LMFDB - Embedded newform 5070.2.a.bc.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5070,2,Mod(1,5070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5070, 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("5070.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5070.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:	$40.4841538248$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 390)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	5070.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +2.82843 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +2.82843 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -5.65685 q^{11} +1.00000 q^{12} -2.82843 q^{14} -1.00000 q^{15} +1.00000 q^{16} +0.828427 q^{17} -1.00000 q^{18} -2.82843 q^{19} -1.00000 q^{20} +2.82843 q^{21} +5.65685 q^{22} -8.48528 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} +2.82843 q^{28} -8.82843 q^{29} +1.00000 q^{30} -4.00000 q^{31} -1.00000 q^{32} -5.65685 q^{33} -0.828427 q^{34} -2.82843 q^{35} +1.00000 q^{36} +11.6569 q^{37} +2.82843 q^{38} +1.00000 q^{40} +7.65685 q^{41} -2.82843 q^{42} +9.65685 q^{43} -5.65685 q^{44} -1.00000 q^{45} +8.48528 q^{46} +8.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +0.828427 q^{51} +13.3137 q^{53} -1.00000 q^{54} +5.65685 q^{55} -2.82843 q^{56} -2.82843 q^{57} +8.82843 q^{58} +2.34315 q^{59} -1.00000 q^{60} +6.00000 q^{61} +4.00000 q^{62} +2.82843 q^{63} +1.00000 q^{64} +5.65685 q^{66} -5.65685 q^{67} +0.828427 q^{68} -8.48528 q^{69} +2.82843 q^{70} +5.65685 q^{71} -1.00000 q^{72} +14.4853 q^{73} -11.6569 q^{74} +1.00000 q^{75} -2.82843 q^{76} -16.0000 q^{77} +2.34315 q^{79} -1.00000 q^{80} +1.00000 q^{81} -7.65685 q^{82} -6.34315 q^{83} +2.82843 q^{84} -0.828427 q^{85} -9.65685 q^{86} -8.82843 q^{87} +5.65685 q^{88} +15.6569 q^{89} +1.00000 q^{90} -8.48528 q^{92} -4.00000 q^{93} -8.00000 q^{94} +2.82843 q^{95} -1.00000 q^{96} +3.17157 q^{97} -1.00000 q^{98} -5.65685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{12} - 2 q^{15} + 2 q^{16} - 4 q^{17} - 2 q^{18} - 2 q^{20} - 2 q^{24} + 2 q^{25} + 2 q^{27} - 12 q^{29} + 2 q^{30} - 8 q^{31} - 2 q^{32} + 4 q^{34} + 2 q^{36} + 12 q^{37} + 2 q^{40} + 4 q^{41} + 8 q^{43} - 2 q^{45} + 16 q^{47} + 2 q^{48} + 2 q^{49} - 2 q^{50} - 4 q^{51} + 4 q^{53} - 2 q^{54} + 12 q^{58} + 16 q^{59} - 2 q^{60} + 12 q^{61} + 8 q^{62} + 2 q^{64} - 4 q^{68} - 2 q^{72} + 12 q^{73} - 12 q^{74} + 2 q^{75} - 32 q^{77} + 16 q^{79} - 2 q^{80} + 2 q^{81} - 4 q^{82} - 24 q^{83} + 4 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{89} + 2 q^{90} - 8 q^{93} - 16 q^{94} - 2 q^{96} + 12 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^12 - 2 * q^15 + 2 * q^16 - 4 * q^17 - 2 * q^18 - 2 * q^20 - 2 * q^24 + 2 * q^25 + 2 * q^27 - 12 * q^29 + 2 * q^30 - 8 * q^31 - 2 * q^32 + 4 * q^34 + 2 * q^36 + 12 * q^37 + 2 * q^40 + 4 * q^41 + 8 * q^43 - 2 * q^45 + 16 * q^47 + 2 * q^48 + 2 * q^49 - 2 * q^50 - 4 * q^51 + 4 * q^53 - 2 * q^54 + 12 * q^58 + 16 * q^59 - 2 * q^60 + 12 * q^61 + 8 * q^62 + 2 * q^64 - 4 * q^68 - 2 * q^72 + 12 * q^73 - 12 * q^74 + 2 * q^75 - 32 * q^77 + 16 * q^79 - 2 * q^80 + 2 * q^81 - 4 * q^82 - 24 * q^83 + 4 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^89 + 2 * q^90 - 8 * q^93 - 16 * q^94 - 2 * q^96 + 12 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	2.82843	1.06904	0.534522	−	0.845154i	$-0.320491\pi$
$7$	2.82843	1.06904	0.534522	+	0.845154i	$0.320491\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−5.65685	−1.70561	−0.852803	−	0.522233i	$-0.825099\pi$
$11$	−5.65685	−1.70561	−0.852803	+	0.522233i	$0.825099\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−2.82843	−0.755929
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	0.828427	0.200923	0.100462	−	0.994941i	$-0.467968\pi$
$17$	0.828427	0.200923	0.100462	+	0.994941i	$0.467968\pi$
$18$	−1.00000	−0.235702
$19$	−2.82843	−0.648886	−0.324443	−	0.945905i	$-0.605177\pi$
$19$	−2.82843	−0.648886	−0.324443	+	0.945905i	$0.605177\pi$
$20$	−1.00000	−0.223607
$21$	2.82843	0.617213
$22$	5.65685	1.20605
$23$	−8.48528	−1.76930	−0.884652	−	0.466252i	$-0.845604\pi$
$23$	−8.48528	−1.76930	−0.884652	+	0.466252i	$0.845604\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	0	0
$27$	1.00000	0.192450
$28$	2.82843	0.534522
$29$	−8.82843	−1.63940	−0.819699	−	0.572795i	$-0.805859\pi$
$29$	−8.82843	−1.63940	−0.819699	+	0.572795i	$0.805859\pi$
$30$	1.00000	0.182574
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000	−0.176777
$33$	−5.65685	−0.984732
$34$	−0.828427	−0.142074
$35$	−2.82843	−0.478091
$36$	1.00000	0.166667
$37$	11.6569	1.91638	0.958188	−	0.286141i	$-0.0923726\pi$
$37$	11.6569	1.91638	0.958188	+	0.286141i	$0.0923726\pi$
$38$	2.82843	0.458831
$39$	0	0
$40$	1.00000	0.158114
$41$	7.65685	1.19580	0.597900	−	0.801571i	$-0.296002\pi$
$41$	7.65685	1.19580	0.597900	+	0.801571i	$0.296002\pi$
$42$	−2.82843	−0.436436
$43$	9.65685	1.47266	0.736328	−	0.676625i	$-0.236558\pi$
$43$	9.65685	1.47266	0.736328	+	0.676625i	$0.236558\pi$
$44$	−5.65685	−0.852803
$45$	−1.00000	−0.149071
$46$	8.48528	1.25109
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	0.828427	0.116003
$52$	0	0
$53$	13.3137	1.82878	0.914389	−	0.404836i	$-0.132671\pi$
$53$	13.3137	1.82878	0.914389	+	0.404836i	$0.132671\pi$
$54$	−1.00000	−0.136083
$55$	5.65685	0.762770
$56$	−2.82843	−0.377964
$57$	−2.82843	−0.374634
$58$	8.82843	1.15923
$59$	2.34315	0.305052	0.152526	−	0.988299i	$-0.451259\pi$
$59$	2.34315	0.305052	0.152526	+	0.988299i	$0.451259\pi$
$60$	−1.00000	−0.129099
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	4.00000	0.508001
$63$	2.82843	0.356348
$64$	1.00000	0.125000
$65$	0	0
$66$	5.65685	0.696311
