LMFDB - Embedded newform 5390.2.a.ca.1.1

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			1.1
Root			$-1.81361$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.10278 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.10278 q^{6} +1.00000 q^{8} +6.62721 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.10278 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.10278 q^{6} +1.00000 q^{8} +6.62721 q^{9} -1.00000 q^{10} +1.00000 q^{11} -3.10278 q^{12} +3.62721 q^{13} +3.10278 q^{15} +1.00000 q^{16} +4.20555 q^{17} +6.62721 q^{18} +8.15165 q^{19} -1.00000 q^{20} +1.00000 q^{22} +0.897225 q^{23} -3.10278 q^{24} +1.00000 q^{25} +3.62721 q^{26} -11.2544 q^{27} -7.30833 q^{29} +3.10278 q^{30} +3.42166 q^{31} +1.00000 q^{32} -3.10278 q^{33} +4.20555 q^{34} +6.62721 q^{36} -1.10278 q^{37} +8.15165 q^{38} -11.2544 q^{39} -1.00000 q^{40} -12.3572 q^{41} +10.6761 q^{43} +1.00000 q^{44} -6.62721 q^{45} +0.897225 q^{46} +1.15667 q^{47} -3.10278 q^{48} +1.00000 q^{50} -13.0489 q^{51} +3.62721 q^{52} +11.3083 q^{53} -11.2544 q^{54} -1.00000 q^{55} -25.2927 q^{57} -7.30833 q^{58} -7.25443 q^{59} +3.10278 q^{60} +3.15667 q^{61} +3.42166 q^{62} +1.00000 q^{64} -3.62721 q^{65} -3.10278 q^{66} -8.41110 q^{67} +4.20555 q^{68} -2.78389 q^{69} -13.0489 q^{71} +6.62721 q^{72} -0.205550 q^{73} -1.10278 q^{74} -3.10278 q^{75} +8.15165 q^{76} -11.2544 q^{78} +12.1517 q^{79} -1.00000 q^{80} +15.0383 q^{81} -12.3572 q^{82} -2.20555 q^{83} -4.20555 q^{85} +10.6761 q^{86} +22.6761 q^{87} +1.00000 q^{88} +7.45998 q^{89} -6.62721 q^{90} +0.897225 q^{92} -10.6167 q^{93} +1.15667 q^{94} -8.15165 q^{95} -3.10278 q^{96} -2.25945 q^{97} +6.62721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.10278	−1.79139	−0.895694	−	0.444671i	$-0.853321\pi$
$3$	−3.10278	−1.79139	−0.895694	+	0.444671i	$0.853321\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.10278	−1.26670
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	6.62721	2.20907
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.10278	−0.895694
$13$	3.62721	1.00601	0.503004	−	0.864284i	$-0.332228\pi$
$13$	3.62721	1.00601	0.503004	+	0.864284i	$0.332228\pi$
$14$	0	0
$15$	3.10278	0.801133
$16$	1.00000	0.250000
$17$	4.20555	1.02000	0.509998	−	0.860176i	$-0.329646\pi$
$17$	4.20555	1.02000	0.509998	+	0.860176i	$0.329646\pi$
$18$	6.62721	1.56205
$19$	8.15165	1.87012	0.935058	−	0.354493i	$-0.115347\pi$
$19$	8.15165	1.87012	0.935058	+	0.354493i	$0.115347\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	1.00000	0.213201
$23$	0.897225	0.187084	0.0935422	−	0.995615i	$-0.470181\pi$
$23$	0.897225	0.187084	0.0935422	+	0.995615i	$0.470181\pi$
$24$	−3.10278	−0.633351
$25$	1.00000	0.200000
$26$	3.62721	0.711355
$27$	−11.2544	−2.16592
$28$	0	0
$29$	−7.30833	−1.35712	−0.678561	−	0.734544i	$-0.737396\pi$
$29$	−7.30833	−1.35712	−0.678561	+	0.734544i	$0.737396\pi$
$30$	3.10278	0.566487
$31$	3.42166	0.614549	0.307274	−	0.951621i	$-0.400583\pi$
$31$	3.42166	0.614549	0.307274	+	0.951621i	$0.400583\pi$
$32$	1.00000	0.176777
$33$	−3.10278	−0.540124
$34$	4.20555	0.721246
$35$	0	0
$36$	6.62721	1.10454
$37$	−1.10278	−0.181295	−0.0906476	−	0.995883i	$-0.528894\pi$
$37$	−1.10278	−0.181295	−0.0906476	+	0.995883i	$0.528894\pi$
$38$	8.15165	1.32237
$39$	−11.2544	−1.80215
$40$	−1.00000	−0.158114
$41$	−12.3572	−1.92987	−0.964935	−	0.262488i	$-0.915457\pi$
$41$	−12.3572	−1.92987	−0.964935	+	0.262488i	$0.915457\pi$
$42$	0	0
$43$	10.6761	1.62809	0.814044	−	0.580803i	$-0.197261\pi$
$43$	10.6761	1.62809	0.814044	+	0.580803i	$0.197261\pi$
$44$	1.00000	0.150756
$45$	−6.62721	−0.987927
$46$	0.897225	0.132289
$47$	1.15667	0.168718	0.0843591	−	0.996435i	$-0.473116\pi$
$47$	1.15667	0.168718	0.0843591	+	0.996435i	$0.473116\pi$
$48$	−3.10278	−0.447847
$49$	0	0
$50$	1.00000	0.141421
$51$	−13.0489	−1.82721
$52$	3.62721	0.503004
$53$	11.3083	1.55332	0.776659	−	0.629921i	$-0.216913\pi$
$53$	11.3083	1.55332	0.776659	+	0.629921i	$0.216913\pi$
$54$	−11.2544	−1.53153
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−25.2927	−3.35011
$58$	−7.30833	−0.959630
$59$	−7.25443	−0.944446	−0.472223	−	0.881479i	$-0.656548\pi$
$59$	−7.25443	−0.944446	−0.472223	+	0.881479i	$0.656548\pi$
$60$	3.10278	0.400567
$61$	3.15667	0.404171	0.202085	−	0.979368i	$-0.435228\pi$
$61$	3.15667	0.404171	0.202085	+	0.979368i	$0.435228\pi$
$62$	3.42166	0.434552
$63$	0	0
$64$	1.00000	0.125000
$65$	−3.62721	−0.449900
$66$	−3.10278	−0.381925
$67$	−8.41110	−1.02758	−0.513790	−	0.857916i	$-0.671759\pi$
$67$	−8.41110	−1.02758	−0.513790	+	0.857916i	$0.671759\pi$
$68$	4.20555	0.509998
$69$	−2.78389	−0.335141
$70$	0	0
$71$	−13.0489	−1.54862	−0.774308	−	0.632809i	$-0.781902\pi$
$71$	−13.0489	−1.54862	−0.774308	+	0.632809i	$0.781902\pi$
$72$	6.62721	0.781025
$73$	−0.205550	−0.0240578	−0.0120289	−	0.999928i	$-0.503829\pi$
$73$	−0.205550	−0.0240578	−0.0120289	+	0.999928i	$0.503829\pi$
$74$	−1.10278	−0.128195
$75$	−3.10278	−0.358278
$76$	8.15165	0.935058
$77$	0	0
$78$	−11.2544	−1.27431
$79$	12.1517	1.36717	0.683584	−	0.729872i	$-0.260420\pi$
$79$	12.1517	1.36717	0.683584	+	0.729872i	$0.260420\pi$
$80$	−1.00000	−0.111803
$81$	15.0383	1.67092
$82$	−12.3572	−1.36462
$83$	−2.20555	−0.242091	−0.121045	−	0.992647i	$-0.538625\pi$
