LMFDB - Embedded newform 6027.2.a.bm.1.15

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			1.15
Root			$-2.11474$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.11474 q^{2} +1.00000 q^{3} +2.47212 q^{4} -0.285010 q^{5} +2.11474 q^{6} +0.998417 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.11474 q^{2} +1.00000 q^{3} +2.47212 q^{4} -0.285010 q^{5} +2.11474 q^{6} +0.998417 q^{8} +1.00000 q^{9} -0.602721 q^{10} -3.38810 q^{11} +2.47212 q^{12} +0.720106 q^{13} -0.285010 q^{15} -2.83285 q^{16} -4.26834 q^{17} +2.11474 q^{18} -6.19369 q^{19} -0.704579 q^{20} -7.16495 q^{22} -3.13345 q^{23} +0.998417 q^{24} -4.91877 q^{25} +1.52284 q^{26} +1.00000 q^{27} +0.696665 q^{29} -0.602721 q^{30} +9.88002 q^{31} -7.98758 q^{32} -3.38810 q^{33} -9.02642 q^{34} +2.47212 q^{36} +0.244950 q^{37} -13.0980 q^{38} +0.720106 q^{39} -0.284558 q^{40} +1.00000 q^{41} -2.01718 q^{43} -8.37580 q^{44} -0.285010 q^{45} -6.62643 q^{46} -8.72811 q^{47} -2.83285 q^{48} -10.4019 q^{50} -4.26834 q^{51} +1.78019 q^{52} -14.1567 q^{53} +2.11474 q^{54} +0.965642 q^{55} -6.19369 q^{57} +1.47327 q^{58} +9.03275 q^{59} -0.704579 q^{60} +3.37394 q^{61} +20.8937 q^{62} -11.2259 q^{64} -0.205237 q^{65} -7.16495 q^{66} +10.3436 q^{67} -10.5519 q^{68} -3.13345 q^{69} +2.17761 q^{71} +0.998417 q^{72} -11.9292 q^{73} +0.518005 q^{74} -4.91877 q^{75} -15.3116 q^{76} +1.52284 q^{78} -11.8004 q^{79} +0.807391 q^{80} +1.00000 q^{81} +2.11474 q^{82} -7.48655 q^{83} +1.21652 q^{85} -4.26581 q^{86} +0.696665 q^{87} -3.38274 q^{88} +5.06017 q^{89} -0.602721 q^{90} -7.74628 q^{92} +9.88002 q^{93} -18.4577 q^{94} +1.76526 q^{95} -7.98758 q^{96} +15.2586 q^{97} -3.38810 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 16 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 16 * q^3 + 12 * q^4 - 12 * q^5 - 4 * q^6 - 12 * q^8 + 16 * q^9	$ 16 q - 4 q^{2} + 16 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{8} + 16 q^{9} - 4 q^{10} - 4 q^{11} + 12 q^{12} - 12 q^{15} - 8 q^{17} - 4 q^{18} + 4 q^{19} - 20 q^{20} - 16 q^{22} - 12 q^{23} - 12 q^{24} - 8 q^{25} - 8 q^{26} + 16 q^{27} - 16 q^{29} - 4 q^{30} - 4 q^{31} - 48 q^{32} - 4 q^{33} + 16 q^{34} + 12 q^{36} - 48 q^{37} - 4 q^{38} + 56 q^{40} + 16 q^{41} - 16 q^{43} - 12 q^{45} - 4 q^{46} - 36 q^{47} - 8 q^{50} - 8 q^{51} - 60 q^{53} - 4 q^{54} + 8 q^{55} + 4 q^{57} - 36 q^{58} - 36 q^{59} - 20 q^{60} - 4 q^{61} - 12 q^{62} + 52 q^{64} - 36 q^{65} - 16 q^{66} - 52 q^{67} - 8 q^{68} - 12 q^{69} - 12 q^{71} - 12 q^{72} - 16 q^{73} + 4 q^{74} - 8 q^{75} + 16 q^{76} - 8 q^{78} - 36 q^{79} - 68 q^{80} + 16 q^{81} - 4 q^{82} - 32 q^{83} - 28 q^{85} - 8 q^{86} - 16 q^{87} - 36 q^{88} - 12 q^{89} - 4 q^{90} - 36 q^{92} - 4 q^{93} + 24 q^{94} - 20 q^{95} - 48 q^{96} + 48 q^{97} - 4 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 + 16 * q^3 + 12 * q^4 - 12 * q^5 - 4 * q^6 - 12 * q^8 + 16 * q^9 - 4 * q^10 - 4 * q^11 + 12 * q^12 - 12 * q^15 - 8 * q^17 - 4 * q^18 + 4 * q^19 - 20 * q^20 - 16 * q^22 - 12 * q^23 - 12 * q^24 - 8 * q^25 - 8 * q^26 + 16 * q^27 - 16 * q^29 - 4 * q^30 - 4 * q^31 - 48 * q^32 - 4 * q^33 + 16 * q^34 + 12 * q^36 - 48 * q^37 - 4 * q^38 + 56 * q^40 + 16 * q^41 - 16 * q^43 - 12 * q^45 - 4 * q^46 - 36 * q^47 - 8 * q^50 - 8 * q^51 - 60 * q^53 - 4 * q^54 + 8 * q^55 + 4 * q^57 - 36 * q^58 - 36 * q^59 - 20 * q^60 - 4 * q^61 - 12 * q^62 + 52 * q^64 - 36 * q^65 - 16 * q^66 - 52 * q^67 - 8 * q^68 - 12 * q^69 - 12 * q^71 - 12 * q^72 - 16 * q^73 + 4 * q^74 - 8 * q^75 + 16 * q^76 - 8 * q^78 - 36 * q^79 - 68 * q^80 + 16 * q^81 - 4 * q^82 - 32 * q^83 - 28 * q^85 - 8 * q^86 - 16 * q^87 - 36 * q^88 - 12 * q^89 - 4 * q^90 - 36 * q^92 - 4 * q^93 + 24 * q^94 - 20 * q^95 - 48 * q^96 + 48 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.11474	1.49535	0.747673	−	0.664067i	$-0.231171\pi$
$2$	2.11474	1.49535	0.747673	+	0.664067i	$0.231171\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.47212	1.23606
$5$	−0.285010	−0.127460	−0.0637301	−	0.997967i	$-0.520300\pi$
$5$	−0.285010	−0.127460	−0.0637301	+	0.997967i	$0.520300\pi$
$6$	2.11474	0.863339
$7$	0	0
$7$	0	0
$8$	0.998417	0.352994
$9$	1.00000	0.333333
$10$	−0.602721	−0.190597
$11$	−3.38810	−1.02155	−0.510776	−	0.859714i	$-0.670642\pi$
$11$	−3.38810	−1.02155	−0.510776	+	0.859714i	$0.670642\pi$
$12$	2.47212	0.713640
$13$	0.720106	0.199721	0.0998607	−	0.995001i	$-0.468160\pi$
$13$	0.720106	0.199721	0.0998607	+	0.995001i	$0.468160\pi$
$14$	0	0
$15$	−0.285010	−0.0735892
$16$	−2.83285	−0.708214
$17$	−4.26834	−1.03522	−0.517612	−	0.855616i	$-0.673179\pi$
$17$	−4.26834	−1.03522	−0.517612	+	0.855616i	$0.673179\pi$
$18$	2.11474	0.498449
$19$	−6.19369	−1.42093	−0.710465	−	0.703733i	$-0.751515\pi$
$19$	−6.19369	−1.42093	−0.710465	+	0.703733i	$0.751515\pi$
$20$	−0.704579	−0.157549
$21$	0	0
$22$	−7.16495	−1.52757
$23$	−3.13345	−0.653370	−0.326685	−	0.945133i	$-0.605932\pi$
$23$	−3.13345	−0.653370	−0.326685	+	0.945133i	$0.605932\pi$
$24$	0.998417	0.203801
$25$	−4.91877	−0.983754
$26$	1.52284	0.298653
$27$	1.00000	0.192450
$28$	0	0
$29$	0.696665	0.129368	0.0646838	−	0.997906i	$-0.479396\pi$
$29$	0.696665	0.129368	0.0646838	+	0.997906i	$0.479396\pi$
$30$	−0.602721	−0.110041
$31$	9.88002	1.77450	0.887252	−	0.461285i	$-0.152612\pi$
$31$	9.88002	1.77450	0.887252	+	0.461285i	$0.152612\pi$
$32$	−7.98758	−1.41202
$33$	−3.38810	−0.589793
$34$	−9.02642	−1.54802
$35$	0	0
$36$	2.47212	0.412020
$37$	0.244950	0.0402695	0.0201348	−	0.999797i	$-0.493590\pi$
$37$	0.244950	0.0402695	0.0201348	+	0.999797i	$0.493590\pi$