$67$	−5.65685	−0.691095	−0.345547	−	0.938401i	$-0.612307\pi$
$67$	−5.65685	−0.691095	−0.345547	+	0.938401i	$0.612307\pi$
$68$	0.828427	0.100462
$69$	−8.48528	−1.02151
$70$	2.82843	0.338062
$71$	5.65685	0.671345	0.335673	−	0.941979i	$-0.391036\pi$
$71$	5.65685	0.671345	0.335673	+	0.941979i	$0.391036\pi$
$72$	−1.00000	−0.117851
$73$	14.4853	1.69537	0.847687	−	0.530497i	$-0.177995\pi$
$73$	14.4853	1.69537	0.847687	+	0.530497i	$0.177995\pi$
$74$	−11.6569	−1.35508
$75$	1.00000	0.115470
$76$	−2.82843	−0.324443
$77$	−16.0000	−1.82337
$78$	0	0
$79$	2.34315	0.263624	0.131812	−	0.991275i	$-0.457920\pi$
$79$	2.34315	0.263624	0.131812	+	0.991275i	$0.457920\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−7.65685	−0.845558
$83$	−6.34315	−0.696251	−0.348125	−	0.937448i	$-0.613182\pi$
$83$	−6.34315	−0.696251	−0.348125	+	0.937448i	$0.613182\pi$
$84$	2.82843	0.308607
$85$	−0.828427	−0.0898555
$86$	−9.65685	−1.04133
$87$	−8.82843	−0.946507
$88$	5.65685	0.603023
$89$	15.6569	1.65962	0.829812	−	0.558044i	$-0.188448\pi$
$89$	15.6569	1.65962	0.829812	+	0.558044i	$0.188448\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	−8.48528	−0.884652
$93$	−4.00000	−0.414781
$94$	−8.00000	−0.825137
$95$	2.82843	0.290191
$96$	−1.00000	−0.102062
$97$	3.17157	0.322024	0.161012	−	0.986952i	$-0.448524\pi$
$97$	3.17157	0.322024	0.161012	+	0.986952i	$0.448524\pi$
$98$	−1.00000	−0.101015
$99$	−5.65685	−0.568535
$100$	1.00000	0.100000
$101$	16.1421	1.60620	0.803101	−	0.595843i	$-0.203182\pi$
$101$	16.1421	1.60620	0.803101	+	0.595843i	$0.203182\pi$
$102$	−0.828427	−0.0820265
$103$	−1.65685	−0.163255	−0.0816274	−	0.996663i	$-0.526012\pi$
$103$	−1.65685	−0.163255	−0.0816274	+	0.996663i	$0.526012\pi$
$104$	0	0
$105$	−2.82843	−0.276026
$106$	−13.3137	−1.29314
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	1.00000	0.0962250
$109$	−8.82843	−0.845610	−0.422805	−	0.906221i	$-0.638954\pi$
$109$	−8.82843	−0.845610	−0.422805	+	0.906221i	$0.638954\pi$
$110$	−5.65685	−0.539360
$111$	11.6569	1.10642
$112$	2.82843	0.267261
$113$	6.48528	0.610084	0.305042	−	0.952339i	$-0.401330\pi$
$113$	6.48528	0.610084	0.305042	+	0.952339i	$0.401330\pi$
$114$	2.82843	0.264906
$115$	8.48528	0.791257
$116$	−8.82843	−0.819699
$117$	0	0
$118$	−2.34315	−0.215704
$119$	2.34315	0.214796
$120$	1.00000	0.0912871
$121$	21.0000	1.90909
$122$	−6.00000	−0.543214
$123$	7.65685	0.690395
$124$	−4.00000	−0.359211
$125$	−1.00000	−0.0894427
$126$	−2.82843	−0.251976
$127$	9.65685	0.856907	0.428454	−	0.903564i	$-0.359059\pi$
$127$	9.65685	0.856907	0.428454	+	0.903564i	$0.359059\pi$
$128$	−1.00000	−0.0883883
$129$	9.65685	0.850239
$130$	0	0
$131$	−6.14214	−0.536641	−0.268320	−	0.963330i	$-0.586469\pi$
$131$	−6.14214	−0.536641	−0.268320	+	0.963330i	$0.586469\pi$
$132$	−5.65685	−0.492366
$133$	−8.00000	−0.693688
$134$	5.65685	0.488678
$135$	−1.00000	−0.0860663
$136$	−0.828427	−0.0710370
$137$	17.3137	1.47921	0.739605	−	0.673041i	$-0.235012\pi$
$137$	17.3137	1.47921	0.739605	+	0.673041i	$0.235012\pi$
$138$	8.48528	0.722315
$139$	6.34315	0.538019	0.269009	−	0.963138i	$-0.413304\pi$
$139$	6.34315	0.538019	0.269009	+	0.963138i	$0.413304\pi$
$140$	−2.82843	−0.239046
$141$	8.00000	0.673722
$142$	−5.65685	−0.474713
$143$	0	0
$144$	1.00000	0.0833333
$145$	8.82843	0.733161
$146$	−14.4853	−1.19881
$147$	1.00000	0.0824786
$148$	11.6569	0.958188
$149$	−3.65685	−0.299581	−0.149791	−	0.988718i	$-0.547860\pi$
$149$	−3.65685	−0.299581	−0.149791	+	0.988718i	$0.547860\pi$
$150$	−1.00000	−0.0816497
$151$	−12.0000	−0.976546	−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000	−0.976546	−0.488273	+	0.872691i	$0.662373\pi$
$152$	2.82843	0.229416
$153$	0.828427	0.0669744
$154$	16.0000	1.28932
$155$	4.00000	0.321288
$156$	0	0
$157$	5.31371	0.424080	0.212040	−	0.977261i	$-0.431989\pi$
$157$	5.31371	0.424080	0.212040	+	0.977261i	$0.431989\pi$
$158$	−2.34315	−0.186411
$159$	13.3137	1.05585
$160$	1.00000	0.0790569
$161$	−24.0000	−1.89146
$162$	−1.00000	−0.0785674
$163$	−11.3137	−0.886158	−0.443079	−	0.896483i	$-0.646114\pi$
$163$	−11.3137	−0.886158	−0.443079	+	0.896483i	$0.646114\pi$
$164$	7.65685	0.597900
$165$	5.65685	0.440386
$166$	6.34315	0.492324
$167$	−8.97056	−0.694163	−0.347081	−	0.937835i	$-0.612827\pi$
$167$	−8.97056	−0.694163	−0.347081	+	0.937835i	$0.612827\pi$
$168$	−2.82843	−0.218218
$169$	0	0
$170$	0.828427	0.0635375
$171$	−2.82843	−0.216295
$172$	9.65685	0.736328
$173$	−9.31371	−0.708108	−0.354054	−	0.935225i	$-0.615197\pi$
$173$	−9.31371	−0.708108	−0.354054	+	0.935225i	$0.615197\pi$
$174$	8.82843	0.669281
$175$	2.82843	0.213809
$176$	−5.65685	−0.426401
$177$	2.34315	0.176122
$178$	−15.6569	−1.17353
$179$	7.51472	0.561676	0.280838	−	0.959755i	$-0.409388\pi$
$179$	7.51472	0.561676	0.280838	+	0.959755i	$0.409388\pi$
$180$	−1.00000	−0.0745356
$181$	−7.65685	−0.569129	−0.284565	−	0.958657i	$-0.591849\pi$
$181$	−7.65685	−0.569129	−0.284565	+	0.958657i	$0.591849\pi$
$182$	0	0
$183$	6.00000	0.443533
$184$	8.48528	0.625543
$185$	−11.6569	−0.857029
$186$	4.00000	0.293294
$187$	−4.68629	−0.342696
$188$	8.00000	0.583460
$189$	2.82843	0.205738
$190$	−2.82843	−0.205196
$191$	11.3137	0.818631	0.409316	−	0.912393i	$-0.365768\pi$
$191$	11.3137	0.818631	0.409316	+	0.912393i	$0.365768\pi$
$192$	1.00000	0.0721688
$193$	−2.48528	−0.178894	−0.0894472	−	0.995992i	$-0.528510\pi$
$193$	−2.48528	−0.178894	−0.0894472	+	0.995992i	$0.528510\pi$
$194$	−3.17157	−0.227706
$195$	0	0
$196$	1.00000	0.0714286
$197$	13.3137	0.948562	0.474281	−	0.880373i	$-0.342708\pi$
$197$	13.3137	0.948562	0.474281	+	0.880373i	$0.342708\pi$
$198$	5.65685	0.402015
$199$	10.3431	0.733206	0.366603	−	0.930377i	$-0.380521\pi$
$199$	10.3431	0.733206	0.366603	+	0.930377i	$0.380521\pi$