$83$	−2.20555	−0.242091	−0.121045	+	0.992647i	$0.538625\pi$
$84$	0	0
$85$	−4.20555	−0.456156
$86$	10.6761	1.15123
$87$	22.6761	2.43113
$88$	1.00000	0.106600
$89$	7.45998	0.790756	0.395378	−	0.918519i	$-0.370614\pi$
$89$	7.45998	0.790756	0.395378	+	0.918519i	$0.370614\pi$
$90$	−6.62721	−0.698570
$91$	0	0
$92$	0.897225	0.0935422
$93$	−10.6167	−1.10090
$94$	1.15667	0.119302
$95$	−8.15165	−0.836342
$96$	−3.10278	−0.316676
$97$	−2.25945	−0.229412	−0.114706	−	0.993399i	$-0.536593\pi$
$97$	−2.25945	−0.229412	−0.114706	+	0.993399i	$0.536593\pi$
$98$	0	0
$99$	6.62721	0.666060
$100$	1.00000	0.100000
$101$	−13.6655	−1.35977	−0.679885	−	0.733318i	$-0.737970\pi$
$101$	−13.6655	−1.35977	−0.679885	+	0.733318i	$0.737970\pi$
$102$	−13.0489	−1.29203
$103$	5.04888	0.497481	0.248740	−	0.968570i	$-0.419983\pi$
$103$	5.04888	0.497481	0.248740	+	0.968570i	$0.419983\pi$
$104$	3.62721	0.355677
$105$	0	0
$106$	11.3083	1.09836
$107$	12.9894	1.25574	0.627868	−	0.778320i	$-0.283928\pi$
$107$	12.9894	1.25574	0.627868	+	0.778320i	$0.283928\pi$
$108$	−11.2544	−1.08296
$109$	5.10278	0.488757	0.244379	−	0.969680i	$-0.421416\pi$
$109$	5.10278	0.488757	0.244379	+	0.969680i	$0.421416\pi$
$110$	−1.00000	−0.0953463
$111$	3.42166	0.324770
$112$	0	0
$113$	−10.4111	−0.979394	−0.489697	−	0.871893i	$-0.662893\pi$
$113$	−10.4111	−0.979394	−0.489697	+	0.871893i	$0.662893\pi$
$114$	−25.2927	−2.36888
$115$	−0.897225	−0.0836667
$116$	−7.30833	−0.678561
$117$	24.0383	2.22234
$118$	−7.25443	−0.667824
$119$	0	0
$120$	3.10278	0.283243
$121$	1.00000	0.0909091
$122$	3.15667	0.285792
$123$	38.3416	3.45715
$124$	3.42166	0.307274
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	3.25443	0.288784	0.144392	−	0.989521i	$-0.453877\pi$
$127$	3.25443	0.288784	0.144392	+	0.989521i	$0.453877\pi$
$128$	1.00000	0.0883883
$129$	−33.1255	−2.91654
$130$	−3.62721	−0.318128
$131$	17.3083	1.51224	0.756118	−	0.654436i	$-0.227094\pi$
$131$	17.3083	1.51224	0.756118	+	0.654436i	$0.227094\pi$
$132$	−3.10278	−0.270062
$133$	0	0
$134$	−8.41110	−0.726608
$135$	11.2544	0.968627
$136$	4.20555	0.360623
$137$	10.0000	0.854358	0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000	0.854358	0.427179	+	0.904167i	$0.359507\pi$
$138$	−2.78389	−0.236980
$139$	−13.2005	−1.11965	−0.559827	−	0.828609i	$-0.689132\pi$
$139$	−13.2005	−1.11965	−0.559827	+	0.828609i	$0.689132\pi$
$140$	0	0
$141$	−3.58890	−0.302240
$142$	−13.0489	−1.09504
$143$	3.62721	0.303323
$144$	6.62721	0.552268
$145$	7.30833	0.606923
$146$	−0.205550	−0.0170114
$147$	0	0
$148$	−1.10278	−0.0906476
$149$	−23.6116	−1.93434	−0.967170	−	0.254131i	$-0.918211\pi$
$149$	−23.6116	−1.93434	−0.967170	+	0.254131i	$0.918211\pi$
$150$	−3.10278	−0.253341
$151$	11.5139	0.936986	0.468493	−	0.883467i	$-0.344797\pi$
$151$	11.5139	0.936986	0.468493	+	0.883467i	$0.344797\pi$
$152$	8.15165	0.661186
$153$	27.8711	2.25324
$154$	0	0
$155$	−3.42166	−0.274835
$156$	−11.2544	−0.901075
$157$	16.2056	1.29334	0.646672	−	0.762768i	$-0.276160\pi$
$157$	16.2056	1.29334	0.646672	+	0.762768i	$0.276160\pi$
$158$	12.1517	0.966733
$159$	−35.0872	−2.78260
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	15.0383	1.18152
$163$	6.31335	0.494500	0.247250	−	0.968952i	$-0.420473\pi$
$163$	6.31335	0.494500	0.247250	+	0.968952i	$0.420473\pi$
$164$	−12.3572	−0.964935
$165$	3.10278	0.241551
$166$	−2.20555	−0.171184
$167$	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
$169$	0.156674	0.0120519
$170$	−4.20555	−0.322551
$171$	54.0227	4.13122
$172$	10.6761	0.814044
$173$	−9.25443	−0.703601	−0.351800	−	0.936075i	$-0.614430\pi$
$173$	−9.25443	−0.703601	−0.351800	+	0.936075i	$0.614430\pi$
$174$	22.6761	1.71907
$175$	0	0
$176$	1.00000	0.0753778
$177$	22.5089	1.69187
$178$	7.45998	0.559149
$179$	4.98944	0.372928	0.186464	−	0.982462i	$-0.440297\pi$
$179$	4.98944	0.372928	0.186464	+	0.982462i	$0.440297\pi$
$180$	−6.62721	−0.493963
$181$	9.66553	0.718433	0.359216	−	0.933254i	$-0.383044\pi$
$181$	9.66553	0.718433	0.359216	+	0.933254i	$0.383044\pi$
$182$	0	0
$183$	−9.79445	−0.724027
$184$	0.897225	0.0661443
$185$	1.10278	0.0810776
$186$	−10.6167	−0.778451
$187$	4.20555	0.307540
$188$	1.15667	0.0843591
$189$	0	0
$190$	−8.15165	−0.591383
$191$	−9.15667	−0.662554	−0.331277	−	0.943534i	$-0.607479\pi$
$191$	−9.15667	−0.662554	−0.331277	+	0.943534i	$0.607479\pi$
$192$	−3.10278	−0.223924
$193$	1.52946	0.110093	0.0550465	−	0.998484i	$-0.482469\pi$
$193$	1.52946	0.110093	0.0550465	+	0.998484i	$0.482469\pi$
$194$	−2.25945	−0.162219
$195$	11.2544	0.805946
$196$	0	0
$197$	14.3033	1.01907	0.509534	−	0.860451i	$-0.329818\pi$
$197$	14.3033	1.01907	0.509534	+	0.860451i	$0.329818\pi$
$198$	6.62721	0.470976
$199$	10.0978	0.715811	0.357905	−	0.933758i	$-0.383491\pi$
$199$	10.0978	0.715811	0.357905	+	0.933758i	$0.383491\pi$
$200$	1.00000	0.0707107
$201$	26.0978	1.84079
$202$	−13.6655	−0.961503
$203$	0	0
$204$	−13.0489	−0.913604
$205$	12.3572	0.863064
$206$	5.04888	0.351772
$207$	5.94610	0.413283
$208$	3.62721	0.251502
$209$	8.15165	0.563861
$210$	0	0
$211$	10.8433	0.746485	0.373243	−	0.927734i	$-0.378246\pi$
$211$	10.8433	0.746485	0.373243	+	0.927734i	$0.378246\pi$
$212$	11.3083	0.776659
$213$	40.4877	2.77417
$214$	12.9894	0.887940
$215$	−10.6761	−0.728103
$216$	−11.2544	−0.765767
$217$	0	0
