LMFDB - Embedded newform 8006.2.a.d.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8006,2,Mod(1,8006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8006 = 2 \cdot 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8006.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:	$63.9282318582$
Analytic rank:	$0$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.20682 q^{3} +1.00000 q^{4} +0.892162 q^{5} -2.20682 q^{6} -0.549139 q^{7} +1.00000 q^{8} +1.87006 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.20682 q^{3} +1.00000 q^{4} +0.892162 q^{5} -2.20682 q^{6} -0.549139 q^{7} +1.00000 q^{8} +1.87006 q^{9} +0.892162 q^{10} +2.29468 q^{11} -2.20682 q^{12} +2.95468 q^{13} -0.549139 q^{14} -1.96884 q^{15} +1.00000 q^{16} +5.83838 q^{17} +1.87006 q^{18} +4.19727 q^{19} +0.892162 q^{20} +1.21185 q^{21} +2.29468 q^{22} +6.28981 q^{23} -2.20682 q^{24} -4.20405 q^{25} +2.95468 q^{26} +2.49357 q^{27} -0.549139 q^{28} +8.78592 q^{29} -1.96884 q^{30} -2.92486 q^{31} +1.00000 q^{32} -5.06395 q^{33} +5.83838 q^{34} -0.489921 q^{35} +1.87006 q^{36} -3.55112 q^{37} +4.19727 q^{38} -6.52045 q^{39} +0.892162 q^{40} -5.59790 q^{41} +1.21185 q^{42} +8.44044 q^{43} +2.29468 q^{44} +1.66840 q^{45} +6.28981 q^{46} -2.57206 q^{47} -2.20682 q^{48} -6.69845 q^{49} -4.20405 q^{50} -12.8843 q^{51} +2.95468 q^{52} +11.5016 q^{53} +2.49357 q^{54} +2.04723 q^{55} -0.549139 q^{56} -9.26262 q^{57} +8.78592 q^{58} -6.52700 q^{59} -1.96884 q^{60} -9.77721 q^{61} -2.92486 q^{62} -1.02692 q^{63} +1.00000 q^{64} +2.63605 q^{65} -5.06395 q^{66} -4.36190 q^{67} +5.83838 q^{68} -13.8805 q^{69} -0.489921 q^{70} +6.91114 q^{71} +1.87006 q^{72} +0.394918 q^{73} -3.55112 q^{74} +9.27758 q^{75} +4.19727 q^{76} -1.26010 q^{77} -6.52045 q^{78} -17.0494 q^{79} +0.892162 q^{80} -11.1131 q^{81} -5.59790 q^{82} +4.55195 q^{83} +1.21185 q^{84} +5.20878 q^{85} +8.44044 q^{86} -19.3890 q^{87} +2.29468 q^{88} +6.45562 q^{89} +1.66840 q^{90} -1.62253 q^{91} +6.28981 q^{92} +6.45464 q^{93} -2.57206 q^{94} +3.74464 q^{95} -2.20682 q^{96} -17.2201 q^{97} -6.69845 q^{98} +4.29119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9}+O(q^{10}) $ 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9	\( 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9} + 4 q^{10} + 51 q^{11} + 16 q^{12} + 31 q^{13} + 29 q^{14} + 57 q^{15} + 98 q^{16} + 35 q^{17} + 130 q^{18} + 77 q^{19} + 4 q^{20} + 46 q^{21} + 51 q^{22} + 73 q^{23} + 16 q^{24} + 150 q^{25} + 31 q^{26} + 52 q^{27} + 29 q^{28} + 20 q^{29} + 57 q^{30} + 59 q^{31} + 98 q^{32} + 27 q^{33} + 35 q^{34} + 48 q^{35} + 130 q^{36} + 41 q^{37} + 77 q^{38} + 64 q^{39} + 4 q^{40} + 29 q^{41} + 46 q^{42} + 94 q^{43} + 51 q^{44} - 3 q^{45} + 73 q^{46} + 58 q^{47} + 16 q^{48} + 149 q^{49} + 150 q^{50} + 58 q^{51} + 31 q^{52} - 11 q^{53} + 52 q^{54} + 56 q^{55} + 29 q^{56} + 64 q^{57} + 20 q^{58} + 45 q^{59} + 57 q^{60} + 73 q^{61} + 59 q^{62} + 53 q^{63} + 98 q^{64} + 39 q^{65} + 27 q^{66} + 133 q^{67} + 35 q^{68} + 13 q^{69} + 48 q^{70} + 67 q^{71} + 130 q^{72} + 42 q^{73} + 41 q^{74} + 36 q^{75} + 77 q^{76} - 25 q^{77} + 64 q^{78} + 154 q^{79} + 4 q^{80} + 198 q^{81} + 29 q^{82} + 69 q^{83} + 46 q^{84} + 81 q^{85} + 94 q^{86} + 25 q^{87} + 51 q^{88} + 32 q^{89} - 3 q^{90} + 95 q^{91} + 73 q^{92} - 23 q^{93} + 58 q^{94} + 50 q^{95} + 16 q^{96} + 76 q^{97} + 149 q^{98} + 149 q^{99}+O(q^{100}) \) 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9 + 4 * q^10 + 51 * q^11 + 16 * q^12 + 31 * q^13 + 29 * q^14 + 57 * q^15 + 98 * q^16 + 35 * q^17 + 130 * q^18 + 77 * q^19 + 4 * q^20 + 46 * q^21 + 51 * q^22 + 73 * q^23 + 16 * q^24 + 150 * q^25 + 31 * q^26 + 52 * q^27 + 29 * q^28 + 20 * q^29 + 57 * q^30 + 59 * q^31 + 98 * q^32 + 27 * q^33 + 35 * q^34 + 48 * q^35 + 130 * q^36 + 41 * q^37 + 77 * q^38 + 64 * q^39 + 4 * q^40 + 29 * q^41 + 46 * q^42 + 94 * q^43 + 51 * q^44 - 3 * q^45 + 73 * q^46 + 58 * q^47 + 16 * q^48 + 149 * q^49 + 150 * q^50 + 58 * q^51 + 31 * q^52 - 11 * q^53 + 52 * q^54 + 56 * q^55 + 29 * q^56 + 64 * q^57 + 20 * q^58 + 45 * q^59 + 57 * q^60 + 73 * q^61 + 59 * q^62 + 53 * q^63 + 98 * q^64 + 39 * q^65 + 27 * q^66 + 133 * q^67 + 35 * q^68 + 13 * q^69 + 48 * q^70 + 67 * q^71 + 130 * q^72 + 42 * q^73 + 41 * q^74 + 36 * q^75 + 77 * q^76 - 25 * q^77 + 64 * q^78 + 154 * q^79 + 4 * q^80 + 198 * q^81 + 29 * q^82 + 69 * q^83 + 46 * q^84 + 81 * q^85 + 94 * q^86 + 25 * q^87 + 51 * q^88 + 32 * q^89 - 3 * q^90 + 95 * q^91 + 73 * q^92 - 23 * q^93 + 58 * q^94 + 50 * q^95 + 16 * q^96 + 76 * q^97 + 149 * q^98 + 149 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.20682	−1.27411	−0.637055	−	0.770819i	$-0.719847\pi$
$3$	−2.20682	−1.27411	−0.637055	+	0.770819i	$0.719847\pi$
$4$	1.00000	0.500000
$5$	0.892162	0.398987	0.199493	−	0.979899i	$-0.436070\pi$
$5$	0.892162	0.398987	0.199493	+	0.979899i	$0.436070\pi$
$6$	−2.20682	−0.900931
$7$	−0.549139	−0.207555	−0.103778	−	0.994601i	$-0.533093\pi$
$7$	−0.549139	−0.207555	−0.103778	+	0.994601i	$0.533093\pi$
$8$	1.00000	0.353553
$9$	1.87006	0.623354
$10$	0.892162	0.282126
$11$	2.29468	0.691872	0.345936	−	0.938258i	$-0.387561\pi$
$11$	2.29468	0.691872	0.345936	+	0.938258i	$0.387561\pi$
$12$	−2.20682	−0.637055
$13$	2.95468	0.819481	0.409740	−	0.912202i	$-0.365619\pi$
$13$	2.95468	0.819481	0.409740	+	0.912202i	$0.365619\pi$
$14$	−0.549139	−0.146764
$15$	−1.96884	−0.508353
$16$	1.00000	0.250000
$17$	5.83838	1.41601	0.708007	−	0.706205i	$-0.249594\pi$
$17$	5.83838	1.41601	0.708007	+	0.706205i	$0.249594\pi$
$18$	1.87006	0.440778
$19$	4.19727	0.962919	0.481460	−	0.876468i	$-0.340107\pi$
$19$	4.19727	0.962919	0.481460	+	0.876468i	$0.340107\pi$
$20$	0.892162	0.199493
$21$	1.21185	0.264448
$22$	2.29468	0.489227
$23$	6.28981	1.31152	0.655758	−	0.754971i	$-0.272349\pi$
$23$	6.28981	1.31152	0.655758	+	0.754971i	$0.272349\pi$
$24$	−2.20682	−0.450466
$25$	−4.20405	−0.840810
$26$	2.95468	0.579460
$27$	2.49357	0.479888
$28$	−0.549139	−0.103778
$29$	8.78592	1.63151	0.815753	−	0.578401i	$-0.196323\pi$
$29$	8.78592	1.63151	0.815753	+	0.578401i	$0.196323\pi$
$30$	−1.96884	−0.359460
$31$	−2.92486	−0.525320	−0.262660	−	0.964888i	$-0.584600\pi$
$31$	−2.92486	−0.525320	−0.262660	+	0.964888i	$0.584600\pi$
