LMFDB - Embedded newform 8015.2.a.i.1.20

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:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-0.508100 q^{2} +2.08594 q^{3} -1.74183 q^{4} +1.00000 q^{5} -1.05987 q^{6} -1.00000 q^{7} +1.90123 q^{8} +1.35113 q^{9} +O(q^{10})$	\(q-0.508100 q^{2} +2.08594 q^{3} -1.74183 q^{4} +1.00000 q^{5} -1.05987 q^{6} -1.00000 q^{7} +1.90123 q^{8} +1.35113 q^{9} -0.508100 q^{10} +0.775468 q^{11} -3.63336 q^{12} -3.72997 q^{13} +0.508100 q^{14} +2.08594 q^{15} +2.51765 q^{16} -4.85946 q^{17} -0.686511 q^{18} +1.98948 q^{19} -1.74183 q^{20} -2.08594 q^{21} -0.394015 q^{22} +3.04302 q^{23} +3.96584 q^{24} +1.00000 q^{25} +1.89520 q^{26} -3.43943 q^{27} +1.74183 q^{28} +2.74198 q^{29} -1.05987 q^{30} +5.21531 q^{31} -5.08167 q^{32} +1.61758 q^{33} +2.46909 q^{34} -1.00000 q^{35} -2.35345 q^{36} -8.76174 q^{37} -1.01085 q^{38} -7.78048 q^{39} +1.90123 q^{40} +2.23023 q^{41} +1.05987 q^{42} +3.57485 q^{43} -1.35074 q^{44} +1.35113 q^{45} -1.54616 q^{46} +3.45526 q^{47} +5.25167 q^{48} +1.00000 q^{49} -0.508100 q^{50} -10.1365 q^{51} +6.49699 q^{52} +7.87848 q^{53} +1.74758 q^{54} +0.775468 q^{55} -1.90123 q^{56} +4.14993 q^{57} -1.39320 q^{58} -7.51394 q^{59} -3.63336 q^{60} +0.864964 q^{61} -2.64990 q^{62} -1.35113 q^{63} -2.45331 q^{64} -3.72997 q^{65} -0.821891 q^{66} -7.24202 q^{67} +8.46437 q^{68} +6.34755 q^{69} +0.508100 q^{70} -8.33101 q^{71} +2.56881 q^{72} +1.08129 q^{73} +4.45184 q^{74} +2.08594 q^{75} -3.46534 q^{76} -0.775468 q^{77} +3.95326 q^{78} -7.23703 q^{79} +2.51765 q^{80} -11.2278 q^{81} -1.13318 q^{82} -4.32857 q^{83} +3.63336 q^{84} -4.85946 q^{85} -1.81638 q^{86} +5.71960 q^{87} +1.47434 q^{88} -0.886633 q^{89} -0.686511 q^{90} +3.72997 q^{91} -5.30044 q^{92} +10.8788 q^{93} -1.75562 q^{94} +1.98948 q^{95} -10.6001 q^{96} +9.26504 q^{97} -0.508100 q^{98} +1.04776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * 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 $

$2$	−0.508100	−0.359281	−0.179641	−	0.983732i	$-0.557493\pi$
$2$	−0.508100	−0.359281	−0.179641	+	0.983732i	$0.557493\pi$
$3$	2.08594	1.20432	0.602158	−	0.798377i	$-0.294308\pi$
$3$	2.08594	1.20432	0.602158	+	0.798377i	$0.294308\pi$
$4$	−1.74183	−0.870917
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.05987	−0.432688
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.90123	0.672185
$9$	1.35113	0.450378
$10$	−0.508100	−0.160675
$11$	0.775468	0.233812	0.116906	−	0.993143i	$-0.462702\pi$
$11$	0.775468	0.233812	0.116906	+	0.993143i	$0.462702\pi$
$12$	−3.63336	−1.04886
$13$	−3.72997	−1.03451	−0.517254	−	0.855832i	$-0.673046\pi$
$13$	−3.72997	−1.03451	−0.517254	+	0.855832i	$0.673046\pi$
$14$	0.508100	0.135796
$15$	2.08594	0.538587
$16$	2.51765	0.629414
$17$	−4.85946	−1.17859	−0.589296	−	0.807917i	$-0.700595\pi$
$17$	−4.85946	−1.17859	−0.589296	+	0.807917i	$0.700595\pi$
$18$	−0.686511	−0.161812
$19$	1.98948	0.456418	0.228209	−	0.973612i	$-0.426713\pi$
$19$	1.98948	0.456418	0.228209	+	0.973612i	$0.426713\pi$
$20$	−1.74183	−0.389486
$21$	−2.08594	−0.455189
$22$	−0.394015	−0.0840044
$23$	3.04302	0.634514	0.317257	−	0.948340i	$-0.397238\pi$
$23$	3.04302	0.634514	0.317257	+	0.948340i	$0.397238\pi$
$24$	3.96584	0.809524
$25$	1.00000	0.200000
$26$	1.89520	0.371679
$27$	−3.43943	−0.661919
$28$	1.74183	0.329176
$29$	2.74198	0.509173	0.254587	−	0.967050i	$-0.418061\pi$
$29$	2.74198	0.509173	0.254587	+	0.967050i	$0.418061\pi$
$30$	−1.05987	−0.193504
$31$	5.21531	0.936697	0.468348	−	0.883544i	$-0.344849\pi$
$31$	5.21531	0.936697	0.468348	+	0.883544i	$0.344849\pi$
$32$	−5.08167	−0.898322
$33$	1.61758	0.281584
$34$	2.46909	0.423446
$35$	−1.00000	−0.169031
$36$	−2.35345	−0.392241
$37$	−8.76174	−1.44042	−0.720210	−	0.693756i	$-0.755955\pi$
$37$	−8.76174	−1.44042	−0.720210	+	0.693756i	$0.755955\pi$
$38$	−1.01085	−0.163982
$39$	−7.78048	−1.24587
$40$	1.90123	0.300610
$41$	2.23023	0.348303	0.174151	−	0.984719i	$-0.444282\pi$
$41$	2.23023	0.348303	0.174151	+	0.984719i	$0.444282\pi$
$42$	1.05987	0.163541
$43$	3.57485	0.545160	0.272580	−	0.962133i	$-0.412123\pi$
$43$	3.57485	0.545160	0.272580	+	0.962133i	$0.412123\pi$
$44$	−1.35074	−0.203631
$45$	1.35113	0.201415
$46$	−1.54616	−0.227969
$47$	3.45526	0.504002	0.252001	−	0.967727i	$-0.418911\pi$
$47$	3.45526	0.504002	0.252001	+	0.967727i	$0.418911\pi$
$48$	5.25167	0.758013
$49$	1.00000	0.142857
$50$	−0.508100	−0.0718562
$51$	−10.1365	−1.41940
$52$	6.49699	0.900970
$53$	7.87848	1.08219	0.541096	−	0.840961i	$-0.318009\pi$
$53$	7.87848	1.08219	0.541096	+	0.840961i	$0.318009\pi$
$54$	1.74758	0.237815
$55$	0.775468	0.104564
$56$	−1.90123	−0.254062
$57$	4.14993	0.549671
$58$	−1.39320	−0.182936
$59$	−7.51394	−0.978232	−0.489116	−	0.872219i	$-0.662680\pi$
$59$	−7.51394	−0.978232	−0.489116	+	0.872219i	$0.662680\pi$
$60$	−3.63336	−0.469064
$61$	0.864964	0.110747	0.0553737	−	0.998466i	$-0.482365\pi$
$61$	0.864964	0.110747	0.0553737	+	0.998466i	$0.482365\pi$
$62$	−2.64990	−0.336537
$63$	−1.35113	−0.170227
$64$	−2.45331	−0.306664
$65$	−3.72997	−0.462646
$66$	−0.821891	−0.101168
$67$	−7.24202	−0.884754	−0.442377	−	0.896829i	$-0.645865\pi$
$67$	−7.24202	−0.884754	−0.442377	+	0.896829i	$0.645865\pi$
$68$	8.46437	1.02646
$69$	6.34755	0.764156
$70$	0.508100	0.0607296
$71$	−8.33101	−0.988708	−0.494354	−	0.869261i	$-0.664595\pi$
$71$	−8.33101	−0.988708	−0.494354	+	0.869261i	$0.664595\pi$
$72$	2.56881	0.302737
$73$	1.08129	0.126555	0.0632776	−	0.997996i	$-0.479845\pi$
$73$	1.08129	0.126555	0.0632776	+	0.997996i	$0.479845\pi$
$74$	4.45184	0.517516
