LMFDB - Embedded newform 6027.2.a.bl.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 14 x^{14} + 68 x^{13} + 64 x^{12} - 456 x^{11} - 54 x^{10} + 1532 x^{9} - 400 x^{8} + \cdots - 49 $ x^16 - 4x^15 - 14x^14 + 68x^13 + 64x^12 - 456x^11 - 54x^10 + 1532x^9 - 400x^8 - 2708x^7 + 1218x^6 + 2424x^5 - 1276x^4 - 960x^3 + 500x^2 + 112*x - 49
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.69180$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69180 q^{2} -1.00000 q^{3} +5.24578 q^{4} +3.62847 q^{5} +2.69180 q^{6} -8.73699 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.69180 q^{2} -1.00000 q^{3} +5.24578 q^{4} +3.62847 q^{5} +2.69180 q^{6} -8.73699 q^{8} +1.00000 q^{9} -9.76712 q^{10} +3.79578 q^{11} -5.24578 q^{12} -0.986924 q^{13} -3.62847 q^{15} +13.0267 q^{16} -1.05753 q^{17} -2.69180 q^{18} +2.81023 q^{19} +19.0342 q^{20} -10.2175 q^{22} -5.66437 q^{23} +8.73699 q^{24} +8.16582 q^{25} +2.65660 q^{26} -1.00000 q^{27} -2.21857 q^{29} +9.76712 q^{30} -10.4547 q^{31} -17.5912 q^{32} -3.79578 q^{33} +2.84664 q^{34} +5.24578 q^{36} -7.86953 q^{37} -7.56457 q^{38} +0.986924 q^{39} -31.7019 q^{40} -1.00000 q^{41} +4.16152 q^{43} +19.9118 q^{44} +3.62847 q^{45} +15.2473 q^{46} +5.08902 q^{47} -13.0267 q^{48} -21.9807 q^{50} +1.05753 q^{51} -5.17719 q^{52} -9.17461 q^{53} +2.69180 q^{54} +13.7729 q^{55} -2.81023 q^{57} +5.97193 q^{58} +7.58471 q^{59} -19.0342 q^{60} -5.96328 q^{61} +28.1420 q^{62} +21.2985 q^{64} -3.58103 q^{65} +10.2175 q^{66} -15.6363 q^{67} -5.54754 q^{68} +5.66437 q^{69} +11.6213 q^{71} -8.73699 q^{72} +3.75487 q^{73} +21.1832 q^{74} -8.16582 q^{75} +14.7418 q^{76} -2.65660 q^{78} -4.83413 q^{79} +47.2669 q^{80} +1.00000 q^{81} +2.69180 q^{82} -7.04509 q^{83} -3.83720 q^{85} -11.2020 q^{86} +2.21857 q^{87} -33.1637 q^{88} -9.53384 q^{89} -9.76712 q^{90} -29.7140 q^{92} +10.4547 q^{93} -13.6986 q^{94} +10.1968 q^{95} +17.5912 q^{96} -14.2834 q^{97} +3.79578 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9	$ 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9} + 4 q^{10} - 4 q^{11} - 12 q^{12} - 12 q^{15} + 8 q^{17} - 4 q^{18} - 4 q^{19} + 20 q^{20} - 16 q^{22} - 12 q^{23} + 12 q^{24} - 8 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29} - 4 q^{30} + 4 q^{31} - 48 q^{32} + 4 q^{33} - 16 q^{34} + 12 q^{36} - 48 q^{37} + 4 q^{38} - 56 q^{40} - 16 q^{41} - 16 q^{43} + 12 q^{45} - 4 q^{46} + 36 q^{47} - 8 q^{50} - 8 q^{51} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 4 q^{57} - 36 q^{58} + 36 q^{59} - 20 q^{60} + 4 q^{61} + 12 q^{62} + 52 q^{64} - 36 q^{65} + 16 q^{66} - 52 q^{67} + 8 q^{68} + 12 q^{69} - 12 q^{71} - 12 q^{72} + 16 q^{73} + 4 q^{74} + 8 q^{75} - 16 q^{76} - 8 q^{78} - 36 q^{79} + 68 q^{80} + 16 q^{81} + 4 q^{82} + 32 q^{83} - 28 q^{85} - 8 q^{86} + 16 q^{87} - 36 q^{88} + 12 q^{89} + 4 q^{90} - 36 q^{92} - 4 q^{93} - 24 q^{94} - 20 q^{95} + 48 q^{96} - 48 q^{97} - 4 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9 + 4 * q^10 - 4 * q^11 - 12 * q^12 - 12 * q^15 + 8 * q^17 - 4 * q^18 - 4 * q^19 + 20 * q^20 - 16 * q^22 - 12 * q^23 + 12 * q^24 - 8 * q^25 + 8 * q^26 - 16 * q^27 - 16 * q^29 - 4 * q^30 + 4 * q^31 - 48 * q^32 + 4 * q^33 - 16 * q^34 + 12 * q^36 - 48 * q^37 + 4 * q^38 - 56 * q^40 - 16 * q^41 - 16 * q^43 + 12 * q^45 - 4 * q^46 + 36 * q^47 - 8 * q^50 - 8 * q^51 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 4 * q^57 - 36 * q^58 + 36 * q^59 - 20 * q^60 + 4 * q^61 + 12 * q^62 + 52 * q^64 - 36 * q^65 + 16 * q^66 - 52 * q^67 + 8 * q^68 + 12 * q^69 - 12 * q^71 - 12 * q^72 + 16 * q^73 + 4 * q^74 + 8 * q^75 - 16 * q^76 - 8 * q^78 - 36 * q^79 + 68 * q^80 + 16 * q^81 + 4 * q^82 + 32 * q^83 - 28 * q^85 - 8 * q^86 + 16 * q^87 - 36 * q^88 + 12 * q^89 + 4 * q^90 - 36 * q^92 - 4 * q^93 - 24 * q^94 - 20 * q^95 + 48 * q^96 - 48 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.69180	−1.90339	−0.951695	−	0.307046i	$-0.900659\pi$
$2$	−2.69180	−1.90339	−0.951695	+	0.307046i	$0.900659\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.24578	2.62289
$5$	3.62847	1.62270	0.811351	−	0.584559i	$-0.198732\pi$
$5$	3.62847	1.62270	0.811351	+	0.584559i	$0.198732\pi$
$6$	2.69180	1.09892
$7$	0	0
$7$	0	0
$8$	−8.73699	−3.08899
$9$	1.00000	0.333333
$10$	−9.76712	−3.08863
$11$	3.79578	1.14447	0.572235	−	0.820090i	$-0.306077\pi$
$11$	3.79578	1.14447	0.572235	+	0.820090i	$0.306077\pi$
$12$	−5.24578	−1.51433
$13$	−0.986924	−0.273723	−0.136862	−	0.990590i	$-0.543702\pi$
$13$	−0.986924	−0.273723	−0.136862	+	0.990590i	$0.543702\pi$
$14$	0	0
$15$	−3.62847	−0.936868
$16$	13.0267	3.25666
$17$	−1.05753	−0.256488	−0.128244	−	0.991743i	$-0.540934\pi$
$17$	−1.05753	−0.256488	−0.128244	+	0.991743i	$0.540934\pi$
$18$	−2.69180	−0.634463
$19$	2.81023	0.644711	0.322355	−	0.946619i	$-0.395525\pi$
$19$	2.81023	0.644711	0.322355	+	0.946619i	$0.395525\pi$
$20$	19.0342	4.25617
$21$	0	0
$22$	−10.2175	−2.17837
$23$	−5.66437	−1.18110	−0.590551	−	0.807000i	$-0.701090\pi$
$23$	−5.66437	−1.18110	−0.590551	+	0.807000i	$0.701090\pi$
$24$	8.73699	1.78343
$25$	8.16582	1.63316
$26$	2.65660	0.521002
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−2.21857	−0.411977	−0.205989	−	0.978554i	$-0.566041\pi$
$29$	−2.21857	−0.411977	−0.205989	+	0.978554i	$0.566041\pi$
$30$	9.76712	1.78322
$31$	−10.4547	−1.87773	−0.938863	−	0.344291i	$-0.888119\pi$
$31$	−10.4547	−1.87773	−0.938863	+	0.344291i	$0.888119\pi$
$32$	−17.5912	−3.10971
$33$	−3.79578	−0.660760
$34$	2.84664	0.488196
$35$	0	0
$36$	5.24578	0.874297
$37$	−7.86953	−1.29374	−0.646871	−	0.762599i	$-0.723923\pi$
$37$	−7.86953	−1.29374	−0.646871	+	0.762599i	$0.723923\pi$
$38$	−7.56457	−1.22714
$39$	0.986924	0.158034
$40$	−31.7019	−5.01251
