LMFDB - Embedded newform 4029.2.a.l.1.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.32
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.74833 q^{2} -1.00000 q^{3} +5.55332 q^{4} +0.373803 q^{5} -2.74833 q^{6} -2.56695 q^{7} +9.76571 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.74833 q^{2} -1.00000 q^{3} +5.55332 q^{4} +0.373803 q^{5} -2.74833 q^{6} -2.56695 q^{7} +9.76571 q^{8} +1.00000 q^{9} +1.02733 q^{10} +5.33080 q^{11} -5.55332 q^{12} +1.62873 q^{13} -7.05484 q^{14} -0.373803 q^{15} +15.7328 q^{16} -1.00000 q^{17} +2.74833 q^{18} +6.40751 q^{19} +2.07585 q^{20} +2.56695 q^{21} +14.6508 q^{22} -8.29053 q^{23} -9.76571 q^{24} -4.86027 q^{25} +4.47629 q^{26} -1.00000 q^{27} -14.2551 q^{28} +7.11963 q^{29} -1.02733 q^{30} -0.319404 q^{31} +23.7074 q^{32} -5.33080 q^{33} -2.74833 q^{34} -0.959535 q^{35} +5.55332 q^{36} -9.68955 q^{37} +17.6100 q^{38} -1.62873 q^{39} +3.65045 q^{40} +10.6895 q^{41} +7.05484 q^{42} -2.22479 q^{43} +29.6037 q^{44} +0.373803 q^{45} -22.7851 q^{46} -1.32238 q^{47} -15.7328 q^{48} -0.410745 q^{49} -13.3576 q^{50} +1.00000 q^{51} +9.04487 q^{52} +0.149084 q^{53} -2.74833 q^{54} +1.99267 q^{55} -25.0681 q^{56} -6.40751 q^{57} +19.5671 q^{58} +0.248068 q^{59} -2.07585 q^{60} +10.9718 q^{61} -0.877828 q^{62} -2.56695 q^{63} +33.6903 q^{64} +0.608824 q^{65} -14.6508 q^{66} +6.82788 q^{67} -5.55332 q^{68} +8.29053 q^{69} -2.63712 q^{70} -9.62623 q^{71} +9.76571 q^{72} +1.57803 q^{73} -26.6301 q^{74} +4.86027 q^{75} +35.5830 q^{76} -13.6839 q^{77} -4.47629 q^{78} +1.00000 q^{79} +5.88095 q^{80} +1.00000 q^{81} +29.3782 q^{82} +17.5951 q^{83} +14.2551 q^{84} -0.373803 q^{85} -6.11445 q^{86} -7.11963 q^{87} +52.0590 q^{88} +14.4784 q^{89} +1.02733 q^{90} -4.18088 q^{91} -46.0400 q^{92} +0.319404 q^{93} -3.63435 q^{94} +2.39515 q^{95} -23.7074 q^{96} -15.6399 q^{97} -1.12886 q^{98} +5.33080 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * 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 $

$2$	2.74833	1.94336	0.971682	−	0.236293i	$-0.0759327\pi$
$2$	2.74833	1.94336	0.971682	+	0.236293i	$0.0759327\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.55332	2.77666
$5$	0.373803	0.167170	0.0835849	−	0.996501i	$-0.473363\pi$
$5$	0.373803	0.167170	0.0835849	+	0.996501i	$0.473363\pi$
$6$	−2.74833	−1.12200
$7$	−2.56695	−0.970218	−0.485109	−	0.874454i	$-0.661220\pi$
$7$	−2.56695	−0.970218	−0.485109	+	0.874454i	$0.661220\pi$
$8$	9.76571	3.45270
$9$	1.00000	0.333333
$10$	1.02733	0.324872
$11$	5.33080	1.60730	0.803648	−	0.595104i	$-0.202889\pi$
$11$	5.33080	1.60730	0.803648	+	0.595104i	$0.202889\pi$
$12$	−5.55332	−1.60311
$13$	1.62873	0.451729	0.225864	−	0.974159i	$-0.427479\pi$
$13$	1.62873	0.451729	0.225864	+	0.974159i	$0.427479\pi$
$14$	−7.05484	−1.88549
$15$	−0.373803	−0.0965155
$16$	15.7328	3.93319
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.74833	0.647788
$19$	6.40751	1.46998	0.734992	−	0.678076i	$-0.237186\pi$
$19$	6.40751	1.46998	0.734992	+	0.678076i	$0.237186\pi$
$20$	2.07585	0.464174
$21$	2.56695	0.560155
$22$	14.6508	3.12356
$23$	−8.29053	−1.72870	−0.864348	−	0.502894i	$-0.832268\pi$
$23$	−8.29053	−1.72870	−0.864348	+	0.502894i	$0.832268\pi$
$24$	−9.76571	−1.99342
$25$	−4.86027	−0.972054
$26$	4.47629	0.877873
$27$	−1.00000	−0.192450
$28$	−14.2551	−2.69397
$29$	7.11963	1.32208	0.661041	−	0.750350i	$-0.270115\pi$
$29$	7.11963	1.32208	0.661041	+	0.750350i	$0.270115\pi$
$30$	−1.02733	−0.187565
$31$	−0.319404	−0.0573666	−0.0286833	−	0.999589i	$-0.509131\pi$
$31$	−0.319404	−0.0573666	−0.0286833	+	0.999589i	$0.509131\pi$
$32$	23.7074	4.19091
$33$	−5.33080	−0.927973
$34$	−2.74833	−0.471335
$35$	−0.959535	−0.162191
$36$	5.55332	0.925554
$37$	−9.68955	−1.59295	−0.796477	−	0.604669i	$-0.793305\pi$
$37$	−9.68955	−1.59295	−0.796477	+	0.604669i	$0.793305\pi$
$38$	17.6100	2.85671
$39$	−1.62873	−0.260806
$40$	3.65045	0.577187
$41$	10.6895	1.66941	0.834707	−	0.550694i	$-0.185637\pi$
$41$	10.6895	1.66941	0.834707	+	0.550694i	$0.185637\pi$
$42$	7.05484	1.08859
$43$	−2.22479	−0.339277	−0.169638	−	0.985506i	$-0.554260\pi$
$43$	−2.22479	−0.339277	−0.169638	+	0.985506i	$0.554260\pi$
$44$	29.6037	4.46292
$45$	0.373803	0.0557233
$46$	−22.7851	−3.35948
$47$	−1.32238	−0.192889	−0.0964447	−	0.995338i	$-0.530747\pi$
$47$	−1.32238	−0.192889	−0.0964447	+	0.995338i	$0.530747\pi$
$48$	−15.7328	−2.27083
$49$	−0.410745	−0.0586778
$50$	−13.3576	−1.88905
$51$	1.00000	0.140028
$52$	9.04487	1.25430
$53$	0.149084	0.0204782	0.0102391	−	0.999948i	$-0.496741\pi$
$53$	0.149084	0.0204782	0.0102391	+	0.999948i	$0.496741\pi$
$54$	−2.74833	−0.374000
$55$	1.99267	0.268691
$56$	−25.0681	−3.34987
$57$	−6.40751	−0.848696
$58$	19.5671	2.56929
$59$	0.248068	0.0322957	0.0161479	−	0.999870i	$-0.494860\pi$
$59$	0.248068	0.0322957	0.0161479	+	0.999870i	$0.494860\pi$
$60$	−2.07585	−0.267991
$61$	10.9718	1.40480	0.702400	−	0.711782i	$-0.252112\pi$
$61$	10.9718	1.40480	0.702400	+	0.711782i	$0.252112\pi$
$62$	−0.877828	−0.111484
$63$	−2.56695	−0.323406
$64$	33.6903	4.21128
$65$	0.608824	0.0755154
$66$	−14.6508	−1.80339
$67$	6.82788	0.834158	0.417079	−	0.908870i	$-0.363054\pi$
$67$	6.82788	0.834158	0.417079	+	0.908870i	$0.363054\pi$
$68$	−5.55332	−0.673439
$69$	8.29053	0.998063
$70$	−2.63712	−0.315196
$71$	−9.62623	−1.14242	−0.571211	−	0.820803i	$-0.693526\pi$
$71$	−9.62623	−1.14242	−0.571211	+	0.820803i	$0.693526\pi$
$72$	9.76571	1.15090
$73$	1.57803	0.184695	0.0923473	−	0.995727i	$-0.470563\pi$
$73$	1.57803	0.184695	0.0923473	+	0.995727i	$0.470563\pi$
