LMFDB - Embedded newform 2057.2.a.bd.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2057,2,Mod(1,2057)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2057, 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("2057.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2057 = 11^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2057.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:	$16.4252276958$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 30 x^{16} + 57 x^{15} + 375 x^{14} - 668 x^{13} - 2533 x^{12} + 4156 x^{11} + \cdots - 781 $ x^18 - 2x^17 - 30x^16 + 57x^15 + 375x^14 - 668x^13 - 2533x^12 + 4156x^11 + 10021x^10 - 14771x^9 - 23513x^8 + 29953x^7 + 31637x^6 - 32426x^5 - 22583x^4 + 15706x^3 + 7598x^2 - 2117*x - 781
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 187)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.62277$ of defining polynomial
Character	$\chi$	$=$	2057.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.62277 q^{2} -2.06455 q^{3} +0.633389 q^{4} +3.65600 q^{5} +3.35029 q^{6} -0.632224 q^{7} +2.21770 q^{8} +1.26235 q^{9} +O(q^{10})$	\(q-1.62277 q^{2} -2.06455 q^{3} +0.633389 q^{4} +3.65600 q^{5} +3.35029 q^{6} -0.632224 q^{7} +2.21770 q^{8} +1.26235 q^{9} -5.93286 q^{10} -1.30766 q^{12} -2.89743 q^{13} +1.02596 q^{14} -7.54799 q^{15} -4.86560 q^{16} +1.00000 q^{17} -2.04851 q^{18} -1.30132 q^{19} +2.31567 q^{20} +1.30526 q^{21} +7.02655 q^{23} -4.57854 q^{24} +8.36637 q^{25} +4.70187 q^{26} +3.58745 q^{27} -0.400444 q^{28} +2.47652 q^{29} +12.2487 q^{30} +5.89344 q^{31} +3.46036 q^{32} -1.62277 q^{34} -2.31141 q^{35} +0.799560 q^{36} -7.63775 q^{37} +2.11174 q^{38} +5.98189 q^{39} +8.10791 q^{40} +0.948733 q^{41} -2.11813 q^{42} -4.42018 q^{43} +4.61517 q^{45} -11.4025 q^{46} +10.1311 q^{47} +10.0453 q^{48} -6.60029 q^{49} -13.5767 q^{50} -2.06455 q^{51} -1.83520 q^{52} -6.23235 q^{53} -5.82162 q^{54} -1.40208 q^{56} +2.68663 q^{57} -4.01883 q^{58} +6.61526 q^{59} -4.78082 q^{60} -12.9799 q^{61} -9.56371 q^{62} -0.798090 q^{63} +4.11582 q^{64} -10.5930 q^{65} -5.11549 q^{67} +0.633389 q^{68} -14.5066 q^{69} +3.75090 q^{70} +3.34255 q^{71} +2.79952 q^{72} -5.33501 q^{73} +12.3943 q^{74} -17.2728 q^{75} -0.824239 q^{76} -9.70724 q^{78} -6.66100 q^{79} -17.7886 q^{80} -11.1935 q^{81} -1.53958 q^{82} +16.7594 q^{83} +0.826735 q^{84} +3.65600 q^{85} +7.17295 q^{86} -5.11289 q^{87} +10.2267 q^{89} -7.48936 q^{90} +1.83183 q^{91} +4.45054 q^{92} -12.1673 q^{93} -16.4405 q^{94} -4.75762 q^{95} -7.14407 q^{96} +11.8347 q^{97} +10.7108 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 7 q^{3} + 28 q^{4} + 8 q^{5} + 3 q^{7} - 9 q^{8} + 29 q^{9}+O(q^{10}) $ 18 * q - 2 * q^2 + 7 * q^3 + 28 * q^4 + 8 * q^5 + 3 * q^7 - 9 * q^8 + 29 * q^9	$ 18 q - 2 q^{2} + 7 q^{3} + 28 q^{4} + 8 q^{5} + 3 q^{7} - 9 q^{8} + 29 q^{9} - 5 q^{10} + 14 q^{12} + q^{13} - 3 q^{14} + 38 q^{15} + 28 q^{16} + 18 q^{17} + 11 q^{18} - 10 q^{19} + 12 q^{20} - 25 q^{21} + 19 q^{23} + 9 q^{24} + 46 q^{25} - 20 q^{26} + 37 q^{27} - 2 q^{28} + 15 q^{29} - 31 q^{30} + 36 q^{31} - 20 q^{32} - 2 q^{34} - q^{35} + 60 q^{36} + 18 q^{37} + 28 q^{39} + 18 q^{40} - 9 q^{41} - 16 q^{42} - 4 q^{43} + 21 q^{45} + q^{46} + 45 q^{47} + 59 q^{48} + 19 q^{49} + 3 q^{50} + 7 q^{51} - 7 q^{52} - 6 q^{53} - 29 q^{54} - 14 q^{56} - 13 q^{57} + 69 q^{58} - 12 q^{59} + 46 q^{60} + 33 q^{61} + 8 q^{62} - 8 q^{63} + 21 q^{64} - 21 q^{65} + 27 q^{67} + 28 q^{68} + 12 q^{69} + 47 q^{70} + 10 q^{71} + 64 q^{72} + 9 q^{73} + 22 q^{74} - 5 q^{75} - 70 q^{76} - 24 q^{78} + 7 q^{79} + 8 q^{80} + 18 q^{81} - 6 q^{82} - 19 q^{83} + 47 q^{84} + 8 q^{85} - 25 q^{86} - 16 q^{87} + 6 q^{89} - 20 q^{90} + 3 q^{91} + 57 q^{92} + 5 q^{93} - 11 q^{94} + 22 q^{95} - 14 q^{96} + 38 q^{97} - 106 q^{98}+O(q^{100}) $ 18 * q - 2 * q^2 + 7 * q^3 + 28 * q^4 + 8 * q^5 + 3 * q^7 - 9 * q^8 + 29 * q^9 - 5 * q^10 + 14 * q^12 + q^13 - 3 * q^14 + 38 * q^15 + 28 * q^16 + 18 * q^17 + 11 * q^18 - 10 * q^19 + 12 * q^20 - 25 * q^21 + 19 * q^23 + 9 * q^24 + 46 * q^25 - 20 * q^26 + 37 * q^27 - 2 * q^28 + 15 * q^29 - 31 * q^30 + 36 * q^31 - 20 * q^32 - 2 * q^34 - q^35 + 60 * q^36 + 18 * q^37 + 28 * q^39 + 18 * q^40 - 9 * q^41 - 16 * q^42 - 4 * q^43 + 21 * q^45 + q^46 + 45 * q^47 + 59 * q^48 + 19 * q^49 + 3 * q^50 + 7 * q^51 - 7 * q^52 - 6 * q^53 - 29 * q^54 - 14 * q^56 - 13 * q^57 + 69 * q^58 - 12 * q^59 + 46 * q^60 + 33 * q^61 + 8 * q^62 - 8 * q^63 + 21 * q^64 - 21 * q^65 + 27 * q^67 + 28 * q^68 + 12 * q^69 + 47 * q^70 + 10 * q^71 + 64 * q^72 + 9 * q^73 + 22 * q^74 - 5 * q^75 - 70 * q^76 - 24 * q^78 + 7 * q^79 + 8 * q^80 + 18 * q^81 - 6 * q^82 - 19 * q^83 + 47 * q^84 + 8 * q^85 - 25 * q^86 - 16 * q^87 + 6 * q^89 - 20 * q^90 + 3 * q^91 + 57 * q^92 + 5 * q^93 - 11 * q^94 + 22 * q^95 - 14 * q^96 + 38 * q^97 - 106 * 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 $

$2$	−1.62277	−1.14747	−0.573737	−	0.819040i	$-0.694507\pi$
$2$	−1.62277	−1.14747	−0.573737	+	0.819040i	$0.694507\pi$
$3$	−2.06455	−1.19197	−0.595983	−	0.802997i	$-0.703238\pi$
$3$	−2.06455	−1.19197	−0.595983	+	0.802997i	$0.703238\pi$
$4$	0.633389	0.316695
$5$	3.65600	1.63501	0.817507	−	0.575918i	$-0.195355\pi$
$5$	3.65600	1.63501	0.817507	+	0.575918i	$0.195355\pi$
$6$	3.35029	1.36775
$7$	−0.632224	−0.238958	−0.119479	−	0.992837i	$-0.538122\pi$
$7$	−0.632224	−0.238958	−0.119479	+	0.992837i	$0.538122\pi$
$8$	2.21770	0.784075
$9$	1.26235	0.420784
$10$	−5.93286	−1.87614
$11$	0	0
$11$	0	0
$12$	−1.30766	−0.377489
$13$	−2.89743	−0.803603	−0.401802	−	0.915727i	$-0.631616\pi$
$13$	−2.89743	−0.803603	−0.401802	+	0.915727i	$0.631616\pi$
$14$	1.02596	0.274198
$15$	−7.54799	−1.94888
$16$	−4.86560	−1.21640
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.04851	−0.482839
$19$	−1.30132	−0.298542	−0.149271	−	0.988796i	$-0.547693\pi$
$19$	−1.30132	−0.298542	−0.149271	+	0.988796i	$0.547693\pi$
$20$	2.31567	0.517800
$21$	1.30526	0.284830
$22$	0	0
$23$	7.02655	1.46514	0.732568	−	0.680693i	$-0.238321\pi$
$23$	7.02655	1.46514	0.732568	+	0.680693i	$0.238321\pi$
