LMFDB - Embedded newform 1859.2.a.s.1.20

Newspace parameters

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$14.8441897358$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	1859.1

$q$-expansion

$f(q)$	$=$	$q+2.70607 q^{2} +0.960218 q^{3} +5.32282 q^{4} +3.57279 q^{5} +2.59842 q^{6} -3.95601 q^{7} +8.99178 q^{8} -2.07798 q^{9} +O(q^{10})$	\(q+2.70607 q^{2} +0.960218 q^{3} +5.32282 q^{4} +3.57279 q^{5} +2.59842 q^{6} -3.95601 q^{7} +8.99178 q^{8} -2.07798 q^{9} +9.66821 q^{10} -1.00000 q^{11} +5.11106 q^{12} -10.7053 q^{14} +3.43065 q^{15} +13.6867 q^{16} +2.79876 q^{17} -5.62316 q^{18} +0.00685455 q^{19} +19.0173 q^{20} -3.79863 q^{21} -2.70607 q^{22} -3.94433 q^{23} +8.63406 q^{24} +7.76481 q^{25} -4.87597 q^{27} -21.0571 q^{28} +6.09411 q^{29} +9.28359 q^{30} -0.242210 q^{31} +19.0537 q^{32} -0.960218 q^{33} +7.57365 q^{34} -14.1340 q^{35} -11.0607 q^{36} -0.801720 q^{37} +0.0185489 q^{38} +32.1257 q^{40} +6.58954 q^{41} -10.2794 q^{42} -6.24920 q^{43} -5.32282 q^{44} -7.42419 q^{45} -10.6736 q^{46} -6.29173 q^{47} +13.1423 q^{48} +8.65004 q^{49} +21.0121 q^{50} +2.68742 q^{51} +9.02538 q^{53} -13.1947 q^{54} -3.57279 q^{55} -35.5716 q^{56} +0.00658186 q^{57} +16.4911 q^{58} -4.00551 q^{59} +18.2607 q^{60} -6.32993 q^{61} -0.655437 q^{62} +8.22052 q^{63} +24.1873 q^{64} -2.59842 q^{66} -8.97718 q^{67} +14.8973 q^{68} -3.78741 q^{69} -38.2476 q^{70} -8.03382 q^{71} -18.6847 q^{72} -0.166373 q^{73} -2.16951 q^{74} +7.45591 q^{75} +0.0364855 q^{76} +3.95601 q^{77} -9.30756 q^{79} +48.8998 q^{80} +1.55195 q^{81} +17.8318 q^{82} -0.547068 q^{83} -20.2194 q^{84} +9.99939 q^{85} -16.9108 q^{86} +5.85167 q^{87} -8.99178 q^{88} -17.0658 q^{89} -20.0904 q^{90} -20.9949 q^{92} -0.232574 q^{93} -17.0259 q^{94} +0.0244899 q^{95} +18.2957 q^{96} -8.78558 q^{97} +23.4076 q^{98} +2.07798 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) $ 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9 + 18 * q^10 - 21 * q^11 + 23 * q^12 + 20 * q^14 - 16 * q^15 + 50 * q^16 + 16 * q^17 - 3 * q^18 + 11 * q^19 - 24 * q^20 + 5 * q^21 - 9 * q^23 + 54 * q^24 + 36 * q^25 + 11 * q^28 + 28 * q^29 + 21 * q^30 - 15 * q^31 + 61 * q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 45 * q^36 + 12 * q^37 + q^38 + 55 * q^40 + 4 * q^41 - 34 * q^42 + 17 * q^43 - 32 * q^44 - 9 * q^45 - 11 * q^46 - 36 * q^47 + 24 * q^48 + 72 * q^49 + 9 * q^50 + 2 * q^51 + 19 * q^53 - q^54 + 7 * q^55 + 44 * q^56 + 4 * q^57 + 33 * q^58 - 54 * q^59 - 64 * q^60 + 98 * q^61 - 29 * q^62 + 81 * q^63 + 63 * q^64 - 19 * q^66 - 25 * q^67 + 4 * q^68 + 89 * q^69 - 65 * q^70 - 37 * q^71 - 55 * q^72 - 8 * q^73 - 11 * q^74 + 24 * q^75 - 13 * q^76 + q^77 + 24 * q^79 - 26 * q^80 + 81 * q^81 + 26 * q^82 + 34 * q^83 + 103 * q^84 + 11 * q^85 - 30 * q^86 + 32 * q^87 - 3 * q^88 - 6 * q^89 + 47 * q^90 - 80 * q^92 - 41 * q^93 + 40 * q^94 + 20 * q^95 + 98 * q^96 + 5 * q^98 - 33 * 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 $

$2$	2.70607	1.91348	0.956740	−	0.290943i	$-0.0939690\pi$
$2$	2.70607	1.91348	0.956740	+	0.290943i	$0.0939690\pi$
$3$	0.960218	0.554382	0.277191	−	0.960815i	$-0.410597\pi$
$3$	0.960218	0.554382	0.277191	+	0.960815i	$0.410597\pi$
$4$	5.32282	2.66141
$5$	3.57279	1.59780	0.798900	−	0.601464i	$-0.205416\pi$
$5$	3.57279	1.59780	0.798900	+	0.601464i	$0.205416\pi$
$6$	2.59842	1.06080
$7$	−3.95601	−1.49523	−0.747616	−	0.664131i	$-0.768802\pi$
$7$	−3.95601	−1.49523	−0.747616	+	0.664131i	$0.768802\pi$
$8$	8.99178	3.17907
$9$	−2.07798	−0.692661
$10$	9.66821	3.05736
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	5.11106	1.47544
$13$	0	0
$13$	0	0
$14$	−10.7053	−2.86110
$15$	3.43065	0.885791
$16$	13.6867	3.42169
$17$	2.79876	0.678800	0.339400	−	0.940642i	$-0.389776\pi$
$17$	2.79876	0.678800	0.339400	+	0.940642i	$0.389776\pi$
$18$	−5.62316	−1.32539
$19$	0.00685455	0.00157254	0.000786271	−	1.00000i	$-0.499750\pi$
$19$	0.00685455	0.00157254	0.000786271		1.00000i	$0.499750\pi$
$20$	19.0173	4.25240
$21$	−3.79863	−0.828930
$22$	−2.70607	−0.576936
$23$	−3.94433	−0.822449	−0.411224	−	0.911534i	$-0.634899\pi$
$23$	−3.94433	−0.822449	−0.411224	+	0.911534i	$0.634899\pi$
$24$	8.63406	1.76242
$25$	7.76481	1.55296
$26$	0	0
$27$	−4.87597	−0.938381
$28$	−21.0571	−3.97942
$29$	6.09411	1.13165	0.565824	−	0.824526i	$-0.308558\pi$
$29$	6.09411	1.13165	0.565824	+	0.824526i	$0.308558\pi$
$30$	9.28359	1.69494
$31$	−0.242210	−0.0435022	−0.0217511	−	0.999763i	$-0.506924\pi$
$31$	−0.242210	−0.0435022	−0.0217511	+	0.999763i	$0.506924\pi$
$32$	19.0537	3.36826
$33$	−0.960218	−0.167152
$34$	7.57365	1.29887
$35$	−14.1340	−2.38908
$36$	−11.0607	−1.84345
$37$	−0.801720	−0.131802	−0.0659010	−	0.997826i	$-0.520992\pi$
$37$	−0.801720	−0.131802	−0.0659010	+	0.997826i	$0.520992\pi$
$38$	0.0185489	0.00300903
$39$	0	0
$40$	32.1257	5.07952
$41$	6.58954	1.02911	0.514557	−	0.857456i	$-0.327956\pi$
$41$	6.58954	1.02911	0.514557	+	0.857456i	$0.327956\pi$
$42$	−10.2794	−1.58614
$43$	−6.24920	−0.952994	−0.476497	−	0.879176i	$-0.658094\pi$
$43$	−6.24920	−0.952994	−0.476497	+	0.879176i	$0.658094\pi$
$44$	−5.32282	−0.802445
$45$	−7.42419	−1.10673
$46$	−10.6736	−1.57374
$47$	−6.29173	−0.917743	−0.458872	−	0.888503i	$-0.651746\pi$
$47$	−6.29173	−0.917743	−0.458872	+	0.888503i	$0.651746\pi$
$48$	13.1423	1.89692
$49$	8.65004	1.23572
$50$	21.0121	2.97156
$51$	2.68742	0.376315
$52$	0	0
$53$	9.02538	1.23973	0.619865	−	0.784708i	$-0.287187\pi$
$53$	9.02538	1.23973	0.619865	+	0.784708i	$0.287187\pi$
$54$	−13.1947	−1.79557
$55$	−3.57279	−0.481755
$56$	−35.5716	−4.75345
$57$	0.00658186	0.000871789 0
$58$	16.4911	2.16539
$59$	−4.00551	−0.521472	−0.260736	−	0.965410i	$-0.583965\pi$
