LMFDB - Embedded newform 3234.2.a.bl.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3234,2,Mod(1,3234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3234, 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("3234.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3234.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:	$25.8236200137$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.4352.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 4x + 2 $ x^4 - 6x^2 - 4x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.334904$ of defining polynomial
Character	$\chi$	$=$	3234.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.473626 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.473626 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.473626 q^{10} +1.00000 q^{11} -1.00000 q^{12} -7.03127 q^{13} -0.473626 q^{15} +1.00000 q^{16} +4.64167 q^{17} +1.00000 q^{18} -6.55765 q^{19} +0.473626 q^{20} +1.00000 q^{22} +1.49824 q^{23} -1.00000 q^{24} -4.77568 q^{25} -7.03127 q^{26} -1.00000 q^{27} -2.11882 q^{29} -0.473626 q^{30} -6.83509 q^{31} +1.00000 q^{32} -1.00000 q^{33} +4.64167 q^{34} +1.00000 q^{36} -4.32666 q^{37} -6.55765 q^{38} +7.03127 q^{39} +0.473626 q^{40} +11.2458 q^{41} +0.158619 q^{43} +1.00000 q^{44} +0.473626 q^{45} +1.49824 q^{46} -0.270780 q^{47} -1.00000 q^{48} -4.77568 q^{50} -4.64167 q^{51} -7.03127 q^{52} -9.66628 q^{53} -1.00000 q^{54} +0.473626 q^{55} +6.55765 q^{57} -2.11882 q^{58} -9.82490 q^{59} -0.473626 q^{60} -15.1993 q^{61} -6.83509 q^{62} +1.00000 q^{64} -3.33019 q^{65} -1.00000 q^{66} -1.21137 q^{67} +4.64167 q^{68} -1.49824 q^{69} +15.0098 q^{71} +1.00000 q^{72} +6.13048 q^{73} -4.32666 q^{74} +4.77568 q^{75} -6.55765 q^{76} +7.03127 q^{78} +11.4420 q^{79} +0.473626 q^{80} +1.00000 q^{81} +11.2458 q^{82} +7.54469 q^{83} +2.19841 q^{85} +0.158619 q^{86} +2.11882 q^{87} +1.00000 q^{88} -16.6881 q^{89} +0.473626 q^{90} +1.49824 q^{92} +6.83509 q^{93} -0.270780 q^{94} -3.10587 q^{95} -1.00000 q^{96} -12.9656 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 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 - 4 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} - 8 q^{13} + 4 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} - 12 q^{19} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 4 q^{24} + 4 q^{25} - 8 q^{26} - 4 q^{27} - 8 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 4 q^{33} - 4 q^{34} + 4 q^{36} + 8 q^{37} - 12 q^{38} + 8 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{43} + 4 q^{44} - 4 q^{45} - 8 q^{46} - 4 q^{47} - 4 q^{48} + 4 q^{50} + 4 q^{51} - 8 q^{52} - 8 q^{53} - 4 q^{54} - 4 q^{55} + 12 q^{57} - 8 q^{58} + 4 q^{60} - 24 q^{61} - 4 q^{62} + 4 q^{64} - 16 q^{65} - 4 q^{66} - 8 q^{67} - 4 q^{68} + 8 q^{69} + 8 q^{71} + 4 q^{72} - 4 q^{73} + 8 q^{74} - 4 q^{75} - 12 q^{76} + 8 q^{78} - 8 q^{79} - 4 q^{80} + 4 q^{81} - 12 q^{82} - 4 q^{83} - 8 q^{85} - 8 q^{86} + 8 q^{87} + 4 q^{88} - 24 q^{89} - 4 q^{90} - 8 q^{92} + 4 q^{93} - 4 q^{94} + 8 q^{95} - 4 q^{96} + 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 - 8 * q^13 + 4 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 - 12 * q^19 - 4 * q^20 + 4 * q^22 - 8 * q^23 - 4 * q^24 + 4 * q^25 - 8 * q^26 - 4 * q^27 - 8 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 4 * q^33 - 4 * q^34 + 4 * q^36 + 8 * q^37 - 12 * q^38 + 8 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^43 + 4 * q^44 - 4 * q^45 - 8 * q^46 - 4 * q^47 - 4 * q^48 + 4 * q^50 + 4 * q^51 - 8 * q^52 - 8 * q^53 - 4 * q^54 - 4 * q^55 + 12 * q^57 - 8 * q^58 + 4 * q^60 - 24 * q^61 - 4 * q^62 + 4 * q^64 - 16 * q^65 - 4 * q^66 - 8 * q^67 - 4 * q^68 + 8 * q^69 + 8 * q^71 + 4 * q^72 - 4 * q^73 + 8 * q^74 - 4 * q^75 - 12 * q^76 + 8 * q^78 - 8 * q^79 - 4 * q^80 + 4 * q^81 - 12 * q^82 - 4 * q^83 - 8 * q^85 - 8 * q^86 + 8 * q^87 + 4 * q^88 - 24 * q^89 - 4 * q^90 - 8 * q^92 + 4 * q^93 - 4 * q^94 + 8 * q^95 - 4 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0.473626	0.211812	0.105906	−	0.994376i	$-0.466226\pi$
$5$	0.473626	0.211812	0.105906	+	0.994376i	$0.466226\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.473626	0.149774
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−7.03127	−1.95012	−0.975062	−	0.221932i	$-0.928764\pi$
$13$	−7.03127	−1.95012	−0.975062	+	0.221932i	$0.928764\pi$
$14$	0	0
$15$	−0.473626	−0.122290
$16$	1.00000	0.250000
$17$	4.64167	1.12577	0.562885	−	0.826535i	$-0.309691\pi$
$17$	4.64167	1.12577	0.562885	+	0.826535i	$0.309691\pi$
$18$	1.00000	0.235702
$19$	−6.55765	−1.50443	−0.752214	−	0.658919i	$-0.771014\pi$
$19$	−6.55765	−1.50443	−0.752214	+	0.658919i	$0.771014\pi$
$20$	0.473626	0.105906
$21$	0	0
$22$	1.00000	0.213201
$23$	1.49824	0.312404	0.156202	−	0.987725i	$-0.450075\pi$
$23$	1.49824	0.312404	0.156202	+	0.987725i	$0.450075\pi$
$24$	−1.00000	−0.204124
$25$	−4.77568	−0.955136
$26$	−7.03127	−1.37895
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−2.11882	−0.393456	−0.196728	−	0.980458i	$-0.563032\pi$
$29$	−2.11882	−0.393456	−0.196728	+	0.980458i	$0.563032\pi$
$30$	−0.473626	−0.0864718
$31$	−6.83509	−1.22762	−0.613809	−	0.789454i	$-0.710364\pi$
$31$	−6.83509	−1.22762	−0.613809	+	0.789454i	$0.710364\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	4.64167	0.796040
$35$	0	0
$36$	1.00000	0.166667
$37$	−4.32666	−0.711299	−0.355649	−	0.934619i	$-0.615740\pi$
$37$	−4.32666	−0.711299	−0.355649	+	0.934619i	$0.615740\pi$
$38$	−6.55765	−1.06379
$39$	7.03127	1.12590
$40$	0.473626	0.0748868
$41$	11.2458	1.75629	0.878147	−	0.478390i	$-0.158779\pi$
$41$	11.2458	1.75629	0.878147	+	0.478390i	$0.158779\pi$
$42$	0	0
$43$	0.158619	0.0241892	0.0120946	−	0.999927i	$-0.496150\pi$
$43$	0.158619	0.0241892	0.0120946	+	0.999927i	$0.496150\pi$
