LMFDB - Embedded newform 6015.2.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.52097 q^{2} -1.00000 q^{3} +0.313357 q^{4} -1.00000 q^{5} +1.52097 q^{6} -2.49520 q^{7} +2.56534 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.52097 q^{2} -1.00000 q^{3} +0.313357 q^{4} -1.00000 q^{5} +1.52097 q^{6} -2.49520 q^{7} +2.56534 q^{8} +1.00000 q^{9} +1.52097 q^{10} -3.05882 q^{11} -0.313357 q^{12} +0.142101 q^{13} +3.79513 q^{14} +1.00000 q^{15} -4.52852 q^{16} +3.56159 q^{17} -1.52097 q^{18} -6.21032 q^{19} -0.313357 q^{20} +2.49520 q^{21} +4.65238 q^{22} -8.69934 q^{23} -2.56534 q^{24} +1.00000 q^{25} -0.216132 q^{26} -1.00000 q^{27} -0.781887 q^{28} -0.813253 q^{29} -1.52097 q^{30} +5.86732 q^{31} +1.75708 q^{32} +3.05882 q^{33} -5.41708 q^{34} +2.49520 q^{35} +0.313357 q^{36} +2.23586 q^{37} +9.44572 q^{38} -0.142101 q^{39} -2.56534 q^{40} +0.462438 q^{41} -3.79513 q^{42} -5.58551 q^{43} -0.958501 q^{44} -1.00000 q^{45} +13.2315 q^{46} -12.0963 q^{47} +4.52852 q^{48} -0.773990 q^{49} -1.52097 q^{50} -3.56159 q^{51} +0.0445284 q^{52} -1.56234 q^{53} +1.52097 q^{54} +3.05882 q^{55} -6.40102 q^{56} +6.21032 q^{57} +1.23694 q^{58} +7.14764 q^{59} +0.313357 q^{60} -11.9090 q^{61} -8.92403 q^{62} -2.49520 q^{63} +6.38457 q^{64} -0.142101 q^{65} -4.65238 q^{66} +10.9569 q^{67} +1.11605 q^{68} +8.69934 q^{69} -3.79513 q^{70} -12.3690 q^{71} +2.56534 q^{72} +2.99541 q^{73} -3.40068 q^{74} -1.00000 q^{75} -1.94604 q^{76} +7.63235 q^{77} +0.216132 q^{78} -12.1521 q^{79} +4.52852 q^{80} +1.00000 q^{81} -0.703356 q^{82} -0.423112 q^{83} +0.781887 q^{84} -3.56159 q^{85} +8.49541 q^{86} +0.813253 q^{87} -7.84690 q^{88} +17.6879 q^{89} +1.52097 q^{90} -0.354571 q^{91} -2.72600 q^{92} -5.86732 q^{93} +18.3981 q^{94} +6.21032 q^{95} -1.75708 q^{96} -15.9859 q^{97} +1.17722 q^{98} -3.05882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - 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 $

$2$	−1.52097	−1.07549	−0.537745	−	0.843108i	$-0.680724\pi$
$2$	−1.52097	−1.07549	−0.537745	+	0.843108i	$0.680724\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.313357	0.156678
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.52097	0.620934
$7$	−2.49520	−0.943096	−0.471548	−	0.881840i	$-0.656305\pi$
$7$	−2.49520	−0.943096	−0.471548	+	0.881840i	$0.656305\pi$
$8$	2.56534	0.906984
$9$	1.00000	0.333333
$10$	1.52097	0.480974
$11$	−3.05882	−0.922268	−0.461134	−	0.887331i	$-0.652557\pi$
$11$	−3.05882	−0.922268	−0.461134	+	0.887331i	$0.652557\pi$
$12$	−0.313357	−0.0904583
$13$	0.142101	0.0394118	0.0197059	−	0.999806i	$-0.493727\pi$
$13$	0.142101	0.0394118	0.0197059	+	0.999806i	$0.493727\pi$
$14$	3.79513	1.01429
$15$	1.00000	0.258199
$16$	−4.52852	−1.13213
$17$	3.56159	0.863813	0.431906	−	0.901918i	$-0.357841\pi$
$17$	3.56159	0.863813	0.431906	+	0.901918i	$0.357841\pi$
$18$	−1.52097	−0.358497
$19$	−6.21032	−1.42474	−0.712372	−	0.701802i	$-0.752379\pi$
$19$	−6.21032	−1.42474	−0.712372	+	0.701802i	$0.752379\pi$
$20$	−0.313357	−0.0700687
$21$	2.49520	0.544497
$22$	4.65238	0.991890
$23$	−8.69934	−1.81394	−0.906969	−	0.421197i	$-0.861610\pi$
$23$	−8.69934	−1.81394	−0.906969	+	0.421197i	$0.861610\pi$
$24$	−2.56534	−0.523647
$25$	1.00000	0.200000
$26$	−0.216132	−0.0423870
$27$	−1.00000	−0.192450
$28$	−0.781887	−0.147763
$29$	−0.813253	−0.151017	−0.0755086	−	0.997145i	$-0.524058\pi$
$29$	−0.813253	−0.151017	−0.0755086	+	0.997145i	$0.524058\pi$
$30$	−1.52097	−0.277690
$31$	5.86732	1.05380	0.526901	−	0.849927i	$-0.323354\pi$
$31$	5.86732	1.05380	0.526901	+	0.849927i	$0.323354\pi$
$32$	1.75708	0.310611
$33$	3.05882	0.532472
$34$	−5.41708	−0.929022
$35$	2.49520	0.421765
$36$	0.313357	0.0522261
$37$	2.23586	0.367573	0.183787	−	0.982966i	$-0.441164\pi$
$37$	2.23586	0.367573	0.183787	+	0.982966i	$0.441164\pi$
$38$	9.44572	1.53230
$39$	−0.142101	−0.0227544
$40$	−2.56534	−0.405616
$41$	0.462438	0.0722207	0.0361103	−	0.999348i	$-0.488503\pi$
$41$	0.462438	0.0722207	0.0361103	+	0.999348i	$0.488503\pi$
$42$	−3.79513	−0.585601
$43$	−5.58551	−0.851783	−0.425891	−	0.904774i	$-0.640039\pi$
$43$	−5.58551	−0.851783	−0.425891	+	0.904774i	$0.640039\pi$
$44$	−0.958501	−0.144499
$45$	−1.00000	−0.149071
$46$	13.2315	1.95087
$47$	−12.0963	−1.76442	−0.882212	−	0.470852i	$-0.843947\pi$
$47$	−12.0963	−1.76442	−0.882212	+	0.470852i	$0.843947\pi$
$48$	4.52852	0.653636
$49$	−0.773990	−0.110570
$50$	−1.52097	−0.215098
$51$	−3.56159	−0.498723
$52$	0.0445284	0.00617497
$53$	−1.56234	−0.214604	−0.107302	−	0.994226i	$-0.534221\pi$
$53$	−1.56234	−0.214604	−0.107302	+	0.994226i	$0.534221\pi$
$54$	1.52097	0.206978
$55$	3.05882	0.412451
$56$	−6.40102	−0.855373
$57$	6.21032	0.822576
$58$	1.23694	0.162418
$59$	7.14764	0.930544	0.465272	−	0.885168i	$-0.345957\pi$
$59$	7.14764	0.930544	0.465272	+	0.885168i	$0.345957\pi$
$60$	0.313357	0.0404542
$61$	−11.9090	−1.52478	−0.762392	−	0.647115i	$-0.775975\pi$
$61$	−11.9090	−1.52478	−0.762392	+	0.647115i	$0.775975\pi$
$62$	−8.92403	−1.13335
$63$	−2.49520	−0.314365
$64$	6.38457	0.798072
$65$	−0.142101	−0.0176255
$66$	−4.65238	−0.572668
$67$	10.9569	1.33860	0.669301	−	0.742991i	$-0.266594\pi$
$67$	10.9569	1.33860	0.669301	+	0.742991i	$0.266594\pi$
$68$	1.11605	0.135341
$69$	8.69934	1.04728
$70$	−3.79513	−0.453604
$71$	−12.3690	−1.46793	−0.733967	−	0.679185i	$-0.762333\pi$
$71$	−12.3690	−1.46793	−0.733967	+	0.679185i	$0.762333\pi$
$72$	2.56534	0.302328
$73$	2.99541	0.350587	0.175293	−	0.984516i	$-0.443913\pi$
$73$	2.99541	0.350587	0.175293	+	0.984516i	$0.443913\pi$
$74$	−3.40068	−0.395321
$75$	−1.00000	−0.115470
