LMFDB - Embedded newform 5239.2.a.m.1.17

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:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 4 x^{16} - 19 x^{15} + 90 x^{14} + 116 x^{13} - 776 x^{12} - 146 x^{11} + 3232 x^{10} + \cdots - 1 $ x^17 - 4x^16 - 19x^15 + 90x^14 + 116x^13 - 776x^12 - 146x^11 + 3232x^10 - 995x^9 - 6763x^8 + 3668x^7 + 6782x^6 - 4160x^5 - 2876x^4 + 1449x^3 + 392x^2 + 6x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 403)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$-2.72325$ of defining polynomial
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)

$f(q)$	$=$	$q+2.72325 q^{2} -2.85287 q^{3} +5.41608 q^{4} -1.48160 q^{5} -7.76907 q^{6} -2.10121 q^{7} +9.30282 q^{8} +5.13886 q^{9} +O(q^{10})$	\(q+2.72325 q^{2} -2.85287 q^{3} +5.41608 q^{4} -1.48160 q^{5} -7.76907 q^{6} -2.10121 q^{7} +9.30282 q^{8} +5.13886 q^{9} -4.03477 q^{10} -3.72756 q^{11} -15.4514 q^{12} -5.72212 q^{14} +4.22682 q^{15} +14.5017 q^{16} +3.93010 q^{17} +13.9944 q^{18} +5.95633 q^{19} -8.02448 q^{20} +5.99448 q^{21} -10.1511 q^{22} -1.89598 q^{23} -26.5397 q^{24} -2.80485 q^{25} -6.10188 q^{27} -11.3803 q^{28} -6.78836 q^{29} +11.5107 q^{30} -1.00000 q^{31} +20.8861 q^{32} +10.6342 q^{33} +10.7026 q^{34} +3.11316 q^{35} +27.8324 q^{36} +2.13082 q^{37} +16.2206 q^{38} -13.7831 q^{40} -6.82335 q^{41} +16.3244 q^{42} -4.82610 q^{43} -20.1887 q^{44} -7.61375 q^{45} -5.16323 q^{46} +8.45973 q^{47} -41.3715 q^{48} -2.58491 q^{49} -7.63830 q^{50} -11.2121 q^{51} -11.1099 q^{53} -16.6169 q^{54} +5.52276 q^{55} -19.5472 q^{56} -16.9926 q^{57} -18.4864 q^{58} +1.70425 q^{59} +22.8928 q^{60} +4.57968 q^{61} -2.72325 q^{62} -10.7978 q^{63} +27.8747 q^{64} +28.9596 q^{66} +8.62745 q^{67} +21.2857 q^{68} +5.40899 q^{69} +8.47791 q^{70} -16.2606 q^{71} +47.8059 q^{72} -2.72582 q^{73} +5.80274 q^{74} +8.00187 q^{75} +32.2599 q^{76} +7.83238 q^{77} +7.19465 q^{79} -21.4858 q^{80} +1.99128 q^{81} -18.5817 q^{82} -11.4569 q^{83} +32.4665 q^{84} -5.82285 q^{85} -13.1427 q^{86} +19.3663 q^{87} -34.6768 q^{88} -14.2119 q^{89} -20.7341 q^{90} -10.2688 q^{92} +2.85287 q^{93} +23.0379 q^{94} -8.82491 q^{95} -59.5854 q^{96} -18.2670 q^{97} -7.03936 q^{98} -19.1554 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9	$ 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9} + 6 q^{10} - 13 q^{11} + 4 q^{12} - 4 q^{15} + 34 q^{16} - 6 q^{17} + 12 q^{18} - 4 q^{19} - 28 q^{20} - 18 q^{21} - 34 q^{22} - 8 q^{23} - 40 q^{24} + 8 q^{25} - 3 q^{27} - 21 q^{28} - 6 q^{29} + 19 q^{30} - 17 q^{31} - 6 q^{32} - 7 q^{33} - 24 q^{34} - 9 q^{35} - 14 q^{37} + 11 q^{38} - 10 q^{40} - 43 q^{41} + 33 q^{42} + 18 q^{43} - 28 q^{44} - 26 q^{45} - 7 q^{46} - 6 q^{47} - 95 q^{48} - q^{49} - 44 q^{50} + 26 q^{51} - 5 q^{53} - 27 q^{54} + 39 q^{55} + 39 q^{56} - 46 q^{57} - 8 q^{58} + q^{59} - 21 q^{60} - 19 q^{61} + 4 q^{62} - 5 q^{63} + 42 q^{64} + 26 q^{66} - 10 q^{67} + 34 q^{68} + 32 q^{69} + 24 q^{70} - 35 q^{71} + 26 q^{72} - 11 q^{73} - 68 q^{74} - 62 q^{75} - 2 q^{76} + 21 q^{77} + q^{79} - 49 q^{80} + 37 q^{81} + 35 q^{82} - 24 q^{83} + 34 q^{84} + 13 q^{85} - 76 q^{86} - 22 q^{87} - 37 q^{88} - 42 q^{89} + 15 q^{90} + 15 q^{92} + 42 q^{94} + 34 q^{95} - 33 q^{96} + 38 q^{97} - 8 q^{98} - 17 q^{99}+O(q^{100}) $ 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9 + 6 * q^10 - 13 * q^11 + 4 * q^12 - 4 * q^15 + 34 * q^16 - 6 * q^17 + 12 * q^18 - 4 * q^19 - 28 * q^20 - 18 * q^21 - 34 * q^22 - 8 * q^23 - 40 * q^24 + 8 * q^25 - 3 * q^27 - 21 * q^28 - 6 * q^29 + 19 * q^30 - 17 * q^31 - 6 * q^32 - 7 * q^33 - 24 * q^34 - 9 * q^35 - 14 * q^37 + 11 * q^38 - 10 * q^40 - 43 * q^41 + 33 * q^42 + 18 * q^43 - 28 * q^44 - 26 * q^45 - 7 * q^46 - 6 * q^47 - 95 * q^48 - q^49 - 44 * q^50 + 26 * q^51 - 5 * q^53 - 27 * q^54 + 39 * q^55 + 39 * q^56 - 46 * q^57 - 8 * q^58 + q^59 - 21 * q^60 - 19 * q^61 + 4 * q^62 - 5 * q^63 + 42 * q^64 + 26 * q^66 - 10 * q^67 + 34 * q^68 + 32 * q^69 + 24 * q^70 - 35 * q^71 + 26 * q^72 - 11 * q^73 - 68 * q^74 - 62 * q^75 - 2 * q^76 + 21 * q^77 + q^79 - 49 * q^80 + 37 * q^81 + 35 * q^82 - 24 * q^83 + 34 * q^84 + 13 * q^85 - 76 * q^86 - 22 * q^87 - 37 * q^88 - 42 * q^89 + 15 * q^90 + 15 * q^92 + 42 * q^94 + 34 * q^95 - 33 * q^96 + 38 * q^97 - 8 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.72325	1.92563	0.962813	−	0.270168i	$-0.0870791\pi$
$2$	2.72325	1.92563	0.962813	+	0.270168i	$0.0870791\pi$
$3$	−2.85287	−1.64710	−0.823552	−	0.567241i	$-0.808011\pi$
$3$	−2.85287	−1.64710	−0.823552	+	0.567241i	$0.808011\pi$
$4$	5.41608	2.70804
$5$	−1.48160	−0.662593	−0.331297	−	0.943527i	$-0.607486\pi$
$5$	−1.48160	−0.662593	−0.331297	+	0.943527i	$0.607486\pi$
$6$	−7.76907	−3.17171
$7$	−2.10121	−0.794183	−0.397092	−	0.917779i	$-0.629980\pi$
$7$	−2.10121	−0.794183	−0.397092	+	0.917779i	$0.629980\pi$
$8$	9.30282	3.28904
$9$	5.13886	1.71295
$10$	−4.03477	−1.27591
$11$	−3.72756	−1.12390	−0.561950	−	0.827171i	$-0.689949\pi$
$11$	−3.72756	−1.12390	−0.561950	+	0.827171i	$0.689949\pi$
$12$	−15.4514	−4.46042
$13$	0	0
$13$	0	0
$14$	−5.72212	−1.52930
$15$	4.22682	1.09136
$16$	14.5017	3.62543
$17$	3.93010	0.953189	0.476594	−	0.879123i	$-0.341871\pi$
$17$	3.93010	0.953189	0.476594	+	0.879123i	$0.341871\pi$
$18$	13.9944	3.29851
$19$	5.95633	1.36648	0.683238	−	0.730196i	$-0.260571\pi$
$19$	5.95633	1.36648	0.683238	+	0.730196i	$0.260571\pi$
$20$	−8.02448	−1.79433
$21$	5.99448	1.30810
$22$	−10.1511	−2.16421
$23$	−1.89598	−0.395340	−0.197670	−	0.980269i	$-0.563337\pi$
$23$	−1.89598	−0.395340	−0.197670	+	0.980269i	$0.563337\pi$
$24$	−26.5397	−5.41740
$25$	−2.80485	−0.560970
$26$	0	0
$27$	−6.10188	−1.17431
$28$	−11.3803	−2.15068
$29$	−6.78836	−1.26057	−0.630284	−	0.776365i	$-0.717061\pi$
$29$	−6.78836	−1.26057	−0.630284	+	0.776365i	$0.717061\pi$
$30$	11.5107	2.10155
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	20.8861	3.69218
