LMFDB - Embedded newform 6002.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.00129 q^{3} +1.00000 q^{4} -0.204934 q^{5} +3.00129 q^{6} -4.79366 q^{7} -1.00000 q^{8} +6.00776 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.00129 q^{3} +1.00000 q^{4} -0.204934 q^{5} +3.00129 q^{6} -4.79366 q^{7} -1.00000 q^{8} +6.00776 q^{9} +0.204934 q^{10} +0.396567 q^{11} -3.00129 q^{12} +6.44086 q^{13} +4.79366 q^{14} +0.615066 q^{15} +1.00000 q^{16} -5.08335 q^{17} -6.00776 q^{18} -1.26261 q^{19} -0.204934 q^{20} +14.3872 q^{21} -0.396567 q^{22} +0.525700 q^{23} +3.00129 q^{24} -4.95800 q^{25} -6.44086 q^{26} -9.02716 q^{27} -4.79366 q^{28} +1.64190 q^{29} -0.615066 q^{30} +0.301674 q^{31} -1.00000 q^{32} -1.19021 q^{33} +5.08335 q^{34} +0.982381 q^{35} +6.00776 q^{36} -10.4971 q^{37} +1.26261 q^{38} -19.3309 q^{39} +0.204934 q^{40} +4.54633 q^{41} -14.3872 q^{42} -2.30467 q^{43} +0.396567 q^{44} -1.23119 q^{45} -0.525700 q^{46} -1.79773 q^{47} -3.00129 q^{48} +15.9791 q^{49} +4.95800 q^{50} +15.2566 q^{51} +6.44086 q^{52} +0.0596552 q^{53} +9.02716 q^{54} -0.0812698 q^{55} +4.79366 q^{56} +3.78947 q^{57} -1.64190 q^{58} -13.2130 q^{59} +0.615066 q^{60} +12.3951 q^{61} -0.301674 q^{62} -28.7991 q^{63} +1.00000 q^{64} -1.31995 q^{65} +1.19021 q^{66} +2.92226 q^{67} -5.08335 q^{68} -1.57778 q^{69} -0.982381 q^{70} +3.98855 q^{71} -6.00776 q^{72} -6.80739 q^{73} +10.4971 q^{74} +14.8804 q^{75} -1.26261 q^{76} -1.90100 q^{77} +19.3309 q^{78} +10.2093 q^{79} -0.204934 q^{80} +9.06988 q^{81} -4.54633 q^{82} +9.28605 q^{83} +14.3872 q^{84} +1.04175 q^{85} +2.30467 q^{86} -4.92783 q^{87} -0.396567 q^{88} +13.5837 q^{89} +1.23119 q^{90} -30.8752 q^{91} +0.525700 q^{92} -0.905412 q^{93} +1.79773 q^{94} +0.258752 q^{95} +3.00129 q^{96} +5.27392 q^{97} -15.9791 q^{98} +2.38248 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) $ 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.00129	−1.73280	−0.866399	−	0.499353i	$-0.833571\pi$
$3$	−3.00129	−1.73280	−0.866399	+	0.499353i	$0.833571\pi$
$4$	1.00000	0.500000
$5$	−0.204934	−0.0916491	−0.0458245	−	0.998950i	$-0.514592\pi$
$5$	−0.204934	−0.0916491	−0.0458245	+	0.998950i	$0.514592\pi$
$6$	3.00129	1.22527
$7$	−4.79366	−1.81183	−0.905916	−	0.423458i	$-0.860816\pi$
$7$	−4.79366	−1.81183	−0.905916	+	0.423458i	$0.860816\pi$
$8$	−1.00000	−0.353553
$9$	6.00776	2.00259
$10$	0.204934	0.0648057
$11$	0.396567	0.119569	0.0597847	−	0.998211i	$-0.480959\pi$
$11$	0.396567	0.119569	0.0597847	+	0.998211i	$0.480959\pi$
$12$	−3.00129	−0.866399
$13$	6.44086	1.78637	0.893186	−	0.449687i	$-0.148465\pi$
$13$	6.44086	1.78637	0.893186	+	0.449687i	$0.148465\pi$
$14$	4.79366	1.28116
$15$	0.615066	0.158809
$16$	1.00000	0.250000
$17$	−5.08335	−1.23289	−0.616446	−	0.787397i	$-0.711428\pi$
$17$	−5.08335	−1.23289	−0.616446	+	0.787397i	$0.711428\pi$
$18$	−6.00776	−1.41604
$19$	−1.26261	−0.289663	−0.144832	−	0.989456i	$-0.546264\pi$
$19$	−1.26261	−0.289663	−0.144832	+	0.989456i	$0.546264\pi$
$20$	−0.204934	−0.0458245
$21$	14.3872	3.13954
$22$	−0.396567	−0.0845483
$23$	0.525700	0.109616	0.0548081	−	0.998497i	$-0.482545\pi$
$23$	0.525700	0.109616	0.0548081	+	0.998497i	$0.482545\pi$
$24$	3.00129	0.612636
$25$	−4.95800	−0.991600
$26$	−6.44086	−1.26316
$27$	−9.02716	−1.73728
$28$	−4.79366	−0.905916
$29$	1.64190	0.304893	0.152447	−	0.988312i	$-0.451285\pi$
$29$	1.64190	0.304893	0.152447	+	0.988312i	$0.451285\pi$
$30$	−0.615066	−0.112295
$31$	0.301674	0.0541823	0.0270911	−	0.999633i	$-0.491376\pi$
$31$	0.301674	0.0541823	0.0270911	+	0.999633i	$0.491376\pi$
$32$	−1.00000	−0.176777
$33$	−1.19021	−0.207189
$34$	5.08335	0.871787
$35$	0.982381	0.166053
$36$	6.00776	1.00129
$37$	−10.4971	−1.72572	−0.862858	−	0.505447i	$-0.831328\pi$
$37$	−10.4971	−1.72572	−0.862858	+	0.505447i	$0.831328\pi$
$38$	1.26261	0.204823
$39$	−19.3309	−3.09542
$40$	0.204934	0.0324028
$41$	4.54633	0.710017	0.355008	−	0.934863i	$-0.384478\pi$
$41$	4.54633	0.710017	0.355008	+	0.934863i	$0.384478\pi$
$42$	−14.3872	−2.21999
$43$	−2.30467	−0.351459	−0.175730	−	0.984438i	$-0.556228\pi$
$43$	−2.30467	−0.351459	−0.175730	+	0.984438i	$0.556228\pi$
$44$	0.396567	0.0597847
$45$	−1.23119	−0.183535
$46$	−0.525700	−0.0775103
$47$	−1.79773	−0.262227	−0.131113	−	0.991367i	$-0.541855\pi$
$47$	−1.79773	−0.262227	−0.131113	+	0.991367i	$0.541855\pi$
$48$	−3.00129	−0.433199
$49$	15.9791	2.28273
$50$	4.95800	0.701167
$51$	15.2566	2.13635
$52$	6.44086	0.893186
$53$	0.0596552	0.00819428	0.00409714	−	0.999992i	$-0.498696\pi$
$53$	0.0596552	0.00819428	0.00409714	+	0.999992i	$0.498696\pi$
$54$	9.02716	1.22844
$55$	−0.0812698	−0.0109584
$56$	4.79366	0.640579
$57$	3.78947	0.501927
$58$	−1.64190	−0.215592
$59$	−13.2130	−1.72019	−0.860096	−	0.510133i	$-0.829596\pi$
$59$	−13.2130	−1.72019	−0.860096	+	0.510133i	$0.829596\pi$
$60$	0.615066	0.0794046
$61$	12.3951	1.58702	0.793512	−	0.608555i	$-0.208250\pi$
$61$	12.3951	1.58702	0.793512	+	0.608555i	$0.208250\pi$
$62$	−0.301674	−0.0383127
$63$	−28.7991	−3.62835
$64$	1.00000	0.125000
$65$	−1.31995	−0.163719
$66$	1.19021	0.146505
$67$	2.92226	0.357011	0.178505	−	0.983939i	$-0.442874\pi$
$67$	2.92226	0.357011	0.178505	+	0.983939i	$0.442874\pi$
$68$	−5.08335	−0.616446
$69$	−1.57778	−0.189943
$70$	−0.982381	−0.117417
$71$	3.98855	0.473354	0.236677	−	0.971588i	$-0.423942\pi$
$71$	3.98855	0.473354	0.236677	+	0.971588i	$0.423942\pi$
$72$	−6.00776	−0.708021
$73$	−6.80739	−0.796745	−0.398372	−	0.917224i	$-0.630425\pi$
$73$	−6.80739	−0.796745	−0.398372	+	0.917224i	$0.630425\pi$
$74$	10.4971	1.22027
$75$	14.8804	1.71824
