LMFDB - Embedded newform 6027.2.a.bk.1.13

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} + \cdots + 16 $ x^14 - 2x^13 - 19x^12 + 36x^11 + 134x^10 - 237x^9 - 438x^8 + 716x^7 + 662x^6 - 1007x^5 - 384x^4 + 579x^3 + 44x^2 - 112*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-2.13271$ 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)

$f(q)$	$=$	$q+2.13271 q^{2} +1.00000 q^{3} +2.54845 q^{4} -0.889988 q^{5} +2.13271 q^{6} +1.16968 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.13271 q^{2} +1.00000 q^{3} +2.54845 q^{4} -0.889988 q^{5} +2.13271 q^{6} +1.16968 q^{8} +1.00000 q^{9} -1.89809 q^{10} +3.41733 q^{11} +2.54845 q^{12} -6.24747 q^{13} -0.889988 q^{15} -2.60231 q^{16} -7.99996 q^{17} +2.13271 q^{18} +0.0729909 q^{19} -2.26809 q^{20} +7.28817 q^{22} +1.57406 q^{23} +1.16968 q^{24} -4.20792 q^{25} -13.3240 q^{26} +1.00000 q^{27} -0.756839 q^{29} -1.89809 q^{30} -2.56122 q^{31} -7.88933 q^{32} +3.41733 q^{33} -17.0616 q^{34} +2.54845 q^{36} -11.1697 q^{37} +0.155668 q^{38} -6.24747 q^{39} -1.04100 q^{40} -1.00000 q^{41} -6.17260 q^{43} +8.70889 q^{44} -0.889988 q^{45} +3.35702 q^{46} -1.59757 q^{47} -2.60231 q^{48} -8.97427 q^{50} -7.99996 q^{51} -15.9214 q^{52} +9.15967 q^{53} +2.13271 q^{54} -3.04138 q^{55} +0.0729909 q^{57} -1.61412 q^{58} +0.919674 q^{59} -2.26809 q^{60} +8.51853 q^{61} -5.46234 q^{62} -11.6210 q^{64} +5.56017 q^{65} +7.28817 q^{66} +2.41279 q^{67} -20.3875 q^{68} +1.57406 q^{69} +8.88392 q^{71} +1.16968 q^{72} -3.64101 q^{73} -23.8216 q^{74} -4.20792 q^{75} +0.186014 q^{76} -13.3240 q^{78} +11.7568 q^{79} +2.31602 q^{80} +1.00000 q^{81} -2.13271 q^{82} -4.03102 q^{83} +7.11987 q^{85} -13.1644 q^{86} -0.756839 q^{87} +3.99719 q^{88} +8.44697 q^{89} -1.89809 q^{90} +4.01141 q^{92} -2.56122 q^{93} -3.40716 q^{94} -0.0649610 q^{95} -7.88933 q^{96} +9.05668 q^{97} +3.41733 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9	$ 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9} - 3 q^{10} - 16 q^{11} + 14 q^{12} - 21 q^{13} - 10 q^{15} + 22 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 40 q^{20} + q^{22} - 7 q^{23} - 6 q^{24} + 22 q^{25} - 2 q^{26} + 14 q^{27} - 16 q^{29} - 3 q^{30} - 8 q^{31} - 19 q^{32} - 16 q^{33} - 33 q^{34} + 14 q^{36} + q^{37} - 32 q^{38} - 21 q^{39} + 13 q^{40} - 14 q^{41} + 14 q^{43} - 36 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} + 22 q^{48} - q^{50} - 12 q^{51} - 60 q^{52} - 20 q^{53} - 2 q^{54} + 11 q^{55} - 2 q^{57} + 21 q^{58} - 25 q^{59} - 40 q^{60} - 26 q^{61} + 33 q^{62} + 42 q^{64} - 8 q^{65} + q^{66} - 22 q^{67} - 15 q^{68} - 7 q^{69} - 36 q^{71} - 6 q^{72} - 31 q^{73} - 65 q^{74} + 22 q^{75} + 2 q^{76} - 2 q^{78} + 12 q^{79} - 112 q^{80} + 14 q^{81} + 2 q^{82} - 20 q^{83} + 40 q^{85} - 9 q^{86} - 16 q^{87} - 54 q^{88} - 39 q^{89} - 3 q^{90} + 63 q^{92} - 8 q^{93} - 14 q^{94} - 55 q^{95} - 19 q^{96} - 18 q^{97} - 16 q^{99}+O(q^{100}) $ 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9 - 3 * q^10 - 16 * q^11 + 14 * q^12 - 21 * q^13 - 10 * q^15 + 22 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 40 * q^20 + q^22 - 7 * q^23 - 6 * q^24 + 22 * q^25 - 2 * q^26 + 14 * q^27 - 16 * q^29 - 3 * q^30 - 8 * q^31 - 19 * q^32 - 16 * q^33 - 33 * q^34 + 14 * q^36 + q^37 - 32 * q^38 - 21 * q^39 + 13 * q^40 - 14 * q^41 + 14 * q^43 - 36 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 + 22 * q^48 - q^50 - 12 * q^51 - 60 * q^52 - 20 * q^53 - 2 * q^54 + 11 * q^55 - 2 * q^57 + 21 * q^58 - 25 * q^59 - 40 * q^60 - 26 * q^61 + 33 * q^62 + 42 * q^64 - 8 * q^65 + q^66 - 22 * q^67 - 15 * q^68 - 7 * q^69 - 36 * q^71 - 6 * q^72 - 31 * q^73 - 65 * q^74 + 22 * q^75 + 2 * q^76 - 2 * q^78 + 12 * q^79 - 112 * q^80 + 14 * q^81 + 2 * q^82 - 20 * q^83 + 40 * q^85 - 9 * q^86 - 16 * q^87 - 54 * q^88 - 39 * q^89 - 3 * q^90 + 63 * q^92 - 8 * q^93 - 14 * q^94 - 55 * q^95 - 19 * q^96 - 18 * q^97 - 16 * 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 $

$2$	2.13271	1.50805	0.754027	−	0.656844i	$-0.228109\pi$
$2$	2.13271	1.50805	0.754027	+	0.656844i	$0.228109\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.54845	1.27422
$5$	−0.889988	−0.398015	−0.199007	−	0.979998i	$-0.563772\pi$
$5$	−0.889988	−0.398015	−0.199007	+	0.979998i	$0.563772\pi$
$6$	2.13271	0.870675
$7$	0	0
$7$	0	0
$8$	1.16968	0.413545
$9$	1.00000	0.333333
$10$	−1.89809	−0.600227
$11$	3.41733	1.03036	0.515182	−	0.857081i	$-0.327724\pi$
$11$	3.41733	1.03036	0.515182	+	0.857081i	$0.327724\pi$
$12$	2.54845	0.735674
$13$	−6.24747	−1.73274	−0.866368	−	0.499406i	$-0.833552\pi$
$13$	−6.24747	−1.73274	−0.866368	+	0.499406i	$0.833552\pi$
$14$	0	0
$15$	−0.889988	−0.229794
$16$	−2.60231	−0.650577
$17$	−7.99996	−1.94027	−0.970137	−	0.242556i	$-0.922014\pi$
$17$	−7.99996	−1.94027	−0.970137	+	0.242556i	$0.922014\pi$
$18$	2.13271	0.502684
$19$	0.0729909	0.0167453	0.00837263	−	0.999965i	$-0.497335\pi$
$19$	0.0729909	0.0167453	0.00837263	+	0.999965i	$0.497335\pi$
$20$	−2.26809	−0.507160
$21$	0	0
$22$	7.28817	1.55384
$23$	1.57406	0.328215	0.164107	−	0.986443i	$-0.447526\pi$
$23$	1.57406	0.328215	0.164107	+	0.986443i	$0.447526\pi$
$24$	1.16968	0.238760
$25$	−4.20792	−0.841584
$26$	−13.3240	−2.61306
$27$	1.00000	0.192450
$28$	0	0
$29$	−0.756839	−0.140541	−0.0702707	−	0.997528i	$-0.522386\pi$
$29$	−0.756839	−0.140541	−0.0702707	+	0.997528i	$0.522386\pi$
$30$	−1.89809	−0.346541
$31$	−2.56122	−0.460009	−0.230004	−	0.973190i	$-0.573874\pi$
$31$	−2.56122	−0.460009	−0.230004	+	0.973190i	$0.573874\pi$
$32$	−7.88933	−1.39465
$33$	3.41733	0.594881
$34$	−17.0616	−2.92604
$35$	0	0
$36$	2.54845	0.424741
$37$	−11.1697	−1.83628	−0.918140	−	0.396257i	$-0.870309\pi$
$37$	−11.1697	−1.83628	−0.918140	+	0.396257i	$0.870309\pi$
$38$	0.155668	0.0252527
$39$	−6.24747	−1.00040
