LMFDB - Embedded newform 6762.2.a.cn.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:	4.4.16448.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 7x^{2} + 8x + 14 $ x^4 - 2x^3 - 7x^2 + 8*x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.18398$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.183979 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.183979 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -0.183979 q^{10} +3.08861 q^{11} -1.00000 q^{12} +5.85838 q^{13} +0.183979 q^{15} +1.00000 q^{16} +6.36796 q^{17} +1.00000 q^{18} +3.41421 q^{19} -0.183979 q^{20} +3.08861 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.96615 q^{25} +5.85838 q^{26} -1.00000 q^{27} -4.68681 q^{29} +0.183979 q^{30} +3.41421 q^{31} +1.00000 q^{32} -3.08861 q^{33} +6.36796 q^{34} +1.00000 q^{36} -1.49042 q^{37} +3.41421 q^{38} -5.85838 q^{39} -0.183979 q^{40} +2.07621 q^{41} +4.94699 q^{43} +3.08861 q^{44} -0.183979 q^{45} -1.00000 q^{46} +5.01241 q^{47} -1.00000 q^{48} -4.96615 q^{50} -6.36796 q^{51} +5.85838 q^{52} -1.79972 q^{53} -1.00000 q^{54} -0.568241 q^{55} -3.41421 q^{57} -4.68681 q^{58} +7.91704 q^{59} +0.183979 q^{60} -2.30254 q^{61} +3.41421 q^{62} +1.00000 q^{64} -1.07782 q^{65} -3.08861 q^{66} -1.53953 q^{67} +6.36796 q^{68} +1.00000 q^{69} -3.08861 q^{71} +1.00000 q^{72} -5.13097 q^{73} -1.49042 q^{74} +4.96615 q^{75} +3.41421 q^{76} -5.85838 q^{78} -9.08861 q^{79} -0.183979 q^{80} +1.00000 q^{81} +2.07621 q^{82} +0.0175454 q^{83} -1.17157 q^{85} +4.94699 q^{86} +4.68681 q^{87} +3.08861 q^{88} -9.63380 q^{89} -0.183979 q^{90} -1.00000 q^{92} -3.41421 q^{93} +5.01241 q^{94} -0.628145 q^{95} -1.00000 q^{96} -4.60385 q^{97} +3.08861 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 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 + 6 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 6 q^{10} - 4 q^{12} + 10 q^{13} - 6 q^{15} + 4 q^{16} + 12 q^{17} + 4 q^{18} + 8 q^{19} + 6 q^{20} - 4 q^{23} - 4 q^{24} + 6 q^{25} + 10 q^{26} - 4 q^{27} + 6 q^{29} - 6 q^{30} + 8 q^{31} + 4 q^{32} + 12 q^{34} + 4 q^{36} - 6 q^{37} + 8 q^{38} - 10 q^{39} + 6 q^{40} + 14 q^{41} - 6 q^{43} + 6 q^{45} - 4 q^{46} + 2 q^{47} - 4 q^{48} + 6 q^{50} - 12 q^{51} + 10 q^{52} - 4 q^{53} - 4 q^{54} + 8 q^{55} - 8 q^{57} + 6 q^{58} + 8 q^{59} - 6 q^{60} + 12 q^{61} + 8 q^{62} + 4 q^{64} + 6 q^{65} - 4 q^{67} + 12 q^{68} + 4 q^{69} + 4 q^{72} + 12 q^{73} - 6 q^{74} - 6 q^{75} + 8 q^{76} - 10 q^{78} - 24 q^{79} + 6 q^{80} + 4 q^{81} + 14 q^{82} + 16 q^{83} - 16 q^{85} - 6 q^{86} - 6 q^{87} + 12 q^{89} + 6 q^{90} - 4 q^{92} - 8 q^{93} + 2 q^{94} + 12 q^{95} - 4 q^{96} + 30 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 6 * q^10 - 4 * q^12 + 10 * q^13 - 6 * q^15 + 4 * q^16 + 12 * q^17 + 4 * q^18 + 8 * q^19 + 6 * q^20 - 4 * q^23 - 4 * q^24 + 6 * q^25 + 10 * q^26 - 4 * q^27 + 6 * q^29 - 6 * q^30 + 8 * q^31 + 4 * q^32 + 12 * q^34 + 4 * q^36 - 6 * q^37 + 8 * q^38 - 10 * q^39 + 6 * q^40 + 14 * q^41 - 6 * q^43 + 6 * q^45 - 4 * q^46 + 2 * q^47 - 4 * q^48 + 6 * q^50 - 12 * q^51 + 10 * q^52 - 4 * q^53 - 4 * q^54 + 8 * q^55 - 8 * q^57 + 6 * q^58 + 8 * q^59 - 6 * q^60 + 12 * q^61 + 8 * q^62 + 4 * q^64 + 6 * q^65 - 4 * q^67 + 12 * q^68 + 4 * q^69 + 4 * q^72 + 12 * q^73 - 6 * q^74 - 6 * q^75 + 8 * q^76 - 10 * q^78 - 24 * q^79 + 6 * q^80 + 4 * q^81 + 14 * q^82 + 16 * q^83 - 16 * q^85 - 6 * q^86 - 6 * q^87 + 12 * q^89 + 6 * q^90 - 4 * q^92 - 8 * q^93 + 2 * q^94 + 12 * q^95 - 4 * q^96 + 30 * q^97

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
$5$	−0.183979	−0.0822781	−0.0411390	−	0.999153i	$-0.513099\pi$
$5$	−0.183979	−0.0822781	−0.0411390	+	0.999153i	$0.513099\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.183979	−0.0581794
$11$	3.08861	0.931252	0.465626	−	0.884982i	$-0.345829\pi$
$11$	3.08861	0.931252	0.465626	+	0.884982i	$0.345829\pi$
$12$	−1.00000	−0.288675
$13$	5.85838	1.62482	0.812411	−	0.583085i	$-0.198155\pi$
$13$	5.85838	1.62482	0.812411	+	0.583085i	$0.198155\pi$
$14$	0	0
$15$	0.183979	0.0475033
$16$	1.00000	0.250000
$17$	6.36796	1.54446	0.772228	−	0.635345i	$-0.219142\pi$
$17$	6.36796	1.54446	0.772228	+	0.635345i	$0.219142\pi$
$18$	1.00000	0.235702
$19$	3.41421	0.783274	0.391637	−	0.920120i	$-0.371909\pi$
$19$	3.41421	0.783274	0.391637	+	0.920120i	$0.371909\pi$
$20$	−0.183979	−0.0411390
$21$	0	0
$22$	3.08861	0.658495
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	−4.96615	−0.993230
$26$	5.85838	1.14892
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−4.68681	−0.870318	−0.435159	−	0.900354i	$-0.643308\pi$
$29$	−4.68681	−0.870318	−0.435159	+	0.900354i	$0.643308\pi$
$30$	0.183979	0.0335899
$31$	3.41421	0.613211	0.306605	−	0.951837i	$-0.400807\pi$
$31$	3.41421	0.613211	0.306605	+	0.951837i	$0.400807\pi$
$32$	1.00000	0.176777
$33$	−3.08861	−0.537659
$34$	6.36796	1.09210
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.49042	−0.245024	−0.122512	−	0.992467i	$-0.539095\pi$
$37$	−1.49042	−0.245024	−0.122512	+	0.992467i	$0.539095\pi$
$38$	3.41421	0.553859
$39$	−5.85838	−0.938091
$40$	−0.183979	−0.0290897
$41$	2.07621	0.324249	0.162125	−	0.986770i	$-0.448165\pi$
$41$	2.07621	0.324249	0.162125	+	0.986770i	$0.448165\pi$
$42$	0	0
$43$	4.94699	0.754409	0.377205	−	0.926130i	$-0.376885\pi$
$43$	4.94699	0.754409	0.377205	+	0.926130i	$0.376885\pi$
$44$	3.08861	0.465626
$45$	−0.183979	−0.0274260
$46$	−1.00000	−0.147442
$47$	5.01241	0.731135	0.365567	−	0.930785i	$-0.380875\pi$
$47$	5.01241	0.731135	0.365567	+	0.930785i	$0.380875\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−4.96615	−0.702320
$51$	−6.36796	−0.891693
$52$	5.85838	0.812411
$53$	−1.79972	−0.247210	−0.123605	−	0.992331i	$-0.539446\pi$
