LMFDB - Embedded newform 5415.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5415,2,Mod(1,5415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5415, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5415 = 3 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5415.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$43.2389926945$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 285)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	5415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.73205 q^{6} +0.732051 q^{7} +1.73205 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.73205 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.73205 q^{6} +0.732051 q^{7} +1.73205 q^{8} +1.00000 q^{9} -1.73205 q^{10} +1.26795 q^{11} -1.00000 q^{12} +2.73205 q^{13} -1.26795 q^{14} -1.00000 q^{15} -5.00000 q^{16} -1.73205 q^{18} +1.00000 q^{20} -0.732051 q^{21} -2.19615 q^{22} -3.46410 q^{23} -1.73205 q^{24} +1.00000 q^{25} -4.73205 q^{26} -1.00000 q^{27} +0.732051 q^{28} +2.19615 q^{29} +1.73205 q^{30} +4.92820 q^{31} +5.19615 q^{32} -1.26795 q^{33} +0.732051 q^{35} +1.00000 q^{36} -4.19615 q^{37} -2.73205 q^{39} +1.73205 q^{40} -4.73205 q^{41} +1.26795 q^{42} -6.19615 q^{43} +1.26795 q^{44} +1.00000 q^{45} +6.00000 q^{46} +3.46410 q^{47} +5.00000 q^{48} -6.46410 q^{49} -1.73205 q^{50} +2.73205 q^{52} +2.53590 q^{53} +1.73205 q^{54} +1.26795 q^{55} +1.26795 q^{56} -3.80385 q^{58} -9.46410 q^{59} -1.00000 q^{60} -13.4641 q^{61} -8.53590 q^{62} +0.732051 q^{63} +1.00000 q^{64} +2.73205 q^{65} +2.19615 q^{66} -8.00000 q^{67} +3.46410 q^{69} -1.26795 q^{70} -16.3923 q^{71} +1.73205 q^{72} -3.07180 q^{73} +7.26795 q^{74} -1.00000 q^{75} +0.928203 q^{77} +4.73205 q^{78} -2.92820 q^{79} -5.00000 q^{80} +1.00000 q^{81} +8.19615 q^{82} +0.928203 q^{83} -0.732051 q^{84} +10.7321 q^{86} -2.19615 q^{87} +2.19615 q^{88} -7.26795 q^{89} -1.73205 q^{90} +2.00000 q^{91} -3.46410 q^{92} -4.92820 q^{93} -6.00000 q^{94} -5.19615 q^{96} -4.19615 q^{97} +11.1962 q^{98} +1.26795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^7 + 2 * q^9	$ 2 q - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{7} + 2 q^{9} + 6 q^{11} - 2 q^{12} + 2 q^{13} - 6 q^{14} - 2 q^{15} - 10 q^{16} + 2 q^{20} + 2 q^{21} + 6 q^{22} + 2 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} - 6 q^{29} - 4 q^{31} - 6 q^{33} - 2 q^{35} + 2 q^{36} + 2 q^{37} - 2 q^{39} - 6 q^{41} + 6 q^{42} - 2 q^{43} + 6 q^{44} + 2 q^{45} + 12 q^{46} + 10 q^{48} - 6 q^{49} + 2 q^{52} + 12 q^{53} + 6 q^{55} + 6 q^{56} - 18 q^{58} - 12 q^{59} - 2 q^{60} - 20 q^{61} - 24 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{65} - 6 q^{66} - 16 q^{67} - 6 q^{70} - 12 q^{71} - 20 q^{73} + 18 q^{74} - 2 q^{75} - 12 q^{77} + 6 q^{78} + 8 q^{79} - 10 q^{80} + 2 q^{81} + 6 q^{82} - 12 q^{83} + 2 q^{84} + 18 q^{86} + 6 q^{87} - 6 q^{88} - 18 q^{89} + 4 q^{91} + 4 q^{93} - 12 q^{94} + 2 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^7 + 2 * q^9 + 6 * q^11 - 2 * q^12 + 2 * q^13 - 6 * q^14 - 2 * q^15 - 10 * q^16 + 2 * q^20 + 2 * q^21 + 6 * q^22 + 2 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 - 6 * q^29 - 4 * q^31 - 6 * q^33 - 2 * q^35 + 2 * q^36 + 2 * q^37 - 2 * q^39 - 6 * q^41 + 6 * q^42 - 2 * q^43 + 6 * q^44 + 2 * q^45 + 12 * q^46 + 10 * q^48 - 6 * q^49 + 2 * q^52 + 12 * q^53 + 6 * q^55 + 6 * q^56 - 18 * q^58 - 12 * q^59 - 2 * q^60 - 20 * q^61 - 24 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^65 - 6 * q^66 - 16 * q^67 - 6 * q^70 - 12 * q^71 - 20 * q^73 + 18 * q^74 - 2 * q^75 - 12 * q^77 + 6 * q^78 + 8 * q^79 - 10 * q^80 + 2 * q^81 + 6 * q^82 - 12 * q^83 + 2 * q^84 + 18 * q^86 + 6 * q^87 - 6 * q^88 - 18 * q^89 + 4 * q^91 + 4 * q^93 - 12 * q^94 + 2 * q^97 + 12 * 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 $

$2$	−1.73205	−1.22474	−0.612372	−	0.790569i	$-0.709785\pi$
$2$	−1.73205	−1.22474	−0.612372	+	0.790569i	$0.709785\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.73205	0.707107
$7$	0.732051	0.276689	0.138345	−	0.990384i	$-0.455822\pi$
$7$	0.732051	0.276689	0.138345	+	0.990384i	$0.455822\pi$
$8$	1.73205	0.612372
$9$	1.00000	0.333333
$10$	−1.73205	−0.547723
$11$	1.26795	0.382301	0.191151	−	0.981561i	$-0.438778\pi$
$11$	1.26795	0.382301	0.191151	+	0.981561i	$0.438778\pi$
$12$	−1.00000	−0.288675
$13$	2.73205	0.757735	0.378867	−	0.925451i	$-0.376314\pi$
$13$	2.73205	0.757735	0.378867	+	0.925451i	$0.376314\pi$
$14$	−1.26795	−0.338874
$15$	−1.00000	−0.258199
$16$	−5.00000	−1.25000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−1.73205	−0.408248
$19$	0	0
$19$	0	0
$20$	1.00000	0.223607
$21$	−0.732051	−0.159747
$22$	−2.19615	−0.468221
$23$	−3.46410	−0.722315	−0.361158	−	0.932505i	$-0.617618\pi$
$23$	−3.46410	−0.722315	−0.361158	+	0.932505i	$0.617618\pi$
$24$	−1.73205	−0.353553
$25$	1.00000	0.200000
$26$	−4.73205	−0.928032
$27$	−1.00000	−0.192450
$28$	0.732051	0.138345
$29$	2.19615	0.407815	0.203908	−	0.978990i	$-0.434636\pi$
$29$	2.19615	0.407815	0.203908	+	0.978990i	$0.434636\pi$
$30$	1.73205	0.316228
$31$	4.92820	0.885131	0.442566	−	0.896736i	$-0.354068\pi$
$31$	4.92820	0.885131	0.442566	+	0.896736i	$0.354068\pi$
$32$	5.19615	0.918559
$33$	−1.26795	−0.220722
$34$	0	0
$35$	0.732051	0.123739
$36$	1.00000	0.166667
$37$	−4.19615	−0.689843	−0.344922	−	0.938631i	$-0.612095\pi$
$37$	−4.19615	−0.689843	−0.344922	+	0.938631i	$0.612095\pi$
$38$	0	0
$39$	−2.73205	−0.437478
$40$	1.73205	0.273861
$41$	−4.73205	−0.739022	−0.369511	−	0.929226i	$-0.620475\pi$
$41$	−4.73205	−0.739022	−0.369511	+	0.929226i	$0.620475\pi$
$42$	1.26795	0.195649
$43$	−6.19615	−0.944904	−0.472452	−	0.881356i	$-0.656631\pi$
$43$	−6.19615	−0.944904	−0.472452	+	0.881356i	$0.656631\pi$
$44$	1.26795	0.191151
$45$	1.00000	0.149071
