LMFDB - Embedded newform 8015.2.a.l.1.53

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.53
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.11453 q^{2} -2.77399 q^{3} +2.47123 q^{4} -1.00000 q^{5} -5.86568 q^{6} -1.00000 q^{7} +0.996433 q^{8} +4.69501 q^{9} +O(q^{10})$	\(q+2.11453 q^{2} -2.77399 q^{3} +2.47123 q^{4} -1.00000 q^{5} -5.86568 q^{6} -1.00000 q^{7} +0.996433 q^{8} +4.69501 q^{9} -2.11453 q^{10} +4.53639 q^{11} -6.85517 q^{12} +5.00491 q^{13} -2.11453 q^{14} +2.77399 q^{15} -2.83548 q^{16} +6.37048 q^{17} +9.92773 q^{18} +1.52323 q^{19} -2.47123 q^{20} +2.77399 q^{21} +9.59233 q^{22} -2.04398 q^{23} -2.76409 q^{24} +1.00000 q^{25} +10.5830 q^{26} -4.70193 q^{27} -2.47123 q^{28} -9.52762 q^{29} +5.86568 q^{30} -4.49195 q^{31} -7.98856 q^{32} -12.5839 q^{33} +13.4706 q^{34} +1.00000 q^{35} +11.6024 q^{36} +2.04175 q^{37} +3.22091 q^{38} -13.8836 q^{39} -0.996433 q^{40} +6.84673 q^{41} +5.86568 q^{42} -3.38647 q^{43} +11.2105 q^{44} -4.69501 q^{45} -4.32206 q^{46} -5.40079 q^{47} +7.86558 q^{48} +1.00000 q^{49} +2.11453 q^{50} -17.6716 q^{51} +12.3683 q^{52} +11.1941 q^{53} -9.94236 q^{54} -4.53639 q^{55} -0.996433 q^{56} -4.22542 q^{57} -20.1464 q^{58} +7.44363 q^{59} +6.85517 q^{60} +13.0216 q^{61} -9.49836 q^{62} -4.69501 q^{63} -11.2211 q^{64} -5.00491 q^{65} -26.6090 q^{66} -5.56782 q^{67} +15.7429 q^{68} +5.66999 q^{69} +2.11453 q^{70} -4.39289 q^{71} +4.67826 q^{72} +8.71633 q^{73} +4.31735 q^{74} -2.77399 q^{75} +3.76425 q^{76} -4.53639 q^{77} -29.3572 q^{78} -10.9171 q^{79} +2.83548 q^{80} -1.04193 q^{81} +14.4776 q^{82} +2.08396 q^{83} +6.85517 q^{84} -6.37048 q^{85} -7.16079 q^{86} +26.4295 q^{87} +4.52021 q^{88} -1.27717 q^{89} -9.92773 q^{90} -5.00491 q^{91} -5.05116 q^{92} +12.4606 q^{93} -11.4201 q^{94} -1.52323 q^{95} +22.1602 q^{96} -9.32565 q^{97} +2.11453 q^{98} +21.2984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	2.11453	1.49520	0.747599	−	0.664151i	$-0.231207\pi$
$2$	2.11453	1.49520	0.747599	+	0.664151i	$0.231207\pi$
$3$	−2.77399	−1.60156	−0.800781	−	0.598957i	$-0.795582\pi$
$3$	−2.77399	−1.60156	−0.800781	+	0.598957i	$0.795582\pi$
$4$	2.47123	1.23562
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−5.86568	−2.39465
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.996433	0.352292
$9$	4.69501	1.56500
$10$	−2.11453	−0.668673
$11$	4.53639	1.36777	0.683887	−	0.729588i	$-0.260288\pi$
$11$	4.53639	1.36777	0.683887	+	0.729588i	$0.260288\pi$
$12$	−6.85517	−1.97892
$13$	5.00491	1.38811	0.694056	−	0.719921i	$-0.255822\pi$
$13$	5.00491	1.38811	0.694056	+	0.719921i	$0.255822\pi$
$14$	−2.11453	−0.565132
$15$	2.77399	0.716240
$16$	−2.83548	−0.708869
$17$	6.37048	1.54507	0.772534	−	0.634974i	$-0.218989\pi$
$17$	6.37048	1.54507	0.772534	+	0.634974i	$0.218989\pi$
$18$	9.92773	2.33999
$19$	1.52323	0.349453	0.174726	−	0.984617i	$-0.444096\pi$
$19$	1.52323	0.349453	0.174726	+	0.984617i	$0.444096\pi$
$20$	−2.47123	−0.552584
$21$	2.77399	0.605334
$22$	9.59233	2.04509
$23$	−2.04398	−0.426200	−0.213100	−	0.977030i	$-0.568356\pi$
$23$	−2.04398	−0.426200	−0.213100	+	0.977030i	$0.568356\pi$
$24$	−2.76409	−0.564218
$25$	1.00000	0.200000
$26$	10.5830	2.07550
$27$	−4.70193	−0.904886
$28$	−2.47123	−0.467019
$29$	−9.52762	−1.76924	−0.884618	−	0.466317i	$-0.845581\pi$
$29$	−9.52762	−1.76924	−0.884618	+	0.466317i	$0.845581\pi$
$30$	5.86568	1.07092
$31$	−4.49195	−0.806778	−0.403389	−	0.915029i	$-0.632168\pi$
$31$	−4.49195	−0.806778	−0.403389	+	0.915029i	$0.632168\pi$
$32$	−7.98856	−1.41219
$33$	−12.5839	−2.19057
$34$	13.4706	2.31018
$35$	1.00000	0.169031
$36$	11.6024	1.93374
$37$	2.04175	0.335662	0.167831	−	0.985816i	$-0.446324\pi$
$37$	2.04175	0.335662	0.167831	+	0.985816i	$0.446324\pi$
$38$	3.22091	0.522501
$39$	−13.8836	−2.22315
$40$	−0.996433	−0.157550
$41$	6.84673	1.06928	0.534640	−	0.845080i	$-0.320447\pi$
$41$	6.84673	1.06928	0.534640	+	0.845080i	$0.320447\pi$
$42$	5.86568	0.905093
$43$	−3.38647	−0.516432	−0.258216	−	0.966087i	$-0.583135\pi$
$43$	−3.38647	−0.516432	−0.258216	+	0.966087i	$0.583135\pi$
$44$	11.2105	1.69004
$45$	−4.69501	−0.699890
$46$	−4.32206	−0.637253
$47$	−5.40079	−0.787787	−0.393893	−	0.919156i	$-0.628872\pi$
$47$	−5.40079	−0.787787	−0.393893	+	0.919156i	$0.628872\pi$
$48$	7.86558	1.13530
$49$	1.00000	0.142857
$50$	2.11453	0.299040
$51$	−17.6716	−2.47452
$52$	12.3683	1.71517
$53$	11.1941	1.53763	0.768815	−	0.639471i	$-0.220847\pi$
$53$	11.1941	1.53763	0.768815	+	0.639471i	$0.220847\pi$
$54$	−9.94236	−1.35298
$55$	−4.53639	−0.611687
$56$	−0.996433	−0.133154
$57$	−4.22542	−0.559671
$58$	−20.1464	−2.64536
$59$	7.44363	0.969078	0.484539	−	0.874770i	$-0.338987\pi$
$59$	7.44363	0.969078	0.484539	+	0.874770i	$0.338987\pi$
$60$	6.85517	0.884998
$61$	13.0216	1.66724	0.833622	−	0.552335i	$-0.186263\pi$
$61$	13.0216	1.66724	0.833622	+	0.552335i	$0.186263\pi$
$62$	−9.49836	−1.20629
$63$	−4.69501	−0.591515
$64$	−11.2211	−1.40264
$65$	−5.00491	−0.620783
$66$	−26.6090	−3.27534
$67$	−5.56782	−0.680218	−0.340109	−	0.940386i	$-0.610464\pi$
$67$	−5.56782	−0.680218	−0.340109	+	0.940386i	$0.610464\pi$
$68$	15.7429	1.90911
$69$	5.66999	0.682586
$70$	2.11453	0.252735
$71$	−4.39289	−0.521340	−0.260670	−	0.965428i	$-0.583943\pi$
$71$	−4.39289	−0.521340	−0.260670	+	0.965428i	$0.583943\pi$
$72$	4.67826	0.551338
$73$	8.71633	1.02017	0.510085	−	0.860124i	$-0.329614\pi$
$73$	8.71633	1.02017	0.510085	+	0.860124i	$0.329614\pi$
$74$	4.31735	0.501881
$75$	−2.77399	−0.320312