$200$	−1.00000	−0.0707107
$201$	−5.65685	−0.399004
$202$	−16.1421	−1.13576
$203$	−24.9706	−1.75259
$204$	0.828427	0.0580015
$205$	−7.65685	−0.534778
$206$	1.65685	0.115439
$207$	−8.48528	−0.589768
$208$	0	0
$209$	16.0000	1.10674
$210$	2.82843	0.195180
$211$	0.686292	0.0472463	0.0236231	−	0.999721i	$-0.492480\pi$
$211$	0.686292	0.0472463	0.0236231	+	0.999721i	$0.492480\pi$
$212$	13.3137	0.914389
$213$	5.65685	0.387601
$214$	4.00000	0.273434
$215$	−9.65685	−0.658592
$216$	−1.00000	−0.0680414
$217$	−11.3137	−0.768025
$218$	8.82843	0.597937
$219$	14.4853	0.978825
$220$	5.65685	0.381385
$221$	0	0
$222$	−11.6569	−0.782357
$223$	−10.8284	−0.725125	−0.362563	−	0.931959i	$-0.618098\pi$
$223$	−10.8284	−0.725125	−0.362563	+	0.931959i	$0.618098\pi$
$224$	−2.82843	−0.188982
$225$	1.00000	0.0666667
$226$	−6.48528	−0.431394
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	−2.82843	−0.187317
$229$	−4.14214	−0.273720	−0.136860	−	0.990590i	$-0.543701\pi$
$229$	−4.14214	−0.273720	−0.136860	+	0.990590i	$0.543701\pi$
$230$	−8.48528	−0.559503
$231$	−16.0000	−1.05272
$232$	8.82843	0.579615
$233$	5.51472	0.361281	0.180641	−	0.983549i	$-0.442183\pi$
$233$	5.51472	0.361281	0.180641	+	0.983549i	$0.442183\pi$
$234$	0	0
$235$	−8.00000	−0.521862
$236$	2.34315	0.152526
$237$	2.34315	0.152204
$238$	−2.34315	−0.151884
$239$	−16.0000	−1.03495	−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000	−1.03495	−0.517477	+	0.855697i	$0.673129\pi$
$240$	−1.00000	−0.0645497
$241$	−5.31371	−0.342286	−0.171143	−	0.985246i	$-0.554746\pi$
$241$	−5.31371	−0.342286	−0.171143	+	0.985246i	$0.554746\pi$
$242$	−21.0000	−1.34993
$243$	1.00000	0.0641500
$244$	6.00000	0.384111
$245$	−1.00000	−0.0638877
$246$	−7.65685	−0.488183
$247$	0	0
$248$	4.00000	0.254000
$249$	−6.34315	−0.401981
$250$	1.00000	0.0632456
$251$	10.8284	0.683484	0.341742	−	0.939794i	$-0.388983\pi$
$251$	10.8284	0.683484	0.341742	+	0.939794i	$0.388983\pi$
$252$	2.82843	0.178174
$253$	48.0000	3.01773
$254$	−9.65685	−0.605925
$255$	−0.828427	−0.0518781
$256$	1.00000	0.0625000
$257$	−4.82843	−0.301189	−0.150595	−	0.988596i	$-0.548119\pi$
$257$	−4.82843	−0.301189	−0.150595	+	0.988596i	$0.548119\pi$
$258$	−9.65685	−0.601209
$259$	32.9706	2.04869
$260$	0	0
$261$	−8.82843	−0.546466
$262$	6.14214	0.379462
$263$	16.4853	1.01653	0.508263	−	0.861202i	$-0.330288\pi$
$263$	16.4853	1.01653	0.508263	+	0.861202i	$0.330288\pi$
$264$	5.65685	0.348155
$265$	−13.3137	−0.817855
$266$	8.00000	0.490511
$267$	15.6569	0.958184
$268$	−5.65685	−0.345547
$269$	−14.4853	−0.883183	−0.441592	−	0.897216i	$-0.645586\pi$
$269$	−14.4853	−0.883183	−0.441592	+	0.897216i	$0.645586\pi$
$270$	1.00000	0.0608581
$271$	−7.31371	−0.444276	−0.222138	−	0.975015i	$-0.571304\pi$
$271$	−7.31371	−0.444276	−0.222138	+	0.975015i	$0.571304\pi$
$272$	0.828427	0.0502308
$273$	0	0
$274$	−17.3137	−1.04596
$275$	−5.65685	−0.341121
$276$	−8.48528	−0.510754
$277$	26.0000	1.56219	0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000	1.56219	0.781094	+	0.624413i	$0.214662\pi$
$278$	−6.34315	−0.380437
$279$	−4.00000	−0.239474
$280$	2.82843	0.169031
$281$	−8.34315	−0.497710	−0.248855	−	0.968541i	$-0.580054\pi$
$281$	−8.34315	−0.497710	−0.248855	+	0.968541i	$0.580054\pi$
$282$	−8.00000	−0.476393
$283$	−17.6569	−1.04959	−0.524796	−	0.851228i	$-0.675858\pi$
$283$	−17.6569	−1.04959	−0.524796	+	0.851228i	$0.675858\pi$
$284$	5.65685	0.335673
$285$	2.82843	0.167542
$286$	0	0
$287$	21.6569	1.27836
$288$	−1.00000	−0.0589256
$289$	−16.3137	−0.959630
$290$	−8.82843	−0.518423
$291$	3.17157	0.185921
$292$	14.4853	0.847687
$293$	16.6274	0.971384	0.485692	−	0.874130i	$-0.338568\pi$
$293$	16.6274	0.971384	0.485692	+	0.874130i	$0.338568\pi$
$294$	−1.00000	−0.0583212
$295$	−2.34315	−0.136423
$296$	−11.6569	−0.677541
$297$	−5.65685	−0.328244
$298$	3.65685	0.211836
$299$	0	0
$300$	1.00000	0.0577350
$301$	27.3137	1.57434
$302$	12.0000	0.690522
$303$	16.1421	0.927341
$304$	−2.82843	−0.162221
$305$	−6.00000	−0.343559
$306$	−0.828427	−0.0473580
$307$	21.6569	1.23602	0.618011	−	0.786169i	$-0.287939\pi$
$307$	21.6569	1.23602	0.618011	+	0.786169i	$0.287939\pi$
$308$	−16.0000	−0.911685
$309$	−1.65685	−0.0942551
$310$	−4.00000	−0.227185
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	0	0
$313$	−30.9706	−1.75056	−0.875280	−	0.483617i	$-0.839323\pi$
$313$	−30.9706	−1.75056	−0.875280	+	0.483617i	$0.839323\pi$
$314$	−5.31371	−0.299870
$315$	−2.82843	−0.159364
$316$	2.34315	0.131812
$317$	−25.3137	−1.42176	−0.710880	−	0.703314i	$-0.751703\pi$
$317$	−25.3137	−1.42176	−0.710880	+	0.703314i	$0.751703\pi$
$318$	−13.3137	−0.746596
$319$	49.9411	2.79617
$320$	−1.00000	−0.0559017
$321$	−4.00000	−0.223258
$322$	24.0000	1.33747
$323$	−2.34315	−0.130376
$324$	1.00000	0.0555556
$325$	0	0
$326$	11.3137	0.626608
$327$	−8.82843	−0.488213
$328$	−7.65685	−0.422779
$329$	22.6274	1.24749
$330$	−5.65685	−0.311400
$331$	8.48528	0.466393	0.233197	−	0.972430i	$-0.425081\pi$
$331$	8.48528	0.466393	0.233197	+	0.972430i	$0.425081\pi$
$332$	−6.34315	−0.348125
$333$	11.6569	0.638792
$334$	8.97056	0.490847
$335$	5.65685	0.309067
$336$	2.82843	0.154303
$337$	10.9706	0.597605	0.298802	−	0.954315i	$-0.403413\pi$
$337$	10.9706	0.597605	0.298802	+	0.954315i	$0.403413\pi$
$338$	0	0
$339$	6.48528	0.352232
$340$	−0.828427	−0.0449278
$341$	22.6274	1.22534
$342$	2.82843	0.152944
$343$	−16.9706	−0.916324
$344$	−9.65685	−0.520663
$345$	8.48528	0.456832
$346$	9.31371	0.500708
$347$	−9.65685	−0.518407	−0.259204	−	0.965823i	$-0.583460\pi$
$347$	−9.65685	−0.518407	−0.259204	+	0.965823i	$0.583460\pi$
$348$	−8.82843	−0.473253
$349$	−12.1421	−0.649954	−0.324977	−	0.945722i	$-0.605356\pi$