$53$	−1.79972	−0.247210	−0.123605	+	0.992331i	$0.539446\pi$
$54$	−1.00000	−0.136083
$55$	−0.568241	−0.0766216
$56$	0	0
$57$	−3.41421	−0.452224
$58$	−4.68681	−0.615408
$59$	7.91704	1.03071	0.515355	−	0.856977i	$-0.327660\pi$
$59$	7.91704	1.03071	0.515355	+	0.856977i	$0.327660\pi$
$60$	0.183979	0.0237516
$61$	−2.30254	−0.294811	−0.147405	−	0.989076i	$-0.547092\pi$
$61$	−2.30254	−0.294811	−0.147405	+	0.989076i	$0.547092\pi$
$62$	3.41421	0.433606
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.07782	−0.133687
$66$	−3.08861	−0.380182
$67$	−1.53953	−0.188084	−0.0940419	−	0.995568i	$-0.529979\pi$
$67$	−1.53953	−0.188084	−0.0940419	+	0.995568i	$0.529979\pi$
$68$	6.36796	0.772228
$69$	1.00000	0.120386
$70$	0	0
$71$	−3.08861	−0.366551	−0.183275	−	0.983062i	$-0.558670\pi$
$71$	−3.08861	−0.366551	−0.183275	+	0.983062i	$0.558670\pi$
$72$	1.00000	0.117851
$73$	−5.13097	−0.600535	−0.300267	−	0.953855i	$-0.597076\pi$
$73$	−5.13097	−0.600535	−0.300267	+	0.953855i	$0.597076\pi$
$74$	−1.49042	−0.173258
$75$	4.96615	0.573442
$76$	3.41421	0.391637
$77$	0	0
$78$	−5.85838	−0.663331
$79$	−9.08861	−1.02255	−0.511274	−	0.859418i	$-0.670826\pi$
$79$	−9.08861	−1.02255	−0.511274	+	0.859418i	$0.670826\pi$
$80$	−0.183979	−0.0205695
$81$	1.00000	0.111111
$82$	2.07621	0.229279
$83$	0.0175454	0.00192586	0.000962929	−	1.00000i	$-0.499693\pi$
$83$	0.0175454	0.00192586	0.000962929		1.00000i	$0.499693\pi$
$84$	0	0
$85$	−1.17157	−0.127075
$86$	4.94699	0.533448
$87$	4.68681	0.502478
$88$	3.08861	0.329247
$89$	−9.63380	−1.02118	−0.510590	−	0.859824i	$-0.670573\pi$
$89$	−9.63380	−1.02118	−0.510590	+	0.859824i	$0.670573\pi$
$90$	−0.183979	−0.0193931
$91$	0	0
$92$	−1.00000	−0.104257
$93$	−3.41421	−0.354037
$94$	5.01241	0.516990
$95$	−0.628145	−0.0644463
$96$	−1.00000	−0.102062
$97$	−4.60385	−0.467450	−0.233725	−	0.972303i	$-0.575092\pi$
$97$	−4.60385	−0.467450	−0.233725	+	0.972303i	$0.575092\pi$
$98$	0	0
$99$	3.08861	0.310417
$100$	−4.96615	−0.496615
$101$	5.39667	0.536989	0.268494	−	0.963281i	$-0.413474\pi$
$101$	5.39667	0.536989	0.268494	+	0.963281i	$0.413474\pi$
$102$	−6.36796	−0.630522
$103$	0.141621	0.0139543	0.00697717	−	0.999976i	$-0.497779\pi$
$103$	0.141621	0.0139543	0.00697717	+	0.999976i	$0.497779\pi$
$104$	5.85838	0.574461
$105$	0	0
$106$	−1.79972	−0.174804
$107$	−16.5452	−1.59948	−0.799742	−	0.600344i	$-0.795030\pi$
$107$	−16.5452	−1.59948	−0.799742	+	0.600344i	$0.795030\pi$
$108$	−1.00000	−0.0962250
$109$	15.9431	1.52707	0.763536	−	0.645765i	$-0.223462\pi$
$109$	15.9431	1.52707	0.763536	+	0.645765i	$0.223462\pi$
$110$	−0.568241	−0.0541797
$111$	1.49042	0.141464
$112$	0	0
$113$	1.42097	0.133673	0.0668366	−	0.997764i	$-0.478709\pi$
$113$	1.42097	0.133673	0.0668366	+	0.997764i	$0.478709\pi$
$114$	−3.41421	−0.319770
$115$	0.183979	0.0171562
$116$	−4.68681	−0.435159
$117$	5.85838	0.541607
$118$	7.91704	0.728823
$119$	0	0
$120$	0.183979	0.0167949
$121$	−1.46047	−0.132770
$122$	−2.30254	−0.208463
$123$	−2.07621	−0.187205
$124$	3.41421	0.306605
$125$	1.83357	0.163999
$126$	0	0
$127$	−12.0356	−1.06799	−0.533994	−	0.845488i	$-0.679309\pi$
$127$	−12.0356	−1.06799	−0.533994	+	0.845488i	$0.679309\pi$
$128$	1.00000	0.0883883
$129$	−4.94699	−0.435558
$130$	−1.07782	−0.0945311
$131$	2.47573	0.216306	0.108153	−	0.994134i	$-0.465506\pi$
$131$	2.47573	0.216306	0.108153	+	0.994134i	$0.465506\pi$
$132$	−3.08861	−0.268829
$133$	0	0
$134$	−1.53953	−0.132995
$135$	0.183979	0.0158344
$136$	6.36796	0.546048
$137$	17.6230	1.50563	0.752817	−	0.658229i	$-0.228694\pi$
$137$	17.6230	1.50563	0.752817	+	0.658229i	$0.228694\pi$
$138$	1.00000	0.0851257
$139$	−17.9526	−1.52272	−0.761362	−	0.648327i	$-0.775469\pi$
$139$	−17.9526	−1.52272	−0.761362	+	0.648327i	$0.775469\pi$
$140$	0	0
$141$	−5.01241	−0.422121
$142$	−3.08861	−0.259191
$143$	18.0943	1.51312
$144$	1.00000	0.0833333
$145$	0.862276	0.0716081
$146$	−5.13097	−0.424642
$147$	0	0
$148$	−1.49042	−0.122512
$149$	1.33925	0.109716	0.0548578	−	0.998494i	$-0.482529\pi$
$149$	1.33925	0.109716	0.0548578	+	0.998494i	$0.482529\pi$
$150$	4.96615	0.405485
$151$	9.05476	0.736866	0.368433	−	0.929654i	$-0.379894\pi$
$151$	9.05476	0.736866	0.368433	+	0.929654i	$0.379894\pi$
$152$	3.41421	0.276929
$153$	6.36796	0.514819
$154$	0	0
$155$	−0.628145	−0.0504538
$156$	−5.85838	−0.469046
$157$	−9.98421	−0.796827	−0.398413	−	0.917206i	$-0.630439\pi$
$157$	−9.98421	−0.796827	−0.398413	+	0.917206i	$0.630439\pi$
$158$	−9.08861	−0.723051
$159$	1.79972	0.142727
$160$	−0.183979	−0.0145448
$161$	0	0
$162$	1.00000	0.0785674
$163$	8.48528	0.664619	0.332309	−	0.943170i	$-0.392172\pi$
$163$	8.48528	0.664619	0.332309	+	0.943170i	$0.392172\pi$
$164$	2.07621	0.162125
$165$	0.568241	0.0442375
$166$	0.0175454	0.00136179
$167$	−12.1845	−0.942864	−0.471432	−	0.881902i	$-0.656263\pi$
$167$	−12.1845	−0.942864	−0.471432	+	0.881902i	$0.656263\pi$
$168$	0	0
$169$	21.3206	1.64005
$170$	−1.17157	−0.0898555
$171$	3.41421	0.261091
$172$	4.94699	0.377205
$173$	−6.21555	−0.472559	−0.236280	−	0.971685i	$-0.575928\pi$
$173$	−6.21555	−0.472559	−0.236280	+	0.971685i	$0.575928\pi$
$174$	4.68681	0.355306
$175$	0	0
$176$	3.08861	0.232813
$177$	−7.91704	−0.595081
$178$	−9.63380	−0.722084
$179$	12.6422	0.944920	0.472460	−	0.881352i	$-0.343366\pi$
$179$	12.6422	0.944920	0.472460	+	0.881352i	$0.343366\pi$
$180$	−0.183979	−0.0137130
$181$	18.4893	1.37430	0.687150	−	0.726515i	$-0.258861\pi$
$181$	18.4893	1.37430	0.687150	+	0.726515i	$0.258861\pi$
$182$	0	0
$183$	2.30254	0.170209
$184$	−1.00000	−0.0737210
$185$	0.274207	0.0201601
$186$	−3.41421	−0.250342
$187$	19.6682	1.43828
$188$	5.01241	0.365567
$189$	0	0
$190$	−0.628145	−0.0455704
