LMFDB - Embedded newform 6035.2.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1897176198$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37029 q^{2} -1.04857 q^{3} +3.61829 q^{4} -1.00000 q^{5} +2.48541 q^{6} +0.282680 q^{7} -3.83582 q^{8} -1.90050 q^{9} +O(q^{10})$	\(q-2.37029 q^{2} -1.04857 q^{3} +3.61829 q^{4} -1.00000 q^{5} +2.48541 q^{6} +0.282680 q^{7} -3.83582 q^{8} -1.90050 q^{9} +2.37029 q^{10} -0.000604399 q^{11} -3.79402 q^{12} +1.98111 q^{13} -0.670036 q^{14} +1.04857 q^{15} +1.85543 q^{16} -1.00000 q^{17} +4.50475 q^{18} +2.43673 q^{19} -3.61829 q^{20} -0.296410 q^{21} +0.00143260 q^{22} -3.59276 q^{23} +4.02211 q^{24} +1.00000 q^{25} -4.69580 q^{26} +5.13851 q^{27} +1.02282 q^{28} -9.49853 q^{29} -2.48541 q^{30} +7.94983 q^{31} +3.27372 q^{32} +0.000633753 q^{33} +2.37029 q^{34} -0.282680 q^{35} -6.87657 q^{36} -2.25248 q^{37} -5.77577 q^{38} -2.07732 q^{39} +3.83582 q^{40} -3.48347 q^{41} +0.702578 q^{42} +10.4154 q^{43} -0.00218689 q^{44} +1.90050 q^{45} +8.51590 q^{46} +2.65015 q^{47} -1.94554 q^{48} -6.92009 q^{49} -2.37029 q^{50} +1.04857 q^{51} +7.16821 q^{52} -7.59462 q^{53} -12.1798 q^{54} +0.000604399 q^{55} -1.08431 q^{56} -2.55508 q^{57} +22.5143 q^{58} +3.89689 q^{59} +3.79402 q^{60} -11.0008 q^{61} -18.8434 q^{62} -0.537236 q^{63} -11.4705 q^{64} -1.98111 q^{65} -0.00150218 q^{66} +13.8861 q^{67} -3.61829 q^{68} +3.76726 q^{69} +0.670036 q^{70} +1.00000 q^{71} +7.28998 q^{72} -9.11858 q^{73} +5.33903 q^{74} -1.04857 q^{75} +8.81679 q^{76} -0.000170852 q^{77} +4.92387 q^{78} +4.38324 q^{79} -1.85543 q^{80} +0.313432 q^{81} +8.25685 q^{82} -8.34659 q^{83} -1.07250 q^{84} +1.00000 q^{85} -24.6877 q^{86} +9.95986 q^{87} +0.00231836 q^{88} +5.50386 q^{89} -4.50475 q^{90} +0.560020 q^{91} -12.9996 q^{92} -8.33594 q^{93} -6.28164 q^{94} -2.43673 q^{95} -3.43272 q^{96} +2.71150 q^{97} +16.4026 q^{98} +0.00114866 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q + 3 q^{2} + 6 q^{3} + 55 q^{4} - 49 q^{5} - 6 q^{6} + 11 q^{7} + 9 q^{8} + 43 q^{9}+O(q^{10}) $ 49 * q + 3 * q^2 + 6 * q^3 + 55 * q^4 - 49 * q^5 - 6 * q^6 + 11 * q^7 + 9 * q^8 + 43 * q^9	\( 49 q + 3 q^{2} + 6 q^{3} + 55 q^{4} - 49 q^{5} - 6 q^{6} + 11 q^{7} + 9 q^{8} + 43 q^{9} - 3 q^{10} - 10 q^{11} + 2 q^{12} + 43 q^{13} - 16 q^{14} - 6 q^{15} + 63 q^{16} - 49 q^{17} + 8 q^{18} + 15 q^{19} - 55 q^{20} + 19 q^{21} - 2 q^{23} - 3 q^{24} + 49 q^{25} + 22 q^{26} + 27 q^{27} + 32 q^{28} - 38 q^{29} + 6 q^{30} + 11 q^{31} + 16 q^{32} + 51 q^{33} - 3 q^{34} - 11 q^{35} + 83 q^{36} + 54 q^{37} + 39 q^{38} - 25 q^{39} - 9 q^{40} - 29 q^{41} + 52 q^{42} + 29 q^{43} - 47 q^{44} - 43 q^{45} + 10 q^{46} + 60 q^{47} + 16 q^{48} + 82 q^{49} + 3 q^{50} - 6 q^{51} + 113 q^{52} + 41 q^{53} + 28 q^{54} + 10 q^{55} - 16 q^{56} + 18 q^{57} + 14 q^{58} + 8 q^{59} - 2 q^{60} + 65 q^{61} + 37 q^{62} - 4 q^{63} + 77 q^{64} - 43 q^{65} + 27 q^{66} + 65 q^{67} - 55 q^{68} + 23 q^{69} + 16 q^{70} + 49 q^{71} + 121 q^{72} + 59 q^{73} - 53 q^{74} + 6 q^{75} + 50 q^{76} + 41 q^{77} + 26 q^{78} + 11 q^{79} - 63 q^{80} + 41 q^{81} + 77 q^{82} + 16 q^{83} + 30 q^{84} + 49 q^{85} - q^{86} + 8 q^{87} + 11 q^{88} - 4 q^{89} - 8 q^{90} + 47 q^{91} + 60 q^{92} + 69 q^{93} + 66 q^{94} - 15 q^{95} - 19 q^{96} + 76 q^{97} + 31 q^{98} - 39 q^{99}+O(q^{100}) \) 49 * q + 3 * q^2 + 6 * q^3 + 55 * q^4 - 49 * q^5 - 6 * q^6 + 11 * q^7 + 9 * q^8 + 43 * q^9 - 3 * q^10 - 10 * q^11 + 2 * q^12 + 43 * q^13 - 16 * q^14 - 6 * q^15 + 63 * q^16 - 49 * q^17 + 8 * q^18 + 15 * q^19 - 55 * q^20 + 19 * q^21 - 2 * q^23 - 3 * q^24 + 49 * q^25 + 22 * q^26 + 27 * q^27 + 32 * q^28 - 38 * q^29 + 6 * q^30 + 11 * q^31 + 16 * q^32 + 51 * q^33 - 3 * q^34 - 11 * q^35 + 83 * q^36 + 54 * q^37 + 39 * q^38 - 25 * q^39 - 9 * q^40 - 29 * q^41 + 52 * q^42 + 29 * q^43 - 47 * q^44 - 43 * q^45 + 10 * q^46 + 60 * q^47 + 16 * q^48 + 82 * q^49 + 3 * q^50 - 6 * q^51 + 113 * q^52 + 41 * q^53 + 28 * q^54 + 10 * q^55 - 16 * q^56 + 18 * q^57 + 14 * q^58 + 8 * q^59 - 2 * q^60 + 65 * q^61 + 37 * q^62 - 4 * q^63 + 77 * q^64 - 43 * q^65 + 27 * q^66 + 65 * q^67 - 55 * q^68 + 23 * q^69 + 16 * q^70 + 49 * q^71 + 121 * q^72 + 59 * q^73 - 53 * q^74 + 6 * q^75 + 50 * q^76 + 41 * q^77 + 26 * q^78 + 11 * q^79 - 63 * q^80 + 41 * q^81 + 77 * q^82 + 16 * q^83 + 30 * q^84 + 49 * q^85 - q^86 + 8 * q^87 + 11 * q^88 - 4 * q^89 - 8 * q^90 + 47 * q^91 + 60 * q^92 + 69 * q^93 + 66 * q^94 - 15 * q^95 - 19 * q^96 + 76 * q^97 + 31 * q^98 - 39 * 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 $

$2$	−2.37029	−1.67605	−0.838025	−	0.545632i	$-0.816290\pi$
$2$	−2.37029	−1.67605	−0.838025	+	0.545632i	$0.816290\pi$
$3$	−1.04857	−0.605391	−0.302696	−	0.953087i	$-0.597887\pi$
$3$	−1.04857	−0.605391	−0.302696	+	0.953087i	$0.597887\pi$
$4$	3.61829	1.80914
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.48541	1.01467
$7$	0.282680	0.106843	0.0534216	−	0.998572i	$-0.482987\pi$
$7$	0.282680	0.106843	0.0534216	+	0.998572i	$0.482987\pi$
$8$	−3.83582	−1.35617
$9$	−1.90050	−0.633502
$10$	2.37029	0.749552
$11$	−0.000604399 0	−0.000182233 0	−9.11165e−5	−	1.00000i	$-0.500029\pi$
$11$	−0.000604399 0	−0.000182233 0	−9.11165e−5		1.00000i	$0.500029\pi$
$12$	−3.79402	−1.09524
$13$	1.98111	0.549460	0.274730	−	0.961521i	$-0.411412\pi$
$13$	1.98111	0.549460	0.274730	+	0.961521i	$0.411412\pi$
$14$	−0.670036	−0.179075
$15$	1.04857	0.270739
$16$	1.85543	0.463857
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	4.50475	1.06178
$19$	2.43673	0.559024	0.279512	−	0.960142i	$-0.409827\pi$
$19$	2.43673	0.559024	0.279512	+	0.960142i	$0.409827\pi$
$20$	−3.61829	−0.809074
$21$	−0.296410	−0.0646819
$22$	0.00143260	0.000305432 0
$23$	−3.59276	−0.749143	−0.374571	−	0.927198i	$-0.622210\pi$
$23$	−3.59276	−0.749143	−0.374571	+	0.927198i	$0.622210\pi$
$24$	4.02211	0.821011
$25$	1.00000	0.200000
$26$	−4.69580	−0.920922
$27$	5.13851	0.988907
$28$	1.02282	0.193295
$29$	−9.49853	−1.76383	−0.881917	−	0.471406i	$-0.843747\pi$
$29$	−9.49853	−1.76383	−0.881917	+	0.471406i	$0.843747\pi$
$30$	−2.48541	−0.453772
$31$	7.94983	1.42783	0.713916	−	0.700232i	$-0.246920\pi$
$31$	7.94983	1.42783	0.713916	+	0.700232i	$0.246920\pi$
$32$	3.27372	0.578717
$33$	0.000633753 0	0.000110322 0
$34$	2.37029	0.406502
$35$	−0.282680	−0.0477817
