LMFDB - Embedded newform 6027.2.a.bk.1.6

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			1.6
Root			$0.766034$ 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)

$f(q)$	$=$	$q-0.766034 q^{2} +1.00000 q^{3} -1.41319 q^{4} +0.561773 q^{5} -0.766034 q^{6} +2.61462 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.766034 q^{2} +1.00000 q^{3} -1.41319 q^{4} +0.561773 q^{5} -0.766034 q^{6} +2.61462 q^{8} +1.00000 q^{9} -0.430337 q^{10} -3.11111 q^{11} -1.41319 q^{12} +5.92656 q^{13} +0.561773 q^{15} +0.823497 q^{16} +3.15286 q^{17} -0.766034 q^{18} -0.142324 q^{19} -0.793894 q^{20} +2.38321 q^{22} -4.62821 q^{23} +2.61462 q^{24} -4.68441 q^{25} -4.53994 q^{26} +1.00000 q^{27} -8.30868 q^{29} -0.430337 q^{30} -0.336298 q^{31} -5.86007 q^{32} -3.11111 q^{33} -2.41520 q^{34} -1.41319 q^{36} -9.44997 q^{37} +0.109025 q^{38} +5.92656 q^{39} +1.46882 q^{40} -1.00000 q^{41} +9.28869 q^{43} +4.39659 q^{44} +0.561773 q^{45} +3.54537 q^{46} -7.35790 q^{47} +0.823497 q^{48} +3.58842 q^{50} +3.15286 q^{51} -8.37537 q^{52} -8.42111 q^{53} -0.766034 q^{54} -1.74774 q^{55} -0.142324 q^{57} +6.36473 q^{58} +0.911205 q^{59} -0.793894 q^{60} -3.48407 q^{61} +0.257615 q^{62} +2.84201 q^{64} +3.32938 q^{65} +2.38321 q^{66} -0.537448 q^{67} -4.45560 q^{68} -4.62821 q^{69} -0.835931 q^{71} +2.61462 q^{72} +8.54657 q^{73} +7.23899 q^{74} -4.68441 q^{75} +0.201131 q^{76} -4.53994 q^{78} -10.4527 q^{79} +0.462619 q^{80} +1.00000 q^{81} +0.766034 q^{82} -5.99692 q^{83} +1.77119 q^{85} -7.11545 q^{86} -8.30868 q^{87} -8.13436 q^{88} +18.7260 q^{89} -0.430337 q^{90} +6.54056 q^{92} -0.336298 q^{93} +5.63640 q^{94} -0.0799537 q^{95} -5.86007 q^{96} +10.9913 q^{97} -3.11111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.766034	−0.541668	−0.270834	−	0.962626i	$-0.587299\pi$
$2$	−0.766034	−0.541668	−0.270834	+	0.962626i	$0.587299\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.41319	−0.706596
$5$	0.561773	0.251233	0.125616	−	0.992079i	$-0.459909\pi$
$5$	0.561773	0.251233	0.125616	+	0.992079i	$0.459909\pi$
$6$	−0.766034	−0.312732
$7$	0	0
$7$	0	0
$8$	2.61462	0.924408
$9$	1.00000	0.333333
$10$	−0.430337	−0.136085
$11$	−3.11111	−0.938034	−0.469017	−	0.883189i	$-0.655392\pi$
$11$	−3.11111	−0.938034	−0.469017	+	0.883189i	$0.655392\pi$
$12$	−1.41319	−0.407953
$13$	5.92656	1.64373	0.821866	−	0.569681i	$-0.192933\pi$
$13$	5.92656	1.64373	0.821866	+	0.569681i	$0.192933\pi$
$14$	0	0
$15$	0.561773	0.145049
$16$	0.823497	0.205874
$17$	3.15286	0.764681	0.382341	−	0.924021i	$-0.375118\pi$
$17$	3.15286	0.764681	0.382341	+	0.924021i	$0.375118\pi$
$18$	−0.766034	−0.180556
$19$	−0.142324	−0.0326513	−0.0163256	−	0.999867i	$-0.505197\pi$
$19$	−0.142324	−0.0326513	−0.0163256	+	0.999867i	$0.505197\pi$
$20$	−0.793894	−0.177520
$21$	0	0
$22$	2.38321	0.508102
$23$	−4.62821	−0.965049	−0.482525	−	0.875882i	$-0.660280\pi$
$23$	−4.62821	−0.965049	−0.482525	+	0.875882i	$0.660280\pi$
$24$	2.61462	0.533707
$25$	−4.68441	−0.936882
$26$	−4.53994	−0.890356
$27$	1.00000	0.192450
$28$	0	0
$29$	−8.30868	−1.54288	−0.771442	−	0.636300i	$-0.780464\pi$
$29$	−8.30868	−1.54288	−0.771442	+	0.636300i	$0.780464\pi$
$30$	−0.430337	−0.0785685
$31$	−0.336298	−0.0604008	−0.0302004	−	0.999544i	$-0.509615\pi$
$31$	−0.336298	−0.0604008	−0.0302004	+	0.999544i	$0.509615\pi$
$32$	−5.86007	−1.03592
$33$	−3.11111	−0.541574
$34$	−2.41520	−0.414203
$35$	0	0
$36$	−1.41319	−0.235532
$37$	−9.44997	−1.55356	−0.776782	−	0.629769i	$-0.783150\pi$
$37$	−9.44997	−1.55356	−0.776782	+	0.629769i	$0.783150\pi$
$38$	0.109025	0.0176861
$39$	5.92656	0.949009
$40$	1.46882	0.232242
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	9.28869	1.41651	0.708256	−	0.705956i	$-0.249482\pi$
$43$	9.28869	1.41651	0.708256	+	0.705956i	$0.249482\pi$
$44$	4.39659	0.662811
$45$	0.561773	0.0837442
$46$	3.54537	0.522736
$47$	−7.35790	−1.07326	−0.536630	−	0.843818i	$-0.680303\pi$
$47$	−7.35790	−1.07326	−0.536630	+	0.843818i	$0.680303\pi$
$48$	0.823497	0.118862
$49$	0	0
$50$	3.58842	0.507479
$51$	3.15286	0.441489
$52$	−8.37537	−1.16145
$53$	−8.42111	−1.15673	−0.578364	−	0.815779i	$-0.696309\pi$
$53$	−8.42111	−1.15673	−0.578364	+	0.815779i	$0.696309\pi$
$54$	−0.766034	−0.104244
$55$	−1.74774	−0.235665
$56$	0	0
$57$	−0.142324	−0.0188512
$58$	6.36473	0.835730
$59$	0.911205	0.118629	0.0593144	−	0.998239i	$-0.481109\pi$
$59$	0.911205	0.118629	0.0593144	+	0.998239i	$0.481109\pi$
$60$	−0.793894	−0.102491
$61$	−3.48407	−0.446090	−0.223045	−	0.974808i	$-0.571600\pi$
$61$	−3.48407	−0.446090	−0.223045	+	0.974808i	$0.571600\pi$
$62$	0.257615	0.0327172
$63$	0	0
$64$	2.84201	0.355252
$65$	3.32938	0.412959
$66$	2.38321	0.293353
$67$	−0.537448	−0.0656597	−0.0328298	−	0.999461i	$-0.510452\pi$
$67$	−0.537448	−0.0656597	−0.0328298	+	0.999461i	$0.510452\pi$
$68$	−4.45560	−0.540321
$69$	−4.62821	−0.557172
$70$	0	0
$71$	−0.835931	−0.0992067	−0.0496034	−	0.998769i	$-0.515796\pi$
$71$	−0.835931	−0.0992067	−0.0496034	+	0.998769i	$0.515796\pi$
$72$	2.61462	0.308136
$73$	8.54657	1.00030	0.500150	−	0.865939i	$-0.333278\pi$
$73$	8.54657	1.00030	0.500150	+	0.865939i	$0.333278\pi$
$74$	7.23899	0.841516
$75$	−4.68441	−0.540909
$76$	0.201131	0.0230713
$77$	0	0
$78$	−4.53994	−0.514047
$79$	−10.4527	−1.17602	−0.588010	−	0.808854i	$-0.700088\pi$
