LMFDB - Embedded newform 8018.2.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.99099 q^{3} +1.00000 q^{4} +3.02780 q^{5} -1.99099 q^{6} -1.37345 q^{7} +1.00000 q^{8} +0.964042 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.99099 q^{3} +1.00000 q^{4} +3.02780 q^{5} -1.99099 q^{6} -1.37345 q^{7} +1.00000 q^{8} +0.964042 q^{9} +3.02780 q^{10} +0.397234 q^{11} -1.99099 q^{12} -4.55614 q^{13} -1.37345 q^{14} -6.02831 q^{15} +1.00000 q^{16} -3.23767 q^{17} +0.964042 q^{18} -1.00000 q^{19} +3.02780 q^{20} +2.73453 q^{21} +0.397234 q^{22} +3.58028 q^{23} -1.99099 q^{24} +4.16755 q^{25} -4.55614 q^{26} +4.05357 q^{27} -1.37345 q^{28} +6.40339 q^{29} -6.02831 q^{30} -3.70594 q^{31} +1.00000 q^{32} -0.790890 q^{33} -3.23767 q^{34} -4.15853 q^{35} +0.964042 q^{36} -9.38701 q^{37} -1.00000 q^{38} +9.07124 q^{39} +3.02780 q^{40} +11.9154 q^{41} +2.73453 q^{42} +12.8122 q^{43} +0.397234 q^{44} +2.91892 q^{45} +3.58028 q^{46} -8.37564 q^{47} -1.99099 q^{48} -5.11363 q^{49} +4.16755 q^{50} +6.44616 q^{51} -4.55614 q^{52} -6.58237 q^{53} +4.05357 q^{54} +1.20274 q^{55} -1.37345 q^{56} +1.99099 q^{57} +6.40339 q^{58} +0.515881 q^{59} -6.02831 q^{60} -6.96657 q^{61} -3.70594 q^{62} -1.32407 q^{63} +1.00000 q^{64} -13.7951 q^{65} -0.790890 q^{66} +0.464573 q^{67} -3.23767 q^{68} -7.12830 q^{69} -4.15853 q^{70} +1.16646 q^{71} +0.964042 q^{72} +11.4898 q^{73} -9.38701 q^{74} -8.29755 q^{75} -1.00000 q^{76} -0.545583 q^{77} +9.07124 q^{78} -2.58832 q^{79} +3.02780 q^{80} -10.9627 q^{81} +11.9154 q^{82} -6.52135 q^{83} +2.73453 q^{84} -9.80300 q^{85} +12.8122 q^{86} -12.7491 q^{87} +0.397234 q^{88} -3.17796 q^{89} +2.91892 q^{90} +6.25765 q^{91} +3.58028 q^{92} +7.37848 q^{93} -8.37564 q^{94} -3.02780 q^{95} -1.99099 q^{96} +8.44539 q^{97} -5.11363 q^{98} +0.382951 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) $ 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * 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
$3$	−1.99099	−1.14950	−0.574749	−	0.818329i	$-0.694900\pi$
$3$	−1.99099	−1.14950	−0.574749	+	0.818329i	$0.694900\pi$
$4$	1.00000	0.500000
$5$	3.02780	1.35407	0.677036	−	0.735950i	$-0.263264\pi$
$5$	3.02780	1.35407	0.677036	+	0.735950i	$0.263264\pi$
$6$	−1.99099	−0.812818
$7$	−1.37345	−0.519116	−0.259558	−	0.965727i	$-0.583577\pi$
$7$	−1.37345	−0.519116	−0.259558	+	0.965727i	$0.583577\pi$
$8$	1.00000	0.353553
$9$	0.964042	0.321347
$10$	3.02780	0.957473
$11$	0.397234	0.119771	0.0598853	−	0.998205i	$-0.480926\pi$
$11$	0.397234	0.119771	0.0598853	+	0.998205i	$0.480926\pi$
$12$	−1.99099	−0.574749
$13$	−4.55614	−1.26365	−0.631823	−	0.775112i	$-0.717693\pi$
$13$	−4.55614	−1.26365	−0.631823	+	0.775112i	$0.717693\pi$
$14$	−1.37345	−0.367071
$15$	−6.02831	−1.55650
$16$	1.00000	0.250000
$17$	−3.23767	−0.785250	−0.392625	−	0.919699i	$-0.628433\pi$
$17$	−3.23767	−0.785250	−0.392625	+	0.919699i	$0.628433\pi$
$18$	0.964042	0.227227
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.02780	0.677036
$21$	2.73453	0.596724
$22$	0.397234	0.0846906
$23$	3.58028	0.746539	0.373270	−	0.927723i	$-0.378237\pi$
$23$	3.58028	0.746539	0.373270	+	0.927723i	$0.378237\pi$
$24$	−1.99099	−0.406409
$25$	4.16755	0.833510
$26$	−4.55614	−0.893533
$27$	4.05357	0.780110
$28$	−1.37345	−0.259558
$29$	6.40339	1.18908	0.594539	−	0.804066i	$-0.297334\pi$
$29$	6.40339	1.18908	0.594539	+	0.804066i	$0.297334\pi$
$30$	−6.02831	−1.10061
$31$	−3.70594	−0.665606	−0.332803	−	0.942996i	$-0.607994\pi$
$31$	−3.70594	−0.665606	−0.332803	+	0.942996i	$0.607994\pi$
$32$	1.00000	0.176777
$33$	−0.790890	−0.137676
$34$	−3.23767	−0.555255
$35$	−4.15853	−0.702921
$36$	0.964042	0.160674
$37$	−9.38701	−1.54321	−0.771607	−	0.636099i	$-0.780547\pi$
$37$	−9.38701	−1.54321	−0.771607	+	0.636099i	$0.780547\pi$
$38$	−1.00000	−0.162221
$39$	9.07124	1.45256
$40$	3.02780	0.478737
$41$	11.9154	1.86087	0.930437	−	0.366452i	$-0.119428\pi$
$41$	11.9154	1.86087	0.930437	+	0.366452i	$0.119428\pi$
$42$	2.73453	0.421947
$43$	12.8122	1.95384	0.976922	−	0.213597i	$-0.0685180\pi$
$43$	12.8122	1.95384	0.976922	+	0.213597i	$0.0685180\pi$
$44$	0.397234	0.0598853
$45$	2.91892	0.435127
$46$	3.58028	0.527883
$47$	−8.37564	−1.22171	−0.610856	−	0.791741i	$-0.709175\pi$
$47$	−8.37564	−1.22171	−0.610856	+	0.791741i	$0.709175\pi$
$48$	−1.99099	−0.287375
$49$	−5.11363	−0.730518
$50$	4.16755	0.589381
$51$	6.44616	0.902644
$52$	−4.55614	−0.631823
$53$	−6.58237	−0.904158	−0.452079	−	0.891978i	$-0.649317\pi$
$53$	−6.58237	−0.904158	−0.452079	+	0.891978i	$0.649317\pi$
$54$	4.05357	0.551621
$55$	1.20274	0.162178
$56$	−1.37345	−0.183535
$57$	1.99099	0.263713
$58$	6.40339	0.840806
$59$	0.515881	0.0671620	0.0335810	−	0.999436i	$-0.489309\pi$
$59$	0.515881	0.0671620	0.0335810	+	0.999436i	$0.489309\pi$
$60$	−6.02831	−0.778252
$61$	−6.96657	−0.891978	−0.445989	−	0.895038i	$-0.647148\pi$
$61$	−6.96657	−0.891978	−0.445989	+	0.895038i	$0.647148\pi$
$62$	−3.70594	−0.470654
$63$	−1.32407	−0.166817
$64$	1.00000	0.125000
$65$	−13.7951	−1.71107
$66$	−0.790890	−0.0973518
$67$	0.464573	0.0567567	0.0283783	−	0.999597i	$-0.490966\pi$
$67$	0.464573	0.0567567	0.0283783	+	0.999597i	$0.490966\pi$
$68$	−3.23767	−0.392625
$69$	−7.12830	−0.858146
$70$	−4.15853	−0.497040
$71$	1.16646	0.138433	0.0692167	−	0.997602i	$-0.477950\pi$
$71$	1.16646	0.138433	0.0692167	+	0.997602i	$0.477950\pi$
$72$	0.964042	0.113613
$73$	11.4898	1.34478	0.672390	−	0.740197i	$-0.265268\pi$
$73$	11.4898	1.34478	0.672390	+	0.740197i	$0.265268\pi$
$74$	−9.38701	−1.09122
$75$	−8.29755	−0.958119
