LMFDB - Embedded newform 4235.2.a.bp.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 28 x^{16} + 54 x^{15} + 317 x^{14} - 580 x^{13} - 1874 x^{12} + 3158 x^{11} + \cdots - 176 $ x^18 - 2x^17 - 28x^16 + 54x^15 + 317x^14 - 580x^13 - 1874x^12 + 3158x^11 + 6290x^10 - 9228x^9 - 12411x^8 + 14224x^7 + 14618x^6 - 10744x^5 - 9817x^4 + 3146x^3 + 3048x^2 - 16*x - 176
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$1.38970$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.38970 q^{2} -1.33908 q^{3} -0.0687332 q^{4} +1.00000 q^{5} -1.86092 q^{6} +1.00000 q^{7} -2.87492 q^{8} -1.20687 q^{9} +O(q^{10})$	\(q+1.38970 q^{2} -1.33908 q^{3} -0.0687332 q^{4} +1.00000 q^{5} -1.86092 q^{6} +1.00000 q^{7} -2.87492 q^{8} -1.20687 q^{9} +1.38970 q^{10} +0.0920392 q^{12} -3.94610 q^{13} +1.38970 q^{14} -1.33908 q^{15} -3.85781 q^{16} -4.78195 q^{17} -1.67718 q^{18} +1.15891 q^{19} -0.0687332 q^{20} -1.33908 q^{21} +7.36414 q^{23} +3.84975 q^{24} +1.00000 q^{25} -5.48389 q^{26} +5.63333 q^{27} -0.0687332 q^{28} -7.46257 q^{29} -1.86092 q^{30} +4.94894 q^{31} +0.388640 q^{32} -6.64548 q^{34} +1.00000 q^{35} +0.0829518 q^{36} -7.98144 q^{37} +1.61054 q^{38} +5.28414 q^{39} -2.87492 q^{40} +7.06899 q^{41} -1.86092 q^{42} +10.3536 q^{43} -1.20687 q^{45} +10.2339 q^{46} -0.463035 q^{47} +5.16591 q^{48} +1.00000 q^{49} +1.38970 q^{50} +6.40341 q^{51} +0.271228 q^{52} +7.83248 q^{53} +7.82864 q^{54} -2.87492 q^{56} -1.55187 q^{57} -10.3707 q^{58} +7.73940 q^{59} +0.0920392 q^{60} +3.97128 q^{61} +6.87754 q^{62} -1.20687 q^{63} +8.25571 q^{64} -3.94610 q^{65} +0.686469 q^{67} +0.328679 q^{68} -9.86117 q^{69} +1.38970 q^{70} +4.07768 q^{71} +3.46964 q^{72} +0.867108 q^{73} -11.0918 q^{74} -1.33908 q^{75} -0.0796556 q^{76} +7.34337 q^{78} -9.16188 q^{79} -3.85781 q^{80} -3.92288 q^{81} +9.82378 q^{82} -13.1810 q^{83} +0.0920392 q^{84} -4.78195 q^{85} +14.3883 q^{86} +9.99298 q^{87} -0.382439 q^{89} -1.67718 q^{90} -3.94610 q^{91} -0.506161 q^{92} -6.62702 q^{93} -0.643480 q^{94} +1.15891 q^{95} -0.520419 q^{96} +16.9086 q^{97} +1.38970 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9}+O(q^{10}) $ 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9} + 2 q^{10} + 15 q^{12} + 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} - 5 q^{17} + 2 q^{18} + 15 q^{19} + 24 q^{20} + 5 q^{21} + 4 q^{23} + 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} + 24 q^{28} - 6 q^{29} - q^{30} + 22 q^{31} - 6 q^{32} + 44 q^{34} + 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} - 38 q^{39} + 6 q^{40} + 7 q^{41} - q^{42} + 10 q^{43} + 37 q^{45} - 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} + 2 q^{50} - 11 q^{51} + 18 q^{52} + 23 q^{53} + 13 q^{54} + 6 q^{56} - 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} + 17 q^{61} + 57 q^{62} + 37 q^{63} + 64 q^{64} + 8 q^{65} + 29 q^{67} - 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} - 77 q^{72} + 3 q^{73} - 48 q^{74} + 5 q^{75} + 47 q^{76} + 10 q^{78} - 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} + 9 q^{83} + 15 q^{84} - 5 q^{85} + 25 q^{86} + 23 q^{87} + 59 q^{89} + 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} - 19 q^{94} + 15 q^{95} + 14 q^{96} + 30 q^{97} + 2 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9 + 2 * q^10 + 15 * q^12 + 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 - 5 * q^17 + 2 * q^18 + 15 * q^19 + 24 * q^20 + 5 * q^21 + 4 * q^23 + 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 + 24 * q^28 - 6 * q^29 - q^30 + 22 * q^31 - 6 * q^32 + 44 * q^34 + 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 - 38 * q^39 + 6 * q^40 + 7 * q^41 - q^42 + 10 * q^43 + 37 * q^45 - 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 + 2 * q^50 - 11 * q^51 + 18 * q^52 + 23 * q^53 + 13 * q^54 + 6 * q^56 - 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 + 17 * q^61 + 57 * q^62 + 37 * q^63 + 64 * q^64 + 8 * q^65 + 29 * q^67 - 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 - 77 * q^72 + 3 * q^73 - 48 * q^74 + 5 * q^75 + 47 * q^76 + 10 * q^78 - 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 + 9 * q^83 + 15 * q^84 - 5 * q^85 + 25 * q^86 + 23 * q^87 + 59 * q^89 + 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 - 19 * q^94 + 15 * q^95 + 14 * q^96 + 30 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.38970	0.982666	0.491333	−	0.870972i	$-0.336510\pi$
$2$	1.38970	0.982666	0.491333	+	0.870972i	$0.336510\pi$
$3$	−1.33908	−0.773118	−0.386559	−	0.922265i	$-0.626336\pi$
$3$	−1.33908	−0.773118	−0.386559	+	0.922265i	$0.626336\pi$
$4$	−0.0687332	−0.0343666
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.86092	−0.759717
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.87492	−1.01644
$9$	−1.20687	−0.402289
$10$	1.38970	0.439462
$11$	0	0
$11$	0	0
$12$	0.0920392	0.0265694
$13$	−3.94610	−1.09445	−0.547225	−	0.836985i	$-0.684316\pi$
$13$	−3.94610	−1.09445	−0.547225	+	0.836985i	$0.684316\pi$
$14$	1.38970	0.371413
$15$	−1.33908	−0.345749
$16$	−3.85781	−0.964452
$17$	−4.78195	−1.15979	−0.579897	−	0.814690i	$-0.696907\pi$
$17$	−4.78195	−1.15979	−0.579897	+	0.814690i	$0.696907\pi$
$18$	−1.67718	−0.395316
$19$	1.15891	0.265872	0.132936	−	0.991125i	$-0.457559\pi$
$19$	1.15891	0.265872	0.132936	+	0.991125i	$0.457559\pi$
$20$	−0.0687332	−0.0153692
$21$	−1.33908	−0.292211
$22$	0	0
$23$	7.36414	1.53553	0.767765	−	0.640732i	$-0.221369\pi$
$23$	7.36414	1.53553	0.767765	+	0.640732i	$0.221369\pi$
$24$	3.84975	0.785826
$25$	1.00000	0.200000
$26$	−5.48389	−1.07548
$27$	5.63333	1.08413
$28$	−0.0687332	−0.0129894
$29$	−7.46257	−1.38577	−0.692883	−	0.721050i	$-0.743660\pi$
$29$	−7.46257	−1.38577	−0.692883	+	0.721050i	$0.743660\pi$
$30$	−1.86092	−0.339756
$31$	4.94894	0.888855	0.444428	−	0.895815i	$-0.353407\pi$
$31$	4.94894	0.888855	0.444428	+	0.895815i	$0.353407\pi$
$32$	0.388640	0.0687024
$33$	0	0
$34$	−6.64548	−1.13969
$35$	1.00000	0.169031
$36$	0.0829518	0.0138253
$37$	−7.98144	−1.31214	−0.656071	−	0.754699i	$-0.727783\pi$