$36$	−6.87657	−1.14610
$37$	−2.25248	−0.370305	−0.185152	−	0.982710i	$-0.559278\pi$
$37$	−2.25248	−0.370305	−0.185152	+	0.982710i	$0.559278\pi$
$38$	−5.77577	−0.936953
$39$	−2.07732	−0.332638
$40$	3.83582	0.606496
$41$	−3.48347	−0.544027	−0.272014	−	0.962293i	$-0.587690\pi$
$41$	−3.48347	−0.544027	−0.272014	+	0.962293i	$0.587690\pi$
$42$	0.702578	0.108410
$43$	10.4154	1.58834	0.794170	−	0.607695i	$-0.207906\pi$
$43$	10.4154	1.58834	0.794170	+	0.607695i	$0.207906\pi$
$44$	−0.00218689	−0.000329686 0
$45$	1.90050	0.283311
$46$	8.51590	1.25560
$47$	2.65015	0.386565	0.193282	−	0.981143i	$-0.438087\pi$
$47$	2.65015	0.386565	0.193282	+	0.981143i	$0.438087\pi$
$48$	−1.94554	−0.280815
$49$	−6.92009	−0.988585
$50$	−2.37029	−0.335210
$51$	1.04857	0.146829
$52$	7.16821	0.994052
$53$	−7.59462	−1.04320	−0.521601	−	0.853190i	$-0.674665\pi$
$53$	−7.59462	−1.04320	−0.521601	+	0.853190i	$0.674665\pi$
$54$	−12.1798	−1.65746
$55$	0.000604399 0	8.14971e−5 0
$56$	−1.08431	−0.144897
$57$	−2.55508	−0.338428
$58$	22.5143	2.95627
$59$	3.89689	0.507332	0.253666	−	0.967292i	$-0.418364\pi$
$59$	3.89689	0.507332	0.253666	+	0.967292i	$0.418364\pi$
$60$	3.79402	0.489806
$61$	−11.0008	−1.40851	−0.704253	−	0.709949i	$-0.748718\pi$
$61$	−11.0008	−1.40851	−0.704253	+	0.709949i	$0.748718\pi$
$62$	−18.8434	−2.39312
$63$	−0.537236	−0.0676853
$64$	−11.4705	−1.43382
$65$	−1.98111	−0.245726
$66$	−0.00150218	−0.000184906 0
$67$	13.8861	1.69646	0.848228	−	0.529631i	$-0.177669\pi$
$67$	13.8861	1.69646	0.848228	+	0.529631i	$0.177669\pi$
$68$	−3.61829	−0.438782
$69$	3.76726	0.453524
$70$	0.670036	0.0800846
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	7.28998	0.859133
$73$	−9.11858	−1.06725	−0.533625	−	0.845721i	$-0.679170\pi$
$73$	−9.11858	−1.06725	−0.533625	+	0.845721i	$0.679170\pi$
$74$	5.33903	0.620649
$75$	−1.04857	−0.121078
$76$	8.81679	1.01136
$77$	−0.000170852 0	−1.94704e−5 0
$78$	4.92387	0.557518
$79$	4.38324	0.493154	0.246577	−	0.969123i	$-0.420694\pi$
$79$	4.38324	0.493154	0.246577	+	0.969123i	$0.420694\pi$
$80$	−1.85543	−0.207443
$81$	0.313432	0.0348257
$82$	8.25685	0.911817
$83$	−8.34659	−0.916157	−0.458078	−	0.888912i	$-0.651462\pi$
$83$	−8.34659	−0.916157	−0.458078	+	0.888912i	$0.651462\pi$
$84$	−1.07250	−0.117019
$85$	1.00000	0.108465
$86$	−24.6877	−2.66214
$87$	9.95986	1.06781
$88$	0.00231836	0.000247138 0
$89$	5.50386	0.583408	0.291704	−	0.956509i	$-0.405778\pi$
$89$	5.50386	0.583408	0.291704	+	0.956509i	$0.405778\pi$
$90$	−4.50475	−0.474843
$91$	0.560020	0.0587061
$92$	−12.9996	−1.35531
$93$	−8.33594	−0.864396
$94$	−6.28164	−0.647902
$95$	−2.43673	−0.250003
$96$	−3.43272	−0.350350
$97$	2.71150	0.275311	0.137656	−	0.990480i	$-0.456043\pi$
$97$	2.71150	0.275311	0.137656	+	0.990480i	$0.456043\pi$
$98$	16.4026	1.65692
$99$	0.00114866	0.000115445 0
$100$	3.61829	0.361829
$101$	8.21784	0.817706	0.408853	−	0.912600i	$-0.365929\pi$
$101$	8.21784	0.817706	0.408853	+	0.912600i	$0.365929\pi$
$102$	−2.48541	−0.246093
$103$	16.5812	1.63379	0.816897	−	0.576783i	$-0.195692\pi$
$103$	16.5812	1.63379	0.816897	+	0.576783i	$0.195692\pi$
$104$	−7.59916	−0.745159
$105$	0.296410	0.0289266
$106$	18.0015	1.74846
$107$	3.37536	0.326308	0.163154	−	0.986601i	$-0.447833\pi$
$107$	3.37536	0.326308	0.163154	+	0.986601i	$0.447833\pi$
$108$	18.5926	1.78908
$109$	−15.2828	−1.46383	−0.731914	−	0.681398i	$-0.761373\pi$
$109$	−15.2828	−1.46383	−0.731914	+	0.681398i	$0.761373\pi$
$110$	−0.00143260	−0.000136593 0
$111$	2.36187	0.224179
$112$	0.524494	0.0495600
$113$	−7.74190	−0.728296	−0.364148	−	0.931341i	$-0.618640\pi$
$113$	−7.74190	−0.728296	−0.364148	+	0.931341i	$0.618640\pi$
$114$	6.05628	0.567223
$115$	3.59276	0.335027
$116$	−34.3684	−3.19103
$117$	−3.76510	−0.348084
$118$	−9.23677	−0.850314
$119$	−0.282680	−0.0259133
$120$	−4.02211	−0.367167
$121$	−11.0000	−1.00000
$122$	26.0751	2.36073
$123$	3.65266	0.329349
$124$	28.7648	2.58315
$125$	−1.00000	−0.0894427
$126$	1.27341	0.113444
$127$	−13.0673	−1.15954	−0.579770	−	0.814780i	$-0.696858\pi$
$127$	−13.0673	−1.15954	−0.579770	+	0.814780i	$0.696858\pi$
$128$	20.6411	1.82443
$129$	−10.9213	−0.961568
$130$	4.69580	0.411849
$131$	−16.0499	−1.40228	−0.701141	−	0.713022i	$-0.747326\pi$
$131$	−16.0499	−1.40228	−0.701141	+	0.713022i	$0.747326\pi$
$132$	0.00229310	0.000199589 0
$133$	0.688816	0.0597280
$134$	−32.9141	−2.84335
$135$	−5.13851	−0.442253
$136$	3.83582	0.328918
$137$	14.5681	1.24464	0.622319	−	0.782764i	$-0.286191\pi$
$137$	14.5681	1.24464	0.622319	+	0.782764i	$0.286191\pi$
$138$	−8.92950	−0.760130
$139$	−16.7964	−1.42465	−0.712324	−	0.701851i	$-0.752357\pi$
$139$	−16.7964	−1.42465	−0.712324	+	0.701851i	$0.752357\pi$
$140$	−1.02282	−0.0864440
$141$	−2.77887	−0.234023
$142$	−2.37029	−0.198911
$143$	−0.00119738	−0.000100130 0
$144$	−3.52625	−0.293854
$145$	9.49853	0.788810
$146$	21.6137	1.78876
$147$	7.25619	0.598480
$148$	−8.15010	−0.669934
$149$	12.2428	1.00297	0.501486	−	0.865166i	$-0.332787\pi$
$149$	12.2428	1.00297	0.501486	+	0.865166i	$0.332787\pi$
$150$	2.48541	0.202933
$151$	5.92341	0.482040	0.241020	−	0.970520i	$-0.422518\pi$
$151$	5.92341	0.482040	0.241020	+	0.970520i	$0.422518\pi$
$152$	−9.34685	−0.758130
$153$	1.90050	0.153647
$154$	0.000404969 0	3.26333e−5 0
$155$	−7.94983	−0.638546
$156$	−7.51636	−0.601790
$157$	9.25043	0.738264	0.369132	−	0.929377i	$-0.379655\pi$
$157$	9.25043	0.738264	0.369132	+	0.929377i	$0.379655\pi$
$158$	−10.3896	−0.826550
$159$	7.96348	0.631545
$160$	−3.27372	−0.258810
$161$	−1.01560	−0.0800408
$162$	−0.742925	−0.0583697
$163$	−4.53648	−0.355325	−0.177662	−	0.984091i	$-0.556853\pi$
$163$	−4.53648	−0.355325	−0.177662	+	0.984091i	$0.556853\pi$
$164$	−12.6042	−0.984224
$165$	−0.000633753 0	−4.93376e−5 0
$166$	19.7838	1.53552
$167$	16.3095	1.26207	0.631035	−	0.775755i	$-0.282631\pi$
$167$	16.3095	1.26207	0.631035	+	0.775755i	$0.282631\pi$
$168$	1.13697	0.0877194
$169$	−9.07522	−0.698094
$170$	−2.37029	−0.181793
$171$	−4.63102	−0.354143
$172$	37.6861	2.87354
$173$	0.0149121	0.00113374	0.000566872	−	1.00000i	$-0.499820\pi$
$173$	0.0149121	0.00113374	0.000566872		1.00000i	$0.499820\pi$
$174$	−23.6078	−1.78970
$175$	0.282680	0.0213686
$176$	−0.00112142	−8.45302e−5 0
$177$	−4.08616	−0.307134
$178$	−13.0458	−0.977821
