LMFDB - Embedded newform 2535.2.a.ba.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2535,2,Mod(1,2535)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2535, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2535.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2535 = 3 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2535.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:	$20.2420769124$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.756.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 6x - 2 $ x^3 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.26180$ of defining polynomial
Character	$\chi$	$=$	2535.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.26180 q^{2} -1.00000 q^{3} +3.11575 q^{4} -1.00000 q^{5} -2.26180 q^{6} +1.26180 q^{7} +2.52360 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.26180 q^{2} -1.00000 q^{3} +3.11575 q^{4} -1.00000 q^{5} -2.26180 q^{6} +1.26180 q^{7} +2.52360 q^{8} +1.00000 q^{9} -2.26180 q^{10} -4.52360 q^{11} -3.11575 q^{12} +2.85395 q^{14} +1.00000 q^{15} -0.523604 q^{16} -4.49330 q^{17} +2.26180 q^{18} -5.11575 q^{19} -3.11575 q^{20} -1.26180 q^{21} -10.2315 q^{22} +2.23150 q^{23} -2.52360 q^{24} +1.00000 q^{25} -1.00000 q^{27} +3.93146 q^{28} -1.37755 q^{29} +2.26180 q^{30} -8.87085 q^{31} -6.23150 q^{32} +4.52360 q^{33} -10.1630 q^{34} -1.26180 q^{35} +3.11575 q^{36} +0.231499 q^{37} -11.5708 q^{38} -2.52360 q^{40} -1.14605 q^{41} -2.85395 q^{42} +6.37755 q^{43} -14.0944 q^{44} -1.00000 q^{45} +5.04721 q^{46} +10.7854 q^{47} +0.523604 q^{48} -5.40786 q^{49} +2.26180 q^{50} +4.49330 q^{51} +4.52360 q^{53} -2.26180 q^{54} +4.52360 q^{55} +3.18429 q^{56} +5.11575 q^{57} -3.11575 q^{58} +0.853947 q^{59} +3.11575 q^{60} +4.63935 q^{61} -20.0641 q^{62} +1.26180 q^{63} -13.0472 q^{64} +10.2315 q^{66} -13.1327 q^{67} -14.0000 q^{68} -2.23150 q^{69} -2.85395 q^{70} +9.60905 q^{71} +2.52360 q^{72} -13.7854 q^{73} +0.523604 q^{74} -1.00000 q^{75} -15.9394 q^{76} -5.70789 q^{77} -8.87085 q^{79} +0.523604 q^{80} +1.00000 q^{81} -2.59214 q^{82} +8.23150 q^{83} -3.93146 q^{84} +4.49330 q^{85} +14.4248 q^{86} +1.37755 q^{87} -11.4158 q^{88} -6.62245 q^{89} -2.26180 q^{90} +6.95279 q^{92} +8.87085 q^{93} +24.3945 q^{94} +5.11575 q^{95} +6.23150 q^{96} -10.6697 q^{97} -12.2315 q^{98} -4.52360 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^7 - 6 * q^8 + 3 * q^9	$ 3 q - 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{12} + 12 q^{14} + 3 q^{15} + 12 q^{16} - 12 q^{19} - 6 q^{20} + 3 q^{21} - 24 q^{22} + 6 q^{24} + 3 q^{25} - 3 q^{27} - 12 q^{28} + 6 q^{29} - 3 q^{31} - 12 q^{32} + 3 q^{35} + 6 q^{36} - 6 q^{37} + 6 q^{38} + 6 q^{40} - 12 q^{42} + 9 q^{43} + 12 q^{44} - 3 q^{45} - 12 q^{46} + 12 q^{47} - 12 q^{48} - 6 q^{49} + 30 q^{56} + 12 q^{57} - 6 q^{58} + 6 q^{59} + 6 q^{60} - 3 q^{61} - 6 q^{62} - 3 q^{63} - 12 q^{64} + 24 q^{66} - 9 q^{67} - 42 q^{68} - 12 q^{70} + 12 q^{71} - 6 q^{72} - 21 q^{73} - 12 q^{74} - 3 q^{75} - 48 q^{76} - 24 q^{77} - 3 q^{79} - 12 q^{80} + 3 q^{81} - 18 q^{82} + 18 q^{83} + 12 q^{84} + 6 q^{86} - 6 q^{87} - 48 q^{88} - 30 q^{89} + 48 q^{92} + 3 q^{93} + 36 q^{94} + 12 q^{95} + 12 q^{96} - 15 q^{97} - 30 q^{98}+O(q^{100}) $ 3 * q - 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^12 + 12 * q^14 + 3 * q^15 + 12 * q^16 - 12 * q^19 - 6 * q^20 + 3 * q^21 - 24 * q^22 + 6 * q^24 + 3 * q^25 - 3 * q^27 - 12 * q^28 + 6 * q^29 - 3 * q^31 - 12 * q^32 + 3 * q^35 + 6 * q^36 - 6 * q^37 + 6 * q^38 + 6 * q^40 - 12 * q^42 + 9 * q^43 + 12 * q^44 - 3 * q^45 - 12 * q^46 + 12 * q^47 - 12 * q^48 - 6 * q^49 + 30 * q^56 + 12 * q^57 - 6 * q^58 + 6 * q^59 + 6 * q^60 - 3 * q^61 - 6 * q^62 - 3 * q^63 - 12 * q^64 + 24 * q^66 - 9 * q^67 - 42 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^72 - 21 * q^73 - 12 * q^74 - 3 * q^75 - 48 * q^76 - 24 * q^77 - 3 * q^79 - 12 * q^80 + 3 * q^81 - 18 * q^82 + 18 * q^83 + 12 * q^84 + 6 * q^86 - 6 * q^87 - 48 * q^88 - 30 * q^89 + 48 * q^92 + 3 * q^93 + 36 * q^94 + 12 * q^95 + 12 * q^96 - 15 * q^97 - 30 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.26180	1.59934	0.799668	−	0.600443i	$-0.205009\pi$
$2$	2.26180	1.59934	0.799668	+	0.600443i	$0.205009\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.11575	1.55787
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.26180	−0.923377
$7$	1.26180	0.476916	0.238458	−	0.971153i	$-0.423358\pi$
$7$	1.26180	0.476916	0.238458	+	0.971153i	$0.423358\pi$
$8$	2.52360	0.892229
$9$	1.00000	0.333333
$10$	−2.26180	−0.715245
$11$	−4.52360	−1.36392	−0.681959	−	0.731390i	$-0.738872\pi$
$11$	−4.52360	−1.36392	−0.681959	+	0.731390i	$0.738872\pi$
$12$	−3.11575	−0.899439
$13$	0	0
$13$	0	0
$14$	2.85395	0.762749
$15$	1.00000	0.258199
$16$	−0.523604	−0.130901
$17$	−4.49330	−1.08979	−0.544893	−	0.838506i	$-0.683430\pi$
$17$	−4.49330	−1.08979	−0.544893	+	0.838506i	$0.683430\pi$
$18$	2.26180	0.533112
$19$	−5.11575	−1.17363	−0.586817	−	0.809720i	$-0.699619\pi$
$19$	−5.11575	−1.17363	−0.586817	+	0.809720i	$0.699619\pi$
$20$	−3.11575	−0.696703
$21$	−1.26180	−0.275348
$22$	−10.2315	−2.18136
$23$	2.23150	0.465300	0.232650	−	0.972561i	$-0.425260\pi$
$23$	2.23150	0.465300	0.232650	+	0.972561i	$0.425260\pi$
$24$	−2.52360	−0.515129
$25$	1.00000	0.200000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	3.93146	0.742976
$29$	−1.37755	−0.255805	−0.127902	−	0.991787i	$-0.540824\pi$
$29$	−1.37755	−0.255805	−0.127902	+	0.991787i	$0.540824\pi$
$30$	2.26180	0.412947
$31$	−8.87085	−1.59325	−0.796626	−	0.604472i	$-0.793384\pi$
$31$	−8.87085	−1.59325	−0.796626	+	0.604472i	$0.793384\pi$
$32$	−6.23150	−1.10158
$33$	4.52360	0.787458
$34$	−10.1630	−1.74293
$35$	−1.26180	−0.213284
$36$	3.11575	0.519292
$37$	0.231499	0.0380582	0.0190291	−	0.999819i	$-0.493942\pi$
$37$	0.231499	0.0380582	0.0190291	+	0.999819i	$0.493942\pi$
$38$	−11.5708	−1.87703
$39$	0	0
$40$	−2.52360	−0.399017
$41$	−1.14605	−0.178983	−0.0894917	−	0.995988i	$-0.528524\pi$