$76$	3.76425	0.431790
$77$	−4.53639	−0.516970
$78$	−29.3572	−3.32405
$79$	−10.9171	−1.22828	−0.614138	−	0.789199i	$-0.710496\pi$
$79$	−10.9171	−1.22828	−0.614138	+	0.789199i	$0.710496\pi$
$80$	2.83548	0.317016
$81$	−1.04193	−0.115771
$82$	14.4776	1.59879
$83$	2.08396	0.228744	0.114372	−	0.993438i	$-0.463514\pi$
$83$	2.08396	0.228744	0.114372	+	0.993438i	$0.463514\pi$
$84$	6.85517	0.747960
$85$	−6.37048	−0.690975
$86$	−7.16079	−0.772168
$87$	26.4295	2.83354
$88$	4.52021	0.481856
$89$	−1.27717	−0.135380	−0.0676898	−	0.997706i	$-0.521563\pi$
$89$	−1.27717	−0.135380	−0.0676898	+	0.997706i	$0.521563\pi$
$90$	−9.92773	−1.04647
$91$	−5.00491	−0.524657
$92$	−5.05116	−0.526620
$93$	12.4606	1.29211
$94$	−11.4201	−1.17790
$95$	−1.52323	−0.156280
$96$	22.1602	2.26171
$97$	−9.32565	−0.946876	−0.473438	−	0.880827i	$-0.656987\pi$
$97$	−9.32565	−0.946876	−0.473438	+	0.880827i	$0.656987\pi$
$98$	2.11453	0.213600
$99$	21.2984	2.14057
$100$	2.47123	0.247123
$101$	−4.40127	−0.437943	−0.218972	−	0.975731i	$-0.570270\pi$
$101$	−4.40127	−0.437943	−0.218972	+	0.975731i	$0.570270\pi$
$102$	−37.3671	−3.69990
$103$	−11.1776	−1.10137	−0.550683	−	0.834715i	$-0.685633\pi$
$103$	−11.1776	−1.10137	−0.550683	+	0.834715i	$0.685633\pi$
$104$	4.98706	0.489021
$105$	−2.77399	−0.270713
$106$	23.6703	2.29906
$107$	−10.8833	−1.05213	−0.526065	−	0.850444i	$-0.676333\pi$
$107$	−10.8833	−1.05213	−0.526065	+	0.850444i	$0.676333\pi$
$108$	−11.6195	−1.11809
$109$	2.98412	0.285827	0.142914	−	0.989735i	$-0.454353\pi$
$109$	2.98412	0.285827	0.142914	+	0.989735i	$0.454353\pi$
$110$	−9.59233	−0.914593
$111$	−5.66380	−0.537584
$112$	2.83548	0.267927
$113$	16.7466	1.57539	0.787693	−	0.616068i	$-0.211275\pi$
$113$	16.7466	1.57539	0.787693	+	0.616068i	$0.211275\pi$
$114$	−8.93477	−0.836818
$115$	2.04398	0.190602
$116$	−23.5450	−2.18610
$117$	23.4981	2.17240
$118$	15.7398	1.44896
$119$	−6.37048	−0.583981
$120$	2.76409	0.252326
$121$	9.57884	0.870804
$122$	27.5345	2.49286
$123$	−18.9928	−1.71252
$124$	−11.1006	−0.996868
$125$	−1.00000	−0.0894427
$126$	−9.92773	−0.884432
$127$	3.94166	0.349766	0.174883	−	0.984589i	$-0.444045\pi$
$127$	3.94166	0.349766	0.174883	+	0.984589i	$0.444045\pi$
$128$	−7.75019	−0.685027
$129$	9.39403	0.827098
$130$	−10.5830	−0.928193
$131$	19.8568	1.73490	0.867449	−	0.497526i	$-0.165758\pi$
$131$	19.8568	1.73490	0.867449	+	0.497526i	$0.165758\pi$
$132$	−31.0977	−2.70671
$133$	−1.52323	−0.132081
$134$	−11.7733	−1.01706
$135$	4.70193	0.404677
$136$	6.34775	0.544315
$137$	3.33683	0.285085	0.142542	−	0.989789i	$-0.454472\pi$
$137$	3.33683	0.285085	0.142542	+	0.989789i	$0.454472\pi$
$138$	11.9893	1.02060
$139$	16.6919	1.41579	0.707895	−	0.706318i	$-0.249645\pi$
$139$	16.6919	1.41579	0.707895	+	0.706318i	$0.249645\pi$
$140$	2.47123	0.208857
$141$	14.9817	1.26169
$142$	−9.28888	−0.779506
$143$	22.7042	1.89862
$144$	−13.3126	−1.10938
$145$	9.52762	0.791226
$146$	18.4309	1.52535
$147$	−2.77399	−0.228795
$148$	5.04564	0.414749
$149$	−1.80328	−0.147731	−0.0738653	−	0.997268i	$-0.523533\pi$
$149$	−1.80328	−0.147731	−0.0738653	+	0.997268i	$0.523533\pi$
$150$	−5.86568	−0.478930
$151$	−12.2444	−0.996438	−0.498219	−	0.867051i	$-0.666012\pi$
$151$	−12.2444	−0.996438	−0.498219	+	0.867051i	$0.666012\pi$
$152$	1.51780	0.123110
$153$	29.9094	2.41803
$154$	−9.59233	−0.772972
$155$	4.49195	0.360802
$156$	−34.3095	−2.74696
$157$	−1.44303	−0.115166	−0.0575832	−	0.998341i	$-0.518339\pi$
$157$	−1.44303	−0.115166	−0.0575832	+	0.998341i	$0.518339\pi$
$158$	−23.0846	−1.83651
$159$	−31.0523	−2.46261
$160$	7.98856	0.631551
$161$	2.04398	0.161088
$162$	−2.20320	−0.173100
$163$	17.2617	1.35204	0.676020	−	0.736884i	$-0.263703\pi$
$163$	17.2617	1.35204	0.676020	+	0.736884i	$0.263703\pi$
$164$	16.9199	1.32122
$165$	12.5839	0.979655
$166$	4.40659	0.342018
$167$	2.90141	0.224518	0.112259	−	0.993679i	$-0.464191\pi$
$167$	2.90141	0.224518	0.112259	+	0.993679i	$0.464191\pi$
$168$	2.76409	0.213254
$169$	12.0491	0.926856
$170$	−13.4706	−1.03314
$171$	7.15157	0.546895
$172$	−8.36875	−0.638112
$173$	10.0954	0.767539	0.383770	−	0.923429i	$-0.374626\pi$
$173$	10.0954	0.767539	0.383770	+	0.923429i	$0.374626\pi$
$174$	55.8860	4.23670
$175$	−1.00000	−0.0755929
$176$	−12.8628	−0.969573
$177$	−20.6485	−1.55204
$178$	−2.70061	−0.202419
$179$	21.0779	1.57544	0.787719	−	0.616035i	$-0.211262\pi$
$179$	21.0779	1.57544	0.787719	+	0.616035i	$0.211262\pi$
$180$	−11.6024	−0.864795
$181$	−17.1971	−1.27825	−0.639124	−	0.769104i	$-0.720703\pi$
$181$	−17.1971	−1.27825	−0.639124	+	0.769104i	$0.720703\pi$
$182$	−10.5830	−0.784466
$183$	−36.1217	−2.67020
$184$	−2.03669	−0.150147
$185$	−2.04175	−0.150113
$186$	26.3483	1.93195
$187$	28.8990	2.11330
$188$	−13.3466	−0.973402
$189$	4.70193	0.342015
$190$	−3.22091	−0.233670
$191$	−6.36081	−0.460252	−0.230126	−	0.973161i	$-0.573914\pi$
$191$	−6.36081	−0.460252	−0.230126	+	0.973161i	$0.573914\pi$
$192$	31.1272	2.24641
$193$	20.6184	1.48414	0.742071	−	0.670321i	$-0.233844\pi$
$193$	20.6184	1.48414	0.742071	+	0.670321i	$0.233844\pi$
$194$	−19.7194	−1.41577
$195$	13.8836	0.994222
$196$	2.47123	0.176517
$197$	1.73117	0.123341	0.0616704	−	0.998097i	$-0.480357\pi$
$197$	1.73117	0.123341	0.0616704	+	0.998097i	$0.480357\pi$
$198$	45.0360	3.20057
$199$	−5.29923	−0.375653	−0.187826	−	0.982202i	$-0.560144\pi$
$199$	−5.29923	−0.375653	−0.187826	+	0.982202i	$0.560144\pi$
$200$	0.996433	0.0704584
$201$	15.4451	1.08941
$202$	−9.30662	−0.654812
$203$	9.52762	0.668708
$204$	−43.6707	−3.05756
