LMFDB - Embedded newform 6027.2.a.be.1.5

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:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 11x^{8} + 56x^{7} + 26x^{6} - 266x^{5} + 52x^{4} + 526x^{3} - 255x^{2} - 372x + 239 $ x^10 - 4x^9 - 11x^8 + 56x^7 + 26x^6 - 266x^5 + 52x^4 + 526x^3 - 255x^2 - 372*x + 239
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.775610$ 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)

$f(q)$	$=$	$q+0.775610 q^{2} +1.00000 q^{3} -1.39843 q^{4} +2.32372 q^{5} +0.775610 q^{6} -2.63586 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.775610 q^{2} +1.00000 q^{3} -1.39843 q^{4} +2.32372 q^{5} +0.775610 q^{6} -2.63586 q^{8} +1.00000 q^{9} +1.80230 q^{10} +0.760190 q^{11} -1.39843 q^{12} +5.49099 q^{13} +2.32372 q^{15} +0.752463 q^{16} +0.343275 q^{17} +0.775610 q^{18} +4.11329 q^{19} -3.24955 q^{20} +0.589611 q^{22} -2.25692 q^{23} -2.63586 q^{24} +0.399659 q^{25} +4.25887 q^{26} +1.00000 q^{27} -2.50209 q^{29} +1.80230 q^{30} +9.19269 q^{31} +5.85533 q^{32} +0.760190 q^{33} +0.266248 q^{34} -1.39843 q^{36} -3.66914 q^{37} +3.19031 q^{38} +5.49099 q^{39} -6.12498 q^{40} +1.00000 q^{41} -10.6199 q^{43} -1.06307 q^{44} +2.32372 q^{45} -1.75049 q^{46} +2.71630 q^{47} +0.752463 q^{48} +0.309979 q^{50} +0.343275 q^{51} -7.67876 q^{52} +13.4616 q^{53} +0.775610 q^{54} +1.76647 q^{55} +4.11329 q^{57} -1.94064 q^{58} +1.48497 q^{59} -3.24955 q^{60} -1.90957 q^{61} +7.12994 q^{62} +3.03652 q^{64} +12.7595 q^{65} +0.589611 q^{66} -7.92467 q^{67} -0.480046 q^{68} -2.25692 q^{69} -9.05365 q^{71} -2.63586 q^{72} -9.45548 q^{73} -2.84582 q^{74} +0.399659 q^{75} -5.75215 q^{76} +4.25887 q^{78} -3.15388 q^{79} +1.74851 q^{80} +1.00000 q^{81} +0.775610 q^{82} +1.77106 q^{83} +0.797674 q^{85} -8.23693 q^{86} -2.50209 q^{87} -2.00375 q^{88} +17.7374 q^{89} +1.80230 q^{90} +3.15615 q^{92} +9.19269 q^{93} +2.10679 q^{94} +9.55812 q^{95} +5.85533 q^{96} +17.8216 q^{97} +0.760190 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	$ 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 2 q^{10} - 2 q^{11} + 18 q^{12} + 6 q^{15} + 14 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + 20 q^{20} + 2 q^{22} + 12 q^{24} + 10 q^{25} + 16 q^{26} + 10 q^{27} + 16 q^{29} + 2 q^{30} + 2 q^{31} + 38 q^{32} - 2 q^{33} - 4 q^{34} + 18 q^{36} + 24 q^{37} - 26 q^{38} + 40 q^{40} + 10 q^{41} + 8 q^{43} - 8 q^{44} + 6 q^{45} + 4 q^{46} - 8 q^{47} + 14 q^{48} + 44 q^{50} + 8 q^{51} - 30 q^{52} + 24 q^{53} + 4 q^{54} + 6 q^{57} - 14 q^{58} + 6 q^{59} + 20 q^{60} - 14 q^{61} - 2 q^{62} + 86 q^{64} + 28 q^{65} + 2 q^{66} + 26 q^{67} - 6 q^{68} + 14 q^{71} + 12 q^{72} - 36 q^{73} + 18 q^{74} + 10 q^{75} - 32 q^{76} + 16 q^{78} + 20 q^{79} + 70 q^{80} + 10 q^{81} + 4 q^{82} + 40 q^{83} + 24 q^{85} - 36 q^{86} + 16 q^{87} + 14 q^{88} + 2 q^{89} + 2 q^{90} + 8 q^{92} + 2 q^{93} - 54 q^{94} - 24 q^{95} + 38 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 2 * q^10 - 2 * q^11 + 18 * q^12 + 6 * q^15 + 14 * q^16 + 8 * q^17 + 4 * q^18 + 6 * q^19 + 20 * q^20 + 2 * q^22 + 12 * q^24 + 10 * q^25 + 16 * q^26 + 10 * q^27 + 16 * q^29 + 2 * q^30 + 2 * q^31 + 38 * q^32 - 2 * q^33 - 4 * q^34 + 18 * q^36 + 24 * q^37 - 26 * q^38 + 40 * q^40 + 10 * q^41 + 8 * q^43 - 8 * q^44 + 6 * q^45 + 4 * q^46 - 8 * q^47 + 14 * q^48 + 44 * q^50 + 8 * q^51 - 30 * q^52 + 24 * q^53 + 4 * q^54 + 6 * q^57 - 14 * q^58 + 6 * q^59 + 20 * q^60 - 14 * q^61 - 2 * q^62 + 86 * q^64 + 28 * q^65 + 2 * q^66 + 26 * q^67 - 6 * q^68 + 14 * q^71 + 12 * q^72 - 36 * q^73 + 18 * q^74 + 10 * q^75 - 32 * q^76 + 16 * q^78 + 20 * q^79 + 70 * q^80 + 10 * q^81 + 4 * q^82 + 40 * q^83 + 24 * q^85 - 36 * q^86 + 16 * q^87 + 14 * q^88 + 2 * q^89 + 2 * q^90 + 8 * q^92 + 2 * q^93 - 54 * q^94 - 24 * q^95 + 38 * q^96 + 16 * q^97 - 2 * 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 $

$2$	0.775610	0.548439	0.274220	−	0.961667i	$-0.411581\pi$
$2$	0.775610	0.548439	0.274220	+	0.961667i	$0.411581\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.39843	−0.699215
$5$	2.32372	1.03920	0.519599	−	0.854410i	$-0.326081\pi$
$5$	2.32372	1.03920	0.519599	+	0.854410i	$0.326081\pi$
$6$	0.775610	0.316641
$7$	0	0
$7$	0	0
$8$	−2.63586	−0.931916
$9$	1.00000	0.333333
$10$	1.80230	0.569937
$11$	0.760190	0.229206	0.114603	−	0.993411i	$-0.463440\pi$
$11$	0.760190	0.229206	0.114603	+	0.993411i	$0.463440\pi$
$12$	−1.39843	−0.403692
$13$	5.49099	1.52293	0.761464	−	0.648208i	$-0.224481\pi$
$13$	5.49099	1.52293	0.761464	+	0.648208i	$0.224481\pi$
$14$	0	0
$15$	2.32372	0.599981
$16$	0.752463	0.188116
$17$	0.343275	0.0832565	0.0416282	−	0.999133i	$-0.486745\pi$
$17$	0.343275	0.0832565	0.0416282	+	0.999133i	$0.486745\pi$
$18$	0.775610	0.182813
$19$	4.11329	0.943654	0.471827	−	0.881691i	$-0.343595\pi$
$19$	4.11329	0.943654	0.471827	+	0.881691i	$0.343595\pi$
$20$	−3.24955	−0.726622
$21$	0	0
$22$	0.589611	0.125705
$23$	−2.25692	−0.470601	−0.235300	−	0.971923i	$-0.575607\pi$
$23$	−2.25692	−0.470601	−0.235300	+	0.971923i	$0.575607\pi$
$24$	−2.63586	−0.538042
$25$	0.399659	0.0799317
$26$	4.25887	0.835233
$27$	1.00000	0.192450
$28$	0	0
$29$	−2.50209	−0.464626	−0.232313	−	0.972641i	$-0.574629\pi$
$29$	−2.50209	−0.464626	−0.232313	+	0.972641i	$0.574629\pi$
$30$	1.80230	0.329053
$31$	9.19269	1.65106	0.825528	−	0.564361i	$-0.190878\pi$
$31$	9.19269	1.65106	0.825528	+	0.564361i	$0.190878\pi$
$32$	5.85533	1.03509
$33$	0.760190	0.132332
$34$	0.266248	0.0456611
$35$	0	0
$36$	−1.39843	−0.233072
$37$	−3.66914	−0.603202	−0.301601	−	0.953434i	$-0.597521\pi$
$37$	−3.66914	−0.603202	−0.301601	+	0.953434i	$0.597521\pi$
$38$	3.19031	0.517537
$39$	5.49099	0.879262
$40$	−6.12498	−0.968444
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−10.6199	−1.61953	−0.809763	−	0.586757i	$-0.800404\pi$