$41$	−1.14605	−0.178983	−0.0894917	+	0.995988i	$0.528524\pi$
$42$	−2.85395	−0.440374
$43$	6.37755	0.972568	0.486284	−	0.873801i	$-0.338352\pi$
$43$	6.37755	0.972568	0.486284	+	0.873801i	$0.338352\pi$
$44$	−14.0944	−2.12481
$45$	−1.00000	−0.149071
$46$	5.04721	0.744170
$47$	10.7854	1.57321	0.786607	−	0.617454i	$-0.211836\pi$
$47$	10.7854	1.57321	0.786607	+	0.617454i	$0.211836\pi$
$48$	0.523604	0.0755758
$49$	−5.40786	−0.772551
$50$	2.26180	0.319867
$51$	4.49330	0.629188
$52$	0	0
$53$	4.52360	0.621365	0.310682	−	0.950514i	$-0.399442\pi$
$53$	4.52360	0.621365	0.310682	+	0.950514i	$0.399442\pi$
$54$	−2.26180	−0.307792
$55$	4.52360	0.609963
$56$	3.18429	0.425519
$57$	5.11575	0.677598
$58$	−3.11575	−0.409118
$59$	0.853947	0.111174	0.0555872	−	0.998454i	$-0.482297\pi$
$59$	0.853947	0.111174	0.0555872	+	0.998454i	$0.482297\pi$
$60$	3.11575	0.402242
$61$	4.63935	0.594008	0.297004	−	0.954876i	$-0.404012\pi$
$61$	4.63935	0.594008	0.297004	+	0.954876i	$0.404012\pi$
$62$	−20.0641	−2.54815
$63$	1.26180	0.158972
$64$	−13.0472	−1.63090
$65$	0	0
$66$	10.2315	1.25941
$67$	−13.1327	−1.60441	−0.802205	−	0.597049i	$-0.796340\pi$
$67$	−13.1327	−1.60441	−0.802205	+	0.597049i	$0.796340\pi$
$68$	−14.0000	−1.69775
$69$	−2.23150	−0.268641
$70$	−2.85395	−0.341112
$71$	9.60905	1.14038	0.570192	−	0.821511i	$-0.306869\pi$
$71$	9.60905	1.14038	0.570192	+	0.821511i	$0.306869\pi$
$72$	2.52360	0.297410
$73$	−13.7854	−1.61346	−0.806730	−	0.590920i	$-0.798765\pi$
$73$	−13.7854	−1.61346	−0.806730	+	0.590920i	$0.798765\pi$
$74$	0.523604	0.0608678
$75$	−1.00000	−0.115470
$76$	−15.9394	−1.82837
$77$	−5.70789	−0.650475
$78$	0	0
$79$	−8.87085	−0.998049	−0.499024	−	0.866588i	$-0.666308\pi$
$79$	−8.87085	−0.998049	−0.499024	+	0.866588i	$0.666308\pi$
$80$	0.523604	0.0585408
$81$	1.00000	0.111111
$82$	−2.59214	−0.286255
$83$	8.23150	0.903524	0.451762	−	0.892138i	$-0.350796\pi$
$83$	8.23150	0.903524	0.451762	+	0.892138i	$0.350796\pi$
$84$	−3.93146	−0.428957
$85$	4.49330	0.487367
$86$	14.4248	1.55546
$87$	1.37755	0.147689
$88$	−11.4158	−1.21693
$89$	−6.62245	−0.701978	−0.350989	−	0.936380i	$-0.614155\pi$
$89$	−6.62245	−0.701978	−0.350989	+	0.936380i	$0.614155\pi$
$90$	−2.26180	−0.238415
$91$	0	0
$92$	6.95279	0.724879
$93$	8.87085	0.919865
$94$	24.3945	2.51610
$95$	5.11575	0.524865
$96$	6.23150	0.636000
$97$	−10.6697	−1.08334	−0.541670	−	0.840591i	$-0.682208\pi$
$97$	−10.6697	−1.08334	−0.541670	+	0.840591i	$0.682208\pi$
$98$	−12.2315	−1.23557
$99$	−4.52360	−0.454639
$100$	3.11575	0.311575
$101$	−17.0472	−1.69626	−0.848130	−	0.529788i	$-0.822272\pi$
$101$	−17.0472	−1.69626	−0.848130	+	0.529788i	$0.822272\pi$
$102$	10.1630	1.00628
$103$	−13.9484	−1.37437	−0.687187	−	0.726481i	$-0.741155\pi$
$103$	−13.9484	−1.37437	−0.687187	+	0.726481i	$0.741155\pi$
$104$	0	0
$105$	1.26180	0.123139
$106$	10.2315	0.993771
$107$	12.4933	1.20777	0.603886	−	0.797070i	$-0.293618\pi$
$107$	12.4933	1.20777	0.603886	+	0.797070i	$0.293618\pi$
$108$	−3.11575	−0.299813
$109$	2.27871	0.218261	0.109130	−	0.994027i	$-0.465193\pi$
$109$	2.27871	0.218261	0.109130	+	0.994027i	$0.465193\pi$
$110$	10.2315	0.975535
$111$	−0.231499	−0.0219729
$112$	−0.660685	−0.0624289
$113$	−1.47640	−0.138888	−0.0694438	−	0.997586i	$-0.522122\pi$
$113$	−1.47640	−0.138888	−0.0694438	+	0.997586i	$0.522122\pi$
$114$	11.5708	1.08371
$115$	−2.23150	−0.208088
$116$	−4.29211	−0.398512
$117$	0	0
$118$	1.93146	0.177805
$119$	−5.66966	−0.519737
$120$	2.52360	0.230373
$121$	9.46300	0.860273
$122$	10.4933	0.950019
$123$	1.14605	0.103336
$124$	−27.6394	−2.48209
$125$	−1.00000	−0.0894427
$126$	2.85395	0.254250
$127$	−17.7854	−1.57820	−0.789100	−	0.614265i	$-0.789453\pi$
$127$	−17.7854	−1.57820	−0.789100	+	0.614265i	$0.789453\pi$
$128$	−17.0472	−1.50677
$129$	−6.37755	−0.561512
$130$	0	0
$131$	11.6697	1.01958	0.509791	−	0.860298i	$-0.329723\pi$
$131$	11.6697	1.01958	0.509791	+	0.860298i	$0.329723\pi$
$132$	14.0944	1.22676
$133$	−6.45506	−0.559725
$134$	−29.7035	−2.56599
$135$	1.00000	0.0860663
$136$	−11.3393	−0.972338
$137$	20.0641	1.71419	0.857096	−	0.515156i	$-0.172266\pi$
$137$	20.0641	1.71419	0.857096	+	0.515156i	$0.172266\pi$
$138$	−5.04721	−0.429647
$139$	16.3393	1.38588	0.692941	−	0.720994i	$-0.256314\pi$
$139$	16.3393	1.38588	0.692941	+	0.720994i	$0.256314\pi$
$140$	−3.93146	−0.332269
$141$	−10.7854	−0.908295
$142$	21.7338	1.82386
$143$	0	0
$144$	−0.523604	−0.0436337
$145$	1.37755	0.114399
$146$	−31.1799	−2.58046
$147$	5.40786	0.446032
$148$	0.721292	0.0592899
$149$	3.24490	0.265832	0.132916	−	0.991127i	$-0.457566\pi$
$149$	3.24490	0.265832	0.132916	+	0.991127i	$0.457566\pi$
$150$	−2.26180	−0.184675
$151$	−5.69996	−0.463856	−0.231928	−	0.972733i	$-0.574503\pi$
$151$	−5.69996	−0.463856	−0.231928	+	0.972733i	$0.574503\pi$
$152$	−12.9101	−1.04715
$153$	−4.49330	−0.363262
$154$	−12.9101	−1.04033
$155$	8.87085	0.712524
$156$	0	0
$157$	−3.85395	−0.307578	−0.153789	−	0.988104i	$-0.549148\pi$
$157$	−3.85395	−0.307578	−0.153789	+	0.988104i	$0.549148\pi$
$158$	−20.0641	−1.59622
$159$	−4.52360	−0.358745
$160$	6.23150	0.492643
$161$	2.81571	0.221909
$162$	2.26180	0.177704
$163$	9.72480	0.761705	0.380853	−	0.924636i	$-0.375631\pi$
$163$	9.72480	0.761705	0.380853	+	0.924636i	$0.375631\pi$
$164$	−3.57081	−0.278834
$165$	−4.52360	−0.352162
$166$	18.6180	1.44504
$167$	19.2787	1.49183	0.745916	−	0.666040i	$-0.232012\pi$
$167$	19.2787	1.49183	0.745916	+	0.666040i	$0.232012\pi$
$168$	−3.18429	−0.245673
$169$	0	0
$170$	10.1630	0.779463
$171$	−5.11575	−0.391211
$172$	19.8709	1.51514
$173$	−3.01691	−0.229371	−0.114686	−	0.993402i	$-0.536586\pi$
$173$	−3.01691	−0.229371	−0.114686	+	0.993402i	$0.536586\pi$
$174$	3.11575	0.236204
$175$	1.26180	0.0953833
$176$	2.36858	0.178538
$177$	−0.853947	−0.0641866
$178$	−14.9787	−1.12270
$179$	−5.31694	−0.397407	−0.198704	−	0.980060i	$-0.563673\pi$
$179$	−5.31694	−0.397407	−0.198704	+	0.980060i	$0.563673\pi$
$180$	−3.11575	−0.232234
$181$	25.8709	1.92297	0.961483	−	0.274866i	$-0.0886333\pi$