$205$	−6.84673	−0.478197
$206$	−23.6354	−1.64676
$207$	−9.59652	−0.667004
$208$	−14.1913	−0.983990
$209$	6.90997	0.477972
$210$	−5.86568	−0.404770
$211$	22.1566	1.52532	0.762661	−	0.646799i	$-0.223893\pi$
$211$	22.1566	1.52532	0.762661	+	0.646799i	$0.223893\pi$
$212$	27.6633	1.89992
$213$	12.1858	0.834958
$214$	−23.0131	−1.57314
$215$	3.38647	0.230955
$216$	−4.68515	−0.318784
$217$	4.49195	0.304933
$218$	6.31002	0.427368
$219$	−24.1790	−1.63386
$220$	−11.2105	−0.755810
$221$	31.8837	2.14473
$222$	−11.9763	−0.803794
$223$	11.9524	0.800394	0.400197	−	0.916429i	$-0.368942\pi$
$223$	11.9524	0.800394	0.400197	+	0.916429i	$0.368942\pi$
$224$	7.98856	0.533758
$225$	4.69501	0.313000
$226$	35.4111	2.35551
$227$	−16.0218	−1.06340	−0.531701	−	0.846932i	$-0.678447\pi$
$227$	−16.0218	−1.06340	−0.531701	+	0.846932i	$0.678447\pi$
$228$	−10.4420	−0.691538
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	4.32206	0.284988
$231$	12.5839	0.827959
$232$	−9.49364	−0.623288
$233$	−10.7925	−0.707041	−0.353521	−	0.935427i	$-0.615016\pi$
$233$	−10.7925	−0.707041	−0.353521	+	0.935427i	$0.615016\pi$
$234$	49.6874	3.24817
$235$	5.40079	0.352309
$236$	18.3949	1.19741
$237$	30.2840	1.96716
$238$	−13.4706	−0.873166
$239$	−3.07503	−0.198907	−0.0994535	−	0.995042i	$-0.531709\pi$
$239$	−3.07503	−0.198907	−0.0994535	+	0.995042i	$0.531709\pi$
$240$	−7.86558	−0.507721
$241$	12.8381	0.826972	0.413486	−	0.910511i	$-0.364311\pi$
$241$	12.8381	0.826972	0.413486	+	0.910511i	$0.364311\pi$
$242$	20.2547	1.30202
$243$	16.9961	1.09030
$244$	32.1794	2.06007
$245$	−1.00000	−0.0638877
$246$	−40.1607	−2.56055
$247$	7.62363	0.485080
$248$	−4.47593	−0.284222
$249$	−5.78087	−0.366348
$250$	−2.11453	−0.133735
$251$	25.8710	1.63296	0.816482	−	0.577371i	$-0.195922\pi$
$251$	25.8710	1.63296	0.816482	+	0.577371i	$0.195922\pi$
$252$	−11.6024	−0.730886
$253$	−9.27231	−0.582945
$254$	8.33476	0.522969
$255$	17.6716	1.10664
$256$	6.05418	0.378386
$257$	17.1194	1.06788	0.533938	−	0.845523i	$-0.320711\pi$
$257$	17.1194	1.06788	0.533938	+	0.845523i	$0.320711\pi$
$258$	19.8639	1.23668
$259$	−2.04175	−0.126868
$260$	−12.3683	−0.767049
$261$	−44.7323	−2.76886
$262$	41.9878	2.59401
$263$	24.2501	1.49533	0.747663	−	0.664078i	$-0.231176\pi$
$263$	24.2501	1.49533	0.747663	+	0.664078i	$0.231176\pi$
$264$	−12.5390	−0.771722
$265$	−11.1941	−0.687649
$266$	−3.22091	−0.197487
$267$	3.54285	0.216819
$268$	−13.7594	−0.840488
$269$	−25.8726	−1.57748	−0.788740	−	0.614727i	$-0.789266\pi$
$269$	−25.8726	−1.57748	−0.788740	+	0.614727i	$0.789266\pi$
$270$	9.94236	0.605073
$271$	24.6376	1.49663	0.748315	−	0.663344i	$-0.230863\pi$
$271$	24.6376	1.49663	0.748315	+	0.663344i	$0.230863\pi$
$272$	−18.0633	−1.09525
$273$	13.8836	0.840271
$274$	7.05583	0.426258
$275$	4.53639	0.273555
$276$	14.0118	0.843414
$277$	−1.74062	−0.104584	−0.0522918	−	0.998632i	$-0.516653\pi$
$277$	−1.74062	−0.104584	−0.0522918	+	0.998632i	$0.516653\pi$
$278$	35.2955	2.11689
$279$	−21.0897	−1.26261
$280$	0.996433	0.0595482
$281$	16.5133	0.985103	0.492551	−	0.870283i	$-0.336064\pi$
$281$	16.5133	0.985103	0.492551	+	0.870283i	$0.336064\pi$
$282$	31.6793	1.88648
$283$	11.2747	0.670211	0.335106	−	0.942181i	$-0.391228\pi$
$283$	11.2747	0.670211	0.335106	+	0.942181i	$0.391228\pi$
$284$	−10.8558	−0.644175
$285$	4.22542	0.250292
$286$	48.0087	2.83882
$287$	−6.84673	−0.404150
$288$	−37.5064	−2.21008
$289$	23.5830	1.38723
$290$	20.1464	1.18304
$291$	25.8692	1.51648
$292$	21.5401	1.26054
$293$	−8.81104	−0.514746	−0.257373	−	0.966312i	$-0.582857\pi$
$293$	−8.81104	−0.514746	−0.257373	+	0.966312i	$0.582857\pi$
$294$	−5.86568	−0.342093
$295$	−7.44363	−0.433385
$296$	2.03447	0.118251
$297$	−21.3298	−1.23768
$298$	−3.81309	−0.220886
$299$	−10.2300	−0.591614
$300$	−6.85517	−0.395783
$301$	3.38647	0.195193
$302$	−25.8912	−1.48987
$303$	12.2091	0.701393
$304$	−4.31908	−0.247717
$305$	−13.0216	−0.745614
$306$	63.2443	3.61544
$307$	−2.39240	−0.136541	−0.0682707	−	0.997667i	$-0.521748\pi$
$307$	−2.39240	−0.136541	−0.0682707	+	0.997667i	$0.521748\pi$
$308$	−11.2105	−0.638776
$309$	31.0066	1.76390
$310$	9.49836	0.539470
$311$	18.4588	1.04670	0.523350	−	0.852118i	$-0.324682\pi$
$311$	18.4588	1.04670	0.523350	+	0.852118i	$0.324682\pi$
$312$	−13.8340	−0.783198
$313$	15.3111	0.865435	0.432717	−	0.901530i	$-0.357555\pi$
$313$	15.3111	0.865435	0.432717	+	0.901530i	$0.357555\pi$
$314$	−3.05133	−0.172197
$315$	4.69501	0.264534
$316$	−26.9788	−1.51768
$317$	−5.64871	−0.317263	−0.158632	−	0.987338i	$-0.550708\pi$
$317$	−5.64871	−0.317263	−0.158632	+	0.987338i	$0.550708\pi$
$318$	−65.6611	−3.68209
$319$	−43.2210	−2.41991
$320$	11.2211	0.627278
$321$	30.1902	1.68505
$322$	4.32206	0.240859
$323$	9.70370	0.539928
$324$	−2.57486	−0.143048
$325$	5.00491	0.277622
$326$	36.5003	2.02157
$327$	−8.27792	−0.457770
$328$	6.82231	0.376699
$329$	5.40079	0.297755
$330$	26.6090	1.46478
$331$	22.5115	1.23735	0.618673	−	0.785649i	$-0.287671\pi$
$331$	22.5115	1.23735	0.618673	+	0.785649i	$0.287671\pi$
$332$	5.14994	0.282640
$333$	9.58604	0.525312
$334$	6.13512	0.335699
$335$	5.56782	0.304203
$336$	−7.86558	−0.429103
$337$	0.912983	0.0497333	0.0248667	−	0.999691i	$-0.492084\pi$
$337$	0.912983	0.0497333	0.0248667	+	0.999691i	$0.492084\pi$
$338$	25.4782	1.38583
$339$	−46.4548	−2.52308
$340$	−15.7429	−0.853780
$341$	−20.3772	−1.10349
$342$	15.1222	0.817715
$343$	−1.00000	−0.0539949
$344$	−3.37439	−0.181935
$345$	−5.66999	−0.305262
$346$	21.3470	1.14762