$32$	1.00000	0.176777
$33$	−5.06395	−0.881521
$34$	5.83838	1.00127
$35$	−0.489921	−0.0828117
$36$	1.87006	0.311677
$37$	−3.55112	−0.583800	−0.291900	−	0.956449i	$-0.594288\pi$
$37$	−3.55112	−0.583800	−0.291900	+	0.956449i	$0.594288\pi$
$38$	4.19727	0.680887
$39$	−6.52045	−1.04411
$40$	0.892162	0.141063
$41$	−5.59790	−0.874246	−0.437123	−	0.899402i	$-0.644003\pi$
$41$	−5.59790	−0.874246	−0.437123	+	0.899402i	$0.644003\pi$
$42$	1.21185	0.186993
$43$	8.44044	1.28715	0.643577	−	0.765381i	$-0.277449\pi$
$43$	8.44044	1.28715	0.643577	+	0.765381i	$0.277449\pi$
$44$	2.29468	0.345936
$45$	1.66840	0.248710
$46$	6.28981	0.927381
$47$	−2.57206	−0.375173	−0.187587	−	0.982248i	$-0.560067\pi$
$47$	−2.57206	−0.375173	−0.187587	+	0.982248i	$0.560067\pi$
$48$	−2.20682	−0.318527
$49$	−6.69845	−0.956921
$50$	−4.20405	−0.594542
$51$	−12.8843	−1.80416
$52$	2.95468	0.409740
$53$	11.5016	1.57987	0.789936	−	0.613190i	$-0.210114\pi$
$53$	11.5016	1.57987	0.789936	+	0.613190i	$0.210114\pi$
$54$	2.49357	0.339332
$55$	2.04723	0.276048
$56$	−0.549139	−0.0733818
$57$	−9.26262	−1.22686
$58$	8.78592	1.15365
$59$	−6.52700	−0.849742	−0.424871	−	0.905254i	$-0.639681\pi$
$59$	−6.52700	−0.849742	−0.424871	+	0.905254i	$0.639681\pi$
$60$	−1.96884	−0.254176
$61$	−9.77721	−1.25184	−0.625921	−	0.779886i	$-0.715277\pi$
$61$	−9.77721	−1.25184	−0.625921	+	0.779886i	$0.715277\pi$
$62$	−2.92486	−0.371457
$63$	−1.02692	−0.129380
$64$	1.00000	0.125000
$65$	2.63605	0.326962
$66$	−5.06395	−0.623329
$67$	−4.36190	−0.532891	−0.266446	−	0.963850i	$-0.585849\pi$
$67$	−4.36190	−0.532891	−0.266446	+	0.963850i	$0.585849\pi$
$68$	5.83838	0.708007
$69$	−13.8805	−1.67101
$70$	−0.489921	−0.0585567
$71$	6.91114	0.820201	0.410101	−	0.912040i	$-0.365494\pi$
$71$	6.91114	0.820201	0.410101	+	0.912040i	$0.365494\pi$
$72$	1.87006	0.220389
$73$	0.394918	0.0462217	0.0231108	−	0.999733i	$-0.492643\pi$
$73$	0.394918	0.0462217	0.0231108	+	0.999733i	$0.492643\pi$
$74$	−3.55112	−0.412809
$75$	9.27758	1.07128
$76$	4.19727	0.481460
$77$	−1.26010	−0.143602
$78$	−6.52045	−0.738296
$79$	−17.0494	−1.91821	−0.959103	−	0.283057i	$-0.908651\pi$
$79$	−17.0494	−1.91821	−0.959103	+	0.283057i	$0.908651\pi$
$80$	0.892162	0.0997467
$81$	−11.1131	−1.23478
$82$	−5.59790	−0.618185
$83$	4.55195	0.499642	0.249821	−	0.968292i	$-0.419628\pi$
$83$	4.55195	0.499642	0.249821	+	0.968292i	$0.419628\pi$
$84$	1.21185	0.132224
$85$	5.20878	0.564971
$86$	8.44044	0.910156
$87$	−19.3890	−2.07872
$88$	2.29468	0.244614
$89$	6.45562	0.684294	0.342147	−	0.939646i	$-0.388846\pi$
$89$	6.45562	0.684294	0.342147	+	0.939646i	$0.388846\pi$
$90$	1.66840	0.175865
$91$	−1.62253	−0.170087
$92$	6.28981	0.655758
$93$	6.45464	0.669315
$94$	−2.57206	−0.265288
$95$	3.74464	0.384192
$96$	−2.20682	−0.225233
$97$	−17.2201	−1.74844	−0.874220	−	0.485529i	$-0.838627\pi$
$97$	−17.2201	−1.74844	−0.874220	+	0.485529i	$0.838627\pi$
$98$	−6.69845	−0.676645
$99$	4.29119	0.431281
$100$	−4.20405	−0.420405
$101$	−0.0488438	−0.00486014	−0.00243007	−	0.999997i	$-0.500774\pi$
$101$	−0.0488438	−0.00486014	−0.00243007	+	0.999997i	$0.500774\pi$
$102$	−12.8843	−1.27573
$103$	11.6578	1.14868	0.574340	−	0.818617i	$-0.305259\pi$
$103$	11.6578	1.14868	0.574340	+	0.818617i	$0.305259\pi$
$104$	2.95468	0.289730
$105$	1.08117	0.105511
$106$	11.5016	1.11714
$107$	12.3356	1.19252	0.596261	−	0.802790i	$-0.296652\pi$
$107$	12.3356	1.19252	0.596261	+	0.802790i	$0.296652\pi$
$108$	2.49357	0.239944
$109$	13.5360	1.29651	0.648255	−	0.761424i	$-0.275499\pi$
$109$	13.5360	1.29651	0.648255	+	0.761424i	$0.275499\pi$
$110$	2.04723	0.195195
$111$	7.83669	0.743825
$112$	−0.549139	−0.0518888
$113$	1.59064	0.149634	0.0748172	−	0.997197i	$-0.476163\pi$
$113$	1.59064	0.149634	0.0748172	+	0.997197i	$0.476163\pi$
$114$	−9.26262	−0.867524
$115$	5.61152	0.523277
$116$	8.78592	0.815753
$117$	5.52544	0.510827
$118$	−6.52700	−0.600859
$119$	−3.20608	−0.293901
$120$	−1.96884	−0.179730
$121$	−5.73444	−0.521313
$122$	−9.77721	−0.885187
$123$	12.3536	1.11388
$124$	−2.92486	−0.262660
$125$	−8.21150	−0.734459
$126$	−1.02692	−0.0914857
$127$	−5.06913	−0.449812	−0.224906	−	0.974380i	$-0.572208\pi$
$127$	−5.06913	−0.449812	−0.224906	+	0.974380i	$0.572208\pi$
$128$	1.00000	0.0883883
$129$	−18.6265	−1.63998
$130$	2.63605	0.231197
$131$	−0.509807	−0.0445421	−0.0222710	−	0.999752i	$-0.507090\pi$
$131$	−0.509807	−0.0445421	−0.0222710	+	0.999752i	$0.507090\pi$
$132$	−5.06395	−0.440760
$133$	−2.30488	−0.199859
$134$	−4.36190	−0.376811
$135$	2.22467	0.191469
$136$	5.83838	0.500637
$137$	6.48358	0.553930	0.276965	−	0.960880i	$-0.410671\pi$
$137$	6.48358	0.553930	0.276965	+	0.960880i	$0.410671\pi$
$138$	−13.8805	−1.18159
$139$	10.0921	0.856004	0.428002	−	0.903778i	$-0.359218\pi$
$139$	10.0921	0.856004	0.428002	+	0.903778i	$0.359218\pi$
$140$	−0.489921	−0.0414059
$141$	5.67608	0.478012
$142$	6.91114	0.579970
$143$	6.78005	0.566976
$144$	1.87006	0.155839
$145$	7.83846	0.650949
$146$	0.394918	0.0326837
$147$	14.7823	1.21922
$148$	−3.55112	−0.291900
$149$	−0.650798	−0.0533154	−0.0266577	−	0.999645i	$-0.508486\pi$
$149$	−0.650798	−0.0533154	−0.0266577	+	0.999645i	$0.508486\pi$
$150$	9.27758	0.757512
$151$	16.7614	1.36402	0.682010	−	0.731343i	$-0.261106\pi$
$151$	16.7614	1.36402	0.682010	+	0.731343i	$0.261106\pi$
$152$	4.19727	0.340443
$153$	10.9181	0.882679
$154$	−1.26010	−0.101542
$155$	−2.60945	−0.209596
$156$	−6.52045	−0.522054
$157$	−7.77539	−0.620544	−0.310272	−	0.950648i	$-0.600420\pi$
$157$	−7.77539	−0.620544	−0.310272	+	0.950648i	$0.600420\pi$
$158$	−17.0494	−1.35638
$159$	−25.3821	−2.01293
$160$	0.892162	0.0705316
$161$	−3.45398	−0.272212
$162$	−11.1131	−0.873124
$163$	−8.37598	−0.656058	−0.328029	−	0.944668i	$-0.606384\pi$
$163$	−8.37598	−0.656058	−0.328029	+	0.944668i	$0.606384\pi$
$164$	−5.59790	−0.437123
$165$	−4.51786	−0.351715
$166$	4.55195	0.353300
$167$	9.37779	0.725675	0.362838	−	0.931852i	$-0.381808\pi$
$167$	9.37779	0.725675	0.362838	+	0.931852i	$0.381808\pi$
$168$	1.21185	0.0934964
$169$	−4.26986	−0.328451
$170$	5.20878	0.399495
$171$	7.84915	0.600240
$172$	8.44044	0.643577
$173$	24.1534	1.83635	0.918176	−	0.396173i	$-0.129662\pi$