$74$	−26.6301	−3.09569
$75$	4.86027	0.561216
$76$	35.5830	4.08165
$77$	−13.6839	−1.55943
$78$	−4.47629	−0.506840
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	5.88095	0.657510
$81$	1.00000	0.111111
$82$	29.3782	3.24428
$83$	17.5951	1.93132	0.965658	−	0.259817i	$-0.0836624\pi$
$83$	17.5951	1.93132	0.965658	+	0.259817i	$0.0836624\pi$
$84$	14.2551	1.55536
$85$	−0.373803	−0.0405446
$86$	−6.11445	−0.659338
$87$	−7.11963	−0.763305
$88$	52.0590	5.54951
$89$	14.4784	1.53471	0.767354	−	0.641223i	$-0.221573\pi$
$89$	14.4784	1.53471	0.767354	+	0.641223i	$0.221573\pi$
$90$	1.02733	0.108291
$91$	−4.18088	−0.438275
$92$	−46.0400	−4.80000
$93$	0.319404	0.0331206
$94$	−3.63435	−0.374854
$95$	2.39515	0.245737
$96$	−23.7074	−2.41963
$97$	−15.6399	−1.58799	−0.793993	−	0.607927i	$-0.792001\pi$
$97$	−15.6399	−1.58799	−0.793993	+	0.607927i	$0.792001\pi$
$98$	−1.12886	−0.114032
$99$	5.33080	0.535766
$100$	−26.9907	−2.69907
$101$	−17.8744	−1.77857	−0.889286	−	0.457352i	$-0.848798\pi$
$101$	−17.8744	−1.77857	−0.889286	+	0.457352i	$0.848798\pi$
$102$	2.74833	0.272125
$103$	8.14100	0.802156	0.401078	−	0.916044i	$-0.368636\pi$
$103$	8.14100	0.802156	0.401078	+	0.916044i	$0.368636\pi$
$104$	15.9057	1.55968
$105$	0.959535	0.0936410
$106$	0.409731	0.0397966
$107$	−0.591829	−0.0572143	−0.0286071	−	0.999591i	$-0.509107\pi$
$107$	−0.591829	−0.0572143	−0.0286071	+	0.999591i	$0.509107\pi$
$108$	−5.55332	−0.534369
$109$	−8.27027	−0.792148	−0.396074	−	0.918219i	$-0.629628\pi$
$109$	−8.27027	−0.792148	−0.396074	+	0.918219i	$0.629628\pi$
$110$	5.47651	0.522165
$111$	9.68955	0.919692
$112$	−40.3853	−3.81605
$113$	−2.16838	−0.203984	−0.101992	−	0.994785i	$-0.532522\pi$
$113$	−2.16838	−0.203984	−0.101992	+	0.994785i	$0.532522\pi$
$114$	−17.6100	−1.64932
$115$	−3.09903	−0.288986
$116$	39.5376	3.67098
$117$	1.62873	0.150576
$118$	0.681773	0.0627623
$119$	2.56695	0.235312
$120$	−3.65045	−0.333239
$121$	17.4174	1.58340
$122$	30.1543	2.73004
$123$	−10.6895	−0.963837
$124$	−1.77375	−0.159288
$125$	−3.68580	−0.329668
$126$	−7.05484	−0.628495
$127$	17.9434	1.59222	0.796110	−	0.605152i	$-0.206888\pi$
$127$	17.9434	1.59222	0.796110	+	0.605152i	$0.206888\pi$
$128$	45.1772	3.99314
$129$	2.22479	0.195882
$130$	1.67325	0.146754
$131$	17.8875	1.56284	0.781420	−	0.624005i	$-0.214496\pi$
$131$	17.8875	1.56284	0.781420	+	0.624005i	$0.214496\pi$
$132$	−29.6037	−2.57667
$133$	−16.4478	−1.42620
$134$	18.7653	1.62107
$135$	−0.373803	−0.0321718
$136$	−9.76571	−0.837403
$137$	1.72142	0.147071	0.0735355	−	0.997293i	$-0.476572\pi$
$137$	1.72142	0.147071	0.0735355	+	0.997293i	$0.476572\pi$
$138$	22.7851	1.93960
$139$	−8.00475	−0.678954	−0.339477	−	0.940614i	$-0.610250\pi$
$139$	−8.00475	−0.678954	−0.339477	+	0.940614i	$0.610250\pi$
$140$	−5.32861	−0.450350
$141$	1.32238	0.111365
$142$	−26.4561	−2.22014
$143$	8.68244	0.726062
$144$	15.7328	1.31106
$145$	2.66134	0.221012
$146$	4.33695	0.358929
$147$	0.410745	0.0338777
$148$	−53.8092	−4.42309
$149$	−18.5362	−1.51854	−0.759271	−	0.650775i	$-0.774444\pi$
$149$	−18.5362	−1.51854	−0.759271	+	0.650775i	$0.774444\pi$
$150$	13.3576	1.09065
$151$	3.63863	0.296107	0.148054	−	0.988979i	$-0.452699\pi$
$151$	3.63863	0.296107	0.148054	+	0.988979i	$0.452699\pi$
$152$	62.5739	5.07541
$153$	−1.00000	−0.0808452
$154$	−37.6079	−3.03053
$155$	−0.119394	−0.00958997
$156$	−9.04487	−0.724169
$157$	8.19091	0.653706	0.326853	−	0.945075i	$-0.394012\pi$
$157$	8.19091	0.653706	0.326853	+	0.945075i	$0.394012\pi$
$158$	2.74833	0.218645
$159$	−0.149084	−0.0118231
$160$	8.86189	0.700594
$161$	21.2814	1.67721
$162$	2.74833	0.215929
$163$	−5.79651	−0.454018	−0.227009	−	0.973893i	$-0.572895\pi$
$163$	−5.79651	−0.454018	−0.227009	+	0.973893i	$0.572895\pi$
$164$	59.3621	4.63540
$165$	−1.99267	−0.155129
$166$	48.3572	3.75325
$167$	9.67616	0.748763	0.374382	−	0.927275i	$-0.377855\pi$
$167$	9.67616	0.748763	0.374382	+	0.927275i	$0.377855\pi$
$168$	25.0681	1.93405
$169$	−10.3472	−0.795941
$170$	−1.02733	−0.0787929
$171$	6.40751	0.489995
$172$	−12.3550	−0.942057
$173$	−18.4489	−1.40265	−0.701323	−	0.712843i	$-0.747407\pi$
$173$	−18.4489	−1.40265	−0.701323	+	0.712843i	$0.747407\pi$
$174$	−19.5671	−1.48338
$175$	12.4761	0.943104
$176$	83.8682	6.32180
$177$	−0.248068	−0.0186459
$178$	39.7915	2.98250
$179$	11.9693	0.894626	0.447313	−	0.894377i	$-0.352381\pi$
$179$	11.9693	0.894626	0.447313	+	0.894377i	$0.352381\pi$
$180$	2.07585	0.154725
$181$	−19.5566	−1.45363	−0.726815	−	0.686833i	$-0.759000\pi$
$181$	−19.5566	−1.45363	−0.726815	+	0.686833i	$0.759000\pi$
$182$	−11.4904	−0.851728
$183$	−10.9718	−0.811062
$184$	−80.9629	−5.96867
$185$	−3.62198	−0.266294
$186$	0.877828	0.0643654
$187$	−5.33080	−0.389827
$188$	−7.34362	−0.535589
$189$	2.56695	0.186718
$190$	6.58266	0.477556
$191$	−15.7826	−1.14199	−0.570993	−	0.820955i	$-0.693442\pi$
$191$	−15.7826	−1.14199	−0.570993	+	0.820955i	$0.693442\pi$
$192$	−33.6903	−2.43138
$193$	8.56277	0.616362	0.308181	−	0.951328i	$-0.400280\pi$
$193$	8.56277	0.616362	0.308181	+	0.951328i	$0.400280\pi$
$194$	−42.9835	−3.08603
$195$	−0.608824	−0.0435988
$196$	−2.28100	−0.162929
$197$	−11.6567	−0.830507	−0.415253	−	0.909706i	$-0.636307\pi$
$197$	−11.6567	−0.830507	−0.415253	+	0.909706i	$0.636307\pi$
$198$	14.6508	1.04119
$199$	−17.5984	−1.24752	−0.623760	−	0.781616i	$-0.714396\pi$
$199$	−17.5984	−1.24752	−0.623760	+	0.781616i	$0.714396\pi$
$200$	−47.4640	−3.35621
$201$	−6.82788	−0.481602
$202$	−49.1248	−3.45641
$203$	−18.2758	−1.28271
$204$	5.55332	0.388810
$205$	3.99575	0.279076