$37$	−7.98144	−1.31214	−0.656071	+	0.754699i	$0.727783\pi$
$38$	1.61054	0.261264
$39$	5.28414	0.846139
$40$	−2.87492	−0.454565
$41$	7.06899	1.10399	0.551995	−	0.833847i	$-0.313867\pi$
$41$	7.06899	1.10399	0.551995	+	0.833847i	$0.313867\pi$
$42$	−1.86092	−0.287146
$43$	10.3536	1.57890	0.789452	−	0.613813i	$-0.210365\pi$
$43$	10.3536	1.57890	0.789452	+	0.613813i	$0.210365\pi$
$44$	0	0
$45$	−1.20687	−0.179909
$46$	10.2339	1.50891
$47$	−0.463035	−0.0675406	−0.0337703	−	0.999430i	$-0.510751\pi$
$47$	−0.463035	−0.0675406	−0.0337703	+	0.999430i	$0.510751\pi$
$48$	5.16591	0.745635
$49$	1.00000	0.142857
$50$	1.38970	0.196533
$51$	6.40341	0.896657
$52$	0.271228	0.0376125
$53$	7.83248	1.07587	0.537937	−	0.842985i	$-0.319204\pi$
$53$	7.83248	1.07587	0.537937	+	0.842985i	$0.319204\pi$
$54$	7.82864	1.06534
$55$	0	0
$56$	−2.87492	−0.384177
$57$	−1.55187	−0.205551
$58$	−10.3707	−1.36174
$59$	7.73940	1.00758	0.503792	−	0.863825i	$-0.331938\pi$
$59$	7.73940	1.00758	0.503792	+	0.863825i	$0.331938\pi$
$60$	0.0920392	0.0118822
$61$	3.97128	0.508470	0.254235	−	0.967142i	$-0.418176\pi$
$61$	3.97128	0.508470	0.254235	+	0.967142i	$0.418176\pi$
$62$	6.87754	0.873448
$63$	−1.20687	−0.152051
$64$	8.25571	1.03196
$65$	−3.94610	−0.489453
$66$	0	0
$67$	0.686469	0.0838655	0.0419327	−	0.999120i	$-0.486648\pi$
$67$	0.686469	0.0838655	0.0419327	+	0.999120i	$0.486648\pi$
$68$	0.328679	0.0398582
$69$	−9.86117	−1.18715
$70$	1.38970	0.166101
$71$	4.07768	0.483931	0.241966	−	0.970285i	$-0.422208\pi$
$71$	4.07768	0.483931	0.241966	+	0.970285i	$0.422208\pi$
$72$	3.46964	0.408901
$73$	0.867108	0.101487	0.0507437	−	0.998712i	$-0.483841\pi$
$73$	0.867108	0.101487	0.0507437	+	0.998712i	$0.483841\pi$
$74$	−11.0918	−1.28940
$75$	−1.33908	−0.154624
$76$	−0.0796556	−0.00913712
$77$	0	0
$78$	7.34337	0.831473
$79$	−9.16188	−1.03079	−0.515396	−	0.856952i	$-0.672355\pi$
$79$	−9.16188	−1.03079	−0.515396	+	0.856952i	$0.672355\pi$
$80$	−3.85781	−0.431316
$81$	−3.92288	−0.435875
$82$	9.82378	1.08485
$83$	−13.1810	−1.44680	−0.723399	−	0.690430i	$-0.757421\pi$
$83$	−13.1810	−1.44680	−0.723399	+	0.690430i	$0.757421\pi$
$84$	0.0920392	0.0100423
$85$	−4.78195	−0.518676
$86$	14.3883	1.55154
$87$	9.99298	1.07136
$88$	0	0
$89$	−0.382439	−0.0405385	−0.0202692	−	0.999795i	$-0.506452\pi$
$89$	−0.382439	−0.0405385	−0.0202692	+	0.999795i	$0.506452\pi$
$90$	−1.67718	−0.176791
$91$	−3.94610	−0.413663
$92$	−0.506161	−0.0527709
$93$	−6.62702	−0.687190
$94$	−0.643480	−0.0663698
$95$	1.15891	0.118902
$96$	−0.520419	−0.0531151
$97$	16.9086	1.71681	0.858405	−	0.512972i	$-0.171456\pi$
$97$	16.9086	1.71681	0.858405	+	0.512972i	$0.171456\pi$
$98$	1.38970	0.140381
$99$	0	0
$100$	−0.0687332	−0.00687332
$101$	−0.551012	−0.0548278	−0.0274139	−	0.999624i	$-0.508727\pi$
$101$	−0.551012	−0.0548278	−0.0274139	+	0.999624i	$0.508727\pi$
$102$	8.89883	0.881115
$103$	−16.1292	−1.58926	−0.794629	−	0.607096i	$-0.792334\pi$
$103$	−16.1292	−1.58926	−0.794629	+	0.607096i	$0.792334\pi$
$104$	11.3447	1.11244
$105$	−1.33908	−0.130681
$106$	10.8848	1.05723
$107$	16.5565	1.60058	0.800288	−	0.599616i	$-0.204680\pi$
$107$	16.5565	1.60058	0.800288	+	0.599616i	$0.204680\pi$
$108$	−0.387197	−0.0372580
$109$	7.43500	0.712144	0.356072	−	0.934459i	$-0.384116\pi$
$109$	7.43500	0.712144	0.356072	+	0.934459i	$0.384116\pi$
$110$	0	0
$111$	10.6878	1.01444
$112$	−3.85781	−0.364529
$113$	−8.60374	−0.809372	−0.404686	−	0.914456i	$-0.632619\pi$
$113$	−8.60374	−0.809372	−0.404686	+	0.914456i	$0.632619\pi$
$114$	−2.15664	−0.201988
$115$	7.36414	0.686710
$116$	0.512927	0.0476240
$117$	4.76241	0.440285
$118$	10.7555	0.990120
$119$	−4.78195	−0.438361
$120$	3.84975	0.351432
$121$	0	0
$122$	5.51888	0.499656
$123$	−9.46594	−0.853515
$124$	−0.340156	−0.0305469
$125$	1.00000	0.0894427
$126$	−1.67718	−0.149415
$127$	17.4984	1.55273	0.776364	−	0.630284i	$-0.217062\pi$
$127$	17.4984	1.55273	0.776364	+	0.630284i	$0.217062\pi$
$128$	10.6957	0.945374
$129$	−13.8642	−1.22068
$130$	−5.48389	−0.480969
$131$	20.8724	1.82363	0.911814	−	0.410603i	$-0.134682\pi$
$131$	20.8724	1.82363	0.911814	+	0.410603i	$0.134682\pi$
$132$	0	0
$133$	1.15891	0.100490
$134$	0.953986	0.0824118
$135$	5.63333	0.484840
$136$	13.7477	1.17886
$137$	−11.8714	−1.01424	−0.507121	−	0.861875i	$-0.669290\pi$
$137$	−11.8714	−1.01424	−0.507121	+	0.861875i	$0.669290\pi$
$138$	−13.7041	−1.16657
$139$	−4.84576	−0.411012	−0.205506	−	0.978656i	$-0.565884\pi$
$139$	−4.84576	−0.411012	−0.205506	+	0.978656i	$0.565884\pi$
$140$	−0.0687332	−0.00580902
$141$	0.620040	0.0522168
$142$	5.66675	0.475543
$143$	0	0
$144$	4.65586	0.387988
$145$	−7.46257	−0.619733
$146$	1.20502	0.0997282
$147$	−1.33908	−0.110445
$148$	0.548590	0.0450938
$149$	−11.1873	−0.916499	−0.458250	−	0.888824i	$-0.651523\pi$
$149$	−11.1873	−0.916499	−0.458250	+	0.888824i	$0.651523\pi$
$150$	−1.86092	−0.151943
$151$	2.89151	0.235308	0.117654	−	0.993055i	$-0.462463\pi$
$151$	2.89151	0.235308	0.117654	+	0.993055i	$0.462463\pi$
$152$	−3.33177	−0.270242
$153$	5.77118	0.466572
$154$	0	0
$155$	4.94894	0.397508
$156$	−0.363196	−0.0290789
$157$	9.74290	0.777568	0.388784	−	0.921329i	$-0.372895\pi$
$157$	9.74290	0.777568	0.388784	+	0.921329i	$0.372895\pi$
$158$	−12.7323	−1.01293
$159$	−10.4883	−0.831778
$160$	0.388640	0.0307247
$161$	7.36414	0.580376
$162$	−5.45162	−0.428320
$163$	−10.4088	−0.815281	−0.407640	−	0.913143i	$-0.633648\pi$
$163$	−10.4088	−0.815281	−0.407640	+	0.913143i	$0.633648\pi$
$164$	−0.485874	−0.0379404
$165$	0	0
$166$	−18.3176	−1.42172
$167$	18.0290	1.39512	0.697561	−	0.716525i	$-0.254269\pi$
$167$	18.0290	1.39512	0.697561	+	0.716525i	$0.254269\pi$
$168$	3.84975	0.297014
$169$	2.57168	0.197822
$170$	−6.64548	−0.509685
$171$	−1.39865	−0.106957
$172$	−0.711633	−0.0542615
$173$	−4.23728	−0.322154	−0.161077	−	0.986942i	$-0.551497\pi$
$173$	−4.23728	−0.322154	−0.161077	+	0.986942i	$0.551497\pi$
$174$	13.8872	1.05279
$175$	1.00000	0.0755929
$176$	0	0
$177$	−10.3637	−0.778982
$178$	−0.531476	−0.0398358
