LMFDB - Embedded newform 2415.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2415,2,Mod(1,2415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2415, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2415 = 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2415.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:	$19.2838720881$
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:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	2415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73205 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.73205 q^{6} -1.00000 q^{7} -1.73205 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.73205 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.73205 q^{6} -1.00000 q^{7} -1.73205 q^{8} +1.00000 q^{9} -1.73205 q^{10} +2.73205 q^{11} +1.00000 q^{12} -4.73205 q^{13} -1.73205 q^{14} -1.00000 q^{15} -5.00000 q^{16} -7.46410 q^{17} +1.73205 q^{18} -3.46410 q^{19} -1.00000 q^{20} -1.00000 q^{21} +4.73205 q^{22} +1.00000 q^{23} -1.73205 q^{24} +1.00000 q^{25} -8.19615 q^{26} +1.00000 q^{27} -1.00000 q^{28} -1.73205 q^{30} -1.26795 q^{31} -5.19615 q^{32} +2.73205 q^{33} -12.9282 q^{34} +1.00000 q^{35} +1.00000 q^{36} -1.26795 q^{37} -6.00000 q^{38} -4.73205 q^{39} +1.73205 q^{40} -3.46410 q^{41} -1.73205 q^{42} +6.92820 q^{43} +2.73205 q^{44} -1.00000 q^{45} +1.73205 q^{46} -8.39230 q^{47} -5.00000 q^{48} +1.00000 q^{49} +1.73205 q^{50} -7.46410 q^{51} -4.73205 q^{52} +0.732051 q^{53} +1.73205 q^{54} -2.73205 q^{55} +1.73205 q^{56} -3.46410 q^{57} +2.19615 q^{59} -1.00000 q^{60} +4.00000 q^{61} -2.19615 q^{62} -1.00000 q^{63} +1.00000 q^{64} +4.73205 q^{65} +4.73205 q^{66} -14.9282 q^{67} -7.46410 q^{68} +1.00000 q^{69} +1.73205 q^{70} -6.00000 q^{71} -1.73205 q^{72} +3.66025 q^{73} -2.19615 q^{74} +1.00000 q^{75} -3.46410 q^{76} -2.73205 q^{77} -8.19615 q^{78} +10.1962 q^{79} +5.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -2.00000 q^{83} -1.00000 q^{84} +7.46410 q^{85} +12.0000 q^{86} -4.73205 q^{88} +6.53590 q^{89} -1.73205 q^{90} +4.73205 q^{91} +1.00000 q^{92} -1.26795 q^{93} -14.5359 q^{94} +3.46410 q^{95} -5.19615 q^{96} +2.92820 q^{97} +1.73205 q^{98} +2.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 2 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{15} - 10 q^{16} - 8 q^{17} - 2 q^{20} - 2 q^{21} + 6 q^{22} + 2 q^{23} + 2 q^{25} - 6 q^{26} + 2 q^{27} - 2 q^{28} - 6 q^{31} + 2 q^{33} - 12 q^{34} + 2 q^{35} + 2 q^{36} - 6 q^{37} - 12 q^{38} - 6 q^{39} + 2 q^{44} - 2 q^{45} + 4 q^{47} - 10 q^{48} + 2 q^{49} - 8 q^{51} - 6 q^{52} - 2 q^{53} - 2 q^{55} - 6 q^{59} - 2 q^{60} + 8 q^{61} + 6 q^{62} - 2 q^{63} + 2 q^{64} + 6 q^{65} + 6 q^{66} - 16 q^{67} - 8 q^{68} + 2 q^{69} - 12 q^{71} - 10 q^{73} + 6 q^{74} + 2 q^{75} - 2 q^{77} - 6 q^{78} + 10 q^{79} + 10 q^{80} + 2 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 8 q^{85} + 24 q^{86} - 6 q^{88} + 20 q^{89} + 6 q^{91} + 2 q^{92} - 6 q^{93} - 36 q^{94} - 8 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^7 + 2 * q^9 + 2 * q^11 + 2 * q^12 - 6 * q^13 - 2 * q^15 - 10 * q^16 - 8 * q^17 - 2 * q^20 - 2 * q^21 + 6 * q^22 + 2 * q^23 + 2 * q^25 - 6 * q^26 + 2 * q^27 - 2 * q^28 - 6 * q^31 + 2 * q^33 - 12 * q^34 + 2 * q^35 + 2 * q^36 - 6 * q^37 - 12 * q^38 - 6 * q^39 + 2 * q^44 - 2 * q^45 + 4 * q^47 - 10 * q^48 + 2 * q^49 - 8 * q^51 - 6 * q^52 - 2 * q^53 - 2 * q^55 - 6 * q^59 - 2 * q^60 + 8 * q^61 + 6 * q^62 - 2 * q^63 + 2 * q^64 + 6 * q^65 + 6 * q^66 - 16 * q^67 - 8 * q^68 + 2 * q^69 - 12 * q^71 - 10 * q^73 + 6 * q^74 + 2 * q^75 - 2 * q^77 - 6 * q^78 + 10 * q^79 + 10 * q^80 + 2 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 8 * q^85 + 24 * q^86 - 6 * q^88 + 20 * q^89 + 6 * q^91 + 2 * q^92 - 6 * q^93 - 36 * q^94 - 8 * q^97 + 2 * 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	$-0.290215\pi$
$2$	1.73205	1.22474	0.612372	+	0.790569i	$0.290215\pi$
$3$	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
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.73205	−0.612372
$9$	1.00000	0.333333
$10$	−1.73205	−0.547723
$11$	2.73205	0.823744	0.411872	−	0.911242i	$-0.364875\pi$
$11$	2.73205	0.823744	0.411872	+	0.911242i	$0.364875\pi$
$12$	1.00000	0.288675
$13$	−4.73205	−1.31243	−0.656217	−	0.754572i	$-0.727845\pi$
$13$	−4.73205	−1.31243	−0.656217	+	0.754572i	$0.727845\pi$
$14$	−1.73205	−0.462910
$15$	−1.00000	−0.258199
$16$	−5.00000	−1.25000
$17$	−7.46410	−1.81031	−0.905155	−	0.425081i	$-0.860246\pi$
$17$	−7.46410	−1.81031	−0.905155	+	0.425081i	$0.860246\pi$
$18$	1.73205	0.408248
$19$	−3.46410	−0.794719	−0.397360	−	0.917663i	$-0.630073\pi$
$19$	−3.46410	−0.794719	−0.397360	+	0.917663i	$0.630073\pi$
$20$	−1.00000	−0.223607
$21$	−1.00000	−0.218218
$22$	4.73205	1.00888
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.73205	−0.353553
$25$	1.00000	0.200000
$26$	−8.19615	−1.60740
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	−1.73205	−0.316228
$31$	−1.26795	−0.227730	−0.113865	−	0.993496i	$-0.536323\pi$
$31$	−1.26795	−0.227730	−0.113865	+	0.993496i	$0.536323\pi$
$32$	−5.19615	−0.918559
$33$	2.73205	0.475589
$34$	−12.9282	−2.21717
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	−1.26795	−0.208450	−0.104225	−	0.994554i	$-0.533236\pi$
$37$	−1.26795	−0.208450	−0.104225	+	0.994554i	$0.533236\pi$
$38$	−6.00000	−0.973329
$39$	−4.73205	−0.757735
$40$	1.73205	0.273861
$41$	−3.46410	−0.541002	−0.270501	−	0.962720i	$-0.587189\pi$
$41$	−3.46410	−0.541002	−0.270501	+	0.962720i	$0.587189\pi$
$42$	−1.73205	−0.267261
$43$	6.92820	1.05654	0.528271	−	0.849076i	$-0.322841\pi$
$43$	6.92820	1.05654	0.528271	+	0.849076i	$0.322841\pi$
$44$	2.73205	0.411872
$45$	−1.00000	−0.149071
$46$	1.73205	0.255377
$47$	−8.39230	−1.22414	−0.612072	−	0.790802i	$-0.709664\pi$
$47$	−8.39230	−1.22414	−0.612072	+	0.790802i	$0.709664\pi$
