LMFDB - Embedded newform 8047.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8047,2,Mod(1,8047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8047, 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("8047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8047 = 13 \cdot 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8047.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:	$64.2556185065$
Analytic rank:	$1$
Dimension:	$142$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74745 q^{2} -2.94528 q^{3} +5.54847 q^{4} +1.95253 q^{5} +8.09201 q^{6} +3.66595 q^{7} -9.74923 q^{8} +5.67469 q^{9} +O(q^{10})$	\(q-2.74745 q^{2} -2.94528 q^{3} +5.54847 q^{4} +1.95253 q^{5} +8.09201 q^{6} +3.66595 q^{7} -9.74923 q^{8} +5.67469 q^{9} -5.36448 q^{10} +2.28522 q^{11} -16.3418 q^{12} +1.00000 q^{13} -10.0720 q^{14} -5.75076 q^{15} +15.6885 q^{16} -5.27543 q^{17} -15.5909 q^{18} -6.83843 q^{19} +10.8336 q^{20} -10.7973 q^{21} -6.27851 q^{22} -5.42234 q^{23} +28.7142 q^{24} -1.18762 q^{25} -2.74745 q^{26} -7.87771 q^{27} +20.3404 q^{28} +3.26310 q^{29} +15.7999 q^{30} +4.92936 q^{31} -23.6050 q^{32} -6.73061 q^{33} +14.4940 q^{34} +7.15788 q^{35} +31.4858 q^{36} -0.423081 q^{37} +18.7882 q^{38} -2.94528 q^{39} -19.0357 q^{40} +1.80363 q^{41} +29.6649 q^{42} -7.67491 q^{43} +12.6794 q^{44} +11.0800 q^{45} +14.8976 q^{46} -1.57661 q^{47} -46.2072 q^{48} +6.43917 q^{49} +3.26293 q^{50} +15.5376 q^{51} +5.54847 q^{52} +8.57399 q^{53} +21.6436 q^{54} +4.46196 q^{55} -35.7402 q^{56} +20.1411 q^{57} -8.96521 q^{58} -0.00498498 q^{59} -31.9079 q^{60} -3.15109 q^{61} -13.5432 q^{62} +20.8031 q^{63} +33.4764 q^{64} +1.95253 q^{65} +18.4920 q^{66} +7.35369 q^{67} -29.2705 q^{68} +15.9703 q^{69} -19.6659 q^{70} +5.73892 q^{71} -55.3238 q^{72} -14.0956 q^{73} +1.16239 q^{74} +3.49788 q^{75} -37.9428 q^{76} +8.37748 q^{77} +8.09201 q^{78} +16.4326 q^{79} +30.6324 q^{80} +6.17802 q^{81} -4.95537 q^{82} -2.90991 q^{83} -59.9082 q^{84} -10.3004 q^{85} +21.0864 q^{86} -9.61076 q^{87} -22.2791 q^{88} -14.5759 q^{89} -30.4417 q^{90} +3.66595 q^{91} -30.0857 q^{92} -14.5184 q^{93} +4.33165 q^{94} -13.3523 q^{95} +69.5234 q^{96} -0.448125 q^{97} -17.6913 q^{98} +12.9679 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 142 q - 13 q^{2} - 26 q^{3} + 129 q^{4} - 37 q^{5} - 15 q^{6} - 14 q^{7} - 39 q^{8} + 98 q^{9}+O(q^{10}) $ 142 * q - 13 * q^2 - 26 * q^3 + 129 * q^4 - 37 * q^5 - 15 * q^6 - 14 * q^7 - 39 * q^8 + 98 * q^9	\( 142 q - 13 q^{2} - 26 q^{3} + 129 q^{4} - 37 q^{5} - 15 q^{6} - 14 q^{7} - 39 q^{8} + 98 q^{9} - 25 q^{10} - 25 q^{11} - 62 q^{12} + 142 q^{13} - 57 q^{14} - 14 q^{15} + 111 q^{16} - 141 q^{17} - 29 q^{18} - 3 q^{19} - 87 q^{20} - 19 q^{21} - 24 q^{22} - 69 q^{23} - 40 q^{24} + 87 q^{25} - 13 q^{26} - 95 q^{27} - 34 q^{28} - 147 q^{29} - 2 q^{30} - 21 q^{31} - 66 q^{32} - 62 q^{33} - 6 q^{34} - 59 q^{35} + 74 q^{36} - 37 q^{37} - 76 q^{38} - 26 q^{39} - 61 q^{40} - 97 q^{41} - 29 q^{42} - 33 q^{43} - 57 q^{44} - 86 q^{45} - q^{46} - 102 q^{47} - 141 q^{48} + 70 q^{49} - 28 q^{50} - 13 q^{51} + 129 q^{52} - 137 q^{53} - 29 q^{54} - 24 q^{55} - 130 q^{56} - 65 q^{57} - 15 q^{58} - 56 q^{59} + 11 q^{60} - 77 q^{61} - 150 q^{62} - 32 q^{63} + 73 q^{64} - 37 q^{65} - 32 q^{66} - 9 q^{67} - 226 q^{68} - 113 q^{69} + 6 q^{70} - 18 q^{71} - 82 q^{72} - 117 q^{73} - 70 q^{74} - 83 q^{75} + 40 q^{76} - 214 q^{77} - 15 q^{78} - 52 q^{79} - 161 q^{80} - 10 q^{81} - 36 q^{82} - 74 q^{83} + 53 q^{84} + 2 q^{85} + 17 q^{86} - 49 q^{87} - 29 q^{88} - 171 q^{89} - 57 q^{90} - 14 q^{91} - 187 q^{92} - 39 q^{93} + 13 q^{94} - 150 q^{95} - 47 q^{96} - 126 q^{97} - 85 q^{98}+O(q^{100}) \) 142 * q - 13 * q^2 - 26 * q^3 + 129 * q^4 - 37 * q^5 - 15 * q^6 - 14 * q^7 - 39 * q^8 + 98 * q^9 - 25 * q^10 - 25 * q^11 - 62 * q^12 + 142 * q^13 - 57 * q^14 - 14 * q^15 + 111 * q^16 - 141 * q^17 - 29 * q^18 - 3 * q^19 - 87 * q^20 - 19 * q^21 - 24 * q^22 - 69 * q^23 - 40 * q^24 + 87 * q^25 - 13 * q^26 - 95 * q^27 - 34 * q^28 - 147 * q^29 - 2 * q^30 - 21 * q^31 - 66 * q^32 - 62 * q^33 - 6 * q^34 - 59 * q^35 + 74 * q^36 - 37 * q^37 - 76 * q^38 - 26 * q^39 - 61 * q^40 - 97 * q^41 - 29 * q^42 - 33 * q^43 - 57 * q^44 - 86 * q^45 - q^46 - 102 * q^47 - 141 * q^48 + 70 * q^49 - 28 * q^50 - 13 * q^51 + 129 * q^52 - 137 * q^53 - 29 * q^54 - 24 * q^55 - 130 * q^56 - 65 * q^57 - 15 * q^58 - 56 * q^59 + 11 * q^60 - 77 * q^61 - 150 * q^62 - 32 * q^63 + 73 * q^64 - 37 * q^65 - 32 * q^66 - 9 * q^67 - 226 * q^68 - 113 * q^69 + 6 * q^70 - 18 * q^71 - 82 * q^72 - 117 * q^73 - 70 * q^74 - 83 * q^75 + 40 * q^76 - 214 * q^77 - 15 * q^78 - 52 * q^79 - 161 * q^80 - 10 * q^81 - 36 * q^82 - 74 * q^83 + 53 * q^84 + 2 * q^85 + 17 * q^86 - 49 * q^87 - 29 * q^88 - 171 * q^89 - 57 * q^90 - 14 * q^91 - 187 * q^92 - 39 * q^93 + 13 * q^94 - 150 * q^95 - 47 * q^96 - 126 * q^97 - 85 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.74745	−1.94274	−0.971369	−	0.237575i	$-0.923648\pi$
$2$	−2.74745	−1.94274	−0.971369	+	0.237575i	$0.923648\pi$
$3$	−2.94528	−1.70046	−0.850230	−	0.526412i	$-0.823537\pi$
$3$	−2.94528	−1.70046	−0.850230	+	0.526412i	$0.823537\pi$
$4$	5.54847	2.77423
$5$	1.95253	0.873199	0.436599	−	0.899656i	$-0.356183\pi$
$5$	1.95253	0.873199	0.436599	+	0.899656i	$0.356183\pi$
$6$	8.09201	3.30355
$7$	3.66595	1.38560	0.692799	−	0.721131i	$-0.256377\pi$
$7$	3.66595	1.38560	0.692799	+	0.721131i	$0.256377\pi$
$8$	−9.74923	−3.44687
$9$	5.67469	1.89156
$10$	−5.36448	−1.69640
$11$	2.28522	0.689019	0.344509	−	0.938783i	$-0.388045\pi$
$11$	2.28522	0.689019	0.344509	+	0.938783i	$0.388045\pi$
$12$	−16.3418	−4.71747
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−10.0720	−2.69185
$15$	−5.75076	−1.48484
$16$	15.6885	3.92214
$17$	−5.27543	−1.27948	−0.639739	−	0.768592i	$-0.720958\pi$
$17$	−5.27543	−1.27948	−0.639739	+	0.768592i	$0.720958\pi$
$18$	−15.5909	−3.67481
$19$	−6.83843	−1.56884	−0.784422	−	0.620228i	$-0.787040\pi$
$19$	−6.83843	−1.56884	−0.784422	+	0.620228i	$0.787040\pi$
$20$	10.8336	2.42246
$21$	−10.7973	−2.35615
$22$	−6.27851	−1.33858
$23$	−5.42234	−1.13064	−0.565318	−	0.824873i	$-0.691246\pi$
$23$	−5.42234	−1.13064	−0.565318	+	0.824873i	$0.691246\pi$