$46$	6.00000	0.884652
$47$	3.46410	0.505291	0.252646	−	0.967559i	$-0.418699\pi$
$47$	3.46410	0.505291	0.252646	+	0.967559i	$0.418699\pi$
$48$	5.00000	0.721688
$49$	−6.46410	−0.923443
$50$	−1.73205	−0.244949
$51$	0	0
$52$	2.73205	0.378867
$53$	2.53590	0.348332	0.174166	−	0.984716i	$-0.444277\pi$
$53$	2.53590	0.348332	0.174166	+	0.984716i	$0.444277\pi$
$54$	1.73205	0.235702
$55$	1.26795	0.170970
$56$	1.26795	0.169437
$57$	0	0
$58$	−3.80385	−0.499470
$59$	−9.46410	−1.23212	−0.616061	−	0.787699i	$-0.711272\pi$
$59$	−9.46410	−1.23212	−0.616061	+	0.787699i	$0.711272\pi$
$60$	−1.00000	−0.129099
$61$	−13.4641	−1.72390	−0.861951	−	0.506992i	$-0.830757\pi$
$61$	−13.4641	−1.72390	−0.861951	+	0.506992i	$0.830757\pi$
$62$	−8.53590	−1.08406
$63$	0.732051	0.0922297
$64$	1.00000	0.125000
$65$	2.73205	0.338869
$66$	2.19615	0.270328
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	0	0
$69$	3.46410	0.417029
$70$	−1.26795	−0.151549
$71$	−16.3923	−1.94541	−0.972704	−	0.232048i	$-0.925457\pi$
$71$	−16.3923	−1.94541	−0.972704	+	0.232048i	$0.925457\pi$
$72$	1.73205	0.204124
$73$	−3.07180	−0.359527	−0.179763	−	0.983710i	$-0.557533\pi$
$73$	−3.07180	−0.359527	−0.179763	+	0.983710i	$0.557533\pi$
$74$	7.26795	0.844882
$75$	−1.00000	−0.115470
$76$	0	0
$77$	0.928203	0.105779
$78$	4.73205	0.535799
$79$	−2.92820	−0.329449	−0.164724	−	0.986340i	$-0.552673\pi$
$79$	−2.92820	−0.329449	−0.164724	+	0.986340i	$0.552673\pi$
$80$	−5.00000	−0.559017
$81$	1.00000	0.111111
$82$	8.19615	0.905114
$83$	0.928203	0.101884	0.0509418	−	0.998702i	$-0.483778\pi$
$83$	0.928203	0.101884	0.0509418	+	0.998702i	$0.483778\pi$
$84$	−0.732051	−0.0798733
$85$	0	0
$86$	10.7321	1.15727
$87$	−2.19615	−0.235452
$88$	2.19615	0.234111
$89$	−7.26795	−0.770401	−0.385201	−	0.922833i	$-0.625868\pi$
$89$	−7.26795	−0.770401	−0.385201	+	0.922833i	$0.625868\pi$
$90$	−1.73205	−0.182574
$91$	2.00000	0.209657
$92$	−3.46410	−0.361158
$93$	−4.92820	−0.511031
$94$	−6.00000	−0.618853
$95$	0	0
$96$	−5.19615	−0.530330
$97$	−4.19615	−0.426055	−0.213027	−	0.977046i	$-0.568332\pi$
$97$	−4.19615	−0.426055	−0.213027	+	0.977046i	$0.568332\pi$
$98$	11.1962	1.13098
$99$	1.26795	0.127434
$100$	1.00000	0.100000
$101$	10.3923	1.03407	0.517036	−	0.855963i	$-0.327035\pi$
$101$	10.3923	1.03407	0.517036	+	0.855963i	$0.327035\pi$
$102$	0	0
$103$	17.8564	1.75944	0.879722	−	0.475488i	$-0.157729\pi$
$103$	17.8564	1.75944	0.879722	+	0.475488i	$0.157729\pi$
$104$	4.73205	0.464016
$105$	−0.732051	−0.0714408
$106$	−4.39230	−0.426618
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	−1.00000	−0.0962250
$109$	−6.39230	−0.612272	−0.306136	−	0.951988i	$-0.599036\pi$
$109$	−6.39230	−0.612272	−0.306136	+	0.951988i	$0.599036\pi$
$110$	−2.19615	−0.209395
$111$	4.19615	0.398281
$112$	−3.66025	−0.345861
$113$	−5.07180	−0.477115	−0.238557	−	0.971128i	$-0.576674\pi$
$113$	−5.07180	−0.477115	−0.238557	+	0.971128i	$0.576674\pi$
$114$	0	0
$115$	−3.46410	−0.323029
$116$	2.19615	0.203908
$117$	2.73205	0.252578
$118$	16.3923	1.50903
$119$	0	0
$120$	−1.73205	−0.158114
$121$	−9.39230	−0.853846
$122$	23.3205	2.11134
$123$	4.73205	0.426675
$124$	4.92820	0.442566
$125$	1.00000	0.0894427
$126$	−1.26795	−0.112958
$127$	4.00000	0.354943	0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000	0.354943	0.177471	+	0.984126i	$0.443208\pi$
$128$	−12.1244	−1.07165
$129$	6.19615	0.545541
$130$	−4.73205	−0.415028
$131$	15.1244	1.32142	0.660711	−	0.750641i	$-0.270255\pi$
$131$	15.1244	1.32142	0.660711	+	0.750641i	$0.270255\pi$
$132$	−1.26795	−0.110361
$133$	0	0
$134$	13.8564	1.19701
$135$	−1.00000	−0.0860663
$136$	0	0
$137$	−7.85641	−0.671218	−0.335609	−	0.942001i	$-0.608942\pi$
$137$	−7.85641	−0.671218	−0.335609	+	0.942001i	$0.608942\pi$
$138$	−6.00000	−0.510754
$139$	12.3923	1.05110	0.525551	−	0.850762i	$-0.323859\pi$
$139$	12.3923	1.05110	0.525551	+	0.850762i	$0.323859\pi$
$140$	0.732051	0.0618696
$141$	−3.46410	−0.291730
$142$	28.3923	2.38263
$143$	3.46410	0.289683
$144$	−5.00000	−0.416667
$145$	2.19615	0.182381
$146$	5.32051	0.440328
$147$	6.46410	0.533150
$148$	−4.19615	−0.344922
$149$	7.85641	0.643622	0.321811	−	0.946804i	$-0.395708\pi$
$149$	7.85641	0.643622	0.321811	+	0.946804i	$0.395708\pi$
$150$	1.73205	0.141421
$151$	−14.0000	−1.13930	−0.569652	−	0.821886i	$-0.692922\pi$
$151$	−14.0000	−1.13930	−0.569652	+	0.821886i	$0.692922\pi$
$152$	0	0
$153$	0	0
$154$	−1.60770	−0.129552
$155$	4.92820	0.395843
$156$	−2.73205	−0.218739
$157$	−14.3923	−1.14863	−0.574315	−	0.818634i	$-0.694732\pi$
$157$	−14.3923	−1.14863	−0.574315	+	0.818634i	$0.694732\pi$
$158$	5.07180	0.403490
$159$	−2.53590	−0.201110
$160$	5.19615	0.410792
$161$	−2.53590	−0.199857
$162$	−1.73205	−0.136083
$163$	12.7321	0.997251	0.498626	−	0.866817i	$-0.333838\pi$
$163$	12.7321	0.997251	0.498626	+	0.866817i	$0.333838\pi$
$164$	−4.73205	−0.369511
$165$	−1.26795	−0.0987097
$166$	−1.60770	−0.124781
$167$	3.46410	0.268060	0.134030	−	0.990977i	$-0.457208\pi$
$167$	3.46410	0.268060	0.134030	+	0.990977i	$0.457208\pi$
$168$	−1.26795	−0.0978244
$169$	−5.53590	−0.425838
$170$	0	0
$171$	0	0
$172$	−6.19615	−0.472452
$173$	6.92820	0.526742	0.263371	−	0.964695i	$-0.415166\pi$
$173$	6.92820	0.526742	0.263371	+	0.964695i	$0.415166\pi$
$174$	3.80385	0.288369
$175$	0.732051	0.0553378
$176$	−6.33975	−0.477876
$177$	9.46410	0.711365
$178$	12.5885	0.943545
$179$	11.3205	0.846135	0.423067	−	0.906098i	$-0.360953\pi$
$179$	11.3205	0.846135	0.423067	+	0.906098i	$0.360953\pi$
$180$	1.00000	0.0745356
$181$	−18.3923	−1.36709	−0.683545	−	0.729909i	$-0.739563\pi$
$181$	−18.3923	−1.36709	−0.683545	+	0.729909i	$0.739563\pi$
$182$	−3.46410	−0.256776
$183$	13.4641	0.995295
$184$	−6.00000	−0.442326
$185$	−4.19615	−0.308507
$186$	8.53590	0.625882
$187$	0	0
$188$	3.46410	0.252646
