LMFDB - Embedded newform 6762.2.a.bv.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6762,2,Mod(1,6762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6762, 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("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6762.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:	$53.9948418468$
Analytic rank:	$1$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 966)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	6762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.414214 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.414214 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -0.414214 q^{10} +2.00000 q^{11} +1.00000 q^{12} -1.82843 q^{13} +0.414214 q^{15} +1.00000 q^{16} -3.24264 q^{17} -1.00000 q^{18} +3.65685 q^{19} +0.414214 q^{20} -2.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} -4.82843 q^{25} +1.82843 q^{26} +1.00000 q^{27} -1.17157 q^{29} -0.414214 q^{30} -2.00000 q^{31} -1.00000 q^{32} +2.00000 q^{33} +3.24264 q^{34} +1.00000 q^{36} -3.17157 q^{37} -3.65685 q^{38} -1.82843 q^{39} -0.414214 q^{40} -10.8284 q^{41} -11.6569 q^{43} +2.00000 q^{44} +0.414214 q^{45} -1.00000 q^{46} +9.00000 q^{47} +1.00000 q^{48} +4.82843 q^{50} -3.24264 q^{51} -1.82843 q^{52} -10.0711 q^{53} -1.00000 q^{54} +0.828427 q^{55} +3.65685 q^{57} +1.17157 q^{58} +1.65685 q^{59} +0.414214 q^{60} -2.00000 q^{61} +2.00000 q^{62} +1.00000 q^{64} -0.757359 q^{65} -2.00000 q^{66} +14.8995 q^{67} -3.24264 q^{68} +1.00000 q^{69} -9.82843 q^{71} -1.00000 q^{72} -10.6569 q^{73} +3.17157 q^{74} -4.82843 q^{75} +3.65685 q^{76} +1.82843 q^{78} -10.0000 q^{79} +0.414214 q^{80} +1.00000 q^{81} +10.8284 q^{82} +12.8284 q^{83} -1.34315 q^{85} +11.6569 q^{86} -1.17157 q^{87} -2.00000 q^{88} +1.17157 q^{89} -0.414214 q^{90} +1.00000 q^{92} -2.00000 q^{93} -9.00000 q^{94} +1.51472 q^{95} -1.00000 q^{96} -9.65685 q^{97} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 4 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} - 4 q^{19} - 2 q^{20} - 4 q^{22} + 2 q^{23} - 2 q^{24} - 4 q^{25} - 2 q^{26} + 2 q^{27} - 8 q^{29} + 2 q^{30} - 4 q^{31} - 2 q^{32} + 4 q^{33} - 2 q^{34} + 2 q^{36} - 12 q^{37} + 4 q^{38} + 2 q^{39} + 2 q^{40} - 16 q^{41} - 12 q^{43} + 4 q^{44} - 2 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} + 4 q^{50} + 2 q^{51} + 2 q^{52} - 6 q^{53} - 2 q^{54} - 4 q^{55} - 4 q^{57} + 8 q^{58} - 8 q^{59} - 2 q^{60} - 4 q^{61} + 4 q^{62} + 2 q^{64} - 10 q^{65} - 4 q^{66} + 10 q^{67} + 2 q^{68} + 2 q^{69} - 14 q^{71} - 2 q^{72} - 10 q^{73} + 12 q^{74} - 4 q^{75} - 4 q^{76} - 2 q^{78} - 20 q^{79} - 2 q^{80} + 2 q^{81} + 16 q^{82} + 20 q^{83} - 14 q^{85} + 12 q^{86} - 8 q^{87} - 4 q^{88} + 8 q^{89} + 2 q^{90} + 2 q^{92} - 4 q^{93} - 18 q^{94} + 20 q^{95} - 2 q^{96} - 8 q^{97} + 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 - 4 * q^19 - 2 * q^20 - 4 * q^22 + 2 * q^23 - 2 * q^24 - 4 * q^25 - 2 * q^26 + 2 * q^27 - 8 * q^29 + 2 * q^30 - 4 * q^31 - 2 * q^32 + 4 * q^33 - 2 * q^34 + 2 * q^36 - 12 * q^37 + 4 * q^38 + 2 * q^39 + 2 * q^40 - 16 * q^41 - 12 * q^43 + 4 * q^44 - 2 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 + 4 * q^50 + 2 * q^51 + 2 * q^52 - 6 * q^53 - 2 * q^54 - 4 * q^55 - 4 * q^57 + 8 * q^58 - 8 * q^59 - 2 * q^60 - 4 * q^61 + 4 * q^62 + 2 * q^64 - 10 * q^65 - 4 * q^66 + 10 * q^67 + 2 * q^68 + 2 * q^69 - 14 * q^71 - 2 * q^72 - 10 * q^73 + 12 * q^74 - 4 * q^75 - 4 * q^76 - 2 * q^78 - 20 * q^79 - 2 * q^80 + 2 * q^81 + 16 * q^82 + 20 * q^83 - 14 * q^85 + 12 * q^86 - 8 * q^87 - 4 * q^88 + 8 * q^89 + 2 * q^90 + 2 * q^92 - 4 * q^93 - 18 * q^94 + 20 * q^95 - 2 * q^96 - 8 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.414214	0.185242	0.0926210	−	0.995701i	$-0.470476\pi$
$5$	0.414214	0.185242	0.0926210	+	0.995701i	$0.470476\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.414214	−0.130986
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	1.00000	0.288675
$13$	−1.82843	−0.507114	−0.253557	−	0.967320i	$-0.581601\pi$
$13$	−1.82843	−0.507114	−0.253557	+	0.967320i	$0.581601\pi$
$14$	0	0
$15$	0.414214	0.106949
$16$	1.00000	0.250000
$17$	−3.24264	−0.786456	−0.393228	−	0.919441i	$-0.628642\pi$
$17$	−3.24264	−0.786456	−0.393228	+	0.919441i	$0.628642\pi$
$18$	−1.00000	−0.235702
$19$	3.65685	0.838940	0.419470	−	0.907769i	$-0.362216\pi$
$19$	3.65685	0.838940	0.419470	+	0.907769i	$0.362216\pi$
$20$	0.414214	0.0926210
$21$	0	0
$22$	−2.00000	−0.426401
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	−4.82843	−0.965685
$26$	1.82843	0.358584
$27$	1.00000	0.192450
$28$	0	0
$29$	−1.17157	−0.217556	−0.108778	−	0.994066i	$-0.534694\pi$
$29$	−1.17157	−0.217556	−0.108778	+	0.994066i	$0.534694\pi$
$30$	−0.414214	−0.0756247
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−1.00000	−0.176777
$33$	2.00000	0.348155
$34$	3.24264	0.556108
$35$	0	0
$36$	1.00000	0.166667
$37$	−3.17157	−0.521403	−0.260702	−	0.965419i	$-0.583954\pi$
$37$	−3.17157	−0.521403	−0.260702	+	0.965419i	$0.583954\pi$
$38$	−3.65685	−0.593220
$39$	−1.82843	−0.292783
$40$	−0.414214	−0.0654929
$41$	−10.8284	−1.69112	−0.845558	−	0.533883i	$-0.820732\pi$
$41$	−10.8284	−1.69112	−0.845558	+	0.533883i	$0.820732\pi$
$42$	0	0
$43$	−11.6569	−1.77765	−0.888827	−	0.458243i	$-0.848479\pi$
$43$	−11.6569	−1.77765	−0.888827	+	0.458243i	$0.848479\pi$
$44$	2.00000	0.301511
$45$	0.414214	0.0617473
$46$	−1.00000	−0.147442
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	4.82843	0.682843
$51$	−3.24264	−0.454061
$52$	−1.82843	−0.253557
$53$	−10.0711	−1.38337	−0.691684	−	0.722200i	$-0.743131\pi$
$53$	−10.0711	−1.38337	−0.691684	+	0.722200i	$0.743131\pi$
