LMFDB - Embedded newform 5390.2.a.ca.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5390,2,Mod(1,5390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5390, 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("5390.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5390.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:	$43.0393666895$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.470683$ of defining polynomial
Character	$\chi$	$=$	5390.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.24914 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.24914 q^{6} +1.00000 q^{8} +2.05863 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.24914 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.24914 q^{6} +1.00000 q^{8} +2.05863 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.24914 q^{12} -0.941367 q^{13} -2.24914 q^{15} +1.00000 q^{16} -6.49828 q^{17} +2.05863 q^{18} +4.36641 q^{19} -1.00000 q^{20} +1.00000 q^{22} +6.24914 q^{23} +2.24914 q^{24} +1.00000 q^{25} -0.941367 q^{26} -2.11727 q^{27} +8.74742 q^{29} -2.24914 q^{30} +9.55691 q^{31} +1.00000 q^{32} +2.24914 q^{33} -6.49828 q^{34} +2.05863 q^{36} +4.24914 q^{37} +4.36641 q^{38} -2.11727 q^{39} -1.00000 q^{40} +2.13187 q^{41} +7.67418 q^{43} +1.00000 q^{44} -2.05863 q^{45} +6.24914 q^{46} -11.1138 q^{47} +2.24914 q^{48} +1.00000 q^{50} -14.6155 q^{51} -0.941367 q^{52} -4.74742 q^{53} -2.11727 q^{54} -1.00000 q^{55} +9.82066 q^{57} +8.74742 q^{58} +1.88273 q^{59} -2.24914 q^{60} -9.11383 q^{61} +9.55691 q^{62} +1.00000 q^{64} +0.941367 q^{65} +2.24914 q^{66} +12.9966 q^{67} -6.49828 q^{68} +14.0552 q^{69} -14.6155 q^{71} +2.05863 q^{72} +10.4983 q^{73} +4.24914 q^{74} +2.24914 q^{75} +4.36641 q^{76} -2.11727 q^{78} +8.36641 q^{79} -1.00000 q^{80} -10.9379 q^{81} +2.13187 q^{82} +8.49828 q^{83} +6.49828 q^{85} +7.67418 q^{86} +19.6742 q^{87} +1.00000 q^{88} -12.3810 q^{89} -2.05863 q^{90} +6.24914 q^{92} +21.4948 q^{93} -11.1138 q^{94} -4.36641 q^{95} +2.24914 q^{96} +15.3630 q^{97} +2.05863 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} - 2 q^{6} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 - 3 * q^5 - 2 * q^6 + 3 * q^8 + 7 * q^9	$ 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} - 2 q^{6} + 3 q^{8} + 7 q^{9} - 3 q^{10} + 3 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{15} + 3 q^{16} - 2 q^{17} + 7 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{22} + 10 q^{23} - 2 q^{24} + 3 q^{25} - 2 q^{26} - 8 q^{27} + 2 q^{30} + 12 q^{31} + 3 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{36} + 4 q^{37} + 6 q^{38} - 8 q^{39} - 3 q^{40} - 4 q^{41} + 8 q^{43} + 3 q^{44} - 7 q^{45} + 10 q^{46} - 2 q^{48} + 3 q^{50} - 28 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 3 q^{55} - 8 q^{57} + 4 q^{59} + 2 q^{60} + 6 q^{61} + 12 q^{62} + 3 q^{64} + 2 q^{65} - 2 q^{66} + 4 q^{67} - 2 q^{68} + 8 q^{69} - 28 q^{71} + 7 q^{72} + 14 q^{73} + 4 q^{74} - 2 q^{75} + 6 q^{76} - 8 q^{78} + 18 q^{79} - 3 q^{80} + 3 q^{81} - 4 q^{82} + 8 q^{83} + 2 q^{85} + 8 q^{86} + 44 q^{87} + 3 q^{88} - 18 q^{89} - 7 q^{90} + 10 q^{92} + 12 q^{93} - 6 q^{95} - 2 q^{96} + 4 q^{97} + 7 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 - 3 * q^5 - 2 * q^6 + 3 * q^8 + 7 * q^9 - 3 * q^10 + 3 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^15 + 3 * q^16 - 2 * q^17 + 7 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^22 + 10 * q^23 - 2 * q^24 + 3 * q^25 - 2 * q^26 - 8 * q^27 + 2 * q^30 + 12 * q^31 + 3 * q^32 - 2 * q^33 - 2 * q^34 + 7 * q^36 + 4 * q^37 + 6 * q^38 - 8 * q^39 - 3 * q^40 - 4 * q^41 + 8 * q^43 + 3 * q^44 - 7 * q^45 + 10 * q^46 - 2 * q^48 + 3 * q^50 - 28 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 3 * q^55 - 8 * q^57 + 4 * q^59 + 2 * q^60 + 6 * q^61 + 12 * q^62 + 3 * q^64 + 2 * q^65 - 2 * q^66 + 4 * q^67 - 2 * q^68 + 8 * q^69 - 28 * q^71 + 7 * q^72 + 14 * q^73 + 4 * q^74 - 2 * q^75 + 6 * q^76 - 8 * q^78 + 18 * q^79 - 3 * q^80 + 3 * q^81 - 4 * q^82 + 8 * q^83 + 2 * q^85 + 8 * q^86 + 44 * q^87 + 3 * q^88 - 18 * q^89 - 7 * q^90 + 10 * q^92 + 12 * q^93 - 6 * q^95 - 2 * q^96 + 4 * q^97 + 7 * 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
$3$	2.24914	1.29854	0.649271	−	0.760557i	$-0.275074\pi$
$3$	2.24914	1.29854	0.649271	+	0.760557i	$0.275074\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.24914	0.918208
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	2.05863	0.686211
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.24914	0.649271
$13$	−0.941367	−0.261088	−0.130544	−	0.991443i	$-0.541672\pi$
$13$	−0.941367	−0.261088	−0.130544	+	0.991443i	$0.541672\pi$
$14$	0	0
$15$	−2.24914	−0.580726
$16$	1.00000	0.250000
$17$	−6.49828	−1.57606	−0.788032	−	0.615634i	$-0.788900\pi$
$17$	−6.49828	−1.57606	−0.788032	+	0.615634i	$0.788900\pi$
$18$	2.05863	0.485224
$19$	4.36641	1.00172	0.500861	−	0.865528i	$-0.333017\pi$
$19$	4.36641	1.00172	0.500861	+	0.865528i	$0.333017\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	1.00000	0.213201
$23$	6.24914	1.30304	0.651518	−	0.758633i	$-0.274133\pi$
$23$	6.24914	1.30304	0.651518	+	0.758633i	$0.274133\pi$
$24$	2.24914	0.459104
$25$	1.00000	0.200000
$26$	−0.941367	−0.184617
$27$	−2.11727	−0.407468
$28$	0	0
$29$	8.74742	1.62436	0.812178	−	0.583410i	$-0.198282\pi$
$29$	8.74742	1.62436	0.812178	+	0.583410i	$0.198282\pi$
$30$	−2.24914	−0.410635
$31$	9.55691	1.71647	0.858236	−	0.513255i	$-0.171560\pi$
$31$	9.55691	1.71647	0.858236	+	0.513255i	$0.171560\pi$
$32$	1.00000	0.176777
$33$	2.24914	0.391525
$34$	−6.49828	−1.11445
$35$	0	0
$36$	2.05863	0.343106
$37$	4.24914	0.698554	0.349277	−	0.937019i	$-0.386427\pi$
$37$	4.24914	0.698554	0.349277	+	0.937019i	$0.386427\pi$
$38$	4.36641	0.708325
$39$	−2.11727	−0.339034
$40$	−1.00000	−0.158114
$41$	2.13187	0.332943	0.166471	−	0.986046i	$-0.446763\pi$