$191$	−13.1230	−0.949545	−0.474773	−	0.880108i	$-0.657470\pi$
$191$	−13.1230	−0.949545	−0.474773	+	0.880108i	$0.657470\pi$
$192$	−1.00000	−0.0721688
$193$	14.6038	1.05121	0.525604	−	0.850729i	$-0.323839\pi$
$193$	14.6038	1.05121	0.525604	+	0.850729i	$0.323839\pi$
$194$	−4.60385	−0.330537
$195$	1.07782	0.0771843
$196$	0	0
$197$	17.5751	1.25218	0.626088	−	0.779752i	$-0.284655\pi$
$197$	17.5751	1.25218	0.626088	+	0.779752i	$0.284655\pi$
$198$	3.08861	0.219498
$199$	−1.39791	−0.0990953	−0.0495476	−	0.998772i	$-0.515778\pi$
$199$	−1.39791	−0.0990953	−0.0495476	+	0.998772i	$0.515778\pi$
$200$	−4.96615	−0.351160
$201$	1.53953	0.108590
$202$	5.39667	0.379708
$203$	0	0
$204$	−6.36796	−0.445846
$205$	−0.381979	−0.0266786
$206$	0.141621	0.00986720
$207$	−1.00000	−0.0695048
$208$	5.85838	0.406205
$209$	10.5452	0.729426
$210$	0	0
$211$	−17.9419	−1.23517	−0.617584	−	0.786505i	$-0.711888\pi$
$211$	−17.9419	−1.23517	−0.617584	+	0.786505i	$0.711888\pi$
$212$	−1.79972	−0.123605
$213$	3.08861	0.211628
$214$	−16.5452	−1.13101
$215$	−0.910144	−0.0620713
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	15.9431	1.07980
$219$	5.13097	0.346719
$220$	−0.568241	−0.0383108
$221$	37.3059	2.50947
$222$	1.49042	0.100030
$223$	23.9013	1.60055	0.800273	−	0.599636i	$-0.204688\pi$
$223$	23.9013	1.60055	0.800273	+	0.599636i	$0.204688\pi$
$224$	0	0
$225$	−4.96615	−0.331077
$226$	1.42097	0.0945213
$227$	−8.81212	−0.584881	−0.292441	−	0.956284i	$-0.594467\pi$
$227$	−8.81212	−0.584881	−0.292441	+	0.956284i	$0.594467\pi$
$228$	−3.41421	−0.226112
$229$	−0.194772	−0.0128709	−0.00643544	−	0.999979i	$-0.502048\pi$
$229$	−0.194772	−0.0128709	−0.00643544	+	0.999979i	$0.502048\pi$
$230$	0.183979	0.0121312
$231$	0	0
$232$	−4.68681	−0.307704
$233$	9.79972	0.642001	0.321000	−	0.947079i	$-0.395981\pi$
$233$	9.79972	0.642001	0.321000	+	0.947079i	$0.395981\pi$
$234$	5.85838	0.382974
$235$	−0.922179	−0.0601563
$236$	7.91704	0.515355
$237$	9.08861	0.590369
$238$	0	0
$239$	10.5835	0.684590	0.342295	−	0.939593i	$-0.388796\pi$
$239$	10.5835	0.684590	0.342295	+	0.939593i	$0.388796\pi$
$240$	0.183979	0.0118758
$241$	6.17847	0.397990	0.198995	−	0.980000i	$-0.436232\pi$
$241$	6.17847	0.397990	0.198995	+	0.980000i	$0.436232\pi$
$242$	−1.46047	−0.0938825
$243$	−1.00000	−0.0641500
$244$	−2.30254	−0.147405
$245$	0	0
$246$	−2.07621	−0.132374
$247$	20.0018	1.27268
$248$	3.41421	0.216803
$249$	−0.0175454	−0.00111189
$250$	1.83357	0.115965
$251$	18.6845	1.17936	0.589678	−	0.807638i	$-0.299255\pi$
$251$	18.6845	1.17936	0.589678	+	0.807638i	$0.299255\pi$
$252$	0	0
$253$	−3.08861	−0.194179
$254$	−12.0356	−0.755181
$255$	1.17157	0.0733667
$256$	1.00000	0.0625000
$257$	−1.76691	−0.110217	−0.0551084	−	0.998480i	$-0.517550\pi$
$257$	−1.76691	−0.110217	−0.0551084	+	0.998480i	$0.517550\pi$
$258$	−4.94699	−0.307986
$259$	0	0
$260$	−1.07782	−0.0668436
$261$	−4.68681	−0.290106
$262$	2.47573	0.152951
$263$	−7.58864	−0.467936	−0.233968	−	0.972244i	$-0.575171\pi$
$263$	−7.58864	−0.467936	−0.233968	+	0.972244i	$0.575171\pi$
$264$	−3.08861	−0.190091
$265$	0.331111	0.0203400
$266$	0	0
$267$	9.63380	0.589579
$268$	−1.53953	−0.0940419
$269$	24.6452	1.50264	0.751321	−	0.659937i	$-0.229417\pi$
$269$	24.6452	1.50264	0.751321	+	0.659937i	$0.229417\pi$
$270$	0.183979	0.0111966
$271$	−18.8261	−1.14361	−0.571803	−	0.820391i	$-0.693756\pi$
$271$	−18.8261	−1.14361	−0.571803	+	0.820391i	$0.693756\pi$
$272$	6.36796	0.386114
$273$	0	0
$274$	17.6230	1.06464
$275$	−15.3385	−0.924948
$276$	1.00000	0.0601929
$277$	11.8571	0.712426	0.356213	−	0.934405i	$-0.384068\pi$
$277$	11.8571	0.712426	0.356213	+	0.934405i	$0.384068\pi$
$278$	−17.9526	−1.07673
$279$	3.41421	0.204404
$280$	0	0
$281$	8.48652	0.506264	0.253132	−	0.967432i	$-0.418539\pi$
$281$	8.48652	0.506264	0.253132	+	0.967432i	$0.418539\pi$
$282$	−5.01241	−0.298484
$283$	5.34329	0.317626	0.158813	−	0.987309i	$-0.449233\pi$
$283$	5.34329	0.317626	0.158813	+	0.987309i	$0.449233\pi$
$284$	−3.08861	−0.183275
$285$	0.628145	0.0372081
$286$	18.0943	1.06994
$287$	0	0
$288$	1.00000	0.0589256
$289$	23.5509	1.38535
$290$	0.862276	0.0506346
$291$	4.60385	0.269882
$292$	−5.13097	−0.300267
$293$	17.9148	1.04659	0.523296	−	0.852151i	$-0.324702\pi$
$293$	17.9148	1.04659	0.523296	+	0.852151i	$0.324702\pi$
$294$	0	0
$295$	−1.45657	−0.0848049
$296$	−1.49042	−0.0866289
$297$	−3.08861	−0.179220
$298$	1.33925	0.0775806
$299$	−5.85838	−0.338799
$300$	4.96615	0.286721
$301$	0	0
$302$	9.05476	0.521043
$303$	−5.39667	−0.310030
$304$	3.41421	0.195819
$305$	0.423621	0.0242564
$306$	6.36796	0.364032
$307$	−6.99339	−0.399134	−0.199567	−	0.979884i	$-0.563954\pi$
$307$	−6.99339	−0.399134	−0.199567	+	0.979884i	$0.563954\pi$
$308$	0	0
$309$	−0.141621	−0.00805654
$310$	−0.628145	−0.0356762
$311$	19.9013	1.12850	0.564248	−	0.825605i	$-0.309166\pi$
$311$	19.9013	1.12850	0.564248	+	0.825605i	$0.309166\pi$
$312$	−5.85838	−0.331665
$313$	17.0440	0.963382	0.481691	−	0.876341i	$-0.340023\pi$
$313$	17.0440	0.963382	0.481691	+	0.876341i	$0.340023\pi$
$314$	−9.98421	−0.563442
$315$	0	0
$316$	−9.08861	−0.511274
$317$	−6.47449	−0.363644	−0.181822	−	0.983332i	$-0.558199\pi$
$317$	−6.47449	−0.363644	−0.181822	+	0.983332i	$0.558199\pi$
$318$	1.79972	0.100923
$319$	−14.4757	−0.810485
$320$	−0.183979	−0.0102848
$321$	16.5452	0.923462
$322$	0	0
$323$	21.7416	1.20973
$324$	1.00000	0.0555556
$325$	−29.0936	−1.61382
$326$	8.48528	0.469956
$327$	−15.9431	−0.881655
$328$	2.07621	0.114639
$329$	0	0
$330$	0.568241	0.0312806
$331$	−17.4909	−0.961389	−0.480694	−	0.876888i	$-0.659615\pi$
$331$	−17.4909	−0.961389	−0.480694	+	0.876888i	$0.659615\pi$
$332$	0.0175454	0.000962929 0
$333$	−1.49042	−0.0816745
