LMFDB - Embedded newform 5577.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5577, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5577.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$44.5325692073$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1019601.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 10x^{3} - x^{2} + 24x + 7 $ x^5 - 10x^3 - x^2 + 24x + 7
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 429)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.48141$ of defining polynomial
Character	$\chi$	$=$	5577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48141 q^{2} -1.00000 q^{3} +4.15740 q^{4} -1.71458 q^{5} +2.48141 q^{6} +2.09718 q^{7} -5.35339 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.48141 q^{2} -1.00000 q^{3} +4.15740 q^{4} -1.71458 q^{5} +2.48141 q^{6} +2.09718 q^{7} -5.35339 q^{8} +1.00000 q^{9} +4.25457 q^{10} +1.00000 q^{11} -4.15740 q^{12} -5.20396 q^{14} +1.71458 q^{15} +4.96915 q^{16} -8.12818 q^{17} -2.48141 q^{18} +4.57859 q^{19} -7.12818 q^{20} -2.09718 q^{21} -2.48141 q^{22} -6.60796 q^{23} +5.35339 q^{24} -2.06022 q^{25} -1.00000 q^{27} +8.71880 q^{28} -7.27598 q^{29} -4.25457 q^{30} -9.14162 q^{31} -1.62373 q^{32} -1.00000 q^{33} +20.1694 q^{34} -3.59577 q^{35} +4.15740 q^{36} +3.29339 q^{37} -11.3614 q^{38} +9.17880 q^{40} -3.87198 q^{41} +5.20396 q^{42} -1.30683 q^{43} +4.15740 q^{44} -1.71458 q^{45} +16.3971 q^{46} +6.30683 q^{47} -4.96915 q^{48} -2.60185 q^{49} +5.11225 q^{50} +8.12818 q^{51} +13.5637 q^{53} +2.48141 q^{54} -1.71458 q^{55} -11.2270 q^{56} -4.57859 q^{57} +18.0547 q^{58} -5.22309 q^{59} +7.12818 q^{60} -5.13577 q^{61} +22.6841 q^{62} +2.09718 q^{63} -5.90915 q^{64} +2.48141 q^{66} +2.71621 q^{67} -33.7921 q^{68} +6.60796 q^{69} +8.92259 q^{70} -6.59289 q^{71} -5.35339 q^{72} +8.00164 q^{73} -8.17225 q^{74} +2.06022 q^{75} +19.0350 q^{76} +2.09718 q^{77} +2.75886 q^{79} -8.52000 q^{80} +1.00000 q^{81} +9.60796 q^{82} +1.20254 q^{83} -8.71880 q^{84} +13.9364 q^{85} +3.24277 q^{86} +7.27598 q^{87} -5.35339 q^{88} -0.162093 q^{89} +4.25457 q^{90} -27.4719 q^{92} +9.14162 q^{93} -15.6498 q^{94} -7.85035 q^{95} +1.62373 q^{96} -12.0081 q^{97} +6.45626 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^7 + 3 * q^8 + 5 * q^9	$ 5 q - 5 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{7} + 3 q^{8} + 5 q^{9} + 7 q^{10} + 5 q^{11} - 10 q^{12} + q^{14} + 2 q^{15} + 4 q^{16} + 3 q^{17} + 7 q^{19} + 8 q^{20} - 7 q^{21} + 11 q^{23} - 3 q^{24} - 3 q^{25} - 5 q^{27} + 5 q^{28} - 2 q^{29} - 7 q^{30} + 10 q^{31} - 9 q^{32} - 5 q^{33} + 29 q^{34} - 14 q^{35} + 10 q^{36} + 15 q^{37} - 19 q^{38} + 15 q^{40} - 2 q^{41} - q^{42} + 7 q^{43} + 10 q^{44} - 2 q^{45} + 20 q^{46} + 18 q^{47} - 4 q^{48} + 14 q^{49} - 2 q^{50} - 3 q^{51} + 15 q^{53} - 2 q^{55} + 3 q^{56} - 7 q^{57} + 5 q^{58} - 4 q^{59} - 8 q^{60} - 14 q^{61} + 46 q^{62} + 7 q^{63} - 37 q^{64} - 5 q^{67} - 24 q^{68} - 11 q^{69} + 40 q^{70} - 13 q^{71} + 3 q^{72} + 28 q^{73} + 15 q^{74} + 3 q^{75} + 2 q^{76} + 7 q^{77} + 16 q^{79} - 22 q^{80} + 5 q^{81} + 4 q^{82} + 12 q^{83} - 5 q^{84} + 13 q^{85} + 2 q^{86} + 2 q^{87} + 3 q^{88} - 6 q^{89} + 7 q^{90} - 2 q^{92} - 10 q^{93} - 2 q^{94} - 21 q^{95} + 9 q^{96} + 9 q^{97} + 16 q^{98} + 5 q^{99}+O(q^{100}) $ 5 * q - 5 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^7 + 3 * q^8 + 5 * q^9 + 7 * q^10 + 5 * q^11 - 10 * q^12 + q^14 + 2 * q^15 + 4 * q^16 + 3 * q^17 + 7 * q^19 + 8 * q^20 - 7 * q^21 + 11 * q^23 - 3 * q^24 - 3 * q^25 - 5 * q^27 + 5 * q^28 - 2 * q^29 - 7 * q^30 + 10 * q^31 - 9 * q^32 - 5 * q^33 + 29 * q^34 - 14 * q^35 + 10 * q^36 + 15 * q^37 - 19 * q^38 + 15 * q^40 - 2 * q^41 - q^42 + 7 * q^43 + 10 * q^44 - 2 * q^45 + 20 * q^46 + 18 * q^47 - 4 * q^48 + 14 * q^49 - 2 * q^50 - 3 * q^51 + 15 * q^53 - 2 * q^55 + 3 * q^56 - 7 * q^57 + 5 * q^58 - 4 * q^59 - 8 * q^60 - 14 * q^61 + 46 * q^62 + 7 * q^63 - 37 * q^64 - 5 * q^67 - 24 * q^68 - 11 * q^69 + 40 * q^70 - 13 * q^71 + 3 * q^72 + 28 * q^73 + 15 * q^74 + 3 * q^75 + 2 * q^76 + 7 * q^77 + 16 * q^79 - 22 * q^80 + 5 * q^81 + 4 * q^82 + 12 * q^83 - 5 * q^84 + 13 * q^85 + 2 * q^86 + 2 * q^87 + 3 * q^88 - 6 * q^89 + 7 * q^90 - 2 * q^92 - 10 * q^93 - 2 * q^94 - 21 * q^95 + 9 * q^96 + 9 * q^97 + 16 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.48141	−1.75462	−0.877311	−	0.479922i	$-0.840665\pi$
$2$	−2.48141	−1.75462	−0.877311	+	0.479922i	$0.840665\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.15740	2.07870
$5$	−1.71458	−0.766783	−0.383391	−	0.923586i	$-0.625244\pi$
$5$	−1.71458	−0.766783	−0.383391	+	0.923586i	$0.625244\pi$
$6$	2.48141	1.01303
$7$	2.09718	0.792658	0.396329	−	0.918108i	$-0.370284\pi$
$7$	2.09718	0.792658	0.396329	+	0.918108i	$0.370284\pi$
$8$	−5.35339	−1.89271
$9$	1.00000	0.333333
$10$	4.25457	1.34541
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.15740	−1.20014
$13$	0	0
$13$	0	0
$14$	−5.20396	−1.39082
$15$	1.71458	0.442702
$16$	4.96915	1.24229
$17$	−8.12818	−1.97137	−0.985687	−	0.168585i	$-0.946080\pi$
$17$	−8.12818	−1.97137	−0.985687	+	0.168585i	$0.946080\pi$
$18$	−2.48141	−0.584874
$19$	4.57859	1.05040	0.525200	−	0.850979i	$-0.323991\pi$
$19$	4.57859	1.05040	0.525200	+	0.850979i	$0.323991\pi$
$20$	−7.12818	−1.59391
$21$	−2.09718	−0.457642
$22$	−2.48141	−0.529038
$23$	−6.60796	−1.37785	−0.688927	−	0.724830i	$-0.741918\pi$
$23$	−6.60796	−1.37785	−0.688927	+	0.724830i	$0.741918\pi$
$24$	5.35339	1.09276
$25$	−2.06022	−0.412044
$26$	0	0
$27$	−1.00000	−0.192450
$28$	8.71880	1.64770
$29$	−7.27598	−1.35112	−0.675558	−	0.737307i	$-0.736097\pi$
$29$	−7.27598	−1.35112	−0.675558	+	0.737307i	$0.736097\pi$
$30$	−4.25457	−0.776775
$31$	−9.14162	−1.64188	−0.820942	−	0.571012i	$-0.806551\pi$
$31$	−9.14162	−1.64188	−0.820942	+	0.571012i	$0.806551\pi$
$32$	−1.62373	−0.287038
$33$	−1.00000	−0.174078
$34$	20.1694	3.45902
$35$	−3.59577	−0.607797
$36$	4.15740	0.692899