$48$	−5.00000	−0.721688
$49$	1.00000	0.142857
$50$	1.73205	0.244949
$51$	−7.46410	−1.04518
$52$	−4.73205	−0.656217
$53$	0.732051	0.100555	0.0502775	−	0.998735i	$-0.483989\pi$
$53$	0.732051	0.100555	0.0502775	+	0.998735i	$0.483989\pi$
$54$	1.73205	0.235702
$55$	−2.73205	−0.368390
$56$	1.73205	0.231455
$57$	−3.46410	−0.458831
$58$	0	0
$59$	2.19615	0.285915	0.142957	−	0.989729i	$-0.454339\pi$
$59$	2.19615	0.285915	0.142957	+	0.989729i	$0.454339\pi$
$60$	−1.00000	−0.129099
$61$	4.00000	0.512148	0.256074	−	0.966657i	$-0.417571\pi$
$61$	4.00000	0.512148	0.256074	+	0.966657i	$0.417571\pi$
$62$	−2.19615	−0.278912
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	4.73205	0.586939
$66$	4.73205	0.582475
$67$	−14.9282	−1.82377	−0.911885	−	0.410445i	$-0.865373\pi$
$67$	−14.9282	−1.82377	−0.911885	+	0.410445i	$0.865373\pi$
$68$	−7.46410	−0.905155
$69$	1.00000	0.120386
$70$	1.73205	0.207020
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	−1.73205	−0.204124
$73$	3.66025	0.428400	0.214200	−	0.976790i	$-0.431286\pi$
$73$	3.66025	0.428400	0.214200	+	0.976790i	$0.431286\pi$
$74$	−2.19615	−0.255298
$75$	1.00000	0.115470
$76$	−3.46410	−0.397360
$77$	−2.73205	−0.311346
$78$	−8.19615	−0.928032
$79$	10.1962	1.14716	0.573578	−	0.819151i	$-0.305555\pi$
$79$	10.1962	1.14716	0.573578	+	0.819151i	$0.305555\pi$
$80$	5.00000	0.559017
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	−2.00000	−0.219529	−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000	−0.219529	−0.109764	+	0.993958i	$0.535010\pi$
$84$	−1.00000	−0.109109
$85$	7.46410	0.809595
$86$	12.0000	1.29399
$87$	0	0
$88$	−4.73205	−0.504438
$89$	6.53590	0.692804	0.346402	−	0.938086i	$-0.387403\pi$
$89$	6.53590	0.692804	0.346402	+	0.938086i	$0.387403\pi$
$90$	−1.73205	−0.182574
$91$	4.73205	0.496054
$92$	1.00000	0.104257
$93$	−1.26795	−0.131480
$94$	−14.5359	−1.49926
$95$	3.46410	0.355409
$96$	−5.19615	−0.530330
$97$	2.92820	0.297314	0.148657	−	0.988889i	$-0.452505\pi$
$97$	2.92820	0.297314	0.148657	+	0.988889i	$0.452505\pi$
$98$	1.73205	0.174964
$99$	2.73205	0.274581
$100$	1.00000	0.100000
$101$	7.46410	0.742706	0.371353	−	0.928492i	$-0.378894\pi$
$101$	7.46410	0.742706	0.371353	+	0.928492i	$0.378894\pi$
$102$	−12.9282	−1.28008
$103$	−7.46410	−0.735460	−0.367730	−	0.929933i	$-0.619865\pi$
$103$	−7.46410	−0.735460	−0.367730	+	0.929933i	$0.619865\pi$
$104$	8.19615	0.803699
$105$	1.00000	0.0975900
$106$	1.26795	0.123154
$107$	−1.46410	−0.141540	−0.0707700	−	0.997493i	$-0.522546\pi$
$107$	−1.46410	−0.141540	−0.0707700	+	0.997493i	$0.522546\pi$
$108$	1.00000	0.0962250
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	−4.73205	−0.451183
$111$	−1.26795	−0.120348
$112$	5.00000	0.472456
$113$	−7.26795	−0.683711	−0.341856	−	0.939753i	$-0.611055\pi$
$113$	−7.26795	−0.683711	−0.341856	+	0.939753i	$0.611055\pi$
$114$	−6.00000	−0.561951
$115$	−1.00000	−0.0932505
$116$	0	0
$117$	−4.73205	−0.437478
$118$	3.80385	0.350173
$119$	7.46410	0.684233
$120$	1.73205	0.158114
$121$	−3.53590	−0.321445
$122$	6.92820	0.627250
$123$	−3.46410	−0.312348
$124$	−1.26795	−0.113865
$125$	−1.00000	−0.0894427
$126$	−1.73205	−0.154303
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	12.1244	1.07165
$129$	6.92820	0.609994
$130$	8.19615	0.718850
$131$	−7.26795	−0.635004	−0.317502	−	0.948258i	$-0.602844\pi$
$131$	−7.26795	−0.635004	−0.317502	+	0.948258i	$0.602844\pi$
$132$	2.73205	0.237795
$133$	3.46410	0.300376
$134$	−25.8564	−2.23365
$135$	−1.00000	−0.0860663
$136$	12.9282	1.10858
$137$	−4.73205	−0.404286	−0.202143	−	0.979356i	$-0.564791\pi$
$137$	−4.73205	−0.404286	−0.202143	+	0.979356i	$0.564791\pi$
$138$	1.73205	0.147442
$139$	−22.7321	−1.92811	−0.964054	−	0.265708i	$-0.914394\pi$
$139$	−22.7321	−1.92811	−0.964054	+	0.265708i	$0.914394\pi$
$140$	1.00000	0.0845154
$141$	−8.39230	−0.706760
$142$	−10.3923	−0.872103
$143$	−12.9282	−1.08111
$144$	−5.00000	−0.416667
$145$	0	0
$146$	6.33975	0.524681
$147$	1.00000	0.0824786
$148$	−1.26795	−0.104225
$149$	7.46410	0.611483	0.305742	−	0.952115i	$-0.401096\pi$
$149$	7.46410	0.611483	0.305742	+	0.952115i	$0.401096\pi$
$150$	1.73205	0.141421
$151$	4.39230	0.357441	0.178720	−	0.983900i	$-0.442804\pi$
$151$	4.39230	0.357441	0.178720	+	0.983900i	$0.442804\pi$
$152$	6.00000	0.486664
$153$	−7.46410	−0.603437
$154$	−4.73205	−0.381320
$155$	1.26795	0.101844
$156$	−4.73205	−0.378867
$157$	−17.4641	−1.39379	−0.696894	−	0.717175i	$-0.745435\pi$
$157$	−17.4641	−1.39379	−0.696894	+	0.717175i	$0.745435\pi$
$158$	17.6603	1.40497
$159$	0.732051	0.0580554
$160$	5.19615	0.410792
$161$	−1.00000	−0.0788110
$162$	1.73205	0.136083
$163$	−14.9282	−1.16927	−0.584634	−	0.811297i	$-0.698762\pi$
$163$	−14.9282	−1.16927	−0.584634	+	0.811297i	$0.698762\pi$
$164$	−3.46410	−0.270501
$165$	−2.73205	−0.212690
$166$	−3.46410	−0.268866
$167$	10.9282	0.845650	0.422825	−	0.906211i	$-0.361039\pi$
$167$	10.9282	0.845650	0.422825	+	0.906211i	$0.361039\pi$
$168$	1.73205	0.133631
$169$	9.39230	0.722485
$170$	12.9282	0.991548
$171$	−3.46410	−0.264906
$172$	6.92820	0.528271
$173$	17.6603	1.34268	0.671342	−	0.741148i	$-0.265718\pi$
$173$	17.6603	1.34268	0.671342	+	0.741148i	$0.265718\pi$
$174$	0	0
$175$	−1.00000	−0.0755929
$176$	−13.6603	−1.02968
$177$	2.19615	0.165073
$178$	11.3205	0.848508
$179$	−15.8564	−1.18516	−0.592582	−	0.805510i	$-0.701891\pi$
$179$	−15.8564	−1.18516	−0.592582	+	0.805510i	$0.701891\pi$
$180$	−1.00000	−0.0745356
$181$	3.07180	0.228325	0.114162	−	0.993462i	$-0.463582\pi$
$181$	3.07180	0.228325	0.114162	+	0.993462i	$0.463582\pi$
$182$	8.19615	0.607539
$183$	4.00000	0.295689
$184$	−1.73205	−0.127688
$185$	1.26795	0.0932215
$186$	−2.19615	−0.161030
$187$	−20.3923	−1.49123
$188$	−8.39230	−0.612072
$189$	−1.00000	−0.0727393
$190$	6.00000	0.435286
$191$	22.7321	1.64483	0.822417	−	0.568886i	$-0.192625\pi$