$347$	−34.0698	−1.82896	−0.914481	−	0.404630i	$-0.867400\pi$
$347$	−34.0698	−1.82896	−0.914481	+	0.404630i	$0.867400\pi$
$348$	65.3134	3.50117
$349$	−30.3306	−1.62356	−0.811780	−	0.583964i	$-0.801501\pi$
$349$	−30.3306	−1.62356	−0.811780	+	0.583964i	$0.801501\pi$
$350$	−2.11453	−0.113026
$351$	−23.5327	−1.25608
$352$	−36.2393	−1.93156
$353$	−4.99889	−0.266064	−0.133032	−	0.991112i	$-0.542471\pi$
$353$	−4.99889	−0.266064	−0.133032	+	0.991112i	$0.542471\pi$
$354$	−43.6619	−2.32060
$355$	4.39289	0.233150
$356$	−3.15618	−0.167277
$357$	17.6716	0.935281
$358$	44.5699	2.35559
$359$	1.51174	0.0797864	0.0398932	−	0.999204i	$-0.487298\pi$
$359$	1.51174	0.0797864	0.0398932	+	0.999204i	$0.487298\pi$
$360$	−4.67826	−0.246566
$361$	−16.6798	−0.877883
$362$	−36.3637	−1.91123
$363$	−26.5716	−1.39465
$364$	−12.3683	−0.648275
$365$	−8.71633	−0.456234
$366$	−76.3804	−3.99247
$367$	7.87025	0.410824	0.205412	−	0.978676i	$-0.434147\pi$
$367$	7.87025	0.410824	0.205412	+	0.978676i	$0.434147\pi$
$368$	5.79567	0.302120
$369$	32.1455	1.67343
$370$	−4.31735	−0.224448
$371$	−11.1941	−0.581170
$372$	30.7931	1.59655
$373$	28.0248	1.45107	0.725534	−	0.688186i	$-0.241593\pi$
$373$	28.0248	1.45107	0.725534	+	0.688186i	$0.241593\pi$
$374$	61.1077	3.15980
$375$	2.77399	0.143248
$376$	−5.38153	−0.277531
$377$	−47.6849	−2.45590
$378$	9.94236	0.511380
$379$	−25.0989	−1.28925	−0.644623	−	0.764501i	$-0.722985\pi$
$379$	−25.0989	−1.28925	−0.644623	+	0.764501i	$0.722985\pi$
$380$	−3.76425	−0.193102
$381$	−10.9341	−0.560172
$382$	−13.4501	−0.688168
$383$	36.2805	1.85384	0.926922	−	0.375253i	$-0.122444\pi$
$383$	36.2805	1.85384	0.926922	+	0.375253i	$0.122444\pi$
$384$	21.4989	1.09711
$385$	4.53639	0.231196
$386$	43.5981	2.21909
$387$	−15.8995	−0.808217
$388$	−23.0458	−1.16998
$389$	7.06651	0.358286	0.179143	−	0.983823i	$-0.442667\pi$
$389$	7.06651	0.358286	0.179143	+	0.983823i	$0.442667\pi$
$390$	29.3572	1.48656
$391$	−13.0211	−0.658508
$392$	0.996433	0.0503275
$393$	−55.0825	−2.77855
$394$	3.66061	0.184419
$395$	10.9171	0.549301
$396$	52.6332	2.64492
$397$	28.7212	1.44147	0.720737	−	0.693208i	$-0.243803\pi$
$397$	28.7212	1.44147	0.720737	+	0.693208i	$0.243803\pi$
$398$	−11.2054	−0.561675
$399$	4.22542	0.211536
$400$	−2.83548	−0.141774
$401$	−5.33183	−0.266259	−0.133130	−	0.991099i	$-0.542503\pi$
$401$	−5.33183	−0.266259	−0.133130	+	0.991099i	$0.542503\pi$
$402$	32.6590	1.62888
$403$	−22.4818	−1.11990
$404$	−10.8766	−0.541129
$405$	1.04193	0.0517742
$406$	20.1464	0.999851
$407$	9.26219	0.459110
$408$	−17.6086	−0.871755
$409$	−16.6103	−0.821324	−0.410662	−	0.911788i	$-0.634702\pi$
$409$	−16.6103	−0.821324	−0.410662	+	0.911788i	$0.634702\pi$
$410$	−14.4776	−0.714999
$411$	−9.25633	−0.456581
$412$	−27.6225	−1.36086
$413$	−7.44363	−0.366277
$414$	−20.2921	−0.997303
$415$	−2.08396	−0.102297
$416$	−39.9820	−1.96028
$417$	−46.3032	−2.26748
$418$	14.6113	0.714663
$419$	−19.7911	−0.966859	−0.483430	−	0.875383i	$-0.660609\pi$
$419$	−19.7911	−0.966859	−0.483430	+	0.875383i	$0.660609\pi$
$420$	−6.85517	−0.334498
$421$	−6.46224	−0.314950	−0.157475	−	0.987523i	$-0.550335\pi$
$421$	−6.46224	−0.314950	−0.157475	+	0.987523i	$0.550335\pi$
$422$	46.8507	2.28066
$423$	−25.3568	−1.23289
$424$	11.1542	0.541695
$425$	6.37048	0.309013
$426$	25.7672	1.24843
$427$	−13.0216	−0.630159
$428$	−26.8952	−1.30003
$429$	−62.9813	−3.04076
$430$	7.16079	0.345324
$431$	−17.2503	−0.830917	−0.415459	−	0.909612i	$-0.636379\pi$
$431$	−17.2503	−0.830917	−0.415459	+	0.909612i	$0.636379\pi$
$432$	13.3322	0.641446
$433$	24.4221	1.17365	0.586826	−	0.809713i	$-0.300377\pi$
$433$	24.4221	1.17365	0.586826	+	0.809713i	$0.300377\pi$
$434$	9.49836	0.455936
$435$	−26.4295	−1.26720
$436$	7.37446	0.353173
$437$	−3.11346	−0.148937
$438$	−51.1272	−2.44295
$439$	−14.7613	−0.704521	−0.352260	−	0.935902i	$-0.614587\pi$
$439$	−14.7613	−0.704521	−0.352260	+	0.935902i	$0.614587\pi$
$440$	−4.52021	−0.215492
$441$	4.69501	0.223572
$442$	67.4189	3.20679
$443$	4.98945	0.237056	0.118528	−	0.992951i	$-0.462182\pi$
$443$	4.98945	0.237056	0.118528	+	0.992951i	$0.462182\pi$
$444$	−13.9966	−0.664247
$445$	1.27717	0.0605436
$446$	25.2738	1.19675
$447$	5.00228	0.236600
$448$	11.2211	0.530147
$449$	2.41343	0.113897	0.0569485	−	0.998377i	$-0.481863\pi$
$449$	2.41343	0.113897	0.0569485	+	0.998377i	$0.481863\pi$
$450$	9.92773	0.467997
$451$	31.0595	1.46253
$452$	41.3847	1.94657
$453$	33.9659	1.59586
$454$	−33.8785	−1.59000
$455$	5.00491	0.234634
$456$	−4.21035	−0.197168
$457$	35.0547	1.63979	0.819895	−	0.572514i	$-0.194032\pi$
$457$	35.0547	1.63979	0.819895	+	0.572514i	$0.194032\pi$
$458$	2.11453	0.0988054
$459$	−29.9535	−1.39811
$460$	5.05116	0.235511
$461$	1.74901	0.0814593	0.0407296	−	0.999170i	$-0.487032\pi$
$461$	1.74901	0.0814593	0.0407296	+	0.999170i	$0.487032\pi$
$462$	26.6090	1.23796
$463$	−20.6997	−0.961998	−0.480999	−	0.876721i	$-0.659726\pi$
$463$	−20.6997	−0.961998	−0.480999	+	0.876721i	$0.659726\pi$
$464$	27.0154	1.25416
$465$	−12.4606	−0.577847
$466$	−22.8211	−1.05717
$467$	−0.629312	−0.0291211	−0.0145605	−	0.999894i	$-0.504635\pi$
$467$	−0.629312	−0.0291211	−0.0145605	+	0.999894i	$0.504635\pi$
$468$	58.0692	2.68425
$469$	5.56782	0.257098
$470$	11.4201	0.526771
$471$	4.00295	0.184446
$472$	7.41707	0.341399
$473$	−15.3624	−0.706362
$474$	64.0365	2.94129
$475$	1.52323	0.0698906
$476$	−15.7429	−0.721576
$477$	52.5565	2.40639
$478$	−6.50224	−0.297405
$479$	−21.9714	−1.00390	−0.501949	−	0.864897i	$-0.667383\pi$
