LMFDB - Embedded newform 5566.2.a.bt.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5566,2,Mod(1,5566)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5566, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5566.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5566 = 2 \cdot 11^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5566.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:	$44.4447337650$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 14x^{8} + 50x^{7} + 85x^{6} - 188x^{5} - 248x^{4} + 186x^{3} + 260x^{2} + 52x - 4 $ x^10 - 4x^9 - 14x^8 + 50x^7 + 85x^6 - 188x^5 - 248x^4 + 186x^3 + 260x^2 + 52*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 506)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.81018$ of defining polynomial
Character	$\chi$	$=$	5566.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.81018 q^{3} +1.00000 q^{4} +2.25015 q^{5} +2.81018 q^{6} +3.09785 q^{7} -1.00000 q^{8} +4.89711 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.81018 q^{3} +1.00000 q^{4} +2.25015 q^{5} +2.81018 q^{6} +3.09785 q^{7} -1.00000 q^{8} +4.89711 q^{9} -2.25015 q^{10} -2.81018 q^{12} +5.01243 q^{13} -3.09785 q^{14} -6.32332 q^{15} +1.00000 q^{16} +7.75477 q^{17} -4.89711 q^{18} -5.94284 q^{19} +2.25015 q^{20} -8.70552 q^{21} -1.00000 q^{23} +2.81018 q^{24} +0.0631591 q^{25} -5.01243 q^{26} -5.33122 q^{27} +3.09785 q^{28} +4.80351 q^{29} +6.32332 q^{30} +1.49254 q^{31} -1.00000 q^{32} -7.75477 q^{34} +6.97062 q^{35} +4.89711 q^{36} +9.28931 q^{37} +5.94284 q^{38} -14.0858 q^{39} -2.25015 q^{40} -3.83583 q^{41} +8.70552 q^{42} +9.79625 q^{43} +11.0192 q^{45} +1.00000 q^{46} +4.63169 q^{47} -2.81018 q^{48} +2.59668 q^{49} -0.0631591 q^{50} -21.7923 q^{51} +5.01243 q^{52} +0.614988 q^{53} +5.33122 q^{54} -3.09785 q^{56} +16.7004 q^{57} -4.80351 q^{58} +6.99032 q^{59} -6.32332 q^{60} -0.886579 q^{61} -1.49254 q^{62} +15.1705 q^{63} +1.00000 q^{64} +11.2787 q^{65} -1.43348 q^{67} +7.75477 q^{68} +2.81018 q^{69} -6.97062 q^{70} +9.56151 q^{71} -4.89711 q^{72} +8.88793 q^{73} -9.28931 q^{74} -0.177489 q^{75} -5.94284 q^{76} +14.0858 q^{78} -13.9740 q^{79} +2.25015 q^{80} +0.290366 q^{81} +3.83583 q^{82} -16.3708 q^{83} -8.70552 q^{84} +17.4494 q^{85} -9.79625 q^{86} -13.4987 q^{87} +11.8016 q^{89} -11.0192 q^{90} +15.5278 q^{91} -1.00000 q^{92} -4.19431 q^{93} -4.63169 q^{94} -13.3723 q^{95} +2.81018 q^{96} +8.16993 q^{97} -2.59668 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9	$ 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9} - 12 q^{10} + 6 q^{12} + 3 q^{13} + 4 q^{14} + 6 q^{15} + 10 q^{16} + 4 q^{17} - 16 q^{18} - 8 q^{19} + 12 q^{20} - 8 q^{21} - 10 q^{23} - 6 q^{24} + 34 q^{25} - 3 q^{26} + 12 q^{27} - 4 q^{28} + 15 q^{29} - 6 q^{30} - 10 q^{32} - 4 q^{34} - 8 q^{35} + 16 q^{36} + 18 q^{37} + 8 q^{38} - 29 q^{39} - 12 q^{40} - 3 q^{41} + 8 q^{42} - 4 q^{43} + 72 q^{45} + 10 q^{46} + 42 q^{47} + 6 q^{48} + 12 q^{49} - 34 q^{50} - 18 q^{51} + 3 q^{52} + 11 q^{53} - 12 q^{54} + 4 q^{56} - 16 q^{57} - 15 q^{58} + 54 q^{59} + 6 q^{60} - 6 q^{61} + 10 q^{64} + 31 q^{65} + 24 q^{67} + 4 q^{68} - 6 q^{69} + 8 q^{70} + 37 q^{71} - 16 q^{72} + 42 q^{73} - 18 q^{74} - 12 q^{75} - 8 q^{76} + 29 q^{78} - 37 q^{79} + 12 q^{80} + 10 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} + 20 q^{85} + 4 q^{86} - 15 q^{87} + 63 q^{89} - 72 q^{90} + 11 q^{91} - 10 q^{92} + 8 q^{93} - 42 q^{94} + 30 q^{95} - 6 q^{96} + 2 q^{97} - 12 q^{98}+O(q^{100}) $ 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9 - 12 * q^10 + 6 * q^12 + 3 * q^13 + 4 * q^14 + 6 * q^15 + 10 * q^16 + 4 * q^17 - 16 * q^18 - 8 * q^19 + 12 * q^20 - 8 * q^21 - 10 * q^23 - 6 * q^24 + 34 * q^25 - 3 * q^26 + 12 * q^27 - 4 * q^28 + 15 * q^29 - 6 * q^30 - 10 * q^32 - 4 * q^34 - 8 * q^35 + 16 * q^36 + 18 * q^37 + 8 * q^38 - 29 * q^39 - 12 * q^40 - 3 * q^41 + 8 * q^42 - 4 * q^43 + 72 * q^45 + 10 * q^46 + 42 * q^47 + 6 * q^48 + 12 * q^49 - 34 * q^50 - 18 * q^51 + 3 * q^52 + 11 * q^53 - 12 * q^54 + 4 * q^56 - 16 * q^57 - 15 * q^58 + 54 * q^59 + 6 * q^60 - 6 * q^61 + 10 * q^64 + 31 * q^65 + 24 * q^67 + 4 * q^68 - 6 * q^69 + 8 * q^70 + 37 * q^71 - 16 * q^72 + 42 * q^73 - 18 * q^74 - 12 * q^75 - 8 * q^76 + 29 * q^78 - 37 * q^79 + 12 * q^80 + 10 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 + 20 * q^85 + 4 * q^86 - 15 * q^87 + 63 * q^89 - 72 * q^90 + 11 * q^91 - 10 * q^92 + 8 * q^93 - 42 * q^94 + 30 * q^95 - 6 * q^96 + 2 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.81018	−1.62246	−0.811229	−	0.584728i	$-0.801201\pi$
$3$	−2.81018	−1.62246	−0.811229	+	0.584728i	$0.801201\pi$
$4$	1.00000	0.500000
$5$	2.25015	1.00630	0.503148	−	0.864200i	$-0.332175\pi$
$5$	2.25015	1.00630	0.503148	+	0.864200i	$0.332175\pi$
$6$	2.81018	1.14725
$7$	3.09785	1.17088	0.585439	−	0.810717i	$-0.300922\pi$
$7$	3.09785	1.17088	0.585439	+	0.810717i	$0.300922\pi$
$8$	−1.00000	−0.353553
$9$	4.89711	1.63237
$10$	−2.25015	−0.711559
$11$	0	0
$11$	0	0
$12$	−2.81018	−0.811229
$13$	5.01243	1.39020	0.695099	−	0.718914i	$-0.255361\pi$
$13$	5.01243	1.39020	0.695099	+	0.718914i	$0.255361\pi$
$14$	−3.09785	−0.827936
$15$	−6.32332	−1.63267
$16$	1.00000	0.250000
$17$	7.75477	1.88081	0.940404	−	0.340058i	$-0.110447\pi$
$17$	7.75477	1.88081	0.940404	+	0.340058i	$0.110447\pi$
$18$	−4.89711	−1.15426
$19$	−5.94284	−1.36338	−0.681690	−	0.731641i	$-0.738755\pi$
$19$	−5.94284	−1.36338	−0.681690	+	0.731641i	$0.738755\pi$
$20$	2.25015	0.503148
$21$	−8.70552	−1.89970
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.81018	0.573626
$25$	0.0631591	0.0126318
$26$	−5.01243	−0.983018
$27$	−5.33122	−1.02599
$28$	3.09785	0.585439
$29$	4.80351	0.891990	0.445995	−	0.895036i	$-0.352850\pi$
$29$	4.80351	0.891990	0.445995	+	0.895036i	$0.352850\pi$
$30$	6.32332	1.15447
$31$	1.49254	0.268068	0.134034	−	0.990977i	$-0.457207\pi$
$31$	1.49254	0.268068	0.134034	+	0.990977i	$0.457207\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−7.75477	−1.32993
