7.15745	0.286298
$626$	−54.7229	−2.18717
$627$	7.67886	0.306664
$628$	57.3714	2.28937
$629$	−17.0752	−0.680833
$630$	8.97928	0.357743
$631$	−11.0386	−0.439441	−0.219721	−	0.975563i	$-0.570515\pi$
$631$	−11.0386	−0.439441	−0.219721	+	0.975563i	$0.570515\pi$
$632$	22.4111	0.891465
$633$	−23.5992	−0.937982
$634$	39.9636	1.58716
$635$	−24.4314	−0.969529
$636$	13.1944	0.523193
$637$	0	0
$638$	5.01271	0.198455
$639$	−12.1582	−0.480972
$640$	−48.3658	−1.91183
$641$	11.2924	0.446022	0.223011	−	0.974816i	$-0.428411\pi$
$641$	11.2924	0.446022	0.223011	+	0.974816i	$0.428411\pi$
$642$	20.4221	0.805996
$643$	−2.73168	−0.107727	−0.0538634	−	0.998548i	$-0.517154\pi$
$643$	−2.73168	−0.107727	−0.0538634	+	0.998548i	$0.517154\pi$
$644$	−17.8265	−0.702463
$645$	−19.4715	−0.766691
$646$	−40.0013	−1.57383
$647$	−10.3135	−0.405465	−0.202733	−	0.979234i	$-0.564982\pi$
$647$	−10.3135	−0.405465	−0.202733	+	0.979234i	$0.564982\pi$
$648$	−6.14151	−0.241261
$649$	−12.3548	−0.484968
$650$	0	0
$651$	10.0971	0.395735
$652$	−82.6616	−3.23728
$653$	−1.95601	−0.0765446	−0.0382723	−	0.999267i	$-0.512185\pi$
$653$	−1.95601	−0.0765446	−0.0382723	+	0.999267i	$0.512185\pi$
$654$	−36.3942	−1.42313
$655$	−21.5058	−0.840303
$656$	35.1480	1.37230
$657$	3.32573	0.129749
$658$	−3.02437	−0.117902
$659$	−21.0277	−0.819121	−0.409561	−	0.912283i	$-0.634318\pi$
$659$	−21.0277	−0.819121	−0.409561	+	0.912283i	$0.634318\pi$
$660$	16.3704	0.637218
$661$	−25.7516	−1.00162	−0.500810	−	0.865557i	$-0.666964\pi$
$661$	−25.7516	−1.00162	−0.500810	+	0.865557i	$0.666964\pi$
$662$	29.5517	1.14856
$663$	0	0
$664$	20.3872	0.791176
$665$	27.2058	1.05499
$666$	−21.0544	−0.815841
$667$	−8.32673	−0.322412
$668$	−110.767	−4.28570
$669$	14.7201	0.569111
$670$	−13.1966	−0.509830
$671$	0.183851	0.00709748
$672$	−4.54213	−0.175217
$673$	−18.2077	−0.701856	−0.350928	−	0.936403i	$-0.614134\pi$
$673$	−18.2077	−0.701856	−0.350928	+	0.936403i	$0.614134\pi$
$674$	19.3504	0.745351
$675$	8.69737	0.334762
$676$	0	0
$677$	−10.3281	−0.396941	−0.198470	−	0.980107i	$-0.563597\pi$
$677$	−10.3281	−0.396941	−0.198470	+	0.980107i	$0.563597\pi$
$678$	−47.3112	−1.81697
$679$	−9.40344	−0.360871
$680$	−46.7191	−1.79160
$681$	−0.0358913	−0.00137536
$682$	26.7317	1.02361
$683$	33.4285	1.27911	0.639553	−	0.768747i	$-0.279119\pi$
$683$	33.4285	1.27911	0.639553	+	0.768747i	$0.279119\pi$
$684$	−33.9655	−1.29870
$685$	20.8813	0.797834
$686$	31.7431	1.21196
$687$	−8.37257	−0.319433
$688$	35.3478	1.34762
$689$	0	0
$690$	−39.4889	−1.50332
$691$	38.8290	1.47712	0.738562	−	0.674186i	$-0.235505\pi$
$691$	38.8290	1.47712	0.738562	+	0.674186i	$0.235505\pi$
$692$	−13.9922	−0.531903
$693$	−0.957295	−0.0363646
$694$	45.0678	1.71075
$695$	16.5368	0.627276