$173$	24.1534	1.83635	0.918176	+	0.396173i	$0.129662\pi$
$174$	−19.3890	−1.46987
$175$	2.30861	0.174514
$176$	2.29468	0.172968
$177$	14.4039	1.08266
$178$	6.45562	0.483869
$179$	−9.40111	−0.702672	−0.351336	−	0.936249i	$-0.614273\pi$
$179$	−9.40111	−0.702672	−0.351336	+	0.936249i	$0.614273\pi$
$180$	1.66840	0.124355
$181$	−21.2271	−1.57780	−0.788899	−	0.614523i	$-0.789348\pi$
$181$	−21.2271	−1.57780	−0.788899	+	0.614523i	$0.789348\pi$
$182$	−1.62253	−0.120270
$183$	21.5766	1.59498
$184$	6.28981	0.463691
$185$	−3.16817	−0.232929
$186$	6.45464	0.473277
$187$	13.3972	0.979701
$188$	−2.57206	−0.187587
$189$	−1.36932	−0.0996032
$190$	3.74464	0.271665
$191$	8.25101	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$191$	8.25101	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$192$	−2.20682	−0.159264
$193$	−11.1472	−0.802394	−0.401197	−	0.915992i	$-0.631406\pi$
$193$	−11.1472	−0.802394	−0.401197	+	0.915992i	$0.631406\pi$
$194$	−17.2201	−1.23633
$195$	−5.81730	−0.416585
$196$	−6.69845	−0.478460
$197$	7.48297	0.533140	0.266570	−	0.963816i	$-0.414110\pi$
$197$	7.48297	0.533140	0.266570	+	0.963816i	$0.414110\pi$
$198$	4.29119	0.304962
$199$	7.26404	0.514934	0.257467	−	0.966287i	$-0.417112\pi$
$199$	7.26404	0.514934	0.257467	+	0.966287i	$0.417112\pi$
$200$	−4.20405	−0.297271
$201$	9.62594	0.678962
$202$	−0.0488438	−0.00343664
$203$	−4.82469	−0.338627
$204$	−12.8843	−0.902079
$205$	−4.99424	−0.348813
$206$	11.6578	0.812240
$207$	11.7623	0.817538
$208$	2.95468	0.204870
$209$	9.63138	0.666217
$210$	1.08117	0.0746077
$211$	24.2822	1.67165	0.835826	−	0.548994i	$-0.184989\pi$
$211$	24.2822	1.67165	0.835826	+	0.548994i	$0.184989\pi$
$212$	11.5016	0.789936
$213$	−15.2517	−1.04503
$214$	12.3356	0.843241
$215$	7.53023	0.513558
$216$	2.49357	0.169666
$217$	1.60615	0.109033
$218$	13.5360	0.916771
$219$	−0.871514	−0.0588915
$220$	2.04723	0.138024
$221$	17.2505	1.16040
$222$	7.83669	0.525964
$223$	−25.8892	−1.73367	−0.866835	−	0.498596i	$-0.833849\pi$
$223$	−25.8892	−1.73367	−0.866835	+	0.498596i	$0.833849\pi$
$224$	−0.549139	−0.0366909
$225$	−7.86183	−0.524122
$226$	1.59064	0.105807
$227$	9.63050	0.639199	0.319599	−	0.947553i	$-0.396452\pi$
$227$	9.63050	0.639199	0.319599	+	0.947553i	$0.396452\pi$
$228$	−9.26262	−0.613432
$229$	8.46571	0.559430	0.279715	−	0.960083i	$-0.409760\pi$
$229$	8.46571	0.559430	0.279715	+	0.960083i	$0.409760\pi$
$230$	5.61152	0.370013
$231$	2.78081	0.182964
$232$	8.78592	0.576824
$233$	−21.0223	−1.37721	−0.688607	−	0.725135i	$-0.741778\pi$
$233$	−21.0223	−1.37721	−0.688607	+	0.725135i	$0.741778\pi$
$234$	5.52544	0.361209
$235$	−2.29469	−0.149689
$236$	−6.52700	−0.424871
$237$	37.6250	2.44400
$238$	−3.20608	−0.207819
$239$	−20.9656	−1.35615	−0.678075	−	0.734992i	$-0.737186\pi$
$239$	−20.9656	−1.35615	−0.678075	+	0.734992i	$0.737186\pi$
$240$	−1.96884	−0.127088
$241$	5.98986	0.385841	0.192920	−	0.981214i	$-0.438204\pi$
$241$	5.98986	0.385841	0.192920	+	0.981214i	$0.438204\pi$
$242$	−5.73444	−0.368624
$243$	17.0438	1.09336
$244$	−9.77721	−0.625921
$245$	−5.97610	−0.381799
$246$	12.3536	0.787635
$247$	12.4016	0.789094
$248$	−2.92486	−0.185729
$249$	−10.0453	−0.636598
$250$	−8.21150	−0.519341
$251$	10.1703	0.641946	0.320973	−	0.947088i	$-0.395990\pi$
$251$	10.1703	0.641946	0.320973	+	0.947088i	$0.395990\pi$
$252$	−1.02692	−0.0646902
$253$	14.4331	0.907401
$254$	−5.06913	−0.318065
$255$	−11.4948	−0.719835
$256$	1.00000	0.0625000
$257$	16.2330	1.01258	0.506292	−	0.862362i	$-0.331016\pi$
$257$	16.2330	1.01258	0.506292	+	0.862362i	$0.331016\pi$
$258$	−18.6265	−1.15964
$259$	1.95006	0.121171
$260$	2.63605	0.163481
$261$	16.4302	1.01701
$262$	−0.509807	−0.0314960
$263$	−11.1192	−0.685637	−0.342818	−	0.939402i	$-0.611382\pi$
$263$	−11.1192	−0.685637	−0.342818	+	0.939402i	$0.611382\pi$
$264$	−5.06395	−0.311665
$265$	10.2613	0.630348
$266$	−2.30488	−0.141321
$267$	−14.2464	−0.871866
$268$	−4.36190	−0.266446
$269$	−12.8214	−0.781736	−0.390868	−	0.920447i	$-0.627825\pi$
$269$	−12.8214	−0.781736	−0.390868	+	0.920447i	$0.627825\pi$
$270$	2.22467	0.135389
$271$	24.0423	1.46047	0.730234	−	0.683197i	$-0.239411\pi$
$271$	24.0423	1.46047	0.730234	+	0.683197i	$0.239411\pi$
$272$	5.83838	0.354004
$273$	3.58064	0.216710
$274$	6.48358	0.391688
$275$	−9.64694	−0.581733
$276$	−13.8805	−0.835507
$277$	−8.00151	−0.480764	−0.240382	−	0.970678i	$-0.577273\pi$
$277$	−8.00151	−0.480764	−0.240382	+	0.970678i	$0.577273\pi$
$278$	10.0921	0.605286
$279$	−5.46967	−0.327460
$280$	−0.489921	−0.0292784
$281$	−5.09013	−0.303651	−0.151826	−	0.988407i	$-0.548515\pi$
$281$	−5.09013	−0.303651	−0.151826	+	0.988407i	$0.548515\pi$
$282$	5.67608	0.338005
$283$	−11.9028	−0.707550	−0.353775	−	0.935331i	$-0.615102\pi$
$283$	−11.9028	−0.707550	−0.353775	+	0.935331i	$0.615102\pi$
$284$	6.91114	0.410101
$285$	−8.26375	−0.489503
$286$	6.78005	0.400913
$287$	3.07403	0.181454
$288$	1.87006	0.110194
$289$	17.0867	1.00510
$290$	7.83846	0.460290
$291$	38.0018	2.22770
$292$	0.394918	0.0231108
$293$	23.0018	1.34378	0.671891	−	0.740650i	$-0.265482\pi$
$293$	23.0018	1.34378	0.671891	+	0.740650i	$0.265482\pi$
$294$	14.7823	0.862120
$295$	−5.82314	−0.339036
$296$	−3.55112	−0.206405
$297$	5.72195	0.332021
$298$	−0.650798	−0.0376997
$299$	18.5844	1.07476
$300$	9.27758	0.535642
$301$	−4.63497	−0.267155
$302$	16.7614	0.964508
$303$	0.107790	0.00619235
$304$	4.19727	0.240730
$305$	−8.72285	−0.499469
$306$	10.9181	0.624148
$307$	−6.73472	−0.384371	−0.192185	−	0.981359i	$-0.561558\pi$
$307$	−6.73472	−0.384371	−0.192185	+	0.981359i	$0.561558\pi$
$308$	−1.26010	−0.0718008
$309$	−25.7268	−1.46354
$310$	−2.60945	−0.148207
$311$	22.9400	1.30081	0.650404	−	0.759588i	$-0.274599\pi$
$311$	22.9400	1.30081	0.650404	+	0.759588i	$0.274599\pi$
$312$	−6.52045	−0.369148
$313$	12.9615	0.732628	0.366314	−	0.930491i	$-0.380620\pi$
$313$	12.9615	0.732628	0.366314	+	0.930491i	$0.380620\pi$
$314$	−7.77539	−0.438791
$315$	−0.916183	−0.0516210
$316$	−17.0494	−0.959103
$317$	5.42877	0.304910	0.152455	−	0.988310i	$-0.451282\pi$
$317$	5.42877	0.304910	0.152455	+	0.988310i	$0.451282\pi$
$318$	−25.3821	−1.42336
$319$	20.1609	1.12879
$320$	0.892162	0.0498733
$321$	−27.2224	−1.51940
$322$	−3.45398	−0.192483
