LMFDB - Embedded newform 8015.2.a.o.1.15

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:	$73$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-1.86693 q^{2} -0.178602 q^{3} +1.48541 q^{4} +1.00000 q^{5} +0.333437 q^{6} +1.00000 q^{7} +0.960700 q^{8} -2.96810 q^{9} +O(q^{10})$	\(q-1.86693 q^{2} -0.178602 q^{3} +1.48541 q^{4} +1.00000 q^{5} +0.333437 q^{6} +1.00000 q^{7} +0.960700 q^{8} -2.96810 q^{9} -1.86693 q^{10} +6.52236 q^{11} -0.265298 q^{12} +3.33389 q^{13} -1.86693 q^{14} -0.178602 q^{15} -4.76438 q^{16} +3.94052 q^{17} +5.54122 q^{18} -3.03563 q^{19} +1.48541 q^{20} -0.178602 q^{21} -12.1768 q^{22} -2.54700 q^{23} -0.171583 q^{24} +1.00000 q^{25} -6.22413 q^{26} +1.06592 q^{27} +1.48541 q^{28} -7.17557 q^{29} +0.333437 q^{30} -8.61035 q^{31} +6.97334 q^{32} -1.16491 q^{33} -7.35665 q^{34} +1.00000 q^{35} -4.40885 q^{36} +8.56403 q^{37} +5.66729 q^{38} -0.595442 q^{39} +0.960700 q^{40} +0.468490 q^{41} +0.333437 q^{42} +0.800583 q^{43} +9.68838 q^{44} -2.96810 q^{45} +4.75507 q^{46} +4.61726 q^{47} +0.850929 q^{48} +1.00000 q^{49} -1.86693 q^{50} -0.703786 q^{51} +4.95220 q^{52} -1.95848 q^{53} -1.98999 q^{54} +6.52236 q^{55} +0.960700 q^{56} +0.542170 q^{57} +13.3962 q^{58} +9.89533 q^{59} -0.265298 q^{60} -11.3677 q^{61} +16.0749 q^{62} -2.96810 q^{63} -3.48994 q^{64} +3.33389 q^{65} +2.17480 q^{66} +9.93960 q^{67} +5.85329 q^{68} +0.454901 q^{69} -1.86693 q^{70} +11.9535 q^{71} -2.85146 q^{72} -7.50733 q^{73} -15.9884 q^{74} -0.178602 q^{75} -4.50915 q^{76} +6.52236 q^{77} +1.11165 q^{78} +5.55752 q^{79} -4.76438 q^{80} +8.71393 q^{81} -0.874635 q^{82} +3.74509 q^{83} -0.265298 q^{84} +3.94052 q^{85} -1.49463 q^{86} +1.28157 q^{87} +6.26603 q^{88} +17.6795 q^{89} +5.54122 q^{90} +3.33389 q^{91} -3.78335 q^{92} +1.53783 q^{93} -8.62009 q^{94} -3.03563 q^{95} -1.24545 q^{96} +0.713150 q^{97} -1.86693 q^{98} -19.3590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) $ 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.86693	−1.32012	−0.660058	−	0.751215i	$-0.729468\pi$
$2$	−1.86693	−1.32012	−0.660058	+	0.751215i	$0.729468\pi$
$3$	−0.178602	−0.103116	−0.0515581	−	0.998670i	$-0.516419\pi$
$3$	−0.178602	−0.103116	−0.0515581	+	0.998670i	$0.516419\pi$
$4$	1.48541	0.742705
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.333437	0.136125
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.960700	0.339659
$9$	−2.96810	−0.989367
$10$	−1.86693	−0.590374
$11$	6.52236	1.96657	0.983283	−	0.182084i	$-0.0582844\pi$
$11$	6.52236	1.96657	0.983283	+	0.182084i	$0.0582844\pi$
$12$	−0.265298	−0.0765849
$13$	3.33389	0.924656	0.462328	−	0.886709i	$-0.347014\pi$
$13$	3.33389	0.924656	0.462328	+	0.886709i	$0.347014\pi$
$14$	−1.86693	−0.498957
$15$	−0.178602	−0.0461150
$16$	−4.76438	−1.19109
$17$	3.94052	0.955716	0.477858	−	0.878437i	$-0.341413\pi$
$17$	3.94052	0.955716	0.477858	+	0.878437i	$0.341413\pi$
$18$	5.54122	1.30608
$19$	−3.03563	−0.696421	−0.348210	−	0.937416i	$-0.613210\pi$
$19$	−3.03563	−0.696421	−0.348210	+	0.937416i	$0.613210\pi$
$20$	1.48541	0.332148
$21$	−0.178602	−0.0389743
$22$	−12.1768	−2.59609
$23$	−2.54700	−0.531087	−0.265543	−	0.964099i	$-0.585551\pi$
$23$	−2.54700	−0.531087	−0.265543	+	0.964099i	$0.585551\pi$
$24$	−0.171583	−0.0350243
$25$	1.00000	0.200000
$26$	−6.22413	−1.22065
$27$	1.06592	0.205136
$28$	1.48541	0.280716
$29$	−7.17557	−1.33247	−0.666235	−	0.745742i	$-0.732095\pi$
$29$	−7.17557	−1.33247	−0.666235	+	0.745742i	$0.732095\pi$
$30$	0.333437	0.0608771
$31$	−8.61035	−1.54646	−0.773232	−	0.634123i	$-0.781361\pi$
$31$	−8.61035	−1.54646	−0.773232	+	0.634123i	$0.781361\pi$
$32$	6.97334	1.23272
$33$	−1.16491	−0.202785
$34$	−7.35665	−1.26166
$35$	1.00000	0.169031
$36$	−4.40885	−0.734808
$37$	8.56403	1.40792	0.703959	−	0.710241i	$-0.251414\pi$
$37$	8.56403	1.40792	0.703959	+	0.710241i	$0.251414\pi$
$38$	5.66729	0.919356
$39$	−0.595442	−0.0953470
$40$	0.960700	0.151900
$41$	0.468490	0.0731658	0.0365829	−	0.999331i	$-0.488353\pi$
$41$	0.468490	0.0731658	0.0365829	+	0.999331i	$0.488353\pi$
$42$	0.333437	0.0514505
$43$	0.800583	0.122088	0.0610439	−	0.998135i	$-0.480557\pi$
$43$	0.800583	0.122088	0.0610439	+	0.998135i	$0.480557\pi$
$44$	9.68838	1.46058
$45$	−2.96810	−0.442458
$46$	4.75507	0.701096
$47$	4.61726	0.673497	0.336749	−	0.941595i	$-0.390673\pi$
$47$	4.61726	0.673497	0.336749	+	0.941595i	$0.390673\pi$
$48$	0.850929	0.122821
$49$	1.00000	0.142857
$50$	−1.86693	−0.264023
$51$	−0.703786	−0.0985498
$52$	4.95220	0.686747
$53$	−1.95848	−0.269018	−0.134509	−	0.990912i	$-0.542946\pi$
$53$	−1.95848	−0.269018	−0.134509	+	0.990912i	$0.542946\pi$
$54$	−1.98999	−0.270803
$55$	6.52236	0.879475
$56$	0.960700	0.128379
$57$	0.542170	0.0718122
$58$	13.3962	1.75901
$59$	9.89533	1.28826	0.644131	−	0.764915i	$-0.277219\pi$
$59$	9.89533	1.28826	0.644131	+	0.764915i	$0.277219\pi$
$60$	−0.265298	−0.0342498
$61$	−11.3677	−1.45549	−0.727745	−	0.685847i	$-0.759432\pi$
$61$	−11.3677	−1.45549	−0.727745	+	0.685847i	$0.759432\pi$
$62$	16.0749	2.04151
$63$	−2.96810	−0.373946
$64$	−3.48994	−0.436243
$65$	3.33389	0.413519
$66$	2.17480	0.267699
$67$	9.93960	1.21432	0.607158	−	0.794581i	$-0.292310\pi$
$67$	9.93960	1.21432	0.607158	+	0.794581i	$0.292310\pi$
$68$	5.85329	0.709815
$69$	0.454901	0.0547637
$70$	−1.86693	−0.223140
$71$	11.9535	1.41862	0.709311	−	0.704896i	$-0.249006\pi$
$71$	11.9535	1.41862	0.709311	+	0.704896i	$0.249006\pi$
$72$	−2.85146	−0.336047
$73$	−7.50733	−0.878666	−0.439333	−	0.898324i	$-0.644785\pi$
$73$	−7.50733	−0.878666	−0.439333	+	0.898324i	$0.644785\pi$