$75$	2.08594	0.240863
$76$	−3.46534	−0.397502
$77$	−0.775468	−0.0883727
$78$	3.95326	0.447619
$79$	−7.23703	−0.814229	−0.407115	−	0.913377i	$-0.633465\pi$
$79$	−7.23703	−0.814229	−0.407115	+	0.913377i	$0.633465\pi$
$80$	2.51765	0.281482
$81$	−11.2278	−1.24754
$82$	−1.13318	−0.125139
$83$	−4.32857	−0.475123	−0.237561	−	0.971373i	$-0.576348\pi$
$83$	−4.32857	−0.475123	−0.237561	+	0.971373i	$0.576348\pi$
$84$	3.63336	0.396432
$85$	−4.85946	−0.527082
$86$	−1.81638	−0.195866
$87$	5.71960	0.613206
$88$	1.47434	0.157165
$89$	−0.886633	−0.0939829	−0.0469915	−	0.998895i	$-0.514963\pi$
$89$	−0.886633	−0.0939829	−0.0469915	+	0.998895i	$0.514963\pi$
$90$	−0.686511	−0.0723646
$91$	3.72997	0.391007
$92$	−5.30044	−0.552609
$93$	10.8788	1.12808
$94$	−1.75562	−0.181078
$95$	1.98948	0.204116
$96$	−10.6001	−1.08186
$97$	9.26504	0.940722	0.470361	−	0.882474i	$-0.344124\pi$
$97$	9.26504	0.940722	0.470361	+	0.882474i	$0.344124\pi$
$98$	−0.508100	−0.0513259
$99$	1.04776	0.105304
$100$	−1.74183	−0.174183
$101$	−17.1887	−1.71034	−0.855168	−	0.518350i	$-0.826546\pi$
$101$	−17.1887	−1.71034	−0.855168	+	0.518350i	$0.826546\pi$
$102$	5.15037	0.509963
$103$	−3.14120	−0.309511	−0.154756	−	0.987953i	$-0.549459\pi$
$103$	−3.14120	−0.309511	−0.154756	+	0.987953i	$0.549459\pi$
$104$	−7.09152	−0.695381
$105$	−2.08594	−0.203567
$106$	−4.00306	−0.388811
$107$	15.6913	1.51694	0.758468	−	0.651710i	$-0.225948\pi$
$107$	15.6913	1.51694	0.758468	+	0.651710i	$0.225948\pi$
$108$	5.99092	0.576477
$109$	−5.01098	−0.479965	−0.239983	−	0.970777i	$-0.577142\pi$
$109$	−5.01098	−0.479965	−0.239983	+	0.970777i	$0.577142\pi$
$110$	−0.394015	−0.0375679
$111$	−18.2764	−1.73472
$112$	−2.51765	−0.237896
$113$	5.31486	0.499980	0.249990	−	0.968248i	$-0.419573\pi$
$113$	5.31486	0.499980	0.249990	+	0.968248i	$0.419573\pi$
$114$	−2.10858	−0.197486
$115$	3.04302	0.283763
$116$	−4.77608	−0.443448
$117$	−5.03968	−0.465919
$118$	3.81783	0.351460
$119$	4.85946	0.445466
$120$	3.96584	0.362030
$121$	−10.3986	−0.945332
$122$	−0.439489	−0.0397894
$123$	4.65211	0.419467
$124$	−9.08420	−0.815785
$125$	1.00000	0.0894427
$126$	0.686511	0.0611592
$127$	0.481467	0.0427232	0.0213616	−	0.999772i	$-0.493200\pi$
$127$	0.481467	0.0427232	0.0213616	+	0.999772i	$0.493200\pi$
$128$	11.4099	1.00850
$129$	7.45692	0.656545
$130$	1.89520	0.166220
$131$	0.748551	0.0654012	0.0327006	−	0.999465i	$-0.489589\pi$
$131$	0.748551	0.0654012	0.0327006	+	0.999465i	$0.489589\pi$
$132$	−2.81755	−0.245236
$133$	−1.98948	−0.172510
$134$	3.67967	0.317875
$135$	−3.43943	−0.296019
$136$	−9.23893	−0.792232
$137$	−18.4579	−1.57696	−0.788481	−	0.615059i	$-0.789132\pi$
$137$	−18.4579	−1.57696	−0.788481	+	0.615059i	$0.789132\pi$
$138$	−3.22519	−0.274547
$139$	−18.3549	−1.55684	−0.778422	−	0.627742i	$-0.783979\pi$
$139$	−18.3549	−1.55684	−0.778422	+	0.627742i	$0.783979\pi$
$140$	1.74183	0.147212
$141$	7.20746	0.606978
$142$	4.23299	0.355224
$143$	−2.89247	−0.241881
$144$	3.40169	0.283474
$145$	2.74198	0.227709
$146$	−0.549403	−0.0454689
$147$	2.08594	0.172045
$148$	15.2615	1.25449
$149$	−19.2111	−1.57383	−0.786916	−	0.617061i	$-0.788323\pi$
$149$	−19.2111	−1.57383	−0.786916	+	0.617061i	$0.788323\pi$
$150$	−1.05987	−0.0865376
$151$	3.66050	0.297887	0.148944	−	0.988846i	$-0.452413\pi$
$151$	3.66050	0.297887	0.148944	+	0.988846i	$0.452413\pi$
$152$	3.78245	0.306797
$153$	−6.56577	−0.530811
$154$	0.394015	0.0317507
$155$	5.21531	0.418903
$156$	13.5523	1.08505
$157$	−7.24880	−0.578518	−0.289259	−	0.957251i	$-0.593409\pi$
$157$	−7.24880	−0.578518	−0.289259	+	0.957251i	$0.593409\pi$
$158$	3.67714	0.292537
$159$	16.4340	1.30330
$160$	−5.08167	−0.401742
$161$	−3.04302	−0.239824
$162$	5.70487	0.448217
$163$	−20.7871	−1.62817	−0.814085	−	0.580746i	$-0.802761\pi$
$163$	−20.7871	−1.62817	−0.814085	+	0.580746i	$0.802761\pi$
$164$	−3.88468	−0.303343
$165$	1.61758	0.125928
$166$	2.19935	0.170703
$167$	−16.1595	−1.25046	−0.625230	−	0.780440i	$-0.714995\pi$
$167$	−16.1595	−1.25046	−0.625230	+	0.780440i	$0.714995\pi$
$168$	−3.96584	−0.305971
$169$	0.912676	0.0702058
$170$	2.46909	0.189371
$171$	2.68805	0.205560
$172$	−6.22680	−0.474789
$173$	0.819248	0.0622862	0.0311431	−	0.999515i	$-0.490085\pi$
$173$	0.819248	0.0622862	0.0311431	+	0.999515i	$0.490085\pi$
$174$	−2.90613	−0.220313
$175$	−1.00000	−0.0755929
$176$	1.95236	0.147165
$177$	−15.6736	−1.17810
$178$	0.450499	0.0337663
$179$	−3.27699	−0.244934	−0.122467	−	0.992473i	$-0.539081\pi$
$179$	−3.27699	−0.244934	−0.122467	+	0.992473i	$0.539081\pi$
$180$	−2.35345	−0.175416
$181$	−5.27452	−0.392052	−0.196026	−	0.980599i	$-0.562804\pi$
$181$	−5.27452	−0.392052	−0.196026	+	0.980599i	$0.562804\pi$
$182$	−1.89520	−0.140481
$183$	1.80426	0.133375
$184$	5.78548	0.426511
$185$	−8.76174	−0.644176
$186$	−5.52752	−0.405297
$187$	−3.76835	−0.275569
$188$	−6.01849	−0.438944
$189$	3.43943	0.250182
$190$	−1.01085	−0.0733351
$191$	−0.730228	−0.0528375	−0.0264187	−	0.999651i	$-0.508410\pi$
$191$	−0.730228	−0.0528375	−0.0264187	+	0.999651i	$0.508410\pi$
$192$	−5.11745	−0.369320
$193$	0.252705	0.0181901	0.00909504	−	0.999959i	$-0.497105\pi$
$193$	0.252705	0.0181901	0.00909504	+	0.999959i	$0.497105\pi$
$194$	−4.70757	−0.337984
$195$	−7.78048	−0.557172
$196$	−1.74183	−0.124417
$197$	19.9879	1.42408	0.712040	−	0.702139i	$-0.247771\pi$
$197$	19.9879	1.42408	0.712040	+	0.702139i	$0.247771\pi$
$198$	−0.532367	−0.0378337
$199$	18.7485	1.32905	0.664523	−	0.747268i	$-0.268635\pi$
$199$	18.7485	1.32905	0.664523	+	0.747268i	$0.268635\pi$
$200$	1.90123	0.134437
$201$	−15.1064	−1.06552
