LMFDB - Embedded newform 4598.2.a.ca.1.4

Newspace parameters

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
Defining polynomial:	$ x^{8} - 2x^{7} - 10x^{6} + 16x^{5} + 26x^{4} - 32x^{3} - 16x^{2} + 20x - 4 $ x^8 - 2x^7 - 10x^6 + 16x^5 + 26x^4 - 32x^3 - 16x^2 + 20*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.488861$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

$f(q)$	$=$	$q+1.00000 q^{2} +0.158731 q^{3} +1.00000 q^{4} +3.07692 q^{5} +0.158731 q^{6} +1.35199 q^{7} +1.00000 q^{8} -2.97480 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.158731 q^{3} +1.00000 q^{4} +3.07692 q^{5} +0.158731 q^{6} +1.35199 q^{7} +1.00000 q^{8} -2.97480 q^{9} +3.07692 q^{10} +0.158731 q^{12} -0.526746 q^{13} +1.35199 q^{14} +0.488401 q^{15} +1.00000 q^{16} +7.23593 q^{17} -2.97480 q^{18} -1.00000 q^{19} +3.07692 q^{20} +0.214602 q^{21} +2.09183 q^{23} +0.158731 q^{24} +4.46742 q^{25} -0.526746 q^{26} -0.948385 q^{27} +1.35199 q^{28} -0.277873 q^{29} +0.488401 q^{30} -1.72447 q^{31} +1.00000 q^{32} +7.23593 q^{34} +4.15995 q^{35} -2.97480 q^{36} +8.91226 q^{37} -1.00000 q^{38} -0.0836108 q^{39} +3.07692 q^{40} -8.37354 q^{41} +0.214602 q^{42} +6.30119 q^{43} -9.15323 q^{45} +2.09183 q^{46} +1.96711 q^{47} +0.158731 q^{48} -5.17213 q^{49} +4.46742 q^{50} +1.14856 q^{51} -0.526746 q^{52} -2.20703 q^{53} -0.948385 q^{54} +1.35199 q^{56} -0.158731 q^{57} -0.277873 q^{58} +8.72295 q^{59} +0.488401 q^{60} +6.38710 q^{61} -1.72447 q^{62} -4.02190 q^{63} +1.00000 q^{64} -1.62075 q^{65} -1.02001 q^{67} +7.23593 q^{68} +0.332037 q^{69} +4.15995 q^{70} -3.71385 q^{71} -2.97480 q^{72} +1.72161 q^{73} +8.91226 q^{74} +0.709116 q^{75} -1.00000 q^{76} -0.0836108 q^{78} +7.53423 q^{79} +3.07692 q^{80} +8.77388 q^{81} -8.37354 q^{82} +6.49693 q^{83} +0.214602 q^{84} +22.2643 q^{85} +6.30119 q^{86} -0.0441070 q^{87} -10.3518 q^{89} -9.15323 q^{90} -0.712155 q^{91} +2.09183 q^{92} -0.273726 q^{93} +1.96711 q^{94} -3.07692 q^{95} +0.158731 q^{96} -10.4421 q^{97} -5.17213 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9	$ 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9} + 2 q^{10} + 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} - 8 q^{19} + 2 q^{20} + 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} + 8 q^{28} + 14 q^{29} + 10 q^{30} - 2 q^{31} + 8 q^{32} + 4 q^{34} + 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} - 4 q^{39} + 2 q^{40} + 8 q^{41} + 14 q^{42} + 28 q^{43} - 28 q^{45} + 12 q^{46} + 6 q^{47} + 32 q^{49} - 12 q^{51} + 18 q^{52} - 24 q^{53} - 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} - 24 q^{61} - 2 q^{62} + 30 q^{63} + 8 q^{64} - 16 q^{65} - 22 q^{67} + 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} + 20 q^{72} + 16 q^{73} - 22 q^{74} + 6 q^{75} - 8 q^{76} - 4 q^{78} + 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} + 12 q^{83} + 14 q^{84} + 48 q^{85} + 28 q^{86} + 42 q^{87} - 28 q^{89} - 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} + 6 q^{94} - 2 q^{95} - 22 q^{97} + 32 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9 + 2 * q^10 + 18 * q^13 + 8 * q^14 + 10 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 - 8 * q^19 + 2 * q^20 + 14 * q^21 + 12 * q^23 + 18 * q^26 - 24 * q^27 + 8 * q^28 + 14 * q^29 + 10 * q^30 - 2 * q^31 + 8 * q^32 + 4 * q^34 + 40 * q^35 + 20 * q^36 - 22 * q^37 - 8 * q^38 - 4 * q^39 + 2 * q^40 + 8 * q^41 + 14 * q^42 + 28 * q^43 - 28 * q^45 + 12 * q^46 + 6 * q^47 + 32 * q^49 - 12 * q^51 + 18 * q^52 - 24 * q^53 - 24 * q^54 + 8 * q^56 + 14 * q^58 + 46 * q^59 + 10 * q^60 - 24 * q^61 - 2 * q^62 + 30 * q^63 + 8 * q^64 - 16 * q^65 - 22 * q^67 + 4 * q^68 - 38 * q^69 + 40 * q^70 + 8 * q^71 + 20 * q^72 + 16 * q^73 - 22 * q^74 + 6 * q^75 - 8 * q^76 - 4 * q^78 + 4 * q^79 + 2 * q^80 + 28 * q^81 + 8 * q^82 + 12 * q^83 + 14 * q^84 + 48 * q^85 + 28 * q^86 + 42 * q^87 - 28 * q^89 - 28 * q^90 - 12 * q^91 + 12 * q^92 + 22 * q^93 + 6 * q^94 - 2 * q^95 - 22 * q^97 + 32 * q^98

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.158731	0.0916432	0.0458216	−	0.998950i	$-0.485409\pi$
$3$	0.158731	0.0916432	0.0458216	+	0.998950i	$0.485409\pi$
$4$	1.00000	0.500000
$5$	3.07692	1.37604	0.688019	−	0.725692i	$-0.258480\pi$
$5$	3.07692	1.37604	0.688019	+	0.725692i	$0.258480\pi$
$6$	0.158731	0.0648015
$7$	1.35199	0.511003	0.255502	−	0.966809i	$-0.417759\pi$
$7$	1.35199	0.511003	0.255502	+	0.966809i	$0.417759\pi$
$8$	1.00000	0.353553
$9$	−2.97480	−0.991602
$10$	3.07692	0.973007
$11$	0	0
$11$	0	0
$12$	0.158731	0.0458216
$13$	−0.526746	−0.146093	−0.0730466	−	0.997329i	$-0.523272\pi$
$13$	−0.526746	−0.146093	−0.0730466	+	0.997329i	$0.523272\pi$
$14$	1.35199	0.361334
$15$	0.488401	0.126105
$16$	1.00000	0.250000
$17$	7.23593	1.75497	0.877485	−	0.479604i	$-0.159220\pi$
$17$	7.23593	1.75497	0.877485	+	0.479604i	$0.159220\pi$
$18$	−2.97480	−0.701168
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.07692	0.688019
$21$	0.214602	0.0468300
$22$	0	0
$23$	2.09183	0.436176	0.218088	−	0.975929i	$-0.430018\pi$
$23$	2.09183	0.436176	0.218088	+	0.975929i	$0.430018\pi$
$24$	0.158731	0.0324008
$25$	4.46742	0.893483
$26$	−0.526746	−0.103303
$27$	−0.948385	−0.182517
$28$	1.35199	0.255502
$29$	−0.277873	−0.0515998	−0.0257999	−	0.999667i	$-0.508213\pi$
$29$	−0.277873	−0.0515998	−0.0257999	+	0.999667i	$0.508213\pi$
$30$	0.488401	0.0891694
$31$	−1.72447	−0.309724	−0.154862	−	0.987936i	$-0.549493\pi$
$31$	−1.72447	−0.309724	−0.154862	+	0.987936i	$0.549493\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	7.23593	1.24095
$35$	4.15995	0.703161
$36$	−2.97480	−0.495801
$37$	8.91226	1.46517	0.732584	−	0.680677i	$-0.238314\pi$
$37$	8.91226	1.46517	0.732584	+	0.680677i	$0.238314\pi$
$38$	−1.00000	−0.162221
$39$	−0.0836108	−0.0133884
$40$	3.07692	0.486503
$41$	−8.37354	−1.30773	−0.653864	−	0.756612i	$-0.726853\pi$
$41$	−8.37354	−1.30773	−0.653864	+	0.756612i	$0.726853\pi$
$42$	0.214602	0.0331138