$54$	−1.00000	−0.136083
$55$	0.828427	0.111705
$56$	0	0
$57$	3.65685	0.484362
$58$	1.17157	0.153835
$59$	1.65685	0.215704	0.107852	−	0.994167i	$-0.465603\pi$
$59$	1.65685	0.215704	0.107852	+	0.994167i	$0.465603\pi$
$60$	0.414214	0.0534747
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	2.00000	0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	−0.757359	−0.0939389
$66$	−2.00000	−0.246183
$67$	14.8995	1.82026	0.910132	−	0.414319i	$-0.135980\pi$
$67$	14.8995	1.82026	0.910132	+	0.414319i	$0.135980\pi$
$68$	−3.24264	−0.393228
$69$	1.00000	0.120386
$70$	0	0
$71$	−9.82843	−1.16642	−0.583210	−	0.812322i	$-0.698203\pi$
$71$	−9.82843	−1.16642	−0.583210	+	0.812322i	$0.698203\pi$
$72$	−1.00000	−0.117851
$73$	−10.6569	−1.24729	−0.623645	−	0.781708i	$-0.714349\pi$
$73$	−10.6569	−1.24729	−0.623645	+	0.781708i	$0.714349\pi$
$74$	3.17157	0.368688
$75$	−4.82843	−0.557539
$76$	3.65685	0.419470
$77$	0	0
$78$	1.82843	0.207029
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	0.414214	0.0463105
$81$	1.00000	0.111111
$82$	10.8284	1.19580
$83$	12.8284	1.40810	0.704051	−	0.710149i	$-0.251372\pi$
$83$	12.8284	1.40810	0.704051	+	0.710149i	$0.251372\pi$
$84$	0	0
$85$	−1.34315	−0.145685
$86$	11.6569	1.25699
$87$	−1.17157	−0.125606
$88$	−2.00000	−0.213201
$89$	1.17157	0.124186	0.0620932	−	0.998070i	$-0.480222\pi$
$89$	1.17157	0.124186	0.0620932	+	0.998070i	$0.480222\pi$
$90$	−0.414214	−0.0436619
$91$	0	0
$92$	1.00000	0.104257
$93$	−2.00000	−0.207390
$94$	−9.00000	−0.928279
$95$	1.51472	0.155407
$96$	−1.00000	−0.102062
$97$	−9.65685	−0.980505	−0.490252	−	0.871580i	$-0.663095\pi$
$97$	−9.65685	−0.980505	−0.490252	+	0.871580i	$0.663095\pi$
$98$	0	0
$99$	2.00000	0.201008
$100$	−4.82843	−0.482843
$101$	3.17157	0.315583	0.157792	−	0.987472i	$-0.449563\pi$
$101$	3.17157	0.315583	0.157792	+	0.987472i	$0.449563\pi$
$102$	3.24264	0.321069
$103$	−8.89949	−0.876893	−0.438447	−	0.898757i	$-0.644471\pi$
$103$	−8.89949	−0.876893	−0.438447	+	0.898757i	$0.644471\pi$
$104$	1.82843	0.179292
$105$	0	0
$106$	10.0711	0.978189
$107$	5.65685	0.546869	0.273434	−	0.961891i	$-0.411840\pi$
$107$	5.65685	0.546869	0.273434	+	0.961891i	$0.411840\pi$
$108$	1.00000	0.0962250
$109$	14.8284	1.42031	0.710153	−	0.704048i	$-0.248626\pi$
$109$	14.8284	1.42031	0.710153	+	0.704048i	$0.248626\pi$
$110$	−0.828427	−0.0789874
$111$	−3.17157	−0.301032
$112$	0	0
$113$	−13.7279	−1.29141	−0.645707	−	0.763585i	$-0.723437\pi$
$113$	−13.7279	−1.29141	−0.645707	+	0.763585i	$0.723437\pi$
$114$	−3.65685	−0.342496
$115$	0.414214	0.0386256
$116$	−1.17157	−0.108778
$117$	−1.82843	−0.169038
$118$	−1.65685	−0.152526
$119$	0	0
$120$	−0.414214	−0.0378124
$121$	−7.00000	−0.636364
$122$	2.00000	0.181071
$123$	−10.8284	−0.976366
$124$	−2.00000	−0.179605
$125$	−4.07107	−0.364127
$126$	0	0
$127$	4.82843	0.428454	0.214227	−	0.976784i	$-0.431277\pi$
$127$	4.82843	0.428454	0.214227	+	0.976784i	$0.431277\pi$
$128$	−1.00000	−0.0883883
$129$	−11.6569	−1.02633
$130$	0.757359	0.0664248
$131$	19.1421	1.67246	0.836228	−	0.548382i	$-0.184756\pi$
$131$	19.1421	1.67246	0.836228	+	0.548382i	$0.184756\pi$
$132$	2.00000	0.174078
$133$	0	0
$134$	−14.8995	−1.28712
$135$	0.414214	0.0356498
$136$	3.24264	0.278054
$137$	−10.4142	−0.889746	−0.444873	−	0.895594i	$-0.646751\pi$
$137$	−10.4142	−0.889746	−0.444873	+	0.895594i	$0.646751\pi$
$138$	−1.00000	−0.0851257
$139$	−13.3137	−1.12925	−0.564627	−	0.825346i	$-0.690980\pi$
$139$	−13.3137	−1.12925	−0.564627	+	0.825346i	$0.690980\pi$
$140$	0	0
$141$	9.00000	0.757937
$142$	9.82843	0.824783
$143$	−3.65685	−0.305802
$144$	1.00000	0.0833333
$145$	−0.485281	−0.0403004
$146$	10.6569	0.881968
$147$	0	0
$148$	−3.17157	−0.260702
$149$	0.757359	0.0620453	0.0310226	−	0.999519i	$-0.490124\pi$
$149$	0.757359	0.0620453	0.0310226	+	0.999519i	$0.490124\pi$
$150$	4.82843	0.394239
$151$	14.1421	1.15087	0.575435	−	0.817847i	$-0.304833\pi$
$151$	14.1421	1.15087	0.575435	+	0.817847i	$0.304833\pi$
$152$	−3.65685	−0.296610
$153$	−3.24264	−0.262152
$154$	0	0
$155$	−0.828427	−0.0665409
$156$	−1.82843	−0.146391
$157$	−4.34315	−0.346621	−0.173310	−	0.984867i	$-0.555446\pi$
$157$	−4.34315	−0.346621	−0.173310	+	0.984867i	$0.555446\pi$
$158$	10.0000	0.795557
$159$	−10.0711	−0.798688
$160$	−0.414214	−0.0327465
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−9.65685	−0.756383	−0.378192	−	0.925727i	$-0.623454\pi$
$163$	−9.65685	−0.756383	−0.378192	+	0.925727i	$0.623454\pi$
$164$	−10.8284	−0.845558
$165$	0.828427	0.0644930
$166$	−12.8284	−0.995679
$167$	−14.7990	−1.14518	−0.572590	−	0.819842i	$-0.694061\pi$
$167$	−14.7990	−1.14518	−0.572590	+	0.819842i	$0.694061\pi$
$168$	0	0
$169$	−9.65685	−0.742835
$170$	1.34315	0.103015
$171$	3.65685	0.279647
$172$	−11.6569	−0.888827
$173$	15.3137	1.16428	0.582140	−	0.813089i	$-0.302216\pi$
$173$	15.3137	1.16428	0.582140	+	0.813089i	$0.302216\pi$
$174$	1.17157	0.0888167
$175$	0	0
$176$	2.00000	0.150756
$177$	1.65685	0.124537
$178$	−1.17157	−0.0878131
$179$	11.9706	0.894722	0.447361	−	0.894354i	$-0.352364\pi$
$179$	11.9706	0.894722	0.447361	+	0.894354i	$0.352364\pi$
$180$	0.414214	0.0308737
$181$	13.3137	0.989600	0.494800	−	0.869007i	$-0.335241\pi$
$181$	13.3137	0.989600	0.494800	+	0.869007i	$0.335241\pi$
$182$	0	0
$183$	−2.00000	−0.147844
$184$	−1.00000	−0.0737210
$185$	−1.31371	−0.0965858
$186$	2.00000	0.146647
$187$	−6.48528	−0.474251
$188$	9.00000	0.656392
$189$	0	0
$190$	−1.51472	−0.109889
$191$	−10.8284	−0.783517	−0.391759	−	0.920068i	$-0.628133\pi$
$191$	−10.8284	−0.783517	−0.391759	+	0.920068i	$0.628133\pi$
$192$	1.00000	0.0721688