$37$	3.29339	0.541430	0.270715	−	0.962660i	$-0.412740\pi$
$37$	3.29339	0.541430	0.270715	+	0.962660i	$0.412740\pi$
$38$	−11.3614	−1.84305
$39$	0	0
$40$	9.17880	1.45130
$41$	−3.87198	−0.604701	−0.302350	−	0.953197i	$-0.597771\pi$
$41$	−3.87198	−0.604701	−0.302350	+	0.953197i	$0.597771\pi$
$42$	5.20396	0.802988
$43$	−1.30683	−0.199289	−0.0996445	−	0.995023i	$-0.531771\pi$
$43$	−1.30683	−0.199289	−0.0996445	+	0.995023i	$0.531771\pi$
$44$	4.15740	0.626751
$45$	−1.71458	−0.255594
$46$	16.3971	2.41761
$47$	6.30683	0.919945	0.459973	−	0.887933i	$-0.347859\pi$
$47$	6.30683	0.919945	0.459973	+	0.887933i	$0.347859\pi$
$48$	−4.96915	−0.717235
$49$	−2.60185	−0.371693
$50$	5.11225	0.722981
$51$	8.12818	1.13817
$52$	0	0
$53$	13.5637	1.86311	0.931557	−	0.363596i	$-0.118451\pi$
$53$	13.5637	1.86311	0.931557	+	0.363596i	$0.118451\pi$
$54$	2.48141	0.337677
$55$	−1.71458	−0.231194
$56$	−11.2270	−1.50027
$57$	−4.57859	−0.606449
$58$	18.0547	2.37070
$59$	−5.22309	−0.679988	−0.339994	−	0.940428i	$-0.610425\pi$
$59$	−5.22309	−0.679988	−0.339994	+	0.940428i	$0.610425\pi$
$60$	7.12818	0.920245
$61$	−5.13577	−0.657568	−0.328784	−	0.944405i	$-0.606639\pi$
$61$	−5.13577	−0.657568	−0.328784	+	0.944405i	$0.606639\pi$
$62$	22.6841	2.88089
$63$	2.09718	0.264219
$64$	−5.90915	−0.738644
$65$	0	0
$66$	2.48141	0.305440
$67$	2.71621	0.331838	0.165919	−	0.986139i	$-0.446941\pi$
$67$	2.71621	0.331838	0.165919	+	0.986139i	$0.446941\pi$
$68$	−33.7921	−4.09789
$69$	6.60796	0.795505
$70$	8.92259	1.06645
$71$	−6.59289	−0.782432	−0.391216	−	0.920299i	$-0.627945\pi$
$71$	−6.59289	−0.782432	−0.391216	+	0.920299i	$0.627945\pi$
$72$	−5.35339	−0.630903
$73$	8.00164	0.936521	0.468260	−	0.883591i	$-0.344881\pi$
$73$	8.00164	0.936521	0.468260	+	0.883591i	$0.344881\pi$
$74$	−8.17225	−0.950004
$75$	2.06022	0.237894
$76$	19.0350	2.18346
$77$	2.09718	0.238995
$78$	0	0
$79$	2.75886	0.310396	0.155198	−	0.987883i	$-0.450398\pi$
$79$	2.75886	0.310396	0.155198	+	0.987883i	$0.450398\pi$
$80$	−8.52000	−0.952565
$81$	1.00000	0.111111
$82$	9.60796	1.06102
$83$	1.20254	0.131996	0.0659981	−	0.997820i	$-0.478977\pi$
$83$	1.20254	0.131996	0.0659981	+	0.997820i	$0.478977\pi$
$84$	−8.71880	−0.951299
$85$	13.9364	1.51162
$86$	3.24277	0.349677
$87$	7.27598	0.780067
$88$	−5.35339	−0.570673
$89$	−0.162093	−0.0171818	−0.00859090	−	0.999963i	$-0.502735\pi$
$89$	−0.162093	−0.0171818	−0.00859090	+	0.999963i	$0.502735\pi$
$90$	4.25457	0.448471
$91$	0	0
$92$	−27.4719	−2.86414
$93$	9.14162	0.947942
$94$	−15.6498	−1.61416
$95$	−7.85035	−0.805429
$96$	1.62373	0.165722
$97$	−12.0081	−1.21924	−0.609620	−	0.792694i	$-0.708678\pi$
$97$	−12.0081	−1.21924	−0.609620	+	0.792694i	$0.708678\pi$
$98$	6.45626	0.652180
$99$	1.00000	0.100504
$100$	−8.56515	−0.856515
$101$	12.9670	1.29027	0.645134	−	0.764069i	$-0.276801\pi$
$101$	12.9670	1.29027	0.645134	+	0.764069i	$0.276801\pi$
$102$	−20.1694	−1.99706
$103$	−4.89993	−0.482805	−0.241402	−	0.970425i	$-0.577607\pi$
$103$	−4.89993	−0.482805	−0.241402	+	0.970425i	$0.577607\pi$
$104$	0	0
$105$	3.59577	0.350912
$106$	−33.6570	−3.26906
$107$	17.0107	1.64449	0.822244	−	0.569136i	$-0.192722\pi$
$107$	17.0107	1.64449	0.822244	+	0.569136i	$0.192722\pi$
$108$	−4.15740	−0.400046
$109$	−5.95485	−0.570372	−0.285186	−	0.958472i	$-0.592055\pi$
$109$	−5.95485	−0.570372	−0.285186	+	0.958472i	$0.592055\pi$
$110$	4.25457	0.405658
$111$	−3.29339	−0.312595
$112$	10.4212	0.984710
$113$	12.2811	1.15530	0.577652	−	0.816283i	$-0.303969\pi$
$113$	12.2811	1.15530	0.577652	+	0.816283i	$0.303969\pi$
$114$	11.3614	1.06409
$115$	11.3299	1.05652
$116$	−30.2491	−2.80856
$117$	0	0
$118$	12.9606	1.19312
$119$	−17.0462	−1.56263
$120$	−9.17880	−0.837906
$121$	1.00000	0.0909091
$122$	12.7440	1.15378
$123$	3.87198	0.349124
$124$	−38.0053	−3.41298
$125$	12.1053	1.08273
$126$	−5.20396	−0.463605
$127$	−5.48000	−0.486271	−0.243136	−	0.969992i	$-0.578176\pi$
$127$	−5.48000	−0.486271	−0.243136	+	0.969992i	$0.578176\pi$
$128$	17.9105	1.58308
$129$	1.30683	0.115060
$130$	0	0
$131$	−11.7454	−1.02620	−0.513099	−	0.858330i	$-0.671502\pi$
$131$	−11.7454	−1.02620	−0.513099	+	0.858330i	$0.671502\pi$
$132$	−4.15740	−0.361855
$133$	9.60211	0.832608
$134$	−6.74004	−0.582251
$135$	1.71458	0.147567
$136$	43.5133	3.73123
$137$	−4.49993	−0.384455	−0.192227	−	0.981350i	$-0.561571\pi$
$137$	−4.49993	−0.384455	−0.192227	+	0.981350i	$0.561571\pi$
$138$	−16.3971	−1.39581
$139$	−2.18191	−0.185067	−0.0925337	−	0.995710i	$-0.529497\pi$
$139$	−2.18191	−0.185067	−0.0925337	+	0.995710i	$0.529497\pi$
$140$	−14.9491	−1.26343
$141$	−6.30683	−0.531131
$142$	16.3597	1.37287
$143$	0	0
$144$	4.96915	0.414096
$145$	12.4752	1.03601
$146$	−19.8553	−1.64324
$147$	2.60185	0.214597
$148$	13.6919	1.12547
$149$	−0.681457	−0.0558271	−0.0279136	−	0.999610i	$-0.508886\pi$
$149$	−0.681457	−0.0558271	−0.0279136	+	0.999610i	$0.508886\pi$
$150$	−5.11225	−0.417413
$151$	−6.17333	−0.502379	−0.251189	−	0.967938i	$-0.580822\pi$
$151$	−6.17333	−0.502379	−0.251189	+	0.967938i	$0.580822\pi$
$152$	−24.5109	−1.98810
$153$	−8.12818	−0.657125
$154$	−5.20396	−0.419347
$155$	15.6740	1.25897
$156$	0	0
$157$	17.5114	1.39756	0.698782	−	0.715335i	$-0.253726\pi$
$157$	17.5114	1.39756	0.698782	+	0.715335i	$0.253726\pi$
$158$	−6.84587	−0.544629
$159$	−13.5637	−1.07567
$160$	2.78402	0.220096
$161$	−13.8581	−1.09217
$162$	−2.48141	−0.194958
$163$	16.3550	1.28102	0.640512	−	0.767948i	$-0.278722\pi$
$163$	16.3550	1.28102	0.640512	+	0.767948i	$0.278722\pi$
$164$	−16.0973	−1.25699
$165$	1.71458	0.133480
$166$	−2.98400	−0.231604
$167$	−11.7305	−0.907734	−0.453867	−	0.891069i	$-0.649956\pi$
$167$	−11.7305	−0.907734	−0.453867	+	0.891069i	$0.649956\pi$
$168$	11.2270	0.866182
$169$	0	0
$170$	−34.5820	−2.65231
$171$	4.57859	0.350133
$172$	−5.43299	−0.414262
$173$	−3.41056	−0.259300	−0.129650	−	0.991560i	$-0.541385\pi$
$173$	−3.41056	−0.259300	−0.129650	+	0.991560i	$0.541385\pi$
$174$	−18.0547	−1.36872
$175$	−4.32064	−0.326610
$176$	4.96915	0.374564
