LMFDB - Embedded newform 4334.2.a.f.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.56353 q^{3} +1.00000 q^{4} -2.07613 q^{5} +1.56353 q^{6} +4.64853 q^{7} +1.00000 q^{8} -0.555380 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.56353 q^{3} +1.00000 q^{4} -2.07613 q^{5} +1.56353 q^{6} +4.64853 q^{7} +1.00000 q^{8} -0.555380 q^{9} -2.07613 q^{10} -1.00000 q^{11} +1.56353 q^{12} +6.09472 q^{13} +4.64853 q^{14} -3.24609 q^{15} +1.00000 q^{16} +1.78758 q^{17} -0.555380 q^{18} +6.90819 q^{19} -2.07613 q^{20} +7.26811 q^{21} -1.00000 q^{22} -5.48372 q^{23} +1.56353 q^{24} -0.689686 q^{25} +6.09472 q^{26} -5.55894 q^{27} +4.64853 q^{28} -4.90520 q^{29} -3.24609 q^{30} +1.11165 q^{31} +1.00000 q^{32} -1.56353 q^{33} +1.78758 q^{34} -9.65096 q^{35} -0.555380 q^{36} +0.379289 q^{37} +6.90819 q^{38} +9.52927 q^{39} -2.07613 q^{40} +2.79267 q^{41} +7.26811 q^{42} +4.01165 q^{43} -1.00000 q^{44} +1.15304 q^{45} -5.48372 q^{46} +4.54670 q^{47} +1.56353 q^{48} +14.6089 q^{49} -0.689686 q^{50} +2.79493 q^{51} +6.09472 q^{52} +7.21426 q^{53} -5.55894 q^{54} +2.07613 q^{55} +4.64853 q^{56} +10.8011 q^{57} -4.90520 q^{58} +7.85452 q^{59} -3.24609 q^{60} -11.0838 q^{61} +1.11165 q^{62} -2.58170 q^{63} +1.00000 q^{64} -12.6534 q^{65} -1.56353 q^{66} -3.73165 q^{67} +1.78758 q^{68} -8.57395 q^{69} -9.65096 q^{70} +2.38774 q^{71} -0.555380 q^{72} -10.3830 q^{73} +0.379289 q^{74} -1.07834 q^{75} +6.90819 q^{76} -4.64853 q^{77} +9.52927 q^{78} +14.2434 q^{79} -2.07613 q^{80} -7.02541 q^{81} +2.79267 q^{82} -6.38129 q^{83} +7.26811 q^{84} -3.71125 q^{85} +4.01165 q^{86} -7.66942 q^{87} -1.00000 q^{88} -1.41310 q^{89} +1.15304 q^{90} +28.3315 q^{91} -5.48372 q^{92} +1.73809 q^{93} +4.54670 q^{94} -14.3423 q^{95} +1.56353 q^{96} -9.85860 q^{97} +14.6089 q^{98} +0.555380 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) $ 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9 - 24 * q^11 + 8 * q^12 + 9 * q^13 + 11 * q^14 + 6 * q^15 + 24 * q^16 - q^17 + 28 * q^18 + 35 * q^19 + 21 * q^21 - 24 * q^22 + 13 * q^23 + 8 * q^24 + 38 * q^25 + 9 * q^26 + 23 * q^27 + 11 * q^28 + 15 * q^29 + 6 * q^30 + 31 * q^31 + 24 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 28 * q^36 + 13 * q^37 + 35 * q^38 + 31 * q^39 + 16 * q^41 + 21 * q^42 + 35 * q^43 - 24 * q^44 + 13 * q^45 + 13 * q^46 + 46 * q^47 + 8 * q^48 + 55 * q^49 + 38 * q^50 + 18 * q^51 + 9 * q^52 + 6 * q^53 + 23 * q^54 + 11 * q^56 + 18 * q^57 + 15 * q^58 + 13 * q^59 + 6 * q^60 + 60 * q^61 + 31 * q^62 + 52 * q^63 + 24 * q^64 - 9 * q^65 - 8 * q^66 + 28 * q^67 - q^68 + 21 * q^69 + 28 * q^70 + 10 * q^71 + 28 * q^72 + 3 * q^73 + 13 * q^74 + 48 * q^75 + 35 * q^76 - 11 * q^77 + 31 * q^78 + 47 * q^79 + 16 * q^81 + 16 * q^82 + 66 * q^83 + 21 * q^84 + 37 * q^85 + 35 * q^86 + 34 * q^87 - 24 * q^88 - 5 * q^89 + 13 * q^90 + q^91 + 13 * q^92 - 16 * q^93 + 46 * q^94 + 9 * q^95 + 8 * q^96 + 24 * q^97 + 55 * q^98 - 28 * 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
$3$	1.56353	0.902703	0.451352	−	0.892346i	$-0.350942\pi$
$3$	1.56353	0.902703	0.451352	+	0.892346i	$0.350942\pi$
$4$	1.00000	0.500000
$5$	−2.07613	−0.928473	−0.464237	−	0.885711i	$-0.653671\pi$
$5$	−2.07613	−0.928473	−0.464237	+	0.885711i	$0.653671\pi$
$6$	1.56353	0.638308
$7$	4.64853	1.75698	0.878490	−	0.477761i	$-0.158551\pi$
$7$	4.64853	1.75698	0.878490	+	0.477761i	$0.158551\pi$
$8$	1.00000	0.353553
$9$	−0.555380	−0.185127
$10$	−2.07613	−0.656530
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.56353	0.451352
$13$	6.09472	1.69037	0.845186	−	0.534473i	$-0.179490\pi$
$13$	6.09472	1.69037	0.845186	+	0.534473i	$0.179490\pi$
$14$	4.64853	1.24237
$15$	−3.24609	−0.838136
$16$	1.00000	0.250000
$17$	1.78758	0.433552	0.216776	−	0.976221i	$-0.430446\pi$
$17$	1.78758	0.433552	0.216776	+	0.976221i	$0.430446\pi$
$18$	−0.555380	−0.130904
$19$	6.90819	1.58485	0.792423	−	0.609972i	$-0.208819\pi$
$19$	6.90819	1.58485	0.792423	+	0.609972i	$0.208819\pi$
$20$	−2.07613	−0.464237
$21$	7.26811	1.58603
$22$	−1.00000	−0.213201
$23$	−5.48372	−1.14343	−0.571717	−	0.820451i	$-0.693723\pi$
$23$	−5.48372	−1.14343	−0.571717	+	0.820451i	$0.693723\pi$
$24$	1.56353	0.319154
$25$	−0.689686	−0.137937
$26$	6.09472	1.19527
$27$	−5.55894	−1.06982
$28$	4.64853	0.878490
$29$	−4.90520	−0.910873	−0.455436	−	0.890268i	$-0.650517\pi$
$29$	−4.90520	−0.910873	−0.455436	+	0.890268i	$0.650517\pi$
$30$	−3.24609	−0.592652
$31$	1.11165	0.199658	0.0998290	−	0.995005i	$-0.468170\pi$
$31$	1.11165	0.199658	0.0998290	+	0.995005i	$0.468170\pi$
$32$	1.00000	0.176777
$33$	−1.56353	−0.272175
$34$	1.78758	0.306567
$35$	−9.65096	−1.63131
$36$	−0.555380	−0.0925634
$37$	0.379289	0.0623548	0.0311774	−	0.999514i	$-0.490074\pi$
$37$	0.379289	0.0623548	0.0311774	+	0.999514i	$0.490074\pi$
$38$	6.90819	1.12066
$39$	9.52927	1.52590
$40$	−2.07613	−0.328265
$41$	2.79267	0.436142	0.218071	−	0.975933i	$-0.430023\pi$
$41$	2.79267	0.436142	0.218071	+	0.975933i	$0.430023\pi$
$42$	7.26811	1.12149
$43$	4.01165	0.611771	0.305885	−	0.952068i	$-0.401048\pi$
$43$	4.01165	0.611771	0.305885	+	0.952068i	$0.401048\pi$
$44$	−1.00000	−0.150756
$45$	1.15304	0.171885
$46$	−5.48372	−0.808530
$47$	4.54670	0.663204	0.331602	−	0.943419i	$-0.392411\pi$
$47$	4.54670	0.663204	0.331602	+	0.943419i	$0.392411\pi$
$48$	1.56353	0.225676
$49$	14.6089	2.08698
$50$	−0.689686	−0.0975363
$51$	2.79493	0.391369
$52$	6.09472	0.845186
$53$	7.21426	0.990954	0.495477	−	0.868621i	$-0.334993\pi$
$53$	7.21426	0.990954	0.495477	+	0.868621i	$0.334993\pi$
$54$	−5.55894	−0.756475
$55$	2.07613	0.279945
$56$	4.64853	0.621186
$57$	10.8011	1.43065
$58$	−4.90520	−0.644084
$59$	7.85452	1.02257	0.511286	−	0.859411i	$-0.329169\pi$
$59$	7.85452	1.02257	0.511286	+	0.859411i	$0.329169\pi$
$60$	−3.24609	−0.419068
$61$	−11.0838	−1.41913	−0.709565	−	0.704640i	$-0.751109\pi$
