LMFDB - Embedded newform 3750.2.a.u.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3750,2,Mod(1,3750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3750, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3750.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3750 = 2 \cdot 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3750.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:	$29.9439007580$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.71684000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 18x^{6} + 10x^{5} + 101x^{4} + 40x^{3} - 132x^{2} - 96x - 4 $ x^8 - 2x^7 - 18x^6 + 10x^5 + 101x^4 + 40x^3 - 132x^2 - 96*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 150)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.852282$ of defining polynomial
Character	$\chi$	$=$	3750.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +3.52206 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +3.52206 q^{7} -1.00000 q^{8} +1.00000 q^{9} +5.25498 q^{11} -1.00000 q^{12} -0.619103 q^{13} -3.52206 q^{14} +1.00000 q^{16} -3.44557 q^{17} -1.00000 q^{18} +2.27431 q^{19} -3.52206 q^{21} -5.25498 q^{22} +8.95380 q^{23} +1.00000 q^{24} +0.619103 q^{26} -1.00000 q^{27} +3.52206 q^{28} -2.68163 q^{29} +9.76875 q^{31} -1.00000 q^{32} -5.25498 q^{33} +3.44557 q^{34} +1.00000 q^{36} +1.00173 q^{37} -2.27431 q^{38} +0.619103 q^{39} +6.29687 q^{41} +3.52206 q^{42} +1.51251 q^{43} +5.25498 q^{44} -8.95380 q^{46} -10.6760 q^{47} -1.00000 q^{48} +5.40494 q^{49} +3.44557 q^{51} -0.619103 q^{52} -0.553365 q^{53} +1.00000 q^{54} -3.52206 q^{56} -2.27431 q^{57} +2.68163 q^{58} +0.278771 q^{59} +3.68218 q^{61} -9.76875 q^{62} +3.52206 q^{63} +1.00000 q^{64} +5.25498 q^{66} +11.9121 q^{67} -3.44557 q^{68} -8.95380 q^{69} +4.74858 q^{71} -1.00000 q^{72} -9.83408 q^{73} -1.00173 q^{74} +2.27431 q^{76} +18.5084 q^{77} -0.619103 q^{78} +6.52057 q^{79} +1.00000 q^{81} -6.29687 q^{82} -2.65973 q^{83} -3.52206 q^{84} -1.51251 q^{86} +2.68163 q^{87} -5.25498 q^{88} -13.3860 q^{89} -2.18052 q^{91} +8.95380 q^{92} -9.76875 q^{93} +10.6760 q^{94} +1.00000 q^{96} -4.37205 q^{97} -5.40494 q^{98} +5.25498 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9} + 6 q^{11} - 8 q^{12} - 2 q^{13} + 4 q^{14} + 8 q^{16} - 14 q^{17} - 8 q^{18} + 10 q^{19} + 4 q^{21} - 6 q^{22} - 12 q^{23} + 8 q^{24} + 2 q^{26} - 8 q^{27} - 4 q^{28} + 10 q^{29} + 16 q^{31} - 8 q^{32} - 6 q^{33} + 14 q^{34} + 8 q^{36} + 6 q^{37} - 10 q^{38} + 2 q^{39} + 6 q^{41} - 4 q^{42} - 2 q^{43} + 6 q^{44} + 12 q^{46} - 14 q^{47} - 8 q^{48} + 26 q^{49} + 14 q^{51} - 2 q^{52} - 12 q^{53} + 8 q^{54} + 4 q^{56} - 10 q^{57} - 10 q^{58} + 16 q^{61} - 16 q^{62} - 4 q^{63} + 8 q^{64} + 6 q^{66} + 6 q^{67} - 14 q^{68} + 12 q^{69} + 6 q^{71} - 8 q^{72} + 8 q^{73} - 6 q^{74} + 10 q^{76} - 8 q^{77} - 2 q^{78} + 10 q^{79} + 8 q^{81} - 6 q^{82} - 22 q^{83} + 4 q^{84} + 2 q^{86} - 10 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{91} - 12 q^{92} - 16 q^{93} + 14 q^{94} + 8 q^{96} + 16 q^{97} - 26 q^{98} + 6 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9 + 6 * q^11 - 8 * q^12 - 2 * q^13 + 4 * q^14 + 8 * q^16 - 14 * q^17 - 8 * q^18 + 10 * q^19 + 4 * q^21 - 6 * q^22 - 12 * q^23 + 8 * q^24 + 2 * q^26 - 8 * q^27 - 4 * q^28 + 10 * q^29 + 16 * q^31 - 8 * q^32 - 6 * q^33 + 14 * q^34 + 8 * q^36 + 6 * q^37 - 10 * q^38 + 2 * q^39 + 6 * q^41 - 4 * q^42 - 2 * q^43 + 6 * q^44 + 12 * q^46 - 14 * q^47 - 8 * q^48 + 26 * q^49 + 14 * q^51 - 2 * q^52 - 12 * q^53 + 8 * q^54 + 4 * q^56 - 10 * q^57 - 10 * q^58 + 16 * q^61 - 16 * q^62 - 4 * q^63 + 8 * q^64 + 6 * q^66 + 6 * q^67 - 14 * q^68 + 12 * q^69 + 6 * q^71 - 8 * q^72 + 8 * q^73 - 6 * q^74 + 10 * q^76 - 8 * q^77 - 2 * q^78 + 10 * q^79 + 8 * q^81 - 6 * q^82 - 22 * q^83 + 4 * q^84 + 2 * q^86 - 10 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^91 - 12 * q^92 - 16 * q^93 + 14 * q^94 + 8 * q^96 + 16 * q^97 - 26 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	3.52206	1.33122	0.665608	−	0.746302i	$-0.268172\pi$
$7$	3.52206	1.33122	0.665608	+	0.746302i	$0.268172\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	5.25498	1.58444	0.792219	−	0.610237i	$-0.208926\pi$
$11$	5.25498	1.58444	0.792219	+	0.610237i	$0.208926\pi$
$12$	−1.00000	−0.288675
$13$	−0.619103	−0.171708	−0.0858542	−	0.996308i	$-0.527362\pi$
$13$	−0.619103	−0.171708	−0.0858542	+	0.996308i	$0.527362\pi$
$14$	−3.52206	−0.941311
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.44557	−0.835673	−0.417836	−	0.908522i	$-0.637211\pi$
$17$	−3.44557	−0.835673	−0.417836	+	0.908522i	$0.637211\pi$
$18$	−1.00000	−0.235702
$19$	2.27431	0.521762	0.260881	−	0.965371i	$-0.415987\pi$
$19$	2.27431	0.521762	0.260881	+	0.965371i	$0.415987\pi$
$20$	0	0
$21$	−3.52206	−0.768578
$22$	−5.25498	−1.12037
$23$	8.95380	1.86700	0.933499	−	0.358581i	$-0.116739\pi$
$23$	8.95380	1.86700	0.933499	+	0.358581i	$0.116739\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	0.619103	0.121416
$27$	−1.00000	−0.192450
$28$	3.52206	0.665608
$29$	−2.68163	−0.497967	−0.248983	−	0.968508i	$-0.580096\pi$
$29$	−2.68163	−0.497967	−0.248983	+	0.968508i	$0.580096\pi$
$30$	0	0
$31$	9.76875	1.75452	0.877260	−	0.480015i	$-0.159369\pi$
$31$	9.76875	1.75452	0.877260	+	0.480015i	$0.159369\pi$
$32$	−1.00000	−0.176777
$33$	−5.25498	−0.914775
$34$	3.44557	0.590910
$35$	0	0
$36$	1.00000	0.166667
$37$	1.00173	0.164683	0.0823417	−	0.996604i	$-0.473760\pi$
$37$	1.00173	0.164683	0.0823417	+	0.996604i	$0.473760\pi$
$38$	−2.27431	−0.368941
$39$	0.619103	0.0991358
$40$	0	0
$41$	6.29687	0.983406	0.491703	−	0.870763i	$-0.336375\pi$
$41$	6.29687	0.983406	0.491703	+	0.870763i	$0.336375\pi$
$42$	3.52206	0.543466
$43$	1.51251	0.230656	0.115328	−	0.993327i	$-0.463208\pi$