$334$	−12.1845	−0.666706
$335$	0.283242	0.0154752
$336$	0	0
$337$	−21.0999	−1.14939	−0.574693	−	0.818369i	$-0.694879\pi$
$337$	−21.0999	−1.14939	−0.574693	+	0.818369i	$0.694879\pi$
$338$	21.3206	1.15969
$339$	−1.42097	−0.0771763
$340$	−1.17157	−0.0635375
$341$	10.5452	0.571054
$342$	3.41421	0.184620
$343$	0	0
$344$	4.94699	0.266724
$345$	−0.183979	−0.00990512
$346$	−6.21555	−0.334150
$347$	12.1976	0.654800	0.327400	−	0.944886i	$-0.393828\pi$
$347$	12.1976	0.654800	0.327400	+	0.944886i	$0.393828\pi$
$348$	4.68681	0.251239
$349$	25.3353	1.35617	0.678084	−	0.734985i	$-0.262811\pi$
$349$	25.3353	1.35617	0.678084	+	0.734985i	$0.262811\pi$
$350$	0	0
$351$	−5.85838	−0.312697
$352$	3.08861	0.164624
$353$	−26.9816	−1.43608	−0.718042	−	0.696000i	$-0.754961\pi$
$353$	−26.9816	−1.43608	−0.718042	+	0.696000i	$0.754961\pi$
$354$	−7.91704	−0.420786
$355$	0.568241	0.0301591
$356$	−9.63380	−0.510590
$357$	0	0
$358$	12.6422	0.668159
$359$	3.43623	0.181357	0.0906786	−	0.995880i	$-0.471096\pi$
$359$	3.43623	0.181357	0.0906786	+	0.995880i	$0.471096\pi$
$360$	−0.183979	−0.00969656
$361$	−7.34315	−0.386481
$362$	18.4893	0.971777
$363$	1.46047	0.0766547
$364$	0	0
$365$	0.943993	0.0494108
$366$	2.30254	0.120356
$367$	−21.8481	−1.14046	−0.570231	−	0.821485i	$-0.693146\pi$
$367$	−21.8481	−1.14046	−0.570231	+	0.821485i	$0.693146\pi$
$368$	−1.00000	−0.0521286
$369$	2.07621	0.108083
$370$	0.274207	0.0142553
$371$	0	0
$372$	−3.41421	−0.177019
$373$	−33.9436	−1.75753	−0.878767	−	0.477251i	$-0.841633\pi$
$373$	−33.9436	−1.75753	−0.878767	+	0.477251i	$0.841633\pi$
$374$	19.6682	1.01702
$375$	−1.83357	−0.0946849
$376$	5.01241	0.258495
$377$	−27.4571	−1.41411
$378$	0	0
$379$	−28.7563	−1.47711	−0.738555	−	0.674193i	$-0.764491\pi$
$379$	−28.7563	−1.47711	−0.738555	+	0.674193i	$0.764491\pi$
$380$	−0.628145	−0.0322231
$381$	12.0356	0.616603
$382$	−13.1230	−0.671430
$383$	2.94648	0.150558	0.0752790	−	0.997163i	$-0.476015\pi$
$383$	2.94648	0.150558	0.0752790	+	0.997163i	$0.476015\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	14.6038	0.743316
$387$	4.94699	0.251470
$388$	−4.60385	−0.233725
$389$	17.7742	0.901187	0.450593	−	0.892729i	$-0.351212\pi$
$389$	17.7742	0.901187	0.450593	+	0.892729i	$0.351212\pi$
$390$	1.07782	0.0545776
$391$	−6.36796	−0.322042
$392$	0	0
$393$	−2.47573	−0.124884
$394$	17.5751	0.885423
$395$	1.67212	0.0841333
$396$	3.08861	0.155209
$397$	22.6026	1.13439	0.567196	−	0.823583i	$-0.308028\pi$
$397$	22.6026	1.13439	0.567196	+	0.823583i	$0.308028\pi$
$398$	−1.39791	−0.0700709
$399$	0	0
$400$	−4.96615	−0.248308
$401$	−31.8047	−1.58825	−0.794126	−	0.607754i	$-0.792071\pi$
$401$	−31.8047	−1.58825	−0.794126	+	0.607754i	$0.792071\pi$
$402$	1.53953	0.0767849
$403$	20.0018	0.996358
$404$	5.39667	0.268494
$405$	−0.183979	−0.00914201
$406$	0	0
$407$	−4.60333	−0.228179
$408$	−6.36796	−0.315261
$409$	11.3082	0.559154	0.279577	−	0.960123i	$-0.409806\pi$
$409$	11.3082	0.559154	0.279577	+	0.960123i	$0.409806\pi$
$410$	−0.381979	−0.0188646
$411$	−17.6230	−0.869279
$412$	0.141621	0.00697717
$413$	0	0
$414$	−1.00000	−0.0491473
$415$	−0.00322799	−0.000158456 0
$416$	5.85838	0.287231
$417$	17.9526	0.879145
$418$	10.5452	0.515782
$419$	−30.3833	−1.48432	−0.742161	−	0.670222i	$-0.766199\pi$
$419$	−30.3833	−1.48432	−0.742161	+	0.670222i	$0.766199\pi$
$420$	0	0
$421$	18.4149	0.897486	0.448743	−	0.893661i	$-0.351872\pi$
$421$	18.4149	0.897486	0.448743	+	0.893661i	$0.351872\pi$
$422$	−17.9419	−0.873396
$423$	5.01241	0.243712
$424$	−1.79972	−0.0874020
$425$	−31.6242	−1.53400
$426$	3.08861	0.149644
$427$	0	0
$428$	−16.5452	−0.799742
$429$	−18.0943	−0.873599
$430$	−0.910144	−0.0438911
$431$	−0.811922	−0.0391089	−0.0195544	−	0.999809i	$-0.506225\pi$
$431$	−0.811922	−0.0391089	−0.0195544	+	0.999809i	$0.506225\pi$
$432$	−1.00000	−0.0481125
$433$	35.7020	1.71573	0.857865	−	0.513876i	$-0.171791\pi$
$433$	35.7020	1.71573	0.857865	+	0.513876i	$0.171791\pi$
$434$	0	0
$435$	−0.862276	−0.0413429
$436$	15.9431	0.763536
$437$	−3.41421	−0.163324
$438$	5.13097	0.245167
$439$	12.0193	0.573650	0.286825	−	0.957983i	$-0.407400\pi$
$439$	12.0193	0.573650	0.286825	+	0.957983i	$0.407400\pi$
$440$	−0.568241	−0.0270898
$441$	0	0
$442$	37.3059	1.77446
$443$	−36.0622	−1.71337	−0.856683	−	0.515844i	$-0.827479\pi$
$443$	−36.0622	−1.71337	−0.856683	+	0.515844i	$0.827479\pi$
$444$	1.49042	0.0707322
$445$	1.77242	0.0840208
$446$	23.9013	1.13176
$447$	−1.33925	−0.0633443
$448$	0	0
$449$	0.0867970	0.00409620	0.00204810	−	0.999998i	$-0.499348\pi$
$449$	0.0867970	0.00409620	0.00204810	+	0.999998i	$0.499348\pi$
$450$	−4.96615	−0.234107
$451$	6.41260	0.301958
$452$	1.42097	0.0668366
$453$	−9.05476	−0.425430
$454$	−8.81212	−0.413573
$455$	0	0
$456$	−3.41421	−0.159885
$457$	−37.6005	−1.75888	−0.879438	−	0.476014i	$-0.842081\pi$
$457$	−37.6005	−1.75888	−0.879438	+	0.476014i	$0.842081\pi$
$458$	−0.194772	−0.00910109
$459$	−6.36796	−0.297231
$460$	0.183979	0.00857808
$461$	−33.2804	−1.55002	−0.775011	−	0.631948i	$-0.782256\pi$
$461$	−33.2804	−1.55002	−0.775011	+	0.631948i	$0.782256\pi$
$462$	0	0
$463$	−18.4036	−0.855286	−0.427643	−	0.903948i	$-0.640656\pi$
$463$	−18.4036	−0.855286	−0.427643	+	0.903948i	$0.640656\pi$
$464$	−4.68681	−0.217580
$465$	0.628145	0.0291295
$466$	9.79972	0.453963
$467$	32.6327	1.51006	0.755031	−	0.655690i	$-0.227622\pi$
$467$	32.6327	1.51006	0.755031	+	0.655690i	$0.227622\pi$
$468$	5.85838	0.270804
$469$	0	0
$470$	−0.922179	−0.0425370
$471$	9.98421	0.460048
$472$	7.91704	0.364411
$473$	15.2793	0.702545
$474$	9.08861	0.417454
$475$	−16.9555	−0.777972
$476$	0	0
$477$	−1.79972	−0.0824034
$478$	10.5835	0.484078
$479$	−33.0578	−1.51045	−0.755224	−	0.655467i	$-0.772472\pi$