$43$	6.30119	0.960923	0.480461	−	0.877016i	$-0.340469\pi$
$43$	6.30119	0.960923	0.480461	+	0.877016i	$0.340469\pi$
$44$	0	0
$45$	−9.15323	−1.36448
$46$	2.09183	0.308423
$47$	1.96711	0.286933	0.143466	−	0.989655i	$-0.454175\pi$
$47$	1.96711	0.286933	0.143466	+	0.989655i	$0.454175\pi$
$48$	0.158731	0.0229108
$49$	−5.17213	−0.738875
$50$	4.46742	0.631788
$51$	1.14856	0.160831
$52$	−0.526746	−0.0730466
$53$	−2.20703	−0.303158	−0.151579	−	0.988445i	$-0.548436\pi$
$53$	−2.20703	−0.303158	−0.151579	+	0.988445i	$0.548436\pi$
$54$	−0.948385	−0.129059
$55$	0	0
$56$	1.35199	0.180667
$57$	−0.158731	−0.0210244
$58$	−0.277873	−0.0364866
$59$	8.72295	1.13563	0.567816	−	0.823156i	$-0.307789\pi$
$59$	8.72295	1.13563	0.567816	+	0.823156i	$0.307789\pi$
$60$	0.488401	0.0630523
$61$	6.38710	0.817785	0.408892	−	0.912583i	$-0.365915\pi$
$61$	6.38710	0.817785	0.408892	+	0.912583i	$0.365915\pi$
$62$	−1.72447	−0.219008
$63$	−4.02190	−0.506712
$64$	1.00000	0.125000
$65$	−1.62075	−0.201030
$66$	0	0
$67$	−1.02001	−0.124614	−0.0623071	−	0.998057i	$-0.519846\pi$
$67$	−1.02001	−0.124614	−0.0623071	+	0.998057i	$0.519846\pi$
$68$	7.23593	0.877485
$69$	0.332037	0.0399726
$70$	4.15995	0.497210
$71$	−3.71385	−0.440753	−0.220376	−	0.975415i	$-0.570729\pi$
$71$	−3.71385	−0.440753	−0.220376	+	0.975415i	$0.570729\pi$
$72$	−2.97480	−0.350584
$73$	1.72161	0.201499	0.100750	−	0.994912i	$-0.467876\pi$
$73$	1.72161	0.201499	0.100750	+	0.994912i	$0.467876\pi$
$74$	8.91226	1.03603
$75$	0.709116	0.0818817
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−0.0836108	−0.00946706
$79$	7.53423	0.847667	0.423833	−	0.905740i	$-0.360684\pi$
$79$	7.53423	0.847667	0.423833	+	0.905740i	$0.360684\pi$
$80$	3.07692	0.344010
$81$	8.77388	0.974875
$82$	−8.37354	−0.924703
$83$	6.49693	0.713131	0.356565	−	0.934270i	$-0.383948\pi$
$83$	6.49693	0.713131	0.356565	+	0.934270i	$0.383948\pi$
$84$	0.214602	0.0234150
$85$	22.2643	2.41491
$86$	6.30119	0.679475
$87$	−0.0441070	−0.00472877
$88$	0	0
$89$	−10.3518	−1.09728	−0.548642	−	0.836057i	$-0.684855\pi$
$89$	−10.3518	−1.09728	−0.548642	+	0.836057i	$0.684855\pi$
$90$	−9.15323	−0.964835
$91$	−0.712155	−0.0746541
$92$	2.09183	0.218088
$93$	−0.273726	−0.0283841
$94$	1.96711	0.202892
$95$	−3.07692	−0.315685
$96$	0.158731	0.0162004
$97$	−10.4421	−1.06023	−0.530116	−	0.847925i	$-0.677852\pi$
$97$	−10.4421	−1.06023	−0.530116	+	0.847925i	$0.677852\pi$
$98$	−5.17213	−0.522464
$99$	0	0
$100$	4.46742	0.446742
$101$	16.6075	1.65251	0.826254	−	0.563298i	$-0.190468\pi$
$101$	16.6075	1.65251	0.826254	+	0.563298i	$0.190468\pi$
$102$	1.14856	0.113725
$103$	−6.30847	−0.621592	−0.310796	−	0.950477i	$-0.600596\pi$
$103$	−6.30847	−0.621592	−0.310796	+	0.950477i	$0.600596\pi$
$104$	−0.526746	−0.0516517
$105$	0.660313	0.0644399
$106$	−2.20703	−0.214365
$107$	13.1999	1.27608	0.638041	−	0.770002i	$-0.279745\pi$
$107$	13.1999	1.27608	0.638041	+	0.770002i	$0.279745\pi$
$108$	−0.948385	−0.0912584
$109$	4.47355	0.428488	0.214244	−	0.976780i	$-0.431271\pi$
$109$	4.47355	0.428488	0.214244	+	0.976780i	$0.431271\pi$
$110$	0	0
$111$	1.41465	0.134273
$112$	1.35199	0.127751
$113$	−12.5601	−1.18156	−0.590778	−	0.806834i	$-0.701179\pi$
$113$	−12.5601	−1.18156	−0.590778	+	0.806834i	$0.701179\pi$
$114$	−0.158731	−0.0148665
$115$	6.43637	0.600195
$116$	−0.277873	−0.0257999
$117$	1.56697	0.144866
$118$	8.72295	0.803012
$119$	9.78288	0.896796
$120$	0.488401	0.0445847
$121$	0	0
$122$	6.38710	0.578261
$123$	−1.32914	−0.119844
$124$	−1.72447	−0.154862
$125$	−1.63872	−0.146571
$126$	−4.02190	−0.358299
$127$	−16.4582	−1.46042	−0.730212	−	0.683220i	$-0.760579\pi$
$127$	−16.4582	−1.46042	−0.730212	+	0.683220i	$0.760579\pi$
$128$	1.00000	0.0883883
$129$	1.00019	0.0880621
$130$	−1.62075	−0.142150
$131$	15.1571	1.32428	0.662140	−	0.749380i	$-0.269648\pi$
$131$	15.1571	1.32428	0.662140	+	0.749380i	$0.269648\pi$
$132$	0	0
$133$	−1.35199	−0.117232
$134$	−1.02001	−0.0881156
$135$	−2.91810	−0.251150
$136$	7.23593	0.620475
$137$	−5.46038	−0.466512	−0.233256	−	0.972415i	$-0.574938\pi$
$137$	−5.46038	−0.466512	−0.233256	+	0.972415i	$0.574938\pi$
$138$	0.332037	0.0282649
$139$	−9.22943	−0.782830	−0.391415	−	0.920214i	$-0.628014\pi$
$139$	−9.22943	−0.782830	−0.391415	+	0.920214i	$0.628014\pi$
$140$	4.15995	0.351580
$141$	0.312241	0.0262954
$142$	−3.71385	−0.311659
$143$	0	0
$144$	−2.97480	−0.247900
$145$	−0.854993	−0.0710033
$146$	1.72161	0.142481
$147$	−0.820976	−0.0677129
$148$	8.91226	0.732584
$149$	−12.3302	−1.01013	−0.505065	−	0.863081i	$-0.668531\pi$
$149$	−12.3302	−1.01013	−0.505065	+	0.863081i	$0.668531\pi$
$150$	0.709116	0.0578991
$151$	3.63459	0.295779	0.147889	−	0.989004i	$-0.452752\pi$
$151$	3.63459	0.295779	0.147889	+	0.989004i	$0.452752\pi$
$152$	−1.00000	−0.0811107
$153$	−21.5255	−1.74023
$154$	0	0
$155$	−5.30605	−0.426192
$156$	−0.0836108	−0.00669422
$157$	−0.871549	−0.0695572	−0.0347786	−	0.999395i	$-0.511073\pi$
$157$	−0.871549	−0.0695572	−0.0347786	+	0.999395i	$0.511073\pi$
$158$	7.53423	0.599391
$159$	−0.350323	−0.0277824
$160$	3.07692	0.243252
$161$	2.82812	0.222887
$162$	8.77388	0.689341
$163$	−7.73571	−0.605908	−0.302954	−	0.953005i	$-0.597973\pi$
$163$	−7.73571	−0.605908	−0.302954	+	0.953005i	$0.597973\pi$
$164$	−8.37354	−0.653864
$165$	0	0
$166$	6.49693	0.504259
$167$	21.8284	1.68913	0.844566	−	0.535451i	$-0.179858\pi$
$167$	21.8284	1.68913	0.844566	+	0.535451i	$0.179858\pi$
$168$	0.214602	0.0165569
$169$	−12.7225	−0.978657
$170$	22.2643	1.70760
$171$	2.97480	0.227489
$172$	6.30119	0.480461
$173$	−11.0102	−0.837086	−0.418543	−	0.908197i	$-0.637459\pi$
$173$	−11.0102	−0.837086	−0.418543	+	0.908197i	$0.637459\pi$
$174$	−0.0441070	−0.00334375
$175$	6.03989	0.456573
$176$	0	0
$177$	1.38460	0.104073
$178$	−10.3518	−0.775897
$179$	−12.5527	−0.938233	−0.469116	−	0.883136i	$-0.655428\pi$
$179$	−12.5527	−0.938233	−0.469116	+	0.883136i	$0.655428\pi$
$180$	−9.15323	−0.682241
$181$	−3.45298	−0.256658	−0.128329	−	0.991732i	$-0.540961\pi$