$61$	−11.0838	−1.41913	−0.709565	+	0.704640i	$0.751109\pi$
$62$	1.11165	0.141180
$63$	−2.58170	−0.325264
$64$	1.00000	0.125000
$65$	−12.6534	−1.56946
$66$	−1.56353	−0.192457
$67$	−3.73165	−0.455894	−0.227947	−	0.973674i	$-0.573201\pi$
$67$	−3.73165	−0.455894	−0.227947	+	0.973674i	$0.573201\pi$
$68$	1.78758	0.216776
$69$	−8.57395	−1.03218
$70$	−9.65096	−1.15351
$71$	2.38774	0.283373	0.141687	−	0.989912i	$-0.454748\pi$
$71$	2.38774	0.283373	0.141687	+	0.989912i	$0.454748\pi$
$72$	−0.555380	−0.0654522
$73$	−10.3830	−1.21524	−0.607618	−	0.794229i	$-0.707875\pi$
$73$	−10.3830	−1.21524	−0.607618	+	0.794229i	$0.707875\pi$
$74$	0.379289	0.0440915
$75$	−1.07834	−0.124516
$76$	6.90819	0.792423
$77$	−4.64853	−0.529749
$78$	9.52927	1.07898
$79$	14.2434	1.60250	0.801251	−	0.598328i	$-0.204168\pi$
$79$	14.2434	1.60250	0.801251	+	0.598328i	$0.204168\pi$
$80$	−2.07613	−0.232118
$81$	−7.02541	−0.780601
$82$	2.79267	0.308399
$83$	−6.38129	−0.700437	−0.350219	−	0.936668i	$-0.613893\pi$
$83$	−6.38129	−0.700437	−0.350219	+	0.936668i	$0.613893\pi$
$84$	7.26811	0.793016
$85$	−3.71125	−0.402541
$86$	4.01165	0.432587
$87$	−7.66942	−0.822248
$88$	−1.00000	−0.106600
$89$	−1.41310	−0.149788	−0.0748942	−	0.997191i	$-0.523862\pi$
$89$	−1.41310	−0.149788	−0.0748942	+	0.997191i	$0.523862\pi$
$90$	1.15304	0.121541
$91$	28.3315	2.96995
$92$	−5.48372	−0.571717
$93$	1.73809	0.180232
$94$	4.54670	0.468956
$95$	−14.3423	−1.47149
$96$	1.56353	0.159577
$97$	−9.85860	−1.00099	−0.500494	−	0.865740i	$-0.666848\pi$
$97$	−9.85860	−1.00099	−0.500494	+	0.865740i	$0.666848\pi$
$98$	14.6089	1.47572
$99$	0.555380	0.0558178
$100$	−0.689686	−0.0689686
$101$	−13.7562	−1.36879	−0.684395	−	0.729111i	$-0.739934\pi$
$101$	−13.7562	−1.36879	−0.684395	+	0.729111i	$0.739934\pi$
$102$	2.79493	0.276739
$103$	−0.599524	−0.0590728	−0.0295364	−	0.999564i	$-0.509403\pi$
$103$	−0.599524	−0.0590728	−0.0295364	+	0.999564i	$0.509403\pi$
$104$	6.09472	0.597636
$105$	−15.0895	−1.47259
$106$	7.21426	0.700711
$107$	−17.0407	−1.64739	−0.823694	−	0.567034i	$-0.808091\pi$
$107$	−17.0407	−1.64739	−0.823694	+	0.567034i	$0.808091\pi$
$108$	−5.55894	−0.534909
$109$	−0.297502	−0.0284955	−0.0142477	−	0.999898i	$-0.504535\pi$
$109$	−0.297502	−0.0284955	−0.0142477	+	0.999898i	$0.504535\pi$
$110$	2.07613	0.197951
$111$	0.593030	0.0562879
$112$	4.64853	0.439245
$113$	14.0142	1.31835	0.659174	−	0.751990i	$-0.270906\pi$
$113$	14.0142	1.31835	0.659174	+	0.751990i	$0.270906\pi$
$114$	10.8011	1.01162
$115$	11.3849	1.06165
$116$	−4.90520	−0.455436
$117$	−3.38489	−0.312933
$118$	7.85452	0.723067
$119$	8.30962	0.761742
$120$	−3.24609	−0.296326
$121$	1.00000	0.0909091
$122$	−11.0838	−1.00348
$123$	4.36642	0.393707
$124$	1.11165	0.0998290
$125$	11.8125	1.05654
$126$	−2.58170	−0.229996
$127$	5.00798	0.444387	0.222193	−	0.975003i	$-0.428678\pi$
$127$	5.00798	0.444387	0.222193	+	0.975003i	$0.428678\pi$
$128$	1.00000	0.0883883
$129$	6.27233	0.552248
$130$	−12.6534	−1.10978
$131$	10.5088	0.918160	0.459080	−	0.888395i	$-0.348179\pi$
$131$	10.5088	0.918160	0.459080	+	0.888395i	$0.348179\pi$
$132$	−1.56353	−0.136088
$133$	32.1129	2.78454
$134$	−3.73165	−0.322366
$135$	11.5411	0.993297
$136$	1.78758	0.153284
$137$	16.9568	1.44871	0.724357	−	0.689426i	$-0.242137\pi$
$137$	16.9568	1.44871	0.724357	+	0.689426i	$0.242137\pi$
$138$	−8.57395	−0.729863
$139$	5.83698	0.495086	0.247543	−	0.968877i	$-0.420377\pi$
$139$	5.83698	0.495086	0.247543	+	0.968877i	$0.420377\pi$
$140$	−9.65096	−0.815655
$141$	7.10889	0.598676
$142$	2.38774	0.200375
$143$	−6.09472	−0.509666
$144$	−0.555380	−0.0462817
$145$	10.1838	0.845721
$146$	−10.3830	−0.859302
$147$	22.8414	1.88392
$148$	0.379289	0.0311774
$149$	17.7402	1.45333	0.726665	−	0.686992i	$-0.241069\pi$
$149$	17.7402	1.45333	0.726665	+	0.686992i	$0.241069\pi$
$150$	−1.07834	−0.0880463
$151$	14.6159	1.18943	0.594714	−	0.803938i	$-0.297265\pi$
$151$	14.6159	1.18943	0.594714	+	0.803938i	$0.297265\pi$
$152$	6.90819	0.560328
$153$	−0.992786	−0.0802620
$154$	−4.64853	−0.374589
$155$	−2.30793	−0.185377
$156$	9.52927	0.762952
$157$	−17.1218	−1.36647	−0.683235	−	0.730199i	$-0.739427\pi$
$157$	−17.1218	−1.36647	−0.683235	+	0.730199i	$0.739427\pi$
$158$	14.2434	1.13314
$159$	11.2797	0.894538
$160$	−2.07613	−0.164132
$161$	−25.4912	−2.00899
$162$	−7.02541	−0.551969
$163$	−8.94600	−0.700705	−0.350353	−	0.936618i	$-0.613938\pi$
$163$	−8.94600	−0.700705	−0.350353	+	0.936618i	$0.613938\pi$
$164$	2.79267	0.218071
$165$	3.24609	0.252708
$166$	−6.38129	−0.495284
$167$	−20.7439	−1.60521	−0.802607	−	0.596508i	$-0.796554\pi$
$167$	−20.7439	−1.60521	−0.802607	+	0.596508i	$0.796554\pi$
$168$	7.26811	0.560747
$169$	24.1456	1.85735
$170$	−3.71125	−0.284640
$171$	−3.83667	−0.293397
$172$	4.01165	0.305885
$173$	9.26366	0.704303	0.352152	−	0.935943i	$-0.385450\pi$
$173$	9.26366	0.704303	0.352152	+	0.935943i	$0.385450\pi$
$174$	−7.66942	−0.581417
$175$	−3.20603	−0.242353
$176$	−1.00000	−0.0753778
$177$	12.2808	0.923079
$178$	−1.41310	−0.105916
$179$	−22.9244	−1.71345	−0.856726	−	0.515772i	$-0.827505\pi$
$179$	−22.9244	−1.71345	−0.856726	+	0.515772i	$0.827505\pi$
$180$	1.15304	0.0859426
$181$	26.0187	1.93396	0.966979	−	0.254856i	$-0.0820279\pi$
$181$	26.0187	1.93396	0.966979	+	0.254856i	$0.0820279\pi$
$182$	28.3315	2.10007
$183$	−17.3298	−1.28105
$184$	−5.48372	−0.404265
$185$	−0.787454	−0.0578948
$186$	1.73809	0.127443
$187$	−1.78758	−0.130721
$188$	4.54670	0.331602
$189$	−25.8409	−1.87965
$190$	−14.3423	−1.04050
$191$	−13.7191	−0.992682	−0.496341	−	0.868128i	$-0.665323\pi$
$191$	−13.7191	−0.992682	−0.496341	+	0.868128i	$0.665323\pi$
$192$	1.56353	0.112838
$193$	−1.73617	−0.124972	−0.0624862	−	0.998046i	$-0.519903\pi$
$193$	−1.73617	−0.124972	−0.0624862	+	0.998046i	$0.519903\pi$
$194$	−9.85860	−0.707806