$349$	−12.1421	−0.649954	−0.324977	+	0.945722i	$0.605356\pi$
$350$	−2.82843	−0.151186
$351$	0	0
$352$	5.65685	0.301511
$353$	−5.31371	−0.282820	−0.141410	−	0.989951i	$-0.545164\pi$
$353$	−5.31371	−0.282820	−0.141410	+	0.989951i	$0.545164\pi$
$354$	−2.34315	−0.124537
$355$	−5.65685	−0.300235
$356$	15.6569	0.829812
$357$	2.34315	0.124012
$358$	−7.51472	−0.397165
$359$	28.2843	1.49279	0.746393	−	0.665505i	$-0.231784\pi$
$359$	28.2843	1.49279	0.746393	+	0.665505i	$0.231784\pi$
$360$	1.00000	0.0527046
$361$	−11.0000	−0.578947
$362$	7.65685	0.402435
$363$	21.0000	1.10221
$364$	0	0
$365$	−14.4853	−0.758194
$366$	−6.00000	−0.313625
$367$	25.6569	1.33928	0.669638	−	0.742687i	$-0.266449\pi$
$367$	25.6569	1.33928	0.669638	+	0.742687i	$0.266449\pi$
$368$	−8.48528	−0.442326
$369$	7.65685	0.398600
$370$	11.6569	0.606011
$371$	37.6569	1.95505
$372$	−4.00000	−0.207390
$373$	−2.68629	−0.139091	−0.0695455	−	0.997579i	$-0.522155\pi$
$373$	−2.68629	−0.139091	−0.0695455	+	0.997579i	$0.522155\pi$
$374$	4.68629	0.242322
$375$	−1.00000	−0.0516398
$376$	−8.00000	−0.412568
$377$	0	0
$378$	−2.82843	−0.145479
$379$	7.51472	0.386005	0.193003	−	0.981198i	$-0.438177\pi$
$379$	7.51472	0.386005	0.193003	+	0.981198i	$0.438177\pi$
$380$	2.82843	0.145095
$381$	9.65685	0.494736
$382$	−11.3137	−0.578860
$383$	29.6569	1.51539	0.757697	−	0.652606i	$-0.226324\pi$
$383$	29.6569	1.51539	0.757697	+	0.652606i	$0.226324\pi$
$384$	−1.00000	−0.0510310
$385$	16.0000	0.815436
$386$	2.48528	0.126497
$387$	9.65685	0.490885
$388$	3.17157	0.161012
$389$	−6.48528	−0.328817	−0.164408	−	0.986392i	$-0.552571\pi$
$389$	−6.48528	−0.328817	−0.164408	+	0.986392i	$0.552571\pi$
$390$	0	0
$391$	−7.02944	−0.355494
$392$	−1.00000	−0.0505076
$393$	−6.14214	−0.309830
$394$	−13.3137	−0.670735
$395$	−2.34315	−0.117896
$396$	−5.65685	−0.284268
$397$	−30.2843	−1.51992	−0.759962	−	0.649968i	$-0.774782\pi$
$397$	−30.2843	−1.51992	−0.759962	+	0.649968i	$0.774782\pi$
$398$	−10.3431	−0.518455
$399$	−8.00000	−0.400501
$400$	1.00000	0.0500000
$401$	26.9706	1.34685	0.673423	−	0.739258i	$-0.264823\pi$
$401$	26.9706	1.34685	0.673423	+	0.739258i	$0.264823\pi$
$402$	5.65685	0.282138
$403$	0	0
$404$	16.1421	0.803101
$405$	−1.00000	−0.0496904
$406$	24.9706	1.23927
$407$	−65.9411	−3.26858
$408$	−0.828427	−0.0410133
$409$	3.65685	0.180820	0.0904099	−	0.995905i	$-0.471182\pi$
$409$	3.65685	0.180820	0.0904099	+	0.995905i	$0.471182\pi$
$410$	7.65685	0.378145
$411$	17.3137	0.854022
$412$	−1.65685	−0.0816274
$413$	6.62742	0.326114
$414$	8.48528	0.417029
$415$	6.34315	0.311373
$416$	0	0
$417$	6.34315	0.310625
$418$	−16.0000	−0.782586
$419$	−10.8284	−0.529003	−0.264502	−	0.964385i	$-0.585207\pi$
$419$	−10.8284	−0.529003	−0.264502	+	0.964385i	$0.585207\pi$
$420$	−2.82843	−0.138013
$421$	24.1421	1.17662	0.588308	−	0.808637i	$-0.299794\pi$
$421$	24.1421	1.17662	0.588308	+	0.808637i	$0.299794\pi$
$422$	−0.686292	−0.0334081
$423$	8.00000	0.388973
$424$	−13.3137	−0.646571
$425$	0.828427	0.0401846
$426$	−5.65685	−0.274075
$427$	16.9706	0.821263
$428$	−4.00000	−0.193347
$429$	0	0
$430$	9.65685	0.465695
$431$	16.0000	0.770693	0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000	0.770693	0.385346	+	0.922772i	$0.374082\pi$
$432$	1.00000	0.0481125
$433$	−22.9706	−1.10389	−0.551947	−	0.833879i	$-0.686115\pi$
$433$	−22.9706	−1.10389	−0.551947	+	0.833879i	$0.686115\pi$
$434$	11.3137	0.543075
$435$	8.82843	0.423291
$436$	−8.82843	−0.422805
$437$	24.0000	1.14808
$438$	−14.4853	−0.692134
$439$	22.6274	1.07995	0.539974	−	0.841682i	$-0.318434\pi$
$439$	22.6274	1.07995	0.539974	+	0.841682i	$0.318434\pi$
$440$	−5.65685	−0.269680
$441$	1.00000	0.0476190
$442$	0	0
$443$	30.3431	1.44165	0.720823	−	0.693119i	$-0.243764\pi$
$443$	30.3431	1.44165	0.720823	+	0.693119i	$0.243764\pi$
$444$	11.6569	0.553210
$445$	−15.6569	−0.742206
$446$	10.8284	0.512741
$447$	−3.65685	−0.172963
$448$	2.82843	0.133631
$449$	−26.2843	−1.24043	−0.620216	−	0.784431i	$-0.712955\pi$
$449$	−26.2843	−1.24043	−0.620216	+	0.784431i	$0.712955\pi$
$450$	−1.00000	−0.0471405
$451$	−43.3137	−2.03956
$452$	6.48528	0.305042
$453$	−12.0000	−0.563809
$454$	4.00000	0.187729
$455$	0	0
$456$	2.82843	0.132453
$457$	−20.8284	−0.974313	−0.487156	−	0.873315i	$-0.661966\pi$
$457$	−20.8284	−0.974313	−0.487156	+	0.873315i	$0.661966\pi$
$458$	4.14214	0.193549
$459$	0.828427	0.0386677
$460$	8.48528	0.395628
$461$	−14.0000	−0.652045	−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000	−0.652045	−0.326023	+	0.945362i	$0.605709\pi$
$462$	16.0000	0.744387
$463$	3.79899	0.176554	0.0882770	−	0.996096i	$-0.471864\pi$
$463$	3.79899	0.176554	0.0882770	+	0.996096i	$0.471864\pi$
$464$	−8.82843	−0.409849
$465$	4.00000	0.185496
$466$	−5.51472	−0.255464
$467$	7.31371	0.338438	0.169219	−	0.985578i	$-0.445875\pi$
$467$	7.31371	0.338438	0.169219	+	0.985578i	$0.445875\pi$
$468$	0	0
$469$	−16.0000	−0.738811
$470$	8.00000	0.369012
$471$	5.31371	0.244843
$472$	−2.34315	−0.107852
$473$	−54.6274	−2.51177
$474$	−2.34315	−0.107624
$475$	−2.82843	−0.129777
$476$	2.34315	0.107398
$477$	13.3137	0.609593
$478$	16.0000	0.731823
$479$	11.3137	0.516937	0.258468	−	0.966020i	$-0.416782\pi$
$479$	11.3137	0.516937	0.258468	+	0.966020i	$0.416782\pi$
$480$	1.00000	0.0456435
$481$	0	0
$482$	5.31371	0.242033
$483$	−24.0000	−1.09204
$484$	21.0000	0.954545
$485$	−3.17157	−0.144014
$486$	−1.00000	−0.0453609
$487$	−16.4853	−0.747019	−0.373510	−	0.927626i	$-0.621846\pi$
$487$	−16.4853	−0.747019	−0.373510	+	0.927626i	$0.621846\pi$
$488$	−6.00000	−0.271607
$489$	−11.3137	−0.511624
$490$	1.00000	0.0451754
$491$	−38.1421	−1.72133	−0.860665	−	0.509171i	$-0.829952\pi$
$491$	−38.1421	−1.72133	−0.860665	+	0.509171i	$0.829952\pi$
$492$	7.65685	0.345198
$493$	−7.31371	−0.329393