$181$	−3.45298	−0.256658	−0.128329	+	0.991732i	$0.540961\pi$
$182$	−0.712155	−0.0527884
$183$	1.01383	0.0749444
$184$	2.09183	0.154211
$185$	27.4223	2.01613
$186$	−0.273726	−0.0200706
$187$	0	0
$188$	1.96711	0.143466
$189$	−1.28221	−0.0932667
$190$	−3.07692	−0.223223
$191$	21.3218	1.54279	0.771397	−	0.636354i	$-0.219558\pi$
$191$	21.3218	1.54279	0.771397	+	0.636354i	$0.219558\pi$
$192$	0.158731	0.0114554
$193$	23.4522	1.68813	0.844063	−	0.536243i	$-0.180157\pi$
$193$	23.4522	1.68813	0.844063	+	0.536243i	$0.180157\pi$
$194$	−10.4421	−0.749697
$195$	−0.257263	−0.0184230
$196$	−5.17213	−0.369438
$197$	−7.79605	−0.555445	−0.277723	−	0.960661i	$-0.589580\pi$
$197$	−7.79605	−0.555445	−0.277723	+	0.960661i	$0.589580\pi$
$198$	0	0
$199$	−9.48281	−0.672219	−0.336109	−	0.941823i	$-0.609111\pi$
$199$	−9.48281	−0.672219	−0.336109	+	0.941823i	$0.609111\pi$
$200$	4.46742	0.315894
$201$	−0.161907	−0.0114200
$202$	16.6075	1.16850
$203$	−0.375681	−0.0263677
$204$	1.14856	0.0804155
$205$	−25.7647	−1.79948
$206$	−6.30847	−0.439532
$207$	−6.22277	−0.432513
$208$	−0.526746	−0.0365233
$209$	0	0
$210$	0.660313	0.0455659
$211$	15.5951	1.07361	0.536805	−	0.843707i	$-0.319631\pi$
$211$	15.5951	1.07361	0.536805	+	0.843707i	$0.319631\pi$
$212$	−2.20703	−0.151579
$213$	−0.589502	−0.0403920
$214$	13.1999	0.902327
$215$	19.3882	1.32227
$216$	−0.948385	−0.0645294
$217$	−2.33146	−0.158270
$218$	4.47355	0.302987
$219$	0.273272	0.0184660
$220$	0	0
$221$	−3.81150	−0.256389
$222$	1.41465	0.0949451
$223$	−24.4375	−1.63646	−0.818230	−	0.574892i	$-0.805044\pi$
$223$	−24.4375	−1.63646	−0.818230	+	0.574892i	$0.805044\pi$
$224$	1.35199	0.0903335
$225$	−13.2897	−0.885979
$226$	−12.5601	−0.835486
$227$	−23.2524	−1.54332	−0.771659	−	0.636037i	$-0.780573\pi$
$227$	−23.2524	−1.54332	−0.771659	+	0.636037i	$0.780573\pi$
$228$	−0.158731	−0.0105122
$229$	−1.94364	−0.128439	−0.0642197	−	0.997936i	$-0.520456\pi$
$229$	−1.94364	−0.128439	−0.0642197	+	0.997936i	$0.520456\pi$
$230$	6.43637	0.424402
$231$	0	0
$232$	−0.277873	−0.0182433
$233$	5.46260	0.357867	0.178933	−	0.983861i	$-0.442735\pi$
$233$	5.46260	0.357867	0.178933	+	0.983861i	$0.442735\pi$
$234$	1.56697	0.102436
$235$	6.05264	0.394831
$236$	8.72295	0.567816
$237$	1.19591	0.0776829
$238$	9.78288	0.634130
$239$	−16.1582	−1.04519	−0.522595	−	0.852581i	$-0.675036\pi$
$239$	−16.1582	−1.04519	−0.522595	+	0.852581i	$0.675036\pi$
$240$	0.488401	0.0315262
$241$	−17.9215	−1.15442	−0.577212	−	0.816594i	$-0.695859\pi$
$241$	−17.9215	−1.15442	−0.577212	+	0.816594i	$0.695859\pi$
$242$	0	0
$243$	4.23784	0.271857
$244$	6.38710	0.408892
$245$	−15.9142	−1.01672
$246$	−1.32914	−0.0847428
$247$	0.526746	0.0335161
$248$	−1.72447	−0.109504
$249$	1.03126	0.0653536
$250$	−1.63872	−0.103641
$251$	26.9550	1.70139	0.850693	−	0.525663i	$-0.176183\pi$
$251$	26.9550	1.70139	0.850693	+	0.525663i	$0.176183\pi$
$252$	−4.02190	−0.253356
$253$	0	0
$254$	−16.4582	−1.03268
$255$	3.53403	0.221310
$256$	1.00000	0.0625000
$257$	−22.2307	−1.38671	−0.693357	−	0.720594i	$-0.743869\pi$
$257$	−22.2307	−1.38671	−0.693357	+	0.720594i	$0.743869\pi$
$258$	1.00019	0.0622693
$259$	12.0493	0.748706
$260$	−1.62075	−0.100515
$261$	0.826619	0.0511664
$262$	15.1571	0.936407
$263$	−0.840832	−0.0518479	−0.0259240	−	0.999664i	$-0.508253\pi$
$263$	−0.840832	−0.0518479	−0.0259240	+	0.999664i	$0.508253\pi$
$264$	0	0
$265$	−6.79084	−0.417158
$266$	−1.35199	−0.0828957
$267$	−1.64314	−0.100559
$268$	−1.02001	−0.0623071
$269$	26.6280	1.62354	0.811770	−	0.583978i	$-0.198504\pi$
$269$	26.6280	1.62354	0.811770	+	0.583978i	$0.198504\pi$
$270$	−2.91810	−0.177590
$271$	−25.3809	−1.54178	−0.770889	−	0.636970i	$-0.780188\pi$
$271$	−25.3809	−1.54178	−0.770889	+	0.636970i	$0.780188\pi$
$272$	7.23593	0.438742
$273$	−0.113041	−0.00684154
$274$	−5.46038	−0.329874
$275$	0	0
$276$	0.332037	0.0199863
$277$	−30.1812	−1.81341	−0.906706	−	0.421763i	$-0.861411\pi$
$277$	−30.1812	−1.81341	−0.906706	+	0.421763i	$0.861411\pi$
$278$	−9.22943	−0.553544
$279$	5.12996	0.307123
$280$	4.15995	0.248605
$281$	16.8269	1.00381	0.501904	−	0.864923i	$-0.332633\pi$
$281$	16.8269	1.00381	0.501904	+	0.864923i	$0.332633\pi$
$282$	0.312241	0.0185937
$283$	−10.4403	−0.620611	−0.310305	−	0.950637i	$-0.600431\pi$
$283$	−10.4403	−0.620611	−0.310305	+	0.950637i	$0.600431\pi$
$284$	−3.71385	−0.220376
$285$	−0.488401	−0.0289304
$286$	0	0
$287$	−11.3209	−0.668253
$288$	−2.97480	−0.175292
$289$	35.3586	2.07992
$290$	−0.854993	−0.0502069
$291$	−1.65748	−0.0971631
$292$	1.72161	0.100750
$293$	13.4022	0.782965	0.391482	−	0.920186i	$-0.371962\pi$
$293$	13.4022	0.782965	0.391482	+	0.920186i	$0.371962\pi$
$294$	−0.820976	−0.0478803
$295$	26.8398	1.56267
$296$	8.91226	0.518015
$297$	0	0
$298$	−12.3302	−0.714270
$299$	−1.10186	−0.0637223
$300$	0.709116	0.0409408
$301$	8.51914	0.491035
$302$	3.63459	0.209147
$303$	2.63612	0.151441
$304$	−1.00000	−0.0573539
$305$	19.6526	1.12530
$306$	−21.5255	−1.23053
$307$	−18.9800	−1.08325	−0.541623	−	0.840622i	$-0.682190\pi$
$307$	−18.9800	−1.08325	−0.541623	+	0.840622i	$0.682190\pi$
$308$	0	0
$309$	−1.00135	−0.0569646
$310$	−5.30605	−0.301363
$311$	12.4757	0.707430	0.353715	−	0.935353i	$-0.384918\pi$
$311$	12.4757	0.707430	0.353715	+	0.935353i	$0.384918\pi$
$312$	−0.0836108	−0.00473353
$313$	−18.2742	−1.03292	−0.516459	−	0.856312i	$-0.672750\pi$
$313$	−18.2742	−1.03292	−0.516459	+	0.856312i	$0.672750\pi$
$314$	−0.871549	−0.0491844
$315$	−12.3751	−0.697255
$316$	7.53423	0.423833
$317$	−13.1830	−0.740432	−0.370216	−	0.928946i	$-0.620716\pi$
$317$	−13.1830	−0.740432	−0.370216	+	0.928946i	$0.620716\pi$
$318$	−0.350323	−0.0196451
$319$	0	0
$320$	3.07692	0.172005
$321$	2.09523	0.116944
$322$	2.82812	0.157605
$323$	−7.23593	−0.402618
$324$	8.77388	0.487438
$325$	−2.35319	−0.130532
$326$	−7.73571	−0.428441
$327$	0.710090	0.0392681
$328$	−8.37354	−0.462352
$329$	2.65951	0.146624
$330$	0	0
$331$	3.69222	0.202943	0.101471	−	0.994838i	$-0.467645\pi$