$33$	10.6342	1.85118
$34$	10.7026	1.83549
$35$	3.11316	0.526220
$36$	27.8324	4.63874
$37$	2.13082	0.350304	0.175152	−	0.984541i	$-0.443958\pi$
$37$	2.13082	0.350304	0.175152	+	0.984541i	$0.443958\pi$
$38$	16.2206	2.63132
$39$	0	0
$40$	−13.7831	−2.17930
$41$	−6.82335	−1.06563	−0.532814	−	0.846232i	$-0.678866\pi$
$41$	−6.82335	−1.06563	−0.532814	+	0.846232i	$0.678866\pi$
$42$	16.3244	2.51892
$43$	−4.82610	−0.735973	−0.367987	−	0.929831i	$-0.619953\pi$
$43$	−4.82610	−0.735973	−0.367987	+	0.929831i	$0.619953\pi$
$44$	−20.1887	−3.04356
$45$	−7.61375	−1.13499
$46$	−5.16323	−0.761277
$47$	8.45973	1.23398	0.616989	−	0.786972i	$-0.288352\pi$
$47$	8.45973	1.23398	0.616989	+	0.786972i	$0.288352\pi$
$48$	−41.3715	−5.97146
$49$	−2.58491	−0.369273
$50$	−7.63830	−1.08022
$51$	−11.2121	−1.57000
$52$	0	0
$53$	−11.1099	−1.52607	−0.763034	−	0.646359i	$-0.776291\pi$
$53$	−11.1099	−1.52607	−0.763034	+	0.646359i	$0.776291\pi$
$54$	−16.6169	−2.26128
$55$	5.52276	0.744689
$56$	−19.5472	−2.61210
$57$	−16.9926	−2.25073
$58$	−18.4864	−2.42738
$59$	1.70425	0.221875	0.110937	−	0.993827i	$-0.464615\pi$
$59$	1.70425	0.221875	0.110937	+	0.993827i	$0.464615\pi$
$60$	22.8928	2.95544
$61$	4.57968	0.586368	0.293184	−	0.956056i	$-0.405285\pi$
$61$	4.57968	0.586368	0.293184	+	0.956056i	$0.405285\pi$
$62$	−2.72325	−0.345853
$63$	−10.7978	−1.36040
$64$	27.8747	3.48434
$65$	0	0
$66$	28.9596	3.56468
$67$	8.62745	1.05401	0.527005	−	0.849862i	$-0.323315\pi$
$67$	8.62745	1.05401	0.527005	+	0.849862i	$0.323315\pi$
$68$	21.2857	2.58127
$69$	5.40899	0.651166
$70$	8.47791	1.01330
$71$	−16.2606	−1.92978	−0.964890	−	0.262655i	$-0.915402\pi$
$71$	−16.2606	−1.92978	−0.964890	+	0.262655i	$0.915402\pi$
$72$	47.8059	5.63397
$73$	−2.72582	−0.319034	−0.159517	−	0.987195i	$-0.550994\pi$
$73$	−2.72582	−0.319034	−0.159517	+	0.987195i	$0.550994\pi$
$74$	5.80274	0.674555
$75$	8.00187	0.923976
$76$	32.2599	3.70047
$77$	7.83238	0.892583
$78$	0	0
$79$	7.19465	0.809462	0.404731	−	0.914436i	$-0.367365\pi$
$79$	7.19465	0.809462	0.404731	+	0.914436i	$0.367365\pi$
$80$	−21.4858	−2.40219
$81$	1.99128	0.221253
$82$	−18.5817	−2.05200
$83$	−11.4569	−1.25756	−0.628779	−	0.777584i	$-0.716445\pi$
$83$	−11.4569	−1.25756	−0.628779	+	0.777584i	$0.716445\pi$
$84$	32.4665	3.54239
$85$	−5.82285	−0.631576
$86$	−13.1427	−1.41721
$87$	19.3663	2.07629
$88$	−34.6768	−3.69656
$89$	−14.2119	−1.50646	−0.753229	−	0.657759i	$-0.771505\pi$
$89$	−14.2119	−1.50646	−0.753229	+	0.657759i	$0.771505\pi$
$90$	−20.7341	−2.18557
$91$	0	0
$92$	−10.2688	−1.07060
$93$	2.85287	0.295829
$94$	23.0379	2.37618
$95$	−8.82491	−0.905417
$96$	−59.5854	−6.08141
$97$	−18.2670	−1.85473	−0.927366	−	0.374155i	$-0.877933\pi$
$97$	−18.2670	−1.85473	−0.927366	+	0.374155i	$0.877933\pi$
$98$	−7.03936	−0.711082
$99$	−19.1554	−1.92519
$100$	−15.1913	−1.51913
$101$	7.86112	0.782211	0.391105	−	0.920346i	$-0.372093\pi$
$101$	7.86112	0.782211	0.391105	+	0.920346i	$0.372093\pi$
$102$	−30.5332	−3.02324
$103$	1.97209	0.194316	0.0971580	−	0.995269i	$-0.469025\pi$
$103$	1.97209	0.194316	0.0971580	+	0.995269i	$0.469025\pi$
$104$	0	0
$105$	−8.88144	−0.866740
$106$	−30.2551	−2.93864
$107$	−12.5743	−1.21561	−0.607804	−	0.794087i	$-0.707949\pi$
$107$	−12.5743	−1.21561	−0.607804	+	0.794087i	$0.707949\pi$
$108$	−33.0482	−3.18007
$109$	−3.40791	−0.326418	−0.163209	−	0.986592i	$-0.552185\pi$
$109$	−3.40791	−0.326418	−0.163209	+	0.986592i	$0.552185\pi$
$110$	15.0398	1.43399
$111$	−6.07894	−0.576987
$112$	−30.4712	−2.87926
$113$	−1.54187	−0.145047	−0.0725233	−	0.997367i	$-0.523105\pi$
$113$	−1.54187	−0.145047	−0.0725233	+	0.997367i	$0.523105\pi$
$114$	−46.2751	−4.33406
$115$	2.80910	0.261950
$116$	−36.7663	−3.41366
$117$	0	0
$118$	4.64110	0.427248
$119$	−8.25796	−0.757006
$120$	39.3213	3.58953
$121$	2.89467	0.263152
$122$	12.4716	1.12913
$123$	19.4661	1.75520
$124$	−5.41608	−0.486378
$125$	11.5637	1.03429
$126$	−29.4051	−2.61962
$127$	−12.6306	−1.12079	−0.560394	−	0.828226i	$-0.689350\pi$
$127$	−12.6306	−1.12079	−0.560394	+	0.828226i	$0.689350\pi$
$128$	34.1374	3.01735
$129$	13.7682	1.21222
$130$	0	0
$131$	9.79673	0.855945	0.427972	−	0.903792i	$-0.359228\pi$
$131$	9.79673	0.855945	0.427972	+	0.903792i	$0.359228\pi$
$132$	57.5958	5.01307
$133$	−12.5155	−1.08523
$134$	23.4947	2.02963
$135$	9.04056	0.778088
$136$	36.5610	3.13508
$137$	−19.3871	−1.65635	−0.828175	−	0.560469i	$-0.810621\pi$
$137$	−19.3871	−1.65635	−0.828175	+	0.560469i	$0.810621\pi$
$138$	14.7300	1.25390
$139$	−4.79081	−0.406351	−0.203176	−	0.979142i	$-0.565126\pi$
$139$	−4.79081	−0.406351	−0.203176	+	0.979142i	$0.565126\pi$
$140$	16.8611	1.42502
$141$	−24.1345	−2.03249
$142$	−44.2817	−3.71604
$143$	0	0
$144$	74.5223	6.21019
$145$	10.0577	0.835243
$146$	−7.42309	−0.614340
$147$	7.37442	0.608232
$148$	11.5407	0.948637
$149$	−17.5569	−1.43832	−0.719160	−	0.694845i	$-0.755473\pi$
$149$	−17.5569	−1.43832	−0.719160	+	0.694845i	$0.755473\pi$
$150$	21.7911	1.77923
$151$	3.58365	0.291633	0.145817	−	0.989312i	$-0.453419\pi$
$151$	3.58365	0.291633	0.145817	+	0.989312i	$0.453419\pi$
$152$	55.4106	4.49440
$153$	20.1962	1.63277
$154$	21.3295	1.71878
$155$	1.48160	0.119005
$156$	0	0
$157$	10.6833	0.852619	0.426309	−	0.904577i	$-0.359813\pi$
$157$	10.6833	0.852619	0.426309	+	0.904577i	$0.359813\pi$
$158$	19.5928	1.55872
$159$	31.6952	2.51359
$160$	−30.9450	−2.44642
$161$	3.98386	0.313972
$162$	5.42275	0.426052
$163$	4.79921	0.375903	0.187952	−	0.982178i	$-0.439815\pi$
$163$	4.79921	0.375903	0.187952	+	0.982178i	$0.439815\pi$
$164$	−36.9558	−2.88576
$165$	−15.7557	−1.22658
$166$	−31.2000	−2.42159
$167$	−1.61082	−0.124649	−0.0623247	−	0.998056i	$-0.519851\pi$
$167$	−1.61082	−0.124649	−0.0623247	+	0.998056i	$0.519851\pi$
$168$	55.7655	4.30240
$169$	0	0
$170$	−15.8570	−1.21618
$171$	30.6087	2.34071
$172$	−26.1385	−1.99304
$173$	−1.80290	−0.137072	−0.0685360	−	0.997649i	$-0.521833\pi$
