LMFDB - Embedded newform 5239.2.a.q.1.8

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:	$34$
Twist minimal:	no (minimal twist has level 403)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-2.12811 q^{2} +0.449534 q^{3} +2.52886 q^{4} -3.56888 q^{5} -0.956659 q^{6} -3.15924 q^{7} -1.12547 q^{8} -2.79792 q^{9} +O(q^{10})$	\(q-2.12811 q^{2} +0.449534 q^{3} +2.52886 q^{4} -3.56888 q^{5} -0.956659 q^{6} -3.15924 q^{7} -1.12547 q^{8} -2.79792 q^{9} +7.59498 q^{10} -1.75064 q^{11} +1.13681 q^{12} +6.72321 q^{14} -1.60433 q^{15} -2.66259 q^{16} +0.689133 q^{17} +5.95429 q^{18} -4.35519 q^{19} -9.02521 q^{20} -1.42018 q^{21} +3.72556 q^{22} +0.320385 q^{23} -0.505939 q^{24} +7.73692 q^{25} -2.60636 q^{27} -7.98926 q^{28} +4.08746 q^{29} +3.41420 q^{30} +1.00000 q^{31} +7.91723 q^{32} -0.786972 q^{33} -1.46655 q^{34} +11.2749 q^{35} -7.07555 q^{36} +3.95398 q^{37} +9.26833 q^{38} +4.01669 q^{40} +9.06843 q^{41} +3.02231 q^{42} +10.4851 q^{43} -4.42712 q^{44} +9.98544 q^{45} -0.681815 q^{46} -2.36996 q^{47} -1.19692 q^{48} +2.98077 q^{49} -16.4650 q^{50} +0.309789 q^{51} -13.6814 q^{53} +5.54663 q^{54} +6.24783 q^{55} +3.55564 q^{56} -1.95781 q^{57} -8.69857 q^{58} -10.0692 q^{59} -4.05714 q^{60} +4.85319 q^{61} -2.12811 q^{62} +8.83929 q^{63} -11.5236 q^{64} +1.67476 q^{66} +6.85143 q^{67} +1.74272 q^{68} +0.144024 q^{69} -23.9943 q^{70} +6.66163 q^{71} +3.14899 q^{72} +5.83029 q^{73} -8.41451 q^{74} +3.47801 q^{75} -11.0137 q^{76} +5.53068 q^{77} +10.2315 q^{79} +9.50246 q^{80} +7.22211 q^{81} -19.2986 q^{82} -5.52078 q^{83} -3.59145 q^{84} -2.45943 q^{85} -22.3135 q^{86} +1.83745 q^{87} +1.97030 q^{88} -5.43790 q^{89} -21.2501 q^{90} +0.810209 q^{92} +0.449534 q^{93} +5.04354 q^{94} +15.5432 q^{95} +3.55906 q^{96} -3.29840 q^{97} -6.34341 q^{98} +4.89815 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 8 q^{2} + 32 q^{4} - 16 q^{5} - 12 q^{6} - 8 q^{7} - 24 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q - 8 * q^2 + 32 * q^4 - 16 * q^5 - 12 * q^6 - 8 * q^7 - 24 * q^8 + 34 * q^9	\( 34 q - 8 q^{2} + 32 q^{4} - 16 q^{5} - 12 q^{6} - 8 q^{7} - 24 q^{8} + 34 q^{9} + 8 q^{10} - 26 q^{11} + 8 q^{12} - 4 q^{14} - 16 q^{15} + 36 q^{16} - 6 q^{17} - 64 q^{18} - 4 q^{19} - 40 q^{20} - 32 q^{21} + 20 q^{22} - 8 q^{23} + 16 q^{24} + 36 q^{25} - 6 q^{27} - 24 q^{28} + 32 q^{30} + 34 q^{31} - 36 q^{32} - 40 q^{33} - 16 q^{34} - 30 q^{35} + 40 q^{36} - 2 q^{37} + 18 q^{38} + 4 q^{40} - 80 q^{41} + 16 q^{42} + 12 q^{43} - 108 q^{44} - 12 q^{45} - 48 q^{46} - 24 q^{47} + 46 q^{48} + 22 q^{49} + 44 q^{50} - 28 q^{51} + 10 q^{53} - 48 q^{54} + 6 q^{55} - 2 q^{56} - 66 q^{57} + 44 q^{58} - 64 q^{59} - 48 q^{60} - 6 q^{61} - 8 q^{62} + 52 q^{63} - 12 q^{64} + 4 q^{66} - 16 q^{67} - 58 q^{68} - 28 q^{69} - 72 q^{70} - 52 q^{71} - 152 q^{72} - 42 q^{73} - 8 q^{74} - 4 q^{75} + 48 q^{76} + 10 q^{77} + 8 q^{79} - 48 q^{80} + 58 q^{81} - 42 q^{82} - 44 q^{83} + 8 q^{84} - 96 q^{85} - 16 q^{86} + 20 q^{87} + 64 q^{88} - 74 q^{89} - 26 q^{90} + 24 q^{92} - 8 q^{94} - 32 q^{95} - 50 q^{96} - 40 q^{97} - 72 q^{98} - 74 q^{99}+O(q^{100}) \) 34 * q - 8 * q^2 + 32 * q^4 - 16 * q^5 - 12 * q^6 - 8 * q^7 - 24 * q^8 + 34 * q^9 + 8 * q^10 - 26 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 36 * q^16 - 6 * q^17 - 64 * q^18 - 4 * q^19 - 40 * q^20 - 32 * q^21 + 20 * q^22 - 8 * q^23 + 16 * q^24 + 36 * q^25 - 6 * q^27 - 24 * q^28 + 32 * q^30 + 34 * q^31 - 36 * q^32 - 40 * q^33 - 16 * q^34 - 30 * q^35 + 40 * q^36 - 2 * q^37 + 18 * q^38 + 4 * q^40 - 80 * q^41 + 16 * q^42 + 12 * q^43 - 108 * q^44 - 12 * q^45 - 48 * q^46 - 24 * q^47 + 46 * q^48 + 22 * q^49 + 44 * q^50 - 28 * q^51 + 10 * q^53 - 48 * q^54 + 6 * q^55 - 2 * q^56 - 66 * q^57 + 44 * q^58 - 64 * q^59 - 48 * q^60 - 6 * q^61 - 8 * q^62 + 52 * q^63 - 12 * q^64 + 4 * q^66 - 16 * q^67 - 58 * q^68 - 28 * q^69 - 72 * q^70 - 52 * q^71 - 152 * q^72 - 42 * q^73 - 8 * q^74 - 4 * q^75 + 48 * q^76 + 10 * q^77 + 8 * q^79 - 48 * q^80 + 58 * q^81 - 42 * q^82 - 44 * q^83 + 8 * q^84 - 96 * q^85 - 16 * q^86 + 20 * q^87 + 64 * q^88 - 74 * q^89 - 26 * q^90 + 24 * q^92 - 8 * q^94 - 32 * q^95 - 50 * q^96 - 40 * q^97 - 72 * q^98 - 74 * 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 $

$2$	−2.12811	−1.50480	−0.752401	−	0.658705i	$-0.771104\pi$
$2$	−2.12811	−1.50480	−0.752401	+	0.658705i	$0.771104\pi$
$3$	0.449534	0.259539	0.129769	−	0.991544i	$-0.458576\pi$
$3$	0.449534	0.259539	0.129769	+	0.991544i	$0.458576\pi$
$4$	2.52886	1.26443
$5$	−3.56888	−1.59605	−0.798026	−	0.602623i	$-0.794122\pi$
$5$	−3.56888	−1.59605	−0.798026	+	0.602623i	$0.794122\pi$
$6$	−0.956659	−0.390554
$7$	−3.15924	−1.19408	−0.597039	−	0.802212i	$-0.703656\pi$
$7$	−3.15924	−1.19408	−0.597039	+	0.802212i	$0.703656\pi$
$8$	−1.12547	−0.397915
$9$	−2.79792	−0.932640
$10$	7.59498	2.40174
$11$	−1.75064	−0.527838	−0.263919	−	0.964545i	$-0.585015\pi$
$11$	−1.75064	−0.527838	−0.263919	+	0.964545i	$0.585015\pi$
$12$	1.13681	0.328168
$13$	0	0
$13$	0	0
$14$	6.72321	1.79685
$15$	−1.60433	−0.414237
$16$	−2.66259	−0.665646
$17$	0.689133	0.167139	0.0835697	−	0.996502i	$-0.473368\pi$
$17$	0.689133	0.167139	0.0835697	+	0.996502i	$0.473368\pi$
$18$	5.95429	1.40344
$19$	−4.35519	−0.999149	−0.499575	−	0.866271i	$-0.666510\pi$
$19$	−4.35519	−0.999149	−0.499575	+	0.866271i	$0.666510\pi$
$20$	−9.02521	−2.01810
$21$	−1.42018	−0.309909
$22$	3.72556	0.794291
$23$	0.320385	0.0668049	0.0334024	−	0.999442i	$-0.489366\pi$
$23$	0.320385	0.0668049	0.0334024	+	0.999442i	$0.489366\pi$
$24$	−0.505939	−0.103274
$25$	7.73692	1.54738
$26$	0	0
$27$	−2.60636	−0.501595
$28$	−7.98926	−1.50983
$29$	4.08746	0.759022	0.379511	−	0.925187i	$-0.376092\pi$
$29$	4.08746	0.759022	0.379511	+	0.925187i	$0.376092\pi$
$30$	3.41420	0.623345
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	7.91723	1.39958
$33$	−0.786972	−0.136994
$34$	−1.46655	−0.251512
$35$	11.2749	1.90581
$36$	−7.07555	−1.17926
$37$	3.95398	0.650030	0.325015	−	0.945709i	$-0.394631\pi$