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	4.16152	0.634625	0.317313	−	0.948321i	$-0.397220\pi$
$43$	4.16152	0.634625	0.317313	+	0.948321i	$0.397220\pi$
$44$	19.9118	3.00182
$45$	3.62847	0.540901
$46$	15.2473	2.24810
$47$	5.08902	0.742309	0.371155	−	0.928571i	$-0.378962\pi$
$47$	5.08902	0.742309	0.371155	+	0.928571i	$0.378962\pi$
$48$	−13.0267	−1.88024
$49$	0	0
$50$	−21.9807	−3.10854
$51$	1.05753	0.148083
$52$	−5.17719	−0.717946
$53$	−9.17461	−1.26023	−0.630115	−	0.776502i	$-0.716992\pi$
$53$	−9.17461	−1.26023	−0.630115	+	0.776502i	$0.716992\pi$
$54$	2.69180	0.366307
$55$	13.7729	1.85713
$56$	0	0
$57$	−2.81023	−0.372224
$58$	5.97193	0.784153
$59$	7.58471	0.987446	0.493723	−	0.869619i	$-0.335636\pi$
$59$	7.58471	0.987446	0.493723	+	0.869619i	$0.335636\pi$
$60$	−19.0342	−2.45730
$61$	−5.96328	−0.763520	−0.381760	−	0.924262i	$-0.624682\pi$
$61$	−5.96328	−0.763520	−0.381760	+	0.924262i	$0.624682\pi$
$62$	28.1420	3.57404
$63$	0	0
$64$	21.2985	2.66232
$65$	−3.58103	−0.444172
$66$	10.2175	1.25768
$67$	−15.6363	−1.91027	−0.955137	−	0.296165i	$-0.904292\pi$
$67$	−15.6363	−1.91027	−0.955137	+	0.296165i	$0.904292\pi$
$68$	−5.54754	−0.672739
$69$	5.66437	0.681909
$70$	0	0
$71$	11.6213	1.37920	0.689600	−	0.724190i	$-0.257786\pi$
$71$	11.6213	1.37920	0.689600	+	0.724190i	$0.257786\pi$
$72$	−8.73699	−1.02966
$73$	3.75487	0.439475	0.219737	−	0.975559i	$-0.429480\pi$
$73$	3.75487	0.439475	0.219737	+	0.975559i	$0.429480\pi$
$74$	21.1832	2.46250
$75$	−8.16582	−0.942907
$76$	14.7418	1.69101
$77$	0	0
$78$	−2.65660	−0.300801
$79$	−4.83413	−0.543883	−0.271941	−	0.962314i	$-0.587666\pi$
$79$	−4.83413	−0.543883	−0.271941	+	0.962314i	$0.587666\pi$
$80$	47.2669	5.28460
$81$	1.00000	0.111111
$82$	2.69180	0.297259
$83$	−7.04509	−0.773299	−0.386649	−	0.922227i	$-0.626368\pi$
$83$	−7.04509	−0.773299	−0.386649	+	0.922227i	$0.626368\pi$
$84$	0	0
$85$	−3.83720	−0.416203
$86$	−11.2020	−1.20794
$87$	2.21857	0.237855
$88$	−33.1637	−3.53526
$89$	−9.53384	−1.01059	−0.505293	−	0.862948i	$-0.668615\pi$
$89$	−9.53384	−1.01059	−0.505293	+	0.862948i	$0.668615\pi$
$90$	−9.76712	−1.02954
$91$	0	0
$92$	−29.7140	−3.09790
$93$	10.4547	1.08411
$94$	−13.6986	−1.41290
$95$	10.1968	1.04617
$96$	17.5912	1.79539
$97$	−14.2834	−1.45026	−0.725130	−	0.688612i	$-0.758221\pi$
$97$	−14.2834	−1.45026	−0.725130	+	0.688612i	$0.758221\pi$
$98$	0	0
$99$	3.79578	0.381490
$100$	42.8361	4.28361
$101$	−1.27838	−0.127203	−0.0636017	−	0.997975i	$-0.520259\pi$
$101$	−1.27838	−0.127203	−0.0636017	+	0.997975i	$0.520259\pi$
$102$	−2.84664	−0.281860
$103$	−11.9906	−1.18147	−0.590737	−	0.806864i	$-0.701163\pi$
$103$	−11.9906	−1.18147	−0.590737	+	0.806864i	$0.701163\pi$
$104$	8.62274	0.845529
$105$	0	0
$106$	24.6962	2.39871
$107$	−18.0089	−1.74098	−0.870491	−	0.492185i	$-0.836198\pi$
$107$	−18.0089	−1.74098	−0.870491	+	0.492185i	$0.836198\pi$
$108$	−5.24578	−0.504775
$109$	−14.0107	−1.34198	−0.670992	−	0.741464i	$-0.734132\pi$
$109$	−14.0107	−1.34198	−0.670992	+	0.741464i	$0.734132\pi$
$110$	−37.0738	−3.53485
$111$	7.86953	0.746943
$112$	0	0
$113$	13.5638	1.27597	0.637986	−	0.770048i	$-0.279768\pi$
$113$	13.5638	1.27597	0.637986	+	0.770048i	$0.279768\pi$
$114$	7.56457	0.708487
$115$	−20.5530	−1.91658
$116$	−11.6381	−1.08057
$117$	−0.986924	−0.0912411
$118$	−20.4165	−1.87949
$119$	0	0
$120$	31.7019	2.89398
$121$	3.40793	0.309812
$122$	16.0519	1.45328
$123$	1.00000	0.0901670
$124$	−54.8433	−4.92507
$125$	11.4871	1.02744
$126$	0	0
$127$	12.6460	1.12215	0.561076	−	0.827764i	$-0.310387\pi$
$127$	12.6460	1.12215	0.561076	+	0.827764i	$0.310387\pi$
$128$	−22.1491	−1.95772
$129$	−4.16152	−0.366401
$130$	9.63940	0.845431
$131$	−21.8687	−1.91068	−0.955340	−	0.295509i	$-0.904511\pi$
$131$	−21.8687	−1.91068	−0.955340	+	0.295509i	$0.904511\pi$
$132$	−19.9118	−1.73310
$133$	0	0
$134$	42.0897	3.63599
$135$	−3.62847	−0.312289
$136$	9.23959	0.792288
$137$	−4.28037	−0.365697	−0.182848	−	0.983141i	$-0.558532\pi$
$137$	−4.28037	−0.365697	−0.182848	+	0.983141i	$0.558532\pi$
$138$	−15.2473	−1.29794
$139$	−0.0145030	−0.00123013	−0.000615064	−	1.00000i	$-0.500196\pi$
$139$	−0.0145030	−0.00123013	−0.000615064		1.00000i	$0.500196\pi$
$140$	0	0
$141$	−5.08902	−0.428572
$142$	−31.2823	−2.62515
$143$	−3.74614	−0.313268
$144$	13.0267	1.08555
$145$	−8.05001	−0.668517
$146$	−10.1074	−0.836491
$147$	0	0
$148$	−41.2818	−3.39335
$149$	−14.7596	−1.20915	−0.604577	−	0.796547i	$-0.706658\pi$
$149$	−14.7596	−1.20915	−0.604577	+	0.796547i	$0.706658\pi$
$150$	21.9807	1.79472
$151$	−6.86221	−0.558438	−0.279219	−	0.960227i	$-0.590076\pi$
$151$	−6.86221	−0.558438	−0.279219	+	0.960227i	$0.590076\pi$
$152$	−24.5529	−1.99151
$153$	−1.05753	−0.0854958
$154$	0	0
$155$	−37.9347	−3.04699
$156$	5.17719	0.414507
$157$	−4.17576	−0.333262	−0.166631	−	0.986019i	$-0.553289\pi$
$157$	−4.17576	−0.333262	−0.166631	+	0.986019i	$0.553289\pi$
$158$	13.0125	1.03522
$159$	9.17461	0.727594
$160$	−63.8290	−5.04613
$161$	0	0
$162$	−2.69180	−0.211488
$163$	−23.5210	−1.84231	−0.921155	−	0.389195i	$-0.872753\pi$
$163$	−23.5210	−1.84231	−0.921155	+	0.389195i	$0.872753\pi$
$164$	−5.24578	−0.409627
$165$	−13.7729	−1.07222
$166$	18.9640	1.47189
$167$	15.7070	1.21544	0.607722	−	0.794150i	$-0.292083\pi$
$167$	15.7070	1.21544	0.607722	+	0.794150i	$0.292083\pi$
$168$	0	0
$169$	−12.0260	−0.925076
$170$	10.3290	0.792196
$171$	2.81023	0.214904
$172$	21.8304	1.66455
$173$	5.89269	0.448013	0.224006	−	0.974588i	$-0.428086\pi$
$173$	5.89269	0.448013	0.224006	+	0.974588i	$0.428086\pi$
$174$	−5.97193	−0.452731
$175$	0	0
$176$	49.4463	3.72715
$177$	−7.58471	−0.570102
$178$	25.6632	1.92354
$179$	4.67222	0.349218	0.174609	−	0.984638i	$-0.444134\pi$
$179$	4.67222	0.349218	0.174609	+	0.984638i	$0.444134\pi$