$181$	25.8709	1.92297	0.961483	+	0.274866i	$0.0886333\pi$
$182$	0	0
$183$	−4.63935	−0.342951
$184$	5.63142	0.415154
$185$	−0.231499	−0.0170201
$186$	20.0641	1.47117
$187$	20.3259	1.48638
$188$	33.6046	2.45087
$189$	−1.26180	−0.0917826
$190$	11.5708	0.839435
$191$	10.6563	0.771060	0.385530	−	0.922695i	$-0.374019\pi$
$191$	10.6563	0.771060	0.385530	+	0.922695i	$0.374019\pi$
$192$	13.0472	0.941601
$193$	−7.98309	−0.574636	−0.287318	−	0.957835i	$-0.592764\pi$
$193$	−7.98309	−0.574636	−0.287318	+	0.957835i	$0.592764\pi$
$194$	−24.1327	−1.73262
$195$	0	0
$196$	−16.8495	−1.20354
$197$	−17.3393	−1.23538	−0.617688	−	0.786424i	$-0.711930\pi$
$197$	−17.3393	−1.23538	−0.617688	+	0.786424i	$0.711930\pi$
$198$	−10.2315	−0.727121
$199$	−1.23150	−0.0872986	−0.0436493	−	0.999047i	$-0.513898\pi$
$199$	−1.23150	−0.0872986	−0.0436493	+	0.999047i	$0.513898\pi$
$200$	2.52360	0.178446
$201$	13.1327	0.926306
$202$	−38.5574	−2.71289
$203$	−1.73820	−0.121998
$204$	14.0000	0.980196
$205$	1.14605	0.0800438
$206$	−31.5484	−2.19808
$207$	2.23150	0.155100
$208$	0	0
$209$	23.1416	1.60074
$210$	2.85395	0.196941
$211$	10.3393	0.711788	0.355894	−	0.934526i	$-0.384176\pi$
$211$	10.3393	0.711788	0.355894	+	0.934526i	$0.384176\pi$
$212$	14.0944	0.968009
$213$	−9.60905	−0.658401
$214$	28.2574	1.93163
$215$	−6.37755	−0.434945
$216$	−2.52360	−0.171710
$217$	−11.1933	−0.759848
$218$	5.15399	0.349072
$219$	13.7854	0.931531
$220$	14.0944	0.950245
$221$	0	0
$222$	−0.523604	−0.0351420
$223$	−21.5708	−1.44449	−0.722244	−	0.691638i	$-0.756889\pi$
$223$	−21.5708	−1.44449	−0.722244	+	0.691638i	$0.756889\pi$
$224$	−7.86292	−0.525363
$225$	1.00000	0.0666667
$226$	−3.33931	−0.222128
$227$	−5.44609	−0.361470	−0.180735	−	0.983532i	$-0.557848\pi$
$227$	−5.44609	−0.361470	−0.180735	+	0.983532i	$0.557848\pi$
$228$	15.9394	1.05561
$229$	−21.9315	−1.44927	−0.724636	−	0.689132i	$-0.757992\pi$
$229$	−21.9315	−1.44927	−0.724636	+	0.689132i	$0.757992\pi$
$230$	−5.04721	−0.332803
$231$	5.70789	0.375552
$232$	−3.47640	−0.228237
$233$	25.3125	1.65828	0.829139	−	0.559042i	$-0.188831\pi$
$233$	25.3125	1.65828	0.829139	+	0.559042i	$0.188831\pi$
$234$	0	0
$235$	−10.7854	−0.703562
$236$	2.66069	0.173196
$237$	8.87085	0.576224
$238$	−12.8236	−0.831233
$239$	−22.5236	−1.45693	−0.728465	−	0.685083i	$-0.759766\pi$
$239$	−22.5236	−1.45693	−0.728465	+	0.685083i	$0.759766\pi$
$240$	−0.523604	−0.0337985
$241$	−11.1157	−0.716028	−0.358014	−	0.933716i	$-0.616546\pi$
$241$	−11.1157	−0.716028	−0.358014	+	0.933716i	$0.616546\pi$
$242$	21.4034	1.37586
$243$	−1.00000	−0.0641500
$244$	14.4551	0.925391
$245$	5.40786	0.345495
$246$	2.59214	0.165269
$247$	0	0
$248$	−22.3865	−1.42155
$249$	−8.23150	−0.521650
$250$	−2.26180	−0.143049
$251$	11.0472	0.697294	0.348647	−	0.937254i	$-0.386641\pi$
$251$	11.0472	0.697294	0.348647	+	0.937254i	$0.386641\pi$
$252$	3.93146	0.247659
$253$	−10.0944	−0.634631
$254$	−40.2271	−2.52407
$255$	−4.49330	−0.281381
$256$	−12.4630	−0.778937
$257$	−2.03030	−0.126647	−0.0633234	−	0.997993i	$-0.520170\pi$
$257$	−2.03030	−0.126647	−0.0633234	+	0.997993i	$0.520170\pi$
$258$	−14.4248	−0.898046
$259$	0.292106	0.0181506
$260$	0	0
$261$	−1.37755	−0.0852683
$262$	26.3945	1.63066
$263$	3.24840	0.200305	0.100153	−	0.994972i	$-0.468067\pi$
$263$	3.24840	0.200305	0.100153	+	0.994972i	$0.468067\pi$
$264$	11.4158	0.702593
$265$	−4.52360	−0.277883
$266$	−14.6001	−0.895188
$267$	6.62245	0.405287
$268$	−40.9181	−2.49947
$269$	26.9484	1.64307	0.821535	−	0.570157i	$-0.193118\pi$
$269$	26.9484	1.64307	0.821535	+	0.570157i	$0.193118\pi$
$270$	2.26180	0.137649
$271$	19.8495	1.20577	0.602886	−	0.797827i	$-0.294017\pi$
$271$	19.8495	1.20577	0.602886	+	0.797827i	$0.294017\pi$
$272$	2.35271	0.142654
$273$	0	0
$274$	45.3811	2.74157
$275$	−4.52360	−0.272784
$276$	−6.95279	−0.418509
$277$	16.0944	0.967020	0.483510	−	0.875339i	$-0.339362\pi$
$277$	16.0944	0.967020	0.483510	+	0.875339i	$0.339362\pi$
$278$	36.9563	2.21649
$279$	−8.87085	−0.531084
$280$	−3.18429	−0.190298
$281$	5.37755	0.320798	0.160399	−	0.987052i	$-0.448722\pi$
$281$	5.37755	0.320798	0.160399	+	0.987052i	$0.448722\pi$
$282$	−24.3945	−1.45267
$283$	26.8664	1.59704	0.798522	−	0.601966i	$-0.205616\pi$
$283$	26.8664	1.59704	0.798522	+	0.601966i	$0.205616\pi$
$284$	29.9394	1.77658
$285$	−5.11575	−0.303031
$286$	0	0
$287$	−1.44609	−0.0853601
$288$	−6.23150	−0.367195
$289$	3.18975	0.187633
$290$	3.11575	0.182963
$291$	10.6697	0.625466
$292$	−42.9519	−2.51357
$293$	−21.4193	−1.25133	−0.625664	−	0.780092i	$-0.715172\pi$
$293$	−21.4193	−1.25133	−0.625664	+	0.780092i	$0.715172\pi$
$294$	12.2315	0.713355
$295$	−0.853947	−0.0497187
$296$	0.584211	0.0339566
$297$	4.52360	0.262486
$298$	7.33931	0.425155
$299$	0	0
$300$	−3.11575	−0.179888
$301$	8.04721	0.463833
$302$	−12.8922	−0.741862
$303$	17.0472	0.979337
$304$	2.67863	0.153630
$305$	−4.63935	−0.265649
$306$	−10.1630	−0.580978
$307$	7.85395	0.448248	0.224124	−	0.974561i	$-0.428048\pi$
$307$	7.85395	0.448248	0.224124	+	0.974561i	$0.428048\pi$
$308$	−17.7844	−1.01336
$309$	13.9484	0.793495
$310$	20.0641	1.13957
$311$	−27.8744	−1.58061	−0.790305	−	0.612714i	$-0.790078\pi$
$311$	−27.8744	−1.58061	−0.790305	+	0.612714i	$0.790078\pi$
$312$	0	0
$313$	7.88776	0.445842	0.222921	−	0.974836i	$-0.428441\pi$
$313$	7.88776	0.445842	0.222921	+	0.974836i	$0.428441\pi$
$314$	−8.71687	−0.491921
$315$	−1.26180	−0.0710945
$316$	−27.6394	−1.55484
$317$	−13.2181	−0.742403	−0.371201	−	0.928552i	$-0.621054\pi$
$317$	−13.2181	−0.742403	−0.371201	+	0.928552i	$0.621054\pi$
$318$	−10.2315	−0.573754
$319$	6.23150	0.348897
$320$	13.0472	0.729361
$321$	−12.4933	−0.697308
$322$	6.36858	0.354907
$323$	22.9866	1.27901
$324$	3.11575	0.173097
$325$	0	0
$326$	21.9956	1.21822
$327$	−2.27871	−0.126013
$328$	−2.89218	−0.159694
$329$	13.6091	0.750291
$330$	−10.2315	−0.563225
$331$	23.8495	1.31089	0.655444	−	0.755244i	$-0.272481\pi$
$331$	23.8495	1.31089	0.655444	+	0.755244i	$0.272481\pi$
$332$	25.6473	1.40758
$333$	0.231499	0.0126861