$76$	−1.26261	−0.144832
$77$	−1.90100	−0.216639
$78$	19.3309	2.18879
$79$	10.2093	1.14864	0.574318	−	0.818632i	$-0.305267\pi$
$79$	10.2093	1.14864	0.574318	+	0.818632i	$0.305267\pi$
$80$	−0.204934	−0.0229123
$81$	9.06988	1.00776
$82$	−4.54633	−0.502058
$83$	9.28605	1.01928	0.509638	−	0.860389i	$-0.329779\pi$
$83$	9.28605	1.01928	0.509638	+	0.860389i	$0.329779\pi$
$84$	14.3872	1.56977
$85$	1.04175	0.112993
$86$	2.30467	0.248519
$87$	−4.92783	−0.528318
$88$	−0.396567	−0.0422741
$89$	13.5837	1.43987	0.719933	−	0.694044i	$-0.244172\pi$
$89$	13.5837	1.43987	0.719933	+	0.694044i	$0.244172\pi$
$90$	1.23119	0.129779
$91$	−30.8752	−3.23660
$92$	0.525700	0.0548081
$93$	−0.905412	−0.0938869
$94$	1.79773	0.185422
$95$	0.258752	0.0265474
$96$	3.00129	0.306318
$97$	5.27392	0.535486	0.267743	−	0.963490i	$-0.413722\pi$
$97$	5.27392	0.535486	0.267743	+	0.963490i	$0.413722\pi$
$98$	−15.9791	−1.61414
$99$	2.38248	0.239448
$100$	−4.95800	−0.495800
$101$	0.694824	0.0691376	0.0345688	−	0.999402i	$-0.488994\pi$
$101$	0.694824	0.0691376	0.0345688	+	0.999402i	$0.488994\pi$
$102$	−15.2566	−1.51063
$103$	11.7870	1.16141	0.580704	−	0.814115i	$-0.302777\pi$
$103$	11.7870	1.16141	0.580704	+	0.814115i	$0.302777\pi$
$104$	−6.44086	−0.631578
$105$	−2.94841	−0.287736
$106$	−0.0596552	−0.00579423
$107$	16.7976	1.62389	0.811945	−	0.583735i	$-0.198409\pi$
$107$	16.7976	1.62389	0.811945	+	0.583735i	$0.198409\pi$
$108$	−9.02716	−0.868639
$109$	5.63077	0.539330	0.269665	−	0.962954i	$-0.413087\pi$
$109$	5.63077	0.539330	0.269665	+	0.962954i	$0.413087\pi$
$110$	0.0812698	0.00774877
$111$	31.5049	2.99032
$112$	−4.79366	−0.452958
$113$	19.0209	1.78934	0.894669	−	0.446730i	$-0.147412\pi$
$113$	19.0209	1.78934	0.894669	+	0.446730i	$0.147412\pi$
$114$	−3.78947	−0.354916
$115$	−0.107734	−0.0100462
$116$	1.64190	0.152447
$117$	38.6951	3.57736
$118$	13.2130	1.21636
$119$	24.3678	2.23379
$120$	−0.615066	−0.0561476
$121$	−10.8427	−0.985703
$122$	−12.3951	−1.12220
$123$	−13.6449	−1.23032
$124$	0.301674	0.0270911
$125$	2.04073	0.182528
$126$	28.7991	2.56563
$127$	−15.9183	−1.41252	−0.706260	−	0.707953i	$-0.749619\pi$
$127$	−15.9183	−1.41252	−0.706260	+	0.707953i	$0.749619\pi$
$128$	−1.00000	−0.0883883
$129$	6.91700	0.609008
$130$	1.31995	0.115767
$131$	−18.2329	−1.59301	−0.796506	−	0.604630i	$-0.793321\pi$
$131$	−18.2329	−1.59301	−0.796506	+	0.604630i	$0.793321\pi$
$132$	−1.19021	−0.103595
$133$	6.05253	0.524821
$134$	−2.92226	−0.252445
$135$	1.84997	0.159220
$136$	5.08335	0.435893
$137$	9.70397	0.829066	0.414533	−	0.910034i	$-0.363945\pi$
$137$	9.70397	0.829066	0.414533	+	0.910034i	$0.363945\pi$
$138$	1.57778	0.134310
$139$	5.44265	0.461640	0.230820	−	0.972996i	$-0.425859\pi$
$139$	5.44265	0.461640	0.230820	+	0.972996i	$0.425859\pi$
$140$	0.982381	0.0830263
$141$	5.39553	0.454385
$142$	−3.98855	−0.334712
$143$	2.55423	0.213595
$144$	6.00776	0.500646
$145$	−0.336481	−0.0279432
$146$	6.80739	0.563384
$147$	−47.9580	−3.95551
$148$	−10.4971	−0.862858
$149$	−1.61084	−0.131965	−0.0659825	−	0.997821i	$-0.521018\pi$
$149$	−1.61084	−0.131965	−0.0659825	+	0.997821i	$0.521018\pi$
$150$	−14.8804	−1.21498
$151$	−6.88855	−0.560582	−0.280291	−	0.959915i	$-0.590431\pi$
$151$	−6.88855	−0.560582	−0.280291	+	0.959915i	$0.590431\pi$
$152$	1.26261	0.102411
$153$	−30.5395	−2.46897
$154$	1.90100	0.153187
$155$	−0.0618231	−0.00496575
$156$	−19.3309	−1.54771
$157$	−19.8048	−1.58059	−0.790296	−	0.612725i	$-0.790073\pi$
$157$	−19.8048	−1.58059	−0.790296	+	0.612725i	$0.790073\pi$
$158$	−10.2093	−0.812209
$159$	−0.179043	−0.0141990
$160$	0.204934	0.0162014
$161$	−2.52003	−0.198606
$162$	−9.06988	−0.712597
$163$	−8.50049	−0.665810	−0.332905	−	0.942960i	$-0.608029\pi$
$163$	−8.50049	−0.665810	−0.332905	+	0.942960i	$0.608029\pi$
$164$	4.54633	0.355008
$165$	0.243914	0.0189887
$166$	−9.28605	−0.720738
$167$	−18.6389	−1.44232	−0.721161	−	0.692768i	$-0.756391\pi$
$167$	−18.6389	−1.44232	−0.721161	+	0.692768i	$0.756391\pi$
$168$	−14.3872	−1.10999
$169$	28.4846	2.19112
$170$	−1.04175	−0.0798984
$171$	−7.58547	−0.580075
$172$	−2.30467	−0.175730
$173$	16.0401	1.21951	0.609753	−	0.792591i	$-0.291269\pi$
$173$	16.0401	1.21951	0.609753	+	0.792591i	$0.291269\pi$
$174$	4.92783	0.373578
$175$	23.7670	1.79661
$176$	0.396567	0.0298923
$177$	39.6562	2.98074
$178$	−13.5837	−1.01814
$179$	−2.49688	−0.186625	−0.0933127	−	0.995637i	$-0.529746\pi$
$179$	−2.49688	−0.186625	−0.0933127	+	0.995637i	$0.529746\pi$
$180$	−1.23119	−0.0917676
$181$	−5.90552	−0.438954	−0.219477	−	0.975618i	$-0.570435\pi$
$181$	−5.90552	−0.438954	−0.219477	+	0.975618i	$0.570435\pi$
$182$	30.8752	2.28863
$183$	−37.2012	−2.74999
$184$	−0.525700	−0.0387552
$185$	2.15121	0.158160
$186$	0.905412	0.0663881
$187$	−2.01589	−0.147416
$188$	−1.79773	−0.131113
$189$	43.2731	3.14765
$190$	−0.258752	−0.0187718
$191$	−9.53565	−0.689975	−0.344988	−	0.938607i	$-0.612117\pi$
$191$	−9.53565	−0.689975	−0.344988	+	0.938607i	$0.612117\pi$
$192$	−3.00129	−0.216600
$193$	19.9539	1.43631	0.718156	−	0.695883i	$-0.244987\pi$
$193$	19.9539	1.43631	0.718156	+	0.695883i	$0.244987\pi$
$194$	−5.27392	−0.378646
$195$	3.96155	0.283692
$196$	15.9791	1.14137
$197$	−6.41647	−0.457155	−0.228577	−	0.973526i	$-0.573407\pi$
$197$	−6.41647	−0.457155	−0.228577	+	0.973526i	$0.573407\pi$
$198$	−2.38248	−0.169315
$199$	8.40475	0.595797	0.297898	−	0.954598i	$-0.403714\pi$
$199$	8.40475	0.595797	0.297898	+	0.954598i	$0.403714\pi$
$200$	4.95800	0.350584
$201$	−8.77055	−0.618627
$202$	−0.694824	−0.0488877
$203$	−7.87071	−0.552415
$204$	15.2566	1.06818