$44$	1.00000	0.150756
$45$	0.473626	0.0706040
$46$	1.49824	0.220903
$47$	−0.270780	−0.0394973	−0.0197486	−	0.999805i	$-0.506287\pi$
$47$	−0.270780	−0.0394973	−0.0197486	+	0.999805i	$0.506287\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−4.77568	−0.675383
$51$	−4.64167	−0.649964
$52$	−7.03127	−0.975062
$53$	−9.66628	−1.32777	−0.663883	−	0.747837i	$-0.731093\pi$
$53$	−9.66628	−1.32777	−0.663883	+	0.747837i	$0.731093\pi$
$54$	−1.00000	−0.136083
$55$	0.473626	0.0638637
$56$	0	0
$57$	6.55765	0.868582
$58$	−2.11882	−0.278215
$59$	−9.82490	−1.27909	−0.639546	−	0.768753i	$-0.720878\pi$
$59$	−9.82490	−1.27909	−0.639546	+	0.768753i	$0.720878\pi$
$60$	−0.473626	−0.0611448
$61$	−15.1993	−1.94607	−0.973037	−	0.230651i	$-0.925914\pi$
$61$	−15.1993	−1.94607	−0.973037	+	0.230651i	$0.925914\pi$
$62$	−6.83509	−0.868057
$63$	0	0
$64$	1.00000	0.125000
$65$	−3.33019	−0.413059
$66$	−1.00000	−0.123091
$67$	−1.21137	−0.147992	−0.0739961	−	0.997259i	$-0.523575\pi$
$67$	−1.21137	−0.147992	−0.0739961	+	0.997259i	$0.523575\pi$
$68$	4.64167	0.562885
$69$	−1.49824	−0.180366
$70$	0	0
$71$	15.0098	1.78134	0.890668	−	0.454655i	$-0.150237\pi$
$71$	15.0098	1.78134	0.890668	+	0.454655i	$0.150237\pi$
$72$	1.00000	0.117851
$73$	6.13048	0.717518	0.358759	−	0.933430i	$-0.383200\pi$
$73$	6.13048	0.717518	0.358759	+	0.933430i	$0.383200\pi$
$74$	−4.32666	−0.502964
$75$	4.77568	0.551448
$76$	−6.55765	−0.752214
$77$	0	0
$78$	7.03127	0.796135
$79$	11.4420	1.28732	0.643660	−	0.765311i	$-0.277415\pi$
$79$	11.4420	1.28732	0.643660	+	0.765311i	$0.277415\pi$
$80$	0.473626	0.0529530
$81$	1.00000	0.111111
$82$	11.2458	1.24189
$83$	7.54469	0.828138	0.414069	−	0.910246i	$-0.364107\pi$
$83$	7.54469	0.828138	0.414069	+	0.910246i	$0.364107\pi$
$84$	0	0
$85$	2.19841	0.238451
$86$	0.158619	0.0171043
$87$	2.11882	0.227162
$88$	1.00000	0.106600
$89$	−16.6881	−1.76894	−0.884469	−	0.466599i	$-0.845479\pi$
$89$	−16.6881	−1.76894	−0.884469	+	0.466599i	$0.845479\pi$
$90$	0.473626	0.0499245
$91$	0	0
$92$	1.49824	0.156202
$93$	6.83509	0.708766
$94$	−0.270780	−0.0279288
$95$	−3.10587	−0.318656
$96$	−1.00000	−0.102062
$97$	−12.9656	−1.31645	−0.658227	−	0.752819i	$-0.728693\pi$
$97$	−12.9656	−1.31645	−0.658227	+	0.752819i	$0.728693\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	−4.77568	−0.477568
$101$	−0.298919	−0.0297436	−0.0148718	−	0.999889i	$-0.504734\pi$
$101$	−0.298919	−0.0297436	−0.0148718	+	0.999889i	$0.504734\pi$
$102$	−4.64167	−0.459594
$103$	7.39550	0.728700	0.364350	−	0.931262i	$-0.381291\pi$
$103$	7.39550	0.728700	0.364350	+	0.931262i	$0.381291\pi$
$104$	−7.03127	−0.689473
$105$	0	0
$106$	−9.66628	−0.938872
$107$	−15.3231	−1.48134	−0.740672	−	0.671867i	$-0.765493\pi$
$107$	−15.3231	−1.48134	−0.740672	+	0.671867i	$0.765493\pi$
$108$	−1.00000	−0.0962250
$109$	−0.422735	−0.0404907	−0.0202453	−	0.999795i	$-0.506445\pi$
$109$	−0.422735	−0.0404907	−0.0202453	+	0.999795i	$0.506445\pi$
$110$	0.473626	0.0451584
$111$	4.32666	0.410669
$112$	0	0
$113$	−8.40569	−0.790741	−0.395370	−	0.918522i	$-0.629384\pi$
$113$	−8.40569	−0.790741	−0.395370	+	0.918522i	$0.629384\pi$
$114$	6.55765	0.614180
$115$	0.709603	0.0661708
$116$	−2.11882	−0.196728
$117$	−7.03127	−0.650041
$118$	−9.82490	−0.904455
$119$	0	0
$120$	−0.473626	−0.0432359
$121$	1.00000	0.0909091
$122$	−15.1993	−1.37608
$123$	−11.2458	−1.01400
$124$	−6.83509	−0.613809
$125$	−4.63001	−0.414121
$126$	0	0
$127$	10.1023	0.896438	0.448219	−	0.893924i	$-0.352059\pi$
$127$	10.1023	0.896438	0.448219	+	0.893924i	$0.352059\pi$
$128$	1.00000	0.0883883
$129$	−0.158619	−0.0139656
$130$	−3.33019	−0.292077
$131$	−20.8843	−1.82467	−0.912335	−	0.409444i	$-0.865723\pi$
$131$	−20.8843	−1.82467	−0.912335	+	0.409444i	$0.865723\pi$
$132$	−1.00000	−0.0870388
$133$	0	0
$134$	−1.21137	−0.104646
$135$	−0.473626	−0.0407632
$136$	4.64167	0.398020
$137$	7.35294	0.628204	0.314102	−	0.949389i	$-0.398297\pi$
$137$	7.35294	0.628204	0.314102	+	0.949389i	$0.398297\pi$
$138$	−1.49824	−0.127538
$139$	4.67647	0.396653	0.198327	−	0.980136i	$-0.436449\pi$
$139$	4.67647	0.396653	0.198327	+	0.980136i	$0.436449\pi$
$140$	0	0
$141$	0.270780	0.0228038
$142$	15.0098	1.25959
$143$	−7.03127	−0.587985
$144$	1.00000	0.0833333
$145$	−1.00353	−0.0833386
$146$	6.13048	0.507362
$147$	0	0
$148$	−4.32666	−0.355649
$149$	4.89097	0.400684	0.200342	−	0.979726i	$-0.435795\pi$
$149$	4.89097	0.400684	0.200342	+	0.979726i	$0.435795\pi$
$150$	4.77568	0.389933
$151$	−16.6533	−1.35523	−0.677614	−	0.735418i	$-0.736986\pi$
$151$	−16.6533	−1.35523	−0.677614	+	0.735418i	$0.736986\pi$
$152$	−6.55765	−0.531895
$153$	4.64167	0.375257
$154$	0	0
$155$	−3.23728	−0.260024
$156$	7.03127	0.562952
$157$	14.5228	1.15905	0.579525	−	0.814955i	$-0.303238\pi$
$157$	14.5228	1.15905	0.579525	+	0.814955i	$0.303238\pi$
$158$	11.4420	0.910273
$159$	9.66628	0.766586
$160$	0.473626	0.0374434
$161$	0	0
$162$	1.00000	0.0785674
$163$	−8.33609	−0.652933	−0.326466	−	0.945209i	$-0.605858\pi$
$163$	−8.33609	−0.652933	−0.326466	+	0.945209i	$0.605858\pi$
$164$	11.2458	0.878147
$165$	−0.473626	−0.0368717
$166$	7.54469	0.585582
$167$	−2.84727	−0.220329	−0.110164	−	0.993913i	$-0.535138\pi$
$167$	−2.84727	−0.220329	−0.110164	+	0.993913i	$0.535138\pi$
$168$	0	0
$169$	36.4388	2.80298
$170$	2.19841	0.168611
$171$	−6.55765	−0.501476
$172$	0.158619	0.0120946
$173$	−9.17656	−0.697681	−0.348841	−	0.937182i	$-0.613425\pi$
$173$	−9.17656	−0.697681	−0.348841	+	0.937182i	$0.613425\pi$
$174$	2.11882	0.160628
$175$	0	0
$176$	1.00000	0.0753778
$177$	9.82490	0.738485
$178$	−16.6881	−1.25083
$179$	−5.76625	−0.430990	−0.215495	−	0.976505i	$-0.569137\pi$
$179$	−5.76625	−0.430990	−0.215495	+	0.976505i	$0.569137\pi$
$180$	0.473626	0.0353020
