LMFDB - Embedded newform 5239.2.a.t.1.21

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			1.21
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)

$f(q)$	$=$	$q+0.753306 q^{2} -2.56519 q^{3} -1.43253 q^{4} -3.00378 q^{5} -1.93237 q^{6} -1.71928 q^{7} -2.58575 q^{8} +3.58019 q^{9} +O(q^{10})$	\(q+0.753306 q^{2} -2.56519 q^{3} -1.43253 q^{4} -3.00378 q^{5} -1.93237 q^{6} -1.71928 q^{7} -2.58575 q^{8} +3.58019 q^{9} -2.26276 q^{10} -2.41529 q^{11} +3.67471 q^{12} -1.29514 q^{14} +7.70525 q^{15} +0.917200 q^{16} +0.538152 q^{17} +2.69698 q^{18} -4.10746 q^{19} +4.30300 q^{20} +4.41027 q^{21} -1.81945 q^{22} -4.29565 q^{23} +6.63293 q^{24} +4.02267 q^{25} -1.48830 q^{27} +2.46291 q^{28} +0.243664 q^{29} +5.80442 q^{30} -1.00000 q^{31} +5.86243 q^{32} +6.19567 q^{33} +0.405393 q^{34} +5.16432 q^{35} -5.12873 q^{36} +4.01880 q^{37} -3.09417 q^{38} +7.76700 q^{40} +12.3788 q^{41} +3.32228 q^{42} -0.328492 q^{43} +3.45997 q^{44} -10.7541 q^{45} -3.23594 q^{46} +10.1186 q^{47} -2.35279 q^{48} -4.04409 q^{49} +3.03031 q^{50} -1.38046 q^{51} -1.10278 q^{53} -1.12115 q^{54} +7.25498 q^{55} +4.44561 q^{56} +10.5364 q^{57} +0.183553 q^{58} +9.12070 q^{59} -11.0380 q^{60} -8.62851 q^{61} -0.753306 q^{62} -6.15534 q^{63} +2.58180 q^{64} +4.66723 q^{66} +10.2626 q^{67} -0.770918 q^{68} +11.0191 q^{69} +3.89032 q^{70} +0.724013 q^{71} -9.25747 q^{72} -10.8130 q^{73} +3.02739 q^{74} -10.3189 q^{75} +5.88406 q^{76} +4.15254 q^{77} +0.534099 q^{79} -2.75506 q^{80} -6.92280 q^{81} +9.32506 q^{82} +8.64796 q^{83} -6.31784 q^{84} -1.61649 q^{85} -0.247455 q^{86} -0.625043 q^{87} +6.24532 q^{88} +2.59593 q^{89} -8.10113 q^{90} +6.15364 q^{92} +2.56519 q^{93} +7.62242 q^{94} +12.3379 q^{95} -15.0382 q^{96} -10.3773 q^{97} -3.04644 q^{98} -8.64719 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.753306	0.532668	0.266334	−	0.963881i	$-0.414188\pi$
$2$	0.753306	0.532668	0.266334	+	0.963881i	$0.414188\pi$
$3$	−2.56519	−1.48101	−0.740506	−	0.672050i	$-0.765414\pi$
$3$	−2.56519	−1.48101	−0.740506	+	0.672050i	$0.765414\pi$
$4$	−1.43253	−0.716265
$5$	−3.00378	−1.34333	−0.671665	−	0.740855i	$-0.734421\pi$
$5$	−3.00378	−1.34333	−0.671665	+	0.740855i	$0.734421\pi$
$6$	−1.93237	−0.788888
$7$	−1.71928	−0.649825	−0.324913	−	0.945744i	$-0.605335\pi$
$7$	−1.71928	−0.649825	−0.324913	+	0.945744i	$0.605335\pi$
$8$	−2.58575	−0.914199
$9$	3.58019	1.19340
$10$	−2.26276	−0.715549
$11$	−2.41529	−0.728236	−0.364118	−	0.931353i	$-0.618630\pi$
$11$	−2.41529	−0.728236	−0.364118	+	0.931353i	$0.618630\pi$
$12$	3.67471	1.06080
$13$	0	0
$13$	0	0
$14$	−1.29514	−0.346141
$15$	7.70525	1.98949
$16$	0.917200	0.229300
$17$	0.538152	0.130521	0.0652605	−	0.997868i	$-0.479212\pi$
$17$	0.538152	0.130521	0.0652605	+	0.997868i	$0.479212\pi$
$18$	2.69698	0.635685
$19$	−4.10746	−0.942316	−0.471158	−	0.882049i	$-0.656164\pi$
$19$	−4.10746	−0.942316	−0.471158	+	0.882049i	$0.656164\pi$
$20$	4.30300	0.962180
$21$	4.41027	0.962399
$22$	−1.81945	−0.387908
$23$	−4.29565	−0.895704	−0.447852	−	0.894108i	$-0.647811\pi$
$23$	−4.29565	−0.895704	−0.447852	+	0.894108i	$0.647811\pi$
$24$	6.63293	1.35394
$25$	4.02267	0.804535
$26$	0	0
$27$	−1.48830	−0.286424
$28$	2.46291	0.465447
$29$	0.243664	0.0452472	0.0226236	−	0.999744i	$-0.492798\pi$
$29$	0.243664	0.0452472	0.0226236	+	0.999744i	$0.492798\pi$
$30$	5.80442	1.05974
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	5.86243	1.03634
$33$	6.19567	1.07853
$34$	0.405393	0.0695244
$35$	5.16432	0.872929
$36$	−5.12873	−0.854789
$37$	4.01880	0.660686	0.330343	−	0.943861i	$-0.392836\pi$
$37$	4.01880	0.660686	0.330343	+	0.943861i	$0.392836\pi$
$38$	−3.09417	−0.501941
$39$	0	0
$40$	7.76700	1.22807
$41$	12.3788	1.93325	0.966625	−	0.256195i	$-0.0824690\pi$
$41$	12.3788	1.93325	0.966625	+	0.256195i	$0.0824690\pi$
$42$	3.32228	0.512639
$43$	−0.328492	−0.0500945	−0.0250473	−	0.999686i	$-0.507974\pi$
$43$	−0.328492	−0.0500945	−0.0250473	+	0.999686i	$0.507974\pi$
$44$	3.45997	0.521610
$45$	−10.7541	−1.60313
$46$	−3.23594	−0.477113
$47$	10.1186	1.47595	0.737976	−	0.674827i	$-0.235782\pi$
$47$	10.1186	1.47595	0.737976	+	0.674827i	$0.235782\pi$
$48$	−2.35279	−0.339596
$49$	−4.04409	−0.577727
$50$	3.03031	0.428550
$51$	−1.38046	−0.193303
$52$	0	0
$53$	−1.10278	−0.151479	−0.0757396	−	0.997128i	$-0.524132\pi$
$53$	−1.10278	−0.151479	−0.0757396	+	0.997128i	$0.524132\pi$
$54$	−1.12115	−0.152569
$55$	7.25498	0.978262
$56$	4.44561	0.594070
$57$	10.5364	1.39558
$58$	0.183553	0.0241017
$59$	9.12070	1.18741	0.593707	−	0.804681i	$-0.297664\pi$
$59$	9.12070	1.18741	0.593707	+	0.804681i	$0.297664\pi$
$60$	−11.0380	−1.42500
$61$	−8.62851	−1.10477	−0.552384	−	0.833590i	$-0.686282\pi$
$61$	−8.62851	−1.10477	−0.552384	+	0.833590i	$0.686282\pi$
$62$	−0.753306	−0.0956700
$63$	−6.15534	−0.775500
$64$	2.58180	0.322725
$65$	0	0
$66$	4.66723	0.574497
$67$	10.2626	1.25378	0.626889	−	0.779108i	$-0.284328\pi$
$67$	10.2626	1.25378	0.626889	+	0.779108i	$0.284328\pi$
$68$	−0.770918	−0.0934876
$69$	11.0191	1.32655
$70$	3.89032	0.464982
$71$	0.724013	0.0859245	0.0429622	−	0.999077i	$-0.486320\pi$
$71$	0.724013	0.0859245	0.0429622	+	0.999077i	$0.486320\pi$
$72$	−9.25747	−1.09100
$73$	−10.8130	−1.26557	−0.632784	−	0.774328i	$-0.718088\pi$
$73$	−10.8130	−1.26557	−0.632784	+	0.774328i	$0.718088\pi$
$74$	3.02739	0.351927
$75$	−10.3189	−1.19153
$76$	5.88406	0.674947
$77$	4.15254	0.473226