$43$	1.51251	0.230656	0.115328	+	0.993327i	$0.463208\pi$
$44$	5.25498	0.792219
$45$	0	0
$46$	−8.95380	−1.32017
$47$	−10.6760	−1.55726	−0.778630	−	0.627483i	$-0.784085\pi$
$47$	−10.6760	−1.55726	−0.778630	+	0.627483i	$0.784085\pi$
$48$	−1.00000	−0.144338
$49$	5.40494	0.772134
$50$	0	0
$51$	3.44557	0.482476
$52$	−0.619103	−0.0858542
$53$	−0.553365	−0.0760105	−0.0380052	−	0.999278i	$-0.512100\pi$
$53$	−0.553365	−0.0760105	−0.0380052	+	0.999278i	$0.512100\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−3.52206	−0.470656
$57$	−2.27431	−0.301239
$58$	2.68163	0.352116
$59$	0.278771	0.0362929	0.0181465	−	0.999835i	$-0.494223\pi$
$59$	0.278771	0.0362929	0.0181465	+	0.999835i	$0.494223\pi$
$60$	0	0
$61$	3.68218	0.471455	0.235727	−	0.971819i	$-0.424253\pi$
$61$	3.68218	0.471455	0.235727	+	0.971819i	$0.424253\pi$
$62$	−9.76875	−1.24063
$63$	3.52206	0.443738
$64$	1.00000	0.125000
$65$	0	0
$66$	5.25498	0.646844
$67$	11.9121	1.45530	0.727648	−	0.685951i	$-0.240614\pi$
$67$	11.9121	1.45530	0.727648	+	0.685951i	$0.240614\pi$
$68$	−3.44557	−0.417836
$69$	−8.95380	−1.07791
$70$	0	0
$71$	4.74858	0.563553	0.281776	−	0.959480i	$-0.409076\pi$
$71$	4.74858	0.563553	0.281776	+	0.959480i	$0.409076\pi$
$72$	−1.00000	−0.117851
$73$	−9.83408	−1.15099	−0.575496	−	0.817804i	$-0.695191\pi$
$73$	−9.83408	−1.15099	−0.575496	+	0.817804i	$0.695191\pi$
$74$	−1.00173	−0.116449
$75$	0	0
$76$	2.27431	0.260881
$77$	18.5084	2.10923
$78$	−0.619103	−0.0700996
$79$	6.52057	0.733621	0.366810	−	0.930296i	$-0.380450\pi$
$79$	6.52057	0.733621	0.366810	+	0.930296i	$0.380450\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−6.29687	−0.695373
$83$	−2.65973	−0.291943	−0.145972	−	0.989289i	$-0.546631\pi$
$83$	−2.65973	−0.291943	−0.145972	+	0.989289i	$0.546631\pi$
$84$	−3.52206	−0.384289
$85$	0	0
$86$	−1.51251	−0.163098
$87$	2.68163	0.287501
$88$	−5.25498	−0.560183
$89$	−13.3860	−1.41891	−0.709455	−	0.704751i	$-0.751059\pi$
$89$	−13.3860	−1.41891	−0.709455	+	0.704751i	$0.751059\pi$
$90$	0	0
$91$	−2.18052	−0.228581
$92$	8.95380	0.933499
$93$	−9.76875	−1.01297
$94$	10.6760	1.10115
$95$	0	0
$96$	1.00000	0.102062
$97$	−4.37205	−0.443914	−0.221957	−	0.975056i	$-0.571244\pi$
$97$	−4.37205	−0.443914	−0.221957	+	0.975056i	$0.571244\pi$
$98$	−5.40494	−0.545981
$99$	5.25498	0.528146
$100$	0	0
$101$	−14.2687	−1.41979	−0.709893	−	0.704309i	$-0.751257\pi$
$101$	−14.2687	−1.41979	−0.709893	+	0.704309i	$0.751257\pi$
$102$	−3.44557	−0.341162
$103$	−17.6683	−1.74091	−0.870454	−	0.492250i	$-0.836175\pi$
$103$	−17.6683	−1.74091	−0.870454	+	0.492250i	$0.836175\pi$
$104$	0.619103	0.0607081
$105$	0	0
$106$	0.553365	0.0537475
$107$	−0.723713	−0.0699640	−0.0349820	−	0.999388i	$-0.511137\pi$
$107$	−0.723713	−0.0699640	−0.0349820	+	0.999388i	$0.511137\pi$
$108$	−1.00000	−0.0962250
$109$	−2.57331	−0.246479	−0.123239	−	0.992377i	$-0.539328\pi$
$109$	−2.57331	−0.246479	−0.123239	+	0.992377i	$0.539328\pi$
$110$	0	0
$111$	−1.00173	−0.0950800
$112$	3.52206	0.332804
$113$	−15.1881	−1.42878	−0.714390	−	0.699748i	$-0.753296\pi$
$113$	−15.1881	−1.42878	−0.714390	+	0.699748i	$0.753296\pi$
$114$	2.27431	0.213008
$115$	0	0
$116$	−2.68163	−0.248983
$117$	−0.619103	−0.0572361
$118$	−0.278771	−0.0256630
$119$	−12.1355	−1.11246
$120$	0	0
$121$	16.6149	1.51044
$122$	−3.68218	−0.333369
$123$	−6.29687	−0.567770
$124$	9.76875	0.877260
$125$	0	0
$126$	−3.52206	−0.313770
$127$	4.36385	0.387229	0.193615	−	0.981078i	$-0.437979\pi$
$127$	4.36385	0.387229	0.193615	+	0.981078i	$0.437979\pi$
$128$	−1.00000	−0.0883883
$129$	−1.51251	−0.133169
$130$	0	0
$131$	−0.617783	−0.0539760	−0.0269880	−	0.999636i	$-0.508592\pi$
$131$	−0.617783	−0.0539760	−0.0269880	+	0.999636i	$0.508592\pi$
$132$	−5.25498	−0.457388
$133$	8.01025	0.694577
$134$	−11.9121	−1.02905
$135$	0	0
$136$	3.44557	0.295455
$137$	−9.27162	−0.792128	−0.396064	−	0.918223i	$-0.629624\pi$
$137$	−9.27162	−0.792128	−0.396064	+	0.918223i	$0.629624\pi$
$138$	8.95380	0.762198
$139$	18.7619	1.59136	0.795680	−	0.605717i	$-0.207114\pi$
$139$	18.7619	1.59136	0.795680	+	0.605717i	$0.207114\pi$
$140$	0	0
$141$	10.6760	0.899085
$142$	−4.74858	−0.398492
$143$	−3.25338	−0.272061
$144$	1.00000	0.0833333
$145$	0	0
$146$	9.83408	0.813875
$147$	−5.40494	−0.445792
$148$	1.00173	0.0823417
$149$	−16.8396	−1.37955	−0.689777	−	0.724022i	$-0.742291\pi$
$149$	−16.8396	−1.37955	−0.689777	+	0.724022i	$0.742291\pi$
$150$	0	0
$151$	16.7932	1.36661	0.683305	−	0.730133i	$-0.260542\pi$
$151$	16.7932	1.36661	0.683305	+	0.730133i	$0.260542\pi$
$152$	−2.27431	−0.184471
$153$	−3.44557	−0.278558
$154$	−18.5084	−1.49145
$155$	0	0
$156$	0.619103	0.0495679
$157$	−4.55451	−0.363489	−0.181745	−	0.983346i	$-0.558174\pi$
$157$	−4.55451	−0.363489	−0.181745	+	0.983346i	$0.558174\pi$
$158$	−6.52057	−0.518748
$159$	0.553365	0.0438847
$160$	0	0
$161$	31.5359	2.48538
$162$	−1.00000	−0.0785674
$163$	20.2133	1.58322	0.791612	−	0.611024i	$-0.209242\pi$
$163$	20.2133	1.58322	0.791612	+	0.611024i	$0.209242\pi$
$164$	6.29687	0.491703
$165$	0	0
$166$	2.65973	0.206435
$167$	7.19183	0.556520	0.278260	−	0.960506i	$-0.410242\pi$
$167$	7.19183	0.556520	0.278260	+	0.960506i	$0.410242\pi$
$168$	3.52206	0.271733
$169$	−12.6167	−0.970516
$170$	0	0
$171$	2.27431	0.173921
$172$	1.51251	0.115328
$173$	−6.13155	−0.466173	−0.233086	−	0.972456i	$-0.574883\pi$
$173$	−6.13155	−0.466173	−0.233086	+	0.972456i	$0.574883\pi$
$174$	−2.68163	−0.203294
$175$	0	0
$176$	5.25498	0.396109
$177$	−0.278771	−0.0209537
$178$	13.3860	1.00332
$179$	14.3297	1.07105	0.535527	−	0.844518i	$-0.320113\pi$
$179$	14.3297	1.07105	0.535527	+	0.844518i	$0.320113\pi$
$180$	0	0
$181$	15.7294	1.16916	0.584580	−	0.811336i	$-0.301259\pi$
$181$	15.7294	1.16916	0.584580	+	0.811336i	$0.301259\pi$