$76$	−1.94604	−0.223227
$77$	7.63235	0.869787
$78$	0.216132	0.0244721
$79$	−12.1521	−1.36722	−0.683611	−	0.729846i	$-0.739592\pi$
$79$	−12.1521	−1.36722	−0.683611	+	0.729846i	$0.739592\pi$
$80$	4.52852	0.506304
$81$	1.00000	0.111111
$82$	−0.703356	−0.0776726
$83$	−0.423112	−0.0464425	−0.0232213	−	0.999730i	$-0.507392\pi$
$83$	−0.423112	−0.0464425	−0.0232213	+	0.999730i	$0.507392\pi$
$84$	0.781887	0.0853109
$85$	−3.56159	−0.386309
$86$	8.49541	0.916084
$87$	0.813253	0.0871899
$88$	−7.84690	−0.836482
$89$	17.6879	1.87491	0.937455	−	0.348106i	$-0.113175\pi$
$89$	17.6879	1.87491	0.937455	+	0.348106i	$0.113175\pi$
$90$	1.52097	0.160325
$91$	−0.354571	−0.0371691
$92$	−2.72600	−0.284205
$93$	−5.86732	−0.608412
$94$	18.3981	1.89762
$95$	6.21032	0.637165
$96$	−1.75708	−0.179331
$97$	−15.9859	−1.62312	−0.811562	−	0.584266i	$-0.801382\pi$
$97$	−15.9859	−1.62312	−0.811562	+	0.584266i	$0.801382\pi$
$98$	1.17722	0.118917
$99$	−3.05882	−0.307423
$100$	0.313357	0.0313357
$101$	−12.5751	−1.25127	−0.625635	−	0.780116i	$-0.715160\pi$
$101$	−12.5751	−1.25127	−0.625635	+	0.780116i	$0.715160\pi$
$102$	5.41708	0.536371
$103$	−0.526436	−0.0518713	−0.0259356	−	0.999664i	$-0.508256\pi$
$103$	−0.526436	−0.0518713	−0.0259356	+	0.999664i	$0.508256\pi$
$104$	0.364538	0.0357459
$105$	−2.49520	−0.243506
$106$	2.37628	0.230805
$107$	0.781482	0.0755487	0.0377744	−	0.999286i	$-0.487973\pi$
$107$	0.781482	0.0755487	0.0377744	+	0.999286i	$0.487973\pi$
$108$	−0.313357	−0.0301528
$109$	−7.52099	−0.720381	−0.360190	−	0.932879i	$-0.617288\pi$
$109$	−7.52099	−0.720381	−0.360190	+	0.932879i	$0.617288\pi$
$110$	−4.65238	−0.443587
$111$	−2.23586	−0.212218
$112$	11.2996	1.06771
$113$	10.4826	0.986119	0.493059	−	0.869996i	$-0.335879\pi$
$113$	10.4826	0.986119	0.493059	+	0.869996i	$0.335879\pi$
$114$	−9.44572	−0.884672
$115$	8.69934	0.811218
$116$	−0.254838	−0.0236611
$117$	0.142101	0.0131373
$118$	−10.8714	−1.00079
$119$	−8.88687	−0.814658
$120$	2.56534	0.234182
$121$	−1.64364	−0.149422
$122$	18.1132	1.63989
$123$	−0.462438	−0.0416966
$124$	1.83856	0.165108
$125$	−1.00000	−0.0894427
$126$	3.79513	0.338097
$127$	−17.0659	−1.51435	−0.757177	−	0.653210i	$-0.773422\pi$
$127$	−17.0659	−1.51435	−0.757177	+	0.653210i	$0.773422\pi$
$128$	−13.2249	−1.16893
$129$	5.58551	0.491777
$130$	0.216132	0.0189560
$131$	−13.9235	−1.21650	−0.608249	−	0.793746i	$-0.708128\pi$
$131$	−13.9235	−1.21650	−0.608249	+	0.793746i	$0.708128\pi$
$132$	0.958501	0.0834268
$133$	15.4960	1.34367
$134$	−16.6652	−1.43965
$135$	1.00000	0.0860663
$136$	9.13668	0.783464
$137$	−17.0076	−1.45306	−0.726529	−	0.687135i	$-0.758868\pi$
$137$	−17.0076	−1.45306	−0.726529	+	0.687135i	$0.758868\pi$
$138$	−13.2315	−1.12634
$139$	−0.472599	−0.0400853	−0.0200426	−	0.999799i	$-0.506380\pi$
$139$	−0.472599	−0.0400853	−0.0200426	+	0.999799i	$0.506380\pi$
$140$	0.781887	0.0660815
$141$	12.0963	1.01869
$142$	18.8129	1.57875
$143$	−0.434662	−0.0363482
$144$	−4.52852	−0.377377
$145$	0.813253	0.0675370
$146$	−4.55594	−0.377052
$147$	0.773990	0.0638376
$148$	0.700622	0.0575907
$149$	−8.83247	−0.723584	−0.361792	−	0.932259i	$-0.617835\pi$
$149$	−8.83247	−0.723584	−0.361792	+	0.932259i	$0.617835\pi$
$150$	1.52097	0.124187
$151$	−19.1377	−1.55740	−0.778702	−	0.627394i	$-0.784121\pi$
$151$	−19.1377	−1.55740	−0.778702	+	0.627394i	$0.784121\pi$
$152$	−15.9316	−1.29222
$153$	3.56159	0.287938
$154$	−11.6086	−0.935447
$155$	−5.86732	−0.471274
$156$	−0.0445284	−0.00356512
$157$	2.62674	0.209637	0.104818	−	0.994491i	$-0.466574\pi$
$157$	2.62674	0.209637	0.104818	+	0.994491i	$0.466574\pi$
$158$	18.4831	1.47043
$159$	1.56234	0.123902
$160$	−1.75708	−0.138909
$161$	21.7066	1.71072
$162$	−1.52097	−0.119499
$163$	−0.186249	−0.0145881	−0.00729407	−	0.999973i	$-0.502322\pi$
$163$	−0.186249	−0.0145881	−0.00729407	+	0.999973i	$0.502322\pi$
$164$	0.144908	0.0113154
$165$	−3.05882	−0.238129
$166$	0.643541	0.0499485
$167$	−2.04523	−0.158265	−0.0791324	−	0.996864i	$-0.525215\pi$
$167$	−2.04523	−0.158265	−0.0791324	+	0.996864i	$0.525215\pi$
$168$	6.40102	0.493850
$169$	−12.9798	−0.998447
$170$	5.41708	0.415471
$171$	−6.21032	−0.474915
$172$	−1.75026	−0.133456
$173$	21.8501	1.66123	0.830616	−	0.556845i	$-0.187988\pi$
$173$	21.8501	1.66123	0.830616	+	0.556845i	$0.187988\pi$
$174$	−1.23694	−0.0937718
$175$	−2.49520	−0.188619
$176$	13.8519	1.04413
$177$	−7.14764	−0.537250
$178$	−26.9028	−2.01645
$179$	−4.36265	−0.326080	−0.163040	−	0.986619i	$-0.552130\pi$
$179$	−4.36265	−0.326080	−0.163040	+	0.986619i	$0.552130\pi$
$180$	−0.313357	−0.0233562
$181$	−10.2005	−0.758195	−0.379098	−	0.925357i	$-0.623766\pi$
$181$	−10.2005	−0.758195	−0.379098	+	0.925357i	$0.623766\pi$
$182$	0.539292	0.0399750
$183$	11.9090	0.880335
$184$	−22.3168	−1.64521
$185$	−2.23586	−0.164384
$186$	8.92403	0.654341
$187$	−10.8943	−0.796667
$188$	−3.79045	−0.276447
$189$	2.49520	0.181499
$190$	−9.44572	−0.685264
$191$	20.2836	1.46767	0.733835	−	0.679328i	$-0.237729\pi$
$191$	20.2836	1.46767	0.733835	+	0.679328i	$0.237729\pi$
$192$	−6.38457	−0.460767
$193$	13.2764	0.955659	0.477830	−	0.878453i	$-0.341424\pi$
$193$	13.2764	0.955659	0.477830	+	0.878453i	$0.341424\pi$
$194$	24.3141	1.74565
$195$	0.142101	0.0101761
$196$	−0.242535	−0.0173239
$197$	7.22841	0.515003	0.257501	−	0.966278i	$-0.417101\pi$
$197$	7.22841	0.515003	0.257501	+	0.966278i	$0.417101\pi$
$198$	4.65238	0.330630
$199$	−25.9616	−1.84037	−0.920184	−	0.391485i	$-0.871961\pi$
$199$	−25.9616	−1.84037	−0.920184	+	0.391485i	$0.871961\pi$
$200$	2.56534	0.181397
$201$	−10.9569	−0.772843
$202$	19.1264	1.34573