$41$	2.13187	0.332943	0.166471	+	0.986046i	$0.446763\pi$
$42$	0	0
$43$	7.67418	1.17030	0.585151	−	0.810925i	$-0.301035\pi$
$43$	7.67418	1.17030	0.585151	+	0.810925i	$0.301035\pi$
$44$	1.00000	0.150756
$45$	−2.05863	−0.306883
$46$	6.24914	0.921386
$47$	−11.1138	−1.62112	−0.810559	−	0.585657i	$-0.800837\pi$
$47$	−11.1138	−1.62112	−0.810559	+	0.585657i	$0.800837\pi$
$48$	2.24914	0.324635
$49$	0	0
$50$	1.00000	0.141421
$51$	−14.6155	−2.04659
$52$	−0.941367	−0.130544
$53$	−4.74742	−0.652109	−0.326054	−	0.945351i	$-0.605719\pi$
$53$	−4.74742	−0.652109	−0.326054	+	0.945351i	$0.605719\pi$
$54$	−2.11727	−0.288123
$55$	−1.00000	−0.134840
$56$	0	0
$57$	9.82066	1.30078
$58$	8.74742	1.14859
$59$	1.88273	0.245111	0.122556	−	0.992462i	$-0.460891\pi$
$59$	1.88273	0.245111	0.122556	+	0.992462i	$0.460891\pi$
$60$	−2.24914	−0.290363
$61$	−9.11383	−1.16691	−0.583453	−	0.812147i	$-0.698299\pi$
$61$	−9.11383	−1.16691	−0.583453	+	0.812147i	$0.698299\pi$
$62$	9.55691	1.21373
$63$	0	0
$64$	1.00000	0.125000
$65$	0.941367	0.116762
$66$	2.24914	0.276850
$67$	12.9966	1.58778	0.793891	−	0.608060i	$-0.208052\pi$
$67$	12.9966	1.58778	0.793891	+	0.608060i	$0.208052\pi$
$68$	−6.49828	−0.788032
$69$	14.0552	1.69205
$70$	0	0
$71$	−14.6155	−1.73455	−0.867273	−	0.497833i	$-0.834129\pi$
$71$	−14.6155	−1.73455	−0.867273	+	0.497833i	$0.834129\pi$
$72$	2.05863	0.242612
$73$	10.4983	1.22873	0.614365	−	0.789022i	$-0.289412\pi$
$73$	10.4983	1.22873	0.614365	+	0.789022i	$0.289412\pi$
$74$	4.24914	0.493953
$75$	2.24914	0.259708
$76$	4.36641	0.500861
$77$	0	0
$78$	−2.11727	−0.239733
$79$	8.36641	0.941294	0.470647	−	0.882322i	$-0.344020\pi$
$79$	8.36641	0.941294	0.470647	+	0.882322i	$0.344020\pi$
$80$	−1.00000	−0.111803
$81$	−10.9379	−1.21533
$82$	2.13187	0.235426
$83$	8.49828	0.932808	0.466404	−	0.884572i	$-0.345549\pi$
$83$	8.49828	0.932808	0.466404	+	0.884572i	$0.345549\pi$
$84$	0	0
$85$	6.49828	0.704838
$86$	7.67418	0.827528
$87$	19.6742	2.10929
$88$	1.00000	0.106600
$89$	−12.3810	−1.31238	−0.656192	−	0.754594i	$-0.727834\pi$
$89$	−12.3810	−1.31238	−0.656192	+	0.754594i	$0.727834\pi$
$90$	−2.05863	−0.216999
$91$	0	0
$92$	6.24914	0.651518
$93$	21.4948	2.22891
$94$	−11.1138	−1.14630
$95$	−4.36641	−0.447984
$96$	2.24914	0.229552
$97$	15.3630	1.55987	0.779937	−	0.625859i	$-0.215251\pi$
$97$	15.3630	1.55987	0.779937	+	0.625859i	$0.215251\pi$
$98$	0	0
$99$	2.05863	0.206900
$100$	1.00000	0.100000
$101$	16.8793	1.67955	0.839776	−	0.542932i	$-0.182686\pi$
$101$	16.8793	1.67955	0.839776	+	0.542932i	$0.182686\pi$
$102$	−14.6155	−1.44715
$103$	6.61555	0.651849	0.325925	−	0.945396i	$-0.394324\pi$
$103$	6.61555	0.651849	0.325925	+	0.945396i	$0.394324\pi$
$104$	−0.941367	−0.0923086
$105$	0	0
$106$	−4.74742	−0.461110
$107$	−14.5535	−1.40694	−0.703469	−	0.710726i	$-0.748367\pi$
$107$	−14.5535	−1.40694	−0.703469	+	0.710726i	$0.748367\pi$
$108$	−2.11727	−0.203734
$109$	−0.249141	−0.0238633	−0.0119317	−	0.999929i	$-0.503798\pi$
$109$	−0.249141	−0.0238633	−0.0119317	+	0.999929i	$0.503798\pi$
$110$	−1.00000	−0.0953463
$111$	9.55691	0.907102
$112$	0	0
$113$	10.9966	1.03447	0.517235	−	0.855844i	$-0.326961\pi$
$113$	10.9966	1.03447	0.517235	+	0.855844i	$0.326961\pi$
$114$	9.82066	0.919789
$115$	−6.24914	−0.582735
$116$	8.74742	0.812178
$117$	−1.93793	−0.179162
$118$	1.88273	0.173320
$119$	0	0
$120$	−2.24914	−0.205318
$121$	1.00000	0.0909091
$122$	−9.11383	−0.825127
$123$	4.79488	0.432340
$124$	9.55691	0.858236
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−5.88273	−0.522008	−0.261004	−	0.965338i	$-0.584054\pi$
$127$	−5.88273	−0.522008	−0.261004	+	0.965338i	$0.584054\pi$
$128$	1.00000	0.0883883
$129$	17.2603	1.51969
$130$	0.941367	0.0825633
$131$	1.25258	0.109438	0.0547191	−	0.998502i	$-0.482574\pi$
$131$	1.25258	0.109438	0.0547191	+	0.998502i	$0.482574\pi$
$132$	2.24914	0.195763
$133$	0	0
$134$	12.9966	1.12273
$135$	2.11727	0.182225
$136$	−6.49828	−0.557223
$137$	10.0000	0.854358	0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000	0.854358	0.427179	+	0.904167i	$0.359507\pi$
$138$	14.0552	1.19646
$139$	−10.9820	−0.931477	−0.465739	−	0.884922i	$-0.654211\pi$
$139$	−10.9820	−0.931477	−0.465739	+	0.884922i	$0.654211\pi$
$140$	0	0
$141$	−24.9966	−2.10509
$142$	−14.6155	−1.22651
$143$	−0.941367	−0.0787210
$144$	2.05863	0.171553
$145$	−8.74742	−0.726434
$146$	10.4983	0.868844
$147$	0	0
$148$	4.24914	0.349277
$149$	0.0146079	0.00119673	0.000598363	−	1.00000i	$-0.499810\pi$
$149$	0.0146079	0.00119673	0.000598363		1.00000i	$0.499810\pi$
$150$	2.24914	0.183642
$151$	−15.2457	−1.24068	−0.620339	−	0.784334i	$-0.713005\pi$
$151$	−15.2457	−1.24068	−0.620339	+	0.784334i	$0.713005\pi$
$152$	4.36641	0.354162
$153$	−13.3776	−1.08151
$154$	0	0
$155$	−9.55691	−0.767630
$156$	−2.11727	−0.169517
$157$	5.50172	0.439085	0.219542	−	0.975603i	$-0.429544\pi$
$157$	5.50172	0.439085	0.219542	+	0.975603i	$0.429544\pi$
$158$	8.36641	0.665596
$159$	−10.6776	−0.846790
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−10.9379	−0.859365
$163$	−18.2277	−1.42770	−0.713850	−	0.700298i	$-0.753050\pi$
$163$	−18.2277	−1.42770	−0.713850	+	0.700298i	$0.753050\pi$
$164$	2.13187	0.166471
$165$	−2.24914	−0.175095
$166$	8.49828	0.659595
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	0	0
$169$	−12.1138	−0.931833
$170$	6.49828	0.498395
$171$	8.98883	0.687393
$172$	7.67418	0.585151
$173$	−0.117266	−0.00891559	−0.00445780	−	0.999990i	$-0.501419\pi$
$173$	−0.117266	−0.00891559	−0.00445780	+	0.999990i	$0.501419\pi$
$174$	19.6742	1.49150
$175$	0	0
$176$	1.00000	0.0753778
$177$	4.23453	0.318287
$178$	−12.3810	−0.927996
$179$	−22.5535	−1.68573	−0.842863	−	0.538128i	$-0.819132\pi$
$179$	−22.5535	−1.68573	−0.842863	+	0.538128i	$0.819132\pi$
$180$	−2.05863	−0.153441
$181$	−20.8793	−1.55195	−0.775973	−	0.630766i	$-0.782741\pi$
$181$	−20.8793	−1.55195	−0.775973	+	0.630766i	$0.782741\pi$