$173$	−1.80290	−0.137072	−0.0685360	+	0.997649i	$0.521833\pi$
$174$	52.7392	3.99815
$175$	5.89358	0.445513
$176$	−54.0560	−4.07462
$177$	−4.86201	−0.365451
$178$	−38.7025	−2.90087
$179$	9.56216	0.714709	0.357355	−	0.933969i	$-0.383679\pi$
$179$	9.56216	0.714709	0.357355	+	0.933969i	$0.383679\pi$
$180$	−41.2366	−3.07360
$181$	−10.8096	−0.803468	−0.401734	−	0.915756i	$-0.631592\pi$
$181$	−10.8096	−0.803468	−0.401734	+	0.915756i	$0.631592\pi$
$182$	0	0
$183$	−13.0652	−0.965809
$184$	−17.6380	−1.30029
$185$	−3.15702	−0.232109
$186$	7.76907	0.569656
$187$	−14.6497	−1.07129
$188$	45.8185	3.34166
$189$	12.8213	0.932615
$190$	−24.0324	−1.74350
$191$	13.7731	0.996588	0.498294	−	0.867008i	$-0.333960\pi$
$191$	13.7731	0.996588	0.498294	+	0.867008i	$0.333960\pi$
$192$	−79.5228	−5.73906
$193$	15.2664	1.09890	0.549451	−	0.835526i	$-0.314837\pi$
$193$	15.2664	1.09890	0.549451	+	0.835526i	$0.314837\pi$
$194$	−49.7455	−3.57152
$195$	0	0
$196$	−14.0001	−1.00001
$197$	−10.6280	−0.757216	−0.378608	−	0.925557i	$-0.623597\pi$
$197$	−10.6280	−0.757216	−0.378608	+	0.925557i	$0.623597\pi$
$198$	−52.1648	−3.70719
$199$	5.39666	0.382559	0.191279	−	0.981536i	$-0.438736\pi$
$199$	5.39666	0.382559	0.191279	+	0.981536i	$0.438736\pi$
$200$	−26.0930	−1.84506
$201$	−24.6130	−1.73607
$202$	21.4078	1.50625
$203$	14.2638	1.00112
$204$	−60.7253	−4.25162
$205$	10.1095	0.706078
$206$	5.37049	0.374180
$207$	−9.74319	−0.677199
$208$	0	0
$209$	−22.2025	−1.53578
$210$	−24.1864	−1.66902
$211$	1.43832	0.0990183	0.0495092	−	0.998774i	$-0.484234\pi$
$211$	1.43832	0.0990183	0.0495092	+	0.998774i	$0.484234\pi$
$212$	−60.1723	−4.13265
$213$	46.3894	3.17855
$214$	−34.2430	−2.34081
$215$	7.15036	0.487651
$216$	−56.7647	−3.86235
$217$	2.10121	0.142639
$218$	−9.28057	−0.628560
$219$	7.77642	0.525482
$220$	29.9117	2.01665
$221$	0	0
$222$	−16.5545	−1.11106
$223$	−11.5067	−0.770546	−0.385273	−	0.922803i	$-0.625893\pi$
$223$	−11.5067	−0.770546	−0.385273	+	0.922803i	$0.625893\pi$
$224$	−43.8862	−2.93227
$225$	−14.4137	−0.960915
$226$	−4.19889	−0.279306
$227$	0.691629	0.0459051	0.0229525	−	0.999737i	$-0.492693\pi$
$227$	0.691629	0.0459051	0.0229525	+	0.999737i	$0.492693\pi$
$228$	−92.0333	−6.09505
$229$	−19.1306	−1.26419	−0.632093	−	0.774893i	$-0.717804\pi$
$229$	−19.1306	−1.26419	−0.632093	+	0.774893i	$0.717804\pi$
$230$	7.64987	0.504417
$231$	−22.3447	−1.47018
$232$	−63.1509	−4.14606
$233$	24.4339	1.60072	0.800358	−	0.599522i	$-0.204643\pi$
$233$	24.4339	1.60072	0.800358	+	0.599522i	$0.204643\pi$
$234$	0	0
$235$	−12.5340	−0.817626
$236$	9.23036	0.600845
$237$	−20.5254	−1.33327
$238$	−22.4885	−1.45771
$239$	11.7124	0.757613	0.378807	−	0.925476i	$-0.376335\pi$
$239$	11.7124	0.757613	0.378807	+	0.925476i	$0.376335\pi$
$240$	61.2962	3.95665
$241$	23.4773	1.51230	0.756152	−	0.654396i	$-0.227077\pi$
$241$	23.4773	1.51230	0.756152	+	0.654396i	$0.227077\pi$
$242$	7.88291	0.506732
$243$	12.6248	0.809879
$244$	24.8039	1.58791
$245$	3.82982	0.244678
$246$	53.0111	3.37986
$247$	0	0
$248$	−9.30282	−0.590730
$249$	32.6850	2.07133
$250$	31.4908	1.99165
$251$	−3.29038	−0.207687	−0.103843	−	0.994594i	$-0.533114\pi$
$251$	−3.29038	−0.207687	−0.103843	+	0.994594i	$0.533114\pi$
$252$	−58.4818	−3.68401
$253$	7.06739	0.444323
$254$	−34.3963	−2.15822
$255$	16.6118	1.04027
$256$	37.2151	2.32595
$257$	−2.30720	−0.143919	−0.0719596	−	0.997408i	$-0.522925\pi$
$257$	−2.30720	−0.143919	−0.0719596	+	0.997408i	$0.522925\pi$
$258$	37.4943	2.33429
$259$	−4.47729	−0.278206
$260$	0	0
$261$	−34.8844	−2.15929
$262$	26.6789	1.64823
$263$	2.31128	0.142520	0.0712598	−	0.997458i	$-0.477298\pi$
$263$	2.31128	0.142520	0.0712598	+	0.997458i	$0.477298\pi$
$264$	98.9283	6.08861
$265$	16.4605	1.01116
$266$	−34.0828	−2.08975
$267$	40.5446	2.48129
$268$	46.7269	2.85430
$269$	3.87780	0.236434	0.118217	−	0.992988i	$-0.462282\pi$
$269$	3.87780	0.236434	0.118217	+	0.992988i	$0.462282\pi$
$270$	24.6197	1.49831
$271$	−2.46831	−0.149939	−0.0749696	−	0.997186i	$-0.523886\pi$
$271$	−2.46831	−0.149939	−0.0749696	+	0.997186i	$0.523886\pi$
$272$	56.9932	3.45572
$273$	0	0
$274$	−52.7958	−3.18951
$275$	10.4552	0.630475
$276$	29.2955	1.76338
$277$	−7.64965	−0.459623	−0.229811	−	0.973235i	$-0.573811\pi$
$277$	−7.64965	−0.459623	−0.229811	+	0.973235i	$0.573811\pi$
$278$	−13.0466	−0.782481
$279$	−5.13886	−0.307655
$280$	28.9612	1.73076
$281$	−22.4921	−1.34177	−0.670884	−	0.741563i	$-0.734085\pi$
$281$	−22.4921	−1.34177	−0.670884	+	0.741563i	$0.734085\pi$
$282$	−65.7242	−3.91382
$283$	−4.86600	−0.289254	−0.144627	−	0.989486i	$-0.546198\pi$
$283$	−4.86600	−0.289254	−0.144627	+	0.989486i	$0.546198\pi$
$284$	−88.0687	−5.22592
$285$	25.1763	1.49132
$286$	0	0
$287$	14.3373	0.846304
$288$	107.331	6.32453
$289$	−1.55433	−0.0914313
$290$	27.3895	1.60837
$291$	52.1133	3.05494
$292$	−14.7633	−0.863955
$293$	2.96271	0.173083	0.0865416	−	0.996248i	$-0.472418\pi$
$293$	2.96271	0.173083	0.0865416	+	0.996248i	$0.472418\pi$
$294$	20.0824	1.17123
$295$	−2.52502	−0.147013
$296$	19.8226	1.15217
$297$	22.7451	1.31980
$298$	−47.8119	−2.76967
$299$	0	0
$300$	43.3387	2.50216
$301$	10.1406	0.584497
$302$	9.75916	0.561576
$303$	−22.4267	−1.28838
$304$	86.3770	4.95406
$305$	−6.78527	−0.388523
$306$	54.9993	3.14410
$307$	8.33149	0.475503	0.237752	−	0.971326i	$-0.423590\pi$
$307$	8.33149	0.475503	0.237752	+	0.971326i	$0.423590\pi$
$308$	42.4208	2.41715
$309$	−5.62612	−0.320059
$310$	4.03477	0.229160
$311$	−10.8995	−0.618053	−0.309026	−	0.951053i	$-0.600003\pi$
$311$	−10.8995	−0.618053	−0.309026	+	0.951053i	$0.600003\pi$
$312$	0	0
$313$	13.6878	0.773680	0.386840	−	0.922147i	$-0.373567\pi$
$313$	13.6878	0.773680	0.386840	+	0.922147i	$0.373567\pi$
$314$	29.0932	1.64183
$315$	15.9981	0.901390
$316$	38.9668	2.19205
$317$	−12.7083	−0.713771	−0.356885	−	0.934148i	$-0.616161\pi$
$317$	−12.7083	−0.713771	−0.356885	+	0.934148i	$0.616161\pi$
$318$	86.3139	4.84024
$319$	25.3040	1.41675
$320$	−41.2992	−2.30870