$334$	43.6046	2.38594
$335$	13.1327	0.717514
$336$	0.660685	0.0360433
$337$	5.68306	0.309576	0.154788	−	0.987948i	$-0.450531\pi$
$337$	5.68306	0.309576	0.154788	+	0.987948i	$0.450531\pi$
$338$	0	0
$339$	1.47640	0.0801868
$340$	14.0000	0.759257
$341$	40.1282	2.17307
$342$	−11.5708	−0.625678
$343$	−15.6563	−0.845359
$344$	16.0944	0.867753
$345$	2.23150	0.120140
$346$	−6.82364	−0.366841
$347$	−21.4496	−1.15147	−0.575737	−	0.817635i	$-0.695285\pi$
$347$	−21.4496	−1.15147	−0.575737	+	0.817635i	$0.695285\pi$
$348$	4.29211	0.230081
$349$	−6.87085	−0.367788	−0.183894	−	0.982946i	$-0.558870\pi$
$349$	−6.87085	−0.367788	−0.183894	+	0.982946i	$0.558870\pi$
$350$	2.85395	0.152550
$351$	0	0
$352$	28.1888	1.50247
$353$	−34.4968	−1.83608	−0.918040	−	0.396488i	$-0.870229\pi$
$353$	−34.4968	−1.83608	−0.918040	+	0.396488i	$0.870229\pi$
$354$	−1.93146	−0.102656
$355$	−9.60905	−0.509995
$356$	−20.6339	−1.09359
$357$	5.66966	0.300070
$358$	−12.0259	−0.635587
$359$	8.15945	0.430639	0.215320	−	0.976544i	$-0.430921\pi$
$359$	8.15945	0.430639	0.215320	+	0.976544i	$0.430921\pi$
$360$	−2.52360	−0.133006
$361$	7.17089	0.377415
$362$	58.5148	3.07547
$363$	−9.46300	−0.496679
$364$	0	0
$365$	13.7854	0.721561
$366$	−10.4933	−0.548494
$367$	−6.84055	−0.357074	−0.178537	−	0.983933i	$-0.557136\pi$
$367$	−6.84055	−0.357074	−0.178537	+	0.983933i	$0.557136\pi$
$368$	−1.16842	−0.0609082
$369$	−1.14605	−0.0596611
$370$	−0.523604	−0.0272209
$371$	5.70789	0.296339
$372$	27.6394	1.43303
$373$	13.8192	0.715532	0.357766	−	0.933811i	$-0.383539\pi$
$373$	13.8192	0.715532	0.357766	+	0.933811i	$0.383539\pi$
$374$	45.9732	2.37722
$375$	1.00000	0.0516398
$376$	27.2181	1.40367
$377$	0	0
$378$	−2.85395	−0.146791
$379$	−11.5157	−0.591520	−0.295760	−	0.955262i	$-0.595573\pi$
$379$	−11.5157	−0.591520	−0.295760	+	0.955262i	$0.595573\pi$
$380$	15.9394	0.817674
$381$	17.7854	0.911174
$382$	24.1024	1.23318
$383$	−22.8798	−1.16910	−0.584552	−	0.811356i	$-0.698730\pi$
$383$	−22.8798	−1.16910	−0.584552	+	0.811356i	$0.698730\pi$
$384$	17.0472	0.869937
$385$	5.70789	0.290901
$386$	−18.0562	−0.919035
$387$	6.37755	0.324189
$388$	−33.2440	−1.68771
$389$	−4.35271	−0.220691	−0.110346	−	0.993893i	$-0.535196\pi$
$389$	−4.35271	−0.220691	−0.110346	+	0.993893i	$0.535196\pi$
$390$	0	0
$391$	−10.0268	−0.507077
$392$	−13.6473	−0.689292
$393$	−11.6697	−0.588656
$394$	−39.2181	−1.97578
$395$	8.87085	0.446341
$396$	−14.0944	−0.708271
$397$	−7.62245	−0.382560	−0.191280	−	0.981536i	$-0.561264\pi$
$397$	−7.62245	−0.382560	−0.191280	+	0.981536i	$0.561264\pi$
$398$	−2.78541	−0.139620
$399$	6.45506	0.323157
$400$	−0.523604	−0.0261802
$401$	−20.8495	−1.04118	−0.520588	−	0.853808i	$-0.674287\pi$
$401$	−20.8495	−1.04118	−0.520588	+	0.853808i	$0.674287\pi$
$402$	29.7035	1.48147
$403$	0	0
$404$	−53.1148	−2.64256
$405$	−1.00000	−0.0496904
$406$	−3.93146	−0.195115
$407$	−1.04721	−0.0519082
$408$	11.3393	0.561380
$409$	16.9653	0.838879	0.419439	−	0.907783i	$-0.362227\pi$
$409$	16.9653	0.838879	0.419439	+	0.907783i	$0.362227\pi$
$410$	2.59214	0.128017
$411$	−20.0641	−0.989690
$412$	−43.4596	−2.14110
$413$	1.07751	0.0530209
$414$	5.04721	0.248057
$415$	−8.23150	−0.404068
$416$	0	0
$417$	−16.3393	−0.800140
$418$	52.3418	2.56012
$419$	2.09884	0.102535	0.0512676	−	0.998685i	$-0.483674\pi$
$419$	2.09884	0.102535	0.0512676	+	0.998685i	$0.483674\pi$
$420$	3.93146	0.191836
$421$	39.6598	1.93290	0.966449	−	0.256857i	$-0.0826870\pi$
$421$	39.6598	1.93290	0.966449	+	0.256857i	$0.0826870\pi$
$422$	23.3855	1.13839
$423$	10.7854	0.524404
$424$	11.4158	0.554400
$425$	−4.49330	−0.217957
$426$	−21.7338	−1.05300
$427$	5.85395	0.283292
$428$	38.9260	1.88156
$429$	0	0
$430$	−14.4248	−0.695624
$431$	22.1282	1.06588	0.532940	−	0.846153i	$-0.321087\pi$
$431$	22.1282	1.06588	0.532940	+	0.846153i	$0.321087\pi$
$432$	0.523604	0.0251919
$433$	−31.3562	−1.50688	−0.753442	−	0.657515i	$-0.771608\pi$
$433$	−31.3562	−1.50688	−0.753442	+	0.657515i	$0.771608\pi$
$434$	−25.3169	−1.21525
$435$	−1.37755	−0.0660485
$436$	7.09988	0.340023
$437$	−11.4158	−0.546091
$438$	31.1799	1.48983
$439$	4.31344	0.205869	0.102935	−	0.994688i	$-0.467177\pi$
$439$	4.31344	0.205869	0.102935	+	0.994688i	$0.467177\pi$
$440$	11.4158	0.544226
$441$	−5.40786	−0.257517
$442$	0	0
$443$	0.493301	0.0234374	0.0117187	−	0.999931i	$-0.496270\pi$
$443$	0.493301	0.0234374	0.0117187	+	0.999931i	$0.496270\pi$
$444$	−0.721292	−0.0342310
$445$	6.62245	0.313934
$446$	−48.7889	−2.31022
$447$	−3.24490	−0.153478
$448$	−16.4630	−0.777804
$449$	23.3125	1.10019	0.550093	−	0.835103i	$-0.314592\pi$
$449$	23.3125	1.10019	0.550093	+	0.835103i	$0.314592\pi$
$450$	2.26180	0.106622
$451$	5.18429	0.244119
$452$	−4.60008	−0.216369
$453$	5.69996	0.267808
$454$	−12.3180	−0.578112
$455$	0	0
$456$	12.9101	0.604572
$457$	−6.66966	−0.311993	−0.155997	−	0.987758i	$-0.549859\pi$
$457$	−6.66966	−0.311993	−0.155997	+	0.987758i	$0.549859\pi$
$458$	−49.6046	−2.31787
$459$	4.49330	0.209729
$460$	−6.95279	−0.324176
$461$	−29.1193	−1.35622	−0.678110	−	0.734961i	$-0.737200\pi$
$461$	−29.1193	−1.35622	−0.678110	+	0.734961i	$0.737200\pi$
$462$	12.9101	0.600634
$463$	1.79334	0.0833436	0.0416718	−	0.999131i	$-0.486732\pi$
$463$	1.79334	0.0833436	0.0416718	+	0.999131i	$0.486732\pi$
$464$	0.721292	0.0334852
$465$	−8.87085	−0.411376
$466$	57.2519	2.65214
$467$	16.8192	0.778301	0.389150	−	0.921174i	$-0.372769\pi$
$467$	16.8192	0.778301	0.389150	+	0.921174i	$0.372769\pi$
$468$	0	0
$469$	−16.5708	−0.765169
$470$	−24.3945	−1.12523
$471$	3.85395	0.177581
$472$	2.15502	0.0991931
$473$	−28.8495	−1.32650
$474$	20.0641	0.921575
$475$	−5.11575	−0.234727
$476$	−17.6652	−0.809685
$477$	4.52360	0.207122
$478$	−50.9439	−2.33012
$479$	−35.1531	−1.60618	−0.803092	−	0.595855i	$-0.796813\pi$
$479$	−35.1531	−1.60618	−0.803092	+	0.595855i	$0.796813\pi$
$480$	−6.23150	−0.284428
$481$	0	0
$482$	−25.1416	−1.14517
$483$	−2.81571	−0.128119
$484$	29.4843	1.34020
$485$	10.6697	0.484484
$486$	−2.26180	−0.102597