$40$	−1.04100	−0.164597
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−6.17260	−0.941312	−0.470656	−	0.882317i	$-0.655983\pi$
$43$	−6.17260	−0.941312	−0.470656	+	0.882317i	$0.655983\pi$
$44$	8.70889	1.31291
$45$	−0.889988	−0.132672
$46$	3.35702	0.494965
$47$	−1.59757	−0.233030	−0.116515	−	0.993189i	$-0.537172\pi$
$47$	−1.59757	−0.233030	−0.116515	+	0.993189i	$0.537172\pi$
$48$	−2.60231	−0.375611
$49$	0	0
$50$	−8.97427	−1.26915
$51$	−7.99996	−1.12022
$52$	−15.9214	−2.20789
$53$	9.15967	1.25818	0.629088	−	0.777334i	$-0.283428\pi$
$53$	9.15967	1.25818	0.629088	+	0.777334i	$0.283428\pi$
$54$	2.13271	0.290225
$55$	−3.04138	−0.410100
$56$	0	0
$57$	0.0729909	0.00966788
$58$	−1.61412	−0.211944
$59$	0.919674	0.119731	0.0598657	−	0.998206i	$-0.480933\pi$
$59$	0.919674	0.119731	0.0598657	+	0.998206i	$0.480933\pi$
$60$	−2.26809	−0.292809
$61$	8.51853	1.09069	0.545343	−	0.838213i	$-0.316399\pi$
$61$	8.51853	1.09069	0.545343	+	0.838213i	$0.316399\pi$
$62$	−5.46234	−0.693717
$63$	0	0
$64$	−11.6210	−1.45263
$65$	5.56017	0.689655
$66$	7.28817	0.897112
$67$	2.41279	0.294770	0.147385	−	0.989079i	$-0.452914\pi$
$67$	2.41279	0.294770	0.147385	+	0.989079i	$0.452914\pi$
$68$	−20.3875	−2.47235
$69$	1.57406	0.189495
$70$	0	0
$71$	8.88392	1.05433	0.527163	−	0.849764i	$-0.323256\pi$
$71$	8.88392	1.05433	0.527163	+	0.849764i	$0.323256\pi$
$72$	1.16968	0.137848
$73$	−3.64101	−0.426148	−0.213074	−	0.977036i	$-0.568348\pi$
$73$	−3.64101	−0.426148	−0.213074	+	0.977036i	$0.568348\pi$
$74$	−23.8216	−2.76921
$75$	−4.20792	−0.485889
$76$	0.186014	0.0213372
$77$	0	0
$78$	−13.3240	−1.50865
$79$	11.7568	1.32274	0.661371	−	0.750059i	$-0.269975\pi$
$79$	11.7568	1.32274	0.661371	+	0.750059i	$0.269975\pi$
$80$	2.31602	0.258939
$81$	1.00000	0.111111
$82$	−2.13271	−0.235518
$83$	−4.03102	−0.442462	−0.221231	−	0.975221i	$-0.571008\pi$
$83$	−4.03102	−0.442462	−0.221231	+	0.975221i	$0.571008\pi$
$84$	0	0
$85$	7.11987	0.772258
$86$	−13.1644	−1.41955
$87$	−0.756839	−0.0811417
$88$	3.99719	0.426101
$89$	8.44697	0.895377	0.447688	−	0.894190i	$-0.352247\pi$
$89$	8.44697	0.895377	0.447688	+	0.894190i	$0.352247\pi$
$90$	−1.89809	−0.200076
$91$	0	0
$92$	4.01141	0.418219
$93$	−2.56122	−0.265586
$94$	−3.40716	−0.351421
$95$	−0.0649610	−0.00666486
$96$	−7.88933	−0.805201
$97$	9.05668	0.919567	0.459783	−	0.888031i	$-0.347927\pi$
$97$	9.05668	0.919567	0.459783	+	0.888031i	$0.347927\pi$
$98$	0	0
$99$	3.41733	0.343455
$100$	−10.7237	−1.07237
$101$	−10.8514	−1.07976	−0.539879	−	0.841742i	$-0.681530\pi$
$101$	−10.8514	−1.07976	−0.539879	+	0.841742i	$0.681530\pi$
$102$	−17.0616	−1.68935
$103$	3.12953	0.308362	0.154181	−	0.988043i	$-0.450726\pi$
$103$	3.12953	0.308362	0.154181	+	0.988043i	$0.450726\pi$
$104$	−7.30755	−0.716564
$105$	0	0
$106$	19.5349	1.89740
$107$	3.35731	0.324564	0.162282	−	0.986744i	$-0.448115\pi$
$107$	3.35731	0.324564	0.162282	+	0.986744i	$0.448115\pi$
$108$	2.54845	0.245225
$109$	0.403889	0.0386856	0.0193428	−	0.999813i	$-0.493843\pi$
$109$	0.403889	0.0386856	0.0193428	+	0.999813i	$0.493843\pi$
$110$	−6.48638	−0.618453
$111$	−11.1697	−1.06018
$112$	0	0
$113$	5.43878	0.511637	0.255818	−	0.966725i	$-0.417655\pi$
$113$	5.43878	0.511637	0.255818	+	0.966725i	$0.417655\pi$
$114$	0.155668	0.0145797
$115$	−1.40090	−0.130634
$116$	−1.92877	−0.179081
$117$	−6.24747	−0.577579
$118$	1.96140	0.180561
$119$	0	0
$120$	−1.04100	−0.0950301
$121$	0.678140	0.0616491
$122$	18.1675	1.64481
$123$	−1.00000	−0.0901670
$124$	−6.52713	−0.586154
$125$	8.19494	0.732978
$126$	0	0
$127$	−5.15902	−0.457789	−0.228895	−	0.973451i	$-0.573511\pi$
$127$	−5.15902	−0.457789	−0.228895	+	0.973451i	$0.573511\pi$
$128$	−9.00561	−0.795991
$129$	−6.17260	−0.543467
$130$	11.8582	1.04004
$131$	−11.9242	−1.04182	−0.520911	−	0.853611i	$-0.674408\pi$
$131$	−11.9242	−1.04182	−0.520911	+	0.853611i	$0.674408\pi$
$132$	8.70889	0.758011
$133$	0	0
$134$	5.14579	0.444528
$135$	−0.889988	−0.0765980
$136$	−9.35740	−0.802390
$137$	4.57666	0.391010	0.195505	−	0.980703i	$-0.437365\pi$
$137$	4.57666	0.391010	0.195505	+	0.980703i	$0.437365\pi$
$138$	3.35702	0.285768
$139$	−14.6408	−1.24181	−0.620906	−	0.783885i	$-0.713235\pi$
$139$	−14.6408	−1.24181	−0.620906	+	0.783885i	$0.713235\pi$
$140$	0	0
$141$	−1.59757	−0.134540
$142$	18.9468	1.58998
$143$	−21.3497	−1.78535
$144$	−2.60231	−0.216859
$145$	0.673578	0.0559376
$146$	−7.76522	−0.642654
$147$	0	0
$148$	−28.4653	−2.33983
$149$	2.31277	0.189470	0.0947348	−	0.995503i	$-0.469800\pi$
$149$	2.31277	0.189470	0.0947348	+	0.995503i	$0.469800\pi$
$150$	−8.97427	−0.732746
$151$	1.08733	0.0884857	0.0442428	−	0.999021i	$-0.485912\pi$
$151$	1.08733	0.0884857	0.0442428	+	0.999021i	$0.485912\pi$
$152$	0.0853761	0.00692491
$153$	−7.99996	−0.646758
$154$	0	0
$155$	2.27945	0.183090
$156$	−15.9214	−1.27473
$157$	−24.5214	−1.95702	−0.978512	−	0.206192i	$-0.933893\pi$
$157$	−24.5214	−1.95702	−0.978512	+	0.206192i	$0.933893\pi$
$158$	25.0738	1.99477
$159$	9.15967	0.726409
$160$	7.02141	0.555091
$161$	0	0
$162$	2.13271	0.167561
$163$	−20.7325	−1.62390	−0.811948	−	0.583730i	$-0.801593\pi$
$163$	−20.7325	−1.62390	−0.811948	+	0.583730i	$0.801593\pi$
$164$	−2.54845	−0.199000
$165$	−3.04138	−0.236771
$166$	−8.59700	−0.667257
$167$	9.83140	0.760776	0.380388	−	0.924827i	$-0.375790\pi$
$167$	9.83140	0.760776	0.380388	+	0.924827i	$0.375790\pi$
$168$	0	0
$169$	26.0309	2.00238
$170$	15.1846	1.16461
$171$	0.0729909	0.00558175
$172$	−15.7305	−1.19944
$173$	−19.3348	−1.47000	−0.734998	−	0.678070i	$-0.762817\pi$
$173$	−19.3348	−1.47000	−0.734998	+	0.678070i	$0.762817\pi$
$174$	−1.61412	−0.122366
$175$	0	0
$176$	−8.89294	−0.670331
$177$	0.919674	0.0691269
$178$	18.0149	1.35028
$179$	16.3998	1.22578	0.612888	−	0.790170i	$-0.290008\pi$
$179$	16.3998	1.22578	0.612888	+	0.790170i	$0.290008\pi$