$180$	19.0342	1.41872
$181$	13.2354	0.983776	0.491888	−	0.870658i	$-0.336307\pi$
$181$	13.2354	0.983776	0.491888	+	0.870658i	$0.336307\pi$
$182$	0	0
$183$	5.96328	0.440818
$184$	49.4895	3.64841
$185$	−28.5544	−2.09936
$186$	−28.1420	−2.06348
$187$	−4.01413	−0.293542
$188$	26.6959	1.94700
$189$	0	0
$190$	−27.4478	−1.99127
$191$	18.4336	1.33381	0.666903	−	0.745145i	$-0.267620\pi$
$191$	18.4336	1.33381	0.666903	+	0.745145i	$0.267620\pi$
$192$	−21.2985	−1.53709
$193$	11.4648	0.825254	0.412627	−	0.910900i	$-0.364611\pi$
$193$	11.4648	0.825254	0.412627	+	0.910900i	$0.364611\pi$
$194$	38.4481	2.76041
$195$	3.58103	0.256443
$196$	0	0
$197$	2.88305	0.205408	0.102704	−	0.994712i	$-0.467250\pi$
$197$	2.88305	0.205408	0.102704	+	0.994712i	$0.467250\pi$
$198$	−10.2175	−0.726124
$199$	−18.6674	−1.32330	−0.661650	−	0.749813i	$-0.730144\pi$
$199$	−18.6674	−1.32330	−0.661650	+	0.749813i	$0.730144\pi$
$200$	−71.3446	−5.04483
$201$	15.6363	1.10290
$202$	3.44114	0.242118
$203$	0	0
$204$	5.54754	0.388406
$205$	−3.62847	−0.253424
$206$	32.2764	2.24880
$207$	−5.66437	−0.393701
$208$	−12.8563	−0.891425
$209$	10.6670	0.737852
$210$	0	0
$211$	−3.09415	−0.213010	−0.106505	−	0.994312i	$-0.533966\pi$
$211$	−3.09415	−0.213010	−0.106505	+	0.994312i	$0.533966\pi$
$212$	−48.1280	−3.30544
$213$	−11.6213	−0.796282
$214$	48.4762	3.31377
$215$	15.1000	1.02981
$216$	8.73699	0.594477
$217$	0	0
$218$	37.7141	2.55432
$219$	−3.75487	−0.253731
$220$	72.2495	4.87106
$221$	1.04370	0.0702066
$222$	−21.1832	−1.42172
$223$	−20.2026	−1.35286	−0.676432	−	0.736505i	$-0.736475\pi$
$223$	−20.2026	−1.35286	−0.676432	+	0.736505i	$0.736475\pi$
$224$	0	0
$225$	8.16582	0.544388
$226$	−36.5109	−2.42867
$227$	23.1892	1.53912	0.769559	−	0.638575i	$-0.220476\pi$
$227$	23.1892	1.53912	0.769559	+	0.638575i	$0.220476\pi$
$228$	−14.7418	−0.976302
$229$	14.8334	0.980219	0.490109	−	0.871661i	$-0.336957\pi$
$229$	14.8334	0.980219	0.490109	+	0.871661i	$0.336957\pi$
$230$	55.3245	3.64799
$231$	0	0
$232$	19.3836	1.27259
$233$	23.8864	1.56485	0.782426	−	0.622744i	$-0.213982\pi$
$233$	23.8864	1.56485	0.782426	+	0.622744i	$0.213982\pi$
$234$	2.65660	0.173667
$235$	18.4654	1.20455
$236$	39.7877	2.58996
$237$	4.83413	0.314011
$238$	0	0
$239$	17.1844	1.11156	0.555782	−	0.831328i	$-0.312419\pi$
$239$	17.1844	1.11156	0.555782	+	0.831328i	$0.312419\pi$
$240$	−47.2669	−3.05106
$241$	−6.16967	−0.397423	−0.198712	−	0.980058i	$-0.563676\pi$
$241$	−6.16967	−0.397423	−0.198712	+	0.980058i	$0.563676\pi$
$242$	−9.17345	−0.589692
$243$	−1.00000	−0.0641500
$244$	−31.2821	−2.00263
$245$	0	0
$246$	−2.69180	−0.171623
$247$	−2.77348	−0.176472
$248$	91.3429	5.80028
$249$	7.04509	0.446464
$250$	−30.9209	−1.95561
$251$	21.2207	1.33944	0.669720	−	0.742614i	$-0.266414\pi$
$251$	21.2207	1.33944	0.669720	+	0.742614i	$0.266414\pi$
$252$	0	0
$253$	−21.5007	−1.35174
$254$	−34.0405	−2.13589
$255$	3.83720	0.240295
$256$	17.0238	1.06399
$257$	−23.2708	−1.45159	−0.725796	−	0.687910i	$-0.758528\pi$
$257$	−23.2708	−1.45159	−0.725796	+	0.687910i	$0.758528\pi$
$258$	11.2020	0.697404
$259$	0	0
$260$	−18.7853	−1.16501
$261$	−2.21857	−0.137326
$262$	58.8662	3.63677
$263$	−30.5369	−1.88299	−0.941493	−	0.337033i	$-0.890577\pi$
$263$	−30.5369	−1.88299	−0.941493	+	0.337033i	$0.890577\pi$
$264$	33.1637	2.04108
$265$	−33.2898	−2.04498
$266$	0	0
$267$	9.53384	0.583462
$268$	−82.0244	−5.01044
$269$	4.54700	0.277235	0.138618	−	0.990346i	$-0.455734\pi$
$269$	4.54700	0.277235	0.138618	+	0.990346i	$0.455734\pi$
$270$	9.76712	0.594408
$271$	21.0582	1.27919	0.639597	−	0.768711i	$-0.279101\pi$
$271$	21.0582	1.27919	0.639597	+	0.768711i	$0.279101\pi$
$272$	−13.7760	−0.835294
$273$	0	0
$274$	11.5219	0.696063
$275$	30.9956	1.86911
$276$	29.7140	1.78857
$277$	−1.16773	−0.0701620	−0.0350810	−	0.999384i	$-0.511169\pi$
$277$	−1.16773	−0.0701620	−0.0350810	+	0.999384i	$0.511169\pi$
$278$	0.0390392	0.00234141
$279$	−10.4547	−0.625909
$280$	0	0
$281$	−16.8177	−1.00326	−0.501631	−	0.865082i	$-0.667266\pi$
$281$	−16.8177	−1.00326	−0.501631	+	0.865082i	$0.667266\pi$
$282$	13.6986	0.815740
$283$	−32.2924	−1.91958	−0.959791	−	0.280715i	$-0.909428\pi$
$283$	−32.2924	−1.91958	−0.959791	+	0.280715i	$0.909428\pi$
$284$	60.9630	3.61749
$285$	−10.1968	−0.604008
$286$	10.0839	0.596271
$287$	0	0
$288$	−17.5912	−1.03657
$289$	−15.8816	−0.934214
$290$	21.6690	1.27245
$291$	14.2834	0.837309
$292$	19.6972	1.15269
$293$	22.4014	1.30871	0.654353	−	0.756189i	$-0.272941\pi$
$293$	22.4014	1.30871	0.654353	+	0.756189i	$0.272941\pi$
$294$	0	0
$295$	27.5209	1.60233
$296$	68.7560	3.99636
$297$	−3.79578	−0.220253
$298$	39.7299	2.30149
$299$	5.59030	0.323295
$300$	−42.8361	−2.47314
$301$	0	0
$302$	18.4717	1.06293
$303$	1.27838	0.0734409
$304$	36.6079	2.09961
$305$	−21.6376	−1.23897
$306$	2.84664	0.162732
$307$	15.5675	0.888481	0.444241	−	0.895907i	$-0.353474\pi$
$307$	15.5675	0.888481	0.444241	+	0.895907i	$0.353474\pi$
$308$	0	0
$309$	11.9906	0.682124
$310$	102.113	5.79961
$311$	20.2286	1.14706	0.573531	−	0.819184i	$-0.305573\pi$
$311$	20.2286	1.14706	0.573531	+	0.819184i	$0.305573\pi$
$312$	−8.62274	−0.488167
$313$	13.2244	0.747490	0.373745	−	0.927532i	$-0.378074\pi$
$313$	13.2244	0.747490	0.373745	+	0.927532i	$0.378074\pi$
$314$	11.2403	0.634328
$315$	0	0
$316$	−25.3588	−1.42654
$317$	−17.4307	−0.979004	−0.489502	−	0.872002i	$-0.662821\pi$
$317$	−17.4307	−0.979004	−0.489502	+	0.872002i	$0.662821\pi$
$318$	−24.6962	−1.38489
$319$	−8.42118	−0.471496
$320$	77.2812	4.32015
$321$	18.0089	1.00516
$322$	0	0
$323$	−2.97189	−0.165360
$324$	5.24578	0.291432
$325$	−8.05904	−0.447035
$326$	63.3139	3.50663
$327$	14.0107	0.774795
$328$	8.73699	0.482420
$329$	0	0