$79$	−10.4527	−1.17602	−0.588010	+	0.808854i	$0.700088\pi$
$80$	0.462619	0.0517224
$81$	1.00000	0.111111
$82$	0.766034	0.0845943
$83$	−5.99692	−0.658248	−0.329124	−	0.944287i	$-0.606753\pi$
$83$	−5.99692	−0.658248	−0.329124	+	0.944287i	$0.606753\pi$
$84$	0	0
$85$	1.77119	0.192113
$86$	−7.11545	−0.767279
$87$	−8.30868	−0.890784
$88$	−8.13436	−0.867126
$89$	18.7260	1.98495	0.992474	−	0.122457i	$-0.0390774\pi$
$89$	18.7260	1.98495	0.992474	+	0.122457i	$0.0390774\pi$
$90$	−0.430337	−0.0453615
$91$	0	0
$92$	6.54056	0.681900
$93$	−0.336298	−0.0348724
$94$	5.63640	0.581350
$95$	−0.0799537	−0.00820307
$96$	−5.86007	−0.598091
$97$	10.9913	1.11599	0.557996	−	0.829843i	$-0.311570\pi$
$97$	10.9913	1.11599	0.557996	+	0.829843i	$0.311570\pi$
$98$	0	0
$99$	−3.11111	−0.312678
$100$	6.61997	0.661997
$101$	0.288673	0.0287241	0.0143620	−	0.999897i	$-0.495428\pi$
$101$	0.288673	0.0287241	0.0143620	+	0.999897i	$0.495428\pi$
$102$	−2.41520	−0.239140
$103$	15.6537	1.54241	0.771205	−	0.636587i	$-0.219655\pi$
$103$	15.6537	1.54241	0.771205	+	0.636587i	$0.219655\pi$
$104$	15.4957	1.51948
$105$	0	0
$106$	6.45086	0.626562
$107$	11.0431	1.06758	0.533790	−	0.845617i	$-0.320767\pi$
$107$	11.0431	1.06758	0.533790	+	0.845617i	$0.320767\pi$
$108$	−1.41319	−0.135984
$109$	−16.4108	−1.57187	−0.785934	−	0.618311i	$-0.787817\pi$
$109$	−16.4108	−1.57187	−0.785934	+	0.618311i	$0.787817\pi$
$110$	1.33883	0.127652
$111$	−9.44997	−0.896951
$112$	0	0
$113$	8.10161	0.762136	0.381068	−	0.924547i	$-0.375556\pi$
$113$	8.10161	0.762136	0.381068	+	0.924547i	$0.375556\pi$
$114$	0.109025	0.0102111
$115$	−2.60001	−0.242452
$116$	11.7418	1.09020
$117$	5.92656	0.547910
$118$	−0.698014	−0.0642574
$119$	0	0
$120$	1.46882	0.134085
$121$	−1.32102	−0.120093
$122$	2.66892	0.241632
$123$	−1.00000	−0.0901670
$124$	0.475253	0.0426790
$125$	−5.44045	−0.486608
$126$	0	0
$127$	−13.5484	−1.20223	−0.601113	−	0.799164i	$-0.705276\pi$
$127$	−13.5484	−1.20223	−0.601113	+	0.799164i	$0.705276\pi$
$128$	9.54306	0.843495
$129$	9.28869	0.817824
$130$	−2.55042	−0.223687
$131$	17.4438	1.52407	0.762037	−	0.647533i	$-0.224199\pi$
$131$	17.4438	1.52407	0.762037	+	0.647533i	$0.224199\pi$
$132$	4.39659	0.382674
$133$	0	0
$134$	0.411703	0.0355657
$135$	0.561773	0.0483498
$136$	8.24354	0.706877
$137$	−20.2741	−1.73214	−0.866069	−	0.499925i	$-0.833361\pi$
$137$	−20.2741	−1.73214	−0.866069	+	0.499925i	$0.833361\pi$
$138$	3.54537	0.301802
$139$	−9.45159	−0.801674	−0.400837	−	0.916149i	$-0.631281\pi$
$139$	−9.45159	−0.801674	−0.400837	+	0.916149i	$0.631281\pi$
$140$	0	0
$141$	−7.35790	−0.619647
$142$	0.640351	0.0537371
$143$	−18.4381	−1.54188
$144$	0.823497	0.0686248
$145$	−4.66760	−0.387623
$146$	−6.54696	−0.541830
$147$	0	0
$148$	13.3546	1.09774
$149$	−19.7136	−1.61500	−0.807501	−	0.589866i	$-0.799181\pi$
$149$	−19.7136	−1.61500	−0.807501	+	0.589866i	$0.799181\pi$
$150$	3.58842	0.292993
$151$	19.6751	1.60114	0.800570	−	0.599240i	$-0.204530\pi$
$151$	19.6751	1.60114	0.800570	+	0.599240i	$0.204530\pi$
$152$	−0.372122	−0.0301831
$153$	3.15286	0.254894
$154$	0	0
$155$	−0.188923	−0.0151747
$156$	−8.37537	−0.670566
$157$	−16.7932	−1.34025	−0.670123	−	0.742250i	$-0.733759\pi$
$157$	−16.7932	−1.34025	−0.670123	+	0.742250i	$0.733759\pi$
$158$	8.00712	0.637012
$159$	−8.42111	−0.667838
$160$	−3.29203	−0.260258
$161$	0	0
$162$	−0.766034	−0.0601853
$163$	−2.83566	−0.222106	−0.111053	−	0.993814i	$-0.535422\pi$
$163$	−2.83566	−0.222106	−0.111053	+	0.993814i	$0.535422\pi$
$164$	1.41319	0.110352
$165$	−1.74774	−0.136061
$166$	4.59384	0.356551
$167$	6.23667	0.482608	0.241304	−	0.970450i	$-0.422425\pi$
$167$	6.23667	0.482608	0.241304	+	0.970450i	$0.422425\pi$
$168$	0	0
$169$	22.1241	1.70185
$170$	−1.35679	−0.104061
$171$	−0.142324	−0.0108838
$172$	−13.1267	−1.00090
$173$	−24.1412	−1.83542	−0.917709	−	0.397252i	$-0.869964\pi$
$173$	−24.1412	−1.83542	−0.917709	+	0.397252i	$0.869964\pi$
$174$	6.36473	0.482509
$175$	0	0
$176$	−2.56199	−0.193117
$177$	0.911205	0.0684903
$178$	−14.3447	−1.07518
$179$	−14.3311	−1.07116	−0.535580	−	0.844485i	$-0.679907\pi$
$179$	−14.3311	−1.07116	−0.535580	+	0.844485i	$0.679907\pi$
$180$	−0.793894	−0.0591734
$181$	−7.16449	−0.532532	−0.266266	−	0.963900i	$-0.585790\pi$
$181$	−7.16449	−0.532532	−0.266266	+	0.963900i	$0.585790\pi$
$182$	0	0
$183$	−3.48407	−0.257550
$184$	−12.1010	−0.892099
$185$	−5.30874	−0.390306
$186$	0.257615	0.0188893
$187$	−9.80888	−0.717297
$188$	10.3981	0.758361
$189$	0	0
$190$	0.0612472	0.00444334
$191$	−17.8171	−1.28920	−0.644601	−	0.764519i	$-0.722976\pi$
$191$	−17.8171	−1.28920	−0.644601	+	0.764519i	$0.722976\pi$
$192$	2.84201	0.205105
$193$	17.8976	1.28830	0.644150	−	0.764899i	$-0.277211\pi$
$193$	17.8976	1.28830	0.644150	+	0.764899i	$0.277211\pi$
$194$	−8.41967	−0.604497
$195$	3.32938	0.238422
$196$	0	0
$197$	−1.27454	−0.0908069	−0.0454034	−	0.998969i	$-0.514457\pi$
$197$	−1.27454	−0.0908069	−0.0454034	+	0.998969i	$0.514457\pi$
$198$	2.38321	0.169367
$199$	−26.9626	−1.91133	−0.955666	−	0.294454i	$-0.904862\pi$
$199$	−26.9626	−1.91133	−0.955666	+	0.294454i	$0.904862\pi$
$200$	−12.2480	−0.866061
$201$	−0.537448	−0.0379086
$202$	−0.221134	−0.0155589
$203$	0	0
$204$	−4.45560	−0.311954
$205$	−0.561773	−0.0392360
$206$	−11.9913	−0.835473
$207$	−4.62821	−0.321683
$208$	4.88050	0.338402