$191$	22.7321	1.64483	0.822417	+	0.568886i	$0.192625\pi$
$192$	1.00000	0.0721688
$193$	2.39230	0.172202	0.0861009	−	0.996286i	$-0.472559\pi$
$193$	2.39230	0.172202	0.0861009	+	0.996286i	$0.472559\pi$
$194$	5.07180	0.364134
$195$	4.73205	0.338869
$196$	1.00000	0.0714286
$197$	6.53590	0.465663	0.232832	−	0.972517i	$-0.425201\pi$
$197$	6.53590	0.465663	0.232832	+	0.972517i	$0.425201\pi$
$198$	4.73205	0.336292
$199$	14.3923	1.02024	0.510122	−	0.860102i	$-0.329600\pi$
$199$	14.3923	1.02024	0.510122	+	0.860102i	$0.329600\pi$
$200$	−1.73205	−0.122474
$201$	−14.9282	−1.05295
$202$	12.9282	0.909625
$203$	0	0
$204$	−7.46410	−0.522592
$205$	3.46410	0.241943
$206$	−12.9282	−0.900751
$207$	1.00000	0.0695048
$208$	23.6603	1.64054
$209$	−9.46410	−0.654646
$210$	1.73205	0.119523
$211$	−4.39230	−0.302379	−0.151189	−	0.988505i	$-0.548310\pi$
$211$	−4.39230	−0.302379	−0.151189	+	0.988505i	$0.548310\pi$
$212$	0.732051	0.0502775
$213$	−6.00000	−0.411113
$214$	−2.53590	−0.173350
$215$	−6.92820	−0.472500
$216$	−1.73205	−0.117851
$217$	1.26795	0.0860740
$218$	10.3923	0.703856
$219$	3.66025	0.247337
$220$	−2.73205	−0.184195
$221$	35.3205	2.37591
$222$	−2.19615	−0.147396
$223$	22.2487	1.48988	0.744942	−	0.667129i	$-0.232477\pi$
$223$	22.2487	1.48988	0.744942	+	0.667129i	$0.232477\pi$
$224$	5.19615	0.347183
$225$	1.00000	0.0666667
$226$	−12.5885	−0.837372
$227$	9.85641	0.654193	0.327096	−	0.944991i	$-0.393930\pi$
$227$	9.85641	0.654193	0.327096	+	0.944991i	$0.393930\pi$
$228$	−3.46410	−0.229416
$229$	18.9282	1.25081	0.625405	−	0.780300i	$-0.284934\pi$
$229$	18.9282	1.25081	0.625405	+	0.780300i	$0.284934\pi$
$230$	−1.73205	−0.114208
$231$	−2.73205	−0.179756
$232$	0	0
$233$	5.46410	0.357965	0.178983	−	0.983852i	$-0.442719\pi$
$233$	5.46410	0.357965	0.178983	+	0.983852i	$0.442719\pi$
$234$	−8.19615	−0.535799
$235$	8.39230	0.547454
$236$	2.19615	0.142957
$237$	10.1962	0.662311
$238$	12.9282	0.838011
$239$	−0.928203	−0.0600405	−0.0300202	−	0.999549i	$-0.509557\pi$
$239$	−0.928203	−0.0600405	−0.0300202	+	0.999549i	$0.509557\pi$
$240$	5.00000	0.322749
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	−6.12436	−0.393688
$243$	1.00000	0.0641500
$244$	4.00000	0.256074
$245$	−1.00000	−0.0638877
$246$	−6.00000	−0.382546
$247$	16.3923	1.04302
$248$	2.19615	0.139456
$249$	−2.00000	−0.126745
$250$	−1.73205	−0.109545
$251$	8.39230	0.529718	0.264859	−	0.964287i	$-0.414675\pi$
$251$	8.39230	0.529718	0.264859	+	0.964287i	$0.414675\pi$
$252$	−1.00000	−0.0629941
$253$	2.73205	0.171763
$254$	−13.8564	−0.869428
$255$	7.46410	0.467420
$256$	19.0000	1.18750
$257$	−11.8038	−0.736304	−0.368152	−	0.929766i	$-0.620009\pi$
$257$	−11.8038	−0.736304	−0.368152	+	0.929766i	$0.620009\pi$
$258$	12.0000	0.747087
$259$	1.26795	0.0787865
$260$	4.73205	0.293469
$261$	0	0
$262$	−12.5885	−0.777717
$263$	23.3205	1.43800	0.719002	−	0.695008i	$-0.244599\pi$
$263$	23.3205	1.43800	0.719002	+	0.695008i	$0.244599\pi$
$264$	−4.73205	−0.291238
$265$	−0.732051	−0.0449695
$266$	6.00000	0.367884
$267$	6.53590	0.399990
$268$	−14.9282	−0.911885
$269$	−27.4641	−1.67452	−0.837258	−	0.546808i	$-0.815843\pi$
$269$	−27.4641	−1.67452	−0.837258	+	0.546808i	$0.815843\pi$
$270$	−1.73205	−0.105409
$271$	−28.5885	−1.73663	−0.868313	−	0.496017i	$-0.834795\pi$
$271$	−28.5885	−1.73663	−0.868313	+	0.496017i	$0.834795\pi$
$272$	37.3205	2.26289
$273$	4.73205	0.286397
$274$	−8.19615	−0.495148
$275$	2.73205	0.164749
$276$	1.00000	0.0601929
$277$	6.39230	0.384076	0.192038	−	0.981387i	$-0.438490\pi$
$277$	6.39230	0.384076	0.192038	+	0.981387i	$0.438490\pi$
$278$	−39.3731	−2.36144
$279$	−1.26795	−0.0759101
$280$	−1.73205	−0.103510
$281$	−10.0000	−0.596550	−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000	−0.596550	−0.298275	+	0.954480i	$0.596411\pi$
$282$	−14.5359	−0.865600
$283$	−27.4641	−1.63257	−0.816286	−	0.577648i	$-0.803970\pi$
$283$	−27.4641	−1.63257	−0.816286	+	0.577648i	$0.803970\pi$
$284$	−6.00000	−0.356034
$285$	3.46410	0.205196
$286$	−22.3923	−1.32408
$287$	3.46410	0.204479
$288$	−5.19615	−0.306186
$289$	38.7128	2.27722
$290$	0	0
$291$	2.92820	0.171654
$292$	3.66025	0.214200
$293$	14.7846	0.863726	0.431863	−	0.901939i	$-0.357856\pi$
$293$	14.7846	0.863726	0.431863	+	0.901939i	$0.357856\pi$
$294$	1.73205	0.101015
$295$	−2.19615	−0.127865
$296$	2.19615	0.127649
$297$	2.73205	0.158530
$298$	12.9282	0.748911
$299$	−4.73205	−0.273662
$300$	1.00000	0.0577350
$301$	−6.92820	−0.399335
$302$	7.60770	0.437774
$303$	7.46410	0.428801
$304$	17.3205	0.993399
$305$	−4.00000	−0.229039
$306$	−12.9282	−0.739056
$307$	−2.53590	−0.144731	−0.0723657	−	0.997378i	$-0.523055\pi$
$307$	−2.53590	−0.144731	−0.0723657	+	0.997378i	$0.523055\pi$
$308$	−2.73205	−0.155673
$309$	−7.46410	−0.424618
$310$	2.19615	0.124733
$311$	−18.1962	−1.03181	−0.515905	−	0.856646i	$-0.672544\pi$
$311$	−18.1962	−1.03181	−0.515905	+	0.856646i	$0.672544\pi$
$312$	8.19615	0.464016
$313$	−29.4641	−1.66541	−0.832705	−	0.553717i	$-0.813209\pi$
$313$	−29.4641	−1.66541	−0.832705	+	0.553717i	$0.813209\pi$
$314$	−30.2487	−1.70703
$315$	1.00000	0.0563436
$316$	10.1962	0.573578
$317$	−27.3205	−1.53447	−0.767236	−	0.641365i	$-0.778369\pi$
$317$	−27.3205	−1.53447	−0.767236	+	0.641365i	$0.778369\pi$
$318$	1.26795	0.0711031
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−1.46410	−0.0817182
$322$	−1.73205	−0.0965234
$323$	25.8564	1.43869
$324$	1.00000	0.0555556
$325$	−4.73205	−0.262487
$326$	−25.8564	−1.43205
$327$	6.00000	0.331801
$328$	6.00000	0.331295
$329$	8.39230	0.462683
$330$	−4.73205	−0.260491
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	−2.00000	−0.109764
$333$	−1.26795	−0.0694832
$334$	18.9282	1.03571
$335$	14.9282	0.815615
$336$	5.00000	0.272772
$337$	−10.7321	−0.584612	−0.292306	−	0.956325i	$-0.594423\pi$
$337$	−10.7321	−0.584612	−0.292306	+	0.956325i	$0.594423\pi$
$338$	16.2679	0.884860