$205$	−0.931695	−0.0650724
$206$	−11.7870	−0.821240
$207$	3.15828	0.219516
$208$	6.44086	0.446593
$209$	−0.500710	−0.0346348
$210$	2.94841	0.203460
$211$	11.4478	0.788101	0.394051	−	0.919089i	$-0.371073\pi$
$211$	11.4478	0.788101	0.394051	+	0.919089i	$0.371073\pi$
$212$	0.0596552	0.00409714
$213$	−11.9708	−0.820227
$214$	−16.7976	−1.14826
$215$	0.472305	0.0322109
$216$	9.02716	0.614221
$217$	−1.44612	−0.0981691
$218$	−5.63077	−0.381364
$219$	20.4310	1.38060
$220$	−0.0812698	−0.00547921
$221$	−32.7411	−2.20240
$222$	−31.5049	−2.11447
$223$	5.32609	0.356662	0.178331	−	0.983971i	$-0.442930\pi$
$223$	5.32609	0.356662	0.178331	+	0.983971i	$0.442930\pi$
$224$	4.79366	0.320290
$225$	−29.7865	−1.98577
$226$	−19.0209	−1.26525
$227$	−23.3986	−1.55302	−0.776510	−	0.630105i	$-0.783012\pi$
$227$	−23.3986	−1.55302	−0.776510	+	0.630105i	$0.783012\pi$
$228$	3.78947	0.250964
$229$	−6.45479	−0.426544	−0.213272	−	0.976993i	$-0.568412\pi$
$229$	−6.45479	−0.426544	−0.213272	+	0.976993i	$0.568412\pi$
$230$	0.107734	0.00710375
$231$	5.70547	0.375392
$232$	−1.64190	−0.107796
$233$	20.3881	1.33567	0.667836	−	0.744309i	$-0.267221\pi$
$233$	20.3881	1.33567	0.667836	+	0.744309i	$0.267221\pi$
$234$	−38.6951	−2.52958
$235$	0.368416	0.0240328
$236$	−13.2130	−0.860096
$237$	−30.6411	−1.99035
$238$	−24.3678	−1.57953
$239$	10.6977	0.691975	0.345987	−	0.938239i	$-0.387544\pi$
$239$	10.6977	0.691975	0.345987	+	0.938239i	$0.387544\pi$
$240$	0.615066	0.0397023
$241$	13.2150	0.851253	0.425626	−	0.904899i	$-0.360054\pi$
$241$	13.2150	0.851253	0.425626	+	0.904899i	$0.360054\pi$
$242$	10.8427	0.696997
$243$	−0.139879	−0.00897324
$244$	12.3951	0.793512
$245$	−3.27466	−0.209210
$246$	13.6449	0.869964
$247$	−8.13230	−0.517446
$248$	−0.301674	−0.0191563
$249$	−27.8702	−1.76620
$250$	−2.04073	−0.129067
$251$	8.17495	0.515998	0.257999	−	0.966145i	$-0.416937\pi$
$251$	8.17495	0.515998	0.257999	+	0.966145i	$0.416937\pi$
$252$	−28.7991	−1.81417
$253$	0.208475	0.0131067
$254$	15.9183	0.998802
$255$	−3.12659	−0.195795
$256$	1.00000	0.0625000
$257$	−3.71888	−0.231977	−0.115989	−	0.993251i	$-0.537004\pi$
$257$	−3.71888	−0.231977	−0.115989	+	0.993251i	$0.537004\pi$
$258$	−6.91700	−0.430634
$259$	50.3196	3.12671
$260$	−1.31995	−0.0818597
$261$	9.86415	0.610575
$262$	18.2329	1.12643
$263$	−5.97313	−0.368319	−0.184160	−	0.982896i	$-0.558956\pi$
$263$	−5.97313	−0.368319	−0.184160	+	0.982896i	$0.558956\pi$
$264$	1.19021	0.0732525
$265$	−0.0122254	−0.000750998 0
$266$	−6.05253	−0.371104
$267$	−40.7686	−2.49500
$268$	2.92226	0.178505
$269$	28.5177	1.73875	0.869377	−	0.494149i	$-0.164520\pi$
$269$	28.5177	1.73875	0.869377	+	0.494149i	$0.164520\pi$
$270$	−1.84997	−0.112585
$271$	13.3117	0.808628	0.404314	−	0.914620i	$-0.367510\pi$
$271$	13.3117	0.808628	0.404314	+	0.914620i	$0.367510\pi$
$272$	−5.08335	−0.308223
$273$	92.6656	5.60838
$274$	−9.70397	−0.586238
$275$	−1.96618	−0.118565
$276$	−1.57778	−0.0949713
$277$	3.58447	0.215370	0.107685	−	0.994185i	$-0.465656\pi$
$277$	3.58447	0.215370	0.107685	+	0.994185i	$0.465656\pi$
$278$	−5.44265	−0.326429
$279$	1.81238	0.108505
$280$	−0.982381	−0.0587085
$281$	−12.9974	−0.775362	−0.387681	−	0.921794i	$-0.626724\pi$
$281$	−12.9974	−0.775362	−0.387681	+	0.921794i	$0.626724\pi$
$282$	−5.39553	−0.321299
$283$	−13.5719	−0.806768	−0.403384	−	0.915031i	$-0.632166\pi$
$283$	−13.5719	−0.806768	−0.403384	+	0.915031i	$0.632166\pi$
$284$	3.98855	0.236677
$285$	−0.776589	−0.0460012
$286$	−2.55423	−0.151035
$287$	−21.7935	−1.28643
$288$	−6.00776	−0.354011
$289$	8.84041	0.520024
$290$	0.336481	0.0197588
$291$	−15.8286	−0.927888
$292$	−6.80739	−0.398372
$293$	−9.01018	−0.526380	−0.263190	−	0.964744i	$-0.584775\pi$
$293$	−9.01018	−0.526380	−0.263190	+	0.964744i	$0.584775\pi$
$294$	47.9580	2.79697
$295$	2.70780	0.157654
$296$	10.4971	0.610133
$297$	−3.57987	−0.207725
$298$	1.61084	0.0933134
$299$	3.38596	0.195815
$300$	14.8804	0.859121
$301$	11.0478	0.636785
$302$	6.88855	0.396392
$303$	−2.08537	−0.119801
$304$	−1.26261	−0.0724158
$305$	−2.54016	−0.145449
$306$	30.5395	1.74583
$307$	−16.3584	−0.933622	−0.466811	−	0.884357i	$-0.654597\pi$
$307$	−16.3584	−0.933622	−0.466811	+	0.884357i	$0.654597\pi$
$308$	−1.90100	−0.108320
$309$	−35.3763	−2.01248
$310$	0.0618231	0.00351132
$311$	−3.38771	−0.192099	−0.0960497	−	0.995377i	$-0.530621\pi$
$311$	−3.38771	−0.192099	−0.0960497	+	0.995377i	$0.530621\pi$
$312$	19.3309	1.09440
$313$	−18.2529	−1.03172	−0.515858	−	0.856674i	$-0.672527\pi$
$313$	−18.2529	−1.03172	−0.515858	+	0.856674i	$0.672527\pi$
$314$	19.8048	1.11765
$315$	5.90191	0.332535
$316$	10.2093	0.574318
$317$	28.2213	1.58506	0.792532	−	0.609830i	$-0.208762\pi$
$317$	28.2213	1.58506	0.792532	+	0.609830i	$0.208762\pi$
$318$	0.179043	0.0100402
$319$	0.651123	0.0364559
$320$	−0.204934	−0.0114561
$321$	−50.4146	−2.81387
$322$	2.52003	0.140436
$323$	6.41829	0.357123
$324$	9.06988	0.503882
$325$	−31.9338	−1.77137
$326$	8.50049	0.470799
$327$	−16.8996	−0.934550
$328$	−4.54633	−0.251029
$329$	8.61772	0.475110
$330$	−0.243914	−0.0134270
$331$	13.8786	0.762835	0.381417	−	0.924403i	$-0.375436\pi$
$331$	13.8786	0.762835	0.381417	+	0.924403i	$0.375436\pi$
$332$	9.28605	0.509638
$333$	−63.0641	−3.45589
$334$	18.6389	1.01988
$335$	−0.598869	−0.0327197
$336$	14.3872	0.784884
$337$	−3.16150	−0.172218	−0.0861088	−	0.996286i	$-0.527443\pi$
$337$	−3.16150	−0.172218	−0.0861088	+	0.996286i	$0.527443\pi$
$338$	−28.4846	−1.54936
$339$	−57.0873	−3.10056
$340$	1.04175	0.0564967
$341$	0.119634	0.00647854
$342$	7.58547	0.410175
$343$	−43.0429	−2.32410
$344$	2.30467	0.124260