$330$	37.0738	2.04085
$331$	20.7539	1.14074	0.570369	−	0.821389i	$-0.306800\pi$
$331$	20.7539	1.14074	0.570369	+	0.821389i	$0.306800\pi$
$332$	−36.9570	−2.02828
$333$	−7.86953	−0.431248
$334$	−42.2801	−2.31346
$335$	−56.7358	−3.09981
$336$	0	0
$337$	−3.56654	−0.194282	−0.0971409	−	0.995271i	$-0.530970\pi$
$337$	−3.56654	−0.194282	−0.0971409	+	0.995271i	$0.530970\pi$
$338$	32.3715	1.76078
$339$	−13.5638	−0.736682
$340$	−20.1291	−1.09165
$341$	−39.6839	−2.14900
$342$	−7.56457	−0.409045
$343$	0	0
$344$	−36.3591	−1.96035
$345$	20.5530	1.10654
$346$	−15.8619	−0.852743
$347$	11.9328	0.640586	0.320293	−	0.947319i	$-0.396219\pi$
$347$	11.9328	0.640586	0.320293	+	0.947319i	$0.396219\pi$
$348$	11.6381	0.623868
$349$	6.91055	0.369913	0.184957	−	0.982747i	$-0.440786\pi$
$349$	6.91055	0.369913	0.184957	+	0.982747i	$0.440786\pi$
$350$	0	0
$351$	0.986924	0.0526781
$352$	−66.7721	−3.55897
$353$	−3.75498	−0.199858	−0.0999288	−	0.994995i	$-0.531861\pi$
$353$	−3.75498	−0.199858	−0.0999288	+	0.994995i	$0.531861\pi$
$354$	20.4165	1.08513
$355$	42.1677	2.23803
$356$	−50.0125	−2.65066
$357$	0	0
$358$	−12.5767	−0.664698
$359$	9.38283	0.495207	0.247603	−	0.968861i	$-0.420357\pi$
$359$	9.38283	0.495207	0.247603	+	0.968861i	$0.420357\pi$
$360$	−31.7019	−1.67084
$361$	−11.1026	−0.584348
$362$	−35.6269	−1.87251
$363$	−3.40793	−0.178870
$364$	0	0
$365$	13.6245	0.713136
$366$	−16.0519	−0.839049
$367$	26.7028	1.39388	0.696938	−	0.717132i	$-0.254545\pi$
$367$	26.7028	1.39388	0.696938	+	0.717132i	$0.254545\pi$
$368$	−73.7877	−3.84645
$369$	−1.00000	−0.0520579
$370$	76.8626	3.99590
$371$	0	0
$372$	54.8433	2.84349
$373$	6.05227	0.313375	0.156687	−	0.987648i	$-0.449919\pi$
$373$	6.05227	0.313375	0.156687	+	0.987648i	$0.449919\pi$
$374$	10.8052	0.558725
$375$	−11.4871	−0.593190
$376$	−44.4627	−2.29299
$377$	2.18956	0.112768
$378$	0	0
$379$	−4.68737	−0.240774	−0.120387	−	0.992727i	$-0.538414\pi$
$379$	−4.68737	−0.240774	−0.120387	+	0.992727i	$0.538414\pi$
$380$	53.4904	2.74400
$381$	−12.6460	−0.647875
$382$	−49.6194	−2.53875
$383$	34.5205	1.76391	0.881957	−	0.471330i	$-0.156226\pi$
$383$	34.5205	1.76391	0.881957	+	0.471330i	$0.156226\pi$
$384$	22.1491	1.13029
$385$	0	0
$386$	−30.8609	−1.57078
$387$	4.16152	0.211542
$388$	−74.9277	−3.80388
$389$	1.71421	0.0869137	0.0434569	−	0.999055i	$-0.486163\pi$
$389$	1.71421	0.0869137	0.0434569	+	0.999055i	$0.486163\pi$
$390$	−9.63940	−0.488110
$391$	5.99021	0.302938
$392$	0	0
$393$	21.8687	1.10313
$394$	−7.76058	−0.390972
$395$	−17.5405	−0.882560
$396$	19.9118	1.00061
$397$	−14.5925	−0.732377	−0.366189	−	0.930541i	$-0.619338\pi$
$397$	−14.5925	−0.732377	−0.366189	+	0.930541i	$0.619338\pi$
$398$	50.2490	2.51876
$399$	0	0
$400$	106.373	5.31866
$401$	10.9102	0.544829	0.272415	−	0.962180i	$-0.412178\pi$
$401$	10.9102	0.544829	0.272415	+	0.962180i	$0.412178\pi$
$402$	−42.0897	−2.09924
$403$	10.3180	0.513978
$404$	−6.70609	−0.333641
$405$	3.62847	0.180300
$406$	0	0
$407$	−29.8710	−1.48065
$408$	−9.23959	−0.457428
$409$	14.5454	0.719224	0.359612	−	0.933102i	$-0.382909\pi$
$409$	14.5454	0.719224	0.359612	+	0.933102i	$0.382909\pi$
$410$	9.76712	0.482364
$411$	4.28037	0.211135
$412$	−62.9003	−3.09888
$413$	0	0
$414$	15.2473	0.749365
$415$	−25.5629	−1.25483
$416$	17.3611	0.851199
$417$	0.0145030	0.000710215 0
$418$	−28.7134	−1.40442
$419$	18.6549	0.911353	0.455676	−	0.890146i	$-0.349397\pi$
$419$	18.6549	0.911353	0.455676	+	0.890146i	$0.349397\pi$
$420$	0	0
$421$	−30.2812	−1.47582	−0.737909	−	0.674900i	$-0.764187\pi$
$421$	−30.2812	−1.47582	−0.737909	+	0.674900i	$0.764187\pi$
$422$	8.32884	0.405441
$423$	5.08902	0.247436
$424$	80.1584	3.89284
$425$	−8.63555	−0.418886
$426$	31.2823	1.51563
$427$	0	0
$428$	−94.4705	−4.56640
$429$	3.74614	0.180865
$430$	−40.6460	−1.96013
$431$	12.4541	0.599895	0.299948	−	0.953956i	$-0.403031\pi$
$431$	12.4541	0.599895	0.299948	+	0.953956i	$0.403031\pi$
$432$	−13.0267	−0.626745
$433$	6.80377	0.326968	0.163484	−	0.986546i	$-0.447727\pi$
$433$	6.80377	0.326968	0.163484	+	0.986546i	$0.447727\pi$
$434$	0	0
$435$	8.05001	0.385968
$436$	−73.4972	−3.51988
$437$	−15.9182	−0.761469
$438$	10.1074	0.482948
$439$	23.6472	1.12862	0.564310	−	0.825563i	$-0.309142\pi$
$439$	23.6472	1.12862	0.564310	+	0.825563i	$0.309142\pi$
$440$	−120.333	−5.73667
$441$	0	0
$442$	−2.80942	−0.133631
$443$	14.4599	0.687009	0.343505	−	0.939151i	$-0.388386\pi$
$443$	14.4599	0.687009	0.343505	+	0.939151i	$0.388386\pi$
$444$	41.2818	1.95915
$445$	−34.5933	−1.63988
$446$	54.3812	2.57503
$447$	14.7596	0.698105
$448$	0	0
$449$	−14.7644	−0.696777	−0.348388	−	0.937350i	$-0.613271\pi$
$449$	−14.7644	−0.696777	−0.348388	+	0.937350i	$0.613271\pi$
$450$	−21.9807	−1.03618
$451$	−3.79578	−0.178736
$452$	71.1525	3.34673
$453$	6.86221	0.322415
$454$	−62.4205	−2.92954
$455$	0	0
$456$	24.5529	1.14980
$457$	−7.93084	−0.370989	−0.185495	−	0.982645i	$-0.559389\pi$
$457$	−7.93084	−0.370989	−0.185495	+	0.982645i	$0.559389\pi$
$458$	−39.9285	−1.86574
$459$	1.05753	0.0493610
$460$	−107.817	−5.02697
$461$	−9.83013	−0.457835	−0.228917	−	0.973446i	$-0.573519\pi$
$461$	−9.83013	−0.457835	−0.228917	+	0.973446i	$0.573519\pi$
$462$	0	0
$463$	−6.47631	−0.300980	−0.150490	−	0.988612i	$-0.548085\pi$
$463$	−6.47631	−0.300980	−0.150490	+	0.988612i	$0.548085\pi$
$464$	−28.9005	−1.34167
$465$	37.9347	1.75918
$466$	−64.2975	−2.97852
$467$	−2.17951	−0.100856	−0.0504278	−	0.998728i	$-0.516058\pi$
$467$	−2.17951	−0.100856	−0.0504278	+	0.998728i	$0.516058\pi$
$468$	−5.17719	−0.239315
$469$	0	0
$470$	−49.7050	−2.29272
$471$	4.17576	0.192409
$472$	−66.2676	−3.05021
$473$	15.7962	0.726310
$474$	−13.0125	−0.597685
$475$	22.9478	1.05292
$476$	0	0
$477$	−9.17461	−0.420076
$478$	−46.2569	−2.11574