$339$	−7.26795	−0.394741
$340$	7.46410	0.404798
$341$	−3.46410	−0.187592
$342$	−6.00000	−0.324443
$343$	−1.00000	−0.0539949
$344$	−12.0000	−0.646997
$345$	−1.00000	−0.0538382
$346$	30.5885	1.64445
$347$	−4.00000	−0.214731	−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000	−0.214731	−0.107366	+	0.994220i	$0.534242\pi$
$348$	0	0
$349$	19.4641	1.04189	0.520945	−	0.853590i	$-0.325580\pi$
$349$	19.4641	1.04189	0.520945	+	0.853590i	$0.325580\pi$
$350$	−1.73205	−0.0925820
$351$	−4.73205	−0.252578
$352$	−14.1962	−0.756657
$353$	9.66025	0.514163	0.257082	−	0.966390i	$-0.417239\pi$
$353$	9.66025	0.514163	0.257082	+	0.966390i	$0.417239\pi$
$354$	3.80385	0.202172
$355$	6.00000	0.318447
$356$	6.53590	0.346402
$357$	7.46410	0.395042
$358$	−27.4641	−1.45152
$359$	−12.1962	−0.643688	−0.321844	−	0.946793i	$-0.604303\pi$
$359$	−12.1962	−0.643688	−0.321844	+	0.946793i	$0.604303\pi$
$360$	1.73205	0.0912871
$361$	−7.00000	−0.368421
$362$	5.32051	0.279640
$363$	−3.53590	−0.185587
$364$	4.73205	0.248027
$365$	−3.66025	−0.191586
$366$	6.92820	0.362143
$367$	17.8564	0.932097	0.466048	−	0.884759i	$-0.345677\pi$
$367$	17.8564	0.932097	0.466048	+	0.884759i	$0.345677\pi$
$368$	−5.00000	−0.260643
$369$	−3.46410	−0.180334
$370$	2.19615	0.114173
$371$	−0.732051	−0.0380062
$372$	−1.26795	−0.0657401
$373$	−1.66025	−0.0859647	−0.0429823	−	0.999076i	$-0.513686\pi$
$373$	−1.66025	−0.0859647	−0.0429823	+	0.999076i	$0.513686\pi$
$374$	−35.3205	−1.82638
$375$	−1.00000	−0.0516398
$376$	14.5359	0.749632
$377$	0	0
$378$	−1.73205	−0.0890871
$379$	5.80385	0.298124	0.149062	−	0.988828i	$-0.452375\pi$
$379$	5.80385	0.298124	0.149062	+	0.988828i	$0.452375\pi$
$380$	3.46410	0.177705
$381$	−8.00000	−0.409852
$382$	39.3731	2.01450
$383$	7.85641	0.401444	0.200722	−	0.979648i	$-0.435671\pi$
$383$	7.85641	0.401444	0.200722	+	0.979648i	$0.435671\pi$
$384$	12.1244	0.618718
$385$	2.73205	0.139238
$386$	4.14359	0.210903
$387$	6.92820	0.352180
$388$	2.92820	0.148657
$389$	−8.53590	−0.432787	−0.216394	−	0.976306i	$-0.569429\pi$
$389$	−8.53590	−0.432787	−0.216394	+	0.976306i	$0.569429\pi$
$390$	8.19615	0.415028
$391$	−7.46410	−0.377476
$392$	−1.73205	−0.0874818
$393$	−7.26795	−0.366620
$394$	11.3205	0.570319
$395$	−10.1962	−0.513024
$396$	2.73205	0.137291
$397$	−28.4449	−1.42761	−0.713803	−	0.700346i	$-0.753029\pi$
$397$	−28.4449	−1.42761	−0.713803	+	0.700346i	$0.753029\pi$
$398$	24.9282	1.24954
$399$	3.46410	0.173422
$400$	−5.00000	−0.250000
$401$	20.2487	1.01117	0.505586	−	0.862776i	$-0.331276\pi$
$401$	20.2487	1.01117	0.505586	+	0.862776i	$0.331276\pi$
$402$	−25.8564	−1.28960
$403$	6.00000	0.298881
$404$	7.46410	0.371353
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−3.46410	−0.171709
$408$	12.9282	0.640041
$409$	−18.3923	−0.909441	−0.454720	−	0.890634i	$-0.650261\pi$
$409$	−18.3923	−0.909441	−0.454720	+	0.890634i	$0.650261\pi$
$410$	6.00000	0.296319
$411$	−4.73205	−0.233415
$412$	−7.46410	−0.367730
$413$	−2.19615	−0.108066
$414$	1.73205	0.0851257
$415$	2.00000	0.0981761
$416$	24.5885	1.20555
$417$	−22.7321	−1.11319
$418$	−16.3923	−0.801774
$419$	26.9282	1.31553	0.657764	−	0.753224i	$-0.271502\pi$
$419$	26.9282	1.31553	0.657764	+	0.753224i	$0.271502\pi$
$420$	1.00000	0.0487950
$421$	−7.85641	−0.382898	−0.191449	−	0.981503i	$-0.561319\pi$
$421$	−7.85641	−0.382898	−0.191449	+	0.981503i	$0.561319\pi$
$422$	−7.60770	−0.370337
$423$	−8.39230	−0.408048
$424$	−1.26795	−0.0615771
$425$	−7.46410	−0.362062
$426$	−10.3923	−0.503509
$427$	−4.00000	−0.193574
$428$	−1.46410	−0.0707700
$429$	−12.9282	−0.624180
$430$	−12.0000	−0.578691
$431$	15.8038	0.761245	0.380622	−	0.924731i	$-0.375710\pi$
$431$	15.8038	0.761245	0.380622	+	0.924731i	$0.375710\pi$
$432$	−5.00000	−0.240563
$433$	−5.85641	−0.281441	−0.140720	−	0.990049i	$-0.544942\pi$
$433$	−5.85641	−0.281441	−0.140720	+	0.990049i	$0.544942\pi$
$434$	2.19615	0.105419
$435$	0	0
$436$	6.00000	0.287348
$437$	−3.46410	−0.165710
$438$	6.33975	0.302925
$439$	−30.4449	−1.45305	−0.726527	−	0.687138i	$-0.758867\pi$
$439$	−30.4449	−1.45305	−0.726527	+	0.687138i	$0.758867\pi$
$440$	4.73205	0.225592
$441$	1.00000	0.0476190
$442$	61.1769	2.90989
$443$	33.3205	1.58311	0.791553	−	0.611101i	$-0.209273\pi$
$443$	33.3205	1.58311	0.791553	+	0.611101i	$0.209273\pi$
$444$	−1.26795	−0.0601742
$445$	−6.53590	−0.309831
$446$	38.5359	1.82473
$447$	7.46410	0.353040
$448$	−1.00000	−0.0472456
$449$	12.0000	0.566315	0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000	0.566315	0.283158	+	0.959073i	$0.408618\pi$
$450$	1.73205	0.0816497
$451$	−9.46410	−0.445647
$452$	−7.26795	−0.341856
$453$	4.39230	0.206368
$454$	17.0718	0.801219
$455$	−4.73205	−0.221842
$456$	6.00000	0.280976
$457$	1.26795	0.0593122	0.0296561	−	0.999560i	$-0.490559\pi$
$457$	1.26795	0.0593122	0.0296561	+	0.999560i	$0.490559\pi$
$458$	32.7846	1.53192
$459$	−7.46410	−0.348394
$460$	−1.00000	−0.0466252
$461$	−4.92820	−0.229529	−0.114765	−	0.993393i	$-0.536611\pi$
$461$	−4.92820	−0.229529	−0.114765	+	0.993393i	$0.536611\pi$
$462$	−4.73205	−0.220155
$463$	30.7846	1.43068	0.715341	−	0.698775i	$-0.246271\pi$
$463$	30.7846	1.43068	0.715341	+	0.698775i	$0.246271\pi$
$464$	0	0
$465$	1.26795	0.0587997
$466$	9.46410	0.438416
$467$	−23.7128	−1.09730	−0.548649	−	0.836053i	$-0.684858\pi$
$467$	−23.7128	−1.09730	−0.548649	+	0.836053i	$0.684858\pi$
$468$	−4.73205	−0.218739
$469$	14.9282	0.689320
$470$	14.5359	0.670491
$471$	−17.4641	−0.804703
$472$	−3.80385	−0.175086
$473$	18.9282	0.870320
$474$	17.6603	0.811162
$475$	−3.46410	−0.158944
$476$	7.46410	0.342117
$477$	0.732051	0.0335183
$478$	−1.60770	−0.0735343
$479$	−25.1769	−1.15036	−0.575181	−	0.818026i	$-0.695068\pi$
$479$	−25.1769	−1.15036	−0.575181	+	0.818026i	$0.695068\pi$
$480$	5.19615	0.237171
$481$	6.00000	0.273576
$482$	17.3205	0.788928
$483$	−1.00000	−0.0455016