$24$	28.7142	5.86127
$25$	−1.18762	−0.237524
$26$	−2.74745	−0.538819
$27$	−7.87771	−1.51607
$28$	20.3404	3.84397
$29$	3.26310	0.605943	0.302972	−	0.953000i	$-0.402021\pi$
$29$	3.26310	0.605943	0.302972	+	0.953000i	$0.402021\pi$
$30$	15.7999	2.88465
$31$	4.92936	0.885340	0.442670	−	0.896685i	$-0.354031\pi$
$31$	4.92936	0.885340	0.442670	+	0.896685i	$0.354031\pi$
$32$	−23.6050	−4.17282
$33$	−6.73061	−1.17165
$34$	14.4940	2.48569
$35$	7.15788	1.20990
$36$	31.4858	5.24764
$37$	−0.423081	−0.0695541	−0.0347771	−	0.999395i	$-0.511072\pi$
$37$	−0.423081	−0.0695541	−0.0347771	+	0.999395i	$0.511072\pi$
$38$	18.7882	3.04785
$39$	−2.94528	−0.471623
$40$	−19.0357	−3.00980
$41$	1.80363	0.281679	0.140840	−	0.990032i	$-0.455020\pi$
$41$	1.80363	0.281679	0.140840	+	0.990032i	$0.455020\pi$
$42$	29.6649	4.57739
$43$	−7.67491	−1.17041	−0.585206	−	0.810884i	$-0.698986\pi$
$43$	−7.67491	−1.17041	−0.585206	+	0.810884i	$0.698986\pi$
$44$	12.6794	1.91150
$45$	11.0800	1.65171
$46$	14.8976	2.19653
$47$	−1.57661	−0.229972	−0.114986	−	0.993367i	$-0.536682\pi$
$47$	−1.57661	−0.229972	−0.114986	+	0.993367i	$0.536682\pi$
$48$	−46.2072	−6.66944
$49$	6.43917	0.919882
$50$	3.26293	0.461448
$51$	15.5376	2.17570
$52$	5.54847	0.769434
$53$	8.57399	1.17773	0.588864	−	0.808232i	$-0.299575\pi$
$53$	8.57399	1.17773	0.588864	+	0.808232i	$0.299575\pi$
$54$	21.6436	2.94532
$55$	4.46196	0.601650
$56$	−35.7402	−4.77598
$57$	20.1411	2.66776
$58$	−8.96521	−1.17719
$59$	−0.00498498	−0.000648989 0	−0.000324494	−	1.00000i	$-0.500103\pi$
$59$	−0.00498498	−0.000648989 0	−0.000324494		1.00000i	$0.500103\pi$
$60$	−31.9079	−4.11929
$61$	−3.15109	−0.403456	−0.201728	−	0.979442i	$-0.564656\pi$
$61$	−3.15109	−0.403456	−0.201728	+	0.979442i	$0.564656\pi$
$62$	−13.5432	−1.71998
$63$	20.8031	2.62095
$64$	33.4764	4.18455
$65$	1.95253	0.242182
$66$	18.4920	2.27621
$67$	7.35369	0.898396	0.449198	−	0.893432i	$-0.351710\pi$
$67$	7.35369	0.898396	0.449198	+	0.893432i	$0.351710\pi$
$68$	−29.2705	−3.54957
$69$	15.9703	1.92260
$70$	−19.6659	−2.35052
$71$	5.73892	0.681085	0.340542	−	0.940229i	$-0.389389\pi$
$71$	5.73892	0.681085	0.340542	+	0.940229i	$0.389389\pi$
$72$	−55.3238	−6.51997
$73$	−14.0956	−1.64976	−0.824882	−	0.565304i	$-0.808759\pi$
$73$	−14.0956	−1.64976	−0.824882	+	0.565304i	$0.808759\pi$
$74$	1.16239	0.135125
$75$	3.49788	0.403901
$76$	−37.9428	−4.35234
$77$	8.37748	0.954703
$78$	8.09201	0.916239
$79$	16.4326	1.84881	0.924404	−	0.381415i	$-0.124563\pi$
$79$	16.4326	1.84881	0.924404	+	0.381415i	$0.124563\pi$
$80$	30.6324	3.42480
$81$	6.17802	0.686446
$82$	−4.95537	−0.547229
$83$	−2.90991	−0.319404	−0.159702	−	0.987165i	$-0.551053\pi$
$83$	−2.90991	−0.319404	−0.159702	+	0.987165i	$0.551053\pi$
$84$	−59.9082	−6.53652
$85$	−10.3004	−1.11724
$86$	21.0864	2.27381
$87$	−9.61076	−1.03038
$88$	−22.2791	−2.37496
$89$	−14.5759	−1.54504	−0.772519	−	0.634992i	$-0.781004\pi$
$89$	−14.5759	−1.54504	−0.772519	+	0.634992i	$0.781004\pi$
$90$	−30.4417	−3.20884
$91$	3.66595	0.384296
$92$	−30.0857	−3.13665
$93$	−14.5184	−1.50548
$94$	4.33165	0.446776
$95$	−13.3523	−1.36991
$96$	69.5234	7.09570
$97$	−0.448125	−0.0455002	−0.0227501	−	0.999741i	$-0.507242\pi$
$97$	−0.448125	−0.0455002	−0.0227501	+	0.999741i	$0.507242\pi$
$98$	−17.6913	−1.78709
$99$	12.9679	1.30332
$100$	−6.58948	−0.658948
$101$	5.04151	0.501649	0.250825	−	0.968033i	$-0.419298\pi$
$101$	5.04151	0.501649	0.250825	+	0.968033i	$0.419298\pi$
$102$	−42.6888	−4.22682
$103$	18.1746	1.79079	0.895397	−	0.445268i	$-0.146892\pi$
$103$	18.1746	1.79079	0.895397	+	0.445268i	$0.146892\pi$
$104$	−9.74923	−0.955990
$105$	−21.0820	−2.05739
$106$	−23.5566	−2.28802
$107$	−0.259001	−0.0250386	−0.0125193	−	0.999922i	$-0.503985\pi$
$107$	−0.259001	−0.0250386	−0.0125193	+	0.999922i	$0.503985\pi$
$108$	−43.7092	−4.20592
$109$	15.6963	1.50344	0.751718	−	0.659485i	$-0.229226\pi$
$109$	15.6963	1.50344	0.751718	+	0.659485i	$0.229226\pi$
$110$	−12.2590	−1.16885
$111$	1.24609	0.118274
$112$	57.5134	5.43451
$113$	−12.4639	−1.17250	−0.586251	−	0.810129i	$-0.699397\pi$
$113$	−12.4639	−1.17250	−0.586251	+	0.810129i	$0.699397\pi$
$114$	−55.3366	−5.18275
$115$	−10.5873	−0.987269
$116$	18.1052	1.68103
$117$	5.67469	0.524625
$118$	0.0136960	0.00126082
$119$	−19.3394	−1.77284
$120$	56.0654	5.11805
$121$	−5.77779	−0.525253
$122$	8.65746	0.783810
$123$	−5.31219	−0.478984
$124$	27.3504	2.45614
$125$	−12.0815	−1.08060
$126$	−57.1554	−5.09181
$127$	20.1869	1.79129	0.895647	−	0.444765i	$-0.146713\pi$
$127$	20.1869	1.79129	0.895647	+	0.444765i	$0.146713\pi$
$128$	−44.7647	−3.95668
$129$	22.6048	1.99024
$130$	−5.36448	−0.470496
$131$	−13.4179	−1.17233	−0.586163	−	0.810193i	$-0.699362\pi$
$131$	−13.4179	−1.17233	−0.586163	+	0.810193i	$0.699362\pi$
$132$	−37.3445	−3.25043
$133$	−25.0693	−2.17379
$134$	−20.2039	−1.74535
$135$	−15.3815	−1.32383
$136$	51.4313	4.41020
$137$	−4.99604	−0.426840	−0.213420	−	0.976961i	$-0.568460\pi$
$137$	−4.99604	−0.426840	−0.213420	+	0.976961i	$0.568460\pi$
$138$	−43.8776	−3.73511
$139$	3.68590	0.312634	0.156317	−	0.987707i	$-0.450038\pi$
$139$	3.68590	0.312634	0.156317	+	0.987707i	$0.450038\pi$
$140$	39.7152	3.35655
$141$	4.64356	0.391058
$142$	−15.7674	−1.32317
$143$	2.28522	0.191099
$144$	89.0276	7.41897
$145$	6.37131	0.529109
$146$	38.7269	3.20506
$147$	−18.9652	−1.56422
$148$	−2.34745	−0.192959
$149$	−9.50558	−0.778728	−0.389364	−	0.921084i	$-0.627305\pi$
$149$	−9.50558	−0.778728	−0.389364	+	0.921084i	$0.627305\pi$
$150$	−9.61024	−0.784673
$151$	4.01953	0.327104	0.163552	−	0.986535i	$-0.447705\pi$
$151$	4.01953	0.327104	0.163552	+	0.986535i	$0.447705\pi$
$152$	66.6694	5.40760
$153$	−29.9364	−2.42021
$154$	−23.0167	−1.85474
$155$	9.62474	0.773078
$156$	−16.3418	−1.30839
$157$	10.8566	0.866453	0.433226	−	0.901285i	$-0.357375\pi$
$157$	10.8566	0.866453	0.433226	+	0.901285i	$0.357375\pi$
$158$	−45.1476	−3.59175
$159$	−25.2528	−2.00268
$160$	−46.0895	−3.64370
$161$	−19.8780	−1.56661
$162$	−16.9738	−1.33359
$163$	1.67072	0.130861	0.0654304	−	0.997857i	$-0.479158\pi$
$163$	1.67072	0.130861	0.0654304	+	0.997857i	$0.479158\pi$
$164$	10.0074	0.781443
$165$	−13.1417	−1.02308
$166$	7.99481	0.620518
$167$	−24.3283	−1.88258	−0.941292	−	0.337594i	$-0.890387\pi$