$179$	19.2805	1.44110	0.720548	−	0.693405i	$-0.243891\pi$
$179$	19.2805	1.44110	0.720548	+	0.693405i	$0.243891\pi$
$180$	0.0829518	0.00618286
$181$	11.3763	0.845592	0.422796	−	0.906225i	$-0.361049\pi$
$181$	11.3763	0.845592	0.422796	+	0.906225i	$0.361049\pi$
$182$	−5.48389	−0.406493
$183$	−5.31786	−0.393107
$184$	−21.1713	−1.56077
$185$	−7.98144	−0.586807
$186$	−9.20957	−0.675279
$187$	0	0
$188$	0.0318259	0.00232114
$189$	5.63333	0.409764
$190$	1.61054	0.116841
$191$	12.5852	0.910633	0.455316	−	0.890330i	$-0.349526\pi$
$191$	12.5852	0.910633	0.455316	+	0.890330i	$0.349526\pi$
$192$	−11.0551	−0.797830
$193$	−5.52570	−0.397749	−0.198874	−	0.980025i	$-0.563729\pi$
$193$	−5.52570	−0.397749	−0.198874	+	0.980025i	$0.563729\pi$
$194$	23.4979	1.68705
$195$	5.28414	0.378405
$196$	−0.0687332	−0.00490951
$197$	−10.2918	−0.733257	−0.366629	−	0.930367i	$-0.619488\pi$
$197$	−10.2918	−0.733257	−0.366629	+	0.930367i	$0.619488\pi$
$198$	0	0
$199$	−1.58408	−0.112293	−0.0561464	−	0.998423i	$-0.517881\pi$
$199$	−1.58408	−0.112293	−0.0561464	+	0.998423i	$0.517881\pi$
$200$	−2.87492	−0.203287
$201$	−0.919236	−0.0648379
$202$	−0.765742	−0.0538774
$203$	−7.46257	−0.523770
$204$	−0.440127	−0.0308151
$205$	7.06899	0.493720
$206$	−22.4148	−1.56171
$207$	−8.88753	−0.617726
$208$	15.2233	1.05555
$209$	0	0
$210$	−1.86092	−0.128416
$211$	16.2131	1.11615	0.558077	−	0.829789i	$-0.311539\pi$
$211$	16.2131	1.11615	0.558077	+	0.829789i	$0.311539\pi$
$212$	−0.538352	−0.0369742
$213$	−5.46034	−0.374136
$214$	23.0086	1.57283
$215$	10.3536	0.706107
$216$	−16.1954	−1.10195
$217$	4.94894	0.335956
$218$	10.3324	0.699800
$219$	−1.16113	−0.0784617
$220$	0	0
$221$	18.8700	1.26934
$222$	14.8528	0.996856
$223$	20.7492	1.38947	0.694734	−	0.719266i	$-0.255522\pi$
$223$	20.7492	1.38947	0.694734	+	0.719266i	$0.255522\pi$
$224$	0.388640	0.0259671
$225$	−1.20687	−0.0804577
$226$	−11.9566	−0.795343
$227$	−12.8887	−0.855452	−0.427726	−	0.903908i	$-0.640685\pi$
$227$	−12.8887	−0.855452	−0.427726	+	0.903908i	$0.640685\pi$
$228$	0.106665	0.00706407
$229$	14.4560	0.955282	0.477641	−	0.878555i	$-0.341492\pi$
$229$	14.4560	0.955282	0.477641	+	0.878555i	$0.341492\pi$
$230$	10.2339	0.674807
$231$	0	0
$232$	21.4543	1.40854
$233$	−23.5678	−1.54398	−0.771990	−	0.635635i	$-0.780738\pi$
$233$	−23.5678	−1.54398	−0.771990	+	0.635635i	$0.780738\pi$
$234$	6.61832	0.432653
$235$	−0.463035	−0.0302051
$236$	−0.531954	−0.0346273
$237$	12.2685	0.796924
$238$	−6.64548	−0.430762
$239$	−10.7182	−0.693303	−0.346652	−	0.937994i	$-0.612681\pi$
$239$	−10.7182	−0.693303	−0.346652	+	0.937994i	$0.612681\pi$
$240$	5.16591	0.333458
$241$	−18.4240	−1.18680	−0.593398	−	0.804909i	$-0.702214\pi$
$241$	−18.4240	−1.18680	−0.593398	+	0.804909i	$0.702214\pi$
$242$	0	0
$243$	−11.6469	−0.747152
$244$	−0.272959	−0.0174744
$245$	1.00000	0.0638877
$246$	−13.1548	−0.838721
$247$	−4.57317	−0.290984
$248$	−14.2278	−0.903466
$249$	17.6504	1.11855
$250$	1.38970	0.0878924
$251$	18.6051	1.17435	0.587173	−	0.809462i	$-0.300241\pi$
$251$	18.6051	1.17435	0.587173	+	0.809462i	$0.300241\pi$
$252$	0.0829518	0.00522547
$253$	0	0
$254$	24.3175	1.52581
$255$	6.40341	0.400997
$256$	−1.64763	−0.102977
$257$	9.29366	0.579723	0.289861	−	0.957069i	$-0.406391\pi$
$257$	9.29366	0.579723	0.289861	+	0.957069i	$0.406391\pi$
$258$	−19.2671	−1.19952
$259$	−7.98144	−0.495943
$260$	0.271228	0.0168208
$261$	9.00633	0.557478
$262$	29.0063	1.79202
$263$	27.4069	1.68998	0.844991	−	0.534781i	$-0.179606\pi$
$263$	27.4069	1.68998	0.844991	+	0.534781i	$0.179606\pi$
$264$	0	0
$265$	7.83248	0.481146
$266$	1.61054	0.0987484
$267$	0.512116	0.0313410
$268$	−0.0471832	−0.00288217
$269$	22.5141	1.37271	0.686353	−	0.727268i	$-0.259210\pi$
$269$	22.5141	1.37271	0.686353	+	0.727268i	$0.259210\pi$
$270$	7.82864	0.476436
$271$	20.1822	1.22598	0.612991	−	0.790090i	$-0.289966\pi$
$271$	20.1822	1.22598	0.612991	+	0.790090i	$0.289966\pi$
$272$	18.4479	1.11857
$273$	5.28414	0.319811
$274$	−16.4977	−0.996662
$275$	0	0
$276$	0.677790	0.0407982
$277$	−4.93354	−0.296427	−0.148214	−	0.988955i	$-0.547352\pi$
$277$	−4.93354	−0.296427	−0.148214	+	0.988955i	$0.547352\pi$
$278$	−6.73415	−0.403888
$279$	−5.97270	−0.357576
$280$	−2.87492	−0.171809
$281$	−25.1591	−1.50087	−0.750433	−	0.660947i	$-0.770155\pi$
$281$	−25.1591	−1.50087	−0.750433	+	0.660947i	$0.770155\pi$
$282$	0.861670	0.0513117
$283$	7.83461	0.465719	0.232859	−	0.972510i	$-0.425192\pi$
$283$	7.83461	0.465719	0.232859	+	0.972510i	$0.425192\pi$
$284$	−0.280272	−0.0166311
$285$	−1.55187	−0.0919250
$286$	0	0
$287$	7.06899	0.417269
$288$	−0.469036	−0.0276382
$289$	5.86707	0.345121
$290$	−10.3707	−0.608991
$291$	−22.6420	−1.32730
$292$	−0.0595991	−0.00348778
$293$	19.5486	1.14204	0.571021	−	0.820936i	$-0.306548\pi$
$293$	19.5486	1.14204	0.571021	+	0.820936i	$0.306548\pi$
$294$	−1.86092	−0.108531
$295$	7.73940	0.450605
$296$	22.9460	1.33371
$297$	0	0
$298$	−15.5470	−0.900613
$299$	−29.0596	−1.68056
$300$	0.0920392	0.00531389
$301$	10.3536	0.596769
$302$	4.01833	0.231229
$303$	0.737849	0.0423883
$304$	−4.47085	−0.256421
$305$	3.97128	0.227395
$306$	8.02020	0.458485
$307$	−6.34372	−0.362055	−0.181028	−	0.983478i	$-0.557942\pi$
$307$	−6.34372	−0.362055	−0.181028	+	0.983478i	$0.557942\pi$
$308$	0	0
$309$	21.5983	1.22868
$310$	6.87754	0.390618
$311$	8.29035	0.470103	0.235051	−	0.971983i	$-0.424474\pi$
$311$	8.29035	0.470103	0.235051	+	0.971983i	$0.424474\pi$
$312$	−15.1915	−0.860048
$313$	2.06948	0.116974	0.0584871	−	0.998288i	$-0.481372\pi$
$313$	2.06948	0.116974	0.0584871	+	0.998288i	$0.481372\pi$
$314$	13.5397	0.764090
$315$	−1.20687	−0.0679992
$316$	0.629726	0.0354248
$317$	−14.8944	−0.836551	−0.418276	−	0.908320i	$-0.637365\pi$
$317$	−14.8944	−0.836551	−0.418276	+	0.908320i	$0.637365\pi$
$318$	−14.5756	−0.817360
$319$	0	0
$320$	8.25571	0.461508
$321$	−22.1705	−1.23743
$322$	10.2339	0.570316
$323$	−5.54185	−0.308357
$324$	0.269632	0.0149795
$325$	−3.94610	−0.218890
$326$	−14.4651	−0.801149
$327$	−9.95606	−0.550571
