LMFDB - Embedded newform 1078.2.a.w.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(1,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, 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("1078.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 154)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	1078.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +3.23607 q^{3} +1.00000 q^{4} -3.23607 q^{5} +3.23607 q^{6} +1.00000 q^{8} +7.47214 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.23607 q^{3} +1.00000 q^{4} -3.23607 q^{5} +3.23607 q^{6} +1.00000 q^{8} +7.47214 q^{9} -3.23607 q^{10} +1.00000 q^{11} +3.23607 q^{12} -1.23607 q^{13} -10.4721 q^{15} +1.00000 q^{16} +6.47214 q^{17} +7.47214 q^{18} +2.76393 q^{19} -3.23607 q^{20} +1.00000 q^{22} +4.00000 q^{23} +3.23607 q^{24} +5.47214 q^{25} -1.23607 q^{26} +14.4721 q^{27} -4.47214 q^{29} -10.4721 q^{30} -2.00000 q^{31} +1.00000 q^{32} +3.23607 q^{33} +6.47214 q^{34} +7.47214 q^{36} -10.9443 q^{37} +2.76393 q^{38} -4.00000 q^{39} -3.23607 q^{40} -6.47214 q^{41} -1.52786 q^{43} +1.00000 q^{44} -24.1803 q^{45} +4.00000 q^{46} +2.00000 q^{47} +3.23607 q^{48} +5.47214 q^{50} +20.9443 q^{51} -1.23607 q^{52} -0.472136 q^{53} +14.4721 q^{54} -3.23607 q^{55} +8.94427 q^{57} -4.47214 q^{58} -7.23607 q^{59} -10.4721 q^{60} +5.23607 q^{61} -2.00000 q^{62} +1.00000 q^{64} +4.00000 q^{65} +3.23607 q^{66} -15.4164 q^{67} +6.47214 q^{68} +12.9443 q^{69} -2.47214 q^{71} +7.47214 q^{72} +4.94427 q^{73} -10.9443 q^{74} +17.7082 q^{75} +2.76393 q^{76} -4.00000 q^{78} -3.23607 q^{80} +24.4164 q^{81} -6.47214 q^{82} -10.1803 q^{83} -20.9443 q^{85} -1.52786 q^{86} -14.4721 q^{87} +1.00000 q^{88} -10.0000 q^{89} -24.1803 q^{90} +4.00000 q^{92} -6.47214 q^{93} +2.00000 q^{94} -8.94427 q^{95} +3.23607 q^{96} -3.52786 q^{97} +7.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} + 6 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 + 6 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} + 6 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 2 q^{13} - 12 q^{15} + 2 q^{16} + 4 q^{17} + 6 q^{18} + 10 q^{19} - 2 q^{20} + 2 q^{22} + 8 q^{23} + 2 q^{24} + 2 q^{25} + 2 q^{26} + 20 q^{27} - 12 q^{30} - 4 q^{31} + 2 q^{32} + 2 q^{33} + 4 q^{34} + 6 q^{36} - 4 q^{37} + 10 q^{38} - 8 q^{39} - 2 q^{40} - 4 q^{41} - 12 q^{43} + 2 q^{44} - 26 q^{45} + 8 q^{46} + 4 q^{47} + 2 q^{48} + 2 q^{50} + 24 q^{51} + 2 q^{52} + 8 q^{53} + 20 q^{54} - 2 q^{55} - 10 q^{59} - 12 q^{60} + 6 q^{61} - 4 q^{62} + 2 q^{64} + 8 q^{65} + 2 q^{66} - 4 q^{67} + 4 q^{68} + 8 q^{69} + 4 q^{71} + 6 q^{72} - 8 q^{73} - 4 q^{74} + 22 q^{75} + 10 q^{76} - 8 q^{78} - 2 q^{80} + 22 q^{81} - 4 q^{82} + 2 q^{83} - 24 q^{85} - 12 q^{86} - 20 q^{87} + 2 q^{88} - 20 q^{89} - 26 q^{90} + 8 q^{92} - 4 q^{93} + 4 q^{94} + 2 q^{96} - 16 q^{97} + 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 + 6 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 + 2 * q^13 - 12 * q^15 + 2 * q^16 + 4 * q^17 + 6 * q^18 + 10 * q^19 - 2 * q^20 + 2 * q^22 + 8 * q^23 + 2 * q^24 + 2 * q^25 + 2 * q^26 + 20 * q^27 - 12 * q^30 - 4 * q^31 + 2 * q^32 + 2 * q^33 + 4 * q^34 + 6 * q^36 - 4 * q^37 + 10 * q^38 - 8 * q^39 - 2 * q^40 - 4 * q^41 - 12 * q^43 + 2 * q^44 - 26 * q^45 + 8 * q^46 + 4 * q^47 + 2 * q^48 + 2 * q^50 + 24 * q^51 + 2 * q^52 + 8 * q^53 + 20 * q^54 - 2 * q^55 - 10 * q^59 - 12 * q^60 + 6 * q^61 - 4 * q^62 + 2 * q^64 + 8 * q^65 + 2 * q^66 - 4 * q^67 + 4 * q^68 + 8 * q^69 + 4 * q^71 + 6 * q^72 - 8 * q^73 - 4 * q^74 + 22 * q^75 + 10 * q^76 - 8 * q^78 - 2 * q^80 + 22 * q^81 - 4 * q^82 + 2 * q^83 - 24 * q^85 - 12 * q^86 - 20 * q^87 + 2 * q^88 - 20 * q^89 - 26 * q^90 + 8 * q^92 - 4 * q^93 + 4 * q^94 + 2 * q^96 - 16 * q^97 + 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
$3$	3.23607	1.86834	0.934172	−	0.356822i	$-0.116140\pi$
$3$	3.23607	1.86834	0.934172	+	0.356822i	$0.116140\pi$
$4$	1.00000	0.500000
$5$	−3.23607	−1.44721	−0.723607	−	0.690212i	$-0.757517\pi$
$5$	−3.23607	−1.44721	−0.723607	+	0.690212i	$0.757517\pi$
$6$	3.23607	1.32112
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	7.47214	2.49071
$10$	−3.23607	−1.02333
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.23607	0.934172
$13$	−1.23607	−0.342824	−0.171412	−	0.985199i	$-0.554833\pi$
$13$	−1.23607	−0.342824	−0.171412	+	0.985199i	$0.554833\pi$
$14$	0	0
$15$	−10.4721	−2.70389
$16$	1.00000	0.250000
$17$	6.47214	1.56972	0.784862	−	0.619671i	$-0.212734\pi$
$17$	6.47214	1.56972	0.784862	+	0.619671i	$0.212734\pi$
$18$	7.47214	1.76120
$19$	2.76393	0.634089	0.317045	−	0.948411i	$-0.397309\pi$
$19$	2.76393	0.634089	0.317045	+	0.948411i	$0.397309\pi$
$20$	−3.23607	−0.723607
$21$	0	0
$22$	1.00000	0.213201
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	3.23607	0.660560
$25$	5.47214	1.09443
$26$	−1.23607	−0.242413
$27$	14.4721	2.78516
$28$	0	0
$29$	−4.47214	−0.830455	−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214	−0.830455	−0.415227	+	0.909718i	$0.636298\pi$
$30$	−10.4721	−1.91194
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	1.00000	0.176777
$33$	3.23607	0.563327
$34$	6.47214	1.10996
$35$	0	0
$36$	7.47214	1.24536
$37$	−10.9443	−1.79923	−0.899614	−	0.436687i	$-0.856152\pi$
$37$	−10.9443	−1.79923	−0.899614	+	0.436687i	$0.856152\pi$
$38$	2.76393	0.448369
$39$	−4.00000	−0.640513
$40$	−3.23607	−0.511667
$41$	−6.47214	−1.01078	−0.505389	−	0.862892i	$-0.668651\pi$
$41$	−6.47214	−1.01078	−0.505389	+	0.862892i	$0.668651\pi$
$42$	0	0
$43$	−1.52786	−0.232997	−0.116499	−	0.993191i	$-0.537167\pi$
$43$	−1.52786	−0.232997	−0.116499	+	0.993191i	$0.537167\pi$
$44$	1.00000	0.150756
$45$	−24.1803	−3.60459
$46$	4.00000	0.589768