$167$	−24.3283	−1.88258	−0.941292	+	0.337594i	$0.890387\pi$
$168$	105.265	8.12136
$169$	1.00000	0.0769231
$170$	28.2999	2.17050
$171$	−38.8060	−2.96757
$172$	−42.5840	−3.24700
$173$	−10.6576	−0.810279	−0.405140	−	0.914255i	$-0.632777\pi$
$173$	−10.6576	−0.810279	−0.405140	+	0.914255i	$0.632777\pi$
$174$	26.4051	2.00176
$175$	−4.35376	−0.329113
$176$	35.8517	2.70243
$177$	0.0146822	0.00110358
$178$	40.0464	3.00160
$179$	−18.7878	−1.40427	−0.702134	−	0.712045i	$-0.747769\pi$
$179$	−18.7878	−1.40427	−0.702134	+	0.712045i	$0.747769\pi$
$180$	61.4770	4.58223
$181$	−17.9591	−1.33489	−0.667443	−	0.744661i	$-0.732611\pi$
$181$	−17.9591	−1.33489	−0.667443	+	0.744661i	$0.732611\pi$
$182$	−10.0720	−0.746586
$183$	9.28086	0.686061
$184$	52.8636	3.89716
$185$	−0.826079	−0.0607346
$186$	39.8885	2.92476
$187$	−12.0555	−0.881585
$188$	−8.74776	−0.637996
$189$	−28.8793	−2.10066
$190$	36.6846	2.66138
$191$	−4.22235	−0.305518	−0.152759	−	0.988263i	$-0.548816\pi$
$191$	−4.22235	−0.305518	−0.152759	+	0.988263i	$0.548816\pi$
$192$	−98.5975	−7.11566
$193$	12.8962	0.928285	0.464143	−	0.885760i	$-0.346362\pi$
$193$	12.8962	0.928285	0.464143	+	0.885760i	$0.346362\pi$
$194$	1.23120	0.0883951
$195$	−5.75076	−0.411820
$196$	35.7275	2.55197
$197$	8.13195	0.579377	0.289689	−	0.957121i	$-0.406448\pi$
$197$	8.13195	0.579377	0.289689	+	0.957121i	$0.406448\pi$
$198$	−35.6286	−2.53201
$199$	−7.14405	−0.506429	−0.253214	−	0.967410i	$-0.581488\pi$
$199$	−7.14405	−0.506429	−0.253214	+	0.967410i	$0.581488\pi$
$200$	11.5784	0.818716
$201$	−21.6587	−1.52769
$202$	−13.8513	−0.974573
$203$	11.9624	0.839594
$204$	86.2100	6.03590
$205$	3.52164	0.245962
$206$	−49.9337	−3.47905
$207$	−30.7701	−2.13867
$208$	15.6885	1.08781
$209$	−15.6273	−1.08096
$210$	57.9216	3.99697
$211$	15.7847	1.08666	0.543331	−	0.839519i	$-0.317163\pi$
$211$	15.7847	1.08666	0.543331	+	0.839519i	$0.317163\pi$
$212$	47.5725	3.26729
$213$	−16.9027	−1.15816
$214$	0.711592	0.0486434
$215$	−14.9855	−1.02200
$216$	76.8016	5.22568
$217$	18.0708	1.22673
$218$	−43.1248	−2.92078
$219$	41.5155	2.80536
$220$	24.7570	1.66912
$221$	−5.27543	−0.354864
$222$	−3.42358	−0.229775
$223$	−14.8024	−0.991240	−0.495620	−	0.868539i	$-0.665059\pi$
$223$	−14.8024	−0.991240	−0.495620	+	0.868539i	$0.665059\pi$
$224$	−86.5347	−5.78185
$225$	−6.73938	−0.449292
$226$	34.2438	2.27787
$227$	−4.82453	−0.320215	−0.160108	−	0.987100i	$-0.551184\pi$
$227$	−4.82453	−0.320215	−0.160108	+	0.987100i	$0.551184\pi$
$228$	111.752	7.40098
$229$	20.5700	1.35930	0.679652	−	0.733535i	$-0.262131\pi$
$229$	20.5700	1.35930	0.679652	+	0.733535i	$0.262131\pi$
$230$	29.0880	1.91801
$231$	−24.6741	−1.62343
$232$	−31.8127	−2.08861
$233$	13.2007	0.864809	0.432405	−	0.901680i	$-0.357665\pi$
$233$	13.2007	0.864809	0.432405	+	0.901680i	$0.357665\pi$
$234$	−15.5909	−1.01921
$235$	−3.07838	−0.200811
$236$	−0.0276590	−0.00180045
$237$	−48.3985	−3.14382
$238$	53.1341	3.44417
$239$	−0.793102	−0.0513015	−0.0256508	−	0.999671i	$-0.508166\pi$
$239$	−0.793102	−0.0513015	−0.0256508	+	0.999671i	$0.508166\pi$
$240$	−90.2210	−5.82374
$241$	−9.18842	−0.591878	−0.295939	−	0.955207i	$-0.595633\pi$
$241$	−9.18842	−0.591878	−0.295939	+	0.955207i	$0.595633\pi$
$242$	15.8742	1.02043
$243$	5.43713	0.348792
$244$	−17.4837	−1.11928
$245$	12.5727	0.803240
$246$	14.5950	0.930540
$247$	−6.83843	−0.435119
$248$	−48.0575	−3.05165
$249$	8.57050	0.543133
$250$	33.1934	2.09933
$251$	−24.1779	−1.52610	−0.763048	−	0.646342i	$-0.776298\pi$
$251$	−24.1779	−1.52610	−0.763048	+	0.646342i	$0.776298\pi$
$252$	115.425	7.27111
$253$	−12.3912	−0.779029
$254$	−55.4623	−3.48002
$255$	30.3377	1.89982
$256$	56.0358	3.50224
$257$	−3.74302	−0.233483	−0.116742	−	0.993162i	$-0.537245\pi$
$257$	−3.74302	−0.233483	−0.116742	+	0.993162i	$0.537245\pi$
$258$	−62.1054	−3.86651
$259$	−1.55099	−0.0963741
$260$	10.8336	0.671869
$261$	18.5171	1.14618
$262$	36.8649	2.27752
$263$	12.8466	0.792156	0.396078	−	0.918217i	$-0.370371\pi$
$263$	12.8466	0.792156	0.396078	+	0.918217i	$0.370371\pi$
$264$	65.6182	4.03852
$265$	16.7410	1.02839
$266$	68.8767	4.22310
$267$	42.9300	2.62727
$268$	40.8017	2.49236
$269$	7.59445	0.463042	0.231521	−	0.972830i	$-0.425630\pi$
$269$	7.59445	0.463042	0.231521	+	0.972830i	$0.425630\pi$
$270$	42.2598	2.57185
$271$	25.5517	1.55216	0.776079	−	0.630636i	$-0.217206\pi$
$271$	25.5517	1.55216	0.776079	+	0.630636i	$0.217206\pi$
$272$	−82.7638	−5.01829
$273$	−10.7973	−0.653479
$274$	13.7263	0.829239
$275$	−2.71397	−0.163659
$276$	88.6108	5.33374
$277$	−3.06330	−0.184056	−0.0920280	−	0.995756i	$-0.529335\pi$
$277$	−3.06330	−0.184056	−0.0920280	+	0.995756i	$0.529335\pi$
$278$	−10.1268	−0.607366
$279$	27.9726	1.67468
$280$	−69.7838	−4.17038
$281$	32.1505	1.91794	0.958968	−	0.283515i	$-0.0915004\pi$
$281$	32.1505	1.91794	0.958968	+	0.283515i	$0.0915004\pi$
$282$	−12.7579	−0.759724
$283$	22.9498	1.36423	0.682113	−	0.731247i	$-0.261061\pi$
$283$	22.9498	1.36423	0.682113	+	0.731247i	$0.261061\pi$
$284$	31.8422	1.88949
$285$	39.3261	2.32948
$286$	−6.27851	−0.371256
$287$	6.61200	0.390294
$288$	−133.951	−7.89314
$289$	10.8301	0.637066
$290$	−17.5048	−1.02792
$291$	1.31986	0.0773713
$292$	−78.2090	−4.57683
$293$	−11.9804	−0.699901	−0.349950	−	0.936768i	$-0.613802\pi$
$293$	−11.9804	−0.699901	−0.349950	+	0.936768i	$0.613802\pi$
$294$	52.1058	3.03887
$295$	−0.00973332	−0.000566696 0
$296$	4.12471	0.239744
$297$	−18.0023	−1.04460
$298$	26.1161	1.51286
$299$	−5.42234	−0.313582
$300$	19.4079	1.12051
$301$	−28.1358	−1.62172
$302$	−11.0434	−0.635478
$303$	−14.8487	−0.853034
$304$	−107.285	−6.15322
$305$	−6.15261	−0.352297
$306$	82.2487	4.70184
$307$	−31.1310	−1.77674	−0.888371	−	0.459127i	$-0.848162\pi$
$307$	−31.1310	−1.77674	−0.888371	+	0.459127i	$0.848162\pi$
$308$	46.4822	2.64857
$309$	−53.5293	−3.04517
$310$	−26.4435	−1.50189
$311$	−5.40376	−0.306419	−0.153210	−	0.988194i	$-0.548961\pi$
$311$	−5.40376	−0.306419	−0.153210	+	0.988194i	$0.548961\pi$
$312$	28.7142	1.62562
$313$	−29.1137	−1.64561	−0.822803	−	0.568327i	$-0.807591\pi$
$313$	−29.1137	−1.64561	−0.822803	+	0.568327i	$0.807591\pi$
$314$	−29.8280	−1.68329
$315$	40.6187	2.28861
$316$	91.1755	5.12903
