LMFDB - Embedded newform 5239.2.a.t.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5239,2,Mod(1,5239)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5239, 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("5239.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.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:	$41.8336256189$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	5239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.709075 q^{2} -2.87369 q^{3} -1.49721 q^{4} -2.11332 q^{5} +2.03766 q^{6} -0.783955 q^{7} +2.47979 q^{8} +5.25811 q^{9} +O(q^{10})$	\(q-0.709075 q^{2} -2.87369 q^{3} -1.49721 q^{4} -2.11332 q^{5} +2.03766 q^{6} -0.783955 q^{7} +2.47979 q^{8} +5.25811 q^{9} +1.49850 q^{10} -1.64979 q^{11} +4.30253 q^{12} +0.555883 q^{14} +6.07304 q^{15} +1.23607 q^{16} -2.10026 q^{17} -3.72840 q^{18} -1.79114 q^{19} +3.16409 q^{20} +2.25284 q^{21} +1.16983 q^{22} -4.11635 q^{23} -7.12615 q^{24} -0.533870 q^{25} -6.48911 q^{27} +1.17375 q^{28} -8.45542 q^{29} -4.30624 q^{30} -1.00000 q^{31} -5.83604 q^{32} +4.74100 q^{33} +1.48924 q^{34} +1.65675 q^{35} -7.87250 q^{36} -0.960200 q^{37} +1.27005 q^{38} -5.24059 q^{40} +2.63807 q^{41} -1.59744 q^{42} +5.00533 q^{43} +2.47009 q^{44} -11.1121 q^{45} +2.91880 q^{46} -4.39676 q^{47} -3.55208 q^{48} -6.38542 q^{49} +0.378554 q^{50} +6.03550 q^{51} +10.0103 q^{53} +4.60127 q^{54} +3.48654 q^{55} -1.94404 q^{56} +5.14718 q^{57} +5.99553 q^{58} +6.60885 q^{59} -9.09262 q^{60} +12.7226 q^{61} +0.709075 q^{62} -4.12212 q^{63} +1.66606 q^{64} -3.36172 q^{66} +3.08130 q^{67} +3.14453 q^{68} +11.8291 q^{69} -1.17476 q^{70} +4.93002 q^{71} +13.0390 q^{72} +4.65497 q^{73} +0.680854 q^{74} +1.53418 q^{75} +2.68171 q^{76} +1.29336 q^{77} +15.9886 q^{79} -2.61221 q^{80} +2.87337 q^{81} -1.87059 q^{82} +6.55669 q^{83} -3.37299 q^{84} +4.43853 q^{85} -3.54916 q^{86} +24.2983 q^{87} -4.09113 q^{88} -2.84594 q^{89} +7.87930 q^{90} +6.16305 q^{92} +2.87369 q^{93} +3.11763 q^{94} +3.78525 q^{95} +16.7710 q^{96} -3.61767 q^{97} +4.52774 q^{98} -8.67478 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 5 q^{3} + 28 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 36 * q + 2 * q^2 - 5 * q^3 + 28 * q^4 + 5 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	\( 36 q + 2 q^{2} - 5 q^{3} + 28 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - 15 q^{10} - q^{11} - 13 q^{12} - 19 q^{14} - 10 q^{15} + 4 q^{16} - 46 q^{17} - 9 q^{18} + 8 q^{19} - 5 q^{20} - 16 q^{21} - 21 q^{22} - 24 q^{23} + 57 q^{24} + 5 q^{25} - 11 q^{27} - 32 q^{28} - 73 q^{29} - 31 q^{30} - 36 q^{31} + 3 q^{32} - 8 q^{33} - 37 q^{34} - 31 q^{35} - 31 q^{36} + 6 q^{37} - 25 q^{38} - 22 q^{40} + 6 q^{41} - 37 q^{42} - 37 q^{43} - 16 q^{45} - 45 q^{46} + 13 q^{47} - 46 q^{48} - 5 q^{49} + 24 q^{50} - 46 q^{51} - 42 q^{53} - 26 q^{54} - 47 q^{55} - 95 q^{56} + 33 q^{57} + 9 q^{58} + 20 q^{59} - 40 q^{60} - 48 q^{61} - 2 q^{62} + 52 q^{63} + 21 q^{64} - 4 q^{66} - 50 q^{67} - 76 q^{68} - 33 q^{69} + 93 q^{70} + 16 q^{71} - 52 q^{72} - 43 q^{73} - 76 q^{74} - 40 q^{75} + 62 q^{76} - 47 q^{77} - 43 q^{79} - 46 q^{80} - 96 q^{81} + 7 q^{82} + 9 q^{83} - 77 q^{84} - 5 q^{85} + 64 q^{86} - 8 q^{87} - 54 q^{88} + 6 q^{89} + 27 q^{90} - 35 q^{92} + 5 q^{93} - 76 q^{94} - 63 q^{95} + 72 q^{96} - 4 q^{97} - 41 q^{98} - 47 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 5 * q^3 + 28 * q^4 + 5 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - 15 * q^10 - q^11 - 13 * q^12 - 19 * q^14 - 10 * q^15 + 4 * q^16 - 46 * q^17 - 9 * q^18 + 8 * q^19 - 5 * q^20 - 16 * q^21 - 21 * q^22 - 24 * q^23 + 57 * q^24 + 5 * q^25 - 11 * q^27 - 32 * q^28 - 73 * q^29 - 31 * q^30 - 36 * q^31 + 3 * q^32 - 8 * q^33 - 37 * q^34 - 31 * q^35 - 31 * q^36 + 6 * q^37 - 25 * q^38 - 22 * q^40 + 6 * q^41 - 37 * q^42 - 37 * q^43 - 16 * q^45 - 45 * q^46 + 13 * q^47 - 46 * q^48 - 5 * q^49 + 24 * q^50 - 46 * q^51 - 42 * q^53 - 26 * q^54 - 47 * q^55 - 95 * q^56 + 33 * q^57 + 9 * q^58 + 20 * q^59 - 40 * q^60 - 48 * q^61 - 2 * q^62 + 52 * q^63 + 21 * q^64 - 4 * q^66 - 50 * q^67 - 76 * q^68 - 33 * q^69 + 93 * q^70 + 16 * q^71 - 52 * q^72 - 43 * q^73 - 76 * q^74 - 40 * q^75 + 62 * q^76 - 47 * q^77 - 43 * q^79 - 46 * q^80 - 96 * q^81 + 7 * q^82 + 9 * q^83 - 77 * q^84 - 5 * q^85 + 64 * q^86 - 8 * q^87 - 54 * q^88 + 6 * q^89 + 27 * q^90 - 35 * q^92 + 5 * q^93 - 76 * q^94 - 63 * q^95 + 72 * q^96 - 4 * q^97 - 41 * q^98 - 47 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.709075	−0.501392	−0.250696	−	0.968066i	$-0.580659\pi$
$2$	−0.709075	−0.501392	−0.250696	+	0.968066i	$0.580659\pi$
$3$	−2.87369	−1.65913	−0.829564	−	0.558412i	$-0.811411\pi$
$3$	−2.87369	−1.65913	−0.829564	+	0.558412i	$0.811411\pi$
$4$	−1.49721	−0.748606
$5$	−2.11332	−0.945106	−0.472553	−	0.881302i	$-0.656668\pi$
$5$	−2.11332	−0.945106	−0.472553	+	0.881302i	$0.656668\pi$
$6$	2.03766	0.831873
$7$	−0.783955	−0.296307	−0.148153	−	0.988964i	$-0.547333\pi$
$7$	−0.783955	−0.296307	−0.148153	+	0.988964i	$0.547333\pi$
$8$	2.47979	0.876737
$9$	5.25811	1.75270
$10$	1.49850	0.473869
$11$	−1.64979	−0.497431	−0.248716	−	0.968577i	$-0.580008\pi$
$11$	−1.64979	−0.497431	−0.248716	+	0.968577i	$0.580008\pi$
$12$	4.30253	1.24203
$13$	0	0
$13$	0	0
$14$	0.555883	0.148566
$15$	6.07304	1.56805
$16$	1.23607	0.309017
$17$	−2.10026	−0.509388	−0.254694	−	0.967022i	$-0.581975\pi$
$17$	−2.10026	−0.509388	−0.254694	+	0.967022i	$0.581975\pi$
$18$	−3.72840	−0.878791
$19$	−1.79114	−0.410915	−0.205458	−	0.978666i	$-0.565868\pi$
$19$	−1.79114	−0.410915	−0.205458	+	0.978666i	$0.565868\pi$
$20$	3.16409	0.707512
$21$	2.25284	0.491611
$22$	1.16983	0.249408
$23$	−4.11635	−0.858318	−0.429159	−	0.903229i	$-0.641190\pi$
$23$	−4.11635	−0.858318	−0.429159	+	0.903229i	$0.641190\pi$
$24$	−7.12615	−1.45462
$25$	−0.533870	−0.106774
$26$	0	0
$27$	−6.48911	−1.24883
$28$	1.17375	0.221817
$29$	−8.45542	−1.57013	−0.785066	−	0.619413i	$-0.787371\pi$
$29$	−8.45542	−1.57013	−0.785066	+	0.619413i	$0.787371\pi$