$202$	8.73357	0.614492
$203$	−2.74198	−0.192449
$204$	17.6561	1.23618
$205$	2.23023	0.155766
$206$	1.59604	0.111202
$207$	4.11153	0.285771
$208$	−9.39078	−0.651133
$209$	1.54278	0.106716
$210$	1.05987	0.0731376
$211$	12.3474	0.850031	0.425016	−	0.905186i	$-0.360269\pi$
$211$	12.3474	0.850031	0.425016	+	0.905186i	$0.360269\pi$
$212$	−13.7230	−0.942500
$213$	−17.3780	−1.19072
$214$	−7.97276	−0.545007
$215$	3.57485	0.243803
$216$	−6.53914	−0.444932
$217$	−5.21531	−0.354038
$218$	2.54608	0.172442
$219$	2.25550	0.152413
$220$	−1.35074	−0.0910666
$221$	18.1256	1.21926
$222$	9.28626	0.623253
$223$	−5.87323	−0.393301	−0.196650	−	0.980474i	$-0.563006\pi$
$223$	−5.87323	−0.393301	−0.196650	+	0.980474i	$0.563006\pi$
$224$	5.08167	0.339534
$225$	1.35113	0.0900755
$226$	−2.70048	−0.179633
$227$	−28.6956	−1.90460	−0.952298	−	0.305168i	$-0.901287\pi$
$227$	−28.6956	−1.90460	−0.952298	+	0.305168i	$0.901287\pi$
$228$	−7.22848	−0.478718
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−1.54616	−0.101951
$231$	−1.61758	−0.106429
$232$	5.21313	0.342259
$233$	5.59626	0.366623	0.183312	−	0.983055i	$-0.441318\pi$
$233$	5.59626	0.366623	0.183312	+	0.983055i	$0.441318\pi$
$234$	2.56066	0.167396
$235$	3.45526	0.225396
$236$	13.0880	0.851959
$237$	−15.0960	−0.980590
$238$	−2.46909	−0.160047
$239$	−23.9851	−1.55146	−0.775732	−	0.631063i	$-0.782619\pi$
$239$	−23.9851	−1.55146	−0.775732	+	0.631063i	$0.782619\pi$
$240$	5.25167	0.338994
$241$	7.79824	0.502329	0.251164	−	0.967944i	$-0.419187\pi$
$241$	7.79824	0.502329	0.251164	+	0.967944i	$0.419187\pi$
$242$	5.28356	0.339640
$243$	−13.1023	−0.840511
$244$	−1.50662	−0.0964517
$245$	1.00000	0.0638877
$246$	−2.36374	−0.150706
$247$	−7.42069	−0.472167
$248$	9.91548	0.629634
$249$	−9.02913	−0.572198
$250$	−0.508100	−0.0321351
$251$	0.384111	0.0242449	0.0121224	−	0.999927i	$-0.496141\pi$
$251$	0.384111	0.0242449	0.0121224	+	0.999927i	$0.496141\pi$
$252$	2.35345	0.148253
$253$	2.35977	0.148357
$254$	−0.244633	−0.0153497
$255$	−10.1365	−0.634774
$256$	−0.890744	−0.0556715
$257$	−15.6187	−0.974267	−0.487134	−	0.873327i	$-0.661958\pi$
$257$	−15.6187	−0.974267	−0.487134	+	0.873327i	$0.661958\pi$
$258$	−3.78886	−0.235884
$259$	8.76174	0.544428
$260$	6.49699	0.402926
$261$	3.70478	0.229320
$262$	−0.380339	−0.0234974
$263$	21.2354	1.30943	0.654716	−	0.755875i	$-0.272788\pi$
$263$	21.2354	1.30943	0.654716	+	0.755875i	$0.272788\pi$
$264$	3.07538	0.189277
$265$	7.87848	0.483971
$266$	1.01085	0.0619795
$267$	−1.84946	−0.113185
$268$	12.6144	0.770547
$269$	−22.9950	−1.40203	−0.701016	−	0.713146i	$-0.747270\pi$
$269$	−22.9950	−1.40203	−0.701016	+	0.713146i	$0.747270\pi$
$270$	1.74758	0.106354
$271$	−10.3957	−0.631491	−0.315746	−	0.948844i	$-0.602255\pi$
$271$	−10.3957	−0.631491	−0.315746	+	0.948844i	$0.602255\pi$
$272$	−12.2344	−0.741822
$273$	7.78048	0.470896
$274$	9.37845	0.566573
$275$	0.775468	0.0467625
$276$	−11.0564	−0.665516
$277$	17.2553	1.03677	0.518385	−	0.855147i	$-0.326533\pi$
$277$	17.2553	1.03677	0.518385	+	0.855147i	$0.326533\pi$
$278$	9.32613	0.559344
$279$	7.04657	0.421867
$280$	−1.90123	−0.113620
$281$	4.43878	0.264795	0.132398	−	0.991197i	$-0.457732\pi$
$281$	4.43878	0.264795	0.132398	+	0.991197i	$0.457732\pi$
$282$	−3.66211	−0.218076
$283$	8.42022	0.500530	0.250265	−	0.968177i	$-0.419482\pi$
$283$	8.42022	0.500530	0.250265	+	0.968177i	$0.419482\pi$
$284$	14.5112	0.861083
$285$	4.14993	0.245820
$286$	1.46967	0.0869031
$287$	−2.23023	−0.131646
$288$	−6.86602	−0.404584
$289$	6.61433	0.389078
$290$	−1.39320	−0.0818116
$291$	19.3263	1.13293
$292$	−1.88342	−0.110219
$293$	−18.0793	−1.05620	−0.528102	−	0.849181i	$-0.677096\pi$
$293$	−18.0793	−1.05620	−0.528102	+	0.849181i	$0.677096\pi$
$294$	−1.05987	−0.0618126
$295$	−7.51394	−0.437478
$296$	−16.6580	−0.968229
$297$	−2.66717	−0.154765
$298$	9.76114	0.565448
$299$	−11.3504	−0.656410
$300$	−3.63336	−0.209772
$301$	−3.57485	−0.206051
$302$	−1.85990	−0.107025
$303$	−35.8545	−2.05979
$304$	5.00882	0.287275
$305$	0.864964	0.0495277
$306$	3.33607	0.190710
$307$	15.5055	0.884947	0.442474	−	0.896781i	$-0.354101\pi$
$307$	15.5055	0.884947	0.442474	+	0.896781i	$0.354101\pi$
$308$	1.35074	0.0769653
$309$	−6.55234	−0.372750
$310$	−2.64990	−0.150504
$311$	−23.6446	−1.34076	−0.670382	−	0.742016i	$-0.733870\pi$
$311$	−23.6446	−1.34076	−0.670382	+	0.742016i	$0.733870\pi$
$312$	−14.7925	−0.837458
$313$	4.09786	0.231625	0.115812	−	0.993271i	$-0.463053\pi$
$313$	4.09786	0.231625	0.115812	+	0.993271i	$0.463053\pi$
$314$	3.68312	0.207850
$315$	−1.35113	−0.0761277
$316$	12.6057	0.709126
$317$	22.3050	1.25278	0.626388	−	0.779511i	$-0.284533\pi$
$317$	22.3050	1.25278	0.626388	+	0.779511i	$0.284533\pi$
$318$	−8.35013	−0.468252
$319$	2.12632	0.119051
$320$	−2.45331	−0.137144
$321$	32.7311	1.82687
$322$	1.54616	0.0861642
$323$	−9.66778	−0.537930
$324$	19.5570	1.08650
$325$	−3.72997	−0.206902
$326$	10.5619	0.584971
$327$	−10.4526	−0.578030
$328$	4.24016	0.234124
$329$	−3.45526	−0.190495
$330$	−0.821891	−0.0452436
$331$	−17.4733	−0.960418	−0.480209	−	0.877154i	$-0.659439\pi$
$331$	−17.4733	−0.960418	−0.480209	+	0.877154i	$0.659439\pi$
$332$	7.53966	0.413792
$333$	−11.8383	−0.648733
$334$	8.21065	0.449267
$335$	−7.24202	−0.395674
$336$	−5.25167	−0.286502
$337$	17.8090	0.970116	0.485058	−	0.874482i	$-0.338799\pi$
$337$	17.8090	0.970116	0.485058	+	0.874482i	$0.338799\pi$
$338$	−0.463731	−0.0252236
$339$	11.0865	0.602134
$340$	8.46437	0.459045
$341$	4.04430	0.219011
$342$	−1.36580	−0.0738539
$343$	−1.00000	−0.0539949
$344$	6.79661	0.366449
$345$	6.34755	0.341741