$180$	−2.26809	−0.169053
$181$	−16.4233	−1.22073	−0.610366	−	0.792119i	$-0.708978\pi$
$181$	−16.4233	−1.22073	−0.610366	+	0.792119i	$0.708978\pi$
$182$	0	0
$183$	8.51853	0.629708
$184$	1.84115	0.135731
$185$	9.94086	0.730866
$186$	−5.46234	−0.400518
$187$	−27.3385	−1.99919
$188$	−4.07133	−0.296932
$189$	0	0
$190$	−0.138543	−0.0100510
$191$	−25.9485	−1.87757	−0.938785	−	0.344503i	$-0.888047\pi$
$191$	−25.9485	−1.87757	−0.938785	+	0.344503i	$0.888047\pi$
$192$	−11.6210	−0.838675
$193$	26.2201	1.88737	0.943683	−	0.330850i	$-0.107335\pi$
$193$	26.2201	1.88737	0.943683	+	0.330850i	$0.107335\pi$
$194$	19.3153	1.38676
$195$	5.56017	0.398172
$196$	0	0
$197$	5.03749	0.358906	0.179453	−	0.983767i	$-0.442567\pi$
$197$	5.03749	0.358906	0.179453	+	0.983767i	$0.442567\pi$
$198$	7.28817	0.517948
$199$	2.53705	0.179847	0.0899234	−	0.995949i	$-0.471338\pi$
$199$	2.53705	0.179847	0.0899234	+	0.995949i	$0.471338\pi$
$200$	−4.92193	−0.348033
$201$	2.41279	0.170185
$202$	−23.1430	−1.62833
$203$	0	0
$204$	−20.3875	−1.42741
$205$	0.889988	0.0621595
$206$	6.67438	0.465026
$207$	1.57406	0.109405
$208$	16.2578	1.12728
$209$	0.249434	0.0172537
$210$	0	0
$211$	−23.1162	−1.59139	−0.795693	−	0.605700i	$-0.792893\pi$
$211$	−23.1162	−1.59139	−0.795693	+	0.605700i	$0.792893\pi$
$212$	23.3429	1.60320
$213$	8.88392	0.608716
$214$	7.16017	0.489459
$215$	5.49354	0.374656
$216$	1.16968	0.0795867
$217$	0	0
$218$	0.861378	0.0583399
$219$	−3.64101	−0.246037
$220$	−7.75081	−0.522559
$221$	49.9795	3.36198
$222$	−23.8216	−1.59880
$223$	0.239630	0.0160468	0.00802341	−	0.999968i	$-0.497446\pi$
$223$	0.239630	0.0160468	0.00802341	+	0.999968i	$0.497446\pi$
$224$	0	0
$225$	−4.20792	−0.280528
$226$	11.5993	0.771576
$227$	3.70162	0.245685	0.122843	−	0.992426i	$-0.460799\pi$
$227$	3.70162	0.245685	0.122843	+	0.992426i	$0.460799\pi$
$228$	0.186014	0.0123190
$229$	−6.25848	−0.413572	−0.206786	−	0.978386i	$-0.566300\pi$
$229$	−6.25848	−0.413572	−0.206786	+	0.978386i	$0.566300\pi$
$230$	−2.98770	−0.197003
$231$	0	0
$232$	−0.885260	−0.0581202
$233$	−25.6456	−1.68010	−0.840050	−	0.542509i	$-0.817474\pi$
$233$	−25.6456	−1.68010	−0.840050	+	0.542509i	$0.817474\pi$
$234$	−13.3240	−0.871020
$235$	1.42182	0.0927493
$236$	2.34374	0.152565
$237$	11.7568	0.763686
$238$	0	0
$239$	−17.7843	−1.15037	−0.575185	−	0.818023i	$-0.695070\pi$
$239$	−17.7843	−1.15037	−0.575185	+	0.818023i	$0.695070\pi$
$240$	2.31602	0.149499
$241$	7.64067	0.492179	0.246089	−	0.969247i	$-0.420854\pi$
$241$	7.64067	0.492179	0.246089	+	0.969247i	$0.420854\pi$
$242$	1.44627	0.0929700
$243$	1.00000	0.0641500
$244$	21.7090	1.38978
$245$	0	0
$246$	−2.13271	−0.135977
$247$	−0.456008	−0.0290151
$248$	−2.99581	−0.190234
$249$	−4.03102	−0.255456
$250$	17.4774	1.10537
$251$	−2.01280	−0.127047	−0.0635235	−	0.997980i	$-0.520234\pi$
$251$	−2.01280	−0.127047	−0.0635235	+	0.997980i	$0.520234\pi$
$252$	0	0
$253$	5.37909	0.338180
$254$	−11.0027	−0.690370
$255$	7.11987	0.445863
$256$	4.03570	0.252231
$257$	−6.23662	−0.389030	−0.194515	−	0.980900i	$-0.562313\pi$
$257$	−6.23662	−0.389030	−0.194515	+	0.980900i	$0.562313\pi$
$258$	−13.1644	−0.819577
$259$	0	0
$260$	14.1698	0.878775
$261$	−0.756839	−0.0468472
$262$	−25.4309	−1.57112
$263$	−8.13880	−0.501860	−0.250930	−	0.968005i	$-0.580736\pi$
$263$	−8.13880	−0.501860	−0.250930	+	0.968005i	$0.580736\pi$
$264$	3.99719	0.246010
$265$	−8.15199	−0.500773
$266$	0	0
$267$	8.44697	0.516946
$268$	6.14888	0.375603
$269$	25.6694	1.56509	0.782544	−	0.622595i	$-0.213921\pi$
$269$	25.6694	1.56509	0.782544	+	0.622595i	$0.213921\pi$
$270$	−1.89809	−0.115514
$271$	30.0299	1.82419	0.912093	−	0.409983i	$-0.134465\pi$
$271$	30.0299	1.82419	0.912093	+	0.409983i	$0.134465\pi$
$272$	20.8184	1.26230
$273$	0	0
$274$	9.76068	0.589664
$275$	−14.3799	−0.867138
$276$	4.01141	0.241459
$277$	−10.2884	−0.618169	−0.309085	−	0.951035i	$-0.600023\pi$
$277$	−10.2884	−0.618169	−0.309085	+	0.951035i	$0.600023\pi$
$278$	−31.2245	−1.87272
$279$	−2.56122	−0.153336
$280$	0	0
$281$	11.9838	0.714894	0.357447	−	0.933933i	$-0.383647\pi$
$281$	11.9838	0.714894	0.357447	+	0.933933i	$0.383647\pi$
$282$	−3.40716	−0.202893
$283$	15.2539	0.906752	0.453376	−	0.891319i	$-0.350219\pi$
$283$	15.2539	0.906752	0.453376	+	0.891319i	$0.350219\pi$
$284$	22.6402	1.34345
$285$	−0.0649610	−0.00384796
$286$	−45.5326	−2.69240
$287$	0	0
$288$	−7.88933	−0.464883
$289$	46.9993	2.76467
$290$	1.43655	0.0843569
$291$	9.05668	0.530912
$292$	−9.27893	−0.543008
$293$	29.2216	1.70714	0.853571	−	0.520976i	$-0.174432\pi$
$293$	29.2216	1.70714	0.853571	+	0.520976i	$0.174432\pi$
$294$	0	0
$295$	−0.818499	−0.0476548
$296$	−13.0649	−0.759384
$297$	3.41733	0.198294
$298$	4.93247	0.285730
$299$	−9.83390	−0.568709
$300$	−10.7237	−0.619131
$301$	0	0
$302$	2.31896	0.133441
$303$	−10.8514	−0.623399
$304$	−0.189945	−0.0108941
$305$	−7.58139	−0.434109
$306$	−17.0616	−0.975346
$307$	27.7393	1.58317	0.791584	−	0.611061i	$-0.209257\pi$
$307$	27.7393	1.58317	0.791584	+	0.611061i	$0.209257\pi$
$308$	0	0
$309$	3.12953	0.178033
$310$	4.86141	0.276110
$311$	13.6882	0.776187	0.388093	−	0.921620i	$-0.373134\pi$
$311$	13.6882	0.776187	0.388093	+	0.921620i	$0.373134\pi$
$312$	−7.30755	−0.413708
$313$	−21.4280	−1.21118	−0.605590	−	0.795777i	$-0.707063\pi$
$313$	−21.4280	−1.21118	−0.605590	+	0.795777i	$0.707063\pi$
$314$	−52.2971	−2.95129
$315$	0	0
$316$	29.9616	1.68547
$317$	−27.6310	−1.55191	−0.775956	−	0.630786i	$-0.782732\pi$
$317$	−27.6310	−1.55191	−0.775956	+	0.630786i	$0.782732\pi$
$318$	19.5349	1.09546
$319$	−2.58637	−0.144809
$320$	10.3426	0.578168
$321$	3.35731	0.187387
$322$	0	0
$323$	−0.583924	−0.0324904
$324$	2.54845	0.141580
$325$	26.2889	1.45824
$326$	−44.2164	−2.44892
$327$	0.403889	0.0223351
$328$	−1.16968	−0.0645848