$317$	−13.7518	−0.772380	−0.386190	−	0.922419i	$-0.626209\pi$
$317$	−13.7518	−0.772380	−0.386190	+	0.922419i	$0.626209\pi$
$318$	69.3808	3.89068
$319$	7.45690	0.417506
$320$	65.3638	3.65395
$321$	0.762831	0.0425771
$322$	54.6138	3.04351
$323$	36.0756	2.00730
$324$	34.2785	1.90436
$325$	−1.18762	−0.0658774
$326$	−4.59021	−0.254228
$327$	−46.2301	−2.55653
$328$	−17.5840	−0.970912
$329$	−5.77977	−0.318649
$330$	36.1062	1.98758
$331$	−19.8673	−1.09200	−0.546002	−	0.837784i	$-0.683851\pi$
$331$	−19.8673	−1.09200	−0.546002	+	0.837784i	$0.683851\pi$
$332$	−16.1455	−0.886100
$333$	−2.40085	−0.131566
$334$	66.8408	3.65737
$335$	14.3583	0.784478
$336$	−169.393	−9.24116
$337$	−14.0276	−0.764134	−0.382067	−	0.924135i	$-0.624788\pi$
$337$	−14.0276	−0.764134	−0.382067	+	0.924135i	$0.624788\pi$
$338$	−2.74745	−0.149441
$339$	36.7096	1.99379
$340$	−57.1516	−3.09948
$341$	11.2647	0.610016
$342$	106.617	5.76521
$343$	−2.05596	−0.111011
$344$	74.8244	4.03426
$345$	31.1825	1.67881
$346$	29.2811	1.57416
$347$	11.0188	0.591519	0.295760	−	0.955262i	$-0.404427\pi$
$347$	11.0188	0.591519	0.295760	+	0.955262i	$0.404427\pi$
$348$	−53.3250	−2.85852
$349$	−26.0618	−1.39505	−0.697527	−	0.716558i	$-0.745716\pi$
$349$	−26.0618	−1.39505	−0.697527	+	0.716558i	$0.745716\pi$
$350$	11.9617	0.639381
$351$	−7.87771	−0.420481
$352$	−53.9426	−2.87515
$353$	−13.0911	−0.696766	−0.348383	−	0.937352i	$-0.613269\pi$
$353$	−13.0911	−0.696766	−0.348383	+	0.937352i	$0.613269\pi$
$354$	−0.0403385	−0.00214397
$355$	11.2054	0.594722
$356$	−80.8737	−4.28630
$357$	56.9601	3.01465
$358$	51.6186	2.72813
$359$	5.11130	0.269764	0.134882	−	0.990862i	$-0.456934\pi$
$359$	5.11130	0.269764	0.134882	+	0.990862i	$0.456934\pi$
$360$	−108.021	−5.69323
$361$	27.7641	1.46127
$362$	49.3416	2.59333
$363$	17.0172	0.893172
$364$	20.3404	1.06613
$365$	−27.5221	−1.44057
$366$	−25.4987	−1.33284
$367$	17.1910	0.897362	0.448681	−	0.893692i	$-0.351894\pi$
$367$	17.1910	0.897362	0.448681	+	0.893692i	$0.351894\pi$
$368$	−85.0686	−4.43451
$369$	10.2350	0.532814
$370$	2.26961	0.117991
$371$	31.4318	1.63186
$372$	−80.5547	−4.17657
$373$	−22.3103	−1.15518	−0.577592	−	0.816325i	$-0.696008\pi$
$373$	−22.3103	−1.15518	−0.577592	+	0.816325i	$0.696008\pi$
$374$	33.1218	1.71269
$375$	35.5835	1.83752
$376$	15.3707	0.792684
$377$	3.26310	0.168058
$378$	79.3443	4.08103
$379$	−37.6487	−1.93389	−0.966943	−	0.254994i	$-0.917926\pi$
$379$	−37.6487	−1.93389	−0.966943	+	0.254994i	$0.917926\pi$
$380$	−74.0845	−3.80046
$381$	−59.4560	−3.04602
$382$	11.6007	0.593542
$383$	−4.99819	−0.255395	−0.127698	−	0.991813i	$-0.540759\pi$
$383$	−4.99819	−0.255395	−0.127698	+	0.991813i	$0.540759\pi$
$384$	131.845	6.72817
$385$	16.3573	0.833645
$386$	−35.4315	−1.80342
$387$	−43.5527	−2.21391
$388$	−2.48641	−0.126228
$389$	13.1940	0.668961	0.334480	−	0.942403i	$-0.391439\pi$
$389$	13.1940	0.668961	0.334480	+	0.942403i	$0.391439\pi$
$390$	15.7999	0.800059
$391$	28.6051	1.44662
$392$	−62.7770	−3.17072
$393$	39.5194	1.99349
$394$	−22.3421	−1.12558
$395$	32.0851	1.61438
$396$	71.9519	3.61572
$397$	−38.9759	−1.95615	−0.978073	−	0.208262i	$-0.933219\pi$
$397$	−38.9759	−1.95615	−0.978073	+	0.208262i	$0.933219\pi$
$398$	19.6279	0.983858
$399$	73.8363	3.69644
$400$	−18.6321	−0.931603
$401$	8.30201	0.414583	0.207291	−	0.978279i	$-0.433535\pi$
$401$	8.30201	0.414583	0.207291	+	0.978279i	$0.433535\pi$
$402$	59.5061	2.96790
$403$	4.92936	0.245549
$404$	27.9727	1.39169
$405$	12.0628	0.599404
$406$	−32.8660	−1.63111
$407$	−0.966832	−0.0479241
$408$	−151.480	−7.49937
$409$	7.88315	0.389797	0.194898	−	0.980823i	$-0.437562\pi$
$409$	7.88315	0.389797	0.194898	+	0.980823i	$0.437562\pi$
$410$	−9.67551	−0.477839
$411$	14.7147	0.725825
$412$	100.841	4.96808
$413$	−0.0182747	−0.000899237 0
$414$	84.5392	4.15487
$415$	−5.68168	−0.278903
$416$	−23.6050	−1.15733
$417$	−10.8560	−0.531621
$418$	42.9352	2.10003
$419$	−5.54539	−0.270910	−0.135455	−	0.990783i	$-0.543250\pi$
$419$	−5.54539	−0.270910	−0.135455	+	0.990783i	$0.543250\pi$
$420$	−116.973	−5.70768
$421$	−8.09794	−0.394670	−0.197335	−	0.980336i	$-0.563229\pi$
$421$	−8.09794	−0.394670	−0.197335	+	0.980336i	$0.563229\pi$
$422$	−43.3675	−2.11110
$423$	−8.94676	−0.435007
$424$	−83.5897	−4.05948
$425$	6.26521	0.303907
$426$	46.4394	2.25000
$427$	−11.5517	−0.559028
$428$	−1.43706	−0.0694628
$429$	−6.73061	−0.324957
$430$	41.1719	1.98548
$431$	−4.46152	−0.214904	−0.107452	−	0.994210i	$-0.534269\pi$
$431$	−4.46152	−0.214904	−0.107452	+	0.994210i	$0.534269\pi$
$432$	−123.590	−5.94622
$433$	−25.8081	−1.24026	−0.620128	−	0.784501i	$-0.712919\pi$
$433$	−25.8081	−1.24026	−0.620128	+	0.784501i	$0.712919\pi$
$434$	−49.6485	−2.38321
$435$	−18.7653	−0.899728
$436$	87.0906	4.17088
$437$	37.0803	1.77379
$438$	−114.062	−5.45008
$439$	23.3538	1.11462	0.557309	−	0.830305i	$-0.311834\pi$
$439$	23.3538	1.11462	0.557309	+	0.830305i	$0.311834\pi$
$440$	−43.5006	−2.07381
$441$	36.5403	1.74001
$442$	14.4940	0.689407
$443$	−29.1327	−1.38413	−0.692067	−	0.721833i	$-0.743300\pi$
$443$	−29.1327	−1.38413	−0.692067	+	0.721833i	$0.743300\pi$
$444$	6.91391	0.328120
$445$	−28.4598	−1.34912
$446$	40.6688	1.92572
$447$	27.9966	1.32420
$448$	122.723	5.79811
$449$	−21.7596	−1.02690	−0.513449	−	0.858120i	$-0.671633\pi$
$449$	−21.7596	−1.02690	−0.513449	+	0.858120i	$0.671633\pi$
$450$	18.5161	0.872857
$451$	4.12168	0.194082
$452$	−69.1554	−3.25280
$453$	−11.8386	−0.556228
$454$	13.2551	0.622094
$455$	7.15788	0.335566
$456$	−196.360	−9.19541
$457$	10.5026	0.491290	0.245645	−	0.969360i	$-0.421000\pi$
$457$	10.5026	0.491290	0.245645	+	0.969360i	$0.421000\pi$
$458$	−56.5150	−2.64077
$459$	41.5583	1.93977
$460$	−58.7432	−2.73892
$461$	12.3527	0.575322	0.287661	−	0.957732i	$-0.407122\pi$
$461$	12.3527	0.575322	0.287661	+	0.957732i	$0.407122\pi$
$462$	67.7907	3.15391
$463$	31.2732	1.45339	0.726694	−	0.686961i	$-0.241056\pi$
$463$	31.2732	1.45339	0.726694	+	0.686961i	$0.241056\pi$
$464$	51.1934	2.37659
$465$	−28.3476	−1.31459
$466$	−36.2683	−1.68010
$467$	−18.9404	−0.876456	−0.438228	−	0.898864i	$-0.644394\pi$
$467$	−18.9404	−0.876456	−0.438228	+	0.898864i	$0.644394\pi$
$468$	31.4858	1.45543
$469$	26.9583	1.24482
$470$	8.45768	0.390124
$471$	−31.9758	−1.47337
