LMFDB - Embedded newform 1859.4.a.n.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.98336 q^{2} +6.46359 q^{3} +7.86718 q^{4} -1.70678 q^{5} -25.7468 q^{6} +18.7420 q^{7} +0.529060 q^{8} +14.7780 q^{9} +O(q^{10})$	\(q-3.98336 q^{2} +6.46359 q^{3} +7.86718 q^{4} -1.70678 q^{5} -25.7468 q^{6} +18.7420 q^{7} +0.529060 q^{8} +14.7780 q^{9} +6.79871 q^{10} +11.0000 q^{11} +50.8502 q^{12} -74.6562 q^{14} -11.0319 q^{15} -65.0449 q^{16} -24.0995 q^{17} -58.8660 q^{18} -10.9329 q^{19} -13.4275 q^{20} +121.141 q^{21} -43.8170 q^{22} +150.505 q^{23} +3.41962 q^{24} -122.087 q^{25} -78.9983 q^{27} +147.447 q^{28} -231.485 q^{29} +43.9441 q^{30} +86.4697 q^{31} +254.865 q^{32} +71.0995 q^{33} +95.9972 q^{34} -31.9884 q^{35} +116.261 q^{36} +22.2361 q^{37} +43.5496 q^{38} -0.902987 q^{40} -272.123 q^{41} -482.547 q^{42} -234.774 q^{43} +86.5390 q^{44} -25.2227 q^{45} -599.517 q^{46} +128.141 q^{47} -420.423 q^{48} +8.26294 q^{49} +486.317 q^{50} -155.769 q^{51} -534.401 q^{53} +314.679 q^{54} -18.7745 q^{55} +9.91564 q^{56} -70.6656 q^{57} +922.088 q^{58} -699.879 q^{59} -86.7900 q^{60} -42.4158 q^{61} -344.440 q^{62} +276.969 q^{63} -494.861 q^{64} -283.215 q^{66} +36.2575 q^{67} -189.595 q^{68} +972.803 q^{69} +127.422 q^{70} -90.9950 q^{71} +7.81842 q^{72} -177.627 q^{73} -88.5743 q^{74} -789.119 q^{75} -86.0110 q^{76} +206.162 q^{77} +8.76078 q^{79} +111.017 q^{80} -909.617 q^{81} +1083.97 q^{82} +502.622 q^{83} +953.035 q^{84} +41.1325 q^{85} +935.190 q^{86} -1496.22 q^{87} +5.81966 q^{88} +1091.56 q^{89} +100.471 q^{90} +1184.05 q^{92} +558.904 q^{93} -510.432 q^{94} +18.6600 q^{95} +1647.34 q^{96} -636.713 q^{97} -32.9143 q^{98} +162.557 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9}+O(q^{10}) $ 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9} - 158 q^{10} + 429 q^{11} - 351 q^{12} - 176 q^{14} - 30 q^{15} + 230 q^{16} - 244 q^{17} - 21 q^{18} + 70 q^{19} - 366 q^{20} + 142 q^{21} - 47 q^{23} - 846 q^{24} + 322 q^{25} - 416 q^{27} - 1131 q^{28} - 838 q^{29} - 293 q^{30} - 507 q^{31} + 1433 q^{32} - 253 q^{33} - 166 q^{34} - 498 q^{35} + 815 q^{36} - 89 q^{37} + 81 q^{38} - 2917 q^{40} - 618 q^{41} - 318 q^{42} - 1064 q^{43} + 1254 q^{44} - 238 q^{45} + 1331 q^{46} - 1499 q^{47} - 1460 q^{48} - 413 q^{49} + 2459 q^{50} - 2350 q^{51} - 2745 q^{53} + 845 q^{54} - 253 q^{55} - 2904 q^{56} - 1450 q^{57} + 2509 q^{58} - 2285 q^{59} + 3566 q^{60} - 6218 q^{61} - 911 q^{62} + 1930 q^{63} + 67 q^{64} - 847 q^{66} - 546 q^{67} - 170 q^{68} - 5254 q^{69} + 2195 q^{70} + 263 q^{71} + 2393 q^{72} + 1148 q^{73} + 775 q^{74} - 5385 q^{75} + 7247 q^{76} + 44 q^{77} - 3666 q^{79} - 5594 q^{80} - 1901 q^{81} - 4414 q^{82} - 2722 q^{83} + 9971 q^{84} - 1858 q^{85} - 2478 q^{86} - 2284 q^{87} + 231 q^{88} - 13 q^{89} - 6771 q^{90} - 2232 q^{92} + 1082 q^{93} - 7330 q^{94} - 2352 q^{95} - 5770 q^{96} + 1197 q^{97} - 6813 q^{98} + 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9 - 158 * q^10 + 429 * q^11 - 351 * q^12 - 176 * q^14 - 30 * q^15 + 230 * q^16 - 244 * q^17 - 21 * q^18 + 70 * q^19 - 366 * q^20 + 142 * q^21 - 47 * q^23 - 846 * q^24 + 322 * q^25 - 416 * q^27 - 1131 * q^28 - 838 * q^29 - 293 * q^30 - 507 * q^31 + 1433 * q^32 - 253 * q^33 - 166 * q^34 - 498 * q^35 + 815 * q^36 - 89 * q^37 + 81 * q^38 - 2917 * q^40 - 618 * q^41 - 318 * q^42 - 1064 * q^43 + 1254 * q^44 - 238 * q^45 + 1331 * q^46 - 1499 * q^47 - 1460 * q^48 - 413 * q^49 + 2459 * q^50 - 2350 * q^51 - 2745 * q^53 + 845 * q^54 - 253 * q^55 - 2904 * q^56 - 