$24$	−4.57854	−0.934591
$25$	8.36637	1.67327
$26$	4.70187	0.922113
$27$	3.58745	0.690406
$28$	−0.400444	−0.0756768
$29$	2.47652	0.459878	0.229939	−	0.973205i	$-0.426147\pi$
$29$	2.47652	0.459878	0.229939	+	0.973205i	$0.426147\pi$
$30$	12.2487	2.23629
$31$	5.89344	1.05849	0.529246	−	0.848468i	$-0.322475\pi$
$31$	5.89344	1.05849	0.529246	+	0.848468i	$0.322475\pi$
$32$	3.46036	0.611711
$33$	0	0
$34$	−1.62277	−0.278303
$35$	−2.31141	−0.390700
$36$	0.799560	0.133260
$37$	−7.63775	−1.25564	−0.627819	−	0.778359i	$-0.716052\pi$
$37$	−7.63775	−1.25564	−0.627819	+	0.778359i	$0.716052\pi$
$38$	2.11174	0.342569
$39$	5.98189	0.957868
$40$	8.10791	1.28197
$41$	0.948733	0.148167	0.0740836	−	0.997252i	$-0.476397\pi$
$41$	0.948733	0.148167	0.0740836	+	0.997252i	$0.476397\pi$
$42$	−2.11813	−0.326835
$43$	−4.42018	−0.674071	−0.337036	−	0.941492i	$-0.609424\pi$
$43$	−4.42018	−0.674071	−0.337036	+	0.941492i	$0.609424\pi$
$44$	0	0
$45$	4.61517	0.687988
$46$	−11.4025	−1.68121
$47$	10.1311	1.47778	0.738889	−	0.673827i	$-0.235351\pi$
$47$	10.1311	1.47778	0.738889	+	0.673827i	$0.235351\pi$
$48$	10.0453	1.44991
$49$	−6.60029	−0.942899
$50$	−13.5767	−1.92004
$51$	−2.06455	−0.289094
$52$	−1.83520	−0.254497
$53$	−6.23235	−0.856079	−0.428040	−	0.903760i	$-0.640796\pi$
$53$	−6.23235	−0.856079	−0.428040	+	0.903760i	$0.640796\pi$
$54$	−5.82162	−0.792222
$55$	0	0
$56$	−1.40208	−0.187361
$57$	2.68663	0.355852
$58$	−4.01883	−0.527698
$59$	6.61526	0.861234	0.430617	−	0.902535i	$-0.358296\pi$
$59$	6.61526	0.861234	0.430617	+	0.902535i	$0.358296\pi$
$60$	−4.78082	−0.617201
$61$	−12.9799	−1.66191	−0.830955	−	0.556340i	$-0.812205\pi$
$61$	−12.9799	−1.66191	−0.830955	+	0.556340i	$0.812205\pi$
$62$	−9.56371	−1.21459
$63$	−0.798090	−0.100550
$64$	4.11582	0.514478
$65$	−10.5930	−1.31390
$66$	0	0
$67$	−5.11549	−0.624956	−0.312478	−	0.949925i	$-0.601159\pi$
$67$	−5.11549	−0.624956	−0.312478	+	0.949925i	$0.601159\pi$
$68$	0.633389	0.0768097
$69$	−14.5066	−1.74639
$70$	3.75090	0.448318
$71$	3.34255	0.396688	0.198344	−	0.980133i	$-0.436444\pi$
$71$	3.34255	0.396688	0.198344	+	0.980133i	$0.436444\pi$
$72$	2.79952	0.329926
$73$	−5.33501	−0.624415	−0.312208	−	0.950014i	$-0.601068\pi$
$73$	−5.33501	−0.624415	−0.312208	+	0.950014i	$0.601068\pi$
$74$	12.3943	1.44081
$75$	−17.2728	−1.99449
$76$	−0.824239	−0.0945467
$77$	0	0
$78$	−9.70724	−1.09913
$79$	−6.66100	−0.749421	−0.374711	−	0.927142i	$-0.622258\pi$
$79$	−6.66100	−0.749421	−0.374711	+	0.927142i	$0.622258\pi$
$80$	−17.7886	−1.98883
$81$	−11.1935	−1.24372
$82$	−1.53958	−0.170018
$83$	16.7594	1.83959	0.919793	−	0.392403i	$-0.128356\pi$
$83$	16.7594	1.83959	0.919793	+	0.392403i	$0.128356\pi$
$84$	0.826735	0.0902042
$85$	3.65600	0.396549
$86$	7.17295	0.773479
$87$	−5.11289	−0.548159
$88$	0	0
$89$	10.2267	1.08403	0.542016	−	0.840368i	$-0.317661\pi$
$89$	10.2267	1.08403	0.542016	+	0.840368i	$0.317661\pi$
$90$	−7.48936	−0.789448
$91$	1.83183	0.192028
$92$	4.45054	0.464001
$93$	−12.1673	−1.26169
$94$	−16.4405	−1.69571
$95$	−4.75762	−0.488121
$96$	−7.14407	−0.729139
$97$	11.8347	1.20163	0.600816	−	0.799388i	$-0.294843\pi$
$97$	11.8347	1.20163	0.600816	+	0.799388i	$0.294843\pi$
$98$	10.7108	1.08195
$99$	0	0
$100$	5.29917	0.529917
$101$	9.90198	0.985284	0.492642	−	0.870232i	$-0.336031\pi$
$101$	9.90198	0.985284	0.492642	+	0.870232i	$0.336031\pi$
$102$	3.35029	0.331728
$103$	18.9622	1.86840	0.934202	−	0.356745i	$-0.116114\pi$
$103$	18.9622	1.86840	0.934202	+	0.356745i	$0.116114\pi$
$104$	−6.42563	−0.630085
$105$	4.77202	0.465702
$106$	10.1137	0.982328
$107$	−11.4209	−1.10410	−0.552048	−	0.833812i	$-0.686154\pi$
$107$	−11.4209	−1.10410	−0.552048	+	0.833812i	$0.686154\pi$
$108$	2.27225	0.218648
$109$	−3.22026	−0.308445	−0.154222	−	0.988036i	$-0.549287\pi$
$109$	−3.22026	−0.308445	−0.154222	+	0.988036i	$0.549287\pi$
$110$	0	0
$111$	15.7685	1.49668
$112$	3.07615	0.290669
$113$	−5.12487	−0.482107	−0.241054	−	0.970512i	$-0.577493\pi$
$113$	−5.12487	−0.482107	−0.241054	+	0.970512i	$0.577493\pi$
$114$	−4.35978	−0.408331
$115$	25.6891	2.39552
$116$	1.56860	0.145641
$117$	−3.65758	−0.338144
$118$	−10.7351	−0.988242
$119$	−0.632224	−0.0579559
$120$	−16.7392	−1.52807
$121$	0	0
$122$	21.0635	1.90700
$123$	−1.95870	−0.176610
$124$	3.73284	0.335219
$125$	12.3075	1.10081
$126$	1.29512	0.115378
$127$	14.0721	1.24870	0.624350	−	0.781145i	$-0.285364\pi$
$127$	14.0721	1.24870	0.624350	+	0.781145i	$0.285364\pi$
$128$	−13.5998	−1.20206
$129$	9.12567	0.803471
$130$	17.1901	1.50767
$131$	10.0036	0.874020	0.437010	−	0.899457i	$-0.356037\pi$
$131$	10.0036	0.874020	0.437010	+	0.899457i	$0.356037\pi$
$132$	0	0
$133$	0.822723	0.0713391
$134$	8.30127	0.717120
$135$	13.1157	1.12882
$136$	2.21770	0.190166
$137$	3.54146	0.302568	0.151284	−	0.988490i	$-0.451659\pi$
$137$	3.54146	0.302568	0.151284	+	0.988490i	$0.451659\pi$
$138$	23.5410	2.00394
$139$	−13.1767	−1.11764	−0.558818	−	0.829290i	$-0.688745\pi$
$139$	−13.1767	−1.11764	−0.558818	+	0.829290i	$0.688745\pi$
$140$	−1.46402	−0.123733
$141$	−20.9162	−1.76146
$142$	−5.42419	−0.455188
$143$	0	0
$144$	−6.14210	−0.511842
$145$	9.05416	0.751907
$146$	8.65750	0.716500
$147$	13.6266	1.12390
$148$	−4.83767	−0.397654
$149$	−20.6433	−1.69117	−0.845584	−	0.533842i	$-0.820748\pi$
$149$	−20.6433	−1.69117	−0.845584	+	0.533842i	$0.820748\pi$
$150$	28.0297	2.28862
$151$	4.71508	0.383707	0.191854	−	0.981424i	$-0.438550\pi$
$151$	4.71508	0.383707	0.191854	+	0.981424i	$0.438550\pi$
$152$	−2.88593	−0.234079
$153$	1.26235	0.102055
$154$	0	0
$155$	21.5464	1.73065
$156$	3.78886	0.303352
$157$	4.46819	0.356601	0.178300	−	0.983976i	$-0.442940\pi$
$157$	4.46819	0.356601	0.178300	+	0.983976i	$0.442940\pi$
$158$	10.8093	0.859941
$159$	12.8670	1.02042
$160$	12.6511	1.00016
$161$	−4.44235	−0.350106
$162$	18.1645	1.42714
$163$	−12.7576	−0.999254	−0.499627	−	0.866241i	$-0.666530\pi$
$163$	−12.7576	−0.999254	−0.499627	+	0.866241i	$0.666530\pi$
$164$	0.600917	0.0469238
$165$	0	0
$166$	−27.1967	−2.11088
$167$	12.6063	0.975501	0.487751	−	0.872983i	$-0.337818\pi$