$78$	0	0
$79$	0.534099	0.0600908	0.0300454	−	0.999549i	$-0.490435\pi$
$79$	0.534099	0.0600908	0.0300454	+	0.999549i	$0.490435\pi$
$80$	−2.75506	−0.308025
$81$	−6.92280	−0.769200
$82$	9.32506	1.02978
$83$	8.64796	0.949237	0.474618	−	0.880192i	$-0.342586\pi$
$83$	8.64796	0.949237	0.474618	+	0.880192i	$0.342586\pi$
$84$	−6.31784	−0.689333
$85$	−1.61649	−0.175333
$86$	−0.247455	−0.0266838
$87$	−0.625043	−0.0670117
$88$	6.24532	0.665753
$89$	2.59593	0.275168	0.137584	−	0.990490i	$-0.456066\pi$
$89$	2.59593	0.275168	0.137584	+	0.990490i	$0.456066\pi$
$90$	−8.10113	−0.853934
$91$	0	0
$92$	6.15364	0.641561
$93$	2.56519	0.265998
$94$	7.62242	0.786192
$95$	12.3379	1.26584
$96$	−15.0382	−1.53483
$97$	−10.3773	−1.05365	−0.526826	−	0.849973i	$-0.676618\pi$
$97$	−10.3773	−1.05365	−0.526826	+	0.849973i	$0.676618\pi$
$98$	−3.04644	−0.307737
$99$	−8.64719	−0.869076
$100$	−5.76260	−0.576260
$101$	−6.16934	−0.613872	−0.306936	−	0.951730i	$-0.599304\pi$
$101$	−6.16934	−0.613872	−0.306936	+	0.951730i	$0.599304\pi$
$102$	−1.03991	−0.102966
$103$	−1.74950	−0.172383	−0.0861916	−	0.996279i	$-0.527470\pi$
$103$	−1.74950	−0.172383	−0.0861916	+	0.996279i	$0.527470\pi$
$104$	0	0
$105$	−13.2475	−1.29282
$106$	−0.830735	−0.0806881
$107$	5.63492	0.544748	0.272374	−	0.962191i	$-0.412191\pi$
$107$	5.63492	0.544748	0.272374	+	0.962191i	$0.412191\pi$
$108$	2.13204	0.205156
$109$	9.20616	0.881790	0.440895	−	0.897559i	$-0.354661\pi$
$109$	9.20616	0.881790	0.440895	+	0.897559i	$0.354661\pi$
$110$	5.46522	0.521089
$111$	−10.3090	−0.978485
$112$	−1.57692	−0.149005
$113$	−9.68417	−0.911010	−0.455505	−	0.890233i	$-0.650541\pi$
$113$	−9.68417	−0.911010	−0.455505	+	0.890233i	$0.650541\pi$
$114$	7.93714	0.743381
$115$	12.9032	1.20323
$116$	−0.349055	−0.0324090
$117$	0	0
$118$	6.87069	0.632498
$119$	−0.925232	−0.0848158
$120$	−19.9238	−1.81879
$121$	−5.16639	−0.469672
$122$	−6.49991	−0.588475
$123$	−31.7541	−2.86317
$124$	1.43253	0.128645
$125$	2.93567	0.262574
$126$	−4.63686	−0.413084
$127$	15.2395	1.35228	0.676141	−	0.736772i	$-0.263651\pi$
$127$	15.2395	1.35228	0.676141	+	0.736772i	$0.263651\pi$
$128$	−9.77996	−0.864435
$129$	0.842644	0.0741906
$130$	0	0
$131$	19.4002	1.69500	0.847501	−	0.530794i	$-0.178106\pi$
$131$	19.4002	1.69500	0.847501	+	0.530794i	$0.178106\pi$
$132$	−8.87547	−0.772511
$133$	7.06185	0.612340
$134$	7.73090	0.667848
$135$	4.47053	0.384762
$136$	−1.39152	−0.119322
$137$	−13.0335	−1.11353	−0.556764	−	0.830671i	$-0.687957\pi$
$137$	−13.0335	−1.11353	−0.556764	+	0.830671i	$0.687957\pi$
$138$	8.30079	0.706610
$139$	−2.70512	−0.229445	−0.114723	−	0.993398i	$-0.536598\pi$
$139$	−2.70512	−0.229445	−0.114723	+	0.993398i	$0.536598\pi$
$140$	−7.39804	−0.625249
$141$	−25.9562	−2.18590
$142$	0.545403	0.0457692
$143$	0	0
$144$	3.28375	0.273646
$145$	−0.731911	−0.0607819
$146$	−8.14552	−0.674128
$147$	10.3739	0.855621
$148$	−5.75705	−0.473226
$149$	−5.12241	−0.419644	−0.209822	−	0.977740i	$-0.567288\pi$
$149$	−5.12241	−0.419644	−0.209822	+	0.977740i	$0.567288\pi$
$150$	−7.77331	−0.634688
$151$	17.5113	1.42505	0.712524	−	0.701648i	$-0.247552\pi$
$151$	17.5113	1.42505	0.712524	+	0.701648i	$0.247552\pi$
$152$	10.6208	0.861464
$153$	1.92669	0.155763
$154$	3.12814	0.252073
$155$	3.00378	0.241269
$156$	0	0
$157$	2.92979	0.233823	0.116912	−	0.993142i	$-0.462701\pi$
$157$	2.92979	0.233823	0.116912	+	0.993142i	$0.462701\pi$
$158$	0.402340	0.0320084
$159$	2.82885	0.224342
$160$	−17.6094	−1.39215
$161$	7.38540	0.582051
$162$	−5.21499	−0.409728
$163$	11.5202	0.902335	0.451167	−	0.892439i	$-0.351008\pi$
$163$	11.5202	0.902335	0.451167	+	0.892439i	$0.351008\pi$
$164$	−17.7331	−1.38472
$165$	−18.6104	−1.44882
$166$	6.51456	0.505628
$167$	−22.0174	−1.70376	−0.851880	−	0.523737i	$-0.824537\pi$
$167$	−22.0174	−1.70376	−0.851880	+	0.523737i	$0.824537\pi$
$168$	−11.4038	−0.879825
$169$	0	0
$170$	−1.21771	−0.0933942
$171$	−14.7055	−1.12456
$172$	0.470574	0.0358810
$173$	−22.5599	−1.71520	−0.857601	−	0.514316i	$-0.828046\pi$
$173$	−22.5599	−1.71520	−0.857601	+	0.514316i	$0.828046\pi$
$174$	−0.470849	−0.0356950
$175$	−6.91609	−0.522807
$176$	−2.21530	−0.166985
$177$	−23.3963	−1.75858
$178$	1.95553	0.146573
$179$	−3.62608	−0.271026	−0.135513	−	0.990776i	$-0.543268\pi$
$179$	−3.62608	−0.271026	−0.135513	+	0.990776i	$0.543268\pi$
$180$	15.4056	1.14826
$181$	1.42609	0.106000	0.0530002	−	0.998595i	$-0.483122\pi$
$181$	1.42609	0.106000	0.0530002	+	0.998595i	$0.483122\pi$
$182$	0	0
$183$	22.1338	1.63617
$184$	11.1075	0.818852
$185$	−12.0716	−0.887520
$186$	1.93237	0.141688
$187$	−1.29979	−0.0950501
$188$	−14.4952	−1.05717
$189$	2.55881	0.186126
$190$	9.29421	0.674273
$191$	−10.1375	−0.733522	−0.366761	−	0.930315i	$-0.619533\pi$
$191$	−10.1375	−0.733522	−0.366761	+	0.930315i	$0.619533\pi$
$192$	−6.62281	−0.477960
$193$	−13.0276	−0.937748	−0.468874	−	0.883265i	$-0.655340\pi$
$193$	−13.0276	−0.937748	−0.468874	+	0.883265i	$0.655340\pi$
$194$	−7.81726	−0.561247
$195$	0	0
$196$	5.79328	0.413806
$197$	25.0100	1.78189	0.890944	−	0.454113i	$-0.150044\pi$
$197$	25.0100	1.78189	0.890944	+	0.454113i	$0.150044\pi$
$198$	−6.51399	−0.462929
$199$	−26.6335	−1.88800	−0.944000	−	0.329946i	$-0.892970\pi$
$199$	−26.6335	−1.88800	−0.944000	+	0.329946i	$0.892970\pi$
$200$	−10.4016	−0.735505
$201$	−26.3256	−1.85686
$202$	−4.64740	−0.326990
$203$	−0.418925	−0.0294028
$204$	1.97755	0.138456
$205$	−37.1833	−2.59699