$696$	−12.1471	−0.460433
$697$	−10.7528	−0.407290
$698$	30.8343	1.16710
$699$	−18.0020	−0.680897
$700$	36.8277	1.39196
$701$	47.5275	1.79509	0.897544	−	0.440925i	$-0.145350\pi$
$701$	47.5275	1.79509	0.897544	+	0.440925i	$0.145350\pi$
$702$	0	0
$703$	−63.7914	−2.40594
$704$	1.41208	0.0532199
$705$	−4.61350	−0.173755
$706$	−83.3886	−3.13837
$707$	−8.06365	−0.303265
$708$	54.6483	2.05381
$709$	28.9052	1.08556	0.542780	−	0.839875i	$-0.317372\pi$
$709$	28.9052	1.08556	0.542780	+	0.839875i	$0.317372\pi$
$710$	−114.042	−4.27993
$711$	−3.64911	−0.136852
$712$	32.2001	1.20675
$713$	−44.4046	−1.66297
$714$	4.98682	0.186627
$715$	0	0
$716$	5.52805	0.206593
$717$	5.74497	0.214550
$718$	18.4951	0.690233
$719$	47.9212	1.78716	0.893579	−	0.448906i	$-0.148186\pi$
$719$	47.9212	1.78716	0.893579	+	0.448906i	$0.148186\pi$
$720$	−24.8656	−0.926687
$721$	−12.8305	−0.477834
$722$	−101.287	−3.76953
$723$	16.1458	0.600469
$724$	71.0869	2.64192
$725$	17.2022	0.638873
$726$	−2.53441	−0.0940609
$727$	23.4347	0.869146	0.434573	−	0.900636i	$-0.356899\pi$
$727$	23.4347	0.869146	0.434573	+	0.900636i	$0.356899\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	31.1949	1.15457
$731$	−10.8139	−0.399966
$732$	−0.813218	−0.0300574
$733$	−38.8733	−1.43582	−0.717910	−	0.696136i	$-0.754901\pi$
$733$	−38.8733	−1.43582	−0.717910	+	0.696136i	$0.754901\pi$
$734$	22.6809	0.837167
$735$	22.5153	0.830491
$736$	19.9753	0.736299
$737$	1.40691	0.0518242
$738$	−13.2586	−0.488055
$739$	−29.3240	−1.07870	−0.539350	−	0.842082i	$-0.681330\pi$
$739$	−29.3240	−1.07870	−0.539350	+	0.842082i	$0.681330\pi$
$740$	−135.996	−4.99930
$741$	0	0
$742$	−7.23723	−0.265687
$743$	−40.8183	−1.49748	−0.748740	−	0.662864i	$-0.769341\pi$
$743$	−40.8183	−1.49748	−0.748740	+	0.662864i	$0.769341\pi$
$744$	−64.7776	−2.37486
$745$	−27.3781	−1.00305
$746$	46.1042	1.68799
$747$	−3.31957	−0.121457
$748$	9.09163	0.332423
$749$	−7.71380	−0.281856
$750$	34.6808	1.26636
$751$	4.36042	0.159114	0.0795570	−	0.996830i	$-0.474649\pi$
$751$	4.36042	0.159114	0.0795570	+	0.996830i	$0.474649\pi$
$752$	8.37515	0.305410
$753$	−6.83631	−0.249129
$754$	0	0
$755$	87.8817	3.19834
$756$	4.23435	0.154002
$757$	40.1387	1.45887	0.729433	−	0.684052i	$-0.239784\pi$
$757$	40.1387	1.45887	0.729433	+	0.684052i	$0.239784\pi$
$758$	50.9577	1.85087
$759$	4.20997	0.152812
$760$	−174.538	−6.33117
$761$	38.2425	1.38629	0.693144	−	0.720799i	$-0.256225\pi$
$761$	38.2425	1.38629	0.693144	+	0.720799i	$0.256225\pi$
$762$	−16.7304	−0.606079
$763$	13.7468	0.497667
$764$	67.6357	2.44697
$765$	7.60710	0.275035
$766$	−20.2523	−0.731745
$767$	0	0
$768$	−30.2963	−1.09323
$769$	35.0140	1.26264	0.631319	−	0.775523i	$-0.282514\pi$
$769$	35.0140	1.26264	0.631319	+	0.775523i	$0.282514\pi$