$38$	−13.0980	−2.12478
$39$	0.720106	0.115309
$40$	−0.284558	−0.0449926
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−2.01718	−0.307617	−0.153809	−	0.988101i	$-0.549154\pi$
$43$	−2.01718	−0.307617	−0.153809	+	0.988101i	$0.549154\pi$
$44$	−8.37580	−1.26270
$45$	−0.285010	−0.0424867
$46$	−6.62643	−0.977014
$47$	−8.72811	−1.27313	−0.636563	−	0.771225i	$-0.719644\pi$
$47$	−8.72811	−1.27313	−0.636563	+	0.771225i	$0.719644\pi$
$48$	−2.83285	−0.408887
$49$	0	0
$50$	−10.4019	−1.47105
$51$	−4.26834	−0.597687
$52$	1.78019	0.246868
$53$	−14.1567	−1.94457	−0.972283	−	0.233805i	$-0.924882\pi$
$53$	−14.1567	−1.94457	−0.972283	+	0.233805i	$0.924882\pi$
$54$	2.11474	0.287780
$55$	0.965642	0.130207
$56$	0	0
$57$	−6.19369	−0.820374
$58$	1.47327	0.193449
$59$	9.03275	1.17596	0.587982	−	0.808874i	$-0.299923\pi$
$59$	9.03275	1.17596	0.587982	+	0.808874i	$0.299923\pi$
$60$	−0.704579	−0.0909607
$61$	3.37394	0.431988	0.215994	−	0.976395i	$-0.430701\pi$
$61$	3.37394	0.431988	0.215994	+	0.976395i	$0.430701\pi$
$62$	20.8937	2.65350
$63$	0	0
$64$	−11.2259	−1.40324
$65$	−0.205237	−0.0254565
$66$	−7.16495	−0.881945
$67$	10.3436	1.26367	0.631837	−	0.775101i	$-0.282301\pi$
$67$	10.3436	1.26367	0.631837	+	0.775101i	$0.282301\pi$
$68$	−10.5519	−1.27960
$69$	−3.13345	−0.377223
$70$	0	0
$71$	2.17761	0.258435	0.129217	−	0.991616i	$-0.458754\pi$
$71$	2.17761	0.258435	0.129217	+	0.991616i	$0.458754\pi$
$72$	0.998417	0.117665
$73$	−11.9292	−1.39621	−0.698106	−	0.715994i	$-0.745974\pi$
$73$	−11.9292	−1.39621	−0.698106	+	0.715994i	$0.745974\pi$
$74$	0.518005	0.0602169
$75$	−4.91877	−0.567971
$76$	−15.3116	−1.75636
$77$	0	0
$78$	1.52284	0.172427
$79$	−11.8004	−1.32764	−0.663822	−	0.747891i	$-0.731067\pi$
$79$	−11.8004	−1.32764	−0.663822	+	0.747891i	$0.731067\pi$
$80$	0.807391	0.0902690
$81$	1.00000	0.111111
$82$	2.11474	0.233534
$83$	−7.48655	−0.821756	−0.410878	−	0.911690i	$-0.634778\pi$
$83$	−7.48655	−0.821756	−0.410878	+	0.911690i	$0.634778\pi$
$84$	0	0
$85$	1.21652	0.131950
$86$	−4.26581	−0.459995
$87$	0.696665	0.0746904
$88$	−3.38274	−0.360601
$89$	5.06017	0.536377	0.268188	−	0.963367i	$-0.413575\pi$
$89$	5.06017	0.536377	0.268188	+	0.963367i	$0.413575\pi$
$90$	−0.602721	−0.0635324
$91$	0	0
$92$	−7.74628	−0.807605
$93$	9.88002	1.02451
$94$	−18.4577	−1.90376
$95$	1.76526	0.181112
$96$	−7.98758	−0.815229
$97$	15.2586	1.54928	0.774639	−	0.632404i	$-0.217932\pi$
$97$	15.2586	1.54928	0.774639	+	0.632404i	$0.217932\pi$
$98$	0	0
$99$	−3.38810	−0.340517
$100$	−12.1598	−1.21598
$101$	16.7781	1.66948	0.834741	−	0.550642i	$-0.185617\pi$
$101$	16.7781	1.66948	0.834741	+	0.550642i	$0.185617\pi$
$102$	−9.02642	−0.893749
$103$	7.17037	0.706518	0.353259	−	0.935526i	$-0.385073\pi$
$103$	7.17037	0.706518	0.353259	+	0.935526i	$0.385073\pi$
$104$	0.718966	0.0705004
$105$	0	0
$106$	−29.9376	−2.90780
$107$	−2.30396	−0.222733	−0.111366	−	0.993779i	$-0.535523\pi$
$107$	−2.30396	−0.222733	−0.111366	+	0.993779i	$0.535523\pi$
$108$	2.47212	0.237880
$109$	−5.22043	−0.500026	−0.250013	−	0.968242i	$-0.580435\pi$
$109$	−5.22043	−0.500026	−0.250013	+	0.968242i	$0.580435\pi$
$110$	2.04208	0.194705
$111$	0.244950	0.0232496
$112$	0	0
$113$	−10.1900	−0.958591	−0.479295	−	0.877654i	$-0.659108\pi$
$113$	−10.1900	−0.958591	−0.479295	+	0.877654i	$0.659108\pi$
$114$	−13.0980	−1.22674
$115$	0.893064	0.0832786
$116$	1.72224	0.159906
$117$	0.720106	0.0665738
$118$	19.1019	1.75847
$119$	0	0
$120$	−0.284558	−0.0259765
$121$	0.479235	0.0435668
$122$	7.13500	0.645972
$123$	1.00000	0.0901670
$124$	24.4246	2.19340
$125$	2.82694	0.252850
$126$	0	0
$127$	−19.7843	−1.75557	−0.877785	−	0.479054i	$-0.840980\pi$
$127$	−19.7843	−1.75557	−0.877785	+	0.479054i	$0.840980\pi$
$128$	−7.76479	−0.686317
$129$	−2.01718	−0.177603
$130$	−0.434023	−0.0380663
$131$	−11.9961	−1.04811	−0.524054	−	0.851685i	$-0.675581\pi$
$131$	−11.9961	−1.04811	−0.524054	+	0.851685i	$0.675581\pi$
$132$	−8.37580	−0.729020
$133$	0	0
$134$	21.8741	1.88963
$135$	−0.285010	−0.0245297
$136$	−4.26158	−0.365427
$137$	−7.01086	−0.598978	−0.299489	−	0.954100i	$-0.596816\pi$
$137$	−7.01086	−0.598978	−0.299489	+	0.954100i	$0.596816\pi$
$138$	−6.62643	−0.564079
$139$	−8.32435	−0.706062	−0.353031	−	0.935612i	$-0.614849\pi$
$139$	−8.32435	−0.706062	−0.353031	+	0.935612i	$0.614849\pi$
$140$	0	0
$141$	−8.72811	−0.735039
$142$	4.60507	0.386449
$143$	−2.43979	−0.204026
$144$	−2.83285	−0.236071
$145$	−0.198556	−0.0164892
$146$	−25.2272	−2.08782
$147$	0	0
$148$	0.605546	0.0497756
$149$	17.2597	1.41397	0.706987	−	0.707227i	$-0.250054\pi$
$149$	17.2597	1.41397	0.706987	+	0.707227i	$0.250054\pi$
$150$	−10.4019	−0.849313
$151$	17.2443	1.40332	0.701661	−	0.712511i	$-0.252442\pi$
$151$	17.2443	1.40332	0.701661	+	0.712511i	$0.252442\pi$
$152$	−6.18388	−0.501579
$153$	−4.26834	−0.345075
$154$	0	0
$155$	−2.81590	−0.226179
$156$	1.78019	0.142529
$157$	11.2308	0.896319	0.448160	−	0.893954i	$-0.352080\pi$
$157$	11.2308	0.896319	0.448160	+	0.893954i	$0.352080\pi$
$158$	−24.9547	−1.98529
$159$	−14.1567	−1.12270
$160$	2.27654	0.179976
$161$	0	0
$162$	2.11474	0.166150
$163$	5.68152	0.445011	0.222506	−	0.974931i	$-0.428576\pi$
$163$	5.68152	0.445011	0.222506	+	0.974931i	$0.428576\pi$
$164$	2.47212	0.193040
$165$	0.965642	0.0751751
$166$	−15.8321	−1.22881
$167$	15.7473	1.21856	0.609281	−	0.792954i	$-0.291458\pi$
$167$	15.7473	1.21856	0.609281	+	0.792954i	$0.291458\pi$
$168$	0	0
$169$	−12.4814	−0.960111
$170$	2.57262	0.197311
$171$	−6.19369	−0.473643
$172$	−4.98672	−0.380234