$195$	−19.7840	−1.41676
$196$	14.6089	1.04349
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	0.555380	0.0394691
$199$	−9.28306	−0.658059	−0.329029	−	0.944320i	$-0.606722\pi$
$199$	−9.28306	−0.658059	−0.329029	+	0.944320i	$0.606722\pi$
$200$	−0.689686	−0.0487681
$201$	−5.83454	−0.411537
$202$	−13.7562	−0.967881
$203$	−22.8020	−1.60039
$204$	2.79493	0.195684
$205$	−5.79795	−0.404947
$206$	−0.599524	−0.0417708
$207$	3.04555	0.211680
$208$	6.09472	0.422593
$209$	−6.90819	−0.477849
$210$	−15.0895	−1.04128
$211$	26.6206	1.83264	0.916318	−	0.400451i	$-0.131147\pi$
$211$	26.6206	1.83264	0.916318	+	0.400451i	$0.131147\pi$
$212$	7.21426	0.495477
$213$	3.73330	0.255802
$214$	−17.0407	−1.16488
$215$	−8.32870	−0.568013
$216$	−5.55894	−0.378238
$217$	5.16753	0.350795
$218$	−0.297502	−0.0201493
$219$	−16.2341	−1.09700
$220$	2.07613	0.139973
$221$	10.8948	0.732863
$222$	0.593030	0.0398015
$223$	−18.9028	−1.26583	−0.632913	−	0.774223i	$-0.718141\pi$
$223$	−18.9028	−1.26583	−0.632913	+	0.774223i	$0.718141\pi$
$224$	4.64853	0.310593
$225$	0.383038	0.0255358
$226$	14.0142	0.932213
$227$	−0.843402	−0.0559786	−0.0279893	−	0.999608i	$-0.508910\pi$
$227$	−0.843402	−0.0559786	−0.0279893	+	0.999608i	$0.508910\pi$
$228$	10.8011	0.715323
$229$	14.1329	0.933928	0.466964	−	0.884276i	$-0.345348\pi$
$229$	14.1329	0.933928	0.466964	+	0.884276i	$0.345348\pi$
$230$	11.3849	0.750699
$231$	−7.26811	−0.478207
$232$	−4.90520	−0.322042
$233$	1.15831	0.0758831	0.0379416	−	0.999280i	$-0.487920\pi$
$233$	1.15831	0.0758831	0.0379416	+	0.999280i	$0.487920\pi$
$234$	−3.38489	−0.221277
$235$	−9.43953	−0.615767
$236$	7.85452	0.511286
$237$	22.2699	1.44658
$238$	8.30962	0.538633
$239$	−15.0282	−0.972092	−0.486046	−	0.873933i	$-0.661561\pi$
$239$	−15.0282	−0.972092	−0.486046	+	0.873933i	$0.661561\pi$
$240$	−3.24609	−0.209534
$241$	−0.00171999	−0.000110794 0	−5.53970e−5	−	1.00000i	$-0.500018\pi$
$241$	−0.00171999	−0.000110794 0	−5.53970e−5		1.00000i	$0.500018\pi$
$242$	1.00000	0.0642824
$243$	5.69238	0.365166
$244$	−11.0838	−0.709565
$245$	−30.3299	−1.93770
$246$	4.36642	0.278393
$247$	42.1035	2.67898
$248$	1.11165	0.0705898
$249$	−9.97732	−0.632287
$250$	11.8125	0.747090
$251$	22.9715	1.44995	0.724974	−	0.688776i	$-0.241852\pi$
$251$	22.9715	1.44995	0.724974	+	0.688776i	$0.241852\pi$
$252$	−2.58170	−0.162632
$253$	5.48372	0.344759
$254$	5.00798	0.314229
$255$	−5.80264	−0.363375
$256$	1.00000	0.0625000
$257$	5.79523	0.361497	0.180748	−	0.983529i	$-0.442148\pi$
$257$	5.79523	0.361497	0.180748	+	0.983529i	$0.442148\pi$
$258$	6.27233	0.390498
$259$	1.76314	0.109556
$260$	−12.6534	−0.784732
$261$	2.72425	0.168627
$262$	10.5088	0.649237
$263$	−15.8336	−0.976339	−0.488170	−	0.872749i	$-0.662335\pi$
$263$	−15.8336	−0.976339	−0.488170	+	0.872749i	$0.662335\pi$
$264$	−1.56353	−0.0962285
$265$	−14.9777	−0.920075
$266$	32.1129	1.96897
$267$	−2.20942	−0.135214
$268$	−3.73165	−0.227947
$269$	−1.86193	−0.113524	−0.0567619	−	0.998388i	$-0.518078\pi$
$269$	−1.86193	−0.113524	−0.0567619	+	0.998388i	$0.518078\pi$
$270$	11.5411	0.702367
$271$	−20.4378	−1.24151	−0.620753	−	0.784007i	$-0.713173\pi$
$271$	−20.4378	−1.24151	−0.620753	+	0.784007i	$0.713173\pi$
$272$	1.78758	0.108388
$273$	44.2971	2.68098
$274$	16.9568	1.02439
$275$	0.689686	0.0415896
$276$	−8.57395	−0.516091
$277$	11.0419	0.663441	0.331720	−	0.943378i	$-0.392371\pi$
$277$	11.0419	0.663441	0.331720	+	0.943378i	$0.392371\pi$
$278$	5.83698	0.350079
$279$	−0.617388	−0.0369620
$280$	−9.65096	−0.576755
$281$	−2.68057	−0.159909	−0.0799547	−	0.996799i	$-0.525478\pi$
$281$	−2.68057	−0.159909	−0.0799547	+	0.996799i	$0.525478\pi$
$282$	7.10889	0.423328
$283$	−8.91685	−0.530052	−0.265026	−	0.964241i	$-0.585381\pi$
$283$	−8.91685	−0.530052	−0.265026	+	0.964241i	$0.585381\pi$
$284$	2.38774	0.141687
$285$	−22.4246	−1.32832
$286$	−6.09472	−0.360388
$287$	12.9818	0.766294
$288$	−0.555380	−0.0327261
$289$	−13.8046	−0.812033
$290$	10.1838	0.598015
$291$	−15.4142	−0.903596
$292$	−10.3830	−0.607618
$293$	−31.2844	−1.82765	−0.913826	−	0.406105i	$-0.866887\pi$
$293$	−31.2844	−1.82765	−0.913826	+	0.406105i	$0.866887\pi$
$294$	22.8414	1.33213
$295$	−16.3070	−0.949431
$296$	0.379289	0.0220457
$297$	5.55894	0.322562
$298$	17.7402	1.02766
$299$	−33.4217	−1.93283
$300$	−1.07834	−0.0622581
$301$	18.6483	1.07487
$302$	14.6159	0.841052
$303$	−21.5082	−1.23561
$304$	6.90819	0.396212
$305$	23.0113	1.31762
$306$	−0.992786	−0.0567538
$307$	−6.22595	−0.355334	−0.177667	−	0.984091i	$-0.556855\pi$
$307$	−6.22595	−0.355334	−0.177667	+	0.984091i	$0.556855\pi$
$308$	−4.64853	−0.264875
$309$	−0.937372	−0.0533252
$310$	−2.30793	−0.131081
$311$	−20.4167	−1.15772	−0.578862	−	0.815426i	$-0.696503\pi$
$311$	−20.4167	−1.15772	−0.578862	+	0.815426i	$0.696503\pi$
$312$	9.52927	0.539488
$313$	−4.92535	−0.278397	−0.139199	−	0.990264i	$-0.544453\pi$
$313$	−4.92535	−0.278397	−0.139199	+	0.990264i	$0.544453\pi$
$314$	−17.1218	−0.966240
$315$	5.35995	0.301999
$316$	14.2434	0.801251
$317$	3.10764	0.174542	0.0872712	−	0.996185i	$-0.472185\pi$
$317$	3.10764	0.174542	0.0872712	+	0.996185i	$0.472185\pi$
$318$	11.2797	0.632534
$319$	4.90520	0.274639
$320$	−2.07613	−0.116059
$321$	−26.6436	−1.48710
$322$	−25.4912	−1.42057
$323$	12.3489	0.687113
$324$	−7.02541	−0.390301
$325$	−4.20344	−0.233165
$326$	−8.94600	−0.495473
$327$	−0.465152	−0.0257230
$328$	2.79267	0.154200
$329$	21.1355	1.16524
$330$	3.24609	0.178691
$331$	−0.366644	−0.0201525	−0.0100763	−	0.999949i	$-0.503207\pi$
$331$	−0.366644	−0.0201525	−0.0100763	+	0.999949i	$0.503207\pi$
$332$	−6.38129	−0.350219
$333$	−0.210650	−0.0115435
$334$	−20.7439	−1.13506
$335$	7.74739	0.423285
$336$	7.26811	0.396508
$337$	−32.5731	−1.77437	−0.887184	−	0.461416i	$-0.847342\pi$
$337$	−32.5731	−1.77437	−0.887184	+	0.461416i	$0.847342\pi$
