LMFDB - Embedded newform 4017.2.a.k.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.13224 q^{2} +1.00000 q^{3} +2.54643 q^{4} -4.09989 q^{5} -2.13224 q^{6} +4.42610 q^{7} -1.16513 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.13224 q^{2} +1.00000 q^{3} +2.54643 q^{4} -4.09989 q^{5} -2.13224 q^{6} +4.42610 q^{7} -1.16513 q^{8} +1.00000 q^{9} +8.74193 q^{10} -3.18976 q^{11} +2.54643 q^{12} +1.00000 q^{13} -9.43750 q^{14} -4.09989 q^{15} -2.60854 q^{16} +0.564744 q^{17} -2.13224 q^{18} -3.52703 q^{19} -10.4401 q^{20} +4.42610 q^{21} +6.80133 q^{22} -4.29050 q^{23} -1.16513 q^{24} +11.8091 q^{25} -2.13224 q^{26} +1.00000 q^{27} +11.2708 q^{28} -5.66978 q^{29} +8.74193 q^{30} -0.408569 q^{31} +7.89228 q^{32} -3.18976 q^{33} -1.20417 q^{34} -18.1465 q^{35} +2.54643 q^{36} +3.45521 q^{37} +7.52047 q^{38} +1.00000 q^{39} +4.77689 q^{40} +9.10892 q^{41} -9.43750 q^{42} -7.77010 q^{43} -8.12252 q^{44} -4.09989 q^{45} +9.14836 q^{46} +10.4828 q^{47} -2.60854 q^{48} +12.5904 q^{49} -25.1797 q^{50} +0.564744 q^{51} +2.54643 q^{52} -8.95119 q^{53} -2.13224 q^{54} +13.0777 q^{55} -5.15697 q^{56} -3.52703 q^{57} +12.0893 q^{58} +12.0559 q^{59} -10.4401 q^{60} -1.13112 q^{61} +0.871165 q^{62} +4.42610 q^{63} -11.6111 q^{64} -4.09989 q^{65} +6.80133 q^{66} -6.48364 q^{67} +1.43808 q^{68} -4.29050 q^{69} +38.6927 q^{70} +14.4727 q^{71} -1.16513 q^{72} +9.97568 q^{73} -7.36732 q^{74} +11.8091 q^{75} -8.98136 q^{76} -14.1182 q^{77} -2.13224 q^{78} -9.05613 q^{79} +10.6947 q^{80} +1.00000 q^{81} -19.4224 q^{82} +6.20521 q^{83} +11.2708 q^{84} -2.31539 q^{85} +16.5677 q^{86} -5.66978 q^{87} +3.71648 q^{88} -9.20347 q^{89} +8.74193 q^{90} +4.42610 q^{91} -10.9255 q^{92} -0.408569 q^{93} -22.3519 q^{94} +14.4604 q^{95} +7.89228 q^{96} -15.1598 q^{97} -26.8457 q^{98} -3.18976 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.13224	−1.50772	−0.753860	−	0.657036i	$-0.771810\pi$
$2$	−2.13224	−1.50772	−0.753860	+	0.657036i	$0.771810\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.54643	1.27322
$5$	−4.09989	−1.83353	−0.916763	−	0.399433i	$-0.869207\pi$
$5$	−4.09989	−1.83353	−0.916763	+	0.399433i	$0.869207\pi$
$6$	−2.13224	−0.870482
$7$	4.42610	1.67291	0.836455	−	0.548036i	$-0.184624\pi$
$7$	4.42610	1.67291	0.836455	+	0.548036i	$0.184624\pi$
$8$	−1.16513	−0.411935
$9$	1.00000	0.333333
$10$	8.74193	2.76444
$11$	−3.18976	−0.961750	−0.480875	−	0.876789i	$-0.659681\pi$
$11$	−3.18976	−0.961750	−0.480875	+	0.876789i	$0.659681\pi$
$12$	2.54643	0.735092
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−9.43750	−2.52228
$15$	−4.09989	−1.05859
$16$	−2.60854	−0.652135
$17$	0.564744	0.136970	0.0684852	−	0.997652i	$-0.478183\pi$
$17$	0.564744	0.136970	0.0684852	+	0.997652i	$0.478183\pi$
$18$	−2.13224	−0.502573
$19$	−3.52703	−0.809157	−0.404578	−	0.914503i	$-0.632582\pi$
$19$	−3.52703	−0.809157	−0.404578	+	0.914503i	$0.632582\pi$
$20$	−10.4401	−2.33448
$21$	4.42610	0.965855
$22$	6.80133	1.45005
$23$	−4.29050	−0.894631	−0.447315	−	0.894376i	$-0.647620\pi$
$23$	−4.29050	−0.894631	−0.447315	+	0.894376i	$0.647620\pi$
$24$	−1.16513	−0.237831
$25$	11.8091	2.36181
$26$	−2.13224	−0.418166
$27$	1.00000	0.192450
$28$	11.2708	2.12998
$29$	−5.66978	−1.05285	−0.526426	−	0.850221i	$-0.676468\pi$
$29$	−5.66978	−1.05285	−0.526426	+	0.850221i	$0.676468\pi$
$30$	8.74193	1.59605
$31$	−0.408569	−0.0733811	−0.0366905	−	0.999327i	$-0.511682\pi$
$31$	−0.408569	−0.0733811	−0.0366905	+	0.999327i	$0.511682\pi$
$32$	7.89228	1.39517
$33$	−3.18976	−0.555267
$34$	−1.20417	−0.206513
$35$	−18.1465	−3.06732
$36$	2.54643	0.424406
$37$	3.45521	0.568032	0.284016	−	0.958819i	$-0.408333\pi$
$37$	3.45521	0.568032	0.284016	+	0.958819i	$0.408333\pi$
$38$	7.52047	1.21998
$39$	1.00000	0.160128
$40$	4.77689	0.755292
$41$	9.10892	1.42257	0.711287	−	0.702901i	$-0.248112\pi$
$41$	9.10892	1.42257	0.711287	+	0.702901i	$0.248112\pi$
$42$	−9.43750	−1.45624
$43$	−7.77010	−1.18493	−0.592465	−	0.805596i	$-0.701845\pi$
$43$	−7.77010	−1.18493	−0.592465	+	0.805596i	$0.701845\pi$
$44$	−8.12252	−1.22452
$45$	−4.09989	−0.611175
$46$	9.14836	1.34885
$47$	10.4828	1.52908	0.764538	−	0.644578i	$-0.222967\pi$
$47$	10.4828	1.52908	0.764538	+	0.644578i	$0.222967\pi$
$48$	−2.60854	−0.376511
$49$	12.5904	1.79863
$50$	−25.1797	−3.56095
$51$	0.564744	0.0790799
$52$	2.54643	0.353127
$53$	−8.95119	−1.22954	−0.614770	−	0.788706i	$-0.710751\pi$
$53$	−8.95119	−1.22954	−0.614770	+	0.788706i	$0.710751\pi$
$54$	−2.13224	−0.290161
$55$	13.0777	1.76339
$56$	−5.15697	−0.689129
$57$	−3.52703	−0.467167
$58$	12.0893	1.58741
$59$	12.0559	1.56954	0.784771	−	0.619786i	$-0.212781\pi$
$59$	12.0559	1.56954	0.784771	+	0.619786i	$0.212781\pi$
$60$	−10.4401	−1.34781
$61$	−1.13112	−0.144825	−0.0724127	−	0.997375i	$-0.523070\pi$
$61$	−1.13112	−0.144825	−0.0724127	+	0.997375i	$0.523070\pi$
$62$	0.871165	0.110638
$63$	4.42610	0.557637
$64$	−11.6111	−1.45139
$65$	−4.09989	−0.508528
$66$	6.80133	0.837186
$67$	−6.48364	−0.792103	−0.396052	−	0.918228i	$-0.629620\pi$
$67$	−6.48364	−0.792103	−0.396052	+	0.918228i	$0.629620\pi$
$68$	1.43808	0.174393
$69$	−4.29050	−0.516515
$70$	38.6927	4.62466
$71$	14.4727	1.71760	0.858798	−	0.512315i	$-0.171212\pi$
$71$	14.4727	1.71760	0.858798	+	0.512315i	$0.171212\pi$
$72$	−1.16513	−0.137312
$73$	9.97568	1.16757	0.583783	−	0.811910i	$-0.301572\pi$
$73$	9.97568	1.16757	0.583783	+	0.811910i	$0.301572\pi$
$74$	−7.36732	−0.856433
$75$	11.8091	1.36359
$76$	−8.98136	−1.03023
$77$	−14.1182	−1.60892
