LMFDB - Embedded newform 8013.2.a.d.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41705 q^{2} +1.00000 q^{3} +3.84214 q^{4} -2.77464 q^{5} -2.41705 q^{6} +0.900586 q^{7} -4.45255 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.41705 q^{2} +1.00000 q^{3} +3.84214 q^{4} -2.77464 q^{5} -2.41705 q^{6} +0.900586 q^{7} -4.45255 q^{8} +1.00000 q^{9} +6.70646 q^{10} -1.27387 q^{11} +3.84214 q^{12} -5.58494 q^{13} -2.17676 q^{14} -2.77464 q^{15} +3.07777 q^{16} -2.93223 q^{17} -2.41705 q^{18} -1.37714 q^{19} -10.6606 q^{20} +0.900586 q^{21} +3.07901 q^{22} -9.43206 q^{23} -4.45255 q^{24} +2.69865 q^{25} +13.4991 q^{26} +1.00000 q^{27} +3.46018 q^{28} -1.09717 q^{29} +6.70646 q^{30} +1.22262 q^{31} +1.46598 q^{32} -1.27387 q^{33} +7.08736 q^{34} -2.49881 q^{35} +3.84214 q^{36} +0.111472 q^{37} +3.32861 q^{38} -5.58494 q^{39} +12.3542 q^{40} -6.36057 q^{41} -2.17676 q^{42} +8.45869 q^{43} -4.89439 q^{44} -2.77464 q^{45} +22.7978 q^{46} -9.34739 q^{47} +3.07777 q^{48} -6.18894 q^{49} -6.52278 q^{50} -2.93223 q^{51} -21.4581 q^{52} -0.694746 q^{53} -2.41705 q^{54} +3.53454 q^{55} -4.00991 q^{56} -1.37714 q^{57} +2.65191 q^{58} -13.1818 q^{59} -10.6606 q^{60} -4.89206 q^{61} -2.95514 q^{62} +0.900586 q^{63} -9.69888 q^{64} +15.4962 q^{65} +3.07901 q^{66} -2.71553 q^{67} -11.2661 q^{68} -9.43206 q^{69} +6.03974 q^{70} +2.87878 q^{71} -4.45255 q^{72} -8.94958 q^{73} -0.269434 q^{74} +2.69865 q^{75} -5.29116 q^{76} -1.14723 q^{77} +13.4991 q^{78} +8.01421 q^{79} -8.53971 q^{80} +1.00000 q^{81} +15.3738 q^{82} -0.206750 q^{83} +3.46018 q^{84} +8.13590 q^{85} -20.4451 q^{86} -1.09717 q^{87} +5.67197 q^{88} +13.6189 q^{89} +6.70646 q^{90} -5.02972 q^{91} -36.2393 q^{92} +1.22262 q^{93} +22.5931 q^{94} +3.82107 q^{95} +1.46598 q^{96} +3.46030 q^{97} +14.9590 q^{98} -1.27387 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * 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 $

$2$	−2.41705	−1.70911	−0.854557	−	0.519358i	$-0.826171\pi$
$2$	−2.41705	−1.70911	−0.854557	+	0.519358i	$0.826171\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.84214	1.92107
$5$	−2.77464	−1.24086	−0.620429	−	0.784262i	$-0.713042\pi$
$5$	−2.77464	−1.24086	−0.620429	+	0.784262i	$0.713042\pi$
$6$	−2.41705	−0.986757
$7$	0.900586	0.340390	0.170195	−	0.985410i	$-0.445560\pi$
$7$	0.900586	0.340390	0.170195	+	0.985410i	$0.445560\pi$
$8$	−4.45255	−1.57421
$9$	1.00000	0.333333
$10$	6.70646	2.12077
$11$	−1.27387	−0.384086	−0.192043	−	0.981386i	$-0.561511\pi$
$11$	−1.27387	−0.384086	−0.192043	+	0.981386i	$0.561511\pi$
$12$	3.84214	1.10913
$13$	−5.58494	−1.54898	−0.774491	−	0.632585i	$-0.781994\pi$
$13$	−5.58494	−1.54898	−0.774491	+	0.632585i	$0.781994\pi$
$14$	−2.17676	−0.581764
$15$	−2.77464	−0.716410
$16$	3.07777	0.769442
$17$	−2.93223	−0.711171	−0.355585	−	0.934644i	$-0.615718\pi$
$17$	−2.93223	−0.711171	−0.355585	+	0.934644i	$0.615718\pi$
$18$	−2.41705	−0.569705
$19$	−1.37714	−0.315937	−0.157968	−	0.987444i	$-0.550494\pi$
$19$	−1.37714	−0.315937	−0.157968	+	0.987444i	$0.550494\pi$
$20$	−10.6606	−2.38378
$21$	0.900586	0.196524
$22$	3.07901	0.656447
$23$	−9.43206	−1.96672	−0.983361	−	0.181665i	$-0.941852\pi$
$23$	−9.43206	−1.96672	−0.983361	+	0.181665i	$0.941852\pi$
$24$	−4.45255	−0.908873
$25$	2.69865	0.539730
$26$	13.4991	2.64739
$27$	1.00000	0.192450
$28$	3.46018	0.653912
$29$	−1.09717	−0.203738	−0.101869	−	0.994798i	$-0.532482\pi$
$29$	−1.09717	−0.203738	−0.101869	+	0.994798i	$0.532482\pi$
$30$	6.70646	1.22443
$31$	1.22262	0.219589	0.109794	−	0.993954i	$-0.464981\pi$
$31$	1.22262	0.219589	0.109794	+	0.993954i	$0.464981\pi$
$32$	1.46598	0.259151
$33$	−1.27387	−0.221752
$34$	7.08736	1.21547
$35$	−2.49881	−0.422375
$36$	3.84214	0.640357
$37$	0.111472	0.0183259	0.00916296	−	0.999958i	$-0.497083\pi$
$37$	0.111472	0.0183259	0.00916296	+	0.999958i	$0.497083\pi$
$38$	3.32861	0.539972
$39$	−5.58494	−0.894305
$40$	12.3542	1.95338
$41$	−6.36057	−0.993353	−0.496677	−	0.867936i	$-0.665447\pi$
$41$	−6.36057	−0.993353	−0.496677	+	0.867936i	$0.665447\pi$
$42$	−2.17676	−0.335882
$43$	8.45869	1.28994	0.644969	−	0.764209i	$-0.276870\pi$
$43$	8.45869	1.28994	0.644969	+	0.764209i	$0.276870\pi$
$44$	−4.89439	−0.737857
$45$	−2.77464	−0.413620
$46$	22.7978	3.36135
$47$	−9.34739	−1.36346	−0.681729	−	0.731605i	$-0.738771\pi$
$47$	−9.34739	−1.36346	−0.681729	+	0.731605i	$0.738771\pi$
$48$	3.07777	0.444237
$49$	−6.18894	−0.884135
$50$	−6.52278	−0.922461
$51$	−2.93223	−0.410595
$52$	−21.4581	−2.97570
$53$	−0.694746	−0.0954307	−0.0477153	−	0.998861i	$-0.515194\pi$
$53$	−0.694746	−0.0954307	−0.0477153	+	0.998861i	$0.515194\pi$
$54$	−2.41705	−0.328919
$55$	3.53454	0.476597
$56$	−4.00991	−0.535846
$57$	−1.37714	−0.182406
$58$	2.65191	0.348212
$59$	−13.1818	−1.71613	−0.858064	−	0.513543i	$-0.828333\pi$
$59$	−13.1818	−1.71613	−0.858064	+	0.513543i	$0.828333\pi$
$60$	−10.6606	−1.37627
$61$	−4.89206	−0.626364	−0.313182	−	0.949693i	$-0.601395\pi$
$61$	−4.89206	−0.626364	−0.313182	+	0.949693i	$0.601395\pi$
$62$	−2.95514	−0.375303
$63$	0.900586	0.113463
$64$	−9.69888	−1.21236
$65$	15.4962	1.92207
$66$	3.07901	0.379000
$67$	−2.71553	−0.331755	−0.165878	−	0.986146i	$-0.553046\pi$
$67$	−2.71553	−0.331755	−0.165878	+	0.986146i	$0.553046\pi$
$68$	−11.2661	−1.36621
$69$	−9.43206	−1.13549
$70$	6.03974	0.721888
$71$	2.87878	0.341648	0.170824	−	0.985302i	$-0.445357\pi$
$71$	2.87878	0.341648	0.170824	+	0.985302i	$0.445357\pi$
$72$	−4.45255	−0.524738
$73$	−8.94958	−1.04747	−0.523734	−	0.851882i	$-0.675462\pi$