$472$	0.0485996	0.00223698
$473$	−17.5388	−0.806436
$474$	132.972	6.10763
$475$	8.12147	0.372639
$476$	−107.304	−4.91828
$477$	48.6547	2.22775
$478$	2.17901	0.0996654
$479$	−1.41694	−0.0647415	−0.0323708	−	0.999476i	$-0.510306\pi$
$479$	−1.41694	−0.0647415	−0.0323708	+	0.999476i	$0.510306\pi$
$480$	135.747	6.19596
$481$	−0.423081	−0.0192908
$482$	25.2447	1.14986
$483$	58.5463	2.66395
$484$	−32.0579	−1.45718
$485$	−0.874979	−0.0397307
$486$	−14.9382	−0.677612
$487$	−15.3165	−0.694056	−0.347028	−	0.937855i	$-0.612809\pi$
$487$	−15.3165	−0.694056	−0.347028	+	0.937855i	$0.612809\pi$
$488$	30.7207	1.39066
$489$	−4.92074	−0.222523
$490$	−34.5428	−1.56048
$491$	−6.60220	−0.297953	−0.148977	−	0.988841i	$-0.547598\pi$
$491$	−6.60220	−0.297953	−0.148977	+	0.988841i	$0.547598\pi$
$492$	−29.4745	−1.32881
$493$	−17.2143	−0.775291
$494$	18.7882	0.845322
$495$	25.3202	1.13806
$496$	77.3346	3.47242
$497$	21.0386	0.943709
$498$	−23.5470	−1.05517
$499$	38.0051	1.70134	0.850672	−	0.525698i	$-0.176196\pi$
$499$	38.0051	1.70134	0.850672	+	0.525698i	$0.176196\pi$
$500$	−67.0339	−2.99785
$501$	71.6538	3.20126
$502$	66.4275	2.96481
$503$	33.0104	1.47186	0.735930	−	0.677058i	$-0.236745\pi$
$503$	33.0104	1.47186	0.735930	+	0.677058i	$0.236745\pi$
$504$	−202.814	−9.03406
$505$	9.84371	0.438039
$506$	34.0442	1.51345
$507$	−2.94528	−0.130805
$508$	112.006	4.96947
$509$	43.4360	1.92527	0.962633	−	0.270809i	$-0.0872913\pi$
$509$	43.4360	1.92527	0.962633	+	0.270809i	$0.0872913\pi$
$510$	−83.3512	−3.69085
$511$	−51.6737	−2.28591
$512$	−64.4260	−2.84725
$513$	53.8712	2.37847
$514$	10.2837	0.453597
$515$	35.4864	1.56372
$516$	125.422	5.52139
$517$	−3.60289	−0.158455
$518$	4.26127	0.187230
$519$	31.3895	1.37785
$520$	−19.0357	−0.834769
$521$	−21.6497	−0.948489	−0.474244	−	0.880393i	$-0.657279\pi$
$521$	−21.6497	−0.948489	−0.474244	+	0.880393i	$0.657279\pi$
$522$	−50.8747	−2.22673
$523$	33.9561	1.48480	0.742399	−	0.669958i	$-0.233688\pi$
$523$	33.9561	1.48480	0.742399	+	0.669958i	$0.233688\pi$
$524$	−74.4486	−3.25230
$525$	12.8230	0.559644
$526$	−35.2954	−1.53895
$527$	−26.0045	−1.13277
$528$	−105.593	−4.59536
$529$	6.40175	0.278337
$530$	−45.9950	−1.99789
$531$	−0.0282882	−0.00122760
$532$	−139.096	−6.03059
$533$	1.80363	0.0781237
$534$	−117.948	−5.10411
$535$	−0.505708	−0.0218636
$536$	−71.6928	−3.09666
$537$	55.3354	2.38790
$538$	−20.8653	−0.899569
$539$	14.7149	0.633816
$540$	−85.3436	−3.67260
$541$	−21.9583	−0.944063	−0.472031	−	0.881582i	$-0.656479\pi$
$541$	−21.9583	−0.944063	−0.472031	+	0.881582i	$0.656479\pi$
$542$	−70.2021	−3.01544
$543$	52.8945	2.26992
$544$	124.527	5.33903
$545$	30.6476	1.31280
$546$	29.6649	1.26954
$547$	−31.5933	−1.35083	−0.675417	−	0.737436i	$-0.736036\pi$
$547$	−31.5933	−1.35083	−0.675417	+	0.737436i	$0.736036\pi$
$548$	−27.7203	−1.18415
$549$	−17.8815	−0.763162
$550$	7.45649	0.317946
$551$	−22.3145	−0.950630
$552$	−155.698	−6.62696
$553$	60.2409	2.56170
$554$	8.41626	0.357573
$555$	2.43304	0.103277
$556$	20.4511	0.867319
$557$	20.3956	0.864191	0.432095	−	0.901828i	$-0.357774\pi$
$557$	20.3956	0.864191	0.432095	+	0.901828i	$0.357774\pi$
$558$	−76.8532	−3.25346
$559$	−7.67491	−0.324614
$560$	112.297	4.74540
$561$	35.5068	1.49910
$562$	−88.3317	−3.72605
$563$	−8.69222	−0.366333	−0.183167	−	0.983082i	$-0.558635\pi$
$563$	−8.69222	−0.366333	−0.183167	+	0.983082i	$0.558635\pi$
$564$	25.7646	1.08489
$565$	−24.3361	−1.02383
$566$	−63.0534	−2.65033
$567$	22.6483	0.951139
$568$	−55.9500	−2.34761
$569$	14.7472	0.618236	0.309118	−	0.951024i	$-0.399966\pi$
$569$	14.7472	0.618236	0.309118	+	0.951024i	$0.399966\pi$
$570$	−108.047	−4.52557
$571$	−6.55340	−0.274251	−0.137126	−	0.990554i	$-0.543786\pi$
$571$	−6.55340	−0.274251	−0.137126	+	0.990554i	$0.543786\pi$
$572$	12.6794	0.530154
$573$	12.4360	0.519521
$574$	−18.1661	−0.758239
$575$	6.43969	0.268553
$576$	189.968	7.91534
$577$	−38.9643	−1.62210	−0.811052	−	0.584974i	$-0.801105\pi$
$577$	−38.9643	−1.62210	−0.811052	+	0.584974i	$0.801105\pi$
$578$	−29.7552	−1.23765
$579$	−37.9828	−1.57851
$580$	35.3510	1.46787
$581$	−10.6676	−0.442565
$582$	−3.62623	−0.150312
$583$	19.5934	0.811476
$584$	137.421	5.68653
$585$	11.0800	0.458102
$586$	32.9154	1.35972
$587$	18.1136	0.747630	0.373815	−	0.927503i	$-0.378050\pi$
$587$	18.1136	0.747630	0.373815	+	0.927503i	$0.378050\pi$
$588$	−105.228	−4.33952
$589$	−33.7091	−1.38896
$590$	0.0267418	0.00110094
$591$	−23.9509	−0.985208
$592$	−6.63753	−0.272801
$593$	−33.0794	−1.35841	−0.679205	−	0.733949i	$-0.737675\pi$
$593$	−33.0794	−1.35841	−0.679205	+	0.733949i	$0.737675\pi$
$594$	49.4603	2.02938
$595$	−37.7609	−1.54804
$596$	−52.7414	−2.16037
$597$	21.0413	0.861161
$598$	14.8976	0.609208
$599$	−34.0427	−1.39095	−0.695473	−	0.718552i	$-0.744805\pi$
$599$	−34.0427	−1.39095	−0.695473	+	0.718552i	$0.744805\pi$
$600$	−34.1016	−1.39219
$601$	−32.0597	−1.30774	−0.653871	−	0.756606i	$-0.726856\pi$
$601$	−32.0597	−1.30774	−0.653871	+	0.756606i	$0.726856\pi$
$602$	77.3017	3.15058
$603$	41.7299	1.69937
$604$	22.3022	0.907464
$605$	−11.2813	−0.458651
$606$	40.7959	1.65722
$607$	−15.5548	−0.631348	−0.315674	−	0.948868i	$-0.602231\pi$
$607$	−15.5548	−0.631348	−0.315674	+	0.948868i	$0.602231\pi$
$608$	161.421	6.54650
$609$	−35.2325	−1.42769
$610$	16.9040	0.684421
$611$	−1.57661	−0.0637828
$612$	−166.101	−6.71424
$613$	−23.7847	−0.960657	−0.480328	−	0.877089i	$-0.659483\pi$
$613$	−23.7847	−0.960657	−0.480328	+	0.877089i	$0.659483\pi$
$614$	85.5309	3.45174
$615$	−10.3722	−0.418248
$616$	−81.6740	−3.29074
$617$	18.0367	0.726131	0.363065	−	0.931764i	$-0.381730\pi$
$617$	18.0367	0.726131	0.363065	+	0.931764i	$0.381730\pi$
$618$	147.069	5.91598
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	53.4025	2.14470
$621$	42.7156	1.71412
$622$	14.8465	0.595292
$623$	−53.4343	−2.14080
$624$	−46.2072	−1.84977
$625$	−17.6514	−0.706058
$626$	79.9884	3.19698
$627$	46.0268	1.83813
$628$	60.2376	2.40374
$629$	2.23193	0.0889930
$630$	−111.598	−4.44616
$631$	−48.9443	−1.94844	−0.974222	−	0.225593i	$-0.927568\pi$
$631$	−48.9443	−1.94844	−0.974222	+	0.225593i	$0.927568\pi$
$632$	−160.205	−6.37260
$633$	−46.4903	−1.84782
$634$	37.7824	1.50053
$635$	39.4155	1.56416