$189$	−0.732051	−0.0532489
$190$	0	0
$191$	17.6603	1.27785	0.638926	−	0.769269i	$-0.279379\pi$
$191$	17.6603	1.27785	0.638926	+	0.769269i	$0.279379\pi$
$192$	−1.00000	−0.0721688
$193$	7.12436	0.512822	0.256411	−	0.966568i	$-0.417460\pi$
$193$	7.12436	0.512822	0.256411	+	0.966568i	$0.417460\pi$
$194$	7.26795	0.521808
$195$	−2.73205	−0.195646
$196$	−6.46410	−0.461722
$197$	−24.0000	−1.70993	−0.854965	−	0.518686i	$-0.826421\pi$
$197$	−24.0000	−1.70993	−0.854965	+	0.518686i	$0.826421\pi$
$198$	−2.19615	−0.156074
$199$	19.3205	1.36959	0.684797	−	0.728734i	$-0.259891\pi$
$199$	19.3205	1.36959	0.684797	+	0.728734i	$0.259891\pi$
$200$	1.73205	0.122474
$201$	8.00000	0.564276
$202$	−18.0000	−1.26648
$203$	1.60770	0.112838
$204$	0	0
$205$	−4.73205	−0.330501
$206$	−30.9282	−2.15487
$207$	−3.46410	−0.240772
$208$	−13.6603	−0.947168
$209$	0	0
$210$	1.26795	0.0874968
$211$	−14.9282	−1.02770	−0.513850	−	0.857880i	$-0.671781\pi$
$211$	−14.9282	−1.02770	−0.513850	+	0.857880i	$0.671781\pi$
$212$	2.53590	0.174166
$213$	16.3923	1.12318
$214$	0	0
$215$	−6.19615	−0.422574
$216$	−1.73205	−0.117851
$217$	3.60770	0.244906
$218$	11.0718	0.749877
$219$	3.07180	0.207573
$220$	1.26795	0.0854851
$221$	0	0
$222$	−7.26795	−0.487793
$223$	−9.85641	−0.660034	−0.330017	−	0.943975i	$-0.607054\pi$
$223$	−9.85641	−0.660034	−0.330017	+	0.943975i	$0.607054\pi$
$224$	3.80385	0.254155
$225$	1.00000	0.0666667
$226$	8.78461	0.584344
$227$	10.3923	0.689761	0.344881	−	0.938647i	$-0.387919\pi$
$227$	10.3923	0.689761	0.344881	+	0.938647i	$0.387919\pi$
$228$	0	0
$229$	−25.4641	−1.68272	−0.841358	−	0.540479i	$-0.818243\pi$
$229$	−25.4641	−1.68272	−0.841358	+	0.540479i	$0.818243\pi$
$230$	6.00000	0.395628
$231$	−0.928203	−0.0610713
$232$	3.80385	0.249735
$233$	19.8564	1.30084	0.650418	−	0.759576i	$-0.274594\pi$
$233$	19.8564	1.30084	0.650418	+	0.759576i	$0.274594\pi$
$234$	−4.73205	−0.309344
$235$	3.46410	0.225973
$236$	−9.46410	−0.616061
$237$	2.92820	0.190207
$238$	0	0
$239$	−20.1962	−1.30638	−0.653190	−	0.757194i	$-0.726570\pi$
$239$	−20.1962	−1.30638	−0.653190	+	0.757194i	$0.726570\pi$
$240$	5.00000	0.322749
$241$	16.9282	1.09044	0.545221	−	0.838293i	$-0.316446\pi$
$241$	16.9282	1.09044	0.545221	+	0.838293i	$0.316446\pi$
$242$	16.2679	1.04574
$243$	−1.00000	−0.0641500
$244$	−13.4641	−0.861951
$245$	−6.46410	−0.412976
$246$	−8.19615	−0.522568
$247$	0	0
$248$	8.53590	0.542030
$249$	−0.928203	−0.0588225
$250$	−1.73205	−0.109545
$251$	−10.0526	−0.634512	−0.317256	−	0.948340i	$-0.602761\pi$
$251$	−10.0526	−0.634512	−0.317256	+	0.948340i	$0.602761\pi$
$252$	0.732051	0.0461149
$253$	−4.39230	−0.276142
$254$	−6.92820	−0.434714
$255$	0	0
$256$	19.0000	1.18750
$257$	24.0000	1.49708	0.748539	−	0.663090i	$-0.230755\pi$
$257$	24.0000	1.49708	0.748539	+	0.663090i	$0.230755\pi$
$258$	−10.7321	−0.668148
$259$	−3.07180	−0.190872
$260$	2.73205	0.169435
$261$	2.19615	0.135938
$262$	−26.1962	−1.61840
$263$	6.00000	0.369976	0.184988	−	0.982741i	$-0.440775\pi$
$263$	6.00000	0.369976	0.184988	+	0.982741i	$0.440775\pi$
$264$	−2.19615	−0.135164
$265$	2.53590	0.155779
$266$	0	0
$267$	7.26795	0.444791
$268$	−8.00000	−0.488678
$269$	30.5885	1.86501	0.932506	−	0.361156i	$-0.117618\pi$
$269$	30.5885	1.86501	0.932506	+	0.361156i	$0.117618\pi$
$270$	1.73205	0.105409
$271$	−20.3923	−1.23874	−0.619372	−	0.785098i	$-0.712613\pi$
$271$	−20.3923	−1.23874	−0.619372	+	0.785098i	$0.712613\pi$
$272$	0	0
$273$	−2.00000	−0.121046
$274$	13.6077	0.822071
$275$	1.26795	0.0764602
$276$	3.46410	0.208514
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	−21.4641	−1.28733
$279$	4.92820	0.295044
$280$	1.26795	0.0757745
$281$	−4.73205	−0.282290	−0.141145	−	0.989989i	$-0.545078\pi$
$281$	−4.73205	−0.282290	−0.141145	+	0.989989i	$0.545078\pi$
$282$	6.00000	0.357295
$283$	−26.9808	−1.60384	−0.801920	−	0.597432i	$-0.796188\pi$
$283$	−26.9808	−1.60384	−0.801920	+	0.597432i	$0.796188\pi$
$284$	−16.3923	−0.972704
$285$	0	0
$286$	−6.00000	−0.354787
$287$	−3.46410	−0.204479
$288$	5.19615	0.306186
$289$	−17.0000	−1.00000
$290$	−3.80385	−0.223370
$291$	4.19615	0.245983
$292$	−3.07180	−0.179763
$293$	27.7128	1.61900	0.809500	−	0.587120i	$-0.199738\pi$
$293$	27.7128	1.61900	0.809500	+	0.587120i	$0.199738\pi$
$294$	−11.1962	−0.652973
$295$	−9.46410	−0.551021
$296$	−7.26795	−0.422441
$297$	−1.26795	−0.0735739
$298$	−13.6077	−0.788273
$299$	−9.46410	−0.547323
$300$	−1.00000	−0.0577350
$301$	−4.53590	−0.261445
$302$	24.2487	1.39536
$303$	−10.3923	−0.597022
$304$	0	0
$305$	−13.4641	−0.770952
$306$	0	0
$307$	11.6077	0.662486	0.331243	−	0.943545i	$-0.392532\pi$
$307$	11.6077	0.662486	0.331243	+	0.943545i	$0.392532\pi$
$308$	0.928203	0.0528893
$309$	−17.8564	−1.01582
$310$	−8.53590	−0.484806
$311$	−26.4449	−1.49955	−0.749775	−	0.661692i	$-0.769838\pi$
$311$	−26.4449	−1.49955	−0.749775	+	0.661692i	$0.769838\pi$
$312$	−4.73205	−0.267900
$313$	−14.3923	−0.813501	−0.406751	−	0.913539i	$-0.633338\pi$
$313$	−14.3923	−0.813501	−0.406751	+	0.913539i	$0.633338\pi$
$314$	24.9282	1.40678
$315$	0.732051	0.0412464
$316$	−2.92820	−0.164724
$317$	−23.3205	−1.30981	−0.654905	−	0.755711i	$-0.727291\pi$
$317$	−23.3205	−1.30981	−0.654905	+	0.755711i	$0.727291\pi$
$318$	4.39230	0.246308
$319$	2.78461	0.155908
$320$	1.00000	0.0559017
$321$	0	0
$322$	4.39230	0.244774
$323$	0	0
$324$	1.00000	0.0555556
$325$	2.73205	0.151547
$326$	−22.0526	−1.22138
$327$	6.39230	0.353495
$328$	−8.19615	−0.452557
$329$	2.53590	0.139809
$330$	2.19615	0.120894
$331$	−29.7128	−1.63316	−0.816582	−	0.577230i	$-0.804134\pi$
$331$	−29.7128	−1.63316	−0.816582	+	0.577230i	$0.804134\pi$
$332$	0.928203	0.0509418
$333$	−4.19615	−0.229948
$334$	−6.00000	−0.328305
$335$	−8.00000	−0.437087
$336$	3.66025	0.199683