$321$	35.8729	2.00223
$322$	10.8490	0.604594
$323$	23.4089	1.30251
$324$	10.7849	0.599163
$325$	0	0
$326$	13.0694	0.723849
$327$	9.72231	0.537645
$328$	−63.4764	−3.50490
$329$	−17.7757	−0.980005
$330$	−42.9067	−2.36193
$331$	15.5108	0.852549	0.426275	−	0.904594i	$-0.359826\pi$
$331$	15.5108	0.852549	0.426275	+	0.904594i	$0.359826\pi$
$332$	−62.0515	−3.40552
$333$	10.9500	0.600054
$334$	−4.38667	−0.240028
$335$	−12.7825	−0.698380
$336$	86.9303	4.74243
$337$	−1.13512	−0.0618337	−0.0309168	−	0.999522i	$-0.509843\pi$
$337$	−1.13512	−0.0618337	−0.0309168	+	0.999522i	$0.509843\pi$
$338$	0	0
$339$	4.39874	0.238907
$340$	−31.5370	−1.71033
$341$	3.72756	0.201858
$342$	83.3551	4.50733
$343$	20.1399	1.08745
$344$	−44.8963	−2.42065
$345$	−8.01398	−0.431458
$346$	−4.90974	−0.263949
$347$	31.3723	1.68415	0.842076	−	0.539358i	$-0.181333\pi$
$347$	31.3723	1.68415	0.842076	+	0.539358i	$0.181333\pi$
$348$	104.889	5.62266
$349$	−3.55015	−0.190035	−0.0950177	−	0.995476i	$-0.530291\pi$
$349$	−3.55015	−0.190035	−0.0950177	+	0.995476i	$0.530291\pi$
$350$	16.0497	0.857892
$351$	0	0
$352$	−77.8543	−4.14965
$353$	−25.5828	−1.36164	−0.680818	−	0.732453i	$-0.738375\pi$
$353$	−25.5828	−1.36164	−0.680818	+	0.732453i	$0.738375\pi$
$354$	−13.2404	−0.703722
$355$	24.0918	1.27866
$356$	−76.9727	−4.07954
$357$	23.5589	1.24687
$358$	26.0401	1.37626
$359$	−27.6723	−1.46049	−0.730243	−	0.683187i	$-0.760593\pi$
$359$	−27.6723	−1.46049	−0.730243	+	0.683187i	$0.760593\pi$
$360$	−70.8293	−3.73303
$361$	16.4778	0.867254
$362$	−29.4371	−1.54718
$363$	−8.25812	−0.433439
$364$	0	0
$365$	4.03859	0.211390
$366$	−35.5798	−1.85979
$367$	2.06313	0.107694	0.0538472	−	0.998549i	$-0.482852\pi$
$367$	2.06313	0.107694	0.0538472	+	0.998549i	$0.482852\pi$
$368$	−27.4950	−1.43328
$369$	−35.0642	−1.82537
$370$	−8.59736	−0.446955
$371$	23.3443	1.21198
$372$	15.4514	0.801115
$373$	8.19109	0.424119	0.212059	−	0.977257i	$-0.431983\pi$
$373$	8.19109	0.424119	0.212059	+	0.977257i	$0.431983\pi$
$374$	−39.8946	−2.06290
$375$	−32.9897	−1.70358
$376$	78.6993	4.05861
$377$	0	0
$378$	34.9157	1.79587
$379$	0.979392	0.0503080	0.0251540	−	0.999684i	$-0.491992\pi$
$379$	0.979392	0.0503080	0.0251540	+	0.999684i	$0.491992\pi$
$380$	−47.7964	−2.45190
$381$	36.0335	1.84605
$382$	37.5076	1.91906
$383$	5.62317	0.287330	0.143665	−	0.989626i	$-0.454111\pi$
$383$	5.62317	0.287330	0.143665	+	0.989626i	$0.454111\pi$
$384$	−97.3894	−4.96988
$385$	−11.6045	−0.591419
$386$	41.5743	2.11608
$387$	−24.8006	−1.26069
$388$	−98.9354	−5.02268
$389$	15.6021	0.791057	0.395528	−	0.918454i	$-0.370562\pi$
$389$	15.6021	0.791057	0.395528	+	0.918454i	$0.370562\pi$
$390$	0	0
$391$	−7.45140	−0.376834
$392$	−24.0470	−1.21456
$393$	−27.9488	−1.40983
$394$	−28.9428	−1.45812
$395$	−10.6596	−0.536344
$396$	−103.747	−5.21348
$397$	−36.7053	−1.84219	−0.921093	−	0.389342i	$-0.872702\pi$
$397$	−36.7053	−1.84219	−0.921093	+	0.389342i	$0.872702\pi$
$398$	14.6964	0.736665
$399$	35.7051	1.78749
$400$	−40.6752	−2.03376
$401$	−1.11897	−0.0558785	−0.0279392	−	0.999610i	$-0.508894\pi$
$401$	−1.11897	−0.0558785	−0.0279392	+	0.999610i	$0.508894\pi$
$402$	−67.0272	−3.34301
$403$	0	0
$404$	42.5764	2.11826
$405$	−2.95029	−0.146601
$406$	38.8438	1.92779
$407$	−7.94274	−0.393707
$408$	−104.304	−5.16380
$409$	−14.7181	−0.727766	−0.363883	−	0.931445i	$-0.618549\pi$
$409$	−14.7181	−0.727766	−0.363883	+	0.931445i	$0.618549\pi$
$410$	27.5307	1.35964
$411$	55.3088	2.72818
$412$	10.6810	0.526215
$413$	−3.58099	−0.176209
$414$	−26.5331	−1.30403
$415$	16.9746	0.833250
$416$	0	0
$417$	13.6676	0.669303
$418$	−60.4630	−2.95734
$419$	11.9990	0.586188	0.293094	−	0.956084i	$-0.405315\pi$
$419$	11.9990	0.586188	0.293094	+	0.956084i	$0.405315\pi$
$420$	−48.1025	−2.34716
$421$	12.2208	0.595606	0.297803	−	0.954627i	$-0.403746\pi$
$421$	12.2208	0.595606	0.297803	+	0.954627i	$0.403746\pi$
$422$	3.91691	0.190672
$423$	43.4733	2.11375
$424$	−103.354	−5.01930
$425$	−11.0233	−0.534711
$426$	126.330	6.12070
$427$	−9.62287	−0.465683
$428$	−68.1036	−3.29191
$429$	0	0
$430$	19.4722	0.939033
$431$	−20.7605	−0.999996	−0.499998	−	0.866026i	$-0.666666\pi$
$431$	−20.7605	−0.999996	−0.499998	+	0.866026i	$0.666666\pi$
$432$	−88.4877	−4.25737
$433$	9.49393	0.456249	0.228125	−	0.973632i	$-0.426741\pi$
$433$	9.49393	0.456249	0.228125	+	0.973632i	$0.426741\pi$
$434$	5.72212	0.274670
$435$	−28.6932	−1.37573
$436$	−18.4575	−0.883953
$437$	−11.2931	−0.540222
$438$	21.1771	1.01188
$439$	37.3614	1.78316	0.891581	−	0.452861i	$-0.149596\pi$
$439$	37.3614	1.78316	0.891581	+	0.452861i	$0.149596\pi$
$440$	51.3772	2.44931
$441$	−13.2835	−0.632547
$442$	0	0
$443$	4.91644	0.233587	0.116794	−	0.993156i	$-0.462738\pi$
$443$	4.91644	0.233587	0.116794	+	0.993156i	$0.462738\pi$
$444$	−32.9240	−1.56250
$445$	21.0564	0.998168
$446$	−31.3356	−1.48378
$447$	50.0876	2.36906
$448$	−58.5706	−2.76720
$449$	−23.2621	−1.09780	−0.548902	−	0.835887i	$-0.684954\pi$
$449$	−23.2621	−1.09780	−0.548902	+	0.835887i	$0.684954\pi$
$450$	−39.2522	−1.85036
$451$	25.4344	1.19766
$452$	−8.35087	−0.392792
$453$	−10.2237	−0.480350
$454$	1.88348	0.0883960
$455$	0	0
$456$	−158.079	−7.40274
$457$	12.6016	0.589479	0.294740	−	0.955578i	$-0.404767\pi$
$457$	12.6016	0.589479	0.294740	+	0.955578i	$0.404767\pi$
$458$	−52.0973	−2.43435
$459$	−23.9810	−1.11934
$460$	15.2143	0.709370
$461$	34.8173	1.62160	0.810801	−	0.585322i	$-0.199032\pi$
$461$	34.8173	1.62160	0.810801	+	0.585322i	$0.199032\pi$
$462$	−60.8503	−2.83101
$463$	2.50847	0.116579	0.0582893	−	0.998300i	$-0.481435\pi$
$463$	2.50847	0.116579	0.0582893	+	0.998300i	$0.481435\pi$
$464$	−98.4429	−4.57010
$465$	−4.22682	−0.196014
$466$	66.5395	3.08238
$467$	−3.17663	−0.146997	−0.0734984	−	0.997295i	$-0.523416\pi$
$467$	−3.17663	−0.146997	−0.0734984	+	0.997295i	$0.523416\pi$
$468$	0	0
$469$	−18.1281	−0.837077
$470$	−34.1331	−1.57444
$471$	−30.4780	−1.40435