$209$	0.442784	0.0306280
$210$	0	0
$211$	−8.25353	−0.568196	−0.284098	−	0.958795i	$-0.591694\pi$
$211$	−8.25353	−0.568196	−0.284098	+	0.958795i	$0.591694\pi$
$212$	11.9006	0.817340
$213$	−0.835931	−0.0572770
$214$	−8.45942	−0.578274
$215$	5.21814	0.355874
$216$	2.61462	0.177902
$217$	0	0
$218$	12.5712	0.851430
$219$	8.54657	0.577524
$220$	2.46989	0.166520
$221$	18.6856	1.25693
$222$	7.23899	0.485849
$223$	9.94467	0.665944	0.332972	−	0.942937i	$-0.391948\pi$
$223$	9.94467	0.665944	0.332972	+	0.942937i	$0.391948\pi$
$224$	0	0
$225$	−4.68441	−0.312294
$226$	−6.20611	−0.412824
$227$	−8.59955	−0.570772	−0.285386	−	0.958413i	$-0.592122\pi$
$227$	−8.59955	−0.570772	−0.285386	+	0.958413i	$0.592122\pi$
$228$	0.201131	0.0133202
$229$	−7.01808	−0.463768	−0.231884	−	0.972743i	$-0.574489\pi$
$229$	−7.01808	−0.463768	−0.231884	+	0.972743i	$0.574489\pi$
$230$	1.99169	0.131328
$231$	0	0
$232$	−21.7240	−1.42625
$233$	0.664006	0.0435005	0.0217502	−	0.999763i	$-0.493076\pi$
$233$	0.664006	0.0435005	0.0217502	+	0.999763i	$0.493076\pi$
$234$	−4.53994	−0.296785
$235$	−4.13347	−0.269638
$236$	−1.28771	−0.0838226
$237$	−10.4527	−0.678975
$238$	0	0
$239$	3.89087	0.251679	0.125840	−	0.992051i	$-0.459837\pi$
$239$	3.89087	0.251679	0.125840	+	0.992051i	$0.459837\pi$
$240$	0.462619	0.0298619
$241$	−1.93117	−0.124398	−0.0621989	−	0.998064i	$-0.519811\pi$
$241$	−1.93117	−0.124398	−0.0621989	+	0.998064i	$0.519811\pi$
$242$	1.01195	0.0650505
$243$	1.00000	0.0641500
$244$	4.92366	0.315205
$245$	0	0
$246$	0.766034	0.0488405
$247$	−0.843490	−0.0536700
$248$	−0.879290	−0.0558350
$249$	−5.99692	−0.380039
$250$	4.16756	0.263580
$251$	19.7811	1.24857	0.624285	−	0.781197i	$-0.285390\pi$
$251$	19.7811	1.24857	0.624285	+	0.781197i	$0.285390\pi$
$252$	0	0
$253$	14.3989	0.905249
$254$	10.3785	0.651207
$255$	1.77119	0.110916
$256$	−12.9943	−0.812146
$257$	−10.8991	−0.679866	−0.339933	−	0.940450i	$-0.610404\pi$
$257$	−10.8991	−0.679866	−0.339933	+	0.940450i	$0.610404\pi$
$258$	−7.11545	−0.442989
$259$	0	0
$260$	−4.70506	−0.291795
$261$	−8.30868	−0.514294
$262$	−13.3626	−0.825542
$263$	−12.8647	−0.793268	−0.396634	−	0.917977i	$-0.629822\pi$
$263$	−12.8647	−0.793268	−0.396634	+	0.917977i	$0.629822\pi$
$264$	−8.13436	−0.500635
$265$	−4.73076	−0.290608
$266$	0	0
$267$	18.7260	1.14601
$268$	0.759517	0.0463949
$269$	1.49766	0.0913140	0.0456570	−	0.998957i	$-0.485462\pi$
$269$	1.49766	0.0913140	0.0456570	+	0.998957i	$0.485462\pi$
$270$	−0.430337	−0.0261895
$271$	−16.3381	−0.992466	−0.496233	−	0.868189i	$-0.665284\pi$
$271$	−16.3381	−0.992466	−0.496233	+	0.868189i	$0.665284\pi$
$272$	2.59637	0.157428
$273$	0	0
$274$	15.5307	0.938243
$275$	14.5737	0.878827
$276$	6.54056	0.393695
$277$	0.682460	0.0410051	0.0205025	−	0.999790i	$-0.493473\pi$
$277$	0.682460	0.0410051	0.0205025	+	0.999790i	$0.493473\pi$
$278$	7.24024	0.434241
$279$	−0.336298	−0.0201336
$280$	0	0
$281$	−18.5463	−1.10638	−0.553190	−	0.833055i	$-0.686590\pi$
$281$	−18.5463	−1.10638	−0.553190	+	0.833055i	$0.686590\pi$
$282$	5.63640	0.335643
$283$	−6.11849	−0.363707	−0.181853	−	0.983326i	$-0.558210\pi$
$283$	−6.11849	−0.363707	−0.181853	+	0.983326i	$0.558210\pi$
$284$	1.18133	0.0700991
$285$	−0.0799537	−0.00473605
$286$	14.1242	0.835184
$287$	0	0
$288$	−5.86007	−0.345308
$289$	−7.05946	−0.415263
$290$	3.57554	0.209963
$291$	10.9913	0.644319
$292$	−12.0779	−0.706808
$293$	−24.0482	−1.40491	−0.702456	−	0.711727i	$-0.747913\pi$
$293$	−24.0482	−1.40491	−0.702456	+	0.711727i	$0.747913\pi$
$294$	0	0
$295$	0.511891	0.0298034
$296$	−24.7081	−1.43613
$297$	−3.11111	−0.180525
$298$	15.1013	0.874795
$299$	−27.4294	−1.58628
$300$	6.61997	0.382204
$301$	0	0
$302$	−15.0718	−0.867286
$303$	0.288673	0.0165839
$304$	−0.117203	−0.00672206
$305$	−1.95726	−0.112072
$306$	−2.41520	−0.138068
$307$	24.2257	1.38263	0.691317	−	0.722551i	$-0.257031\pi$
$307$	24.2257	1.38263	0.691317	+	0.722551i	$0.257031\pi$
$308$	0	0
$309$	15.6537	0.890510
$310$	0.144721	0.00821962
$311$	17.6804	1.00257	0.501283	−	0.865284i	$-0.332862\pi$
$311$	17.6804	1.00257	0.501283	+	0.865284i	$0.332862\pi$
$312$	15.4957	0.877271
$313$	22.0256	1.24496	0.622480	−	0.782635i	$-0.286125\pi$
$313$	22.0256	1.24496	0.622480	+	0.782635i	$0.286125\pi$
$314$	12.8642	0.725968
$315$	0	0
$316$	14.7717	0.830971
$317$	3.06800	0.172316	0.0861579	−	0.996281i	$-0.472541\pi$
$317$	3.06800	0.172316	0.0861579	+	0.996281i	$0.472541\pi$
$318$	6.45086	0.361746
$319$	25.8492	1.44728
$320$	1.59657	0.0892509
$321$	11.0431	0.616368
$322$	0	0
$323$	−0.448727	−0.0249678
$324$	−1.41319	−0.0785107
$325$	−27.7624	−1.53998
$326$	2.17221	0.120308
$327$	−16.4108	−0.907518
$328$	−2.61462	−0.144368
$329$	0	0
$330$	1.33883	0.0736999
$331$	−25.9353	−1.42553	−0.712765	−	0.701403i	$-0.752558\pi$
$331$	−25.9353	−1.42553	−0.712765	+	0.701403i	$0.752558\pi$
$332$	8.47480	0.465115
$333$	−9.44997	−0.517855
$334$	−4.77750	−0.261413
$335$	−0.301924	−0.0164959
$336$	0	0
$337$	23.2651	1.26733	0.633666	−	0.773606i	$-0.281549\pi$
$337$	23.2651	1.26733	0.633666	+	0.773606i	$0.281549\pi$
$338$	−16.9478	−0.921839
$339$	8.10161	0.440019
$340$	−2.50304	−0.135746
$341$	1.04626	0.0566580
$342$	0.109025	0.00589538
$343$	0	0
$344$	24.2864	1.30943
$345$	−2.60001	−0.139980
$346$	18.4929	0.994187