$78$	−2.13224	−0.241428
$79$	−9.05613	−1.01889	−0.509447	−	0.860502i	$-0.670150\pi$
$79$	−9.05613	−1.01889	−0.509447	+	0.860502i	$0.670150\pi$
$80$	10.6947	1.19571
$81$	1.00000	0.111111
$82$	−19.4224	−2.14484
$83$	6.20521	0.681110	0.340555	−	0.940225i	$-0.389385\pi$
$83$	6.20521	0.681110	0.340555	+	0.940225i	$0.389385\pi$
$84$	11.2708	1.22974
$85$	−2.31539	−0.251139
$86$	16.5677	1.78654
$87$	−5.66978	−0.607865
$88$	3.71648	0.396178
$89$	−9.20347	−0.975566	−0.487783	−	0.872965i	$-0.662194\pi$
$89$	−9.20347	−0.975566	−0.487783	+	0.872965i	$0.662194\pi$
$90$	8.74193	0.921480
$91$	4.42610	0.463982
$92$	−10.9255	−1.13906
$93$	−0.408569	−0.0423666
$94$	−22.3519	−2.30542
$95$	14.4604	1.48361
$96$	7.89228	0.805503
$97$	−15.1598	−1.53925	−0.769623	−	0.638499i	$-0.779556\pi$
$97$	−15.1598	−1.53925	−0.769623	+	0.638499i	$0.779556\pi$
$98$	−26.8457	−2.71183
$99$	−3.18976	−0.320583
$100$	30.0710	3.00710
$101$	3.08904	0.307371	0.153686	−	0.988120i	$-0.450886\pi$
$101$	3.08904	0.307371	0.153686	+	0.988120i	$0.450886\pi$
$102$	−1.20417	−0.119230
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.16513	−0.114250
$105$	−18.1465	−1.77092
$106$	19.0860	1.85380
$107$	−16.3302	−1.57870	−0.789351	−	0.613943i	$-0.789583\pi$
$107$	−16.3302	−1.57870	−0.789351	+	0.613943i	$0.789583\pi$
$108$	2.54643	0.245031
$109$	−3.14926	−0.301644	−0.150822	−	0.988561i	$-0.548192\pi$
$109$	−3.14926	−0.301644	−0.150822	+	0.988561i	$0.548192\pi$
$110$	−27.8847	−2.65870
$111$	3.45521	0.327954
$112$	−11.5457	−1.09096
$113$	−5.40135	−0.508116	−0.254058	−	0.967189i	$-0.581765\pi$
$113$	−5.40135	−0.508116	−0.254058	+	0.967189i	$0.581765\pi$
$114$	7.52047	0.704356
$115$	17.5906	1.64033
$116$	−14.4377	−1.34051
$117$	1.00000	0.0924500
$118$	−25.7060	−2.36643
$119$	2.49961	0.229139
$120$	4.77689	0.436068
$121$	−0.825405	−0.0750368
$122$	2.41182	0.218356
$123$	9.10892	0.821324
$124$	−1.04039	−0.0934300
$125$	−27.9164	−2.49692
$126$	−9.43750	−0.840760
$127$	9.64530	0.855882	0.427941	−	0.903807i	$-0.359239\pi$
$127$	9.64530	0.855882	0.427941	+	0.903807i	$0.359239\pi$
$128$	8.97312	0.793119
$129$	−7.77010	−0.684119
$130$	8.74193	0.766718
$131$	1.28931	0.112647	0.0563236	−	0.998413i	$-0.482062\pi$
$131$	1.28931	0.112647	0.0563236	+	0.998413i	$0.482062\pi$
$132$	−8.12252	−0.706975
$133$	−15.6110	−1.35365
$134$	13.8247	1.19427
$135$	−4.09989	−0.352862
$136$	−0.657998	−0.0564229
$137$	13.2405	1.13121	0.565606	−	0.824676i	$-0.308642\pi$
$137$	13.2405	1.13121	0.565606	+	0.824676i	$0.308642\pi$
$138$	9.14836	0.778760
$139$	−7.67432	−0.650927	−0.325463	−	0.945555i	$-0.605520\pi$
$139$	−7.67432	−0.650927	−0.325463	+	0.945555i	$0.605520\pi$
$140$	−46.2089	−3.90537
$141$	10.4828	0.882813
$142$	−30.8593	−2.58965
$143$	−3.18976	−0.266741
$144$	−2.60854	−0.217378
$145$	23.2455	1.93043
$146$	−21.2705	−1.76036
$147$	12.5904	1.03844
$148$	8.79845	0.723228
$149$	1.45362	0.119085	0.0595424	−	0.998226i	$-0.481036\pi$
$149$	1.45362	0.119085	0.0595424	+	0.998226i	$0.481036\pi$
$150$	−25.1797	−2.05592
$151$	1.56690	0.127513	0.0637563	−	0.997966i	$-0.479692\pi$
$151$	1.56690	0.127513	0.0637563	+	0.997966i	$0.479692\pi$
$152$	4.10944	0.333320
$153$	0.564744	0.0456568
$154$	30.1034	2.42580
$155$	1.67508	0.134546
$156$	2.54643	0.203878
$157$	22.7109	1.81253	0.906265	−	0.422710i	$-0.138921\pi$
$157$	22.7109	1.81253	0.906265	+	0.422710i	$0.138921\pi$
$158$	19.3098	1.53621
$159$	−8.95119	−0.709875
$160$	−32.3575	−2.55808
$161$	−18.9902	−1.49664
$162$	−2.13224	−0.167524
$163$	16.0518	1.25728	0.628638	−	0.777698i	$-0.283613\pi$
$163$	16.0518	1.25728	0.628638	+	0.777698i	$0.283613\pi$
$164$	23.1953	1.81125
$165$	13.0777	1.01810
$166$	−13.2310	−1.02692
$167$	−17.8685	−1.38271	−0.691354	−	0.722516i	$-0.742986\pi$
$167$	−17.8685	−1.38271	−0.691354	+	0.722516i	$0.742986\pi$
$168$	−5.15697	−0.397869
$169$	1.00000	0.0769231
$170$	4.93695	0.378647
$171$	−3.52703	−0.269719
$172$	−19.7861	−1.50867
$173$	0.114145	0.00867828	0.00433914	−	0.999991i	$-0.498619\pi$
$173$	0.114145	0.00867828	0.00433914	+	0.999991i	$0.498619\pi$
$174$	12.0893	0.916489
$175$	52.2682	3.95110
$176$	8.32063	0.627191
$177$	12.0559	0.906175
$178$	19.6240	1.47088
$179$	17.1574	1.28240	0.641200	−	0.767373i	$-0.278437\pi$
$179$	17.1574	1.28240	0.641200	+	0.767373i	$0.278437\pi$
$180$	−10.4401	−0.778158
$181$	14.2966	1.06266	0.531331	−	0.847165i	$-0.321692\pi$
$181$	14.2966	1.06266	0.531331	+	0.847165i	$0.321692\pi$
$182$	−9.43750	−0.699554
$183$	−1.13112	−0.0836150
$184$	4.99897	0.368529
$185$	−14.1660	−1.04150
$186$	0.871165	0.0638769
$187$	−1.80140	−0.131731
$188$	26.6938	1.94685
$189$	4.42610	0.321952
$190$	−30.8331	−2.23687
$191$	22.2951	1.61322	0.806609	−	0.591085i	$-0.201300\pi$
$191$	22.2951	1.61322	0.806609	+	0.591085i	$0.201300\pi$
$192$	−11.6111	−0.837961
$193$	−22.2387	−1.60077	−0.800387	−	0.599484i	$-0.795372\pi$
$193$	−22.2387	−1.60077	−0.800387	+	0.599484i	$0.795372\pi$
$194$	32.3243	2.32075
$195$	−4.09989	−0.293599
$196$	32.0606	2.29004
$197$	10.6340	0.757643	0.378822	−	0.925470i	$-0.376329\pi$
$197$	10.6340	0.757643	0.378822	+	0.925470i	$0.376329\pi$
$198$	6.80133	0.483350
$199$	7.50040	0.531689	0.265845	−	0.964016i	$-0.414349\pi$
$199$	7.50040	0.531689	0.265845	+	0.964016i	$0.414349\pi$
$200$	−13.7591	−0.972913
$201$	−6.48364	−0.457321
$202$	−6.58657	−0.463429
$203$	−25.0951	−1.76133
$204$	1.43808	0.100686
$205$	−37.3455	−2.60833
$206$	−2.13224	−0.148560
$207$	−4.29050	−0.298210
$208$	−2.60854	−0.180870
$209$	11.2504	0.778206