$59$	−4.00551	−0.521472	−0.260736	+	0.965410i	$0.583965\pi$
$60$	18.2607	2.35745
$61$	−6.32993	−0.810464	−0.405232	−	0.914214i	$-0.632809\pi$
$61$	−6.32993	−0.810464	−0.405232	+	0.914214i	$0.632809\pi$
$62$	−0.655437	−0.0832405
$63$	8.22052	1.03569
$64$	24.1873	3.02341
$65$	0	0
$66$	−2.59842	−0.319843
$67$	−8.97718	−1.09674	−0.548368	−	0.836237i	$-0.684751\pi$
$67$	−8.97718	−1.09674	−0.548368	+	0.836237i	$0.684751\pi$
$68$	14.8973	1.80656
$69$	−3.78741	−0.455951
$70$	−38.2476	−4.57146
$71$	−8.03382	−0.953439	−0.476720	−	0.879055i	$-0.658174\pi$
$71$	−8.03382	−0.953439	−0.476720	+	0.879055i	$0.658174\pi$
$72$	−18.6847	−2.20202
$73$	−0.166373	−0.0194725	−0.00973623	−	0.999953i	$-0.503099\pi$
$73$	−0.166373	−0.0194725	−0.00973623	+	0.999953i	$0.503099\pi$
$74$	−2.16951	−0.252200
$75$	7.45591	0.860934
$76$	0.0364855	0.00418518
$77$	3.95601	0.450830
$78$	0	0
$79$	−9.30756	−1.04718	−0.523591	−	0.851970i	$-0.675408\pi$
$79$	−9.30756	−1.04718	−0.523591	+	0.851970i	$0.675408\pi$
$80$	48.8998	5.46717
$81$	1.55195	0.172439
$82$	17.8318	1.96919
$83$	−0.547068	−0.0600485	−0.0300242	−	0.999549i	$-0.509558\pi$
$83$	−0.547068	−0.0600485	−0.0300242	+	0.999549i	$0.509558\pi$
$84$	−20.2194	−2.20612
$85$	9.99939	1.08459
$86$	−16.9108	−1.82354
$87$	5.85167	0.627365
$88$	−8.99178	−0.958527
$89$	−17.0658	−1.80897	−0.904487	−	0.426502i	$-0.859746\pi$
$89$	−17.0658	−1.80897	−0.904487	+	0.426502i	$0.859746\pi$
$90$	−20.0904	−2.11771
$91$	0	0
$92$	−20.9949	−2.18887
$93$	−0.232574	−0.0241168
$94$	−17.0259	−1.75608
$95$	0.0244899	0.00251261
$96$	18.2957	1.86730
$97$	−8.78558	−0.892040	−0.446020	−	0.895023i	$-0.647159\pi$
$97$	−8.78558	−0.892040	−0.446020	+	0.895023i	$0.647159\pi$
$98$	23.4076	2.36453
$99$	2.07798	0.208845
$100$	41.3307	4.13307
$101$	−0.664826	−0.0661527	−0.0330763	−	0.999453i	$-0.510530\pi$
$101$	−0.664826	−0.0661527	−0.0330763	+	0.999453i	$0.510530\pi$
$102$	7.27236	0.720071
$103$	−14.3916	−1.41804	−0.709021	−	0.705187i	$-0.750863\pi$
$103$	−14.3916	−1.41804	−0.709021	+	0.705187i	$0.750863\pi$
$104$	0	0
$105$	−13.5717	−1.32446
$106$	24.4233	2.37220
$107$	7.11634	0.687962	0.343981	−	0.938977i	$-0.388224\pi$
$107$	7.11634	0.687962	0.343981	+	0.938977i	$0.388224\pi$
$108$	−25.9539	−2.49741
$109$	7.76979	0.744211	0.372105	−	0.928191i	$-0.378636\pi$
$109$	7.76979	0.744211	0.372105	+	0.928191i	$0.378636\pi$
$110$	−9.66821	−0.921828
$111$	−0.769826	−0.0730686
$112$	−54.1450	−5.11622
$113$	−13.4649	−1.26667	−0.633334	−	0.773878i	$-0.718314\pi$
$113$	−13.4649	−1.26667	−0.633334	+	0.773878i	$0.718314\pi$
$114$	0.0178110	0.00166815
$115$	−14.0922	−1.31411
$116$	32.4378	3.01178
$117$	0	0
$118$	−10.8392	−0.997827
$119$	−11.0720	−1.01496
$120$	30.8477	2.81599
$121$	1.00000	0.0909091
$122$	−17.1292	−1.55081
$123$	6.32740	0.570522
$124$	−1.28924	−0.115777
$125$	9.87808	0.883523
$126$	22.2453	1.98177
$127$	13.1288	1.16499	0.582495	−	0.812834i	$-0.302076\pi$
$127$	13.1288	1.16499	0.582495	+	0.812834i	$0.302076\pi$
$128$	27.3450	2.41698
$129$	−6.00059	−0.528323
$130$	0	0
$131$	16.5571	1.44660	0.723300	−	0.690534i	$-0.242625\pi$
$131$	16.5571	1.44660	0.723300	+	0.690534i	$0.242625\pi$
$132$	−5.11106	−0.444861
$133$	−0.0271167	−0.00235132
$134$	−24.2929	−2.09859
$135$	−17.4208	−1.49934
$136$	25.1659	2.15796
$137$	17.9393	1.53266	0.766330	−	0.642447i	$-0.222081\pi$
$137$	17.9393	1.53266	0.766330	+	0.642447i	$0.222081\pi$
$138$	−10.2490	−0.872453
$139$	8.20712	0.696119	0.348059	−	0.937473i	$-0.386841\pi$
$139$	8.20712	0.696119	0.348059	+	0.937473i	$0.386841\pi$
$140$	−75.2327	−6.35832
$141$	−6.04143	−0.508780
$142$	−21.7401	−1.82439
$143$	0	0
$144$	−28.4408	−2.37007
$145$	21.7730	1.80815
$146$	−0.450216	−0.0372602
$147$	8.30592	0.685061
$148$	−4.26741	−0.350779
$149$	−6.02019	−0.493193	−0.246597	−	0.969118i	$-0.579312\pi$
$149$	−6.02019	−0.493193	−0.246597	+	0.969118i	$0.579312\pi$
$150$	20.1762	1.64738
$151$	9.53009	0.775547	0.387774	−	0.921755i	$-0.373244\pi$
$151$	9.53009	0.775547	0.387774	+	0.921755i	$0.373244\pi$
$152$	0.0616346	0.00499923
$153$	−5.81578	−0.470178
$154$	10.7053	0.862654
$155$	−0.865364	−0.0695077
$156$	0	0
$157$	7.58684	0.605496	0.302748	−	0.953071i	$-0.402096\pi$
$157$	7.58684	0.605496	0.302748	+	0.953071i	$0.402096\pi$
$158$	−25.1869	−2.00376
$159$	8.66633	0.687284
$160$	68.0750	5.38180
$161$	15.6038	1.22975
$162$	4.19969	0.329959
$163$	−0.420278	−0.0329187	−0.0164594	−	0.999865i	$-0.505239\pi$
$163$	−0.420278	−0.0329187	−0.0164594	+	0.999865i	$0.505239\pi$
$164$	35.0749	2.73889
$165$	−3.43065	−0.267076
$166$	−1.48040	−0.114902
$167$	15.9576	1.23484	0.617420	−	0.786634i	$-0.288178\pi$
$167$	15.9576	1.23484	0.617420	+	0.786634i	$0.288178\pi$
$168$	−34.1565	−2.63523
$169$	0	0
$170$	27.0591	2.07534
$171$	−0.0142436	−0.00108924
$172$	−33.2633	−2.53631
$173$	−1.43723	−0.109270	−0.0546352	−	0.998506i	$-0.517400\pi$
$173$	−1.43723	−0.109270	−0.0546352	+	0.998506i	$0.517400\pi$
$174$	15.8350	1.20045
$175$	−30.7177	−2.32204
$176$	−13.6867	−1.03168
$177$	−3.84616	−0.289095
$178$	−46.1813	−3.46144
$179$	16.8302	1.25795	0.628973	−	0.777427i	$-0.283476\pi$
$179$	16.8302	1.25795	0.628973	+	0.777427i	$0.283476\pi$
$180$	−39.5176	−2.94547
$181$	4.85465	0.360843	0.180422	−	0.983589i	$-0.442254\pi$
$181$	4.85465	0.360843	0.180422	+	0.983589i	$0.442254\pi$
$182$	0	0
$183$	−6.07811	−0.449307
$184$	−35.4665	−2.61462
$185$	−2.86437	−0.210593
$186$	−0.629362	−0.0461471
$187$	−2.79876	−0.204666
$188$	−33.4897	−2.44249
$189$	19.2894	1.40310
$190$	0.0662713	0.00480782
$191$	11.5662	0.836898	0.418449	−	0.908240i	$-0.362574\pi$
$191$	11.5662	0.836898	0.418449	+	0.908240i	$0.362574\pi$