$47$	2.00000	0.291730	0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000	0.291730	0.145865	+	0.989305i	$0.453403\pi$
$48$	3.23607	0.467086
$49$	0	0
$50$	5.47214	0.773877
$51$	20.9443	2.93278
$52$	−1.23607	−0.171412
$53$	−0.472136	−0.0648529	−0.0324264	−	0.999474i	$-0.510323\pi$
$53$	−0.472136	−0.0648529	−0.0324264	+	0.999474i	$0.510323\pi$
$54$	14.4721	1.96941
$55$	−3.23607	−0.436351
$56$	0	0
$57$	8.94427	1.18470
$58$	−4.47214	−0.587220
$59$	−7.23607	−0.942056	−0.471028	−	0.882118i	$-0.656117\pi$
$59$	−7.23607	−0.942056	−0.471028	+	0.882118i	$0.656117\pi$
$60$	−10.4721	−1.35195
$61$	5.23607	0.670410	0.335205	−	0.942145i	$-0.391194\pi$
$61$	5.23607	0.670410	0.335205	+	0.942145i	$0.391194\pi$
$62$	−2.00000	−0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	3.23607	0.398332
$67$	−15.4164	−1.88341	−0.941707	−	0.336434i	$-0.890779\pi$
$67$	−15.4164	−1.88341	−0.941707	+	0.336434i	$0.890779\pi$
$68$	6.47214	0.784862
$69$	12.9443	1.55831
$70$	0	0
$71$	−2.47214	−0.293389	−0.146694	−	0.989182i	$-0.546863\pi$
$71$	−2.47214	−0.293389	−0.146694	+	0.989182i	$0.546863\pi$
$72$	7.47214	0.880600
$73$	4.94427	0.578683	0.289342	−	0.957226i	$-0.406564\pi$
$73$	4.94427	0.578683	0.289342	+	0.957226i	$0.406564\pi$
$74$	−10.9443	−1.27225
$75$	17.7082	2.04477
$76$	2.76393	0.317045
$77$	0	0
$78$	−4.00000	−0.452911
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−3.23607	−0.361803
$81$	24.4164	2.71293
$82$	−6.47214	−0.714728
$83$	−10.1803	−1.11744	−0.558719	−	0.829357i	$-0.688707\pi$
$83$	−10.1803	−1.11744	−0.558719	+	0.829357i	$0.688707\pi$
$84$	0	0
$85$	−20.9443	−2.27173
$86$	−1.52786	−0.164754
$87$	−14.4721	−1.55158
$88$	1.00000	0.106600
$89$	−10.0000	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$90$	−24.1803	−2.54883
$91$	0	0
$92$	4.00000	0.417029
$93$	−6.47214	−0.671129
$94$	2.00000	0.206284
$95$	−8.94427	−0.917663
$96$	3.23607	0.330280
$97$	−3.52786	−0.358200	−0.179100	−	0.983831i	$-0.557319\pi$
$97$	−3.52786	−0.358200	−0.179100	+	0.983831i	$0.557319\pi$
$98$	0	0
$99$	7.47214	0.750978
$100$	5.47214	0.547214
$101$	14.1803	1.41100	0.705498	−	0.708712i	$-0.250723\pi$
$101$	14.1803	1.41100	0.705498	+	0.708712i	$0.250723\pi$
$102$	20.9443	2.07379
$103$	−2.94427	−0.290108	−0.145054	−	0.989424i	$-0.546336\pi$
$103$	−2.94427	−0.290108	−0.145054	+	0.989424i	$0.546336\pi$
$104$	−1.23607	−0.121206
$105$	0	0
$106$	−0.472136	−0.0458579
$107$	−6.47214	−0.625685	−0.312842	−	0.949805i	$-0.601281\pi$
$107$	−6.47214	−0.625685	−0.312842	+	0.949805i	$0.601281\pi$
$108$	14.4721	1.39258
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	−3.23607	−0.308547
$111$	−35.4164	−3.36158
$112$	0	0
$113$	8.47214	0.796992	0.398496	−	0.917170i	$-0.369532\pi$
$113$	8.47214	0.796992	0.398496	+	0.917170i	$0.369532\pi$
$114$	8.94427	0.837708
$115$	−12.9443	−1.20706
$116$	−4.47214	−0.415227
$117$	−9.23607	−0.853875
$118$	−7.23607	−0.666134
$119$	0	0
$120$	−10.4721	−0.955971
$121$	1.00000	0.0909091
$122$	5.23607	0.474051
$123$	−20.9443	−1.88848
$124$	−2.00000	−0.179605
$125$	−1.52786	−0.136656
$126$	0	0
$127$	−12.0000	−1.06483	−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000	−1.06483	−0.532414	+	0.846484i	$0.678715\pi$
$128$	1.00000	0.0883883
$129$	−4.94427	−0.435319
$130$	4.00000	0.350823
$131$	−9.23607	−0.806959	−0.403480	−	0.914989i	$-0.632199\pi$
$131$	−9.23607	−0.806959	−0.403480	+	0.914989i	$0.632199\pi$
$132$	3.23607	0.281664
$133$	0	0
$134$	−15.4164	−1.33177
$135$	−46.8328	−4.03073
$136$	6.47214	0.554981
$137$	15.8885	1.35745	0.678725	−	0.734393i	$-0.262533\pi$
$137$	15.8885	1.35745	0.678725	+	0.734393i	$0.262533\pi$
$138$	12.9443	1.10189
$139$	8.29180	0.703301	0.351650	−	0.936131i	$-0.385621\pi$
$139$	8.29180	0.703301	0.351650	+	0.936131i	$0.385621\pi$
$140$	0	0
$141$	6.47214	0.545052
$142$	−2.47214	−0.207457
$143$	−1.23607	−0.103365
$144$	7.47214	0.622678
$145$	14.4721	1.20185
$146$	4.94427	0.409191
$147$	0	0
$148$	−10.9443	−0.899614
$149$	22.3607	1.83186	0.915929	−	0.401340i	$-0.131455\pi$
$149$	22.3607	1.83186	0.915929	+	0.401340i	$0.131455\pi$
$150$	17.7082	1.44587
$151$	12.0000	0.976546	0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000	0.976546	0.488273	+	0.872691i	$0.337627\pi$
$152$	2.76393	0.224184
$153$	48.3607	3.90973
$154$	0	0
$155$	6.47214	0.519854
$156$	−4.00000	−0.320256
$157$	−18.6525	−1.48863	−0.744315	−	0.667829i	$-0.767224\pi$
$157$	−18.6525	−1.48863	−0.744315	+	0.667829i	$0.767224\pi$
$158$	0	0
$159$	−1.52786	−0.121168
$160$	−3.23607	−0.255834
$161$	0	0
$162$	24.4164	1.91833
$163$	7.41641	0.580898	0.290449	−	0.956890i	$-0.406195\pi$
$163$	7.41641	0.580898	0.290449	+	0.956890i	$0.406195\pi$
$164$	−6.47214	−0.505389
$165$	−10.4721	−0.815255
$166$	−10.1803	−0.790148
$167$	15.4164	1.19296	0.596479	−	0.802629i	$-0.296566\pi$
$167$	15.4164	1.19296	0.596479	+	0.802629i	$0.296566\pi$
$168$	0	0
$169$	−11.4721	−0.882472
$170$	−20.9443	−1.60635
$171$	20.6525	1.57933
$172$	−1.52786	−0.116499
$173$	−1.23607	−0.0939765	−0.0469883	−	0.998895i	$-0.514962\pi$
$173$	−1.23607	−0.0939765	−0.0469883	+	0.998895i	$0.514962\pi$
$174$	−14.4721	−1.09713
$175$	0	0
$176$	1.00000	0.0753778
$177$	−23.4164	−1.76008
$178$	−10.0000	−0.749532
$179$	8.94427	0.668526	0.334263	−	0.942480i	$-0.391513\pi$
$179$	8.94427	0.668526	0.334263	+	0.942480i	$0.391513\pi$
$180$	−24.1803	−1.80230
$181$	−4.76393	−0.354100	−0.177050	−	0.984202i	$-0.556655\pi$
$181$	−4.76393	−0.354100	−0.177050	+	0.984202i	$0.556655\pi$
$182$	0	0
$183$	16.9443	1.25256
$184$	4.00000	0.294884
$185$	35.4164	2.60387
$186$	−6.47214	−0.474560
$187$	6.47214	0.473289
$188$	2.00000	0.145865
$189$	0	0
$190$	−8.94427	−0.648886
$191$	6.47214	0.468307	0.234154	−	0.972200i	$-0.424768\pi$
$191$	6.47214	0.468307	0.234154	+	0.972200i	$0.424768\pi$
