LMFDB - Embedded newform 6762.2.a.cg.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:	$0$
Dimension:	$4$
Coefficient field:	4.4.138768.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 11x^{2} + 12x + 8 $ x^4 - 2x^3 - 11x^2 + 12*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
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			$-0.479029$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.479029 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.479029 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +0.479029 q^{10} -5.35023 q^{11} -1.00000 q^{12} -4.70448 q^{13} +0.479029 q^{15} +1.00000 q^{16} -2.16672 q^{17} -1.00000 q^{18} -3.74642 q^{19} -0.479029 q^{20} +5.35023 q^{22} +1.00000 q^{23} +1.00000 q^{24} -4.77053 q^{25} +4.70448 q^{26} -1.00000 q^{27} -4.74642 q^{29} -0.479029 q^{30} -9.77053 q^{31} -1.00000 q^{32} +5.35023 q^{33} +2.16672 q^{34} +1.00000 q^{36} -2.70448 q^{37} +3.74642 q^{38} +4.70448 q^{39} +0.479029 q^{40} +0.253580 q^{41} +2.00000 q^{43} -5.35023 q^{44} -0.479029 q^{45} -1.00000 q^{46} -9.92993 q^{47} -1.00000 q^{48} +4.77053 q^{50} +2.16672 q^{51} -4.70448 q^{52} +2.47903 q^{53} +1.00000 q^{54} +2.56291 q^{55} +3.74642 q^{57} +4.74642 q^{58} +12.5589 q^{59} +0.479029 q^{60} -8.95806 q^{61} +9.77053 q^{62} +1.00000 q^{64} +2.25358 q^{65} -5.35023 q^{66} -6.70046 q^{67} -2.16672 q^{68} -1.00000 q^{69} +0.774551 q^{71} -1.00000 q^{72} -11.2214 q^{73} +2.70448 q^{74} +4.77053 q^{75} -3.74642 q^{76} -4.70448 q^{78} +0.847088 q^{79} -0.479029 q^{80} +1.00000 q^{81} -0.253580 q^{82} +10.9299 q^{83} +1.03792 q^{85} -2.00000 q^{86} +4.74642 q^{87} +5.35023 q^{88} -3.21164 q^{89} +0.479029 q^{90} +1.00000 q^{92} +9.77053 q^{93} +9.92993 q^{94} +1.79464 q^{95} +1.00000 q^{96} +13.0098 q^{97} -5.35023 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 - 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{8} + 4 q^{9} - 2 q^{10} + 6 q^{11} - 4 q^{12} - 2 q^{13} - 2 q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} - 6 q^{19} + 2 q^{20} - 6 q^{22} + 4 q^{23} + 4 q^{24} + 6 q^{25} + 2 q^{26} - 4 q^{27} - 10 q^{29} + 2 q^{30} - 14 q^{31} - 4 q^{32} - 6 q^{33} + 2 q^{34} + 4 q^{36} + 6 q^{37} + 6 q^{38} + 2 q^{39} - 2 q^{40} + 10 q^{41} + 8 q^{43} + 6 q^{44} + 2 q^{45} - 4 q^{46} - 10 q^{47} - 4 q^{48} - 6 q^{50} + 2 q^{51} - 2 q^{52} + 6 q^{53} + 4 q^{54} + 22 q^{55} + 6 q^{57} + 10 q^{58} + 24 q^{59} - 2 q^{60} - 28 q^{61} + 14 q^{62} + 4 q^{64} + 18 q^{65} + 6 q^{66} + 28 q^{67} - 2 q^{68} - 4 q^{69} + 16 q^{71} - 4 q^{72} + 6 q^{73} - 6 q^{74} - 6 q^{75} - 6 q^{76} - 2 q^{78} - 4 q^{79} + 2 q^{80} + 4 q^{81} - 10 q^{82} + 14 q^{83} - 26 q^{85} - 8 q^{86} + 10 q^{87} - 6 q^{88} - 14 q^{89} - 2 q^{90} + 4 q^{92} + 14 q^{93} + 10 q^{94} - 34 q^{95} + 4 q^{96} + 6 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 - 4 * q^8 + 4 * q^9 - 2 * q^10 + 6 * q^11 - 4 * q^12 - 2 * q^13 - 2 * q^15 + 4 * q^16 - 2 * q^17 - 4 * q^18 - 6 * q^19 + 2 * q^20 - 6 * q^22 + 4 * q^23 + 4 * q^24 + 6 * q^25 + 2 * q^26 - 4 * q^27 - 10 * q^29 + 2 * q^30 - 14 * q^31 - 4 * q^32 - 6 * q^33 + 2 * q^34 + 4 * q^36 + 6 * q^37 + 6 * q^38 + 2 * q^39 - 2 * q^40 + 10 * q^41 + 8 * q^43 + 6 * q^44 + 2 * q^45 - 4 * q^46 - 10 * q^47 - 4 * q^48 - 6 * q^50 + 2 * q^51 - 2 * q^52 + 6 * q^53 + 4 * q^54 + 22 * q^55 + 6 * q^57 + 10 * q^58 + 24 * q^59 - 2 * q^60 - 28 * q^61 + 14 * q^62 + 4 * q^64 + 18 * q^65 + 6 * q^66 + 28 * q^67 - 2 * q^68 - 4 * q^69 + 16 * q^71 - 4 * q^72 + 6 * q^73 - 6 * q^74 - 6 * q^75 - 6 * q^76 - 2 * q^78 - 4 * q^79 + 2 * q^80 + 4 * q^81 - 10 * q^82 + 14 * q^83 - 26 * q^85 - 8 * q^86 + 10 * q^87 - 6 * q^88 - 14 * q^89 - 2 * q^90 + 4 * q^92 + 14 * q^93 + 10 * q^94 - 34 * q^95 + 4 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−0.479029	−0.214228	−0.107114	−	0.994247i	$-0.534161\pi$
$5$	−0.479029	−0.214228	−0.107114	+	0.994247i	$0.534161\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.479029	0.151482
$11$	−5.35023	−1.61315	−0.806577	−	0.591129i	$-0.798683\pi$
$11$	−5.35023	−1.61315	−0.806577	+	0.591129i	$0.798683\pi$
$12$	−1.00000	−0.288675
$13$	−4.70448	−1.30479	−0.652394	−	0.757880i	$-0.726235\pi$
$13$	−4.70448	−1.30479	−0.652394	+	0.757880i	$0.726235\pi$
$14$	0	0
$15$	0.479029	0.123685
$16$	1.00000	0.250000
$17$	−2.16672	−0.525507	−0.262754	−	0.964863i	$-0.584631\pi$
$17$	−2.16672	−0.525507	−0.262754	+	0.964863i	$0.584631\pi$
$18$	−1.00000	−0.235702
$19$	−3.74642	−0.859488	−0.429744	−	0.902951i	$-0.641396\pi$
$19$	−3.74642	−0.859488	−0.429744	+	0.902951i	$0.641396\pi$
$20$	−0.479029	−0.107114
$21$	0	0
$22$	5.35023	1.14067
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	−4.77053	−0.954106
$26$	4.70448	0.922624
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−4.74642	−0.881388	−0.440694	−	0.897657i	$-0.645268\pi$
$29$	−4.74642	−0.881388	−0.440694	+	0.897657i	$0.645268\pi$
$30$	−0.479029	−0.0874583
$31$	−9.77053	−1.75484	−0.877420	−	0.479724i	$-0.840737\pi$
$31$	−9.77053	−1.75484	−0.877420	+	0.479724i	$0.840737\pi$
$32$	−1.00000	−0.176777
$33$	5.35023	0.931355
$34$	2.16672	0.371590
$35$	0	0
$36$	1.00000	0.166667
$37$	−2.70448	−0.444613	−0.222307	−	0.974977i	$-0.571359\pi$
$37$	−2.70448	−0.444613	−0.222307	+	0.974977i	$0.571359\pi$
$38$	3.74642	0.607750
$39$	4.70448	0.753319
$40$	0.479029	0.0757411
$41$	0.253580	0.0396026	0.0198013	−	0.999804i	$-0.493697\pi$
$41$	0.253580	0.0396026	0.0198013	+	0.999804i	$0.493697\pi$
$42$	0	0
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	−5.35023	−0.806577
$45$	−0.479029	−0.0714094
$46$	−1.00000	−0.147442
$47$	−9.92993	−1.44843	−0.724214	−	0.689575i	$-0.757797\pi$
$47$	−9.92993	−1.44843	−0.724214	+	0.689575i	$0.757797\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	4.77053	0.674655