$328$	−20.3228	−1.12214
$329$	−0.463035	−0.0255279
$330$	0	0
$331$	−6.83550	−0.375713	−0.187857	−	0.982196i	$-0.560154\pi$
$331$	−6.83550	−0.375713	−0.187857	+	0.982196i	$0.560154\pi$
$332$	0.905970	0.0497215
$333$	9.63253	0.527860
$334$	25.0548	1.37094
$335$	0.686469	0.0375058
$336$	5.16591	0.281824
$337$	0.336838	0.0183487	0.00917437	−	0.999958i	$-0.497080\pi$
$337$	0.336838	0.0183487	0.00917437	+	0.999958i	$0.497080\pi$
$338$	3.57387	0.194393
$339$	11.5211	0.625740
$340$	0.328679	0.0178251
$341$	0	0
$342$	−1.94370	−0.105103
$343$	1.00000	0.0539949
$344$	−29.7656	−1.60486
$345$	−9.86117	−0.530908
$346$	−5.88855	−0.316570
$347$	−2.54307	−0.136519	−0.0682595	−	0.997668i	$-0.521745\pi$
$347$	−2.54307	−0.136519	−0.0682595	+	0.997668i	$0.521745\pi$
$348$	−0.686850	−0.0368190
$349$	−1.74424	−0.0933668	−0.0466834	−	0.998910i	$-0.514865\pi$
$349$	−1.74424	−0.0933668	−0.0466834	+	0.998910i	$0.514865\pi$
$350$	1.38970	0.0742826
$351$	−22.2297	−1.18653
$352$	0	0
$353$	15.9185	0.847254	0.423627	−	0.905837i	$-0.360757\pi$
$353$	15.9185	0.847254	0.423627	+	0.905837i	$0.360757\pi$
$354$	−14.4024	−0.765479
$355$	4.07768	0.216421
$356$	0.0262863	0.00139317
$357$	6.40341	0.338905
$358$	26.7942	1.41612
$359$	−19.5669	−1.03270	−0.516352	−	0.856376i	$-0.672710\pi$
$359$	−19.5669	−1.03270	−0.516352	+	0.856376i	$0.672710\pi$
$360$	3.46964	0.182866
$361$	−17.6569	−0.929312
$362$	15.8096	0.830935
$363$	0	0
$364$	0.271228	0.0142162
$365$	0.867108	0.0453865
$366$	−7.39023	−0.386293
$367$	−3.50279	−0.182844	−0.0914220	−	0.995812i	$-0.529141\pi$
$367$	−3.50279	−0.182844	−0.0914220	+	0.995812i	$0.529141\pi$
$368$	−28.4095	−1.48095
$369$	−8.53132	−0.444123
$370$	−11.0918	−0.576636
$371$	7.83248	0.406642
$372$	0.455496	0.0236164
$373$	−16.6995	−0.864667	−0.432334	−	0.901714i	$-0.642310\pi$
$373$	−16.6995	−0.864667	−0.432334	+	0.901714i	$0.642310\pi$
$374$	0	0
$375$	−1.33908	−0.0691498
$376$	1.33119	0.0686508
$377$	29.4480	1.51665
$378$	7.82864	0.402662
$379$	−0.125195	−0.00643083	−0.00321542	−	0.999995i	$-0.501024\pi$
$379$	−0.125195	−0.00643083	−0.00321542	+	0.999995i	$0.501024\pi$
$380$	−0.0796556	−0.00408625
$381$	−23.4317	−1.20044
$382$	17.4896	0.894848
$383$	−30.4292	−1.55486	−0.777429	−	0.628971i	$-0.783476\pi$
$383$	−30.4292	−1.55486	−0.777429	+	0.628971i	$0.783476\pi$
$384$	−14.3224	−0.730886
$385$	0	0
$386$	−7.67907	−0.390854
$387$	−12.4954	−0.635175
$388$	−1.16218	−0.0590009
$389$	20.5595	1.04241	0.521205	−	0.853432i	$-0.325483\pi$
$389$	20.5595	1.04241	0.521205	+	0.853432i	$0.325483\pi$
$390$	7.34337	0.371846
$391$	−35.2150	−1.78090
$392$	−2.87492	−0.145205
$393$	−27.9498	−1.40988
$394$	−14.3025	−0.720547
$395$	−9.16188	−0.460984
$396$	0	0
$397$	28.5802	1.43440	0.717200	−	0.696867i	$-0.245423\pi$
$397$	28.5802	1.43440	0.717200	+	0.696867i	$0.245423\pi$
$398$	−2.20140	−0.110346
$399$	−1.55187	−0.0776908
$400$	−3.85781	−0.192890
$401$	−6.18045	−0.308637	−0.154318	−	0.988021i	$-0.549318\pi$
$401$	−6.18045	−0.308637	−0.154318	+	0.988021i	$0.549318\pi$
$402$	−1.27746	−0.0637140
$403$	−19.5290	−0.972808
$404$	0.0378729	0.00188424
$405$	−3.92288	−0.194929
$406$	−10.3707	−0.514691
$407$	0	0
$408$	−18.4093	−0.911396
$409$	−1.48361	−0.0733597	−0.0366798	−	0.999327i	$-0.511678\pi$
$409$	−1.48361	−0.0733597	−0.0366798	+	0.999327i	$0.511678\pi$
$410$	9.82378	0.485162
$411$	15.8968	0.784129
$412$	1.10861	0.0546174
$413$	7.73940	0.380831
$414$	−12.3510	−0.607019
$415$	−13.1810	−0.647028
$416$	−1.53361	−0.0751914
$417$	6.48886	0.317761
$418$	0	0
$419$	−9.88917	−0.483117	−0.241559	−	0.970386i	$-0.577659\pi$
$419$	−9.88917	−0.483117	−0.241559	+	0.970386i	$0.577659\pi$
$420$	0.0920392	0.00449105
$421$	22.0180	1.07309	0.536546	−	0.843871i	$-0.319729\pi$
$421$	22.0180	1.07309	0.536546	+	0.843871i	$0.319729\pi$
$422$	22.5313	1.09681
$423$	0.558821	0.0271708
$424$	−22.5178	−1.09356
$425$	−4.78195	−0.231959
$426$	−7.58823	−0.367651
$427$	3.97128	0.192184
$428$	−1.13798	−0.0550064
$429$	0	0
$430$	14.3883	0.693868
$431$	−25.8082	−1.24314	−0.621568	−	0.783360i	$-0.713504\pi$
$431$	−25.8082	−1.24314	−0.621568	+	0.783360i	$0.713504\pi$
$432$	−21.7323	−1.04560
$433$	38.1154	1.83171	0.915855	−	0.401510i	$-0.131514\pi$
$433$	38.1154	1.83171	0.915855	+	0.401510i	$0.131514\pi$
$434$	6.87754	0.330132
$435$	9.99298	0.479127
$436$	−0.511031	−0.0244740
$437$	8.53438	0.408255
$438$	−1.61362	−0.0771017
$439$	−1.15055	−0.0549126	−0.0274563	−	0.999623i	$-0.508741\pi$
$439$	−1.15055	−0.0549126	−0.0274563	+	0.999623i	$0.508741\pi$
$440$	0	0
$441$	−1.20687	−0.0574698
$442$	26.2237	1.24733
$443$	30.4328	1.44591	0.722954	−	0.690897i	$-0.242784\pi$
$443$	30.4328	1.44591	0.722954	+	0.690897i	$0.242784\pi$
$444$	−0.734606	−0.0348629
$445$	−0.382439	−0.0181294
$446$	28.8352	1.36538
$447$	14.9807	0.708562
$448$	8.25571	0.390046
$449$	13.4484	0.634669	0.317335	−	0.948314i	$-0.397212\pi$
$449$	13.4484	0.634669	0.317335	+	0.948314i	$0.397212\pi$
$450$	−1.67718	−0.0790631
$451$	0	0
$452$	0.591363	0.0278154
$453$	−3.87196	−0.181921
$454$	−17.9114	−0.840624
$455$	−3.94610	−0.184996
$456$	4.46151	0.208929
$457$	−10.7377	−0.502288	−0.251144	−	0.967950i	$-0.580807\pi$
$457$	−10.7377	−0.502288	−0.251144	+	0.967950i	$0.580807\pi$
$458$	20.0896	0.938724
$459$	−26.9383	−1.25737
$460$	−0.506161	−0.0235999
$461$	9.94825	0.463336	0.231668	−	0.972795i	$-0.425582\pi$
$461$	9.94825	0.463336	0.231668	+	0.972795i	$0.425582\pi$
$462$	0	0
$463$	−27.8064	−1.29227	−0.646136	−	0.763223i	$-0.723616\pi$
$463$	−27.8064	−1.29227	−0.646136	+	0.763223i	$0.723616\pi$
$464$	28.7892	1.33650
$465$	−6.62702	−0.307321
$466$	−32.7522	−1.51722
$467$	−20.5492	−0.950905	−0.475453	−	0.879741i	$-0.657716\pi$
$467$	−20.5492	−0.950905	−0.475453	+	0.879741i	$0.657716\pi$
$468$	−0.327336	−0.0151311
$469$	0.686469	0.0316982
$470$	−0.643480	−0.0296815
$471$	−13.0465	−0.601152
$472$	−22.2502	−1.02415
$473$	0	0
$474$	17.0495	0.783111
$475$	1.15891	0.0531744
$476$	0.328679	0.0150650
$477$	−9.45276	−0.432812