$167$	12.6063	0.975501	0.487751	+	0.872983i	$0.337818\pi$
$168$	2.89466	0.223328
$169$	−4.60488	−0.354222
$170$	−5.93286	−0.455030
$171$	−1.64272	−0.125622
$172$	−2.79970	−0.213475
$173$	4.05468	0.308271	0.154136	−	0.988050i	$-0.450741\pi$
$173$	4.05468	0.308271	0.154136	+	0.988050i	$0.450741\pi$
$174$	8.29705	0.628998
$175$	−5.28942	−0.399842
$176$	0	0
$177$	−13.6575	−1.02656
$178$	−16.5957	−1.24390
$179$	14.5724	1.08919	0.544597	−	0.838698i	$-0.316683\pi$
$179$	14.5724	1.08919	0.544597	+	0.838698i	$0.316683\pi$
$180$	2.92320	0.217882
$181$	−9.77087	−0.726263	−0.363132	−	0.931738i	$-0.618292\pi$
$181$	−9.77087	−0.726263	−0.363132	+	0.931738i	$0.618292\pi$
$182$	−2.97264	−0.220347
$183$	26.7977	1.98094
$184$	15.5828	1.14878
$185$	−27.9237	−2.05299
$186$	19.7447	1.44775
$187$	0	0
$188$	6.41695	0.468004
$189$	−2.26807	−0.164978
$190$	7.72053	0.560106
$191$	−1.30681	−0.0945578	−0.0472789	−	0.998882i	$-0.515055\pi$
$191$	−1.30681	−0.0945578	−0.0472789	+	0.998882i	$0.515055\pi$
$192$	−8.49730	−0.613240
$193$	20.9491	1.50795	0.753974	−	0.656904i	$-0.228134\pi$
$193$	20.9491	1.50795	0.753974	+	0.656904i	$0.228134\pi$
$194$	−19.2050	−1.37884
$195$	21.8698	1.56613
$196$	−4.18055	−0.298611
$197$	21.0368	1.49881	0.749407	−	0.662110i	$-0.230339\pi$
$197$	21.0368	1.49881	0.749407	+	0.662110i	$0.230339\pi$
$198$	0	0
$199$	−0.377720	−0.0267759	−0.0133879	−	0.999910i	$-0.504262\pi$
$199$	−0.377720	−0.0267759	−0.0133879	+	0.999910i	$0.504262\pi$
$200$	18.5541	1.31197
$201$	10.5612	0.744927
$202$	−16.0687	−1.13059
$203$	−1.56571	−0.109892
$204$	−1.30766	−0.0915546
$205$	3.46857	0.242256
$206$	−30.7714	−2.14394
$207$	8.86998	0.616506
$208$	14.0977	0.977502
$209$	0	0
$210$	−7.74390	−0.534380
$211$	17.5850	1.21060	0.605302	−	0.795996i	$-0.293052\pi$
$211$	17.5850	1.21060	0.605302	+	0.795996i	$0.293052\pi$
$212$	−3.94750	−0.271116
$213$	−6.90085	−0.472838
$214$	18.5335	1.26692
$215$	−16.1602	−1.10212
$216$	7.95589	0.541330
$217$	−3.72597	−0.252936
$218$	5.22574	0.353932
$219$	11.0144	0.744282
$220$	0	0
$221$	−2.89743	−0.194902
$222$	−25.5887	−1.71740
$223$	23.3962	1.56673	0.783364	−	0.621563i	$-0.213502\pi$
$223$	23.3962	1.56673	0.783364	+	0.621563i	$0.213502\pi$
$224$	−2.18772	−0.146173
$225$	10.5613	0.704087
$226$	8.31650	0.553205
$227$	−10.1730	−0.675205	−0.337602	−	0.941289i	$-0.609616\pi$
$227$	−10.1730	−0.675205	−0.337602	+	0.941289i	$0.609616\pi$
$228$	1.70168	0.112697
$229$	−2.94662	−0.194718	−0.0973591	−	0.995249i	$-0.531040\pi$
$229$	−2.94662	−0.194718	−0.0973591	+	0.995249i	$0.531040\pi$
$230$	−41.6875	−2.74880
$231$	0	0
$232$	5.49217	0.360579
$233$	23.5886	1.54534	0.772669	−	0.634809i	$-0.218921\pi$
$233$	23.5886	1.54534	0.772669	+	0.634809i	$0.218921\pi$
$234$	5.93542	0.388011
$235$	37.0395	2.41619
$236$	4.19003	0.272748
$237$	13.7519	0.893285
$238$	1.02596	0.0665028
$239$	−1.72645	−0.111674	−0.0558372	−	0.998440i	$-0.517783\pi$
$239$	−1.72645	−0.111674	−0.0558372	+	0.998440i	$0.517783\pi$
$240$	36.7255	2.37062
$241$	23.9463	1.54252	0.771258	−	0.636523i	$-0.219628\pi$
$241$	23.9463	1.54252	0.771258	+	0.636523i	$0.219628\pi$
$242$	0	0
$243$	12.3472	0.792073
$244$	−8.22135	−0.526318
$245$	−24.1307	−1.54165
$246$	3.17853	0.202656
$247$	3.77047	0.239910
$248$	13.0699	0.829937
$249$	−34.6006	−2.19273
$250$	−19.9722	−1.26315
$251$	−4.15751	−0.262420	−0.131210	−	0.991355i	$-0.541886\pi$
$251$	−4.15751	−0.262420	−0.131210	+	0.991355i	$0.541886\pi$
$252$	−0.505501	−0.0318436
$253$	0	0
$254$	−22.8359	−1.43285
$255$	−7.54799	−0.472674
$256$	13.8377	0.864854
$257$	−4.68216	−0.292065	−0.146032	−	0.989280i	$-0.546650\pi$
$257$	−4.68216	−0.292065	−0.146032	+	0.989280i	$0.546650\pi$
$258$	−14.8089	−0.921961
$259$	4.82877	0.300045
$260$	−6.70951	−0.416106
$261$	3.12624	0.193509
$262$	−16.2336	−1.00291
$263$	−8.16857	−0.503695	−0.251848	−	0.967767i	$-0.581038\pi$
$263$	−8.16857	−0.503695	−0.251848	+	0.967767i	$0.581038\pi$
$264$	0	0
$265$	−22.7855	−1.39970
$266$	−1.33509	−0.0818597
$267$	−21.1136	−1.29213
$268$	−3.24009	−0.197920
$269$	7.59953	0.463351	0.231676	−	0.972793i	$-0.425579\pi$
$269$	7.59953	0.463351	0.231676	+	0.972793i	$0.425579\pi$
$270$	−21.2839	−1.29529
$271$	11.5024	0.698722	0.349361	−	0.936988i	$-0.386399\pi$
$271$	11.5024	0.698722	0.349361	+	0.936988i	$0.386399\pi$
$272$	−4.86560	−0.295020
$273$	−3.78189	−0.228890
$274$	−5.74699	−0.347188
$275$	0	0
$276$	−9.18835	−0.553074
$277$	26.3924	1.58577	0.792884	−	0.609373i	$-0.208579\pi$
$277$	26.3924	1.58577	0.792884	+	0.609373i	$0.208579\pi$
$278$	21.3829	1.28246
$279$	7.43960	0.445397
$280$	−5.12602	−0.306338
$281$	25.6882	1.53243	0.766214	−	0.642586i	$-0.222138\pi$
$281$	25.6882	1.53243	0.766214	+	0.642586i	$0.222138\pi$
$282$	33.9422	2.02123
$283$	−9.07138	−0.539237	−0.269619	−	0.962967i	$-0.586898\pi$
$283$	−9.07138	−0.539237	−0.269619	+	0.962967i	$0.586898\pi$
$284$	2.11713	0.125629
$285$	9.82232	0.581824
$286$	0	0
$287$	−0.599812	−0.0354058
$288$	4.36819	0.257398
$289$	1.00000	0.0588235
$290$	−14.6928	−0.862794
$291$	−24.4333	−1.43230
$292$	−3.37913	−0.197749
$293$	6.23789	0.364421	0.182211	−	0.983260i	$-0.441675\pi$
$293$	6.23789	0.364421	0.182211	+	0.983260i	$0.441675\pi$
$294$	−22.1129	−1.28965
$295$	24.1854	1.40813
$296$	−16.9382	−0.984514
$297$	0	0
$298$	33.4994	1.94057
$299$	−20.3590	−1.17739
$300$	−10.9404	−0.631643
$301$	2.79455	0.161075
$302$	−7.65149	−0.440294
$303$	−20.4431	−1.17443
$304$	6.33168	0.363147
$305$	−47.4547	−2.71725
$306$	−2.04851	−0.117106
$307$	8.42949	0.481096	0.240548	−	0.970637i	$-0.422673\pi$
$307$	8.42949	0.481096	0.240548	+	0.970637i	$0.422673\pi$
$308$	0	0
$309$	−39.1484	−2.22707
$310$	−34.9649	−1.98588
$311$	−33.9671	−1.92610	−0.963048	−	0.269331i	$-0.913197\pi$
$311$	−33.9671	−1.92610	−0.963048	+	0.269331i	$0.913197\pi$
$312$	13.2660	0.751040
$313$	−9.67803	−0.547035	−0.273517	−	0.961867i	$-0.588187\pi$
$313$	−9.67803	−0.547035	−0.273517	+	0.961867i	$0.588187\pi$
$314$	−7.25086	−0.409190
$315$	−2.91782	−0.164401
$316$	−4.21901	−0.237338