$770$	−8.97928	−0.323591
$771$	−26.8038	−0.965315
$772$	−29.9079	−1.07641
$773$	5.69564	0.204858	0.102429	−	0.994740i	$-0.467339\pi$
$773$	5.69564	0.204858	0.102429	+	0.994740i	$0.467339\pi$
$774$	−13.3340	−0.479279
$775$	91.7355	3.29524
$776$	60.3277	2.16564
$777$	7.95264	0.285299
$778$	−10.9390	−0.392181
$779$	−40.1713	−1.43929
$780$	0	0
$781$	12.1582	0.435055
$782$	−21.9309	−0.784248
$783$	1.97786	0.0706830
$784$	−40.8734	−1.45976
$785$	−48.0035	−1.71332
$786$	−14.7270	−0.525296
$787$	−31.2092	−1.11249	−0.556244	−	0.831019i	$-0.687758\pi$
$787$	−31.2092	−1.11249	−0.556244	+	0.831019i	$0.687758\pi$
$788$	50.1244	1.78561
$789$	−11.9518	−0.425496
$790$	−34.2282	−1.21778
$791$	17.8703	0.635395
$792$	6.14151	0.218229
$793$	0	0
$794$	59.4472	2.10970
$795$	−11.0400	−0.391547
$796$	95.3836	3.38078
$797$	−42.7214	−1.51327	−0.756634	−	0.653839i	$-0.773157\pi$
$797$	−42.7214	−1.51327	−0.756634	+	0.653839i	$0.773157\pi$
$798$	18.6303	0.659505
$799$	−2.56220	−0.0906440
$800$	−41.2669	−1.45901
$801$	−5.24302	−0.185253
$802$	−6.03786	−0.213204
$803$	−3.32573	−0.117362
$804$	−6.22311	−0.219472
$805$	14.9157	0.525709
$806$	0	0
$807$	4.59663	0.161809
$808$	51.7323	1.81993
$809$	−13.3241	−0.468449	−0.234225	−	0.972182i	$-0.575255\pi$
$809$	−13.3241	−0.468449	−0.234225	+	0.972182i	$0.575255\pi$
$810$	9.37985	0.329574
$811$	−41.9849	−1.47429	−0.737144	−	0.675735i	$-0.763826\pi$
$811$	−41.9849	−1.47429	−0.737144	+	0.675735i	$0.763826\pi$
$812$	8.37496	0.293903
$813$	−19.8969	−0.697815
$814$	21.0544	0.737956
$815$	69.1642	2.42272
$816$	−13.8096	−0.483433
$817$	−40.3997	−1.41341
$818$	−26.3439	−0.921092
$819$	0	0
$820$	−85.6406	−2.99070
$821$	−10.0872	−0.352047	−0.176023	−	0.984386i	$-0.556323\pi$
$821$	−10.0872	−0.352047	−0.176023	+	0.984386i	$0.556323\pi$
$822$	14.2994	0.498748
$823$	−1.16139	−0.0404835	−0.0202418	−	0.999795i	$-0.506444\pi$
$823$	−1.16139	−0.0404835	−0.0202418	+	0.999795i	$0.506444\pi$
$824$	82.3142	2.86755
$825$	−8.69737	−0.302804
$826$	−29.9749	−1.04296
$827$	5.42242	0.188556	0.0942781	−	0.995546i	$-0.469946\pi$
$827$	5.42242	0.188556	0.0942781	+	0.995546i	$0.469946\pi$
$828$	−18.6217	−0.647151
$829$	−16.1881	−0.562237	−0.281119	−	0.959673i	$-0.590705\pi$
$829$	−16.1881	−0.562237	−0.281119	+	0.959673i	$0.590705\pi$
$830$	−31.1371	−1.08078
$831$	−11.2319	−0.389629
$832$	0	0
$833$	12.5043	0.433249
$834$	11.3243	0.392127
$835$	92.6803	3.20734
$836$	33.9655	1.17472
$837$	10.5475	0.364575
$838$	−34.5812	−1.19459
$839$	−13.1144	−0.452759	−0.226379	−	0.974039i	$-0.572689\pi$
$839$	−13.1144	−0.452759	−0.226379	+	0.974039i	$0.572689\pi$
$840$	21.7590	0.750758
$841$	−25.0881	−0.865106
$842$	16.2466	0.559895
$843$	30.2946	1.04340