$346$	−0.416260	−0.0223783
$347$	23.2589	1.24860	0.624302	−	0.781183i	$-0.285384\pi$
$347$	23.2589	1.24860	0.624302	+	0.781183i	$0.285384\pi$
$348$	−9.96260	−0.534051
$349$	5.48690	0.293707	0.146853	−	0.989158i	$-0.453085\pi$
$349$	5.48690	0.293707	0.146853	+	0.989158i	$0.453085\pi$
$350$	0.508100	0.0271591
$351$	12.8290	0.684760
$352$	−3.94067	−0.210039
$353$	21.8965	1.16543	0.582716	−	0.812676i	$-0.301990\pi$
$353$	21.8965	1.16543	0.582716	+	0.812676i	$0.301990\pi$
$354$	7.96376	0.423269
$355$	−8.33101	−0.442164
$356$	1.54437	0.0818513
$357$	10.1365	0.536482
$358$	1.66504	0.0880001
$359$	−3.55244	−0.187491	−0.0937454	−	0.995596i	$-0.529884\pi$
$359$	−3.55244	−0.187491	−0.0937454	+	0.995596i	$0.529884\pi$
$360$	2.56881	0.135388
$361$	−15.0420	−0.791683
$362$	2.67998	0.140857
$363$	−21.6909	−1.13848
$364$	−6.49699	−0.340535
$365$	1.08129	0.0565972
$366$	−0.916746	−0.0479191
$367$	−15.8835	−0.829112	−0.414556	−	0.910024i	$-0.636063\pi$
$367$	−15.8835	−0.829112	−0.414556	+	0.910024i	$0.636063\pi$
$368$	7.66128	0.399372
$369$	3.01333	0.156868
$370$	4.45184	0.231440
$371$	−7.87848	−0.409030
$372$	−18.9491	−0.982463
$373$	29.6682	1.53616	0.768081	−	0.640352i	$-0.221212\pi$
$373$	29.6682	1.53616	0.768081	+	0.640352i	$0.221212\pi$
$374$	1.91470	0.0990068
$375$	2.08594	0.107717
$376$	6.56924	0.338783
$377$	−10.2275	−0.526744
$378$	−1.74758	−0.0898857
$379$	12.0198	0.617417	0.308709	−	0.951157i	$-0.400103\pi$
$379$	12.0198	0.617417	0.308709	+	0.951157i	$0.400103\pi$
$380$	−3.46534	−0.177768
$381$	1.00431	0.0514523
$382$	0.371029	0.0189835
$383$	12.9653	0.662498	0.331249	−	0.943543i	$-0.392530\pi$
$383$	12.9653	0.662498	0.331249	+	0.943543i	$0.392530\pi$
$384$	23.8003	1.21455
$385$	−0.775468	−0.0395215
$386$	−0.128399	−0.00653535
$387$	4.83010	0.245528
$388$	−16.1382	−0.819291
$389$	−27.0276	−1.37035	−0.685177	−	0.728376i	$-0.740275\pi$
$389$	−27.0276	−1.37035	−0.685177	+	0.728376i	$0.740275\pi$
$390$	3.95326	0.200181
$391$	−14.7874	−0.747833
$392$	1.90123	0.0960265
$393$	1.56143	0.0787638
$394$	−10.1559	−0.511645
$395$	−7.23703	−0.364134
$396$	−1.82502	−0.0917109
$397$	−1.67756	−0.0841942	−0.0420971	−	0.999114i	$-0.513404\pi$
$397$	−1.67756	−0.0841942	−0.0420971	+	0.999114i	$0.513404\pi$
$398$	−9.52612	−0.477501
$399$	−4.14993	−0.207756
$400$	2.51765	0.125883
$401$	−10.3213	−0.515420	−0.257710	−	0.966222i	$-0.582968\pi$
$401$	−10.3213	−0.515420	−0.257710	+	0.966222i	$0.582968\pi$
$402$	7.67557	0.382823
$403$	−19.4529	−0.969020
$404$	29.9398	1.48956
$405$	−11.2278	−0.557916
$406$	1.39320	0.0691435
$407$	−6.79444	−0.336788
$408$	−19.2718	−0.954098
$409$	−5.95337	−0.294375	−0.147188	−	0.989109i	$-0.547022\pi$
$409$	−5.95337	−0.294375	−0.147188	+	0.989109i	$0.547022\pi$
$410$	−1.13318	−0.0559637
$411$	−38.5019	−1.89916
$412$	5.47144	0.269559
$413$	7.51394	0.369737
$414$	−2.08907	−0.102672
$415$	−4.32857	−0.212481
$416$	18.9545	0.929321
$417$	−38.2872	−1.87493
$418$	−0.783885	−0.0383411
$419$	−7.36938	−0.360018	−0.180009	−	0.983665i	$-0.557613\pi$
$419$	−7.36938	−0.360018	−0.180009	+	0.983665i	$0.557613\pi$
$420$	3.63336	0.177290
$421$	−14.1115	−0.687753	−0.343877	−	0.939015i	$-0.611740\pi$
$421$	−14.1115	−0.687753	−0.343877	+	0.939015i	$0.611740\pi$
$422$	−6.27373	−0.305400
$423$	4.66852	0.226991
$424$	14.9788	0.727434
$425$	−4.85946	−0.235718
$426$	8.82974	0.427802
$427$	−0.864964	−0.0418586
$428$	−27.3317	−1.32113
$429$	−6.03351	−0.291301
$430$	−1.81638	−0.0875938
$431$	−33.2075	−1.59955	−0.799774	−	0.600302i	$-0.795047\pi$
$431$	−33.2075	−1.59955	−0.799774	+	0.600302i	$0.795047\pi$
$432$	−8.65930	−0.416621
$433$	3.40640	0.163701	0.0818506	−	0.996645i	$-0.473917\pi$
$433$	3.40640	0.163701	0.0818506	+	0.996645i	$0.473917\pi$
$434$	2.64990	0.127199
$435$	5.71960	0.274234
$436$	8.72830	0.418010
$437$	6.05403	0.289603
$438$	−1.14602	−0.0547589
$439$	32.6409	1.55786	0.778932	−	0.627109i	$-0.215762\pi$
$439$	32.6409	1.55786	0.778932	+	0.627109i	$0.215762\pi$
$440$	1.47434	0.0702864
$441$	1.35113	0.0643396
$442$	−9.20964	−0.438058
$443$	4.05022	0.192432	0.0962158	−	0.995360i	$-0.469326\pi$
$443$	4.05022	0.192432	0.0962158	+	0.995360i	$0.469326\pi$
$444$	31.8345	1.51080
$445$	−0.886633	−0.0420304
$446$	2.98419	0.141306
$447$	−40.0731	−1.89539
$448$	2.45331	0.115908
$449$	23.5910	1.11333	0.556664	−	0.830738i	$-0.312081\pi$
$449$	23.5910	1.11333	0.556664	+	0.830738i	$0.312081\pi$
$450$	−0.686511	−0.0323624
$451$	1.72947	0.0814375
$452$	−9.25760	−0.435441
$453$	7.63557	0.358750
$454$	14.5803	0.684286
$455$	3.72997	0.174864
$456$	7.88995	0.369481
$457$	−13.0592	−0.610885	−0.305442	−	0.952211i	$-0.598804\pi$
$457$	−13.0592	−0.610885	−0.305442	+	0.952211i	$0.598804\pi$
$458$	−0.508100	−0.0237420
$459$	16.7138	0.780132
$460$	−5.30044	−0.247134
$461$	−32.2758	−1.50323	−0.751617	−	0.659600i	$-0.770726\pi$
$461$	−32.2758	−1.50323	−0.751617	+	0.659600i	$0.770726\pi$
$462$	0.821891	0.0382378
$463$	−36.9787	−1.71854	−0.859272	−	0.511519i	$-0.829083\pi$
$463$	−36.9787	−1.71854	−0.859272	+	0.511519i	$0.829083\pi$
$464$	6.90337	0.320481
$465$	10.8788	0.504492
$466$	−2.84346	−0.131721
$467$	−4.88656	−0.226123	−0.113062	−	0.993588i	$-0.536066\pi$
$467$	−4.88656	−0.226123	−0.113062	+	0.993588i	$0.536066\pi$
$468$	8.77829	0.405777
$469$	7.24202	0.334406
$470$	−1.75562	−0.0809807
$471$	−15.1205	−0.696718
$472$	−14.2857	−0.657553
$473$	2.77218	0.127465
$474$	7.67028	0.352307
$475$	1.98948	0.0912835
$476$	−8.46437	−0.387964
$477$	10.6449	0.487395
$478$	12.1868	0.557412
$479$	−34.7852	−1.58938	−0.794688	−	0.607018i	$-0.792366\pi$