$218$	5.10278	0.345604
$219$	0.637776	0.0430969
$220$	−1.00000	−0.0674200
$221$	15.2544	1.02612
$222$	3.42166	0.229647
$223$	9.45998	0.633487	0.316743	−	0.948511i	$-0.397411\pi$
$223$	9.45998	0.633487	0.316743	+	0.948511i	$0.397411\pi$
$224$	0	0
$225$	6.62721	0.441814
$226$	−10.4111	−0.692536
$227$	17.5678	1.16601	0.583007	−	0.812467i	$-0.301876\pi$
$227$	17.5678	1.16601	0.583007	+	0.812467i	$0.301876\pi$
$228$	−25.2927	−1.67505
$229$	−25.7250	−1.69995	−0.849977	−	0.526820i	$-0.823384\pi$
$229$	−25.7250	−1.69995	−0.849977	+	0.526820i	$0.823384\pi$
$230$	−0.897225	−0.0591613
$231$	0	0
$232$	−7.30833	−0.479815
$233$	19.1567	1.25500	0.627498	−	0.778618i	$-0.284079\pi$
$233$	19.1567	1.25500	0.627498	+	0.778618i	$0.284079\pi$
$234$	24.0383	1.57143
$235$	−1.15667	−0.0754531
$236$	−7.25443	−0.472223
$237$	−37.7038	−2.44913
$238$	0	0
$239$	−18.0539	−1.16781	−0.583905	−	0.811822i	$-0.698476\pi$
$239$	−18.0539	−1.16781	−0.583905	+	0.811822i	$0.698476\pi$
$240$	3.10278	0.200283
$241$	−6.15165	−0.396263	−0.198131	−	0.980175i	$-0.563487\pi$
$241$	−6.15165	−0.396263	−0.198131	+	0.980175i	$0.563487\pi$
$242$	1.00000	0.0642824
$243$	−12.8972	−0.827357
$244$	3.15667	0.202085
$245$	0	0
$246$	38.3416	2.44457
$247$	29.5678	1.88135
$248$	3.42166	0.217276
$249$	6.84333	0.433678
$250$	−1.00000	−0.0632456
$251$	29.9789	1.89225	0.946125	−	0.323802i	$-0.104961\pi$
$251$	29.9789	1.89225	0.946125	+	0.323802i	$0.104961\pi$
$252$	0	0
$253$	0.897225	0.0564080
$254$	3.25443	0.204201
$255$	13.0489	0.817152
$256$	1.00000	0.0625000
$257$	−4.05390	−0.252875	−0.126438	−	0.991975i	$-0.540354\pi$
$257$	−4.05390	−0.252875	−0.126438	+	0.991975i	$0.540354\pi$
$258$	−33.1255	−2.06230
$259$	0	0
$260$	−3.62721	−0.224950
$261$	−48.4338	−2.99798
$262$	17.3083	1.06931
$263$	−14.5089	−0.894654	−0.447327	−	0.894370i	$-0.647624\pi$
$263$	−14.5089	−0.894654	−0.447327	+	0.894370i	$0.647624\pi$
$264$	−3.10278	−0.190963
$265$	−11.3083	−0.694665
$266$	0	0
$267$	−23.1466	−1.41655
$268$	−8.41110	−0.513790
$269$	−4.37279	−0.266614	−0.133307	−	0.991075i	$-0.542560\pi$
$269$	−4.37279	−0.266614	−0.133307	+	0.991075i	$0.542560\pi$
$270$	11.2544	0.684923
$271$	10.6167	0.644916	0.322458	−	0.946584i	$-0.395491\pi$
$271$	10.6167	0.644916	0.322458	+	0.946584i	$0.395491\pi$
$272$	4.20555	0.254999
$273$	0	0
$274$	10.0000	0.604122
$275$	1.00000	0.0603023
$276$	−2.78389	−0.167570
$277$	−19.7633	−1.18746	−0.593730	−	0.804664i	$-0.702345\pi$
$277$	−19.7633	−1.18746	−0.593730	+	0.804664i	$0.702345\pi$
$278$	−13.2005	−0.791715
$279$	22.6761	1.35758
$280$	0	0
$281$	−27.0489	−1.61360	−0.806800	−	0.590824i	$-0.798803\pi$
$281$	−27.0489	−1.61360	−0.806800	+	0.590824i	$0.798803\pi$
$282$	−3.58890	−0.213716
$283$	−27.6655	−1.64454	−0.822272	−	0.569094i	$-0.807294\pi$
$283$	−27.6655	−1.64454	−0.822272	+	0.569094i	$0.807294\pi$
$284$	−13.0489	−0.774308
$285$	25.2927	1.49821
$286$	3.62721	0.214482
$287$	0	0
$288$	6.62721	0.390512
$289$	0.686652	0.0403913
$290$	7.30833	0.429160
$291$	7.01056	0.410966
$292$	−0.205550	−0.0120289
$293$	8.37279	0.489143	0.244572	−	0.969631i	$-0.421353\pi$
$293$	8.37279	0.489143	0.244572	+	0.969631i	$0.421353\pi$
$294$	0	0
$295$	7.25443	0.422369
$296$	−1.10278	−0.0640975
$297$	−11.2544	−0.653048
$298$	−23.6116	−1.36778
$299$	3.25443	0.188208
$300$	−3.10278	−0.179139
$301$	0	0
$302$	11.5139	0.662549
$303$	42.4011	2.43588
$304$	8.15165	0.467529
$305$	−3.15667	−0.180751
$306$	27.8711	1.59328
$307$	10.2056	0.582462	0.291231	−	0.956653i	$-0.405935\pi$
$307$	10.2056	0.582462	0.291231	+	0.956653i	$0.405935\pi$
$308$	0	0
$309$	−15.6655	−0.891181
$310$	−3.42166	−0.194337
$311$	8.16724	0.463122	0.231561	−	0.972820i	$-0.425617\pi$
$311$	8.16724	0.463122	0.231561	+	0.972820i	$0.425617\pi$
$312$	−11.2544	−0.637156
$313$	−34.5628	−1.95360	−0.976801	−	0.214149i	$-0.931302\pi$
$313$	−34.5628	−1.95360	−0.976801	+	0.214149i	$0.931302\pi$
$314$	16.2056	0.914532
$315$	0	0
$316$	12.1517	0.683584
$317$	9.21057	0.517317	0.258659	−	0.965969i	$-0.416720\pi$
$317$	9.21057	0.517317	0.258659	+	0.965969i	$0.416720\pi$
$318$	−35.0872	−1.96759
$319$	−7.30833	−0.409188
$320$	−1.00000	−0.0559017
$321$	−40.3033	−2.24951
$322$	0	0
$323$	34.2822	1.90751
$324$	15.0383	0.835462
$325$	3.62721	0.201202
$326$	6.31335	0.349664
$327$	−15.8328	−0.875554
$328$	−12.3572	−0.682312
$329$	0	0
$330$	3.10278	0.170802
$331$	16.2439	0.892843	0.446422	−	0.894823i	$-0.352698\pi$
$331$	16.2439	0.892843	0.446422	+	0.894823i	$0.352698\pi$
$332$	−2.20555	−0.121045
$333$	−7.30833	−0.400494
$334$	8.00000	0.437741
$335$	8.41110	0.459547
$336$	0	0
$337$	−1.25443	−0.0683329	−0.0341665	−	0.999416i	$-0.510878\pi$
$337$	−1.25443	−0.0683329	−0.0341665	+	0.999416i	$0.510878\pi$
$338$	0.156674	0.00852195
$339$	32.3033	1.75447
$340$	−4.20555	−0.228078
$341$	3.42166	0.185293
$342$	54.0227	2.92121
$343$	0	0
$344$	10.6761	0.575616
$345$	2.78389	0.149879
$346$	−9.25443	−0.497521
$347$	7.42166	0.398416	0.199208	−	0.979957i	$-0.436163\pi$
$347$	7.42166	0.398416	0.199208	+	0.979957i	$0.436163\pi$
$348$	22.6761	1.21557
$349$	18.3033	0.979753	0.489877	−	0.871792i	$-0.337042\pi$
$349$	18.3033	0.979753	0.489877	+	0.871792i	$0.337042\pi$
$350$	0	0
$351$	−40.8222	−2.17893
$352$	1.00000	0.0533002