$30$	−4.30624	−0.786209
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−5.83604	−1.03168
$33$	4.74100	0.825301
$34$	1.48924	0.255403
$35$	1.65675	0.280042
$36$	−7.87250	−1.31208
$37$	−0.960200	−0.157856	−0.0789280	−	0.996880i	$-0.525150\pi$
$37$	−0.960200	−0.157856	−0.0789280	+	0.996880i	$0.525150\pi$
$38$	1.27005	0.206030
$39$	0	0
$40$	−5.24059	−0.828610
$41$	2.63807	0.411997	0.205999	−	0.978552i	$-0.433956\pi$
$41$	2.63807	0.411997	0.205999	+	0.978552i	$0.433956\pi$
$42$	−1.59744	−0.246490
$43$	5.00533	0.763306	0.381653	−	0.924306i	$-0.375355\pi$
$43$	5.00533	0.763306	0.381653	+	0.924306i	$0.375355\pi$
$44$	2.47009	0.372380
$45$	−11.1121	−1.65649
$46$	2.91880	0.430354
$47$	−4.39676	−0.641333	−0.320667	−	0.947192i	$-0.603907\pi$
$47$	−4.39676	−0.641333	−0.320667	+	0.947192i	$0.603907\pi$
$48$	−3.55208	−0.512698
$49$	−6.38542	−0.912202
$50$	0.378554	0.0535357
$51$	6.03550	0.845139
$52$	0	0
$53$	10.0103	1.37501	0.687507	−	0.726178i	$-0.258705\pi$
$53$	10.0103	1.37501	0.687507	+	0.726178i	$0.258705\pi$
$54$	4.60127	0.626153
$55$	3.48654	0.470125
$56$	−1.94404	−0.259783
$57$	5.14718	0.681761
$58$	5.99553	0.787251
$59$	6.60885	0.860399	0.430200	−	0.902734i	$-0.358443\pi$
$59$	6.60885	0.860399	0.430200	+	0.902734i	$0.358443\pi$
$60$	−9.09262	−1.17385
$61$	12.7226	1.62896	0.814479	−	0.580193i	$-0.197023\pi$
$61$	12.7226	1.62896	0.814479	+	0.580193i	$0.197023\pi$
$62$	0.709075	0.0900527
$63$	−4.12212	−0.519338
$64$	1.66606	0.208257
$65$	0	0
$66$	−3.36172	−0.413800
$67$	3.08130	0.376441	0.188221	−	0.982127i	$-0.439728\pi$
$67$	3.08130	0.376441	0.188221	+	0.982127i	$0.439728\pi$
$68$	3.14453	0.381331
$69$	11.8291	1.42406
$70$	−1.17476	−0.140411
$71$	4.93002	0.585085	0.292543	−	0.956252i	$-0.405499\pi$
$71$	4.93002	0.585085	0.292543	+	0.956252i	$0.405499\pi$
$72$	13.0390	1.53666
$73$	4.65497	0.544823	0.272411	−	0.962181i	$-0.412179\pi$
$73$	4.65497	0.544823	0.272411	+	0.962181i	$0.412179\pi$
$74$	0.680854	0.0791477
$75$	1.53418	0.177152
$76$	2.68171	0.307614
$77$	1.29336	0.147392
$78$	0	0
$79$	15.9886	1.79886	0.899431	−	0.437062i	$-0.143981\pi$
$79$	15.9886	1.79886	0.899431	+	0.437062i	$0.143981\pi$
$80$	−2.61221	−0.292054
$81$	2.87337	0.319264
$82$	−1.87059	−0.206572
$83$	6.55669	0.719690	0.359845	−	0.933012i	$-0.382830\pi$
$83$	6.55669	0.719690	0.359845	+	0.933012i	$0.382830\pi$
$84$	−3.37299	−0.368023
$85$	4.43853	0.481426
$86$	−3.54916	−0.382716
$87$	24.2983	2.60505
$88$	−4.09113	−0.436116
$89$	−2.84594	−0.301669	−0.150834	−	0.988559i	$-0.548196\pi$
$89$	−2.84594	−0.301669	−0.150834	+	0.988559i	$0.548196\pi$
$90$	7.87930	0.830551
$91$	0	0
$92$	6.16305	0.642542
$93$	2.87369	0.297988
$94$	3.11763	0.321559
$95$	3.78525	0.388359
$96$	16.7710	1.71168
$97$	−3.61767	−0.367318	−0.183659	−	0.982990i	$-0.558794\pi$
$97$	−3.61767	−0.367318	−0.183659	+	0.982990i	$0.558794\pi$
$98$	4.52774	0.457371
$99$	−8.67478	−0.871849
$100$	0.799317	0.0799317
$101$	−4.20610	−0.418523	−0.209261	−	0.977860i	$-0.567106\pi$
$101$	−4.20610	−0.418523	−0.209261	+	0.977860i	$0.567106\pi$
$102$	−4.27963	−0.423746
$103$	6.33423	0.624131	0.312065	−	0.950061i	$-0.398979\pi$
$103$	6.33423	0.624131	0.312065	+	0.950061i	$0.398979\pi$
$104$	0	0
$105$	−4.76098	−0.464625
$106$	−7.09802	−0.689421
$107$	−14.5503	−1.40663	−0.703316	−	0.710877i	$-0.748298\pi$
$107$	−14.5503	−1.40663	−0.703316	+	0.710877i	$0.748298\pi$
$108$	9.71557	0.934881
$109$	−0.330287	−0.0316358	−0.0158179	−	0.999875i	$-0.505035\pi$
$109$	−0.330287	−0.0316358	−0.0158179	+	0.999875i	$0.505035\pi$
$110$	−2.47222	−0.235717
$111$	2.75932	0.261903
$112$	−0.969021	−0.0915639
$113$	6.62402	0.623135	0.311568	−	0.950224i	$-0.399146\pi$
$113$	6.62402	0.623135	0.311568	+	0.950224i	$0.399146\pi$
$114$	−3.64974	−0.341830
$115$	8.69917	0.811202
$116$	12.6595	1.17541
$117$	0	0
$118$	−4.68617	−0.431397
$119$	1.64651	0.150935
$120$	15.0598	1.37477
$121$	−8.27819	−0.752562
$122$	−9.02126	−0.816746
$123$	−7.58100	−0.683555
$124$	1.49721	0.134454
$125$	11.6948	1.04602
$126$	2.92289	0.260392
$127$	4.13545	0.366962	0.183481	−	0.983023i	$-0.441263\pi$
$127$	4.13545	0.366962	0.183481	+	0.983023i	$0.441263\pi$
$128$	10.4907	0.927257
$129$	−14.3838	−1.26642
$130$	0	0
$131$	−9.42052	−0.823075	−0.411537	−	0.911393i	$-0.635008\pi$
$131$	−9.42052	−0.823075	−0.411537	+	0.911393i	$0.635008\pi$
$132$	−7.09827	−0.617826
$133$	1.40417	0.121757
$134$	−2.18488	−0.188745
$135$	13.7136	1.18028
$136$	−5.20820	−0.446599
$137$	−10.1263	−0.865145	−0.432572	−	0.901599i	$-0.642394\pi$
$137$	−10.1263	−0.865145	−0.432572	+	0.901599i	$0.642394\pi$
$138$	−8.38774	−0.714012
$139$	11.1723	0.947625	0.473813	−	0.880626i	$-0.342877\pi$
$139$	11.1723	0.947625	0.473813	+	0.880626i	$0.342877\pi$
$140$	−2.48050	−0.209641
$141$	12.6349	1.06405
$142$	−3.49575	−0.293357
$143$	0	0
$144$	6.49938	0.541615
$145$	17.8690	1.48394
$146$	−3.30072	−0.273170
$147$	18.3497	1.51346
$148$	1.43762	0.118172
$149$	16.6102	1.36076	0.680381	−	0.732858i	$-0.261814\pi$
$149$	16.6102	1.36076	0.680381	+	0.732858i	$0.261814\pi$
$150$	−1.08785	−0.0888225
$151$	−23.6104	−1.92139	−0.960695	−	0.277608i	$-0.910458\pi$
$151$	−23.6104	−1.92139	−0.960695	+	0.277608i	$0.910458\pi$
$152$	−4.44164	−0.360265
$153$	−11.0434	−0.892806
$154$	−0.917091	−0.0739013
$155$	2.11332	0.169746
$156$	0	0
$157$	4.24171	0.338525	0.169262	−	0.985571i	$-0.445861\pi$
$157$	4.24171	0.338525	0.169262	+	0.985571i	$0.445861\pi$
$158$	−11.3372	−0.901935
$159$	−28.7664	−2.28132
$160$	12.3334	0.975043
$161$	3.22703	0.254326
$162$	−2.03744	−0.160076
$163$	18.5814	1.45541	0.727705	−	0.685890i	$-0.240587\pi$
$163$	18.5814	1.45541	0.727705	+	0.685890i	$0.240587\pi$
$164$	−3.94975	−0.308423
$165$	−10.0192	−0.779997
$166$	−4.64919	−0.360847
$167$	19.4675	1.50644	0.753221	−	0.657767i	$-0.228499\pi$
$167$	19.4675	1.50644	0.753221	+	0.657767i	$0.228499\pi$
$168$	5.58657	0.431014
$169$	0	0
$170$	−3.14725	−0.241383
$171$	−9.41800	−0.720213
$172$	−7.49405	−0.571416
$173$	−17.8920	−1.36030	−0.680150	−	0.733073i	$-0.738085\pi$