$844$	−104.385	−3.59308
$845$	0	0
$846$	−3.15929	−0.108619
$847$	0.957295	0.0328930
$848$	20.0415	0.688227
$849$	−15.3889	−0.528147
$850$	45.3071	1.55402
$851$	−34.9739	−1.19889
$852$	−53.7788	−1.84243
$853$	8.66325	0.296624	0.148312	−	0.988941i	$-0.452616\pi$
$853$	8.66325	0.296624	0.148312	+	0.988941i	$0.452616\pi$
$854$	0.446055	0.0152637
$855$	28.4194	0.971924
$856$	49.4878	1.69146
$857$	−28.1435	−0.961365	−0.480683	−	0.876895i	$-0.659611\pi$
$857$	−28.1435	−0.961365	−0.480683	+	0.876895i	$0.659611\pi$
$858$	0	0
$859$	11.7375	0.400479	0.200240	−	0.979747i	$-0.435828\pi$
$859$	11.7375	0.400479	0.200240	+	0.979747i	$0.435828\pi$
$860$	−86.1275	−2.93692
$861$	5.00801	0.170673
$862$	40.1325	1.36692
$863$	14.6715	0.499424	0.249712	−	0.968320i	$-0.419664\pi$
$863$	14.6715	0.499424	0.249712	+	0.968320i	$0.419664\pi$
$864$	−4.74476	−0.161420
$865$	11.7075	0.398066
$866$	26.9340	0.915254
$867$	−12.7753	−0.433870
$868$	44.6618	1.51592
$869$	3.64911	0.123788
$870$	18.5520	0.628973
$871$	0	0
$872$	−88.1922	−2.98657
$873$	−9.82293	−0.332456
$874$	−81.9319	−2.77139
$875$	−13.0996	−0.442847
$876$	14.7105	0.497023
$877$	18.0884	0.610803	0.305402	−	0.952224i	$-0.401209\pi$
$877$	18.0884	0.610803	0.305402	+	0.952224i	$0.401209\pi$
$878$	43.6413	1.47282
$879$	−6.95822	−0.234695
$880$	24.8656	0.838220
$881$	−31.0695	−1.04676	−0.523379	−	0.852100i	$-0.675329\pi$
$881$	−31.0695	−1.04676	−0.523379	+	0.852100i	$0.675329\pi$
$882$	15.4183	0.519162
$883$	34.4102	1.15799	0.578997	−	0.815330i	$-0.303444\pi$
$883$	34.4102	1.15799	0.578997	+	0.815330i	$0.303444\pi$
$884$	0	0
$885$	−45.7250	−1.53703
$886$	63.7047	2.14020
$887$	−24.0600	−0.807857	−0.403928	−	0.914791i	$-0.632355\pi$
$887$	−24.0600	−0.807857	−0.403928	+	0.914791i	$0.632355\pi$
$888$	−51.0200	−1.71212
$889$	6.31938	0.211945
$890$	−49.1788	−1.64848
$891$	−1.00000	−0.0335013
$892$	65.1106	2.18006
$893$	−9.57213	−0.320319
$894$	−18.7483	−0.627036
$895$	−4.62540	−0.154610
$896$	12.5102	0.417938
$897$	0	0
$898$	−5.10928	−0.170499
$899$	20.8615	0.695769
$900$	38.4706	1.28235
$901$	−6.13126	−0.204262
$902$	13.2586	0.441462
$903$	5.03648	0.167604
$904$	−114.647	−3.81309
$905$	−59.4794	−1.97716
$906$	60.1807	1.99937
$907$	−7.79308	−0.258765	−0.129382	−	0.991595i	$-0.541299\pi$
$907$	−7.79308	−0.258765	−0.129382	+	0.991595i	$0.541299\pi$
$908$	−0.158756	−0.00526851
$909$	−8.42338	−0.279386
$910$	0	0
$911$	−4.88300	−0.161781	−0.0808904	−	0.996723i	$-0.525776\pi$
$911$	−4.88300	−0.161781	−0.0808904	+	0.996723i	$0.525776\pi$
$912$	−51.5914	−1.70836
$913$	3.31957	0.109862
$914$	85.5768	2.83063
$915$	0.680431	0.0224944
$916$	−37.0339	−1.22364
$917$	5.56267	0.183696
$918$	5.20928	0.171932
$919$	−53.5402	−1.76613	−0.883065	−	0.469251i	$-0.844524\pi$