$337$	19.1244	1.04177	0.520885	−	0.853627i	$-0.325602\pi$
$337$	19.1244	1.04177	0.520885	+	0.853627i	$0.325602\pi$
$338$	9.58846	0.521543
$339$	5.07180	0.275462
$340$	0	0
$341$	6.24871	0.338387
$342$	0	0
$343$	−9.85641	−0.532196
$344$	−10.7321	−0.578633
$345$	3.46410	0.186501
$346$	−12.0000	−0.645124
$347$	12.9282	0.694022	0.347011	−	0.937861i	$-0.387197\pi$
$347$	12.9282	0.694022	0.347011	+	0.937861i	$0.387197\pi$
$348$	−2.19615	−0.117726
$349$	−22.0000	−1.17763	−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000	−1.17763	−0.588817	+	0.808267i	$0.700406\pi$
$350$	−1.26795	−0.0677747
$351$	−2.73205	−0.145826
$352$	6.58846	0.351166
$353$	26.7846	1.42560	0.712800	−	0.701367i	$-0.247427\pi$
$353$	26.7846	1.42560	0.712800	+	0.701367i	$0.247427\pi$
$354$	−16.3923	−0.871241
$355$	−16.3923	−0.870013
$356$	−7.26795	−0.385201
$357$	0	0
$358$	−19.6077	−1.03630
$359$	17.6603	0.932073	0.466036	−	0.884766i	$-0.345682\pi$
$359$	17.6603	0.932073	0.466036	+	0.884766i	$0.345682\pi$
$360$	1.73205	0.0912871
$361$	0	0
$362$	31.8564	1.67434
$363$	9.39230	0.492968
$364$	2.00000	0.104828
$365$	−3.07180	−0.160785
$366$	−23.3205	−1.21898
$367$	5.80385	0.302958	0.151479	−	0.988460i	$-0.451596\pi$
$367$	5.80385	0.302958	0.151479	+	0.988460i	$0.451596\pi$
$368$	17.3205	0.902894
$369$	−4.73205	−0.246341
$370$	7.26795	0.377843
$371$	1.85641	0.0963798
$372$	−4.92820	−0.255515
$373$	−4.19615	−0.217269	−0.108634	−	0.994082i	$-0.534648\pi$
$373$	−4.19615	−0.217269	−0.108634	+	0.994082i	$0.534648\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	6.00000	0.309426
$377$	6.00000	0.309016
$378$	1.26795	0.0652163
$379$	−7.07180	−0.363254	−0.181627	−	0.983368i	$-0.558136\pi$
$379$	−7.07180	−0.363254	−0.181627	+	0.983368i	$0.558136\pi$
$380$	0	0
$381$	−4.00000	−0.204926
$382$	−30.5885	−1.56504
$383$	30.9282	1.58036	0.790179	−	0.612877i	$-0.209988\pi$
$383$	30.9282	1.58036	0.790179	+	0.612877i	$0.209988\pi$
$384$	12.1244	0.618718
$385$	0.928203	0.0473056
$386$	−12.3397	−0.628077
$387$	−6.19615	−0.314968
$388$	−4.19615	−0.213027
$389$	−19.8564	−1.00676	−0.503380	−	0.864065i	$-0.667910\pi$
$389$	−19.8564	−1.00676	−0.503380	+	0.864065i	$0.667910\pi$
$390$	4.73205	0.239617
$391$	0	0
$392$	−11.1962	−0.565491
$393$	−15.1244	−0.762923
$394$	41.5692	2.09423
$395$	−2.92820	−0.147334
$396$	1.26795	0.0637168
$397$	−4.92820	−0.247339	−0.123670	−	0.992323i	$-0.539466\pi$
$397$	−4.92820	−0.247339	−0.123670	+	0.992323i	$0.539466\pi$
$398$	−33.4641	−1.67740
$399$	0	0
$400$	−5.00000	−0.250000
$401$	−4.05256	−0.202375	−0.101188	−	0.994867i	$-0.532264\pi$
$401$	−4.05256	−0.202375	−0.101188	+	0.994867i	$0.532264\pi$
$402$	−13.8564	−0.691095
$403$	13.4641	0.670695
$404$	10.3923	0.517036
$405$	1.00000	0.0496904
$406$	−2.78461	−0.138198
$407$	−5.32051	−0.263728
$408$	0	0
$409$	5.60770	0.277283	0.138641	−	0.990343i	$-0.455726\pi$
$409$	5.60770	0.277283	0.138641	+	0.990343i	$0.455726\pi$
$410$	8.19615	0.404779
$411$	7.85641	0.387528
$412$	17.8564	0.879722
$413$	−6.92820	−0.340915
$414$	6.00000	0.294884
$415$	0.928203	0.0455637
$416$	14.1962	0.696024
$417$	−12.3923	−0.606854
$418$	0	0
$419$	10.0526	0.491100	0.245550	−	0.969384i	$-0.421032\pi$
$419$	10.0526	0.491100	0.245550	+	0.969384i	$0.421032\pi$
$420$	−0.732051	−0.0357204
$421$	−22.7846	−1.11045	−0.555227	−	0.831699i	$-0.687369\pi$
$421$	−22.7846	−1.11045	−0.555227	+	0.831699i	$0.687369\pi$
$422$	25.8564	1.25867
$423$	3.46410	0.168430
$424$	4.39230	0.213309
$425$	0	0
$426$	−28.3923	−1.37561
$427$	−9.85641	−0.476985
$428$	0	0
$429$	−3.46410	−0.167248
$430$	10.7321	0.517545
$431$	−23.3205	−1.12331	−0.561655	−	0.827372i	$-0.689835\pi$
$431$	−23.3205	−1.12331	−0.561655	+	0.827372i	$0.689835\pi$
$432$	5.00000	0.240563
$433$	−20.5885	−0.989418	−0.494709	−	0.869059i	$-0.664725\pi$
$433$	−20.5885	−0.989418	−0.494709	+	0.869059i	$0.664725\pi$
$434$	−6.24871	−0.299948
$435$	−2.19615	−0.105297
$436$	−6.39230	−0.306136
$437$	0	0
$438$	−5.32051	−0.254224
$439$	−13.0718	−0.623883	−0.311941	−	0.950101i	$-0.600979\pi$
$439$	−13.0718	−0.623883	−0.311941	+	0.950101i	$0.600979\pi$
$440$	2.19615	0.104697
$441$	−6.46410	−0.307814
$442$	0	0
$443$	29.3205	1.39306	0.696530	−	0.717528i	$-0.254726\pi$
$443$	29.3205	1.39306	0.696530	+	0.717528i	$0.254726\pi$
$444$	4.19615	0.199141
$445$	−7.26795	−0.344534
$446$	17.0718	0.808373
$447$	−7.85641	−0.371595
$448$	0.732051	0.0345861
$449$	−11.6603	−0.550281	−0.275141	−	0.961404i	$-0.588724\pi$
$449$	−11.6603	−0.550281	−0.275141	+	0.961404i	$0.588724\pi$
$450$	−1.73205	−0.0816497
$451$	−6.00000	−0.282529
$452$	−5.07180	−0.238557
$453$	14.0000	0.657777
$454$	−18.0000	−0.844782
$455$	2.00000	0.0937614
$456$	0	0
$457$	11.4641	0.536268	0.268134	−	0.963382i	$-0.413593\pi$
$457$	11.4641	0.536268	0.268134	+	0.963382i	$0.413593\pi$
$458$	44.1051	2.06090
$459$	0	0
$460$	−3.46410	−0.161515
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	1.60770	0.0747967
$463$	9.51666	0.442277	0.221138	−	0.975242i	$-0.429023\pi$
$463$	9.51666	0.442277	0.221138	+	0.975242i	$0.429023\pi$
$464$	−10.9808	−0.509769
$465$	−4.92820	−0.228540
$466$	−34.3923	−1.59319
$467$	27.4641	1.27089	0.635444	−	0.772147i	$-0.280817\pi$
$467$	27.4641	1.27089	0.635444	+	0.772147i	$0.280817\pi$
$468$	2.73205	0.126289
$469$	−5.85641	−0.270424
$470$	−6.00000	−0.276759
$471$	14.3923	0.663162
$472$	−16.3923	−0.754517
$473$	−7.85641	−0.361238
$474$	−5.07180	−0.232955
$475$	0	0
$476$	0	0
$477$	2.53590	0.116111
$478$	34.9808	1.59998
$479$	−19.5167	−0.891739	−0.445869	−	0.895098i	$-0.647105\pi$
$479$	−19.5167	−0.891739	−0.445869	+	0.895098i	$0.647105\pi$
$480$	−5.19615	−0.237171
$481$	−11.4641	−0.522718
$482$	−29.3205	−1.33551
$483$	2.53590	0.115387
$484$	−9.39230	−0.426923
$485$	−4.19615	−0.190537
$486$	1.73205	0.0785674