$181$	−3.38164	−0.251356	−0.125678	−	0.992071i	$-0.540111\pi$
$181$	−3.38164	−0.251356	−0.125678	+	0.992071i	$0.540111\pi$
$182$	0	0
$183$	15.1993	1.12357
$184$	1.49824	0.110451
$185$	−2.04922	−0.150662
$186$	6.83509	0.501173
$187$	4.64167	0.339432
$188$	−0.270780	−0.0197486
$189$	0	0
$190$	−3.10587	−0.225324
$191$	−16.1586	−1.16920	−0.584598	−	0.811323i	$-0.698748\pi$
$191$	−16.1586	−1.16920	−0.584598	+	0.811323i	$0.698748\pi$
$192$	−1.00000	−0.0721688
$193$	−24.8651	−1.78983	−0.894913	−	0.446240i	$-0.852763\pi$
$193$	−24.8651	−1.78983	−0.894913	+	0.446240i	$0.852763\pi$
$194$	−12.9656	−0.930874
$195$	3.33019	0.238480
$196$	0	0
$197$	10.4290	0.743036	0.371518	−	0.928426i	$-0.378837\pi$
$197$	10.4290	0.743036	0.371518	+	0.928426i	$0.378837\pi$
$198$	1.00000	0.0710669
$199$	13.2712	0.940767	0.470384	−	0.882462i	$-0.344116\pi$
$199$	13.2712	0.940767	0.470384	+	0.882462i	$0.344116\pi$
$200$	−4.77568	−0.337691
$201$	1.21137	0.0854433
$202$	−0.298919	−0.0210319
$203$	0	0
$204$	−4.64167	−0.324982
$205$	5.32629	0.372004
$206$	7.39550	0.515269
$207$	1.49824	0.104135
$208$	−7.03127	−0.487531
$209$	−6.55765	−0.453602
$210$	0	0
$211$	−24.2837	−1.67176	−0.835880	−	0.548912i	$-0.815042\pi$
$211$	−24.2837	−1.67176	−0.835880	+	0.548912i	$0.815042\pi$
$212$	−9.66628	−0.663883
$213$	−15.0098	−1.02845
$214$	−15.3231	−1.04747
$215$	0.0751261	0.00512356
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−0.422735	−0.0286312
$219$	−6.13048	−0.414259
$220$	0.473626	0.0319318
$221$	−32.6368	−2.19539
$222$	4.32666	0.290387
$223$	3.82529	0.256161	0.128080	−	0.991764i	$-0.459118\pi$
$223$	3.82529	0.256161	0.128080	+	0.991764i	$0.459118\pi$
$224$	0	0
$225$	−4.77568	−0.318379
$226$	−8.40569	−0.559138
$227$	12.3106	0.817082	0.408541	−	0.912740i	$-0.366038\pi$
$227$	12.3106	0.817082	0.408541	+	0.912740i	$0.366038\pi$
$228$	6.55765	0.434291
$229$	20.2726	1.33965	0.669826	−	0.742518i	$-0.266369\pi$
$229$	20.2726	1.33965	0.669826	+	0.742518i	$0.266369\pi$
$230$	0.709603	0.0467898
$231$	0	0
$232$	−2.11882	−0.139108
$233$	−10.8114	−0.708277	−0.354139	−	0.935193i	$-0.615226\pi$
$233$	−10.8114	−0.708277	−0.354139	+	0.935193i	$0.615226\pi$
$234$	−7.03127	−0.459649
$235$	−0.128248	−0.00836600
$236$	−9.82490	−0.639546
$237$	−11.4420	−0.743235
$238$	0	0
$239$	4.07959	0.263887	0.131943	−	0.991257i	$-0.457878\pi$
$239$	4.07959	0.263887	0.131943	+	0.991257i	$0.457878\pi$
$240$	−0.473626	−0.0305724
$241$	−21.9946	−1.41680	−0.708399	−	0.705812i	$-0.750582\pi$
$241$	−21.9946	−1.41680	−0.708399	+	0.705812i	$0.750582\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−15.1993	−0.973037
$245$	0	0
$246$	−11.2458	−0.717004
$247$	46.1086	2.93382
$248$	−6.83509	−0.434029
$249$	−7.54469	−0.478126
$250$	−4.63001	−0.292828
$251$	23.1082	1.45858	0.729289	−	0.684205i	$-0.239851\pi$
$251$	23.1082	1.45858	0.729289	+	0.684205i	$0.239851\pi$
$252$	0	0
$253$	1.49824	0.0941932
$254$	10.1023	0.633877
$255$	−2.19841	−0.137670
$256$	1.00000	0.0625000
$257$	7.75420	0.483694	0.241847	−	0.970314i	$-0.422247\pi$
$257$	7.75420	0.483694	0.241847	+	0.970314i	$0.422247\pi$
$258$	−0.158619	−0.00987520
$259$	0	0
$260$	−3.33019	−0.206530
$261$	−2.11882	−0.131152
$262$	−20.8843	−1.29024
$263$	−13.7851	−0.850026	−0.425013	−	0.905187i	$-0.639730\pi$
$263$	−13.7851	−0.850026	−0.425013	+	0.905187i	$0.639730\pi$
$264$	−1.00000	−0.0615457
$265$	−4.57820	−0.281236
$266$	0	0
$267$	16.6881	1.02130
$268$	−1.21137	−0.0739961
$269$	6.13048	0.373782	0.186891	−	0.982381i	$-0.440159\pi$
$269$	6.13048	0.373782	0.186891	+	0.982381i	$0.440159\pi$
$270$	−0.473626	−0.0288239
$271$	11.0661	0.672216	0.336108	−	0.941823i	$-0.390889\pi$
$271$	11.0661	0.672216	0.336108	+	0.941823i	$0.390889\pi$
$272$	4.64167	0.281443
$273$	0	0
$274$	7.35294	0.444208
$275$	−4.77568	−0.287984
$276$	−1.49824	−0.0901832
$277$	−16.4986	−0.991305	−0.495653	−	0.868521i	$-0.665071\pi$
$277$	−16.4986	−0.991305	−0.495653	+	0.868521i	$0.665071\pi$
$278$	4.67647	0.280476
$279$	−6.83509	−0.409206
$280$	0	0
$281$	−17.2341	−1.02810	−0.514051	−	0.857760i	$-0.671856\pi$
$281$	−17.2341	−1.02810	−0.514051	+	0.857760i	$0.671856\pi$
$282$	0.270780	0.0161247
$283$	18.3333	1.08980	0.544902	−	0.838500i	$-0.316567\pi$
$283$	18.3333	1.08980	0.544902	+	0.838500i	$0.316567\pi$
$284$	15.0098	0.890668
$285$	3.10587	0.183976
$286$	−7.03127	−0.415768
$287$	0	0
$288$	1.00000	0.0589256
$289$	4.54509	0.267358
$290$	−1.00353	−0.0589293
$291$	12.9656	0.760055
$292$	6.13048	0.358759
$293$	26.1560	1.52805	0.764025	−	0.645187i	$-0.223221\pi$
$293$	26.1560	1.52805	0.764025	+	0.645187i	$0.223221\pi$
$294$	0	0
$295$	−4.65332	−0.270927
$296$	−4.32666	−0.251482
$297$	−1.00000	−0.0580259
$298$	4.89097	0.283326
$299$	−10.5345	−0.609226
$300$	4.77568	0.275724
$301$	0	0
$302$	−16.6533	−0.958291
$303$	0.298919	0.0171724
$304$	−6.55765	−0.376107
$305$	−7.19879	−0.412201
$306$	4.64167	0.265347
$307$	−25.3109	−1.44457	−0.722286	−	0.691594i	$-0.756909\pi$
$307$	−25.3109	−1.44457	−0.722286	+	0.691594i	$0.756909\pi$
$308$	0	0
$309$	−7.39550	−0.420715
$310$	−3.23728	−0.183865
$311$	24.6202	1.39608	0.698042	−	0.716057i	$-0.254055\pi$
$311$	24.6202	1.39608	0.698042	+	0.716057i	$0.254055\pi$
$312$	7.03127	0.398067
$313$	−19.2713	−1.08928	−0.544639	−	0.838671i	$-0.683333\pi$
$313$	−19.2713	−1.08928	−0.544639	+	0.838671i	$0.683333\pi$
$314$	14.5228	0.819572
$315$	0	0
$316$	11.4420	0.643660
$317$	4.34551	0.244068	0.122034	−	0.992526i	$-0.461058\pi$
$317$	4.34551	0.244068	0.122034	+	0.992526i	$0.461058\pi$
$318$	9.66628	0.542058
$319$	−2.11882	−0.118631
$320$	0.473626	0.0264765
$321$	15.3231	0.855254
$322$	0	0
$323$	−30.4384	−1.69364
$324$	1.00000	0.0555556
$325$	33.5791	1.86263
$326$	−8.33609	−0.461693
$327$	0.422735	0.0233773
$328$	11.2458	0.620944