$37$	3.95398	0.650030	0.325015	+	0.945709i	$0.394631\pi$
$38$	9.26833	1.50352
$39$	0	0
$40$	4.01669	0.635094
$41$	9.06843	1.41625	0.708125	−	0.706087i	$-0.249541\pi$
$41$	9.06843	1.41625	0.708125	+	0.706087i	$0.249541\pi$
$42$	3.02231	0.466352
$43$	10.4851	1.59897	0.799483	−	0.600688i	$-0.205107\pi$
$43$	10.4851	1.59897	0.799483	+	0.600688i	$0.205107\pi$
$44$	−4.42712	−0.667414
$45$	9.98544	1.48854
$46$	−0.681815	−0.100528
$47$	−2.36996	−0.345694	−0.172847	−	0.984949i	$-0.555297\pi$
$47$	−2.36996	−0.345694	−0.172847	+	0.984949i	$0.555297\pi$
$48$	−1.19692	−0.172761
$49$	2.98077	0.425824
$50$	−16.4650	−2.32851
$51$	0.309789	0.0433791
$52$	0	0
$53$	−13.6814	−1.87928	−0.939640	−	0.342164i	$-0.888840\pi$
$53$	−13.6814	−1.87928	−0.939640	+	0.342164i	$0.888840\pi$
$54$	5.54663	0.754801
$55$	6.24783	0.842457
$56$	3.55564	0.475142
$57$	−1.95781	−0.259318
$58$	−8.69857	−1.14218
$59$	−10.0692	−1.31090	−0.655448	−	0.755240i	$-0.727520\pi$
$59$	−10.0692	−1.31090	−0.655448	+	0.755240i	$0.727520\pi$
$60$	−4.05714	−0.523774
$61$	4.85319	0.621387	0.310694	−	0.950510i	$-0.399439\pi$
$61$	4.85319	0.621387	0.310694	+	0.950510i	$0.399439\pi$
$62$	−2.12811	−0.270270
$63$	8.83929	1.11365
$64$	−11.5236	−1.44045
$65$	0	0
$66$	1.67476	0.206149
$67$	6.85143	0.837035	0.418518	−	0.908209i	$-0.362550\pi$
$67$	6.85143	0.837035	0.418518	+	0.908209i	$0.362550\pi$
$68$	1.74272	0.211336
$69$	0.144024	0.0173384
$70$	−23.9943	−2.86787
$71$	6.66163	0.790590	0.395295	−	0.918554i	$-0.370642\pi$
$71$	6.66163	0.790590	0.395295	+	0.918554i	$0.370642\pi$
$72$	3.14899	0.371112
$73$	5.83029	0.682384	0.341192	−	0.939994i	$-0.389169\pi$
$73$	5.83029	0.682384	0.341192	+	0.939994i	$0.389169\pi$
$74$	−8.41451	−0.978166
$75$	3.47801	0.401606
$76$	−11.0137	−1.26335
$77$	5.53068	0.630280
$78$	0	0
$79$	10.2315	1.15114	0.575568	−	0.817754i	$-0.304781\pi$
$79$	10.2315	1.15114	0.575568	+	0.817754i	$0.304781\pi$
$80$	9.50246	1.06241
$81$	7.22211	0.802457
$82$	−19.2986	−2.13118
$83$	−5.52078	−0.605984	−0.302992	−	0.952993i	$-0.597986\pi$
$83$	−5.52078	−0.605984	−0.302992	+	0.952993i	$0.597986\pi$
$84$	−3.59145	−0.391859
$85$	−2.45943	−0.266763
$86$	−22.3135	−2.40613
$87$	1.83745	0.196996
$88$	1.97030	0.210035
$89$	−5.43790	−0.576416	−0.288208	−	0.957568i	$-0.593060\pi$
$89$	−5.43790	−0.576416	−0.288208	+	0.957568i	$0.593060\pi$
$90$	−21.2501	−2.23996
$91$	0	0
$92$	0.810209	0.0844701
$93$	0.449534	0.0466145
$94$	5.04354	0.520201
$95$	15.5432	1.59470
$96$	3.55906	0.363245
$97$	−3.29840	−0.334902	−0.167451	−	0.985880i	$-0.553554\pi$
$97$	−3.29840	−0.334902	−0.167451	+	0.985880i	$0.553554\pi$
$98$	−6.34341	−0.640781
$99$	4.89815	0.492282
$100$	19.5656	1.95656
$101$	6.31085	0.627953	0.313976	−	0.949431i	$-0.398339\pi$
$101$	6.31085	0.627953	0.313976	+	0.949431i	$0.398339\pi$
$102$	−0.659265	−0.0652770
$103$	−6.84933	−0.674885	−0.337442	−	0.941346i	$-0.609562\pi$
$103$	−6.84933	−0.674885	−0.337442	+	0.941346i	$0.609562\pi$
$104$	0	0
$105$	5.06847	0.494632
$106$	29.1155	2.82795
$107$	14.7895	1.42975	0.714876	−	0.699251i	$-0.246483\pi$
$107$	14.7895	1.42975	0.714876	+	0.699251i	$0.246483\pi$
$108$	−6.59112	−0.634231
$109$	18.4288	1.76515	0.882577	−	0.470168i	$-0.155807\pi$
$109$	18.4288	1.76515	0.882577	+	0.470168i	$0.155807\pi$
$110$	−13.2961	−1.26773
$111$	1.77745	0.168708
$112$	8.41174	0.794834
$113$	−7.55052	−0.710293	−0.355147	−	0.934811i	$-0.615569\pi$
$113$	−7.55052	−0.710293	−0.355147	+	0.934811i	$0.615569\pi$
$114$	4.16643	0.390222
$115$	−1.14342	−0.106624
$116$	10.3366	0.959731
$117$	0	0
$118$	21.4284	1.97264
$119$	−2.17713	−0.199577
$120$	1.80564	0.164831
$121$	−7.93526	−0.721387
$122$	−10.3281	−0.935065
$123$	4.07657	0.367572
$124$	2.52886	0.227098
$125$	−9.76775	−0.873654
$126$	−18.8110	−1.67582
$127$	−13.2049	−1.17175	−0.585874	−	0.810402i	$-0.699249\pi$
$127$	−13.2049	−1.17175	−0.585874	+	0.810402i	$0.699249\pi$
$128$	8.68901	0.768007
$129$	4.71342	0.414993
$130$	0	0
$131$	−1.63644	−0.142977	−0.0714883	−	0.997441i	$-0.522775\pi$
$131$	−1.63644	−0.142977	−0.0714883	+	0.997441i	$0.522775\pi$
$132$	−1.99014	−0.173220
$133$	13.7591	1.19306
$134$	−14.5806	−1.25957
$135$	9.30180	0.800571
$136$	−0.775601	−0.0665073
$137$	−10.8446	−0.926520	−0.463260	−	0.886222i	$-0.653320\pi$
$137$	−10.8446	−0.926520	−0.463260	+	0.886222i	$0.653320\pi$
$138$	−0.306499	−0.0260909
$139$	12.3632	1.04863	0.524316	−	0.851524i	$-0.324321\pi$
$139$	12.3632	1.04863	0.524316	+	0.851524i	$0.324321\pi$
$140$	28.5127	2.40977
$141$	−1.06538	−0.0897209
$142$	−14.1767	−1.18968
$143$	0	0
$144$	7.44970	0.620808
$145$	−14.5877	−1.21144
$146$	−12.4075	−1.02685
$147$	1.33996	0.110518
$148$	9.99906	0.821917
$149$	1.24011	0.101594	0.0507969	−	0.998709i	$-0.483824\pi$
$149$	1.24011	0.101594	0.0507969	+	0.998709i	$0.483824\pi$
$150$	−7.40159	−0.604338
$151$	5.98598	0.487132	0.243566	−	0.969884i	$-0.421683\pi$
$151$	5.98598	0.487132	0.243566	+	0.969884i	$0.421683\pi$
$152$	4.90165	0.397577
$153$	−1.92814	−0.155881
$154$	−11.7699	−0.948446
$155$	−3.56888	−0.286660
$156$	0	0
$157$	−22.1325	−1.76637	−0.883185	−	0.469025i	$-0.844605\pi$
$157$	−22.1325	−1.76637	−0.883185	+	0.469025i	$0.844605\pi$
$158$	−21.7738	−1.73223
$159$	−6.15024	−0.487746
$160$	−28.2557	−2.23381
$161$	−1.01217	−0.0797703
$162$	−15.3695	−1.20754
$163$	−16.6619	−1.30506	−0.652529	−	0.757764i	$-0.726292\pi$
$163$	−16.6619	−1.30506	−0.652529	+	0.757764i	$0.726292\pi$
$164$	22.9328	1.79075
$165$	2.80861	0.218650
$166$	11.7488	0.911886
$167$	22.0272	1.70452	0.852258	−	0.523121i	$-0.175233\pi$
$167$	22.0272	1.70452	0.852258	+	0.523121i	$0.175233\pi$
$168$	1.59838	0.123318
$169$	0	0
$170$	5.23395	0.401426
$171$	12.1855	0.931846
$172$	26.5154	2.02178
$173$	−16.6650	−1.26701	−0.633507	−	0.773737i	$-0.718385\pi$
$173$	−16.6650	−1.26701	−0.633507	+	0.773737i	$0.718385\pi$
$174$	−3.91030	−0.296439
$175$	−24.4428	−1.84770
$176$	4.66123	0.351353
$177$	−4.52644	−0.340228
$178$	11.5725	0.867393
$179$	−0.949981	−0.0710049	−0.0355025	−	0.999370i	$-0.511303\pi$