$345$	0.323340	0.0174081
$346$	−16.0401	−0.862321
$347$	−17.6960	−0.949969	−0.474985	−	0.879994i	$-0.657546\pi$
$347$	−17.6960	−0.949969	−0.474985	+	0.879994i	$0.657546\pi$
$348$	−4.92783	−0.264159
$349$	−25.3453	−1.35670	−0.678352	−	0.734737i	$-0.737306\pi$
$349$	−25.3453	−1.35670	−0.678352	+	0.734737i	$0.737306\pi$
$350$	−23.7670	−1.27040
$351$	−58.1426	−3.10342
$352$	−0.396567	−0.0211371
$353$	20.2664	1.07867	0.539335	−	0.842091i	$-0.318676\pi$
$353$	20.2664	1.07867	0.539335	+	0.842091i	$0.318676\pi$
$354$	−39.6562	−2.10770
$355$	−0.817389	−0.0433825
$356$	13.5837	0.719933
$357$	−73.1349	−3.87071
$358$	2.49688	0.131964
$359$	−0.839992	−0.0443331	−0.0221665	−	0.999754i	$-0.507056\pi$
$359$	−0.839992	−0.0443331	−0.0221665	+	0.999754i	$0.507056\pi$
$360$	1.23119	0.0648895
$361$	−17.4058	−0.916095
$362$	5.90552	0.310387
$363$	32.5422	1.70802
$364$	−30.8752	−1.61830
$365$	1.39506	0.0730209
$366$	37.2012	1.94454
$367$	−8.92375	−0.465816	−0.232908	−	0.972499i	$-0.574824\pi$
$367$	−8.92375	−0.465816	−0.232908	+	0.972499i	$0.574824\pi$
$368$	0.525700	0.0274040
$369$	27.3132	1.42187
$370$	−2.15121	−0.111836
$371$	−0.285967	−0.0148466
$372$	−0.905412	−0.0469434
$373$	1.84070	0.0953079	0.0476539	−	0.998864i	$-0.484826\pi$
$373$	1.84070	0.0953079	0.0476539	+	0.998864i	$0.484826\pi$
$374$	2.01589	0.104239
$375$	−6.12482	−0.316285
$376$	1.79773	0.0927111
$377$	10.5753	0.544653
$378$	−43.2731	−2.22573
$379$	28.6685	1.47260	0.736301	−	0.676654i	$-0.236571\pi$
$379$	28.6685	1.47260	0.736301	+	0.676654i	$0.236571\pi$
$380$	0.258752	0.0132737
$381$	47.7754	2.44761
$382$	9.53565	0.487886
$383$	0.942020	0.0481350	0.0240675	−	0.999710i	$-0.492338\pi$
$383$	0.942020	0.0481350	0.0240675	+	0.999710i	$0.492338\pi$
$384$	3.00129	0.153159
$385$	0.389579	0.0198548
$386$	−19.9539	−1.01563
$387$	−13.8459	−0.703828
$388$	5.27392	0.267743
$389$	−27.6069	−1.39973	−0.699864	−	0.714277i	$-0.746756\pi$
$389$	−27.6069	−1.39973	−0.699864	+	0.714277i	$0.746756\pi$
$390$	−3.96155	−0.200601
$391$	−2.67232	−0.135145
$392$	−15.9791	−0.807068
$393$	54.7222	2.76037
$394$	6.41647	0.323257
$395$	−2.09223	−0.105272
$396$	2.38248	0.119724
$397$	3.50554	0.175938	0.0879691	−	0.996123i	$-0.471962\pi$
$397$	3.50554	0.175938	0.0879691	+	0.996123i	$0.471962\pi$
$398$	−8.40475	−0.421292
$399$	−18.1654	−0.909408
$400$	−4.95800	−0.247900
$401$	−2.87844	−0.143742	−0.0718712	−	0.997414i	$-0.522897\pi$
$401$	−2.87844	−0.143742	−0.0718712	+	0.997414i	$0.522897\pi$
$402$	8.77055	0.437435
$403$	1.94304	0.0967897
$404$	0.694824	0.0345688
$405$	−1.85872	−0.0923607
$406$	7.87071	0.390617
$407$	−4.16281	−0.206343
$408$	−15.2566	−0.755315
$409$	2.40053	0.118699	0.0593493	−	0.998237i	$-0.481097\pi$
$409$	2.40053	0.118699	0.0593493	+	0.998237i	$0.481097\pi$
$410$	0.931695	0.0460131
$411$	−29.1245	−1.43660
$412$	11.7870	0.580704
$413$	63.3388	3.11670
$414$	−3.15828	−0.155221
$415$	−1.90302	−0.0934158
$416$	−6.44086	−0.315789
$417$	−16.3350	−0.799928
$418$	0.500710	0.0244905
$419$	−33.9798	−1.66002	−0.830012	−	0.557745i	$-0.811667\pi$
$419$	−33.9798	−1.66002	−0.830012	+	0.557745i	$0.811667\pi$
$420$	−2.94841	−0.143868
$421$	22.0073	1.07257	0.536284	−	0.844037i	$-0.319827\pi$
$421$	22.0073	1.07257	0.536284	+	0.844037i	$0.319827\pi$
$422$	−11.4478	−0.557272
$423$	−10.8004	−0.525131
$424$	−0.0596552	−0.00289711
$425$	25.2032	1.22254
$426$	11.9708	0.579988
$427$	−59.4176	−2.87542
$428$	16.7976	0.811945
$429$	−7.66599	−0.370117
$430$	−0.472305	−0.0227766
$431$	20.5352	0.989146	0.494573	−	0.869136i	$-0.335324\pi$
$431$	20.5352	0.989146	0.494573	+	0.869136i	$0.335324\pi$
$432$	−9.02716	−0.434319
$433$	−25.4294	−1.22206	−0.611030	−	0.791607i	$-0.709245\pi$
$433$	−25.4294	−1.22206	−0.611030	+	0.791607i	$0.709245\pi$
$434$	1.44612	0.0694161
$435$	1.00988	0.0484199
$436$	5.63077	0.269665
$437$	−0.663756	−0.0317517
$438$	−20.4310	−0.976229
$439$	−28.2533	−1.34846	−0.674228	−	0.738523i	$-0.735524\pi$
$439$	−28.2533	−1.34846	−0.674228	+	0.738523i	$0.735524\pi$
$440$	0.0812698	0.00387439
$441$	95.9987	4.57137
$442$	32.7411	1.55734
$443$	−20.3899	−0.968754	−0.484377	−	0.874859i	$-0.660954\pi$
$443$	−20.3899	−0.968754	−0.484377	+	0.874859i	$0.660954\pi$
$444$	31.5049	1.49516
$445$	−2.78375	−0.131962
$446$	−5.32609	−0.252198
$447$	4.83460	0.228669
$448$	−4.79366	−0.226479
$449$	−6.82589	−0.322133	−0.161067	−	0.986944i	$-0.551493\pi$
$449$	−6.82589	−0.322133	−0.161067	+	0.986944i	$0.551493\pi$
$450$	29.7865	1.40415
$451$	1.80292	0.0848962
$452$	19.0209	0.894669
$453$	20.6746	0.971376
$454$	23.3986	1.09815
$455$	6.32737	0.296632
$456$	−3.78947	−0.177458
$457$	−37.0843	−1.73473	−0.867365	−	0.497673i	$-0.834188\pi$
$457$	−37.0843	−1.73473	−0.867365	+	0.497673i	$0.834188\pi$
$458$	6.45479	0.301612
$459$	45.8882	2.14188
$460$	−0.107734	−0.00502311
$461$	37.0523	1.72570	0.862848	−	0.505463i	$-0.168678\pi$
$461$	37.0523	1.72570	0.862848	+	0.505463i	$0.168678\pi$
$462$	−5.70547	−0.265442
$463$	−1.92050	−0.0892532	−0.0446266	−	0.999004i	$-0.514210\pi$
$463$	−1.92050	−0.0892532	−0.0446266	+	0.999004i	$0.514210\pi$
$464$	1.64190	0.0762234
$465$	0.185549	0.00860465
$466$	−20.3881	−0.944463
$467$	2.26048	0.104603	0.0523013	−	0.998631i	$-0.483344\pi$
$467$	2.26048	0.104603	0.0523013	+	0.998631i	$0.483344\pi$
$468$	38.6951	1.78868
$469$	−14.0083	−0.646843
$470$	−0.368416	−0.0169938
$471$	59.4399	2.73885
$472$	13.2130	0.608179
$473$	−0.913957	−0.0420238
$474$	30.6411	1.40739
$475$	6.26003	0.287230
$476$	24.3678	1.11690
$477$	0.358394	0.0164097
$478$	−10.6977	−0.489300