$74$	−15.9884	−1.85861
$75$	−0.178602	−0.0206232
$76$	−4.50915	−0.517235
$77$	6.52236	0.743292
$78$	1.11165	0.125869
$79$	5.55752	0.625270	0.312635	−	0.949873i	$-0.398788\pi$
$79$	5.55752	0.625270	0.312635	+	0.949873i	$0.398788\pi$
$80$	−4.76438	−0.532674
$81$	8.71393	0.968214
$82$	−0.874635	−0.0965873
$83$	3.74509	0.411077	0.205539	−	0.978649i	$-0.434105\pi$
$83$	3.74509	0.411077	0.205539	+	0.978649i	$0.434105\pi$
$84$	−0.265298	−0.0289464
$85$	3.94052	0.427409
$86$	−1.49463	−0.161170
$87$	1.28157	0.137399
$88$	6.26603	0.667961
$89$	17.6795	1.87402	0.937011	−	0.349299i	$-0.113580\pi$
$89$	17.6795	1.87402	0.937011	+	0.349299i	$0.113580\pi$
$90$	5.54122	0.584096
$91$	3.33389	0.349487
$92$	−3.78335	−0.394441
$93$	1.53783	0.159465
$94$	−8.62009	−0.889094
$95$	−3.03563	−0.311449
$96$	−1.24545	−0.127114
$97$	0.713150	0.0724095	0.0362047	−	0.999344i	$-0.488473\pi$
$97$	0.713150	0.0724095	0.0362047	+	0.999344i	$0.488473\pi$
$98$	−1.86693	−0.188588
$99$	−19.3590	−1.94566
$100$	1.48541	0.148541
$101$	11.0582	1.10033	0.550166	−	0.835055i	$-0.314564\pi$
$101$	11.0582	1.10033	0.550166	+	0.835055i	$0.314564\pi$
$102$	1.31392	0.130097
$103$	−17.2307	−1.69779	−0.848896	−	0.528560i	$-0.822732\pi$
$103$	−17.2307	−1.69779	−0.848896	+	0.528560i	$0.822732\pi$
$104$	3.20287	0.314067
$105$	−0.178602	−0.0174298
$106$	3.65633	0.355134
$107$	1.93107	0.186684	0.0933419	−	0.995634i	$-0.470245\pi$
$107$	1.93107	0.186684	0.0933419	+	0.995634i	$0.470245\pi$
$108$	1.58333	0.152356
$109$	10.8530	1.03952	0.519762	−	0.854311i	$-0.326021\pi$
$109$	10.8530	1.03952	0.519762	+	0.854311i	$0.326021\pi$
$110$	−12.1768	−1.16101
$111$	−1.52956	−0.145179
$112$	−4.76438	−0.450191
$113$	−7.74448	−0.728539	−0.364270	−	0.931294i	$-0.618681\pi$
$113$	−7.74448	−0.728539	−0.364270	+	0.931294i	$0.618681\pi$
$114$	−1.01219	−0.0948004
$115$	−2.54700	−0.237509
$116$	−10.6587	−0.989632
$117$	−9.89533	−0.914824
$118$	−18.4739	−1.70066
$119$	3.94052	0.361227
$120$	−0.171583	−0.0156634
$121$	31.5412	2.86738
$122$	21.2227	1.92142
$123$	−0.0836734	−0.00754458
$124$	−12.7899	−1.14857
$125$	1.00000	0.0894427
$126$	5.54122	0.493651
$127$	−8.15990	−0.724074	−0.362037	−	0.932164i	$-0.617919\pi$
$127$	−8.15990	−0.724074	−0.362037	+	0.932164i	$0.617919\pi$
$128$	−7.43121	−0.656832
$129$	−0.142986	−0.0125892
$130$	−6.22413	−0.545892
$131$	−9.66966	−0.844842	−0.422421	−	0.906400i	$-0.638820\pi$
$131$	−9.66966	−0.844842	−0.422421	+	0.906400i	$0.638820\pi$
$132$	−1.73037	−0.150609
$133$	−3.03563	−0.263222
$134$	−18.5565	−1.60304
$135$	1.06592	0.0917396
$136$	3.78566	0.324617
$137$	3.99947	0.341698	0.170849	−	0.985297i	$-0.445349\pi$
$137$	3.99947	0.341698	0.170849	+	0.985297i	$0.445349\pi$
$138$	−0.849266	−0.0722944
$139$	−13.1127	−1.11221	−0.556104	−	0.831112i	$-0.687705\pi$
$139$	−13.1127	−1.11221	−0.556104	+	0.831112i	$0.687705\pi$
$140$	1.48541	0.125540
$141$	−0.824655	−0.0694485
$142$	−22.3163	−1.87274
$143$	21.7449	1.81840
$144$	14.1412	1.17843
$145$	−7.17557	−0.595898
$146$	14.0156	1.15994
$147$	−0.178602	−0.0147309
$148$	12.7211	1.04567
$149$	−21.8638	−1.79116	−0.895578	−	0.444904i	$-0.853238\pi$
$149$	−21.8638	−1.79116	−0.895578	+	0.444904i	$0.853238\pi$
$150$	0.333437	0.0272251
$151$	1.41103	0.114828	0.0574141	−	0.998350i	$-0.481714\pi$
$151$	1.41103	0.114828	0.0574141	+	0.998350i	$0.481714\pi$
$152$	−2.91633	−0.236545
$153$	−11.6959	−0.945554
$154$	−12.1768	−0.981231
$155$	−8.61035	−0.691600
$156$	−0.884475	−0.0708147
$157$	18.8664	1.50570	0.752852	−	0.658190i	$-0.228678\pi$
$157$	18.8664	1.50570	0.752852	+	0.658190i	$0.228678\pi$
$158$	−10.3755	−0.825429
$159$	0.349789	0.0277401
$160$	6.97334	0.551291
$161$	−2.54700	−0.200732
$162$	−16.2683	−1.27815
$163$	7.40459	0.579972	0.289986	−	0.957031i	$-0.406349\pi$
$163$	7.40459	0.579972	0.289986	+	0.957031i	$0.406349\pi$
$164$	0.695899	0.0543406
$165$	−1.16491	−0.0906881
$166$	−6.99181	−0.542669
$167$	−4.48617	−0.347151	−0.173575	−	0.984821i	$-0.555532\pi$
$167$	−4.48617	−0.347151	−0.173575	+	0.984821i	$0.555532\pi$
$168$	−0.171583	−0.0132380
$169$	−1.88515	−0.145012
$170$	−7.35665	−0.564230
$171$	9.01005	0.689016
$172$	1.18919	0.0906752
$173$	−1.04523	−0.0794674	−0.0397337	−	0.999210i	$-0.512651\pi$
$173$	−1.04523	−0.0794674	−0.0397337	+	0.999210i	$0.512651\pi$
$174$	−2.39260	−0.181383
$175$	1.00000	0.0755929
$176$	−31.0750	−2.34237
$177$	−1.76733	−0.132841
$178$	−33.0063	−2.47393
$179$	12.0848	0.903259	0.451629	−	0.892206i	$-0.350843\pi$
$179$	12.0848	0.903259	0.451629	+	0.892206i	$0.350843\pi$
$180$	−4.40885	−0.328616
$181$	7.45985	0.554486	0.277243	−	0.960800i	$-0.410579\pi$
$181$	7.45985	0.554486	0.277243	+	0.960800i	$0.410579\pi$
$182$	−6.22413	−0.461363
$183$	2.03031	0.150085
$184$	−2.44691	−0.180388
$185$	8.56403	0.629640
$186$	−2.87101	−0.210513
$187$	25.7015	1.87948
$188$	6.85853	0.500210
$189$	1.06592	0.0775341
$190$	5.66729	0.411148
$191$	13.9674	1.01065	0.505325	−	0.862929i	$-0.331373\pi$
$191$	13.9674	1.01065	0.505325	+	0.862929i	$0.331373\pi$
$192$	0.623313	0.0449837
$193$	−13.3450	−0.960596	−0.480298	−	0.877105i	$-0.659471\pi$
$193$	−13.3450	−0.960596	−0.480298	+	0.877105i	$0.659471\pi$
$194$	−1.33140	−0.0955889
$195$	−0.595442	−0.0426405
$196$	1.48541	0.106101
$197$	−15.1820	−1.08167	−0.540837	−	0.841127i	$-0.681893\pi$
$197$	−15.1820	−1.08167	−0.540837	+	0.841127i	$0.681893\pi$
$198$	36.1419	2.56849
$199$	−6.50229	−0.460935	−0.230468	−	0.973080i	$-0.574026\pi$
$199$	−6.50229	−0.460935	−0.230468	+	0.973080i	$0.574026\pi$
$200$	0.960700	0.0679318
$201$	−1.77524	−0.125216
$202$	−20.6448	−1.45257