$192$	3.23607	0.233543
$193$	2.94427	0.211933	0.105967	−	0.994370i	$-0.466206\pi$
$193$	2.94427	0.211933	0.105967	+	0.994370i	$0.466206\pi$
$194$	−3.52786	−0.253286
$195$	12.9443	0.926959
$196$	0	0
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	7.47214	0.531022
$199$	−1.05573	−0.0748386	−0.0374193	−	0.999300i	$-0.511914\pi$
$199$	−1.05573	−0.0748386	−0.0374193	+	0.999300i	$0.511914\pi$
$200$	5.47214	0.386938
$201$	−49.8885	−3.51887
$202$	14.1803	0.997725
$203$	0	0
$204$	20.9443	1.46639
$205$	20.9443	1.46281
$206$	−2.94427	−0.205137
$207$	29.8885	2.07740
$208$	−1.23607	−0.0857059
$209$	2.76393	0.191185
$210$	0	0
$211$	−22.4721	−1.54705	−0.773523	−	0.633768i	$-0.781507\pi$
$211$	−22.4721	−1.54705	−0.773523	+	0.633768i	$0.781507\pi$
$212$	−0.472136	−0.0324264
$213$	−8.00000	−0.548151
$214$	−6.47214	−0.442426
$215$	4.94427	0.337197
$216$	14.4721	0.984704
$217$	0	0
$218$	−10.0000	−0.677285
$219$	16.0000	1.08118
$220$	−3.23607	−0.218176
$221$	−8.00000	−0.538138
$222$	−35.4164	−2.37699
$223$	−8.47214	−0.567336	−0.283668	−	0.958923i	$-0.591551\pi$
$223$	−8.47214	−0.567336	−0.283668	+	0.958923i	$0.591551\pi$
$224$	0	0
$225$	40.8885	2.72590
$226$	8.47214	0.563558
$227$	14.7639	0.979917	0.489958	−	0.871746i	$-0.337012\pi$
$227$	14.7639	0.979917	0.489958	+	0.871746i	$0.337012\pi$
$228$	8.94427	0.592349
$229$	−12.7639	−0.843464	−0.421732	−	0.906720i	$-0.638578\pi$
$229$	−12.7639	−0.843464	−0.421732	+	0.906720i	$0.638578\pi$
$230$	−12.9443	−0.853520
$231$	0	0
$232$	−4.47214	−0.293610
$233$	2.94427	0.192886	0.0964428	−	0.995339i	$-0.469254\pi$
$233$	2.94427	0.192886	0.0964428	+	0.995339i	$0.469254\pi$
$234$	−9.23607	−0.603781
$235$	−6.47214	−0.422196
$236$	−7.23607	−0.471028
$237$	0	0
$238$	0	0
$239$	20.0000	1.29369	0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000	1.29369	0.646846	+	0.762620i	$0.276088\pi$
$240$	−10.4721	−0.675973
$241$	11.4164	0.735395	0.367698	−	0.929945i	$-0.380146\pi$
$241$	11.4164	0.735395	0.367698	+	0.929945i	$0.380146\pi$
$242$	1.00000	0.0642824
$243$	35.5967	2.28353
$244$	5.23607	0.335205
$245$	0	0
$246$	−20.9443	−1.33536
$247$	−3.41641	−0.217381
$248$	−2.00000	−0.127000
$249$	−32.9443	−2.08776
$250$	−1.52786	−0.0966306
$251$	−24.7639	−1.56309	−0.781543	−	0.623852i	$-0.785567\pi$
$251$	−24.7639	−1.56309	−0.781543	+	0.623852i	$0.785567\pi$
$252$	0	0
$253$	4.00000	0.251478
$254$	−12.0000	−0.752947
$255$	−67.7771	−4.24437
$256$	1.00000	0.0625000
$257$	10.9443	0.682685	0.341342	−	0.939939i	$-0.389118\pi$
$257$	10.9443	0.682685	0.341342	+	0.939939i	$0.389118\pi$
$258$	−4.94427	−0.307817
$259$	0	0
$260$	4.00000	0.248069
$261$	−33.4164	−2.06842
$262$	−9.23607	−0.570606
$263$	12.9443	0.798178	0.399089	−	0.916912i	$-0.369326\pi$
$263$	12.9443	0.798178	0.399089	+	0.916912i	$0.369326\pi$
$264$	3.23607	0.199166
$265$	1.52786	0.0938559
$266$	0	0
$267$	−32.3607	−1.98044
$268$	−15.4164	−0.941707
$269$	27.2361	1.66061	0.830306	−	0.557307i	$-0.188166\pi$
$269$	27.2361	1.66061	0.830306	+	0.557307i	$0.188166\pi$
$270$	−46.8328	−2.85015
$271$	16.9443	1.02929	0.514646	−	0.857403i	$-0.327924\pi$
$271$	16.9443	1.02929	0.514646	+	0.857403i	$0.327924\pi$
$272$	6.47214	0.392431
$273$	0	0
$274$	15.8885	0.959862
$275$	5.47214	0.329982
$276$	12.9443	0.779154
$277$	12.4721	0.749378	0.374689	−	0.927151i	$-0.377749\pi$
$277$	12.4721	0.749378	0.374689	+	0.927151i	$0.377749\pi$
$278$	8.29180	0.497309
$279$	−14.9443	−0.894690
$280$	0	0
$281$	−24.8328	−1.48140	−0.740701	−	0.671835i	$-0.765506\pi$
$281$	−24.8328	−1.48140	−0.740701	+	0.671835i	$0.765506\pi$
$282$	6.47214	0.385410
$283$	16.6525	0.989887	0.494943	−	0.868925i	$-0.335189\pi$
$283$	16.6525	0.989887	0.494943	+	0.868925i	$0.335189\pi$
$284$	−2.47214	−0.146694
$285$	−28.9443	−1.71451
$286$	−1.23607	−0.0730902
$287$	0	0
$288$	7.47214	0.440300
$289$	24.8885	1.46403
$290$	14.4721	0.849833
$291$	−11.4164	−0.669242
$292$	4.94427	0.289342
$293$	−4.65248	−0.271801	−0.135900	−	0.990723i	$-0.543393\pi$
$293$	−4.65248	−0.271801	−0.135900	+	0.990723i	$0.543393\pi$
$294$	0	0
$295$	23.4164	1.36336
$296$	−10.9443	−0.636123
$297$	14.4721	0.839759
$298$	22.3607	1.29532
$299$	−4.94427	−0.285935
$300$	17.7082	1.02238
$301$	0	0
$302$	12.0000	0.690522
$303$	45.8885	2.63623
$304$	2.76393	0.158522
$305$	−16.9443	−0.970226
$306$	48.3607	2.76460
$307$	−32.0689	−1.83027	−0.915134	−	0.403150i	$-0.867915\pi$
$307$	−32.0689	−1.83027	−0.915134	+	0.403150i	$0.867915\pi$
$308$	0	0
$309$	−9.52786	−0.542021
$310$	6.47214	0.367593
$311$	−5.41641	−0.307136	−0.153568	−	0.988138i	$-0.549076\pi$
$311$	−5.41641	−0.307136	−0.153568	+	0.988138i	$0.549076\pi$
$312$	−4.00000	−0.226455
$313$	−28.4721	−1.60934	−0.804670	−	0.593722i	$-0.797658\pi$
$313$	−28.4721	−1.60934	−0.804670	+	0.593722i	$0.797658\pi$
$314$	−18.6525	−1.05262
$315$	0	0
$316$	0	0
$317$	−13.0557	−0.733283	−0.366641	−	0.930362i	$-0.619492\pi$
$317$	−13.0557	−0.733283	−0.366641	+	0.930362i	$0.619492\pi$
$318$	−1.52786	−0.0856784
$319$	−4.47214	−0.250392
$320$	−3.23607	−0.180902
$321$	−20.9443	−1.16900
$322$	0	0
$323$	17.8885	0.995345
$324$	24.4164	1.35647
$325$	−6.76393	−0.375195
$326$	7.41641	0.410757
$327$	−32.3607	−1.78955
$328$	−6.47214	−0.357364
$329$	0	0
$330$	−10.4721	−0.576472
$331$	0.944272	0.0519019	0.0259509	−	0.999663i	$-0.491739\pi$
$331$	0.944272	0.0519019	0.0259509	+	0.999663i	$0.491739\pi$
$332$	−10.1803	−0.558719
$333$	−81.7771	−4.48136
$334$	15.4164	0.843548
$335$	49.8885	2.72570
$336$	0	0
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	−11.4721	−0.624002
$339$	27.4164	1.48905
$340$	−20.9443	−1.13586
$341$	−2.00000	−0.108306
$342$	20.6525	1.11676
$343$	0	0
$344$	−1.52786	−0.0823769
$345$	−41.8885	−2.25520