$192$	23.2251	1.67612
$193$	−26.9954	−1.94317	−0.971584	−	0.236693i	$-0.923936\pi$
$193$	−26.9954	−1.94317	−0.971584	+	0.236693i	$0.923936\pi$
$194$	−23.7744	−1.70690
$195$	0	0
$196$	46.0426	3.28876
$197$	−16.7441	−1.19297	−0.596483	−	0.802626i	$-0.703436\pi$
$197$	−16.7441	−1.19297	−0.596483	+	0.802626i	$0.703436\pi$
$198$	5.62316	0.399621
$199$	24.3915	1.72907	0.864535	−	0.502572i	$-0.167613\pi$
$199$	24.3915	1.72907	0.864535	+	0.502572i	$0.167613\pi$
$200$	69.8194	4.93698
$201$	−8.62005	−0.608011
$202$	−1.79907	−0.126582
$203$	−24.1084	−1.69208
$204$	14.3047	1.00153
$205$	23.5430	1.64432
$206$	−38.9446	−2.71340
$207$	8.19624	0.569678
$208$	0	0
$209$	−0.00685455	−0.000474139 0
$210$	−36.7260	−2.53434
$211$	20.9742	1.44392	0.721961	−	0.691934i	$-0.243241\pi$
$211$	20.9742	1.44392	0.721961	+	0.691934i	$0.243241\pi$
$212$	48.0404	3.29943
$213$	−7.71422	−0.528570
$214$	19.2573	1.31640
$215$	−22.3271	−1.52269
$216$	−43.8436	−2.98318
$217$	0.958185	0.0650458
$218$	21.0256	1.42403
$219$	−0.159754	−0.0107952
$220$	−19.0173	−1.28215
$221$	0	0
$222$	−2.08320	−0.139815
$223$	2.16005	0.144647	0.0723237	−	0.997381i	$-0.476959\pi$
$223$	2.16005	0.144647	0.0723237	+	0.997381i	$0.476959\pi$
$224$	−75.3769	−5.03633
$225$	−16.1351	−1.07568
$226$	−36.4369	−2.42375
$227$	19.0617	1.26517	0.632586	−	0.774490i	$-0.281994\pi$
$227$	19.0617	1.26517	0.632586	+	0.774490i	$0.281994\pi$
$228$	0.0350340	0.00232019
$229$	−18.7054	−1.23609	−0.618043	−	0.786144i	$-0.712074\pi$
$229$	−18.7054	−1.23609	−0.618043	+	0.786144i	$0.712074\pi$
$230$	−38.1346	−2.51452
$231$	3.79863	0.249932
$232$	54.7969	3.59759
$233$	29.4725	1.93081	0.965404	−	0.260758i	$-0.0839725\pi$
$233$	29.4725	1.93081	0.965404	+	0.260758i	$0.0839725\pi$
$234$	0	0
$235$	−22.4790	−1.46637
$236$	−21.3206	−1.38785
$237$	−8.93728	−0.580539
$238$	−29.9615	−1.94211
$239$	0.858675	0.0555431	0.0277715	−	0.999614i	$-0.491159\pi$
$239$	0.858675	0.0555431	0.0277715	+	0.999614i	$0.491159\pi$
$240$	46.9545	3.03090
$241$	−6.76007	−0.435454	−0.217727	−	0.976010i	$-0.569864\pi$
$241$	−6.76007	−0.435454	−0.217727	+	0.976010i	$0.569864\pi$
$242$	2.70607	0.173953
$243$	16.1181	1.03398
$244$	−33.6931	−2.15698
$245$	30.9048	1.97443
$246$	17.1224	1.09168
$247$	0	0
$248$	−2.17790	−0.138297
$249$	−0.525304	−0.0332898
$250$	26.7308	1.69060
$251$	24.1131	1.52200	0.761002	−	0.648749i	$-0.224707\pi$
$251$	24.1131	1.52200	0.761002	+	0.648749i	$0.224707\pi$
$252$	43.7563	2.75639
$253$	3.94433	0.247978
$254$	35.5274	2.22919
$255$	9.60159	0.601275
$256$	25.6229	1.60143
$257$	11.8561	0.739563	0.369781	−	0.929119i	$-0.379433\pi$
$257$	11.8561	0.739563	0.369781	+	0.929119i	$0.379433\pi$
$258$	−16.2380	−1.01094
$259$	3.17161	0.197075
$260$	0	0
$261$	−12.6634	−0.783848
$262$	44.8046	2.76804
$263$	11.5619	0.712939	0.356470	−	0.934307i	$-0.383980\pi$
$263$	11.5619	0.712939	0.356470	+	0.934307i	$0.383980\pi$
$264$	−8.63406	−0.531390
$265$	32.2458	1.98084
$266$	−0.0733797	−0.00449920
$267$	−16.3869	−1.00286
$268$	−47.7839	−2.91887
$269$	24.0669	1.46739	0.733693	−	0.679481i	$-0.237795\pi$
$269$	24.0669	1.46739	0.733693	+	0.679481i	$0.237795\pi$
$270$	−47.1419	−2.86897
$271$	−18.6610	−1.13357	−0.566787	−	0.823864i	$-0.691814\pi$
$271$	−18.6610	−1.13357	−0.566787	+	0.823864i	$0.691814\pi$
$272$	38.3060	2.32264
$273$	0	0
$274$	48.5451	2.93272
$275$	−7.76481	−0.468236
$276$	−20.1597	−1.21347
$277$	0.407769	0.0245005	0.0122502	−	0.999925i	$-0.496101\pi$
$277$	0.407769	0.0245005	0.0122502	+	0.999925i	$0.496101\pi$
$278$	22.2090	1.33201
$279$	0.503307	0.0301322
$280$	−127.090	−7.59506
$281$	30.5675	1.82350	0.911752	−	0.410741i	$-0.134730\pi$
$281$	30.5675	1.82350	0.911752	+	0.410741i	$0.134730\pi$
$282$	−16.3485	−0.973541
$283$	14.5967	0.867683	0.433841	−	0.900989i	$-0.357158\pi$
$283$	14.5967	0.867683	0.433841	+	0.900989i	$0.357158\pi$
$284$	−42.7626	−2.53749
$285$	0.0235156	0.00139294
$286$	0	0
$287$	−26.0683	−1.53876
$288$	−39.5933	−2.33306
$289$	−9.16691	−0.539230
$290$	58.9191	3.45985
$291$	−8.43607	−0.494531
$292$	−0.885572	−0.0518242
$293$	29.1102	1.70064	0.850319	−	0.526268i	$-0.176409\pi$
$293$	29.1102	1.70064	0.850319	+	0.526268i	$0.176409\pi$
$294$	22.4764	1.31085
$295$	−14.3108	−0.833208
$296$	−7.20889	−0.419008
$297$	4.87597	0.282932
$298$	−16.2911	−0.943715
$299$	0	0
$300$	39.6864	2.29130
$301$	24.7219	1.42495
$302$	25.7891	1.48399
$303$	−0.638378	−0.0366738
$304$	0.0938165	0.00538075
$305$	−22.6155	−1.29496
$306$	−15.7379	−0.899677
$307$	−24.4200	−1.39372	−0.696861	−	0.717207i	$-0.745420\pi$
$307$	−24.4200	−1.39372	−0.696861	+	0.717207i	$0.745420\pi$
$308$	21.0571	1.19984
$309$	−13.8190	−0.786137
$310$	−2.34174	−0.133002
$311$	26.3470	1.49400	0.747002	−	0.664822i	$-0.231493\pi$
$311$	26.3470	1.49400	0.747002	+	0.664822i	$0.231493\pi$
$312$	0	0
$313$	−29.2630	−1.65404	−0.827021	−	0.562171i	$-0.809966\pi$
$313$	−29.2630	−1.65404	−0.827021	+	0.562171i	$0.809966\pi$
$314$	20.5305	1.15860
$315$	29.3702	1.65482
$316$	−49.5424	−2.78698
$317$	16.1999	0.909875	0.454937	−	0.890523i	$-0.349662\pi$
$317$	16.1999	0.909875	0.454937	+	0.890523i	$0.349662\pi$
$318$	23.4517	1.31511
$319$	−6.09411	−0.341205
$320$	86.4160	4.83080
$321$	6.83323	0.381394
$322$	42.2250	2.35311
$323$	0.0191843	0.00106744
$324$	8.26076	0.458931
$325$	0	0
$326$	−1.13730	−0.0629893
$327$	7.46069	0.412577
$328$	59.2517	3.27163
$329$	24.8902	1.37224
$330$	−9.28359	−0.511045
$331$	−9.41075	−0.517262	−0.258631	−	0.965976i	$-0.583271\pi$
$331$	−9.41075	−0.517262	−0.258631	+	0.965976i	$0.583271\pi$
$332$	−2.91194	−0.159814
$333$	1.66596	0.0912940
$334$	43.1825	2.36284