$338$	24.1456	1.31335
$339$	21.9116	1.19008
$340$	−3.71125	−0.201271
$341$	−1.11165	−0.0601991
$342$	−3.83667	−0.207463
$343$	35.3700	1.90980
$344$	4.01165	0.216294
$345$	17.8006	0.958354
$346$	9.26366	0.498018
$347$	−18.6166	−0.999390	−0.499695	−	0.866201i	$-0.666555\pi$
$347$	−18.6166	−0.999390	−0.499695	+	0.866201i	$0.666555\pi$
$348$	−7.66942	−0.411124
$349$	−22.8704	−1.22422	−0.612111	−	0.790772i	$-0.709679\pi$
$349$	−22.8704	−1.22422	−0.612111	+	0.790772i	$0.709679\pi$
$350$	−3.20603	−0.171369
$351$	−33.8802	−1.80839
$352$	−1.00000	−0.0533002
$353$	1.36064	0.0724193	0.0362097	−	0.999344i	$-0.488472\pi$
$353$	1.36064	0.0724193	0.0362097	+	0.999344i	$0.488472\pi$
$354$	12.2808	0.652715
$355$	−4.95727	−0.263104
$356$	−1.41310	−0.0748942
$357$	12.9923	0.687627
$358$	−22.9244	−1.21159
$359$	23.1148	1.21995	0.609977	−	0.792419i	$-0.291179\pi$
$359$	23.1148	1.21995	0.609977	+	0.792419i	$0.291179\pi$
$360$	1.15304	0.0607706
$361$	28.7230	1.51174
$362$	26.0187	1.36752
$363$	1.56353	0.0820639
$364$	28.3315	1.48497
$365$	21.5564	1.12832
$366$	−17.3298	−0.905842
$367$	−21.5987	−1.12744	−0.563721	−	0.825965i	$-0.690631\pi$
$367$	−21.5987	−1.12744	−0.563721	+	0.825965i	$0.690631\pi$
$368$	−5.48372	−0.285859
$369$	−1.55100	−0.0807416
$370$	−0.787454	−0.0409378
$371$	33.5357	1.74109
$372$	1.73809	0.0901160
$373$	−8.95058	−0.463444	−0.231722	−	0.972782i	$-0.574436\pi$
$373$	−8.95058	−0.463444	−0.231722	+	0.972782i	$0.574436\pi$
$374$	−1.78758	−0.0924335
$375$	18.4692	0.953746
$376$	4.54670	0.234478
$377$	−29.8958	−1.53971
$378$	−25.8409	−1.32911
$379$	−17.5642	−0.902215	−0.451107	−	0.892470i	$-0.648971\pi$
$379$	−17.5642	−0.902215	−0.451107	+	0.892470i	$0.648971\pi$
$380$	−14.3423	−0.735744
$381$	7.83012	0.401149
$382$	−13.7191	−0.701932
$383$	−4.18459	−0.213823	−0.106911	−	0.994269i	$-0.534096\pi$
$383$	−4.18459	−0.213823	−0.106911	+	0.994269i	$0.534096\pi$
$384$	1.56353	0.0797885
$385$	9.65096	0.491858
$386$	−1.73617	−0.0883688
$387$	−2.22799	−0.113255
$388$	−9.85860	−0.500494
$389$	−13.4447	−0.681675	−0.340838	−	0.940122i	$-0.610711\pi$
$389$	−13.4447	−0.681675	−0.340838	+	0.940122i	$0.610711\pi$
$390$	−19.7840	−1.00180
$391$	−9.80258	−0.495738
$392$	14.6089	0.737859
$393$	16.4308	0.828826
$394$	−1.00000	−0.0503793
$395$	−29.5710	−1.48788
$396$	0.555380	0.0279089
$397$	31.7230	1.59213	0.796067	−	0.605209i	$-0.206911\pi$
$397$	31.7230	1.59213	0.796067	+	0.605209i	$0.206911\pi$
$398$	−9.28306	−0.465318
$399$	50.2095	2.51362
$400$	−0.689686	−0.0344843
$401$	15.6697	0.782509	0.391254	−	0.920283i	$-0.372041\pi$
$401$	15.6697	0.782509	0.391254	+	0.920283i	$0.372041\pi$
$402$	−5.83454	−0.291000
$403$	6.77519	0.337496
$404$	−13.7562	−0.684395
$405$	14.5857	0.724768
$406$	−22.8020	−1.13164
$407$	−0.379289	−0.0188007
$408$	2.79493	0.138370
$409$	21.2975	1.05309	0.526547	−	0.850146i	$-0.323486\pi$
$409$	21.2975	1.05309	0.526547	+	0.850146i	$0.323486\pi$
$410$	−5.79795	−0.286341
$411$	26.5124	1.30776
$412$	−0.599524	−0.0295364
$413$	36.5120	1.79664
$414$	3.04555	0.149681
$415$	13.2484	0.650337
$416$	6.09472	0.298818
$417$	9.12628	0.446916
$418$	−6.90819	−0.337890
$419$	−0.569174	−0.0278060	−0.0139030	−	0.999903i	$-0.504426\pi$
$419$	−0.569174	−0.0278060	−0.0139030	+	0.999903i	$0.504426\pi$
$420$	−15.0895	−0.736294
$421$	−32.4773	−1.58285	−0.791424	−	0.611267i	$-0.790660\pi$
$421$	−32.4773	−1.58285	−0.791424	+	0.611267i	$0.790660\pi$
$422$	26.6206	1.29587
$423$	−2.52515	−0.122777
$424$	7.21426	0.350355
$425$	−1.23287	−0.0598029
$426$	3.73330	0.180879
$427$	−51.5232	−2.49338
$428$	−17.0407	−0.823694
$429$	−9.52927	−0.460077
$430$	−8.32870	−0.401646
$431$	−2.24052	−0.107922	−0.0539610	−	0.998543i	$-0.517185\pi$
$431$	−2.24052	−0.107922	−0.0539610	+	0.998543i	$0.517185\pi$
$432$	−5.55894	−0.267454
$433$	−8.26995	−0.397428	−0.198714	−	0.980057i	$-0.563677\pi$
$433$	−8.26995	−0.397428	−0.198714	+	0.980057i	$0.563677\pi$
$434$	5.16753	0.248050
$435$	15.9227	0.763435
$436$	−0.297502	−0.0142477
$437$	−37.8826	−1.81217
$438$	−16.2341	−0.775695
$439$	40.2920	1.92303	0.961517	−	0.274746i	$-0.0885937\pi$
$439$	40.2920	1.92303	0.961517	+	0.274746i	$0.0885937\pi$
$440$	2.07613	0.0989756
$441$	−8.11347	−0.386356
$442$	10.8948	0.518213
$443$	−0.0881844	−0.00418977	−0.00209488	−	0.999998i	$-0.500667\pi$
$443$	−0.0881844	−0.00418977	−0.00209488	+	0.999998i	$0.500667\pi$
$444$	0.593030	0.0281439
$445$	2.93378	0.139074
$446$	−18.9028	−0.895075
$447$	27.7372	1.31193
$448$	4.64853	0.219623
$449$	−29.6553	−1.39952	−0.699760	−	0.714378i	$-0.746710\pi$
$449$	−29.6553	−1.39952	−0.699760	+	0.714378i	$0.746710\pi$
$450$	0.383038	0.0180566
$451$	−2.79267	−0.131502
$452$	14.0142	0.659174
$453$	22.8524	1.07370
$454$	−0.843402	−0.0395828
$455$	−58.8199	−2.75752
$456$	10.8011	0.505810
$457$	37.8637	1.77119	0.885594	−	0.464460i	$-0.153752\pi$
$457$	37.8637	1.77119	0.885594	+	0.464460i	$0.153752\pi$
$458$	14.1329	0.660387
$459$	−9.93704	−0.463821
$460$	11.3849	0.530824
$461$	−2.52437	−0.117572	−0.0587858	−	0.998271i	$-0.518723\pi$
$461$	−2.52437	−0.117572	−0.0587858	+	0.998271i	$0.518723\pi$
$462$	−7.26811	−0.338143
$463$	−20.8350	−0.968283	−0.484141	−	0.874990i	$-0.660868\pi$
$463$	−20.8350	−0.968283	−0.484141	+	0.874990i	$0.660868\pi$
$464$	−4.90520	−0.227718
$465$	−3.60851	−0.167341
$466$	1.15831	0.0536575
$467$	−13.2139	−0.611465	−0.305733	−	0.952117i	$-0.598901\pi$
$467$	−13.2139	−0.611465	−0.305733	+	0.952117i	$0.598901\pi$
$468$	−3.38489	−0.156466
$469$	−17.3467	−0.800996
$470$	−9.43953	−0.435413
$471$	−26.7704	−1.23352
$472$	7.85452	0.361534
$473$	−4.01165	−0.184456
$474$	22.2699	1.02289
$475$	−4.76448	−0.218609
$476$	8.30962	0.380871
$477$	−4.00666	−0.183452
$478$	−15.0282	−0.687373
$479$	−4.87270	−0.222639	−0.111320	−	0.993785i	$-0.535508\pi$