$206$	22.3742	1.55888
$207$	−8.29053	−0.576232
$208$	25.6244	1.77673
$209$	34.1572	2.36270
$210$	2.63712	0.181979
$211$	−24.6862	−1.69947	−0.849733	−	0.527213i	$-0.823237\pi$
$211$	−24.6862	−1.69947	−0.849733	+	0.527213i	$0.823237\pi$
$212$	0.827910	0.0568611
$213$	9.62623	0.659578
$214$	−1.62654	−0.111188
$215$	−0.831632	−0.0567169
$216$	−9.76571	−0.664472
$217$	0.819895	0.0556581
$218$	−22.7294	−1.53943
$219$	−1.57803	−0.106633
$220$	11.0659	0.746065
$221$	−1.62873	−0.109560
$222$	26.6301	1.78730
$223$	−6.86018	−0.459391	−0.229696	−	0.973263i	$-0.573773\pi$
$223$	−6.86018	−0.459391	−0.229696	+	0.973263i	$0.573773\pi$
$224$	−60.8558	−4.06610
$225$	−4.86027	−0.324018
$226$	−5.95944	−0.396416
$227$	−9.87021	−0.655109	−0.327554	−	0.944832i	$-0.606224\pi$
$227$	−9.87021	−0.655109	−0.327554	+	0.944832i	$0.606224\pi$
$228$	−35.5830	−2.35654
$229$	−14.7541	−0.974976	−0.487488	−	0.873130i	$-0.662087\pi$
$229$	−14.7541	−0.974976	−0.487488	+	0.873130i	$0.662087\pi$
$230$	−8.51715	−0.561604
$231$	13.6839	0.900336
$232$	69.5282	4.56475
$233$	−16.1279	−1.05658	−0.528289	−	0.849065i	$-0.677166\pi$
$233$	−16.1279	−1.05658	−0.528289	+	0.849065i	$0.677166\pi$
$234$	4.47629	0.292624
$235$	−0.494311	−0.0322453
$236$	1.37760	0.0896742
$237$	−1.00000	−0.0649570
$238$	7.05484	0.457297
$239$	−30.8739	−1.99706	−0.998532	−	0.0541703i	$-0.982749\pi$
$239$	−30.8739	−1.99706	−0.998532	+	0.0541703i	$0.982749\pi$
$240$	−5.88095	−0.379614
$241$	7.78762	0.501645	0.250822	−	0.968033i	$-0.419299\pi$
$241$	7.78762	0.501645	0.250822	+	0.968033i	$0.419299\pi$
$242$	47.8689	3.07713
$243$	−1.00000	−0.0641500
$244$	60.9302	3.90066
$245$	−0.153538	−0.00980916
$246$	−29.3782	−1.87308
$247$	10.4361	0.664034
$248$	−3.11921	−0.198070
$249$	−17.5951	−1.11505
$250$	−10.1298	−0.640664
$251$	17.3058	1.09233	0.546167	−	0.837676i	$-0.316086\pi$
$251$	17.3058	1.09233	0.546167	+	0.837676i	$0.316086\pi$
$252$	−14.2551	−0.897989
$253$	−44.1952	−2.77853
$254$	49.3144	3.09426
$255$	0.373803	0.0234085
$256$	56.7814	3.54883
$257$	4.96971	0.310002	0.155001	−	0.987914i	$-0.450462\pi$
$257$	4.96971	0.310002	0.155001	+	0.987914i	$0.450462\pi$
$258$	6.11445	0.380669
$259$	24.8726	1.54551
$260$	3.38100	0.209681
$261$	7.11963	0.440694
$262$	49.1608	3.03717
$263$	−27.5432	−1.69839	−0.849193	−	0.528083i	$-0.822911\pi$
$263$	−27.5432	−1.69839	−0.849193	+	0.528083i	$0.822911\pi$
$264$	−52.0590	−3.20401
$265$	0.0557279	0.00342334
$266$	−45.2040	−2.77163
$267$	−14.4784	−0.886064
$268$	37.9174	2.31618
$269$	10.1279	0.617509	0.308755	−	0.951142i	$-0.400088\pi$
$269$	10.1279	0.617509	0.308755	+	0.951142i	$0.400088\pi$
$270$	−1.02733	−0.0625216
$271$	−1.32119	−0.0802568	−0.0401284	−	0.999195i	$-0.512777\pi$
$271$	−1.32119	−0.0802568	−0.0401284	+	0.999195i	$0.512777\pi$
$272$	−15.7328	−0.953938
$273$	4.18088	0.253038
$274$	4.73103	0.285812
$275$	−25.9091	−1.56238
$276$	46.0400	2.77128
$277$	0.795932	0.0478229	0.0239115	−	0.999714i	$-0.492388\pi$
$277$	0.795932	0.0478229	0.0239115	+	0.999714i	$0.492388\pi$
$278$	−21.9997	−1.31945
$279$	−0.319404	−0.0191222
$280$	−9.37054	−0.559997
$281$	11.6674	0.696020	0.348010	−	0.937491i	$-0.386858\pi$
$281$	11.6674	0.696020	0.348010	+	0.937491i	$0.386858\pi$
$282$	3.63435	0.216422
$283$	−28.7465	−1.70880	−0.854400	−	0.519616i	$-0.826075\pi$
$283$	−28.7465	−1.70880	−0.854400	+	0.519616i	$0.826075\pi$
$284$	−53.4575	−3.17212
$285$	−2.39515	−0.141876
$286$	23.8622	1.41100
$287$	−27.4394	−1.61969
$288$	23.7074	1.39697
$289$	1.00000	0.0588235
$290$	7.31424	0.429507
$291$	15.6399	0.916824
$292$	8.76332	0.512834
$293$	1.52782	0.0892559	0.0446280	−	0.999004i	$-0.485790\pi$
$293$	1.52782	0.0892559	0.0446280	+	0.999004i	$0.485790\pi$
$294$	1.12886	0.0658366
$295$	0.0927286	0.00539887
$296$	−94.6254	−5.49999
$297$	−5.33080	−0.309324
$298$	−50.9435	−2.95108
$299$	−13.5030	−0.780901
$300$	26.9907	1.55831
$301$	5.71093	0.329172
$302$	10.0002	0.575444
$303$	17.8744	1.02686
$304$	100.808	5.78172
$305$	4.10131	0.234840
$306$	−2.74833	−0.157112
$307$	−18.2538	−1.04180	−0.520900	−	0.853618i	$-0.674404\pi$
$307$	−18.2538	−1.04180	−0.520900	+	0.853618i	$0.674404\pi$
$308$	−75.9912	−4.33000
$309$	−8.14100	−0.463125
$310$	−0.328135	−0.0186368
$311$	28.4096	1.61096	0.805479	−	0.592624i	$-0.201908\pi$
$311$	28.4096	1.61096	0.805479	+	0.592624i	$0.201908\pi$
$312$	−15.9057	−0.900483
$313$	−9.69798	−0.548162	−0.274081	−	0.961707i	$-0.588374\pi$
$313$	−9.69798	−0.548162	−0.274081	+	0.961707i	$0.588374\pi$
$314$	22.5113	1.27039
$315$	−0.959535	−0.0540637
$316$	5.55332	0.312399
$317$	21.1700	1.18902	0.594512	−	0.804087i	$-0.297345\pi$
$317$	21.1700	1.18902	0.594512	+	0.804087i	$0.297345\pi$
$318$	−0.409731	−0.0229766
$319$	37.9533	2.12498
$320$	12.5935	0.703999
$321$	0.591829	0.0330327
$322$	58.4884	3.25943
$323$	−6.40751	−0.356524
$324$	5.55332	0.308518
$325$	−7.91607	−0.439105
$326$	−15.9307	−0.882321
$327$	8.27027	0.457347
$328$	104.390	5.76398
$329$	3.39450	0.187145
$330$	−5.47651	−0.301472
$331$	−21.6099	−1.18779	−0.593895	−	0.804543i	$-0.702410\pi$
$331$	−21.6099	−1.18779	−0.593895	+	0.804543i	$0.702410\pi$
$332$	97.7114	5.36261
$333$	−9.68955	−0.530984
$334$	26.5933	1.45512
$335$	2.55228	0.139446
$336$	40.3853	2.20320
$337$	−29.5121	−1.60763	−0.803813	−	0.594882i	$-0.797199\pi$
$337$	−29.5121	−1.60763	−0.803813	+	0.594882i	$0.797199\pi$
$338$	−28.4376	−1.54680
$339$	2.16838	0.117770
$340$	−2.07585	−0.112579
$341$	−1.70268	−0.0922052
$342$	17.6100	0.952238
$343$	19.0230	1.02715
$344$	−21.7266	−1.17142