$335$	−32.0736	−1.75237
$336$	−51.9909	−2.83634
$337$	−34.4623	−1.87728	−0.938640	−	0.344900i	$-0.887913\pi$
$337$	−34.4623	−1.87728	−0.938640	+	0.344900i	$0.887913\pi$
$338$	0	0
$339$	−12.9292	−0.702218
$340$	53.2249	2.88653
$341$	0.242210	0.0131164
$342$	−0.0385443	−0.00208424
$343$	−6.52758	−0.352456
$344$	−56.1914	−3.02964
$345$	−13.5316	−0.728518
$346$	−3.88924	−0.209087
$347$	−17.3788	−0.932945	−0.466473	−	0.884536i	$-0.654475\pi$
$347$	−17.3788	−0.932945	−0.466473	+	0.884536i	$0.654475\pi$
$348$	31.1474	1.66967
$349$	−1.75565	−0.0939780	−0.0469890	−	0.998895i	$-0.514963\pi$
$349$	−1.75565	−0.0939780	−0.0469890	+	0.998895i	$0.514963\pi$
$350$	−83.1242	−4.44318
$351$	0	0
$352$	−19.0537	−1.01557
$353$	9.12962	0.485921	0.242960	−	0.970036i	$-0.421882\pi$
$353$	9.12962	0.485921	0.242960	+	0.970036i	$0.421882\pi$
$354$	−10.4080	−0.553178
$355$	−28.7031	−1.52340
$356$	−90.8383	−4.81442
$357$	−10.6315	−0.562678
$358$	45.5436	2.40706
$359$	5.56656	0.293792	0.146896	−	0.989152i	$-0.453072\pi$
$359$	5.56656	0.293792	0.146896	+	0.989152i	$0.453072\pi$
$360$	−66.7566	−3.51838
$361$	−19.0000	−0.999998
$362$	13.1370	0.690467
$363$	0.960218	0.0503984
$364$	0	0
$365$	−0.594415	−0.0311131
$366$	−16.4478	−0.859740
$367$	−10.8050	−0.564017	−0.282009	−	0.959412i	$-0.591001\pi$
$367$	−10.8050	−0.564017	−0.282009	+	0.959412i	$0.591001\pi$
$368$	−53.9850	−2.81416
$369$	−13.6930	−0.712827
$370$	−7.75120	−0.402966
$371$	−35.7045	−1.85369
$372$	−1.23795	−0.0641847
$373$	3.71923	0.192574	0.0962872	−	0.995354i	$-0.469303\pi$
$373$	3.71923	0.192574	0.0962872	+	0.995354i	$0.469303\pi$
$374$	−7.57365	−0.391624
$375$	9.48511	0.489809
$376$	−56.5738	−2.91757
$377$	0	0
$378$	52.1985	2.68480
$379$	−6.49327	−0.333537	−0.166768	−	0.985996i	$-0.553333\pi$
$379$	−6.49327	−0.333537	−0.166768	+	0.985996i	$0.553333\pi$
$380$	0.130355	0.00668707
$381$	12.6065	0.645850
$382$	31.2988	1.60139
$383$	−4.15841	−0.212485	−0.106242	−	0.994340i	$-0.533882\pi$
$383$	−4.15841	−0.212485	−0.106242	+	0.994340i	$0.533882\pi$
$384$	26.2572	1.33993
$385$	14.1340	0.720335
$386$	−73.0514	−3.71822
$387$	12.9857	0.660101
$388$	−46.7640	−2.37408
$389$	12.5597	0.636803	0.318402	−	0.947956i	$-0.396854\pi$
$389$	12.5597	0.636803	0.318402	+	0.947956i	$0.396854\pi$
$390$	0	0
$391$	−11.0392	−0.558278
$392$	77.7792	3.92844
$393$	15.8984	0.801969
$394$	−45.3106	−2.28272
$395$	−33.2539	−1.67319
$396$	11.0607	0.555822
$397$	−18.0947	−0.908147	−0.454073	−	0.890964i	$-0.650030\pi$
$397$	−18.0947	−0.908147	−0.454073	+	0.890964i	$0.650030\pi$
$398$	66.0052	3.30854
$399$	−0.0260379	−0.00130353
$400$	106.275	5.31375
$401$	8.08415	0.403703	0.201852	−	0.979416i	$-0.435304\pi$
$401$	8.08415	0.403703	0.201852	+	0.979416i	$0.435304\pi$
$402$	−23.3265	−1.16342
$403$	0	0
$404$	−3.53875	−0.176059
$405$	5.54480	0.275523
$406$	−65.2389	−3.23775
$407$	0.801720	0.0397398
$408$	24.1647	1.19633
$409$	18.9341	0.936233	0.468116	−	0.883667i	$-0.344933\pi$
$409$	18.9341	0.936233	0.468116	+	0.883667i	$0.344933\pi$
$410$	63.7091	3.14637
$411$	17.2257	0.849679
$412$	−76.6036	−3.77399
$413$	15.8458	0.779722
$414$	22.1796	1.09007
$415$	−1.95456	−0.0959454
$416$	0	0
$417$	7.88062	0.385916
$418$	−0.0185489	−0.000907256 0
$419$	−22.2827	−1.08858	−0.544292	−	0.838896i	$-0.683202\pi$
$419$	−22.2827	−1.08858	−0.544292	+	0.838896i	$0.683202\pi$
$420$	−72.2397	−3.52494
$421$	−16.8899	−0.823161	−0.411581	−	0.911373i	$-0.635023\pi$
$421$	−16.8899	−0.823161	−0.411581	+	0.911373i	$0.635023\pi$
$422$	56.7576	2.76292
$423$	13.0741	0.635685
$424$	81.1542	3.94119
$425$	21.7319	1.05415
$426$	−20.8752	−1.01141
$427$	25.0413	1.21183
$428$	37.8790	1.83095
$429$	0	0
$430$	−60.4186	−2.91364
$431$	12.8476	0.618846	0.309423	−	0.950924i	$-0.399864\pi$
$431$	12.8476	0.618846	0.309423	+	0.950924i	$0.399864\pi$
$432$	−66.7361	−3.21084
$433$	12.3159	0.591865	0.295933	−	0.955209i	$-0.404370\pi$
$433$	12.3159	0.591865	0.295933	+	0.955209i	$0.404370\pi$
$434$	2.59292	0.124464
$435$	20.9068	1.00240
$436$	41.3572	1.98065
$437$	−0.0270366	−0.00129333
$438$	−0.432306	−0.0206564
$439$	−5.79480	−0.276571	−0.138285	−	0.990392i	$-0.544159\pi$
$439$	−5.79480	−0.276571	−0.138285	+	0.990392i	$0.544159\pi$
$440$	−32.1257	−1.53153
$441$	−17.9746	−0.855935
$442$	0	0
$443$	−25.9984	−1.23522	−0.617612	−	0.786483i	$-0.711900\pi$
$443$	−25.9984	−1.23522	−0.617612	+	0.786483i	$0.711900\pi$
$444$	−4.09764	−0.194465
$445$	−60.9726	−2.89038
$446$	5.84524	0.276780
$447$	−5.78069	−0.273417
$448$	−95.6852	−4.52070
$449$	−23.8705	−1.12652	−0.563258	−	0.826281i	$-0.690452\pi$
$449$	−23.8705	−1.12652	−0.563258	+	0.826281i	$0.690452\pi$
$450$	−43.6628	−2.05828
$451$	−6.58954	−0.310290
$452$	−71.6711	−3.37112
$453$	9.15096	0.429949
$454$	51.5824	2.42088
$455$	0	0
$456$	0.0591826	0.00277148
$457$	−6.67322	−0.312160	−0.156080	−	0.987744i	$-0.549886\pi$
$457$	−6.67322	−0.312160	−0.156080	+	0.987744i	$0.549886\pi$
$458$	−50.6181	−2.36523
$459$	−13.6467	−0.636973
$460$	−75.0104	−3.49738
$461$	−16.3391	−0.760989	−0.380495	−	0.924783i	$-0.624246\pi$
$461$	−16.3391	−0.760989	−0.380495	+	0.924783i	$0.624246\pi$
$462$	10.2794	0.478240
$463$	−31.3751	−1.45812	−0.729062	−	0.684447i	$-0.760044\pi$
$463$	−31.3751	−1.45812	−0.729062	+	0.684447i	$0.760044\pi$
$464$	83.4085	3.87214
$465$	−0.830938	−0.0385338
$466$	79.7547	3.69456
$467$	−5.90578	−0.273287	−0.136643	−	0.990620i	$-0.543631\pi$
$467$	−5.90578	−0.273287	−0.136643	+	0.990620i	$0.543631\pi$
$468$	0	0
$469$	35.5138	1.63988
$470$	−60.8298	−2.80587
$471$	7.28502	0.335676
$472$	−36.0166	−1.65780
$473$	6.24920	0.287338
$474$	−24.1849	−1.11085
$475$	0.0532243	0.00244210
$476$	−58.9340	−2.70123