$479$	−4.87270	−0.222639	−0.111320	+	0.993785i	$0.535508\pi$
$480$	−3.24609	−0.148163
$481$	2.31166	0.105403
$482$	−0.00171999	−7.83432e−5 0
$483$	−39.8563	−1.81352
$484$	1.00000	0.0454545
$485$	20.4677	0.929391
$486$	5.69238	0.258212
$487$	−41.0312	−1.85930	−0.929651	−	0.368440i	$-0.879892\pi$
$487$	−41.0312	−1.85930	−0.929651	+	0.368440i	$0.879892\pi$
$488$	−11.0838	−0.501738
$489$	−13.9873	−0.632529
$490$	−30.3299	−1.37016
$491$	8.14454	0.367558	0.183779	−	0.982968i	$-0.441167\pi$
$491$	8.14454	0.367558	0.183779	+	0.982968i	$0.441167\pi$
$492$	4.36642	0.196854
$493$	−8.76843	−0.394910
$494$	42.1035	1.89432
$495$	−1.15304	−0.0518254
$496$	1.11165	0.0499145
$497$	11.0995	0.497881
$498$	−9.97732	−0.447094
$499$	−0.179072	−0.00801636	−0.00400818	−	0.999992i	$-0.501276\pi$
$499$	−0.179072	−0.00801636	−0.00400818	+	0.999992i	$0.501276\pi$
$500$	11.8125	0.528272
$501$	−32.4337	−1.44903
$502$	22.9715	1.02527
$503$	2.26208	0.100861	0.0504305	−	0.998728i	$-0.483941\pi$
$503$	2.26208	0.100861	0.0504305	+	0.998728i	$0.483941\pi$
$504$	−2.58170	−0.114998
$505$	28.5596	1.27089
$506$	5.48372	0.243781
$507$	37.7523	1.67664
$508$	5.00798	0.222193
$509$	−18.0905	−0.801847	−0.400924	−	0.916112i	$-0.631311\pi$
$509$	−18.0905	−0.801847	−0.400924	+	0.916112i	$0.631311\pi$
$510$	−5.80264	−0.256945
$511$	−48.2657	−2.13515
$512$	1.00000	0.0441942
$513$	−38.4022	−1.69550
$514$	5.79523	0.255617
$515$	1.24469	0.0548475
$516$	6.27233	0.276124
$517$	−4.54670	−0.199964
$518$	1.76314	0.0774679
$519$	14.4840	0.635777
$520$	−12.6534	−0.554890
$521$	−9.46180	−0.414529	−0.207264	−	0.978285i	$-0.566456\pi$
$521$	−9.46180	−0.414529	−0.207264	+	0.978285i	$0.566456\pi$
$522$	2.72425	0.119237
$523$	23.4640	1.02601	0.513004	−	0.858386i	$-0.328533\pi$
$523$	23.4640	1.02601	0.513004	+	0.858386i	$0.328533\pi$
$524$	10.5088	0.459080
$525$	−5.01271	−0.218773
$526$	−15.8336	−0.690376
$527$	1.98716	0.0865620
$528$	−1.56353	−0.0680438
$529$	7.07118	0.307443
$530$	−14.9777	−0.650591
$531$	−4.36225	−0.189305
$532$	32.1129	1.39227
$533$	17.0206	0.737243
$534$	−2.20942	−0.0956110
$535$	35.3787	1.52956
$536$	−3.73165	−0.161183
$537$	−35.8430	−1.54674
$538$	−1.86193	−0.0802734
$539$	−14.6089	−0.629248
$540$	11.5411	0.496649
$541$	−9.21812	−0.396318	−0.198159	−	0.980170i	$-0.563496\pi$
$541$	−9.21812	−0.396318	−0.198159	+	0.980170i	$0.563496\pi$
$542$	−20.4378	−0.877877
$543$	40.6810	1.74579
$544$	1.78758	0.0766418
$545$	0.617652	0.0264573
$546$	44.2971	1.89574
$547$	−1.58912	−0.0679460	−0.0339730	−	0.999423i	$-0.510816\pi$
$547$	−1.58912	−0.0679460	−0.0339730	+	0.999423i	$0.510816\pi$
$548$	16.9568	0.724357
$549$	6.15570	0.262719
$550$	0.689686	0.0294083
$551$	−33.8860	−1.44359
$552$	−8.57395	−0.364932
$553$	66.2107	2.81556
$554$	11.0419	0.469123
$555$	−1.23121	−0.0522618
$556$	5.83698	0.247543
$557$	−22.9814	−0.973753	−0.486876	−	0.873471i	$-0.661864\pi$
$557$	−22.9814	−0.973753	−0.486876	+	0.873471i	$0.661864\pi$
$558$	−0.617388	−0.0261361
$559$	24.4499	1.03412
$560$	−9.65096	−0.407827
$561$	−2.79493	−0.118002
$562$	−2.68057	−0.113073
$563$	−37.3913	−1.57585	−0.787927	−	0.615769i	$-0.788846\pi$
$563$	−37.3913	−1.57585	−0.787927	+	0.615769i	$0.788846\pi$
$564$	7.10889	0.299338
$565$	−29.0954	−1.22405
$566$	−8.91685	−0.374803
$567$	−32.6579	−1.37150
$568$	2.38774	0.100187
$569$	27.6306	1.15833	0.579167	−	0.815209i	$-0.303378\pi$
$569$	27.6306	1.15833	0.579167	+	0.815209i	$0.303378\pi$
$570$	−22.4246	−0.939262
$571$	36.2240	1.51593	0.757963	−	0.652297i	$-0.226195\pi$
$571$	36.2240	1.51593	0.757963	+	0.652297i	$0.226195\pi$
$572$	−6.09472	−0.254833
$573$	−21.4502	−0.896097
$574$	12.9818	0.541851
$575$	3.78204	0.157722
$576$	−0.555380	−0.0231408
$577$	28.5994	1.19061	0.595304	−	0.803501i	$-0.297032\pi$
$577$	28.5994	1.19061	0.595304	+	0.803501i	$0.297032\pi$
$578$	−13.8046	−0.574194
$579$	−2.71455	−0.112813
$580$	10.1838	0.422861
$581$	−29.6636	−1.23065
$582$	−15.4142	−0.638939
$583$	−7.21426	−0.298784
$584$	−10.3830	−0.429651
$585$	7.02746	0.290550
$586$	−31.2844	−1.29235
$587$	2.66224	0.109883	0.0549413	−	0.998490i	$-0.482503\pi$
$587$	2.66224	0.109883	0.0549413	+	0.998490i	$0.482503\pi$
$588$	22.8414	0.941962
$589$	7.67948	0.316427
$590$	−16.3070	−0.671349
$591$	−1.56353	−0.0643149
$592$	0.379289	0.0155887
$593$	−4.07572	−0.167370	−0.0836848	−	0.996492i	$-0.526669\pi$
$593$	−4.07572	−0.167370	−0.0836848	+	0.996492i	$0.526669\pi$
$594$	5.55894	0.228086
$595$	−17.2518	−0.707257
$596$	17.7402	0.726665
$597$	−14.5143	−0.594032
$598$	−33.4217	−1.36672
$599$	−11.9631	−0.488800	−0.244400	−	0.969675i	$-0.578591\pi$
$599$	−11.9631	−0.488800	−0.244400	+	0.969675i	$0.578591\pi$
$600$	−1.07834	−0.0440232
$601$	−36.9186	−1.50594	−0.752970	−	0.658055i	$-0.771379\pi$
$601$	−36.9186	−1.50594	−0.752970	+	0.658055i	$0.771379\pi$
$602$	18.6483	0.760047
$603$	2.07248	0.0843981
$604$	14.6159	0.594714
$605$	−2.07613	−0.0844067
$606$	−21.5082	−0.873709
$607$	−29.0879	−1.18064	−0.590322	−	0.807168i	$-0.700999\pi$
$607$	−29.0879	−1.18064	−0.590322	+	0.807168i	$0.700999\pi$
$608$	6.90819	0.280164
$609$	−35.6515	−1.44467
$610$	23.0113	0.931702
$611$	27.7108	1.12106
$612$	−0.992786	−0.0401310
$613$	−0.534474	−0.0215872	−0.0107936	−	0.999942i	$-0.503436\pi$
$613$	−0.534474	−0.0215872	−0.0107936	+	0.999942i	$0.503436\pi$
$614$	−6.22595	−0.251259
$615$	−9.06526	−0.365547
$616$	−4.64853	−0.187295
$617$	−11.1447	−0.448670	−0.224335	−	0.974512i	$-0.572021\pi$
$617$	−11.1447	−0.448670	−0.224335	+	0.974512i	$0.572021\pi$
$618$	−0.937372	−0.0377066
$619$	−22.4316	−0.901604	−0.450802	−	0.892624i	$-0.648862\pi$
$619$	−22.4316	−0.901604	−0.450802	+	0.892624i	$0.648862\pi$
$620$	−2.30793	−0.0926886
$621$	30.4836	1.22327
$622$	−20.4167	−0.818634
$623$	−6.56884	−0.263175
$624$	9.52927	0.381476
$625$	−21.0759	−0.843036