$479$	−34.7852	−1.58938	−0.794688	+	0.607018i	$0.792366\pi$
$480$	−10.6001	−0.483824
$481$	32.6810	1.49013
$482$	−3.96229	−0.180477
$483$	−6.34755	−0.288824
$484$	18.1127	0.823306
$485$	9.26504	0.420704
$486$	6.65726	0.301980
$487$	−14.7048	−0.666340	−0.333170	−	0.942867i	$-0.608118\pi$
$487$	−14.7048	−0.666340	−0.333170	+	0.942867i	$0.608118\pi$
$488$	1.64449	0.0744427
$489$	−43.3605	−1.96083
$490$	−0.508100	−0.0229536
$491$	−7.70290	−0.347627	−0.173814	−	0.984779i	$-0.555609\pi$
$491$	−7.70290	−0.347627	−0.173814	+	0.984779i	$0.555609\pi$
$492$	−8.10320	−0.365321
$493$	−13.3245	−0.600108
$494$	3.77046	0.169641
$495$	1.04776	0.0470933
$496$	13.1303	0.589570
$497$	8.33101	0.373697
$498$	4.58770	0.205580
$499$	−2.07225	−0.0927668	−0.0463834	−	0.998924i	$-0.514770\pi$
$499$	−2.07225	−0.0927668	−0.0463834	+	0.998924i	$0.514770\pi$
$500$	−1.74183	−0.0778972
$501$	−33.7077	−1.50595
$502$	−0.195167	−0.00871072
$503$	−11.4295	−0.509617	−0.254808	−	0.966992i	$-0.582012\pi$
$503$	−11.4295	−0.509617	−0.254808	+	0.966992i	$0.582012\pi$
$504$	−2.56881	−0.114424
$505$	−17.1887	−0.764886
$506$	−1.19900	−0.0533019
$507$	1.90378	0.0845500
$508$	−0.838635	−0.0372084
$509$	19.5942	0.868498	0.434249	−	0.900793i	$-0.357014\pi$
$509$	19.5942	0.868498	0.434249	+	0.900793i	$0.357014\pi$
$510$	5.15037	0.228062
$511$	−1.08129	−0.0478334
$512$	−22.3672	−0.988498
$513$	−6.84268	−0.302112
$514$	7.93586	0.350036
$515$	−3.14120	−0.138418
$516$	−12.9887	−0.571797
$517$	2.67944	0.117842
$518$	−4.45184	−0.195603
$519$	1.70890	0.0750123
$520$	−7.09152	−0.310984
$521$	34.5947	1.51562	0.757810	−	0.652475i	$-0.226269\pi$
$521$	34.5947	1.51562	0.757810	+	0.652475i	$0.226269\pi$
$522$	−1.88240	−0.0823905
$523$	−30.1226	−1.31717	−0.658585	−	0.752507i	$-0.728845\pi$
$523$	−30.1226	−1.31717	−0.658585	+	0.752507i	$0.728845\pi$
$524$	−1.30385	−0.0569590
$525$	−2.08594	−0.0910377
$526$	−10.7897	−0.470454
$527$	−25.3436	−1.10398
$528$	4.07250	0.177233
$529$	−13.7400	−0.597392
$530$	−4.00306	−0.173882
$531$	−10.1523	−0.440574
$532$	3.46534	0.150242
$533$	−8.31867	−0.360322
$534$	0.939712	0.0406653
$535$	15.6913	0.678395
$536$	−13.7687	−0.594719
$537$	−6.83559	−0.294978
$538$	11.6838	0.503724
$539$	0.775468	0.0334018
$540$	5.99092	0.257808
$541$	9.13676	0.392820	0.196410	−	0.980522i	$-0.437072\pi$
$541$	9.13676	0.392820	0.196410	+	0.980522i	$0.437072\pi$
$542$	5.28204	0.226883
$543$	−11.0023	−0.472154
$544$	24.6942	1.05875
$545$	−5.01098	−0.214647
$546$	−3.95326	−0.169184
$547$	5.69658	0.243568	0.121784	−	0.992557i	$-0.461138\pi$
$547$	5.69658	0.243568	0.121784	+	0.992557i	$0.461138\pi$
$548$	32.1505	1.37340
$549$	1.16868	0.0498781
$550$	−0.394015	−0.0168009
$551$	5.45511	0.232396
$552$	12.0681	0.513654
$553$	7.23703	0.307750
$554$	−8.76743	−0.372492
$555$	−18.2764	−0.775791
$556$	31.9712	1.35588
$557$	−18.8511	−0.798746	−0.399373	−	0.916789i	$-0.630772\pi$
$557$	−18.8511	−0.798746	−0.399373	+	0.916789i	$0.630772\pi$
$558$	−3.58036	−0.151569
$559$	−13.3341	−0.563972
$560$	−2.51765	−0.106390
$561$	−7.86055	−0.331872
$562$	−2.25534	−0.0951359
$563$	−38.5074	−1.62289	−0.811447	−	0.584426i	$-0.801320\pi$
$563$	−38.5074	−1.62289	−0.811447	+	0.584426i	$0.801320\pi$
$564$	−12.5542	−0.528627
$565$	5.31486	0.223598
$566$	−4.27832	−0.179831
$567$	11.2278	0.471525
$568$	−15.8391	−0.664595
$569$	38.1117	1.59773	0.798863	−	0.601513i	$-0.205435\pi$
$569$	38.1117	1.59773	0.798863	+	0.601513i	$0.205435\pi$
$570$	−2.10858	−0.0883186
$571$	−30.6504	−1.28268	−0.641339	−	0.767257i	$-0.721621\pi$
$571$	−30.6504	−1.28268	−0.641339	+	0.767257i	$0.721621\pi$
$572$	5.03821	0.210658
$573$	−1.52321	−0.0636330
$574$	1.13318	0.0472979
$575$	3.04302	0.126903
$576$	−3.31475	−0.138114
$577$	−2.85921	−0.119030	−0.0595152	−	0.998227i	$-0.518955\pi$
$577$	−2.85921	−0.119030	−0.0595152	+	0.998227i	$0.518955\pi$
$578$	−3.36074	−0.139788
$579$	0.527126	0.0219066
$580$	−4.77608	−0.198316
$581$	4.32857	0.179579
$582$	−9.81969	−0.407039
$583$	6.10951	0.253030
$584$	2.05577	0.0850685
$585$	−5.03968	−0.208365
$586$	9.18609	0.379474
$587$	3.94065	0.162648	0.0813240	−	0.996688i	$-0.474085\pi$
$587$	3.94065	0.162648	0.0813240	+	0.996688i	$0.474085\pi$
$588$	−3.63336	−0.149837
$589$	10.3757	0.427525
$590$	3.81783	0.157178
$591$	41.6935	1.71504
$592$	−22.0590	−0.906620
$593$	3.02377	0.124172	0.0620858	−	0.998071i	$-0.480225\pi$
$593$	3.02377	0.124172	0.0620858	+	0.998071i	$0.480225\pi$
$594$	1.35519	0.0556041
$595$	4.85946	0.199218
$596$	33.4625	1.37068
$597$	39.1082	1.60059
$598$	5.76713	0.235836
$599$	24.2692	0.991612	0.495806	−	0.868433i	$-0.334873\pi$
$599$	24.2692	0.991612	0.495806	+	0.868433i	$0.334873\pi$
$600$	3.96584	0.161905
$601$	−5.96581	−0.243351	−0.121675	−	0.992570i	$-0.538827\pi$
$601$	−5.96581	−0.243351	−0.121675	+	0.992570i	$0.538827\pi$
$602$	1.81638	0.0740303
$603$	−9.78493	−0.398473
$604$	−6.37598	−0.259435
$605$	−10.3986	−0.422765
$606$	18.2177	0.740042
$607$	23.8061	0.966258	0.483129	−	0.875549i	$-0.339500\pi$
$607$	23.8061	0.966258	0.483129	+	0.875549i	$0.339500\pi$
$608$	−10.1099	−0.410010
$609$	−5.71960	−0.231770
$610$	−0.439489	−0.0177944
$611$	−12.8880	−0.521394
$612$	11.4365	0.462293
$613$	47.2453	1.90822	0.954110	−	0.299455i	$-0.0968050\pi$
$613$	47.2453	1.90822	0.954110	+	0.299455i	$0.0968050\pi$
$614$	−7.87836	−0.317945
$615$	4.65211	0.187591
$616$	−1.47434	−0.0594029
$617$	−20.0199	−0.805972	−0.402986	−	0.915206i	$-0.632028\pi$
$617$	−20.0199	−0.805972	−0.402986	+	0.915206i	$0.632028\pi$
$618$	3.32925	0.133922
