LMFDB - Embedded newform 6027.2.a.bm.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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 14 x^{14} + 68 x^{13} + 64 x^{12} - 456 x^{11} - 54 x^{10} + 1532 x^{9} - 400 x^{8} + \cdots - 49 $ x^16 - 4x^15 - 14x^14 + 68x^13 + 64x^12 - 456x^11 - 54x^10 + 1532x^9 - 400x^8 - 2708x^7 + 1218x^6 + 2424x^5 - 1276x^4 - 960x^3 + 500x^2 + 112*x - 49
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.44011$ 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)

$f(q)$	$=$	$q-1.44011 q^{2} +1.00000 q^{3} +0.0739309 q^{4} +3.20961 q^{5} -1.44011 q^{6} +2.77376 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.44011 q^{2} +1.00000 q^{3} +0.0739309 q^{4} +3.20961 q^{5} -1.44011 q^{6} +2.77376 q^{8} +1.00000 q^{9} -4.62221 q^{10} -3.71531 q^{11} +0.0739309 q^{12} +1.13302 q^{13} +3.20961 q^{15} -4.14240 q^{16} -5.67373 q^{17} -1.44011 q^{18} +3.14749 q^{19} +0.237290 q^{20} +5.35047 q^{22} -4.86181 q^{23} +2.77376 q^{24} +5.30163 q^{25} -1.63167 q^{26} +1.00000 q^{27} +2.25032 q^{29} -4.62221 q^{30} -1.73959 q^{31} +0.418005 q^{32} -3.71531 q^{33} +8.17082 q^{34} +0.0739309 q^{36} -4.53215 q^{37} -4.53274 q^{38} +1.13302 q^{39} +8.90270 q^{40} +1.00000 q^{41} -6.99210 q^{43} -0.274676 q^{44} +3.20961 q^{45} +7.00157 q^{46} -6.44011 q^{47} -4.14240 q^{48} -7.63495 q^{50} -5.67373 q^{51} +0.0837649 q^{52} +3.39697 q^{53} -1.44011 q^{54} -11.9247 q^{55} +3.14749 q^{57} -3.24072 q^{58} -3.87745 q^{59} +0.237290 q^{60} +8.17051 q^{61} +2.50520 q^{62} +7.68282 q^{64} +3.63655 q^{65} +5.35047 q^{66} -4.36043 q^{67} -0.419464 q^{68} -4.86181 q^{69} +7.54065 q^{71} +2.77376 q^{72} -9.11677 q^{73} +6.52682 q^{74} +5.30163 q^{75} +0.232697 q^{76} -1.63167 q^{78} +0.0474074 q^{79} -13.2955 q^{80} +1.00000 q^{81} -1.44011 q^{82} -8.03200 q^{83} -18.2105 q^{85} +10.0694 q^{86} +2.25032 q^{87} -10.3054 q^{88} -9.30187 q^{89} -4.62221 q^{90} -0.359438 q^{92} -1.73959 q^{93} +9.27450 q^{94} +10.1022 q^{95} +0.418005 q^{96} -17.8996 q^{97} -3.71531 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 16 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 16 * q^3 + 12 * q^4 - 12 * q^5 - 4 * q^6 - 12 * q^8 + 16 * q^9	$ 16 q - 4 q^{2} + 16 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{8} + 16 q^{9} - 4 q^{10} - 4 q^{11} + 12 q^{12} - 12 q^{15} - 8 q^{17} - 4 q^{18} + 4 q^{19} - 20 q^{20} - 16 q^{22} - 12 q^{23} - 12 q^{24} - 8 q^{25} - 8 q^{26} + 16 q^{27} - 16 q^{29} - 4 q^{30} - 4 q^{31} - 48 q^{32} - 4 q^{33} + 16 q^{34} + 12 q^{36} - 48 q^{37} - 4 q^{38} + 56 q^{40} + 16 q^{41} - 16 q^{43} - 12 q^{45} - 4 q^{46} - 36 q^{47} - 8 q^{50} - 8 q^{51} - 60 q^{53} - 4 q^{54} + 8 q^{55} + 4 q^{57} - 36 q^{58} - 36 q^{59} - 20 q^{60} - 4 q^{61} - 12 q^{62} + 52 q^{64} - 36 q^{65} - 16 q^{66} - 52 q^{67} - 8 q^{68} - 12 q^{69} - 12 q^{71} - 12 q^{72} - 16 q^{73} + 4 q^{74} - 8 q^{75} + 16 q^{76} - 8 q^{78} - 36 q^{79} - 68 q^{80} + 16 q^{81} - 4 q^{82} - 32 q^{83} - 28 q^{85} - 8 q^{86} - 16 q^{87} - 36 q^{88} - 12 q^{89} - 4 q^{90} - 36 q^{92} - 4 q^{93} + 24 q^{94} - 20 q^{95} - 48 q^{96} + 48 q^{97} - 4 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 + 16 * q^3 + 12 * q^4 - 12 * q^5 - 4 * q^6 - 12 * q^8 + 16 * q^9 - 4 * q^10 - 4 * q^11 + 12 * q^12 - 12 * q^15 - 8 * q^17 - 4 * q^18 + 4 * q^19 - 20 * q^20 - 16 * q^22 - 12 * q^23 - 12 * q^24 - 8 * q^25 - 8 * q^26 + 16 * q^27 - 16 * q^29 - 4 * q^30 - 4 * q^31 - 48 * q^32 - 4 * q^33 + 16 * q^34 + 12 * q^36 - 48 * q^37 - 4 * q^38 + 56 * q^40 + 16 * q^41 - 16 * q^43 - 12 * q^45 - 4 * q^46 - 36 * q^47 - 8 * q^50 - 8 * q^51 - 60 * q^53 - 4 * q^54 + 8 * q^55 + 4 * q^57 - 36 * q^58 - 36 * q^59 - 20 * q^60 - 4 * q^61 - 12 * q^62 + 52 * q^64 - 36 * q^65 - 16 * q^66 - 52 * q^67 - 8 * q^68 - 12 * q^69 - 12 * q^71 - 12 * q^72 - 16 * q^73 + 4 * q^74 - 8 * q^75 + 16 * q^76 - 8 * q^78 - 36 * q^79 - 68 * q^80 + 16 * q^81 - 4 * q^82 - 32 * q^83 - 28 * q^85 - 8 * q^86 - 16 * q^87 - 36 * q^88 - 12 * q^89 - 4 * q^90 - 36 * q^92 - 4 * q^93 + 24 * q^94 - 20 * q^95 - 48 * q^96 + 48 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.44011	−1.01832	−0.509158	−	0.860673i	$-0.670043\pi$
$2$	−1.44011	−1.01832	−0.509158	+	0.860673i	$0.670043\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.0739309	0.0369655
$5$	3.20961	1.43538	0.717692	−	0.696361i	$-0.245199\pi$
$5$	3.20961	1.43538	0.717692	+	0.696361i	$0.245199\pi$
$6$	−1.44011	−0.587924
$7$	0	0
$7$	0	0
$8$	2.77376	0.980673
$9$	1.00000	0.333333
$10$	−4.62221	−1.46167
$11$	−3.71531	−1.12021	−0.560103	−	0.828423i	$-0.689239\pi$
$11$	−3.71531	−1.12021	−0.560103	+	0.828423i	$0.689239\pi$
$12$	0.0739309	0.0213420
$13$	1.13302	0.314242	0.157121	−	0.987579i	$-0.449779\pi$
$13$	1.13302	0.314242	0.157121	+	0.987579i	$0.449779\pi$
$14$	0	0
$15$	3.20961	0.828719
$16$	−4.14240	−1.03560
$17$	−5.67373	−1.37608	−0.688041	−	0.725672i	$-0.741529\pi$
$17$	−5.67373	−1.37608	−0.688041	+	0.725672i	$0.741529\pi$
$18$	−1.44011	−0.339438
$19$	3.14749	0.722083	0.361041	−	0.932550i	$-0.382421\pi$
$19$	3.14749	0.722083	0.361041	+	0.932550i	$0.382421\pi$
$20$	0.237290	0.0530596
$21$	0	0
$22$	5.35047	1.14072
$23$	−4.86181	−1.01376	−0.506879	−	0.862017i	$-0.669201\pi$
$23$	−4.86181	−1.01376	−0.506879	+	0.862017i	$0.669201\pi$
$24$	2.77376	0.566192
$25$	5.30163	1.06033
$26$	−1.63167	−0.319998
$27$	1.00000	0.192450
$28$	0	0
$29$	2.25032	0.417874	0.208937	−	0.977929i	$-0.433000\pi$
$29$	2.25032	0.417874	0.208937	+	0.977929i	$0.433000\pi$
$30$	−4.62221	−0.843897
$31$	−1.73959	−0.312439	−0.156219	−	0.987722i	$-0.549931\pi$
$31$	−1.73959	−0.312439	−0.156219	+	0.987722i	$0.549931\pi$
$32$	0.418005	0.0738935
$33$	−3.71531	−0.646752
$34$	8.17082	1.40128
$35$	0	0
$36$	0.0739309	0.0123218
$37$	−4.53215	−0.745081	−0.372540	−	0.928016i	$-0.621513\pi$