$347$	−3.95967	−0.212566	−0.106283	−	0.994336i	$-0.533895\pi$
$347$	−3.95967	−0.212566	−0.106283	+	0.994336i	$0.533895\pi$
$348$	11.7418	0.629425
$349$	−21.7095	−1.16209	−0.581043	−	0.813873i	$-0.697355\pi$
$349$	−21.7095	−1.16209	−0.581043	+	0.813873i	$0.697355\pi$
$350$	0	0
$351$	5.92656	0.316336
$352$	18.2313	0.971731
$353$	4.27161	0.227355	0.113677	−	0.993518i	$-0.463737\pi$
$353$	4.27161	0.227355	0.113677	+	0.993518i	$0.463737\pi$
$354$	−0.698014	−0.0370990
$355$	−0.469604	−0.0249240
$356$	−26.4634	−1.40256
$357$	0	0
$358$	10.9781	0.580212
$359$	−2.51480	−0.132726	−0.0663631	−	0.997796i	$-0.521140\pi$
$359$	−2.51480	−0.132726	−0.0663631	+	0.997796i	$0.521140\pi$
$360$	1.46882	0.0774138
$361$	−18.9797	−0.998934
$362$	5.48824	0.288455
$363$	−1.32102	−0.0693358
$364$	0	0
$365$	4.80124	0.251308
$366$	2.66892	0.139506
$367$	7.53136	0.393134	0.196567	−	0.980490i	$-0.437021\pi$
$367$	7.53136	0.393134	0.196567	+	0.980490i	$0.437021\pi$
$368$	−3.81132	−0.198679
$369$	−1.00000	−0.0520579
$370$	4.06667	0.211416
$371$	0	0
$372$	0.475253	0.0246407
$373$	30.3545	1.57170	0.785849	−	0.618419i	$-0.212226\pi$
$373$	30.3545	1.57170	0.785849	+	0.618419i	$0.212226\pi$
$374$	7.51394	0.388536
$375$	−5.44045	−0.280943
$376$	−19.2381	−0.992130
$377$	−49.2419	−2.53609
$378$	0	0
$379$	13.9206	0.715054	0.357527	−	0.933903i	$-0.383620\pi$
$379$	13.9206	0.715054	0.357527	+	0.933903i	$0.383620\pi$
$380$	0.112990	0.00579626
$381$	−13.5484	−0.694106
$382$	13.6485	0.698319
$383$	−12.3726	−0.632209	−0.316104	−	0.948724i	$-0.602375\pi$
$383$	−12.3726	−0.632209	−0.316104	+	0.948724i	$0.602375\pi$
$384$	9.54306	0.486992
$385$	0	0
$386$	−13.7102	−0.697831
$387$	9.28869	0.472171
$388$	−15.5328	−0.788556
$389$	−21.3306	−1.08151	−0.540753	−	0.841182i	$-0.681860\pi$
$389$	−21.3306	−1.08151	−0.540753	+	0.841182i	$0.681860\pi$
$390$	−2.55042	−0.129146
$391$	−14.5921	−0.737955
$392$	0	0
$393$	17.4438	0.879925
$394$	0.976337	0.0491871
$395$	−5.87205	−0.295455
$396$	4.39659	0.220937
$397$	−32.1083	−1.61147	−0.805736	−	0.592275i	$-0.798230\pi$
$397$	−32.1083	−1.61147	−0.805736	+	0.592275i	$0.798230\pi$
$398$	20.6543	1.03531
$399$	0	0
$400$	−3.85760	−0.192880
$401$	11.0839	0.553503	0.276751	−	0.960942i	$-0.410742\pi$
$401$	11.0839	0.553503	0.276751	+	0.960942i	$0.410742\pi$
$402$	0.411703	0.0205339
$403$	−1.99309	−0.0992827
$404$	−0.407951	−0.0202963
$405$	0.561773	0.0279147
$406$	0	0
$407$	29.3998	1.45730
$408$	8.24354	0.408116
$409$	−14.2017	−0.702229	−0.351114	−	0.936333i	$-0.614197\pi$
$409$	−14.2017	−0.702229	−0.351114	+	0.936333i	$0.614197\pi$
$410$	0.430337	0.0212529
$411$	−20.2741	−1.00005
$412$	−22.1217	−1.08986
$413$	0	0
$414$	3.54537	0.174245
$415$	−3.36891	−0.165373
$416$	−34.7300	−1.70278
$417$	−9.45159	−0.462846
$418$	−0.339187	−0.0165902
$419$	−17.9651	−0.877654	−0.438827	−	0.898572i	$-0.644606\pi$
$419$	−17.9651	−0.877654	−0.438827	+	0.898572i	$0.644606\pi$
$420$	0	0
$421$	15.4655	0.753741	0.376871	−	0.926266i	$-0.377000\pi$
$421$	15.4655	0.753741	0.376871	+	0.926266i	$0.377000\pi$
$422$	6.32248	0.307774
$423$	−7.35790	−0.357753
$424$	−22.0180	−1.06929
$425$	−14.7693	−0.716416
$426$	0.640351	0.0310251
$427$	0	0
$428$	−15.6061	−0.754348
$429$	−18.4381	−0.890202
$430$	−3.99727	−0.192766
$431$	10.7203	0.516378	0.258189	−	0.966094i	$-0.416874\pi$
$431$	10.7203	0.516378	0.258189	+	0.966094i	$0.416874\pi$
$432$	0.823497	0.0396205
$433$	17.0262	0.818228	0.409114	−	0.912483i	$-0.365838\pi$
$433$	17.0262	0.818228	0.409114	+	0.912483i	$0.365838\pi$
$434$	0	0
$435$	−4.66760	−0.223794
$436$	23.1916	1.11068
$437$	0.658705	0.0315101
$438$	−6.54696	−0.312826
$439$	−9.07115	−0.432942	−0.216471	−	0.976289i	$-0.569455\pi$
$439$	−9.07115	−0.432942	−0.216471	+	0.976289i	$0.569455\pi$
$440$	−4.56967	−0.217850
$441$	0	0
$442$	−14.3138	−0.680839
$443$	19.4595	0.924548	0.462274	−	0.886737i	$-0.347034\pi$
$443$	19.4595	0.924548	0.462274	+	0.886737i	$0.347034\pi$
$444$	13.3546	0.633782
$445$	10.5197	0.498684
$446$	−7.61795	−0.360721
$447$	−19.7136	−0.932422
$448$	0	0
$449$	−26.9820	−1.27336	−0.636680	−	0.771129i	$-0.719693\pi$
$449$	−26.9820	−1.27336	−0.636680	+	0.771129i	$0.719693\pi$
$450$	3.58842	0.169160
$451$	3.11111	0.146496
$452$	−11.4491	−0.538522
$453$	19.6751	0.924418
$454$	6.58755	0.309169
$455$	0	0
$456$	−0.372122	−0.0174262
$457$	−5.46329	−0.255562	−0.127781	−	0.991802i	$-0.540785\pi$
$457$	−5.46329	−0.255562	−0.127781	+	0.991802i	$0.540785\pi$
$458$	5.37609	0.251208
$459$	3.15286	0.147163
$460$	3.67431	0.171316
$461$	−37.0737	−1.72669	−0.863347	−	0.504610i	$-0.831636\pi$
$461$	−37.0737	−1.72669	−0.863347	+	0.504610i	$0.831636\pi$
$462$	0	0
$463$	24.7212	1.14889	0.574446	−	0.818542i	$-0.305217\pi$
$463$	24.7212	1.14889	0.574446	+	0.818542i	$0.305217\pi$
$464$	−6.84218	−0.317640
$465$	−0.188923	−0.00876110
$466$	−0.508651	−0.0235628
$467$	14.3275	0.662999	0.331499	−	0.943455i	$-0.392446\pi$
$467$	14.3275	0.662999	0.331499	+	0.943455i	$0.392446\pi$
$468$	−8.37537	−0.387151
$469$	0	0
$470$	3.16638	0.146054
$471$	−16.7932	−0.773792
$472$	2.38245	0.109661
$473$	−28.8981	−1.32874
$474$	8.00712	0.367779
$475$	0.666703	0.0305904
$476$	0	0
$477$	−8.42111	−0.385576
$478$	−2.98054	−0.136327
$479$	27.6827	1.26485	0.632427	−	0.774620i	$-0.282059\pi$
$479$	27.6827	1.26485	0.632427	+	0.774620i	$0.282059\pi$