$331$	3.69222	0.202943	0.101471	+	0.994838i	$0.467645\pi$
$332$	6.49693	0.356565
$333$	−26.5122	−1.45286
$334$	21.8284	1.19440
$335$	−3.13849	−0.171474
$336$	0.214602	0.0117075
$337$	26.2983	1.43256	0.716279	−	0.697814i	$-0.245844\pi$
$337$	26.2983	1.43256	0.716279	+	0.697814i	$0.245844\pi$
$338$	−12.7225	−0.692015
$339$	−1.99368	−0.108282
$340$	22.2643	1.20745
$341$	0	0
$342$	2.97480	0.160859
$343$	−16.4566	−0.888571
$344$	6.30119	0.339738
$345$	1.02165	0.0550038
$346$	−11.0102	−0.591909
$347$	−5.33343	−0.286313	−0.143157	−	0.989700i	$-0.545725\pi$
$347$	−5.33343	−0.286313	−0.143157	+	0.989700i	$0.545725\pi$
$348$	−0.0441070	−0.00236439
$349$	19.4450	1.04087	0.520433	−	0.853903i	$-0.325771\pi$
$349$	19.4450	1.04087	0.520433	+	0.853903i	$0.325771\pi$
$350$	6.03989	0.322846
$351$	0.499558	0.0266644
$352$	0	0
$353$	−27.8728	−1.48352	−0.741761	−	0.670665i	$-0.766009\pi$
$353$	−27.8728	−1.48352	−0.741761	+	0.670665i	$0.766009\pi$
$354$	1.38460	0.0735906
$355$	−11.4272	−0.606493
$356$	−10.3518	−0.548642
$357$	1.55284	0.0821852
$358$	−12.5527	−0.663431
$359$	35.7338	1.88596	0.942978	−	0.332856i	$-0.108012\pi$
$359$	35.7338	1.88596	0.942978	+	0.332856i	$0.108012\pi$
$360$	−9.15323	−0.482417
$361$	1.00000	0.0526316
$362$	−3.45298	−0.181485
$363$	0	0
$364$	−0.712155	−0.0373270
$365$	5.29725	0.277271
$366$	1.01383	0.0529937
$367$	37.8147	1.97391	0.986956	−	0.160991i	$-0.0514691\pi$
$367$	37.8147	1.97391	0.986956	+	0.160991i	$0.0514691\pi$
$368$	2.09183	0.109044
$369$	24.9097	1.29675
$370$	27.4223	1.42562
$371$	−2.98387	−0.154915
$372$	−0.273726	−0.0141920
$373$	−20.1806	−1.04491	−0.522456	−	0.852667i	$-0.674984\pi$
$373$	−20.1806	−1.04491	−0.522456	+	0.852667i	$0.674984\pi$
$374$	0	0
$375$	−0.260114	−0.0134322
$376$	1.96711	0.101446
$377$	0.146369	0.00753837
$378$	−1.28221	−0.0659495
$379$	−32.7152	−1.68047	−0.840233	−	0.542225i	$-0.817582\pi$
$379$	−32.7152	−1.68047	−0.840233	+	0.542225i	$0.817582\pi$
$380$	−3.07692	−0.157842
$381$	−2.61241	−0.133838
$382$	21.3218	1.09092
$383$	−25.6817	−1.31227	−0.656136	−	0.754643i	$-0.727810\pi$
$383$	−25.6817	−1.31227	−0.656136	+	0.754643i	$0.727810\pi$
$384$	0.158731	0.00810019
$385$	0	0
$386$	23.4522	1.19369
$387$	−18.7448	−0.952853
$388$	−10.4421	−0.530116
$389$	−4.46845	−0.226559	−0.113280	−	0.993563i	$-0.536136\pi$
$389$	−4.46845	−0.226559	−0.113280	+	0.993563i	$0.536136\pi$
$390$	−0.257263	−0.0130270
$391$	15.1363	0.765475
$392$	−5.17213	−0.261232
$393$	2.40589	0.121361
$394$	−7.79605	−0.392759
$395$	23.1822	1.16642
$396$	0	0
$397$	28.8810	1.44950	0.724748	−	0.689014i	$-0.241956\pi$
$397$	28.8810	1.44950	0.724748	+	0.689014i	$0.241956\pi$
$398$	−9.48281	−0.475330
$399$	−0.214602	−0.0107435
$400$	4.46742	0.223371
$401$	0.797439	0.0398222	0.0199111	−	0.999802i	$-0.493662\pi$
$401$	0.797439	0.0398222	0.0199111	+	0.999802i	$0.493662\pi$
$402$	−0.161907	−0.00807519
$403$	0.908358	0.0452485
$404$	16.6075	0.826254
$405$	26.9965	1.34147
$406$	−0.375681	−0.0186448
$407$	0	0
$408$	1.14856	0.0568624
$409$	22.7240	1.12363	0.561814	−	0.827263i	$-0.310103\pi$
$409$	22.7240	1.12363	0.561814	+	0.827263i	$0.310103\pi$
$410$	−25.7647	−1.27243
$411$	−0.866730	−0.0427527
$412$	−6.30847	−0.310796
$413$	11.7933	0.580311
$414$	−6.22277	−0.305833
$415$	19.9905	0.981296
$416$	−0.526746	−0.0258259
$417$	−1.46499	−0.0717410
$418$	0	0
$419$	−0.427754	−0.0208971	−0.0104486	−	0.999945i	$-0.503326\pi$
$419$	−0.427754	−0.0208971	−0.0104486	+	0.999945i	$0.503326\pi$
$420$	0.660313	0.0322200
$421$	−9.69726	−0.472615	−0.236308	−	0.971678i	$-0.575937\pi$
$421$	−9.69726	−0.472615	−0.236308	+	0.971678i	$0.575937\pi$
$422$	15.5951	0.759156
$423$	−5.85177	−0.284523
$424$	−2.20703	−0.107183
$425$	32.3259	1.56804
$426$	−0.589502	−0.0285615
$427$	8.63529	0.417891
$428$	13.1999	0.638041
$429$	0	0
$430$	19.3882	0.934984
$431$	−6.70352	−0.322897	−0.161449	−	0.986881i	$-0.551617\pi$
$431$	−6.70352	−0.322897	−0.161449	+	0.986881i	$0.551617\pi$
$432$	−0.948385	−0.0456292
$433$	−15.3773	−0.738988	−0.369494	−	0.929233i	$-0.620469\pi$
$433$	−15.3773	−0.738988	−0.369494	+	0.929233i	$0.620469\pi$
$434$	−2.33146	−0.111914
$435$	−0.135714	−0.00650697
$436$	4.47355	0.214244
$437$	−2.09183	−0.100066
$438$	0.273272	0.0130575
$439$	−2.15073	−0.102649	−0.0513244	−	0.998682i	$-0.516344\pi$
$439$	−2.15073	−0.102649	−0.0513244	+	0.998682i	$0.516344\pi$
$440$	0	0
$441$	15.3861	0.732670
$442$	−3.81150	−0.181294
$443$	30.3841	1.44359	0.721797	−	0.692105i	$-0.243317\pi$
$443$	30.3841	1.44359	0.721797	+	0.692105i	$0.243317\pi$
$444$	1.41465	0.0671363
$445$	−31.8515	−1.50991
$446$	−24.4375	−1.15715
$447$	−1.95718	−0.0925715
$448$	1.35199	0.0638754
$449$	3.34155	0.157698	0.0788488	−	0.996887i	$-0.474876\pi$
$449$	3.34155	0.157698	0.0788488	+	0.996887i	$0.474876\pi$
$450$	−13.2897	−0.626482
$451$	0	0
$452$	−12.5601	−0.590778
$453$	0.576921	0.0271061
$454$	−23.2524	−1.09129
$455$	−2.19124	−0.102727
$456$	−0.158731	−0.00743325
$457$	29.3880	1.37471	0.687356	−	0.726321i	$-0.258771\pi$
$457$	29.3880	1.37471	0.687356	+	0.726321i	$0.258771\pi$
$458$	−1.94364	−0.0908204
$459$	−6.86244	−0.320311
$460$	6.43637	0.300097
$461$	−1.74308	−0.0811833	−0.0405917	−	0.999176i	$-0.512924\pi$
$461$	−1.74308	−0.0811833	−0.0405917	+	0.999176i	$0.512924\pi$
$462$	0	0
$463$	−31.2015	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$463$	−31.2015	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$464$	−0.277873	−0.0128999
$465$	−0.842233	−0.0390576
$466$	5.46260	0.253050
$467$	26.0733	1.20653	0.603264	−	0.797542i	$-0.293867\pi$
$467$	26.0733	1.20653	0.603264	+	0.797542i	$0.293867\pi$
$468$	1.56697	0.0724331
$469$	−1.37904	−0.0636783
$470$	6.05264	0.279187
$471$	−0.138342	−0.00637444
$472$	8.72295	0.401506
$473$	0	0
$474$	1.19591	0.0549301
$475$	−4.46742	−0.204979
$476$	9.78288	0.448398
$477$	6.56547	0.300612
$478$	−16.1582	−0.739061
$479$	−29.3946	−1.34307	−0.671536	−	0.740972i	$-0.734365\pi$
