LMFDB - Embedded newform 8013.2.a.c.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9841271397$
Analytic rank:	$1$
Dimension:	$116$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20341 q^{2} -1.00000 q^{3} +2.85502 q^{4} -0.504029 q^{5} +2.20341 q^{6} -3.35275 q^{7} -1.88396 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.20341 q^{2} -1.00000 q^{3} +2.85502 q^{4} -0.504029 q^{5} +2.20341 q^{6} -3.35275 q^{7} -1.88396 q^{8} +1.00000 q^{9} +1.11058 q^{10} +1.05945 q^{11} -2.85502 q^{12} -3.97609 q^{13} +7.38748 q^{14} +0.504029 q^{15} -1.55890 q^{16} -4.88714 q^{17} -2.20341 q^{18} -2.88330 q^{19} -1.43901 q^{20} +3.35275 q^{21} -2.33440 q^{22} -3.63705 q^{23} +1.88396 q^{24} -4.74595 q^{25} +8.76096 q^{26} -1.00000 q^{27} -9.57215 q^{28} -0.102473 q^{29} -1.11058 q^{30} +3.68423 q^{31} +7.20282 q^{32} -1.05945 q^{33} +10.7684 q^{34} +1.68988 q^{35} +2.85502 q^{36} +8.85222 q^{37} +6.35309 q^{38} +3.97609 q^{39} +0.949570 q^{40} +9.04429 q^{41} -7.38748 q^{42} +6.44418 q^{43} +3.02475 q^{44} -0.504029 q^{45} +8.01391 q^{46} +8.28920 q^{47} +1.55890 q^{48} +4.24090 q^{49} +10.4573 q^{50} +4.88714 q^{51} -11.3518 q^{52} -7.33259 q^{53} +2.20341 q^{54} -0.533993 q^{55} +6.31644 q^{56} +2.88330 q^{57} +0.225790 q^{58} -7.83997 q^{59} +1.43901 q^{60} +0.0555462 q^{61} -8.11786 q^{62} -3.35275 q^{63} -12.7530 q^{64} +2.00406 q^{65} +2.33440 q^{66} +7.57174 q^{67} -13.9529 q^{68} +3.63705 q^{69} -3.72350 q^{70} +15.2961 q^{71} -1.88396 q^{72} +6.54789 q^{73} -19.5051 q^{74} +4.74595 q^{75} -8.23187 q^{76} -3.55206 q^{77} -8.76096 q^{78} +0.672310 q^{79} +0.785732 q^{80} +1.00000 q^{81} -19.9283 q^{82} -1.36416 q^{83} +9.57215 q^{84} +2.46326 q^{85} -14.1992 q^{86} +0.102473 q^{87} -1.99596 q^{88} +1.35945 q^{89} +1.11058 q^{90} +13.3308 q^{91} -10.3838 q^{92} -3.68423 q^{93} -18.2645 q^{94} +1.45327 q^{95} -7.20282 q^{96} +12.8151 q^{97} -9.34445 q^{98} +1.05945 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9}+O(q^{10}) $ 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9} + 3 q^{10} - 57 q^{11} - 116 q^{12} + 6 q^{13} - 9 q^{14} + 20 q^{15} + 112 q^{16} - 30 q^{17} - 16 q^{18} + 3 q^{19} - 54 q^{20} + 33 q^{21} - 22 q^{22} - 58 q^{23} + 45 q^{24} + 126 q^{25} - 21 q^{26} - 116 q^{27} - 77 q^{28} - 38 q^{29} - 3 q^{30} + 17 q^{31} - 106 q^{32} + 57 q^{33} + 35 q^{34} - 72 q^{35} + 116 q^{36} - 41 q^{37} - 45 q^{38} - 6 q^{39} + 5 q^{40} - 39 q^{41} + 9 q^{42} - 118 q^{43} - 103 q^{44} - 20 q^{45} - 8 q^{46} - 65 q^{47} - 112 q^{48} + 165 q^{49} - 72 q^{50} + 30 q^{51} - 10 q^{52} - 58 q^{53} + 16 q^{54} + 14 q^{55} - 23 q^{56} - 3 q^{57} - 27 q^{58} - 75 q^{59} + 54 q^{60} + 45 q^{61} - 73 q^{62} - 33 q^{63} + 111 q^{64} - 86 q^{65} + 22 q^{66} - 127 q^{67} - 94 q^{68} + 58 q^{69} - 7 q^{70} - 61 q^{71} - 45 q^{72} + 15 q^{73} - 51 q^{74} - 126 q^{75} + 96 q^{76} - 57 q^{77} + 21 q^{78} + 7 q^{79} - 144 q^{80} + 116 q^{81} - 37 q^{82} - 194 q^{83} + 77 q^{84} + 3 q^{85} - 57 q^{86} + 38 q^{87} - 42 q^{88} - 56 q^{89} + 3 q^{90} - 39 q^{91} - 138 q^{92} - 17 q^{93} + 51 q^{94} - 127 q^{95} + 106 q^{96} + 57 q^{97} - 105 q^{98} - 57 q^{99}+O(q^{100}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9 + 3 * q^10 - 57 * q^11 - 116 * q^12 + 6 * q^13 - 9 * q^14 + 20 * q^15 + 112 * q^16 - 30 * q^17 - 16 * q^18 + 3 * q^19 - 54 * q^20 + 33 * q^21 - 22 * q^22 - 58 * q^23 + 45 * q^24 + 126 * q^25 - 21 * q^26 - 116 * q^27 - 77 * q^28 - 38 * q^29 - 3 * q^30 + 17 * q^31 - 106 * q^32 + 57 * q^33 + 35 * q^34 - 72 * q^35 + 116 * q^36 - 41 * q^37 - 45 * q^38 - 6 * q^39 + 5 * q^40 - 39 * q^41 + 9 * q^42 - 118 * q^43 - 103 * q^44 - 20 * q^45 - 8 * q^46 - 65 * q^47 - 112 * q^48 + 165 * q^49 - 72 * q^50 + 30 * q^51 - 10 * q^52 - 58 * q^53 + 16 * q^54 + 14 * q^55 - 23 * q^56 - 3 * q^57 - 27 * q^58 - 75 * q^59 + 54 * q^60 + 45 * q^61 - 73 * q^62 - 33 * q^63 + 111 * q^64 - 86 * q^65 + 22 * q^66 - 127 * q^67 - 94 * q^68 + 58 * q^69 - 7 * q^70 - 61 * q^71 - 45 * q^72 + 15 * q^73 - 51 * q^74 - 126 * q^75 + 96 * q^76 - 57 * q^77 + 21 * q^78 + 7 * q^79 - 144 * q^80 + 116 * q^81 - 37 * q^82 - 194 * q^83 + 77 * q^84 + 3 * q^85 - 57 * q^86 + 38 * q^87 - 42 * q^88 - 56 * q^89 + 3 * q^90 - 39 * q^91 - 138 * q^92 - 17 * q^93 + 51 * q^94 - 127 * q^95 + 106 * q^96 + 57 * q^97 - 105 * q^98 - 57 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.20341	−1.55805	−0.779023	−	0.626995i	$-0.784285\pi$
$2$	−2.20341	−1.55805	−0.779023	+	0.626995i	$0.784285\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.85502	1.42751
$5$	−0.504029	−0.225409	−0.112704	−	0.993629i	$-0.535951\pi$
$5$	−0.504029	−0.225409	−0.112704	+	0.993629i	$0.535951\pi$
$6$	2.20341	0.899539
$7$	−3.35275	−1.26722	−0.633609	−	0.773653i	$-0.718427\pi$
$7$	−3.35275	−1.26722	−0.633609	+	0.773653i	$0.718427\pi$
$8$	−1.88396	−0.666080
$9$	1.00000	0.333333
$10$	1.11058	0.351197
$11$	1.05945	0.319436	0.159718	−	0.987163i	$-0.448942\pi$
$11$	1.05945	0.319436	0.159718	+	0.987163i	$0.448942\pi$
$12$	−2.85502	−0.824173
$13$	−3.97609	−1.10277	−0.551384	−	0.834251i	$-0.685900\pi$
$13$	−3.97609	−1.10277	−0.551384	+	0.834251i	$0.685900\pi$
$14$	7.38748	1.97439
$15$	0.504029	0.130140
$16$	−1.55890	−0.389726
$17$	−4.88714	−1.18531	−0.592653	−	0.805458i	$-0.701920\pi$
$17$	−4.88714	−1.18531	−0.592653	+	0.805458i	$0.701920\pi$
$18$	−2.20341	−0.519349
$19$	−2.88330	−0.661474	−0.330737	−	0.943723i	$-0.607297\pi$
$19$	−2.88330	−0.661474	−0.330737	+	0.943723i	$0.607297\pi$
$20$	−1.43901	−0.321773
$21$	3.35275	0.731629
$22$	−2.33440	−0.497696
$23$	−3.63705	−0.758377	−0.379188	−	0.925319i	$-0.623797\pi$
$23$	−3.63705	−0.758377	−0.379188	+	0.925319i	$0.623797\pi$
$24$	1.88396	0.384562
$25$	−4.74595	−0.949191
$26$	8.76096	1.71816
$27$	−1.00000	−0.192450
$28$	−9.57215	−1.80897
$29$	−0.102473	−0.0190287	−0.00951437	−	0.999955i	$-0.503029\pi$
$29$	−0.102473	−0.0190287	−0.00951437	+	0.999955i	$0.503029\pi$
$30$	−1.11058	−0.202764
$31$	3.68423	0.661706	0.330853	−	0.943682i	$-0.392664\pi$
$31$	3.68423	0.661706	0.330853	+	0.943682i	$0.392664\pi$
$32$	7.20282	1.27329
$33$	−1.05945	−0.184426
$34$	10.7684	1.84676
$35$	1.68988	0.285642