$37$	−4.53215	−0.745081	−0.372540	+	0.928016i	$0.621513\pi$
$38$	−4.53274	−0.735308
$39$	1.13302	0.181428
$40$	8.90270	1.40764
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−6.99210	−1.06629	−0.533143	−	0.846025i	$-0.678989\pi$
$43$	−6.99210	−1.06629	−0.533143	+	0.846025i	$0.678989\pi$
$44$	−0.274676	−0.0414090
$45$	3.20961	0.478461
$46$	7.00157	1.03232
$47$	−6.44011	−0.939387	−0.469694	−	0.882830i	$-0.655636\pi$
$47$	−6.44011	−0.939387	−0.469694	+	0.882830i	$0.655636\pi$
$48$	−4.14240	−0.597903
$49$	0	0
$50$	−7.63495	−1.07975
$51$	−5.67373	−0.794481
$52$	0.0837649	0.0116161
$53$	3.39697	0.466610	0.233305	−	0.972404i	$-0.425046\pi$
$53$	3.39697	0.466610	0.233305	+	0.972404i	$0.425046\pi$
$54$	−1.44011	−0.195975
$55$	−11.9247	−1.60793
$56$	0	0
$57$	3.14749	0.416895
$58$	−3.24072	−0.425528
$59$	−3.87745	−0.504800	−0.252400	−	0.967623i	$-0.581220\pi$
$59$	−3.87745	−0.504800	−0.252400	+	0.967623i	$0.581220\pi$
$60$	0.237290	0.0306340
$61$	8.17051	1.04613	0.523063	−	0.852294i	$-0.324789\pi$
$61$	8.17051	1.04613	0.523063	+	0.852294i	$0.324789\pi$
$62$	2.50520	0.318161
$63$	0	0
$64$	7.68282	0.960352
$65$	3.63655	0.451058
$66$	5.35047	0.658597
$67$	−4.36043	−0.532712	−0.266356	−	0.963875i	$-0.585820\pi$
$67$	−4.36043	−0.532712	−0.266356	+	0.963875i	$0.585820\pi$
$68$	−0.419464	−0.0508675
$69$	−4.86181	−0.585293
$70$	0	0
$71$	7.54065	0.894910	0.447455	−	0.894306i	$-0.352330\pi$
$71$	7.54065	0.894910	0.447455	+	0.894306i	$0.352330\pi$
$72$	2.77376	0.326891
$73$	−9.11677	−1.06704	−0.533519	−	0.845788i	$-0.679131\pi$
$73$	−9.11677	−1.06704	−0.533519	+	0.845788i	$0.679131\pi$
$74$	6.52682	0.758727
$75$	5.30163	0.612179
$76$	0.232697	0.0266921
$77$	0	0
$78$	−1.63167	−0.184751
$79$	0.0474074	0.00533375	0.00266688	−	0.999996i	$-0.499151\pi$
$79$	0.0474074	0.00533375	0.00266688	+	0.999996i	$0.499151\pi$
$80$	−13.2955	−1.48648
$81$	1.00000	0.111111
$82$	−1.44011	−0.159034
$83$	−8.03200	−0.881626	−0.440813	−	0.897599i	$-0.645310\pi$
$83$	−8.03200	−0.881626	−0.440813	+	0.897599i	$0.645310\pi$
$84$	0	0
$85$	−18.2105	−1.97520
$86$	10.0694	1.08581
$87$	2.25032	0.241260
$88$	−10.3054	−1.09856
$89$	−9.30187	−0.985996	−0.492998	−	0.870030i	$-0.664099\pi$
$89$	−9.30187	−0.985996	−0.492998	+	0.870030i	$0.664099\pi$
$90$	−4.62221	−0.487224
$91$	0	0
$92$	−0.359438	−0.0374740
$93$	−1.73959	−0.180387
$94$	9.27450	0.956592
$95$	10.1022	1.03647
$96$	0.418005	0.0426624
$97$	−17.8996	−1.81743	−0.908714	−	0.417420i	$-0.862934\pi$
$97$	−17.8996	−1.81743	−0.908714	+	0.417420i	$0.862934\pi$
$98$	0	0
$99$	−3.71531	−0.373402
$100$	0.391954	0.0391954
$101$	−3.11847	−0.310300	−0.155150	−	0.987891i	$-0.549586\pi$
$101$	−3.11847	−0.310300	−0.155150	+	0.987891i	$0.549586\pi$
$102$	8.17082	0.809032
$103$	2.85378	0.281192	0.140596	−	0.990067i	$-0.455098\pi$
$103$	2.85378	0.281192	0.140596	+	0.990067i	$0.455098\pi$
$104$	3.14272	0.308169
$105$	0	0
$106$	−4.89203	−0.475156
$107$	12.8370	1.24100	0.620500	−	0.784206i	$-0.286930\pi$
$107$	12.8370	1.24100	0.620500	+	0.784206i	$0.286930\pi$
$108$	0.0739309	0.00711401
$109$	−19.4326	−1.86131	−0.930655	−	0.365899i	$-0.880762\pi$
$109$	−19.4326	−1.86131	−0.930655	+	0.365899i	$0.880762\pi$
$110$	17.1729	1.63738
$111$	−4.53215	−0.430173
$112$	0	0
$113$	−8.96160	−0.843037	−0.421518	−	0.906820i	$-0.638503\pi$
$113$	−8.96160	−0.843037	−0.421518	+	0.906820i	$0.638503\pi$
$114$	−4.53274	−0.424530
$115$	−15.6045	−1.45513
$116$	0.166368	0.0154469
$117$	1.13302	0.104747
$118$	5.58397	0.514046
$119$	0	0
$120$	8.90270	0.812702
$121$	2.80350	0.254863
$122$	−11.7665	−1.06529
$123$	1.00000	0.0901670
$124$	−0.128609	−0.0115495
$125$	0.968108	0.0865902
$126$	0	0
$127$	15.5846	1.38291	0.691455	−	0.722420i	$-0.256970\pi$
$127$	15.5846	1.38291	0.691455	+	0.722420i	$0.256970\pi$
$128$	−11.9001	−1.05183
$129$	−6.99210	−0.615620
$130$	−5.23704	−0.459319
$131$	11.1927	0.977913	0.488957	−	0.872308i	$-0.337378\pi$
$131$	11.1927	0.977913	0.488957	+	0.872308i	$0.337378\pi$
$132$	−0.274676	−0.0239075
$133$	0	0
$134$	6.27953	0.542468
$135$	3.20961	0.276240
$136$	−15.7376	−1.34949
$137$	−9.63284	−0.822989	−0.411494	−	0.911412i	$-0.634993\pi$
$137$	−9.63284	−0.822989	−0.411494	+	0.911412i	$0.634993\pi$
$138$	7.00157	0.596013
$139$	−12.4957	−1.05987	−0.529935	−	0.848039i	$-0.677784\pi$
$139$	−12.4957	−1.05987	−0.529935	+	0.848039i	$0.677784\pi$
$140$	0	0
$141$	−6.44011	−0.542355
$142$	−10.8594	−0.911301
$143$	−4.20950	−0.352016
$144$	−4.14240	−0.345200
$145$	7.22267	0.599810
$146$	13.1292	1.08658
$147$	0	0
$148$	−0.335066	−0.0275423
$149$	−13.7960	−1.13021	−0.565105	−	0.825019i	$-0.691165\pi$
$149$	−13.7960	−1.13021	−0.565105	+	0.825019i	$0.691165\pi$
$150$	−7.63495	−0.623391
$151$	15.3274	1.24733	0.623663	−	0.781694i	$-0.285644\pi$
$151$	15.3274	1.24733	0.623663	+	0.781694i	$0.285644\pi$
$152$	8.73037	0.708127
$153$	−5.67373	−0.458694
$154$	0	0
$155$	−5.58340	−0.448470
$156$	0.0837649	0.00670656
$157$	−5.91126	−0.471770	−0.235885	−	0.971781i	$-0.575799\pi$
$157$	−5.91126	−0.471770	−0.235885	+	0.971781i	$0.575799\pi$
$158$	−0.0682721	−0.00543144
$159$	3.39697	0.269398
$160$	1.34163	0.106066
$161$	0	0
$162$	−1.44011	−0.113146
$163$	9.18322	0.719285	0.359643	−	0.933090i	$-0.382899\pi$
$163$	9.18322	0.719285	0.359643	+	0.933090i	$0.382899\pi$
$164$	0.0739309	0.00577304
$165$	−11.9247	−0.928337
$166$	11.5670	0.897773
$167$	−20.1802	−1.56159	−0.780795	−	0.624787i	$-0.785186\pi$
$167$	−20.1802	−1.56159	−0.780795	+	0.624787i	$0.785186\pi$
$168$	0	0
$169$	−11.7163	−0.901252
$170$	26.2252	2.01138
$171$	3.14749	0.240694
$172$	−0.516932	−0.0394157
$173$	−22.8081	−1.73407	−0.867033	−	0.498250i	$-0.833976\pi$
$173$	−22.8081	−1.73407	−0.867033	+	0.498250i	$0.833976\pi$
$174$	−3.24072	−0.245679
$175$	0	0
$176$	15.3903	1.16009
$177$	−3.87745	−0.291447
$178$	13.3958	1.00405