$317$	25.5845	1.43697	0.718484	−	0.695543i	$-0.244836\pi$
$317$	25.5845	1.43697	0.718484	+	0.695543i	$0.244836\pi$
$318$	−20.8802	−1.17090
$319$	0	0
$320$	15.0475	0.841178
$321$	23.5789	1.31605
$322$	7.20893	0.401738
$323$	−1.30132	−0.0724071
$324$	−7.08986	−0.393881
$325$	−24.2410	−1.34465
$326$	20.7027	1.14662
$327$	6.64837	0.367656
$328$	2.10400	0.116174
$329$	−6.40515	−0.353127
$330$	0	0
$331$	−1.49552	−0.0822012	−0.0411006	−	0.999155i	$-0.513086\pi$
$331$	−1.49552	−0.0822012	−0.0411006	+	0.999155i	$0.513086\pi$
$332$	10.6152	0.582587
$333$	−9.64154	−0.528353
$334$	−20.4571	−1.11936
$335$	−18.7022	−1.02181
$336$	−6.35085	−0.346467
$337$	22.7861	1.24124	0.620620	−	0.784111i	$-0.286881\pi$
$337$	22.7861	1.24124	0.620620	+	0.784111i	$0.286881\pi$
$338$	7.47268	0.406460
$339$	10.5805	0.574656
$340$	2.31567	0.125585
$341$	0	0
$342$	2.66576	0.144148
$343$	8.59843	0.464272
$344$	−9.80263	−0.528522
$345$	−53.0363	−2.85538
$346$	−6.57981	−0.353733
$347$	21.3919	1.14838	0.574188	−	0.818723i	$-0.305318\pi$
$347$	21.3919	1.14838	0.574188	+	0.818723i	$0.305318\pi$
$348$	−3.23845	−0.173599
$349$	6.94102	0.371545	0.185772	−	0.982593i	$-0.440521\pi$
$349$	6.94102	0.371545	0.185772	+	0.982593i	$0.440521\pi$
$350$	8.58352	0.458809
$351$	−10.3944	−0.554812
$352$	0	0
$353$	14.1565	0.753472	0.376736	−	0.926321i	$-0.377046\pi$
$353$	14.1565	0.753472	0.376736	+	0.926321i	$0.377046\pi$
$354$	22.1630	1.17795
$355$	12.2204	0.648590
$356$	6.47751	0.343307
$357$	1.30526	0.0690815
$358$	−23.6477	−1.24982
$359$	−15.4256	−0.814134	−0.407067	−	0.913398i	$-0.633448\pi$
$359$	−15.4256	−0.814134	−0.407067	+	0.913398i	$0.633448\pi$
$360$	10.2350	0.539434
$361$	−17.3066	−0.910872
$362$	15.8559	0.833368
$363$	0	0
$364$	1.16026	0.0608141
$365$	−19.5048	−1.02093
$366$	−43.4865	−2.27308
$367$	−24.2277	−1.26468	−0.632339	−	0.774692i	$-0.717905\pi$
$367$	−24.2277	−1.26468	−0.632339	+	0.774692i	$0.717905\pi$
$368$	−34.1884	−1.78219
$369$	1.19764	0.0623465
$370$	45.3137	2.35575
$371$	3.94024	0.204567
$372$	−7.70662	−0.399570
$373$	3.97837	0.205992	0.102996	−	0.994682i	$-0.467157\pi$
$373$	3.97837	0.205992	0.102996	+	0.994682i	$0.467157\pi$
$374$	0	0
$375$	−25.4093	−1.31213
$376$	22.4678	1.15869
$377$	−7.17555	−0.369559
$378$	3.68057	0.189308
$379$	12.2938	0.631490	0.315745	−	0.948844i	$-0.397746\pi$
$379$	12.2938	0.631490	0.315745	+	0.948844i	$0.397746\pi$
$380$	−3.01342	−0.154585
$381$	−29.0526	−1.48841
$382$	2.12066	0.108503
$383$	24.5675	1.25534	0.627670	−	0.778479i	$-0.284009\pi$
$383$	24.5675	1.25534	0.627670	+	0.778479i	$0.284009\pi$
$384$	28.0773	1.43282
$385$	0	0
$386$	−33.9956	−1.73033
$387$	−5.57983	−0.283639
$388$	7.49597	0.380550
$389$	7.21967	0.366052	0.183026	−	0.983108i	$-0.441411\pi$
$389$	7.21967	0.366052	0.183026	+	0.983108i	$0.441411\pi$
$390$	−35.4897	−1.79709
$391$	7.02655	0.355348
$392$	−14.6375	−0.739303
$393$	−20.6529	−1.04180
$394$	−34.1380	−1.71985
$395$	−24.3527	−1.22531
$396$	0	0
$397$	15.9590	0.800959	0.400480	−	0.916306i	$-0.368844\pi$
$397$	15.9590	0.800959	0.400480	+	0.916306i	$0.368844\pi$
$398$	0.612954	0.0307246
$399$	−1.69855	−0.0850339
$400$	−40.7074	−2.03537
$401$	4.79458	0.239430	0.119715	−	0.992808i	$-0.461802\pi$
$401$	4.79458	0.239430	0.119715	+	0.992808i	$0.461802\pi$
$402$	−17.1384	−0.854784
$403$	−17.0758	−0.850608
$404$	6.27181	0.312034
$405$	−40.9236	−2.03351
$406$	2.54080	0.126098
$407$	0	0
$408$	−4.57854	−0.226672
$409$	−15.3256	−0.757801	−0.378900	−	0.925437i	$-0.623698\pi$
$409$	−15.3256	−0.757801	−0.378900	+	0.925437i	$0.623698\pi$
$410$	−5.62870	−0.277982
$411$	−7.31152	−0.360651
$412$	12.0105	0.591713
$413$	−4.18233	−0.205799
$414$	−14.3940	−0.707425
$415$	61.2726	3.00775
$416$	−10.0262	−0.491573
$417$	27.2040	1.33219
$418$	0	0
$419$	−12.7816	−0.624421	−0.312210	−	0.950013i	$-0.601069\pi$
$419$	−12.7816	−0.624421	−0.312210	+	0.950013i	$0.601069\pi$
$420$	3.02255	0.147485
$421$	10.6119	0.517190	0.258595	−	0.965986i	$-0.416740\pi$
$421$	10.6119	0.517190	0.258595	+	0.965986i	$0.416740\pi$
$422$	−28.5365	−1.38914
$423$	12.7891	0.621826
$424$	−13.8215	−0.671230
$425$	8.36637	0.405828
$426$	11.1985	0.542569
$427$	8.20622	0.397127
$428$	−7.23385	−0.349661
$429$	0	0
$430$	26.2243	1.26465
$431$	−22.1194	−1.06545	−0.532727	−	0.846287i	$-0.678833\pi$
$431$	−22.1194	−1.06545	−0.532727	+	0.846287i	$0.678833\pi$
$432$	−17.4551	−0.839809
$433$	30.3821	1.46007	0.730036	−	0.683409i	$-0.239503\pi$
$433$	30.3821	1.46007	0.730036	+	0.683409i	$0.239503\pi$
$434$	6.04640	0.290237
$435$	−18.6927	−0.896248
$436$	−2.03968	−0.0976828
$437$	−9.14376	−0.437405
$438$	−17.8738	−0.854044
$439$	16.6236	0.793402	0.396701	−	0.917948i	$-0.370155\pi$
$439$	16.6236	0.793402	0.396701	+	0.917948i	$0.370155\pi$
$440$	0	0
$441$	−8.33190	−0.396757
$442$	4.70187	0.223645
$443$	−30.7505	−1.46100	−0.730501	−	0.682912i	$-0.760713\pi$
$443$	−30.7505	−1.46100	−0.730501	+	0.682912i	$0.760713\pi$
$444$	9.98759	0.473990
$445$	37.3890	1.77241
$446$	−37.9668	−1.79778
$447$	42.6191	2.01582
$448$	−2.60212	−0.122939
$449$	−6.34406	−0.299395	−0.149697	−	0.988732i	$-0.547830\pi$
$449$	−6.34406	−0.299395	−0.149697	+	0.988732i	$0.547830\pi$
$450$	−17.1386	−0.807921
$451$	0	0
$452$	−3.24604	−0.152681
$453$	−9.73449	−0.457366
$454$	16.5084	0.774779
$455$	6.69717	0.313968
$456$	5.95813	0.279015
$457$	−11.9668	−0.559784	−0.279892	−	0.960032i	$-0.590299\pi$
$457$	−11.9668	−0.559784	−0.279892	+	0.960032i	$0.590299\pi$
$458$	4.78170	0.223434
$459$	3.58745	0.167448
$460$	16.2712	0.758648
$461$	−10.4704	−0.487653	−0.243827	−	0.969819i	$-0.578403\pi$
$461$	−10.4704	−0.487653	−0.243827	+	0.969819i	$0.578403\pi$
$462$	0	0
$463$	−16.4699	−0.765420	−0.382710	−	0.923869i	$-0.625009\pi$
$463$	−16.4699	−0.765420	−0.382710	+	0.923869i	$0.625009\pi$
$464$	−12.0497	−0.559395
$465$	−44.4836	−2.06288
$466$	−38.2788	−1.77323
$467$	28.0689	1.29887	0.649437	−	0.760416i	$-0.275005\pi$
$467$	28.0689	1.29887	0.649437	+	0.760416i	$0.275005\pi$
$468$	−2.31667	−0.107088
$469$	3.23413	0.149338
$470$	−60.1066	−2.77251