1450 * q^57 + 2509 * q^58 - 2285 * q^59 + 3566 * q^60 - 6218 * q^61 - 911 * q^62 + 1930 * q^63 + 67 * q^64 - 847 * q^66 - 546 * q^67 - 170 * q^68 - 5254 * q^69 + 2195 * q^70 + 263 * q^71 + 2393 * q^72 + 1148 * q^73 + 775 * q^74 - 5385 * q^75 + 7247 * q^76 + 44 * q^77 - 3666 * q^79 - 5594 * q^80 - 1901 * q^81 - 4414 * q^82 - 2722 * q^83 + 9971 * q^84 - 1858 * q^85 - 2478 * q^86 - 2284 * q^87 + 231 * q^88 - 13 * q^89 - 6771 * q^90 - 2232 * q^92 + 1082 * q^93 - 7330 * q^94 - 2352 * q^95 - 5770 * q^96 + 1197 * q^97 - 6813 * q^98 + 2860 * 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 $

$2$	−3.98336	−1.40833	−0.704166	−	0.710036i	$-0.748679\pi$
$2$	−3.98336	−1.40833	−0.704166	+	0.710036i	$0.748679\pi$
$3$	6.46359	1.24392	0.621959	−	0.783050i	$-0.286337\pi$
$3$	6.46359	1.24392	0.621959	+	0.783050i	$0.286337\pi$
$4$	7.86718	0.983398
$5$	−1.70678	−0.152659	−0.0763294	−	0.997083i	$-0.524320\pi$
$5$	−1.70678	−0.152659	−0.0763294	+	0.997083i	$0.524320\pi$
$6$	−25.7468	−1.75185
$7$	18.7420	1.01197	0.505987	−	0.862541i	$-0.331128\pi$
$7$	18.7420	1.01197	0.505987	+	0.862541i	$0.331128\pi$
$8$	0.529060	0.0233814
$9$	14.7780	0.547332
$10$	6.79871	0.214994
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	50.8502	1.22327
$13$	0	0
$13$	0	0
$14$	−74.6562	−1.42519
$15$	−11.0319	−0.189895
$16$	−65.0449	−1.01633
$17$	−24.0995	−0.343823	−0.171912	−	0.985112i	$-0.554994\pi$
$17$	−24.0995	−0.343823	−0.171912	+	0.985112i	$0.554994\pi$
$18$	−58.8660	−0.770824
$19$	−10.9329	−0.132009	−0.0660046	−	0.997819i	$-0.521025\pi$
$19$	−10.9329	−0.132009	−0.0660046	+	0.997819i	$0.521025\pi$
$20$	−13.4275	−0.150124
$21$	121.141	1.25881
$22$	−43.8170	−0.424628
$23$	150.505	1.36446	0.682228	−	0.731139i	$-0.261011\pi$
$23$	150.505	1.36446	0.682228	+	0.731139i	$0.261011\pi$
$24$	3.41962	0.0290845
$25$	−122.087	−0.976695
$26$	0	0
$27$	−78.9983	−0.563082
$28$	147.447	0.995172
$29$	−231.485	−1.48226	−0.741132	−	0.671360i	$-0.765711\pi$
$29$	−231.485	−1.48226	−0.741132	+	0.671360i	$0.765711\pi$
$30$	43.9441	0.267435
$31$	86.4697	0.500981	0.250491	−	0.968119i	$-0.419408\pi$
$31$	86.4697	0.500981	0.250491	+	0.968119i	$0.419408\pi$
$32$	254.865	1.40794
$33$	71.0995	0.375055
$34$	95.9972	0.484217
$35$	−31.9884	−0.154487
$36$	116.261	0.538245
$37$	22.2361	0.0987996	0.0493998	−	0.998779i	$-0.484269\pi$
$37$	22.2361	0.0987996	0.0493998	+	0.998779i	$0.484269\pi$
$38$	43.5496	0.185913
$39$	0	0
$40$	−0.902987	−0.00356937
$41$	−272.123	−1.03655	−0.518274	−	0.855214i	$-0.673425\pi$
$41$	−272.123	−1.03655	−0.518274	+	0.855214i	$0.673425\pi$
$42$	−482.547	−1.77282
$43$	−234.774	−0.832621	−0.416311	−	0.909222i	$-0.636677\pi$
$43$	−234.774	−0.832621	−0.416311	+	0.909222i	$0.636677\pi$
$44$	86.5390	0.296506
$45$	−25.2227	−0.0835549
$46$	−599.517	−1.92161
$47$	128.141	0.397687	0.198843	−	0.980031i	$-0.436282\pi$
$47$	128.141	0.397687	0.198843	+	0.980031i	$0.436282\pi$
$48$	−420.423	−1.26423
$49$	8.26294	0.0240902
$50$	486.317	1.37551
$51$	−155.769	−0.427688
$52$	0	0
$53$	−534.401	−1.38501	−0.692506	−	0.721412i	$-0.743493\pi$
$53$	−534.401	−1.38501	−0.692506	+	0.721412i	$0.743493\pi$
$54$	314.679	0.793007
$55$	−18.7745	−0.0460283
$56$	9.91564	0.0236613
$57$	−70.6656	−0.164209
$58$	922.088	2.08752
$59$	−699.879	−1.54435	−0.772174	−	0.635412i	$-0.780830\pi$
$59$	−699.879	−1.54435	−0.772174	+	0.635412i	$0.780830\pi$
$60$	−86.7900	−0.186742
$61$	−42.4158	−0.0890293	−0.0445147	−	0.999009i	$-0.514174\pi$
$61$	−42.4158	−0.0890293	−0.0445147	+	0.999009i	$0.514174\pi$
$62$	−344.440	−0.705548