$487$	11.6077	0.525995	0.262997	−	0.964797i	$-0.415289\pi$
$487$	11.6077	0.525995	0.262997	+	0.964797i	$0.415289\pi$
$488$	−23.3205	−1.05567
$489$	−12.7321	−0.575763
$490$	11.1962	0.505791
$491$	−22.0526	−0.995218	−0.497609	−	0.867401i	$-0.665789\pi$
$491$	−22.0526	−0.995218	−0.497609	+	0.867401i	$0.665789\pi$
$492$	4.73205	0.213337
$493$	0	0
$494$	0	0
$495$	1.26795	0.0569901
$496$	−24.6410	−1.10641
$497$	−12.0000	−0.538274
$498$	1.60770	0.0720425
$499$	17.4641	0.781801	0.390900	−	0.920433i	$-0.372164\pi$
$499$	17.4641	0.781801	0.390900	+	0.920433i	$0.372164\pi$
$500$	1.00000	0.0447214
$501$	−3.46410	−0.154765
$502$	17.4115	0.777115
$503$	−36.9282	−1.64655	−0.823274	−	0.567645i	$-0.807855\pi$
$503$	−36.9282	−1.64655	−0.823274	+	0.567645i	$0.807855\pi$
$504$	1.26795	0.0564789
$505$	10.3923	0.462451
$506$	7.60770	0.338203
$507$	5.53590	0.245858
$508$	4.00000	0.177471
$509$	−28.0526	−1.24341	−0.621704	−	0.783252i	$-0.713559\pi$
$509$	−28.0526	−1.24341	−0.621704	+	0.783252i	$0.713559\pi$
$510$	0	0
$511$	−2.24871	−0.0994771
$512$	−8.66025	−0.382733
$513$	0	0
$514$	−41.5692	−1.83354
$515$	17.8564	0.786847
$516$	6.19615	0.272770
$517$	4.39230	0.193173
$518$	5.32051	0.233770
$519$	−6.92820	−0.304114
$520$	4.73205	0.207514
$521$	−40.7321	−1.78450	−0.892252	−	0.451538i	$-0.850875\pi$
$521$	−40.7321	−1.78450	−0.892252	+	0.451538i	$0.850875\pi$
$522$	−3.80385	−0.166490
$523$	−43.3205	−1.89427	−0.947137	−	0.320830i	$-0.896038\pi$
$523$	−43.3205	−1.89427	−0.947137	+	0.320830i	$0.896038\pi$
$524$	15.1244	0.660711
$525$	−0.732051	−0.0319493
$526$	−10.3923	−0.453126
$527$	0	0
$528$	6.33975	0.275902
$529$	−11.0000	−0.478261
$530$	−4.39230	−0.190790
$531$	−9.46410	−0.410707
$532$	0	0
$533$	−12.9282	−0.559983
$534$	−12.5885	−0.544756
$535$	0	0
$536$	−13.8564	−0.598506
$537$	−11.3205	−0.488516
$538$	−52.9808	−2.28416
$539$	−8.19615	−0.353033
$540$	−1.00000	−0.0430331
$541$	−13.7128	−0.589560	−0.294780	−	0.955565i	$-0.595246\pi$
$541$	−13.7128	−0.589560	−0.294780	+	0.955565i	$0.595246\pi$
$542$	35.3205	1.51715
$543$	18.3923	0.789289
$544$	0	0
$545$	−6.39230	−0.273816
$546$	3.46410	0.148250
$547$	−8.67949	−0.371108	−0.185554	−	0.982634i	$-0.559408\pi$
$547$	−8.67949	−0.371108	−0.185554	+	0.982634i	$0.559408\pi$
$548$	−7.85641	−0.335609
$549$	−13.4641	−0.574634
$550$	−2.19615	−0.0936443
$551$	0	0
$552$	6.00000	0.255377
$553$	−2.14359	−0.0911549
$554$	−3.46410	−0.147176
$555$	4.19615	0.178117
$556$	12.3923	0.525551
$557$	−12.9282	−0.547786	−0.273893	−	0.961760i	$-0.588311\pi$
$557$	−12.9282	−0.547786	−0.273893	+	0.961760i	$0.588311\pi$
$558$	−8.53590	−0.361353
$559$	−16.9282	−0.715987
$560$	−3.66025	−0.154674
$561$	0	0
$562$	8.19615	0.345734
$563$	20.5359	0.865485	0.432742	−	0.901518i	$-0.357546\pi$
$563$	20.5359	0.865485	0.432742	+	0.901518i	$0.357546\pi$
$564$	−3.46410	−0.145865
$565$	−5.07180	−0.213372
$566$	46.7321	1.96429
$567$	0.732051	0.0307432
$568$	−28.3923	−1.19131
$569$	16.0526	0.672958	0.336479	−	0.941691i	$-0.390764\pi$
$569$	16.0526	0.672958	0.336479	+	0.941691i	$0.390764\pi$
$570$	0	0
$571$	14.2487	0.596290	0.298145	−	0.954521i	$-0.403632\pi$
$571$	14.2487	0.596290	0.298145	+	0.954521i	$0.403632\pi$
$572$	3.46410	0.144841
$573$	−17.6603	−0.737768
$574$	6.00000	0.250435
$575$	−3.46410	−0.144463
$576$	1.00000	0.0416667
$577$	−47.1769	−1.96400	−0.982000	−	0.188879i	$-0.939515\pi$
$577$	−47.1769	−1.96400	−0.982000	+	0.188879i	$0.939515\pi$
$578$	29.4449	1.22474
$579$	−7.12436	−0.296078
$580$	2.19615	0.0911903
$581$	0.679492	0.0281901
$582$	−7.26795	−0.301266
$583$	3.21539	0.133168
$584$	−5.32051	−0.220164
$585$	2.73205	0.112956
$586$	−48.0000	−1.98286
$587$	3.46410	0.142979	0.0714894	−	0.997441i	$-0.477225\pi$
$587$	3.46410	0.142979	0.0714894	+	0.997441i	$0.477225\pi$
$588$	6.46410	0.266575
$589$	0	0
$590$	16.3923	0.674861
$591$	24.0000	0.987228
$592$	20.9808	0.862304
$593$	2.78461	0.114350	0.0571751	−	0.998364i	$-0.481791\pi$
$593$	2.78461	0.114350	0.0571751	+	0.998364i	$0.481791\pi$
$594$	2.19615	0.0901092
$595$	0	0
$596$	7.85641	0.321811
$597$	−19.3205	−0.790736
$598$	16.3923	0.670331
$599$	−13.8564	−0.566157	−0.283079	−	0.959097i	$-0.591356\pi$
$599$	−13.8564	−0.566157	−0.283079	+	0.959097i	$0.591356\pi$
$600$	−1.73205	−0.0707107
$601$	−15.1769	−0.619079	−0.309540	−	0.950887i	$-0.600175\pi$
$601$	−15.1769	−0.619079	−0.309540	+	0.950887i	$0.600175\pi$
$602$	7.85641	0.320203
$603$	−8.00000	−0.325785
$604$	−14.0000	−0.569652
$605$	−9.39230	−0.381851
$606$	18.0000	0.731200
$607$	32.3923	1.31476	0.657382	−	0.753558i	$-0.271664\pi$
$607$	32.3923	1.31476	0.657382	+	0.753558i	$0.271664\pi$
$608$	0	0
$609$	−1.60770	−0.0651471
$610$	23.3205	0.944220
$611$	9.46410	0.382877
$612$	0	0
$613$	21.6077	0.872727	0.436363	−	0.899771i	$-0.356266\pi$
$613$	21.6077	0.872727	0.436363	+	0.899771i	$0.356266\pi$
$614$	−20.1051	−0.811377
$615$	4.73205	0.190815
$616$	1.60770	0.0647759
$617$	−27.7128	−1.11568	−0.557838	−	0.829950i	$-0.688369\pi$
$617$	−27.7128	−1.11568	−0.557838	+	0.829950i	$0.688369\pi$
$618$	30.9282	1.24411
$619$	19.3205	0.776557	0.388278	−	0.921542i	$-0.373070\pi$
$619$	19.3205	0.776557	0.388278	+	0.921542i	$0.373070\pi$
$620$	4.92820	0.197921
$621$	3.46410	0.139010
$622$	45.8038	1.83657
$623$	−5.32051	−0.213162
$624$	13.6603	0.546848
$625$	1.00000	0.0400000
$626$	24.9282	0.996331
$627$	0	0
$628$	−14.3923	−0.574315
$629$	0	0
$630$	−1.26795	−0.0505163
$631$	−21.0718	−0.838855	−0.419427	−	0.907789i	$-0.637769\pi$
$631$	−21.0718	−0.838855	−0.419427	+	0.907789i	$0.637769\pi$
$632$	−5.07180	−0.201745
$633$	14.9282	0.593343
$634$	40.3923	1.60418
$635$	4.00000	0.158735
$636$	−2.53590	−0.100555
$637$	−17.6603	−0.699725
$638$	−4.82309	−0.190948
$639$	−16.3923	−0.648470
$640$	−12.1244	−0.479257