$203$	2.02923	0.142424
$204$	−1.11605	−0.0781390
$205$	−0.462438	−0.0322981
$206$	0.800695	0.0557871
$207$	−8.69934	−0.604646
$208$	−0.643508	−0.0446193
$209$	18.9962	1.31400
$210$	3.79513	0.261889
$211$	15.2988	1.05321	0.526605	−	0.850110i	$-0.323465\pi$
$211$	15.2988	1.05321	0.526605	+	0.850110i	$0.323465\pi$
$212$	−0.489570	−0.0336238
$213$	12.3690	0.847512
$214$	−1.18861	−0.0812519
$215$	5.58551	0.380929
$216$	−2.56534	−0.174549
$217$	−14.6401	−0.993836
$218$	11.4392	0.774762
$219$	−2.99541	−0.202411
$220$	0.958501	0.0646221
$221$	0.506106	0.0340444
$222$	3.40068	0.228239
$223$	−8.92853	−0.597898	−0.298949	−	0.954269i	$-0.596636\pi$
$223$	−8.92853	−0.597898	−0.298949	+	0.954269i	$0.596636\pi$
$224$	−4.38426	−0.292936
$225$	1.00000	0.0666667
$226$	−15.9437	−1.06056
$227$	6.79938	0.451291	0.225645	−	0.974210i	$-0.427551\pi$
$227$	6.79938	0.451291	0.225645	+	0.974210i	$0.427551\pi$
$228$	1.94604	0.128880
$229$	−13.0836	−0.864590	−0.432295	−	0.901732i	$-0.642296\pi$
$229$	−13.0836	−0.864590	−0.432295	+	0.901732i	$0.642296\pi$
$230$	−13.2315	−0.872457
$231$	−7.63235	−0.502172
$232$	−2.08627	−0.136970
$233$	23.0216	1.50819	0.754096	−	0.656764i	$-0.228075\pi$
$233$	23.0216	1.50819	0.754096	+	0.656764i	$0.228075\pi$
$234$	−0.216132	−0.0141290
$235$	12.0963	0.789075
$236$	2.23976	0.145796
$237$	12.1521	0.789366
$238$	13.5167	0.876157
$239$	4.85678	0.314159	0.157080	−	0.987586i	$-0.449792\pi$
$239$	4.85678	0.314159	0.157080	+	0.987586i	$0.449792\pi$
$240$	−4.52852	−0.292315
$241$	9.12446	0.587758	0.293879	−	0.955843i	$-0.405054\pi$
$241$	9.12446	0.587758	0.293879	+	0.955843i	$0.405054\pi$
$242$	2.49993	0.160701
$243$	−1.00000	−0.0641500
$244$	−3.73175	−0.238901
$245$	0.773990	0.0494484
$246$	0.703356	0.0448443
$247$	−0.882493	−0.0561517
$248$	15.0517	0.955781
$249$	0.423112	0.0268136
$250$	1.52097	0.0961947
$251$	−12.5076	−0.789475	−0.394738	−	0.918794i	$-0.629165\pi$
$251$	−12.5076	−0.789475	−0.394738	+	0.918794i	$0.629165\pi$
$252$	−0.781887	−0.0492542
$253$	26.6097	1.67294
$254$	25.9568	1.62867
$255$	3.56159	0.223035
$256$	7.34559	0.459099
$257$	−18.2390	−1.13772	−0.568858	−	0.822436i	$-0.692615\pi$
$257$	−18.2390	−1.13772	−0.568858	+	0.822436i	$0.692615\pi$
$258$	−8.49541	−0.528901
$259$	−5.57891	−0.346657
$260$	−0.0445284	−0.00276153
$261$	−0.813253	−0.0503391
$262$	21.1772	1.30833
$263$	23.0284	1.41999	0.709997	−	0.704205i	$-0.248696\pi$
$263$	23.0284	1.41999	0.709997	+	0.704205i	$0.248696\pi$
$264$	7.84690	0.482943
$265$	1.56234	0.0959739
$266$	−23.5689	−1.44510
$267$	−17.6879	−1.08248
$268$	3.43343	0.209730
$269$	−16.5281	−1.00774	−0.503868	−	0.863781i	$-0.668090\pi$
$269$	−16.5281	−1.00774	−0.503868	+	0.863781i	$0.668090\pi$
$270$	−1.52097	−0.0925634
$271$	−29.4328	−1.78792	−0.893959	−	0.448149i	$-0.852083\pi$
$271$	−29.4328	−1.78792	−0.893959	+	0.448149i	$0.852083\pi$
$272$	−16.1287	−0.977949
$273$	0.354571	0.0214596
$274$	25.8681	1.56275
$275$	−3.05882	−0.184454
$276$	2.72600	0.164086
$277$	14.5842	0.876279	0.438139	−	0.898907i	$-0.355638\pi$
$277$	14.5842	0.876279	0.438139	+	0.898907i	$0.355638\pi$
$278$	0.718809	0.0431113
$279$	5.86732	0.351267
$280$	6.40102	0.382534
$281$	31.4206	1.87439	0.937197	−	0.348800i	$-0.113411\pi$
$281$	31.4206	1.87439	0.937197	+	0.348800i	$0.113411\pi$
$282$	−18.3981	−1.09559
$283$	18.8797	1.12228	0.561140	−	0.827721i	$-0.310363\pi$
$283$	18.8797	1.12228	0.561140	+	0.827721i	$0.310363\pi$
$284$	−3.87592	−0.229993
$285$	−6.21032	−0.367867
$286$	0.661108	0.0390922
$287$	−1.15387	−0.0681111
$288$	1.75708	0.103537
$289$	−4.31507	−0.253828
$290$	−1.23694	−0.0726353
$291$	15.9859	0.937111
$292$	0.938633	0.0549293
$293$	−9.26832	−0.541461	−0.270731	−	0.962655i	$-0.587265\pi$
$293$	−9.26832	−0.541461	−0.270731	+	0.962655i	$0.587265\pi$
$294$	−1.17722	−0.0686567
$295$	−7.14764	−0.416152
$296$	5.73573	0.333383
$297$	3.05882	0.177491
$298$	13.4339	0.778207
$299$	−1.23619	−0.0714906
$300$	−0.313357	−0.0180917
$301$	13.9370	0.803313
$302$	29.1079	1.67497
$303$	12.5751	0.722422
$304$	28.1235	1.61300
$305$	11.9090	0.681905
$306$	−5.41708	−0.309674
$307$	−3.05011	−0.174079	−0.0870393	−	0.996205i	$-0.527741\pi$
$307$	−3.05011	−0.174079	−0.0870393	+	0.996205i	$0.527741\pi$
$308$	2.39165	0.136277
$309$	0.526436	0.0299479
$310$	8.92403	0.506851
$311$	−29.2996	−1.66143	−0.830713	−	0.556700i	$-0.812067\pi$
$311$	−29.2996	−1.66143	−0.830713	+	0.556700i	$0.812067\pi$
$312$	−0.364538	−0.0206379
$313$	−4.27141	−0.241435	−0.120717	−	0.992687i	$-0.538519\pi$
$313$	−4.27141	−0.241435	−0.120717	+	0.992687i	$0.538519\pi$
$314$	−3.99520	−0.225462
$315$	2.49520	0.140588
$316$	−3.80795	−0.214214
$317$	25.1086	1.41024	0.705119	−	0.709089i	$-0.250894\pi$
$317$	25.1086	1.41024	0.705119	+	0.709089i	$0.250894\pi$
$318$	−2.37628	−0.133255
$319$	2.48759	0.139278
$320$	−6.38457	−0.356908
$321$	−0.781482	−0.0436181
$322$	−33.0151	−1.83986
$323$	−22.1186	−1.23071
$324$	0.313357	0.0174087
$325$	0.142101	0.00788236
$326$	0.283279	0.0156894
$327$	7.52099	0.415912
$328$	1.18631	0.0655030
$329$	30.1826	1.66402
$330$	4.65238	0.256105
$331$	−33.2745	−1.82893	−0.914465	−	0.404665i	$-0.867388\pi$
$331$	−33.2745	−1.82893	−0.914465	+	0.404665i	$0.867388\pi$
$332$	−0.132585	−0.00727654
$333$	2.23586	0.122524
$334$	3.11074	0.170212
$335$	−10.9569	−0.598641
$336$	−11.2996	−0.616441
$337$	−13.9132	−0.757900	−0.378950	−	0.925417i	$-0.623715\pi$
$337$	−13.9132	−0.757900	−0.378950	+	0.925417i	$0.623715\pi$
$338$	19.7419	1.07382
$339$	−10.4826	−0.569336
$340$	−1.11605	−0.0605262
$341$	−17.9471	−0.971887