$323$	24.5052	1.36351
$324$	−11.1131	−0.617392
$325$	−12.4216	−0.689027
$326$	−8.37598	−0.463903
$327$	−29.8714	−1.65189
$328$	−5.59790	−0.309093
$329$	1.41242	0.0778691
$330$	−4.51786	−0.248700
$331$	−30.2525	−1.66283	−0.831415	−	0.555652i	$-0.812469\pi$
$331$	−30.2525	−1.66283	−0.831415	+	0.555652i	$0.812469\pi$
$332$	4.55195	0.249821
$333$	−6.64081	−0.363914
$334$	9.37779	0.513130
$335$	−3.89152	−0.212617
$336$	1.21185	0.0661120
$337$	−25.3103	−1.37874	−0.689371	−	0.724409i	$-0.742113\pi$
$337$	−25.3103	−1.37874	−0.689371	+	0.724409i	$0.742113\pi$
$338$	−4.26986	−0.232250
$339$	−3.51025	−0.190651
$340$	5.20878	0.282486
$341$	−6.71161	−0.363454
$342$	7.84915	0.424433
$343$	7.52235	0.406169
$344$	8.44044	0.455078
$345$	−12.3836	−0.666712
$346$	24.1534	1.29850
$347$	−7.51674	−0.403520	−0.201760	−	0.979435i	$-0.564666\pi$
$347$	−7.51674	−0.403520	−0.201760	+	0.979435i	$0.564666\pi$
$348$	−19.3890	−1.03936
$349$	−0.148365	−0.00794180	−0.00397090	−	0.999992i	$-0.501264\pi$
$349$	−0.148365	−0.00794180	−0.00397090	+	0.999992i	$0.501264\pi$
$350$	2.30861	0.123400
$351$	7.36771	0.393259
$352$	2.29468	0.122307
$353$	−20.1156	−1.07064	−0.535322	−	0.844648i	$-0.679810\pi$
$353$	−20.1156	−1.07064	−0.535322	+	0.844648i	$0.679810\pi$
$354$	14.4039	0.765560
$355$	6.16585	0.327250
$356$	6.45562	0.342147
$357$	7.07525	0.374462
$358$	−9.40111	−0.496864
$359$	21.9025	1.15597	0.577984	−	0.816048i	$-0.303840\pi$
$359$	21.9025	1.15597	0.577984	+	0.816048i	$0.303840\pi$
$360$	1.66840	0.0879323
$361$	−1.38295	−0.0727870
$362$	−21.2271	−1.11567
$363$	12.6549	0.664210
$364$	−1.62253	−0.0850437
$365$	0.352331	0.0184418
$366$	21.5766	1.12782
$367$	−0.673632	−0.0351633	−0.0175816	−	0.999845i	$-0.505597\pi$
$367$	−0.673632	−0.0351633	−0.0175816	+	0.999845i	$0.505597\pi$
$368$	6.28981	0.327879
$369$	−10.4684	−0.544965
$370$	−3.16817	−0.164705
$371$	−6.31600	−0.327910
$372$	6.45464	0.334658
$373$	36.2933	1.87920	0.939598	−	0.342279i	$-0.111199\pi$
$373$	36.2933	1.87920	0.939598	+	0.342279i	$0.111199\pi$
$374$	13.3972	0.692753
$375$	18.1213	0.935781
$376$	−2.57206	−0.132644
$377$	25.9596	1.33699
$378$	−1.36932	−0.0704301
$379$	30.2139	1.55198	0.775992	−	0.630742i	$-0.217250\pi$
$379$	30.2139	1.55198	0.775992	+	0.630742i	$0.217250\pi$
$380$	3.74464	0.192096
$381$	11.1867	0.573110
$382$	8.25101	0.422158
$383$	8.16474	0.417199	0.208599	−	0.978001i	$-0.433110\pi$
$383$	8.16474	0.417199	0.208599	+	0.978001i	$0.433110\pi$
$384$	−2.20682	−0.112616
$385$	−1.12421	−0.0572951
$386$	−11.1472	−0.567378
$387$	15.7841	0.802353
$388$	−17.2201	−0.874220
$389$	33.7255	1.70995	0.854976	−	0.518668i	$-0.173572\pi$
$389$	33.7255	1.70995	0.854976	+	0.518668i	$0.173572\pi$
$390$	−5.81730	−0.294570
$391$	36.7223	1.85713
$392$	−6.69845	−0.338323
$393$	1.12505	0.0567514
$394$	7.48297	0.376987
$395$	−15.2108	−0.765339
$396$	4.29119	0.215641
$397$	−4.97751	−0.249814	−0.124907	−	0.992168i	$-0.539863\pi$
$397$	−4.97751	−0.249814	−0.124907	+	0.992168i	$0.539863\pi$
$398$	7.26404	0.364113
$399$	5.08647	0.254642
$400$	−4.20405	−0.210202
$401$	−32.1996	−1.60797	−0.803985	−	0.594650i	$-0.797291\pi$
$401$	−32.1996	−1.60797	−0.803985	+	0.594650i	$0.797291\pi$
$402$	9.62594	0.480098
$403$	−8.64202	−0.430490
$404$	−0.0488438	−0.00243007
$405$	−9.91464	−0.492662
$406$	−4.82469	−0.239446
$407$	−8.14868	−0.403915
$408$	−12.8843	−0.637866
$409$	−25.5021	−1.26100	−0.630498	−	0.776191i	$-0.717149\pi$
$409$	−25.5021	−1.26100	−0.630498	+	0.776191i	$0.717149\pi$
$410$	−4.99424	−0.246648
$411$	−14.3081	−0.705767
$412$	11.6578	0.574340
$413$	3.58423	0.176368
$414$	11.7623	0.578087
$415$	4.06108	0.199350
$416$	2.95468	0.144865
$417$	−22.2715	−1.09064
$418$	9.63138	0.471086
$419$	0.208915	0.0102062	0.00510309	−	0.999987i	$-0.498376\pi$
$419$	0.208915	0.0102062	0.00510309	+	0.999987i	$0.498376\pi$
$420$	1.08117	0.0527556
$421$	−31.9879	−1.55900	−0.779498	−	0.626405i	$-0.784526\pi$
$421$	−31.9879	−1.55900	−0.779498	+	0.626405i	$0.784526\pi$
$422$	24.2822	1.18204
$423$	−4.80991	−0.233866
$424$	11.5016	0.558569
$425$	−24.5448	−1.19060
$426$	−15.2517	−0.738945
$427$	5.36905	0.259826
$428$	12.3356	0.596261
$429$	−14.9624	−0.722389
$430$	7.53023	0.363140
$431$	14.1530	0.681726	0.340863	−	0.940113i	$-0.389281\pi$
$431$	14.1530	0.681726	0.340863	+	0.940113i	$0.389281\pi$
$432$	2.49357	0.119972
$433$	−15.4314	−0.741585	−0.370792	−	0.928716i	$-0.620914\pi$
$433$	−15.4314	−0.741585	−0.370792	+	0.928716i	$0.620914\pi$
$434$	1.60615	0.0770979
$435$	−17.2981	−0.829380
$436$	13.5360	0.648255
$437$	26.4000	1.26288
$438$	−0.871514	−0.0416426
$439$	−23.7333	−1.13273	−0.566365	−	0.824155i	$-0.691651\pi$
$439$	−23.7333	−1.13273	−0.566365	+	0.824155i	$0.691651\pi$
$440$	2.04723	0.0975976
$441$	−12.5265	−0.596501
$442$	17.2505	0.820525
$443$	4.73581	0.225005	0.112503	−	0.993651i	$-0.464113\pi$
$443$	4.73581	0.225005	0.112503	+	0.993651i	$0.464113\pi$
$444$	7.83669	0.371913
$445$	5.75946	0.273024
$446$	−25.8892	−1.22589
$447$	1.43620	0.0679297
$448$	−0.549139	−0.0259444
$449$	29.8305	1.40779	0.703893	−	0.710306i	$-0.251443\pi$
$449$	29.8305	1.40779	0.703893	+	0.710306i	$0.251443\pi$
$450$	−7.86183	−0.370610
$451$	−12.8454	−0.604866
$452$	1.59064	0.0748172
$453$	−36.9893	−1.73791
$454$	9.63050	0.451982
$455$	−1.44756	−0.0678626
$456$	−9.26262	−0.433762
$457$	−13.7508	−0.643234	−0.321617	−	0.946870i	$-0.604226\pi$
$457$	−13.7508	−0.643234	−0.321617	+	0.946870i	$0.604226\pi$
$458$	8.46571	0.395577
$459$	14.5584	0.679529
$460$	5.61152	0.261639
$461$	−18.5705	−0.864913	−0.432456	−	0.901655i	$-0.642353\pi$
$461$	−18.5705	−0.864913	−0.432456	+	0.901655i	$0.642353\pi$
$462$	2.78081	0.129375
$463$	22.2182	1.03257	0.516285	−	0.856417i	$-0.327315\pi$
$463$	22.2182	1.03257	0.516285	+	0.856417i	$0.327315\pi$
$464$	8.78592	0.407876
$465$	5.75858	0.267048
$466$	−21.0223	−0.973838
$467$	0.252699	0.0116935	0.00584675	−	0.999983i	$-0.498139\pi$
$467$	0.252699	0.0116935	0.00584675	+	0.999983i	$0.498139\pi$
$468$	5.52544	0.255413
$469$	2.39529	0.110604
$470$	−2.29469	−0.105846
$471$	17.1589	0.790641
$472$	−6.52700	−0.300429
$473$	19.3681	0.890546
$474$	37.6250	1.72817
$475$	−17.6455	−0.809631
$476$	−3.20608	−0.146951