$193$	11.4853	0.826729	0.413364	−	0.910566i	$-0.364354\pi$
$193$	11.4853	0.826729	0.413364	+	0.910566i	$0.364354\pi$
$194$	9.65685	0.693322
$195$	−0.757359	−0.0542356
$196$	0	0
$197$	−7.17157	−0.510953	−0.255477	−	0.966815i	$-0.582232\pi$
$197$	−7.17157	−0.510953	−0.255477	+	0.966815i	$0.582232\pi$
$198$	−2.00000	−0.142134
$199$	−16.3431	−1.15853	−0.579267	−	0.815138i	$-0.696661\pi$
$199$	−16.3431	−1.15853	−0.579267	+	0.815138i	$0.696661\pi$
$200$	4.82843	0.341421
$201$	14.8995	1.05093
$202$	−3.17157	−0.223151
$203$	0	0
$204$	−3.24264	−0.227030
$205$	−4.48528	−0.313266
$206$	8.89949	0.620057
$207$	1.00000	0.0695048
$208$	−1.82843	−0.126779
$209$	7.31371	0.505900
$210$	0	0
$211$	−16.8284	−1.15852	−0.579258	−	0.815144i	$-0.696658\pi$
$211$	−16.8284	−1.15852	−0.579258	+	0.815144i	$0.696658\pi$
$212$	−10.0711	−0.691684
$213$	−9.82843	−0.673433
$214$	−5.65685	−0.386695
$215$	−4.82843	−0.329296
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−14.8284	−1.00431
$219$	−10.6569	−0.720123
$220$	0.828427	0.0558525
$221$	5.92893	0.398823
$222$	3.17157	0.212862
$223$	4.48528	0.300357	0.150178	−	0.988659i	$-0.452015\pi$
$223$	4.48528	0.300357	0.150178	+	0.988659i	$0.452015\pi$
$224$	0	0
$225$	−4.82843	−0.321895
$226$	13.7279	0.913168
$227$	22.9706	1.52461	0.762305	−	0.647218i	$-0.224068\pi$
$227$	22.9706	1.52461	0.762305	+	0.647218i	$0.224068\pi$
$228$	3.65685	0.242181
$229$	−26.1421	−1.72752	−0.863760	−	0.503903i	$-0.831897\pi$
$229$	−26.1421	−1.72752	−0.863760	+	0.503903i	$0.831897\pi$
$230$	−0.414214	−0.0273124
$231$	0	0
$232$	1.17157	0.0769175
$233$	−8.00000	−0.524097	−0.262049	−	0.965055i	$-0.584398\pi$
$233$	−8.00000	−0.524097	−0.262049	+	0.965055i	$0.584398\pi$
$234$	1.82843	0.119528
$235$	3.72792	0.243183
$236$	1.65685	0.107852
$237$	−10.0000	−0.649570
$238$	0	0
$239$	21.6569	1.40087	0.700433	−	0.713718i	$-0.252990\pi$
$239$	21.6569	1.40087	0.700433	+	0.713718i	$0.252990\pi$
$240$	0.414214	0.0267374
$241$	−7.17157	−0.461962	−0.230981	−	0.972958i	$-0.574193\pi$
$241$	−7.17157	−0.461962	−0.230981	+	0.972958i	$0.574193\pi$
$242$	7.00000	0.449977
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	0	0
$246$	10.8284	0.690395
$247$	−6.68629	−0.425439
$248$	2.00000	0.127000
$249$	12.8284	0.812969
$250$	4.07107	0.257477
$251$	−5.31371	−0.335398	−0.167699	−	0.985838i	$-0.553634\pi$
$251$	−5.31371	−0.335398	−0.167699	+	0.985838i	$0.553634\pi$
$252$	0	0
$253$	2.00000	0.125739
$254$	−4.82843	−0.302962
$255$	−1.34315	−0.0841110
$256$	1.00000	0.0625000
$257$	22.4853	1.40259	0.701297	−	0.712870i	$-0.252605\pi$
$257$	22.4853	1.40259	0.701297	+	0.712870i	$0.252605\pi$
$258$	11.6569	0.725724
$259$	0	0
$260$	−0.757359	−0.0469694
$261$	−1.17157	−0.0725185
$262$	−19.1421	−1.18261
$263$	−3.31371	−0.204332	−0.102166	−	0.994767i	$-0.532577\pi$
$263$	−3.31371	−0.204332	−0.102166	+	0.994767i	$0.532577\pi$
$264$	−2.00000	−0.123091
$265$	−4.17157	−0.256258
$266$	0	0
$267$	1.17157	0.0716991
$268$	14.8995	0.910132
$269$	−12.0000	−0.731653	−0.365826	−	0.930683i	$-0.619214\pi$
$269$	−12.0000	−0.731653	−0.365826	+	0.930683i	$0.619214\pi$
$270$	−0.414214	−0.0252082
$271$	26.2843	1.59666	0.798328	−	0.602223i	$-0.205718\pi$
$271$	26.2843	1.59666	0.798328	+	0.602223i	$0.205718\pi$
$272$	−3.24264	−0.196614
$273$	0	0
$274$	10.4142	0.629146
$275$	−9.65685	−0.582330
$276$	1.00000	0.0601929
$277$	−31.2843	−1.87969	−0.939845	−	0.341602i	$-0.889031\pi$
$277$	−31.2843	−1.87969	−0.939845	+	0.341602i	$0.889031\pi$
$278$	13.3137	0.798503
$279$	−2.00000	−0.119737
$280$	0	0
$281$	−16.4142	−0.979190	−0.489595	−	0.871950i	$-0.662855\pi$
$281$	−16.4142	−0.979190	−0.489595	+	0.871950i	$0.662855\pi$
$282$	−9.00000	−0.535942
$283$	7.38478	0.438979	0.219490	−	0.975615i	$-0.429561\pi$
$283$	7.38478	0.438979	0.219490	+	0.975615i	$0.429561\pi$
$284$	−9.82843	−0.583210
$285$	1.51472	0.0897242
$286$	3.65685	0.216234
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−6.48528	−0.381487
$290$	0.485281	0.0284967
$291$	−9.65685	−0.566095
$292$	−10.6569	−0.623645
$293$	−6.41421	−0.374722	−0.187361	−	0.982291i	$-0.559993\pi$
$293$	−6.41421	−0.374722	−0.187361	+	0.982291i	$0.559993\pi$
$294$	0	0
$295$	0.686292	0.0399574
$296$	3.17157	0.184344
$297$	2.00000	0.116052
$298$	−0.757359	−0.0438726
$299$	−1.82843	−0.105741
$300$	−4.82843	−0.278769
$301$	0	0
$302$	−14.1421	−0.813788
$303$	3.17157	0.182202
$304$	3.65685	0.209735
$305$	−0.828427	−0.0474356
$306$	3.24264	0.185369
$307$	14.1421	0.807134	0.403567	−	0.914950i	$-0.367770\pi$
$307$	14.1421	0.807134	0.403567	+	0.914950i	$0.367770\pi$
$308$	0	0
$309$	−8.89949	−0.506275
$310$	0.828427	0.0470515
$311$	6.31371	0.358018	0.179009	−	0.983847i	$-0.442711\pi$
$311$	6.31371	0.358018	0.179009	+	0.983847i	$0.442711\pi$
$312$	1.82843	0.103514
$313$	−0.970563	−0.0548595	−0.0274297	−	0.999624i	$-0.508732\pi$
$313$	−0.970563	−0.0548595	−0.0274297	+	0.999624i	$0.508732\pi$
$314$	4.34315	0.245098
$315$	0	0
$316$	−10.0000	−0.562544
$317$	12.6274	0.709226	0.354613	−	0.935013i	$-0.384613\pi$
$317$	12.6274	0.709226	0.354613	+	0.935013i	$0.384613\pi$
$318$	10.0711	0.564757
$319$	−2.34315	−0.131191
$320$	0.414214	0.0231552
$321$	5.65685	0.315735
$322$	0	0
$323$	−11.8579	−0.659789
$324$	1.00000	0.0555556
$325$	8.82843	0.489713
$326$	9.65685	0.534844
$327$	14.8284	0.820014
$328$	10.8284	0.597900
$329$	0	0
$330$	−0.828427	−0.0456034
$331$	−17.5147	−0.962696	−0.481348	−	0.876530i	$-0.659853\pi$
$331$	−17.5147	−0.962696	−0.481348	+	0.876530i	$0.659853\pi$
$332$	12.8284	0.704051
$333$	−3.17157	−0.173801
$334$	14.7990	0.809765
$335$	6.17157	0.337189
$336$	0	0
$337$	0	0		−	1.00000i	$-0.5\pi$
$337$	0	0			1.00000i	$0.5\pi$