$342$	9.44572	0.510766
$343$	19.3976	1.04737
$344$	−14.3287	−0.772553
$345$	−8.69934	−0.468357
$346$	−33.2334	−1.78664
$347$	20.6973	1.11109	0.555545	−	0.831487i	$-0.312510\pi$
$347$	20.6973	1.11109	0.555545	+	0.831487i	$0.312510\pi$
$348$	0.254838	0.0136608
$349$	1.30717	0.0699714	0.0349857	−	0.999388i	$-0.488861\pi$
$349$	1.30717	0.0699714	0.0349857	+	0.999388i	$0.488861\pi$
$350$	3.79513	0.202858
$351$	−0.142101	−0.00758480
$352$	−5.37458	−0.286466
$353$	25.8704	1.37694	0.688470	−	0.725264i	$-0.258283\pi$
$353$	25.8704	1.37694	0.688470	+	0.725264i	$0.258283\pi$
$354$	10.8714	0.577806
$355$	12.3690	0.656480
$356$	5.54261	0.293758
$357$	8.88687	0.470343
$358$	6.63547	0.350695
$359$	−5.01739	−0.264808	−0.132404	−	0.991196i	$-0.542270\pi$
$359$	−5.01739	−0.264808	−0.132404	+	0.991196i	$0.542270\pi$
$360$	−2.56534	−0.135205
$361$	19.5680	1.02990
$362$	15.5146	0.815431
$363$	1.64364	0.0862686
$364$	−0.111107	−0.00582359
$365$	−2.99541	−0.156787
$366$	−18.1132	−0.946791
$367$	28.2083	1.47246	0.736231	−	0.676731i	$-0.236604\pi$
$367$	28.2083	1.47246	0.736231	+	0.676731i	$0.236604\pi$
$368$	39.3952	2.05361
$369$	0.462438	0.0240736
$370$	3.40068	0.176793
$371$	3.89835	0.202392
$372$	−1.83856	−0.0953251
$373$	−30.1932	−1.56335	−0.781674	−	0.623688i	$-0.785634\pi$
$373$	−30.1932	−1.56335	−0.781674	+	0.623688i	$0.785634\pi$
$374$	16.5699	0.856807
$375$	1.00000	0.0516398
$376$	−31.0311	−1.60030
$377$	−0.115564	−0.00595186
$378$	−3.79513	−0.195200
$379$	18.0115	0.925191	0.462595	−	0.886569i	$-0.346918\pi$
$379$	18.0115	0.925191	0.462595	+	0.886569i	$0.346918\pi$
$380$	1.94604	0.0998300
$381$	17.0659	0.874312
$382$	−30.8508	−1.57846
$383$	4.21222	0.215234	0.107617	−	0.994192i	$-0.465678\pi$
$383$	4.21222	0.215234	0.107617	+	0.994192i	$0.465678\pi$
$384$	13.2249	0.674881
$385$	−7.63235	−0.388981
$386$	−20.1931	−1.02780
$387$	−5.58551	−0.283928
$388$	−5.00929	−0.254308
$389$	14.3438	0.727260	0.363630	−	0.931543i	$-0.381537\pi$
$389$	14.3438	0.727260	0.363630	+	0.931543i	$0.381537\pi$
$390$	−0.216132	−0.0109443
$391$	−30.9835	−1.56690
$392$	−1.98554	−0.100285
$393$	13.9235	0.702345
$394$	−10.9942	−0.553880
$395$	12.1521	0.611440
$396$	−0.958501	−0.0481665
$397$	−31.1145	−1.56159	−0.780796	−	0.624786i	$-0.785186\pi$
$397$	−31.1145	−1.56159	−0.780796	+	0.624786i	$0.785186\pi$
$398$	39.4869	1.97930
$399$	−15.4960	−0.775768
$400$	−4.52852	−0.226426
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	16.6652	0.831184
$403$	0.833753	0.0415322
$404$	−3.94050	−0.196047
$405$	−1.00000	−0.0496904
$406$	−3.08640	−0.153175
$407$	−6.83908	−0.339001
$408$	−9.13668	−0.452333
$409$	26.7225	1.32134	0.660671	−	0.750676i	$-0.270272\pi$
$409$	26.7225	1.32134	0.660671	+	0.750676i	$0.270272\pi$
$410$	0.703356	0.0347363
$411$	17.0076	0.838924
$412$	−0.164962	−0.00812711
$413$	−17.8348	−0.877592
$414$	13.2315	0.650291
$415$	0.423112	0.0207697
$416$	0.249683	0.0122417
$417$	0.472599	0.0231433
$418$	−28.8927	−1.41319
$419$	−32.5976	−1.59250	−0.796249	−	0.604969i	$-0.793185\pi$
$419$	−32.5976	−1.59250	−0.796249	+	0.604969i	$0.793185\pi$
$420$	−0.781887	−0.0381522
$421$	−24.0701	−1.17310	−0.586552	−	0.809911i	$-0.699515\pi$
$421$	−24.0701	−1.17310	−0.586552	+	0.809911i	$0.699515\pi$
$422$	−23.2690	−1.13272
$423$	−12.0963	−0.588142
$424$	−4.00793	−0.194643
$425$	3.56159	0.172763
$426$	−18.8129	−0.911490
$427$	29.7152	1.43802
$428$	0.244883	0.0118369
$429$	0.434662	0.0209857
$430$	−8.49541	−0.409685
$431$	4.57406	0.220325	0.110162	−	0.993914i	$-0.464863\pi$
$431$	4.57406	0.220325	0.110162	+	0.993914i	$0.464863\pi$
$432$	4.52852	0.217879
$433$	19.4323	0.933855	0.466928	−	0.884296i	$-0.345361\pi$
$433$	19.4323	0.933855	0.466928	+	0.884296i	$0.345361\pi$
$434$	22.2672	1.06886
$435$	−0.813253	−0.0389925
$436$	−2.35675	−0.112868
$437$	54.0257	2.58440
$438$	4.55594	0.217691
$439$	34.3383	1.63888	0.819439	−	0.573167i	$-0.194285\pi$
$439$	34.3383	1.63888	0.819439	+	0.573167i	$0.194285\pi$
$440$	7.84690	0.374086
$441$	−0.773990	−0.0368566
$442$	−0.769774	−0.0366144
$443$	18.2855	0.868772	0.434386	−	0.900727i	$-0.356965\pi$
$443$	18.2855	0.868772	0.434386	+	0.900727i	$0.356965\pi$
$444$	−0.700622	−0.0332500
$445$	−17.6879	−0.838485
$446$	13.5800	0.643034
$447$	8.83247	0.417761
$448$	−15.9308	−0.752658
$449$	3.78030	0.178403	0.0892016	−	0.996014i	$-0.471568\pi$
$449$	3.78030	0.178403	0.0892016	+	0.996014i	$0.471568\pi$
$450$	−1.52097	−0.0716993
$451$	−1.41451	−0.0666068
$452$	3.28479	0.154503
$453$	19.1377	0.899167
$454$	−10.3417	−0.485358
$455$	0.354571	0.0166225
$456$	15.9316	0.746063
$457$	12.6090	0.589822	0.294911	−	0.955525i	$-0.404710\pi$
$457$	12.6090	0.589822	0.294911	+	0.955525i	$0.404710\pi$
$458$	19.8998	0.929858
$459$	−3.56159	−0.166241
$460$	2.72600	0.127100
$461$	−11.5175	−0.536425	−0.268212	−	0.963360i	$-0.586433\pi$
$461$	−11.5175	−0.536425	−0.268212	+	0.963360i	$0.586433\pi$
$462$	11.6086	0.540081
$463$	−12.8880	−0.598955	−0.299477	−	0.954103i	$-0.596812\pi$
$463$	−12.8880	−0.598955	−0.299477	+	0.954103i	$0.596812\pi$
$464$	3.68283	0.170971
$465$	5.86732	0.272090
$466$	−35.0151	−1.62205
$467$	9.97540	0.461606	0.230803	−	0.973000i	$-0.425865\pi$
$467$	9.97540	0.461606	0.230803	+	0.973000i	$0.425865\pi$
$468$	0.0445284	0.00205832
$469$	−27.3397	−1.26243
$470$	−18.3981	−0.848642
$471$	−2.62674	−0.121034
$472$	18.3361	0.843988
$473$	17.0851	0.785572
$474$	−18.4831	−0.848955
$475$	−6.21032	−0.284949
$476$	−2.78476	−0.127639
$477$	−1.56234	−0.0715347
$478$	−7.38703	−0.337875
$479$	26.6188	1.21625	0.608123	−	0.793843i	$-0.291923\pi$