$641$	−17.4115	−0.687715	−0.343857	−	0.939022i	$-0.611734\pi$
$641$	−17.4115	−0.687715	−0.343857	+	0.939022i	$0.611734\pi$
$642$	0	0
$643$	−1.80385	−0.0711368	−0.0355684	−	0.999367i	$-0.511324\pi$
$643$	−1.80385	−0.0711368	−0.0355684	+	0.999367i	$0.511324\pi$
$644$	−2.53590	−0.0999284
$645$	6.19615	0.243973
$646$	0	0
$647$	−31.8564	−1.25240	−0.626202	−	0.779661i	$-0.715392\pi$
$647$	−31.8564	−1.25240	−0.626202	+	0.779661i	$0.715392\pi$
$648$	1.73205	0.0680414
$649$	−12.0000	−0.471041
$650$	−4.73205	−0.185606
$651$	−3.60770	−0.141397
$652$	12.7321	0.498626
$653$	30.9282	1.21031	0.605157	−	0.796106i	$-0.293110\pi$
$653$	30.9282	1.21031	0.605157	+	0.796106i	$0.293110\pi$
$654$	−11.0718	−0.432942
$655$	15.1244	0.590957
$656$	23.6603	0.923778
$657$	−3.07180	−0.119842
$658$	−4.39230	−0.171230
$659$	−18.9282	−0.737338	−0.368669	−	0.929561i	$-0.620186\pi$
$659$	−18.9282	−0.737338	−0.368669	+	0.929561i	$0.620186\pi$
$660$	−1.26795	−0.0493549
$661$	23.1769	0.901477	0.450739	−	0.892656i	$-0.351161\pi$
$661$	23.1769	0.901477	0.450739	+	0.892656i	$0.351161\pi$
$662$	51.4641	2.00021
$663$	0	0
$664$	1.60770	0.0623907
$665$	0	0
$666$	7.26795	0.281627
$667$	−7.60770	−0.294571
$668$	3.46410	0.134030
$669$	9.85641	0.381071
$670$	13.8564	0.535320
$671$	−17.0718	−0.659049
$672$	−3.80385	−0.146737
$673$	7.12436	0.274624	0.137312	−	0.990528i	$-0.456154\pi$
$673$	7.12436	0.274624	0.137312	+	0.990528i	$0.456154\pi$
$674$	−33.1244	−1.27590
$675$	−1.00000	−0.0384900
$676$	−5.53590	−0.212919
$677$	−35.3205	−1.35748	−0.678739	−	0.734380i	$-0.737473\pi$
$677$	−35.3205	−1.35748	−0.678739	+	0.734380i	$0.737473\pi$
$678$	−8.78461	−0.337371
$679$	−3.07180	−0.117885
$680$	0	0
$681$	−10.3923	−0.398234
$682$	−10.8231	−0.414437
$683$	18.9282	0.724268	0.362134	−	0.932126i	$-0.382048\pi$
$683$	18.9282	0.724268	0.362134	+	0.932126i	$0.382048\pi$
$684$	0	0
$685$	−7.85641	−0.300178
$686$	17.0718	0.651804
$687$	25.4641	0.971516
$688$	30.9808	1.18113
$689$	6.92820	0.263944
$690$	−6.00000	−0.228416
$691$	−8.39230	−0.319258	−0.159629	−	0.987177i	$-0.551030\pi$
$691$	−8.39230	−0.319258	−0.159629	+	0.987177i	$0.551030\pi$
$692$	6.92820	0.263371
$693$	0.928203	0.0352595
$694$	−22.3923	−0.850000
$695$	12.3923	0.470067
$696$	−3.80385	−0.144184
$697$	0	0
$698$	38.1051	1.44230
$699$	−19.8564	−0.751038
$700$	0.732051	0.0276689
$701$	21.7128	0.820082	0.410041	−	0.912067i	$-0.365514\pi$
$701$	21.7128	0.820082	0.410041	+	0.912067i	$0.365514\pi$
$702$	4.73205	0.178600
$703$	0	0
$704$	1.26795	0.0477876
$705$	−3.46410	−0.130466
$706$	−46.3923	−1.74600
$707$	7.60770	0.286117
$708$	9.46410	0.355683
$709$	33.1769	1.24599	0.622993	−	0.782228i	$-0.285917\pi$
$709$	33.1769	1.24599	0.622993	+	0.782228i	$0.285917\pi$
$710$	28.3923	1.06554
$711$	−2.92820	−0.109816
$712$	−12.5885	−0.471772
$713$	−17.0718	−0.639344
$714$	0	0
$715$	3.46410	0.129550
$716$	11.3205	0.423067
$717$	20.1962	0.754239
$718$	−30.5885	−1.14155
$719$	5.66025	0.211092	0.105546	−	0.994414i	$-0.466341\pi$
$719$	5.66025	0.211092	0.105546	+	0.994414i	$0.466341\pi$
$720$	−5.00000	−0.186339
$721$	13.0718	0.486819
$722$	0	0
$723$	−16.9282	−0.629567
$724$	−18.3923	−0.683545
$725$	2.19615	0.0815631
$726$	−16.2679	−0.603760
$727$	8.33975	0.309304	0.154652	−	0.987969i	$-0.450574\pi$
$727$	8.33975	0.309304	0.154652	+	0.987969i	$0.450574\pi$
$728$	3.46410	0.128388
$729$	1.00000	0.0370370
$730$	5.32051	0.196921
$731$	0	0
$732$	13.4641	0.497648
$733$	22.7846	0.841569	0.420784	−	0.907161i	$-0.361755\pi$
$733$	22.7846	0.841569	0.420784	+	0.907161i	$0.361755\pi$
$734$	−10.0526	−0.371047
$735$	6.46410	0.238432
$736$	−18.0000	−0.663489
$737$	−10.1436	−0.373644
$738$	8.19615	0.301705
$739$	33.8564	1.24543	0.622714	−	0.782450i	$-0.286030\pi$
$739$	33.8564	1.24543	0.622714	+	0.782450i	$0.286030\pi$
$740$	−4.19615	−0.154254
$741$	0	0
$742$	−3.21539	−0.118041
$743$	44.7846	1.64299	0.821494	−	0.570217i	$-0.193141\pi$
$743$	44.7846	1.64299	0.821494	+	0.570217i	$0.193141\pi$
$744$	−8.53590	−0.312941
$745$	7.85641	0.287836
$746$	7.26795	0.266099
$747$	0.928203	0.0339612
$748$	0	0
$749$	0	0
$750$	1.73205	0.0632456
$751$	−26.0000	−0.948753	−0.474377	−	0.880322i	$-0.657327\pi$
$751$	−26.0000	−0.948753	−0.474377	+	0.880322i	$0.657327\pi$
$752$	−17.3205	−0.631614
$753$	10.0526	0.366336
$754$	−10.3923	−0.378465
$755$	−14.0000	−0.509512
$756$	−0.732051	−0.0266244
$757$	−16.2487	−0.590569	−0.295285	−	0.955409i	$-0.595415\pi$
$757$	−16.2487	−0.590569	−0.295285	+	0.955409i	$0.595415\pi$
$758$	12.2487	0.444893
$759$	4.39230	0.159431
$760$	0	0
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	6.92820	0.250982
$763$	−4.67949	−0.169409
$764$	17.6603	0.638926
$765$	0	0
$766$	−53.5692	−1.93553
$767$	−25.8564	−0.933621
$768$	−19.0000	−0.685603
$769$	48.6410	1.75404	0.877020	−	0.480454i	$-0.159528\pi$
$769$	48.6410	1.75404	0.877020	+	0.480454i	$0.159528\pi$
$770$	−1.60770	−0.0579373
$771$	−24.0000	−0.864339
$772$	7.12436	0.256411
$773$	−37.1769	−1.33716	−0.668580	−	0.743640i	$-0.733098\pi$
$773$	−37.1769	−1.33716	−0.668580	+	0.743640i	$0.733098\pi$
$774$	10.7321	0.385756
$775$	4.92820	0.177026
$776$	−7.26795	−0.260904
$777$	3.07180	0.110200
$778$	34.3923	1.23302
$779$	0	0
$780$	−2.73205	−0.0978231
$781$	−20.7846	−0.743732
$782$	0	0
$783$	−2.19615	−0.0784841
$784$	32.3205	1.15430
$785$	−14.3923	−0.513683
$786$	26.1962	0.934386
$787$	−43.3205	−1.54421	−0.772105	−	0.635495i	$-0.780796\pi$
$787$	−43.3205	−1.54421	−0.772105	+	0.635495i	$0.780796\pi$
$788$	−24.0000	−0.854965
$789$	−6.00000	−0.213606
$790$	5.07180	0.180446
$791$	−3.71281	−0.132012
$792$	2.19615	0.0780369
$793$	−36.7846	−1.30626
$794$	8.53590	0.302928
$795$	−2.53590	−0.0899390
$796$	19.3205	0.684797
$797$	−3.21539	−0.113895	−0.0569475	−	0.998377i	$-0.518137\pi$