$487$	8.62596	0.390879	0.195440	−	0.980716i	$-0.437387\pi$
$487$	8.62596	0.390879	0.195440	+	0.980716i	$0.437387\pi$
$488$	11.7079	0.529991
$489$	−9.72480	−0.439771
$490$	12.2315	0.552563
$491$	−23.2137	−1.04762	−0.523809	−	0.851836i	$-0.675490\pi$
$491$	−23.2137	−1.04762	−0.523809	+	0.851836i	$0.675490\pi$
$492$	3.57081	0.160985
$493$	6.18975	0.278773
$494$	0	0
$495$	4.52360	0.203321
$496$	4.64482	0.208558
$497$	12.1247	0.543868
$498$	−18.6180	−0.834294
$499$	−29.0393	−1.29998	−0.649988	−	0.759944i	$-0.725226\pi$
$499$	−29.0393	−1.29998	−0.649988	+	0.759944i	$0.725226\pi$
$500$	−3.11575	−0.139341
$501$	−19.2787	−0.861309
$502$	24.9866	1.11521
$503$	−17.3999	−0.775824	−0.387912	−	0.921696i	$-0.626804\pi$
$503$	−17.3999	−0.775824	−0.387912	+	0.921696i	$0.626804\pi$
$504$	3.18429	0.141840
$505$	17.0472	0.758591
$506$	−22.8316	−1.01499
$507$	0	0
$508$	−55.4149	−2.45864
$509$	22.8763	1.01397	0.506987	−	0.861953i	$-0.330759\pi$
$509$	22.8763	1.01397	0.506987	+	0.861953i	$0.330759\pi$
$510$	−10.1630	−0.450023
$511$	−17.3945	−0.769485
$512$	5.90558	0.260992
$513$	5.11575	0.225866
$514$	−4.59214	−0.202551
$515$	13.9484	0.614638
$516$	−19.8709	−0.874766
$517$	−48.7889	−2.14573
$518$	0.660685	0.0290288
$519$	3.01691	0.132427
$520$	0	0
$521$	−26.3642	−1.15503	−0.577517	−	0.816378i	$-0.695978\pi$
$521$	−26.3642	−1.15503	−0.577517	+	0.816378i	$0.695978\pi$
$522$	−3.11575	−0.136373
$523$	−26.2921	−1.14967	−0.574837	−	0.818268i	$-0.694934\pi$
$523$	−26.2921	−1.14967	−0.574837	+	0.818268i	$0.694934\pi$
$524$	36.3597	1.58838
$525$	−1.26180	−0.0550696
$526$	7.34725	0.320355
$527$	39.8594	1.73630
$528$	−2.36858	−0.103079
$529$	−18.0204	−0.783496
$530$	−10.2315	−0.444428
$531$	0.853947	0.0370581
$532$	−20.1124	−0.871981
$533$	0	0
$534$	14.9787	0.648190
$535$	−12.4933	−0.540133
$536$	−33.1416	−1.43150
$537$	5.31694	0.229443
$538$	60.9519	2.62782
$539$	24.4630	1.05370
$540$	3.11575	0.134081
$541$	0.107816	0.00463537	0.00231768	−	0.999997i	$-0.499262\pi$
$541$	0.107816	0.00463537	0.00231768	+	0.999997i	$0.499262\pi$
$542$	44.8957	1.92844
$543$	−25.8709	−1.11022
$544$	28.0000	1.20049
$545$	−2.27871	−0.0976091
$546$	0	0
$547$	12.1193	0.518182	0.259091	−	0.965853i	$-0.416577\pi$
$547$	12.1193	0.518182	0.259091	+	0.965853i	$0.416577\pi$
$548$	62.5148	2.67050
$549$	4.63935	0.198003
$550$	−10.2315	−0.436273
$551$	7.04721	0.300221
$552$	−5.63142	−0.239689
$553$	−11.1933	−0.475986
$554$	36.4024	1.54659
$555$	0.231499	0.00982658
$556$	50.9092	2.15903
$557$	−38.0070	−1.61041	−0.805204	−	0.592997i	$-0.797944\pi$
$557$	−38.0070	−1.61041	−0.805204	+	0.592997i	$0.797944\pi$
$558$	−20.0641	−0.849382
$559$	0	0
$560$	0.660685	0.0279191
$561$	−20.3259	−0.858161
$562$	12.1630	0.513063
$563$	15.5102	0.653677	0.326839	−	0.945080i	$-0.394017\pi$
$563$	15.5102	0.653677	0.326839	+	0.945080i	$0.394017\pi$
$564$	−33.6046	−1.41501
$565$	1.47640	0.0621124
$566$	60.7665	2.55421
$567$	1.26180	0.0529907
$568$	24.2494	1.01748
$569$	19.2405	0.806602	0.403301	−	0.915067i	$-0.367863\pi$
$569$	19.2405	0.806602	0.403301	+	0.915067i	$0.367863\pi$
$570$	−11.5708	−0.484648
$571$	27.7338	1.16062	0.580311	−	0.814395i	$-0.302931\pi$
$571$	27.7338	1.16062	0.580311	+	0.814395i	$0.302931\pi$
$572$	0	0
$573$	−10.6563	−0.445172
$574$	−3.27077	−0.136519
$575$	2.23150	0.0930599
$576$	−13.0472	−0.543634
$577$	−26.9866	−1.12347	−0.561733	−	0.827318i	$-0.689865\pi$
$577$	−26.9866	−1.12347	−0.561733	+	0.827318i	$0.689865\pi$
$578$	7.21459	0.300088
$579$	7.98309	0.331766
$580$	4.29211	0.178220
$581$	10.3865	0.430906
$582$	24.1327	1.00033
$583$	−20.4630	−0.847491
$584$	−34.7889	−1.43958
$585$	0	0
$586$	−48.4462	−2.00129
$587$	30.8530	1.27344	0.636720	−	0.771095i	$-0.280291\pi$
$587$	30.8530	1.27344	0.636720	+	0.771095i	$0.280291\pi$
$588$	16.8495	0.694863
$589$	45.3811	1.86989
$590$	−1.93146	−0.0795169
$591$	17.3393	0.713244
$592$	−0.121214	−0.00498186
$593$	−4.29211	−0.176256	−0.0881278	−	0.996109i	$-0.528088\pi$
$593$	−4.29211	−0.176256	−0.0881278	+	0.996109i	$0.528088\pi$
$594$	10.2315	0.419803
$595$	5.66966	0.232433
$596$	10.1103	0.414133
$597$	1.23150	0.0504019
$598$	0	0
$599$	−24.0224	−0.981527	−0.490764	−	0.871293i	$-0.663282\pi$
$599$	−24.0224	−0.981527	−0.490764	+	0.871293i	$0.663282\pi$
$600$	−2.52360	−0.103026
$601$	2.53154	0.103264	0.0516318	−	0.998666i	$-0.483558\pi$
$601$	2.53154	0.103264	0.0516318	+	0.998666i	$0.483558\pi$
$602$	18.2012	0.741825
$603$	−13.1327	−0.534803
$604$	−17.7596	−0.722630
$605$	−9.46300	−0.384726
$606$	38.5574	1.56629
$607$	11.4417	0.464403	0.232201	−	0.972668i	$-0.425407\pi$
$607$	11.4417	0.464403	0.232201	+	0.972668i	$0.425407\pi$
$608$	31.8788	1.29286
$609$	1.73820	0.0704353
$610$	−10.4933	−0.424861
$611$	0	0
$612$	−14.0000	−0.565916
$613$	7.19326	0.290533	0.145267	−	0.989393i	$-0.453596\pi$
$613$	7.19326	0.290533	0.145267	+	0.989393i	$0.453596\pi$
$614$	17.7641	0.716900
$615$	−1.14605	−0.0462133
$616$	−14.4045	−0.580373
$617$	−25.5708	−1.02944	−0.514721	−	0.857358i	$-0.672105\pi$
$617$	−25.5708	−1.02944	−0.514721	+	0.857358i	$0.672105\pi$
$618$	31.5484	1.26906
$619$	−5.98660	−0.240622	−0.120311	−	0.992736i	$-0.538389\pi$
$619$	−5.98660	−0.240622	−0.120311	+	0.992736i	$0.538389\pi$
$620$	27.6394	1.11002
$621$	−2.23150	−0.0895470
$622$	−63.0463	−2.52793
$623$	−8.35622	−0.334785
$624$	0	0
$625$	1.00000	0.0400000
$626$	17.8405	0.713052
$627$	−23.1416	−0.924188
$628$	−12.0079	−0.479169
$629$	−1.04019	−0.0414752
$630$	−2.85395	−0.113704
$631$	43.0259	1.71283	0.856417	−	0.516285i	$-0.172686\pi$
$631$	43.0259	1.71283	0.856417	+	0.516285i	$0.172686\pi$
$632$	−22.3865	−0.890488
$633$	−10.3393	−0.410951
$634$	−29.8967	−1.18735
$635$	17.7854	0.705792
$636$	−14.0944	−0.558880
$637$	0	0
$638$	14.0944	0.558003
$639$	9.60905	0.380128
$640$	17.0472	0.673850
$641$	−6.69450	−0.264417	−0.132208	−	0.991222i	$-0.542207\pi$
$641$	−6.69450	−0.264417	−0.132208	+	0.991222i	$0.542207\pi$
$642$	−28.2574	−1.11523
$643$	−8.18078	−0.322619	−0.161309	−	0.986904i	$-0.551572\pi$