$210$	38.6927	2.67005
$211$	7.63296	0.525475	0.262737	−	0.964867i	$-0.415375\pi$
$211$	7.63296	0.525475	0.262737	+	0.964867i	$0.415375\pi$
$212$	−22.7936	−1.56547
$213$	14.4727	0.991654
$214$	34.8199	2.38024
$215$	31.8565	2.17260
$216$	−1.16513	−0.0792768
$217$	−1.80837	−0.122760
$218$	6.71496	0.454794
$219$	9.97568	0.674094
$220$	33.3014	2.24518
$221$	0.564744	0.0379888
$222$	−7.36732	−0.494462
$223$	−6.00848	−0.402357	−0.201179	−	0.979555i	$-0.564477\pi$
$223$	−6.00848	−0.402357	−0.201179	+	0.979555i	$0.564477\pi$
$224$	34.9321	2.33400
$225$	11.8091	0.787271
$226$	11.5170	0.766097
$227$	21.0128	1.39467	0.697335	−	0.716745i	$-0.254369\pi$
$227$	21.0128	1.39467	0.697335	+	0.716745i	$0.254369\pi$
$228$	−8.98136	−0.594805
$229$	−14.7916	−0.977455	−0.488728	−	0.872436i	$-0.662539\pi$
$229$	−14.7916	−0.977455	−0.488728	+	0.872436i	$0.662539\pi$
$230$	−37.5072	−2.47315
$231$	−14.1182	−0.928911
$232$	6.60602	0.433706
$233$	22.4264	1.46920	0.734602	−	0.678499i	$-0.237369\pi$
$233$	22.4264	1.46920	0.734602	+	0.678499i	$0.237369\pi$
$234$	−2.13224	−0.139389
$235$	−42.9784	−2.80360
$236$	30.6995	1.99837
$237$	−9.05613	−0.588259
$238$	−5.32977	−0.345478
$239$	8.56098	0.553764	0.276882	−	0.960904i	$-0.410699\pi$
$239$	8.56098	0.553764	0.276882	+	0.960904i	$0.410699\pi$
$240$	10.6947	0.690342
$241$	25.4811	1.64138	0.820691	−	0.571373i	$-0.193589\pi$
$241$	25.4811	1.64138	0.820691	+	0.571373i	$0.193589\pi$
$242$	1.75996	0.113134
$243$	1.00000	0.0641500
$244$	−2.88033	−0.184394
$245$	−51.6192	−3.29783
$246$	−19.4224	−1.23833
$247$	−3.52703	−0.224420
$248$	0.476034	0.0302282
$249$	6.20521	0.393239
$250$	59.5244	3.76466
$251$	16.9061	1.06710	0.533551	−	0.845768i	$-0.320857\pi$
$251$	16.9061	1.06710	0.533551	+	0.845768i	$0.320857\pi$
$252$	11.2708	0.709993
$253$	13.6857	0.860411
$254$	−20.5661	−1.29043
$255$	−2.31539	−0.144995
$256$	4.08945	0.255591
$257$	−14.5064	−0.904883	−0.452441	−	0.891794i	$-0.649447\pi$
$257$	−14.5064	−0.904883	−0.452441	+	0.891794i	$0.649447\pi$
$258$	16.5677	1.03146
$259$	15.2931	0.950267
$260$	−10.4401	−0.647467
$261$	−5.66978	−0.350951
$262$	−2.74911	−0.169840
$263$	2.98355	0.183974	0.0919869	−	0.995760i	$-0.470678\pi$
$263$	2.98355	0.183974	0.0919869	+	0.995760i	$0.470678\pi$
$264$	3.71648	0.228734
$265$	36.6988	2.25439
$266$	33.2864	2.04092
$267$	−9.20347	−0.563243
$268$	−16.5102	−1.00852
$269$	22.2538	1.35684	0.678418	−	0.734677i	$-0.262666\pi$
$269$	22.2538	1.35684	0.678418	+	0.734677i	$0.262666\pi$
$270$	8.74193	0.532017
$271$	8.80145	0.534650	0.267325	−	0.963606i	$-0.413860\pi$
$271$	8.80145	0.534650	0.267325	+	0.963606i	$0.413860\pi$
$272$	−1.47316	−0.0893233
$273$	4.42610	0.267880
$274$	−28.2319	−1.70555
$275$	−37.6682	−2.27148
$276$	−10.9255	−0.657636
$277$	9.55548	0.574133	0.287067	−	0.957911i	$-0.407320\pi$
$277$	9.55548	0.574133	0.287067	+	0.957911i	$0.407320\pi$
$278$	16.3635	0.981415
$279$	−0.408569	−0.0244604
$280$	21.1430	1.26354
$281$	8.61699	0.514047	0.257023	−	0.966405i	$-0.417258\pi$
$281$	8.61699	0.514047	0.257023	+	0.966405i	$0.417258\pi$
$282$	−22.3519	−1.33103
$283$	−20.0940	−1.19447	−0.597233	−	0.802068i	$-0.703733\pi$
$283$	−20.0940	−1.19447	−0.597233	+	0.802068i	$0.703733\pi$
$284$	36.8538	2.18687
$285$	14.4604	0.856562
$286$	6.80133	0.402171
$287$	40.3170	2.37984
$288$	7.89228	0.465057
$289$	−16.6811	−0.981239
$290$	−49.5649	−2.91055
$291$	−15.1598	−0.888684
$292$	25.4024	1.48656
$293$	−8.58420	−0.501494	−0.250747	−	0.968053i	$-0.580676\pi$
$293$	−8.58420	−0.501494	−0.250747	+	0.968053i	$0.580676\pi$
$294$	−26.8457	−1.56567
$295$	−49.4277	−2.87779
$296$	−4.02575	−0.233992
$297$	−3.18976	−0.185089
$298$	−3.09945	−0.179546
$299$	−4.29050	−0.248126
$300$	30.0710	1.73615
$301$	−34.3913	−1.98228
$302$	−3.34100	−0.192253
$303$	3.08904	0.177461
$304$	9.20041	0.527680
$305$	4.63747	0.265541
$306$	−1.20417	−0.0688377
$307$	10.0774	0.575149	0.287575	−	0.957758i	$-0.407151\pi$
$307$	10.0774	0.575149	0.287575	+	0.957758i	$0.407151\pi$
$308$	−35.9511	−2.04851
$309$	1.00000	0.0568880
$310$	−3.57168	−0.202858
$311$	−24.0566	−1.36412	−0.682061	−	0.731295i	$-0.738916\pi$
$311$	−24.0566	−1.36412	−0.682061	+	0.731295i	$0.738916\pi$
$312$	−1.16513	−0.0659623
$313$	26.1431	1.47770	0.738848	−	0.673872i	$-0.235370\pi$
$313$	26.1431	1.47770	0.738848	+	0.673872i	$0.235370\pi$
$314$	−48.4251	−2.73279
$315$	−18.1465	−1.02244
$316$	−23.0608	−1.29727
$317$	−14.8853	−0.836040	−0.418020	−	0.908438i	$-0.637276\pi$
$317$	−14.8853	−0.836040	−0.418020	+	0.908438i	$0.637276\pi$
$318$	19.0860	1.07029
$319$	18.0853	1.01258
$320$	47.6043	2.66116
$321$	−16.3302	−0.911464
$322$	40.4916	2.25651
$323$	−1.99187	−0.110831
$324$	2.54643	0.141469
$325$	11.8091	0.655049
$326$	−34.2263	−1.89562
$327$	−3.14926	−0.174154
$328$	−10.6130	−0.586008
$329$	46.3981	2.55801
$330$	−27.8847	−1.53500
$331$	4.87697	0.268062	0.134031	−	0.990977i	$-0.457208\pi$
$331$	4.87697	0.268062	0.134031	+	0.990977i	$0.457208\pi$
$332$	15.8012	0.867201
$333$	3.45521	0.189344
$334$	38.0999	2.08474
$335$	26.5822	1.45234
$336$	−11.5457	−0.629868
$337$	−12.2129	−0.665278	−0.332639	−	0.943054i	$-0.607939\pi$
$337$	−12.2129	−0.665278	−0.332639	+	0.943054i	$0.607939\pi$
$338$	−2.13224	−0.115978
$339$	−5.40135	−0.293361
$340$	−5.89598	−0.319754
$341$	1.30324	0.0705743
$342$	7.52047	0.406660
$343$	24.7437	1.33603
$344$	9.05316	0.488113
$345$	17.5906	0.947044
$346$	−0.243384	−0.0130844
$347$	−2.30245	−0.123602	−0.0618010	−	0.998088i	$-0.519684\pi$