$182$	2.18052	0.161631
$183$	−3.68218	−0.272195
$184$	−8.95380	−0.660083
$185$	0	0
$186$	9.76875	0.716280
$187$	−18.1064	−1.32407
$188$	−10.6760	−0.778630
$189$	−3.52206	−0.256193
$190$	0	0
$191$	−3.62240	−0.262108	−0.131054	−	0.991375i	$-0.541836\pi$
$191$	−3.62240	−0.262108	−0.131054	+	0.991375i	$0.541836\pi$
$192$	−1.00000	−0.0721688
$193$	9.72486	0.700010	0.350005	−	0.936748i	$-0.386180\pi$
$193$	9.72486	0.700010	0.350005	+	0.936748i	$0.386180\pi$
$194$	4.37205	0.313895
$195$	0	0
$196$	5.40494	0.386067
$197$	7.07377	0.503985	0.251992	−	0.967729i	$-0.418914\pi$
$197$	7.07377	0.503985	0.251992	+	0.967729i	$0.418914\pi$
$198$	−5.25498	−0.373455
$199$	−17.6745	−1.25291	−0.626455	−	0.779457i	$-0.715495\pi$
$199$	−17.6745	−1.25291	−0.626455	+	0.779457i	$0.715495\pi$
$200$	0	0
$201$	−11.9121	−0.840215
$202$	14.2687	1.00394
$203$	−9.44489	−0.662901
$204$	3.44557	0.241238
$205$	0	0
$206$	17.6683	1.23101
$207$	8.95380	0.622332
$208$	−0.619103	−0.0429271
$209$	11.9514	0.826698
$210$	0	0
$211$	−11.7638	−0.809855	−0.404927	−	0.914349i	$-0.632703\pi$
$211$	−11.7638	−0.809855	−0.404927	+	0.914349i	$0.632703\pi$
$212$	−0.553365	−0.0380052
$213$	−4.74858	−0.325367
$214$	0.723713	0.0494720
$215$	0	0
$216$	1.00000	0.0680414
$217$	34.4062	2.33564
$218$	2.57331	0.174287
$219$	9.83408	0.664526
$220$	0	0
$221$	2.13316	0.143492
$222$	1.00173	0.0672317
$223$	12.7005	0.850486	0.425243	−	0.905079i	$-0.360189\pi$
$223$	12.7005	0.850486	0.425243	+	0.905079i	$0.360189\pi$
$224$	−3.52206	−0.235328
$225$	0	0
$226$	15.1881	1.01030
$227$	14.2661	0.946877	0.473438	−	0.880827i	$-0.343013\pi$
$227$	14.2661	0.946877	0.473438	+	0.880827i	$0.343013\pi$
$228$	−2.27431	−0.150620
$229$	8.80308	0.581724	0.290862	−	0.956765i	$-0.406058\pi$
$229$	8.80308	0.581724	0.290862	+	0.956765i	$0.406058\pi$
$230$	0	0
$231$	−18.5084	−1.21776
$232$	2.68163	0.176058
$233$	15.0762	0.987676	0.493838	−	0.869554i	$-0.335594\pi$
$233$	15.0762	0.987676	0.493838	+	0.869554i	$0.335594\pi$
$234$	0.619103	0.0404720
$235$	0	0
$236$	0.278771	0.0181465
$237$	−6.52057	−0.423556
$238$	12.1355	0.786628
$239$	−6.24583	−0.404009	−0.202004	−	0.979385i	$-0.564746\pi$
$239$	−6.24583	−0.404009	−0.202004	+	0.979385i	$0.564746\pi$
$240$	0	0
$241$	−14.8094	−0.953959	−0.476979	−	0.878914i	$-0.658268\pi$
$241$	−14.8094	−0.953959	−0.476979	+	0.878914i	$0.658268\pi$
$242$	−16.6149	−1.06804
$243$	−1.00000	−0.0641500
$244$	3.68218	0.235727
$245$	0	0
$246$	6.29687	0.401474
$247$	−1.40803	−0.0895908
$248$	−9.76875	−0.620317
$249$	2.65973	0.168554
$250$	0	0
$251$	18.2744	1.15347	0.576735	−	0.816931i	$-0.304327\pi$
$251$	18.2744	1.15347	0.576735	+	0.816931i	$0.304327\pi$
$252$	3.52206	0.221869
$253$	47.0521	2.95814
$254$	−4.36385	−0.273812
$255$	0	0
$256$	1.00000	0.0625000
$257$	1.80149	0.112374	0.0561868	−	0.998420i	$-0.482106\pi$
$257$	1.80149	0.112374	0.0561868	+	0.998420i	$0.482106\pi$
$258$	1.51251	0.0941649
$259$	3.52816	0.219229
$260$	0	0
$261$	−2.68163	−0.165989
$262$	0.617783	0.0381668
$263$	−14.2039	−0.875848	−0.437924	−	0.899012i	$-0.644286\pi$
$263$	−14.2039	−0.875848	−0.437924	+	0.899012i	$0.644286\pi$
$264$	5.25498	0.323422
$265$	0	0
$266$	−8.01025	−0.491140
$267$	13.3860	0.819208
$268$	11.9121	0.727648
$269$	−6.24307	−0.380647	−0.190323	−	0.981721i	$-0.560954\pi$
$269$	−6.24307	−0.380647	−0.190323	+	0.981721i	$0.560954\pi$
$270$	0	0
$271$	−23.8469	−1.44860	−0.724299	−	0.689486i	$-0.757836\pi$
$271$	−23.8469	−1.44860	−0.724299	+	0.689486i	$0.757836\pi$
$272$	−3.44557	−0.208918
$273$	2.18052	0.131971
$274$	9.27162	0.560119
$275$	0	0
$276$	−8.95380	−0.538956
$277$	6.97357	0.419001	0.209501	−	0.977809i	$-0.432816\pi$
$277$	6.97357	0.419001	0.209501	+	0.977809i	$0.432816\pi$
$278$	−18.7619	−1.12526
$279$	9.76875	0.584840
$280$	0	0
$281$	11.6338	0.694013	0.347007	−	0.937863i	$-0.387198\pi$
$281$	11.6338	0.694013	0.347007	+	0.937863i	$0.387198\pi$
$282$	−10.6760	−0.635749
$283$	−9.60500	−0.570958	−0.285479	−	0.958385i	$-0.592153\pi$
$283$	−9.60500	−0.570958	−0.285479	+	0.958385i	$0.592153\pi$
$284$	4.74858	0.281776
$285$	0	0
$286$	3.25338	0.192376
$287$	22.1780	1.30912
$288$	−1.00000	−0.0589256
$289$	−5.12807	−0.301651
$290$	0	0
$291$	4.37205	0.256294
$292$	−9.83408	−0.575496
$293$	8.52716	0.498162	0.249081	−	0.968483i	$-0.419871\pi$
$293$	8.52716	0.498162	0.249081	+	0.968483i	$0.419871\pi$
$294$	5.40494	0.315222
$295$	0	0
$296$	−1.00173	−0.0582244
$297$	−5.25498	−0.304925
$298$	16.8396	0.975492
$299$	−5.54333	−0.320579
$300$	0	0
$301$	5.32717	0.307053
$302$	−16.7932	−0.966339
$303$	14.2687	0.819714
$304$	2.27431	0.130440
$305$	0	0
$306$	3.44557	0.196970
$307$	2.85794	0.163111	0.0815557	−	0.996669i	$-0.474011\pi$
$307$	2.85794	0.163111	0.0815557	+	0.996669i	$0.474011\pi$
$308$	18.5084	1.05461
$309$	17.6683	1.00511
$310$	0	0
$311$	−10.1618	−0.576223	−0.288111	−	0.957597i	$-0.593027\pi$
$311$	−10.1618	−0.576223	−0.288111	+	0.957597i	$0.593027\pi$
$312$	−0.619103	−0.0350498
$313$	18.2036	1.02893	0.514465	−	0.857512i	$-0.327991\pi$
$313$	18.2036	1.02893	0.514465	+	0.857512i	$0.327991\pi$
$314$	4.55451	0.257026
$315$	0	0
$316$	6.52057	0.366810
$317$	31.2764	1.75666	0.878328	−	0.478059i	$-0.158660\pi$
$317$	31.2764	1.75666	0.878328	+	0.478059i	$0.158660\pi$
$318$	−0.553365	−0.0310312
$319$	−14.0919	−0.788997
$320$	0	0
$321$	0.723713	0.0403937
$322$	−31.5359	−1.75743
$323$	−7.83627	−0.436022
$324$	1.00000	0.0555556
$325$	0	0
$326$	−20.2133	−1.11951
$327$	2.57331	0.142305
$328$	−6.29687	−0.347686
$329$	−37.6017	−2.07305
$330$	0	0
$331$	3.43194	0.188637	0.0943183	−	0.995542i	$-0.469933\pi$
$331$	3.43194	0.188637	0.0943183	+	0.995542i	$0.469933\pi$
$332$	−2.65973	−0.145972
$333$	1.00173	0.0548945
$334$	−7.19183	−0.393519