$643$	−8.18078	−0.322619	−0.161309	+	0.986904i	$0.551572\pi$
$644$	8.77305	0.345706
$645$	6.37755	0.251116
$646$	51.9911	2.04556
$647$	−11.2787	−0.443412	−0.221706	−	0.975114i	$-0.571162\pi$
$647$	−11.2787	−0.443412	−0.221706	+	0.975114i	$0.571162\pi$
$648$	2.52360	0.0991365
$649$	−3.86292	−0.151633
$650$	0	0
$651$	11.1933	0.438699
$652$	30.3000	1.18664
$653$	27.2484	1.06631	0.533156	−	0.846017i	$-0.321006\pi$
$653$	27.2484	1.06631	0.533156	+	0.846017i	$0.321006\pi$
$654$	−5.15399	−0.201537
$655$	−11.6697	−0.455971
$656$	0.600078	0.0234291
$657$	−13.7854	−0.537820
$658$	30.7810	1.19997
$659$	6.75510	0.263141	0.131571	−	0.991307i	$-0.457998\pi$
$659$	6.75510	0.263141	0.131571	+	0.991307i	$0.457998\pi$
$660$	−14.0944	−0.548624
$661$	26.5102	1.03113	0.515564	−	0.856851i	$-0.327583\pi$
$661$	26.5102	1.03113	0.515564	+	0.856851i	$0.327583\pi$
$662$	53.9429	2.09655
$663$	0	0
$664$	20.7730	0.806151
$665$	6.45506	0.250317
$666$	0.523604	0.0202893
$667$	−3.07400	−0.119026
$668$	60.0676	2.32409
$669$	21.5708	0.833976
$670$	29.7035	1.14755
$671$	−20.9866	−0.810179
$672$	7.86292	0.303319
$673$	−0.677591	−0.0261192	−0.0130596	−	0.999915i	$-0.504157\pi$
$673$	−0.677591	−0.0261192	−0.0130596	+	0.999915i	$0.504157\pi$
$674$	12.8539	0.495116
$675$	−1.00000	−0.0384900
$676$	0	0
$677$	−10.4630	−0.402126	−0.201063	−	0.979578i	$-0.564440\pi$
$677$	−10.4630	−0.402126	−0.201063	+	0.979578i	$0.564440\pi$
$678$	3.33931	0.128246
$679$	−13.4630	−0.516662
$680$	11.3393	0.434843
$681$	5.44609	0.208695
$682$	90.7621	3.47546
$683$	18.7516	0.717510	0.358755	−	0.933432i	$-0.383201\pi$
$683$	18.7516	0.717510	0.358755	+	0.933432i	$0.383201\pi$
$684$	−15.9394	−0.609458
$685$	−20.0641	−0.766610
$686$	−35.4114	−1.35201
$687$	21.9315	0.836737
$688$	−3.33931	−0.127310
$689$	0	0
$690$	5.04721	0.192144
$691$	−43.5653	−1.65730	−0.828652	−	0.559764i	$-0.810892\pi$
$691$	−43.5653	−1.65730	−0.828652	+	0.559764i	$0.810892\pi$
$692$	−9.39992	−0.357331
$693$	−5.70789	−0.216825
$694$	−48.5148	−1.84159
$695$	−16.3393	−0.619786
$696$	3.47640	0.131772
$697$	5.14956	0.195054
$698$	−15.5405	−0.588217
$699$	−25.3125	−0.957407
$700$	3.93146	0.148595
$701$	−19.0810	−0.720680	−0.360340	−	0.932821i	$-0.617339\pi$
$701$	−19.0810	−0.720680	−0.360340	+	0.932821i	$0.617339\pi$
$702$	0	0
$703$	−1.18429	−0.0446663
$704$	59.0204	2.22442
$705$	10.7854	0.406202
$706$	−78.0250	−2.93651
$707$	−21.5102	−0.808975
$708$	−2.66069	−0.0999947
$709$	−44.6046	−1.67516	−0.837581	−	0.546313i	$-0.816031\pi$
$709$	−44.6046	−1.67516	−0.837581	+	0.546313i	$0.816031\pi$
$710$	−21.7338	−0.815654
$711$	−8.87085	−0.332683
$712$	−16.7124	−0.626325
$713$	−19.7953	−0.741340
$714$	12.8236	0.479913
$715$	0	0
$716$	−16.5663	−0.619110
$717$	22.5236	0.841159
$718$	18.4551	0.688737
$719$	−12.9822	−0.484153	−0.242077	−	0.970257i	$-0.577829\pi$
$719$	−12.9822	−0.484153	−0.242077	+	0.970257i	$0.577829\pi$
$720$	0.523604	0.0195136
$721$	−17.6001	−0.655461
$722$	16.2191	0.603614
$723$	11.1157	0.413399
$724$	80.6071	2.99574
$725$	−1.37755	−0.0511610
$726$	−21.4034	−0.794356
$727$	17.3980	0.645255	0.322627	−	0.946526i	$-0.395434\pi$
$727$	17.3980	0.645255	0.322627	+	0.946526i	$0.395434\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	31.1799	1.15402
$731$	−28.6563	−1.05989
$732$	−14.4551	−0.534275
$733$	−45.8272	−1.69266	−0.846332	−	0.532655i	$-0.821194\pi$
$733$	−45.8272	−1.69266	−0.846332	+	0.532655i	$0.821194\pi$
$734$	−15.4720	−0.571081
$735$	−5.40786	−0.199472
$736$	−13.9056	−0.512567
$737$	59.4069	2.18828
$738$	−2.59214	−0.0954182
$739$	−17.5708	−0.646353	−0.323176	−	0.946339i	$-0.604751\pi$
$739$	−17.5708	−0.646353	−0.323176	+	0.946339i	$0.604751\pi$
$740$	−0.721292	−0.0265152
$741$	0	0
$742$	12.9101	0.473946
$743$	30.3562	1.11366	0.556831	−	0.830626i	$-0.312017\pi$
$743$	30.3562	1.11366	0.556831	+	0.830626i	$0.312017\pi$
$744$	22.3865	0.820730
$745$	−3.24490	−0.118884
$746$	31.2563	1.14438
$747$	8.23150	0.301175
$748$	63.3305	2.31559
$749$	15.7641	0.576007
$750$	2.26180	0.0825893
$751$	3.80323	0.138782	0.0693909	−	0.997590i	$-0.477894\pi$
$751$	3.80323	0.138782	0.0693909	+	0.997590i	$0.477894\pi$
$752$	−5.64729	−0.205935
$753$	−11.0472	−0.402583
$754$	0	0
$755$	5.69996	0.207443
$756$	−3.93146	−0.142986
$757$	−3.40786	−0.123861	−0.0619303	−	0.998080i	$-0.519726\pi$
$757$	−3.40786	−0.123861	−0.0619303	+	0.998080i	$0.519726\pi$
$758$	−26.0462	−0.946040
$759$	10.0944	0.366404
$760$	12.9101	0.468300
$761$	−7.24490	−0.262627	−0.131314	−	0.991341i	$-0.541919\pi$
$761$	−7.24490	−0.262627	−0.131314	+	0.991341i	$0.541919\pi$
$762$	40.2271	1.45727
$763$	2.87528	0.104092
$764$	33.2022	1.20121
$765$	4.49330	0.162456
$766$	−51.7496	−1.86979
$767$	0	0
$768$	12.4630	0.449720
$769$	−31.1764	−1.12425	−0.562124	−	0.827053i	$-0.690016\pi$
$769$	−31.1764	−1.12425	−0.562124	+	0.827053i	$0.690016\pi$
$770$	12.9101	0.465249
$771$	2.03030	0.0731196
$772$	−24.8733	−0.895210
$773$	−19.4605	−0.699947	−0.349973	−	0.936760i	$-0.613809\pi$
$773$	−19.4605	−0.699947	−0.349973	+	0.936760i	$0.613809\pi$
$774$	14.4248	0.518487
$775$	−8.87085	−0.318650
$776$	−26.9260	−0.966587
$777$	−0.292106	−0.0104792
$778$	−9.84498	−0.352959
$779$	5.86292	0.210061
$780$	0	0
$781$	−43.4675	−1.55539
$782$	−22.6786	−0.810986
$783$	1.37755	0.0492297
$784$	2.83158	0.101128
$785$	3.85395	0.137553
$786$	−26.3945	−0.941459
$787$	−14.4034	−0.513427	−0.256713	−	0.966488i	$-0.582640\pi$
$787$	−14.4034	−0.513427	−0.256713	+	0.966488i	$0.582640\pi$
$788$	−54.0250	−1.92456
$789$	−3.24840	−0.115646
$790$	20.0641	0.713849
$791$	−1.86292	−0.0662378
$792$	−11.4158	−0.405642
$793$	0	0
$794$	−17.2405	−0.611841
$795$	4.52360	0.160436
$796$	−3.83704	−0.136000
$797$	−23.6011	−0.835994	−0.417997	−	0.908448i	$-0.637268\pi$
$797$	−23.6011	−0.835994	−0.417997	+	0.908448i	$0.637268\pi$
$798$	14.6001	0.516837
$799$	−48.4621	−1.71447
$800$	−6.23150	−0.220317
$801$	−6.62245	−0.233993
$802$	−47.1575	−1.66519
$803$	62.3597	2.20063
$804$	40.9181	1.44307