$182$	0	0
$183$	−20.4983	−1.51528
$184$	6.24914	0.460693
$185$	−4.24914	−0.312403
$186$	21.4948	1.57608
$187$	−6.49828	−0.475201
$188$	−11.1138	−0.810559
$189$	0	0
$190$	−4.36641	−0.316772
$191$	3.11383	0.225309	0.112654	−	0.993634i	$-0.464065\pi$
$191$	3.11383	0.225309	0.112654	+	0.993634i	$0.464065\pi$
$192$	2.24914	0.162318
$193$	−6.17246	−0.444304	−0.222152	−	0.975012i	$-0.571308\pi$
$193$	−6.17246	−0.444304	−0.222152	+	0.975012i	$0.571308\pi$
$194$	15.3630	1.10300
$195$	2.11727	0.151621
$196$	0	0
$197$	6.73281	0.479693	0.239847	−	0.970811i	$-0.422903\pi$
$197$	6.73281	0.479693	0.239847	+	0.970811i	$0.422903\pi$
$198$	2.05863	0.146301
$199$	13.2311	0.937927	0.468964	−	0.883217i	$-0.344627\pi$
$199$	13.2311	0.937927	0.468964	+	0.883217i	$0.344627\pi$
$200$	1.00000	0.0707107
$201$	29.2311	2.06180
$202$	16.8793	1.18762
$203$	0	0
$204$	−14.6155	−1.02329
$205$	−2.13187	−0.148897
$206$	6.61555	0.460927
$207$	12.8647	0.894158
$208$	−0.941367	−0.0652720
$209$	4.36641	0.302031
$210$	0	0
$211$	23.1138	1.59122	0.795611	−	0.605808i	$-0.207150\pi$
$211$	23.1138	1.59122	0.795611	+	0.605808i	$0.207150\pi$
$212$	−4.74742	−0.326054
$213$	−32.8724	−2.25238
$214$	−14.5535	−0.994855
$215$	−7.67418	−0.523375
$216$	−2.11727	−0.144062
$217$	0	0
$218$	−0.249141	−0.0168739
$219$	23.6121	1.59556
$220$	−1.00000	−0.0674200
$221$	6.11727	0.411492
$222$	9.55691	0.641418
$223$	−10.3810	−0.695164	−0.347582	−	0.937650i	$-0.612997\pi$
$223$	−10.3810	−0.695164	−0.347582	+	0.937650i	$0.612997\pi$
$224$	0	0
$225$	2.05863	0.137242
$226$	10.9966	0.731480
$227$	−16.1104	−1.06928	−0.534642	−	0.845079i	$-0.679554\pi$
$227$	−16.1104	−1.06928	−0.534642	+	0.845079i	$0.679554\pi$
$228$	9.82066	0.650389
$229$	−24.2897	−1.60511	−0.802555	−	0.596578i	$-0.796527\pi$
$229$	−24.2897	−1.60511	−0.802555	+	0.596578i	$0.796527\pi$
$230$	−6.24914	−0.412056
$231$	0	0
$232$	8.74742	0.574296
$233$	6.88617	0.451128	0.225564	−	0.974228i	$-0.427578\pi$
$233$	6.88617	0.451128	0.225564	+	0.974228i	$0.427578\pi$
$234$	−1.93793	−0.126686
$235$	11.1138	0.724986
$236$	1.88273	0.122556
$237$	18.8172	1.22231
$238$	0	0
$239$	−11.1353	−0.720283	−0.360142	−	0.932898i	$-0.617272\pi$
$239$	−11.1353	−0.720283	−0.360142	+	0.932898i	$0.617272\pi$
$240$	−2.24914	−0.145181
$241$	−2.36641	−0.152434	−0.0762168	−	0.997091i	$-0.524284\pi$
$241$	−2.36641	−0.152434	−0.0762168	+	0.997091i	$0.524284\pi$
$242$	1.00000	0.0642824
$243$	−18.2491	−1.17068
$244$	−9.11383	−0.583453
$245$	0	0
$246$	4.79488	0.305711
$247$	−4.11039	−0.261538
$248$	9.55691	0.606865
$249$	19.1138	1.21129
$250$	−1.00000	−0.0632456
$251$	−25.1070	−1.58474	−0.792368	−	0.610043i	$-0.791152\pi$
$251$	−25.1070	−1.58474	−0.792368	+	0.610043i	$0.791152\pi$
$252$	0	0
$253$	6.24914	0.392880
$254$	−5.88273	−0.369116
$255$	14.6155	0.915261
$256$	1.00000	0.0625000
$257$	2.86469	0.178694	0.0893472	−	0.996001i	$-0.471522\pi$
$257$	2.86469	0.178694	0.0893472	+	0.996001i	$0.471522\pi$
$258$	17.2603	1.07458
$259$	0	0
$260$	0.941367	0.0583811
$261$	18.0077	1.11465
$262$	1.25258	0.0773846
$263$	3.76547	0.232189	0.116094	−	0.993238i	$-0.462963\pi$
$263$	3.76547	0.232189	0.116094	+	0.993238i	$0.462963\pi$
$264$	2.24914	0.138425
$265$	4.74742	0.291632
$266$	0	0
$267$	−27.8466	−1.70419
$268$	12.9966	0.793891
$269$	−8.94137	−0.545165	−0.272582	−	0.962132i	$-0.587878\pi$
$269$	−8.94137	−0.545165	−0.272582	+	0.962132i	$0.587878\pi$
$270$	2.11727	0.128853
$271$	−21.4948	−1.30572	−0.652859	−	0.757479i	$-0.726431\pi$
$271$	−21.4948	−1.30572	−0.652859	+	0.757479i	$0.726431\pi$
$272$	−6.49828	−0.394016
$273$	0	0
$274$	10.0000	0.604122
$275$	1.00000	0.0603023
$276$	14.0552	0.846023
$277$	7.64820	0.459536	0.229768	−	0.973245i	$-0.426203\pi$
$277$	7.64820	0.459536	0.229768	+	0.973245i	$0.426203\pi$
$278$	−10.9820	−0.658654
$279$	19.6742	1.17786
$280$	0	0
$281$	−28.6155	−1.70706	−0.853530	−	0.521043i	$-0.825543\pi$
$281$	−28.6155	−1.70706	−0.853530	+	0.521043i	$0.825543\pi$
$282$	−24.9966	−1.48852
$283$	2.87930	0.171156	0.0855782	−	0.996331i	$-0.472726\pi$
$283$	2.87930	0.171156	0.0855782	+	0.996331i	$0.472726\pi$
$284$	−14.6155	−0.867273
$285$	−9.82066	−0.581726
$286$	−0.941367	−0.0556642
$287$	0	0
$288$	2.05863	0.121306
$289$	25.2277	1.48398
$290$	−8.74742	−0.513666
$291$	34.5535	2.02556
$292$	10.4983	0.614365
$293$	12.9414	0.756043	0.378021	−	0.925797i	$-0.376605\pi$
$293$	12.9414	0.756043	0.378021	+	0.925797i	$0.376605\pi$
$294$	0	0
$295$	−1.88273	−0.109617
$296$	4.24914	0.246976
$297$	−2.11727	−0.122856
$298$	0.0146079	0.000846213 0
$299$	−5.88273	−0.340207
$300$	2.24914	0.129854
$301$	0	0
$302$	−15.2457	−0.877292
$303$	37.9639	2.18097
$304$	4.36641	0.250431
$305$	9.11383	0.521856
$306$	−13.3776	−0.764745
$307$	−0.498281	−0.0284384	−0.0142192	−	0.999899i	$-0.504526\pi$
$307$	−0.498281	−0.0284384	−0.0142192	+	0.999899i	$0.504526\pi$
$308$	0	0
$309$	14.8793	0.846454
$310$	−9.55691	−0.542796
$311$	23.4396	1.32914	0.664570	−	0.747226i	$-0.268615\pi$
$311$	23.4396	1.32914	0.664570	+	0.747226i	$0.268615\pi$
$312$	−2.11727	−0.119867
$313$	−9.36984	−0.529615	−0.264807	−	0.964301i	$-0.585308\pi$
$313$	−9.36984	−0.529615	−0.264807	+	0.964301i	$0.585308\pi$
$314$	5.50172	0.310480
$315$	0	0
$316$	8.36641	0.470647
$317$	−9.97852	−0.560449	−0.280225	−	0.959934i	$-0.590409\pi$
$317$	−9.97852	−0.560449	−0.280225	+	0.959934i	$0.590409\pi$
$318$	−10.6776	−0.598771
$319$	8.74742	0.489762
$320$	−1.00000	−0.0559017
$321$	−32.7328	−1.82697
$322$	0	0
$323$	−28.3741	−1.57878
$324$	−10.9379	−0.607663
$325$	−0.941367	−0.0522176
$326$	−18.2277	−1.00954
$327$	−0.560352	−0.0309875
$328$	2.13187	0.117713
$329$	0	0
$330$	−2.24914	−0.123811
$331$	−20.4362	−1.12328	−0.561638	−	0.827383i	$-0.689829\pi$
$331$	−20.4362	−1.12328	−0.561638	+	0.827383i	$0.689829\pi$
$332$	8.49828	0.466404
$333$	8.74742	0.479356