$479$	−21.9714	−1.00390	−0.501949	+	0.864897i	$0.667383\pi$
$480$	−22.1602	−1.01147
$481$	10.2188	0.465937
$482$	27.1464	1.23649
$483$	−5.66999	−0.257993
$484$	23.6715	1.07598
$485$	9.32565	0.423456
$486$	35.9387	1.63021
$487$	29.1812	1.32233	0.661163	−	0.750242i	$-0.270063\pi$
$487$	29.1812	1.32233	0.661163	+	0.750242i	$0.270063\pi$
$488$	12.9751	0.587357
$489$	−47.8837	−2.16538
$490$	−2.11453	−0.0955247
$491$	−24.2620	−1.09493	−0.547465	−	0.836829i	$-0.684407\pi$
$491$	−24.2620	−1.09493	−0.547465	+	0.836829i	$0.684407\pi$
$492$	−46.9355	−2.11602
$493$	−60.6955	−2.73359
$494$	16.1204	0.725290
$495$	−21.2984	−0.957291
$496$	12.7368	0.571900
$497$	4.39289	0.197048
$498$	−12.2238	−0.547763
$499$	−28.3371	−1.26854	−0.634272	−	0.773110i	$-0.718700\pi$
$499$	−28.3371	−1.26854	−0.634272	+	0.773110i	$0.718700\pi$
$500$	−2.47123	−0.110517
$501$	−8.04849	−0.359580
$502$	54.7050	2.44160
$503$	−44.6739	−1.99191	−0.995955	−	0.0898532i	$-0.971360\pi$
$503$	−44.6739	−1.99191	−0.995955	+	0.0898532i	$0.971360\pi$
$504$	−4.67826	−0.208386
$505$	4.40127	0.195854
$506$	−19.6066	−0.871618
$507$	−33.4241	−1.48442
$508$	9.74076	0.432177
$509$	−10.4258	−0.462114	−0.231057	−	0.972940i	$-0.574218\pi$
$509$	−10.4258	−0.462114	−0.231057	+	0.972940i	$0.574218\pi$
$510$	37.3671	1.65465
$511$	−8.71633	−0.385588
$512$	28.3021	1.25079
$513$	−7.16212	−0.316215
$514$	36.1994	1.59669
$515$	11.1776	0.492545
$516$	23.2148	1.02198
$517$	−24.5001	−1.07751
$518$	−4.31735	−0.189693
$519$	−28.0045	−1.22926
$520$	−4.98706	−0.218697
$521$	−39.0560	−1.71107	−0.855537	−	0.517742i	$-0.826773\pi$
$521$	−39.0560	−1.71107	−0.855537	+	0.517742i	$0.826773\pi$
$522$	−94.5876	−4.13999
$523$	−7.37453	−0.322466	−0.161233	−	0.986916i	$-0.551547\pi$
$523$	−7.37453	−0.322466	−0.161233	+	0.986916i	$0.551547\pi$
$524$	49.0708	2.14367
$525$	2.77399	0.121067
$526$	51.2776	2.23581
$527$	−28.6159	−1.24653
$528$	35.6813	1.55283
$529$	−18.8221	−0.818354
$530$	−23.6703	−1.02817
$531$	34.9479	1.51661
$532$	−3.76425	−0.163201
$533$	34.2673	1.48428
$534$	7.49146	0.324187
$535$	10.8833	0.470527
$536$	−5.54796	−0.239635
$537$	−58.4699	−2.52316
$538$	−54.7083	−2.35864
$539$	4.53639	0.195396
$540$	11.6195	0.500026
$541$	−21.5199	−0.925212	−0.462606	−	0.886564i	$-0.653086\pi$
$541$	−21.5199	−0.925212	−0.462606	+	0.886564i	$0.653086\pi$
$542$	52.0970	2.23776
$543$	47.7044	2.04719
$544$	−50.8910	−2.18193
$545$	−2.98412	−0.127826
$546$	29.3572	1.25637
$547$	−9.33707	−0.399224	−0.199612	−	0.979875i	$-0.563968\pi$
$547$	−9.33707	−0.399224	−0.199612	+	0.979875i	$0.563968\pi$
$548$	8.24609	0.352255
$549$	61.1365	2.60924
$550$	9.59233	0.409018
$551$	−14.5128	−0.618265
$552$	5.64976	0.240470
$553$	10.9171	0.464244
$554$	−3.68059	−0.156373
$555$	5.66380	0.240415
$556$	41.2496	1.74937
$557$	42.6513	1.80719	0.903597	−	0.428383i	$-0.140917\pi$
$557$	42.6513	1.80719	0.903597	+	0.428383i	$0.140917\pi$
$558$	−44.5948	−1.88785
$559$	−16.9490	−0.716866
$560$	−2.83548	−0.119821
$561$	−80.1654	−3.38459
$562$	34.9179	1.47292
$563$	29.6589	1.24997	0.624986	−	0.780636i	$-0.285105\pi$
$563$	29.6589	1.24997	0.624986	+	0.780636i	$0.285105\pi$
$564$	37.0233	1.55896
$565$	−16.7466	−0.704534
$566$	23.8407	1.00210
$567$	1.04193	0.0437572
$568$	−4.37721	−0.183664
$569$	22.8690	0.958719	0.479359	−	0.877619i	$-0.340869\pi$
$569$	22.8690	0.958719	0.479359	+	0.877619i	$0.340869\pi$
$570$	8.93477	0.374237
$571$	2.19067	0.0916765	0.0458382	−	0.998949i	$-0.485404\pi$
$571$	2.19067	0.0916765	0.0458382	+	0.998949i	$0.485404\pi$
$572$	56.1074	2.34597
$573$	17.6448	0.737122
$574$	−14.4776	−0.604284
$575$	−2.04398	−0.0852400
$576$	−52.6831	−2.19513
$577$	−29.1413	−1.21317	−0.606585	−	0.795019i	$-0.707461\pi$
$577$	−29.1413	−1.21317	−0.606585	+	0.795019i	$0.707461\pi$
$578$	49.8669	2.07419
$579$	−57.1951	−2.37695
$580$	23.5450	0.977652
$581$	−2.08396	−0.0864572
$582$	54.7012	2.26744
$583$	50.7809	2.10313
$584$	8.68524	0.359398
$585$	−23.4981	−0.971526
$586$	−18.6312	−0.769648
$587$	11.5862	0.478215	0.239107	−	0.970993i	$-0.423145\pi$
$587$	11.5862	0.478215	0.239107	+	0.970993i	$0.423145\pi$
$588$	−6.85517	−0.282702
$589$	−6.84227	−0.281931
$590$	−15.7398	−0.647996
$591$	−4.80224	−0.197538
$592$	−5.78934	−0.237941
$593$	21.8371	0.896742	0.448371	−	0.893848i	$-0.352004\pi$
$593$	21.8371	0.896742	0.448371	+	0.893848i	$0.352004\pi$
$594$	−45.1024	−1.85057
$595$	6.37048	0.261164
$596$	−4.45633	−0.182538
$597$	14.7000	0.601631
$598$	−21.6315	−0.884579
$599$	30.1002	1.22986	0.614930	−	0.788582i	$-0.289184\pi$
$599$	30.1002	1.22986	0.614930	+	0.788582i	$0.289184\pi$
$600$	−2.76409	−0.112844
$601$	−33.5967	−1.37044	−0.685219	−	0.728337i	$-0.740293\pi$
$601$	−33.5967	−1.37044	−0.685219	+	0.728337i	$0.740293\pi$
$602$	7.16079	0.291852
$603$	−26.1410	−1.06454
$604$	−30.2588	−1.23121
$605$	−9.57884	−0.389435
$606$	25.8164	1.04872
$607$	7.67036	0.311330	0.155665	−	0.987810i	$-0.450248\pi$
$607$	7.67036	0.311330	0.155665	+	0.987810i	$0.450248\pi$
$608$	−12.1684	−0.493495
$609$	−26.4295	−1.07098
$610$	−27.5345	−1.11484
$611$	−27.0305	−1.09354
$612$	73.9131	2.98776
$613$	15.5992	0.630048	0.315024	−	0.949084i	$-0.397987\pi$
$613$	15.5992	0.630048	0.315024	+	0.949084i	$0.397987\pi$
$614$	−5.05879	−0.204156
$615$	18.9928	0.765862
$616$	−4.52021	−0.182124
$617$	12.5666	0.505914	0.252957	−	0.967478i	$-0.418597\pi$
$617$	12.5666	0.505914	0.252957	+	0.967478i	$0.418597\pi$
$618$	65.5644	2.63739
$619$	−17.4444	−0.701148	−0.350574	−	0.936535i	$-0.614014\pi$