$477$	−18.7546	−0.858713
$478$	2.32363	0.106281
$479$	−5.29228	−0.241811	−0.120905	−	0.992664i	$-0.538580\pi$
$479$	−5.29228	−0.241811	−0.120905	+	0.992664i	$0.538580\pi$
$480$	65.3668	2.98357
$481$	0	0
$482$	−18.2932	−0.833234
$483$	14.9830	0.681752
$484$	5.32282	0.241946
$485$	−31.3890	−1.42530
$486$	43.6168	1.97850
$487$	15.4866	0.701763	0.350881	−	0.936420i	$-0.385882\pi$
$487$	15.4866	0.701763	0.350881	+	0.936420i	$0.385882\pi$
$488$	−56.9173	−2.57653
$489$	−0.403558	−0.0182495
$490$	83.6305	3.77804
$491$	−31.9189	−1.44048	−0.720240	−	0.693725i	$-0.755968\pi$
$491$	−31.9189	−1.44048	−0.720240	+	0.693725i	$0.755968\pi$
$492$	33.6796	1.51839
$493$	17.0560	0.768162
$494$	0	0
$495$	7.42419	0.333692
$496$	−3.31506	−0.148851
$497$	31.7819	1.42561
$498$	−1.42151	−0.0636994
$499$	5.83312	0.261126	0.130563	−	0.991440i	$-0.458321\pi$
$499$	5.83312	0.261126	0.130563	+	0.991440i	$0.458321\pi$
$500$	52.5792	2.35141
$501$	15.3228	0.684573
$502$	65.2517	2.91233
$503$	0.285275	0.0127198	0.00635990	−	0.999980i	$-0.497976\pi$
$503$	0.285275	0.0127198	0.00635990	+	0.999980i	$0.497976\pi$
$504$	73.9171	3.29253
$505$	−2.37528	−0.105699
$506$	10.6736	0.474500
$507$	0	0
$508$	69.8821	3.10052
$509$	−34.6860	−1.53743	−0.768714	−	0.639592i	$-0.779103\pi$
$509$	−34.6860	−1.53743	−0.768714	+	0.639592i	$0.779103\pi$
$510$	25.9826	1.15053
$511$	0.658173	0.0291159
$512$	14.6475	0.647332
$513$	−0.0334226	−0.00147564
$514$	32.0834	1.41514
$515$	−51.4180	−2.26575
$516$	−31.9401	−1.40608
$517$	6.29173	0.276710
$518$	8.58261	0.377098
$519$	−1.38005	−0.0605775
$520$	0	0
$521$	36.6073	1.60379	0.801897	−	0.597463i	$-0.203824\pi$
$521$	36.6073	1.60379	0.801897	+	0.597463i	$0.203824\pi$
$522$	−34.2682	−1.49988
$523$	−1.29679	−0.0567048	−0.0283524	−	0.999598i	$-0.509026\pi$
$523$	−1.29679	−0.0567048	−0.0283524	+	0.999598i	$0.509026\pi$
$524$	88.1303	3.84999
$525$	−29.4957	−1.28730
$526$	31.2874	1.36420
$527$	−0.677888	−0.0295293
$528$	−13.1423	−0.571943
$529$	−7.44230	−0.323578
$530$	87.2593	3.79030
$531$	8.32337	0.361203
$532$	−0.144337	−0.00625781
$533$	0	0
$534$	−44.3441	−1.91896
$535$	25.4252	1.09923
$536$	−80.7208	−3.48661
$537$	16.1606	0.697383
$538$	65.1268	2.80781
$539$	−8.65004	−0.372584
$540$	−92.7277	−3.99037
$541$	23.0243	0.989893	0.494947	−	0.868923i	$-0.335188\pi$
$541$	23.0243	0.989893	0.494947	+	0.868923i	$0.335188\pi$
$542$	−50.4980	−2.16907
$543$	4.66152	0.200045
$544$	53.3270	2.28637
$545$	27.7598	1.18910
$546$	0	0
$547$	16.9199	0.723441	0.361721	−	0.932287i	$-0.382189\pi$
$547$	16.9199	0.723441	0.361721	+	0.932287i	$0.382189\pi$
$548$	95.4878	4.07904
$549$	13.1535	0.561377
$550$	−21.0121	−0.895960
$551$	0.0417724	0.00177956
$552$	−34.0556	−1.44950
$553$	36.8208	1.56578
$554$	1.10345	0.0468811
$555$	−2.75042	−0.116749
$556$	43.6850	1.85266
$557$	9.45511	0.400626	0.200313	−	0.979732i	$-0.435804\pi$
$557$	9.45511	0.400626	0.200313	+	0.979732i	$0.435804\pi$
$558$	1.36199	0.0576574
$559$	0	0
$560$	−193.448	−8.17469
$561$	−2.68742	−0.113463
$562$	82.7178	3.48924
$563$	−41.4269	−1.74593	−0.872967	−	0.487779i	$-0.837807\pi$
$563$	−41.4269	−1.74593	−0.872967	+	0.487779i	$0.837807\pi$
$564$	−32.1574	−1.35407
$565$	−48.1071	−2.02388
$566$	39.4997	1.66029
$567$	−6.13955	−0.257837
$568$	−72.2383	−3.03105
$569$	−9.18281	−0.384963	−0.192482	−	0.981301i	$-0.561654\pi$
$569$	−9.18281	−0.384963	−0.192482	+	0.981301i	$0.561654\pi$
$570$	0.0636349	0.00266537
$571$	−17.2362	−0.721311	−0.360655	−	0.932699i	$-0.617447\pi$
$571$	−17.2362	−0.721311	−0.360655	+	0.932699i	$0.617447\pi$
$572$	0	0
$573$	11.1060	0.463961
$574$	−70.5427	−2.94440
$575$	−30.6269	−1.27723
$576$	−50.2607	−2.09420
$577$	23.4108	0.974603	0.487301	−	0.873234i	$-0.337981\pi$
$577$	23.4108	0.974603	0.487301	+	0.873234i	$0.337981\pi$
$578$	−24.8063	−1.03181
$579$	−25.9214	−1.07726
$580$	115.893	4.81221
$581$	2.16421	0.0897864
$582$	−22.8286	−0.946276
$583$	−9.02538	−0.373793
$584$	−1.49599	−0.0619044
$585$	0	0
$586$	78.7743	3.25414
$587$	23.3954	0.965633	0.482817	−	0.875721i	$-0.339614\pi$
$587$	23.3954	0.965633	0.482817	+	0.875721i	$0.339614\pi$
$588$	44.2109	1.82323
$589$	−0.00166024	−6.84090e−5 0
$590$	−38.7261	−1.59433
$591$	−16.0780	−0.661359
$592$	−10.9729	−0.450985
$593$	37.8389	1.55386	0.776929	−	0.629588i	$-0.216776\pi$
$593$	37.8389	1.55386	0.776929	+	0.629588i	$0.216776\pi$
$594$	13.1947	0.541386
$595$	−39.5577	−1.62171
$596$	−32.0444	−1.31259
$597$	23.4212	0.958566
$598$	0	0
$599$	24.6076	1.00544	0.502720	−	0.864449i	$-0.332333\pi$
$599$	24.6076	1.00544	0.502720	+	0.864449i	$0.332333\pi$
$600$	67.0419	2.73697
$601$	31.6065	1.28926	0.644628	−	0.764496i	$-0.277012\pi$
$601$	31.6065	1.28926	0.644628	+	0.764496i	$0.277012\pi$
$602$	66.8992	2.72661
$603$	18.6544	0.759666
$604$	50.7269	2.06405
$605$	3.57279	0.145254
$606$	−1.72750	−0.0701747
$607$	4.05847	0.164728	0.0823640	−	0.996602i	$-0.473753\pi$
$607$	4.05847	0.164728	0.0823640	+	0.996602i	$0.473753\pi$
$608$	0.130605	0.00529673
$609$	−23.1493	−0.938056
$610$	−61.1991	−2.47788
$611$	0	0
$612$	−30.9563	−1.25134
$613$	−30.8970	−1.24792	−0.623959	−	0.781457i	$-0.714477\pi$
$613$	−30.8970	−1.24792	−0.623959	+	0.781457i	$0.714477\pi$
$614$	−66.0822	−2.66686
$615$	22.6064	0.911580
$616$	35.5716	1.43322
$617$	33.9704	1.36759	0.683797	−	0.729672i	$-0.260327\pi$
$617$	33.9704	1.36759	0.683797	+	0.729672i	$0.260327\pi$
$618$	−37.3953	−1.50426
$619$	10.1642	0.408535	0.204267	−	0.978915i	$-0.434519\pi$
$619$	10.1642	0.408535	0.204267	+	0.978915i	$0.434519\pi$
$620$	−4.60617	−0.184988
$621$	19.2324	0.771770
$622$	71.2970	2.85875
$623$	67.5126	2.70484
$624$	0	0