$179$	17.5265	1.30999	0.654997	−	0.755631i	$-0.272670\pi$
$179$	17.5265	1.30999	0.654997	+	0.755631i	$0.272670\pi$
$180$	6.87657	0.512549
$181$	−8.57762	−0.637569	−0.318785	−	0.947827i	$-0.603275\pi$
$181$	−8.57762	−0.637569	−0.318785	+	0.947827i	$0.603275\pi$
$182$	−1.32741	−0.0983943
$183$	11.5351	0.852697
$184$	13.7812	1.01596
$185$	2.25248	0.165605
$186$	19.7586	1.44877
$187$	0.000604399 0	4.41980e−5 0
$188$	9.58902	0.699351
$189$	1.45256	0.105658
$190$	5.77577	0.419018
$191$	−12.7936	−0.925711	−0.462855	−	0.886434i	$-0.653175\pi$
$191$	−12.7936	−0.925711	−0.462855	+	0.886434i	$0.653175\pi$
$192$	12.0276	0.868020
$193$	12.4949	0.899402	0.449701	−	0.893179i	$-0.351531\pi$
$193$	12.4949	0.899402	0.449701	+	0.893179i	$0.351531\pi$
$194$	−6.42705	−0.461435
$195$	2.07732	0.148760
$196$	−25.0389	−1.78849
$197$	7.47347	0.532463	0.266231	−	0.963909i	$-0.414221\pi$
$197$	7.47347	0.532463	0.266231	+	0.963909i	$0.414221\pi$
$198$	−0.00272267	−0.000193491 0
$199$	−0.0233494	−0.00165520	−0.000827598	−	1.00000i	$-0.500263\pi$
$199$	−0.0233494	−0.00165520	−0.000827598		1.00000i	$0.500263\pi$
$200$	−3.83582	−0.271233
$201$	−14.5605	−1.02702
$202$	−19.4787	−1.37052
$203$	−2.68505	−0.188454
$204$	3.79402	0.265635
$205$	3.48347	0.243296
$206$	−39.3023	−2.73832
$207$	6.82806	0.474583
$208$	3.67580	0.254871
$209$	−0.00147276	−0.000101873 0
$210$	−0.702578	−0.0484825
$211$	9.27160	0.638283	0.319142	−	0.947707i	$-0.396605\pi$
$211$	9.27160	0.638283	0.319142	+	0.947707i	$0.396605\pi$
$212$	−27.4795	−1.88730
$213$	−1.04857	−0.0718467
$214$	−8.00059	−0.546909
$215$	−10.4154	−0.710328
$216$	−19.7104	−1.34112
$217$	2.24726	0.152554
$218$	36.2247	2.45345
$219$	9.56145	0.646103
$220$	0.00218689	0.000147440 0
$221$	−1.98111	−0.133264
$222$	−5.59833	−0.375735
$223$	9.65933	0.646836	0.323418	−	0.946256i	$-0.395168\pi$
$223$	9.65933	0.646836	0.323418	+	0.946256i	$0.395168\pi$
$224$	0.925416	0.0618320
$225$	−1.90050	−0.126700
$226$	18.3506	1.22066
$227$	5.24580	0.348176	0.174088	−	0.984730i	$-0.444302\pi$
$227$	5.24580	0.348176	0.174088	+	0.984730i	$0.444302\pi$
$228$	−9.24501	−0.612266
$229$	−2.89799	−0.191504	−0.0957522	−	0.995405i	$-0.530526\pi$
$229$	−2.89799	−0.191504	−0.0957522	+	0.995405i	$0.530526\pi$
$230$	−8.51590	−0.561522
$231$	0.000179150 0	1.17872e−5 0
$232$	36.4346	2.39205
$233$	−7.58630	−0.496995	−0.248497	−	0.968633i	$-0.579937\pi$
$233$	−7.58630	−0.496995	−0.248497	+	0.968633i	$0.579937\pi$
$234$	8.92439	0.583406
$235$	−2.65015	−0.172877
$236$	14.1001	0.917837
$237$	−4.59613	−0.298551
$238$	0.670036	0.0434320
$239$	−12.8970	−0.834236	−0.417118	−	0.908852i	$-0.636960\pi$
$239$	−12.8970	−0.834236	−0.417118	+	0.908852i	$0.636960\pi$
$240$	1.94554	0.125584
$241$	−12.6779	−0.816657	−0.408328	−	0.912835i	$-0.633888\pi$
$241$	−12.6779	−0.816657	−0.408328	+	0.912835i	$0.633888\pi$
$242$	26.0732	1.67605
$243$	−15.7442	−1.00999
$244$	−39.8040	−2.54819
$245$	6.92009	0.442108
$246$	−8.65787	−0.552006
$247$	4.82742	0.307162
$248$	−30.4941	−1.93638
$249$	8.75196	0.554633
$250$	2.37029	0.149910
$251$	4.83549	0.305214	0.152607	−	0.988287i	$-0.451233\pi$
$251$	4.83549	0.305214	0.152607	+	0.988287i	$0.451233\pi$
$252$	−1.94387	−0.122452
$253$	0.00217146	0.000136519 0
$254$	30.9734	1.94345
$255$	−1.04857	−0.0656639
$256$	−25.9843	−1.62402
$257$	−17.6953	−1.10380	−0.551901	−	0.833910i	$-0.686097\pi$
$257$	−17.6953	−1.10380	−0.551901	+	0.833910i	$0.686097\pi$
$258$	25.8867	1.61164
$259$	−0.636731	−0.0395645
$260$	−7.16821	−0.444554
$261$	18.0520	1.11739
$262$	38.0429	2.35030
$263$	−18.4662	−1.13868	−0.569339	−	0.822103i	$-0.692801\pi$
$263$	−18.4662	−1.13868	−0.569339	+	0.822103i	$0.692801\pi$
$264$	−0.00243096	−0.000149615 0
$265$	7.59462	0.466534
$266$	−1.63270	−0.100107
$267$	−5.77117	−0.353190
$268$	50.2439	3.06913
$269$	−25.8829	−1.57811	−0.789055	−	0.614322i	$-0.789430\pi$
$269$	−25.8829	−1.57811	−0.789055	+	0.614322i	$0.789430\pi$
$270$	12.1798	0.741238
$271$	−6.68719	−0.406218	−0.203109	−	0.979156i	$-0.565105\pi$
$271$	−6.68719	−0.406218	−0.203109	+	0.979156i	$0.565105\pi$
$272$	−1.85543	−0.112502
$273$	−0.587219	−0.0355401
$274$	−34.5307	−2.08608
$275$	−0.000604399 0	−3.64466e−5 0
$276$	13.6310	0.820491
$277$	−16.5084	−0.991891	−0.495946	−	0.868354i	$-0.665178\pi$
$277$	−16.5084	−0.991891	−0.495946	+	0.868354i	$0.665178\pi$
$278$	39.8123	2.38778
$279$	−15.1087	−0.904533
$280$	1.08431	0.0647999
$281$	−4.03466	−0.240688	−0.120344	−	0.992732i	$-0.538400\pi$
$281$	−4.03466	−0.240688	−0.120344	+	0.992732i	$0.538400\pi$
$282$	6.58673	0.392234
$283$	12.1085	0.719776	0.359888	−	0.932996i	$-0.382815\pi$
$283$	12.1085	0.719776	0.359888	+	0.932996i	$0.382815\pi$
$284$	3.61829	0.214706
$285$	2.55508	0.151350
$286$	0.00283814	0.000167823 0
$287$	−0.984710	−0.0581256
$288$	−6.22172	−0.366618
$289$	1.00000	0.0588235
$290$	−22.5143	−1.32209
$291$	−2.84319	−0.166671
$292$	−32.9936	−1.93081
$293$	−5.93654	−0.346816	−0.173408	−	0.984850i	$-0.555478\pi$
$293$	−5.93654	−0.346816	−0.173408	+	0.984850i	$0.555478\pi$
$294$	−17.1993	−1.00308
$295$	−3.89689	−0.226886
$296$	8.64008	0.502194
$297$	−0.00310571	−0.000180212 0
$298$	−29.0191	−1.68103
$299$	−7.11764	−0.411624
$300$	−3.79402	−0.219048
$301$	2.94424	0.169703
$302$	−14.0402	−0.807924
$303$	−8.61697	−0.495032
$304$	4.52118	0.259308
$305$	11.0008	0.629903
$306$	−4.50475	−0.257520
$307$	−12.5572	−0.716680	−0.358340	−	0.933591i	$-0.616657\pi$
$307$	−12.5572	−0.716680	−0.358340	+	0.933591i	$0.616657\pi$
$308$	−0.000618191 0	−3.52247e−5 0
$309$	−17.3865	−0.989085
$310$	18.8434	1.07023
$311$	−28.4188	−1.61148	−0.805742	−	0.592266i	$-0.798233\pi$
$311$	−28.4188	−1.61148	−0.805742	+	0.592266i	$0.798233\pi$
$312$	7.96823	0.451112
$313$	12.3391	0.697445	0.348723	−	0.937226i	$-0.386616\pi$
$313$	12.3391	0.697445	0.348723	+	0.937226i	$0.386616\pi$
$314$	−21.9262	−1.23737
$315$	0.537236	0.0302698
$316$	15.8598	0.892186
$317$	20.6207	1.15817	0.579087	−	0.815266i	$-0.303409\pi$
$317$	20.6207	1.15817	0.579087	+	0.815266i	$0.303409\pi$
$318$	−18.8758	−1.05850
$319$	0.00574090	0.000321429 0
$320$	11.4705	0.641222
$321$	−3.53930	−0.197544
$322$	2.40728	0.134152
$323$	−2.43673	−0.135583
$324$	1.13409	0.0630048
$325$	1.98111	0.109892
$326$	10.7528	0.595542