$35$	6.97062	1.17825
$36$	4.89711	0.816185
$37$	9.28931	1.52715	0.763577	−	0.645717i	$-0.223441\pi$
$37$	9.28931	1.52715	0.763577	+	0.645717i	$0.223441\pi$
$38$	5.94284	0.964056
$39$	−14.0858	−2.25554
$40$	−2.25015	−0.355779
$41$	−3.83583	−0.599056	−0.299528	−	0.954087i	$-0.596829\pi$
$41$	−3.83583	−0.599056	−0.299528	+	0.954087i	$0.596829\pi$
$42$	8.70552	1.34329
$43$	9.79625	1.49391	0.746957	−	0.664872i	$-0.231514\pi$
$43$	9.79625	1.49391	0.746957	+	0.664872i	$0.231514\pi$
$44$	0	0
$45$	11.0192	1.64265
$46$	1.00000	0.147442
$47$	4.63169	0.675601	0.337800	−	0.941218i	$-0.390317\pi$
$47$	4.63169	0.675601	0.337800	+	0.941218i	$0.390317\pi$
$48$	−2.81018	−0.405615
$49$	2.59668	0.370955
$50$	−0.0631591	−0.00893205
$51$	−21.7923	−3.05153
$52$	5.01243	0.695099
$53$	0.614988	0.0844750	0.0422375	−	0.999108i	$-0.486551\pi$
$53$	0.614988	0.0844750	0.0422375	+	0.999108i	$0.486551\pi$
$54$	5.33122	0.725488
$55$	0	0
$56$	−3.09785	−0.413968
$57$	16.7004	2.21203
$58$	−4.80351	−0.630732
$59$	6.99032	0.910062	0.455031	−	0.890476i	$-0.349628\pi$
$59$	6.99032	0.910062	0.455031	+	0.890476i	$0.349628\pi$
$60$	−6.32332	−0.816337
$61$	−0.886579	−0.113515	−0.0567574	−	0.998388i	$-0.518076\pi$
$61$	−0.886579	−0.113515	−0.0567574	+	0.998388i	$0.518076\pi$
$62$	−1.49254	−0.189553
$63$	15.1705	1.91131
$64$	1.00000	0.125000
$65$	11.2787	1.39895
$66$	0	0
$67$	−1.43348	−0.175127	−0.0875634	−	0.996159i	$-0.527908\pi$
$67$	−1.43348	−0.175127	−0.0875634	+	0.996159i	$0.527908\pi$
$68$	7.75477	0.940404
$69$	2.81018	0.338306
$70$	−6.97062	−0.833148
$71$	9.56151	1.13474	0.567371	−	0.823462i	$-0.307961\pi$
$71$	9.56151	1.13474	0.567371	+	0.823462i	$0.307961\pi$
$72$	−4.89711	−0.577130
$73$	8.88793	1.04025	0.520127	−	0.854089i	$-0.325885\pi$
$73$	8.88793	1.04025	0.520127	+	0.854089i	$0.325885\pi$
$74$	−9.28931	−1.07986
$75$	−0.177489	−0.0204946
$76$	−5.94284	−0.681690
$77$	0	0
$78$	14.0858	1.59491
$79$	−13.9740	−1.57220	−0.786100	−	0.618100i	$-0.787903\pi$
$79$	−13.9740	−1.57220	−0.786100	+	0.618100i	$0.787903\pi$
$80$	2.25015	0.251574
$81$	0.290366	0.0322629
$82$	3.83583	0.423597
$83$	−16.3708	−1.79693	−0.898467	−	0.439042i	$-0.855318\pi$
$83$	−16.3708	−1.79693	−0.898467	+	0.439042i	$0.855318\pi$
$84$	−8.70552	−0.949850
$85$	17.4494	1.89265
$86$	−9.79625	−1.05636
$87$	−13.4987	−1.44722
$88$	0	0
$89$	11.8016	1.25097	0.625483	−	0.780238i	$-0.284902\pi$
$89$	11.8016	1.25097	0.625483	+	0.780238i	$0.284902\pi$
$90$	−11.0192	−1.16153
$91$	15.5278	1.62775
$92$	−1.00000	−0.104257
$93$	−4.19431	−0.434929
$94$	−4.63169	−0.477722
$95$	−13.3723	−1.37196
$96$	2.81018	0.286813
$97$	8.16993	0.829530	0.414765	−	0.909928i	$-0.363864\pi$
$97$	8.16993	0.829530	0.414765	+	0.909928i	$0.363864\pi$
$98$	−2.59668	−0.262305
$99$	0	0
$100$	0.0631591	0.00631591
$101$	5.12658	0.510114	0.255057	−	0.966926i	$-0.417906\pi$
$101$	5.12658	0.510114	0.255057	+	0.966926i	$0.417906\pi$
$102$	21.7923	2.15776
$103$	0.293842	0.0289531	0.0144766	−	0.999895i	$-0.495392\pi$
$103$	0.293842	0.0289531	0.0144766	+	0.999895i	$0.495392\pi$
$104$	−5.01243	−0.491509
$105$	−19.5887	−1.91166
$106$	−0.614988	−0.0597329
$107$	10.7943	1.04352	0.521762	−	0.853091i	$-0.325275\pi$
$107$	10.7943	1.04352	0.521762	+	0.853091i	$0.325275\pi$
$108$	−5.33122	−0.512997
$109$	10.5072	1.00640	0.503202	−	0.864169i	$-0.332155\pi$
$109$	10.5072	1.00640	0.503202	+	0.864169i	$0.332155\pi$
$110$	0	0
$111$	−26.1046	−2.47774
$112$	3.09785	0.292719
$113$	−16.7961	−1.58004	−0.790020	−	0.613080i	$-0.789930\pi$
$113$	−16.7961	−1.58004	−0.790020	+	0.613080i	$0.789930\pi$
$114$	−16.7004	−1.56414
$115$	−2.25015	−0.209827
$116$	4.80351	0.445995
$117$	24.5464	2.26932
$118$	−6.99032	−0.643511
$119$	24.0231	2.20220
$120$	6.32332	0.577237
$121$	0	0
$122$	0.886579	0.0802671
$123$	10.7794	0.971943
$124$	1.49254	0.134034
$125$	−11.1086	−0.993585
$126$	−15.1705	−1.35150
$127$	−9.97814	−0.885417	−0.442709	−	0.896666i	$-0.645982\pi$
$127$	−9.97814	−0.885417	−0.442709	+	0.896666i	$0.645982\pi$
$128$	−1.00000	−0.0883883
$129$	−27.5292	−2.42381
$130$	−11.2787	−0.989207
$131$	−5.19650	−0.454020	−0.227010	−	0.973892i	$-0.572895\pi$
$131$	−5.19650	−0.454020	−0.227010	+	0.973892i	$0.572895\pi$
$132$	0	0
$133$	−18.4100	−1.59635
$134$	1.43348	0.123833
$135$	−11.9960	−1.03245
$136$	−7.75477	−0.664966
$137$	0.138469	0.0118302	0.00591510	−	0.999983i	$-0.498117\pi$
$137$	0.138469	0.0118302	0.00591510	+	0.999983i	$0.498117\pi$
$138$	−2.81018	−0.239218
$139$	1.74854	0.148309	0.0741547	−	0.997247i	$-0.476374\pi$
$139$	1.74854	0.148309	0.0741547	+	0.997247i	$0.476374\pi$
$140$	6.97062	0.589125
$141$	−13.0159	−1.09613
$142$	−9.56151	−0.802384
$143$	0	0
$144$	4.89711	0.408093
$145$	10.8086	0.897606
$146$	−8.88793	−0.735570
$147$	−7.29715	−0.601859
$148$	9.28931	0.763577
$149$	−8.79464	−0.720485	−0.360243	−	0.932859i	$-0.617306\pi$
$149$	−8.79464	−0.720485	−0.360243	+	0.932859i	$0.617306\pi$
$150$	0.177489	0.0144919
$151$	−18.4774	−1.50367	−0.751836	−	0.659350i	$-0.770832\pi$
$151$	−18.4774	−1.50367	−0.751836	+	0.659350i	$0.770832\pi$
$152$	5.94284	0.482028
$153$	37.9760	3.07018
$154$	0	0
$155$	3.35843	0.269756
$156$	−14.0858	−1.12777
$157$	−2.68693	−0.214440	−0.107220	−	0.994235i	$-0.534195\pi$
$157$	−2.68693	−0.214440	−0.107220	+	0.994235i	$0.534195\pi$
$158$	13.9740	1.11171
$159$	−1.72823	−0.137057
$160$	−2.25015	−0.177890
$161$	−3.09785	−0.244145
$162$	−0.290366	−0.0228133
$163$	5.27927	0.413504	0.206752	−	0.978393i	$-0.433711\pi$
$163$	5.27927	0.413504	0.206752	+	0.978393i	$0.433711\pi$
$164$	−3.83583	−0.299528
$165$	0	0
$166$	16.3708	1.27062
$167$	−0.708355	−0.0548142	−0.0274071	−	0.999624i	$-0.508725\pi$
$167$	−0.708355	−0.0548142	−0.0274071	+	0.999624i	$0.508725\pi$
$168$	8.70552	0.671645
$169$	12.1244	0.932650
$170$	−17.4494	−1.33831
$171$	−29.1027	−2.22554
$172$	9.79625	0.746957
$173$	−18.5378	−1.40940	−0.704701	−	0.709504i	$-0.748919\pi$
$173$	−18.5378	−1.40940	−0.704701	+	0.709504i	$0.748919\pi$