$636$	−140.114	−5.55590
$637$	6.43917	0.255129
$638$	−20.4874	−0.811105
$639$	32.5666	1.28831
$640$	−87.4045	−3.45497
$641$	−21.5215	−0.850047	−0.425024	−	0.905182i	$-0.639734\pi$
$641$	−21.5215	−0.850047	−0.425024	+	0.905182i	$0.639734\pi$
$642$	−2.09584	−0.0827161
$643$	32.7317	1.29081	0.645406	−	0.763839i	$-0.276688\pi$
$643$	32.7317	1.29081	0.645406	+	0.763839i	$0.276688\pi$
$644$	−110.292	−4.34613
$645$	44.1365	1.73787
$646$	−99.1159	−3.89966
$647$	−40.2120	−1.58090	−0.790449	−	0.612528i	$-0.790153\pi$
$647$	−40.2120	−1.58090	−0.790449	+	0.612528i	$0.790153\pi$
$648$	−60.2309	−2.36609
$649$	−0.0113917	−0.000447165 0
$650$	3.26293	0.127983
$651$	−53.2236	−2.08600
$652$	9.26992	0.363038
$653$	−17.5689	−0.687524	−0.343762	−	0.939057i	$-0.611701\pi$
$653$	−17.5689	−0.687524	−0.343762	+	0.939057i	$0.611701\pi$
$654$	127.015	4.96667
$655$	−26.1988	−1.02367
$656$	28.2963	1.10478
$657$	−79.9881	−3.12063
$658$	15.8796	0.619052
$659$	28.9532	1.12786	0.563928	−	0.825824i	$-0.309290\pi$
$659$	28.9532	1.12786	0.563928	+	0.825824i	$0.309290\pi$
$660$	−72.9164	−2.83827
$661$	−8.96440	−0.348675	−0.174337	−	0.984686i	$-0.555778\pi$
$661$	−8.96440	−0.348675	−0.174337	+	0.984686i	$0.555778\pi$
$662$	54.5843	2.12148
$663$	15.5376	0.603431
$664$	28.3693	1.10094
$665$	−48.9487	−1.89815
$666$	6.59622	0.255598
$667$	−17.6937	−0.685101
$668$	−134.985	−5.22273
$669$	43.5972	1.68556
$670$	−39.4487	−1.52404
$671$	−7.20093	−0.277989
$672$	254.869	9.83179
$673$	−9.87647	−0.380710	−0.190355	−	0.981715i	$-0.560964\pi$
$673$	−9.87647	−0.380710	−0.190355	+	0.981715i	$0.560964\pi$
$674$	38.5402	1.48451
$675$	9.35574	0.360103
$676$	5.54847	0.213403
$677$	23.6149	0.907594	0.453797	−	0.891105i	$-0.350069\pi$
$677$	23.6149	0.907594	0.453797	+	0.891105i	$0.350069\pi$
$678$	−100.858	−3.87342
$679$	−1.64280	−0.0630450
$680$	100.421	3.85098
$681$	14.2096	0.544513
$682$	−30.9491	−1.18510
$683$	−8.81004	−0.337107	−0.168553	−	0.985693i	$-0.553910\pi$
$683$	−8.81004	−0.337107	−0.168553	+	0.985693i	$0.553910\pi$
$684$	−215.314	−8.23272
$685$	−9.75492	−0.372716
$686$	5.64864	0.215666
$687$	−60.5845	−2.31144
$688$	−120.408	−4.59052
$689$	8.57399	0.326643
$690$	−85.6724	−3.26149
$691$	12.3878	0.471255	0.235628	−	0.971843i	$-0.424285\pi$
$691$	12.3878	0.471255	0.235628	+	0.971843i	$0.424285\pi$
$692$	−59.1331	−2.24790
$693$	47.5396	1.80588
$694$	−30.2735	−1.14917
$695$	7.19683	0.272991
$696$	93.6975	3.55159
$697$	−9.51490	−0.360402
$698$	71.6033	2.71023
$699$	−38.8799	−1.47057
$700$	−24.1567	−0.913037
$701$	20.5655	0.776748	0.388374	−	0.921502i	$-0.373037\pi$
$701$	20.5655	0.776748	0.388374	+	0.921502i	$0.373037\pi$
$702$	21.6436	0.816885
$703$	2.89321	0.109120
$704$	76.5009	2.88323
$705$	9.06669	0.341471
$706$	35.9670	1.35364
$707$	18.4819	0.695084
$708$	0.0814635	0.00306158
$709$	−33.9503	−1.27503	−0.637515	−	0.770438i	$-0.720037\pi$
$709$	−33.9503	−1.27503	−0.637515	+	0.770438i	$0.720037\pi$
$710$	−30.7863	−1.15539
$711$	93.2497	3.49714
$712$	142.103	5.32555
$713$	−26.7287	−1.00100
$714$	−156.495	−5.85667
$715$	4.46196	0.166868
$716$	−104.244	−3.89577
$717$	2.33591	0.0872362
$718$	−14.0430	−0.524081
$719$	−32.0988	−1.19708	−0.598541	−	0.801092i	$-0.704253\pi$
$719$	−32.0988	−1.19708	−0.598541	+	0.801092i	$0.704253\pi$
$720$	173.829	6.47823
$721$	66.6270	2.48132
$722$	−76.2805	−2.83887
$723$	27.0625	1.00646
$724$	−99.6452	−3.70329
$725$	−3.87533	−0.143926
$726$	−46.7539	−1.73520
$727$	15.9916	0.593096	0.296548	−	0.955018i	$-0.404165\pi$
$727$	15.9916	0.593096	0.296548	+	0.955018i	$0.404165\pi$
$728$	−35.7402	−1.32462
$729$	−34.5479	−1.27955
$730$	75.6155	2.79866
$731$	40.4884	1.49752
$732$	51.4945	1.90329
$733$	27.8783	1.02971	0.514855	−	0.857277i	$-0.327846\pi$
$733$	27.8783	1.02971	0.514855	+	0.857277i	$0.327846\pi$
$734$	−47.2313	−1.74334
$735$	−37.0301	−1.36588
$736$	127.994	4.71793
$737$	16.8048	0.619012
$738$	−28.1202	−1.03512
$739$	−46.7004	−1.71790	−0.858952	−	0.512056i	$-0.828884\pi$
$739$	−46.7004	−1.71790	−0.858952	+	0.512056i	$0.828884\pi$
$740$	−4.58347	−0.168492
$741$	20.1411	0.739902
$742$	−86.3572	−3.17027
$743$	−30.2815	−1.11092	−0.555461	−	0.831543i	$-0.687458\pi$
$743$	−30.2815	−1.11092	−0.555461	+	0.831543i	$0.687458\pi$
$744$	141.543	5.18921
$745$	−18.5600	−0.679984
$746$	61.2964	2.24422
$747$	−16.5128	−0.604172
$748$	−66.8895	−2.44572
$749$	−0.949484	−0.0346934
$750$	−97.7638	−3.56983
$751$	5.32180	0.194195	0.0970976	−	0.995275i	$-0.469044\pi$
$751$	5.32180	0.194195	0.0970976	+	0.995275i	$0.469044\pi$
$752$	−24.7347	−0.901982
$753$	71.2108	2.59506
$754$	−8.96521	−0.326494
$755$	7.84825	0.285627
$756$	−160.236	−5.82772
$757$	−9.83335	−0.357399	−0.178700	−	0.983904i	$-0.557189\pi$
$757$	−9.83335	−0.357399	−0.178700	+	0.983904i	$0.557189\pi$
$758$	103.438	3.75703
$759$	36.4956	1.32471
$760$	130.174	4.72191
$761$	3.86812	0.140219	0.0701096	−	0.997539i	$-0.477665\pi$
$761$	3.86812	0.140219	0.0701096	+	0.997539i	$0.477665\pi$
$762$	163.352	5.91763
$763$	57.5419	2.08316
$764$	−23.4275	−0.847579
$765$	−58.4517	−2.11333
$766$	13.7323	0.496167
$767$	−0.00498498	−0.000179997 0
$768$	−165.041	−5.95541
$769$	−33.4631	−1.20671	−0.603354	−	0.797473i	$-0.706170\pi$
$769$	−33.4631	−1.20671	−0.603354	+	0.797473i	$0.706170\pi$
$770$	−44.9408	−1.61955
$771$	11.0242	0.397029
$772$	71.5539	2.57528
$773$	−34.1128	−1.22695	−0.613476	−	0.789713i	$-0.710229\pi$
$773$	−34.1128	−1.22695	−0.613476	+	0.789713i	$0.710229\pi$
$774$	119.659	4.30105
$775$	−5.85422	−0.210290
$776$	4.36887	0.156833
$777$	4.56811	0.163880
$778$	−36.2497	−1.29962
$779$	−12.3340	−0.441910
$780$	−31.9079	−1.14249
$781$	13.1147	0.469280
$782$	−78.5911	−2.81041
$783$	−25.7058	−0.918650
$784$	101.021	3.60790
$785$	21.1979	0.756585
$786$	−108.578	−3.87283
$787$	29.0325	1.03490	0.517448	−	0.855715i	$-0.326882\pi$
$787$	29.0325	1.03490	0.517448	+	0.855715i	$0.326882\pi$
$788$	45.1198	1.60733
$789$	−37.8369	−1.34703
$790$	−88.1521	−3.13631
$791$	−45.6919	−1.62462
$792$	−126.427	−4.49238
$793$	−3.15109	−0.111899
$794$	107.084	3.80028
$795$	−49.3069	−1.74874
$796$	−39.6385	−1.40495
$797$	−1.33539	−0.0473018	−0.0236509	−	0.999720i	$-0.507529\pi$
$797$	−1.33539	−0.0473018	−0.0236509	+	0.999720i	$0.507529\pi$