$36$	2.85502	0.475837
$37$	8.85222	1.45530	0.727648	−	0.685950i	$-0.240613\pi$
$37$	8.85222	1.45530	0.727648	+	0.685950i	$0.240613\pi$
$38$	6.35309	1.03061
$39$	3.97609	0.636684
$40$	0.949570	0.150140
$41$	9.04429	1.41248	0.706241	−	0.707972i	$-0.250390\pi$
$41$	9.04429	1.41248	0.706241	+	0.707972i	$0.250390\pi$
$42$	−7.38748	−1.13991
$43$	6.44418	0.982728	0.491364	−	0.870954i	$-0.336498\pi$
$43$	6.44418	0.982728	0.491364	+	0.870954i	$0.336498\pi$
$44$	3.02475	0.455998
$45$	−0.504029	−0.0751362
$46$	8.01391	1.18159
$47$	8.28920	1.20910	0.604552	−	0.796566i	$-0.293352\pi$
$47$	8.28920	1.20910	0.604552	+	0.796566i	$0.293352\pi$
$48$	1.55890	0.225008
$49$	4.24090	0.605843
$50$	10.4573	1.47888
$51$	4.88714	0.684337
$52$	−11.3518	−1.57421
$53$	−7.33259	−1.00721	−0.503605	−	0.863934i	$-0.667993\pi$
$53$	−7.33259	−1.00721	−0.503605	+	0.863934i	$0.667993\pi$
$54$	2.20341	0.299846
$55$	−0.533993	−0.0720036
$56$	6.31644	0.844069
$57$	2.88330	0.381902
$58$	0.225790	0.0296477
$59$	−7.83997	−1.02068	−0.510339	−	0.859974i	$-0.670480\pi$
$59$	−7.83997	−1.02068	−0.510339	+	0.859974i	$0.670480\pi$
$60$	1.43901	0.185776
$61$	0.0555462	0.00711196	0.00355598	−	0.999994i	$-0.498868\pi$
$61$	0.0555462	0.00711196	0.00355598	+	0.999994i	$0.498868\pi$
$62$	−8.11786	−1.03097
$63$	−3.35275	−0.422406
$64$	−12.7530	−1.59412
$65$	2.00406	0.248573
$66$	2.33440	0.287345
$67$	7.57174	0.925036	0.462518	−	0.886610i	$-0.346946\pi$
$67$	7.57174	0.925036	0.462518	+	0.886610i	$0.346946\pi$
$68$	−13.9529	−1.69204
$69$	3.63705	0.437849
$70$	−3.72350	−0.445043
$71$	15.2961	1.81531	0.907654	−	0.419719i	$-0.137871\pi$
$71$	15.2961	1.81531	0.907654	+	0.419719i	$0.137871\pi$
$72$	−1.88396	−0.222027
$73$	6.54789	0.766373	0.383186	−	0.923671i	$-0.374827\pi$
$73$	6.54789	0.766373	0.383186	+	0.923671i	$0.374827\pi$
$74$	−19.5051	−2.26742
$75$	4.74595	0.548016
$76$	−8.23187	−0.944260
$77$	−3.55206	−0.404795
$78$	−8.76096	−0.991983
$79$	0.672310	0.0756408	0.0378204	−	0.999285i	$-0.487959\pi$
$79$	0.672310	0.0756408	0.0378204	+	0.999285i	$0.487959\pi$
$80$	0.785732	0.0878475
$81$	1.00000	0.111111
$82$	−19.9283	−2.20071
$83$	−1.36416	−0.149736	−0.0748682	−	0.997193i	$-0.523854\pi$
$83$	−1.36416	−0.149736	−0.0748682	+	0.997193i	$0.523854\pi$
$84$	9.57215	1.04441
$85$	2.46326	0.267178
$86$	−14.1992	−1.53114
$87$	0.102473	0.0109862
$88$	−1.99596	−0.212770
$89$	1.35945	0.144101	0.0720505	−	0.997401i	$-0.477046\pi$
$89$	1.35945	0.144101	0.0720505	+	0.997401i	$0.477046\pi$
$90$	1.11058	0.117066
$91$	13.3308	1.39745
$92$	−10.3838	−1.08259
$93$	−3.68423	−0.382036
$94$	−18.2645	−1.88384
$95$	1.45327	0.149102
$96$	−7.20282	−0.735135
$97$	12.8151	1.30118	0.650589	−	0.759430i	$-0.274522\pi$
$97$	12.8151	1.30118	0.650589	+	0.759430i	$0.274522\pi$
$98$	−9.34445	−0.943932
$99$	1.05945	0.106479
$100$	−13.5498	−1.35498
$101$	−4.92004	−0.489562	−0.244781	−	0.969578i	$-0.578716\pi$
$101$	−4.92004	−0.489562	−0.244781	+	0.969578i	$0.578716\pi$
$102$	−10.7684	−1.06623
$103$	−11.4983	−1.13297	−0.566483	−	0.824074i	$-0.691696\pi$
$103$	−11.4983	−1.13297	−0.566483	+	0.824074i	$0.691696\pi$
$104$	7.49079	0.734532
$105$	−1.68988	−0.164915
$106$	16.1567	1.56928
$107$	−6.27725	−0.606845	−0.303423	−	0.952856i	$-0.598129\pi$
$107$	−6.27725	−0.606845	−0.303423	+	0.952856i	$0.598129\pi$
$108$	−2.85502	−0.274724
$109$	−14.7627	−1.41401	−0.707005	−	0.707208i	$-0.749954\pi$
$109$	−14.7627	−1.41401	−0.707005	+	0.707208i	$0.749954\pi$
$110$	1.17661	0.112185
$111$	−8.85222	−0.840216
$112$	5.22660	0.493867
$113$	−11.3162	−1.06453	−0.532267	−	0.846576i	$-0.678660\pi$
$113$	−11.3162	−1.06453	−0.532267	+	0.846576i	$0.678660\pi$
$114$	−6.35309	−0.595021
$115$	1.83318	0.170945
$116$	−0.292562	−0.0271637
$117$	−3.97609	−0.367590
$118$	17.2747	1.59026
$119$	16.3853	1.50204
$120$	−0.949570	−0.0866835
$121$	−9.87757	−0.897961
$122$	−0.122391	−0.0110808
$123$	−9.04429	−0.815497
$124$	10.5185	0.944592
$125$	4.91224	0.439364
$126$	7.38748	0.658129
$127$	2.09965	0.186314	0.0931568	−	0.995651i	$-0.470304\pi$
$127$	2.09965	0.186314	0.0931568	+	0.995651i	$0.470304\pi$
$128$	13.6944	1.21042
$129$	−6.44418	−0.567378
$130$	−4.41577	−0.387289
$131$	12.9058	1.12759	0.563793	−	0.825916i	$-0.309341\pi$
$131$	12.9058	1.12759	0.563793	+	0.825916i	$0.309341\pi$
$132$	−3.02475	−0.263271
$133$	9.66696	0.838232
$134$	−16.6837	−1.44125
$135$	0.504029	0.0433799
$136$	9.20718	0.789509
$137$	−8.10768	−0.692686	−0.346343	−	0.938108i	$-0.612577\pi$
$137$	−8.10768	−0.692686	−0.346343	+	0.938108i	$0.612577\pi$
$138$	−8.01391	−0.682189
$139$	17.6737	1.49907	0.749533	−	0.661967i	$-0.230278\pi$
$139$	17.6737	1.49907	0.749533	+	0.661967i	$0.230278\pi$
$140$	4.82464	0.407757
$141$	−8.28920	−0.698077
$142$	−33.7035	−2.82834
$143$	−4.21246	−0.352264
$144$	−1.55890	−0.129909
$145$	0.0516493	0.00428924
$146$	−14.4277	−1.19404
$147$	−4.24090	−0.349784
$148$	25.2733	2.07745
$149$	23.0845	1.89115	0.945576	−	0.325401i	$-0.105499\pi$
$149$	23.0845	1.89115	0.945576	+	0.325401i	$0.105499\pi$
$150$	−10.4573	−0.853834
$151$	7.04932	0.573666	0.286833	−	0.957981i	$-0.407398\pi$
$151$	7.04932	0.573666	0.286833	+	0.957981i	$0.407398\pi$
$152$	5.43202	0.440595
$153$	−4.88714	−0.395102
$154$	7.82665	0.630690
$155$	−1.85696	−0.149154
$156$	11.3518	0.908872
$157$	2.33627	0.186454	0.0932272	−	0.995645i	$-0.470282\pi$
$157$	2.33627	0.186454	0.0932272	+	0.995645i	$0.470282\pi$
$158$	−1.48138	−0.117852
$159$	7.33259	0.581512
$160$	−3.63043	−0.287011
$161$	12.1941	0.961029
$162$	−2.20341	−0.173116
$163$	15.1564	1.18714	0.593571	−	0.804782i	$-0.297718\pi$
$163$	15.1564	1.18714	0.593571	+	0.804782i	$0.297718\pi$
$164$	25.8216	2.01633
$165$	0.533993	0.0415713
$166$	3.00581	0.233296
$167$	−23.0248	−1.78172	−0.890858	−	0.454283i	$-0.849896\pi$
$167$	−23.0248	−1.78172	−0.890858	+	0.454283i	$0.849896\pi$
$168$	−6.31644	−0.487324
$169$	2.80928	0.216098
$170$	−5.42758	−0.416276
$171$	−2.88330	−0.220491
$172$	18.3983	1.40285
$173$	1.98555	0.150959	0.0754793	−	0.997147i	$-0.475951\pi$
$173$	1.98555	0.150959	0.0754793	+	0.997147i	$0.475951\pi$
$174$	−0.225790	−0.0171171
$175$	15.9120	1.20283
$176$	−1.65158	−0.124492
$177$	7.83997	0.589288