$173$	−17.8920	−1.36030	−0.680150	+	0.733073i	$0.738085\pi$
$174$	−17.2293	−1.30615
$175$	0.418530	0.0316379
$176$	−2.03926	−0.153715
$177$	−18.9918	−1.42751
$178$	2.01799	0.151254
$179$	1.92359	0.143776	0.0718880	−	0.997413i	$-0.477098\pi$
$179$	1.92359	0.143776	0.0718880	+	0.997413i	$0.477098\pi$
$180$	16.6371	1.24006
$181$	−23.8458	−1.77244	−0.886221	−	0.463263i	$-0.846678\pi$
$181$	−23.8458	−1.77244	−0.886221	+	0.463263i	$0.846678\pi$
$182$	0	0
$183$	−36.5607	−2.70265
$184$	−10.2077	−0.752519
$185$	2.02921	0.149191
$186$	−2.03766	−0.149409
$187$	3.46499	0.253385
$188$	6.58288	0.480106
$189$	5.08716	0.370037
$190$	−2.68403	−0.194720
$191$	−2.66551	−0.192870	−0.0964349	−	0.995339i	$-0.530744\pi$
$191$	−2.66551	−0.192870	−0.0964349	+	0.995339i	$0.530744\pi$
$192$	−4.78773	−0.345525
$193$	10.9967	0.791559	0.395779	−	0.918346i	$-0.370475\pi$
$193$	10.9967	0.791559	0.395779	+	0.918346i	$0.370475\pi$
$194$	2.56520	0.184171
$195$	0	0
$196$	9.56032	0.682880
$197$	−3.76446	−0.268206	−0.134103	−	0.990967i	$-0.542815\pi$
$197$	−3.76446	−0.268206	−0.134103	+	0.990967i	$0.542815\pi$
$198$	6.15108	0.437138
$199$	−1.46227	−0.103658	−0.0518289	−	0.998656i	$-0.516505\pi$
$199$	−1.46227	−0.103658	−0.0518289	+	0.998656i	$0.516505\pi$
$200$	−1.32388	−0.0936128
$201$	−8.85472	−0.624564
$202$	2.98244	0.209844
$203$	6.62866	0.465241
$204$	−9.03643	−0.632676
$205$	−5.57509	−0.389381
$206$	−4.49145	−0.312934
$207$	−21.6442	−1.50438
$208$	0	0
$209$	2.95501	0.204402
$210$	3.37590	0.232959
$211$	13.9102	0.957615	0.478808	−	0.877920i	$-0.341069\pi$
$211$	13.9102	0.957615	0.478808	+	0.877920i	$0.341069\pi$
$212$	−14.9875	−1.02934
$213$	−14.1674	−0.970731
$214$	10.3173	0.705274
$215$	−10.5779	−0.721405
$216$	−16.0916	−1.09489
$217$	0.783955	0.0532183
$218$	0.234198	0.0158619
$219$	−13.3770	−0.903931
$220$	−5.22009	−0.351939
$221$	0	0
$222$	−1.95657	−0.131316
$223$	9.87731	0.661434	0.330717	−	0.943730i	$-0.392710\pi$
$223$	9.87731	0.661434	0.330717	+	0.943730i	$0.392710\pi$
$224$	4.57519	0.305693
$225$	−2.80715	−0.187143
$226$	−4.69693	−0.312435
$227$	−12.4069	−0.823475	−0.411738	−	0.911302i	$-0.635078\pi$
$227$	−12.4069	−0.823475	−0.411738	+	0.911302i	$0.635078\pi$
$228$	−7.70642	−0.510370
$229$	8.61792	0.569488	0.284744	−	0.958604i	$-0.408091\pi$
$229$	8.61792	0.569488	0.284744	+	0.958604i	$0.408091\pi$
$230$	−6.16837	−0.406730
$231$	−3.71672	−0.244543
$232$	−20.9676	−1.37659
$233$	0.899255	0.0589122	0.0294561	−	0.999566i	$-0.490622\pi$
$233$	0.899255	0.0589122	0.0294561	+	0.999566i	$0.490622\pi$
$234$	0	0
$235$	9.29177	0.606128
$236$	−9.89485	−0.644100
$237$	−45.9464	−2.98454
$238$	−1.16750	−0.0756777
$239$	28.8292	1.86481	0.932403	−	0.361422i	$-0.117708\pi$
$239$	28.8292	1.86481	0.932403	+	0.361422i	$0.117708\pi$
$240$	7.50669	0.484555
$241$	21.2358	1.36792	0.683958	−	0.729522i	$-0.260257\pi$
$241$	21.2358	1.36792	0.683958	+	0.729522i	$0.260257\pi$
$242$	5.86986	0.377329
$243$	11.2101	0.719130
$244$	−19.0484	−1.21945
$245$	13.4944	0.862128
$246$	5.37550	0.342729
$247$	0	0
$248$	−2.47979	−0.157467
$249$	−18.8419	−1.19406
$250$	−8.29253	−0.524466
$251$	2.43630	0.153778	0.0768890	−	0.997040i	$-0.475501\pi$
$251$	2.43630	0.153778	0.0768890	+	0.997040i	$0.475501\pi$
$252$	6.17168	0.388780
$253$	6.79112	0.426954
$254$	−2.93235	−0.183992
$255$	−12.7550	−0.798746
$256$	−10.7708	−0.673177
$257$	16.5771	1.03405	0.517027	−	0.855969i	$-0.327039\pi$
$257$	16.5771	1.03405	0.517027	+	0.855969i	$0.327039\pi$
$258$	10.1992	0.634974
$259$	0.752753	0.0467738
$260$	0	0
$261$	−44.4595	−2.75197
$262$	6.67986	0.412683
$263$	−0.578689	−0.0356835	−0.0178418	−	0.999841i	$-0.505680\pi$
$263$	−0.578689	−0.0356835	−0.0178418	+	0.999841i	$0.505680\pi$
$264$	11.7567	0.723572
$265$	−21.1549	−1.29953
$266$	−0.995664	−0.0610481
$267$	8.17835	0.500507
$268$	−4.61337	−0.281806
$269$	−27.4959	−1.67646	−0.838228	−	0.545320i	$-0.816408\pi$
$269$	−27.4959	−1.67646	−0.838228	+	0.545320i	$0.816408\pi$
$270$	−9.72396	−0.591781
$271$	−22.2428	−1.35115	−0.675577	−	0.737290i	$-0.736105\pi$
$271$	−22.2428	−1.35115	−0.675577	+	0.737290i	$0.736105\pi$
$272$	−2.59606	−0.157410
$273$	0	0
$274$	7.18028	0.433777
$275$	0.880775	0.0531127
$276$	−17.7107	−1.06606
$277$	−3.62111	−0.217571	−0.108786	−	0.994065i	$-0.534696\pi$
$277$	−3.62111	−0.217571	−0.108786	+	0.994065i	$0.534696\pi$
$278$	−7.92203	−0.475132
$279$	−5.25811	−0.314795
$280$	4.10838	0.245523
$281$	31.8859	1.90215	0.951076	−	0.308957i	$-0.0999801\pi$
$281$	31.8859	1.90215	0.951076	+	0.308957i	$0.0999801\pi$
$282$	−8.95912	−0.533508
$283$	17.1848	1.02153	0.510764	−	0.859721i	$-0.329363\pi$
$283$	17.1848	1.02153	0.510764	+	0.859721i	$0.329363\pi$
$284$	−7.38128	−0.437998
$285$	−10.8777	−0.644337
$286$	0	0
$287$	−2.06813	−0.122078
$288$	−30.6865	−1.80822
$289$	−12.5889	−0.740524
$290$	−12.6705	−0.744036
$291$	10.3961	0.609428
$292$	−6.96948	−0.407858
$293$	29.2099	1.70646	0.853230	−	0.521535i	$-0.174640\pi$
$293$	29.2099	1.70646	0.853230	+	0.521535i	$0.174640\pi$
$294$	−13.0113	−0.758836
$295$	−13.9666	−0.813169
$296$	−2.38109	−0.138398
$297$	10.7057	0.621206
$298$	−11.7779	−0.682276
$299$	0	0
$300$	−2.29699	−0.132617
$301$	−3.92395	−0.226173
$302$	16.7416	0.963369
$303$	12.0870	0.694382
$304$	−2.21397	−0.126980
$305$	−26.8869	−1.53954
$306$	7.83060	0.447646
$307$	25.3394	1.44620	0.723099	−	0.690745i	$-0.242717\pi$
$307$	25.3394	1.44620	0.723099	+	0.690745i	$0.242717\pi$
$308$	−1.93644	−0.110339
$309$	−18.2026	−1.03551
$310$	−1.49850	−0.0851093
$311$	−24.2942	−1.37760	−0.688798	−	0.724953i	$-0.741861\pi$
$311$	−24.2942	−1.37760	−0.688798	+	0.724953i	$0.741861\pi$
$312$	0	0
$313$	−12.7169	−0.718804	−0.359402	−	0.933183i	$-0.617019\pi$
$313$	−12.7169	−0.718804	−0.359402	+	0.933183i	$0.617019\pi$
$314$	−3.00769	−0.169734
$315$	8.71136	0.490830
$316$	−23.9384	−1.34664
$317$	−23.9226	−1.34363	−0.671815	−	0.740719i	$-0.734485\pi$
$317$	−23.9226	−1.34363	−0.671815	+	0.740719i	$0.734485\pi$
$318$	20.3975	1.14384
$319$	13.9497	0.781032