$76$	−1.00000	−0.114708
$77$	−0.545583	−0.0621749
$78$	9.07124	1.02712
$79$	−2.58832	−0.291209	−0.145605	−	0.989343i	$-0.546513\pi$
$79$	−2.58832	−0.291209	−0.145605	+	0.989343i	$0.546513\pi$
$80$	3.02780	0.338518
$81$	−10.9627	−1.21808
$82$	11.9154	1.31584
$83$	−6.52135	−0.715811	−0.357905	−	0.933758i	$-0.616509\pi$
$83$	−6.52135	−0.715811	−0.357905	+	0.933758i	$0.616509\pi$
$84$	2.73453	0.298362
$85$	−9.80300	−1.06328
$86$	12.8122	1.38158
$87$	−12.7491	−1.36684
$88$	0.397234	0.0423453
$89$	−3.17796	−0.336863	−0.168431	−	0.985713i	$-0.553870\pi$
$89$	−3.17796	−0.336863	−0.168431	+	0.985713i	$0.553870\pi$
$90$	2.91892	0.307682
$91$	6.25765	0.655980
$92$	3.58028	0.373270
$93$	7.37848	0.765113
$94$	−8.37564	−0.863881
$95$	−3.02780	−0.310645
$96$	−1.99099	−0.203205
$97$	8.44539	0.857499	0.428750	−	0.903423i	$-0.358954\pi$
$97$	8.44539	0.857499	0.428750	+	0.903423i	$0.358954\pi$
$98$	−5.11363	−0.516554
$99$	0.382951	0.0384880
$100$	4.16755	0.416755
$101$	−7.51579	−0.747849	−0.373924	−	0.927459i	$-0.621988\pi$
$101$	−7.51579	−0.747849	−0.373924	+	0.927459i	$0.621988\pi$
$102$	6.44616	0.638265
$103$	−17.6420	−1.73832	−0.869161	−	0.494529i	$-0.835341\pi$
$103$	−17.6420	−1.73832	−0.869161	+	0.494529i	$0.835341\pi$
$104$	−4.55614	−0.446767
$105$	8.27960	0.808006
$106$	−6.58237	−0.639336
$107$	−14.3177	−1.38414	−0.692072	−	0.721828i	$-0.743302\pi$
$107$	−14.3177	−1.38414	−0.692072	+	0.721828i	$0.743302\pi$
$108$	4.05357	0.390055
$109$	−12.8699	−1.23271	−0.616355	−	0.787468i	$-0.711391\pi$
$109$	−12.8699	−1.23271	−0.616355	+	0.787468i	$0.711391\pi$
$110$	1.20274	0.114677
$111$	18.6894	1.77392
$112$	−1.37345	−0.129779
$113$	−12.9516	−1.21838	−0.609190	−	0.793024i	$-0.708505\pi$
$113$	−12.9516	−1.21838	−0.609190	+	0.793024i	$0.708505\pi$
$114$	1.99099	0.186473
$115$	10.8403	1.01087
$116$	6.40339	0.594539
$117$	−4.39232	−0.406070
$118$	0.515881	0.0474907
$119$	4.44678	0.407636
$120$	−6.02831	−0.550307
$121$	−10.8422	−0.985655
$122$	−6.96657	−0.630724
$123$	−23.7235	−2.13907
$124$	−3.70594	−0.332803
$125$	−2.52049	−0.225439
$126$	−1.32407	−0.117957
$127$	−19.1157	−1.69624	−0.848121	−	0.529803i	$-0.822266\pi$
$127$	−19.1157	−1.69624	−0.848121	+	0.529803i	$0.822266\pi$
$128$	1.00000	0.0883883
$129$	−25.5090	−2.24594
$130$	−13.7951	−1.20991
$131$	15.9092	1.38999	0.694995	−	0.719015i	$-0.255407\pi$
$131$	15.9092	1.38999	0.694995	+	0.719015i	$0.255407\pi$
$132$	−0.790890	−0.0688381
$133$	1.37345	0.119093
$134$	0.464573	0.0401330
$135$	12.2734	1.05633
$136$	−3.23767	−0.277628
$137$	2.55812	0.218555	0.109277	−	0.994011i	$-0.465146\pi$
$137$	2.55812	0.218555	0.109277	+	0.994011i	$0.465146\pi$
$138$	−7.12830	−0.606801
$139$	−12.2545	−1.03941	−0.519705	−	0.854346i	$-0.673958\pi$
$139$	−12.2545	−1.03941	−0.519705	+	0.854346i	$0.673958\pi$
$140$	−4.15853	−0.351460
$141$	16.6758	1.40436
$142$	1.16646	0.0978872
$143$	−1.80986	−0.151348
$144$	0.964042	0.0803369
$145$	19.3881	1.61010
$146$	11.4898	0.950903
$147$	10.1812	0.839730
$148$	−9.38701	−0.771607
$149$	2.00321	0.164110	0.0820548	−	0.996628i	$-0.473852\pi$
$149$	2.00321	0.164110	0.0820548	+	0.996628i	$0.473852\pi$
$150$	−8.29755	−0.677492
$151$	3.35528	0.273049	0.136524	−	0.990637i	$-0.456407\pi$
$151$	3.35528	0.273049	0.136524	+	0.990637i	$0.456407\pi$
$152$	−1.00000	−0.0811107
$153$	−3.12125	−0.252338
$154$	−0.545583	−0.0439643
$155$	−11.2208	−0.901278
$156$	9.07124	0.726280
$157$	8.44890	0.674296	0.337148	−	0.941452i	$-0.390538\pi$
$157$	8.44890	0.674296	0.337148	+	0.941452i	$0.390538\pi$
$158$	−2.58832	−0.205916
$159$	13.1054	1.03933
$160$	3.02780	0.239368
$161$	−4.91734	−0.387541
$162$	−10.9627	−0.861315
$163$	2.83126	0.221761	0.110881	−	0.993834i	$-0.464633\pi$
$163$	2.83126	0.221761	0.110881	+	0.993834i	$0.464633\pi$
$164$	11.9154	0.930437
$165$	−2.39465	−0.186423
$166$	−6.52135	−0.506155
$167$	−3.94910	−0.305590	−0.152795	−	0.988258i	$-0.548827\pi$
$167$	−3.94910	−0.305590	−0.152795	+	0.988258i	$0.548827\pi$
$168$	2.73453	0.210974
$169$	7.75844	0.596803
$170$	−9.80300	−0.751856
$171$	−0.964042	−0.0737222
$172$	12.8122	0.976922
$173$	3.89334	0.296005	0.148003	−	0.988987i	$-0.452716\pi$
$173$	3.89334	0.296005	0.148003	+	0.988987i	$0.452716\pi$
$174$	−12.7491	−0.966505
$175$	−5.72393	−0.432689
$176$	0.397234	0.0299427
$177$	−1.02711	−0.0772027
$178$	−3.17796	−0.238198
$179$	−13.6821	−1.02265	−0.511323	−	0.859389i	$-0.670844\pi$
$179$	−13.6821	−1.02265	−0.511323	+	0.859389i	$0.670844\pi$
$180$	2.91892	0.217564
$181$	−2.35410	−0.174979	−0.0874893	−	0.996165i	$-0.527884\pi$
$181$	−2.35410	−0.174979	−0.0874893	+	0.996165i	$0.527884\pi$
$182$	6.25765	0.463848
$183$	13.8704	1.02533
$184$	3.58028	0.263942
$185$	−28.4220	−2.08962
$186$	7.37848	0.541016
$187$	−1.28611	−0.0940499
$188$	−8.37564	−0.610856
$189$	−5.56739	−0.404968
$190$	−3.02780	−0.219659
$191$	10.4205	0.754002	0.377001	−	0.926213i	$-0.376955\pi$
$191$	10.4205	0.754002	0.377001	+	0.926213i	$0.376955\pi$
$192$	−1.99099	−0.143687
$193$	−14.7752	−1.06354	−0.531772	−	0.846888i	$-0.678474\pi$
$193$	−14.7752	−1.06354	−0.531772	+	0.846888i	$0.678474\pi$
$194$	8.44539	0.606344
$195$	27.4659	1.96687
$196$	−5.11363	−0.365259
$197$	−14.6513	−1.04386	−0.521932	−	0.852987i	$-0.674789\pi$
$197$	−14.6513	−1.04386	−0.521932	+	0.852987i	$0.674789\pi$
$198$	0.382951	0.0272151
$199$	21.0659	1.49332	0.746661	−	0.665204i	$-0.231656\pi$
$199$	21.0659	1.49332	0.746661	+	0.665204i	$0.231656\pi$
$200$	4.16755	0.294690
$201$	−0.924961	−0.0652417
$202$	−7.51579	−0.528809
$203$	−8.79475	−0.617270