$345$	3.09903	0.166846
$346$	−50.7038	−2.72585
$347$	−20.7743	−1.11522	−0.557612	−	0.830101i	$-0.688282\pi$
$347$	−20.7743	−1.11522	−0.557612	+	0.830101i	$0.688282\pi$
$348$	−39.5376	−2.11944
$349$	−25.9885	−1.39113	−0.695567	−	0.718462i	$-0.744847\pi$
$349$	−25.9885	−1.39113	−0.695567	+	0.718462i	$0.744847\pi$
$350$	34.2884	1.83279
$351$	−1.62873	−0.0869352
$352$	126.379	6.73604
$353$	2.38009	0.126679	0.0633397	−	0.997992i	$-0.479825\pi$
$353$	2.38009	0.126679	0.0633397	+	0.997992i	$0.479825\pi$
$354$	−0.681773	−0.0362358
$355$	−3.59831	−0.190979
$356$	80.4033	4.26137
$357$	−2.56695	−0.135858
$358$	32.8956	1.73858
$359$	20.0137	1.05628	0.528141	−	0.849157i	$-0.322889\pi$
$359$	20.0137	1.05628	0.528141	+	0.849157i	$0.322889\pi$
$360$	3.65045	0.192396
$361$	22.0562	1.16085
$362$	−53.7480	−2.82493
$363$	−17.4174	−0.914178
$364$	−23.2178	−1.21694
$365$	0.589873	0.0308754
$366$	−30.1543	−1.57619
$367$	17.7943	0.928855	0.464427	−	0.885611i	$-0.346260\pi$
$367$	17.7943	0.928855	0.464427	+	0.885611i	$0.346260\pi$
$368$	−130.433	−6.79928
$369$	10.6895	0.556471
$370$	−9.95441	−0.517505
$371$	−0.382691	−0.0198683
$372$	1.77375	0.0919648
$373$	1.70830	0.0884525	0.0442262	−	0.999022i	$-0.485918\pi$
$373$	1.70830	0.0884525	0.0442262	+	0.999022i	$0.485918\pi$
$374$	−14.6508	−0.757575
$375$	3.68580	0.190334
$376$	−12.9140	−0.665989
$377$	11.5960	0.597222
$378$	7.05484	0.362862
$379$	−5.47785	−0.281378	−0.140689	−	0.990054i	$-0.544932\pi$
$379$	−5.47785	−0.281378	−0.140689	+	0.990054i	$0.544932\pi$
$380$	13.3010	0.682328
$381$	−17.9434	−0.919269
$382$	−43.3757	−2.21929
$383$	−23.6109	−1.20646	−0.603230	−	0.797567i	$-0.706120\pi$
$383$	−23.6109	−1.20646	−0.603230	+	0.797567i	$0.706120\pi$
$384$	−45.1772	−2.30544
$385$	−5.11509	−0.260689
$386$	23.5333	1.19781
$387$	−2.22479	−0.113092
$388$	−86.8531	−4.40930
$389$	20.5160	1.04020	0.520101	−	0.854105i	$-0.325894\pi$
$389$	20.5160	1.04020	0.520101	+	0.854105i	$0.325894\pi$
$390$	−1.67325	−0.0847284
$391$	8.29053	0.419270
$392$	−4.01121	−0.202597
$393$	−17.8875	−0.902306
$394$	−32.0365	−1.61398
$395$	0.373803	0.0188081
$396$	29.6037	1.48764
$397$	14.9466	0.750150	0.375075	−	0.926994i	$-0.377617\pi$
$397$	14.9466	0.750150	0.375075	+	0.926994i	$0.377617\pi$
$398$	−48.3663	−2.42438
$399$	16.4478	0.823419
$400$	−76.4654	−3.82327
$401$	6.18443	0.308836	0.154418	−	0.988006i	$-0.450650\pi$
$401$	6.18443	0.308836	0.154418	+	0.988006i	$0.450650\pi$
$402$	−18.7653	−0.935927
$403$	−0.520223	−0.0259142
$404$	−99.2624	−4.93849
$405$	0.373803	0.0185744
$406$	−50.2279	−2.49277
$407$	−51.6531	−2.56035
$408$	9.76571	0.483475
$409$	2.32025	0.114729	0.0573645	−	0.998353i	$-0.481730\pi$
$409$	2.32025	0.114729	0.0573645	+	0.998353i	$0.481730\pi$
$410$	10.9817	0.542345
$411$	−1.72142	−0.0849114
$412$	45.2096	2.22732
$413$	−0.636779	−0.0313339
$414$	−22.7851	−1.11983
$415$	6.57711	0.322858
$416$	38.6130	1.89316
$417$	8.00475	0.391994
$418$	93.8752	4.59159
$419$	3.12902	0.152863	0.0764313	−	0.997075i	$-0.475647\pi$
$419$	3.12902	0.152863	0.0764313	+	0.997075i	$0.475647\pi$
$420$	5.32861	0.260009
$421$	5.74274	0.279884	0.139942	−	0.990160i	$-0.455308\pi$
$421$	5.74274	0.279884	0.139942	+	0.990160i	$0.455308\pi$
$422$	−67.8458	−3.30268
$423$	−1.32238	−0.0642965
$424$	1.45591	0.0707051
$425$	4.86027	0.235758
$426$	26.4561	1.28180
$427$	−28.1642	−1.36296
$428$	−3.28662	−0.158865
$429$	−8.68244	−0.419192
$430$	−2.28560	−0.110221
$431$	17.9769	0.865916	0.432958	−	0.901414i	$-0.357470\pi$
$431$	17.9769	0.865916	0.432958	+	0.901414i	$0.357470\pi$
$432$	−15.7328	−0.756942
$433$	−0.911900	−0.0438231	−0.0219116	−	0.999760i	$-0.506975\pi$
$433$	−0.911900	−0.0438231	−0.0219116	+	0.999760i	$0.506975\pi$
$434$	2.25334	0.108164
$435$	−2.66134	−0.127601
$436$	−45.9275	−2.19953
$437$	−53.1217	−2.54116
$438$	−4.33695	−0.207228
$439$	9.84132	0.469701	0.234850	−	0.972032i	$-0.424540\pi$
$439$	9.84132	0.469701	0.234850	+	0.972032i	$0.424540\pi$
$440$	19.4598	0.927711
$441$	−0.410745	−0.0195593
$442$	−4.47629	−0.212915
$443$	29.2452	1.38948	0.694740	−	0.719261i	$-0.255519\pi$
$443$	29.2452	1.38948	0.694740	+	0.719261i	$0.255519\pi$
$444$	53.8092	2.55367
$445$	5.41207	0.256557
$446$	−18.8540	−0.892764
$447$	18.5362	0.876730
$448$	−86.4813	−4.08586
$449$	10.8120	0.510249	0.255125	−	0.966908i	$-0.417884\pi$
$449$	10.8120	0.510249	0.255125	+	0.966908i	$0.417884\pi$
$450$	−13.3576	−0.629685
$451$	56.9834	2.68324
$452$	−12.0417	−0.566396
$453$	−3.63863	−0.170958
$454$	−27.1266	−1.27311
$455$	−1.56282	−0.0732663
$456$	−62.5739	−2.93029
$457$	−8.60055	−0.402317	−0.201158	−	0.979559i	$-0.564471\pi$
$457$	−8.60055	−0.402317	−0.201158	+	0.979559i	$0.564471\pi$
$458$	−40.5490	−1.89473
$459$	1.00000	0.0466760
$460$	−17.2099	−0.802415
$461$	−36.5940	−1.70435	−0.852177	−	0.523254i	$-0.824718\pi$
$461$	−36.5940	−1.70435	−0.852177	+	0.523254i	$0.824718\pi$
$462$	37.6079	1.74968
$463$	−7.77200	−0.361195	−0.180598	−	0.983557i	$-0.557803\pi$
$463$	−7.77200	−0.361195	−0.180598	+	0.983557i	$0.557803\pi$
$464$	112.011	5.20000
$465$	0.119394	0.00553677
$466$	−44.3249	−2.05331
$467$	1.56128	0.0722474	0.0361237	−	0.999347i	$-0.488499\pi$
$467$	1.56128	0.0722474	0.0361237	+	0.999347i	$0.488499\pi$
$468$	9.04487	0.418099
$469$	−17.5269	−0.809315
$470$	−1.35853	−0.0626643
$471$	−8.19091	−0.377417
$472$	2.42256	0.111507
$473$	−11.8599	−0.545319
$474$	−2.74833	−0.126235
$475$	−31.1422	−1.42890
$476$	14.2551	0.653383
$477$	0.149084	0.00682607
$478$	−84.8516	−3.88102