$477$	21.5088	0.984819
$478$	−20.9656	−0.958943
$479$	−1.08921	−0.0497671	−0.0248836	−	0.999690i	$-0.507921\pi$
$479$	−1.08921	−0.0497671	−0.0248836	+	0.999690i	$0.507921\pi$
$480$	−1.96884	−0.0898649
$481$	−10.4924	−0.478413
$482$	5.98986	0.272831
$483$	7.62232	0.346827
$484$	−5.73444	−0.260657
$485$	−15.3632	−0.697605
$486$	17.0438	0.773123
$487$	−14.6810	−0.665259	−0.332629	−	0.943058i	$-0.607936\pi$
$487$	−14.6810	−0.665259	−0.332629	+	0.943058i	$0.607936\pi$
$488$	−9.77721	−0.442593
$489$	18.4843	0.835889
$490$	−5.97610	−0.269973
$491$	33.3549	1.50528	0.752642	−	0.658430i	$-0.228779\pi$
$491$	33.3549	1.50528	0.752642	+	0.658430i	$0.228779\pi$
$492$	12.3536	0.556942
$493$	51.2956	2.31024
$494$	12.4016	0.557973
$495$	3.82844	0.172076
$496$	−2.92486	−0.131330
$497$	−3.79518	−0.170237
$498$	−10.0453	−0.450143
$499$	36.7264	1.64410	0.822049	−	0.569417i	$-0.192831\pi$
$499$	36.7264	1.64410	0.822049	+	0.569417i	$0.192831\pi$
$500$	−8.21150	−0.367229
$501$	−20.6951	−0.924590
$502$	10.1703	0.453924
$503$	−27.0927	−1.20800	−0.604002	−	0.796983i	$-0.706428\pi$
$503$	−27.0927	−1.20800	−0.604002	+	0.796983i	$0.706428\pi$
$504$	−1.02692	−0.0457429
$505$	−0.0435766	−0.00193913
$506$	14.4331	0.641629
$507$	9.42283	0.418483
$508$	−5.06913	−0.224906
$509$	−4.59655	−0.203738	−0.101869	−	0.994798i	$-0.532482\pi$
$509$	−4.59655	−0.203738	−0.101869	+	0.994798i	$0.532482\pi$
$510$	−11.4948	−0.509000
$511$	−0.216865	−0.00959355
$512$	1.00000	0.0441942
$513$	10.4662	0.462093
$514$	16.2330	0.716005
$515$	10.4007	0.458308
$516$	−18.6265	−0.819988
$517$	−5.90205	−0.259572
$518$	1.95006	0.0856806
$519$	−53.3023	−2.33971
$520$	2.63605	0.115599
$521$	−10.4002	−0.455642	−0.227821	−	0.973703i	$-0.573160\pi$
$521$	−10.4002	−0.455642	−0.227821	+	0.973703i	$0.573160\pi$
$522$	16.4302	0.719131
$523$	2.52837	0.110558	0.0552790	−	0.998471i	$-0.482395\pi$
$523$	2.52837	0.110558	0.0552790	+	0.998471i	$0.482395\pi$
$524$	−0.509807	−0.0222710
$525$	−5.09468	−0.222350
$526$	−11.1192	−0.484818
$527$	−17.0764	−0.743861
$528$	−5.06395	−0.220380
$529$	16.5617	0.720073
$530$	10.2613	0.445723
$531$	−12.2059	−0.529690
$532$	−2.30488	−0.0999294
$533$	−16.5400	−0.716428
$534$	−14.2464	−0.616502
$535$	11.0053	0.475801
$536$	−4.36190	−0.188406
$537$	20.7466	0.895281
$538$	−12.8214	−0.552771
$539$	−15.3708	−0.662067
$540$	2.22467	0.0957345
$541$	19.4294	0.835333	0.417667	−	0.908600i	$-0.362848\pi$
$541$	19.4294	0.835333	0.417667	+	0.908600i	$0.362848\pi$
$542$	24.0423	1.03271
$543$	46.8444	2.01029
$544$	5.83838	0.250318
$545$	12.0763	0.517290
$546$	3.58064	0.153237
$547$	6.37577	0.272608	0.136304	−	0.990667i	$-0.456478\pi$
$547$	6.37577	0.272608	0.136304	+	0.990667i	$0.456478\pi$
$548$	6.48358	0.276965
$549$	−18.2840	−0.780341
$550$	−9.64694	−0.411347
$551$	36.8769	1.57101
$552$	−13.8805	−0.590793
$553$	9.36249	0.398133
$554$	−8.00151	−0.339952
$555$	6.99159	0.296776
$556$	10.0921	0.428002
$557$	9.24859	0.391875	0.195938	−	0.980616i	$-0.437225\pi$
$557$	9.24859	0.391875	0.195938	+	0.980616i	$0.437225\pi$
$558$	−5.46967	−0.231549
$559$	24.9388	1.05480
$560$	−0.489921	−0.0207029
$561$	−29.5653	−1.24825
$562$	−5.09013	−0.214714
$563$	9.37455	0.395090	0.197545	−	0.980294i	$-0.436703\pi$
$563$	9.37455	0.395090	0.197545	+	0.980294i	$0.436703\pi$
$564$	5.67608	0.239006
$565$	1.41910	0.0597021
$566$	−11.9028	−0.500314
$567$	6.10261	0.256286
$568$	6.91114	0.289985
$569$	16.2048	0.679343	0.339671	−	0.940544i	$-0.389684\pi$
$569$	16.2048	0.679343	0.339671	+	0.940544i	$0.389684\pi$
$570$	−8.26375	−0.346131
$571$	−30.1733	−1.26271	−0.631357	−	0.775492i	$-0.717502\pi$
$571$	−30.1733	−1.26271	−0.631357	+	0.775492i	$0.717502\pi$
$572$	6.78005	0.283488
$573$	−18.2085	−0.760671
$574$	3.07403	0.128307
$575$	−26.4426	−1.10273
$576$	1.87006	0.0779193
$577$	−0.0253670	−0.00105604	−0.000528020	−	1.00000i	$-0.500168\pi$
$577$	−0.0253670	−0.00105604	−0.000528020		1.00000i	$0.500168\pi$
$578$	17.0867	0.710712
$579$	24.5999	1.02234
$580$	7.83846	0.325474
$581$	−2.49965	−0.103703
$582$	38.0018	1.57522
$583$	26.3926	1.09307
$584$	0.394918	0.0163418
$585$	4.92958	0.203813
$586$	23.0018	0.950197
$587$	13.4704	0.555981	0.277991	−	0.960584i	$-0.410332\pi$
$587$	13.4704	0.555981	0.277991	+	0.960584i	$0.410332\pi$
$588$	14.7823	0.609611
$589$	−12.2764	−0.505841
$590$	−5.82314	−0.239735
$591$	−16.5136	−0.679278
$592$	−3.55112	−0.145950
$593$	30.7237	1.26167	0.630836	−	0.775916i	$-0.282712\pi$
$593$	30.7237	1.26167	0.630836	+	0.775916i	$0.282712\pi$
$594$	5.72195	0.234774
$595$	−2.86034	−0.117263
$596$	−0.650798	−0.0266577
$597$	−16.0304	−0.656082
$598$	18.5844	0.759971
$599$	18.7502	0.766113	0.383057	−	0.923725i	$-0.374871\pi$
$599$	18.7502	0.766113	0.383057	+	0.923725i	$0.374871\pi$
$600$	9.27758	0.378756
$601$	−12.0858	−0.492991	−0.246496	−	0.969144i	$-0.579279\pi$
$601$	−12.0858	−0.492991	−0.246496	+	0.969144i	$0.579279\pi$
$602$	−4.63497	−0.188907
$603$	−8.15703	−0.332180
$604$	16.7614	0.682010
$605$	−5.11605	−0.207997
$606$	0.107790	0.00437866
$607$	9.24432	0.375215	0.187608	−	0.982244i	$-0.439927\pi$
$607$	9.24432	0.375215	0.187608	+	0.982244i	$0.439927\pi$
$608$	4.19727	0.170222
$609$	10.6472	0.431448
$610$	−8.72285	−0.353178
$611$	−7.59961	−0.307447
$612$	10.9181	0.441339
$613$	−34.3725	−1.38829	−0.694146	−	0.719834i	$-0.744218\pi$
$613$	−34.3725	−1.38829	−0.694146	+	0.719834i	$0.744218\pi$
$614$	−6.73472	−0.271791
$615$	11.0214	0.444425
$616$	−1.26010	−0.0507708
$617$	32.8632	1.32302	0.661511	−	0.749935i	$-0.269915\pi$
$617$	32.8632	1.32302	0.661511	+	0.749935i	$0.269915\pi$
$618$	−25.7268	−1.03488
$619$	35.3054	1.41904	0.709521	−	0.704684i	$-0.248911\pi$
$619$	35.3054	1.41904	0.709521	+	0.704684i	$0.248911\pi$
$620$	−2.60945	−0.104798
$621$	15.6841	0.629380
$622$	22.9400	0.919811
$623$	−3.54503	−0.142029
$624$	−6.52045	−0.261027
$625$	13.6943	0.547770
$626$	12.9615	0.518046
$627$	−21.2547	−0.848833
$628$	−7.77539	−0.310272
$629$	−20.7328	−0.826670
$630$	−0.916183	−0.0365016
$631$	5.85395	0.233042	0.116521	−	0.993188i	$-0.462826\pi$
$631$	5.85395	0.233042	0.116521	+	0.993188i	$0.462826\pi$
$632$	−17.0494	−0.678188
$633$	−53.5864	−2.12987
$634$	5.42877	0.215604
