LMFDB - Embedded newform 5577.2.a.ba.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5577,2,Mod(1,5577)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5577, 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("5577.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5577 = 3 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5577.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:	$44.5325692073$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 14 x^{10} + 13 x^{9} + 70 x^{8} - 61 x^{7} - 152 x^{6} + 127 x^{5} + 138 x^{4} + \cdots + 1 $ x^12 - x^11 - 14x^10 + 13x^9 + 70x^8 - 61x^7 - 152x^6 + 127x^5 + 138x^4 - 110x^3 - 40x^2 + 29x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.679772$ of defining polynomial
Character	$\chi$	$=$	5577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.679772 q^{2} -1.00000 q^{3} -1.53791 q^{4} -3.36496 q^{5} -0.679772 q^{6} +0.0622521 q^{7} -2.40497 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.679772 q^{2} -1.00000 q^{3} -1.53791 q^{4} -3.36496 q^{5} -0.679772 q^{6} +0.0622521 q^{7} -2.40497 q^{8} +1.00000 q^{9} -2.28741 q^{10} -1.00000 q^{11} +1.53791 q^{12} +0.0423172 q^{14} +3.36496 q^{15} +1.44099 q^{16} -2.45300 q^{17} +0.679772 q^{18} -0.283042 q^{19} +5.17501 q^{20} -0.0622521 q^{21} -0.679772 q^{22} +1.33715 q^{23} +2.40497 q^{24} +6.32297 q^{25} -1.00000 q^{27} -0.0957381 q^{28} +2.25549 q^{29} +2.28741 q^{30} +6.67832 q^{31} +5.78949 q^{32} +1.00000 q^{33} -1.66748 q^{34} -0.209476 q^{35} -1.53791 q^{36} +3.56253 q^{37} -0.192404 q^{38} +8.09264 q^{40} +10.0209 q^{41} -0.0423172 q^{42} -8.65994 q^{43} +1.53791 q^{44} -3.36496 q^{45} +0.908955 q^{46} -4.79855 q^{47} -1.44099 q^{48} -6.99612 q^{49} +4.29818 q^{50} +2.45300 q^{51} +4.34343 q^{53} -0.679772 q^{54} +3.36496 q^{55} -0.149715 q^{56} +0.283042 q^{57} +1.53322 q^{58} +13.7575 q^{59} -5.17501 q^{60} +2.03838 q^{61} +4.53974 q^{62} +0.0622521 q^{63} +1.05356 q^{64} +0.679772 q^{66} -2.33966 q^{67} +3.77250 q^{68} -1.33715 q^{69} -0.142396 q^{70} +8.74173 q^{71} -2.40497 q^{72} -13.1075 q^{73} +2.42171 q^{74} -6.32297 q^{75} +0.435293 q^{76} -0.0622521 q^{77} +1.65672 q^{79} -4.84886 q^{80} +1.00000 q^{81} +6.81195 q^{82} +5.86499 q^{83} +0.0957381 q^{84} +8.25426 q^{85} -5.88679 q^{86} -2.25549 q^{87} +2.40497 q^{88} +7.18799 q^{89} -2.28741 q^{90} -2.05641 q^{92} -6.67832 q^{93} -3.26192 q^{94} +0.952425 q^{95} -5.78949 q^{96} -8.30250 q^{97} -4.75577 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} - 12 q^{3} + 5 q^{4} + 6 q^{5} + q^{6} + q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q - q^2 - 12 * q^3 + 5 * q^4 + 6 * q^5 + q^6 + q^7 + 12 * q^9	$ 12 q - q^{2} - 12 q^{3} + 5 q^{4} + 6 q^{5} + q^{6} + q^{7} + 12 q^{9} - 11 q^{10} - 12 q^{11} - 5 q^{12} + 9 q^{14} - 6 q^{15} - 9 q^{16} + 3 q^{17} - q^{18} - 6 q^{19} + 20 q^{20} - q^{21} + q^{22} - 22 q^{23} - 2 q^{25} - 12 q^{27} + 11 q^{28} + 13 q^{29} + 11 q^{30} - 2 q^{31} - 11 q^{32} + 12 q^{33} - 10 q^{34} - 14 q^{35} + 5 q^{36} - 3 q^{37} - 18 q^{38} - 18 q^{40} - 4 q^{41} - 9 q^{42} - 26 q^{43} - 5 q^{44} + 6 q^{45} + 18 q^{46} + 9 q^{47} + 9 q^{48} - 3 q^{49} - 29 q^{50} - 3 q^{51} - 5 q^{53} + q^{54} - 6 q^{55} + 5 q^{56} + 6 q^{57} - 37 q^{58} + 22 q^{59} - 20 q^{60} - 11 q^{61} - 18 q^{62} + q^{63} - 10 q^{64} - q^{66} + 28 q^{67} + 12 q^{68} + 22 q^{69} + 29 q^{70} - 10 q^{71} + 7 q^{73} - 6 q^{74} + 2 q^{75} - 32 q^{76} - q^{77} - 40 q^{79} - 30 q^{80} + 12 q^{81} + 26 q^{82} - q^{83} - 11 q^{84} + 32 q^{85} + 9 q^{86} - 13 q^{87} - 11 q^{89} - 11 q^{90} - 38 q^{92} + 2 q^{93} - 25 q^{94} - 10 q^{95} + 11 q^{96} - 7 q^{97} - 28 q^{98} - 12 q^{99}+O(q^{100}) $ 12 * q - q^2 - 12 * q^3 + 5 * q^4 + 6 * q^5 + q^6 + q^7 + 12 * q^9 - 11 * q^10 - 12 * q^11 - 5 * q^12 + 9 * q^14 - 6 * q^15 - 9 * q^16 + 3 * q^17 - q^18 - 6 * q^19 + 20 * q^20 - q^21 + q^22 - 22 * q^23 - 2 * q^25 - 12 * q^27 + 11 * q^28 + 13 * q^29 + 11 * q^30 - 2 * q^31 - 11 * q^32 + 12 * q^33 - 10 * q^34 - 14 * q^35 + 5 * q^36 - 3 * q^37 - 18 * q^38 - 18 * q^40 - 4 * q^41 - 9 * q^42 - 26 * q^43 - 5 * q^44 + 6 * q^45 + 18 * q^46 + 9 * q^47 + 9 * q^48 - 3 * q^49 - 29 * q^50 - 3 * q^51 - 5 * q^53 + q^54 - 6 * q^55 + 5 * q^56 + 6 * q^57 - 37 * q^58 + 22 * q^59 - 20 * q^60 - 11 * q^61 - 18 * q^62 + q^63 - 10 * q^64 - q^66 + 28 * q^67 + 12 * q^68 + 22 * q^69 + 29 * q^70 - 10 * q^71 + 7 * q^73 - 6 * q^74 + 2 * q^75 - 32 * q^76 - q^77 - 40 * q^79 - 30 * q^80 + 12 * q^81 + 26 * q^82 - q^83 - 11 * q^84 + 32 * q^85 + 9 * q^86 - 13 * q^87 - 11 * q^89 - 11 * q^90 - 38 * q^92 + 2 * q^93 - 25 * q^94 - 10 * q^95 + 11 * q^96 - 7 * q^97 - 28 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.679772	0.480672	0.240336	−	0.970690i	$-0.422742\pi$
$2$	0.679772	0.480672	0.240336	+	0.970690i	$0.422742\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.53791	−0.768955
$5$	−3.36496	−1.50486	−0.752428	−	0.658674i	$-0.771118\pi$
$5$	−3.36496	−1.50486	−0.752428	+	0.658674i	$0.771118\pi$
$6$	−0.679772	−0.277516
$7$	0.0622521	0.0235291	0.0117645	−	0.999931i	$-0.496255\pi$
$7$	0.0622521	0.0235291	0.0117645	+	0.999931i	$0.496255\pi$
$8$	−2.40497	−0.850286
$9$	1.00000	0.333333
$10$	−2.28741	−0.723342
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.53791	0.443956
$13$	0	0
$13$	0	0
$14$	0.0423172	0.0113098
$15$	3.36496	0.868829
$16$	1.44099	0.360246
$17$	−2.45300	−0.594941	−0.297470	−	0.954731i	$-0.596143\pi$
$17$	−2.45300	−0.594941	−0.297470	+	0.954731i	$0.596143\pi$
$18$	0.679772	0.160224
$19$	−0.283042	−0.0649343	−0.0324671	−	0.999473i	$-0.510336\pi$
$19$	−0.283042	−0.0649343	−0.0324671	+	0.999473i	$0.510336\pi$
$20$	5.17501	1.15717
$21$	−0.0622521	−0.0135845
$22$	−0.679772	−0.144928
$23$	1.33715	0.278814	0.139407	−	0.990235i	$-0.455480\pi$
$23$	1.33715	0.278814	0.139407	+	0.990235i	$0.455480\pi$
$24$	2.40497	0.490913
$25$	6.32297	1.26459
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−0.0957381	−0.0180928
$29$	2.25549	0.418834	0.209417	−	0.977826i	$-0.432843\pi$
$29$	2.25549	0.418834	0.209417	+	0.977826i	$0.432843\pi$
$30$	2.28741	0.417622