$478$	−14.8951	−0.681286
$479$	−8.24927	−0.376919	−0.188459	−	0.982081i	$-0.560349\pi$
$479$	−8.24927	−0.376919	−0.188459	+	0.982081i	$0.560349\pi$
$480$	−0.520419	−0.0237538
$481$	31.4956	1.43607
$482$	−25.6039	−1.16623
$483$	−9.86117	−0.448699
$484$	0	0
$485$	16.9086	0.767781
$486$	−16.1858	−0.734201
$487$	8.60750	0.390043	0.195022	−	0.980799i	$-0.437522\pi$
$487$	8.60750	0.390043	0.195022	+	0.980799i	$0.437522\pi$
$488$	−11.4171	−0.516828
$489$	13.9382	0.630308
$490$	1.38970	0.0627803
$491$	−4.87862	−0.220169	−0.110085	−	0.993922i	$-0.535112\pi$
$491$	−4.87862	−0.220169	−0.110085	+	0.993922i	$0.535112\pi$
$492$	0.650624	0.0293324
$493$	35.6857	1.60720
$494$	−6.35534	−0.285940
$495$	0	0
$496$	−19.0921	−0.857259
$497$	4.07768	0.182909
$498$	24.5287	1.09916
$499$	38.0320	1.70255	0.851273	−	0.524723i	$-0.175831\pi$
$499$	38.0320	1.70255	0.851273	+	0.524723i	$0.175831\pi$
$500$	−0.0687332	−0.00307384
$501$	−24.1422	−1.07859
$502$	25.8556	1.15399
$503$	25.7799	1.14947	0.574734	−	0.818340i	$-0.305105\pi$
$503$	25.7799	1.14947	0.574734	+	0.818340i	$0.305105\pi$
$504$	3.46964	0.154550
$505$	−0.551012	−0.0245197
$506$	0	0
$507$	−3.44369	−0.152940
$508$	−1.20272	−0.0533620
$509$	−41.8301	−1.85409	−0.927043	−	0.374954i	$-0.877659\pi$
$509$	−41.8301	−1.85409	−0.927043	+	0.374954i	$0.877659\pi$
$510$	8.89883	0.394047
$511$	0.867108	0.0383586
$512$	−23.6811	−1.04657
$513$	6.52852	0.288241
$514$	12.9154	0.569674
$515$	−16.1292	−0.710737
$516$	0.952934	0.0419506
$517$	0	0
$518$	−11.0918	−0.487346
$519$	5.67405	0.249063
$520$	11.3447	0.497498
$521$	44.2656	1.93931	0.969655	−	0.244478i	$-0.0786167\pi$
$521$	44.2656	1.93931	0.969655	+	0.244478i	$0.0786167\pi$
$522$	12.5161	0.547815
$523$	−26.0456	−1.13890	−0.569448	−	0.822027i	$-0.692843\pi$
$523$	−26.0456	−1.13890	−0.569448	+	0.822027i	$0.692843\pi$
$524$	−1.43463	−0.0626719
$525$	−1.33908	−0.0584422
$526$	38.0874	1.66069
$527$	−23.6656	−1.03089
$528$	0	0
$529$	31.2306	1.35785
$530$	10.8848	0.472806
$531$	−9.34042	−0.405340
$532$	−0.0796556	−0.00345351
$533$	−27.8949	−1.20826
$534$	0.711688	0.0307978
$535$	16.5565	0.715799
$536$	−1.97354	−0.0852440
$537$	−25.8182	−1.11414
$538$	31.2878	1.34891
$539$	0	0
$540$	−0.387197	−0.0166623
$541$	34.4716	1.48205	0.741024	−	0.671478i	$-0.234340\pi$
$541$	34.4716	1.48205	0.741024	+	0.671478i	$0.234340\pi$
$542$	28.0472	1.20473
$543$	−15.2337	−0.653742
$544$	−1.85846	−0.0796806
$545$	7.43500	0.318480
$546$	7.34337	0.314267
$547$	−6.38611	−0.273050	−0.136525	−	0.990637i	$-0.543593\pi$
$547$	−6.38611	−0.273050	−0.136525	+	0.990637i	$0.543593\pi$
$548$	0.815960	0.0348561
$549$	−4.79280	−0.204552
$550$	0	0
$551$	−8.64845	−0.368436
$552$	28.3501	1.20666
$553$	−9.16188	−0.389603
$554$	−6.85614	−0.291289
$555$	10.6878	0.453671
$556$	0.333065	0.0141251
$557$	−15.0788	−0.638911	−0.319455	−	0.947601i	$-0.603500\pi$
$557$	−15.0788	−0.638911	−0.319455	+	0.947601i	$0.603500\pi$
$558$	−8.30027	−0.351378
$559$	−40.8562	−1.72803
$560$	−3.85781	−0.163022
$561$	0	0
$562$	−34.9636	−1.47485
$563$	8.80139	0.370934	0.185467	−	0.982650i	$-0.440620\pi$
$563$	8.80139	0.370934	0.185467	+	0.982650i	$0.440620\pi$
$564$	−0.0426174	−0.00179451
$565$	−8.60374	−0.361962
$566$	10.8878	0.457646
$567$	−3.92288	−0.164745
$568$	−11.7230	−0.491886
$569$	6.40967	0.268707	0.134354	−	0.990933i	$-0.457104\pi$
$569$	6.40967	0.268707	0.134354	+	0.990933i	$0.457104\pi$
$570$	−2.15664	−0.0903316
$571$	−13.6983	−0.573254	−0.286627	−	0.958042i	$-0.592534\pi$
$571$	−13.6983	−0.573254	−0.286627	+	0.958042i	$0.592534\pi$
$572$	0	0
$573$	−16.8526	−0.704026
$574$	9.82378	0.410037
$575$	7.36414	0.307106
$576$	−9.96354	−0.415147
$577$	−14.9248	−0.621326	−0.310663	−	0.950520i	$-0.600551\pi$
$577$	−14.9248	−0.621326	−0.310663	+	0.950520i	$0.600551\pi$
$578$	8.15346	0.339139
$579$	7.39936	0.307507
$580$	0.512927	0.0212981
$581$	−13.1810	−0.546838
$582$	−31.4656	−1.30429
$583$	0	0
$584$	−2.49287	−0.103156
$585$	4.76241	0.196901
$586$	27.1667	1.12225
$587$	−12.4819	−0.515185	−0.257593	−	0.966254i	$-0.582929\pi$
$587$	−12.4819	−0.515185	−0.257593	+	0.966254i	$0.582929\pi$
$588$	0.0920392	0.00379563
$589$	5.73537	0.236322
$590$	10.7555	0.442795
$591$	13.7815	0.566894
$592$	30.7909	1.26550
$593$	−3.74417	−0.153755	−0.0768773	−	0.997041i	$-0.524495\pi$
$593$	−3.74417	−0.153755	−0.0768773	+	0.997041i	$0.524495\pi$
$594$	0	0
$595$	−4.78195	−0.196041
$596$	0.768939	0.0314970
$597$	2.12121	0.0868155
$598$	−40.3842	−1.65143
$599$	−40.5923	−1.65856	−0.829278	−	0.558836i	$-0.811248\pi$
$599$	−40.5923	−1.65856	−0.829278	+	0.558836i	$0.811248\pi$
$600$	3.84975	0.157165
$601$	22.3363	0.911118	0.455559	−	0.890206i	$-0.349439\pi$
$601$	22.3363	0.911118	0.455559	+	0.890206i	$0.349439\pi$
$602$	14.3883	0.586425
$603$	−0.828476	−0.0337381
$604$	−0.198743	−0.00808672
$605$	0	0
$606$	1.02539	0.0416536
$607$	−43.6562	−1.77195	−0.885976	−	0.463732i	$-0.846510\pi$
$607$	−43.6562	−1.77195	−0.885976	+	0.463732i	$0.846510\pi$
$608$	0.450398	0.0182661
$609$	9.99298	0.404936
$610$	5.51888	0.223453
$611$	1.82718	0.0739198
$612$	−0.396671	−0.0160345
$613$	−32.4296	−1.30982	−0.654909	−	0.755708i	$-0.727293\pi$
$613$	−32.4296	−1.30982	−0.654909	+	0.755708i	$0.727293\pi$
$614$	−8.81587	−0.355780
$615$	−9.46594	−0.381704
$616$	0	0
$617$	−7.01816	−0.282541	−0.141270	−	0.989971i	$-0.545119\pi$
$617$	−7.01816	−0.282541	−0.141270	+	0.989971i	$0.545119\pi$
$618$	30.0151	1.20739
$619$	−27.6132	−1.10987	−0.554935	−	0.831894i	$-0.687257\pi$
$619$	−27.6132	−1.10987	−0.554935	+	0.831894i	$0.687257\pi$
$620$	−0.340156	−0.0136610
$621$	41.4846	1.66472
$622$	11.5211	0.461954
$623$	−0.382439	−0.0153221
$624$	−20.3852	−0.816061
$625$	1.00000	0.0400000
$626$	2.87596	0.114947
$627$	0	0
$628$	−0.669661	−0.0267224
$629$	38.1669	1.52181
$630$	−1.67718	−0.0668205
$631$	6.35717	0.253075	0.126537	−	0.991962i	$-0.459614\pi$
$631$	6.35717	0.253075	0.126537	+	0.991962i	$0.459614\pi$
$632$	26.3397	1.04774
$633$	−21.7106	−0.862919
$634$	−20.6987	−0.822051