$179$	−0.949981	−0.0710049	−0.0355025	+	0.999370i	$0.511303\pi$
$180$	25.2518	1.88216
$181$	6.82270	0.507127	0.253564	−	0.967319i	$-0.418397\pi$
$181$	6.82270	0.507127	0.253564	+	0.967319i	$0.418397\pi$
$182$	0	0
$183$	2.18167	0.161274
$184$	−0.360585	−0.0265827
$185$	−14.1113	−1.03748
$186$	−0.956659	−0.0701456
$187$	−1.20642	−0.0882224
$188$	−5.99329	−0.437106
$189$	8.23411	0.598943
$190$	−33.0776	−2.39970
$191$	−9.90992	−0.717057	−0.358528	−	0.933519i	$-0.616721\pi$
$191$	−9.90992	−0.717057	−0.358528	+	0.933519i	$0.616721\pi$
$192$	−5.18024	−0.373852
$193$	11.6904	0.841494	0.420747	−	0.907178i	$-0.361768\pi$
$193$	11.6904	0.841494	0.420747	+	0.907178i	$0.361768\pi$
$194$	7.01938	0.503962
$195$	0	0
$196$	7.53794	0.538425
$197$	14.5003	1.03310	0.516550	−	0.856257i	$-0.327216\pi$
$197$	14.5003	1.03310	0.516550	+	0.856257i	$0.327216\pi$
$198$	−10.4238	−0.740788
$199$	13.2198	0.937127	0.468564	−	0.883430i	$-0.344772\pi$
$199$	13.2198	0.937127	0.468564	+	0.883430i	$0.344772\pi$
$200$	−8.70771	−0.615728
$201$	3.07995	0.217243
$202$	−13.4302	−0.944945
$203$	−12.9132	−0.906332
$204$	0.783412	0.0548498
$205$	−32.3641	−2.26041
$206$	14.5761	1.01557
$207$	−0.896411	−0.0623049
$208$	0	0
$209$	7.62437	0.527389
$210$	−10.7863	−0.744323
$211$	−12.9687	−0.892802	−0.446401	−	0.894833i	$-0.647295\pi$
$211$	−12.9687	−0.892802	−0.446401	+	0.894833i	$0.647295\pi$
$212$	−34.5983	−2.37622
$213$	2.99463	0.205189
$214$	−31.4736	−2.15149
$215$	−37.4202	−2.55203
$216$	2.93339	0.199592
$217$	−3.15924	−0.214463
$218$	−39.2184	−2.65621
$219$	2.62091	0.177105
$220$	15.7999	1.06523
$221$	0	0
$222$	−3.78261	−0.253872
$223$	29.6729	1.98704	0.993521	−	0.113647i	$-0.0362532\pi$
$223$	29.6729	1.98704	0.993521	+	0.113647i	$0.0362532\pi$
$224$	−25.0124	−1.67121
$225$	−21.6473	−1.44315
$226$	16.0684	1.06885
$227$	3.79323	0.251765	0.125883	−	0.992045i	$-0.459824\pi$
$227$	3.79323	0.251765	0.125883	+	0.992045i	$0.459824\pi$
$228$	−4.95102	−0.327889
$229$	−18.4653	−1.22022	−0.610110	−	0.792316i	$-0.708875\pi$
$229$	−18.4653	−1.22022	−0.610110	+	0.792316i	$0.708875\pi$
$230$	2.43332	0.160448
$231$	2.48623	0.163582
$232$	−4.60033	−0.302026
$233$	−25.1397	−1.64696	−0.823479	−	0.567347i	$-0.807970\pi$
$233$	−25.1397	−1.64696	−0.823479	+	0.567347i	$0.807970\pi$
$234$	0	0
$235$	8.45810	0.551746
$236$	−25.4636	−1.65754
$237$	4.59942	0.298764
$238$	4.63318	0.300325
$239$	−22.6641	−1.46602	−0.733010	−	0.680218i	$-0.761885\pi$
$239$	−22.6641	−1.46602	−0.733010	+	0.680218i	$0.761885\pi$
$240$	4.27168	0.275736
$241$	−9.20188	−0.592745	−0.296373	−	0.955072i	$-0.595777\pi$
$241$	−9.20188	−0.592745	−0.296373	+	0.955072i	$0.595777\pi$
$242$	16.8871	1.08555
$243$	11.0657	0.709863
$244$	12.2730	0.785701
$245$	−10.6380	−0.679637
$246$	−8.67539	−0.553123
$247$	0	0
$248$	−1.12547	−0.0714677
$249$	−2.48178	−0.157276
$250$	20.7869	1.31468
$251$	2.58758	0.163326	0.0816632	−	0.996660i	$-0.473977\pi$
$251$	2.58758	0.163326	0.0816632	+	0.996660i	$0.473977\pi$
$252$	22.3533	1.40813
$253$	−0.560878	−0.0352621
$254$	28.1016	1.76325
$255$	−1.10560	−0.0692353
$256$	4.55598	0.284749
$257$	29.9074	1.86557	0.932785	−	0.360434i	$-0.117371\pi$
$257$	29.9074	1.86557	0.932785	+	0.360434i	$0.117371\pi$
$258$	−10.0307	−0.624483
$259$	−12.4915	−0.776187
$260$	0	0
$261$	−11.4364	−0.707894
$262$	3.48253	0.215151
$263$	−26.1929	−1.61513	−0.807563	−	0.589781i	$-0.799214\pi$
$263$	−26.1929	−1.61513	−0.807563	+	0.589781i	$0.799214\pi$
$264$	0.885716	0.0545121
$265$	48.8272	2.99943
$266$	−29.2808	−1.79532
$267$	−2.44452	−0.149602
$268$	17.3263	1.05837
$269$	−8.51944	−0.519439	−0.259720	−	0.965684i	$-0.583630\pi$
$269$	−8.51944	−0.519439	−0.259720	+	0.965684i	$0.583630\pi$
$270$	−19.7953	−1.20470
$271$	22.5862	1.37201	0.686007	−	0.727595i	$-0.259362\pi$
$271$	22.5862	1.37201	0.686007	+	0.727595i	$0.259362\pi$
$272$	−1.83488	−0.111256
$273$	0	0
$274$	23.0786	1.39423
$275$	−13.5446	−0.816768
$276$	0.364216	0.0219233
$277$	23.2709	1.39821	0.699107	−	0.715017i	$-0.253581\pi$
$277$	23.2709	1.39821	0.699107	+	0.715017i	$0.253581\pi$
$278$	−26.3102	−1.57798
$279$	−2.79792	−0.167507
$280$	−12.6897	−0.758352
$281$	−21.1691	−1.26284	−0.631421	−	0.775440i	$-0.717528\pi$
$281$	−21.1691	−1.26284	−0.631421	+	0.775440i	$0.717528\pi$
$282$	2.26724	0.135012
$283$	27.5167	1.63570	0.817848	−	0.575435i	$-0.195167\pi$
$283$	27.5167	1.63570	0.817848	+	0.575435i	$0.195167\pi$
$284$	16.8463	0.999646
$285$	6.98718	0.413885
$286$	0	0
$287$	−28.6493	−1.69111
$288$	−22.1518	−1.30531
$289$	−16.5251	−0.972064
$290$	31.0442	1.82298
$291$	−1.48275	−0.0869201
$292$	14.7440	0.862827
$293$	−12.2724	−0.716960	−0.358480	−	0.933537i	$-0.616705\pi$
$293$	−12.2724	−0.716960	−0.358480	+	0.933537i	$0.616705\pi$
$294$	−2.85158	−0.166307
$295$	35.9358	2.09226
$296$	−4.45010	−0.258657
$297$	4.56280	0.264760
$298$	−2.63909	−0.152879
$299$	0	0
$300$	8.79540	0.507803
$301$	−33.1250	−1.90929
$302$	−12.7388	−0.733038
$303$	2.83694	0.162978
$304$	11.5961	0.665080
$305$	−17.3205	−0.991767
$306$	4.10329	0.234570
$307$	21.0610	1.20201	0.601007	−	0.799244i	$-0.294766\pi$
$307$	21.0610	1.20201	0.601007	+	0.799244i	$0.294766\pi$
$308$	13.9863	0.796945
$309$	−3.07901	−0.175159
$310$	7.59498	0.431366
$311$	1.06484	0.0603814	0.0301907	−	0.999544i	$-0.490389\pi$
$311$	1.06484	0.0603814	0.0301907	+	0.999544i	$0.490389\pi$
$312$	0	0
$313$	22.9321	1.29620	0.648100	−	0.761556i	$-0.275564\pi$
$313$	22.9321	1.29620	0.648100	+	0.761556i	$0.275564\pi$
$314$	47.1005	2.65804
$315$	−31.5464	−1.77744
$316$	25.8741	1.45553
$317$	−4.55800	−0.256003	−0.128001	−	0.991774i	$-0.540856\pi$
$317$	−4.55800	−0.256003	−0.128001	+	0.991774i	$0.540856\pi$
$318$	13.0884	0.733961
$319$	−7.15567	−0.400640
$320$	41.1263	2.29903
$321$	6.64837	0.371076
$322$	2.15401	0.120039
$323$	−3.00131	−0.166997
$324$	18.2637	1.01465
$325$	0	0
$326$	35.4583	1.96385
$327$	8.28435	0.458126
$328$	−10.2063	−0.563548
$329$	7.48726	0.412786
$330$	−5.97704	−0.329025