$43$	−10.6199	−1.61953	−0.809763	+	0.586757i	$0.800404\pi$
$44$	−1.06307	−0.160264
$45$	2.32372	0.346399
$46$	−1.75049	−0.258096
$47$	2.71630	0.396213	0.198107	−	0.980180i	$-0.436521\pi$
$47$	2.71630	0.396213	0.198107	+	0.980180i	$0.436521\pi$
$48$	0.752463	0.108609
$49$	0	0
$50$	0.309979	0.0438377
$51$	0.343275	0.0480681
$52$	−7.67876	−1.06485
$53$	13.4616	1.84909	0.924544	−	0.381076i	$-0.124446\pi$
$53$	13.4616	1.84909	0.924544	+	0.381076i	$0.124446\pi$
$54$	0.775610	0.105547
$55$	1.76647	0.238190
$56$	0	0
$57$	4.11329	0.544819
$58$	−1.94064	−0.254819
$59$	1.48497	0.193327	0.0966636	−	0.995317i	$-0.469183\pi$
$59$	1.48497	0.193327	0.0966636	+	0.995317i	$0.469183\pi$
$60$	−3.24955	−0.419516
$61$	−1.90957	−0.244496	−0.122248	−	0.992500i	$-0.539010\pi$
$61$	−1.90957	−0.244496	−0.122248	+	0.992500i	$0.539010\pi$
$62$	7.12994	0.905503
$63$	0	0
$64$	3.03652	0.379566
$65$	12.7595	1.58262
$66$	0.589611	0.0725761
$67$	−7.92467	−0.968152	−0.484076	−	0.875026i	$-0.660844\pi$
$67$	−7.92467	−0.968152	−0.484076	+	0.875026i	$0.660844\pi$
$68$	−0.480046	−0.0582141
$69$	−2.25692	−0.271701
$70$	0	0
$71$	−9.05365	−1.07447	−0.537235	−	0.843432i	$-0.680531\pi$
$71$	−9.05365	−1.07447	−0.537235	+	0.843432i	$0.680531\pi$
$72$	−2.63586	−0.310639
$73$	−9.45548	−1.10668	−0.553340	−	0.832955i	$-0.686647\pi$
$73$	−9.45548	−1.10668	−0.553340	+	0.832955i	$0.686647\pi$
$74$	−2.84582	−0.330820
$75$	0.399659	0.0461486
$76$	−5.75215	−0.659817
$77$	0	0
$78$	4.25887	0.482222
$79$	−3.15388	−0.354840	−0.177420	−	0.984135i	$-0.556775\pi$
$79$	−3.15388	−0.354840	−0.177420	+	0.984135i	$0.556775\pi$
$80$	1.74851	0.195489
$81$	1.00000	0.111111
$82$	0.775610	0.0856518
$83$	1.77106	0.194399	0.0971994	−	0.995265i	$-0.469012\pi$
$83$	1.77106	0.194399	0.0971994	+	0.995265i	$0.469012\pi$
$84$	0	0
$85$	0.797674	0.0865199
$86$	−8.23693	−0.888211
$87$	−2.50209	−0.268252
$88$	−2.00375	−0.213600
$89$	17.7374	1.88016	0.940078	−	0.340959i	$-0.110752\pi$
$89$	17.7374	1.88016	0.940078	+	0.340959i	$0.110752\pi$
$90$	1.80230	0.189979
$91$	0	0
$92$	3.15615	0.329051
$93$	9.19269	0.953237
$94$	2.10679	0.217299
$95$	9.55812	0.980643
$96$	5.85533	0.597607
$97$	17.8216	1.80951	0.904754	−	0.425934i	$-0.140054\pi$
$97$	17.8216	1.80951	0.904754	+	0.425934i	$0.140054\pi$
$98$	0	0
$99$	0.760190	0.0764019
$100$	−0.558894	−0.0558894
$101$	7.40000	0.736327	0.368164	−	0.929761i	$-0.379987\pi$
$101$	7.40000	0.736327	0.368164	+	0.929761i	$0.379987\pi$
$102$	0.266248	0.0263624
$103$	6.69028	0.659213	0.329607	−	0.944118i	$-0.393084\pi$
$103$	6.69028	0.659213	0.329607	+	0.944118i	$0.393084\pi$
$104$	−14.4735	−1.41924
$105$	0	0
$106$	10.4409	1.01411
$107$	−3.96952	−0.383748	−0.191874	−	0.981420i	$-0.561457\pi$
$107$	−3.96952	−0.383748	−0.191874	+	0.981420i	$0.561457\pi$
$108$	−1.39843	−0.134564
$109$	16.7744	1.60670	0.803349	−	0.595509i	$-0.203050\pi$
$109$	16.7744	1.60670	0.803349	+	0.595509i	$0.203050\pi$
$110$	1.37009	0.130633
$111$	−3.66914	−0.348259
$112$	0	0
$113$	−2.86702	−0.269706	−0.134853	−	0.990866i	$-0.543056\pi$
$113$	−2.86702	−0.269706	−0.134853	+	0.990866i	$0.543056\pi$
$114$	3.19031	0.298800
$115$	−5.24445	−0.489047
$116$	3.49899	0.324873
$117$	5.49099	0.507642
$118$	1.15176	0.106028
$119$	0	0
$120$	−6.12498	−0.559132
$121$	−10.4221	−0.947465
$122$	−1.48108	−0.134091
$123$	1.00000	0.0901670
$124$	−12.8553	−1.15444
$125$	−10.6899	−0.956133
$126$	0	0
$127$	−0.720763	−0.0639574	−0.0319787	−	0.999489i	$-0.510181\pi$
$127$	−0.720763	−0.0639574	−0.0319787	+	0.999489i	$0.510181\pi$
$128$	−9.35550	−0.826917
$129$	−10.6199	−0.935034
$130$	9.89640	0.867972
$131$	8.88804	0.776552	0.388276	−	0.921543i	$-0.373071\pi$
$131$	8.88804	0.776552	0.388276	+	0.921543i	$0.373071\pi$
$132$	−1.06307	−0.0925285
$133$	0	0
$134$	−6.14645	−0.530972
$135$	2.32372	0.199994
$136$	−0.904824	−0.0775880
$137$	8.11913	0.693664	0.346832	−	0.937927i	$-0.387257\pi$
$137$	8.11913	0.693664	0.346832	+	0.937927i	$0.387257\pi$
$138$	−1.75049	−0.149012
$139$	−13.2889	−1.12715	−0.563576	−	0.826065i	$-0.690575\pi$
$139$	−13.2889	−1.12715	−0.563576	+	0.826065i	$0.690575\pi$
$140$	0	0
$141$	2.71630	0.228754
$142$	−7.02210	−0.589282
$143$	4.17420	0.349064
$144$	0.752463	0.0627053
$145$	−5.81414	−0.482838
$146$	−7.33377	−0.606947
$147$	0	0
$148$	5.13103	0.421768
$149$	−6.17294	−0.505707	−0.252853	−	0.967505i	$-0.581369\pi$
$149$	−6.17294	−0.505707	−0.252853	+	0.967505i	$0.581369\pi$
$150$	0.309979	0.0253097
$151$	16.9531	1.37962	0.689812	−	0.723989i	$-0.257693\pi$
$151$	16.9531	1.37962	0.689812	+	0.723989i	$0.257693\pi$
$152$	−10.8420	−0.879406
$153$	0.343275	0.0277522
$154$	0	0
$155$	21.3612	1.71577
$156$	−7.67876	−0.614793
$157$	5.87013	0.468488	0.234244	−	0.972178i	$-0.424739\pi$
$157$	5.87013	0.468488	0.234244	+	0.972178i	$0.424739\pi$
$158$	−2.44618	−0.194608
$159$	13.4616	1.06757
$160$	13.6061	1.07566
$161$	0	0
$162$	0.775610	0.0609377
$163$	22.5599	1.76703	0.883516	−	0.468401i	$-0.155170\pi$
$163$	22.5599	1.76703	0.883516	+	0.468401i	$0.155170\pi$
$164$	−1.39843	−0.109199
$165$	1.76647	0.137519
$166$	1.37365	0.106616
$167$	−13.6071	−1.05295	−0.526476	−	0.850190i	$-0.676487\pi$
$167$	−13.6071	−1.05295	−0.526476	+	0.850190i	$0.676487\pi$
$168$	0	0
$169$	17.1510	1.31931
$170$	0.618684	0.0474509
$171$	4.11329	0.314551
$172$	14.8512	1.13240
$173$	−12.8290	−0.975374	−0.487687	−	0.873018i	$-0.662159\pi$
$173$	−12.8290	−0.975374	−0.487687	+	0.873018i	$0.662159\pi$
$174$	−1.94064	−0.147120
$175$	0	0
$176$	0.572015	0.0431172
$177$	1.48497	0.111617
$178$	13.7573	1.03115
$179$	17.6606	1.32001	0.660006	−	0.751261i	$-0.270554\pi$
$179$	17.6606	1.32001	0.660006	+	0.751261i	$0.270554\pi$
$180$	−3.24955	−0.242207
$181$	6.92754	0.514920	0.257460	−	0.966289i	$-0.417114\pi$