$73$	−8.94958	−1.04747	−0.523734	+	0.851882i	$0.675462\pi$
$74$	−0.269434	−0.0313211
$75$	2.69865	0.311614
$76$	−5.29116	−0.606937
$77$	−1.14723	−0.130739
$78$	13.4991	1.52847
$79$	8.01421	0.901669	0.450835	−	0.892607i	$-0.351126\pi$
$79$	8.01421	0.901669	0.450835	+	0.892607i	$0.351126\pi$
$80$	−8.53971	−0.954769
$81$	1.00000	0.111111
$82$	15.3738	1.69775
$83$	−0.206750	−0.0226938	−0.0113469	−	0.999936i	$-0.503612\pi$
$83$	−0.206750	−0.0226938	−0.0113469	+	0.999936i	$0.503612\pi$
$84$	3.46018	0.377536
$85$	8.13590	0.882462
$86$	−20.4451	−2.20465
$87$	−1.09717	−0.117628
$88$	5.67197	0.604634
$89$	13.6189	1.44360	0.721801	−	0.692101i	$-0.243315\pi$
$89$	13.6189	1.44360	0.721801	+	0.692101i	$0.243315\pi$
$90$	6.70646	0.706923
$91$	−5.02972	−0.527257
$92$	−36.2393	−3.77821
$93$	1.22262	0.126780
$94$	22.5931	2.33030
$95$	3.82107	0.392033
$96$	1.46598	0.149621
$97$	3.46030	0.351340	0.175670	−	0.984449i	$-0.443791\pi$
$97$	3.46030	0.351340	0.175670	+	0.984449i	$0.443791\pi$
$98$	14.9590	1.51109
$99$	−1.27387	−0.128029
$100$	10.3686	1.03686
$101$	−8.67687	−0.863381	−0.431690	−	0.902022i	$-0.642083\pi$
$101$	−8.67687	−0.863381	−0.431690	+	0.902022i	$0.642083\pi$
$102$	7.08736	0.701753
$103$	7.66574	0.755328	0.377664	−	0.925943i	$-0.376727\pi$
$103$	7.66574	0.755328	0.377664	+	0.925943i	$0.376727\pi$
$104$	24.8672	2.43843
$105$	−2.49881	−0.243859
$106$	1.67924	0.163102
$107$	2.63298	0.254539	0.127270	−	0.991868i	$-0.459379\pi$
$107$	2.63298	0.254539	0.127270	+	0.991868i	$0.459379\pi$
$108$	3.84214	0.369710
$109$	−11.3577	−1.08787	−0.543934	−	0.839128i	$-0.683066\pi$
$109$	−11.3577	−1.08787	−0.543934	+	0.839128i	$0.683066\pi$
$110$	−8.54316	−0.814558
$111$	0.111472	0.0105805
$112$	2.77179	0.261910
$113$	5.64352	0.530897	0.265449	−	0.964125i	$-0.414480\pi$
$113$	5.64352	0.530897	0.265449	+	0.964125i	$0.414480\pi$
$114$	3.32861	0.311753
$115$	26.1706	2.44042
$116$	−4.21546	−0.391396
$117$	−5.58494	−0.516328
$118$	31.8612	2.93306
$119$	−2.64073	−0.242075
$120$	12.3542	1.12778
$121$	−9.37726	−0.852478
$122$	11.8244	1.07053
$123$	−6.36057	−0.573513
$124$	4.69748	0.421846
$125$	6.38542	0.571129
$126$	−2.17676	−0.193921
$127$	10.7700	0.955682	0.477841	−	0.878446i	$-0.341419\pi$
$127$	10.7700	0.955682	0.477841	+	0.878446i	$0.341419\pi$
$128$	20.5107	1.81291
$129$	8.45869	0.744746
$130$	−37.4552	−3.28503
$131$	−13.3198	−1.16375	−0.581876	−	0.813277i	$-0.697681\pi$
$131$	−13.3198	−1.16375	−0.581876	+	0.813277i	$0.697681\pi$
$132$	−4.89439	−0.426002
$133$	−1.24023	−0.107542
$134$	6.56359	0.567008
$135$	−2.77464	−0.238803
$136$	13.0559	1.11954
$137$	−3.15516	−0.269564	−0.134782	−	0.990875i	$-0.543033\pi$
$137$	−3.15516	−0.269564	−0.134782	+	0.990875i	$0.543033\pi$
$138$	22.7978	1.94068
$139$	−11.1880	−0.948952	−0.474476	−	0.880268i	$-0.657363\pi$
$139$	−11.1880	−0.948952	−0.474476	+	0.880268i	$0.657363\pi$
$140$	−9.60077	−0.811413
$141$	−9.34739	−0.787192
$142$	−6.95816	−0.583916
$143$	7.11448	0.594943
$144$	3.07777	0.256481
$145$	3.04424	0.252811
$146$	21.6316	1.79024
$147$	−6.18894	−0.510456
$148$	0.428292	0.0352054
$149$	23.2434	1.90418	0.952088	−	0.305824i	$-0.0989318\pi$
$149$	23.2434	1.90418	0.952088	+	0.305824i	$0.0989318\pi$
$150$	−6.52278	−0.532583
$151$	14.3304	1.16619	0.583096	−	0.812403i	$-0.301841\pi$
$151$	14.3304	1.16619	0.583096	+	0.812403i	$0.301841\pi$
$152$	6.13177	0.497353
$153$	−2.93223	−0.237057
$154$	2.77291	0.223448
$155$	−3.39233	−0.272479
$156$	−21.4581	−1.71802
$157$	17.0943	1.36428	0.682138	−	0.731224i	$-0.261050\pi$
$157$	17.0943	1.36428	0.682138	+	0.731224i	$0.261050\pi$
$158$	−19.3708	−1.54106
$159$	−0.694746	−0.0550969
$160$	−4.06757	−0.321570
$161$	−8.49438	−0.669451
$162$	−2.41705	−0.189902
$163$	15.9899	1.25243	0.626214	−	0.779651i	$-0.284604\pi$
$163$	15.9899	1.25243	0.626214	+	0.779651i	$0.284604\pi$
$164$	−24.4382	−1.90830
$165$	3.53454	0.275163
$166$	0.499726	0.0387862
$167$	−17.1243	−1.32512	−0.662560	−	0.749009i	$-0.730530\pi$
$167$	−17.1243	−1.32512	−0.662560	+	0.749009i	$0.730530\pi$
$168$	−4.00991	−0.309371
$169$	18.1915	1.39935
$170$	−19.6649	−1.50823
$171$	−1.37714	−0.105312
$172$	32.4995	2.47806
$173$	4.42061	0.336092	0.168046	−	0.985779i	$-0.446254\pi$
$173$	4.42061	0.336092	0.168046	+	0.985779i	$0.446254\pi$
$174$	2.65191	0.201040
$175$	2.43037	0.183719
$176$	−3.92068	−0.295532
$177$	−13.1818	−0.990807
$178$	−32.9176	−2.46728
$179$	6.66218	0.497954	0.248977	−	0.968509i	$-0.419906\pi$
$179$	6.66218	0.497954	0.248977	+	0.968509i	$0.419906\pi$
$180$	−10.6606	−0.794592
$181$	−12.3817	−0.920323	−0.460162	−	0.887835i	$-0.652209\pi$
$181$	−12.3817	−0.920323	−0.460162	+	0.887835i	$0.652209\pi$
$182$	12.1571	0.901143
$183$	−4.89206	−0.361632
$184$	41.9968	3.09604
$185$	−0.309296	−0.0227399
$186$	−2.95514	−0.216681
$187$	3.73528	0.273151
$188$	−35.9140	−2.61930
$189$	0.900586	0.0655080
$190$	−9.23572	−0.670029
$191$	−26.5656	−1.92222	−0.961111	−	0.276162i	$-0.910938\pi$
$191$	−26.5656	−1.92222	−0.961111	+	0.276162i	$0.910938\pi$
$192$	−9.69888	−0.699957
$193$	14.1004	1.01497	0.507486	−	0.861660i	$-0.330575\pi$
$193$	14.1004	1.01497	0.507486	+	0.861660i	$0.330575\pi$
$194$	−8.36372	−0.600480
$195$	15.4962	1.10971
$196$	−23.7788	−1.69849
$197$	7.60149	0.541584	0.270792	−	0.962638i	$-0.412714\pi$
$197$	7.60149	0.541584	0.270792	+	0.962638i	$0.412714\pi$
$198$	3.07901	0.218816
$199$	−17.7245	−1.25646	−0.628229	−	0.778029i	$-0.716220\pi$
$199$	−17.7245	−1.25646	−0.628229	+	0.778029i	$0.716220\pi$
$200$	−12.0159	−0.849652
$201$	−2.71553	−0.191539