$329$	0	0
$330$	−0.473626	−0.0260722
$331$	−5.46786	−0.300541	−0.150270	−	0.988645i	$-0.548014\pi$
$331$	−5.46786	−0.300541	−0.150270	+	0.988645i	$0.548014\pi$
$332$	7.54469	0.414069
$333$	−4.32666	−0.237100
$334$	−2.84727	−0.155796
$335$	−0.573735	−0.0313465
$336$	0	0
$337$	7.43569	0.405048	0.202524	−	0.979277i	$-0.435086\pi$
$337$	7.43569	0.405048	0.202524	+	0.979277i	$0.435086\pi$
$338$	36.4388	1.98201
$339$	8.40569	0.456535
$340$	2.19841	0.119226
$341$	−6.83509	−0.370141
$342$	−6.55765	−0.354597
$343$	0	0
$344$	0.158619	0.00855217
$345$	−0.709603	−0.0382037
$346$	−9.17656	−0.493335
$347$	5.88508	0.315928	0.157964	−	0.987445i	$-0.449507\pi$
$347$	5.88508	0.315928	0.157964	+	0.987445i	$0.449507\pi$
$348$	2.11882	0.113581
$349$	−17.5658	−0.940274	−0.470137	−	0.882593i	$-0.655796\pi$
$349$	−17.5658	−0.940274	−0.470137	+	0.882593i	$0.655796\pi$
$350$	0	0
$351$	7.03127	0.375302
$352$	1.00000	0.0533002
$353$	1.45401	0.0773891	0.0386945	−	0.999251i	$-0.487680\pi$
$353$	1.45401	0.0773891	0.0386945	+	0.999251i	$0.487680\pi$
$354$	9.82490	0.522187
$355$	7.10903	0.377308
$356$	−16.6881	−0.884469
$357$	0	0
$358$	−5.76625	−0.304756
$359$	19.6796	1.03865	0.519325	−	0.854577i	$-0.326183\pi$
$359$	19.6796	1.03865	0.519325	+	0.854577i	$0.326183\pi$
$360$	0.473626	0.0249623
$361$	24.0027	1.26330
$362$	−3.38164	−0.177735
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	2.90355	0.151979
$366$	15.1993	0.794481
$367$	18.0692	0.943205	0.471603	−	0.881811i	$-0.343676\pi$
$367$	18.0692	0.943205	0.471603	+	0.881811i	$0.343676\pi$
$368$	1.49824	0.0781009
$369$	11.2458	0.585432
$370$	−2.04922	−0.106534
$371$	0	0
$372$	6.83509	0.354383
$373$	−21.3459	−1.10525	−0.552624	−	0.833431i	$-0.686373\pi$
$373$	−21.3459	−1.10525	−0.552624	+	0.833431i	$0.686373\pi$
$374$	4.64167	0.240015
$375$	4.63001	0.239093
$376$	−0.270780	−0.0139644
$377$	14.8980	0.767288
$378$	0	0
$379$	−4.63448	−0.238057	−0.119029	−	0.992891i	$-0.537978\pi$
$379$	−4.63448	−0.238057	−0.119029	+	0.992891i	$0.537978\pi$
$380$	−3.10587	−0.159328
$381$	−10.1023	−0.517559
$382$	−16.1586	−0.826747
$383$	7.37981	0.377091	0.188545	−	0.982065i	$-0.439623\pi$
$383$	7.37981	0.377091	0.188545	+	0.982065i	$0.439623\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−24.8651	−1.26560
$387$	0.158619	0.00806306
$388$	−12.9656	−0.658227
$389$	−1.34668	−0.0682792	−0.0341396	−	0.999417i	$-0.510869\pi$
$389$	−1.34668	−0.0682792	−0.0341396	+	0.999417i	$0.510869\pi$
$390$	3.33019	0.168631
$391$	6.95431	0.351695
$392$	0	0
$393$	20.8843	1.05347
$394$	10.4290	0.525406
$395$	5.41921	0.272670
$396$	1.00000	0.0502519
$397$	20.7346	1.04064	0.520320	−	0.853972i	$-0.325813\pi$
$397$	20.7346	1.04064	0.520320	+	0.853972i	$0.325813\pi$
$398$	13.2712	0.665223
$399$	0	0
$400$	−4.77568	−0.238784
$401$	7.96077	0.397542	0.198771	−	0.980046i	$-0.436305\pi$
$401$	7.96077	0.397542	0.198771	+	0.980046i	$0.436305\pi$
$402$	1.21137	0.0604175
$403$	48.0594	2.39401
$404$	−0.298919	−0.0148718
$405$	0.473626	0.0235347
$406$	0	0
$407$	−4.32666	−0.214465
$408$	−4.64167	−0.229797
$409$	−30.1438	−1.49052	−0.745258	−	0.666777i	$-0.767674\pi$
$409$	−30.1438	−1.49052	−0.745258	+	0.666777i	$0.767674\pi$
$410$	5.32629	0.263047
$411$	−7.35294	−0.362694
$412$	7.39550	0.364350
$413$	0	0
$414$	1.49824	0.0736342
$415$	3.57336	0.175409
$416$	−7.03127	−0.344737
$417$	−4.67647	−0.229008
$418$	−6.55765	−0.320745
$419$	26.7025	1.30450	0.652252	−	0.758002i	$-0.273824\pi$
$419$	26.7025	1.30450	0.652252	+	0.758002i	$0.273824\pi$
$420$	0	0
$421$	8.44158	0.411418	0.205709	−	0.978613i	$-0.434050\pi$
$421$	8.44158	0.411418	0.205709	+	0.978613i	$0.434050\pi$
$422$	−24.2837	−1.18211
$423$	−0.270780	−0.0131658
$424$	−9.66628	−0.469436
$425$	−22.1671	−1.07526
$426$	−15.0098	−0.727227
$427$	0	0
$428$	−15.3231	−0.740672
$429$	7.03127	0.339473
$430$	0.0751261	0.00362290
$431$	18.5510	0.893569	0.446785	−	0.894642i	$-0.352569\pi$
$431$	18.5510	0.893569	0.446785	+	0.894642i	$0.352569\pi$
$432$	−1.00000	−0.0481125
$433$	4.19969	0.201824	0.100912	−	0.994895i	$-0.467824\pi$
$433$	4.19969	0.201824	0.100912	+	0.994895i	$0.467824\pi$
$434$	0	0
$435$	1.00353	0.0481156
$436$	−0.422735	−0.0202453
$437$	−9.82490	−0.469989
$438$	−6.13048	−0.292926
$439$	3.48175	0.166175	0.0830875	−	0.996542i	$-0.473522\pi$
$439$	3.48175	0.166175	0.0830875	+	0.996542i	$0.473522\pi$
$440$	0.473626	0.0225792
$441$	0	0
$442$	−32.6368	−1.55238
$443$	24.6690	1.17206	0.586030	−	0.810289i	$-0.300690\pi$
$443$	24.6690	1.17206	0.586030	+	0.810289i	$0.300690\pi$
$444$	4.32666	0.205334
$445$	−7.90393	−0.374682
$446$	3.82529	0.181133
$447$	−4.89097	−0.231335
$448$	0	0
$449$	6.39863	0.301970	0.150985	−	0.988536i	$-0.451755\pi$
$449$	6.39863	0.301970	0.150985	+	0.988536i	$0.451755\pi$
$450$	−4.77568	−0.225128
$451$	11.2458	0.529543
$452$	−8.40569	−0.395370
$453$	16.6533	0.782441
$454$	12.3106	0.577764
$455$	0	0
$456$	6.55765	0.307090
$457$	14.5549	0.680849	0.340424	−	0.940272i	$-0.389429\pi$
$457$	14.5549	0.680849	0.340424	+	0.940272i	$0.389429\pi$
$458$	20.2726	0.947277
$459$	−4.64167	−0.216655
$460$	0.709603	0.0330854
$461$	16.3115	0.759700	0.379850	−	0.925048i	$-0.375976\pi$
$461$	16.3115	0.759700	0.379850	+	0.925048i	$0.375976\pi$
$462$	0	0
$463$	8.81138	0.409500	0.204750	−	0.978814i	$-0.434362\pi$
$463$	8.81138	0.409500	0.204750	+	0.978814i	$0.434362\pi$
$464$	−2.11882	−0.0983640
$465$	3.23728	0.150125
$466$	−10.8114	−0.500828
$467$	−8.20468	−0.379667	−0.189834	−	0.981816i	$-0.560795\pi$
$467$	−8.20468	−0.379667	−0.189834	+	0.981816i	$0.560795\pi$
$468$	−7.03127	−0.325021
$469$	0	0
$470$	−0.128248	−0.00591565
$471$	−14.5228	−0.669177
$472$	−9.82490	−0.452228
$473$	0.158619	0.00729332
$474$	−11.4420	−0.525546
$475$	31.3172	1.43693
$476$	0	0