$479$	26.6188	1.21625	0.608123	+	0.793843i	$0.291923\pi$
$480$	1.75708	0.0801993
$481$	0.317718	0.0144867
$482$	−13.8781	−0.632128
$483$	−21.7066	−0.987684
$484$	−0.515045	−0.0234111
$485$	15.9859	0.725883
$486$	1.52097	0.0689927
$487$	−1.03938	−0.0470987	−0.0235493	−	0.999723i	$-0.507497\pi$
$487$	−1.03938	−0.0470987	−0.0235493	+	0.999723i	$0.507497\pi$
$488$	−30.5505	−1.38296
$489$	0.186249	0.00842246
$490$	−1.17722	−0.0531812
$491$	−8.60531	−0.388352	−0.194176	−	0.980967i	$-0.562203\pi$
$491$	−8.60531	−0.388352	−0.194176	+	0.980967i	$0.562203\pi$
$492$	−0.144908	−0.00653296
$493$	−2.89647	−0.130451
$494$	1.34225	0.0603906
$495$	3.05882	0.137484
$496$	−26.5703	−1.19304
$497$	30.8632	1.38440
$498$	−0.643541	−0.0288378
$499$	28.8542	1.29169	0.645845	−	0.763468i	$-0.276505\pi$
$499$	28.8542	1.29169	0.645845	+	0.763468i	$0.276505\pi$
$500$	−0.313357	−0.0140137
$501$	2.04523	0.0913742
$502$	19.0238	0.849073
$503$	29.3505	1.30868	0.654338	−	0.756202i	$-0.272947\pi$
$503$	29.3505	1.30868	0.654338	+	0.756202i	$0.272947\pi$
$504$	−6.40102	−0.285124
$505$	12.5751	0.559585
$506$	−40.4726	−1.79923
$507$	12.9798	0.576453
$508$	−5.34771	−0.237266
$509$	1.43043	0.0634029	0.0317014	−	0.999497i	$-0.489907\pi$
$509$	1.43043	0.0634029	0.0317014	+	0.999497i	$0.489907\pi$
$510$	−5.41708	−0.239872
$511$	−7.47415	−0.330637
$512$	15.2774	0.675172
$513$	6.21032	0.274192
$514$	27.7410	1.22360
$515$	0.526436	0.0231975
$516$	1.75026	0.0770508
$517$	37.0003	1.62727
$518$	8.48537	0.372826
$519$	−21.8501	−0.959113
$520$	−0.364538	−0.0159860
$521$	−27.0467	−1.18494	−0.592469	−	0.805593i	$-0.701847\pi$
$521$	−27.0467	−1.18494	−0.592469	+	0.805593i	$0.701847\pi$
$522$	1.23694	0.0541392
$523$	24.8443	1.08636	0.543182	−	0.839615i	$-0.317220\pi$
$523$	24.8443	1.08636	0.543182	+	0.839615i	$0.317220\pi$
$524$	−4.36301	−0.190599
$525$	2.49520	0.108899
$526$	−35.0256	−1.52719
$527$	20.8970	0.910287
$528$	−13.8519	−0.602827
$529$	52.6786	2.29037
$530$	−2.37628	−0.103219
$531$	7.14764	0.310181
$532$	4.85576	0.210524
$533$	0.0657130	0.00284635
$534$	26.9028	1.16420
$535$	−0.781482	−0.0337864
$536$	28.1082	1.21409
$537$	4.36265	0.188262
$538$	25.1388	1.08381
$539$	2.36749	0.101975
$540$	0.313357	0.0134847
$541$	43.0551	1.85108	0.925541	−	0.378648i	$-0.123611\pi$
$541$	43.0551	1.85108	0.925541	+	0.378648i	$0.123611\pi$
$542$	44.7665	1.92289
$543$	10.2005	0.437744
$544$	6.25800	0.268310
$545$	7.52099	0.322164
$546$	−0.539292	−0.0230796
$547$	−11.3035	−0.483303	−0.241652	−	0.970363i	$-0.577689\pi$
$547$	−11.3035	−0.483303	−0.241652	+	0.970363i	$0.577689\pi$
$548$	−5.32945	−0.227663
$549$	−11.9090	−0.508262
$550$	4.65238	0.198378
$551$	5.05056	0.215161
$552$	22.3168	0.949864
$553$	30.3220	1.28942
$554$	−22.1821	−0.942429
$555$	2.23586	0.0949069
$556$	−0.148092	−0.00628050
$557$	−34.6856	−1.46968	−0.734838	−	0.678243i	$-0.762742\pi$
$557$	−34.6856	−1.46968	−0.734838	+	0.678243i	$0.762742\pi$
$558$	−8.92403	−0.377784
$559$	−0.793708	−0.0335703
$560$	−11.2996	−0.477493
$561$	10.8943	0.459956
$562$	−47.7898	−2.01589
$563$	15.9689	0.673011	0.336505	−	0.941682i	$-0.390755\pi$
$563$	15.9689	0.673011	0.336505	+	0.941682i	$0.390755\pi$
$564$	3.79045	0.159607
$565$	−10.4826	−0.441006
$566$	−28.7155	−1.20700
$567$	−2.49520	−0.104788
$568$	−31.7307	−1.33139
$569$	17.6136	0.738402	0.369201	−	0.929350i	$-0.379631\pi$
$569$	17.6136	0.738402	0.369201	+	0.929350i	$0.379631\pi$
$570$	9.44572	0.395638
$571$	−43.6865	−1.82822	−0.914111	−	0.405464i	$-0.867110\pi$
$571$	−43.6865	−1.82822	−0.914111	+	0.405464i	$0.867110\pi$
$572$	−0.136204	−0.00569498
$573$	−20.2836	−0.847359
$574$	1.75501	0.0732527
$575$	−8.69934	−0.362788
$576$	6.38457	0.266024
$577$	26.3447	1.09674	0.548371	−	0.836235i	$-0.315248\pi$
$577$	26.3447	1.09674	0.548371	+	0.836235i	$0.315248\pi$
$578$	6.56310	0.272989
$579$	−13.2764	−0.551750
$580$	0.254838	0.0105816
$581$	1.05575	0.0437998
$582$	−24.3141	−1.00785
$583$	4.77892	0.197923
$584$	7.68425	0.317976
$585$	−0.142101	−0.00587516
$586$	14.0969	0.582336
$587$	0.814412	0.0336144	0.0168072	−	0.999859i	$-0.494650\pi$
$587$	0.814412	0.0336144	0.0168072	+	0.999859i	$0.494650\pi$
$588$	0.242535	0.0100020
$589$	−36.4379	−1.50140
$590$	10.8714	0.447567
$591$	−7.22841	−0.297337
$592$	−10.1251	−0.416141
$593$	1.87240	0.0768901	0.0384450	−	0.999261i	$-0.487760\pi$
$593$	1.87240	0.0768901	0.0384450	+	0.999261i	$0.487760\pi$
$594$	−4.65238	−0.190889
$595$	8.88687	0.364326
$596$	−2.76771	−0.113370
$597$	25.9616	1.06254
$598$	1.88021	0.0768874
$599$	33.0534	1.35053	0.675263	−	0.737577i	$-0.264030\pi$
$599$	33.0534	1.35053	0.675263	+	0.737577i	$0.264030\pi$
$600$	−2.56534	−0.104729
$601$	17.9458	0.732023	0.366012	−	0.930610i	$-0.380723\pi$
$601$	17.9458	0.732023	0.366012	+	0.930610i	$0.380723\pi$
$602$	−21.1977	−0.863955
$603$	10.9569	0.446201
$604$	−5.99692	−0.244011
$605$	1.64364	0.0668234
$606$	−19.1264	−0.776957
$607$	−3.09114	−0.125466	−0.0627328	−	0.998030i	$-0.519982\pi$
$607$	−3.09114	−0.125466	−0.0627328	+	0.998030i	$0.519982\pi$
$608$	−10.9120	−0.442541
$609$	−2.02923	−0.0822284
$610$	−18.1132	−0.733381
$611$	−1.71890	−0.0695391
$612$	1.11605	0.0451136
$613$	−24.9351	−1.00712	−0.503560	−	0.863961i	$-0.667977\pi$
$613$	−24.9351	−1.00712	−0.503560	+	0.863961i	$0.667977\pi$
$614$	4.63913	0.187220
$615$	0.462438	0.0186473
$616$	19.5796	0.788883
$617$	0.900429	0.0362499	0.0181250	−	0.999836i	$-0.494230\pi$
$617$	0.900429	0.0362499	0.0181250	+	0.999836i	$0.494230\pi$
$618$	−0.800695	−0.0322087
$619$	−4.28574	−0.172258	−0.0861292	−	0.996284i	$-0.527450\pi$