$181$	6.92754	0.514920	0.257460	+	0.966289i	$0.417114\pi$
$182$	0	0
$183$	−1.90957	−0.141160
$184$	5.94892	0.438560
$185$	−8.52603	−0.626846
$186$	7.12994	0.522793
$187$	0.260954	0.0190829
$188$	−3.79856	−0.277038
$189$	0	0
$190$	7.41338	0.537823
$191$	−12.5688	−0.909448	−0.454724	−	0.890632i	$-0.650262\pi$
$191$	−12.5688	−0.909448	−0.454724	+	0.890632i	$0.650262\pi$
$192$	3.03652	0.219142
$193$	1.78824	0.128720	0.0643600	−	0.997927i	$-0.479499\pi$
$193$	1.78824	0.128720	0.0643600	+	0.997927i	$0.479499\pi$
$194$	13.8226	0.992405
$195$	12.7595	0.913727
$196$	0	0
$197$	3.12996	0.223001	0.111500	−	0.993764i	$-0.464434\pi$
$197$	3.12996	0.223001	0.111500	+	0.993764i	$0.464434\pi$
$198$	0.589611	0.0419018
$199$	−13.9364	−0.987925	−0.493963	−	0.869483i	$-0.664452\pi$
$199$	−13.9364	−0.987925	−0.493963	+	0.869483i	$0.664452\pi$
$200$	−1.05344	−0.0744896
$201$	−7.92467	−0.558963
$202$	5.73951	0.403831
$203$	0	0
$204$	−0.480046	−0.0336099
$205$	2.32372	0.162295
$206$	5.18905	0.361538
$207$	−2.25692	−0.156867
$208$	4.13177	0.286487
$209$	3.12688	0.216291
$210$	0	0
$211$	14.6116	1.00591	0.502953	−	0.864314i	$-0.332247\pi$
$211$	14.6116	1.00591	0.502953	+	0.864314i	$0.332247\pi$
$212$	−18.8250	−1.29291
$213$	−9.05365	−0.620346
$214$	−3.07880	−0.210462
$215$	−24.6777	−1.68301
$216$	−2.63586	−0.179347
$217$	0	0
$218$	13.0104	0.881176
$219$	−9.45548	−0.638942
$220$	−2.47028	−0.166546
$221$	1.88492	0.126794
$222$	−2.84582	−0.190999
$223$	11.9533	0.800451	0.400226	−	0.916417i	$-0.368932\pi$
$223$	11.9533	0.800451	0.400226	+	0.916417i	$0.368932\pi$
$224$	0	0
$225$	0.399659	0.0266439
$226$	−2.22369	−0.147917
$227$	7.88865	0.523588	0.261794	−	0.965124i	$-0.415686\pi$
$227$	7.88865	0.523588	0.261794	+	0.965124i	$0.415686\pi$
$228$	−5.75215	−0.380945
$229$	−17.0903	−1.12936	−0.564679	−	0.825311i	$-0.691000\pi$
$229$	−17.0903	−1.12936	−0.564679	+	0.825311i	$0.691000\pi$
$230$	−4.06765	−0.268213
$231$	0	0
$232$	6.59514	0.432992
$233$	11.8187	0.774271	0.387136	−	0.922023i	$-0.373465\pi$
$233$	11.8187	0.774271	0.387136	+	0.922023i	$0.373465\pi$
$234$	4.25887	0.278411
$235$	6.31191	0.411744
$236$	−2.07663	−0.135177
$237$	−3.15388	−0.204867
$238$	0	0
$239$	−20.1219	−1.30158	−0.650788	−	0.759260i	$-0.725561\pi$
$239$	−20.1219	−1.30158	−0.650788	+	0.759260i	$0.725561\pi$
$240$	1.74851	0.112866
$241$	−17.7351	−1.14242	−0.571210	−	0.820804i	$-0.693526\pi$
$241$	−17.7351	−1.14242	−0.571210	+	0.820804i	$0.693526\pi$
$242$	−8.08349	−0.519627
$243$	1.00000	0.0641500
$244$	2.67040	0.170955
$245$	0	0
$246$	0.775610	0.0494511
$247$	22.5861	1.43712
$248$	−24.2306	−1.53864
$249$	1.77106	0.112236
$250$	−8.29118	−0.524381
$251$	18.3801	1.16014	0.580071	−	0.814566i	$-0.303025\pi$
$251$	18.3801	1.16014	0.580071	+	0.814566i	$0.303025\pi$
$252$	0	0
$253$	−1.71569	−0.107864
$254$	−0.559031	−0.0350767
$255$	0.797674	0.0499523
$256$	−13.3293	−0.833079
$257$	9.32564	0.581717	0.290859	−	0.956766i	$-0.406059\pi$
$257$	9.32564	0.581717	0.290859	+	0.956766i	$0.406059\pi$
$258$	−8.23693	−0.512809
$259$	0	0
$260$	−17.8433	−1.10659
$261$	−2.50209	−0.154875
$262$	6.89365	0.425891
$263$	25.7805	1.58969	0.794845	−	0.606812i	$-0.207552\pi$
$263$	25.7805	1.58969	0.794845	+	0.606812i	$0.207552\pi$
$264$	−2.00375	−0.123322
$265$	31.2809	1.92157
$266$	0	0
$267$	17.7374	1.08551
$268$	11.0821	0.676946
$269$	−7.94764	−0.484576	−0.242288	−	0.970204i	$-0.577898\pi$
$269$	−7.94764	−0.484576	−0.242288	+	0.970204i	$0.577898\pi$
$270$	1.80230	0.109684
$271$	−19.6003	−1.19063	−0.595316	−	0.803492i	$-0.702973\pi$
$271$	−19.6003	−1.19063	−0.595316	+	0.803492i	$0.702973\pi$
$272$	0.258302	0.0156619
$273$	0	0
$274$	6.29727	0.380432
$275$	0.303816	0.0183208
$276$	3.15615	0.189978
$277$	21.9242	1.31730	0.658649	−	0.752450i	$-0.271128\pi$
$277$	21.9242	1.31730	0.658649	+	0.752450i	$0.271128\pi$
$278$	−10.3070	−0.618174
$279$	9.19269	0.550352
$280$	0	0
$281$	22.6021	1.34833	0.674165	−	0.738581i	$-0.264504\pi$
$281$	22.6021	1.34833	0.674165	+	0.738581i	$0.264504\pi$
$282$	2.10679	0.125458
$283$	−8.49810	−0.505159	−0.252580	−	0.967576i	$-0.581279\pi$
$283$	−8.49810	−0.505159	−0.252580	+	0.967576i	$0.581279\pi$
$284$	12.6609	0.751285
$285$	9.55812	0.566174
$286$	3.23755	0.191440
$287$	0	0
$288$	5.85533	0.345029
$289$	−16.8822	−0.993068
$290$	−4.50950	−0.264807
$291$	17.8216	1.04472
$292$	13.2228	0.773807
$293$	20.7777	1.21385	0.606923	−	0.794761i	$-0.292404\pi$
$293$	20.7777	1.21385	0.606923	+	0.794761i	$0.292404\pi$
$294$	0	0
$295$	3.45066	0.200905
$296$	9.67131	0.562134
$297$	0.760190	0.0441107
$298$	−4.78779	−0.277349
$299$	−12.3927	−0.716691
$300$	−0.558894	−0.0322678
$301$	0	0
$302$	13.1490	0.756639
$303$	7.40000	0.425119
$304$	3.09510	0.177516
$305$	−4.43730	−0.254079
$306$	0.266248	0.0152204
$307$	−1.65867	−0.0946656	−0.0473328	−	0.998879i	$-0.515072\pi$
$307$	−1.65867	−0.0946656	−0.0473328	+	0.998879i	$0.515072\pi$
$308$	0	0
$309$	6.69028	0.380597
$310$	16.5680	0.940997
$311$	28.7365	1.62950	0.814750	−	0.579813i	$-0.196874\pi$
$311$	28.7365	1.62950	0.814750	+	0.579813i	$0.196874\pi$
$312$	−14.4735	−0.819398
$313$	−12.6429	−0.714617	−0.357308	−	0.933986i	$-0.616305\pi$
$313$	−12.6429	−0.714617	−0.357308	+	0.933986i	$0.616305\pi$
$314$	4.55293	0.256937
$315$	0	0
$316$	4.41048	0.248109
$317$	−23.3711	−1.31265	−0.656325	−	0.754478i	$-0.727890\pi$
$317$	−23.3711	−1.31265	−0.656325	+	0.754478i	$0.727890\pi$
$318$	10.4409	0.585498
$319$	−1.90206	−0.106495
$320$	7.05602	0.394444
$321$	−3.96952	−0.221557
$322$	0	0
$323$	1.41199	0.0785653
$324$	−1.39843	−0.0776905
$325$	2.19452	0.121730
$326$	17.4977	0.969109
$327$	16.7744	0.927627
$328$	−2.63586	−0.145541
$329$	0	0
$330$	1.37009	0.0754209
$331$	16.3855	0.900626	0.450313	−	0.892871i	$-0.351312\pi$