$625$	−3.53176	−0.141271
$626$	−79.1877	−3.16498
$627$	−0.00658186	−0.000262854 0
$628$	40.3834	1.61147
$629$	−2.24383	−0.0894672
$630$	79.4778	3.16647
$631$	−0.696721	−0.0277360	−0.0138680	−	0.999904i	$-0.504414\pi$
$631$	−0.696721	−0.0277360	−0.0138680	+	0.999904i	$0.504414\pi$
$632$	−83.6915	−3.32907
$633$	20.1398	0.800485
$634$	43.8380	1.74103
$635$	46.9063	1.86142
$636$	46.1293	1.82914
$637$	0	0
$638$	−16.4911	−0.652888
$639$	16.6941	0.660410
$640$	97.6979	3.86185
$641$	−40.2357	−1.58922	−0.794608	−	0.607123i	$-0.792323\pi$
$641$	−40.2357	−1.58922	−0.794608	+	0.607123i	$0.792323\pi$
$642$	18.4912	0.729790
$643$	17.1540	0.676486	0.338243	−	0.941059i	$-0.390167\pi$
$643$	17.1540	0.676486	0.338243	+	0.941059i	$0.390167\pi$
$644$	83.0562	3.27287
$645$	−21.4388	−0.844154
$646$	0.0519140	0.00204253
$647$	−27.6409	−1.08668	−0.543338	−	0.839514i	$-0.682840\pi$
$647$	−27.6409	−1.08668	−0.543338	+	0.839514i	$0.682840\pi$
$648$	13.9548	0.548197
$649$	4.00551	0.157230
$650$	0	0
$651$	0.920066	0.0360602
$652$	−2.23706	−0.0876101
$653$	−31.7645	−1.24304	−0.621520	−	0.783398i	$-0.713485\pi$
$653$	−31.7645	−1.24304	−0.621520	+	0.783398i	$0.713485\pi$
$654$	20.1891	0.789458
$655$	59.1549	2.31138
$656$	90.1894	3.52131
$657$	0.345720	0.0134878
$658$	67.3546	2.62575
$659$	23.2018	0.903813	0.451907	−	0.892065i	$-0.350744\pi$
$659$	23.2018	0.903813	0.451907	+	0.892065i	$0.350744\pi$
$660$	−18.2607	−0.710799
$661$	−31.7645	−1.23550	−0.617749	−	0.786376i	$-0.711955\pi$
$661$	−31.7645	−1.23550	−0.617749	+	0.786376i	$0.711955\pi$
$662$	−25.4661	−0.989770
$663$	0	0
$664$	−4.91911	−0.190898
$665$	−0.0968822	−0.00375693
$666$	4.50820	0.174689
$667$	−24.0371	−0.930722
$668$	84.9396	3.28641
$669$	2.07412	0.0801899
$670$	−86.7933	−3.35312
$671$	6.32993	0.244364
$672$	−72.3782	−2.79205
$673$	−17.8907	−0.689635	−0.344817	−	0.938670i	$-0.612059\pi$
$673$	−17.8907	−0.689635	−0.344817	+	0.938670i	$0.612059\pi$
$674$	−93.2573	−3.59214
$675$	−37.8610	−1.45727
$676$	0	0
$677$	6.49534	0.249636	0.124818	−	0.992180i	$-0.460165\pi$
$677$	6.49534	0.249636	0.124818	+	0.992180i	$0.460165\pi$
$678$	−34.9874	−1.34368
$679$	34.7559	1.33381
$680$	89.9123	3.44798
$681$	18.3034	0.701388
$682$	0.655437	0.0250980
$683$	−18.8733	−0.722169	−0.361084	−	0.932533i	$-0.617593\pi$
$683$	−18.8733	−0.722169	−0.361084	+	0.932533i	$0.617593\pi$
$684$	−0.0758162	−0.00289891
$685$	64.0934	2.44888
$686$	−17.6641	−0.674418
$687$	−17.9612	−0.685264
$688$	−85.5312	−3.26085
$689$	0	0
$690$	−36.6175	−1.39400
$691$	−15.6086	−0.593781	−0.296890	−	0.954912i	$-0.595950\pi$
$691$	−15.6086	−0.593781	−0.296890	+	0.954912i	$0.595950\pi$
$692$	−7.65010	−0.290813
$693$	−8.22052	−0.312272
$694$	−47.0284	−1.78517
$695$	29.3223	1.11226
$696$	52.6169	1.99444
$697$	18.4426	0.698563
$698$	−4.75092	−0.179825
$699$	28.3000	1.07041
$700$	−163.505	−6.17990
$701$	−28.0280	−1.05860	−0.529301	−	0.848434i	$-0.677546\pi$
$701$	−28.0280	−1.05860	−0.529301	+	0.848434i	$0.677546\pi$
$702$	0	0
$703$	−0.00549543	−0.000207264 0
$704$	−24.1873	−0.911593
$705$	−21.5848	−0.812929
$706$	24.7054	0.929800
$707$	2.63006	0.0989136
$708$	−20.4724	−0.769400
$709$	−23.0101	−0.864161	−0.432081	−	0.901835i	$-0.642220\pi$
$709$	−23.0101	−0.864161	−0.432081	+	0.901835i	$0.642220\pi$
$710$	−77.6727	−2.91501
$711$	19.3409	0.725342
$712$	−153.452	−5.75086
$713$	0.955354	0.0357783
$714$	−28.7695	−1.07667
$715$	0	0
$716$	89.5839	3.34791
$717$	0.824515	0.0307921
$718$	15.0635	0.562165
$719$	−10.3567	−0.386239	−0.193120	−	0.981175i	$-0.561861\pi$
$719$	−10.3567	−0.386239	−0.193120	+	0.981175i	$0.561861\pi$
$720$	−101.613	−3.78689
$721$	56.9332	2.12030
$722$	−51.4152	−1.91348
$723$	−6.49114	−0.241408
$724$	25.8404	0.960351
$725$	47.3196	1.75741
$726$	2.59842	0.0964363
$727$	4.61443	0.171140	0.0855699	−	0.996332i	$-0.472729\pi$
$727$	4.61443	0.171140	0.0855699	+	0.996332i	$0.472729\pi$
$728$	0	0
$729$	10.8210	0.400779
$730$	−1.60853	−0.0595343
$731$	−17.4900	−0.646892
$732$	−32.3527	−1.19579
$733$	18.5479	0.685081	0.342541	−	0.939503i	$-0.388713\pi$
$733$	18.5479	0.685081	0.342541	+	0.939503i	$0.388713\pi$
$734$	−29.2391	−1.07924
$735$	29.6753	1.09459
$736$	−75.1542	−2.77022
$737$	8.97718	0.330679
$738$	−37.0541	−1.36398
$739$	−11.4875	−0.422573	−0.211286	−	0.977424i	$-0.567765\pi$
$739$	−11.4875	−0.422573	−0.211286	+	0.977424i	$0.567765\pi$
$740$	−15.2465	−0.560474
$741$	0	0
$742$	−96.6189	−3.54699
$743$	−6.95186	−0.255039	−0.127519	−	0.991836i	$-0.540702\pi$
$743$	−6.95186	−0.255039	−0.127519	+	0.991836i	$0.540702\pi$
$744$	−2.09125	−0.0766691
$745$	−21.5089	−0.788023
$746$	10.0645	0.368487
$747$	1.13680	0.0415932
$748$	−14.8973	−0.544700
$749$	−28.1523	−1.02866
$750$	25.6674	0.937240
$751$	9.67208	0.352939	0.176470	−	0.984306i	$-0.443532\pi$
$751$	9.67208	0.352939	0.176470	+	0.984306i	$0.443532\pi$
$752$	−86.1133	−3.14023
$753$	23.1538	0.843772
$754$	0	0
$755$	34.0490	1.23917
$756$	102.674	3.73421
$757$	−6.61489	−0.240422	−0.120211	−	0.992748i	$-0.538357\pi$
$757$	−6.61489	−0.240422	−0.120211	+	0.992748i	$0.538357\pi$
$758$	−17.5712	−0.638217
$759$	3.78741	0.137474
$760$	0.220207	0.00798776
$761$	22.0974	0.801031	0.400515	−	0.916290i	$-0.368831\pi$
$761$	22.0974	0.801031	0.400515	+	0.916290i	$0.368831\pi$
$762$	34.1140	1.23582
$763$	−30.7374	−1.11277
$764$	61.5646	2.22733
$765$	−20.7786	−0.751250
$766$	−11.2529	−0.406585
$767$	0	0
$768$	24.6036	0.887806
$769$	−2.23113	−0.0804564	−0.0402282	−	0.999191i	$-0.512808\pi$
$769$	−2.23113	−0.0804564	−0.0402282	+	0.999191i	$0.512808\pi$
$770$	38.2476	1.37835
$771$	11.3844	0.410000
$772$	−143.691	−5.17157
$773$	11.1675	0.401667	0.200833	−	0.979625i	$-0.435635\pi$