$471$	−9.22480	−0.425056
$472$	14.6706	0.675271
$473$	0	0
$474$	−22.3163	−1.02502
$475$	−10.8873	−0.499543
$476$	−0.400444	−0.0183543
$477$	−7.86743	−0.360225
$478$	2.80163	0.128143
$479$	22.2784	1.01793	0.508963	−	0.860788i	$-0.330029\pi$
$479$	22.2784	1.01793	0.508963	+	0.860788i	$0.330029\pi$
$480$	−26.1188	−1.19215
$481$	22.1299	1.00904
$482$	−38.8594	−1.77000
$483$	9.17145	0.417315
$484$	0	0
$485$	43.2677	1.96469
$486$	−20.0367	−0.908882
$487$	9.12630	0.413552	0.206776	−	0.978388i	$-0.433703\pi$
$487$	9.12630	0.413552	0.206776	+	0.978388i	$0.433703\pi$
$488$	−28.7856	−1.30306
$489$	26.3387	1.19108
$490$	39.1586	1.76901
$491$	33.2044	1.49850	0.749248	−	0.662290i	$-0.230415\pi$
$491$	33.2044	1.49850	0.749248	+	0.662290i	$0.230415\pi$
$492$	−1.24062	−0.0559316
$493$	2.47652	0.111537
$494$	−6.11862	−0.275290
$495$	0	0
$496$	−28.6751	−1.28755
$497$	−2.11324	−0.0947918
$498$	56.1489	2.51609
$499$	−22.4456	−1.00480	−0.502402	−	0.864634i	$-0.667550\pi$
$499$	−22.4456	−1.00480	−0.502402	+	0.864634i	$0.667550\pi$
$500$	7.79541	0.348621
$501$	−26.0262	−1.16276
$502$	6.74669	0.301120
$503$	28.4240	1.26736	0.633681	−	0.773594i	$-0.281543\pi$
$503$	28.4240	1.26736	0.633681	+	0.773594i	$0.281543\pi$
$504$	−1.76992	−0.0788386
$505$	36.2017	1.61095
$506$	0	0
$507$	9.50700	0.422221
$508$	8.91314	0.395457
$509$	−19.1159	−0.847297	−0.423648	−	0.905827i	$-0.639251\pi$
$509$	−19.1159	−0.847297	−0.423648	+	0.905827i	$0.639251\pi$
$510$	12.2487	0.542380
$511$	3.37292	0.149209
$512$	4.74414	0.209663
$513$	−4.66841	−0.206115
$514$	7.59807	0.335137
$515$	69.3260	3.05487
$516$	5.78010	0.254455
$517$	0	0
$518$	−7.83599	−0.344294
$519$	−8.37107	−0.367449
$520$	−23.4921	−1.03020
$521$	−15.6023	−0.683548	−0.341774	−	0.939782i	$-0.611028\pi$
$521$	−15.6023	−0.683548	−0.341774	+	0.939782i	$0.611028\pi$
$522$	−5.07318	−0.222047
$523$	2.69152	0.117692	0.0588459	−	0.998267i	$-0.481258\pi$
$523$	2.69152	0.117692	0.0588459	+	0.998267i	$0.481258\pi$
$524$	6.33618	0.276797
$525$	10.9203	0.476599
$526$	13.2557	0.577977
$527$	5.89344	0.256722
$528$	0	0
$529$	26.3724	1.14663
$530$	36.9757	1.60612
$531$	8.35079	0.362394
$532$	0.521104	0.0225927
$533$	−2.74889	−0.119068
$534$	34.2625	1.48268
$535$	−41.7547	−1.80521
$536$	−11.3446	−0.490012
$537$	−30.0854	−1.29828
$538$	−12.3323	−0.531683
$539$	0	0
$540$	8.30737	0.357492
$541$	40.8684	1.75707	0.878534	−	0.477679i	$-0.158522\pi$
$541$	40.8684	1.75707	0.878534	+	0.477679i	$0.158522\pi$
$542$	−18.6658	−0.801765
$543$	20.1724	0.865682
$544$	3.46036	0.148362
$545$	−11.7733	−0.504312
$546$	6.13715	0.262646
$547$	−24.2993	−1.03896	−0.519482	−	0.854481i	$-0.673875\pi$
$547$	−24.2993	−1.03896	−0.519482	+	0.854481i	$0.673875\pi$
$548$	2.24313	0.0958216
$549$	−16.3853	−0.699305
$550$	0	0
$551$	−3.22273	−0.137293
$552$	−32.1713	−1.36930
$553$	4.21125	0.179080
$554$	−42.8289	−1.81963
$555$	57.6497	2.44709
$556$	−8.34601	−0.353950
$557$	−37.4457	−1.58662	−0.793312	−	0.608815i	$-0.791645\pi$
$557$	−37.4457	−1.58662	−0.793312	+	0.608815i	$0.791645\pi$
$558$	−12.0728	−0.511081
$559$	12.8072	0.541686
$560$	11.2464	0.475247
$561$	0	0
$562$	−41.6860	−1.75842
$563$	22.5488	0.950319	0.475159	−	0.879900i	$-0.342390\pi$
$563$	22.5488	0.950319	0.475159	+	0.879900i	$0.342390\pi$
$564$	−13.2481	−0.557845
$565$	−18.7366	−0.788253
$566$	14.7208	0.618760
$567$	7.07681	0.297198
$568$	7.41276	0.311033
$569$	−11.4471	−0.479885	−0.239943	−	0.970787i	$-0.577129\pi$
$569$	−11.4471	−0.479885	−0.239943	+	0.970787i	$0.577129\pi$
$570$	−15.9394	−0.667627
$571$	−8.54691	−0.357677	−0.178839	−	0.983878i	$-0.557234\pi$
$571$	−8.54691	−0.357677	−0.178839	+	0.983878i	$0.557234\pi$
$572$	0	0
$573$	2.69798	0.112710
$574$	0.973358	0.0406272
$575$	58.7867	2.45157
$576$	5.19562	0.216484
$577$	−6.41032	−0.266865	−0.133433	−	0.991058i	$-0.542600\pi$
$577$	−6.41032	−0.266865	−0.133433	+	0.991058i	$0.542600\pi$
$578$	−1.62277	−0.0674984
$579$	−43.2504	−1.79742
$580$	5.73481	0.238125
$581$	−10.5957	−0.439584
$582$	39.6496	1.64353
$583$	0	0
$584$	−11.8314	−0.489588
$585$	−13.3721	−0.552870
$586$	−10.1227	−0.418164
$587$	10.9838	0.453348	0.226674	−	0.973971i	$-0.427215\pi$
$587$	10.9838	0.453348	0.226674	+	0.973971i	$0.427215\pi$
$588$	8.63095	0.355934
$589$	−7.66922	−0.316005
$590$	−39.2474	−1.61579
$591$	−43.4315	−1.78654
$592$	37.1622	1.52736
$593$	−40.2318	−1.65212	−0.826062	−	0.563580i	$-0.809424\pi$
$593$	−40.2318	−1.65212	−0.826062	+	0.563580i	$0.809424\pi$
$594$	0	0
$595$	−2.31141	−0.0947587
$596$	−13.0753	−0.535584
$597$	0.779821	0.0319159
$598$	33.0379	1.35102
$599$	−21.1492	−0.864134	−0.432067	−	0.901842i	$-0.642216\pi$
$599$	−21.1492	−0.864134	−0.432067	+	0.901842i	$0.642216\pi$
$600$	−38.3058	−1.56383
$601$	−26.5757	−1.08405	−0.542023	−	0.840364i	$-0.682341\pi$
$601$	−26.5757	−1.08405	−0.542023	+	0.840364i	$0.682341\pi$
$602$	−4.53491	−0.184829
$603$	−6.45755	−0.262972
$604$	2.98648	0.121518
$605$	0	0
$606$	33.1745	1.34762
$607$	−39.9113	−1.61995	−0.809976	−	0.586463i	$-0.800520\pi$
$607$	−39.9113	−1.61995	−0.809976	+	0.586463i	$0.800520\pi$
$608$	−4.50302	−0.182622
$609$	3.23249	0.130987
$610$	77.0081	3.11797
$611$	−29.3543	−1.18755
$612$	0.799560	0.0323203
$613$	−23.8791	−0.964468	−0.482234	−	0.876042i	$-0.660175\pi$
$613$	−23.8791	−0.964468	−0.482234	+	0.876042i	$0.660175\pi$
$614$	−13.6791	−0.552045
$615$	−7.16103	−0.288761
$616$	0	0
$617$	28.2081	1.13562	0.567809	−	0.823161i	$-0.307791\pi$
$617$	28.2081	1.13562	0.567809	+	0.823161i	$0.307791\pi$
$618$	63.5289	2.55551
$619$	−13.9369	−0.560172	−0.280086	−	0.959975i	$-0.590363\pi$
$619$	−13.9369	−0.560172	−0.280086	+	0.959975i	$0.590363\pi$
$620$	13.6473	0.548088
$621$	25.2074	1.01154
$622$	55.1208	2.21014
$623$	−6.46559	−0.259038
$624$	−29.1054	−1.16515
$625$	3.16427	0.126571
$626$	15.7052	0.627708
$627$	0	0
$628$	2.83011	0.112934
$629$	−7.63775	−0.304537
$630$	4.73496	0.188645
$631$	1.51109	0.0601557	0.0300778	−	0.999548i	$-0.490424\pi$
$631$	1.51109	0.0601557	0.0300778	+	0.999548i	$0.490424\pi$
$632$	−14.7721	−0.587602