$797$	−3.21539	−0.113895	−0.0569475	+	0.998377i	$0.518137\pi$
$798$	0	0
$799$	0	0
$800$	5.19615	0.183712
$801$	−7.26795	−0.256800
$802$	7.01924	0.247858
$803$	−3.89488	−0.137447
$804$	8.00000	0.282138
$805$	−2.53590	−0.0893787
$806$	−23.3205	−0.821430
$807$	−30.5885	−1.07676
$808$	18.0000	0.633238
$809$	−26.7846	−0.941697	−0.470848	−	0.882214i	$-0.656052\pi$
$809$	−26.7846	−0.941697	−0.470848	+	0.882214i	$0.656052\pi$
$810$	−1.73205	−0.0608581
$811$	45.5692	1.60015	0.800076	−	0.599899i	$-0.204793\pi$
$811$	45.5692	1.60015	0.800076	+	0.599899i	$0.204793\pi$
$812$	1.60770	0.0564190
$813$	20.3923	0.715189
$814$	9.21539	0.322999
$815$	12.7321	0.445984
$816$	0	0
$817$	0	0
$818$	−9.71281	−0.339601
$819$	2.00000	0.0698857
$820$	−4.73205	−0.165250
$821$	−39.4641	−1.37731	−0.688653	−	0.725091i	$-0.741798\pi$
$821$	−39.4641	−1.37731	−0.688653	+	0.725091i	$0.741798\pi$
$822$	−13.6077	−0.474623
$823$	−38.9808	−1.35878	−0.679392	−	0.733776i	$-0.737756\pi$
$823$	−38.9808	−1.35878	−0.679392	+	0.733776i	$0.737756\pi$
$824$	30.9282	1.07744
$825$	−1.26795	−0.0441443
$826$	12.0000	0.417533
$827$	−29.3205	−1.01957	−0.509787	−	0.860301i	$-0.670276\pi$
$827$	−29.3205	−1.01957	−0.509787	+	0.860301i	$0.670276\pi$
$828$	−3.46410	−0.120386
$829$	42.1051	1.46237	0.731186	−	0.682179i	$-0.238967\pi$
$829$	42.1051	1.46237	0.731186	+	0.682179i	$0.238967\pi$
$830$	−1.60770	−0.0558039
$831$	−2.00000	−0.0693792
$832$	2.73205	0.0947168
$833$	0	0
$834$	21.4641	0.743241
$835$	3.46410	0.119880
$836$	0	0
$837$	−4.92820	−0.170344
$838$	−17.4115	−0.601472
$839$	40.3923	1.39450	0.697249	−	0.716829i	$-0.254407\pi$
$839$	40.3923	1.39450	0.697249	+	0.716829i	$0.254407\pi$
$840$	−1.26795	−0.0437484
$841$	−24.1769	−0.833687
$842$	39.4641	1.36002
$843$	4.73205	0.162980
$844$	−14.9282	−0.513850
$845$	−5.53590	−0.190441
$846$	−6.00000	−0.206284
$847$	−6.87564	−0.236250
$848$	−12.6795	−0.435416
$849$	26.9808	0.925977
$850$	0	0
$851$	14.5359	0.498284
$852$	16.3923	0.561591
$853$	−35.1769	−1.20443	−0.602217	−	0.798332i	$-0.705716\pi$
$853$	−35.1769	−1.20443	−0.602217	+	0.798332i	$0.705716\pi$
$854$	17.0718	0.584185
$855$	0	0
$856$	0	0
$857$	−6.24871	−0.213452	−0.106726	−	0.994288i	$-0.534037\pi$
$857$	−6.24871	−0.213452	−0.106726	+	0.994288i	$0.534037\pi$
$858$	6.00000	0.204837
$859$	32.0000	1.09183	0.545913	−	0.837842i	$-0.316183\pi$
$859$	32.0000	1.09183	0.545913	+	0.837842i	$0.316183\pi$
$860$	−6.19615	−0.211287
$861$	3.46410	0.118056
$862$	40.3923	1.37577
$863$	12.0000	0.408485	0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000	0.408485	0.204242	+	0.978920i	$0.434527\pi$
$864$	−5.19615	−0.176777
$865$	6.92820	0.235566
$866$	35.6603	1.21178
$867$	17.0000	0.577350
$868$	3.60770	0.122453
$869$	−3.71281	−0.125949
$870$	3.80385	0.128963
$871$	−21.8564	−0.740576
$872$	−11.0718	−0.374938
$873$	−4.19615	−0.142018
$874$	0	0
$875$	0.732051	0.0247478
$876$	3.07180	0.103786
$877$	−28.8756	−0.975061	−0.487531	−	0.873106i	$-0.662102\pi$
$877$	−28.8756	−0.975061	−0.487531	+	0.873106i	$0.662102\pi$
$878$	22.6410	0.764097
$879$	−27.7128	−0.934730
$880$	−6.33975	−0.213713
$881$	15.4641	0.520999	0.260499	−	0.965474i	$-0.416113\pi$
$881$	15.4641	0.520999	0.260499	+	0.965474i	$0.416113\pi$
$882$	11.1962	0.376994
$883$	−14.9808	−0.504143	−0.252071	−	0.967709i	$-0.581112\pi$
$883$	−14.9808	−0.504143	−0.252071	+	0.967709i	$0.581112\pi$
$884$	0	0
$885$	9.46410	0.318132
$886$	−50.7846	−1.70614
$887$	24.0000	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$888$	7.26795	0.243896
$889$	2.92820	0.0982088
$890$	12.5885	0.421966
$891$	1.26795	0.0424779
$892$	−9.85641	−0.330017
$893$	0	0
$894$	13.6077	0.455109
$895$	11.3205	0.378403
$896$	−8.87564	−0.296514
$897$	9.46410	0.315997
$898$	20.1962	0.673954
$899$	10.8231	0.360970
$900$	1.00000	0.0333333
$901$	0	0
$902$	10.3923	0.346026
$903$	4.53590	0.150945
$904$	−8.78461	−0.292172
$905$	−18.3923	−0.611381
$906$	−24.2487	−0.805609
$907$	11.6077	0.385427	0.192714	−	0.981255i	$-0.438271\pi$
$907$	11.6077	0.385427	0.192714	+	0.981255i	$0.438271\pi$
$908$	10.3923	0.344881
$909$	10.3923	0.344691
$910$	−3.46410	−0.114834
$911$	41.0718	1.36077	0.680385	−	0.732855i	$-0.261813\pi$
$911$	41.0718	1.36077	0.680385	+	0.732855i	$0.261813\pi$
$912$	0	0
$913$	1.17691	0.0389502
$914$	−19.8564	−0.656792
$915$	13.4641	0.445109
$916$	−25.4641	−0.841358
$917$	11.0718	0.365623
$918$	0	0
$919$	−59.4256	−1.96027	−0.980135	−	0.198330i	$-0.936448\pi$
$919$	−59.4256	−1.96027	−0.980135	+	0.198330i	$0.936448\pi$
$920$	−6.00000	−0.197814
$921$	−11.6077	−0.382487
$922$	−10.3923	−0.342252
$923$	−44.7846	−1.47410
$924$	−0.928203	−0.0305356
$925$	−4.19615	−0.137969
$926$	−16.4833	−0.541676
$927$	17.8564	0.586481
$928$	11.4115	0.374602
$929$	−22.3923	−0.734668	−0.367334	−	0.930089i	$-0.619729\pi$
$929$	−22.3923	−0.734668	−0.367334	+	0.930089i	$0.619729\pi$
$930$	8.53590	0.279903
$931$	0	0
$932$	19.8564	0.650418
$933$	26.4449	0.865766
$934$	−47.5692	−1.55651
$935$	0	0
$936$	4.73205	0.154672
$937$	32.2487	1.05352	0.526760	−	0.850014i	$-0.323407\pi$
$937$	32.2487	1.05352	0.526760	+	0.850014i	$0.323407\pi$
$938$	10.1436	0.331200
$939$	14.3923	0.469675
$940$	3.46410	0.112987
$941$	30.5885	0.997155	0.498578	−	0.866845i	$-0.333856\pi$
$941$	30.5885	0.997155	0.498578	+	0.866845i	$0.333856\pi$
$942$	−24.9282	−0.812205
$943$	16.3923	0.533807
$944$	47.3205	1.54015
$945$	−0.732051	−0.0238136
$946$	13.6077	0.442424
$947$	55.8564	1.81509	0.907545	−	0.419956i	$-0.137954\pi$
$947$	55.8564	1.81509	0.907545	+	0.419956i	$0.137954\pi$
$948$	2.92820	0.0951036
$949$	−8.39230	−0.272426
$950$	0	0
$951$	23.3205	0.756219
$952$	0	0
$953$	−10.1436	−0.328583	−0.164292	−	0.986412i	$-0.552534\pi$
$953$	−10.1436	−0.328583	−0.164292	+	0.986412i	$0.552534\pi$