$479$	23.3346	1.06619	0.533093	−	0.846057i	$-0.321030\pi$
$479$	23.3346	1.06619	0.533093	+	0.846057i	$0.321030\pi$
$480$	63.8290	2.91338
$481$	7.76663	0.354128
$482$	16.6075	0.756451
$483$	0	0
$484$	17.8772	0.812602
$485$	−51.8270	−2.35334
$486$	2.69180	0.122102
$487$	−0.181820	−0.00823903	−0.00411952	−	0.999992i	$-0.501311\pi$
$487$	−0.181820	−0.00823903	−0.00411952	+	0.999992i	$0.501311\pi$
$488$	52.1011	2.35851
$489$	23.5210	1.06366
$490$	0	0
$491$	19.2932	0.870688	0.435344	−	0.900264i	$-0.356627\pi$
$491$	19.2932	0.870688	0.435344	+	0.900264i	$0.356627\pi$
$492$	5.24578	0.236498
$493$	2.34619	0.105667
$494$	7.46565	0.335896
$495$	13.7729	0.619045
$496$	−136.190	−6.11512
$497$	0	0
$498$	−18.9640	−0.849795
$499$	9.27958	0.415411	0.207706	−	0.978191i	$-0.433400\pi$
$499$	9.27958	0.415411	0.207706	+	0.978191i	$0.433400\pi$
$500$	60.2587	2.69485
$501$	−15.7070	−0.701737
$502$	−57.1219	−2.54948
$503$	−19.7484	−0.880537	−0.440269	−	0.897866i	$-0.645117\pi$
$503$	−19.7484	−0.880537	−0.440269	+	0.897866i	$0.645117\pi$
$504$	0	0
$505$	−4.63856	−0.206413
$506$	57.8755	2.57288
$507$	12.0260	0.534093
$508$	66.3383	2.94328
$509$	−10.5926	−0.469510	−0.234755	−	0.972055i	$-0.575429\pi$
$509$	−10.5926	−0.469510	−0.234755	+	0.972055i	$0.575429\pi$
$510$	−10.3290	−0.457375
$511$	0	0
$512$	−1.52644	−0.0674599
$513$	−2.81023	−0.124075
$514$	62.6403	2.76294
$515$	−43.5077	−1.91718
$516$	−21.8304	−0.961030
$517$	19.3168	0.849551
$518$	0	0
$519$	−5.89269	−0.258660
$520$	31.2874	1.37204
$521$	−27.2068	−1.19195	−0.595976	−	0.803002i	$-0.703235\pi$
$521$	−27.2068	−1.19195	−0.595976	+	0.803002i	$0.703235\pi$
$522$	5.97193	0.261384
$523$	43.2412	1.89081	0.945403	−	0.325904i	$-0.105669\pi$
$523$	43.2412	1.89081	0.945403	+	0.325904i	$0.105669\pi$
$524$	−114.719	−5.01150
$525$	0	0
$526$	82.1992	3.58406
$527$	11.0561	0.481613
$528$	−49.4463	−2.15187
$529$	9.08504	0.395002
$530$	89.6095	3.89239
$531$	7.58471	0.329149
$532$	0	0
$533$	0.986924	0.0427484
$534$	−25.6632	−1.11055
$535$	−65.3446	−2.82510
$536$	136.614	5.90082
$537$	−4.67222	−0.201621
$538$	−12.2396	−0.527687
$539$	0	0
$540$	−19.0342	−0.819100
$541$	11.1859	0.480919	0.240459	−	0.970659i	$-0.422702\pi$
$541$	11.1859	0.480919	0.240459	+	0.970659i	$0.422702\pi$
$542$	−56.6844	−2.43480
$543$	−13.2354	−0.567983
$544$	18.6031	0.797601
$545$	−50.8375	−2.17764
$546$	0	0
$547$	34.4215	1.47176	0.735878	−	0.677115i	$-0.236770\pi$
$547$	34.4215	1.47176	0.735878	+	0.677115i	$0.236770\pi$
$548$	−22.4539	−0.959183
$549$	−5.96328	−0.254507
$550$	−83.4340	−3.55764
$551$	−6.23468	−0.265606
$552$	−49.4895	−2.10641
$553$	0	0
$554$	3.14329	0.133546
$555$	28.5544	1.21207
$556$	−0.0760796	−0.00322649
$557$	37.0851	1.57134	0.785672	−	0.618643i	$-0.212317\pi$
$557$	37.0851	1.57134	0.785672	+	0.618643i	$0.212317\pi$
$558$	28.1420	1.19135
$559$	−4.10710	−0.173712
$560$	0	0
$561$	4.01413	0.169477
$562$	45.2699	1.90960
$563$	−0.795779	−0.0335381	−0.0167690	−	0.999859i	$-0.505338\pi$
$563$	−0.795779	−0.0335381	−0.0167690	+	0.999859i	$0.505338\pi$
$564$	−26.6959	−1.12410
$565$	49.2157	2.07052
$566$	86.9246	3.65371
$567$	0	0
$568$	−101.536	−4.26034
$569$	11.2518	0.471701	0.235850	−	0.971789i	$-0.424212\pi$
$569$	11.2518	0.471701	0.235850	+	0.971789i	$0.424212\pi$
$570$	27.4478	1.14966
$571$	−39.0794	−1.63542	−0.817711	−	0.575629i	$-0.804757\pi$
$571$	−39.0794	−1.63542	−0.817711	+	0.575629i	$0.804757\pi$
$572$	−19.6514	−0.821668
$573$	−18.4336	−0.770073
$574$	0	0
$575$	−46.2542	−1.92893
$576$	21.2985	0.887439
$577$	11.3745	0.473527	0.236763	−	0.971567i	$-0.423913\pi$
$577$	11.3745	0.473527	0.236763	+	0.971567i	$0.423913\pi$
$578$	42.7502	1.77817
$579$	−11.4648	−0.476461
$580$	−42.2286	−1.75345
$581$	0	0
$582$	−38.4481	−1.59372
$583$	−34.8248	−1.44229
$584$	−32.8063	−1.35753
$585$	−3.58103	−0.148057
$586$	−60.3002	−2.49098
$587$	1.19831	0.0494595	0.0247297	−	0.999694i	$-0.492127\pi$
$587$	1.19831	0.0494595	0.0247297	+	0.999694i	$0.492127\pi$
$588$	0	0
$589$	−29.3802	−1.21059
$590$	−74.0808	−3.04986
$591$	−2.88305	−0.118593
$592$	−102.514	−4.21329
$593$	−24.6608	−1.01270	−0.506349	−	0.862329i	$-0.669005\pi$
$593$	−24.6608	−1.01270	−0.506349	+	0.862329i	$0.669005\pi$
$594$	10.2175	0.419228
$595$	0	0
$596$	−77.4256	−3.17148
$597$	18.6674	0.764008
$598$	−15.0480	−0.615357
$599$	−25.4843	−1.04126	−0.520630	−	0.853783i	$-0.674303\pi$
$599$	−25.4843	−1.04126	−0.520630	+	0.853783i	$0.674303\pi$
$600$	71.3446	2.91263
$601$	0.495078	0.0201947	0.0100973	−	0.999949i	$-0.496786\pi$
$601$	0.495078	0.0201947	0.0100973	+	0.999949i	$0.496786\pi$
$602$	0	0
$603$	−15.6363	−0.636758
$604$	−35.9976	−1.46472
$605$	12.3656	0.502732
$606$	−3.44114	−0.139787
$607$	47.8430	1.94189	0.970943	−	0.239309i	$-0.0769209\pi$
$607$	47.8430	1.94189	0.970943	+	0.239309i	$0.0769209\pi$
$608$	−49.4352	−2.00486
$609$	0	0
$610$	58.2441	2.35823
$611$	−5.02247	−0.203187
$612$	−5.54754	−0.224246
$613$	−38.3710	−1.54979	−0.774895	−	0.632090i	$-0.782197\pi$
$613$	−38.3710	−1.54979	−0.774895	+	0.632090i	$0.782197\pi$
$614$	−41.9044	−1.69113
$615$	3.62847	0.146314
$616$	0	0
$617$	−9.52594	−0.383500	−0.191750	−	0.981444i	$-0.561416\pi$
$617$	−9.52594	−0.383500	−0.191750	+	0.981444i	$0.561416\pi$
$618$	−32.2764	−1.29835
$619$	33.0989	1.33036	0.665179	−	0.746684i	$-0.268355\pi$
$619$	33.0989	1.33036	0.665179	+	0.746684i	$0.268355\pi$
$620$	−198.997	−7.99192
$621$	5.66437	0.227303
$622$	−54.4515	−2.18330
$623$	0	0
$624$	12.8563	0.514665
$625$	0.851461	0.0340584
$626$	−35.5976	−1.42276
$627$	−10.6670	−0.425999
$628$	−21.9051	−0.874110
$629$	8.32223	0.331829
$630$	0	0
$631$	−7.62134	−0.303401	−0.151700	−	0.988427i	$-0.548475\pi$
$631$	−7.62134	−0.303401	−0.151700	+	0.988427i	$0.548475\pi$