$619$	−4.28574	−0.172258	−0.0861292	+	0.996284i	$0.527450\pi$
$620$	−1.83856	−0.0738385
$621$	8.69934	0.349093
$622$	44.5638	1.78685
$623$	−44.1347	−1.76822
$624$	0.643508	0.0257609
$625$	1.00000	0.0400000
$626$	6.49670	0.259660
$627$	−18.9962	−0.758636
$628$	0.823108	0.0328456
$629$	7.96322	0.317514
$630$	−3.79513	−0.151201
$631$	26.7059	1.06314	0.531572	−	0.847013i	$-0.321601\pi$
$631$	26.7059	1.06314	0.531572	+	0.847013i	$0.321601\pi$
$632$	−31.1743	−1.24005
$633$	−15.2988	−0.608071
$634$	−38.1894	−1.51670
$635$	17.0659	0.677239
$636$	0.489570	0.0194127
$637$	−0.109985	−0.00435776
$638$	−3.78356	−0.149793
$639$	−12.3690	−0.489311
$640$	13.2249	0.522761
$641$	−0.234671	−0.00926895	−0.00463447	−	0.999989i	$-0.501475\pi$
$641$	−0.234671	−0.00926895	−0.00463447	+	0.999989i	$0.501475\pi$
$642$	1.18861	0.0469108
$643$	−13.6764	−0.539344	−0.269672	−	0.962952i	$-0.586915\pi$
$643$	−13.6764	−0.539344	−0.269672	+	0.962952i	$0.586915\pi$
$644$	6.80190	0.268033
$645$	−5.58551	−0.219929
$646$	33.6418	1.32362
$647$	27.8194	1.09369	0.546846	−	0.837233i	$-0.315828\pi$
$647$	27.8194	1.09369	0.546846	+	0.837233i	$0.315828\pi$
$648$	2.56534	0.100776
$649$	−21.8633	−0.858211
$650$	−0.216132	−0.00847739
$651$	14.6401	0.573791
$652$	−0.0583623	−0.00228564
$653$	1.75417	0.0686460	0.0343230	−	0.999411i	$-0.489072\pi$
$653$	1.75417	0.0686460	0.0343230	+	0.999411i	$0.489072\pi$
$654$	−11.4392	−0.447309
$655$	13.9235	0.544034
$656$	−2.09416	−0.0817632
$657$	2.99541	0.116862
$658$	−45.9069	−1.78964
$659$	37.2826	1.45232	0.726162	−	0.687524i	$-0.241302\pi$
$659$	37.2826	1.45232	0.726162	+	0.687524i	$0.241302\pi$
$660$	−0.958501	−0.0373096
$661$	19.8186	0.770853	0.385427	−	0.922738i	$-0.374054\pi$
$661$	19.8186	0.770853	0.385427	+	0.922738i	$0.374054\pi$
$662$	50.6095	1.96700
$663$	−0.506106	−0.0196555
$664$	−1.08542	−0.0421226
$665$	−15.4960	−0.600908
$666$	−3.40068	−0.131774
$667$	7.07477	0.273936
$668$	−0.640887	−0.0247967
$669$	8.92853	0.345197
$670$	16.6652	0.643833
$671$	36.4273	1.40626
$672$	4.38426	0.169127
$673$	−44.2498	−1.70571	−0.852853	−	0.522151i	$-0.825130\pi$
$673$	−44.2498	−1.70571	−0.852853	+	0.522151i	$0.825130\pi$
$674$	21.1616	0.815114
$675$	−1.00000	−0.0384900
$676$	−4.06731	−0.156435
$677$	−13.5380	−0.520308	−0.260154	−	0.965567i	$-0.583773\pi$
$677$	−13.5380	−0.520308	−0.260154	+	0.965567i	$0.583773\pi$
$678$	15.9437	0.612315
$679$	39.8880	1.53076
$680$	−9.13668	−0.350376
$681$	−6.79938	−0.260553
$682$	27.2970	1.04525
$683$	−38.4462	−1.47110	−0.735551	−	0.677470i	$-0.763076\pi$
$683$	−38.4462	−1.47110	−0.735551	+	0.677470i	$0.763076\pi$
$684$	−1.94604	−0.0744089
$685$	17.0076	0.649828
$686$	−29.5033	−1.12644
$687$	13.0836	0.499171
$688$	25.2941	0.964329
$689$	−0.222011	−0.00845793
$690$	13.2315	0.503713
$691$	17.3348	0.659447	0.329724	−	0.944077i	$-0.393044\pi$
$691$	17.3348	0.659447	0.329724	+	0.944077i	$0.393044\pi$
$692$	6.84688	0.260279
$693$	7.63235	0.289929
$694$	−31.4800	−1.19497
$695$	0.472599	0.0179267
$696$	2.08627	0.0790798
$697$	1.64702	0.0623852
$698$	−1.98818	−0.0752536
$699$	−23.0216	−0.870755
$700$	−0.781887	−0.0295525
$701$	1.08838	0.0411074	0.0205537	−	0.999789i	$-0.493457\pi$
$701$	1.08838	0.0411074	0.0205537	+	0.999789i	$0.493457\pi$
$702$	0.216132	0.00815738
$703$	−13.8854	−0.523697
$704$	−19.5292	−0.736036
$705$	−12.0963	−0.455573
$706$	−39.3481	−1.48089
$707$	31.3774	1.18007
$708$	−2.23976	−0.0841754
$709$	12.5305	0.470593	0.235297	−	0.971924i	$-0.424394\pi$
$709$	12.5305	0.470593	0.235297	+	0.971924i	$0.424394\pi$
$710$	−18.8129	−0.706037
$711$	−12.1521	−0.455741
$712$	45.3754	1.70051
$713$	−51.0418	−1.91153
$714$	−13.5167	−0.505849
$715$	0.434662	0.0162554
$716$	−1.36707	−0.0510896
$717$	−4.85678	−0.181380
$718$	7.63131	0.284798
$719$	24.0674	0.897561	0.448780	−	0.893642i	$-0.351859\pi$
$719$	24.0674	0.897561	0.448780	+	0.893642i	$0.351859\pi$
$720$	4.52852	0.168768
$721$	1.31356	0.0489196
$722$	−29.7624	−1.10764
$723$	−9.12446	−0.339342
$724$	−3.19639	−0.118793
$725$	−0.813253	−0.0302035
$726$	−2.49993	−0.0927810
$727$	−43.1149	−1.59904	−0.799522	−	0.600637i	$-0.794914\pi$
$727$	−43.1149	−1.59904	−0.799522	+	0.600637i	$0.794914\pi$
$728$	−0.909593	−0.0337118
$729$	1.00000	0.0370370
$730$	4.55594	0.168623
$731$	−19.8933	−0.735781
$732$	3.73175	0.137929
$733$	14.4466	0.533597	0.266799	−	0.963752i	$-0.414034\pi$
$733$	14.4466	0.533597	0.266799	+	0.963752i	$0.414034\pi$
$734$	−42.9040	−1.58362
$735$	−0.773990	−0.0285490
$736$	−15.2854	−0.563429
$737$	−33.5153	−1.23455
$738$	−0.703356	−0.0258909
$739$	−44.0990	−1.62221	−0.811104	−	0.584902i	$-0.801133\pi$
$739$	−44.0990	−1.62221	−0.811104	+	0.584902i	$0.801133\pi$
$740$	−0.700622	−0.0257554
$741$	0.882493	0.0324192
$742$	−5.92929	−0.217671
$743$	32.4885	1.19189	0.595944	−	0.803026i	$-0.296778\pi$
$743$	32.4885	1.19189	0.595944	+	0.803026i	$0.296778\pi$
$744$	−15.0517	−0.551820
$745$	8.83247	0.323597
$746$	45.9231	1.68136
$747$	−0.423112	−0.0154808
$748$	−3.41379	−0.124820
$749$	−1.94995	−0.0712497
$750$	−1.52097	−0.0555381
$751$	28.8576	1.05303	0.526514	−	0.850167i	$-0.323499\pi$
$751$	28.8576	1.05303	0.526514	+	0.850167i	$0.323499\pi$
$752$	54.7783	1.99756
$753$	12.5076	0.455804
$754$	0.175770	0.00640117
$755$	19.1377	0.696492
$756$	0.781887	0.0284370
$757$	31.2946	1.13742	0.568711	−	0.822537i	$-0.307442\pi$
$757$	31.2946	1.13742	0.568711	+	0.822537i	$0.307442\pi$
$758$	−27.3951	−0.995033
$759$	−26.6097	−0.965871
$760$	15.9316	0.577898
$761$	−24.4072	−0.884760	−0.442380	−	0.896828i	$-0.645866\pi$