$477$	−9.66628	−0.442588
$478$	4.07959	0.186596
$479$	−6.72920	−0.307465	−0.153732	−	0.988113i	$-0.549129\pi$
$479$	−6.72920	−0.307465	−0.153732	+	0.988113i	$0.549129\pi$
$480$	−0.473626	−0.0216180
$481$	30.4219	1.38712
$482$	−21.9946	−1.00183
$483$	0	0
$484$	1.00000	0.0454545
$485$	−6.14083	−0.278841
$486$	−1.00000	−0.0453609
$487$	18.9870	0.860385	0.430193	−	0.902737i	$-0.358446\pi$
$487$	18.9870	0.860385	0.430193	+	0.902737i	$0.358446\pi$
$488$	−15.1993	−0.688041
$489$	8.33609	0.376971
$490$	0	0
$491$	19.1027	0.862093	0.431047	−	0.902330i	$-0.358144\pi$
$491$	19.1027	0.862093	0.431047	+	0.902330i	$0.358144\pi$
$492$	−11.2458	−0.506999
$493$	−9.83488	−0.442941
$494$	46.1086	2.07452
$495$	0.473626	0.0212879
$496$	−6.83509	−0.306905
$497$	0	0
$498$	−7.54469	−0.338086
$499$	−38.6243	−1.72906	−0.864530	−	0.502582i	$-0.832384\pi$
$499$	−38.6243	−1.72906	−0.864530	+	0.502582i	$0.832384\pi$
$500$	−4.63001	−0.207060
$501$	2.84727	0.127207
$502$	23.1082	1.03137
$503$	−2.53784	−0.113157	−0.0565784	−	0.998398i	$-0.518019\pi$
$503$	−2.53784	−0.113157	−0.0565784	+	0.998398i	$0.518019\pi$
$504$	0	0
$505$	−0.141576	−0.00630004
$506$	1.49824	0.0666047
$507$	−36.4388	−1.61830
$508$	10.1023	0.448219
$509$	28.5987	1.26762	0.633808	−	0.773490i	$-0.281491\pi$
$509$	28.5987	1.26762	0.633808	+	0.773490i	$0.281491\pi$
$510$	−2.19841	−0.0973474
$511$	0	0
$512$	1.00000	0.0441942
$513$	6.55765	0.289527
$514$	7.75420	0.342023
$515$	3.50270	0.154347
$516$	−0.158619	−0.00698282
$517$	−0.270780	−0.0119089
$518$	0	0
$519$	9.17656	0.402806
$520$	−3.33019	−0.146039
$521$	−15.2789	−0.669381	−0.334691	−	0.942328i	$-0.608632\pi$
$521$	−15.2789	−0.669381	−0.334691	+	0.942328i	$0.608632\pi$
$522$	−2.11882	−0.0927384
$523$	34.6031	1.51309	0.756545	−	0.653942i	$-0.226886\pi$
$523$	34.6031	1.51309	0.756545	+	0.653942i	$0.226886\pi$
$524$	−20.8843	−0.912335
$525$	0	0
$526$	−13.7851	−0.601059
$527$	−31.7262	−1.38202
$528$	−1.00000	−0.0435194
$529$	−20.7553	−0.902404
$530$	−4.57820	−0.198864
$531$	−9.82490	−0.426364
$532$	0	0
$533$	−79.0721	−3.42499
$534$	16.6881	0.722166
$535$	−7.25743	−0.313766
$536$	−1.21137	−0.0523231
$537$	5.76625	0.248832
$538$	6.13048	0.264304
$539$	0	0
$540$	−0.473626	−0.0203816
$541$	11.1153	0.477884	0.238942	−	0.971034i	$-0.423199\pi$
$541$	11.1153	0.477884	0.238942	+	0.971034i	$0.423199\pi$
$542$	11.0661	0.475329
$543$	3.38164	0.145120
$544$	4.64167	0.199010
$545$	−0.200218	−0.00857641
$546$	0	0
$547$	41.5576	1.77688	0.888438	−	0.458997i	$-0.151791\pi$
$547$	41.5576	1.77688	0.888438	+	0.458997i	$0.151791\pi$
$548$	7.35294	0.314102
$549$	−15.1993	−0.648691
$550$	−4.77568	−0.203636
$551$	13.8945	0.591926
$552$	−1.49824	−0.0637691
$553$	0	0
$554$	−16.4986	−0.700959
$555$	2.04922	0.0869845
$556$	4.67647	0.198327
$557$	4.19841	0.177893	0.0889463	−	0.996036i	$-0.471650\pi$
$557$	4.19841	0.177893	0.0889463	+	0.996036i	$0.471650\pi$
$558$	−6.83509	−0.289352
$559$	−1.11529	−0.0471719
$560$	0	0
$561$	−4.64167	−0.195971
$562$	−17.2341	−0.726977
$563$	−5.10311	−0.215070	−0.107535	−	0.994201i	$-0.534296\pi$
$563$	−5.10311	−0.215070	−0.107535	+	0.994201i	$0.534296\pi$
$564$	0.270780	0.0114019
$565$	−3.98115	−0.167488
$566$	18.3333	0.770607
$567$	0	0
$568$	15.0098	0.629797
$569$	−36.9635	−1.54959	−0.774795	−	0.632212i	$-0.782147\pi$
$569$	−36.9635	−1.54959	−0.774795	+	0.632212i	$0.782147\pi$
$570$	3.10587	0.130091
$571$	16.7462	0.700808	0.350404	−	0.936599i	$-0.386044\pi$
$571$	16.7462	0.700808	0.350404	+	0.936599i	$0.386044\pi$
$572$	−7.03127	−0.293992
$573$	16.1586	0.675036
$574$	0	0
$575$	−7.15509	−0.298388
$576$	1.00000	0.0416667
$577$	20.9889	0.873779	0.436889	−	0.899515i	$-0.356080\pi$
$577$	20.9889	0.873779	0.436889	+	0.899515i	$0.356080\pi$
$578$	4.54509	0.189051
$579$	24.8651	1.03336
$580$	−1.00353	−0.0416693
$581$	0	0
$582$	12.9656	0.537440
$583$	−9.66628	−0.400336
$584$	6.13048	0.253681
$585$	−3.33019	−0.137686
$586$	26.1560	1.08049
$587$	−2.56747	−0.105971	−0.0529854	−	0.998595i	$-0.516874\pi$
$587$	−2.56747	−0.105971	−0.0529854	+	0.998595i	$0.516874\pi$
$588$	0	0
$589$	44.8221	1.84686
$590$	−4.65332	−0.191574
$591$	−10.4290	−0.428992
$592$	−4.32666	−0.177825
$593$	−27.7177	−1.13823	−0.569115	−	0.822258i	$-0.692714\pi$
$593$	−27.7177	−1.13823	−0.569115	+	0.822258i	$0.692714\pi$
$594$	−1.00000	−0.0410305
$595$	0	0
$596$	4.89097	0.200342
$597$	−13.2712	−0.543152
$598$	−10.5345	−0.430788
$599$	26.2173	1.07121	0.535604	−	0.844469i	$-0.320084\pi$
$599$	26.2173	1.07121	0.535604	+	0.844469i	$0.320084\pi$
$600$	4.77568	0.194966
$601$	−20.5621	−0.838745	−0.419372	−	0.907814i	$-0.637750\pi$
$601$	−20.5621	−0.838745	−0.419372	+	0.907814i	$0.637750\pi$
$602$	0	0
$603$	−1.21137	−0.0493307
$604$	−16.6533	−0.677614
$605$	0.473626	0.0192556
$606$	0.298919	0.0121428
$607$	−22.8839	−0.928829	−0.464415	−	0.885618i	$-0.653735\pi$
$607$	−22.8839	−0.928829	−0.464415	+	0.885618i	$0.653735\pi$
$608$	−6.55765	−0.265948
$609$	0	0
$610$	−7.19879	−0.291470
$611$	1.90393	0.0770246
$612$	4.64167	0.187628
$613$	6.82843	0.275798	0.137899	−	0.990446i	$-0.455965\pi$
$613$	6.82843	0.275798	0.137899	+	0.990446i	$0.455965\pi$
$614$	−25.3109	−1.02147
$615$	−5.32629	−0.214777
$616$	0	0
$617$	22.4120	0.902272	0.451136	−	0.892455i	$-0.351019\pi$
$617$	22.4120	0.902272	0.451136	+	0.892455i	$0.351019\pi$
$618$	−7.39550	−0.297491
$619$	15.6076	0.627324	0.313662	−	0.949535i	$-0.398444\pi$
$619$	15.6076	0.627324	0.313662	+	0.949535i	$0.398444\pi$
$620$	−3.23728	−0.130012
$621$	−1.49824	−0.0601221
$622$	24.6202	0.987180
$623$	0	0
$624$	7.03127	0.281476
$625$	21.6855	0.867420
$626$	−19.2713	−0.770236
$627$	6.55765	0.261887
$628$	14.5228	0.579525
$629$	−20.0829	−0.800759
$630$	0	0
$631$	−18.4588	−0.734834	−0.367417	−	0.930056i	$-0.619758\pi$