$346$	−1.23607	−0.0664514
$347$	−6.47214	−0.347442	−0.173721	−	0.984795i	$-0.555579\pi$
$347$	−6.47214	−0.347442	−0.173721	+	0.984795i	$0.555579\pi$
$348$	−14.4721	−0.775788
$349$	−8.29180	−0.443850	−0.221925	−	0.975064i	$-0.571234\pi$
$349$	−8.29180	−0.443850	−0.221925	+	0.975064i	$0.571234\pi$
$350$	0	0
$351$	−17.8885	−0.954820
$352$	1.00000	0.0533002
$353$	34.9443	1.85990	0.929948	−	0.367691i	$-0.119852\pi$
$353$	34.9443	1.85990	0.929948	+	0.367691i	$0.119852\pi$
$354$	−23.4164	−1.24457
$355$	8.00000	0.424596
$356$	−10.0000	−0.529999
$357$	0	0
$358$	8.94427	0.472719
$359$	−26.8328	−1.41618	−0.708091	−	0.706121i	$-0.750443\pi$
$359$	−26.8328	−1.41618	−0.708091	+	0.706121i	$0.750443\pi$
$360$	−24.1803	−1.27442
$361$	−11.3607	−0.597931
$362$	−4.76393	−0.250387
$363$	3.23607	0.169850
$364$	0	0
$365$	−16.0000	−0.837478
$366$	16.9443	0.885691
$367$	−21.4164	−1.11793	−0.558964	−	0.829192i	$-0.688801\pi$
$367$	−21.4164	−1.11793	−0.558964	+	0.829192i	$0.688801\pi$
$368$	4.00000	0.208514
$369$	−48.3607	−2.51756
$370$	35.4164	1.84121
$371$	0	0
$372$	−6.47214	−0.335565
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	6.47214	0.334666
$375$	−4.94427	−0.255321
$376$	2.00000	0.103142
$377$	5.52786	0.284699
$378$	0	0
$379$	5.52786	0.283947	0.141974	−	0.989870i	$-0.454655\pi$
$379$	5.52786	0.283947	0.141974	+	0.989870i	$0.454655\pi$
$380$	−8.94427	−0.458831
$381$	−38.8328	−1.98947
$382$	6.47214	0.331143
$383$	−11.8885	−0.607476	−0.303738	−	0.952756i	$-0.598235\pi$
$383$	−11.8885	−0.607476	−0.303738	+	0.952756i	$0.598235\pi$
$384$	3.23607	0.165140
$385$	0	0
$386$	2.94427	0.149859
$387$	−11.4164	−0.580329
$388$	−3.52786	−0.179100
$389$	6.58359	0.333801	0.166901	−	0.985974i	$-0.446624\pi$
$389$	6.58359	0.333801	0.166901	+	0.985974i	$0.446624\pi$
$390$	12.9443	0.655459
$391$	25.8885	1.30924
$392$	0	0
$393$	−29.8885	−1.50768
$394$	18.0000	0.906827
$395$	0	0
$396$	7.47214	0.375489
$397$	10.2918	0.516530	0.258265	−	0.966074i	$-0.416849\pi$
$397$	10.2918	0.516530	0.258265	+	0.966074i	$0.416849\pi$
$398$	−1.05573	−0.0529189
$399$	0	0
$400$	5.47214	0.273607
$401$	−30.3607	−1.51614	−0.758070	−	0.652173i	$-0.773857\pi$
$401$	−30.3607	−1.51614	−0.758070	+	0.652173i	$0.773857\pi$
$402$	−49.8885	−2.48821
$403$	2.47214	0.123146
$404$	14.1803	0.705498
$405$	−79.0132	−3.92620
$406$	0	0
$407$	−10.9443	−0.542487
$408$	20.9443	1.03690
$409$	23.4164	1.15787	0.578933	−	0.815375i	$-0.303469\pi$
$409$	23.4164	1.15787	0.578933	+	0.815375i	$0.303469\pi$
$410$	20.9443	1.03436
$411$	51.4164	2.53618
$412$	−2.94427	−0.145054
$413$	0	0
$414$	29.8885	1.46894
$415$	32.9443	1.61717
$416$	−1.23607	−0.0606032
$417$	26.8328	1.31401
$418$	2.76393	0.135188
$419$	−12.7639	−0.623559	−0.311779	−	0.950155i	$-0.600925\pi$
$419$	−12.7639	−0.623559	−0.311779	+	0.950155i	$0.600925\pi$
$420$	0	0
$421$	7.52786	0.366886	0.183443	−	0.983030i	$-0.441276\pi$
$421$	7.52786	0.366886	0.183443	+	0.983030i	$0.441276\pi$
$422$	−22.4721	−1.09393
$423$	14.9443	0.726615
$424$	−0.472136	−0.0229289
$425$	35.4164	1.71795
$426$	−8.00000	−0.387601
$427$	0	0
$428$	−6.47214	−0.312842
$429$	−4.00000	−0.193122
$430$	4.94427	0.238434
$431$	40.9443	1.97222	0.986108	−	0.166105i	$-0.0531190\pi$
$431$	40.9443	1.97222	0.986108	+	0.166105i	$0.0531190\pi$
$432$	14.4721	0.696291
$433$	−19.5279	−0.938449	−0.469225	−	0.883079i	$-0.655467\pi$
$433$	−19.5279	−0.938449	−0.469225	+	0.883079i	$0.655467\pi$
$434$	0	0
$435$	46.8328	2.24546
$436$	−10.0000	−0.478913
$437$	11.0557	0.528867
$438$	16.0000	0.764510
$439$	8.94427	0.426887	0.213443	−	0.976955i	$-0.431532\pi$
$439$	8.94427	0.426887	0.213443	+	0.976955i	$0.431532\pi$
$440$	−3.23607	−0.154273
$441$	0	0
$442$	−8.00000	−0.380521
$443$	−7.05573	−0.335228	−0.167614	−	0.985853i	$-0.553606\pi$
$443$	−7.05573	−0.335228	−0.167614	+	0.985853i	$0.553606\pi$
$444$	−35.4164	−1.68079
$445$	32.3607	1.53404
$446$	−8.47214	−0.401167
$447$	72.3607	3.42254
$448$	0	0
$449$	1.05573	0.0498229	0.0249114	−	0.999690i	$-0.492070\pi$
$449$	1.05573	0.0498229	0.0249114	+	0.999690i	$0.492070\pi$
$450$	40.8885	1.92750
$451$	−6.47214	−0.304761
$452$	8.47214	0.398496
$453$	38.8328	1.82452
$454$	14.7639	0.692906
$455$	0	0
$456$	8.94427	0.418854
$457$	9.05573	0.423609	0.211805	−	0.977312i	$-0.432066\pi$
$457$	9.05573	0.423609	0.211805	+	0.977312i	$0.432066\pi$
$458$	−12.7639	−0.596419
$459$	93.6656	4.37194
$460$	−12.9443	−0.603530
$461$	−29.2361	−1.36166	−0.680830	−	0.732442i	$-0.738381\pi$
$461$	−29.2361	−1.36166	−0.680830	+	0.732442i	$0.738381\pi$
$462$	0	0
$463$	−21.5279	−1.00048	−0.500242	−	0.865885i	$-0.666756\pi$
$463$	−21.5279	−1.00048	−0.500242	+	0.865885i	$0.666756\pi$
$464$	−4.47214	−0.207614
$465$	20.9443	0.971267
$466$	2.94427	0.136391
$467$	−13.1246	−0.607335	−0.303667	−	0.952778i	$-0.598211\pi$
$467$	−13.1246	−0.607335	−0.303667	+	0.952778i	$0.598211\pi$
$468$	−9.23607	−0.426937
$469$	0	0
$470$	−6.47214	−0.298537
$471$	−60.3607	−2.78127
$472$	−7.23607	−0.333067
$473$	−1.52786	−0.0702513
$474$	0	0
$475$	15.1246	0.693965
$476$	0	0
$477$	−3.52786	−0.161530
$478$	20.0000	0.914779
$479$	32.3607	1.47860	0.739299	−	0.673378i	$-0.235157\pi$
$479$	32.3607	1.47860	0.739299	+	0.673378i	$0.235157\pi$
$480$	−10.4721	−0.477985
$481$	13.5279	0.616818
$482$	11.4164	0.520003
$483$	0	0
$484$	1.00000	0.0454545
$485$	11.4164	0.518392
$486$	35.5967	1.61470
$487$	−0.944272	−0.0427890	−0.0213945	−	0.999771i	$-0.506811\pi$
$487$	−0.944272	−0.0427890	−0.0213945	+	0.999771i	$0.506811\pi$
$488$	5.23607	0.237026
$489$	24.0000	1.08532
$490$	0	0
$491$	0.944272	0.0426144	0.0213072	−	0.999773i	$-0.493217\pi$
$491$	0.944272	0.0426144	0.0213072	+	0.999773i	$0.493217\pi$
$492$	−20.9443	−0.944241
$493$	−28.9443	−1.30358