$173$	−13.6448	−1.03739	−0.518696	−	0.854959i	$-0.673582\pi$
$173$	−13.6448	−1.03739	−0.518696	+	0.854959i	$0.673582\pi$
$174$	1.47327	0.111688
$175$	0	0
$176$	9.59800	0.723476
$177$	9.03275	0.678943
$178$	10.7009	0.802069
$179$	−9.11935	−0.681612	−0.340806	−	0.940134i	$-0.610700\pi$
$179$	−9.11935	−0.681612	−0.340806	+	0.940134i	$0.610700\pi$
$180$	−0.704579	−0.0525162
$181$	25.5291	1.89756	0.948782	−	0.315932i	$-0.102317\pi$
$181$	25.5291	1.89756	0.948782	+	0.315932i	$0.102317\pi$
$182$	0	0
$183$	3.37394	0.249409
$184$	−3.12849	−0.230635
$185$	−0.0698131	−0.00513276
$186$	20.8937	1.53200
$187$	14.4616	1.05753
$188$	−21.5770	−1.57366
$189$	0	0
$190$	3.73307	0.270825
$191$	−8.35959	−0.604879	−0.302440	−	0.953169i	$-0.597801\pi$
$191$	−8.35959	−0.604879	−0.302440	+	0.953169i	$0.597801\pi$
$192$	−11.2259	−0.810163
$193$	19.4805	1.40224	0.701118	−	0.713045i	$-0.252685\pi$
$193$	19.4805	1.40224	0.701118	+	0.713045i	$0.252685\pi$
$194$	32.2680	2.31671
$195$	−0.205237	−0.0146973
$196$	0	0
$197$	12.4743	0.888757	0.444378	−	0.895839i	$-0.353425\pi$
$197$	12.4743	0.888757	0.444378	+	0.895839i	$0.353425\pi$
$198$	−7.16495	−0.509191
$199$	2.86737	0.203263	0.101631	−	0.994822i	$-0.467594\pi$
$199$	2.86737	0.203263	0.101631	+	0.994822i	$0.467594\pi$
$200$	−4.91098	−0.347259
$201$	10.3436	0.729582
$202$	35.4813	2.49646
$203$	0	0
$204$	−10.5519	−0.738777
$205$	−0.285010	−0.0199059
$206$	15.1635	1.05649
$207$	−3.13345	−0.217790
$208$	−2.03995	−0.141445
$209$	20.9849	1.45155
$210$	0	0
$211$	7.31043	0.503270	0.251635	−	0.967822i	$-0.419032\pi$
$211$	7.31043	0.503270	0.251635	+	0.967822i	$0.419032\pi$
$212$	−34.9970	−2.40360
$213$	2.17761	0.149207
$214$	−4.87228	−0.333062
$215$	0.574916	0.0392090
$216$	0.998417	0.0679337
$217$	0	0
$218$	−11.0398	−0.747713
$219$	−11.9292	−0.806104
$220$	2.38718	0.160944
$221$	−3.07365	−0.206756
$222$	0.518005	0.0347662
$223$	0.374802	0.0250986	0.0125493	−	0.999921i	$-0.496005\pi$
$223$	0.374802	0.0250986	0.0125493	+	0.999921i	$0.496005\pi$
$224$	0	0
$225$	−4.91877	−0.327918
$226$	−21.5491	−1.43343
$227$	−15.8874	−1.05448	−0.527240	−	0.849716i	$-0.676773\pi$
$227$	−15.8874	−1.05448	−0.527240	+	0.849716i	$0.676773\pi$
$228$	−15.3116	−1.01403
$229$	19.5385	1.29114	0.645571	−	0.763701i	$-0.276620\pi$
$229$	19.5385	1.29114	0.645571	+	0.763701i	$0.276620\pi$
$230$	1.88860	0.124530
$231$	0	0
$232$	0.695562	0.0456659
$233$	−17.0909	−1.11966	−0.559832	−	0.828606i	$-0.689134\pi$
$233$	−17.0909	−1.11966	−0.559832	+	0.828606i	$0.689134\pi$
$234$	1.52284	0.0995509
$235$	2.48760	0.162273
$236$	22.3301	1.45356
$237$	−11.8004	−0.766515
$238$	0	0
$239$	15.0447	0.973162	0.486581	−	0.873636i	$-0.338244\pi$
$239$	15.0447	0.973162	0.486581	+	0.873636i	$0.338244\pi$
$240$	0.807391	0.0521168
$241$	−0.539340	−0.0347419	−0.0173710	−	0.999849i	$-0.505530\pi$
$241$	−0.539340	−0.0347419	−0.0173710	+	0.999849i	$0.505530\pi$
$242$	1.01346	0.0651475
$243$	1.00000	0.0641500
$244$	8.34079	0.533964
$245$	0	0
$246$	2.11474	0.134831
$247$	−4.46011	−0.283790
$248$	9.86438	0.626389
$249$	−7.48655	−0.474441
$250$	5.97825	0.378098
$251$	12.9971	0.820368	0.410184	−	0.912003i	$-0.365464\pi$
$251$	12.9971	0.820368	0.410184	+	0.912003i	$0.365464\pi$
$252$	0	0
$253$	10.6165	0.667451
$254$	−41.8386	−2.62519
$255$	1.21652	0.0761812
$256$	6.03139	0.376962
$257$	−29.5500	−1.84328	−0.921640	−	0.388046i	$-0.873150\pi$
$257$	−29.5500	−1.84328	−0.921640	+	0.388046i	$0.873150\pi$
$258$	−4.26581	−0.265578
$259$	0	0
$260$	−0.507371	−0.0314658
$261$	0.696665	0.0431225
$262$	−25.3687	−1.56728
$263$	16.5947	1.02327	0.511637	−	0.859202i	$-0.329039\pi$
$263$	16.5947	1.02327	0.511637	+	0.859202i	$0.329039\pi$
$264$	−3.38274	−0.208193
$265$	4.03478	0.247855
$266$	0	0
$267$	5.06017	0.309677
$268$	25.5707	1.56198
$269$	−23.9750	−1.46178	−0.730891	−	0.682495i	$-0.760895\pi$
$269$	−23.9750	−1.46178	−0.730891	+	0.682495i	$0.760895\pi$
$270$	−0.602721	−0.0366804
$271$	−4.41087	−0.267941	−0.133971	−	0.990985i	$-0.542773\pi$
$271$	−4.41087	−0.267941	−0.133971	+	0.990985i	$0.542773\pi$
$272$	12.0916	0.733159
$273$	0	0
$274$	−14.8261	−0.895680
$275$	16.6653	1.00495
$276$	−7.74628	−0.466271
$277$	−23.4865	−1.41117	−0.705584	−	0.708626i	$-0.749315\pi$
$277$	−23.4865	−1.41117	−0.705584	+	0.708626i	$0.749315\pi$
$278$	−17.6038	−1.05581
$279$	9.88002	0.591501
$280$	0	0
$281$	−23.5640	−1.40571	−0.702856	−	0.711332i	$-0.748092\pi$
$281$	−23.5640	−1.40571	−0.702856	+	0.711332i	$0.748092\pi$
$282$	−18.4577	−1.09914
$283$	−19.1984	−1.14123	−0.570614	−	0.821219i	$-0.693295\pi$
$283$	−19.1984	−1.14123	−0.570614	+	0.821219i	$0.693295\pi$
$284$	5.38331	0.319441
$285$	1.76526	0.104565
$286$	−5.15952	−0.305089
$287$	0	0
$288$	−7.98758	−0.470673
$289$	1.21870	0.0716880
$290$	−0.419895	−0.0246571
$291$	15.2586	0.894476
$292$	−29.4906	−1.72580
$293$	15.8156	0.923960	0.461980	−	0.886890i	$-0.347139\pi$
$293$	15.8156	0.923960	0.461980	+	0.886890i	$0.347139\pi$
$294$	0	0
$295$	−2.57442	−0.149889
$296$	0.244562	0.0142149
$297$	−3.38810	−0.196598
$298$	36.4999	2.11438
$299$	−2.25642	−0.130492
$300$	−12.1598	−0.702047
$301$	0	0
$302$	36.4672	2.09845
$303$	16.7781	0.963876
$304$	17.5458	1.00632
$305$	−0.961604	−0.0550613
$306$	−9.02642	−0.516006
$307$	1.88472	0.107567	0.0537834	−	0.998553i	$-0.482872\pi$
$307$	1.88472	0.107567	0.0537834	+	0.998553i	$0.482872\pi$
$308$	0	0
$309$	7.17037	0.407908
$310$	−5.95489	−0.338215
$311$	−5.69831	−0.323122	−0.161561	−	0.986863i	$-0.551653\pi$