$31$	6.67832	1.19946	0.599731	−	0.800202i	$-0.295274\pi$
$31$	6.67832	1.19946	0.599731	+	0.800202i	$0.295274\pi$
$32$	5.78949	1.02345
$33$	1.00000	0.174078
$34$	−1.66748	−0.285971
$35$	−0.209476	−0.0354079
$36$	−1.53791	−0.256318
$37$	3.56253	0.585677	0.292838	−	0.956162i	$-0.405400\pi$
$37$	3.56253	0.585677	0.292838	+	0.956162i	$0.405400\pi$
$38$	−0.192404	−0.0312121
$39$	0	0
$40$	8.09264	1.27956
$41$	10.0209	1.56501	0.782503	−	0.622647i	$-0.213943\pi$
$41$	10.0209	1.56501	0.782503	+	0.622647i	$0.213943\pi$
$42$	−0.0423172	−0.00652969
$43$	−8.65994	−1.32063	−0.660314	−	0.750989i	$-0.729577\pi$
$43$	−8.65994	−1.32063	−0.660314	+	0.750989i	$0.729577\pi$
$44$	1.53791	0.231849
$45$	−3.36496	−0.501619
$46$	0.908955	0.134018
$47$	−4.79855	−0.699940	−0.349970	−	0.936761i	$-0.613808\pi$
$47$	−4.79855	−0.699940	−0.349970	+	0.936761i	$0.613808\pi$
$48$	−1.44099	−0.207988
$49$	−6.99612	−0.999446
$50$	4.29818	0.607854
$51$	2.45300	0.343489
$52$	0	0
$53$	4.34343	0.596616	0.298308	−	0.954470i	$-0.403578\pi$
$53$	4.34343	0.596616	0.298308	+	0.954470i	$0.403578\pi$
$54$	−0.679772	−0.0925053
$55$	3.36496	0.453731
$56$	−0.149715	−0.0200065
$57$	0.283042	0.0374898
$58$	1.53322	0.201322
$59$	13.7575	1.79108	0.895539	−	0.444983i	$-0.146790\pi$
$59$	13.7575	1.79108	0.895539	+	0.444983i	$0.146790\pi$
$60$	−5.17501	−0.668091
$61$	2.03838	0.260987	0.130494	−	0.991449i	$-0.458344\pi$
$61$	2.03838	0.260987	0.130494	+	0.991449i	$0.458344\pi$
$62$	4.53974	0.576547
$63$	0.0622521	0.00784303
$64$	1.05356	0.131695
$65$	0	0
$66$	0.679772	0.0836742
$67$	−2.33966	−0.285835	−0.142918	−	0.989735i	$-0.545648\pi$
$67$	−2.33966	−0.285835	−0.142918	+	0.989735i	$0.545648\pi$
$68$	3.77250	0.457483
$69$	−1.33715	−0.160974
$70$	−0.142396	−0.0170196
$71$	8.74173	1.03745	0.518726	−	0.854940i	$-0.326406\pi$
$71$	8.74173	1.03745	0.518726	+	0.854940i	$0.326406\pi$
$72$	−2.40497	−0.283429
$73$	−13.1075	−1.53411	−0.767057	−	0.641579i	$-0.778279\pi$
$73$	−13.1075	−1.53411	−0.767057	+	0.641579i	$0.778279\pi$
$74$	2.42171	0.281518
$75$	−6.32297	−0.730114
$76$	0.435293	0.0499315
$77$	−0.0622521	−0.00709428
$78$	0	0
$79$	1.65672	0.186396	0.0931979	−	0.995648i	$-0.470291\pi$
$79$	1.65672	0.186396	0.0931979	+	0.995648i	$0.470291\pi$
$80$	−4.84886	−0.542119
$81$	1.00000	0.111111
$82$	6.81195	0.752254
$83$	5.86499	0.643767	0.321883	−	0.946779i	$-0.395684\pi$
$83$	5.86499	0.643767	0.321883	+	0.946779i	$0.395684\pi$
$84$	0.0957381	0.0104459
$85$	8.25426	0.895301
$86$	−5.88679	−0.634789
$87$	−2.25549	−0.241814
$88$	2.40497	0.256371
$89$	7.18799	0.761925	0.380963	−	0.924590i	$-0.375593\pi$
$89$	7.18799	0.761925	0.380963	+	0.924590i	$0.375593\pi$
$90$	−2.28741	−0.241114
$91$	0	0
$92$	−2.05641	−0.214396
$93$	−6.67832	−0.692510
$94$	−3.26192	−0.336441
$95$	0.952425	0.0977168
$96$	−5.78949	−0.590887
$97$	−8.30250	−0.842991	−0.421495	−	0.906831i	$-0.638495\pi$
$97$	−8.30250	−0.842991	−0.421495	+	0.906831i	$0.638495\pi$
$98$	−4.75577	−0.480405
$99$	−1.00000	−0.100504
$100$	−9.72416	−0.972416
$101$	−1.60575	−0.159778	−0.0798890	−	0.996804i	$-0.525457\pi$
$101$	−1.60575	−0.159778	−0.0798890	+	0.996804i	$0.525457\pi$
$102$	1.66748	0.165106
$103$	−7.09787	−0.699374	−0.349687	−	0.936867i	$-0.613712\pi$
$103$	−7.09787	−0.699374	−0.349687	+	0.936867i	$0.613712\pi$
$104$	0	0
$105$	0.209476	0.0204428
$106$	2.95254	0.286776
$107$	−8.02814	−0.776110	−0.388055	−	0.921636i	$-0.626853\pi$
$107$	−8.02814	−0.776110	−0.388055	+	0.921636i	$0.626853\pi$
$108$	1.53791	0.147985
$109$	−0.0538086	−0.00515393	−0.00257696	−	0.999997i	$-0.500820\pi$
$109$	−0.0538086	−0.00515393	−0.00257696	+	0.999997i	$0.500820\pi$
$110$	2.28741	0.218096
$111$	−3.56253	−0.338141
$112$	0.0897044	0.00847627
$113$	−3.42218	−0.321931	−0.160966	−	0.986960i	$-0.551461\pi$
$113$	−3.42218	−0.321931	−0.160966	+	0.986960i	$0.551461\pi$
$114$	0.192404	0.0180203
$115$	−4.49945	−0.419576
$116$	−3.46874	−0.322065
$117$	0	0
$118$	9.35199	0.860920
$119$	−0.152705	−0.0139984
$120$	−8.09264	−0.738754
$121$	1.00000	0.0909091
$122$	1.38563	0.125449
$123$	−10.0209	−0.903556
$124$	−10.2707	−0.922332
$125$	−4.45174	−0.398176
$126$	0.0423172	0.00376992
$127$	−13.5267	−1.20030	−0.600150	−	0.799888i	$-0.704892\pi$
$127$	−13.5267	−1.20030	−0.600150	+	0.799888i	$0.704892\pi$
$128$	−10.8628	−0.960144
$129$	8.65994	0.762465
$130$	0	0
$131$	−18.4271	−1.60999	−0.804993	−	0.593284i	$-0.797831\pi$
$131$	−18.4271	−1.60999	−0.804993	+	0.593284i	$0.797831\pi$
$132$	−1.53791	−0.133858
$133$	−0.0176200	−0.00152784
$134$	−1.59044	−0.137393
$135$	3.36496	0.289610
$136$	5.89941	0.505870
$137$	16.5528	1.41420	0.707102	−	0.707112i	$-0.250002\pi$
$137$	16.5528	1.41420	0.707102	+	0.707112i	$0.250002\pi$
$138$	−0.908955	−0.0773754
$139$	16.7090	1.41724	0.708619	−	0.705591i	$-0.249318\pi$
$139$	16.7090	1.41724	0.708619	+	0.705591i	$0.249318\pi$
$140$	0.322155	0.0272271
$141$	4.79855	0.404111
$142$	5.94239	0.498674
$143$	0	0
$144$	1.44099	0.120082
$145$	−7.58964	−0.630286
$146$	−8.91009	−0.737405
$147$	6.99612	0.577031
$148$	−5.47885	−0.450359
$149$	−6.37375	−0.522158	−0.261079	−	0.965317i	$-0.584078\pi$
$149$	−6.37375	−0.522158	−0.261079	+	0.965317i	$0.584078\pi$
$150$	−4.29818	−0.350945
$151$	−20.4640	−1.66534	−0.832670	−	0.553770i	$-0.813189\pi$
$151$	−20.4640	−1.66534	−0.832670	+	0.553770i	$0.813189\pi$
$152$	0.680708	0.0552127
$153$	−2.45300	−0.198314
$154$	−0.0423172	−0.00341002
$155$	−22.4723	−1.80502
$156$	0	0
$157$	0.501348	0.0400119	0.0200060	−	0.999800i	$-0.493631\pi$
$157$	0.501348	0.0400119	0.0200060	+	0.999800i	$0.493631\pi$
$158$	1.12619	0.0895952
$159$	−4.34343	−0.344456
$160$	−19.4814	−1.54014
$161$	0.0832402	0.00656025
$162$	0.679772	0.0534080
$163$	9.68039	0.758227	0.379113	−	0.925350i	$-0.376229\pi$
$163$	9.68039	0.758227	0.379113	+	0.925350i	$0.376229\pi$
$164$	−15.4113	−1.20342
$165$	−3.36496	−0.261962
$166$	3.98686	0.309440
$167$	3.66836	0.283866	0.141933	−	0.989876i	$-0.454668\pi$
$167$	3.66836	0.283866	0.141933	+	0.989876i	$0.454668\pi$
$168$	0.149715	0.0115507
$169$	0	0
$170$	5.61102	0.430346
$171$	−0.283042	−0.0216448