$63$	276.969	0.553885
$64$	−494.861	−0.966525
$65$	0	0
$66$	−283.215	−0.528202
$67$	36.2575	0.0661128	0.0330564	−	0.999453i	$-0.489476\pi$
$67$	36.2575	0.0661128	0.0330564	+	0.999453i	$0.489476\pi$
$68$	−189.595	−0.338115
$69$	972.803	1.69727
$70$	127.422	0.217568
$71$	−90.9950	−0.152100	−0.0760501	−	0.997104i	$-0.524231\pi$
$71$	−90.9950	−0.152100	−0.0760501	+	0.997104i	$0.524231\pi$
$72$	7.81842	0.0127974
$73$	−177.627	−0.284790	−0.142395	−	0.989810i	$-0.545480\pi$
$73$	−177.627	−0.284790	−0.142395	+	0.989810i	$0.545480\pi$
$74$	−88.5743	−0.139143
$75$	−789.119	−1.21493
$76$	−86.0110	−0.129818
$77$	206.162	0.305121
$78$	0	0
$79$	8.76078	0.0124768	0.00623838	−	0.999981i	$-0.498014\pi$
$79$	8.76078	0.0124768	0.00623838	+	0.999981i	$0.498014\pi$
$80$	111.017	0.155151
$81$	−909.617	−1.24776
$82$	1083.97	1.45980
$83$	502.622	0.664698	0.332349	−	0.943156i	$-0.392159\pi$
$83$	502.622	0.664698	0.332349	+	0.943156i	$0.392159\pi$
$84$	953.035	1.23791
$85$	41.1325	0.0524876
$86$	935.190	1.17261
$87$	−1496.22	−1.84381
$88$	5.81966	0.00704974
$89$	1091.56	1.30006	0.650028	−	0.759910i	$-0.274757\pi$
$89$	1091.56	1.30006	0.650028	+	0.759910i	$0.274757\pi$
$90$	100.471	0.117673
$91$	0	0
$92$	1184.05	1.34180
$93$	558.904	0.623179
$94$	−510.432	−0.560075
$95$	18.6600	0.0201524
$96$	1647.34	1.75137
$97$	−636.713	−0.666478	−0.333239	−	0.942842i	$-0.608142\pi$
$97$	−636.713	−0.666478	−0.333239	+	0.942842i	$0.608142\pi$
$98$	−32.9143	−0.0339270
$99$	162.557	0.165027
$100$	−960.480	−0.960480
$101$	−21.2887	−0.0209733	−0.0104867	−	0.999945i	$-0.503338\pi$
$101$	−21.2887	−0.0209733	−0.0104867	+	0.999945i	$0.503338\pi$
$102$	620.486	0.602326
$103$	−158.384	−0.151515	−0.0757574	−	0.997126i	$-0.524137\pi$
$103$	−158.384	−0.151515	−0.0757574	+	0.997126i	$0.524137\pi$
$104$	0	0
$105$	−206.760	−0.192169
$106$	2128.71	1.95056
$107$	−435.778	−0.393722	−0.196861	−	0.980431i	$-0.563075\pi$
$107$	−435.778	−0.393722	−0.196861	+	0.980431i	$0.563075\pi$
$108$	−621.494	−0.553734
$109$	−1207.40	−1.06099	−0.530496	−	0.847687i	$-0.677994\pi$
$109$	−1207.40	−1.06099	−0.530496	+	0.847687i	$0.677994\pi$
$110$	74.7858	0.0648232
$111$	143.725	0.122899
$112$	−1219.07	−1.02850
$113$	−1063.40	−0.885279	−0.442640	−	0.896700i	$-0.645958\pi$
$113$	−1063.40	−0.885279	−0.442640	+	0.896700i	$0.645958\pi$
$114$	281.487	0.231260
$115$	−256.879	−0.208296
$116$	−1821.13	−1.45765
$117$	0	0
$118$	2787.87	2.17495
$119$	−451.674	−0.347940
$120$	−5.83653	−0.00444000
$121$	121.000	0.0909091
$122$	168.958	0.125383
$123$	−1758.89	−1.28938
$124$	680.273	0.492664
$125$	421.722	0.301760
$126$	−1103.27	−0.780054
$127$	−1404.39	−0.981254	−0.490627	−	0.871370i	$-0.663232\pi$
$127$	−1404.39	−0.981254	−0.490627	+	0.871370i	$0.663232\pi$
$128$	−67.7103	−0.0467563
$129$	−1517.48	−1.03571
$130$	0	0
$131$	2071.15	1.38135	0.690675	−	0.723165i	$-0.257314\pi$
$131$	2071.15	1.38135	0.690675	+	0.723165i	$0.257314\pi$
$132$	559.352	0.368829
$133$	−204.904	−0.133590
$134$	−144.427	−0.0931087
$135$	134.832	0.0859594
$136$	−12.7501	−0.00803905
$137$	−1765.19	−1.10081	−0.550404	−	0.834898i	$-0.685526\pi$
$137$	−1765.19	−1.10081	−0.550404	+	0.834898i	$0.685526\pi$
$138$	−3875.03	−2.39032
$139$	−1380.18	−0.842195	−0.421097	−	0.907015i	$-0.638355\pi$
$139$	−1380.18	−0.842195	−0.421097	+	0.907015i	$0.638355\pi$
$140$	−251.659	−0.151922
$141$	828.250	0.494689
$142$	362.466	0.214208
$143$	0	0
$144$	−961.230	−0.556268
$145$	395.093	0.226280
$146$	707.553	0.401079
$147$	53.4083	0.0299663
$148$	174.935	0.0971594