$206$	−1.31791	−0.0918231
$207$	−15.3792	−1.06893
$208$	0	0
$209$	9.92069	0.686228
$210$	−9.97939	−0.688644
$211$	26.0382	1.79255	0.896273	−	0.443504i	$-0.146265\pi$
$211$	26.0382	1.79255	0.896273	+	0.443504i	$0.146265\pi$
$212$	1.57977	0.108499
$213$	−1.85723	−0.127255
$214$	4.24482	0.290170
$215$	0.986716	0.0672935
$216$	3.84838	0.261849
$217$	1.71928	0.116712
$218$	6.93506	0.469702
$219$	27.7374	1.87432
$220$	−10.3930	−0.700694
$221$	0	0
$222$	−7.76582	−0.521208
$223$	1.76510	0.118200	0.0590999	−	0.998252i	$-0.481177\pi$
$223$	1.76510	0.118200	0.0590999	+	0.998252i	$0.481177\pi$
$224$	−10.0791	−0.673440
$225$	14.4020	0.960130
$226$	−7.29515	−0.485266
$227$	−5.17208	−0.343283	−0.171641	−	0.985159i	$-0.554907\pi$
$227$	−5.17208	−0.343283	−0.171641	+	0.985159i	$0.554907\pi$
$228$	−15.0937	−0.999606
$229$	8.60451	0.568602	0.284301	−	0.958735i	$-0.408239\pi$
$229$	8.60451	0.568602	0.284301	+	0.958735i	$0.408239\pi$
$230$	9.72004	0.640920
$231$	−10.6521	−0.700854
$232$	−0.630052	−0.0413650
$233$	−27.3582	−1.79229	−0.896147	−	0.443756i	$-0.853646\pi$
$233$	−27.3582	−1.79229	−0.896147	+	0.443756i	$0.853646\pi$
$234$	0	0
$235$	−30.3941	−1.98269
$236$	−13.0657	−0.850503
$237$	−1.37006	−0.0889952
$238$	−0.696983	−0.0451787
$239$	−28.2618	−1.82810	−0.914052	−	0.405598i	$-0.867063\pi$
$239$	−28.2618	−1.82810	−0.914052	+	0.405598i	$0.867063\pi$
$240$	7.06726	0.456189
$241$	5.27603	0.339859	0.169929	−	0.985456i	$-0.445646\pi$
$241$	5.27603	0.339859	0.169929	+	0.985456i	$0.445646\pi$
$242$	−3.89187	−0.250179
$243$	22.2232	1.42562
$244$	12.3606	0.791306
$245$	12.1475	0.776078
$246$	−23.9205	−1.52512
$247$	0	0
$248$	2.58575	0.164195
$249$	−22.1836	−1.40583
$250$	2.21146	0.139865
$251$	−21.8523	−1.37930	−0.689651	−	0.724141i	$-0.742236\pi$
$251$	−21.8523	−1.37930	−0.689651	+	0.724141i	$0.742236\pi$
$252$	8.81770	0.555463
$253$	10.3752	0.652284
$254$	11.4800	0.720318
$255$	4.14660	0.259670
$256$	−12.5309	−0.783182
$257$	−9.56534	−0.596669	−0.298335	−	0.954461i	$-0.596431\pi$
$257$	−9.56534	−0.596669	−0.298335	+	0.954461i	$0.596431\pi$
$258$	0.634769	0.0395190
$259$	−6.90942	−0.429331
$260$	0	0
$261$	0.872363	0.0539979
$262$	14.6143	0.902873
$263$	12.4665	0.768717	0.384359	−	0.923184i	$-0.374423\pi$
$263$	12.4665	0.768717	0.384359	+	0.923184i	$0.374423\pi$
$264$	−16.0204	−0.985989
$265$	3.31252	0.203486
$266$	5.31974	0.326174
$267$	−6.65905	−0.407527
$268$	−14.7015	−0.898037
$269$	26.1429	1.59396	0.796980	−	0.604006i	$-0.206430\pi$
$269$	26.1429	1.59396	0.796980	+	0.604006i	$0.206430\pi$
$270$	3.36768	0.204951
$271$	19.2573	1.16980	0.584900	−	0.811106i	$-0.301134\pi$
$271$	19.2573	1.16980	0.584900	+	0.811106i	$0.301134\pi$
$272$	0.493593	0.0299285
$273$	0	0
$274$	−9.81822	−0.593140
$275$	−9.71591	−0.585892
$276$	−15.7853	−0.950160
$277$	−21.7768	−1.30844	−0.654220	−	0.756304i	$-0.727003\pi$
$277$	−21.7768	−1.30844	−0.654220	+	0.756304i	$0.727003\pi$
$278$	−2.03779	−0.122218
$279$	−3.58019	−0.214341
$280$	−13.3536	−0.798032
$281$	5.31074	0.316812	0.158406	−	0.987374i	$-0.449364\pi$
$281$	5.31074	0.316812	0.158406	+	0.987374i	$0.449364\pi$
$282$	−19.5529	−1.16436
$283$	16.3794	0.973654	0.486827	−	0.873499i	$-0.338154\pi$
$283$	16.3794	0.973654	0.486827	+	0.873499i	$0.338154\pi$
$284$	−1.03717	−0.0615447
$285$	−31.6490	−1.87473
$286$	0	0
$287$	−21.2826	−1.25627
$288$	20.9886	1.23677
$289$	−16.7104	−0.982964
$290$	−0.551353	−0.0323766
$291$	26.6196	1.56047
$292$	15.4900	0.906482
$293$	−15.5008	−0.905564	−0.452782	−	0.891621i	$-0.649568\pi$
$293$	−15.5008	−0.905564	−0.452782	+	0.891621i	$0.649568\pi$
$294$	7.81469	0.455762
$295$	−27.3966	−1.59509
$296$	−10.3916	−0.603999
$297$	3.59468	0.208585
$298$	−3.85874	−0.223531
$299$	0	0
$300$	14.7822	0.853448
$301$	0.564768	0.0325527
$302$	13.1914	0.759078
$303$	15.8255	0.909152
$304$	−3.76736	−0.216073
$305$	25.9181	1.48407
$306$	1.45139	0.0829702
$307$	3.95640	0.225803	0.112902	−	0.993606i	$-0.463985\pi$
$307$	3.95640	0.225803	0.112902	+	0.993606i	$0.463985\pi$
$308$	−5.94864	−0.338955
$309$	4.48780	0.255302
$310$	2.26276	0.128516
$311$	11.7972	0.668956	0.334478	−	0.942404i	$-0.391440\pi$
$311$	11.7972	0.668956	0.334478	+	0.942404i	$0.391440\pi$
$312$	0	0
$313$	0.650669	0.0367780	0.0183890	−	0.999831i	$-0.494146\pi$
$313$	0.650669	0.0367780	0.0183890	+	0.999831i	$0.494146\pi$
$314$	2.20703	0.124550
$315$	18.4893	1.04175
$316$	−0.765112	−0.0430409
$317$	19.4835	1.09430	0.547151	−	0.837034i	$-0.315712\pi$
$317$	19.4835	1.09430	0.547151	+	0.837034i	$0.315712\pi$
$318$	2.13099	0.119500
$319$	−0.588517	−0.0329507
$320$	−7.75516	−0.433527
$321$	−14.4546	−0.806778
$322$	5.56347	0.310040
$323$	−2.21044	−0.122992
$324$	9.91711	0.550951
$325$	0	0
$326$	8.67827	0.480645
$327$	−23.6155	−1.30594
$328$	−32.0085	−1.76738
$329$	−17.3967	−0.959110
$330$	−14.0193	−0.771739
$331$	34.6419	1.90409	0.952047	−	0.305953i	$-0.0989749\pi$
$331$	34.6419	1.90409	0.952047	+	0.305953i	$0.0989749\pi$
$332$	−12.3885	−0.679905
$333$	14.3881	0.788462
$334$	−16.5859	−0.907538
$335$	−30.8266	−1.68424
$336$	4.04510	0.220678
$337$	25.1335	1.36911	0.684555	−	0.728962i	$-0.259997\pi$
$337$	25.1335	1.36911	0.684555	+	0.728962i	$0.259997\pi$
$338$	0	0
$339$	24.8417	1.34922
$340$	2.31567	0.125585
$341$	2.41529	0.130795
$342$	−11.0777	−0.599016
$343$	18.9878	1.02525
$344$	0.849397	0.0457964
$345$	−33.0991	−1.78199
$346$	−16.9946	−0.913633