$179$	22.3973	1.67405	0.837025	−	0.547165i	$-0.184293\pi$
$179$	22.3973	1.67405	0.837025	+	0.547165i	$0.184293\pi$
$180$	0.237290	0.0176865
$181$	18.9086	1.40546	0.702732	−	0.711455i	$-0.251963\pi$
$181$	18.9086	1.40546	0.702732	+	0.711455i	$0.251963\pi$
$182$	0	0
$183$	8.17051	0.603981
$184$	−13.4855	−0.994165
$185$	−14.5465	−1.06948
$186$	2.50520	0.183691
$187$	21.0796	1.54150
$188$	−0.476124	−0.0347249
$189$	0	0
$190$	−14.5484	−1.05545
$191$	19.3875	1.40283	0.701416	−	0.712752i	$-0.252552\pi$
$191$	19.3875	1.40283	0.701416	+	0.712752i	$0.252552\pi$
$192$	7.68282	0.554460
$193$	−8.99357	−0.647371	−0.323686	−	0.946165i	$-0.604922\pi$
$193$	−8.99357	−0.647371	−0.323686	+	0.946165i	$0.604922\pi$
$194$	25.7775	1.85071
$195$	3.63655	0.260418
$196$	0	0
$197$	−16.6318	−1.18497	−0.592484	−	0.805583i	$-0.701852\pi$
$197$	−16.6318	−1.18497	−0.592484	+	0.805583i	$0.701852\pi$
$198$	5.35047	0.380241
$199$	8.98803	0.637144	0.318572	−	0.947899i	$-0.396797\pi$
$199$	8.98803	0.637144	0.318572	+	0.947899i	$0.396797\pi$
$200$	14.7054	1.03983
$201$	−4.36043	−0.307561
$202$	4.49096	0.315983
$203$	0	0
$204$	−0.419464	−0.0293684
$205$	3.20961	0.224169
$206$	−4.10978	−0.286342
$207$	−4.86181	−0.337919
$208$	−4.69340	−0.325429
$209$	−11.6939	−0.808882
$210$	0	0
$211$	25.8993	1.78298	0.891490	−	0.453040i	$-0.149661\pi$
$211$	25.8993	1.78298	0.891490	+	0.453040i	$0.149661\pi$
$212$	0.251141	0.0172485
$213$	7.54065	0.516677
$214$	−18.4868	−1.26373
$215$	−22.4419	−1.53053
$216$	2.77376	0.188731
$217$	0	0
$218$	27.9852	1.89540
$219$	−9.11677	−0.616054
$220$	−0.881604	−0.0594377
$221$	−6.42843	−0.432423
$222$	6.52682	0.438051
$223$	18.1127	1.21292	0.606458	−	0.795115i	$-0.292590\pi$
$223$	18.1127	1.21292	0.606458	+	0.795115i	$0.292590\pi$
$224$	0	0
$225$	5.30163	0.353442
$226$	12.9057	0.858477
$227$	−12.9994	−0.862802	−0.431401	−	0.902160i	$-0.641981\pi$
$227$	−12.9994	−0.862802	−0.431401	+	0.902160i	$0.641981\pi$
$228$	0.232697	0.0154107
$229$	5.48370	0.362373	0.181187	−	0.983449i	$-0.442006\pi$
$229$	5.48370	0.362373	0.181187	+	0.983449i	$0.442006\pi$
$230$	22.4723	1.48178
$231$	0	0
$232$	6.24186	0.409798
$233$	9.19946	0.602676	0.301338	−	0.953517i	$-0.402567\pi$
$233$	9.19946	0.602676	0.301338	+	0.953517i	$0.402567\pi$
$234$	−1.63167	−0.106666
$235$	−20.6703	−1.34838
$236$	−0.286663	−0.0186602
$237$	0.0474074	0.00307944
$238$	0	0
$239$	0.823059	0.0532393	0.0266196	−	0.999646i	$-0.491526\pi$
$239$	0.823059	0.0532393	0.0266196	+	0.999646i	$0.491526\pi$
$240$	−13.2955	−0.858221
$241$	6.48256	0.417578	0.208789	−	0.977961i	$-0.433048\pi$
$241$	6.48256	0.417578	0.208789	+	0.977961i	$0.433048\pi$
$242$	−4.03736	−0.259531
$243$	1.00000	0.0641500
$244$	0.604053	0.0386706
$245$	0	0
$246$	−1.44011	−0.0918184
$247$	3.56615	0.226909
$248$	−4.82520	−0.306400
$249$	−8.03200	−0.509007
$250$	−1.39419	−0.0881761
$251$	11.0992	0.700575	0.350287	−	0.936642i	$-0.386084\pi$
$251$	11.0992	0.700575	0.350287	+	0.936642i	$0.386084\pi$
$252$	0	0
$253$	18.0631	1.13562
$254$	−22.4436	−1.40824
$255$	−18.2105	−1.14039
$256$	1.77195	0.110747
$257$	−9.44160	−0.588951	−0.294475	−	0.955659i	$-0.595145\pi$
$257$	−9.44160	−0.588951	−0.294475	+	0.955659i	$0.595145\pi$
$258$	10.0694	0.626895
$259$	0	0
$260$	0.268853	0.0166736
$261$	2.25032	0.139291
$262$	−16.1188	−0.995824
$263$	−12.5414	−0.773333	−0.386666	−	0.922220i	$-0.626374\pi$
$263$	−12.5414	−0.773333	−0.386666	+	0.922220i	$0.626374\pi$
$264$	−10.3054	−0.634252
$265$	10.9030	0.669765
$266$	0	0
$267$	−9.30187	−0.569265
$268$	−0.322371	−0.0196919
$269$	2.28195	0.139133	0.0695666	−	0.997577i	$-0.477838\pi$
$269$	2.28195	0.139133	0.0695666	+	0.997577i	$0.477838\pi$
$270$	−4.62221	−0.281299
$271$	−12.2113	−0.741781	−0.370891	−	0.928677i	$-0.620948\pi$
$271$	−12.2113	−0.741781	−0.370891	+	0.928677i	$0.620948\pi$
$272$	23.5028	1.42507
$273$	0	0
$274$	13.8724	0.838062
$275$	−19.6972	−1.18778
$276$	−0.359438	−0.0216356
$277$	−24.7287	−1.48580	−0.742901	−	0.669401i	$-0.766551\pi$
$277$	−24.7287	−1.48580	−0.742901	+	0.669401i	$0.766551\pi$
$278$	17.9952	1.07928
$279$	−1.73959	−0.104146
$280$	0	0
$281$	−4.87088	−0.290572	−0.145286	−	0.989390i	$-0.546410\pi$
$281$	−4.87088	−0.290572	−0.145286	+	0.989390i	$0.546410\pi$
$282$	9.27450	0.552289
$283$	4.43504	0.263636	0.131818	−	0.991274i	$-0.457919\pi$
$283$	4.43504	0.263636	0.131818	+	0.991274i	$0.457919\pi$
$284$	0.557487	0.0330808
$285$	10.1022	0.598404
$286$	6.06217	0.358463
$287$	0	0
$288$	0.418005	0.0246312
$289$	15.1912	0.893601
$290$	−10.4015	−0.610795
$291$	−17.8996	−1.04929
$292$	−0.674011	−0.0394435
$293$	10.4636	0.611289	0.305644	−	0.952146i	$-0.401128\pi$
$293$	10.4636	0.611289	0.305644	+	0.952146i	$0.401128\pi$
$294$	0	0
$295$	−12.4451	−0.724582
$296$	−12.5711	−0.730680
$297$	−3.71531	−0.215584
$298$	19.8678	1.15091
$299$	−5.50851	−0.318566
$300$	0.391954	0.0226295
$301$	0	0
$302$	−22.0732	−1.27017
$303$	−3.11847	−0.179152
$304$	−13.0381	−0.747788
$305$	26.2242	1.50159
$306$	8.17082	0.467095
$307$	−4.63816	−0.264714	−0.132357	−	0.991202i	$-0.542254\pi$
$307$	−4.63816	−0.264714	−0.132357	+	0.991202i	$0.542254\pi$
$308$	0	0
$309$	2.85378	0.162346
$310$	8.04074	0.456683
$311$	4.98755	0.282818	0.141409	−	0.989951i	$-0.454837\pi$
$311$	4.98755	0.282818	0.141409	+	0.989951i	$0.454837\pi$
$312$	3.14272	0.177921
$313$	12.0497	0.681087	0.340544	−	0.940229i	$-0.389389\pi$
$313$	12.0497	0.681087	0.340544	+	0.940229i	$0.389389\pi$
$314$	8.51289	0.480410
$315$	0	0
$316$	0.00350487	0.000197165 0
$317$	17.2675	0.969840	0.484920	−	0.874559i	$-0.338849\pi$
$317$	17.2675	0.969840	0.484920	+	0.874559i	$0.338849\pi$
$318$	−4.89203	−0.274332
$319$	−8.36064	−0.468106
$320$	24.6589	1.37847
$321$	12.8370	0.716492
$322$	0	0
$323$	−17.8580	−0.993645
$324$	0.0739309	0.00410727
$325$	6.00683	0.333199