$479$	−29.3946	−1.34307	−0.671536	+	0.740972i	$0.734365\pi$
$480$	0.488401	0.0222924
$481$	−4.69450	−0.214051
$482$	−17.9215	−0.816301
$483$	0.448910	0.0204261
$484$	0	0
$485$	−32.1294	−1.45892
$486$	4.23784	0.192232
$487$	43.0919	1.95268	0.976340	−	0.216242i	$-0.0693801\pi$
$487$	43.0919	1.95268	0.976340	+	0.216242i	$0.0693801\pi$
$488$	6.38710	0.289131
$489$	−1.22790	−0.0555273
$490$	−15.9142	−0.718931
$491$	−29.5401	−1.33313	−0.666563	−	0.745449i	$-0.732235\pi$
$491$	−29.5401	−1.33313	−0.666563	+	0.745449i	$0.732235\pi$
$492$	−1.32914	−0.0599222
$493$	−2.01067	−0.0905561
$494$	0.526746	0.0236994
$495$	0	0
$496$	−1.72447	−0.0774309
$497$	−5.02108	−0.225226
$498$	1.03126	0.0462120
$499$	−27.8915	−1.24859	−0.624297	−	0.781187i	$-0.714615\pi$
$499$	−27.8915	−1.24859	−0.624297	+	0.781187i	$0.714615\pi$
$500$	−1.63872	−0.0732856
$501$	3.46484	0.154798
$502$	26.9550	1.20306
$503$	0.0484888	0.00216201	0.00108100	−	0.999999i	$-0.499656\pi$
$503$	0.0484888	0.00216201	0.00108100	+	0.999999i	$0.499656\pi$
$504$	−4.02190	−0.179150
$505$	51.0999	2.27392
$506$	0	0
$507$	−2.01946	−0.0896873
$508$	−16.4582	−0.730212
$509$	9.75291	0.432290	0.216145	−	0.976361i	$-0.430652\pi$
$509$	9.75291	0.432290	0.216145	+	0.976361i	$0.430652\pi$
$510$	3.53403	0.156490
$511$	2.32759	0.102967
$512$	1.00000	0.0441942
$513$	0.948385	0.0418722
$514$	−22.2307	−0.980555
$515$	−19.4106	−0.855334
$516$	1.00019	0.0440310
$517$	0	0
$518$	12.0493	0.529415
$519$	−1.74765	−0.0767133
$520$	−1.62075	−0.0710748
$521$	−40.4077	−1.77029	−0.885147	−	0.465312i	$-0.845942\pi$
$521$	−40.4077	−1.77029	−0.885147	+	0.465312i	$0.845942\pi$
$522$	0.826619	0.0361801
$523$	22.7718	0.995742	0.497871	−	0.867251i	$-0.334115\pi$
$523$	22.7718	0.995742	0.497871	+	0.867251i	$0.334115\pi$
$524$	15.1571	0.662140
$525$	0.958717	0.0418418
$526$	−0.840832	−0.0366620
$527$	−12.4781	−0.543556
$528$	0	0
$529$	−18.6243	−0.809751
$530$	−6.79084	−0.294975
$531$	−25.9491	−1.12609
$532$	−1.35199	−0.0586161
$533$	4.41073	0.191050
$534$	−1.64314	−0.0711057
$535$	40.6150	1.75594
$536$	−1.02001	−0.0440578
$537$	−1.99250	−0.0859827
$538$	26.6280	1.14802
$539$	0	0
$540$	−2.91810	−0.125575
$541$	−7.41552	−0.318818	−0.159409	−	0.987213i	$-0.550959\pi$
$541$	−7.41552	−0.318818	−0.159409	+	0.987213i	$0.550959\pi$
$542$	−25.3809	−1.09020
$543$	−0.548094	−0.0235210
$544$	7.23593	0.310238
$545$	13.7647	0.589617
$546$	−0.113041	−0.00483770
$547$	2.41910	0.103433	0.0517167	−	0.998662i	$-0.483531\pi$
$547$	2.41910	0.103433	0.0517167	+	0.998662i	$0.483531\pi$
$548$	−5.46038	−0.233256
$549$	−19.0004	−0.810917
$550$	0	0
$551$	0.277873	0.0118378
$552$	0.332037	0.0141324
$553$	10.1862	0.433161
$554$	−30.1812	−1.28228
$555$	4.35276	0.184764
$556$	−9.22943	−0.391415
$557$	0.412176	0.0174645	0.00873224	−	0.999962i	$-0.497220\pi$
$557$	0.412176	0.0174645	0.00873224	+	0.999962i	$0.497220\pi$
$558$	5.12996	0.217168
$559$	−3.31913	−0.140384
$560$	4.15995	0.175790
$561$	0	0
$562$	16.8269	0.709800
$563$	4.49045	0.189250	0.0946249	−	0.995513i	$-0.469835\pi$
$563$	4.49045	0.189250	0.0946249	+	0.995513i	$0.469835\pi$
$564$	0.312241	0.0131477
$565$	−38.6464	−1.62587
$566$	−10.4403	−0.438838
$567$	11.8622	0.498165
$568$	−3.71385	−0.155830
$569$	−32.6319	−1.36800	−0.684000	−	0.729482i	$-0.739761\pi$
$569$	−32.6319	−1.36800	−0.684000	+	0.729482i	$0.739761\pi$
$570$	−0.488401	−0.0204569
$571$	18.1484	0.759486	0.379743	−	0.925092i	$-0.376012\pi$
$571$	18.1484	0.759486	0.379743	+	0.925092i	$0.376012\pi$
$572$	0	0
$573$	3.38443	0.141387
$574$	−11.3209	−0.472527
$575$	9.34506	0.389716
$576$	−2.97480	−0.123950
$577$	−21.9198	−0.912532	−0.456266	−	0.889843i	$-0.650814\pi$
$577$	−21.9198	−0.912532	−0.456266	+	0.889843i	$0.650814\pi$
$578$	35.3586	1.47072
$579$	3.72259	0.154705
$580$	−0.854993	−0.0355017
$581$	8.78377	0.364412
$582$	−1.65748	−0.0687047
$583$	0	0
$584$	1.72161	0.0712407
$585$	4.82143	0.199341
$586$	13.4022	0.553640
$587$	16.9253	0.698581	0.349291	−	0.937014i	$-0.386423\pi$
$587$	16.9253	0.698581	0.349291	+	0.937014i	$0.386423\pi$
$588$	−0.820976	−0.0338565
$589$	1.72447	0.0710555
$590$	26.8398	1.10498
$591$	−1.23747	−0.0509028
$592$	8.91226	0.366292
$593$	9.83301	0.403793	0.201897	−	0.979407i	$-0.435290\pi$
$593$	9.83301	0.403793	0.201897	+	0.979407i	$0.435290\pi$
$594$	0	0
$595$	30.1011	1.23403
$596$	−12.3302	−0.505065
$597$	−1.50521	−0.0616043
$598$	−1.10186	−0.0450585
$599$	43.2136	1.76566	0.882829	−	0.469694i	$-0.155636\pi$
$599$	43.2136	1.76566	0.882829	+	0.469694i	$0.155636\pi$
$600$	0.709116	0.0289495
$601$	−6.60416	−0.269389	−0.134695	−	0.990887i	$-0.543005\pi$
$601$	−6.60416	−0.269389	−0.134695	+	0.990887i	$0.543005\pi$
$602$	8.51914	0.347214
$603$	3.03433	0.123568
$604$	3.63459	0.147889
$605$	0	0
$606$	2.63612	0.107085
$607$	19.6695	0.798359	0.399180	−	0.916873i	$-0.369295\pi$
$607$	19.6695	0.798359	0.399180	+	0.916873i	$0.369295\pi$
$608$	−1.00000	−0.0405554
$609$	−0.0596322	−0.00241642
$610$	19.6526	0.795710
$611$	−1.03617	−0.0419189
$612$	−21.5255	−0.870115
$613$	−1.55586	−0.0628407	−0.0314203	−	0.999506i	$-0.510003\pi$
$613$	−1.55586	−0.0628407	−0.0314203	+	0.999506i	$0.510003\pi$
$614$	−18.9800	−0.765970
$615$	−4.08965	−0.164911
$616$	0	0
$617$	−43.2521	−1.74126	−0.870632	−	0.491935i	$-0.836290\pi$
$617$	−43.2521	−1.74126	−0.870632	+	0.491935i	$0.836290\pi$
$618$	−1.00135	−0.0402801
$619$	3.26969	0.131420	0.0657100	−	0.997839i	$-0.479069\pi$
$619$	3.26969	0.131420	0.0657100	+	0.997839i	$0.479069\pi$
$620$	−5.30605	−0.213096
$621$	−1.98386	−0.0796094
$622$	12.4757	0.500228
$623$	−13.9955	−0.560716
$624$	−0.0836108	−0.00334711
$625$	−27.3793	−1.09517
$626$	−18.2742	−0.730383
$627$	0	0
$628$	−0.871549	−0.0347786
$629$	64.4885	2.57132
$630$	−12.3751	−0.493034
$631$	27.6628	1.10124	0.550620	−	0.834756i	$-0.314391\pi$
$631$	27.6628	1.10124	0.550620	+	0.834756i	$0.314391\pi$
$632$	7.53423	0.299695
$633$	2.47542	0.0983890