$149$	−1339.73	−0.736611	−0.368305	−	0.929705i	$-0.620062\pi$
$149$	−1339.73	−0.736611	−0.368305	+	0.929705i	$0.620062\pi$
$150$	3143.35	1.71102
$151$	2936.86	1.58277	0.791386	−	0.611316i	$-0.209360\pi$
$151$	2936.86	1.58277	0.791386	+	0.611316i	$0.209360\pi$
$152$	−5.78415	−0.00308655
$153$	−356.142	−0.188185
$154$	−821.219	−0.429712
$155$	−147.584	−0.0764792
$156$	0	0
$157$	2026.61	1.03020	0.515099	−	0.857131i	$-0.327755\pi$
$157$	2026.61	1.03020	0.515099	+	0.857131i	$0.327755\pi$
$158$	−34.8974	−0.0175714
$159$	−3454.15	−1.72284
$160$	−434.998	−0.214935
$161$	2820.77	1.38079
$162$	3623.33	1.75726
$163$	−1974.54	−0.948823	−0.474412	−	0.880303i	$-0.657339\pi$
$163$	−1974.54	−0.948823	−0.474412	+	0.880303i	$0.657339\pi$
$164$	−2140.84	−1.01934
$165$	−121.351	−0.0572555
$166$	−2002.13	−0.936115
$167$	2197.20	1.01811	0.509056	−	0.860733i	$-0.329995\pi$
$167$	2197.20	1.01811	0.509056	+	0.860733i	$0.329995\pi$
$168$	64.0906	0.0294327
$169$	0	0
$170$	−163.846	−0.0739200
$171$	−161.566	−0.0722528
$172$	−1847.01	−0.818798
$173$	1104.88	0.485563	0.242782	−	0.970081i	$-0.421940\pi$
$173$	1104.88	0.485563	0.242782	+	0.970081i	$0.421940\pi$
$174$	5959.99	2.59670
$175$	−2288.15	−0.988390
$176$	−715.494	−0.306434
$177$	−4523.73	−1.92104
$178$	−4348.07	−1.83091
$179$	−1759.48	−0.734693	−0.367346	−	0.930084i	$-0.619734\pi$
$179$	−1759.48	−0.734693	−0.367346	+	0.930084i	$0.619734\pi$
$180$	−198.431	−0.0821678
$181$	4337.52	1.78125	0.890623	−	0.454742i	$-0.150269\pi$
$181$	4337.52	1.78125	0.890623	+	0.454742i	$0.150269\pi$
$182$	0	0
$183$	−274.158	−0.110745
$184$	79.6262	0.0319028
$185$	−37.9520	−0.0150826
$186$	−2226.32	−0.877643
$187$	−265.095	−0.103667
$188$	1008.11	0.391084
$189$	−1480.59	−0.569824
$190$	−74.3295	−0.0283812
$191$	−3343.27	−1.26655	−0.633274	−	0.773928i	$-0.718289\pi$
$191$	−3343.27	−1.26655	−0.633274	+	0.773928i	$0.718289\pi$
$192$	−3198.57	−1.20228
$193$	−515.425	−0.192234	−0.0961169	−	0.995370i	$-0.530642\pi$
$193$	−515.425	−0.192234	−0.0961169	+	0.995370i	$0.530642\pi$
$194$	2536.26	0.938622
$195$	0	0
$196$	65.0061	0.0236903
$197$	2842.81	1.02813	0.514066	−	0.857750i	$-0.328139\pi$
$197$	2842.81	1.02813	0.514066	+	0.857750i	$0.328139\pi$
$198$	−647.525	−0.232412
$199$	1484.48	0.528804	0.264402	−	0.964413i	$-0.414825\pi$
$199$	1484.48	0.528804	0.264402	+	0.964413i	$0.414825\pi$
$200$	−64.5913	−0.0228365
$201$	234.353	0.0822389
$202$	84.8007	0.0295374
$203$	−4338.49	−1.50001
$204$	−1225.47	−0.420587
$205$	464.453	0.158238
$206$	630.900	0.213383
$207$	2224.16	0.746810
$208$	0	0
$209$	−120.262	−0.0398023
$210$	823.600	0.270637
$211$	−1246.31	−0.406632	−0.203316	−	0.979113i	$-0.565172\pi$
$211$	−1246.31	−0.406632	−0.203316	+	0.979113i	$0.565172\pi$
$212$	−4204.23	−1.36202
$213$	−588.154	−0.189200
$214$	1735.86	0.554492
$215$	400.707	0.127107
$216$	−41.7948	−0.0131656
$217$	1620.62	0.506980
$218$	4809.52	1.49423
$219$	−1148.11	−0.354255
$220$	−147.703	−0.0452642
$221$	0	0
$222$	−572.508	−0.173082
$223$	−4764.28	−1.43067	−0.715336	−	0.698781i	$-0.753726\pi$
$223$	−4764.28	−1.43067	−0.715336	+	0.698781i	$0.753726\pi$
$224$	4776.68	1.42480
$225$	−1804.19	−0.534576
$226$	4235.92	1.24677
$227$	2667.21	0.779863	0.389932	−	0.920844i	$-0.372499\pi$
$227$	2667.21	0.779863	0.389932	+	0.920844i	$0.372499\pi$
$228$	−555.939	−0.161482
$229$	2908.85	0.839397	0.419698	−	0.907664i	$-0.362136\pi$
$229$	2908.85	0.839397	0.419698	+	0.907664i	$0.362136\pi$
$230$	1023.24	0.293350
$231$	1332.55	0.379546
$232$	−122.469	−0.0346573