$326$	−13.2249	−0.732459
$327$	−19.4326	−1.07463
$328$	2.77376	0.153155
$329$	0	0
$330$	17.1729	0.945339
$331$	−11.7004	−0.643110	−0.321555	−	0.946891i	$-0.604205\pi$
$331$	−11.7004	−0.643110	−0.321555	+	0.946891i	$0.604205\pi$
$332$	−0.593813	−0.0325897
$333$	−4.53215	−0.248360
$334$	29.0618	1.59019
$335$	−13.9953	−0.764646
$336$	0	0
$337$	12.6186	0.687377	0.343689	−	0.939084i	$-0.388324\pi$
$337$	12.6186	0.687377	0.343689	+	0.939084i	$0.388324\pi$
$338$	16.8728	0.917758
$339$	−8.96160	−0.486728
$340$	−1.34632	−0.0730144
$341$	6.46310	0.349996
$342$	−4.53274	−0.245103
$343$	0	0
$344$	−19.3944	−1.04568
$345$	−15.6045	−0.840120
$346$	32.8463	1.76583
$347$	−22.2243	−1.19306	−0.596530	−	0.802591i	$-0.703454\pi$
$347$	−22.2243	−1.19306	−0.596530	+	0.802591i	$0.703454\pi$
$348$	0.166368	0.00891828
$349$	27.5451	1.47445	0.737227	−	0.675645i	$-0.236135\pi$
$349$	27.5451	1.47445	0.737227	+	0.675645i	$0.236135\pi$
$350$	0	0
$351$	1.13302	0.0604759
$352$	−1.55302	−0.0827760
$353$	−8.11789	−0.432072	−0.216036	−	0.976385i	$-0.569313\pi$
$353$	−8.11789	−0.432072	−0.216036	+	0.976385i	$0.569313\pi$
$354$	5.58397	0.296785
$355$	24.2026	1.28454
$356$	−0.687696	−0.0364478
$357$	0	0
$358$	−32.2546	−1.70471
$359$	−16.6316	−0.877782	−0.438891	−	0.898540i	$-0.644629\pi$
$359$	−16.6316	−0.877782	−0.438891	+	0.898540i	$0.644629\pi$
$360$	8.90270	0.469214
$361$	−9.09334	−0.478597
$362$	−27.2305	−1.43121
$363$	2.80350	0.147145
$364$	0	0
$365$	−29.2613	−1.53161
$366$	−11.7665	−0.615043
$367$	23.5211	1.22779	0.613897	−	0.789386i	$-0.289601\pi$
$367$	23.5211	1.22779	0.613897	+	0.789386i	$0.289601\pi$
$368$	20.1396	1.04985
$369$	1.00000	0.0520579
$370$	20.9486	1.08906
$371$	0	0
$372$	−0.128609	−0.00666808
$373$	14.4062	0.745923	0.372962	−	0.927847i	$-0.378342\pi$
$373$	14.4062	0.745923	0.372962	+	0.927847i	$0.378342\pi$
$374$	−30.3571	−1.56973
$375$	0.968108	0.0499929
$376$	−17.8633	−0.921231
$377$	2.54965	0.131314
$378$	0	0
$379$	4.88799	0.251079	0.125540	−	0.992089i	$-0.459934\pi$
$379$	4.88799	0.251079	0.125540	+	0.992089i	$0.459934\pi$
$380$	0.746866	0.0383134
$381$	15.5846	0.798423
$382$	−27.9203	−1.42852
$383$	22.8952	1.16989	0.584944	−	0.811074i	$-0.301116\pi$
$383$	22.8952	1.16989	0.584944	+	0.811074i	$0.301116\pi$
$384$	−11.9001	−0.607277
$385$	0	0
$386$	12.9518	0.659228
$387$	−6.99210	−0.355428
$388$	−1.32333	−0.0671821
$389$	13.6469	0.691925	0.345962	−	0.938248i	$-0.387553\pi$
$389$	13.6469	0.691925	0.345962	+	0.938248i	$0.387553\pi$
$390$	−5.23704	−0.265188
$391$	27.5846	1.39501
$392$	0	0
$393$	11.1927	0.564599
$394$	23.9517	1.20667
$395$	0.152160	0.00765598
$396$	−0.274676	−0.0138030
$397$	7.08009	0.355339	0.177670	−	0.984090i	$-0.443144\pi$
$397$	7.08009	0.355339	0.177670	+	0.984090i	$0.443144\pi$
$398$	−12.9438	−0.648814
$399$	0	0
$400$	−21.9614	−1.09807
$401$	−29.9703	−1.49665	−0.748323	−	0.663335i	$-0.769141\pi$
$401$	−29.9703	−1.49665	−0.748323	+	0.663335i	$0.769141\pi$
$402$	6.27953	0.313194
$403$	−1.97098	−0.0981815
$404$	−0.230552	−0.0114704
$405$	3.20961	0.159487
$406$	0	0
$407$	16.8383	0.834645
$408$	−15.7376	−0.779126
$409$	−13.3731	−0.661258	−0.330629	−	0.943761i	$-0.607261\pi$
$409$	−13.3731	−0.661258	−0.330629	+	0.943761i	$0.607261\pi$
$410$	−4.62221	−0.228275
$411$	−9.63284	−0.475153
$412$	0.210983	0.0103944
$413$	0	0
$414$	7.00157	0.344108
$415$	−25.7796	−1.26547
$416$	0.473606	0.0232205
$417$	−12.4957	−0.611916
$418$	16.8405	0.823697
$419$	−24.2251	−1.18348	−0.591738	−	0.806131i	$-0.701558\pi$
$419$	−24.2251	−1.18348	−0.591738	+	0.806131i	$0.701558\pi$
$420$	0	0
$421$	−13.2818	−0.647314	−0.323657	−	0.946174i	$-0.604912\pi$
$421$	−13.2818	−0.647314	−0.323657	+	0.946174i	$0.604912\pi$
$422$	−37.2979	−1.81564
$423$	−6.44011	−0.313129
$424$	9.42239	0.457592
$425$	−30.0800	−1.45909
$426$	−10.8594	−0.526140
$427$	0	0
$428$	0.949052	0.0458742
$429$	−4.20950	−0.203237
$430$	32.3190	1.55856
$431$	16.2256	0.781562	0.390781	−	0.920484i	$-0.372205\pi$
$431$	16.2256	0.781562	0.390781	+	0.920484i	$0.372205\pi$
$432$	−4.14240	−0.199301
$433$	−1.61340	−0.0775351	−0.0387675	−	0.999248i	$-0.512343\pi$
$433$	−1.61340	−0.0775351	−0.0387675	+	0.999248i	$0.512343\pi$
$434$	0	0
$435$	7.22267	0.346300
$436$	−1.43667	−0.0688042
$437$	−15.3025	−0.732017
$438$	13.1292	0.627337
$439$	−15.4861	−0.739113	−0.369556	−	0.929208i	$-0.620490\pi$
$439$	−15.4861	−0.739113	−0.369556	+	0.929208i	$0.620490\pi$
$440$	−33.0763	−1.57685
$441$	0	0
$442$	9.25768	0.440343
$443$	−12.9825	−0.616817	−0.308409	−	0.951254i	$-0.599796\pi$
$443$	−12.9825	−0.616817	−0.308409	+	0.951254i	$0.599796\pi$
$444$	−0.335066	−0.0159015
$445$	−29.8554	−1.41528
$446$	−26.0844	−1.23513
$447$	−13.7960	−0.652528
$448$	0	0
$449$	−25.4508	−1.20110	−0.600549	−	0.799588i	$-0.705051\pi$
$449$	−25.4508	−1.20110	−0.600549	+	0.799588i	$0.705051\pi$
$450$	−7.63495	−0.359915
$451$	−3.71531	−0.174947
$452$	−0.662540	−0.0311633
$453$	15.3274	0.720144
$454$	18.7207	0.878604
$455$	0	0
$456$	8.73037	0.408837
$457$	14.1521	0.662009	0.331004	−	0.943629i	$-0.392613\pi$
$457$	14.1521	0.662009	0.331004	+	0.943629i	$0.392613\pi$
$458$	−7.89716	−0.369010
$459$	−5.67373	−0.264827
$460$	−1.15366	−0.0537896
$461$	1.10138	0.0512963	0.0256481	−	0.999671i	$-0.491835\pi$
$461$	1.10138	0.0512963	0.0256481	+	0.999671i	$0.491835\pi$
$462$	0	0
$463$	−18.5041	−0.859958	−0.429979	−	0.902839i	$-0.641479\pi$
$463$	−18.5041	−0.859958	−0.429979	+	0.902839i	$0.641479\pi$
$464$	−9.32173	−0.432750
$465$	−5.58340	−0.258924
$466$	−13.2483	−0.613714
$467$	26.1402	1.20962	0.604812	−	0.796368i	$-0.293248\pi$
$467$	26.1402	1.20962	0.604812	+	0.796368i	$0.293248\pi$
$468$	0.0837649	0.00387204
$469$	0	0
$470$	29.7676	1.37308
$471$	−5.91126	−0.272377
$472$	−10.7551	−0.495044
$473$	25.9778	1.19446
$474$	−0.0682721	−0.00313584