$177$	5.22309	0.392591
$178$	0.402219	0.0301476
$179$	−0.647031	−0.0483614	−0.0241807	−	0.999708i	$-0.507698\pi$
$179$	−0.647031	−0.0483614	−0.0241807	+	0.999708i	$0.507698\pi$
$180$	−7.12818	−0.531303
$181$	5.81214	0.432013	0.216006	−	0.976392i	$-0.430697\pi$
$181$	5.81214	0.432013	0.216006	+	0.976392i	$0.430697\pi$
$182$	0	0
$183$	5.13577	0.379647
$184$	35.3749	2.60788
$185$	−5.64677	−0.415159
$186$	−22.6841	−1.66328
$187$	−8.12818	−0.594392
$188$	26.2200	1.91229
$189$	−2.09718	−0.152547
$190$	19.4799	1.41322
$191$	−20.1781	−1.46004	−0.730018	−	0.683428i	$-0.760488\pi$
$191$	−20.1781	−1.46004	−0.730018	+	0.683428i	$0.760488\pi$
$192$	5.90915	0.426457
$193$	6.09007	0.438373	0.219186	−	0.975683i	$-0.429660\pi$
$193$	6.09007	0.438373	0.219186	+	0.975683i	$0.429660\pi$
$194$	29.7971	2.13931
$195$	0	0
$196$	−10.8169	−0.772637
$197$	20.0594	1.42917	0.714586	−	0.699548i	$-0.246615\pi$
$197$	20.0594	1.42917	0.714586	+	0.699548i	$0.246615\pi$
$198$	−2.48141	−0.176346
$199$	−0.361130	−0.0255998	−0.0127999	−	0.999918i	$-0.504074\pi$
$199$	−0.361130	−0.0255998	−0.0127999	+	0.999918i	$0.504074\pi$
$200$	11.0291	0.779879
$201$	−2.71621	−0.191587
$202$	−32.1765	−2.26393
$203$	−15.2590	−1.07097
$204$	33.7921	2.36592
$205$	6.63881	0.463674
$206$	12.1587	0.847140
$207$	−6.60796	−0.459285
$208$	0	0
$209$	4.57859	0.316707
$210$	−8.92259	−0.615717
$211$	−7.03937	−0.484610	−0.242305	−	0.970200i	$-0.577903\pi$
$211$	−7.03937	−0.484610	−0.242305	+	0.970200i	$0.577903\pi$
$212$	56.3896	3.87285
$213$	6.59289	0.451737
$214$	−42.2105	−2.88545
$215$	2.24066	0.152811
$216$	5.35339	0.364252
$217$	−19.1716	−1.30145
$218$	14.7764	1.00079
$219$	−8.00164	−0.540700
$220$	−7.12818	−0.480582
$221$	0	0
$222$	8.17225	0.548485
$223$	23.4591	1.57094	0.785468	−	0.618902i	$-0.212422\pi$
$223$	23.4591	1.57094	0.785468	+	0.618902i	$0.212422\pi$
$224$	−3.40526	−0.227523
$225$	−2.06022	−0.137348
$226$	−30.4743	−2.02712
$227$	17.7437	1.17769	0.588845	−	0.808246i	$-0.299583\pi$
$227$	17.7437	1.17769	0.588845	+	0.808246i	$0.299583\pi$
$228$	−19.0350	−1.26062
$229$	−10.7707	−0.711751	−0.355875	−	0.934533i	$-0.615817\pi$
$229$	−10.7707	−0.711751	−0.355875	+	0.934533i	$0.615817\pi$
$230$	−28.1140	−1.85379
$231$	−2.09718	−0.137984
$232$	38.9511	2.55727
$233$	−20.3286	−1.33177	−0.665887	−	0.746053i	$-0.731947\pi$
$233$	−20.3286	−1.33177	−0.665887	+	0.746053i	$0.731947\pi$
$234$	0	0
$235$	−10.8135	−0.705398
$236$	−21.7144	−1.41349
$237$	−2.75886	−0.179207
$238$	42.2987	2.74182
$239$	11.6449	0.753247	0.376623	−	0.926366i	$-0.377085\pi$
$239$	11.6449	0.753247	0.376623	+	0.926366i	$0.377085\pi$
$240$	8.52000	0.549964
$241$	3.56615	0.229716	0.114858	−	0.993382i	$-0.463359\pi$
$241$	3.56615	0.229716	0.114858	+	0.993382i	$0.463359\pi$
$242$	−2.48141	−0.159511
$243$	−1.00000	−0.0641500
$244$	−21.3514	−1.36689
$245$	4.46108	0.285008
$246$	−9.60796	−0.612581
$247$	0	0
$248$	48.9386	3.10761
$249$	−1.20254	−0.0762081
$250$	−30.0382	−1.89978
$251$	−11.1818	−0.705792	−0.352896	−	0.935663i	$-0.614803\pi$
$251$	−11.1818	−0.705792	−0.352896	+	0.935663i	$0.614803\pi$
$252$	8.71880	0.549232
$253$	−6.60796	−0.415439
$254$	13.5981	0.853222
$255$	−13.9364	−0.872732
$256$	−32.6250	−2.03906
$257$	9.95627	0.621055	0.310527	−	0.950564i	$-0.399494\pi$
$257$	9.95627	0.621055	0.310527	+	0.950564i	$0.399494\pi$
$258$	−3.24277	−0.201886
$259$	6.90682	0.429169
$260$	0	0
$261$	−7.27598	−0.450372
$262$	29.1451	1.80059
$263$	−14.1421	−0.872039	−0.436020	−	0.899937i	$-0.643612\pi$
$263$	−14.1421	−0.872039	−0.436020	+	0.899937i	$0.643612\pi$
$264$	5.35339	0.329478
$265$	−23.2560	−1.42860
$266$	−23.8268	−1.46091
$267$	0.162093	0.00991992
$268$	11.2924	0.689792
$269$	−27.0016	−1.64631	−0.823157	−	0.567813i	$-0.807790\pi$
$269$	−27.0016	−1.64631	−0.823157	+	0.567813i	$0.807790\pi$
$270$	−4.25457	−0.258925
$271$	−9.74003	−0.591665	−0.295832	−	0.955240i	$-0.595597\pi$
$271$	−9.74003	−0.591665	−0.295832	+	0.955240i	$0.595597\pi$
$272$	−40.3902	−2.44901
$273$	0	0
$274$	11.1662	0.674572
$275$	−2.06022	−0.124236
$276$	27.4719	1.65361
$277$	32.8308	1.97261	0.986306	−	0.164923i	$-0.0527375\pi$
$277$	32.8308	1.97261	0.986306	+	0.164923i	$0.0527375\pi$
$278$	5.41422	0.324723
$279$	−9.14162	−0.547295
$280$	19.2496	1.15038
$281$	−13.6637	−0.815108	−0.407554	−	0.913181i	$-0.633618\pi$
$281$	−13.6637	−0.815108	−0.407554	+	0.913181i	$0.633618\pi$
$282$	15.6498	0.931933
$283$	−21.4777	−1.27671	−0.638357	−	0.769740i	$-0.720386\pi$
$283$	−21.4777	−1.27671	−0.638357	+	0.769740i	$0.720386\pi$
$284$	−27.4092	−1.62644
$285$	7.85035	0.465014
$286$	0	0
$287$	−8.12022	−0.479321
$288$	−1.62373	−0.0956794
$289$	49.0674	2.88632
$290$	−30.9562	−1.81781
$291$	12.0081	0.703929
$292$	33.2660	1.94674
$293$	20.4329	1.19370	0.596852	−	0.802351i	$-0.296418\pi$
$293$	20.4329	1.19370	0.596852	+	0.802351i	$0.296418\pi$
$294$	−6.45626	−0.376536
$295$	8.95539	0.521403
$296$	−17.6308	−1.02477
$297$	−1.00000	−0.0580259
$298$	1.69097	0.0979555
$299$	0	0
$300$	8.56515	0.494509
$301$	−2.74064	−0.157968
$302$	15.3186	0.881484
$303$	−12.9670	−0.744937
$304$	22.7517	1.30490
$305$	8.80568	0.504212
$306$	20.1694	1.15301
$307$	−9.82605	−0.560803	−0.280401	−	0.959883i	$-0.590468\pi$
$307$	−9.82605	−0.560803	−0.280401	+	0.959883i	$0.590468\pi$
$308$	8.71880	0.496799
$309$	4.89993	0.278748
$310$	−38.8937	−2.20901
$311$	29.7164	1.68506	0.842530	−	0.538649i	$-0.181065\pi$
$311$	29.7164	1.68506	0.842530	+	0.538649i	$0.181065\pi$
$312$	0	0
$313$	20.6042	1.16462	0.582309	−	0.812967i	$-0.302149\pi$
$313$	20.6042	1.16462	0.582309	+	0.812967i	$0.302149\pi$
$314$	−43.4530	−2.45220
$315$	−3.59577	−0.202599
$316$	11.4697	0.645221
$317$	−20.2447	−1.13705	−0.568527	−	0.822664i	$-0.692487\pi$
$317$	−20.2447	−1.13705	−0.568527	+	0.822664i	$0.692487\pi$
$318$	33.6570	1.88739
$319$	−7.27598	−0.407377
$320$	10.1317	0.566380
$321$	−17.0107	−0.949445
$322$	34.3875	1.91634
$323$	−37.2156	−2.07073
$324$	4.15740	0.230966