$334$	8.00000	0.437741
$335$	−12.9966	−0.710078
$336$	0	0
$337$	7.88273	0.429400	0.214700	−	0.976680i	$-0.431123\pi$
$337$	7.88273	0.429400	0.214700	+	0.976680i	$0.431123\pi$
$338$	−12.1138	−0.658905
$339$	24.7328	1.34330
$340$	6.49828	0.352419
$341$	9.55691	0.517536
$342$	8.98883	0.486060
$343$	0	0
$344$	7.67418	0.413764
$345$	−14.0552	−0.756706
$346$	−0.117266	−0.00630428
$347$	13.5569	0.727773	0.363887	−	0.931443i	$-0.381450\pi$
$347$	13.5569	0.727773	0.363887	+	0.931443i	$0.381450\pi$
$348$	19.6742	1.05465
$349$	10.7328	0.574514	0.287257	−	0.957853i	$-0.407257\pi$
$349$	10.7328	0.574514	0.287257	+	0.957853i	$0.407257\pi$
$350$	0	0
$351$	1.99312	0.106385
$352$	1.00000	0.0533002
$353$	20.8578	1.11015	0.555075	−	0.831801i	$-0.312690\pi$
$353$	20.8578	1.11015	0.555075	+	0.831801i	$0.312690\pi$
$354$	4.23453	0.225063
$355$	14.6155	0.775713
$356$	−12.3810	−0.656192
$357$	0	0
$358$	−22.5535	−1.19199
$359$	0.366407	0.0193382	0.00966911	−	0.999953i	$-0.496922\pi$
$359$	0.366407	0.0193382	0.00966911	+	0.999953i	$0.496922\pi$
$360$	−2.05863	−0.108499
$361$	0.0655089	0.00344783
$362$	−20.8793	−1.09739
$363$	2.24914	0.118049
$364$	0	0
$365$	−10.4983	−0.549505
$366$	−20.4983	−1.07146
$367$	−20.8432	−1.08801	−0.544003	−	0.839083i	$-0.683092\pi$
$367$	−20.8432	−1.08801	−0.544003	+	0.839083i	$0.683092\pi$
$368$	6.24914	0.325759
$369$	4.38875	0.228469
$370$	−4.24914	−0.220902
$371$	0	0
$372$	21.4948	1.11446
$373$	−5.37758	−0.278440	−0.139220	−	0.990261i	$-0.544460\pi$
$373$	−5.37758	−0.278440	−0.139220	+	0.990261i	$0.544460\pi$
$374$	−6.49828	−0.336018
$375$	−2.24914	−0.116145
$376$	−11.1138	−0.573152
$377$	−8.23453	−0.424100
$378$	0	0
$379$	3.53093	0.181372	0.0906860	−	0.995880i	$-0.471094\pi$
$379$	3.53093	0.181372	0.0906860	+	0.995880i	$0.471094\pi$
$380$	−4.36641	−0.223992
$381$	−13.2311	−0.677850
$382$	3.11383	0.159317
$383$	−1.38445	−0.0707422	−0.0353711	−	0.999374i	$-0.511261\pi$
$383$	−1.38445	−0.0707422	−0.0353711	+	0.999374i	$0.511261\pi$
$384$	2.24914	0.114776
$385$	0	0
$386$	−6.17246	−0.314170
$387$	15.7983	0.803074
$388$	15.3630	0.779937
$389$	15.7294	0.797511	0.398756	−	0.917057i	$-0.369442\pi$
$389$	15.7294	0.797511	0.398756	+	0.917057i	$0.369442\pi$
$390$	2.11727	0.107212
$391$	−40.6087	−2.05367
$392$	0	0
$393$	2.81722	0.142110
$394$	6.73281	0.339194
$395$	−8.36641	−0.420960
$396$	2.05863	0.103450
$397$	17.6121	0.883926	0.441963	−	0.897033i	$-0.354282\pi$
$397$	17.6121	0.883926	0.441963	+	0.897033i	$0.354282\pi$
$398$	13.2311	0.663215
$399$	0	0
$400$	1.00000	0.0500000
$401$	−32.8172	−1.63881	−0.819407	−	0.573212i	$-0.805697\pi$
$401$	−32.8172	−1.63881	−0.819407	+	0.573212i	$0.805697\pi$
$402$	29.2311	1.45791
$403$	−8.99656	−0.448151
$404$	16.8793	0.839776
$405$	10.9379	0.543510
$406$	0	0
$407$	4.24914	0.210622
$408$	−14.6155	−0.723577
$409$	33.3561	1.64935	0.824676	−	0.565605i	$-0.191357\pi$
$409$	33.3561	1.64935	0.824676	+	0.565605i	$0.191357\pi$
$410$	−2.13187	−0.105286
$411$	22.4914	1.10942
$412$	6.61555	0.325925
$413$	0	0
$414$	12.8647	0.632265
$415$	−8.49828	−0.417164
$416$	−0.941367	−0.0461543
$417$	−24.7000	−1.20956
$418$	4.36641	0.213568
$419$	−12.3449	−0.603089	−0.301544	−	0.953452i	$-0.597502\pi$
$419$	−12.3449	−0.603089	−0.301544	+	0.953452i	$0.597502\pi$
$420$	0	0
$421$	−8.87930	−0.432750	−0.216375	−	0.976310i	$-0.569423\pi$
$421$	−8.87930	−0.432750	−0.216375	+	0.976310i	$0.569423\pi$
$422$	23.1138	1.12516
$423$	−22.8793	−1.11243
$424$	−4.74742	−0.230555
$425$	−6.49828	−0.315213
$426$	−32.8724	−1.59267
$427$	0	0
$428$	−14.5535	−0.703469
$429$	−2.11727	−0.102223
$430$	−7.67418	−0.370082
$431$	18.2784	0.880437	0.440219	−	0.897891i	$-0.354901\pi$
$431$	18.2784	0.880437	0.440219	+	0.897891i	$0.354901\pi$
$432$	−2.11727	−0.101867
$433$	−6.86469	−0.329896	−0.164948	−	0.986302i	$-0.552746\pi$
$433$	−6.86469	−0.329896	−0.164948	+	0.986302i	$0.552746\pi$
$434$	0	0
$435$	−19.6742	−0.943305
$436$	−0.249141	−0.0119317
$437$	27.2863	1.30528
$438$	23.6121	1.12823
$439$	11.8466	0.565409	0.282705	−	0.959207i	$-0.408768\pi$
$439$	11.8466	0.565409	0.282705	+	0.959207i	$0.408768\pi$
$440$	−1.00000	−0.0476731
$441$	0	0
$442$	6.11727	0.290969
$443$	17.8827	0.849634	0.424817	−	0.905279i	$-0.360338\pi$
$443$	17.8827	0.849634	0.424817	+	0.905279i	$0.360338\pi$
$444$	9.55691	0.453551
$445$	12.3810	0.586916
$446$	−10.3810	−0.491555
$447$	0.0328552	0.00155400
$448$	0	0
$449$	−16.8172	−0.793654	−0.396827	−	0.917893i	$-0.629889\pi$
$449$	−16.8172	−0.793654	−0.396827	+	0.917893i	$0.629889\pi$
$450$	2.05863	0.0970449
$451$	2.13187	0.100386
$452$	10.9966	0.517235
$453$	−34.2897	−1.61107
$454$	−16.1104	−0.756098
$455$	0	0
$456$	9.82066	0.459895
$457$	−12.2277	−0.571986	−0.285993	−	0.958232i	$-0.592323\pi$
$457$	−12.2277	−0.571986	−0.285993	+	0.958232i	$0.592323\pi$
$458$	−24.2897	−1.13498
$459$	13.7586	0.642196
$460$	−6.24914	−0.291368
$461$	16.6155	0.773863	0.386932	−	0.922108i	$-0.373535\pi$
$461$	16.6155	0.773863	0.386932	+	0.922108i	$0.373535\pi$
$462$	0	0
$463$	18.4837	0.859009	0.429505	−	0.903065i	$-0.358688\pi$
$463$	18.4837	0.859009	0.429505	+	0.903065i	$0.358688\pi$
$464$	8.74742	0.406089
$465$	−21.4948	−0.996799
$466$	6.88617	0.318996
$467$	−24.3956	−1.12889	−0.564447	−	0.825469i	$-0.690911\pi$
$467$	−24.3956	−1.12889	−0.564447	+	0.825469i	$0.690911\pi$
$468$	−1.93793	−0.0895808
$469$	0	0
$470$	11.1138	0.512643
$471$	12.3741	0.570170
$472$	1.88273	0.0866598
$473$	7.67418	0.352859
$474$	18.8172	0.864304
$475$	4.36641	0.200344
$476$	0	0
$477$	−9.77320	−0.447484
$478$	−11.1353	−0.509317
$479$	27.7655	1.26864	0.634318	−	0.773072i	$-0.281281\pi$
$479$	27.7655	1.26864	0.634318	+	0.773072i	$0.281281\pi$
$480$	−2.24914	−0.102659
$481$	−4.00000	−0.182384
$482$	−2.36641	−0.107787
$483$	0	0
$484$	1.00000	0.0454545
$485$	−15.3630	−0.697596
$486$	−18.2491	−0.827798