$178$	−2.99542	−0.224516
$179$	−7.61148	−0.568909	−0.284454	−	0.958690i	$-0.591812\pi$
$179$	−7.61148	−0.568909	−0.284454	+	0.958690i	$0.591812\pi$
$180$	−1.43901	−0.107258
$181$	24.5355	1.82371	0.911855	−	0.410513i	$-0.134650\pi$
$181$	24.5355	1.82371	0.911855	+	0.410513i	$0.134650\pi$
$182$	−29.3733	−2.17729
$183$	−0.0555462	−0.00410609
$184$	6.85205	0.505140
$185$	−4.46178	−0.328036
$186$	8.11786	0.595231
$187$	−5.17768	−0.378630
$188$	23.6658	1.72601
$189$	3.35275	0.243876
$190$	−3.20214	−0.232308
$191$	0.0232831	0.00168470	0.000842351	−	1.00000i	$-0.499732\pi$
$191$	0.0232831	0.00168470	0.000842351		1.00000i	$0.499732\pi$
$192$	12.7530	0.920366
$193$	9.23830	0.664988	0.332494	−	0.943105i	$-0.392110\pi$
$193$	9.23830	0.664988	0.332494	+	0.943105i	$0.392110\pi$
$194$	−28.2370	−2.02730
$195$	−2.00406	−0.143514
$196$	12.1079	0.864847
$197$	−18.2497	−1.30024	−0.650118	−	0.759833i	$-0.725280\pi$
$197$	−18.2497	−1.30024	−0.650118	+	0.759833i	$0.725280\pi$
$198$	−2.33440	−0.165899
$199$	−0.461043	−0.0326825	−0.0163412	−	0.999866i	$-0.505202\pi$
$199$	−0.461043	−0.0326825	−0.0163412	+	0.999866i	$0.505202\pi$
$200$	8.94119	0.632237
$201$	−7.57174	−0.534070
$202$	10.8409	0.762760
$203$	0.343565	0.0241136
$204$	13.9529	0.976898
$205$	−4.55859	−0.318385
$206$	25.3356	1.76521
$207$	−3.63705	−0.252792
$208$	6.19833	0.429777
$209$	−3.05471	−0.211299
$210$	3.72350	0.256946
$211$	7.97527	0.549040	0.274520	−	0.961581i	$-0.411481\pi$
$211$	7.97527	0.549040	0.274520	+	0.961581i	$0.411481\pi$
$212$	−20.9347	−1.43780
$213$	−15.2961	−1.04807
$214$	13.8314	0.945493
$215$	−3.24805	−0.221515
$216$	1.88396	0.128187
$217$	−12.3523	−0.838527
$218$	32.5283	2.20310
$219$	−6.54789	−0.442466
$220$	−1.52456	−0.102786
$221$	19.4317	1.30712
$222$	19.5051	1.30910
$223$	2.21917	0.148606	0.0743032	−	0.997236i	$-0.476327\pi$
$223$	2.21917	0.148606	0.0743032	+	0.997236i	$0.476327\pi$
$224$	−24.1492	−1.61354
$225$	−4.74595	−0.316397
$226$	24.9342	1.65860
$227$	−8.25597	−0.547968	−0.273984	−	0.961734i	$-0.588342\pi$
$227$	−8.25597	−0.547968	−0.273984	+	0.961734i	$0.588342\pi$
$228$	8.23187	0.545169
$229$	26.4098	1.74521	0.872605	−	0.488427i	$-0.162429\pi$
$229$	26.4098	1.74521	0.872605	+	0.488427i	$0.162429\pi$
$230$	−4.03924	−0.266340
$231$	3.55206	0.233709
$232$	0.193055	0.0126747
$233$	−20.5282	−1.34485	−0.672423	−	0.740167i	$-0.734747\pi$
$233$	−20.5282	−1.34485	−0.672423	+	0.740167i	$0.734747\pi$
$234$	8.76096	0.572722
$235$	−4.17800	−0.272542
$236$	−22.3833	−1.45703
$237$	−0.672310	−0.0436712
$238$	−36.1037	−2.34025
$239$	−11.8095	−0.763895	−0.381948	−	0.924184i	$-0.624747\pi$
$239$	−11.8095	−0.763895	−0.381948	+	0.924184i	$0.624747\pi$
$240$	−0.785732	−0.0507188
$241$	25.2773	1.62826	0.814128	−	0.580685i	$-0.197215\pi$
$241$	25.2773	1.62826	0.814128	+	0.580685i	$0.197215\pi$
$242$	21.7643	1.39906
$243$	−1.00000	−0.0641500
$244$	0.158585	0.0101524
$245$	−2.13754	−0.136562
$246$	19.9283	1.27058
$247$	11.4642	0.729453
$248$	−6.94093	−0.440750
$249$	1.36416	0.0864504
$250$	−10.8237	−0.684550
$251$	−16.7012	−1.05417	−0.527085	−	0.849813i	$-0.676715\pi$
$251$	−16.7012	−1.05417	−0.527085	+	0.849813i	$0.676715\pi$
$252$	−9.57215	−0.602989
$253$	−3.85327	−0.242253
$254$	−4.62639	−0.290285
$255$	−2.46326	−0.154255
$256$	−4.66843	−0.291777
$257$	28.0381	1.74897	0.874483	−	0.485055i	$-0.161201\pi$
$257$	28.0381	1.74897	0.874483	+	0.485055i	$0.161201\pi$
$258$	14.1992	0.884002
$259$	−29.6793	−1.84418
$260$	5.72164	0.354841
$261$	−0.102473	−0.00634291
$262$	−28.4368	−1.75683
$263$	−1.98299	−0.122276	−0.0611381	−	0.998129i	$-0.519473\pi$
$263$	−1.98299	−0.122276	−0.0611381	+	0.998129i	$0.519473\pi$
$264$	1.99596	0.122843
$265$	3.69584	0.227034
$266$	−21.3003	−1.30600
$267$	−1.35945	−0.0831967
$268$	21.6175	1.32050
$269$	−15.8491	−0.966339	−0.483170	−	0.875527i	$-0.660515\pi$
$269$	−15.8491	−0.966339	−0.483170	+	0.875527i	$0.660515\pi$
$270$	−1.11058	−0.0675879
$271$	−14.4347	−0.876846	−0.438423	−	0.898769i	$-0.644463\pi$
$271$	−14.4347	−0.876846	−0.438423	+	0.898769i	$0.644463\pi$
$272$	7.61858	0.461944
$273$	−13.3308	−0.806817
$274$	17.8646	1.07924
$275$	−5.02810	−0.303206
$276$	10.3838	0.625034
$277$	6.48601	0.389707	0.194853	−	0.980832i	$-0.437577\pi$
$277$	6.48601	0.389707	0.194853	+	0.980832i	$0.437577\pi$
$278$	−38.9425	−2.33561
$279$	3.68423	0.220569
$280$	−3.18367	−0.190260
$281$	18.0800	1.07856	0.539282	−	0.842125i	$-0.318696\pi$
$281$	18.0800	1.07856	0.539282	+	0.842125i	$0.318696\pi$
$282$	18.2645	1.08764
$283$	−22.1215	−1.31499	−0.657493	−	0.753460i	$-0.728383\pi$
$283$	−22.1215	−1.31499	−0.657493	+	0.753460i	$0.728383\pi$
$284$	43.6706	2.59137
$285$	−1.45327	−0.0860840
$286$	9.28179	0.548844
$287$	−30.3232	−1.78992
$288$	7.20282	0.424430
$289$	6.88418	0.404952
$290$	−0.113805	−0.00668284
$291$	−12.8151	−0.751235
$292$	18.6944	1.09400
$293$	−26.7255	−1.56132	−0.780661	−	0.624955i	$-0.785117\pi$
$293$	−26.7255	−1.56132	−0.780661	+	0.624955i	$0.785117\pi$
$294$	9.34445	0.544979
$295$	3.95157	0.230069
$296$	−16.6772	−0.969345
$297$	−1.05945	−0.0614755
$298$	−50.8645	−2.94650
$299$	14.4612	0.836314
$300$	13.5498	0.782298
$301$	−21.6057	−1.24533
$302$	−15.5326	−0.893798
$303$	4.92004	0.282649
$304$	4.49478	0.257793
$305$	−0.0279969	−0.00160310
$306$	10.7684	0.615588
$307$	−25.3945	−1.44934	−0.724669	−	0.689097i	$-0.758008\pi$
$307$	−25.3945	−1.44934	−0.724669	+	0.689097i	$0.758008\pi$
$308$	−10.1412	−0.577849
$309$	11.4983	0.654118
$310$	4.09164	0.232389
$311$	−6.78536	−0.384762	−0.192381	−	0.981320i	$-0.561621\pi$
$311$	−6.78536	−0.384762	−0.192381	+	0.981320i	$0.561621\pi$
$312$	−7.49079	−0.424082
$313$	−0.0695236	−0.00392970	−0.00196485	−	0.999998i	$-0.500625\pi$
$313$	−0.0695236	−0.00392970	−0.00196485	+	0.999998i	$0.500625\pi$
$314$	−5.14776	−0.290505
$315$	1.68988	0.0952140
$316$	1.91946	0.107978
$317$	−0.515794	−0.0289699	−0.0144849	−	0.999895i	$-0.504611\pi$
$317$	−0.515794	−0.0289699	−0.0144849	+	0.999895i	$0.504611\pi$
$318$	−16.1567	−0.906024
$319$	−0.108565	−0.00607846
$320$	6.42786	0.359329
$321$	6.27725	0.350362
$322$	−26.8686	−1.49733
$323$	14.0911	0.784049
$324$	2.85502	0.158612