$631$	−18.4588	−0.734834	−0.367417	+	0.930056i	$0.619758\pi$
$632$	11.4420	0.455137
$633$	24.2837	0.965191
$634$	4.34551	0.172582
$635$	4.78473	0.189876
$636$	9.66628	0.383293
$637$	0	0
$638$	−2.11882	−0.0838851
$639$	15.0098	0.593778
$640$	0.473626	0.0187217
$641$	−29.6006	−1.16915	−0.584576	−	0.811339i	$-0.698739\pi$
$641$	−29.6006	−1.16915	−0.584576	+	0.811339i	$0.698739\pi$
$642$	15.3231	0.604756
$643$	7.93039	0.312744	0.156372	−	0.987698i	$-0.450020\pi$
$643$	7.93039	0.312744	0.156372	+	0.987698i	$0.450020\pi$
$644$	0	0
$645$	−0.0751261	−0.00295809
$646$	−30.4384	−1.19758
$647$	40.4810	1.59147	0.795736	−	0.605644i	$-0.207084\pi$
$647$	40.4810	1.59147	0.795736	+	0.605644i	$0.207084\pi$
$648$	1.00000	0.0392837
$649$	−9.82490	−0.385661
$650$	33.5791	1.31708
$651$	0	0
$652$	−8.33609	−0.326466
$653$	−22.8643	−0.894750	−0.447375	−	0.894346i	$-0.647641\pi$
$653$	−22.8643	−0.894750	−0.447375	+	0.894346i	$0.647641\pi$
$654$	0.422735	0.0165303
$655$	−9.89135	−0.386487
$656$	11.2458	0.439074
$657$	6.13048	0.239173
$658$	0	0
$659$	8.96114	0.349076	0.174538	−	0.984650i	$-0.444157\pi$
$659$	8.96114	0.349076	0.174538	+	0.984650i	$0.444157\pi$
$660$	−0.473626	−0.0184359
$661$	−8.95891	−0.348461	−0.174231	−	0.984705i	$-0.555744\pi$
$661$	−8.95891	−0.348461	−0.174231	+	0.984705i	$0.555744\pi$
$662$	−5.46786	−0.212515
$663$	32.6368	1.26751
$664$	7.54469	0.292791
$665$	0	0
$666$	−4.32666	−0.167655
$667$	−3.17450	−0.122917
$668$	−2.84727	−0.110164
$669$	−3.82529	−0.147894
$670$	−0.573735	−0.0221653
$671$	−15.1993	−0.586763
$672$	0	0
$673$	−32.2141	−1.24176	−0.620881	−	0.783905i	$-0.713225\pi$
$673$	−32.2141	−1.24176	−0.620881	+	0.783905i	$0.713225\pi$
$674$	7.43569	0.286412
$675$	4.77568	0.183816
$676$	36.4388	1.40149
$677$	2.96482	0.113947	0.0569737	−	0.998376i	$-0.481855\pi$
$677$	2.96482	0.113947	0.0569737	+	0.998376i	$0.481855\pi$
$678$	8.40569	0.322819
$679$	0	0
$680$	2.19841	0.0843053
$681$	−12.3106	−0.471742
$682$	−6.83509	−0.261729
$683$	25.4616	0.974259	0.487130	−	0.873330i	$-0.338044\pi$
$683$	25.4616	0.974259	0.487130	+	0.873330i	$0.338044\pi$
$684$	−6.55765	−0.250738
$685$	3.48254	0.133061
$686$	0	0
$687$	−20.2726	−0.773449
$688$	0.158619	0.00604730
$689$	67.9662	2.58931
$690$	−0.709603	−0.0270141
$691$	−8.44785	−0.321371	−0.160686	−	0.987006i	$-0.551371\pi$
$691$	−8.44785	−0.321371	−0.160686	+	0.987006i	$0.551371\pi$
$692$	−9.17656	−0.348841
$693$	0	0
$694$	5.88508	0.223395
$695$	2.21490	0.0840158
$696$	2.11882	0.0803138
$697$	52.1992	1.97718
$698$	−17.5658	−0.664874
$699$	10.8114	0.408924
$700$	0	0
$701$	49.0886	1.85405	0.927025	−	0.374999i	$-0.122357\pi$
$701$	49.0886	1.85405	0.927025	+	0.374999i	$0.122357\pi$
$702$	7.03127	0.265378
$703$	28.3727	1.07010
$704$	1.00000	0.0376889
$705$	0.128248	0.00483011
$706$	1.45401	0.0547223
$707$	0	0
$708$	9.82490	0.369242
$709$	−0.167483	−0.00628996	−0.00314498	−	0.999995i	$-0.501001\pi$
$709$	−0.167483	−0.00628996	−0.00314498	+	0.999995i	$0.501001\pi$
$710$	7.10903	0.266797
$711$	11.4420	0.429107
$712$	−16.6881	−0.625414
$713$	−10.2406	−0.383512
$714$	0	0
$715$	−3.33019	−0.124542
$716$	−5.76625	−0.215495
$717$	−4.07959	−0.152355
$718$	19.6796	0.734436
$719$	1.83472	0.0684234	0.0342117	−	0.999415i	$-0.489108\pi$
$719$	1.83472	0.0684234	0.0342117	+	0.999415i	$0.489108\pi$
$720$	0.473626	0.0176510
$721$	0	0
$722$	24.0027	0.893289
$723$	21.9946	0.817988
$724$	−3.38164	−0.125678
$725$	10.1188	0.375804
$726$	−1.00000	−0.0371135
$727$	27.7394	1.02880	0.514399	−	0.857551i	$-0.328015\pi$
$727$	27.7394	1.02880	0.514399	+	0.857551i	$0.328015\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.90355	0.107465
$731$	0.736258	0.0272315
$732$	15.1993	0.561783
$733$	−41.5283	−1.53388	−0.766942	−	0.641716i	$-0.778223\pi$
$733$	−41.5283	−1.53388	−0.766942	+	0.641716i	$0.778223\pi$
$734$	18.0692	0.666947
$735$	0	0
$736$	1.49824	0.0552257
$737$	−1.21137	−0.0446213
$738$	11.2458	0.413963
$739$	1.19488	0.0439545	0.0219773	−	0.999758i	$-0.493004\pi$
$739$	1.19488	0.0439545	0.0219773	+	0.999758i	$0.493004\pi$
$740$	−2.04922	−0.0753308
$741$	−46.1086	−1.69384
$742$	0	0
$743$	4.25650	0.156156	0.0780779	−	0.996947i	$-0.475122\pi$
$743$	4.25650	0.156156	0.0780779	+	0.996947i	$0.475122\pi$
$744$	6.83509	0.250587
$745$	2.31649	0.0848697
$746$	−21.3459	−0.781528
$747$	7.54469	0.276046
$748$	4.64167	0.169716
$749$	0	0
$750$	4.63001	0.169064
$751$	−13.0925	−0.477754	−0.238877	−	0.971050i	$-0.576779\pi$
$751$	−13.0925	−0.477754	−0.238877	+	0.971050i	$0.576779\pi$
$752$	−0.270780	−0.00987432
$753$	−23.1082	−0.842111
$754$	14.8980	0.542554
$755$	−7.88744	−0.287053
$756$	0	0
$757$	−4.21411	−0.153164	−0.0765821	−	0.997063i	$-0.524401\pi$
$757$	−4.21411	−0.153164	−0.0765821	+	0.997063i	$0.524401\pi$
$758$	−4.63448	−0.168332
$759$	−1.49824	−0.0543825
$760$	−3.10587	−0.112662
$761$	−45.8587	−1.66238	−0.831189	−	0.555990i	$-0.812339\pi$
$761$	−45.8587	−1.66238	−0.831189	+	0.555990i	$0.812339\pi$
$762$	−10.1023	−0.365969
$763$	0	0
$764$	−16.1586	−0.584598
$765$	2.19841	0.0794838
$766$	7.37981	0.266643
$767$	69.0815	2.49439
$768$	−1.00000	−0.0360844
$769$	−53.7185	−1.93714	−0.968569	−	0.248745i	$-0.919982\pi$
$769$	−53.7185	−1.93714	−0.968569	+	0.248745i	$0.919982\pi$
$770$	0	0
$771$	−7.75420	−0.279261
$772$	−24.8651	−0.894913
$773$	−6.90523	−0.248364	−0.124182	−	0.992259i	$-0.539631\pi$
$773$	−6.90523	−0.248364	−0.124182	+	0.992259i	$0.539631\pi$
$774$	0.158619	0.00570145
$775$	32.6422	1.17254
$776$	−12.9656	−0.465437
$777$	0	0
$778$	−1.34668	−0.0482807
$779$	−73.7458	−2.64222
$780$	3.33019	0.119240
$781$	15.0098	0.537093
$782$	6.95431	0.248686
$783$	2.11882	0.0757206
$784$	0	0
$785$	6.87839	0.245500
$786$	20.8843	0.744919