$338$	9.65685	0.525264
$339$	−13.7279	−0.745598
$340$	−1.34315	−0.0728423
$341$	−4.00000	−0.216612
$342$	−3.65685	−0.197740
$343$	0	0
$344$	11.6569	0.628495
$345$	0.414214	0.0223005
$346$	−15.3137	−0.823270
$347$	−21.3431	−1.14576	−0.572880	−	0.819639i	$-0.694174\pi$
$347$	−21.3431	−1.14576	−0.572880	+	0.819639i	$0.694174\pi$
$348$	−1.17157	−0.0628029
$349$	3.14214	0.168195	0.0840973	−	0.996458i	$-0.473199\pi$
$349$	3.14214	0.168195	0.0840973	+	0.996458i	$0.473199\pi$
$350$	0	0
$351$	−1.82843	−0.0975942
$352$	−2.00000	−0.106600
$353$	−26.1421	−1.39141	−0.695703	−	0.718330i	$-0.744907\pi$
$353$	−26.1421	−1.39141	−0.695703	+	0.718330i	$0.744907\pi$
$354$	−1.65685	−0.0880608
$355$	−4.07107	−0.216070
$356$	1.17157	0.0620932
$357$	0	0
$358$	−11.9706	−0.632664
$359$	−6.97056	−0.367892	−0.183946	−	0.982936i	$-0.558887\pi$
$359$	−6.97056	−0.367892	−0.183946	+	0.982936i	$0.558887\pi$
$360$	−0.414214	−0.0218310
$361$	−5.62742	−0.296180
$362$	−13.3137	−0.699753
$363$	−7.00000	−0.367405
$364$	0	0
$365$	−4.41421	−0.231050
$366$	2.00000	0.104542
$367$	−32.6985	−1.70685	−0.853424	−	0.521218i	$-0.825478\pi$
$367$	−32.6985	−1.70685	−0.853424	+	0.521218i	$0.825478\pi$
$368$	1.00000	0.0521286
$369$	−10.8284	−0.563705
$370$	1.31371	0.0682965
$371$	0	0
$372$	−2.00000	−0.103695
$373$	−11.6569	−0.603569	−0.301785	−	0.953376i	$-0.597582\pi$
$373$	−11.6569	−0.603569	−0.301785	+	0.953376i	$0.597582\pi$
$374$	6.48528	0.335346
$375$	−4.07107	−0.210229
$376$	−9.00000	−0.464140
$377$	2.14214	0.110326
$378$	0	0
$379$	0.899495	0.0462040	0.0231020	−	0.999733i	$-0.492646\pi$
$379$	0.899495	0.0462040	0.0231020	+	0.999733i	$0.492646\pi$
$380$	1.51472	0.0777034
$381$	4.82843	0.247368
$382$	10.8284	0.554031
$383$	−7.65685	−0.391247	−0.195623	−	0.980679i	$-0.562673\pi$
$383$	−7.65685	−0.391247	−0.195623	+	0.980679i	$0.562673\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−11.4853	−0.584585
$387$	−11.6569	−0.592551
$388$	−9.65685	−0.490252
$389$	13.4558	0.682238	0.341119	−	0.940020i	$-0.389194\pi$
$389$	13.4558	0.682238	0.341119	+	0.940020i	$0.389194\pi$
$390$	0.757359	0.0383504
$391$	−3.24264	−0.163987
$392$	0	0
$393$	19.1421	0.965593
$394$	7.17157	0.361299
$395$	−4.14214	−0.208413
$396$	2.00000	0.100504
$397$	2.65685	0.133344	0.0666718	−	0.997775i	$-0.478762\pi$
$397$	2.65685	0.133344	0.0666718	+	0.997775i	$0.478762\pi$
$398$	16.3431	0.819208
$399$	0	0
$400$	−4.82843	−0.241421
$401$	26.6985	1.33326	0.666629	−	0.745389i	$-0.267736\pi$
$401$	26.6985	1.33326	0.666629	+	0.745389i	$0.267736\pi$
$402$	−14.8995	−0.743119
$403$	3.65685	0.182161
$404$	3.17157	0.157792
$405$	0.414214	0.0205824
$406$	0	0
$407$	−6.34315	−0.314418
$408$	3.24264	0.160535
$409$	12.7990	0.632869	0.316435	−	0.948614i	$-0.397514\pi$
$409$	12.7990	0.632869	0.316435	+	0.948614i	$0.397514\pi$
$410$	4.48528	0.221512
$411$	−10.4142	−0.513695
$412$	−8.89949	−0.438447
$413$	0	0
$414$	−1.00000	−0.0491473
$415$	5.31371	0.260840
$416$	1.82843	0.0896460
$417$	−13.3137	−0.651975
$418$	−7.31371	−0.357725
$419$	24.4853	1.19618	0.598092	−	0.801427i	$-0.295926\pi$
$419$	24.4853	1.19618	0.598092	+	0.801427i	$0.295926\pi$
$420$	0	0
$421$	15.3137	0.746344	0.373172	−	0.927762i	$-0.378270\pi$
$421$	15.3137	0.746344	0.373172	+	0.927762i	$0.378270\pi$
$422$	16.8284	0.819195
$423$	9.00000	0.437595
$424$	10.0711	0.489094
$425$	15.6569	0.759469
$426$	9.82843	0.476189
$427$	0	0
$428$	5.65685	0.273434
$429$	−3.65685	−0.176555
$430$	4.82843	0.232847
$431$	−4.68629	−0.225731	−0.112865	−	0.993610i	$-0.536003\pi$
$431$	−4.68629	−0.225731	−0.112865	+	0.993610i	$0.536003\pi$
$432$	1.00000	0.0481125
$433$	−14.0000	−0.672797	−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000	−0.672797	−0.336399	+	0.941720i	$0.609209\pi$
$434$	0	0
$435$	−0.485281	−0.0232675
$436$	14.8284	0.710153
$437$	3.65685	0.174931
$438$	10.6569	0.509204
$439$	−2.97056	−0.141777	−0.0708886	−	0.997484i	$-0.522583\pi$
$439$	−2.97056	−0.141777	−0.0708886	+	0.997484i	$0.522583\pi$
$440$	−0.828427	−0.0394937
$441$	0	0
$442$	−5.92893	−0.282011
$443$	−17.1421	−0.814447	−0.407224	−	0.913328i	$-0.633503\pi$
$443$	−17.1421	−0.814447	−0.407224	+	0.913328i	$0.633503\pi$
$444$	−3.17157	−0.150516
$445$	0.485281	0.0230045
$446$	−4.48528	−0.212384
$447$	0.757359	0.0358219
$448$	0	0
$449$	26.4853	1.24992	0.624959	−	0.780658i	$-0.285116\pi$
$449$	26.4853	1.24992	0.624959	+	0.780658i	$0.285116\pi$
$450$	4.82843	0.227614
$451$	−21.6569	−1.01978
$452$	−13.7279	−0.645707
$453$	14.1421	0.664455
$454$	−22.9706	−1.07806
$455$	0	0
$456$	−3.65685	−0.171248
$457$	0	0		−	1.00000i	$-0.5\pi$
$457$	0	0			1.00000i	$0.5\pi$
$458$	26.1421	1.22154
$459$	−3.24264	−0.151354
$460$	0.414214	0.0193128
$461$	14.0000	0.652045	0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000	0.652045	0.326023	+	0.945362i	$0.394291\pi$
$462$	0	0
$463$	10.6274	0.493898	0.246949	−	0.969028i	$-0.420572\pi$
$463$	10.6274	0.493898	0.246949	+	0.969028i	$0.420572\pi$
$464$	−1.17157	−0.0543889
$465$	−0.828427	−0.0384174
$466$	8.00000	0.370593
$467$	10.3431	0.478624	0.239312	−	0.970943i	$-0.423078\pi$
$467$	10.3431	0.478624	0.239312	+	0.970943i	$0.423078\pi$
$468$	−1.82843	−0.0845191
$469$	0	0
$470$	−3.72792	−0.171956
$471$	−4.34315	−0.200122
$472$	−1.65685	−0.0762629
$473$	−23.3137	−1.07197
$474$	10.0000	0.459315
$475$	−17.6569	−0.810152
$476$	0	0
$477$	−10.0711	−0.461123
$478$	−21.6569	−0.990561
$479$	34.1421	1.55999	0.779997	−	0.625783i	$-0.215221\pi$
$479$	34.1421	1.55999	0.779997	+	0.625783i	$0.215221\pi$
$480$	−0.414214	−0.0189062
$481$	5.79899	0.264411
$482$	7.17157	0.326656
$483$	0	0
$484$	−7.00000	−0.318182