$635$	−4.52248	−0.179469
$636$	−25.3821	−1.00646
$637$	−19.7918	−0.784178
$638$	20.1609	0.798177
$639$	12.9243	0.511276
$640$	0.892162	0.0352658
$641$	21.0283	0.830568	0.415284	−	0.909692i	$-0.363682\pi$
$641$	21.0283	0.830568	0.415284	+	0.909692i	$0.363682\pi$
$642$	−27.2224	−1.07438
$643$	12.7665	0.503462	0.251731	−	0.967797i	$-0.419000\pi$
$643$	12.7665	0.503462	0.251731	+	0.967797i	$0.419000\pi$
$644$	−3.45398	−0.136106
$645$	−16.6179	−0.654329
$646$	24.5052	0.964146
$647$	−19.5060	−0.766860	−0.383430	−	0.923570i	$-0.625257\pi$
$647$	−19.5060	−0.766860	−0.383430	+	0.923570i	$0.625257\pi$
$648$	−11.1131	−0.436562
$649$	−14.9774	−0.587913
$650$	−12.4216	−0.487216
$651$	−3.54450	−0.138920
$652$	−8.37598	−0.328029
$653$	−10.9678	−0.429203	−0.214602	−	0.976702i	$-0.568845\pi$
$653$	−10.9678	−0.429203	−0.214602	+	0.976702i	$0.568845\pi$
$654$	−29.8714	−1.16807
$655$	−0.454830	−0.0177717
$656$	−5.59790	−0.218561
$657$	0.738522	0.0288125
$658$	1.41242	0.0550618
$659$	−33.8985	−1.32050	−0.660249	−	0.751047i	$-0.729549\pi$
$659$	−33.8985	−1.32050	−0.660249	+	0.751047i	$0.729549\pi$
$660$	−4.51786	−0.175858
$661$	20.5116	0.797809	0.398904	−	0.916993i	$-0.369391\pi$
$661$	20.5116	0.797809	0.398904	+	0.916993i	$0.369391\pi$
$662$	−30.2525	−1.17580
$663$	−38.0689	−1.47847
$664$	4.55195	0.176650
$665$	−2.05633	−0.0797410
$666$	−6.64081	−0.257326
$667$	55.2618	2.13974
$668$	9.37779	0.362838
$669$	57.1329	2.20888
$670$	−3.89152	−0.150343
$671$	−22.4356	−0.866115
$672$	1.21185	0.0467482
$673$	13.8098	0.532328	0.266164	−	0.963928i	$-0.414244\pi$
$673$	13.8098	0.532328	0.266164	+	0.963928i	$0.414244\pi$
$674$	−25.3103	−0.974917
$675$	−10.4831	−0.403494
$676$	−4.26986	−0.164226
$677$	−48.2434	−1.85414	−0.927072	−	0.374884i	$-0.877683\pi$
$677$	−48.2434	−1.85414	−0.927072	+	0.374884i	$0.877683\pi$
$678$	−3.51025	−0.134810
$679$	9.45626	0.362898
$680$	5.20878	0.199748
$681$	−21.2528	−0.814409
$682$	−6.71161	−0.257001
$683$	−27.4306	−1.04960	−0.524800	−	0.851225i	$-0.675860\pi$
$683$	−27.4306	−1.04960	−0.524800	+	0.851225i	$0.675860\pi$
$684$	7.84915	0.300120
$685$	5.78441	0.221011
$686$	7.52235	0.287205
$687$	−18.6823	−0.712774
$688$	8.44044	0.321789
$689$	33.9837	1.29467
$690$	−12.3836	−0.471437
$691$	−12.5859	−0.478791	−0.239395	−	0.970922i	$-0.576949\pi$
$691$	−12.5859	−0.478791	−0.239395	+	0.970922i	$0.576949\pi$
$692$	24.1534	0.918176
$693$	−2.35646	−0.0895146
$694$	−7.51674	−0.285332
$695$	9.00382	0.341534
$696$	−19.3890	−0.734937
$697$	−32.6827	−1.23795
$698$	−0.148365	−0.00561570
$699$	46.3924	1.75472
$700$	2.30861	0.0872571
$701$	12.1609	0.459312	0.229656	−	0.973272i	$-0.426240\pi$
$701$	12.1609	0.459312	0.229656	+	0.973272i	$0.426240\pi$
$702$	7.36771	0.278076
$703$	−14.9050	−0.562152
$704$	2.29468	0.0864840
$705$	5.06398	0.190720
$706$	−20.1156	−0.757060
$707$	0.0268221	0.00100875
$708$	14.4039	0.541332
$709$	−36.1971	−1.35941	−0.679706	−	0.733485i	$-0.737893\pi$
$709$	−36.1971	−1.35941	−0.679706	+	0.733485i	$0.737893\pi$
$710$	6.16585	0.231400
$711$	−31.8834	−1.19572
$712$	6.45562	0.241935
$713$	−18.3968	−0.688965
$714$	7.07525	0.264785
$715$	6.04890	0.226216
$716$	−9.40111	−0.351336
$717$	46.2673	1.72788
$718$	21.9025	0.817392
$719$	2.87357	0.107166	0.0535830	−	0.998563i	$-0.482936\pi$
$719$	2.87357	0.107166	0.0535830	+	0.998563i	$0.482936\pi$
$720$	1.66840	0.0621775
$721$	−6.40177	−0.238415
$722$	−1.38295	−0.0514682
$723$	−13.2186	−0.491603
$724$	−21.2271	−0.788899
$725$	−36.9364	−1.37178
$726$	12.6549	0.469667
$727$	47.0710	1.74577	0.872884	−	0.487928i	$-0.162247\pi$
$727$	47.0710	1.74577	0.872884	+	0.487928i	$0.162247\pi$
$728$	−1.62253	−0.0601350
$729$	−4.27350	−0.158278
$730$	0.352331	0.0130404
$731$	49.2785	1.82263
$732$	21.5766	0.797492
$733$	−35.6021	−1.31500	−0.657498	−	0.753457i	$-0.728385\pi$
$733$	−35.6021	−1.31500	−0.657498	+	0.753457i	$0.728385\pi$
$734$	−0.673632	−0.0248642
$735$	13.1882	0.486453
$736$	6.28981	0.231845
$737$	−10.0092	−0.368693
$738$	−10.4684	−0.385348
$739$	−11.3766	−0.418495	−0.209247	−	0.977863i	$-0.567101\pi$
$739$	−11.3766	−0.418495	−0.209247	+	0.977863i	$0.567101\pi$
$740$	−3.16817	−0.116464
$741$	−27.3681	−1.00539
$742$	−6.31600	−0.231868
$743$	22.5232	0.826296	0.413148	−	0.910664i	$-0.364429\pi$
$743$	22.5232	0.826296	0.413148	+	0.910664i	$0.364429\pi$
$744$	6.45464	0.236639
$745$	−0.580617	−0.0212722
$746$	36.2933	1.32879
$747$	8.51243	0.311454
$748$	13.3972	0.489851
$749$	−6.77393	−0.247514
$750$	18.1213	0.661697
$751$	21.8177	0.796137	0.398069	−	0.917356i	$-0.369681\pi$
$751$	21.8177	0.796137	0.398069	+	0.917356i	$0.369681\pi$
$752$	−2.57206	−0.0937933
$753$	−22.4441	−0.817909
$754$	25.9596	0.945393
$755$	14.9538	0.544226
$756$	−1.36932	−0.0498016
$757$	15.0847	0.548262	0.274131	−	0.961692i	$-0.411610\pi$
$757$	15.0847	0.548262	0.274131	+	0.961692i	$0.411610\pi$
$758$	30.2139	1.09742
$759$	−31.8513	−1.15613
$760$	3.74464	0.135832
$761$	0.751027	0.0272247	0.0136124	−	0.999907i	$-0.495667\pi$
$761$	0.751027	0.0272247	0.0136124	+	0.999907i	$0.495667\pi$
$762$	11.1867	0.405250
$763$	−7.43312	−0.269097
$764$	8.25101	0.298511
$765$	9.74074	0.352177
$766$	8.16474	0.295004
$767$	−19.2852	−0.696348
$768$	−2.20682	−0.0796318
$769$	7.04426	0.254023	0.127011	−	0.991901i	$-0.459462\pi$
$769$	7.04426	0.254023	0.127011	+	0.991901i	$0.459462\pi$
$770$	−1.12421	−0.0405138
$771$	−35.8232	−1.29014
$772$	−11.1472	−0.401197
$773$	−24.3740	−0.876672	−0.438336	−	0.898811i	$-0.644432\pi$
$773$	−24.3740	−0.876672	−0.438336	+	0.898811i	$0.644432\pi$
$774$	15.7841	0.567349
$775$	12.2962	0.441694
$776$	−17.2201	−0.618167
$777$	−4.30343	−0.154385
$778$	33.7255	1.20912
$779$	−23.4959	−0.841828
$780$	−5.81730	−0.208293
$781$	15.8589	0.567474
$782$	36.7223	1.31319
$783$	21.9083	0.782940
$784$	−6.69845	−0.239230
$785$	−6.93691	−0.247589
$786$	1.12505	0.0401293
$787$	−17.6235	−0.628209	−0.314105	−	0.949388i	$-0.601704\pi$
$787$	−17.6235	−0.628209	−0.314105	+	0.949388i	$0.601704\pi$
$788$	7.48297	0.266570
$789$	24.5380	0.873576
$790$	−15.2108	−0.541176
$791$	−0.873480	−0.0310574
$792$	4.29119	0.152481
$793$	−28.8885	−1.02586
$794$	−4.97751	−0.176645
$795$	−22.6449	−0.803132