$480$	−3.29203	−0.150260
$481$	−56.0058	−2.55364
$482$	1.47934	0.0673823
$483$	0	0
$484$	1.86686	0.0848573
$485$	6.17459	0.280374
$486$	−0.766034	−0.0347480
$487$	9.78574	0.443434	0.221717	−	0.975111i	$-0.428834\pi$
$487$	9.78574	0.443434	0.221717	+	0.975111i	$0.428834\pi$
$488$	−9.10952	−0.412369
$489$	−2.83566	−0.128233
$490$	0	0
$491$	−23.0245	−1.03908	−0.519541	−	0.854445i	$-0.673897\pi$
$491$	−23.0245	−1.03908	−0.519541	+	0.854445i	$0.673897\pi$
$492$	1.41319	0.0637116
$493$	−26.1961	−1.17981
$494$	0.646141	0.0290713
$495$	−1.74774	−0.0785549
$496$	−0.276940	−0.0124350
$497$	0	0
$498$	4.59384	0.205855
$499$	26.0648	1.16682	0.583410	−	0.812178i	$-0.301718\pi$
$499$	26.0648	1.16682	0.583410	+	0.812178i	$0.301718\pi$
$500$	7.68840	0.343835
$501$	6.23667	0.278634
$502$	−15.1530	−0.676310
$503$	5.13546	0.228979	0.114489	−	0.993424i	$-0.463477\pi$
$503$	5.13546	0.228979	0.114489	+	0.993424i	$0.463477\pi$
$504$	0	0
$505$	0.162169	0.00721643
$506$	−11.0300	−0.490344
$507$	22.1241	0.982565
$508$	19.1465	0.849488
$509$	24.5525	1.08827	0.544135	−	0.838997i	$-0.316858\pi$
$509$	24.5525	1.08827	0.544135	+	0.838997i	$0.316858\pi$
$510$	−1.35679	−0.0600799
$511$	0	0
$512$	−9.13201	−0.403582
$513$	−0.142324	−0.00628374
$514$	8.34906	0.368261
$515$	8.79386	0.387504
$516$	−13.1267	−0.577871
$517$	22.8912	1.00675
$518$	0	0
$519$	−24.1412	−1.05968
$520$	8.70507	0.381743
$521$	1.40704	0.0616437	0.0308219	−	0.999525i	$-0.490188\pi$
$521$	1.40704	0.0616437	0.0308219	+	0.999525i	$0.490188\pi$
$522$	6.36473	0.278577
$523$	4.67309	0.204340	0.102170	−	0.994767i	$-0.467421\pi$
$523$	4.67309	0.204340	0.102170	+	0.994767i	$0.467421\pi$
$524$	−24.6515	−1.07691
$525$	0	0
$526$	9.85476	0.429688
$527$	−1.06030	−0.0461874
$528$	−2.56199	−0.111496
$529$	−1.57963	−0.0686795
$530$	3.62392	0.157413
$531$	0.911205	0.0395429
$532$	0	0
$533$	−5.92656	−0.256708
$534$	−14.3447	−0.620757
$535$	6.20374	0.268211
$536$	−1.40522	−0.0606963
$537$	−14.3311	−0.618434
$538$	−1.14726	−0.0494619
$539$	0	0
$540$	−0.793894	−0.0341638
$541$	34.9134	1.50105	0.750523	−	0.660844i	$-0.229802\pi$
$541$	34.9134	1.50105	0.750523	+	0.660844i	$0.229802\pi$
$542$	12.5155	0.537587
$543$	−7.16449	−0.307458
$544$	−18.4760	−0.792151
$545$	−9.21914	−0.394904
$546$	0	0
$547$	12.6091	0.539128	0.269564	−	0.962982i	$-0.413120\pi$
$547$	12.6091	0.539128	0.269564	+	0.962982i	$0.413120\pi$
$548$	28.6513	1.22392
$549$	−3.48407	−0.148697
$550$	−11.1639	−0.476032
$551$	1.18252	0.0503771
$552$	−12.1010	−0.515054
$553$	0	0
$554$	−0.522788	−0.0222111
$555$	−5.30874	−0.225343
$556$	13.3569	0.566460
$557$	11.4906	0.486872	0.243436	−	0.969917i	$-0.421725\pi$
$557$	11.4906	0.486872	0.243436	+	0.969917i	$0.421725\pi$
$558$	0.257615	0.0109057
$559$	55.0500	2.32837
$560$	0	0
$561$	−9.80888	−0.414131
$562$	14.2071	0.599290
$563$	−7.94311	−0.334762	−0.167381	−	0.985892i	$-0.553531\pi$
$563$	−7.94311	−0.334762	−0.167381	+	0.985892i	$0.553531\pi$
$564$	10.3981	0.437840
$565$	4.55127	0.191473
$566$	4.68697	0.197008
$567$	0	0
$568$	−2.18564	−0.0917075
$569$	−20.4591	−0.857688	−0.428844	−	0.903379i	$-0.641079\pi$
$569$	−20.4591	−0.857688	−0.428844	+	0.903379i	$0.641079\pi$
$570$	0.0612472	0.00256536
$571$	24.9522	1.04422	0.522108	−	0.852879i	$-0.325146\pi$
$571$	24.9522	1.04422	0.522108	+	0.852879i	$0.325146\pi$
$572$	26.0566	1.08948
$573$	−17.8171	−0.744321
$574$	0	0
$575$	21.6805	0.904138
$576$	2.84201	0.118417
$577$	5.42180	0.225712	0.112856	−	0.993611i	$-0.464000\pi$
$577$	5.42180	0.225712	0.112856	+	0.993611i	$0.464000\pi$
$578$	5.40779	0.224934
$579$	17.8976	0.743801
$580$	6.59621	0.273893
$581$	0	0
$582$	−8.41967	−0.349007
$583$	26.1990	1.08505
$584$	22.3460	0.924686
$585$	3.32938	0.137653
$586$	18.4217	0.760995
$587$	−3.53886	−0.146064	−0.0730322	−	0.997330i	$-0.523268\pi$
$587$	−3.53886	−0.146064	−0.0730322	+	0.997330i	$0.523268\pi$
$588$	0	0
$589$	0.0478631	0.00197217
$590$	−0.392126	−0.0161436
$591$	−1.27454	−0.0524274
$592$	−7.78202	−0.319839
$593$	−6.19628	−0.254451	−0.127225	−	0.991874i	$-0.540607\pi$
$593$	−6.19628	−0.254451	−0.127225	+	0.991874i	$0.540607\pi$
$594$	2.38321	0.0977844
$595$	0	0
$596$	27.8591	1.14115
$597$	−26.9626	−1.10351
$598$	21.0118	0.859238
$599$	0.570423	0.0233068	0.0116534	−	0.999932i	$-0.496291\pi$
$599$	0.570423	0.0233068	0.0116534	+	0.999932i	$0.496291\pi$
$600$	−12.2480	−0.500021
$601$	−6.47851	−0.264264	−0.132132	−	0.991232i	$-0.542182\pi$
$601$	−6.47851	−0.264264	−0.132132	+	0.991232i	$0.542182\pi$
$602$	0	0
$603$	−0.537448	−0.0218866
$604$	−27.8047	−1.13136
$605$	−0.742116	−0.0301713
$606$	−0.221134	−0.00898294
$607$	6.62026	0.268708	0.134354	−	0.990933i	$-0.457104\pi$
$607$	6.62026	0.268708	0.134354	+	0.990933i	$0.457104\pi$
$608$	0.834026	0.0338242
$609$	0	0
$610$	1.49933	0.0607059
$611$	−43.6070	−1.76415
$612$	−4.45560	−0.180107
$613$	14.0034	0.565592	0.282796	−	0.959180i	$-0.408738\pi$
$613$	14.0034	0.565592	0.282796	+	0.959180i	$0.408738\pi$
$614$	−18.5577	−0.748928
$615$	−0.561773	−0.0226529
$616$	0	0
$617$	−37.3456	−1.50348	−0.751739	−	0.659460i	$-0.770785\pi$
$617$	−37.3456	−1.50348	−0.751739	+	0.659460i	$0.770785\pi$
$618$	−11.9913	−0.482361
$619$	−24.8145	−0.997377	−0.498689	−	0.866781i	$-0.666185\pi$
$619$	−24.8145	−0.997377	−0.498689	+	0.866781i	$0.666185\pi$