$327$	16.0251	0.886188
$328$	13.3620	0.737791
$329$	0.749147	0.0413018
$330$	0.00150218	8.26923e−5 0
$331$	11.8345	0.650481	0.325241	−	0.945631i	$-0.394555\pi$
$331$	11.8345	0.650481	0.325241	+	0.945631i	$0.394555\pi$
$332$	−30.2003	−1.65746
$333$	4.28084	0.234589
$334$	−38.6584	−2.11529
$335$	−13.8861	−0.758678
$336$	−0.549968	−0.0300032
$337$	6.45529	0.351642	0.175821	−	0.984422i	$-0.443742\pi$
$337$	6.45529	0.351642	0.175821	+	0.984422i	$0.443742\pi$
$338$	21.5109	1.17004
$339$	8.11791	0.440904
$340$	3.61829	0.196229
$341$	−0.00480487	−0.000260198 0
$342$	10.9769	0.593561
$343$	−3.93494	−0.212467
$344$	−39.9517	−2.15405
$345$	−3.76726	−0.202822
$346$	−0.0353460	−0.00190021
$347$	−27.8455	−1.49483	−0.747413	−	0.664359i	$-0.768704\pi$
$347$	−27.8455	−1.49483	−0.747413	+	0.664359i	$0.768704\pi$
$348$	36.0376	1.93182
$349$	31.9098	1.70809	0.854047	−	0.520195i	$-0.174141\pi$
$349$	31.9098	1.70809	0.854047	+	0.520195i	$0.174141\pi$
$350$	−0.670036	−0.0358149
$351$	10.1799	0.543365
$352$	−0.00197863	−0.000105461 0
$353$	−13.4707	−0.716973	−0.358486	−	0.933535i	$-0.616707\pi$
$353$	−13.4707	−0.716973	−0.358486	+	0.933535i	$0.616707\pi$
$354$	9.68539	0.514773
$355$	−1.00000	−0.0530745
$356$	19.9145	1.05547
$357$	0.296410	0.0156877
$358$	−41.5430	−2.19562
$359$	4.63288	0.244514	0.122257	−	0.992498i	$-0.460987\pi$
$359$	4.63288	0.244514	0.122257	+	0.992498i	$0.460987\pi$
$360$	−7.28998	−0.384216
$361$	−13.0623	−0.687492
$362$	20.3315	1.06860
$363$	11.5343	0.605391
$364$	2.02631	0.106208
$365$	9.11858	0.477288
$366$	−27.3415	−1.42916
$367$	−0.859994	−0.0448913	−0.0224457	−	0.999748i	$-0.507145\pi$
$367$	−0.859994	−0.0448913	−0.0224457	+	0.999748i	$0.507145\pi$
$368$	−6.66612	−0.347495
$369$	6.62036	0.344642
$370$	−5.33903	−0.277563
$371$	−2.14685	−0.111459
$372$	−30.1618	−1.56382
$373$	27.5536	1.42667	0.713335	−	0.700824i	$-0.247184\pi$
$373$	27.5536	1.42667	0.713335	+	0.700824i	$0.247184\pi$
$374$	−0.00143260	−7.40781e−5 0
$375$	1.04857	0.0541478
$376$	−10.1655	−0.524246
$377$	−18.8176	−0.969156
$378$	−3.44299	−0.177088
$379$	24.1852	1.24231	0.621155	−	0.783688i	$-0.286664\pi$
$379$	24.1852	1.24231	0.621155	+	0.783688i	$0.286664\pi$
$380$	−8.81679	−0.452292
$381$	13.7020	0.701975
$382$	30.3245	1.55154
$383$	−34.2783	−1.75154	−0.875770	−	0.482729i	$-0.839645\pi$
$383$	−34.2783	−1.75154	−0.875770	+	0.482729i	$0.839645\pi$
$384$	−21.6436	−1.10449
$385$	0.000170852 0	8.70741e−6 0
$386$	−29.6165	−1.50744
$387$	−19.7946	−1.00622
$388$	9.81099	0.498077
$389$	33.3911	1.69299	0.846497	−	0.532393i	$-0.178707\pi$
$389$	33.3911	1.69299	0.846497	+	0.532393i	$0.178707\pi$
$390$	−4.92387	−0.249330
$391$	3.59276	0.181694
$392$	26.5442	1.34068
$393$	16.8294	0.848930
$394$	−17.7143	−0.892434
$395$	−4.38324	−0.220545
$396$	0.00415619	0.000208856 0
$397$	37.4037	1.87724	0.938619	−	0.344955i	$-0.112106\pi$
$397$	37.4037	1.87724	0.938619	+	0.344955i	$0.112106\pi$
$398$	0.0553450	0.00277419
$399$	−0.722271	−0.0361588
$400$	1.85543	0.0927715
$401$	38.5478	1.92499	0.962493	−	0.271307i	$-0.0874557\pi$
$401$	38.5478	1.92499	0.962493	+	0.271307i	$0.0874557\pi$
$402$	34.5127	1.72134
$403$	15.7495	0.784536
$404$	29.7345	1.47935
$405$	−0.313432	−0.0155745
$406$	6.36435	0.315858
$407$	0.00136139	6.74817e−5 0
$408$	−4.02211	−0.199124
$409$	5.06758	0.250576	0.125288	−	0.992120i	$-0.460015\pi$
$409$	5.06758	0.250576	0.125288	+	0.992120i	$0.460015\pi$
$410$	−8.25685	−0.407777
$411$	−15.2757	−0.753493
$412$	59.9956	2.95577
$413$	1.10158	0.0542050
$414$	−16.1845	−0.795425
$415$	8.34659	0.409718
$416$	6.48558	0.317982
$417$	17.6121	0.862469
$418$	0.00349087	0.000170744 0
$419$	−14.1712	−0.692308	−0.346154	−	0.938178i	$-0.612513\pi$
$419$	−14.1712	−0.692308	−0.346154	+	0.938178i	$0.612513\pi$
$420$	1.07250	0.0523324
$421$	−10.5163	−0.512536	−0.256268	−	0.966606i	$-0.582493\pi$
$421$	−10.5163	−0.512536	−0.256268	+	0.966606i	$0.582493\pi$
$422$	−21.9764	−1.06979
$423$	−5.03663	−0.244889
$424$	29.1316	1.41475
$425$	−1.00000	−0.0485071
$426$	2.48541	0.120419
$427$	−3.10971	−0.150489
$428$	12.2130	0.590339
$429$	0.00125553	6.06177e−5 0
$430$	24.6877	1.19054
$431$	24.9149	1.20011	0.600054	−	0.799960i	$-0.295146\pi$
$431$	24.9149	1.20011	0.600054	+	0.799960i	$0.295146\pi$
$432$	9.53415	0.458712
$433$	−25.6624	−1.23326	−0.616628	−	0.787254i	$-0.711502\pi$
$433$	−25.6624	−1.23326	−0.616628	+	0.787254i	$0.711502\pi$
$434$	−5.32667	−0.255688
$435$	−9.95986	−0.477539
$436$	−55.2976	−2.64827
$437$	−8.75460	−0.418789
$438$	−22.6634	−1.08290
$439$	21.2328	1.01339	0.506694	−	0.862126i	$-0.330867\pi$
$439$	21.2328	1.01339	0.506694	+	0.862126i	$0.330867\pi$
$440$	−0.00231836	−0.000110524 0
$441$	13.1517	0.626270
$442$	4.69580	0.223356
$443$	14.1243	0.671064	0.335532	−	0.942029i	$-0.391084\pi$
$443$	14.1243	0.671064	0.335532	+	0.942029i	$0.391084\pi$
$444$	8.54594	0.405572
$445$	−5.50386	−0.260908
$446$	−22.8954	−1.08413
$447$	−12.8374	−0.607190
$448$	−3.24250	−0.153194
$449$	−5.69406	−0.268719	−0.134360	−	0.990933i	$-0.542898\pi$
$449$	−5.69406	−0.268719	−0.134360	+	0.990933i	$0.542898\pi$
$450$	4.50475	0.212356
$451$	0.00210541	9.91397e−5 0
$452$	−28.0124	−1.31759
$453$	−6.21110	−0.291823
$454$	−12.4341	−0.583560
$455$	−0.560020	−0.0262541
$456$	9.80081	0.458965
$457$	30.3508	1.41975	0.709875	−	0.704328i	$-0.248751\pi$
$457$	30.3508	1.41975	0.709875	+	0.704328i	$0.248751\pi$
$458$	6.86908	0.320971
$459$	−5.13851	−0.239845
$460$	12.9996	0.606112
$461$	−2.65079	−0.123459	−0.0617297	−	0.998093i	$-0.519662\pi$
$461$	−2.65079	−0.123459	−0.0617297	+	0.998093i	$0.519662\pi$
$462$	−0.000424637 0	−1.97559e−5 0
$463$	27.3884	1.27285	0.636423	−	0.771341i	$-0.280413\pi$
$463$	27.3884	1.27285	0.636423	+	0.771341i	$0.280413\pi$
$464$	−17.6239	−0.818167
$465$	8.33594	0.386570
$466$	17.9817	0.832988
$467$	−8.16536	−0.377848	−0.188924	−	0.981992i	$-0.560500\pi$
$467$	−8.16536	−0.377848	−0.188924	+	0.981992i	$0.560500\pi$
$468$	−13.6232	−0.629734
$469$	3.92533	0.181255
$470$	6.28164	0.289751
$471$	−9.69970	−0.446939
$472$	−14.9478	−0.688026
$473$	−0.00629508	−0.000289448 0
$474$	10.8942	0.500386
$475$	2.43673	0.111805
$476$	−1.02282	−0.0468808
$477$	14.4336	0.660870
$478$	30.5696	1.39822
$479$	24.0124	1.09715	0.548577	−	0.836100i	$-0.315170\pi$