$329$	0	0
$330$	−6.48638	−0.357064
$331$	−17.5293	−0.963498	−0.481749	−	0.876309i	$-0.659998\pi$
$331$	−17.5293	−0.963498	−0.481749	+	0.876309i	$0.659998\pi$
$332$	−10.2729	−0.563796
$333$	−11.1697	−0.612093
$334$	20.9675	1.14729
$335$	−2.14736	−0.117323
$336$	0	0
$337$	13.3142	0.725272	0.362636	−	0.931931i	$-0.381877\pi$
$337$	13.3142	0.725272	0.362636	+	0.931931i	$0.381877\pi$
$338$	55.5163	3.01969
$339$	5.43878	0.295394
$340$	18.1446	0.984030
$341$	−8.75253	−0.473976
$342$	0.155668	0.00841758
$343$	0	0
$344$	−7.21997	−0.389275
$345$	−1.40090	−0.0754217
$346$	−41.2354	−2.21683
$347$	−3.91557	−0.210199	−0.105099	−	0.994462i	$-0.533516\pi$
$347$	−3.91557	−0.210199	−0.105099	+	0.994462i	$0.533516\pi$
$348$	−1.92877	−0.103393
$349$	20.1583	1.07905	0.539524	−	0.841970i	$-0.318604\pi$
$349$	20.1583	1.07905	0.539524	+	0.841970i	$0.318604\pi$
$350$	0	0
$351$	−6.24747	−0.333465
$352$	−26.9604	−1.43700
$353$	−20.7285	−1.10327	−0.551633	−	0.834087i	$-0.685995\pi$
$353$	−20.7285	−1.10327	−0.551633	+	0.834087i	$0.685995\pi$
$354$	1.96140	0.104247
$355$	−7.90658	−0.419638
$356$	21.5267	1.14091
$357$	0	0
$358$	34.9759	1.84854
$359$	−34.7155	−1.83221	−0.916107	−	0.400934i	$-0.868686\pi$
$359$	−34.7155	−1.83221	−0.916107	+	0.400934i	$0.868686\pi$
$360$	−1.04100	−0.0548656
$361$	−18.9947	−0.999720
$362$	−35.0261	−1.84093
$363$	0.678140	0.0355931
$364$	0	0
$365$	3.24046	0.169613
$366$	18.1675	0.949633
$367$	22.9795	1.19952	0.599761	−	0.800179i	$-0.295262\pi$
$367$	22.9795	1.19952	0.599761	+	0.800179i	$0.295262\pi$
$368$	−4.09619	−0.213529
$369$	−1.00000	−0.0520579
$370$	21.2010	1.10219
$371$	0	0
$372$	−6.52713	−0.338416
$373$	9.55192	0.494580	0.247290	−	0.968942i	$-0.420460\pi$
$373$	9.55192	0.494580	0.247290	+	0.968942i	$0.420460\pi$
$374$	−58.3051	−3.01488
$375$	8.19494	0.423185
$376$	−1.86865	−0.0963683
$377$	4.72833	0.243521
$378$	0	0
$379$	−16.6032	−0.852847	−0.426423	−	0.904524i	$-0.640227\pi$
$379$	−16.6032	−0.852847	−0.426423	+	0.904524i	$0.640227\pi$
$380$	−0.165550	−0.00849253
$381$	−5.15902	−0.264305
$382$	−55.3407	−2.83148
$383$	−37.5062	−1.91648	−0.958239	−	0.285969i	$-0.907685\pi$
$383$	−37.5062	−1.91648	−0.958239	+	0.285969i	$0.907685\pi$
$384$	−9.00561	−0.459566
$385$	0	0
$386$	55.9199	2.84625
$387$	−6.17260	−0.313771
$388$	23.0805	1.17173
$389$	−1.49006	−0.0755488	−0.0377744	−	0.999286i	$-0.512027\pi$
$389$	−1.49006	−0.0755488	−0.0377744	+	0.999286i	$0.512027\pi$
$390$	11.8582	0.600465
$391$	−12.5924	−0.636826
$392$	0	0
$393$	−11.9242	−0.601496
$394$	10.7435	0.541250
$395$	−10.4634	−0.526471
$396$	8.70889	0.437638
$397$	−6.71173	−0.336852	−0.168426	−	0.985714i	$-0.553868\pi$
$397$	−6.71173	−0.336852	−0.168426	+	0.985714i	$0.553868\pi$
$398$	5.41079	0.271218
$399$	0	0
$400$	10.9503	0.547515
$401$	−3.68773	−0.184157	−0.0920783	−	0.995752i	$-0.529351\pi$
$401$	−3.68773	−0.184157	−0.0920783	+	0.995752i	$0.529351\pi$
$402$	5.14579	0.256648
$403$	16.0011	0.797074
$404$	−27.6543	−1.37585
$405$	−0.889988	−0.0442239
$406$	0	0
$407$	−38.1704	−1.89204
$408$	−9.35740	−0.463260
$409$	6.90268	0.341316	0.170658	−	0.985330i	$-0.445411\pi$
$409$	6.90268	0.341316	0.170658	+	0.985330i	$0.445411\pi$
$410$	1.89809	0.0937398
$411$	4.57666	0.225750
$412$	7.97544	0.392922
$413$	0	0
$414$	3.35702	0.164988
$415$	3.58756	0.176107
$416$	49.2883	2.41656
$417$	−14.6408	−0.716961
$418$	0.531970	0.0260195
$419$	−7.45445	−0.364174	−0.182087	−	0.983282i	$-0.558285\pi$
$419$	−7.45445	−0.364174	−0.182087	+	0.983282i	$0.558285\pi$
$420$	0	0
$421$	7.74992	0.377708	0.188854	−	0.982005i	$-0.439523\pi$
$421$	7.74992	0.377708	0.188854	+	0.982005i	$0.439523\pi$
$422$	−49.3002	−2.39989
$423$	−1.59757	−0.0776766
$424$	10.7139	0.520312
$425$	33.6632	1.63290
$426$	18.9468	0.917976
$427$	0	0
$428$	8.55594	0.413567
$429$	−21.3497	−1.03077
$430$	11.7161	0.565001
$431$	8.87444	0.427467	0.213733	−	0.976892i	$-0.431438\pi$
$431$	8.87444	0.427467	0.213733	+	0.976892i	$0.431438\pi$
$432$	−2.60231	−0.125204
$433$	15.3304	0.736734	0.368367	−	0.929681i	$-0.379917\pi$
$433$	15.3304	0.736734	0.368367	+	0.929681i	$0.379917\pi$
$434$	0	0
$435$	0.673578	0.0322956
$436$	1.02929	0.0492941
$437$	0.114892	0.00549604
$438$	−7.76522	−0.371037
$439$	−27.4686	−1.31100	−0.655501	−	0.755194i	$-0.727543\pi$
$439$	−27.4686	−1.31100	−0.655501	+	0.755194i	$0.727543\pi$
$440$	−3.55745	−0.169595
$441$	0	0
$442$	106.592	5.07005
$443$	−1.87494	−0.0890811	−0.0445406	−	0.999008i	$-0.514182\pi$
$443$	−1.87494	−0.0890811	−0.0445406	+	0.999008i	$0.514182\pi$
$444$	−28.4653	−1.35090
$445$	−7.51770	−0.356373
$446$	0.511062	0.0241995
$447$	2.31277	0.109390
$448$	0	0
$449$	29.4978	1.39209	0.696043	−	0.718001i	$-0.254942\pi$
$449$	29.4978	1.39209	0.696043	+	0.718001i	$0.254942\pi$
$450$	−8.97427	−0.423051
$451$	−3.41733	−0.160916
$452$	13.8604	0.651940
$453$	1.08733	0.0510872
$454$	7.89449	0.370507
$455$	0	0
$456$	0.0853761	0.00399810
$457$	30.2742	1.41617	0.708084	−	0.706129i	$-0.249560\pi$
$457$	30.2742	1.41617	0.708084	+	0.706129i	$0.249560\pi$
$458$	−13.3475	−0.623689
$459$	−7.99996	−0.373406
$460$	−3.57011	−0.166457
$461$	−23.7455	−1.10594	−0.552968	−	0.833202i	$-0.686505\pi$
$461$	−23.7455	−1.10594	−0.552968	+	0.833202i	$0.686505\pi$
$462$	0	0
$463$	−21.6384	−1.00562	−0.502811	−	0.864396i	$-0.667701\pi$
$463$	−21.6384	−1.00562	−0.502811	+	0.864396i	$0.667701\pi$
$464$	1.96953	0.0914330
$465$	2.27945	0.105707
$466$	−54.6946	−2.53368
$467$	−4.37189	−0.202307	−0.101153	−	0.994871i	$-0.532253\pi$
$467$	−4.37189	−0.202307	−0.101153	+	0.994871i	$0.532253\pi$
$468$	−15.9214	−0.735965
$469$	0	0
$470$	3.03233	0.139871
$471$	−24.5214	−1.12989
$472$	1.07572	0.0495142
$473$	−21.0938	−0.969894
$474$	25.0738	1.15168
$475$	−0.307140	−0.0140925
$476$	0	0
$477$	9.15967	0.419392