$203$	−7.17557	−0.503626
$204$	−1.04541	−0.0731935
$205$	0.468490	0.0327207
$206$	32.1685	2.24128
$207$	7.55976	0.525440
$208$	−15.8839	−1.10135
$209$	−19.7995	−1.36956
$210$	0.333437	0.0230094
$211$	2.36052	0.162505	0.0812525	−	0.996694i	$-0.474108\pi$
$211$	2.36052	0.162505	0.0812525	+	0.996694i	$0.474108\pi$
$212$	−2.90914	−0.199801
$213$	−2.13493	−0.146283
$214$	−3.60517	−0.246444
$215$	0.800583	0.0545993
$216$	1.02403	0.0696762
$217$	−8.61035	−0.584508
$218$	−20.2617	−1.37229
$219$	1.34083	0.0906047
$220$	9.68838	0.653191
$221$	13.1373	0.883708
$222$	2.85557	0.191653
$223$	−19.5584	−1.30973	−0.654863	−	0.755748i	$-0.727274\pi$
$223$	−19.5584	−1.30973	−0.654863	+	0.755748i	$0.727274\pi$
$224$	6.97334	0.465926
$225$	−2.96810	−0.197873
$226$	14.4584	0.961756
$227$	19.7616	1.31162	0.655812	−	0.754924i	$-0.272326\pi$
$227$	19.7616	1.31162	0.655812	+	0.754924i	$0.272326\pi$
$228$	0.805346	0.0533353
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	4.75507	0.313540
$231$	−1.16491	−0.0766454
$232$	−6.89357	−0.452585
$233$	14.7625	0.967125	0.483562	−	0.875310i	$-0.339343\pi$
$233$	14.7625	0.967125	0.483562	+	0.875310i	$0.339343\pi$
$234$	18.4738	1.20767
$235$	4.61726	0.301197
$236$	14.6986	0.956800
$237$	−0.992587	−0.0644755
$238$	−7.35665	−0.476861
$239$	22.4302	1.45089	0.725443	−	0.688282i	$-0.241635\pi$
$239$	22.4302	1.45089	0.725443	+	0.688282i	$0.241635\pi$
$240$	0.850929	0.0549273
$241$	7.50896	0.483695	0.241847	−	0.970314i	$-0.422247\pi$
$241$	7.50896	0.483695	0.241847	+	0.970314i	$0.422247\pi$
$242$	−58.8851	−3.78527
$243$	−4.75408	−0.304975
$244$	−16.8858	−1.08100
$245$	1.00000	0.0638877
$246$	0.156212	0.00995971
$247$	−10.1205	−0.643949
$248$	−8.27196	−0.525270
$249$	−0.668883	−0.0423887
$250$	−1.86693	−0.118075
$251$	16.1136	1.01708	0.508541	−	0.861038i	$-0.330185\pi$
$251$	16.1136	1.01708	0.508541	+	0.861038i	$0.330185\pi$
$252$	−4.40885	−0.277731
$253$	−16.6125	−1.04442
$254$	15.2339	0.955862
$255$	−0.703786	−0.0440728
$256$	20.8534	1.30334
$257$	−3.97052	−0.247674	−0.123837	−	0.992303i	$-0.539520\pi$
$257$	−3.97052	−0.247674	−0.123837	+	0.992303i	$0.539520\pi$
$258$	0.266944	0.0166192
$259$	8.56403	0.532143
$260$	4.95220	0.307122
$261$	21.2978	1.31830
$262$	18.0525	1.11529
$263$	−17.2589	−1.06423	−0.532114	−	0.846672i	$-0.678602\pi$
$263$	−17.2589	−1.06423	−0.532114	+	0.846672i	$0.678602\pi$
$264$	−1.11913	−0.0688776
$265$	−1.95848	−0.120308
$266$	5.66729	0.347484
$267$	−3.15760	−0.193242
$268$	14.7644	0.901878
$269$	0.850845	0.0518770	0.0259385	−	0.999664i	$-0.491743\pi$
$269$	0.850845	0.0518770	0.0259385	+	0.999664i	$0.491743\pi$
$270$	−1.98999	−0.121107
$271$	1.04139	0.0632599	0.0316299	−	0.999500i	$-0.489930\pi$
$271$	1.04139	0.0632599	0.0316299	+	0.999500i	$0.489930\pi$
$272$	−18.7741	−1.13835
$273$	−0.595442	−0.0360378
$274$	−7.46671	−0.451080
$275$	6.52236	0.393313
$276$	0.675715	0.0406733
$277$	26.9528	1.61944	0.809718	−	0.586820i	$-0.199620\pi$
$277$	26.9528	1.61944	0.809718	+	0.586820i	$0.199620\pi$
$278$	24.4805	1.46824
$279$	25.5564	1.53002
$280$	0.960700	0.0574128
$281$	2.04057	0.121730	0.0608651	−	0.998146i	$-0.480614\pi$
$281$	2.04057	0.121730	0.0608651	+	0.998146i	$0.480614\pi$
$282$	1.53957	0.0916800
$283$	−18.9506	−1.12649	−0.563247	−	0.826289i	$-0.690448\pi$
$283$	−18.9506	−1.12649	−0.563247	+	0.826289i	$0.690448\pi$
$284$	17.7559	1.05362
$285$	0.542170	0.0321154
$286$	−40.5960	−2.40049
$287$	0.468490	0.0276541
$288$	−20.6976	−1.21962
$289$	−1.47231	−0.0866067
$290$	13.3962	0.786655
$291$	−0.127370	−0.00746659
$292$	−11.1515	−0.652590
$293$	16.7905	0.980914	0.490457	−	0.871466i	$-0.336830\pi$
$293$	16.7905	0.980914	0.490457	+	0.871466i	$0.336830\pi$
$294$	0.333437	0.0194465
$295$	9.89533	0.576129
$296$	8.22746	0.478212
$297$	6.95230	0.403413
$298$	40.8182	2.36453
$299$	−8.49144	−0.491073
$300$	−0.265298	−0.0153170
$301$	0.800583	0.0461448
$302$	−2.63429	−0.151587
$303$	−1.97502	−0.113462
$304$	14.4629	0.829502
$305$	−11.3677	−0.650915
$306$	21.8353	1.24824
$307$	15.8010	0.901811	0.450906	−	0.892572i	$-0.351101\pi$
$307$	15.8010	0.901811	0.450906	+	0.892572i	$0.351101\pi$
$308$	9.68838	0.552047
$309$	3.07745	0.175070
$310$	16.0749	0.912991
$311$	−8.64552	−0.490242	−0.245121	−	0.969492i	$-0.578828\pi$
$311$	−8.64552	−0.490242	−0.245121	+	0.969492i	$0.578828\pi$
$312$	−0.572041	−0.0323854
$313$	20.8576	1.17894	0.589472	−	0.807789i	$-0.299336\pi$
$313$	20.8576	1.17894	0.589472	+	0.807789i	$0.299336\pi$
$314$	−35.2222	−1.98770
$315$	−2.96810	−0.167234
$316$	8.25520	0.464391
$317$	−29.4945	−1.65658	−0.828288	−	0.560302i	$-0.810685\pi$
$317$	−29.4945	−1.65658	−0.828288	+	0.560302i	$0.810685\pi$
$318$	−0.653030	−0.0366201
$319$	−46.8016	−2.62039
$320$	−3.48994	−0.195094
$321$	−0.344894	−0.0192501
$322$	4.75507	0.264989
$323$	−11.9619	−0.665580
$324$	12.9438	0.719098
$325$	3.33389	0.184931
$326$	−13.8238	−0.765630
$327$	−1.93836	−0.107192
$328$	0.450078	0.0248514
$329$	4.61726	0.254558
$330$	2.17480	0.119719
$331$	0.473951	0.0260507	0.0130254	−	0.999915i	$-0.495854\pi$
$331$	0.473951	0.0260507	0.0130254	+	0.999915i	$0.495854\pi$
$332$	5.56300	0.305309
$333$	−25.4189	−1.39295
$334$	8.37535	0.458279
$335$	9.93960	0.543058
$336$	0.850929	0.0464220
$337$	31.7598	1.73006	0.865032	−	0.501716i	$-0.167298\pi$
$337$	31.7598	1.73006	0.865032	+	0.501716i	$0.167298\pi$
$338$	3.51944	0.191432
$339$	1.38318	0.0751242
$340$	5.85329	0.317439
$341$	−56.1598	−3.04122
$342$	−16.8211	−0.909580
$343$	1.00000	0.0539949
$344$	0.769120	0.0414682
$345$	0.454901	0.0244911