$619$	−17.4444	−0.701148	−0.350574	+	0.936535i	$0.614014\pi$
$620$	11.1006	0.445813
$621$	9.61066	0.385663
$622$	39.0316	1.56502
$623$	1.27717	0.0511687
$624$	39.3665	1.57592
$625$	1.00000	0.0400000
$626$	32.3758	1.29400
$627$	−19.1682	−0.765503
$628$	−3.56606	−0.142301
$629$	13.0069	0.518621
$630$	9.92773	0.395530
$631$	−24.3491	−0.969321	−0.484660	−	0.874702i	$-0.661057\pi$
$631$	−24.3491	−0.969321	−0.484660	+	0.874702i	$0.661057\pi$
$632$	−10.8782	−0.432712
$633$	−61.4621	−2.44290
$634$	−11.9444	−0.474371
$635$	−3.94166	−0.156420
$636$	−76.7375	−3.04284
$637$	5.00491	0.198302
$638$	−91.3921	−3.61825
$639$	−20.6246	−0.815898
$640$	7.75019	0.306353
$641$	−28.6277	−1.13072	−0.565362	−	0.824843i	$-0.691264\pi$
$641$	−28.6277	−1.13072	−0.565362	+	0.824843i	$0.691264\pi$
$642$	63.8380	2.51948
$643$	−34.1050	−1.34497	−0.672486	−	0.740110i	$-0.734773\pi$
$643$	−34.1050	−1.34497	−0.672486	+	0.740110i	$0.734773\pi$
$644$	5.05116	0.199043
$645$	−9.39403	−0.369889
$646$	20.5188	0.807300
$647$	40.7560	1.60229	0.801143	−	0.598473i	$-0.204226\pi$
$647$	40.7560	1.60229	0.801143	+	0.598473i	$0.204226\pi$
$648$	−1.03822	−0.0407851
$649$	33.7672	1.32548
$650$	10.5830	0.415100
$651$	−12.4606	−0.488370
$652$	42.6576	1.67060
$653$	−18.0164	−0.705037	−0.352518	−	0.935805i	$-0.614675\pi$
$653$	−18.0164	−0.705037	−0.352518	+	0.935805i	$0.614675\pi$
$654$	−17.5039	−0.684457
$655$	−19.8568	−0.775870
$656$	−19.4138	−0.757980
$657$	40.9232	1.59657
$658$	11.4201	0.445203
$659$	−25.4889	−0.992907	−0.496453	−	0.868063i	$-0.665365\pi$
$659$	−25.4889	−0.992907	−0.496453	+	0.868063i	$0.665365\pi$
$660$	31.0977	1.21048
$661$	29.2232	1.13665	0.568325	−	0.822804i	$-0.307592\pi$
$661$	29.2232	1.13665	0.568325	+	0.822804i	$0.307592\pi$
$662$	47.6013	1.85008
$663$	−88.4449	−3.43491
$664$	2.07652	0.0805848
$665$	1.52323	0.0590683
$666$	20.2700	0.785445
$667$	19.4743	0.754048
$668$	7.17007	0.277418
$669$	−33.1559	−1.28188
$670$	11.7733	0.454843
$671$	59.0710	2.28041
$672$	−22.1602	−0.854847
$673$	44.6022	1.71929	0.859644	−	0.510893i	$-0.170685\pi$
$673$	44.6022	1.71929	0.859644	+	0.510893i	$0.170685\pi$
$674$	1.93053	0.0743612
$675$	−4.70193	−0.180977
$676$	29.7762	1.14524
$677$	12.2997	0.472718	0.236359	−	0.971666i	$-0.424046\pi$
$677$	12.2997	0.472718	0.236359	+	0.971666i	$0.424046\pi$
$678$	−98.2301	−3.77250
$679$	9.32565	0.357886
$680$	−6.34775	−0.243425
$681$	44.4442	1.70310
$682$	−43.0883	−1.64993
$683$	28.9302	1.10698	0.553492	−	0.832854i	$-0.313295\pi$
$683$	28.9302	1.10698	0.553492	+	0.832854i	$0.313295\pi$
$684$	17.6732	0.675752
$685$	−3.33683	−0.127494
$686$	−2.11453	−0.0807331
$687$	−2.77399	−0.105834
$688$	9.60226	0.366083
$689$	56.0256	2.13440
$690$	−11.9893	−0.456427
$691$	−22.8650	−0.869825	−0.434913	−	0.900473i	$-0.643221\pi$
$691$	−22.8650	−0.869825	−0.434913	+	0.900473i	$0.643221\pi$
$692$	24.9481	0.948384
$693$	−21.2984	−0.809059
$694$	−72.0415	−2.73466
$695$	−16.6919	−0.633160
$696$	26.3352	0.998234
$697$	43.6170	1.65211
$698$	−64.1349	−2.42754
$699$	29.9383	1.13237
$700$	−2.47123	−0.0934038
$701$	−29.1680	−1.10166	−0.550830	−	0.834617i	$-0.685689\pi$
$701$	−29.1680	−1.10166	−0.550830	+	0.834617i	$0.685689\pi$
$702$	−49.7606	−1.87809
$703$	3.11006	0.117298
$704$	−50.9033	−1.91849
$705$	−14.9817	−0.564245
$706$	−10.5703	−0.397819
$707$	4.40127	0.165527
$708$	−51.0273	−1.91772
$709$	−29.7709	−1.11807	−0.559034	−	0.829144i	$-0.688828\pi$
$709$	−29.7709	−1.11807	−0.559034	+	0.829144i	$0.688828\pi$
$710$	9.28888	0.348606
$711$	−51.2561	−1.92225
$712$	−1.27261	−0.0476932
$713$	9.18147	0.343849
$714$	37.3671	1.39843
$715$	−22.7042	−0.849090
$716$	52.0884	1.94664
$717$	8.53009	0.318562
$718$	3.19661	0.119296
$719$	18.6006	0.693687	0.346844	−	0.937923i	$-0.387253\pi$
$719$	18.6006	0.693687	0.346844	+	0.937923i	$0.387253\pi$
$720$	13.3126	0.496131
$721$	11.1776	0.416277
$722$	−35.2699	−1.31261
$723$	−35.6126	−1.32445
$724$	−42.4979	−1.57942
$725$	−9.52762	−0.353847
$726$	−56.1864	−2.08527
$727$	31.4828	1.16763	0.583816	−	0.811886i	$-0.301559\pi$
$727$	31.4828	1.16763	0.583816	+	0.811886i	$0.301559\pi$
$728$	−4.98706	−0.184833
$729$	−44.0211	−1.63041
$730$	−18.4309	−0.682159
$731$	−21.5734	−0.797922
$732$	−89.2652	−3.29934
$733$	27.5305	1.01686	0.508431	−	0.861103i	$-0.330226\pi$
$733$	27.5305	1.01686	0.508431	+	0.861103i	$0.330226\pi$
$734$	16.6419	0.614263
$735$	2.77399	0.102320
$736$	16.3285	0.601876
$737$	−25.2578	−0.930383
$738$	67.9725	2.50210
$739$	33.1578	1.21973	0.609865	−	0.792505i	$-0.291224\pi$
$739$	33.1578	1.21973	0.609865	+	0.792505i	$0.291224\pi$
$740$	−5.04564	−0.185482
$741$	−21.1479	−0.776886
$742$	−23.6703	−0.868963
$743$	29.1849	1.07069	0.535344	−	0.844634i	$-0.320182\pi$
$743$	29.1849	1.07069	0.535344	+	0.844634i	$0.320182\pi$
$744$	12.4162	0.455199
$745$	1.80328	0.0660671
$746$	59.2592	2.16963
$747$	9.78420	0.357985
$748$	71.4160	2.61123
$749$	10.8833	0.397668
$750$	5.86568	0.214184
$751$	14.6743	0.535471	0.267736	−	0.963492i	$-0.413725\pi$
$751$	14.6743	0.535471	0.267736	+	0.963492i	$0.413725\pi$
$752$	15.3138	0.558438
$753$	−71.7658	−2.61529
$754$	−100.831	−3.67205
$755$	12.2444	0.445620
$756$	11.6195	0.422599
$757$	−30.0394	−1.09180	−0.545901	−	0.837850i	$-0.683813\pi$
$757$	−30.0394	−1.09180	−0.545901	+	0.837850i	$0.683813\pi$
$758$	−53.0724	−1.92768
$759$	25.7213	0.933623
$760$	−1.51780	−0.0550563
$761$	15.9968	0.579884	0.289942	−	0.957044i	$-0.406364\pi$
$761$	15.9968	0.579884	0.289942	+	0.957044i	$0.406364\pi$