$619$	29.2570	1.17594	0.587969	−	0.808884i	$-0.299928\pi$
$619$	29.2570	1.17594	0.587969	+	0.808884i	$0.299928\pi$
$620$	−9.08420	−0.364830
$621$	−10.4663	−0.419997
$622$	12.0138	0.481711
$623$	0.886633	0.0355222
$624$	−19.5886	−0.784170
$625$	1.00000	0.0400000
$626$	−2.08213	−0.0832185
$627$	3.21813	0.128520
$628$	12.6262	0.503841
$629$	42.5773	1.69767
$630$	0.686511	0.0273512
$631$	10.5126	0.418499	0.209249	−	0.977862i	$-0.432898\pi$
$631$	10.5126	0.418499	0.209249	+	0.977862i	$0.432898\pi$
$632$	−13.7592	−0.547313
$633$	25.7559	1.02371
$634$	−11.3332	−0.450099
$635$	0.481467	0.0191064
$636$	−28.6253	−1.13507
$637$	−3.72997	−0.147787
$638$	−1.08038	−0.0427728
$639$	−11.2563	−0.445292
$640$	11.4099	0.451015
$641$	−7.67607	−0.303186	−0.151593	−	0.988443i	$-0.548440\pi$
$641$	−7.67607	−0.303186	−0.151593	+	0.988443i	$0.548440\pi$
$642$	−16.6307	−0.656360
$643$	−28.7364	−1.13325	−0.566626	−	0.823975i	$-0.691752\pi$
$643$	−28.7364	−1.13325	−0.566626	+	0.823975i	$0.691752\pi$
$644$	5.30044	0.208867
$645$	7.45692	0.293616
$646$	4.91220	0.193268
$647$	−15.5183	−0.610085	−0.305043	−	0.952339i	$-0.598671\pi$
$647$	−15.5183	−0.610085	−0.305043	+	0.952339i	$0.598671\pi$
$648$	−21.3467	−0.838576
$649$	−5.82682	−0.228723
$650$	1.89520	0.0743358
$651$	−10.8788	−0.426374
$652$	36.2076	1.41800
$653$	0.739461	0.0289373	0.0144687	−	0.999895i	$-0.495394\pi$
$653$	0.739461	0.0289373	0.0144687	+	0.999895i	$0.495394\pi$
$654$	5.31097	0.207675
$655$	0.748551	0.0292483
$656$	5.61494	0.219226
$657$	1.46096	0.0569976
$658$	1.75562	0.0684412
$659$	8.85169	0.344813	0.172406	−	0.985026i	$-0.444846\pi$
$659$	8.85169	0.344813	0.172406	+	0.985026i	$0.444846\pi$
$660$	−2.81755	−0.109673
$661$	45.9314	1.78652	0.893261	−	0.449538i	$-0.148411\pi$
$661$	45.9314	1.78652	0.893261	+	0.449538i	$0.148411\pi$
$662$	8.87817	0.345060
$663$	37.8089	1.46838
$664$	−8.22960	−0.319370
$665$	−1.98948	−0.0771486
$666$	6.01503	0.233078
$667$	8.34392	0.323078
$668$	28.1472	1.08905
$669$	−12.2512	−0.473659
$670$	3.67967	0.142158
$671$	0.670752	0.0258941
$672$	10.6001	0.408906
$673$	−21.6790	−0.835664	−0.417832	−	0.908524i	$-0.637210\pi$
$673$	−21.6790	−0.835664	−0.417832	+	0.908524i	$0.637210\pi$
$674$	−9.04874	−0.348544
$675$	−3.43943	−0.132384
$676$	−1.58973	−0.0611435
$677$	38.3161	1.47261	0.736305	−	0.676650i	$-0.236569\pi$
$677$	38.3161	1.47261	0.736305	+	0.676650i	$0.236569\pi$
$678$	−5.63303	−0.216335
$679$	−9.26504	−0.355559
$680$	−9.23893	−0.354297
$681$	−59.8573	−2.29374
$682$	−2.05491	−0.0786866
$683$	6.65593	0.254682	0.127341	−	0.991859i	$-0.459356\pi$
$683$	6.65593	0.254682	0.127341	+	0.991859i	$0.459356\pi$
$684$	−4.68213	−0.179026
$685$	−18.4579	−0.705239
$686$	0.508100	0.0193994
$687$	2.08594	0.0795835
$688$	9.00025	0.343131
$689$	−29.3865	−1.11954
$690$	−3.22519	−0.122781
$691$	35.5110	1.35090	0.675450	−	0.737405i	$-0.263949\pi$
$691$	35.5110	1.35090	0.675450	+	0.737405i	$0.263949\pi$
$692$	−1.42699	−0.0542461
$693$	−1.04776	−0.0398011
$694$	−11.8179	−0.448600
$695$	−18.3549	−0.696241
$696$	10.8743	0.412188
$697$	−10.8377	−0.410507
$698$	−2.78789	−0.105523
$699$	11.6735	0.441530
$700$	1.74183	0.0658351
$701$	−14.0776	−0.531704	−0.265852	−	0.964014i	$-0.585653\pi$
$701$	−14.0776	−0.531704	−0.265852	+	0.964014i	$0.585653\pi$
$702$	−6.51841	−0.246022
$703$	−17.4313	−0.657433
$704$	−1.90246	−0.0717017
$705$	7.20746	0.271449
$706$	−11.1256	−0.418718
$707$	17.1887	0.646447
$708$	27.3008	1.02603
$709$	−16.6431	−0.625046	−0.312523	−	0.949910i	$-0.601174\pi$
$709$	−16.6431	−0.625046	−0.312523	+	0.949910i	$0.601174\pi$
$710$	4.23299	0.158861
$711$	−9.77819	−0.366711
$712$	−1.68569	−0.0631739
$713$	15.8703	0.594347
$714$	−5.15037	−0.192748
$715$	−2.89247	−0.108172
$716$	5.70797	0.213317
$717$	−50.0313	−1.86845
$718$	1.80500	0.0673619
$719$	25.5609	0.953260	0.476630	−	0.879104i	$-0.341858\pi$
$719$	25.5609	0.953260	0.476630	+	0.879104i	$0.341858\pi$
$720$	3.40169	0.126773
$721$	3.14120	0.116984
$722$	7.64283	0.284437
$723$	16.2666	0.604962
$724$	9.18733	0.341445
$725$	2.74198	0.101835
$726$	11.0212	0.409034
$727$	−17.4622	−0.647635	−0.323818	−	0.946120i	$-0.604966\pi$
$727$	−17.4622	−0.647635	−0.323818	+	0.946120i	$0.604966\pi$
$728$	7.09152	0.262829
$729$	6.35302	0.235297
$730$	−0.549403	−0.0203343
$731$	−17.3719	−0.642521
$732$	−3.14272	−0.116158
$733$	42.1719	1.55766	0.778828	−	0.627238i	$-0.215815\pi$
$733$	42.1719	1.55766	0.778828	+	0.627238i	$0.215815\pi$
$734$	8.07041	0.297884
$735$	2.08594	0.0769409
$736$	−15.4636	−0.569998
$737$	−5.61596	−0.206866
$738$	−1.53107	−0.0563596
$739$	44.1632	1.62457	0.812284	−	0.583262i	$-0.198224\pi$
$739$	44.1632	1.62457	0.812284	+	0.583262i	$0.198224\pi$
$740$	15.2615	0.561024
$741$	−15.4791	−0.568639
$742$	4.00306	0.146957
$743$	19.5220	0.716194	0.358097	−	0.933684i	$-0.383426\pi$
$743$	19.5220	0.716194	0.358097	+	0.933684i	$0.383426\pi$
$744$	20.6831	0.758278
$745$	−19.2111	−0.703839
$746$	−15.0744	−0.551914
$747$	−5.84848	−0.213985
$748$	6.56385	0.239998
$749$	−15.6913	−0.573348
$750$	−1.05987	−0.0387008
$751$	2.91407	0.106336	0.0531680	−	0.998586i	$-0.483068\pi$
$751$	2.91407	0.106336	0.0531680	+	0.998586i	$0.483068\pi$
$752$	8.69916	0.317226
$753$	0.801231	0.0291985
$754$	5.19660	0.189249
$755$	3.66050	0.133219
$756$	−5.99092	−0.217888
$757$	−3.66609	−0.133246	−0.0666231	−	0.997778i	$-0.521223\pi$
$757$	−3.66609	−0.133246	−0.0666231	+	0.997778i	$0.521223\pi$
$758$	−6.10728	−0.221826
$759$	4.92232	0.178669
$760$	3.78245	0.137204
$761$	−40.9765	−1.48540	−0.742699	−	0.669625i	$-0.766455\pi$