$335$	0	0
$336$	−3.52206	−0.192144
$337$	11.7235	0.638622	0.319311	−	0.947650i	$-0.396549\pi$
$337$	11.7235	0.638622	0.319311	+	0.947650i	$0.396549\pi$
$338$	12.6167	0.686259
$339$	15.1881	0.824907
$340$	0	0
$341$	51.3346	2.77993
$342$	−2.27431	−0.122980
$343$	−5.61791	−0.303339
$344$	−1.51251	−0.0815492
$345$	0	0
$346$	6.13155	0.329634
$347$	−32.4102	−1.73987	−0.869935	−	0.493167i	$-0.835839\pi$
$347$	−32.4102	−1.73987	−0.869935	+	0.493167i	$0.835839\pi$
$348$	2.68163	0.143751
$349$	−11.3708	−0.608665	−0.304333	−	0.952566i	$-0.598433\pi$
$349$	−11.3708	−0.608665	−0.304333	+	0.952566i	$0.598433\pi$
$350$	0	0
$351$	0.619103	0.0330453
$352$	−5.25498	−0.280092
$353$	−2.08723	−0.111092	−0.0555461	−	0.998456i	$-0.517690\pi$
$353$	−2.08723	−0.111092	−0.0555461	+	0.998456i	$0.517690\pi$
$354$	0.278771	0.0148165
$355$	0	0
$356$	−13.3860	−0.709455
$357$	12.1355	0.642279
$358$	−14.3297	−0.757349
$359$	6.81215	0.359532	0.179766	−	0.983709i	$-0.442466\pi$
$359$	6.81215	0.359532	0.179766	+	0.983709i	$0.442466\pi$
$360$	0	0
$361$	−13.8275	−0.727765
$362$	−15.7294	−0.826722
$363$	−16.6149	−0.872054
$364$	−2.18052	−0.114290
$365$	0	0
$366$	3.68218	0.192471
$367$	0.155337	0.00810850	0.00405425	−	0.999992i	$-0.498709\pi$
$367$	0.155337	0.00810850	0.00405425	+	0.999992i	$0.498709\pi$
$368$	8.95380	0.466749
$369$	6.29687	0.327802
$370$	0	0
$371$	−1.94899	−0.101186
$372$	−9.76875	−0.506486
$373$	29.7460	1.54019	0.770096	−	0.637928i	$-0.220208\pi$
$373$	29.7460	1.54019	0.770096	+	0.637928i	$0.220208\pi$
$374$	18.1064	0.936259
$375$	0	0
$376$	10.6760	0.550575
$377$	1.66021	0.0855051
$378$	3.52206	0.181155
$379$	−16.6822	−0.856910	−0.428455	−	0.903563i	$-0.640942\pi$
$379$	−16.6822	−0.856910	−0.428455	+	0.903563i	$0.640942\pi$
$380$	0	0
$381$	−4.36385	−0.223567
$382$	3.62240	0.185338
$383$	11.2792	0.576338	0.288169	−	0.957580i	$-0.406954\pi$
$383$	11.2792	0.576338	0.288169	+	0.957580i	$0.406954\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−9.72486	−0.494982
$387$	1.51251	0.0768853
$388$	−4.37205	−0.221957
$389$	6.66140	0.337746	0.168873	−	0.985638i	$-0.445987\pi$
$389$	6.66140	0.337746	0.168873	+	0.985638i	$0.445987\pi$
$390$	0	0
$391$	−30.8509	−1.56020
$392$	−5.40494	−0.272991
$393$	0.617783	0.0311630
$394$	−7.07377	−0.356371
$395$	0	0
$396$	5.25498	0.264073
$397$	37.2235	1.86819	0.934097	−	0.357020i	$-0.116207\pi$
$397$	37.2235	1.86819	0.934097	+	0.357020i	$0.116207\pi$
$398$	17.6745	0.885942
$399$	−8.01025	−0.401014
$400$	0	0
$401$	19.6891	0.983228	0.491614	−	0.870813i	$-0.336407\pi$
$401$	19.6891	0.983228	0.491614	+	0.870813i	$0.336407\pi$
$402$	11.9121	0.594122
$403$	−6.04787	−0.301266
$404$	−14.2687	−0.709893
$405$	0	0
$406$	9.44489	0.468742
$407$	5.26407	0.260930
$408$	−3.44557	−0.170581
$409$	29.5602	1.46166	0.730828	−	0.682561i	$-0.239134\pi$
$409$	29.5602	1.46166	0.730828	+	0.682561i	$0.239134\pi$
$410$	0	0
$411$	9.27162	0.457335
$412$	−17.6683	−0.870454
$413$	0.981851	0.0483137
$414$	−8.95380	−0.440055
$415$	0	0
$416$	0.619103	0.0303540
$417$	−18.7619	−0.918772
$418$	−11.9514	−0.584564
$419$	−1.17027	−0.0571714	−0.0285857	−	0.999591i	$-0.509100\pi$
$419$	−1.17027	−0.0571714	−0.0285857	+	0.999591i	$0.509100\pi$
$420$	0	0
$421$	8.33013	0.405986	0.202993	−	0.979180i	$-0.434933\pi$
$421$	8.33013	0.405986	0.202993	+	0.979180i	$0.434933\pi$
$422$	11.7638	0.572654
$423$	−10.6760	−0.519087
$424$	0.553365	0.0268738
$425$	0	0
$426$	4.74858	0.230069
$427$	12.9689	0.627608
$428$	−0.723713	−0.0349820
$429$	3.25338	0.157075
$430$	0	0
$431$	−18.6927	−0.900395	−0.450198	−	0.892929i	$-0.648646\pi$
$431$	−18.6927	−0.900395	−0.450198	+	0.892929i	$0.648646\pi$
$432$	−1.00000	−0.0481125
$433$	18.9083	0.908676	0.454338	−	0.890829i	$-0.349876\pi$
$433$	18.9083	0.908676	0.454338	+	0.890829i	$0.349876\pi$
$434$	−34.4062	−1.65155
$435$	0	0
$436$	−2.57331	−0.123239
$437$	20.3637	0.974127
$438$	−9.83408	−0.469891
$439$	−40.8600	−1.95014	−0.975070	−	0.221895i	$-0.928776\pi$
$439$	−40.8600	−1.95014	−0.975070	+	0.221895i	$0.928776\pi$
$440$	0	0
$441$	5.40494	0.257378
$442$	−2.13316	−0.101464
$443$	−5.99083	−0.284633	−0.142317	−	0.989821i	$-0.545455\pi$
$443$	−5.99083	−0.284633	−0.142317	+	0.989821i	$0.545455\pi$
$444$	−1.00173	−0.0475400
$445$	0	0
$446$	−12.7005	−0.601384
$447$	16.8396	0.796486
$448$	3.52206	0.166402
$449$	12.4505	0.587574	0.293787	−	0.955871i	$-0.405084\pi$
$449$	12.4505	0.587574	0.293787	+	0.955871i	$0.405084\pi$
$450$	0	0
$451$	33.0899	1.55814
$452$	−15.1881	−0.714390
$453$	−16.7932	−0.789013
$454$	−14.2661	−0.669543
$455$	0	0
$456$	2.27431	0.106504
$457$	−1.11807	−0.0523011	−0.0261506	−	0.999658i	$-0.508325\pi$
$457$	−1.11807	−0.0523011	−0.0261506	+	0.999658i	$0.508325\pi$
$458$	−8.80308	−0.411341
$459$	3.44557	0.160825
$460$	0	0
$461$	−30.0946	−1.40164	−0.700822	−	0.713336i	$-0.747183\pi$
$461$	−30.0946	−1.40164	−0.700822	+	0.713336i	$0.747183\pi$
$462$	18.5084	0.861088
$463$	21.0358	0.977616	0.488808	−	0.872391i	$-0.337432\pi$
$463$	21.0358	0.977616	0.488808	+	0.872391i	$0.337432\pi$
$464$	−2.68163	−0.124492
$465$	0	0
$466$	−15.0762	−0.698393
$467$	3.53614	0.163633	0.0818166	−	0.996647i	$-0.473928\pi$
$467$	3.53614	0.163633	0.0818166	+	0.996647i	$0.473928\pi$
$468$	−0.619103	−0.0286181
$469$	41.9552	1.93731
$470$	0	0
$471$	4.55451	0.209861
$472$	−0.278771	−0.0128315
$473$	7.94823	0.365460
$474$	6.52057	0.299499
$475$	0	0
$476$	−12.1355	−0.556230
$477$	−0.553365	−0.0253368
$478$	6.24583	0.285677
$479$	40.4357	1.84756	0.923778	−	0.382929i	$-0.125085\pi$
$479$	40.4357	1.84756	0.923778	+	0.382929i	$0.125085\pi$
$480$	0	0
$481$	−0.620174	−0.0282775
$482$	14.8094	0.674551
$483$	−31.5359	−1.43493
$484$	16.6149	0.755221
$485$	0	0
$486$	1.00000	0.0453609