$919$	−53.5402	−1.76613	−0.883065	+	0.469251i	$0.844524\pi$
$920$	−95.6914	−3.15485
$921$	12.6233	0.415950
$922$	42.4766	1.39889
$923$	0	0
$924$	−4.23435	−0.139300
$925$	72.2526	2.37565
$926$	69.8095	2.29408
$927$	−13.4029	−0.440209
$928$	−9.38447	−0.308060
$929$	35.1499	1.15323	0.576616	−	0.817015i	$-0.304373\pi$
$929$	35.1499	1.15323	0.576616	+	0.817015i	$0.304373\pi$
$930$	98.9339	3.24417
$931$	46.7150	1.53102
$932$	−79.6272	−2.60828
$933$	2.12116	0.0694435
$934$	−58.1185	−1.90170
$935$	−7.60710	−0.248779
$936$	0	0
$937$	12.6307	0.412626	0.206313	−	0.978486i	$-0.433854\pi$
$937$	12.6307	0.412626	0.206313	+	0.978486i	$0.433854\pi$
$938$	3.41342	0.111452
$939$	21.5919	0.704626
$940$	−20.4067	−0.665592
$941$	39.6660	1.29308	0.646538	−	0.762882i	$-0.276216\pi$
$941$	39.6660	1.29308	0.646538	+	0.762882i	$0.276216\pi$
$942$	−32.8724	−1.07104
$943$	−22.0241	−0.717204
$944$	83.0072	2.70165
$945$	−3.54294	−0.115252
$946$	13.3340	0.433524
$947$	−6.08586	−0.197764	−0.0988819	−	0.995099i	$-0.531527\pi$
$947$	−6.08586	−0.197764	−0.0988819	+	0.995099i	$0.531527\pi$
$948$	−16.1409	−0.524233
$949$	0	0
$950$	169.263	5.49162
$951$	−15.7684	−0.511324
$952$	12.0843	0.391654
$953$	−29.8978	−0.968484	−0.484242	−	0.874934i	$-0.660904\pi$
$953$	−29.8978	−0.968484	−0.484242	+	0.874934i	$0.660904\pi$
$954$	−7.56008	−0.244767
$955$	−56.5917	−1.83127
$956$	25.4114	0.821865
$957$	−1.97786	−0.0639351
$958$	−14.4840	−0.467958
$959$	−5.40113	−0.174412
$960$	5.22612	0.168672
$961$	80.2496	2.58870
$962$	0	0
$963$	−8.05792	−0.259663
$964$	71.4170	2.30019
$965$	25.0244	0.805563
$966$	10.2141	0.328635
$967$	−23.5725	−0.758039	−0.379020	−	0.925389i	$-0.623739\pi$
$967$	−23.5725	−0.758039	−0.379020	+	0.925389i	$0.623739\pi$
$968$	−6.14151	−0.197396
$969$	15.7833	0.507032
$970$	−92.1377	−2.95836
$971$	31.0731	0.997182	0.498591	−	0.866837i	$-0.333851\pi$
$971$	31.0731	0.997182	0.498591	+	0.866837i	$0.333851\pi$
$972$	4.42325	0.141876
$973$	−4.27738	−0.137126
$974$	26.6081	0.852578
$975$	0	0
$976$	−1.23523	−0.0395386
$977$	−18.8934	−0.604454	−0.302227	−	0.953236i	$-0.597730\pi$
$977$	−18.8934	−0.604454	−0.302227	+	0.953236i	$0.597730\pi$
$978$	47.3631	1.51450
$979$	5.24302	0.167568
$980$	99.5909	3.18132
$981$	14.3600	0.458480
$982$	−33.0633	−1.05509
$983$	−32.8458	−1.04762	−0.523809	−	0.851836i	$-0.675489\pi$
$983$	−32.8458	−1.04762	−0.523809	+	0.851836i	$0.675489\pi$
$984$	−32.1288	−1.02423
$985$	−41.9398	−1.33631
$986$	10.3032	0.328122
$987$	1.19332	0.0379839
$988$	0	0
$989$	−22.1493	−0.704308
$990$	−9.37985	−0.298111
$991$	−15.1204	−0.480316	−0.240158	−	0.970734i	$-0.577199\pi$
$991$	−15.1204	−0.480316	−0.240158	+	0.970734i	$0.577199\pi$
$992$	−50.0453	−1.58894