$485$	−4.00000	−0.181631
$486$	−1.00000	−0.0453609
$487$	−32.7696	−1.48493	−0.742465	−	0.669885i	$-0.766343\pi$
$487$	−32.7696	−1.48493	−0.742465	+	0.669885i	$0.766343\pi$
$488$	2.00000	0.0905357
$489$	−9.65685	−0.436698
$490$	0	0
$491$	−11.3431	−0.511909	−0.255955	−	0.966689i	$-0.582390\pi$
$491$	−11.3431	−0.511909	−0.255955	+	0.966689i	$0.582390\pi$
$492$	−10.8284	−0.488183
$493$	3.79899	0.171098
$494$	6.68629	0.300830
$495$	0.828427	0.0372350
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	−12.8284	−0.574856
$499$	1.17157	0.0524468	0.0262234	−	0.999656i	$-0.491652\pi$
$499$	1.17157	0.0524468	0.0262234	+	0.999656i	$0.491652\pi$
$500$	−4.07107	−0.182064
$501$	−14.7990	−0.661170
$502$	5.31371	0.237162
$503$	43.6569	1.94656	0.973281	−	0.229615i	$-0.0737468\pi$
$503$	43.6569	1.94656	0.973281	+	0.229615i	$0.0737468\pi$
$504$	0	0
$505$	1.31371	0.0584593
$506$	−2.00000	−0.0889108
$507$	−9.65685	−0.428876
$508$	4.82843	0.214227
$509$	15.8579	0.702887	0.351444	−	0.936209i	$-0.385691\pi$
$509$	15.8579	0.702887	0.351444	+	0.936209i	$0.385691\pi$
$510$	1.34315	0.0594755
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	3.65685	0.161454
$514$	−22.4853	−0.991783
$515$	−3.68629	−0.162437
$516$	−11.6569	−0.513164
$517$	18.0000	0.791639
$518$	0	0
$519$	15.3137	0.672197
$520$	0.757359	0.0332124
$521$	25.5858	1.12093	0.560467	−	0.828177i	$-0.310622\pi$
$521$	25.5858	1.12093	0.560467	+	0.828177i	$0.310622\pi$
$522$	1.17157	0.0512784
$523$	−14.0711	−0.615285	−0.307642	−	0.951502i	$-0.599540\pi$
$523$	−14.0711	−0.615285	−0.307642	+	0.951502i	$0.599540\pi$
$524$	19.1421	0.836228
$525$	0	0
$526$	3.31371	0.144485
$527$	6.48528	0.282503
$528$	2.00000	0.0870388
$529$	1.00000	0.0434783
$530$	4.17157	0.181202
$531$	1.65685	0.0719014
$532$	0	0
$533$	19.7990	0.857589
$534$	−1.17157	−0.0506989
$535$	2.34315	0.101303
$536$	−14.8995	−0.643560
$537$	11.9706	0.516568
$538$	12.0000	0.517357
$539$	0	0
$540$	0.414214	0.0178249
$541$	12.8579	0.552803	0.276401	−	0.961042i	$-0.410858\pi$
$541$	12.8579	0.552803	0.276401	+	0.961042i	$0.410858\pi$
$542$	−26.2843	−1.12901
$543$	13.3137	0.571346
$544$	3.24264	0.139027
$545$	6.14214	0.263100
$546$	0	0
$547$	−34.2843	−1.46589	−0.732945	−	0.680288i	$-0.761855\pi$
$547$	−34.2843	−1.46589	−0.732945	+	0.680288i	$0.761855\pi$
$548$	−10.4142	−0.444873
$549$	−2.00000	−0.0853579
$550$	9.65685	0.411770
$551$	−4.28427	−0.182516
$552$	−1.00000	−0.0425628
$553$	0	0
$554$	31.2843	1.32914
$555$	−1.31371	−0.0557638
$556$	−13.3137	−0.564627
$557$	−23.7990	−1.00840	−0.504198	−	0.863588i	$-0.668212\pi$
$557$	−23.7990	−1.00840	−0.504198	+	0.863588i	$0.668212\pi$
$558$	2.00000	0.0846668
$559$	21.3137	0.901474
$560$	0	0
$561$	−6.48528	−0.273809
$562$	16.4142	0.692392
$563$	−5.45584	−0.229936	−0.114968	−	0.993369i	$-0.536677\pi$
$563$	−5.45584	−0.229936	−0.114968	+	0.993369i	$0.536677\pi$
$564$	9.00000	0.378968
$565$	−5.68629	−0.239224
$566$	−7.38478	−0.310405
$567$	0	0
$568$	9.82843	0.412392
$569$	10.4142	0.436587	0.218293	−	0.975883i	$-0.429951\pi$
$569$	10.4142	0.436587	0.218293	+	0.975883i	$0.429951\pi$
$570$	−1.51472	−0.0634446
$571$	−20.8995	−0.874617	−0.437308	−	0.899312i	$-0.644068\pi$
$571$	−20.8995	−0.874617	−0.437308	+	0.899312i	$0.644068\pi$
$572$	−3.65685	−0.152901
$573$	−10.8284	−0.452364
$574$	0	0
$575$	−4.82843	−0.201359
$576$	1.00000	0.0416667
$577$	−31.9411	−1.32973	−0.664863	−	0.746965i	$-0.731510\pi$
$577$	−31.9411	−1.32973	−0.664863	+	0.746965i	$0.731510\pi$
$578$	6.48528	0.269752
$579$	11.4853	0.477312
$580$	−0.485281	−0.0201502
$581$	0	0
$582$	9.65685	0.400289
$583$	−20.1421	−0.834202
$584$	10.6569	0.440984
$585$	−0.757359	−0.0313130
$586$	6.41421	0.264969
$587$	1.14214	0.0471410	0.0235705	−	0.999722i	$-0.492497\pi$
$587$	1.14214	0.0471410	0.0235705	+	0.999722i	$0.492497\pi$
$588$	0	0
$589$	−7.31371	−0.301356
$590$	−0.686292	−0.0282542
$591$	−7.17157	−0.294999
$592$	−3.17157	−0.130351
$593$	−3.85786	−0.158424	−0.0792118	−	0.996858i	$-0.525240\pi$
$593$	−3.85786	−0.158424	−0.0792118	+	0.996858i	$0.525240\pi$
$594$	−2.00000	−0.0820610
$595$	0	0
$596$	0.757359	0.0310226
$597$	−16.3431	−0.668880
$598$	1.82843	0.0747699
$599$	−6.17157	−0.252164	−0.126082	−	0.992020i	$-0.540240\pi$
$599$	−6.17157	−0.252164	−0.126082	+	0.992020i	$0.540240\pi$
$600$	4.82843	0.197120
$601$	−14.2843	−0.582668	−0.291334	−	0.956621i	$-0.594099\pi$
$601$	−14.2843	−0.582668	−0.291334	+	0.956621i	$0.594099\pi$
$602$	0	0
$603$	14.8995	0.606754
$604$	14.1421	0.575435
$605$	−2.89949	−0.117881
$606$	−3.17157	−0.128836
$607$	36.1421	1.46696	0.733482	−	0.679709i	$-0.237894\pi$
$607$	36.1421	1.46696	0.733482	+	0.679709i	$0.237894\pi$
$608$	−3.65685	−0.148305
$609$	0	0
$610$	0.828427	0.0335420
$611$	−16.4558	−0.665732
$612$	−3.24264	−0.131076
$613$	−17.7990	−0.718894	−0.359447	−	0.933165i	$-0.617035\pi$
$613$	−17.7990	−0.718894	−0.359447	+	0.933165i	$0.617035\pi$
$614$	−14.1421	−0.570730
$615$	−4.48528	−0.180864
$616$	0	0
$617$	−36.0711	−1.45217	−0.726083	−	0.687607i	$-0.758661\pi$
$617$	−36.0711	−1.45217	−0.726083	+	0.687607i	$0.758661\pi$
$618$	8.89949	0.357990
$619$	29.9289	1.20295	0.601473	−	0.798893i	$-0.294581\pi$
$619$	29.9289	1.20295	0.601473	+	0.798893i	$0.294581\pi$
$620$	−0.828427	−0.0332704
$621$	1.00000	0.0401286
$622$	−6.31371	−0.253157
$623$	0	0
$624$	−1.82843	−0.0731957
$625$	22.4558	0.898234
$626$	0.970563	0.0387915
$627$	7.31371	0.292081
$628$	−4.34315	−0.173310
$629$	10.2843	0.410061
$630$	0	0
$631$	−46.5563	−1.85338	−0.926689	−	0.375828i	$-0.877358\pi$
$631$	−46.5563	−1.85338	−0.926689	+	0.375828i	$0.877358\pi$
$632$	10.0000	0.397779
$633$	−16.8284	−0.668870