$487$	26.7043	1.21009	0.605044	−	0.796192i	$-0.293156\pi$
$487$	26.7043	1.21009	0.605044	+	0.796192i	$0.293156\pi$
$488$	−3.68218	−0.166685
$489$	−20.2133	−0.914075
$490$	0	0
$491$	33.1096	1.49421	0.747107	−	0.664704i	$-0.231442\pi$
$491$	33.1096	1.49421	0.747107	+	0.664704i	$0.231442\pi$
$492$	−6.29687	−0.283885
$493$	9.23975	0.416137
$494$	1.40803	0.0633503
$495$	0	0
$496$	9.76875	0.438630
$497$	16.7248	0.750210
$498$	−2.65973	−0.119185
$499$	6.01303	0.269180	0.134590	−	0.990901i	$-0.457028\pi$
$499$	6.01303	0.269180	0.134590	+	0.990901i	$0.457028\pi$
$500$	0	0
$501$	−7.19183	−0.321307
$502$	−18.2744	−0.815626
$503$	−6.66724	−0.297277	−0.148639	−	0.988892i	$-0.547489\pi$
$503$	−6.66724	−0.297277	−0.148639	+	0.988892i	$0.547489\pi$
$504$	−3.52206	−0.156885
$505$	0	0
$506$	−47.0521	−2.09172
$507$	12.6167	0.560328
$508$	4.36385	0.193615
$509$	−17.6023	−0.780208	−0.390104	−	0.920771i	$-0.627561\pi$
$509$	−17.6023	−0.780208	−0.390104	+	0.920771i	$0.627561\pi$
$510$	0	0
$511$	−34.6363	−1.53222
$512$	−1.00000	−0.0441942
$513$	−2.27431	−0.100413
$514$	−1.80149	−0.0794601
$515$	0	0
$516$	−1.51251	−0.0665846
$517$	−56.1024	−2.46738
$518$	−3.52816	−0.155018
$519$	6.13155	0.269145
$520$	0	0
$521$	18.4407	0.807900	0.403950	−	0.914781i	$-0.367637\pi$
$521$	18.4407	0.807900	0.403950	+	0.914781i	$0.367637\pi$
$522$	2.68163	0.117372
$523$	10.3150	0.451044	0.225522	−	0.974238i	$-0.427591\pi$
$523$	10.3150	0.451044	0.225522	+	0.974238i	$0.427591\pi$
$524$	−0.617783	−0.0269880
$525$	0	0
$526$	14.2039	0.619318
$527$	−33.6589	−1.46620
$528$	−5.25498	−0.228694
$529$	57.1706	2.48568
$530$	0	0
$531$	0.278771	0.0120976
$532$	8.01025	0.347288
$533$	−3.89841	−0.168859
$534$	−13.3860	−0.579268
$535$	0	0
$536$	−11.9121	−0.514525
$537$	−14.3297	−0.618373
$538$	6.24307	0.269158
$539$	28.4029	1.22340
$540$	0	0
$541$	−37.4596	−1.61051	−0.805256	−	0.592927i	$-0.797972\pi$
$541$	−37.4596	−1.61051	−0.805256	+	0.592927i	$0.797972\pi$
$542$	23.8469	1.02431
$543$	−15.7294	−0.675015
$544$	3.44557	0.147727
$545$	0	0
$546$	−2.18052	−0.0933177
$547$	−11.0459	−0.472288	−0.236144	−	0.971718i	$-0.575884\pi$
$547$	−11.0459	−0.472288	−0.236144	+	0.971718i	$0.575884\pi$
$548$	−9.27162	−0.396064
$549$	3.68218	0.157152
$550$	0	0
$551$	−6.09886	−0.259820
$552$	8.95380	0.381099
$553$	22.9659	0.976607
$554$	−6.97357	−0.296278
$555$	0	0
$556$	18.7619	0.795680
$557$	−29.7087	−1.25880	−0.629400	−	0.777082i	$-0.716699\pi$
$557$	−29.7087	−1.25880	−0.629400	+	0.777082i	$0.716699\pi$
$558$	−9.76875	−0.413544
$559$	−0.936401	−0.0396055
$560$	0	0
$561$	18.1064	0.764453
$562$	−11.6338	−0.490741
$563$	−18.3303	−0.772532	−0.386266	−	0.922387i	$-0.626235\pi$
$563$	−18.3303	−0.772532	−0.386266	+	0.922387i	$0.626235\pi$
$564$	10.6760	0.449542
$565$	0	0
$566$	9.60500	0.403728
$567$	3.52206	0.147913
$568$	−4.74858	−0.199246
$569$	−21.9915	−0.921933	−0.460966	−	0.887418i	$-0.652497\pi$
$569$	−21.9915	−0.921933	−0.460966	+	0.887418i	$0.652497\pi$
$570$	0	0
$571$	25.0786	1.04951	0.524754	−	0.851254i	$-0.324157\pi$
$571$	25.0786	1.04951	0.524754	+	0.851254i	$0.324157\pi$
$572$	−3.25338	−0.136031
$573$	3.62240	0.151328
$574$	−22.1780	−0.925691
$575$	0	0
$576$	1.00000	0.0416667
$577$	−34.9875	−1.45655	−0.728275	−	0.685285i	$-0.759678\pi$
$577$	−34.9875	−1.45655	−0.728275	+	0.685285i	$0.759678\pi$
$578$	5.12807	0.213300
$579$	−9.72486	−0.404151
$580$	0	0
$581$	−9.36774	−0.388639
$582$	−4.37205	−0.181227
$583$	−2.90792	−0.120434
$584$	9.83408	0.406937
$585$	0	0
$586$	−8.52716	−0.352254
$587$	−10.3857	−0.428664	−0.214332	−	0.976761i	$-0.568757\pi$
$587$	−10.3857	−0.428664	−0.214332	+	0.976761i	$0.568757\pi$
$588$	−5.40494	−0.222896
$589$	22.2171	0.915441
$590$	0	0
$591$	−7.07377	−0.290976
$592$	1.00173	0.0411708
$593$	0.948200	0.0389379	0.0194690	−	0.999810i	$-0.493802\pi$
$593$	0.948200	0.0389379	0.0194690	+	0.999810i	$0.493802\pi$
$594$	5.25498	0.215615
$595$	0	0
$596$	−16.8396	−0.689777
$597$	17.6745	0.723368
$598$	5.54333	0.226684
$599$	25.4901	1.04150	0.520748	−	0.853710i	$-0.325653\pi$
$599$	25.4901	1.04150	0.520748	+	0.853710i	$0.325653\pi$
$600$	0	0
$601$	−16.6409	−0.678797	−0.339399	−	0.940643i	$-0.610224\pi$
$601$	−16.6409	−0.678797	−0.339399	+	0.940643i	$0.610224\pi$
$602$	−5.32717	−0.217119
$603$	11.9121	0.485098
$604$	16.7932	0.683305
$605$	0	0
$606$	−14.2687	−0.579625
$607$	33.2662	1.35023	0.675116	−	0.737712i	$-0.264094\pi$
$607$	33.2662	1.35023	0.675116	+	0.737712i	$0.264094\pi$
$608$	−2.27431	−0.0922353
$609$	9.44489	0.382726
$610$	0	0
$611$	6.60957	0.267395
$612$	−3.44557	−0.139279
$613$	−16.2821	−0.657626	−0.328813	−	0.944395i	$-0.606649\pi$
$613$	−16.2821	−0.657626	−0.328813	+	0.944395i	$0.606649\pi$
$614$	−2.85794	−0.115337
$615$	0	0
$616$	−18.5084	−0.745724
$617$	−48.5284	−1.95368	−0.976839	−	0.213974i	$-0.931359\pi$
$617$	−48.5284	−1.95368	−0.976839	+	0.213974i	$0.931359\pi$
$618$	−17.6683	−0.710723
$619$	−24.6659	−0.991408	−0.495704	−	0.868492i	$-0.665090\pi$
$619$	−24.6659	−0.991408	−0.495704	+	0.868492i	$0.665090\pi$
$620$	0	0
$621$	−8.95380	−0.359304
$622$	10.1618	0.407451
$623$	−47.1463	−1.88887
$624$	0.619103	0.0247840
$625$	0	0
$626$	−18.2036	−0.727563
$627$	−11.9514	−0.477295
$628$	−4.55451	−0.181745
$629$	−3.45153	−0.137621
$630$	0	0
$631$	−11.7933	−0.469485	−0.234742	−	0.972058i	$-0.575425\pi$
$631$	−11.7933	−0.469485	−0.234742	+	0.972058i	$0.575425\pi$
$632$	−6.52057	−0.259374
$633$	11.7638	0.467570
$634$	−31.2764	−1.24214
$635$	0	0
$636$	0.553365	0.0219423
$637$	−3.34621	−0.132582
$638$	14.0919	0.557905
$639$	4.74858	0.187851
$640$	0	0
$641$	−13.6031	−0.537291	−0.268645	−	0.963239i	$-0.586576\pi$
$641$	−13.6031	−0.537291	−0.268645	+	0.963239i	$0.586576\pi$
$642$	−0.723713	−0.0285627