$479$	15.9877	0.730498	0.365249	−	0.930910i	$-0.380984\pi$
$479$	15.9877	0.730498	0.365249	+	0.930910i	$0.380984\pi$
$480$	−0.615066	−0.0280738
$481$	−67.6104	−3.08277
$482$	−13.2150	−0.601927
$483$	7.56334	0.344144
$484$	−10.8427	−0.492852
$485$	−1.08080	−0.0490768
$486$	0.139879	0.00634504
$487$	−15.6977	−0.711329	−0.355665	−	0.934614i	$-0.615745\pi$
$487$	−15.6977	−0.711329	−0.355665	+	0.934614i	$0.615745\pi$
$488$	−12.3951	−0.561098
$489$	25.5125	1.15371
$490$	3.27466	0.147934
$491$	−38.0663	−1.71791	−0.858955	−	0.512051i	$-0.828886\pi$
$491$	−38.0663	−1.71791	−0.858955	+	0.512051i	$0.828886\pi$
$492$	−13.6449	−0.615158
$493$	−8.34635	−0.375901
$494$	8.13230	0.365890
$495$	−0.488249	−0.0219452
$496$	0.301674	0.0135456
$497$	−19.1198	−0.857638
$498$	27.8702	1.24889
$499$	11.1696	0.500018	0.250009	−	0.968243i	$-0.419566\pi$
$499$	11.1696	0.500018	0.250009	+	0.968243i	$0.419566\pi$
$500$	2.04073	0.0912642
$501$	55.9408	2.49925
$502$	−8.17495	−0.364866
$503$	13.6309	0.607774	0.303887	−	0.952708i	$-0.401716\pi$
$503$	13.6309	0.607774	0.303887	+	0.952708i	$0.401716\pi$
$504$	28.7991	1.28281
$505$	−0.142393	−0.00633640
$506$	−0.208475	−0.00926786
$507$	−85.4907	−3.79677
$508$	−15.9183	−0.706260
$509$	−26.3549	−1.16816	−0.584081	−	0.811695i	$-0.698545\pi$
$509$	−26.3549	−1.16816	−0.584081	+	0.811695i	$0.698545\pi$
$510$	3.12659	0.138448
$511$	32.6323	1.44357
$512$	−1.00000	−0.0441942
$513$	11.3978	0.503225
$514$	3.71888	0.164033
$515$	−2.41555	−0.106442
$516$	6.91700	0.304504
$517$	−0.712922	−0.0313543
$518$	−50.3196	−2.21091
$519$	−48.1410	−2.11316
$520$	1.31995	0.0578835
$521$	−14.1231	−0.618743	−0.309372	−	0.950941i	$-0.600119\pi$
$521$	−14.1231	−0.618743	−0.309372	+	0.950941i	$0.600119\pi$
$522$	−9.86415	−0.431742
$523$	−24.3950	−1.06672	−0.533360	−	0.845889i	$-0.679071\pi$
$523$	−24.3950	−1.06672	−0.533360	+	0.845889i	$0.679071\pi$
$524$	−18.2329	−0.796506
$525$	−71.3316	−3.11317
$526$	5.97313	0.260441
$527$	−1.53351	−0.0668009
$528$	−1.19021	−0.0517973
$529$	−22.7236	−0.987984
$530$	0.0122254	0.000531036 0
$531$	−79.3807	−3.44483
$532$	6.05253	0.262410
$533$	29.2822	1.26835
$534$	40.7686	1.76423
$535$	−3.44240	−0.148828
$536$	−2.92226	−0.126222
$537$	7.49386	0.323384
$538$	−28.5177	−1.22948
$539$	6.33679	0.272945
$540$	1.84997	0.0796100
$541$	32.7470	1.40790	0.703952	−	0.710248i	$-0.251417\pi$
$541$	32.7470	1.40790	0.703952	+	0.710248i	$0.251417\pi$
$542$	−13.3117	−0.571786
$543$	17.7242	0.760618
$544$	5.08335	0.217947
$545$	−1.15393	−0.0494291
$546$	−92.6656	−3.96572
$547$	−29.4148	−1.25769	−0.628844	−	0.777532i	$-0.716471\pi$
$547$	−29.4148	−1.25769	−0.628844	+	0.777532i	$0.716471\pi$
$548$	9.70397	0.414533
$549$	74.4665	3.17815
$550$	1.96618	0.0838381
$551$	−2.07308	−0.0883164
$552$	1.57778	0.0671548
$553$	−48.9399	−2.08114
$554$	−3.58447	−0.152290
$555$	−6.45642	−0.274060
$556$	5.44265	0.230820
$557$	−21.3448	−0.904406	−0.452203	−	0.891915i	$-0.649362\pi$
$557$	−21.3448	−0.904406	−0.452203	+	0.891915i	$0.649362\pi$
$558$	−1.81238	−0.0767244
$559$	−14.8441	−0.627837
$560$	0.982381	0.0415132
$561$	6.05026	0.255442
$562$	12.9974	0.548264
$563$	37.1759	1.56678	0.783389	−	0.621532i	$-0.213490\pi$
$563$	37.1759	1.56678	0.783389	+	0.621532i	$0.213490\pi$
$564$	5.39553	0.227193
$565$	−3.89802	−0.163991
$566$	13.5719	0.570471
$567$	−43.4779	−1.82590
$568$	−3.98855	−0.167356
$569$	−35.1444	−1.47333	−0.736664	−	0.676259i	$-0.763600\pi$
$569$	−35.1444	−1.47333	−0.736664	+	0.676259i	$0.763600\pi$
$570$	0.776589	0.0325277
$571$	−33.4099	−1.39816	−0.699081	−	0.715042i	$-0.746407\pi$
$571$	−33.4099	−1.39816	−0.699081	+	0.715042i	$0.746407\pi$
$572$	2.55423	0.106798
$573$	28.6193	1.19559
$574$	21.7935	0.909644
$575$	−2.60642	−0.108695
$576$	6.00776	0.250323
$577$	34.5839	1.43975	0.719874	−	0.694105i	$-0.244200\pi$
$577$	34.5839	1.43975	0.719874	+	0.694105i	$0.244200\pi$
$578$	−8.84041	−0.367713
$579$	−59.8874	−2.48884
$580$	−0.336481	−0.0139716
$581$	−44.5141	−1.84676
$582$	15.8286	0.656116
$583$	0.0236573	0.000979784 0
$584$	6.80739	0.281692
$585$	−7.92992	−0.327862
$586$	9.01018	0.372207
$587$	31.7920	1.31220	0.656099	−	0.754675i	$-0.272205\pi$
$587$	31.7920	1.31220	0.656099	+	0.754675i	$0.272205\pi$
$588$	−47.9580	−1.97776
$589$	−0.380897	−0.0156946
$590$	−2.70780	−0.111478
$591$	19.2577	0.792156
$592$	−10.4971	−0.431429
$593$	−36.9868	−1.51887	−0.759433	−	0.650585i	$-0.774524\pi$
$593$	−36.9868	−1.51887	−0.759433	+	0.650585i	$0.774524\pi$
$594$	3.57987	0.146884
$595$	−4.99378	−0.204725
$596$	−1.61084	−0.0659825
$597$	−25.2251	−1.03240
$598$	−3.38596	−0.138462
$599$	−16.5455	−0.676032	−0.338016	−	0.941140i	$-0.609756\pi$
$599$	−16.5455	−0.676032	−0.338016	+	0.941140i	$0.609756\pi$
$600$	−14.8804	−0.607490
$601$	−38.9446	−1.58858	−0.794291	−	0.607537i	$-0.792158\pi$
$601$	−38.9446	−1.58858	−0.794291	+	0.607537i	$0.792158\pi$
$602$	−11.0478	−0.450275
$603$	17.5562	0.714944
$604$	−6.88855	−0.280291
$605$	2.22204	0.0903388
$606$	2.08537	0.0847124
$607$	32.9825	1.33872	0.669360	−	0.742939i	$-0.266569\pi$
$607$	32.9825	1.33872	0.669360	+	0.742939i	$0.266569\pi$
$608$	1.26261	0.0512057
$609$	23.6223	0.957224
$610$	2.54016	0.102848
$611$	−11.5789	−0.468434
$612$	−30.5395	−1.23449
$613$	−40.9191	−1.65271	−0.826354	−	0.563151i	$-0.809589\pi$
$613$	−40.9191	−1.65271	−0.826354	+	0.563151i	$0.809589\pi$
$614$	16.3584	0.660170
$615$	2.79629	0.112757
$616$	1.90100	0.0765936
$617$	−11.8187	−0.475805	−0.237902	−	0.971289i	$-0.576460\pi$
$617$	−11.8187	−0.475805	−0.237902	+	0.971289i	$0.576460\pi$
$618$	35.3763	1.42304