$635$	17.4984	0.694401
$636$	0.720896	0.0285854
$637$	−3.94610	−0.156350
$638$	0	0
$639$	−4.92121	−0.194680
$640$	10.6957	0.422784
$641$	−5.54954	−0.219194	−0.109597	−	0.993976i	$-0.534956\pi$
$641$	−5.54954	−0.219194	−0.109597	+	0.993976i	$0.534956\pi$
$642$	−30.8103	−1.21599
$643$	39.6480	1.56356	0.781782	−	0.623551i	$-0.214311\pi$
$643$	39.6480	1.56356	0.781782	+	0.623551i	$0.214311\pi$
$644$	−0.506161	−0.0199455
$645$	−13.8642	−0.545904
$646$	−7.70151	−0.303012
$647$	−13.5756	−0.533714	−0.266857	−	0.963736i	$-0.585985\pi$
$647$	−13.5756	−0.533714	−0.266857	+	0.963736i	$0.585985\pi$
$648$	11.2780	0.443040
$649$	0	0
$650$	−5.48389	−0.215096
$651$	−6.62702	−0.259733
$652$	0.715431	0.0280184
$653$	−7.54721	−0.295345	−0.147673	−	0.989036i	$-0.547178\pi$
$653$	−7.54721	−0.295345	−0.147673	+	0.989036i	$0.547178\pi$
$654$	−13.8359	−0.541028
$655$	20.8724	0.815551
$656$	−27.2708	−1.06475
$657$	−1.04648	−0.0408272
$658$	−0.643480	−0.0250854
$659$	28.5719	1.11300	0.556502	−	0.830846i	$-0.312143\pi$
$659$	28.5719	1.11300	0.556502	+	0.830846i	$0.312143\pi$
$660$	0	0
$661$	−23.9965	−0.933355	−0.466677	−	0.884428i	$-0.654549\pi$
$661$	−23.9965	−0.933355	−0.466677	+	0.884428i	$0.654549\pi$
$662$	−9.49930	−0.369201
$663$	−25.2685	−0.981347
$664$	37.8942	1.47058
$665$	1.15891	0.0449406
$666$	13.3863	0.518710
$667$	−54.9554	−2.12788
$668$	−1.23919	−0.0479456
$669$	−27.7848	−1.07422
$670$	0.953986	0.0368557
$671$	0	0
$672$	−0.520419	−0.0200756
$673$	−43.8794	−1.69142	−0.845712	−	0.533639i	$-0.820824\pi$
$673$	−43.8794	−1.69142	−0.845712	+	0.533639i	$0.820824\pi$
$674$	0.468104	0.0180307
$675$	5.63333	0.216827
$676$	−0.176760	−0.00679846
$677$	41.3579	1.58951	0.794756	−	0.606930i	$-0.207599\pi$
$677$	41.3579	1.58951	0.794756	+	0.606930i	$0.207599\pi$
$678$	16.0109	0.614894
$679$	16.9086	0.648893
$680$	13.7477	0.527201
$681$	17.2590	0.661365
$682$	0	0
$683$	−41.8181	−1.60012	−0.800062	−	0.599917i	$-0.795200\pi$
$683$	−41.8181	−1.60012	−0.800062	+	0.599917i	$0.795200\pi$
$684$	0.0961336	0.00367576
$685$	−11.8714	−0.453583
$686$	1.38970	0.0530590
$687$	−19.3578	−0.738546
$688$	−39.9421	−1.52278
$689$	−30.9077	−1.17749
$690$	−13.7041	−0.521705
$691$	−14.5859	−0.554875	−0.277438	−	0.960744i	$-0.589485\pi$
$691$	−14.5859	−0.554875	−0.277438	+	0.960744i	$0.589485\pi$
$692$	0.291242	0.0110713
$693$	0	0
$694$	−3.53410	−0.134153
$695$	−4.84576	−0.183810
$696$	−28.7290	−1.08897
$697$	−33.8036	−1.28040
$698$	−2.42397	−0.0917485
$699$	31.5592	1.19368
$700$	−0.0687332	−0.00259787
$701$	8.20599	0.309936	0.154968	−	0.987920i	$-0.450473\pi$
$701$	8.20599	0.309936	0.154968	+	0.987920i	$0.450473\pi$
$702$	−30.8926	−1.16596
$703$	−9.24978	−0.348862
$704$	0	0
$705$	0.620040	0.0233521
$706$	22.1219	0.832568
$707$	−0.551012	−0.0207230
$708$	0.712329	0.0267710
$709$	37.5612	1.41064	0.705321	−	0.708888i	$-0.250803\pi$
$709$	37.5612	1.41064	0.705321	+	0.708888i	$0.250803\pi$
$710$	5.66675	0.212669
$711$	11.0572	0.414676
$712$	1.09948	0.0412048
$713$	36.4447	1.36486
$714$	8.89883	0.333030
$715$	0	0
$716$	−1.32521	−0.0495255
$717$	14.3525	0.536005
$718$	−27.1922	−1.01480
$719$	3.29737	0.122971	0.0614855	−	0.998108i	$-0.480416\pi$
$719$	3.29737	0.122971	0.0614855	+	0.998108i	$0.480416\pi$
$720$	4.65586	0.173514
$721$	−16.1292	−0.600683
$722$	−24.5378	−0.913204
$723$	24.6712	0.917534
$724$	−0.781928	−0.0290601
$725$	−7.46257	−0.277153
$726$	0	0
$727$	15.9781	0.592596	0.296298	−	0.955096i	$-0.404248\pi$
$727$	15.9781	0.592596	0.296298	+	0.955096i	$0.404248\pi$
$728$	11.3447	0.420463
$729$	27.3648	1.01351
$730$	1.20502	0.0445998
$731$	−49.5102	−1.83120
$732$	0.365513	0.0135098
$733$	17.3106	0.639383	0.319691	−	0.947522i	$-0.396421\pi$
$733$	17.3106	0.639383	0.319691	+	0.947522i	$0.396421\pi$
$734$	−4.86782	−0.179675
$735$	−1.33908	−0.0493927
$736$	2.86200	0.105495
$737$	0	0
$738$	−11.8560	−0.436425
$739$	−21.9231	−0.806454	−0.403227	−	0.915100i	$-0.632111\pi$
$739$	−21.9231	−0.806454	−0.403227	+	0.915100i	$0.632111\pi$
$740$	0.548590	0.0201666
$741$	6.12384	0.224965
$742$	10.8848	0.399594
$743$	−22.4883	−0.825015	−0.412508	−	0.910954i	$-0.635347\pi$
$743$	−22.4883	−0.825015	−0.412508	+	0.910954i	$0.635347\pi$
$744$	19.0521	0.698486
$745$	−11.1873	−0.409871
$746$	−23.2073	−0.849680
$747$	15.9077	0.582031
$748$	0	0
$749$	16.5565	0.604961
$750$	−1.86092	−0.0679512
$751$	−12.4353	−0.453772	−0.226886	−	0.973921i	$-0.572854\pi$
$751$	−12.4353	−0.453772	−0.226886	+	0.973921i	$0.572854\pi$
$752$	1.78630	0.0651397
$753$	−24.9137	−0.907907
$754$	40.9239	1.49036
$755$	2.89151	0.105233
$756$	−0.387197	−0.0140822
$757$	13.6815	0.497263	0.248631	−	0.968598i	$-0.420019\pi$
$757$	13.6815	0.497263	0.248631	+	0.968598i	$0.420019\pi$
$758$	−0.173983	−0.00631936
$759$	0	0
$760$	−3.33177	−0.120856
$761$	5.36529	0.194492	0.0972458	−	0.995260i	$-0.468997\pi$
$761$	5.36529	0.194492	0.0972458	+	0.995260i	$0.468997\pi$
$762$	−32.5630	−1.17963
$763$	7.43500	0.269165
$764$	−0.865021	−0.0312954
$765$	5.77118	0.208657
$766$	−42.2874	−1.52791
$767$	−30.5404	−1.10275
$768$	2.20630	0.0796131
$769$	−35.1400	−1.26718	−0.633591	−	0.773668i	$-0.718420\pi$
$769$	−35.1400	−1.26718	−0.633591	+	0.773668i	$0.718420\pi$
$770$	0	0
$771$	−12.4450	−0.448194
$772$	0.379799	0.0136693
$773$	−22.2719	−0.801065	−0.400532	−	0.916283i	$-0.631175\pi$
$773$	−22.2719	−0.801065	−0.400532	+	0.916283i	$0.631175\pi$
$774$	−17.3648	−0.624165
$775$	4.94894	0.177771
$776$	−48.6109	−1.74503
$777$	10.6878	0.383422
$778$	28.5716	1.02434
$779$	8.19232	0.293520
$780$	−0.363196	−0.0130045
$781$	0	0
$782$	−48.9383	−1.75003
$783$	−42.0391	−1.50236
$784$	−3.85781	−0.137779
$785$	9.74290	0.347739
$786$	−38.8418	−1.38544
$787$	40.5577	1.44573	0.722864	−	0.690991i	$-0.242825\pi$
$787$	40.5577	1.44573	0.722864	+	0.690991i	$0.242825\pi$
$788$	0.707385	0.0251996
$789$	−36.7000	−1.30656
$790$	−12.7323	−0.452994
$791$	−8.60374	−0.305914
$792$	0	0
$793$	−15.6710	−0.556495
$794$	39.7179	1.40954
$795$	−10.4883	−0.371982