$643$	20.9102	0.824617	0.412308	−	0.911044i	$-0.364723\pi$
$643$	20.9102	0.824617	0.412308	+	0.911044i	$0.364723\pi$
$644$	31.5359	1.24269
$645$	0	0
$646$	7.83627	0.308314
$647$	45.8878	1.80404	0.902018	−	0.431699i	$-0.142086\pi$
$647$	45.8878	1.80404	0.902018	+	0.431699i	$0.142086\pi$
$648$	−1.00000	−0.0392837
$649$	1.46494	0.0575039
$650$	0	0
$651$	−34.4062	−1.34848
$652$	20.2133	0.791612
$653$	2.60610	0.101985	0.0509923	−	0.998699i	$-0.483762\pi$
$653$	2.60610	0.101985	0.0509923	+	0.998699i	$0.483762\pi$
$654$	−2.57331	−0.100625
$655$	0	0
$656$	6.29687	0.245851
$657$	−9.83408	−0.383664
$658$	37.6017	1.46587
$659$	23.9462	0.932810	0.466405	−	0.884571i	$-0.345549\pi$
$659$	23.9462	0.932810	0.466405	+	0.884571i	$0.345549\pi$
$660$	0	0
$661$	25.9503	1.00935	0.504674	−	0.863310i	$-0.331613\pi$
$661$	25.9503	1.00935	0.504674	+	0.863310i	$0.331613\pi$
$662$	−3.43194	−0.133386
$663$	−2.13316	−0.0828451
$664$	2.65973	0.103218
$665$	0	0
$666$	−1.00173	−0.0388162
$667$	−24.0108	−0.929703
$668$	7.19183	0.278260
$669$	−12.7005	−0.491028
$670$	0	0
$671$	19.3498	0.746991
$672$	3.52206	0.135867
$673$	−14.8093	−0.570856	−0.285428	−	0.958400i	$-0.592136\pi$
$673$	−14.8093	−0.570856	−0.285428	+	0.958400i	$0.592136\pi$
$674$	−11.7235	−0.451574
$675$	0	0
$676$	−12.6167	−0.485258
$677$	34.9321	1.34255	0.671274	−	0.741209i	$-0.265747\pi$
$677$	34.9321	1.34255	0.671274	+	0.741209i	$0.265747\pi$
$678$	−15.1881	−0.583297
$679$	−15.3986	−0.590945
$680$	0	0
$681$	−14.2661	−0.546680
$682$	−51.3346	−1.96571
$683$	−21.0086	−0.803871	−0.401936	−	0.915668i	$-0.631662\pi$
$683$	−21.0086	−0.803871	−0.401936	+	0.915668i	$0.631662\pi$
$684$	2.27431	0.0869603
$685$	0	0
$686$	5.61791	0.214493
$687$	−8.80308	−0.335859
$688$	1.51251	0.0576640
$689$	0.342590	0.0130516
$690$	0	0
$691$	−23.4042	−0.890339	−0.445170	−	0.895446i	$-0.646857\pi$
$691$	−23.4042	−0.890339	−0.445170	+	0.895446i	$0.646857\pi$
$692$	−6.13155	−0.233086
$693$	18.5084	0.703076
$694$	32.4102	1.23027
$695$	0	0
$696$	−2.68163	−0.101647
$697$	−21.6963	−0.821805
$698$	11.3708	0.430391
$699$	−15.0762	−0.570235
$700$	0	0
$701$	−43.2849	−1.63485	−0.817424	−	0.576037i	$-0.804598\pi$
$701$	−43.2849	−1.63485	−0.817424	+	0.576037i	$0.804598\pi$
$702$	−0.619103	−0.0233665
$703$	2.27824	0.0859255
$704$	5.25498	0.198055
$705$	0	0
$706$	2.08723	0.0785541
$707$	−50.2552	−1.89004
$708$	−0.278771	−0.0104769
$709$	−25.0146	−0.939442	−0.469721	−	0.882815i	$-0.655645\pi$
$709$	−25.0146	−0.939442	−0.469721	+	0.882815i	$0.655645\pi$
$710$	0	0
$711$	6.52057	0.244540
$712$	13.3860	0.501661
$713$	87.4675	3.27568
$714$	−12.1355	−0.454160
$715$	0	0
$716$	14.3297	0.535527
$717$	6.24583	0.233255
$718$	−6.81215	−0.254227
$719$	−30.8440	−1.15029	−0.575143	−	0.818053i	$-0.695054\pi$
$719$	−30.8440	−1.15029	−0.575143	+	0.818053i	$0.695054\pi$
$720$	0	0
$721$	−62.2288	−2.31752
$722$	13.8275	0.514607
$723$	14.8094	0.550768
$724$	15.7294	0.584580
$725$	0	0
$726$	16.6149	0.616635
$727$	0.655542	0.0243127	0.0121564	−	0.999926i	$-0.496130\pi$
$727$	0.655542	0.0243127	0.0121564	+	0.999926i	$0.496130\pi$
$728$	2.18052	0.0808155
$729$	1.00000	0.0370370
$730$	0	0
$731$	−5.21146	−0.192753
$732$	−3.68218	−0.136097
$733$	13.7121	0.506467	0.253233	−	0.967405i	$-0.418506\pi$
$733$	13.7121	0.506467	0.253233	+	0.967405i	$0.418506\pi$
$734$	−0.155337	−0.00573358
$735$	0	0
$736$	−8.95380	−0.330042
$737$	62.5979	2.30582
$738$	−6.29687	−0.231791
$739$	−10.9570	−0.403059	−0.201530	−	0.979482i	$-0.564591\pi$
$739$	−10.9570	−0.403059	−0.201530	+	0.979482i	$0.564591\pi$
$740$	0	0
$741$	1.40803	0.0517253
$742$	1.94899	0.0715495
$743$	5.67053	0.208032	0.104016	−	0.994576i	$-0.466831\pi$
$743$	5.67053	0.208032	0.104016	+	0.994576i	$0.466831\pi$
$744$	9.76875	0.358140
$745$	0	0
$746$	−29.7460	−1.08908
$747$	−2.65973	−0.0973144
$748$	−18.1064	−0.662035
$749$	−2.54896	−0.0931371
$750$	0	0
$751$	−22.2909	−0.813408	−0.406704	−	0.913560i	$-0.633322\pi$
$751$	−22.2909	−0.813408	−0.406704	+	0.913560i	$0.633322\pi$
$752$	−10.6760	−0.389315
$753$	−18.2744	−0.665956
$754$	−1.66021	−0.0604612
$755$	0	0
$756$	−3.52206	−0.128096
$757$	−17.3894	−0.632030	−0.316015	−	0.948754i	$-0.602345\pi$
$757$	−17.3894	−0.632030	−0.316015	+	0.948754i	$0.602345\pi$
$758$	16.6822	0.605927
$759$	−47.0521	−1.70788
$760$	0	0
$761$	15.4947	0.561682	0.280841	−	0.959754i	$-0.409387\pi$
$761$	15.4947	0.561682	0.280841	+	0.959754i	$0.409387\pi$
$762$	4.36385	0.158086
$763$	−9.06338	−0.328116
$764$	−3.62240	−0.131054
$765$	0	0
$766$	−11.2792	−0.407532
$767$	−0.172588	−0.00623180
$768$	−1.00000	−0.0360844
$769$	−48.8512	−1.76162	−0.880810	−	0.473469i	$-0.843002\pi$
$769$	−48.8512	−1.76162	−0.880810	+	0.473469i	$0.843002\pi$
$770$	0	0
$771$	−1.80149	−0.0648789
$772$	9.72486	0.350005
$773$	1.07544	0.0386810	0.0193405	−	0.999813i	$-0.493843\pi$
$773$	1.07544	0.0386810	0.0193405	+	0.999813i	$0.493843\pi$
$774$	−1.51251	−0.0543661
$775$	0	0
$776$	4.37205	0.156947
$777$	−3.52816	−0.126572
$778$	−6.66140	−0.238823
$779$	14.3210	0.513103
$780$	0	0
$781$	24.9537	0.892914
$782$	30.8509	1.10323
$783$	2.68163	0.0958338
$784$	5.40494	0.193034
$785$	0	0
$786$	−0.617783	−0.0220356
$787$	−37.8477	−1.34913	−0.674563	−	0.738217i	$-0.735668\pi$
$787$	−37.8477	−1.34913	−0.674563	+	0.738217i	$0.735668\pi$
$788$	7.07377	0.251992
$789$	14.2039	0.505671
$790$	0	0
$791$	−53.4936	−1.90201
$792$	−5.25498	−0.186728
$793$	−2.27965	−0.0809527
$794$	−37.2235	−1.32101
$795$	0	0
$796$	−17.6745	−0.626455
$797$	11.5577	0.409395	0.204697	−	0.978825i	$-0.434379\pi$
$797$	11.5577	0.409395	0.204697	+	0.978825i	$0.434379\pi$
$798$	8.01025	0.283560
$799$	36.7850	1.30136
$800$	0	0
$801$	−13.3860	−0.472970
$802$	−19.6891	−0.695247
$803$	−51.6780	−1.82368