$347$	−2.30245	−0.123602	−0.0618010	+	0.998088i	$0.519684\pi$
$348$	−14.4377	−0.773944
$349$	15.1458	0.810737	0.405369	−	0.914153i	$-0.367143\pi$
$349$	15.1458	0.810737	0.405369	+	0.914153i	$0.367143\pi$
$350$	−111.448	−5.95715
$351$	1.00000	0.0533761
$352$	−25.1745	−1.34181
$353$	−4.21706	−0.224451	−0.112226	−	0.993683i	$-0.535798\pi$
$353$	−4.21706	−0.224451	−0.112226	+	0.993683i	$0.535798\pi$
$354$	−25.7060	−1.36626
$355$	−59.3365	−3.14925
$356$	−23.4360	−1.24211
$357$	2.49961	0.132294
$358$	−36.5835	−1.93350
$359$	13.1895	0.696114	0.348057	−	0.937473i	$-0.386842\pi$
$359$	13.1895	0.696114	0.348057	+	0.937473i	$0.386842\pi$
$360$	4.77689	0.251764
$361$	−6.56004	−0.345265
$362$	−30.4838	−1.60219
$363$	−0.825405	−0.0433225
$364$	11.2708	0.590749
$365$	−40.8992	−2.14076
$366$	2.41182	0.126068
$367$	26.4586	1.38113	0.690563	−	0.723272i	$-0.257363\pi$
$367$	26.4586	1.38113	0.690563	+	0.723272i	$0.257363\pi$
$368$	11.1919	0.583420
$369$	9.10892	0.474192
$370$	30.2052	1.57029
$371$	−39.6189	−2.05691
$372$	−1.04039	−0.0539419
$373$	1.23862	0.0641331	0.0320666	−	0.999486i	$-0.489791\pi$
$373$	1.23862	0.0641331	0.0320666	+	0.999486i	$0.489791\pi$
$374$	3.84101	0.198614
$375$	−27.9164	−1.44160
$376$	−12.2138	−0.629880
$377$	−5.66978	−0.292009
$378$	−9.43750	−0.485413
$379$	−24.3541	−1.25098	−0.625492	−	0.780231i	$-0.715102\pi$
$379$	−24.3541	−1.25098	−0.625492	+	0.780231i	$0.715102\pi$
$380$	36.8225	1.88896
$381$	9.64530	0.494144
$382$	−47.5385	−2.43228
$383$	−23.1632	−1.18359	−0.591793	−	0.806090i	$-0.701580\pi$
$383$	−23.1632	−1.18359	−0.591793	+	0.806090i	$0.701580\pi$
$384$	8.97312	0.457908
$385$	57.8831	2.95000
$386$	47.4181	2.41352
$387$	−7.77010	−0.394977
$388$	−38.6035	−1.95979
$389$	8.81661	0.447020	0.223510	−	0.974702i	$-0.428249\pi$
$389$	8.81661	0.447020	0.223510	+	0.974702i	$0.428249\pi$
$390$	8.74193	0.442665
$391$	−2.42303	−0.122538
$392$	−14.6694	−0.740917
$393$	1.28931	0.0650369
$394$	−22.6743	−1.14231
$395$	37.1291	1.86817
$396$	−8.12252	−0.408172
$397$	2.31292	0.116082	0.0580412	−	0.998314i	$-0.481515\pi$
$397$	2.31292	0.116082	0.0580412	+	0.998314i	$0.481515\pi$
$398$	−15.9926	−0.801638
$399$	−15.6110	−0.781528
$400$	−30.8045	−1.54022
$401$	0.239699	0.0119700	0.00598500	−	0.999982i	$-0.498095\pi$
$401$	0.239699	0.0119700	0.00598500	+	0.999982i	$0.498095\pi$
$402$	13.8247	0.689512
$403$	−0.408569	−0.0203522
$404$	7.86604	0.391350
$405$	−4.09989	−0.203725
$406$	53.5086	2.65559
$407$	−11.0213	−0.546305
$408$	−0.657998	−0.0325758
$409$	18.3766	0.908663	0.454331	−	0.890833i	$-0.349878\pi$
$409$	18.3766	0.908663	0.454331	+	0.890833i	$0.349878\pi$
$410$	79.6296	3.93262
$411$	13.2405	0.653105
$412$	2.54643	0.125454
$413$	53.3606	2.62570
$414$	9.14836	0.449617
$415$	−25.4407	−1.24883
$416$	7.89228	0.386951
$417$	−7.67432	−0.375813
$418$	−23.9885	−1.17332
$419$	26.2691	1.28333	0.641665	−	0.766985i	$-0.278244\pi$
$419$	26.2691	1.28333	0.641665	+	0.766985i	$0.278244\pi$
$420$	−46.2089	−2.25476
$421$	9.49465	0.462741	0.231370	−	0.972866i	$-0.425679\pi$
$421$	9.49465	0.462741	0.231370	+	0.972866i	$0.425679\pi$
$422$	−16.2753	−0.792268
$423$	10.4828	0.509692
$424$	10.4293	0.506490
$425$	6.66910	0.323499
$426$	−30.8593	−1.49514
$427$	−5.00647	−0.242280
$428$	−41.5838	−2.01003
$429$	−3.18976	−0.154003
$430$	−67.9257	−3.27567
$431$	−9.65046	−0.464846	−0.232423	−	0.972615i	$-0.574665\pi$
$431$	−9.65046	−0.464846	−0.232423	+	0.972615i	$0.574665\pi$
$432$	−2.60854	−0.125504
$433$	35.4059	1.70150	0.850750	−	0.525570i	$-0.176148\pi$
$433$	35.4059	1.70150	0.850750	+	0.525570i	$0.176148\pi$
$434$	3.85587	0.185088
$435$	23.2455	1.11454
$436$	−8.01937	−0.384058
$437$	15.1327	0.723896
$438$	−21.2705	−1.01634
$439$	27.1542	1.29600	0.648000	−	0.761640i	$-0.275606\pi$
$439$	27.1542	1.29600	0.648000	+	0.761640i	$0.275606\pi$
$440$	−15.2371	−0.726402
$441$	12.5904	0.599543
$442$	−1.20417	−0.0572764
$443$	38.8758	1.84704	0.923522	−	0.383544i	$-0.125297\pi$
$443$	38.8758	1.84704	0.923522	+	0.383544i	$0.125297\pi$
$444$	8.79845	0.417556
$445$	37.7332	1.78873
$446$	12.8115	0.606642
$447$	1.45362	0.0687536
$448$	−51.3921	−2.42805
$449$	9.21063	0.434676	0.217338	−	0.976096i	$-0.430263\pi$
$449$	9.21063	0.434676	0.217338	+	0.976096i	$0.430263\pi$
$450$	−25.1797	−1.18698
$451$	−29.0553	−1.36816
$452$	−13.7542	−0.646942
$453$	1.56690	0.0736194
$454$	−44.8043	−2.10277
$455$	−18.1465	−0.850722
$456$	4.10944	0.192442
$457$	34.2749	1.60331	0.801655	−	0.597786i	$-0.203953\pi$
$457$	34.2749	1.60331	0.801655	+	0.597786i	$0.203953\pi$
$458$	31.5391	1.47373
$459$	0.564744	0.0263600
$460$	44.7932	2.08849
$461$	34.1992	1.59282	0.796409	−	0.604758i	$-0.206730\pi$
$461$	34.1992	1.59282	0.796409	+	0.604758i	$0.206730\pi$
$462$	30.1034	1.40054
$463$	0.415236	0.0192977	0.00964883	−	0.999953i	$-0.496929\pi$
$463$	0.415236	0.0192977	0.00964883	+	0.999953i	$0.496929\pi$
$464$	14.7899	0.686602
$465$	1.67508	0.0776802
$466$	−47.8184	−2.21515
$467$	−34.2317	−1.58405	−0.792026	−	0.610487i	$-0.790974\pi$
$467$	−34.2317	−1.58405	−0.792026	+	0.610487i	$0.790974\pi$
$468$	2.54643	0.117709
$469$	−28.6973	−1.32512
$470$	91.6401	4.22704
$471$	22.7109	1.04646
$472$	−14.0466	−0.646548
$473$	24.7848	1.13961
$474$	19.3098	0.886929
$475$	−41.6510	−1.91108
$476$	6.36510	0.291744
$477$	−8.95119	−0.409847
$478$	−18.2540	−0.834921
$479$	−3.03093	−0.138487	−0.0692434	−	0.997600i	$-0.522058\pi$
$479$	−3.03093	−0.138487	−0.0692434	+	0.997600i	$0.522058\pi$
$480$	−32.3575	−1.47691