$487$	10.0958	0.457484	0.228742	−	0.973487i	$-0.426539\pi$
$487$	10.0958	0.457484	0.228742	+	0.973487i	$0.426539\pi$
$488$	−9.11383	−0.412564
$489$	−40.9966	−1.85393
$490$	0	0
$491$	−32.1104	−1.44912	−0.724561	−	0.689211i	$-0.757957\pi$
$491$	−32.1104	−1.44912	−0.724561	+	0.689211i	$0.757957\pi$
$492$	4.79488	0.216170
$493$	−56.8432	−2.56009
$494$	−4.11039	−0.184935
$495$	−2.05863	−0.0925287
$496$	9.55691	0.429118
$497$	0	0
$498$	19.1138	0.856511
$499$	−8.79488	−0.393713	−0.196857	−	0.980432i	$-0.563073\pi$
$499$	−8.79488	−0.393713	−0.196857	+	0.980432i	$0.563073\pi$
$500$	−1.00000	−0.0447214
$501$	17.9931	0.803874
$502$	−25.1070	−1.12058
$503$	15.0034	0.668970	0.334485	−	0.942401i	$-0.391438\pi$
$503$	15.0034	0.668970	0.334485	+	0.942401i	$0.391438\pi$
$504$	0	0
$505$	−16.8793	−0.751119
$506$	6.24914	0.277808
$507$	−27.2457	−1.21002
$508$	−5.88273	−0.261004
$509$	−21.8759	−0.969630	−0.484815	−	0.874617i	$-0.661113\pi$
$509$	−21.8759	−0.969630	−0.484815	+	0.874617i	$0.661113\pi$
$510$	14.6155	0.647187
$511$	0	0
$512$	1.00000	0.0441942
$513$	−9.24485	−0.408170
$514$	2.86469	0.126356
$515$	−6.61555	−0.291516
$516$	17.2603	0.759843
$517$	−11.1138	−0.488786
$518$	0	0
$519$	−0.263748	−0.0115773
$520$	0.941367	0.0412817
$521$	−14.0292	−0.614631	−0.307316	−	0.951608i	$-0.599431\pi$
$521$	−14.0292	−0.614631	−0.307316	+	0.951608i	$0.599431\pi$
$522$	18.0077	0.788177
$523$	−1.14992	−0.0502825	−0.0251412	−	0.999684i	$-0.508004\pi$
$523$	−1.14992	−0.0502825	−0.0251412	+	0.999684i	$0.508004\pi$
$524$	1.25258	0.0547191
$525$	0	0
$526$	3.76547	0.164182
$527$	−62.1035	−2.70527
$528$	2.24914	0.0978813
$529$	16.0518	0.697902
$530$	4.74742	0.206215
$531$	3.87586	0.168198
$532$	0	0
$533$	−2.00688	−0.0869274
$534$	−27.8466	−1.20504
$535$	14.5535	0.629202
$536$	12.9966	0.561366
$537$	−50.7259	−2.18899
$538$	−8.94137	−0.385490
$539$	0	0
$540$	2.11727	0.0911126
$541$	−6.47680	−0.278459	−0.139230	−	0.990260i	$-0.544463\pi$
$541$	−6.47680	−0.278459	−0.139230	+	0.990260i	$0.544463\pi$
$542$	−21.4948	−0.923283
$543$	−46.9605	−2.01527
$544$	−6.49828	−0.278612
$545$	0.249141	0.0106720
$546$	0	0
$547$	12.9966	0.555693	0.277846	−	0.960626i	$-0.410379\pi$
$547$	12.9966	0.555693	0.277846	+	0.960626i	$0.410379\pi$
$548$	10.0000	0.427179
$549$	−18.7620	−0.800744
$550$	1.00000	0.0426401
$551$	38.1948	1.62715
$552$	14.0552	0.598229
$553$	0	0
$554$	7.64820	0.324941
$555$	−9.55691	−0.405668
$556$	−10.9820	−0.465739
$557$	−16.4914	−0.698763	−0.349382	−	0.936981i	$-0.613608\pi$
$557$	−16.4914	−0.698763	−0.349382	+	0.936981i	$0.613608\pi$
$558$	19.6742	0.832874
$559$	−7.22422	−0.305552
$560$	0	0
$561$	−14.6155	−0.617069
$562$	−28.6155	−1.20707
$563$	16.7620	0.706435	0.353218	−	0.935541i	$-0.385088\pi$
$563$	16.7620	0.706435	0.353218	+	0.935541i	$0.385088\pi$
$564$	−24.9966	−1.05255
$565$	−10.9966	−0.462629
$566$	2.87930	0.121026
$567$	0	0
$568$	−14.6155	−0.613255
$569$	−22.0000	−0.922288	−0.461144	−	0.887325i	$-0.652561\pi$
$569$	−22.0000	−0.922288	−0.461144	+	0.887325i	$0.652561\pi$
$570$	−9.82066	−0.411342
$571$	12.7328	0.532852	0.266426	−	0.963855i	$-0.414157\pi$
$571$	12.7328	0.532852	0.266426	+	0.963855i	$0.414157\pi$
$572$	−0.941367	−0.0393605
$573$	7.00344	0.292573
$574$	0	0
$575$	6.24914	0.260607
$576$	2.05863	0.0857764
$577$	11.8613	0.493790	0.246895	−	0.969042i	$-0.420590\pi$
$577$	11.8613	0.493790	0.246895	+	0.969042i	$0.420590\pi$
$578$	25.2277	1.04933
$579$	−13.8827	−0.576947
$580$	−8.74742	−0.363217
$581$	0	0
$582$	34.5535	1.43229
$583$	−4.74742	−0.196618
$584$	10.4983	0.434422
$585$	1.93793	0.0801235
$586$	12.9414	0.534603
$587$	8.60094	0.354999	0.177499	−	0.984121i	$-0.443199\pi$
$587$	8.60094	0.354999	0.177499	+	0.984121i	$0.443199\pi$
$588$	0	0
$589$	41.7294	1.71943
$590$	−1.88273	−0.0775109
$591$	15.1430	0.622902
$592$	4.24914	0.174639
$593$	−10.7328	−0.440744	−0.220372	−	0.975416i	$-0.570727\pi$
$593$	−10.7328	−0.440744	−0.220372	+	0.975416i	$0.570727\pi$
$594$	−2.11727	−0.0868725
$595$	0	0
$596$	0.0146079	0.000598363 0
$597$	29.7586	1.21794
$598$	−5.88273	−0.240563
$599$	16.0812	0.657059	0.328529	−	0.944494i	$-0.393447\pi$
$599$	16.0812	0.657059	0.328529	+	0.944494i	$0.393447\pi$
$600$	2.24914	0.0918208
$601$	34.0889	1.39052	0.695258	−	0.718760i	$-0.255290\pi$
$601$	34.0889	1.39052	0.695258	+	0.718760i	$0.255290\pi$
$602$	0	0
$603$	26.7552	1.08955
$604$	−15.2457	−0.620339
$605$	−1.00000	−0.0406558
$606$	37.9639	1.54218
$607$	−11.6742	−0.473840	−0.236920	−	0.971529i	$-0.576138\pi$
$607$	−11.6742	−0.473840	−0.236920	+	0.971529i	$0.576138\pi$
$608$	4.36641	0.177081
$609$	0	0
$610$	9.11383	0.369008
$611$	10.4622	0.423255
$612$	−13.3776	−0.540756
$613$	−34.2637	−1.38390	−0.691950	−	0.721946i	$-0.743248\pi$
$613$	−34.2637	−1.38390	−0.691950	+	0.721946i	$0.743248\pi$
$614$	−0.498281	−0.0201090
$615$	−4.79488	−0.193348
$616$	0	0
$617$	39.3707	1.58500	0.792502	−	0.609869i	$-0.208778\pi$
$617$	39.3707	1.58500	0.792502	+	0.609869i	$0.208778\pi$
$618$	14.8793	0.598533
$619$	−16.1104	−0.647531	−0.323766	−	0.946137i	$-0.604949\pi$
$619$	−16.1104	−0.647531	−0.323766	+	0.946137i	$0.604949\pi$
$620$	−9.55691	−0.383815
$621$	−13.2311	−0.530946
$622$	23.4396	0.939844
$623$	0	0
$624$	−2.11727	−0.0847585
$625$	1.00000	0.0400000
$626$	−9.36984	−0.374494
$627$	9.82066	0.392199
$628$	5.50172	0.219542
$629$	−27.6121	−1.10097
$630$	0	0
$631$	13.8827	0.552663	0.276331	−	0.961062i	$-0.410881\pi$
$631$	13.8827	0.552663	0.276331	+	0.961062i	$0.410881\pi$
$632$	8.36641	0.332798
$633$	51.9862	2.06627
$634$	−9.97852	−0.396298
$635$	5.88273	0.233449
$636$	−10.6776	−0.423395
$637$	0	0
$638$	8.74742	0.346314
$639$	−30.0881	−1.19026
$640$	−1.00000	−0.0395285
$641$	−39.3415	−1.55390	−0.776948	−	0.629565i	$-0.783233\pi$
$641$	−39.3415	−1.55390	−0.776948	+	0.629565i	$0.783233\pi$
$642$	−32.7328	−1.29186