$346$	1.95137	0.104906
$347$	−11.6338	−0.624537	−0.312269	−	0.949994i	$-0.601089\pi$
$347$	−11.6338	−0.624537	−0.312269	+	0.949994i	$0.601089\pi$
$348$	1.90366	0.102047
$349$	24.9890	1.33763	0.668814	−	0.743430i	$-0.266802\pi$
$349$	24.9890	1.33763	0.668814	+	0.743430i	$0.266802\pi$
$350$	−1.86693	−0.0997914
$351$	3.55366	0.189680
$352$	45.4826	2.42423
$353$	1.98763	0.105791	0.0528955	−	0.998600i	$-0.483155\pi$
$353$	1.98763	0.105791	0.0528955	+	0.998600i	$0.483155\pi$
$354$	3.29948	0.175365
$355$	11.9535	0.634427
$356$	26.2613	1.39185
$357$	−0.703786	−0.0372483
$358$	−22.5614	−1.19241
$359$	15.2335	0.803993	0.401997	−	0.915641i	$-0.368316\pi$
$359$	15.2335	0.803993	0.401997	+	0.915641i	$0.368316\pi$
$360$	−2.85146	−0.150285
$361$	−9.78497	−0.514998
$362$	−13.9270	−0.731986
$363$	−5.63334	−0.295673
$364$	4.95220	0.259566
$365$	−7.50733	−0.392951
$366$	−3.79043	−0.198129
$367$	7.99510	0.417341	0.208670	−	0.977986i	$-0.433086\pi$
$367$	7.99510	0.417341	0.208670	+	0.977986i	$0.433086\pi$
$368$	12.1349	0.632575
$369$	−1.39052	−0.0723878
$370$	−15.9884	−0.831197
$371$	−1.95848	−0.101679
$372$	2.28431	0.118436
$373$	−20.5940	−1.06632	−0.533159	−	0.846015i	$-0.678995\pi$
$373$	−20.5940	−1.06632	−0.533159	+	0.846015i	$0.678995\pi$
$374$	−47.9828	−2.48113
$375$	−0.178602	−0.00922299
$376$	4.43581	0.228759
$377$	−23.9226	−1.23208
$378$	−1.98999	−0.102354
$379$	10.2735	0.527715	0.263858	−	0.964562i	$-0.415005\pi$
$379$	10.2735	0.527715	0.263858	+	0.964562i	$0.415005\pi$
$380$	−4.50915	−0.231315
$381$	1.45738	0.0746638
$382$	−26.0762	−1.33417
$383$	5.74248	0.293427	0.146713	−	0.989179i	$-0.453130\pi$
$383$	5.74248	0.293427	0.146713	+	0.989179i	$0.453130\pi$
$384$	1.32723	0.0677300
$385$	6.52236	0.332410
$386$	24.9142	1.26810
$387$	−2.37621	−0.120790
$388$	1.05932	0.0537789
$389$	−11.0661	−0.561071	−0.280536	−	0.959844i	$-0.590512\pi$
$389$	−11.0661	−0.561071	−0.280536	+	0.959844i	$0.590512\pi$
$390$	1.11165	0.0562903
$391$	−10.0365	−0.507568
$392$	0.960700	0.0485227
$393$	1.72703	0.0871169
$394$	28.3437	1.42794
$395$	5.55752	0.279629
$396$	−28.7561	−1.44505
$397$	−1.07527	−0.0539663	−0.0269832	−	0.999636i	$-0.508590\pi$
$397$	−1.07527	−0.0539663	−0.0269832	+	0.999636i	$0.508590\pi$
$398$	12.1393	0.608488
$399$	0.542170	0.0271425
$400$	−4.76438	−0.238219
$401$	−1.55163	−0.0774846	−0.0387423	−	0.999249i	$-0.512335\pi$
$401$	−1.55163	−0.0774846	−0.0387423	+	0.999249i	$0.512335\pi$
$402$	3.31424	0.165299
$403$	−28.7060	−1.42995
$404$	16.4260	0.817223
$405$	8.71393	0.432999
$406$	13.3962	0.664845
$407$	55.8577	2.76876
$408$	−0.676128	−0.0334733
$409$	1.10024	0.0544035	0.0272018	−	0.999630i	$-0.491340\pi$
$409$	1.10024	0.0544035	0.0272018	+	0.999630i	$0.491340\pi$
$410$	−0.874635	−0.0431951
$411$	−0.714315	−0.0352345
$412$	−25.5947	−1.26096
$413$	9.89533	0.486918
$414$	−14.1135	−0.693641
$415$	3.74509	0.183839
$416$	23.2484	1.13984
$417$	2.34197	0.114687
$418$	36.9641	1.80797
$419$	5.84787	0.285687	0.142844	−	0.989745i	$-0.454375\pi$
$419$	5.84787	0.285687	0.142844	+	0.989745i	$0.454375\pi$
$420$	−0.265298	−0.0129452
$421$	−10.9791	−0.535089	−0.267544	−	0.963546i	$-0.586212\pi$
$421$	−10.9791	−0.535089	−0.267544	+	0.963546i	$0.586212\pi$
$422$	−4.40692	−0.214525
$423$	−13.7045	−0.666336
$424$	−1.88151	−0.0913742
$425$	3.94052	0.191143
$426$	3.98575	0.193110
$427$	−11.3677	−0.550124
$428$	2.86844	0.138651
$429$	−3.88369	−0.187506
$430$	−1.49463	−0.0720774
$431$	−38.4932	−1.85415	−0.927077	−	0.374871i	$-0.877687\pi$
$431$	−38.4932	−1.85415	−0.927077	+	0.374871i	$0.877687\pi$
$432$	−5.07843	−0.244336
$433$	−8.85866	−0.425720	−0.212860	−	0.977083i	$-0.568278\pi$
$433$	−8.85866	−0.425720	−0.212860	+	0.977083i	$0.568278\pi$
$434$	16.0749	0.771619
$435$	1.28157	0.0614468
$436$	16.1211	0.772060
$437$	7.73175	0.369860
$438$	−2.50322	−0.119609
$439$	−30.9093	−1.47522	−0.737611	−	0.675226i	$-0.764046\pi$
$439$	−30.9093	−1.47522	−0.737611	+	0.675226i	$0.764046\pi$
$440$	6.26603	0.298721
$441$	−2.96810	−0.141338
$442$	−24.5263	−1.16660
$443$	21.9059	1.04078	0.520390	−	0.853929i	$-0.325787\pi$
$443$	21.9059	1.04078	0.520390	+	0.853929i	$0.325787\pi$
$444$	−2.27202	−0.107825
$445$	17.6795	0.838088
$446$	36.5140	1.72899
$447$	3.90494	0.184697
$448$	−3.48994	−0.164884
$449$	−3.88963	−0.183563	−0.0917816	−	0.995779i	$-0.529256\pi$
$449$	−3.88963	−0.183563	−0.0917816	+	0.995779i	$0.529256\pi$
$450$	5.54122	0.261216
$451$	3.05566	0.143885
$452$	−11.5037	−0.541090
$453$	−0.252014	−0.0118407
$454$	−36.8935	−1.73150
$455$	3.33389	0.156295
$456$	0.520863	0.0243917
$457$	−14.2670	−0.667382	−0.333691	−	0.942682i	$-0.608294\pi$
$457$	−14.2670	−0.667382	−0.333691	+	0.942682i	$0.608294\pi$
$458$	−1.86693	−0.0872357
$459$	4.20027	0.196052
$460$	−3.78335	−0.176399
$461$	−18.0110	−0.838855	−0.419427	−	0.907789i	$-0.637769\pi$
$461$	−18.0110	−0.838855	−0.419427	+	0.907789i	$0.637769\pi$
$462$	2.17480	0.101181
$463$	−1.26085	−0.0585967	−0.0292984	−	0.999571i	$-0.509327\pi$
$463$	−1.26085	−0.0585967	−0.0292984	+	0.999571i	$0.509327\pi$
$464$	34.1871	1.58710
$465$	1.53783	0.0713151
$466$	−27.5605	−1.27672
$467$	5.66665	0.262221	0.131111	−	0.991368i	$-0.458146\pi$
$467$	5.66665	0.262221	0.131111	+	0.991368i	$0.458146\pi$
$468$	−14.6986	−0.679444
$469$	9.93960	0.458968
$470$	−8.62009	−0.397615
$471$	−3.36959	−0.155262
$472$	9.50645	0.437570
$473$	5.22169	0.240094
$474$	1.85309	0.0851151
$475$	−3.03563	−0.139284
$476$	5.85329	0.268285
$477$	5.81296	0.266157
$478$	−41.8754	−1.91534
$479$	−13.2839	−0.606957	−0.303478	−	0.952838i	$-0.598148\pi$