$479$	5.06415	0.231387	0.115693	−	0.993285i	$-0.463091\pi$
$479$	5.06415	0.231387	0.115693	+	0.993285i	$0.463091\pi$
$480$	−8.86189	−0.404488
$481$	−15.7817	−0.719583
$482$	21.4030	0.974878
$483$	−21.2814	−0.968338
$484$	96.7247	4.39658
$485$	−5.84622	−0.265463
$486$	−2.74833	−0.124667
$487$	−16.7417	−0.758638	−0.379319	−	0.925266i	$-0.623842\pi$
$487$	−16.7417	−0.758638	−0.379319	+	0.925266i	$0.623842\pi$
$488$	107.148	4.85035
$489$	5.79651	0.262127
$490$	−0.421972	−0.0190628
$491$	−14.3112	−0.645856	−0.322928	−	0.946424i	$-0.604667\pi$
$491$	−14.3112	−0.645856	−0.322928	+	0.946424i	$0.604667\pi$
$492$	−59.3621	−2.67625
$493$	−7.11963	−0.320652
$494$	28.6819	1.29046
$495$	1.99267	0.0895638
$496$	−5.02510	−0.225634
$497$	24.7101	1.10840
$498$	−48.3572	−2.16694
$499$	39.9530	1.78854	0.894270	−	0.447528i	$-0.147695\pi$
$499$	39.9530	1.78854	0.894270	+	0.447528i	$0.147695\pi$
$500$	−20.4684	−0.915376
$501$	−9.67616	−0.432299
$502$	47.5621	2.12280
$503$	33.3391	1.48652	0.743258	−	0.669005i	$-0.233280\pi$
$503$	33.3391	1.48652	0.743258	+	0.669005i	$0.233280\pi$
$504$	−25.0681	−1.11662
$505$	−6.68151	−0.297323
$506$	−121.463	−5.39969
$507$	10.3472	0.459537
$508$	99.6455	4.42106
$509$	−31.5900	−1.40020	−0.700101	−	0.714044i	$-0.746862\pi$
$509$	−31.5900	−1.40020	−0.700101	+	0.714044i	$0.746862\pi$
$510$	1.02733	0.0454911
$511$	−4.05073	−0.179194
$512$	65.6996	2.90354
$513$	−6.40751	−0.282899
$514$	13.6584	0.602446
$515$	3.04313	0.134096
$516$	12.3550	0.543897
$517$	−7.04936	−0.310031
$518$	68.3583	3.00349
$519$	18.4489	0.809818
$520$	5.94560	0.260732
$521$	−20.7956	−0.911072	−0.455536	−	0.890217i	$-0.650552\pi$
$521$	−20.7956	−0.911072	−0.455536	+	0.890217i	$0.650552\pi$
$522$	19.5671	0.856429
$523$	6.58581	0.287977	0.143989	−	0.989579i	$-0.454007\pi$
$523$	6.58581	0.287977	0.143989	+	0.989579i	$0.454007\pi$
$524$	99.3352	4.33948
$525$	−12.4761	−0.544501
$526$	−75.6978	−3.30058
$527$	0.319404	0.0139135
$528$	−83.8682	−3.64989
$529$	45.7329	1.98839
$530$	0.153159	0.00665279
$531$	0.248068	0.0107652
$532$	−91.3399	−3.96009
$533$	17.4103	0.754122
$534$	−39.7915	−1.72195
$535$	−0.221227	−0.00956450
$536$	66.6791	2.88010
$537$	−11.9693	−0.516513
$538$	27.8348	1.20005
$539$	−2.18960	−0.0943127
$540$	−2.07585	−0.0893303
$541$	31.9817	1.37500	0.687501	−	0.726184i	$-0.258708\pi$
$541$	31.9817	1.37500	0.687501	+	0.726184i	$0.258708\pi$
$542$	−3.63108	−0.155968
$543$	19.5566	0.839254
$544$	−23.7074	−1.01645
$545$	−3.09145	−0.132423
$546$	11.4904	0.491745
$547$	4.25604	0.181975	0.0909875	−	0.995852i	$-0.470998\pi$
$547$	4.25604	0.181975	0.0909875	+	0.995852i	$0.470998\pi$
$548$	9.55961	0.408366
$549$	10.9718	0.468267
$550$	−71.2069	−3.03627
$551$	45.6191	1.94344
$552$	80.9629	3.44601
$553$	−2.56695	−0.109158
$554$	2.18748	0.0929373
$555$	3.62198	0.153745
$556$	−44.4530	−1.88523
$557$	−17.8387	−0.755849	−0.377925	−	0.925836i	$-0.623362\pi$
$557$	−17.8387	−0.755849	−0.377925	+	0.925836i	$0.623362\pi$
$558$	−0.877828	−0.0371614
$559$	−3.62358	−0.153261
$560$	−15.0961	−0.637928
$561$	5.33080	0.225067
$562$	32.0659	1.35262
$563$	−35.5431	−1.49796	−0.748982	−	0.662591i	$-0.769457\pi$
$563$	−35.5431	−1.49796	−0.748982	+	0.662591i	$0.769457\pi$
$564$	7.34362	0.309222
$565$	−0.810548	−0.0341000
$566$	−79.0048	−3.32082
$567$	−2.56695	−0.107802
$568$	−94.0069	−3.94444
$569$	−33.9869	−1.42481	−0.712403	−	0.701770i	$-0.752393\pi$
$569$	−33.9869	−1.42481	−0.712403	+	0.701770i	$0.752393\pi$
$570$	−6.58266	−0.275717
$571$	29.5150	1.23516	0.617582	−	0.786506i	$-0.288112\pi$
$571$	29.5150	1.23516	0.617582	+	0.786506i	$0.288112\pi$
$572$	48.2164	2.01603
$573$	15.7826	0.659326
$574$	−75.4125	−3.14766
$575$	40.2942	1.68039
$576$	33.6903	1.40376
$577$	0.756942	0.0315119	0.0157560	−	0.999876i	$-0.494985\pi$
$577$	0.756942	0.0315119	0.0157560	+	0.999876i	$0.494985\pi$
$578$	2.74833	0.114315
$579$	−8.56277	−0.355857
$580$	14.7793	0.613676
$581$	−45.1659	−1.87380
$582$	42.9835	1.78172
$583$	0.794735	0.0329146
$584$	15.4106	0.637695
$585$	0.608824	0.0251718
$586$	4.19894	0.173457
$587$	1.94843	0.0804202	0.0402101	−	0.999191i	$-0.487197\pi$
$587$	1.94843	0.0804202	0.0402101	+	0.999191i	$0.487197\pi$
$588$	2.28100	0.0940668
$589$	−2.04658	−0.0843280
$590$	0.254849	0.0104920
$591$	11.6567	0.479493
$592$	−152.443	−6.26538
$593$	8.41287	0.345475	0.172737	−	0.984968i	$-0.444739\pi$
$593$	8.41287	0.345475	0.172737	+	0.984968i	$0.444739\pi$
$594$	−14.6508	−0.601130
$595$	0.959535	0.0393371
$596$	−102.937	−4.21648
$597$	17.5984	0.720256
$598$	−37.1108	−1.51758
$599$	−27.4110	−1.11998	−0.559991	−	0.828499i	$-0.689195\pi$
$599$	−27.4110	−1.11998	−0.559991	+	0.828499i	$0.689195\pi$
$600$	47.4640	1.93771
$601$	7.09004	0.289209	0.144604	−	0.989490i	$-0.453809\pi$
$601$	7.09004	0.289209	0.144604	+	0.989490i	$0.453809\pi$
$602$	15.6955	0.639702
$603$	6.82788	0.278053
$604$	20.2065	0.822190
$605$	6.51069	0.264697
$606$	49.1248	1.99556
$607$	4.23643	0.171951	0.0859757	−	0.996297i	$-0.472599\pi$
$607$	4.23643	0.171951	0.0859757	+	0.996297i	$0.472599\pi$
$608$	151.905	6.16058
$609$	18.2758	0.740572
$610$	11.2717	0.456380
$611$	−2.15381	−0.0871337
$612$	−5.55332	−0.224480
$613$	38.2966	1.54678	0.773392	−	0.633928i	$-0.218558\pi$
$613$	38.2966	1.54678	0.773392	+	0.633928i	$0.218558\pi$
$614$	−50.1675	−2.02460
$615$	−3.99575	−0.161124
$616$	−133.633	−5.38423
$617$	−20.6285	−0.830471	−0.415236	−	0.909714i	$-0.636301\pi$
$617$	−20.6285	−0.830471	−0.415236	+	0.909714i	$0.636301\pi$
$618$	−22.3742	−0.900020
$619$	37.7983	1.51924	0.759620	−	0.650367i	$-0.225385\pi$