$472$	15.8543	0.729755
$473$	17.9895	0.827160
$474$	−55.8957	−2.56738
$475$	−16.7066	−0.766552
$476$	−44.7258	−2.05000
$477$	−57.0924	−2.61408
$478$	31.8958	1.45888
$479$	6.17300	0.282052	0.141026	−	0.990006i	$-0.454960\pi$
$479$	6.17300	0.282052	0.141026	+	0.990006i	$0.454960\pi$
$480$	88.2820	4.02950
$481$	0	0
$482$	63.9344	2.91213
$483$	−11.3654	−0.517145
$484$	15.6778	0.712625
$485$	27.0644	1.22893
$486$	34.3804	1.55953
$487$	−10.9599	−0.496639	−0.248319	−	0.968678i	$-0.579878\pi$
$487$	−10.9599	−0.496639	−0.248319	+	0.968678i	$0.579878\pi$
$488$	42.6039	1.92859
$489$	−13.6915	−0.619151
$490$	10.4295	0.471158
$491$	−17.1228	−0.772743	−0.386372	−	0.922343i	$-0.626272\pi$
$491$	−17.1228	−0.772743	−0.386372	+	0.922343i	$0.626272\pi$
$492$	105.430	4.75315
$493$	−26.6789	−1.20156
$494$	0	0
$495$	28.3807	1.27562
$496$	−14.5017	−0.651147
$497$	34.1670	1.53260
$498$	89.0095	3.98861
$499$	−11.6532	−0.521669	−0.260835	−	0.965383i	$-0.583998\pi$
$499$	−11.6532	−0.521669	−0.260835	+	0.965383i	$0.583998\pi$
$500$	62.6298	2.80089
$501$	4.59547	0.205310
$502$	−8.96052	−0.399927
$503$	6.97224	0.310877	0.155438	−	0.987846i	$-0.450321\pi$
$503$	6.97224	0.310877	0.155438	+	0.987846i	$0.450321\pi$
$504$	−100.450	−4.47441
$505$	−11.6471	−0.518287
$506$	19.2462	0.855600
$507$	0	0
$508$	−68.4085	−3.03513
$509$	2.18913	0.0970315	0.0485158	−	0.998822i	$-0.484551\pi$
$509$	2.18913	0.0970315	0.0485158	+	0.998822i	$0.484551\pi$
$510$	45.2381	2.00318
$511$	5.72753	0.253371
$512$	33.0713	1.46156
$513$	−36.3448	−1.60466
$514$	−6.28308	−0.277135
$515$	−2.92186	−0.128752
$516$	74.5697	3.28275
$517$	−31.5341	−1.38687
$518$	−12.1928	−0.535720
$519$	5.14344	0.225772
$520$	0	0
$521$	41.7337	1.82839	0.914193	−	0.405279i	$-0.132826\pi$
$521$	41.7337	1.82839	0.914193	+	0.405279i	$0.132826\pi$
$522$	−94.9989	−4.15799
$523$	−32.2448	−1.40997	−0.704983	−	0.709224i	$-0.749045\pi$
$523$	−32.2448	−1.40997	−0.704983	+	0.709224i	$0.749045\pi$
$524$	53.0599	2.31793
$525$	−16.8136	−0.733807
$526$	6.29418	0.274439
$527$	−3.93010	−0.171198
$528$	154.215	6.71133
$529$	−19.4052	−0.843706
$530$	44.8261	1.94712
$531$	8.75791	0.380061
$532$	−67.7849	−2.93885
$533$	0	0
$534$	110.413	4.77804
$535$	18.6302	0.805453
$536$	80.2596	3.46669
$537$	−27.2796	−1.17720
$538$	10.5602	0.455283
$539$	9.63541	0.415026
$540$	48.9644	2.10709
$541$	−42.1436	−1.81189	−0.905947	−	0.423390i	$-0.860840\pi$
$541$	−42.1436	−1.81189	−0.905947	+	0.423390i	$0.860840\pi$
$542$	−6.72182	−0.288727
$543$	30.8382	1.32339
$544$	82.0846	3.51935
$545$	5.04917	0.216282
$546$	0	0
$547$	32.5367	1.39117	0.695585	−	0.718444i	$-0.255145\pi$
$547$	32.5367	1.39117	0.695585	+	0.718444i	$0.255145\pi$
$548$	−105.002	−4.48546
$549$	23.5343	1.00442
$550$	28.4722	1.21406
$551$	−40.4337	−1.72253
$552$	50.3189	2.14171
$553$	−15.1175	−0.642861
$554$	−20.8319	−0.885062
$555$	9.00658	0.382308
$556$	−25.9474	−1.10042
$557$	−14.6402	−0.620326	−0.310163	−	0.950683i	$-0.600384\pi$
$557$	−14.6402	−0.620326	−0.310163	+	0.950683i	$0.600384\pi$
$558$	−13.9944	−0.592429
$559$	0	0
$560$	45.1462	1.90778
$561$	41.7935	1.76452
$562$	−61.2516	−2.58374
$563$	20.2904	0.855137	0.427569	−	0.903983i	$-0.359370\pi$
$563$	20.2904	0.855137	0.427569	+	0.903983i	$0.359370\pi$
$564$	−130.714	−5.50406
$565$	2.28444	0.0961069
$566$	−13.2513	−0.556994
$567$	−4.18410	−0.175716
$568$	−151.270	−6.34713
$569$	−33.4043	−1.40038	−0.700192	−	0.713955i	$-0.746902\pi$
$569$	−33.4043	−1.40038	−0.700192	+	0.713955i	$0.746902\pi$
$570$	68.5613	2.87172
$571$	−5.79670	−0.242584	−0.121292	−	0.992617i	$-0.538704\pi$
$571$	−5.79670	−0.242584	−0.121292	+	0.992617i	$0.538704\pi$
$572$	0	0
$573$	−39.2929	−1.64148
$574$	39.0440	1.62967
$575$	5.31795	0.221774
$576$	143.244	5.96850
$577$	−36.9609	−1.53870	−0.769352	−	0.638825i	$-0.779421\pi$
$577$	−36.9609	−1.53870	−0.769352	+	0.638825i	$0.779421\pi$
$578$	−4.23283	−0.176063
$579$	−43.5532	−1.81001
$580$	54.4730	2.26187
$581$	24.0734	0.998732
$582$	141.917	5.88267
$583$	41.4129	1.71515
$584$	−25.3579	−1.04932
$585$	0	0
$586$	8.06818	0.333294
$587$	26.2265	1.08248	0.541242	−	0.840867i	$-0.317954\pi$
$587$	26.2265	1.08248	0.541242	+	0.840867i	$0.317954\pi$
$588$	39.9404	1.64711
$589$	−5.95633	−0.245426
$590$	−6.87627	−0.283091
$591$	30.3204	1.24721
$592$	30.9005	1.27000
$593$	26.8828	1.10394	0.551972	−	0.833862i	$-0.313875\pi$
$593$	26.8828	1.10394	0.551972	+	0.833862i	$0.313875\pi$
$594$	61.9405	2.54145
$595$	12.2350	0.501587
$596$	−95.0897	−3.89502
$597$	−15.3959	−0.630114
$598$	0	0
$599$	−13.5483	−0.553567	−0.276784	−	0.960932i	$-0.589269\pi$
$599$	−13.5483	−0.553567	−0.276784	+	0.960932i	$0.589269\pi$
$600$	74.4400	3.03900
$601$	45.4539	1.85410	0.927052	−	0.374934i	$-0.122334\pi$
$601$	45.4539	1.85410	0.927052	+	0.374934i	$0.122334\pi$
$602$	27.6155	1.12552
$603$	44.3352	1.80547
$604$	19.4093	0.789753
$605$	−4.28875	−0.174363
$606$	−61.0736	−2.48094
$607$	9.84075	0.399424	0.199712	−	0.979855i	$-0.435999\pi$
$607$	9.84075	0.399424	0.199712	+	0.979855i	$0.435999\pi$
$608$	124.405	5.04528
$609$	−40.6927	−1.64895
$610$	−18.4780	−0.748151
$611$	0	0
$612$	109.384	4.42159
$613$	17.6935	0.714633	0.357316	−	0.933983i	$-0.383692\pi$
$613$	17.6935	0.714633	0.357316	+	0.933983i	$0.383692\pi$
$614$	22.6887	0.915641
$615$	−28.8411	−1.16298
$616$	72.8632	2.93574
$617$	−9.67643	−0.389559	−0.194779	−	0.980847i	$-0.562399\pi$
$617$	−9.67643	−0.389559	−0.194779	+	0.980847i	$0.562399\pi$
$618$	−15.3213	−0.616314
$619$	20.0237	0.804820	0.402410	−	0.915460i	$-0.368173\pi$
$619$	20.0237	0.804820	0.402410	+	0.915460i	$0.368173\pi$
$620$	8.02448	0.322271
$621$	11.5691	0.464251
$622$	−29.6820	−1.19014
$623$	29.8622	1.19640
$624$	0	0
$625$	−3.10855	−0.124342
$626$	37.2753	1.48982
$627$	63.3409	2.52959
$628$	57.8615	2.30892
$629$	8.37432	0.333906
$630$	43.5668	1.73574
$631$	−23.5980	−0.939422	−0.469711	−	0.882820i	$-0.655642\pi$