$331$	16.3855	0.900626	0.450313	+	0.892871i	$0.351312\pi$
$332$	−2.47670	−0.135927
$333$	−3.66914	−0.201067
$334$	−10.5538	−0.577480
$335$	−18.4147	−1.00610
$336$	0	0
$337$	−29.8514	−1.62611	−0.813055	−	0.582187i	$-0.802197\pi$
$337$	−29.8514	−1.62611	−0.813055	+	0.582187i	$0.802197\pi$
$338$	13.3025	0.723560
$339$	−2.86702	−0.155715
$340$	−1.11549	−0.0604960
$341$	6.98819	0.378432
$342$	3.19031	0.172512
$343$	0	0
$344$	27.9926	1.50926
$345$	−5.24445	−0.282352
$346$	−9.95034	−0.534933
$347$	−27.5058	−1.47659	−0.738295	−	0.674478i	$-0.764369\pi$
$347$	−27.5058	−1.47659	−0.738295	+	0.674478i	$0.764369\pi$
$348$	3.49899	0.187566
$349$	0.348415	0.0186502	0.00932512	−	0.999957i	$-0.497032\pi$
$349$	0.348415	0.0186502	0.00932512	+	0.999957i	$0.497032\pi$
$350$	0	0
$351$	5.49099	0.293087
$352$	4.45116	0.237248
$353$	15.1421	0.805932	0.402966	−	0.915215i	$-0.367979\pi$
$353$	15.1421	0.805932	0.402966	+	0.915215i	$0.367979\pi$
$354$	1.15176	0.0612154
$355$	−21.0381	−1.11659
$356$	−24.8044	−1.31463
$357$	0	0
$358$	13.6977	0.723946
$359$	−2.84933	−0.150382	−0.0751909	−	0.997169i	$-0.523957\pi$
$359$	−2.84933	−0.150382	−0.0751909	+	0.997169i	$0.523957\pi$
$360$	−6.12498	−0.322815
$361$	−2.08083	−0.109517
$362$	5.37307	0.282402
$363$	−10.4221	−0.547019
$364$	0	0
$365$	−21.9719	−1.15006
$366$	−1.48108	−0.0774174
$367$	0.608968	0.0317879	0.0158939	−	0.999874i	$-0.494941\pi$
$367$	0.608968	0.0317879	0.0158939	+	0.999874i	$0.494941\pi$
$368$	−1.69825	−0.0885274
$369$	1.00000	0.0520579
$370$	−6.61288	−0.343787
$371$	0	0
$372$	−12.8553	−0.666518
$373$	−7.26112	−0.375967	−0.187983	−	0.982172i	$-0.560195\pi$
$373$	−7.26112	−0.375967	−0.187983	+	0.982172i	$0.560195\pi$
$374$	0.202399	0.0104658
$375$	−10.6899	−0.552024
$376$	−7.15978	−0.369237
$377$	−13.7389	−0.707591
$378$	0	0
$379$	14.5784	0.748845	0.374422	−	0.927258i	$-0.377841\pi$
$379$	14.5784	0.748845	0.374422	+	0.927258i	$0.377841\pi$
$380$	−13.3664	−0.685680
$381$	−0.720763	−0.0369258
$382$	−9.74850	−0.498777
$383$	−15.3796	−0.785861	−0.392930	−	0.919568i	$-0.628539\pi$
$383$	−15.3796	−0.785861	−0.392930	+	0.919568i	$0.628539\pi$
$384$	−9.35550	−0.477421
$385$	0	0
$386$	1.38697	0.0705951
$387$	−10.6199	−0.539842
$388$	−24.9222	−1.26523
$389$	−10.6534	−0.540147	−0.270074	−	0.962840i	$-0.587048\pi$
$389$	−10.6534	−0.540147	−0.270074	+	0.962840i	$0.587048\pi$
$390$	9.89640	0.501124
$391$	−0.774745	−0.0391806
$392$	0	0
$393$	8.88804	0.448342
$394$	2.42763	0.122302
$395$	−7.32873	−0.368749
$396$	−1.06307	−0.0534214
$397$	6.13371	0.307842	0.153921	−	0.988083i	$-0.450810\pi$
$397$	6.13371	0.307842	0.153921	+	0.988083i	$0.450810\pi$
$398$	−10.8092	−0.541817
$399$	0	0
$400$	0.300728	0.0150364
$401$	−10.9247	−0.545555	−0.272778	−	0.962077i	$-0.587942\pi$
$401$	−10.9247	−0.545555	−0.272778	+	0.962077i	$0.587942\pi$
$402$	−6.14645	−0.306557
$403$	50.4770	2.51444
$404$	−10.3484	−0.514851
$405$	2.32372	0.115466
$406$	0	0
$407$	−2.78924	−0.138257
$408$	−0.904824	−0.0447955
$409$	−1.51340	−0.0748328	−0.0374164	−	0.999300i	$-0.511913\pi$
$409$	−1.51340	−0.0748328	−0.0374164	+	0.999300i	$0.511913\pi$
$410$	1.80230	0.0890091
$411$	8.11913	0.400487
$412$	−9.35589	−0.460932
$413$	0	0
$414$	−1.75049	−0.0860319
$415$	4.11544	0.202019
$416$	32.1516	1.57636
$417$	−13.2889	−0.650761
$418$	2.42524	0.118622
$419$	−22.7774	−1.11275	−0.556374	−	0.830932i	$-0.687808\pi$
$419$	−22.7774	−1.11275	−0.556374	+	0.830932i	$0.687808\pi$
$420$	0	0
$421$	−30.2061	−1.47215	−0.736076	−	0.676898i	$-0.763324\pi$
$421$	−30.2061	−1.47215	−0.736076	+	0.676898i	$0.763324\pi$
$422$	11.3329	0.551678
$423$	2.71630	0.132071
$424$	−35.4827	−1.72319
$425$	0.137193	0.00665483
$426$	−7.02210	−0.340222
$427$	0	0
$428$	5.55109	0.268322
$429$	4.17420	0.201532
$430$	−19.1403	−0.923027
$431$	−29.6181	−1.42666	−0.713328	−	0.700831i	$-0.752813\pi$
$431$	−29.6181	−1.42666	−0.713328	+	0.700831i	$0.752813\pi$
$432$	0.752463	0.0362029
$433$	−2.89012	−0.138890	−0.0694451	−	0.997586i	$-0.522123\pi$
$433$	−2.89012	−0.138890	−0.0694451	+	0.997586i	$0.522123\pi$
$434$	0	0
$435$	−5.81414	−0.278767
$436$	−23.4578	−1.12343
$437$	−9.28338	−0.444084
$438$	−7.33377	−0.350421
$439$	−13.4203	−0.640517	−0.320259	−	0.947330i	$-0.603770\pi$
$439$	−13.4203	−0.640517	−0.320259	+	0.947330i	$0.603770\pi$
$440$	−4.65615	−0.221973
$441$	0	0
$442$	1.46196	0.0695385
$443$	1.87862	0.0892560	0.0446280	−	0.999004i	$-0.485790\pi$
$443$	1.87862	0.0892560	0.0446280	+	0.999004i	$0.485790\pi$
$444$	5.13103	0.243508
$445$	41.2166	1.95385
$446$	9.27109	0.438999
$447$	−6.17294	−0.291970
$448$	0	0
$449$	−6.03380	−0.284753	−0.142376	−	0.989813i	$-0.545474\pi$
$449$	−6.03380	−0.284753	−0.142376	+	0.989813i	$0.545474\pi$
$450$	0.309979	0.0146126
$451$	0.760190	0.0357959
$452$	4.00932	0.188583
$453$	16.9531	0.796526
$454$	6.11851	0.287156
$455$	0	0
$456$	−10.8420	−0.507725
$457$	1.97465	0.0923701	0.0461851	−	0.998933i	$-0.485294\pi$
$457$	1.97465	0.0923701	0.0461851	+	0.998933i	$0.485294\pi$
$458$	−13.2554	−0.619384
$459$	0.343275	0.0160227
$460$	7.33399	0.341949
$461$	11.6577	0.542953	0.271477	−	0.962445i	$-0.412488\pi$
$461$	11.6577	0.542953	0.271477	+	0.962445i	$0.412488\pi$
$462$	0	0
$463$	−6.43173	−0.298908	−0.149454	−	0.988769i	$-0.547752\pi$
$463$	−6.43173	−0.298908	−0.149454	+	0.988769i	$0.547752\pi$
$464$	−1.88273	−0.0874034
$465$	21.3612	0.990602
$466$	9.16673	0.424640
$467$	12.7103	0.588164	0.294082	−	0.955780i	$-0.404986\pi$
$467$	12.7103	0.588164	0.294082	+	0.955780i	$0.404986\pi$
$468$	−7.67876	−0.354951
$469$	0	0
$470$	4.89558	0.225816
$471$	5.87013	0.270481
$472$	−3.91418	−0.180165
$473$	−8.07317	−0.371205
$474$	−2.44618	−0.112357
$475$	1.64391	0.0754279
$476$	0	0
$477$	13.4616	0.616363
$478$	−15.6067	−0.713835