$478$	−37.9287	−1.73482
$479$	−16.5420	−0.755824	−0.377912	−	0.925842i	$-0.623358\pi$
$479$	−16.5420	−0.755824	−0.377912	+	0.925842i	$0.623358\pi$
$480$	7.02141	0.320482
$481$	69.7821	3.18179
$482$	16.2953	0.742232
$483$	0	0
$484$	1.72820	0.0785547
$485$	−8.06034	−0.366001
$486$	2.13271	0.0967417
$487$	−21.6708	−0.981998	−0.490999	−	0.871160i	$-0.663368\pi$
$487$	−21.6708	−0.981998	−0.490999	+	0.871160i	$0.663368\pi$
$488$	9.96396	0.451047
$489$	−20.7325	−0.937557
$490$	0	0
$491$	2.65513	0.119824	0.0599121	−	0.998204i	$-0.480918\pi$
$491$	2.65513	0.119824	0.0599121	+	0.998204i	$0.480918\pi$
$492$	−2.54845	−0.114893
$493$	6.05468	0.272689
$494$	−0.972533	−0.0437563
$495$	−3.04138	−0.136700
$496$	6.66508	0.299271
$497$	0	0
$498$	−8.59700	−0.385241
$499$	−3.67247	−0.164402	−0.0822012	−	0.996616i	$-0.526195\pi$
$499$	−3.67247	−0.164402	−0.0822012	+	0.996616i	$0.526195\pi$
$500$	20.8844	0.933978
$501$	9.83140	0.439234
$502$	−4.29272	−0.191594
$503$	23.5718	1.05101	0.525506	−	0.850790i	$-0.323876\pi$
$503$	23.5718	1.05101	0.525506	+	0.850790i	$0.323876\pi$
$504$	0	0
$505$	9.65766	0.429760
$506$	11.4720	0.509994
$507$	26.0309	1.15607
$508$	−13.1475	−0.583326
$509$	−34.8559	−1.54496	−0.772481	−	0.635037i	$-0.780985\pi$
$509$	−34.8559	−1.54496	−0.772481	+	0.635037i	$0.780985\pi$
$510$	15.1846	0.672386
$511$	0	0
$512$	26.6182	1.17637
$513$	0.0729909	0.00322263
$514$	−13.3009	−0.586677
$515$	−2.78524	−0.122733
$516$	−15.7305	−0.692498
$517$	−5.45943	−0.240105
$518$	0	0
$519$	−19.3348	−0.848702
$520$	6.50363	0.285203
$521$	39.0969	1.71287	0.856434	−	0.516257i	$-0.172675\pi$
$521$	39.0969	1.71287	0.856434	+	0.516257i	$0.172675\pi$
$522$	−1.61412	−0.0706480
$523$	−10.0083	−0.437632	−0.218816	−	0.975766i	$-0.570219\pi$
$523$	−10.0083	−0.437632	−0.218816	+	0.975766i	$0.570219\pi$
$524$	−30.3882	−1.32752
$525$	0	0
$526$	−17.3577	−0.756831
$527$	20.4896	0.892543
$528$	−8.89294	−0.387016
$529$	−20.5223	−0.892275
$530$	−17.3858	−0.755192
$531$	0.919674	0.0399104
$532$	0	0
$533$	6.24747	0.270608
$534$	18.0149	0.779582
$535$	−2.98797	−0.129181
$536$	2.82220	0.121900
$537$	16.3998	0.707702
$538$	54.7453	2.36024
$539$	0	0
$540$	−2.26809	−0.0976030
$541$	22.2218	0.955390	0.477695	−	0.878526i	$-0.341472\pi$
$541$	22.2218	0.955390	0.477695	+	0.878526i	$0.341472\pi$
$542$	64.0450	2.75097
$543$	−16.4233	−0.704790
$544$	63.1143	2.70600
$545$	−0.359457	−0.0153974
$546$	0	0
$547$	26.4397	1.13048	0.565240	−	0.824927i	$-0.308784\pi$
$547$	26.4397	1.13048	0.565240	+	0.824927i	$0.308784\pi$
$548$	11.6634	0.498235
$549$	8.51853	0.363562
$550$	−30.6680	−1.30769
$551$	−0.0552424	−0.00235340
$552$	1.84115	0.0783645
$553$	0	0
$554$	−21.9421	−0.932232
$555$	9.94086	0.421966
$556$	−37.3112	−1.58235
$557$	25.7136	1.08952	0.544759	−	0.838593i	$-0.316621\pi$
$557$	25.7136	1.08952	0.544759	+	0.838593i	$0.316621\pi$
$558$	−5.46234	−0.231239
$559$	38.5631	1.63105
$560$	0	0
$561$	−27.3385	−1.15423
$562$	25.5580	1.07810
$563$	31.4548	1.32566	0.662830	−	0.748770i	$-0.269355\pi$
$563$	31.4548	1.32566	0.662830	+	0.748770i	$0.269355\pi$
$564$	−4.07133	−0.171434
$565$	−4.84045	−0.203639
$566$	32.5322	1.36743
$567$	0	0
$568$	10.3913	0.436011
$569$	−26.4186	−1.10752	−0.553762	−	0.832675i	$-0.686808\pi$
$569$	−26.4186	−1.10752	−0.553762	+	0.832675i	$0.686808\pi$
$570$	−0.138543	−0.00580293
$571$	4.76235	0.199298	0.0996491	−	0.995023i	$-0.468228\pi$
$571$	4.76235	0.199298	0.0996491	+	0.995023i	$0.468228\pi$
$572$	−54.4085	−2.27493
$573$	−25.9485	−1.08402
$574$	0	0
$575$	−6.62353	−0.276220
$576$	−11.6210	−0.484209
$577$	−7.27641	−0.302921	−0.151460	−	0.988463i	$-0.548398\pi$
$577$	−7.27641	−0.302921	−0.151460	+	0.988463i	$0.548398\pi$
$578$	100.236	4.16926
$579$	26.2201	1.08967
$580$	1.71658	0.0712770
$581$	0	0
$582$	19.3153	0.800644
$583$	31.3016	1.29638
$584$	−4.25882	−0.176231
$585$	5.56017	0.229885
$586$	62.3211	2.57446
$587$	1.48111	0.0611320	0.0305660	−	0.999533i	$-0.490269\pi$
$587$	1.48111	0.0611320	0.0305660	+	0.999533i	$0.490269\pi$
$588$	0	0
$589$	−0.186946	−0.00770296
$590$	−1.74562	−0.0718660
$591$	5.03749	0.207215
$592$	29.0669	1.19464
$593$	0.770893	0.0316568	0.0158284	−	0.999875i	$-0.494961\pi$
$593$	0.770893	0.0316568	0.0158284	+	0.999875i	$0.494961\pi$
$594$	7.28817	0.299037
$595$	0	0
$596$	5.89398	0.241427
$597$	2.53705	0.103835
$598$	−20.9729	−0.857644
$599$	2.95056	0.120557	0.0602783	−	0.998182i	$-0.480801\pi$
$599$	2.95056	0.120557	0.0602783	+	0.998182i	$0.480801\pi$
$600$	−4.92193	−0.200937
$601$	−14.1523	−0.577285	−0.288642	−	0.957437i	$-0.593204\pi$
$601$	−14.1523	−0.577285	−0.288642	+	0.957437i	$0.593204\pi$
$602$	0	0
$603$	2.41279	0.0982565
$604$	2.77100	0.112751
$605$	−0.603536	−0.0245372
$606$	−23.1430	−0.940119
$607$	−39.5171	−1.60395	−0.801975	−	0.597358i	$-0.796217\pi$
$607$	−39.5171	−1.60395	−0.801975	+	0.597358i	$0.796217\pi$
$608$	−0.575849	−0.0233538
$609$	0	0
$610$	−16.1689	−0.654660
$611$	9.98078	0.403779
$612$	−20.3875	−0.824115
$613$	41.8648	1.69091	0.845453	−	0.534050i	$-0.179331\pi$
$613$	41.8648	1.69091	0.845453	+	0.534050i	$0.179331\pi$
$614$	59.1599	2.38750
$615$	0.889988	0.0358878
$616$	0	0
$617$	24.9542	1.00462	0.502310	−	0.864688i	$-0.332484\pi$
$617$	24.9542	1.00462	0.502310	+	0.864688i	$0.332484\pi$
$618$	6.67438	0.268483
$619$	−5.05747	−0.203277	−0.101638	−	0.994821i	$-0.532408\pi$
$619$	−5.05747	−0.203277	−0.101638	+	0.994821i	$0.532408\pi$
$620$	5.80907	0.233298
$621$	1.57406	0.0631649
$622$	29.1929	1.17053
$623$	0	0
$624$	16.2578	0.650834
$625$	13.7462	0.549848
$626$	−45.6996	−1.82652
$627$	0.249434	0.00996143
$628$	−62.4916	−2.49369
$629$	89.3568	3.56289
$630$	0	0
$631$	−16.8805	−0.672000	−0.336000	−	0.941862i	$-0.609074\pi$
$631$	−16.8805	−0.672000	−0.336000	+	0.941862i	$0.609074\pi$