$51$	2.16672	0.303402
$52$	−4.70448	−0.652394
$53$	2.47903	0.340521	0.170260	−	0.985399i	$-0.445539\pi$
$53$	2.47903	0.340521	0.170260	+	0.985399i	$0.445539\pi$
$54$	1.00000	0.136083
$55$	2.56291	0.345583
$56$	0	0
$57$	3.74642	0.496225
$58$	4.74642	0.623235
$59$	12.5589	1.63503	0.817514	−	0.575908i	$-0.195351\pi$
$59$	12.5589	1.63503	0.817514	+	0.575908i	$0.195351\pi$
$60$	0.479029	0.0618424
$61$	−8.95806	−1.14696	−0.573481	−	0.819219i	$-0.694407\pi$
$61$	−8.95806	−1.14696	−0.573481	+	0.819219i	$0.694407\pi$
$62$	9.77053	1.24086
$63$	0	0
$64$	1.00000	0.125000
$65$	2.25358	0.279522
$66$	−5.35023	−0.658568
$67$	−6.70046	−0.818591	−0.409296	−	0.912402i	$-0.634226\pi$
$67$	−6.70046	−0.818591	−0.409296	+	0.912402i	$0.634226\pi$
$68$	−2.16672	−0.262754
$69$	−1.00000	−0.120386
$70$	0	0
$71$	0.774551	0.0919223	0.0459612	−	0.998943i	$-0.485365\pi$
$71$	0.774551	0.0919223	0.0459612	+	0.998943i	$0.485365\pi$
$72$	−1.00000	−0.117851
$73$	−11.2214	−1.31337	−0.656684	−	0.754165i	$-0.728042\pi$
$73$	−11.2214	−1.31337	−0.656684	+	0.754165i	$0.728042\pi$
$74$	2.70448	0.314389
$75$	4.77053	0.550854
$76$	−3.74642	−0.429744
$77$	0	0
$78$	−4.70448	−0.532677
$79$	0.847088	0.0953049	0.0476524	−	0.998864i	$-0.484826\pi$
$79$	0.847088	0.0953049	0.0476524	+	0.998864i	$0.484826\pi$
$80$	−0.479029	−0.0535570
$81$	1.00000	0.111111
$82$	−0.253580	−0.0280032
$83$	10.9299	1.19972	0.599858	−	0.800107i	$-0.295224\pi$
$83$	10.9299	1.19972	0.599858	+	0.800107i	$0.295224\pi$
$84$	0	0
$85$	1.03792	0.112578
$86$	−2.00000	−0.215666
$87$	4.74642	0.508870
$88$	5.35023	0.570336
$89$	−3.21164	−0.340433	−0.170216	−	0.985407i	$-0.554447\pi$
$89$	−3.21164	−0.340433	−0.170216	+	0.985407i	$0.554447\pi$
$90$	0.479029	0.0504941
$91$	0	0
$92$	1.00000	0.104257
$93$	9.77053	1.01316
$94$	9.92993	1.02419
$95$	1.79464	0.184126
$96$	1.00000	0.102062
$97$	13.0098	1.32094	0.660472	−	0.750851i	$-0.270356\pi$
$97$	13.0098	1.32094	0.660472	+	0.750851i	$0.270356\pi$
$98$	0	0
$99$	−5.35023	−0.537718
$100$	−4.77053	−0.477053
$101$	4.77053	0.474686	0.237343	−	0.971426i	$-0.423724\pi$
$101$	4.77053	0.474686	0.237343	+	0.971426i	$0.423724\pi$
$102$	−2.16672	−0.214537
$103$	−7.37836	−0.727011	−0.363506	−	0.931592i	$-0.618420\pi$
$103$	−7.37836	−0.727011	−0.363506	+	0.931592i	$0.618420\pi$
$104$	4.70448	0.461312
$105$	0	0
$106$	−2.47903	−0.240785
$107$	14.9299	1.44333	0.721665	−	0.692242i	$-0.243377\pi$
$107$	14.9299	1.44333	0.721665	+	0.692242i	$0.243377\pi$
$108$	−1.00000	−0.0962250
$109$	4.53775	0.434638	0.217319	−	0.976101i	$-0.430269\pi$
$109$	4.53775	0.434638	0.217319	+	0.976101i	$0.430269\pi$
$110$	−2.56291	−0.244364
$111$	2.70448	0.256698
$112$	0	0
$113$	−14.2455	−1.34011	−0.670054	−	0.742312i	$-0.733729\pi$
$113$	−14.2455	−1.34011	−0.670054	+	0.742312i	$0.733729\pi$
$114$	−3.74642	−0.350884
$115$	−0.479029	−0.0446697
$116$	−4.74642	−0.440694
$117$	−4.70448	−0.434929
$118$	−12.5589	−1.15614
$119$	0	0
$120$	−0.479029	−0.0437291
$121$	17.6249	1.60227
$122$	8.95806	0.811024
$123$	−0.253580	−0.0228646
$124$	−9.77053	−0.877420
$125$	4.68037	0.418625
$126$	0	0
$127$	−12.3053	−1.09192	−0.545960	−	0.837811i	$-0.683835\pi$
$127$	−12.3053	−1.09192	−0.545960	+	0.837811i	$0.683835\pi$
$128$	−1.00000	−0.0883883
$129$	−2.00000	−0.176090
$130$	−2.25358	−0.197652
$131$	−9.31561	−0.813909	−0.406954	−	0.913448i	$-0.633409\pi$
$131$	−9.31561	−0.813909	−0.406954	+	0.913448i	$0.633409\pi$
$132$	5.35023	0.465678
$133$	0	0
$134$	6.70046	0.578831
$135$	0.479029	0.0412282
$136$	2.16672	0.185795
$137$	13.2046	1.12815	0.564074	−	0.825724i	$-0.309233\pi$
$137$	13.2046	1.12815	0.564074	+	0.825724i	$0.309233\pi$
$138$	1.00000	0.0851257
$139$	−5.92993	−0.502970	−0.251485	−	0.967861i	$-0.580919\pi$
$139$	−5.92993	−0.502970	−0.251485	+	0.967861i	$0.580919\pi$
$140$	0	0
$141$	9.92993	0.836251
$142$	−0.774551	−0.0649989
$143$	25.1700	2.10482
$144$	1.00000	0.0833333
$145$	2.27367	0.188818
$146$	11.2214	0.928692
$147$	0	0
$148$	−2.70448	−0.222307
$149$	−1.17405	−0.0961820	−0.0480910	−	0.998843i	$-0.515314\pi$
$149$	−1.17405	−0.0961820	−0.0480910	+	0.998843i	$0.515314\pi$
$150$	−4.77053	−0.389512
$151$	6.30531	0.513119	0.256560	−	0.966528i	$-0.417411\pi$
$151$	6.30531	0.513119	0.256560	+	0.966528i	$0.417411\pi$
$152$	3.74642	0.303875
$153$	−2.16672	−0.175169
$154$	0	0
$155$	4.68037	0.375936
$156$	4.70448	0.376660
$157$	2.28417	0.182297	0.0911485	−	0.995837i	$-0.470946\pi$
$157$	2.28417	0.182297	0.0911485	+	0.995837i	$0.470946\pi$
$158$	−0.847088	−0.0673907
$159$	−2.47903	−0.196600
$160$	0.479029	0.0378706
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	4.77455	0.373972	0.186986	−	0.982363i	$-0.440128\pi$
$163$	4.77455	0.373972	0.186986	+	0.982363i	$0.440128\pi$
$164$	0.253580	0.0198013
$165$	−2.56291	−0.199523
$166$	−10.9299	−0.848327
$167$	−20.9500	−1.62116	−0.810581	−	0.585627i	$-0.800848\pi$
$167$	−20.9500	−1.62116	−0.810581	+	0.585627i	$0.800848\pi$
$168$	0	0
$169$	9.13211	0.702470
$170$	−1.03792	−0.0796050
$171$	−3.74642	−0.286496
$172$	2.00000	0.152499
$173$	−17.2214	−1.30932	−0.654660	−	0.755923i	$-0.727188\pi$
$173$	−17.2214	−1.30932	−0.654660	+	0.755923i	$0.727188\pi$
$174$	−4.74642	−0.359825
$175$	0	0
$176$	−5.35023	−0.403289
$177$	−12.5589	−0.943984
$178$	3.21164	0.240722
$179$	24.5267	1.83321	0.916607	−	0.399789i	$-0.130916\pi$
$179$	24.5267	1.83321	0.916607	+	0.399789i	$0.130916\pi$
$180$	−0.479029	−0.0357047
$181$	−20.4123	−1.51723	−0.758616	−	0.651538i	$-0.774124\pi$
$181$	−20.4123	−1.51723	−0.758616	+	0.651538i	$0.774124\pi$
$182$	0	0
$183$	8.95806	0.662199
$184$	−1.00000	−0.0737210
$185$	1.29552	0.0952487
$186$	−9.77053	−0.716410