$174$	13.4987	1.02334
$175$	0.195658	0.0147903
$176$	0	0
$177$	−19.6441	−1.47654
$178$	−11.8016	−0.884566
$179$	−17.1726	−1.28354	−0.641770	−	0.766897i	$-0.721800\pi$
$179$	−17.1726	−1.28354	−0.641770	+	0.766897i	$0.721800\pi$
$180$	11.0192	0.821324
$181$	−8.86577	−0.658988	−0.329494	−	0.944158i	$-0.606878\pi$
$181$	−8.86577	−0.658988	−0.329494	+	0.944158i	$0.606878\pi$
$182$	−15.5278	−1.15099
$183$	2.49145	0.184173
$184$	1.00000	0.0737210
$185$	20.9023	1.53677
$186$	4.19431	0.307541
$187$	0	0
$188$	4.63169	0.337800
$189$	−16.5153	−1.20131
$190$	13.3723	0.970125
$191$	18.7919	1.35973	0.679866	−	0.733336i	$-0.262038\pi$
$191$	18.7919	1.35973	0.679866	+	0.733336i	$0.262038\pi$
$192$	−2.81018	−0.202807
$193$	−19.4982	−1.40351	−0.701754	−	0.712420i	$-0.747599\pi$
$193$	−19.4982	−1.40351	−0.701754	+	0.712420i	$0.747599\pi$
$194$	−8.16993	−0.586567
$195$	−31.6952	−2.26974
$196$	2.59668	0.185477
$197$	4.40813	0.314066	0.157033	−	0.987593i	$-0.449807\pi$
$197$	4.40813	0.314066	0.157033	+	0.987593i	$0.449807\pi$
$198$	0	0
$199$	−5.78447	−0.410050	−0.205025	−	0.978757i	$-0.565728\pi$
$199$	−5.78447	−0.410050	−0.205025	+	0.978757i	$0.565728\pi$
$200$	−0.0631591	−0.00446602
$201$	4.02832	0.284136
$202$	−5.12658	−0.360705
$203$	14.8806	1.04441
$204$	−21.7923	−1.52577
$205$	−8.63118	−0.602828
$206$	−0.293842	−0.0204730
$207$	−4.89711	−0.340373
$208$	5.01243	0.347549
$209$	0	0
$210$	19.5887	1.35175
$211$	−3.38865	−0.233285	−0.116642	−	0.993174i	$-0.537213\pi$
$211$	−3.38865	−0.233285	−0.116642	+	0.993174i	$0.537213\pi$
$212$	0.614988	0.0422375
$213$	−26.8696	−1.84107
$214$	−10.7943	−0.737883
$215$	22.0430	1.50332
$216$	5.33122	0.362744
$217$	4.62367	0.313875
$218$	−10.5072	−0.711636
$219$	−24.9767	−1.68777
$220$	0	0
$221$	38.8703	2.61470
$222$	26.1046	1.75203
$223$	−3.49298	−0.233907	−0.116954	−	0.993137i	$-0.537313\pi$
$223$	−3.49298	−0.233907	−0.116954	+	0.993137i	$0.537313\pi$
$224$	−3.09785	−0.206984
$225$	0.309297	0.0206198
$226$	16.7961	1.11726
$227$	−27.1982	−1.80521	−0.902603	−	0.430474i	$-0.858346\pi$
$227$	−27.1982	−1.80521	−0.902603	+	0.430474i	$0.858346\pi$
$228$	16.7004	1.10601
$229$	−11.1372	−0.735968	−0.367984	−	0.929832i	$-0.619952\pi$
$229$	−11.1372	−0.735968	−0.367984	+	0.929832i	$0.619952\pi$
$230$	2.25015	0.148370
$231$	0	0
$232$	−4.80351	−0.315366
$233$	−9.71632	−0.636537	−0.318269	−	0.948001i	$-0.603101\pi$
$233$	−9.71632	−0.636537	−0.318269	+	0.948001i	$0.603101\pi$
$234$	−24.5464	−1.60465
$235$	10.4220	0.679855
$236$	6.99032	0.455031
$237$	39.2695	2.55083
$238$	−24.0231	−1.55719
$239$	26.8646	1.73772	0.868862	−	0.495054i	$-0.164852\pi$
$239$	26.8646	1.73772	0.868862	+	0.495054i	$0.164852\pi$
$240$	−6.32332	−0.408168
$241$	−4.47315	−0.288141	−0.144071	−	0.989567i	$-0.546019\pi$
$241$	−4.47315	−0.288141	−0.144071	+	0.989567i	$0.546019\pi$
$242$	0	0
$243$	15.1777	0.973649
$244$	−0.886579	−0.0567574
$245$	5.84292	0.373290
$246$	−10.7794	−0.687268
$247$	−29.7881	−1.89537
$248$	−1.49254	−0.0947764
$249$	46.0050	2.91545
$250$	11.1086	0.702571
$251$	14.0859	0.889096	0.444548	−	0.895755i	$-0.353364\pi$
$251$	14.0859	0.889096	0.444548	+	0.895755i	$0.353364\pi$
$252$	15.1705	0.955653
$253$	0	0
$254$	9.97814	0.626084
$255$	−49.0359	−3.07075
$256$	1.00000	0.0625000
$257$	9.00362	0.561631	0.280815	−	0.959762i	$-0.409395\pi$
$257$	9.00362	0.561631	0.280815	+	0.959762i	$0.409395\pi$
$258$	27.5292	1.71390
$259$	28.7769	1.78811
$260$	11.2787	0.699475
$261$	23.5233	1.45606
$262$	5.19650	0.321041
$263$	22.1216	1.36408	0.682038	−	0.731317i	$-0.261094\pi$
$263$	22.1216	1.36408	0.682038	+	0.731317i	$0.261094\pi$
$264$	0	0
$265$	1.38381	0.0850069
$266$	18.4100	1.12879
$267$	−33.1646	−2.02964
$268$	−1.43348	−0.0875634
$269$	8.92181	0.543972	0.271986	−	0.962301i	$-0.412319\pi$
$269$	8.92181	0.543972	0.271986	+	0.962301i	$0.412319\pi$
$270$	11.9960	0.730056
$271$	9.96830	0.605531	0.302766	−	0.953065i	$-0.402090\pi$
$271$	9.96830	0.605531	0.302766	+	0.953065i	$0.402090\pi$
$272$	7.75477	0.470202
$273$	−43.6358	−2.64096
$274$	−0.138469	−0.00836521
$275$	0	0
$276$	2.81018	0.169153
$277$	−16.5830	−0.996378	−0.498189	−	0.867068i	$-0.666001\pi$
$277$	−16.5830	−0.996378	−0.498189	+	0.867068i	$0.666001\pi$
$278$	−1.74854	−0.104871
$279$	7.30913	0.437586
$280$	−6.97062	−0.416574
$281$	−14.4228	−0.860394	−0.430197	−	0.902735i	$-0.641556\pi$
$281$	−14.4228	−0.860394	−0.430197	+	0.902735i	$0.641556\pi$
$282$	13.0159	0.775084
$283$	−27.1744	−1.61535	−0.807675	−	0.589628i	$-0.799275\pi$
$283$	−27.1744	−1.61535	−0.807675	+	0.589628i	$0.799275\pi$
$284$	9.56151	0.567371
$285$	37.5784	2.22595
$286$	0	0
$287$	−11.8828	−0.701421
$288$	−4.89711	−0.288565
$289$	43.1365	2.53744
$290$	−10.8086	−0.634703
$291$	−22.9590	−1.34588
$292$	8.88793	0.520127
$293$	−3.48229	−0.203438	−0.101719	−	0.994813i	$-0.532434\pi$
$293$	−3.48229	−0.203438	−0.101719	+	0.994813i	$0.532434\pi$
$294$	7.29715	0.425578
$295$	15.7292	0.915792
$296$	−9.28931	−0.539930
$297$	0	0
$298$	8.79464	0.509460
$299$	−5.01243	−0.289876
$300$	−0.177489	−0.0102473
$301$	30.3473	1.74919
$302$	18.4774	1.06326
$303$	−14.4066	−0.827639
$304$	−5.94284	−0.340845
$305$	−1.99493	−0.114230
$306$	−37.9760	−2.17094
$307$	−28.2862	−1.61438	−0.807188	−	0.590294i	$-0.799012\pi$
$307$	−28.2862	−1.61438	−0.807188	+	0.590294i	$0.799012\pi$
$308$	0	0
$309$	−0.825750	−0.0469753
$310$	−3.35843	−0.190746
$311$	14.3867	0.815797	0.407898	−	0.913027i	$-0.366262\pi$
$311$	14.3867	0.815797	0.407898	+	0.913027i	$0.366262\pi$
$312$	14.0858	0.797453
$313$	0.746479	0.0421935	0.0210967	−	0.999777i	$-0.493284\pi$
$313$	0.746479	0.0421935	0.0210967	+	0.999777i	$0.493284\pi$
$314$	2.68693	0.151632
$315$	34.1359	1.92334
$316$	−13.9740	−0.786100
$317$	−8.86497	−0.497906	−0.248953	−	0.968516i	$-0.580087\pi$
$317$	−8.86497	−0.497906	−0.248953	+	0.968516i	$0.580087\pi$
$318$	1.72823	0.0969141
$319$	0	0
$320$	2.25015	0.125787
$321$	−30.3339	−1.69307
$322$	3.09785	0.172637
$323$	−46.0854	−2.56426