$787$	3.06703	0.109328	0.0546639	−	0.998505i	$-0.482591\pi$
$787$	3.06703	0.109328	0.0546639	+	0.998505i	$0.482591\pi$
$788$	10.4290	0.371518
$789$	13.7851	0.490763
$790$	5.41921	0.192807
$791$	0	0
$792$	1.00000	0.0355335
$793$	106.871	3.79508
$794$	20.7346	0.735843
$795$	4.57820	0.162372
$796$	13.2712	0.470384
$797$	41.1028	1.45594	0.727969	−	0.685610i	$-0.240465\pi$
$797$	41.1028	1.45594	0.727969	+	0.685610i	$0.240465\pi$
$798$	0	0
$799$	−1.25687	−0.0444649
$800$	−4.77568	−0.168846
$801$	−16.6881	−0.589646
$802$	7.96077	0.281104
$803$	6.13048	0.216340
$804$	1.21137	0.0427216
$805$	0	0
$806$	48.0594	1.69282
$807$	−6.13048	−0.215803
$808$	−0.298919	−0.0105159
$809$	−36.2141	−1.27322	−0.636610	−	0.771186i	$-0.719664\pi$
$809$	−36.2141	−1.27322	−0.636610	+	0.771186i	$0.719664\pi$
$810$	0.473626	0.0166415
$811$	−12.2752	−0.431042	−0.215521	−	0.976499i	$-0.569145\pi$
$811$	−12.2752	−0.431042	−0.215521	+	0.976499i	$0.569145\pi$
$812$	0	0
$813$	−11.0661	−0.388104
$814$	−4.32666	−0.151649
$815$	−3.94819	−0.138299
$816$	−4.64167	−0.162491
$817$	−1.04017	−0.0363909
$818$	−30.1438	−1.05395
$819$	0	0
$820$	5.32629	0.186002
$821$	−43.0697	−1.50314	−0.751572	−	0.659651i	$-0.770704\pi$
$821$	−43.0697	−1.50314	−0.751572	+	0.659651i	$0.770704\pi$
$822$	−7.35294	−0.256463
$823$	26.9541	0.939560	0.469780	−	0.882783i	$-0.344333\pi$
$823$	26.9541	0.939560	0.469780	+	0.882783i	$0.344333\pi$
$824$	7.39550	0.257634
$825$	4.77568	0.166268
$826$	0	0
$827$	−34.9902	−1.21673	−0.608364	−	0.793659i	$-0.708174\pi$
$827$	−34.9902	−1.21673	−0.608364	+	0.793659i	$0.708174\pi$
$828$	1.49824	0.0520673
$829$	−20.7246	−0.719795	−0.359898	−	0.932992i	$-0.617188\pi$
$829$	−20.7246	−0.719795	−0.359898	+	0.932992i	$0.617188\pi$
$830$	3.57336	0.124033
$831$	16.4986	0.572330
$832$	−7.03127	−0.243766
$833$	0	0
$834$	−4.67647	−0.161933
$835$	−1.34854	−0.0466682
$836$	−6.55765	−0.226801
$837$	6.83509	0.236255
$838$	26.7025	0.922424
$839$	31.3128	1.08104	0.540518	−	0.841332i	$-0.318228\pi$
$839$	31.3128	1.08104	0.540518	+	0.841332i	$0.318228\pi$
$840$	0	0
$841$	−24.5106	−0.845193
$842$	8.44158	0.290916
$843$	17.2341	0.593575
$844$	−24.2837	−0.835880
$845$	17.2584	0.593705
$846$	−0.270780	−0.00930960
$847$	0	0
$848$	−9.66628	−0.331941
$849$	−18.3333	−0.629198
$850$	−22.1671	−0.760326
$851$	−6.48236	−0.222212
$852$	−15.0098	−0.514227
$853$	29.5524	1.01186	0.505928	−	0.862576i	$-0.331150\pi$
$853$	29.5524	1.01186	0.505928	+	0.862576i	$0.331150\pi$
$854$	0	0
$855$	−3.10587	−0.106219
$856$	−15.3231	−0.523734
$857$	36.7050	1.25382	0.626909	−	0.779093i	$-0.284320\pi$
$857$	36.7050	1.25382	0.626909	+	0.779093i	$0.284320\pi$
$858$	7.03127	0.240044
$859$	−0.326102	−0.0111265	−0.00556323	−	0.999985i	$-0.501771\pi$
$859$	−0.326102	−0.0111265	−0.00556323	+	0.999985i	$0.501771\pi$
$860$	0.0751261	0.00256178
$861$	0	0
$862$	18.5510	0.631849
$863$	16.8727	0.574353	0.287176	−	0.957878i	$-0.407283\pi$
$863$	16.8727	0.574353	0.287176	+	0.957878i	$0.407283\pi$
$864$	−1.00000	−0.0340207
$865$	−4.34626	−0.147777
$866$	4.19969	0.142711
$867$	−4.54509	−0.154359
$868$	0	0
$869$	11.4420	0.388142
$870$	1.00353	0.0340228
$871$	8.51746	0.288603
$872$	−0.422735	−0.0143156
$873$	−12.9656	−0.438818
$874$	−9.82490	−0.332332
$875$	0	0
$876$	−6.13048	−0.207130
$877$	−9.71054	−0.327902	−0.163951	−	0.986469i	$-0.552424\pi$
$877$	−9.71054	−0.327902	−0.163951	+	0.986469i	$0.552424\pi$
$878$	3.48175	0.117503
$879$	−26.1560	−0.882220
$880$	0.473626	0.0159659
$881$	−22.2976	−0.751224	−0.375612	−	0.926777i	$-0.622567\pi$
$881$	−22.2976	−0.751224	−0.375612	+	0.926777i	$0.622567\pi$
$882$	0	0
$883$	6.70589	0.225671	0.112836	−	0.993614i	$-0.464007\pi$
$883$	6.70589	0.225671	0.112836	+	0.993614i	$0.464007\pi$
$884$	−32.6368	−1.09770
$885$	4.65332	0.156420
$886$	24.6690	0.828772
$887$	58.3368	1.95876	0.979380	−	0.202029i	$-0.0647535\pi$
$887$	58.3368	1.95876	0.979380	+	0.202029i	$0.0647535\pi$
$888$	4.32666	0.145193
$889$	0	0
$890$	−7.90393	−0.264940
$891$	1.00000	0.0335013
$892$	3.82529	0.128080
$893$	1.77568	0.0594208
$894$	−4.89097	−0.163579
$895$	−2.73105	−0.0912888
$896$	0	0
$897$	10.5345	0.351737
$898$	6.39863	0.213525
$899$	14.4824	0.483014
$900$	−4.77568	−0.159189
$901$	−44.8677	−1.49476
$902$	11.2458	0.374443
$903$	0	0
$904$	−8.40569	−0.279569
$905$	−1.60163	−0.0532401
$906$	16.6533	0.553270
$907$	46.2804	1.53671	0.768357	−	0.640021i	$-0.221074\pi$
$907$	46.2804	1.53671	0.768357	+	0.640021i	$0.221074\pi$
$908$	12.3106	0.408541
$909$	−0.298919	−0.00991452
$910$	0	0
$911$	−55.3864	−1.83503	−0.917517	−	0.397696i	$-0.869810\pi$
$911$	−55.3864	−1.83503	−0.917517	+	0.397696i	$0.869810\pi$
$912$	6.55765	0.217145
$913$	7.54469	0.249693
$914$	14.5549	0.481433
$915$	7.19879	0.237985
$916$	20.2726	0.669826
$917$	0	0
$918$	−4.64167	−0.153198
$919$	14.1851	0.467923	0.233961	−	0.972246i	$-0.424831\pi$
$919$	14.1851	0.467923	0.233961	+	0.972246i	$0.424831\pi$
$920$	0.709603	0.0233949
$921$	25.3109	0.834024
$922$	16.3115	0.537189
$923$	−105.538	−3.47383
$924$	0	0
$925$	20.6627	0.679387
$926$	8.81138	0.289560
$927$	7.39550	0.242900
$928$	−2.11882	−0.0695538
$929$	31.0150	1.01757	0.508784	−	0.860894i	$-0.330095\pi$
$929$	31.0150	1.01757	0.508784	+	0.860894i	$0.330095\pi$
$930$	3.23728	0.106154
$931$	0	0
$932$	−10.8114	−0.354139
$933$	−24.6202	−0.806029
$934$	−8.20468	−0.268465
$935$	2.19841	0.0718958
$936$	−7.03127	−0.229824
$937$	−33.5238	−1.09517	−0.547587	−	0.836749i	$-0.684454\pi$
$937$	−33.5238	−1.09517	−0.547587	+	0.836749i	$0.684454\pi$
$938$	0	0
$939$	19.2713	0.628895
$940$	−0.128248	−0.00418300
$941$	−32.2097	−1.05001	−0.525003	−	0.851101i	$-0.675936\pi$
$941$	−32.2097	−1.05001	−0.525003	+	0.851101i	$0.675936\pi$
$942$	−14.5228	−0.473180
$943$	16.8488	0.548673