$202$	20.9725	1.47562
$203$	−0.988091	−0.0693504
$204$	−11.2661	−0.788781
$205$	17.6483	1.23261
$206$	−18.5285	−1.29094
$207$	−9.43206	−0.655574
$208$	−17.1891	−1.19185
$209$	1.75429	0.121347
$210$	6.03974	0.416782
$211$	−23.1567	−1.59418	−0.797088	−	0.603863i	$-0.793627\pi$
$211$	−23.1567	−1.59418	−0.797088	+	0.603863i	$0.793627\pi$
$212$	−2.66931	−0.183329
$213$	2.87878	0.197251
$214$	−6.36404	−0.435037
$215$	−23.4699	−1.60063
$216$	−4.45255	−0.302958
$217$	1.10107	0.0747458
$218$	27.4521	1.85929
$219$	−8.94958	−0.604756
$220$	13.5802	0.915576
$221$	16.3763	1.10159
$222$	−0.269434	−0.0180832
$223$	23.9637	1.60473	0.802365	−	0.596833i	$-0.203575\pi$
$223$	23.9637	1.60473	0.802365	+	0.596833i	$0.203575\pi$
$224$	1.32024	0.0882123
$225$	2.69865	0.179910
$226$	−13.6407	−0.907364
$227$	10.1059	0.670755	0.335377	−	0.942084i	$-0.391136\pi$
$227$	10.1059	0.670755	0.335377	+	0.942084i	$0.391136\pi$
$228$	−5.29116	−0.350415
$229$	−26.9013	−1.77769	−0.888844	−	0.458211i	$-0.848490\pi$
$229$	−26.9013	−1.77769	−0.888844	+	0.458211i	$0.848490\pi$
$230$	−63.2558	−4.17096
$231$	−1.14723	−0.0754821
$232$	4.88518	0.320728
$233$	−2.47081	−0.161868	−0.0809340	−	0.996719i	$-0.525790\pi$
$233$	−2.47081	−0.161868	−0.0809340	+	0.996719i	$0.525790\pi$
$234$	13.4991	0.882463
$235$	25.9357	1.69186
$236$	−50.6464	−3.29680
$237$	8.01421	0.520579
$238$	6.38278	0.413734
$239$	−2.94597	−0.190559	−0.0952793	−	0.995451i	$-0.530374\pi$
$239$	−2.94597	−0.190559	−0.0952793	+	0.995451i	$0.530374\pi$
$240$	−8.53971	−0.551236
$241$	−5.51845	−0.355475	−0.177737	−	0.984078i	$-0.556878\pi$
$241$	−5.51845	−0.355475	−0.177737	+	0.984078i	$0.556878\pi$
$242$	22.6653	1.45698
$243$	1.00000	0.0641500
$244$	−18.7960	−1.20329
$245$	17.1721	1.09709
$246$	15.3738	0.980199
$247$	7.69122	0.489381
$248$	−5.44378	−0.345680
$249$	−0.206750	−0.0131023
$250$	−15.4339	−0.976125
$251$	13.9211	0.878691	0.439345	−	0.898318i	$-0.355210\pi$
$251$	13.9211	0.878691	0.439345	+	0.898318i	$0.355210\pi$
$252$	3.46018	0.217971
$253$	12.0152	0.755390
$254$	−26.0316	−1.63337
$255$	8.13590	0.509490
$256$	−30.1778	−1.88611
$257$	15.5978	0.972964	0.486482	−	0.873691i	$-0.338280\pi$
$257$	15.5978	0.972964	0.486482	+	0.873691i	$0.338280\pi$
$258$	−20.4451	−1.27286
$259$	0.100390	0.00623795
$260$	59.5386	3.69243
$261$	−1.09717	−0.0679128
$262$	32.1946	1.98899
$263$	−24.4979	−1.51060	−0.755302	−	0.655377i	$-0.772510\pi$
$263$	−24.4979	−1.51060	−0.755302	+	0.655377i	$0.772510\pi$
$264$	5.67197	0.349086
$265$	1.92767	0.118416
$266$	2.99770	0.183801
$267$	13.6189	0.833464
$268$	−10.4335	−0.637325
$269$	−3.34574	−0.203993	−0.101997	−	0.994785i	$-0.532523\pi$
$269$	−3.34574	−0.203993	−0.101997	+	0.994785i	$0.532523\pi$
$270$	6.70646	0.408142
$271$	9.27925	0.563674	0.281837	−	0.959462i	$-0.409056\pi$
$271$	9.27925	0.563674	0.281837	+	0.959462i	$0.409056\pi$
$272$	−9.02473	−0.547205
$273$	−5.02972	−0.304412
$274$	7.62619	0.460715
$275$	−3.43773	−0.207303
$276$	−36.2393	−2.18135
$277$	−25.6603	−1.54178	−0.770890	−	0.636968i	$-0.780188\pi$
$277$	−25.6603	−1.54178	−0.770890	+	0.636968i	$0.780188\pi$
$278$	27.0419	1.62187
$279$	1.22262	0.0731963
$280$	11.1261	0.664909
$281$	−14.7166	−0.877920	−0.438960	−	0.898507i	$-0.644653\pi$
$281$	−14.7166	−0.877920	−0.438960	+	0.898507i	$0.644653\pi$
$282$	22.5931	1.34540
$283$	1.36979	0.0814254	0.0407127	−	0.999171i	$-0.487037\pi$
$283$	1.36979	0.0814254	0.0407127	+	0.999171i	$0.487037\pi$
$284$	11.0607	0.656331
$285$	3.82107	0.226340
$286$	−17.1961	−1.01683
$287$	−5.72824	−0.338127
$288$	1.46598	0.0863836
$289$	−8.40201	−0.494236
$290$	−7.35809	−0.432082
$291$	3.46030	0.202846
$292$	−34.3855	−2.01226
$293$	−33.2586	−1.94299	−0.971494	−	0.237063i	$-0.923815\pi$
$293$	−33.2586	−1.94299	−0.971494	+	0.237063i	$0.923815\pi$
$294$	14.9590	0.872427
$295$	36.5749	2.12947
$296$	−0.496336	−0.0288489
$297$	−1.27387	−0.0739174
$298$	−56.1806	−3.25445
$299$	52.6775	3.04642
$300$	10.3686	0.598632
$301$	7.61778	0.439081
$302$	−34.6373	−1.99316
$303$	−8.67687	−0.498473
$304$	−4.23851	−0.243095
$305$	13.5737	0.777230
$306$	7.08736	0.405157
$307$	26.7870	1.52881	0.764407	−	0.644734i	$-0.223032\pi$
$307$	26.7870	1.52881	0.764407	+	0.644734i	$0.223032\pi$
$308$	−4.40782	−0.251159
$309$	7.66574	0.436089
$310$	8.19945	0.465697
$311$	31.7867	1.80246	0.901229	−	0.433344i	$-0.142666\pi$
$311$	31.7867	1.80246	0.901229	+	0.433344i	$0.142666\pi$
$312$	24.8672	1.40783
$313$	29.8834	1.68911	0.844555	−	0.535469i	$-0.179865\pi$
$313$	29.8834	1.68911	0.844555	+	0.535469i	$0.179865\pi$
$314$	−41.3179	−2.33170
$315$	−2.49881	−0.140792
$316$	30.7917	1.73217
$317$	6.29224	0.353408	0.176704	−	0.984264i	$-0.443457\pi$
$317$	6.29224	0.353408	0.176704	+	0.984264i	$0.443457\pi$
$318$	1.67924	0.0941669
$319$	1.39765	0.0782531
$320$	26.9110	1.50437
$321$	2.63298	0.146958
$322$	20.5314	1.14417
$323$	4.03809	0.224685
$324$	3.84214	0.213452
$325$	−15.0718	−0.836033
$326$	−38.6485	−2.14054
$327$	−11.3577	−0.628080
$328$	28.3207	1.56375
$329$	−8.41813	−0.464106
$330$	−8.54316	−0.470285
$331$	17.7939	0.978042	0.489021	−	0.872272i	$-0.337354\pi$
$331$	17.7939	0.978042	0.489021	+	0.872272i	$0.337354\pi$
$332$	−0.794363	−0.0435963
$333$	0.111472	0.00610864
$334$	41.3904	2.26478
$335$	7.53464	0.411661
$336$	2.77179	0.151214
$337$	34.8773	1.89989	0.949944	−	0.312420i	$-0.101140\pi$
$337$	34.8773	1.89989	0.949944	+	0.312420i	$0.101140\pi$
$338$	−43.9698	−2.39164
$339$	5.64352	0.306514
$340$	31.2593	1.69527
$341$	−1.55746	−0.0843411
$342$	3.32861	0.179991