$632$	42.2358	1.68005
$633$	3.09415	0.122982
$634$	46.9199	1.86343
$635$	45.8857	1.82092
$636$	48.1280	1.90840
$637$	0	0
$638$	22.6681	0.897440
$639$	11.6213	0.459733
$640$	−80.3673	−3.17680
$641$	−33.7943	−1.33479	−0.667397	−	0.744702i	$-0.732592\pi$
$641$	−33.7943	−1.33479	−0.667397	+	0.744702i	$0.732592\pi$
$642$	−48.4762	−1.91320
$643$	−6.60324	−0.260406	−0.130203	−	0.991487i	$-0.541563\pi$
$643$	−6.60324	−0.260406	−0.130203	+	0.991487i	$0.541563\pi$
$644$	0	0
$645$	−15.1000	−0.594560
$646$	7.99972	0.314745
$647$	12.2008	0.479663	0.239832	−	0.970815i	$-0.422908\pi$
$647$	12.2008	0.479663	0.239832	+	0.970815i	$0.422908\pi$
$648$	−8.73699	−0.343221
$649$	28.7899	1.13010
$650$	21.6933	0.850881
$651$	0	0
$652$	−123.386	−4.83218
$653$	−37.3586	−1.46195	−0.730977	−	0.682402i	$-0.760936\pi$
$653$	−37.3586	−1.46195	−0.730977	+	0.682402i	$0.760936\pi$
$654$	−37.7141	−1.47474
$655$	−79.3501	−3.10046
$656$	−13.0267	−0.508605
$657$	3.75487	0.146492
$658$	0	0
$659$	17.0668	0.664829	0.332414	−	0.943133i	$-0.392137\pi$
$659$	17.0668	0.664829	0.332414	+	0.943133i	$0.392137\pi$
$660$	−72.2495	−2.81231
$661$	−9.34986	−0.363668	−0.181834	−	0.983329i	$-0.558203\pi$
$661$	−9.34986	−0.363668	−0.181834	+	0.983329i	$0.558203\pi$
$662$	−55.8653	−2.17127
$663$	−1.04370	−0.0405338
$664$	61.5528	2.38871
$665$	0	0
$666$	21.1832	0.820832
$667$	12.5668	0.486587
$668$	82.3955	3.18798
$669$	20.2026	0.781076
$670$	152.721	5.90014
$671$	−22.6353	−0.873825
$672$	0	0
$673$	7.36902	0.284055	0.142027	−	0.989863i	$-0.454638\pi$
$673$	7.36902	0.284055	0.142027	+	0.989863i	$0.454638\pi$
$674$	9.60040	0.369794
$675$	−8.16582	−0.314302
$676$	−63.0857	−2.42637
$677$	−18.2593	−0.701762	−0.350881	−	0.936420i	$-0.614118\pi$
$677$	−18.2593	−0.701762	−0.350881	+	0.936420i	$0.614118\pi$
$678$	36.5109	1.40219
$679$	0	0
$680$	33.5256	1.28565
$681$	−23.1892	−0.888610
$682$	106.821	4.09039
$683$	5.22095	0.199774	0.0998870	−	0.994999i	$-0.468152\pi$
$683$	5.22095	0.199774	0.0998870	+	0.994999i	$0.468152\pi$
$684$	14.7418	0.563668
$685$	−15.5312	−0.593417
$686$	0	0
$687$	−14.8334	−0.565929
$688$	54.2107	2.06676
$689$	9.05464	0.344954
$690$	−55.3245	−2.10617
$691$	1.84487	0.0701823	0.0350912	−	0.999384i	$-0.488828\pi$
$691$	1.84487	0.0701823	0.0350912	+	0.999384i	$0.488828\pi$
$692$	30.9117	1.17509
$693$	0	0
$694$	−32.1207	−1.21928
$695$	−0.0526237	−0.00199613
$696$	−19.3836	−0.734733
$697$	1.05753	0.0400566
$698$	−18.6018	−0.704089
$699$	−23.8864	−0.903468
$700$	0	0
$701$	−30.6724	−1.15848	−0.579240	−	0.815157i	$-0.696651\pi$
$701$	−30.6724	−1.15848	−0.579240	+	0.815157i	$0.696651\pi$
$702$	−2.65660	−0.100267
$703$	−22.1152	−0.834090
$704$	80.8445	3.04694
$705$	−18.4654	−0.695446
$706$	10.1077	0.380407
$707$	0	0
$708$	−39.7877	−1.49531
$709$	−29.3623	−1.10273	−0.551363	−	0.834266i	$-0.685892\pi$
$709$	−29.3623	−1.10273	−0.551363	+	0.834266i	$0.685892\pi$
$710$	−113.507	−4.25984
$711$	−4.83413	−0.181294
$712$	83.2971	3.12169
$713$	59.2195	2.21779
$714$	0	0
$715$	−13.5928	−0.508341
$716$	24.5094	0.915961
$717$	−17.1844	−0.641762
$718$	−25.2567	−0.942572
$719$	−13.0625	−0.487148	−0.243574	−	0.969882i	$-0.578320\pi$
$719$	−13.0625	−0.487148	−0.243574	+	0.969882i	$0.578320\pi$
$720$	47.2669	1.76153
$721$	0	0
$722$	29.8860	1.11224
$723$	6.16967	0.229452
$724$	69.4298	2.58034
$725$	−18.1164	−0.672826
$726$	9.17345	0.340459
$727$	18.2556	0.677064	0.338532	−	0.940955i	$-0.390070\pi$
$727$	18.2556	0.677064	0.338532	+	0.940955i	$0.390070\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−36.6743	−1.35738
$731$	−4.40091	−0.162773
$732$	31.2821	1.15622
$733$	−21.0158	−0.776235	−0.388117	−	0.921610i	$-0.626874\pi$
$733$	−21.0158	−0.776235	−0.388117	+	0.921610i	$0.626874\pi$
$734$	−71.8786	−2.65309
$735$	0	0
$736$	99.6427	3.67288
$737$	−59.3518	−2.18625
$738$	2.69180	0.0990865
$739$	42.2094	1.55270	0.776348	−	0.630304i	$-0.217070\pi$
$739$	42.2094	1.55270	0.776348	+	0.630304i	$0.217070\pi$
$740$	−149.790	−5.50639
$741$	2.77348	0.101886
$742$	0	0
$743$	−52.7446	−1.93501	−0.967505	−	0.252852i	$-0.918632\pi$
$743$	−52.7446	−1.93501	−0.967505	+	0.252852i	$0.918632\pi$
$744$	−91.3429	−3.34879
$745$	−53.5548	−1.96210
$746$	−16.2915	−0.596474
$747$	−7.04509	−0.257766
$748$	−21.0572	−0.769929
$749$	0	0
$750$	30.9209	1.12907
$751$	−26.7511	−0.976160	−0.488080	−	0.872799i	$-0.662303\pi$
$751$	−26.7511	−0.976160	−0.488080	+	0.872799i	$0.662303\pi$
$752$	66.2929	2.41745
$753$	−21.2207	−0.773326
$754$	−5.89384	−0.214641
$755$	−24.8993	−0.906179
$756$	0	0
$757$	46.6901	1.69698	0.848489	−	0.529212i	$-0.177512\pi$
$757$	46.6901	1.69698	0.848489	+	0.529212i	$0.177512\pi$
$758$	12.6175	0.458287
$759$	21.5007	0.780425
$760$	−89.0896	−3.23162
$761$	−39.3776	−1.42744	−0.713718	−	0.700433i	$-0.752990\pi$
$761$	−39.3776	−1.42744	−0.713718	+	0.700433i	$0.752990\pi$
$762$	34.0405	1.23316
$763$	0	0
$764$	96.6984	3.49843
$765$	−3.83720	−0.138734
$766$	−92.9222	−3.35742
$767$	−7.48553	−0.270287
$768$	−17.0238	−0.614293
$769$	40.4050	1.45704	0.728520	−	0.685025i	$-0.240209\pi$
$769$	40.4050	1.45704	0.728520	+	0.685025i	$0.240209\pi$
$770$	0	0
$771$	23.2708	0.838077
$772$	60.1418	2.16455
$773$	16.5528	0.595364	0.297682	−	0.954665i	$-0.403786\pi$
$773$	16.5528	0.595364	0.297682	+	0.954665i	$0.403786\pi$
$774$	−11.2020	−0.402646
$775$	−85.3715	−3.06663
$776$	124.794	4.47984
$777$	0	0
$778$	−4.61430	−0.165431
$779$	−2.81023	−0.100687
$780$	18.7853	0.672621
$781$	44.1120	1.57845
$782$	−16.1244	−0.576609
$783$	2.21857	0.0792851
$784$	0	0
$785$	−15.1516	−0.540785
$786$	−58.8662	−2.09969
$787$	41.3752	1.47487	0.737433	−	0.675420i	$-0.236038\pi$
$787$	41.3752	1.47487	0.737433	+	0.675420i	$0.236038\pi$