$633$	−36.3051	−1.44300
$634$	−41.5178	−1.64888
$635$	51.4478	2.04164
$636$	8.14981	0.323161
$637$	19.1239	0.757717
$638$	0	0
$639$	4.21948	0.166920
$640$	−49.7208	−1.96539
$641$	3.93727	0.155513	0.0777563	−	0.996972i	$-0.475224\pi$
$641$	3.93727	0.155513	0.0777563	+	0.996972i	$0.475224\pi$
$642$	−38.2632	−1.51013
$643$	−22.1817	−0.874759	−0.437380	−	0.899277i	$-0.644093\pi$
$643$	−22.1817	−0.874759	−0.437380	+	0.899277i	$0.644093\pi$
$644$	−2.81374	−0.110877
$645$	33.3635	1.31369
$646$	2.11174	0.0830853
$647$	−12.8892	−0.506726	−0.253363	−	0.967371i	$-0.581537\pi$
$647$	−12.8892	−0.506726	−0.253363	+	0.967371i	$0.581537\pi$
$648$	−24.8239	−0.975173
$649$	0	0
$650$	39.3376	1.54295
$651$	7.69244	0.301491
$652$	−8.08054	−0.316458
$653$	48.6061	1.90210	0.951051	−	0.309033i	$-0.100005\pi$
$653$	48.6061	1.90210	0.951051	+	0.309033i	$0.100005\pi$
$654$	−10.7888	−0.421875
$655$	36.5733	1.42904
$656$	−4.61615	−0.180231
$657$	−6.73466	−0.262744
$658$	10.3941	0.405204
$659$	−0.655855	−0.0255485	−0.0127742	−	0.999918i	$-0.504066\pi$
$659$	−0.655855	−0.0255485	−0.0127742	+	0.999918i	$0.504066\pi$
$660$	0	0
$661$	2.10351	0.0818172	0.0409086	−	0.999163i	$-0.486975\pi$
$661$	2.10351	0.0818172	0.0409086	+	0.999163i	$0.486975\pi$
$662$	2.42689	0.0943236
$663$	5.98189	0.232317
$664$	37.1674	1.44237
$665$	3.00788	0.116641
$666$	15.6460	0.606271
$667$	17.4014	0.673784
$668$	7.98466	0.308936
$669$	−48.3026	−1.86749
$670$	30.3495	1.17250
$671$	0	0
$672$	4.51665	0.174234
$673$	−14.6242	−0.563723	−0.281862	−	0.959455i	$-0.590952\pi$
$673$	−14.6242	−0.563723	−0.281862	+	0.959455i	$0.590952\pi$
$674$	−36.9767	−1.42429
$675$	30.0140	1.15524
$676$	−2.91668	−0.112180
$677$	30.5212	1.17303	0.586513	−	0.809940i	$-0.300500\pi$
$677$	30.5212	1.17303	0.586513	+	0.809940i	$0.300500\pi$
$678$	−17.1698	−0.659402
$679$	−7.48218	−0.287140
$680$	8.10791	0.310924
$681$	21.0026	0.804821
$682$	0	0
$683$	23.1910	0.887380	0.443690	−	0.896180i	$-0.353669\pi$
$683$	23.1910	0.887380	0.443690	+	0.896180i	$0.353669\pi$
$684$	−1.04048	−0.0397838
$685$	12.9476	0.494703
$686$	−13.9533	−0.532739
$687$	6.08344	0.232098
$688$	21.5068	0.819940
$689$	18.0578	0.687948
$690$	86.0659	3.27647
$691$	19.2345	0.731714	0.365857	−	0.930671i	$-0.380776\pi$
$691$	19.2345	0.731714	0.365857	+	0.930671i	$0.380776\pi$
$692$	2.56819	0.0976278
$693$	0	0
$694$	−34.7141	−1.31773
$695$	−48.1742	−1.82735
$696$	−11.3388	−0.429798
$697$	0.948733	0.0359358
$698$	−11.2637	−0.426337
$699$	−48.6997	−1.84199
$700$	−3.35026	−0.126628
$701$	−16.3461	−0.617384	−0.308692	−	0.951162i	$-0.599891\pi$
$701$	−16.3461	−0.617384	−0.308692	+	0.951162i	$0.599891\pi$
$702$	16.8678	0.636632
$703$	9.93913	0.374861
$704$	0	0
$705$	−76.4697	−2.88002
$706$	−22.9727	−0.864589
$707$	−6.26027	−0.235442
$708$	−8.65052	−0.325106
$709$	−37.2342	−1.39836	−0.699179	−	0.714946i	$-0.746451\pi$
$709$	−37.2342	−1.39836	−0.699179	+	0.714946i	$0.746451\pi$
$710$	−19.8309	−0.744240
$711$	−8.40853	−0.315345
$712$	22.6798	0.849962
$713$	41.4105	1.55084
$714$	−2.11813	−0.0792691
$715$	0	0
$716$	9.23001	0.344942
$717$	3.56433	0.133112
$718$	25.0323	0.934197
$719$	−1.52985	−0.0570536	−0.0285268	−	0.999593i	$-0.509082\pi$
$719$	−1.52985	−0.0570536	−0.0285268	+	0.999593i	$0.509082\pi$
$720$	−22.4555	−0.836869
$721$	−11.9884	−0.446470
$722$	28.0846	1.04520
$723$	−49.4382	−1.83863
$724$	−6.18877	−0.230004
$725$	20.7195	0.769502
$726$	0	0
$727$	19.2169	0.712717	0.356358	−	0.934349i	$-0.384018\pi$
$727$	19.2169	0.712717	0.356358	+	0.934349i	$0.384018\pi$
$728$	4.06244	0.150564
$729$	8.08922	0.299601
$730$	31.6519	1.17149
$731$	−4.42018	−0.163486
$732$	16.9734	0.627353
$733$	41.3494	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$733$	41.3494	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$734$	39.3161	1.45118
$735$	49.8190	1.83760
$736$	24.3144	0.896240
$737$	0	0
$738$	−1.94349	−0.0715409
$739$	−8.84010	−0.325189	−0.162594	−	0.986693i	$-0.551986\pi$
$739$	−8.84010	−0.325189	−0.162594	+	0.986693i	$0.551986\pi$
$740$	−17.6865	−0.650170
$741$	−7.78432	−0.285964
$742$	−6.39412	−0.234735
$743$	−0.109408	−0.00401378	−0.00200689	−	0.999998i	$-0.500639\pi$
$743$	−0.109408	−0.00401378	−0.00200689	+	0.999998i	$0.500639\pi$
$744$	−26.9833	−0.989257
$745$	−75.4721	−2.76509
$746$	−6.45599	−0.236371
$747$	21.1563	0.774069
$748$	0	0
$749$	7.22055	0.263833
$750$	41.2335	1.50564
$751$	2.01423	0.0735003	0.0367501	−	0.999324i	$-0.488299\pi$
$751$	2.01423	0.0735003	0.0367501	+	0.999324i	$0.488299\pi$
$752$	−49.2940	−1.79757
$753$	8.58338	0.312796
$754$	11.6443	0.424060
$755$	17.2383	0.627367
$756$	−1.43657	−0.0522477
$757$	2.78983	0.101398	0.0506990	−	0.998714i	$-0.483855\pi$
$757$	2.78983	0.101398	0.0506990	+	0.998714i	$0.483855\pi$
$758$	−19.9500	−0.724618
$759$	0	0
$760$	−10.5510	−0.382723
$761$	42.2031	1.52986	0.764931	−	0.644112i	$-0.222773\pi$
$761$	42.2031	1.52986	0.764931	+	0.644112i	$0.222773\pi$
$762$	47.1457	1.70791
$763$	2.03592	0.0737054
$764$	−0.827722	−0.0299459
$765$	4.61517	0.166862
$766$	−39.8674	−1.44047
$767$	−19.1673	−0.692090
$768$	−28.5685	−1.03088
$769$	−37.8018	−1.36317	−0.681584	−	0.731740i	$-0.738709\pi$
$769$	−37.8018	−1.36317	−0.681584	+	0.731740i	$0.738709\pi$
$770$	0	0
$771$	9.66653	0.348132
$772$	13.2689	0.477559
$773$	−17.3421	−0.623753	−0.311876	−	0.950123i	$-0.600958\pi$
$773$	−17.3421	−0.623753	−0.311876	+	0.950123i	$0.600958\pi$
$774$	9.05479	0.325468
$775$	49.3067	1.77115
$776$	26.2458	0.942169
$777$	−9.96922	−0.357644
$778$	−11.7159	−0.420035
$779$	−1.23460	−0.0442342
$780$	13.8521	0.495984
$781$	0	0
$782$	−11.4025	−0.407752
$783$	8.88440	0.317502
$784$	32.1144	1.14694
$785$	16.3357	0.583048
$786$	33.5150	1.19544
$787$	−22.0728	−0.786811	−0.393406	−	0.919365i	$-0.628703\pi$
$787$	−22.0728	−0.786811	−0.393406	+	0.919365i	$0.628703\pi$
$788$	13.3245	0.474666
$789$	16.8644	0.600388
$790$	39.5188	1.40602
$791$	3.24007	0.115204
$792$	0	0
$793$	37.6085	1.33552
$794$	−25.8978	−0.919079
$795$	47.0417	1.66840
$796$	−0.239244	−0.00847978