$311$	−5.69831	−0.323122	−0.161561	+	0.986863i	$0.551653\pi$
$312$	0.718966	0.0407034
$313$	−29.2119	−1.65116	−0.825578	−	0.564289i	$-0.809150\pi$
$313$	−29.2119	−1.65116	−0.825578	+	0.564289i	$0.809150\pi$
$314$	23.7503	1.34031
$315$	0	0
$316$	−29.1719	−1.64105
$317$	−32.9071	−1.84825	−0.924123	−	0.382096i	$-0.875202\pi$
$317$	−32.9071	−1.84825	−0.924123	+	0.382096i	$0.875202\pi$
$318$	−29.9376	−1.67882
$319$	−2.36037	−0.132156
$320$	3.19950	0.178858
$321$	−2.30396	−0.128595
$322$	0	0
$323$	26.4368	1.47098
$324$	2.47212	0.137340
$325$	−3.54203	−0.196477
$326$	12.0149	0.665446
$327$	−5.22043	−0.288690
$328$	0.998417	0.0551283
$329$	0	0
$330$	2.04208	0.112413
$331$	−17.9603	−0.987188	−0.493594	−	0.869692i	$-0.664317\pi$
$331$	−17.9603	−0.987188	−0.493594	+	0.869692i	$0.664317\pi$
$332$	−18.5077	−1.01574
$333$	0.244950	0.0134232
$334$	33.3014	1.82217
$335$	−2.94803	−0.161068
$336$	0	0
$337$	−1.91719	−0.104436	−0.0522180	−	0.998636i	$-0.516629\pi$
$337$	−1.91719	−0.104436	−0.0522180	+	0.998636i	$0.516629\pi$
$338$	−26.3950	−1.43570
$339$	−10.1900	−0.553443
$340$	3.00738	0.163098
$341$	−33.4745	−1.81275
$342$	−13.0980	−0.708261
$343$	0	0
$344$	−2.01399	−0.108587
$345$	0.893064	0.0480809
$346$	−28.8551	−1.55126
$347$	3.05347	0.163919	0.0819595	−	0.996636i	$-0.473882\pi$
$347$	3.05347	0.163919	0.0819595	+	0.996636i	$0.473882\pi$
$348$	1.72224	0.0923219
$349$	18.5504	0.992981	0.496491	−	0.868042i	$-0.334622\pi$
$349$	18.5504	0.992981	0.496491	+	0.868042i	$0.334622\pi$
$350$	0	0
$351$	0.720106	0.0384364
$352$	27.0627	1.44245
$353$	−10.4653	−0.557010	−0.278505	−	0.960435i	$-0.589839\pi$
$353$	−10.4653	−0.557010	−0.278505	+	0.960435i	$0.589839\pi$
$354$	19.1019	1.01526
$355$	−0.620639	−0.0329401
$356$	12.5094	0.662995
$357$	0	0
$358$	−19.2851	−1.01925
$359$	23.0278	1.21536	0.607682	−	0.794181i	$-0.292100\pi$
$359$	23.0278	1.21536	0.607682	+	0.794181i	$0.292100\pi$
$360$	−0.284558	−0.0149975
$361$	19.3618	1.01904
$362$	53.9874	2.83751
$363$	0.479235	0.0251533
$364$	0	0
$365$	3.39995	0.177961
$366$	7.13500	0.372952
$367$	−23.9454	−1.24994	−0.624970	−	0.780648i	$-0.714889\pi$
$367$	−23.9454	−1.24994	−0.624970	+	0.780648i	$0.714889\pi$
$368$	8.87661	0.462725
$369$	1.00000	0.0520579
$370$	−0.147637	−0.00767526
$371$	0	0
$372$	24.4246	1.26636
$373$	−21.8958	−1.13372	−0.566860	−	0.823814i	$-0.691842\pi$
$373$	−21.8958	−1.13372	−0.566860	+	0.823814i	$0.691842\pi$
$374$	30.5824	1.58138
$375$	2.82694	0.145983
$376$	−8.71429	−0.449405
$377$	0.501673	0.0258375
$378$	0	0
$379$	14.7773	0.759058	0.379529	−	0.925180i	$-0.376086\pi$
$379$	14.7773	0.759058	0.379529	+	0.925180i	$0.376086\pi$
$380$	4.36394	0.223866
$381$	−19.7843	−1.01358
$382$	−17.6784	−0.904504
$383$	−13.4489	−0.687206	−0.343603	−	0.939115i	$-0.611647\pi$
$383$	−13.4489	−0.687206	−0.343603	+	0.939115i	$0.611647\pi$
$384$	−7.76479	−0.396245
$385$	0	0
$386$	41.1962	2.09683
$387$	−2.01718	−0.102539
$388$	37.7212	1.91500
$389$	−10.7324	−0.544156	−0.272078	−	0.962275i	$-0.587711\pi$
$389$	−10.7324	−0.544156	−0.272078	+	0.962275i	$0.587711\pi$
$390$	−0.434023	−0.0219776
$391$	13.3746	0.676384
$392$	0	0
$393$	−11.9961	−0.605125
$394$	26.3799	1.32900
$395$	3.36321	0.169222
$396$	−8.37580	−0.420900
$397$	−21.5444	−1.08128	−0.540641	−	0.841253i	$-0.681818\pi$
$397$	−21.5444	−1.08128	−0.540641	+	0.841253i	$0.681818\pi$
$398$	6.06374	0.303948
$399$	0	0
$400$	13.9342	0.696708
$401$	28.5605	1.42625	0.713123	−	0.701039i	$-0.247280\pi$
$401$	28.5605	1.42625	0.713123	+	0.701039i	$0.247280\pi$
$402$	21.8741	1.09098
$403$	7.11466	0.354406
$404$	41.4775	2.06358
$405$	−0.285010	−0.0141622
$406$	0	0
$407$	−0.829916	−0.0411374
$408$	−4.26158	−0.210980
$409$	1.61277	0.0797462	0.0398731	−	0.999205i	$-0.487305\pi$
$409$	1.61277	0.0797462	0.0398731	+	0.999205i	$0.487305\pi$
$410$	−0.602721	−0.0297663
$411$	−7.01086	−0.345820
$412$	17.7260	0.873300
$413$	0	0
$414$	−6.62643	−0.325671
$415$	2.13374	0.104741
$416$	−5.75190	−0.282010
$417$	−8.32435	−0.407645
$418$	44.3775	2.17057
$419$	−0.829572	−0.0405272	−0.0202636	−	0.999795i	$-0.506451\pi$
$419$	−0.829572	−0.0405272	−0.0202636	+	0.999795i	$0.506451\pi$
$420$	0	0
$421$	−3.10283	−0.151223	−0.0756113	−	0.997137i	$-0.524091\pi$
$421$	−3.10283	−0.151223	−0.0756113	+	0.997137i	$0.524091\pi$
$422$	15.4596	0.752564
$423$	−8.72811	−0.424375
$424$	−14.1342	−0.686420
$425$	20.9950	1.01841
$426$	4.60507	0.223117
$427$	0	0
$428$	−5.69568	−0.275311
$429$	−2.43979	−0.117794
$430$	1.21580	0.0586310
$431$	−27.8777	−1.34282	−0.671411	−	0.741085i	$-0.734312\pi$
$431$	−27.8777	−1.34282	−0.671411	+	0.741085i	$0.734312\pi$
$432$	−2.83285	−0.136296
$433$	−28.4561	−1.36751	−0.683755	−	0.729711i	$-0.739654\pi$
$433$	−28.4561	−1.36751	−0.683755	+	0.729711i	$0.739654\pi$
$434$	0	0
$435$	−0.198556	−0.00952005
$436$	−12.9055	−0.618063
$437$	19.4076	0.928393
$438$	−25.2272	−1.20540
$439$	25.2640	1.20579	0.602893	−	0.797822i	$-0.294014\pi$
$439$	25.2640	1.20579	0.602893	+	0.797822i	$0.294014\pi$
$440$	0.964113	0.0459623
$441$	0	0
$442$	−6.49998	−0.309172
$443$	−25.4878	−1.21096	−0.605480	−	0.795860i	$-0.707019\pi$
$443$	−25.4878	−1.21096	−0.605480	+	0.795860i	$0.707019\pi$
$444$	0.605546	0.0287380
$445$	−1.44220	−0.0683667
$446$	0.792608	0.0375311
$447$	17.2597	0.816358
$448$	0	0
$449$	27.7044	1.30745	0.653726	−	0.756731i	$-0.273205\pi$
$449$	27.7044	1.30745	0.653726	+	0.756731i	$0.273205\pi$
$450$	−10.4019	−0.490351
$451$	−3.38810	−0.159539
$452$	−25.1908	−1.18488
$453$	17.2443	0.810208
$454$	−33.5976	−1.57681
$455$	0	0