$479$	−13.2839	−0.606957	−0.303478	+	0.952838i	$0.598148\pi$
$480$	−1.24545	−0.0568470
$481$	28.5516	1.30184
$482$	−14.0187	−0.638533
$483$	0.454901	0.0206987
$484$	46.8516	2.12962
$485$	0.713150	0.0323825
$486$	8.87552	0.402602
$487$	−5.81838	−0.263656	−0.131828	−	0.991273i	$-0.542085\pi$
$487$	−5.81838	−0.263656	−0.131828	+	0.991273i	$0.542085\pi$
$488$	−10.9210	−0.494370
$489$	−1.32248	−0.0598045
$490$	−1.86693	−0.0843391
$491$	−23.1767	−1.04595	−0.522975	−	0.852348i	$-0.675178\pi$
$491$	−23.1767	−1.04595	−0.522975	+	0.852348i	$0.675178\pi$
$492$	−0.124289	−0.00560340
$493$	−28.2754	−1.27346
$494$	18.8941	0.850087
$495$	−19.3590	−0.870124
$496$	41.0229	1.84198
$497$	11.9535	0.536189
$498$	1.24875	0.0559580
$499$	32.4473	1.45254	0.726270	−	0.687410i	$-0.241252\pi$
$499$	32.4473	1.45254	0.726270	+	0.687410i	$0.241252\pi$
$500$	1.48541	0.0664296
$501$	0.801242	0.0357968
$502$	−30.0829	−1.34267
$503$	−1.74629	−0.0778633	−0.0389316	−	0.999242i	$-0.512395\pi$
$503$	−1.74629	−0.0778633	−0.0389316	+	0.999242i	$0.512395\pi$
$504$	−2.85146	−0.127014
$505$	11.0582	0.492084
$506$	31.0143	1.37875
$507$	0.336693	0.0149531
$508$	−12.1208	−0.537774
$509$	−1.29610	−0.0574486	−0.0287243	−	0.999587i	$-0.509144\pi$
$509$	−1.29610	−0.0574486	−0.0287243	+	0.999587i	$0.509144\pi$
$510$	1.31392	0.0581812
$511$	−7.50733	−0.332105
$512$	−24.0693	−1.06372
$513$	−3.23573	−0.142861
$514$	7.41267	0.326959
$515$	−17.2307	−0.759276
$516$	−0.212393	−0.00935008
$517$	30.1155	1.32448
$518$	−15.9884	−0.702490
$519$	0.186681	0.00819437
$520$	3.20287	0.140455
$521$	−20.5200	−0.898999	−0.449500	−	0.893281i	$-0.648398\pi$
$521$	−20.5200	−0.898999	−0.449500	+	0.893281i	$0.648398\pi$
$522$	−39.7614	−1.74031
$523$	41.5496	1.81684	0.908419	−	0.418061i	$-0.137290\pi$
$523$	41.5496	1.81684	0.908419	+	0.418061i	$0.137290\pi$
$524$	−14.3634	−0.627469
$525$	−0.178602	−0.00779485
$526$	32.2211	1.40491
$527$	−33.9292	−1.47798
$528$	5.55007	0.241536
$529$	−16.5128	−0.717947
$530$	3.65633	0.158821
$531$	−29.3704	−1.27456
$532$	−4.50915	−0.195497
$533$	1.56189	0.0676532
$534$	5.89501	0.255102
$535$	1.93107	0.0834876
$536$	9.54898	0.412453
$537$	−2.15837	−0.0931406
$538$	−1.58846	−0.0684836
$539$	6.52236	0.280938
$540$	1.58333	0.0681355
$541$	17.4360	0.749632	0.374816	−	0.927099i	$-0.377706\pi$
$541$	17.4360	0.749632	0.374816	+	0.927099i	$0.377706\pi$
$542$	−1.94420	−0.0835104
$543$	−1.33235	−0.0571765
$544$	27.4786	1.17813
$545$	10.8530	0.464889
$546$	1.11165	0.0475740
$547$	−28.5398	−1.22028	−0.610138	−	0.792295i	$-0.708886\pi$
$547$	−28.5398	−1.22028	−0.610138	+	0.792295i	$0.708886\pi$
$548$	5.94085	0.253781
$549$	33.7406	1.44001
$550$	−12.1768	−0.519219
$551$	21.7823	0.927959
$552$	0.437024	0.0186010
$553$	5.55752	0.236330
$554$	−50.3188	−2.13784
$555$	−1.52956	−0.0649261
$556$	−19.4778	−0.826043
$557$	−3.06816	−0.130002	−0.0650011	−	0.997885i	$-0.520705\pi$
$557$	−3.06816	−0.130002	−0.0650011	+	0.997885i	$0.520705\pi$
$558$	−47.7119	−2.01980
$559$	2.66906	0.112889
$560$	−4.76438	−0.201332
$561$	−4.59035	−0.193805
$562$	−3.80959	−0.160698
$563$	4.79710	0.202174	0.101087	−	0.994878i	$-0.467768\pi$
$563$	4.79710	0.202174	0.101087	+	0.994878i	$0.467768\pi$
$564$	−1.22495	−0.0515797
$565$	−7.74448	−0.325813
$566$	35.3793	1.48710
$567$	8.71393	0.365951
$568$	11.4837	0.481847
$569$	34.3017	1.43800	0.719001	−	0.695009i	$-0.244600\pi$
$569$	34.3017	1.43800	0.719001	+	0.695009i	$0.244600\pi$
$570$	−1.01219	−0.0423960
$571$	40.6947	1.70302	0.851509	−	0.524339i	$-0.175688\pi$
$571$	40.6947	1.70302	0.851509	+	0.524339i	$0.175688\pi$
$572$	32.3000	1.35053
$573$	−2.49462	−0.104214
$574$	−0.874635	−0.0365066
$575$	−2.54700	−0.106217
$576$	10.3585	0.431604
$577$	26.0092	1.08278	0.541389	−	0.840772i	$-0.317899\pi$
$577$	26.0092	1.08278	0.541389	+	0.840772i	$0.317899\pi$
$578$	2.74870	0.114331
$579$	2.38345	0.0990530
$580$	−10.6587	−0.442577
$581$	3.74509	0.155373
$582$	0.237791	0.00985676
$583$	−12.7739	−0.529041
$584$	−7.21229	−0.298447
$585$	−9.89533	−0.409122
$586$	−31.3467	−1.29492
$587$	−41.8694	−1.72813	−0.864067	−	0.503376i	$-0.832091\pi$
$587$	−41.8694	−1.72813	−0.864067	+	0.503376i	$0.832091\pi$
$588$	−0.265298	−0.0109407
$589$	26.1378	1.07699
$590$	−18.4739	−0.760556
$591$	2.71155	0.111538
$592$	−40.8023	−1.67696
$593$	20.7691	0.852884	0.426442	−	0.904515i	$-0.359767\pi$
$593$	20.7691	0.852884	0.426442	+	0.904515i	$0.359767\pi$
$594$	−12.9794	−0.532552
$595$	3.94052	0.161546
$596$	−32.4768	−1.33030
$597$	1.16133	0.0475299
$598$	15.8529	0.648273
$599$	34.4422	1.40727	0.703634	−	0.710562i	$-0.251559\pi$
$599$	34.4422	1.40727	0.703634	+	0.710562i	$0.251559\pi$
$600$	−0.171583	−0.00700487
$601$	−16.0486	−0.654638	−0.327319	−	0.944914i	$-0.606145\pi$
$601$	−16.0486	−0.654638	−0.327319	+	0.944914i	$0.606145\pi$
$602$	−1.49463	−0.0609165
$603$	−29.5017	−1.20140
$604$	2.09596	0.0852836
$605$	31.5412	1.28233
$606$	3.68722	0.149783
$607$	11.3182	0.459390	0.229695	−	0.973263i	$-0.426227\pi$
$607$	11.3182	0.459390	0.229695	+	0.973263i	$0.426227\pi$
$608$	−21.1684	−0.858494
$609$	1.28157	0.0519320
$610$	21.2227	0.859283
$611$	15.3935	0.622753
$612$	−17.3731	−0.702268
$613$	28.6140	1.15571	0.577855	−	0.816139i	$-0.303890\pi$
$613$	28.6140	1.15571	0.577855	+	0.816139i	$0.303890\pi$
$614$	−29.4993	−1.19050
$615$	−0.0836734	−0.00337404
$616$	6.26603	0.252466
$617$	44.0269	1.77246	0.886228	−	0.463249i	$-0.153316\pi$
$617$	44.0269	1.77246	0.886228	+	0.463249i	$0.153316\pi$
$618$	−5.74537	−0.231112
$619$	25.6932	1.03270	0.516348	−	0.856379i	$-0.327291\pi$