$761$	−40.9765	−1.48540	−0.742699	+	0.669625i	$0.766455\pi$
$762$	−0.510290	−0.0184858
$763$	5.01098	0.181410
$764$	1.27194	0.0460171
$765$	−6.56577	−0.237386
$766$	−6.58769	−0.238023
$767$	28.0268	1.01199
$768$	−1.85804	−0.0670461
$769$	−13.4614	−0.485429	−0.242715	−	0.970098i	$-0.578038\pi$
$769$	−13.4614	−0.485429	−0.242715	+	0.970098i	$0.578038\pi$
$770$	0.394015	0.0141993
$771$	−32.5796	−1.17333
$772$	−0.440170	−0.0158421
$773$	26.4404	0.950994	0.475497	−	0.879717i	$-0.342268\pi$
$773$	26.4404	0.950994	0.475497	+	0.879717i	$0.342268\pi$
$774$	−2.45418	−0.0882136
$775$	5.21531	0.187339
$776$	17.6149	0.632339
$777$	18.2764	0.655663
$778$	13.7327	0.492343
$779$	4.43698	0.158971
$780$	13.5523	0.485250
$781$	−6.46043	−0.231172
$782$	7.51350	0.268682
$783$	−9.43087	−0.337032
$784$	2.51765	0.0899162
$785$	−7.24880	−0.258721
$786$	−0.793363	−0.0282983
$787$	−17.6424	−0.628882	−0.314441	−	0.949277i	$-0.601817\pi$
$787$	−17.6424	−0.628882	−0.314441	+	0.949277i	$0.601817\pi$
$788$	−34.8156	−1.24026
$789$	44.2957	1.57697
$790$	3.67714	0.130827
$791$	−5.31486	−0.188975
$792$	1.99203	0.0707837
$793$	−3.22629	−0.114569
$794$	0.852368	0.0302494
$795$	16.4340	0.582854
$796$	−32.6568	−1.15749
$797$	−10.7901	−0.382206	−0.191103	−	0.981570i	$-0.561206\pi$
$797$	−10.7901	−0.382206	−0.191103	+	0.981570i	$0.561206\pi$
$798$	2.10858	0.0746429
$799$	−16.7907	−0.594012
$800$	−5.08167	−0.179664
$801$	−1.19796	−0.0423278
$802$	5.24424	0.185181
$803$	0.838504	0.0295902
$804$	26.3128	0.927983
$805$	−3.04302	−0.107252
$806$	9.88404	0.348151
$807$	−47.9662	−1.68849
$808$	−32.6796	−1.14966
$809$	30.9989	1.08986	0.544932	−	0.838480i	$-0.316556\pi$
$809$	30.9989	1.08986	0.544932	+	0.838480i	$0.316556\pi$
$810$	5.70487	0.200449
$811$	−22.0099	−0.772871	−0.386436	−	0.922316i	$-0.626294\pi$
$811$	−22.0099	−0.772871	−0.386436	+	0.922316i	$0.626294\pi$
$812$	4.77608	0.167608
$813$	−21.6847	−0.760515
$814$	3.45226	0.121002
$815$	−20.7871	−0.728140
$816$	−25.5203	−0.893388
$817$	7.11210	0.248821
$818$	3.02491	0.105763
$819$	5.03968	0.176101
$820$	−3.88468	−0.135659
$821$	−8.95685	−0.312596	−0.156298	−	0.987710i	$-0.549956\pi$
$821$	−8.95685	−0.312596	−0.156298	+	0.987710i	$0.549956\pi$
$822$	19.5628	0.682333
$823$	23.7876	0.829185	0.414592	−	0.910007i	$-0.363924\pi$
$823$	23.7876	0.829185	0.414592	+	0.910007i	$0.363924\pi$
$824$	−5.97213	−0.208049
$825$	1.61758	0.0563168
$826$	−3.81783	−0.132839
$827$	−35.3978	−1.23090	−0.615451	−	0.788175i	$-0.711026\pi$
$827$	−35.3978	−1.23090	−0.615451	+	0.788175i	$0.711026\pi$
$828$	−7.16160	−0.248883
$829$	36.8583	1.28014	0.640071	−	0.768316i	$-0.278905\pi$
$829$	36.8583	1.28014	0.640071	+	0.768316i	$0.278905\pi$
$830$	2.19935	0.0763405
$831$	35.9935	1.24860
$832$	9.15077	0.317246
$833$	−4.85946	−0.168370
$834$	19.4537	0.673627
$835$	−16.1595	−0.559223
$836$	−2.68726	−0.0929408
$837$	−17.9377	−0.620018
$838$	3.74438	0.129348
$839$	−21.7285	−0.750151	−0.375076	−	0.926994i	$-0.622383\pi$
$839$	−21.7285	−0.750151	−0.375076	+	0.926994i	$0.622383\pi$
$840$	−3.96584	−0.136834
$841$	−21.4815	−0.740742
$842$	7.17007	0.247097
$843$	9.25900	0.318897
$844$	−21.5072	−0.740307
$845$	0.912676	0.0313970
$846$	−2.37207	−0.0815536
$847$	10.3986	0.357302
$848$	19.8353	0.681147
$849$	17.5641	0.602797
$850$	2.46909	0.0846891
$851$	−26.6622	−0.913967
$852$	30.2695	1.03702
$853$	−18.2290	−0.624150	−0.312075	−	0.950057i	$-0.601024\pi$
$853$	−18.2290	−0.624150	−0.312075	+	0.950057i	$0.601024\pi$
$854$	0.439489	0.0150390
$855$	2.68805	0.0919293
$856$	29.8328	1.01966
$857$	3.80168	0.129863	0.0649315	−	0.997890i	$-0.479317\pi$
$857$	3.80168	0.129863	0.0649315	+	0.997890i	$0.479317\pi$
$858$	3.06563	0.104659
$859$	−16.3600	−0.558194	−0.279097	−	0.960263i	$-0.590035\pi$
$859$	−16.3600	−0.558194	−0.279097	+	0.960263i	$0.590035\pi$
$860$	−6.22680	−0.212332
$861$	−4.65211	−0.158543
$862$	16.8727	0.574687
$863$	32.4734	1.10541	0.552704	−	0.833378i	$-0.313596\pi$
$863$	32.4734	1.10541	0.552704	+	0.833378i	$0.313596\pi$
$864$	17.4781	0.594616
$865$	0.819248	0.0278553
$866$	−1.73079	−0.0588147
$867$	13.7971	0.468573
$868$	9.08420	0.308338
$869$	−5.61208	−0.190377
$870$	−2.90613	−0.0985271
$871$	27.0125	0.915285
$872$	−9.52702	−0.322626
$873$	12.5183	0.423680
$874$	−3.07605	−0.104049
$875$	−1.00000	−0.0338062
$876$	−3.92871	−0.132739
$877$	25.2181	0.851554	0.425777	−	0.904828i	$-0.360001\pi$
$877$	25.2181	0.851554	0.425777	+	0.904828i	$0.360001\pi$
$878$	−16.5848	−0.559711
$879$	−37.7123	−1.27200
$880$	1.95236	0.0658140
$881$	−57.1433	−1.92521	−0.962603	−	0.270916i	$-0.912673\pi$
$881$	−57.1433	−1.92521	−0.962603	+	0.270916i	$0.912673\pi$
$882$	−0.686511	−0.0231160
$883$	26.6799	0.897851	0.448925	−	0.893569i	$-0.351807\pi$
$883$	26.6799	0.897851	0.448925	+	0.893569i	$0.351807\pi$
$884$	−31.5718	−1.06188
$885$	−15.6736	−0.526862
$886$	−2.05792	−0.0691371
$887$	40.1235	1.34722	0.673608	−	0.739089i	$-0.264744\pi$
$887$	40.1235	1.34722	0.673608	+	0.739089i	$0.264744\pi$
$888$	−34.7476	−1.16605
$889$	−0.481467	−0.0161479
$890$	0.450499	0.0151007
$891$	−8.70683	−0.291690
$892$	10.2302	0.342532
$893$	6.87417	0.230035
$894$	20.3611	0.680978
$895$	−3.27699	−0.109538
$896$	−11.4099	−0.381177
$897$	−23.6762	−0.790525
$898$	−11.9866	−0.399998
$899$	14.3003	0.476941
$900$	−2.35345	−0.0784483
$901$	−38.2851	−1.27546
$902$	−0.878743	−0.0292589
$903$	−7.45692	−0.248151
$904$	10.1047	0.336079
$905$	−5.27452	−0.175331
$906$	−3.87964	−0.128892
$907$	−42.9248	−1.42529	−0.712646	−	0.701523i	$-0.752504\pi$
$907$	−42.9248	−1.42529	−0.712646	+	0.701523i	$0.752504\pi$