$456$	−6.18388	−0.289587
$457$	−12.9935	−0.607808	−0.303904	−	0.952703i	$-0.598290\pi$
$457$	−12.9935	−0.607808	−0.303904	+	0.952703i	$0.598290\pi$
$458$	41.3189	1.93070
$459$	−4.26834	−0.199229
$460$	2.20776	0.102937
$461$	5.41356	0.252135	0.126067	−	0.992022i	$-0.459764\pi$
$461$	5.41356	0.252135	0.126067	+	0.992022i	$0.459764\pi$
$462$	0	0
$463$	31.4718	1.46262	0.731309	−	0.682047i	$-0.238910\pi$
$463$	31.4718	1.46262	0.731309	+	0.682047i	$0.238910\pi$
$464$	−1.97355	−0.0916198
$465$	−2.81590	−0.130584
$466$	−36.1429	−1.67429
$467$	−22.4929	−1.04085	−0.520425	−	0.853908i	$-0.674226\pi$
$467$	−22.4929	−1.04085	−0.520425	+	0.853908i	$0.674226\pi$
$468$	1.78019	0.0822893
$469$	0	0
$470$	5.26062	0.242654
$471$	11.2308	0.517490
$472$	9.01845	0.415108
$473$	6.83442	0.314247
$474$	−24.9547	−1.14621
$475$	30.4653	1.39785
$476$	0	0
$477$	−14.1567	−0.648189
$478$	31.8157	1.45521
$479$	6.12855	0.280021	0.140010	−	0.990150i	$-0.455286\pi$
$479$	6.12855	0.280021	0.140010	+	0.990150i	$0.455286\pi$
$480$	2.27654	0.103909
$481$	0.176390	0.00804269
$482$	−1.14056	−0.0519512
$483$	0	0
$484$	1.18473	0.0538512
$485$	−4.34885	−0.197471
$486$	2.11474	0.0959265
$487$	−29.9158	−1.35561	−0.677807	−	0.735240i	$-0.737069\pi$
$487$	−29.9158	−1.35561	−0.677807	+	0.735240i	$0.737069\pi$
$488$	3.36860	0.152489
$489$	5.68152	0.256927
$490$	0	0
$491$	20.4886	0.924639	0.462319	−	0.886713i	$-0.347017\pi$
$491$	20.4886	0.924639	0.462319	+	0.886713i	$0.347017\pi$
$492$	2.47212	0.111452
$493$	−2.97360	−0.133924
$494$	−9.43197	−0.424364
$495$	0.965642	0.0434024
$496$	−27.9887	−1.25673
$497$	0	0
$498$	−15.8321	−0.709454
$499$	32.9368	1.47445	0.737227	−	0.675645i	$-0.236135\pi$
$499$	32.9368	1.47445	0.737227	+	0.675645i	$0.236135\pi$
$500$	6.98855	0.312538
$501$	15.7473	0.703537
$502$	27.4854	1.22673
$503$	5.20938	0.232275	0.116137	−	0.993233i	$-0.462949\pi$
$503$	5.20938	0.232275	0.116137	+	0.993233i	$0.462949\pi$
$504$	0	0
$505$	−4.78192	−0.212793
$506$	22.4510	0.998070
$507$	−12.4814	−0.554321
$508$	−48.9092	−2.16999
$509$	6.97305	0.309075	0.154537	−	0.987987i	$-0.450611\pi$
$509$	6.97305	0.309075	0.154537	+	0.987987i	$0.450611\pi$
$510$	2.57262	0.113917
$511$	0	0
$512$	28.2844	1.25001
$513$	−6.19369	−0.273458
$514$	−62.4906	−2.75634
$515$	−2.04363	−0.0900529
$516$	−4.98672	−0.219528
$517$	29.5717	1.30056
$518$	0	0
$519$	−13.6448	−0.598938
$520$	−0.204912	−0.00898599
$521$	−21.7662	−0.953596	−0.476798	−	0.879013i	$-0.658203\pi$
$521$	−21.7662	−0.953596	−0.476798	+	0.879013i	$0.658203\pi$
$522$	1.47327	0.0644831
$523$	4.63146	0.202520	0.101260	−	0.994860i	$-0.467713\pi$
$523$	4.63146	0.202520	0.101260	+	0.994860i	$0.467713\pi$
$524$	−29.6559	−1.29553
$525$	0	0
$526$	35.0935	1.53015
$527$	−42.1712	−1.83701
$528$	9.59800	0.417699
$529$	−13.1815	−0.573108
$530$	8.53252	0.370629
$531$	9.03275	0.391988
$532$	0	0
$533$	0.720106	0.0311912
$534$	10.7009	0.463075
$535$	0.656652	0.0283895
$536$	10.3272	0.446069
$537$	−9.11935	−0.393529
$538$	−50.7009	−2.18587
$539$	0	0
$540$	−0.704579	−0.0303202
$541$	34.2767	1.47367	0.736836	−	0.676072i	$-0.236319\pi$
$541$	34.2767	1.47367	0.736836	+	0.676072i	$0.236319\pi$
$542$	−9.32783	−0.400665
$543$	25.5291	1.09556
$544$	34.0937	1.46175
$545$	1.48787	0.0637335
$546$	0	0
$547$	−27.1805	−1.16215	−0.581077	−	0.813848i	$-0.697369\pi$
$547$	−27.1805	−1.16215	−0.581077	+	0.813848i	$0.697369\pi$
$548$	−17.3317	−0.740374
$549$	3.37394	0.143996
$550$	35.2428	1.50276
$551$	−4.31493	−0.183822
$552$	−3.12849	−0.133157
$553$	0	0
$554$	−49.6679	−2.11019
$555$	−0.0698131	−0.00296340
$556$	−20.5788	−0.872736
$557$	14.9699	0.634295	0.317147	−	0.948376i	$-0.397275\pi$
$557$	14.9699	0.634295	0.317147	+	0.948376i	$0.397275\pi$
$558$	20.8937	0.884499
$559$	−1.45258	−0.0614378
$560$	0	0
$561$	14.4616	0.610568
$562$	−49.8318	−2.10203
$563$	22.5397	0.949936	0.474968	−	0.880003i	$-0.342460\pi$
$563$	22.5397	0.949936	0.474968	+	0.880003i	$0.342460\pi$
$564$	−21.5770	−0.908554
$565$	2.90424	0.122182
$566$	−40.5997	−1.70653
$567$	0	0
$568$	2.17416	0.0912257
$569$	−14.3436	−0.601316	−0.300658	−	0.953732i	$-0.597206\pi$
$569$	−14.3436	−0.601316	−0.300658	+	0.953732i	$0.597206\pi$
$570$	3.73307	0.156361
$571$	35.6984	1.49393	0.746966	−	0.664862i	$-0.231510\pi$
$571$	35.6984	1.49393	0.746966	+	0.664862i	$0.231510\pi$
$572$	−6.03146	−0.252188
$573$	−8.35959	−0.349227
$574$	0	0
$575$	15.4127	0.642755
$576$	−11.2259	−0.467748
$577$	12.4868	0.519834	0.259917	−	0.965631i	$-0.416305\pi$
$577$	12.4868	0.519834	0.259917	+	0.965631i	$0.416305\pi$
$578$	2.57723	0.107198
$579$	19.4805	0.809581
$580$	−0.490856	−0.0203817
$581$	0	0
$582$	32.2680	1.33755
$583$	47.9642	1.98647
$584$	−11.9104	−0.492854
$585$	−0.205237	−0.00848551
$586$	33.4460	1.38164
$587$	0.691794	0.0285534	0.0142767	−	0.999898i	$-0.495455\pi$
$587$	0.691794	0.0285534	0.0142767	+	0.999898i	$0.495455\pi$
$588$	0	0
$589$	−61.1938	−2.52145
$590$	−5.44423	−0.224135
$591$	12.4743	0.513124
$592$	−0.693908	−0.0285194
$593$	28.8261	1.18375	0.591873	−	0.806031i	$-0.298389\pi$
$593$	28.8261	1.18375	0.591873	+	0.806031i	$0.298389\pi$
$594$	−7.16495	−0.293982
$595$	0	0
$596$	42.6682	1.74776
$597$	2.86737	0.117354
$598$	−4.77173	−0.195131
$599$	19.2475	0.786430	0.393215	−	0.919447i	$-0.371363\pi$
$599$	19.2475	0.786430	0.393215	+	0.919447i	$0.371363\pi$
$600$	−4.91098	−0.200490
$601$	39.9895	1.63120	0.815602	−	0.578613i	$-0.196406\pi$
$601$	39.9895	1.63120	0.815602	+	0.578613i	$0.196406\pi$
$602$	0	0
$603$	10.3436	0.421225
$604$	42.6300	1.73459