$233$	6673.15	1.87628	0.938139	−	0.346259i	$-0.112548\pi$
$233$	6673.15	1.87628	0.938139	+	0.346259i	$0.112548\pi$
$234$	0	0
$235$	−218.708	−0.0607103
$236$	−5506.08	−1.51871
$237$	56.6260	0.0155201
$238$	1799.18	0.490015
$239$	5829.65	1.57778	0.788888	−	0.614536i	$-0.210657\pi$
$239$	5829.65	1.57778	0.788888	+	0.614536i	$0.210657\pi$
$240$	717.569	0.192995
$241$	−7316.01	−1.95546	−0.977729	−	0.209871i	$-0.932696\pi$
$241$	−7316.01	−1.95546	−0.977729	+	0.209871i	$0.932696\pi$
$242$	−481.987	−0.128030
$243$	−3746.43	−0.989028
$244$	−333.693	−0.0875512
$245$	−14.1030	−0.00367758
$246$	7006.30	1.81588
$247$	0	0
$248$	45.7476	0.0117136
$249$	3248.74	0.826830
$250$	−1679.87	−0.424978
$251$	−2882.67	−0.724910	−0.362455	−	0.932001i	$-0.618061\pi$
$251$	−2882.67	−0.724910	−0.362455	+	0.932001i	$0.618061\pi$
$252$	2178.96	0.544689
$253$	1655.56	0.411399
$254$	5594.18	1.38193
$255$	265.864	0.0652903
$256$	4228.60	1.03237
$257$	7144.14	1.73401	0.867003	−	0.498303i	$-0.166043\pi$
$257$	7144.14	1.73401	0.867003	+	0.498303i	$0.166043\pi$
$258$	6044.68	1.45863
$259$	416.749	0.0999826
$260$	0	0
$261$	−3420.87	−0.811289
$262$	−8250.13	−1.94540
$263$	6382.66	1.49647	0.748236	−	0.663433i	$-0.230901\pi$
$263$	6382.66	1.49647	0.748236	+	0.663433i	$0.230901\pi$
$264$	37.6159	0.00876930
$265$	912.103	0.211434
$266$	816.208	0.188139
$267$	7055.38	1.61716
$268$	285.244	0.0650152
$269$	5590.09	1.26704	0.633520	−	0.773727i	$-0.281610\pi$
$269$	5590.09	1.26704	0.633520	+	0.773727i	$0.281610\pi$
$270$	−537.086	−0.121059
$271$	−1726.28	−0.386953	−0.193476	−	0.981105i	$-0.561976\pi$
$271$	−1726.28	−0.386953	−0.193476	+	0.981105i	$0.561976\pi$
$272$	1567.55	0.349437
$273$	0	0
$274$	7031.41	1.55030
$275$	−1342.96	−0.294485
$276$	7653.22	1.66909
$277$	−5924.27	−1.28503	−0.642517	−	0.766271i	$-0.722110\pi$
$277$	−5924.27	−1.28503	−0.642517	+	0.766271i	$0.722110\pi$
$278$	5497.75	1.18609
$279$	1277.85	0.274203
$280$	−16.9238	−0.00361211
$281$	3462.22	0.735014	0.367507	−	0.930021i	$-0.380211\pi$
$281$	3462.22	0.735014	0.367507	+	0.930021i	$0.380211\pi$
$282$	−3299.22	−0.696687
$283$	125.801	0.0264244	0.0132122	−	0.999913i	$-0.495794\pi$
$283$	125.801	0.0264244	0.0132122	+	0.999913i	$0.495794\pi$
$284$	−715.874	−0.149575
$285$	120.610	0.0250679
$286$	0	0
$287$	−5100.13	−1.04896
$288$	3766.38	0.770612
$289$	−4332.21	−0.881786
$290$	−1573.80	−0.318678
$291$	−4115.45	−0.829044
$292$	−1397.42	−0.280062
$293$	−6129.37	−1.22212	−0.611061	−	0.791584i	$-0.709257\pi$
$293$	−6129.37	−1.22212	−0.611061	+	0.791584i	$0.709257\pi$
$294$	−212.745	−0.0422024
$295$	1194.54	0.235758
$296$	11.7642	0.00231007
$297$	−868.981	−0.169776
$298$	5336.63	1.03739
$299$	0	0
$300$	−6208.15	−1.19476
$301$	−4400.14	−0.842590
$302$	−11698.6	−2.22907
$303$	−137.602	−0.0260891
$304$	711.128	0.134164
$305$	72.3943	0.0135911
$306$	1418.64	0.265027
$307$	4514.57	0.839283	0.419642	−	0.907690i	$-0.362156\pi$
$307$	4514.57	0.839283	0.419642	+	0.907690i	$0.362156\pi$
$308$	1621.91	0.300056
$309$	−1023.73	−0.188472
$310$	587.883	0.107708
$311$	2093.87	0.381776	0.190888	−	0.981612i	$-0.438863\pi$
$311$	2093.87	0.381776	0.190888	+	0.981612i	$0.438863\pi$
$312$	0	0
$313$	−7221.81	−1.30416	−0.652078	−	0.758152i	$-0.726102\pi$
$313$	−7221.81	−1.30416	−0.652078	+	0.758152i	$0.726102\pi$
$314$	−8072.72	−1.45086
$315$	−472.723	−0.0845554
$316$	68.9226	0.0122696
$317$	−5459.08	−0.967232	−0.483616	−	0.875280i	$-0.660677\pi$
$317$	−5459.08	−0.967232	−0.483616	+	0.875280i	$0.660677\pi$
$318$	13759.1	2.42633
$319$	−2546.33	−0.446919