$643$	−38.3595	−1.51275	−0.756376	−	0.654137i	$-0.773032\pi$
$643$	−38.3595	−1.51275	−0.756376	+	0.654137i	$0.773032\pi$
$644$	0	0
$645$	−17.2603	−0.679624
$646$	−28.3741	−1.11637
$647$	−25.7294	−1.01153	−0.505763	−	0.862672i	$-0.668789\pi$
$647$	−25.7294	−1.01153	−0.505763	+	0.862672i	$0.668789\pi$
$648$	−10.9379	−0.429682
$649$	1.88273	0.0739038
$650$	−0.941367	−0.0369234
$651$	0	0
$652$	−18.2277	−0.713850
$653$	18.4768	0.723053	0.361526	−	0.932362i	$-0.382256\pi$
$653$	18.4768	0.723053	0.361526	+	0.932362i	$0.382256\pi$
$654$	−0.560352	−0.0219115
$655$	−1.25258	−0.0489423
$656$	2.13187	0.0832357
$657$	21.6121	0.843169
$658$	0	0
$659$	−39.3776	−1.53393	−0.766966	−	0.641687i	$-0.778235\pi$
$659$	−39.3776	−1.53393	−0.766966	+	0.641687i	$0.778235\pi$
$660$	−2.24914	−0.0875477
$661$	34.2208	1.33103	0.665517	−	0.746383i	$-0.268211\pi$
$661$	34.2208	1.33103	0.665517	+	0.746383i	$0.268211\pi$
$662$	−20.4362	−0.794276
$663$	13.7586	0.534339
$664$	8.49828	0.329797
$665$	0	0
$666$	8.74742	0.338956
$667$	54.6639	2.11659
$668$	8.00000	0.309529
$669$	−23.3484	−0.902700
$670$	−12.9966	−0.502101
$671$	−9.11383	−0.351835
$672$	0	0
$673$	−24.4622	−0.942948	−0.471474	−	0.881880i	$-0.656278\pi$
$673$	−24.4622	−0.942948	−0.471474	+	0.881880i	$0.656278\pi$
$674$	7.88273	0.303632
$675$	−2.11727	−0.0814936
$676$	−12.1138	−0.465916
$677$	39.1070	1.50300	0.751501	−	0.659732i	$-0.229330\pi$
$677$	39.1070	1.50300	0.751501	+	0.659732i	$0.229330\pi$
$678$	24.7328	0.949858
$679$	0	0
$680$	6.49828	0.249198
$681$	−36.2345	−1.38851
$682$	9.55691	0.365953
$683$	23.3776	0.894518	0.447259	−	0.894404i	$-0.352400\pi$
$683$	23.3776	0.894518	0.447259	+	0.894404i	$0.352400\pi$
$684$	8.98883	0.343697
$685$	−10.0000	−0.382080
$686$	0	0
$687$	−54.6310	−2.08430
$688$	7.67418	0.292575
$689$	4.46907	0.170258
$690$	−14.0552	−0.535072
$691$	−8.49828	−0.323290	−0.161645	−	0.986849i	$-0.551680\pi$
$691$	−8.49828	−0.323290	−0.161645	+	0.986849i	$0.551680\pi$
$692$	−0.117266	−0.00445780
$693$	0	0
$694$	13.5569	0.514613
$695$	10.9820	0.416569
$696$	19.6742	0.745748
$697$	−13.8535	−0.524739
$698$	10.7328	0.406243
$699$	15.4880	0.585809
$700$	0	0
$701$	14.9751	0.565601	0.282800	−	0.959179i	$-0.408737\pi$
$701$	14.9751	0.565601	0.282800	+	0.959179i	$0.408737\pi$
$702$	1.99312	0.0752256
$703$	18.5535	0.699758
$704$	1.00000	0.0376889
$705$	24.9966	0.941425
$706$	20.8578	0.784994
$707$	0	0
$708$	4.23453	0.159143
$709$	40.7259	1.52949	0.764747	−	0.644330i	$-0.222864\pi$
$709$	40.7259	1.52949	0.764747	+	0.644330i	$0.222864\pi$
$710$	14.6155	0.548512
$711$	17.2234	0.645927
$712$	−12.3810	−0.463998
$713$	59.7225	2.23663
$714$	0	0
$715$	0.941367	0.0352051
$716$	−22.5535	−0.842863
$717$	−25.0449	−0.935318
$718$	0.366407	0.0136742
$719$	8.00000	0.298350	0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000	0.298350	0.149175	+	0.988811i	$0.452338\pi$
$720$	−2.05863	−0.0767207
$721$	0	0
$722$	0.0655089	0.00243799
$723$	−5.32238	−0.197942
$724$	−20.8793	−0.775973
$725$	8.74742	0.324871
$726$	2.24914	0.0834734
$727$	51.6413	1.91527	0.957635	−	0.287984i	$-0.0929848\pi$
$727$	51.6413	1.91527	0.957635	+	0.287984i	$0.0929848\pi$
$728$	0	0
$729$	−8.23109	−0.304855
$730$	−10.4983	−0.388559
$731$	−49.8690	−1.84447
$732$	−20.4983	−0.757638
$733$	42.0000	1.55131	0.775653	−	0.631160i	$-0.217421\pi$
$733$	42.0000	1.55131	0.775653	+	0.631160i	$0.217421\pi$
$734$	−20.8432	−0.769337
$735$	0	0
$736$	6.24914	0.230346
$737$	12.9966	0.478735
$738$	4.38875	0.161552
$739$	−49.1070	−1.80643	−0.903214	−	0.429190i	$-0.858799\pi$
$739$	−49.1070	−1.80643	−0.903214	+	0.429190i	$0.858799\pi$
$740$	−4.24914	−0.156202
$741$	−9.24485	−0.339618
$742$	0	0
$743$	−53.2311	−1.95286	−0.976430	−	0.215836i	$-0.930752\pi$
$743$	−53.2311	−1.95286	−0.976430	+	0.215836i	$0.930752\pi$
$744$	21.4948	0.788039
$745$	−0.0146079	−0.000535192 0
$746$	−5.37758	−0.196887
$747$	17.4948	0.640103
$748$	−6.49828	−0.237601
$749$	0	0
$750$	−2.24914	−0.0821270
$751$	−31.6121	−1.15354	−0.576771	−	0.816906i	$-0.695688\pi$
$751$	−31.6121	−1.15354	−0.576771	+	0.816906i	$0.695688\pi$
$752$	−11.1138	−0.405280
$753$	−56.4691	−2.05785
$754$	−8.23453	−0.299884
$755$	15.2457	0.554848
$756$	0	0
$757$	−1.24570	−0.0452758	−0.0226379	−	0.999744i	$-0.507206\pi$
$757$	−1.24570	−0.0452758	−0.0226379	+	0.999744i	$0.507206\pi$
$758$	3.53093	0.128249
$759$	14.0552	0.510171
$760$	−4.36641	−0.158386
$761$	10.6009	0.384284	0.192142	−	0.981367i	$-0.438457\pi$
$761$	10.6009	0.384284	0.192142	+	0.981367i	$0.438457\pi$
$762$	−13.2311	−0.479312
$763$	0	0
$764$	3.11383	0.112654
$765$	13.3776	0.483667
$766$	−1.38445	−0.0500223
$767$	−1.77234	−0.0639956
$768$	2.24914	0.0811589
$769$	19.1284	0.689789	0.344895	−	0.938641i	$-0.387915\pi$
$769$	19.1284	0.689789	0.344895	+	0.938641i	$0.387915\pi$
$770$	0	0
$771$	6.44309	0.232042
$772$	−6.17246	−0.222152
$773$	−39.9931	−1.43845	−0.719226	−	0.694776i	$-0.755504\pi$
$773$	−39.9931	−1.43845	−0.719226	+	0.694776i	$0.755504\pi$
$774$	15.7983	0.567859
$775$	9.55691	0.343294
$776$	15.3630	0.551498
$777$	0	0
$778$	15.7294	0.563925
$779$	9.30863	0.333516
$780$	2.11727	0.0758103
$781$	−14.6155	−0.522985
$782$	−40.6087	−1.45216
$783$	−18.5206	−0.661873
$784$	0	0
$785$	−5.50172	−0.196365
$786$	2.81722	0.100487
$787$	−37.9931	−1.35431	−0.677154	−	0.735841i	$-0.736787\pi$
$787$	−37.9931	−1.35431	−0.677154	+	0.735841i	$0.736787\pi$
$788$	6.73281	0.239847
$789$	8.46907	0.301507
$790$	−8.36641	−0.297663
$791$	0	0
$792$	2.05863	0.0731503
$793$	8.57946	0.304665
$794$	17.6121	0.625030
$795$	10.6776	0.378696
$796$	13.2311	0.468964
$797$	20.3810	0.721933	0.360966	−	0.932579i	$-0.382447\pi$
$797$	20.3810	0.721933	0.360966	+	0.932579i	$0.382447\pi$
$798$	0	0
$799$	72.2208	2.55499
$800$	1.00000	0.0353553
$801$	−25.4880	−0.900573
$802$	−32.8172	−1.15882
$803$	10.4983	0.370476