$331$	−4.42902	−0.243441	−0.121721	−	0.992564i	$-0.538841\pi$
$331$	−4.42902	−0.243441	−0.121721	+	0.992564i	$0.538841\pi$
$332$	−13.9613	−0.766224
$333$	−11.0629	−0.606244
$334$	−46.8764	−2.56496
$335$	−24.4519	−1.33595
$336$	3.78136	0.206290
$337$	29.9143	1.62954	0.814769	−	0.579786i	$-0.196864\pi$
$337$	29.9143	1.62954	0.814769	+	0.579786i	$0.196864\pi$
$338$	0	0
$339$	−3.39422	−0.184349
$340$	−6.21957	−0.337303
$341$	−1.75064	−0.0948024
$342$	−25.9320	−1.40224
$343$	12.6977	0.685611
$344$	−11.8007	−0.636253
$345$	−0.514004	−0.0276731
$346$	35.4649	1.90660
$347$	10.0391	0.538928	0.269464	−	0.963011i	$-0.413154\pi$
$347$	10.0391	0.538928	0.269464	+	0.963011i	$0.413154\pi$
$348$	4.64666	0.249087
$349$	−3.93884	−0.210841	−0.105421	−	0.994428i	$-0.533619\pi$
$349$	−3.93884	−0.210841	−0.105421	+	0.994428i	$0.533619\pi$
$350$	52.0169	2.78042
$351$	0	0
$352$	−13.8602	−0.738752
$353$	−13.5847	−0.723042	−0.361521	−	0.932364i	$-0.617742\pi$
$353$	−13.5847	−0.723042	−0.361521	+	0.932364i	$0.617742\pi$
$354$	9.63278	0.511976
$355$	−23.7746	−1.26182
$356$	−13.7517	−0.728838
$357$	−0.978695	−0.0517981
$358$	2.02167	0.106848
$359$	0.759052	0.0400612	0.0200306	−	0.999799i	$-0.493624\pi$
$359$	0.759052	0.0400612	0.0200306	+	0.999799i	$0.493624\pi$
$360$	−11.2384	−0.592314
$361$	−0.0323121	−0.00170064
$362$	−14.5195	−0.763126
$363$	−3.56717	−0.187228
$364$	0	0
$365$	−20.8076	−1.08912
$366$	−4.64285	−0.242685
$367$	−14.9717	−0.781518	−0.390759	−	0.920493i	$-0.627787\pi$
$367$	−14.9717	−0.781518	−0.390759	+	0.920493i	$0.627787\pi$
$368$	−0.853052	−0.0444684
$369$	−25.3727	−1.32085
$370$	30.0304	1.56121
$371$	43.2227	2.24401
$372$	1.13681	0.0589408
$373$	7.68648	0.397991	0.198995	−	0.980000i	$-0.436232\pi$
$373$	7.68648	0.397991	0.198995	+	0.980000i	$0.436232\pi$
$374$	2.56740	0.132757
$375$	−4.39094	−0.226747
$376$	2.66733	0.137557
$377$	0	0
$378$	−17.5231	−0.901291
$379$	−25.0653	−1.28752	−0.643758	−	0.765229i	$-0.722626\pi$
$379$	−25.0653	−1.28752	−0.643758	+	0.765229i	$0.722626\pi$
$380$	39.3065	2.01638
$381$	−5.93606	−0.304114
$382$	21.0894	1.07903
$383$	−9.99309	−0.510623	−0.255312	−	0.966859i	$-0.582178\pi$
$383$	−9.99309	−0.510623	−0.255312	+	0.966859i	$0.582178\pi$
$384$	3.90600	0.199327
$385$	−19.7384	−1.00596
$386$	−24.8785	−1.26628
$387$	−29.3365	−1.49126
$388$	−8.34121	−0.423461
$389$	−12.6266	−0.640192	−0.320096	−	0.947385i	$-0.603715\pi$
$389$	−12.6266	−0.640192	−0.320096	+	0.947385i	$0.603715\pi$
$390$	0	0
$391$	0.220788	0.0111657
$392$	−3.35478	−0.169442
$393$	−0.735636	−0.0371079
$394$	−30.8582	−1.55461
$395$	−36.5151	−1.83727
$396$	12.3867	0.622457
$397$	20.9489	1.05140	0.525698	−	0.850671i	$-0.323804\pi$
$397$	20.9489	1.05140	0.525698	+	0.850671i	$0.323804\pi$
$398$	−28.1332	−1.41019
$399$	6.18517	0.309646
$400$	−20.6002	−1.03001
$401$	−36.7354	−1.83448	−0.917240	−	0.398336i	$-0.869588\pi$
$401$	−36.7354	−1.83448	−0.917240	+	0.398336i	$0.869588\pi$
$402$	−6.55448	−0.326908
$403$	0	0
$404$	15.9593	0.794002
$405$	−25.7749	−1.28076
$406$	27.4808	1.36385
$407$	−6.92199	−0.343110
$408$	−0.348659	−0.0172612
$409$	−1.06065	−0.0524457	−0.0262228	−	0.999656i	$-0.508348\pi$
$409$	−1.06065	−0.0524457	−0.0262228	+	0.999656i	$0.508348\pi$
$410$	68.8745	3.40147
$411$	−4.87503	−0.240468
$412$	−17.3210	−0.853344
$413$	31.8109	1.56531
$414$	1.90766	0.0937565
$415$	19.7030	0.967182
$416$	0	0
$417$	5.55767	0.272160
$418$	−16.2255	−0.793616
$419$	6.82050	0.333203	0.166602	−	0.986024i	$-0.446721\pi$
$419$	6.82050	0.333203	0.166602	+	0.986024i	$0.446721\pi$
$420$	12.8174	0.625427
$421$	23.0197	1.12191	0.560957	−	0.827845i	$-0.310433\pi$
$421$	23.0197	1.12191	0.560957	+	0.827845i	$0.310433\pi$
$422$	27.5988	1.34349
$423$	6.63095	0.322408
$424$	15.3980	0.747794
$425$	5.33177	0.258629
$426$	−6.37290	−0.308768
$427$	−15.3324	−0.741985
$428$	37.4005	1.80782
$429$	0	0
$430$	79.6343	3.84031
$431$	14.3079	0.689188	0.344594	−	0.938752i	$-0.388017\pi$
$431$	14.3079	0.689188	0.344594	+	0.938752i	$0.388017\pi$
$432$	6.93966	0.333885
$433$	−27.3554	−1.31462	−0.657309	−	0.753622i	$-0.728305\pi$
$433$	−27.3554	−1.31462	−0.657309	+	0.753622i	$0.728305\pi$
$434$	6.72321	0.322724
$435$	−6.55765	−0.314415
$436$	46.6037	2.23191
$437$	−1.39534	−0.0667481
$438$	−5.57760	−0.266508
$439$	−23.3649	−1.11515	−0.557573	−	0.830128i	$-0.688267\pi$
$439$	−23.3649	−1.11515	−0.557573	+	0.830128i	$0.688267\pi$
$440$	−7.03177	−0.335226
$441$	−8.33995	−0.397140
$442$	0	0
$443$	−14.9327	−0.709475	−0.354737	−	0.934966i	$-0.615430\pi$
$443$	−14.9327	−0.709475	−0.354737	+	0.934966i	$0.615430\pi$
$444$	4.49492	0.213319
$445$	19.4072	0.919991
$446$	−63.1472	−2.99011
$447$	0.557472	0.0263675
$448$	36.4057	1.72001
$449$	14.2209	0.671126	0.335563	−	0.942018i	$-0.391073\pi$
$449$	14.2209	0.671126	0.335563	+	0.942018i	$0.391073\pi$
$450$	46.0678	2.17166
$451$	−15.8755	−0.747550
$452$	−19.0942	−0.898117
$453$	2.69090	0.126430
$454$	−8.07241	−0.378857
$455$	0	0
$456$	2.20346	0.103186
$457$	25.5343	1.19445	0.597223	−	0.802075i	$-0.296271\pi$
$457$	25.5343	1.19445	0.597223	+	0.802075i	$0.296271\pi$
$458$	39.2962	1.83619
$459$	−1.79613	−0.0838362
$460$	−2.89154	−0.134819
$461$	−19.0846	−0.888857	−0.444429	−	0.895814i	$-0.646593\pi$
$461$	−19.0846	−0.888857	−0.444429	+	0.895814i	$0.646593\pi$
$462$	−5.29097	−0.246158
$463$	−3.27928	−0.152401	−0.0762005	−	0.997093i	$-0.524279\pi$
$463$	−3.27928	−0.152401	−0.0762005	+	0.997093i	$0.524279\pi$
$464$	−10.8832	−0.505240
$465$	−1.60433	−0.0743992
$466$	53.5001	2.47835
$467$	10.0092	0.463168	0.231584	−	0.972815i	$-0.425609\pi$
$467$	10.0092	0.463168	0.231584	+	0.972815i	$0.425609\pi$
$468$	0	0
$469$	−21.6453	−0.999486
$470$	−17.9998	−0.830268
$471$	−9.94933	−0.458441
$472$	11.3326	0.521626
$473$	−18.3557	−0.843995
$474$	−9.78807	−0.449581
$475$	−33.6958	−1.54607
$476$	−5.50567	−0.252352
$477$	38.2794	1.75269
$478$	48.2318	2.20607
$479$	−7.25510	−0.331494	−0.165747	−	0.986168i	$-0.553004\pi$