$634$	−13.1830	−0.523565
$635$	−50.6404	−2.00960
$636$	−0.350323	−0.0138912
$637$	2.72440	0.107945
$638$	0	0
$639$	11.0480	0.437051
$640$	3.07692	0.121626
$641$	−40.1504	−1.58585	−0.792924	−	0.609321i	$-0.791442\pi$
$641$	−40.1504	−1.58585	−0.792924	+	0.609321i	$0.791442\pi$
$642$	2.09523	0.0826921
$643$	−29.3892	−1.15900	−0.579499	−	0.814973i	$-0.696752\pi$
$643$	−29.3892	−1.15900	−0.579499	+	0.814973i	$0.696752\pi$
$644$	2.82812	0.111444
$645$	3.07751	0.121177
$646$	−7.23593	−0.284694
$647$	3.63135	0.142763	0.0713816	−	0.997449i	$-0.477259\pi$
$647$	3.63135	0.142763	0.0713816	+	0.997449i	$0.477259\pi$
$648$	8.77388	0.344670
$649$	0	0
$650$	−2.35319	−0.0922999
$651$	−0.370075	−0.0145044
$652$	−7.73571	−0.302954
$653$	−25.9076	−1.01384	−0.506921	−	0.861992i	$-0.669217\pi$
$653$	−25.9076	−1.01384	−0.506921	+	0.861992i	$0.669217\pi$
$654$	0.710090	0.0277667
$655$	46.6371	1.82226
$656$	−8.37354	−0.326932
$657$	−5.12145	−0.199807
$658$	2.65951	0.103679
$659$	−22.9664	−0.894644	−0.447322	−	0.894373i	$-0.647622\pi$
$659$	−22.9664	−0.894644	−0.447322	+	0.894373i	$0.647622\pi$
$660$	0	0
$661$	43.4685	1.69073	0.845365	−	0.534189i	$-0.179383\pi$
$661$	43.4685	1.69073	0.845365	+	0.534189i	$0.179383\pi$
$662$	3.69222	0.143502
$663$	−0.605002	−0.0234963
$664$	6.49693	0.252130
$665$	−4.15995	−0.161316
$666$	−26.5122	−1.02733
$667$	−0.581263	−0.0225066
$668$	21.8284	0.844566
$669$	−3.87899	−0.149970
$670$	−3.13849	−0.121250
$671$	0	0
$672$	0.214602	0.00827845
$673$	−29.2936	−1.12918	−0.564592	−	0.825370i	$-0.690967\pi$
$673$	−29.2936	−1.12918	−0.564592	+	0.825370i	$0.690967\pi$
$674$	26.2983	1.01297
$675$	−4.23683	−0.163076
$676$	−12.7225	−0.489328
$677$	−38.9988	−1.49884	−0.749422	−	0.662093i	$-0.769669\pi$
$677$	−38.9988	−1.49884	−0.749422	+	0.662093i	$0.769669\pi$
$678$	−1.99368	−0.0765667
$679$	−14.1176	−0.541782
$680$	22.2643	0.853798
$681$	−3.69087	−0.141435
$682$	0	0
$683$	−13.6716	−0.523130	−0.261565	−	0.965186i	$-0.584239\pi$
$683$	−13.6716	−0.523130	−0.261565	+	0.965186i	$0.584239\pi$
$684$	2.97480	0.113744
$685$	−16.8011	−0.641939
$686$	−16.4566	−0.628315
$687$	−0.308515	−0.0117706
$688$	6.30119	0.240231
$689$	1.16254	0.0442894
$690$	1.02165	0.0388936
$691$	8.06092	0.306652	0.153326	−	0.988176i	$-0.451002\pi$
$691$	8.06092	0.306652	0.153326	+	0.988176i	$0.451002\pi$
$692$	−11.0102	−0.418543
$693$	0	0
$694$	−5.33343	−0.202454
$695$	−28.3982	−1.07720
$696$	−0.0441070	−0.00167187
$697$	−60.5903	−2.29502
$698$	19.4450	0.736003
$699$	0.867082	0.0327961
$700$	6.03989	0.228287
$701$	−11.0066	−0.415713	−0.207857	−	0.978159i	$-0.566649\pi$
$701$	−11.0066	−0.415713	−0.207857	+	0.978159i	$0.566649\pi$
$702$	0.499558	0.0188546
$703$	−8.91226	−0.336132
$704$	0	0
$705$	0.960740	0.0361836
$706$	−27.8728	−1.04901
$707$	22.4531	0.844437
$708$	1.38460	0.0520364
$709$	3.81971	0.143452	0.0717260	−	0.997424i	$-0.477149\pi$
$709$	3.81971	0.143452	0.0717260	+	0.997424i	$0.477149\pi$
$710$	−11.4272	−0.428855
$711$	−22.4129	−0.840548
$712$	−10.3518	−0.387948
$713$	−3.60729	−0.135094
$714$	1.55284	0.0581137
$715$	0	0
$716$	−12.5527	−0.469116
$717$	−2.56481	−0.0957846
$718$	35.7338	1.33357
$719$	12.4943	0.465958	0.232979	−	0.972482i	$-0.425153\pi$
$719$	12.4943	0.465958	0.232979	+	0.972482i	$0.425153\pi$
$720$	−9.15323	−0.341121
$721$	−8.52897	−0.317635
$722$	1.00000	0.0372161
$723$	−2.84469	−0.105795
$724$	−3.45298	−0.128329
$725$	−1.24138	−0.0461036
$726$	0	0
$727$	21.9023	0.812311	0.406155	−	0.913804i	$-0.366869\pi$
$727$	21.9023	0.812311	0.406155	+	0.913804i	$0.366869\pi$
$728$	−0.712155	−0.0263942
$729$	−25.6490	−0.949961
$730$	5.29725	0.196060
$731$	45.5950	1.68639
$732$	1.01383	0.0374722
$733$	27.3319	1.00953	0.504764	−	0.863257i	$-0.331579\pi$
$733$	27.3319	1.00953	0.504764	+	0.863257i	$0.331579\pi$
$734$	37.8147	1.39577
$735$	−2.52607	−0.0931756
$736$	2.09183	0.0771057
$737$	0	0
$738$	24.9097	0.916937
$739$	−6.87044	−0.252733	−0.126367	−	0.991984i	$-0.540332\pi$
$739$	−6.87044	−0.252733	−0.126367	+	0.991984i	$0.540332\pi$
$740$	27.4223	1.00806
$741$	0.0836108	0.00307152
$742$	−2.98387	−0.109541
$743$	−38.5332	−1.41365	−0.706824	−	0.707390i	$-0.749873\pi$
$743$	−38.5332	−1.41365	−0.706824	+	0.707390i	$0.749873\pi$
$744$	−0.273726	−0.0100353
$745$	−37.9390	−1.38998
$746$	−20.1806	−0.738864
$747$	−19.3271	−0.707141
$748$	0	0
$749$	17.8461	0.652083
$750$	−0.260114	−0.00949803
$751$	19.0301	0.694418	0.347209	−	0.937788i	$-0.387130\pi$
$751$	19.0301	0.694418	0.347209	+	0.937788i	$0.387130\pi$
$752$	1.96711	0.0717332
$753$	4.27859	0.155920
$754$	0.146369	0.00533044
$755$	11.1833	0.407003
$756$	−1.28221	−0.0466333
$757$	−42.0004	−1.52653	−0.763266	−	0.646084i	$-0.776405\pi$
$757$	−42.0004	−1.52653	−0.763266	+	0.646084i	$0.776405\pi$
$758$	−32.7152	−1.18827
$759$	0	0
$760$	−3.07692	−0.111612
$761$	−21.9298	−0.794955	−0.397477	−	0.917612i	$-0.630114\pi$
$761$	−21.9298	−0.794955	−0.397477	+	0.917612i	$0.630114\pi$
$762$	−2.61241	−0.0946378
$763$	6.04819	0.218959
$764$	21.3218	0.771397
$765$	−66.2321	−2.39463
$766$	−25.6817	−0.927917
$767$	−4.59478	−0.165908
$768$	0.158731	0.00572770
$769$	−20.9969	−0.757167	−0.378584	−	0.925567i	$-0.623589\pi$
$769$	−20.9969	−0.757167	−0.378584	+	0.925567i	$0.623589\pi$
$770$	0	0
$771$	−3.52870	−0.127083
$772$	23.4522	0.844063
$773$	38.3380	1.37892	0.689460	−	0.724323i	$-0.257848\pi$
$773$	38.3380	1.37892	0.689460	+	0.724323i	$0.257848\pi$
$774$	−18.7448	−0.673769
$775$	−7.70392	−0.276733
$776$	−10.4421	−0.374849
$777$	1.91259	0.0686138
$778$	−4.46845	−0.160202
$779$	8.37354	0.300013
$780$	−0.257263	−0.00921151
$781$	0	0
$782$	15.1363	0.541273
$783$	0.263531	0.00941783
$784$	−5.17213	−0.184719
$785$	−2.68168	−0.0957134
$786$	2.40589	0.0858154
$787$	3.85555	0.137435	0.0687177	−	0.997636i	$-0.478109\pi$
$787$	3.85555	0.137435	0.0687177	+	0.997636i	$0.478109\pi$
$788$	−7.79605	−0.277723
$789$	−0.133466	−0.00475151
$790$	23.1822	0.824785