$494$	−3.41641	−0.153711
$495$	−24.1803	−1.08683
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	−32.9443	−1.47627
$499$	12.3607	0.553340	0.276670	−	0.960965i	$-0.410769\pi$
$499$	12.3607	0.553340	0.276670	+	0.960965i	$0.410769\pi$
$500$	−1.52786	−0.0683282
$501$	49.8885	2.22886
$502$	−24.7639	−1.10527
$503$	−4.00000	−0.178351	−0.0891756	−	0.996016i	$-0.528423\pi$
$503$	−4.00000	−0.178351	−0.0891756	+	0.996016i	$0.528423\pi$
$504$	0	0
$505$	−45.8885	−2.04201
$506$	4.00000	0.177822
$507$	−37.1246	−1.64876
$508$	−12.0000	−0.532414
$509$	34.0689	1.51008	0.755038	−	0.655681i	$-0.227618\pi$
$509$	34.0689	1.51008	0.755038	+	0.655681i	$0.227618\pi$
$510$	−67.7771	−3.00122
$511$	0	0
$512$	1.00000	0.0441942
$513$	40.0000	1.76604
$514$	10.9443	0.482731
$515$	9.52786	0.419848
$516$	−4.94427	−0.217659
$517$	2.00000	0.0879599
$518$	0	0
$519$	−4.00000	−0.175581
$520$	4.00000	0.175412
$521$	−34.3607	−1.50537	−0.752684	−	0.658382i	$-0.771241\pi$
$521$	−34.3607	−1.50537	−0.752684	+	0.658382i	$0.771241\pi$
$522$	−33.4164	−1.46260
$523$	27.7082	1.21160	0.605798	−	0.795619i	$-0.292854\pi$
$523$	27.7082	1.21160	0.605798	+	0.795619i	$0.292854\pi$
$524$	−9.23607	−0.403480
$525$	0	0
$526$	12.9443	0.564397
$527$	−12.9443	−0.563861
$528$	3.23607	0.140832
$529$	−7.00000	−0.304348
$530$	1.52786	0.0663662
$531$	−54.0689	−2.34639
$532$	0	0
$533$	8.00000	0.346518
$534$	−32.3607	−1.40038
$535$	20.9443	0.905500
$536$	−15.4164	−0.665887
$537$	28.9443	1.24904
$538$	27.2361	1.17423
$539$	0	0
$540$	−46.8328	−2.01536
$541$	−9.05573	−0.389336	−0.194668	−	0.980869i	$-0.562363\pi$
$541$	−9.05573	−0.389336	−0.194668	+	0.980869i	$0.562363\pi$
$542$	16.9443	0.727819
$543$	−15.4164	−0.661581
$544$	6.47214	0.277491
$545$	32.3607	1.38618
$546$	0	0
$547$	16.9443	0.724485	0.362242	−	0.932084i	$-0.382011\pi$
$547$	16.9443	0.724485	0.362242	+	0.932084i	$0.382011\pi$
$548$	15.8885	0.678725
$549$	39.1246	1.66980
$550$	5.47214	0.233333
$551$	−12.3607	−0.526583
$552$	12.9443	0.550945
$553$	0	0
$554$	12.4721	0.529890
$555$	114.610	4.86492
$556$	8.29180	0.351650
$557$	−28.8328	−1.22169	−0.610843	−	0.791752i	$-0.709169\pi$
$557$	−28.8328	−1.22169	−0.610843	+	0.791752i	$0.709169\pi$
$558$	−14.9443	−0.632641
$559$	1.88854	0.0798769
$560$	0	0
$561$	20.9443	0.884268
$562$	−24.8328	−1.04751
$563$	−26.7639	−1.12797	−0.563983	−	0.825787i	$-0.690732\pi$
$563$	−26.7639	−1.12797	−0.563983	+	0.825787i	$0.690732\pi$
$564$	6.47214	0.272526
$565$	−27.4164	−1.15342
$566$	16.6525	0.699956
$567$	0	0
$568$	−2.47214	−0.103729
$569$	16.8328	0.705668	0.352834	−	0.935686i	$-0.385218\pi$
$569$	16.8328	0.705668	0.352834	+	0.935686i	$0.385218\pi$
$570$	−28.9443	−1.21234
$571$	−45.8885	−1.92038	−0.960188	−	0.279355i	$-0.909879\pi$
$571$	−45.8885	−1.92038	−0.960188	+	0.279355i	$0.909879\pi$
$572$	−1.23607	−0.0516826
$573$	20.9443	0.874960
$574$	0	0
$575$	21.8885	0.912815
$576$	7.47214	0.311339
$577$	−9.05573	−0.376995	−0.188497	−	0.982074i	$-0.560362\pi$
$577$	−9.05573	−0.376995	−0.188497	+	0.982074i	$0.560362\pi$
$578$	24.8885	1.03523
$579$	9.52786	0.395965
$580$	14.4721	0.600923
$581$	0	0
$582$	−11.4164	−0.473225
$583$	−0.472136	−0.0195539
$584$	4.94427	0.204595
$585$	29.8885	1.23574
$586$	−4.65248	−0.192192
$587$	28.1803	1.16313	0.581564	−	0.813501i	$-0.302441\pi$
$587$	28.1803	1.16313	0.581564	+	0.813501i	$0.302441\pi$
$588$	0	0
$589$	−5.52786	−0.227772
$590$	23.4164	0.964038
$591$	58.2492	2.39605
$592$	−10.9443	−0.449807
$593$	−24.0000	−0.985562	−0.492781	−	0.870153i	$-0.664020\pi$
$593$	−24.0000	−0.985562	−0.492781	+	0.870153i	$0.664020\pi$
$594$	14.4721	0.593799
$595$	0	0
$596$	22.3607	0.915929
$597$	−3.41641	−0.139824
$598$	−4.94427	−0.202186
$599$	12.3607	0.505044	0.252522	−	0.967591i	$-0.418740\pi$
$599$	12.3607	0.505044	0.252522	+	0.967591i	$0.418740\pi$
$600$	17.7082	0.722934
$601$	−18.8328	−0.768207	−0.384103	−	0.923290i	$-0.625489\pi$
$601$	−18.8328	−0.768207	−0.384103	+	0.923290i	$0.625489\pi$
$602$	0	0
$603$	−115.193	−4.69104
$604$	12.0000	0.488273
$605$	−3.23607	−0.131565
$606$	45.8885	1.86409
$607$	32.0000	1.29884	0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000	1.29884	0.649420	+	0.760430i	$0.275012\pi$
$608$	2.76393	0.112092
$609$	0	0
$610$	−16.9443	−0.686054
$611$	−2.47214	−0.100012
$612$	48.3607	1.95486
$613$	19.5279	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$613$	19.5279	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$614$	−32.0689	−1.29419
$615$	67.7771	2.73304
$616$	0	0
$617$	−5.41641	−0.218056	−0.109028	−	0.994039i	$-0.534774\pi$
$617$	−5.41641	−0.218056	−0.109028	+	0.994039i	$0.534774\pi$
$618$	−9.52786	−0.383267
$619$	48.5410	1.95103	0.975514	−	0.219937i	$-0.0705851\pi$
$619$	48.5410	1.95103	0.975514	+	0.219937i	$0.0705851\pi$
$620$	6.47214	0.259927
$621$	57.8885	2.32299
$622$	−5.41641	−0.217178
$623$	0	0
$624$	−4.00000	−0.160128
$625$	−22.4164	−0.896656
$626$	−28.4721	−1.13798
$627$	8.94427	0.357200
$628$	−18.6525	−0.744315
$629$	−70.8328	−2.82429
$630$	0	0
$631$	−4.58359	−0.182470	−0.0912350	−	0.995829i	$-0.529081\pi$
$631$	−4.58359	−0.182470	−0.0912350	+	0.995829i	$0.529081\pi$
$632$	0	0
$633$	−72.7214	−2.89041
$634$	−13.0557	−0.518509
$635$	38.8328	1.54103
$636$	−1.52786	−0.0605838
$637$	0	0
$638$	−4.47214	−0.177054
$639$	−18.4721	−0.730746
$640$	−3.23607	−0.127917
$641$	36.4721	1.44056	0.720281	−	0.693682i	$-0.244013\pi$
$641$	36.4721	1.44056	0.720281	+	0.693682i	$0.244013\pi$
$642$	−20.9443	−0.826604
$643$	23.2361	0.916341	0.458171	−	0.888864i	$-0.348505\pi$
$643$	23.2361	0.916341	0.458171	+	0.888864i	$0.348505\pi$
$644$	0	0
$645$	16.0000	0.629999
$646$	17.8885	0.703815
$647$	−24.8328	−0.976279	−0.488139	−	0.872766i	$-0.662324\pi$