$798$	−202.861	−7.18121
$799$	8.31729	0.294244
$800$	28.0338	0.991145
$801$	−82.7134	−2.92254
$802$	−22.8093	−0.805426
$803$	−32.2115	−1.13672
$804$	−120.173	−4.23816
$805$	−38.8124	−1.36796
$806$	−13.5432	−0.477038
$807$	−22.3678	−0.787384
$808$	−49.1508	−1.72912
$809$	−17.1935	−0.604492	−0.302246	−	0.953230i	$-0.597736\pi$
$809$	−17.1935	−0.604492	−0.302246	+	0.953230i	$0.597736\pi$
$810$	−33.1418	−1.16448
$811$	−27.8669	−0.978538	−0.489269	−	0.872133i	$-0.662736\pi$
$811$	−27.8669	−0.978538	−0.489269	+	0.872133i	$0.662736\pi$
$812$	66.3728	2.32923
$813$	−75.2571	−2.63938
$814$	2.65632	0.0931040
$815$	3.26213	0.114267
$816$	243.763	8.53340
$817$	52.4843	1.83619
$818$	−21.6586	−0.757273
$819$	20.8031	0.726919
$820$	19.5397	0.682355
$821$	3.27481	0.114292	0.0571459	−	0.998366i	$-0.481800\pi$
$821$	3.27481	0.114292	0.0571459	+	0.998366i	$0.481800\pi$
$822$	−40.4280	−1.41009
$823$	15.9129	0.554688	0.277344	−	0.960771i	$-0.410546\pi$
$823$	15.9129	0.554688	0.277344	+	0.960771i	$0.410546\pi$
$824$	−177.188	−6.17264
$825$	7.99341	0.278295
$826$	0.0502087	0.00174698
$827$	16.1047	0.560015	0.280007	−	0.959998i	$-0.409663\pi$
$827$	16.1047	0.560015	0.280007	+	0.959998i	$0.409663\pi$
$828$	−170.727	−5.93316
$829$	11.2435	0.390504	0.195252	−	0.980753i	$-0.437447\pi$
$829$	11.2435	0.390504	0.195252	+	0.980753i	$0.437447\pi$
$830$	15.6101	0.541835
$831$	9.02229	0.312980
$832$	33.4764	1.16059
$833$	−33.9694	−1.17697
$834$	29.8263	1.03280
$835$	−47.5018	−1.64387
$836$	−86.7075	−2.99884
$837$	−38.8321	−1.34223
$838$	15.2357	0.526308
$839$	20.6361	0.712439	0.356219	−	0.934402i	$-0.384066\pi$
$839$	20.6361	0.712439	0.356219	+	0.934402i	$0.384066\pi$
$840$	205.533	7.09156
$841$	−18.3522	−0.632833
$842$	22.2487	0.766740
$843$	−94.6922	−3.26137
$844$	87.5807	3.01465
$845$	1.95253	0.0671691
$846$	24.5808	0.845104
$847$	−21.1811	−0.727790
$848$	134.513	4.61921
$849$	−67.5937	−2.31981
$850$	−17.2133	−0.590413
$851$	2.29409	0.0786404
$852$	−93.7843	−3.21300
$853$	3.44542	0.117969	0.0589845	−	0.998259i	$-0.481214\pi$
$853$	3.44542	0.117969	0.0589845	+	0.998259i	$0.481214\pi$
$854$	31.7378	1.08604
$855$	−75.7699	−2.59127
$856$	2.52506	0.0863047
$857$	−34.9011	−1.19220	−0.596100	−	0.802910i	$-0.703284\pi$
$857$	−34.9011	−1.19220	−0.596100	+	0.802910i	$0.703284\pi$
$858$	18.4920	0.631306
$859$	19.5148	0.665836	0.332918	−	0.942956i	$-0.391967\pi$
$859$	19.5148	0.665836	0.332918	+	0.942956i	$0.391967\pi$
$860$	−83.1465	−2.83527
$861$	−19.4742	−0.663679
$862$	12.2578	0.417502
$863$	−21.0744	−0.717380	−0.358690	−	0.933457i	$-0.616776\pi$
$863$	−21.0744	−0.717380	−0.358690	+	0.933457i	$0.616776\pi$
$864$	185.953	6.32626
$865$	−20.8092	−0.707535
$866$	70.9063	2.40949
$867$	−31.8978	−1.08330
$868$	100.265	3.40322
$869$	37.5520	1.27386
$870$	51.5567	1.74794
$871$	7.35369	0.249170
$872$	−153.027	−5.18215
$873$	−2.54297	−0.0860665
$874$	−101.876	−3.44601
$875$	−44.2902	−1.49728
$876$	230.347	7.78272
$877$	39.2382	1.32498	0.662491	−	0.749070i	$-0.269499\pi$
$877$	39.2382	1.32498	0.662491	+	0.749070i	$0.269499\pi$
$878$	−64.1634	−2.16541
$879$	35.2856	1.19015
$880$	70.0016	2.35975
$881$	21.2169	0.714816	0.357408	−	0.933948i	$-0.383661\pi$
$881$	21.2169	0.714816	0.357408	+	0.933948i	$0.383661\pi$
$882$	−100.393	−3.38039
$883$	12.5950	0.423855	0.211927	−	0.977285i	$-0.432026\pi$
$883$	12.5950	0.423855	0.211927	+	0.977285i	$0.432026\pi$
$884$	−29.2705	−0.984474
$885$	0.0286674	0.000963643 0
$886$	80.0405	2.68901
$887$	50.0128	1.67927	0.839633	−	0.543154i	$-0.182770\pi$
$887$	50.0128	1.67927	0.839633	+	0.543154i	$0.182770\pi$
$888$	−12.1484	−0.407675
$889$	74.0040	2.48201
$890$	78.1919	2.62100
$891$	14.1181	0.472974
$892$	−82.1305	−2.74993
$893$	10.7815	0.360790
$894$	−76.9193	−2.57257
$895$	−36.6838	−1.22620
$896$	−164.105	−5.48237
$897$	15.9703	0.533233
$898$	59.7833	1.99500
$899$	16.0850	0.536466
$900$	−37.3932	−1.24644
$901$	−45.2314	−1.50688
$902$	−11.3241	−0.377051
$903$	82.8679	2.75767
$904$	121.513	4.04147
$905$	−35.0656	−1.16562
$906$	32.5260	1.08061
$907$	13.3568	0.443505	0.221752	−	0.975103i	$-0.428822\pi$
$907$	13.3568	0.443505	0.221752	+	0.975103i	$0.428822\pi$
$908$	−26.7687	−0.888352
$909$	28.6090	0.948900
$910$	−19.6659	−0.651918
$911$	−46.2227	−1.53143	−0.765714	−	0.643182i	$-0.777614\pi$
$911$	−46.2227	−1.53143	−0.765714	+	0.643182i	$0.777614\pi$
$912$	315.985	10.4633
$913$	−6.64976	−0.220075
$914$	−28.8553	−0.954448
$915$	18.1212	0.599067
$916$	114.132	3.77103
$917$	−49.1892	−1.62437
$918$	−114.179	−3.76847
$919$	−38.8304	−1.28090	−0.640449	−	0.768001i	$-0.721252\pi$
$919$	−38.8304	−1.28090	−0.640449	+	0.768001i	$0.721252\pi$
$920$	103.218	3.40299
$921$	91.6897	3.02128
$922$	−33.9383	−1.11770
$923$	5.73892	0.188899
$924$	−136.903	−4.50378
$925$	0.502460	0.0165208
$926$	−85.9214	−2.82355
$927$	103.135	3.38740
$928$	−77.0256	−2.52849
$929$	−6.97428	−0.228819	−0.114409	−	0.993434i	$-0.536498\pi$
$929$	−6.97428	−0.228819	−0.114409	+	0.993434i	$0.536498\pi$
$930$	77.8835	2.55390
$931$	−44.0338	−1.44315
$932$	73.2439	2.39918
$933$	15.9156	0.521053
$934$	52.0377	1.70272
$935$	−23.5387	−0.769798
$936$	−55.3238	−1.80832
$937$	−16.6437	−0.543726	−0.271863	−	0.962336i	$-0.587640\pi$
$937$	−16.6437	−0.543726	−0.271863	+	0.962336i	$0.587640\pi$
$938$	−74.0664	−2.41835
$939$	85.7481	2.79829
$940$	−17.0803	−0.557097
$941$	−29.1680	−0.950850	−0.475425	−	0.879756i	$-0.657706\pi$
$941$	−29.1680	−0.950850	−0.475425	+	0.879756i	$0.657706\pi$
$942$	87.8519	2.86237
$943$	−9.77987	−0.318476
$944$	−0.0782070	−0.00254542
$945$	−56.3877	−1.83429
$946$	48.1870	1.56669
$947$	−48.3674	−1.57173	−0.785865	−	0.618398i	$-0.787782\pi$
$947$	−48.3674	−1.57173	−0.785865	+	0.618398i	$0.787782\pi$
$948$	−268.538	−8.72170
$949$	−14.0956	−0.457562
$950$	−22.3133	−0.723939
$951$	40.5030	1.31340
$952$	188.545	6.11076
$953$	−18.7614	−0.607742	−0.303871	−	0.952713i	$-0.598279\pi$
$953$	−18.7614	−0.607742	−0.303871	+	0.952713i	$0.598279\pi$
$954$	−133.676	−4.32793
$955$	−8.24426	−0.266778
$956$	−4.40050	−0.142322
$957$	−21.9627	−0.709952
$958$	3.89296	0.125776
$959$	−18.3152	−0.591429
$960$	−192.515	−6.21339
$961$	−6.70137	−0.216173