$484$	−3.53590	−0.160723
$485$	−2.92820	−0.132963
$486$	1.73205	0.0785674
$487$	−36.6410	−1.66036	−0.830181	−	0.557493i	$-0.811763\pi$
$487$	−36.6410	−1.66036	−0.830181	+	0.557493i	$0.811763\pi$
$488$	−6.92820	−0.313625
$489$	−14.9282	−0.675077
$490$	−1.73205	−0.0782461
$491$	26.7846	1.20877	0.604386	−	0.796691i	$-0.293418\pi$
$491$	26.7846	1.20877	0.604386	+	0.796691i	$0.293418\pi$
$492$	−3.46410	−0.156174
$493$	0	0
$494$	28.3923	1.27743
$495$	−2.73205	−0.122797
$496$	6.33975	0.284663
$497$	6.00000	0.269137
$498$	−3.46410	−0.155230
$499$	−36.3923	−1.62914	−0.814572	−	0.580063i	$-0.803028\pi$
$499$	−36.3923	−1.62914	−0.814572	+	0.580063i	$0.803028\pi$
$500$	−1.00000	−0.0447214
$501$	10.9282	0.488236
$502$	14.5359	0.648769
$503$	26.7846	1.19427	0.597133	−	0.802142i	$-0.296306\pi$
$503$	26.7846	1.19427	0.597133	+	0.802142i	$0.296306\pi$
$504$	1.73205	0.0771517
$505$	−7.46410	−0.332148
$506$	4.73205	0.210365
$507$	9.39230	0.417127
$508$	−8.00000	−0.354943
$509$	8.92820	0.395736	0.197868	−	0.980229i	$-0.436598\pi$
$509$	8.92820	0.395736	0.197868	+	0.980229i	$0.436598\pi$
$510$	12.9282	0.572470
$511$	−3.66025	−0.161920
$512$	8.66025	0.382733
$513$	−3.46410	−0.152944
$514$	−20.4449	−0.901784
$515$	7.46410	0.328908
$516$	6.92820	0.304997
$517$	−22.9282	−1.00838
$518$	2.19615	0.0964934
$519$	17.6603	0.775199
$520$	−8.19615	−0.359425
$521$	−11.3205	−0.495960	−0.247980	−	0.968765i	$-0.579767\pi$
$521$	−11.3205	−0.495960	−0.247980	+	0.968765i	$0.579767\pi$
$522$	0	0
$523$	−32.7846	−1.43357	−0.716785	−	0.697294i	$-0.754387\pi$
$523$	−32.7846	−1.43357	−0.716785	+	0.697294i	$0.754387\pi$
$524$	−7.26795	−0.317502
$525$	−1.00000	−0.0436436
$526$	40.3923	1.76119
$527$	9.46410	0.412263
$528$	−13.6603	−0.594486
$529$	1.00000	0.0434783
$530$	−1.26795	−0.0550762
$531$	2.19615	0.0953049
$532$	3.46410	0.150188
$533$	16.3923	0.710030
$534$	11.3205	0.489886
$535$	1.46410	0.0632986
$536$	25.8564	1.11683
$537$	−15.8564	−0.684254
$538$	−47.5692	−2.05085
$539$	2.73205	0.117678
$540$	−1.00000	−0.0430331
$541$	−44.3923	−1.90857	−0.954287	−	0.298891i	$-0.903383\pi$
$541$	−44.3923	−1.90857	−0.954287	+	0.298891i	$0.903383\pi$
$542$	−49.5167	−2.12692
$543$	3.07180	0.131823
$544$	38.7846	1.66288
$545$	−6.00000	−0.257012
$546$	8.19615	0.350763
$547$	−20.9282	−0.894825	−0.447413	−	0.894328i	$-0.647654\pi$
$547$	−20.9282	−0.894825	−0.447413	+	0.894328i	$0.647654\pi$
$548$	−4.73205	−0.202143
$549$	4.00000	0.170716
$550$	4.73205	0.201775
$551$	0	0
$552$	−1.73205	−0.0737210
$553$	−10.1962	−0.433585
$554$	11.0718	0.470396
$555$	1.26795	0.0538214
$556$	−22.7321	−0.964054
$557$	−2.19615	−0.0930540	−0.0465270	−	0.998917i	$-0.514815\pi$
$557$	−2.19615	−0.0930540	−0.0465270	+	0.998917i	$0.514815\pi$
$558$	−2.19615	−0.0929705
$559$	−32.7846	−1.38664
$560$	−5.00000	−0.211289
$561$	−20.3923	−0.860964
$562$	−17.3205	−0.730622
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	−8.39230	−0.353380
$565$	7.26795	0.305765
$566$	−47.5692	−1.99948
$567$	−1.00000	−0.0419961
$568$	10.3923	0.436051
$569$	−35.8564	−1.50318	−0.751589	−	0.659631i	$-0.770712\pi$
$569$	−35.8564	−1.50318	−0.751589	+	0.659631i	$0.770712\pi$
$570$	6.00000	0.251312
$571$	27.6603	1.15755	0.578773	−	0.815489i	$-0.303532\pi$
$571$	27.6603	1.15755	0.578773	+	0.815489i	$0.303532\pi$
$572$	−12.9282	−0.540555
$573$	22.7321	0.949645
$574$	6.00000	0.250435
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	32.4449	1.35070	0.675349	−	0.737499i	$-0.263993\pi$
$577$	32.4449	1.35070	0.675349	+	0.737499i	$0.263993\pi$
$578$	67.0526	2.78902
$579$	2.39230	0.0994208
$580$	0	0
$581$	2.00000	0.0829740
$582$	5.07180	0.210233
$583$	2.00000	0.0828315
$584$	−6.33975	−0.262341
$585$	4.73205	0.195646
$586$	25.6077	1.05784
$587$	−30.9282	−1.27654	−0.638272	−	0.769811i	$-0.720350\pi$
$587$	−30.9282	−1.27654	−0.638272	+	0.769811i	$0.720350\pi$
$588$	1.00000	0.0412393
$589$	4.39230	0.180982
$590$	−3.80385	−0.156602
$591$	6.53590	0.268851
$592$	6.33975	0.260562
$593$	−39.9090	−1.63886	−0.819432	−	0.573176i	$-0.805711\pi$
$593$	−39.9090	−1.63886	−0.819432	+	0.573176i	$0.805711\pi$
$594$	4.73205	0.194158
$595$	−7.46410	−0.305998
$596$	7.46410	0.305742
$597$	14.3923	0.589038
$598$	−8.19615	−0.335166
$599$	−2.39230	−0.0977469	−0.0488735	−	0.998805i	$-0.515563\pi$
$599$	−2.39230	−0.0977469	−0.0488735	+	0.998805i	$0.515563\pi$
$600$	−1.73205	−0.0707107
$601$	−32.6410	−1.33145	−0.665727	−	0.746195i	$-0.731879\pi$
$601$	−32.6410	−1.33145	−0.665727	+	0.746195i	$0.731879\pi$
$602$	−12.0000	−0.489083
$603$	−14.9282	−0.607923
$604$	4.39230	0.178720
$605$	3.53590	0.143755
$606$	12.9282	0.525172
$607$	−37.1769	−1.50896	−0.754482	−	0.656321i	$-0.772112\pi$
$607$	−37.1769	−1.50896	−0.754482	+	0.656321i	$0.772112\pi$
$608$	18.0000	0.729996
$609$	0	0
$610$	−6.92820	−0.280515
$611$	39.7128	1.60661
$612$	−7.46410	−0.301718
$613$	19.1244	0.772425	0.386213	−	0.922410i	$-0.373783\pi$
$613$	19.1244	0.772425	0.386213	+	0.922410i	$0.373783\pi$
$614$	−4.39230	−0.177259
$615$	3.46410	0.139686
$616$	4.73205	0.190660
$617$	−46.3013	−1.86402	−0.932009	−	0.362434i	$-0.881946\pi$
$617$	−46.3013	−1.86402	−0.932009	+	0.362434i	$0.881946\pi$
$618$	−12.9282	−0.520049
$619$	8.24871	0.331544	0.165772	−	0.986164i	$-0.446988\pi$
$619$	8.24871	0.331544	0.165772	+	0.986164i	$0.446988\pi$
$620$	1.26795	0.0509221
$621$	1.00000	0.0401286
$622$	−31.5167	−1.26370
$623$	−6.53590	−0.261855
$624$	23.6603	0.947168
$625$	1.00000	0.0400000
$626$	−51.0333	−2.03970
$627$	−9.46410	−0.377960
$628$	−17.4641	−0.696894
$629$	9.46410	0.377358
$630$	1.73205	0.0690066
$631$	6.87564	0.273715	0.136858	−	0.990591i	$-0.456300\pi$
$631$	6.87564	0.273715	0.136858	+	0.990591i	$0.456300\pi$
$632$	−17.6603	−0.702487
$633$	−4.39230	−0.174578
$634$	−47.3205	−1.87934
$635$	8.00000	0.317470
$636$	0.732051	0.0290277
$637$	−4.73205	−0.187491