$481$	3.45521	0.157544
$482$	−54.3317	−2.47474
$483$	−18.9902	−0.864083
$484$	−2.10184	−0.0955382
$485$	62.1535	2.82225
$486$	−2.13224	−0.0967202
$487$	28.7549	1.30301	0.651505	−	0.758644i	$-0.274138\pi$
$487$	28.7549	1.30301	0.651505	+	0.758644i	$0.274138\pi$
$488$	1.31790	0.0596586
$489$	16.0518	0.725888
$490$	110.064	4.97220
$491$	−8.60938	−0.388536	−0.194268	−	0.980948i	$-0.562233\pi$
$491$	−8.60938	−0.388536	−0.194268	+	0.980948i	$0.562233\pi$
$492$	23.1953	1.04572
$493$	−3.20198	−0.144210
$494$	7.52047	0.338362
$495$	13.0777	0.587798
$496$	1.06577	0.0478544
$497$	64.0578	2.87338
$498$	−13.2310	−0.592894
$499$	−8.50367	−0.380677	−0.190338	−	0.981719i	$-0.560959\pi$
$499$	−8.50367	−0.380677	−0.190338	+	0.981719i	$0.560959\pi$
$500$	−71.0873	−3.17912
$501$	−17.8685	−0.798307
$502$	−36.0478	−1.60889
$503$	3.88796	0.173355	0.0866777	−	0.996236i	$-0.472375\pi$
$503$	3.88796	0.173355	0.0866777	+	0.996236i	$0.472375\pi$
$504$	−5.15697	−0.229710
$505$	−12.6647	−0.563572
$506$	−29.1811	−1.29726
$507$	1.00000	0.0444116
$508$	24.5611	1.08972
$509$	−1.23635	−0.0548002	−0.0274001	−	0.999625i	$-0.508723\pi$
$509$	−1.23635	−0.0548002	−0.0274001	+	0.999625i	$0.508723\pi$
$510$	4.93695	0.218612
$511$	44.1534	1.95323
$512$	−26.6659	−1.17848
$513$	−3.52703	−0.155722
$514$	30.9310	1.36431
$515$	−4.09989	−0.180663
$516$	−19.7861	−0.871033
$517$	−33.4377	−1.47059
$518$	−32.6085	−1.43274
$519$	0.114145	0.00501041
$520$	4.77689	0.209480
$521$	27.3108	1.19651	0.598253	−	0.801307i	$-0.295862\pi$
$521$	27.3108	1.19651	0.598253	+	0.801307i	$0.295862\pi$
$522$	12.0893	0.529135
$523$	27.0096	1.18105	0.590523	−	0.807021i	$-0.298921\pi$
$523$	27.0096	1.18105	0.590523	+	0.807021i	$0.298921\pi$
$524$	3.28313	0.143424
$525$	52.2682	2.28117
$526$	−6.36164	−0.277381
$527$	−0.230737	−0.0100510
$528$	8.32063	0.362109
$529$	−4.59163	−0.199636
$530$	−78.2506	−3.39899
$531$	12.0559	0.523181
$532$	−39.7524	−1.72349
$533$	9.10892	0.394551
$534$	19.6240	0.849213
$535$	66.9520	2.89459
$536$	7.55427	0.326295
$537$	17.1574	0.740395
$538$	−47.4503	−2.04573
$539$	−40.1604	−1.72983
$540$	−10.4401	−0.449270
$541$	5.18112	0.222754	0.111377	−	0.993778i	$-0.464474\pi$
$541$	5.18112	0.222754	0.111377	+	0.993778i	$0.464474\pi$
$542$	−18.7668	−0.806102
$543$	14.2966	0.613528
$544$	4.45712	0.191097
$545$	12.9116	0.553072
$546$	−9.43750	−0.403888
$547$	10.8197	0.462617	0.231308	−	0.972881i	$-0.425699\pi$
$547$	10.8197	0.462617	0.231308	+	0.972881i	$0.425699\pi$
$548$	33.7160	1.44028
$549$	−1.13112	−0.0482751
$550$	80.3174	3.42475
$551$	19.9975	0.851923
$552$	4.99897	0.212770
$553$	−40.0834	−1.70452
$554$	−20.3745	−0.865631
$555$	−14.1660	−0.601311
$556$	−19.5421	−0.828771
$557$	−34.6024	−1.46615	−0.733076	−	0.680147i	$-0.761916\pi$
$557$	−34.6024	−1.46615	−0.733076	+	0.680147i	$0.761916\pi$
$558$	0.871165	0.0368793
$559$	−7.77010	−0.328640
$560$	47.3360	2.00031
$561$	−1.80140	−0.0760551
$562$	−18.3735	−0.775038
$563$	−13.9077	−0.586139	−0.293070	−	0.956091i	$-0.594677\pi$
$563$	−13.9077	−0.586139	−0.293070	+	0.956091i	$0.594677\pi$
$564$	26.6938	1.12401
$565$	22.1449	0.931644
$566$	42.8452	1.80092
$567$	4.42610	0.185879
$568$	−16.8626	−0.707537
$569$	−15.6171	−0.654704	−0.327352	−	0.944902i	$-0.606156\pi$
$569$	−15.6171	−0.654704	−0.327352	+	0.944902i	$0.606156\pi$
$570$	−30.8331	−1.29146
$571$	15.5805	0.652022	0.326011	−	0.945366i	$-0.394295\pi$
$571$	15.5805	0.652022	0.326011	+	0.945366i	$0.394295\pi$
$572$	−8.12252	−0.339620
$573$	22.2951	0.931392
$574$	−85.9655	−3.58813
$575$	−50.6668	−2.11295
$576$	−11.6111	−0.483797
$577$	34.7317	1.44590	0.722949	−	0.690901i	$-0.242786\pi$
$577$	34.7317	1.44590	0.722949	+	0.690901i	$0.242786\pi$
$578$	35.5680	1.47943
$579$	−22.2387	−0.924207
$580$	59.1931	2.45786
$581$	27.4649	1.13944
$582$	32.3243	1.33989
$583$	28.5522	1.18251
$584$	−11.6229	−0.480960
$585$	−4.09989	−0.169509
$586$	18.3035	0.756113
$587$	−45.6179	−1.88285	−0.941427	−	0.337217i	$-0.890514\pi$
$587$	−45.6179	−1.88285	−0.941427	+	0.337217i	$0.890514\pi$
$588$	32.0606	1.32216
$589$	1.44103	0.0593768
$590$	105.392	4.33891
$591$	10.6340	0.437426
$592$	−9.01305	−0.370434
$593$	−6.08956	−0.250068	−0.125034	−	0.992152i	$-0.539904\pi$
$593$	−6.08956	−0.250068	−0.125034	+	0.992152i	$0.539904\pi$
$594$	6.80133	0.279062
$595$	−10.2481	−0.420133
$596$	3.70154	0.151621
$597$	7.50040	0.306971
$598$	9.14836	0.374104
$599$	−25.7042	−1.05024	−0.525122	−	0.851027i	$-0.675980\pi$
$599$	−25.7042	−1.05024	−0.525122	+	0.851027i	$0.675980\pi$
$600$	−13.7591	−0.561712
$601$	17.6833	0.721318	0.360659	−	0.932698i	$-0.382552\pi$
$601$	17.6833	0.721318	0.360659	+	0.932698i	$0.382552\pi$
$602$	73.3304	2.98872
$603$	−6.48364	−0.264034
$604$	3.99001	0.162351
$605$	3.38407	0.137582
$606$	−6.58657	−0.267561
$607$	−11.4694	−0.465529	−0.232764	−	0.972533i	$-0.574777\pi$
$607$	−11.4694	−0.465529	−0.232764	+	0.972533i	$0.574777\pi$
$608$	−27.8363	−1.12891
$609$	−25.0951	−1.01690
$610$	−9.88819	−0.400361
$611$	10.4828	0.424090
$612$	1.43808	0.0581311
$613$	−0.400133	−0.0161612	−0.00808061	−	0.999967i	$-0.502572\pi$
$613$	−0.400133	−0.0161612	−0.00808061	+	0.999967i	$0.502572\pi$
$614$	−21.4875	−0.867163
$615$	−37.3455	−1.50592
$616$	16.4495	0.662770
$617$	−2.34910	−0.0945712	−0.0472856	−	0.998881i	$-0.515057\pi$
$617$	−2.34910	−0.0945712	−0.0472856	+	0.998881i	$0.515057\pi$
$618$	−2.13224	−0.0857711
$619$	−14.9046	−0.599066	−0.299533	−	0.954086i	$-0.596831\pi$