$647$	−24.8328	−0.976279	−0.488139	+	0.872766i	$0.662324\pi$
$648$	24.4164	0.959167
$649$	−7.23607	−0.284041
$650$	−6.76393	−0.265303
$651$	0	0
$652$	7.41641	0.290449
$653$	1.63932	0.0641516	0.0320758	−	0.999485i	$-0.489788\pi$
$653$	1.63932	0.0641516	0.0320758	+	0.999485i	$0.489788\pi$
$654$	−32.3607	−1.26540
$655$	29.8885	1.16784
$656$	−6.47214	−0.252694
$657$	36.9443	1.44133
$658$	0	0
$659$	43.4164	1.69126	0.845632	−	0.533767i	$-0.179224\pi$
$659$	43.4164	1.69126	0.845632	+	0.533767i	$0.179224\pi$
$660$	−10.4721	−0.407627
$661$	−37.1246	−1.44398	−0.721990	−	0.691903i	$-0.756772\pi$
$661$	−37.1246	−1.44398	−0.721990	+	0.691903i	$0.756772\pi$
$662$	0.944272	0.0367002
$663$	−25.8885	−1.00543
$664$	−10.1803	−0.395074
$665$	0	0
$666$	−81.7771	−3.16880
$667$	−17.8885	−0.692647
$668$	15.4164	0.596479
$669$	−27.4164	−1.05998
$670$	49.8885	1.92736
$671$	5.23607	0.202136
$672$	0	0
$673$	31.8885	1.22921	0.614607	−	0.788834i	$-0.289315\pi$
$673$	31.8885	1.22921	0.614607	+	0.788834i	$0.289315\pi$
$674$	18.0000	0.693334
$675$	79.1935	3.04816
$676$	−11.4721	−0.441236
$677$	−32.0689	−1.23251	−0.616254	−	0.787548i	$-0.711350\pi$
$677$	−32.0689	−1.23251	−0.616254	+	0.787548i	$0.711350\pi$
$678$	27.4164	1.05292
$679$	0	0
$680$	−20.9443	−0.803176
$681$	47.7771	1.83082
$682$	−2.00000	−0.0765840
$683$	15.0557	0.576091	0.288046	−	0.957617i	$-0.406994\pi$
$683$	15.0557	0.576091	0.288046	+	0.957617i	$0.406994\pi$
$684$	20.6525	0.789667
$685$	−51.4164	−1.96452
$686$	0	0
$687$	−41.3050	−1.57588
$688$	−1.52786	−0.0582493
$689$	0.583592	0.0222331
$690$	−41.8885	−1.59467
$691$	18.6525	0.709574	0.354787	−	0.934947i	$-0.384553\pi$
$691$	18.6525	0.709574	0.354787	+	0.934947i	$0.384553\pi$
$692$	−1.23607	−0.0469883
$693$	0	0
$694$	−6.47214	−0.245679
$695$	−26.8328	−1.01783
$696$	−14.4721	−0.548565
$697$	−41.8885	−1.58664
$698$	−8.29180	−0.313849
$699$	9.52786	0.360377
$700$	0	0
$701$	46.7214	1.76464	0.882321	−	0.470649i	$-0.155980\pi$
$701$	46.7214	1.76464	0.882321	+	0.470649i	$0.155980\pi$
$702$	−17.8885	−0.675160
$703$	−30.2492	−1.14087
$704$	1.00000	0.0376889
$705$	−20.9443	−0.788807
$706$	34.9443	1.31515
$707$	0	0
$708$	−23.4164	−0.880042
$709$	−4.47214	−0.167955	−0.0839773	−	0.996468i	$-0.526762\pi$
$709$	−4.47214	−0.167955	−0.0839773	+	0.996468i	$0.526762\pi$
$710$	8.00000	0.300235
$711$	0	0
$712$	−10.0000	−0.374766
$713$	−8.00000	−0.299602
$714$	0	0
$715$	4.00000	0.149592
$716$	8.94427	0.334263
$717$	64.7214	2.41706
$718$	−26.8328	−1.00139
$719$	36.8328	1.37363	0.686816	−	0.726831i	$-0.259008\pi$
$719$	36.8328	1.37363	0.686816	+	0.726831i	$0.259008\pi$
$720$	−24.1803	−0.901148
$721$	0	0
$722$	−11.3607	−0.422801
$723$	36.9443	1.37397
$724$	−4.76393	−0.177050
$725$	−24.4721	−0.908872
$726$	3.23607	0.120102
$727$	−18.0000	−0.667583	−0.333792	−	0.942647i	$-0.608328\pi$
$727$	−18.0000	−0.667583	−0.333792	+	0.942647i	$0.608328\pi$
$728$	0	0
$729$	41.9443	1.55349
$730$	−16.0000	−0.592187
$731$	−9.88854	−0.365741
$732$	16.9443	0.626278
$733$	−8.87539	−0.327820	−0.163910	−	0.986475i	$-0.552411\pi$
$733$	−8.87539	−0.327820	−0.163910	+	0.986475i	$0.552411\pi$
$734$	−21.4164	−0.790494
$735$	0	0
$736$	4.00000	0.147442
$737$	−15.4164	−0.567871
$738$	−48.3607	−1.78018
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	35.4164	1.30193
$741$	−11.0557	−0.406142
$742$	0	0
$743$	−13.8885	−0.509521	−0.254761	−	0.967004i	$-0.581997\pi$
$743$	−13.8885	−0.509521	−0.254761	+	0.967004i	$0.581997\pi$
$744$	−6.47214	−0.237280
$745$	−72.3607	−2.65109
$746$	−6.00000	−0.219676
$747$	−76.0689	−2.78321
$748$	6.47214	0.236645
$749$	0	0
$750$	−4.94427	−0.180539
$751$	0.944272	0.0344570	0.0172285	−	0.999852i	$-0.494516\pi$
$751$	0.944272	0.0344570	0.0172285	+	0.999852i	$0.494516\pi$
$752$	2.00000	0.0729325
$753$	−80.1378	−2.92038
$754$	5.52786	0.201313
$755$	−38.8328	−1.41327
$756$	0	0
$757$	39.3050	1.42856	0.714281	−	0.699859i	$-0.246754\pi$
$757$	39.3050	1.42856	0.714281	+	0.699859i	$0.246754\pi$
$758$	5.52786	0.200781
$759$	12.9443	0.469847
$760$	−8.94427	−0.324443
$761$	−15.4164	−0.558844	−0.279422	−	0.960168i	$-0.590143\pi$
$761$	−15.4164	−0.558844	−0.279422	+	0.960168i	$0.590143\pi$
$762$	−38.8328	−1.40676
$763$	0	0
$764$	6.47214	0.234154
$765$	−156.498	−5.65821
$766$	−11.8885	−0.429551
$767$	8.94427	0.322959
$768$	3.23607	0.116772
$769$	16.5836	0.598020	0.299010	−	0.954250i	$-0.403344\pi$
$769$	16.5836	0.598020	0.299010	+	0.954250i	$0.403344\pi$
$770$	0	0
$771$	35.4164	1.27549
$772$	2.94427	0.105967
$773$	−2.29180	−0.0824302	−0.0412151	−	0.999150i	$-0.513123\pi$
$773$	−2.29180	−0.0824302	−0.0412151	+	0.999150i	$0.513123\pi$
$774$	−11.4164	−0.410354
$775$	−10.9443	−0.393130
$776$	−3.52786	−0.126643
$777$	0	0
$778$	6.58359	0.236033
$779$	−17.8885	−0.640924
$780$	12.9443	0.463479
$781$	−2.47214	−0.0884600
$782$	25.8885	0.925772
$783$	−64.7214	−2.31295
$784$	0	0
$785$	60.3607	2.15437
$786$	−29.8885	−1.06609
$787$	5.81966	0.207448	0.103724	−	0.994606i	$-0.466924\pi$
$787$	5.81966	0.207448	0.103724	+	0.994606i	$0.466924\pi$
$788$	18.0000	0.641223
$789$	41.8885	1.49127
$790$	0	0
$791$	0	0
$792$	7.47214	0.265511
$793$	−6.47214	−0.229832
$794$	10.2918	0.365242
$795$	4.94427	0.175355
$796$	−1.05573	−0.0374193
$797$	−7.59675	−0.269091	−0.134545	−	0.990907i	$-0.542957\pi$
$797$	−7.59675	−0.269091	−0.134545	+	0.990907i	$0.542957\pi$
$798$	0	0
$799$	12.9443	0.457935
$800$	5.47214	0.193469
$801$	−74.7214	−2.64015
$802$	−30.3607	−1.07207
$803$	4.94427	0.174480
$804$	−49.8885	−1.75943
$805$	0	0
$806$	2.47214	0.0870773
$807$	88.1378	3.10260
$808$	14.1803	0.498863
$809$	−38.9443	−1.36921	−0.684604	−	0.728915i	$-0.740025\pi$
$809$	−38.9443	−1.36921	−0.684604	+	0.728915i	$0.740025\pi$
$810$	−79.0132	−2.77624