$605$	−0.136586	−0.00555303
$606$	35.4813	1.44133
$607$	18.0747	0.733631	0.366816	−	0.930294i	$-0.380448\pi$
$607$	18.0747	0.733631	0.366816	+	0.930294i	$0.380448\pi$
$608$	49.4726	2.00638
$609$	0	0
$610$	−2.03354	−0.0823357
$611$	−6.28516	−0.254270
$612$	−10.5519	−0.426533
$613$	−8.41473	−0.339868	−0.169934	−	0.985455i	$-0.554355\pi$
$613$	−8.41473	−0.339868	−0.169934	+	0.985455i	$0.554355\pi$
$614$	3.98569	0.160850
$615$	−0.285010	−0.0114927
$616$	0	0
$617$	25.3196	1.01933	0.509665	−	0.860373i	$-0.329769\pi$
$617$	25.3196	1.01933	0.509665	+	0.860373i	$0.329769\pi$
$618$	15.1635	0.609964
$619$	−6.35528	−0.255440	−0.127720	−	0.991810i	$-0.540766\pi$
$619$	−6.35528	−0.255440	−0.127720	+	0.991810i	$0.540766\pi$
$620$	−6.96125	−0.279571
$621$	−3.13345	−0.125741
$622$	−12.0504	−0.483179
$623$	0	0
$624$	−2.03995	−0.0816635
$625$	23.7881	0.951526
$626$	−61.7756	−2.46905
$627$	20.9849	0.838054
$628$	27.7640	1.10791
$629$	−1.04553	−0.0416880
$630$	0	0
$631$	0.544315	0.0216688	0.0108344	−	0.999941i	$-0.496551\pi$
$631$	0.544315	0.0216688	0.0108344	+	0.999941i	$0.496551\pi$
$632$	−11.7817	−0.468650
$633$	7.31043	0.290563
$634$	−69.5899	−2.76377
$635$	5.63871	0.223765
$636$	−34.9970	−1.38772
$637$	0	0
$638$	−4.99157	−0.197618
$639$	2.17761	0.0861448
$640$	2.21304	0.0874781
$641$	−5.08501	−0.200846	−0.100423	−	0.994945i	$-0.532020\pi$
$641$	−5.08501	−0.200846	−0.100423	+	0.994945i	$0.532020\pi$
$642$	−4.87228	−0.192294
$643$	−21.2796	−0.839186	−0.419593	−	0.907712i	$-0.637827\pi$
$643$	−21.2796	−0.839186	−0.419593	+	0.907712i	$0.637827\pi$
$644$	0	0
$645$	0.574916	0.0226373
$646$	55.9068	2.19963
$647$	1.39928	0.0550115	0.0275057	−	0.999622i	$-0.491244\pi$
$647$	1.39928	0.0550115	0.0275057	+	0.999622i	$0.491244\pi$
$648$	0.998417	0.0392215
$649$	−30.6039	−1.20131
$650$	−7.49048	−0.293801
$651$	0	0
$652$	14.0454	0.550061
$653$	1.68680	0.0660096	0.0330048	−	0.999455i	$-0.489492\pi$
$653$	1.68680	0.0660096	0.0330048	+	0.999455i	$0.489492\pi$
$654$	−11.0398	−0.431692
$655$	3.41901	0.133592
$656$	−2.83285	−0.110604
$657$	−11.9292	−0.465404
$658$	0	0
$659$	−4.28966	−0.167101	−0.0835507	−	0.996504i	$-0.526626\pi$
$659$	−4.28966	−0.167101	−0.0835507	+	0.996504i	$0.526626\pi$
$660$	2.38718	0.0929210
$661$	30.5094	1.18668	0.593340	−	0.804952i	$-0.297809\pi$
$661$	30.5094	1.18668	0.593340	+	0.804952i	$0.297809\pi$
$662$	−37.9814	−1.47619
$663$	−3.07365	−0.119371
$664$	−7.47470	−0.290075
$665$	0	0
$666$	0.518005	0.0200723
$667$	−2.18297	−0.0845248
$668$	38.9292	1.50622
$669$	0.374802	0.0144907
$670$	−6.23432	−0.240853
$671$	−11.4312	−0.441298
$672$	0	0
$673$	10.9216	0.420996	0.210498	−	0.977594i	$-0.432492\pi$
$673$	10.9216	0.420996	0.210498	+	0.977594i	$0.432492\pi$
$674$	−4.05436	−0.156168
$675$	−4.91877	−0.189324
$676$	−30.8557	−1.18676
$677$	−37.4920	−1.44093	−0.720467	−	0.693490i	$-0.756072\pi$
$677$	−37.4920	−1.44093	−0.720467	+	0.693490i	$0.756072\pi$
$678$	−21.5491	−0.827589
$679$	0	0
$680$	1.21459	0.0465774
$681$	−15.8874	−0.608805
$682$	−70.7899	−2.71068
$683$	−36.5776	−1.39960	−0.699802	−	0.714337i	$-0.746728\pi$
$683$	−36.5776	−1.39960	−0.699802	+	0.714337i	$0.746728\pi$
$684$	−15.3116	−0.585452
$685$	1.99816	0.0763459
$686$	0	0
$687$	19.5385	0.745441
$688$	5.71438	0.217859
$689$	−10.1943	−0.388372
$690$	1.88860	0.0718977
$691$	−15.2245	−0.579167	−0.289584	−	0.957153i	$-0.593517\pi$
$691$	−15.2245	−0.579167	−0.289584	+	0.957153i	$0.593517\pi$
$692$	−33.7315	−1.28228
$693$	0	0
$694$	6.45730	0.245116
$695$	2.37252	0.0899948
$696$	0.695562	0.0263652
$697$	−4.26834	−0.161675
$698$	39.2293	1.48485
$699$	−17.0909	−0.646438
$700$	0	0
$701$	−1.07207	−0.0404915	−0.0202457	−	0.999795i	$-0.506445\pi$
$701$	−1.07207	−0.0404915	−0.0202457	+	0.999795i	$0.506445\pi$
$702$	1.52284	0.0574757
$703$	−1.51714	−0.0572202
$704$	38.0347	1.43348
$705$	2.48760	0.0936883
$706$	−22.1313	−0.832923
$707$	0	0
$708$	22.3301	0.839215
$709$	−33.4908	−1.25777	−0.628887	−	0.777497i	$-0.716489\pi$
$709$	−33.4908	−1.25777	−0.628887	+	0.777497i	$0.716489\pi$
$710$	−1.31249	−0.0492569
$711$	−11.8004	−0.442548
$712$	5.05216	0.189338
$713$	−30.9586	−1.15941
$714$	0	0
$715$	0.695364	0.0260051
$716$	−22.5442	−0.842515
$717$	15.0447	0.561855
$718$	48.6979	1.81739
$719$	−9.94539	−0.370900	−0.185450	−	0.982654i	$-0.559374\pi$
$719$	−9.94539	−0.370900	−0.185450	+	0.982654i	$0.559374\pi$
$720$	0.807391	0.0300897
$721$	0	0
$722$	40.9451	1.52382
$723$	−0.539340	−0.0200583
$724$	63.1111	2.34550
$725$	−3.42674	−0.127266
$726$	1.01346	0.0376129
$727$	4.95164	0.183646	0.0918231	−	0.995775i	$-0.470731\pi$
$727$	4.95164	0.183646	0.0918231	+	0.995775i	$0.470731\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	7.19001	0.266114
$731$	8.61001	0.318453
$732$	8.34079	0.308284
$733$	−18.1609	−0.670787	−0.335394	−	0.942078i	$-0.608869\pi$
$733$	−18.1609	−0.670787	−0.335394	+	0.942078i	$0.608869\pi$
$734$	−50.6383	−1.86909
$735$	0	0
$736$	25.0287	0.922570
$737$	−35.0452	−1.29091
$738$	2.11474	0.0778446
$739$	13.5342	0.497864	0.248932	−	0.968521i	$-0.419920\pi$
$739$	13.5342	0.497864	0.248932	+	0.968521i	$0.419920\pi$
$740$	−0.172587	−0.00634441
$741$	−4.46011	−0.163846
$742$	0	0
$743$	22.1427	0.812335	0.406168	−	0.913799i	$-0.366865\pi$
$743$	22.1427	0.812335	0.406168	+	0.913799i	$0.366865\pi$
$744$	9.86438	0.361646
$745$	−4.91919	−0.180225
$746$	−46.3038	−1.69530
$747$	−7.48655	−0.273919
$748$	35.7508	1.30718
$749$	0	0
$750$	5.97825	0.218295
$751$	10.7043	0.390607	0.195304	−	0.980743i	$-0.437431\pi$