$908$	49.9831	1.65875
$909$	−23.2242	−0.770297
$910$	−1.89520	−0.0628252
$911$	−32.3759	−1.07266	−0.536331	−	0.844007i	$-0.680190\pi$
$911$	−32.3759	−1.07266	−0.536331	+	0.844007i	$0.680190\pi$
$912$	10.4481	0.345970
$913$	−3.35667	−0.111090
$914$	6.63539	0.219479
$915$	1.80426	0.0596470
$916$	−1.74183	−0.0575518
$917$	−0.748551	−0.0247193
$918$	−8.49228	−0.280287
$919$	−58.1456	−1.91805	−0.959024	−	0.283325i	$-0.908562\pi$
$919$	−58.1456	−1.91805	−0.959024	+	0.283325i	$0.908562\pi$
$920$	5.78548	0.190741
$921$	32.3436	1.06576
$922$	16.3993	0.540083
$923$	31.0744	1.02283
$924$	2.81755	0.0926906
$925$	−8.76174	−0.288084
$926$	18.7889	0.617440
$927$	−4.24417	−0.139397
$928$	−13.9339	−0.457402
$929$	−27.5591	−0.904186	−0.452093	−	0.891971i	$-0.649322\pi$
$929$	−27.5591	−0.904186	−0.452093	+	0.891971i	$0.649322\pi$
$930$	−5.52752	−0.181255
$931$	1.98948	0.0652025
$932$	−9.74776	−0.319299
$933$	−49.3212	−1.61470
$934$	2.48286	0.0812417
$935$	−3.76835	−0.123238
$936$	−9.58158	−0.313184
$937$	55.1530	1.80177	0.900885	−	0.434058i	$-0.142919\pi$
$937$	55.1530	1.80177	0.900885	+	0.434058i	$0.142919\pi$
$938$	−3.67967	−0.120146
$939$	8.54788	0.278950
$940$	−6.01849	−0.196302
$941$	47.1301	1.53640	0.768198	−	0.640212i	$-0.221153\pi$
$941$	47.1301	1.53640	0.768198	+	0.640212i	$0.221153\pi$
$942$	7.68275	0.250318
$943$	6.78663	0.221003
$944$	−18.9175	−0.615712
$945$	3.43943	0.111885
$946$	−1.40855	−0.0457958
$947$	−50.8823	−1.65345	−0.826726	−	0.562605i	$-0.809799\pi$
$947$	−50.8823	−1.65345	−0.826726	+	0.562605i	$0.809799\pi$
$948$	26.2947	0.854012
$949$	−4.03317	−0.130922
$950$	−1.01085	−0.0327964
$951$	46.5269	1.50874
$952$	9.23893	0.299435
$953$	17.4595	0.565568	0.282784	−	0.959184i	$-0.408742\pi$
$953$	17.4595	0.565568	0.282784	+	0.959184i	$0.408742\pi$
$954$	−5.40866	−0.175112
$955$	−0.730228	−0.0236296
$956$	41.7780	1.35120
$957$	4.43537	0.143375
$958$	17.6744	0.571033
$959$	18.4579	0.596036
$960$	−5.11745	−0.165165
$961$	−3.80058	−0.122599
$962$	−16.6052	−0.535374
$963$	21.2010	0.683194
$964$	−13.5832	−0.437487
$965$	0.252705	0.00813485
$966$	3.22519	0.103769
$967$	−10.0038	−0.321701	−0.160850	−	0.986979i	$-0.551424\pi$
$967$	−10.0038	−0.321701	−0.160850	+	0.986979i	$0.551424\pi$
$968$	−19.7702	−0.635438
$969$	−20.1664	−0.647838
$970$	−4.70757	−0.151151
$971$	−40.6604	−1.30485	−0.652426	−	0.757852i	$-0.726249\pi$
$971$	−40.6604	−1.30485	−0.652426	+	0.757852i	$0.726249\pi$
$972$	22.8220	0.732015
$973$	18.3549	0.588431
$974$	7.47154	0.239403
$975$	−7.78048	−0.249175
$976$	2.17768	0.0697059
$977$	3.79967	0.121562	0.0607811	−	0.998151i	$-0.480641\pi$
$977$	3.79967	0.121562	0.0607811	+	0.998151i	$0.480641\pi$
$978$	22.0315	0.704490
$979$	−0.687555	−0.0219744
$980$	−1.74183	−0.0556409
$981$	−6.77050	−0.216166
$982$	3.91385	0.124896
$983$	−9.78912	−0.312224	−0.156112	−	0.987739i	$-0.549896\pi$
$983$	−9.78912	−0.312224	−0.156112	+	0.987739i	$0.549896\pi$
$984$	8.84471	0.281959
$985$	19.9879	0.636868
$986$	6.77021	0.215607
$987$	−7.20746	−0.229416
$988$	12.9256	0.411219
$989$	10.8784	0.345912
$990$	−0.532367	−0.0169197
$991$	−7.60662	−0.241632	−0.120816	−	0.992675i	$-0.538551\pi$
$991$	−7.60662	−0.241632	−0.120816	+	0.992675i	$0.538551\pi$
$992$	−26.5025	−0.841455
$993$	−36.4481	−1.15665
$994$	−4.23299	−0.134262
$995$	18.7485	0.594367
$996$	15.7272	0.498337
$997$	43.4601	1.37640	0.688198	−	0.725523i	$-0.258402\pi$
$997$	43.4601	1.37640	0.688198	+	0.725523i	$0.258402\pi$
$998$	1.05291	0.0333294
$999$	30.1354	0.953442

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.i.1.20	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.i.1.20	✓	44	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)

\(f(q)\)	\(=\)	\(q-0.508100 q^{2} +2.08594 q^{3} -1.74183 q^{4} +1.00000 q^{5} -1.05987 q^{6} -1.00000 q^{7} +1.90123 q^{8} +1.35113 q^{9} +O(q^{10})\)	\(q-0.508100 q^{2} +2.08594 q^{3} -1.74183 q^{4} +1.00000 q^{5} -1.05987 q^{6} -1.00000 q^{7} +1.90123 q^{8} +1.35113 q^{9} -0.508100 q^{10} +0.775468 q^{11} -3.63336 q^{12} -3.72997 q^{13} +0.508100 q^{14} +2.08594 q^{15} +2.51765 q^{16} -4.85946 q^{17} -0.686511 q^{18} +1.98948 q^{19} -1.74183 q^{20} -2.08594 q^{21} -0.394015 q^{22} +3.04302 q^{23} +3.96584 q^{24} +1.00000 q^{25} +1.89520 q^{26} -3.43943 q^{27} +1.74183 q^{28} +2.74198 q^{29} -1.05987 q^{30} +5.21531 q^{31} -5.08167 q^{32} +1.61758 q^{33} +2.46909 q^{34} -1.00000 q^{35} -2.35345 q^{36} -8.76174 q^{37} -1.01085 q^{38} -7.78048 q^{39} +1.90123 q^{40} +2.23023 q^{41} +1.05987 q^{42} +3.57485 q^{43} -1.35074 q^{44} +1.35113 q^{45} -1.54616 q^{46} +3.45526 q^{47} +5.25167 q^{48} +1.00000 q^{49} -0.508100 q^{50} -10.1365 q^{51} +6.49699 q^{52} +7.87848 q^{53} +1.74758 q^{54} +0.775468 q^{55} -1.90123 q^{56} +4.14993 q^{57} -1.39320 q^{58} -7.51394 q^{59} -3.63336 q^{60} +0.864964 q^{61} -2.64990 q^{62} -1.35113 q^{63} -2.45331 q^{64} -3.72997 q^{65} -0.821891 q^{66} -7.24202 q^{67} +8.46437 q^{68} +6.34755 q^{69} +0.508100 q^{70} -8.33101 q^{71} +2.56881 q^{72} +1.08129 q^{73} +4.45184 q^{74} +2.08594 q^{75} -3.46534 q^{76} -0.775468 q^{77} +3.95326 q^{78} -7.23703 q^{79} +2.51765 q^{80} -11.2278 q^{81} -1.13318 q^{82} -4.32857 q^{83} +3.63336 q^{84} -4.85946 q^{85} -1.81638 q^{86} +5.71960 q^{87} +1.47434 q^{88} -0.886633 q^{89} -0.686511 q^{90} +3.72997 q^{91} -5.30044 q^{92} +10.8788 q^{93} -1.75562 q^{94} +1.98948 q^{95} -10.6001 q^{96} +9.26504 q^{97} -0.508100 q^{98} +1.04776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

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