$632$	13.7517	0.547013
$633$	−23.1162	−0.918787
$634$	−58.9289	−2.34037
$635$	4.59147	0.182207
$636$	23.3429	0.925608
$637$	0	0
$638$	−5.51597	−0.218379
$639$	8.88392	0.351442
$640$	8.01489	0.316816
$641$	−32.4571	−1.28198	−0.640990	−	0.767549i	$-0.721476\pi$
$641$	−32.4571	−1.28198	−0.640990	+	0.767549i	$0.721476\pi$
$642$	7.16017	0.282590
$643$	−32.8318	−1.29476	−0.647381	−	0.762167i	$-0.724136\pi$
$643$	−32.8318	−1.29476	−0.647381	+	0.762167i	$0.724136\pi$
$644$	0	0
$645$	5.49354	0.216308
$646$	−1.24534	−0.0489973
$647$	7.44564	0.292718	0.146359	−	0.989232i	$-0.453245\pi$
$647$	7.44564	0.292718	0.146359	+	0.989232i	$0.453245\pi$
$648$	1.16968	0.0459494
$649$	3.14283	0.123367
$650$	56.0665	2.19911
$651$	0	0
$652$	−52.8357	−2.06921
$653$	−14.6003	−0.571353	−0.285676	−	0.958326i	$-0.592218\pi$
$653$	−14.6003	−0.571353	−0.285676	+	0.958326i	$0.592218\pi$
$654$	0.861378	0.0336826
$655$	10.6124	0.414661
$656$	2.60231	0.101603
$657$	−3.64101	−0.142049
$658$	0	0
$659$	7.79447	0.303629	0.151815	−	0.988409i	$-0.451488\pi$
$659$	7.79447	0.303629	0.151815	+	0.988409i	$0.451488\pi$
$660$	−7.75081	−0.301700
$661$	−13.7123	−0.533345	−0.266673	−	0.963787i	$-0.585924\pi$
$661$	−13.7123	−0.533345	−0.266673	+	0.963787i	$0.585924\pi$
$662$	−37.3849	−1.45301
$663$	49.9795	1.94104
$664$	−4.71501	−0.182978
$665$	0	0
$666$	−23.8216	−0.923069
$667$	−1.19131	−0.0461278
$668$	25.0548	0.969400
$669$	0.239630	0.00926464
$670$	−4.57969	−0.176929
$671$	29.1106	1.12380
$672$	0	0
$673$	−31.7957	−1.22563	−0.612817	−	0.790225i	$-0.709964\pi$
$673$	−31.7957	−1.22563	−0.612817	+	0.790225i	$0.709964\pi$
$674$	28.3953	1.09375
$675$	−4.20792	−0.161963
$676$	66.3384	2.55148
$677$	15.6921	0.603095	0.301547	−	0.953451i	$-0.402497\pi$
$677$	15.6921	0.603095	0.301547	+	0.953451i	$0.402497\pi$
$678$	11.5993	0.445469
$679$	0	0
$680$	8.32798	0.319363
$681$	3.70162	0.141847
$682$	−18.6666	−0.714781
$683$	−45.4953	−1.74083	−0.870415	−	0.492320i	$-0.836149\pi$
$683$	−45.4953	−1.74083	−0.870415	+	0.492320i	$0.836149\pi$
$684$	0.186014	0.00711241
$685$	−4.07317	−0.155628
$686$	0	0
$687$	−6.25848	−0.238776
$688$	16.0630	0.612396
$689$	−57.2247	−2.18009
$690$	−2.98770	−0.113740
$691$	33.1928	1.26271	0.631356	−	0.775493i	$-0.282499\pi$
$691$	33.1928	1.26271	0.631356	+	0.775493i	$0.282499\pi$
$692$	−49.2737	−1.87310
$693$	0	0
$694$	−8.35077	−0.316991
$695$	13.0301	0.494260
$696$	−0.885260	−0.0335557
$697$	7.99996	0.303020
$698$	42.9918	1.62726
$699$	−25.6456	−0.970006
$700$	0	0
$701$	17.9370	0.677470	0.338735	−	0.940882i	$-0.390001\pi$
$701$	17.9370	0.677470	0.338735	+	0.940882i	$0.390001\pi$
$702$	−13.3240	−0.502883
$703$	−0.815283	−0.0307490
$704$	−39.7129	−1.49674
$705$	1.42182	0.0535488
$706$	−44.2078	−1.66378
$707$	0	0
$708$	2.34374	0.0880832
$709$	−19.7437	−0.741492	−0.370746	−	0.928734i	$-0.620898\pi$
$709$	−19.7437	−0.741492	−0.370746	+	0.928734i	$0.620898\pi$
$710$	−16.8624	−0.632836
$711$	11.7568	0.440914
$712$	9.88026	0.370278
$713$	−4.03152	−0.150981
$714$	0	0
$715$	19.0009	0.710595
$716$	41.7940	1.56191
$717$	−17.7843	−0.664167
$718$	−74.0381	−2.76308
$719$	−42.0245	−1.56725	−0.783625	−	0.621234i	$-0.786632\pi$
$719$	−42.0245	−1.56725	−0.783625	+	0.621234i	$0.786632\pi$
$720$	2.31602	0.0863131
$721$	0	0
$722$	−40.5101	−1.50763
$723$	7.64067	0.284160
$724$	−41.8539	−1.55549
$725$	3.18472	0.118277
$726$	1.44627	0.0536763
$727$	32.6634	1.21142	0.605709	−	0.795686i	$-0.292890\pi$
$727$	32.6634	1.21142	0.605709	+	0.795686i	$0.292890\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	6.91095	0.255786
$731$	49.3805	1.82640
$732$	21.7090	0.802389
$733$	36.1097	1.33374	0.666870	−	0.745174i	$-0.267634\pi$
$733$	36.1097	1.33374	0.666870	+	0.745174i	$0.267634\pi$
$734$	49.0087	1.80894
$735$	0	0
$736$	−12.4183	−0.457744
$737$	8.24531	0.303720
$738$	−2.13271	−0.0785061
$739$	26.6713	0.981118	0.490559	−	0.871408i	$-0.336793\pi$
$739$	26.6713	0.981118	0.490559	+	0.871408i	$0.336793\pi$
$740$	25.3338	0.931288
$741$	−0.456008	−0.0167519
$742$	0	0
$743$	−32.0519	−1.17587	−0.587935	−	0.808908i	$-0.700059\pi$
$743$	−32.0519	−1.17587	−0.587935	+	0.808908i	$0.700059\pi$
$744$	−2.99581	−0.109832
$745$	−2.05834	−0.0754117
$746$	20.3715	0.745853
$747$	−4.03102	−0.147487
$748$	−69.6707	−2.54741
$749$	0	0
$750$	17.4774	0.638185
$751$	11.2233	0.409545	0.204772	−	0.978810i	$-0.434355\pi$
$751$	11.2233	0.409545	0.204772	+	0.978810i	$0.434355\pi$
$752$	4.15737	0.151604
$753$	−2.01280	−0.0733506
$754$	10.0842	0.367243
$755$	−0.967711	−0.0352186
$756$	0	0
$757$	−11.3051	−0.410890	−0.205445	−	0.978669i	$-0.565864\pi$
$757$	−11.3051	−0.410890	−0.205445	+	0.978669i	$0.565864\pi$
$758$	−35.4097	−1.28614
$759$	5.37909	0.195248
$760$	−0.0759837	−0.00275622
$761$	14.9745	0.542826	0.271413	−	0.962463i	$-0.412509\pi$
$761$	14.9745	0.542826	0.271413	+	0.962463i	$0.412509\pi$
$762$	−11.0027	−0.398586
$763$	0	0
$764$	−66.1285	−2.39245
$765$	7.11987	0.257419
$766$	−79.9898	−2.89015
$767$	−5.74563	−0.207463
$768$	4.03570	0.145626
$769$	−29.8781	−1.07743	−0.538716	−	0.842487i	$-0.681090\pi$
$769$	−29.8781	−1.07743	−0.538716	+	0.842487i	$0.681090\pi$
$770$	0	0
$771$	−6.23662	−0.224606
$772$	66.8207	2.40493
$773$	6.39402	0.229977	0.114989	−	0.993367i	$-0.463317\pi$
$773$	6.39402	0.229977	0.114989	+	0.993367i	$0.463317\pi$
$774$	−13.1644	−0.473183
$775$	10.7774	0.387136
$776$	10.5934	0.380282
$777$	0	0
$778$	−3.17786	−0.113932
$779$	−0.0729909	−0.00261517
$780$	14.1698	0.507361
$781$	30.3593	1.08634
$782$	−26.8560	−0.960368
$783$	−0.756839	−0.0270472
$784$	0	0
$785$	21.8238	0.778924
$786$	−25.4309	−0.907089
$787$	40.7910	1.45404	0.727021	−	0.686615i	$-0.240904\pi$
$787$	40.7910	1.45404	0.727021	+	0.686615i	$0.240904\pi$
$788$	12.8378	0.457327
$789$	−8.13880	−0.289749
$790$	−22.3154	−0.793947