$634$	−12.6274	−0.501499
$635$	2.00000	0.0793676
$636$	−10.0711	−0.399344
$637$	0	0
$638$	2.34315	0.0927660
$639$	−9.82843	−0.388807
$640$	−0.414214	−0.0163732
$641$	−10.6152	−0.419276	−0.209638	−	0.977779i	$-0.567229\pi$
$641$	−10.6152	−0.419276	−0.209638	+	0.977779i	$0.567229\pi$
$642$	−5.65685	−0.223258
$643$	6.68629	0.263682	0.131841	−	0.991271i	$-0.457911\pi$
$643$	6.68629	0.263682	0.131841	+	0.991271i	$0.457911\pi$
$644$	0	0
$645$	−4.82843	−0.190119
$646$	11.8579	0.466541
$647$	−21.6569	−0.851419	−0.425709	−	0.904860i	$-0.639975\pi$
$647$	−21.6569	−0.851419	−0.425709	+	0.904860i	$0.639975\pi$
$648$	−1.00000	−0.0392837
$649$	3.31371	0.130074
$650$	−8.82843	−0.346279
$651$	0	0
$652$	−9.65685	−0.378192
$653$	−31.9411	−1.24995	−0.624976	−	0.780644i	$-0.714891\pi$
$653$	−31.9411	−1.24995	−0.624976	+	0.780644i	$0.714891\pi$
$654$	−14.8284	−0.579837
$655$	7.92893	0.309809
$656$	−10.8284	−0.422779
$657$	−10.6569	−0.415763
$658$	0	0
$659$	27.4558	1.06953	0.534764	−	0.845002i	$-0.320401\pi$
$659$	27.4558	1.06953	0.534764	+	0.845002i	$0.320401\pi$
$660$	0.828427	0.0322465
$661$	17.4558	0.678954	0.339477	−	0.940614i	$-0.389750\pi$
$661$	17.4558	0.678954	0.339477	+	0.940614i	$0.389750\pi$
$662$	17.5147	0.680729
$663$	5.92893	0.230261
$664$	−12.8284	−0.497840
$665$	0	0
$666$	3.17157	0.122896
$667$	−1.17157	−0.0453635
$668$	−14.7990	−0.572590
$669$	4.48528	0.173411
$670$	−6.17157	−0.238429
$671$	−4.00000	−0.154418
$672$	0	0
$673$	−29.3137	−1.12996	−0.564980	−	0.825104i	$-0.691116\pi$
$673$	−29.3137	−1.12996	−0.564980	+	0.825104i	$0.691116\pi$
$674$	0	0
$675$	−4.82843	−0.185846
$676$	−9.65685	−0.371417
$677$	−20.2721	−0.779119	−0.389560	−	0.921001i	$-0.627373\pi$
$677$	−20.2721	−0.779119	−0.389560	+	0.921001i	$0.627373\pi$
$678$	13.7279	0.527218
$679$	0	0
$680$	1.34315	0.0515073
$681$	22.9706	0.880234
$682$	4.00000	0.153168
$683$	−45.1421	−1.72732	−0.863658	−	0.504078i	$-0.831832\pi$
$683$	−45.1421	−1.72732	−0.863658	+	0.504078i	$0.831832\pi$
$684$	3.65685	0.139823
$685$	−4.31371	−0.164818
$686$	0	0
$687$	−26.1421	−0.997385
$688$	−11.6569	−0.444413
$689$	18.4142	0.701526
$690$	−0.414214	−0.0157688
$691$	16.1421	0.614076	0.307038	−	0.951697i	$-0.400662\pi$
$691$	16.1421	0.614076	0.307038	+	0.951697i	$0.400662\pi$
$692$	15.3137	0.582140
$693$	0	0
$694$	21.3431	0.810175
$695$	−5.51472	−0.209185
$696$	1.17157	0.0444084
$697$	35.1127	1.32999
$698$	−3.14214	−0.118932
$699$	−8.00000	−0.302588
$700$	0	0
$701$	45.3848	1.71416	0.857080	−	0.515184i	$-0.172276\pi$
$701$	45.3848	1.71416	0.857080	+	0.515184i	$0.172276\pi$
$702$	1.82843	0.0690095
$703$	−11.5980	−0.437426
$704$	2.00000	0.0753778
$705$	3.72792	0.140402
$706$	26.1421	0.983872
$707$	0	0
$708$	1.65685	0.0622684
$709$	−38.1421	−1.43246	−0.716229	−	0.697865i	$-0.754133\pi$
$709$	−38.1421	−1.43246	−0.716229	+	0.697865i	$0.754133\pi$
$710$	4.07107	0.152784
$711$	−10.0000	−0.375029
$712$	−1.17157	−0.0439065
$713$	−2.00000	−0.0749006
$714$	0	0
$715$	−1.51472	−0.0566473
$716$	11.9706	0.447361
$717$	21.6569	0.808790
$718$	6.97056	0.260139
$719$	3.34315	0.124678	0.0623391	−	0.998055i	$-0.480144\pi$
$719$	3.34315	0.124678	0.0623391	+	0.998055i	$0.480144\pi$
$720$	0.414214	0.0154368
$721$	0	0
$722$	5.62742	0.209431
$723$	−7.17157	−0.266714
$724$	13.3137	0.494800
$725$	5.65685	0.210090
$726$	7.00000	0.259794
$727$	−42.0000	−1.55769	−0.778847	−	0.627214i	$-0.784195\pi$
$727$	−42.0000	−1.55769	−0.778847	+	0.627214i	$0.784195\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	4.41421	0.163377
$731$	37.7990	1.39805
$732$	−2.00000	−0.0739221
$733$	8.48528	0.313411	0.156706	−	0.987645i	$-0.449913\pi$
$733$	8.48528	0.313411	0.156706	+	0.987645i	$0.449913\pi$
$734$	32.6985	1.20692
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	29.7990	1.09766
$738$	10.8284	0.398600
$739$	45.2548	1.66473	0.832363	−	0.554231i	$-0.186988\pi$
$739$	45.2548	1.66473	0.832363	+	0.554231i	$0.186988\pi$
$740$	−1.31371	−0.0482929
$741$	−6.68629	−0.245627
$742$	0	0
$743$	−35.4558	−1.30075	−0.650374	−	0.759614i	$-0.725388\pi$
$743$	−35.4558	−1.30075	−0.650374	+	0.759614i	$0.725388\pi$
$744$	2.00000	0.0733236
$745$	0.313708	0.0114934
$746$	11.6569	0.426788
$747$	12.8284	0.469368
$748$	−6.48528	−0.237125
$749$	0	0
$750$	4.07107	0.148654
$751$	−41.5980	−1.51793	−0.758966	−	0.651130i	$-0.774295\pi$
$751$	−41.5980	−1.51793	−0.758966	+	0.651130i	$0.774295\pi$
$752$	9.00000	0.328196
$753$	−5.31371	−0.193642
$754$	−2.14214	−0.0780120
$755$	5.85786	0.213190
$756$	0	0
$757$	−4.97056	−0.180658	−0.0903291	−	0.995912i	$-0.528792\pi$
$757$	−4.97056	−0.180658	−0.0903291	+	0.995912i	$0.528792\pi$
$758$	−0.899495	−0.0326711
$759$	2.00000	0.0725954
$760$	−1.51472	−0.0549446
$761$	−10.3431	−0.374939	−0.187469	−	0.982270i	$-0.560029\pi$
$761$	−10.3431	−0.374939	−0.187469	+	0.982270i	$0.560029\pi$
$762$	−4.82843	−0.174915
$763$	0	0
$764$	−10.8284	−0.391759
$765$	−1.34315	−0.0485615
$766$	7.65685	0.276653
$767$	−3.02944	−0.109387
$768$	1.00000	0.0360844
$769$	10.6863	0.385358	0.192679	−	0.981262i	$-0.438282\pi$
$769$	10.6863	0.385358	0.192679	+	0.981262i	$0.438282\pi$
$770$	0	0
$771$	22.4853	0.809788
$772$	11.4853	0.413364
$773$	−9.24264	−0.332435	−0.166217	−	0.986089i	$-0.553155\pi$
$773$	−9.24264	−0.332435	−0.166217	+	0.986089i	$0.553155\pi$
$774$	11.6569	0.418997
$775$	9.65685	0.346884
$776$	9.65685	0.346661
$777$	0	0
$778$	−13.4558	−0.482415
$779$	−39.5980	−1.41874
$780$	−0.757359	−0.0271178
$781$	−19.6569	−0.703378
$782$	3.24264	0.115957
$783$	−1.17157	−0.0418686
$784$	0	0
$785$	−1.79899	−0.0642087
$786$	−19.1421	−0.682777
$787$	11.0416	0.393592	0.196796	−	0.980444i	$-0.436946\pi$