$954$	−4.39230	−0.142206
$955$	17.6603	0.571472
$956$	−20.1962	−0.653190
$957$	−2.78461	−0.0900136
$958$	33.8038	1.09215
$959$	−5.75129	−0.185719
$960$	−1.00000	−0.0322749
$961$	−6.71281	−0.216542
$962$	19.8564	0.640196
$963$	0	0
$964$	16.9282	0.545221
$965$	7.12436	0.229341
$966$	−4.39230	−0.141320
$967$	29.1244	0.936576	0.468288	−	0.883576i	$-0.344871\pi$
$967$	29.1244	0.936576	0.468288	+	0.883576i	$0.344871\pi$
$968$	−16.2679	−0.522872
$969$	0	0
$970$	7.26795	0.233360
$971$	−27.7128	−0.889346	−0.444673	−	0.895693i	$-0.646680\pi$
$971$	−27.7128	−0.889346	−0.444673	+	0.895693i	$0.646680\pi$
$972$	−1.00000	−0.0320750
$973$	9.07180	0.290828
$974$	−20.1051	−0.644210
$975$	−2.73205	−0.0874957
$976$	67.3205	2.15488
$977$	−51.0333	−1.63270	−0.816350	−	0.577557i	$-0.804006\pi$
$977$	−51.0333	−1.63270	−0.816350	+	0.577557i	$0.804006\pi$
$978$	22.0526	0.705163
$979$	−9.21539	−0.294525
$980$	−6.46410	−0.206488
$981$	−6.39230	−0.204091
$982$	38.1962	1.21889
$983$	6.67949	0.213043	0.106521	−	0.994310i	$-0.466029\pi$
$983$	6.67949	0.213043	0.106521	+	0.994310i	$0.466029\pi$
$984$	8.19615	0.261284
$985$	−24.0000	−0.764704
$986$	0	0
$987$	−2.53590	−0.0807185
$988$	0	0
$989$	21.4641	0.682519
$990$	−2.19615	−0.0697983
$991$	−26.9282	−0.855403	−0.427701	−	0.903920i	$-0.640676\pi$
$991$	−26.9282	−0.855403	−0.427701	+	0.903920i	$0.640676\pi$
$992$	25.6077	0.813045
$993$	29.7128	0.942908
$994$	20.7846	0.659248
$995$	19.3205	0.612501
$996$	−0.928203	−0.0294112
$997$	−38.3923	−1.21590	−0.607948	−	0.793977i	$-0.708007\pi$
$997$	−38.3923	−1.21590	−0.607948	+	0.793977i	$0.708007\pi$
$998$	−30.2487	−0.957506
$999$	4.19615	0.132760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5415.2.a.r.1.1		2
19.18	odd	2		285.2.a.e.1.2	✓	2
57.56	even	2		855.2.a.f.1.1		2
76.75	even	2		4560.2.a.bh.1.1		2
95.18	even	4		1425.2.c.k.799.2		4
95.37	even	4		1425.2.c.k.799.3		4
95.94	odd	2		1425.2.a.o.1.1		2
285.284	even	2		4275.2.a.t.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.a.e.1.2	✓	2	19.18	odd	2
855.2.a.f.1.1		2	57.56	even	2
1425.2.a.o.1.1		2	95.94	odd	2
1425.2.c.k.799.2		4	95.18	even	4
1425.2.c.k.799.3		4	95.37	even	4
4275.2.a.t.1.2		2	285.284	even	2
4560.2.a.bh.1.1		2	76.75	even	2
5415.2.a.r.1.1		2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5415 = 3 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5415.a (trivial)

\(f(q)\)	\(=\)	\(q-1.73205 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.73205 q^{6} +0.732051 q^{7} +1.73205 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.73205 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.73205 q^{6} +0.732051 q^{7} +1.73205 q^{8} +1.00000 q^{9} -1.73205 q^{10} +1.26795 q^{11} -1.00000 q^{12} +2.73205 q^{13} -1.26795 q^{14} -1.00000 q^{15} -5.00000 q^{16} -1.73205 q^{18} +1.00000 q^{20} -0.732051 q^{21} -2.19615 q^{22} -3.46410 q^{23} -1.73205 q^{24} +1.00000 q^{25} -4.73205 q^{26} -1.00000 q^{27} +0.732051 q^{28} +2.19615 q^{29} +1.73205 q^{30} +4.92820 q^{31} +5.19615 q^{32} -1.26795 q^{33} +0.732051 q^{35} +1.00000 q^{36} -4.19615 q^{37} -2.73205 q^{39} +1.73205 q^{40} -4.73205 q^{41} +1.26795 q^{42} -6.19615 q^{43} +1.26795 q^{44} +1.00000 q^{45} +6.00000 q^{46} +3.46410 q^{47} +5.00000 q^{48} -6.46410 q^{49} -1.73205 q^{50} +2.73205 q^{52} +2.53590 q^{53} +1.73205 q^{54} +1.26795 q^{55} +1.26795 q^{56} -3.80385 q^{58} -9.46410 q^{59} -1.00000 q^{60} -13.4641 q^{61} -8.53590 q^{62} +0.732051 q^{63} +1.00000 q^{64} +2.73205 q^{65} +2.19615 q^{66} -8.00000 q^{67} +3.46410 q^{69} -1.26795 q^{70} -16.3923 q^{71} +1.73205 q^{72} -3.07180 q^{73} +7.26795 q^{74} -1.00000 q^{75} +0.928203 q^{77} +4.73205 q^{78} -2.92820 q^{79} -5.00000 q^{80} +1.00000 q^{81} +8.19615 q^{82} +0.928203 q^{83} -0.732051 q^{84} +10.7321 q^{86} -2.19615 q^{87} +2.19615 q^{88} -7.26795 q^{89} -1.73205 q^{90} +2.00000 q^{91} -3.46410 q^{92} -4.92820 q^{93} -6.00000 q^{94} -5.19615 q^{96} -4.19615 q^{97} +11.1962 q^{98} +1.26795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^7 + 2 * q^9	\( 2 q - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{7} + 2 q^{9} + 6 q^{11} - 2 q^{12} + 2 q^{13} - 6 q^{14} - 2 q^{15} - 10 q^{16} + 2 q^{20} + 2 q^{21} + 6 q^{22} + 2 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} - 6 q^{29} - 4 q^{31} - 6 q^{33} - 2 q^{35} + 2 q^{36} + 2 q^{37} - 2 q^{39} - 6 q^{41} + 6 q^{42} - 2 q^{43} + 6 q^{44} + 2 q^{45} + 12 q^{46} + 10 q^{48} - 6 q^{49} + 2 q^{52} + 12 q^{53} + 6 q^{55} + 6 q^{56} - 18 q^{58} - 12 q^{59} - 2 q^{60} - 20 q^{61} - 24 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{65} - 6 q^{66} - 16 q^{67} - 6 q^{70} - 12 q^{71} - 20 q^{73} + 18 q^{74} - 2 q^{75} - 12 q^{77} + 6 q^{78} + 8 q^{79} - 10 q^{80} + 2 q^{81} + 6 q^{82} - 12 q^{83} + 2 q^{84} + 18 q^{86} + 6 q^{87} - 6 q^{88} - 18 q^{89} + 4 q^{91} + 4 q^{93} - 12 q^{94} + 2 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^7 + 2 * q^9 + 6 * q^11 - 2 * q^12 + 2 * q^13 - 6 * q^14 - 2 * q^15 - 10 * q^16 + 2 * q^20 + 2 * q^21 + 6 * q^22 + 2 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 - 6 * q^29 - 4 * q^31 - 6 * q^33 - 2 * q^35 + 2 * q^36 + 2 * q^37 - 2 * q^39 - 6 * q^41 + 6 * q^42 - 2 * q^43 + 6 * q^44 + 2 * q^45 + 12 * q^46 + 10 * q^48 - 6 * q^49 + 2 * q^52 + 12 * q^53 + 6 * q^55 + 6 * q^56 - 18 * q^58 - 12 * q^59 - 2 * q^60 - 20 * q^61 - 24 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^65 - 6 * q^66 - 16 * q^67 - 6 * q^70 - 12 * q^71 - 20 * q^73 + 18 * q^74 - 2 * q^75 - 12 * q^77 + 6 * q^78 + 8 * q^79 - 10 * q^80 + 2 * q^81 + 6 * q^82 - 12 * q^83 + 2 * q^84 + 18 * q^86 + 6 * q^87 - 6 * q^88 - 18 * q^89 + 4 * q^91 + 4 * q^93 - 12 * q^94 + 2 * q^97 + 12 * q^98 + 6 * q^99

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