$479$	−7.25510	−0.331494	−0.165747	+	0.986168i	$0.553004\pi$
$480$	−12.7019	−0.579759
$481$	0	0
$482$	19.5826	0.891964
$483$	−0.455005	−0.0207035
$484$	−20.0672	−0.912144
$485$	11.7716	0.534522
$486$	−23.5490	−1.06820
$487$	32.8054	1.48656	0.743278	−	0.668983i	$-0.233270\pi$
$487$	32.8054	1.48656	0.743278	+	0.668983i	$0.233270\pi$
$488$	−5.46214	−0.247260
$489$	−7.49007	−0.338713
$490$	22.6389	1.02272
$491$	26.8317	1.21090	0.605449	−	0.795884i	$-0.292994\pi$
$491$	26.8317	1.21090	0.605449	+	0.795884i	$0.292994\pi$
$492$	10.3091	0.464769
$493$	2.81680	0.126862
$494$	0	0
$495$	−17.4809	−0.785709
$496$	−2.66259	−0.119554
$497$	−21.0456	−0.944026
$498$	5.28150	0.236670
$499$	−13.3585	−0.598007	−0.299004	−	0.954252i	$-0.596654\pi$
$499$	−13.3585	−0.598007	−0.299004	+	0.954252i	$0.596654\pi$
$500$	−24.7013	−1.10468
$501$	9.90198	0.442388
$502$	−5.50665	−0.245774
$503$	−18.0161	−0.803298	−0.401649	−	0.915794i	$-0.631563\pi$
$503$	−18.0161	−0.803298	−0.401649	+	0.915794i	$0.631563\pi$
$504$	−9.94839	−0.443136
$505$	−22.5227	−1.00225
$506$	1.19361	0.0530625
$507$	0	0
$508$	−33.3934	−1.48159
$509$	23.2385	1.03003	0.515014	−	0.857182i	$-0.327787\pi$
$509$	23.2385	1.03003	0.515014	+	0.857182i	$0.327787\pi$
$510$	2.35284	0.104185
$511$	−18.4193	−0.814820
$512$	−27.0736	−1.19650
$513$	11.3512	0.501168
$514$	−63.6462	−2.80731
$515$	24.4445	1.07715
$516$	11.9196	0.524730
$517$	4.14894	0.182470
$518$	26.5834	1.16801
$519$	−7.49146	−0.328839
$520$	0	0
$521$	17.9979	0.788502	0.394251	−	0.919003i	$-0.371004\pi$
$521$	17.9979	0.788502	0.394251	+	0.919003i	$0.371004\pi$
$522$	24.3379	1.06524
$523$	37.3164	1.63173	0.815865	−	0.578242i	$-0.196261\pi$
$523$	37.3164	1.63173	0.815865	+	0.578242i	$0.196261\pi$
$524$	−4.13833	−0.180784
$525$	−10.9878	−0.479549
$526$	55.7415	2.43045
$527$	0.689133	0.0300191
$528$	2.09538	0.0911897
$529$	−22.8974	−0.995537
$530$	−103.910	−4.51355
$531$	28.1728	1.22259
$532$	34.7948	1.50854
$533$	0	0
$534$	5.20221	0.225122
$535$	−52.7819	−2.28196
$536$	−7.71111	−0.333069
$537$	−0.427049	−0.0184285
$538$	18.1303	0.781653
$539$	−5.21825	−0.224766
$540$	23.5229	1.01227
$541$	−6.53779	−0.281082	−0.140541	−	0.990075i	$-0.544884\pi$
$541$	−6.53779	−0.281082	−0.140541	+	0.990075i	$0.544884\pi$
$542$	−48.0660	−2.06461
$543$	3.06703	0.131619
$544$	5.45602	0.233925
$545$	−65.7701	−2.81728
$546$	0	0
$547$	−19.9689	−0.853807	−0.426903	−	0.904297i	$-0.640396\pi$
$547$	−19.9689	−0.853807	−0.426903	+	0.904297i	$0.640396\pi$
$548$	−27.4246	−1.17152
$549$	−13.5788	−0.579531
$550$	28.8243	1.22907
$551$	−17.8017	−0.758377
$552$	−0.162095	−0.00689923
$553$	−32.3238	−1.37455
$554$	−49.5231	−2.10404
$555$	−6.34350	−0.269267
$556$	31.2648	1.32592
$557$	4.62487	0.195962	0.0979811	−	0.995188i	$-0.468762\pi$
$557$	4.62487	0.195962	0.0979811	+	0.995188i	$0.468762\pi$
$558$	5.95429	0.252065
$559$	0	0
$560$	−30.0205	−1.26860
$561$	−0.542328	−0.0228971
$562$	45.0502	1.90033
$563$	23.6637	0.997307	0.498653	−	0.866801i	$-0.333828\pi$
$563$	23.6637	0.997307	0.498653	+	0.866801i	$0.333828\pi$
$564$	−2.69419	−0.113446
$565$	26.9469	1.13367
$566$	−58.5585	−2.46140
$567$	−22.8163	−0.958196
$568$	−7.49749	−0.314588
$569$	−47.5497	−1.99339	−0.996694	−	0.0812459i	$-0.974110\pi$
$569$	−47.5497	−1.99339	−0.996694	+	0.0812459i	$0.974110\pi$
$570$	−14.8695	−0.622815
$571$	−21.0304	−0.880093	−0.440047	−	0.897975i	$-0.645038\pi$
$571$	−21.0304	−0.880093	−0.440047	+	0.897975i	$0.645038\pi$
$572$	0	0
$573$	−4.45485	−0.186104
$574$	60.9689	2.54479
$575$	2.47879	0.103373
$576$	32.2420	1.34342
$577$	21.6212	0.900103	0.450052	−	0.893003i	$-0.351406\pi$
$577$	21.6212	0.900103	0.450052	+	0.893003i	$0.351406\pi$
$578$	35.1673	1.46276
$579$	5.25523	0.218400
$580$	−36.8902	−1.53178
$581$	17.4414	0.723592
$582$	3.15545	0.130798
$583$	23.9511	0.991955
$584$	−6.56184	−0.271531
$585$	0	0
$586$	26.1170	1.07888
$587$	17.4802	0.721485	0.360742	−	0.932666i	$-0.382523\pi$
$587$	17.4802	0.721485	0.360742	+	0.932666i	$0.382523\pi$
$588$	3.38856	0.139742
$589$	−4.35519	−0.179453
$590$	−76.4753	−3.14844
$591$	6.51836	0.268129
$592$	−10.5278	−0.432690
$593$	−6.77062	−0.278036	−0.139018	−	0.990290i	$-0.544395\pi$
$593$	−6.77062	−0.278036	−0.139018	+	0.990290i	$0.544395\pi$
$594$	−9.71015	−0.398412
$595$	7.76993	0.318536
$596$	3.13607	0.128458
$597$	5.94275	0.243221
$598$	0	0
$599$	−9.93934	−0.406111	−0.203055	−	0.979167i	$-0.565087\pi$
$599$	−9.93934	−0.406111	−0.203055	+	0.979167i	$0.565087\pi$
$600$	−3.91441	−0.159805
$601$	33.1660	1.35287	0.676435	−	0.736503i	$-0.263524\pi$
$601$	33.1660	1.35287	0.676435	+	0.736503i	$0.263524\pi$
$602$	70.4937	2.87311
$603$	−19.1697	−0.780652
$604$	15.1377	0.615945
$605$	28.3200	1.15137
$606$	−6.03733	−0.245250
$607$	4.35086	0.176596	0.0882980	−	0.996094i	$-0.471857\pi$
$607$	4.35086	0.176596	0.0882980	+	0.996094i	$0.471857\pi$
$608$	−34.4810	−1.39839
$609$	−5.80494	−0.235228
$610$	36.8599	1.49241
$611$	0	0
$612$	−4.87599	−0.197100
$613$	18.1146	0.731640	0.365820	−	0.930686i	$-0.380789\pi$
$613$	18.1146	0.731640	0.365820	+	0.930686i	$0.380789\pi$
$614$	−44.8201	−1.80879
$615$	−14.5488	−0.586664
$616$	−6.22464	−0.250798
$617$	14.7600	0.594215	0.297107	−	0.954844i	$-0.403978\pi$
$617$	14.7600	0.594215	0.297107	+	0.954844i	$0.403978\pi$
$618$	6.55247	0.263579
$619$	−31.5046	−1.26628	−0.633139	−	0.774038i	$-0.718234\pi$
$619$	−31.5046	−1.26628	−0.633139	+	0.774038i	$0.718234\pi$
$620$	−9.02521	−0.362461
$621$	−0.835039	−0.0335090
$622$	−2.26609	−0.0908621
$623$	17.1796	0.688286
$624$	0	0
$625$	−3.82465	−0.152986
$626$	−48.8021	−1.95052
$627$	3.42741	0.136878
$628$	−55.9701	−2.23345
$629$	2.72482	0.108646
$630$	67.1342	2.67469
$631$	−25.5343	−1.01651	−0.508253	−	0.861208i	$-0.669709\pi$
$631$	−25.5343	−1.01651	−0.508253	+	0.861208i	$0.669709\pi$
$632$	−11.5153	−0.458055
$633$	−5.82987	−0.231717
$634$	9.69994	0.385234
$635$	47.1268	1.87017
$636$	−15.5531	−0.616720
$637$	0	0
$638$	15.2281	0.602885
$639$	−18.6387	−0.737335
$640$	−31.0100	−1.22578