$475$	16.6868	0.765643
$476$	0	0
$477$	3.39697	0.155537
$478$	−1.18530	−0.0542143
$479$	−31.4816	−1.43843	−0.719216	−	0.694787i	$-0.755499\pi$
$479$	−31.4816	−1.43843	−0.719216	+	0.694787i	$0.755499\pi$
$480$	1.34163	0.0612369
$481$	−5.13500	−0.234136
$482$	−9.33563	−0.425226
$483$	0	0
$484$	0.207265	0.00942115
$485$	−57.4508	−2.60871
$486$	−1.44011	−0.0653249
$487$	14.3104	0.648468	0.324234	−	0.945977i	$-0.394893\pi$
$487$	14.3104	0.648468	0.324234	+	0.945977i	$0.394893\pi$
$488$	22.6630	1.02591
$489$	9.18322	0.415279
$490$	0	0
$491$	−21.7811	−0.982969	−0.491485	−	0.870886i	$-0.663546\pi$
$491$	−21.7811	−0.982969	−0.491485	+	0.870886i	$0.663546\pi$
$492$	0.0739309	0.00333306
$493$	−12.7677	−0.575029
$494$	−5.13567	−0.231065
$495$	−11.9247	−0.535975
$496$	7.20606	0.323561
$497$	0	0
$498$	11.5670	0.518330
$499$	−6.73070	−0.301308	−0.150654	−	0.988587i	$-0.548138\pi$
$499$	−6.73070	−0.301308	−0.150654	+	0.988587i	$0.548138\pi$
$500$	0.0715731	0.00320085
$501$	−20.1802	−0.901585
$502$	−15.9841	−0.713406
$503$	14.8815	0.663535	0.331768	−	0.943361i	$-0.392355\pi$
$503$	14.8815	0.663535	0.331768	+	0.943361i	$0.392355\pi$
$504$	0	0
$505$	−10.0091	−0.445399
$506$	−26.0130	−1.15642
$507$	−11.7163	−0.520338
$508$	1.15218	0.0511199
$509$	1.57147	0.0696542	0.0348271	−	0.999393i	$-0.488912\pi$
$509$	1.57147	0.0696542	0.0348271	+	0.999393i	$0.488912\pi$
$510$	26.2252	1.16127
$511$	0	0
$512$	21.2485	0.939059
$513$	3.14749	0.138965
$514$	13.5970	0.599737
$515$	9.15954	0.403618
$516$	−0.516932	−0.0227567
$517$	23.9270	1.05231
$518$	0	0
$519$	−22.8081	−1.00116
$520$	10.0869	0.442340
$521$	4.01664	0.175972	0.0879861	−	0.996122i	$-0.471957\pi$
$521$	4.01664	0.175972	0.0879861	+	0.996122i	$0.471957\pi$
$522$	−3.24072	−0.141843
$523$	−8.94282	−0.391042	−0.195521	−	0.980699i	$-0.562640\pi$
$523$	−8.94282	−0.391042	−0.195521	+	0.980699i	$0.562640\pi$
$524$	0.827489	0.0361490
$525$	0	0
$526$	18.0610	0.787496
$527$	9.86995	0.429942
$528$	15.3903	0.669775
$529$	0.637219	0.0277052
$530$	−15.7015	−0.682031
$531$	−3.87745	−0.168267
$532$	0	0
$533$	1.13302	0.0490764
$534$	13.3958	0.579691
$535$	41.2019	1.78131
$536$	−12.0948	−0.522416
$537$	22.3973	0.966513
$538$	−3.28628	−0.141681
$539$	0	0
$540$	0.237290	0.0102113
$541$	22.1175	0.950907	0.475453	−	0.879741i	$-0.342284\pi$
$541$	22.1175	0.950907	0.475453	+	0.879741i	$0.342284\pi$
$542$	17.5856	0.755367
$543$	18.9086	0.811445
$544$	−2.37165	−0.101683
$545$	−62.3713	−2.67169
$546$	0	0
$547$	−3.20726	−0.137133	−0.0685663	−	0.997647i	$-0.521842\pi$
$547$	−3.20726	−0.137133	−0.0685663	+	0.997647i	$0.521842\pi$
$548$	−0.712165	−0.0304222
$549$	8.17051	0.348709
$550$	28.3662	1.20954
$551$	7.08286	0.301740
$552$	−13.4855	−0.573981
$553$	0	0
$554$	35.6121	1.51302
$555$	−14.5465	−0.617463
$556$	−0.923817	−0.0391786
$557$	−36.1547	−1.53192	−0.765962	−	0.642886i	$-0.777737\pi$
$557$	−36.1547	−1.53192	−0.765962	+	0.642886i	$0.777737\pi$
$558$	2.50520	0.106054
$559$	−7.92216	−0.335072
$560$	0	0
$561$	21.0796	0.889983
$562$	7.01463	0.295894
$563$	37.3991	1.57619	0.788093	−	0.615557i	$-0.211069\pi$
$563$	37.3991	1.57619	0.788093	+	0.615557i	$0.211069\pi$
$564$	−0.476124	−0.0200484
$565$	−28.7633	−1.21008
$566$	−6.38697	−0.268464
$567$	0	0
$568$	20.9160	0.877614
$569$	−38.4021	−1.60990	−0.804950	−	0.593342i	$-0.797808\pi$
$569$	−38.4021	−1.60990	−0.804950	+	0.593342i	$0.797808\pi$
$570$	−14.5484	−0.609363
$571$	35.3708	1.48022	0.740112	−	0.672484i	$-0.234773\pi$
$571$	35.3708	1.48022	0.740112	+	0.672484i	$0.234773\pi$
$572$	−0.311212	−0.0130124
$573$	19.3875	0.809925
$574$	0	0
$575$	−25.7755	−1.07491
$576$	7.68282	0.320117
$577$	7.03644	0.292931	0.146465	−	0.989216i	$-0.453210\pi$
$577$	7.03644	0.292931	0.146465	+	0.989216i	$0.453210\pi$
$578$	−21.8771	−0.909967
$579$	−8.99357	−0.373760
$580$	0.533979	0.0221723
$581$	0	0
$582$	25.7775	1.06851
$583$	−12.6208	−0.522700
$584$	−25.2877	−1.04641
$585$	3.63655	0.150353
$586$	−15.0687	−0.622484
$587$	−42.9014	−1.77073	−0.885365	−	0.464897i	$-0.846091\pi$
$587$	−42.9014	−1.77073	−0.885365	+	0.464897i	$0.846091\pi$
$588$	0	0
$589$	−5.47532	−0.225607
$590$	17.9224	0.737853
$591$	−16.6318	−0.684141
$592$	18.7740	0.771605
$593$	−29.8073	−1.22404	−0.612019	−	0.790843i	$-0.709642\pi$
$593$	−29.8073	−1.22404	−0.612019	+	0.790843i	$0.709642\pi$
$594$	5.35047	0.219532
$595$	0	0
$596$	−1.01995	−0.0417788
$597$	8.98803	0.367855
$598$	7.93289	0.324400
$599$	−4.94543	−0.202065	−0.101032	−	0.994883i	$-0.532215\pi$
$599$	−4.94543	−0.202065	−0.101032	+	0.994883i	$0.532215\pi$
$600$	14.7054	0.600347
$601$	31.4634	1.28342	0.641709	−	0.766948i	$-0.278226\pi$
$601$	31.4634	1.28342	0.641709	+	0.766948i	$0.278226\pi$
$602$	0	0
$603$	−4.36043	−0.177571
$604$	1.13317	0.0461080
$605$	8.99815	0.365827
$606$	4.49096	0.182433
$607$	19.3517	0.785461	0.392730	−	0.919654i	$-0.371531\pi$
$607$	19.3517	0.785461	0.392730	+	0.919654i	$0.371531\pi$
$608$	1.31566	0.0533572
$609$	0	0
$610$	−37.7658	−1.52909
$611$	−7.29675	−0.295195
$612$	−0.419464	−0.0169558
$613$	−24.5783	−0.992708	−0.496354	−	0.868120i	$-0.665328\pi$
$613$	−24.5783	−0.992708	−0.496354	+	0.868120i	$0.665328\pi$
$614$	6.67948	0.269562
$615$	3.20961	0.129424
$616$	0	0
$617$	−41.2037	−1.65880	−0.829399	−	0.558657i	$-0.811317\pi$
$617$	−41.2037	−1.65880	−0.829399	+	0.558657i	$0.811317\pi$
$618$	−4.10978	−0.165319
$619$	10.0042	0.402102	0.201051	−	0.979581i	$-0.435564\pi$
$619$	10.0042	0.402102	0.201051	+	0.979581i	$0.435564\pi$
$620$	−0.412786	−0.0165779
$621$	−4.86181	−0.195098
$622$	−7.18264	−0.287998
$623$	0	0
$624$	−4.69340	−0.187886
$625$	−23.4009	−0.936035
$626$	−17.3529	−0.693561
$627$	−11.6939	−0.467008
$628$	−0.437025	−0.0174392
$629$	25.7142	1.02529
$630$	0	0
$631$	−20.0998	−0.800162	−0.400081	−	0.916480i	$-0.631018\pi$