$353$	−28.8761	−1.53692	−0.768460	−	0.639898i	$-0.778977\pi$
$353$	−28.8761	−1.53692	−0.768460	+	0.639898i	$0.778977\pi$
$354$	22.5089	1.19633
$355$	13.0489	0.692562
$356$	7.45998	0.395378
$357$	0	0
$358$	4.98944	0.263700
$359$	4.15165	0.219116	0.109558	−	0.993980i	$-0.465057\pi$
$359$	4.15165	0.219116	0.109558	+	0.993980i	$0.465057\pi$
$360$	−6.62721	−0.349285
$361$	47.4494	2.49734
$362$	9.66553	0.508009
$363$	−3.10278	−0.162853
$364$	0	0
$365$	0.205550	0.0107590
$366$	−9.79445	−0.511964
$367$	5.26447	0.274803	0.137402	−	0.990515i	$-0.456125\pi$
$367$	5.26447	0.274803	0.137402	+	0.990515i	$0.456125\pi$
$368$	0.897225	0.0467711
$369$	−81.8938	−4.26322
$370$	1.10278	0.0573305
$371$	0	0
$372$	−10.6167	−0.550448
$373$	35.8711	1.85733	0.928667	−	0.370915i	$-0.120956\pi$
$373$	35.8711	1.85733	0.928667	+	0.370915i	$0.120956\pi$
$374$	4.20555	0.217464
$375$	3.10278	0.160227
$376$	1.15667	0.0596509
$377$	−26.5089	−1.36528
$378$	0	0
$379$	−33.0177	−1.69601	−0.848003	−	0.529992i	$-0.822195\pi$
$379$	−33.0177	−1.69601	−0.848003	+	0.529992i	$0.822195\pi$
$380$	−8.15165	−0.418171
$381$	−10.0978	−0.517323
$382$	−9.15667	−0.468496
$383$	−2.95112	−0.150795	−0.0753977	−	0.997154i	$-0.524023\pi$
$383$	−2.95112	−0.150795	−0.0753977	+	0.997154i	$0.524023\pi$
$384$	−3.10278	−0.158338
$385$	0	0
$386$	1.52946	0.0778475
$387$	70.7527	3.59656
$388$	−2.25945	−0.114706
$389$	1.89220	0.0959384	0.0479692	−	0.998849i	$-0.484725\pi$
$389$	1.89220	0.0959384	0.0479692	+	0.998849i	$0.484725\pi$
$390$	11.2544	0.569890
$391$	3.77332	0.190825
$392$	0	0
$393$	−53.7038	−2.70900
$394$	14.3033	0.720590
$395$	−12.1517	−0.611416
$396$	6.62721	0.333030
$397$	−5.36222	−0.269122	−0.134561	−	0.990905i	$-0.542962\pi$
$397$	−5.36222	−0.269122	−0.134561	+	0.990905i	$0.542962\pi$
$398$	10.0978	0.506155
$399$	0	0
$400$	1.00000	0.0500000
$401$	23.7038	1.18371	0.591857	−	0.806043i	$-0.298395\pi$
$401$	23.7038	1.18371	0.591857	+	0.806043i	$0.298395\pi$
$402$	26.0978	1.30164
$403$	12.4111	0.618241
$404$	−13.6655	−0.679885
$405$	−15.0383	−0.747260
$406$	0	0
$407$	−1.10278	−0.0546625
$408$	−13.0489	−0.646016
$409$	−27.0816	−1.33910	−0.669551	−	0.742766i	$-0.733513\pi$
$409$	−27.0816	−1.33910	−0.669551	+	0.742766i	$0.733513\pi$
$410$	12.3572	0.610279
$411$	−31.0278	−1.53049
$412$	5.04888	0.248740
$413$	0	0
$414$	5.94610	0.292235
$415$	2.20555	0.108266
$416$	3.62721	0.177839
$417$	40.9583	2.00573
$418$	8.15165	0.398710
$419$	3.05892	0.149438	0.0747191	−	0.997205i	$-0.476194\pi$
$419$	3.05892	0.149438	0.0747191	+	0.997205i	$0.476194\pi$
$420$	0	0
$421$	21.6655	1.05591	0.527957	−	0.849271i	$-0.322958\pi$
$421$	21.6655	1.05591	0.527957	+	0.849271i	$0.322958\pi$
$422$	10.8433	0.527845
$423$	7.66553	0.372711
$424$	11.3083	0.549181
$425$	4.20555	0.203999
$426$	40.4877	1.96164
$427$	0	0
$428$	12.9894	0.627868
$429$	−11.2544	−0.543369
$430$	−10.6761	−0.514847
$431$	−34.3260	−1.65343	−0.826713	−	0.562623i	$-0.809792\pi$
$431$	−34.3260	−1.65343	−0.826713	+	0.562623i	$0.809792\pi$
$432$	−11.2544	−0.541479
$433$	0.0538991	0.00259023	0.00129511	−	0.999999i	$-0.499588\pi$
$433$	0.0538991	0.00259023	0.00129511	+	0.999999i	$0.499588\pi$
$434$	0	0
$435$	−22.6761	−1.08724
$436$	5.10278	0.244379
$437$	7.31386	0.349870
$438$	0.637776	0.0304741
$439$	7.14663	0.341090	0.170545	−	0.985350i	$-0.445447\pi$
$439$	7.14663	0.341090	0.170545	+	0.985350i	$0.445447\pi$
$440$	−1.00000	−0.0476731
$441$	0	0
$442$	15.2544	0.725579
$443$	8.74557	0.415515	0.207757	−	0.978180i	$-0.433384\pi$
$443$	8.74557	0.415515	0.207757	+	0.978180i	$0.433384\pi$
$444$	3.42166	0.162385
$445$	−7.45998	−0.353637
$446$	9.45998	0.447943
$447$	73.2616	3.46515
$448$	0	0
$449$	39.7038	1.87374	0.936870	−	0.349678i	$-0.113709\pi$
$449$	39.7038	1.87374	0.936870	+	0.349678i	$0.113709\pi$
$450$	6.62721	0.312410
$451$	−12.3572	−0.581878
$452$	−10.4111	−0.489697
$453$	−35.7250	−1.67851
$454$	17.5678	0.824497
$455$	0	0
$456$	−25.2927	−1.18444
$457$	12.3133	0.575994	0.287997	−	0.957631i	$-0.407011\pi$
$457$	12.3133	0.575994	0.287997	+	0.957631i	$0.407011\pi$
$458$	−25.7250	−1.20205
$459$	−47.3311	−2.20922
$460$	−0.897225	−0.0418333
$461$	15.0489	0.700896	0.350448	−	0.936582i	$-0.386029\pi$
$461$	15.0489	0.700896	0.350448	+	0.936582i	$0.386029\pi$
$462$	0	0
$463$	31.4061	1.45956	0.729782	−	0.683680i	$-0.239622\pi$
$463$	31.4061	1.45956	0.729782	+	0.683680i	$0.239622\pi$
$464$	−7.30833	−0.339280
$465$	10.6167	0.492335
$466$	19.1567	0.887416
$467$	19.0716	0.882529	0.441264	−	0.897377i	$-0.354530\pi$
$467$	19.0716	0.882529	0.441264	+	0.897377i	$0.354530\pi$
$468$	24.0383	1.11117
$469$	0	0
$470$	−1.15667	−0.0533534
$471$	−50.2822	−2.31688
$472$	−7.25443	−0.333912
$473$	10.6761	0.490887
$474$	−37.7038	−1.73179
$475$	8.15165	0.374023
$476$	0	0
$477$	74.9427	3.43139
$478$	−18.0539	−0.825766
$479$	9.49115	0.433662	0.216831	−	0.976209i	$-0.430428\pi$
$479$	9.49115	0.433662	0.216831	+	0.976209i	$0.430428\pi$
$480$	3.10278	0.141622
$481$	−4.00000	−0.182384
$482$	−6.15165	−0.280200
$483$	0	0
$484$	1.00000	0.0454545
$485$	2.25945	0.102596
$486$	−12.8972	−0.585030
$487$	0.0438527	0.00198715	0.000993577	−	1.00000i	$-0.499684\pi$
$487$	0.0438527	0.00198715	0.000993577		1.00000i	$0.499684\pi$
$488$	3.15667	0.142896
$489$	−19.5889	−0.885841
$490$	0	0