$494$	0	0
$495$	5.65685	0.254257
$496$	−4.00000	−0.179605
$497$	16.0000	0.717698
$498$	6.34315	0.284243
$499$	−0.485281	−0.0217242	−0.0108621	−	0.999941i	$-0.503458\pi$
$499$	−0.485281	−0.0217242	−0.0108621	+	0.999941i	$0.503458\pi$
$500$	−1.00000	−0.0447214
$501$	−8.97056	−0.400775
$502$	−10.8284	−0.483296
$503$	−23.5147	−1.04847	−0.524235	−	0.851574i	$-0.675649\pi$
$503$	−23.5147	−1.04847	−0.524235	+	0.851574i	$0.675649\pi$
$504$	−2.82843	−0.125988
$505$	−16.1421	−0.718316
$506$	−48.0000	−2.13386
$507$	0	0
$508$	9.65685	0.428454
$509$	37.3137	1.65390	0.826951	−	0.562275i	$-0.190074\pi$
$509$	37.3137	1.65390	0.826951	+	0.562275i	$0.190074\pi$
$510$	0.828427	0.0366834
$511$	40.9706	1.81243
$512$	−1.00000	−0.0441942
$513$	−2.82843	−0.124878
$514$	4.82843	0.212973
$515$	1.65685	0.0730097
$516$	9.65685	0.425119
$517$	−45.2548	−1.99031
$518$	−32.9706	−1.44864
$519$	−9.31371	−0.408826
$520$	0	0
$521$	26.9706	1.18160	0.590801	−	0.806817i	$-0.298812\pi$
$521$	26.9706	1.18160	0.590801	+	0.806817i	$0.298812\pi$
$522$	8.82843	0.386410
$523$	−10.6274	−0.464704	−0.232352	−	0.972632i	$-0.574642\pi$
$523$	−10.6274	−0.464704	−0.232352	+	0.972632i	$0.574642\pi$
$524$	−6.14214	−0.268320
$525$	2.82843	0.123443
$526$	−16.4853	−0.718792
$527$	−3.31371	−0.144347
$528$	−5.65685	−0.246183
$529$	49.0000	2.13043
$530$	13.3137	0.578311
$531$	2.34315	0.101684
$532$	−8.00000	−0.346844
$533$	0	0
$534$	−15.6569	−0.677538
$535$	4.00000	0.172935
$536$	5.65685	0.244339
$537$	7.51472	0.324284
$538$	14.4853	0.624505
$539$	−5.65685	−0.243658
$540$	−1.00000	−0.0430331
$541$	−14.4853	−0.622771	−0.311385	−	0.950284i	$-0.600793\pi$
$541$	−14.4853	−0.622771	−0.311385	+	0.950284i	$0.600793\pi$
$542$	7.31371	0.314151
$543$	−7.65685	−0.328587
$544$	−0.828427	−0.0355185
$545$	8.82843	0.378168
$546$	0	0
$547$	0.686292	0.0293437	0.0146719	−	0.999892i	$-0.495330\pi$
$547$	0.686292	0.0293437	0.0146719	+	0.999892i	$0.495330\pi$
$548$	17.3137	0.739605
$549$	6.00000	0.256074
$550$	5.65685	0.241209
$551$	24.9706	1.06378
$552$	8.48528	0.361158
$553$	6.62742	0.281826
$554$	−26.0000	−1.10463
$555$	−11.6569	−0.494806
$556$	6.34315	0.269009
$557$	−10.6863	−0.452793	−0.226396	−	0.974035i	$-0.572694\pi$
$557$	−10.6863	−0.452793	−0.226396	+	0.974035i	$0.572694\pi$
$558$	4.00000	0.169334
$559$	0	0
$560$	−2.82843	−0.119523
$561$	−4.68629	−0.197855
$562$	8.34315	0.351934
$563$	−30.3431	−1.27881	−0.639406	−	0.768870i	$-0.720819\pi$
$563$	−30.3431	−1.27881	−0.639406	+	0.768870i	$0.720819\pi$
$564$	8.00000	0.336861
$565$	−6.48528	−0.272838
$566$	17.6569	0.742173
$567$	2.82843	0.118783
$568$	−5.65685	−0.237356
$569$	31.6569	1.32712	0.663562	−	0.748121i	$-0.269044\pi$
$569$	31.6569	1.32712	0.663562	+	0.748121i	$0.269044\pi$
$570$	−2.82843	−0.118470
$571$	20.9706	0.877591	0.438795	−	0.898587i	$-0.355405\pi$
$571$	20.9706	0.877591	0.438795	+	0.898587i	$0.355405\pi$
$572$	0	0
$573$	11.3137	0.472637
$574$	−21.6569	−0.903940
$575$	−8.48528	−0.353861
$576$	1.00000	0.0416667
$577$	23.4558	0.976480	0.488240	−	0.872710i	$-0.337639\pi$
$577$	23.4558	0.976480	0.488240	+	0.872710i	$0.337639\pi$
$578$	16.3137	0.678561
$579$	−2.48528	−0.103285
$580$	8.82843	0.366580
$581$	−17.9411	−0.744323
$582$	−3.17157	−0.131466
$583$	−75.3137	−3.11918
$584$	−14.4853	−0.599405
$585$	0	0
$586$	−16.6274	−0.686872
$587$	−2.62742	−0.108445	−0.0542226	−	0.998529i	$-0.517268\pi$
$587$	−2.62742	−0.108445	−0.0542226	+	0.998529i	$0.517268\pi$
$588$	1.00000	0.0412393
$589$	11.3137	0.466173
$590$	2.34315	0.0964658
$591$	13.3137	0.547653
$592$	11.6569	0.479094
$593$	0.343146	0.0140913	0.00704565	−	0.999975i	$-0.497757\pi$
$593$	0.343146	0.0140913	0.00704565	+	0.999975i	$0.497757\pi$
$594$	5.65685	0.232104
$595$	−2.34315	−0.0960596
$596$	−3.65685	−0.149791
$597$	10.3431	0.423317
$598$	0	0
$599$	40.0000	1.63436	0.817178	−	0.576386i	$-0.195537\pi$
$599$	40.0000	1.63436	0.817178	+	0.576386i	$0.195537\pi$
$600$	−1.00000	−0.0408248
$601$	29.3137	1.19573	0.597866	−	0.801596i	$-0.296016\pi$
$601$	29.3137	1.19573	0.597866	+	0.801596i	$0.296016\pi$
$602$	−27.3137	−1.11322
$603$	−5.65685	−0.230365
$604$	−12.0000	−0.488273
$605$	−21.0000	−0.853771
$606$	−16.1421	−0.655729
$607$	28.9706	1.17588	0.587939	−	0.808905i	$-0.299939\pi$
$607$	28.9706	1.17588	0.587939	+	0.808905i	$0.299939\pi$
$608$	2.82843	0.114708
$609$	−24.9706	−1.01186
$610$	6.00000	0.242933
$611$	0	0
$612$	0.828427	0.0334872
$613$	−22.2843	−0.900053	−0.450027	−	0.893015i	$-0.648586\pi$
$613$	−22.2843	−0.900053	−0.450027	+	0.893015i	$0.648586\pi$
$614$	−21.6569	−0.874000
$615$	−7.65685	−0.308754
$616$	16.0000	0.644658
$617$	−2.00000	−0.0805170	−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000	−0.0805170	−0.0402585	+	0.999189i	$0.512818\pi$
$618$	1.65685	0.0666485
$619$	34.8284	1.39987	0.699936	−	0.714205i	$-0.253212\pi$
$619$	34.8284	1.39987	0.699936	+	0.714205i	$0.253212\pi$
$620$	4.00000	0.160644
$621$	−8.48528	−0.340503
$622$	24.0000	0.962312
$623$	44.2843	1.77421
$624$	0	0
$625$	1.00000	0.0400000
$626$	30.9706	1.23783
$627$	16.0000	0.638978
$628$	5.31371	0.212040
$629$	9.65685	0.385044
$630$	2.82843	0.112687
$631$	33.6569	1.33986	0.669929	−	0.742425i	$-0.266324\pi$
$631$	33.6569	1.33986	0.669929	+	0.742425i	$0.266324\pi$
$632$	−2.34315	−0.0932053
$633$	0.686292	0.0272776
$634$	25.3137	1.00534
$635$	−9.65685	−0.383221
$636$	13.3137	0.527923
$637$	0	0
$638$	−49.9411	−1.97719
$639$	5.65685	0.223782
$640$	1.00000	0.0395285
$641$	−4.62742	−0.182772	−0.0913860	−	0.995816i	$-0.529130\pi$
$641$	−4.62742	−0.182772	−0.0913860	+	0.995816i	$0.529130\pi$
$642$	4.00000	0.157867
$643$	−39.5980	−1.56159	−0.780796	−	0.624786i	$-0.785186\pi$
$643$	−39.5980	−1.56159	−0.780796	+	0.624786i	$0.785186\pi$