$631$	−20.0998	−0.800162	−0.400081	+	0.916480i	$0.631018\pi$
$632$	0.131497	0.00523066
$633$	25.8993	1.02940
$634$	−24.8672	−0.987603
$635$	50.0205	1.98500
$636$	0.251141	0.00995841
$637$	0	0
$638$	12.0403	0.476679
$639$	7.54065	0.298303
$640$	−38.1949	−1.50979
$641$	11.2048	0.442564	0.221282	−	0.975210i	$-0.428976\pi$
$641$	11.2048	0.442564	0.221282	+	0.975210i	$0.428976\pi$
$642$	−18.4868	−0.729615
$643$	−11.0643	−0.436334	−0.218167	−	0.975911i	$-0.570008\pi$
$643$	−11.0643	−0.436334	−0.218167	+	0.975911i	$0.570008\pi$
$644$	0	0
$645$	−22.4419	−0.883651
$646$	25.7175	1.01184
$647$	−0.620088	−0.0243782	−0.0121891	−	0.999926i	$-0.503880\pi$
$647$	−0.620088	−0.0243782	−0.0121891	+	0.999926i	$0.503880\pi$
$648$	2.77376	0.108964
$649$	14.4059	0.565481
$650$	−8.65053	−0.339302
$651$	0	0
$652$	0.678924	0.0265887
$653$	32.5395	1.27337	0.636684	−	0.771125i	$-0.280306\pi$
$653$	32.5395	1.27337	0.636684	+	0.771125i	$0.280306\pi$
$654$	27.9852	1.09431
$655$	35.9244	1.40368
$656$	−4.14240	−0.161733
$657$	−9.11677	−0.355679
$658$	0	0
$659$	−40.2250	−1.56694	−0.783472	−	0.621427i	$-0.786553\pi$
$659$	−40.2250	−1.56694	−0.783472	+	0.621427i	$0.786553\pi$
$660$	−0.881604	−0.0343164
$661$	8.07046	0.313904	0.156952	−	0.987606i	$-0.449833\pi$
$661$	8.07046	0.313904	0.156952	+	0.987606i	$0.449833\pi$
$662$	16.8499	0.654888
$663$	−6.42843	−0.249659
$664$	−22.2788	−0.864587
$665$	0	0
$666$	6.52682	0.252909
$667$	−10.9406	−0.423623
$668$	−1.49194	−0.0577249
$669$	18.1127	0.700278
$670$	20.1549	0.778650
$671$	−30.3559	−1.17188
$672$	0	0
$673$	−8.65901	−0.333780	−0.166890	−	0.985976i	$-0.553373\pi$
$673$	−8.65901	−0.333780	−0.166890	+	0.985976i	$0.553373\pi$
$674$	−18.1722	−0.699967
$675$	5.30163	0.204060
$676$	−0.866195	−0.0333152
$677$	−41.8965	−1.61021	−0.805106	−	0.593131i	$-0.797892\pi$
$677$	−41.8965	−1.61021	−0.805106	+	0.593131i	$0.797892\pi$
$678$	12.9057	0.495642
$679$	0	0
$680$	−50.5115	−1.93703
$681$	−12.9994	−0.498139
$682$	−9.30760	−0.356406
$683$	3.33986	0.127796	0.0638981	−	0.997956i	$-0.479647\pi$
$683$	3.33986	0.127796	0.0638981	+	0.997956i	$0.479647\pi$
$684$	0.232697	0.00889737
$685$	−30.9177	−1.18130
$686$	0	0
$687$	5.48370	0.209216
$688$	28.9640	1.10424
$689$	3.84883	0.146629
$690$	22.4723	0.855507
$691$	−37.2226	−1.41602	−0.708008	−	0.706205i	$-0.750406\pi$
$691$	−37.2226	−1.41602	−0.708008	+	0.706205i	$0.750406\pi$
$692$	−1.68622	−0.0641006
$693$	0	0
$694$	32.0055	1.21491
$695$	−40.1063	−1.52132
$696$	6.24186	0.236597
$697$	−5.67373	−0.214908
$698$	−39.6681	−1.50146
$699$	9.19946	0.347955
$700$	0	0
$701$	9.14668	0.345465	0.172733	−	0.984969i	$-0.444740\pi$
$701$	9.14668	0.345465	0.172733	+	0.984969i	$0.444740\pi$
$702$	−1.63167	−0.0615836
$703$	−14.2649	−0.538010
$704$	−28.5440	−1.07579
$705$	−20.6703	−0.778488
$706$	11.6907	0.439985
$707$	0	0
$708$	−0.286663	−0.0107735
$709$	−6.00600	−0.225560	−0.112780	−	0.993620i	$-0.535976\pi$
$709$	−6.00600	−0.225560	−0.112780	+	0.993620i	$0.535976\pi$
$710$	−34.8545	−1.30807
$711$	0.0474074	0.00177792
$712$	−25.8012	−0.966939
$713$	8.45754	0.316737
$714$	0	0
$715$	−13.5109	−0.505278
$716$	1.65585	0.0618820
$717$	0.823059	0.0307377
$718$	23.9514	0.893859
$719$	−33.9920	−1.26769	−0.633844	−	0.773461i	$-0.718524\pi$
$719$	−33.9920	−1.26769	−0.633844	+	0.773461i	$0.718524\pi$
$720$	−13.2955	−0.495494
$721$	0	0
$722$	13.0954	0.487362
$723$	6.48256	0.241089
$724$	1.39793	0.0519536
$725$	11.9304	0.443083
$726$	−4.03736	−0.149840
$727$	−16.9197	−0.627516	−0.313758	−	0.949503i	$-0.601588\pi$
$727$	−16.9197	−0.627516	−0.313758	+	0.949503i	$0.601588\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	42.1397	1.55966
$731$	39.6713	1.46730
$732$	0.604053	0.0223265
$733$	41.7959	1.54377	0.771884	−	0.635763i	$-0.219315\pi$
$733$	41.7959	1.54377	0.771884	+	0.635763i	$0.219315\pi$
$734$	−33.8731	−1.25028
$735$	0	0
$736$	−2.03226	−0.0749101
$737$	16.2003	0.596747
$738$	−1.44011	−0.0530114
$739$	−9.12094	−0.335519	−0.167760	−	0.985828i	$-0.553653\pi$
$739$	−9.12094	−0.335519	−0.167760	+	0.985828i	$0.553653\pi$
$740$	−1.07543	−0.0395337
$741$	3.56615	0.131006
$742$	0	0
$743$	31.7676	1.16544	0.582720	−	0.812673i	$-0.301988\pi$
$743$	31.7676	1.16544	0.582720	+	0.812673i	$0.301988\pi$
$744$	−4.82520	−0.176900
$745$	−44.2798	−1.62229
$746$	−20.7465	−0.759585
$747$	−8.03200	−0.293875
$748$	1.55844	0.0569821
$749$	0	0
$750$	−1.39419	−0.0509085
$751$	−2.28714	−0.0834590	−0.0417295	−	0.999129i	$-0.513287\pi$
$751$	−2.28714	−0.0834590	−0.0417295	+	0.999129i	$0.513287\pi$
$752$	26.6775	0.972828
$753$	11.0992	0.404477
$754$	−3.67179	−0.133719
$755$	49.1950	1.79039
$756$	0	0
$757$	34.8962	1.26832	0.634162	−	0.773201i	$-0.281345\pi$
$757$	34.8962	1.26832	0.634162	+	0.773201i	$0.281345\pi$
$758$	−7.03927	−0.255678
$759$	18.0631	0.655650
$760$	28.0211	1.01643
$761$	−21.0081	−0.761544	−0.380772	−	0.924669i	$-0.624342\pi$
$761$	−21.0081	−0.761544	−0.380772	+	0.924669i	$0.624342\pi$
$762$	−22.4436	−0.813046
$763$	0	0
$764$	1.43334	0.0518563
$765$	−18.2105	−0.658402
$766$	−32.9717	−1.19131
$767$	−4.39321	−0.158630
$768$	1.77195	0.0639397
$769$	18.4285	0.664548	0.332274	−	0.943183i	$-0.392184\pi$
$769$	18.4285	0.664548	0.332274	+	0.943183i	$0.392184\pi$
$770$	0	0
$771$	−9.44160	−0.340031
$772$	−0.664903	−0.0239304
$773$	53.0919	1.90958	0.954791	−	0.297277i	$-0.0960783\pi$
$773$	53.0919	1.90958	0.954791	+	0.297277i	$0.0960783\pi$
$774$	10.0694	0.361938
$775$	−9.22264	−0.331287
$776$	−49.6492	−1.78230
$777$	0	0
$778$	−19.6531	−0.704597
$779$	3.14749	0.112770
$780$	0.268853	0.00962649
$781$	−28.0158	−1.00248
$782$	−39.7250	−1.42056
$783$	2.25032	0.0804200
$784$	0	0
$785$	−18.9729	−0.677171
$786$	−16.1188	−0.574939
$787$	23.7459	0.846451	0.423226	−	0.906024i	$-0.360898\pi$
$787$	23.7459	0.846451	0.423226	+	0.906024i	$0.360898\pi$
$788$	−1.22960	−0.0438029