$479$	−18.5088	−0.845688	−0.422844	−	0.906203i	$-0.638968\pi$
$479$	−18.5088	−0.845688	−0.422844	+	0.906203i	$0.638968\pi$
$480$	13.6061	0.621032
$481$	−20.1472	−0.918633
$482$	−13.7555	−0.626547
$483$	0	0
$484$	14.5746	0.662481
$485$	41.4123	1.88044
$486$	0.775610	0.0351824
$487$	−15.3201	−0.694222	−0.347111	−	0.937824i	$-0.612837\pi$
$487$	−15.3201	−0.694222	−0.347111	+	0.937824i	$0.612837\pi$
$488$	5.03335	0.227849
$489$	22.5599	1.02020
$490$	0	0
$491$	16.1924	0.730752	0.365376	−	0.930860i	$-0.380940\pi$
$491$	16.1924	0.730752	0.365376	+	0.930860i	$0.380940\pi$
$492$	−1.39843	−0.0630461
$493$	−0.858904	−0.0386831
$494$	17.5180	0.788171
$495$	1.76647	0.0793967
$496$	6.91716	0.310590
$497$	0	0
$498$	1.37365	0.0615547
$499$	−29.6732	−1.32835	−0.664177	−	0.747575i	$-0.731218\pi$
$499$	−29.6732	−1.32835	−0.664177	+	0.747575i	$0.731218\pi$
$500$	14.9491	0.668542
$501$	−13.6071	−0.607923
$502$	14.2558	0.636268
$503$	−16.9217	−0.754501	−0.377251	−	0.926111i	$-0.623130\pi$
$503$	−16.9217	−0.754501	−0.377251	+	0.926111i	$0.623130\pi$
$504$	0	0
$505$	17.1955	0.765189
$506$	−1.33071	−0.0591571
$507$	17.1510	0.761703
$508$	1.00794	0.0447199
$509$	−20.0722	−0.889684	−0.444842	−	0.895609i	$-0.646740\pi$
$509$	−20.0722	−0.889684	−0.444842	+	0.895609i	$0.646740\pi$
$510$	0.618684	0.0273958
$511$	0	0
$512$	8.37269	0.370024
$513$	4.11329	0.181606
$514$	7.23306	0.319036
$515$	15.5463	0.685053
$516$	14.8512	0.653789
$517$	2.06490	0.0908144
$518$	0	0
$519$	−12.8290	−0.563133
$520$	−33.6322	−1.47487
$521$	43.2896	1.89655	0.948276	−	0.317448i	$-0.102826\pi$
$521$	43.2896	1.89655	0.948276	+	0.317448i	$0.102826\pi$
$522$	−1.94064	−0.0849396
$523$	−13.0076	−0.568784	−0.284392	−	0.958708i	$-0.591792\pi$
$523$	−13.0076	−0.568784	−0.284392	+	0.958708i	$0.591792\pi$
$524$	−12.4293	−0.542976
$525$	0	0
$526$	19.9956	0.871849
$527$	3.15562	0.137461
$528$	0.572015	0.0248937
$529$	−17.9063	−0.778535
$530$	24.2617	1.05386
$531$	1.48497	0.0644424
$532$	0	0
$533$	5.49099	0.237841
$534$	13.7573	0.595335
$535$	−9.22404	−0.398790
$536$	20.8883	0.902236
$537$	17.6606	0.762109
$538$	−6.16427	−0.265761
$539$	0	0
$540$	−3.24955	−0.139839
$541$	−37.2906	−1.60325	−0.801624	−	0.597828i	$-0.796031\pi$
$541$	−37.2906	−1.60325	−0.801624	+	0.597828i	$0.796031\pi$
$542$	−15.2022	−0.652989
$543$	6.92754	0.297289
$544$	2.00999	0.0861776
$545$	38.9790	1.66968
$546$	0	0
$547$	−18.1855	−0.777555	−0.388777	−	0.921332i	$-0.627102\pi$
$547$	−18.1855	−0.777555	−0.388777	+	0.921332i	$0.627102\pi$
$548$	−11.3540	−0.485020
$549$	−1.90957	−0.0814985
$550$	0.235643	0.0100479
$551$	−10.2918	−0.438446
$552$	5.94892	0.253203
$553$	0	0
$554$	17.0046	0.722457
$555$	−8.52603	−0.361910
$556$	18.5836	0.788121
$557$	7.24631	0.307036	0.153518	−	0.988146i	$-0.450940\pi$
$557$	7.24631	0.307036	0.153518	+	0.988146i	$0.450940\pi$
$558$	7.12994	0.301834
$559$	−58.3140	−2.46642
$560$	0	0
$561$	0.260954	0.0110175
$562$	17.5304	0.739476
$563$	−23.1660	−0.976332	−0.488166	−	0.872751i	$-0.662334\pi$
$563$	−23.1660	−0.976332	−0.488166	+	0.872751i	$0.662334\pi$
$564$	−3.79856	−0.159948
$565$	−6.66213	−0.280278
$566$	−6.59121	−0.277049
$567$	0	0
$568$	23.8641	1.00132
$569$	14.8263	0.621550	0.310775	−	0.950483i	$-0.399411\pi$
$569$	14.8263	0.621550	0.310775	+	0.950483i	$0.399411\pi$
$570$	7.41338	0.310512
$571$	−4.25462	−0.178050	−0.0890251	−	0.996029i	$-0.528375\pi$
$571$	−4.25462	−0.178050	−0.0890251	+	0.996029i	$0.528375\pi$
$572$	−5.83732	−0.244071
$573$	−12.5688	−0.525070
$574$	0	0
$575$	−0.901998	−0.0376159
$576$	3.03652	0.126522
$577$	20.3581	0.847518	0.423759	−	0.905775i	$-0.360710\pi$
$577$	20.3581	0.847518	0.423759	+	0.905775i	$0.360710\pi$
$578$	−13.0940	−0.544637
$579$	1.78824	0.0743166
$580$	8.13066	0.337607
$581$	0	0
$582$	13.8226	0.572965
$583$	10.2333	0.423822
$584$	24.9233	1.03133
$585$	12.7595	0.527541
$586$	16.1154	0.665720
$587$	−0.786770	−0.0324735	−0.0162367	−	0.999868i	$-0.505169\pi$
$587$	−0.786770	−0.0324735	−0.0162367	+	0.999868i	$0.505169\pi$
$588$	0	0
$589$	37.8122	1.55803
$590$	2.67637	0.110184
$591$	3.12996	0.128749
$592$	−2.76089	−0.113472
$593$	−7.63352	−0.313471	−0.156735	−	0.987641i	$-0.550097\pi$
$593$	−7.63352	−0.313471	−0.156735	+	0.987641i	$0.550097\pi$
$594$	0.589611	0.0241920
$595$	0	0
$596$	8.63242	0.353598
$597$	−13.9364	−0.570379
$598$	−9.61193	−0.393061
$599$	−39.0847	−1.59696	−0.798478	−	0.602023i	$-0.794361\pi$
$599$	−39.0847	−1.59696	−0.798478	+	0.602023i	$0.794361\pi$
$600$	−1.05344	−0.0430066
$601$	−6.03068	−0.245997	−0.122998	−	0.992407i	$-0.539251\pi$
$601$	−6.03068	−0.245997	−0.122998	+	0.992407i	$0.539251\pi$
$602$	0	0
$603$	−7.92467	−0.322717
$604$	−23.7077	−0.964653
$605$	−24.2180	−0.984603
$606$	5.73951	0.233152
$607$	23.0814	0.936845	0.468423	−	0.883504i	$-0.344822\pi$
$607$	23.0814	0.936845	0.468423	+	0.883504i	$0.344822\pi$
$608$	24.0847	0.976763
$609$	0	0
$610$	−3.44162	−0.139347
$611$	14.9152	0.603404
$612$	−0.480046	−0.0194047
$613$	48.2137	1.94733	0.973666	−	0.227981i	$-0.0732123\pi$
$613$	48.2137	1.94733	0.973666	+	0.227981i	$0.0732123\pi$
$614$	−1.28648	−0.0519183
$615$	2.32372	0.0937013
$616$	0	0
$617$	−6.03090	−0.242795	−0.121397	−	0.992604i	$-0.538738\pi$
$617$	−6.03090	−0.242795	−0.121397	+	0.992604i	$0.538738\pi$
$618$	5.18905	0.208734
$619$	9.84681	0.395777	0.197888	−	0.980225i	$-0.436592\pi$
$619$	9.84681	0.395777	0.197888	+	0.980225i	$0.436592\pi$
$620$	−29.8721	−1.19969
$621$	−2.25692	−0.0905672
$622$	22.2883	0.893681
$623$	0	0
$624$	4.13177	0.165403
$625$	−26.8386	−1.07354
$626$	−9.80593	−0.391924
$627$	3.12688	0.124876
$628$	−8.20897	−0.327573
$629$	−1.25952	−0.0502205
$630$	0	0
$631$	−41.2519	−1.64221	−0.821107	−	0.570775i	$-0.806643\pi$
$631$	−41.2519	−1.64221	−0.821107	+	0.570775i	$0.806643\pi$