$343$	−11.8778	−0.641340
$344$	−37.6627	−2.03064
$345$	26.1706	1.40898
$346$	−10.6848	−0.574420
$347$	−23.5893	−1.26634	−0.633171	−	0.774012i	$-0.718247\pi$
$347$	−23.5893	−1.26634	−0.633171	+	0.774012i	$0.718247\pi$
$348$	−4.21546	−0.225973
$349$	13.8322	0.740421	0.370211	−	0.928948i	$-0.379286\pi$
$349$	13.8322	0.740421	0.370211	+	0.928948i	$0.379286\pi$
$350$	−5.87433	−0.313996
$351$	−5.58494	−0.298102
$352$	−1.86747	−0.0995363
$353$	−30.7694	−1.63769	−0.818844	−	0.574016i	$-0.805385\pi$
$353$	−30.7694	−1.63769	−0.818844	+	0.574016i	$0.805385\pi$
$354$	31.8612	1.69340
$355$	−7.98759	−0.423937
$356$	52.3258	2.77326
$357$	−2.64073	−0.139762
$358$	−16.1028	−0.851061
$359$	18.8217	0.993373	0.496686	−	0.867930i	$-0.334550\pi$
$359$	18.8217	0.993373	0.496686	+	0.867930i	$0.334550\pi$
$360$	12.3542	0.651126
$361$	−17.1035	−0.900184
$362$	29.9272	1.57294
$363$	−9.37726	−0.492178
$364$	−19.3249	−1.01290
$365$	24.8319	1.29976
$366$	11.8244	0.618070
$367$	−16.7292	−0.873255	−0.436628	−	0.899642i	$-0.643827\pi$
$367$	−16.7292	−0.873255	−0.436628	+	0.899642i	$0.643827\pi$
$368$	−29.0297	−1.51328
$369$	−6.36057	−0.331118
$370$	0.747584	0.0388650
$371$	−0.625678	−0.0324836
$372$	4.69748	0.243553
$373$	11.2213	0.581015	0.290508	−	0.956873i	$-0.406176\pi$
$373$	11.2213	0.581015	0.290508	+	0.956873i	$0.406176\pi$
$374$	−9.02837	−0.466846
$375$	6.38542	0.329742
$376$	41.6197	2.14637
$377$	6.12760	0.315587
$378$	−2.17676	−0.111961
$379$	6.04118	0.310314	0.155157	−	0.987890i	$-0.450412\pi$
$379$	6.04118	0.310314	0.155157	+	0.987890i	$0.450412\pi$
$380$	14.6811	0.753123
$381$	10.7700	0.551763
$382$	64.2105	3.28530
$383$	−21.9862	−1.12344	−0.561721	−	0.827327i	$-0.689860\pi$
$383$	−21.9862	−1.12344	−0.561721	+	0.827327i	$0.689860\pi$
$384$	20.5107	1.04668
$385$	3.18315	0.162229
$386$	−34.0815	−1.73470
$387$	8.45869	0.429979
$388$	13.2950	0.674949
$389$	−13.0933	−0.663854	−0.331927	−	0.943305i	$-0.607699\pi$
$389$	−13.0933	−0.663854	−0.331927	+	0.943305i	$0.607699\pi$
$390$	−37.4552	−1.89662
$391$	27.6570	1.39867
$392$	27.5566	1.39182
$393$	−13.3198	−0.671893
$394$	−18.3732	−0.925628
$395$	−22.2366	−1.11884
$396$	−4.89439	−0.245952
$397$	29.2781	1.46942	0.734712	−	0.678379i	$-0.237317\pi$
$397$	29.2781	1.46942	0.734712	+	0.678379i	$0.237317\pi$
$398$	42.8411	2.14743
$399$	−1.24023	−0.0620892
$400$	8.30582	0.415291
$401$	−31.7755	−1.58680	−0.793398	−	0.608704i	$-0.791690\pi$
$401$	−31.7755	−1.58680	−0.793398	+	0.608704i	$0.791690\pi$
$402$	6.56359	0.327362
$403$	−6.82825	−0.340139
$404$	−33.3378	−1.65862
$405$	−2.77464	−0.137873
$406$	2.38827	0.118528
$407$	−0.142001	−0.00703873
$408$	13.0559	0.646364
$409$	−21.9147	−1.08361	−0.541805	−	0.840504i	$-0.682259\pi$
$409$	−21.9147	−1.08361	−0.541805	+	0.840504i	$0.682259\pi$
$410$	−42.6569	−2.10667
$411$	−3.15516	−0.155633
$412$	29.4529	1.45104
$413$	−11.8714	−0.584152
$414$	22.7978	1.12045
$415$	0.573658	0.0281598
$416$	−8.18740	−0.401420
$417$	−11.1880	−0.547878
$418$	−4.24022	−0.207396
$419$	−18.7123	−0.914158	−0.457079	−	0.889426i	$-0.651104\pi$
$419$	−18.7123	−0.914158	−0.457079	+	0.889426i	$0.651104\pi$
$420$	−9.60077	−0.468469
$421$	−11.0842	−0.540211	−0.270106	−	0.962831i	$-0.587059\pi$
$421$	−11.0842	−0.540211	−0.270106	+	0.962831i	$0.587059\pi$
$422$	55.9711	2.72463
$423$	−9.34739	−0.454486
$424$	3.09339	0.150228
$425$	−7.91308	−0.383841
$426$	−6.95816	−0.337124
$427$	−4.40572	−0.213208
$428$	10.1163	0.488988
$429$	7.11448	0.343490
$430$	56.7279	2.73566
$431$	2.06580	0.0995060	0.0497530	−	0.998762i	$-0.484157\pi$
$431$	2.06580	0.0995060	0.0497530	+	0.998762i	$0.484157\pi$
$432$	3.07777	0.148079
$433$	−15.8105	−0.759805	−0.379903	−	0.925027i	$-0.624042\pi$
$433$	−15.8105	−0.759805	−0.379903	+	0.925027i	$0.624042\pi$
$434$	−2.66135	−0.127749
$435$	3.04424	0.145960
$436$	−43.6378	−2.08987
$437$	12.9892	0.621360
$438$	21.6316	1.03360
$439$	−1.71192	−0.0817056	−0.0408528	−	0.999165i	$-0.513007\pi$
$439$	−1.71192	−0.0817056	−0.0408528	+	0.999165i	$0.513007\pi$
$440$	−15.7377	−0.750266
$441$	−6.18894	−0.294712
$442$	−39.5824	−1.88274
$443$	14.4599	0.687009	0.343505	−	0.939151i	$-0.388386\pi$
$443$	14.4599	0.687009	0.343505	+	0.939151i	$0.388386\pi$
$444$	0.428292	0.0203258
$445$	−37.7877	−1.79131
$446$	−57.9216	−2.74267
$447$	23.2434	1.09938
$448$	−8.73468	−0.412675
$449$	39.5760	1.86771	0.933854	−	0.357654i	$-0.116423\pi$
$449$	39.5760	1.86771	0.933854	+	0.357654i	$0.116423\pi$
$450$	−6.52278	−0.307487
$451$	8.10253	0.381533
$452$	21.6832	1.01989
$453$	14.3304	0.673301
$454$	−24.4266	−1.14640
$455$	13.9557	0.654252
$456$	6.13177	0.287147
$457$	−37.8797	−1.77194	−0.885968	−	0.463746i	$-0.846505\pi$
$457$	−37.8797	−1.77194	−0.885968	+	0.463746i	$0.846505\pi$
$458$	65.0218	3.03827
$459$	−2.93223	−0.136865
$460$	100.551	4.68823
$461$	10.6913	0.497942	0.248971	−	0.968511i	$-0.419908\pi$
$461$	10.6913	0.497942	0.248971	+	0.968511i	$0.419908\pi$
$462$	2.77291	0.129008
$463$	0.454352	0.0211155	0.0105578	−	0.999944i	$-0.496639\pi$
$463$	0.454352	0.0211155	0.0105578	+	0.999944i	$0.496639\pi$
$464$	−3.37682	−0.156765
$465$	−3.39233	−0.157316
$466$	5.97207	0.276651
$467$	15.7674	0.729627	0.364814	−	0.931081i	$-0.381133\pi$
$467$	15.7674	0.729627	0.364814	+	0.931081i	$0.381133\pi$
$468$	−21.4581	−0.991902
$469$	−2.44557	−0.112926
$470$	−62.6879	−2.89158
$471$	17.0943	0.787665
$472$	58.6928	2.70155
$473$	−10.7753	−0.495447
$474$	−19.3708	−0.889729
$475$	−3.71641	−0.170521
$476$	−10.1460	−0.465043
$477$	−0.694746	−0.0318102
$478$	7.12055	0.325686