$644$	−24.0000	−0.945732
$645$	−9.65685	−0.380238
$646$	2.34315	0.0921898
$647$	8.48528	0.333591	0.166795	−	0.985992i	$-0.446658\pi$
$647$	8.48528	0.333591	0.166795	+	0.985992i	$0.446658\pi$
$648$	−1.00000	−0.0392837
$649$	−13.2548	−0.520298
$650$	0	0
$651$	−11.3137	−0.443419
$652$	−11.3137	−0.443079
$653$	−42.2843	−1.65471	−0.827356	−	0.561678i	$-0.810156\pi$
$653$	−42.2843	−1.65471	−0.827356	+	0.561678i	$0.810156\pi$
$654$	8.82843	0.345219
$655$	6.14214	0.239993
$656$	7.65685	0.298950
$657$	14.4853	0.565125
$658$	−22.6274	−0.882109
$659$	−7.51472	−0.292732	−0.146366	−	0.989231i	$-0.546758\pi$
$659$	−7.51472	−0.292732	−0.146366	+	0.989231i	$0.546758\pi$
$660$	5.65685	0.220193
$661$	8.14214	0.316692	0.158346	−	0.987384i	$-0.449384\pi$
$661$	8.14214	0.316692	0.158346	+	0.987384i	$0.449384\pi$
$662$	−8.48528	−0.329790
$663$	0	0
$664$	6.34315	0.246162
$665$	8.00000	0.310227
$666$	−11.6569	−0.451694
$667$	74.9117	2.90059
$668$	−8.97056	−0.347081
$669$	−10.8284	−0.418651
$670$	−5.65685	−0.218543
$671$	−33.9411	−1.31028
$672$	−2.82843	−0.109109
$673$	32.6274	1.25769	0.628847	−	0.777529i	$-0.283527\pi$
$673$	32.6274	1.25769	0.628847	+	0.777529i	$0.283527\pi$
$674$	−10.9706	−0.422570
$675$	1.00000	0.0384900
$676$	0	0
$677$	12.3431	0.474386	0.237193	−	0.971463i	$-0.423773\pi$
$677$	12.3431	0.474386	0.237193	+	0.971463i	$0.423773\pi$
$678$	−6.48528	−0.249066
$679$	8.97056	0.344259
$680$	0.828427	0.0317687
$681$	−4.00000	−0.153280
$682$	−22.6274	−0.866449
$683$	−33.6569	−1.28784	−0.643922	−	0.765091i	$-0.722694\pi$
$683$	−33.6569	−1.28784	−0.643922	+	0.765091i	$0.722694\pi$
$684$	−2.82843	−0.108148
$685$	−17.3137	−0.661523
$686$	16.9706	0.647939
$687$	−4.14214	−0.158032
$688$	9.65685	0.368164
$689$	0	0
$690$	−8.48528	−0.323029
$691$	27.7990	1.05752	0.528762	−	0.848770i	$-0.322657\pi$
$691$	27.7990	1.05752	0.528762	+	0.848770i	$0.322657\pi$
$692$	−9.31371	−0.354054
$693$	−16.0000	−0.607790
$694$	9.65685	0.366569
$695$	−6.34315	−0.240609
$696$	8.82843	0.334641
$697$	6.34315	0.240264
$698$	12.1421	0.459587
$699$	5.51472	0.208586
$700$	2.82843	0.106904
$701$	0.142136	0.00536839	0.00268419	−	0.999996i	$-0.499146\pi$
$701$	0.142136	0.00536839	0.00268419	+	0.999996i	$0.499146\pi$
$702$	0	0
$703$	−32.9706	−1.24351
$704$	−5.65685	−0.213201
$705$	−8.00000	−0.301297
$706$	5.31371	0.199984
$707$	45.6569	1.71710
$708$	2.34315	0.0880608
$709$	7.17157	0.269334	0.134667	−	0.990891i	$-0.457004\pi$
$709$	7.17157	0.269334	0.134667	+	0.990891i	$0.457004\pi$
$710$	5.65685	0.212298
$711$	2.34315	0.0878748
$712$	−15.6569	−0.586765
$713$	33.9411	1.27111
$714$	−2.34315	−0.0876900
$715$	0	0
$716$	7.51472	0.280838
$717$	−16.0000	−0.597531
$718$	−28.2843	−1.05556
$719$	−29.6569	−1.10601	−0.553007	−	0.833177i	$-0.686520\pi$
$719$	−29.6569	−1.10601	−0.553007	+	0.833177i	$0.686520\pi$
$720$	−1.00000	−0.0372678
$721$	−4.68629	−0.174527
$722$	11.0000	0.409378
$723$	−5.31371	−0.197619
$724$	−7.65685	−0.284565
$725$	−8.82843	−0.327880
$726$	−21.0000	−0.779383
$727$	−45.9411	−1.70386	−0.851931	−	0.523654i	$-0.824568\pi$
$727$	−45.9411	−1.70386	−0.851931	+	0.523654i	$0.824568\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	14.4853	0.536124
$731$	8.00000	0.295891
$732$	6.00000	0.221766
$733$	0.343146	0.0126744	0.00633719	−	0.999980i	$-0.497983\pi$
$733$	0.343146	0.0126744	0.00633719	+	0.999980i	$0.497983\pi$
$734$	−25.6569	−0.947012
$735$	−1.00000	−0.0368856
$736$	8.48528	0.312772
$737$	32.0000	1.17874
$738$	−7.65685	−0.281853
$739$	14.1421	0.520227	0.260113	−	0.965578i	$-0.416240\pi$
$739$	14.1421	0.520227	0.260113	+	0.965578i	$0.416240\pi$
$740$	−11.6569	−0.428514
$741$	0	0
$742$	−37.6569	−1.38243
$743$	36.2843	1.33114	0.665570	−	0.746335i	$-0.268188\pi$
$743$	36.2843	1.33114	0.665570	+	0.746335i	$0.268188\pi$
$744$	4.00000	0.146647
$745$	3.65685	0.133977
$746$	2.68629	0.0983521
$747$	−6.34315	−0.232084
$748$	−4.68629	−0.171348
$749$	−11.3137	−0.413394
$750$	1.00000	0.0365148
$751$	11.3137	0.412843	0.206422	−	0.978463i	$-0.433818\pi$
$751$	11.3137	0.412843	0.206422	+	0.978463i	$0.433818\pi$
$752$	8.00000	0.291730
$753$	10.8284	0.394610
$754$	0	0
$755$	12.0000	0.436725
$756$	2.82843	0.102869
$757$	19.9411	0.724773	0.362386	−	0.932028i	$-0.381962\pi$
$757$	19.9411	0.724773	0.362386	+	0.932028i	$0.381962\pi$
$758$	−7.51472	−0.272947
$759$	48.0000	1.74229
$760$	−2.82843	−0.102598
$761$	−27.6569	−1.00256	−0.501280	−	0.865285i	$-0.667137\pi$
$761$	−27.6569	−1.00256	−0.501280	+	0.865285i	$0.667137\pi$
$762$	−9.65685	−0.349831
$763$	−24.9706	−0.903995
$764$	11.3137	0.409316
$765$	−0.828427	−0.0299518
$766$	−29.6569	−1.07155
$767$	0	0
$768$	1.00000	0.0360844
$769$	14.0000	0.504853	0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000	0.504853	0.252426	+	0.967616i	$0.418771\pi$
$770$	−16.0000	−0.576600
$771$	−4.82843	−0.173892
$772$	−2.48528	−0.0894472
$773$	53.3137	1.91756	0.958780	−	0.284148i	$-0.0917107\pi$
$773$	53.3137	1.91756	0.958780	+	0.284148i	$0.0917107\pi$
$774$	−9.65685	−0.347108
$775$	−4.00000	−0.143684
$776$	−3.17157	−0.113853
$777$	32.9706	1.18281
$778$	6.48528	0.232509
$779$	−21.6569	−0.775937
$780$	0	0
$781$	−32.0000	−1.14505
$782$	7.02944	0.251372
$783$	−8.82843	−0.315502
$784$	1.00000	0.0357143
$785$	−5.31371	−0.189654
$786$	6.14214	0.219083
$787$	24.0000	0.855508	0.427754	−	0.903895i	$-0.359305\pi$
$787$	24.0000	0.855508	0.427754	+	0.903895i	$0.359305\pi$
$788$	13.3137	0.474281
$789$	16.4853	0.586892
$790$	2.34315	0.0833654
$791$	18.3431	0.652207
$792$	5.65685	0.201008
$793$	0	0
$794$	30.2843	1.07475
$795$	−13.3137	−0.472189
$796$	10.3431	0.366603
$797$	16.6274	0.588973	0.294487	−	0.955656i	$-0.404851\pi$