$325$	18.8703	1.04674
$326$	−33.3958	−1.84962
$327$	14.7627	0.816380
$328$	−17.0391	−0.940826
$329$	−27.7916	−1.53220
$330$	−1.17661	−0.0647700
$331$	−12.6921	−0.697619	−0.348810	−	0.937194i	$-0.613414\pi$
$331$	−12.6921	−0.697619	−0.348810	+	0.937194i	$0.613414\pi$
$332$	−3.89471	−0.213750
$333$	8.85222	0.485099
$334$	50.7332	2.77600
$335$	−3.81638	−0.208511
$336$	−5.22660	−0.285134
$337$	8.72249	0.475144	0.237572	−	0.971370i	$-0.423648\pi$
$337$	8.72249	0.475144	0.237572	+	0.971370i	$0.423648\pi$
$338$	−6.19000	−0.336691
$339$	11.3162	0.614609
$340$	7.03266	0.381400
$341$	3.90325	0.211373
$342$	6.35309	0.343536
$343$	9.25056	0.499483
$344$	−12.1406	−0.654576
$345$	−1.83318	−0.0986949
$346$	−4.37498	−0.235201
$347$	−14.9066	−0.800229	−0.400114	−	0.916465i	$-0.631030\pi$
$347$	−14.9066	−0.800229	−0.400114	+	0.916465i	$0.631030\pi$
$348$	0.292562	0.0156830
$349$	34.7926	1.86241	0.931203	−	0.364500i	$-0.118760\pi$
$349$	34.7926	1.86241	0.931203	+	0.364500i	$0.118760\pi$
$350$	−35.0606	−1.87407
$351$	3.97609	0.212228
$352$	7.63102	0.406735
$353$	−8.02470	−0.427112	−0.213556	−	0.976931i	$-0.568505\pi$
$353$	−8.02470	−0.427112	−0.213556	+	0.976931i	$0.568505\pi$
$354$	−17.2747	−0.918139
$355$	−7.70966	−0.409186
$356$	3.88124	0.205706
$357$	−16.3853	−0.867205
$358$	16.7712	0.886387
$359$	−7.38095	−0.389552	−0.194776	−	0.980848i	$-0.562398\pi$
$359$	−7.38095	−0.389552	−0.194776	+	0.980848i	$0.562398\pi$
$360$	0.949570	0.0500467
$361$	−10.6866	−0.562452
$362$	−54.0618	−2.84142
$363$	9.87757	0.518438
$364$	38.0597	1.99487
$365$	−3.30033	−0.172747
$366$	0.122391	0.00639748
$367$	−1.85716	−0.0969430	−0.0484715	−	0.998825i	$-0.515435\pi$
$367$	−1.85716	−0.0969430	−0.0484715	+	0.998825i	$0.515435\pi$
$368$	5.66980	0.295559
$369$	9.04429	0.470827
$370$	9.83113	0.511096
$371$	24.5843	1.27635
$372$	−10.5185	−0.545361
$373$	−22.1439	−1.14657	−0.573284	−	0.819357i	$-0.694331\pi$
$373$	−22.1439	−1.14657	−0.573284	+	0.819357i	$0.694331\pi$
$374$	11.4086	0.589923
$375$	−4.91224	−0.253667
$376$	−15.6165	−0.805361
$377$	0.407441	0.0209843
$378$	−7.38748	−0.379971
$379$	1.24219	0.0638069	0.0319034	−	0.999491i	$-0.489843\pi$
$379$	1.24219	0.0638069	0.0319034	+	0.999491i	$0.489843\pi$
$380$	4.14910	0.212844
$381$	−2.09965	−0.107568
$382$	−0.0513021	−0.00262485
$383$	−3.58442	−0.183155	−0.0915777	−	0.995798i	$-0.529191\pi$
$383$	−3.58442	−0.183155	−0.0915777	+	0.995798i	$0.529191\pi$
$384$	−13.6944	−0.698839
$385$	1.79034	0.0912443
$386$	−20.3558	−1.03608
$387$	6.44418	0.327576
$388$	36.5874	1.85744
$389$	21.3099	1.08045	0.540227	−	0.841519i	$-0.318338\pi$
$389$	21.3099	1.08045	0.540227	+	0.841519i	$0.318338\pi$
$390$	4.41577	0.223601
$391$	17.7748	0.898909
$392$	−7.98969	−0.403540
$393$	−12.9058	−0.651013
$394$	40.2115	2.02583
$395$	−0.338864	−0.0170501
$396$	3.02475	0.151999
$397$	10.5813	0.531059	0.265530	−	0.964103i	$-0.414453\pi$
$397$	10.5813	0.531059	0.265530	+	0.964103i	$0.414453\pi$
$398$	1.01587	0.0509208
$399$	−9.66696	−0.483953
$400$	7.39848	0.369924
$401$	−4.22983	−0.211228	−0.105614	−	0.994407i	$-0.533681\pi$
$401$	−4.22983	−0.211228	−0.105614	+	0.994407i	$0.533681\pi$
$402$	16.6837	0.832105
$403$	−14.6488	−0.729709
$404$	−14.0468	−0.698854
$405$	−0.504029	−0.0250454
$406$	−0.757016	−0.0375701
$407$	9.37848	0.464874
$408$	−9.20718	−0.455823
$409$	−12.2151	−0.603997	−0.301999	−	0.953308i	$-0.597654\pi$
$409$	−12.2151	−0.603997	−0.301999	+	0.953308i	$0.597654\pi$
$410$	10.0444	0.496059
$411$	8.10768	0.399922
$412$	−32.8280	−1.61732
$413$	26.2854	1.29342
$414$	8.01391	0.393862
$415$	0.687578	0.0337519
$416$	−28.6391	−1.40415
$417$	−17.6737	−0.865486
$418$	6.73078	0.329213
$419$	28.5979	1.39710	0.698549	−	0.715562i	$-0.253829\pi$
$419$	28.5979	1.39710	0.698549	+	0.715562i	$0.253829\pi$
$420$	−4.82464	−0.235418
$421$	−13.5829	−0.661991	−0.330995	−	0.943632i	$-0.607384\pi$
$421$	−13.5829	−0.661991	−0.330995	+	0.943632i	$0.607384\pi$
$422$	−17.5728	−0.855430
$423$	8.28920	0.403035
$424$	13.8143	0.670882
$425$	23.1942	1.12508
$426$	33.7035	1.63294
$427$	−0.186232	−0.00901241
$428$	−17.9217	−0.866277
$429$	4.21246	0.203380
$430$	7.15679	0.345131
$431$	33.0674	1.59280	0.796400	−	0.604770i	$-0.206735\pi$
$431$	33.0674	1.59280	0.796400	+	0.604770i	$0.206735\pi$
$432$	1.55890	0.0750027
$433$	10.3763	0.498655	0.249327	−	0.968419i	$-0.419790\pi$
$433$	10.3763	0.498655	0.249327	+	0.968419i	$0.419790\pi$
$434$	27.2171	1.30646
$435$	−0.0516493	−0.00247639
$436$	−42.1478	−2.01851
$437$	10.4867	0.501646
$438$	14.4277	0.689382
$439$	4.42521	0.211204	0.105602	−	0.994408i	$-0.466323\pi$
$439$	4.42521	0.211204	0.105602	+	0.994408i	$0.466323\pi$
$440$	1.00602	0.0479602
$441$	4.24090	0.201948
$442$	−42.8161	−2.03655
$443$	7.89951	0.375317	0.187658	−	0.982234i	$-0.439910\pi$
$443$	7.89951	0.375317	0.187658	+	0.982234i	$0.439910\pi$
$444$	−25.2733	−1.19942
$445$	−0.685200	−0.0324816
$446$	−4.88974	−0.231536
$447$	−23.0845	−1.09186
$448$	42.7575	2.02010
$449$	11.1314	0.525324	0.262662	−	0.964888i	$-0.415400\pi$
$449$	11.1314	0.525324	0.262662	+	0.964888i	$0.415400\pi$
$450$	10.4573	0.492961
$451$	9.58197	0.451197
$452$	−32.3079	−1.51963
$453$	−7.04932	−0.331206
$454$	18.1913	0.853760
$455$	−6.71911	−0.314997
$456$	−5.43202	−0.254377
$457$	39.2864	1.83774	0.918869	−	0.394562i	$-0.129104\pi$
$457$	39.2864	1.83774	0.918869	+	0.394562i	$0.129104\pi$
$458$	−58.1917	−2.71912
$459$	4.88714	0.228112
$460$	5.23376	0.244025
$461$	19.6929	0.917192	0.458596	−	0.888645i	$-0.348353\pi$
$461$	19.6929	0.917192	0.458596	+	0.888645i	$0.348353\pi$
$462$	−7.82665	−0.364129
$463$	13.5531	0.629864	0.314932	−	0.949114i	$-0.398018\pi$
$463$	13.5531	0.629864	0.314932	+	0.949114i	$0.398018\pi$
$464$	0.159745	0.00741598
$465$	1.85696	0.0861143
$466$	45.2320	2.09533
$467$	−26.6904	−1.23509	−0.617543	−	0.786537i	$-0.711872\pi$
$467$	−26.6904	−1.23509	−0.617543	+	0.786537i	$0.711872\pi$
$468$	−11.3518	−0.524738
$469$	−25.3861	−1.17222
$470$	9.20584	0.424634
$471$	−2.33627	−0.107649
$472$	14.7702	0.679853
$473$	6.82728	0.313919
$474$	1.48138	0.0680418
$475$	13.6840	0.627865
$476$	46.7805	2.14418
$477$	−7.33259	−0.335736