$479$	−8.14081	−0.371963	−0.185981	−	0.982553i	$-0.559546\pi$
$479$	−8.14081	−0.371963	−0.185981	+	0.982553i	$0.559546\pi$
$480$	−4.06757	−0.185658
$481$	−0.622565	−0.0283865
$482$	13.3384	0.607547
$483$	−8.49438	−0.386508
$484$	−36.0287	−1.63767
$485$	−9.60110	−0.435963
$486$	−2.41705	−0.109640
$487$	−9.11338	−0.412966	−0.206483	−	0.978450i	$-0.566202\pi$
$487$	−9.11338	−0.412966	−0.206483	+	0.978450i	$0.566202\pi$
$488$	21.7822	0.986032
$489$	15.9899	0.723090
$490$	−41.5059	−1.87505
$491$	36.7897	1.66030	0.830149	−	0.557542i	$-0.188255\pi$
$491$	36.7897	1.66030	0.830149	+	0.557542i	$0.188255\pi$
$492$	−24.4382	−1.10176
$493$	3.21714	0.144893
$494$	−18.5901	−0.836408
$495$	3.53454	0.158866
$496$	3.76294	0.168961
$497$	2.59259	0.116294
$498$	0.499726	0.0223933
$499$	−15.3142	−0.685558	−0.342779	−	0.939416i	$-0.611368\pi$
$499$	−15.3142	−0.685558	−0.342779	+	0.939416i	$0.611368\pi$
$500$	24.5337	1.09718
$501$	−17.1243	−0.765058
$502$	−33.6480	−1.50178
$503$	−36.2116	−1.61460	−0.807298	−	0.590144i	$-0.799071\pi$
$503$	−36.2116	−1.61460	−0.807298	+	0.590144i	$0.799071\pi$
$504$	−4.00991	−0.178615
$505$	24.0752	1.07133
$506$	−29.0414	−1.29105
$507$	18.1915	0.807913
$508$	41.3798	1.83593
$509$	27.6719	1.22654	0.613268	−	0.789875i	$-0.289855\pi$
$509$	27.6719	1.22654	0.613268	+	0.789875i	$0.289855\pi$
$510$	−19.6649	−0.870776
$511$	−8.05986	−0.356547
$512$	31.9198	1.41067
$513$	−1.37714	−0.0608021
$514$	−37.7007	−1.66291
$515$	−21.2697	−0.937256
$516$	32.4995	1.43071
$517$	11.9074	0.523685
$518$	−0.242649	−0.0106614
$519$	4.42061	0.194043
$520$	−68.9977	−3.02575
$521$	25.5272	1.11837	0.559184	−	0.829044i	$-0.311115\pi$
$521$	25.5272	1.11837	0.559184	+	0.829044i	$0.311115\pi$
$522$	2.65191	0.116071
$523$	−21.8509	−0.955475	−0.477737	−	0.878503i	$-0.658543\pi$
$523$	−21.8509	−0.955475	−0.477737	+	0.878503i	$0.658543\pi$
$524$	−51.1764	−2.23565
$525$	2.43037	0.106070
$526$	59.2127	2.58179
$527$	−3.58500	−0.156165
$528$	−3.92068	−0.170625
$529$	65.9638	2.86799
$530$	−4.65928	−0.202386
$531$	−13.1818	−0.572043
$532$	−4.76514	−0.206595
$533$	35.5233	1.53869
$534$	−32.9176	−1.42449
$535$	−7.30557	−0.315848
$536$	12.0911	0.522254
$537$	6.66218	0.287494
$538$	8.08683	0.348648
$539$	7.88391	0.339584
$540$	−10.6606	−0.458758
$541$	−26.4902	−1.13890	−0.569451	−	0.822026i	$-0.692844\pi$
$541$	−26.4902	−1.13890	−0.569451	+	0.822026i	$0.692844\pi$
$542$	−22.4284	−0.963383
$543$	−12.3817	−0.531349
$544$	−4.29859	−0.184301
$545$	31.5135	1.34989
$546$	12.1571	0.520275
$547$	36.2723	1.55089	0.775447	−	0.631413i	$-0.217525\pi$
$547$	36.2723	1.55089	0.775447	+	0.631413i	$0.217525\pi$
$548$	−12.1226	−0.517851
$549$	−4.89206	−0.208788
$550$	8.30918	0.354305
$551$	1.51095	0.0643685
$552$	41.9968	1.78750
$553$	7.21749	0.306919
$554$	62.0224	2.63508
$555$	−0.309296	−0.0131289
$556$	−42.9858	−1.82300
$557$	−2.94719	−0.124877	−0.0624383	−	0.998049i	$-0.519888\pi$
$557$	−2.94719	−0.124877	−0.0624383	+	0.998049i	$0.519888\pi$
$558$	−2.95514	−0.125101
$559$	−47.2412	−1.99809
$560$	−7.69074	−0.324993
$561$	3.73528	0.157704
$562$	35.5709	1.50047
$563$	21.5956	0.910146	0.455073	−	0.890454i	$-0.349613\pi$
$563$	21.5956	0.910146	0.455073	+	0.890454i	$0.349613\pi$
$564$	−35.9140	−1.51225
$565$	−15.6588	−0.658769
$566$	−3.31085	−0.139165
$567$	0.900586	0.0378211
$568$	−12.8179	−0.537828
$569$	3.86761	0.162139	0.0810694	−	0.996708i	$-0.474166\pi$
$569$	3.86761	0.162139	0.0810694	+	0.996708i	$0.474166\pi$
$570$	−9.23572	−0.386842
$571$	−39.9902	−1.67354	−0.836768	−	0.547557i	$-0.815558\pi$
$571$	−39.9902	−1.67354	−0.836768	+	0.547557i	$0.815558\pi$
$572$	27.3348	1.14293
$573$	−26.5656	−1.10980
$574$	13.8454	0.577898
$575$	−25.4539	−1.06150
$576$	−9.69888	−0.404120
$577$	−32.9209	−1.37051	−0.685257	−	0.728301i	$-0.740310\pi$
$577$	−32.9209	−1.37051	−0.685257	+	0.728301i	$0.740310\pi$
$578$	20.3081	0.844706
$579$	14.1004	0.585994
$580$	11.6964	0.485667
$581$	−0.186196	−0.00772472
$582$	−8.36372	−0.346687
$583$	0.885016	0.0366536
$584$	39.8485	1.64894
$585$	15.4962	0.640690
$586$	80.3878	3.32079
$587$	16.2240	0.669636	0.334818	−	0.942283i	$-0.391325\pi$
$587$	16.2240	0.669636	0.334818	+	0.942283i	$0.391325\pi$
$588$	−23.7788	−0.980621
$589$	−1.68371	−0.0693763
$590$	−88.4034	−3.63951
$591$	7.60149	0.312684
$592$	0.343085	0.0141007
$593$	5.43644	0.223248	0.111624	−	0.993751i	$-0.464395\pi$
$593$	5.43644	0.223248	0.111624	+	0.993751i	$0.464395\pi$
$594$	3.07901	0.126333
$595$	7.32708	0.300381
$596$	89.3046	3.65806
$597$	−17.7245	−0.725416
$598$	−127.324	−5.20667
$599$	−4.42338	−0.180735	−0.0903673	−	0.995909i	$-0.528804\pi$
$599$	−4.42338	−0.180735	−0.0903673	+	0.995909i	$0.528804\pi$
$600$	−12.0159	−0.490547
$601$	16.8558	0.687563	0.343781	−	0.939050i	$-0.388292\pi$
$601$	16.8558	0.687563	0.343781	+	0.939050i	$0.388292\pi$
$602$	−18.4126	−0.750440
$603$	−2.71553	−0.110585
$604$	55.0595	2.24034
$605$	26.0186	1.05780
$606$	20.9725	0.851948
$607$	−35.6191	−1.44573	−0.722867	−	0.690987i	$-0.757176\pi$
$607$	−35.6191	−1.44573	−0.722867	+	0.690987i	$0.757176\pi$
$608$	−2.01885	−0.0818754
$609$	−0.988091	−0.0400395
$610$	−32.8084	−1.32837
$611$	52.2046	2.11197
$612$	−11.2661	−0.455403
$613$	0.854413	0.0345094	0.0172547	−	0.999851i	$-0.494507\pi$
$613$	0.854413	0.0345094	0.0172547	+	0.999851i	$0.494507\pi$
$614$	−64.7456	−2.61292
$615$	17.6483	0.711648
$616$	5.10810	0.205811
$617$	31.4495	1.26611	0.633054	−	0.774108i	$-0.281801\pi$
$617$	31.4495	1.26611	0.633054	+	0.774108i	$0.281801\pi$