$632$	8.31318	0.330681
$633$	14.6116	0.580760
$634$	−18.1268	−0.719908
$635$	−1.67485	−0.0664643
$636$	−18.8250	−0.746461
$637$	0	0
$638$	−1.47526	−0.0584060
$639$	−9.05365	−0.358157
$640$	−21.7395	−0.859330
$641$	33.5265	1.32422	0.662110	−	0.749407i	$-0.269661\pi$
$641$	33.5265	1.32422	0.662110	+	0.749407i	$0.269661\pi$
$642$	−3.07880	−0.121511
$643$	19.6386	0.774472	0.387236	−	0.921981i	$-0.373430\pi$
$643$	19.6386	0.774472	0.387236	+	0.921981i	$0.373430\pi$
$644$	0	0
$645$	−24.6777	−0.971685
$646$	1.09515	0.0430883
$647$	34.8073	1.36842	0.684209	−	0.729286i	$-0.260148\pi$
$647$	34.8073	1.36842	0.684209	+	0.729286i	$0.260148\pi$
$648$	−2.63586	−0.103546
$649$	1.12886	0.0443117
$650$	1.70209	0.0667616
$651$	0	0
$652$	−31.5485	−1.23553
$653$	−0.467797	−0.0183063	−0.00915315	−	0.999958i	$-0.502914\pi$
$653$	−0.467797	−0.0183063	−0.00915315	+	0.999958i	$0.502914\pi$
$654$	13.0104	0.508747
$655$	20.6533	0.806991
$656$	0.752463	0.0293787
$657$	−9.45548	−0.368893
$658$	0	0
$659$	−39.9725	−1.55711	−0.778554	−	0.627577i	$-0.784047\pi$
$659$	−39.9725	−1.55711	−0.778554	+	0.627577i	$0.784047\pi$
$660$	−2.47028	−0.0961554
$661$	43.8448	1.70537	0.852683	−	0.522429i	$-0.174974\pi$
$661$	43.8448	1.70537	0.852683	+	0.522429i	$0.174974\pi$
$662$	12.7087	0.493938
$663$	1.88492	0.0732043
$664$	−4.66825	−0.181163
$665$	0	0
$666$	−2.84582	−0.110273
$667$	5.64701	0.218653
$668$	19.0286	0.736240
$669$	11.9533	0.462141
$670$	−14.2826	−0.551785
$671$	−1.45164	−0.0560398
$672$	0	0
$673$	21.7056	0.836690	0.418345	−	0.908288i	$-0.362610\pi$
$673$	21.7056	0.836690	0.418345	+	0.908288i	$0.362610\pi$
$674$	−23.1531	−0.891822
$675$	0.399659	0.0153829
$676$	−23.9845	−0.922479
$677$	−17.1365	−0.658610	−0.329305	−	0.944224i	$-0.606814\pi$
$677$	−17.1365	−0.658610	−0.329305	+	0.944224i	$0.606814\pi$
$678$	−2.22369	−0.0854002
$679$	0	0
$680$	−2.10255	−0.0806293
$681$	7.88865	0.302294
$682$	5.42011	0.207547
$683$	−4.55778	−0.174399	−0.0871994	−	0.996191i	$-0.527792\pi$
$683$	−4.55778	−0.174399	−0.0871994	+	0.996191i	$0.527792\pi$
$684$	−5.75215	−0.219939
$685$	18.8665	0.720854
$686$	0	0
$687$	−17.0903	−0.652035
$688$	−7.99112	−0.304658
$689$	73.9173	2.81603
$690$	−4.06765	−0.154853
$691$	29.3151	1.11520	0.557600	−	0.830110i	$-0.311722\pi$
$691$	29.3151	1.11520	0.557600	+	0.830110i	$0.311722\pi$
$692$	17.9405	0.681996
$693$	0	0
$694$	−21.3338	−0.809819
$695$	−30.8797	−1.17133
$696$	6.59514	0.249988
$697$	0.343275	0.0130025
$698$	0.270234	0.0102285
$699$	11.8187	0.447026
$700$	0	0
$701$	21.1570	0.799088	0.399544	−	0.916714i	$-0.369169\pi$
$701$	21.1570	0.799088	0.399544	+	0.916714i	$0.369169\pi$
$702$	4.25887	0.160741
$703$	−15.0922	−0.569214
$704$	2.30833	0.0869986
$705$	6.31191	0.237720
$706$	11.7444	0.442005
$707$	0	0
$708$	−2.07663	−0.0780446
$709$	33.8220	1.27021	0.635107	−	0.772425i	$-0.280956\pi$
$709$	33.8220	1.27021	0.635107	+	0.772425i	$0.280956\pi$
$710$	−16.3174	−0.612380
$711$	−3.15388	−0.118280
$712$	−46.7531	−1.75215
$713$	−20.7472	−0.776988
$714$	0	0
$715$	9.69965	0.362746
$716$	−24.6970	−0.922971
$717$	−20.1219	−0.751465
$718$	−2.20997	−0.0824752
$719$	8.11869	0.302776	0.151388	−	0.988474i	$-0.451626\pi$
$719$	8.11869	0.302776	0.151388	+	0.988474i	$0.451626\pi$
$720$	1.74851	0.0651632
$721$	0	0
$722$	−1.61391	−0.0600636
$723$	−17.7351	−0.659576
$724$	−9.68768	−0.360040
$725$	−0.999980	−0.0371383
$726$	−8.08349	−0.300007
$727$	0.581872	0.0215805	0.0107902	−	0.999942i	$-0.496565\pi$
$727$	0.581872	0.0215805	0.0107902	+	0.999942i	$0.496565\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−17.0416	−0.630738
$731$	−3.64556	−0.134836
$732$	2.67040	0.0987008
$733$	−11.4298	−0.422170	−0.211085	−	0.977468i	$-0.567700\pi$
$733$	−11.4298	−0.422170	−0.211085	+	0.977468i	$0.567700\pi$
$734$	0.472322	0.0174337
$735$	0	0
$736$	−13.2150	−0.487112
$737$	−6.02425	−0.221906
$738$	0.775610	0.0285506
$739$	−26.0004	−0.956439	−0.478220	−	0.878240i	$-0.658718\pi$
$739$	−26.0004	−0.956439	−0.478220	+	0.878240i	$0.658718\pi$
$740$	11.9231	0.438300
$741$	22.5861	0.829719
$742$	0	0
$743$	4.57518	0.167847	0.0839235	−	0.996472i	$-0.473255\pi$
$743$	4.57518	0.167847	0.0839235	+	0.996472i	$0.473255\pi$
$744$	−24.2306	−0.888337
$745$	−14.3442	−0.525529
$746$	−5.63180	−0.206195
$747$	1.77106	0.0647996
$748$	−0.364926	−0.0133430
$749$	0	0
$750$	−8.29118	−0.302751
$751$	−28.7808	−1.05023	−0.525113	−	0.851032i	$-0.675977\pi$
$751$	−28.7808	−1.05023	−0.525113	+	0.851032i	$0.675977\pi$
$752$	2.04392	0.0745340
$753$	18.3801	0.669809
$754$	−10.6561	−0.388071
$755$	39.3942	1.43370
$756$	0	0
$757$	27.3918	0.995573	0.497787	−	0.867299i	$-0.334146\pi$
$757$	27.3918	0.995573	0.497787	+	0.867299i	$0.334146\pi$
$758$	11.3072	0.410696
$759$	−1.71569	−0.0622756
$760$	−25.1938	−0.913876
$761$	−2.80913	−0.101831	−0.0509155	−	0.998703i	$-0.516214\pi$
$761$	−2.80913	−0.101831	−0.0509155	+	0.998703i	$0.516214\pi$
$762$	−0.559031	−0.0202515
$763$	0	0
$764$	17.5766	0.635899
$765$	0.797674	0.0288400
$766$	−11.9286	−0.430997
$767$	8.15398	0.294423
$768$	−13.3293	−0.480978
$769$	36.1335	1.30301	0.651504	−	0.758645i	$-0.274138\pi$
$769$	36.1335	1.30301	0.651504	+	0.758645i	$0.274138\pi$
$770$	0	0
$771$	9.32564	0.335855
$772$	−2.50072	−0.0900030
$773$	−1.84459	−0.0663451	−0.0331726	−	0.999450i	$-0.510561\pi$
$773$	−1.84459	−0.0663451	−0.0331726	+	0.999450i	$0.510561\pi$
$774$	−8.23693	−0.296070
$775$	3.67394	0.131972
$776$	−46.9751	−1.68631
$777$	0	0
$778$	−8.26286	−0.296238
$779$	4.11329	0.147374
$780$	−17.8433	−0.638892
$781$	−6.88249	−0.246275
$782$	−0.600900	−0.0214881
$783$	−2.50209	−0.0894173
$784$	0	0
$785$	13.6405	0.486851
$786$	6.89365	0.245888
$787$	−37.8377	−1.34877	−0.674385	−	0.738380i	$-0.735591\pi$