$347$	−5.03446	−0.270264	−0.135132	−	0.990828i	$-0.543146\pi$
$347$	−5.03446	−0.270264	−0.135132	+	0.990828i	$0.543146\pi$
$348$	0.895393	0.0479981
$349$	−1.12415	−0.0601744	−0.0300872	−	0.999547i	$-0.509578\pi$
$349$	−1.12415	−0.0601744	−0.0300872	+	0.999547i	$0.509578\pi$
$350$	−5.20993	−0.278483
$351$	0	0
$352$	−14.1594	−0.754701
$353$	22.5001	1.19756	0.598780	−	0.800914i	$-0.295653\pi$
$353$	22.5001	1.19756	0.598780	+	0.800914i	$0.295653\pi$
$354$	−17.6246	−0.936737
$355$	−2.17477	−0.115425
$356$	−3.71874	−0.197093
$357$	2.37339	0.125613
$358$	−2.73155	−0.144367
$359$	7.73787	0.408389	0.204195	−	0.978930i	$-0.434542\pi$
$359$	7.73787	0.408389	0.204195	+	0.978930i	$0.434542\pi$
$360$	27.8074	1.46558
$361$	−2.12878	−0.112041
$362$	1.07428	0.0564630
$363$	13.2528	0.695590
$364$	0	0
$365$	32.4799	1.70008
$366$	16.6735	0.871538
$367$	30.5145	1.59285	0.796423	−	0.604740i	$-0.206723\pi$
$367$	30.5145	1.59285	0.796423	+	0.604740i	$0.206723\pi$
$368$	−3.93997	−0.205385
$369$	44.3186	2.30714
$370$	−9.09359	−0.472753
$371$	1.89599	0.0984349
$372$	−3.67471	−0.190525
$373$	16.9987	0.880158	0.440079	−	0.897959i	$-0.354950\pi$
$373$	16.9987	0.880158	0.440079	+	0.897959i	$0.354950\pi$
$374$	−0.979141	−0.0506302
$375$	−7.53054	−0.388875
$376$	−26.1642	−1.34931
$377$	0	0
$378$	1.92756	0.0991432
$379$	−23.6534	−1.21499	−0.607495	−	0.794323i	$-0.707826\pi$
$379$	−23.6534	−1.21499	−0.607495	+	0.794323i	$0.707826\pi$
$380$	−17.6744	−0.906677
$381$	−39.0921	−2.00275
$382$	−7.63663	−0.390724
$383$	15.7676	0.805687	0.402844	−	0.915269i	$-0.368022\pi$
$383$	15.7676	0.805687	0.402844	+	0.915269i	$0.368022\pi$
$384$	25.0874	1.28024
$385$	−12.4733	−0.635699
$386$	−9.81378	−0.499508
$387$	−1.17606	−0.0597827
$388$	14.8657	0.754693
$389$	−10.2232	−0.518335	−0.259167	−	0.965832i	$-0.583448\pi$
$389$	−10.2232	−0.518335	−0.259167	+	0.965832i	$0.583448\pi$
$390$	0	0
$391$	−2.31171	−0.116908
$392$	10.4570	0.528158
$393$	−49.7651	−2.51032
$394$	18.8402	0.949155
$395$	−1.60431	−0.0807217
$396$	12.3874	0.622488
$397$	16.0521	0.805634	0.402817	−	0.915281i	$-0.368031\pi$
$397$	16.0521	0.805634	0.402817	+	0.915281i	$0.368031\pi$
$398$	−20.0632	−1.00568
$399$	−18.1150	−0.906884
$400$	3.68960	0.184480
$401$	−36.4893	−1.82219	−0.911095	−	0.412197i	$-0.864761\pi$
$401$	−36.4893	−1.82219	−0.911095	+	0.412197i	$0.864761\pi$
$402$	−19.8312	−0.989091
$403$	0	0
$404$	8.83776	0.439695
$405$	20.7945	1.03329
$406$	−0.315579	−0.0156619
$407$	−9.70655	−0.481136
$408$	3.56952	0.176718
$409$	−2.42281	−0.119800	−0.0599000	−	0.998204i	$-0.519078\pi$
$409$	−2.42281	−0.119800	−0.0599000	+	0.998204i	$0.519078\pi$
$410$	−28.0104	−1.38333
$411$	33.4334	1.64915
$412$	2.50621	0.123472
$413$	−15.6810	−0.771612
$414$	−11.5853	−0.569386
$415$	−25.9765	−1.27514
$416$	0	0
$417$	6.93915	0.339812
$418$	7.47332	0.365532
$419$	13.0375	0.636921	0.318461	−	0.947936i	$-0.396834\pi$
$419$	13.0375	0.636921	0.318461	+	0.947936i	$0.396834\pi$
$420$	18.9774	0.926001
$421$	34.8023	1.69616	0.848081	−	0.529867i	$-0.177758\pi$
$421$	34.8023	1.69616	0.848081	+	0.529867i	$0.177758\pi$
$422$	19.6148	0.954832
$423$	36.2266	1.76140
$424$	2.85152	0.138482
$425$	2.16481	0.105009
$426$	−1.39906	−0.0677848
$427$	14.8348	0.717906
$428$	−8.07218	−0.390184
$429$	0	0
$430$	0.743300	0.0358451
$431$	−25.7869	−1.24211	−0.621056	−	0.783766i	$-0.713296\pi$
$431$	−25.7869	−1.24211	−0.621056	+	0.783766i	$0.713296\pi$
$432$	−1.36507	−0.0656771
$433$	38.6581	1.85779	0.928895	−	0.370344i	$-0.120760\pi$
$433$	38.6581	1.85779	0.928895	+	0.370344i	$0.120760\pi$
$434$	1.29514	0.0621688
$435$	1.87749	0.0900188
$436$	−13.1881	−0.631595
$437$	17.6442	0.844036
$438$	20.8948	0.998392
$439$	14.7054	0.701852	0.350926	−	0.936403i	$-0.385867\pi$
$439$	14.7054	0.701852	0.350926	+	0.936403i	$0.385867\pi$
$440$	−18.7595	−0.894326
$441$	−14.4786	−0.689458
$442$	0	0
$443$	3.92410	0.186440	0.0932198	−	0.995646i	$-0.470284\pi$
$443$	3.92410	0.186440	0.0932198	+	0.995646i	$0.470284\pi$
$444$	14.7679	0.700854
$445$	−7.79759	−0.369641
$446$	1.32966	0.0629613
$447$	13.1399	0.621498
$448$	−4.43883	−0.209715
$449$	−10.7056	−0.505229	−0.252615	−	0.967567i	$-0.581291\pi$
$449$	−10.7056	−0.505229	−0.252615	+	0.967567i	$0.581291\pi$
$450$	10.8491	0.511431
$451$	−29.8984	−1.40786
$452$	13.8729	0.652525
$453$	−44.9198	−2.11051
$454$	−3.89616	−0.182856
$455$	0	0
$456$	−27.2445	−1.27584
$457$	14.7034	0.687798	0.343899	−	0.939007i	$-0.388252\pi$
$457$	14.7034	0.687798	0.343899	+	0.939007i	$0.388252\pi$
$458$	6.48183	0.302876
$459$	−0.800934	−0.0373844
$460$	−18.4842	−0.861829
$461$	24.9281	1.16102	0.580508	−	0.814254i	$-0.302854\pi$
$461$	24.9281	1.16102	0.580508	+	0.814254i	$0.302854\pi$
$462$	−8.02426	−0.373323
$463$	−12.0814	−0.561471	−0.280735	−	0.959785i	$-0.590578\pi$
$463$	−12.0814	−0.561471	−0.280735	+	0.959785i	$0.590578\pi$
$464$	0.223488	0.0103752
$465$	−7.70525	−0.357323
$466$	−20.6091	−0.954698
$467$	−27.5898	−1.27670	−0.638351	−	0.769745i	$-0.720383\pi$
$467$	−27.5898	−1.27670	−0.638351	+	0.769745i	$0.720383\pi$
$468$	0	0
$469$	−17.6443	−0.814737
$470$	−22.8960	−1.05612
$471$	−7.51548	−0.346295
$472$	−23.5838	−1.08553
$473$	0.793402	0.0364807
$474$	−1.03208	−0.0474049
$475$	−16.5230	−0.758126
$476$	1.32542	0.0607506
$477$	−3.94818	−0.180775
$478$	−21.2898	−0.973772
$479$	−2.12342	−0.0970213	−0.0485107	−	0.998823i	$-0.515447\pi$