$479$	24.0124	1.09715	0.548577	+	0.836100i	$0.315170\pi$
$480$	3.43272	0.156681
$481$	−4.46239	−0.203468
$482$	30.0504	1.36876
$483$	1.06493	0.0484560
$484$	−39.8012	−1.80914
$485$	−2.71150	−0.123123
$486$	37.3184	1.69279
$487$	24.3121	1.10169	0.550844	−	0.834608i	$-0.314306\pi$
$487$	24.3121	1.10169	0.550844	+	0.834608i	$0.314306\pi$
$488$	42.1970	1.91017
$489$	4.75681	0.215110
$490$	−16.4026	−0.740996
$491$	−26.3829	−1.19064	−0.595321	−	0.803488i	$-0.702975\pi$
$491$	−26.3829	−1.19064	−0.595321	+	0.803488i	$0.702975\pi$
$492$	13.2164	0.595840
$493$	9.49853	0.427792
$494$	−11.4424	−0.514818
$495$	−0.00114866	−5.16285e−5 0
$496$	14.7503	0.662310
$497$	0.282680	0.0126800
$498$	−20.7447	−0.929593
$499$	−19.8156	−0.887069	−0.443535	−	0.896257i	$-0.646276\pi$
$499$	−19.8156	−0.887069	−0.443535	+	0.896257i	$0.646276\pi$
$500$	−3.61829	−0.161815
$501$	−17.1017	−0.764046
$502$	−11.4615	−0.511553
$503$	14.2382	0.634848	0.317424	−	0.948284i	$-0.397182\pi$
$503$	14.2382	0.634848	0.317424	+	0.948284i	$0.397182\pi$
$504$	2.06074	0.0917925
$505$	−8.21784	−0.365689
$506$	−0.00514700	−0.000228812 0
$507$	9.51599	0.422620
$508$	−47.2814	−2.09777
$509$	−4.32969	−0.191910	−0.0959551	−	0.995386i	$-0.530591\pi$
$509$	−4.32969	−0.191910	−0.0959551	+	0.995386i	$0.530591\pi$
$510$	2.48541	0.110056
$511$	−2.57765	−0.114028
$512$	20.3083	0.897510
$513$	12.5212	0.552823
$514$	41.9430	1.85003
$515$	−16.5812	−0.730655
$516$	−39.5164	−1.73961
$517$	−0.00160175	−7.04449e−5 0
$518$	1.50924	0.0663121
$519$	−0.0156363	−0.000686359 0
$520$	7.59916	0.333245
$521$	41.1120	1.80115	0.900576	−	0.434699i	$-0.143145\pi$
$521$	41.1120	1.80115	0.900576	+	0.434699i	$0.143145\pi$
$522$	−42.7885	−1.87280
$523$	−5.50737	−0.240820	−0.120410	−	0.992724i	$-0.538421\pi$
$523$	−5.50737	−0.240820	−0.120410	+	0.992724i	$0.538421\pi$
$524$	−58.0730	−2.53693
$525$	−0.296410	−0.0129364
$526$	43.7704	1.90848
$527$	−7.94983	−0.346300
$528$	0.00117588	5.11738e−5 0
$529$	−10.0921	−0.438785
$530$	−18.0015	−0.781934
$531$	−7.40606	−0.321396
$532$	2.49234	0.108056
$533$	−6.90113	−0.298921
$534$	13.6794	0.591964
$535$	−3.37536	−0.145930
$536$	−53.2645	−2.30068
$537$	−18.3778	−0.793059
$538$	61.3501	2.64499
$539$	0.00418249	0.000180153 0
$540$	−18.5926	−0.800099
$541$	0.159930	0.00687591	0.00343796	−	0.999994i	$-0.498906\pi$
$541$	0.159930	0.00687591	0.00343796	+	0.999994i	$0.498906\pi$
$542$	15.8506	0.680842
$543$	8.99422	0.385979
$544$	−3.27372	−0.140360
$545$	15.2828	0.654643
$546$	1.39188	0.0595670
$547$	10.6156	0.453892	0.226946	−	0.973907i	$-0.427126\pi$
$547$	10.6156	0.453892	0.226946	+	0.973907i	$0.427126\pi$
$548$	52.7116	2.25173
$549$	20.9070	0.892291
$550$	0.00143260	6.10863e−5 0
$551$	−23.1454	−0.986026
$552$	−14.4505	−0.615054
$553$	1.23906	0.0526901
$554$	39.1296	1.66246
$555$	−2.36187	−0.100256
$556$	−60.7740	−2.57739
$557$	2.67304	0.113261	0.0566303	−	0.998395i	$-0.481964\pi$
$557$	2.67304	0.113261	0.0566303	+	0.998395i	$0.481964\pi$
$558$	35.8120	1.51604
$559$	20.6341	0.872730
$560$	−0.524494	−0.0221639
$561$	−0.000633753 0	−2.67571e−5 0
$562$	9.56332	0.403404
$563$	22.8170	0.961622	0.480811	−	0.876824i	$-0.340342\pi$
$563$	22.8170	0.961622	0.480811	+	0.876824i	$0.340342\pi$
$564$	−10.0547	−0.423381
$565$	7.74190	0.325704
$566$	−28.7007	−1.20638
$567$	0.0886010	0.00372089
$568$	−3.83582	−0.160947
$569$	−9.69926	−0.406614	−0.203307	−	0.979115i	$-0.565169\pi$
$569$	−9.69926	−0.406614	−0.203307	+	0.979115i	$0.565169\pi$
$570$	−6.05628	−0.253670
$571$	28.2723	1.18316	0.591580	−	0.806247i	$-0.298505\pi$
$571$	28.2723	1.18316	0.591580	+	0.806247i	$0.298505\pi$
$572$	−0.00433246	−0.000181149 0
$573$	13.4149	0.560417
$574$	2.33405	0.0974214
$575$	−3.59276	−0.149829
$576$	21.7998	0.908325
$577$	37.8742	1.57672	0.788362	−	0.615211i	$-0.210929\pi$
$577$	37.8742	1.57672	0.788362	+	0.615211i	$0.210929\pi$
$578$	−2.37029	−0.0985912
$579$	−13.1017	−0.544490
$580$	34.3684	1.42707
$581$	−2.35942	−0.0978851
$582$	6.73920	0.279349
$583$	0.00459018	0.000190106 0
$584$	34.9772	1.44737
$585$	3.76510	0.155668
$586$	14.0713	0.581281
$587$	41.9374	1.73094	0.865471	−	0.500960i	$-0.167019\pi$
$587$	41.9374	1.73094	0.865471	+	0.500960i	$0.167019\pi$
$588$	26.2550	1.08274
$589$	19.3716	0.798193
$590$	9.23677	0.380272
$591$	−7.83645	−0.322348
$592$	−4.17931	−0.171769
$593$	23.4929	0.964739	0.482369	−	0.875968i	$-0.339776\pi$
$593$	23.4929	0.964739	0.482369	+	0.875968i	$0.339776\pi$
$594$	0.00736144	0.000302044 0
$595$	0.282680	0.0115888
$596$	44.2981	1.81452
$597$	0.0244835	0.00100204
$598$	16.8709	0.689902
$599$	44.3759	1.81315	0.906574	−	0.422046i	$-0.138688\pi$
$599$	44.3759	1.81315	0.906574	+	0.422046i	$0.138688\pi$
$600$	4.02211	0.164202
$601$	9.66288	0.394157	0.197079	−	0.980388i	$-0.436855\pi$
$601$	9.66288	0.394157	0.197079	+	0.980388i	$0.436855\pi$
$602$	−6.97872	−0.284431
$603$	−26.3906	−1.07471
$604$	21.4326	0.872080
$605$	11.0000	0.447214
$606$	20.4247	0.829698
$607$	19.7743	0.802615	0.401307	−	0.915943i	$-0.368556\pi$
$607$	19.7743	0.802615	0.401307	+	0.915943i	$0.368556\pi$
$608$	7.97717	0.323517
$609$	2.81546	0.114088
$610$	−26.0751	−1.05575
$611$	5.25024	0.212402
$612$	6.87657	0.277969
$613$	4.99115	0.201591	0.100795	−	0.994907i	$-0.467861\pi$
$613$	4.99115	0.201591	0.100795	+	0.994907i	$0.467861\pi$
$614$	29.7643	1.20119
$615$	−3.65266	−0.147289
$616$	0.000655356 0	2.64050e−5 0
$617$	−33.1766	−1.33564	−0.667820	−	0.744323i	$-0.732773\pi$
$617$	−33.1766	−1.33564	−0.667820	+	0.744323i	$0.732773\pi$
$618$	41.2111	1.65776
$619$	−4.05299	−0.162903	−0.0814516	−	0.996677i	$-0.525956\pi$
$619$	−4.05299	−0.162903	−0.0814516	+	0.996677i	$0.525956\pi$
$620$	−28.7648	−1.15522
$621$	−18.4615	−0.740833
$622$	67.3610	2.70093
$623$	1.55583	0.0623332
$624$	−3.85433	−0.154297
$625$	1.00000	0.0400000
$626$	−29.2472	−1.16895
$627$	0.00154429	6.16729e−5 0
$628$	33.4707	1.33563
$629$	2.25248	0.0898121
$630$	−1.27341	−0.0507337
$631$	8.25297	0.328546	0.164273	−	0.986415i	$-0.447472\pi$
$631$	8.25297	0.328546	0.164273	+	0.986415i	$0.447472\pi$
$632$	−16.8133	−0.668798
$633$	−9.72190	−0.386411
$634$	−48.8771	−1.94116
$635$	13.0673	0.518562
$636$	28.8142	1.14256
$637$	−13.7094	−0.543188
$638$	−0.0136076	−0.000538731 0