$773$	11.1675	0.401667	0.200833	+	0.979625i	$0.435635\pi$
$774$	35.1403	1.26309
$775$	−1.88071	−0.0675572
$776$	−78.9980	−2.83586
$777$	3.04544	0.109255
$778$	33.9875	1.21851
$779$	0.0451684	0.00161832
$780$	0	0
$781$	8.03382	0.287473
$782$	−29.8730	−1.06825
$783$	−29.7147	−1.06192
$784$	118.391	4.22825
$785$	27.1062	0.967461
$786$	43.0222	1.53455
$787$	14.6600	0.522572	0.261286	−	0.965261i	$-0.415853\pi$
$787$	14.6600	0.522572	0.261286	+	0.965261i	$0.415853\pi$
$788$	−89.1257	−3.17497
$789$	11.1020	0.395241
$790$	−89.9875	−3.20161
$791$	53.2672	1.89396
$792$	18.6847	0.663934
$793$	0	0
$794$	−48.9655	−1.73772
$795$	30.9629	1.09814
$796$	129.832	4.60176
$797$	0.631320	0.0223625	0.0111813	−	0.999937i	$-0.496441\pi$
$797$	0.631320	0.0223625	0.0111813	+	0.999937i	$0.496441\pi$
$798$	−0.0704605	−0.00249427
$799$	−17.6091	−0.622964
$800$	147.949	5.23078
$801$	35.4625	1.25300
$802$	21.8763	0.772479
$803$	0.166373	0.00587117
$804$	−45.8829	−1.61817
$805$	55.7491	1.96490
$806$	0	0
$807$	23.1095	0.813492
$808$	−5.97797	−0.210304
$809$	6.32576	0.222402	0.111201	−	0.993798i	$-0.464530\pi$
$809$	6.32576	0.222402	0.111201	+	0.993798i	$0.464530\pi$
$810$	15.0046	0.527208
$811$	51.1786	1.79712	0.898562	−	0.438846i	$-0.144613\pi$
$811$	51.1786	1.79712	0.898562	+	0.438846i	$0.144613\pi$
$812$	−128.324	−4.50331
$813$	−17.9186	−0.628433
$814$	2.16951	0.0760413
$815$	−1.50156	−0.0525975
$816$	36.7821	1.28763
$817$	−0.0428355	−0.00149862
$818$	51.2371	1.79146
$819$	0	0
$820$	125.315	4.37620
$821$	−16.8298	−0.587364	−0.293682	−	0.955903i	$-0.594881\pi$
$821$	−16.8298	−0.587364	−0.293682	+	0.955903i	$0.594881\pi$
$822$	46.6139	1.62585
$823$	52.7955	1.84034	0.920168	−	0.391524i	$-0.128052\pi$
$823$	52.7955	1.84034	0.920168	+	0.391524i	$0.128052\pi$
$824$	−129.406	−4.50806
$825$	−7.45591	−0.259581
$826$	42.8799	1.49198
$827$	−8.61118	−0.299440	−0.149720	−	0.988728i	$-0.547837\pi$
$827$	−8.61118	−0.299440	−0.149720	+	0.988728i	$0.547837\pi$
$828$	43.6271	1.51615
$829$	11.2584	0.391021	0.195510	−	0.980702i	$-0.437364\pi$
$829$	11.2584	0.391021	0.195510	+	0.980702i	$0.437364\pi$
$830$	−5.28917	−0.183590
$831$	0.391547	0.0135826
$832$	0	0
$833$	24.2094	0.838807
$834$	21.3255	0.738442
$835$	57.0132	1.97302
$836$	−0.0364855	−0.00126188
$837$	1.18101	0.0408216
$838$	−60.2987	−2.08298
$839$	−8.76246	−0.302514	−0.151257	−	0.988494i	$-0.548332\pi$
$839$	−8.76246	−0.302514	−0.151257	+	0.988494i	$0.548332\pi$
$840$	−122.034	−4.21057
$841$	8.13815	0.280626
$842$	−45.7051	−1.57510
$843$	29.3515	1.01092
$844$	111.642	3.84287
$845$	0	0
$846$	35.3794	1.21637
$847$	−3.95601	−0.135930
$848$	123.528	4.24197
$849$	14.0160	0.481028
$850$	58.8080	2.01710
$851$	3.16224	0.108400
$852$	−41.0614	−1.40674
$853$	−21.4641	−0.734917	−0.367458	−	0.930040i	$-0.619772\pi$
$853$	−21.4641	−0.734917	−0.367458	+	0.930040i	$0.619772\pi$
$854$	67.7635	2.31882
$855$	−0.0508895	−0.00174038
$856$	63.9885	2.18708
$857$	−28.8303	−0.984823	−0.492412	−	0.870362i	$-0.663885\pi$
$857$	−28.8303	−0.984823	−0.492412	+	0.870362i	$0.663885\pi$
$858$	0	0
$859$	−13.5007	−0.460639	−0.230320	−	0.973115i	$-0.573977\pi$
$859$	−13.5007	−0.460639	−0.230320	+	0.973115i	$0.573977\pi$
$860$	−118.843	−4.05251
$861$	−25.0313	−0.853063
$862$	34.7665	1.18415
$863$	37.4769	1.27573	0.637864	−	0.770149i	$-0.279818\pi$
$863$	37.4769	1.27573	0.637864	+	0.770149i	$0.279818\pi$
$864$	−92.9055	−3.16071
$865$	−5.13491	−0.174592
$866$	33.3277	1.13252
$867$	−8.80224	−0.298940
$868$	5.10024	0.173114
$869$	9.30756	0.315737
$870$	56.5752	1.91808
$871$	0	0
$872$	69.8642	2.36590
$873$	18.2563	0.617881
$874$	−0.0731629	−0.00247477
$875$	−39.0778	−1.32107
$876$	−0.850342	−0.0287304
$877$	9.81599	0.331462	0.165731	−	0.986171i	$-0.447002\pi$
$877$	9.81599	0.331462	0.165731	+	0.986171i	$0.447002\pi$
$878$	−15.6811	−0.529213
$879$	27.9522	0.942803
$880$	−48.8998	−1.64841
$881$	37.2709	1.25569	0.627844	−	0.778339i	$-0.283938\pi$
$881$	37.2709	1.25569	0.627844	+	0.778339i	$0.283938\pi$
$882$	−48.6406	−1.63781
$883$	−36.1317	−1.21593	−0.607964	−	0.793965i	$-0.708013\pi$
$883$	−36.1317	−1.21593	−0.607964	+	0.793965i	$0.708013\pi$
$884$	0	0
$885$	−13.7415	−0.461916
$886$	−70.3536	−2.36358
$887$	−50.2943	−1.68872	−0.844358	−	0.535779i	$-0.820018\pi$
$887$	−50.2943	−1.68872	−0.844358	+	0.535779i	$0.820018\pi$
$888$	−6.92210	−0.232291
$889$	−51.9376	−1.74193
$890$	−164.996	−5.53068
$891$	−1.55195	−0.0519924
$892$	11.4975	0.384966
$893$	−0.0431270	−0.00144319
$894$	−15.6430	−0.523179
$895$	60.1306	2.00994
$896$	−108.177	−3.61395
$897$	0	0
$898$	−64.5952	−2.15557
$899$	−1.47605	−0.0492291
$900$	−85.8844	−2.86281
$901$	25.2599	0.841529
$902$	−17.8318	−0.593733
$903$	23.7384	0.789965
$904$	−121.073	−4.02683
$905$	17.3446	0.576555
$906$	24.7631	0.822700
$907$	−12.9985	−0.431609	−0.215805	−	0.976437i	$-0.569237\pi$
$907$	−12.9985	−0.431609	−0.215805	+	0.976437i	$0.569237\pi$
$908$	101.462	3.36714
$909$	1.38150	0.0458213
$910$	0	0
$911$	44.3455	1.46923	0.734616	−	0.678483i	$-0.237362\pi$
$911$	44.3455	1.46923	0.734616	+	0.678483i	$0.237362\pi$
$912$	0.0900843	0.00298299
$913$	0.547068	0.0181053
$914$	−18.0582	−0.597312
$915$	−21.7158	−0.717902
$916$	−99.5653	−3.28973
$917$	−65.5000	−2.16300
$918$	−36.9289	−1.21884
$919$	−47.6103	−1.57052	−0.785260	−	0.619167i	$-0.787471\pi$
$919$	−47.6103	−1.57052	−0.785260	+	0.619167i	$0.787471\pi$
$920$	−126.714	−4.17764
$921$	−23.4485	−0.772654
$922$	−44.2148	−1.45614
$923$	0	0
$924$	20.2194	0.665171
$925$	−6.22520	−0.204683
$926$	−84.9032	−2.79009
$927$	29.9054	0.982222
$928$	116.116	3.81168
$929$	−33.0705	−1.08501	−0.542503	−	0.840054i	$-0.682523\pi$