$172$	13.3182	1.01550
$173$	13.6952	1.04123	0.520615	−	0.853792i	$-0.325703\pi$
$173$	13.6952	1.04123	0.520615	+	0.853792i	$0.325703\pi$
$174$	−1.53322	−0.116233
$175$	0.393618	0.0297547
$176$	−1.44099	−0.108618
$177$	−13.7575	−1.03408
$178$	4.88619	0.366236
$179$	18.7715	1.40305	0.701524	−	0.712646i	$-0.252503\pi$
$179$	18.7715	1.40305	0.701524	+	0.712646i	$0.252503\pi$
$180$	5.17501	0.385722
$181$	−4.63979	−0.344873	−0.172436	−	0.985021i	$-0.555164\pi$
$181$	−4.63979	−0.344873	−0.172436	+	0.985021i	$0.555164\pi$
$182$	0	0
$183$	−2.03838	−0.150681
$184$	−3.21580	−0.237072
$185$	−11.9878	−0.881360
$186$	−4.53974	−0.332870
$187$	2.45300	0.179381
$188$	7.37974	0.538223
$189$	−0.0622521	−0.00452817
$190$	0.647432	0.0469697
$191$	26.3850	1.90915	0.954576	−	0.297968i	$-0.0963089\pi$
$191$	26.3850	1.90915	0.954576	+	0.297968i	$0.0963089\pi$
$192$	−1.05356	−0.0760343
$193$	−16.8077	−1.20985	−0.604923	−	0.796284i	$-0.706796\pi$
$193$	−16.8077	−1.20985	−0.604923	+	0.796284i	$0.706796\pi$
$194$	−5.64381	−0.405202
$195$	0	0
$196$	10.7594	0.768529
$197$	−21.1316	−1.50556	−0.752781	−	0.658271i	$-0.771288\pi$
$197$	−21.1316	−1.50556	−0.752781	+	0.658271i	$0.771288\pi$
$198$	−0.679772	−0.0483093
$199$	−21.7455	−1.54150	−0.770750	−	0.637138i	$-0.780118\pi$
$199$	−21.7455	−1.54150	−0.770750	+	0.637138i	$0.780118\pi$
$200$	−15.2066	−1.07527
$201$	2.33966	0.165027
$202$	−1.09154	−0.0768007
$203$	0.140409	0.00985479
$204$	−3.77250	−0.264128
$205$	−33.7200	−2.35511
$206$	−4.82494	−0.336169
$207$	1.33715	0.0929381
$208$	0	0
$209$	0.283042	0.0195784
$210$	0.142396	0.00982625
$211$	3.29543	0.226867	0.113433	−	0.993546i	$-0.463815\pi$
$211$	3.29543	0.226867	0.113433	+	0.993546i	$0.463815\pi$
$212$	−6.67980	−0.458771
$213$	−8.74173	−0.598974
$214$	−5.45731	−0.373054
$215$	29.1404	1.98736
$216$	2.40497	0.163638
$217$	0.415740	0.0282222
$218$	−0.0365776	−0.00247735
$219$	13.1075	0.885721
$220$	−5.17501	−0.348899
$221$	0	0
$222$	−2.42171	−0.162535
$223$	−21.5223	−1.44124	−0.720619	−	0.693332i	$-0.756142\pi$
$223$	−21.5223	−1.44124	−0.720619	+	0.693332i	$0.756142\pi$
$224$	0.360408	0.0240808
$225$	6.32297	0.421531
$226$	−2.32630	−0.154743
$227$	−8.47294	−0.562369	−0.281184	−	0.959654i	$-0.590727\pi$
$227$	−8.47294	−0.562369	−0.281184	+	0.959654i	$0.590727\pi$
$228$	−0.435293	−0.0288280
$229$	14.9492	0.987870	0.493935	−	0.869499i	$-0.335558\pi$
$229$	14.9492	0.987870	0.493935	+	0.869499i	$0.335558\pi$
$230$	−3.05860	−0.201678
$231$	0.0622521	0.00409589
$232$	−5.42440	−0.356129
$233$	−27.6123	−1.80894	−0.904470	−	0.426538i	$-0.859733\pi$
$233$	−27.6123	−1.80894	−0.904470	+	0.426538i	$0.859733\pi$
$234$	0	0
$235$	16.1469	1.05331
$236$	−21.1578	−1.37726
$237$	−1.65672	−0.107616
$238$	−0.103804	−0.00672864
$239$	3.17249	0.205211	0.102606	−	0.994722i	$-0.467282\pi$
$239$	3.17249	0.205211	0.102606	+	0.994722i	$0.467282\pi$
$240$	4.84886	0.312993
$241$	−3.37747	−0.217562	−0.108781	−	0.994066i	$-0.534695\pi$
$241$	−3.37747	−0.217562	−0.108781	+	0.994066i	$0.534695\pi$
$242$	0.679772	0.0436974
$243$	−1.00000	−0.0641500
$244$	−3.13484	−0.200687
$245$	23.5417	1.50402
$246$	−6.81195	−0.434314
$247$	0	0
$248$	−16.0612	−1.01989
$249$	−5.86499	−0.371679
$250$	−3.02617	−0.191392
$251$	−11.8347	−0.747000	−0.373500	−	0.927630i	$-0.621842\pi$
$251$	−11.8347	−0.747000	−0.373500	+	0.927630i	$0.621842\pi$
$252$	−0.0957381	−0.00603093
$253$	−1.33715	−0.0840657
$254$	−9.19506	−0.576950
$255$	−8.25426	−0.516902
$256$	−9.49135	−0.593209
$257$	4.07570	0.254235	0.127118	−	0.991888i	$-0.459427\pi$
$257$	4.07570	0.254235	0.127118	+	0.991888i	$0.459427\pi$
$258$	5.88679	0.366495
$259$	0.221775	0.0137804
$260$	0	0
$261$	2.25549	0.139611
$262$	−12.5263	−0.773874
$263$	−25.1902	−1.55330	−0.776648	−	0.629934i	$-0.783082\pi$
$263$	−25.1902	−1.55330	−0.776648	+	0.629934i	$0.783082\pi$
$264$	−2.40497	−0.148016
$265$	−14.6155	−0.897821
$266$	−0.0119776	−0.000734391 0
$267$	−7.18799	−0.439898
$268$	3.59819	0.219795
$269$	23.4644	1.43065	0.715325	−	0.698792i	$-0.246279\pi$
$269$	23.4644	1.43065	0.715325	+	0.698792i	$0.246279\pi$
$270$	2.28741	0.139207
$271$	−8.84070	−0.537034	−0.268517	−	0.963275i	$-0.586534\pi$
$271$	−8.84070	−0.537034	−0.268517	+	0.963275i	$0.586534\pi$
$272$	−3.53474	−0.214325
$273$	0	0
$274$	11.2522	0.679768
$275$	−6.32297	−0.381289
$276$	2.05641	0.123781
$277$	3.88461	0.233404	0.116702	−	0.993167i	$-0.462768\pi$
$277$	3.88461	0.233404	0.116702	+	0.993167i	$0.462768\pi$
$278$	11.3583	0.681226
$279$	6.67832	0.399821
$280$	0.503784	0.0301068
$281$	15.4133	0.919480	0.459740	−	0.888054i	$-0.347943\pi$
$281$	15.4133	0.919480	0.459740	+	0.888054i	$0.347943\pi$
$282$	3.26192	0.194245
$283$	−16.1099	−0.957632	−0.478816	−	0.877915i	$-0.658934\pi$
$283$	−16.1099	−0.957632	−0.478816	+	0.877915i	$0.658934\pi$
$284$	−13.4440	−0.797754
$285$	−0.952425	−0.0564168
$286$	0	0
$287$	0.623823	0.0368231
$288$	5.78949	0.341149
$289$	−10.9828	−0.646045
$290$	−5.15923	−0.302960
$291$	8.30250	0.486701
$292$	20.1581	1.17966
$293$	−4.23935	−0.247666	−0.123833	−	0.992303i	$-0.539519\pi$
$293$	−4.23935	−0.247666	−0.123833	+	0.992303i	$0.539519\pi$
$294$	4.75577	0.277362
$295$	−46.2936	−2.69532
$296$	−8.56779	−0.497993
$297$	1.00000	0.0580259
$298$	−4.33270	−0.250987
$299$	0	0
$300$	9.72416	0.561424
$301$	−0.539099	−0.0310732
$302$	−13.9109	−0.800481
$303$	1.60575	0.0922479
$304$	−0.407859	−0.0233923
$305$	−6.85906	−0.392749
$306$	−1.66748	−0.0953237
$307$	27.1091	1.54720	0.773598	−	0.633677i	$-0.218455\pi$
$307$	27.1091	1.54720	0.773598	+	0.633677i	$0.218455\pi$
$308$	0.0957381	0.00545518
$309$	7.09787	0.403784
$310$	−15.2761	−0.867621
$311$	−2.84322	−0.161224	−0.0806122	−	0.996746i	$-0.525688\pi$
$311$	−2.84322	−0.161224	−0.0806122	+	0.996746i	$0.525688\pi$
$312$	0	0
$313$	−27.2591	−1.54077	−0.770387	−	0.637577i	$-0.779937\pi$
$313$	−27.2591	−1.54077	−0.770387	+	0.637577i	$0.779937\pi$
$314$	0.340802	0.0192326
$315$	−0.209476	−0.0118026
$316$	−2.54789	−0.143330
$317$	−10.6977	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$317$	−10.6977	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$318$	−2.95254	−0.165570