$320$	844.616	0.147548
$321$	−2816.69	−0.489758
$322$	−11236.1	−1.94462
$323$	263.477	0.0453878
$324$	−7156.12	−1.22704
$325$	0	0
$326$	7865.33	1.33626
$327$	−7804.15	−1.31979
$328$	−143.969	−0.0242359
$329$	2401.62	0.402448
$330$	483.385	0.0806347
$331$	−4544.86	−0.754706	−0.377353	−	0.926069i	$-0.623166\pi$
$331$	−4544.86	−0.754706	−0.377353	+	0.926069i	$0.623166\pi$
$332$	3954.22	0.653662
$333$	328.604	0.0540762
$334$	−8752.26	−1.43384
$335$	−61.8834	−0.0100927
$336$	−7879.58	−1.27936
$337$	−9056.73	−1.46395	−0.731976	−	0.681331i	$-0.761401\pi$
$337$	−9056.73	−1.46395	−0.731976	+	0.681331i	$0.761401\pi$
$338$	0	0
$339$	−6873.40	−1.10121
$340$	323.597	0.0516162
$341$	951.167	0.151052
$342$	643.574	0.101756
$343$	−6273.65	−0.987595
$344$	−124.209	−0.0194678
$345$	−1660.36	−0.259103
$346$	−4401.14	−0.683834
$347$	−4708.73	−0.728467	−0.364233	−	0.931308i	$-0.618669\pi$
$347$	−4708.73	−0.728467	−0.364233	+	0.931308i	$0.618669\pi$
$348$	−11771.0	−1.81320
$349$	497.434	0.0762952	0.0381476	−	0.999272i	$-0.487854\pi$
$349$	497.434	0.0762952	0.0381476	+	0.999272i	$0.487854\pi$
$350$	9114.55	1.39198
$351$	0	0
$352$	2803.51	0.424511
$353$	−7144.94	−1.07730	−0.538650	−	0.842530i	$-0.681065\pi$
$353$	−7144.94	−1.07730	−0.538650	+	0.842530i	$0.681065\pi$
$354$	18019.7	2.70546
$355$	155.308	0.0232194
$356$	8587.49	1.27847
$357$	−2919.43	−0.432809
$358$	7008.66	1.03469
$359$	4730.95	0.695515	0.347757	−	0.937585i	$-0.386943\pi$
$359$	4730.95	0.695515	0.347757	+	0.937585i	$0.386943\pi$
$360$	−13.3443	−0.00195363
$361$	−6739.47	−0.982574
$362$	−17277.9	−2.50859
$363$	782.094	0.113083
$364$	0	0
$365$	303.169	0.0434757
$366$	1092.07	0.155966
$367$	2037.24	0.289762	0.144881	−	0.989449i	$-0.453720\pi$
$367$	2037.24	0.289762	0.144881	+	0.989449i	$0.453720\pi$
$368$	−9789.59	−1.38673
$369$	−4021.42	−0.567336
$370$	151.177	0.0212413
$371$	−10015.7	−1.40159
$372$	4397.00	0.612833
$373$	−8768.76	−1.21724	−0.608618	−	0.793463i	$-0.708276\pi$
$373$	−8768.76	−1.21724	−0.608618	+	0.793463i	$0.708276\pi$
$374$	1055.97	0.145997
$375$	2725.84	0.375364
$376$	67.7942	0.00929845
$377$	0	0
$378$	5897.71	0.802502
$379$	−5256.68	−0.712447	−0.356223	−	0.934401i	$-0.615936\pi$
$379$	−5256.68	−0.712447	−0.356223	+	0.934401i	$0.615936\pi$
$380$	146.801	0.0198178
$381$	−9077.38	−1.22060
$382$	13317.5	1.78372
$383$	4388.84	0.585533	0.292766	−	0.956184i	$-0.405424\pi$
$383$	4388.84	0.585533	0.292766	+	0.956184i	$0.405424\pi$
$384$	−437.651	−0.0581610
$385$	−351.873	−0.0465795
$386$	2053.13	0.270729
$387$	−3469.48	−0.455720
$388$	−5009.14	−0.655413
$389$	−12511.4	−1.63072	−0.815361	−	0.578952i	$-0.803462\pi$
$389$	−12511.4	−1.63072	−0.815361	+	0.578952i	$0.803462\pi$
$390$	0	0
$391$	−3627.10	−0.469132
$392$	4.37159	0.000563262 0
$393$	13387.0	1.71829
$394$	−11324.0	−1.44795
$395$	−14.9527	−0.00190469
$396$	1278.87	0.162287
$397$	9601.26	1.21379	0.606893	−	0.794783i	$-0.292415\pi$
$397$	9601.26	1.21379	0.606893	+	0.794783i	$0.292415\pi$
$398$	−5913.23	−0.744732
$399$	−1324.42	−0.166175
$400$	7941.13	0.992641
$401$	6626.81	0.825255	0.412627	−	0.910900i	$-0.364611\pi$
$401$	6626.81	0.825255	0.412627	+	0.910900i	$0.364611\pi$
$402$	−933.515	−0.115820
$403$	0	0
$404$	−167.482	−0.0206251
$405$	1552.51	0.190481
$406$	17281.8	2.11251
$407$	244.597	0.0297892
$408$	−82.4113	−0.00999992
$409$	3654.30	0.441794	0.220897	−	0.975297i	$-0.429102\pi$
$409$	3654.30	0.441794	0.220897	+	0.975297i	$0.429102\pi$
$410$	−1850.09	−0.222852
$411$	−11409.5	−1.36932
$412$	−1246.03	−0.148999