$929$	−33.0705	−1.08501	−0.542503	+	0.840054i	$0.682523\pi$
$930$	−2.24858	−0.0737337
$931$	0.0592921	0.00194322
$932$	156.877	5.13867
$933$	25.2989	0.828249
$934$	−15.9815	−0.522929
$935$	−9.99939	−0.327015
$936$	0	0
$937$	−43.8560	−1.43271	−0.716356	−	0.697735i	$-0.754191\pi$
$937$	−43.8560	−1.43271	−0.716356	+	0.697735i	$0.754191\pi$
$938$	96.1029	3.13787
$939$	−28.0989	−0.916971
$940$	−119.652	−3.90261
$941$	27.1576	0.885313	0.442657	−	0.896691i	$-0.354036\pi$
$941$	27.1576	0.885313	0.442657	+	0.896691i	$0.354036\pi$
$942$	19.7138	0.642310
$943$	−25.9913	−0.846393
$944$	−54.8223	−1.78432
$945$	68.9169	2.24187
$946$	16.9108	0.549817
$947$	24.4338	0.793991	0.396996	−	0.917821i	$-0.370053\pi$
$947$	24.4338	0.793991	0.396996	+	0.917821i	$0.370053\pi$
$948$	−47.5715	−1.54505
$949$	0	0
$950$	0.144029	0.00467291
$951$	15.5554	0.504418
$952$	−99.5565	−3.22665
$953$	−0.830376	−0.0268985	−0.0134493	−	0.999910i	$-0.504281\pi$
$953$	−0.830376	−0.0268985	−0.0134493	+	0.999910i	$0.504281\pi$
$954$	−50.7512	−1.64313
$955$	41.3234	1.33720
$956$	4.57057	0.147823
$957$	−5.85167	−0.189158
$958$	−14.3213	−0.462700
$959$	−70.9682	−2.29168
$960$	82.9782	2.67811
$961$	−30.9413	−0.998108
$962$	0	0
$963$	−14.7876	−0.476524
$964$	−35.9826	−1.15892
$965$	−96.4487	−3.10479
$966$	40.5452	1.30452
$967$	−3.68739	−0.118578	−0.0592892	−	0.998241i	$-0.518883\pi$
$967$	−3.68739	−0.118578	−0.0592892	+	0.998241i	$0.518883\pi$
$968$	8.99178	0.289007
$969$	0.0184211	0.000591771 0
$970$	−84.9409	−2.72729
$971$	−10.8602	−0.348520	−0.174260	−	0.984700i	$-0.555753\pi$
$971$	−10.8602	−0.348520	−0.174260	+	0.984700i	$0.555753\pi$
$972$	85.7938	2.75184
$973$	−32.4675	−1.04086
$974$	41.9077	1.34281
$975$	0	0
$976$	−86.6361	−2.77316
$977$	−30.9277	−0.989466	−0.494733	−	0.869045i	$-0.664734\pi$
$977$	−30.9277	−0.989466	−0.494733	+	0.869045i	$0.664734\pi$
$978$	−1.09206	−0.0349201
$979$	17.0658	0.545426
$980$	164.500	5.25477
$981$	−16.1455	−0.515485
$982$	−86.3748	−2.75633
$983$	−12.9691	−0.413650	−0.206825	−	0.978378i	$-0.566313\pi$
$983$	−12.9691	−0.413650	−0.206825	+	0.978378i	$0.566313\pi$
$984$	56.8946	1.81373
$985$	−59.8230	−1.90612
$986$	46.1547	1.46986
$987$	23.9000	0.760745
$988$	0	0
$989$	24.6489	0.783789
$990$	20.0904	0.638514
$991$	5.95855	0.189279	0.0946397	−	0.995512i	$-0.469830\pi$
$991$	5.95855	0.189279	0.0946397	+	0.995512i	$0.469830\pi$
$992$	−4.61500	−0.146527
$993$	−9.03637	−0.286761
$994$	86.0041	2.72788
$995$	87.1458	2.76271
$996$	−2.79610	−0.0885977
$997$	−6.47004	−0.204908	−0.102454	−	0.994738i	$-0.532669\pi$
$997$	−6.47004	−0.204908	−0.102454	+	0.994738i	$0.532669\pi$
$998$	15.7848	0.499660
$999$	3.90916	0.123680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.s.1.20	✓	21
13.12	even	2		1859.2.a.t.1.2	yes	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.20	✓	21	1.1	even	1	trivial
1859.2.a.t.1.2	yes	21	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+2.70607 q^{2} +0.960218 q^{3} +5.32282 q^{4} +3.57279 q^{5} +2.59842 q^{6} -3.95601 q^{7} +8.99178 q^{8} -2.07798 q^{9} +O(q^{10})\)	\(q+2.70607 q^{2} +0.960218 q^{3} +5.32282 q^{4} +3.57279 q^{5} +2.59842 q^{6} -3.95601 q^{7} +8.99178 q^{8} -2.07798 q^{9} +9.66821 q^{10} -1.00000 q^{11} +5.11106 q^{12} -10.7053 q^{14} +3.43065 q^{15} +13.6867 q^{16} +2.79876 q^{17} -5.62316 q^{18} +0.00685455 q^{19} +19.0173 q^{20} -3.79863 q^{21} -2.70607 q^{22} -3.94433 q^{23} +8.63406 q^{24} +7.76481 q^{25} -4.87597 q^{27} -21.0571 q^{28} +6.09411 q^{29} +9.28359 q^{30} -0.242210 q^{31} +19.0537 q^{32} -0.960218 q^{33} +7.57365 q^{34} -14.1340 q^{35} -11.0607 q^{36} -0.801720 q^{37} +0.0185489 q^{38} +32.1257 q^{40} +6.58954 q^{41} -10.2794 q^{42} -6.24920 q^{43} -5.32282 q^{44} -7.42419 q^{45} -10.6736 q^{46} -6.29173 q^{47} +13.1423 q^{48} +8.65004 q^{49} +21.0121 q^{50} +2.68742 q^{51} +9.02538 q^{53} -13.1947 q^{54} -3.57279 q^{55} -35.5716 q^{56} +0.00658186 q^{57} +16.4911 q^{58} -4.00551 q^{59} +18.2607 q^{60} -6.32993 q^{61} -0.655437 q^{62} +8.22052 q^{63} +24.1873 q^{64} -2.59842 q^{66} -8.97718 q^{67} +14.8973 q^{68} -3.78741 q^{69} -38.2476 q^{70} -8.03382 q^{71} -18.6847 q^{72} -0.166373 q^{73} -2.16951 q^{74} +7.45591 q^{75} +0.0364855 q^{76} +3.95601 q^{77} -9.30756 q^{79} +48.8998 q^{80} +1.55195 q^{81} +17.8318 q^{82} -0.547068 q^{83} -20.2194 q^{84} +9.99939 q^{85} -16.9108 q^{86} +5.85167 q^{87} -8.99178 q^{88} -17.0658 q^{89} -20.0904 q^{90} -20.9949 q^{92} -0.232574 q^{93} -17.0259 q^{94} +0.0244899 q^{95} +18.2957 q^{96} -8.78558 q^{97} +23.4076 q^{98} +2.07798 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9 + 18 * q^10 - 21 * q^11 + 23 * q^12 + 20 * q^14 - 16 * q^15 + 50 * q^16 + 16 * q^17 - 3 * q^18 + 11 * q^19 - 24 * q^20 + 5 * q^21 - 9 * q^23 + 54 * q^24 + 36 * q^25 + 11 * q^28 + 28 * q^29 + 21 * q^30 - 15 * q^31 + 61 * q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 45 * q^36 + 12 * q^37 + q^38 + 55 * q^40 + 4 * q^41 - 34 * q^42 + 17 * q^43 - 32 * q^44 - 9 * q^45 - 11 * q^46 - 36 * q^47 + 24 * q^48 + 72 * q^49 + 9 * q^50 + 2 * q^51 + 19 * q^53 - q^54 + 7 * q^55 + 44 * q^56 + 4 * q^57 + 33 * q^58 - 54 * q^59 - 64 * q^60 + 98 * q^61 - 29 * q^62 + 81 * q^63 + 63 * q^64 - 19 * q^66 - 25 * q^67 + 4 * q^68 + 89 * q^69 - 65 * q^70 - 37 * q^71 - 55 * q^72 - 8 * q^73 - 11 * q^74 + 24 * q^75 - 13 * q^76 + q^77 + 24 * q^79 - 26 * q^80 + 81 * q^81 + 26 * q^82 + 34 * q^83 + 103 * q^84 + 11 * q^85 - 30 * q^86 + 32 * q^87 - 3 * q^88 - 6 * q^89 + 47 * q^90 - 80 * q^92 - 41 * q^93 + 40 * q^94 + 20 * q^95 + 98 * q^96 + 5 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more