$479$	−2.12342	−0.0970213	−0.0485107	+	0.998823i	$0.515447\pi$
$480$	45.1715	2.06179
$481$	0	0
$482$	3.97447	0.181032
$483$	−18.9449	−0.862025
$484$	7.40101	0.336409
$485$	31.1710	1.41540
$486$	16.7409	0.759381
$487$	−9.10865	−0.412752	−0.206376	−	0.978473i	$-0.566167\pi$
$487$	−9.10865	−0.412752	−0.206376	+	0.978473i	$0.566167\pi$
$488$	22.3111	1.00998
$489$	−29.5516	−1.33637
$490$	9.15082	0.413392
$491$	30.6933	1.38517	0.692585	−	0.721336i	$-0.256472\pi$
$491$	30.6933	1.38517	0.692585	+	0.721336i	$0.256472\pi$
$492$	45.4886	2.05079
$493$	0.131128	0.00590571
$494$	0	0
$495$	25.9742	1.16746
$496$	−0.917200	−0.0411835
$497$	−1.24478	−0.0558359
$498$	−16.7111	−0.748841
$499$	−26.5369	−1.18795	−0.593977	−	0.804482i	$-0.702443\pi$
$499$	−26.5369	−1.18795	−0.593977	+	0.804482i	$0.702443\pi$
$500$	−4.20543	−0.188073
$501$	56.4789	2.52329
$502$	−16.4615	−0.734711
$503$	19.0148	0.847827	0.423914	−	0.905703i	$-0.360656\pi$
$503$	19.0148	0.847827	0.423914	+	0.905703i	$0.360656\pi$
$504$	15.9161	0.708961
$505$	18.5313	0.824633
$506$	7.81572	0.347451
$507$	0	0
$508$	−21.8310	−0.968593
$509$	−27.4226	−1.21549	−0.607743	−	0.794134i	$-0.707925\pi$
$509$	−27.4226	−1.21549	−0.607743	+	0.794134i	$0.707925\pi$
$510$	3.12366	0.138318
$511$	18.5906	0.822398
$512$	10.1203	0.447259
$513$	6.11315	0.269902
$514$	−7.20563	−0.317827
$515$	5.25511	0.231568
$516$	−1.20711	−0.0531401
$517$	−24.4394	−1.07484
$518$	−5.20491	−0.228691
$519$	57.8705	2.54023
$520$	0	0
$521$	−29.5700	−1.29548	−0.647742	−	0.761859i	$-0.724287\pi$
$521$	−29.5700	−1.29548	−0.647742	+	0.761859i	$0.724287\pi$
$522$	0.657156	0.0287630
$523$	9.72522	0.425254	0.212627	−	0.977133i	$-0.431798\pi$
$523$	9.72522	0.425254	0.212627	+	0.977133i	$0.431798\pi$
$524$	−27.7913	−1.21407
$525$	17.7411	0.774284
$526$	9.39109	0.409471
$527$	−0.538152	−0.0234423
$528$	5.68266	0.247306
$529$	−4.54741	−0.197714
$530$	2.49534	0.108391
$531$	32.6539	1.41706
$532$	−10.1163	−0.438598
$533$	0	0
$534$	−5.01630	−0.217077
$535$	−16.9260	−0.731776
$536$	−26.5365	−1.14620
$537$	9.30159	0.401393
$538$	19.6936	0.849051
$539$	9.76764	0.420722
$540$	−6.40417	−0.275592
$541$	35.2771	1.51668	0.758340	−	0.651859i	$-0.226011\pi$
$541$	35.2771	1.51668	0.758340	+	0.651859i	$0.226011\pi$
$542$	14.5067	0.623115
$543$	−3.65819	−0.156988
$544$	3.15488	0.135264
$545$	−27.6533	−1.18454
$546$	0	0
$547$	−13.1433	−0.561967	−0.280983	−	0.959713i	$-0.590661\pi$
$547$	−13.1433	−0.561967	−0.280983	+	0.959713i	$0.590661\pi$
$548$	18.6709	0.797580
$549$	−30.8917	−1.31843
$550$	−7.31906	−0.312086
$551$	−1.00084	−0.0426371
$552$	−28.4927	−1.21273
$553$	−0.918263	−0.0390485
$554$	−16.4046	−0.696964
$555$	30.9659	1.31443
$556$	3.87517	0.164344
$557$	−33.1100	−1.40291	−0.701457	−	0.712711i	$-0.747467\pi$
$557$	−33.1100	−1.40291	−0.701457	+	0.712711i	$0.747467\pi$
$558$	−2.69698	−0.114172
$559$	0	0
$560$	4.73671	0.200163
$561$	3.33421	0.140770
$562$	4.00062	0.168756
$563$	−17.0254	−0.717535	−0.358767	−	0.933427i	$-0.616803\pi$
$563$	−17.0254	−0.717535	−0.358767	+	0.933427i	$0.616803\pi$
$564$	37.1830	1.56568
$565$	29.0891	1.22379
$566$	12.3387	0.518634
$567$	11.9022	0.499845
$568$	−1.87211	−0.0785521
$569$	−17.2210	−0.721943	−0.360972	−	0.932577i	$-0.617555\pi$
$569$	−17.2210	−0.721943	−0.360972	+	0.932577i	$0.617555\pi$
$570$	−23.8414	−0.998606
$571$	−3.30201	−0.138185	−0.0690924	−	0.997610i	$-0.522010\pi$
$571$	−3.30201	−0.138185	−0.0690924	+	0.997610i	$0.522010\pi$
$572$	0	0
$573$	26.0045	1.08636
$574$	−16.0323	−0.669177
$575$	−17.2800	−0.720625
$576$	9.24335	0.385140
$577$	34.6833	1.44389	0.721943	−	0.691952i	$-0.243249\pi$
$577$	34.6833	1.44389	0.721943	+	0.691952i	$0.243249\pi$
$578$	−12.5880	−0.523594
$579$	33.4183	1.38882
$580$	1.04848	0.0435359
$581$	−14.8682	−0.616838
$582$	20.0527	0.831213
$583$	2.66354	0.110313
$584$	27.9597	1.15698
$585$	0	0
$586$	−11.6768	−0.482365
$587$	29.4705	1.21638	0.608188	−	0.793793i	$-0.291897\pi$
$587$	29.4705	1.21638	0.608188	+	0.793793i	$0.291897\pi$
$588$	−14.8609	−0.612851
$589$	4.10746	0.169245
$590$	−20.6380	−0.849653
$591$	−64.1553	−2.63900
$592$	3.68604	0.151495
$593$	7.00300	0.287579	0.143789	−	0.989608i	$-0.454071\pi$
$593$	7.00300	0.287579	0.143789	+	0.989608i	$0.454071\pi$
$594$	2.70790	0.111106
$595$	2.77919	0.113936
$596$	7.33800	0.300576
$597$	68.3200	2.79615
$598$	0	0
$599$	11.1725	0.456498	0.228249	−	0.973603i	$-0.426700\pi$
$599$	11.1725	0.456498	0.228249	+	0.973603i	$0.426700\pi$
$600$	26.6821	1.08929
$601$	11.8379	0.482879	0.241440	−	0.970416i	$-0.422380\pi$
$601$	11.8379	0.482879	0.241440	+	0.970416i	$0.422380\pi$
$602$	0.425443	0.0173398
$603$	36.7422	1.49626
$604$	−25.0854	−1.02071
$605$	15.5187	0.630924
$606$	11.9215	0.484276
$607$	30.3378	1.23137	0.615687	−	0.787991i	$-0.288879\pi$
$607$	30.3378	1.23137	0.615687	+	0.787991i	$0.288879\pi$
$608$	−24.0797	−0.976559
$609$	1.07462	0.0435459
$610$	19.5243	0.790515
$611$	0	0
$612$	−2.76004	−0.111568
$613$	−14.7816	−0.597024	−0.298512	−	0.954406i	$-0.596490\pi$
$613$	−14.7816	−0.597024	−0.298512	+	0.954406i	$0.596490\pi$
$614$	2.98038	0.120278
$615$	95.3821	3.84618
$616$	−10.7374	−0.432623
$617$	−12.9742	−0.522322	−0.261161	−	0.965295i	$-0.584105\pi$
$617$	−12.9742	−0.522322	−0.261161	+	0.965295i	$0.584105\pi$
$618$	3.38069	0.135991
$619$	−11.6716	−0.469123	−0.234561	−	0.972101i	$-0.575365\pi$
$619$	−11.6716	−0.469123	−0.234561	+	0.972101i	$0.575365\pi$