$791$	0	0
$792$	3.99719	0.142034
$793$	−53.2193	−1.88987
$794$	−14.3142	−0.507991
$795$	−8.15199	−0.289121
$796$	6.46554	0.229165
$797$	−33.0669	−1.17129	−0.585645	−	0.810567i	$-0.699159\pi$
$797$	−33.0669	−1.17129	−0.585645	+	0.810567i	$0.699159\pi$
$798$	0	0
$799$	12.7805	0.452142
$800$	33.1977	1.17371
$801$	8.44697	0.298459
$802$	−7.86486	−0.277718
$803$	−12.4425	−0.439088
$804$	6.14888	0.216854
$805$	0	0
$806$	34.1258	1.20203
$807$	25.6694	0.903604
$808$	−12.6927	−0.446529
$809$	9.54220	0.335486	0.167743	−	0.985831i	$-0.446352\pi$
$809$	9.54220	0.335486	0.167743	+	0.985831i	$0.446352\pi$
$810$	−1.89809	−0.0666919
$811$	2.64941	0.0930333	0.0465166	−	0.998918i	$-0.485188\pi$
$811$	2.64941	0.0930333	0.0465166	+	0.998918i	$0.485188\pi$
$812$	0	0
$813$	30.0299	1.05319
$814$	−81.4063	−2.85329
$815$	18.4517	0.646334
$816$	20.8184	0.728788
$817$	−0.450543	−0.0157625
$818$	14.7214	0.514722
$819$	0	0
$820$	2.26809	0.0792051
$821$	39.2366	1.36937	0.684683	−	0.728841i	$-0.259941\pi$
$821$	39.2366	1.36937	0.684683	+	0.728841i	$0.259941\pi$
$822$	9.76068	0.340443
$823$	−46.2425	−1.61191	−0.805956	−	0.591976i	$-0.798348\pi$
$823$	−46.2425	−1.61191	−0.805956	+	0.591976i	$0.798348\pi$
$824$	3.66055	0.127521
$825$	−14.3799	−0.500642
$826$	0	0
$827$	19.5022	0.678158	0.339079	−	0.940758i	$-0.389885\pi$
$827$	19.5022	0.678158	0.339079	+	0.940758i	$0.389885\pi$
$828$	4.01141	0.139406
$829$	−8.56705	−0.297546	−0.148773	−	0.988871i	$-0.547532\pi$
$829$	−8.56705	−0.297546	−0.148773	+	0.988871i	$0.547532\pi$
$830$	7.65123	0.265578
$831$	−10.2884	−0.356900
$832$	72.6020	2.51702
$833$	0	0
$834$	−31.2245	−1.08121
$835$	−8.74983	−0.302800
$836$	0.635670	0.0219851
$837$	−2.56122	−0.0885287
$838$	−15.8982	−0.549193
$839$	−43.6287	−1.50623	−0.753115	−	0.657888i	$-0.771450\pi$
$839$	−43.6287	−1.50623	−0.753115	+	0.657888i	$0.771450\pi$
$840$	0	0
$841$	−28.4272	−0.980248
$842$	16.5283	0.569603
$843$	11.9838	0.412744
$844$	−58.9105	−2.02778
$845$	−23.1672	−0.796975
$846$	−3.40716	−0.117140
$847$	0	0
$848$	−23.8363	−0.818541
$849$	15.2539	0.523514
$850$	71.7938	2.46251
$851$	−17.5817	−0.602694
$852$	22.6402	0.775641
$853$	3.06449	0.104926	0.0524630	−	0.998623i	$-0.483293\pi$
$853$	3.06449	0.104926	0.0524630	+	0.998623i	$0.483293\pi$
$854$	0	0
$855$	−0.0649610	−0.00222162
$856$	3.92699	0.134222
$857$	10.5860	0.361610	0.180805	−	0.983519i	$-0.442130\pi$
$857$	10.5860	0.361610	0.180805	+	0.983519i	$0.442130\pi$
$858$	−45.5326	−1.55446
$859$	7.65853	0.261306	0.130653	−	0.991428i	$-0.458293\pi$
$859$	7.65853	0.261306	0.130653	+	0.991428i	$0.458293\pi$
$860$	14.0000	0.477396
$861$	0	0
$862$	18.9266	0.644642
$863$	4.80094	0.163426	0.0817129	−	0.996656i	$-0.473961\pi$
$863$	4.80094	0.163426	0.0817129	+	0.996656i	$0.473961\pi$
$864$	−7.88933	−0.268400
$865$	17.2077	0.585080
$866$	32.6954	1.11103
$867$	46.9993	1.59618
$868$	0	0
$869$	40.1768	1.36291
$870$	1.43655	0.0487035
$871$	−15.0739	−0.510758
$872$	0.472422	0.0159982
$873$	9.05668	0.306522
$874$	0.245032	0.00828832
$875$	0	0
$876$	−9.27893	−0.313506
$877$	−52.0697	−1.75827	−0.879135	−	0.476573i	$-0.841879\pi$
$877$	−52.0697	−1.75827	−0.879135	+	0.476573i	$0.841879\pi$
$878$	−58.5824	−1.97706
$879$	29.2216	0.985619
$880$	7.91461	0.266802
$881$	17.6360	0.594171	0.297085	−	0.954851i	$-0.403985\pi$
$881$	17.6360	0.594171	0.297085	+	0.954851i	$0.403985\pi$
$882$	0	0
$883$	12.2941	0.413731	0.206866	−	0.978369i	$-0.433674\pi$
$883$	12.2941	0.413731	0.206866	+	0.978369i	$0.433674\pi$
$884$	127.370	4.28392
$885$	−0.818499	−0.0275135
$886$	−3.99870	−0.134339
$887$	41.9487	1.40850	0.704251	−	0.709952i	$-0.251283\pi$
$887$	41.9487	1.40850	0.704251	+	0.709952i	$0.251283\pi$
$888$	−13.0649	−0.438430
$889$	0	0
$890$	−16.0331	−0.537430
$891$	3.41733	0.114485
$892$	0.610685	0.0204473
$893$	−0.116608	−0.00390215
$894$	4.93247	0.164966
$895$	−14.5956	−0.487877
$896$	0	0
$897$	−9.83390	−0.328344
$898$	62.9101	2.09934
$899$	1.93843	0.0646503
$900$	−10.7237	−0.357456
$901$	−73.2769	−2.44121
$902$	−7.28817	−0.242670
$903$	0	0
$904$	6.36163	0.211585
$905$	14.6165	0.485870
$906$	2.31896	0.0770422
$907$	−0.531208	−0.0176385	−0.00881923	−	0.999961i	$-0.502807\pi$
$907$	−0.531208	−0.0176385	−0.00881923	+	0.999961i	$0.502807\pi$
$908$	9.43340	0.313058
$909$	−10.8514	−0.359920
$910$	0	0
$911$	−19.0477	−0.631078	−0.315539	−	0.948913i	$-0.602185\pi$
$911$	−19.0477	−0.631078	−0.315539	+	0.948913i	$0.602185\pi$
$912$	−0.189945	−0.00628970
$913$	−13.7753	−0.455897
$914$	64.5661	2.13566
$915$	−7.58139	−0.250633
$916$	−15.9494	−0.526984
$917$	0	0
$918$	−17.0616	−0.563116
$919$	9.06567	0.299049	0.149524	−	0.988758i	$-0.452226\pi$
$919$	9.06567	0.299049	0.149524	+	0.988758i	$0.452226\pi$
$920$	−1.63860	−0.0540231
$921$	27.7393	0.914042
$922$	−50.6422	−1.66781
$923$	−55.5020	−1.82687
$924$	0	0
$925$	47.0010	1.54538
$926$	−46.1484	−1.51653
$927$	3.12953	0.102787
$928$	5.97095	0.196006
$929$	9.91561	0.325321	0.162660	−	0.986682i	$-0.447993\pi$
$929$	9.91561	0.325321	0.162660	+	0.986682i	$0.447993\pi$
$930$	4.86141	0.159412
$931$	0	0
$932$	−65.3565	−2.14082
$933$	13.6882	0.448131
$934$	−9.32397	−0.305090
$935$	24.3309	0.795707
$936$	−7.30755	−0.238855
$937$	−22.9798	−0.750718	−0.375359	−	0.926879i	$-0.622481\pi$
$937$	−22.9798	−0.750718	−0.375359	+	0.926879i	$0.622481\pi$
$938$	0	0
$939$	−21.4280	−0.699275
$940$	3.62344	0.118183
$941$	−13.1179	−0.427630	−0.213815	−	0.976874i	$-0.568589\pi$
$941$	−13.1179	−0.427630	−0.213815	+	0.976874i	$0.568589\pi$
$942$	−52.2971	−1.70393
$943$	−1.57406	−0.0512585
$944$	−2.39327	−0.0778944
$945$	0	0
$946$	−44.9869	−1.46265
$947$	−27.6733	−0.899262	−0.449631	−	0.893214i	$-0.648445\pi$
$947$	−27.6733	−0.899262	−0.449631	+	0.893214i	$0.648445\pi$
$948$	29.9616	0.973107