$787$	11.0416	0.393592	0.196796	+	0.980444i	$0.436946\pi$
$788$	−7.17157	−0.255477
$789$	−3.31371	−0.117971
$790$	4.14214	0.147371
$791$	0	0
$792$	−2.00000	−0.0710669
$793$	3.65685	0.129859
$794$	−2.65685	−0.0942882
$795$	−4.17157	−0.147950
$796$	−16.3431	−0.579267
$797$	13.8701	0.491303	0.245651	−	0.969358i	$-0.420998\pi$
$797$	13.8701	0.491303	0.245651	+	0.969358i	$0.420998\pi$
$798$	0	0
$799$	−29.1838	−1.03245
$800$	4.82843	0.170711
$801$	1.17157	0.0413955
$802$	−26.6985	−0.942756
$803$	−21.3137	−0.752144
$804$	14.8995	0.525465
$805$	0	0
$806$	−3.65685	−0.128807
$807$	−12.0000	−0.422420
$808$	−3.17157	−0.111576
$809$	4.14214	0.145630	0.0728149	−	0.997345i	$-0.476802\pi$
$809$	4.14214	0.145630	0.0728149	+	0.997345i	$0.476802\pi$
$810$	−0.414214	−0.0145540
$811$	−41.1127	−1.44366	−0.721831	−	0.692069i	$-0.756699\pi$
$811$	−41.1127	−1.44366	−0.721831	+	0.692069i	$0.756699\pi$
$812$	0	0
$813$	26.2843	0.921830
$814$	6.34315	0.222327
$815$	−4.00000	−0.140114
$816$	−3.24264	−0.113515
$817$	−42.6274	−1.49134
$818$	−12.7990	−0.447506
$819$	0	0
$820$	−4.48528	−0.156633
$821$	54.2843	1.89453	0.947267	−	0.320445i	$-0.103832\pi$
$821$	54.2843	1.89453	0.947267	+	0.320445i	$0.103832\pi$
$822$	10.4142	0.363237
$823$	25.7990	0.899296	0.449648	−	0.893206i	$-0.351549\pi$
$823$	25.7990	0.899296	0.449648	+	0.893206i	$0.351549\pi$
$824$	8.89949	0.310029
$825$	−9.65685	−0.336209
$826$	0	0
$827$	2.62742	0.0913642	0.0456821	−	0.998956i	$-0.485454\pi$
$827$	2.62742	0.0913642	0.0456821	+	0.998956i	$0.485454\pi$
$828$	1.00000	0.0347524
$829$	21.8284	0.758133	0.379066	−	0.925370i	$-0.376245\pi$
$829$	21.8284	0.758133	0.379066	+	0.925370i	$0.376245\pi$
$830$	−5.31371	−0.184442
$831$	−31.2843	−1.08524
$832$	−1.82843	−0.0633893
$833$	0	0
$834$	13.3137	0.461016
$835$	−6.12994	−0.212135
$836$	7.31371	0.252950
$837$	−2.00000	−0.0691301
$838$	−24.4853	−0.845830
$839$	−8.97056	−0.309698	−0.154849	−	0.987938i	$-0.549489\pi$
$839$	−8.97056	−0.309698	−0.154849	+	0.987938i	$0.549489\pi$
$840$	0	0
$841$	−27.6274	−0.952670
$842$	−15.3137	−0.527745
$843$	−16.4142	−0.565336
$844$	−16.8284	−0.579258
$845$	−4.00000	−0.137604
$846$	−9.00000	−0.309426
$847$	0	0
$848$	−10.0711	−0.345842
$849$	7.38478	0.253445
$850$	−15.6569	−0.537026
$851$	−3.17157	−0.108720
$852$	−9.82843	−0.336716
$853$	48.9117	1.67470	0.837352	−	0.546664i	$-0.184102\pi$
$853$	48.9117	1.67470	0.837352	+	0.546664i	$0.184102\pi$
$854$	0	0
$855$	1.51472	0.0518023
$856$	−5.65685	−0.193347
$857$	44.6274	1.52444	0.762222	−	0.647316i	$-0.224109\pi$
$857$	44.6274	1.52444	0.762222	+	0.647316i	$0.224109\pi$
$858$	3.65685	0.124843
$859$	−12.6863	−0.432851	−0.216425	−	0.976299i	$-0.569440\pi$
$859$	−12.6863	−0.432851	−0.216425	+	0.976299i	$0.569440\pi$
$860$	−4.82843	−0.164648
$861$	0	0
$862$	4.68629	0.159616
$863$	31.3431	1.06693	0.533467	−	0.845821i	$-0.320889\pi$
$863$	31.3431	1.06693	0.533467	+	0.845821i	$0.320889\pi$
$864$	−1.00000	−0.0340207
$865$	6.34315	0.215673
$866$	14.0000	0.475739
$867$	−6.48528	−0.220252
$868$	0	0
$869$	−20.0000	−0.678454
$870$	0.485281	0.0164526
$871$	−27.2426	−0.923082
$872$	−14.8284	−0.502154
$873$	−9.65685	−0.326835
$874$	−3.65685	−0.123695
$875$	0	0
$876$	−10.6569	−0.360062
$877$	−40.3137	−1.36130	−0.680649	−	0.732610i	$-0.738302\pi$
$877$	−40.3137	−1.36130	−0.680649	+	0.732610i	$0.738302\pi$
$878$	2.97056	0.100252
$879$	−6.41421	−0.216346
$880$	0.828427	0.0279263
$881$	−31.7279	−1.06894	−0.534470	−	0.845187i	$-0.679489\pi$
$881$	−31.7279	−1.06894	−0.534470	+	0.845187i	$0.679489\pi$
$882$	0	0
$883$	12.2843	0.413399	0.206699	−	0.978405i	$-0.433728\pi$
$883$	12.2843	0.413399	0.206699	+	0.978405i	$0.433728\pi$
$884$	5.92893	0.199412
$885$	0.686292	0.0230694
$886$	17.1421	0.575901
$887$	7.02944	0.236025	0.118013	−	0.993012i	$-0.462348\pi$
$887$	7.02944	0.236025	0.118013	+	0.993012i	$0.462348\pi$
$888$	3.17157	0.106431
$889$	0	0
$890$	−0.485281	−0.0162667
$891$	2.00000	0.0670025
$892$	4.48528	0.150178
$893$	32.9117	1.10135
$894$	−0.757359	−0.0253299
$895$	4.95837	0.165740
$896$	0	0
$897$	−1.82843	−0.0610494
$898$	−26.4853	−0.883825
$899$	2.34315	0.0781483
$900$	−4.82843	−0.160948
$901$	32.6569	1.08796
$902$	21.6569	0.721094
$903$	0	0
$904$	13.7279	0.456584
$905$	5.51472	0.183315
$906$	−14.1421	−0.469841
$907$	23.1005	0.767040	0.383520	−	0.923533i	$-0.374712\pi$
$907$	23.1005	0.767040	0.383520	+	0.923533i	$0.374712\pi$
$908$	22.9706	0.762305
$909$	3.17157	0.105194
$910$	0	0
$911$	−8.48528	−0.281130	−0.140565	−	0.990071i	$-0.544892\pi$
$911$	−8.48528	−0.281130	−0.140565	+	0.990071i	$0.544892\pi$
$912$	3.65685	0.121091
$913$	25.6569	0.849118
$914$	0	0
$915$	−0.828427	−0.0273870
$916$	−26.1421	−0.863760
$917$	0	0
$918$	3.24264	0.107023
$919$	1.72792	0.0569989	0.0284994	−	0.999594i	$-0.490927\pi$
$919$	1.72792	0.0569989	0.0284994	+	0.999594i	$0.490927\pi$
$920$	−0.414214	−0.0136562
$921$	14.1421	0.465999
$922$	−14.0000	−0.461065
$923$	17.9706	0.591508
$924$	0	0
$925$	15.3137	0.503512
$926$	−10.6274	−0.349239
$927$	−8.89949	−0.292298
$928$	1.17157	0.0384588
$929$	−50.6274	−1.66103	−0.830516	−	0.556995i	$-0.811954\pi$
$929$	−50.6274	−1.66103	−0.830516	+	0.556995i	$0.811954\pi$
$930$	0.828427	0.0271652
$931$	0	0
$932$	−8.00000	−0.262049
$933$	6.31371	0.206702
$934$	−10.3431	−0.338438
$935$	−2.68629	−0.0878511
$936$	1.82843	0.0597640
$937$	−12.4853	−0.407876	−0.203938	−	0.978984i	$-0.565374\pi$
$937$	−12.4853	−0.407876	−0.203938	+	0.978984i	$0.565374\pi$
$938$	0	0
$939$	−0.970563	−0.0316731
$940$	3.72792	0.121591
$941$	48.4853	1.58058	0.790288	−	0.612736i	$-0.209931\pi$