$324$	0.290366	0.0161315
$325$	0.316581	0.0175607
$326$	−5.27927	−0.292391
$327$	−29.5270	−1.63285
$328$	3.83583	0.211798
$329$	14.3483	0.791046
$330$	0	0
$331$	−4.33257	−0.238140	−0.119070	−	0.992886i	$-0.537991\pi$
$331$	−4.33257	−0.238140	−0.119070	+	0.992886i	$0.537991\pi$
$332$	−16.3708	−0.898467
$333$	45.4908	2.49288
$334$	0.708355	0.0387595
$335$	−3.22553	−0.176229
$336$	−8.70552	−0.474925
$337$	−1.83289	−0.0998437	−0.0499219	−	0.998753i	$-0.515897\pi$
$337$	−1.83289	−0.0998437	−0.0499219	+	0.998753i	$0.515897\pi$
$338$	−12.1244	−0.659483
$339$	47.2000	2.56355
$340$	17.4494	0.946325
$341$	0	0
$342$	29.1027	1.57370
$343$	−13.6408	−0.736535
$344$	−9.79625	−0.528179
$345$	6.32332	0.340436
$346$	18.5378	0.996598
$347$	27.2229	1.46140	0.730702	−	0.682697i	$-0.239193\pi$
$347$	27.2229	1.46140	0.730702	+	0.682697i	$0.239193\pi$
$348$	−13.4987	−0.723608
$349$	−9.63308	−0.515647	−0.257824	−	0.966192i	$-0.583005\pi$
$349$	−9.63308	−0.515647	−0.257824	+	0.966192i	$0.583005\pi$
$350$	−0.195658	−0.0104583
$351$	−26.7224	−1.42634
$352$	0	0
$353$	13.4800	0.717465	0.358733	−	0.933440i	$-0.383209\pi$
$353$	13.4800	0.717465	0.358733	+	0.933440i	$0.383209\pi$
$354$	19.6441	1.04407
$355$	21.5148	1.14189
$356$	11.8016	0.625483
$357$	−67.5093	−3.57297
$358$	17.1726	0.907600
$359$	10.4305	0.550500	0.275250	−	0.961373i	$-0.411239\pi$
$359$	10.4305	0.550500	0.275250	+	0.961373i	$0.411239\pi$
$360$	−11.0192	−0.580764
$361$	16.3173	0.858806
$362$	8.86577	0.465975
$363$	0	0
$364$	15.5278	0.813876
$365$	19.9991	1.04680
$366$	−2.49145	−0.130230
$367$	9.83913	0.513599	0.256799	−	0.966465i	$-0.417332\pi$
$367$	9.83913	0.513599	0.256799	+	0.966465i	$0.417332\pi$
$368$	−1.00000	−0.0521286
$369$	−18.7845	−0.977881
$370$	−20.9023	−1.08666
$371$	1.90514	0.0989099
$372$	−4.19431	−0.217465
$373$	−20.4789	−1.06036	−0.530178	−	0.847886i	$-0.677875\pi$
$373$	−20.4789	−1.06036	−0.530178	+	0.847886i	$0.677875\pi$
$374$	0	0
$375$	31.2172	1.61205
$376$	−4.63169	−0.238861
$377$	24.0773	1.24004
$378$	16.5153	0.849458
$379$	3.37792	0.173512	0.0867560	−	0.996230i	$-0.472350\pi$
$379$	3.37792	0.173512	0.0867560	+	0.996230i	$0.472350\pi$
$380$	−13.3723	−0.685982
$381$	28.0404	1.43655
$382$	−18.7919	−0.961476
$383$	13.9752	0.714100	0.357050	−	0.934085i	$-0.383783\pi$
$383$	13.9752	0.714100	0.357050	+	0.934085i	$0.383783\pi$
$384$	2.81018	0.143406
$385$	0	0
$386$	19.4982	0.992430
$387$	47.9733	2.43862
$388$	8.16993	0.414765
$389$	−23.3825	−1.18554	−0.592771	−	0.805371i	$-0.701966\pi$
$389$	−23.3825	−1.18554	−0.592771	+	0.805371i	$0.701966\pi$
$390$	31.6952	1.60495
$391$	−7.75477	−0.392176
$392$	−2.59668	−0.131152
$393$	14.6031	0.736629
$394$	−4.40813	−0.222079
$395$	−31.4436	−1.58210
$396$	0	0
$397$	8.06086	0.404563	0.202281	−	0.979327i	$-0.435164\pi$
$397$	8.06086	0.404563	0.202281	+	0.979327i	$0.435164\pi$
$398$	5.78447	0.289949
$399$	51.7355	2.59001
$400$	0.0631591	0.00315796
$401$	36.1950	1.80749	0.903747	−	0.428067i	$-0.140805\pi$
$401$	36.1950	1.80749	0.903747	+	0.428067i	$0.140805\pi$
$402$	−4.02832	−0.200914
$403$	7.48125	0.372668
$404$	5.12658	0.255057
$405$	0.653367	0.0324661
$406$	−14.8806	−0.738510
$407$	0	0
$408$	21.7923	1.07888
$409$	−7.62353	−0.376959	−0.188480	−	0.982077i	$-0.560356\pi$
$409$	−7.62353	−0.376959	−0.188480	+	0.982077i	$0.560356\pi$
$410$	8.63118	0.426264
$411$	−0.389123	−0.0191940
$412$	0.293842	0.0144766
$413$	21.6550	1.06557
$414$	4.89711	0.240680
$415$	−36.8368	−1.80825
$416$	−5.01243	−0.245755
$417$	−4.91371	−0.240626
$418$	0	0
$419$	−6.63406	−0.324095	−0.162048	−	0.986783i	$-0.551810\pi$
$419$	−6.63406	−0.324095	−0.162048	+	0.986783i	$0.551810\pi$
$420$	−19.5887	−0.955830
$421$	−13.0866	−0.637800	−0.318900	−	0.947788i	$-0.603313\pi$
$421$	−13.0866	−0.637800	−0.318900	+	0.947788i	$0.603313\pi$
$422$	3.38865	0.164957
$423$	22.6819	1.10283
$424$	−0.614988	−0.0298664
$425$	0.489785	0.0237581
$426$	26.8696	1.30183
$427$	−2.74649	−0.132912
$428$	10.7943	0.521762
$429$	0	0
$430$	−22.0430	−1.06301
$431$	−17.4541	−0.840734	−0.420367	−	0.907354i	$-0.638099\pi$
$431$	−17.4541	−0.840734	−0.420367	+	0.907354i	$0.638099\pi$
$432$	−5.33122	−0.256499
$433$	−9.83787	−0.472778	−0.236389	−	0.971659i	$-0.575964\pi$
$433$	−9.83787	−0.472778	−0.236389	+	0.971659i	$0.575964\pi$
$434$	−4.62367	−0.221943
$435$	−30.3741	−1.45633
$436$	10.5072	0.503202
$437$	5.94284	0.284284
$438$	24.9767	1.19343
$439$	17.2087	0.821324	0.410662	−	0.911788i	$-0.365298\pi$
$439$	17.2087	0.821324	0.410662	+	0.911788i	$0.365298\pi$
$440$	0	0
$441$	12.7163	0.605536
$442$	−38.8703	−1.84887
$443$	2.07757	0.0987084	0.0493542	−	0.998781i	$-0.484284\pi$
$443$	2.07757	0.0987084	0.0493542	+	0.998781i	$0.484284\pi$
$444$	−26.1046	−1.23887
$445$	26.5553	1.25884
$446$	3.49298	0.165398
$447$	24.7145	1.16896
$448$	3.09785	0.146360
$449$	25.3159	1.19473	0.597367	−	0.801968i	$-0.296214\pi$
$449$	25.3159	1.19473	0.597367	+	0.801968i	$0.296214\pi$
$450$	−0.309297	−0.0145804
$451$	0	0
$452$	−16.7961	−0.790020
$453$	51.9249	2.43965
$454$	27.1982	1.27647
$455$	34.9397	1.63800
$456$	−16.7004	−0.782070
$457$	27.8859	1.30445	0.652224	−	0.758026i	$-0.273836\pi$
$457$	27.8859	1.30445	0.652224	+	0.758026i	$0.273836\pi$
$458$	11.1372	0.520408
$459$	−41.3424	−1.92970
$460$	−2.25015	−0.104914
$461$	−10.0652	−0.468785	−0.234392	−	0.972142i	$-0.575310\pi$
$461$	−10.0652	−0.468785	−0.234392	+	0.972142i	$0.575310\pi$
$462$	0	0
$463$	−6.04419	−0.280897	−0.140449	−	0.990088i	$-0.544855\pi$
$463$	−6.04419	−0.280897	−0.140449	+	0.990088i	$0.544855\pi$
$464$	4.80351	0.222997
$465$	−9.43780	−0.437668
$466$	9.71632	0.450100
$467$	16.4801	0.762610	0.381305	−	0.924449i	$-0.375475\pi$
$467$	16.4801	0.762610	0.381305	+	0.924449i	$0.375475\pi$
$468$	24.5464	1.13466
$469$	−4.44069	−0.205052
$470$	−10.4220	−0.480730
$471$	7.55074	0.347920
$472$	−6.99032	−0.321756
$473$	0	0
$474$	−39.2695	−1.80371
$475$	−0.375344	−0.0172220
$476$	24.0231	1.10110
$477$	3.01166	0.137895
$478$	−26.8646	−1.22876