$204$	6.44616	0.451322
$205$	36.0774	2.51976
$206$	−17.6420	−1.22918
$207$	3.45154	0.239899
$208$	−4.55614	−0.315912
$209$	−0.397234	−0.0274773
$210$	8.27960	0.571347
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−6.58237	−0.452079
$213$	−2.32241	−0.159129
$214$	−14.3177	−0.978738
$215$	38.7928	2.64564
$216$	4.05357	0.275811
$217$	5.08993	0.345527
$218$	−12.8699	−0.871658
$219$	−22.8761	−1.54582
$220$	1.20274	0.0810890
$221$	14.7513	0.992278
$222$	18.6894	1.25435
$223$	24.0295	1.60913	0.804566	−	0.593863i	$-0.202398\pi$
$223$	24.0295	1.60913	0.804566	+	0.593863i	$0.202398\pi$
$224$	−1.37345	−0.0917677
$225$	4.01769	0.267846
$226$	−12.9516	−0.861525
$227$	11.1387	0.739300	0.369650	−	0.929171i	$-0.379478\pi$
$227$	11.1387	0.739300	0.369650	+	0.929171i	$0.379478\pi$
$228$	1.99099	0.131857
$229$	−2.57967	−0.170470	−0.0852348	−	0.996361i	$-0.527164\pi$
$229$	−2.57967	−0.170470	−0.0852348	+	0.996361i	$0.527164\pi$
$230$	10.8403	0.714791
$231$	1.08625	0.0714700
$232$	6.40339	0.420403
$233$	−25.9512	−1.70012	−0.850059	−	0.526688i	$-0.823434\pi$
$233$	−25.9512	−1.70012	−0.850059	+	0.526688i	$0.823434\pi$
$234$	−4.39232	−0.287135
$235$	−25.3597	−1.65429
$236$	0.515881	0.0335810
$237$	5.15333	0.334745
$238$	4.44678	0.288242
$239$	6.55258	0.423851	0.211926	−	0.977286i	$-0.432027\pi$
$239$	6.55258	0.423851	0.211926	+	0.977286i	$0.432027\pi$
$240$	−6.02831	−0.389126
$241$	−16.7731	−1.08045	−0.540225	−	0.841520i	$-0.681661\pi$
$241$	−16.7731	−1.08045	−0.540225	+	0.841520i	$0.681661\pi$
$242$	−10.8422	−0.696963
$243$	9.66601	0.620075
$244$	−6.96657	−0.445989
$245$	−15.4830	−0.989174
$246$	−23.7235	−1.51255
$247$	4.55614	0.289900
$248$	−3.70594	−0.235327
$249$	12.9839	0.822823
$250$	−2.52049	−0.159410
$251$	−26.3403	−1.66259	−0.831293	−	0.555834i	$-0.812399\pi$
$251$	−26.3403	−1.66259	−0.831293	+	0.555834i	$0.812399\pi$
$252$	−1.32407	−0.0834084
$253$	1.42221	0.0894135
$254$	−19.1157	−1.19942
$255$	19.5177	1.22224
$256$	1.00000	0.0625000
$257$	−20.3438	−1.26901	−0.634507	−	0.772917i	$-0.718797\pi$
$257$	−20.3438	−1.26901	−0.634507	+	0.772917i	$0.718797\pi$
$258$	−25.5090	−1.58812
$259$	12.8926	0.801108
$260$	−13.7951	−0.855534
$261$	6.17313	0.382107
$262$	15.9092	0.982871
$263$	−12.7213	−0.784428	−0.392214	−	0.919874i	$-0.628291\pi$
$263$	−12.7213	−0.784428	−0.392214	+	0.919874i	$0.628291\pi$
$264$	−0.790890	−0.0486759
$265$	−19.9301	−1.22429
$266$	1.37345	0.0842118
$267$	6.32728	0.387223
$268$	0.464573	0.0283783
$269$	8.45637	0.515594	0.257797	−	0.966199i	$-0.417003\pi$
$269$	8.45637	0.515594	0.257797	+	0.966199i	$0.417003\pi$
$270$	12.2734	0.746935
$271$	21.8022	1.32439	0.662195	−	0.749331i	$-0.269625\pi$
$271$	21.8022	1.32439	0.662195	+	0.749331i	$0.269625\pi$
$272$	−3.23767	−0.196312
$273$	−12.4589	−0.754048
$274$	2.55812	0.154542
$275$	1.65549	0.0998300
$276$	−7.12830	−0.429073
$277$	−23.8291	−1.43175	−0.715875	−	0.698229i	$-0.753972\pi$
$277$	−23.8291	−1.43175	−0.715875	+	0.698229i	$0.753972\pi$
$278$	−12.2545	−0.734974
$279$	−3.57268	−0.213891
$280$	−4.15853	−0.248520
$281$	−16.2405	−0.968828	−0.484414	−	0.874839i	$-0.660967\pi$
$281$	−16.2405	−0.968828	−0.484414	+	0.874839i	$0.660967\pi$
$282$	16.6758	0.993030
$283$	7.90691	0.470017	0.235008	−	0.971993i	$-0.424488\pi$
$283$	7.90691	0.470017	0.235008	+	0.971993i	$0.424488\pi$
$284$	1.16646	0.0692167
$285$	6.02831	0.357086
$286$	−1.80986	−0.107019
$287$	−16.3652	−0.966010
$288$	0.964042	0.0568067
$289$	−6.51751	−0.383383
$290$	19.3881	1.13851
$291$	−16.8147	−0.985695
$292$	11.4898	0.672390
$293$	−2.19595	−0.128289	−0.0641444	−	0.997941i	$-0.520432\pi$
$293$	−2.19595	−0.128289	−0.0641444	+	0.997941i	$0.520432\pi$
$294$	10.1812	0.593779
$295$	1.56198	0.0909422
$296$	−9.38701	−0.545609
$297$	1.61022	0.0934343
$298$	2.00321	0.116043
$299$	−16.3123	−0.943362
$300$	−8.29755	−0.479059
$301$	−17.5970	−1.01427
$302$	3.35528	0.193074
$303$	14.9639	0.859651
$304$	−1.00000	−0.0573539
$305$	−21.0934	−1.20780
$306$	−3.12125	−0.178430
$307$	1.38686	0.0791524	0.0395762	−	0.999217i	$-0.487399\pi$
$307$	1.38686	0.0791524	0.0395762	+	0.999217i	$0.487399\pi$
$308$	−0.545583	−0.0310874
$309$	35.1251	1.99820
$310$	−11.2208	−0.637300
$311$	18.5752	1.05330	0.526651	−	0.850082i	$-0.323447\pi$
$311$	18.5752	1.05330	0.526651	+	0.850082i	$0.323447\pi$
$312$	9.07124	0.513558
$313$	9.84471	0.556456	0.278228	−	0.960515i	$-0.410253\pi$
$313$	9.84471	0.556456	0.278228	+	0.960515i	$0.410253\pi$
$314$	8.44890	0.476799
$315$	−4.00900	−0.225882
$316$	−2.58832	−0.145605
$317$	33.5375	1.88366	0.941828	−	0.336096i	$-0.109107\pi$
$317$	33.5375	1.88366	0.941828	+	0.336096i	$0.109107\pi$
$318$	13.1054	0.734916
$319$	2.54364	0.142417
$320$	3.02780	0.169259
$321$	28.5064	1.59107
$322$	−4.91734	−0.274033
$323$	3.23767	0.180149
$324$	−10.9627	−0.609042
$325$	−18.9880	−1.05326
$326$	2.83126	0.156809
$327$	25.6238	1.41700
$328$	11.9154	0.657918
$329$	11.5035	0.634211
$330$	−2.39465	−0.131821
$331$	32.7510	1.80016	0.900080	−	0.435725i	$-0.143508\pi$
$331$	32.7510	1.80016	0.900080	+	0.435725i	$0.143508\pi$
$332$	−6.52135	−0.357905
$333$	−9.04948	−0.495908
$334$	−3.94910	−0.216085
$335$	1.40663	0.0768526
$336$	2.73453	0.149181
$337$	12.4477	0.678069	0.339035	−	0.940774i	$-0.389900\pi$
$337$	12.4477	0.678069	0.339035	+	0.940774i	$0.389900\pi$
$338$	7.75844	0.422004
$339$	25.7864	1.40053
$340$	−9.80300	−0.531642
$341$	−1.47212	−0.0797200
$342$	−0.964042	−0.0521294
$343$	16.6375	0.898340
$344$	12.8122	0.690788
$345$	−21.5830	−1.16199
$346$	3.89334	0.209307