$789$	−12.5414	−0.446484
$790$	−0.219127	−0.00779620
$791$	0	0
$792$	−10.3054	−0.366185
$793$	9.25732	0.328737
$794$	−10.1961	−0.361847
$795$	10.9030	0.386689
$796$	0.664493	0.0235523
$797$	49.8669	1.76638	0.883189	−	0.469018i	$-0.155392\pi$
$797$	49.8669	1.76638	0.883189	+	0.469018i	$0.155392\pi$
$798$	0	0
$799$	36.5395	1.29267
$800$	2.21611	0.0783512
$801$	−9.30187	−0.328665
$802$	43.1607	1.52406
$803$	33.8716	1.19530
$804$	−0.322371	−0.0113691
$805$	0	0
$806$	2.83844	0.0999797
$807$	2.28195	0.0803286
$808$	−8.64990	−0.304302
$809$	8.65135	0.304165	0.152083	−	0.988368i	$-0.451402\pi$
$809$	8.65135	0.304165	0.152083	+	0.988368i	$0.451402\pi$
$810$	−4.62221	−0.162408
$811$	42.3391	1.48673	0.743363	−	0.668888i	$-0.233229\pi$
$811$	42.3391	1.48673	0.743363	+	0.668888i	$0.233229\pi$
$812$	0	0
$813$	−12.2113	−0.428268
$814$	−24.2491	−0.849931
$815$	29.4746	1.03245
$816$	23.5028	0.822764
$817$	−22.0075	−0.769946
$818$	19.2588	0.673369
$819$	0	0
$820$	0.237290	0.00828652
$821$	14.9198	0.520703	0.260352	−	0.965514i	$-0.416162\pi$
$821$	14.9198	0.520703	0.260352	+	0.965514i	$0.416162\pi$
$822$	13.8724	0.483855
$823$	−42.3059	−1.47469	−0.737346	−	0.675516i	$-0.763921\pi$
$823$	−42.3059	−1.47469	−0.737346	+	0.675516i	$0.763921\pi$
$824$	7.91571	0.275757
$825$	−19.6972	−0.685767
$826$	0	0
$827$	18.8508	0.655507	0.327754	−	0.944763i	$-0.393708\pi$
$827$	18.8508	0.655507	0.327754	+	0.944763i	$0.393708\pi$
$828$	−0.359438	−0.0124913
$829$	−19.0982	−0.663307	−0.331654	−	0.943401i	$-0.607606\pi$
$829$	−19.0982	−0.663307	−0.331654	+	0.943401i	$0.607606\pi$
$830$	37.1256	1.28865
$831$	−24.7287	−0.857829
$832$	8.70476	0.301783
$833$	0	0
$834$	17.9952	0.623123
$835$	−64.7706	−2.24148
$836$	−0.864539	−0.0299007
$837$	−1.73959	−0.0601289
$838$	34.8870	1.20515
$839$	−48.6318	−1.67895	−0.839477	−	0.543395i	$-0.817139\pi$
$839$	−48.6318	−1.67895	−0.839477	+	0.543395i	$0.817139\pi$
$840$	0	0
$841$	−23.9360	−0.825381
$842$	19.1273	0.659170
$843$	−4.87088	−0.167762
$844$	1.91476	0.0659087
$845$	−37.6047	−1.29364
$846$	9.27450	0.318864
$847$	0	0
$848$	−14.0716	−0.483221
$849$	4.43504	0.152210
$850$	43.3187	1.48582
$851$	22.0345	0.755332
$852$	0.557487	0.0190992
$853$	−44.9375	−1.53863	−0.769316	−	0.638868i	$-0.779403\pi$
$853$	−44.9375	−1.53863	−0.769316	+	0.638868i	$0.779403\pi$
$854$	0	0
$855$	10.1022	0.345488
$856$	35.6068	1.21702
$857$	−5.26810	−0.179955	−0.0899774	−	0.995944i	$-0.528679\pi$
$857$	−5.26810	−0.179955	−0.0899774	+	0.995944i	$0.528679\pi$
$858$	6.06217	0.206959
$859$	−22.2259	−0.758336	−0.379168	−	0.925328i	$-0.623790\pi$
$859$	−22.2259	−0.758336	−0.379168	+	0.925328i	$0.623790\pi$
$860$	−1.65915	−0.0565767
$861$	0	0
$862$	−23.3668	−0.795876
$863$	−1.76373	−0.0600380	−0.0300190	−	0.999549i	$-0.509557\pi$
$863$	−1.76373	−0.0600380	−0.0300190	+	0.999549i	$0.509557\pi$
$864$	0.418005	0.0142208
$865$	−73.2052	−2.48905
$866$	2.32348	0.0789551
$867$	15.1912	0.515921
$868$	0	0
$869$	−0.176133	−0.00597491
$870$	−10.4015	−0.352643
$871$	−4.94044	−0.167401
$872$	−53.9015	−1.82533
$873$	−17.8996	−0.605809
$874$	22.0373	0.745424
$875$	0	0
$876$	−0.674011	−0.0227727
$877$	30.4164	1.02709	0.513544	−	0.858063i	$-0.328332\pi$
$877$	30.4164	1.02709	0.513544	+	0.858063i	$0.328332\pi$
$878$	22.3018	0.752649
$879$	10.4636	0.352928
$880$	49.3968	1.66517
$881$	−30.7584	−1.03628	−0.518138	−	0.855297i	$-0.673375\pi$
$881$	−30.7584	−1.03628	−0.518138	+	0.855297i	$0.673375\pi$
$882$	0	0
$883$	40.3820	1.35896	0.679482	−	0.733693i	$-0.262205\pi$
$883$	40.3820	1.35896	0.679482	+	0.733693i	$0.262205\pi$
$884$	−0.475260	−0.0159847
$885$	−12.4451	−0.418338
$886$	18.6963	0.628114
$887$	−15.3104	−0.514073	−0.257037	−	0.966402i	$-0.582746\pi$
$887$	−15.3104	−0.514073	−0.257037	+	0.966402i	$0.582746\pi$
$888$	−12.5711	−0.421859
$889$	0	0
$890$	42.9952	1.44120
$891$	−3.71531	−0.124467
$892$	1.33909	0.0448360
$893$	−20.2702	−0.678315
$894$	19.8678	0.664479
$895$	71.8866	2.40290
$896$	0	0
$897$	−5.50851	−0.183924
$898$	36.6521	1.22310
$899$	−3.91463	−0.130560
$900$	0.391954	0.0130651
$901$	−19.2735	−0.642094
$902$	5.35047	0.178151
$903$	0	0
$904$	−24.8573	−0.826743
$905$	60.6893	2.01738
$906$	−22.0732	−0.733333
$907$	−37.4485	−1.24346	−0.621728	−	0.783233i	$-0.713569\pi$
$907$	−37.4485	−1.24346	−0.621728	+	0.783233i	$0.713569\pi$
$908$	−0.961060	−0.0318939
$909$	−3.11847	−0.103433
$910$	0	0
$911$	−14.5170	−0.480969	−0.240485	−	0.970653i	$-0.577306\pi$
$911$	−14.5170	−0.480969	−0.240485	+	0.970653i	$0.577306\pi$
$912$	−13.0381	−0.431736
$913$	29.8413	0.987604
$914$	−20.3807	−0.674133
$915$	26.2242	0.866945
$916$	0.405415	0.0133953
$917$	0	0
$918$	8.17082	0.269677
$919$	9.79265	0.323030	0.161515	−	0.986870i	$-0.448362\pi$
$919$	9.79265	0.323030	0.161515	+	0.986870i	$0.448362\pi$
$920$	−43.2833	−1.42701
$921$	−4.63816	−0.152832
$922$	−1.58611	−0.0522357
$923$	8.54368	0.281219
$924$	0	0
$925$	−24.0278	−0.790028
$926$	26.6480	0.875708
$927$	2.85378	0.0937305
$928$	0.940645	0.0308782
$929$	34.6323	1.13625	0.568124	−	0.822943i	$-0.307669\pi$
$929$	34.6323	1.13625	0.568124	+	0.822943i	$0.307669\pi$
$930$	8.04074	0.263666
$931$	0	0
$932$	0.680124	0.0222782
$933$	4.98755	0.163285
$934$	−37.6449	−1.23178
$935$	67.6575	2.21264
$936$	3.14272	0.102723
$937$	26.5941	0.868793	0.434396	−	0.900722i	$-0.356962\pi$
$937$	26.5941	0.868793	0.434396	+	0.900722i	$0.356962\pi$
$938$	0	0
$939$	12.0497	0.393226
$940$	−1.52817	−0.0498435
$941$	48.6579	1.58620	0.793101	−	0.609091i	$-0.208465\pi$
$941$	48.6579	1.58620	0.793101	+	0.609091i	$0.208465\pi$
$942$	8.51289	0.277365
$943$	−4.86181	−0.158322
$944$	16.0619	0.522771
$945$	0	0
$946$	−37.4110	−1.21634
$947$	20.1400	0.654462	0.327231	−	0.944944i	$-0.393885\pi$
$947$	20.1400	0.654462	0.327231	+	0.944944i	$0.393885\pi$
$948$	0.00350487	0.000113833 0