$619$	37.7983	1.51924	0.759620	+	0.650367i	$0.225385\pi$
$620$	−0.663034	−0.0266281
$621$	8.29053	0.332688
$622$	78.0789	3.13068
$623$	−37.1654	−1.48900
$624$	−25.6244	−1.02580
$625$	22.9236	0.916944
$626$	−26.6532	−1.06528
$627$	−34.1572	−1.36411
$628$	45.4868	1.81512
$629$	9.68955	0.386348
$630$	−2.63712	−0.105065
$631$	−19.3557	−0.770538	−0.385269	−	0.922804i	$-0.625891\pi$
$631$	−19.3557	−0.770538	−0.385269	+	0.922804i	$0.625891\pi$
$632$	9.76571	0.388459
$633$	24.6862	0.981187
$634$	58.1821	2.31070
$635$	6.70730	0.266171
$636$	−0.827910	−0.0328287
$637$	−0.668993	−0.0265065
$638$	104.308	4.12961
$639$	−9.62623	−0.380808
$640$	16.8874	0.667532
$641$	46.5183	1.83736	0.918682	−	0.394999i	$-0.129255\pi$
$641$	46.5183	1.83736	0.918682	+	0.394999i	$0.129255\pi$
$642$	1.62654	0.0641945
$643$	31.8736	1.25697	0.628486	−	0.777821i	$-0.283675\pi$
$643$	31.8736	1.25697	0.628486	+	0.777821i	$0.283675\pi$
$644$	118.183	4.65705
$645$	0.831632	0.0327455
$646$	−17.6100	−0.692855
$647$	6.15278	0.241891	0.120945	−	0.992659i	$-0.461407\pi$
$647$	6.15278	0.241891	0.120945	+	0.992659i	$0.461407\pi$
$648$	9.76571	0.383633
$649$	1.32240	0.0519088
$650$	−21.7560	−0.853340
$651$	−0.819895	−0.0321342
$652$	−32.1899	−1.26065
$653$	−24.5966	−0.962538	−0.481269	−	0.876573i	$-0.659824\pi$
$653$	−24.5966	−0.962538	−0.481269	+	0.876573i	$0.659824\pi$
$654$	22.7294	0.888791
$655$	6.68641	0.261260
$656$	168.175	6.56612
$657$	1.57803	0.0615649
$658$	9.32920	0.363690
$659$	22.3348	0.870042	0.435021	−	0.900420i	$-0.356741\pi$
$659$	22.3348	0.870042	0.435021	+	0.900420i	$0.356741\pi$
$660$	−11.0659	−0.430741
$661$	4.22158	0.164200	0.0821002	−	0.996624i	$-0.473837\pi$
$661$	4.22158	0.164200	0.0821002	+	0.996624i	$0.473837\pi$
$662$	−59.3912	−2.30831
$663$	1.62873	0.0632547
$664$	171.829	6.66825
$665$	−6.14823	−0.238418
$666$	−26.6301	−1.03190
$667$	−59.0255	−2.28548
$668$	53.7348	2.07906
$669$	6.86018	0.265230
$670$	7.01452	0.270994
$671$	58.4887	2.25793
$672$	60.8558	2.34756
$673$	29.6046	1.14117	0.570586	−	0.821238i	$-0.306716\pi$
$673$	29.6046	1.14117	0.570586	+	0.821238i	$0.306716\pi$
$674$	−81.1090	−3.12420
$675$	4.86027	0.187072
$676$	−57.4615	−2.21006
$677$	−31.7025	−1.21843	−0.609213	−	0.793007i	$-0.708514\pi$
$677$	−31.7025	−1.21843	−0.609213	+	0.793007i	$0.708514\pi$
$678$	5.95944	0.228871
$679$	40.1468	1.54069
$680$	−3.65045	−0.139988
$681$	9.87021	0.378227
$682$	−4.67952	−0.179188
$683$	−20.2708	−0.775641	−0.387821	−	0.921735i	$-0.626772\pi$
$683$	−20.2708	−0.775641	−0.387821	+	0.921735i	$0.626772\pi$
$684$	35.5830	1.36055
$685$	0.643472	0.0245858
$686$	52.2816	1.99612
$687$	14.7541	0.562903
$688$	−35.0020	−1.33444
$689$	0.242817	0.00925059
$690$	8.51715	0.324242
$691$	1.09078	0.0414953	0.0207477	−	0.999785i	$-0.493395\pi$
$691$	1.09078	0.0414953	0.0207477	+	0.999785i	$0.493395\pi$
$692$	−102.453	−3.89467
$693$	−13.6839	−0.519809
$694$	−57.0948	−2.16729
$695$	−2.99220	−0.113501
$696$	−69.5282	−2.63546
$697$	−10.6895	−0.404892
$698$	−71.4250	−2.70348
$699$	16.1279	0.610015
$700$	69.2838	2.61868
$701$	−36.0337	−1.36097	−0.680487	−	0.732760i	$-0.738232\pi$
$701$	−36.0337	−1.36097	−0.680487	+	0.732760i	$0.738232\pi$
$702$	−4.47629	−0.168947
$703$	−62.0859	−2.34162
$704$	179.596	6.76878
$705$	0.494311	0.0186168
$706$	6.54127	0.246184
$707$	45.8828	1.72560
$708$	−1.37760	−0.0517734
$709$	7.94892	0.298528	0.149264	−	0.988797i	$-0.452310\pi$
$709$	7.94892	0.298528	0.149264	+	0.988797i	$0.452310\pi$
$710$	−9.88935	−0.371141
$711$	1.00000	0.0375029
$712$	141.392	5.29889
$713$	2.64803	0.0991695
$714$	−7.05484	−0.264021
$715$	3.24552	0.121376
$716$	66.4693	2.48407
$717$	30.8739	1.15301
$718$	55.0043	2.05274
$719$	26.6105	0.992404	0.496202	−	0.868207i	$-0.334728\pi$
$719$	26.6105	0.992404	0.496202	+	0.868207i	$0.334728\pi$
$720$	5.88095	0.219170
$721$	−20.8976	−0.778266
$722$	60.6178	2.25596
$723$	−7.78762	−0.289625
$724$	−108.604	−4.03624
$725$	−34.6033	−1.28514
$726$	−47.8689	−1.77658
$727$	−0.269075	−0.00997942	−0.00498971	−	0.999988i	$-0.501588\pi$
$727$	−0.269075	−0.00997942	−0.00498971	+	0.999988i	$0.501588\pi$
$728$	−40.8292	−1.51323
$729$	1.00000	0.0370370
$730$	1.62117	0.0600020
$731$	2.22479	0.0822868
$732$	−60.9302	−2.25204
$733$	25.2754	0.933568	0.466784	−	0.884371i	$-0.345413\pi$
$733$	25.2754	0.933568	0.466784	+	0.884371i	$0.345413\pi$
$734$	48.9046	1.80510
$735$	0.153538	0.00566332
$736$	−196.547	−7.24482
$737$	36.3981	1.34074
$738$	29.3782	1.08143
$739$	5.68610	0.209167	0.104583	−	0.994516i	$-0.466649\pi$
$739$	5.68610	0.209167	0.104583	+	0.994516i	$0.466649\pi$
$740$	−20.1141	−0.739407
$741$	−10.4361	−0.383380
$742$	−1.05176	−0.0386114
$743$	−4.80201	−0.176169	−0.0880843	−	0.996113i	$-0.528074\pi$
$743$	−4.80201	−0.176169	−0.0880843	+	0.996113i	$0.528074\pi$
$744$	3.11921	0.114356
$745$	−6.92887	−0.253854
$746$	4.69498	0.171895
$747$	17.5951	0.643772
$748$	−29.6037	−1.08242
$749$	1.51920	0.0555103
$750$	10.1298	0.369888
$751$	32.7746	1.19596	0.597982	−	0.801510i	$-0.295970\pi$
$751$	32.7746	1.19596	0.597982	+	0.801510i	$0.295970\pi$
$752$	−20.8047	−0.758670
$753$	−17.3058	−0.630659
$754$	31.8695	1.16062
$755$	1.36013	0.0495002
$756$	14.2551	0.518454
$757$	−10.5402	−0.383090	−0.191545	−	0.981484i	$-0.561350\pi$
$757$	−10.5402	−0.383090	−0.191545	+	0.981484i	$0.561350\pi$
$758$	−15.0549	−0.546820
$759$	44.1952	1.60418
$760$	23.3903	0.848456
$761$	34.4028	1.24710	0.623550	−	0.781783i	$-0.285690\pi$
$761$	34.4028	1.24710	0.623550	+	0.781783i	$0.285690\pi$