$479$	−33.0578	−1.51045	−0.755224	+	0.655467i	$0.772472\pi$
$480$	0.183979	0.00839747
$481$	−8.73145	−0.398120
$482$	6.17847	0.281422
$483$	0	0
$484$	−1.46047	−0.0663849
$485$	0.847013	0.0384609
$486$	−1.00000	−0.0453609
$487$	24.1562	1.09462	0.547310	−	0.836930i	$-0.315652\pi$
$487$	24.1562	1.09462	0.547310	+	0.836930i	$0.315652\pi$
$488$	−2.30254	−0.104231
$489$	−8.48528	−0.383718
$490$	0	0
$491$	27.6320	1.24702	0.623508	−	0.781817i	$-0.285707\pi$
$491$	27.6320	1.24702	0.623508	+	0.781817i	$0.285707\pi$
$492$	−2.07621	−0.0936026
$493$	−29.8454	−1.34417
$494$	20.0018	0.899922
$495$	−0.568241	−0.0255405
$496$	3.41421	0.153303
$497$	0	0
$498$	−0.0175454	−0.000786228 0
$499$	−33.9787	−1.52110	−0.760548	−	0.649282i	$-0.775070\pi$
$499$	−33.9787	−1.52110	−0.760548	+	0.649282i	$0.775070\pi$
$500$	1.83357	0.0819996
$501$	12.1845	0.544363
$502$	18.6845	0.833931
$503$	25.6451	1.14346	0.571729	−	0.820442i	$-0.306273\pi$
$503$	25.6451	1.14346	0.571729	+	0.820442i	$0.306273\pi$
$504$	0	0
$505$	−0.992875	−0.0441824
$506$	−3.08861	−0.137306
$507$	−21.3206	−0.946881
$508$	−12.0356	−0.533994
$509$	29.1631	1.29263	0.646315	−	0.763071i	$-0.276309\pi$
$509$	29.1631	1.29263	0.646315	+	0.763071i	$0.276309\pi$
$510$	1.17157	0.0518781
$511$	0	0
$512$	1.00000	0.0441942
$513$	−3.41421	−0.150741
$514$	−1.76691	−0.0779350
$515$	−0.0260553	−0.00114814
$516$	−4.94699	−0.217779
$517$	15.4814	0.680871
$518$	0	0
$519$	6.21555	0.272832
$520$	−1.07782	−0.0472656
$521$	43.0011	1.88391	0.941956	−	0.335736i	$-0.108985\pi$
$521$	43.0011	1.88391	0.941956	+	0.335736i	$0.108985\pi$
$522$	−4.68681	−0.205136
$523$	19.3202	0.844815	0.422407	−	0.906406i	$-0.361185\pi$
$523$	19.3202	0.844815	0.422407	+	0.906406i	$0.361185\pi$
$524$	2.47573	0.108153
$525$	0	0
$526$	−7.58864	−0.330881
$527$	21.7416	0.947078
$528$	−3.08861	−0.134415
$529$	1.00000	0.0434783
$530$	0.331111	0.0143825
$531$	7.91704	0.343570
$532$	0	0
$533$	12.1632	0.526847
$534$	9.63380	0.416895
$535$	3.04397	0.131602
$536$	−1.53953	−0.0664976
$537$	−12.6422	−0.545550
$538$	24.6452	1.06253
$539$	0	0
$540$	0.183979	0.00791721
$541$	−33.7203	−1.44975	−0.724874	−	0.688882i	$-0.758102\pi$
$541$	−33.7203	−1.44975	−0.724874	+	0.688882i	$0.758102\pi$
$542$	−18.8261	−0.808652
$543$	−18.4893	−0.793453
$544$	6.36796	0.273024
$545$	−2.93320	−0.125644
$546$	0	0
$547$	−27.6275	−1.18127	−0.590633	−	0.806940i	$-0.701122\pi$
$547$	−27.6275	−1.18127	−0.590633	+	0.806940i	$0.701122\pi$
$548$	17.6230	0.752817
$549$	−2.30254	−0.0982702
$550$	−15.3385	−0.654037
$551$	−16.0018	−0.681698
$552$	1.00000	0.0425628
$553$	0	0
$554$	11.8571	0.503761
$555$	−0.274207	−0.0116394
$556$	−17.9526	−0.761362
$557$	−1.65685	−0.0702032	−0.0351016	−	0.999384i	$-0.511175\pi$
$557$	−1.65685	−0.0702032	−0.0351016	+	0.999384i	$0.511175\pi$
$558$	3.41421	0.144535
$559$	28.9814	1.22578
$560$	0	0
$561$	−19.6682	−0.830390
$562$	8.48652	0.357982
$563$	−38.9217	−1.64035	−0.820176	−	0.572111i	$-0.806125\pi$
$563$	−38.9217	−1.64035	−0.820176	+	0.572111i	$0.806125\pi$
$564$	−5.01241	−0.211060
$565$	−0.261428	−0.0109984
$566$	5.34329	0.224595
$567$	0	0
$568$	−3.08861	−0.129595
$569$	10.3093	0.432188	0.216094	−	0.976373i	$-0.430668\pi$
$569$	10.3093	0.432188	0.216094	+	0.976373i	$0.430668\pi$
$570$	0.628145	0.0263101
$571$	23.3137	0.975648	0.487824	−	0.872942i	$-0.337791\pi$
$571$	23.3137	0.975648	0.487824	+	0.872942i	$0.337791\pi$
$572$	18.0943	0.756559
$573$	13.1230	0.548220
$574$	0	0
$575$	4.96615	0.207103
$576$	1.00000	0.0416667
$577$	−33.2716	−1.38512	−0.692558	−	0.721362i	$-0.743516\pi$
$577$	−33.2716	−1.38512	−0.692558	+	0.721362i	$0.743516\pi$
$578$	23.5509	0.979588
$579$	−14.6038	−0.606915
$580$	0.862276	0.0358040
$581$	0	0
$582$	4.60385	0.190836
$583$	−5.55863	−0.230215
$584$	−5.13097	−0.212321
$585$	−1.07782	−0.0445624
$586$	17.9148	0.740052
$587$	−35.4328	−1.46247	−0.731234	−	0.682127i	$-0.761055\pi$
$587$	−35.4328	−1.46247	−0.731234	+	0.682127i	$0.761055\pi$
$588$	0	0
$589$	11.6569	0.480312
$590$	−1.45657	−0.0599661
$591$	−17.5751	−0.722945
$592$	−1.49042	−0.0612559
$593$	−8.28604	−0.340267	−0.170133	−	0.985421i	$-0.554420\pi$
$593$	−8.28604	−0.340267	−0.170133	+	0.985421i	$0.554420\pi$
$594$	−3.08861	−0.126727
$595$	0	0
$596$	1.33925	0.0548578
$597$	1.39791	0.0572127
$598$	−5.85838	−0.239567
$599$	17.3392	0.708463	0.354231	−	0.935158i	$-0.384743\pi$
$599$	17.3392	0.708463	0.354231	+	0.935158i	$0.384743\pi$
$600$	4.96615	0.202742
$601$	−18.1214	−0.739186	−0.369593	−	0.929194i	$-0.620503\pi$
$601$	−18.1214	−0.739186	−0.369593	+	0.929194i	$0.620503\pi$
$602$	0	0
$603$	−1.53953	−0.0626946
$604$	9.05476	0.368433
$605$	0.268696	0.0109240
$606$	−5.39667	−0.219225
$607$	−23.3663	−0.948411	−0.474205	−	0.880414i	$-0.657265\pi$
$607$	−23.3663	−0.948411	−0.474205	+	0.880414i	$0.657265\pi$
$608$	3.41421	0.138465
$609$	0	0
$610$	0.423621	0.0171519
$611$	29.3646	1.18796
$612$	6.36796	0.257409
$613$	−37.9353	−1.53219	−0.766096	−	0.642726i	$-0.777803\pi$
$613$	−37.9353	−1.53219	−0.766096	+	0.642726i	$0.777803\pi$
$614$	−6.99339	−0.282230
$615$	0.381979	0.0154029
$616$	0	0
$617$	32.6274	1.31353	0.656765	−	0.754095i	$-0.271924\pi$
$617$	32.6274	1.31353	0.656765	+	0.754095i	$0.271924\pi$
$618$	−0.141621	−0.00569683
$619$	−31.1150	−1.25062	−0.625308	−	0.780378i	$-0.715027\pi$
$619$	−31.1150	−1.25062	−0.625308	+	0.780378i	$0.715027\pi$
$620$	−0.628145	−0.0252269
$621$	1.00000	0.0401286
$622$	19.9013	0.797968
$623$	0	0
$624$	−5.85838	−0.234523
$625$	24.4934	0.979737
$626$	17.0440	0.681214
$627$	−10.5452	−0.421134
$628$	−9.98421	−0.398413
$629$	−9.49093	−0.378428
$630$	0	0
$631$	19.9556	0.794422	0.397211	−	0.917727i	$-0.369978\pi$