$413$	−13117.1	−1.56284
$414$	−8859.63	−1.05176
$415$	−857.863	−0.101472
$416$	0	0
$417$	−8920.89	−1.04762
$418$	479.046	0.0560548
$419$	2264.44	0.264022	0.132011	−	0.991248i	$-0.457857\pi$
$419$	2264.44	0.264022	0.132011	+	0.991248i	$0.457857\pi$
$420$	−1626.62	−0.188978
$421$	−15152.7	−1.75415	−0.877075	−	0.480353i	$-0.840508\pi$
$421$	−15152.7	−1.75415	−0.877075	+	0.480353i	$0.840508\pi$
$422$	4964.49	0.572673
$423$	1893.66	0.217666
$424$	−282.730	−0.0323834
$425$	2942.24	0.335811
$426$	2342.83	0.266457
$427$	−794.958	−0.0900953
$428$	−3428.35	−0.387186
$429$	0	0
$430$	−1596.16	−0.179009
$431$	−5686.13	−0.635478	−0.317739	−	0.948178i	$-0.602924\pi$
$431$	−5686.13	−0.635478	−0.317739	+	0.948178i	$0.602924\pi$
$432$	5138.43	0.572276
$433$	−2446.82	−0.271563	−0.135781	−	0.990739i	$-0.543354\pi$
$433$	−2446.82	−0.271563	−0.135781	+	0.990739i	$0.543354\pi$
$434$	−6455.50	−0.713996
$435$	2553.72	0.281474
$436$	−9498.85	−1.04338
$437$	−1645.45	−0.180121
$438$	4573.33	0.498909
$439$	6812.13	0.740605	0.370302	−	0.928911i	$-0.379254\pi$
$439$	6812.13	0.740605	0.370302	+	0.928911i	$0.379254\pi$
$440$	−9.93285	−0.00107620
$441$	122.109	0.0131853
$442$	0	0
$443$	−18516.3	−1.98586	−0.992932	−	0.118686i	$-0.962132\pi$
$443$	−18516.3	−1.98586	−0.992932	+	0.118686i	$0.962132\pi$
$444$	1130.71	0.120858
$445$	−1863.05	−0.198465
$446$	18977.9	2.01486
$447$	−8659.46	−0.916283
$448$	−9274.68	−0.978097
$449$	−10900.6	−1.14572	−0.572861	−	0.819653i	$-0.694166\pi$
$449$	−10900.6	−1.14572	−0.572861	+	0.819653i	$0.694166\pi$
$450$	7186.76	0.752861
$451$	−2993.35	−0.312531
$452$	−8365.99	−0.870582
$453$	18982.7	1.96884
$454$	−10624.5	−1.09831
$455$	0	0
$456$	−37.3863	−0.00383942
$457$	−2233.04	−0.228572	−0.114286	−	0.993448i	$-0.536458\pi$
$457$	−2233.04	−0.228572	−0.114286	+	0.993448i	$0.536458\pi$
$458$	−11587.0	−1.18215
$459$	1903.82	0.193601
$460$	−2020.91	−0.204838
$461$	11412.4	1.15299	0.576496	−	0.817100i	$-0.304420\pi$
$461$	11412.4	1.15299	0.576496	+	0.817100i	$0.304420\pi$
$462$	−5308.02	−0.534527
$463$	−17901.7	−1.79690	−0.898448	−	0.439080i	$-0.855304\pi$
$463$	−17901.7	−1.79690	−0.898448	+	0.439080i	$0.855304\pi$
$464$	15056.9	1.50646
$465$	−953.925	−0.0951338
$466$	−26581.6	−2.64242
$467$	−16132.0	−1.59850	−0.799249	−	0.601000i	$-0.794769\pi$
$467$	−16132.0	−1.59850	−0.799249	+	0.601000i	$0.794769\pi$
$468$	0	0
$469$	679.538	0.0669044
$470$	871.193	0.0855003
$471$	13099.2	1.28148
$472$	−370.278	−0.0361089
$473$	−2582.51	−0.251045
$474$	−225.562	−0.0218574
$475$	1334.76	0.128933
$476$	−3553.40	−0.342163
$477$	−7897.35	−0.758061
$478$	−23221.6	−2.22203
$479$	18226.1	1.73856	0.869282	−	0.494316i	$-0.164581\pi$
$479$	18226.1	1.73856	0.869282	+	0.494316i	$0.164581\pi$
$480$	−2811.64	−0.267361
$481$	0	0
$482$	29142.3	2.75393
$483$	18232.3	1.71759
$484$	951.929	0.0893998
$485$	1086.73	0.101744
$486$	14923.4	1.39288
$487$	−5785.43	−0.538322	−0.269161	−	0.963095i	$-0.586746\pi$
$487$	−5785.43	−0.538322	−0.269161	+	0.963095i	$0.586746\pi$
$488$	−22.4405	−0.00208163
$489$	−12762.6	−1.18026
$490$	56.1774	0.00517926
$491$	−9670.17	−0.888816	−0.444408	−	0.895824i	$-0.646586\pi$
$491$	−9670.17	−0.888816	−0.444408	+	0.895824i	$0.646586\pi$
$492$	−13837.5	−1.26797
$493$	5578.67	0.509636
$494$	0	0
$495$	−277.449	−0.0251928
$496$	−5624.41	−0.509161
$497$	−1705.43	−0.153921
$498$	−12940.9	−1.16445
$499$	−11679.3	−1.04777	−0.523887	−	0.851788i	$-0.675519\pi$
$499$	−11679.3	−1.04777	−0.523887	+	0.851788i	$0.675519\pi$
$500$	3317.77	0.296750
$501$	14201.8	1.26645