$805$	−2.81571	−0.0992407
$806$	0	0
$807$	−26.9484	−0.948627
$808$	−43.0204	−1.51345
$809$	26.7551	0.940659	0.470330	−	0.882491i	$-0.344135\pi$
$809$	26.7551	0.940659	0.470330	+	0.882491i	$0.344135\pi$
$810$	−2.26180	−0.0794716
$811$	3.58421	0.125859	0.0629293	−	0.998018i	$-0.479956\pi$
$811$	3.58421	0.125859	0.0629293	+	0.998018i	$0.479956\pi$
$812$	−5.41579	−0.190057
$813$	−19.8495	−0.696153
$814$	−2.36858	−0.0830187
$815$	−9.72480	−0.340645
$816$	−2.35271	−0.0823614
$817$	−32.6260	−1.14144
$818$	38.3721	1.34165
$819$	0	0
$820$	3.57081	0.124698
$821$	−15.8361	−0.552685	−0.276342	−	0.961059i	$-0.589122\pi$
$821$	−15.8361	−0.552685	−0.276342	+	0.961059i	$0.589122\pi$
$822$	−45.3811	−1.58285
$823$	7.41579	0.258498	0.129249	−	0.991612i	$-0.458743\pi$
$823$	7.41579	0.258498	0.129249	+	0.991612i	$0.458743\pi$
$824$	−35.2002	−1.22626
$825$	4.52360	0.157492
$826$	2.43712	0.0847983
$827$	16.6036	0.577363	0.288682	−	0.957425i	$-0.406783\pi$
$827$	16.6036	0.577363	0.288682	+	0.957425i	$0.406783\pi$
$828$	6.95279	0.241626
$829$	−29.2842	−1.01708	−0.508541	−	0.861038i	$-0.669815\pi$
$829$	−29.2842	−1.01708	−0.508541	+	0.861038i	$0.669815\pi$
$830$	−18.6180	−0.646241
$831$	−16.0944	−0.558309
$832$	0	0
$833$	24.2991	0.841915
$834$	−36.9563	−1.27969
$835$	−19.2787	−0.667167
$836$	72.1035	2.49375
$837$	8.87085	0.306622
$838$	4.74717	0.163988
$839$	30.1620	1.04131	0.520655	−	0.853767i	$-0.325688\pi$
$839$	30.1620	1.04131	0.520655	+	0.853767i	$0.325688\pi$
$840$	3.18429	0.109868
$841$	−27.1024	−0.934564
$842$	89.7026	3.09135
$843$	−5.37755	−0.185213
$844$	32.2147	1.10888
$845$	0	0
$846$	24.3945	0.838699
$847$	11.9404	0.410278
$848$	−2.36858	−0.0813374
$849$	−26.8664	−0.922053
$850$	−10.1630	−0.348587
$851$	0.516589	0.0177085
$852$	−29.9394	−1.02571
$853$	2.50670	0.0858277	0.0429139	−	0.999079i	$-0.486336\pi$
$853$	2.50670	0.0858277	0.0429139	+	0.999079i	$0.486336\pi$
$854$	13.2405	0.453080
$855$	5.11575	0.174955
$856$	31.5282	1.07761
$857$	−24.4327	−0.834605	−0.417302	−	0.908768i	$-0.637024\pi$
$857$	−24.4327	−0.834605	−0.417302	+	0.908768i	$0.637024\pi$
$858$	0	0
$859$	−7.10235	−0.242329	−0.121165	−	0.992632i	$-0.538663\pi$
$859$	−7.10235	−0.242329	−0.121165	+	0.992632i	$0.538663\pi$
$860$	−19.8709	−0.677590
$861$	1.44609	0.0492827
$862$	50.0497	1.70470
$863$	3.24490	0.110458	0.0552288	−	0.998474i	$-0.482411\pi$
$863$	3.24490	0.110458	0.0552288	+	0.998474i	$0.482411\pi$
$864$	6.23150	0.212000
$865$	3.01691	0.102578
$866$	−70.9216	−2.41001
$867$	−3.18975	−0.108330
$868$	−34.8754	−1.18375
$869$	40.1282	1.36126
$870$	−3.11575	−0.105634
$871$	0	0
$872$	5.75056	0.194738
$873$	−10.6697	−0.361113
$874$	−25.8203	−0.873383
$875$	−1.26180	−0.0426567
$876$	42.9519	1.45121
$877$	−18.9866	−0.641132	−0.320566	−	0.947226i	$-0.603873\pi$
$877$	−18.9866	−0.641132	−0.320566	+	0.947226i	$0.603873\pi$
$878$	9.75614	0.329254
$879$	21.4193	0.722455
$880$	−2.36858	−0.0798448
$881$	−19.4764	−0.656176	−0.328088	−	0.944647i	$-0.606404\pi$
$881$	−19.4764	−0.656176	−0.328088	+	0.944647i	$0.606404\pi$
$882$	−12.2315	−0.411856
$883$	−50.5664	−1.70169	−0.850847	−	0.525413i	$-0.823911\pi$
$883$	−50.5664	−1.70169	−0.850847	+	0.525413i	$0.823911\pi$
$884$	0	0
$885$	0.853947	0.0287051
$886$	1.11575	0.0374843
$887$	−12.5271	−0.420619	−0.210310	−	0.977635i	$-0.567447\pi$
$887$	−12.5271	−0.420619	−0.210310	+	0.977635i	$0.567447\pi$
$888$	−0.584211	−0.0196049
$889$	−22.4417	−0.752669
$890$	14.9787	0.502086
$891$	−4.52360	−0.151546
$892$	−67.2092	−2.25033
$893$	−55.1754	−1.84638
$894$	−7.33931	−0.245463
$895$	5.31694	0.177726
$896$	−21.5102	−0.718606
$897$	0	0
$898$	52.7283	1.75957
$899$	12.2201	0.407562
$900$	3.11575	0.103858
$901$	−20.3259	−0.677154
$902$	11.7258	0.390428
$903$	−8.04721	−0.267794
$904$	−3.72584	−0.123920
$905$	−25.8709	−0.859976
$906$	12.8922	0.428314
$907$	28.0417	0.931111	0.465555	−	0.885019i	$-0.345855\pi$
$907$	28.0417	0.931111	0.465555	+	0.885019i	$0.345855\pi$
$908$	−16.9687	−0.563125
$909$	−17.0472	−0.565420
$910$	0	0
$911$	16.1977	0.536653	0.268327	−	0.963328i	$-0.413529\pi$
$911$	16.1977	0.536653	0.268327	+	0.963328i	$0.413529\pi$
$912$	−2.67863	−0.0886983
$913$	−37.2360	−1.23233
$914$	−15.0854	−0.498982
$915$	4.63935	0.153372
$916$	−68.3329	−2.25778
$917$	14.7248	0.486256
$918$	10.1630	0.335428
$919$	−43.2778	−1.42760	−0.713801	−	0.700348i	$-0.753028\pi$
$919$	−43.2778	−1.42760	−0.713801	+	0.700348i	$0.753028\pi$
$920$	−5.63142	−0.185662
$921$	−7.85395	−0.258796
$922$	−65.8620	−2.16905
$923$	0	0
$924$	17.7844	0.585063
$925$	0.231499	0.00761163
$926$	4.05618	0.133294
$927$	−13.9484	−0.458124
$928$	8.58421	0.281791
$929$	−13.7685	−0.451730	−0.225865	−	0.974159i	$-0.572521\pi$
$929$	−13.7685	−0.451730	−0.225865	+	0.974159i	$0.572521\pi$
$930$	−20.0641	−0.657928
$931$	27.6652	0.906691
$932$	78.8675	2.58339
$933$	27.8744	0.912566
$934$	38.0417	1.24476
$935$	−20.3259	−0.664729
$936$	0	0
$937$	−38.1888	−1.24757	−0.623787	−	0.781594i	$-0.714407\pi$
$937$	−38.1888	−1.24757	−0.623787	+	0.781594i	$0.714407\pi$
$938$	−37.4799	−1.22376
$939$	−7.88776	−0.257407
$940$	−33.6046	−1.09606
$941$	13.9618	0.455140	0.227570	−	0.973762i	$-0.426922\pi$
$941$	13.9618	0.455140	0.227570	+	0.973762i	$0.426922\pi$
$942$	8.71687	0.284011
$943$	−2.55742	−0.0832809
$944$	−0.447131	−0.0145529
$945$	1.26180	0.0410464
$946$	−65.2519	−2.12152
$947$	−7.36962	−0.239480	−0.119740	−	0.992805i	$-0.538206\pi$
$947$	−7.36962	−0.239480	−0.119740	+	0.992805i	$0.538206\pi$
$948$	27.6394	0.897684
$949$	0	0
$950$	−11.5708	−0.375407
$951$	13.2181	0.428626
$952$	−14.3080	−0.463724
$953$	23.2181	0.752108	0.376054	−	0.926598i	$-0.377281\pi$
$953$	23.2181	0.752108	0.376054	+	0.926598i	$0.377281\pi$
$954$	10.2315	0.331257
$955$	−10.6563	−0.344828
$956$	−70.1779	−2.26972
$957$	−6.23150	−0.201436
$958$	−79.5093	−2.56883
$959$	25.3169	0.817527
$960$	−13.0472	−0.421097
$961$	47.6920	1.53845
$962$	0	0
$963$	12.4933	0.402591
$964$	−34.6339	−1.11548
$965$	7.98309	0.256985