$319$	−2.25549	−0.126283
$320$	−3.54520	−0.198182
$321$	8.02814	0.448087
$322$	0.0565844	0.00315332
$323$	0.694303	0.0386321
$324$	−1.53791	−0.0854394
$325$	0	0
$326$	6.58046	0.364458
$327$	0.0538086	0.00297562
$328$	−24.1001	−1.33070
$329$	−0.298720	−0.0164690
$330$	−2.28741	−0.125918
$331$	25.9797	1.42797	0.713987	−	0.700159i	$-0.246888\pi$
$331$	25.9797	1.42797	0.713987	+	0.700159i	$0.246888\pi$
$332$	−9.01983	−0.495027
$333$	3.56253	0.195226
$334$	2.49365	0.136446
$335$	7.87288	0.430141
$336$	−0.0897044	−0.00489377
$337$	−21.6922	−1.18165	−0.590825	−	0.806800i	$-0.701198\pi$
$337$	−21.6922	−1.18165	−0.590825	+	0.806800i	$0.701198\pi$
$338$	0	0
$339$	3.42218	0.185867
$340$	−12.6943	−0.688446
$341$	−6.67832	−0.361652
$342$	−0.192404	−0.0104040
$343$	−0.871288	−0.0470451
$344$	20.8269	1.12291
$345$	4.49945	0.242242
$346$	9.30965	0.500490
$347$	2.68078	0.143912	0.0719560	−	0.997408i	$-0.477076\pi$
$347$	2.68078	0.143912	0.0719560	+	0.997408i	$0.477076\pi$
$348$	3.46874	0.185944
$349$	21.6257	1.15760	0.578799	−	0.815471i	$-0.303522\pi$
$349$	21.6257	1.15760	0.578799	+	0.815471i	$0.303522\pi$
$350$	0.267571	0.0143023
$351$	0	0
$352$	−5.78949	−0.308581
$353$	8.84205	0.470615	0.235307	−	0.971921i	$-0.424390\pi$
$353$	8.84205	0.470615	0.235307	+	0.971921i	$0.424390\pi$
$354$	−9.35199	−0.497052
$355$	−29.4156	−1.56122
$356$	−11.0545	−0.585886
$357$	0.152705	0.00808198
$358$	12.7603	0.674405
$359$	−33.6139	−1.77408	−0.887038	−	0.461697i	$-0.847241\pi$
$359$	−33.6139	−1.77408	−0.887038	+	0.461697i	$0.847241\pi$
$360$	8.09264	0.426520
$361$	−18.9199	−0.995784
$362$	−3.15400	−0.165771
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	44.1061	2.30862
$366$	−1.38563	−0.0724281
$367$	16.4407	0.858200	0.429100	−	0.903257i	$-0.358831\pi$
$367$	16.4407	0.858200	0.429100	+	0.903257i	$0.358831\pi$
$368$	1.92681	0.100442
$369$	10.0209	0.521668
$370$	−8.14897	−0.423645
$371$	0.270388	0.0140378
$372$	10.2707	0.532509
$373$	0.748625	0.0387623	0.0193812	−	0.999812i	$-0.493830\pi$
$373$	0.748625	0.0387623	0.0193812	+	0.999812i	$0.493830\pi$
$374$	1.66748	0.0862235
$375$	4.45174	0.229887
$376$	11.5404	0.595150
$377$	0	0
$378$	−0.0423172	−0.00217656
$379$	22.4141	1.15134	0.575669	−	0.817683i	$-0.304742\pi$
$379$	22.4141	1.15134	0.575669	+	0.817683i	$0.304742\pi$
$380$	−1.46474	−0.0751398
$381$	13.5267	0.692993
$382$	17.9358	0.917675
$383$	22.5514	1.15232	0.576161	−	0.817336i	$-0.304550\pi$
$383$	22.5514	1.15232	0.576161	+	0.817336i	$0.304550\pi$
$384$	10.8628	0.554340
$385$	0.209476	0.0106759
$386$	−11.4254	−0.581539
$387$	−8.65994	−0.440210
$388$	12.7685	0.648222
$389$	−7.51672	−0.381113	−0.190556	−	0.981676i	$-0.561029\pi$
$389$	−7.51672	−0.381113	−0.190556	+	0.981676i	$0.561029\pi$
$390$	0	0
$391$	−3.28003	−0.165878
$392$	16.8255	0.849816
$393$	18.4271	0.929526
$394$	−14.3647	−0.723681
$395$	−5.57481	−0.280499
$396$	1.53791	0.0772829
$397$	18.0969	0.908259	0.454129	−	0.890936i	$-0.349950\pi$
$397$	18.0969	0.908259	0.454129	+	0.890936i	$0.349950\pi$
$398$	−14.7820	−0.740955
$399$	0.0176200	0.000882101 0
$400$	9.11131	0.455565
$401$	5.52026	0.275669	0.137834	−	0.990455i	$-0.455986\pi$
$401$	5.52026	0.275669	0.137834	+	0.990455i	$0.455986\pi$
$402$	1.59044	0.0793239
$403$	0	0
$404$	2.46950	0.122862
$405$	−3.36496	−0.167206
$406$	0.0954462	0.00473692
$407$	−3.56253	−0.176588
$408$	−5.89941	−0.292064
$409$	−27.6153	−1.36549	−0.682744	−	0.730657i	$-0.739214\pi$
$409$	−27.6153	−1.36549	−0.682744	+	0.730657i	$0.739214\pi$
$410$	−22.9219	−1.13203
$411$	−16.5528	−0.816491
$412$	10.9159	0.537787
$413$	0.856435	0.0421424
$414$	0.908955	0.0446727
$415$	−19.7355	−0.968776
$416$	0	0
$417$	−16.7090	−0.818243
$418$	0.192404	0.00941079
$419$	−11.0744	−0.541018	−0.270509	−	0.962717i	$-0.587192\pi$
$419$	−11.0744	−0.541018	−0.270509	+	0.962717i	$0.587192\pi$
$420$	−0.322155	−0.0157196
$421$	29.2020	1.42322	0.711610	−	0.702575i	$-0.247967\pi$
$421$	29.2020	1.42322	0.711610	+	0.702575i	$0.247967\pi$
$422$	2.24014	0.109048
$423$	−4.79855	−0.233313
$424$	−10.4458	−0.507294
$425$	−15.5103	−0.752359
$426$	−5.94239	−0.287910
$427$	0.126893	0.00614079
$428$	12.3466	0.596793
$429$	0	0
$430$	19.8088	0.955266
$431$	7.61037	0.366578	0.183289	−	0.983059i	$-0.441326\pi$
$431$	7.61037	0.366578	0.183289	+	0.983059i	$0.441326\pi$
$432$	−1.44099	−0.0693295
$433$	10.3182	0.495860	0.247930	−	0.968778i	$-0.420250\pi$
$433$	10.3182	0.495860	0.247930	+	0.968778i	$0.420250\pi$
$434$	0.282608	0.0135656
$435$	7.58964	0.363896
$436$	0.0827527	0.00396314
$437$	−0.378469	−0.0181046
$438$	8.91009	0.425741
$439$	−10.7735	−0.514190	−0.257095	−	0.966386i	$-0.582765\pi$
$439$	−10.7735	−0.514190	−0.257095	+	0.966386i	$0.582765\pi$
$440$	−8.09264	−0.385802
$441$	−6.99612	−0.333149
$442$	0	0
$443$	−18.4493	−0.876551	−0.438275	−	0.898841i	$-0.644411\pi$
$443$	−18.4493	−0.876551	−0.438275	+	0.898841i	$0.644411\pi$
$444$	5.47885	0.260015
$445$	−24.1873	−1.14659
$446$	−14.6302	−0.692762
$447$	6.37375	0.301468
$448$	0.0655864	0.00309867
$449$	−35.4123	−1.67121	−0.835605	−	0.549331i	$-0.814882\pi$
$449$	−35.4123	−1.67121	−0.835605	+	0.549331i	$0.814882\pi$
$450$	4.29818	0.202618
$451$	−10.0209	−0.471867
$452$	5.26300	0.247551
$453$	20.4640	0.961484
$454$	−5.75967	−0.270315
$455$	0	0
$456$	−0.680708	−0.0318771
$457$	21.1979	0.991595	0.495798	−	0.868438i	$-0.334876\pi$
$457$	21.1979	0.991595	0.495798	+	0.868438i	$0.334876\pi$
$458$	10.1620	0.474841
$459$	2.45300	0.114496
$460$	6.91974	0.322635
$461$	−34.3108	−1.59801	−0.799006	−	0.601323i	$-0.794641\pi$
$461$	−34.3108	−1.59801	−0.799006	+	0.601323i	$0.794641\pi$
$462$	0.0423172	0.00196878
$463$	−17.7724	−0.825951	−0.412976	−	0.910742i	$-0.635511\pi$
$463$	−17.7724	−0.825951	−0.412976	+	0.910742i	$0.635511\pi$
$464$	3.25013	0.150884
$465$	22.4723	1.04213
$466$	−18.7701	−0.869506
$467$	−8.01133	−0.370720	−0.185360	−	0.982671i	$-0.559345\pi$
$467$	−8.01133	−0.370720	−0.185360	+	0.982671i	$0.559345\pi$
$468$	0	0
$469$	−0.145649	−0.00672544
$470$	10.9762	0.506296