$797$	16.6274	0.588973	0.294487	+	0.955656i	$0.404851\pi$
$798$	8.00000	0.283197
$799$	6.62742	0.234461
$800$	−1.00000	−0.0353553
$801$	15.6569	0.553208
$802$	−26.9706	−0.952364
$803$	−81.9411	−2.89164
$804$	−5.65685	−0.199502
$805$	24.0000	0.845889
$806$	0	0
$807$	−14.4853	−0.509906
$808$	−16.1421	−0.567878
$809$	13.3137	0.468085	0.234043	−	0.972226i	$-0.424804\pi$
$809$	13.3137	0.468085	0.234043	+	0.972226i	$0.424804\pi$
$810$	1.00000	0.0351364
$811$	1.85786	0.0652384	0.0326192	−	0.999468i	$-0.489615\pi$
$811$	1.85786	0.0652384	0.0326192	+	0.999468i	$0.489615\pi$
$812$	−24.9706	−0.876295
$813$	−7.31371	−0.256503
$814$	65.9411	2.31124
$815$	11.3137	0.396302
$816$	0.828427	0.0290008
$817$	−27.3137	−0.955586
$818$	−3.65685	−0.127859
$819$	0	0
$820$	−7.65685	−0.267389
$821$	−34.2843	−1.19653	−0.598265	−	0.801299i	$-0.704143\pi$
$821$	−34.2843	−1.19653	−0.598265	+	0.801299i	$0.704143\pi$
$822$	−17.3137	−0.603885
$823$	−52.9706	−1.84644	−0.923219	−	0.384275i	$-0.874452\pi$
$823$	−52.9706	−1.84644	−0.923219	+	0.384275i	$0.874452\pi$
$824$	1.65685	0.0577193
$825$	−5.65685	−0.196946
$826$	−6.62742	−0.230597
$827$	−9.65685	−0.335802	−0.167901	−	0.985804i	$-0.553699\pi$
$827$	−9.65685	−0.335802	−0.167901	+	0.985804i	$0.553699\pi$
$828$	−8.48528	−0.294884
$829$	−53.3137	−1.85166	−0.925831	−	0.377938i	$-0.876633\pi$
$829$	−53.3137	−1.85166	−0.925831	+	0.377938i	$0.876633\pi$
$830$	−6.34315	−0.220174
$831$	26.0000	0.901930
$832$	0	0
$833$	0.828427	0.0287033
$834$	−6.34315	−0.219645
$835$	8.97056	0.310439
$836$	16.0000	0.553372
$837$	−4.00000	−0.138260
$838$	10.8284	0.374062
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	2.82843	0.0975900
$841$	48.9411	1.68763
$842$	−24.1421	−0.831993
$843$	−8.34315	−0.287353
$844$	0.686292	0.0236231
$845$	0	0
$846$	−8.00000	−0.275046
$847$	59.3970	2.04090
$848$	13.3137	0.457195
$849$	−17.6569	−0.605982
$850$	−0.828427	−0.0284148
$851$	−98.9117	−3.39065
$852$	5.65685	0.193801
$853$	−38.2843	−1.31083	−0.655414	−	0.755270i	$-0.727506\pi$
$853$	−38.2843	−1.31083	−0.655414	+	0.755270i	$0.727506\pi$
$854$	−16.9706	−0.580721
$855$	2.82843	0.0967302
$856$	4.00000	0.136717
$857$	−20.8284	−0.711486	−0.355743	−	0.934584i	$-0.615772\pi$
$857$	−20.8284	−0.711486	−0.355743	+	0.934584i	$0.615772\pi$
$858$	0	0
$859$	37.9411	1.29453	0.647267	−	0.762263i	$-0.275912\pi$
$859$	37.9411	1.29453	0.647267	+	0.762263i	$0.275912\pi$
$860$	−9.65685	−0.329296
$861$	21.6569	0.738064
$862$	−16.0000	−0.544962
$863$	28.2843	0.962808	0.481404	−	0.876499i	$-0.340127\pi$
$863$	28.2843	0.962808	0.481404	+	0.876499i	$0.340127\pi$
$864$	−1.00000	−0.0340207
$865$	9.31371	0.316676
$866$	22.9706	0.780571
$867$	−16.3137	−0.554043
$868$	−11.3137	−0.384012
$869$	−13.2548	−0.449639
$870$	−8.82843	−0.299312
$871$	0	0
$872$	8.82843	0.298968
$873$	3.17157	0.107341
$874$	−24.0000	−0.811812
$875$	−2.82843	−0.0956183
$876$	14.4853	0.489412
$877$	51.2548	1.73075	0.865376	−	0.501122i	$-0.167079\pi$
$877$	51.2548	1.73075	0.865376	+	0.501122i	$0.167079\pi$
$878$	−22.6274	−0.763638
$879$	16.6274	0.560829
$880$	5.65685	0.190693
$881$	−10.2843	−0.346486	−0.173243	−	0.984879i	$-0.555425\pi$
$881$	−10.2843	−0.346486	−0.173243	+	0.984879i	$0.555425\pi$
$882$	−1.00000	−0.0336718
$883$	31.3137	1.05379	0.526895	−	0.849930i	$-0.323356\pi$
$883$	31.3137	1.05379	0.526895	+	0.849930i	$0.323356\pi$
$884$	0	0
$885$	−2.34315	−0.0787640
$886$	−30.3431	−1.01940
$887$	−40.4853	−1.35936	−0.679681	−	0.733508i	$-0.737882\pi$
$887$	−40.4853	−1.35936	−0.679681	+	0.733508i	$0.737882\pi$
$888$	−11.6569	−0.391178
$889$	27.3137	0.916072
$890$	15.6569	0.524819
$891$	−5.65685	−0.189512
$892$	−10.8284	−0.362563
$893$	−22.6274	−0.757198
$894$	3.65685	0.122304
$895$	−7.51472	−0.251189
$896$	−2.82843	−0.0944911
$897$	0	0
$898$	26.2843	0.877117
$899$	35.3137	1.17778
$900$	1.00000	0.0333333
$901$	11.0294	0.367444
$902$	43.3137	1.44219
$903$	27.3137	0.908943
$904$	−6.48528	−0.215697
$905$	7.65685	0.254522
$906$	12.0000	0.398673
$907$	8.28427	0.275075	0.137537	−	0.990497i	$-0.456081\pi$
$907$	8.28427	0.275075	0.137537	+	0.990497i	$0.456081\pi$
$908$	−4.00000	−0.132745
$909$	16.1421	0.535401
$910$	0	0
$911$	24.9706	0.827312	0.413656	−	0.910433i	$-0.364252\pi$
$911$	24.9706	0.827312	0.413656	+	0.910433i	$0.364252\pi$
$912$	−2.82843	−0.0936586
$913$	35.8823	1.18753
$914$	20.8284	0.688943
$915$	−6.00000	−0.198354
$916$	−4.14214	−0.136860
$917$	−17.3726	−0.573693
$918$	−0.828427	−0.0273422
$919$	41.9411	1.38351	0.691755	−	0.722132i	$-0.256838\pi$
$919$	41.9411	1.38351	0.691755	+	0.722132i	$0.256838\pi$
$920$	−8.48528	−0.279751
$921$	21.6569	0.713618
$922$	14.0000	0.461065
$923$	0	0
$924$	−16.0000	−0.526361
$925$	11.6569	0.383275
$926$	−3.79899	−0.124843
$927$	−1.65685	−0.0544182
$928$	8.82843	0.289807
$929$	33.5980	1.10231	0.551157	−	0.834402i	$-0.314187\pi$
$929$	33.5980	1.10231	0.551157	+	0.834402i	$0.314187\pi$
$930$	−4.00000	−0.131165
$931$	−2.82843	−0.0926980
$932$	5.51472	0.180641
$933$	−24.0000	−0.785725
$934$	−7.31371	−0.239312
$935$	4.68629	0.153258
$936$	0	0
$937$	16.6274	0.543194	0.271597	−	0.962411i	$-0.412448\pi$
$937$	16.6274	0.543194	0.271597	+	0.962411i	$0.412448\pi$
$938$	16.0000	0.522419
$939$	−30.9706	−1.01069
$940$	−8.00000	−0.260931
$941$	−54.9706	−1.79199	−0.895995	−	0.444065i	$-0.853536\pi$
$941$	−54.9706	−1.79199	−0.895995	+	0.444065i	$0.853536\pi$
$942$	−5.31371	−0.173130
$943$	−64.9706	−2.11573
$944$	2.34315	0.0762629
$945$	−2.82843	−0.0920087
$946$	54.6274	1.77609
$947$	−30.3431	−0.986020	−0.493010	−	0.870024i	$-0.664103\pi$
$947$	−30.3431	−0.986020	−0.493010	+	0.870024i	$0.664103\pi$
$948$	2.34315	0.0761018
$949$	0	0
$950$	2.82843	0.0917663
$951$	−25.3137	−0.820853