$631$	−23.5980	−0.939422	−0.469711	+	0.882820i	$0.655642\pi$
$632$	66.9305	2.66235
$633$	−4.10335	−0.163093
$634$	−34.6079	−1.37446
$635$	18.7136	0.742626
$636$	171.664	6.80690
$637$	0	0
$638$	68.9090	2.72813
$639$	−83.5610	−3.30562
$640$	−50.5780	−1.99927
$641$	−7.67071	−0.302975	−0.151487	−	0.988459i	$-0.548406\pi$
$641$	−7.67071	−0.302975	−0.151487	+	0.988459i	$0.548406\pi$
$642$	97.6909	3.85555
$643$	−3.81880	−0.150599	−0.0752994	−	0.997161i	$-0.523991\pi$
$643$	−3.81880	−0.150599	−0.0752994	+	0.997161i	$0.523991\pi$
$644$	21.5769	0.850249
$645$	−20.3990	−0.803212
$646$	63.7483	2.50815
$647$	−49.3628	−1.94065	−0.970325	−	0.241804i	$-0.922261\pi$
$647$	−49.3628	−1.94065	−0.970325	+	0.241804i	$0.922261\pi$
$648$	18.5245	0.727712
$649$	−6.35269	−0.249365
$650$	0	0
$651$	−5.99448	−0.234942
$652$	25.9929	1.01796
$653$	19.8840	0.778121	0.389060	−	0.921212i	$-0.372800\pi$
$653$	19.8840	0.778121	0.389060	+	0.921212i	$0.372800\pi$
$654$	26.4762	1.03530
$655$	−14.5149	−0.567143
$656$	−98.9504	−3.86336
$657$	−14.0076	−0.546489
$658$	−48.4076	−1.88712
$659$	3.67642	0.143213	0.0716065	−	0.997433i	$-0.477187\pi$
$659$	3.67642	0.143213	0.0716065	+	0.997433i	$0.477187\pi$
$660$	−85.3341	−3.32162
$661$	3.21490	0.125045	0.0625226	−	0.998044i	$-0.480085\pi$
$661$	3.21490	0.125045	0.0625226	+	0.998044i	$0.480085\pi$
$662$	42.2397	1.64169
$663$	0	0
$664$	−106.582	−4.13617
$665$	18.5430	0.719067
$666$	29.8195	1.15548
$667$	12.8706	0.498353
$668$	−8.72435	−0.337555
$669$	32.8271	1.26917
$670$	−34.8098	−1.34482
$671$	−17.0710	−0.659019
$672$	125.202	4.82975
$673$	9.92828	0.382707	0.191353	−	0.981521i	$-0.438712\pi$
$673$	9.92828	0.382707	0.191353	+	0.981521i	$0.438712\pi$
$674$	−3.09120	−0.119069
$675$	17.1149	0.658751
$676$	0	0
$677$	20.3472	0.782006	0.391003	−	0.920389i	$-0.372128\pi$
$677$	20.3472	0.782006	0.391003	+	0.920389i	$0.372128\pi$
$678$	11.9789	0.460046
$679$	38.3828	1.47300
$680$	−54.1689	−2.07728
$681$	−1.97313	−0.0756104
$682$	10.1511	0.388704
$683$	16.6281	0.636258	0.318129	−	0.948047i	$-0.396946\pi$
$683$	16.6281	0.636258	0.318129	+	0.948047i	$0.396946\pi$
$684$	165.779	6.33872
$685$	28.7240	1.09749
$686$	54.8460	2.09403
$687$	54.5771	2.08224
$688$	−69.9867	−2.66822
$689$	0	0
$690$	−21.8241	−0.830828
$691$	19.8066	0.753478	0.376739	−	0.926319i	$-0.377045\pi$
$691$	19.8066	0.753478	0.376739	+	0.926319i	$0.377045\pi$
$692$	−9.76465	−0.371196
$693$	40.2495	1.52895
$694$	85.4345	3.24305
$695$	7.09808	0.269246
$696$	180.161	6.82899
$697$	−26.8164	−1.01575
$698$	−9.66795	−0.365937
$699$	−69.7066	−2.63655
$700$	31.9201	1.20647
$701$	40.8641	1.54342	0.771709	−	0.635976i	$-0.219402\pi$
$701$	40.8641	1.54342	0.771709	+	0.635976i	$0.219402\pi$
$702$	0	0
$703$	12.6918	0.478682
$704$	−103.904	−3.91605
$705$	35.7577	1.34671
$706$	−69.6683	−2.62200
$707$	−16.5179	−0.621218
$708$	−26.3330	−0.989654
$709$	−8.19242	−0.307673	−0.153836	−	0.988096i	$-0.549163\pi$
$709$	−8.19242	−0.307673	−0.153836	+	0.988096i	$0.549163\pi$
$710$	65.6079	2.46222
$711$	36.9723	1.38657
$712$	−132.211	−4.95480
$713$	1.89598	0.0710052
$714$	64.1567	2.40100
$715$	0	0
$716$	51.7894	1.93546
$717$	−33.4140	−1.24787
$718$	−75.3584	−2.81235
$719$	−38.3462	−1.43007	−0.715036	−	0.699087i	$-0.753590\pi$
$719$	−38.3462	−1.43007	−0.715036	+	0.699087i	$0.753590\pi$
$720$	−110.412	−4.11483
$721$	−4.14378	−0.154322
$722$	44.8732	1.67001
$723$	−66.9775	−2.49092
$724$	−58.5453	−2.17582
$725$	19.0403	0.707141
$726$	−22.4889	−0.834641
$727$	−11.3527	−0.421047	−0.210524	−	0.977589i	$-0.567517\pi$
$727$	−11.3527	−0.421047	−0.210524	+	0.977589i	$0.567517\pi$
$728$	0	0
$729$	−41.9906	−1.55521
$730$	10.9981	0.407057
$731$	−18.9670	−0.701521
$732$	−70.7622	−2.61545
$733$	16.1295	0.595756	0.297878	−	0.954604i	$-0.403721\pi$
$733$	16.1295	0.595756	0.297878	+	0.954604i	$0.403721\pi$
$734$	5.61841	0.207379
$735$	−10.9260	−0.403010
$736$	−39.5998	−1.45967
$737$	−32.1593	−1.18460
$738$	−95.4886	−3.51498
$739$	6.77902	0.249370	0.124685	−	0.992196i	$-0.460208\pi$
$739$	6.77902	0.249370	0.124685	+	0.992196i	$0.460208\pi$
$740$	−17.0987	−0.628560
$741$	0	0
$742$	63.5724	2.33382
$743$	42.0754	1.54360	0.771799	−	0.635866i	$-0.219357\pi$
$743$	42.0754	1.54360	0.771799	+	0.635866i	$0.219357\pi$
$744$	26.5397	0.972993
$745$	26.0124	0.953021
$746$	22.3064	0.816694
$747$	−58.8754	−2.15414
$748$	−79.3437	−2.90109
$749$	26.4213	0.965415
$750$	−89.8391	−3.28046
$751$	6.49814	0.237120	0.118560	−	0.992947i	$-0.462172\pi$
$751$	6.49814	0.237120	0.118560	+	0.992947i	$0.462172\pi$
$752$	122.681	4.47370
$753$	9.38702	0.342082
$754$	0	0
$755$	−5.30954	−0.193234
$756$	69.4413	2.52556
$757$	42.1789	1.53302	0.766508	−	0.642234i	$-0.221992\pi$
$757$	42.1789	1.53302	0.766508	+	0.642234i	$0.221992\pi$
$758$	2.66713	0.0968744
$759$	−20.1623	−0.731846
$760$	−82.0966	−2.97796
$761$	3.76086	0.136331	0.0681655	−	0.997674i	$-0.478285\pi$
$761$	3.76086	0.136331	0.0681655	+	0.997674i	$0.478285\pi$
$762$	98.1282	3.55481
$763$	7.16073	0.259236
$764$	74.5963	2.69880
$765$	−29.9228	−1.08186
$766$	15.3133	0.553291
$767$	0	0
$768$	−106.170	−3.83108
$769$	−50.8913	−1.83519	−0.917594	−	0.397519i	$-0.869871\pi$
$769$	−50.8913	−1.83519	−0.917594	+	0.397519i	$0.869871\pi$
$770$	−31.6019	−1.13885
$771$	6.58214	0.237050
$772$	82.6842	2.97587
$773$	−3.92202	−0.141065	−0.0705326	−	0.997509i	$-0.522470\pi$
$773$	−3.92202	−0.141065	−0.0705326	+	0.997509i	$0.522470\pi$
$774$	−67.5382	−2.42761
$775$	2.80485	0.100753
$776$	−169.935	−6.10029
$777$	12.7731	0.458234
$778$	42.4883	1.52328
$779$	−40.6421	−1.45616
$780$	0	0
$781$	60.6123	2.16888
$782$	−20.2920	−0.725641
$783$	41.4217	1.48029
$784$	−37.4857	−1.33877
$785$	−15.8284	−0.564939
$786$	−76.1115	−2.71481
$787$	20.3376	0.724958	0.362479	−	0.931992i	$-0.381931\pi$
$787$	20.3376	0.724958	0.362479	+	0.931992i	$0.381931\pi$
$788$	−57.5623	−2.05057
$789$	−6.59377	−0.234745
$790$	−29.0288	−1.03280