$347$	−2.05017	−0.110059	−0.0550294	−	0.998485i	$-0.517525\pi$
$347$	−2.05017	−0.110059	−0.0550294	+	0.998485i	$0.517525\pi$
$348$	−12.7491	−0.683422
$349$	26.3137	1.40854	0.704270	−	0.709932i	$-0.251274\pi$
$349$	26.3137	1.40854	0.704270	+	0.709932i	$0.251274\pi$
$350$	−5.72393	−0.305957
$351$	−18.4687	−0.985784
$352$	0.397234	0.0211727
$353$	−17.5587	−0.934556	−0.467278	−	0.884111i	$-0.654765\pi$
$353$	−17.5587	−0.934556	−0.467278	+	0.884111i	$0.654765\pi$
$354$	−1.02711	−0.0545905
$355$	3.53181	0.187449
$356$	−3.17796	−0.168431
$357$	−8.85350	−0.468577
$358$	−13.6821	−0.723120
$359$	−20.2391	−1.06818	−0.534089	−	0.845428i	$-0.679345\pi$
$359$	−20.2391	−1.06818	−0.534089	+	0.845428i	$0.679345\pi$
$360$	2.91892	0.153841
$361$	1.00000	0.0526316
$362$	−2.35410	−0.123729
$363$	21.5867	1.13301
$364$	6.25765	0.327990
$365$	34.7888	1.82093
$366$	13.8704	0.725016
$367$	0.745908	0.0389361	0.0194680	−	0.999810i	$-0.493803\pi$
$367$	0.745908	0.0389361	0.0194680	+	0.999810i	$0.493803\pi$
$368$	3.58028	0.186635
$369$	11.4870	0.597987
$370$	−28.4220	−1.47759
$371$	9.04057	0.469363
$372$	7.37848	0.382556
$373$	−29.2219	−1.51305	−0.756527	−	0.653963i	$-0.773105\pi$
$373$	−29.2219	−1.51305	−0.756527	+	0.653963i	$0.773105\pi$
$374$	−1.28611	−0.0665033
$375$	5.01827	0.259142
$376$	−8.37564	−0.431941
$377$	−29.1747	−1.50258
$378$	−5.56739	−0.286356
$379$	23.4019	1.20208	0.601038	−	0.799220i	$-0.294754\pi$
$379$	23.4019	1.20208	0.601038	+	0.799220i	$0.294754\pi$
$380$	−3.02780	−0.155323
$381$	38.0591	1.94983
$382$	10.4205	0.533160
$383$	−17.3713	−0.887632	−0.443816	−	0.896118i	$-0.646376\pi$
$383$	−17.3713	−0.887632	−0.443816	+	0.896118i	$0.646376\pi$
$384$	−1.99099	−0.101602
$385$	−1.65191	−0.0841893
$386$	−14.7752	−0.752039
$387$	12.3515	0.627863
$388$	8.44539	0.428750
$389$	−0.119745	−0.00607132	−0.00303566	−	0.999995i	$-0.500966\pi$
$389$	−0.119745	−0.00607132	−0.00303566	+	0.999995i	$0.500966\pi$
$390$	27.4659	1.39079
$391$	−11.5917	−0.586220
$392$	−5.11363	−0.258277
$393$	−31.6750	−1.59779
$394$	−14.6513	−0.738123
$395$	−7.83692	−0.394318
$396$	0.382951	0.0192440
$397$	12.5975	0.632252	0.316126	−	0.948717i	$-0.397618\pi$
$397$	12.5975	0.632252	0.316126	+	0.948717i	$0.397618\pi$
$398$	21.0659	1.05594
$399$	−2.73453	−0.136898
$400$	4.16755	0.208377
$401$	−22.6141	−1.12930	−0.564648	−	0.825332i	$-0.690988\pi$
$401$	−22.6141	−1.12930	−0.564648	+	0.825332i	$0.690988\pi$
$402$	−0.924961	−0.0461329
$403$	16.8848	0.841090
$404$	−7.51579	−0.373924
$405$	−33.1930	−1.64937
$406$	−8.79475	−0.436476
$407$	−3.72884	−0.184832
$408$	6.44616	0.319133
$409$	−26.2677	−1.29885	−0.649427	−	0.760424i	$-0.724991\pi$
$409$	−26.2677	−1.29885	−0.649427	+	0.760424i	$0.724991\pi$
$410$	36.0774	1.78174
$411$	−5.09319	−0.251229
$412$	−17.6420	−0.869161
$413$	−0.708539	−0.0348649
$414$	3.45154	0.169634
$415$	−19.7453	−0.969259
$416$	−4.55614	−0.223383
$417$	24.3985	1.19480
$418$	−0.397234	−0.0194294
$419$	19.5333	0.954264	0.477132	−	0.878832i	$-0.341676\pi$
$419$	19.5333	0.954264	0.477132	+	0.878832i	$0.341676\pi$
$420$	8.27960	0.404003
$421$	−37.1077	−1.80852	−0.904260	−	0.426982i	$-0.859577\pi$
$421$	−37.1077	−1.80852	−0.904260	+	0.426982i	$0.859577\pi$
$422$	1.00000	0.0486792
$423$	−8.07447	−0.392594
$424$	−6.58237	−0.319668
$425$	−13.4931	−0.654513
$426$	−2.32241	−0.112521
$427$	9.56825	0.463040
$428$	−14.3177	−0.692072
$429$	3.60341	0.173974
$430$	38.7928	1.87075
$431$	−2.03781	−0.0981578	−0.0490789	−	0.998795i	$-0.515629\pi$
$431$	−2.03781	−0.0981578	−0.0490789	+	0.998795i	$0.515629\pi$
$432$	4.05357	0.195028
$433$	16.1803	0.777576	0.388788	−	0.921327i	$-0.372894\pi$
$433$	16.1803	0.777576	0.388788	+	0.921327i	$0.372894\pi$
$434$	5.08993	0.244324
$435$	−38.6016	−1.85081
$436$	−12.8699	−0.616355
$437$	−3.58028	−0.171268
$438$	−22.8761	−1.09306
$439$	−10.8767	−0.519115	−0.259558	−	0.965728i	$-0.583577\pi$
$439$	−10.8767	−0.519115	−0.259558	+	0.965728i	$0.583577\pi$
$440$	1.20274	0.0573386
$441$	−4.92975	−0.234750
$442$	14.7513	0.701647
$443$	11.9442	0.567488	0.283744	−	0.958900i	$-0.408423\pi$
$443$	11.9442	0.567488	0.283744	+	0.958900i	$0.408423\pi$
$444$	18.6894	0.886962
$445$	−9.62220	−0.456136
$446$	24.0295	1.13783
$447$	−3.98838	−0.188644
$448$	−1.37345	−0.0648895
$449$	4.92790	0.232562	0.116281	−	0.993216i	$-0.462903\pi$
$449$	4.92790	0.232562	0.116281	+	0.993216i	$0.462903\pi$
$450$	4.01769	0.189396
$451$	4.73321	0.222878
$452$	−12.9516	−0.609190
$453$	−6.68032	−0.313869
$454$	11.1387	0.522764
$455$	18.9469	0.888243
$456$	1.99099	0.0932367
$457$	−27.3914	−1.28131	−0.640657	−	0.767827i	$-0.721338\pi$
$457$	−27.3914	−1.28131	−0.640657	+	0.767827i	$0.721338\pi$
$458$	−2.57967	−0.120540
$459$	−13.1241	−0.612581
$460$	10.8403	0.505434
$461$	−28.7098	−1.33715	−0.668573	−	0.743646i	$-0.733095\pi$
$461$	−28.7098	−1.33715	−0.668573	+	0.743646i	$0.733095\pi$
$462$	1.08625	0.0505369
$463$	−7.07073	−0.328605	−0.164302	−	0.986410i	$-0.552537\pi$
$463$	−7.07073	−0.328605	−0.164302	+	0.986410i	$0.552537\pi$
$464$	6.40339	0.297270
$465$	22.3405	1.03602
$466$	−25.9512	−1.20216
$467$	−13.6850	−0.633267	−0.316634	−	0.948548i	$-0.602553\pi$
$467$	−13.6850	−0.633267	−0.316634	+	0.948548i	$0.602553\pi$
$468$	−4.39232	−0.203035
$469$	−0.638069	−0.0294633
$470$	−25.3597	−1.16976
$471$	−16.8217	−0.775102
$472$	0.515881	0.0237454
$473$	5.08945	0.234013
$474$	5.15333	0.236700
$475$	−4.16755	−0.191220
$476$	4.44678	0.203818
$477$	−6.34568	−0.290549
$478$	6.55258	0.299708
$479$	10.7225	0.489922	0.244961	−	0.969533i	$-0.421225\pi$