$187$	11.5925	0.847725
$188$	−9.92993	−0.724214
$189$	0	0
$190$	−1.79464	−0.130197
$191$	−1.23926	−0.0896697	−0.0448348	−	0.998994i	$-0.514276\pi$
$191$	−1.23926	−0.0896697	−0.0448348	+	0.998994i	$0.514276\pi$
$192$	−1.00000	−0.0721688
$193$	−11.1795	−0.804717	−0.402359	−	0.915482i	$-0.631809\pi$
$193$	−11.1795	−0.804717	−0.402359	+	0.915482i	$0.631809\pi$
$194$	−13.0098	−0.934049
$195$	−2.25358	−0.161382
$196$	0	0
$197$	22.0956	1.57425	0.787123	−	0.616796i	$-0.211570\pi$
$197$	22.0956	1.57425	0.787123	+	0.616796i	$0.211570\pi$
$198$	5.35023	0.380224
$199$	8.49615	0.602276	0.301138	−	0.953581i	$-0.402634\pi$
$199$	8.49615	0.602276	0.301138	+	0.953581i	$0.402634\pi$
$200$	4.77053	0.337328
$201$	6.70046	0.472614
$202$	−4.77053	−0.335653
$203$	0	0
$204$	2.16672	0.151701
$205$	−0.121472	−0.00848399
$206$	7.37836	0.514075
$207$	1.00000	0.0695048
$208$	−4.70448	−0.326197
$209$	20.0442	1.38649
$210$	0	0
$211$	20.3808	1.40307	0.701537	−	0.712633i	$-0.252498\pi$
$211$	20.3808	1.40307	0.701537	+	0.712633i	$0.252498\pi$
$212$	2.47903	0.170260
$213$	−0.774551	−0.0530714
$214$	−14.9299	−1.02059
$215$	−0.958058	−0.0653390
$216$	1.00000	0.0680414
$217$	0	0
$218$	−4.53775	−0.307336
$219$	11.2214	0.758274
$220$	2.56291	0.172792
$221$	10.1933	0.685675
$222$	−2.70448	−0.181513
$223$	−3.18753	−0.213453	−0.106726	−	0.994288i	$-0.534037\pi$
$223$	−3.18753	−0.213453	−0.106726	+	0.994288i	$0.534037\pi$
$224$	0	0
$225$	−4.77053	−0.318035
$226$	14.2455	0.947599
$227$	5.35827	0.355641	0.177820	−	0.984063i	$-0.443095\pi$
$227$	5.35827	0.355641	0.177820	+	0.984063i	$0.443095\pi$
$228$	3.74642	0.248113
$229$	−23.4582	−1.55016	−0.775082	−	0.631861i	$-0.782291\pi$
$229$	−23.4582	−1.55016	−0.775082	+	0.631861i	$0.782291\pi$
$230$	0.479029	0.0315862
$231$	0	0
$232$	4.74642	0.311618
$233$	−24.7803	−1.62341	−0.811706	−	0.584066i	$-0.801461\pi$
$233$	−24.7803	−1.62341	−0.811706	+	0.584066i	$0.801461\pi$
$234$	4.70448	0.307541
$235$	4.75672	0.310294
$236$	12.5589	0.817514
$237$	−0.847088	−0.0550243
$238$	0	0
$239$	4.97187	0.321603	0.160802	−	0.986987i	$-0.448592\pi$
$239$	4.97187	0.321603	0.160802	+	0.986987i	$0.448592\pi$
$240$	0.479029	0.0309212
$241$	−7.48338	−0.482047	−0.241024	−	0.970519i	$-0.577483\pi$
$241$	−7.48338	−0.482047	−0.241024	+	0.970519i	$0.577483\pi$
$242$	−17.6249	−1.13297
$243$	−1.00000	−0.0641500
$244$	−8.95806	−0.573481
$245$	0	0
$246$	0.253580	0.0161677
$247$	17.6249	1.12145
$248$	9.77053	0.620429
$249$	−10.9299	−0.692656
$250$	−4.68037	−0.296012
$251$	−14.9752	−0.945225	−0.472612	−	0.881270i	$-0.656689\pi$
$251$	−14.9752	−0.945225	−0.472612	+	0.881270i	$0.656689\pi$
$252$	0	0
$253$	−5.35023	−0.336366
$254$	12.3053	0.772104
$255$	−1.03792	−0.0649972
$256$	1.00000	0.0625000
$257$	0.503140	0.0313850	0.0156925	−	0.999877i	$-0.495005\pi$
$257$	0.503140	0.0313850	0.0156925	+	0.999877i	$0.495005\pi$
$258$	2.00000	0.124515
$259$	0	0
$260$	2.25358	0.139761
$261$	−4.74642	−0.293796
$262$	9.31561	0.575521
$263$	−4.99163	−0.307797	−0.153898	−	0.988087i	$-0.549183\pi$
$263$	−4.99163	−0.307797	−0.153898	+	0.988087i	$0.549183\pi$
$264$	−5.35023	−0.329284
$265$	−1.18753	−0.0729492
$266$	0	0
$267$	3.21164	0.196549
$268$	−6.70046	−0.409296
$269$	4.12775	0.251674	0.125837	−	0.992051i	$-0.459838\pi$
$269$	4.12775	0.251674	0.125837	+	0.992051i	$0.459838\pi$
$270$	−0.479029	−0.0291528
$271$	−2.93797	−0.178469	−0.0892344	−	0.996011i	$-0.528442\pi$
$271$	−2.93797	−0.178469	−0.0892344	+	0.996011i	$0.528442\pi$
$272$	−2.16672	−0.131377
$273$	0	0
$274$	−13.2046	−0.797722
$275$	25.5234	1.53912
$276$	−1.00000	−0.0601929
$277$	−28.6924	−1.72396	−0.861980	−	0.506942i	$-0.830776\pi$
$277$	−28.6924	−1.72396	−0.861980	+	0.506942i	$0.830776\pi$
$278$	5.92993	0.355653
$279$	−9.77053	−0.584946
$280$	0	0
$281$	−14.7833	−0.881897	−0.440949	−	0.897532i	$-0.645358\pi$
$281$	−14.7833	−0.881897	−0.440949	+	0.897532i	$0.645358\pi$
$282$	−9.92993	−0.591318
$283$	−13.1178	−0.779772	−0.389886	−	0.920863i	$-0.627486\pi$
$283$	−13.1178	−0.779772	−0.389886	+	0.920863i	$0.627486\pi$
$284$	0.774551	0.0459612
$285$	−1.79464	−0.106305
$286$	−25.1700	−1.48834
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−12.3053	−0.723842
$290$	−2.27367	−0.133515
$291$	−13.0098	−0.762647
$292$	−11.2214	−0.656684
$293$	−4.38920	−0.256420	−0.128210	−	0.991747i	$-0.540923\pi$
$293$	−4.38920	−0.256420	−0.128210	+	0.991747i	$0.540923\pi$
$294$	0	0
$295$	−6.01607	−0.350269
$296$	2.70448	0.157195
$297$	5.35023	0.310452
$298$	1.17405	0.0680109
$299$	−4.70448	−0.272067
$300$	4.77053	0.275427
$301$	0	0
$302$	−6.30531	−0.362830
$303$	−4.77053	−0.274060
$304$	−3.74642	−0.214872
$305$	4.29117	0.245712
$306$	2.16672	0.123863
$307$	10.1755	0.580745	0.290372	−	0.956914i	$-0.406221\pi$
$307$	10.1755	0.580745	0.290372	+	0.956914i	$0.406221\pi$
$308$	0	0
$309$	7.37836	0.419740
$310$	−4.68037	−0.265827
$311$	−12.5505	−0.711675	−0.355837	−	0.934548i	$-0.615804\pi$
$311$	−12.5505	−0.711675	−0.355837	+	0.934548i	$0.615804\pi$
$312$	−4.70448	−0.266339
$313$	15.8840	0.897815	0.448907	−	0.893578i	$-0.351813\pi$
$313$	15.8840	0.897815	0.448907	+	0.893578i	$0.351813\pi$
$314$	−2.28417	−0.128903
$315$	0	0
$316$	0.847088	0.0476524
$317$	30.5589	1.71636	0.858179	−	0.513350i	$-0.171596\pi$
$317$	30.5589	1.71636	0.858179	+	0.513350i	$0.171596\pi$
$318$	2.47903	0.139017
$319$	25.3944	1.42182
$320$	−0.479029	−0.0267785
$321$	−14.9299	−0.833307
$322$	0	0
$323$	8.11745	0.451667
$324$	1.00000	0.0555556
$325$	22.4429	1.24491
$326$	−4.77455	−0.264438
$327$	−4.53775	−0.250938
$328$	−0.253580	−0.0140016
$329$	0	0
$330$	2.56291	0.141084
$331$	−34.2375	−1.88186	−0.940932	−	0.338597i	$-0.890048\pi$
$331$	−34.2375	−1.88186	−0.940932	+	0.338597i	$0.890048\pi$