$791$	3.23979	0.115194
$792$	−178.199	−6.33203
$793$	0	0
$794$	−99.9576	−3.54736
$795$	−46.9597	−1.66549
$796$	29.2287	1.03598
$797$	54.6383	1.93539	0.967693	−	0.252130i	$-0.0811310\pi$
$797$	54.6383	1.93539	0.967693	+	0.252130i	$0.0811310\pi$
$798$	97.2337	3.44204
$799$	33.2476	1.17621
$800$	−58.5825	−2.07121
$801$	−73.0329	−2.58049
$802$	−3.04722	−0.107601
$803$	10.1607	0.358562
$804$	−133.306	−4.70133
$805$	−5.90251	−0.208036
$806$	0	0
$807$	−11.0629	−0.389431
$808$	73.1306	2.57272
$809$	−3.25818	−0.114552	−0.0572758	−	0.998358i	$-0.518241\pi$
$809$	−3.25818	−0.114552	−0.0572758	+	0.998358i	$0.518241\pi$
$810$	−8.03437	−0.282299
$811$	7.90675	0.277644	0.138822	−	0.990317i	$-0.455668\pi$
$811$	7.90675	0.277644	0.138822	+	0.990317i	$0.455668\pi$
$812$	77.2537	2.71107
$813$	7.04176	0.246965
$814$	−21.6300	−0.758132
$815$	−7.11052	−0.249071
$816$	−162.594	−5.69193
$817$	−28.7458	−1.00569
$818$	−40.0812	−1.40140
$819$	0	0
$820$	54.7538	1.91209
$821$	8.01821	0.279837	0.139919	−	0.990163i	$-0.455316\pi$
$821$	8.01821	0.279837	0.139919	+	0.990163i	$0.455316\pi$
$822$	150.620	5.25346
$823$	−52.3432	−1.82457	−0.912284	−	0.409558i	$-0.865683\pi$
$823$	−52.3432	−1.82457	−0.912284	+	0.409558i	$0.865683\pi$
$824$	18.3460	0.639114
$825$	−29.8274	−1.03846
$826$	−9.75193	−0.339313
$827$	−33.0105	−1.14789	−0.573944	−	0.818895i	$-0.694587\pi$
$827$	−33.0105	−1.14789	−0.573944	+	0.818895i	$0.694587\pi$
$828$	−52.7699	−1.83388
$829$	−54.2238	−1.88327	−0.941634	−	0.336637i	$-0.890710\pi$
$829$	−54.2238	−1.88327	−0.941634	+	0.336637i	$0.890710\pi$
$830$	46.2260	1.60453
$831$	21.8234	0.757047
$832$	0	0
$833$	−10.1590	−0.351987
$834$	37.2201	1.28883
$835$	2.38660	0.0825918
$836$	−120.251	−4.15896
$837$	6.10188	0.210912
$838$	32.6761	1.12878
$839$	−8.07518	−0.278786	−0.139393	−	0.990237i	$-0.544515\pi$
$839$	−8.07518	−0.278786	−0.139393	+	0.990237i	$0.544515\pi$
$840$	−82.6224	−2.85074
$841$	17.0819	0.589029
$842$	33.2803	1.14691
$843$	64.1670	2.21003
$844$	7.79007	0.268145
$845$	0	0
$846$	118.389	4.07029
$847$	−6.08231	−0.208991
$848$	−161.113	−5.53265
$849$	13.8820	0.476431
$850$	−30.0193	−1.02965
$851$	−4.03999	−0.138489
$852$	251.248	8.60763
$853$	46.7327	1.60010	0.800048	−	0.599936i	$-0.204807\pi$
$853$	46.7327	1.60010	0.800048	+	0.599936i	$0.204807\pi$
$854$	−26.2055	−0.896732
$855$	−45.3500	−1.55094
$856$	−116.977	−3.99818
$857$	−32.8329	−1.12155	−0.560775	−	0.827969i	$-0.689497\pi$
$857$	−32.8329	−1.12155	−0.560775	+	0.827969i	$0.689497\pi$
$858$	0	0
$859$	26.8471	0.916013	0.458006	−	0.888949i	$-0.348564\pi$
$859$	26.8471	0.916013	0.458006	+	0.888949i	$0.348564\pi$
$860$	38.7269	1.32058
$861$	−40.9024	−1.39395
$862$	−56.5359	−1.92562
$863$	28.8717	0.982805	0.491402	−	0.870933i	$-0.336484\pi$
$863$	28.8717	0.982805	0.491402	+	0.870933i	$0.336484\pi$
$864$	−127.445	−4.33576
$865$	2.67118	0.0908230
$866$	25.8543	0.878565
$867$	4.43431	0.150597
$868$	11.3803	0.386273
$869$	−26.8185	−0.909754
$870$	−78.1386	−2.64915
$871$	0	0
$872$	−31.7031	−1.07360
$873$	−93.8715	−3.17707
$874$	−30.7539	−1.04027
$875$	−24.2978	−0.821414
$876$	42.1177	1.42302
$877$	37.3786	1.26219	0.631093	−	0.775707i	$-0.282606\pi$
$877$	37.3786	1.26219	0.631093	+	0.775707i	$0.282606\pi$
$878$	101.744	3.43371
$879$	−8.45221	−0.285086
$880$	80.0895	2.69982
$881$	4.88537	0.164592	0.0822961	−	0.996608i	$-0.473775\pi$
$881$	4.88537	0.164592	0.0822961	+	0.996608i	$0.473775\pi$
$882$	−36.1742	−1.21805
$883$	6.40509	0.215548	0.107774	−	0.994175i	$-0.465628\pi$
$883$	6.40509	0.215548	0.107774	+	0.994175i	$0.465628\pi$
$884$	0	0
$885$	7.20356	0.242145
$886$	13.3887	0.449801
$887$	−16.3134	−0.547751	−0.273875	−	0.961765i	$-0.588306\pi$
$887$	−16.3134	−0.547751	−0.273875	+	0.961765i	$0.588306\pi$
$888$	−56.5513	−1.89774
$889$	26.5396	0.890110
$890$	57.3417	1.92210
$891$	−7.42261	−0.248667
$892$	−62.3212	−2.08667
$893$	50.3889	1.68620
$894$	136.401	4.56193
$895$	−14.1673	−0.473561
$896$	−71.7298	−2.39633
$897$	0	0
$898$	−63.3483	−2.11396
$899$	6.78836	0.226405
$900$	−78.0659	−2.60220
$901$	−43.6632	−1.45463
$902$	69.2642	2.30625
$903$	−28.9299	−0.962728
$904$	−14.3437	−0.477065
$905$	16.0155	0.532372
$906$	−27.8416	−0.924975
$907$	44.1291	1.46528	0.732641	−	0.680616i	$-0.238288\pi$
$907$	44.1291	1.46528	0.732641	+	0.680616i	$0.238288\pi$
$908$	3.74592	0.124313
$909$	40.3972	1.33989
$910$	0	0
$911$	−21.0194	−0.696404	−0.348202	−	0.937420i	$-0.613208\pi$
$911$	−21.0194	−0.696404	−0.348202	+	0.937420i	$0.613208\pi$
$912$	−246.422	−8.15986
$913$	42.7063	1.41337
$914$	34.3173	1.13512
$915$	19.3575	0.639938
$916$	−103.613	−3.42346
$917$	−20.5850	−0.679777
$918$	−65.3061	−2.15542
$919$	10.3074	0.340011	0.170005	−	0.985443i	$-0.445621\pi$
$919$	10.3074	0.340011	0.170005	+	0.985443i	$0.445621\pi$
$920$	26.1325	0.861564
$921$	−23.7686	−0.783203
$922$	94.8160	3.12260
$923$	0	0
$924$	−121.021	−3.98129
$925$	−5.97662	−0.196510
$926$	6.83119	0.224487
$927$	10.1343	0.332854
$928$	−141.783	−4.65424
$929$	43.2386	1.41861	0.709306	−	0.704901i	$-0.249008\pi$
$929$	43.2386	1.41861	0.709306	+	0.704901i	$0.249008\pi$
$930$	−11.5107	−0.377450
$931$	−15.3966	−0.504603
$932$	132.336	4.33480
$933$	31.0948	1.01800
$934$	−8.65074	−0.283061
$935$	21.7050	0.709829
$936$	0	0
$937$	−9.89909	−0.323389	−0.161695	−	0.986841i	$-0.551696\pi$
$937$	−9.89909	−0.323389	−0.161695	+	0.986841i	$0.551696\pi$
$938$	−49.3673	−1.61190
$939$	−39.0495	−1.27433
$940$	−67.8849	−2.21416
$941$	38.5248	1.25587	0.627937	−	0.778264i	$-0.283900\pi$
$941$	38.5248	1.25587	0.627937	+	0.778264i	$0.283900\pi$
$942$	−82.9991	−2.70426
$943$	12.9370	0.421286
$944$	24.7146	0.804391
$945$	−18.9961	−0.617944
$946$	48.9900	1.59280
$947$	59.6757	1.93920	0.969599	−	0.244698i	$-0.0786889\pi$
$947$	59.6757	1.93920	0.969599	+	0.244698i	$0.0786889\pi$
$948$	−111.167	−3.61054
$949$	0	0
$950$	−45.4962	−1.47609
$951$	36.2552	1.17566
$952$	−76.8223	−2.48983