$796$	7.26404	0.257467
$797$	−50.5619	−1.79099	−0.895497	−	0.445067i	$-0.853180\pi$
$797$	−50.5619	−1.79099	−0.895497	+	0.445067i	$0.853180\pi$
$798$	5.08647	0.180059
$799$	−15.0167	−0.531251
$800$	−4.20405	−0.148636
$801$	12.0724	0.426558
$802$	−32.1996	−1.13701
$803$	0.906211	0.0319795
$804$	9.62594	0.339481
$805$	−3.08151	−0.108609
$806$	−8.64202	−0.304402
$807$	28.2946	0.996016
$808$	−0.0488438	−0.00171832
$809$	16.0918	0.565759	0.282880	−	0.959155i	$-0.408710\pi$
$809$	16.0918	0.565759	0.282880	+	0.959155i	$0.408710\pi$
$810$	−9.91464	−0.348365
$811$	28.4551	0.999195	0.499598	−	0.866258i	$-0.333481\pi$
$811$	28.4551	0.999195	0.499598	+	0.866258i	$0.333481\pi$
$812$	−4.82469	−0.169314
$813$	−53.0572	−1.86080
$814$	−8.14868	−0.285611
$815$	−7.47273	−0.261758
$816$	−12.8843	−0.451039
$817$	35.4268	1.23943
$818$	−25.5021	−0.891659
$819$	−3.03423	−0.106025
$820$	−4.99424	−0.174406
$821$	25.4569	0.888450	0.444225	−	0.895915i	$-0.353479\pi$
$821$	25.4569	0.888450	0.444225	+	0.895915i	$0.353479\pi$
$822$	−14.3081	−0.499053
$823$	29.2876	1.02090	0.510450	−	0.859907i	$-0.329479\pi$
$823$	29.2876	1.02090	0.510450	+	0.859907i	$0.329479\pi$
$824$	11.6578	0.406120
$825$	21.2891	0.741191
$826$	3.58423	0.124711
$827$	23.3416	0.811669	0.405834	−	0.913947i	$-0.366981\pi$
$827$	23.3416	0.811669	0.405834	+	0.913947i	$0.366981\pi$
$828$	11.7623	0.408769
$829$	53.8467	1.87017	0.935087	−	0.354417i	$-0.115321\pi$
$829$	53.8467	1.87017	0.935087	+	0.354417i	$0.115321\pi$
$830$	4.06108	0.140962
$831$	17.6579	0.612546
$832$	2.95468	0.102435
$833$	−39.1081	−1.35501
$834$	−22.2715	−0.771201
$835$	8.36651	0.289535
$836$	9.63138	0.333108
$837$	−7.29334	−0.252095
$838$	0.208915	0.00721686
$839$	−42.1184	−1.45409	−0.727045	−	0.686590i	$-0.759107\pi$
$839$	−42.1184	−1.45409	−0.727045	+	0.686590i	$0.759107\pi$
$840$	1.08117	0.0373038
$841$	48.1925	1.66181
$842$	−31.9879	−1.10238
$843$	11.2330	0.386885
$844$	24.2822	0.835826
$845$	−3.80941	−0.131048
$846$	−4.80991	−0.165368
$847$	3.14901	0.108201
$848$	11.5016	0.394968
$849$	26.2674	0.901496
$850$	−24.5448	−0.841881
$851$	−22.3359	−0.765663
$852$	−15.2517	−0.522513
$853$	−48.4616	−1.65929	−0.829646	−	0.558289i	$-0.811458\pi$
$853$	−48.4616	−1.65929	−0.829646	+	0.558289i	$0.811458\pi$
$854$	5.36905	0.183725
$855$	7.00271	0.239488
$856$	12.3356	0.421620
$857$	−51.1945	−1.74877	−0.874386	−	0.485231i	$-0.838735\pi$
$857$	−51.1945	−1.74877	−0.874386	+	0.485231i	$0.838735\pi$
$858$	−14.9624	−0.510806
$859$	14.4981	0.494669	0.247334	−	0.968930i	$-0.420445\pi$
$859$	14.4981	0.494669	0.247334	+	0.968930i	$0.420445\pi$
$860$	7.53023	0.256779
$861$	−6.78383	−0.231192
$862$	14.1530	0.482053
$863$	−30.9507	−1.05357	−0.526787	−	0.849998i	$-0.676603\pi$
$863$	−30.9507	−1.05357	−0.526787	+	0.849998i	$0.676603\pi$
$864$	2.49357	0.0848330
$865$	21.5488	0.732680
$866$	−15.4314	−0.524380
$867$	−37.7072	−1.28060
$868$	1.60615	0.0545164
$869$	−39.1229	−1.32715
$870$	−17.2981	−0.586460
$871$	−12.8880	−0.436694
$872$	13.5360	0.458385
$873$	−32.2027	−1.08990
$874$	26.4000	0.892993
$875$	4.50926	0.152441
$876$	−0.871514	−0.0294457
$877$	7.23403	0.244276	0.122138	−	0.992513i	$-0.461025\pi$
$877$	7.23403	0.244276	0.122138	+	0.992513i	$0.461025\pi$
$878$	−23.7333	−0.800961
$879$	−50.7609	−1.71212
$880$	2.04723	0.0690120
$881$	7.96512	0.268352	0.134176	−	0.990958i	$-0.457161\pi$
$881$	7.96512	0.268352	0.134176	+	0.990958i	$0.457161\pi$
$882$	−12.5265	−0.421790
$883$	−41.0750	−1.38228	−0.691142	−	0.722719i	$-0.742892\pi$
$883$	−41.0750	−1.38228	−0.691142	+	0.722719i	$0.742892\pi$
$884$	17.2505	0.580199
$885$	12.8506	0.431969
$886$	4.73581	0.159103
$887$	25.8398	0.867617	0.433809	−	0.901005i	$-0.357169\pi$
$887$	25.8398	0.867617	0.433809	+	0.901005i	$0.357169\pi$
$888$	7.83669	0.262982
$889$	2.78366	0.0933609
$890$	5.75946	0.193057
$891$	−25.5009	−0.854312
$892$	−25.8892	−0.866835
$893$	−10.7956	−0.361262
$894$	1.43620	0.0480336
$895$	−8.38731	−0.280357
$896$	−0.549139	−0.0183455
$897$	−41.0124	−1.36936
$898$	29.8305	0.995455
$899$	−25.6976	−0.857062
$900$	−7.86183	−0.262061
$901$	67.1509	2.23712
$902$	−12.8454	−0.427705
$903$	10.2286	0.340385
$904$	1.59064	0.0529037
$905$	−18.9380	−0.629520
$906$	−36.9893	−1.22889
$907$	−37.4931	−1.24494	−0.622469	−	0.782644i	$-0.713870\pi$
$907$	−37.4931	−1.24494	−0.622469	+	0.782644i	$0.713870\pi$
$908$	9.63050	0.319599
$909$	−0.0913410	−0.00302959
$910$	−1.44756	−0.0479861
$911$	3.21506	0.106520	0.0532598	−	0.998581i	$-0.483039\pi$
$911$	3.21506	0.106520	0.0532598	+	0.998581i	$0.483039\pi$
$912$	−9.26262	−0.306716
$913$	10.4453	0.345688
$914$	−13.7508	−0.454835
$915$	19.2498	0.636378
$916$	8.46571	0.279715
$917$	0.279955	0.00924493
$918$	14.5584	0.480499
$919$	−19.2750	−0.635822	−0.317911	−	0.948121i	$-0.602981\pi$
$919$	−19.2750	−0.635822	−0.317911	+	0.948121i	$0.602981\pi$
$920$	5.61152	0.185006
$921$	14.8623	0.489731
$922$	−18.5705	−0.611586
$923$	20.4202	0.672139
$924$	2.78081	0.0914820
$925$	14.9291	0.490865
$926$	22.2182	0.730137
$927$	21.8009	0.716035
$928$	8.78592	0.288412
$929$	−2.20342	−0.0722918	−0.0361459	−	0.999347i	$-0.511508\pi$
$929$	−2.20342	−0.0722918	−0.0361459	+	0.999347i	$0.511508\pi$
$930$	5.75858	0.188831
$931$	−28.1152	−0.921437
$932$	−21.0223	−0.688607
$933$	−50.6245	−1.65737
$934$	0.252699	0.00826855
$935$	11.9525	0.390888
$936$	5.52544	0.180605
$937$	−31.9852	−1.04491	−0.522456	−	0.852667i	$-0.674984\pi$
$937$	−31.9852	−1.04491	−0.522456	+	0.852667i	$0.674984\pi$
$938$	2.39529	0.0782090
$939$	−28.6037	−0.933447
$940$	−2.29469	−0.0748446
$941$	−2.74283	−0.0894137	−0.0447069	−	0.999000i	$-0.514235\pi$
$941$	−2.74283	−0.0894137	−0.0447069	+	0.999000i	$0.514235\pi$
$942$	17.1589	0.559067
$943$	−35.2097	−1.14659
$944$	−6.52700	−0.212436
$945$	−1.22165	−0.0397404
$946$	19.3681	0.629711
$947$	27.0524	0.879086	0.439543	−	0.898222i	$-0.355140\pi$
$947$	27.0524	0.879086	0.439543	+	0.898222i	$0.355140\pi$
$948$	37.6250	1.22200
$949$	1.16686	0.0378778
$950$	−17.6455	−0.572496
$951$	−11.9803	−0.388489
$952$	−3.20608	−0.103910
$953$	−44.3377	−1.43624	−0.718119	−	0.695921i	$-0.754997\pi$
$953$	−44.3377	−1.43624	−0.718119	+	0.695921i	$0.754997\pi$
$954$	21.5088	0.696372