$761$	−24.4072	−0.884760	−0.442380	+	0.896828i	$0.645866\pi$
$762$	−25.9568	−0.940314
$763$	18.7664	0.679388
$764$	6.35600	0.229952
$765$	−3.56159	−0.128770
$766$	−6.40667	−0.231482
$767$	1.01569	0.0366744
$768$	−7.34559	−0.265061
$769$	52.8668	1.90643	0.953214	−	0.302297i	$-0.0977536\pi$
$769$	52.8668	1.90643	0.953214	+	0.302297i	$0.0977536\pi$
$770$	11.6086	0.418345
$771$	18.2390	0.656861
$772$	4.16026	0.149731
$773$	1.48217	0.0533101	0.0266551	−	0.999645i	$-0.491514\pi$
$773$	1.48217	0.0533101	0.0266551	+	0.999645i	$0.491514\pi$
$774$	8.49541	0.305361
$775$	5.86732	0.210760
$776$	−41.0093	−1.47215
$777$	5.57891	0.200142
$778$	−21.8165	−0.782161
$779$	−2.87189	−0.102896
$780$	0.0445284	0.00159437
$781$	37.8346	1.35383
$782$	47.1251	1.68519
$783$	0.813253	0.0290633
$784$	3.50503	0.125180
$785$	−2.62674	−0.0937525
$786$	−21.1772	−0.755365
$787$	−35.2559	−1.25674	−0.628368	−	0.777916i	$-0.716277\pi$
$787$	−35.2559	−1.25674	−0.628368	+	0.777916i	$0.716277\pi$
$788$	2.26507	0.0806898
$789$	−23.0284	−0.819833
$790$	−18.4831	−0.657598
$791$	−26.1561	−0.930004
$792$	−7.84690	−0.278827
$793$	−1.69228	−0.0600945
$794$	47.3243	1.67948
$795$	−1.56234	−0.0554106
$796$	−8.13524	−0.288346
$797$	19.7099	0.698160	0.349080	−	0.937093i	$-0.386494\pi$
$797$	19.7099	0.698160	0.349080	+	0.937093i	$0.386494\pi$
$798$	23.5689	0.834331
$799$	−43.0820	−1.52413
$800$	1.75708	0.0621221
$801$	17.6879	0.624970
$802$	−1.52097	−0.0537074
$803$	−9.16242	−0.323335
$804$	−3.43343	−0.121088
$805$	−21.7066	−0.765056
$806$	−1.26812	−0.0446674
$807$	16.5281	0.581816
$808$	−32.2594	−1.13488
$809$	−44.6006	−1.56807	−0.784037	−	0.620714i	$-0.786843\pi$
$809$	−44.6006	−1.56807	−0.784037	+	0.620714i	$0.786843\pi$
$810$	1.52097	0.0534415
$811$	−13.4454	−0.472130	−0.236065	−	0.971737i	$-0.575858\pi$
$811$	−13.4454	−0.472130	−0.236065	+	0.971737i	$0.575858\pi$
$812$	0.635872	0.0223147
$813$	29.4328	1.03225
$814$	10.4021	0.364592
$815$	0.186249	0.00652401
$816$	16.1287	0.564619
$817$	34.6878	1.21357
$818$	−40.6441	−1.42109
$819$	−0.354571	−0.0123897
$820$	−0.144908	−0.00506041
$821$	5.07247	0.177030	0.0885152	−	0.996075i	$-0.471788\pi$
$821$	5.07247	0.177030	0.0885152	+	0.996075i	$0.471788\pi$
$822$	−25.8681	−0.902254
$823$	19.4502	0.677990	0.338995	−	0.940788i	$-0.389913\pi$
$823$	19.4502	0.677990	0.338995	+	0.940788i	$0.389913\pi$
$824$	−1.35049	−0.0470464
$825$	3.05882	0.106494
$826$	27.1262	0.943841
$827$	3.16793	0.110160	0.0550799	−	0.998482i	$-0.482459\pi$
$827$	3.16793	0.110160	0.0550799	+	0.998482i	$0.482459\pi$
$828$	−2.72600	−0.0947350
$829$	9.26211	0.321686	0.160843	−	0.986980i	$-0.448579\pi$
$829$	9.26211	0.321686	0.160843	+	0.986980i	$0.448579\pi$
$830$	−0.643541	−0.0223376
$831$	−14.5842	−0.505920
$832$	0.907256	0.0314534
$833$	−2.75663	−0.0955117
$834$	−0.718809	−0.0248903
$835$	2.04523	0.0707782
$836$	5.95259	0.205875
$837$	−5.86732	−0.202804
$838$	49.5801	1.71272
$839$	12.4484	0.429768	0.214884	−	0.976640i	$-0.431063\pi$
$839$	12.4484	0.429768	0.214884	+	0.976640i	$0.431063\pi$
$840$	−6.40102	−0.220856
$841$	−28.3386	−0.977194
$842$	36.6100	1.26166
$843$	−31.4206	−1.08218
$844$	4.79397	0.165015
$845$	12.9798	0.446519
$846$	18.3981	0.632540
$847$	4.10120	0.140919
$848$	7.07510	0.242960
$849$	−18.8797	−0.647949
$850$	−5.41708	−0.185804
$851$	−19.4505	−0.666755
$852$	3.87592	0.132787
$853$	−26.1363	−0.894891	−0.447446	−	0.894311i	$-0.647666\pi$
$853$	−26.1363	−0.894891	−0.447446	+	0.894311i	$0.647666\pi$
$854$	−45.1960	−1.54657
$855$	6.21032	0.212388
$856$	2.00477	0.0685215
$857$	−25.5542	−0.872914	−0.436457	−	0.899725i	$-0.643767\pi$
$857$	−25.5542	−0.872914	−0.436457	+	0.899725i	$0.643767\pi$
$858$	−0.661108	−0.0225699
$859$	11.8308	0.403663	0.201831	−	0.979420i	$-0.435311\pi$
$859$	11.8308	0.403663	0.201831	+	0.979420i	$0.435311\pi$
$860$	1.75026	0.0596833
$861$	1.15387	0.0393239
$862$	−6.95701	−0.236957
$863$	45.3808	1.54478	0.772391	−	0.635148i	$-0.219061\pi$
$863$	45.3808	1.54478	0.772391	+	0.635148i	$0.219061\pi$
$864$	−1.75708	−0.0597771
$865$	−21.8501	−0.742926
$866$	−29.5559	−1.00435
$867$	4.31507	0.146547
$868$	−4.58758	−0.155713
$869$	37.1712	1.26095
$870$	1.23694	0.0419360
$871$	1.55699	0.0527567
$872$	−19.2939	−0.653374
$873$	−15.9859	−0.541041
$874$	−82.1715	−2.77949
$875$	2.49520	0.0843531
$876$	−0.938633	−0.0317135
$877$	−30.5620	−1.03201	−0.516003	−	0.856587i	$-0.672581\pi$
$877$	−30.5620	−1.03201	−0.516003	+	0.856587i	$0.672581\pi$
$878$	−52.2276	−1.76260
$879$	9.26832	0.312613
$880$	−13.8519	−0.466948
$881$	8.45742	0.284938	0.142469	−	0.989799i	$-0.454496\pi$
$881$	8.45742	0.284938	0.142469	+	0.989799i	$0.454496\pi$
$882$	1.17722	0.0396390
$883$	45.3065	1.52469	0.762343	−	0.647173i	$-0.224049\pi$
$883$	45.3065	1.52469	0.762343	+	0.647173i	$0.224049\pi$
$884$	0.158592	0.00533402
$885$	7.14764	0.240265
$886$	−27.8118	−0.934355
$887$	−16.1149	−0.541085	−0.270542	−	0.962708i	$-0.587203\pi$
$887$	−16.1149	−0.541085	−0.270542	+	0.962708i	$0.587203\pi$
$888$	−5.73573	−0.192479
$889$	42.5828	1.42818
$890$	26.9028	0.901782
$891$	−3.05882	−0.102474
$892$	−2.79781	−0.0936778
$893$	75.1218	2.51385
$894$	−13.4339	−0.449298
$895$	4.36265	0.145827
$896$	32.9988	1.10241
$897$	1.23619	0.0412751
$898$	−5.74973	−0.191871
$899$	−4.77161	−0.159142
$900$	0.313357	0.0104452
$901$	−5.56442	−0.185378
$902$	2.15144	0.0716350
$903$	−13.9370	−0.463793
$904$	26.8914	0.894394
$905$	10.2005	0.339075
$906$	−29.1079	−0.967045
$907$	−36.5564	−1.21384	−0.606918	−	0.794764i	$-0.707595\pi$
$907$	−36.5564	−1.21384	−0.606918	+	0.794764i	$0.707595\pi$