$320$	−3.52091	−0.196825
$321$	41.8132	2.33378
$322$	−2.28821	−0.127517
$323$	3.76186	0.209315
$324$	−4.30205	−0.239003
$325$	0	0
$326$	−13.1756	−0.729731
$327$	0.949143	0.0524877
$328$	6.54185	0.361213
$329$	3.44686	0.190032
$330$	7.10440	0.391085
$331$	13.6527	0.750420	0.375210	−	0.926940i	$-0.377571\pi$
$331$	13.6527	0.750420	0.375210	+	0.926940i	$0.377571\pi$
$332$	−9.81676	−0.538765
$333$	−5.04884	−0.276675
$334$	−13.8039	−0.755318
$335$	−6.51179	−0.355777
$336$	2.78467	0.151916
$337$	9.89600	0.539069	0.269535	−	0.962991i	$-0.413130\pi$
$337$	9.89600	0.539069	0.269535	+	0.962991i	$0.413130\pi$
$338$	0	0
$339$	−19.0354	−1.03386
$340$	−6.64541	−0.360398
$341$	1.64979	0.0893413
$342$	6.67807	0.361109
$343$	10.4936	0.566599
$344$	12.4122	0.669219
$345$	−24.9987	−1.34589
$346$	12.6867	0.682044
$347$	−4.63115	−0.248613	−0.124307	−	0.992244i	$-0.539671\pi$
$347$	−4.63115	−0.248613	−0.124307	+	0.992244i	$0.539671\pi$
$348$	−36.3797	−1.95015
$349$	11.7707	0.630071	0.315036	−	0.949080i	$-0.397984\pi$
$349$	11.7707	0.630071	0.315036	+	0.949080i	$0.397984\pi$
$350$	−0.296769	−0.0158630
$351$	0	0
$352$	9.62825	0.513188
$353$	−36.2424	−1.92899	−0.964494	−	0.264103i	$-0.914924\pi$
$353$	−36.2424	−1.92899	−0.964494	+	0.264103i	$0.914924\pi$
$354$	13.4666	0.715743
$355$	−10.4187	−0.552968
$356$	4.26097	0.225831
$357$	−4.73156	−0.250421
$358$	−1.36397	−0.0720882
$359$	17.4838	0.922758	0.461379	−	0.887203i	$-0.347355\pi$
$359$	17.4838	0.922758	0.461379	+	0.887203i	$0.347355\pi$
$360$	−27.5556	−1.45231
$361$	−15.7918	−0.831148
$362$	16.9084	0.888688
$363$	23.7890	1.24860
$364$	0	0
$365$	−9.83745	−0.514916
$366$	25.9243	1.35509
$367$	5.74519	0.299896	0.149948	−	0.988694i	$-0.452089\pi$
$367$	5.74519	0.299896	0.149948	+	0.988694i	$0.452089\pi$
$368$	−5.08809	−0.265235
$369$	13.8712	0.722108
$370$	−1.43886	−0.0748030
$371$	−7.84758	−0.407426
$372$	−4.30253	−0.223076
$373$	−17.7904	−0.921151	−0.460575	−	0.887621i	$-0.652357\pi$
$373$	−17.7904	−0.921151	−0.460575	+	0.887621i	$0.652357\pi$
$374$	−2.45694	−0.127045
$375$	−33.6074	−1.73548
$376$	−10.9030	−0.562281
$377$	0	0
$378$	−3.60718	−0.185534
$379$	−32.4615	−1.66744	−0.833718	−	0.552191i	$-0.813792\pi$
$379$	−32.4615	−1.66744	−0.833718	+	0.552191i	$0.813792\pi$
$380$	−5.66733	−0.290728
$381$	−11.8840	−0.608837
$382$	1.89005	0.0967034
$383$	−15.1790	−0.775612	−0.387806	−	0.921741i	$-0.626767\pi$
$383$	−15.1790	−0.775612	−0.387806	+	0.921741i	$0.626767\pi$
$384$	−30.1471	−1.53844
$385$	−2.73329	−0.139301
$386$	−7.79748	−0.396881
$387$	26.3186	1.33785
$388$	5.41641	0.274977
$389$	−2.78705	−0.141309	−0.0706545	−	0.997501i	$-0.522509\pi$
$389$	−2.78705	−0.141309	−0.0706545	+	0.997501i	$0.522509\pi$
$390$	0	0
$391$	8.64540	0.437217
$392$	−15.8345	−0.799762
$393$	27.0717	1.36559
$394$	2.66928	0.134477
$395$	−33.7891	−1.70012
$396$	12.9880	0.652671
$397$	32.9787	1.65515	0.827576	−	0.561354i	$-0.189719\pi$
$397$	32.9787	1.65515	0.827576	+	0.561354i	$0.189719\pi$
$398$	1.03686	0.0519732
$399$	−4.03516	−0.202011
$400$	−0.659900	−0.0329950
$401$	18.3499	0.916352	0.458176	−	0.888862i	$-0.348503\pi$
$401$	18.3499	0.916352	0.458176	+	0.888862i	$0.348503\pi$
$402$	6.27866	0.313151
$403$	0	0
$404$	6.29742	0.313309
$405$	−6.07236	−0.301738
$406$	−4.70022	−0.233268
$407$	1.58413	0.0785224
$408$	14.9668	0.740965
$409$	−10.6012	−0.524196	−0.262098	−	0.965041i	$-0.584414\pi$
$409$	−10.6012	−0.524196	−0.262098	+	0.965041i	$0.584414\pi$
$410$	3.95316	0.195233
$411$	29.0998	1.43539
$412$	−9.48369	−0.467228
$413$	−5.18104	−0.254942
$414$	15.3474	0.754282
$415$	−13.8564	−0.680184
$416$	0	0
$417$	−32.1059	−1.57223
$418$	−2.09532	−0.102486
$419$	21.3577	1.04339	0.521695	−	0.853132i	$-0.325300\pi$
$419$	21.3577	1.04339	0.521695	+	0.853132i	$0.325300\pi$
$420$	7.12820	0.347821
$421$	−21.7079	−1.05798	−0.528989	−	0.848629i	$-0.677429\pi$
$421$	−21.7079	−1.05798	−0.528989	+	0.848629i	$0.677429\pi$
$422$	−9.86336	−0.480141
$423$	−23.1186	−1.12407
$424$	24.8233	1.20553
$425$	1.12127	0.0543894
$426$	10.0457	0.486717
$427$	−9.97391	−0.482671
$428$	21.7849	1.05301
$429$	0	0
$430$	7.50052	0.361707
$431$	23.8677	1.14966	0.574832	−	0.818271i	$-0.305067\pi$
$431$	23.8677	1.14966	0.574832	+	0.818271i	$0.305067\pi$
$432$	−8.02098	−0.385909
$433$	−31.2737	−1.50292	−0.751459	−	0.659780i	$-0.770650\pi$
$433$	−31.2737	−1.50292	−0.751459	+	0.659780i	$0.770650\pi$
$434$	−0.555883	−0.0266832
$435$	−51.3501	−2.46205
$436$	0.494510	0.0236827
$437$	7.37295	0.352696
$438$	9.48527	0.453224
$439$	−9.33113	−0.445350	−0.222675	−	0.974893i	$-0.571479\pi$
$439$	−9.33113	−0.445350	−0.222675	+	0.974893i	$0.571479\pi$
$440$	8.64588	0.412176
$441$	−33.5752	−1.59882
$442$	0	0
$443$	−25.1538	−1.19509	−0.597546	−	0.801835i	$-0.703857\pi$
$443$	−25.1538	−1.19509	−0.597546	+	0.801835i	$0.703857\pi$
$444$	−4.13129	−0.196062
$445$	6.01439	0.285109
$446$	−7.00376	−0.331638
$447$	−47.7327	−2.25768
$448$	−1.30611	−0.0617080
$449$	−27.8053	−1.31222	−0.656108	−	0.754667i	$-0.727798\pi$
$449$	−27.8053	−1.31222	−0.656108	+	0.754667i	$0.727798\pi$
$450$	1.99048	0.0938321
$451$	−4.35226	−0.204940
$452$	−9.91756	−0.466483
$453$	67.8491	3.18783
$454$	8.79743	0.412884
$455$	0	0
$456$	12.7639	0.597725
$457$	20.4982	0.958865	0.479433	−	0.877579i	$-0.340843\pi$
$457$	20.4982	0.958865	0.479433	+	0.877579i	$0.340843\pi$
$458$	−6.11076	−0.285537
$459$	13.6288	0.636139
$460$	−13.0245	−0.607271
$461$	−27.0762	−1.26107	−0.630533	−	0.776162i	$-0.717164\pi$
$461$	−27.0762	−1.26107	−0.630533	+	0.776162i	$0.717164\pi$
$462$	2.63544	0.122612
$463$	−6.14401	−0.285536	−0.142768	−	0.989756i	$-0.545600\pi$
$463$	−6.14401	−0.285536	−0.142768	+	0.989756i	$0.545600\pi$
$464$	−10.4515	−0.485197
$465$	−6.07304	−0.281630
$466$	−0.637640	−0.0295381
$467$	31.2574	1.44642	0.723209	−	0.690629i	$-0.242666\pi$
$467$	31.2574	1.44642	0.723209	+	0.690629i	$0.242666\pi$
$468$	0	0
$469$	−2.41560	−0.111542
$470$	−6.58857	−0.303908
$471$	−12.1894	−0.561656
$472$	16.3885	0.754344
$473$	−8.25776	−0.379692