$332$	10.9299	0.599858
$333$	−2.70448	−0.148204
$334$	20.9500	1.14633
$335$	3.20971	0.175365
$336$	0	0
$337$	−12.2590	−0.667791	−0.333896	−	0.942610i	$-0.608363\pi$
$337$	−12.2590	−0.667791	−0.333896	+	0.942610i	$0.608363\pi$
$338$	−9.13211	−0.496721
$339$	14.2455	0.773712
$340$	1.03792	0.0562892
$341$	52.2746	2.83083
$342$	3.74642	0.202583
$343$	0	0
$344$	−2.00000	−0.107833
$345$	0.479029	0.0257900
$346$	17.2214	0.925830
$347$	−9.54106	−0.512191	−0.256096	−	0.966651i	$-0.582436\pi$
$347$	−9.54106	−0.512191	−0.256096	+	0.966651i	$0.582436\pi$
$348$	4.74642	0.254435
$349$	−8.44688	−0.452151	−0.226075	−	0.974110i	$-0.572590\pi$
$349$	−8.44688	−0.452151	−0.226075	+	0.974110i	$0.572590\pi$
$350$	0	0
$351$	4.70448	0.251106
$352$	5.35023	0.285168
$353$	24.4804	1.30296	0.651481	−	0.758665i	$-0.274148\pi$
$353$	24.4804	1.30296	0.651481	+	0.758665i	$0.274148\pi$
$354$	12.5589	0.667498
$355$	−0.371032	−0.0196924
$356$	−3.21164	−0.170216
$357$	0	0
$358$	−24.5267	−1.29628
$359$	20.2415	1.06831	0.534153	−	0.845388i	$-0.320631\pi$
$359$	20.2415	1.06831	0.534153	+	0.845388i	$0.320631\pi$
$360$	0.479029	0.0252470
$361$	−4.96434	−0.261281
$362$	20.4123	1.07284
$363$	−17.6249	−0.925070
$364$	0	0
$365$	5.37539	0.281361
$366$	−8.95806	−0.468245
$367$	5.85040	0.305388	0.152694	−	0.988274i	$-0.451205\pi$
$367$	5.85040	0.305388	0.152694	+	0.988274i	$0.451205\pi$
$368$	1.00000	0.0521286
$369$	0.253580	0.0132009
$370$	−1.29552	−0.0673510
$371$	0	0
$372$	9.77053	0.506578
$373$	33.1543	1.71667	0.858333	−	0.513093i	$-0.171500\pi$
$373$	33.1543	1.71667	0.858333	+	0.513093i	$0.171500\pi$
$374$	−11.5925	−0.599432
$375$	−4.68037	−0.241693
$376$	9.92993	0.512097
$377$	22.3294	1.15002
$378$	0	0
$379$	29.1996	1.49988	0.749941	−	0.661505i	$-0.230082\pi$
$379$	29.1996	1.49988	0.749941	+	0.661505i	$0.230082\pi$
$380$	1.79464	0.0920632
$381$	12.3053	0.630420
$382$	1.23926	0.0634060
$383$	−35.2232	−1.79982	−0.899910	−	0.436075i	$-0.856368\pi$
$383$	−35.2232	−1.79982	−0.899910	+	0.436075i	$0.856368\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	11.1795	0.569021
$387$	2.00000	0.101666
$388$	13.0098	0.660472
$389$	−30.6166	−1.55232	−0.776161	−	0.630535i	$-0.782836\pi$
$389$	−30.6166	−1.55232	−0.776161	+	0.630535i	$0.782836\pi$
$390$	2.25358	0.114114
$391$	−2.16672	−0.109576
$392$	0	0
$393$	9.31561	0.469911
$394$	−22.0956	−1.11316
$395$	−0.405780	−0.0204170
$396$	−5.35023	−0.268859
$397$	−16.9058	−0.848479	−0.424239	−	0.905550i	$-0.639458\pi$
$397$	−16.9058	−0.848479	−0.424239	+	0.905550i	$0.639458\pi$
$398$	−8.49615	−0.425873
$399$	0	0
$400$	−4.77053	−0.238527
$401$	−32.4735	−1.62165	−0.810823	−	0.585291i	$-0.800980\pi$
$401$	−32.4735	−1.62165	−0.810823	+	0.585291i	$0.800980\pi$
$402$	−6.70046	−0.334188
$403$	45.9652	2.28969
$404$	4.77053	0.237343
$405$	−0.479029	−0.0238031
$406$	0	0
$407$	14.4696	0.717230
$408$	−2.16672	−0.107269
$409$	−27.0196	−1.33603	−0.668016	−	0.744147i	$-0.732856\pi$
$409$	−27.0196	−1.33603	−0.668016	+	0.744147i	$0.732856\pi$
$410$	0.121472	0.00599908
$411$	−13.2046	−0.651337
$412$	−7.37836	−0.363506
$413$	0	0
$414$	−1.00000	−0.0491473
$415$	−5.23575	−0.257013
$416$	4.70448	0.230656
$417$	5.92993	0.290390
$418$	−20.0442	−0.980394
$419$	2.08686	0.101950	0.0509748	−	0.998700i	$-0.483767\pi$
$419$	2.08686	0.101950	0.0509748	+	0.998700i	$0.483767\pi$
$420$	0	0
$421$	23.2805	1.13462	0.567311	−	0.823504i	$-0.307984\pi$
$421$	23.2805	1.13462	0.567311	+	0.823504i	$0.307984\pi$
$422$	−20.3808	−0.992123
$423$	−9.92993	−0.482810
$424$	−2.47903	−0.120392
$425$	10.3364	0.501390
$426$	0.774551	0.0375271
$427$	0	0
$428$	14.9299	0.721665
$429$	−25.1700	−1.21522
$430$	0.958058	0.0462016
$431$	−26.6106	−1.28179	−0.640894	−	0.767629i	$-0.721436\pi$
$431$	−26.6106	−1.28179	−0.640894	+	0.767629i	$0.721436\pi$
$432$	−1.00000	−0.0481125
$433$	34.9354	1.67889	0.839443	−	0.543447i	$-0.182881\pi$
$433$	34.9354	1.67889	0.839443	+	0.543447i	$0.182881\pi$
$434$	0	0
$435$	−2.27367	−0.109014
$436$	4.53775	0.217319
$437$	−3.74642	−0.179216
$438$	−11.2214	−0.536181
$439$	−7.73696	−0.369265	−0.184633	−	0.982808i	$-0.559110\pi$
$439$	−7.73696	−0.369265	−0.184633	+	0.982808i	$0.559110\pi$
$440$	−2.56291	−0.122182
$441$	0	0
$442$	−10.1933	−0.484846
$443$	19.3432	0.919025	0.459512	−	0.888171i	$-0.348024\pi$
$443$	19.3432	0.919025	0.459512	+	0.888171i	$0.348024\pi$
$444$	2.70448	0.128349
$445$	1.53847	0.0729303
$446$	3.18753	0.150934
$447$	1.17405	0.0555307
$448$	0	0
$449$	16.0718	0.758476	0.379238	−	0.925299i	$-0.376186\pi$
$449$	16.0718	0.758476	0.379238	+	0.925299i	$0.376186\pi$
$450$	4.77053	0.224885
$451$	−1.35671	−0.0638851
$452$	−14.2455	−0.670054
$453$	−6.30531	−0.296249
$454$	−5.35827	−0.251476
$455$	0	0
$456$	−3.74642	−0.175442
$457$	14.9339	0.698581	0.349290	−	0.937015i	$-0.386423\pi$
$457$	14.9339	0.698581	0.349290	+	0.937015i	$0.386423\pi$
$458$	23.4582	1.09613
$459$	2.16672	0.101134
$460$	−0.479029	−0.0223348
$461$	23.1660	1.07895	0.539474	−	0.842002i	$-0.318623\pi$
$461$	23.1660	1.07895	0.539474	+	0.842002i	$0.318623\pi$
$462$	0	0
$463$	40.4429	1.87954	0.939769	−	0.341809i	$-0.111040\pi$
$463$	40.4429	1.87954	0.939769	+	0.341809i	$0.111040\pi$
$464$	−4.74642	−0.220347
$465$	−4.68037	−0.217047
$466$	24.7803	1.14793
$467$	6.42030	0.297096	0.148548	−	0.988905i	$-0.452540\pi$
$467$	6.42030	0.297096	0.148548	+	0.988905i	$0.452540\pi$
$468$	−4.70448	−0.217465
$469$	0	0
$470$	−4.75672	−0.219411
$471$	−2.28417	−0.105249
$472$	−12.5589	−0.578070
$473$	−10.7005	−0.492008
$474$	0.847088	0.0389081
$475$	17.8724	0.820043
$476$	0	0
$477$	2.47903	0.113507
$478$	−4.97187	−0.227408
$479$	8.25358	0.377116	0.188558	−	0.982062i	$-0.439619\pi$