$479$	−3.77861	−0.172649	−0.0863246	−	0.996267i	$-0.527512\pi$
$479$	−3.77861	−0.172649	−0.0863246	+	0.996267i	$0.527512\pi$
$480$	6.32332	0.288619
$481$	46.5620	2.12305
$482$	4.47315	0.203747
$483$	8.70552	0.396115
$484$	0	0
$485$	18.3835	0.834753
$486$	−15.1777	−0.688474
$487$	35.2807	1.59872	0.799360	−	0.600852i	$-0.205172\pi$
$487$	35.2807	1.59872	0.799360	+	0.600852i	$0.205172\pi$
$488$	0.886579	0.0401336
$489$	−14.8357	−0.670893
$490$	−5.84292	−0.263956
$491$	−1.36487	−0.0615955	−0.0307978	−	0.999526i	$-0.509805\pi$
$491$	−1.36487	−0.0615955	−0.0307978	+	0.999526i	$0.509805\pi$
$492$	10.7794	0.485972
$493$	37.2501	1.67766
$494$	29.7881	1.34023
$495$	0	0
$496$	1.49254	0.0670170
$497$	29.6201	1.32864
$498$	−46.0050	−2.06153
$499$	−17.5578	−0.785994	−0.392997	−	0.919540i	$-0.628562\pi$
$499$	−17.5578	−0.785994	−0.392997	+	0.919540i	$0.628562\pi$
$500$	−11.1086	−0.496792
$501$	1.99061	0.0889337
$502$	−14.0859	−0.628686
$503$	30.7106	1.36932	0.684659	−	0.728864i	$-0.259951\pi$
$503$	30.7106	1.36932	0.684659	+	0.728864i	$0.259951\pi$
$504$	−15.1705	−0.675749
$505$	11.5356	0.513326
$506$	0	0
$507$	−34.0719	−1.51319
$508$	−9.97814	−0.442709
$509$	−28.3191	−1.25522	−0.627611	−	0.778527i	$-0.715967\pi$
$509$	−28.3191	−1.25522	−0.627611	+	0.778527i	$0.715967\pi$
$510$	49.0359	2.17135
$511$	27.5335	1.21801
$512$	−1.00000	−0.0441942
$513$	31.6826	1.39882
$514$	−9.00362	−0.397133
$515$	0.661188	0.0291354
$516$	−27.5292	−1.21191
$517$	0	0
$518$	−28.7769	−1.26438
$519$	52.0945	2.28670
$520$	−11.2787	−0.494604
$521$	13.2114	0.578802	0.289401	−	0.957208i	$-0.406544\pi$
$521$	13.2114	0.578802	0.289401	+	0.957208i	$0.406544\pi$
$522$	−23.5233	−1.02959
$523$	−26.8786	−1.17532	−0.587660	−	0.809108i	$-0.699951\pi$
$523$	−26.8786	−1.17532	−0.587660	+	0.809108i	$0.699951\pi$
$524$	−5.19650	−0.227010
$525$	−0.549833	−0.0239967
$526$	−22.1216	−0.964547
$527$	11.5743	0.504185
$528$	0	0
$529$	1.00000	0.0434783
$530$	−1.38381	−0.0601090
$531$	34.2324	1.48556
$532$	−18.4100	−0.798176
$533$	−19.2268	−0.832806
$534$	33.1646	1.43517
$535$	24.2888	1.05009
$536$	1.43348	0.0619167
$537$	48.2581	2.08249
$538$	−8.92181	−0.384647
$539$	0	0
$540$	−11.9960	−0.516227
$541$	−16.8878	−0.726062	−0.363031	−	0.931777i	$-0.618258\pi$
$541$	−16.8878	−0.726062	−0.363031	+	0.931777i	$0.618258\pi$
$542$	−9.96830	−0.428175
$543$	24.9144	1.06918
$544$	−7.75477	−0.332483
$545$	23.6427	1.01274
$546$	43.6358	1.86744
$547$	1.99796	0.0854267	0.0427133	−	0.999087i	$-0.486400\pi$
$547$	1.99796	0.0854267	0.0427133	+	0.999087i	$0.486400\pi$
$548$	0.138469	0.00591510
$549$	−4.34168	−0.185298
$550$	0	0
$551$	−28.5465	−1.21612
$552$	−2.81018	−0.119609
$553$	−43.2894	−1.84085
$554$	16.5830	0.704546
$555$	−58.7393	−2.49334
$556$	1.74854	0.0741547
$557$	−10.0386	−0.425348	−0.212674	−	0.977123i	$-0.568217\pi$
$557$	−10.0386	−0.425348	−0.212674	+	0.977123i	$0.568217\pi$
$558$	−7.30913	−0.309420
$559$	49.1030	2.07684
$560$	6.97062	0.294562
$561$	0	0
$562$	14.4228	0.608390
$563$	12.2018	0.514243	0.257122	−	0.966379i	$-0.417226\pi$
$563$	12.2018	0.514243	0.257122	+	0.966379i	$0.417226\pi$
$564$	−13.0159	−0.548067
$565$	−37.7936	−1.58999
$566$	27.1744	1.14223
$567$	0.899512	0.0377760
$568$	−9.56151	−0.401192
$569$	15.9666	0.669354	0.334677	−	0.942333i	$-0.391373\pi$
$569$	15.9666	0.669354	0.334677	+	0.942333i	$0.391373\pi$
$570$	−37.5784	−1.57399
$571$	26.1387	1.09387	0.546936	−	0.837175i	$-0.315794\pi$
$571$	26.1387	1.09387	0.546936	+	0.837175i	$0.315794\pi$
$572$	0	0
$573$	−52.8085	−2.20611
$574$	11.8828	0.495980
$575$	−0.0631591	−0.00263392
$576$	4.89711	0.204046
$577$	−3.48468	−0.145069	−0.0725345	−	0.997366i	$-0.523109\pi$
$577$	−3.48468	−0.145069	−0.0725345	+	0.997366i	$0.523109\pi$
$578$	−43.1365	−1.79424
$579$	54.7933	2.27713
$580$	10.8086	0.448803
$581$	−50.7144	−2.10399
$582$	22.9590	0.951680
$583$	0	0
$584$	−8.88793	−0.367785
$585$	55.2330	2.28361
$586$	3.48229	0.143852
$587$	2.77548	0.114556	0.0572782	−	0.998358i	$-0.481758\pi$
$587$	2.77548	0.114556	0.0572782	+	0.998358i	$0.481758\pi$
$588$	−7.29715	−0.300929
$589$	−8.86992	−0.365479
$590$	−15.7292	−0.647563
$591$	−12.3876	−0.509560
$592$	9.28931	0.381788
$593$	−4.17701	−0.171529	−0.0857646	−	0.996315i	$-0.527333\pi$
$593$	−4.17701	−0.171529	−0.0857646	+	0.996315i	$0.527333\pi$
$594$	0	0
$595$	54.0556	2.21606
$596$	−8.79464	−0.360243
$597$	16.2554	0.665289
$598$	5.01243	0.204973
$599$	−14.3890	−0.587918	−0.293959	−	0.955818i	$-0.594973\pi$
$599$	−14.3890	−0.587918	−0.293959	+	0.955818i	$0.594973\pi$
$600$	0.177489	0.00724594
$601$	16.7352	0.682645	0.341322	−	0.939946i	$-0.389125\pi$
$601$	16.7352	0.682645	0.341322	+	0.939946i	$0.389125\pi$
$602$	−30.3473	−1.23687
$603$	−7.01989	−0.285872
$604$	−18.4774	−0.751836
$605$	0	0
$606$	14.4066	0.585229
$607$	−41.2966	−1.67618	−0.838090	−	0.545533i	$-0.816327\pi$
$607$	−41.2966	−1.67618	−0.838090	+	0.545533i	$0.816327\pi$
$608$	5.94284	0.241014
$609$	−41.8171	−1.69451
$610$	1.99493	0.0807725
$611$	23.2160	0.939219
$612$	37.9760	1.53509
$613$	21.1499	0.854235	0.427118	−	0.904196i	$-0.359529\pi$
$613$	21.1499	0.854235	0.427118	+	0.904196i	$0.359529\pi$
$614$	28.2862	1.14154
$615$	24.2552	0.978063
$616$	0	0
$617$	25.1597	1.01289	0.506446	−	0.862272i	$-0.330959\pi$
$617$	25.1597	1.01289	0.506446	+	0.862272i	$0.330959\pi$
$618$	0.825750	0.0332165
$619$	38.4097	1.54382	0.771908	−	0.635734i	$-0.219302\pi$
$619$	38.4097	1.54382	0.771908	+	0.635734i	$0.219302\pi$
$620$	3.35843	0.134878
$621$	5.33122	0.213935
$622$	−14.3867	−0.576856
$623$	36.5596	1.46473
$624$	−14.0858	−0.563884
$625$	−25.3118	−1.01247
$626$	−0.746479	−0.0298353
$627$	0	0
$628$	−2.68693	−0.107220
$629$	72.0365	2.87228
$630$	−34.1359	−1.36001
$631$	3.16257	0.125900	0.0629499	−	0.998017i	$-0.479949\pi$
$631$	3.16257	0.125900	0.0629499	+	0.998017i	$0.479949\pi$
$632$	13.9740	0.555856
$633$	9.52273	0.378495
$634$	8.86497	0.352073
$635$	−22.4523	−0.890992
$636$	−1.72823	−0.0685286