$618$	−18.5285	−0.745326
$619$	−2.60090	−0.104539	−0.0522695	−	0.998633i	$-0.516645\pi$
$619$	−2.60090	−0.104539	−0.0522695	+	0.998633i	$0.516645\pi$
$620$	−13.0338	−0.523451
$621$	−9.43206	−0.378496
$622$	−76.8301	−3.08060
$623$	12.2650	0.491387
$624$	−17.1891	−0.688116
$625$	−31.2105	−1.24842
$626$	−72.2298	−2.88688
$627$	1.75429	0.0700597
$628$	65.6788	2.62087
$629$	−0.326862	−0.0130329
$630$	6.03974	0.240629
$631$	−42.8437	−1.70558	−0.852791	−	0.522252i	$-0.825092\pi$
$631$	−42.8437	−1.70558	−0.852791	+	0.522252i	$0.825092\pi$
$632$	−35.6837	−1.41942
$633$	−23.1567	−0.920398
$634$	−15.2087	−0.604014
$635$	−29.8829	−1.18587
$636$	−2.66931	−0.105845
$637$	34.5649	1.36951
$638$	−3.37818	−0.133744
$639$	2.87878	0.113883
$640$	−56.9100	−2.24957
$641$	21.1118	0.833864	0.416932	−	0.908938i	$-0.363105\pi$
$641$	21.1118	0.833864	0.416932	+	0.908938i	$0.363105\pi$
$642$	−6.36404	−0.251169
$643$	−32.8031	−1.29363	−0.646815	−	0.762647i	$-0.723899\pi$
$643$	−32.8031	−1.29363	−0.646815	+	0.762647i	$0.723899\pi$
$644$	−32.6366	−1.28606
$645$	−23.4699	−0.924125
$646$	−9.76026	−0.384012
$647$	−43.1095	−1.69481	−0.847405	−	0.530948i	$-0.821836\pi$
$647$	−43.1095	−1.69481	−0.847405	+	0.530948i	$0.821836\pi$
$648$	−4.45255	−0.174913
$649$	16.7919	0.659141
$650$	36.4293	1.42888
$651$	1.10107	0.0431545
$652$	61.4356	2.40600
$653$	12.0881	0.473044	0.236522	−	0.971626i	$-0.423993\pi$
$653$	12.0881	0.473044	0.236522	+	0.971626i	$0.423993\pi$
$654$	27.4521	1.07346
$655$	36.9576	1.44405
$656$	−19.5763	−0.764328
$657$	−8.94958	−0.349156
$658$	20.3471	0.793211
$659$	9.65204	0.375990	0.187995	−	0.982170i	$-0.439801\pi$
$659$	9.65204	0.375990	0.187995	+	0.982170i	$0.439801\pi$
$660$	13.5802	0.528608
$661$	19.4018	0.754642	0.377321	−	0.926083i	$-0.376845\pi$
$661$	19.4018	0.754642	0.377321	+	0.926083i	$0.376845\pi$
$662$	−43.0088	−1.67159
$663$	16.3763	0.636004
$664$	0.920566	0.0357249
$665$	3.44120	0.133444
$666$	−0.269434	−0.0104404
$667$	10.3485	0.400697
$668$	−65.7941	−2.54565
$669$	23.9637	0.926492
$670$	−18.2116	−0.703576
$671$	6.23185	0.240578
$672$	1.32024	0.0509294
$673$	−3.16594	−0.122038	−0.0610190	−	0.998137i	$-0.519435\pi$
$673$	−3.16594	−0.122038	−0.0610190	+	0.998137i	$0.519435\pi$
$674$	−84.3003	−3.24713
$675$	2.69865	0.103871
$676$	69.8943	2.68824
$677$	8.07463	0.310333	0.155167	−	0.987888i	$-0.450409\pi$
$677$	8.07463	0.310333	0.155167	+	0.987888i	$0.450409\pi$
$678$	−13.6407	−0.523867
$679$	3.11630	0.119592
$680$	−36.2255	−1.38919
$681$	10.1059	0.387261
$682$	3.76446	0.144149
$683$	38.5680	1.47576	0.737882	−	0.674929i	$-0.235826\pi$
$683$	38.5680	1.47576	0.737882	+	0.674929i	$0.235826\pi$
$684$	−5.29116	−0.202312
$685$	8.75445	0.334490
$686$	28.7092	1.09612
$687$	−26.9013	−1.02635
$688$	26.0339	0.992532
$689$	3.88011	0.147820
$690$	−63.2558	−2.40811
$691$	−19.4440	−0.739684	−0.369842	−	0.929095i	$-0.620588\pi$
$691$	−19.4440	−0.739684	−0.369842	+	0.929095i	$0.620588\pi$
$692$	16.9846	0.645657
$693$	−1.14723	−0.0435796
$694$	57.0167	2.16432
$695$	31.0427	1.17752
$696$	4.88518	0.185172
$697$	18.6507	0.706444
$698$	−33.4332	−1.26546
$699$	−2.47081	−0.0934545
$700$	9.33782	0.352936
$701$	−23.3470	−0.881804	−0.440902	−	0.897555i	$-0.645341\pi$
$701$	−23.3470	−0.881804	−0.440902	+	0.897555i	$0.645341\pi$
$702$	13.4991	0.509490
$703$	−0.153512	−0.00578983
$704$	12.3551	0.465651
$705$	25.9357	0.976794
$706$	74.3712	2.79900
$707$	−7.81427	−0.293886
$708$	−50.6464	−1.90341
$709$	20.8957	0.784753	0.392376	−	0.919805i	$-0.371653\pi$
$709$	20.8957	0.784753	0.392376	+	0.919805i	$0.371653\pi$
$710$	19.3064	0.724557
$711$	8.01421	0.300556
$712$	−60.6389	−2.27254
$713$	−11.5318	−0.431870
$714$	6.38278	0.238869
$715$	−19.7402	−0.738240
$716$	25.5970	0.956606
$717$	−2.94597	−0.110019
$718$	−45.4931	−1.69779
$719$	−28.9783	−1.08071	−0.540354	−	0.841438i	$-0.681710\pi$
$719$	−28.9783	−1.08071	−0.540354	+	0.841438i	$0.681710\pi$
$720$	−8.53971	−0.318256
$721$	6.90366	0.257106
$722$	41.3400	1.53852
$723$	−5.51845	−0.205233
$724$	−47.5722	−1.76801
$725$	−2.96087	−0.109964
$726$	22.6653	0.841189
$727$	−23.3937	−0.867623	−0.433812	−	0.901004i	$-0.642832\pi$
$727$	−23.3937	−0.867623	−0.433812	+	0.901004i	$0.642832\pi$
$728$	22.3951	0.830016
$729$	1.00000	0.0370370
$730$	−60.0200	−2.22144
$731$	−24.8028	−0.917366
$732$	−18.7960	−0.694720
$733$	47.0403	1.73747	0.868737	−	0.495274i	$-0.164932\pi$
$733$	47.0403	1.73747	0.868737	+	0.495274i	$0.164932\pi$
$734$	40.4353	1.49249
$735$	17.1721	0.633403
$736$	−13.8272	−0.509678
$737$	3.45924	0.127423
$738$	15.3738	0.565918
$739$	23.5752	0.867228	0.433614	−	0.901099i	$-0.357238\pi$
$739$	23.5752	0.867228	0.433614	+	0.901099i	$0.357238\pi$
$740$	−1.18836	−0.0436849
$741$	7.69122	0.282544
$742$	1.51230	0.0555182
$743$	16.0587	0.589135	0.294568	−	0.955631i	$-0.404824\pi$
$743$	16.0587	0.589135	0.294568	+	0.955631i	$0.404824\pi$
$744$	−5.44378	−0.199579
$745$	−64.4923	−2.36281
$746$	−27.1224	−0.993021
$747$	−0.206750	−0.00756459
$748$	14.3515	0.524742
$749$	2.37122	0.0866426
$750$	−15.4339	−0.563566
$751$	−16.1071	−0.587758	−0.293879	−	0.955843i	$-0.594946\pi$
$751$	−16.1071	−0.587758	−0.293879	+	0.955843i	$0.594946\pi$
$752$	−28.7691	−1.04910
$753$	13.9211	0.507312
$754$	−14.8107	−0.539375
$755$	−39.7618	−1.44708
$756$	3.46018	0.125845
$757$	35.9703	1.30736	0.653682	−	0.756770i	$-0.273223\pi$
$757$	35.9703	1.30736	0.653682	+	0.756770i	$0.273223\pi$
$758$	−14.6018	−0.530363
$759$	12.0152	0.436125
$760$	−17.0135	−0.617144
$761$	7.22549	0.261924	0.130962	−	0.991387i	$-0.458193\pi$