$474$	32.5795	1.49643
$475$	0.956236	0.0438751
$476$	−2.46517	−0.112991
$477$	52.6350	2.40999
$478$	−20.4421	−0.934998
$479$	−4.86212	−0.222156	−0.111078	−	0.993812i	$-0.535430\pi$
$479$	−4.86212	−0.222156	−0.111078	+	0.993812i	$0.535430\pi$
$480$	−35.4425	−1.61772
$481$	0	0
$482$	−15.0577	−0.685862
$483$	−9.27349	−0.421959
$484$	12.3942	0.563373
$485$	7.64530	0.347155
$486$	−7.94883	−0.360566
$487$	−31.9091	−1.44594	−0.722970	−	0.690879i	$-0.757224\pi$
$487$	−31.9091	−1.44594	−0.722970	+	0.690879i	$0.757224\pi$
$488$	31.5493	1.42817
$489$	−53.3973	−2.41471
$490$	−9.56857	−0.432264
$491$	−3.21102	−0.144911	−0.0724557	−	0.997372i	$-0.523084\pi$
$491$	−3.21102	−0.144911	−0.0724557	+	0.997372i	$0.523084\pi$
$492$	11.3504	0.511714
$493$	17.7586	0.799806
$494$	0	0
$495$	18.3326	0.823990
$496$	−1.23607	−0.0555011
$497$	−3.86491	−0.173365
$498$	13.3603	0.598691
$499$	12.0183	0.538013	0.269006	−	0.963138i	$-0.413305\pi$
$499$	12.0183	0.538013	0.269006	+	0.963138i	$0.413305\pi$
$500$	−17.5097	−0.783056
$501$	−55.9437	−2.49938
$502$	−1.72752	−0.0771030
$503$	−8.33682	−0.371720	−0.185860	−	0.982576i	$-0.559507\pi$
$503$	−8.33682	−0.371720	−0.185860	+	0.982576i	$0.559507\pi$
$504$	−10.2220	−0.455323
$505$	8.88884	0.395548
$506$	−4.81542	−0.214071
$507$	0	0
$508$	−6.19165	−0.274710
$509$	26.0740	1.15571	0.577855	−	0.816140i	$-0.303890\pi$
$509$	26.0740	1.15571	0.577855	+	0.816140i	$0.303890\pi$
$510$	9.04423	0.400485
$511$	−3.64928	−0.161435
$512$	−13.3441	−0.589732
$513$	11.6229	0.513163
$514$	−11.7544	−0.518466
$515$	−13.3863	−0.589870
$516$	21.5356	0.948051
$517$	7.25374	0.319019
$518$	−0.533759	−0.0234520
$519$	51.4160	2.25691
$520$	0	0
$521$	−30.6542	−1.34298	−0.671492	−	0.741012i	$-0.734346\pi$
$521$	−30.6542	−1.34298	−0.671492	+	0.741012i	$0.734346\pi$
$522$	31.5251	1.37982
$523$	−5.51176	−0.241013	−0.120506	−	0.992713i	$-0.538452\pi$
$523$	−5.51176	−0.241013	−0.120506	+	0.992713i	$0.538452\pi$
$524$	14.1045	0.616159
$525$	−1.20273	−0.0524913
$526$	0.410334	0.0178914
$527$	2.10026	0.0914888
$528$	5.86019	0.255032
$529$	−6.05567	−0.263290
$530$	15.0004	0.651576
$531$	34.7501	1.50802
$532$	−2.10234	−0.0911481
$533$	0	0
$534$	−5.79907	−0.250950
$535$	30.7495	1.32942
$536$	7.64098	0.330040
$537$	−5.52781	−0.238543
$538$	19.4967	0.840561
$539$	10.5346	0.453758
$540$	−20.5321	−0.883562
$541$	−9.57466	−0.411647	−0.205823	−	0.978589i	$-0.565987\pi$
$541$	−9.57466	−0.411647	−0.205823	+	0.978589i	$0.565987\pi$
$542$	15.7718	0.677458
$543$	68.5254	2.94071
$544$	12.2572	0.525523
$545$	0.698003	0.0298992
$546$	0	0
$547$	26.9614	1.15279	0.576394	−	0.817172i	$-0.304459\pi$
$547$	26.9614	1.15279	0.576394	+	0.817172i	$0.304459\pi$
$548$	15.1612	0.647653
$549$	66.8966	2.85508
$550$	−0.624536	−0.0266303
$551$	15.1448	0.645191
$552$	29.3337	1.24853
$553$	−12.5344	−0.533015
$554$	2.56764	0.109089
$555$	−5.83133	−0.247526
$556$	−16.7274	−0.709398
$557$	−1.25226	−0.0530601	−0.0265301	−	0.999648i	$-0.508446\pi$
$557$	−1.25226	−0.0530601	−0.0265301	+	0.999648i	$0.508446\pi$
$558$	3.72840	0.157836
$559$	0	0
$560$	2.04785	0.0865376
$561$	−9.95732	−0.420399
$562$	−22.6095	−0.953724
$563$	10.6829	0.450232	0.225116	−	0.974332i	$-0.427724\pi$
$563$	10.6829	0.450232	0.225116	+	0.974332i	$0.427724\pi$
$564$	−18.9172	−0.796557
$565$	−13.9987	−0.588929
$566$	−12.1853	−0.512186
$567$	−2.25259	−0.0946001
$568$	12.2254	0.512966
$569$	11.0501	0.463246	0.231623	−	0.972806i	$-0.425596\pi$
$569$	11.0501	0.463246	0.231623	+	0.972806i	$0.425596\pi$
$570$	7.71308	0.323065
$571$	−32.2598	−1.35003	−0.675016	−	0.737803i	$-0.735863\pi$
$571$	−32.2598	−1.35003	−0.675016	+	0.737803i	$0.735863\pi$
$572$	0	0
$573$	7.65987	0.319996
$574$	1.46646	0.0612087
$575$	2.19760	0.0916461
$576$	8.76030	0.365013
$577$	3.67336	0.152924	0.0764620	−	0.997072i	$-0.475638\pi$
$577$	3.67336	0.152924	0.0764620	+	0.997072i	$0.475638\pi$
$578$	8.92648	0.371293
$579$	−31.6011	−1.31330
$580$	−26.7537	−1.11089
$581$	−5.14015	−0.213249
$582$	−7.37159	−0.305562
$583$	−16.5148	−0.683975
$584$	11.5433	0.477667
$585$	0	0
$586$	−20.7120	−0.855605
$587$	−26.5616	−1.09631	−0.548157	−	0.836375i	$-0.684670\pi$
$587$	−26.5616	−1.09631	−0.548157	+	0.836375i	$0.684670\pi$
$588$	−27.4734	−1.13298
$589$	1.79114	0.0738026
$590$	9.90340	0.407716
$591$	10.8179	0.444988
$592$	−1.18687	−0.0487802
$593$	−1.24660	−0.0511919	−0.0255960	−	0.999672i	$-0.508148\pi$
$593$	−1.24660	−0.0511919	−0.0255960	+	0.999672i	$0.508148\pi$
$594$	−7.59113	−0.311468
$595$	−3.47960	−0.142650
$596$	−24.8690	−1.01868
$597$	4.20212	0.171981
$598$	0	0
$599$	27.1300	1.10850	0.554250	−	0.832350i	$-0.313005\pi$
$599$	27.1300	1.10850	0.554250	+	0.832350i	$0.313005\pi$
$600$	3.80444	0.155316
$601$	−14.7636	−0.602218	−0.301109	−	0.953590i	$-0.597357\pi$
$601$	−14.7636	−0.602218	−0.301109	+	0.953590i	$0.597357\pi$
$602$	2.78238	0.113401
$603$	16.2018	0.659789
$604$	35.3498	1.43836
$605$	17.4945	0.711251
$606$	−8.57062	−0.348158
$607$	8.00865	0.325061	0.162530	−	0.986704i	$-0.448034\pi$
$607$	8.00865	0.325061	0.162530	+	0.986704i	$0.448034\pi$
$608$	10.4532	0.423932
$609$	−19.0487	−0.771894
$610$	19.0648	0.771912
$611$	0	0
$612$	16.5343	0.668360
$613$	45.1160	1.82222	0.911109	−	0.412166i	$-0.135227\pi$
$613$	45.1160	1.82222	0.911109	+	0.412166i	$0.135227\pi$
$614$	−17.9676	−0.725112
$615$	16.0211	0.646033
$616$	3.20726	0.129224
$617$	−0.796112	−0.0320502	−0.0160251	−	0.999872i	$-0.505101\pi$
$617$	−0.796112	−0.0320502	−0.0160251	+	0.999872i	$0.505101\pi$
$618$	12.9070	0.519197
$619$	30.8439	1.23972	0.619861	−	0.784712i	$-0.287189\pi$
$619$	30.8439	1.23972	0.619861	+	0.784712i	$0.287189\pi$
$620$	−3.16409	−0.127073
$621$	26.7114	1.07189
$622$	17.2264	0.690716
$623$	2.23109	0.0893866
$624$	0	0
$625$	−22.0456	−0.881825
$626$	9.01727	0.360402
$627$	−8.49178	−0.339129
$628$	−6.35073	−0.253422
$629$	2.01667	0.0804099
$630$	−6.17701	−0.246098
$631$	−39.2945	−1.56429	−0.782145	−	0.623096i	$-0.785875\pi$
$631$	−39.2945	−1.56429	−0.782145	+	0.623096i	$0.785875\pi$