$325$	0	0
$326$	−40.5835	−2.24771
$327$	5.95485	0.329304
$328$	20.7282	1.14452
$329$	13.2265	0.729202
$330$	−4.25457	−0.234207
$331$	27.9741	1.53759	0.768797	−	0.639493i	$-0.220856\pi$
$331$	27.9741	1.53759	0.768797	+	0.639493i	$0.220856\pi$
$332$	4.99945	0.274380
$333$	3.29339	0.180477
$334$	29.1082	1.59273
$335$	−4.65716	−0.254448
$336$	−10.4212	−0.568523
$337$	−17.6006	−0.958764	−0.479382	−	0.877606i	$-0.659139\pi$
$337$	−17.6006	−0.958764	−0.479382	+	0.877606i	$0.659139\pi$
$338$	0	0
$339$	−12.2811	−0.667015
$340$	57.9392	3.14219
$341$	−9.14162	−0.495047
$342$	−11.3614	−0.614352
$343$	−20.1368	−1.08728
$344$	6.99594	0.377196
$345$	−11.3299	−0.609979
$346$	8.46299	0.454973
$347$	−18.6292	−1.00007	−0.500034	−	0.866006i	$-0.666679\pi$
$347$	−18.6292	−1.00007	−0.500034	+	0.866006i	$0.666679\pi$
$348$	30.2491	1.62152
$349$	−0.618348	−0.0330994	−0.0165497	−	0.999863i	$-0.505268\pi$
$349$	−0.618348	−0.0330994	−0.0165497	+	0.999863i	$0.505268\pi$
$350$	10.7213	0.573077
$351$	0	0
$352$	−1.62373	−0.0865453
$353$	5.89565	0.313794	0.156897	−	0.987615i	$-0.449851\pi$
$353$	5.89565	0.313794	0.156897	+	0.987615i	$0.449851\pi$
$354$	−12.9606	−0.688849
$355$	11.3040	0.599955
$356$	−0.673884	−0.0357158
$357$	17.0462	0.902183
$358$	1.60555	0.0848559
$359$	27.1425	1.43253	0.716263	−	0.697831i	$-0.245851\pi$
$359$	27.1425	1.43253	0.716263	+	0.697831i	$0.245851\pi$
$360$	9.17880	0.483765
$361$	1.96346	0.103340
$362$	−14.4223	−0.758019
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	−13.7194	−0.718108
$366$	−12.7440	−0.666137
$367$	−22.3469	−1.16650	−0.583248	−	0.812294i	$-0.698218\pi$
$367$	−22.3469	−1.16650	−0.583248	+	0.812294i	$0.698218\pi$
$368$	−32.8360	−1.71169
$369$	−3.87198	−0.201567
$370$	14.0120	0.728447
$371$	28.4454	1.47681
$372$	38.0053	1.97049
$373$	−11.8585	−0.614012	−0.307006	−	0.951708i	$-0.599327\pi$
$373$	−11.8585	−0.614012	−0.307006	+	0.951708i	$0.599327\pi$
$374$	20.1694	1.04293
$375$	−12.1053	−0.625115
$376$	−33.7629	−1.74119
$377$	0	0
$378$	5.20396	0.267663
$379$	19.5647	1.00497	0.502485	−	0.864586i	$-0.332419\pi$
$379$	19.5647	1.00497	0.502485	+	0.864586i	$0.332419\pi$
$380$	−32.6370	−1.67424
$381$	5.48000	0.280749
$382$	50.0701	2.56181
$383$	3.79004	0.193662	0.0968311	−	0.995301i	$-0.469129\pi$
$383$	3.79004	0.193662	0.0968311	+	0.995301i	$0.469129\pi$
$384$	−17.9105	−0.913992
$385$	−3.59577	−0.183258
$386$	−15.1120	−0.769179
$387$	−1.30683	−0.0664297
$388$	−49.9225	−2.53443
$389$	7.37888	0.374124	0.187062	−	0.982348i	$-0.440103\pi$
$389$	7.37888	0.374124	0.187062	+	0.982348i	$0.440103\pi$
$390$	0	0
$391$	53.7107	2.71627
$392$	13.9287	0.703506
$393$	11.7454	0.592475
$394$	−49.7756	−2.50766
$395$	−4.73029	−0.238007
$396$	4.15740	0.208917
$397$	−10.1461	−0.509221	−0.254610	−	0.967044i	$-0.581947\pi$
$397$	−10.1461	−0.509221	−0.254610	+	0.967044i	$0.581947\pi$
$398$	0.896112	0.0449180
$399$	−9.60211	−0.480707
$400$	−10.2375	−0.511877
$401$	9.75217	0.487000	0.243500	−	0.969901i	$-0.421704\pi$
$401$	9.75217	0.487000	0.243500	+	0.969901i	$0.421704\pi$
$402$	6.74004	0.336163
$403$	0	0
$404$	53.9091	2.68208
$405$	−1.71458	−0.0851981
$406$	37.8639	1.87915
$407$	3.29339	0.163247
$408$	−43.5133	−2.15423
$409$	20.5039	1.01385	0.506927	−	0.861989i	$-0.330781\pi$
$409$	20.5039	1.01385	0.506927	+	0.861989i	$0.330781\pi$
$410$	−16.4736	−0.813573
$411$	4.49993	0.221965
$412$	−20.3710	−1.00361
$413$	−10.9537	−0.538998
$414$	16.3971	0.805871
$415$	−2.06185	−0.101212
$416$	0	0
$417$	2.18191	0.106849
$418$	−11.3614	−0.555702
$419$	31.8533	1.55614	0.778068	−	0.628180i	$-0.216200\pi$
$419$	31.8533	1.55614	0.778068	+	0.628180i	$0.216200\pi$
$420$	14.9491	0.729440
$421$	19.0756	0.929690	0.464845	−	0.885392i	$-0.346110\pi$
$421$	19.0756	0.929690	0.464845	+	0.885392i	$0.346110\pi$
$422$	17.4676	0.850307
$423$	6.30683	0.306648
$424$	−72.6116	−3.52633
$425$	16.7458	0.812293
$426$	−16.3597	−0.792628
$427$	−10.7706	−0.521227
$428$	70.7203	3.41839
$429$	0	0
$430$	−5.55999	−0.268126
$431$	2.21982	0.106925	0.0534624	−	0.998570i	$-0.482974\pi$
$431$	2.21982	0.106925	0.0534624	+	0.998570i	$0.482974\pi$
$432$	−4.96915	−0.239078
$433$	−15.9607	−0.767024	−0.383512	−	0.923536i	$-0.625286\pi$
$433$	−15.9607	−0.767024	−0.383512	+	0.923536i	$0.625286\pi$
$434$	47.5726	2.28356
$435$	−12.4752	−0.598142
$436$	−24.7567	−1.18563
$437$	−30.2551	−1.44730
$438$	19.8553	0.948725
$439$	−16.0428	−0.765682	−0.382841	−	0.923814i	$-0.625054\pi$
$439$	−16.0428	−0.765682	−0.382841	+	0.923814i	$0.625054\pi$
$440$	9.17880	0.437582
$441$	−2.60185	−0.123898
$442$	0	0
$443$	−30.1760	−1.43371	−0.716853	−	0.697225i	$-0.754418\pi$
$443$	−30.1760	−1.43371	−0.716853	+	0.697225i	$0.754418\pi$
$444$	−13.6919	−0.649790
$445$	0.277921	0.0131747
$446$	−58.2116	−2.75640
$447$	0.681457	0.0322318
$448$	−12.3925	−0.585493
$449$	9.91108	0.467733	0.233866	−	0.972269i	$-0.424862\pi$
$449$	9.91108	0.467733	0.233866	+	0.972269i	$0.424862\pi$
$450$	5.11225	0.240994
$451$	−3.87198	−0.182324
$452$	51.0572	2.40153
$453$	6.17333	0.290048
$454$	−44.0294	−2.06640
$455$	0	0
$456$	24.5109	1.14783
$457$	−14.4550	−0.676175	−0.338088	−	0.941115i	$-0.609780\pi$
$457$	−14.4550	−0.676175	−0.338088	+	0.941115i	$0.609780\pi$
$458$	26.7266	1.24885
$459$	8.12818	0.379391
$460$	47.1027	2.19618
$461$	−28.1836	−1.31264	−0.656321	−	0.754482i	$-0.727888\pi$
$461$	−28.1836	−1.31264	−0.656321	+	0.754482i	$0.727888\pi$
$462$	5.20396	0.242110
$463$	20.2581	0.941472	0.470736	−	0.882274i	$-0.343988\pi$
$463$	20.2581	0.941472	0.470736	+	0.882274i	$0.343988\pi$
$464$	−36.1554	−1.67847
$465$	−15.6740	−0.726866
$466$	50.4437	2.33676
$467$	−8.66625	−0.401026	−0.200513	−	0.979691i	$-0.564261\pi$
$467$	−8.66625	−0.401026	−0.200513	+	0.979691i	$0.564261\pi$
$468$	0	0
$469$	5.69638	0.263034
$470$	26.8329	1.23771
$471$	−17.5114	−0.806884
$472$	27.9612	1.28702
$473$	−1.30683	−0.0600879
$474$	6.84587	0.314441
$475$	−9.43289	−0.432811