$639$	−1.90050	−0.0751828
$640$	−20.6411	−0.815910
$641$	12.7155	0.502233	0.251116	−	0.967957i	$-0.419202\pi$
$641$	12.7155	0.502233	0.251116	+	0.967957i	$0.419202\pi$
$642$	8.38917	0.331094
$643$	−16.2549	−0.641029	−0.320515	−	0.947244i	$-0.603856\pi$
$643$	−16.2549	−0.641029	−0.320515	+	0.947244i	$0.603856\pi$
$644$	−3.67475	−0.144805
$645$	10.9213	0.430026
$646$	5.77577	0.227244
$647$	30.6923	1.20664	0.603319	−	0.797500i	$-0.293844\pi$
$647$	30.6923	1.20664	0.603319	+	0.797500i	$0.293844\pi$
$648$	−1.20227	−0.0472295
$649$	−0.00235528	−9.24527e−5 0
$650$	−4.69580	−0.184184
$651$	−2.35641	−0.0923549
$652$	−16.4143	−0.642834
$653$	−13.8304	−0.541225	−0.270613	−	0.962688i	$-0.587226\pi$
$653$	−13.8304	−0.541225	−0.270613	+	0.962688i	$0.587226\pi$
$654$	−37.9841	−1.48530
$655$	16.0499	0.627120
$656$	−6.46334	−0.252351
$657$	17.3299	0.676104
$658$	−1.77570	−0.0692239
$659$	−35.0878	−1.36683	−0.683413	−	0.730032i	$-0.739505\pi$
$659$	−35.0878	−1.36683	−0.683413	+	0.730032i	$0.739505\pi$
$660$	−0.00229310	−8.92589e−5 0
$661$	11.0537	0.429937	0.214969	−	0.976621i	$-0.431035\pi$
$661$	11.0537	0.429937	0.214969	+	0.976621i	$0.431035\pi$
$662$	−28.0512	−1.09024
$663$	2.07732	0.0806766
$664$	32.0160	1.24246
$665$	−0.688816	−0.0267112
$666$	−10.1468	−0.393182
$667$	34.1260	1.32136
$668$	59.0126	2.28326
$669$	−10.1285	−0.391589
$670$	32.9141	1.27158
$671$	0.00664886	0.000256676 0
$672$	−0.970362	−0.0374325
$673$	9.24718	0.356452	0.178226	−	0.983990i	$-0.442964\pi$
$673$	9.24718	0.356452	0.178226	+	0.983990i	$0.442964\pi$
$674$	−15.3009	−0.589370
$675$	5.13851	0.197781
$676$	−32.8368	−1.26295
$677$	33.8996	1.30287	0.651435	−	0.758705i	$-0.274168\pi$
$677$	33.8996	1.30287	0.651435	+	0.758705i	$0.274168\pi$
$678$	−19.2418	−0.738977
$679$	0.766488	0.0294151
$680$	−3.83582	−0.147097
$681$	−5.50058	−0.210783
$682$	0.0113889	0.000436105 0
$683$	−25.2089	−0.964591	−0.482296	−	0.876009i	$-0.660197\pi$
$683$	−25.2089	−0.964591	−0.482296	+	0.876009i	$0.660197\pi$
$684$	−16.7564	−0.640695
$685$	−14.5681	−0.556619
$686$	9.32696	0.356105
$687$	3.03874	0.115935
$688$	19.3251	0.736764
$689$	−15.0458	−0.573197
$690$	8.92950	0.339940
$691$	−1.10877	−0.0421798	−0.0210899	−	0.999778i	$-0.506714\pi$
$691$	−1.10877	−0.0421798	−0.0210899	+	0.999778i	$0.506714\pi$
$692$	0.0539562	0.00205111
$693$	0.000324704 0	1.23345e−5 0
$694$	66.0021	2.50540
$695$	16.7964	0.637122
$696$	−38.2042	−1.44813
$697$	3.48347	0.131946
$698$	−75.6357	−2.86285
$699$	7.95475	0.300876
$700$	1.02282	0.0386589
$701$	11.2032	0.423140	0.211570	−	0.977363i	$-0.432142\pi$
$701$	11.2032	0.423140	0.211570	+	0.977363i	$0.432142\pi$
$702$	−24.1294	−0.910707
$703$	−5.48868	−0.207009
$704$	0.00693277	0.000261289 0
$705$	2.77887	0.104658
$706$	31.9295	1.20168
$707$	2.32302	0.0873663
$708$	−14.7849	−0.555650
$709$	2.63876	0.0991006	0.0495503	−	0.998772i	$-0.484221\pi$
$709$	2.63876	0.0991006	0.0495503	+	0.998772i	$0.484221\pi$
$710$	2.37029	0.0889555
$711$	−8.33038	−0.312414
$712$	−21.1118	−0.791198
$713$	−28.5618	−1.06965
$714$	−0.702578	−0.0262933
$715$	0.00119738	4.47794e−5 0
$716$	63.4160	2.36997
$717$	13.5234	0.505039
$718$	−10.9813	−0.409818
$719$	10.7071	0.399306	0.199653	−	0.979867i	$-0.436018\pi$
$719$	10.7071	0.399306	0.199653	+	0.979867i	$0.436018\pi$
$720$	3.52625	0.131416
$721$	4.68718	0.174560
$722$	30.9616	1.15227
$723$	13.2937	0.494397
$724$	−31.0363	−1.15345
$725$	−9.49853	−0.352767
$726$	−27.3395	−1.01467
$727$	18.9424	0.702535	0.351268	−	0.936275i	$-0.385751\pi$
$727$	18.9424	0.702535	0.351268	+	0.936275i	$0.385751\pi$
$728$	−2.14813	−0.0796151
$729$	15.5686	0.576614
$730$	−21.6137	−0.799959
$731$	−10.4154	−0.385229
$732$	41.7372	1.54265
$733$	−12.5955	−0.465226	−0.232613	−	0.972569i	$-0.574728\pi$
$733$	−12.5955	−0.465226	−0.232613	+	0.972569i	$0.574728\pi$
$734$	2.03844	0.0752401
$735$	−7.25619	−0.267649
$736$	−11.7617	−0.433542
$737$	−0.00839274	−0.000309150 0
$738$	−15.6922	−0.577637
$739$	−7.88014	−0.289876	−0.144938	−	0.989441i	$-0.546298\pi$
$739$	−7.88014	−0.289876	−0.144938	+	0.989441i	$0.546298\pi$
$740$	8.15010	0.299604
$741$	−5.06188	−0.185953
$742$	5.08867	0.186811
$743$	35.4965	1.30224	0.651120	−	0.758975i	$-0.274299\pi$
$743$	35.4965	1.30224	0.651120	+	0.758975i	$0.274299\pi$
$744$	31.9751	1.17226
$745$	−12.2428	−0.448543
$746$	−65.3100	−2.39117
$747$	15.8627	0.580387
$748$	0.00218689	7.99606e−5 0
$749$	0.954148	0.0348638
$750$	−2.48541	−0.0907545
$751$	6.37638	0.232677	0.116339	−	0.993210i	$-0.462884\pi$
$751$	6.37638	0.232677	0.116339	+	0.993210i	$0.462884\pi$
$752$	4.91718	0.179311
$753$	−5.07035	−0.184774
$754$	44.6032	1.62435
$755$	−5.92341	−0.215575
$756$	5.25577	0.191151
$757$	45.0058	1.63576	0.817881	−	0.575387i	$-0.195149\pi$
$757$	45.0058	1.63576	0.817881	+	0.575387i	$0.195149\pi$
$758$	−57.3260	−2.08217
$759$	−0.00227692	−8.26471e−5 0
$760$	9.34685	0.339046
$761$	45.3304	1.64323	0.821613	−	0.570045i	$-0.193074\pi$
$761$	45.3304	1.64323	0.821613	+	0.570045i	$0.193074\pi$
$762$	−32.4778	−1.17655
$763$	−4.32015	−0.156400
$764$	−46.2908	−1.67474
$765$	−1.90050	−0.0687129
$766$	81.2496	2.93567
$767$	7.72016	0.278759
$768$	27.2464	0.983168
$769$	23.8470	0.859945	0.429972	−	0.902842i	$-0.358523\pi$
$769$	23.8470	0.859945	0.429972	+	0.902842i	$0.358523\pi$
$770$	−0.000404969 0	−1.45941e−5 0
$771$	18.5547	0.668232
$772$	45.2101	1.62715
$773$	−38.1499	−1.37216	−0.686078	−	0.727528i	$-0.740669\pi$
$773$	−38.1499	−1.37216	−0.686078	+	0.727528i	$0.740669\pi$
$774$	46.9190	1.68647
$775$	7.94983	0.285566
$776$	−10.4008	−0.373367
$777$	0.667656	0.0239520
$778$	−79.1466	−2.83754
$779$	−8.48829	−0.304125
$780$	7.51636	0.269129
$781$	−0.000604399 0	−2.16271e−5 0
$782$	−8.51590	−0.304528
$783$	−48.8083	−1.74427
$784$	−12.8397	−0.458562
$785$	−9.25043	−0.330162
$786$	−39.8905	−1.42285
$787$	21.8669	0.779471	0.389735	−	0.920927i	$-0.372566\pi$
$787$	21.8669	0.779471	0.389735	+	0.920927i	$0.372566\pi$
$788$	27.0412	0.963302
$789$	19.3631	0.689345
$790$	10.3896	0.369644
$791$	−2.18848	−0.0778135
$792$	−0.00440606	−0.000156562 0
$793$	−21.7937	−0.773918
$794$	−88.6578	−3.14635
$795$	−7.96348	−0.282435
$796$	−0.0844849	−0.00299449
$797$	21.7013	0.768698	0.384349	−	0.923188i	$-0.374426\pi$