$478$	26.0213	1.19018
$479$	11.8043	0.539353	0.269676	−	0.962951i	$-0.413083\pi$
$479$	11.8043	0.539353	0.269676	+	0.962951i	$0.413083\pi$
$480$	3.63043	0.165706
$481$	−35.1972	−1.60486
$482$	−55.6964	−2.53690
$483$	−12.1941	−0.554850
$484$	−28.2006	−1.28185
$485$	−6.45919	−0.293297
$486$	2.20341	0.0999487
$487$	13.9568	0.632445	0.316222	−	0.948685i	$-0.397585\pi$
$487$	13.9568	0.632445	0.316222	+	0.948685i	$0.397585\pi$
$488$	−0.104647	−0.00473714
$489$	−15.1564	−0.685397
$490$	4.70987	0.212770
$491$	−3.67396	−0.165804	−0.0829018	−	0.996558i	$-0.526419\pi$
$491$	−3.67396	−0.165804	−0.0829018	+	0.996558i	$0.526419\pi$
$492$	−25.8216	−1.16413
$493$	0.500800	0.0225549
$494$	−25.2604	−1.13652
$495$	−0.533993	−0.0240012
$496$	−5.74335	−0.257884
$497$	−51.2838	−2.30039
$498$	−3.00581	−0.134694
$499$	24.9891	1.11866	0.559332	−	0.828944i	$-0.311058\pi$
$499$	24.9891	1.11866	0.559332	+	0.828944i	$0.311058\pi$
$500$	14.0245	0.627197
$501$	23.0248	1.02867
$502$	36.7996	1.64245
$503$	−26.7466	−1.19257	−0.596286	−	0.802772i	$-0.703357\pi$
$503$	−26.7466	−1.19257	−0.596286	+	0.802772i	$0.703357\pi$
$504$	6.31644	0.281356
$505$	2.47984	0.110351
$506$	8.49033	0.377441
$507$	−2.80928	−0.124764
$508$	5.99454	0.265965
$509$	−22.2353	−0.985562	−0.492781	−	0.870153i	$-0.664020\pi$
$509$	−22.2353	−0.985562	−0.492781	+	0.870153i	$0.664020\pi$
$510$	5.42758	0.240337
$511$	−21.9534	−0.971162
$512$	−17.1023	−0.755822
$513$	2.88330	0.127301
$514$	−61.7794	−2.72497
$515$	5.79550	0.255380
$516$	−18.3983	−0.809938
$517$	8.78199	0.386231
$518$	65.3956	2.87332
$519$	−1.98555	−0.0871560
$520$	−3.77557	−0.165570
$521$	0.284124	0.0124477	0.00622385	−	0.999981i	$-0.498019\pi$
$521$	0.284124	0.0124477	0.00622385	+	0.999981i	$0.498019\pi$
$522$	0.225790	0.00988255
$523$	−26.1378	−1.14293	−0.571463	−	0.820628i	$-0.693624\pi$
$523$	−26.1378	−1.14293	−0.571463	+	0.820628i	$0.693624\pi$
$524$	36.8464	1.60964
$525$	−15.9120	−0.694456
$526$	4.36934	0.190512
$527$	−18.0053	−0.784325
$528$	1.65158	0.0718757
$529$	−9.77189	−0.424865
$530$	−8.14345	−0.353729
$531$	−7.83997	−0.340226
$532$	27.5994	1.19658
$533$	−35.9609	−1.55764
$534$	2.99542	0.129624
$535$	3.16392	0.136788
$536$	−14.2649	−0.616148
$537$	7.61148	0.328460
$538$	34.9222	1.50560
$539$	4.49302	0.193528
$540$	1.43901	0.0619252
$541$	33.8156	1.45385	0.726924	−	0.686718i	$-0.240949\pi$
$541$	33.8156	1.45385	0.726924	+	0.686718i	$0.240949\pi$
$542$	31.8056	1.36617
$543$	−24.5355	−1.05292
$544$	−35.2012	−1.50924
$545$	7.44083	0.318730
$546$	29.3733	1.25706
$547$	−9.31560	−0.398306	−0.199153	−	0.979968i	$-0.563819\pi$
$547$	−9.31560	−0.398306	−0.199153	+	0.979968i	$0.563819\pi$
$548$	−23.1476	−0.988816
$549$	0.0555462	0.00237065
$550$	11.0790	0.472409
$551$	0.295460	0.0125870
$552$	−6.85205	−0.291643
$553$	−2.25408	−0.0958534
$554$	−14.2913	−0.607181
$555$	4.46178	0.189392
$556$	50.4588	2.13993
$557$	11.6734	0.494620	0.247310	−	0.968936i	$-0.420453\pi$
$557$	11.6734	0.494620	0.247310	+	0.968936i	$0.420453\pi$
$558$	−8.11786	−0.343657
$559$	−25.6226	−1.08372
$560$	−2.63436	−0.111322
$561$	5.17768	0.218602
$562$	−39.8377	−1.68045
$563$	−5.29239	−0.223048	−0.111524	−	0.993762i	$-0.535573\pi$
$563$	−5.29239	−0.223048	−0.111524	+	0.993762i	$0.535573\pi$
$564$	−23.6658	−0.996511
$565$	5.70367	0.239955
$566$	48.7428	2.04881
$567$	−3.35275	−0.140802
$568$	−28.8172	−1.20914
$569$	−22.1981	−0.930595	−0.465297	−	0.885154i	$-0.654053\pi$
$569$	−22.1981	−0.930595	−0.465297	+	0.885154i	$0.654053\pi$
$570$	3.20214	0.134123
$571$	−12.2848	−0.514102	−0.257051	−	0.966398i	$-0.582751\pi$
$571$	−12.2848	−0.514102	−0.257051	+	0.966398i	$0.582751\pi$
$572$	−12.0267	−0.502860
$573$	−0.0232831	−0.000972664 0
$574$	66.8145	2.78878
$575$	17.2613	0.719844
$576$	−12.7530	−0.531374
$577$	32.1466	1.33828	0.669140	−	0.743136i	$-0.266663\pi$
$577$	32.1466	1.33828	0.669140	+	0.743136i	$0.266663\pi$
$578$	−15.1687	−0.630934
$579$	−9.23830	−0.383931
$580$	0.147460	0.00612293
$581$	4.57369	0.189749
$582$	28.2370	1.17046
$583$	−7.76851	−0.321739
$584$	−12.3360	−0.510466
$585$	2.00406	0.0828578
$586$	58.8873	2.43261
$587$	−17.1158	−0.706446	−0.353223	−	0.935539i	$-0.614914\pi$
$587$	−17.1158	−0.706446	−0.353223	+	0.935539i	$0.614914\pi$
$588$	−12.1079	−0.499319
$589$	−10.6227	−0.437701
$590$	−8.70693	−0.358459
$591$	18.2497	0.750691
$592$	−13.7998	−0.567166
$593$	−25.2353	−1.03629	−0.518144	−	0.855293i	$-0.673377\pi$
$593$	−25.2353	−1.03629	−0.518144	+	0.855293i	$0.673377\pi$
$594$	2.33440	0.0957817
$595$	−8.25869	−0.338573
$596$	65.9066	2.69964
$597$	0.461043	0.0188692
$598$	−31.8640	−1.30302
$599$	22.9921	0.939431	0.469715	−	0.882818i	$-0.344357\pi$
$599$	22.9921	0.939431	0.469715	+	0.882818i	$0.344357\pi$
$600$	−8.94119	−0.365022
$601$	−34.7355	−1.41689	−0.708444	−	0.705767i	$-0.750603\pi$
$601$	−34.7355	−1.41689	−0.708444	+	0.705767i	$0.750603\pi$
$602$	47.6062	1.94028
$603$	7.57174	0.308345
$604$	20.1260	0.818914
$605$	4.97858	0.202408
$606$	−10.8409	−0.440380
$607$	45.2027	1.83472	0.917361	−	0.398055i	$-0.130315\pi$
$607$	45.2027	1.83472	0.917361	+	0.398055i	$0.130315\pi$
$608$	−20.7679	−0.842249
$609$	−0.343565	−0.0139220
$610$	0.0616886	0.00249770
$611$	−32.9586	−1.33336
$612$	−13.9529	−0.564012
$613$	−48.7354	−1.96841	−0.984203	−	0.177044i	$-0.943346\pi$
$613$	−48.7354	−1.96841	−0.984203	+	0.177044i	$0.943346\pi$
$614$	55.9544	2.25814
$615$	4.55859	0.183820
$616$	6.69194	0.269626
$617$	−24.3814	−0.981559	−0.490779	−	0.871284i	$-0.663288\pi$
$617$	−24.3814	−0.981559	−0.490779	+	0.871284i	$0.663288\pi$
$618$	−25.3356	−1.01915
$619$	−3.15057	−0.126632	−0.0633160	−	0.997994i	$-0.520168\pi$
$619$	−3.15057	−0.126632	−0.0633160	+	0.997994i	$0.520168\pi$
$620$	−5.30165	−0.212919
$621$	3.63705	0.145950
$622$	14.9509	0.599478
$623$	−4.55788	−0.182607
$624$	−6.19833	−0.248132
$625$	21.2539	0.850155
$626$	0.153189	0.00612266
$627$	3.05471	0.121993
$628$	6.67009	0.266165
$629$	−43.2621	−1.72497
$630$	−3.72350	−0.148348
$631$	−39.9025	−1.58850	−0.794248	−	0.607594i	$-0.792135\pi$
$631$	−39.9025	−1.58850	−0.794248	+	0.607594i	$0.792135\pi$
$632$	−1.26661	−0.0503829
$633$	−7.97527	−0.316988