$479$	10.7225	0.489922	0.244961	+	0.969533i	$0.421225\pi$
$480$	−6.02831	−0.275154
$481$	42.7686	1.95008
$482$	−16.7731	−0.763994
$483$	9.79038	0.445478
$484$	−10.8422	−0.492827
$485$	25.5709	1.16112
$486$	9.66601	0.438459
$487$	6.79903	0.308094	0.154047	−	0.988064i	$-0.450769\pi$
$487$	6.79903	0.308094	0.154047	+	0.988064i	$0.450769\pi$
$488$	−6.96657	−0.315362
$489$	−5.63701	−0.254914
$490$	−15.4830	−0.699452
$491$	−28.7198	−1.29611	−0.648054	−	0.761594i	$-0.724417\pi$
$491$	−28.7198	−1.29611	−0.648054	+	0.761594i	$0.724417\pi$
$492$	−23.7235	−1.06954
$493$	−20.7320	−0.933724
$494$	4.55614	0.204991
$495$	1.15950	0.0521155
$496$	−3.70594	−0.166401
$497$	−1.60208	−0.0718631
$498$	12.9839	0.581824
$499$	−10.1555	−0.454625	−0.227312	−	0.973822i	$-0.572994\pi$
$499$	−10.1555	−0.454625	−0.227312	+	0.973822i	$0.572994\pi$
$500$	−2.52049	−0.112720
$501$	7.86262	0.351276
$502$	−26.3403	−1.17563
$503$	18.9284	0.843975	0.421988	−	0.906602i	$-0.361333\pi$
$503$	18.9284	0.843975	0.421988	+	0.906602i	$0.361333\pi$
$504$	−1.32407	−0.0589786
$505$	−22.7563	−1.01264
$506$	1.42221	0.0632249
$507$	−15.4470	−0.686025
$508$	−19.1157	−0.848121
$509$	24.3908	1.08110	0.540552	−	0.841311i	$-0.318215\pi$
$509$	24.3908	1.08110	0.540552	+	0.841311i	$0.318215\pi$
$510$	19.5177	0.864257
$511$	−15.7807	−0.698097
$512$	1.00000	0.0441942
$513$	−4.05357	−0.178970
$514$	−20.3438	−0.897328
$515$	−53.4165	−2.35381
$516$	−25.5090	−1.12297
$517$	−3.32709	−0.146325
$518$	12.8926	0.566469
$519$	−7.75161	−0.340258
$520$	−13.7951	−0.604954
$521$	−5.10449	−0.223632	−0.111816	−	0.993729i	$-0.535667\pi$
$521$	−5.10449	−0.223632	−0.111816	+	0.993729i	$0.535667\pi$
$522$	6.17313	0.270191
$523$	−10.6680	−0.466480	−0.233240	−	0.972419i	$-0.574933\pi$
$523$	−10.6680	−0.466480	−0.233240	+	0.972419i	$0.574933\pi$
$524$	15.9092	0.694995
$525$	11.3963	0.497375
$526$	−12.7213	−0.554674
$527$	11.9986	0.522667
$528$	−0.790890	−0.0344191
$529$	−10.1816	−0.442679
$530$	−19.9301	−0.865707
$531$	0.497332	0.0215823
$532$	1.37345	0.0595467
$533$	−54.2883	−2.35149
$534$	6.32728	0.273808
$535$	−43.3511	−1.87423
$536$	0.464573	0.0200665
$537$	27.2409	1.17553
$538$	8.45637	0.364580
$539$	−2.03131	−0.0874947
$540$	12.2734	0.528163
$541$	−11.0831	−0.476500	−0.238250	−	0.971204i	$-0.576574\pi$
$541$	−11.0831	−0.476500	−0.238250	+	0.971204i	$0.576574\pi$
$542$	21.8022	0.936486
$543$	4.68698	0.201138
$544$	−3.23767	−0.138814
$545$	−38.9674	−1.66918
$546$	−12.4589	−0.533192
$547$	−26.1914	−1.11986	−0.559931	−	0.828539i	$-0.689173\pi$
$547$	−26.1914	−1.11986	−0.559931	+	0.828539i	$0.689173\pi$
$548$	2.55812	0.109277
$549$	−6.71607	−0.286635
$550$	1.65549	0.0705905
$551$	−6.40339	−0.272793
$552$	−7.12830	−0.303400
$553$	3.55494	0.151171
$554$	−23.8291	−1.01240
$555$	56.5878	2.40202
$556$	−12.2545	−0.519705
$557$	−42.5163	−1.80147	−0.900737	−	0.434365i	$-0.856973\pi$
$557$	−42.5163	−1.80147	−0.900737	+	0.434365i	$0.856973\pi$
$558$	−3.57268	−0.151244
$559$	−58.3743	−2.46897
$560$	−4.15853	−0.175730
$561$	2.56064	0.108110
$562$	−16.2405	−0.685065
$563$	−30.7254	−1.29492	−0.647461	−	0.762098i	$-0.724169\pi$
$563$	−30.7254	−1.29492	−0.647461	+	0.762098i	$0.724169\pi$
$564$	16.6758	0.702179
$565$	−39.2147	−1.64977
$566$	7.90691	0.332352
$567$	15.0568	0.632327
$568$	1.16646	0.0489436
$569$	2.86428	0.120077	0.0600385	−	0.998196i	$-0.480878\pi$
$569$	2.86428	0.120077	0.0600385	+	0.998196i	$0.480878\pi$
$570$	6.02831	0.252498
$571$	42.5497	1.78065	0.890324	−	0.455327i	$-0.150478\pi$
$571$	42.5497	1.78065	0.890324	+	0.455327i	$0.150478\pi$
$572$	−1.80986	−0.0756739
$573$	−20.7471	−0.866724
$574$	−16.3652	−0.683072
$575$	14.9210	0.622248
$576$	0.964042	0.0401684
$577$	−36.3405	−1.51288	−0.756438	−	0.654065i	$-0.773062\pi$
$577$	−36.3405	−1.51288	−0.756438	+	0.654065i	$0.773062\pi$
$578$	−6.51751	−0.271093
$579$	29.4173	1.22254
$580$	19.3881	0.805049
$581$	8.95676	0.371589
$582$	−16.8147	−0.696991
$583$	−2.61474	−0.108292
$584$	11.4898	0.475452
$585$	−13.2990	−0.549847
$586$	−2.19595	−0.0907138
$587$	−2.66692	−0.110076	−0.0550378	−	0.998484i	$-0.517528\pi$
$587$	−2.66692	−0.110076	−0.0550378	+	0.998484i	$0.517528\pi$
$588$	10.1812	0.419865
$589$	3.70594	0.152700
$590$	1.56198	0.0643058
$591$	29.1707	1.19992
$592$	−9.38701	−0.385804
$593$	41.4314	1.70139	0.850693	−	0.525663i	$-0.176183\pi$
$593$	41.4314	1.70139	0.850693	+	0.525663i	$0.176183\pi$
$594$	1.61022	0.0660680
$595$	13.4640	0.551968
$596$	2.00321	0.0820548
$597$	−41.9420	−1.71657
$598$	−16.3123	−0.667058
$599$	11.6196	0.474763	0.237381	−	0.971417i	$-0.423711\pi$
$599$	11.6196	0.474763	0.237381	+	0.971417i	$0.423711\pi$
$600$	−8.29755	−0.338746
$601$	25.0393	1.02138	0.510688	−	0.859766i	$-0.329391\pi$
$601$	25.0393	1.02138	0.510688	+	0.859766i	$0.329391\pi$
$602$	−17.5970	−0.717199
$603$	0.447868	0.0182386
$604$	3.35528	0.136524
$605$	−32.8280	−1.33465
$606$	14.9639	0.607865
$607$	4.89045	0.198497	0.0992485	−	0.995063i	$-0.468356\pi$
$607$	4.89045	0.198497	0.0992485	+	0.995063i	$0.468356\pi$
$608$	−1.00000	−0.0405554
$609$	17.5103	0.709551
$610$	−21.0934	−0.854045
$611$	38.1606	1.54381
$612$	−3.12125	−0.126169
$613$	25.5705	1.03278	0.516391	−	0.856353i	$-0.327275\pi$
$613$	25.5705	1.03278	0.516391	+	0.856353i	$0.327275\pi$
$614$	1.38686	0.0559692
$615$	−71.8298	−2.89646
$616$	−0.545583	−0.0219821
$617$	−26.2168	−1.05545	−0.527724	−	0.849416i	$-0.676955\pi$
$617$	−26.2168	−1.05545	−0.527724	+	0.849416i	$0.676955\pi$
$618$	35.1251	1.41294