$762$	−49.3144	−1.78647
$763$	21.2294	0.768556
$764$	−87.6456	−3.17091
$765$	−0.373803	−0.0135149
$766$	−64.8906	−2.34459
$767$	0.404036	0.0145889
$768$	−56.7814	−2.04892
$769$	−10.3263	−0.372374	−0.186187	−	0.982514i	$-0.559613\pi$
$769$	−10.3263	−0.372374	−0.186187	+	0.982514i	$0.559613\pi$
$770$	−14.0580	−0.506614
$771$	−4.96971	−0.178980
$772$	47.5518	1.71143
$773$	40.6953	1.46371	0.731854	−	0.681461i	$-0.238655\pi$
$773$	40.6953	1.46371	0.731854	+	0.681461i	$0.238655\pi$
$774$	−6.11445	−0.219779
$775$	1.55239	0.0557635
$776$	−152.734	−5.48284
$777$	−24.8726	−0.892301
$778$	56.3847	2.02149
$779$	68.4929	2.45401
$780$	−3.38100	−0.121059
$781$	−51.3155	−1.83621
$782$	22.7851	0.814795
$783$	−7.11963	−0.254435
$784$	−6.46215	−0.230791
$785$	3.06179	0.109280
$786$	−49.1608	−1.75351
$787$	−6.91174	−0.246377	−0.123188	−	0.992383i	$-0.539312\pi$
$787$	−6.91174	−0.246377	−0.123188	+	0.992383i	$0.539312\pi$
$788$	−64.7335	−2.30604
$789$	27.5432	0.980563
$790$	1.02733	0.0365509
$791$	5.56614	0.197909
$792$	52.0590	1.84984
$793$	17.8702	0.634589
$794$	41.0783	1.45781
$795$	−0.0557279	−0.00197647
$796$	−97.7298	−3.46394
$797$	−20.4571	−0.724626	−0.362313	−	0.932056i	$-0.618013\pi$
$797$	−20.4571	−0.724626	−0.362313	+	0.932056i	$0.618013\pi$
$798$	45.2040	1.60020
$799$	1.32238	0.0467826
$800$	−115.224	−4.07380
$801$	14.4784	0.511570
$802$	16.9969	0.600180
$803$	8.41217	0.296859
$804$	−37.9174	−1.33724
$805$	7.95506	0.280379
$806$	−1.42974	−0.0503606
$807$	−10.1279	−0.356519
$808$	−174.556	−6.14087
$809$	−26.2412	−0.922591	−0.461295	−	0.887247i	$-0.652615\pi$
$809$	−26.2412	−0.922591	−0.461295	+	0.887247i	$0.652615\pi$
$810$	1.02733	0.0360968
$811$	−13.8119	−0.485000	−0.242500	−	0.970151i	$-0.577967\pi$
$811$	−13.8119	−0.485000	−0.242500	+	0.970151i	$0.577967\pi$
$812$	−101.491	−3.56164
$813$	1.32119	0.0463363
$814$	−141.960	−4.97569
$815$	−2.16675	−0.0758980
$816$	15.7328	0.550756
$817$	−14.2554	−0.498732
$818$	6.37682	0.222960
$819$	−4.18088	−0.146092
$820$	22.1897	0.774898
$821$	−6.95034	−0.242568	−0.121284	−	0.992618i	$-0.538701\pi$
$821$	−6.95034	−0.242568	−0.121284	+	0.992618i	$0.538701\pi$
$822$	−4.73103	−0.165014
$823$	11.6523	0.406173	0.203087	−	0.979161i	$-0.434903\pi$
$823$	11.6523	0.406173	0.203087	+	0.979161i	$0.434903\pi$
$824$	79.5026	2.76960
$825$	25.9091	0.902040
$826$	−1.75008	−0.0608931
$827$	−4.32909	−0.150537	−0.0752687	−	0.997163i	$-0.523981\pi$
$827$	−4.32909	−0.150537	−0.0752687	+	0.997163i	$0.523981\pi$
$828$	−46.0400	−1.60000
$829$	−48.5640	−1.68670	−0.843349	−	0.537366i	$-0.819419\pi$
$829$	−48.5640	−1.68670	−0.843349	+	0.537366i	$0.819419\pi$
$830$	18.0761	0.627430
$831$	−0.795932	−0.0276106
$832$	54.8724	1.90236
$833$	0.410745	0.0142315
$834$	21.9997	0.761788
$835$	3.61698	0.125171
$836$	189.686	6.56042
$837$	0.319404	0.0110402
$838$	8.59958	0.297068
$839$	6.04404	0.208663	0.104332	−	0.994543i	$-0.466730\pi$
$839$	6.04404	0.208663	0.104332	+	0.994543i	$0.466730\pi$
$840$	9.37054	0.323314
$841$	21.6892	0.747902
$842$	15.7829	0.543916
$843$	−11.6674	−0.401847
$844$	−137.090	−4.71884
$845$	−3.86783	−0.133057
$846$	−3.63435	−0.124951
$847$	−44.7098	−1.53625
$848$	2.34550	0.0805446
$849$	28.7465	0.986576
$850$	13.3576	0.458163
$851$	80.3316	2.75373
$852$	53.4575	1.83143
$853$	17.0646	0.584280	0.292140	−	0.956376i	$-0.405633\pi$
$853$	17.0646	0.584280	0.292140	+	0.956376i	$0.405633\pi$
$854$	−77.4046	−2.64873
$855$	2.39515	0.0819123
$856$	−5.77963	−0.197544
$857$	−9.99478	−0.341415	−0.170708	−	0.985322i	$-0.554605\pi$
$857$	−9.99478	−0.341415	−0.170708	+	0.985322i	$0.554605\pi$
$858$	−23.8622	−0.814643
$859$	14.5088	0.495035	0.247517	−	0.968883i	$-0.420385\pi$
$859$	14.5088	0.495035	0.247517	+	0.968883i	$0.420385\pi$
$860$	−4.61832	−0.157484
$861$	27.4394	0.935131
$862$	49.4064	1.68279
$863$	−26.7850	−0.911773	−0.455887	−	0.890038i	$-0.650678\pi$
$863$	−26.7850	−0.911773	−0.455887	+	0.890038i	$0.650678\pi$
$864$	−23.7074	−0.806542
$865$	−6.89627	−0.234480
$866$	−2.50620	−0.0851643
$867$	−1.00000	−0.0339618
$868$	4.55314	0.154544
$869$	5.33080	0.180835
$870$	−7.31424	−0.247976
$871$	11.1208	0.376813
$872$	−80.7650	−2.73505
$873$	−15.6399	−0.529329
$874$	−145.996	−4.93839
$875$	9.46128	0.319850
$876$	−8.76332	−0.296085
$877$	−13.9883	−0.472351	−0.236175	−	0.971710i	$-0.575894\pi$
$877$	−13.9883	−0.472351	−0.236175	+	0.971710i	$0.575894\pi$
$878$	27.0472	0.912799
$879$	−1.52782	−0.0515319
$880$	31.3502	1.05681
$881$	−58.0873	−1.95701	−0.978506	−	0.206219i	$-0.933884\pi$
$881$	−58.0873	−1.95701	−0.978506	+	0.206219i	$0.933884\pi$
$882$	−1.12886	−0.0380108
$883$	−7.78627	−0.262029	−0.131014	−	0.991380i	$-0.541823\pi$
$883$	−7.78627	−0.262029	−0.131014	+	0.991380i	$0.541823\pi$
$884$	−9.04487	−0.304212
$885$	−0.0927286	−0.00311704
$886$	80.3754	2.70027
$887$	32.6996	1.09794	0.548972	−	0.835841i	$-0.315019\pi$
$887$	32.6996	1.09794	0.548972	+	0.835841i	$0.315019\pi$
$888$	94.6254	3.17542
$889$	−46.0599	−1.54480
$890$	14.8742	0.498583
$891$	5.33080	0.178589
$892$	−38.0968	−1.27557
$893$	−8.47319	−0.283544
$894$	50.9435	1.70381
$895$	4.47415	0.149554
$896$	−115.968	−3.87421
$897$	13.5030	0.450854
$898$	29.7149	0.991600
$899$	−2.27404	−0.0758434
$900$	−26.9907	−0.899689
$901$	−0.149084	−0.00496670
$902$	156.609	5.21452
$903$	−5.71093	−0.190048
$904$	−21.1758	−0.704297
$905$	−7.31031	−0.243003
$906$	−10.0002	−0.332233
$907$	20.5355	0.681870	0.340935	−	0.940087i	$-0.389256\pi$
$907$	20.5355	0.681870	0.340935	+	0.940087i	$0.389256\pi$