$479$	8.25358	0.377116	0.188558	+	0.982062i	$0.439619\pi$
$480$	−0.479029	−0.0218646
$481$	12.7232	0.580126
$482$	7.48338	0.340859
$483$	0	0
$484$	17.6249	0.801134
$485$	−6.23206	−0.282983
$486$	1.00000	0.0453609
$487$	27.4290	1.24293	0.621464	−	0.783442i	$-0.286538\pi$
$487$	27.4290	1.24293	0.621464	+	0.783442i	$0.286538\pi$
$488$	8.95806	0.405512
$489$	−4.77455	−0.215913
$490$	0	0
$491$	15.9067	0.717857	0.358929	−	0.933365i	$-0.383142\pi$
$491$	15.9067	0.717857	0.358929	+	0.933365i	$0.383142\pi$
$492$	−0.253580	−0.0114323
$493$	10.2842	0.463176
$494$	−17.6249	−0.792984
$495$	2.56291	0.115194
$496$	−9.77053	−0.438710
$497$	0	0
$498$	10.9299	0.489782
$499$	−3.27175	−0.146463	−0.0732317	−	0.997315i	$-0.523331\pi$
$499$	−3.27175	−0.146463	−0.0732317	+	0.997315i	$0.523331\pi$
$500$	4.68037	0.209312
$501$	20.9500	0.935978
$502$	14.9752	0.668375
$503$	1.58267	0.0705678	0.0352839	−	0.999377i	$-0.488766\pi$
$503$	1.58267	0.0705678	0.0352839	+	0.999377i	$0.488766\pi$
$504$	0	0
$505$	−2.28522	−0.101691
$506$	5.35023	0.237847
$507$	−9.13211	−0.405571
$508$	−12.3053	−0.545960
$509$	−16.9544	−0.751489	−0.375745	−	0.926723i	$-0.622613\pi$
$509$	−16.9544	−0.751489	−0.375745	+	0.926723i	$0.622613\pi$
$510$	1.03792	0.0459600
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	3.74642	0.165408
$514$	−0.503140	−0.0221926
$515$	3.53445	0.155746
$516$	−2.00000	−0.0880451
$517$	53.1274	2.33654
$518$	0	0
$519$	17.2214	0.755937
$520$	−2.25358	−0.0988260
$521$	−7.54106	−0.330380	−0.165190	−	0.986262i	$-0.552824\pi$
$521$	−7.54106	−0.330380	−0.165190	+	0.986262i	$0.552824\pi$
$522$	4.74642	0.207745
$523$	19.1930	0.839250	0.419625	−	0.907698i	$-0.362162\pi$
$523$	19.1930	0.839250	0.419625	+	0.907698i	$0.362162\pi$
$524$	−9.31561	−0.406954
$525$	0	0
$526$	4.99163	0.217645
$527$	21.1700	0.922181
$528$	5.35023	0.232839
$529$	1.00000	0.0434783
$530$	1.18753	0.0515828
$531$	12.5589	0.545010
$532$	0	0
$533$	−1.19296	−0.0516729
$534$	−3.21164	−0.138981
$535$	−7.15186	−0.309202
$536$	6.70046	0.289416
$537$	−24.5267	−1.05841
$538$	−4.12775	−0.177960
$539$	0	0
$540$	0.479029	0.0206141
$541$	−29.7946	−1.28097	−0.640486	−	0.767970i	$-0.721267\pi$
$541$	−29.7946	−1.28097	−0.640486	+	0.767970i	$0.721267\pi$
$542$	2.93797	0.126196
$543$	20.4123	0.875974
$544$	2.16672	0.0928975
$545$	−2.17372	−0.0931117
$546$	0	0
$547$	−16.6264	−0.710892	−0.355446	−	0.934697i	$-0.615671\pi$
$547$	−16.6264	−0.710892	−0.355446	+	0.934697i	$0.615671\pi$
$548$	13.2046	0.564074
$549$	−8.95806	−0.382321
$550$	−25.5234	−1.08832
$551$	17.7821	0.757542
$552$	1.00000	0.0425628
$553$	0	0
$554$	28.6924	1.21902
$555$	−1.29552	−0.0549919
$556$	−5.92993	−0.251485
$557$	17.2298	0.730050	0.365025	−	0.930998i	$-0.381060\pi$
$557$	17.2298	0.730050	0.365025	+	0.930998i	$0.381060\pi$
$558$	9.77053	0.413620
$559$	−9.40895	−0.397956
$560$	0	0
$561$	−11.5925	−0.489434
$562$	14.7833	0.623596
$563$	29.8011	1.25597	0.627984	−	0.778226i	$-0.283880\pi$
$563$	29.8011	1.25597	0.627984	+	0.778226i	$0.283880\pi$
$564$	9.92993	0.418125
$565$	6.82402	0.287089
$566$	13.1178	0.551382
$567$	0	0
$568$	−0.774551	−0.0324995
$569$	16.6589	0.698375	0.349188	−	0.937053i	$-0.386458\pi$
$569$	16.6589	0.698375	0.349188	+	0.937053i	$0.386458\pi$
$570$	1.79464	0.0751693
$571$	41.5370	1.73827	0.869136	−	0.494574i	$-0.164676\pi$
$571$	41.5370	1.73827	0.869136	+	0.494574i	$0.164676\pi$
$572$	25.1700	1.05241
$573$	1.23926	0.0517708
$574$	0	0
$575$	−4.77053	−0.198945
$576$	1.00000	0.0416667
$577$	−46.0259	−1.91608	−0.958041	−	0.286632i	$-0.907464\pi$
$577$	−46.0259	−1.91608	−0.958041	+	0.286632i	$0.907464\pi$
$578$	12.3053	0.511834
$579$	11.1795	0.464604
$580$	2.27367	0.0944091
$581$	0	0
$582$	13.0098	0.539273
$583$	−13.2634	−0.549313
$584$	11.2214	0.464346
$585$	2.25358	0.0931741
$586$	4.38920	0.181316
$587$	−10.5865	−0.436952	−0.218476	−	0.975842i	$-0.570109\pi$
$587$	−10.5865	−0.436952	−0.218476	+	0.975842i	$0.570109\pi$
$588$	0	0
$589$	36.6045	1.50826
$590$	6.01607	0.247678
$591$	−22.0956	−0.908892
$592$	−2.70448	−0.111153
$593$	41.7263	1.71349	0.856747	−	0.515736i	$-0.172482\pi$
$593$	41.7263	1.71349	0.856747	+	0.515736i	$0.172482\pi$
$594$	−5.35023	−0.219523
$595$	0	0
$596$	−1.17405	−0.0480910
$597$	−8.49615	−0.347724
$598$	4.70448	0.192380
$599$	12.9738	0.530095	0.265047	−	0.964235i	$-0.414612\pi$
$599$	12.9738	0.530095	0.265047	+	0.964235i	$0.414612\pi$
$600$	−4.77053	−0.194756
$601$	15.1795	0.619184	0.309592	−	0.950869i	$-0.399808\pi$
$601$	15.1795	0.619184	0.309592	+	0.950869i	$0.399808\pi$
$602$	0	0
$603$	−6.70046	−0.272864
$604$	6.30531	0.256560
$605$	−8.44286	−0.343251
$606$	4.77053	0.193790
$607$	−43.6786	−1.77286	−0.886430	−	0.462863i	$-0.846822\pi$
$607$	−43.6786	−1.77286	−0.886430	+	0.462863i	$0.846822\pi$
$608$	3.74642	0.151937
$609$	0	0
$610$	−4.29117	−0.173744
$611$	46.7151	1.88989
$612$	−2.16672	−0.0875846
$613$	13.0931	0.528827	0.264413	−	0.964409i	$-0.414822\pi$
$613$	13.0931	0.528827	0.264413	+	0.964409i	$0.414822\pi$
$614$	−10.1755	−0.410648
$615$	0.121472	0.00489823
$616$	0	0
$617$	−6.04525	−0.243373	−0.121686	−	0.992569i	$-0.538830\pi$
$617$	−6.04525	−0.243373	−0.121686	+	0.992569i	$0.538830\pi$
$618$	−7.37836	−0.296801
$619$	9.73838	0.391419	0.195709	−	0.980662i	$-0.437299\pi$
$619$	9.73838	0.391419	0.195709	+	0.980662i	$0.437299\pi$
$620$	4.68037	0.187968
$621$	−1.00000	−0.0401286
$622$	12.5505	0.503230
$623$	0	0
$624$	4.70448	0.188330
$625$	21.6106	0.864425
$626$	−15.8840	−0.634851
$627$	−20.0442	−0.800488
$628$	2.28417	0.0911485
$629$	5.85985	0.233648
$630$	0	0
$631$	−42.7282	−1.70098	−0.850492	−	0.525989i	$-0.823695\pi$
$631$	−42.7282	−1.70098	−0.850492	+	0.525989i	$0.823695\pi$
$632$	−0.847088	−0.0336954