$751$	10.7043	0.390607	0.195304	+	0.980743i	$0.437431\pi$
$752$	24.7255	0.901645
$753$	12.9971	0.473640
$754$	1.06091	0.0386360
$755$	−4.91479	−0.178868
$756$	0	0
$757$	−17.0866	−0.621021	−0.310511	−	0.950570i	$-0.600500\pi$
$757$	−17.0866	−0.621021	−0.310511	+	0.950570i	$0.600500\pi$
$758$	31.2501	1.13506
$759$	10.6165	0.385353
$760$	1.76247	0.0639314
$761$	5.85387	0.212202	0.106101	−	0.994355i	$-0.466163\pi$
$761$	5.85387	0.212202	0.106101	+	0.994355i	$0.466163\pi$
$762$	−41.8386	−1.51565
$763$	0	0
$764$	−20.6659	−0.747668
$765$	1.21652	0.0439833
$766$	−28.4409	−1.02761
$767$	6.50453	0.234865
$768$	6.03139	0.217639
$769$	−16.7698	−0.604736	−0.302368	−	0.953191i	$-0.597777\pi$
$769$	−16.7698	−0.604736	−0.302368	+	0.953191i	$0.597777\pi$
$770$	0	0
$771$	−29.5500	−1.06422
$772$	48.1582	1.73325
$773$	−27.4347	−0.986756	−0.493378	−	0.869815i	$-0.664238\pi$
$773$	−27.4347	−0.986756	−0.493378	+	0.869815i	$0.664238\pi$
$774$	−4.26581	−0.153332
$775$	−48.5975	−1.74567
$776$	15.2345	0.546885
$777$	0	0
$778$	−22.6963	−0.813702
$779$	−6.19369	−0.221912
$780$	−0.507371	−0.0181668
$781$	−7.37796	−0.264004
$782$	28.2838	1.01143
$783$	0.696665	0.0248968
$784$	0	0
$785$	−3.20090	−0.114245
$786$	−25.3687	−0.904872
$787$	21.6137	0.770447	0.385223	−	0.922823i	$-0.374124\pi$
$787$	21.6137	0.770447	0.385223	+	0.922823i	$0.374124\pi$
$788$	30.8380	1.09856
$789$	16.5947	0.590787
$790$	7.11232	0.253045
$791$	0	0
$792$	−3.38274	−0.120200
$793$	2.42959	0.0862773
$794$	−45.5608	−1.61689
$795$	4.03478	0.143099
$796$	7.08849	0.251245
$797$	2.52312	0.0893736	0.0446868	−	0.999001i	$-0.485771\pi$
$797$	2.52312	0.0893736	0.0446868	+	0.999001i	$0.485771\pi$
$798$	0	0
$799$	37.2545	1.31797
$800$	39.2891	1.38908
$801$	5.06017	0.178792
$802$	60.3981	2.13273
$803$	40.4175	1.42630
$804$	25.5707	0.901809
$805$	0	0
$806$	15.0456	0.529960
$807$	−23.9750	−0.843960
$808$	16.7515	0.589317
$809$	15.5598	0.547052	0.273526	−	0.961865i	$-0.411810\pi$
$809$	15.5598	0.547052	0.273526	+	0.961865i	$0.411810\pi$
$810$	−0.602721	−0.0211775
$811$	−30.8517	−1.08335	−0.541674	−	0.840589i	$-0.682209\pi$
$811$	−30.8517	−1.08335	−0.541674	+	0.840589i	$0.682209\pi$
$812$	0	0
$813$	−4.41087	−0.154696
$814$	−1.75506	−0.0615146
$815$	−1.61929	−0.0567212
$816$	12.0916	0.423290
$817$	12.4938	0.437103
$818$	3.41058	0.119248
$819$	0	0
$820$	−0.704579	−0.0246050
$821$	48.8645	1.70538	0.852691	−	0.522415i	$-0.174969\pi$
$821$	48.8645	1.70538	0.852691	+	0.522415i	$0.174969\pi$
$822$	−14.8261	−0.517121
$823$	26.1744	0.912382	0.456191	−	0.889882i	$-0.349213\pi$
$823$	26.1744	0.912382	0.456191	+	0.889882i	$0.349213\pi$
$824$	7.15902	0.249396
$825$	16.6653	0.580211
$826$	0	0
$827$	28.1957	0.980460	0.490230	−	0.871593i	$-0.336913\pi$
$827$	28.1957	0.980460	0.490230	+	0.871593i	$0.336913\pi$
$828$	−7.74628	−0.269202
$829$	15.9005	0.552248	0.276124	−	0.961122i	$-0.410950\pi$
$829$	15.9005	0.552248	0.276124	+	0.961122i	$0.410950\pi$
$830$	4.51230	0.156624
$831$	−23.4865	−0.814739
$832$	−8.08387	−0.280258
$833$	0	0
$834$	−17.6038	−0.609571
$835$	−4.48813	−0.155318
$836$	51.8771	1.79421
$837$	9.88002	0.341503
$838$	−1.75433	−0.0606023
$839$	17.9080	0.618253	0.309127	−	0.951021i	$-0.399963\pi$
$839$	17.9080	0.618253	0.309127	+	0.951021i	$0.399963\pi$
$840$	0	0
$841$	−28.5147	−0.983264
$842$	−6.56167	−0.226130
$843$	−23.5640	−0.811589
$844$	18.0723	0.622073
$845$	3.55733	0.122376
$846$	−18.4577	−0.634588
$847$	0	0
$848$	40.1038	1.37717
$849$	−19.1984	−0.658888
$850$	44.3989	1.52287
$851$	−0.767539	−0.0263109
$852$	5.38331	0.184429
$853$	−0.747942	−0.0256090	−0.0128045	−	0.999918i	$-0.504076\pi$
$853$	−0.747942	−0.0256090	−0.0128045	+	0.999918i	$0.504076\pi$
$854$	0	0
$855$	1.76526	0.0603707
$856$	−2.30032	−0.0786232
$857$	13.6782	0.467237	0.233619	−	0.972328i	$-0.424943\pi$
$857$	13.6782	0.467237	0.233619	+	0.972328i	$0.424943\pi$
$858$	−5.15952	−0.176143
$859$	17.7503	0.605633	0.302817	−	0.953049i	$-0.402073\pi$
$859$	17.7503	0.605633	0.302817	+	0.953049i	$0.402073\pi$
$860$	1.42126	0.0484647
$861$	0	0
$862$	−58.9541	−2.00798
$863$	−26.0933	−0.888226	−0.444113	−	0.895971i	$-0.646481\pi$
$863$	−26.0933	−0.888226	−0.444113	+	0.895971i	$0.646481\pi$
$864$	−7.98758	−0.271743
$865$	3.88889	0.132226
$866$	−60.1771	−2.04490
$867$	1.21870	0.0413891
$868$	0	0
$869$	39.9808	1.35626
$870$	−0.419895	−0.0142358
$871$	7.44850	0.252383
$872$	−5.21216	−0.176506
$873$	15.2586	0.516426
$874$	41.0421	1.38827
$875$	0	0
$876$	−29.4906	−0.996393
$877$	−18.5476	−0.626310	−0.313155	−	0.949702i	$-0.601386\pi$
$877$	−18.5476	−0.626310	−0.313155	+	0.949702i	$0.601386\pi$
$878$	53.4269	1.80307
$879$	15.8156	0.533448
$880$	−2.73552	−0.0922144
$881$	−36.5564	−1.23162	−0.615808	−	0.787896i	$-0.711170\pi$
$881$	−36.5564	−1.23162	−0.615808	+	0.787896i	$0.711170\pi$
$882$	0	0
$883$	−29.5247	−0.993585	−0.496792	−	0.867869i	$-0.665489\pi$
$883$	−29.5247	−0.993585	−0.496792	+	0.867869i	$0.665489\pi$
$884$	−7.59845	−0.255563
$885$	−2.57442	−0.0865382
$886$	−53.9000	−1.81081
$887$	31.5502	1.05935	0.529677	−	0.848200i	$-0.322313\pi$
$887$	31.5502	1.05935	0.529677	+	0.848200i	$0.322313\pi$
$888$	0.244562	0.00820697
$889$	0	0
$890$	−3.04987	−0.102232
$891$	−3.38810	−0.113506
$892$	0.926555	0.0310234
$893$	54.0592	1.80902
$894$	36.4999	1.22074
$895$	2.59910	0.0868784
$896$	0	0
$897$	−2.25642	−0.0753395
$898$	58.5876	1.95509
$899$	6.88307	0.229563
$900$	−12.1598	−0.405327
$901$	60.4254	2.01306
$902$	−7.16495	−0.238567
$903$	0	0
$904$	−10.1738	−0.338376