$471$	−0.501348	−0.0231009
$472$	−33.0865	−1.52293
$473$	8.65994	0.398185
$474$	−1.12619	−0.0517278
$475$	−1.78967	−0.0821155
$476$	0.234846	0.0107641
$477$	4.34343	0.198872
$478$	2.15657	0.0986392
$479$	11.4168	0.521646	0.260823	−	0.965387i	$-0.416006\pi$
$479$	11.4168	0.521646	0.260823	+	0.965387i	$0.416006\pi$
$480$	19.4814	0.889200
$481$	0	0
$482$	−2.29591	−0.104576
$483$	−0.0832402	−0.00378756
$484$	−1.53791	−0.0699050
$485$	27.9376	1.26858
$486$	−0.679772	−0.0308351
$487$	30.6526	1.38900	0.694501	−	0.719492i	$-0.255625\pi$
$487$	30.6526	1.38900	0.694501	+	0.719492i	$0.255625\pi$
$488$	−4.90224	−0.221914
$489$	−9.68039	−0.437762
$490$	16.0030	0.722941
$491$	−28.7518	−1.29755	−0.648775	−	0.760980i	$-0.724718\pi$
$491$	−28.7518	−1.29755	−0.648775	+	0.760980i	$0.724718\pi$
$492$	15.4113	0.694794
$493$	−5.53273	−0.249182
$494$	0	0
$495$	3.36496	0.151244
$496$	9.62337	0.432102
$497$	0.544191	0.0244103
$498$	−3.98686	−0.178655
$499$	0.548949	0.0245743	0.0122872	−	0.999925i	$-0.496089\pi$
$499$	0.548949	0.0245743	0.0122872	+	0.999925i	$0.496089\pi$
$500$	6.84638	0.306179
$501$	−3.66836	−0.163890
$502$	−8.04490	−0.359061
$503$	15.8593	0.707131	0.353566	−	0.935410i	$-0.384969\pi$
$503$	15.8593	0.707131	0.353566	+	0.935410i	$0.384969\pi$
$504$	−0.149715	−0.00666882
$505$	5.40328	0.240443
$506$	−0.908955	−0.0404080
$507$	0	0
$508$	20.8028	0.922976
$509$	−38.1514	−1.69103	−0.845514	−	0.533953i	$-0.820706\pi$
$509$	−38.1514	−1.69103	−0.845514	+	0.533953i	$0.820706\pi$
$510$	−5.61102	−0.248460
$511$	−0.815967	−0.0360963
$512$	15.2736	0.675005
$513$	0.283042	0.0124966
$514$	2.77055	0.122204
$515$	23.8841	1.05246
$516$	−13.3182	−0.586301
$517$	4.79855	0.211040
$518$	0.150757	0.00662386
$519$	−13.6952	−0.601154
$520$	0	0
$521$	19.4297	0.851232	0.425616	−	0.904904i	$-0.360057\pi$
$521$	19.4297	0.851232	0.425616	+	0.904904i	$0.360057\pi$
$522$	1.53322	0.0671073
$523$	21.4060	0.936020	0.468010	−	0.883723i	$-0.344971\pi$
$523$	21.4060	0.936020	0.468010	+	0.883723i	$0.344971\pi$
$524$	28.3393	1.23801
$525$	−0.393618	−0.0171789
$526$	−17.1236	−0.746626
$527$	−16.3820	−0.713609
$528$	1.44099	0.0627108
$529$	−21.2120	−0.922263
$530$	−9.93519	−0.431557
$531$	13.7575	0.597026
$532$	0.0270979	0.00117484
$533$	0	0
$534$	−4.88619	−0.211446
$535$	27.0144	1.16793
$536$	5.62683	0.243042
$537$	−18.7715	−0.810050
$538$	15.9505	0.687673
$539$	6.99612	0.301344
$540$	−5.17501	−0.222697
$541$	3.71159	0.159574	0.0797868	−	0.996812i	$-0.474576\pi$
$541$	3.71159	0.159574	0.0797868	+	0.996812i	$0.474576\pi$
$542$	−6.00966	−0.258137
$543$	4.63979	0.199112
$544$	−14.2016	−0.608890
$545$	0.181064	0.00775592
$546$	0	0
$547$	−40.5420	−1.73345	−0.866725	−	0.498786i	$-0.833779\pi$
$547$	−40.5420	−1.73345	−0.866725	+	0.498786i	$0.833779\pi$
$548$	−25.4568	−1.08746
$549$	2.03838	0.0869958
$550$	−4.29818	−0.183275
$551$	−0.638399	−0.0271967
$552$	3.21580	0.136874
$553$	0.103134	0.00438572
$554$	2.64065	0.112191
$555$	11.9878	0.508853
$556$	−25.6969	−1.08979
$557$	16.3173	0.691386	0.345693	−	0.938348i	$-0.387644\pi$
$557$	16.3173	0.691386	0.345693	+	0.938348i	$0.387644\pi$
$558$	4.53974	0.192182
$559$	0	0
$560$	−0.301852	−0.0127556
$561$	−2.45300	−0.103566
$562$	10.4775	0.441968
$563$	16.0740	0.677439	0.338719	−	0.940887i	$-0.390006\pi$
$563$	16.0740	0.677439	0.338719	+	0.940887i	$0.390006\pi$
$564$	−7.37974	−0.310743
$565$	11.5155	0.484460
$566$	−10.9510	−0.460307
$567$	0.0622521	0.00261434
$568$	−21.0236	−0.882132
$569$	−0.916789	−0.0384338	−0.0192169	−	0.999815i	$-0.506117\pi$
$569$	−0.916789	−0.0384338	−0.0192169	+	0.999815i	$0.506117\pi$
$570$	−0.647432	−0.0271180
$571$	0.906071	0.0379179	0.0189590	−	0.999820i	$-0.493965\pi$
$571$	0.906071	0.0379179	0.0189590	+	0.999820i	$0.493965\pi$
$572$	0	0
$573$	−26.3850	−1.10225
$574$	0.424058	0.0176998
$575$	8.45474	0.352587
$576$	1.05356	0.0438984
$577$	0.545156	0.0226952	0.0113476	−	0.999936i	$-0.496388\pi$
$577$	0.545156	0.0226952	0.0113476	+	0.999936i	$0.496388\pi$
$578$	−7.46578	−0.310536
$579$	16.8077	0.698505
$580$	11.6722	0.484661
$581$	0.365108	0.0151472
$582$	5.64381	0.233943
$583$	−4.34343	−0.179886
$584$	31.5231	1.30444
$585$	0	0
$586$	−2.88180	−0.119046
$587$	39.0656	1.61241	0.806206	−	0.591635i	$-0.201517\pi$
$587$	39.0656	1.61241	0.806206	+	0.591635i	$0.201517\pi$
$588$	−10.7594	−0.443711
$589$	−1.89025	−0.0778862
$590$	−31.4691	−1.29556
$591$	21.1316	0.869236
$592$	5.13356	0.210988
$593$	8.21394	0.337306	0.168653	−	0.985675i	$-0.446058\pi$
$593$	8.21394	0.337306	0.168653	+	0.985675i	$0.446058\pi$
$594$	0.679772	0.0278914
$595$	0.513845	0.0210656
$596$	9.80226	0.401516
$597$	21.7455	0.889985
$598$	0	0
$599$	−4.01963	−0.164237	−0.0821187	−	0.996623i	$-0.526169\pi$
$599$	−4.01963	−0.164237	−0.0821187	+	0.996623i	$0.526169\pi$
$600$	15.2066	0.620806
$601$	41.4912	1.69246	0.846230	−	0.532817i	$-0.178867\pi$
$601$	41.4912	1.69246	0.846230	+	0.532817i	$0.178867\pi$
$602$	−0.366465	−0.0149360
$603$	−2.33966	−0.0952785
$604$	31.4718	1.28057
$605$	−3.36496	−0.136805
$606$	1.09154	0.0443409
$607$	15.9867	0.648881	0.324441	−	0.945906i	$-0.394824\pi$
$607$	15.9867	0.648881	0.324441	+	0.945906i	$0.394824\pi$
$608$	−1.63867	−0.0664568
$609$	−0.140409	−0.00568966
$610$	−4.66260	−0.188783
$611$	0	0
$612$	3.77250	0.152494
$613$	46.0791	1.86112	0.930559	−	0.366142i	$-0.119321\pi$
$613$	46.0791	1.86112	0.930559	+	0.366142i	$0.119321\pi$
$614$	18.4280	0.743693
$615$	33.7200	1.35972
$616$	0.149715	0.00603217
$617$	4.06514	0.163656	0.0818282	−	0.996646i	$-0.473924\pi$
$617$	4.06514	0.163656	0.0818282	+	0.996646i	$0.473924\pi$
$618$	4.82494	0.194087
$619$	−22.4783	−0.903478	−0.451739	−	0.892150i	$-0.649196\pi$
$619$	−22.4783	−0.903478	−0.451739	+	0.892150i	$0.649196\pi$
$620$	34.5604	1.38798
$621$	−1.33715	−0.0536579
$622$	−1.93274	−0.0774960
$623$	0.447467	0.0179274
$624$	0	0
$625$	−16.6349	−0.665396
$626$	−18.5300	−0.740606
$627$	−0.283042	−0.0113036
$628$	−0.771028	−0.0307674
$629$	−8.73891	−0.348443
$630$	−0.142396	−0.00567319
$631$	44.5257	1.77254	0.886270	−	0.463168i	$-0.153287\pi$