$631$	19.9556	0.794422	0.397211	+	0.917727i	$0.369978\pi$
$632$	−9.08861	−0.361526
$633$	17.9419	0.713125
$634$	−6.47449	−0.257135
$635$	2.21430	0.0878719
$636$	1.79972	0.0713634
$637$	0	0
$638$	−14.4757	−0.573100
$639$	−3.08861	−0.122184
$640$	−0.183979	−0.00727242
$641$	−1.72123	−0.0679844	−0.0339922	−	0.999422i	$-0.510822\pi$
$641$	−1.72123	−0.0679844	−0.0339922	+	0.999422i	$0.510822\pi$
$642$	16.5452	0.652986
$643$	6.02885	0.237755	0.118877	−	0.992909i	$-0.462070\pi$
$643$	6.02885	0.237755	0.118877	+	0.992909i	$0.462070\pi$
$644$	0	0
$645$	0.910144	0.0358369
$646$	21.7416	0.855411
$647$	19.9498	0.784309	0.392155	−	0.919899i	$-0.371730\pi$
$647$	19.9498	0.784309	0.392155	+	0.919899i	$0.371730\pi$
$648$	1.00000	0.0392837
$649$	24.4527	0.959851
$650$	−29.0936	−1.14114
$651$	0	0
$652$	8.48528	0.332309
$653$	41.8484	1.63765	0.818827	−	0.574040i	$-0.194625\pi$
$653$	41.8484	1.63765	0.818827	+	0.574040i	$0.194625\pi$
$654$	−15.9431	−0.623424
$655$	−0.455483	−0.0177972
$656$	2.07621	0.0810623
$657$	−5.13097	−0.200178
$658$	0	0
$659$	17.6721	0.688408	0.344204	−	0.938895i	$-0.388149\pi$
$659$	17.6721	0.688408	0.344204	+	0.938895i	$0.388149\pi$
$660$	0.568241	0.0221188
$661$	−45.0019	−1.75037	−0.875186	−	0.483787i	$-0.839261\pi$
$661$	−45.0019	−1.75037	−0.875186	+	0.483787i	$0.839261\pi$
$662$	−17.4909	−0.679804
$663$	−37.3059	−1.44884
$664$	0.0175454	0.000680894 0
$665$	0	0
$666$	−1.49042	−0.0577526
$667$	4.68681	0.181474
$668$	−12.1845	−0.471432
$669$	−23.9013	−0.924076
$670$	0.283242	0.0109426
$671$	−7.11167	−0.274543
$672$	0	0
$673$	18.0948	0.697503	0.348751	−	0.937215i	$-0.386606\pi$
$673$	18.0948	0.697503	0.348751	+	0.937215i	$0.386606\pi$
$674$	−21.0999	−0.812739
$675$	4.96615	0.191147
$676$	21.3206	0.820023
$677$	34.4000	1.32210	0.661050	−	0.750341i	$-0.270111\pi$
$677$	34.4000	1.32210	0.661050	+	0.750341i	$0.270111\pi$
$678$	−1.42097	−0.0545719
$679$	0	0
$680$	−1.17157	−0.0449278
$681$	8.81212	0.337681
$682$	10.5452	0.403796
$683$	−39.2300	−1.50110	−0.750548	−	0.660816i	$-0.770210\pi$
$683$	−39.2300	−1.50110	−0.750548	+	0.660816i	$0.770210\pi$
$684$	3.41421	0.130546
$685$	−3.24227	−0.123881
$686$	0	0
$687$	0.194772	0.00743101
$688$	4.94699	0.188602
$689$	−10.5434	−0.401673
$690$	−0.183979	−0.00700397
$691$	−23.2054	−0.882776	−0.441388	−	0.897316i	$-0.645514\pi$
$691$	−23.2054	−0.882776	−0.441388	+	0.897316i	$0.645514\pi$
$692$	−6.21555	−0.236280
$693$	0	0
$694$	12.1976	0.463013
$695$	3.30292	0.125287
$696$	4.68681	0.177653
$697$	13.2212	0.500789
$698$	25.3353	0.958955
$699$	−9.79972	−0.370659
$700$	0	0
$701$	−6.82271	−0.257690	−0.128845	−	0.991665i	$-0.541127\pi$
$701$	−6.82271	−0.257690	−0.128845	+	0.991665i	$0.541127\pi$
$702$	−5.85838	−0.221110
$703$	−5.08861	−0.191921
$704$	3.08861	0.116406
$705$	0.922179	0.0347313
$706$	−26.9816	−1.01546
$707$	0	0
$708$	−7.91704	−0.297541
$709$	−36.6309	−1.37570	−0.687852	−	0.725851i	$-0.741446\pi$
$709$	−36.6309	−1.37570	−0.687852	+	0.725851i	$0.741446\pi$
$710$	0.568241	0.0213257
$711$	−9.08861	−0.340850
$712$	−9.63380	−0.361042
$713$	−3.41421	−0.127863
$714$	0	0
$715$	−3.32897	−0.124496
$716$	12.6422	0.472460
$717$	−10.5835	−0.395248
$718$	3.43623	0.128239
$719$	−43.5746	−1.62506	−0.812529	−	0.582920i	$-0.801910\pi$
$719$	−43.5746	−1.62506	−0.812529	+	0.582920i	$0.801910\pi$
$720$	−0.183979	−0.00685651
$721$	0	0
$722$	−7.34315	−0.273284
$723$	−6.17847	−0.229780
$724$	18.4893	0.687150
$725$	23.2754	0.864426
$726$	1.46047	0.0542031
$727$	15.5859	0.578050	0.289025	−	0.957322i	$-0.406669\pi$
$727$	15.5859	0.578050	0.289025	+	0.957322i	$0.406669\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0.943993	0.0349387
$731$	31.5022	1.16515
$732$	2.30254	0.0851045
$733$	1.66485	0.0614926	0.0307463	−	0.999527i	$-0.490212\pi$
$733$	1.66485	0.0614926	0.0307463	+	0.999527i	$0.490212\pi$
$734$	−21.8481	−0.806428
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−4.75502	−0.175153
$738$	2.07621	0.0764262
$739$	27.3856	1.00740	0.503699	−	0.863879i	$-0.331972\pi$
$739$	27.3856	1.00740	0.503699	+	0.863879i	$0.331972\pi$
$740$	0.274207	0.0100800
$741$	−20.0018	−0.734783
$742$	0	0
$743$	−28.1775	−1.03373	−0.516866	−	0.856066i	$-0.672902\pi$
$743$	−28.1775	−1.03373	−0.516866	+	0.856066i	$0.672902\pi$
$744$	−3.41421	−0.125171
$745$	−0.246394	−0.00902718
$746$	−33.9436	−1.24276
$747$	0.0175454	0.000641953 0
$748$	19.6682	0.719139
$749$	0	0
$750$	−1.83357	−0.0669524
$751$	22.1439	0.808042	0.404021	−	0.914750i	$-0.367612\pi$
$751$	22.1439	0.808042	0.404021	+	0.914750i	$0.367612\pi$
$752$	5.01241	0.182784
$753$	−18.6845	−0.680902
$754$	−27.4571	−0.999928
$755$	−1.66589	−0.0606279
$756$	0	0
$757$	−11.1748	−0.406155	−0.203078	−	0.979163i	$-0.565094\pi$
$757$	−11.1748	−0.406155	−0.203078	+	0.979163i	$0.565094\pi$
$758$	−28.7563	−1.04447
$759$	3.08861	0.112110
$760$	−0.628145	−0.0227852
$761$	−8.27141	−0.299838	−0.149919	−	0.988698i	$-0.547901\pi$
$761$	−8.27141	−0.299838	−0.149919	+	0.988698i	$0.547901\pi$
$762$	12.0356	0.436004
$763$	0	0
$764$	−13.1230	−0.474773
$765$	−1.17157	−0.0423583
$766$	2.94648	0.106461
$767$	46.3810	1.67472
$768$	−1.00000	−0.0360844
$769$	−5.44007	−0.196174	−0.0980869	−	0.995178i	$-0.531272\pi$
$769$	−5.44007	−0.196174	−0.0980869	+	0.995178i	$0.531272\pi$
$770$	0	0
$771$	1.76691	0.0636337
$772$	14.6038	0.525604
$773$	42.6671	1.53463	0.767314	−	0.641272i	$-0.221593\pi$
$773$	42.6671	1.53463	0.767314	+	0.641272i	$0.221593\pi$
$774$	4.94699	0.177816
$775$	−16.9555	−0.609060
$776$	−4.60385	−0.165268
$777$	0	0
$778$	17.7742	0.637235
$779$	7.08861	0.253976
$780$	1.07782	0.0385922
$781$	−9.53953	−0.341351
$782$	−6.36796	−0.227718
$783$	4.68681	0.167493