$949$	22.7471	0.738403
$950$	−0.655040	−0.0212523
$951$	−27.6310	−0.895997
$952$	0	0
$953$	−14.5017	−0.469757	−0.234878	−	0.972025i	$-0.575469\pi$
$953$	−14.5017	−0.469757	−0.234878	+	0.972025i	$0.575469\pi$
$954$	19.5349	0.632466
$955$	23.0939	0.747301
$956$	−45.3224	−1.46583
$957$	−2.58637	−0.0836054
$958$	−35.2793	−1.13982
$959$	0	0
$960$	10.3426	0.333805
$961$	−24.4402	−0.788392
$962$	148.825	4.79831
$963$	3.35731	0.108188
$964$	19.4719	0.627146
$965$	−23.3356	−0.751200
$966$	0	0
$967$	−4.81409	−0.154811	−0.0774054	−	0.997000i	$-0.524664\pi$
$967$	−4.81409	−0.154811	−0.0774054	+	0.997000i	$0.524664\pi$
$968$	0.793207	0.0254946
$969$	−0.583924	−0.0187583
$970$	−17.1904	−0.551949
$971$	56.7999	1.82279	0.911397	−	0.411527i	$-0.135005\pi$
$971$	56.7999	1.82279	0.911397	+	0.411527i	$0.135005\pi$
$972$	2.54845	0.0817415
$973$	0	0
$974$	−46.2175	−1.48090
$975$	26.2889	0.841917
$976$	−22.1678	−0.709575
$977$	26.0244	0.832595	0.416297	−	0.909229i	$-0.363328\pi$
$977$	26.0244	0.832595	0.416297	+	0.909229i	$0.363328\pi$
$978$	−44.2164	−1.41389
$979$	28.8661	0.922564
$980$	0	0
$981$	0.403889	0.0128952
$982$	5.66261	0.180701
$983$	−59.1340	−1.88608	−0.943041	−	0.332677i	$-0.892048\pi$
$983$	−59.1340	−1.88608	−0.943041	+	0.332677i	$0.892048\pi$
$984$	−1.16968	−0.0372881
$985$	−4.48331	−0.142850
$986$	12.9129	0.411230
$987$	0	0
$988$	−1.16211	−0.0369718
$989$	−9.71604	−0.308952
$990$	−6.48638	−0.206151
$991$	41.2982	1.31188	0.655941	−	0.754812i	$-0.272272\pi$
$991$	41.2982	1.31188	0.655941	+	0.754812i	$0.272272\pi$
$992$	20.2063	0.641550
$993$	−17.5293	−0.556276
$994$	0	0
$995$	−2.25794	−0.0715817
$996$	−10.2729	−0.325508
$997$	12.4930	0.395657	0.197828	−	0.980237i	$-0.436611\pi$
$997$	12.4930	0.395657	0.197828	+	0.980237i	$0.436611\pi$
$998$	−7.83231	−0.247927
$999$	−11.1697	−0.353392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bk.1.13		14
7.3	odd	6		861.2.i.g.247.2	✓	28
7.5	odd	6		861.2.i.g.739.2	yes	28
7.6	odd	2		6027.2.a.bj.1.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.g.247.2	✓	28	7.3	odd	6
861.2.i.g.739.2	yes	28	7.5	odd	6
6027.2.a.bj.1.13		14	7.6	odd	2
6027.2.a.bk.1.13		14	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)

\(f(q)\)	\(=\)	\(q+2.13271 q^{2} +1.00000 q^{3} +2.54845 q^{4} -0.889988 q^{5} +2.13271 q^{6} +1.16968 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.13271 q^{2} +1.00000 q^{3} +2.54845 q^{4} -0.889988 q^{5} +2.13271 q^{6} +1.16968 q^{8} +1.00000 q^{9} -1.89809 q^{10} +3.41733 q^{11} +2.54845 q^{12} -6.24747 q^{13} -0.889988 q^{15} -2.60231 q^{16} -7.99996 q^{17} +2.13271 q^{18} +0.0729909 q^{19} -2.26809 q^{20} +7.28817 q^{22} +1.57406 q^{23} +1.16968 q^{24} -4.20792 q^{25} -13.3240 q^{26} +1.00000 q^{27} -0.756839 q^{29} -1.89809 q^{30} -2.56122 q^{31} -7.88933 q^{32} +3.41733 q^{33} -17.0616 q^{34} +2.54845 q^{36} -11.1697 q^{37} +0.155668 q^{38} -6.24747 q^{39} -1.04100 q^{40} -1.00000 q^{41} -6.17260 q^{43} +8.70889 q^{44} -0.889988 q^{45} +3.35702 q^{46} -1.59757 q^{47} -2.60231 q^{48} -8.97427 q^{50} -7.99996 q^{51} -15.9214 q^{52} +9.15967 q^{53} +2.13271 q^{54} -3.04138 q^{55} +0.0729909 q^{57} -1.61412 q^{58} +0.919674 q^{59} -2.26809 q^{60} +8.51853 q^{61} -5.46234 q^{62} -11.6210 q^{64} +5.56017 q^{65} +7.28817 q^{66} +2.41279 q^{67} -20.3875 q^{68} +1.57406 q^{69} +8.88392 q^{71} +1.16968 q^{72} -3.64101 q^{73} -23.8216 q^{74} -4.20792 q^{75} +0.186014 q^{76} -13.3240 q^{78} +11.7568 q^{79} +2.31602 q^{80} +1.00000 q^{81} -2.13271 q^{82} -4.03102 q^{83} +7.11987 q^{85} -13.1644 q^{86} -0.756839 q^{87} +3.99719 q^{88} +8.44697 q^{89} -1.89809 q^{90} +4.01141 q^{92} -2.56122 q^{93} -3.40716 q^{94} -0.0649610 q^{95} -7.88933 q^{96} +9.05668 q^{97} +3.41733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9} - 3 q^{10} - 16 q^{11} + 14 q^{12} - 21 q^{13} - 10 q^{15} + 22 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 40 q^{20} + q^{22} - 7 q^{23} - 6 q^{24} + 22 q^{25} - 2 q^{26} + 14 q^{27} - 16 q^{29} - 3 q^{30} - 8 q^{31} - 19 q^{32} - 16 q^{33} - 33 q^{34} + 14 q^{36} + q^{37} - 32 q^{38} - 21 q^{39} + 13 q^{40} - 14 q^{41} + 14 q^{43} - 36 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} + 22 q^{48} - q^{50} - 12 q^{51} - 60 q^{52} - 20 q^{53} - 2 q^{54} + 11 q^{55} - 2 q^{57} + 21 q^{58} - 25 q^{59} - 40 q^{60} - 26 q^{61} + 33 q^{62} + 42 q^{64} - 8 q^{65} + q^{66} - 22 q^{67} - 15 q^{68} - 7 q^{69} - 36 q^{71} - 6 q^{72} - 31 q^{73} - 65 q^{74} + 22 q^{75} + 2 q^{76} - 2 q^{78} + 12 q^{79} - 112 q^{80} + 14 q^{81} + 2 q^{82} - 20 q^{83} + 40 q^{85} - 9 q^{86} - 16 q^{87} - 54 q^{88} - 39 q^{89} - 3 q^{90} + 63 q^{92} - 8 q^{93} - 14 q^{94} - 55 q^{95} - 19 q^{96} - 18 q^{97} - 16 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9 - 3 * q^10 - 16 * q^11 + 14 * q^12 - 21 * q^13 - 10 * q^15 + 22 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 40 * q^20 + q^22 - 7 * q^23 - 6 * q^24 + 22 * q^25 - 2 * q^26 + 14 * q^27 - 16 * q^29 - 3 * q^30 - 8 * q^31 - 19 * q^32 - 16 * q^33 - 33 * q^34 + 14 * q^36 + q^37 - 32 * q^38 - 21 * q^39 + 13 * q^40 - 14 * q^41 + 14 * q^43 - 36 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 + 22 * q^48 - q^50 - 12 * q^51 - 60 * q^52 - 20 * q^53 - 2 * q^54 + 11 * q^55 - 2 * q^57 + 21 * q^58 - 25 * q^59 - 40 * q^60 - 26 * q^61 + 33 * q^62 + 42 * q^64 - 8 * q^65 + q^66 - 22 * q^67 - 15 * q^68 - 7 * q^69 - 36 * q^71 - 6 * q^72 - 31 * q^73 - 65 * q^74 + 22 * q^75 + 2 * q^76 - 2 * q^78 + 12 * q^79 - 112 * q^80 + 14 * q^81 + 2 * q^82 - 20 * q^83 + 40 * q^85 - 9 * q^86 - 16 * q^87 - 54 * q^88 - 39 * q^89 - 3 * q^90 + 63 * q^92 - 8 * q^93 - 14 * q^94 - 55 * q^95 - 19 * q^96 - 18 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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