$632$	39.6484	1.57713
$633$	−39.9735	−1.58881
$634$	16.9630	0.673685
$635$	−8.73954	−0.346818
$636$	43.0694	1.70781
$637$	0	0
$638$	−9.89137	−0.391603
$639$	25.9226	1.02548
$640$	−22.1703	−0.876357
$641$	−26.0112	−1.02738	−0.513691	−	0.857975i	$-0.671722\pi$
$641$	−26.0112	−1.02738	−0.513691	+	0.857975i	$0.671722\pi$
$642$	−29.6487	−1.17014
$643$	21.1289	0.833244	0.416622	−	0.909080i	$-0.363214\pi$
$643$	21.1289	0.833244	0.416622	+	0.909080i	$0.363214\pi$
$644$	−4.83155	−0.190390
$645$	30.3976	1.19690
$646$	−2.66744	−0.104949
$647$	33.1213	1.30213	0.651067	−	0.759020i	$-0.274322\pi$
$647$	33.1213	1.30213	0.651067	+	0.759020i	$0.274322\pi$
$648$	7.12536	0.279910
$649$	−10.9032	−0.427989
$650$	0	0
$651$	−2.25284	−0.0882959
$652$	−27.8203	−1.08953
$653$	−21.1686	−0.828392	−0.414196	−	0.910188i	$-0.635937\pi$
$653$	−21.1686	−0.828392	−0.414196	+	0.910188i	$0.635937\pi$
$654$	−0.673014	−0.0263169
$655$	19.9086	0.777893
$656$	3.26083	0.127314
$657$	24.4763	0.954913
$658$	−2.44408	−0.0952803
$659$	−7.88939	−0.307327	−0.153664	−	0.988123i	$-0.549107\pi$
$659$	−7.88939	−0.307327	−0.153664	+	0.988123i	$0.549107\pi$
$660$	15.0009	0.583911
$661$	−3.93626	−0.153103	−0.0765515	−	0.997066i	$-0.524391\pi$
$661$	−3.93626	−0.153103	−0.0765515	+	0.997066i	$0.524391\pi$
$662$	−9.68079	−0.376255
$663$	0	0
$664$	16.2592	0.630979
$665$	−2.96747	−0.115073
$666$	3.58001	0.138722
$667$	34.8054	1.34767
$668$	−29.1470	−1.12773
$669$	−28.3843	−1.09740
$670$	4.61735	0.178384
$671$	−20.9896	−0.810294
$672$	−13.1477	−0.507183
$673$	−48.6562	−1.87556	−0.937779	−	0.347234i	$-0.887121\pi$
$673$	−48.6562	−1.87556	−0.937779	+	0.347234i	$0.887121\pi$
$674$	−7.01701	−0.270285
$675$	3.46434	0.133343
$676$	0	0
$677$	22.2236	0.854123	0.427062	−	0.904223i	$-0.359549\pi$
$677$	22.2236	0.854123	0.427062	+	0.904223i	$0.359549\pi$
$678$	13.4975	0.518370
$679$	2.83609	0.108839
$680$	11.0066	0.422084
$681$	35.6536	1.36625
$682$	−1.16983	−0.0447950
$683$	−39.0166	−1.49293	−0.746464	−	0.665425i	$-0.768250\pi$
$683$	−39.0166	−1.49293	−0.746464	+	0.665425i	$0.768250\pi$
$684$	14.1007	0.539156
$685$	21.4001	0.817654
$686$	−7.44072	−0.284088
$687$	−24.7653	−0.944853
$688$	6.18693	0.235875
$689$	0	0
$690$	17.7260	0.674817
$691$	28.5328	1.08544	0.542720	−	0.839914i	$-0.317395\pi$
$691$	28.5328	1.08544	0.542720	+	0.839914i	$0.317395\pi$
$692$	26.7881	1.01833
$693$	6.80064	0.258335
$694$	3.28384	0.124653
$695$	−23.6107	−0.895607
$696$	60.2545	2.28394
$697$	−5.54063	−0.209866
$698$	−8.34631	−0.315913
$699$	−2.58418	−0.0977427
$700$	−0.626628	−0.0236843
$701$	−41.1148	−1.55289	−0.776443	−	0.630187i	$-0.782978\pi$
$701$	−41.1148	−1.55289	−0.776443	+	0.630187i	$0.782978\pi$
$702$	0	0
$703$	1.71985	0.0648655
$704$	−2.74865	−0.103594
$705$	−26.7017	−1.00564
$706$	25.6986	0.967180
$707$	3.29739	0.124011
$708$	28.4348	1.06864
$709$	41.8480	1.57163	0.785816	−	0.618460i	$-0.212243\pi$
$709$	41.8480	1.57163	0.785816	+	0.618460i	$0.212243\pi$
$710$	7.38765	0.277254
$711$	84.0700	3.15287
$712$	−7.05732	−0.264484
$713$	4.11635	0.154158
$714$	3.35503	0.125559
$715$	0	0
$716$	−2.88003	−0.107632
$717$	−82.8462	−3.09395
$718$	−12.3973	−0.462663
$719$	−47.4012	−1.76776	−0.883882	−	0.467709i	$-0.845079\pi$
$719$	−47.4012	−1.76776	−0.883882	+	0.467709i	$0.845079\pi$
$720$	−13.7353	−0.511884
$721$	−4.96575	−0.184934
$722$	11.1976	0.416731
$723$	−61.0250	−2.26954
$724$	35.7022	1.32686
$725$	4.51410	0.167649
$726$	−16.8682	−0.626036
$727$	−0.734381	−0.0272367	−0.0136183	−	0.999907i	$-0.504335\pi$
$727$	−0.734381	−0.0272367	−0.0136183	+	0.999907i	$0.504335\pi$
$728$	0	0
$729$	−40.8346	−1.51239
$730$	6.97549	0.258175
$731$	−10.5125	−0.388819
$732$	54.7392	2.02322
$733$	19.3298	0.713964	0.356982	−	0.934111i	$-0.383806\pi$
$733$	19.3298	0.713964	0.356982	+	0.934111i	$0.383806\pi$
$734$	−4.07377	−0.150366
$735$	−38.7789	−1.43038
$736$	24.0232	0.885506
$737$	−5.08351	−0.187254
$738$	−9.83576	−0.362059
$739$	−24.0128	−0.883324	−0.441662	−	0.897182i	$-0.645611\pi$
$739$	−24.0128	−0.883324	−0.441662	+	0.897182i	$0.645611\pi$
$740$	−3.03816	−0.111685
$741$	0	0
$742$	5.56453	0.204280
$743$	−1.03395	−0.0379319	−0.0189660	−	0.999820i	$-0.506037\pi$
$743$	−1.03395	−0.0379319	−0.0189660	+	0.999820i	$0.506037\pi$
$744$	7.12615	0.261257
$745$	−35.1028	−1.28607
$746$	12.6147	0.461858
$747$	34.4758	1.26140
$748$	−5.18783	−0.189686
$749$	11.4068	0.416795
$750$	23.8302	0.870155
$751$	−13.4734	−0.491651	−0.245825	−	0.969314i	$-0.579059\pi$
$751$	−13.4734	−0.491651	−0.245825	+	0.969314i	$0.579059\pi$
$752$	−5.43469	−0.198183
$753$	−7.00118	−0.255137
$754$	0	0
$755$	49.8964	1.81592
$756$	−7.61656	−0.277012
$757$	−11.6135	−0.422101	−0.211051	−	0.977475i	$-0.567688\pi$
$757$	−11.6135	−0.422101	−0.211051	+	0.977475i	$0.567688\pi$
$758$	23.0177	0.836039
$759$	−19.5156	−0.708371
$760$	9.38662	0.340489
$761$	−11.6589	−0.422636	−0.211318	−	0.977417i	$-0.567776\pi$
$761$	−11.6589	−0.422636	−0.211318	+	0.977417i	$0.567776\pi$
$762$	8.42666	0.305266
$763$	0.258930	0.00937390
$764$	3.99084	0.144384
$765$	23.3382	0.843796
$766$	10.7631	0.388886
$767$	0	0
$768$	30.9520	1.11689
$769$	15.6244	0.563430	0.281715	−	0.959498i	$-0.409097\pi$
$769$	15.6244	0.563430	0.281715	+	0.959498i	$0.409097\pi$
$770$	1.93811	0.0698446
$771$	−47.6376	−1.71563
$772$	−16.4644	−0.592566
$773$	7.35478	0.264533	0.132267	−	0.991214i	$-0.457775\pi$
$773$	7.35478	0.264533	0.132267	+	0.991214i	$0.457775\pi$
$774$	−18.6619	−0.670787
$775$	0.533870	0.0191772
$776$	−8.97104	−0.322042
$777$	−2.16318	−0.0776037
$778$	1.97623	0.0708512
$779$	−4.72515	−0.169296
$780$	0	0
$781$	−8.13350	−0.291040
$782$	−6.13024	−0.219217
$783$	54.8681	1.96083
$784$	−7.89281	−0.281886
$785$	−8.96409	−0.319942
$786$	−19.1959	−0.684694
$787$	−2.24801	−0.0801329	−0.0400665	−	0.999197i	$-0.512757\pi$
$787$	−2.24801	−0.0801329	−0.0400665	+	0.999197i	$0.512757\pi$
$788$	5.63619	0.200781
$789$	1.66297	0.0592035
$790$	23.9591	0.852425
$791$	−5.19293	−0.184639
$792$	−21.5116	−0.764382