$638$	0	0
$639$	−6.00000	−0.237356
$640$	−12.1244	−0.479257
$641$	29.3205	1.15809	0.579045	−	0.815295i	$-0.303425\pi$
$641$	29.3205	1.15809	0.579045	+	0.815295i	$0.303425\pi$
$642$	−2.53590	−0.100084
$643$	12.5359	0.494368	0.247184	−	0.968969i	$-0.420495\pi$
$643$	12.5359	0.494368	0.247184	+	0.968969i	$0.420495\pi$
$644$	−1.00000	−0.0394055
$645$	−6.92820	−0.272798
$646$	44.7846	1.76203
$647$	28.3923	1.11622	0.558108	−	0.829768i	$-0.311527\pi$
$647$	28.3923	1.11622	0.558108	+	0.829768i	$0.311527\pi$
$648$	−1.73205	−0.0680414
$649$	6.00000	0.235521
$650$	−8.19615	−0.321480
$651$	1.26795	0.0496948
$652$	−14.9282	−0.584634
$653$	−7.32051	−0.286474	−0.143237	−	0.989688i	$-0.545751\pi$
$653$	−7.32051	−0.286474	−0.143237	+	0.989688i	$0.545751\pi$
$654$	10.3923	0.406371
$655$	7.26795	0.283982
$656$	17.3205	0.676252
$657$	3.66025	0.142800
$658$	14.5359	0.566668
$659$	−34.0526	−1.32650	−0.663250	−	0.748398i	$-0.730823\pi$
$659$	−34.0526	−1.32650	−0.663250	+	0.748398i	$0.730823\pi$
$660$	−2.73205	−0.106345
$661$	15.0718	0.586225	0.293112	−	0.956078i	$-0.405309\pi$
$661$	15.0718	0.586225	0.293112	+	0.956078i	$0.405309\pi$
$662$	13.8564	0.538545
$663$	35.3205	1.37173
$664$	3.46410	0.134433
$665$	−3.46410	−0.134332
$666$	−2.19615	−0.0850992
$667$	0	0
$668$	10.9282	0.422825
$669$	22.2487	0.860185
$670$	25.8564	0.998920
$671$	10.9282	0.421879
$672$	5.19615	0.200446
$673$	−20.2487	−0.780530	−0.390265	−	0.920702i	$-0.627617\pi$
$673$	−20.2487	−0.780530	−0.390265	+	0.920702i	$0.627617\pi$
$674$	−18.5885	−0.716001
$675$	1.00000	0.0384900
$676$	9.39230	0.361242
$677$	21.3205	0.819414	0.409707	−	0.912217i	$-0.365631\pi$
$677$	21.3205	0.819414	0.409707	+	0.912217i	$0.365631\pi$
$678$	−12.5885	−0.483457
$679$	−2.92820	−0.112374
$680$	−12.9282	−0.495774
$681$	9.85641	0.377698
$682$	−6.00000	−0.229752
$683$	37.5692	1.43755	0.718773	−	0.695245i	$-0.244704\pi$
$683$	37.5692	1.43755	0.718773	+	0.695245i	$0.244704\pi$
$684$	−3.46410	−0.132453
$685$	4.73205	0.180802
$686$	−1.73205	−0.0661300
$687$	18.9282	0.722156
$688$	−34.6410	−1.32068
$689$	−3.46410	−0.131972
$690$	−1.73205	−0.0659380
$691$	−36.9808	−1.40681	−0.703407	−	0.710787i	$-0.748339\pi$
$691$	−36.9808	−1.40681	−0.703407	+	0.710787i	$0.748339\pi$
$692$	17.6603	0.671342
$693$	−2.73205	−0.103782
$694$	−6.92820	−0.262991
$695$	22.7321	0.862276
$696$	0	0
$697$	25.8564	0.979381
$698$	33.7128	1.27605
$699$	5.46410	0.206671
$700$	−1.00000	−0.0377964
$701$	−33.7128	−1.27332	−0.636658	−	0.771147i	$-0.719684\pi$
$701$	−33.7128	−1.27332	−0.636658	+	0.771147i	$0.719684\pi$
$702$	−8.19615	−0.309344
$703$	4.39230	0.165659
$704$	2.73205	0.102968
$705$	8.39230	0.316072
$706$	16.7321	0.629719
$707$	−7.46410	−0.280716
$708$	2.19615	0.0825365
$709$	12.1436	0.456062	0.228031	−	0.973654i	$-0.426771\pi$
$709$	12.1436	0.456062	0.228031	+	0.973654i	$0.426771\pi$
$710$	10.3923	0.390016
$711$	10.1962	0.382386
$712$	−11.3205	−0.424254
$713$	−1.26795	−0.0474851
$714$	12.9282	0.483826
$715$	12.9282	0.483487
$716$	−15.8564	−0.592582
$717$	−0.928203	−0.0346644
$718$	−21.1244	−0.788354
$719$	0.732051	0.0273009	0.0136504	−	0.999907i	$-0.495655\pi$
$719$	0.732051	0.0273009	0.0136504	+	0.999907i	$0.495655\pi$
$720$	5.00000	0.186339
$721$	7.46410	0.277978
$722$	−12.1244	−0.451222
$723$	10.0000	0.371904
$724$	3.07180	0.114162
$725$	0	0
$726$	−6.12436	−0.227296
$727$	−11.4641	−0.425180	−0.212590	−	0.977141i	$-0.568190\pi$
$727$	−11.4641	−0.425180	−0.212590	+	0.977141i	$0.568190\pi$
$728$	−8.19615	−0.303770
$729$	1.00000	0.0370370
$730$	−6.33975	−0.234645
$731$	−51.7128	−1.91267
$732$	4.00000	0.147844
$733$	−41.8564	−1.54600	−0.773001	−	0.634405i	$-0.781245\pi$
$733$	−41.8564	−1.54600	−0.773001	+	0.634405i	$0.781245\pi$
$734$	30.9282	1.14158
$735$	−1.00000	−0.0368856
$736$	−5.19615	−0.191533
$737$	−40.7846	−1.50232
$738$	−6.00000	−0.220863
$739$	19.3205	0.710716	0.355358	−	0.934730i	$-0.384359\pi$
$739$	19.3205	0.710716	0.355358	+	0.934730i	$0.384359\pi$
$740$	1.26795	0.0466107
$741$	16.3923	0.602186
$742$	−1.26795	−0.0465479
$743$	25.4641	0.934187	0.467094	−	0.884208i	$-0.345301\pi$
$743$	25.4641	0.934187	0.467094	+	0.884208i	$0.345301\pi$
$744$	2.19615	0.0805149
$745$	−7.46410	−0.273464
$746$	−2.87564	−0.105285
$747$	−2.00000	−0.0731762
$748$	−20.3923	−0.745617
$749$	1.46410	0.0534971
$750$	−1.73205	−0.0632456
$751$	−44.0526	−1.60750	−0.803750	−	0.594967i	$-0.797165\pi$
$751$	−44.0526	−1.60750	−0.803750	+	0.594967i	$0.797165\pi$
$752$	41.9615	1.53018
$753$	8.39230	0.305833
$754$	0	0
$755$	−4.39230	−0.159852
$756$	−1.00000	−0.0363696
$757$	−33.6603	−1.22340	−0.611701	−	0.791089i	$-0.709515\pi$
$757$	−33.6603	−1.22340	−0.611701	+	0.791089i	$0.709515\pi$
$758$	10.0526	0.365125
$759$	2.73205	0.0991672
$760$	−6.00000	−0.217643
$761$	24.2487	0.879015	0.439508	−	0.898239i	$-0.355153\pi$
$761$	24.2487	0.879015	0.439508	+	0.898239i	$0.355153\pi$
$762$	−13.8564	−0.501965
$763$	−6.00000	−0.217215
$764$	22.7321	0.822417
$765$	7.46410	0.269865
$766$	13.6077	0.491666
$767$	−10.3923	−0.375244
$768$	19.0000	0.685603
$769$	3.85641	0.139066	0.0695328	−	0.997580i	$-0.477849\pi$
$769$	3.85641	0.139066	0.0695328	+	0.997580i	$0.477849\pi$
$770$	4.73205	0.170531
$771$	−11.8038	−0.425105
$772$	2.39230	0.0861009
$773$	4.24871	0.152816	0.0764078	−	0.997077i	$-0.475655\pi$
$773$	4.24871	0.152816	0.0764078	+	0.997077i	$0.475655\pi$
$774$	12.0000	0.431331
$775$	−1.26795	−0.0455461
$776$	−5.07180	−0.182067
$777$	1.26795	0.0454874
$778$	−14.7846	−0.530054
$779$	12.0000	0.429945
$780$	4.73205	0.169435
$781$	−16.3923	−0.586563
$782$	−12.9282	−0.462312
$783$	0	0
$784$	−5.00000	−0.178571
$785$	17.4641	0.623321
$786$	−12.5885	−0.449015
$787$	28.5359	1.01719	0.508597	−	0.861004i	$-0.330164\pi$
$787$	28.5359	1.01719	0.508597	+	0.861004i	$0.330164\pi$
$788$	6.53590	0.232832