$811$	−9.23607	−0.324322	−0.162161	−	0.986764i	$-0.551846\pi$
$811$	−9.23607	−0.324322	−0.162161	+	0.986764i	$0.551846\pi$
$812$	0	0
$813$	54.8328	1.92307
$814$	−10.9443	−0.383597
$815$	−24.0000	−0.840683
$816$	20.9443	0.733196
$817$	−4.22291	−0.147741
$818$	23.4164	0.818736
$819$	0	0
$820$	20.9443	0.731406
$821$	25.4164	0.887039	0.443519	−	0.896265i	$-0.353730\pi$
$821$	25.4164	0.887039	0.443519	+	0.896265i	$0.353730\pi$
$822$	51.4164	1.79335
$823$	34.2492	1.19385	0.596926	−	0.802296i	$-0.296388\pi$
$823$	34.2492	1.19385	0.596926	+	0.802296i	$0.296388\pi$
$824$	−2.94427	−0.102569
$825$	17.7082	0.616521
$826$	0	0
$827$	−0.944272	−0.0328356	−0.0164178	−	0.999865i	$-0.505226\pi$
$827$	−0.944272	−0.0328356	−0.0164178	+	0.999865i	$0.505226\pi$
$828$	29.8885	1.03870
$829$	1.70820	0.0593284	0.0296642	−	0.999560i	$-0.490556\pi$
$829$	1.70820	0.0593284	0.0296642	+	0.999560i	$0.490556\pi$
$830$	32.9443	1.14351
$831$	40.3607	1.40010
$832$	−1.23607	−0.0428529
$833$	0	0
$834$	26.8328	0.929144
$835$	−49.8885	−1.72646
$836$	2.76393	0.0955926
$837$	−28.9443	−1.00046
$838$	−12.7639	−0.440923
$839$	36.8328	1.27161	0.635805	−	0.771850i	$-0.280668\pi$
$839$	36.8328	1.27161	0.635805	+	0.771850i	$0.280668\pi$
$840$	0	0
$841$	−9.00000	−0.310345
$842$	7.52786	0.259427
$843$	−80.3607	−2.76777
$844$	−22.4721	−0.773523
$845$	37.1246	1.27713
$846$	14.9443	0.513795
$847$	0	0
$848$	−0.472136	−0.0162132
$849$	53.8885	1.84945
$850$	35.4164	1.21477
$851$	−43.7771	−1.50066
$852$	−8.00000	−0.274075
$853$	34.5410	1.18266	0.591331	−	0.806429i	$-0.298603\pi$
$853$	34.5410	1.18266	0.591331	+	0.806429i	$0.298603\pi$
$854$	0	0
$855$	−66.8328	−2.28563
$856$	−6.47214	−0.221213
$857$	37.5279	1.28193	0.640964	−	0.767571i	$-0.278535\pi$
$857$	37.5279	1.28193	0.640964	+	0.767571i	$0.278535\pi$
$858$	−4.00000	−0.136558
$859$	25.1246	0.857241	0.428620	−	0.903485i	$-0.359000\pi$
$859$	25.1246	0.857241	0.428620	+	0.903485i	$0.359000\pi$
$860$	4.94427	0.168598
$861$	0	0
$862$	40.9443	1.39457
$863$	27.4164	0.933265	0.466633	−	0.884451i	$-0.345467\pi$
$863$	27.4164	0.933265	0.466633	+	0.884451i	$0.345467\pi$
$864$	14.4721	0.492352
$865$	4.00000	0.136004
$866$	−19.5279	−0.663584
$867$	80.5410	2.73532
$868$	0	0
$869$	0	0
$870$	46.8328	1.58778
$871$	19.0557	0.645679
$872$	−10.0000	−0.338643
$873$	−26.3607	−0.892174
$874$	11.0557	0.373966
$875$	0	0
$876$	16.0000	0.540590
$877$	26.9443	0.909843	0.454922	−	0.890531i	$-0.349667\pi$
$877$	26.9443	0.909843	0.454922	+	0.890531i	$0.349667\pi$
$878$	8.94427	0.301855
$879$	−15.0557	−0.507817
$880$	−3.23607	−0.109088
$881$	24.8328	0.836639	0.418319	−	0.908300i	$-0.362619\pi$
$881$	24.8328	0.836639	0.418319	+	0.908300i	$0.362619\pi$
$882$	0	0
$883$	50.8328	1.71066	0.855330	−	0.518083i	$-0.173354\pi$
$883$	50.8328	1.71066	0.855330	+	0.518083i	$0.173354\pi$
$884$	−8.00000	−0.269069
$885$	75.7771	2.54722
$886$	−7.05573	−0.237042
$887$	−0.360680	−0.0121104	−0.00605522	−	0.999982i	$-0.501927\pi$
$887$	−0.360680	−0.0121104	−0.00605522	+	0.999982i	$0.501927\pi$
$888$	−35.4164	−1.18850
$889$	0	0
$890$	32.3607	1.08473
$891$	24.4164	0.817980
$892$	−8.47214	−0.283668
$893$	5.52786	0.184983
$894$	72.3607	2.42010
$895$	−28.9443	−0.967500
$896$	0	0
$897$	−16.0000	−0.534224
$898$	1.05573	0.0352301
$899$	8.94427	0.298308
$900$	40.8885	1.36295
$901$	−3.05573	−0.101801
$902$	−6.47214	−0.215499
$903$	0	0
$904$	8.47214	0.281779
$905$	15.4164	0.512459
$906$	38.8328	1.29013
$907$	20.3607	0.676065	0.338033	−	0.941134i	$-0.390239\pi$
$907$	20.3607	0.676065	0.338033	+	0.941134i	$0.390239\pi$
$908$	14.7639	0.489958
$909$	105.957	3.51439
$910$	0	0
$911$	−28.0000	−0.927681	−0.463841	−	0.885919i	$-0.653529\pi$
$911$	−28.0000	−0.927681	−0.463841	+	0.885919i	$0.653529\pi$
$912$	8.94427	0.296174
$913$	−10.1803	−0.336920
$914$	9.05573	0.299537
$915$	−54.8328	−1.81272
$916$	−12.7639	−0.421732
$917$	0	0
$918$	93.6656	3.09143
$919$	−57.8885	−1.90957	−0.954783	−	0.297302i	$-0.903913\pi$
$919$	−57.8885	−1.90957	−0.954783	+	0.297302i	$0.903913\pi$
$920$	−12.9443	−0.426760
$921$	−103.777	−3.41957
$922$	−29.2361	−0.962839
$923$	3.05573	0.100581
$924$	0	0
$925$	−59.8885	−1.96912
$926$	−21.5279	−0.707450
$927$	−22.0000	−0.722575
$928$	−4.47214	−0.146805
$929$	40.2492	1.32053	0.660267	−	0.751031i	$-0.270443\pi$
$929$	40.2492	1.32053	0.660267	+	0.751031i	$0.270443\pi$
$930$	20.9443	0.686790
$931$	0	0
$932$	2.94427	0.0964428
$933$	−17.5279	−0.573837
$934$	−13.1246	−0.429450
$935$	−20.9443	−0.684951
$936$	−9.23607	−0.301890
$937$	20.9443	0.684220	0.342110	−	0.939660i	$-0.388859\pi$
$937$	20.9443	0.684220	0.342110	+	0.939660i	$0.388859\pi$
$938$	0	0
$939$	−92.1378	−3.00680
$940$	−6.47214	−0.211098
$941$	34.1803	1.11425	0.557124	−	0.830430i	$-0.311905\pi$
$941$	34.1803	1.11425	0.557124	+	0.830430i	$0.311905\pi$
$942$	−60.3607	−1.96666
$943$	−25.8885	−0.843047
$944$	−7.23607	−0.235514
$945$	0	0
$946$	−1.52786	−0.0496751
$947$	−0.944272	−0.0306847	−0.0153424	−	0.999882i	$-0.504884\pi$
$947$	−0.944272	−0.0306847	−0.0153424	+	0.999882i	$0.504884\pi$
$948$	0	0
$949$	−6.11146	−0.198386
$950$	15.1246	0.490707
$951$	−42.2492	−1.37002
$952$	0	0
$953$	5.05573	0.163771	0.0818855	−	0.996642i	$-0.473906\pi$
$953$	5.05573	0.163771	0.0818855	+	0.996642i	$0.473906\pi$
$954$	−3.52786	−0.114219
$955$	−20.9443	−0.677741
$956$	20.0000	0.646846
$957$	−14.4721	−0.467818
$958$	32.3607	1.04553
$959$	0	0
$960$	−10.4721	−0.337987
$961$	−27.0000	−0.870968
$962$	13.5279	0.436156
$963$	−48.3607	−1.55840
$964$	11.4164	0.367698
$965$	−9.52786	−0.306713
$966$	0	0
$967$	10.1115	0.325163	0.162581	−	0.986695i	$-0.448018\pi$
$967$	10.1115	0.325163	0.162581	+	0.986695i	$0.448018\pi$
$968$	1.00000	0.0321412
$969$	57.8885	1.85965