$952$	−2.34315	−0.0759418
$953$	−27.8579	−0.902405	−0.451202	−	0.892422i	$-0.649005\pi$
$953$	−27.8579	−0.902405	−0.451202	+	0.892422i	$0.649005\pi$
$954$	−13.3137	−0.431047
$955$	−11.3137	−0.366103
$956$	−16.0000	−0.517477
$957$	49.9411	1.61437
$958$	−11.3137	−0.365529
$959$	48.9706	1.58134
$960$	−1.00000	−0.0322749
$961$	−15.0000	−0.483871
$962$	0	0
$963$	−4.00000	−0.128898
$964$	−5.31371	−0.171143
$965$	2.48528	0.0800040
$966$	24.0000	0.772187
$967$	7.51472	0.241657	0.120829	−	0.992673i	$-0.461445\pi$
$967$	7.51472	0.241657	0.120829	+	0.992673i	$0.461445\pi$
$968$	−21.0000	−0.674966
$969$	−2.34315	−0.0752727
$970$	3.17157	0.101833
$971$	15.5147	0.497891	0.248946	−	0.968517i	$-0.419916\pi$
$971$	15.5147	0.497891	0.248946	+	0.968517i	$0.419916\pi$
$972$	1.00000	0.0320750
$973$	17.9411	0.575166
$974$	16.4853	0.528222
$975$	0	0
$976$	6.00000	0.192055
$977$	8.34315	0.266921	0.133460	−	0.991054i	$-0.457391\pi$
$977$	8.34315	0.266921	0.133460	+	0.991054i	$0.457391\pi$
$978$	11.3137	0.361773
$979$	−88.5685	−2.83066
$980$	−1.00000	−0.0319438
$981$	−8.82843	−0.281870
$982$	38.1421	1.21716
$983$	2.34315	0.0747347	0.0373674	−	0.999302i	$-0.488103\pi$
$983$	2.34315	0.0747347	0.0373674	+	0.999302i	$0.488103\pi$
$984$	−7.65685	−0.244092
$985$	−13.3137	−0.424210
$986$	7.31371	0.232916
$987$	22.6274	0.720239
$988$	0	0
$989$	−81.9411	−2.60558
$990$	−5.65685	−0.179787
$991$	−42.9117	−1.36313	−0.681567	−	0.731755i	$-0.738701\pi$
$991$	−42.9117	−1.36313	−0.681567	+	0.731755i	$0.738701\pi$
$992$	4.00000	0.127000
$993$	8.48528	0.269272
$994$	−16.0000	−0.507489
$995$	−10.3431	−0.327900
$996$	−6.34315	−0.200990
$997$	61.3137	1.94182	0.970912	−	0.239435i	$-0.0769623\pi$
$997$	61.3137	1.94182	0.970912	+	0.239435i	$0.0769623\pi$
$998$	0.485281	0.0153613
$999$	11.6569	0.368807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5070.2.a.bc.1.2		2
13.5	odd	4		5070.2.b.q.1351.4		4
13.8	odd	4		5070.2.b.q.1351.1		4
13.12	even	2		390.2.a.h.1.1	✓	2
39.38	odd	2		1170.2.a.o.1.1		2
52.51	odd	2		3120.2.a.bc.1.2		2
65.12	odd	4		1950.2.e.o.1249.3		4
65.38	odd	4		1950.2.e.o.1249.2		4
65.64	even	2		1950.2.a.bd.1.2		2
156.155	even	2		9360.2.a.ch.1.2		2
195.38	even	4		5850.2.e.bk.5149.4		4
195.77	even	4		5850.2.e.bk.5149.1		4
195.194	odd	2		5850.2.a.cl.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.a.h.1.1	✓	2	13.12	even	2
1170.2.a.o.1.1		2	39.38	odd	2
1950.2.a.bd.1.2		2	65.64	even	2
1950.2.e.o.1249.2		4	65.38	odd	4
1950.2.e.o.1249.3		4	65.12	odd	4
3120.2.a.bc.1.2		2	52.51	odd	2
5070.2.a.bc.1.2		2	1.1	even	1	trivial
5070.2.b.q.1351.1		4	13.8	odd	4
5070.2.b.q.1351.4		4	13.5	odd	4
5850.2.a.cl.1.2		2	195.194	odd	2
5850.2.e.bk.5149.1		4	195.77	even	4
5850.2.e.bk.5149.4		4	195.38	even	4
9360.2.a.ch.1.2		2	156.155	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5070.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +2.82843 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +2.82843 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -5.65685 q^{11} +1.00000 q^{12} -2.82843 q^{14} -1.00000 q^{15} +1.00000 q^{16} +0.828427 q^{17} -1.00000 q^{18} -2.82843 q^{19} -1.00000 q^{20} +2.82843 q^{21} +5.65685 q^{22} -8.48528 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} +2.82843 q^{28} -8.82843 q^{29} +1.00000 q^{30} -4.00000 q^{31} -1.00000 q^{32} -5.65685 q^{33} -0.828427 q^{34} -2.82843 q^{35} +1.00000 q^{36} +11.6569 q^{37} +2.82843 q^{38} +1.00000 q^{40} +7.65685 q^{41} -2.82843 q^{42} +9.65685 q^{43} -5.65685 q^{44} -1.00000 q^{45} +8.48528 q^{46} +8.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +0.828427 q^{51} +13.3137 q^{53} -1.00000 q^{54} +5.65685 q^{55} -2.82843 q^{56} -2.82843 q^{57} +8.82843 q^{58} +2.34315 q^{59} -1.00000 q^{60} +6.00000 q^{61} +4.00000 q^{62} +2.82843 q^{63} +1.00000 q^{64} +5.65685 q^{66} -5.65685 q^{67} +0.828427 q^{68} -8.48528 q^{69} +2.82843 q^{70} +5.65685 q^{71} -1.00000 q^{72} +14.4853 q^{73} -11.6569 q^{74} +1.00000 q^{75} -2.82843 q^{76} -16.0000 q^{77} +2.34315 q^{79} -1.00000 q^{80} +1.00000 q^{81} -7.65685 q^{82} -6.34315 q^{83} +2.82843 q^{84} -0.828427 q^{85} -9.65685 q^{86} -8.82843 q^{87} +5.65685 q^{88} +15.6569 q^{89} +1.00000 q^{90} -8.48528 q^{92} -4.00000 q^{93} -8.00000 q^{94} +2.82843 q^{95} -1.00000 q^{96} +3.17157 q^{97} -1.00000 q^{98} -5.65685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{12} - 2 q^{15} + 2 q^{16} - 4 q^{17} - 2 q^{18} - 2 q^{20} - 2 q^{24} + 2 q^{25} + 2 q^{27} - 12 q^{29} + 2 q^{30} - 8 q^{31} - 2 q^{32} + 4 q^{34} + 2 q^{36} + 12 q^{37} + 2 q^{40} + 4 q^{41} + 8 q^{43} - 2 q^{45} + 16 q^{47} + 2 q^{48} + 2 q^{49} - 2 q^{50} - 4 q^{51} + 4 q^{53} - 2 q^{54} + 12 q^{58} + 16 q^{59} - 2 q^{60} + 12 q^{61} + 8 q^{62} + 2 q^{64} - 4 q^{68} - 2 q^{72} + 12 q^{73} - 12 q^{74} + 2 q^{75} - 32 q^{77} + 16 q^{79} - 2 q^{80} + 2 q^{81} - 4 q^{82} - 24 q^{83} + 4 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{89} + 2 q^{90} - 8 q^{93} - 16 q^{94} - 2 q^{96} + 12 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^12 - 2 * q^15 + 2 * q^16 - 4 * q^17 - 2 * q^18 - 2 * q^20 - 2 * q^24 + 2 * q^25 + 2 * q^27 - 12 * q^29 + 2 * q^30 - 8 * q^31 - 2 * q^32 + 4 * q^34 + 2 * q^36 + 12 * q^37 + 2 * q^40 + 4 * q^41 + 8 * q^43 - 2 * q^45 + 16 * q^47 + 2 * q^48 + 2 * q^49 - 2 * q^50 - 4 * q^51 + 4 * q^53 - 2 * q^54 + 12 * q^58 + 16 * q^59 - 2 * q^60 + 12 * q^61 + 8 * q^62 + 2 * q^64 - 4 * q^68 - 2 * q^72 + 12 * q^73 - 12 * q^74 + 2 * q^75 - 32 * q^77 + 16 * q^79 - 2 * q^80 + 2 * q^81 - 4 * q^82 - 24 * q^83 + 4 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^89 + 2 * q^90 - 8 * q^93 - 16 * q^94 - 2 * q^96 + 12 * q^97 - 2 * q^98

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