$619$	3.47653	0.139733	0.0698667	−	0.997556i	$-0.477743\pi$
$619$	3.47653	0.139733	0.0698667	+	0.997556i	$0.477743\pi$
$620$	−11.2208	−0.450639
$621$	14.5129	0.582383
$622$	18.5752	0.744797
$623$	4.36477	0.174871
$624$	9.07124	0.363140
$625$	−28.4693	−1.13877
$626$	9.84471	0.393474
$627$	0.790890	0.0315851
$628$	8.44890	0.337148
$629$	30.3920	1.21181
$630$	−4.00900	−0.159723
$631$	6.09385	0.242592	0.121296	−	0.992616i	$-0.461295\pi$
$631$	6.09385	0.242592	0.121296	+	0.992616i	$0.461295\pi$
$632$	−2.58832	−0.102958
$633$	−1.99099	−0.0791348
$634$	33.5375	1.33195
$635$	−57.8784	−2.29683
$636$	13.1054	0.519664
$637$	23.2984	0.923117
$638$	2.54364	0.100704
$639$	1.12452	0.0444852
$640$	3.02780	0.119684
$641$	46.5382	1.83815	0.919075	−	0.394083i	$-0.128938\pi$
$641$	46.5382	1.83815	0.919075	+	0.394083i	$0.128938\pi$
$642$	28.5064	1.12506
$643$	−23.0978	−0.910890	−0.455445	−	0.890264i	$-0.650520\pi$
$643$	−23.0978	−0.910890	−0.455445	+	0.890264i	$0.650520\pi$
$644$	−4.91734	−0.193770
$645$	−77.2360	−3.04116
$646$	3.23767	0.127384
$647$	45.2171	1.77767	0.888833	−	0.458231i	$-0.151517\pi$
$647$	45.2171	1.77767	0.888833	+	0.458231i	$0.151517\pi$
$648$	−10.9627	−0.430657
$649$	0.204926	0.00804404
$650$	−18.9880	−0.744769
$651$	−10.1340	−0.397183
$652$	2.83126	0.110881
$653$	−19.7593	−0.773243	−0.386621	−	0.922238i	$-0.626358\pi$
$653$	−19.7593	−0.773243	−0.386621	+	0.922238i	$0.626358\pi$
$654$	25.6238	1.00197
$655$	48.1697	1.88215
$656$	11.9154	0.465218
$657$	11.0767	0.432142
$658$	11.5035	0.448455
$659$	−14.6349	−0.570093	−0.285046	−	0.958514i	$-0.592009\pi$
$659$	−14.6349	−0.570093	−0.285046	+	0.958514i	$0.592009\pi$
$660$	−2.39465	−0.0932117
$661$	8.17451	0.317952	0.158976	−	0.987282i	$-0.449181\pi$
$661$	8.17451	0.317952	0.158976	+	0.987282i	$0.449181\pi$
$662$	32.7510	1.27291
$663$	−29.3697	−1.14062
$664$	−6.52135	−0.253077
$665$	4.15853	0.161261
$666$	−9.04948	−0.350660
$667$	22.9259	0.887694
$668$	−3.94910	−0.152795
$669$	−47.8424	−1.84970
$670$	1.40663	0.0543430
$671$	−2.76736	−0.106833
$672$	2.73453	0.105487
$673$	−40.4561	−1.55947	−0.779733	−	0.626112i	$-0.784645\pi$
$673$	−40.4561	−1.55947	−0.779733	+	0.626112i	$0.784645\pi$
$674$	12.4477	0.479467
$675$	16.8935	0.650230
$676$	7.75844	0.298402
$677$	22.6740	0.871432	0.435716	−	0.900084i	$-0.356495\pi$
$677$	22.6740	0.871432	0.435716	+	0.900084i	$0.356495\pi$
$678$	25.7864	0.990322
$679$	−11.5993	−0.445142
$680$	−9.80300	−0.375928
$681$	−22.1770	−0.849825
$682$	−1.47212	−0.0563706
$683$	0.428261	0.0163870	0.00819348	−	0.999966i	$-0.497392\pi$
$683$	0.428261	0.0163870	0.00819348	+	0.999966i	$0.497392\pi$
$684$	−0.964042	−0.0368611
$685$	7.74547	0.295939
$686$	16.6375	0.635222
$687$	5.13610	0.195955
$688$	12.8122	0.488461
$689$	29.9902	1.14254
$690$	−21.5830	−0.821652
$691$	9.57133	0.364111	0.182055	−	0.983288i	$-0.441725\pi$
$691$	9.57133	0.364111	0.182055	+	0.983288i	$0.441725\pi$
$692$	3.89334	0.148003
$693$	−0.525965	−0.0199797
$694$	−2.05017	−0.0778234
$695$	−37.1040	−1.40744
$696$	−12.7491	−0.483253
$697$	−38.5781	−1.46125
$698$	26.3137	0.995988
$699$	51.6685	1.95428
$700$	−5.72393	−0.216344
$701$	10.1168	0.382106	0.191053	−	0.981580i	$-0.438810\pi$
$701$	10.1168	0.382106	0.191053	+	0.981580i	$0.438810\pi$
$702$	−18.4687	−0.697054
$703$	9.38701	0.354038
$704$	0.397234	0.0149713
$705$	50.4910	1.90160
$706$	−17.5587	−0.660831
$707$	10.3226	0.388220
$708$	−1.02711	−0.0386013
$709$	4.59318	0.172501	0.0862503	−	0.996274i	$-0.472512\pi$
$709$	4.59318	0.172501	0.0862503	+	0.996274i	$0.472512\pi$
$710$	3.53181	0.132546
$711$	−2.49525	−0.0935794
$712$	−3.17796	−0.119099
$713$	−13.2683	−0.496901
$714$	−8.85350	−0.331334
$715$	−5.47988	−0.204936
$716$	−13.6821	−0.511323
$717$	−13.0461	−0.487216
$718$	−20.2391	−0.755317
$719$	−33.5810	−1.25236	−0.626180	−	0.779679i	$-0.715382\pi$
$719$	−33.5810	−1.25236	−0.626180	+	0.779679i	$0.715382\pi$
$720$	2.91892	0.108782
$721$	24.2305	0.902392
$722$	1.00000	0.0372161
$723$	33.3951	1.24198
$724$	−2.35410	−0.0874893
$725$	26.6864	0.991109
$726$	21.5867	0.801158
$727$	28.3434	1.05120	0.525598	−	0.850733i	$-0.323841\pi$
$727$	28.3434	1.05120	0.525598	+	0.850733i	$0.323841\pi$
$728$	6.25765	0.231924
$729$	13.6433	0.505308
$730$	34.7888	1.28759
$731$	−41.4817	−1.53426
$732$	13.8704	0.512664
$733$	27.9008	1.03054	0.515270	−	0.857028i	$-0.327692\pi$
$733$	27.9008	1.03054	0.515270	+	0.857028i	$0.327692\pi$
$734$	0.745908	0.0275320
$735$	30.8265	1.13705
$736$	3.58028	0.131971
$737$	0.184544	0.00679778
$738$	11.4870	0.422841
$739$	51.2124	1.88388	0.941939	−	0.335785i	$-0.109002\pi$
$739$	51.2124	1.88388	0.941939	+	0.335785i	$0.109002\pi$
$740$	−28.4220	−1.04481
$741$	−9.07124	−0.333240
$742$	9.04057	0.331890
$743$	14.9019	0.546699	0.273350	−	0.961915i	$-0.411868\pi$
$743$	14.9019	0.546699	0.273350	+	0.961915i	$0.411868\pi$
$744$	7.37848	0.270508
$745$	6.06532	0.222216
$746$	−29.2219	−1.06989
$747$	−6.28685	−0.230024
$748$	−1.28611	−0.0470249
$749$	19.6647	0.718532
$750$	5.01827	0.183241
$751$	−18.9018	−0.689738	−0.344869	−	0.938651i	$-0.612077\pi$
$751$	−18.9018	−0.689738	−0.344869	+	0.938651i	$0.612077\pi$
$752$	−8.37564	−0.305428
$753$	52.4433	1.91114
$754$	−29.1747	−1.06248
$755$	10.1591	0.369727
$756$	−5.56739	−0.202484
$757$	8.31211	0.302109	0.151054	−	0.988525i	$-0.451733\pi$
$757$	8.31211	0.302109	0.151054	+	0.988525i	$0.451733\pi$
$758$	23.4019	0.849997
$759$	−2.83160	−0.102781
$760$	−3.02780	−0.109830
$761$	−40.6552	−1.47375	−0.736874	−	0.676030i	$-0.763699\pi$