$793$	0	0
$794$	−23.3844	−0.829880
$795$	60.7926	2.15609
$796$	2.18933	0.0775988
$797$	−21.6912	−0.768343	−0.384171	−	0.923262i	$-0.625513\pi$
$797$	−21.6912	−0.768343	−0.384171	+	0.923262i	$0.625513\pi$
$798$	2.86123	0.101286
$799$	9.23434	0.326688
$800$	3.11569	0.110156
$801$	−14.9643	−0.528736
$802$	−13.0115	−0.459451
$803$	−7.67973	−0.271012
$804$	13.2574	0.467552
$805$	−6.81975	−0.240365
$806$	0	0
$807$	79.0148	2.78145
$808$	−10.4302	−0.366934
$809$	−17.9451	−0.630917	−0.315459	−	0.948939i	$-0.602158\pi$
$809$	−17.9451	−0.630917	−0.315459	+	0.948939i	$0.602158\pi$
$810$	4.30576	0.151289
$811$	9.55828	0.335637	0.167818	−	0.985818i	$-0.446328\pi$
$811$	9.55828	0.335637	0.167818	+	0.985818i	$0.446328\pi$
$812$	−9.92451	−0.348282
$813$	63.9190	2.24174
$814$	−1.12327	−0.0393705
$815$	−39.2685	−1.37552
$816$	7.46029	0.261162
$817$	−8.96525	−0.313654
$818$	7.51706	0.262828
$819$	0	0
$820$	8.34709	0.291493
$821$	−6.91481	−0.241328	−0.120664	−	0.992693i	$-0.538502\pi$
$821$	−6.91481	−0.241328	−0.120664	+	0.992693i	$0.538502\pi$
$822$	−20.6339	−0.719691
$823$	−39.1630	−1.36514	−0.682569	−	0.730821i	$-0.739137\pi$
$823$	−39.1630	−1.36514	−0.682569	+	0.730821i	$0.739137\pi$
$824$	15.7076	0.547198
$825$	−2.53108	−0.0881208
$826$	3.67375	0.127826
$827$	17.7084	0.615780	0.307890	−	0.951422i	$-0.400377\pi$
$827$	17.7084	0.615780	0.307890	+	0.951422i	$0.400377\pi$
$828$	32.4060	1.12619
$829$	48.6359	1.68920	0.844598	−	0.535401i	$-0.179840\pi$
$829$	48.6359	1.68920	0.844598	+	0.535401i	$0.179840\pi$
$830$	9.82523	0.341039
$831$	10.4060	0.360979
$832$	0	0
$833$	13.4110	0.464665
$834$	22.7655	0.788304
$835$	−41.1411	−1.42375
$836$	−4.42427	−0.153017
$837$	6.48911	0.224296
$838$	−15.1442	−0.523148
$839$	28.0117	0.967070	0.483535	−	0.875325i	$-0.339353\pi$
$839$	28.0117	0.967070	0.483535	+	0.875325i	$0.339353\pi$
$840$	−11.8062	−0.407354
$841$	42.4940	1.46531
$842$	15.3925	0.530462
$843$	−91.6302	−3.15591
$844$	−20.8265	−0.716877
$845$	0	0
$846$	16.3929	0.563598
$847$	6.48972	0.222989
$848$	12.3734	0.424903
$849$	−49.3837	−1.69484
$850$	−0.795063	−0.0272704
$851$	3.95252	0.135491
$852$	21.2115	0.726695
$853$	−20.2419	−0.693071	−0.346536	−	0.938037i	$-0.612642\pi$
$853$	−20.2419	−0.693071	−0.346536	+	0.938037i	$0.612642\pi$
$854$	7.07226	0.242008
$855$	19.9033	0.680678
$856$	−36.0817	−1.23325
$857$	−9.02467	−0.308277	−0.154139	−	0.988049i	$-0.549260\pi$
$857$	−9.02467	−0.308277	−0.154139	+	0.988049i	$0.549260\pi$
$858$	0	0
$859$	50.6873	1.72943	0.864714	−	0.502265i	$-0.167500\pi$
$859$	50.6873	1.72943	0.864714	+	0.502265i	$0.167500\pi$
$860$	15.8373	0.540048
$861$	5.94316	0.202542
$862$	−16.9240	−0.576433
$863$	−13.3637	−0.454906	−0.227453	−	0.973789i	$-0.573040\pi$
$863$	−13.3637	−0.454906	−0.227453	+	0.973789i	$0.573040\pi$
$864$	37.8707	1.28839
$865$	37.8115	1.28563
$866$	22.1754	0.753551
$867$	36.1766	1.22862
$868$	−1.17375	−0.0398395
$869$	−26.3779	−0.894810
$870$	36.4111	1.23445
$871$	0	0
$872$	−0.819041	−0.0277362
$873$	−19.0221	−0.643800
$874$	−5.22798	−0.176839
$875$	−9.16823	−0.309943
$876$	20.0281	0.676688
$877$	8.02866	0.271109	0.135554	−	0.990770i	$-0.456718\pi$
$877$	8.02866	0.271109	0.135554	+	0.990770i	$0.456718\pi$
$878$	6.61647	0.223295
$879$	−83.9402	−2.83123
$880$	4.30960	0.145277
$881$	−15.4699	−0.521194	−0.260597	−	0.965448i	$-0.583919\pi$
$881$	−15.4699	−0.521194	−0.260597	+	0.965448i	$0.583919\pi$
$882$	23.8074	0.801635
$883$	21.9581	0.738949	0.369474	−	0.929241i	$-0.379538\pi$
$883$	21.9581	0.738949	0.369474	+	0.929241i	$0.379538\pi$
$884$	0	0
$885$	40.1358	1.34915
$886$	17.8359	0.599210
$887$	52.8759	1.77540	0.887699	−	0.460424i	$-0.152303\pi$
$887$	52.8759	1.77540	0.887699	+	0.460424i	$0.152303\pi$
$888$	6.84253	0.229620
$889$	−3.24201	−0.108733
$890$	−4.26465	−0.142951
$891$	−4.74047	−0.158812
$892$	−14.7884	−0.495153
$893$	7.87521	0.263534
$894$	33.8461	1.13198
$895$	−4.06517	−0.135884
$896$	−8.22425	−0.274753
$897$	0	0
$898$	19.7161	0.657934
$899$	8.45542	0.282004
$900$	4.20290	0.140097
$901$	−21.0241	−0.700415
$902$	3.08608	0.102755
$903$	11.2762	0.375250
$904$	16.4262	0.546326
$905$	50.3938	1.67515
$906$	−48.1101	−1.59835
$907$	54.1411	1.79772	0.898862	−	0.438232i	$-0.144395\pi$
$907$	54.1411	1.79772	0.898862	+	0.438232i	$0.144395\pi$
$908$	18.5758	0.616458
$909$	−22.1161	−0.733546
$910$	0	0
$911$	−45.4888	−1.50711	−0.753555	−	0.657384i	$-0.771663\pi$
$911$	−45.4888	−1.50711	−0.753555	+	0.657384i	$0.771663\pi$
$912$	6.36227	0.210676
$913$	−10.8172	−0.357996
$914$	−14.5348	−0.480767
$915$	77.2646	2.55429
$916$	−12.9029	−0.426322
$917$	7.38526	0.243883
$918$	−9.66386	−0.318955
$919$	1.03662	0.0341950	0.0170975	−	0.999854i	$-0.494557\pi$
$919$	1.03662	0.0341950	0.0170975	+	0.999854i	$0.494557\pi$
$920$	21.5721	0.711211
$921$	−72.8177	−2.39943
$922$	19.1991	0.632289
$923$	0	0
$924$	5.56472	0.183066
$925$	0.512622	0.0168549
$926$	4.35657	0.143166
$927$	33.3061	1.09392
$928$	49.3461	1.61987
$929$	−54.1533	−1.77671	−0.888357	−	0.459154i	$-0.848153\pi$
$929$	−54.1533	−1.77671	−0.888357	+	0.459154i	$0.848153\pi$
$930$	4.30624	0.141207
$931$	11.4372	0.374838
$932$	−1.34638	−0.0441020
$933$	69.8140	2.28561
$934$	−22.1638	−0.725222
$935$	−7.32265	−0.239476
$936$	0	0
$937$	46.8956	1.53201	0.766006	−	0.642833i	$-0.222241\pi$
$937$	46.8956	1.53201	0.766006	+	0.642833i	$0.222241\pi$
$938$	1.71284	0.0559263
$939$	36.5446	1.19259
$940$	−13.9118	−0.453751
$941$	−22.0239	−0.717959	−0.358979	−	0.933346i	$-0.616875\pi$
$941$	−22.0239	−0.717959	−0.358979	+	0.933346i	$0.616875\pi$
$942$	8.64317	0.281610
$943$	−10.8592	−0.353625
$944$	8.16899	0.265878
$945$	−10.7508	−0.349724
$946$	5.85537	0.190375
$947$	−34.7986	−1.13080	−0.565401	−	0.824816i	$-0.691278\pi$
$947$	−34.7986	−1.13080	−0.565401	+	0.824816i	$0.691278\pi$
$948$	68.7915	2.23425
$949$	0	0
$950$	−0.678044	−0.0219986
$951$	68.7463	2.22925
$952$	4.08299	0.132330
$953$	12.1587	0.393857	0.196929	−	0.980418i	$-0.436903\pi$
$953$	12.1587	0.393857	0.196929	+	0.980418i	$0.436903\pi$