$905$	−7.27604	−0.241864
$906$	36.4672	1.21154
$907$	0.774377	0.0257128	0.0128564	−	0.999917i	$-0.495908\pi$
$907$	0.774377	0.0257128	0.0128564	+	0.999917i	$0.495908\pi$
$908$	−39.2755	−1.30340
$909$	16.7781	0.556494
$910$	0	0
$911$	−32.0425	−1.06162	−0.530808	−	0.847492i	$-0.678112\pi$
$911$	−32.0425	−1.06162	−0.530808	+	0.847492i	$0.678112\pi$
$912$	17.5458	0.581000
$913$	25.3652	0.839466
$914$	−27.4778	−0.908884
$915$	−0.961604	−0.0317897
$916$	48.3016	1.59593
$917$	0	0
$918$	−9.02642	−0.297916
$919$	−18.5782	−0.612839	−0.306419	−	0.951897i	$-0.599131\pi$
$919$	−18.5782	−0.612839	−0.306419	+	0.951897i	$0.599131\pi$
$920$	0.891650	0.0293968
$921$	1.88472	0.0621037
$922$	11.4483	0.377029
$923$	1.56811	0.0516149
$924$	0	0
$925$	−1.20485	−0.0396153
$926$	66.5546	2.18712
$927$	7.17037	0.235506
$928$	−5.56467	−0.182669
$929$	−24.1583	−0.792607	−0.396303	−	0.918120i	$-0.629707\pi$
$929$	−24.1583	−0.792607	−0.396303	+	0.918120i	$0.629707\pi$
$930$	−5.95489	−0.195269
$931$	0	0
$932$	−42.2509	−1.38397
$933$	−5.69831	−0.186554
$934$	−47.5667	−1.55643
$935$	−4.12168	−0.134793
$936$	0.718966	0.0235001
$937$	28.0378	0.915955	0.457978	−	0.888964i	$-0.348574\pi$
$937$	28.0378	0.915955	0.457978	+	0.888964i	$0.348574\pi$
$938$	0	0
$939$	−29.2119	−0.953295
$940$	6.14964	0.200579
$941$	5.15440	0.168029	0.0840143	−	0.996465i	$-0.473226\pi$
$941$	5.15440	0.168029	0.0840143	+	0.996465i	$0.473226\pi$
$942$	23.7503	0.773827
$943$	−3.13345	−0.102039
$944$	−25.5885	−0.832834
$945$	0	0
$946$	14.4530	0.469908
$947$	41.8074	1.35856	0.679279	−	0.733880i	$-0.262293\pi$
$947$	41.8074	1.35856	0.679279	+	0.733880i	$0.262293\pi$
$948$	−29.1719	−0.947460
$949$	−8.59032	−0.278853
$950$	64.4262	2.09026
$951$	−32.9071	−1.06709
$952$	0	0
$953$	3.18682	0.103231	0.0516157	−	0.998667i	$-0.483563\pi$
$953$	3.18682	0.103231	0.0516157	+	0.998667i	$0.483563\pi$
$954$	−29.9376	−0.969267
$955$	2.38256	0.0770980
$956$	37.1924	1.20289
$957$	−2.36037	−0.0763000
$958$	12.9603	0.418728
$959$	0	0
$960$	3.19950	0.103264
$961$	66.6148	2.14886
$962$	0.373019	0.0120266
$963$	−2.30396	−0.0742442
$964$	−1.33331	−0.0429432
$965$	−5.55213	−0.178729
$966$	0	0
$967$	32.6115	1.04871	0.524357	−	0.851498i	$-0.324306\pi$
$967$	32.6115	1.04871	0.524357	+	0.851498i	$0.324306\pi$
$968$	0.478476	0.0153788
$969$	26.4368	0.849271
$970$	−9.19669	−0.295288
$971$	−32.0671	−1.02908	−0.514542	−	0.857465i	$-0.672038\pi$
$971$	−32.0671	−1.02908	−0.514542	+	0.857465i	$0.672038\pi$
$972$	2.47212	0.0792934
$973$	0	0
$974$	−63.2641	−2.02711
$975$	−3.54203	−0.113436
$976$	−9.55787	−0.305940
$977$	−45.1298	−1.44383	−0.721915	−	0.691982i	$-0.756738\pi$
$977$	−45.1298	−1.44383	−0.721915	+	0.691982i	$0.756738\pi$
$978$	12.0149	0.384195
$979$	−17.1444	−0.547936
$980$	0	0
$981$	−5.22043	−0.166675
$982$	43.3281	1.38266
$983$	−17.6207	−0.562013	−0.281007	−	0.959706i	$-0.590668\pi$
$983$	−17.6207	−0.562013	−0.281007	+	0.959706i	$0.590668\pi$
$984$	0.998417	0.0318284
$985$	−3.55529	−0.113281
$986$	−6.28839	−0.200263
$987$	0	0
$988$	−11.0259	−0.350782
$989$	6.32074	0.200988
$990$	2.04208	0.0649016
$991$	−11.1131	−0.353020	−0.176510	−	0.984299i	$-0.556481\pi$
$991$	−11.1131	−0.353020	−0.176510	+	0.984299i	$0.556481\pi$
$992$	−78.9175	−2.50563
$993$	−17.9603	−0.569953
$994$	0	0
$995$	−0.817228	−0.0259079
$996$	−18.5077	−0.586438
$997$	−12.0055	−0.380219	−0.190109	−	0.981763i	$-0.560884\pi$
$997$	−12.0055	−0.380219	−0.190109	+	0.981763i	$0.560884\pi$
$998$	69.6528	2.20482
$999$	0.244950	0.00774987

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bm.1.15	yes	16
7.6	odd	2		6027.2.a.bl.1.15	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bl.1.15	✓	16	7.6	odd	2
6027.2.a.bm.1.15	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)

\(f(q)\)	\(=\)	\(q+2.11474 q^{2} +1.00000 q^{3} +2.47212 q^{4} -0.285010 q^{5} +2.11474 q^{6} +0.998417 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.11474 q^{2} +1.00000 q^{3} +2.47212 q^{4} -0.285010 q^{5} +2.11474 q^{6} +0.998417 q^{8} +1.00000 q^{9} -0.602721 q^{10} -3.38810 q^{11} +2.47212 q^{12} +0.720106 q^{13} -0.285010 q^{15} -2.83285 q^{16} -4.26834 q^{17} +2.11474 q^{18} -6.19369 q^{19} -0.704579 q^{20} -7.16495 q^{22} -3.13345 q^{23} +0.998417 q^{24} -4.91877 q^{25} +1.52284 q^{26} +1.00000 q^{27} +0.696665 q^{29} -0.602721 q^{30} +9.88002 q^{31} -7.98758 q^{32} -3.38810 q^{33} -9.02642 q^{34} +2.47212 q^{36} +0.244950 q^{37} -13.0980 q^{38} +0.720106 q^{39} -0.284558 q^{40} +1.00000 q^{41} -2.01718 q^{43} -8.37580 q^{44} -0.285010 q^{45} -6.62643 q^{46} -8.72811 q^{47} -2.83285 q^{48} -10.4019 q^{50} -4.26834 q^{51} +1.78019 q^{52} -14.1567 q^{53} +2.11474 q^{54} +0.965642 q^{55} -6.19369 q^{57} +1.47327 q^{58} +9.03275 q^{59} -0.704579 q^{60} +3.37394 q^{61} +20.8937 q^{62} -11.2259 q^{64} -0.205237 q^{65} -7.16495 q^{66} +10.3436 q^{67} -10.5519 q^{68} -3.13345 q^{69} +2.17761 q^{71} +0.998417 q^{72} -11.9292 q^{73} +0.518005 q^{74} -4.91877 q^{75} -15.3116 q^{76} +1.52284 q^{78} -11.8004 q^{79} +0.807391 q^{80} +1.00000 q^{81} +2.11474 q^{82} -7.48655 q^{83} +1.21652 q^{85} -4.26581 q^{86} +0.696665 q^{87} -3.38274 q^{88} +5.06017 q^{89} -0.602721 q^{90} -7.74628 q^{92} +9.88002 q^{93} -18.4577 q^{94} +1.76526 q^{95} -7.98758 q^{96} +15.2586 q^{97} -3.38810 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 16 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) 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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