$620$	−4.30300	−0.172813
$621$	6.39323	0.256551
$622$	8.88688	0.356331
$623$	−4.46312	−0.178811
$624$	0	0
$625$	−28.9315	−1.15726
$626$	0.490153	0.0195905
$627$	−25.4484	−1.01631
$628$	−4.19702	−0.167479
$629$	2.16272	0.0862335
$630$	13.9281	0.554908
$631$	−38.5206	−1.53348	−0.766740	−	0.641958i	$-0.778123\pi$
$631$	−38.5206	−1.53348	−0.766740	+	0.641958i	$0.778123\pi$
$632$	−1.38104	−0.0549350
$633$	−66.7930	−2.65478
$634$	14.6770	0.582900
$635$	−45.7759	−1.81656
$636$	−4.05241	−0.160689
$637$	0	0
$638$	−0.443334	−0.0175518
$639$	2.59210	0.102542
$640$	29.3768	1.16122
$641$	−40.3821	−1.59500	−0.797498	−	0.603321i	$-0.793844\pi$
$641$	−40.3821	−1.59500	−0.797498	+	0.603321i	$0.793844\pi$
$642$	−10.8888	−0.429745
$643$	−8.88234	−0.350285	−0.175143	−	0.984543i	$-0.556039\pi$
$643$	−8.88234	−0.350285	−0.175143	+	0.984543i	$0.556039\pi$
$644$	−10.5798	−0.416903
$645$	−2.53111	−0.0996625
$646$	−1.66514	−0.0655139
$647$	−37.3832	−1.46969	−0.734843	−	0.678237i	$-0.762744\pi$
$647$	−37.3832	−1.46969	−0.734843	+	0.678237i	$0.762744\pi$
$648$	17.9006	0.703202
$649$	−22.0291	−0.864719
$650$	0	0
$651$	−4.41027	−0.172852
$652$	−16.5031	−0.646311
$653$	6.43840	0.251954	0.125977	−	0.992033i	$-0.459793\pi$
$653$	6.43840	0.251954	0.125977	+	0.992033i	$0.459793\pi$
$654$	−17.7897	−0.695634
$655$	−58.2738	−2.27695
$656$	11.3539	0.443294
$657$	−38.7127	−1.51033
$658$	−13.1050	−0.510887
$659$	30.0163	1.16927	0.584634	−	0.811297i	$-0.301238\pi$
$659$	30.0163	1.16927	0.584634	+	0.811297i	$0.301238\pi$
$660$	26.6599	1.03774
$661$	41.9581	1.63198	0.815990	−	0.578066i	$-0.196193\pi$
$661$	41.9581	1.63198	0.815990	+	0.578066i	$0.196193\pi$
$662$	26.0960	1.01425
$663$	0	0
$664$	−22.3614	−0.867792
$665$	−21.2122	−0.822575
$666$	10.8386	0.419988
$667$	−1.04669	−0.0405281
$668$	31.5406	1.22034
$669$	−4.52782	−0.175055
$670$	−23.2219	−0.897140
$671$	20.8403	0.804532
$672$	25.8549	0.997373
$673$	11.6684	0.449783	0.224891	−	0.974384i	$-0.427797\pi$
$673$	11.6684	0.449783	0.224891	+	0.974384i	$0.427797\pi$
$674$	18.9332	0.729281
$675$	−5.98696	−0.230438
$676$	0	0
$677$	17.5998	0.676415	0.338208	−	0.941071i	$-0.390179\pi$
$677$	17.5998	0.676415	0.338208	+	0.941071i	$0.390179\pi$
$678$	18.7134	0.718685
$679$	17.8414	0.684689
$680$	4.17983	0.160289
$681$	13.2674	0.508406
$682$	1.81945	0.0696704
$683$	−24.2463	−0.927759	−0.463879	−	0.885898i	$-0.653543\pi$
$683$	−24.2463	−0.927759	−0.463879	+	0.885898i	$0.653543\pi$
$684$	21.0661	0.805481
$685$	39.1497	1.49583
$686$	14.3037	0.546116
$687$	−22.0722	−0.842106
$688$	−0.301293	−0.0114867
$689$	0	0
$690$	−24.9337	−0.949211
$691$	−23.8452	−0.907114	−0.453557	−	0.891227i	$-0.649845\pi$
$691$	−23.8452	−0.907114	−0.453557	+	0.891227i	$0.649845\pi$
$692$	32.3178	1.22854
$693$	14.8669	0.564747
$694$	−3.79249	−0.143961
$695$	8.12558	0.308221
$696$	1.61620	0.0612620
$697$	6.66170	0.252330
$698$	−0.846830	−0.0320530
$699$	70.1789	2.65441
$700$	9.90750	0.374468
$701$	−20.2431	−0.764571	−0.382286	−	0.924044i	$-0.624863\pi$
$701$	−20.2431	−0.764571	−0.382286	+	0.924044i	$0.624863\pi$
$702$	0	0
$703$	−16.5070	−0.622575
$704$	−6.23579	−0.235020
$705$	77.9665	2.93639
$706$	16.9495	0.637902
$707$	10.6068	0.398910
$708$	33.5159	1.25961
$709$	−10.0203	−0.376320	−0.188160	−	0.982138i	$-0.560252\pi$
$709$	−10.0203	−0.376320	−0.188160	+	0.982138i	$0.560252\pi$
$710$	−1.63827	−0.0614832
$711$	1.91218	0.0717122
$712$	−6.71241	−0.251558
$713$	4.29565	0.160873
$714$	1.78789	0.0669102
$715$	0	0
$716$	5.19447	0.194126
$717$	72.4968	2.70744
$718$	5.82899	0.217536
$719$	35.8972	1.33874	0.669370	−	0.742929i	$-0.266564\pi$
$719$	35.8972	1.33874	0.669370	+	0.742929i	$0.266564\pi$
$720$	−9.86366	−0.367597
$721$	3.00787	0.112019
$722$	−1.60363	−0.0596808
$723$	−13.5340	−0.503335
$724$	−2.04292	−0.0759243
$725$	0.980179	0.0364030
$726$	9.98339	0.370518
$727$	11.4678	0.425315	0.212658	−	0.977127i	$-0.431788\pi$
$727$	11.4678	0.425315	0.212658	+	0.977127i	$0.431788\pi$
$728$	0	0
$729$	−36.2383	−1.34216
$730$	24.4673	0.905576
$731$	−0.176779	−0.00653839
$732$	−31.7073	−1.17193
$733$	−27.1202	−1.00171	−0.500854	−	0.865532i	$-0.666981\pi$
$733$	−27.1202	−1.00171	−0.500854	+	0.865532i	$0.666981\pi$
$734$	22.9868	0.848458
$735$	−31.1607	−1.14938
$736$	−25.1829	−0.928254
$737$	−24.7872	−0.913047
$738$	33.3855	1.22894
$739$	−9.56435	−0.351830	−0.175915	−	0.984405i	$-0.556288\pi$
$739$	−9.56435	−0.351830	−0.175915	+	0.984405i	$0.556288\pi$
$740$	17.2929	0.635699
$741$	0	0
$742$	1.42826	0.0524332
$743$	6.84478	0.251110	0.125555	−	0.992087i	$-0.459929\pi$
$743$	6.84478	0.251110	0.125555	+	0.992087i	$0.459929\pi$
$744$	−6.63293	−0.243175
$745$	15.3866	0.563720
$746$	12.8052	0.468832
$747$	30.9614	1.13282
$748$	1.86199	0.0680811
$749$	−9.68797	−0.353991
$750$	−5.67280	−0.207142
$751$	−48.5495	−1.77160	−0.885798	−	0.464072i	$-0.846388\pi$
$751$	−48.5495	−1.77160	−0.885798	+	0.464072i	$0.846388\pi$
$752$	9.28079	0.338436
$753$	56.0552	2.04276
$754$	0	0
$755$	−52.6000	−1.91431
$756$	−3.66556	−0.133315
$757$	17.8546	0.648937	0.324468	−	0.945897i	$-0.394815\pi$
$757$	17.8546	0.648937	0.324468	+	0.945897i	$0.394815\pi$
$758$	−17.8182	−0.647187
$759$	−26.6144	−0.966041
$760$	−31.9027	−1.15723
$761$	10.1108	0.366518	0.183259	−	0.983065i	$-0.441335\pi$
$761$	10.1108	0.366518	0.183259	+	0.983065i	$0.441335\pi$
$762$	−29.4483	−1.06680
$763$	−15.8279	−0.573010