$966$	−6.36858	−0.204906
$967$	7.54402	0.242599	0.121300	−	0.992616i	$-0.461294\pi$
$967$	7.54402	0.242599	0.121300	+	0.992616i	$0.461294\pi$
$968$	23.8809	0.767560
$969$	−22.9866	−0.738436
$970$	24.1327	0.774853
$971$	−30.5842	−0.981494	−0.490747	−	0.871302i	$-0.663276\pi$
$971$	−30.5842	−0.981494	−0.490747	+	0.871302i	$0.663276\pi$
$972$	−3.11575	−0.0999377
$973$	20.6170	0.660950
$974$	19.5102	0.625147
$975$	0	0
$976$	−2.42919	−0.0777564
$977$	35.6811	1.14154	0.570770	−	0.821110i	$-0.306645\pi$
$977$	35.6811	1.14154	0.570770	+	0.821110i	$0.306645\pi$
$978$	−21.9956	−0.703341
$979$	29.9573	0.957441
$980$	16.8495	0.538238
$981$	2.27871	0.0727535
$982$	−52.5047	−1.67549
$983$	−12.9866	−0.414208	−0.207104	−	0.978319i	$-0.566404\pi$
$983$	−12.9866	−0.414208	−0.207104	+	0.978319i	$0.566404\pi$
$984$	2.89218	0.0921995
$985$	17.3393	0.552477
$986$	14.0000	0.445851
$987$	−13.6091	−0.433181
$988$	0	0
$989$	14.2315	0.452535
$990$	10.2315	0.325178
$991$	−22.7472	−0.722588	−0.361294	−	0.932452i	$-0.617665\pi$
$991$	−22.7472	−0.722588	−0.361294	+	0.932452i	$0.617665\pi$
$992$	55.2787	1.75510
$993$	−23.8495	−0.756842
$994$	27.4237	0.869828
$995$	1.23150	0.0390411
$996$	−25.6473	−0.812665
$997$	−13.8460	−0.438508	−0.219254	−	0.975668i	$-0.570362\pi$
$997$	−13.8460	−0.438508	−0.219254	+	0.975668i	$0.570362\pi$
$998$	−65.6811	−2.07910
$999$	−0.231499	−0.00732430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2535.2.a.ba.1.3		3
3.2	odd	2		7605.2.a.bw.1.1		3
13.4	even	6		195.2.i.d.16.3	✓	6
13.10	even	6		195.2.i.d.61.3	yes	6
13.12	even	2		2535.2.a.bb.1.1		3
39.17	odd	6		585.2.j.f.406.1		6
39.23	odd	6		585.2.j.f.451.1		6
39.38	odd	2		7605.2.a.bv.1.3		3
65.4	even	6		975.2.i.l.601.1		6
65.17	odd	12		975.2.bb.k.874.2		12
65.23	odd	12		975.2.bb.k.724.2		12
65.43	odd	12		975.2.bb.k.874.5		12
65.49	even	6		975.2.i.l.451.1		6
65.62	odd	12		975.2.bb.k.724.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.d.16.3	✓	6	13.4	even	6
195.2.i.d.61.3	yes	6	13.10	even	6
585.2.j.f.406.1		6	39.17	odd	6
585.2.j.f.451.1		6	39.23	odd	6
975.2.i.l.451.1		6	65.49	even	6
975.2.i.l.601.1		6	65.4	even	6
975.2.bb.k.724.2		12	65.23	odd	12
975.2.bb.k.724.5		12	65.62	odd	12
975.2.bb.k.874.2		12	65.17	odd	12
975.2.bb.k.874.5		12	65.43	odd	12
2535.2.a.ba.1.3		3	1.1	even	1	trivial
2535.2.a.bb.1.1		3	13.12	even	2
7605.2.a.bv.1.3		3	39.38	odd	2
7605.2.a.bw.1.1		3	3.2	odd	2

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:	\( N \)	\(=\)	\( 2535 = 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2535.a (trivial)

\(f(q)\)	\(=\)	\(q+2.26180 q^{2} -1.00000 q^{3} +3.11575 q^{4} -1.00000 q^{5} -2.26180 q^{6} +1.26180 q^{7} +2.52360 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.26180 q^{2} -1.00000 q^{3} +3.11575 q^{4} -1.00000 q^{5} -2.26180 q^{6} +1.26180 q^{7} +2.52360 q^{8} +1.00000 q^{9} -2.26180 q^{10} -4.52360 q^{11} -3.11575 q^{12} +2.85395 q^{14} +1.00000 q^{15} -0.523604 q^{16} -4.49330 q^{17} +2.26180 q^{18} -5.11575 q^{19} -3.11575 q^{20} -1.26180 q^{21} -10.2315 q^{22} +2.23150 q^{23} -2.52360 q^{24} +1.00000 q^{25} -1.00000 q^{27} +3.93146 q^{28} -1.37755 q^{29} +2.26180 q^{30} -8.87085 q^{31} -6.23150 q^{32} +4.52360 q^{33} -10.1630 q^{34} -1.26180 q^{35} +3.11575 q^{36} +0.231499 q^{37} -11.5708 q^{38} -2.52360 q^{40} -1.14605 q^{41} -2.85395 q^{42} +6.37755 q^{43} -14.0944 q^{44} -1.00000 q^{45} +5.04721 q^{46} +10.7854 q^{47} +0.523604 q^{48} -5.40786 q^{49} +2.26180 q^{50} +4.49330 q^{51} +4.52360 q^{53} -2.26180 q^{54} +4.52360 q^{55} +3.18429 q^{56} +5.11575 q^{57} -3.11575 q^{58} +0.853947 q^{59} +3.11575 q^{60} +4.63935 q^{61} -20.0641 q^{62} +1.26180 q^{63} -13.0472 q^{64} +10.2315 q^{66} -13.1327 q^{67} -14.0000 q^{68} -2.23150 q^{69} -2.85395 q^{70} +9.60905 q^{71} +2.52360 q^{72} -13.7854 q^{73} +0.523604 q^{74} -1.00000 q^{75} -15.9394 q^{76} -5.70789 q^{77} -8.87085 q^{79} +0.523604 q^{80} +1.00000 q^{81} -2.59214 q^{82} +8.23150 q^{83} -3.93146 q^{84} +4.49330 q^{85} +14.4248 q^{86} +1.37755 q^{87} -11.4158 q^{88} -6.62245 q^{89} -2.26180 q^{90} +6.95279 q^{92} +8.87085 q^{93} +24.3945 q^{94} +5.11575 q^{95} +6.23150 q^{96} -10.6697 q^{97} -12.2315 q^{98} -4.52360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^7 - 6 * q^8 + 3 * q^9	\( 3 q - 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{12} + 12 q^{14} + 3 q^{15} + 12 q^{16} - 12 q^{19} - 6 q^{20} + 3 q^{21} - 24 q^{22} + 6 q^{24} + 3 q^{25} - 3 q^{27} - 12 q^{28} + 6 q^{29} - 3 q^{31} - 12 q^{32} + 3 q^{35} + 6 q^{36} - 6 q^{37} + 6 q^{38} + 6 q^{40} - 12 q^{42} + 9 q^{43} + 12 q^{44} - 3 q^{45} - 12 q^{46} + 12 q^{47} - 12 q^{48} - 6 q^{49} + 30 q^{56} + 12 q^{57} - 6 q^{58} + 6 q^{59} + 6 q^{60} - 3 q^{61} - 6 q^{62} - 3 q^{63} - 12 q^{64} + 24 q^{66} - 9 q^{67} - 42 q^{68} - 12 q^{70} + 12 q^{71} - 6 q^{72} - 21 q^{73} - 12 q^{74} - 3 q^{75} - 48 q^{76} - 24 q^{77} - 3 q^{79} - 12 q^{80} + 3 q^{81} - 18 q^{82} + 18 q^{83} + 12 q^{84} + 6 q^{86} - 6 q^{87} - 48 q^{88} - 30 q^{89} + 48 q^{92} + 3 q^{93} + 36 q^{94} + 12 q^{95} + 12 q^{96} - 15 q^{97} - 30 q^{98}+O(q^{100}) \) 3 * q - 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^12 + 12 * q^14 + 3 * q^15 + 12 * q^16 - 12 * q^19 - 6 * q^20 + 3 * q^21 - 24 * q^22 + 6 * q^24 + 3 * q^25 - 3 * q^27 - 12 * q^28 + 6 * q^29 - 3 * q^31 - 12 * q^32 + 3 * q^35 + 6 * q^36 - 6 * q^37 + 6 * q^38 + 6 * q^40 - 12 * q^42 + 9 * q^43 + 12 * q^44 - 3 * q^45 - 12 * q^46 + 12 * q^47 - 12 * q^48 - 6 * q^49 + 30 * q^56 + 12 * q^57 - 6 * q^58 + 6 * q^59 + 6 * q^60 - 3 * q^61 - 6 * q^62 - 3 * q^63 - 12 * q^64 + 24 * q^66 - 9 * q^67 - 42 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^72 - 21 * q^73 - 12 * q^74 - 3 * q^75 - 48 * q^76 - 24 * q^77 - 3 * q^79 - 12 * q^80 + 3 * q^81 - 18 * q^82 + 18 * q^83 + 12 * q^84 + 6 * q^86 - 6 * q^87 - 48 * q^88 - 30 * q^89 + 48 * q^92 + 3 * q^93 + 36 * q^94 + 12 * q^95 + 12 * q^96 - 15 * q^97 - 30 * q^98

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