$908$	2.13063	0.0707075
$909$	−12.5751	−0.417090
$910$	−0.539292	−0.0178774
$911$	5.52162	0.182939	0.0914697	−	0.995808i	$-0.470844\pi$
$911$	5.52162	0.182939	0.0914697	+	0.995808i	$0.470844\pi$
$912$	−28.1235	−0.931264
$913$	1.29422	0.0428325
$914$	−19.1779	−0.634348
$915$	−11.9090	−0.393698
$916$	−4.09984	−0.135463
$917$	34.7418	1.14727
$918$	5.41708	0.178790
$919$	17.1280	0.565000	0.282500	−	0.959267i	$-0.408836\pi$
$919$	17.1280	0.565000	0.282500	+	0.959267i	$0.408836\pi$
$920$	22.3168	0.735762
$921$	3.05011	0.100504
$922$	17.5178	0.576920
$923$	−1.75765	−0.0578539
$924$	−2.39165	−0.0786795
$925$	2.23586	0.0735146
$926$	19.6022	0.644170
$927$	−0.526436	−0.0172904
$928$	−1.42895	−0.0469076
$929$	54.3868	1.78437	0.892186	−	0.451668i	$-0.149171\pi$
$929$	54.3868	1.78437	0.892186	+	0.451668i	$0.149171\pi$
$930$	−8.92403	−0.292630
$931$	4.80672	0.157534
$932$	7.21396	0.236301
$933$	29.2996	0.959225
$934$	−15.1723	−0.496453
$935$	10.8943	0.356280
$936$	0.364538	0.0119153
$937$	−51.9914	−1.69848	−0.849242	−	0.528003i	$-0.822941\pi$
$937$	−51.9914	−1.69848	−0.849242	+	0.528003i	$0.822941\pi$
$938$	41.5829	1.35773
$939$	4.27141	0.139392
$940$	3.79045	0.123631
$941$	−36.1326	−1.17789	−0.588945	−	0.808173i	$-0.700457\pi$
$941$	−36.1326	−1.17789	−0.588945	+	0.808173i	$0.700457\pi$
$942$	3.99520	0.130171
$943$	−4.02291	−0.131004
$944$	−32.3682	−1.05350
$945$	−2.49520	−0.0811688
$946$	−25.9859	−0.844875
$947$	57.8138	1.87870	0.939349	−	0.342963i	$-0.111431\pi$
$947$	57.8138	1.87870	0.939349	+	0.342963i	$0.111431\pi$
$948$	3.80795	0.123677
$949$	0.425652	0.0138172
$950$	9.44572	0.306460
$951$	−25.1086	−0.814201
$952$	−22.7978	−0.738882
$953$	−12.4955	−0.404770	−0.202385	−	0.979306i	$-0.564869\pi$
$953$	−12.4955	−0.404770	−0.202385	+	0.979306i	$0.564869\pi$
$954$	2.37628	0.0769349
$955$	−20.2836	−0.656362
$956$	1.52191	0.0492219
$957$	−2.48759	−0.0804124
$958$	−40.4865	−1.30806
$959$	42.4374	1.37037
$960$	6.38457	0.206061
$961$	3.42541	0.110497
$962$	−0.483241	−0.0155803
$963$	0.781482	0.0251829
$964$	2.85921	0.0920890
$965$	−13.2764	−0.427384
$966$	33.0151	1.06224
$967$	−26.0918	−0.839054	−0.419527	−	0.907743i	$-0.637804\pi$
$967$	−26.0918	−0.839054	−0.419527	+	0.907743i	$0.637804\pi$
$968$	−4.21649	−0.135523
$969$	22.1186	0.710552
$970$	−24.3141	−0.780680
$971$	−20.4558	−0.656457	−0.328229	−	0.944598i	$-0.606452\pi$
$971$	−20.4558	−0.656457	−0.328229	+	0.944598i	$0.606452\pi$
$972$	−0.313357	−0.0100509
$973$	1.17923	0.0378043
$974$	1.58086	0.0506542
$975$	−0.142101	−0.00455088
$976$	53.9299	1.72626
$977$	36.6375	1.17214	0.586068	−	0.810262i	$-0.300675\pi$
$977$	36.6375	1.17214	0.586068	+	0.810262i	$0.300675\pi$
$978$	−0.283279	−0.00905827
$979$	−54.1040	−1.72917
$980$	0.242535	0.00774749
$981$	−7.52099	−0.240127
$982$	13.0884	0.417669
$983$	−34.4458	−1.09865	−0.549325	−	0.835609i	$-0.685115\pi$
$983$	−34.4458	−1.09865	−0.549325	+	0.835609i	$0.685115\pi$
$984$	−1.18631	−0.0378182
$985$	−7.22841	−0.230316
$986$	4.40546	0.140298
$987$	−30.1826	−0.960724
$988$	−0.276535	−0.00879776
$989$	48.5903	1.54508
$990$	−4.65238	−0.147862
$991$	0.676208	0.0214804	0.0107402	−	0.999942i	$-0.496581\pi$
$991$	0.676208	0.0214804	0.0107402	+	0.999942i	$0.496581\pi$
$992$	10.3093	0.327322
$993$	33.2745	1.05593
$994$	−46.9420	−1.48891
$995$	25.9616	0.823038
$996$	0.132585	0.00420111
$997$	12.9662	0.410644	0.205322	−	0.978694i	$-0.434176\pi$
$997$	12.9662	0.410644	0.205322	+	0.978694i	$0.434176\pi$
$998$	−43.8864	−1.38920
$999$	−2.23586	−0.0707395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.e.1.8	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.e.1.8	✓	31	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.52097 q^{2} -1.00000 q^{3} +0.313357 q^{4} -1.00000 q^{5} +1.52097 q^{6} -2.49520 q^{7} +2.56534 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.52097 q^{2} -1.00000 q^{3} +0.313357 q^{4} -1.00000 q^{5} +1.52097 q^{6} -2.49520 q^{7} +2.56534 q^{8} +1.00000 q^{9} +1.52097 q^{10} -3.05882 q^{11} -0.313357 q^{12} +0.142101 q^{13} +3.79513 q^{14} +1.00000 q^{15} -4.52852 q^{16} +3.56159 q^{17} -1.52097 q^{18} -6.21032 q^{19} -0.313357 q^{20} +2.49520 q^{21} +4.65238 q^{22} -8.69934 q^{23} -2.56534 q^{24} +1.00000 q^{25} -0.216132 q^{26} -1.00000 q^{27} -0.781887 q^{28} -0.813253 q^{29} -1.52097 q^{30} +5.86732 q^{31} +1.75708 q^{32} +3.05882 q^{33} -5.41708 q^{34} +2.49520 q^{35} +0.313357 q^{36} +2.23586 q^{37} +9.44572 q^{38} -0.142101 q^{39} -2.56534 q^{40} +0.462438 q^{41} -3.79513 q^{42} -5.58551 q^{43} -0.958501 q^{44} -1.00000 q^{45} +13.2315 q^{46} -12.0963 q^{47} +4.52852 q^{48} -0.773990 q^{49} -1.52097 q^{50} -3.56159 q^{51} +0.0445284 q^{52} -1.56234 q^{53} +1.52097 q^{54} +3.05882 q^{55} -6.40102 q^{56} +6.21032 q^{57} +1.23694 q^{58} +7.14764 q^{59} +0.313357 q^{60} -11.9090 q^{61} -8.92403 q^{62} -2.49520 q^{63} +6.38457 q^{64} -0.142101 q^{65} -4.65238 q^{66} +10.9569 q^{67} +1.11605 q^{68} +8.69934 q^{69} -3.79513 q^{70} -12.3690 q^{71} +2.56534 q^{72} +2.99541 q^{73} -3.40068 q^{74} -1.00000 q^{75} -1.94604 q^{76} +7.63235 q^{77} +0.216132 q^{78} -12.1521 q^{79} +4.52852 q^{80} +1.00000 q^{81} -0.703356 q^{82} -0.423112 q^{83} +0.781887 q^{84} -3.56159 q^{85} +8.49541 q^{86} +0.813253 q^{87} -7.84690 q^{88} +17.6879 q^{89} +1.52097 q^{90} -0.354571 q^{91} -2.72600 q^{92} -5.86732 q^{93} +18.3981 q^{94} +6.21032 q^{95} -1.75708 q^{96} -15.9859 q^{97} +1.17722 q^{98} -3.05882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - q^99

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