$633$	−20.3808	−0.810065
$634$	−30.5589	−1.21365
$635$	5.89460	0.233920
$636$	−2.47903	−0.0982999
$637$	0	0
$638$	−25.3944	−1.00538
$639$	0.774551	0.0306408
$640$	0.479029	0.0189353
$641$	−14.2149	−0.561457	−0.280728	−	0.959787i	$-0.590576\pi$
$641$	−14.2149	−0.561457	−0.280728	+	0.959787i	$0.590576\pi$
$642$	14.9299	0.589237
$643$	29.3990	1.15938	0.579691	−	0.814836i	$-0.303173\pi$
$643$	29.3990	1.15938	0.579691	+	0.814836i	$0.303173\pi$
$644$	0	0
$645$	0.958058	0.0377235
$646$	−8.11745	−0.319377
$647$	35.1040	1.38008	0.690040	−	0.723771i	$-0.257593\pi$
$647$	35.1040	1.38008	0.690040	+	0.723771i	$0.257593\pi$
$648$	−1.00000	−0.0392837
$649$	−67.1930	−2.63755
$650$	−22.4429	−0.880281
$651$	0	0
$652$	4.77455	0.186986
$653$	15.3294	0.599887	0.299943	−	0.953957i	$-0.403032\pi$
$653$	15.3294	0.599887	0.299943	+	0.953957i	$0.403032\pi$
$654$	4.53775	0.177440
$655$	4.46245	0.174362
$656$	0.253580	0.00990064
$657$	−11.2214	−0.437790
$658$	0	0
$659$	−6.98865	−0.272239	−0.136120	−	0.990692i	$-0.543463\pi$
$659$	−6.98865	−0.272239	−0.136120	+	0.990692i	$0.543463\pi$
$660$	−2.56291	−0.0997613
$661$	−14.2190	−0.553054	−0.276527	−	0.961006i	$-0.589183\pi$
$661$	−14.2190	−0.553054	−0.276527	+	0.961006i	$0.589183\pi$
$662$	34.2375	1.33068
$663$	−10.1933	−0.395875
$664$	−10.9299	−0.424163
$665$	0	0
$666$	2.70448	0.104796
$667$	−4.74642	−0.183782
$668$	−20.9500	−0.810581
$669$	3.18753	0.123237
$670$	−3.20971	−0.124002
$671$	47.9277	1.85023
$672$	0	0
$673$	−14.0339	−0.540967	−0.270484	−	0.962725i	$-0.587184\pi$
$673$	−14.0339	−0.540967	−0.270484	+	0.962725i	$0.587184\pi$
$674$	12.2590	0.472200
$675$	4.77053	0.183618
$676$	9.13211	0.351235
$677$	−23.4707	−0.902051	−0.451025	−	0.892511i	$-0.648942\pi$
$677$	−23.4707	−0.902051	−0.451025	+	0.892511i	$0.648942\pi$
$678$	−14.2455	−0.547097
$679$	0	0
$680$	−1.03792	−0.0398025
$681$	−5.35827	−0.205329
$682$	−52.2746	−2.00170
$683$	−23.9175	−0.915179	−0.457589	−	0.889164i	$-0.651287\pi$
$683$	−23.9175	−0.915179	−0.457589	+	0.889164i	$0.651287\pi$
$684$	−3.74642	−0.143248
$685$	−6.32541	−0.241681
$686$	0	0
$687$	23.4582	0.894987
$688$	2.00000	0.0762493
$689$	−11.6625	−0.444307
$690$	−0.479029	−0.0182363
$691$	14.6826	0.558553	0.279277	−	0.960211i	$-0.409905\pi$
$691$	14.6826	0.558553	0.279277	+	0.960211i	$0.409905\pi$
$692$	−17.2214	−0.654660
$693$	0	0
$694$	9.54106	0.362174
$695$	2.84061	0.107750
$696$	−4.74642	−0.179913
$697$	−0.549438	−0.0208114
$698$	8.44688	0.319719
$699$	24.7803	0.937278
$700$	0	0
$701$	−13.9383	−0.526442	−0.263221	−	0.964736i	$-0.584785\pi$
$701$	−13.9383	−0.526442	−0.263221	+	0.964736i	$0.584785\pi$
$702$	−4.70448	−0.177559
$703$	10.1321	0.382140
$704$	−5.35023	−0.201644
$705$	−4.75672	−0.179148
$706$	−24.4804	−0.921334
$707$	0	0
$708$	−12.5589	−0.471992
$709$	12.9234	0.485350	0.242675	−	0.970108i	$-0.421975\pi$
$709$	12.9234	0.485350	0.242675	+	0.970108i	$0.421975\pi$
$710$	0.371032	0.0139246
$711$	0.847088	0.0317683
$712$	3.21164	0.120361
$713$	−9.77053	−0.365909
$714$	0	0
$715$	−12.0572	−0.450913
$716$	24.5267	0.916607
$717$	−4.97187	−0.185678
$718$	−20.2415	−0.755407
$719$	13.3820	0.499065	0.249532	−	0.968366i	$-0.419723\pi$
$719$	13.3820	0.499065	0.249532	+	0.968366i	$0.419723\pi$
$720$	−0.479029	−0.0178523
$721$	0	0
$722$	4.96434	0.184754
$723$	7.48338	0.278310
$724$	−20.4123	−0.758616
$725$	22.6429	0.840938
$726$	17.6249	0.654123
$727$	−47.9963	−1.78009	−0.890043	−	0.455877i	$-0.849326\pi$
$727$	−47.9963	−1.78009	−0.890043	+	0.455877i	$0.849326\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−5.37539	−0.198952
$731$	−4.33345	−0.160278
$732$	8.95806	0.331099
$733$	25.4918	0.941561	0.470780	−	0.882250i	$-0.343972\pi$
$733$	25.4918	0.941561	0.470780	+	0.882250i	$0.343972\pi$
$734$	−5.85040	−0.215942
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	35.8490	1.32051
$738$	−0.253580	−0.00933441
$739$	24.6174	0.905566	0.452783	−	0.891621i	$-0.350431\pi$
$739$	24.6174	0.905566	0.452783	+	0.891621i	$0.350431\pi$
$740$	1.29552	0.0476244
$741$	−17.6249	−0.647469
$742$	0	0
$743$	−2.89777	−0.106309	−0.0531545	−	0.998586i	$-0.516928\pi$
$743$	−2.89777	−0.106309	−0.0531545	+	0.998586i	$0.516928\pi$
$744$	−9.77053	−0.358205
$745$	0.562404	0.0206049
$746$	−33.1543	−1.21387
$747$	10.9299	0.399905
$748$	11.5925	0.423862
$749$	0	0
$750$	4.68037	0.170903
$751$	−36.8843	−1.34593	−0.672964	−	0.739676i	$-0.734979\pi$
$751$	−36.8843	−1.34593	−0.672964	+	0.739676i	$0.734979\pi$
$752$	−9.92993	−0.362107
$753$	14.9752	0.545726
$754$	−22.3294	−0.813190
$755$	−3.02043	−0.109925
$756$	0	0
$757$	−46.4053	−1.68663	−0.843314	−	0.537421i	$-0.819399\pi$
$757$	−46.4053	−1.68663	−0.843314	+	0.537421i	$0.819399\pi$
$758$	−29.1996	−1.06058
$759$	5.35023	0.194201
$760$	−1.79464	−0.0650985
$761$	−42.1477	−1.52785	−0.763926	−	0.645304i	$-0.776731\pi$
$761$	−42.1477	−1.52785	−0.763926	+	0.645304i	$0.776731\pi$
$762$	−12.3053	−0.445774
$763$	0	0
$764$	−1.23926	−0.0448348
$765$	1.03792	0.0375262
$766$	35.2232	1.27267
$767$	−59.0830	−2.13336
$768$	−1.00000	−0.0360844
$769$	−38.8004	−1.39918	−0.699589	−	0.714545i	$-0.746634\pi$
$769$	−38.8004	−1.39918	−0.699589	+	0.714545i	$0.746634\pi$
$770$	0	0
$771$	−0.503140	−0.0181202
$772$	−11.1795	−0.402359
$773$	6.98568	0.251257	0.125629	−	0.992077i	$-0.459905\pi$
$773$	6.98568	0.251257	0.125629	+	0.992077i	$0.459905\pi$
$774$	−2.00000	−0.0718885
$775$	46.6106	1.67430
$776$	−13.0098	−0.467024
$777$	0	0
$778$	30.6166	1.09766
$779$	−0.950018	−0.0340379
$780$	−2.25358	−0.0806911
$781$	−4.14403	−0.148285
$782$	2.16672	0.0774818
$783$	4.74642	0.169623
$784$	0	0
$785$	−1.09419	−0.0390532
$786$	−9.31561	−0.332277
$787$	31.4701	1.12179	0.560895	−	0.827887i	$-0.310457\pi$