$619$	25.6932	1.03270	0.516348	+	0.856379i	$0.327291\pi$
$620$	−12.7899	−0.513655
$621$	−2.71490	−0.108945
$622$	16.1405	0.647176
$623$	17.6795	0.708314
$624$	2.83691	0.113567
$625$	1.00000	0.0400000
$626$	−38.9397	−1.55634
$627$	3.53623	0.141223
$628$	28.0244	1.11829
$629$	33.7467	1.34557
$630$	5.54122	0.220768
$631$	21.1780	0.843082	0.421541	−	0.906809i	$-0.361489\pi$
$631$	21.1780	0.843082	0.421541	+	0.906809i	$0.361489\pi$
$632$	5.33911	0.212378
$633$	−0.421595	−0.0167569
$634$	55.0641	2.18687
$635$	−8.15990	−0.323816
$636$	0.519580	0.0206027
$637$	3.33389	0.132094
$638$	87.3752	3.45922
$639$	−35.4793	−1.40354
$640$	−7.43121	−0.293744
$641$	−2.81152	−0.111048	−0.0555242	−	0.998457i	$-0.517683\pi$
$641$	−2.81152	−0.111048	−0.0555242	+	0.998457i	$0.517683\pi$
$642$	0.643892	0.0254124
$643$	−38.9735	−1.53696	−0.768482	−	0.639871i	$-0.778988\pi$
$643$	−38.9735	−1.53696	−0.768482	+	0.639871i	$0.778988\pi$
$644$	−3.78335	−0.149085
$645$	−0.142986	−0.00563007
$646$	22.3321	0.878643
$647$	37.2183	1.46320	0.731602	−	0.681732i	$-0.238773\pi$
$647$	37.2183	1.46320	0.731602	+	0.681732i	$0.238773\pi$
$648$	8.37147	0.328863
$649$	64.5409	2.53345
$650$	−6.22413	−0.244130
$651$	1.53783	0.0602723
$652$	10.9989	0.430748
$653$	−39.2223	−1.53489	−0.767444	−	0.641116i	$-0.778472\pi$
$653$	−39.2223	−1.53489	−0.767444	+	0.641116i	$0.778472\pi$
$654$	3.61878	0.141506
$655$	−9.66966	−0.377825
$656$	−2.23206	−0.0871473
$657$	22.2825	0.869323
$658$	−8.62009	−0.336046
$659$	−45.0129	−1.75346	−0.876728	−	0.480987i	$-0.840278\pi$
$659$	−45.0129	−1.75346	−0.876728	+	0.480987i	$0.840278\pi$
$660$	−1.73037	−0.0673545
$661$	−30.9463	−1.20367	−0.601836	−	0.798620i	$-0.705564\pi$
$661$	−30.9463	−1.20367	−0.601836	+	0.798620i	$0.705564\pi$
$662$	−0.884832	−0.0343900
$663$	−2.34635	−0.0911246
$664$	3.59791	0.139626
$665$	−3.03563	−0.117717
$666$	47.4552	1.83885
$667$	18.2762	0.707657
$668$	−6.66381	−0.257831
$669$	3.49317	0.135054
$670$	−18.5565	−0.716900
$671$	−74.1446	−2.86232
$672$	−1.24545	−0.0480445
$673$	41.9174	1.61580	0.807898	−	0.589322i	$-0.200605\pi$
$673$	41.9174	1.61580	0.807898	+	0.589322i	$0.200605\pi$
$674$	−59.2931	−2.28389
$675$	1.06592	0.0410272
$676$	−2.80023	−0.107701
$677$	−42.4468	−1.63136	−0.815682	−	0.578501i	$-0.803638\pi$
$677$	−42.4468	−1.63136	−0.815682	+	0.578501i	$0.803638\pi$
$678$	−2.58230	−0.0991726
$679$	0.713150	0.0273682
$680$	3.78566	0.145173
$681$	−3.52947	−0.135250
$682$	104.846	4.01477
$683$	34.9436	1.33708	0.668540	−	0.743677i	$-0.266920\pi$
$683$	34.9436	1.33708	0.668540	+	0.743677i	$0.266920\pi$
$684$	13.3836	0.511735
$685$	3.99947	0.152812
$686$	−1.86693	−0.0712795
$687$	−0.178602	−0.00681411
$688$	−3.81428	−0.145418
$689$	−6.52936	−0.248749
$690$	−0.849266	−0.0323310
$691$	51.5456	1.96089	0.980443	−	0.196801i	$-0.0630552\pi$
$691$	51.5456	1.96089	0.980443	+	0.196801i	$0.0630552\pi$
$692$	−1.55260	−0.0590208
$693$	−19.3590	−0.735389
$694$	21.7195	0.824461
$695$	−13.1127	−0.497395
$696$	1.23121	0.0466688
$697$	1.84609	0.0699257
$698$	−46.6525	−1.76582
$699$	−2.63662	−0.0997262
$700$	1.48541	0.0561432
$701$	37.9381	1.43290	0.716451	−	0.697637i	$-0.245765\pi$
$701$	37.9381	1.43290	0.716451	+	0.697637i	$0.245765\pi$
$702$	−6.63441	−0.250400
$703$	−25.9972	−0.980503
$704$	−22.7627	−0.857900
$705$	−0.824655	−0.0310583
$706$	−3.71076	−0.139656
$707$	11.0582	0.415887
$708$	−2.62521	−0.0986615
$709$	18.0285	0.677075	0.338538	−	0.940953i	$-0.390068\pi$
$709$	18.0285	0.677075	0.338538	+	0.940953i	$0.390068\pi$
$710$	−22.3163	−0.837517
$711$	−16.4953	−0.618622
$712$	16.9847	0.636528
$713$	21.9306	0.821307
$714$	1.31392	0.0491721
$715$	21.7449	0.813212
$716$	17.9509	0.670855
$717$	−4.00608	−0.149610
$718$	−28.4398	−1.06136
$719$	1.79080	0.0667857	0.0333928	−	0.999442i	$-0.489369\pi$
$719$	1.79080	0.0667857	0.0333928	+	0.999442i	$0.489369\pi$
$720$	14.1412	0.527010
$721$	−17.2307	−0.641705
$722$	18.2678	0.679858
$723$	−1.34112	−0.0498767
$724$	11.0809	0.411820
$725$	−7.17557	−0.266494
$726$	10.5170	0.390323
$727$	2.68170	0.0994588	0.0497294	−	0.998763i	$-0.484164\pi$
$727$	2.68170	0.0994588	0.0497294	+	0.998763i	$0.484164\pi$
$728$	3.20287	0.118706
$729$	−25.2927	−0.936766
$730$	14.0156	0.518741
$731$	3.15471	0.116681
$732$	3.01584	0.111469
$733$	19.9234	0.735889	0.367944	−	0.929848i	$-0.380062\pi$
$733$	19.9234	0.735889	0.367944	+	0.929848i	$0.380062\pi$
$734$	−14.9263	−0.550938
$735$	−0.178602	−0.00658785
$736$	−17.7611	−0.654683
$737$	64.8297	2.38803
$738$	2.59601	0.0955603
$739$	33.2039	1.22142	0.610712	−	0.791853i	$-0.290883\pi$
$739$	33.2039	1.22142	0.610712	+	0.791853i	$0.290883\pi$
$740$	12.7211	0.467637
$741$	1.80754	0.0664016
$742$	3.65633	0.134228
$743$	−20.7341	−0.760659	−0.380329	−	0.924851i	$-0.624189\pi$
$743$	−20.7341	−0.760659	−0.380329	+	0.924851i	$0.624189\pi$
$744$	1.47739	0.0541639
$745$	−21.8638	−0.801029
$746$	38.4475	1.40766
$747$	−11.1158	−0.406706
$748$	38.1773	1.39590
$749$	1.93107	0.0705599
$750$	0.333437	0.0121754
$751$	34.5280	1.25994	0.629972	−	0.776617i	$-0.283066\pi$
$751$	34.5280	1.25994	0.629972	+	0.776617i	$0.283066\pi$
$752$	−21.9984	−0.802198
$753$	−2.87793	−0.104878
$754$	44.6617	1.62648
$755$	1.41103	0.0513528
$756$	1.58333	0.0575850
$757$	−36.7545	−1.33587	−0.667933	−	0.744221i	$-0.732821\pi$
$757$	−36.7545	−1.33587	−0.667933	+	0.744221i	$0.732821\pi$
$758$	−19.1799	−0.696645
$759$	2.96703	0.107696
$760$	−2.91633	−0.105786
$761$	−24.7416	−0.896884	−0.448442	−	0.893812i	$-0.648021\pi$
$761$	−24.7416	−0.896884	−0.448442	+	0.893812i	$0.648021\pi$