$626$	−4.92535	−0.196857
$627$	−10.8011	−0.431356
$628$	−17.1218	−0.683235
$629$	0.678010	0.0270340
$630$	5.35995	0.213546
$631$	26.0624	1.03753	0.518764	−	0.854918i	$-0.326392\pi$
$631$	26.0624	1.03753	0.518764	+	0.854918i	$0.326392\pi$
$632$	14.2434	0.566570
$633$	41.6220	1.65433
$634$	3.10764	0.123420
$635$	−10.3972	−0.412601
$636$	11.2797	0.447269
$637$	89.0369	3.52777
$638$	4.90520	0.194199
$639$	−1.32611	−0.0524599
$640$	−2.07613	−0.0820662
$641$	17.7822	0.702353	0.351177	−	0.936309i	$-0.385782\pi$
$641$	17.7822	0.702353	0.351177	+	0.936309i	$0.385782\pi$
$642$	−26.6436	−1.05154
$643$	−37.9747	−1.49758	−0.748788	−	0.662810i	$-0.769364\pi$
$643$	−37.9747	−1.49758	−0.748788	+	0.662810i	$0.769364\pi$
$644$	−25.4912	−1.00450
$645$	−13.0222	−0.512747
$646$	12.3489	0.485862
$647$	32.9990	1.29732	0.648662	−	0.761077i	$-0.275329\pi$
$647$	32.9990	1.29732	0.648662	+	0.761077i	$0.275329\pi$
$648$	−7.02541	−0.275984
$649$	−7.85452	−0.308317
$650$	−4.20344	−0.164872
$651$	8.07959	0.316664
$652$	−8.94600	−0.350353
$653$	−1.34256	−0.0525385	−0.0262692	−	0.999655i	$-0.508363\pi$
$653$	−1.34256	−0.0525385	−0.0262692	+	0.999655i	$0.508363\pi$
$654$	−0.465152	−0.0181889
$655$	−21.8177	−0.852487
$656$	2.79267	0.109036
$657$	5.76651	0.224973
$658$	21.1355	0.823946
$659$	−40.8055	−1.58956	−0.794778	−	0.606900i	$-0.792413\pi$
$659$	−40.8055	−1.58956	−0.794778	+	0.606900i	$0.792413\pi$
$660$	3.24609	0.126354
$661$	5.79929	0.225566	0.112783	−	0.993620i	$-0.464023\pi$
$661$	5.79929	0.225566	0.112783	+	0.993620i	$0.464023\pi$
$662$	−0.366644	−0.0142500
$663$	17.0343	0.661558
$664$	−6.38129	−0.247642
$665$	−66.6706	−2.58538
$666$	−0.210650	−0.00816251
$667$	26.8987	1.04152
$668$	−20.7439	−0.802607
$669$	−29.5551	−1.14267
$670$	7.74739	0.299308
$671$	11.0838	0.427884
$672$	7.26811	0.280373
$673$	−9.86285	−0.380185	−0.190092	−	0.981766i	$-0.560879\pi$
$673$	−9.86285	−0.380185	−0.190092	+	0.981766i	$0.560879\pi$
$674$	−32.5731	−1.25467
$675$	3.83392	0.147568
$676$	24.1456	0.928677
$677$	3.89062	0.149529	0.0747643	−	0.997201i	$-0.476180\pi$
$677$	3.89062	0.149529	0.0747643	+	0.997201i	$0.476180\pi$
$678$	21.9116	0.841512
$679$	−45.8280	−1.75872
$680$	−3.71125	−0.142320
$681$	−1.31868	−0.0505320
$682$	−1.11165	−0.0425672
$683$	−35.7498	−1.36793	−0.683965	−	0.729515i	$-0.739746\pi$
$683$	−35.7498	−1.36793	−0.683965	+	0.729515i	$0.739746\pi$
$684$	−3.83667	−0.146699
$685$	−35.2044	−1.34509
$686$	35.3700	1.35043
$687$	22.0972	0.843060
$688$	4.01165	0.152943
$689$	43.9689	1.67508
$690$	17.8006	0.677658
$691$	−20.1226	−0.765501	−0.382751	−	0.923852i	$-0.625023\pi$
$691$	−20.1226	−0.765501	−0.382751	+	0.923852i	$0.625023\pi$
$692$	9.26366	0.352152
$693$	2.58170	0.0980708
$694$	−18.6166	−0.706675
$695$	−12.1183	−0.459674
$696$	−7.66942	−0.290709
$697$	4.99213	0.189090
$698$	−22.8704	−0.865656
$699$	1.81104	0.0684999
$700$	−3.20603	−0.121176
$701$	−24.6059	−0.929352	−0.464676	−	0.885481i	$-0.653829\pi$
$701$	−24.6059	−0.929352	−0.464676	+	0.885481i	$0.653829\pi$
$702$	−33.8802	−1.27872
$703$	2.62020	0.0988228
$704$	−1.00000	−0.0376889
$705$	−14.7590	−0.555855
$706$	1.36064	0.0512082
$707$	−63.9460	−2.40494
$708$	12.2808	0.461539
$709$	21.0416	0.790234	0.395117	−	0.918631i	$-0.370704\pi$
$709$	21.0416	0.790234	0.395117	+	0.918631i	$0.370704\pi$
$710$	−4.95727	−0.186043
$711$	−7.91047	−0.296666
$712$	−1.41310	−0.0529582
$713$	−6.09597	−0.228296
$714$	12.9923	0.486225
$715$	12.6534	0.473211
$716$	−22.9244	−0.856726
$717$	−23.4970	−0.877511
$718$	23.1148	0.862638
$719$	−17.6431	−0.657975	−0.328988	−	0.944334i	$-0.606707\pi$
$719$	−17.6431	−0.657975	−0.328988	+	0.944334i	$0.606707\pi$
$720$	1.15304	0.0429713
$721$	−2.78690	−0.103790
$722$	28.7230	1.06896
$723$	−0.00268925	−0.000100014 0
$724$	26.0187	0.966979
$725$	3.38305	0.125643
$726$	1.56353	0.0580280
$727$	20.4077	0.756882	0.378441	−	0.925626i	$-0.376460\pi$
$727$	20.4077	0.756882	0.378441	+	0.925626i	$0.376460\pi$
$728$	28.3315	1.05004
$729$	29.9764	1.11024
$730$	21.5564	0.797839
$731$	7.17114	0.265234
$732$	−17.3298	−0.640527
$733$	−13.7570	−0.508128	−0.254064	−	0.967187i	$-0.581767\pi$
$733$	−13.7570	−0.508128	−0.254064	+	0.967187i	$0.581767\pi$
$734$	−21.5987	−0.797222
$735$	−47.4216	−1.74917
$736$	−5.48372	−0.202133
$737$	3.73165	0.137457
$738$	−1.55100	−0.0570930
$739$	−23.1169	−0.850370	−0.425185	−	0.905107i	$-0.639791\pi$
$739$	−23.1169	−0.850370	−0.425185	+	0.905107i	$0.639791\pi$
$740$	−0.787454	−0.0289474
$741$	65.8299	2.41832
$742$	33.5357	1.23113
$743$	5.12361	0.187967	0.0939834	−	0.995574i	$-0.470040\pi$
$743$	5.12361	0.187967	0.0939834	+	0.995574i	$0.470040\pi$
$744$	1.73809	0.0637216
$745$	−36.8309	−1.34938
$746$	−8.95058	−0.327704
$747$	3.54404	0.129670
$748$	−1.78758	−0.0653604
$749$	−79.2143	−2.89443
$750$	18.4692	0.674400
$751$	31.1713	1.13746	0.568728	−	0.822526i	$-0.307436\pi$
$751$	31.1713	1.13746	0.568728	+	0.822526i	$0.307436\pi$
$752$	4.54670	0.165801
$753$	35.9166	1.30887
$754$	−29.8958	−1.08874
$755$	−30.3446	−1.10435
$756$	−25.8409	−0.939824
$757$	22.8730	0.831332	0.415666	−	0.909517i	$-0.363549\pi$
$757$	22.8730	0.831332	0.415666	+	0.909517i	$0.363549\pi$
$758$	−17.5642	−0.637962
$759$	8.57395	0.311215
$760$	−14.3423	−0.520250
$761$	−45.7912	−1.65993	−0.829965	−	0.557816i	$-0.811640\pi$
$761$	−45.7912	−1.65993	−0.829965	+	0.557816i	$0.811640\pi$
$762$	7.83012	0.283655
$763$	−1.38295	−0.0500660
$764$	−13.7191	−0.496341
$765$	2.06115	0.0745211
$766$	−4.18459	−0.151196
$767$	47.8711	1.72853
$768$	1.56353	0.0564190
$769$	−28.0619	−1.01194	−0.505968	−	0.862552i	$-0.668865\pi$
$769$	−28.0619	−1.01194	−0.505968	+	0.862552i	$0.668865\pi$
$770$	9.65096	0.347796
$771$	9.06101	0.326324
$772$	−1.73617	−0.0624862
$773$	25.6659	0.923139	0.461570	−	0.887104i	$-0.347286\pi$