$787$	−37.8377	−1.34877	−0.674385	+	0.738380i	$0.735591\pi$
$788$	−4.37703	−0.155925
$789$	25.7805	0.917808
$790$	−5.68424	−0.202236
$791$	0	0
$792$	−2.00375	−0.0712002
$793$	−10.4854	−0.372349
$794$	4.75736	0.168832
$795$	31.2809	1.10942
$796$	19.4891	0.690772
$797$	−50.8916	−1.80267	−0.901336	−	0.433121i	$-0.857412\pi$
$797$	−50.8916	−1.80267	−0.901336	+	0.433121i	$0.857412\pi$
$798$	0	0
$799$	0.932439	0.0329873
$800$	2.34013	0.0827362
$801$	17.7374	0.626719
$802$	−8.47333	−0.299204
$803$	−7.18796	−0.253658
$804$	11.0821	0.390835
$805$	0	0
$806$	39.1504	1.37902
$807$	−7.94764	−0.279770
$808$	−19.5053	−0.686195
$809$	−41.8050	−1.46978	−0.734892	−	0.678184i	$-0.762767\pi$
$809$	−41.8050	−1.46978	−0.734892	+	0.678184i	$0.762767\pi$
$810$	1.80230	0.0633263
$811$	−39.6502	−1.39231	−0.696154	−	0.717892i	$-0.745107\pi$
$811$	−39.6502	−1.39231	−0.696154	+	0.717892i	$0.745107\pi$
$812$	0	0
$813$	−19.6003	−0.687412
$814$	−2.16336	−0.0758258
$815$	52.4229	1.83630
$816$	0.258302	0.00904238
$817$	−43.6829	−1.52827
$818$	−1.17381	−0.0410412
$819$	0	0
$820$	−3.24955	−0.113479
$821$	34.7645	1.21329	0.606645	−	0.794973i	$-0.292515\pi$
$821$	34.7645	1.21329	0.606645	+	0.794973i	$0.292515\pi$
$822$	6.29727	0.219643
$823$	−1.17430	−0.0409334	−0.0204667	−	0.999791i	$-0.506515\pi$
$823$	−1.17430	−0.0409334	−0.0204667	+	0.999791i	$0.506515\pi$
$824$	−17.6346	−0.614331
$825$	0.303816	0.0105775
$826$	0	0
$827$	13.0266	0.452979	0.226489	−	0.974014i	$-0.427275\pi$
$827$	13.0266	0.452979	0.226489	+	0.974014i	$0.427275\pi$
$828$	3.15615	0.109684
$829$	−44.8266	−1.55689	−0.778447	−	0.627711i	$-0.783992\pi$
$829$	−44.8266	−1.55689	−0.778447	+	0.627711i	$0.783992\pi$
$830$	3.19197	0.110795
$831$	21.9242	0.760542
$832$	16.6735	0.578051
$833$	0	0
$834$	−10.3070	−0.356903
$835$	−31.6192	−1.09423
$836$	−4.37272	−0.151234
$837$	9.19269	0.317746
$838$	−17.6664	−0.610274
$839$	−15.9347	−0.550127	−0.275064	−	0.961426i	$-0.588699\pi$
$839$	−15.9347	−0.550127	−0.275064	+	0.961426i	$0.588699\pi$
$840$	0	0
$841$	−22.7396	−0.784123
$842$	−23.4281	−0.807386
$843$	22.6021	0.778458
$844$	−20.4333	−0.703344
$845$	39.8541	1.37102
$846$	2.10679	0.0724329
$847$	0	0
$848$	10.1293	0.347843
$849$	−8.49810	−0.291654
$850$	0.106408	0.00364977
$851$	8.28095	0.283867
$852$	12.6609	0.433755
$853$	5.71827	0.195790	0.0978949	−	0.995197i	$-0.468789\pi$
$853$	5.71827	0.195790	0.0978949	+	0.995197i	$0.468789\pi$
$854$	0	0
$855$	9.55812	0.326881
$856$	10.4631	0.357621
$857$	−10.1019	−0.345074	−0.172537	−	0.985003i	$-0.555196\pi$
$857$	−10.1019	−0.345074	−0.172537	+	0.985003i	$0.555196\pi$
$858$	3.23755	0.110528
$859$	0.0100888	0.000344227 0	0.000172113	−	1.00000i	$-0.499945\pi$
$859$	0.0100888	0.000344227 0	0.000172113		1.00000i	$0.499945\pi$
$860$	34.5101	1.17678
$861$	0	0
$862$	−22.9721	−0.782434
$863$	46.6354	1.58749	0.793743	−	0.608253i	$-0.208129\pi$
$863$	46.6354	1.58749	0.793743	+	0.608253i	$0.208129\pi$
$864$	5.85533	0.199202
$865$	−29.8111	−1.01361
$866$	−2.24161	−0.0761729
$867$	−16.8822	−0.573348
$868$	0	0
$869$	−2.39755	−0.0813313
$870$	−4.50950	−0.152886
$871$	−43.5143	−1.47443
$872$	−44.2149	−1.49731
$873$	17.8216	0.603170
$874$	−7.20028	−0.243553
$875$	0	0
$876$	13.2228	0.446758
$877$	0.720970	0.0243454	0.0121727	−	0.999926i	$-0.496125\pi$
$877$	0.720970	0.0243454	0.0121727	+	0.999926i	$0.496125\pi$
$878$	−10.4089	−0.351285
$879$	20.7777	0.700814
$880$	1.32920	0.0448073
$881$	−2.07246	−0.0698231	−0.0349115	−	0.999390i	$-0.511115\pi$
$881$	−2.07246	−0.0698231	−0.0349115	+	0.999390i	$0.511115\pi$
$882$	0	0
$883$	−25.4061	−0.854983	−0.427492	−	0.904019i	$-0.640603\pi$
$883$	−25.4061	−0.854983	−0.427492	+	0.904019i	$0.640603\pi$
$884$	−2.63593	−0.0886559
$885$	3.45066	0.115993
$886$	1.45708	0.0489515
$887$	33.3489	1.11975	0.559873	−	0.828579i	$-0.310850\pi$
$887$	33.3489	1.11975	0.559873	+	0.828579i	$0.310850\pi$
$888$	9.67131	0.324548
$889$	0	0
$890$	31.9680	1.07157
$891$	0.760190	0.0254673
$892$	−16.7158	−0.559687
$893$	11.1729	0.373888
$894$	−4.78779	−0.160128
$895$	41.0381	1.37175
$896$	0	0
$897$	−12.3927	−0.413782
$898$	−4.67988	−0.156170
$899$	−23.0009	−0.767123
$900$	−0.558894	−0.0186298
$901$	4.62102	0.153949
$902$	0.589611	0.0196319
$903$	0	0
$904$	7.55704	0.251343
$905$	16.0976	0.535104
$906$	13.1490	0.436846
$907$	−19.5723	−0.649888	−0.324944	−	0.945733i	$-0.605345\pi$
$907$	−19.5723	−0.649888	−0.324944	+	0.945733i	$0.605345\pi$
$908$	−11.0317	−0.366100
$909$	7.40000	0.245442
$910$	0	0
$911$	−47.3259	−1.56798	−0.783989	−	0.620775i	$-0.786818\pi$
$911$	−47.3259	−1.56798	−0.783989	+	0.620775i	$0.786818\pi$
$912$	3.09510	0.102489
$913$	1.34634	0.0445573
$914$	1.53156	0.0506594
$915$	−4.43730	−0.146693
$916$	23.8996	0.789664
$917$	0	0
$918$	0.266248	0.00878748
$919$	26.6402	0.878780	0.439390	−	0.898296i	$-0.355195\pi$
$919$	26.6402	0.878780	0.439390	+	0.898296i	$0.355195\pi$
$920$	13.8236	0.455751
$921$	−1.65867	−0.0546552
$922$	9.04182	0.297777
$923$	−49.7135	−1.63634
$924$	0	0
$925$	−1.46640	−0.0482150
$926$	−4.98851	−0.163933
$927$	6.69028	0.219738
$928$	−14.6505	−0.480927
$929$	33.7826	1.10837	0.554186	−	0.832393i	$-0.313030\pi$
$929$	33.7826	1.10837	0.554186	+	0.832393i	$0.313030\pi$
$930$	16.5680	0.543285
$931$	0	0
$932$	−16.5277	−0.541382
$933$	28.7365	0.940792
$934$	9.85826	0.322572
$935$	0.606384	0.0198309
$936$	−14.4735	−0.473080
$937$	−21.7512	−0.710582	−0.355291	−	0.934756i	$-0.615618\pi$
$937$	−21.7512	−0.710582	−0.355291	+	0.934756i	$0.615618\pi$
$938$	0	0
$939$	−12.6429	−0.412584
$940$	−8.82677	−0.287897
$941$	−54.9319	−1.79073	−0.895364	−	0.445334i	$-0.853085\pi$
$941$	−54.9319	−1.79073	−0.895364	+	0.445334i	$0.853085\pi$
$942$	4.55293	0.148343
$943$	−2.25692	−0.0734955
$944$	1.11739	0.0363679
$945$	0	0