$761$	−40.6552	−1.47375	−0.736874	+	0.676030i	$0.763699\pi$
$762$	38.0591	1.37874
$763$	17.6762	0.639920
$764$	10.4205	0.377001
$765$	−9.45050	−0.341684
$766$	−17.3713	−0.627651
$767$	−2.35043	−0.0848691
$768$	−1.99099	−0.0718437
$769$	−12.1004	−0.436351	−0.218175	−	0.975910i	$-0.570010\pi$
$769$	−12.1004	−0.436351	−0.218175	+	0.975910i	$0.570010\pi$
$770$	−1.65191	−0.0595308
$771$	40.5044	1.45873
$772$	−14.7752	−0.531772
$773$	−33.6458	−1.21015	−0.605077	−	0.796167i	$-0.706858\pi$
$773$	−33.6458	−1.21015	−0.605077	+	0.796167i	$0.706858\pi$
$774$	12.3515	0.443966
$775$	−15.4447	−0.554789
$776$	8.44539	0.303172
$777$	−25.6691	−0.920873
$778$	−0.119745	−0.00429307
$779$	−11.9154	−0.426914
$780$	27.4659	0.983435
$781$	0.463358	0.0165803
$782$	−11.5917	−0.414520
$783$	25.9566	0.927613
$784$	−5.11363	−0.182630
$785$	25.5816	0.913045
$786$	−31.6750	−1.12981
$787$	−26.5771	−0.947371	−0.473685	−	0.880694i	$-0.657077\pi$
$787$	−26.5771	−0.947371	−0.473685	+	0.880694i	$0.657077\pi$
$788$	−14.6513	−0.521932
$789$	25.3280	0.901699
$790$	−7.83692	−0.278825
$791$	17.7884	0.632481
$792$	0.382951	0.0136076
$793$	31.7407	1.12715
$794$	12.5975	0.447070
$795$	39.6806	1.40732
$796$	21.0659	0.746661
$797$	9.39536	0.332801	0.166400	−	0.986058i	$-0.446786\pi$
$797$	9.39536	0.332801	0.166400	+	0.986058i	$0.446786\pi$
$798$	−2.73453	−0.0968013
$799$	27.1175	0.959349
$800$	4.16755	0.147345
$801$	−3.06368	−0.108250
$802$	−22.6141	−0.798532
$803$	4.56415	0.161065
$804$	−0.924961	−0.0326209
$805$	−14.8887	−0.524758
$806$	16.8848	0.594741
$807$	−16.8366	−0.592675
$808$	−7.51579	−0.264404
$809$	42.0966	1.48004	0.740019	−	0.672586i	$-0.234816\pi$
$809$	42.0966	1.48004	0.740019	+	0.672586i	$0.234816\pi$
$810$	−33.1930	−1.16628
$811$	6.67823	0.234504	0.117252	−	0.993102i	$-0.462591\pi$
$811$	6.67823	0.234504	0.117252	+	0.993102i	$0.462591\pi$
$812$	−8.79475	−0.308635
$813$	−43.4080	−1.52239
$814$	−3.72884	−0.130696
$815$	8.57248	0.300281
$816$	6.44616	0.225661
$817$	−12.8122	−0.448242
$818$	−26.2677	−0.918429
$819$	6.03264	0.210797
$820$	36.0774	1.25988
$821$	26.8180	0.935956	0.467978	−	0.883740i	$-0.344983\pi$
$821$	26.8180	0.935956	0.467978	+	0.883740i	$0.344983\pi$
$822$	−5.09319	−0.177645
$823$	−22.3292	−0.778346	−0.389173	−	0.921165i	$-0.627239\pi$
$823$	−22.3292	−0.778346	−0.389173	+	0.921165i	$0.627239\pi$
$824$	−17.6420	−0.614590
$825$	−3.29607	−0.114754
$826$	−0.708539	−0.0246532
$827$	−35.6128	−1.23838	−0.619188	−	0.785242i	$-0.712538\pi$
$827$	−35.6128	−1.23838	−0.619188	+	0.785242i	$0.712538\pi$
$828$	3.45154	0.119949
$829$	−19.7541	−0.686088	−0.343044	−	0.939319i	$-0.611458\pi$
$829$	−19.7541	−0.686088	−0.343044	+	0.939319i	$0.611458\pi$
$830$	−19.7453	−0.685369
$831$	47.4434	1.64579
$832$	−4.55614	−0.157956
$833$	16.5562	0.573639
$834$	24.3985	0.844852
$835$	−11.9571	−0.413791
$836$	−0.397234	−0.0137386
$837$	−15.0223	−0.519246
$838$	19.5333	0.674767
$839$	−2.66638	−0.0920537	−0.0460269	−	0.998940i	$-0.514656\pi$
$839$	−2.66638	−0.0920537	−0.0460269	+	0.998940i	$0.514656\pi$
$840$	8.27960	0.285673
$841$	12.0033	0.413908
$842$	−37.1077	−1.27882
$843$	32.3347	1.11367
$844$	1.00000	0.0344214
$845$	23.4910	0.808114
$846$	−8.07447	−0.277606
$847$	14.8913	0.511670
$848$	−6.58237	−0.226039
$849$	−15.7426	−0.540284
$850$	−13.4931	−0.462811
$851$	−33.6081	−1.15207
$852$	−2.32241	−0.0795645
$853$	51.8097	1.77393	0.886966	−	0.461835i	$-0.152809\pi$
$853$	51.8097	1.77393	0.886966	+	0.461835i	$0.152809\pi$
$854$	9.56825	0.327419
$855$	−2.91892	−0.0998251
$856$	−14.3177	−0.489369
$857$	10.3281	0.352801	0.176401	−	0.984318i	$-0.443555\pi$
$857$	10.3281	0.352801	0.176401	+	0.984318i	$0.443555\pi$
$858$	3.60341	0.123018
$859$	34.2667	1.16917	0.584583	−	0.811334i	$-0.301258\pi$
$859$	34.2667	1.16917	0.584583	+	0.811334i	$0.301258\pi$
$860$	38.7928	1.32282
$861$	32.5830	1.11043
$862$	−2.03781	−0.0694080
$863$	−38.9827	−1.32699	−0.663493	−	0.748182i	$-0.730927\pi$
$863$	−38.9827	−1.32699	−0.663493	+	0.748182i	$0.730927\pi$
$864$	4.05357	0.137905
$865$	11.7883	0.400813
$866$	16.1803	0.549829
$867$	12.9763	0.440698
$868$	5.08993	0.172763
$869$	−1.02817	−0.0348783
$870$	−38.6016	−1.30872
$871$	−2.11666	−0.0717204
$872$	−12.8699	−0.435829
$873$	8.14171	0.275555
$874$	−3.58028	−0.121105
$875$	3.46177	0.117029
$876$	−22.8761	−0.772912
$877$	11.5497	0.390006	0.195003	−	0.980803i	$-0.437528\pi$
$877$	11.5497	0.390006	0.195003	+	0.980803i	$0.437528\pi$
$878$	−10.8767	−0.367070
$879$	4.37211	0.147468
$880$	1.20274	0.0405445
$881$	30.3682	1.02313	0.511566	−	0.859244i	$-0.329066\pi$
$881$	30.3682	1.02313	0.511566	+	0.859244i	$0.329066\pi$
$882$	−4.92975	−0.165993
$883$	20.4016	0.686570	0.343285	−	0.939231i	$-0.388460\pi$
$883$	20.4016	0.686570	0.343285	+	0.939231i	$0.388460\pi$
$884$	14.7513	0.496139
$885$	−3.10989	−0.104538
$886$	11.9442	0.401274
$887$	19.9924	0.671279	0.335639	−	0.941991i	$-0.391048\pi$
$887$	19.9924	0.671279	0.335639	+	0.941991i	$0.391048\pi$
$888$	18.6894	0.627177
$889$	26.2545	0.880547
$890$	−9.62220	−0.322537
$891$	−4.35478	−0.145891
$892$	24.0295	0.804566
$893$	8.37564	0.280280
$894$	−3.98838	−0.133391
$895$	−41.4265	−1.38474
$896$	−1.37345	−0.0458838
$897$	32.4775	1.08439
$898$	4.92790	0.164446
$899$	−23.7305	−0.791457
$900$	4.01769	0.133923
$901$	21.3115	0.709990
$902$	4.73321	0.157599
$903$	35.0354	1.16590
$904$	−12.9516	−0.430763
$905$	−7.12772	−0.236934
$906$	−6.68032	−0.221939
$907$	39.6229	1.31566	0.657828	−	0.753168i	$-0.271475\pi$
$907$	39.6229	1.31566	0.657828	+	0.753168i	$0.271475\pi$