$773$	25.6659	0.923139	0.461570	+	0.887104i	$0.347286\pi$
$774$	−2.22799	−0.0800835
$775$	−0.766688	−0.0275402
$776$	−9.85860	−0.353903
$777$	2.75672	0.0988967
$778$	−13.4447	−0.482017
$779$	19.2923	0.691219
$780$	−19.7840	−0.708380
$781$	−2.38774	−0.0854402
$782$	−9.80258	−0.350540
$783$	27.2677	0.974468
$784$	14.6089	0.521745
$785$	35.5471	1.26873
$786$	16.4308	0.586068
$787$	25.0074	0.891417	0.445709	−	0.895178i	$-0.352952\pi$
$787$	25.0074	0.891417	0.445709	+	0.895178i	$0.352952\pi$
$788$	−1.00000	−0.0356235
$789$	−24.7562	−0.881345
$790$	−29.5710	−1.05209
$791$	65.1456	2.31631
$792$	0.555380	0.0197346
$793$	−67.5524	−2.39886
$794$	31.7230	1.12581
$795$	−23.4181	−0.830555
$796$	−9.28306	−0.329029
$797$	34.1278	1.20887	0.604435	−	0.796654i	$-0.293399\pi$
$797$	34.1278	1.20887	0.604435	+	0.796654i	$0.293399\pi$
$798$	50.2095	1.77740
$799$	8.12758	0.287533
$800$	−0.689686	−0.0243841
$801$	0.784808	0.0277298
$802$	15.6697	0.553317
$803$	10.3830	0.366408
$804$	−5.83454	−0.205768
$805$	52.9231	1.86530
$806$	6.77519	0.238646
$807$	−2.91118	−0.102478
$808$	−13.7562	−0.483940
$809$	31.1305	1.09449	0.547245	−	0.836972i	$-0.315677\pi$
$809$	31.1305	1.09449	0.547245	+	0.836972i	$0.315677\pi$
$810$	14.5857	0.512488
$811$	27.3547	0.960555	0.480278	−	0.877117i	$-0.340536\pi$
$811$	27.3547	0.960555	0.480278	+	0.877117i	$0.340536\pi$
$812$	−22.8020	−0.800193
$813$	−31.9550	−1.12071
$814$	−0.379289	−0.0132941
$815$	18.5731	0.650586
$816$	2.79493	0.0978421
$817$	27.7132	0.969563
$818$	21.2975	0.744651
$819$	−15.7348	−0.549817
$820$	−5.79795	−0.202473
$821$	39.5173	1.37916	0.689581	−	0.724209i	$-0.257795\pi$
$821$	39.5173	1.37916	0.689581	+	0.724209i	$0.257795\pi$
$822$	26.5124	0.924725
$823$	−36.5741	−1.27489	−0.637447	−	0.770495i	$-0.720009\pi$
$823$	−36.5741	−1.27489	−0.637447	+	0.770495i	$0.720009\pi$
$824$	−0.599524	−0.0208854
$825$	1.07834	0.0375431
$826$	36.5120	1.27042
$827$	0.880793	0.0306282	0.0153141	−	0.999883i	$-0.495125\pi$
$827$	0.880793	0.0306282	0.0153141	+	0.999883i	$0.495125\pi$
$828$	3.04555	0.105840
$829$	−18.7204	−0.650188	−0.325094	−	0.945682i	$-0.605396\pi$
$829$	−18.7204	−0.650188	−0.325094	+	0.945682i	$0.605396\pi$
$830$	13.2484	0.459858
$831$	17.2642	0.598890
$832$	6.09472	0.211296
$833$	26.1145	0.904813
$834$	9.12628	0.316017
$835$	43.0671	1.49040
$836$	−6.90819	−0.238925
$837$	−6.17958	−0.213598
$838$	−0.569174	−0.0196618
$839$	34.3890	1.18724	0.593621	−	0.804745i	$-0.297698\pi$
$839$	34.3890	1.18724	0.593621	+	0.804745i	$0.297698\pi$
$840$	−15.0895	−0.520639
$841$	−4.93901	−0.170311
$842$	−32.4773	−1.11924
$843$	−4.19114	−0.144351
$844$	26.6206	0.916318
$845$	−50.1294	−1.72450
$846$	−2.52515	−0.0868163
$847$	4.64853	0.159725
$848$	7.21426	0.247739
$849$	−13.9417	−0.478480
$850$	−1.23287	−0.0422870
$851$	−2.07992	−0.0712986
$852$	3.73330	0.127901
$853$	−6.09714	−0.208762	−0.104381	−	0.994537i	$-0.533286\pi$
$853$	−6.09714	−0.208762	−0.104381	+	0.994537i	$0.533286\pi$
$854$	−51.5232	−1.76309
$855$	7.96542	0.272412
$856$	−17.0407	−0.582440
$857$	−1.26482	−0.0432054	−0.0216027	−	0.999767i	$-0.506877\pi$
$857$	−1.26482	−0.0432054	−0.0216027	+	0.999767i	$0.506877\pi$
$858$	−9.52927	−0.325324
$859$	11.1236	0.379532	0.189766	−	0.981829i	$-0.439227\pi$
$859$	11.1236	0.379532	0.189766	+	0.981829i	$0.439227\pi$
$860$	−8.32870	−0.284006
$861$	20.2975	0.691736
$862$	−2.24052	−0.0763123
$863$	48.8906	1.66426	0.832128	−	0.554584i	$-0.187122\pi$
$863$	48.8906	1.66426	0.832128	+	0.554584i	$0.187122\pi$
$864$	−5.55894	−0.189119
$865$	−19.2326	−0.653927
$866$	−8.26995	−0.281024
$867$	−21.5838	−0.733025
$868$	5.16753	0.175398
$869$	−14.2434	−0.483173
$870$	15.9227	0.539830
$871$	−22.7434	−0.770630
$872$	−0.297502	−0.0100747
$873$	5.47527	0.185310
$874$	−37.8826	−1.28140
$875$	54.9109	1.85633
$876$	−16.2341	−0.548499
$877$	−9.52902	−0.321772	−0.160886	−	0.986973i	$-0.551435\pi$
$877$	−9.52902	−0.321772	−0.160886	+	0.986973i	$0.551435\pi$
$878$	40.2920	1.35979
$879$	−48.9140	−1.64983
$880$	2.07613	0.0699863
$881$	−30.1396	−1.01543	−0.507715	−	0.861525i	$-0.669510\pi$
$881$	−30.1396	−1.01543	−0.507715	+	0.861525i	$0.669510\pi$
$882$	−8.11347	−0.273195
$883$	30.7657	1.03535	0.517675	−	0.855578i	$-0.326798\pi$
$883$	30.7657	1.03535	0.517675	+	0.855578i	$0.326798\pi$
$884$	10.8948	0.366432
$885$	−25.4965	−0.857054
$886$	−0.0881844	−0.00296261
$887$	6.15519	0.206671	0.103336	−	0.994647i	$-0.467048\pi$
$887$	6.15519	0.206671	0.103336	+	0.994647i	$0.467048\pi$
$888$	0.593030	0.0199008
$889$	23.2798	0.780779
$890$	2.93378	0.0983405
$891$	7.02541	0.235360
$892$	−18.9028	−0.632913
$893$	31.4094	1.05108
$894$	27.7372	0.927672
$895$	47.5941	1.59089
$896$	4.64853	0.155297
$897$	−52.2558	−1.74477
$898$	−29.6553	−0.989611
$899$	−5.45286	−0.181863
$900$	0.383038	0.0127679
$901$	12.8961	0.429630
$902$	−2.79267	−0.0929859
$903$	29.1571	0.970288
$904$	14.0142	0.466106
$905$	−54.0183	−1.79563
$906$	22.8524	0.759220
$907$	−46.3310	−1.53840	−0.769199	−	0.639010i	$-0.779344\pi$
$907$	−46.3310	−1.53840	−0.769199	+	0.639010i	$0.779344\pi$
$908$	−0.843402	−0.0279893
$909$	7.63991	0.253400
$910$	−58.8199	−1.94986
$911$	13.5978	0.450517	0.225258	−	0.974299i	$-0.427677\pi$
$911$	13.5978	0.450517	0.225258	+	0.974299i	$0.427677\pi$
$912$	10.8011	0.357662
$913$	6.38129	0.211190
$914$	37.8637	1.25242
$915$	35.9789	1.18942
$916$	14.1329	0.466964
$917$	48.8506	1.61319
$918$	−9.93704	−0.327971
$919$	−1.79347	−0.0591611	−0.0295806	−	0.999562i	$-0.509417\pi$
$919$	−1.79347	−0.0591611	−0.0295806	+	0.999562i	$0.509417\pi$
$920$	11.3849	0.375349
$921$	−9.73445	−0.320761
$922$	−2.52437	−0.0831356
$923$	14.5526	0.479006
$924$	−7.26811	−0.239103
$925$	−0.261590	−0.00860104
$926$	−20.8350	−0.684679
$927$	0.332964	0.0109360
$928$	−4.90520	−0.161021
$929$	−28.2202	−0.925876	−0.462938	−	0.886391i	$-0.653205\pi$