$789$	23.3205	0.830232
$790$	−17.6603	−0.628324
$791$	7.26795	0.258419
$792$	−4.73205	−0.168146
$793$	−18.9282	−0.672160
$794$	−49.2679	−1.74845
$795$	−0.732051	−0.0259632
$796$	14.3923	0.510122
$797$	3.85641	0.136601	0.0683005	−	0.997665i	$-0.478242\pi$
$797$	3.85641	0.136601	0.0683005	+	0.997665i	$0.478242\pi$
$798$	6.00000	0.212398
$799$	62.6410	2.21608
$800$	−5.19615	−0.183712
$801$	6.53590	0.230935
$802$	35.0718	1.23843
$803$	10.0000	0.352892
$804$	−14.9282	−0.526477
$805$	1.00000	0.0352454
$806$	10.3923	0.366053
$807$	−27.4641	−0.966782
$808$	−12.9282	−0.454813
$809$	7.07180	0.248631	0.124316	−	0.992243i	$-0.460326\pi$
$809$	7.07180	0.248631	0.124316	+	0.992243i	$0.460326\pi$
$810$	−1.73205	−0.0608581
$811$	20.8756	0.733043	0.366522	−	0.930410i	$-0.380549\pi$
$811$	20.8756	0.733043	0.366522	+	0.930410i	$0.380549\pi$
$812$	0	0
$813$	−28.5885	−1.00264
$814$	−6.00000	−0.210300
$815$	14.9282	0.522912
$816$	37.3205	1.30648
$817$	−24.0000	−0.839654
$818$	−31.8564	−1.11383
$819$	4.73205	0.165351
$820$	3.46410	0.120972
$821$	21.7128	0.757782	0.378891	−	0.925441i	$-0.376305\pi$
$821$	21.7128	0.757782	0.378891	+	0.925441i	$0.376305\pi$
$822$	−8.19615	−0.285874
$823$	−31.5692	−1.10043	−0.550217	−	0.835022i	$-0.685455\pi$
$823$	−31.5692	−1.10043	−0.550217	+	0.835022i	$0.685455\pi$
$824$	12.9282	0.450375
$825$	2.73205	0.0951178
$826$	−3.80385	−0.132353
$827$	45.4641	1.58094	0.790471	−	0.612500i	$-0.209836\pi$
$827$	45.4641	1.58094	0.790471	+	0.612500i	$0.209836\pi$
$828$	1.00000	0.0347524
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	3.46410	0.120241
$831$	6.39230	0.221747
$832$	−4.73205	−0.164054
$833$	−7.46410	−0.258616
$834$	−39.3731	−1.36338
$835$	−10.9282	−0.378186
$836$	−9.46410	−0.327323
$837$	−1.26795	−0.0438267
$838$	46.6410	1.61119
$839$	−16.3923	−0.565925	−0.282963	−	0.959131i	$-0.591317\pi$
$839$	−16.3923	−0.565925	−0.282963	+	0.959131i	$0.591317\pi$
$840$	−1.73205	−0.0597614
$841$	−29.0000	−1.00000
$842$	−13.6077	−0.468952
$843$	−10.0000	−0.344418
$844$	−4.39230	−0.151189
$845$	−9.39230	−0.323105
$846$	−14.5359	−0.499754
$847$	3.53590	0.121495
$848$	−3.66025	−0.125694
$849$	−27.4641	−0.942566
$850$	−12.9282	−0.443434
$851$	−1.26795	−0.0434647
$852$	−6.00000	−0.205557
$853$	9.41154	0.322245	0.161123	−	0.986934i	$-0.448489\pi$
$853$	9.41154	0.322245	0.161123	+	0.986934i	$0.448489\pi$
$854$	−6.92820	−0.237078
$855$	3.46410	0.118470
$856$	2.53590	0.0866752
$857$	19.5167	0.666676	0.333338	−	0.942807i	$-0.391825\pi$
$857$	19.5167	0.666676	0.333338	+	0.942807i	$0.391825\pi$
$858$	−22.3923	−0.764461
$859$	−51.5167	−1.75773	−0.878863	−	0.477074i	$-0.841697\pi$
$859$	−51.5167	−1.75773	−0.878863	+	0.477074i	$0.841697\pi$
$860$	−6.92820	−0.236250
$861$	3.46410	0.118056
$862$	27.3731	0.932330
$863$	29.8564	1.01632	0.508162	−	0.861262i	$-0.330325\pi$
$863$	29.8564	1.01632	0.508162	+	0.861262i	$0.330325\pi$
$864$	−5.19615	−0.176777
$865$	−17.6603	−0.600467
$866$	−10.1436	−0.344693
$867$	38.7128	1.31476
$868$	1.26795	0.0430370
$869$	27.8564	0.944964
$870$	0	0
$871$	70.6410	2.39358
$872$	−10.3923	−0.351928
$873$	2.92820	0.0991047
$874$	−6.00000	−0.202953
$875$	1.00000	0.0338062
$876$	3.66025	0.123669
$877$	−43.8564	−1.48093	−0.740463	−	0.672097i	$-0.765394\pi$
$877$	−43.8564	−1.48093	−0.740463	+	0.672097i	$0.765394\pi$
$878$	−52.7321	−1.77962
$879$	14.7846	0.498673
$880$	13.6603	0.460487
$881$	31.8564	1.07327	0.536635	−	0.843815i	$-0.319695\pi$
$881$	31.8564	1.07327	0.536635	+	0.843815i	$0.319695\pi$
$882$	1.73205	0.0583212
$883$	−9.21539	−0.310123	−0.155061	−	0.987905i	$-0.549558\pi$
$883$	−9.21539	−0.310123	−0.155061	+	0.987905i	$0.549558\pi$
$884$	35.3205	1.18796
$885$	−2.19615	−0.0738229
$886$	57.7128	1.93890
$887$	−29.0718	−0.976135	−0.488068	−	0.872806i	$-0.662298\pi$
$887$	−29.0718	−0.976135	−0.488068	+	0.872806i	$0.662298\pi$
$888$	2.19615	0.0736980
$889$	8.00000	0.268311
$890$	−11.3205	−0.379464
$891$	2.73205	0.0915271
$892$	22.2487	0.744942
$893$	29.0718	0.972851
$894$	12.9282	0.432384
$895$	15.8564	0.530021
$896$	−12.1244	−0.405046
$897$	−4.73205	−0.157999
$898$	20.7846	0.693591
$899$	0	0
$900$	1.00000	0.0333333
$901$	−5.46410	−0.182036
$902$	−16.3923	−0.545804
$903$	−6.92820	−0.230556
$904$	12.5885	0.418686
$905$	−3.07180	−0.102110
$906$	7.60770	0.252749
$907$	−43.3205	−1.43843	−0.719217	−	0.694786i	$-0.755499\pi$
$907$	−43.3205	−1.43843	−0.719217	+	0.694786i	$0.755499\pi$
$908$	9.85641	0.327096
$909$	7.46410	0.247569
$910$	−8.19615	−0.271700
$911$	2.33975	0.0775192	0.0387596	−	0.999249i	$-0.487659\pi$
$911$	2.33975	0.0775192	0.0387596	+	0.999249i	$0.487659\pi$
$912$	17.3205	0.573539
$913$	−5.46410	−0.180835
$914$	2.19615	0.0726423
$915$	−4.00000	−0.132236
$916$	18.9282	0.625405
$917$	7.26795	0.240009
$918$	−12.9282	−0.426694
$919$	−18.5885	−0.613177	−0.306588	−	0.951842i	$-0.599187\pi$
$919$	−18.5885	−0.613177	−0.306588	+	0.951842i	$0.599187\pi$
$920$	1.73205	0.0571040
$921$	−2.53590	−0.0835607
$922$	−8.53590	−0.281115
$923$	28.3923	0.934544
$924$	−2.73205	−0.0898779
$925$	−1.26795	−0.0416899
$926$	53.3205	1.75222
$927$	−7.46410	−0.245153
$928$	0	0
$929$	−60.2487	−1.97670	−0.988348	−	0.152211i	$-0.951361\pi$
$929$	−60.2487	−1.97670	−0.988348	+	0.152211i	$0.951361\pi$
$930$	2.19615	0.0720147
$931$	−3.46410	−0.113531
$932$	5.46410	0.178983
$933$	−18.1962	−0.595715
$934$	−41.0718	−1.34391
$935$	20.3923	0.666900
$936$	8.19615	0.267900
$937$	0.784610	0.0256321	0.0128160	−	0.999918i	$-0.495920\pi$
$937$	0.784610	0.0256321	0.0128160	+	0.999918i	$0.495920\pi$
$938$	25.8564	0.844242
$939$	−29.4641	−0.961525
$940$	8.39230	0.273727
$941$	−4.39230	−0.143185	−0.0715925	−	0.997434i	$-0.522808\pi$
$941$	−4.39230	−0.143185	−0.0715925	+	0.997434i	$0.522808\pi$
$942$	−30.2487	−0.985556
$943$	−3.46410	−0.112807
$944$	−10.9808	−0.357393
$945$	1.00000	0.0325300