$761$	7.22549	0.261924	0.130962	+	0.991387i	$0.458193\pi$
$762$	−26.0316	−0.943027
$763$	−10.2286	−0.370299
$764$	−102.069	−3.69273
$765$	8.13590	0.294154
$766$	53.1417	1.92009
$767$	73.6197	2.65825
$768$	−30.1778	−1.08895
$769$	31.5572	1.13798	0.568991	−	0.822344i	$-0.307334\pi$
$769$	31.5572	1.13798	0.568991	+	0.822344i	$0.307334\pi$
$770$	−7.69385	−0.277267
$771$	15.5978	0.561741
$772$	54.1758	1.94983
$773$	−2.13546	−0.0768071	−0.0384036	−	0.999262i	$-0.512227\pi$
$773$	−2.13546	−0.0768071	−0.0384036	+	0.999262i	$0.512227\pi$
$774$	−20.4451	−0.734884
$775$	3.29943	0.118519
$776$	−15.4072	−0.553085
$777$	0.100390	0.00360148
$778$	31.6471	1.13460
$779$	8.75937	0.313837
$780$	59.5386	2.13183
$781$	−3.66719	−0.131222
$782$	−66.8484	−2.39049
$783$	−1.09717	−0.0392095
$784$	−19.0481	−0.680290
$785$	−47.4307	−1.69287
$786$	32.1946	1.14834
$787$	6.15143	0.219275	0.109637	−	0.993972i	$-0.465031\pi$
$787$	6.15143	0.219275	0.109637	+	0.993972i	$0.465031\pi$
$788$	29.2060	1.04042
$789$	−24.4979	−0.872148
$790$	53.7470	1.91223
$791$	5.08247	0.180712
$792$	5.67197	0.201545
$793$	27.3218	0.970227
$794$	−70.7666	−2.51141
$795$	1.92767	0.0683675
$796$	−68.1001	−2.41374
$797$	26.6589	0.944306	0.472153	−	0.881517i	$-0.343477\pi$
$797$	26.6589	0.944306	0.472153	+	0.881517i	$0.343477\pi$
$798$	2.99770	0.106117
$799$	27.4087	0.969651
$800$	3.95617	0.139872
$801$	13.6189	0.481201
$802$	76.8032	2.71201
$803$	11.4006	0.402318
$804$	−10.4335	−0.367960
$805$	23.5689	0.830694
$806$	16.5042	0.581337
$807$	−3.34574	−0.117776
$808$	38.6342	1.35915
$809$	8.64714	0.304017	0.152009	−	0.988379i	$-0.451426\pi$
$809$	8.64714	0.304017	0.152009	+	0.988379i	$0.451426\pi$
$810$	6.70646	0.235641
$811$	−4.91950	−0.172747	−0.0863735	−	0.996263i	$-0.527528\pi$
$811$	−4.91950	−0.172747	−0.0863735	+	0.996263i	$0.527528\pi$
$812$	−3.79639	−0.133227
$813$	9.27925	0.325437
$814$	0.343224	0.0120300
$815$	−44.3664	−1.55409
$816$	−9.02473	−0.315929
$817$	−11.6488	−0.407539
$818$	52.9689	1.85201
$819$	−5.02972	−0.175752
$820$	67.8073	2.36793
$821$	46.7485	1.63154	0.815768	−	0.578380i	$-0.196315\pi$
$821$	46.7485	1.63154	0.815768	+	0.578380i	$0.196315\pi$
$822$	7.62619	0.265994
$823$	8.46325	0.295010	0.147505	−	0.989061i	$-0.452876\pi$
$823$	8.46325	0.295010	0.147505	+	0.989061i	$0.452876\pi$
$824$	−34.1321	−1.18905
$825$	−3.43773	−0.119686
$826$	28.6937	0.998382
$827$	0.780966	0.0271569	0.0135784	−	0.999908i	$-0.495678\pi$
$827$	0.780966	0.0271569	0.0135784	+	0.999908i	$0.495678\pi$
$828$	−36.2393	−1.25940
$829$	−10.9042	−0.378718	−0.189359	−	0.981908i	$-0.560641\pi$
$829$	−10.9042	−0.378718	−0.189359	+	0.981908i	$0.560641\pi$
$830$	−1.38656	−0.0481283
$831$	−25.6603	−0.890147
$832$	54.1676	1.87792
$833$	18.1474	0.628771
$834$	27.0419	0.936386
$835$	47.5139	1.64429
$836$	6.74024	0.233116
$837$	1.22262	0.0422599
$838$	45.2287	1.56240
$839$	−21.3276	−0.736311	−0.368155	−	0.929764i	$-0.620011\pi$
$839$	−21.3276	−0.736311	−0.368155	+	0.929764i	$0.620011\pi$
$840$	11.1261	0.383886
$841$	−27.7962	−0.958491
$842$	26.7911	0.923282
$843$	−14.7166	−0.506868
$844$	−88.9715	−3.06252
$845$	−50.4750	−1.73639
$846$	22.5931	0.776768
$847$	−8.44503	−0.290174
$848$	−2.13827	−0.0734283
$849$	1.36979	0.0470109
$850$	19.1263	0.656027
$851$	−1.05141	−0.0360420
$852$	11.0607	0.378933
$853$	−4.60845	−0.157790	−0.0788952	−	0.996883i	$-0.525139\pi$
$853$	−4.60845	−0.157790	−0.0788952	+	0.996883i	$0.525139\pi$
$854$	10.6489	0.364396
$855$	3.82107	0.130678
$856$	−11.7235	−0.400700
$857$	28.9169	0.987784	0.493892	−	0.869523i	$-0.335574\pi$
$857$	28.9169	0.987784	0.493892	+	0.869523i	$0.335574\pi$
$858$	−17.1961	−0.587064
$859$	−6.03136	−0.205787	−0.102894	−	0.994692i	$-0.532810\pi$
$859$	−6.03136	−0.205787	−0.102894	+	0.994692i	$0.532810\pi$
$860$	−90.1745	−3.07492
$861$	−5.72824	−0.195218
$862$	−4.99314	−0.170067
$863$	30.9864	1.05479	0.527395	−	0.849621i	$-0.323169\pi$
$863$	30.9864	1.05479	0.527395	+	0.849621i	$0.323169\pi$
$864$	1.46598	0.0498736
$865$	−12.2656	−0.417043
$866$	38.2149	1.29859
$867$	−8.40201	−0.285347
$868$	4.23048	0.143592
$869$	−10.2091	−0.346319
$870$	−7.35809	−0.249463
$871$	15.1661	0.513883
$872$	50.5706	1.71254
$873$	3.46030	0.117113
$874$	−31.3957	−1.06197
$875$	5.75062	0.194406
$876$	−34.3855	−1.16178
$877$	−35.2579	−1.19057	−0.595287	−	0.803513i	$-0.702962\pi$
$877$	−35.2579	−1.19057	−0.595287	+	0.803513i	$0.702962\pi$
$878$	4.13781	0.139644
$879$	−33.2586	−1.12178
$880$	10.8785	0.366713
$881$	21.0519	0.709256	0.354628	−	0.935007i	$-0.384607\pi$
$881$	21.0519	0.709256	0.354628	+	0.935007i	$0.384607\pi$
$882$	14.9590	0.503696
$883$	55.5594	1.86972	0.934861	−	0.355014i	$-0.115524\pi$
$883$	55.5594	1.86972	0.934861	+	0.355014i	$0.115524\pi$
$884$	62.9202	2.11623
$885$	36.5749	1.22945
$886$	−34.9503	−1.17418
$887$	26.6500	0.894818	0.447409	−	0.894329i	$-0.352347\pi$
$887$	26.6500	0.894818	0.447409	+	0.894329i	$0.352347\pi$
$888$	−0.496336	−0.0166559
$889$	9.69931	0.325304
$890$	91.3347	3.06155
$891$	−1.27387	−0.0426762
$892$	92.0721	3.08280
$893$	12.8726	0.430766
$894$	−56.1806	−1.87896
$895$	−18.4852	−0.617891
$896$	18.4717	0.617096
$897$	52.6775	1.75885
$898$	−95.6573	−3.19213
$899$	−1.34142	−0.0447387
$900$	10.3686	0.345620
$901$	2.03716	0.0678675
$902$	−19.5842	−0.652084
$903$	7.61778	0.253504
$904$	−25.1281	−0.835747
$905$	34.3548	1.14199
$906$	−34.6373	−1.15075
$907$	−19.2661	−0.639720	−0.319860	−	0.947465i	$-0.603636\pi$
$907$	−19.2661	−0.639720	−0.319860	+	0.947465i	$0.603636\pi$