$641$	−17.5133	−0.691734	−0.345867	−	0.938284i	$-0.612415\pi$
$641$	−17.5133	−0.691734	−0.345867	+	0.938284i	$0.612415\pi$
$642$	−14.1485	−0.558396
$643$	−45.9250	−1.81111	−0.905554	−	0.424232i	$-0.860544\pi$
$643$	−45.9250	−1.81111	−0.905554	+	0.424232i	$0.860544\pi$
$644$	−2.55964	−0.100864
$645$	−16.8216	−0.662351
$646$	6.38711	0.251298
$647$	14.2546	0.560405	0.280202	−	0.959941i	$-0.409598\pi$
$647$	14.2546	0.560405	0.280202	+	0.959941i	$0.409598\pi$
$648$	−8.12830	−0.319310
$649$	17.6275	0.691941
$650$	0	0
$651$	−1.42018	−0.0556614
$652$	−42.1355	−1.65015
$653$	−37.2871	−1.45916	−0.729578	−	0.683897i	$-0.760284\pi$
$653$	−37.2871	−1.45916	−0.729578	+	0.683897i	$0.760284\pi$
$654$	−17.6300	−0.689388
$655$	5.84027	0.228198
$656$	−24.1455	−0.942722
$657$	−16.3127	−0.636418
$658$	−15.9337	−0.621161
$659$	−47.0067	−1.83112	−0.915560	−	0.402181i	$-0.868252\pi$
$659$	−47.0067	−1.83112	−0.915560	+	0.402181i	$0.868252\pi$
$660$	7.10258	0.276468
$661$	−20.5147	−0.797931	−0.398966	−	0.916966i	$-0.630631\pi$
$661$	−20.5147	−0.797931	−0.398966	+	0.916966i	$0.630631\pi$
$662$	9.42546	0.366331
$663$	0	0
$664$	6.21349	0.241130
$665$	−49.1045	−1.90419
$666$	23.5431	0.912277
$667$	1.30956	0.0507064
$668$	55.7037	2.15524
$669$	13.3390	0.515714
$670$	52.0365	2.01034
$671$	−8.49619	−0.327992
$672$	−11.2439	−0.433744
$673$	−39.7872	−1.53369	−0.766843	−	0.641835i	$-0.778173\pi$
$673$	−39.7872	−1.53369	−0.766843	+	0.641835i	$0.778173\pi$
$674$	−63.6610	−2.45213
$675$	−20.1652	−0.776160
$676$	0	0
$677$	7.12165	0.273707	0.136854	−	0.990591i	$-0.456301\pi$
$677$	7.12165	0.273707	0.136854	+	0.990591i	$0.456301\pi$
$678$	7.22327	0.277408
$679$	10.4204	0.399900
$680$	2.76803	0.106149
$681$	1.70518	0.0653428
$682$	3.72556	0.142659
$683$	−10.0348	−0.383972	−0.191986	−	0.981398i	$-0.561493\pi$
$683$	−10.0348	−0.383972	−0.191986	+	0.981398i	$0.561493\pi$
$684$	30.8154	1.17825
$685$	38.7032	1.47877
$686$	−27.0221	−1.03171
$687$	−8.30078	−0.316694
$688$	−27.9175	−1.06435
$689$	0	0
$690$	1.09386	0.0416425
$691$	−32.7159	−1.24457	−0.622286	−	0.782790i	$-0.713796\pi$
$691$	−32.7159	−1.24457	−0.622286	+	0.782790i	$0.713796\pi$
$692$	−42.1434	−1.60205
$693$	−15.4744	−0.587824
$694$	−21.3643	−0.810980
$695$	−44.1227	−1.67367
$696$	−2.06800	−0.0783875
$697$	6.24935	0.236711
$698$	8.38229	0.317274
$699$	−11.3012	−0.427449
$700$	−61.8123	−2.33629
$701$	43.2914	1.63509	0.817546	−	0.575863i	$-0.195334\pi$
$701$	43.2914	1.63509	0.817546	+	0.575863i	$0.195334\pi$
$702$	0	0
$703$	−17.2203	−0.649477
$704$	20.1736	0.760322
$705$	3.80220	0.143199
$706$	28.9098	1.08804
$707$	−19.9375	−0.749825
$708$	−11.4467	−0.430195
$709$	22.5452	0.846704	0.423352	−	0.905965i	$-0.360853\pi$
$709$	22.5452	0.846704	0.423352	+	0.905965i	$0.360853\pi$
$710$	50.5949	1.89879
$711$	−28.6270	−1.07360
$712$	6.12022	0.229365
$713$	0.320385	0.0119985
$714$	2.08277	0.0779458
$715$	0	0
$716$	−2.40237	−0.0897808
$717$	−10.1883	−0.380489
$718$	−1.61535	−0.0602842
$719$	43.1954	1.61092	0.805458	−	0.592653i	$-0.201919\pi$
$719$	43.1954	1.61092	0.805458	+	0.592653i	$0.201919\pi$
$720$	−26.5871	−0.990843
$721$	21.6386	0.805865
$722$	0.0687637	0.00255912
$723$	−4.13656	−0.153840
$724$	17.2536	0.641227
$725$	31.6244	1.17450
$726$	7.59134	0.281741
$727$	17.9641	0.666251	0.333125	−	0.942883i	$-0.391897\pi$
$727$	17.9641	0.666251	0.333125	+	0.942883i	$0.391897\pi$
$728$	0	0
$729$	−16.6919	−0.618220
$730$	44.2809	1.63891
$731$	7.22565	0.267250
$732$	5.51715	0.203920
$733$	−4.62142	−0.170696	−0.0853479	−	0.996351i	$-0.527200\pi$
$733$	−4.62142	−0.170696	−0.0853479	+	0.996351i	$0.527200\pi$
$734$	31.8615	1.17603
$735$	−4.78215	−0.176392
$736$	2.53656	0.0934989
$737$	−11.9944	−0.441819
$738$	53.9960	1.98762
$739$	11.6167	0.427327	0.213663	−	0.976907i	$-0.431460\pi$
$739$	11.6167	0.427327	0.213663	+	0.976907i	$0.431460\pi$
$740$	−35.6855	−1.31182
$741$	0	0
$742$	−91.9827	−3.37679
$743$	−29.5488	−1.08404	−0.542020	−	0.840365i	$-0.682340\pi$
$743$	−29.5488	−1.08404	−0.542020	+	0.840365i	$0.682340\pi$
$744$	−0.505939	−0.0185486
$745$	−4.42581	−0.162149
$746$	−16.3577	−0.598898
$747$	15.4467	0.565165
$748$	−3.05088	−0.111551
$749$	−46.7234	−1.70724
$750$	9.34440	0.341209
$751$	−2.62741	−0.0958757	−0.0479379	−	0.998850i	$-0.515265\pi$
$751$	−2.62741	−0.0958757	−0.0479379	+	0.998850i	$0.515265\pi$
$752$	6.31022	0.230110
$753$	1.16320	0.0423895
$754$	0	0
$755$	−21.3633	−0.777489
$756$	20.8229	0.757322
$757$	−45.0665	−1.63797	−0.818984	−	0.573816i	$-0.805462\pi$
$757$	−45.0665	−1.63797	−0.818984	+	0.573816i	$0.805462\pi$
$758$	53.3417	1.93746
$759$	−0.252134	−0.00915188
$760$	−17.4934	−0.634553
$761$	−39.0241	−1.41462	−0.707312	−	0.706902i	$-0.750092\pi$
$761$	−39.0241	−1.41462	−0.707312	+	0.706902i	$0.750092\pi$
$762$	12.6326	0.457631
$763$	−58.2208	−2.10773
$764$	−25.0608	−0.906669
$765$	6.88130	0.248794
$766$	21.2664	0.768387
$767$	0	0
$768$	2.04807	0.0739033
$769$	−22.5822	−0.814334	−0.407167	−	0.913354i	$-0.633483\pi$
$769$	−22.5822	−0.814334	−0.407167	+	0.913354i	$0.633483\pi$
$770$	42.0054	1.51377
$771$	13.4444	0.484187
$772$	29.5634	1.06401
$773$	−8.21929	−0.295627	−0.147814	−	0.989015i	$-0.547224\pi$
$773$	−8.21929	−0.295627	−0.147814	+	0.989015i	$0.547224\pi$
$774$	62.4314	2.24405
$775$	7.73692	0.277918
$776$	3.71227	0.133263
$777$	−5.61537	−0.201450
$778$	26.8707	0.963363
$779$	−39.4947	−1.41505
$780$	0	0
$781$	−11.6621	−0.417303
$782$	−0.469861	−0.0168022
$783$	−10.6534	−0.380721
$784$	−7.93655	−0.283448
$785$	78.9885	2.81922
$786$	1.56552	0.0558401
$787$	1.50477	0.0536394	0.0268197	−	0.999640i	$-0.491462\pi$
$787$	1.50477	0.0536394	0.0268197	+	0.999640i	$0.491462\pi$
$788$	36.6691	1.30628
$789$	−11.7746	−0.419187
$790$	77.7082	2.76473
$791$	23.8539	0.848146
$792$	−5.51274	−0.195887
$793$	0	0
$794$	−44.5816	−1.58214
$795$	21.9495	0.778468
$796$	33.4310	1.18493
$797$	13.9641	0.494635	0.247317	−	0.968935i	$-0.420451\pi$
$797$	13.9641	0.494635	0.247317	+	0.968935i	$0.420451\pi$