$634$	1.13651	0.0451364
$635$	−1.05828	−0.0419967
$636$	20.9347	0.830115
$637$	−16.8622	−0.668105
$638$	0.239213	0.00947053
$639$	15.2961	0.605103
$640$	−6.90237	−0.272840
$641$	23.2008	0.916377	0.458189	−	0.888855i	$-0.348498\pi$
$641$	23.2008	0.916377	0.458189	+	0.888855i	$0.348498\pi$
$642$	−13.8314	−0.545881
$643$	−34.6174	−1.36518	−0.682589	−	0.730802i	$-0.739146\pi$
$643$	−34.6174	−1.36518	−0.682589	+	0.730802i	$0.739146\pi$
$644$	34.8144	1.37188
$645$	3.24805	0.127892
$646$	−31.0485	−1.22159
$647$	22.7478	0.894310	0.447155	−	0.894457i	$-0.352437\pi$
$647$	22.7478	0.894310	0.447155	+	0.894457i	$0.352437\pi$
$648$	−1.88396	−0.0740089
$649$	−8.30605	−0.326041
$650$	−41.5791	−1.63087
$651$	12.3523	0.484124
$652$	43.2718	1.69466
$653$	−19.1298	−0.748606	−0.374303	−	0.927306i	$-0.622118\pi$
$653$	−19.1298	−0.748606	−0.374303	+	0.927306i	$0.622118\pi$
$654$	−32.5283	−1.27196
$655$	−6.50491	−0.254168
$656$	−14.0992	−0.550480
$657$	6.54789	0.255458
$658$	61.2363	2.38724
$659$	−17.5322	−0.682956	−0.341478	−	0.939890i	$-0.610928\pi$
$659$	−17.5322	−0.682956	−0.341478	+	0.939890i	$0.610928\pi$
$660$	1.52456	0.0593434
$661$	−32.2506	−1.25440	−0.627202	−	0.778856i	$-0.715800\pi$
$661$	−32.2506	−1.25440	−0.627202	+	0.778856i	$0.715800\pi$
$662$	27.9658	1.08692
$663$	−19.4317	−0.754665
$664$	2.57003	0.0997365
$665$	−4.87243	−0.188945
$666$	−19.5051	−0.755807
$667$	0.372699	0.0144310
$668$	−65.7364	−2.54342
$669$	−2.21917	−0.0857979
$670$	8.40905	0.324870
$671$	0.0588484	0.00227182
$672$	24.1492	0.931577
$673$	−13.2936	−0.512430	−0.256215	−	0.966620i	$-0.582476\pi$
$673$	−13.2936	−0.512430	−0.256215	+	0.966620i	$0.582476\pi$
$674$	−19.2192	−0.740297
$675$	4.74595	0.182672
$676$	8.02055	0.308483
$677$	26.9698	1.03654	0.518268	−	0.855218i	$-0.326577\pi$
$677$	26.9698	1.03654	0.518268	+	0.855218i	$0.326577\pi$
$678$	−24.9342	−0.957590
$679$	−42.9658	−1.64888
$680$	−4.64069	−0.177962
$681$	8.25597	0.316369
$682$	−8.60046	−0.329329
$683$	−39.9696	−1.52939	−0.764697	−	0.644390i	$-0.777111\pi$
$683$	−39.9696	−1.52939	−0.764697	+	0.644390i	$0.777111\pi$
$684$	−8.23187	−0.314753
$685$	4.08651	0.156137
$686$	−20.3828	−0.778218
$687$	−26.4098	−1.00760
$688$	−10.0458	−0.382994
$689$	29.1550	1.11072
$690$	4.03924	0.153771
$691$	15.1312	0.575619	0.287810	−	0.957688i	$-0.407073\pi$
$691$	15.1312	0.575619	0.287810	+	0.957688i	$0.407073\pi$
$692$	5.66878	0.215495
$693$	−3.55206	−0.134932
$694$	32.8454	1.24679
$695$	−8.90806	−0.337902
$696$	−0.193055	−0.00731772
$697$	−44.2008	−1.67422
$698$	−76.6625	−2.90172
$699$	20.5282	0.776448
$700$	45.4290	1.71706
$701$	−37.0504	−1.39937	−0.699687	−	0.714450i	$-0.746677\pi$
$701$	−37.0504	−1.39937	−0.699687	+	0.714450i	$0.746677\pi$
$702$	−8.76096	−0.330661
$703$	−25.5236	−0.962641
$704$	−13.5111	−0.509220
$705$	4.17800	0.157352
$706$	17.6817	0.665460
$707$	16.4956	0.620382
$708$	22.3833	0.841215
$709$	29.6990	1.11537	0.557684	−	0.830053i	$-0.311690\pi$
$709$	29.6990	1.11537	0.557684	+	0.830053i	$0.311690\pi$
$710$	16.9875	0.637531
$711$	0.672310	0.0252136
$712$	−2.56114	−0.0959828
$713$	−13.3997	−0.501823
$714$	36.1037	1.35115
$715$	2.12320	0.0794033
$716$	−21.7309	−0.812123
$717$	11.8095	0.441035
$718$	16.2633	0.606940
$719$	27.9513	1.04241	0.521204	−	0.853432i	$-0.325483\pi$
$719$	27.9513	1.04241	0.521204	+	0.853432i	$0.325483\pi$
$720$	0.785732	0.0292825
$721$	38.5510	1.43571
$722$	23.5470	0.876327
$723$	−25.2773	−0.940074
$724$	70.0493	2.60336
$725$	0.486332	0.0180619
$726$	−21.7643	−0.807750
$727$	−30.3151	−1.12432	−0.562162	−	0.827027i	$-0.690030\pi$
$727$	−30.3151	−1.12432	−0.562162	+	0.827027i	$0.690030\pi$
$728$	−25.1147	−0.930813
$729$	1.00000	0.0370370
$730$	7.27198	0.269148
$731$	−31.4936	−1.16483
$732$	−0.158585	−0.00586149
$733$	3.15961	0.116703	0.0583514	−	0.998296i	$-0.481416\pi$
$733$	3.15961	0.116703	0.0583514	+	0.998296i	$0.481416\pi$
$734$	4.09209	0.151042
$735$	2.13754	0.0788442
$736$	−26.1970	−0.965634
$737$	8.02188	0.295490
$738$	−19.9283	−0.733571
$739$	−35.2549	−1.29687	−0.648436	−	0.761270i	$-0.724576\pi$
$739$	−35.2549	−1.29687	−0.648436	+	0.761270i	$0.724576\pi$
$740$	−12.7385	−0.468275
$741$	−11.4642	−0.421150
$742$	−54.1693	−1.98862
$743$	13.2878	0.487483	0.243741	−	0.969840i	$-0.421625\pi$
$743$	13.2878	0.487483	0.243741	+	0.969840i	$0.421625\pi$
$744$	6.94093	0.254467
$745$	−11.6352	−0.426282
$746$	48.7921	1.78641
$747$	−1.36416	−0.0499121
$748$	−14.7824	−0.540497
$749$	21.0460	0.769005
$750$	10.8237	0.395225
$751$	−37.0471	−1.35187	−0.675934	−	0.736963i	$-0.736259\pi$
$751$	−37.0471	−1.35187	−0.675934	+	0.736963i	$0.736259\pi$
$752$	−12.9221	−0.471219
$753$	16.7012	0.608625
$754$	−0.897760	−0.0326945
$755$	−3.55306	−0.129309
$756$	9.57215	0.348136
$757$	−6.32288	−0.229809	−0.114904	−	0.993377i	$-0.536656\pi$
$757$	−6.32288	−0.229809	−0.114904	+	0.993377i	$0.536656\pi$
$758$	−2.73705	−0.0994141
$759$	3.85327	0.139865
$760$	−2.73789	−0.0993138
$761$	17.7896	0.644872	0.322436	−	0.946591i	$-0.395498\pi$
$761$	17.7896	0.644872	0.322436	+	0.946591i	$0.395498\pi$
$762$	4.62639	0.167596
$763$	49.4956	1.79186
$764$	0.0664736	0.00240493
$765$	2.46326	0.0890594
$766$	7.89796	0.285365
$767$	31.1724	1.12557
$768$	4.66843	0.168458
$769$	3.40628	0.122834	0.0614168	−	0.998112i	$-0.480438\pi$
$769$	3.40628	0.122834	0.0614168	+	0.998112i	$0.480438\pi$
$770$	−3.94486	−0.142163
$771$	−28.0381	−1.00977
$772$	26.3755	0.949276
$773$	−21.7917	−0.783795	−0.391897	−	0.920009i	$-0.628181\pi$
$773$	−21.7917	−0.783795	−0.391897	+	0.920009i	$0.628181\pi$
$774$	−14.1992	−0.510379
$775$	−17.4852	−0.628086
$776$	−24.1432	−0.866689
$777$	29.6793	1.06474
$778$	−46.9545	−1.68340
$779$	−26.0774	−0.934320
$780$	−5.72164	−0.204868
$781$	16.2054	0.579875
$782$	−39.1651	−1.40054
$783$	0.102473	0.00366208
$784$	−6.61115	−0.236112
$785$	−1.17755	−0.0420284
$786$	28.4368	1.01431
$787$	26.2746	0.936588	0.468294	−	0.883573i	$-0.344869\pi$
$787$	26.2746	0.936588	0.468294	+	0.883573i	$0.344869\pi$
$788$	−52.1032	−1.85610
$789$	1.98299	0.0705962
$790$	0.746656	0.0265648
$791$	37.9402	1.34900
$792$	−1.99596	−0.0709233
$793$	−0.220857	−0.00784285