$797$	−18.9443	−0.671042	−0.335521	−	0.942033i	$-0.608912\pi$
$797$	−18.9443	−0.671042	−0.335521	+	0.942033i	$0.608912\pi$
$798$	2.75636	0.0975741
$799$	10.1311	0.358414
$800$	28.9506	1.02356
$801$	12.9098	0.456144
$802$	−7.78051	−0.274740
$803$	0	0
$804$	6.68932	0.235914
$805$	−16.2413	−0.572429
$806$	27.7102	0.976050
$807$	−15.6896	−0.552299
$808$	21.9596	0.772536
$809$	−44.2202	−1.55470	−0.777349	−	0.629069i	$-0.783436\pi$
$809$	−44.2202	−1.55470	−0.777349	+	0.629069i	$0.783436\pi$
$810$	66.4096	2.33340
$811$	8.00545	0.281109	0.140555	−	0.990073i	$-0.455111\pi$
$811$	8.00545	0.281109	0.140555	+	0.990073i	$0.455111\pi$
$812$	−0.991707	−0.0348021
$813$	−23.7473	−0.832853
$814$	0	0
$815$	−46.6419	−1.63379
$816$	10.0453	0.351654
$817$	5.75205	0.201239
$818$	24.8699	0.869556
$819$	2.31241	0.0808022
$820$	2.19696	0.0767211
$821$	44.8842	1.56647	0.783234	−	0.621727i	$-0.213568\pi$
$821$	44.8842	1.56647	0.783234	+	0.621727i	$0.213568\pi$
$822$	11.8649	0.413837
$823$	−22.3133	−0.777792	−0.388896	−	0.921282i	$-0.627143\pi$
$823$	−22.3133	−0.777792	−0.388896	+	0.921282i	$0.627143\pi$
$824$	42.0525	1.46497
$825$	0	0
$826$	6.78696	0.236149
$827$	−0.915606	−0.0318387	−0.0159194	−	0.999873i	$-0.505068\pi$
$827$	−0.915606	−0.0318387	−0.0159194	+	0.999873i	$0.505068\pi$
$828$	5.61815	0.195244
$829$	−14.1760	−0.492353	−0.246177	−	0.969225i	$-0.579174\pi$
$829$	−14.1760	−0.492353	−0.246177	+	0.969225i	$0.579174\pi$
$830$	−99.4314	−3.45131
$831$	−54.4884	−1.89018
$832$	−11.9253	−0.413436
$833$	−6.60029	−0.228687
$834$	−44.1459	−1.52865
$835$	46.0885	1.59496
$836$	0	0
$837$	21.1424	0.730789
$838$	20.7416	0.716506
$839$	−0.909594	−0.0314027	−0.0157013	−	0.999877i	$-0.504998\pi$
$839$	−0.909594	−0.0314027	−0.0157013	+	0.999877i	$0.504998\pi$
$840$	10.5829	0.365145
$841$	−22.8669	−0.788512
$842$	−17.2206	−0.593462
$843$	−53.0344	−1.82660
$844$	11.1382	0.383392
$845$	−16.8355	−0.579158
$846$	−20.7537	−0.713528
$847$	0	0
$848$	30.3241	1.04133
$849$	18.7283	0.642753
$850$	−13.5767	−0.465677
$851$	−53.6670	−1.83968
$852$	−4.37092	−0.149745
$853$	−5.47598	−0.187494	−0.0937471	−	0.995596i	$-0.529885\pi$
$853$	−5.47598	−0.187494	−0.0937471	+	0.995596i	$0.529885\pi$
$854$	−13.3168	−0.455693
$855$	−6.00579	−0.205394
$856$	−25.3280	−0.865694
$857$	−58.2602	−1.99013	−0.995066	−	0.0992194i	$-0.968365\pi$
$857$	−58.2602	−1.99013	−0.995066	+	0.0992194i	$0.968365\pi$
$858$	0	0
$859$	−27.2189	−0.928698	−0.464349	−	0.885652i	$-0.653712\pi$
$859$	−27.2189	−0.928698	−0.464349	+	0.885652i	$0.653712\pi$
$860$	−10.2357	−0.349034
$861$	1.23834	0.0422025
$862$	35.8947	1.22258
$863$	1.47222	0.0501150	0.0250575	−	0.999686i	$-0.492023\pi$
$863$	1.47222	0.0501150	0.0250575	+	0.999686i	$0.492023\pi$
$864$	12.4139	0.422329
$865$	14.8239	0.504028
$866$	−49.3033	−1.67539
$867$	−2.06455	−0.0701157
$868$	−2.35999	−0.0801033
$869$	0	0
$870$	30.3341	1.02842
$871$	14.8218	0.502217
$872$	−7.14156	−0.241844
$873$	14.9396	0.505628
$874$	14.8382	0.501911
$875$	−7.78107	−0.263048
$876$	6.97638	0.235710
$877$	−41.7321	−1.40919	−0.704597	−	0.709607i	$-0.748872\pi$
$877$	−41.7321	−1.40919	−0.704597	+	0.709607i	$0.748872\pi$
$878$	−26.9763	−0.910408
$879$	−12.8784	−0.434378
$880$	0	0
$881$	35.5985	1.19934	0.599672	−	0.800246i	$-0.295298\pi$
$881$	35.5985	1.19934	0.599672	+	0.800246i	$0.295298\pi$
$882$	13.5208	0.455268
$883$	47.0227	1.58244	0.791219	−	0.611533i	$-0.209447\pi$
$883$	47.0227	1.58244	0.791219	+	0.611533i	$0.209447\pi$
$884$	−1.83520	−0.0617245
$885$	−49.9319	−1.67844
$886$	49.9011	1.67646
$887$	20.0703	0.673893	0.336947	−	0.941524i	$-0.390606\pi$
$887$	20.0703	0.673893	0.336947	+	0.941524i	$0.390606\pi$
$888$	34.9698	1.17351
$889$	−8.89674	−0.298387
$890$	−60.6738	−2.03379
$891$	0	0
$892$	14.8189	0.496174
$893$	−13.1838	−0.441179
$894$	−69.1611	−2.31309
$895$	53.2768	1.78085
$896$	8.59809	0.287242
$897$	42.0320	1.40341
$898$	10.2950	0.343548
$899$	14.5952	0.486777
$900$	6.68942	0.222981
$901$	−6.23235	−0.207630
$902$	0	0
$903$	−5.76947	−0.191996
$904$	−11.3654	−0.378008
$905$	−35.7224	−1.18745
$906$	15.7969	0.524816
$907$	−5.79417	−0.192392	−0.0961960	−	0.995362i	$-0.530668\pi$
$907$	−5.79417	−0.192392	−0.0961960	+	0.995362i	$0.530668\pi$
$908$	−6.44346	−0.213834
$909$	12.4998	0.414592
$910$	−10.8680	−0.360270
$911$	−9.82129	−0.325394	−0.162697	−	0.986676i	$-0.552019\pi$
$911$	−9.82129	−0.325394	−0.162697	+	0.986676i	$0.552019\pi$
$912$	−13.0720	−0.432859
$913$	0	0
$914$	19.4194	0.642337
$915$	97.9724	3.23887
$916$	−1.86636	−0.0616662
$917$	−6.32453	−0.208854
$918$	−5.82162	−0.192142
$919$	−7.20472	−0.237662	−0.118831	−	0.992915i	$-0.537915\pi$
$919$	−7.20472	−0.237662	−0.118831	+	0.992915i	$0.537915\pi$
$920$	56.9706	1.87827
$921$	−17.4031	−0.573451
$922$	16.9910	0.559569
$923$	−9.68481	−0.318779
$924$	0	0
$925$	−63.9002	−2.10103
$926$	26.7269	0.878299
$927$	23.9370	0.786195
$928$	8.56964	0.281312
$929$	−13.3888	−0.439272	−0.219636	−	0.975582i	$-0.570487\pi$
$929$	−13.3888	−0.439272	−0.219636	+	0.975582i	$0.570487\pi$
$930$	72.1868	2.36710
$931$	8.58906	0.281495
$932$	14.9407	0.489400
$933$	70.1266	2.29584
$934$	−45.5494	−1.49042
$935$	0	0
$936$	−8.11141	−0.265130
$937$	28.5569	0.932912	0.466456	−	0.884544i	$-0.345531\pi$
$937$	28.5569	0.932912	0.466456	+	0.884544i	$0.345531\pi$
$938$	−5.24826	−0.171362
$939$	19.9807	0.652047
$940$	23.4604	0.765194
$941$	50.7571	1.65463	0.827317	−	0.561736i	$-0.189866\pi$
$941$	50.7571	1.65463	0.827317	+	0.561736i	$0.189866\pi$
$942$	14.9697	0.487741
$943$	6.66632	0.217085
$944$	−32.1872	−1.04760
$945$	−8.29209	−0.269742
$946$	0	0
$947$	2.64871	0.0860714	0.0430357	−	0.999074i	$-0.486297\pi$
$947$	2.64871	0.0860714	0.0430357	+	0.999074i	$0.486297\pi$
$948$	8.71033	0.282899
$949$	15.4578	0.501782
$950$	17.6676	0.573212
$951$	−52.8204	−1.71282
$952$	−1.40208	−0.0454417
$953$	−1.10453	−0.0357792	−0.0178896	−	0.999840i	$-0.505695\pi$
$953$	−1.10453	−0.0357792	−0.0178896	+	0.999840i	$0.505695\pi$
$954$	12.7670	0.413348
$955$	−4.77772	−0.154603
$956$	−1.09351	−0.0353667
$957$	0	0