$787$	31.4701	1.12179	0.560895	+	0.827887i	$0.310457\pi$
$788$	22.0956	0.787123
$789$	4.99163	0.177707
$790$	0.405780	0.0144370
$791$	0	0
$792$	5.35023	0.190112
$793$	42.1430	1.49654
$794$	16.9058	0.599965
$795$	1.18753	0.0421172
$796$	8.49615	0.301138
$797$	8.98024	0.318097	0.159048	−	0.987271i	$-0.449157\pi$
$797$	8.98024	0.318097	0.159048	+	0.987271i	$0.449157\pi$
$798$	0	0
$799$	21.5154	0.761160
$800$	4.77053	0.168664
$801$	−3.21164	−0.113478
$802$	32.4735	1.14668
$803$	60.0372	2.11867
$804$	6.70046	0.236307
$805$	0	0
$806$	−45.9652	−1.61906
$807$	−4.12775	−0.145304
$808$	−4.77053	−0.167827
$809$	−33.4196	−1.17497	−0.587485	−	0.809235i	$-0.699882\pi$
$809$	−33.4196	−1.17497	−0.587485	+	0.809235i	$0.699882\pi$
$810$	0.479029	0.0168314
$811$	−54.4130	−1.91070	−0.955349	−	0.295480i	$-0.904520\pi$
$811$	−54.4130	−1.91070	−0.955349	+	0.295480i	$0.904520\pi$
$812$	0	0
$813$	2.93797	0.103039
$814$	−14.4696	−0.507158
$815$	−2.28715	−0.0801153
$816$	2.16672	0.0758505
$817$	−7.49284	−0.262141
$818$	27.0196	0.944718
$819$	0	0
$820$	−0.121472	−0.00424199
$821$	−5.08581	−0.177496	−0.0887480	−	0.996054i	$-0.528287\pi$
$821$	−5.08581	−0.177496	−0.0887480	+	0.996054i	$0.528287\pi$
$822$	13.2046	0.460565
$823$	−10.9084	−0.380243	−0.190122	−	0.981761i	$-0.560888\pi$
$823$	−10.9084	−0.380243	−0.190122	+	0.981761i	$0.560888\pi$
$824$	7.37836	0.257037
$825$	−25.5234	−0.888612
$826$	0	0
$827$	50.5292	1.75707	0.878536	−	0.477676i	$-0.158521\pi$
$827$	50.5292	1.75707	0.878536	+	0.477676i	$0.158521\pi$
$828$	1.00000	0.0347524
$829$	18.1999	0.632109	0.316055	−	0.948741i	$-0.397642\pi$
$829$	18.1999	0.632109	0.316055	+	0.948741i	$0.397642\pi$
$830$	5.23575	0.181736
$831$	28.6924	0.995329
$832$	−4.70448	−0.163098
$833$	0	0
$834$	−5.92993	−0.205337
$835$	10.0357	0.347298
$836$	20.0442	0.693243
$837$	9.77053	0.337719
$838$	−2.08686	−0.0720893
$839$	7.67057	0.264818	0.132409	−	0.991195i	$-0.457729\pi$
$839$	7.67057	0.264818	0.132409	+	0.991195i	$0.457729\pi$
$840$	0	0
$841$	−6.47150	−0.223155
$842$	−23.2805	−0.802299
$843$	14.7833	0.509164
$844$	20.3808	0.701537
$845$	−4.37454	−0.150489
$846$	9.92993	0.341398
$847$	0	0
$848$	2.47903	0.0851302
$849$	13.1178	0.450201
$850$	−10.3364	−0.354536
$851$	−2.70448	−0.0927083
$852$	−0.774551	−0.0265357
$853$	30.6924	1.05089	0.525444	−	0.850828i	$-0.323899\pi$
$853$	30.6924	1.05089	0.525444	+	0.850828i	$0.323899\pi$
$854$	0	0
$855$	1.79464	0.0613755
$856$	−14.9299	−0.510294
$857$	−30.9817	−1.05831	−0.529157	−	0.848524i	$-0.677492\pi$
$857$	−30.9817	−1.05831	−0.529157	+	0.848524i	$0.677492\pi$
$858$	25.1700	0.859291
$859$	−43.2852	−1.47687	−0.738436	−	0.674323i	$-0.764435\pi$
$859$	−43.2852	−1.47687	−0.738436	+	0.674323i	$0.764435\pi$
$860$	−0.958058	−0.0326695
$861$	0	0
$862$	26.6106	0.906362
$863$	12.5103	0.425857	0.212928	−	0.977068i	$-0.431700\pi$
$863$	12.5103	0.425857	0.212928	+	0.977068i	$0.431700\pi$
$864$	1.00000	0.0340207
$865$	8.24956	0.280493
$866$	−34.9354	−1.18715
$867$	12.3053	0.417910
$868$	0	0
$869$	−4.53212	−0.153742
$870$	2.27367	0.0770847
$871$	31.5222	1.06809
$872$	−4.53775	−0.153668
$873$	13.0098	0.440315
$874$	3.74642	0.126725
$875$	0	0
$876$	11.2214	0.379137
$877$	6.48044	0.218829	0.109415	−	0.993996i	$-0.465102\pi$
$877$	6.48044	0.218829	0.109415	+	0.993996i	$0.465102\pi$
$878$	7.73696	0.261110
$879$	4.38920	0.148044
$880$	2.56291	0.0863958
$881$	7.96941	0.268496	0.134248	−	0.990948i	$-0.457138\pi$
$881$	7.96941	0.268496	0.134248	+	0.990948i	$0.457138\pi$
$882$	0	0
$883$	6.75270	0.227246	0.113623	−	0.993524i	$-0.463754\pi$
$883$	6.75270	0.227246	0.113623	+	0.993524i	$0.463754\pi$
$884$	10.1933	0.342838
$885$	6.01607	0.202228
$886$	−19.3432	−0.649849
$887$	55.5388	1.86481	0.932405	−	0.361415i	$-0.117706\pi$
$887$	55.5388	1.86481	0.932405	+	0.361415i	$0.117706\pi$
$888$	−2.70448	−0.0907563
$889$	0	0
$890$	−1.53847	−0.0515695
$891$	−5.35023	−0.179239
$892$	−3.18753	−0.106726
$893$	37.2017	1.24491
$894$	−1.17405	−0.0392661
$895$	−11.7490	−0.392726
$896$	0	0
$897$	4.70448	0.157078
$898$	−16.0718	−0.536324
$899$	46.3750	1.54669
$900$	−4.77053	−0.159018
$901$	−5.37137	−0.178946
$902$	1.35671	0.0451736
$903$	0	0
$904$	14.2455	0.473800
$905$	9.77806	0.325034
$906$	6.30531	0.209480
$907$	−49.6741	−1.64940	−0.824700	−	0.565570i	$-0.808656\pi$
$907$	−49.6741	−1.64940	−0.824700	+	0.565570i	$0.808656\pi$
$908$	5.35827	0.177820
$909$	4.77053	0.158229
$910$	0	0
$911$	−4.22403	−0.139948	−0.0699742	−	0.997549i	$-0.522292\pi$
$911$	−4.22403	−0.139948	−0.0699742	+	0.997549i	$0.522292\pi$
$912$	3.74642	0.124056
$913$	−58.4776	−1.93533
$914$	−14.9339	−0.493971
$915$	−4.29117	−0.141862
$916$	−23.4582	−0.775082
$917$	0	0
$918$	−2.16672	−0.0715125
$919$	−33.6751	−1.11084	−0.555420	−	0.831570i	$-0.687442\pi$
$919$	−33.6751	−1.11084	−0.555420	+	0.831570i	$0.687442\pi$
$920$	0.479029	0.0157931
$921$	−10.1755	−0.335293
$922$	−23.1660	−0.762932
$923$	−3.64386	−0.119939
$924$	0	0
$925$	12.9018	0.424208
$926$	−40.4429	−1.32903
$927$	−7.37836	−0.242337
$928$	4.74642	0.155809
$929$	28.3826	0.931202	0.465601	−	0.884995i	$-0.345838\pi$
$929$	28.3826	0.931202	0.465601	+	0.884995i	$0.345838\pi$
$930$	4.68037	0.153475
$931$	0	0
$932$	−24.7803	−0.811706
$933$	12.5505	0.410886
$934$	−6.42030	−0.210079
$935$	−5.55312	−0.181607
$936$	4.70448	0.153771
$937$	−26.2115	−0.856291	−0.428146	−	0.903710i	$-0.640833\pi$
$937$	−26.2115	−0.856291	−0.428146	+	0.903710i	$0.640833\pi$
$938$	0	0
$939$	−15.8840	−0.518354
$940$	4.75672	0.155147
$941$	38.5046	1.25521	0.627606	−	0.778531i	$-0.284035\pi$
$941$	38.5046	1.25521	0.627606	+	0.778531i	$0.284035\pi$
$942$	2.28417	0.0744224
$943$	0.253580	0.00825771
$944$	12.5589	0.408757
$945$	0	0
$946$	10.7005	0.347902