$946$	−6.26163	−0.203583
$947$	−51.5728	−1.67589	−0.837946	−	0.545754i	$-0.816243\pi$
$947$	−51.5728	−1.67589	−0.837946	+	0.545754i	$0.816243\pi$
$948$	4.41048	0.143246
$949$	−51.9200	−1.68539
$950$	1.27503	0.0413676
$951$	−23.3711	−0.757859
$952$	0	0
$953$	−53.2111	−1.72368	−0.861838	−	0.507184i	$-0.830686\pi$
$953$	−53.2111	−1.72368	−0.861838	+	0.507184i	$0.830686\pi$
$954$	10.4409	0.338037
$955$	−29.2064	−0.945096
$956$	28.1390	0.910081
$957$	−1.90206	−0.0614849
$958$	−14.3556	−0.463808
$959$	0	0
$960$	7.05602	0.227732
$961$	53.5055	1.72599
$962$	−15.6264	−0.503814
$963$	−3.96952	−0.127916
$964$	24.8013	0.798796
$965$	4.15535	0.133766
$966$	0	0
$967$	−37.0894	−1.19271	−0.596357	−	0.802720i	$-0.703386\pi$
$967$	−37.0894	−1.19271	−0.596357	+	0.802720i	$0.703386\pi$
$968$	27.4712	0.882957
$969$	1.41199	0.0453597
$970$	32.1198	1.03131
$971$	43.1989	1.38632	0.693159	−	0.720784i	$-0.256218\pi$
$971$	43.1989	1.38632	0.693159	+	0.720784i	$0.256218\pi$
$972$	−1.39843	−0.0448546
$973$	0	0
$974$	−11.8825	−0.380739
$975$	2.19452	0.0702810
$976$	−1.43688	−0.0459935
$977$	−5.55227	−0.177633	−0.0888164	−	0.996048i	$-0.528308\pi$
$977$	−5.55227	−0.177633	−0.0888164	+	0.996048i	$0.528308\pi$
$978$	17.4977	0.559515
$979$	13.4838	0.430943
$980$	0	0
$981$	16.7744	0.535566
$982$	12.5590	0.400773
$983$	1.61457	0.0514967	0.0257483	−	0.999668i	$-0.491803\pi$
$983$	1.61457	0.0514967	0.0257483	+	0.999668i	$0.491803\pi$
$984$	−2.63586	−0.0840280
$985$	7.27315	0.231742
$986$	−0.666174	−0.0212153
$987$	0	0
$988$	−31.5850	−1.00485
$989$	23.9684	0.762150
$990$	1.37009	0.0435443
$991$	6.17977	0.196307	0.0981534	−	0.995171i	$-0.468706\pi$
$991$	6.17977	0.196307	0.0981534	+	0.995171i	$0.468706\pi$
$992$	53.8262	1.70898
$993$	16.3855	0.519977
$994$	0	0
$995$	−32.3843	−1.02665
$996$	−2.47670	−0.0784772
$997$	−26.7860	−0.848322	−0.424161	−	0.905587i	$-0.639431\pi$
$997$	−26.7860	−0.848322	−0.424161	+	0.905587i	$0.639431\pi$
$998$	−23.0148	−0.728521
$999$	−3.66914	−0.116086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.be.1.5	yes	10
7.6	odd	2		6027.2.a.bd.1.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bd.1.5	✓	10	7.6	odd	2
6027.2.a.be.1.5	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+0.775610 q^{2} +1.00000 q^{3} -1.39843 q^{4} +2.32372 q^{5} +0.775610 q^{6} -2.63586 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.775610 q^{2} +1.00000 q^{3} -1.39843 q^{4} +2.32372 q^{5} +0.775610 q^{6} -2.63586 q^{8} +1.00000 q^{9} +1.80230 q^{10} +0.760190 q^{11} -1.39843 q^{12} +5.49099 q^{13} +2.32372 q^{15} +0.752463 q^{16} +0.343275 q^{17} +0.775610 q^{18} +4.11329 q^{19} -3.24955 q^{20} +0.589611 q^{22} -2.25692 q^{23} -2.63586 q^{24} +0.399659 q^{25} +4.25887 q^{26} +1.00000 q^{27} -2.50209 q^{29} +1.80230 q^{30} +9.19269 q^{31} +5.85533 q^{32} +0.760190 q^{33} +0.266248 q^{34} -1.39843 q^{36} -3.66914 q^{37} +3.19031 q^{38} +5.49099 q^{39} -6.12498 q^{40} +1.00000 q^{41} -10.6199 q^{43} -1.06307 q^{44} +2.32372 q^{45} -1.75049 q^{46} +2.71630 q^{47} +0.752463 q^{48} +0.309979 q^{50} +0.343275 q^{51} -7.67876 q^{52} +13.4616 q^{53} +0.775610 q^{54} +1.76647 q^{55} +4.11329 q^{57} -1.94064 q^{58} +1.48497 q^{59} -3.24955 q^{60} -1.90957 q^{61} +7.12994 q^{62} +3.03652 q^{64} +12.7595 q^{65} +0.589611 q^{66} -7.92467 q^{67} -0.480046 q^{68} -2.25692 q^{69} -9.05365 q^{71} -2.63586 q^{72} -9.45548 q^{73} -2.84582 q^{74} +0.399659 q^{75} -5.75215 q^{76} +4.25887 q^{78} -3.15388 q^{79} +1.74851 q^{80} +1.00000 q^{81} +0.775610 q^{82} +1.77106 q^{83} +0.797674 q^{85} -8.23693 q^{86} -2.50209 q^{87} -2.00375 q^{88} +17.7374 q^{89} +1.80230 q^{90} +3.15615 q^{92} +9.19269 q^{93} +2.10679 q^{94} +9.55812 q^{95} +5.85533 q^{96} +17.8216 q^{97} +0.760190 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	\( 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 2 q^{10} - 2 q^{11} + 18 q^{12} + 6 q^{15} + 14 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + 20 q^{20} + 2 q^{22} + 12 q^{24} + 10 q^{25} + 16 q^{26} + 10 q^{27} + 16 q^{29} + 2 q^{30} + 2 q^{31} + 38 q^{32} - 2 q^{33} - 4 q^{34} + 18 q^{36} + 24 q^{37} - 26 q^{38} + 40 q^{40} + 10 q^{41} + 8 q^{43} - 8 q^{44} + 6 q^{45} + 4 q^{46} - 8 q^{47} + 14 q^{48} + 44 q^{50} + 8 q^{51} - 30 q^{52} + 24 q^{53} + 4 q^{54} + 6 q^{57} - 14 q^{58} + 6 q^{59} + 20 q^{60} - 14 q^{61} - 2 q^{62} + 86 q^{64} + 28 q^{65} + 2 q^{66} + 26 q^{67} - 6 q^{68} + 14 q^{71} + 12 q^{72} - 36 q^{73} + 18 q^{74} + 10 q^{75} - 32 q^{76} + 16 q^{78} + 20 q^{79} + 70 q^{80} + 10 q^{81} + 4 q^{82} + 40 q^{83} + 24 q^{85} - 36 q^{86} + 16 q^{87} + 14 q^{88} + 2 q^{89} + 2 q^{90} + 8 q^{92} + 2 q^{93} - 54 q^{94} - 24 q^{95} + 38 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 2 * q^10 - 2 * q^11 + 18 * q^12 + 6 * q^15 + 14 * q^16 + 8 * q^17 + 4 * q^18 + 6 * q^19 + 20 * q^20 + 2 * q^22 + 12 * q^24 + 10 * q^25 + 16 * q^26 + 10 * q^27 + 16 * q^29 + 2 * q^30 + 2 * q^31 + 38 * q^32 - 2 * q^33 - 4 * q^34 + 18 * q^36 + 24 * q^37 - 26 * q^38 + 40 * q^40 + 10 * q^41 + 8 * q^43 - 8 * q^44 + 6 * q^45 + 4 * q^46 - 8 * q^47 + 14 * q^48 + 44 * q^50 + 8 * q^51 - 30 * q^52 + 24 * q^53 + 4 * q^54 + 6 * q^57 - 14 * q^58 + 6 * q^59 + 20 * q^60 - 14 * q^61 - 2 * q^62 + 86 * q^64 + 28 * q^65 + 2 * q^66 + 26 * q^67 - 6 * q^68 + 14 * q^71 + 12 * q^72 - 36 * q^73 + 18 * q^74 + 10 * q^75 - 32 * q^76 + 16 * q^78 + 20 * q^79 + 70 * q^80 + 10 * q^81 + 4 * q^82 + 40 * q^83 + 24 * q^85 - 36 * q^86 + 16 * q^87 + 14 * q^88 + 2 * q^89 + 2 * q^90 + 8 * q^92 + 2 * q^93 - 54 * q^94 - 24 * q^95 + 38 * q^96 + 16 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

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Database

Properties

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