$619$	22.2472	0.894189	0.447094	−	0.894487i	$-0.352459\pi$
$619$	22.2472	0.894189	0.447094	+	0.894487i	$0.352459\pi$
$620$	−0.0618231	−0.00248288
$621$	−4.74558	−0.190434
$622$	3.38771	0.135835
$623$	−65.1154	−2.60879
$624$	−19.3309	−0.773855
$625$	24.3718	0.974872
$626$	18.2529	0.729534
$627$	1.50278	0.0600151
$628$	−19.8048	−0.790296
$629$	53.3605	2.12762
$630$	−5.90191	−0.235138
$631$	−38.7355	−1.54203	−0.771017	−	0.636815i	$-0.780252\pi$
$631$	−38.7355	−1.54203	−0.771017	+	0.636815i	$0.780252\pi$
$632$	−10.2093	−0.406104
$633$	−34.3583	−1.36562
$634$	−28.2213	−1.12081
$635$	3.26219	0.129456
$636$	−0.179043	−0.00709951
$637$	102.919	4.07781
$638$	−0.651123	−0.0257782
$639$	23.9623	0.947933
$640$	0.204934	0.00810071
$641$	−42.8404	−1.69209	−0.846047	−	0.533108i	$-0.821024\pi$
$641$	−42.8404	−1.69209	−0.846047	+	0.533108i	$0.821024\pi$
$642$	50.4146	1.98971
$643$	24.3971	0.962128	0.481064	−	0.876685i	$-0.340250\pi$
$643$	24.3971	0.962128	0.481064	+	0.876685i	$0.340250\pi$
$644$	−2.52003	−0.0993030
$645$	−1.41753	−0.0558150
$646$	−6.41829	−0.252524
$647$	38.1828	1.50112	0.750561	−	0.660802i	$-0.229784\pi$
$647$	38.1828	1.50112	0.750561	+	0.660802i	$0.229784\pi$
$648$	−9.06988	−0.356299
$649$	−5.23985	−0.205682
$650$	31.9338	1.25255
$651$	4.34023	0.170107
$652$	−8.50049	−0.332905
$653$	16.0378	0.627608	0.313804	−	0.949488i	$-0.398397\pi$
$653$	16.0378	0.627608	0.313804	+	0.949488i	$0.398397\pi$
$654$	16.8996	0.660826
$655$	3.73653	0.145998
$656$	4.54633	0.177504
$657$	−40.8971	−1.59555
$658$	−8.61772	−0.335954
$659$	12.8046	0.498798	0.249399	−	0.968401i	$-0.419767\pi$
$659$	12.8046	0.498798	0.249399	+	0.968401i	$0.419767\pi$
$660$	0.243914	0.00949436
$661$	6.74794	0.262464	0.131232	−	0.991352i	$-0.458107\pi$
$661$	6.74794	0.262464	0.131232	+	0.991352i	$0.458107\pi$
$662$	−13.8786	−0.539406
$663$	98.2656	3.81632
$664$	−9.28605	−0.360369
$665$	−1.24037	−0.0480993
$666$	63.0641	2.44369
$667$	0.863148	0.0334212
$668$	−18.6389	−0.721161
$669$	−15.9852	−0.618022
$670$	0.598869	0.0231363
$671$	4.91546	0.189759
$672$	−14.3872	−0.554997
$673$	−3.01408	−0.116184	−0.0580921	−	0.998311i	$-0.518502\pi$
$673$	−3.01408	−0.116184	−0.0580921	+	0.998311i	$0.518502\pi$
$674$	3.16150	0.121776
$675$	44.7567	1.72269
$676$	28.4846	1.09556
$677$	26.3319	1.01202	0.506009	−	0.862528i	$-0.331120\pi$
$677$	26.3319	1.01202	0.506009	+	0.862528i	$0.331120\pi$
$678$	57.0873	2.19243
$679$	−25.2814	−0.970210
$680$	−1.04175	−0.0399492
$681$	70.2261	2.69107
$682$	−0.119634	−0.00458102
$683$	14.0299	0.536839	0.268420	−	0.963302i	$-0.413499\pi$
$683$	14.0299	0.536839	0.268420	+	0.963302i	$0.413499\pi$
$684$	−7.58547	−0.290038
$685$	−1.98867	−0.0759831
$686$	43.0429	1.64338
$687$	19.3727	0.739115
$688$	−2.30467	−0.0878649
$689$	0.384231	0.0146380
$690$	−0.323340	−0.0123094
$691$	−37.7547	−1.43626	−0.718129	−	0.695910i	$-0.755001\pi$
$691$	−37.7547	−1.43626	−0.718129	+	0.695910i	$0.755001\pi$
$692$	16.0401	0.609753
$693$	−11.4208	−0.433839
$694$	17.6960	0.671730
$695$	−1.11538	−0.0423089
$696$	4.92783	0.186789
$697$	−23.1106	−0.875375
$698$	25.3453	0.959335
$699$	−61.1908	−2.31445
$700$	23.7670	0.898306
$701$	−0.534392	−0.0201837	−0.0100919	−	0.999949i	$-0.503212\pi$
$701$	−0.534392	−0.0201837	−0.0100919	+	0.999949i	$0.503212\pi$
$702$	58.1426	2.19445
$703$	13.2538	0.499876
$704$	0.396567	0.0149462
$705$	−1.10572	−0.0416440
$706$	−20.2664	−0.762735
$707$	−3.33075	−0.125266
$708$	39.6562	1.49037
$709$	−26.1405	−0.981728	−0.490864	−	0.871236i	$-0.663319\pi$
$709$	−26.1405	−0.981728	−0.490864	+	0.871236i	$0.663319\pi$
$710$	0.817389	0.0306760
$711$	61.3351	2.30024
$712$	−13.5837	−0.509070
$713$	0.158590	0.00593925
$714$	73.1349	2.73701
$715$	−0.523447	−0.0195758
$716$	−2.49688	−0.0933127
$717$	−32.1068	−1.19905
$718$	0.839992	0.0313482
$719$	−9.44350	−0.352183	−0.176092	−	0.984374i	$-0.556346\pi$
$719$	−9.44350	−0.352183	−0.176092	+	0.984374i	$0.556346\pi$
$720$	−1.23119	−0.0458838
$721$	−56.5028	−2.10428
$722$	17.4058	0.647777
$723$	−39.6621	−1.47505
$724$	−5.90552	−0.219477
$725$	−8.14055	−0.302332
$726$	−32.5422	−1.20776
$727$	−37.4965	−1.39067	−0.695334	−	0.718687i	$-0.744743\pi$
$727$	−37.4965	−1.39067	−0.695334	+	0.718687i	$0.744743\pi$
$728$	30.8752	1.14431
$729$	−26.7898	−0.992216
$730$	−1.39506	−0.0516336
$731$	11.7155	0.433312
$732$	−37.2012	−1.37500
$733$	−43.2765	−1.59845	−0.799226	−	0.601030i	$-0.794757\pi$
$733$	−43.2765	−1.59845	−0.799226	+	0.601030i	$0.794757\pi$
$734$	8.92375	0.329382
$735$	9.82821	0.362519
$736$	−0.525700	−0.0193776
$737$	1.15887	0.0426875
$738$	−27.3132	−1.00541
$739$	−10.8675	−0.399768	−0.199884	−	0.979820i	$-0.564057\pi$
$739$	−10.8675	−0.399768	−0.199884	+	0.979820i	$0.564057\pi$
$740$	2.15121	0.0790801
$741$	24.4074	0.896629
$742$	0.285967	0.0104982
$743$	0.845107	0.0310040	0.0155020	−	0.999880i	$-0.495065\pi$
$743$	0.845107	0.0310040	0.0155020	+	0.999880i	$0.495065\pi$
$744$	0.905412	0.0331940
$745$	0.330115	0.0120945
$746$	−1.84070	−0.0673928
$747$	55.7884	2.04119
$748$	−2.01589	−0.0737081
$749$	−80.5221	−2.94221
$750$	6.12482	0.223647
$751$	11.4114	0.416409	0.208204	−	0.978085i	$-0.433238\pi$
$751$	11.4114	0.416409	0.208204	+	0.978085i	$0.433238\pi$
$752$	−1.79773	−0.0655566
$753$	−24.5354	−0.894120
$754$	−10.5753	−0.385128
$755$	1.41170	0.0513769
$756$	43.2731	1.57383
$757$	42.4281	1.54208	0.771038	−	0.636789i	$-0.219738\pi$
$757$	42.4281	1.54208	0.771038	+	0.636789i	$0.219738\pi$
$758$	−28.6685	−1.04129
$759$	−0.625695	−0.0227113
$760$	−0.258752	−0.00938591
$761$	47.4268	1.71922	0.859610	−	0.510950i	$-0.170706\pi$