$476$	−70.8680	−3.24823
$477$	13.5637	0.621038
$478$	−28.8958	−1.32166
$479$	−4.01635	−0.183512	−0.0917559	−	0.995782i	$-0.529248\pi$
$479$	−4.01635	−0.183512	−0.0917559	+	0.995782i	$0.529248\pi$
$480$	−2.78402	−0.127073
$481$	0	0
$482$	−8.84907	−0.403064
$483$	13.8581	0.630563
$484$	4.15740	0.188973
$485$	20.5889	0.934893
$486$	2.48141	0.112559
$487$	−1.85912	−0.0842450	−0.0421225	−	0.999112i	$-0.513412\pi$
$487$	−1.85912	−0.0842450	−0.0421225	+	0.999112i	$0.513412\pi$
$488$	27.4938	1.24458
$489$	−16.3550	−0.739600
$490$	−11.0698	−0.500081
$491$	26.2996	1.18688	0.593441	−	0.804877i	$-0.297769\pi$
$491$	26.2996	1.18688	0.593441	+	0.804877i	$0.297769\pi$
$492$	16.0973	0.725724
$493$	59.1405	2.66355
$494$	0	0
$495$	−1.71458	−0.0770646
$496$	−45.4261	−2.03969
$497$	−13.8264	−0.620201
$498$	2.98400	0.133716
$499$	18.2384	0.816464	0.408232	−	0.912878i	$-0.366146\pi$
$499$	18.2384	0.816464	0.408232	+	0.912878i	$0.366146\pi$
$500$	50.3265	2.25067
$501$	11.7305	0.524081
$502$	27.7468	1.23840
$503$	15.2121	0.678273	0.339137	−	0.940737i	$-0.389865\pi$
$503$	15.2121	0.678273	0.339137	+	0.940737i	$0.389865\pi$
$504$	−11.2270	−0.500090
$505$	−22.2330	−0.989356
$506$	16.3971	0.728938
$507$	0	0
$508$	−22.7825	−1.01081
$509$	−32.4934	−1.44024	−0.720122	−	0.693848i	$-0.755914\pi$
$509$	−32.4934	−1.44024	−0.720122	+	0.693848i	$0.755914\pi$
$510$	34.5820	1.53131
$511$	16.7808	0.742341
$512$	45.1350	1.99470
$513$	−4.57859	−0.202150
$514$	−24.7056	−1.08972
$515$	8.40132	0.370207
$516$	5.43299	0.239174
$517$	6.30683	0.277374
$518$	−17.1386	−0.753029
$519$	3.41056	0.149707
$520$	0	0
$521$	23.8625	1.04544	0.522718	−	0.852506i	$-0.324918\pi$
$521$	23.8625	1.04544	0.522718	+	0.852506i	$0.324918\pi$
$522$	18.0547	0.790232
$523$	−3.46744	−0.151621	−0.0758103	−	0.997122i	$-0.524154\pi$
$523$	−3.46744	−0.151621	−0.0758103	+	0.997122i	$0.524154\pi$
$524$	−48.8301	−2.13315
$525$	4.32064	0.188568
$526$	35.0924	1.53010
$527$	74.3048	3.23677
$528$	−4.96915	−0.216255
$529$	20.6651	0.898483
$530$	57.7076	2.50666
$531$	−5.22309	−0.226663
$532$	39.9198	1.73074
$533$	0	0
$534$	−0.402219	−0.0174057
$535$	−29.1662	−1.26096
$536$	−14.5409	−0.628073
$537$	0.647031	0.0279214
$538$	67.0020	2.88866
$539$	−2.60185	−0.112070
$540$	7.12818	0.306748
$541$	−32.6221	−1.40253	−0.701267	−	0.712899i	$-0.747382\pi$
$541$	−32.6221	−1.40253	−0.701267	+	0.712899i	$0.747382\pi$
$542$	24.1690	1.03815
$543$	−5.81214	−0.249423
$544$	13.1980	0.565860
$545$	10.2101	0.437351
$546$	0	0
$547$	−18.2734	−0.781315	−0.390658	−	0.920536i	$-0.627752\pi$
$547$	−18.2734	−0.781315	−0.390658	+	0.920536i	$0.627752\pi$
$548$	−18.7080	−0.799165
$549$	−5.13577	−0.219189
$550$	5.11225	0.217987
$551$	−33.3137	−1.41921
$552$	−35.3749	−1.50566
$553$	5.78583	0.246038
$554$	−81.4667	−3.46119
$555$	5.64677	0.239692
$556$	−9.07108	−0.384699
$557$	−0.201340	−0.00853103	−0.00426551	−	0.999991i	$-0.501358\pi$
$557$	−0.201340	−0.00853103	−0.00426551	+	0.999991i	$0.501358\pi$
$558$	22.6841	0.960295
$559$	0	0
$560$	−17.8680	−0.755059
$561$	8.12818	0.343172
$562$	33.9053	1.43021
$563$	23.4149	0.986822	0.493411	−	0.869796i	$-0.335750\pi$
$563$	23.4149	0.986822	0.493411	+	0.869796i	$0.335750\pi$
$564$	−26.2200	−1.10406
$565$	−21.0568	−0.885868
$566$	53.2949	2.24015
$567$	2.09718	0.0880731
$568$	35.2943	1.48091
$569$	21.1113	0.885034	0.442517	−	0.896760i	$-0.354086\pi$
$569$	21.1113	0.885034	0.442517	+	0.896760i	$0.354086\pi$
$570$	−19.4799	−0.815925
$571$	−35.2696	−1.47599	−0.737993	−	0.674809i	$-0.764226\pi$
$571$	−35.2696	−1.47599	−0.737993	+	0.674809i	$0.764226\pi$
$572$	0	0
$573$	20.1781	0.842952
$574$	20.1496	0.841028
$575$	13.6138	0.567737
$576$	−5.90915	−0.246215
$577$	21.3658	0.889470	0.444735	−	0.895662i	$-0.353298\pi$
$577$	21.3658	0.889470	0.444735	+	0.895662i	$0.353298\pi$
$578$	−121.756	−5.06439
$579$	−6.09007	−0.253095
$580$	51.8645	2.15356
$581$	2.52195	0.104628
$582$	−29.7971	−1.23513
$583$	13.5637	0.561750
$584$	−42.8358	−1.77256
$585$	0	0
$586$	−50.7025	−2.09450
$587$	7.48382	0.308890	0.154445	−	0.988001i	$-0.450641\pi$
$587$	7.48382	0.308890	0.154445	+	0.988001i	$0.450641\pi$
$588$	10.8169	0.446082
$589$	−41.8557	−1.72463
$590$	−22.2220	−0.914865
$591$	−20.0594	−0.825133
$592$	16.3653	0.672612
$593$	25.2441	1.03665	0.518326	−	0.855183i	$-0.326555\pi$
$593$	25.2441	1.03665	0.518326	+	0.855183i	$0.326555\pi$
$594$	2.48141	0.101813
$595$	29.2271	1.19820
$596$	−2.83309	−0.116048
$597$	0.361130	0.0147801
$598$	0	0
$599$	20.1313	0.822543	0.411272	−	0.911513i	$-0.365085\pi$
$599$	20.1313	0.822543	0.411272	+	0.911513i	$0.365085\pi$
$600$	−11.0291	−0.450263
$601$	47.9648	1.95652	0.978262	−	0.207371i	$-0.0664907\pi$
$601$	47.9648	1.95652	0.978262	+	0.207371i	$0.0664907\pi$
$602$	6.80066	0.277174
$603$	2.71621	0.110613
$604$	−25.6650	−1.04429
$605$	−1.71458	−0.0697075
$606$	32.1765	1.30708
$607$	8.30698	0.337170	0.168585	−	0.985687i	$-0.446080\pi$
$607$	8.30698	0.337170	0.168585	+	0.985687i	$0.446080\pi$
$608$	−7.43441	−0.301505
$609$	15.2590	0.618326
$610$	−21.8505	−0.884701
$611$	0	0
$612$	−33.7921	−1.36596
$613$	42.6352	1.72202	0.861011	−	0.508587i	$-0.169832\pi$
$613$	42.6352	1.72202	0.861011	+	0.508587i	$0.169832\pi$
$614$	24.3825	0.983996
$615$	−6.63881	−0.267703
$616$	−11.2270	−0.452349
$617$	18.9852	0.764316	0.382158	−	0.924097i	$-0.375181\pi$
$617$	18.9852	0.764316	0.382158	+	0.924097i	$0.375181\pi$
$618$	−12.1587	−0.489096
$619$	−6.49630	−0.261108	−0.130554	−	0.991441i	$-0.541676\pi$
$619$	−6.49630	−0.261108	−0.130554	+	0.991441i	$0.541676\pi$
$620$	65.1632	2.61702
$621$	6.60796	0.265168
$622$	−73.7385	−2.95664
$623$	−0.339937	−0.0136193
$624$	0	0
$625$	−10.4544	−0.418176
$626$	−51.1275	−2.04347
$627$	−4.57859	−0.182851
$628$	72.8019	2.90511
$629$	−26.7693	−1.06736
$630$	8.92259	0.355485
$631$	34.4462	1.37128	0.685640	−	0.727940i	$-0.259522\pi$
$631$	34.4462	1.37128	0.685640	+	0.727940i	$0.259522\pi$
$632$	−14.7693	−0.587490
$633$	7.03937	0.279790