$796$	0.108879	0.00385912
$797$	−34.4008	−1.21854	−0.609269	−	0.792963i	$-0.708537\pi$
$797$	−34.4008	−1.21854	−0.609269	+	0.792963i	$0.708537\pi$
$798$	−2.15664	−0.0763442
$799$	2.21421	0.0783331
$800$	0.388640	0.0137405
$801$	0.461553	0.0163082
$802$	−8.58897	−0.303287
$803$	0	0
$804$	0.0631820	0.00222826
$805$	7.36414	0.259552
$806$	−27.1394	−0.955946
$807$	−30.1481	−1.06126
$808$	1.58412	0.0557290
$809$	40.0717	1.40885	0.704424	−	0.709780i	$-0.251205\pi$
$809$	40.0717	1.40885	0.704424	+	0.709780i	$0.251205\pi$
$810$	−5.45162	−0.191550
$811$	−0.883979	−0.0310407	−0.0155203	−	0.999880i	$-0.504940\pi$
$811$	−0.883979	−0.0310407	−0.0155203	+	0.999880i	$0.504940\pi$
$812$	0.512927	0.0180002
$813$	−27.0256	−0.947829
$814$	0	0
$815$	−10.4088	−0.364605
$816$	−24.7032	−0.864783
$817$	11.9988	0.419786
$818$	−2.06177	−0.0720881
$819$	4.76241	0.166412
$820$	−0.485874	−0.0169675
$821$	−11.2472	−0.392532	−0.196266	−	0.980551i	$-0.562882\pi$
$821$	−11.2472	−0.392532	−0.196266	+	0.980551i	$0.562882\pi$
$822$	22.0917	0.770538
$823$	8.29076	0.288998	0.144499	−	0.989505i	$-0.453843\pi$
$823$	8.29076	0.288998	0.144499	+	0.989505i	$0.453843\pi$
$824$	46.3701	1.61538
$825$	0	0
$826$	10.7555	0.374230
$827$	4.86048	0.169015	0.0845077	−	0.996423i	$-0.473068\pi$
$827$	4.86048	0.169015	0.0845077	+	0.996423i	$0.473068\pi$
$828$	0.610869	0.0212291
$829$	27.0454	0.939327	0.469663	−	0.882846i	$-0.344375\pi$
$829$	27.0454	0.939327	0.469663	+	0.882846i	$0.344375\pi$
$830$	−18.3176	−0.635813
$831$	6.60640	0.229173
$832$	−32.5778	−1.12943
$833$	−4.78195	−0.165685
$834$	9.01756	0.312253
$835$	18.0290	0.623918
$836$	0	0
$837$	27.8790	0.963639
$838$	−13.7430	−0.474743
$839$	−10.5377	−0.363801	−0.181900	−	0.983317i	$-0.558225\pi$
$839$	−10.5377	−0.363801	−0.181900	+	0.983317i	$0.558225\pi$
$840$	3.84975	0.132829
$841$	26.6900	0.920345
$842$	30.5984	1.05449
$843$	33.6900	1.16035
$844$	−1.11438	−0.0383584
$845$	2.57168	0.0884686
$846$	0.776594	0.0266998
$847$	0	0
$848$	−30.2162	−1.03763
$849$	−10.4912	−0.360056
$850$	−6.64548	−0.227938
$851$	−58.7765	−2.01483
$852$	0.375306	0.0128578
$853$	15.5635	0.532885	0.266442	−	0.963851i	$-0.414152\pi$
$853$	15.5635	0.532885	0.266442	+	0.963851i	$0.414152\pi$
$854$	5.51888	0.188852
$855$	−1.39865	−0.0478328
$856$	−47.5986	−1.62689
$857$	−18.1093	−0.618603	−0.309301	−	0.950964i	$-0.600095\pi$
$857$	−18.1093	−0.618603	−0.309301	+	0.950964i	$0.600095\pi$
$858$	0	0
$859$	37.6193	1.28356	0.641778	−	0.766891i	$-0.278197\pi$
$859$	37.6193	1.28356	0.641778	+	0.766891i	$0.278197\pi$
$860$	−0.711633	−0.0242665
$861$	−9.46594	−0.322598
$862$	−35.8657	−1.22159
$863$	5.67841	0.193295	0.0966476	−	0.995319i	$-0.469188\pi$
$863$	5.67841	0.193295	0.0966476	+	0.995319i	$0.469188\pi$
$864$	2.18933	0.0744827
$865$	−4.23728	−0.144072
$866$	52.9690	1.79996
$867$	−7.85647	−0.266820
$868$	−0.340156	−0.0115457
$869$	0	0
$870$	13.8872	0.470822
$871$	−2.70887	−0.0917866
$872$	−21.3750	−0.723850
$873$	−20.4064	−0.690653
$874$	11.8602	0.401178
$875$	1.00000	0.0338062
$876$	0.0798080	0.00269646
$877$	14.9110	0.503508	0.251754	−	0.967791i	$-0.418993\pi$
$877$	14.9110	0.503508	0.251754	+	0.967791i	$0.418993\pi$
$878$	−1.59892	−0.0539608
$879$	−26.1771	−0.882933
$880$	0	0
$881$	24.8557	0.837409	0.418704	−	0.908123i	$-0.362484\pi$
$881$	24.8557	0.837409	0.418704	+	0.908123i	$0.362484\pi$
$882$	−1.67718	−0.0564737
$883$	−15.5500	−0.523299	−0.261650	−	0.965163i	$-0.584266\pi$
$883$	−15.5500	−0.523299	−0.261650	+	0.965163i	$0.584266\pi$
$884$	−1.29700	−0.0436228
$885$	−10.3637	−0.348371
$886$	42.2925	1.42084
$887$	42.8936	1.44023	0.720113	−	0.693857i	$-0.244090\pi$
$887$	42.8936	1.44023	0.720113	+	0.693857i	$0.244090\pi$
$888$	−30.7265	−1.03111
$889$	17.4984	0.586876
$890$	−0.531476	−0.0178151
$891$	0	0
$892$	−1.42616	−0.0477513
$893$	−0.536616	−0.0179572
$894$	20.8187	0.696280
$895$	19.2805	0.644477
$896$	10.6957	0.357318
$897$	38.9131	1.29927
$898$	18.6893	0.623668
$899$	−36.9318	−1.23174
$900$	0.0829518	0.00276506
$901$	−37.4546	−1.24779
$902$	0	0
$903$	−13.8642	−0.461373
$904$	24.7351	0.822676
$905$	11.3763	0.378160
$906$	−5.38086	−0.178767
$907$	−5.02913	−0.166989	−0.0834947	−	0.996508i	$-0.526608\pi$
$907$	−5.02913	−0.166989	−0.0834947	+	0.996508i	$0.526608\pi$
$908$	0.885881	0.0293990
$909$	0.664998	0.0220566
$910$	−5.48389	−0.181789
$911$	27.5265	0.911993	0.455996	−	0.889982i	$-0.349283\pi$
$911$	27.5265	0.911993	0.455996	+	0.889982i	$0.349283\pi$
$912$	5.98683	0.198244
$913$	0	0
$914$	−14.9222	−0.493582
$915$	−5.31786	−0.175803
$916$	−0.993610	−0.0328298
$917$	20.8724	0.689267
$918$	−37.4362	−1.23558
$919$	−0.901067	−0.0297234	−0.0148617	−	0.999890i	$-0.504731\pi$
$919$	−0.901067	−0.0297234	−0.0148617	+	0.999890i	$0.504731\pi$
$920$	−21.1713	−0.697997
$921$	8.49475	0.279912
$922$	13.8251	0.455305
$923$	−16.0909	−0.529639
$924$	0	0
$925$	−7.98144	−0.262428
$926$	−38.6425	−1.26987
$927$	19.4658	0.639340
$928$	−2.90025	−0.0952054
$929$	51.1499	1.67818	0.839088	−	0.543996i	$-0.183089\pi$
$929$	51.1499	1.67818	0.839088	+	0.543996i	$0.183089\pi$
$930$	−9.20957	−0.301994
$931$	1.15891	0.0379817
$932$	1.61989	0.0530613
$933$	−11.1014	−0.363445
$934$	−28.5573	−0.934423
$935$	0	0
$936$	−13.6915	−0.447522
$937$	12.0865	0.394849	0.197425	−	0.980318i	$-0.436742\pi$
$937$	12.0865	0.394849	0.197425	+	0.980318i	$0.436742\pi$
$938$	0.953986	0.0311487
$939$	−2.77120	−0.0904348
$940$	0.0318259	0.00103805
$941$	48.6975	1.58749	0.793747	−	0.608248i	$-0.208127\pi$
$941$	48.6975	1.58749	0.793747	+	0.608248i	$0.208127\pi$
$942$	−18.1307	−0.590732
$943$	52.0570	1.69521
$944$	−29.8571	−0.971767
$945$	5.63333	0.183252
$946$	0	0
$947$	25.8656	0.840519	0.420260	−	0.907404i	$-0.361939\pi$
$947$	25.8656	0.840519	0.420260	+	0.907404i	$0.361939\pi$
$948$	−0.843253	−0.0273876
$949$	−3.42169	−0.111073
$950$	1.61054	0.0522527
$951$	19.9447	0.646753
$952$	13.7477	0.445566
$953$	−57.3622	−1.85814	−0.929072	−	0.369899i	$-0.879392\pi$
$953$	−57.3622	−1.85814	−0.929072	+	0.369899i	$0.879392\pi$