$764$	14.5222	0.525396
$765$	−5.78734	−0.209242
$766$	11.8778	0.429164
$767$	0	0
$768$	32.1442	1.15990
$769$	29.5663	1.06619	0.533095	−	0.846056i	$-0.321029\pi$
$769$	29.5663	1.06619	0.533095	+	0.846056i	$0.321029\pi$
$770$	−9.39623	−0.338617
$771$	24.5369	0.883675
$772$	18.6624	0.671676
$773$	10.7806	0.387753	0.193876	−	0.981026i	$-0.437894\pi$
$773$	10.7806	0.387753	0.193876	+	0.981026i	$0.437894\pi$
$774$	−0.885937	−0.0318443
$775$	−4.02267	−0.144499
$776$	26.8330	0.963248
$777$	17.7240	0.635844
$778$	−7.70117	−0.276100
$779$	−50.8456	−1.82173
$780$	0	0
$781$	−1.74870	−0.0625733
$782$	−1.74143	−0.0622733
$783$	−0.362646	−0.0129599
$784$	−3.70924	−0.132473
$785$	−8.80045	−0.314101
$786$	−37.4884	−1.33717
$787$	28.4854	1.01539	0.507697	−	0.861535i	$-0.330497\pi$
$787$	28.4854	1.01539	0.507697	+	0.861535i	$0.330497\pi$
$788$	−35.8275	−1.27630
$789$	−31.9789	−1.13848
$790$	−1.20854	−0.0429979
$791$	16.6498	0.591997
$792$	22.3594	0.794508
$793$	0	0
$794$	12.0922	0.429135
$795$	−8.49724	−0.301366
$796$	38.1533	1.35231
$797$	9.08469	0.321796	0.160898	−	0.986971i	$-0.448561\pi$
$797$	9.08469	0.321796	0.160898	+	0.986971i	$0.448561\pi$
$798$	−13.6461	−0.483068
$799$	5.44535	0.192643
$800$	23.5826	0.833772
$801$	9.29392	0.328385
$802$	−27.4876	−0.970622
$803$	26.1165	0.921633
$804$	37.7121	1.33000
$805$	−22.1841	−0.781887
$806$	0	0
$807$	−67.0614	−2.36067
$808$	15.9523	0.561202
$809$	4.53751	0.159530	0.0797652	−	0.996814i	$-0.474583\pi$
$809$	4.53751	0.159530	0.0797652	+	0.996814i	$0.474583\pi$
$810$	15.6647	0.550400
$811$	−36.4155	−1.27872	−0.639360	−	0.768907i	$-0.720801\pi$
$811$	−36.4155	−1.27872	−0.639360	+	0.768907i	$0.720801\pi$
$812$	0.600122	0.0210602
$813$	−49.3987	−1.73249
$814$	−7.31201	−0.256286
$815$	−34.6042	−1.21213
$816$	−1.26616	−0.0443244
$817$	1.34927	0.0472049
$818$	−1.82512	−0.0638137
$819$	0	0
$820$	53.2661	1.86013
$821$	−32.3007	−1.12730	−0.563651	−	0.826013i	$-0.690604\pi$
$821$	−32.3007	−1.12730	−0.563651	+	0.826013i	$0.690604\pi$
$822$	25.1856	0.878448
$823$	41.0556	1.43111	0.715555	−	0.698557i	$-0.246174\pi$
$823$	41.0556	1.43111	0.715555	+	0.698557i	$0.246174\pi$
$824$	4.52376	0.157593
$825$	24.9231	0.867713
$826$	−11.8126	−0.411013
$827$	−27.0046	−0.939043	−0.469522	−	0.882921i	$-0.655574\pi$
$827$	−27.0046	−0.939043	−0.469522	+	0.882921i	$0.655574\pi$
$828$	22.0312	0.765638
$829$	−3.69480	−0.128326	−0.0641628	−	0.997939i	$-0.520438\pi$
$829$	−3.69480	−0.128326	−0.0641628	+	0.997939i	$0.520438\pi$
$830$	−19.5683	−0.679225
$831$	55.8615	1.93782
$832$	0	0
$833$	−2.17634	−0.0754055
$834$	5.22730	0.181007
$835$	66.1354	2.28871
$836$	−14.2117	−0.491521
$837$	1.48830	0.0514433
$838$	9.82120	0.339268
$839$	48.3035	1.66762	0.833811	−	0.552050i	$-0.186154\pi$
$839$	48.3035	1.66762	0.833811	+	0.552050i	$0.186154\pi$
$840$	34.2546	1.18189
$841$	−28.9406	−0.997953
$842$	26.2168	0.903491
$843$	−13.6231	−0.469203
$844$	−37.3005	−1.28394
$845$	0	0
$846$	27.2897	0.938240
$847$	8.88245	0.305205
$848$	−1.01147	−0.0347342
$849$	−42.0162	−1.44199
$850$	1.63077	0.0559348
$851$	−17.2633	−0.591780
$852$	2.66054	0.0911484
$853$	33.8112	1.15767	0.578836	−	0.815444i	$-0.303507\pi$
$853$	33.8112	1.15767	0.578836	+	0.815444i	$0.303507\pi$
$854$	11.1751	0.382406
$855$	44.1720	1.51065
$856$	−14.5705	−0.498008
$857$	−13.9113	−0.475200	−0.237600	−	0.971363i	$-0.576361\pi$
$857$	−13.9113	−0.475200	−0.237600	+	0.971363i	$0.576361\pi$
$858$	0	0
$859$	−22.8335	−0.779070	−0.389535	−	0.921012i	$-0.627364\pi$
$859$	−22.8335	−0.779070	−0.389535	+	0.921012i	$0.627364\pi$
$860$	−1.41350	−0.0482000
$861$	54.5940	1.86056
$862$	−19.4254	−0.661633
$863$	−42.5034	−1.44683	−0.723417	−	0.690411i	$-0.757430\pi$
$863$	−42.5034	−1.44683	−0.723417	+	0.690411i	$0.757430\pi$
$864$	−8.72507	−0.296833
$865$	67.7650	2.30408
$866$	29.1214	0.989585
$867$	42.8653	1.45578
$868$	−2.46291	−0.0835967
$869$	−1.29000	−0.0437603
$870$	1.41433	0.0479501
$871$	0	0
$872$	−23.8048	−0.806132
$873$	−37.1526	−1.25743
$874$	13.2915	0.449591
$875$	−5.04722	−0.170627
$876$	−39.7347	−1.34251
$877$	−20.1513	−0.680462	−0.340231	−	0.940342i	$-0.610505\pi$
$877$	−20.1513	−0.680462	−0.340231	+	0.940342i	$0.610505\pi$
$878$	11.0777	0.373854
$879$	39.7624	1.34115
$880$	6.65427	0.224315
$881$	−22.7069	−0.765016	−0.382508	−	0.923952i	$-0.624940\pi$
$881$	−22.7069	−0.765016	−0.382508	+	0.923952i	$0.624940\pi$
$882$	−10.9068	−0.367252
$883$	1.54467	0.0519822	0.0259911	−	0.999662i	$-0.491726\pi$
$883$	1.54467	0.0519822	0.0259911	+	0.999662i	$0.491726\pi$
$884$	0	0
$885$	70.2773	2.36235
$886$	2.95605	0.0993104
$887$	−28.2111	−0.947234	−0.473617	−	0.880731i	$-0.657052\pi$
$887$	−28.2111	−0.947234	−0.473617	+	0.880731i	$0.657052\pi$
$888$	26.6564	0.894530
$889$	−26.2008	−0.878747
$890$	−5.87397	−0.196896
$891$	16.7205	0.560159
$892$	−2.52856	−0.0846624
$893$	−41.5618	−1.39081
$894$	9.89840	0.331052
$895$	10.8919	0.364077
$896$	16.8145	0.561731
$897$	0	0
$898$	−8.06461	−0.269120
$899$	−0.243664	−0.00812664
$900$	−20.6312	−0.687707
$901$	−0.593466	−0.0197712
$902$	−22.5227	−0.749924
$903$	−1.44874	−0.0482109
$904$	25.0408	0.832845
$905$	−4.28365	−0.142393
$906$	−33.8383	−1.12420
$907$	−6.55975	−0.217813	−0.108906	−	0.994052i	$-0.534735\pi$
$907$	−6.55975	−0.217813	−0.108906	+	0.994052i	$0.534735\pi$
$908$	7.40915	0.245881
$909$	−22.0874	−0.732594
$910$	0	0
$911$	−16.1160	−0.533947	−0.266974	−	0.963704i	$-0.586024\pi$