$634$	50.2354	1.99510
$635$	9.39589	0.372864
$636$	−56.3896	−2.23599
$637$	0	0
$638$	18.0547	0.714792
$639$	−6.59289	−0.260811
$640$	−30.7090	−1.21388
$641$	46.5238	1.83758	0.918789	−	0.394749i	$-0.129168\pi$
$641$	46.5238	1.83758	0.918789	+	0.394749i	$0.129168\pi$
$642$	42.2105	1.66592
$643$	−47.3618	−1.86777	−0.933883	−	0.357580i	$-0.883602\pi$
$643$	−47.3618	−1.86777	−0.933883	+	0.357580i	$0.883602\pi$
$644$	−57.6134	−2.27029
$645$	−2.24066	−0.0882257
$646$	92.3472	3.63335
$647$	7.12810	0.280234	0.140117	−	0.990135i	$-0.455252\pi$
$647$	7.12810	0.280234	0.140117	+	0.990135i	$0.455252\pi$
$648$	−5.35339	−0.210301
$649$	−5.22309	−0.205024
$650$	0	0
$651$	19.1716	0.751394
$652$	67.9943	2.66286
$653$	32.1089	1.25652	0.628259	−	0.778004i	$-0.283768\pi$
$653$	32.1089	1.25652	0.628259	+	0.778004i	$0.283768\pi$
$654$	−14.7764	−0.577804
$655$	20.1384	0.786870
$656$	−19.2404	−0.751213
$657$	8.00164	0.312174
$658$	−32.8204	−1.27947
$659$	−5.00269	−0.194877	−0.0974386	−	0.995242i	$-0.531065\pi$
$659$	−5.00269	−0.194877	−0.0974386	+	0.995242i	$0.531065\pi$
$660$	7.12818	0.277464
$661$	49.3069	1.91781	0.958907	−	0.283720i	$-0.0915685\pi$
$661$	49.3069	1.91781	0.958907	+	0.283720i	$0.0915685\pi$
$662$	−69.4151	−2.69789
$663$	0	0
$664$	−6.43768	−0.249830
$665$	−16.4636	−0.638430
$666$	−8.17225	−0.316668
$667$	48.0794	1.86164
$668$	−48.7684	−1.88691
$669$	−23.4591	−0.906980
$670$	11.5563	0.446460
$671$	−5.13577	−0.198264
$672$	3.40526	0.131361
$673$	−14.2826	−0.550552	−0.275276	−	0.961365i	$-0.588769\pi$
$673$	−14.2826	−0.550552	−0.275276	+	0.961365i	$0.588769\pi$
$674$	43.6742	1.68227
$675$	2.06022	0.0792979
$676$	0	0
$677$	−18.5948	−0.714656	−0.357328	−	0.933979i	$-0.616312\pi$
$677$	−18.5948	−0.714656	−0.357328	+	0.933979i	$0.616312\pi$
$678$	30.4743	1.17036
$679$	−25.1832	−0.966441
$680$	−74.6070	−2.86105
$681$	−17.7437	−0.679940
$682$	22.6841	0.868620
$683$	13.7197	0.524968	0.262484	−	0.964936i	$-0.415458\pi$
$683$	13.7197	0.524968	0.262484	+	0.964936i	$0.415458\pi$
$684$	19.0350	0.727821
$685$	7.71548	0.294793
$686$	49.9676	1.90777
$687$	10.7707	0.410929
$688$	−6.49382	−0.247574
$689$	0	0
$690$	28.1140	1.07028
$691$	−8.81201	−0.335225	−0.167612	−	0.985853i	$-0.553606\pi$
$691$	−8.81201	−0.335225	−0.167612	+	0.985853i	$0.553606\pi$
$692$	−14.1790	−0.539006
$693$	2.09718	0.0796652
$694$	46.2267	1.75474
$695$	3.74106	0.141907
$696$	−38.9511	−1.47644
$697$	31.4721	1.19209
$698$	1.53438	0.0580770
$699$	20.3286	0.768900
$700$	−17.9626	−0.678924
$701$	8.42103	0.318058	0.159029	−	0.987274i	$-0.449164\pi$
$701$	8.42103	0.318058	0.159029	+	0.987274i	$0.449164\pi$
$702$	0	0
$703$	15.0791	0.568718
$704$	−5.90915	−0.222710
$705$	10.8135	0.407262
$706$	−14.6295	−0.550590
$707$	27.1942	1.02274
$708$	21.7144	0.816079
$709$	29.2306	1.09778	0.548889	−	0.835895i	$-0.315051\pi$
$709$	29.2306	1.09778	0.548889	+	0.835895i	$0.315051\pi$
$710$	−28.0499	−1.05269
$711$	2.75886	0.103465
$712$	0.867745	0.0325201
$713$	60.4075	2.26228
$714$	−42.2987	−1.58299
$715$	0	0
$716$	−2.68996	−0.100529
$717$	−11.6449	−0.434887
$718$	−67.3516	−2.51354
$719$	42.2478	1.57558	0.787789	−	0.615946i	$-0.211226\pi$
$719$	42.2478	1.57558	0.787789	+	0.615946i	$0.211226\pi$
$720$	−8.52000	−0.317522
$721$	−10.2760	−0.382699
$722$	−4.87215	−0.181323
$723$	−3.56615	−0.132626
$724$	24.1634	0.898024
$725$	14.9901	0.556719
$726$	2.48141	0.0920938
$727$	28.7391	1.06587	0.532937	−	0.846155i	$-0.321088\pi$
$727$	28.7391	1.06587	0.532937	+	0.846155i	$0.321088\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	34.0435	1.26001
$731$	10.6221	0.392873
$732$	21.3514	0.789172
$733$	−15.8737	−0.586308	−0.293154	−	0.956065i	$-0.594705\pi$
$733$	−15.8737	−0.586308	−0.293154	+	0.956065i	$0.594705\pi$
$734$	55.4517	2.04676
$735$	−4.46108	−0.164549
$736$	10.7296	0.395497
$737$	2.71621	0.100053
$738$	9.60796	0.353674
$739$	9.01314	0.331554	0.165777	−	0.986163i	$-0.446987\pi$
$739$	9.01314	0.331554	0.165777	+	0.986163i	$0.446987\pi$
$740$	−23.4759	−0.862990
$741$	0	0
$742$	−70.5848	−2.59125
$743$	49.0501	1.79947	0.899736	−	0.436434i	$-0.143759\pi$
$743$	49.0501	1.79947	0.899736	+	0.436434i	$0.143759\pi$
$744$	−48.9386	−1.79418
$745$	1.16841	0.0428073
$746$	29.4259	1.07736
$747$	1.20254	0.0439987
$748$	−33.7921	−1.23556
$749$	35.6745	1.30352
$750$	30.0382	1.09684
$751$	8.51725	0.310799	0.155399	−	0.987852i	$-0.450334\pi$
$751$	8.51725	0.310799	0.155399	+	0.987852i	$0.450334\pi$
$752$	31.3396	1.14284
$753$	11.1818	0.407489
$754$	0	0
$755$	10.5847	0.385215
$756$	−8.71880	−0.317100
$757$	−5.68451	−0.206607	−0.103303	−	0.994650i	$-0.532941\pi$
$757$	−5.68451	−0.206607	−0.103303	+	0.994650i	$0.532941\pi$
$758$	−48.5480	−1.76334
$759$	6.60796	0.239854
$760$	42.0259	1.52444
$761$	−34.6252	−1.25516	−0.627582	−	0.778550i	$-0.715955\pi$
$761$	−34.6252	−1.25516	−0.627582	+	0.778550i	$0.715955\pi$
$762$	−13.5981	−0.492608
$763$	−12.4884	−0.452110
$764$	−83.8884	−3.03497
$765$	13.9364	0.503872
$766$	−9.40465	−0.339804
$767$	0	0
$768$	32.6250	1.17725
$769$	−46.0792	−1.66166	−0.830830	−	0.556526i	$-0.812134\pi$
$769$	−46.0792	−1.66166	−0.830830	+	0.556526i	$0.812134\pi$
$770$	8.92259	0.321548
$771$	−9.95627	−0.358566
$772$	25.3188	0.911245
$773$	−14.4105	−0.518309	−0.259154	−	0.965836i	$-0.583444\pi$
$773$	−14.4105	−0.518309	−0.259154	+	0.965836i	$0.583444\pi$
$774$	3.24277	0.116559
$775$	18.8337	0.676528
$776$	64.2841	2.30767
$777$	−6.90682	−0.247781
$778$	−18.3100	−0.656447
$779$	−17.7282	−0.635178
$780$	0	0
$781$	−6.59289	−0.235912
$782$	−133.278	−4.76602
$783$	7.27598	0.260022
$784$	−12.9290	−0.461749
$785$	−30.0247	−1.07163
$786$	−29.1451	−1.03957
$787$	−8.08007	−0.288024	−0.144012	−	0.989576i	$-0.546000\pi$
$787$	−8.08007	−0.288024	−0.144012	+	0.989576i	$0.546000\pi$
$788$	83.3948	2.97082
$789$	14.1421	0.503472
$790$	11.7378	0.417612
$791$	25.7555	0.915762
$792$	−5.35339	−0.190224
$793$	0	0
$794$	25.1768	0.893490