$761$	47.4268	1.71922	0.859610	+	0.510950i	$0.170706\pi$
$762$	−47.7754	−1.73072
$763$	−26.9920	−0.977175
$764$	−9.53565	−0.344988
$765$	6.25857	0.226279
$766$	−0.942020	−0.0340366
$767$	−85.1033	−3.07290
$768$	−3.00129	−0.108300
$769$	−34.0548	−1.22805	−0.614023	−	0.789288i	$-0.710450\pi$
$769$	−34.0548	−1.22805	−0.614023	+	0.789288i	$0.710450\pi$
$770$	−0.389579	−0.0140395
$771$	11.1614	0.401970
$772$	19.9539	0.718156
$773$	−9.80814	−0.352774	−0.176387	−	0.984321i	$-0.556441\pi$
$773$	−9.80814	−0.352774	−0.176387	+	0.984321i	$0.556441\pi$
$774$	13.8459	0.497681
$775$	−1.49570	−0.0537272
$776$	−5.27392	−0.189323
$777$	−151.024	−5.41795
$778$	27.6069	0.989757
$779$	−5.74025	−0.205666
$780$	3.96155	0.141846
$781$	1.58173	0.0565987
$782$	2.67232	0.0955619
$783$	−14.8217	−0.529685
$784$	15.9791	0.570683
$785$	4.05866	0.144860
$786$	−54.7222	−1.95187
$787$	24.0205	0.856239	0.428119	−	0.903722i	$-0.359176\pi$
$787$	24.0205	0.856239	0.428119	+	0.903722i	$0.359176\pi$
$788$	−6.41647	−0.228577
$789$	17.9271	0.638223
$790$	2.09223	0.0744382
$791$	−91.1797	−3.24198
$792$	−2.38248	−0.0846576
$793$	79.8347	2.83501
$794$	−3.50554	−0.124407
$795$	0.0366919	0.00130133
$796$	8.40475	0.297898
$797$	15.6798	0.555407	0.277704	−	0.960667i	$-0.410427\pi$
$797$	15.6798	0.555407	0.277704	+	0.960667i	$0.410427\pi$
$798$	18.1654	0.643048
$799$	9.13851	0.323297
$800$	4.95800	0.175292
$801$	81.6074	2.88346
$802$	2.87844	0.101641
$803$	−2.69958	−0.0952662
$804$	−8.77055	−0.309313
$805$	0.516438	0.0182021
$806$	−1.94304	−0.0684406
$807$	−85.5899	−3.01291
$808$	−0.694824	−0.0244438
$809$	−31.7090	−1.11483	−0.557415	−	0.830234i	$-0.688207\pi$
$809$	−31.7090	−1.11483	−0.557415	+	0.830234i	$0.688207\pi$
$810$	1.85872	0.0653089
$811$	51.3636	1.80362	0.901810	−	0.432132i	$-0.142239\pi$
$811$	51.3636	1.80362	0.901810	+	0.432132i	$0.142239\pi$
$812$	−7.87071	−0.276208
$813$	−39.9523	−1.40119
$814$	4.16281	0.145906
$815$	1.74204	0.0610209
$816$	15.2566	0.534088
$817$	2.90991	0.101805
$818$	−2.40053	−0.0839326
$819$	−185.491	−6.48158
$820$	−0.931695	−0.0325362
$821$	39.1415	1.36605	0.683023	−	0.730396i	$-0.260665\pi$
$821$	39.1415	1.36605	0.683023	+	0.730396i	$0.260665\pi$
$822$	29.1245	1.01583
$823$	7.73791	0.269726	0.134863	−	0.990864i	$-0.456940\pi$
$823$	7.73791	0.269726	0.134863	+	0.990864i	$0.456940\pi$
$824$	−11.7870	−0.410620
$825$	5.90108	0.205449
$826$	−63.3388	−2.20384
$827$	−53.4578	−1.85891	−0.929455	−	0.368934i	$-0.879723\pi$
$827$	−53.4578	−1.85891	−0.929455	+	0.368934i	$0.879723\pi$
$828$	3.15828	0.109758
$829$	39.4992	1.37186	0.685932	−	0.727666i	$-0.259395\pi$
$829$	39.4992	1.37186	0.685932	+	0.727666i	$0.259395\pi$
$830$	1.90302	0.0660549
$831$	−10.7581	−0.373193
$832$	6.44086	0.223296
$833$	−81.2275	−2.81436
$834$	16.3350	0.565635
$835$	3.81974	0.132187
$836$	−0.500710	−0.0173174
$837$	−2.72326	−0.0941297
$838$	33.9798	1.17381
$839$	35.7362	1.23375	0.616874	−	0.787062i	$-0.288399\pi$
$839$	35.7362	1.23375	0.616874	+	0.787062i	$0.288399\pi$
$840$	2.94841	0.101730
$841$	−26.3042	−0.907040
$842$	−22.0073	−0.758421
$843$	39.0091	1.34354
$844$	11.4478	0.394051
$845$	−5.83746	−0.200815
$846$	10.8004	0.371324
$847$	51.9763	1.78593
$848$	0.0596552	0.00204857
$849$	40.7334	1.39797
$850$	−25.2032	−0.864464
$851$	−5.51834	−0.189166
$852$	−11.9708	−0.410113
$853$	10.3693	0.355039	0.177519	−	0.984117i	$-0.443193\pi$
$853$	10.3693	0.355039	0.177519	+	0.984117i	$0.443193\pi$
$854$	59.4176	2.03323
$855$	1.55452	0.0531634
$856$	−16.7976	−0.574131
$857$	−25.1983	−0.860759	−0.430380	−	0.902648i	$-0.641620\pi$
$857$	−25.1983	−0.860759	−0.430380	+	0.902648i	$0.641620\pi$
$858$	7.66599	0.261712
$859$	−40.6213	−1.38598	−0.692991	−	0.720946i	$-0.743708\pi$
$859$	−40.6213	−1.38598	−0.692991	+	0.720946i	$0.743708\pi$
$860$	0.472305	0.0161055
$861$	65.4087	2.22912
$862$	−20.5352	−0.699432
$863$	25.0013	0.851054	0.425527	−	0.904946i	$-0.360089\pi$
$863$	25.0013	0.851054	0.425527	+	0.904946i	$0.360089\pi$
$864$	9.02716	0.307110
$865$	−3.28715	−0.111767
$866$	25.4294	0.864128
$867$	−26.5327	−0.901096
$868$	−1.44612	−0.0490846
$869$	4.04867	0.137342
$870$	−1.00988	−0.0342380
$871$	18.8218	0.637754
$872$	−5.63077	−0.190682
$873$	31.6845	1.07236
$874$	0.663756	0.0224519
$875$	−9.78255	−0.330711
$876$	20.4310	0.690298
$877$	−38.0262	−1.28405	−0.642027	−	0.766682i	$-0.721906\pi$
$877$	−38.0262	−1.28405	−0.642027	+	0.766682i	$0.721906\pi$
$878$	28.2533	0.953503
$879$	27.0422	0.912110
$880$	−0.0812698	−0.00273960
$881$	−34.4122	−1.15938	−0.579689	−	0.814838i	$-0.696826\pi$
$881$	−34.4122	−1.15938	−0.579689	+	0.814838i	$0.696826\pi$
$882$	−95.9987	−3.23245
$883$	−6.36628	−0.214242	−0.107121	−	0.994246i	$-0.534163\pi$
$883$	−6.36628	−0.214242	−0.107121	+	0.994246i	$0.534163\pi$
$884$	−32.7411	−1.10120
$885$	−8.12689	−0.273182
$886$	20.3899	0.685013
$887$	−10.0816	−0.338508	−0.169254	−	0.985573i	$-0.554136\pi$
$887$	−10.0816	−0.338508	−0.169254	+	0.985573i	$0.554136\pi$
$888$	−31.5049	−1.05724
$889$	76.3068	2.55925
$890$	2.78375	0.0933115
$891$	3.59681	0.120498
$892$	5.32609	0.178331
$893$	2.26984	0.0759574
$894$	−4.83460	−0.161693
$895$	0.511694	0.0171040
$896$	4.79366	0.160145
$897$	−10.1623	−0.339308
$898$	6.82589	0.227783
$899$	0.495319	0.0165198
$900$	−29.7865	−0.992883
$901$	−0.303248	−0.0101027
$902$	−1.80292	−0.0600307
$903$	−33.1577	−1.10342
$904$	−19.0209	−0.632626
$905$	1.21024	0.0402297
$906$	−20.6746	−0.686866
$907$	−4.08420	−0.135614	−0.0678069	−	0.997698i	$-0.521600\pi$
$907$	−4.08420	−0.135614	−0.0678069	+	0.997698i	$0.521600\pi$