$794$	−23.3149	−0.827415
$795$	−3.69584	−0.131078
$796$	−1.31629	−0.0466545
$797$	18.4027	0.651855	0.325928	−	0.945395i	$-0.394323\pi$
$797$	18.4027	0.651855	0.325928	+	0.945395i	$0.394323\pi$
$798$	21.3003	0.754022
$799$	−40.5105	−1.43316
$800$	−34.1843	−1.20860
$801$	1.35945	0.0480337
$802$	9.32005	0.329103
$803$	6.93716	0.244807
$804$	−21.6175	−0.762390
$805$	−6.14617	−0.216624
$806$	32.2773	1.13692
$807$	15.8491	0.557916
$808$	9.26915	0.326088
$809$	−28.8581	−1.01460	−0.507298	−	0.861771i	$-0.669356\pi$
$809$	−28.8581	−1.01460	−0.507298	+	0.861771i	$0.669356\pi$
$810$	1.11058	0.0390219
$811$	32.9004	1.15529	0.577645	−	0.816288i	$-0.303972\pi$
$811$	32.9004	1.15529	0.577645	+	0.816288i	$0.303972\pi$
$812$	0.980886	0.0344224
$813$	14.4347	0.506247
$814$	−20.6647	−0.724296
$815$	−7.63927	−0.267592
$816$	−7.61858	−0.266704
$817$	−18.5805	−0.650049
$818$	26.9149	0.941056
$819$	13.3308	0.465816
$820$	−13.0149	−0.454498
$821$	4.89153	0.170716	0.0853578	−	0.996350i	$-0.472797\pi$
$821$	4.89153	0.170716	0.0853578	+	0.996350i	$0.472797\pi$
$822$	−17.8646	−0.623098
$823$	−43.1185	−1.50302	−0.751508	−	0.659723i	$-0.770673\pi$
$823$	−43.1185	−1.50302	−0.751508	+	0.659723i	$0.770673\pi$
$824$	21.6624	0.754646
$825$	5.02810	0.175056
$826$	−57.9176	−2.01521
$827$	−13.8240	−0.480707	−0.240353	−	0.970685i	$-0.577263\pi$
$827$	−13.8240	−0.480707	−0.240353	+	0.970685i	$0.577263\pi$
$828$	−10.3838	−0.360863
$829$	44.7191	1.55316	0.776580	−	0.630019i	$-0.216953\pi$
$829$	44.7191	1.55316	0.776580	+	0.630019i	$0.216953\pi$
$830$	−1.51502	−0.0525870
$831$	−6.48601	−0.224997
$832$	50.7069	1.75795
$833$	−20.7259	−0.718110
$834$	38.9425	1.34847
$835$	11.6052	0.401614
$836$	−8.72125	−0.301631
$837$	−3.68423	−0.127345
$838$	−63.0129	−2.17675
$839$	39.9237	1.37832	0.689160	−	0.724610i	$-0.257980\pi$
$839$	39.9237	1.37832	0.689160	+	0.724610i	$0.257980\pi$
$840$	3.18367	0.109847
$841$	−28.9895	−0.999638
$842$	29.9287	1.03141
$843$	−18.0800	−0.622709
$844$	22.7696	0.783760
$845$	−1.41596	−0.0487104
$846$	−18.2645	−0.627947
$847$	33.1170	1.13791
$848$	11.4308	0.392535
$849$	22.1215	0.759208
$850$	−51.1063	−1.75293
$851$	−32.1960	−1.10366
$852$	−43.6706	−1.49613
$853$	33.6316	1.15152	0.575762	−	0.817617i	$-0.304706\pi$
$853$	33.6316	1.15152	0.575762	+	0.817617i	$0.304706\pi$
$854$	0.410346	0.0140418
$855$	1.45327	0.0497006
$856$	11.8261	0.404208
$857$	18.2153	0.622223	0.311111	−	0.950373i	$-0.399299\pi$
$857$	18.2153	0.622223	0.311111	+	0.950373i	$0.399299\pi$
$858$	−9.28179	−0.316875
$859$	21.2086	0.723627	0.361814	−	0.932250i	$-0.382158\pi$
$859$	21.2086	0.723627	0.361814	+	0.932250i	$0.382158\pi$
$860$	−9.27325	−0.316215
$861$	30.3232	1.03341
$862$	−72.8610	−2.48166
$863$	−7.65349	−0.260528	−0.130264	−	0.991479i	$-0.541582\pi$
$863$	−7.65349	−0.260528	−0.130264	+	0.991479i	$0.541582\pi$
$864$	−7.20282	−0.245045
$865$	−1.00077	−0.0340274
$866$	−22.8633	−0.776928
$867$	−6.88418	−0.233799
$868$	−35.2660	−1.19700
$869$	0.712279	0.0241624
$870$	0.113805	0.00385834
$871$	−30.1059	−1.02010
$872$	27.8123	0.941845
$873$	12.8151	0.433726
$874$	−23.1065	−0.781589
$875$	−16.4695	−0.556771
$876$	−18.6944	−0.631624
$877$	10.0558	0.339559	0.169780	−	0.985482i	$-0.445694\pi$
$877$	10.0558	0.339559	0.169780	+	0.985482i	$0.445694\pi$
$878$	−9.75055	−0.329065
$879$	26.7255	0.901430
$880$	0.832443	0.0280616
$881$	−14.0519	−0.473420	−0.236710	−	0.971580i	$-0.576069\pi$
$881$	−14.0519	−0.473420	−0.236710	+	0.971580i	$0.576069\pi$
$882$	−9.34445	−0.314644
$883$	22.4940	0.756983	0.378491	−	0.925605i	$-0.376443\pi$
$883$	22.4940	0.756983	0.378491	+	0.925605i	$0.376443\pi$
$884$	55.4779	1.86592
$885$	−3.95157	−0.132831
$886$	−17.4059	−0.584761
$887$	−34.6212	−1.16247	−0.581233	−	0.813737i	$-0.697429\pi$
$887$	−34.6212	−1.16247	−0.581233	+	0.813737i	$0.697429\pi$
$888$	16.6772	0.559651
$889$	−7.03959	−0.236100
$890$	1.50978	0.0506078
$891$	1.05945	0.0354929
$892$	6.33576	0.212137
$893$	−23.9002	−0.799791
$894$	50.8645	1.70116
$895$	3.83641	0.128237
$896$	−45.9138	−1.53387
$897$	−14.4612	−0.482846
$898$	−24.5271	−0.818480
$899$	−0.377533	−0.0125914
$900$	−13.5498	−0.451660
$901$	35.8354	1.19385
$902$	−21.1130	−0.702987
$903$	21.6057	0.718992
$904$	21.3192	0.709066
$905$	−12.3666	−0.411080
$906$	15.5326	0.516035
$907$	−20.4404	−0.678714	−0.339357	−	0.940658i	$-0.610209\pi$
$907$	−20.4404	−0.678714	−0.339357	+	0.940658i	$0.610209\pi$
$908$	−23.5710	−0.782230
$909$	−4.92004	−0.163187
$910$	14.8050	0.490780
$911$	−52.0935	−1.72593	−0.862967	−	0.505260i	$-0.831397\pi$
$911$	−52.0935	−1.72593	−0.862967	+	0.505260i	$0.831397\pi$
$912$	−4.49478	−0.148837
$913$	−1.44526	−0.0478312
$914$	−86.5640	−2.86328
$915$	0.0279969	0.000925548 0
$916$	75.4005	2.49130
$917$	−43.2699	−1.42890
$918$	−10.7684	−0.355410
$919$	1.40524	0.0463544	0.0231772	−	0.999731i	$-0.492622\pi$
$919$	1.40524	0.0463544	0.0231772	+	0.999731i	$0.492622\pi$
$920$	−3.45363	−0.113863
$921$	25.3945	0.836776
$922$	−43.3917	−1.42903
$923$	−60.8185	−2.00187
$924$	10.1412	0.333621
$925$	−42.0123	−1.38135
$926$	−29.8630	−0.981357
$927$	−11.4983	−0.377655
$928$	−0.738094	−0.0242291
$929$	39.1288	1.28377	0.641887	−	0.766799i	$-0.278152\pi$
$929$	39.1288	1.28377	0.641887	+	0.766799i	$0.278152\pi$
$930$	−4.09164	−0.134170
$931$	−12.2278	−0.400749
$932$	−58.6084	−1.91978
$933$	6.78536	0.222143
$934$	58.8100	1.92432
$935$	2.60970	0.0853463
$936$	7.49079	0.244844
$937$	5.70803	0.186473	0.0932366	−	0.995644i	$-0.470279\pi$
$937$	5.70803	0.186473	0.0932366	+	0.995644i	$0.470279\pi$
$938$	55.9361	1.82638
$939$	0.0695236	0.00226882
$940$	−11.9283	−0.389057
$941$	2.24716	0.0732552	0.0366276	−	0.999329i	$-0.488338\pi$
$941$	2.24716	0.0732552	0.0366276	+	0.999329i	$0.488338\pi$
$942$	5.14776	0.167723
$943$	−32.8945	−1.07119
$944$	12.2217	0.397784
$945$	−1.68988	−0.0549718
$946$	−15.0433	−0.489100
$947$	46.4839	1.51052	0.755262	−	0.655424i	$-0.227510\pi$
$947$	46.4839	1.51052	0.755262	+	0.655424i	$0.227510\pi$
$948$	−1.91946	−0.0623411
$949$	−26.0350	−0.845132
$950$	−30.1515	−0.978243
$951$	0.515794	0.0167258
$952$	−30.8693	−1.00048
$953$	−56.8726	−1.84228	−0.921142	−	0.389226i	$-0.872743\pi$