$491$	1.56777	0.0707527	0.0353763	−	0.999374i	$-0.488737\pi$
$491$	1.56777	0.0707527	0.0353763	+	0.999374i	$0.488737\pi$
$492$	38.3416	1.72857
$493$	−30.7355	−1.38426
$494$	29.5678	1.33032
$495$	−6.62721	−0.297871
$496$	3.42166	0.153637
$497$	0	0
$498$	6.84333	0.306657
$499$	−42.3416	−1.89547	−0.947736	−	0.319057i	$-0.896634\pi$
$499$	−42.3416	−1.89547	−0.947736	+	0.319057i	$0.896634\pi$
$500$	−1.00000	−0.0447214
$501$	−24.8222	−1.10897
$502$	29.9789	1.33802
$503$	36.4111	1.62349	0.811745	−	0.584012i	$-0.198518\pi$
$503$	36.4111	1.62349	0.811745	+	0.584012i	$0.198518\pi$
$504$	0	0
$505$	13.6655	0.608108
$506$	0.897225	0.0398865
$507$	−0.486125	−0.0215896
$508$	3.25443	0.144392
$509$	30.0766	1.33312	0.666562	−	0.745450i	$-0.267765\pi$
$509$	30.0766	1.33312	0.666562	+	0.745450i	$0.267765\pi$
$510$	13.0489	0.577814
$511$	0	0
$512$	1.00000	0.0441942
$513$	−91.7422	−4.05051
$514$	−4.05390	−0.178810
$515$	−5.04888	−0.222480
$516$	−33.1255	−1.45827
$517$	1.15667	0.0508705
$518$	0	0
$519$	28.7144	1.26042
$520$	−3.62721	−0.159064
$521$	33.2233	1.45554	0.727769	−	0.685823i	$-0.240557\pi$
$521$	33.2233	1.45554	0.727769	+	0.685823i	$0.240557\pi$
$522$	−48.4338	−2.11989
$523$	15.5577	0.680292	0.340146	−	0.940373i	$-0.389524\pi$
$523$	15.5577	0.680292	0.340146	+	0.940373i	$0.389524\pi$
$524$	17.3083	0.756118
$525$	0	0
$526$	−14.5089	−0.632616
$527$	14.3900	0.626837
$528$	−3.10278	−0.135031
$529$	−22.1950	−0.964999
$530$	−11.3083	−0.491202
$531$	−48.0766	−2.08635
$532$	0	0
$533$	−44.8222	−1.94147
$534$	−23.1466	−1.00165
$535$	−12.9894	−0.561582
$536$	−8.41110	−0.363304
$537$	−15.4811	−0.668059
$538$	−4.37279	−0.188524
$539$	0	0
$540$	11.2544	0.484313
$541$	23.4161	1.00674	0.503369	−	0.864072i	$-0.332094\pi$
$541$	23.4161	1.00674	0.503369	+	0.864072i	$0.332094\pi$
$542$	10.6167	0.456024
$543$	−29.9900	−1.28699
$544$	4.20555	0.180311
$545$	−5.10278	−0.218579
$546$	0	0
$547$	−8.41110	−0.359633	−0.179816	−	0.983700i	$-0.557550\pi$
$547$	−8.41110	−0.359633	−0.179816	+	0.983700i	$0.557550\pi$
$548$	10.0000	0.427179
$549$	20.9200	0.892842
$550$	1.00000	0.0426401
$551$	−59.5749	−2.53798
$552$	−2.78389	−0.118490
$553$	0	0
$554$	−19.7633	−0.839661
$555$	−3.42166	−0.145242
$556$	−13.2005	−0.559827
$557$	37.0278	1.56892	0.784458	−	0.620182i	$-0.212941\pi$
$557$	37.0278	1.56892	0.784458	+	0.620182i	$0.212941\pi$
$558$	22.6761	0.959955
$559$	38.7244	1.63787
$560$	0	0
$561$	−13.0489	−0.550924
$562$	−27.0489	−1.14099
$563$	−22.9200	−0.965961	−0.482980	−	0.875631i	$-0.660446\pi$
$563$	−22.9200	−0.965961	−0.482980	+	0.875631i	$0.660446\pi$
$564$	−3.58890	−0.151120
$565$	10.4111	0.437998
$566$	−27.6655	−1.16287
$567$	0	0
$568$	−13.0489	−0.547519
$569$	−22.0000	−0.922288	−0.461144	−	0.887325i	$-0.652561\pi$
$569$	−22.0000	−0.922288	−0.461144	+	0.887325i	$0.652561\pi$
$570$	25.2927	1.05940
$571$	20.3033	0.849667	0.424833	−	0.905272i	$-0.360333\pi$
$571$	20.3033	0.849667	0.424833	+	0.905272i	$0.360333\pi$
$572$	3.62721	0.151661
$573$	28.4111	1.18689
$574$	0	0
$575$	0.897225	0.0374169
$576$	6.62721	0.276134
$577$	−16.4650	−0.685447	−0.342723	−	0.939436i	$-0.611349\pi$
$577$	−16.4650	−0.685447	−0.342723	+	0.939436i	$0.611349\pi$
$578$	0.686652	0.0285609
$579$	−4.74557	−0.197219
$580$	7.30833	0.303462
$581$	0	0
$582$	7.01056	0.290597
$583$	11.3083	0.468343
$584$	−0.205550	−0.00850572
$585$	−24.0383	−0.993862
$586$	8.37279	0.345877
$587$	30.6605	1.26549	0.632747	−	0.774358i	$-0.281927\pi$
$587$	30.6605	1.26549	0.632747	+	0.774358i	$0.281927\pi$
$588$	0	0
$589$	27.8922	1.14928
$590$	7.25443	0.298660
$591$	−44.3799	−1.82555
$592$	−1.10278	−0.0453238
$593$	−18.3033	−0.751627	−0.375813	−	0.926695i	$-0.622637\pi$
$593$	−18.3033	−0.751627	−0.375813	+	0.926695i	$0.622637\pi$
$594$	−11.2544	−0.461775
$595$	0	0
$596$	−23.6116	−0.967170
$597$	−31.3311	−1.28229
$598$	3.25443	0.133083
$599$	29.6555	1.21169	0.605845	−	0.795583i	$-0.292835\pi$
$599$	29.6555	1.21169	0.605845	+	0.795583i	$0.292835\pi$
$600$	−3.10278	−0.126670
$601$	−18.7783	−0.765985	−0.382992	−	0.923751i	$-0.625106\pi$
$601$	−18.7783	−0.765985	−0.382992	+	0.923751i	$0.625106\pi$
$602$	0	0
$603$	−55.7422	−2.27000
$604$	11.5139	0.468493
$605$	−1.00000	−0.0406558
$606$	42.4011	1.72243
$607$	−14.6761	−0.595684	−0.297842	−	0.954615i	$-0.596267\pi$
$607$	−14.6761	−0.595684	−0.297842	+	0.954615i	$0.596267\pi$
$608$	8.15165	0.330593
$609$	0	0
$610$	−3.15667	−0.127810
$611$	4.19550	0.169732
$612$	27.8711	1.12662
$613$	−5.28560	−0.213483	−0.106742	−	0.994287i	$-0.534042\pi$
$613$	−5.28560	−0.213483	−0.106742	+	0.994287i	$0.534042\pi$
$614$	10.2056	0.411862
$615$	−38.3416	−1.54608
$616$	0	0
$617$	−44.6933	−1.79928	−0.899642	−	0.436629i	$-0.856172\pi$
$617$	−44.6933	−1.79928	−0.899642	+	0.436629i	$0.856172\pi$
$618$	−15.6655	−0.630160
$619$	17.5678	0.706108	0.353054	−	0.935603i	$-0.385143\pi$
$619$	17.5678	0.706108	0.353054	+	0.935603i	$0.385143\pi$
$620$	−3.42166	−0.137417
$621$	−10.0978	−0.405209
$622$	8.16724	0.327476
$623$	0	0
$624$	−11.2544	−0.450538
$625$	1.00000	0.0400000
$626$	−34.5628	−1.38141
$627$	−25.2927	−1.01009
$628$	16.2056	0.646672
$629$	−4.63778	−0.184920
$630$	0	0
$631$	4.74557	0.188918	0.0944592	−	0.995529i	$-0.469888\pi$
$631$	4.74557	0.188918	0.0944592	+	0.995529i	$0.469888\pi$