$637$	13.0157	0.515701
$638$	0	0
$639$	46.8238	1.85232
$640$	−2.25015	−0.0889448
$641$	−16.5333	−0.653026	−0.326513	−	0.945193i	$-0.605874\pi$
$641$	−16.5333	−0.653026	−0.326513	+	0.945193i	$0.605874\pi$
$642$	30.3339	1.19718
$643$	20.3102	0.800956	0.400478	−	0.916306i	$-0.368844\pi$
$643$	20.3102	0.800956	0.400478	+	0.916306i	$0.368844\pi$
$644$	−3.09785	−0.122072
$645$	−61.9448	−2.43907
$646$	46.0854	1.81320
$647$	−7.79432	−0.306426	−0.153213	−	0.988193i	$-0.548962\pi$
$647$	−7.79432	−0.306426	−0.153213	+	0.988193i	$0.548962\pi$
$648$	−0.290366	−0.0114067
$649$	0	0
$650$	−0.316581	−0.0124173
$651$	−12.9933	−0.509249
$652$	5.27927	0.206752
$653$	−36.2239	−1.41755	−0.708775	−	0.705434i	$-0.750752\pi$
$653$	−36.2239	−1.41755	−0.708775	+	0.705434i	$0.750752\pi$
$654$	29.5270	1.15460
$655$	−11.6929	−0.456879
$656$	−3.83583	−0.149764
$657$	43.5252	1.69808
$658$	−14.3483	−0.559354
$659$	15.3327	0.597276	0.298638	−	0.954366i	$-0.403468\pi$
$659$	15.3327	0.597276	0.298638	+	0.954366i	$0.403468\pi$
$660$	0	0
$661$	−16.5296	−0.642928	−0.321464	−	0.946922i	$-0.604175\pi$
$661$	−16.5296	−0.642928	−0.321464	+	0.946922i	$0.604175\pi$
$662$	4.33257	0.168390
$663$	−109.232	−4.24224
$664$	16.3708	0.635312
$665$	−41.4253	−1.60640
$666$	−45.4908	−1.76273
$667$	−4.80351	−0.185993
$668$	−0.708355	−0.0274071
$669$	9.81591	0.379505
$670$	3.22553	0.124613
$671$	0	0
$672$	8.70552	0.335823
$673$	21.8197	0.841087	0.420544	−	0.907272i	$-0.361839\pi$
$673$	21.8197	0.841087	0.420544	+	0.907272i	$0.361839\pi$
$674$	1.83289	0.0706002
$675$	−0.336715	−0.0129602
$676$	12.1244	0.466325
$677$	38.1574	1.46651	0.733254	−	0.679955i	$-0.238001\pi$
$677$	38.1574	1.46651	0.733254	+	0.679955i	$0.238001\pi$
$678$	−47.2000	−1.81270
$679$	25.3092	0.971279
$680$	−17.4494	−0.669153
$681$	76.4318	2.92887
$682$	0	0
$683$	−51.7124	−1.97872	−0.989361	−	0.145482i	$-0.953527\pi$
$683$	−51.7124	−1.97872	−0.989361	+	0.145482i	$0.953527\pi$
$684$	−29.1027	−1.11277
$685$	0.311575	0.0119047
$686$	13.6408	0.520809
$687$	31.2976	1.19408
$688$	9.79625	0.373479
$689$	3.08258	0.117437
$690$	−6.32332	−0.240725
$691$	−45.2732	−1.72227	−0.861136	−	0.508374i	$-0.830247\pi$
$691$	−45.2732	−1.72227	−0.861136	+	0.508374i	$0.830247\pi$
$692$	−18.5378	−0.704701
$693$	0	0
$694$	−27.2229	−1.03337
$695$	3.93447	0.149243
$696$	13.4987	0.511668
$697$	−29.7460	−1.12671
$698$	9.63308	0.364618
$699$	27.3046	1.03275
$700$	0.195658	0.00739516
$701$	46.0720	1.74012	0.870058	−	0.492950i	$-0.164081\pi$
$701$	46.0720	1.74012	0.870058	+	0.492950i	$0.164081\pi$
$702$	26.7224	1.00857
$703$	−55.2049	−2.08209
$704$	0	0
$705$	−29.2876	−1.10304
$706$	−13.4800	−0.507325
$707$	15.8814	0.597281
$708$	−19.6441	−0.738269
$709$	41.4247	1.55574	0.777868	−	0.628428i	$-0.216301\pi$
$709$	41.4247	1.55574	0.777868	+	0.628428i	$0.216301\pi$
$710$	−21.5148	−0.807436
$711$	−68.4323	−2.56641
$712$	−11.8016	−0.442283
$713$	−1.49254	−0.0558961
$714$	67.5093	2.52647
$715$	0	0
$716$	−17.1726	−0.641770
$717$	−75.4943	−2.81939
$718$	−10.4305	−0.389263
$719$	−5.33639	−0.199014	−0.0995069	−	0.995037i	$-0.531727\pi$
$719$	−5.33639	−0.199014	−0.0995069	+	0.995037i	$0.531727\pi$
$720$	11.0192	0.410662
$721$	0.910280	0.0339006
$722$	−16.3173	−0.607268
$723$	12.5704	0.467497
$724$	−8.86577	−0.329494
$725$	0.303386	0.0112675
$726$	0	0
$727$	−36.5141	−1.35423	−0.677116	−	0.735876i	$-0.736770\pi$
$727$	−36.5141	−1.35423	−0.677116	+	0.735876i	$0.736770\pi$
$728$	−15.5278	−0.575497
$729$	−43.5231	−1.61197
$730$	−19.9991	−0.740202
$731$	75.9677	2.80977
$732$	2.49145	0.0920865
$733$	−48.4535	−1.78967	−0.894836	−	0.446396i	$-0.852707\pi$
$733$	−48.4535	−1.78967	−0.894836	+	0.446396i	$0.852707\pi$
$734$	−9.83913	−0.363169
$735$	−16.4197	−0.605648
$736$	1.00000	0.0368605
$737$	0	0
$738$	18.7845	0.691467
$739$	−33.6232	−1.23685	−0.618425	−	0.785844i	$-0.712229\pi$
$739$	−33.6232	−1.23685	−0.618425	+	0.785844i	$0.712229\pi$
$740$	20.9023	0.768384
$741$	83.7098	3.07516
$742$	−1.90514	−0.0699399
$743$	17.2577	0.633123	0.316562	−	0.948572i	$-0.397472\pi$
$743$	17.2577	0.633123	0.316562	+	0.948572i	$0.397472\pi$
$744$	4.19431	0.153771
$745$	−19.7892	−0.725021
$746$	20.4789	0.749785
$747$	−80.1698	−2.93326
$748$	0	0
$749$	33.4391	1.22184
$750$	−31.2172	−1.13989
$751$	−44.9350	−1.63970	−0.819850	−	0.572578i	$-0.805943\pi$
$751$	−44.9350	−1.63970	−0.819850	+	0.572578i	$0.805943\pi$
$752$	4.63169	0.168900
$753$	−39.5840	−1.44252
$754$	−24.0773	−0.876842
$755$	−41.5769	−1.51314
$756$	−16.5153	−0.600657
$757$	17.7007	0.643341	0.321671	−	0.946852i	$-0.395756\pi$
$757$	17.7007	0.643341	0.321671	+	0.946852i	$0.395756\pi$
$758$	−3.37792	−0.122692
$759$	0	0
$760$	13.3723	0.485063
$761$	−42.1203	−1.52686	−0.763429	−	0.645892i	$-0.776486\pi$
$761$	−42.1203	−1.52686	−0.763429	+	0.645892i	$0.776486\pi$
$762$	−28.0404	−1.01580
$763$	32.5497	1.17838
$764$	18.7919	0.679866
$765$	85.4515	3.08951
$766$	−13.9752	−0.504945
$767$	35.0385	1.26517
$768$	−2.81018	−0.101404
$769$	38.0927	1.37366	0.686829	−	0.726819i	$-0.259002\pi$
$769$	38.0927	1.37366	0.686829	+	0.726819i	$0.259002\pi$
$770$	0	0
$771$	−25.3018	−0.911222
$772$	−19.4982	−0.701754
$773$	−13.4259	−0.482896	−0.241448	−	0.970414i	$-0.577622\pi$
$773$	−13.4259	−0.482896	−0.241448	+	0.970414i	$0.577622\pi$
$774$	−47.9733	−1.72437
$775$	0.0942675	0.00338619
$776$	−8.16993	−0.293283
$777$	−80.8683	−2.90113
$778$	23.3825	0.838304
$779$	22.7957	0.816741
$780$	−31.6952	−1.13487
$781$	0	0
$782$	7.75477	0.277310
$783$	−25.6086	−0.915177
$784$	2.59668	0.0927387
$785$	−6.04598	−0.215790
$786$	−14.6031	−0.520875
$787$	−27.9859	−0.997588	−0.498794	−	0.866721i	$-0.666224\pi$
$787$	−27.9859	−0.997588	−0.498794	+	0.866721i	$0.666224\pi$
$788$	4.40813	0.157033
$789$	−62.1657	−2.21316
$790$	31.4436	1.11871
$791$	−52.0317	−1.85003
$792$	0	0
$793$	−4.44392	−0.157808
$794$	−8.06086	−0.286069
$795$	−3.88876	−0.137920
$796$	−5.78447	−0.205025
$797$	44.4739	1.57535	0.787674	−	0.616093i	$-0.211285\pi$