$953$	39.4648	1.27839	0.639196	−	0.769044i	$-0.279267\pi$
$953$	39.4648	1.27839	0.639196	+	0.769044i	$0.279267\pi$
$954$	−155.477	−5.03374
$955$	−20.4063	−0.660333
$956$	63.4353	2.05165
$957$	−72.1890	−2.33354
$958$	16.8106	0.543126
$959$	40.7364	1.31545
$960$	117.821	3.80266
$961$	1.00000	0.0322581
$962$	0	0
$963$	−64.6177	−2.08228
$964$	127.155	4.09538
$965$	−22.6188	−0.728125
$966$	−30.9509	−0.995829
$967$	−26.7494	−0.860203	−0.430102	−	0.902781i	$-0.641522\pi$
$967$	−26.7494	−0.860203	−0.430102	+	0.902781i	$0.641522\pi$
$968$	26.9286	0.865518
$969$	−66.7826	−2.14537
$970$	73.7032	2.36647
$971$	−39.8704	−1.27950	−0.639751	−	0.768582i	$-0.720963\pi$
$971$	−39.8704	−1.27950	−0.639751	+	0.768582i	$0.720963\pi$
$972$	68.3767	2.19318
$973$	10.0665	0.322717
$974$	−29.8464	−0.956340
$975$	0	0
$976$	66.4132	2.12584
$977$	−43.6452	−1.39633	−0.698166	−	0.715935i	$-0.746000\pi$
$977$	−43.6452	−1.39633	−0.698166	+	0.715935i	$0.746000\pi$
$978$	−37.2854	−1.19225
$979$	52.9756	1.69311
$980$	20.7426	0.662597
$981$	−17.5127	−0.559139
$982$	−46.6297	−1.48801
$983$	12.2883	0.391937	0.195969	−	0.980610i	$-0.437215\pi$
$983$	12.2883	0.391937	0.195969	+	0.980610i	$0.437215\pi$
$984$	181.090	5.77293
$985$	15.7465	0.501726
$986$	−72.6533	−2.31375
$987$	50.7117	1.61417
$988$	0	0
$989$	9.15021	0.290960
$990$	77.2876	2.45636
$991$	−35.4177	−1.12508	−0.562541	−	0.826770i	$-0.690176\pi$
$991$	−35.4177	−1.12508	−0.562541	+	0.826770i	$0.690176\pi$
$992$	−20.8861	−0.663136
$993$	−44.2502	−1.40424
$994$	93.0451	2.95121
$995$	−7.99570	−0.253481
$996$	177.025	5.60924
$997$	23.4119	0.741462	0.370731	−	0.928740i	$-0.379107\pi$
$997$	23.4119	0.741462	0.370731	+	0.928740i	$0.379107\pi$
$998$	−31.7346	−1.00454
$999$	−13.0020	−0.411364

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.m.1.17		17
13.3	even	3		403.2.f.b.373.1	yes	34
13.9	even	3		403.2.f.b.94.1	✓	34
13.12	even	2		5239.2.a.n.1.1		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.b.94.1	✓	34	13.9	even	3
403.2.f.b.373.1	yes	34	13.3	even	3
5239.2.a.m.1.17		17	1.1	even	1	trivial
5239.2.a.n.1.1		17	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.72325 q^{2} -2.85287 q^{3} +5.41608 q^{4} -1.48160 q^{5} -7.76907 q^{6} -2.10121 q^{7} +9.30282 q^{8} +5.13886 q^{9} +O(q^{10})\)	\(q+2.72325 q^{2} -2.85287 q^{3} +5.41608 q^{4} -1.48160 q^{5} -7.76907 q^{6} -2.10121 q^{7} +9.30282 q^{8} +5.13886 q^{9} -4.03477 q^{10} -3.72756 q^{11} -15.4514 q^{12} -5.72212 q^{14} +4.22682 q^{15} +14.5017 q^{16} +3.93010 q^{17} +13.9944 q^{18} +5.95633 q^{19} -8.02448 q^{20} +5.99448 q^{21} -10.1511 q^{22} -1.89598 q^{23} -26.5397 q^{24} -2.80485 q^{25} -6.10188 q^{27} -11.3803 q^{28} -6.78836 q^{29} +11.5107 q^{30} -1.00000 q^{31} +20.8861 q^{32} +10.6342 q^{33} +10.7026 q^{34} +3.11316 q^{35} +27.8324 q^{36} +2.13082 q^{37} +16.2206 q^{38} -13.7831 q^{40} -6.82335 q^{41} +16.3244 q^{42} -4.82610 q^{43} -20.1887 q^{44} -7.61375 q^{45} -5.16323 q^{46} +8.45973 q^{47} -41.3715 q^{48} -2.58491 q^{49} -7.63830 q^{50} -11.2121 q^{51} -11.1099 q^{53} -16.6169 q^{54} +5.52276 q^{55} -19.5472 q^{56} -16.9926 q^{57} -18.4864 q^{58} +1.70425 q^{59} +22.8928 q^{60} +4.57968 q^{61} -2.72325 q^{62} -10.7978 q^{63} +27.8747 q^{64} +28.9596 q^{66} +8.62745 q^{67} +21.2857 q^{68} +5.40899 q^{69} +8.47791 q^{70} -16.2606 q^{71} +47.8059 q^{72} -2.72582 q^{73} +5.80274 q^{74} +8.00187 q^{75} +32.2599 q^{76} +7.83238 q^{77} +7.19465 q^{79} -21.4858 q^{80} +1.99128 q^{81} -18.5817 q^{82} -11.4569 q^{83} +32.4665 q^{84} -5.82285 q^{85} -13.1427 q^{86} +19.3663 q^{87} -34.6768 q^{88} -14.2119 q^{89} -20.7341 q^{90} -10.2688 q^{92} +2.85287 q^{93} +23.0379 q^{94} -8.82491 q^{95} -59.5854 q^{96} -18.2670 q^{97} -7.03936 q^{98} -19.1554 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9	\( 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9} + 6 q^{10} - 13 q^{11} + 4 q^{12} - 4 q^{15} + 34 q^{16} - 6 q^{17} + 12 q^{18} - 4 q^{19} - 28 q^{20} - 18 q^{21} - 34 q^{22} - 8 q^{23} - 40 q^{24} + 8 q^{25} - 3 q^{27} - 21 q^{28} - 6 q^{29} + 19 q^{30} - 17 q^{31} - 6 q^{32} - 7 q^{33} - 24 q^{34} - 9 q^{35} - 14 q^{37} + 11 q^{38} - 10 q^{40} - 43 q^{41} + 33 q^{42} + 18 q^{43} - 28 q^{44} - 26 q^{45} - 7 q^{46} - 6 q^{47} - 95 q^{48} - q^{49} - 44 q^{50} + 26 q^{51} - 5 q^{53} - 27 q^{54} + 39 q^{55} + 39 q^{56} - 46 q^{57} - 8 q^{58} + q^{59} - 21 q^{60} - 19 q^{61} + 4 q^{62} - 5 q^{63} + 42 q^{64} + 26 q^{66} - 10 q^{67} + 34 q^{68} + 32 q^{69} + 24 q^{70} - 35 q^{71} + 26 q^{72} - 11 q^{73} - 68 q^{74} - 62 q^{75} - 2 q^{76} + 21 q^{77} + q^{79} - 49 q^{80} + 37 q^{81} + 35 q^{82} - 24 q^{83} + 34 q^{84} + 13 q^{85} - 76 q^{86} - 22 q^{87} - 37 q^{88} - 42 q^{89} + 15 q^{90} + 15 q^{92} + 42 q^{94} + 34 q^{95} - 33 q^{96} + 38 q^{97} - 8 q^{98} - 17 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9 + 6 * q^10 - 13 * q^11 + 4 * q^12 - 4 * q^15 + 34 * q^16 - 6 * q^17 + 12 * q^18 - 4 * q^19 - 28 * q^20 - 18 * q^21 - 34 * q^22 - 8 * q^23 - 40 * q^24 + 8 * q^25 - 3 * q^27 - 21 * q^28 - 6 * q^29 + 19 * q^30 - 17 * q^31 - 6 * q^32 - 7 * q^33 - 24 * q^34 - 9 * q^35 - 14 * q^37 + 11 * q^38 - 10 * q^40 - 43 * q^41 + 33 * q^42 + 18 * q^43 - 28 * q^44 - 26 * q^45 - 7 * q^46 - 6 * q^47 - 95 * q^48 - q^49 - 44 * q^50 + 26 * q^51 - 5 * q^53 - 27 * q^54 + 39 * q^55 + 39 * q^56 - 46 * q^57 - 8 * q^58 + q^59 - 21 * q^60 - 19 * q^61 + 4 * q^62 - 5 * q^63 + 42 * q^64 + 26 * q^66 - 10 * q^67 + 34 * q^68 + 32 * q^69 + 24 * q^70 - 35 * q^71 + 26 * q^72 - 11 * q^73 - 68 * q^74 - 62 * q^75 - 2 * q^76 + 21 * q^77 + q^79 - 49 * q^80 + 37 * q^81 + 35 * q^82 - 24 * q^83 + 34 * q^84 + 13 * q^85 - 76 * q^86 - 22 * q^87 - 37 * q^88 - 42 * q^89 + 15 * q^90 + 15 * q^92 + 42 * q^94 + 34 * q^95 - 33 * q^96 + 38 * q^97 - 8 * q^98 - 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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