$619$	−14.9046	−0.599066	−0.299533	+	0.954086i	$0.596831\pi$
$620$	4.26549	0.171306
$621$	−4.29050	−0.172172
$622$	51.2943	2.05671
$623$	−40.7355	−1.63203
$624$	−2.60854	−0.104425
$625$	55.4088	2.21635
$626$	−55.7433	−2.22795
$627$	11.2504	0.449298
$628$	57.8319	2.30774
$629$	1.95131	0.0778037
$630$	38.6927	1.54155
$631$	33.1005	1.31771	0.658855	−	0.752270i	$-0.271041\pi$
$631$	33.1005	1.31771	0.658855	+	0.752270i	$0.271041\pi$
$632$	10.5515	0.419718
$633$	7.63296	0.303383
$634$	31.7389	1.26051
$635$	−39.5447	−1.56928
$636$	−22.7936	−0.903825
$637$	12.5904	0.498850
$638$	−38.5621	−1.52669
$639$	14.4727	0.572532
$640$	−36.7888	−1.45420
$641$	−32.9055	−1.29969	−0.649845	−	0.760066i	$-0.725166\pi$
$641$	−32.9055	−1.29969	−0.649845	+	0.760066i	$0.725166\pi$
$642$	34.8199	1.37423
$643$	27.8166	1.09698	0.548491	−	0.836157i	$-0.315203\pi$
$643$	27.8166	1.09698	0.548491	+	0.836157i	$0.315203\pi$
$644$	−48.3573	−1.90554
$645$	31.8565	1.25435
$646$	4.24714	0.167101
$647$	36.6533	1.44099	0.720495	−	0.693460i	$-0.243914\pi$
$647$	36.6533	1.44099	0.720495	+	0.693460i	$0.243914\pi$
$648$	−1.16513	−0.0457705
$649$	−38.4554	−1.50951
$650$	−25.1797	−0.987631
$651$	−1.80837	−0.0708755
$652$	40.8749	1.60078
$653$	22.2440	0.870473	0.435237	−	0.900316i	$-0.356665\pi$
$653$	22.2440	0.870473	0.435237	+	0.900316i	$0.356665\pi$
$654$	6.71496	0.262576
$655$	−5.28601	−0.206542
$656$	−23.7610	−0.927711
$657$	9.97568	0.389188
$658$	−98.9317	−3.85676
$659$	−43.7442	−1.70403	−0.852015	−	0.523517i	$-0.824620\pi$
$659$	−43.7442	−1.70403	−0.852015	+	0.523517i	$0.824620\pi$
$660$	33.3014	1.29626
$661$	−26.1914	−1.01873	−0.509365	−	0.860551i	$-0.670120\pi$
$661$	−26.1914	−1.01873	−0.509365	+	0.860551i	$0.670120\pi$
$662$	−10.3989	−0.404163
$663$	0.564744	0.0219328
$664$	−7.22986	−0.280573
$665$	64.0034	2.48194
$666$	−7.36732	−0.285478
$667$	24.3262	0.941914
$668$	−45.5010	−1.76049
$669$	−6.00848	−0.232301
$670$	−56.6796	−2.18972
$671$	3.60801	0.139286
$672$	34.9321	1.34753
$673$	−4.60033	−0.177330	−0.0886648	−	0.996062i	$-0.528260\pi$
$673$	−4.60033	−0.177330	−0.0886648	+	0.996062i	$0.528260\pi$
$674$	26.0407	1.00305
$675$	11.8091	0.454531
$676$	2.54643	0.0979398
$677$	30.8148	1.18431	0.592154	−	0.805825i	$-0.298278\pi$
$677$	30.8148	1.18431	0.592154	+	0.805825i	$0.298278\pi$
$678$	11.5170	0.442306
$679$	−67.0989	−2.57502
$680$	2.69772	0.103453
$681$	21.0128	0.805213
$682$	−2.77881	−0.106406
$683$	38.4616	1.47169	0.735845	−	0.677150i	$-0.236785\pi$
$683$	38.4616	1.47169	0.735845	+	0.677150i	$0.236785\pi$
$684$	−8.98136	−0.343411
$685$	−54.2845	−2.07410
$686$	−52.7594	−2.01436
$687$	−14.7916	−0.564334
$688$	20.2686	0.772735
$689$	−8.95119	−0.341013
$690$	−37.5072	−1.42788
$691$	−15.9478	−0.606683	−0.303342	−	0.952882i	$-0.598102\pi$
$691$	−15.9478	−0.606683	−0.303342	+	0.952882i	$0.598102\pi$
$692$	0.290663	0.0110493
$693$	−14.1182	−0.536307
$694$	4.90937	0.186357
$695$	31.4638	1.19349
$696$	6.60602	0.250400
$697$	5.14421	0.194851
$698$	−32.2945	−1.22236
$699$	22.4264	0.848245
$700$	133.097	5.03061
$701$	−39.1974	−1.48047	−0.740233	−	0.672350i	$-0.765285\pi$
$701$	−39.1974	−1.48047	−0.740233	+	0.672350i	$0.765285\pi$
$702$	−2.13224	−0.0804761
$703$	−12.1866	−0.459627
$704$	37.0368	1.39588
$705$	−42.9784	−1.61866
$706$	8.99176	0.338410
$707$	13.6724	0.514204
$708$	30.6995	1.15376
$709$	19.1884	0.720636	0.360318	−	0.932829i	$-0.382668\pi$
$709$	19.1884	0.720636	0.360318	+	0.932829i	$0.382668\pi$
$710$	126.519	4.74819
$711$	−9.05613	−0.339631
$712$	10.7232	0.401869
$713$	1.75296	0.0656489
$714$	−5.32977	−0.199462
$715$	13.0777	0.489077
$716$	43.6901	1.63277
$717$	8.56098	0.319716
$718$	−28.1231	−1.04954
$719$	−6.63329	−0.247380	−0.123690	−	0.992321i	$-0.539473\pi$
$719$	−6.63329	−0.247380	−0.123690	+	0.992321i	$0.539473\pi$
$720$	10.6947	0.398569
$721$	4.42610	0.164837
$722$	13.9876	0.520563
$723$	25.4811	0.947652
$724$	36.4055	1.35300
$725$	−66.9549	−2.48664
$726$	1.75996	0.0653182
$727$	−27.2552	−1.01084	−0.505420	−	0.862873i	$-0.668663\pi$
$727$	−27.2552	−1.01084	−0.505420	+	0.862873i	$0.668663\pi$
$728$	−5.15697	−0.191130
$729$	1.00000	0.0370370
$730$	87.2067	3.22766
$731$	−4.38812	−0.162300
$732$	−2.88033	−0.106460
$733$	22.5117	0.831490	0.415745	−	0.909481i	$-0.363521\pi$
$733$	22.5117	0.831490	0.415745	+	0.909481i	$0.363521\pi$
$734$	−56.4159	−2.08235
$735$	−51.6192	−1.90400
$736$	−33.8618	−1.24816
$737$	20.6813	0.761805
$738$	−19.4224	−0.714948
$739$	2.47547	0.0910617	0.0455308	−	0.998963i	$-0.485502\pi$
$739$	2.47547	0.0910617	0.0455308	+	0.998963i	$0.485502\pi$
$740$	−36.0727	−1.32606
$741$	−3.52703	−0.129569
$742$	84.4768	3.10124
$743$	45.7884	1.67981	0.839907	−	0.542730i	$-0.182609\pi$
$743$	45.7884	1.67981	0.839907	+	0.542730i	$0.182609\pi$
$744$	0.476034	0.0174523
$745$	−5.95966	−0.218345
$746$	−2.64102	−0.0966948
$747$	6.20521	0.227037
$748$	−4.58714	−0.167723
$749$	−72.2792	−2.64103
$750$	59.5244	2.17352
$751$	−49.0324	−1.78922	−0.894608	−	0.446852i	$-0.852545\pi$
$751$	−49.0324	−1.78922	−0.894608	+	0.446852i	$0.852545\pi$
$752$	−27.3449	−0.997165
$753$	16.9061	0.616092
$754$	12.0893	0.440267
$755$	−6.42411	−0.233797
$756$	11.2708	0.409914
$757$	−23.2512	−0.845080	−0.422540	−	0.906344i	$-0.638861\pi$
$757$	−23.2512	−0.845080	−0.422540	+	0.906344i	$0.638861\pi$
$758$	51.9286	1.88613
$759$	13.6857	0.496758
$760$	−16.8482	−0.611150
$761$	0.431979	0.0156592	0.00782961	−	0.999969i	$-0.497508\pi$
$761$	0.431979	0.0156592	0.00782961	+	0.999969i	$0.497508\pi$