$631$	44.5257	1.77254	0.886270	+	0.463168i	$0.153287\pi$
$632$	−3.98437	−0.158490
$633$	−3.29543	−0.130981
$634$	−7.27199	−0.288808
$635$	45.5168	1.80628
$636$	6.67980	0.264871
$637$	0	0
$638$	−1.53322	−0.0607008
$639$	8.74173	0.345818
$640$	36.5529	1.44488
$641$	21.9038	0.865147	0.432573	−	0.901599i	$-0.357606\pi$
$641$	21.9038	0.865147	0.432573	+	0.901599i	$0.357606\pi$
$642$	5.45731	0.215383
$643$	−38.3705	−1.51319	−0.756593	−	0.653886i	$-0.773138\pi$
$643$	−38.3705	−1.51319	−0.756593	+	0.653886i	$0.773138\pi$
$644$	−0.128016	−0.00504453
$645$	−29.1404	−1.14740
$646$	0.471968	0.0185693
$647$	−9.35693	−0.367859	−0.183929	−	0.982939i	$-0.558882\pi$
$647$	−9.35693	−0.367859	−0.183929	+	0.982939i	$0.558882\pi$
$648$	−2.40497	−0.0944763
$649$	−13.7575	−0.540030
$650$	0	0
$651$	−0.415740	−0.0162941
$652$	−14.8876	−0.583042
$653$	−42.1669	−1.65012	−0.825059	−	0.565047i	$-0.808858\pi$
$653$	−42.1669	−1.65012	−0.825059	+	0.565047i	$0.808858\pi$
$654$	0.0365776	0.00143030
$655$	62.0066	2.42280
$656$	14.4400	0.563788
$657$	−13.1075	−0.511371
$658$	−0.203061	−0.00791616
$659$	−22.1040	−0.861048	−0.430524	−	0.902579i	$-0.641671\pi$
$659$	−22.1040	−0.861048	−0.430524	+	0.902579i	$0.641671\pi$
$660$	5.17501	0.201437
$661$	−39.4885	−1.53592	−0.767962	−	0.640496i	$-0.778729\pi$
$661$	−39.4885	−1.53592	−0.767962	+	0.640496i	$0.778729\pi$
$662$	17.6603	0.686386
$663$	0	0
$664$	−14.1051	−0.547386
$665$	0.0592905	0.00229919
$666$	2.42171	0.0938394
$667$	3.01592	0.116777
$668$	−5.64160	−0.218280
$669$	21.5223	0.832099
$670$	5.35176	0.206757
$671$	−2.03838	−0.0786906
$672$	−0.360408	−0.0139030
$673$	−22.9059	−0.882959	−0.441479	−	0.897271i	$-0.645546\pi$
$673$	−22.9059	−0.882959	−0.441479	+	0.897271i	$0.645546\pi$
$674$	−14.7458	−0.567986
$675$	−6.32297	−0.243371
$676$	0	0
$677$	−12.1550	−0.467155	−0.233578	−	0.972338i	$-0.575043\pi$
$677$	−12.1550	−0.467155	−0.233578	+	0.972338i	$0.575043\pi$
$678$	2.32630	0.0893410
$679$	−0.516848	−0.0198348
$680$	−19.8513	−0.761262
$681$	8.47294	0.324684
$682$	−4.53974	−0.173836
$683$	17.5269	0.670650	0.335325	−	0.942103i	$-0.391154\pi$
$683$	17.5269	0.670650	0.335325	+	0.942103i	$0.391154\pi$
$684$	0.435293	0.0166438
$685$	−55.6997	−2.12817
$686$	−0.592277	−0.0226133
$687$	−14.9492	−0.570347
$688$	−12.4789	−0.475752
$689$	0	0
$690$	3.05860	0.116439
$691$	34.0368	1.29482	0.647411	−	0.762141i	$-0.275852\pi$
$691$	34.0368	1.29482	0.647411	+	0.762141i	$0.275852\pi$
$692$	−21.0620	−0.800659
$693$	−0.0622521	−0.00236476
$694$	1.82232	0.0691744
$695$	−56.2251	−2.13274
$696$	5.42440	0.205611
$697$	−24.5814	−0.931086
$698$	14.7006	0.556424
$699$	27.6123	1.04439
$700$	−0.605349	−0.0228800
$701$	39.7219	1.50027	0.750137	−	0.661283i	$-0.229988\pi$
$701$	39.7219	1.50027	0.750137	+	0.661283i	$0.229988\pi$
$702$	0	0
$703$	−1.00835	−0.0380305
$704$	−1.05356	−0.0397076
$705$	−16.1469	−0.608129
$706$	6.01058	0.226211
$707$	−0.0999612	−0.00375943
$708$	21.1578	0.795160
$709$	−22.0079	−0.826524	−0.413262	−	0.910612i	$-0.635611\pi$
$709$	−22.0079	−0.826524	−0.413262	+	0.910612i	$0.635611\pi$
$710$	−19.9959	−0.750433
$711$	1.65672	0.0621319
$712$	−17.2869	−0.647855
$713$	8.92990	0.334427
$714$	0.103804	0.00388478
$715$	0	0
$716$	−28.8689	−1.07888
$717$	−3.17249	−0.118479
$718$	−22.8498	−0.852748
$719$	5.74870	0.214390	0.107195	−	0.994238i	$-0.465813\pi$
$719$	5.74870	0.214390	0.107195	+	0.994238i	$0.465813\pi$
$720$	−4.84886	−0.180706
$721$	−0.441857	−0.0164556
$722$	−12.8612	−0.478645
$723$	3.37747	0.125610
$724$	7.13558	0.265192
$725$	14.2614	0.529655
$726$	−0.679772	−0.0252287
$727$	21.1337	0.783805	0.391903	−	0.920007i	$-0.371817\pi$
$727$	21.1337	0.783805	0.391903	+	0.920007i	$0.371817\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	29.9821	1.10969
$731$	21.2429	0.785696
$732$	3.13484	0.115867
$733$	−36.7004	−1.35556	−0.677780	−	0.735265i	$-0.737058\pi$
$733$	−36.7004	−1.35556	−0.677780	+	0.735265i	$0.737058\pi$
$734$	11.1760	0.412512
$735$	−23.5417	−0.868348
$736$	7.74139	0.285352
$737$	2.33966	0.0861826
$738$	6.81195	0.250751
$739$	−29.1613	−1.07272	−0.536358	−	0.843990i	$-0.680200\pi$
$739$	−29.1613	−1.07272	−0.536358	+	0.843990i	$0.680200\pi$
$740$	18.4361	0.677726
$741$	0	0
$742$	0.183802	0.00674758
$743$	−13.3594	−0.490109	−0.245054	−	0.969509i	$-0.578806\pi$
$743$	−13.3594	−0.490109	−0.245054	+	0.969509i	$0.578806\pi$
$744$	16.0612	0.588832
$745$	21.4474	0.785773
$746$	0.508895	0.0186320
$747$	5.86499	0.214589
$748$	−3.77250	−0.137936
$749$	−0.499768	−0.0182611
$750$	3.02617	0.110500
$751$	−6.99106	−0.255107	−0.127554	−	0.991832i	$-0.540713\pi$
$751$	−6.99106	−0.255107	−0.127554	+	0.991832i	$0.540713\pi$
$752$	−6.91464	−0.252151
$753$	11.8347	0.431280
$754$	0	0
$755$	68.8607	2.50610
$756$	0.0957381	0.00348196
$757$	3.67122	0.133433	0.0667164	−	0.997772i	$-0.478748\pi$
$757$	3.67122	0.133433	0.0667164	+	0.997772i	$0.478748\pi$
$758$	15.2365	0.553415
$759$	1.33715	0.0485354
$760$	−2.29056	−0.0830872
$761$	−12.5202	−0.453857	−0.226928	−	0.973911i	$-0.572868\pi$
$761$	−12.5202	−0.453857	−0.226928	+	0.973911i	$0.572868\pi$
$762$	9.19506	0.333102
$763$	−0.00334970	−0.000121267 0
$764$	−40.5777	−1.46805
$765$	8.25426	0.298434
$766$	15.3298	0.553889
$767$	0	0
$768$	9.49135	0.342490
$769$	−45.6176	−1.64501	−0.822507	−	0.568755i	$-0.807425\pi$
$769$	−45.6176	−1.64501	−0.822507	+	0.568755i	$0.807425\pi$
$770$	0.142396	0.00513159
$771$	−4.07570	−0.146783
$772$	25.8488	0.930317
$773$	4.28007	0.153944	0.0769718	−	0.997033i	$-0.475475\pi$
$773$	4.28007	0.153944	0.0769718	+	0.997033i	$0.475475\pi$
$774$	−5.88679	−0.211596
$775$	42.2268	1.51683
$776$	19.9673	0.716783
$777$	−0.221775	−0.00795614
$778$	−5.10966	−0.183190
$779$	−2.83634	−0.101622
$780$	0	0
$781$	−8.74173	−0.312804
$782$	−2.22967	−0.0797329
$783$	−2.25549	−0.0806047
$784$	−10.0813	−0.360047
$785$	−1.68702	−0.0602122
$786$	12.5263	0.446797
$787$	14.3385	0.511113	0.255557	−	0.966794i	$-0.417741\pi$
$787$	14.3385	0.511113	0.255557	+	0.966794i	$0.417741\pi$
$788$	32.4984	1.15771
$789$	25.1902	0.896796
$790$	−3.78960	−0.134828