$911$	−16.1160	−0.533947	−0.266974	+	0.963704i	$0.586024\pi$
$912$	9.66399	0.320007
$913$	−20.8873	−0.691269
$914$	11.0762	0.366368
$915$	−66.4849	−2.19792
$916$	−12.3262	−0.407270
$917$	−33.3542	−1.10145
$918$	−0.603348	−0.0199135
$919$	10.4052	0.343235	0.171618	−	0.985164i	$-0.445101\pi$
$919$	10.4052	0.343235	0.171618	+	0.985164i	$0.445101\pi$
$920$	−33.3643	−1.09999
$921$	−10.1489	−0.334418
$922$	18.7785	0.618437
$923$	0	0
$924$	15.2594	0.501997
$925$	16.1663	0.531545
$926$	−9.10100	−0.299077
$927$	−6.26354	−0.205722
$928$	1.42846	0.0468915
$929$	5.28212	0.173301	0.0866504	−	0.996239i	$-0.472384\pi$
$929$	5.28212	0.173301	0.0866504	+	0.996239i	$0.472384\pi$
$930$	−5.80442	−0.190334
$931$	16.6109	0.544401
$932$	39.1914	1.28376
$933$	−30.2619	−0.990732
$934$	−20.7835	−0.680058
$935$	3.90428	0.127684
$936$	0	0
$937$	52.8498	1.72653	0.863264	−	0.504753i	$-0.168416\pi$
$937$	52.8498	1.72653	0.863264	+	0.504753i	$0.168416\pi$
$938$	−13.2915	−0.433984
$939$	−1.66909	−0.0544686
$940$	43.5404	1.42013
$941$	−28.9332	−0.943195	−0.471597	−	0.881814i	$-0.656322\pi$
$941$	−28.9332	−0.943195	−0.471597	+	0.881814i	$0.656322\pi$
$942$	−5.66146	−0.184460
$943$	−53.1751	−1.73162
$944$	8.36551	0.272274
$945$	−7.68608	−0.250028
$946$	0.597675	0.0194321
$947$	35.1437	1.14202	0.571009	−	0.820944i	$-0.306552\pi$
$947$	35.1437	1.14202	0.571009	+	0.820944i	$0.306552\pi$
$948$	1.96266	0.0637441
$949$	0	0
$950$	−12.4469	−0.403829
$951$	−49.9789	−1.62068
$952$	2.39241	0.0775386
$953$	8.39531	0.271951	0.135975	−	0.990712i	$-0.456583\pi$
$953$	8.39531	0.271951	0.135975	+	0.990712i	$0.456583\pi$
$954$	−2.97419	−0.0962930
$955$	30.4507	0.985362
$956$	40.4858	1.30941
$957$	1.50966	0.0488003
$958$	−1.59958	−0.0516802
$959$	22.4082	0.723598
$960$	19.8934	0.642058
$961$	1.00000	0.0322581
$962$	0	0
$963$	20.1741	0.650101
$964$	−7.55807	−0.243429
$965$	39.1320	1.25970
$966$	−14.2714	−0.459173
$967$	9.87400	0.317526	0.158763	−	0.987317i	$-0.449249\pi$
$967$	9.87400	0.317526	0.158763	+	0.987317i	$0.449249\pi$
$968$	13.3590	0.429374
$969$	5.67019	0.182153
$970$	23.4813	0.753939
$971$	−38.1392	−1.22395	−0.611973	−	0.790879i	$-0.709624\pi$
$971$	−38.1392	−1.22395	−0.611973	+	0.790879i	$0.709624\pi$
$972$	−31.8354	−1.02112
$973$	4.65085	0.149099
$974$	−6.86160	−0.219860
$975$	0	0
$976$	−7.91407	−0.253323
$977$	43.7583	1.39995	0.699976	−	0.714166i	$-0.253194\pi$
$977$	43.7583	1.39995	0.699976	+	0.714166i	$0.253194\pi$
$978$	−22.2614	−0.711841
$979$	−6.26991	−0.200387
$980$	−17.4017	−0.555877
$981$	32.9598	1.05233
$982$	23.1215	0.737836
$983$	−58.5667	−1.86799	−0.933994	−	0.357288i	$-0.883701\pi$
$983$	−58.5667	−1.86799	−0.933994	+	0.357288i	$0.883701\pi$
$984$	82.1079	2.61751
$985$	−75.1244	−2.39366
$986$	0.0987796	0.00314578
$987$	44.6258	1.42045
$988$	0	0
$989$	1.41109	0.0448699
$990$	19.5666	0.621866
$991$	−37.6603	−1.19632	−0.598159	−	0.801377i	$-0.704101\pi$
$991$	−37.6603	−1.19632	−0.598159	+	0.801377i	$0.704101\pi$
$992$	−5.86243	−0.186132
$993$	−88.8631	−2.81999
$994$	−0.937699	−0.0297420
$995$	80.0011	2.53621
$996$	31.7787	1.00695
$997$	27.8661	0.882529	0.441265	−	0.897377i	$-0.354530\pi$
$997$	27.8661	0.882529	0.441265	+	0.897377i	$0.354530\pi$
$998$	−19.9904	−0.632785
$999$	−5.98119	−0.189237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.t.1.21	yes	36
13.12	even	2		5239.2.a.s.1.16	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.s.1.16	✓	36	13.12	even	2
5239.2.a.t.1.21	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)

\(f(q)\)	\(=\)	\(q+0.753306 q^{2} -2.56519 q^{3} -1.43253 q^{4} -3.00378 q^{5} -1.93237 q^{6} -1.71928 q^{7} -2.58575 q^{8} +3.58019 q^{9} +O(q^{10})\)	\(q+0.753306 q^{2} -2.56519 q^{3} -1.43253 q^{4} -3.00378 q^{5} -1.93237 q^{6} -1.71928 q^{7} -2.58575 q^{8} +3.58019 q^{9} -2.26276 q^{10} -2.41529 q^{11} +3.67471 q^{12} -1.29514 q^{14} +7.70525 q^{15} +0.917200 q^{16} +0.538152 q^{17} +2.69698 q^{18} -4.10746 q^{19} +4.30300 q^{20} +4.41027 q^{21} -1.81945 q^{22} -4.29565 q^{23} +6.63293 q^{24} +4.02267 q^{25} -1.48830 q^{27} +2.46291 q^{28} +0.243664 q^{29} +5.80442 q^{30} -1.00000 q^{31} +5.86243 q^{32} +6.19567 q^{33} +0.405393 q^{34} +5.16432 q^{35} -5.12873 q^{36} +4.01880 q^{37} -3.09417 q^{38} +7.76700 q^{40} +12.3788 q^{41} +3.32228 q^{42} -0.328492 q^{43} +3.45997 q^{44} -10.7541 q^{45} -3.23594 q^{46} +10.1186 q^{47} -2.35279 q^{48} -4.04409 q^{49} +3.03031 q^{50} -1.38046 q^{51} -1.10278 q^{53} -1.12115 q^{54} +7.25498 q^{55} +4.44561 q^{56} +10.5364 q^{57} +0.183553 q^{58} +9.12070 q^{59} -11.0380 q^{60} -8.62851 q^{61} -0.753306 q^{62} -6.15534 q^{63} +2.58180 q^{64} +4.66723 q^{66} +10.2626 q^{67} -0.770918 q^{68} +11.0191 q^{69} +3.89032 q^{70} +0.724013 q^{71} -9.25747 q^{72} -10.8130 q^{73} +3.02739 q^{74} -10.3189 q^{75} +5.88406 q^{76} +4.15254 q^{77} +0.534099 q^{79} -2.75506 q^{80} -6.92280 q^{81} +9.32506 q^{82} +8.64796 q^{83} -6.31784 q^{84} -1.61649 q^{85} -0.247455 q^{86} -0.625043 q^{87} +6.24532 q^{88} +2.59593 q^{89} -8.10113 q^{90} +6.15364 q^{92} +2.56519 q^{93} +7.62242 q^{94} +12.3379 q^{95} -15.0382 q^{96} -10.3773 q^{97} -3.04644 q^{98} -8.64719 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 5 q^{3} + 28 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 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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