$946$	32.7846	1.06592
$947$	28.5359	0.927292	0.463646	−	0.886021i	$-0.346541\pi$
$947$	28.5359	0.927292	0.463646	+	0.886021i	$0.346541\pi$
$948$	10.1962	0.331156
$949$	−17.3205	−0.562247
$950$	−6.00000	−0.194666
$951$	−27.3205	−0.885928
$952$	−12.9282	−0.419005
$953$	4.33975	0.140578	0.0702891	−	0.997527i	$-0.477608\pi$
$953$	4.33975	0.140578	0.0702891	+	0.997527i	$0.477608\pi$
$954$	1.26795	0.0410514
$955$	−22.7321	−0.735592
$956$	−0.928203	−0.0300202
$957$	0	0
$958$	−43.6077	−1.40890
$959$	4.73205	0.152806
$960$	−1.00000	−0.0322749
$961$	−29.3923	−0.948139
$962$	10.3923	0.335061
$963$	−1.46410	−0.0471800
$964$	10.0000	0.322078
$965$	−2.39230	−0.0770110
$966$	−1.73205	−0.0557278
$967$	7.21539	0.232031	0.116016	−	0.993247i	$-0.462988\pi$
$967$	7.21539	0.232031	0.116016	+	0.993247i	$0.462988\pi$
$968$	6.12436	0.196844
$969$	25.8564	0.830627
$970$	−5.07180	−0.162846
$971$	51.0333	1.63774	0.818869	−	0.573981i	$-0.194602\pi$
$971$	51.0333	1.63774	0.818869	+	0.573981i	$0.194602\pi$
$972$	1.00000	0.0320750
$973$	22.7321	0.728756
$974$	−63.4641	−2.03352
$975$	−4.73205	−0.151547
$976$	−20.0000	−0.640184
$977$	49.1244	1.57163	0.785814	−	0.618463i	$-0.212244\pi$
$977$	49.1244	1.57163	0.785814	+	0.618463i	$0.212244\pi$
$978$	−25.8564	−0.826797
$979$	17.8564	0.570693
$980$	−1.00000	−0.0319438
$981$	6.00000	0.191565
$982$	46.3923	1.48044
$983$	−12.9282	−0.412346	−0.206173	−	0.978516i	$-0.566101\pi$
$983$	−12.9282	−0.412346	−0.206173	+	0.978516i	$0.566101\pi$
$984$	6.00000	0.191273
$985$	−6.53590	−0.208251
$986$	0	0
$987$	8.39230	0.267130
$988$	16.3923	0.521509
$989$	6.92820	0.220304
$990$	−4.73205	−0.150394
$991$	51.0333	1.62113	0.810563	−	0.585651i	$-0.199161\pi$
$991$	51.0333	1.62113	0.810563	+	0.585651i	$0.199161\pi$
$992$	6.58846	0.209184
$993$	8.00000	0.253872
$994$	10.3923	0.329624
$995$	−14.3923	−0.456267
$996$	−2.00000	−0.0633724
$997$	17.1244	0.542334	0.271167	−	0.962532i	$-0.412590\pi$
$997$	17.1244	0.542334	0.271167	+	0.962532i	$0.412590\pi$
$998$	−63.0333	−1.99528
$999$	−1.26795	−0.0401161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.j.1.2	✓	2
3.2	odd	2		7245.2.a.w.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.j.1.2	✓	2	1.1	even	1	trivial
7245.2.a.w.1.1		2	3.2	odd	2

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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2415.a (trivial)

\(f(q)\)	\(=\)	\(q+1.73205 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.73205 q^{6} -1.00000 q^{7} -1.73205 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.73205 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.73205 q^{6} -1.00000 q^{7} -1.73205 q^{8} +1.00000 q^{9} -1.73205 q^{10} +2.73205 q^{11} +1.00000 q^{12} -4.73205 q^{13} -1.73205 q^{14} -1.00000 q^{15} -5.00000 q^{16} -7.46410 q^{17} +1.73205 q^{18} -3.46410 q^{19} -1.00000 q^{20} -1.00000 q^{21} +4.73205 q^{22} +1.00000 q^{23} -1.73205 q^{24} +1.00000 q^{25} -8.19615 q^{26} +1.00000 q^{27} -1.00000 q^{28} -1.73205 q^{30} -1.26795 q^{31} -5.19615 q^{32} +2.73205 q^{33} -12.9282 q^{34} +1.00000 q^{35} +1.00000 q^{36} -1.26795 q^{37} -6.00000 q^{38} -4.73205 q^{39} +1.73205 q^{40} -3.46410 q^{41} -1.73205 q^{42} +6.92820 q^{43} +2.73205 q^{44} -1.00000 q^{45} +1.73205 q^{46} -8.39230 q^{47} -5.00000 q^{48} +1.00000 q^{49} +1.73205 q^{50} -7.46410 q^{51} -4.73205 q^{52} +0.732051 q^{53} +1.73205 q^{54} -2.73205 q^{55} +1.73205 q^{56} -3.46410 q^{57} +2.19615 q^{59} -1.00000 q^{60} +4.00000 q^{61} -2.19615 q^{62} -1.00000 q^{63} +1.00000 q^{64} +4.73205 q^{65} +4.73205 q^{66} -14.9282 q^{67} -7.46410 q^{68} +1.00000 q^{69} +1.73205 q^{70} -6.00000 q^{71} -1.73205 q^{72} +3.66025 q^{73} -2.19615 q^{74} +1.00000 q^{75} -3.46410 q^{76} -2.73205 q^{77} -8.19615 q^{78} +10.1962 q^{79} +5.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -2.00000 q^{83} -1.00000 q^{84} +7.46410 q^{85} +12.0000 q^{86} -4.73205 q^{88} +6.53590 q^{89} -1.73205 q^{90} +4.73205 q^{91} +1.00000 q^{92} -1.26795 q^{93} -14.5359 q^{94} +3.46410 q^{95} -5.19615 q^{96} +2.92820 q^{97} +1.73205 q^{98} +2.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^7 + 2 * q^9	\( 2 q + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{7} + 2 q^{9} + 2 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{15} - 10 q^{16} - 8 q^{17} - 2 q^{20} - 2 q^{21} + 6 q^{22} + 2 q^{23} + 2 q^{25} - 6 q^{26} + 2 q^{27} - 2 q^{28} - 6 q^{31} + 2 q^{33} - 12 q^{34} + 2 q^{35} + 2 q^{36} - 6 q^{37} - 12 q^{38} - 6 q^{39} + 2 q^{44} - 2 q^{45} + 4 q^{47} - 10 q^{48} + 2 q^{49} - 8 q^{51} - 6 q^{52} - 2 q^{53} - 2 q^{55} - 6 q^{59} - 2 q^{60} + 8 q^{61} + 6 q^{62} - 2 q^{63} + 2 q^{64} + 6 q^{65} + 6 q^{66} - 16 q^{67} - 8 q^{68} + 2 q^{69} - 12 q^{71} - 10 q^{73} + 6 q^{74} + 2 q^{75} - 2 q^{77} - 6 q^{78} + 10 q^{79} + 10 q^{80} + 2 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 8 q^{85} + 24 q^{86} - 6 q^{88} + 20 q^{89} + 6 q^{91} + 2 q^{92} - 6 q^{93} - 36 q^{94} - 8 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^7 + 2 * q^9 + 2 * q^11 + 2 * q^12 - 6 * q^13 - 2 * q^15 - 10 * q^16 - 8 * q^17 - 2 * q^20 - 2 * q^21 + 6 * q^22 + 2 * q^23 + 2 * q^25 - 6 * q^26 + 2 * q^27 - 2 * q^28 - 6 * q^31 + 2 * q^33 - 12 * q^34 + 2 * q^35 + 2 * q^36 - 6 * q^37 - 12 * q^38 - 6 * q^39 + 2 * q^44 - 2 * q^45 + 4 * q^47 - 10 * q^48 + 2 * q^49 - 8 * q^51 - 6 * q^52 - 2 * q^53 - 2 * q^55 - 6 * q^59 - 2 * q^60 + 8 * q^61 + 6 * q^62 - 2 * q^63 + 2 * q^64 + 6 * q^65 + 6 * q^66 - 16 * q^67 - 8 * q^68 + 2 * q^69 - 12 * q^71 - 10 * q^73 + 6 * q^74 + 2 * q^75 - 2 * q^77 - 6 * q^78 + 10 * q^79 + 10 * q^80 + 2 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 8 * q^85 + 24 * q^86 - 6 * q^88 + 20 * q^89 + 6 * q^91 + 2 * q^92 - 6 * q^93 - 36 * q^94 - 8 * q^97 + 2 * q^99

Introduction

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