$762$	−2.72082	−0.0985648
$763$	10.8530	0.392903
$764$	20.7474	0.750614
$765$	−11.6959	−0.422865
$766$	−10.7208	−0.387357
$767$	32.9900	1.19120
$768$	−3.72447	−0.134395
$769$	33.1066	1.19385	0.596927	−	0.802296i	$-0.296388\pi$
$769$	33.1066	1.19385	0.596927	+	0.802296i	$0.296388\pi$
$770$	−12.1768	−0.438820
$771$	0.709145	0.0255392
$772$	−19.8228	−0.713440
$773$	0.648661	0.0233307	0.0116654	−	0.999932i	$-0.496287\pi$
$773$	0.648661	0.0233307	0.0116654	+	0.999932i	$0.496287\pi$
$774$	4.43621	0.159456
$775$	−8.61035	−0.309293
$776$	0.685124	0.0245945
$777$	−1.52956	−0.0548725
$778$	20.6595	0.740679
$779$	−1.42216	−0.0509541
$780$	−0.884475	−0.0316693
$781$	77.9652	2.78981
$782$	18.7374	0.670049
$783$	−7.64856	−0.273337
$784$	−4.76438	−0.170156
$785$	18.8664	0.673371
$786$	−3.22423	−0.115004
$787$	−16.1020	−0.573973	−0.286987	−	0.957935i	$-0.592654\pi$
$787$	−16.1020	−0.573973	−0.286987	+	0.957935i	$0.592654\pi$
$788$	−22.5515	−0.803365
$789$	3.08248	0.109739
$790$	−10.3755	−0.369143
$791$	−7.74448	−0.275362
$792$	−18.5982	−0.660859
$793$	−37.8989	−1.34583
$794$	2.00745	0.0712418
$795$	0.349789	0.0124057
$796$	−9.65857	−0.342339
$797$	24.0818	0.853023	0.426511	−	0.904482i	$-0.359742\pi$
$797$	24.0818	0.853023	0.426511	+	0.904482i	$0.359742\pi$
$798$	−1.01219	−0.0358312
$799$	18.1944	0.643672
$800$	6.97334	0.246545
$801$	−52.4745	−1.85410
$802$	2.89677	0.102289
$803$	−48.9655	−1.72795
$804$	−2.63696	−0.0929983
$805$	−2.54700	−0.0897701
$806$	53.5919	1.88769
$807$	−0.151963	−0.00534935
$808$	10.6236	0.373738
$809$	−8.66131	−0.304516	−0.152258	−	0.988341i	$-0.548654\pi$
$809$	−8.66131	−0.304516	−0.152258	+	0.988341i	$0.548654\pi$
$810$	−16.2683	−0.571608
$811$	27.5475	0.967322	0.483661	−	0.875255i	$-0.339307\pi$
$811$	27.5475	0.967322	0.483661	+	0.875255i	$0.339307\pi$
$812$	−10.6587	−0.374046
$813$	−0.185995	−0.00652312
$814$	−104.282	−3.65509
$815$	7.40459	0.259371
$816$	3.35310	0.117382
$817$	−2.43027	−0.0850244
$818$	−2.05407	−0.0718189
$819$	−9.89533	−0.345771
$820$	0.695899	0.0243019
$821$	18.0714	0.630695	0.315348	−	0.948976i	$-0.397879\pi$
$821$	18.0714	0.630695	0.315348	+	0.948976i	$0.397879\pi$
$822$	1.33357	0.0465137
$823$	−48.8596	−1.70314	−0.851570	−	0.524242i	$-0.824349\pi$
$823$	−48.8596	−1.70314	−0.851570	+	0.524242i	$0.824349\pi$
$824$	−16.5536	−0.576670
$825$	−1.16491	−0.0405570
$826$	−18.4739	−0.642788
$827$	−28.4127	−0.988005	−0.494003	−	0.869460i	$-0.664467\pi$
$827$	−28.4127	−0.988005	−0.494003	+	0.869460i	$0.664467\pi$
$828$	11.2294	0.390247
$829$	−7.90684	−0.274616	−0.137308	−	0.990528i	$-0.543845\pi$
$829$	−7.90684	−0.274616	−0.137308	+	0.990528i	$0.543845\pi$
$830$	−6.99181	−0.242689
$831$	−4.81383	−0.166990
$832$	−11.6351	−0.403374
$833$	3.94052	0.136531
$834$	−4.37228	−0.151400
$835$	−4.48617	−0.155250
$836$	−29.4103	−1.01718
$837$	−9.17792	−0.317235
$838$	−10.9175	−0.377140
$839$	−1.59891	−0.0552005	−0.0276002	−	0.999619i	$-0.508787\pi$
$839$	−1.59891	−0.0552005	−0.0276002	+	0.999619i	$0.508787\pi$
$840$	−0.171583	−0.00592019
$841$	22.4887	0.775474
$842$	20.4972	0.706379
$843$	−0.364451	−0.0125524
$844$	3.50634	0.120693
$845$	−1.88515	−0.0648513
$846$	25.5853	0.879640
$847$	31.5412	1.08377
$848$	9.33093	0.320425
$849$	3.38462	0.116160
$850$	−7.35665	−0.252331
$851$	−21.8126	−0.747727
$852$	−3.17124	−0.108645
$853$	12.6539	0.433260	0.216630	−	0.976254i	$-0.430493\pi$
$853$	12.6539	0.433260	0.216630	+	0.976254i	$0.430493\pi$
$854$	21.2227	0.726227
$855$	9.01005	0.308137
$856$	1.85518	0.0634088
$857$	−36.4290	−1.24439	−0.622196	−	0.782862i	$-0.713759\pi$
$857$	−36.4290	−1.24439	−0.622196	+	0.782862i	$0.713759\pi$
$858$	7.25055	0.247530
$859$	39.5688	1.35007	0.675036	−	0.737785i	$-0.264128\pi$
$859$	39.5688	1.35007	0.675036	+	0.737785i	$0.264128\pi$
$860$	1.18919	0.0405512
$861$	−0.0836734	−0.00285158
$862$	71.8640	2.44770
$863$	1.38397	0.0471110	0.0235555	−	0.999723i	$-0.492501\pi$
$863$	1.38397	0.0471110	0.0235555	+	0.999723i	$0.492501\pi$
$864$	7.43300	0.252876
$865$	−1.04523	−0.0355389
$866$	16.5385	0.562000
$867$	0.262959	0.00893056
$868$	−12.7899	−0.434117
$869$	36.2482	1.22963
$870$	−2.39260	−0.0811168
$871$	33.1376	1.12282
$872$	10.4264	0.353084
$873$	−2.11670	−0.0716395
$874$	−14.4346	−0.488258
$875$	1.00000	0.0338062
$876$	1.99168	0.0672926
$877$	5.59270	0.188852	0.0944260	−	0.995532i	$-0.469898\pi$
$877$	5.59270	0.188852	0.0944260	+	0.995532i	$0.469898\pi$
$878$	57.7054	1.94746
$879$	−2.99883	−0.101148
$880$	−31.0750	−1.04754
$881$	−17.2325	−0.580577	−0.290288	−	0.956939i	$-0.593751\pi$
$881$	−17.2325	−0.580577	−0.290288	+	0.956939i	$0.593751\pi$
$882$	5.54122	0.186583
$883$	−4.20557	−0.141529	−0.0707643	−	0.997493i	$-0.522544\pi$
$883$	−4.20557	−0.141529	−0.0707643	+	0.997493i	$0.522544\pi$
$884$	19.5142	0.656335
$885$	−1.76733	−0.0594082
$886$	−40.8967	−1.37395
$887$	−53.8964	−1.80966	−0.904832	−	0.425769i	$-0.860004\pi$
$887$	−53.8964	−1.80966	−0.904832	+	0.425769i	$0.860004\pi$
$888$	−1.46945	−0.0493114
$889$	−8.15990	−0.273674
$890$	−33.0063	−1.10637
$891$	56.8354	1.90406
$892$	−29.0522	−0.972740
$893$	−14.0163	−0.469037
$894$	−7.29023	−0.243822
$895$	12.0848	0.403950
$896$	−7.43121	−0.248259
$897$	1.51659	0.0506375
$898$	7.26166	0.242325
$899$	61.7841	2.06062
$900$	−4.40885	−0.146962
$901$	−7.71742	−0.257104
$902$	−5.70469	−0.189945
$903$	−0.142986	−0.00475828
$904$	−7.44012	−0.247455
$905$	7.45985	0.247974
$906$	0.470491	0.0156310
$907$	37.6052	1.24866	0.624331	−	0.781160i	$-0.285372\pi$
$907$	37.6052	1.24866	0.624331	+	0.781160i	$0.285372\pi$
$908$	29.3541	0.974150