$908$	38.8285	1.28857
$909$	−8.67687	−0.287794
$910$	−33.7316	−1.11819
$911$	28.5841	0.947035	0.473517	−	0.880784i	$-0.342984\pi$
$911$	28.5841	0.947035	0.473517	+	0.880784i	$0.342984\pi$
$912$	−4.23851	−0.140351
$913$	0.263373	0.00871637
$914$	91.5572	3.02844
$915$	13.5737	0.448734
$916$	−103.359	−3.41506
$917$	−11.9956	−0.396129
$918$	7.08736	0.233918
$919$	−39.7266	−1.31046	−0.655229	−	0.755430i	$-0.727428\pi$
$919$	−39.7266	−1.31046	−0.655229	+	0.755430i	$0.727428\pi$
$920$	−116.526	−3.84175
$921$	26.7870	0.882662
$922$	−25.8414	−0.851040
$923$	−16.0778	−0.529207
$924$	−4.40782	−0.145007
$925$	0.300825	0.00989105
$926$	−1.09819	−0.0360888
$927$	7.66574	0.251776
$928$	−1.60842	−0.0527990
$929$	24.1331	0.791782	0.395891	−	0.918298i	$-0.370436\pi$
$929$	24.1331	0.791782	0.395891	+	0.918298i	$0.370436\pi$
$930$	8.19945	0.268871
$931$	8.52303	0.279331
$932$	−9.49319	−0.310960
$933$	31.7867	1.04065
$934$	−38.1106	−1.24702
$935$	−10.3641	−0.338942
$936$	24.8672	0.812810
$937$	30.2673	0.988788	0.494394	−	0.869238i	$-0.335390\pi$
$937$	30.2673	0.988788	0.494394	+	0.869238i	$0.335390\pi$
$938$	5.91108	0.193003
$939$	29.8834	0.975208
$940$	99.6486	3.25018
$941$	−24.3518	−0.793847	−0.396924	−	0.917852i	$-0.629922\pi$
$941$	−24.3518	−0.793847	−0.396924	+	0.917852i	$0.629922\pi$
$942$	−41.3179	−1.34621
$943$	59.9933	1.95365
$944$	−40.5706	−1.32046
$945$	−2.49881	−0.0812862
$946$	26.0444	0.846776
$947$	24.2958	0.789509	0.394754	−	0.918787i	$-0.370830\pi$
$947$	24.2958	0.789509	0.394754	+	0.918787i	$0.370830\pi$
$948$	30.7917	1.00007
$949$	49.9828	1.62251
$950$	8.98277	0.291439
$951$	6.29224	0.204040
$952$	11.7580	0.381078
$953$	47.7775	1.54766	0.773832	−	0.633391i	$-0.218337\pi$
$953$	47.7775	1.54766	0.773832	+	0.633391i	$0.218337\pi$
$954$	1.67924	0.0543673
$955$	73.7102	2.38521
$956$	−11.3188	−0.366077
$957$	1.39765	0.0451795
$958$	19.6768	0.635727
$959$	−2.84149	−0.0917566
$960$	26.9110	0.868547
$961$	−29.5052	−0.951781
$962$	1.50477	0.0485158
$963$	2.63298	0.0848465
$964$	−21.2027	−0.682892
$965$	−39.1237	−1.25944
$966$	20.5314	0.660586
$967$	19.5303	0.628053	0.314026	−	0.949414i	$-0.398322\pi$
$967$	19.5303	0.628053	0.314026	+	0.949414i	$0.398322\pi$
$968$	41.7527	1.34198
$969$	4.03809	0.129722
$970$	23.2063	0.745111
$971$	−11.2206	−0.360087	−0.180044	−	0.983659i	$-0.557624\pi$
$971$	−11.2206	−0.360087	−0.180044	+	0.983659i	$0.557624\pi$
$972$	3.84214	0.123237
$973$	−10.0757	−0.323013
$974$	22.0275	0.705807
$975$	−15.0718	−0.482684
$976$	−15.0566	−0.481951
$977$	−16.9933	−0.543665	−0.271832	−	0.962345i	$-0.587630\pi$
$977$	−16.9933	−0.543665	−0.271832	+	0.962345i	$0.587630\pi$
$978$	−38.6485	−1.23584
$979$	−17.3487	−0.554468
$980$	65.9777	2.10758
$981$	−11.3577	−0.362622
$982$	−88.9227	−2.83764
$983$	−10.9037	−0.347775	−0.173887	−	0.984766i	$-0.555633\pi$
$983$	−10.9037	−0.347775	−0.173887	+	0.984766i	$0.555633\pi$
$984$	28.3207	0.902832
$985$	−21.0914	−0.672029
$986$	−7.77600	−0.247638
$987$	−8.41813	−0.267952
$988$	29.5508	0.940135
$989$	−79.7829	−2.53695
$990$	−8.54316	−0.271519
$991$	20.2693	0.643876	0.321938	−	0.946761i	$-0.395666\pi$
$991$	20.2693	0.643876	0.321938	+	0.946761i	$0.395666\pi$
$992$	1.79233	0.0569067
$993$	17.7939	0.564673
$994$	−6.26642	−0.198759
$995$	49.1792	1.55909
$996$	−0.794363	−0.0251704
$997$	−10.7616	−0.340822	−0.170411	−	0.985373i	$-0.554510\pi$
$997$	−10.7616	−0.340822	−0.170411	+	0.985373i	$0.554510\pi$
$998$	37.0152	1.17170
$999$	0.111472	0.00352682

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.d.1.12	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.d.1.12	✓	129	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41705 q^{2} +1.00000 q^{3} +3.84214 q^{4} -2.77464 q^{5} -2.41705 q^{6} +0.900586 q^{7} -4.45255 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.41705 q^{2} +1.00000 q^{3} +3.84214 q^{4} -2.77464 q^{5} -2.41705 q^{6} +0.900586 q^{7} -4.45255 q^{8} +1.00000 q^{9} +6.70646 q^{10} -1.27387 q^{11} +3.84214 q^{12} -5.58494 q^{13} -2.17676 q^{14} -2.77464 q^{15} +3.07777 q^{16} -2.93223 q^{17} -2.41705 q^{18} -1.37714 q^{19} -10.6606 q^{20} +0.900586 q^{21} +3.07901 q^{22} -9.43206 q^{23} -4.45255 q^{24} +2.69865 q^{25} +13.4991 q^{26} +1.00000 q^{27} +3.46018 q^{28} -1.09717 q^{29} +6.70646 q^{30} +1.22262 q^{31} +1.46598 q^{32} -1.27387 q^{33} +7.08736 q^{34} -2.49881 q^{35} +3.84214 q^{36} +0.111472 q^{37} +3.32861 q^{38} -5.58494 q^{39} +12.3542 q^{40} -6.36057 q^{41} -2.17676 q^{42} +8.45869 q^{43} -4.89439 q^{44} -2.77464 q^{45} +22.7978 q^{46} -9.34739 q^{47} +3.07777 q^{48} -6.18894 q^{49} -6.52278 q^{50} -2.93223 q^{51} -21.4581 q^{52} -0.694746 q^{53} -2.41705 q^{54} +3.53454 q^{55} -4.00991 q^{56} -1.37714 q^{57} +2.65191 q^{58} -13.1818 q^{59} -10.6606 q^{60} -4.89206 q^{61} -2.95514 q^{62} +0.900586 q^{63} -9.69888 q^{64} +15.4962 q^{65} +3.07901 q^{66} -2.71553 q^{67} -11.2661 q^{68} -9.43206 q^{69} +6.03974 q^{70} +2.87878 q^{71} -4.45255 q^{72} -8.94958 q^{73} -0.269434 q^{74} +2.69865 q^{75} -5.29116 q^{76} -1.14723 q^{77} +13.4991 q^{78} +8.01421 q^{79} -8.53971 q^{80} +1.00000 q^{81} +15.3738 q^{82} -0.206750 q^{83} +3.46018 q^{84} +8.13590 q^{85} -20.4451 q^{86} -1.09717 q^{87} +5.67197 q^{88} +13.6189 q^{89} +6.70646 q^{90} -5.02972 q^{91} -36.2393 q^{92} +1.22262 q^{93} +22.5931 q^{94} +3.82107 q^{95} +1.46598 q^{96} +3.46030 q^{97} +14.9590 q^{98} -1.27387 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * q^99

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