$791$	−0.213038	−0.00757475
$792$	2.40497	0.0854570
$793$	0	0
$794$	12.3018	0.436574
$795$	14.6155	0.518357
$796$	33.4427	1.18534
$797$	22.2788	0.789157	0.394578	−	0.918862i	$-0.370891\pi$
$797$	22.2788	0.789157	0.394578	+	0.918862i	$0.370891\pi$
$798$	0.0119776	0.000424001 0
$799$	11.7709	0.416423
$800$	36.6068	1.29424
$801$	7.18799	0.253975
$802$	3.75252	0.132506
$803$	13.1075	0.462553
$804$	−3.59819	−0.126898
$805$	−0.280100	−0.00987223
$806$	0	0
$807$	−23.4644	−0.825986
$808$	3.86178	0.135857
$809$	18.7900	0.660622	0.330311	−	0.943872i	$-0.392846\pi$
$809$	18.7900	0.660622	0.330311	+	0.943872i	$0.392846\pi$
$810$	−2.28741	−0.0803713
$811$	37.7256	1.32472	0.662362	−	0.749184i	$-0.269554\pi$
$811$	37.7256	1.32472	0.662362	+	0.749184i	$0.269554\pi$
$812$	−0.215936	−0.00757789
$813$	8.84070	0.310057
$814$	−2.42171	−0.0848809
$815$	−32.5741	−1.14102
$816$	3.53474	0.123741
$817$	2.45113	0.0857541
$818$	−18.7721	−0.656352
$819$	0	0
$820$	51.8584	1.81097
$821$	37.1959	1.29815	0.649073	−	0.760726i	$-0.275157\pi$
$821$	37.1959	1.29815	0.649073	+	0.760726i	$0.275157\pi$
$822$	−11.2522	−0.392464
$823$	48.8280	1.70204	0.851018	−	0.525137i	$-0.175986\pi$
$823$	48.8280	1.70204	0.851018	+	0.525137i	$0.175986\pi$
$824$	17.0702	0.594668
$825$	6.32297	0.220138
$826$	0.582181	0.0202567
$827$	18.9284	0.658204	0.329102	−	0.944294i	$-0.393254\pi$
$827$	18.9284	0.658204	0.329102	+	0.944294i	$0.393254\pi$
$828$	−2.05641	−0.0714652
$829$	42.2999	1.46914	0.734568	−	0.678535i	$-0.237385\pi$
$829$	42.2999	1.46914	0.734568	+	0.678535i	$0.237385\pi$
$830$	−13.4156	−0.465663
$831$	−3.88461	−0.134756
$832$	0	0
$833$	17.1615	0.594611
$834$	−11.3583	−0.393306
$835$	−12.3439	−0.427178
$836$	−0.435293	−0.0150549
$837$	−6.67832	−0.230837
$838$	−7.52805	−0.260052
$839$	−40.3172	−1.39191	−0.695953	−	0.718088i	$-0.745018\pi$
$839$	−40.3172	−1.39191	−0.695953	+	0.718088i	$0.745018\pi$
$840$	−0.503784	−0.0173822
$841$	−23.9128	−0.824578
$842$	19.8507	0.684101
$843$	−15.4133	−0.530862
$844$	−5.06807	−0.174450
$845$	0	0
$846$	−3.26192	−0.112147
$847$	0.0622521	0.00213901
$848$	6.25882	0.214929
$849$	16.1099	0.552889
$850$	−10.5435	−0.361637
$851$	4.76363	0.163295
$852$	13.4440	0.460584
$853$	24.6591	0.844313	0.422157	−	0.906523i	$-0.361273\pi$
$853$	24.6591	0.844313	0.422157	+	0.906523i	$0.361273\pi$
$854$	0.0862585	0.00295170
$855$	0.952425	0.0325723
$856$	19.3075	0.659915
$857$	42.7014	1.45865	0.729326	−	0.684166i	$-0.239834\pi$
$857$	42.7014	1.45865	0.729326	+	0.684166i	$0.239834\pi$
$858$	0	0
$859$	1.44298	0.0492339	0.0246170	−	0.999697i	$-0.492163\pi$
$859$	1.44298	0.0492339	0.0246170	+	0.999697i	$0.492163\pi$
$860$	−44.8153	−1.52819
$861$	−0.623823	−0.0212598
$862$	5.17332	0.176204
$863$	−42.5985	−1.45007	−0.725034	−	0.688713i	$-0.758176\pi$
$863$	−42.5985	−1.45007	−0.725034	+	0.688713i	$0.758176\pi$
$864$	−5.78949	−0.196962
$865$	−46.0840	−1.56690
$866$	7.01401	0.238346
$867$	10.9828	0.372995
$868$	−0.639370	−0.0217016
$869$	−1.65672	−0.0562005
$870$	5.15923	0.174914
$871$	0	0
$872$	0.129408	0.00438231
$873$	−8.30250	−0.280997
$874$	−0.257272	−0.00870237
$875$	−0.277130	−0.00936872
$876$	−20.1581	−0.681079
$877$	−58.0496	−1.96020	−0.980098	−	0.198515i	$-0.936388\pi$
$877$	−58.0496	−1.96020	−0.980098	+	0.198515i	$0.936388\pi$
$878$	−7.32351	−0.247157
$879$	4.23935	0.142990
$880$	4.84886	0.163455
$881$	−23.0071	−0.775128	−0.387564	−	0.921843i	$-0.626683\pi$
$881$	−23.0071	−0.775128	−0.387564	+	0.921843i	$0.626683\pi$
$882$	−4.75577	−0.160135
$883$	−32.9518	−1.10892	−0.554459	−	0.832211i	$-0.687075\pi$
$883$	−32.9518	−1.10892	−0.554459	+	0.832211i	$0.687075\pi$
$884$	0	0
$885$	46.2936	1.55614
$886$	−12.5413	−0.421333
$887$	−2.90304	−0.0974746	−0.0487373	−	0.998812i	$-0.515520\pi$
$887$	−2.90304	−0.0974746	−0.0487373	+	0.998812i	$0.515520\pi$
$888$	8.56779	0.287516
$889$	−0.842064	−0.0282419
$890$	−16.4419	−0.551132
$891$	−1.00000	−0.0335013
$892$	33.0993	1.10825
$893$	1.35819	0.0454501
$894$	4.33270	0.144907
$895$	−63.1654	−2.11139
$896$	−0.676232	−0.0225913
$897$	0	0
$898$	−24.0723	−0.803303
$899$	15.0629	0.502376
$900$	−9.72416	−0.324139
$901$	−10.6544	−0.354951
$902$	−6.81195	−0.226813
$903$	0.539099	0.0179401
$904$	8.23024	0.273734
$905$	15.6127	0.518984
$906$	13.9109	0.462158
$907$	23.3724	0.776068	0.388034	−	0.921645i	$-0.373154\pi$
$907$	23.3724	0.776068	0.388034	+	0.921645i	$0.373154\pi$
$908$	13.0306	0.432436
$909$	−1.60575	−0.0532593
$910$	0	0
$911$	−13.1517	−0.435734	−0.217867	−	0.975978i	$-0.569910\pi$
$911$	−13.1517	−0.435734	−0.217867	+	0.975978i	$0.569910\pi$
$912$	0.407859	0.0135056
$913$	−5.86499	−0.194103
$914$	14.4097	0.476632
$915$	6.85906	0.226753
$916$	−22.9905	−0.759627
$917$	−1.14713	−0.0378815
$918$	1.66748	0.0550352
$919$	19.4954	0.643095	0.321547	−	0.946893i	$-0.395797\pi$
$919$	19.4954	0.643095	0.321547	+	0.946893i	$0.395797\pi$
$920$	10.8211	0.356759
$921$	−27.1091	−0.893274
$922$	−23.3235	−0.768119
$923$	0	0
$924$	−0.0957381	−0.00314955
$925$	22.5258	0.740643
$926$	−12.0812	−0.397011
$927$	−7.09787	−0.233125
$928$	13.0581	0.428655
$929$	−9.95694	−0.326677	−0.163338	−	0.986570i	$-0.552226\pi$
$929$	−9.95694	−0.326677	−0.163338	+	0.986570i	$0.552226\pi$
$930$	15.2761	0.500921
$931$	1.98020	0.0648983
$932$	42.4652	1.39099
$933$	2.84322	0.0930829
$934$	−5.44588	−0.178195
$935$	−8.25426	−0.269943
$936$	0	0
$937$	29.3817	0.959858	0.479929	−	0.877307i	$-0.340662\pi$
$937$	29.3817	0.959858	0.479929	+	0.877307i	$0.340662\pi$
$938$	−0.0990081	−0.00323273
$939$	27.2591	0.889566
$940$	−24.8325	−0.809948
$941$	29.1121	0.949027	0.474514	−	0.880248i	$-0.342624\pi$
$941$	29.1121	0.949027	0.474514	+	0.880248i	$0.342624\pi$
$942$	−0.340802	−0.0111039
$943$	13.3994	0.436346
$944$	19.8244	0.645229
$945$	0.209476	0.00681425
$946$	5.88679	0.191396
$947$	−20.7275	−0.673552	−0.336776	−	0.941585i	$-0.609337\pi$
$947$	−20.7275	−0.673552	−0.336776	+	0.941585i	$0.609337\pi$
$948$	2.54789	0.0827516
$949$	0	0
$950$	−1.21657	−0.0394706
$951$	10.6977	0.346896
$952$	0.367250	0.0119027
$953$	36.6806	1.18820	0.594100	−	0.804391i	$-0.297508\pi$