$791$	−16.9811	−0.603779
$792$	0	0
$793$	−3.36438	−0.119473
$794$	28.8810	1.02495
$795$	−1.07791	−0.0382297
$796$	−9.48281	−0.336109
$797$	7.72685	0.273699	0.136850	−	0.990592i	$-0.456302\pi$
$797$	7.72685	0.273699	0.136850	+	0.990592i	$0.456302\pi$
$798$	−0.214602	−0.00759683
$799$	14.2339	0.503558
$800$	4.46742	0.157947
$801$	30.7945	1.08807
$802$	0.797439	0.0281586
$803$	0	0
$804$	−0.161907	−0.00571002
$805$	8.70190	0.306702
$806$	0.908358	0.0319955
$807$	4.22669	0.148786
$808$	16.6075	0.584250
$809$	−45.8483	−1.61194	−0.805970	−	0.591957i	$-0.798356\pi$
$809$	−45.8483	−1.61194	−0.805970	+	0.591957i	$0.798356\pi$
$810$	26.9965	0.948560
$811$	−11.9071	−0.418115	−0.209058	−	0.977903i	$-0.567040\pi$
$811$	−11.9071	−0.418115	−0.209058	+	0.977903i	$0.567040\pi$
$812$	−0.375681	−0.0131838
$813$	−4.02872	−0.141293
$814$	0	0
$815$	−23.8021	−0.833753
$816$	1.14856	0.0402078
$817$	−6.30119	−0.220451
$818$	22.7240	0.794526
$819$	2.11852	0.0740271
$820$	−25.7647	−0.899742
$821$	−25.0389	−0.873865	−0.436932	−	0.899494i	$-0.643935\pi$
$821$	−25.0389	−0.873865	−0.436932	+	0.899494i	$0.643935\pi$
$822$	−0.866730	−0.0302307
$823$	−4.14621	−0.144528	−0.0722639	−	0.997386i	$-0.523022\pi$
$823$	−4.14621	−0.144528	−0.0722639	+	0.997386i	$0.523022\pi$
$824$	−6.30847	−0.219766
$825$	0	0
$826$	11.7933	0.410342
$827$	−47.6070	−1.65546	−0.827729	−	0.561127i	$-0.810368\pi$
$827$	−47.6070	−1.65546	−0.827729	+	0.561127i	$0.810368\pi$
$828$	−6.22277	−0.216256
$829$	5.19254	0.180344	0.0901722	−	0.995926i	$-0.471258\pi$
$829$	5.19254	0.180344	0.0901722	+	0.995926i	$0.471258\pi$
$830$	19.9905	0.693881
$831$	−4.79068	−0.166187
$832$	−0.526746	−0.0182616
$833$	−37.4251	−1.29670
$834$	−1.46499	−0.0507286
$835$	67.1642	2.32431
$836$	0	0
$837$	1.63546	0.0565298
$838$	−0.427754	−0.0147765
$839$	−43.4560	−1.50027	−0.750133	−	0.661287i	$-0.770011\pi$
$839$	−43.4560	−1.50027	−0.750133	+	0.661287i	$0.770011\pi$
$840$	0.660313	0.0227829
$841$	−28.9228	−0.997337
$842$	−9.69726	−0.334190
$843$	2.67094	0.0919922
$844$	15.5951	0.536805
$845$	−39.1462	−1.34667
$846$	−5.85177	−0.201188
$847$	0	0
$848$	−2.20703	−0.0757896
$849$	−1.65719	−0.0568748
$850$	32.3259	1.10877
$851$	18.6429	0.639071
$852$	−0.589502	−0.0201960
$853$	−29.3178	−1.00382	−0.501911	−	0.864919i	$-0.667369\pi$
$853$	−29.3178	−1.00382	−0.501911	+	0.864919i	$0.667369\pi$
$854$	8.63529	0.295493
$855$	9.15323	0.313034
$856$	13.1999	0.451163
$857$	3.67262	0.125454	0.0627272	−	0.998031i	$-0.480020\pi$
$857$	3.67262	0.125454	0.0627272	+	0.998031i	$0.480020\pi$
$858$	0	0
$859$	−19.7758	−0.674742	−0.337371	−	0.941372i	$-0.609538\pi$
$859$	−19.7758	−0.674742	−0.337371	+	0.941372i	$0.609538\pi$
$860$	19.3882	0.661134
$861$	−1.79698	−0.0612409
$862$	−6.70352	−0.228323
$863$	−33.2555	−1.13203	−0.566015	−	0.824395i	$-0.691516\pi$
$863$	−33.2555	−1.13203	−0.566015	+	0.824395i	$0.691516\pi$
$864$	−0.948385	−0.0322647
$865$	−33.8773	−1.15186
$866$	−15.3773	−0.522544
$867$	5.61250	0.190610
$868$	−2.33146	−0.0791350
$869$	0	0
$870$	−0.135714	−0.00460112
$871$	0.537287	0.0182053
$872$	4.47355	0.151494
$873$	31.0631	1.05133
$874$	−2.09183	−0.0707571
$875$	−2.21552	−0.0748984
$876$	0.273272	0.00923301
$877$	−14.7200	−0.497060	−0.248530	−	0.968624i	$-0.579948\pi$
$877$	−14.7200	−0.497060	−0.248530	+	0.968624i	$0.579948\pi$
$878$	−2.15073	−0.0725837
$879$	2.12734	0.0717534
$880$	0	0
$881$	−2.16151	−0.0728230	−0.0364115	−	0.999337i	$-0.511593\pi$
$881$	−2.16151	−0.0728230	−0.0364115	+	0.999337i	$0.511593\pi$
$882$	15.3861	0.518076
$883$	−11.6171	−0.390947	−0.195473	−	0.980709i	$-0.562624\pi$
$883$	−11.6171	−0.390947	−0.195473	+	0.980709i	$0.562624\pi$
$884$	−3.81150	−0.128194
$885$	4.26030	0.143208
$886$	30.3841	1.02077
$887$	22.5487	0.757111	0.378555	−	0.925579i	$-0.376421\pi$
$887$	22.5487	0.757111	0.378555	+	0.925579i	$0.376421\pi$
$888$	1.41465	0.0474725
$889$	−22.2512	−0.746282
$890$	−31.8515	−1.06766
$891$	0	0
$892$	−24.4375	−0.818230
$893$	−1.96711	−0.0658269
$894$	−1.95718	−0.0654580
$895$	−38.6236	−1.29104
$896$	1.35199	0.0451668
$897$	−0.174899	−0.00583971
$898$	3.34155	0.111509
$899$	0.479184	0.0159817
$900$	−13.2897	−0.442990
$901$	−15.9699	−0.532034
$902$	0	0
$903$	1.35225	0.0450000
$904$	−12.5601	−0.417743
$905$	−10.6245	−0.353171
$906$	0.576921	0.0191669
$907$	18.3913	0.610672	0.305336	−	0.952245i	$-0.401231\pi$
$907$	18.3913	0.610672	0.305336	+	0.952245i	$0.401231\pi$
$908$	−23.2524	−0.771659
$909$	−49.4041	−1.63863
$910$	−2.19124	−0.0726389
$911$	47.2453	1.56531	0.782654	−	0.622458i	$-0.213866\pi$
$911$	47.2453	1.56531	0.782654	+	0.622458i	$0.213866\pi$
$912$	−0.158731	−0.00525610
$913$	0	0
$914$	29.3880	0.972068
$915$	3.11947	0.103126
$916$	−1.94364	−0.0642197
$917$	20.4922	0.676712
$918$	−6.86244	−0.226494
$919$	−9.79492	−0.323105	−0.161552	−	0.986864i	$-0.551650\pi$
$919$	−9.79492	−0.323105	−0.161552	+	0.986864i	$0.551650\pi$
$920$	6.43637	0.212201
$921$	−3.01271	−0.0992721
$922$	−1.74308	−0.0574053
$923$	1.95626	0.0643910
$924$	0	0
$925$	39.8148	1.30910
$926$	−31.2015	−1.02535
$927$	18.7665	0.616371
$928$	−0.277873	−0.00912164
$929$	22.9921	0.754346	0.377173	−	0.926143i	$-0.376896\pi$
$929$	22.9921	0.754346	0.377173	+	0.926143i	$0.376896\pi$
$930$	−0.842233	−0.0276179
$931$	5.17213	0.169510
$932$	5.46260	0.178933
$933$	1.98027	0.0648311
$934$	26.0733	0.853144
$935$	0	0
$936$	1.56697	0.0512179
$937$	36.6455	1.19716	0.598578	−	0.801065i	$-0.295733\pi$
$937$	36.6455	1.19716	0.598578	+	0.801065i	$0.295733\pi$
$938$	−1.37904	−0.0450274
$939$	−2.90067	−0.0946599
$940$	6.05264	0.197415
$941$	−14.2908	−0.465868	−0.232934	−	0.972493i	$-0.574833\pi$
$941$	−14.2908	−0.465868	−0.232934	+	0.972493i	$0.574833\pi$
$942$	−0.138342	−0.00450741
$943$	−17.5160	−0.570399
$944$	8.72295	0.283908
$945$	−3.94524	−0.128339
$946$	0	0
$947$	49.0452	1.59375	0.796877	−	0.604142i	$-0.206484\pi$
$947$	49.0452	1.59375	0.796877	+	0.604142i	$0.206484\pi$
$948$	1.19591	0.0388414