$762$	−20.5661	−0.745030
$763$	−13.9389	−0.504623
$764$	56.7730	2.05398
$765$	−2.31539	−0.0837129
$766$	49.3895	1.78451
$767$	12.0559	0.435313
$768$	4.08945	0.147565
$769$	0.303144	0.0109317	0.00546583	−	0.999985i	$-0.498260\pi$
$769$	0.303144	0.0109317	0.00546583	+	0.999985i	$0.498260\pi$
$770$	−123.421	−4.44777
$771$	−14.5064	−0.522434
$772$	−56.6293	−2.03813
$773$	−49.1276	−1.76700	−0.883499	−	0.468433i	$-0.844819\pi$
$773$	−49.1276	−1.76700	−0.883499	+	0.468433i	$0.844819\pi$
$774$	16.5677	0.595514
$775$	−4.82482	−0.173312
$776$	17.6631	0.634068
$777$	15.2931	0.548637
$778$	−18.7991	−0.673980
$779$	−32.1275	−1.15109
$780$	−10.4401	−0.373815
$781$	−46.1646	−1.65190
$782$	5.16648	0.184753
$783$	−5.66978	−0.202622
$784$	−32.8426	−1.17295
$785$	−93.1122	−3.32332
$786$	−2.74911	−0.0980574
$787$	15.6063	0.556303	0.278152	−	0.960537i	$-0.410278\pi$
$787$	15.6063	0.556303	0.278152	+	0.960537i	$0.410278\pi$
$788$	27.0789	0.964645
$789$	2.98355	0.106217
$790$	−79.1680	−2.81667
$791$	−23.9069	−0.850033
$792$	3.71648	0.132059
$793$	−1.13112	−0.0401673
$794$	−4.93170	−0.175020
$795$	36.6988	1.30157
$796$	19.0993	0.676956
$797$	25.5032	0.903369	0.451684	−	0.892178i	$-0.350823\pi$
$797$	25.5032	0.903369	0.451684	+	0.892178i	$0.350823\pi$
$798$	33.2864	1.17832
$799$	5.92011	0.209438
$800$	93.2005	3.29514
$801$	−9.20347	−0.325189
$802$	−0.511095	−0.0180474
$803$	−31.8201	−1.12291
$804$	−16.5102	−0.582269
$805$	77.8576	2.74412
$806$	0.871165	0.0306855
$807$	22.2538	0.783369
$808$	−3.59912	−0.126617
$809$	41.7097	1.46643	0.733217	−	0.679994i	$-0.238018\pi$
$809$	41.7097	1.46643	0.733217	+	0.679994i	$0.238018\pi$
$810$	8.74193	0.307160
$811$	52.7943	1.85386	0.926930	−	0.375234i	$-0.122438\pi$
$811$	52.7943	1.85386	0.926930	+	0.375234i	$0.122438\pi$
$812$	−63.9029	−2.24255
$813$	8.80145	0.308680
$814$	23.5000	0.823675
$815$	−65.8106	−2.30525
$816$	−1.47316	−0.0515708
$817$	27.4054	0.958794
$818$	−39.1832	−1.37001
$819$	4.42610	0.154661
$820$	−95.0980	−3.32097
$821$	−3.40835	−0.118952	−0.0594761	−	0.998230i	$-0.518943\pi$
$821$	−3.40835	−0.118952	−0.0594761	+	0.998230i	$0.518943\pi$
$822$	−28.2319	−0.984699
$823$	53.8325	1.87648	0.938242	−	0.345979i	$-0.112453\pi$
$823$	53.8325	1.87648	0.938242	+	0.345979i	$0.112453\pi$
$824$	−1.16513	−0.0405891
$825$	−37.6682	−1.31144
$826$	−113.777	−3.95882
$827$	12.2317	0.425339	0.212670	−	0.977124i	$-0.431784\pi$
$827$	12.2317	0.425339	0.212670	+	0.977124i	$0.431784\pi$
$828$	−10.9255	−0.379686
$829$	38.7001	1.34411	0.672055	−	0.740501i	$-0.265412\pi$
$829$	38.7001	1.34411	0.672055	+	0.740501i	$0.265412\pi$
$830$	54.2455	1.88289
$831$	9.55548	0.331476
$832$	−11.6111	−0.402544
$833$	7.11035	0.246359
$834$	16.3635	0.566620
$835$	73.2589	2.53523
$836$	28.6484	0.990826
$837$	−0.408569	−0.0141222
$838$	−56.0119	−1.93490
$839$	−41.6061	−1.43640	−0.718200	−	0.695836i	$-0.755034\pi$
$839$	−41.6061	−1.43640	−0.718200	+	0.695836i	$0.755034\pi$
$840$	21.1430	0.729503
$841$	3.14645	0.108498
$842$	−20.2448	−0.697683
$843$	8.61699	0.296785
$844$	19.4368	0.669043
$845$	−4.09989	−0.141040
$846$	−22.3519	−0.768473
$847$	−3.65333	−0.125530
$848$	23.3495	0.801827
$849$	−20.0940	−0.689625
$850$	−14.2201	−0.487745
$851$	−14.8246	−0.508179
$852$	36.8538	1.26259
$853$	−17.1507	−0.587229	−0.293615	−	0.955924i	$-0.594858\pi$
$853$	−17.1507	−0.587229	−0.293615	+	0.955924i	$0.594858\pi$
$854$	10.6750	0.365290
$855$	14.4604	0.494536
$856$	19.0268	0.650322
$857$	31.6005	1.07945	0.539725	−	0.841841i	$-0.318528\pi$
$857$	31.6005	1.07945	0.539725	+	0.841841i	$0.318528\pi$
$858$	6.80133	0.232194
$859$	−30.4802	−1.03997	−0.519986	−	0.854175i	$-0.674063\pi$
$859$	−30.4802	−1.03997	−0.519986	+	0.854175i	$0.674063\pi$
$860$	81.1206	2.76619
$861$	40.3170	1.37400
$862$	20.5771	0.700858
$863$	−49.0199	−1.66866	−0.834328	−	0.551268i	$-0.814144\pi$
$863$	−49.0199	−1.66866	−0.834328	+	0.551268i	$0.814144\pi$
$864$	7.89228	0.268501
$865$	−0.467981	−0.0159118
$866$	−75.4938	−2.56538
$867$	−16.6811	−0.566519
$868$	−4.60489	−0.156300
$869$	28.8869	0.979921
$870$	−49.5649	−1.68041
$871$	−6.48364	−0.219690
$872$	3.66928	0.124258
$873$	−15.1598	−0.513082
$874$	−32.2665	−1.09143
$875$	−123.561	−4.17712
$876$	25.4024	0.858268
$877$	50.1049	1.69192	0.845961	−	0.533245i	$-0.179028\pi$
$877$	50.1049	1.69192	0.845961	+	0.533245i	$0.179028\pi$
$878$	−57.8992	−1.95400
$879$	−8.58420	−0.289538
$880$	−34.1137	−1.14997
$881$	−14.3988	−0.485107	−0.242553	−	0.970138i	$-0.577985\pi$
$881$	−14.3988	−0.485107	−0.242553	+	0.970138i	$0.577985\pi$
$882$	−26.8457	−0.903942
$883$	−39.4229	−1.32669	−0.663343	−	0.748315i	$-0.730863\pi$
$883$	−39.4229	−1.32669	−0.663343	+	0.748315i	$0.730863\pi$
$884$	1.43808	0.0483680
$885$	−49.4277	−1.66150
$886$	−82.8924	−2.78483
$887$	−8.20423	−0.275471	−0.137736	−	0.990469i	$-0.543982\pi$
$887$	−8.20423	−0.275471	−0.137736	+	0.990469i	$0.543982\pi$
$888$	−4.02575	−0.135095
$889$	42.6911	1.43181
$890$	−80.4561	−2.69690
$891$	−3.18976	−0.106861
$892$	−15.3002	−0.512288
$893$	−36.9733	−1.23726
$894$	−3.09945	−0.103661
$895$	−70.3432	−2.35131
$896$	39.7160	1.32682
$897$	−4.29050	−0.143256
$898$	−19.6392	−0.655370
$899$	2.31650	0.0772594
$900$	30.0710	1.00237
$901$	−5.05513	−0.168411
$902$	61.9528	2.06280
$903$	−34.3913	−1.14447
$904$	6.29326	0.209311
$905$	−58.6146	−1.94842
$906$	−3.34100	−0.110997
$907$	54.6292	1.81393	0.906967	−	0.421202i	$-0.138392\pi$
$907$	54.6292	1.81393	0.906967	+	0.421202i	$0.138392\pi$
$908$	53.5078	1.77572