$929$	−28.2202	−0.925876	−0.462938	+	0.886391i	$0.653205\pi$
$930$	−3.60851	−0.118328
$931$	100.921	3.30754
$932$	1.15831	0.0379416
$933$	−31.9220	−1.04508
$934$	−13.2139	−0.432371
$935$	3.71125	0.121371
$936$	−3.38489	−0.110638
$937$	24.9976	0.816637	0.408318	−	0.912840i	$-0.366115\pi$
$937$	24.9976	0.816637	0.408318	+	0.912840i	$0.366115\pi$
$938$	−17.3467	−0.566390
$939$	−7.70093	−0.251310
$940$	−9.43953	−0.307884
$941$	−33.2005	−1.08231	−0.541153	−	0.840924i	$-0.682012\pi$
$941$	−33.2005	−1.08231	−0.541153	+	0.840924i	$0.682012\pi$
$942$	−26.7704	−0.872228
$943$	−15.3142	−0.498700
$944$	7.85452	0.255643
$945$	53.6491	1.74520
$946$	−4.01165	−0.130430
$947$	−2.95296	−0.0959584	−0.0479792	−	0.998848i	$-0.515278\pi$
$947$	−2.95296	−0.0959584	−0.0479792	+	0.998848i	$0.515278\pi$
$948$	22.2699	0.723292
$949$	−63.2814	−2.05420
$950$	−4.76448	−0.154580
$951$	4.85888	0.157560
$952$	8.30962	0.269316
$953$	−4.32231	−0.140013	−0.0700067	−	0.997547i	$-0.522302\pi$
$953$	−4.32231	−0.140013	−0.0700067	+	0.997547i	$0.522302\pi$
$954$	−4.00666	−0.129720
$955$	28.4827	0.921678
$956$	−15.0282	−0.486046
$957$	7.66942	0.247917
$958$	−4.87270	−0.157430
$959$	78.8240	2.54536
$960$	−3.24609	−0.104767
$961$	−29.7642	−0.960137
$962$	2.31166	0.0745310
$963$	9.46408	0.304976
$964$	−0.00171999	−5.53970e−5 0
$965$	3.60452	0.116034
$966$	−39.8563	−1.28235
$967$	−41.8739	−1.34657	−0.673287	−	0.739381i	$-0.735118\pi$
$967$	−41.8739	−1.34657	−0.673287	+	0.739381i	$0.735118\pi$
$968$	1.00000	0.0321412
$969$	19.3079	0.620259
$970$	20.4677	0.657179
$971$	−32.9897	−1.05869	−0.529345	−	0.848406i	$-0.677562\pi$
$971$	−32.9897	−1.05869	−0.529345	+	0.848406i	$0.677562\pi$
$972$	5.69238	0.182583
$973$	27.1334	0.869856
$974$	−41.0312	−1.31473
$975$	−6.57220	−0.210479
$976$	−11.0838	−0.354783
$977$	38.3852	1.22805	0.614026	−	0.789286i	$-0.289549\pi$
$977$	38.3852	1.22805	0.614026	+	0.789286i	$0.289549\pi$
$978$	−13.9873	−0.447265
$979$	1.41310	0.0451629
$980$	−30.3299	−0.968852
$981$	0.165226	0.00527527
$982$	8.14454	0.259903
$983$	−17.7353	−0.565667	−0.282834	−	0.959169i	$-0.591274\pi$
$983$	−17.7353	−0.565667	−0.282834	+	0.959169i	$0.591274\pi$
$984$	4.36642	0.139197
$985$	2.07613	0.0661510
$986$	−8.76843	−0.279244
$987$	33.0459	1.05186
$988$	42.1035	1.33949
$989$	−21.9988	−0.699520
$990$	−1.15304	−0.0366461
$991$	36.6948	1.16565	0.582824	−	0.812598i	$-0.301948\pi$
$991$	36.6948	1.16565	0.582824	+	0.812598i	$0.301948\pi$
$992$	1.11165	0.0352949
$993$	−0.573257	−0.0181918
$994$	11.0995	0.352055
$995$	19.2728	0.610990
$996$	−9.97732	−0.316143
$997$	8.37319	0.265182	0.132591	−	0.991171i	$-0.457670\pi$
$997$	8.37319	0.265182	0.132591	+	0.991171i	$0.457670\pi$
$998$	−0.179072	−0.00566842
$999$	−2.10845	−0.0667083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.f.1.16	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.f.1.16	✓	24	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.56353 q^{3} +1.00000 q^{4} -2.07613 q^{5} +1.56353 q^{6} +4.64853 q^{7} +1.00000 q^{8} -0.555380 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.56353 q^{3} +1.00000 q^{4} -2.07613 q^{5} +1.56353 q^{6} +4.64853 q^{7} +1.00000 q^{8} -0.555380 q^{9} -2.07613 q^{10} -1.00000 q^{11} +1.56353 q^{12} +6.09472 q^{13} +4.64853 q^{14} -3.24609 q^{15} +1.00000 q^{16} +1.78758 q^{17} -0.555380 q^{18} +6.90819 q^{19} -2.07613 q^{20} +7.26811 q^{21} -1.00000 q^{22} -5.48372 q^{23} +1.56353 q^{24} -0.689686 q^{25} +6.09472 q^{26} -5.55894 q^{27} +4.64853 q^{28} -4.90520 q^{29} -3.24609 q^{30} +1.11165 q^{31} +1.00000 q^{32} -1.56353 q^{33} +1.78758 q^{34} -9.65096 q^{35} -0.555380 q^{36} +0.379289 q^{37} +6.90819 q^{38} +9.52927 q^{39} -2.07613 q^{40} +2.79267 q^{41} +7.26811 q^{42} +4.01165 q^{43} -1.00000 q^{44} +1.15304 q^{45} -5.48372 q^{46} +4.54670 q^{47} +1.56353 q^{48} +14.6089 q^{49} -0.689686 q^{50} +2.79493 q^{51} +6.09472 q^{52} +7.21426 q^{53} -5.55894 q^{54} +2.07613 q^{55} +4.64853 q^{56} +10.8011 q^{57} -4.90520 q^{58} +7.85452 q^{59} -3.24609 q^{60} -11.0838 q^{61} +1.11165 q^{62} -2.58170 q^{63} +1.00000 q^{64} -12.6534 q^{65} -1.56353 q^{66} -3.73165 q^{67} +1.78758 q^{68} -8.57395 q^{69} -9.65096 q^{70} +2.38774 q^{71} -0.555380 q^{72} -10.3830 q^{73} +0.379289 q^{74} -1.07834 q^{75} +6.90819 q^{76} -4.64853 q^{77} +9.52927 q^{78} +14.2434 q^{79} -2.07613 q^{80} -7.02541 q^{81} +2.79267 q^{82} -6.38129 q^{83} +7.26811 q^{84} -3.71125 q^{85} +4.01165 q^{86} -7.66942 q^{87} -1.00000 q^{88} -1.41310 q^{89} +1.15304 q^{90} +28.3315 q^{91} -5.48372 q^{92} +1.73809 q^{93} +4.54670 q^{94} -14.3423 q^{95} +1.56353 q^{96} -9.85860 q^{97} +14.6089 q^{98} +0.555380 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9 - 24 * q^11 + 8 * q^12 + 9 * q^13 + 11 * q^14 + 6 * q^15 + 24 * q^16 - q^17 + 28 * q^18 + 35 * q^19 + 21 * q^21 - 24 * q^22 + 13 * q^23 + 8 * q^24 + 38 * q^25 + 9 * q^26 + 23 * q^27 + 11 * q^28 + 15 * q^29 + 6 * q^30 + 31 * q^31 + 24 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 28 * q^36 + 13 * q^37 + 35 * q^38 + 31 * q^39 + 16 * q^41 + 21 * q^42 + 35 * q^43 - 24 * q^44 + 13 * q^45 + 13 * q^46 + 46 * q^47 + 8 * q^48 + 55 * q^49 + 38 * q^50 + 18 * q^51 + 9 * q^52 + 6 * q^53 + 23 * q^54 + 11 * q^56 + 18 * q^57 + 15 * q^58 + 13 * q^59 + 6 * q^60 + 60 * q^61 + 31 * q^62 + 52 * q^63 + 24 * q^64 - 9 * q^65 - 8 * q^66 + 28 * q^67 - q^68 + 21 * q^69 + 28 * q^70 + 10 * q^71 + 28 * q^72 + 3 * q^73 + 13 * q^74 + 48 * q^75 + 35 * q^76 - 11 * q^77 + 31 * q^78 + 47 * q^79 + 16 * q^81 + 16 * q^82 + 66 * q^83 + 21 * q^84 + 37 * q^85 + 35 * q^86 + 34 * q^87 - 24 * q^88 - 5 * q^89 + 13 * q^90 + q^91 + 13 * q^92 - 16 * q^93 + 46 * q^94 + 9 * q^95 + 8 * q^96 + 24 * q^97 + 55 * q^98 - 28 * q^99

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