$632$	12.1517	0.483367
$633$	−33.6444	−1.33724
$634$	9.21057	0.365799
$635$	−3.25443	−0.129148
$636$	−35.0872	−1.39130
$637$	0	0
$638$	−7.30833	−0.289339
$639$	−86.4777	−3.42100
$640$	−1.00000	−0.0395285
$641$	−2.52998	−0.0999281	−0.0499641	−	0.998751i	$-0.515911\pi$
$641$	−2.52998	−0.0999281	−0.0499641	+	0.998751i	$0.515911\pi$
$642$	−40.3033	−1.59064
$643$	0.670549	0.0264439	0.0132219	−	0.999913i	$-0.495791\pi$
$643$	0.670549	0.0264439	0.0132219	+	0.999913i	$0.495791\pi$
$644$	0	0
$645$	33.1255	1.30432
$646$	34.2822	1.34881
$647$	−11.8922	−0.467531	−0.233765	−	0.972293i	$-0.575105\pi$
$647$	−11.8922	−0.467531	−0.233765	+	0.972293i	$0.575105\pi$
$648$	15.0383	0.590761
$649$	−7.25443	−0.284761
$650$	3.62721	0.142271
$651$	0	0
$652$	6.31335	0.247250
$653$	−11.4161	−0.446747	−0.223374	−	0.974733i	$-0.571707\pi$
$653$	−11.4161	−0.446747	−0.223374	+	0.974733i	$0.571707\pi$
$654$	−15.8328	−0.619110
$655$	−17.3083	−0.676292
$656$	−12.3572	−0.482468
$657$	−1.36222	−0.0531454
$658$	0	0
$659$	1.87108	0.0728868	0.0364434	−	0.999336i	$-0.488397\pi$
$659$	1.87108	0.0728868	0.0364434	+	0.999336i	$0.488397\pi$
$660$	3.10278	0.120775
$661$	−33.1355	−1.28882	−0.644412	−	0.764679i	$-0.722898\pi$
$661$	−33.1355	−1.28882	−0.644412	+	0.764679i	$0.722898\pi$
$662$	16.2439	0.631336
$663$	−47.3311	−1.83819
$664$	−2.20555	−0.0855919
$665$	0	0
$666$	−7.30833	−0.283192
$667$	−6.55721	−0.253896
$668$	8.00000	0.309529
$669$	−29.3522	−1.13482
$670$	8.41110	0.324949
$671$	3.15667	0.121862
$672$	0	0
$673$	−18.1955	−0.701385	−0.350693	−	0.936491i	$-0.614054\pi$
$673$	−18.1955	−0.701385	−0.350693	+	0.936491i	$0.614054\pi$
$674$	−1.25443	−0.0483187
$675$	−11.2544	−0.433183
$676$	0.156674	0.00602593
$677$	−15.9789	−0.614118	−0.307059	−	0.951690i	$-0.599345\pi$
$677$	−15.9789	−0.614118	−0.307059	+	0.951690i	$0.599345\pi$
$678$	32.3033	1.24060
$679$	0	0
$680$	−4.20555	−0.161275
$681$	−54.5089	−2.08878
$682$	3.42166	0.131022
$683$	−17.8711	−0.683818	−0.341909	−	0.939733i	$-0.611073\pi$
$683$	−17.8711	−0.683818	−0.341909	+	0.939733i	$0.611073\pi$
$684$	54.0227	2.06561
$685$	−10.0000	−0.382080
$686$	0	0
$687$	79.8188	3.04528
$688$	10.6761	0.407022
$689$	41.0177	1.56265
$690$	2.78389	0.105981
$691$	2.20555	0.0839031	0.0419515	−	0.999120i	$-0.486642\pi$
$691$	2.20555	0.0839031	0.0419515	+	0.999120i	$0.486642\pi$
$692$	−9.25443	−0.351800
$693$	0	0
$694$	7.42166	0.281722
$695$	13.2005	0.500725
$696$	22.6761	0.859535
$697$	−51.9688	−1.96846
$698$	18.3033	0.692790
$699$	−59.4389	−2.24818
$700$	0	0
$701$	−25.6217	−0.967717	−0.483859	−	0.875146i	$-0.660765\pi$
$701$	−25.6217	−0.967717	−0.483859	+	0.875146i	$0.660765\pi$
$702$	−40.8222	−1.54073
$703$	−8.98944	−0.339043
$704$	1.00000	0.0376889
$705$	3.58890	0.135166
$706$	−28.8761	−1.08677
$707$	0	0
$708$	22.5089	0.845934
$709$	5.48110	0.205847	0.102924	−	0.994689i	$-0.467180\pi$
$709$	5.48110	0.205847	0.102924	+	0.994689i	$0.467180\pi$
$710$	13.0489	0.489716
$711$	80.5316	3.02017
$712$	7.45998	0.279574
$713$	3.07000	0.114972
$714$	0	0
$715$	−3.62721	−0.135650
$716$	4.98944	0.186464
$717$	56.0172	2.09200
$718$	4.15165	0.154938
$719$	8.00000	0.298350	0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000	0.298350	0.149175	+	0.988811i	$0.452338\pi$
$720$	−6.62721	−0.246982
$721$	0	0
$722$	47.4494	1.76588
$723$	19.0872	0.709860
$724$	9.66553	0.359216
$725$	−7.30833	−0.271424
$726$	−3.10278	−0.115155
$727$	−18.5855	−0.689297	−0.344649	−	0.938732i	$-0.612002\pi$
$727$	−18.5855	−0.689297	−0.344649	+	0.938732i	$0.612002\pi$
$728$	0	0
$729$	−5.09775	−0.188806
$730$	0.205550	0.00760775
$731$	44.8988	1.66064
$732$	−9.79445	−0.362013
$733$	42.0000	1.55131	0.775653	−	0.631160i	$-0.217421\pi$
$733$	42.0000	1.55131	0.775653	+	0.631160i	$0.217421\pi$
$734$	5.26447	0.194315
$735$	0	0
$736$	0.897225	0.0330722
$737$	−8.41110	−0.309827
$738$	−81.8938	−3.01455
$739$	5.97887	0.219936	0.109968	−	0.993935i	$-0.464925\pi$
$739$	5.97887	0.219936	0.109968	+	0.993935i	$0.464925\pi$
$740$	1.10278	0.0405388
$741$	−91.7422	−3.37023
$742$	0	0
$743$	−50.0978	−1.83791	−0.918954	−	0.394364i	$-0.870965\pi$
$743$	−50.0978	−1.83791	−0.918954	+	0.394364i	$0.870965\pi$
$744$	−10.6167	−0.389225
$745$	23.6116	0.865063
$746$	35.8711	1.31333
$747$	−14.6167	−0.534795
$748$	4.20555	0.153770
$749$	0	0
$750$	3.10278	0.113297
$751$	−8.63778	−0.315197	−0.157598	−	0.987503i	$-0.550375\pi$
$751$	−8.63778	−0.315197	−0.157598	+	0.987503i	$0.550375\pi$
$752$	1.15667	0.0421796
$753$	−93.0177	−3.38975
$754$	−26.5089	−0.965395
$755$	−11.5139	−0.419033
$756$	0	0
$757$	25.5139	0.927318	0.463659	−	0.886014i	$-0.346536\pi$
$757$	25.5139	0.927318	0.463659	+	0.886014i	$0.346536\pi$
$758$	−33.0177	−1.19926
$759$	−2.78389	−0.101049
$760$	−8.15165	−0.295691
$761$	32.6605	1.18394	0.591971	−	0.805959i	$-0.298350\pi$
$761$	32.6605	1.18394	0.591971	+	0.805959i	$0.298350\pi$
$762$	−10.0978	−0.365803
$763$	0	0
$764$	−9.15667	−0.331277
$765$	−27.8711	−1.00768
$766$	−2.95112	−0.106628
$767$	−26.3133	−0.950120
$768$	−3.10278	−0.111962
$769$	−16.7683	−0.604680	−0.302340	−	0.953200i	$-0.597768\pi$
$769$	−16.7683	−0.604680	−0.302340	+	0.953200i	$0.597768\pi$
$770$	0	0
$771$	12.5783	0.452998
$772$	1.52946	0.0550465
$773$	2.82220	0.101507	0.0507537	−	0.998711i	$-0.483838\pi$