$795$	23.2560	0.824805
$796$	−1.50136	−0.0532143
$797$	1.71386	0.0607079	0.0303539	−	0.999539i	$-0.490337\pi$
$797$	1.71386	0.0607079	0.0303539	+	0.999539i	$0.490337\pi$
$798$	23.8268	0.843458
$799$	−51.2630	−1.81356
$800$	3.34525	0.118272
$801$	−0.162093	−0.00572727
$802$	−24.1991	−0.854502
$803$	8.00164	0.282372
$804$	−11.2924	−0.398251
$805$	23.7607	0.837456
$806$	0	0
$807$	27.0016	0.950500
$808$	−69.4175	−2.44210
$809$	−27.5775	−0.969573	−0.484786	−	0.874633i	$-0.661103\pi$
$809$	−27.5775	−0.969573	−0.484786	+	0.874633i	$0.661103\pi$
$810$	4.25457	0.149490
$811$	40.1330	1.40926	0.704630	−	0.709575i	$-0.251113\pi$
$811$	40.1330	1.40926	0.704630	+	0.709575i	$0.251113\pi$
$812$	−63.4378	−2.22623
$813$	9.74003	0.341598
$814$	−8.17225	−0.286437
$815$	−28.0420	−0.982267
$816$	40.3902	1.41394
$817$	−5.98342	−0.209333
$818$	−50.8786	−1.77893
$819$	0	0
$820$	27.6002	0.963839
$821$	−9.71294	−0.338984	−0.169492	−	0.985532i	$-0.554213\pi$
$821$	−9.71294	−0.338984	−0.169492	+	0.985532i	$0.554213\pi$
$822$	−11.1662	−0.389465
$823$	16.8883	0.588690	0.294345	−	0.955699i	$-0.404899\pi$
$823$	16.8883	0.588690	0.294345	+	0.955699i	$0.404899\pi$
$824$	26.2312	0.913808
$825$	2.06022	0.0717276
$826$	27.1807	0.945738
$827$	32.3586	1.12522	0.562610	−	0.826723i	$-0.309797\pi$
$827$	32.3586	1.12522	0.562610	+	0.826723i	$0.309797\pi$
$828$	−27.4719	−0.954715
$829$	7.60061	0.263980	0.131990	−	0.991251i	$-0.457863\pi$
$829$	7.60061	0.263980	0.131990	+	0.991251i	$0.457863\pi$
$830$	5.11631	0.177590
$831$	−32.8308	−1.13889
$832$	0	0
$833$	21.1483	0.732745
$834$	−5.41422	−0.187479
$835$	20.1129	0.696035
$836$	19.0350	0.658339
$837$	9.14162	0.315981
$838$	−79.0411	−2.73043
$839$	−19.8829	−0.686435	−0.343218	−	0.939256i	$-0.611517\pi$
$839$	−19.8829	−0.686435	−0.343218	+	0.939256i	$0.611517\pi$
$840$	−19.2496	−0.664173
$841$	23.9399	0.825512
$842$	−47.3345	−1.63125
$843$	13.6637	0.470603
$844$	−29.2654	−1.00736
$845$	0	0
$846$	−15.6498	−0.538052
$847$	2.09718	0.0720598
$848$	67.4000	2.31452
$849$	21.4777	0.737111
$850$	−41.5533	−1.42527
$851$	−21.7626	−0.746011
$852$	27.4092	0.939025
$853$	−3.32953	−0.114001	−0.0570006	−	0.998374i	$-0.518154\pi$
$853$	−3.32953	−0.114001	−0.0570006	+	0.998374i	$0.518154\pi$
$854$	26.7263	0.914556
$855$	−7.85035	−0.268476
$856$	−91.0649	−3.11253
$857$	−15.5857	−0.532397	−0.266198	−	0.963918i	$-0.585768\pi$
$857$	−15.5857	−0.532397	−0.266198	+	0.963918i	$0.585768\pi$
$858$	0	0
$859$	−53.7857	−1.83515	−0.917573	−	0.397568i	$-0.869854\pi$
$859$	−53.7857	−1.83515	−0.917573	+	0.397568i	$0.869854\pi$
$860$	9.31529	0.317649
$861$	8.12022	0.276736
$862$	−5.50827	−0.187613
$863$	50.6790	1.72513	0.862567	−	0.505944i	$-0.168856\pi$
$863$	50.6790	1.72513	0.862567	+	0.505944i	$0.168856\pi$
$864$	1.62373	0.0552405
$865$	5.84767	0.198827
$866$	39.6051	1.34584
$867$	−49.0674	−1.66642
$868$	−79.7039	−2.70533
$869$	2.75886	0.0935881
$870$	30.9562	1.04951
$871$	0	0
$872$	31.8786	1.07955
$873$	−12.0081	−0.406413
$874$	75.0753	2.53946
$875$	25.3870	0.858236
$876$	−33.2660	−1.12395
$877$	−19.7990	−0.668563	−0.334282	−	0.942473i	$-0.608494\pi$
$877$	−19.7990	−0.668563	−0.334282	+	0.942473i	$0.608494\pi$
$878$	39.8088	1.34348
$879$	−20.4329	−0.689186
$880$	−8.52000	−0.287209
$881$	13.5030	0.454926	0.227463	−	0.973787i	$-0.426957\pi$
$881$	13.5030	0.454926	0.227463	+	0.973787i	$0.426957\pi$
$882$	6.45626	0.217393
$883$	−29.4402	−0.990743	−0.495372	−	0.868681i	$-0.664968\pi$
$883$	−29.4402	−0.990743	−0.495372	+	0.868681i	$0.664968\pi$
$884$	0	0
$885$	−8.95539	−0.301032
$886$	74.8791	2.51561
$887$	−12.8606	−0.431817	−0.215909	−	0.976414i	$-0.569271\pi$
$887$	−12.8606	−0.431817	−0.215909	+	0.976414i	$0.569271\pi$
$888$	17.6308	0.591650
$889$	−11.4925	−0.385447
$890$	−0.689636	−0.0231166
$891$	1.00000	0.0335013
$892$	97.5287	3.26550
$893$	28.8764	0.966310
$894$	−1.69097	−0.0565546
$895$	1.10939	0.0370827
$896$	37.5615	1.25484
$897$	0	0
$898$	−24.5935	−0.820695
$899$	66.5142	2.21837
$900$	−8.56515	−0.285505
$901$	−110.248	−3.67289
$902$	9.60796	0.319910
$903$	2.74064	0.0912030
$904$	−65.7452	−2.18665
$905$	−9.96537	−0.331260
$906$	−15.3186	−0.508925
$907$	3.13447	0.104078	0.0520391	−	0.998645i	$-0.483428\pi$
$907$	3.13447	0.104078	0.0520391	+	0.998645i	$0.483428\pi$
$908$	73.7676	2.44806
$909$	12.9670	0.430089
$910$	0	0
$911$	13.6385	0.451864	0.225932	−	0.974143i	$-0.427457\pi$
$911$	13.6385	0.451864	0.225932	+	0.974143i	$0.427457\pi$
$912$	−22.7517	−0.753384
$913$	1.20254	0.0397984
$914$	35.8687	1.18643
$915$	−8.80568	−0.291107
$916$	−44.7782	−1.47951
$917$	−24.6321	−0.813424
$918$	−20.1694	−0.665688
$919$	−50.0438	−1.65079	−0.825397	−	0.564553i	$-0.809049\pi$
$919$	−50.0438	−1.65079	−0.825397	+	0.564553i	$0.809049\pi$
$920$	−60.6531	−1.99967
$921$	9.82605	0.323779
$922$	69.9351	2.30319
$923$	0	0
$924$	−8.71880	−0.286827
$925$	−6.78510	−0.223093
$926$	−50.2686	−1.65193
$927$	−4.89993	−0.160935
$928$	11.8143	0.387822
$929$	50.1404	1.64505	0.822527	−	0.568726i	$-0.192563\pi$
$929$	50.1404	1.64505	0.822527	+	0.568726i	$0.192563\pi$
$930$	38.8937	1.27537
$931$	−11.9128	−0.390426
$932$	−84.5142	−2.76836
$933$	−29.7164	−0.972870
$934$	21.5045	0.703649
$935$	13.9364	0.455769
$936$	0	0
$937$	24.1277	0.788216	0.394108	−	0.919064i	$-0.371054\pi$
$937$	24.1277	0.788216	0.394108	+	0.919064i	$0.371054\pi$
$938$	−14.1351	−0.461526
$939$	−20.6042	−0.672393
$940$	−44.9562	−1.46631
$941$	−20.2804	−0.661123	−0.330562	−	0.943784i	$-0.607238\pi$
$941$	−20.2804	−0.661123	−0.330562	+	0.943784i	$0.607238\pi$
$942$	43.4530	1.41578
$943$	25.5859	0.833190
$944$	−25.9543	−0.844741
$945$	3.59577	0.116971
$946$	3.24277	0.105432
$947$	16.5269	0.537052	0.268526	−	0.963272i	$-0.413463\pi$
$947$	16.5269	0.537052	0.268526	+	0.963272i	$0.413463\pi$
$948$	−11.4697	−0.372518
$949$	0	0
$950$	23.4069	0.759419
$951$	20.2447	0.656479
$952$	91.2551	2.95759
$953$	−37.4256	−1.21233	−0.606167	−	0.795338i	$-0.707293\pi$