$762$	−23.1205	−0.837568
$763$	−2.98412	−0.108033
$764$	−15.7190	−0.568695
$765$	−29.9094	−1.08138
$766$	76.7161	2.77186
$767$	37.2547	1.34519
$768$	−16.7942	−0.606009
$769$	−18.9162	−0.682137	−0.341068	−	0.940038i	$-0.610789\pi$
$769$	−18.9162	−0.682137	−0.341068	+	0.940038i	$0.610789\pi$
$770$	9.59233	0.345684
$771$	−47.4889	−1.71027
$772$	50.9527	1.83383
$773$	5.47300	0.196850	0.0984251	−	0.995144i	$-0.468620\pi$
$773$	5.47300	0.196850	0.0984251	+	0.995144i	$0.468620\pi$
$774$	−33.6200	−1.20844
$775$	−4.49195	−0.161356
$776$	−9.29238	−0.333577
$777$	5.66380	0.203188
$778$	14.9423	0.535709
$779$	10.4292	0.373663
$780$	34.3095	1.22848
$781$	−19.9278	−0.713074
$782$	−27.5336	−0.984599
$783$	44.7982	1.60096
$784$	−2.83548	−0.101267
$785$	1.44303	0.0515040
$786$	−116.474	−4.15448
$787$	9.03353	0.322010	0.161005	−	0.986954i	$-0.448526\pi$
$787$	9.03353	0.322010	0.161005	+	0.986954i	$0.448526\pi$
$788$	4.27812	0.152402
$789$	−67.2695	−2.39486
$790$	23.0846	0.821314
$791$	−16.7466	−0.595440
$792$	21.2224	0.754105
$793$	65.1719	2.31432
$794$	60.7318	2.15529
$795$	31.0523	1.10131
$796$	−13.0956	−0.464162
$797$	−26.7751	−0.948423	−0.474212	−	0.880411i	$-0.657267\pi$
$797$	−26.7751	−0.948423	−0.474212	+	0.880411i	$0.657267\pi$
$798$	8.93477	0.316288
$799$	−34.4056	−1.21718
$800$	−7.98856	−0.282438
$801$	−5.99631	−0.211869
$802$	−11.2743	−0.398110
$803$	39.5407	1.39536
$804$	38.1683	1.34609
$805$	−2.04398	−0.0720410
$806$	−47.5384	−1.67447
$807$	71.7702	2.52643
$808$	−4.38557	−0.154284
$809$	24.4374	0.859174	0.429587	−	0.903026i	$-0.358659\pi$
$809$	24.4374	0.859174	0.429587	+	0.903026i	$0.358659\pi$
$810$	2.20320	0.0774126
$811$	8.67868	0.304750	0.152375	−	0.988323i	$-0.451308\pi$
$811$	8.67868	0.304750	0.152375	+	0.988323i	$0.451308\pi$
$812$	23.5450	0.826266
$813$	−68.3445	−2.39695
$814$	19.5852	0.686460
$815$	−17.2617	−0.604650
$816$	50.1075	1.75411
$817$	−5.15837	−0.180469
$818$	−35.1229	−1.22804
$819$	−23.4981	−0.821090
$820$	−16.9199	−0.590867
$821$	−22.8269	−0.796665	−0.398333	−	0.917241i	$-0.630411\pi$
$821$	−22.8269	−0.796665	−0.398333	+	0.917241i	$0.630411\pi$
$822$	−19.5728	−0.682679
$823$	−24.1544	−0.841969	−0.420984	−	0.907068i	$-0.638315\pi$
$823$	−24.1544	−0.841969	−0.420984	+	0.907068i	$0.638315\pi$
$824$	−11.1378	−0.388002
$825$	−12.5839	−0.438115
$826$	−15.7398	−0.547656
$827$	33.1616	1.15314	0.576571	−	0.817047i	$-0.304390\pi$
$827$	33.1616	1.15314	0.576571	+	0.817047i	$0.304390\pi$
$828$	−23.7152	−0.824161
$829$	26.6091	0.924172	0.462086	−	0.886835i	$-0.347101\pi$
$829$	26.6091	0.924172	0.462086	+	0.886835i	$0.347101\pi$
$830$	−4.40659	−0.152955
$831$	4.82845	0.167497
$832$	−56.1606	−1.94702
$833$	6.37048	0.220724
$834$	−97.9094	−3.39032
$835$	−2.90141	−0.100408
$836$	17.0761	0.590590
$837$	21.1208	0.730042
$838$	−41.8489	−1.44565
$839$	−39.8978	−1.37742	−0.688712	−	0.725035i	$-0.741824\pi$
$839$	−39.8978	−1.37742	−0.688712	+	0.725035i	$0.741824\pi$
$840$	−2.76409	−0.0953702
$841$	61.7756	2.13019
$842$	−13.6646	−0.470913
$843$	−45.8078	−1.57770
$844$	54.7540	1.88471
$845$	−12.0491	−0.414503
$846$	−53.6176	−1.84341
$847$	−9.57884	−0.329133
$848$	−31.7407	−1.08998
$849$	−31.2759	−1.07338
$850$	13.4706	0.462036
$851$	−4.17331	−0.143059
$852$	30.1140	1.03169
$853$	−22.7539	−0.779078	−0.389539	−	0.921010i	$-0.627366\pi$
$853$	−22.7539	−0.779078	−0.389539	+	0.921010i	$0.627366\pi$
$854$	−27.5345	−0.942212
$855$	−7.15157	−0.244579
$856$	−10.8445	−0.370657
$857$	51.4636	1.75796	0.878982	−	0.476855i	$-0.158223\pi$
$857$	51.4636	1.75796	0.878982	+	0.476855i	$0.158223\pi$
$858$	−133.176	−4.54654
$859$	41.3429	1.41060	0.705301	−	0.708908i	$-0.250812\pi$
$859$	41.3429	1.41060	0.705301	+	0.708908i	$0.250812\pi$
$860$	8.36875	0.285372
$861$	18.9928	0.647271
$862$	−36.4762	−1.24239
$863$	−22.0809	−0.751644	−0.375822	−	0.926692i	$-0.622640\pi$
$863$	−22.0809	−0.751644	−0.375822	+	0.926692i	$0.622640\pi$
$864$	37.5616	1.27787
$865$	−10.0954	−0.343254
$866$	51.6413	1.75484
$867$	−65.4188	−2.22174
$868$	11.1006	0.376781
$869$	−49.5245	−1.68000
$870$	−55.8860	−1.89471
$871$	−27.8664	−0.944218
$872$	2.97348	0.100695
$873$	−43.7840	−1.48186
$874$	−6.58350	−0.222690
$875$	1.00000	0.0338062
$876$	−59.7519	−2.01883
$877$	−41.4408	−1.39936	−0.699679	−	0.714457i	$-0.746674\pi$
$877$	−41.4408	−1.39936	−0.699679	+	0.714457i	$0.746674\pi$
$878$	−31.2133	−1.05340
$879$	24.4417	0.824399
$880$	12.8628	0.433606
$881$	−25.4755	−0.858293	−0.429146	−	0.903235i	$-0.641186\pi$
$881$	−25.4755	−0.858293	−0.429146	+	0.903235i	$0.641186\pi$
$882$	9.92773	0.334284
$883$	−18.9663	−0.638268	−0.319134	−	0.947710i	$-0.603392\pi$
$883$	−18.9663	−0.638268	−0.319134	+	0.947710i	$0.603392\pi$
$884$	78.7919	2.65006
$885$	20.6485	0.694093
$886$	10.5503	0.354446
$887$	−22.6669	−0.761081	−0.380540	−	0.924764i	$-0.624262\pi$
$887$	−22.6669	−0.761081	−0.380540	+	0.924764i	$0.624262\pi$
$888$	−5.64359	−0.189387
$889$	−3.94166	−0.132199
$890$	2.70061	0.0905246
$891$	−4.72662	−0.158348
$892$	29.5372	0.988980
$893$	−8.22665	−0.275294
$894$	10.5775	0.353763
$895$	−21.0779	−0.704557
$896$	7.75019	0.258916
$897$	28.3778	0.947506
$898$	5.10327	0.170298
$899$	42.7976	1.42738
$900$	11.6024	0.386748
$901$	71.3119	2.37574
$902$	65.6761	2.18678
$903$	−9.39403	−0.312614
$904$	16.6868	0.554996
$905$	17.1971	0.571650
$906$	71.8219	2.38612
$907$	−33.5545	−1.11416	−0.557080	−	0.830459i	$-0.688078\pi$
$907$	−33.5545	−1.11416	−0.557080	+	0.830459i	$0.688078\pi$