$804$	29.2311	1.03090
$805$	0	0
$806$	−8.99656	−0.316890
$807$	−20.1104	−0.707919
$808$	16.8793	0.593812
$809$	−31.7294	−1.11555	−0.557773	−	0.829994i	$-0.688344\pi$
$809$	−31.7294	−1.11555	−0.557773	+	0.829994i	$0.688344\pi$
$810$	10.9379	0.384320
$811$	−43.5095	−1.52782	−0.763912	−	0.645321i	$-0.776724\pi$
$811$	−43.5095	−1.52782	−0.763912	+	0.645321i	$0.776724\pi$
$812$	0	0
$813$	−48.3449	−1.69553
$814$	4.24914	0.148932
$815$	18.2277	0.638487
$816$	−14.6155	−0.511646
$817$	33.5086	1.17232
$818$	33.3561	1.16627
$819$	0	0
$820$	−2.13187	−0.0744483
$821$	−24.7766	−0.864711	−0.432355	−	0.901703i	$-0.642317\pi$
$821$	−24.7766	−0.864711	−0.432355	+	0.901703i	$0.642317\pi$
$822$	22.4914	0.784478
$823$	28.8647	1.00616	0.503080	−	0.864240i	$-0.332200\pi$
$823$	28.8647	1.00616	0.503080	+	0.864240i	$0.332200\pi$
$824$	6.61555	0.230464
$825$	2.24914	0.0783050
$826$	0	0
$827$	34.2277	1.19021	0.595106	−	0.803647i	$-0.297110\pi$
$827$	34.2277	1.19021	0.595106	+	0.803647i	$0.297110\pi$
$828$	12.8647	0.447079
$829$	−23.6381	−0.820985	−0.410492	−	0.911864i	$-0.634643\pi$
$829$	−23.6381	−0.820985	−0.410492	+	0.911864i	$0.634643\pi$
$830$	−8.49828	−0.294980
$831$	17.2019	0.596727
$832$	−0.941367	−0.0326360
$833$	0	0
$834$	−24.7000	−0.855290
$835$	−8.00000	−0.276851
$836$	4.36641	0.151015
$837$	−20.2345	−0.699408
$838$	−12.3449	−0.426448
$839$	24.9053	0.859826	0.429913	−	0.902870i	$-0.358544\pi$
$839$	24.9053	0.859826	0.429913	+	0.902870i	$0.358544\pi$
$840$	0	0
$841$	47.5174	1.63853
$842$	−8.87930	−0.306001
$843$	−64.3604	−2.21669
$844$	23.1138	0.795611
$845$	12.1138	0.416728
$846$	−22.8793	−0.786606
$847$	0	0
$848$	−4.74742	−0.163027
$849$	6.47594	0.222254
$850$	−6.49828	−0.222889
$851$	26.5535	0.910241
$852$	−32.8724	−1.12619
$853$	−22.9966	−0.787387	−0.393694	−	0.919242i	$-0.628803\pi$
$853$	−22.9966	−0.787387	−0.393694	+	0.919242i	$0.628803\pi$
$854$	0	0
$855$	−8.98883	−0.307411
$856$	−14.5535	−0.497428
$857$	31.2603	1.06783	0.533916	−	0.845538i	$-0.320720\pi$
$857$	31.2603	1.06783	0.533916	+	0.845538i	$0.320720\pi$
$858$	−2.11727	−0.0722823
$859$	−20.3449	−0.694160	−0.347080	−	0.937836i	$-0.612827\pi$
$859$	−20.3449	−0.694160	−0.347080	+	0.937836i	$0.612827\pi$
$860$	−7.67418	−0.261687
$861$	0	0
$862$	18.2784	0.622563
$863$	−58.3595	−1.98658	−0.993291	−	0.115644i	$-0.963107\pi$
$863$	−58.3595	−1.98658	−0.993291	+	0.115644i	$0.963107\pi$
$864$	−2.11727	−0.0720309
$865$	0.117266	0.00398717
$866$	−6.86469	−0.233272
$867$	56.7405	1.92701
$868$	0	0
$869$	8.36641	0.283811
$870$	−19.6742	−0.667017
$871$	−12.2345	−0.414551
$872$	−0.249141	−0.00843696
$873$	31.6267	1.07040
$874$	27.2863	0.922973
$875$	0	0
$876$	23.6121	0.797779
$877$	11.9639	0.403992	0.201996	−	0.979386i	$-0.435257\pi$
$877$	11.9639	0.403992	0.201996	+	0.979386i	$0.435257\pi$
$878$	11.8466	0.399805
$879$	29.1070	0.981753
$880$	−1.00000	−0.0337100
$881$	−5.88961	−0.198426	−0.0992130	−	0.995066i	$-0.531633\pi$
$881$	−5.88961	−0.198426	−0.0992130	+	0.995066i	$0.531633\pi$
$882$	0	0
$883$	−19.4880	−0.655822	−0.327911	−	0.944709i	$-0.606345\pi$
$883$	−19.4880	−0.655822	−0.327911	+	0.944709i	$0.606345\pi$
$884$	6.11727	0.205746
$885$	−4.23453	−0.142342
$886$	17.8827	0.600782
$887$	−50.4622	−1.69435	−0.847177	−	0.531310i	$-0.821700\pi$
$887$	−50.4622	−1.69435	−0.847177	+	0.531310i	$0.821700\pi$
$888$	9.55691	0.320709
$889$	0	0
$890$	12.3810	0.415013
$891$	−10.9379	−0.366434
$892$	−10.3810	−0.347582
$893$	−48.5275	−1.62391
$894$	0.0328552	0.00109884
$895$	22.5535	0.753880
$896$	0	0
$897$	−13.2311	−0.441773
$898$	−16.8172	−0.561198
$899$	83.5984	2.78816
$900$	2.05863	0.0686211
$901$	30.8501	1.02777
$902$	2.13187	0.0709836
$903$	0	0
$904$	10.9966	0.365740
$905$	20.8793	0.694051
$906$	−34.2897	−1.13920
$907$	−16.8432	−0.559269	−0.279635	−	0.960106i	$-0.590213\pi$
$907$	−16.8432	−0.559269	−0.279635	+	0.960106i	$0.590213\pi$
$908$	−16.1104	−0.534642
$909$	34.7483	1.15253
$910$	0	0
$911$	−38.6155	−1.27939	−0.639695	−	0.768629i	$-0.720939\pi$
$911$	−38.6155	−1.27939	−0.639695	+	0.768629i	$0.720939\pi$
$912$	9.82066	0.325195
$913$	8.49828	0.281252
$914$	−12.2277	−0.404455
$915$	20.4983	0.677652
$916$	−24.2897	−0.802555
$917$	0	0
$918$	13.7586	0.454101
$919$	17.2818	0.570074	0.285037	−	0.958517i	$-0.407994\pi$
$919$	17.2818	0.570074	0.285037	+	0.958517i	$0.407994\pi$
$920$	−6.24914	−0.206028
$921$	−1.12070	−0.0369285
$922$	16.6155	0.547204
$923$	13.7586	0.452870
$924$	0	0
$925$	4.24914	0.139711
$926$	18.4837	0.607411
$927$	13.6190	0.447306
$928$	8.74742	0.287148
$929$	−2.91539	−0.0956508	−0.0478254	−	0.998856i	$-0.515229\pi$
$929$	−2.91539	−0.0956508	−0.0478254	+	0.998856i	$0.515229\pi$
$930$	−21.4948	−0.704844
$931$	0	0
$932$	6.88617	0.225564
$933$	52.7191	1.72594
$934$	−24.3956	−0.798249
$935$	6.49828	0.212517
$936$	−1.93793	−0.0633432
$937$	−22.5795	−0.737639	−0.368819	−	0.929501i	$-0.620238\pi$
$937$	−22.5795	−0.737639	−0.368819	+	0.929501i	$0.620238\pi$
$938$	0	0
$939$	−21.0741	−0.687727
$940$	11.1138	0.362493
$941$	21.7655	0.709534	0.354767	−	0.934955i	$-0.384560\pi$
$941$	21.7655	0.709534	0.354767	+	0.934955i	$0.384560\pi$
$942$	12.3741	0.403171
$943$	13.3224	0.433836
$944$	1.88273	0.0612778
$945$	0	0
$946$	7.67418	0.249509
$947$	−1.49484	−0.0485759	−0.0242879	−	0.999705i	$-0.507732\pi$
$947$	−1.49484	−0.0485759	−0.0242879	+	0.999705i	$0.507732\pi$
$948$	18.8172	0.611155
$949$	−9.88273	−0.320807
$950$	4.36641	0.141665
$951$	−22.4431	−0.727767
$952$	0	0
$953$	−4.83098	−0.156491	−0.0782453	−	0.996934i	$-0.524932\pi$
$953$	−4.83098	−0.156491	−0.0782453	+	0.996934i	$0.524932\pi$
$954$	−9.77320	−0.316419
$955$	−3.11383	−0.100761
$956$	−11.1353	−0.360142
$957$	19.6742	0.635976
$958$	27.7655	0.897062
$959$	0	0
$960$	−2.24914	−0.0725907
$961$	60.3346	1.94628
$962$	−4.00000	−0.128965
$963$	−29.9603	−0.965456
$964$	−2.36641	−0.0762168