$784$	0	0
$785$	1.83689	0.0655614
$786$	−2.47573	−0.0883064
$787$	−7.86897	−0.280498	−0.140249	−	0.990116i	$-0.544790\pi$
$787$	−7.86897	−0.280498	−0.140249	+	0.990116i	$0.544790\pi$
$788$	17.5751	0.626088
$789$	7.58864	0.270163
$790$	1.67212	0.0594913
$791$	0	0
$792$	3.08861	0.109749
$793$	−13.4892	−0.479015
$794$	22.6026	0.802136
$795$	−0.331111	−0.0117433
$796$	−1.39791	−0.0495476
$797$	13.0748	0.463133	0.231567	−	0.972819i	$-0.425615\pi$
$797$	13.0748	0.463133	0.231567	+	0.972819i	$0.425615\pi$
$798$	0	0
$799$	31.9188	1.12921
$800$	−4.96615	−0.175580
$801$	−9.63380	−0.340394
$802$	−31.8047	−1.12306
$803$	−15.8476	−0.559249
$804$	1.53953	0.0542951
$805$	0	0
$806$	20.0018	0.704532
$807$	−24.6452	−0.867551
$808$	5.39667	0.189854
$809$	−28.0188	−0.985088	−0.492544	−	0.870288i	$-0.663933\pi$
$809$	−28.0188	−0.985088	−0.492544	+	0.870288i	$0.663933\pi$
$810$	−0.183979	−0.00646438
$811$	−17.1104	−0.600828	−0.300414	−	0.953809i	$-0.597125\pi$
$811$	−17.1104	−0.600828	−0.300414	+	0.953809i	$0.597125\pi$
$812$	0	0
$813$	18.8261	0.660262
$814$	−4.60333	−0.161347
$815$	−1.56112	−0.0546835
$816$	−6.36796	−0.222923
$817$	16.8901	0.590909
$818$	11.3082	0.395382
$819$	0	0
$820$	−0.381979	−0.0133393
$821$	18.0857	0.631197	0.315598	−	0.948893i	$-0.397795\pi$
$821$	18.0857	0.631197	0.315598	+	0.948893i	$0.397795\pi$
$822$	−17.6230	−0.614673
$823$	−24.7219	−0.861751	−0.430876	−	0.902411i	$-0.641795\pi$
$823$	−24.7219	−0.861751	−0.430876	+	0.902411i	$0.641795\pi$
$824$	0.141621	0.00493360
$825$	15.3385	0.534019
$826$	0	0
$827$	9.39843	0.326815	0.163408	−	0.986559i	$-0.447751\pi$
$827$	9.39843	0.326815	0.163408	+	0.986559i	$0.447751\pi$
$828$	−1.00000	−0.0347524
$829$	−2.43566	−0.0845938	−0.0422969	−	0.999105i	$-0.513468\pi$
$829$	−2.43566	−0.0845938	−0.0422969	+	0.999105i	$0.513468\pi$
$830$	−0.00322799	−0.000112045 0
$831$	−11.8571	−0.411320
$832$	5.85838	0.203103
$833$	0	0
$834$	17.9526	0.621649
$835$	2.24170	0.0775771
$836$	10.5452	0.364713
$837$	−3.41421	−0.118012
$838$	−30.3833	−1.04957
$839$	−6.62007	−0.228550	−0.114275	−	0.993449i	$-0.536455\pi$
$839$	−6.62007	−0.228550	−0.114275	+	0.993449i	$0.536455\pi$
$840$	0	0
$841$	−7.03385	−0.242546
$842$	18.4149	0.634618
$843$	−8.48652	−0.292291
$844$	−17.9419	−0.617584
$845$	−3.92255	−0.134940
$846$	5.01241	0.172330
$847$	0	0
$848$	−1.79972	−0.0618026
$849$	−5.34329	−0.183381
$850$	−31.6242	−1.08470
$851$	1.49042	0.0510909
$852$	3.08861	0.105814
$853$	7.63256	0.261334	0.130667	−	0.991426i	$-0.458288\pi$
$853$	7.63256	0.261334	0.130667	+	0.991426i	$0.458288\pi$
$854$	0	0
$855$	−0.628145	−0.0214821
$856$	−16.5452	−0.565503
$857$	14.0772	0.480869	0.240435	−	0.970665i	$-0.422710\pi$
$857$	14.0772	0.480869	0.240435	+	0.970665i	$0.422710\pi$
$858$	−18.0943	−0.617728
$859$	−2.16468	−0.0738578	−0.0369289	−	0.999318i	$-0.511758\pi$
$859$	−2.16468	−0.0738578	−0.0369289	+	0.999318i	$0.511758\pi$
$860$	−0.910144	−0.0310357
$861$	0	0
$862$	−0.811922	−0.0276542
$863$	−4.31054	−0.146732	−0.0733662	−	0.997305i	$-0.523374\pi$
$863$	−4.31054	−0.146732	−0.0733662	+	0.997305i	$0.523374\pi$
$864$	−1.00000	−0.0340207
$865$	1.14353	0.0388813
$866$	35.7020	1.21320
$867$	−23.5509	−0.799830
$868$	0	0
$869$	−28.0712	−0.952251
$870$	−0.862276	−0.0292339
$871$	−9.01916	−0.305603
$872$	15.9431	0.539901
$873$	−4.60385	−0.155817
$874$	−3.41421	−0.115487
$875$	0	0
$876$	5.13097	0.173359
$877$	−13.8015	−0.466043	−0.233021	−	0.972472i	$-0.574861\pi$
$877$	−13.8015	−0.466043	−0.233021	+	0.972472i	$0.574861\pi$
$878$	12.0193	0.405632
$879$	−17.9148	−0.604250
$880$	−0.568241	−0.0191554
$881$	−23.6955	−0.798320	−0.399160	−	0.916881i	$-0.630698\pi$
$881$	−23.6955	−0.798320	−0.399160	+	0.916881i	$0.630698\pi$
$882$	0	0
$883$	54.3484	1.82897	0.914485	−	0.404620i	$-0.132596\pi$
$883$	54.3484	1.82897	0.914485	+	0.404620i	$0.132596\pi$
$884$	37.3059	1.25473
$885$	1.45657	0.0489621
$886$	−36.0622	−1.21153
$887$	14.5547	0.488697	0.244349	−	0.969687i	$-0.421426\pi$
$887$	14.5547	0.488697	0.244349	+	0.969687i	$0.421426\pi$
$888$	1.49042	0.0500152
$889$	0	0
$890$	1.77242	0.0594117
$891$	3.08861	0.103472
$892$	23.9013	0.800273
$893$	17.1134	0.572679
$894$	−1.33925	−0.0447912
$895$	−2.32590	−0.0777462
$896$	0	0
$897$	5.85838	0.195606
$898$	0.0867970	0.00289645
$899$	−16.0018	−0.533688
$900$	−4.96615	−0.165538
$901$	−11.4605	−0.381806
$902$	6.41260	0.213516
$903$	0	0
$904$	1.42097	0.0472606
$905$	−3.40165	−0.113075
$906$	−9.05476	−0.300824
$907$	−6.69884	−0.222431	−0.111216	−	0.993796i	$-0.535474\pi$
$907$	−6.69884	−0.222431	−0.111216	+	0.993796i	$0.535474\pi$
$908$	−8.81212	−0.292441
$909$	5.39667	0.178996
$910$	0	0
$911$	−14.3660	−0.475966	−0.237983	−	0.971269i	$-0.576486\pi$
$911$	−14.3660	−0.475966	−0.237983	+	0.971269i	$0.576486\pi$
$912$	−3.41421	−0.113056
$913$	0.0541910	0.00179346
$914$	−37.6005	−1.24371
$915$	−0.423621	−0.0140045
$916$	−0.194772	−0.00643544
$917$	0	0
$918$	−6.36796	−0.210174
$919$	26.4314	0.871891	0.435945	−	0.899973i	$-0.356414\pi$
$919$	26.4314	0.871891	0.435945	+	0.899973i	$0.356414\pi$
$920$	0.183979	0.00606562
$921$	6.99339	0.230440
$922$	−33.2804	−1.09603
$923$	−18.0943	−0.595580
$924$	0	0
$925$	7.40165	0.243365
$926$	−18.4036	−0.604779
$927$	0.141621	0.00465144
$928$	−4.68681	−0.153852
$929$	−42.6352	−1.39882	−0.699408	−	0.714723i	$-0.746553\pi$
$929$	−42.6352	−1.39882	−0.699408	+	0.714723i	$0.746553\pi$
$930$	0.628145	0.0205977
$931$	0	0
$932$	9.79972	0.321000
$933$	−19.9013	−0.651538
$934$	32.6327	1.06777
$935$	−3.61854	−0.118339
$936$	5.85838	0.191487
$937$	15.7651	0.515025	0.257512	−	0.966275i	$-0.417097\pi$
$937$	15.7651	0.515025	0.257512	+	0.966275i	$0.417097\pi$
$938$	0	0