$908$	−23.3986	−0.776510
$909$	4.17434	0.138454
$910$	−6.32737	−0.209750
$911$	−27.8747	−0.923530	−0.461765	−	0.887002i	$-0.652784\pi$
$911$	−27.8747	−0.923530	−0.461765	+	0.887002i	$0.652784\pi$
$912$	3.78947	0.125482
$913$	3.68254	0.121874
$914$	37.0843	1.22664
$915$	7.62377	0.252034
$916$	−6.45479	−0.213272
$917$	87.4021	2.88627
$918$	−45.8882	−1.51454
$919$	−35.1454	−1.15934	−0.579669	−	0.814852i	$-0.696818\pi$
$919$	−35.1454	−1.15934	−0.579669	+	0.814852i	$0.696818\pi$
$920$	0.107734	0.00355187
$921$	49.0963	1.61778
$922$	−37.0523	−1.22025
$923$	25.6897	0.845587
$924$	5.70547	0.187696
$925$	52.0447	1.71122
$926$	1.92050	0.0631116
$927$	70.8135	2.32582
$928$	−1.64190	−0.0538981
$929$	38.0991	1.24999	0.624995	−	0.780629i	$-0.285101\pi$
$929$	38.0991	1.24999	0.624995	+	0.780629i	$0.285101\pi$
$930$	−0.185549	−0.00608440
$931$	−20.1754	−0.661223
$932$	20.3881	0.667836
$933$	10.1675	0.332869
$934$	−2.26048	−0.0739652
$935$	0.413123	0.0135106
$936$	−38.6951	−1.26479
$937$	−20.4865	−0.669266	−0.334633	−	0.942349i	$-0.608612\pi$
$937$	−20.4865	−0.669266	−0.334633	+	0.942349i	$0.608612\pi$
$938$	14.0083	0.457387
$939$	54.7824	1.78776
$940$	0.368416	0.0120164
$941$	13.9004	0.453139	0.226569	−	0.973995i	$-0.427249\pi$
$941$	13.9004	0.453139	0.226569	+	0.973995i	$0.427249\pi$
$942$	−59.4399	−1.93666
$943$	2.39001	0.0778293
$944$	−13.2130	−0.430048
$945$	−8.86811	−0.288480
$946$	0.913957	0.0297153
$947$	−8.79804	−0.285898	−0.142949	−	0.989730i	$-0.545658\pi$
$947$	−8.79804	−0.285898	−0.142949	+	0.989730i	$0.545658\pi$
$948$	−30.6411	−0.995177
$949$	−43.8454	−1.42328
$950$	−6.26003	−0.203102
$951$	−84.7003	−2.74660
$952$	−24.3678	−0.789765
$953$	−19.4529	−0.630140	−0.315070	−	0.949068i	$-0.602028\pi$
$953$	−19.4529	−0.630140	−0.315070	+	0.949068i	$0.602028\pi$
$954$	−0.358394	−0.0116034
$955$	1.95417	0.0632356
$956$	10.6977	0.345987
$957$	−1.95421	−0.0631707
$958$	−15.9877	−0.516540
$959$	−46.5175	−1.50213
$960$	0.615066	0.0198512
$961$	−30.9090	−0.997064
$962$	67.6104	2.17985
$963$	100.916	3.25198
$964$	13.2150	0.425626
$965$	−4.08922	−0.131637
$966$	−7.56334	−0.243346
$967$	28.0985	0.903587	0.451794	−	0.892122i	$-0.350784\pi$
$967$	28.0985	0.903587	0.451794	+	0.892122i	$0.350784\pi$
$968$	10.8427	0.348499
$969$	−19.2632	−0.618823
$970$	1.08080	0.0347025
$971$	39.0283	1.25248	0.626239	−	0.779631i	$-0.284594\pi$
$971$	39.0283	1.25248	0.626239	+	0.779631i	$0.284594\pi$
$972$	−0.139879	−0.00448662
$973$	−26.0902	−0.836414
$974$	15.6977	0.502986
$975$	95.8426	3.06942
$976$	12.3951	0.396756
$977$	−4.49323	−0.143751	−0.0718756	−	0.997414i	$-0.522898\pi$
$977$	−4.49323	−0.143751	−0.0718756	+	0.997414i	$0.522898\pi$
$978$	−25.5125	−0.815799
$979$	5.38683	0.172164
$980$	−3.27466	−0.104605
$981$	33.8283	1.08005
$982$	38.0663	1.21475
$983$	40.3933	1.28834	0.644172	−	0.764880i	$-0.277202\pi$
$983$	40.3933	1.28834	0.644172	+	0.764880i	$0.277202\pi$
$984$	13.6449	0.434982
$985$	1.31495	0.0418978
$986$	8.34635	0.265802
$987$	−25.8643	−0.823270
$988$	−8.13230	−0.258723
$989$	−1.21157	−0.0385256
$990$	0.488249	0.0155176
$991$	11.8488	0.376390	0.188195	−	0.982132i	$-0.439736\pi$
$991$	11.8488	0.376390	0.188195	+	0.982132i	$0.439736\pi$
$992$	−0.301674	−0.00957816
$993$	−41.6536	−1.32184
$994$	19.1198	0.606442
$995$	−1.72242	−0.0546042
$996$	−27.8702	−0.883100
$997$	−34.5957	−1.09566	−0.547828	−	0.836591i	$-0.684545\pi$
$997$	−34.5957	−1.09566	−0.547828	+	0.836591i	$0.684545\pi$
$998$	−11.1696	−0.353566
$999$	94.7592	2.99805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.b.1.5	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.b.1.5	✓	56	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.00129 q^{3} +1.00000 q^{4} -0.204934 q^{5} +3.00129 q^{6} -4.79366 q^{7} -1.00000 q^{8} +6.00776 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.00129 q^{3} +1.00000 q^{4} -0.204934 q^{5} +3.00129 q^{6} -4.79366 q^{7} -1.00000 q^{8} +6.00776 q^{9} +0.204934 q^{10} +0.396567 q^{11} -3.00129 q^{12} +6.44086 q^{13} +4.79366 q^{14} +0.615066 q^{15} +1.00000 q^{16} -5.08335 q^{17} -6.00776 q^{18} -1.26261 q^{19} -0.204934 q^{20} +14.3872 q^{21} -0.396567 q^{22} +0.525700 q^{23} +3.00129 q^{24} -4.95800 q^{25} -6.44086 q^{26} -9.02716 q^{27} -4.79366 q^{28} +1.64190 q^{29} -0.615066 q^{30} +0.301674 q^{31} -1.00000 q^{32} -1.19021 q^{33} +5.08335 q^{34} +0.982381 q^{35} +6.00776 q^{36} -10.4971 q^{37} +1.26261 q^{38} -19.3309 q^{39} +0.204934 q^{40} +4.54633 q^{41} -14.3872 q^{42} -2.30467 q^{43} +0.396567 q^{44} -1.23119 q^{45} -0.525700 q^{46} -1.79773 q^{47} -3.00129 q^{48} +15.9791 q^{49} +4.95800 q^{50} +15.2566 q^{51} +6.44086 q^{52} +0.0596552 q^{53} +9.02716 q^{54} -0.0812698 q^{55} +4.79366 q^{56} +3.78947 q^{57} -1.64190 q^{58} -13.2130 q^{59} +0.615066 q^{60} +12.3951 q^{61} -0.301674 q^{62} -28.7991 q^{63} +1.00000 q^{64} -1.31995 q^{65} +1.19021 q^{66} +2.92226 q^{67} -5.08335 q^{68} -1.57778 q^{69} -0.982381 q^{70} +3.98855 q^{71} -6.00776 q^{72} -6.80739 q^{73} +10.4971 q^{74} +14.8804 q^{75} -1.26261 q^{76} -1.90100 q^{77} +19.3309 q^{78} +10.2093 q^{79} -0.204934 q^{80} +9.06988 q^{81} -4.54633 q^{82} +9.28605 q^{83} +14.3872 q^{84} +1.04175 q^{85} +2.30467 q^{86} -4.92783 q^{87} -0.396567 q^{88} +13.5837 q^{89} +1.23119 q^{90} -30.8752 q^{91} +0.525700 q^{92} -0.905412 q^{93} +1.79773 q^{94} +0.258752 q^{95} +3.00129 q^{96} +5.27392 q^{97} -15.9791 q^{98} +2.38248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

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