$773$	2.82220	0.101507	0.0507537	+	0.998711i	$0.483838\pi$
$774$	70.7527	2.54315
$775$	3.42166	0.122910
$776$	−2.25945	−0.0811095
$777$	0	0
$778$	1.89220	0.0678387
$779$	−100.732	−3.60908
$780$	11.2544	0.402973
$781$	−13.0489	−0.466925
$782$	3.77332	0.134934
$783$	82.2510	2.93941
$784$	0	0
$785$	−16.2056	−0.578401
$786$	−53.7038	−1.91555
$787$	4.82220	0.171893	0.0859464	−	0.996300i	$-0.472609\pi$
$787$	4.82220	0.171893	0.0859464	+	0.996300i	$0.472609\pi$
$788$	14.3033	0.509534
$789$	45.0177	1.60267
$790$	−12.1517	−0.432336
$791$	0	0
$792$	6.62721	0.235488
$793$	11.4499	0.406599
$794$	−5.36222	−0.190298
$795$	35.0872	1.24441
$796$	10.0978	0.357905
$797$	0.540024	0.0191286	0.00956431	−	0.999954i	$-0.496956\pi$
$797$	0.540024	0.0191286	0.00956431	+	0.999954i	$0.496956\pi$
$798$	0	0
$799$	4.86445	0.172092
$800$	1.00000	0.0353553
$801$	49.4389	1.74684
$802$	23.7038	0.837012
$803$	−0.205550	−0.00725371
$804$	26.0978	0.920397
$805$	0	0
$806$	12.4111	0.437162
$807$	13.5678	0.477608
$808$	−13.6655	−0.480752
$809$	−17.8922	−0.629056	−0.314528	−	0.949248i	$-0.601846\pi$
$809$	−17.8922	−0.629056	−0.314528	+	0.949248i	$0.601846\pi$
$810$	−15.0383	−0.528392
$811$	12.2283	0.429393	0.214696	−	0.976681i	$-0.431124\pi$
$811$	12.2283	0.429393	0.214696	+	0.976681i	$0.431124\pi$
$812$	0	0
$813$	−32.9411	−1.15529
$814$	−1.10278	−0.0386522
$815$	−6.31335	−0.221147
$816$	−13.0489	−0.456802
$817$	87.0278	3.04472
$818$	−27.0816	−0.946888
$819$	0	0
$820$	12.3572	0.431532
$821$	38.5316	1.34476	0.672381	−	0.740206i	$-0.265272\pi$
$821$	38.5316	1.34476	0.672381	+	0.740206i	$0.265272\pi$
$822$	−31.0278	−1.08222
$823$	21.9461	0.764993	0.382496	−	0.923957i	$-0.375064\pi$
$823$	21.9461	0.764993	0.382496	+	0.923957i	$0.375064\pi$
$824$	5.04888	0.175886
$825$	−3.10278	−0.108025
$826$	0	0
$827$	9.68665	0.336838	0.168419	−	0.985716i	$-0.446134\pi$
$827$	9.68665	0.336838	0.168419	+	0.985716i	$0.446134\pi$
$828$	5.94610	0.206641
$829$	−31.0771	−1.07935	−0.539677	−	0.841872i	$-0.681454\pi$
$829$	−31.0771	−1.07935	−0.539677	+	0.841872i	$0.681454\pi$
$830$	2.20555	0.0765558
$831$	61.3210	2.12720
$832$	3.62721	0.125751
$833$	0	0
$834$	40.9583	1.41827
$835$	−8.00000	−0.276851
$836$	8.15165	0.281931
$837$	−38.5089	−1.33106
$838$	3.05892	0.105669
$839$	24.7738	0.855288	0.427644	−	0.903947i	$-0.359344\pi$
$839$	24.7738	0.855288	0.427644	+	0.903947i	$0.359344\pi$
$840$	0	0
$841$	24.4116	0.841780
$842$	21.6655	0.746643
$843$	83.9266	2.89058
$844$	10.8433	0.373243
$845$	−0.156674	−0.00538976
$846$	7.66553	0.263546
$847$	0	0
$848$	11.3083	0.388329
$849$	85.8399	2.94602
$850$	4.20555	0.144249
$851$	−0.989437	−0.0339175
$852$	40.4877	1.38709
$853$	−1.58890	−0.0544029	−0.0272014	−	0.999630i	$-0.508660\pi$
$853$	−1.58890	−0.0544029	−0.0272014	+	0.999630i	$0.508660\pi$
$854$	0	0
$855$	−54.0227	−1.84754
$856$	12.9894	0.443970
$857$	−19.1255	−0.653315	−0.326657	−	0.945143i	$-0.605922\pi$
$857$	−19.1255	−0.653315	−0.326657	+	0.945143i	$0.605922\pi$
$858$	−11.2544	−0.384220
$859$	−4.94108	−0.168587	−0.0842937	−	0.996441i	$-0.526863\pi$
$859$	−4.94108	−0.168587	−0.0842937	+	0.996441i	$0.526863\pi$
$860$	−10.6761	−0.364052
$861$	0	0
$862$	−34.3260	−1.16915
$863$	−19.3295	−0.657982	−0.328991	−	0.944333i	$-0.606709\pi$
$863$	−19.3295	−0.657982	−0.328991	+	0.944333i	$0.606709\pi$
$864$	−11.2544	−0.382883
$865$	9.25443	0.314660
$866$	0.0538991	0.00183157
$867$	−2.13053	−0.0723564
$868$	0	0
$869$	12.1517	0.412217
$870$	−22.6761	−0.768791
$871$	−30.5089	−1.03375
$872$	5.10278	0.172802
$873$	−14.9739	−0.506788
$874$	7.31386	0.247395
$875$	0	0
$876$	0.637776	0.0215484
$877$	16.4011	0.553824	0.276912	−	0.960895i	$-0.410689\pi$
$877$	16.4011	0.553824	0.276912	+	0.960895i	$0.410689\pi$
$878$	7.14663	0.241187
$879$	−25.9789	−0.876246
$880$	−1.00000	−0.0337100
$881$	−39.5678	−1.33307	−0.666536	−	0.745473i	$-0.732224\pi$
$881$	−39.5678	−1.33307	−0.666536	+	0.745473i	$0.732224\pi$
$882$	0	0
$883$	55.4389	1.86567	0.932833	−	0.360309i	$-0.117329\pi$
$883$	55.4389	1.86567	0.932833	+	0.360309i	$0.117329\pi$
$884$	15.2544	0.513062
$885$	−22.5089	−0.756627
$886$	8.74557	0.293813
$887$	−44.1955	−1.48394	−0.741970	−	0.670433i	$-0.766108\pi$
$887$	−44.1955	−1.48394	−0.741970	+	0.670433i	$0.766108\pi$
$888$	3.42166	0.114823
$889$	0	0
$890$	−7.45998	−0.250059
$891$	15.0383	0.503802
$892$	9.45998	0.316743
$893$	9.42880	0.315523
$894$	73.2616	2.45023
$895$	−4.98944	−0.166778
$896$	0	0
$897$	−10.0978	−0.337154
$898$	39.7038	1.32493
$899$	−25.0066	−0.834018
$900$	6.62721	0.220907
$901$	47.5577	1.58438
$902$	−12.3572	−0.411450
$903$	0	0
$904$	−10.4111	−0.346268
$905$	−9.66553	−0.321293
$906$	−35.7250	−1.18688
$907$	9.26447	0.307622	0.153811	−	0.988100i	$-0.450845\pi$
$907$	9.26447	0.307622	0.153811	+	0.988100i	$0.450845\pi$
$908$	17.5678	0.583007
$909$	−90.5644	−3.00383
$910$	0	0
$911$	−37.0489	−1.22748	−0.613742	−	0.789507i	$-0.710336\pi$
$911$	−37.0489	−1.22748	−0.613742	+	0.789507i	$0.710336\pi$
$912$	−25.2927	−0.837526
$913$	−2.20555	−0.0729931
$914$	12.3133	0.407289
$915$	9.79445	0.323795
$916$	−25.7250	−0.849977
$917$	0	0
$918$	−47.3311	−1.56216
$919$	−13.9149	−0.459011	−0.229506	−	0.973307i	$-0.573711\pi$
$919$	−13.9149	−0.459011	−0.229506	+	0.973307i	$0.573711\pi$