$908$	−39.5935	−1.31396
$909$	−20.6640	−0.685382
$910$	10.5830	0.350824
$911$	−21.5556	−0.714168	−0.357084	−	0.934072i	$-0.616229\pi$
$911$	−21.5556	−0.714168	−0.357084	+	0.934072i	$0.616229\pi$
$912$	11.9811	0.396733
$913$	9.45365	0.312870
$914$	74.1242	2.45181
$915$	36.1217	1.19415
$916$	2.47123	0.0816518
$917$	−19.8568	−0.655730
$918$	−63.3376	−2.09045
$919$	−25.9749	−0.856834	−0.428417	−	0.903581i	$-0.640929\pi$
$919$	−25.9749	−0.856834	−0.428417	+	0.903581i	$0.640929\pi$
$920$	2.03669	0.0671478
$921$	6.63648	0.218680
$922$	3.69832	0.121798
$923$	−21.9860	−0.723678
$924$	31.0977	1.02304
$925$	2.04175	0.0671324
$926$	−43.7702	−1.43838
$927$	−52.4791	−1.72364
$928$	76.1120	2.49850
$929$	19.5937	0.642848	0.321424	−	0.946935i	$-0.395838\pi$
$929$	19.5937	0.642848	0.321424	+	0.946935i	$0.395838\pi$
$930$	−26.3483	−0.863995
$931$	1.52323	0.0499219
$932$	−26.6708	−0.873631
$933$	−51.2044	−1.67636
$934$	−1.33070	−0.0435418
$935$	−28.8990	−0.945097
$936$	23.4143	0.765319
$937$	25.9639	0.848205	0.424103	−	0.905614i	$-0.360590\pi$
$937$	25.9639	0.848205	0.424103	+	0.905614i	$0.360590\pi$
$938$	11.7733	0.384412
$939$	−42.4728	−1.38605
$940$	13.3466	0.435318
$941$	0.188381	0.00614106	0.00307053	−	0.999995i	$-0.499023\pi$
$941$	0.188381	0.00614106	0.00307053	+	0.999995i	$0.499023\pi$
$942$	8.46435	0.275783
$943$	−13.9946	−0.455727
$944$	−21.1062	−0.686950
$945$	−4.70193	−0.152954
$946$	−32.4841	−1.05615
$947$	−35.5644	−1.15569	−0.577844	−	0.816147i	$-0.696106\pi$
$947$	−35.5644	−1.15569	−0.577844	+	0.816147i	$0.696106\pi$
$948$	74.8389	2.43065
$949$	43.6245	1.41611
$950$	3.22091	0.104500
$951$	15.6695	0.508117
$952$	−6.34775	−0.205732
$953$	40.5427	1.31331	0.656654	−	0.754192i	$-0.271971\pi$
$953$	40.5427	1.31331	0.656654	+	0.754192i	$0.271971\pi$
$954$	111.132	3.59804
$955$	6.36081	0.205831
$956$	−7.59911	−0.245773
$957$	119.895	3.87564
$958$	−46.4591	−1.50103
$959$	−3.33683	−0.107752
$960$	−31.1272	−1.00463
$961$	−10.8224	−0.349109
$962$	21.6079	0.696667
$963$	−51.0972	−1.64659
$964$	31.7258	1.02182
$965$	−20.6184	−0.663728
$966$	−11.9893	−0.385751
$967$	−8.41159	−0.270498	−0.135249	−	0.990812i	$-0.543184\pi$
$967$	−8.41159	−0.270498	−0.135249	+	0.990812i	$0.543184\pi$
$968$	9.54467	0.306777
$969$	−26.9179	−0.864729
$970$	19.7194	0.633150
$971$	25.5983	0.821490	0.410745	−	0.911750i	$-0.365269\pi$
$971$	25.5983	0.821490	0.410745	+	0.911750i	$0.365269\pi$
$972$	42.0013	1.34719
$973$	−16.6919	−0.535118
$974$	61.7044	1.97714
$975$	−13.8836	−0.444630
$976$	−36.9224	−1.18186
$977$	55.4297	1.77335	0.886676	−	0.462391i	$-0.153008\pi$
$977$	55.4297	1.77335	0.886676	+	0.462391i	$0.153008\pi$
$978$	−101.251	−3.23766
$979$	−5.79373	−0.185169
$980$	−2.47123	−0.0789406
$981$	14.0105	0.447320
$982$	−51.3027	−1.63714
$983$	22.5803	0.720199	0.360100	−	0.932914i	$-0.382743\pi$
$983$	22.5803	0.720199	0.360100	+	0.932914i	$0.382743\pi$
$984$	−18.9250	−0.603307
$985$	−1.73117	−0.0551596
$986$	−128.342	−4.08725
$987$	−14.9817	−0.476874
$988$	18.8398	0.599372
$989$	6.92189	0.220103
$990$	−45.0360	−1.43134
$991$	−21.2983	−0.676564	−0.338282	−	0.941045i	$-0.609846\pi$
$991$	−21.2983	−0.676564	−0.338282	+	0.941045i	$0.609846\pi$
$992$	35.8842	1.13933
$993$	−62.4467	−1.98169
$994$	9.28888	0.294625
$995$	5.29923	0.167997
$996$	−14.2859	−0.452665
$997$	−49.3983	−1.56446	−0.782230	−	0.622990i	$-0.785918\pi$
$997$	−49.3983	−1.56446	−0.782230	+	0.622990i	$0.785918\pi$
$998$	−59.9197	−1.89673
$999$	−9.60017	−0.303736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.53	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.53	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q+2.11453 q^{2} -2.77399 q^{3} +2.47123 q^{4} -1.00000 q^{5} -5.86568 q^{6} -1.00000 q^{7} +0.996433 q^{8} +4.69501 q^{9} +O(q^{10})\)	\(q+2.11453 q^{2} -2.77399 q^{3} +2.47123 q^{4} -1.00000 q^{5} -5.86568 q^{6} -1.00000 q^{7} +0.996433 q^{8} +4.69501 q^{9} -2.11453 q^{10} +4.53639 q^{11} -6.85517 q^{12} +5.00491 q^{13} -2.11453 q^{14} +2.77399 q^{15} -2.83548 q^{16} +6.37048 q^{17} +9.92773 q^{18} +1.52323 q^{19} -2.47123 q^{20} +2.77399 q^{21} +9.59233 q^{22} -2.04398 q^{23} -2.76409 q^{24} +1.00000 q^{25} +10.5830 q^{26} -4.70193 q^{27} -2.47123 q^{28} -9.52762 q^{29} +5.86568 q^{30} -4.49195 q^{31} -7.98856 q^{32} -12.5839 q^{33} +13.4706 q^{34} +1.00000 q^{35} +11.6024 q^{36} +2.04175 q^{37} +3.22091 q^{38} -13.8836 q^{39} -0.996433 q^{40} +6.84673 q^{41} +5.86568 q^{42} -3.38647 q^{43} +11.2105 q^{44} -4.69501 q^{45} -4.32206 q^{46} -5.40079 q^{47} +7.86558 q^{48} +1.00000 q^{49} +2.11453 q^{50} -17.6716 q^{51} +12.3683 q^{52} +11.1941 q^{53} -9.94236 q^{54} -4.53639 q^{55} -0.996433 q^{56} -4.22542 q^{57} -20.1464 q^{58} +7.44363 q^{59} +6.85517 q^{60} +13.0216 q^{61} -9.49836 q^{62} -4.69501 q^{63} -11.2211 q^{64} -5.00491 q^{65} -26.6090 q^{66} -5.56782 q^{67} +15.7429 q^{68} +5.66999 q^{69} +2.11453 q^{70} -4.39289 q^{71} +4.67826 q^{72} +8.71633 q^{73} +4.31735 q^{74} -2.77399 q^{75} +3.76425 q^{76} -4.53639 q^{77} -29.3572 q^{78} -10.9171 q^{79} +2.83548 q^{80} -1.04193 q^{81} +14.4776 q^{82} +2.08396 q^{83} +6.85517 q^{84} -6.37048 q^{85} -7.16079 q^{86} +26.4295 q^{87} +4.52021 q^{88} -1.27717 q^{89} -9.92773 q^{90} -5.00491 q^{91} -5.05116 q^{92} +12.4606 q^{93} -11.4201 q^{94} -1.52323 q^{95} +22.1602 q^{96} -9.32565 q^{97} +2.11453 q^{98} +21.2984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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