$797$	21.7013	0.768698	0.384349	+	0.923188i	$0.374426\pi$
$798$	1.71199	0.0606039
$799$	−2.65015	−0.0937557
$800$	3.27372	0.115743
$801$	−10.4601	−0.369590
$802$	−91.3696	−3.22637
$803$	0.00551126	0.000194488 0
$804$	−52.6841	−1.85803
$805$	1.01560	0.0357953
$806$	−37.3308	−1.31492
$807$	27.1400	0.955374
$808$	−31.5221	−1.10894
$809$	32.6662	1.14848	0.574241	−	0.818686i	$-0.305297\pi$
$809$	32.6662	1.14848	0.574241	+	0.818686i	$0.305297\pi$
$810$	0.742925	0.0261037
$811$	39.0310	1.37056	0.685282	−	0.728277i	$-0.259679\pi$
$811$	39.0310	1.37056	0.685282	+	0.728277i	$0.259679\pi$
$812$	−9.71528	−0.340940
$813$	7.01198	0.245921
$814$	−0.00322690	−0.000113103 0
$815$	4.53648	0.158906
$816$	1.94554	0.0681077
$817$	25.3796	0.887921
$818$	−12.0116	−0.419977
$819$	−1.06432	−0.0371904
$820$	12.6042	0.440158
$821$	39.8870	1.39206	0.696032	−	0.718010i	$-0.254947\pi$
$821$	39.8870	1.39206	0.696032	+	0.718010i	$0.254947\pi$
$822$	36.2078	1.26289
$823$	−16.9927	−0.592327	−0.296163	−	0.955137i	$-0.595707\pi$
$823$	−16.9927	−0.592327	−0.296163	+	0.955137i	$0.595707\pi$
$824$	−63.6024	−2.21570
$825$	0.000633753 0	2.20645e−5 0
$826$	−2.61106	−0.0908503
$827$	−16.9841	−0.590594	−0.295297	−	0.955406i	$-0.595419\pi$
$827$	−16.9841	−0.590594	−0.295297	+	0.955406i	$0.595419\pi$
$828$	24.7059	0.858589
$829$	−15.7947	−0.548572	−0.274286	−	0.961648i	$-0.588442\pi$
$829$	−15.7947	−0.548572	−0.274286	+	0.961648i	$0.588442\pi$
$830$	−19.7838	−0.686707
$831$	17.3101	0.600482
$832$	−22.7243	−0.787825
$833$	6.92009	0.239767
$834$	−41.7459	−1.44554
$835$	−16.3095	−0.564415
$836$	−0.00532886	−0.000184302 0
$837$	40.8503	1.41199
$838$	33.5899	1.16034
$839$	6.76677	0.233615	0.116807	−	0.993155i	$-0.462734\pi$
$839$	6.76677	0.233615	0.116807	+	0.993155i	$0.462734\pi$
$840$	−1.13697	−0.0392293
$841$	61.2221	2.11111
$842$	24.9268	0.859035
$843$	4.23061	0.145710
$844$	33.5473	1.15475
$845$	9.07522	0.312197
$846$	11.9383	0.410447
$847$	−3.10949	−0.106843
$848$	−14.0913	−0.483897
$849$	−12.6966	−0.435746
$850$	2.37029	0.0813004
$851$	8.09261	0.277411
$852$	−3.79402	−0.129981
$853$	−5.84731	−0.200208	−0.100104	−	0.994977i	$-0.531918\pi$
$853$	−5.84731	−0.200208	−0.100104	+	0.994977i	$0.531918\pi$
$854$	7.37092	0.252228
$855$	4.63102	0.158377
$856$	−12.9473	−0.442528
$857$	9.10492	0.311018	0.155509	−	0.987834i	$-0.450298\pi$
$857$	9.10492	0.311018	0.155509	+	0.987834i	$0.450298\pi$
$858$	−0.00297598	−0.000101598 0
$859$	−4.36976	−0.149094	−0.0745471	−	0.997217i	$-0.523751\pi$
$859$	−4.36976	−0.149094	−0.0745471	+	0.997217i	$0.523751\pi$
$860$	−37.6861	−1.28508
$861$	1.03254	0.0351887
$862$	−59.0556	−2.01144
$863$	49.6512	1.69015	0.845073	−	0.534651i	$-0.179557\pi$
$863$	49.6512	1.69015	0.845073	+	0.534651i	$0.179557\pi$
$864$	16.8220	0.572298
$865$	−0.0149121	−0.000507026 0
$866$	60.8274	2.06700
$867$	−1.04857	−0.0356112
$868$	8.13124	0.275992
$869$	−0.00264923	−8.98689e−5 0
$870$	23.6078	0.800379
$871$	27.5098	0.932135
$872$	58.6220	1.98519
$873$	−5.15322	−0.174410
$874$	20.7510	0.701911
$875$	−0.282680	−0.00955634
$876$	34.5961	1.16889
$877$	8.45179	0.285397	0.142698	−	0.989766i	$-0.454422\pi$
$877$	8.45179	0.285397	0.142698	+	0.989766i	$0.454422\pi$
$878$	−50.3280	−1.69849
$879$	6.22486	0.209959
$880$	0.00112142	3.78030e−5 0
$881$	−10.9718	−0.369648	−0.184824	−	0.982772i	$-0.559172\pi$
$881$	−10.9718	−0.369648	−0.184824	+	0.982772i	$0.559172\pi$
$882$	−31.1733	−1.04966
$883$	0.205234	0.00690669	0.00345334	−	0.999994i	$-0.498901\pi$
$883$	0.205234	0.00690669	0.00345334	+	0.999994i	$0.498901\pi$
$884$	−7.16821	−0.241093
$885$	4.08616	0.137355
$886$	−33.4786	−1.12474
$887$	−0.664267	−0.0223039	−0.0111520	−	0.999938i	$-0.503550\pi$
$887$	−0.664267	−0.0223039	−0.0111520	+	0.999938i	$0.503550\pi$
$888$	−9.05971	−0.304024
$889$	−3.69388	−0.123889
$890$	13.0458	0.437295
$891$	−0.000189438 0	−6.34640e−6 0
$892$	34.9502	1.17022
$893$	6.45771	0.216099
$894$	30.4285	1.01768
$895$	−17.5265	−0.585847
$896$	5.83483	0.194928
$897$	7.46333	0.249193
$898$	13.4966	0.450387
$899$	−75.5117	−2.51846
$900$	−6.87657	−0.229219
$901$	7.59462	0.253014
$902$	−0.00499043	−0.000166163 0
$903$	−3.08724	−0.102737
$904$	29.6965	0.987690
$905$	8.57762	0.285130
$906$	14.7221	0.489110
$907$	6.32817	0.210123	0.105062	−	0.994466i	$-0.466496\pi$
$907$	6.32817	0.210123	0.105062	+	0.994466i	$0.466496\pi$
$908$	18.9808	0.629900
$909$	−15.6180	−0.518018
$910$	1.32741	0.0440033
$911$	−20.3238	−0.673359	−0.336679	−	0.941619i	$-0.609304\pi$
$911$	−20.3238	−0.673359	−0.336679	+	0.941619i	$0.609304\pi$
$912$	−4.74077	−0.156983
$913$	0.00504466	0.000166954 0
$914$	−71.9403	−2.37957
$915$	−11.5351	−0.381338
$916$	−10.4858	−0.346459
$917$	−4.53698	−0.149824
$918$	12.1798	0.401993
$919$	18.6130	0.613988	0.306994	−	0.951711i	$-0.400677\pi$
$919$	18.6130	0.613988	0.306994	+	0.951711i	$0.400677\pi$
$920$	−13.7812	−0.454352
$921$	13.1671	0.433872
$922$	6.28314	0.206924
$923$	1.98111	0.0652089
$924$	0.000648215 0	2.13247e−5 0
$925$	−2.25248	−0.0740609
$926$	−64.9184	−2.13335
$927$	−31.5126	−1.03501
$928$	−31.0955	−1.02076
$929$	−47.6623	−1.56375	−0.781875	−	0.623436i	$-0.785736\pi$
$929$	−47.6623	−1.56375	−0.781875	+	0.623436i	$0.785736\pi$
$930$	−19.7586	−0.647910
$931$	−16.8624	−0.552643
$932$	−27.4494	−0.899135
$933$	29.7991	0.975579
$934$	19.3543	0.633292
$935$	−0.000604399 0	−1.97659e−5 0
$936$	14.4422	0.472059
$937$	5.62874	0.183883	0.0919414	−	0.995764i	$-0.470693\pi$
$937$	5.62874	0.183883	0.0919414	+	0.995764i	$0.470693\pi$
$938$	−9.30418	−0.303792
$939$	−12.9384	−0.422227
$940$	−9.58902	−0.312759
$941$	0.0575816	0.00187711	0.000938553	−	1.00000i	$-0.499701\pi$
$941$	0.0575816	0.00187711	0.000938553		1.00000i	$0.499701\pi$
$942$	22.9911	0.749092
$943$	12.5153	0.407554
$944$	7.23041	0.235330
$945$	−1.45256	−0.0472517
$946$	0.0149212	0.000485130 0
$947$	22.4710	0.730210	0.365105	−	0.930966i	$-0.381033\pi$
$947$	22.4710	0.730210	0.365105	+	0.930966i	$0.381033\pi$
$948$	−16.6301	−0.540121
$949$	−18.0649	−0.586411
$950$	−5.77577	−0.187391
$951$	−21.6222	−0.701148
$952$	1.08431	0.0351427
$953$	−17.9550	−0.581619	−0.290810	−	0.956781i	$-0.593925\pi$
$953$	−17.9550	−0.581619	−0.290810	+	0.956781i	$0.593925\pi$
$954$	−34.2119	−1.10765
$955$	12.7936	0.413990