$953$	−37.4256	−1.21233	−0.606167	+	0.795338i	$0.707293\pi$
$954$	−33.6570	−1.08969
$955$	34.5969	1.11953
$956$	48.4125	1.56577
$957$	7.27598	0.235199
$958$	9.96621	0.321994
$959$	−9.43714	−0.304741
$960$	−10.1317	−0.327000
$961$	52.5692	1.69578
$962$	0	0
$963$	17.0107	0.548162
$964$	14.8259	0.477510
$965$	−10.4419	−0.336137
$966$	−34.3875	−1.10640
$967$	−24.9551	−0.802502	−0.401251	−	0.915968i	$-0.631425\pi$
$967$	−24.9551	−0.802502	−0.401251	+	0.915968i	$0.631425\pi$
$968$	−5.35339	−0.172064
$969$	37.2156	1.19554
$970$	−51.0895	−1.64038
$971$	−29.3222	−0.940995	−0.470497	−	0.882401i	$-0.655925\pi$
$971$	−29.3222	−0.940995	−0.470497	+	0.882401i	$0.655925\pi$
$972$	−4.15740	−0.133349
$973$	−4.57586	−0.146695
$974$	4.61325	0.147818
$975$	0	0
$976$	−25.5204	−0.816889
$977$	−11.5113	−0.368280	−0.184140	−	0.982900i	$-0.558950\pi$
$977$	−11.5113	−0.368280	−0.184140	+	0.982900i	$0.558950\pi$
$978$	40.5835	1.29772
$979$	−0.162093	−0.00518051
$980$	18.5465	0.592445
$981$	−5.95485	−0.190124
$982$	−65.2600	−2.08253
$983$	15.2590	0.486686	0.243343	−	0.969940i	$-0.421756\pi$
$983$	15.2590	0.486686	0.243343	+	0.969940i	$0.421756\pi$
$984$	−20.7282	−0.660790
$985$	−34.3934	−1.09586
$986$	−146.752	−4.67353
$987$	−13.2265	−0.421005
$988$	0	0
$989$	8.63545	0.274591
$990$	4.25457	0.135219
$991$	11.7127	0.372066	0.186033	−	0.982543i	$-0.440437\pi$
$991$	11.7127	0.372066	0.186033	+	0.982543i	$0.440437\pi$
$992$	14.8436	0.471283
$993$	−27.9741	−0.887730
$994$	34.3091	1.08822
$995$	0.619186	0.0196295
$996$	−4.99945	−0.158414
$997$	4.97378	0.157521	0.0787605	−	0.996894i	$-0.474904\pi$
$997$	4.97378	0.157521	0.0787605	+	0.996894i	$0.474904\pi$
$998$	−45.2570	−1.43259
$999$	−3.29339	−0.104198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.r.1.1		5
13.3	even	3		429.2.i.d.100.5	✓	10
13.9	even	3		429.2.i.d.133.5	yes	10
13.12	even	2		5577.2.a.s.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.d.100.5	✓	10	13.3	even	3
429.2.i.d.133.5	yes	10	13.9	even	3
5577.2.a.r.1.1		5	1.1	even	1	trivial
5577.2.a.s.1.5		5	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-2.48141 q^{2} -1.00000 q^{3} +4.15740 q^{4} -1.71458 q^{5} +2.48141 q^{6} +2.09718 q^{7} -5.35339 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.48141 q^{2} -1.00000 q^{3} +4.15740 q^{4} -1.71458 q^{5} +2.48141 q^{6} +2.09718 q^{7} -5.35339 q^{8} +1.00000 q^{9} +4.25457 q^{10} +1.00000 q^{11} -4.15740 q^{12} -5.20396 q^{14} +1.71458 q^{15} +4.96915 q^{16} -8.12818 q^{17} -2.48141 q^{18} +4.57859 q^{19} -7.12818 q^{20} -2.09718 q^{21} -2.48141 q^{22} -6.60796 q^{23} +5.35339 q^{24} -2.06022 q^{25} -1.00000 q^{27} +8.71880 q^{28} -7.27598 q^{29} -4.25457 q^{30} -9.14162 q^{31} -1.62373 q^{32} -1.00000 q^{33} +20.1694 q^{34} -3.59577 q^{35} +4.15740 q^{36} +3.29339 q^{37} -11.3614 q^{38} +9.17880 q^{40} -3.87198 q^{41} +5.20396 q^{42} -1.30683 q^{43} +4.15740 q^{44} -1.71458 q^{45} +16.3971 q^{46} +6.30683 q^{47} -4.96915 q^{48} -2.60185 q^{49} +5.11225 q^{50} +8.12818 q^{51} +13.5637 q^{53} +2.48141 q^{54} -1.71458 q^{55} -11.2270 q^{56} -4.57859 q^{57} +18.0547 q^{58} -5.22309 q^{59} +7.12818 q^{60} -5.13577 q^{61} +22.6841 q^{62} +2.09718 q^{63} -5.90915 q^{64} +2.48141 q^{66} +2.71621 q^{67} -33.7921 q^{68} +6.60796 q^{69} +8.92259 q^{70} -6.59289 q^{71} -5.35339 q^{72} +8.00164 q^{73} -8.17225 q^{74} +2.06022 q^{75} +19.0350 q^{76} +2.09718 q^{77} +2.75886 q^{79} -8.52000 q^{80} +1.00000 q^{81} +9.60796 q^{82} +1.20254 q^{83} -8.71880 q^{84} +13.9364 q^{85} +3.24277 q^{86} +7.27598 q^{87} -5.35339 q^{88} -0.162093 q^{89} +4.25457 q^{90} -27.4719 q^{92} +9.14162 q^{93} -15.6498 q^{94} -7.85035 q^{95} +1.62373 q^{96} -12.0081 q^{97} +6.45626 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^7 + 3 * q^8 + 5 * q^9	\( 5 q - 5 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{7} + 3 q^{8} + 5 q^{9} + 7 q^{10} + 5 q^{11} - 10 q^{12} + q^{14} + 2 q^{15} + 4 q^{16} + 3 q^{17} + 7 q^{19} + 8 q^{20} - 7 q^{21} + 11 q^{23} - 3 q^{24} - 3 q^{25} - 5 q^{27} + 5 q^{28} - 2 q^{29} - 7 q^{30} + 10 q^{31} - 9 q^{32} - 5 q^{33} + 29 q^{34} - 14 q^{35} + 10 q^{36} + 15 q^{37} - 19 q^{38} + 15 q^{40} - 2 q^{41} - q^{42} + 7 q^{43} + 10 q^{44} - 2 q^{45} + 20 q^{46} + 18 q^{47} - 4 q^{48} + 14 q^{49} - 2 q^{50} - 3 q^{51} + 15 q^{53} - 2 q^{55} + 3 q^{56} - 7 q^{57} + 5 q^{58} - 4 q^{59} - 8 q^{60} - 14 q^{61} + 46 q^{62} + 7 q^{63} - 37 q^{64} - 5 q^{67} - 24 q^{68} - 11 q^{69} + 40 q^{70} - 13 q^{71} + 3 q^{72} + 28 q^{73} + 15 q^{74} + 3 q^{75} + 2 q^{76} + 7 q^{77} + 16 q^{79} - 22 q^{80} + 5 q^{81} + 4 q^{82} + 12 q^{83} - 5 q^{84} + 13 q^{85} + 2 q^{86} + 2 q^{87} + 3 q^{88} - 6 q^{89} + 7 q^{90} - 2 q^{92} - 10 q^{93} - 2 q^{94} - 21 q^{95} + 9 q^{96} + 9 q^{97} + 16 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q - 5 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^7 + 3 * q^8 + 5 * q^9 + 7 * q^10 + 5 * q^11 - 10 * q^12 + q^14 + 2 * q^15 + 4 * q^16 + 3 * q^17 + 7 * q^19 + 8 * q^20 - 7 * q^21 + 11 * q^23 - 3 * q^24 - 3 * q^25 - 5 * q^27 + 5 * q^28 - 2 * q^29 - 7 * q^30 + 10 * q^31 - 9 * q^32 - 5 * q^33 + 29 * q^34 - 14 * q^35 + 10 * q^36 + 15 * q^37 - 19 * q^38 + 15 * q^40 - 2 * q^41 - q^42 + 7 * q^43 + 10 * q^44 - 2 * q^45 + 20 * q^46 + 18 * q^47 - 4 * q^48 + 14 * q^49 - 2 * q^50 - 3 * q^51 + 15 * q^53 - 2 * q^55 + 3 * q^56 - 7 * q^57 + 5 * q^58 - 4 * q^59 - 8 * q^60 - 14 * q^61 + 46 * q^62 + 7 * q^63 - 37 * q^64 - 5 * q^67 - 24 * q^68 - 11 * q^69 + 40 * q^70 - 13 * q^71 + 3 * q^72 + 28 * q^73 + 15 * q^74 + 3 * q^75 + 2 * q^76 + 7 * q^77 + 16 * q^79 - 22 * q^80 + 5 * q^81 + 4 * q^82 + 12 * q^83 - 5 * q^84 + 13 * q^85 + 2 * q^86 + 2 * q^87 + 3 * q^88 - 6 * q^89 + 7 * q^90 - 2 * q^92 - 10 * q^93 - 2 * q^94 - 21 * q^95 + 9 * q^96 + 9 * q^97 + 16 * q^98 + 5 * q^99

Introduction

L-functions

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Database

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