$954$	−37.3222	−1.20835
$955$	5.63309	0.182283
$956$	−43.1634	−1.39600
$957$	−40.0871	−1.29583
$958$	3.44761	0.111387
$959$	7.93853	0.256348
$960$	10.1180	0.326558
$961$	1.00000	0.0322581
$962$	0	0
$963$	−76.5072	−2.46541
$964$	−31.7944	−1.02403
$965$	−23.2395	−0.748107
$966$	6.57561	0.211567
$967$	−35.2183	−1.13254	−0.566271	−	0.824219i	$-0.691615\pi$
$967$	−35.2183	−1.13254	−0.566271	+	0.824219i	$0.691615\pi$
$968$	−20.5281	−0.659799
$969$	−10.8104	−0.347281
$970$	−5.42109	−0.174061
$971$	−36.9499	−1.18578	−0.592890	−	0.805284i	$-0.702013\pi$
$971$	−36.9499	−1.18578	−0.592890	+	0.805284i	$0.702013\pi$
$972$	−16.7839	−0.538345
$973$	−8.75861	−0.280788
$974$	22.6260	0.724983
$975$	0	0
$976$	15.7260	0.503376
$977$	−35.8733	−1.14769	−0.573845	−	0.818964i	$-0.694549\pi$
$977$	−35.8733	−1.14769	−0.573845	+	0.818964i	$0.694549\pi$
$978$	37.8627	1.21072
$979$	4.69521	0.150060
$980$	−20.2040	−0.645394
$981$	−1.73668	−0.0554481
$982$	2.27686	0.0726574
$983$	6.33667	0.202109	0.101054	−	0.994881i	$-0.467778\pi$
$983$	6.33667	0.202109	0.101054	+	0.994881i	$0.467778\pi$
$984$	−18.7993	−0.599298
$985$	7.95551	0.253483
$986$	−12.5922	−0.401016
$987$	−9.90522	−0.315287
$988$	0	0
$989$	−20.6037	−0.655159
$990$	−12.9992	−0.413142
$991$	−30.4329	−0.966734	−0.483367	−	0.875418i	$-0.660586\pi$
$991$	−30.4329	−0.966734	−0.483367	+	0.875418i	$0.660586\pi$
$992$	5.83604	0.185294
$993$	−39.2337	−1.24504
$994$	2.74051	0.0869238
$995$	3.09025	0.0979676
$996$	28.2103	0.893879
$997$	42.1117	1.33369	0.666846	−	0.745195i	$-0.267644\pi$
$997$	42.1117	1.33369	0.666846	+	0.745195i	$0.267644\pi$
$998$	−8.52187	−0.269755
$999$	6.23084	0.197135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.t.1.14	yes	36
13.12	even	2		5239.2.a.s.1.23	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.s.1.23	✓	36	13.12	even	2
5239.2.a.t.1.14	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q-0.709075 q^{2} -2.87369 q^{3} -1.49721 q^{4} -2.11332 q^{5} +2.03766 q^{6} -0.783955 q^{7} +2.47979 q^{8} +5.25811 q^{9} +O(q^{10})\)	\(q-0.709075 q^{2} -2.87369 q^{3} -1.49721 q^{4} -2.11332 q^{5} +2.03766 q^{6} -0.783955 q^{7} +2.47979 q^{8} +5.25811 q^{9} +1.49850 q^{10} -1.64979 q^{11} +4.30253 q^{12} +0.555883 q^{14} +6.07304 q^{15} +1.23607 q^{16} -2.10026 q^{17} -3.72840 q^{18} -1.79114 q^{19} +3.16409 q^{20} +2.25284 q^{21} +1.16983 q^{22} -4.11635 q^{23} -7.12615 q^{24} -0.533870 q^{25} -6.48911 q^{27} +1.17375 q^{28} -8.45542 q^{29} -4.30624 q^{30} -1.00000 q^{31} -5.83604 q^{32} +4.74100 q^{33} +1.48924 q^{34} +1.65675 q^{35} -7.87250 q^{36} -0.960200 q^{37} +1.27005 q^{38} -5.24059 q^{40} +2.63807 q^{41} -1.59744 q^{42} +5.00533 q^{43} +2.47009 q^{44} -11.1121 q^{45} +2.91880 q^{46} -4.39676 q^{47} -3.55208 q^{48} -6.38542 q^{49} +0.378554 q^{50} +6.03550 q^{51} +10.0103 q^{53} +4.60127 q^{54} +3.48654 q^{55} -1.94404 q^{56} +5.14718 q^{57} +5.99553 q^{58} +6.60885 q^{59} -9.09262 q^{60} +12.7226 q^{61} +0.709075 q^{62} -4.12212 q^{63} +1.66606 q^{64} -3.36172 q^{66} +3.08130 q^{67} +3.14453 q^{68} +11.8291 q^{69} -1.17476 q^{70} +4.93002 q^{71} +13.0390 q^{72} +4.65497 q^{73} +0.680854 q^{74} +1.53418 q^{75} +2.68171 q^{76} +1.29336 q^{77} +15.9886 q^{79} -2.61221 q^{80} +2.87337 q^{81} -1.87059 q^{82} +6.55669 q^{83} -3.37299 q^{84} +4.43853 q^{85} -3.54916 q^{86} +24.2983 q^{87} -4.09113 q^{88} -2.84594 q^{89} +7.87930 q^{90} +6.16305 q^{92} +2.87369 q^{93} +3.11763 q^{94} +3.78525 q^{95} +16.7710 q^{96} -3.61767 q^{97} +4.52774 q^{98} -8.67478 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 5 q^{3} + 28 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 36 * q + 2 * q^2 - 5 * q^3 + 28 * q^4 + 5 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	\( 36 q + 2 q^{2} - 5 q^{3} + 28 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - 15 q^{10} - q^{11} - 13 q^{12} - 19 q^{14} - 10 q^{15} + 4 q^{16} - 46 q^{17} - 9 q^{18} + 8 q^{19} - 5 q^{20} - 16 q^{21} - 21 q^{22} - 24 q^{23} + 57 q^{24} + 5 q^{25} - 11 q^{27} - 32 q^{28} - 73 q^{29} - 31 q^{30} - 36 q^{31} + 3 q^{32} - 8 q^{33} - 37 q^{34} - 31 q^{35} - 31 q^{36} + 6 q^{37} - 25 q^{38} - 22 q^{40} + 6 q^{41} - 37 q^{42} - 37 q^{43} - 16 q^{45} - 45 q^{46} + 13 q^{47} - 46 q^{48} - 5 q^{49} + 24 q^{50} - 46 q^{51} - 42 q^{53} - 26 q^{54} - 47 q^{55} - 95 q^{56} + 33 q^{57} + 9 q^{58} + 20 q^{59} - 40 q^{60} - 48 q^{61} - 2 q^{62} + 52 q^{63} + 21 q^{64} - 4 q^{66} - 50 q^{67} - 76 q^{68} - 33 q^{69} + 93 q^{70} + 16 q^{71} - 52 q^{72} - 43 q^{73} - 76 q^{74} - 40 q^{75} + 62 q^{76} - 47 q^{77} - 43 q^{79} - 46 q^{80} - 96 q^{81} + 7 q^{82} + 9 q^{83} - 77 q^{84} - 5 q^{85} + 64 q^{86} - 8 q^{87} - 54 q^{88} + 6 q^{89} + 27 q^{90} - 35 q^{92} + 5 q^{93} - 76 q^{94} - 63 q^{95} + 72 q^{96} - 4 q^{97} - 41 q^{98} - 47 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 5 * q^3 + 28 * q^4 + 5 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - 15 * q^10 - q^11 - 13 * q^12 - 19 * q^14 - 10 * q^15 + 4 * q^16 - 46 * q^17 - 9 * q^18 + 8 * q^19 - 5 * q^20 - 16 * q^21 - 21 * q^22 - 24 * q^23 + 57 * q^24 + 5 * q^25 - 11 * q^27 - 32 * q^28 - 73 * q^29 - 31 * q^30 - 36 * q^31 + 3 * q^32 - 8 * q^33 - 37 * q^34 - 31 * q^35 - 31 * q^36 + 6 * q^37 - 25 * q^38 - 22 * q^40 + 6 * q^41 - 37 * q^42 - 37 * q^43 - 16 * q^45 - 45 * q^46 + 13 * q^47 - 46 * q^48 - 5 * q^49 + 24 * q^50 - 46 * q^51 - 42 * q^53 - 26 * q^54 - 47 * q^55 - 95 * q^56 + 33 * q^57 + 9 * q^58 + 20 * q^59 - 40 * q^60 - 48 * q^61 - 2 * q^62 + 52 * q^63 + 21 * q^64 - 4 * q^66 - 50 * q^67 - 76 * q^68 - 33 * q^69 + 93 * q^70 + 16 * q^71 - 52 * q^72 - 43 * q^73 - 76 * q^74 - 40 * q^75 + 62 * q^76 - 47 * q^77 - 43 * q^79 - 46 * q^80 - 96 * q^81 + 7 * q^82 + 9 * q^83 - 77 * q^84 - 5 * q^85 + 64 * q^86 - 8 * q^87 - 54 * q^88 + 6 * q^89 + 27 * q^90 - 35 * q^92 + 5 * q^93 - 76 * q^94 - 63 * q^95 + 72 * q^96 - 4 * q^97 - 41 * q^98 - 47 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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