$944$	−9.82490	−0.319773
$945$	0	0
$946$	0.158619	0.00515715
$947$	−45.4459	−1.47679	−0.738396	−	0.674367i	$-0.764416\pi$
$947$	−45.4459	−1.47679	−0.738396	+	0.674367i	$0.764416\pi$
$948$	−11.4420	−0.371617
$949$	−43.1051	−1.39925
$950$	31.3172	1.01606
$951$	−4.34551	−0.140913
$952$	0	0
$953$	−38.5651	−1.24924	−0.624622	−	0.780927i	$-0.714747\pi$
$953$	−38.5651	−1.24924	−0.624622	+	0.780927i	$0.714747\pi$
$954$	−9.66628	−0.312957
$955$	−7.65314	−0.247650
$956$	4.07959	0.131943
$957$	2.11882	0.0684919
$958$	−6.72920	−0.217411
$959$	0	0
$960$	−0.473626	−0.0152862
$961$	15.7185	0.507047
$962$	30.4219	0.980843
$963$	−15.3231	−0.493781
$964$	−21.9946	−0.708399
$965$	−11.7767	−0.379107
$966$	0	0
$967$	30.4086	0.977875	0.488938	−	0.872319i	$-0.337385\pi$
$967$	30.4086	0.977875	0.488938	+	0.872319i	$0.337385\pi$
$968$	1.00000	0.0321412
$969$	30.4384	0.977823
$970$	−6.14083	−0.197170
$971$	18.1366	0.582032	0.291016	−	0.956718i	$-0.406007\pi$
$971$	18.1366	0.582032	0.291016	+	0.956718i	$0.406007\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	18.9870	0.608384
$975$	−33.5791	−1.07539
$976$	−15.1993	−0.486518
$977$	2.68370	0.0858590	0.0429295	−	0.999078i	$-0.486331\pi$
$977$	2.68370	0.0858590	0.0429295	+	0.999078i	$0.486331\pi$
$978$	8.33609	0.266559
$979$	−16.6881	−0.533355
$980$	0	0
$981$	−0.422735	−0.0134969
$982$	19.1027	0.609592
$983$	−39.2806	−1.25286	−0.626428	−	0.779479i	$-0.715484\pi$
$983$	−39.2806	−1.25286	−0.626428	+	0.779479i	$0.715484\pi$
$984$	−11.2458	−0.358502
$985$	4.93944	0.157384
$986$	−9.83488	−0.313206
$987$	0	0
$988$	46.1086	1.46691
$989$	0.237649	0.00755679
$990$	0.473626	0.0150528
$991$	−48.8051	−1.55034	−0.775172	−	0.631750i	$-0.782337\pi$
$991$	−48.8051	−1.55034	−0.775172	+	0.631750i	$0.782337\pi$
$992$	−6.83509	−0.217014
$993$	5.46786	0.173517
$994$	0	0
$995$	6.28556	0.199266
$996$	−7.54469	−0.239063
$997$	0.552259	0.0174902	0.00874512	−	0.999962i	$-0.497216\pi$
$997$	0.552259	0.0174902	0.00874512	+	0.999962i	$0.497216\pi$
$998$	−38.6243	−1.22263
$999$	4.32666	0.136890

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.a.bl.1.3	✓	4
3.2	odd	2		9702.2.a.ea.1.2		4
7.6	odd	2		3234.2.a.bm.1.2	yes	4
21.20	even	2		9702.2.a.dz.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3234.2.a.bl.1.3	✓	4	1.1	even	1	trivial
3234.2.a.bm.1.2	yes	4	7.6	odd	2
9702.2.a.dz.1.3		4	21.20	even	2
9702.2.a.ea.1.2		4	3.2	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:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.473626 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.473626 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.473626 q^{10} +1.00000 q^{11} -1.00000 q^{12} -7.03127 q^{13} -0.473626 q^{15} +1.00000 q^{16} +4.64167 q^{17} +1.00000 q^{18} -6.55765 q^{19} +0.473626 q^{20} +1.00000 q^{22} +1.49824 q^{23} -1.00000 q^{24} -4.77568 q^{25} -7.03127 q^{26} -1.00000 q^{27} -2.11882 q^{29} -0.473626 q^{30} -6.83509 q^{31} +1.00000 q^{32} -1.00000 q^{33} +4.64167 q^{34} +1.00000 q^{36} -4.32666 q^{37} -6.55765 q^{38} +7.03127 q^{39} +0.473626 q^{40} +11.2458 q^{41} +0.158619 q^{43} +1.00000 q^{44} +0.473626 q^{45} +1.49824 q^{46} -0.270780 q^{47} -1.00000 q^{48} -4.77568 q^{50} -4.64167 q^{51} -7.03127 q^{52} -9.66628 q^{53} -1.00000 q^{54} +0.473626 q^{55} +6.55765 q^{57} -2.11882 q^{58} -9.82490 q^{59} -0.473626 q^{60} -15.1993 q^{61} -6.83509 q^{62} +1.00000 q^{64} -3.33019 q^{65} -1.00000 q^{66} -1.21137 q^{67} +4.64167 q^{68} -1.49824 q^{69} +15.0098 q^{71} +1.00000 q^{72} +6.13048 q^{73} -4.32666 q^{74} +4.77568 q^{75} -6.55765 q^{76} +7.03127 q^{78} +11.4420 q^{79} +0.473626 q^{80} +1.00000 q^{81} +11.2458 q^{82} +7.54469 q^{83} +2.19841 q^{85} +0.158619 q^{86} +2.11882 q^{87} +1.00000 q^{88} -16.6881 q^{89} +0.473626 q^{90} +1.49824 q^{92} +6.83509 q^{93} -0.270780 q^{94} -3.10587 q^{95} -1.00000 q^{96} -12.9656 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} - 8 q^{13} + 4 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} - 12 q^{19} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 4 q^{24} + 4 q^{25} - 8 q^{26} - 4 q^{27} - 8 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 4 q^{33} - 4 q^{34} + 4 q^{36} + 8 q^{37} - 12 q^{38} + 8 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{43} + 4 q^{44} - 4 q^{45} - 8 q^{46} - 4 q^{47} - 4 q^{48} + 4 q^{50} + 4 q^{51} - 8 q^{52} - 8 q^{53} - 4 q^{54} - 4 q^{55} + 12 q^{57} - 8 q^{58} + 4 q^{60} - 24 q^{61} - 4 q^{62} + 4 q^{64} - 16 q^{65} - 4 q^{66} - 8 q^{67} - 4 q^{68} + 8 q^{69} + 8 q^{71} + 4 q^{72} - 4 q^{73} + 8 q^{74} - 4 q^{75} - 12 q^{76} + 8 q^{78} - 8 q^{79} - 4 q^{80} + 4 q^{81} - 12 q^{82} - 4 q^{83} - 8 q^{85} - 8 q^{86} + 8 q^{87} + 4 q^{88} - 24 q^{89} - 4 q^{90} - 8 q^{92} + 4 q^{93} - 4 q^{94} + 8 q^{95} - 4 q^{96} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 - 8 * q^13 + 4 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 - 12 * q^19 - 4 * q^20 + 4 * q^22 - 8 * q^23 - 4 * q^24 + 4 * q^25 - 8 * q^26 - 4 * q^27 - 8 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 4 * q^33 - 4 * q^34 + 4 * q^36 + 8 * q^37 - 12 * q^38 + 8 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^43 + 4 * q^44 - 4 * q^45 - 8 * q^46 - 4 * q^47 - 4 * q^48 + 4 * q^50 + 4 * q^51 - 8 * q^52 - 8 * q^53 - 4 * q^54 - 4 * q^55 + 12 * q^57 - 8 * q^58 + 4 * q^60 - 24 * q^61 - 4 * q^62 + 4 * q^64 - 16 * q^65 - 4 * q^66 - 8 * q^67 - 4 * q^68 + 8 * q^69 + 8 * q^71 + 4 * q^72 - 4 * q^73 + 8 * q^74 - 4 * q^75 - 12 * q^76 + 8 * q^78 - 8 * q^79 - 4 * q^80 + 4 * q^81 - 12 * q^82 - 4 * q^83 - 8 * q^85 - 8 * q^86 + 8 * q^87 + 4 * q^88 - 24 * q^89 - 4 * q^90 - 8 * q^92 + 4 * q^93 - 4 * q^94 + 8 * q^95 - 4 * q^96 + 4 * q^99

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