$797$	44.4739	1.57535	0.787674	+	0.616093i	$0.211285\pi$
$798$	−51.7355	−1.83142
$799$	35.9177	1.27068
$800$	−0.0631591	−0.00223301
$801$	57.7937	2.04204
$802$	−36.1950	−1.27809
$803$	0	0
$804$	4.02832	0.142068
$805$	−6.97062	−0.245682
$806$	−7.48125	−0.263516
$807$	−25.0719	−0.882573
$808$	−5.12658	−0.180353
$809$	21.5007	0.755926	0.377963	−	0.925821i	$-0.376625\pi$
$809$	21.5007	0.755926	0.377963	+	0.925821i	$0.376625\pi$
$810$	−0.653367	−0.0229570
$811$	14.4011	0.505692	0.252846	−	0.967506i	$-0.418633\pi$
$811$	14.4011	0.505692	0.252846	+	0.967506i	$0.418633\pi$
$812$	14.8806	0.522206
$813$	−28.0127	−0.982449
$814$	0	0
$815$	11.8791	0.416107
$816$	−21.7923	−0.762883
$817$	−58.2175	−2.03677
$818$	7.62353	0.266551
$819$	76.0412	2.65709
$820$	−8.63118	−0.301414
$821$	17.6841	0.617179	0.308590	−	0.951195i	$-0.400143\pi$
$821$	17.6841	0.617179	0.308590	+	0.951195i	$0.400143\pi$
$822$	0.389123	0.0135722
$823$	−11.7231	−0.408641	−0.204320	−	0.978904i	$-0.565498\pi$
$823$	−11.7231	−0.408641	−0.204320	+	0.978904i	$0.565498\pi$
$824$	−0.293842	−0.0102365
$825$	0	0
$826$	−21.6550	−0.753473
$827$	21.8456	0.759647	0.379823	−	0.925059i	$-0.375985\pi$
$827$	21.8456	0.759647	0.379823	+	0.925059i	$0.375985\pi$
$828$	−4.89711	−0.170186
$829$	−21.8365	−0.758413	−0.379207	−	0.925312i	$-0.623803\pi$
$829$	−21.8365	−0.758413	−0.379207	+	0.925312i	$0.623803\pi$
$830$	36.8368	1.27862
$831$	46.6013	1.61658
$832$	5.01243	0.173775
$833$	20.1367	0.697695
$834$	4.91371	0.170148
$835$	−1.59390	−0.0551593
$836$	0	0
$837$	−7.95706	−0.275036
$838$	6.63406	0.229170
$839$	12.9461	0.446948	0.223474	−	0.974710i	$-0.428260\pi$
$839$	12.9461	0.446948	0.223474	+	0.974710i	$0.428260\pi$
$840$	19.5887	0.675874
$841$	−5.92627	−0.204354
$842$	13.0866	0.450993
$843$	40.5307	1.39595
$844$	−3.38865	−0.116642
$845$	27.2818	0.938522
$846$	−22.6819	−0.779819
$847$	0	0
$848$	0.614988	0.0211188
$849$	76.3650	2.62084
$850$	−0.489785	−0.0167995
$851$	−9.28931	−0.318434
$852$	−26.8696	−0.920536
$853$	2.97260	0.101780	0.0508900	−	0.998704i	$-0.483794\pi$
$853$	2.97260	0.101780	0.0508900	+	0.998704i	$0.483794\pi$
$854$	2.74649	0.0939830
$855$	−65.4854	−2.23955
$856$	−10.7943	−0.368942
$857$	8.23533	0.281314	0.140657	−	0.990058i	$-0.455079\pi$
$857$	8.23533	0.281314	0.140657	+	0.990058i	$0.455079\pi$
$858$	0	0
$859$	26.5013	0.904214	0.452107	−	0.891964i	$-0.350673\pi$
$859$	26.5013	0.904214	0.452107	+	0.891964i	$0.350673\pi$
$860$	22.0430	0.751660
$861$	33.3929	1.13803
$862$	17.4541	0.594489
$863$	−3.31557	−0.112863	−0.0564317	−	0.998406i	$-0.517972\pi$
$863$	−3.31557	−0.112863	−0.0564317	+	0.998406i	$0.517972\pi$
$864$	5.33122	0.181372
$865$	−41.7128	−1.41828
$866$	9.83787	0.334304
$867$	−121.221	−4.11689
$868$	4.62367	0.156937
$869$	0	0
$870$	30.3741	1.02978
$871$	−7.18519	−0.243461
$872$	−10.5072	−0.355818
$873$	40.0090	1.35410
$874$	−5.94284	−0.201019
$875$	−34.4128	−1.16337
$876$	−24.9767	−0.843884
$877$	−35.3709	−1.19439	−0.597195	−	0.802096i	$-0.703718\pi$
$877$	−35.3709	−1.19439	−0.597195	+	0.802096i	$0.703718\pi$
$878$	−17.2087	−0.580764
$879$	9.78587	0.330069
$880$	0	0
$881$	−8.13324	−0.274016	−0.137008	−	0.990570i	$-0.543749\pi$
$881$	−8.13324	−0.274016	−0.137008	+	0.990570i	$0.543749\pi$
$882$	−12.7163	−0.428178
$883$	39.6405	1.33401	0.667004	−	0.745054i	$-0.267577\pi$
$883$	39.6405	1.33401	0.667004	+	0.745054i	$0.267577\pi$
$884$	38.8703	1.30735
$885$	−44.2020	−1.48583
$886$	−2.07757	−0.0697974
$887$	13.0961	0.439724	0.219862	−	0.975531i	$-0.429439\pi$
$887$	13.0961	0.439724	0.219862	+	0.975531i	$0.429439\pi$
$888$	26.1046	0.876014
$889$	−30.9108	−1.03672
$890$	−26.5553	−0.890136
$891$	0	0
$892$	−3.49298	−0.116954
$893$	−27.5254	−0.921101
$894$	−24.7145	−0.826577
$895$	−38.6408	−1.29162
$896$	−3.09785	−0.103492
$897$	14.0858	0.470312
$898$	−25.3159	−0.844804
$899$	7.16943	0.239114
$900$	0.309297	0.0103099
$901$	4.76909	0.158881
$902$	0	0
$903$	−85.2815	−2.83799
$904$	16.7961	0.558629
$905$	−19.9493	−0.663137
$906$	−51.9249	−1.72509
$907$	−45.9809	−1.52677	−0.763385	−	0.645943i	$-0.776464\pi$
$907$	−45.9809	−1.52677	−0.763385	+	0.645943i	$0.776464\pi$
$908$	−27.1982	−0.902603
$909$	25.1054	0.832695
$910$	−34.9397	−1.15824
$911$	5.92029	0.196148	0.0980739	−	0.995179i	$-0.468732\pi$
$911$	5.92029	0.196148	0.0980739	+	0.995179i	$0.468732\pi$
$912$	16.7004	0.553007
$913$	0	0
$914$	−27.8859	−0.922385
$915$	5.60612	0.185333
$916$	−11.1372	−0.367984
$917$	−16.0980	−0.531602
$918$	41.3424	1.36450
$919$	−11.5796	−0.381977	−0.190988	−	0.981592i	$-0.561169\pi$
$919$	−11.5796	−0.381977	−0.190988	+	0.981592i	$0.561169\pi$
$920$	2.25015	0.0741851
$921$	79.4892	2.61926
$922$	10.0652	0.331481
$923$	47.9264	1.57752
$924$	0	0
$925$	0.586705	0.0192907
$926$	6.04419	0.198624
$927$	1.43898	0.0472622
$928$	−4.80351	−0.157683
$929$	4.64030	0.152243	0.0761216	−	0.997099i	$-0.475746\pi$
$929$	4.64030	0.152243	0.0761216	+	0.997099i	$0.475746\pi$
$930$	9.43780	0.309478
$931$	−15.4317	−0.505753
$932$	−9.71632	−0.318269
$933$	−40.4293	−1.32360
$934$	−16.4801	−0.539247
$935$	0	0
$936$	−24.5464	−0.802325
$937$	12.4986	0.408310	0.204155	−	0.978939i	$-0.434555\pi$
$937$	12.4986	0.408310	0.204155	+	0.978939i	$0.434555\pi$
$938$	4.44069	0.144994
$939$	−2.09774	−0.0684571
$940$	10.4220	0.339927
$941$	−59.2106	−1.93021	−0.965106	−	0.261860i	$-0.915664\pi$
$941$	−59.2106	−1.93021	−0.965106	+	0.261860i	$0.915664\pi$
$942$	−7.55074	−0.246017
$943$	3.83583	0.124912
$944$	6.99032	0.227516
$945$	−37.1619	−1.20888
$946$	0	0
$947$	−0.333681	−0.0108432	−0.00542158	−	0.999985i	$-0.501726\pi$
$947$	−0.333681	−0.0108432	−0.00542158	+	0.999985i	$0.501726\pi$
$948$	39.2695	1.27541
$949$	44.5501	1.44616
$950$	0.375344	0.0121778
$951$	24.9122	0.807832
$952$	−24.0231	−0.778594
$953$	−15.9425	−0.516427	−0.258214	−	0.966088i	$-0.583134\pi$
$953$	−15.9425	−0.516427	−0.258214	+	0.966088i	$0.583134\pi$
$954$	−3.01166	−0.0975062
$955$	42.2845	1.36829
$956$	26.8646	0.868862
$957$	0	0