$804$	−11.9121	−0.420108
$805$	0	0
$806$	6.04787	0.213027
$807$	6.24307	0.219767
$808$	14.2687	0.501970
$809$	−20.1993	−0.710168	−0.355084	−	0.934834i	$-0.615548\pi$
$809$	−20.1993	−0.710168	−0.355084	+	0.934834i	$0.615548\pi$
$810$	0	0
$811$	−41.6812	−1.46363	−0.731813	−	0.681506i	$-0.761326\pi$
$811$	−41.6812	−1.46363	−0.731813	+	0.681506i	$0.761326\pi$
$812$	−9.44489	−0.331451
$813$	23.8469	0.836348
$814$	−5.26407	−0.184506
$815$	0	0
$816$	3.44557	0.120619
$817$	3.43992	0.120347
$818$	−29.5602	−1.03355
$819$	−2.18052	−0.0761936
$820$	0	0
$821$	−32.7199	−1.14193	−0.570967	−	0.820973i	$-0.693432\pi$
$821$	−32.7199	−1.14193	−0.570967	+	0.820973i	$0.693432\pi$
$822$	−9.27162	−0.323385
$823$	−33.4849	−1.16721	−0.583604	−	0.812038i	$-0.698358\pi$
$823$	−33.4849	−1.16721	−0.583604	+	0.812038i	$0.698358\pi$
$824$	17.6683	0.615504
$825$	0	0
$826$	−0.981851	−0.0341630
$827$	8.74872	0.304223	0.152111	−	0.988363i	$-0.451393\pi$
$827$	8.74872	0.304223	0.152111	+	0.988363i	$0.451393\pi$
$828$	8.95380	0.311166
$829$	18.9492	0.658134	0.329067	−	0.944307i	$-0.393266\pi$
$829$	18.9492	0.658134	0.329067	+	0.944307i	$0.393266\pi$
$830$	0	0
$831$	−6.97357	−0.241910
$832$	−0.619103	−0.0214635
$833$	−18.6231	−0.645251
$834$	18.7619	0.649670
$835$	0	0
$836$	11.9514	0.413349
$837$	−9.76875	−0.337658
$838$	1.17027	0.0404263
$839$	−11.4769	−0.396228	−0.198114	−	0.980179i	$-0.563482\pi$
$839$	−11.4769	−0.396228	−0.198114	+	0.980179i	$0.563482\pi$
$840$	0	0
$841$	−21.8088	−0.752029
$842$	−8.33013	−0.287075
$843$	−11.6338	−0.400689
$844$	−11.7638	−0.404927
$845$	0	0
$846$	10.6760	0.367050
$847$	58.5186	2.01072
$848$	−0.553365	−0.0190026
$849$	9.60500	0.329643
$850$	0	0
$851$	8.96929	0.307463
$852$	−4.74858	−0.162684
$853$	10.3817	0.355464	0.177732	−	0.984079i	$-0.443124\pi$
$853$	10.3817	0.355464	0.177732	+	0.984079i	$0.443124\pi$
$854$	−12.9689	−0.443786
$855$	0	0
$856$	0.723713	0.0247360
$857$	32.7252	1.11787	0.558936	−	0.829211i	$-0.311210\pi$
$857$	32.7252	1.11787	0.558936	+	0.829211i	$0.311210\pi$
$858$	−3.25338	−0.111068
$859$	20.6685	0.705201	0.352601	−	0.935774i	$-0.385297\pi$
$859$	20.6685	0.705201	0.352601	+	0.935774i	$0.385297\pi$
$860$	0	0
$861$	−22.1780	−0.755824
$862$	18.6927	0.636676
$863$	−56.3209	−1.91718	−0.958592	−	0.284782i	$-0.908079\pi$
$863$	−56.3209	−1.91718	−0.958592	+	0.284782i	$0.908079\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−18.9083	−0.642531
$867$	5.12807	0.174159
$868$	34.4062	1.16782
$869$	34.2655	1.16238
$870$	0	0
$871$	−7.37482	−0.249886
$872$	2.57331	0.0871434
$873$	−4.37205	−0.147971
$874$	−20.3637	−0.688812
$875$	0	0
$876$	9.83408	0.332263
$877$	−45.0842	−1.52239	−0.761193	−	0.648525i	$-0.775386\pi$
$877$	−45.0842	−1.52239	−0.761193	+	0.648525i	$0.775386\pi$
$878$	40.8600	1.37896
$879$	−8.52716	−0.287614
$880$	0	0
$881$	31.2421	1.05257	0.526287	−	0.850307i	$-0.323584\pi$
$881$	31.2421	1.05257	0.526287	+	0.850307i	$0.323584\pi$
$882$	−5.40494	−0.181994
$883$	26.8539	0.903705	0.451853	−	0.892093i	$-0.350763\pi$
$883$	26.8539	0.903705	0.451853	+	0.892093i	$0.350763\pi$
$884$	2.13316	0.0717460
$885$	0	0
$886$	5.99083	0.201266
$887$	−14.5890	−0.489851	−0.244925	−	0.969542i	$-0.578763\pi$
$887$	−14.5890	−0.489851	−0.244925	+	0.969542i	$0.578763\pi$
$888$	1.00173	0.0336159
$889$	15.3698	0.515485
$890$	0	0
$891$	5.25498	0.176049
$892$	12.7005	0.425243
$893$	−24.2806	−0.812519
$894$	−16.8396	−0.563201
$895$	0	0
$896$	−3.52206	−0.117664
$897$	5.54333	0.185086
$898$	−12.4505	−0.415477
$899$	−26.1962	−0.873693
$900$	0	0
$901$	1.90665	0.0635199
$902$	−33.0899	−1.10177
$903$	−5.32717	−0.177277
$904$	15.1881	0.505150
$905$	0	0
$906$	16.7932	0.557916
$907$	29.5506	0.981211	0.490606	−	0.871382i	$-0.336776\pi$
$907$	29.5506	0.981211	0.490606	+	0.871382i	$0.336776\pi$
$908$	14.2661	0.473438
$909$	−14.2687	−0.473262
$910$	0	0
$911$	4.21713	0.139720	0.0698598	−	0.997557i	$-0.477745\pi$
$911$	4.21713	0.139720	0.0698598	+	0.997557i	$0.477745\pi$
$912$	−2.27431	−0.0753098
$913$	−13.9768	−0.462566
$914$	1.11807	0.0369825
$915$	0	0
$916$	8.80308	0.290862
$917$	−2.17587	−0.0718536
$918$	−3.44557	−0.113721
$919$	28.4580	0.938743	0.469371	−	0.883001i	$-0.344481\pi$
$919$	28.4580	0.938743	0.469371	+	0.883001i	$0.344481\pi$
$920$	0	0
$921$	−2.85794	−0.0941724
$922$	30.0946	0.991112
$923$	−2.93986	−0.0967667
$924$	−18.5084	−0.608881
$925$	0	0
$926$	−21.0358	−0.691279
$927$	−17.6683	−0.580303
$928$	2.68163	0.0880290
$929$	−26.2514	−0.861282	−0.430641	−	0.902523i	$-0.641712\pi$
$929$	−26.2514	−0.861282	−0.430641	+	0.902523i	$0.641712\pi$
$930$	0	0
$931$	12.2925	0.402870
$932$	15.0762	0.493838
$933$	10.1618	0.332682
$934$	−3.53614	−0.115706
$935$	0	0
$936$	0.619103	0.0202360
$937$	−5.33219	−0.174195	−0.0870975	−	0.996200i	$-0.527759\pi$
$937$	−5.33219	−0.174195	−0.0870975	+	0.996200i	$0.527759\pi$
$938$	−41.9552	−1.36989
$939$	−18.2036	−0.594053
$940$	0	0
$941$	−8.50265	−0.277179	−0.138589	−	0.990350i	$-0.544257\pi$
$941$	−8.50265	−0.277179	−0.138589	+	0.990350i	$0.544257\pi$
$942$	−4.55451	−0.148394
$943$	56.3809	1.83602
$944$	0.278771	0.00907324
$945$	0	0
$946$	−7.94823	−0.258419
$947$	−22.3295	−0.725612	−0.362806	−	0.931865i	$-0.618181\pi$
$947$	−22.3295	−0.725612	−0.362806	+	0.931865i	$0.618181\pi$
$948$	−6.52057	−0.211778
$949$	6.08831	0.197635
$950$	0	0
$951$	−31.2764	−1.01421
$952$	12.1355	0.393314
$953$	13.6596	0.442479	0.221240	−	0.975219i	$-0.428990\pi$
$953$	13.6596	0.442479	0.221240	+	0.975219i	$0.428990\pi$
$954$	0.553365	0.0179158
$955$	0	0
$956$	−6.24583	−0.202004
$957$	14.0919	0.455528
$958$	−40.4357	−1.30642
$959$	−32.6553	−1.05449
$960$	0	0
$961$	64.4286	2.07834
$962$	0.620174	0.0199952
$963$	−0.723713	−0.0233213
$964$	−14.8094	−0.476979