$788$	15.1238	0.538764
$789$	30.5369	1.08714
$790$	47.2156	1.67985
$791$	0	0
$792$	−33.1637	−1.17842
$793$	5.88530	0.208993
$794$	39.2801	1.39400
$795$	33.2898	1.18067
$796$	−97.9253	−3.47087
$797$	30.5376	1.08170	0.540849	−	0.841119i	$-0.318103\pi$
$797$	30.5376	1.08170	0.540849	+	0.841119i	$0.318103\pi$
$798$	0	0
$799$	−5.38176	−0.190393
$800$	−143.646	−5.07866
$801$	−9.53384	−0.336862
$802$	−29.3680	−1.03702
$803$	14.2527	0.502965
$804$	82.0244	2.89278
$805$	0	0
$806$	−27.7741	−0.978299
$807$	−4.54700	−0.160062
$808$	11.1692	0.392930
$809$	−23.0463	−0.810264	−0.405132	−	0.914258i	$-0.632774\pi$
$809$	−23.0463	−0.810264	−0.405132	+	0.914258i	$0.632774\pi$
$810$	−9.76712	−0.343182
$811$	16.0147	0.562352	0.281176	−	0.959656i	$-0.409275\pi$
$811$	16.0147	0.562352	0.281176	+	0.959656i	$0.409275\pi$
$812$	0	0
$813$	−21.0582	−0.738543
$814$	80.4067	2.81825
$815$	−85.3455	−2.98952
$816$	13.7760	0.482257
$817$	11.6948	0.409150
$818$	−39.1533	−1.36896
$819$	0	0
$820$	−19.0342	−0.664702
$821$	26.8925	0.938553	0.469277	−	0.883051i	$-0.344515\pi$
$821$	26.8925	0.938553	0.469277	+	0.883051i	$0.344515\pi$
$822$	−11.5219	−0.401872
$823$	−49.1148	−1.71203	−0.856017	−	0.516947i	$-0.827068\pi$
$823$	−49.1148	−1.71203	−0.856017	+	0.516947i	$0.827068\pi$
$824$	104.762	3.64956
$825$	−30.9956	−1.07913
$826$	0	0
$827$	−5.37580	−0.186935	−0.0934675	−	0.995622i	$-0.529795\pi$
$827$	−5.37580	−0.186935	−0.0934675	+	0.995622i	$0.529795\pi$
$828$	−29.7140	−1.03263
$829$	−24.9271	−0.865754	−0.432877	−	0.901453i	$-0.642502\pi$
$829$	−24.9271	−0.865754	−0.432877	+	0.901453i	$0.642502\pi$
$830$	68.8102	2.38844
$831$	1.16773	0.0405081
$832$	−21.0200	−0.728739
$833$	0	0
$834$	−0.0390392	−0.00135182
$835$	56.9924	1.97230
$836$	55.9567	1.93530
$837$	10.4547	0.361369
$838$	−50.2153	−1.73466
$839$	12.8146	0.442408	0.221204	−	0.975228i	$-0.429001\pi$
$839$	12.8146	0.442408	0.221204	+	0.975228i	$0.429001\pi$
$840$	0	0
$841$	−24.0780	−0.830275
$842$	81.5110	2.80906
$843$	16.8177	0.579233
$844$	−16.2312	−0.558702
$845$	−43.6359	−1.50112
$846$	−13.6986	−0.470968
$847$	0	0
$848$	−119.514	−4.10414
$849$	32.2924	1.10827
$850$	23.2452	0.797303
$851$	44.5759	1.52804
$852$	−60.9630	−2.08856
$853$	55.5740	1.90282	0.951409	−	0.307930i	$-0.0996364\pi$
$853$	55.5740	1.90282	0.951409	+	0.307930i	$0.0996364\pi$
$854$	0	0
$855$	10.1968	0.348724
$856$	157.343	5.37788
$857$	18.9766	0.648228	0.324114	−	0.946018i	$-0.394934\pi$
$857$	18.9766	0.648228	0.324114	+	0.946018i	$0.394934\pi$
$858$	−10.0839	−0.344257
$859$	−6.24592	−0.213108	−0.106554	−	0.994307i	$-0.533982\pi$
$859$	−6.24592	−0.213108	−0.106554	+	0.994307i	$0.533982\pi$
$860$	79.2110	2.70107
$861$	0	0
$862$	−33.5241	−1.14183
$863$	−33.6361	−1.14499	−0.572494	−	0.819909i	$-0.694024\pi$
$863$	−33.6361	−1.14499	−0.572494	+	0.819909i	$0.694024\pi$
$864$	17.5912	0.598463
$865$	21.3815	0.726991
$866$	−18.3144	−0.622348
$867$	15.8816	0.539369
$868$	0	0
$869$	−18.3493	−0.622457
$870$	−21.6690	−0.734648
$871$	15.4318	0.522887
$872$	122.412	4.14538
$873$	−14.2834	−0.483420
$874$	42.8485	1.44937
$875$	0	0
$876$	−19.6972	−0.665508
$877$	−12.4187	−0.419351	−0.209676	−	0.977771i	$-0.567241\pi$
$877$	−12.4187	−0.419351	−0.209676	+	0.977771i	$0.567241\pi$
$878$	−63.6535	−2.14820
$879$	−22.4014	−0.755582
$880$	179.414	6.04806
$881$	−20.7551	−0.699258	−0.349629	−	0.936888i	$-0.613692\pi$
$881$	−20.7551	−0.699258	−0.349629	+	0.936888i	$0.613692\pi$
$882$	0	0
$883$	−6.14363	−0.206750	−0.103375	−	0.994642i	$-0.532964\pi$
$883$	−6.14363	−0.206750	−0.103375	+	0.994642i	$0.532964\pi$
$884$	5.47500	0.184144
$885$	−27.5209	−0.925106
$886$	−38.9231	−1.30765
$887$	−15.6800	−0.526482	−0.263241	−	0.964730i	$-0.584791\pi$
$887$	−15.6800	−0.526482	−0.263241	+	0.964730i	$0.584791\pi$
$888$	−68.7560	−2.30730
$889$	0	0
$890$	93.1182	3.12133
$891$	3.79578	0.127163
$892$	−105.978	−3.54841
$893$	14.3013	0.478575
$894$	−39.7299	−1.32877
$895$	16.9530	0.566677
$896$	0	0
$897$	−5.59030	−0.186655
$898$	39.7429	1.32624
$899$	23.1945	0.773581
$900$	42.8361	1.42787
$901$	9.70238	0.323233
$902$	10.2175	0.340205
$903$	0	0
$904$	−118.506	−3.94146
$905$	48.0241	1.59638
$906$	−18.4717	−0.613680
$907$	−51.5516	−1.71174	−0.855871	−	0.517190i	$-0.826978\pi$
$907$	−51.5516	−1.71174	−0.855871	+	0.517190i	$0.826978\pi$
$908$	121.645	4.03694
$909$	−1.27838	−0.0424011
$910$	0	0
$911$	−25.3620	−0.840280	−0.420140	−	0.907459i	$-0.638019\pi$
$911$	−25.3620	−0.840280	−0.420140	+	0.907459i	$0.638019\pi$
$912$	−36.6079	−1.21221
$913$	−26.7416	−0.885017
$914$	21.3482	0.706137
$915$	21.6376	0.715317
$916$	77.8128	2.57101
$917$	0	0
$918$	−2.84664	−0.0939533
$919$	−14.9540	−0.493288	−0.246644	−	0.969106i	$-0.579328\pi$
$919$	−14.9540	−0.493288	−0.246644	+	0.969106i	$0.579328\pi$
$920$	179.571	5.92029
$921$	−15.5675	−0.512965
$922$	26.4607	0.871438
$923$	−11.4694	−0.377519
$924$	0	0
$925$	−64.2611	−2.11289
$926$	17.4329	0.572882
$927$	−11.9906	−0.393825
$928$	39.0271	1.28113
$929$	−22.0282	−0.722722	−0.361361	−	0.932426i	$-0.617688\pi$
$929$	−22.0282	−0.722722	−0.361361	+	0.932426i	$0.617688\pi$
$930$	−102.113	−3.34841
$931$	0	0
$932$	125.303	4.10443
$933$	−20.2286	−0.662256
$934$	5.86680	0.191967
$935$	−14.5652	−0.476332
$936$	8.62274	0.281843
$937$	−15.4016	−0.503149	−0.251575	−	0.967838i	$-0.580948\pi$
$937$	−15.4016	−0.503149	−0.251575	+	0.967838i	$0.580948\pi$
$938$	0	0
$939$	−13.2244	−0.431564
$940$	96.8652	3.15940
$941$	−21.8930	−0.713692	−0.356846	−	0.934163i	$-0.616148\pi$
$941$	−21.8930	−0.713692	−0.356846	+	0.934163i	$0.616148\pi$
$942$	−11.2403	−0.366229
$943$	5.66437	0.184457
$944$	98.8034	3.21578
$945$	0	0
$946$	−42.5202	−1.38245