$965$	6.17246	0.198699
$966$	0	0
$967$	−51.9278	−1.66989	−0.834943	−	0.550336i	$-0.814499\pi$
$967$	−51.9278	−1.66989	−0.834943	+	0.550336i	$0.814499\pi$
$968$	1.00000	0.0321412
$969$	−63.8174	−2.05011
$970$	−15.3630	−0.493275
$971$	−59.6933	−1.91565	−0.957824	−	0.287354i	$-0.907224\pi$
$971$	−59.6933	−1.91565	−0.957824	+	0.287354i	$0.907224\pi$
$972$	−18.2491	−0.585341
$973$	0	0
$974$	10.0958	0.323490
$975$	−2.11727	−0.0678068
$976$	−9.11383	−0.291727
$977$	31.2311	0.999171	0.499586	−	0.866265i	$-0.333486\pi$
$977$	31.2311	0.999171	0.499586	+	0.866265i	$0.333486\pi$
$978$	−40.9966	−1.31093
$979$	−12.3810	−0.395699
$980$	0	0
$981$	−0.512889	−0.0163753
$982$	−32.1104	−1.02468
$983$	22.6155	0.721324	0.360662	−	0.932697i	$-0.382551\pi$
$983$	22.6155	0.721324	0.360662	+	0.932697i	$0.382551\pi$
$984$	4.79488	0.152855
$985$	−6.73281	−0.214525
$986$	−56.8432	−1.81026
$987$	0	0
$988$	−4.11039	−0.130769
$989$	47.9570	1.52494
$990$	−2.05863	−0.0654277
$991$	22.4102	0.711884	0.355942	−	0.934508i	$-0.384160\pi$
$991$	22.4102	0.711884	0.355942	+	0.934508i	$0.384160\pi$
$992$	9.55691	0.303432
$993$	−45.9639	−1.45862
$994$	0	0
$995$	−13.2311	−0.419454
$996$	19.1138	0.605645
$997$	27.3415	0.865914	0.432957	−	0.901415i	$-0.357470\pi$
$997$	27.3415	0.865914	0.432957	+	0.901415i	$0.357470\pi$
$998$	−8.79488	−0.278397
$999$	−8.99656	−0.284639

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5390.2.a.ca.1.3		3
7.6	odd	2		770.2.a.m.1.1	✓	3
21.20	even	2		6930.2.a.ce.1.2		3
28.27	even	2		6160.2.a.bf.1.3		3
35.13	even	4		3850.2.c.ba.1849.1		6
35.27	even	4		3850.2.c.ba.1849.6		6
35.34	odd	2		3850.2.a.bt.1.3		3
77.76	even	2		8470.2.a.ci.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.m.1.1	✓	3	7.6	odd	2
3850.2.a.bt.1.3		3	35.34	odd	2
3850.2.c.ba.1849.1		6	35.13	even	4
3850.2.c.ba.1849.6		6	35.27	even	4
5390.2.a.ca.1.3		3	1.1	even	1	trivial
6160.2.a.bf.1.3		3	28.27	even	2
6930.2.a.ce.1.2		3	21.20	even	2
8470.2.a.ci.1.1		3	77.76	even	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:	\( N \)	\(=\)	\( 5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5390.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.24914 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.24914 q^{6} +1.00000 q^{8} +2.05863 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.24914 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.24914 q^{6} +1.00000 q^{8} +2.05863 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.24914 q^{12} -0.941367 q^{13} -2.24914 q^{15} +1.00000 q^{16} -6.49828 q^{17} +2.05863 q^{18} +4.36641 q^{19} -1.00000 q^{20} +1.00000 q^{22} +6.24914 q^{23} +2.24914 q^{24} +1.00000 q^{25} -0.941367 q^{26} -2.11727 q^{27} +8.74742 q^{29} -2.24914 q^{30} +9.55691 q^{31} +1.00000 q^{32} +2.24914 q^{33} -6.49828 q^{34} +2.05863 q^{36} +4.24914 q^{37} +4.36641 q^{38} -2.11727 q^{39} -1.00000 q^{40} +2.13187 q^{41} +7.67418 q^{43} +1.00000 q^{44} -2.05863 q^{45} +6.24914 q^{46} -11.1138 q^{47} +2.24914 q^{48} +1.00000 q^{50} -14.6155 q^{51} -0.941367 q^{52} -4.74742 q^{53} -2.11727 q^{54} -1.00000 q^{55} +9.82066 q^{57} +8.74742 q^{58} +1.88273 q^{59} -2.24914 q^{60} -9.11383 q^{61} +9.55691 q^{62} +1.00000 q^{64} +0.941367 q^{65} +2.24914 q^{66} +12.9966 q^{67} -6.49828 q^{68} +14.0552 q^{69} -14.6155 q^{71} +2.05863 q^{72} +10.4983 q^{73} +4.24914 q^{74} +2.24914 q^{75} +4.36641 q^{76} -2.11727 q^{78} +8.36641 q^{79} -1.00000 q^{80} -10.9379 q^{81} +2.13187 q^{82} +8.49828 q^{83} +6.49828 q^{85} +7.67418 q^{86} +19.6742 q^{87} +1.00000 q^{88} -12.3810 q^{89} -2.05863 q^{90} +6.24914 q^{92} +21.4948 q^{93} -11.1138 q^{94} -4.36641 q^{95} +2.24914 q^{96} +15.3630 q^{97} +2.05863 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} - 2 q^{6} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 - 3 * q^5 - 2 * q^6 + 3 * q^8 + 7 * q^9	\( 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} - 2 q^{6} + 3 q^{8} + 7 q^{9} - 3 q^{10} + 3 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{15} + 3 q^{16} - 2 q^{17} + 7 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{22} + 10 q^{23} - 2 q^{24} + 3 q^{25} - 2 q^{26} - 8 q^{27} + 2 q^{30} + 12 q^{31} + 3 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{36} + 4 q^{37} + 6 q^{38} - 8 q^{39} - 3 q^{40} - 4 q^{41} + 8 q^{43} + 3 q^{44} - 7 q^{45} + 10 q^{46} - 2 q^{48} + 3 q^{50} - 28 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 3 q^{55} - 8 q^{57} + 4 q^{59} + 2 q^{60} + 6 q^{61} + 12 q^{62} + 3 q^{64} + 2 q^{65} - 2 q^{66} + 4 q^{67} - 2 q^{68} + 8 q^{69} - 28 q^{71} + 7 q^{72} + 14 q^{73} + 4 q^{74} - 2 q^{75} + 6 q^{76} - 8 q^{78} + 18 q^{79} - 3 q^{80} + 3 q^{81} - 4 q^{82} + 8 q^{83} + 2 q^{85} + 8 q^{86} + 44 q^{87} + 3 q^{88} - 18 q^{89} - 7 q^{90} + 10 q^{92} + 12 q^{93} - 6 q^{95} - 2 q^{96} + 4 q^{97} + 7 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 - 3 * q^5 - 2 * q^6 + 3 * q^8 + 7 * q^9 - 3 * q^10 + 3 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^15 + 3 * q^16 - 2 * q^17 + 7 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^22 + 10 * q^23 - 2 * q^24 + 3 * q^25 - 2 * q^26 - 8 * q^27 + 2 * q^30 + 12 * q^31 + 3 * q^32 - 2 * q^33 - 2 * q^34 + 7 * q^36 + 4 * q^37 + 6 * q^38 - 8 * q^39 - 3 * q^40 - 4 * q^41 + 8 * q^43 + 3 * q^44 - 7 * q^45 + 10 * q^46 - 2 * q^48 + 3 * q^50 - 28 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 3 * q^55 - 8 * q^57 + 4 * q^59 + 2 * q^60 + 6 * q^61 + 12 * q^62 + 3 * q^64 + 2 * q^65 - 2 * q^66 + 4 * q^67 - 2 * q^68 + 8 * q^69 - 28 * q^71 + 7 * q^72 + 14 * q^73 + 4 * q^74 - 2 * q^75 + 6 * q^76 - 8 * q^78 + 18 * q^79 - 3 * q^80 + 3 * q^81 - 4 * q^82 + 8 * q^83 + 2 * q^85 + 8 * q^86 + 44 * q^87 + 3 * q^88 - 18 * q^89 - 7 * q^90 + 10 * q^92 + 12 * q^93 - 6 * q^95 - 2 * q^96 + 4 * q^97 + 7 * q^99

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