$949$	−10.3294	−0.335308
$950$	−24.0309	−0.779665
$951$	17.2675	0.559937
$952$	0	0
$953$	2.71373	0.0879063	0.0439531	−	0.999034i	$-0.486005\pi$
$953$	2.71373	0.0879063	0.0439531	+	0.999034i	$0.486005\pi$
$954$	−4.89203	−0.158385
$955$	62.2265	2.01360
$956$	0.0608495	0.00196801
$957$	−8.36064	−0.270261
$958$	45.3371	1.46478
$959$	0	0
$960$	24.6589	0.795862
$961$	−27.9738	−0.902382
$962$	7.39499	0.238424
$963$	12.8370	0.413667
$964$	0.479262	0.0154360
$965$	−28.8659	−0.929226
$966$	0	0
$967$	−45.3281	−1.45765	−0.728827	−	0.684698i	$-0.759934\pi$
$967$	−45.3281	−1.45765	−0.728827	+	0.684698i	$0.759934\pi$
$968$	7.77623	0.249938
$969$	−17.8580	−0.573681
$970$	82.7357	2.65648
$971$	−55.2056	−1.77163	−0.885816	−	0.464036i	$-0.846401\pi$
$971$	−55.2056	−1.77163	−0.885816	+	0.464036i	$0.846401\pi$
$972$	0.0739309	0.00237134
$973$	0	0
$974$	−20.6087	−0.660345
$975$	6.00683	0.192373
$976$	−33.8455	−1.08337
$977$	−26.8269	−0.858268	−0.429134	−	0.903241i	$-0.641181\pi$
$977$	−26.8269	−0.858268	−0.429134	+	0.903241i	$0.641181\pi$
$978$	−13.2249	−0.422885
$979$	34.5593	1.10452
$980$	0	0
$981$	−19.4326	−0.620436
$982$	31.3673	1.00097
$983$	19.9926	0.637664	0.318832	−	0.947811i	$-0.396709\pi$
$983$	19.9926	0.637664	0.318832	+	0.947811i	$0.396709\pi$
$984$	2.77376	0.0884243
$985$	−53.3817	−1.70088
$986$	18.3870	0.585561
$987$	0	0
$988$	0.263649	0.00838779
$989$	33.9943	1.08095
$990$	17.1729	0.545792
$991$	11.1839	0.355267	0.177633	−	0.984097i	$-0.443156\pi$
$991$	11.1839	0.355267	0.177633	+	0.984097i	$0.443156\pi$
$992$	−0.727156	−0.0230872
$993$	−11.7004	−0.371300
$994$	0	0
$995$	28.8481	0.914546
$996$	−0.593813	−0.0188157
$997$	45.4682	1.43999	0.719996	−	0.693979i	$-0.244144\pi$
$997$	45.4682	1.43999	0.719996	+	0.693979i	$0.244144\pi$
$998$	9.69298	0.306826
$999$	−4.53215	−0.143391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bm.1.6	yes	16
7.6	odd	2		6027.2.a.bl.1.6	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bl.1.6	✓	16	7.6	odd	2
6027.2.a.bm.1.6	yes	16	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)

\(f(q)\)	\(=\)	\(q-1.44011 q^{2} +1.00000 q^{3} +0.0739309 q^{4} +3.20961 q^{5} -1.44011 q^{6} +2.77376 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.44011 q^{2} +1.00000 q^{3} +0.0739309 q^{4} +3.20961 q^{5} -1.44011 q^{6} +2.77376 q^{8} +1.00000 q^{9} -4.62221 q^{10} -3.71531 q^{11} +0.0739309 q^{12} +1.13302 q^{13} +3.20961 q^{15} -4.14240 q^{16} -5.67373 q^{17} -1.44011 q^{18} +3.14749 q^{19} +0.237290 q^{20} +5.35047 q^{22} -4.86181 q^{23} +2.77376 q^{24} +5.30163 q^{25} -1.63167 q^{26} +1.00000 q^{27} +2.25032 q^{29} -4.62221 q^{30} -1.73959 q^{31} +0.418005 q^{32} -3.71531 q^{33} +8.17082 q^{34} +0.0739309 q^{36} -4.53215 q^{37} -4.53274 q^{38} +1.13302 q^{39} +8.90270 q^{40} +1.00000 q^{41} -6.99210 q^{43} -0.274676 q^{44} +3.20961 q^{45} +7.00157 q^{46} -6.44011 q^{47} -4.14240 q^{48} -7.63495 q^{50} -5.67373 q^{51} +0.0837649 q^{52} +3.39697 q^{53} -1.44011 q^{54} -11.9247 q^{55} +3.14749 q^{57} -3.24072 q^{58} -3.87745 q^{59} +0.237290 q^{60} +8.17051 q^{61} +2.50520 q^{62} +7.68282 q^{64} +3.63655 q^{65} +5.35047 q^{66} -4.36043 q^{67} -0.419464 q^{68} -4.86181 q^{69} +7.54065 q^{71} +2.77376 q^{72} -9.11677 q^{73} +6.52682 q^{74} +5.30163 q^{75} +0.232697 q^{76} -1.63167 q^{78} +0.0474074 q^{79} -13.2955 q^{80} +1.00000 q^{81} -1.44011 q^{82} -8.03200 q^{83} -18.2105 q^{85} +10.0694 q^{86} +2.25032 q^{87} -10.3054 q^{88} -9.30187 q^{89} -4.62221 q^{90} -0.359438 q^{92} -1.73959 q^{93} +9.27450 q^{94} +10.1022 q^{95} +0.418005 q^{96} -17.8996 q^{97} -3.71531 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 16 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 16 * q^3 + 12 * q^4 - 12 * q^5 - 4 * q^6 - 12 * q^8 + 16 * q^9	\( 16 q - 4 q^{2} + 16 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{8} + 16 q^{9} - 4 q^{10} - 4 q^{11} + 12 q^{12} - 12 q^{15} - 8 q^{17} - 4 q^{18} + 4 q^{19} - 20 q^{20} - 16 q^{22} - 12 q^{23} - 12 q^{24} - 8 q^{25} - 8 q^{26} + 16 q^{27} - 16 q^{29} - 4 q^{30} - 4 q^{31} - 48 q^{32} - 4 q^{33} + 16 q^{34} + 12 q^{36} - 48 q^{37} - 4 q^{38} + 56 q^{40} + 16 q^{41} - 16 q^{43} - 12 q^{45} - 4 q^{46} - 36 q^{47} - 8 q^{50} - 8 q^{51} - 60 q^{53} - 4 q^{54} + 8 q^{55} + 4 q^{57} - 36 q^{58} - 36 q^{59} - 20 q^{60} - 4 q^{61} - 12 q^{62} + 52 q^{64} - 36 q^{65} - 16 q^{66} - 52 q^{67} - 8 q^{68} - 12 q^{69} - 12 q^{71} - 12 q^{72} - 16 q^{73} + 4 q^{74} - 8 q^{75} + 16 q^{76} - 8 q^{78} - 36 q^{79} - 68 q^{80} + 16 q^{81} - 4 q^{82} - 32 q^{83} - 28 q^{85} - 8 q^{86} - 16 q^{87} - 36 q^{88} - 12 q^{89} - 4 q^{90} - 36 q^{92} - 4 q^{93} + 24 q^{94} - 20 q^{95} - 48 q^{96} + 48 q^{97} - 4 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 16 * q^3 + 12 * q^4 - 12 * q^5 - 4 * q^6 - 12 * q^8 + 16 * q^9 - 4 * q^10 - 4 * q^11 + 12 * q^12 - 12 * q^15 - 8 * q^17 - 4 * q^18 + 4 * q^19 - 20 * q^20 - 16 * q^22 - 12 * q^23 - 12 * q^24 - 8 * q^25 - 8 * q^26 + 16 * q^27 - 16 * q^29 - 4 * q^30 - 4 * q^31 - 48 * q^32 - 4 * q^33 + 16 * q^34 + 12 * q^36 - 48 * q^37 - 4 * q^38 + 56 * q^40 + 16 * q^41 - 16 * q^43 - 12 * q^45 - 4 * q^46 - 36 * q^47 - 8 * q^50 - 8 * q^51 - 60 * q^53 - 4 * q^54 + 8 * q^55 + 4 * q^57 - 36 * q^58 - 36 * q^59 - 20 * q^60 - 4 * q^61 - 12 * q^62 + 52 * q^64 - 36 * q^65 - 16 * q^66 - 52 * q^67 - 8 * q^68 - 12 * q^69 - 12 * q^71 - 12 * q^72 - 16 * q^73 + 4 * q^74 - 8 * q^75 + 16 * q^76 - 8 * q^78 - 36 * q^79 - 68 * q^80 + 16 * q^81 - 4 * q^82 - 32 * q^83 - 28 * q^85 - 8 * q^86 - 16 * q^87 - 36 * q^88 - 12 * q^89 - 4 * q^90 - 36 * q^92 - 4 * q^93 + 24 * q^94 - 20 * q^95 - 48 * q^96 + 48 * q^97 - 4 * q^99

Introduction

L-functions

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Database

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