$947$	14.4736	0.470329	0.235164	−	0.971956i	$-0.424437\pi$
$947$	14.4736	0.470329	0.235164	+	0.971956i	$0.424437\pi$
$948$	−0.847088	−0.0275122
$949$	52.7910	1.71367
$950$	−17.8724	−0.579858
$951$	−30.5589	−0.990940
$952$	0	0
$953$	−53.2578	−1.72519	−0.862595	−	0.505896i	$-0.831162\pi$
$953$	−53.2578	−1.72519	−0.862595	+	0.505896i	$0.831162\pi$
$954$	−2.47903	−0.0802615
$955$	0.593641	0.0192098
$956$	4.97187	0.160802
$957$	−25.3944	−0.820885
$958$	−8.25358	−0.266661
$959$	0	0
$960$	0.479029	0.0154606
$961$	64.4633	2.07946
$962$	−12.7232	−0.410211
$963$	14.9299	0.481110
$964$	−7.48338	−0.241024
$965$	5.35530	0.172393
$966$	0	0
$967$	52.5804	1.69087	0.845436	−	0.534077i	$-0.179341\pi$
$967$	52.5804	1.69087	0.845436	+	0.534077i	$0.179341\pi$
$968$	−17.6249	−0.566487
$969$	−8.11745	−0.260770
$970$	6.23206	0.200100
$971$	−37.1203	−1.19125	−0.595623	−	0.803264i	$-0.703095\pi$
$971$	−37.1203	−1.19125	−0.595623	+	0.803264i	$0.703095\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−27.4290	−0.878883
$975$	−22.4429	−0.718747
$976$	−8.95806	−0.286740
$977$	−2.20728	−0.0706172	−0.0353086	−	0.999376i	$-0.511241\pi$
$977$	−2.20728	−0.0706172	−0.0353086	+	0.999376i	$0.511241\pi$
$978$	4.77455	0.152673
$979$	17.1830	0.549171
$980$	0	0
$981$	4.53775	0.144879
$982$	−15.9067	−0.507602
$983$	0.142074	0.00453144	0.00226572	−	0.999997i	$-0.499279\pi$
$983$	0.142074	0.00453144	0.00226572	+	0.999997i	$0.499279\pi$
$984$	0.253580	0.00808384
$985$	−10.5844	−0.337248
$986$	−10.2842	−0.327515
$987$	0	0
$988$	17.6249	0.560724
$989$	2.00000	0.0635963
$990$	−2.56291	−0.0814547
$991$	48.2763	1.53355	0.766773	−	0.641918i	$-0.221861\pi$
$991$	48.2763	1.53355	0.766773	+	0.641918i	$0.221861\pi$
$992$	9.77053	0.310215
$993$	34.2375	1.08649
$994$	0	0
$995$	−4.06990	−0.129024
$996$	−10.9299	−0.346328
$997$	−34.5920	−1.09554	−0.547769	−	0.836630i	$-0.684523\pi$
$997$	−34.5920	−1.09554	−0.547769	+	0.836630i	$0.684523\pi$
$998$	3.27175	0.103565
$999$	2.70448	0.0855659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.cg.1.2		4
7.2	even	3		966.2.i.n.277.3	✓	8
7.4	even	3		966.2.i.n.415.3	yes	8
7.6	odd	2		6762.2.a.ch.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.n.277.3	✓	8	7.2	even	3
966.2.i.n.415.3	yes	8	7.4	even	3
6762.2.a.cg.1.2		4	1.1	even	1	trivial
6762.2.a.ch.1.3		4	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.479029 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.479029 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +0.479029 q^{10} -5.35023 q^{11} -1.00000 q^{12} -4.70448 q^{13} +0.479029 q^{15} +1.00000 q^{16} -2.16672 q^{17} -1.00000 q^{18} -3.74642 q^{19} -0.479029 q^{20} +5.35023 q^{22} +1.00000 q^{23} +1.00000 q^{24} -4.77053 q^{25} +4.70448 q^{26} -1.00000 q^{27} -4.74642 q^{29} -0.479029 q^{30} -9.77053 q^{31} -1.00000 q^{32} +5.35023 q^{33} +2.16672 q^{34} +1.00000 q^{36} -2.70448 q^{37} +3.74642 q^{38} +4.70448 q^{39} +0.479029 q^{40} +0.253580 q^{41} +2.00000 q^{43} -5.35023 q^{44} -0.479029 q^{45} -1.00000 q^{46} -9.92993 q^{47} -1.00000 q^{48} +4.77053 q^{50} +2.16672 q^{51} -4.70448 q^{52} +2.47903 q^{53} +1.00000 q^{54} +2.56291 q^{55} +3.74642 q^{57} +4.74642 q^{58} +12.5589 q^{59} +0.479029 q^{60} -8.95806 q^{61} +9.77053 q^{62} +1.00000 q^{64} +2.25358 q^{65} -5.35023 q^{66} -6.70046 q^{67} -2.16672 q^{68} -1.00000 q^{69} +0.774551 q^{71} -1.00000 q^{72} -11.2214 q^{73} +2.70448 q^{74} +4.77053 q^{75} -3.74642 q^{76} -4.70448 q^{78} +0.847088 q^{79} -0.479029 q^{80} +1.00000 q^{81} -0.253580 q^{82} +10.9299 q^{83} +1.03792 q^{85} -2.00000 q^{86} +4.74642 q^{87} +5.35023 q^{88} -3.21164 q^{89} +0.479029 q^{90} +1.00000 q^{92} +9.77053 q^{93} +9.92993 q^{94} +1.79464 q^{95} +1.00000 q^{96} +13.0098 q^{97} -5.35023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{8} + 4 q^{9} - 2 q^{10} + 6 q^{11} - 4 q^{12} - 2 q^{13} - 2 q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} - 6 q^{19} + 2 q^{20} - 6 q^{22} + 4 q^{23} + 4 q^{24} + 6 q^{25} + 2 q^{26} - 4 q^{27} - 10 q^{29} + 2 q^{30} - 14 q^{31} - 4 q^{32} - 6 q^{33} + 2 q^{34} + 4 q^{36} + 6 q^{37} + 6 q^{38} + 2 q^{39} - 2 q^{40} + 10 q^{41} + 8 q^{43} + 6 q^{44} + 2 q^{45} - 4 q^{46} - 10 q^{47} - 4 q^{48} - 6 q^{50} + 2 q^{51} - 2 q^{52} + 6 q^{53} + 4 q^{54} + 22 q^{55} + 6 q^{57} + 10 q^{58} + 24 q^{59} - 2 q^{60} - 28 q^{61} + 14 q^{62} + 4 q^{64} + 18 q^{65} + 6 q^{66} + 28 q^{67} - 2 q^{68} - 4 q^{69} + 16 q^{71} - 4 q^{72} + 6 q^{73} - 6 q^{74} - 6 q^{75} - 6 q^{76} - 2 q^{78} - 4 q^{79} + 2 q^{80} + 4 q^{81} - 10 q^{82} + 14 q^{83} - 26 q^{85} - 8 q^{86} + 10 q^{87} - 6 q^{88} - 14 q^{89} - 2 q^{90} + 4 q^{92} + 14 q^{93} + 10 q^{94} - 34 q^{95} + 4 q^{96} + 6 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 - 4 * q^8 + 4 * q^9 - 2 * q^10 + 6 * q^11 - 4 * q^12 - 2 * q^13 - 2 * q^15 + 4 * q^16 - 2 * q^17 - 4 * q^18 - 6 * q^19 + 2 * q^20 - 6 * q^22 + 4 * q^23 + 4 * q^24 + 6 * q^25 + 2 * q^26 - 4 * q^27 - 10 * q^29 + 2 * q^30 - 14 * q^31 - 4 * q^32 - 6 * q^33 + 2 * q^34 + 4 * q^36 + 6 * q^37 + 6 * q^38 + 2 * q^39 - 2 * q^40 + 10 * q^41 + 8 * q^43 + 6 * q^44 + 2 * q^45 - 4 * q^46 - 10 * q^47 - 4 * q^48 - 6 * q^50 + 2 * q^51 - 2 * q^52 + 6 * q^53 + 4 * q^54 + 22 * q^55 + 6 * q^57 + 10 * q^58 + 24 * q^59 - 2 * q^60 - 28 * q^61 + 14 * q^62 + 4 * q^64 + 18 * q^65 + 6 * q^66 + 28 * q^67 - 2 * q^68 - 4 * q^69 + 16 * q^71 - 4 * q^72 + 6 * q^73 - 6 * q^74 - 6 * q^75 - 6 * q^76 - 2 * q^78 - 4 * q^79 + 2 * q^80 + 4 * q^81 - 10 * q^82 + 14 * q^83 - 26 * q^85 - 8 * q^86 + 10 * q^87 - 6 * q^88 - 14 * q^89 - 2 * q^90 + 4 * q^92 + 14 * q^93 + 10 * q^94 - 34 * q^95 + 4 * q^96 + 6 * q^99

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