$798$	−13.1627	−0.465956
$799$	−1.63322	−0.0577790
$800$	61.2550	2.16569
$801$	15.2148	0.537589
$802$	78.1771	2.76053
$803$	−10.2067	−0.360188
$804$	7.78876	0.274689
$805$	3.61232	0.127318
$806$	0	0
$807$	−3.82978	−0.134814
$808$	−7.10270	−0.249872
$809$	−26.2080	−0.921423	−0.460711	−	0.887550i	$-0.652406\pi$
$809$	−26.2080	−0.921423	−0.460711	+	0.887550i	$0.652406\pi$
$810$	54.8518	1.92730
$811$	−16.4140	−0.576372	−0.288186	−	0.957574i	$-0.593052\pi$
$811$	−16.4140	−0.576372	−0.288186	+	0.957574i	$0.593052\pi$
$812$	−32.6558	−1.14599
$813$	10.1533	0.356091
$814$	14.7308	0.516313
$815$	59.4642	2.08294
$816$	−0.824839	−0.0288751
$817$	−45.6647	−1.59761
$818$	2.25718	0.0789204
$819$	0	0
$820$	−81.8444	−2.85813
$821$	−11.4271	−0.398809	−0.199404	−	0.979917i	$-0.563901\pi$
$821$	−11.4271	−0.398809	−0.199404	+	0.979917i	$0.563901\pi$
$822$	10.3746	0.361856
$823$	−42.2545	−1.47290	−0.736450	−	0.676492i	$-0.763499\pi$
$823$	−42.2545	−1.47290	−0.736450	+	0.676492i	$0.763499\pi$
$824$	7.70874	0.268547
$825$	−6.08874	−0.211983
$826$	−67.6972	−2.35549
$827$	−9.46884	−0.329264	−0.164632	−	0.986355i	$-0.552644\pi$
$827$	−9.46884	−0.329264	−0.164632	+	0.986355i	$0.552644\pi$
$828$	−2.26690	−0.0787802
$829$	34.2652	1.19008	0.595040	−	0.803696i	$-0.297136\pi$
$829$	34.2652	1.19008	0.595040	+	0.803696i	$0.297136\pi$
$830$	−41.9302	−1.45542
$831$	10.4611	0.362891
$832$	0	0
$833$	2.05415	0.0711719
$834$	−11.8273	−0.409547
$835$	−78.6125	−2.72050
$836$	19.2810	0.666846
$837$	−2.60636	−0.0900890
$838$	−14.5148	−0.501405
$839$	34.2981	1.18410	0.592051	−	0.805900i	$-0.298318\pi$
$839$	34.2981	1.18410	0.592051	+	0.805900i	$0.298318\pi$
$840$	−5.70443	−0.196822
$841$	−12.2927	−0.423885
$842$	−48.9886	−1.68826
$843$	−9.51623	−0.327756
$844$	−32.7960	−1.12889
$845$	0	0
$846$	−14.1114	−0.485160
$847$	25.0694	0.861393
$848$	36.4278	1.25094
$849$	12.3697	0.424526
$850$	−11.3466	−0.389185
$851$	1.26679	0.0434252
$852$	7.57300	0.259447
$853$	10.6489	0.364612	0.182306	−	0.983242i	$-0.441644\pi$
$853$	10.6489	0.364612	0.182306	+	0.983242i	$0.441644\pi$
$854$	32.6290	1.11654
$855$	−43.4885	−1.48728
$856$	−16.6452	−0.568920
$857$	18.2123	0.622121	0.311061	−	0.950390i	$-0.399316\pi$
$857$	18.2123	0.622121	0.311061	+	0.950390i	$0.399316\pi$
$858$	0	0
$859$	−13.4772	−0.459835	−0.229917	−	0.973210i	$-0.573846\pi$
$859$	−13.4772	−0.459835	−0.229917	+	0.973210i	$0.573846\pi$
$860$	−94.6304	−3.22687
$861$	−12.8788	−0.438909
$862$	−30.4489	−1.03709
$863$	45.0092	1.53213	0.766065	−	0.642763i	$-0.222212\pi$
$863$	45.0092	1.53213	0.766065	+	0.642763i	$0.222212\pi$
$864$	−20.6352	−0.702022
$865$	59.4753	2.02222
$866$	58.2154	1.97824
$867$	−7.42859	−0.252288
$868$	−7.98926	−0.271173
$869$	−17.9117	−0.607613
$870$	13.9554	0.473133
$871$	0	0
$872$	−20.7411	−0.702382
$873$	9.22867	0.312343
$874$	2.96943	0.100443
$875$	30.8586	1.04321
$876$	6.62792	0.223937
$877$	44.5989	1.50600	0.752999	−	0.658022i	$-0.228607\pi$
$877$	44.5989	1.50600	0.752999	+	0.658022i	$0.228607\pi$
$878$	49.7231	1.67807
$879$	−5.51685	−0.186079
$880$	−16.6354	−0.560778
$881$	26.3171	0.886646	0.443323	−	0.896362i	$-0.353799\pi$
$881$	26.3171	0.886646	0.443323	+	0.896362i	$0.353799\pi$
$882$	17.7483	0.597618
$883$	11.3669	0.382527	0.191263	−	0.981539i	$-0.438742\pi$
$883$	11.3669	0.382527	0.191263	+	0.981539i	$0.438742\pi$
$884$	0	0
$885$	16.1543	0.543022
$886$	31.7785	1.06762
$887$	−29.6569	−0.995782	−0.497891	−	0.867240i	$-0.665892\pi$
$887$	−29.6569	−0.995782	−0.497891	+	0.867240i	$0.665892\pi$
$888$	−2.00047	−0.0671314
$889$	41.7175	1.39916
$890$	−41.3008	−1.38440
$891$	−12.6433	−0.423567
$892$	75.0386	2.51248
$893$	10.3216	0.345400
$894$	−1.18636	−0.0396779
$895$	3.39037	0.113328
$896$	−27.4506	−0.917061
$897$	0	0
$898$	−30.2637	−1.00991
$899$	4.08746	0.136324
$900$	−54.7430	−1.82477
$901$	−9.42828	−0.314102
$902$	33.7849	1.12492
$903$	−14.8908	−0.495535
$904$	8.49792	0.282637
$905$	−24.3494	−0.809402
$906$	−5.72654	−0.190252
$907$	23.8046	0.790420	0.395210	−	0.918591i	$-0.370672\pi$
$907$	23.8046	0.790420	0.395210	+	0.918591i	$0.370672\pi$
$908$	9.59254	0.318340
$909$	−17.6572	−0.585654
$910$	0	0
$911$	−12.1893	−0.403851	−0.201925	−	0.979401i	$-0.564720\pi$
$911$	−12.1893	−0.403851	−0.201925	+	0.979401i	$0.564720\pi$
$912$	5.21283	0.172614
$913$	9.66489	0.319861
$914$	−54.3399	−1.79741
$915$	−7.78614	−0.257402
$916$	−46.6961	−1.54288
$917$	5.16990	0.170725
$918$	3.82237	0.126157
$919$	−3.22323	−0.106325	−0.0531623	−	0.998586i	$-0.516930\pi$
$919$	−3.22323	−0.106325	−0.0531623	+	0.998586i	$0.516930\pi$
$920$	1.28689	0.0424274
$921$	9.46762	0.311969
$922$	40.6141	1.33755
$923$	0	0
$924$	6.28733	0.206838
$925$	30.5916	1.00585
$926$	6.97867	0.229333
$927$	19.1639	0.629424
$928$	32.3614	1.06231
$929$	−14.0603	−0.461305	−0.230652	−	0.973036i	$-0.574086\pi$
$929$	−14.0603	−0.461305	−0.230652	+	0.973036i	$0.574086\pi$
$930$	3.41420	0.111956
$931$	−12.9818	−0.425462
$932$	−63.5748	−2.08246
$933$	0.478681	0.0156713
$934$	−21.3006	−0.696977
$935$	4.30558	0.140808
$936$	0	0
$937$	2.91292	0.0951611	0.0475805	−	0.998867i	$-0.484849\pi$
$937$	2.91292	0.0951611	0.0475805	+	0.998867i	$0.484849\pi$
$938$	46.0636	1.50403
$939$	10.3088	0.336414
$940$	21.3894	0.697644
$941$	38.5019	1.25513	0.627563	−	0.778566i	$-0.284053\pi$
$941$	38.5019	1.25513	0.627563	+	0.778566i	$0.284053\pi$
$942$	21.1733	0.689863
$943$	2.90539	0.0946124
$944$	26.8101	0.872594
$945$	−29.3866	−0.955945
$946$	39.0629	1.27005
$947$	−43.9153	−1.42705	−0.713527	−	0.700627i	$-0.752904\pi$
$947$	−43.9153	−1.42705	−0.713527	+	0.700627i	$0.752904\pi$
$948$	11.6313	0.377766
$949$	0	0
$950$	71.7084	2.32653
$951$	−2.04898	−0.0664426
$952$	2.45031	0.0794149
$953$	7.27878	0.235783	0.117891	−	0.993026i	$-0.462387\pi$
$953$	7.27878	0.235783	0.117891	+	0.993026i	$0.462387\pi$
$954$	−81.4628	−2.63745
$955$	35.3674	1.14446
$956$	−57.3144	−1.85368
$957$	−3.21672	−0.103982
$958$	15.4397	0.498833
$959$	34.2608	1.10634
$960$	18.4877	0.596687