$955$	7.36123	0.238204
$956$	−20.9656	−0.678075
$957$	−44.4915	−1.43821
$958$	−1.08921	−0.0351907
$959$	−3.56039	−0.114971
$960$	−1.96884	−0.0635441
$961$	−22.4452	−0.724039
$962$	−10.4924	−0.338289
$963$	23.0683	0.743364
$964$	5.98986	0.192920
$965$	−9.94512	−0.320145
$966$	7.62232	0.245244
$967$	21.3948	0.688012	0.344006	−	0.938968i	$-0.388216\pi$
$967$	21.3948	0.688012	0.344006	+	0.938968i	$0.388216\pi$
$968$	−5.73444	−0.184312
$969$	−54.0787	−1.73726
$970$	−15.3632	−0.493281
$971$	−12.7796	−0.410118	−0.205059	−	0.978750i	$-0.565739\pi$
$971$	−12.7796	−0.410118	−0.205059	+	0.978750i	$0.565739\pi$
$972$	17.0438	0.546681
$973$	−5.54199	−0.177668
$974$	−14.6810	−0.470409
$975$	27.4123	0.877896
$976$	−9.77721	−0.312961
$977$	22.3513	0.715081	0.357540	−	0.933898i	$-0.383615\pi$
$977$	22.3513	0.715081	0.357540	+	0.933898i	$0.383615\pi$
$978$	18.4843	0.591063
$979$	14.8136	0.473444
$980$	−5.97610	−0.190899
$981$	25.3131	0.808184
$982$	33.3549	1.06440
$983$	−53.0289	−1.69136	−0.845680	−	0.533691i	$-0.820805\pi$
$983$	−53.0289	−1.69136	−0.845680	+	0.533691i	$0.820805\pi$
$984$	12.3536	0.393818
$985$	6.67602	0.212716
$986$	51.2956	1.63358
$987$	−3.11696	−0.0992138
$988$	12.4016	0.394547
$989$	53.0887	1.68812
$990$	3.82844	0.121676
$991$	29.9673	0.951944	0.475972	−	0.879461i	$-0.342096\pi$
$991$	29.9673	0.951944	0.475972	+	0.879461i	$0.342096\pi$
$992$	−2.92486	−0.0928643
$993$	66.7619	2.11863
$994$	−3.79518	−0.120376
$995$	6.48070	0.205452
$996$	−10.0453	−0.318299
$997$	−16.9202	−0.535867	−0.267933	−	0.963437i	$-0.586341\pi$
$997$	−16.9202	−0.535867	−0.267933	+	0.963437i	$0.586341\pi$
$998$	36.7264	1.16255
$999$	−8.85497	−0.280159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.d.1.20	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.d.1.20	✓	98	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:	\( N \)	\(=\)	\( 8006 = 2 \cdot 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.20682 q^{3} +1.00000 q^{4} +0.892162 q^{5} -2.20682 q^{6} -0.549139 q^{7} +1.00000 q^{8} +1.87006 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.20682 q^{3} +1.00000 q^{4} +0.892162 q^{5} -2.20682 q^{6} -0.549139 q^{7} +1.00000 q^{8} +1.87006 q^{9} +0.892162 q^{10} +2.29468 q^{11} -2.20682 q^{12} +2.95468 q^{13} -0.549139 q^{14} -1.96884 q^{15} +1.00000 q^{16} +5.83838 q^{17} +1.87006 q^{18} +4.19727 q^{19} +0.892162 q^{20} +1.21185 q^{21} +2.29468 q^{22} +6.28981 q^{23} -2.20682 q^{24} -4.20405 q^{25} +2.95468 q^{26} +2.49357 q^{27} -0.549139 q^{28} +8.78592 q^{29} -1.96884 q^{30} -2.92486 q^{31} +1.00000 q^{32} -5.06395 q^{33} +5.83838 q^{34} -0.489921 q^{35} +1.87006 q^{36} -3.55112 q^{37} +4.19727 q^{38} -6.52045 q^{39} +0.892162 q^{40} -5.59790 q^{41} +1.21185 q^{42} +8.44044 q^{43} +2.29468 q^{44} +1.66840 q^{45} +6.28981 q^{46} -2.57206 q^{47} -2.20682 q^{48} -6.69845 q^{49} -4.20405 q^{50} -12.8843 q^{51} +2.95468 q^{52} +11.5016 q^{53} +2.49357 q^{54} +2.04723 q^{55} -0.549139 q^{56} -9.26262 q^{57} +8.78592 q^{58} -6.52700 q^{59} -1.96884 q^{60} -9.77721 q^{61} -2.92486 q^{62} -1.02692 q^{63} +1.00000 q^{64} +2.63605 q^{65} -5.06395 q^{66} -4.36190 q^{67} +5.83838 q^{68} -13.8805 q^{69} -0.489921 q^{70} +6.91114 q^{71} +1.87006 q^{72} +0.394918 q^{73} -3.55112 q^{74} +9.27758 q^{75} +4.19727 q^{76} -1.26010 q^{77} -6.52045 q^{78} -17.0494 q^{79} +0.892162 q^{80} -11.1131 q^{81} -5.59790 q^{82} +4.55195 q^{83} +1.21185 q^{84} +5.20878 q^{85} +8.44044 q^{86} -19.3890 q^{87} +2.29468 q^{88} +6.45562 q^{89} +1.66840 q^{90} -1.62253 q^{91} +6.28981 q^{92} +6.45464 q^{93} -2.57206 q^{94} +3.74464 q^{95} -2.20682 q^{96} -17.2201 q^{97} -6.69845 q^{98} +4.29119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9}+O(q^{10}) \) 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9	\( 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9} + 4 q^{10} + 51 q^{11} + 16 q^{12} + 31 q^{13} + 29 q^{14} + 57 q^{15} + 98 q^{16} + 35 q^{17} + 130 q^{18} + 77 q^{19} + 4 q^{20} + 46 q^{21} + 51 q^{22} + 73 q^{23} + 16 q^{24} + 150 q^{25} + 31 q^{26} + 52 q^{27} + 29 q^{28} + 20 q^{29} + 57 q^{30} + 59 q^{31} + 98 q^{32} + 27 q^{33} + 35 q^{34} + 48 q^{35} + 130 q^{36} + 41 q^{37} + 77 q^{38} + 64 q^{39} + 4 q^{40} + 29 q^{41} + 46 q^{42} + 94 q^{43} + 51 q^{44} - 3 q^{45} + 73 q^{46} + 58 q^{47} + 16 q^{48} + 149 q^{49} + 150 q^{50} + 58 q^{51} + 31 q^{52} - 11 q^{53} + 52 q^{54} + 56 q^{55} + 29 q^{56} + 64 q^{57} + 20 q^{58} + 45 q^{59} + 57 q^{60} + 73 q^{61} + 59 q^{62} + 53 q^{63} + 98 q^{64} + 39 q^{65} + 27 q^{66} + 133 q^{67} + 35 q^{68} + 13 q^{69} + 48 q^{70} + 67 q^{71} + 130 q^{72} + 42 q^{73} + 41 q^{74} + 36 q^{75} + 77 q^{76} - 25 q^{77} + 64 q^{78} + 154 q^{79} + 4 q^{80} + 198 q^{81} + 29 q^{82} + 69 q^{83} + 46 q^{84} + 81 q^{85} + 94 q^{86} + 25 q^{87} + 51 q^{88} + 32 q^{89} - 3 q^{90} + 95 q^{91} + 73 q^{92} - 23 q^{93} + 58 q^{94} + 50 q^{95} + 16 q^{96} + 76 q^{97} + 149 q^{98} + 149 q^{99}+O(q^{100}) \) 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9 + 4 * q^10 + 51 * q^11 + 16 * q^12 + 31 * q^13 + 29 * q^14 + 57 * q^15 + 98 * q^16 + 35 * q^17 + 130 * q^18 + 77 * q^19 + 4 * q^20 + 46 * q^21 + 51 * q^22 + 73 * q^23 + 16 * q^24 + 150 * q^25 + 31 * q^26 + 52 * q^27 + 29 * q^28 + 20 * q^29 + 57 * q^30 + 59 * q^31 + 98 * q^32 + 27 * q^33 + 35 * q^34 + 48 * q^35 + 130 * q^36 + 41 * q^37 + 77 * q^38 + 64 * q^39 + 4 * q^40 + 29 * q^41 + 46 * q^42 + 94 * q^43 + 51 * q^44 - 3 * q^45 + 73 * q^46 + 58 * q^47 + 16 * q^48 + 149 * q^49 + 150 * q^50 + 58 * q^51 + 31 * q^52 - 11 * q^53 + 52 * q^54 + 56 * q^55 + 29 * q^56 + 64 * q^57 + 20 * q^58 + 45 * q^59 + 57 * q^60 + 73 * q^61 + 59 * q^62 + 53 * q^63 + 98 * q^64 + 39 * q^65 + 27 * q^66 + 133 * q^67 + 35 * q^68 + 13 * q^69 + 48 * q^70 + 67 * q^71 + 130 * q^72 + 42 * q^73 + 41 * q^74 + 36 * q^75 + 77 * q^76 - 25 * q^77 + 64 * q^78 + 154 * q^79 + 4 * q^80 + 198 * q^81 + 29 * q^82 + 69 * q^83 + 46 * q^84 + 81 * q^85 + 94 * q^86 + 25 * q^87 + 51 * q^88 + 32 * q^89 - 3 * q^90 + 95 * q^91 + 73 * q^92 - 23 * q^93 + 58 * q^94 + 50 * q^95 + 16 * q^96 + 76 * q^97 + 149 * q^98 + 149 * q^99

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