$958$	−36.1528	−1.16804
$959$	−2.23900	−0.0723010
$960$	−31.0662	−1.00266
$961$	3.73260	0.120407
$962$	−35.9117	−1.15784
$963$	−14.4172	−0.464587
$964$	15.1673	0.488506
$965$	76.5900	2.46552
$966$	−14.8832	−0.478858
$967$	−30.0816	−0.967360	−0.483680	−	0.875245i	$-0.660700\pi$
$967$	−30.0816	−0.967360	−0.483680	+	0.875245i	$0.660700\pi$
$968$	0	0
$969$	2.68663	0.0863069
$970$	−70.2136	−2.25442
$971$	−32.6635	−1.04822	−0.524111	−	0.851650i	$-0.675602\pi$
$971$	−32.6635	−1.04822	−0.524111	+	0.851650i	$0.675602\pi$
$972$	7.82058	0.250845
$973$	8.33066	0.267069
$974$	−14.8099	−0.474540
$975$	50.0467	1.60278
$976$	63.1551	2.02155
$977$	−12.5841	−0.402600	−0.201300	−	0.979530i	$-0.564517\pi$
$977$	−12.5841	−0.402600	−0.201300	+	0.979530i	$0.564517\pi$
$978$	−42.7417	−1.36673
$979$	0	0
$980$	−15.2841	−0.488233
$981$	−4.06510	−0.129789
$982$	−53.8832	−1.71948
$983$	−27.7317	−0.884504	−0.442252	−	0.896891i	$-0.645820\pi$
$983$	−27.7317	−0.884504	−0.442252	+	0.896891i	$0.645820\pi$
$984$	−4.34381	−0.138476
$985$	76.9108	2.45058
$986$	−4.01883	−0.127985
$987$	13.2237	0.420916
$988$	2.38818	0.0759781
$989$	−31.0586	−0.987607
$990$	0	0
$991$	37.2665	1.18381	0.591905	−	0.806007i	$-0.298376\pi$
$991$	37.2665	1.18381	0.591905	+	0.806007i	$0.298376\pi$
$992$	20.3934	0.647491
$993$	3.08757	0.0979810
$994$	3.42931	0.108771
$995$	−1.38095	−0.0437790
$996$	−21.9157	−0.694424
$997$	−30.1142	−0.953727	−0.476864	−	0.878977i	$-0.658226\pi$
$997$	−30.1142	−0.953727	−0.476864	+	0.878977i	$0.658226\pi$
$998$	36.4241	1.15298
$999$	−27.4001	−0.866900

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2057.2.a.bd.1.6		18
11.5	even	5		187.2.g.f.69.7	✓	36
11.9	even	5		187.2.g.f.103.7	yes	36
11.10	odd	2		2057.2.a.be.1.13		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.f.69.7	✓	36	11.5	even	5
187.2.g.f.103.7	yes	36	11.9	even	5
2057.2.a.bd.1.6		18	1.1	even	1	trivial
2057.2.a.be.1.13		18	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:	\( N \)	\(=\)	\( 2057 = 11^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2057.a (trivial)

\(f(q)\)	\(=\)	\(q-1.62277 q^{2} -2.06455 q^{3} +0.633389 q^{4} +3.65600 q^{5} +3.35029 q^{6} -0.632224 q^{7} +2.21770 q^{8} +1.26235 q^{9} +O(q^{10})\)	\(q-1.62277 q^{2} -2.06455 q^{3} +0.633389 q^{4} +3.65600 q^{5} +3.35029 q^{6} -0.632224 q^{7} +2.21770 q^{8} +1.26235 q^{9} -5.93286 q^{10} -1.30766 q^{12} -2.89743 q^{13} +1.02596 q^{14} -7.54799 q^{15} -4.86560 q^{16} +1.00000 q^{17} -2.04851 q^{18} -1.30132 q^{19} +2.31567 q^{20} +1.30526 q^{21} +7.02655 q^{23} -4.57854 q^{24} +8.36637 q^{25} +4.70187 q^{26} +3.58745 q^{27} -0.400444 q^{28} +2.47652 q^{29} +12.2487 q^{30} +5.89344 q^{31} +3.46036 q^{32} -1.62277 q^{34} -2.31141 q^{35} +0.799560 q^{36} -7.63775 q^{37} +2.11174 q^{38} +5.98189 q^{39} +8.10791 q^{40} +0.948733 q^{41} -2.11813 q^{42} -4.42018 q^{43} +4.61517 q^{45} -11.4025 q^{46} +10.1311 q^{47} +10.0453 q^{48} -6.60029 q^{49} -13.5767 q^{50} -2.06455 q^{51} -1.83520 q^{52} -6.23235 q^{53} -5.82162 q^{54} -1.40208 q^{56} +2.68663 q^{57} -4.01883 q^{58} +6.61526 q^{59} -4.78082 q^{60} -12.9799 q^{61} -9.56371 q^{62} -0.798090 q^{63} +4.11582 q^{64} -10.5930 q^{65} -5.11549 q^{67} +0.633389 q^{68} -14.5066 q^{69} +3.75090 q^{70} +3.34255 q^{71} +2.79952 q^{72} -5.33501 q^{73} +12.3943 q^{74} -17.2728 q^{75} -0.824239 q^{76} -9.70724 q^{78} -6.66100 q^{79} -17.7886 q^{80} -11.1935 q^{81} -1.53958 q^{82} +16.7594 q^{83} +0.826735 q^{84} +3.65600 q^{85} +7.17295 q^{86} -5.11289 q^{87} +10.2267 q^{89} -7.48936 q^{90} +1.83183 q^{91} +4.45054 q^{92} -12.1673 q^{93} -16.4405 q^{94} -4.75762 q^{95} -7.14407 q^{96} +11.8347 q^{97} +10.7108 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 7 q^{3} + 28 q^{4} + 8 q^{5} + 3 q^{7} - 9 q^{8} + 29 q^{9}+O(q^{10}) \) 18 * q - 2 * q^2 + 7 * q^3 + 28 * q^4 + 8 * q^5 + 3 * q^7 - 9 * q^8 + 29 * q^9	\( 18 q - 2 q^{2} + 7 q^{3} + 28 q^{4} + 8 q^{5} + 3 q^{7} - 9 q^{8} + 29 q^{9} - 5 q^{10} + 14 q^{12} + q^{13} - 3 q^{14} + 38 q^{15} + 28 q^{16} + 18 q^{17} + 11 q^{18} - 10 q^{19} + 12 q^{20} - 25 q^{21} + 19 q^{23} + 9 q^{24} + 46 q^{25} - 20 q^{26} + 37 q^{27} - 2 q^{28} + 15 q^{29} - 31 q^{30} + 36 q^{31} - 20 q^{32} - 2 q^{34} - q^{35} + 60 q^{36} + 18 q^{37} + 28 q^{39} + 18 q^{40} - 9 q^{41} - 16 q^{42} - 4 q^{43} + 21 q^{45} + q^{46} + 45 q^{47} + 59 q^{48} + 19 q^{49} + 3 q^{50} + 7 q^{51} - 7 q^{52} - 6 q^{53} - 29 q^{54} - 14 q^{56} - 13 q^{57} + 69 q^{58} - 12 q^{59} + 46 q^{60} + 33 q^{61} + 8 q^{62} - 8 q^{63} + 21 q^{64} - 21 q^{65} + 27 q^{67} + 28 q^{68} + 12 q^{69} + 47 q^{70} + 10 q^{71} + 64 q^{72} + 9 q^{73} + 22 q^{74} - 5 q^{75} - 70 q^{76} - 24 q^{78} + 7 q^{79} + 8 q^{80} + 18 q^{81} - 6 q^{82} - 19 q^{83} + 47 q^{84} + 8 q^{85} - 25 q^{86} - 16 q^{87} + 6 q^{89} - 20 q^{90} + 3 q^{91} + 57 q^{92} + 5 q^{93} - 11 q^{94} + 22 q^{95} - 14 q^{96} + 38 q^{97} - 106 q^{98}+O(q^{100}) \) 18 * q - 2 * q^2 + 7 * q^3 + 28 * q^4 + 8 * q^5 + 3 * q^7 - 9 * q^8 + 29 * q^9 - 5 * q^10 + 14 * q^12 + q^13 - 3 * q^14 + 38 * q^15 + 28 * q^16 + 18 * q^17 + 11 * q^18 - 10 * q^19 + 12 * q^20 - 25 * q^21 + 19 * q^23 + 9 * q^24 + 46 * q^25 - 20 * q^26 + 37 * q^27 - 2 * q^28 + 15 * q^29 - 31 * q^30 + 36 * q^31 - 20 * q^32 - 2 * q^34 - q^35 + 60 * q^36 + 18 * q^37 + 28 * q^39 + 18 * q^40 - 9 * q^41 - 16 * q^42 - 4 * q^43 + 21 * q^45 + q^46 + 45 * q^47 + 59 * q^48 + 19 * q^49 + 3 * q^50 + 7 * q^51 - 7 * q^52 - 6 * q^53 - 29 * q^54 - 14 * q^56 - 13 * q^57 + 69 * q^58 - 12 * q^59 + 46 * q^60 + 33 * q^61 + 8 * q^62 - 8 * q^63 + 21 * q^64 - 21 * q^65 + 27 * q^67 + 28 * q^68 + 12 * q^69 + 47 * q^70 + 10 * q^71 + 64 * q^72 + 9 * q^73 + 22 * q^74 - 5 * q^75 - 70 * q^76 - 24 * q^78 + 7 * q^79 + 8 * q^80 + 18 * q^81 - 6 * q^82 - 19 * q^83 + 47 * q^84 + 8 * q^85 - 25 * q^86 - 16 * q^87 + 6 * q^89 - 20 * q^90 + 3 * q^91 + 57 * q^92 + 5 * q^93 - 11 * q^94 + 22 * q^95 - 14 * q^96 + 38 * q^97 - 106 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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