$993$	−11.6602	−0.370025
$994$	29.4980	0.935620
$995$	−79.8088	−2.53011
$996$	−14.6833	−0.465257
$997$	−2.12151	−0.0671889	−0.0335945	−	0.999436i	$-0.510695\pi$
$997$	−2.12151	−0.0671889	−0.0335945	+	0.999436i	$0.510695\pi$
$998$	−97.9284	−3.09987
$999$	8.30741	0.262835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.x.1.2		7
13.5	odd	4		429.2.b.b.298.13	yes	14
13.8	odd	4		429.2.b.b.298.2	✓	14
13.12	even	2		5577.2.a.y.1.6		7
39.5	even	4		1287.2.b.c.298.2		14
39.8	even	4		1287.2.b.c.298.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.b.b.298.2	✓	14	13.8	odd	4
429.2.b.b.298.13	yes	14	13.5	odd	4
1287.2.b.c.298.2		14	39.5	even	4
1287.2.b.c.298.13		14	39.8	even	4
5577.2.a.x.1.2		7	1.1	even	1	trivial
5577.2.a.y.1.6		7	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5577.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53441 q^{2} +1.00000 q^{3} +4.42325 q^{4} -3.70100 q^{5} -2.53441 q^{6} +0.957295 q^{7} -6.14151 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.53441 q^{2} +1.00000 q^{3} +4.42325 q^{4} -3.70100 q^{5} -2.53441 q^{6} +0.957295 q^{7} -6.14151 q^{8} +1.00000 q^{9} +9.37985 q^{10} -1.00000 q^{11} +4.42325 q^{12} -2.42618 q^{14} -3.70100 q^{15} +6.71863 q^{16} -2.05542 q^{17} -2.53441 q^{18} -7.67886 q^{19} -16.3704 q^{20} +0.957295 q^{21} +2.53441 q^{22} -4.20997 q^{23} -6.14151 q^{24} +8.69737 q^{25} +1.00000 q^{27} +4.23435 q^{28} +1.97786 q^{29} +9.37985 q^{30} +10.5475 q^{31} -4.74476 q^{32} -1.00000 q^{33} +5.20928 q^{34} -3.54294 q^{35} +4.42325 q^{36} +8.30741 q^{37} +19.4614 q^{38} +22.7297 q^{40} +5.23142 q^{41} -2.42618 q^{42} +5.26116 q^{43} -4.42325 q^{44} -3.70100 q^{45} +10.6698 q^{46} +1.24656 q^{47} +6.71863 q^{48} -6.08359 q^{49} -22.0427 q^{50} -2.05542 q^{51} +2.98297 q^{53} -2.53441 q^{54} +3.70100 q^{55} -5.87924 q^{56} -7.67886 q^{57} -5.01271 q^{58} +12.3548 q^{59} -16.3704 q^{60} -0.183851 q^{61} -26.7317 q^{62} +0.957295 q^{63} -1.41208 q^{64} +2.53441 q^{66} -1.40691 q^{67} -9.09163 q^{68} -4.20997 q^{69} +8.97928 q^{70} -12.1582 q^{71} -6.14151 q^{72} +3.32573 q^{73} -21.0544 q^{74} +8.69737 q^{75} -33.9655 q^{76} -0.957295 q^{77} -3.64911 q^{79} -24.8656 q^{80} +1.00000 q^{81} -13.2586 q^{82} -3.31957 q^{83} +4.23435 q^{84} +7.60710 q^{85} -13.3340 q^{86} +1.97786 q^{87} +6.14151 q^{88} -5.24302 q^{89} +9.37985 q^{90} -18.6217 q^{92} +10.5475 q^{93} -3.15929 q^{94} +28.4194 q^{95} -4.74476 q^{96} -9.82293 q^{97} +15.4183 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 3 q^{2} + 7 q^{3} + 9 q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{7} - 15 q^{8} + 7 q^{9}+O(q^{10}) \) 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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