$953$	36.6806	1.18820	0.594100	+	0.804391i	$0.297508\pi$
$954$	2.95254	0.0955921
$955$	−88.7845	−2.87300
$956$	−4.87900	−0.157798
$957$	2.25549	0.0729097
$958$	7.76081	0.250741
$959$	1.03045	0.0332749
$960$	3.54520	0.114421
$961$	13.6000	0.438710
$962$	0	0
$963$	−8.02814	−0.258703
$964$	5.19425	0.167295
$965$	56.5574	1.82065
$966$	−0.0565844	−0.00182057
$967$	−29.5774	−0.951144	−0.475572	−	0.879677i	$-0.657759\pi$
$967$	−29.5774	−0.951144	−0.475572	+	0.879677i	$0.657759\pi$
$968$	−2.40497	−0.0772988
$969$	−0.694303	−0.0223042
$970$	18.9912	0.609770
$971$	−20.2417	−0.649586	−0.324793	−	0.945785i	$-0.605295\pi$
$971$	−20.2417	−0.649586	−0.324793	+	0.945785i	$0.605295\pi$
$972$	1.53791	0.0493285
$973$	1.04017	0.0333463
$974$	20.8368	0.667653
$975$	0	0
$976$	2.93727	0.0940197
$977$	−42.2256	−1.35092	−0.675459	−	0.737398i	$-0.736054\pi$
$977$	−42.2256	−1.35092	−0.675459	+	0.737398i	$0.736054\pi$
$978$	−6.58046	−0.210420
$979$	−7.18799	−0.229729
$980$	−36.2050	−1.15653
$981$	−0.0538086	−0.00171798
$982$	−19.5447	−0.623695
$983$	2.26617	0.0722796	0.0361398	−	0.999347i	$-0.488494\pi$
$983$	2.26617	0.0722796	0.0361398	+	0.999347i	$0.488494\pi$
$984$	24.1001	0.768282
$985$	71.1069	2.26565
$986$	−3.76100	−0.119775
$987$	0.298720	0.00950836
$988$	0	0
$989$	−11.5796	−0.368210
$990$	2.28741	0.0726986
$991$	−36.1269	−1.14761	−0.573804	−	0.818993i	$-0.694533\pi$
$991$	−36.1269	−1.14761	−0.573804	+	0.818993i	$0.694533\pi$
$992$	38.6641	1.22759
$993$	−25.9797	−0.824441
$994$	0.369926	0.0117333
$995$	73.1729	2.31974
$996$	9.01983	0.285804
$997$	−17.0560	−0.540168	−0.270084	−	0.962837i	$-0.587051\pi$
$997$	−17.0560	−0.540168	−0.270084	+	0.962837i	$0.587051\pi$
$998$	0.373160	0.0118122
$999$	−3.56253	−0.112714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.ba.1.8	✓	12
13.12	even	2		5577.2.a.bc.1.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5577.2.a.ba.1.8	✓	12	1.1	even	1	trivial
5577.2.a.bc.1.5	yes	12	13.12	even	2

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:	\( N \)	\(=\)	\( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5577.a (trivial)

\(f(q)\)	\(=\)	\(q+0.679772 q^{2} -1.00000 q^{3} -1.53791 q^{4} -3.36496 q^{5} -0.679772 q^{6} +0.0622521 q^{7} -2.40497 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.679772 q^{2} -1.00000 q^{3} -1.53791 q^{4} -3.36496 q^{5} -0.679772 q^{6} +0.0622521 q^{7} -2.40497 q^{8} +1.00000 q^{9} -2.28741 q^{10} -1.00000 q^{11} +1.53791 q^{12} +0.0423172 q^{14} +3.36496 q^{15} +1.44099 q^{16} -2.45300 q^{17} +0.679772 q^{18} -0.283042 q^{19} +5.17501 q^{20} -0.0622521 q^{21} -0.679772 q^{22} +1.33715 q^{23} +2.40497 q^{24} +6.32297 q^{25} -1.00000 q^{27} -0.0957381 q^{28} +2.25549 q^{29} +2.28741 q^{30} +6.67832 q^{31} +5.78949 q^{32} +1.00000 q^{33} -1.66748 q^{34} -0.209476 q^{35} -1.53791 q^{36} +3.56253 q^{37} -0.192404 q^{38} +8.09264 q^{40} +10.0209 q^{41} -0.0423172 q^{42} -8.65994 q^{43} +1.53791 q^{44} -3.36496 q^{45} +0.908955 q^{46} -4.79855 q^{47} -1.44099 q^{48} -6.99612 q^{49} +4.29818 q^{50} +2.45300 q^{51} +4.34343 q^{53} -0.679772 q^{54} +3.36496 q^{55} -0.149715 q^{56} +0.283042 q^{57} +1.53322 q^{58} +13.7575 q^{59} -5.17501 q^{60} +2.03838 q^{61} +4.53974 q^{62} +0.0622521 q^{63} +1.05356 q^{64} +0.679772 q^{66} -2.33966 q^{67} +3.77250 q^{68} -1.33715 q^{69} -0.142396 q^{70} +8.74173 q^{71} -2.40497 q^{72} -13.1075 q^{73} +2.42171 q^{74} -6.32297 q^{75} +0.435293 q^{76} -0.0622521 q^{77} +1.65672 q^{79} -4.84886 q^{80} +1.00000 q^{81} +6.81195 q^{82} +5.86499 q^{83} +0.0957381 q^{84} +8.25426 q^{85} -5.88679 q^{86} -2.25549 q^{87} +2.40497 q^{88} +7.18799 q^{89} -2.28741 q^{90} -2.05641 q^{92} -6.67832 q^{93} -3.26192 q^{94} +0.952425 q^{95} -5.78949 q^{96} -8.30250 q^{97} -4.75577 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} - 12 q^{3} + 5 q^{4} + 6 q^{5} + q^{6} + q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q - q^2 - 12 * q^3 + 5 * q^4 + 6 * q^5 + q^6 + q^7 + 12 * q^9	\( 12 q - q^{2} - 12 q^{3} + 5 q^{4} + 6 q^{5} + q^{6} + q^{7} + 12 q^{9} - 11 q^{10} - 12 q^{11} - 5 q^{12} + 9 q^{14} - 6 q^{15} - 9 q^{16} + 3 q^{17} - q^{18} - 6 q^{19} + 20 q^{20} - q^{21} + q^{22} - 22 q^{23} - 2 q^{25} - 12 q^{27} + 11 q^{28} + 13 q^{29} + 11 q^{30} - 2 q^{31} - 11 q^{32} + 12 q^{33} - 10 q^{34} - 14 q^{35} + 5 q^{36} - 3 q^{37} - 18 q^{38} - 18 q^{40} - 4 q^{41} - 9 q^{42} - 26 q^{43} - 5 q^{44} + 6 q^{45} + 18 q^{46} + 9 q^{47} + 9 q^{48} - 3 q^{49} - 29 q^{50} - 3 q^{51} - 5 q^{53} + q^{54} - 6 q^{55} + 5 q^{56} + 6 q^{57} - 37 q^{58} + 22 q^{59} - 20 q^{60} - 11 q^{61} - 18 q^{62} + q^{63} - 10 q^{64} - q^{66} + 28 q^{67} + 12 q^{68} + 22 q^{69} + 29 q^{70} - 10 q^{71} + 7 q^{73} - 6 q^{74} + 2 q^{75} - 32 q^{76} - q^{77} - 40 q^{79} - 30 q^{80} + 12 q^{81} + 26 q^{82} - q^{83} - 11 q^{84} + 32 q^{85} + 9 q^{86} - 13 q^{87} - 11 q^{89} - 11 q^{90} - 38 q^{92} + 2 q^{93} - 25 q^{94} - 10 q^{95} + 11 q^{96} - 7 q^{97} - 28 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q - q^2 - 12 * q^3 + 5 * q^4 + 6 * q^5 + q^6 + q^7 + 12 * q^9 - 11 * q^10 - 12 * q^11 - 5 * q^12 + 9 * q^14 - 6 * q^15 - 9 * q^16 + 3 * q^17 - q^18 - 6 * q^19 + 20 * q^20 - q^21 + q^22 - 22 * q^23 - 2 * q^25 - 12 * q^27 + 11 * q^28 + 13 * q^29 + 11 * q^30 - 2 * q^31 - 11 * q^32 + 12 * q^33 - 10 * q^34 - 14 * q^35 + 5 * q^36 - 3 * q^37 - 18 * q^38 - 18 * q^40 - 4 * q^41 - 9 * q^42 - 26 * q^43 - 5 * q^44 + 6 * q^45 + 18 * q^46 + 9 * q^47 + 9 * q^48 - 3 * q^49 - 29 * q^50 - 3 * q^51 - 5 * q^53 + q^54 - 6 * q^55 + 5 * q^56 + 6 * q^57 - 37 * q^58 + 22 * q^59 - 20 * q^60 - 11 * q^61 - 18 * q^62 + q^63 - 10 * q^64 - q^66 + 28 * q^67 + 12 * q^68 + 22 * q^69 + 29 * q^70 - 10 * q^71 + 7 * q^73 - 6 * q^74 + 2 * q^75 - 32 * q^76 - q^77 - 40 * q^79 - 30 * q^80 + 12 * q^81 + 26 * q^82 - q^83 - 11 * q^84 + 32 * q^85 + 9 * q^86 - 13 * q^87 - 11 * q^89 - 11 * q^90 - 38 * q^92 + 2 * q^93 - 25 * q^94 - 10 * q^95 + 11 * q^96 - 7 * q^97 - 28 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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