$939$	−17.0440	−0.556209
$940$	−0.922179	−0.0300782
$941$	−24.8387	−0.809718	−0.404859	−	0.914379i	$-0.632679\pi$
$941$	−24.8387	−0.809718	−0.404859	+	0.914379i	$0.632679\pi$
$942$	9.98421	0.325303
$943$	−2.07621	−0.0676106
$944$	7.91704	0.257678
$945$	0	0
$946$	15.2793	0.496774
$947$	−27.4245	−0.891176	−0.445588	−	0.895238i	$-0.647005\pi$
$947$	−27.4245	−0.891176	−0.445588	+	0.895238i	$0.647005\pi$
$948$	9.08861	0.295184
$949$	−30.0592	−0.975762
$950$	−16.9555	−0.550109
$951$	6.47449	0.209950
$952$	0	0
$953$	−13.2045	−0.427735	−0.213867	−	0.976863i	$-0.568606\pi$
$953$	−13.2045	−0.427735	−0.213867	+	0.976863i	$0.568606\pi$
$954$	−1.79972	−0.0582680
$955$	2.41436	0.0781267
$956$	10.5835	0.342295
$957$	14.4757	0.467934
$958$	−33.0578	−1.06805
$959$	0	0
$960$	0.183979	0.00593791
$961$	−19.3431	−0.623972
$962$	−8.73145	−0.281513
$963$	−16.5452	−0.533161
$964$	6.17847	0.198995
$965$	−2.68681	−0.0864913
$966$	0	0
$967$	−45.8950	−1.47588	−0.737942	−	0.674864i	$-0.764202\pi$
$967$	−45.8950	−1.47588	−0.737942	+	0.674864i	$0.764202\pi$
$968$	−1.46047	−0.0469412
$969$	−21.7416	−0.698440
$970$	0.847013	0.0271959
$971$	22.5411	0.723380	0.361690	−	0.932298i	$-0.382200\pi$
$971$	22.5411	0.723380	0.361690	+	0.932298i	$0.382200\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	24.1562	0.774013
$975$	29.0936	0.931741
$976$	−2.30254	−0.0737027
$977$	25.9073	0.828847	0.414424	−	0.910084i	$-0.363983\pi$
$977$	25.9073	0.828847	0.414424	+	0.910084i	$0.363983\pi$
$978$	−8.48528	−0.271329
$979$	−29.7551	−0.950976
$980$	0	0
$981$	15.9431	0.509024
$982$	27.6320	0.881774
$983$	34.7320	1.10778	0.553889	−	0.832591i	$-0.313143\pi$
$983$	34.7320	1.10778	0.553889	+	0.832591i	$0.313143\pi$
$984$	−2.07621	−0.0661871
$985$	−3.23346	−0.103027
$986$	−29.8454	−0.950471
$987$	0	0
$988$	20.0018	0.636341
$989$	−4.94699	−0.157305
$990$	−0.568241	−0.0180599
$991$	−32.9187	−1.04570	−0.522849	−	0.852425i	$-0.675131\pi$
$991$	−32.9187	−1.04570	−0.522849	+	0.852425i	$0.675131\pi$
$992$	3.41421	0.108401
$993$	17.4909	0.555058
$994$	0	0
$995$	0.257187	0.00815337
$996$	−0.0175454	−0.000555947 0
$997$	−12.6320	−0.400059	−0.200029	−	0.979790i	$-0.564104\pi$
$997$	−12.6320	−0.400059	−0.200029	+	0.979790i	$0.564104\pi$
$998$	−33.9787	−1.07558
$999$	1.49042	0.0471548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.cn.1.2	✓	4
7.6	odd	2		6762.2.a.co.1.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6762.2.a.cn.1.2	✓	4	1.1	even	1	trivial
6762.2.a.co.1.3	yes	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.183979 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.183979 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -0.183979 q^{10} +3.08861 q^{11} -1.00000 q^{12} +5.85838 q^{13} +0.183979 q^{15} +1.00000 q^{16} +6.36796 q^{17} +1.00000 q^{18} +3.41421 q^{19} -0.183979 q^{20} +3.08861 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.96615 q^{25} +5.85838 q^{26} -1.00000 q^{27} -4.68681 q^{29} +0.183979 q^{30} +3.41421 q^{31} +1.00000 q^{32} -3.08861 q^{33} +6.36796 q^{34} +1.00000 q^{36} -1.49042 q^{37} +3.41421 q^{38} -5.85838 q^{39} -0.183979 q^{40} +2.07621 q^{41} +4.94699 q^{43} +3.08861 q^{44} -0.183979 q^{45} -1.00000 q^{46} +5.01241 q^{47} -1.00000 q^{48} -4.96615 q^{50} -6.36796 q^{51} +5.85838 q^{52} -1.79972 q^{53} -1.00000 q^{54} -0.568241 q^{55} -3.41421 q^{57} -4.68681 q^{58} +7.91704 q^{59} +0.183979 q^{60} -2.30254 q^{61} +3.41421 q^{62} +1.00000 q^{64} -1.07782 q^{65} -3.08861 q^{66} -1.53953 q^{67} +6.36796 q^{68} +1.00000 q^{69} -3.08861 q^{71} +1.00000 q^{72} -5.13097 q^{73} -1.49042 q^{74} +4.96615 q^{75} +3.41421 q^{76} -5.85838 q^{78} -9.08861 q^{79} -0.183979 q^{80} +1.00000 q^{81} +2.07621 q^{82} +0.0175454 q^{83} -1.17157 q^{85} +4.94699 q^{86} +4.68681 q^{87} +3.08861 q^{88} -9.63380 q^{89} -0.183979 q^{90} -1.00000 q^{92} -3.41421 q^{93} +5.01241 q^{94} -0.628145 q^{95} -1.00000 q^{96} -4.60385 q^{97} +3.08861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 6 q^{10} - 4 q^{12} + 10 q^{13} - 6 q^{15} + 4 q^{16} + 12 q^{17} + 4 q^{18} + 8 q^{19} + 6 q^{20} - 4 q^{23} - 4 q^{24} + 6 q^{25} + 10 q^{26} - 4 q^{27} + 6 q^{29} - 6 q^{30} + 8 q^{31} + 4 q^{32} + 12 q^{34} + 4 q^{36} - 6 q^{37} + 8 q^{38} - 10 q^{39} + 6 q^{40} + 14 q^{41} - 6 q^{43} + 6 q^{45} - 4 q^{46} + 2 q^{47} - 4 q^{48} + 6 q^{50} - 12 q^{51} + 10 q^{52} - 4 q^{53} - 4 q^{54} + 8 q^{55} - 8 q^{57} + 6 q^{58} + 8 q^{59} - 6 q^{60} + 12 q^{61} + 8 q^{62} + 4 q^{64} + 6 q^{65} - 4 q^{67} + 12 q^{68} + 4 q^{69} + 4 q^{72} + 12 q^{73} - 6 q^{74} - 6 q^{75} + 8 q^{76} - 10 q^{78} - 24 q^{79} + 6 q^{80} + 4 q^{81} + 14 q^{82} + 16 q^{83} - 16 q^{85} - 6 q^{86} - 6 q^{87} + 12 q^{89} + 6 q^{90} - 4 q^{92} - 8 q^{93} + 2 q^{94} + 12 q^{95} - 4 q^{96} + 30 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 6 * q^10 - 4 * q^12 + 10 * q^13 - 6 * q^15 + 4 * q^16 + 12 * q^17 + 4 * q^18 + 8 * q^19 + 6 * q^20 - 4 * q^23 - 4 * q^24 + 6 * q^25 + 10 * q^26 - 4 * q^27 + 6 * q^29 - 6 * q^30 + 8 * q^31 + 4 * q^32 + 12 * q^34 + 4 * q^36 - 6 * q^37 + 8 * q^38 - 10 * q^39 + 6 * q^40 + 14 * q^41 - 6 * q^43 + 6 * q^45 - 4 * q^46 + 2 * q^47 - 4 * q^48 + 6 * q^50 - 12 * q^51 + 10 * q^52 - 4 * q^53 - 4 * q^54 + 8 * q^55 - 8 * q^57 + 6 * q^58 + 8 * q^59 - 6 * q^60 + 12 * q^61 + 8 * q^62 + 4 * q^64 + 6 * q^65 - 4 * q^67 + 12 * q^68 + 4 * q^69 + 4 * q^72 + 12 * q^73 - 6 * q^74 - 6 * q^75 + 8 * q^76 - 10 * q^78 - 24 * q^79 + 6 * q^80 + 4 * q^81 + 14 * q^82 + 16 * q^83 - 16 * q^85 - 6 * q^86 - 6 * q^87 + 12 * q^89 + 6 * q^90 - 4 * q^92 - 8 * q^93 + 2 * q^94 + 12 * q^95 - 4 * q^96 + 30 * q^97

Introduction

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