$908$	11.1387	0.369650
$909$	−7.24554	−0.240319
$910$	18.9469	0.628083
$911$	26.0001	0.861422	0.430711	−	0.902490i	$-0.358263\pi$
$911$	26.0001	0.861422	0.430711	+	0.902490i	$0.358263\pi$
$912$	1.99099	0.0659283
$913$	−2.59050	−0.0857331
$914$	−27.3914	−0.906026
$915$	41.9967	1.38837
$916$	−2.57967	−0.0852348
$917$	−21.8505	−0.721566
$918$	−13.1241	−0.433160
$919$	22.2662	0.734495	0.367248	−	0.930123i	$-0.380300\pi$
$919$	22.2662	0.734495	0.367248	+	0.930123i	$0.380300\pi$
$920$	10.8403	0.357396
$921$	−2.76123	−0.0909856
$922$	−28.7098	−0.945505
$923$	−5.31456	−0.174931
$924$	1.08625	0.0357350
$925$	−39.1208	−1.28628
$926$	−7.07073	−0.232359
$927$	−17.0077	−0.558606
$928$	6.40339	0.210201
$929$	5.42407	0.177958	0.0889790	−	0.996034i	$-0.471640\pi$
$929$	5.42407	0.177958	0.0889790	+	0.996034i	$0.471640\pi$
$930$	22.3405	0.732575
$931$	5.11363	0.167592
$932$	−25.9512	−0.850059
$933$	−36.9830	−1.21077
$934$	−13.6850	−0.447788
$935$	−3.89409	−0.127350
$936$	−4.39232	−0.143567
$937$	−46.3383	−1.51381	−0.756903	−	0.653527i	$-0.773289\pi$
$937$	−46.3383	−1.51381	−0.756903	+	0.653527i	$0.773289\pi$
$938$	−0.638069	−0.0208337
$939$	−19.6007	−0.639646
$940$	−25.3597	−0.827143
$941$	27.7273	0.903884	0.451942	−	0.892047i	$-0.350731\pi$
$941$	27.7273	0.903884	0.451942	+	0.892047i	$0.350731\pi$
$942$	−16.8217	−0.548080
$943$	42.6605	1.38922
$944$	0.515881	0.0167905
$945$	−16.8569	−0.548356
$946$	5.08945	0.165472
$947$	−55.8908	−1.81621	−0.908103	−	0.418747i	$-0.862469\pi$
$947$	−55.8908	−1.81621	−0.908103	+	0.418747i	$0.862469\pi$
$948$	5.15333	0.167372
$949$	−52.3492	−1.69933
$950$	−4.16755	−0.135213
$951$	−66.7729	−2.16526
$952$	4.44678	0.144121
$953$	−57.0501	−1.84803	−0.924016	−	0.382353i	$-0.875114\pi$
$953$	−57.0501	−1.84803	−0.924016	+	0.382353i	$0.875114\pi$
$954$	−6.34568	−0.205449
$955$	31.5512	1.02097
$956$	6.55258	0.211926
$957$	−5.06437	−0.163708
$958$	10.7225	0.346427
$959$	−3.51346	−0.113455
$960$	−6.02831	−0.194563
$961$	−17.2660	−0.556969
$962$	42.7686	1.37891
$963$	−13.8029	−0.444791
$964$	−16.7731	−0.540225
$965$	−44.7363	−1.44011
$966$	9.79038	0.315000
$967$	36.2466	1.16561	0.582806	−	0.812611i	$-0.301955\pi$
$967$	36.2466	1.16561	0.582806	+	0.812611i	$0.301955\pi$
$968$	−10.8422	−0.348482
$969$	−6.44616	−0.207081
$970$	25.5709	0.821033
$971$	−0.308725	−0.00990744	−0.00495372	−	0.999988i	$-0.501577\pi$
$971$	−0.308725	−0.00990744	−0.00495372	+	0.999988i	$0.501577\pi$
$972$	9.66601	0.310037
$973$	16.8309	0.539575
$974$	6.79903	0.217855
$975$	37.8048	1.21072
$976$	−6.96657	−0.222994
$977$	−48.0136	−1.53609	−0.768046	−	0.640395i	$-0.778771\pi$
$977$	−48.0136	−1.53609	−0.768046	+	0.640395i	$0.778771\pi$
$978$	−5.63701	−0.180252
$979$	−1.26239	−0.0403463
$980$	−15.4830	−0.494587
$981$	−12.4071	−0.396128
$982$	−28.7198	−0.916487
$983$	46.3390	1.47798	0.738992	−	0.673714i	$-0.235302\pi$
$983$	46.3390	1.47798	0.738992	+	0.673714i	$0.235302\pi$
$984$	−23.7235	−0.756276
$985$	−44.3612	−1.41347
$986$	−20.7320	−0.660242
$987$	−22.9034	−0.729025
$988$	4.55614	0.144950
$989$	45.8713	1.45862
$990$	1.15950	0.0368512
$991$	56.6124	1.79835	0.899176	−	0.437587i	$-0.144167\pi$
$991$	56.6124	1.79835	0.899176	+	0.437587i	$0.144167\pi$
$992$	−3.70594	−0.117664
$993$	−65.2070	−2.06928
$994$	−1.60208	−0.0508149
$995$	63.7833	2.02207
$996$	12.9839	0.411412
$997$	7.57727	0.239974	0.119987	−	0.992775i	$-0.461715\pi$
$997$	7.57727	0.239974	0.119987	+	0.992775i	$0.461715\pi$
$998$	−10.1555	−0.321468
$999$	−38.0509	−1.20388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.e.1.7	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.e.1.7	✓	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.99099 q^{3} +1.00000 q^{4} +3.02780 q^{5} -1.99099 q^{6} -1.37345 q^{7} +1.00000 q^{8} +0.964042 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.99099 q^{3} +1.00000 q^{4} +3.02780 q^{5} -1.99099 q^{6} -1.37345 q^{7} +1.00000 q^{8} +0.964042 q^{9} +3.02780 q^{10} +0.397234 q^{11} -1.99099 q^{12} -4.55614 q^{13} -1.37345 q^{14} -6.02831 q^{15} +1.00000 q^{16} -3.23767 q^{17} +0.964042 q^{18} -1.00000 q^{19} +3.02780 q^{20} +2.73453 q^{21} +0.397234 q^{22} +3.58028 q^{23} -1.99099 q^{24} +4.16755 q^{25} -4.55614 q^{26} +4.05357 q^{27} -1.37345 q^{28} +6.40339 q^{29} -6.02831 q^{30} -3.70594 q^{31} +1.00000 q^{32} -0.790890 q^{33} -3.23767 q^{34} -4.15853 q^{35} +0.964042 q^{36} -9.38701 q^{37} -1.00000 q^{38} +9.07124 q^{39} +3.02780 q^{40} +11.9154 q^{41} +2.73453 q^{42} +12.8122 q^{43} +0.397234 q^{44} +2.91892 q^{45} +3.58028 q^{46} -8.37564 q^{47} -1.99099 q^{48} -5.11363 q^{49} +4.16755 q^{50} +6.44616 q^{51} -4.55614 q^{52} -6.58237 q^{53} +4.05357 q^{54} +1.20274 q^{55} -1.37345 q^{56} +1.99099 q^{57} +6.40339 q^{58} +0.515881 q^{59} -6.02831 q^{60} -6.96657 q^{61} -3.70594 q^{62} -1.32407 q^{63} +1.00000 q^{64} -13.7951 q^{65} -0.790890 q^{66} +0.464573 q^{67} -3.23767 q^{68} -7.12830 q^{69} -4.15853 q^{70} +1.16646 q^{71} +0.964042 q^{72} +11.4898 q^{73} -9.38701 q^{74} -8.29755 q^{75} -1.00000 q^{76} -0.545583 q^{77} +9.07124 q^{78} -2.58832 q^{79} +3.02780 q^{80} -10.9627 q^{81} +11.9154 q^{82} -6.52135 q^{83} +2.73453 q^{84} -9.80300 q^{85} +12.8122 q^{86} -12.7491 q^{87} +0.397234 q^{88} -3.17796 q^{89} +2.91892 q^{90} +6.25765 q^{91} +3.58028 q^{92} +7.37848 q^{93} -8.37564 q^{94} -3.02780 q^{95} -1.99099 q^{96} +8.44539 q^{97} -5.11363 q^{98} +0.382951 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * q^99

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