$970$	11.4164	0.366559
$971$	16.5410	0.530827	0.265413	−	0.964135i	$-0.414492\pi$
$971$	16.5410	0.530827	0.265413	+	0.964135i	$0.414492\pi$
$972$	35.5967	1.14177
$973$	0	0
$974$	−0.944272	−0.0302564
$975$	−21.8885	−0.700994
$976$	5.23607	0.167602
$977$	24.8328	0.794472	0.397236	−	0.917716i	$-0.369969\pi$
$977$	24.8328	0.794472	0.397236	+	0.917716i	$0.369969\pi$
$978$	24.0000	0.767435
$979$	−10.0000	−0.319601
$980$	0	0
$981$	−74.7214	−2.38567
$982$	0.944272	0.0301329
$983$	−14.0000	−0.446531	−0.223265	−	0.974758i	$-0.571672\pi$
$983$	−14.0000	−0.446531	−0.223265	+	0.974758i	$0.571672\pi$
$984$	−20.9443	−0.667679
$985$	−58.2492	−1.85597
$986$	−28.9443	−0.921773
$987$	0	0
$988$	−3.41641	−0.108690
$989$	−6.11146	−0.194333
$990$	−24.1803	−0.768502
$991$	44.3607	1.40916	0.704582	−	0.709623i	$-0.251135\pi$
$991$	44.3607	1.40916	0.704582	+	0.709623i	$0.251135\pi$
$992$	−2.00000	−0.0635001
$993$	3.05573	0.0969706
$994$	0	0
$995$	3.41641	0.108307
$996$	−32.9443	−1.04388
$997$	−1.81966	−0.0576292	−0.0288146	−	0.999585i	$-0.509173\pi$
$997$	−1.81966	−0.0576292	−0.0288146	+	0.999585i	$0.509173\pi$
$998$	12.3607	0.391270
$999$	−158.387	−5.01114

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.a.w.1.2		2
3.2	odd	2		9702.2.a.cu.1.2		2
4.3	odd	2		8624.2.a.bf.1.1		2
7.2	even	3		1078.2.e.n.67.1		4
7.3	odd	6		1078.2.e.q.177.2		4
7.4	even	3		1078.2.e.n.177.1		4
7.5	odd	6		1078.2.e.q.67.2		4
7.6	odd	2		154.2.a.d.1.1	✓	2
21.20	even	2		1386.2.a.m.1.1		2
28.27	even	2		1232.2.a.p.1.2		2
35.13	even	4		3850.2.c.q.1849.1		4
35.27	even	4		3850.2.c.q.1849.4		4
35.34	odd	2		3850.2.a.bj.1.2		2
56.13	odd	2		4928.2.a.bt.1.2		2
56.27	even	2		4928.2.a.bk.1.1		2
77.76	even	2		1694.2.a.l.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.a.d.1.1	✓	2	7.6	odd	2
1078.2.a.w.1.2		2	1.1	even	1	trivial
1078.2.e.n.67.1		4	7.2	even	3
1078.2.e.n.177.1		4	7.4	even	3
1078.2.e.q.67.2		4	7.5	odd	6
1078.2.e.q.177.2		4	7.3	odd	6
1232.2.a.p.1.2		2	28.27	even	2
1386.2.a.m.1.1		2	21.20	even	2
1694.2.a.l.1.1		2	77.76	even	2
3850.2.a.bj.1.2		2	35.34	odd	2
3850.2.c.q.1849.1		4	35.13	even	4
3850.2.c.q.1849.4		4	35.27	even	4
4928.2.a.bk.1.1		2	56.27	even	2
4928.2.a.bt.1.2		2	56.13	odd	2
8624.2.a.bf.1.1		2	4.3	odd	2
9702.2.a.cu.1.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.23607 q^{3} +1.00000 q^{4} -3.23607 q^{5} +3.23607 q^{6} +1.00000 q^{8} +7.47214 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.23607 q^{3} +1.00000 q^{4} -3.23607 q^{5} +3.23607 q^{6} +1.00000 q^{8} +7.47214 q^{9} -3.23607 q^{10} +1.00000 q^{11} +3.23607 q^{12} -1.23607 q^{13} -10.4721 q^{15} +1.00000 q^{16} +6.47214 q^{17} +7.47214 q^{18} +2.76393 q^{19} -3.23607 q^{20} +1.00000 q^{22} +4.00000 q^{23} +3.23607 q^{24} +5.47214 q^{25} -1.23607 q^{26} +14.4721 q^{27} -4.47214 q^{29} -10.4721 q^{30} -2.00000 q^{31} +1.00000 q^{32} +3.23607 q^{33} +6.47214 q^{34} +7.47214 q^{36} -10.9443 q^{37} +2.76393 q^{38} -4.00000 q^{39} -3.23607 q^{40} -6.47214 q^{41} -1.52786 q^{43} +1.00000 q^{44} -24.1803 q^{45} +4.00000 q^{46} +2.00000 q^{47} +3.23607 q^{48} +5.47214 q^{50} +20.9443 q^{51} -1.23607 q^{52} -0.472136 q^{53} +14.4721 q^{54} -3.23607 q^{55} +8.94427 q^{57} -4.47214 q^{58} -7.23607 q^{59} -10.4721 q^{60} +5.23607 q^{61} -2.00000 q^{62} +1.00000 q^{64} +4.00000 q^{65} +3.23607 q^{66} -15.4164 q^{67} +6.47214 q^{68} +12.9443 q^{69} -2.47214 q^{71} +7.47214 q^{72} +4.94427 q^{73} -10.9443 q^{74} +17.7082 q^{75} +2.76393 q^{76} -4.00000 q^{78} -3.23607 q^{80} +24.4164 q^{81} -6.47214 q^{82} -10.1803 q^{83} -20.9443 q^{85} -1.52786 q^{86} -14.4721 q^{87} +1.00000 q^{88} -10.0000 q^{89} -24.1803 q^{90} +4.00000 q^{92} -6.47214 q^{93} +2.00000 q^{94} -8.94427 q^{95} +3.23607 q^{96} -3.52786 q^{97} +7.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} + 6 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 + 6 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} + 6 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 2 q^{13} - 12 q^{15} + 2 q^{16} + 4 q^{17} + 6 q^{18} + 10 q^{19} - 2 q^{20} + 2 q^{22} + 8 q^{23} + 2 q^{24} + 2 q^{25} + 2 q^{26} + 20 q^{27} - 12 q^{30} - 4 q^{31} + 2 q^{32} + 2 q^{33} + 4 q^{34} + 6 q^{36} - 4 q^{37} + 10 q^{38} - 8 q^{39} - 2 q^{40} - 4 q^{41} - 12 q^{43} + 2 q^{44} - 26 q^{45} + 8 q^{46} + 4 q^{47} + 2 q^{48} + 2 q^{50} + 24 q^{51} + 2 q^{52} + 8 q^{53} + 20 q^{54} - 2 q^{55} - 10 q^{59} - 12 q^{60} + 6 q^{61} - 4 q^{62} + 2 q^{64} + 8 q^{65} + 2 q^{66} - 4 q^{67} + 4 q^{68} + 8 q^{69} + 4 q^{71} + 6 q^{72} - 8 q^{73} - 4 q^{74} + 22 q^{75} + 10 q^{76} - 8 q^{78} - 2 q^{80} + 22 q^{81} - 4 q^{82} + 2 q^{83} - 24 q^{85} - 12 q^{86} - 20 q^{87} + 2 q^{88} - 20 q^{89} - 26 q^{90} + 8 q^{92} - 4 q^{93} + 4 q^{94} + 2 q^{96} - 16 q^{97} + 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 + 6 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 + 2 * q^13 - 12 * q^15 + 2 * q^16 + 4 * q^17 + 6 * q^18 + 10 * q^19 - 2 * q^20 + 2 * q^22 + 8 * q^23 + 2 * q^24 + 2 * q^25 + 2 * q^26 + 20 * q^27 - 12 * q^30 - 4 * q^31 + 2 * q^32 + 2 * q^33 + 4 * q^34 + 6 * q^36 - 4 * q^37 + 10 * q^38 - 8 * q^39 - 2 * q^40 - 4 * q^41 - 12 * q^43 + 2 * q^44 - 26 * q^45 + 8 * q^46 + 4 * q^47 + 2 * q^48 + 2 * q^50 + 24 * q^51 + 2 * q^52 + 8 * q^53 + 20 * q^54 - 2 * q^55 - 10 * q^59 - 12 * q^60 + 6 * q^61 - 4 * q^62 + 2 * q^64 + 8 * q^65 + 2 * q^66 - 4 * q^67 + 4 * q^68 + 8 * q^69 + 4 * q^71 + 6 * q^72 - 8 * q^73 - 4 * q^74 + 22 * q^75 + 10 * q^76 - 8 * q^78 - 2 * q^80 + 22 * q^81 - 4 * q^82 + 2 * q^83 - 24 * q^85 - 12 * q^86 - 20 * q^87 + 2 * q^88 - 20 * q^89 - 26 * q^90 + 8 * q^92 - 4 * q^93 + 4 * q^94 + 2 * q^96 - 16 * q^97 + 6 * q^99

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