$947$	−24.2765	−0.788881	−0.394441	−	0.918921i	$-0.629062\pi$
$947$	−24.2765	−0.788881	−0.394441	+	0.918921i	$0.629062\pi$
$948$	25.3588	0.823616
$949$	−3.70577	−0.120294
$950$	−61.7709	−2.00411
$951$	17.4307	0.565228
$952$	0	0
$953$	26.1321	0.846503	0.423251	−	0.906012i	$-0.360889\pi$
$953$	26.1321	0.846503	0.423251	+	0.906012i	$0.360889\pi$
$954$	24.6962	0.799569
$955$	66.8857	2.16437
$956$	90.1455	2.91551
$957$	8.42118	0.272218
$958$	−62.8121	−2.02937
$959$	0	0
$960$	−77.2812	−2.49424
$961$	78.3015	2.52586
$962$	−20.9062	−0.674043
$963$	−18.0089	−0.580327
$964$	−32.3647	−1.04240
$965$	41.5997	1.33914
$966$	0	0
$967$	−22.4692	−0.722561	−0.361280	−	0.932457i	$-0.617660\pi$
$967$	−22.4692	−0.722561	−0.361280	+	0.932457i	$0.617660\pi$
$968$	−29.7750	−0.957005
$969$	2.97189	0.0954708
$970$	139.508	4.47933
$971$	6.12283	0.196491	0.0982454	−	0.995162i	$-0.468677\pi$
$971$	6.12283	0.196491	0.0982454	+	0.995162i	$0.468677\pi$
$972$	−5.24578	−0.168258
$973$	0	0
$974$	0.489422	0.0156821
$975$	8.05904	0.258096
$976$	−77.6816	−2.48653
$977$	6.50369	0.208071	0.104036	−	0.994574i	$-0.466824\pi$
$977$	6.50369	0.208071	0.104036	+	0.994574i	$0.466824\pi$
$978$	−63.3139	−2.02456
$979$	−36.1884	−1.15658
$980$	0	0
$981$	−14.0107	−0.447328
$982$	−51.9333	−1.65726
$983$	45.8232	1.46153	0.730766	−	0.682628i	$-0.239163\pi$
$983$	45.8232	1.46153	0.730766	+	0.682628i	$0.239163\pi$
$984$	−8.73699	−0.278525
$985$	10.4611	0.333317
$986$	−6.31547	−0.201125
$987$	0	0
$988$	−14.5491	−0.462868
$989$	−23.5724	−0.749557
$990$	−37.0738	−1.17828
$991$	23.9854	0.761920	0.380960	−	0.924591i	$-0.375594\pi$
$991$	23.9854	0.761920	0.380960	+	0.924591i	$0.375594\pi$
$992$	183.911	5.83918
$993$	−20.7539	−0.658605
$994$	0	0
$995$	−67.7343	−2.14732
$996$	36.9570	1.17103
$997$	9.44196	0.299030	0.149515	−	0.988759i	$-0.452229\pi$
$997$	9.44196	0.299030	0.149515	+	0.988759i	$0.452229\pi$
$998$	−24.9788	−0.790689
$999$	7.86953	0.248981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bl.1.2	✓	16
7.6	odd	2		6027.2.a.bm.1.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bl.1.2	✓	16	1.1	even	1	trivial
6027.2.a.bm.1.2	yes	16	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69180 q^{2} -1.00000 q^{3} +5.24578 q^{4} +3.62847 q^{5} +2.69180 q^{6} -8.73699 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.69180 q^{2} -1.00000 q^{3} +5.24578 q^{4} +3.62847 q^{5} +2.69180 q^{6} -8.73699 q^{8} +1.00000 q^{9} -9.76712 q^{10} +3.79578 q^{11} -5.24578 q^{12} -0.986924 q^{13} -3.62847 q^{15} +13.0267 q^{16} -1.05753 q^{17} -2.69180 q^{18} +2.81023 q^{19} +19.0342 q^{20} -10.2175 q^{22} -5.66437 q^{23} +8.73699 q^{24} +8.16582 q^{25} +2.65660 q^{26} -1.00000 q^{27} -2.21857 q^{29} +9.76712 q^{30} -10.4547 q^{31} -17.5912 q^{32} -3.79578 q^{33} +2.84664 q^{34} +5.24578 q^{36} -7.86953 q^{37} -7.56457 q^{38} +0.986924 q^{39} -31.7019 q^{40} -1.00000 q^{41} +4.16152 q^{43} +19.9118 q^{44} +3.62847 q^{45} +15.2473 q^{46} +5.08902 q^{47} -13.0267 q^{48} -21.9807 q^{50} +1.05753 q^{51} -5.17719 q^{52} -9.17461 q^{53} +2.69180 q^{54} +13.7729 q^{55} -2.81023 q^{57} +5.97193 q^{58} +7.58471 q^{59} -19.0342 q^{60} -5.96328 q^{61} +28.1420 q^{62} +21.2985 q^{64} -3.58103 q^{65} +10.2175 q^{66} -15.6363 q^{67} -5.54754 q^{68} +5.66437 q^{69} +11.6213 q^{71} -8.73699 q^{72} +3.75487 q^{73} +21.1832 q^{74} -8.16582 q^{75} +14.7418 q^{76} -2.65660 q^{78} -4.83413 q^{79} +47.2669 q^{80} +1.00000 q^{81} +2.69180 q^{82} -7.04509 q^{83} -3.83720 q^{85} -11.2020 q^{86} +2.21857 q^{87} -33.1637 q^{88} -9.53384 q^{89} -9.76712 q^{90} -29.7140 q^{92} +10.4547 q^{93} -13.6986 q^{94} +10.1968 q^{95} +17.5912 q^{96} -14.2834 q^{97} +3.79578 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9	\( 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9} + 4 q^{10} - 4 q^{11} - 12 q^{12} - 12 q^{15} + 8 q^{17} - 4 q^{18} - 4 q^{19} + 20 q^{20} - 16 q^{22} - 12 q^{23} + 12 q^{24} - 8 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29} - 4 q^{30} + 4 q^{31} - 48 q^{32} + 4 q^{33} - 16 q^{34} + 12 q^{36} - 48 q^{37} + 4 q^{38} - 56 q^{40} - 16 q^{41} - 16 q^{43} + 12 q^{45} - 4 q^{46} + 36 q^{47} - 8 q^{50} - 8 q^{51} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 4 q^{57} - 36 q^{58} + 36 q^{59} - 20 q^{60} + 4 q^{61} + 12 q^{62} + 52 q^{64} - 36 q^{65} + 16 q^{66} - 52 q^{67} + 8 q^{68} + 12 q^{69} - 12 q^{71} - 12 q^{72} + 16 q^{73} + 4 q^{74} + 8 q^{75} - 16 q^{76} - 8 q^{78} - 36 q^{79} + 68 q^{80} + 16 q^{81} + 4 q^{82} + 32 q^{83} - 28 q^{85} - 8 q^{86} + 16 q^{87} - 36 q^{88} + 12 q^{89} + 4 q^{90} - 36 q^{92} - 4 q^{93} - 24 q^{94} - 20 q^{95} + 48 q^{96} - 48 q^{97} - 4 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9 + 4 * q^10 - 4 * q^11 - 12 * q^12 - 12 * q^15 + 8 * q^17 - 4 * q^18 - 4 * q^19 + 20 * q^20 - 16 * q^22 - 12 * q^23 + 12 * q^24 - 8 * q^25 + 8 * q^26 - 16 * q^27 - 16 * q^29 - 4 * q^30 + 4 * q^31 - 48 * q^32 + 4 * q^33 - 16 * q^34 + 12 * q^36 - 48 * q^37 + 4 * q^38 - 56 * q^40 - 16 * q^41 - 16 * q^43 + 12 * q^45 - 4 * q^46 + 36 * q^47 - 8 * q^50 - 8 * q^51 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 4 * q^57 - 36 * q^58 + 36 * q^59 - 20 * q^60 + 4 * q^61 + 12 * q^62 + 52 * q^64 - 36 * q^65 + 16 * q^66 - 52 * q^67 + 8 * q^68 + 12 * q^69 - 12 * q^71 - 12 * q^72 + 16 * q^73 + 4 * q^74 + 8 * q^75 - 16 * q^76 - 8 * q^78 - 36 * q^79 + 68 * q^80 + 16 * q^81 + 4 * q^82 + 32 * q^83 - 28 * q^85 - 8 * q^86 + 16 * q^87 - 36 * q^88 + 12 * q^89 + 4 * q^90 - 36 * q^92 - 4 * q^93 - 24 * q^94 - 20 * q^95 + 48 * q^96 - 48 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

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Database

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