$909$	3.08904	0.102457
$910$	38.6927	1.28265
$911$	−15.7990	−0.523444	−0.261722	−	0.965143i	$-0.584290\pi$
$911$	−15.7990	−0.523444	−0.261722	+	0.965143i	$0.584290\pi$
$912$	9.20041	0.304656
$913$	−19.7932	−0.655058
$914$	−73.0821	−2.41734
$915$	4.63747	0.153310
$916$	−37.6658	−1.24451
$917$	5.70660	0.188449
$918$	−1.20417	−0.0397435
$919$	−26.8064	−0.884262	−0.442131	−	0.896950i	$-0.645777\pi$
$919$	−26.8064	−0.884262	−0.442131	+	0.896950i	$0.645777\pi$
$920$	−20.4952	−0.675708
$921$	10.0774	0.332063
$922$	−72.9209	−2.40152
$923$	14.4727	0.476375
$924$	−35.9511	−1.18271
$925$	40.8028	1.34159
$926$	−0.885381	−0.0290954
$927$	1.00000	0.0328443
$928$	−44.7475	−1.46891
$929$	30.1854	0.990352	0.495176	−	0.868793i	$-0.335103\pi$
$929$	30.1854	0.990352	0.495176	+	0.868793i	$0.335103\pi$
$930$	−3.57168	−0.117120
$931$	−44.4067	−1.45537
$932$	57.1074	1.87061
$933$	−24.0566	−0.787576
$934$	72.9900	2.38831
$935$	7.38553	0.241533
$936$	−1.16513	−0.0380834
$937$	−15.1175	−0.493868	−0.246934	−	0.969032i	$-0.579423\pi$
$937$	−15.1175	−0.493868	−0.246934	+	0.969032i	$0.579423\pi$
$938$	61.1894	1.99791
$939$	26.1431	0.853149
$940$	−109.442	−3.56959
$941$	−7.83194	−0.255314	−0.127657	−	0.991818i	$-0.540746\pi$
$941$	−7.83194	−0.255314	−0.127657	+	0.991818i	$0.540746\pi$
$942$	−48.4251	−1.57777
$943$	−39.0818	−1.27268
$944$	−31.4483	−1.02355
$945$	−18.1465	−0.590307
$946$	−52.8471	−1.71821
$947$	39.7497	1.29169	0.645846	−	0.763468i	$-0.276505\pi$
$947$	39.7497	1.29169	0.645846	+	0.763468i	$0.276505\pi$
$948$	−23.0608	−0.748981
$949$	9.97568	0.323824
$950$	88.8098	2.88137
$951$	−14.8853	−0.482688
$952$	−2.91237	−0.0943904
$953$	−18.2167	−0.590095	−0.295048	−	0.955483i	$-0.595336\pi$
$953$	−18.2167	−0.590095	−0.295048	+	0.955483i	$0.595336\pi$
$954$	19.0860	0.617934
$955$	−91.4075	−2.95788
$956$	21.8000	0.705062
$957$	18.0853	0.584614
$958$	6.46266	0.208799
$959$	58.6038	1.89241
$960$	47.6043	1.53642
$961$	−30.8331	−0.994615
$962$	−7.36732	−0.237532
$963$	−16.3302	−0.526234
$964$	64.8859	2.08984
$965$	91.1760	2.93506
$966$	40.4916	1.30280
$967$	−7.36461	−0.236830	−0.118415	−	0.992964i	$-0.537781\pi$
$967$	−7.36461	−0.236830	−0.118415	+	0.992964i	$0.537781\pi$
$968$	0.961702	0.0309103
$969$	−1.99187	−0.0639881
$970$	−132.526	−4.25515
$971$	−30.5106	−0.979133	−0.489566	−	0.871966i	$-0.662845\pi$
$971$	−30.5106	−0.979133	−0.489566	+	0.871966i	$0.662845\pi$
$972$	2.54643	0.0816769
$973$	−33.9673	−1.08894
$974$	−61.3123	−1.96457
$975$	11.8091	0.378193
$976$	2.95058	0.0944458
$977$	−40.7260	−1.30294	−0.651470	−	0.758675i	$-0.725847\pi$
$977$	−40.7260	−1.30294	−0.651470	+	0.758675i	$0.725847\pi$
$978$	−34.2263	−1.09444
$979$	29.3569	0.938251
$980$	−131.445	−4.19885
$981$	−3.14926	−0.100548
$982$	18.3572	0.585803
$983$	52.9674	1.68940	0.844699	−	0.535241i	$-0.179779\pi$
$983$	52.9674	1.68940	0.844699	+	0.535241i	$0.179779\pi$
$984$	−10.6130	−0.338332
$985$	−43.5983	−1.38916
$986$	6.82737	0.217428
$987$	46.3981	1.47687
$988$	−8.98136	−0.285735
$989$	33.3376	1.06007
$990$	−27.8847	−0.886234
$991$	5.40069	0.171559	0.0857793	−	0.996314i	$-0.472662\pi$
$991$	5.40069	0.171559	0.0857793	+	0.996314i	$0.472662\pi$
$992$	−3.22454	−0.102379
$993$	4.87697	0.154766
$994$	−136.586	−4.33225
$995$	−30.7508	−0.974866
$996$	15.8012	0.500679
$997$	6.01531	0.190507	0.0952533	−	0.995453i	$-0.469634\pi$
$997$	6.01531	0.190507	0.0952533	+	0.995453i	$0.469634\pi$
$998$	18.1318	0.573954
$999$	3.45521	0.109318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.k.1.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.k.1.6	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.13224 q^{2} +1.00000 q^{3} +2.54643 q^{4} -4.09989 q^{5} -2.13224 q^{6} +4.42610 q^{7} -1.16513 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.13224 q^{2} +1.00000 q^{3} +2.54643 q^{4} -4.09989 q^{5} -2.13224 q^{6} +4.42610 q^{7} -1.16513 q^{8} +1.00000 q^{9} +8.74193 q^{10} -3.18976 q^{11} +2.54643 q^{12} +1.00000 q^{13} -9.43750 q^{14} -4.09989 q^{15} -2.60854 q^{16} +0.564744 q^{17} -2.13224 q^{18} -3.52703 q^{19} -10.4401 q^{20} +4.42610 q^{21} +6.80133 q^{22} -4.29050 q^{23} -1.16513 q^{24} +11.8091 q^{25} -2.13224 q^{26} +1.00000 q^{27} +11.2708 q^{28} -5.66978 q^{29} +8.74193 q^{30} -0.408569 q^{31} +7.89228 q^{32} -3.18976 q^{33} -1.20417 q^{34} -18.1465 q^{35} +2.54643 q^{36} +3.45521 q^{37} +7.52047 q^{38} +1.00000 q^{39} +4.77689 q^{40} +9.10892 q^{41} -9.43750 q^{42} -7.77010 q^{43} -8.12252 q^{44} -4.09989 q^{45} +9.14836 q^{46} +10.4828 q^{47} -2.60854 q^{48} +12.5904 q^{49} -25.1797 q^{50} +0.564744 q^{51} +2.54643 q^{52} -8.95119 q^{53} -2.13224 q^{54} +13.0777 q^{55} -5.15697 q^{56} -3.52703 q^{57} +12.0893 q^{58} +12.0559 q^{59} -10.4401 q^{60} -1.13112 q^{61} +0.871165 q^{62} +4.42610 q^{63} -11.6111 q^{64} -4.09989 q^{65} +6.80133 q^{66} -6.48364 q^{67} +1.43808 q^{68} -4.29050 q^{69} +38.6927 q^{70} +14.4727 q^{71} -1.16513 q^{72} +9.97568 q^{73} -7.36732 q^{74} +11.8091 q^{75} -8.98136 q^{76} -14.1182 q^{77} -2.13224 q^{78} -9.05613 q^{79} +10.6947 q^{80} +1.00000 q^{81} -19.4224 q^{82} +6.20521 q^{83} +11.2708 q^{84} -2.31539 q^{85} +16.5677 q^{86} -5.66978 q^{87} +3.71648 q^{88} -9.20347 q^{89} +8.74193 q^{90} +4.42610 q^{91} -10.9255 q^{92} -0.408569 q^{93} -22.3519 q^{94} +14.4604 q^{95} +7.89228 q^{96} -15.1598 q^{97} -26.8457 q^{98} -3.18976 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

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