$909$	−32.8219	−1.08863
$910$	−6.22413	−0.206328
$911$	48.0009	1.59034	0.795170	−	0.606387i	$-0.207382\pi$
$911$	48.0009	1.59034	0.795170	+	0.606387i	$0.207382\pi$
$912$	−2.58310	−0.0855351
$913$	24.4268	0.808410
$914$	26.6354	0.881022
$915$	2.03031	0.0671199
$916$	1.48541	0.0490793
$917$	−9.66966	−0.319320
$918$	−7.84159	−0.258811
$919$	57.3858	1.89298	0.946491	−	0.322730i	$-0.104601\pi$
$919$	57.3858	1.89298	0.946491	+	0.322730i	$0.104601\pi$
$920$	−2.44691	−0.0806721
$921$	−2.82210	−0.0929914
$922$	33.6251	1.10739
$923$	39.8518	1.31174
$924$	−1.73037	−0.0569250
$925$	8.56403	0.281584
$926$	2.35392	0.0773545
$927$	51.1425	1.67974
$928$	−50.0376	−1.64257
$929$	−48.6125	−1.59492	−0.797462	−	0.603369i	$-0.793825\pi$
$929$	−48.6125	−1.59492	−0.797462	+	0.603369i	$0.793825\pi$
$930$	−2.87101	−0.0941442
$931$	−3.03563	−0.0994886
$932$	21.9284	0.718289
$933$	1.54411	0.0505519
$934$	−10.5792	−0.346163
$935$	25.7015	0.840528
$936$	−9.50645	−0.310728
$937$	3.11906	0.101895	0.0509476	−	0.998701i	$-0.483776\pi$
$937$	3.11906	0.101895	0.0509476	+	0.998701i	$0.483776\pi$
$938$	−18.5565	−0.605891
$939$	−3.72523	−0.121568
$940$	6.85853	0.223701
$941$	23.2752	0.758749	0.379374	−	0.925243i	$-0.376139\pi$
$941$	23.2752	0.758749	0.379374	+	0.925243i	$0.376139\pi$
$942$	6.29077	0.204964
$943$	−1.19324	−0.0388574
$944$	−47.1451	−1.53444
$945$	1.06592	0.0346743
$946$	−9.74851	−0.316951
$947$	26.1012	0.848177	0.424088	−	0.905621i	$-0.360595\pi$
$947$	26.1012	0.848177	0.424088	+	0.905621i	$0.360595\pi$
$948$	−1.47440	−0.0478863
$949$	−25.0286	−0.812464
$950$	5.66729	0.183871
$951$	5.26779	0.170820
$952$	3.78566	0.122694
$953$	−7.83534	−0.253812	−0.126906	−	0.991915i	$-0.540505\pi$
$953$	−7.83534	−0.253812	−0.126906	+	0.991915i	$0.540505\pi$
$954$	−10.8524	−0.351358
$955$	13.9674	0.451976
$956$	33.3180	1.07758
$957$	8.35889	0.270204
$958$	24.8000	0.801253
$959$	3.99947	0.129150
$960$	0.623313	0.0201173
$961$	43.1381	1.39155
$962$	−53.3036	−1.71858
$963$	−5.73162	−0.184699
$964$	11.1539	0.359242
$965$	−13.3450	−0.429592
$966$	−0.849266	−0.0273247
$967$	−5.63438	−0.181189	−0.0905947	−	0.995888i	$-0.528877\pi$
$967$	−5.63438	−0.181189	−0.0905947	+	0.995888i	$0.528877\pi$
$968$	30.3016	0.973931
$969$	2.13643	0.0686321
$970$	−1.33140	−0.0427486
$971$	36.3164	1.16545	0.582724	−	0.812670i	$-0.301987\pi$
$971$	36.3164	1.16545	0.582724	+	0.812670i	$0.301987\pi$
$972$	−7.06176	−0.226506
$973$	−13.1127	−0.420375
$974$	10.8625	0.348056
$975$	−0.595442	−0.0190694
$976$	54.1602	1.73363
$977$	26.1532	0.836716	0.418358	−	0.908282i	$-0.362606\pi$
$977$	26.1532	0.836716	0.418358	+	0.908282i	$0.362606\pi$
$978$	2.46897	0.0789489
$979$	115.312	3.68539
$980$	1.48541	0.0474497
$981$	−32.2127	−1.02847
$982$	43.2692	1.38078
$983$	−2.09778	−0.0669089	−0.0334544	−	0.999440i	$-0.510651\pi$
$983$	−2.09778	−0.0669089	−0.0334544	+	0.999440i	$0.510651\pi$
$984$	−0.0803851	−0.00256258
$985$	−15.1820	−0.483740
$986$	52.7882	1.68112
$987$	−0.824655	−0.0262490
$988$	−15.0330	−0.478264
$989$	−2.03909	−0.0648392
$990$	36.1419	1.14866
$991$	−27.2220	−0.864736	−0.432368	−	0.901697i	$-0.642322\pi$
$991$	−27.2220	−0.864736	−0.432368	+	0.901697i	$0.642322\pi$
$992$	−60.0428	−1.90636
$993$	−0.0846489	−0.00268625
$994$	−22.3163	−0.707831
$995$	−6.50229	−0.206136
$996$	−0.993565	−0.0314823
$997$	44.7130	1.41608	0.708038	−	0.706175i	$-0.249581\pi$
$997$	44.7130	1.41608	0.708038	+	0.706175i	$0.249581\pi$
$998$	−60.5766	−1.91752
$999$	9.12855	0.288814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.o.1.15	✓	73

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.o.1.15	✓	73	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)

\(f(q)\)	\(=\)	\(q-1.86693 q^{2} -0.178602 q^{3} +1.48541 q^{4} +1.00000 q^{5} +0.333437 q^{6} +1.00000 q^{7} +0.960700 q^{8} -2.96810 q^{9} +O(q^{10})\)	\(q-1.86693 q^{2} -0.178602 q^{3} +1.48541 q^{4} +1.00000 q^{5} +0.333437 q^{6} +1.00000 q^{7} +0.960700 q^{8} -2.96810 q^{9} -1.86693 q^{10} +6.52236 q^{11} -0.265298 q^{12} +3.33389 q^{13} -1.86693 q^{14} -0.178602 q^{15} -4.76438 q^{16} +3.94052 q^{17} +5.54122 q^{18} -3.03563 q^{19} +1.48541 q^{20} -0.178602 q^{21} -12.1768 q^{22} -2.54700 q^{23} -0.171583 q^{24} +1.00000 q^{25} -6.22413 q^{26} +1.06592 q^{27} +1.48541 q^{28} -7.17557 q^{29} +0.333437 q^{30} -8.61035 q^{31} +6.97334 q^{32} -1.16491 q^{33} -7.35665 q^{34} +1.00000 q^{35} -4.40885 q^{36} +8.56403 q^{37} +5.66729 q^{38} -0.595442 q^{39} +0.960700 q^{40} +0.468490 q^{41} +0.333437 q^{42} +0.800583 q^{43} +9.68838 q^{44} -2.96810 q^{45} +4.75507 q^{46} +4.61726 q^{47} +0.850929 q^{48} +1.00000 q^{49} -1.86693 q^{50} -0.703786 q^{51} +4.95220 q^{52} -1.95848 q^{53} -1.98999 q^{54} +6.52236 q^{55} +0.960700 q^{56} +0.542170 q^{57} +13.3962 q^{58} +9.89533 q^{59} -0.265298 q^{60} -11.3677 q^{61} +16.0749 q^{62} -2.96810 q^{63} -3.48994 q^{64} +3.33389 q^{65} +2.17480 q^{66} +9.93960 q^{67} +5.85329 q^{68} +0.454901 q^{69} -1.86693 q^{70} +11.9535 q^{71} -2.85146 q^{72} -7.50733 q^{73} -15.9884 q^{74} -0.178602 q^{75} -4.50915 q^{76} +6.52236 q^{77} +1.11165 q^{78} +5.55752 q^{79} -4.76438 q^{80} +8.71393 q^{81} -0.874635 q^{82} +3.74509 q^{83} -0.265298 q^{84} +3.94052 q^{85} -1.49463 q^{86} +1.28157 q^{87} +6.26603 q^{88} +17.6795 q^{89} +5.54122 q^{90} +3.33389 q^{91} -3.78335 q^{92} +1.53783 q^{93} -8.62009 q^{94} -3.03563 q^{95} -1.24545 q^{96} +0.713150 q^{97} -1.86693 q^{98} -19.3590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * q^99

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