$941$	48.4853	1.58058	0.790288	+	0.612736i	$0.209931\pi$
$942$	4.34315	0.141507
$943$	−10.8284	−0.352622
$944$	1.65685	0.0539260
$945$	0	0
$946$	23.3137	0.757994
$947$	−34.3137	−1.11505	−0.557523	−	0.830162i	$-0.688248\pi$
$947$	−34.3137	−1.11505	−0.557523	+	0.830162i	$0.688248\pi$
$948$	−10.0000	−0.324785
$949$	19.4853	0.632519
$950$	17.6569	0.572864
$951$	12.6274	0.409472
$952$	0	0
$953$	−27.7990	−0.900498	−0.450249	−	0.892903i	$-0.648665\pi$
$953$	−27.7990	−0.900498	−0.450249	+	0.892903i	$0.648665\pi$
$954$	10.0711	0.326063
$955$	−4.48528	−0.145140
$956$	21.6569	0.700433
$957$	−2.34315	−0.0757431
$958$	−34.1421	−1.10308
$959$	0	0
$960$	0.414214	0.0133687
$961$	−27.0000	−0.870968
$962$	−5.79899	−0.186967
$963$	5.65685	0.182290
$964$	−7.17157	−0.230981
$965$	4.75736	0.153145
$966$	0	0
$967$	−5.17157	−0.166307	−0.0831533	−	0.996537i	$-0.526499\pi$
$967$	−5.17157	−0.166307	−0.0831533	+	0.996537i	$0.526499\pi$
$968$	7.00000	0.224989
$969$	−11.8579	−0.380929
$970$	4.00000	0.128432
$971$	2.34315	0.0751951	0.0375976	−	0.999293i	$-0.488030\pi$
$971$	2.34315	0.0751951	0.0375976	+	0.999293i	$0.488030\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	32.7696	1.05000
$975$	8.82843	0.282736
$976$	−2.00000	−0.0640184
$977$	−46.3553	−1.48304	−0.741519	−	0.670931i	$-0.765894\pi$
$977$	−46.3553	−1.48304	−0.741519	+	0.670931i	$0.765894\pi$
$978$	9.65685	0.308792
$979$	2.34315	0.0748873
$980$	0	0
$981$	14.8284	0.473435
$982$	11.3431	0.361974
$983$	51.4558	1.64119	0.820593	−	0.571513i	$-0.193643\pi$
$983$	51.4558	1.64119	0.820593	+	0.571513i	$0.193643\pi$
$984$	10.8284	0.345198
$985$	−2.97056	−0.0946500
$986$	−3.79899	−0.120984
$987$	0	0
$988$	−6.68629	−0.212719
$989$	−11.6569	−0.370666
$990$	−0.828427	−0.0263291
$991$	−47.9411	−1.52290	−0.761450	−	0.648224i	$-0.775512\pi$
$991$	−47.9411	−1.52290	−0.761450	+	0.648224i	$0.775512\pi$
$992$	2.00000	0.0635001
$993$	−17.5147	−0.555813
$994$	0	0
$995$	−6.76955	−0.214609
$996$	12.8284	0.406484
$997$	20.6274	0.653277	0.326638	−	0.945149i	$-0.394084\pi$
$997$	20.6274	0.653277	0.326638	+	0.945149i	$0.394084\pi$
$998$	−1.17157	−0.0370855
$999$	−3.17157	−0.100344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.bv.1.2		2
7.2	even	3		966.2.i.j.277.1	✓	4
7.4	even	3		966.2.i.j.415.1	yes	4
7.6	odd	2		6762.2.a.bt.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.j.277.1	✓	4	7.2	even	3
966.2.i.j.415.1	yes	4	7.4	even	3
6762.2.a.bt.1.1		2	7.6	odd	2
6762.2.a.bv.1.2		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.414214 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.414214 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -0.414214 q^{10} +2.00000 q^{11} +1.00000 q^{12} -1.82843 q^{13} +0.414214 q^{15} +1.00000 q^{16} -3.24264 q^{17} -1.00000 q^{18} +3.65685 q^{19} +0.414214 q^{20} -2.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} -4.82843 q^{25} +1.82843 q^{26} +1.00000 q^{27} -1.17157 q^{29} -0.414214 q^{30} -2.00000 q^{31} -1.00000 q^{32} +2.00000 q^{33} +3.24264 q^{34} +1.00000 q^{36} -3.17157 q^{37} -3.65685 q^{38} -1.82843 q^{39} -0.414214 q^{40} -10.8284 q^{41} -11.6569 q^{43} +2.00000 q^{44} +0.414214 q^{45} -1.00000 q^{46} +9.00000 q^{47} +1.00000 q^{48} +4.82843 q^{50} -3.24264 q^{51} -1.82843 q^{52} -10.0711 q^{53} -1.00000 q^{54} +0.828427 q^{55} +3.65685 q^{57} +1.17157 q^{58} +1.65685 q^{59} +0.414214 q^{60} -2.00000 q^{61} +2.00000 q^{62} +1.00000 q^{64} -0.757359 q^{65} -2.00000 q^{66} +14.8995 q^{67} -3.24264 q^{68} +1.00000 q^{69} -9.82843 q^{71} -1.00000 q^{72} -10.6569 q^{73} +3.17157 q^{74} -4.82843 q^{75} +3.65685 q^{76} +1.82843 q^{78} -10.0000 q^{79} +0.414214 q^{80} +1.00000 q^{81} +10.8284 q^{82} +12.8284 q^{83} -1.34315 q^{85} +11.6569 q^{86} -1.17157 q^{87} -2.00000 q^{88} +1.17157 q^{89} -0.414214 q^{90} +1.00000 q^{92} -2.00000 q^{93} -9.00000 q^{94} +1.51472 q^{95} -1.00000 q^{96} -9.65685 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} - 4 q^{19} - 2 q^{20} - 4 q^{22} + 2 q^{23} - 2 q^{24} - 4 q^{25} - 2 q^{26} + 2 q^{27} - 8 q^{29} + 2 q^{30} - 4 q^{31} - 2 q^{32} + 4 q^{33} - 2 q^{34} + 2 q^{36} - 12 q^{37} + 4 q^{38} + 2 q^{39} + 2 q^{40} - 16 q^{41} - 12 q^{43} + 4 q^{44} - 2 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} + 4 q^{50} + 2 q^{51} + 2 q^{52} - 6 q^{53} - 2 q^{54} - 4 q^{55} - 4 q^{57} + 8 q^{58} - 8 q^{59} - 2 q^{60} - 4 q^{61} + 4 q^{62} + 2 q^{64} - 10 q^{65} - 4 q^{66} + 10 q^{67} + 2 q^{68} + 2 q^{69} - 14 q^{71} - 2 q^{72} - 10 q^{73} + 12 q^{74} - 4 q^{75} - 4 q^{76} - 2 q^{78} - 20 q^{79} - 2 q^{80} + 2 q^{81} + 16 q^{82} + 20 q^{83} - 14 q^{85} + 12 q^{86} - 8 q^{87} - 4 q^{88} + 8 q^{89} + 2 q^{90} + 2 q^{92} - 4 q^{93} - 18 q^{94} + 20 q^{95} - 2 q^{96} - 8 q^{97} + 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 - 4 * q^19 - 2 * q^20 - 4 * q^22 + 2 * q^23 - 2 * q^24 - 4 * q^25 - 2 * q^26 + 2 * q^27 - 8 * q^29 + 2 * q^30 - 4 * q^31 - 2 * q^32 + 4 * q^33 - 2 * q^34 + 2 * q^36 - 12 * q^37 + 4 * q^38 + 2 * q^39 + 2 * q^40 - 16 * q^41 - 12 * q^43 + 4 * q^44 - 2 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 + 4 * q^50 + 2 * q^51 + 2 * q^52 - 6 * q^53 - 2 * q^54 - 4 * q^55 - 4 * q^57 + 8 * q^58 - 8 * q^59 - 2 * q^60 - 4 * q^61 + 4 * q^62 + 2 * q^64 - 10 * q^65 - 4 * q^66 + 10 * q^67 + 2 * q^68 + 2 * q^69 - 14 * q^71 - 2 * q^72 - 10 * q^73 + 12 * q^74 - 4 * q^75 - 4 * q^76 - 2 * q^78 - 20 * q^79 - 2 * q^80 + 2 * q^81 + 16 * q^82 + 20 * q^83 - 14 * q^85 + 12 * q^86 - 8 * q^87 - 4 * q^88 + 8 * q^89 + 2 * q^90 + 2 * q^92 - 4 * q^93 - 18 * q^94 + 20 * q^95 - 2 * q^96 - 8 * q^97 + 4 * q^99

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