$956$	−46.6650	−1.50925
$957$	−0.00601973	−0.000194590 0
$958$	−56.9163	−1.83888
$959$	4.11812	0.132981
$960$	−12.0276	−0.388190
$961$	32.1998	1.03870
$962$	10.5772	0.341022
$963$	−6.41489	−0.206717
$964$	−45.8724	−1.47745
$965$	−12.4949	−0.402225
$966$	−2.52420	−0.0812147
$967$	−30.2252	−0.971977	−0.485988	−	0.873965i	$-0.661540\pi$
$967$	−30.2252	−0.971977	−0.485988	+	0.873965i	$0.661540\pi$
$968$	42.1940	1.35617
$969$	2.55508	0.0820810
$970$	6.42705	0.206360
$971$	−2.04882	−0.0657498	−0.0328749	−	0.999459i	$-0.510466\pi$
$971$	−2.04882	−0.0657498	−0.0328749	+	0.999459i	$0.510466\pi$
$972$	−56.9670	−1.82722
$973$	−4.74800	−0.152214
$974$	−57.6269	−1.84649
$975$	−2.07732	−0.0665276
$976$	−20.4112	−0.653346
$977$	−5.99943	−0.191939	−0.0959694	−	0.995384i	$-0.530595\pi$
$977$	−5.99943	−0.191939	−0.0959694	+	0.995384i	$0.530595\pi$
$978$	−11.2750	−0.360536
$979$	−0.00332653	−0.000106316 0
$980$	25.0389	0.799838
$981$	29.0450	0.927337
$982$	62.5352	1.99558
$983$	56.8133	1.81206	0.906032	−	0.423209i	$-0.139097\pi$
$983$	56.8133	1.81206	0.906032	+	0.423209i	$0.139097\pi$
$984$	−14.0109	−0.446652
$985$	−7.47347	−0.238125
$986$	−22.5143	−0.717001
$987$	−0.785532	−0.0250038
$988$	17.4670	0.555699
$989$	−37.4202	−1.18989
$990$	0.00272267	8.65320e−5 0
$991$	9.52712	0.302639	0.151319	−	0.988485i	$-0.451648\pi$
$991$	9.52712	0.302639	0.151319	+	0.988485i	$0.451648\pi$
$992$	26.0255	0.826310
$993$	−12.4093	−0.393796
$994$	−0.670036	−0.0212522
$995$	0.0233494	0.000740226 0
$996$	31.6671	1.00341
$997$	−27.2014	−0.861478	−0.430739	−	0.902477i	$-0.641747\pi$
$997$	−27.2014	−0.861478	−0.430739	+	0.902477i	$0.641747\pi$
$998$	46.9688	1.48677
$999$	−11.5744	−0.366197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.f.1.5	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.f.1.5	✓	49	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37029 q^{2} -1.04857 q^{3} +3.61829 q^{4} -1.00000 q^{5} +2.48541 q^{6} +0.282680 q^{7} -3.83582 q^{8} -1.90050 q^{9} +O(q^{10})\)	\(q-2.37029 q^{2} -1.04857 q^{3} +3.61829 q^{4} -1.00000 q^{5} +2.48541 q^{6} +0.282680 q^{7} -3.83582 q^{8} -1.90050 q^{9} +2.37029 q^{10} -0.000604399 q^{11} -3.79402 q^{12} +1.98111 q^{13} -0.670036 q^{14} +1.04857 q^{15} +1.85543 q^{16} -1.00000 q^{17} +4.50475 q^{18} +2.43673 q^{19} -3.61829 q^{20} -0.296410 q^{21} +0.00143260 q^{22} -3.59276 q^{23} +4.02211 q^{24} +1.00000 q^{25} -4.69580 q^{26} +5.13851 q^{27} +1.02282 q^{28} -9.49853 q^{29} -2.48541 q^{30} +7.94983 q^{31} +3.27372 q^{32} +0.000633753 q^{33} +2.37029 q^{34} -0.282680 q^{35} -6.87657 q^{36} -2.25248 q^{37} -5.77577 q^{38} -2.07732 q^{39} +3.83582 q^{40} -3.48347 q^{41} +0.702578 q^{42} +10.4154 q^{43} -0.00218689 q^{44} +1.90050 q^{45} +8.51590 q^{46} +2.65015 q^{47} -1.94554 q^{48} -6.92009 q^{49} -2.37029 q^{50} +1.04857 q^{51} +7.16821 q^{52} -7.59462 q^{53} -12.1798 q^{54} +0.000604399 q^{55} -1.08431 q^{56} -2.55508 q^{57} +22.5143 q^{58} +3.89689 q^{59} +3.79402 q^{60} -11.0008 q^{61} -18.8434 q^{62} -0.537236 q^{63} -11.4705 q^{64} -1.98111 q^{65} -0.00150218 q^{66} +13.8861 q^{67} -3.61829 q^{68} +3.76726 q^{69} +0.670036 q^{70} +1.00000 q^{71} +7.28998 q^{72} -9.11858 q^{73} +5.33903 q^{74} -1.04857 q^{75} +8.81679 q^{76} -0.000170852 q^{77} +4.92387 q^{78} +4.38324 q^{79} -1.85543 q^{80} +0.313432 q^{81} +8.25685 q^{82} -8.34659 q^{83} -1.07250 q^{84} +1.00000 q^{85} -24.6877 q^{86} +9.95986 q^{87} +0.00231836 q^{88} +5.50386 q^{89} -4.50475 q^{90} +0.560020 q^{91} -12.9996 q^{92} -8.33594 q^{93} -6.28164 q^{94} -2.43673 q^{95} -3.43272 q^{96} +2.71150 q^{97} +16.4026 q^{98} +0.00114866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q + 3 q^{2} + 6 q^{3} + 55 q^{4} - 49 q^{5} - 6 q^{6} + 11 q^{7} + 9 q^{8} + 43 q^{9}+O(q^{10}) \) 49 * q + 3 * q^2 + 6 * q^3 + 55 * q^4 - 49 * q^5 - 6 * q^6 + 11 * q^7 + 9 * q^8 + 43 * q^9	\( 49 q + 3 q^{2} + 6 q^{3} + 55 q^{4} - 49 q^{5} - 6 q^{6} + 11 q^{7} + 9 q^{8} + 43 q^{9} - 3 q^{10} - 10 q^{11} + 2 q^{12} + 43 q^{13} - 16 q^{14} - 6 q^{15} + 63 q^{16} - 49 q^{17} + 8 q^{18} + 15 q^{19} - 55 q^{20} + 19 q^{21} - 2 q^{23} - 3 q^{24} + 49 q^{25} + 22 q^{26} + 27 q^{27} + 32 q^{28} - 38 q^{29} + 6 q^{30} + 11 q^{31} + 16 q^{32} + 51 q^{33} - 3 q^{34} - 11 q^{35} + 83 q^{36} + 54 q^{37} + 39 q^{38} - 25 q^{39} - 9 q^{40} - 29 q^{41} + 52 q^{42} + 29 q^{43} - 47 q^{44} - 43 q^{45} + 10 q^{46} + 60 q^{47} + 16 q^{48} + 82 q^{49} + 3 q^{50} - 6 q^{51} + 113 q^{52} + 41 q^{53} + 28 q^{54} + 10 q^{55} - 16 q^{56} + 18 q^{57} + 14 q^{58} + 8 q^{59} - 2 q^{60} + 65 q^{61} + 37 q^{62} - 4 q^{63} + 77 q^{64} - 43 q^{65} + 27 q^{66} + 65 q^{67} - 55 q^{68} + 23 q^{69} + 16 q^{70} + 49 q^{71} + 121 q^{72} + 59 q^{73} - 53 q^{74} + 6 q^{75} + 50 q^{76} + 41 q^{77} + 26 q^{78} + 11 q^{79} - 63 q^{80} + 41 q^{81} + 77 q^{82} + 16 q^{83} + 30 q^{84} + 49 q^{85} - q^{86} + 8 q^{87} + 11 q^{88} - 4 q^{89} - 8 q^{90} + 47 q^{91} + 60 q^{92} + 69 q^{93} + 66 q^{94} - 15 q^{95} - 19 q^{96} + 76 q^{97} + 31 q^{98} - 39 q^{99}+O(q^{100}) \) 49 * q + 3 * q^2 + 6 * q^3 + 55 * q^4 - 49 * q^5 - 6 * q^6 + 11 * q^7 + 9 * q^8 + 43 * q^9 - 3 * q^10 - 10 * q^11 + 2 * q^12 + 43 * q^13 - 16 * q^14 - 6 * q^15 + 63 * q^16 - 49 * q^17 + 8 * q^18 + 15 * q^19 - 55 * q^20 + 19 * q^21 - 2 * q^23 - 3 * q^24 + 49 * q^25 + 22 * q^26 + 27 * q^27 + 32 * q^28 - 38 * q^29 + 6 * q^30 + 11 * q^31 + 16 * q^32 + 51 * q^33 - 3 * q^34 - 11 * q^35 + 83 * q^36 + 54 * q^37 + 39 * q^38 - 25 * q^39 - 9 * q^40 - 29 * q^41 + 52 * q^42 + 29 * q^43 - 47 * q^44 - 43 * q^45 + 10 * q^46 + 60 * q^47 + 16 * q^48 + 82 * q^49 + 3 * q^50 - 6 * q^51 + 113 * q^52 + 41 * q^53 + 28 * q^54 + 10 * q^55 - 16 * q^56 + 18 * q^57 + 14 * q^58 + 8 * q^59 - 2 * q^60 + 65 * q^61 + 37 * q^62 - 4 * q^63 + 77 * q^64 - 43 * q^65 + 27 * q^66 + 65 * q^67 - 55 * q^68 + 23 * q^69 + 16 * q^70 + 49 * q^71 + 121 * q^72 + 59 * q^73 - 53 * q^74 + 6 * q^75 + 50 * q^76 + 41 * q^77 + 26 * q^78 + 11 * q^79 - 63 * q^80 + 41 * q^81 + 77 * q^82 + 16 * q^83 + 30 * q^84 + 49 * q^85 - q^86 + 8 * q^87 + 11 * q^88 - 4 * q^89 - 8 * q^90 + 47 * q^91 + 60 * q^92 + 69 * q^93 + 66 * q^94 - 15 * q^95 - 19 * q^96 + 76 * q^97 + 31 * q^98 - 39 * q^99

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