$620$	0.266985	0.0107224
$621$	−4.62821	−0.185724
$622$	−13.5438	−0.543057
$623$	0	0
$624$	4.88050	0.195377
$625$	20.3658	0.814630
$626$	−16.8724	−0.674355
$627$	0.442784	0.0176831
$628$	23.7321	0.947013
$629$	−29.7944	−1.18798
$630$	0	0
$631$	−41.0974	−1.63606	−0.818031	−	0.575173i	$-0.804935\pi$
$631$	−41.0974	−1.63606	−0.818031	+	0.575173i	$0.804935\pi$
$632$	−27.3298	−1.08712
$633$	−8.25353	−0.328048
$634$	−2.35019	−0.0933379
$635$	−7.61113	−0.302039
$636$	11.9006	0.471891
$637$	0	0
$638$	−19.8013	−0.783943
$639$	−0.835931	−0.0330689
$640$	5.36104	0.211914
$641$	3.33905	0.131884	0.0659422	−	0.997823i	$-0.478995\pi$
$641$	3.33905	0.131884	0.0659422	+	0.997823i	$0.478995\pi$
$642$	−8.45942	−0.333867
$643$	27.6056	1.08866	0.544330	−	0.838871i	$-0.316784\pi$
$643$	27.6056	1.08866	0.544330	+	0.838871i	$0.316784\pi$
$644$	0	0
$645$	5.21814	0.205464
$646$	0.343740	0.0135243
$647$	27.3768	1.07629	0.538147	−	0.842851i	$-0.319124\pi$
$647$	27.3768	1.07629	0.538147	+	0.842851i	$0.319124\pi$
$648$	2.61462	0.102712
$649$	−2.83485	−0.111278
$650$	21.2670	0.834159
$651$	0	0
$652$	4.00733	0.156939
$653$	−50.3901	−1.97192	−0.985959	−	0.166985i	$-0.946597\pi$
$653$	−50.3901	−1.97192	−0.985959	+	0.166985i	$0.946597\pi$
$654$	12.5712	0.491573
$655$	9.79948	0.382897
$656$	−0.823497	−0.0321522
$657$	8.54657	0.333433
$658$	0	0
$659$	1.97744	0.0770303	0.0385152	−	0.999258i	$-0.487737\pi$
$659$	1.97744	0.0770303	0.0385152	+	0.999258i	$0.487737\pi$
$660$	2.46989	0.0961403
$661$	−34.6552	−1.34793	−0.673965	−	0.738763i	$-0.735410\pi$
$661$	−34.6552	−1.34793	−0.673965	+	0.738763i	$0.735410\pi$
$662$	19.8673	0.772164
$663$	18.6856	0.725689
$664$	−15.6797	−0.608489
$665$	0	0
$666$	7.23899	0.280505
$667$	38.4544	1.48896
$668$	−8.81361	−0.341009
$669$	9.94467	0.384483
$670$	0.231284	0.00893527
$671$	10.8393	0.418447
$672$	0	0
$673$	−9.37694	−0.361455	−0.180727	−	0.983533i	$-0.557845\pi$
$673$	−9.37694	−0.361455	−0.180727	+	0.983533i	$0.557845\pi$
$674$	−17.8219	−0.686473
$675$	−4.68441	−0.180303
$676$	−31.2656	−1.20252
$677$	−9.75240	−0.374815	−0.187408	−	0.982282i	$-0.560009\pi$
$677$	−9.75240	−0.374815	−0.187408	+	0.982282i	$0.560009\pi$
$678$	−6.20611	−0.238344
$679$	0	0
$680$	4.63100	0.177591
$681$	−8.59955	−0.329536
$682$	−0.801468	−0.0306898
$683$	15.3801	0.588502	0.294251	−	0.955728i	$-0.404930\pi$
$683$	15.3801	0.588502	0.294251	+	0.955728i	$0.404930\pi$
$684$	0.201131	0.00769043
$685$	−11.3895	−0.435170
$686$	0	0
$687$	−7.01808	−0.267757
$688$	7.64921	0.291623
$689$	−49.9082	−1.90135
$690$	1.99169	0.0758225
$691$	33.8947	1.28942	0.644708	−	0.764429i	$-0.276979\pi$
$691$	33.8947	1.28942	0.644708	+	0.764429i	$0.276979\pi$
$692$	34.1161	1.29690
$693$	0	0
$694$	3.03324	0.115140
$695$	−5.30965	−0.201407
$696$	−21.7240	−0.823448
$697$	−3.15286	−0.119423
$698$	16.6302	0.629464
$699$	0.664006	0.0251150
$700$	0	0
$701$	−31.8433	−1.20271	−0.601353	−	0.798984i	$-0.705371\pi$
$701$	−31.8433	−1.20271	−0.601353	+	0.798984i	$0.705371\pi$
$702$	−4.53994	−0.171349
$703$	1.34495	0.0507259
$704$	−8.84181	−0.333238
$705$	−4.13347	−0.155676
$706$	−3.27220	−0.123151
$707$	0	0
$708$	−1.28771	−0.0483950
$709$	11.2444	0.422292	0.211146	−	0.977455i	$-0.432280\pi$
$709$	11.2444	0.422292	0.211146	+	0.977455i	$0.432280\pi$
$710$	0.359732	0.0135005
$711$	−10.4527	−0.392007
$712$	48.9613	1.83490
$713$	1.55646	0.0582898
$714$	0	0
$715$	−10.3581	−0.387370
$716$	20.2527	0.756877
$717$	3.89087	0.145307
$718$	1.92642	0.0718935
$719$	−32.1389	−1.19858	−0.599289	−	0.800532i	$-0.704550\pi$
$719$	−32.1389	−1.19858	−0.599289	+	0.800532i	$0.704550\pi$
$720$	0.462619	0.0172408
$721$	0	0
$722$	14.5391	0.541090
$723$	−1.93117	−0.0718211
$724$	10.1248	0.376285
$725$	38.9213	1.44550
$726$	1.01195	0.0375569
$727$	20.1797	0.748425	0.374212	−	0.927343i	$-0.377913\pi$
$727$	20.1797	0.748425	0.374212	+	0.927343i	$0.377913\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−3.67791	−0.136126
$731$	29.2860	1.08318
$732$	4.92366	0.181984
$733$	−49.0009	−1.80989	−0.904944	−	0.425530i	$-0.860088\pi$
$733$	−49.0009	−1.80989	−0.904944	+	0.425530i	$0.860088\pi$
$734$	−5.76928	−0.212948
$735$	0	0
$736$	27.1217	0.999717
$737$	1.67206	0.0615910
$738$	0.766034	0.0281981
$739$	−18.4871	−0.680060	−0.340030	−	0.940415i	$-0.610437\pi$
$739$	−18.4871	−0.680060	−0.340030	+	0.940415i	$0.610437\pi$
$740$	7.50227	0.275789
$741$	−0.843490	−0.0309864
$742$	0	0
$743$	−0.0512035	−0.00187847	−0.000939237	−	1.00000i	$-0.500299\pi$
$743$	−0.0512035	−0.00187847	−0.000939237		1.00000i	$0.500299\pi$
$744$	−0.879290	−0.0322364
$745$	−11.0746	−0.405742
$746$	−23.2526	−0.851338
$747$	−5.99692	−0.219416
$748$	13.8618	0.506839
$749$	0	0
$750$	4.16756	0.152178
$751$	−22.4662	−0.819802	−0.409901	−	0.912130i	$-0.634437\pi$
$751$	−22.4662	−0.819802	−0.409901	+	0.912130i	$0.634437\pi$
$752$	−6.05921	−0.220957
$753$	19.7811	0.720862
$754$	37.7209	1.37372
$755$	11.0530	0.402259
$756$	0	0
$757$	9.36483	0.340370	0.170185	−	0.985412i	$-0.445563\pi$
$757$	9.36483	0.340370	0.170185	+	0.985412i	$0.445563\pi$
$758$	−10.6637	−0.387322
$759$	14.3989	0.522646
$760$	−0.209049	−0.00758299
$761$	−8.28605	−0.300369	−0.150185	−	0.988658i	$-0.547987\pi$
$761$	−8.28605	−0.300369	−0.150185	+	0.988658i	$0.547987\pi$