$961$	1.00000	0.0322581
$962$	0	0
$963$	−41.3797	−1.33344
$964$	−23.2703	−0.749485
$965$	−41.7217	−1.34307
$966$	0.968303	0.0311546
$967$	−10.3547	−0.332986	−0.166493	−	0.986043i	$-0.553244\pi$
$967$	−10.3547	−0.332986	−0.166493	+	0.986043i	$0.553244\pi$
$968$	8.93093	0.287051
$969$	−1.34919	−0.0433422
$970$	−25.0513	−0.804350
$971$	6.32919	0.203113	0.101557	−	0.994830i	$-0.467618\pi$
$971$	6.32919	0.203113	0.101557	+	0.994830i	$0.467618\pi$
$972$	27.9835	0.897572
$973$	−39.0582	−1.25215
$974$	−69.8136	−2.23697
$975$	0	0
$976$	−12.9220	−0.413624
$977$	52.8706	1.69148	0.845740	−	0.533595i	$-0.179159\pi$
$977$	52.8706	1.69148	0.845740	+	0.533595i	$0.179159\pi$
$978$	15.9397	0.509696
$979$	9.51980	0.304254
$980$	−26.9020	−0.859354
$981$	−51.5622	−1.64625
$982$	−57.1009	−1.82216
$983$	56.2102	1.79283	0.896414	−	0.443218i	$-0.146163\pi$
$983$	56.2102	1.79283	0.896414	+	0.443218i	$0.146163\pi$
$984$	−4.58807	−0.146262
$985$	−51.7497	−1.64888
$986$	−5.99447	−0.190903
$987$	3.36578	0.107134
$988$	0	0
$989$	3.35928	0.106819
$990$	37.2013	1.18234
$991$	1.34074	0.0425900	0.0212950	−	0.999773i	$-0.493221\pi$
$991$	1.34074	0.0425900	0.0212950	+	0.999773i	$0.493221\pi$
$992$	7.91723	0.251372
$993$	−1.99100	−0.0631823
$994$	44.7875	1.42057
$995$	−47.1799	−1.49570
$996$	−6.27607	−0.198865
$997$	−15.8230	−0.501120	−0.250560	−	0.968101i	$-0.580615\pi$
$997$	−15.8230	−0.501120	−0.250560	+	0.968101i	$0.580615\pi$
$998$	28.4283	0.899883
$999$	−10.3055	−0.326051

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.q.1.8		34
13.6	odd	12		403.2.r.a.218.30	✓	68
13.11	odd	12		403.2.r.a.342.30	yes	68
13.12	even	2		5239.2.a.r.1.27		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.30	✓	68	13.6	odd	12
403.2.r.a.342.30	yes	68	13.11	odd	12
5239.2.a.q.1.8		34	1.1	even	1	trivial
5239.2.a.r.1.27		34	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)

\(f(q)\)	\(=\)	\(q-2.12811 q^{2} +0.449534 q^{3} +2.52886 q^{4} -3.56888 q^{5} -0.956659 q^{6} -3.15924 q^{7} -1.12547 q^{8} -2.79792 q^{9} +O(q^{10})\)	\(q-2.12811 q^{2} +0.449534 q^{3} +2.52886 q^{4} -3.56888 q^{5} -0.956659 q^{6} -3.15924 q^{7} -1.12547 q^{8} -2.79792 q^{9} +7.59498 q^{10} -1.75064 q^{11} +1.13681 q^{12} +6.72321 q^{14} -1.60433 q^{15} -2.66259 q^{16} +0.689133 q^{17} +5.95429 q^{18} -4.35519 q^{19} -9.02521 q^{20} -1.42018 q^{21} +3.72556 q^{22} +0.320385 q^{23} -0.505939 q^{24} +7.73692 q^{25} -2.60636 q^{27} -7.98926 q^{28} +4.08746 q^{29} +3.41420 q^{30} +1.00000 q^{31} +7.91723 q^{32} -0.786972 q^{33} -1.46655 q^{34} +11.2749 q^{35} -7.07555 q^{36} +3.95398 q^{37} +9.26833 q^{38} +4.01669 q^{40} +9.06843 q^{41} +3.02231 q^{42} +10.4851 q^{43} -4.42712 q^{44} +9.98544 q^{45} -0.681815 q^{46} -2.36996 q^{47} -1.19692 q^{48} +2.98077 q^{49} -16.4650 q^{50} +0.309789 q^{51} -13.6814 q^{53} +5.54663 q^{54} +6.24783 q^{55} +3.55564 q^{56} -1.95781 q^{57} -8.69857 q^{58} -10.0692 q^{59} -4.05714 q^{60} +4.85319 q^{61} -2.12811 q^{62} +8.83929 q^{63} -11.5236 q^{64} +1.67476 q^{66} +6.85143 q^{67} +1.74272 q^{68} +0.144024 q^{69} -23.9943 q^{70} +6.66163 q^{71} +3.14899 q^{72} +5.83029 q^{73} -8.41451 q^{74} +3.47801 q^{75} -11.0137 q^{76} +5.53068 q^{77} +10.2315 q^{79} +9.50246 q^{80} +7.22211 q^{81} -19.2986 q^{82} -5.52078 q^{83} -3.59145 q^{84} -2.45943 q^{85} -22.3135 q^{86} +1.83745 q^{87} +1.97030 q^{88} -5.43790 q^{89} -21.2501 q^{90} +0.810209 q^{92} +0.449534 q^{93} +5.04354 q^{94} +15.5432 q^{95} +3.55906 q^{96} -3.29840 q^{97} -6.34341 q^{98} +4.89815 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 8 q^{2} + 32 q^{4} - 16 q^{5} - 12 q^{6} - 8 q^{7} - 24 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q - 8 * q^2 + 32 * q^4 - 16 * q^5 - 12 * q^6 - 8 * q^7 - 24 * q^8 + 34 * q^9	\( 34 q - 8 q^{2} + 32 q^{4} - 16 q^{5} - 12 q^{6} - 8 q^{7} - 24 q^{8} + 34 q^{9} + 8 q^{10} - 26 q^{11} + 8 q^{12} - 4 q^{14} - 16 q^{15} + 36 q^{16} - 6 q^{17} - 64 q^{18} - 4 q^{19} - 40 q^{20} - 32 q^{21} + 20 q^{22} - 8 q^{23} + 16 q^{24} + 36 q^{25} - 6 q^{27} - 24 q^{28} + 32 q^{30} + 34 q^{31} - 36 q^{32} - 40 q^{33} - 16 q^{34} - 30 q^{35} + 40 q^{36} - 2 q^{37} + 18 q^{38} + 4 q^{40} - 80 q^{41} + 16 q^{42} + 12 q^{43} - 108 q^{44} - 12 q^{45} - 48 q^{46} - 24 q^{47} + 46 q^{48} + 22 q^{49} + 44 q^{50} - 28 q^{51} + 10 q^{53} - 48 q^{54} + 6 q^{55} - 2 q^{56} - 66 q^{57} + 44 q^{58} - 64 q^{59} - 48 q^{60} - 6 q^{61} - 8 q^{62} + 52 q^{63} - 12 q^{64} + 4 q^{66} - 16 q^{67} - 58 q^{68} - 28 q^{69} - 72 q^{70} - 52 q^{71} - 152 q^{72} - 42 q^{73} - 8 q^{74} - 4 q^{75} + 48 q^{76} + 10 q^{77} + 8 q^{79} - 48 q^{80} + 58 q^{81} - 42 q^{82} - 44 q^{83} + 8 q^{84} - 96 q^{85} - 16 q^{86} + 20 q^{87} + 64 q^{88} - 74 q^{89} - 26 q^{90} + 24 q^{92} - 8 q^{94} - 32 q^{95} - 50 q^{96} - 40 q^{97} - 72 q^{98} - 74 q^{99}+O(q^{100}) \) 34 * q - 8 * q^2 + 32 * q^4 - 16 * q^5 - 12 * q^6 - 8 * q^7 - 24 * q^8 + 34 * q^9 + 8 * q^10 - 26 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 36 * q^16 - 6 * q^17 - 64 * q^18 - 4 * q^19 - 40 * q^20 - 32 * q^21 + 20 * q^22 - 8 * q^23 + 16 * q^24 + 36 * q^25 - 6 * q^27 - 24 * q^28 + 32 * q^30 + 34 * q^31 - 36 * q^32 - 40 * q^33 - 16 * q^34 - 30 * q^35 + 40 * q^36 - 2 * q^37 + 18 * q^38 + 4 * q^40 - 80 * q^41 + 16 * q^42 + 12 * q^43 - 108 * q^44 - 12 * q^45 - 48 * q^46 - 24 * q^47 + 46 * q^48 + 22 * q^49 + 44 * q^50 - 28 * q^51 + 10 * q^53 - 48 * q^54 + 6 * q^55 - 2 * q^56 - 66 * q^57 + 44 * q^58 - 64 * q^59 - 48 * q^60 - 6 * q^61 - 8 * q^62 + 52 * q^63 - 12 * q^64 + 4 * q^66 - 16 * q^67 - 58 * q^68 - 28 * q^69 - 72 * q^70 - 52 * q^71 - 152 * q^72 - 42 * q^73 - 8 * q^74 - 4 * q^75 + 48 * q^76 + 10 * q^77 + 8 * q^79 - 48 * q^80 + 58 * q^81 - 42 * q^82 - 44 * q^83 + 8 * q^84 - 96 * q^85 - 16 * q^86 + 20 * q^87 + 64 * q^88 - 74 * q^89 - 26 * q^90 + 24 * q^92 - 8 * q^94 - 32 * q^95 - 50 * q^96 - 40 * q^97 - 72 * q^98 - 74 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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