$962$	1.16239	0.0374771
$963$	−1.46975	−0.0473620
$964$	−50.9816	−1.64201
$965$	25.1801	0.810577
$966$	−160.853	−5.17536
$967$	6.12036	0.196818	0.0984088	−	0.995146i	$-0.468625\pi$
$967$	6.12036	0.196818	0.0984088	+	0.995146i	$0.468625\pi$
$968$	56.3290	1.81048
$969$	−106.253	−3.41334
$970$	2.40396	0.0771864
$971$	7.84953	0.251903	0.125952	−	0.992036i	$-0.459802\pi$
$971$	7.84953	0.251903	0.125952	+	0.992036i	$0.459802\pi$
$972$	30.1677	0.967630
$973$	13.5123	0.433185
$974$	42.0812	1.34837
$975$	3.49788	0.112022
$976$	−49.4361	−1.58241
$977$	−41.4827	−1.32715	−0.663575	−	0.748110i	$-0.730962\pi$
$977$	−41.4827	−1.32715	−0.663575	+	0.748110i	$0.730962\pi$
$978$	13.5195	0.432305
$979$	−33.3090	−1.06456
$980$	69.7591	2.22837
$981$	89.0718	2.84384
$982$	18.1392	0.578845
$983$	−43.3280	−1.38195	−0.690974	−	0.722880i	$-0.742818\pi$
$983$	−43.3280	−1.38195	−0.690974	+	0.722880i	$0.742818\pi$
$984$	51.7897	1.65100
$985$	15.8779	0.505911
$986$	47.2953	1.50619
$987$	17.0230	0.541850
$988$	−37.9428	−1.20712
$989$	41.6159	1.32331
$990$	−69.5659	−2.21095
$991$	−54.8689	−1.74297	−0.871484	−	0.490424i	$-0.836842\pi$
$991$	−54.8689	−1.74297	−0.871484	+	0.490424i	$0.836842\pi$
$992$	−116.358	−3.69436
$993$	58.5147	1.85691
$994$	−57.8024	−1.83338
$995$	−13.9490	−0.442213
$996$	47.5531	1.50678
$997$	−32.7353	−1.03674	−0.518369	−	0.855157i	$-0.673460\pi$
$997$	−32.7353	−1.03674	−0.518369	+	0.855157i	$0.673460\pi$
$998$	−104.417	−3.30526
$999$	3.33291	0.105449

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8047.2.a.b.1.3	✓	142

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8047.2.a.b.1.3	✓	142	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:	\( N \)	\(=\)	\( 8047 = 13 \cdot 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74745 q^{2} -2.94528 q^{3} +5.54847 q^{4} +1.95253 q^{5} +8.09201 q^{6} +3.66595 q^{7} -9.74923 q^{8} +5.67469 q^{9} +O(q^{10})\)	\(q-2.74745 q^{2} -2.94528 q^{3} +5.54847 q^{4} +1.95253 q^{5} +8.09201 q^{6} +3.66595 q^{7} -9.74923 q^{8} +5.67469 q^{9} -5.36448 q^{10} +2.28522 q^{11} -16.3418 q^{12} +1.00000 q^{13} -10.0720 q^{14} -5.75076 q^{15} +15.6885 q^{16} -5.27543 q^{17} -15.5909 q^{18} -6.83843 q^{19} +10.8336 q^{20} -10.7973 q^{21} -6.27851 q^{22} -5.42234 q^{23} +28.7142 q^{24} -1.18762 q^{25} -2.74745 q^{26} -7.87771 q^{27} +20.3404 q^{28} +3.26310 q^{29} +15.7999 q^{30} +4.92936 q^{31} -23.6050 q^{32} -6.73061 q^{33} +14.4940 q^{34} +7.15788 q^{35} +31.4858 q^{36} -0.423081 q^{37} +18.7882 q^{38} -2.94528 q^{39} -19.0357 q^{40} +1.80363 q^{41} +29.6649 q^{42} -7.67491 q^{43} +12.6794 q^{44} +11.0800 q^{45} +14.8976 q^{46} -1.57661 q^{47} -46.2072 q^{48} +6.43917 q^{49} +3.26293 q^{50} +15.5376 q^{51} +5.54847 q^{52} +8.57399 q^{53} +21.6436 q^{54} +4.46196 q^{55} -35.7402 q^{56} +20.1411 q^{57} -8.96521 q^{58} -0.00498498 q^{59} -31.9079 q^{60} -3.15109 q^{61} -13.5432 q^{62} +20.8031 q^{63} +33.4764 q^{64} +1.95253 q^{65} +18.4920 q^{66} +7.35369 q^{67} -29.2705 q^{68} +15.9703 q^{69} -19.6659 q^{70} +5.73892 q^{71} -55.3238 q^{72} -14.0956 q^{73} +1.16239 q^{74} +3.49788 q^{75} -37.9428 q^{76} +8.37748 q^{77} +8.09201 q^{78} +16.4326 q^{79} +30.6324 q^{80} +6.17802 q^{81} -4.95537 q^{82} -2.90991 q^{83} -59.9082 q^{84} -10.3004 q^{85} +21.0864 q^{86} -9.61076 q^{87} -22.2791 q^{88} -14.5759 q^{89} -30.4417 q^{90} +3.66595 q^{91} -30.0857 q^{92} -14.5184 q^{93} +4.33165 q^{94} -13.3523 q^{95} +69.5234 q^{96} -0.448125 q^{97} -17.6913 q^{98} +12.9679 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 142 q - 13 q^{2} - 26 q^{3} + 129 q^{4} - 37 q^{5} - 15 q^{6} - 14 q^{7} - 39 q^{8} + 98 q^{9}+O(q^{10}) \) 142 * q - 13 * q^2 - 26 * q^3 + 129 * q^4 - 37 * q^5 - 15 * q^6 - 14 * q^7 - 39 * q^8 + 98 * q^9	\( 142 q - 13 q^{2} - 26 q^{3} + 129 q^{4} - 37 q^{5} - 15 q^{6} - 14 q^{7} - 39 q^{8} + 98 q^{9} - 25 q^{10} - 25 q^{11} - 62 q^{12} + 142 q^{13} - 57 q^{14} - 14 q^{15} + 111 q^{16} - 141 q^{17} - 29 q^{18} - 3 q^{19} - 87 q^{20} - 19 q^{21} - 24 q^{22} - 69 q^{23} - 40 q^{24} + 87 q^{25} - 13 q^{26} - 95 q^{27} - 34 q^{28} - 147 q^{29} - 2 q^{30} - 21 q^{31} - 66 q^{32} - 62 q^{33} - 6 q^{34} - 59 q^{35} + 74 q^{36} - 37 q^{37} - 76 q^{38} - 26 q^{39} - 61 q^{40} - 97 q^{41} - 29 q^{42} - 33 q^{43} - 57 q^{44} - 86 q^{45} - q^{46} - 102 q^{47} - 141 q^{48} + 70 q^{49} - 28 q^{50} - 13 q^{51} + 129 q^{52} - 137 q^{53} - 29 q^{54} - 24 q^{55} - 130 q^{56} - 65 q^{57} - 15 q^{58} - 56 q^{59} + 11 q^{60} - 77 q^{61} - 150 q^{62} - 32 q^{63} + 73 q^{64} - 37 q^{65} - 32 q^{66} - 9 q^{67} - 226 q^{68} - 113 q^{69} + 6 q^{70} - 18 q^{71} - 82 q^{72} - 117 q^{73} - 70 q^{74} - 83 q^{75} + 40 q^{76} - 214 q^{77} - 15 q^{78} - 52 q^{79} - 161 q^{80} - 10 q^{81} - 36 q^{82} - 74 q^{83} + 53 q^{84} + 2 q^{85} + 17 q^{86} - 49 q^{87} - 29 q^{88} - 171 q^{89} - 57 q^{90} - 14 q^{91} - 187 q^{92} - 39 q^{93} + 13 q^{94} - 150 q^{95} - 47 q^{96} - 126 q^{97} - 85 q^{98}+O(q^{100}) \) 142 * q - 13 * q^2 - 26 * q^3 + 129 * q^4 - 37 * q^5 - 15 * q^6 - 14 * q^7 - 39 * q^8 + 98 * q^9 - 25 * q^10 - 25 * q^11 - 62 * q^12 + 142 * q^13 - 57 * q^14 - 14 * q^15 + 111 * q^16 - 141 * q^17 - 29 * q^18 - 3 * q^19 - 87 * q^20 - 19 * q^21 - 24 * q^22 - 69 * q^23 - 40 * q^24 + 87 * q^25 - 13 * q^26 - 95 * q^27 - 34 * q^28 - 147 * q^29 - 2 * q^30 - 21 * q^31 - 66 * q^32 - 62 * q^33 - 6 * q^34 - 59 * q^35 + 74 * q^36 - 37 * q^37 - 76 * q^38 - 26 * q^39 - 61 * q^40 - 97 * q^41 - 29 * q^42 - 33 * q^43 - 57 * q^44 - 86 * q^45 - q^46 - 102 * q^47 - 141 * q^48 + 70 * q^49 - 28 * q^50 - 13 * q^51 + 129 * q^52 - 137 * q^53 - 29 * q^54 - 24 * q^55 - 130 * q^56 - 65 * q^57 - 15 * q^58 - 56 * q^59 + 11 * q^60 - 77 * q^61 - 150 * q^62 - 32 * q^63 + 73 * q^64 - 37 * q^65 - 32 * q^66 - 9 * q^67 - 226 * q^68 - 113 * q^69 + 6 * q^70 - 18 * q^71 - 82 * q^72 - 117 * q^73 - 70 * q^74 - 83 * q^75 + 40 * q^76 - 214 * q^77 - 15 * q^78 - 52 * q^79 - 161 * q^80 - 10 * q^81 - 36 * q^82 - 74 * q^83 + 53 * q^84 + 2 * q^85 + 17 * q^86 - 49 * q^87 - 29 * q^88 - 171 * q^89 - 57 * q^90 - 14 * q^91 - 187 * q^92 - 39 * q^93 + 13 * q^94 - 150 * q^95 - 47 * q^96 - 126 * q^97 - 85 * q^98

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