$908$	−54.8124	−1.81901
$909$	−17.8744	−0.592857
$910$	−4.29516	−0.142383
$911$	−32.2160	−1.06737	−0.533683	−	0.845685i	$-0.679192\pi$
$911$	−32.2160	−1.06737	−0.533683	+	0.845685i	$0.679192\pi$
$912$	−100.808	−3.33808
$913$	93.7961	3.10420
$914$	−23.6371	−0.781847
$915$	−4.10131	−0.135585
$916$	−81.9341	−2.70718
$917$	−45.9165	−1.51630
$918$	2.74833	0.0907084
$919$	21.1769	0.698561	0.349280	−	0.937018i	$-0.386426\pi$
$919$	21.1769	0.698561	0.349280	+	0.937018i	$0.386426\pi$
$920$	−30.2642	−0.997781
$921$	18.2538	0.601483
$922$	−100.572	−3.31218
$923$	−15.6785	−0.516065
$924$	75.9912	2.49993
$925$	47.0939	1.54844
$926$	−21.3600	−0.701934
$927$	8.14100	0.267385
$928$	168.788	5.54073
$929$	4.41948	0.144998	0.0724992	−	0.997368i	$-0.476903\pi$
$929$	4.41948	0.144998	0.0724992	+	0.997368i	$0.476903\pi$
$930$	0.328135	0.0107600
$931$	−2.63185	−0.0862555
$932$	−89.5637	−2.93376
$933$	−28.4096	−0.930087
$934$	4.29091	0.140403
$935$	−1.99267	−0.0651673
$936$	15.9057	0.519894
$937$	17.6203	0.575630	0.287815	−	0.957686i	$-0.407071\pi$
$937$	17.6203	0.575630	0.287815	+	0.957686i	$0.407071\pi$
$938$	−48.1696	−1.57279
$939$	9.69798	0.316481
$940$	−2.74507	−0.0895342
$941$	48.3348	1.57567	0.787835	−	0.615886i	$-0.211202\pi$
$941$	48.3348	1.57567	0.787835	+	0.615886i	$0.211202\pi$
$942$	−22.5113	−0.733459
$943$	−88.6214	−2.88591
$944$	3.90279	0.127025
$945$	0.959535	0.0312137
$946$	−32.5949	−1.05975
$947$	−30.4385	−0.989118	−0.494559	−	0.869144i	$-0.664670\pi$
$947$	−30.4385	−0.989118	−0.494559	+	0.869144i	$0.664670\pi$
$948$	−5.55332	−0.180364
$949$	2.57019	0.0834318
$950$	−85.5892	−2.77688
$951$	−21.1700	−0.686483
$952$	25.0681	0.812463
$953$	−7.67649	−0.248666	−0.124333	−	0.992241i	$-0.539679\pi$
$953$	−7.67649	−0.248666	−0.124333	+	0.992241i	$0.539679\pi$
$954$	0.409731	0.0132655
$955$	−5.89957	−0.190905
$956$	−171.452	−5.54517
$957$	−37.9533	−1.22686
$958$	13.9180	0.449669
$959$	−4.41881	−0.142691
$960$	−12.5935	−0.406454
$961$	−30.8980	−0.996709
$962$	−43.3733	−1.39841
$963$	−0.591829	−0.0190714
$964$	43.2472	1.39290
$965$	3.20079	0.103037
$966$	−58.4884	−1.88183
$967$	35.4487	1.13995	0.569977	−	0.821660i	$-0.306952\pi$
$967$	35.4487	1.13995	0.569977	+	0.821660i	$0.306952\pi$
$968$	170.094	5.46702
$969$	6.40751	0.205839
$970$	−16.0674	−0.515892
$971$	0.843630	0.0270734	0.0135367	−	0.999908i	$-0.495691\pi$
$971$	0.843630	0.0270734	0.0135367	+	0.999908i	$0.495691\pi$
$972$	−5.55332	−0.178123
$973$	20.5478	0.658733
$974$	−46.0117	−1.47431
$975$	7.91607	0.253517
$976$	172.617	5.52534
$977$	−24.8192	−0.794036	−0.397018	−	0.917811i	$-0.629955\pi$
$977$	−24.8192	−0.794036	−0.397018	+	0.917811i	$0.629955\pi$
$978$	15.9307	0.509408
$979$	77.1815	2.46673
$980$	−0.852644	−0.0272367
$981$	−8.27027	−0.264049
$982$	−39.3319	−1.25513
$983$	17.2037	0.548712	0.274356	−	0.961628i	$-0.411535\pi$
$983$	17.2037	0.548712	0.274356	+	0.961628i	$0.411535\pi$
$984$	−104.390	−3.32784
$985$	−4.35732	−0.138836
$986$	−19.5671	−0.623144
$987$	−3.39450	−0.108048
$988$	57.9551	1.84380
$989$	18.4447	0.586507
$990$	5.47651	0.174055
$991$	−50.5285	−1.60509	−0.802545	−	0.596591i	$-0.796522\pi$
$991$	−50.5285	−1.60509	−0.802545	+	0.596591i	$0.796522\pi$
$992$	−7.57223	−0.240419
$993$	21.6099	0.685770
$994$	67.9115	2.15402
$995$	−6.57835	−0.208548
$996$	−97.7114	−3.09610
$997$	−4.96068	−0.157106	−0.0785532	−	0.996910i	$-0.525030\pi$
$997$	−4.96068	−0.157106	−0.0785532	+	0.996910i	$0.525030\pi$
$998$	109.804	3.47578
$999$	9.68955	0.306564

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.32	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.32	✓	32	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+2.74833 q^{2} -1.00000 q^{3} +5.55332 q^{4} +0.373803 q^{5} -2.74833 q^{6} -2.56695 q^{7} +9.76571 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.74833 q^{2} -1.00000 q^{3} +5.55332 q^{4} +0.373803 q^{5} -2.74833 q^{6} -2.56695 q^{7} +9.76571 q^{8} +1.00000 q^{9} +1.02733 q^{10} +5.33080 q^{11} -5.55332 q^{12} +1.62873 q^{13} -7.05484 q^{14} -0.373803 q^{15} +15.7328 q^{16} -1.00000 q^{17} +2.74833 q^{18} +6.40751 q^{19} +2.07585 q^{20} +2.56695 q^{21} +14.6508 q^{22} -8.29053 q^{23} -9.76571 q^{24} -4.86027 q^{25} +4.47629 q^{26} -1.00000 q^{27} -14.2551 q^{28} +7.11963 q^{29} -1.02733 q^{30} -0.319404 q^{31} +23.7074 q^{32} -5.33080 q^{33} -2.74833 q^{34} -0.959535 q^{35} +5.55332 q^{36} -9.68955 q^{37} +17.6100 q^{38} -1.62873 q^{39} +3.65045 q^{40} +10.6895 q^{41} +7.05484 q^{42} -2.22479 q^{43} +29.6037 q^{44} +0.373803 q^{45} -22.7851 q^{46} -1.32238 q^{47} -15.7328 q^{48} -0.410745 q^{49} -13.3576 q^{50} +1.00000 q^{51} +9.04487 q^{52} +0.149084 q^{53} -2.74833 q^{54} +1.99267 q^{55} -25.0681 q^{56} -6.40751 q^{57} +19.5671 q^{58} +0.248068 q^{59} -2.07585 q^{60} +10.9718 q^{61} -0.877828 q^{62} -2.56695 q^{63} +33.6903 q^{64} +0.608824 q^{65} -14.6508 q^{66} +6.82788 q^{67} -5.55332 q^{68} +8.29053 q^{69} -2.63712 q^{70} -9.62623 q^{71} +9.76571 q^{72} +1.57803 q^{73} -26.6301 q^{74} +4.86027 q^{75} +35.5830 q^{76} -13.6839 q^{77} -4.47629 q^{78} +1.00000 q^{79} +5.88095 q^{80} +1.00000 q^{81} +29.3782 q^{82} +17.5951 q^{83} +14.2551 q^{84} -0.373803 q^{85} -6.11445 q^{86} -7.11963 q^{87} +52.0590 q^{88} +14.4784 q^{89} +1.02733 q^{90} -4.18088 q^{91} -46.0400 q^{92} +0.319404 q^{93} -3.63435 q^{94} +2.39515 q^{95} -23.7074 q^{96} -15.6399 q^{97} -1.12886 q^{98} +5.33080 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

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