$762$	10.3785	0.375975
$763$	0	0
$764$	25.1790	0.910945
$765$	1.77119	0.0640377
$766$	9.47781	0.342447
$767$	5.40031	0.194994
$768$	−12.9943	−0.468893
$769$	−8.71914	−0.314420	−0.157210	−	0.987565i	$-0.550250\pi$
$769$	−8.71914	−0.314420	−0.157210	+	0.987565i	$0.550250\pi$
$770$	0	0
$771$	−10.8991	−0.392521
$772$	−25.2928	−0.910308
$773$	39.2093	1.41026	0.705130	−	0.709078i	$-0.250889\pi$
$773$	39.2093	1.41026	0.705130	+	0.709078i	$0.250889\pi$
$774$	−7.11545	−0.255760
$775$	1.57536	0.0565885
$776$	28.7380	1.03163
$777$	0	0
$778$	16.3400	0.585816
$779$	0.142324	0.00509928
$780$	−4.70506	−0.168468
$781$	2.60067	0.0930592
$782$	11.1781	0.399726
$783$	−8.30868	−0.296928
$784$	0	0
$785$	−9.43400	−0.336714
$786$	−13.3626	−0.476627
$787$	29.7849	1.06172	0.530858	−	0.847461i	$-0.321870\pi$
$787$	29.7849	1.06172	0.530858	+	0.847461i	$0.321870\pi$
$788$	1.80116	0.0641638
$789$	−12.8647	−0.457994
$790$	4.49819	0.160038
$791$	0	0
$792$	−8.13436	−0.289042
$793$	−20.6485	−0.733251
$794$	24.5961	0.872882
$795$	−4.73076	−0.167783
$796$	38.1034	1.35054
$797$	−10.9573	−0.388127	−0.194063	−	0.980989i	$-0.562167\pi$
$797$	−10.9573	−0.388127	−0.194063	+	0.980989i	$0.562167\pi$
$798$	0	0
$799$	−23.1984	−0.820702
$800$	27.4510	0.970538
$801$	18.7260	0.661649
$802$	−8.49063	−0.299814
$803$	−26.5893	−0.938315
$804$	0.759517	0.0267861
$805$	0	0
$806$	1.52677	0.0537782
$807$	1.49766	0.0527202
$808$	0.754771	0.0265528
$809$	−35.3162	−1.24165	−0.620826	−	0.783949i	$-0.713203\pi$
$809$	−35.3162	−1.24165	−0.620826	+	0.783949i	$0.713203\pi$
$810$	−0.430337	−0.0151205
$811$	16.1352	0.566582	0.283291	−	0.959034i	$-0.408574\pi$
$811$	16.1352	0.566582	0.283291	+	0.959034i	$0.408574\pi$
$812$	0	0
$813$	−16.3381	−0.573000
$814$	−22.5213	−0.789370
$815$	−1.59300	−0.0558003
$816$	2.59637	0.0908912
$817$	−1.32200	−0.0462510
$818$	10.8790	0.380374
$819$	0	0
$820$	0.793894	0.0277240
$821$	5.76072	0.201050	0.100525	−	0.994935i	$-0.467948\pi$
$821$	5.76072	0.201050	0.100525	+	0.994935i	$0.467948\pi$
$822$	15.5307	0.541695
$823$	49.8189	1.73658	0.868290	−	0.496057i	$-0.165219\pi$
$823$	49.8189	1.73658	0.868290	+	0.496057i	$0.165219\pi$
$824$	40.9286	1.42582
$825$	14.5737	0.507391
$826$	0	0
$827$	−56.4094	−1.96155	−0.980773	−	0.195151i	$-0.937480\pi$
$827$	−56.4094	−1.96155	−0.980773	+	0.195151i	$0.937480\pi$
$828$	6.54056	0.227300
$829$	−18.1146	−0.629144	−0.314572	−	0.949234i	$-0.601861\pi$
$829$	−18.1146	−0.629144	−0.314572	+	0.949234i	$0.601861\pi$
$830$	2.58070	0.0895774
$831$	0.682460	0.0236743
$832$	16.8434	0.583939
$833$	0	0
$834$	7.24024	0.250709
$835$	3.50360	0.121247
$836$	−0.625739	−0.0216416
$837$	−0.336298	−0.0116241
$838$	13.7619	0.475397
$839$	−7.52465	−0.259780	−0.129890	−	0.991528i	$-0.541462\pi$
$839$	−7.52465	−0.259780	−0.129890	+	0.991528i	$0.541462\pi$
$840$	0	0
$841$	40.0342	1.38049
$842$	−11.8471	−0.408277
$843$	−18.5463	−0.638768
$844$	11.6638	0.401485
$845$	12.4287	0.427561
$846$	5.63640	0.193783
$847$	0	0
$848$	−6.93476	−0.238141
$849$	−6.11849	−0.209986
$850$	11.3138	0.388059
$851$	43.7365	1.49927
$852$	1.18133	0.0404717
$853$	2.09284	0.0716576	0.0358288	−	0.999358i	$-0.488593\pi$
$853$	2.09284	0.0716576	0.0358288	+	0.999358i	$0.488593\pi$
$854$	0	0
$855$	−0.0799537	−0.00273436
$856$	28.8736	0.986880
$857$	−29.6948	−1.01436	−0.507178	−	0.861841i	$-0.669311\pi$
$857$	−29.6948	−1.01436	−0.507178	+	0.861841i	$0.669311\pi$
$858$	14.1242	0.482194
$859$	55.8092	1.90419	0.952093	−	0.305809i	$-0.0989268\pi$
$859$	55.8092	1.90419	0.952093	+	0.305809i	$0.0989268\pi$
$860$	−7.37424	−0.251459
$861$	0	0
$862$	−8.21210	−0.279705
$863$	−33.0298	−1.12435	−0.562173	−	0.827020i	$-0.690035\pi$
$863$	−33.0298	−1.12435	−0.562173	+	0.827020i	$0.690035\pi$
$864$	−5.86007	−0.199364
$865$	−13.5619	−0.461117
$866$	−13.0427	−0.443207
$867$	−7.05946	−0.239752
$868$	0	0
$869$	32.5194	1.10315
$870$	3.57554	0.121222
$871$	−3.18521	−0.107927
$872$	−42.9079	−1.45305
$873$	10.9913	0.371998
$874$	−0.504590	−0.0170680
$875$	0	0
$876$	−12.0779	−0.408076
$877$	35.0276	1.18280	0.591398	−	0.806380i	$-0.298576\pi$
$877$	35.0276	1.18280	0.591398	+	0.806380i	$0.298576\pi$
$878$	6.94881	0.234511
$879$	−24.0482	−0.811126
$880$	−1.43926	−0.0485173
$881$	−9.28557	−0.312839	−0.156419	−	0.987691i	$-0.549995\pi$
$881$	−9.28557	−0.312839	−0.156419	+	0.987691i	$0.549995\pi$
$882$	0	0
$883$	−14.6176	−0.491920	−0.245960	−	0.969280i	$-0.579103\pi$
$883$	−14.6176	−0.491920	−0.245960	+	0.969280i	$0.579103\pi$
$884$	−26.4064	−0.888142
$885$	0.511891	0.0172070
$886$	−14.9066	−0.500798
$887$	4.58271	0.153872	0.0769361	−	0.997036i	$-0.475486\pi$
$887$	4.58271	0.153872	0.0769361	+	0.997036i	$0.475486\pi$
$888$	−24.7081	−0.829149
$889$	0	0
$890$	−8.05848	−0.270121
$891$	−3.11111	−0.104226
$892$	−14.0537	−0.470554
$893$	1.04720	0.0350433
$894$	15.1013	0.505063
$895$	−8.05085	−0.269110
$896$	0	0
$897$	−27.4294	−0.915840
$898$	20.6691	0.689737
$899$	2.79419	0.0931914
$900$	6.61997	0.220666
$901$	−26.5506	−0.884529
$902$	−2.38321	−0.0793523
$903$	0	0
$904$	21.1826	0.704524
$905$	−4.02482	−0.133790
$906$	−15.0718	−0.500728
$907$	50.5590	1.67879	0.839393	−	0.543525i	$-0.182911\pi$
$907$	50.5590	1.67879	0.839393	+	0.543525i	$0.182911\pi$
$908$	12.1528	0.403306
$909$	0.288673	0.00957469
$910$	0	0