$954$	−13.1365	−0.425310
$955$	12.5852	0.407247
$956$	0.736697	0.0238265
$957$	0	0
$958$	−11.4640	−0.370386
$959$	−11.8714	−0.383348
$960$	−11.0551	−0.356800
$961$	−6.50802	−0.209936
$962$	43.7694	1.41118
$963$	−19.9815	−0.643894
$964$	1.26634	0.0407862
$965$	−5.52570	−0.177879
$966$	−13.7041	−0.440921
$967$	−8.61525	−0.277048	−0.138524	−	0.990359i	$-0.544236\pi$
$967$	−8.61525	−0.277048	−0.138524	+	0.990359i	$0.544236\pi$
$968$	0	0
$969$	7.42098	0.238396
$970$	23.4979	0.754473
$971$	39.0476	1.25310	0.626548	−	0.779383i	$-0.284467\pi$
$971$	39.0476	1.25310	0.626548	+	0.779383i	$0.284467\pi$
$972$	0.800532	0.0256771
$973$	−4.84576	−0.155348
$974$	11.9619	0.383282
$975$	5.28414	0.169228
$976$	−15.3204	−0.490395
$977$	−36.6711	−1.17321	−0.586606	−	0.809873i	$-0.699536\pi$
$977$	−36.6711	−1.17321	−0.586606	+	0.809873i	$0.699536\pi$
$978$	19.3700	0.619383
$979$	0	0
$980$	−0.0687332	−0.00219560
$981$	−8.97305	−0.286487
$982$	−6.77983	−0.216353
$983$	−28.1976	−0.899365	−0.449682	−	0.893189i	$-0.648463\pi$
$983$	−28.1976	−0.899365	−0.449682	+	0.893189i	$0.648463\pi$
$984$	27.2138	0.867545
$985$	−10.2918	−0.327923
$986$	49.5924	1.57934
$987$	0.620040	0.0197361
$988$	0.314329	0.0100001
$989$	76.2451	2.42445
$990$	0	0
$991$	11.8021	0.374907	0.187454	−	0.982273i	$-0.439977\pi$
$991$	11.8021	0.374907	0.187454	+	0.982273i	$0.439977\pi$
$992$	1.92335	0.0610665
$993$	9.15328	0.290471
$994$	5.66675	0.179738
$995$	−1.58408	−0.0502188
$996$	−1.21317	−0.0384406
$997$	−6.87124	−0.217614	−0.108807	−	0.994063i	$-0.534703\pi$
$997$	−6.87124	−0.217614	−0.108807	+	0.994063i	$0.534703\pi$
$998$	52.8531	1.67303
$999$	−44.9621	−1.42254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bp.1.13		18
11.7	odd	10		385.2.n.f.71.3	✓	36
11.8	odd	10		385.2.n.f.141.3	yes	36
11.10	odd	2		4235.2.a.bo.1.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.71.3	✓	36	11.7	odd	10
385.2.n.f.141.3	yes	36	11.8	odd	10
4235.2.a.bo.1.6		18	11.10	odd	2
4235.2.a.bp.1.13		18	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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+1.38970 q^{2} -1.33908 q^{3} -0.0687332 q^{4} +1.00000 q^{5} -1.86092 q^{6} +1.00000 q^{7} -2.87492 q^{8} -1.20687 q^{9} +O(q^{10})\)	\(q+1.38970 q^{2} -1.33908 q^{3} -0.0687332 q^{4} +1.00000 q^{5} -1.86092 q^{6} +1.00000 q^{7} -2.87492 q^{8} -1.20687 q^{9} +1.38970 q^{10} +0.0920392 q^{12} -3.94610 q^{13} +1.38970 q^{14} -1.33908 q^{15} -3.85781 q^{16} -4.78195 q^{17} -1.67718 q^{18} +1.15891 q^{19} -0.0687332 q^{20} -1.33908 q^{21} +7.36414 q^{23} +3.84975 q^{24} +1.00000 q^{25} -5.48389 q^{26} +5.63333 q^{27} -0.0687332 q^{28} -7.46257 q^{29} -1.86092 q^{30} +4.94894 q^{31} +0.388640 q^{32} -6.64548 q^{34} +1.00000 q^{35} +0.0829518 q^{36} -7.98144 q^{37} +1.61054 q^{38} +5.28414 q^{39} -2.87492 q^{40} +7.06899 q^{41} -1.86092 q^{42} +10.3536 q^{43} -1.20687 q^{45} +10.2339 q^{46} -0.463035 q^{47} +5.16591 q^{48} +1.00000 q^{49} +1.38970 q^{50} +6.40341 q^{51} +0.271228 q^{52} +7.83248 q^{53} +7.82864 q^{54} -2.87492 q^{56} -1.55187 q^{57} -10.3707 q^{58} +7.73940 q^{59} +0.0920392 q^{60} +3.97128 q^{61} +6.87754 q^{62} -1.20687 q^{63} +8.25571 q^{64} -3.94610 q^{65} +0.686469 q^{67} +0.328679 q^{68} -9.86117 q^{69} +1.38970 q^{70} +4.07768 q^{71} +3.46964 q^{72} +0.867108 q^{73} -11.0918 q^{74} -1.33908 q^{75} -0.0796556 q^{76} +7.34337 q^{78} -9.16188 q^{79} -3.85781 q^{80} -3.92288 q^{81} +9.82378 q^{82} -13.1810 q^{83} +0.0920392 q^{84} -4.78195 q^{85} +14.3883 q^{86} +9.99298 q^{87} -0.382439 q^{89} -1.67718 q^{90} -3.94610 q^{91} -0.506161 q^{92} -6.62702 q^{93} -0.643480 q^{94} +1.15891 q^{95} -0.520419 q^{96} +16.9086 q^{97} +1.38970 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9}+O(q^{10}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9} + 2 q^{10} + 15 q^{12} + 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} - 5 q^{17} + 2 q^{18} + 15 q^{19} + 24 q^{20} + 5 q^{21} + 4 q^{23} + 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} + 24 q^{28} - 6 q^{29} - q^{30} + 22 q^{31} - 6 q^{32} + 44 q^{34} + 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} - 38 q^{39} + 6 q^{40} + 7 q^{41} - q^{42} + 10 q^{43} + 37 q^{45} - 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} + 2 q^{50} - 11 q^{51} + 18 q^{52} + 23 q^{53} + 13 q^{54} + 6 q^{56} - 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} + 17 q^{61} + 57 q^{62} + 37 q^{63} + 64 q^{64} + 8 q^{65} + 29 q^{67} - 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} - 77 q^{72} + 3 q^{73} - 48 q^{74} + 5 q^{75} + 47 q^{76} + 10 q^{78} - 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} + 9 q^{83} + 15 q^{84} - 5 q^{85} + 25 q^{86} + 23 q^{87} + 59 q^{89} + 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} - 19 q^{94} + 15 q^{95} + 14 q^{96} + 30 q^{97} + 2 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9 + 2 * q^10 + 15 * q^12 + 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 - 5 * q^17 + 2 * q^18 + 15 * q^19 + 24 * q^20 + 5 * q^21 + 4 * q^23 + 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 + 24 * q^28 - 6 * q^29 - q^30 + 22 * q^31 - 6 * q^32 + 44 * q^34 + 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 - 38 * q^39 + 6 * q^40 + 7 * q^41 - q^42 + 10 * q^43 + 37 * q^45 - 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 + 2 * q^50 - 11 * q^51 + 18 * q^52 + 23 * q^53 + 13 * q^54 + 6 * q^56 - 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 + 17 * q^61 + 57 * q^62 + 37 * q^63 + 64 * q^64 + 8 * q^65 + 29 * q^67 - 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 - 77 * q^72 + 3 * q^73 - 48 * q^74 + 5 * q^75 + 47 * q^76 + 10 * q^78 - 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 + 9 * q^83 + 15 * q^84 - 5 * q^85 + 25 * q^86 + 23 * q^87 + 59 * q^89 + 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 - 19 * q^94 + 15 * q^95 + 14 * q^96 + 30 * q^97 + 2 * q^98

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