$953$	−56.8726	−1.84228	−0.921142	+	0.389226i	$0.872743\pi$
$954$	16.1567	0.523093
$955$	−0.0117353	−0.000379746 0
$956$	−33.7165	−1.09047
$957$	0.108565	0.00350940
$958$	−26.0098	−0.840337
$959$	27.1830	0.877785
$960$	−6.42786	−0.207458
$961$	−17.4265	−0.562145
$962$	77.5540	2.50044
$963$	−6.27725	−0.202282
$964$	72.1673	2.32435
$965$	−4.65637	−0.149894
$966$	26.8686	0.864483
$967$	−1.88598	−0.0606492	−0.0303246	−	0.999540i	$-0.509654\pi$
$967$	−1.88598	−0.0606492	−0.0303246	+	0.999540i	$0.509654\pi$
$968$	18.6089	0.598114
$969$	−14.0911	−0.452671
$970$	14.2322	0.456970
$971$	−39.8449	−1.27868	−0.639342	−	0.768922i	$-0.720793\pi$
$971$	−39.8449	−1.27868	−0.639342	+	0.768922i	$0.720793\pi$
$972$	−2.85502	−0.0915748
$973$	−59.2555	−1.89964
$974$	−30.7526	−0.985378
$975$	−18.8703	−0.604334
$976$	−0.0865911	−0.00277171
$977$	42.1404	1.34819	0.674096	−	0.738644i	$-0.264533\pi$
$977$	42.1404	1.34819	0.674096	+	0.738644i	$0.264533\pi$
$978$	33.3958	1.06788
$979$	1.44026	0.0460310
$980$	−6.10271	−0.194944
$981$	−14.7627	−0.471337
$982$	8.09524	0.258330
$983$	31.6983	1.01102	0.505510	−	0.862821i	$-0.331304\pi$
$983$	31.6983	1.01102	0.505510	+	0.862821i	$0.331304\pi$
$984$	17.0391	0.543186
$985$	9.19836	0.293084
$986$	−1.10347	−0.0351416
$987$	27.7916	0.884616
$988$	32.7306	1.04130
$989$	−23.4378	−0.745278
$990$	1.17661	0.0373950
$991$	−54.4923	−1.73100	−0.865502	−	0.500905i	$-0.833000\pi$
$991$	−54.4923	−1.73100	−0.865502	+	0.500905i	$0.833000\pi$
$992$	26.5368	0.842545
$993$	12.6921	0.402771
$994$	112.999	3.58412
$995$	0.232379	0.00736691
$996$	3.89471	0.123409
$997$	−49.2064	−1.55838	−0.779192	−	0.626786i	$-0.784370\pi$
$997$	−49.2064	−1.55838	−0.779192	+	0.626786i	$0.784370\pi$
$998$	−55.0612	−1.74293
$999$	−8.85222	−0.280072

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.c.1.18	✓	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.c.1.18	✓	116	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20341 q^{2} -1.00000 q^{3} +2.85502 q^{4} -0.504029 q^{5} +2.20341 q^{6} -3.35275 q^{7} -1.88396 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.20341 q^{2} -1.00000 q^{3} +2.85502 q^{4} -0.504029 q^{5} +2.20341 q^{6} -3.35275 q^{7} -1.88396 q^{8} +1.00000 q^{9} +1.11058 q^{10} +1.05945 q^{11} -2.85502 q^{12} -3.97609 q^{13} +7.38748 q^{14} +0.504029 q^{15} -1.55890 q^{16} -4.88714 q^{17} -2.20341 q^{18} -2.88330 q^{19} -1.43901 q^{20} +3.35275 q^{21} -2.33440 q^{22} -3.63705 q^{23} +1.88396 q^{24} -4.74595 q^{25} +8.76096 q^{26} -1.00000 q^{27} -9.57215 q^{28} -0.102473 q^{29} -1.11058 q^{30} +3.68423 q^{31} +7.20282 q^{32} -1.05945 q^{33} +10.7684 q^{34} +1.68988 q^{35} +2.85502 q^{36} +8.85222 q^{37} +6.35309 q^{38} +3.97609 q^{39} +0.949570 q^{40} +9.04429 q^{41} -7.38748 q^{42} +6.44418 q^{43} +3.02475 q^{44} -0.504029 q^{45} +8.01391 q^{46} +8.28920 q^{47} +1.55890 q^{48} +4.24090 q^{49} +10.4573 q^{50} +4.88714 q^{51} -11.3518 q^{52} -7.33259 q^{53} +2.20341 q^{54} -0.533993 q^{55} +6.31644 q^{56} +2.88330 q^{57} +0.225790 q^{58} -7.83997 q^{59} +1.43901 q^{60} +0.0555462 q^{61} -8.11786 q^{62} -3.35275 q^{63} -12.7530 q^{64} +2.00406 q^{65} +2.33440 q^{66} +7.57174 q^{67} -13.9529 q^{68} +3.63705 q^{69} -3.72350 q^{70} +15.2961 q^{71} -1.88396 q^{72} +6.54789 q^{73} -19.5051 q^{74} +4.74595 q^{75} -8.23187 q^{76} -3.55206 q^{77} -8.76096 q^{78} +0.672310 q^{79} +0.785732 q^{80} +1.00000 q^{81} -19.9283 q^{82} -1.36416 q^{83} +9.57215 q^{84} +2.46326 q^{85} -14.1992 q^{86} +0.102473 q^{87} -1.99596 q^{88} +1.35945 q^{89} +1.11058 q^{90} +13.3308 q^{91} -10.3838 q^{92} -3.68423 q^{93} -18.2645 q^{94} +1.45327 q^{95} -7.20282 q^{96} +12.8151 q^{97} -9.34445 q^{98} +1.05945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9}+O(q^{10}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9} + 3 q^{10} - 57 q^{11} - 116 q^{12} + 6 q^{13} - 9 q^{14} + 20 q^{15} + 112 q^{16} - 30 q^{17} - 16 q^{18} + 3 q^{19} - 54 q^{20} + 33 q^{21} - 22 q^{22} - 58 q^{23} + 45 q^{24} + 126 q^{25} - 21 q^{26} - 116 q^{27} - 77 q^{28} - 38 q^{29} - 3 q^{30} + 17 q^{31} - 106 q^{32} + 57 q^{33} + 35 q^{34} - 72 q^{35} + 116 q^{36} - 41 q^{37} - 45 q^{38} - 6 q^{39} + 5 q^{40} - 39 q^{41} + 9 q^{42} - 118 q^{43} - 103 q^{44} - 20 q^{45} - 8 q^{46} - 65 q^{47} - 112 q^{48} + 165 q^{49} - 72 q^{50} + 30 q^{51} - 10 q^{52} - 58 q^{53} + 16 q^{54} + 14 q^{55} - 23 q^{56} - 3 q^{57} - 27 q^{58} - 75 q^{59} + 54 q^{60} + 45 q^{61} - 73 q^{62} - 33 q^{63} + 111 q^{64} - 86 q^{65} + 22 q^{66} - 127 q^{67} - 94 q^{68} + 58 q^{69} - 7 q^{70} - 61 q^{71} - 45 q^{72} + 15 q^{73} - 51 q^{74} - 126 q^{75} + 96 q^{76} - 57 q^{77} + 21 q^{78} + 7 q^{79} - 144 q^{80} + 116 q^{81} - 37 q^{82} - 194 q^{83} + 77 q^{84} + 3 q^{85} - 57 q^{86} + 38 q^{87} - 42 q^{88} - 56 q^{89} + 3 q^{90} - 39 q^{91} - 138 q^{92} - 17 q^{93} + 51 q^{94} - 127 q^{95} + 106 q^{96} + 57 q^{97} - 105 q^{98} - 57 q^{99}+O(q^{100}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9 + 3 * q^10 - 57 * q^11 - 116 * q^12 + 6 * q^13 - 9 * q^14 + 20 * q^15 + 112 * q^16 - 30 * q^17 - 16 * q^18 + 3 * q^19 - 54 * q^20 + 33 * q^21 - 22 * q^22 - 58 * q^23 + 45 * q^24 + 126 * q^25 - 21 * q^26 - 116 * q^27 - 77 * q^28 - 38 * q^29 - 3 * q^30 + 17 * q^31 - 106 * q^32 + 57 * q^33 + 35 * q^34 - 72 * q^35 + 116 * q^36 - 41 * q^37 - 45 * q^38 - 6 * q^39 + 5 * q^40 - 39 * q^41 + 9 * q^42 - 118 * q^43 - 103 * q^44 - 20 * q^45 - 8 * q^46 - 65 * q^47 - 112 * q^48 + 165 * q^49 - 72 * q^50 + 30 * q^51 - 10 * q^52 - 58 * q^53 + 16 * q^54 + 14 * q^55 - 23 * q^56 - 3 * q^57 - 27 * q^58 - 75 * q^59 + 54 * q^60 + 45 * q^61 - 73 * q^62 - 33 * q^63 + 111 * q^64 - 86 * q^65 + 22 * q^66 - 127 * q^67 - 94 * q^68 + 58 * q^69 - 7 * q^70 - 61 * q^71 - 45 * q^72 + 15 * q^73 - 51 * q^74 - 126 * q^75 + 96 * q^76 - 57 * q^77 + 21 * q^78 + 7 * q^79 - 144 * q^80 + 116 * q^81 - 37 * q^82 - 194 * q^83 + 77 * q^84 + 3 * q^85 - 57 * q^86 + 38 * q^87 - 42 * q^88 - 56 * q^89 + 3 * q^90 - 39 * q^91 - 138 * q^92 - 17 * q^93 + 51 * q^94 - 127 * q^95 + 106 * q^96 + 57 * q^97 - 105 * q^98 - 57 * q^99

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