$958$	3.77861	0.122081
$959$	0.428956	0.0138517
$960$	−6.32332	−0.204084
$961$	−28.7723	−0.928140
$962$	−46.5620	−1.50122
$963$	52.8609	1.70342
$964$	−4.47315	−0.144071
$965$	−43.8737	−1.41234
$966$	−8.70552	−0.280096
$967$	50.6405	1.62849	0.814244	−	0.580523i	$-0.197152\pi$
$967$	50.6405	1.62849	0.814244	+	0.580523i	$0.197152\pi$
$968$	0	0
$969$	129.508	4.16040
$970$	−18.3835	−0.590260
$971$	0.866270	0.0277999	0.0139000	−	0.999903i	$-0.495575\pi$
$971$	0.866270	0.0277999	0.0139000	+	0.999903i	$0.495575\pi$
$972$	15.1777	0.486825
$973$	5.41672	0.173652
$974$	−35.2807	−1.13047
$975$	−0.889649	−0.0284916
$976$	−0.886579	−0.0283787
$977$	−16.9898	−0.543552	−0.271776	−	0.962361i	$-0.587611\pi$
$977$	−16.9898	−0.543552	−0.271776	+	0.962361i	$0.587611\pi$
$978$	14.8357	0.474393
$979$	0	0
$980$	5.84292	0.186645
$981$	51.4548	1.64283
$982$	1.36487	0.0435546
$983$	30.0146	0.957318	0.478659	−	0.878001i	$-0.341123\pi$
$983$	30.0146	0.957318	0.478659	+	0.878001i	$0.341123\pi$
$984$	−10.7794	−0.343634
$985$	9.91894	0.316044
$986$	−37.2501	−1.18629
$987$	−40.3212	−1.28344
$988$	−29.7881	−0.947684
$989$	−9.79625	−0.311503
$990$	0	0
$991$	24.3548	0.773657	0.386828	−	0.922152i	$-0.373571\pi$
$991$	24.3548	0.773657	0.386828	+	0.922152i	$0.373571\pi$
$992$	−1.49254	−0.0473882
$993$	12.1753	0.386372
$994$	−29.6201	−0.939494
$995$	−13.0159	−0.412632
$996$	46.0050	1.45772
$997$	−6.36881	−0.201702	−0.100851	−	0.994902i	$-0.532157\pi$
$997$	−6.36881	−0.201702	−0.100851	+	0.994902i	$0.532157\pi$
$998$	17.5578	0.555781
$999$	−49.5234	−1.56685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5566.2.a.bt.1.1		10
11.7	odd	10		506.2.e.h.93.5	✓	20
11.8	odd	10		506.2.e.h.185.5	yes	20
11.10	odd	2		5566.2.a.bu.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
506.2.e.h.93.5	✓	20	11.7	odd	10
506.2.e.h.185.5	yes	20	11.8	odd	10
5566.2.a.bt.1.1		10	1.1	even	1	trivial
5566.2.a.bu.1.1		10	11.10	odd	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:	\( N \)	\(=\)	\( 5566 = 2 \cdot 11^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5566.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.81018 q^{3} +1.00000 q^{4} +2.25015 q^{5} +2.81018 q^{6} +3.09785 q^{7} -1.00000 q^{8} +4.89711 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.81018 q^{3} +1.00000 q^{4} +2.25015 q^{5} +2.81018 q^{6} +3.09785 q^{7} -1.00000 q^{8} +4.89711 q^{9} -2.25015 q^{10} -2.81018 q^{12} +5.01243 q^{13} -3.09785 q^{14} -6.32332 q^{15} +1.00000 q^{16} +7.75477 q^{17} -4.89711 q^{18} -5.94284 q^{19} +2.25015 q^{20} -8.70552 q^{21} -1.00000 q^{23} +2.81018 q^{24} +0.0631591 q^{25} -5.01243 q^{26} -5.33122 q^{27} +3.09785 q^{28} +4.80351 q^{29} +6.32332 q^{30} +1.49254 q^{31} -1.00000 q^{32} -7.75477 q^{34} +6.97062 q^{35} +4.89711 q^{36} +9.28931 q^{37} +5.94284 q^{38} -14.0858 q^{39} -2.25015 q^{40} -3.83583 q^{41} +8.70552 q^{42} +9.79625 q^{43} +11.0192 q^{45} +1.00000 q^{46} +4.63169 q^{47} -2.81018 q^{48} +2.59668 q^{49} -0.0631591 q^{50} -21.7923 q^{51} +5.01243 q^{52} +0.614988 q^{53} +5.33122 q^{54} -3.09785 q^{56} +16.7004 q^{57} -4.80351 q^{58} +6.99032 q^{59} -6.32332 q^{60} -0.886579 q^{61} -1.49254 q^{62} +15.1705 q^{63} +1.00000 q^{64} +11.2787 q^{65} -1.43348 q^{67} +7.75477 q^{68} +2.81018 q^{69} -6.97062 q^{70} +9.56151 q^{71} -4.89711 q^{72} +8.88793 q^{73} -9.28931 q^{74} -0.177489 q^{75} -5.94284 q^{76} +14.0858 q^{78} -13.9740 q^{79} +2.25015 q^{80} +0.290366 q^{81} +3.83583 q^{82} -16.3708 q^{83} -8.70552 q^{84} +17.4494 q^{85} -9.79625 q^{86} -13.4987 q^{87} +11.8016 q^{89} -11.0192 q^{90} +15.5278 q^{91} -1.00000 q^{92} -4.19431 q^{93} -4.63169 q^{94} -13.3723 q^{95} +2.81018 q^{96} +8.16993 q^{97} -2.59668 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9	\( 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9} - 12 q^{10} + 6 q^{12} + 3 q^{13} + 4 q^{14} + 6 q^{15} + 10 q^{16} + 4 q^{17} - 16 q^{18} - 8 q^{19} + 12 q^{20} - 8 q^{21} - 10 q^{23} - 6 q^{24} + 34 q^{25} - 3 q^{26} + 12 q^{27} - 4 q^{28} + 15 q^{29} - 6 q^{30} - 10 q^{32} - 4 q^{34} - 8 q^{35} + 16 q^{36} + 18 q^{37} + 8 q^{38} - 29 q^{39} - 12 q^{40} - 3 q^{41} + 8 q^{42} - 4 q^{43} + 72 q^{45} + 10 q^{46} + 42 q^{47} + 6 q^{48} + 12 q^{49} - 34 q^{50} - 18 q^{51} + 3 q^{52} + 11 q^{53} - 12 q^{54} + 4 q^{56} - 16 q^{57} - 15 q^{58} + 54 q^{59} + 6 q^{60} - 6 q^{61} + 10 q^{64} + 31 q^{65} + 24 q^{67} + 4 q^{68} - 6 q^{69} + 8 q^{70} + 37 q^{71} - 16 q^{72} + 42 q^{73} - 18 q^{74} - 12 q^{75} - 8 q^{76} + 29 q^{78} - 37 q^{79} + 12 q^{80} + 10 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} + 20 q^{85} + 4 q^{86} - 15 q^{87} + 63 q^{89} - 72 q^{90} + 11 q^{91} - 10 q^{92} + 8 q^{93} - 42 q^{94} + 30 q^{95} - 6 q^{96} + 2 q^{97} - 12 q^{98}+O(q^{100}) \) 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9 - 12 * q^10 + 6 * q^12 + 3 * q^13 + 4 * q^14 + 6 * q^15 + 10 * q^16 + 4 * q^17 - 16 * q^18 - 8 * q^19 + 12 * q^20 - 8 * q^21 - 10 * q^23 - 6 * q^24 + 34 * q^25 - 3 * q^26 + 12 * q^27 - 4 * q^28 + 15 * q^29 - 6 * q^30 - 10 * q^32 - 4 * q^34 - 8 * q^35 + 16 * q^36 + 18 * q^37 + 8 * q^38 - 29 * q^39 - 12 * q^40 - 3 * q^41 + 8 * q^42 - 4 * q^43 + 72 * q^45 + 10 * q^46 + 42 * q^47 + 6 * q^48 + 12 * q^49 - 34 * q^50 - 18 * q^51 + 3 * q^52 + 11 * q^53 - 12 * q^54 + 4 * q^56 - 16 * q^57 - 15 * q^58 + 54 * q^59 + 6 * q^60 - 6 * q^61 + 10 * q^64 + 31 * q^65 + 24 * q^67 + 4 * q^68 - 6 * q^69 + 8 * q^70 + 37 * q^71 - 16 * q^72 + 42 * q^73 - 18 * q^74 - 12 * q^75 - 8 * q^76 + 29 * q^78 - 37 * q^79 + 12 * q^80 + 10 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 + 20 * q^85 + 4 * q^86 - 15 * q^87 + 63 * q^89 - 72 * q^90 + 11 * q^91 - 10 * q^92 + 8 * q^93 - 42 * q^94 + 30 * q^95 - 6 * q^96 + 2 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

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Representations

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Database

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