$965$	0	0
$966$	31.5359	1.01465
$967$	−31.4473	−1.01128	−0.505639	−	0.862745i	$-0.668743\pi$
$967$	−31.4473	−1.01128	−0.505639	+	0.862745i	$0.668743\pi$
$968$	−16.6149	−0.534022
$969$	7.83627	0.251737
$970$	0	0
$971$	−4.21244	−0.135184	−0.0675918	−	0.997713i	$-0.521532\pi$
$971$	−4.21244	−0.135184	−0.0675918	+	0.997713i	$0.521532\pi$
$972$	−1.00000	−0.0320750
$973$	66.0805	2.11844
$974$	−26.7043	−0.855661
$975$	0	0
$976$	3.68218	0.117864
$977$	−14.2028	−0.454389	−0.227194	−	0.973849i	$-0.572955\pi$
$977$	−14.2028	−0.454389	−0.227194	+	0.973849i	$0.572955\pi$
$978$	20.2133	0.646349
$979$	−70.3431	−2.24817
$980$	0	0
$981$	−2.57331	−0.0821596
$982$	−33.1096	−1.05657
$983$	−32.1814	−1.02643	−0.513214	−	0.858261i	$-0.671545\pi$
$983$	−32.1814	−1.02643	−0.513214	+	0.858261i	$0.671545\pi$
$984$	6.29687	0.200737
$985$	0	0
$986$	−9.23975	−0.294254
$987$	37.6017	1.19688
$988$	−1.40803	−0.0447954
$989$	13.5427	0.430634
$990$	0	0
$991$	39.5440	1.25616	0.628078	−	0.778150i	$-0.283842\pi$
$991$	39.5440	1.25616	0.628078	+	0.778150i	$0.283842\pi$
$992$	−9.76875	−0.310158
$993$	−3.43194	−0.108909
$994$	−16.7248	−0.530479
$995$	0	0
$996$	2.65973	0.0842768
$997$	−2.83693	−0.0898464	−0.0449232	−	0.998990i	$-0.514304\pi$
$997$	−2.83693	−0.0898464	−0.0449232	+	0.998990i	$0.514304\pi$
$998$	−6.01303	−0.190339
$999$	−1.00173	−0.0316933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3750.2.a.u.1.7		8
5.2	odd	4		3750.2.c.k.1249.7		16
5.3	odd	4		3750.2.c.k.1249.10		16
5.4	even	2		3750.2.a.v.1.2		8
25.2	odd	20		150.2.h.b.79.2	yes	16
25.9	even	10		750.2.g.f.151.1		16
25.11	even	5		750.2.g.g.601.4		16
25.12	odd	20		750.2.h.d.349.4		16
25.13	odd	20		150.2.h.b.19.2	✓	16
25.14	even	10		750.2.g.f.601.1		16
25.16	even	5		750.2.g.g.151.4		16
25.23	odd	20		750.2.h.d.649.3		16
75.2	even	20		450.2.l.c.379.3		16
75.38	even	20		450.2.l.c.19.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.19.2	✓	16	25.13	odd	20
150.2.h.b.79.2	yes	16	25.2	odd	20
450.2.l.c.19.3		16	75.38	even	20
450.2.l.c.379.3		16	75.2	even	20
750.2.g.f.151.1		16	25.9	even	10
750.2.g.f.601.1		16	25.14	even	10
750.2.g.g.151.4		16	25.16	even	5
750.2.g.g.601.4		16	25.11	even	5
750.2.h.d.349.4		16	25.12	odd	20
750.2.h.d.649.3		16	25.23	odd	20
3750.2.a.u.1.7		8	1.1	even	1	trivial
3750.2.a.v.1.2		8	5.4	even	2
3750.2.c.k.1249.7		16	5.2	odd	4
3750.2.c.k.1249.10		16	5.3	odd	4

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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:	\( N \)	\(=\)	\( 3750 = 2 \cdot 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3750.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +3.52206 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +3.52206 q^{7} -1.00000 q^{8} +1.00000 q^{9} +5.25498 q^{11} -1.00000 q^{12} -0.619103 q^{13} -3.52206 q^{14} +1.00000 q^{16} -3.44557 q^{17} -1.00000 q^{18} +2.27431 q^{19} -3.52206 q^{21} -5.25498 q^{22} +8.95380 q^{23} +1.00000 q^{24} +0.619103 q^{26} -1.00000 q^{27} +3.52206 q^{28} -2.68163 q^{29} +9.76875 q^{31} -1.00000 q^{32} -5.25498 q^{33} +3.44557 q^{34} +1.00000 q^{36} +1.00173 q^{37} -2.27431 q^{38} +0.619103 q^{39} +6.29687 q^{41} +3.52206 q^{42} +1.51251 q^{43} +5.25498 q^{44} -8.95380 q^{46} -10.6760 q^{47} -1.00000 q^{48} +5.40494 q^{49} +3.44557 q^{51} -0.619103 q^{52} -0.553365 q^{53} +1.00000 q^{54} -3.52206 q^{56} -2.27431 q^{57} +2.68163 q^{58} +0.278771 q^{59} +3.68218 q^{61} -9.76875 q^{62} +3.52206 q^{63} +1.00000 q^{64} +5.25498 q^{66} +11.9121 q^{67} -3.44557 q^{68} -8.95380 q^{69} +4.74858 q^{71} -1.00000 q^{72} -9.83408 q^{73} -1.00173 q^{74} +2.27431 q^{76} +18.5084 q^{77} -0.619103 q^{78} +6.52057 q^{79} +1.00000 q^{81} -6.29687 q^{82} -2.65973 q^{83} -3.52206 q^{84} -1.51251 q^{86} +2.68163 q^{87} -5.25498 q^{88} -13.3860 q^{89} -2.18052 q^{91} +8.95380 q^{92} -9.76875 q^{93} +10.6760 q^{94} +1.00000 q^{96} -4.37205 q^{97} -5.40494 q^{98} +5.25498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9} + 6 q^{11} - 8 q^{12} - 2 q^{13} + 4 q^{14} + 8 q^{16} - 14 q^{17} - 8 q^{18} + 10 q^{19} + 4 q^{21} - 6 q^{22} - 12 q^{23} + 8 q^{24} + 2 q^{26} - 8 q^{27} - 4 q^{28} + 10 q^{29} + 16 q^{31} - 8 q^{32} - 6 q^{33} + 14 q^{34} + 8 q^{36} + 6 q^{37} - 10 q^{38} + 2 q^{39} + 6 q^{41} - 4 q^{42} - 2 q^{43} + 6 q^{44} + 12 q^{46} - 14 q^{47} - 8 q^{48} + 26 q^{49} + 14 q^{51} - 2 q^{52} - 12 q^{53} + 8 q^{54} + 4 q^{56} - 10 q^{57} - 10 q^{58} + 16 q^{61} - 16 q^{62} - 4 q^{63} + 8 q^{64} + 6 q^{66} + 6 q^{67} - 14 q^{68} + 12 q^{69} + 6 q^{71} - 8 q^{72} + 8 q^{73} - 6 q^{74} + 10 q^{76} - 8 q^{77} - 2 q^{78} + 10 q^{79} + 8 q^{81} - 6 q^{82} - 22 q^{83} + 4 q^{84} + 2 q^{86} - 10 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{91} - 12 q^{92} - 16 q^{93} + 14 q^{94} + 8 q^{96} + 16 q^{97} - 26 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9 + 6 * q^11 - 8 * q^12 - 2 * q^13 + 4 * q^14 + 8 * q^16 - 14 * q^17 - 8 * q^18 + 10 * q^19 + 4 * q^21 - 6 * q^22 - 12 * q^23 + 8 * q^24 + 2 * q^26 - 8 * q^27 - 4 * q^28 + 10 * q^29 + 16 * q^31 - 8 * q^32 - 6 * q^33 + 14 * q^34 + 8 * q^36 + 6 * q^37 - 10 * q^38 + 2 * q^39 + 6 * q^41 - 4 * q^42 - 2 * q^43 + 6 * q^44 + 12 * q^46 - 14 * q^47 - 8 * q^48 + 26 * q^49 + 14 * q^51 - 2 * q^52 - 12 * q^53 + 8 * q^54 + 4 * q^56 - 10 * q^57 - 10 * q^58 + 16 * q^61 - 16 * q^62 - 4 * q^63 + 8 * q^64 + 6 * q^66 + 6 * q^67 - 14 * q^68 + 12 * q^69 + 6 * q^71 - 8 * q^72 + 8 * q^73 - 6 * q^74 + 10 * q^76 - 8 * q^77 - 2 * q^78 + 10 * q^79 + 8 * q^81 - 6 * q^82 - 22 * q^83 + 4 * q^84 + 2 * q^86 - 10 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^91 - 12 * q^92 - 16 * q^93 + 14 * q^94 + 8 * q^96 + 16 * q^97 - 26 * q^98 + 6 * q^99

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