$949$	−0.906851	−0.0294376
$950$	−4.46742	−0.144942
$951$	−2.09255	−0.0678556
$952$	9.78288	0.317065
$953$	−9.95579	−0.322500	−0.161250	−	0.986914i	$-0.551553\pi$
$953$	−9.95579	−0.322500	−0.161250	+	0.986914i	$0.551553\pi$
$954$	6.56547	0.212565
$955$	65.6055	2.12294
$956$	−16.1582	−0.522595
$957$	0	0
$958$	−29.3946	−0.949695
$959$	−7.38237	−0.238389
$960$	0.488401	0.0157631
$961$	−28.0262	−0.904071
$962$	−4.69450	−0.151357
$963$	−39.2671	−1.26537
$964$	−17.9215	−0.577212
$965$	72.1605	2.32293
$966$	0.448910	0.0144434
$967$	−12.0203	−0.386546	−0.193273	−	0.981145i	$-0.561910\pi$
$967$	−12.0203	−0.386546	−0.193273	+	0.981145i	$0.561910\pi$
$968$	0	0
$969$	−1.14856	−0.0368972
$970$	−32.1294	−1.03161
$971$	51.9013	1.66559	0.832796	−	0.553580i	$-0.186739\pi$
$971$	51.9013	1.66559	0.832796	+	0.553580i	$0.186739\pi$
$972$	4.23784	0.135929
$973$	−12.4781	−0.400029
$974$	43.0919	1.38075
$975$	−0.373524	−0.0119624
$976$	6.38710	0.204446
$977$	−28.7379	−0.919407	−0.459703	−	0.888073i	$-0.652044\pi$
$977$	−28.7379	−0.919407	−0.459703	+	0.888073i	$0.652044\pi$
$978$	−1.22790	−0.0392638
$979$	0	0
$980$	−15.9142	−0.508361
$981$	−13.3079	−0.424890
$982$	−29.5401	−0.942662
$983$	36.7856	1.17328	0.586639	−	0.809849i	$-0.300451\pi$
$983$	36.7856	1.17328	0.586639	+	0.809849i	$0.300451\pi$
$984$	−1.32914	−0.0423714
$985$	−23.9878	−0.764315
$986$	−2.01067	−0.0640328
$987$	0.422146	0.0134371
$988$	0.526746	0.0167580
$989$	13.1810	0.419131
$990$	0	0
$991$	−59.5095	−1.89038	−0.945191	−	0.326517i	$-0.894125\pi$
$991$	−59.5095	−1.89038	−0.945191	+	0.326517i	$0.894125\pi$
$992$	−1.72447	−0.0547519
$993$	0.586069	0.0185983
$994$	−5.02108	−0.159259
$995$	−29.1778	−0.924999
$996$	1.03126	0.0326768
$997$	−27.5241	−0.871697	−0.435848	−	0.900020i	$-0.643552\pi$
$997$	−27.5241	−0.871697	−0.435848	+	0.900020i	$0.643552\pi$
$998$	−27.8915	−0.882889
$999$	−8.45226	−0.267418

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.ca.1.4		8
11.3	even	5		418.2.f.f.229.3	yes	16
11.4	even	5		418.2.f.f.115.3	✓	16
11.10	odd	2		4598.2.a.bx.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.f.115.3	✓	16	11.4	even	5
418.2.f.f.229.3	yes	16	11.3	even	5
4598.2.a.bx.1.4		8	11.10	odd	2
4598.2.a.ca.1.4		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.158731 q^{3} +1.00000 q^{4} +3.07692 q^{5} +0.158731 q^{6} +1.35199 q^{7} +1.00000 q^{8} -2.97480 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.158731 q^{3} +1.00000 q^{4} +3.07692 q^{5} +0.158731 q^{6} +1.35199 q^{7} +1.00000 q^{8} -2.97480 q^{9} +3.07692 q^{10} +0.158731 q^{12} -0.526746 q^{13} +1.35199 q^{14} +0.488401 q^{15} +1.00000 q^{16} +7.23593 q^{17} -2.97480 q^{18} -1.00000 q^{19} +3.07692 q^{20} +0.214602 q^{21} +2.09183 q^{23} +0.158731 q^{24} +4.46742 q^{25} -0.526746 q^{26} -0.948385 q^{27} +1.35199 q^{28} -0.277873 q^{29} +0.488401 q^{30} -1.72447 q^{31} +1.00000 q^{32} +7.23593 q^{34} +4.15995 q^{35} -2.97480 q^{36} +8.91226 q^{37} -1.00000 q^{38} -0.0836108 q^{39} +3.07692 q^{40} -8.37354 q^{41} +0.214602 q^{42} +6.30119 q^{43} -9.15323 q^{45} +2.09183 q^{46} +1.96711 q^{47} +0.158731 q^{48} -5.17213 q^{49} +4.46742 q^{50} +1.14856 q^{51} -0.526746 q^{52} -2.20703 q^{53} -0.948385 q^{54} +1.35199 q^{56} -0.158731 q^{57} -0.277873 q^{58} +8.72295 q^{59} +0.488401 q^{60} +6.38710 q^{61} -1.72447 q^{62} -4.02190 q^{63} +1.00000 q^{64} -1.62075 q^{65} -1.02001 q^{67} +7.23593 q^{68} +0.332037 q^{69} +4.15995 q^{70} -3.71385 q^{71} -2.97480 q^{72} +1.72161 q^{73} +8.91226 q^{74} +0.709116 q^{75} -1.00000 q^{76} -0.0836108 q^{78} +7.53423 q^{79} +3.07692 q^{80} +8.77388 q^{81} -8.37354 q^{82} +6.49693 q^{83} +0.214602 q^{84} +22.2643 q^{85} +6.30119 q^{86} -0.0441070 q^{87} -10.3518 q^{89} -9.15323 q^{90} -0.712155 q^{91} +2.09183 q^{92} -0.273726 q^{93} +1.96711 q^{94} -3.07692 q^{95} +0.158731 q^{96} -10.4421 q^{97} -5.17213 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9	\( 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9} + 2 q^{10} + 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} - 8 q^{19} + 2 q^{20} + 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} + 8 q^{28} + 14 q^{29} + 10 q^{30} - 2 q^{31} + 8 q^{32} + 4 q^{34} + 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} - 4 q^{39} + 2 q^{40} + 8 q^{41} + 14 q^{42} + 28 q^{43} - 28 q^{45} + 12 q^{46} + 6 q^{47} + 32 q^{49} - 12 q^{51} + 18 q^{52} - 24 q^{53} - 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} - 24 q^{61} - 2 q^{62} + 30 q^{63} + 8 q^{64} - 16 q^{65} - 22 q^{67} + 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} + 20 q^{72} + 16 q^{73} - 22 q^{74} + 6 q^{75} - 8 q^{76} - 4 q^{78} + 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} + 12 q^{83} + 14 q^{84} + 48 q^{85} + 28 q^{86} + 42 q^{87} - 28 q^{89} - 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} + 6 q^{94} - 2 q^{95} - 22 q^{97} + 32 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9 + 2 * q^10 + 18 * q^13 + 8 * q^14 + 10 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 - 8 * q^19 + 2 * q^20 + 14 * q^21 + 12 * q^23 + 18 * q^26 - 24 * q^27 + 8 * q^28 + 14 * q^29 + 10 * q^30 - 2 * q^31 + 8 * q^32 + 4 * q^34 + 40 * q^35 + 20 * q^36 - 22 * q^37 - 8 * q^38 - 4 * q^39 + 2 * q^40 + 8 * q^41 + 14 * q^42 + 28 * q^43 - 28 * q^45 + 12 * q^46 + 6 * q^47 + 32 * q^49 - 12 * q^51 + 18 * q^52 - 24 * q^53 - 24 * q^54 + 8 * q^56 + 14 * q^58 + 46 * q^59 + 10 * q^60 - 24 * q^61 - 2 * q^62 + 30 * q^63 + 8 * q^64 - 16 * q^65 - 22 * q^67 + 4 * q^68 - 38 * q^69 + 40 * q^70 + 8 * q^71 + 20 * q^72 + 16 * q^73 - 22 * q^74 + 6 * q^75 - 8 * q^76 - 4 * q^78 + 4 * q^79 + 2 * q^80 + 28 * q^81 + 8 * q^82 + 12 * q^83 + 14 * q^84 + 48 * q^85 + 28 * q^86 + 42 * q^87 - 28 * q^89 - 28 * q^90 - 12 * q^91 + 12 * q^92 + 22 * q^93 + 6 * q^94 - 2 * q^95 - 22 * q^97 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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