$911$	−0.442249	−0.0146524	−0.00732618	−	0.999973i	$-0.502332\pi$
$911$	−0.442249	−0.0146524	−0.00732618	+	0.999973i	$0.502332\pi$
$912$	−0.117203	−0.00388098
$913$	18.6571	0.617458
$914$	4.18506	0.138430
$915$	−1.95726	−0.0647050
$916$	9.91790	0.327697
$917$	0	0
$918$	−2.41520	−0.0797134
$919$	−18.0403	−0.595095	−0.297547	−	0.954707i	$-0.596169\pi$
$919$	−18.0403	−0.595095	−0.297547	+	0.954707i	$0.596169\pi$
$920$	−6.79803	−0.224125
$921$	24.2257	0.798264
$922$	28.3997	0.935295
$923$	−4.95419	−0.163069
$924$	0	0
$925$	44.2675	1.45551
$926$	−18.9373	−0.622318
$927$	15.6537	0.514136
$928$	48.6894	1.59831
$929$	38.6217	1.26714	0.633569	−	0.773687i	$-0.281589\pi$
$929$	38.6217	1.26714	0.633569	+	0.773687i	$0.281589\pi$
$930$	0.144721	0.00474560
$931$	0	0
$932$	−0.938368	−0.0307373
$933$	17.6804	0.578831
$934$	−10.9754	−0.359125
$935$	−5.51037	−0.180208
$936$	15.4957	0.506493
$937$	−5.99551	−0.195865	−0.0979324	−	0.995193i	$-0.531223\pi$
$937$	−5.99551	−0.195865	−0.0979324	+	0.995193i	$0.531223\pi$
$938$	0	0
$939$	22.0256	0.718778
$940$	5.84139	0.190525
$941$	−28.1503	−0.917674	−0.458837	−	0.888520i	$-0.651734\pi$
$941$	−28.1503	−0.917674	−0.458837	+	0.888520i	$0.651734\pi$
$942$	12.8642	0.419138
$943$	4.62821	0.150715
$944$	0.750375	0.0244226
$945$	0	0
$946$	22.1369	0.719733
$947$	−26.4200	−0.858534	−0.429267	−	0.903178i	$-0.641228\pi$
$947$	−26.4200	−0.858534	−0.429267	+	0.903178i	$0.641228\pi$
$948$	14.7717	0.479761
$949$	50.6517	1.64423
$950$	−0.510717	−0.0165698
$951$	3.06800	0.0994866
$952$	0	0
$953$	19.0038	0.615592	0.307796	−	0.951452i	$-0.400409\pi$
$953$	19.0038	0.615592	0.307796	+	0.951452i	$0.400409\pi$
$954$	6.45086	0.208854
$955$	−10.0092	−0.323890
$956$	−5.49855	−0.177836
$957$	25.8492	0.835585
$958$	−21.2059	−0.685130
$959$	0	0
$960$	1.59657	0.0515290
$961$	−30.8869	−0.996352
$962$	42.9023	1.38323
$963$	11.0431	0.355860
$964$	2.72912	0.0878991
$965$	10.0544	0.323663
$966$	0	0
$967$	−38.9197	−1.25157	−0.625787	−	0.779994i	$-0.715222\pi$
$967$	−38.9197	−1.25157	−0.625787	+	0.779994i	$0.715222\pi$
$968$	−3.45398	−0.111015
$969$	−0.448727	−0.0144152
$970$	−4.72995	−0.151869
$971$	−48.6690	−1.56186	−0.780931	−	0.624617i	$-0.785255\pi$
$971$	−48.6690	−1.56186	−0.780931	+	0.624617i	$0.785255\pi$
$972$	−1.41319	−0.0453282
$973$	0	0
$974$	−7.49620	−0.240194
$975$	−27.7624	−0.889109
$976$	−2.86912	−0.0918384
$977$	19.6134	0.627490	0.313745	−	0.949507i	$-0.398416\pi$
$977$	19.6134	0.627490	0.313745	+	0.949507i	$0.398416\pi$
$978$	2.17221	0.0694596
$979$	−58.2584	−1.86195
$980$	0	0
$981$	−16.4108	−0.523956
$982$	17.6376	0.562838
$983$	3.19009	0.101748	0.0508741	−	0.998705i	$-0.483799\pi$
$983$	3.19009	0.101748	0.0508741	+	0.998705i	$0.483799\pi$
$984$	−2.61462	−0.0833511
$985$	−0.716000	−0.0228137
$986$	20.0671	0.639067
$987$	0	0
$988$	1.19201	0.0379230
$989$	−42.9901	−1.36700
$990$	1.33883	0.0425507
$991$	58.7305	1.86564	0.932819	−	0.360346i	$-0.117342\pi$
$991$	58.7305	1.86564	0.932819	+	0.360346i	$0.117342\pi$
$992$	1.97073	0.0625706
$993$	−25.9353	−0.823030
$994$	0	0
$995$	−15.1469	−0.480189
$996$	8.47480	0.268534
$997$	46.2376	1.46436	0.732179	−	0.681112i	$-0.238503\pi$
$997$	46.2376	1.46436	0.732179	+	0.681112i	$0.238503\pi$
$998$	−19.9665	−0.632029
$999$	−9.44997	−0.298984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bk.1.6		14
7.3	odd	6		861.2.i.g.247.9	✓	28
7.5	odd	6		861.2.i.g.739.9	yes	28
7.6	odd	2		6027.2.a.bj.1.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.g.247.9	✓	28	7.3	odd	6
861.2.i.g.739.9	yes	28	7.5	odd	6
6027.2.a.bj.1.6		14	7.6	odd	2
6027.2.a.bk.1.6		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)

\(f(q)\)	\(=\)	\(q-0.766034 q^{2} +1.00000 q^{3} -1.41319 q^{4} +0.561773 q^{5} -0.766034 q^{6} +2.61462 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.766034 q^{2} +1.00000 q^{3} -1.41319 q^{4} +0.561773 q^{5} -0.766034 q^{6} +2.61462 q^{8} +1.00000 q^{9} -0.430337 q^{10} -3.11111 q^{11} -1.41319 q^{12} +5.92656 q^{13} +0.561773 q^{15} +0.823497 q^{16} +3.15286 q^{17} -0.766034 q^{18} -0.142324 q^{19} -0.793894 q^{20} +2.38321 q^{22} -4.62821 q^{23} +2.61462 q^{24} -4.68441 q^{25} -4.53994 q^{26} +1.00000 q^{27} -8.30868 q^{29} -0.430337 q^{30} -0.336298 q^{31} -5.86007 q^{32} -3.11111 q^{33} -2.41520 q^{34} -1.41319 q^{36} -9.44997 q^{37} +0.109025 q^{38} +5.92656 q^{39} +1.46882 q^{40} -1.00000 q^{41} +9.28869 q^{43} +4.39659 q^{44} +0.561773 q^{45} +3.54537 q^{46} -7.35790 q^{47} +0.823497 q^{48} +3.58842 q^{50} +3.15286 q^{51} -8.37537 q^{52} -8.42111 q^{53} -0.766034 q^{54} -1.74774 q^{55} -0.142324 q^{57} +6.36473 q^{58} +0.911205 q^{59} -0.793894 q^{60} -3.48407 q^{61} +0.257615 q^{62} +2.84201 q^{64} +3.32938 q^{65} +2.38321 q^{66} -0.537448 q^{67} -4.45560 q^{68} -4.62821 q^{69} -0.835931 q^{71} +2.61462 q^{72} +8.54657 q^{73} +7.23899 q^{74} -4.68441 q^{75} +0.201131 q^{76} -4.53994 q^{78} -10.4527 q^{79} +0.462619 q^{80} +1.00000 q^{81} +0.766034 q^{82} -5.99692 q^{83} +1.77119 q^{85} -7.11545 q^{86} -8.30868 q^{87} -8.13436 q^{88} +18.7260 q^{89} -0.430337 q^{90} +6.54056 q^{92} -0.336298 q^{93} +5.63640 q^{94} -0.0799537 q^{95} -5.86007 q^{96} +10.9913 q^{97} -3.11111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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