$920$	−0.897225	−0.0295806
$921$	−31.6655	−1.04341
$922$	15.0489	0.495608
$923$	−47.3311	−1.55792
$924$	0	0
$925$	−1.10278	−0.0362590
$926$	31.4061	1.03207
$927$	33.4600	1.09897
$928$	−7.30833	−0.239908
$929$	32.0666	1.05207	0.526035	−	0.850463i	$-0.323678\pi$
$929$	32.0666	1.05207	0.526035	+	0.850463i	$0.323678\pi$
$930$	10.6167	0.348134
$931$	0	0
$932$	19.1567	0.627498
$933$	−25.3411	−0.829630
$934$	19.0716	0.624042
$935$	−4.20555	−0.137536
$936$	24.0383	0.785717
$937$	−25.4499	−0.831413	−0.415706	−	0.909499i	$-0.636466\pi$
$937$	−25.4499	−0.831413	−0.415706	+	0.909499i	$0.636466\pi$
$938$	0	0
$939$	107.240	3.49966
$940$	−1.15667	−0.0377266
$941$	3.49115	0.113808	0.0569041	−	0.998380i	$-0.481877\pi$
$941$	3.49115	0.113808	0.0569041	+	0.998380i	$0.481877\pi$
$942$	−50.2822	−1.63828
$943$	−11.0872	−0.361049
$944$	−7.25443	−0.236111
$945$	0	0
$946$	10.6761	0.347110
$947$	30.6167	0.994907	0.497454	−	0.867491i	$-0.334268\pi$
$947$	30.6167	0.994907	0.497454	+	0.867491i	$0.334268\pi$
$948$	−37.7038	−1.22456
$949$	−0.745574	−0.0242024
$950$	8.15165	0.264474
$951$	−28.5783	−0.926716
$952$	0	0
$953$	−33.9406	−1.09944	−0.549721	−	0.835348i	$-0.685266\pi$
$953$	−33.9406	−1.09944	−0.549721	+	0.835348i	$0.685266\pi$
$954$	74.9427	2.42636
$955$	9.15667	0.296303
$956$	−18.0539	−0.583905
$957$	22.6761	0.733014
$958$	9.49115	0.306645
$959$	0	0
$960$	3.10278	0.100142
$961$	−19.2922	−0.622330
$962$	−4.00000	−0.128965
$963$	86.0838	2.77401
$964$	−6.15165	−0.198131
$965$	−1.52946	−0.0492351
$966$	0	0
$967$	−60.8021	−1.95526	−0.977632	−	0.210323i	$-0.932548\pi$
$967$	−60.8021	−1.95526	−0.977632	+	0.210323i	$0.932548\pi$
$968$	1.00000	0.0321412
$969$	−106.370	−3.41709
$970$	2.25945	0.0725465
$971$	−50.2933	−1.61399	−0.806994	−	0.590560i	$-0.798907\pi$
$971$	−50.2933	−1.61399	−0.806994	+	0.590560i	$0.798907\pi$
$972$	−12.8972	−0.413679
$973$	0	0
$974$	0.0438527	0.00140513
$975$	−11.2544	−0.360430
$976$	3.15667	0.101043
$977$	28.0978	0.898927	0.449463	−	0.893299i	$-0.351615\pi$
$977$	28.0978	0.898927	0.449463	+	0.893299i	$0.351615\pi$
$978$	−19.5889	−0.626384
$979$	7.45998	0.238422
$980$	0	0
$981$	33.8172	1.07970
$982$	1.56777	0.0500297
$983$	21.0489	0.671355	0.335677	−	0.941977i	$-0.391035\pi$
$983$	21.0489	0.671355	0.335677	+	0.941977i	$0.391035\pi$
$984$	38.3416	1.22229
$985$	−14.3033	−0.455741
$986$	−30.7355	−0.978819
$987$	0	0
$988$	29.5678	0.940676
$989$	9.57885	0.304590
$990$	−6.62721	−0.210627
$991$	−44.6832	−1.41941	−0.709705	−	0.704499i	$-0.751172\pi$
$991$	−44.6832	−1.41941	−0.709705	+	0.704499i	$0.751172\pi$
$992$	3.42166	0.108638
$993$	−50.4011	−1.59943
$994$	0	0
$995$	−10.0978	−0.320120
$996$	6.84333	0.216839
$997$	−9.47002	−0.299919	−0.149959	−	0.988692i	$-0.547914\pi$
$997$	−9.47002	−0.299919	−0.149959	+	0.988692i	$0.547914\pi$
$998$	−42.3416	−1.34030
$999$	12.4111	0.392670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5390.2.a.ca.1.1		3
7.6	odd	2		770.2.a.m.1.3	✓	3
21.20	even	2		6930.2.a.ce.1.1		3
28.27	even	2		6160.2.a.bf.1.1		3
35.13	even	4		3850.2.c.ba.1849.3		6
35.27	even	4		3850.2.c.ba.1849.4		6
35.34	odd	2		3850.2.a.bt.1.1		3
77.76	even	2		8470.2.a.ci.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.m.1.3	✓	3	7.6	odd	2
3850.2.a.bt.1.1		3	35.34	odd	2
3850.2.c.ba.1849.3		6	35.13	even	4
3850.2.c.ba.1849.4		6	35.27	even	4
5390.2.a.ca.1.1		3	1.1	even	1	trivial
6160.2.a.bf.1.1		3	28.27	even	2
6930.2.a.ce.1.1		3	21.20	even	2
8470.2.a.ci.1.3		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.10278 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.10278 q^{6} +1.00000 q^{8} +6.62721 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.10278 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.10278 q^{6} +1.00000 q^{8} +6.62721 q^{9} -1.00000 q^{10} +1.00000 q^{11} -3.10278 q^{12} +3.62721 q^{13} +3.10278 q^{15} +1.00000 q^{16} +4.20555 q^{17} +6.62721 q^{18} +8.15165 q^{19} -1.00000 q^{20} +1.00000 q^{22} +0.897225 q^{23} -3.10278 q^{24} +1.00000 q^{25} +3.62721 q^{26} -11.2544 q^{27} -7.30833 q^{29} +3.10278 q^{30} +3.42166 q^{31} +1.00000 q^{32} -3.10278 q^{33} +4.20555 q^{34} +6.62721 q^{36} -1.10278 q^{37} +8.15165 q^{38} -11.2544 q^{39} -1.00000 q^{40} -12.3572 q^{41} +10.6761 q^{43} +1.00000 q^{44} -6.62721 q^{45} +0.897225 q^{46} +1.15667 q^{47} -3.10278 q^{48} +1.00000 q^{50} -13.0489 q^{51} +3.62721 q^{52} +11.3083 q^{53} -11.2544 q^{54} -1.00000 q^{55} -25.2927 q^{57} -7.30833 q^{58} -7.25443 q^{59} +3.10278 q^{60} +3.15667 q^{61} +3.42166 q^{62} +1.00000 q^{64} -3.62721 q^{65} -3.10278 q^{66} -8.41110 q^{67} +4.20555 q^{68} -2.78389 q^{69} -13.0489 q^{71} +6.62721 q^{72} -0.205550 q^{73} -1.10278 q^{74} -3.10278 q^{75} +8.15165 q^{76} -11.2544 q^{78} +12.1517 q^{79} -1.00000 q^{80} +15.0383 q^{81} -12.3572 q^{82} -2.20555 q^{83} -4.20555 q^{85} +10.6761 q^{86} +22.6761 q^{87} +1.00000 q^{88} +7.45998 q^{89} -6.62721 q^{90} +0.897225 q^{92} -10.6167 q^{93} +1.15667 q^{94} -8.15165 q^{95} -3.10278 q^{96} -2.25945 q^{97} +6.62721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} - 2 q^{6} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 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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