$502$	11482.7	1.02091
$503$	8609.69	0.763195	0.381598	−	0.924329i	$-0.375374\pi$
$503$	8609.69	0.763195	0.381598	+	0.924329i	$0.375374\pi$
$504$	146.533	0.0129506
$505$	36.3351	0.00320176
$506$	−6594.68	−0.579386
$507$	0	0
$508$	−11048.6	−0.964963
$509$	542.091	0.0472058	0.0236029	−	0.999721i	$-0.492486\pi$
$509$	542.091	0.0472058	0.0236029	+	0.999721i	$0.492486\pi$
$510$	−1059.03	−0.0919504
$511$	−3329.09	−0.288200
$512$	−16302.4	−1.40717
$513$	863.678	0.0743320
$514$	−28457.7	−2.44205
$515$	270.326	0.0231301
$516$	−11938.3	−1.01852
$517$	1409.55	0.119907
$518$	−1660.06	−0.140809
$519$	7141.48	0.604001
$520$	0	0
$521$	16283.2	1.36925	0.684626	−	0.728895i	$-0.259966\pi$
$521$	16283.2	1.36925	0.684626	+	0.728895i	$0.259966\pi$
$522$	13626.6	1.14256
$523$	−15857.3	−1.32579	−0.662896	−	0.748712i	$-0.730673\pi$
$523$	−15857.3	−1.32579	−0.662896	+	0.748712i	$0.730673\pi$
$524$	16294.1	1.35842
$525$	−14789.7	−1.22948
$526$	−25424.5	−2.10753
$527$	−2083.88	−0.172249
$528$	−4624.66	−0.381179
$529$	10484.8	0.861741
$530$	−3633.24	−0.297769
$531$	−10342.8	−0.845270
$532$	−1612.02	−0.131372
$533$	0	0
$534$	−28104.1	−2.27750
$535$	743.776	0.0601051
$536$	19.1824	0.00154581
$537$	−11372.6	−0.913897
$538$	−22267.3	−1.78441
$539$	90.8924	0.00726347
$540$	1060.75	0.0845323
$541$	9050.52	0.719246	0.359623	−	0.933098i	$-0.382905\pi$
$541$	9050.52	0.719246	0.359623	+	0.933098i	$0.382905\pi$
$542$	6876.41	0.544958
$543$	28036.0	2.21572
$544$	−6142.13	−0.484084
$545$	2060.77	0.161970
$546$	0	0
$547$	16990.1	1.32805	0.664026	−	0.747710i	$-0.268846\pi$
$547$	16990.1	1.32805	0.664026	+	0.747710i	$0.268846\pi$
$548$	−13887.1	−1.08253
$549$	−626.819	−0.0487286
$550$	5349.48	0.414732
$551$	2530.79	0.195672
$552$	514.671	0.0396845
$553$	164.195	0.0126262
$554$	23598.5	1.80976
$555$	−245.306	−0.0187615
$556$	−10858.1	−0.828213
$557$	16179.4	1.23078	0.615389	−	0.788224i	$-0.288999\pi$
$557$	16179.4	1.23078	0.615389	+	0.788224i	$0.288999\pi$
$558$	−5090.12	−0.386169
$559$	0	0
$560$	2080.68	0.157009
$561$	−1713.46	−0.128953
$562$	−13791.3	−1.03514
$563$	−3582.30	−0.268164	−0.134082	−	0.990970i	$-0.542808\pi$
$563$	−3582.30	−0.268164	−0.134082	+	0.990970i	$0.542808\pi$
$564$	6515.99	0.486476
$565$	1814.99	0.135146
$566$	−501.111	−0.0372143
$567$	−17048.0	−1.26270
$568$	−48.1418	−0.00355631
$569$	15068.4	1.11019	0.555096	−	0.831786i	$-0.312682\pi$
$569$	15068.4	1.11019	0.555096	+	0.831786i	$0.312682\pi$
$570$	−480.435	−0.0353039
$571$	2048.47	0.150132	0.0750662	−	0.997179i	$-0.476083\pi$
$571$	2048.47	0.150132	0.0750662	+	0.997179i	$0.476083\pi$
$572$	0	0
$573$	−21609.5	−1.57548
$574$	20315.7	1.47728
$575$	−18374.7	−1.33266
$576$	−7313.03	−0.529009
$577$	−3204.16	−0.231180	−0.115590	−	0.993297i	$-0.536876\pi$
$577$	−3204.16	−0.231180	−0.115590	+	0.993297i	$0.536876\pi$
$578$	17256.8	1.24185
$579$	−3331.50	−0.239123
$580$	3108.27	0.222524
$581$	9420.15	0.672657
$582$	16393.3	1.16757
$583$	−5878.41	−0.417597
$584$	−93.9752	−0.00665877
$585$	0	0
$586$	24415.5	1.72115
$587$	−18832.4	−1.32419	−0.662093	−	0.749422i	$-0.730332\pi$
$587$	−18832.4	−1.32419	−0.662093	+	0.749422i	$0.730332\pi$
$588$	420.173	0.0294687
$589$	−945.363	−0.0661341
$590$	−4758.28	−0.332026
$591$	18374.8	1.27891
$592$	−1446.34	−0.100413
$593$	19389.3	1.34270	0.671350	−	0.741140i	$-0.265715\pi$
$593$	19389.3	1.34270	0.671350	+	0.741140i	$0.265715\pi$
$594$	3461.47	0.239100
$595$	770.906	0.0531161
$596$	−10539.9	−0.724381
$597$	9595.07	0.657789
$598$	0	0
$599$	−23397.9	−1.59602	−0.798008	−	0.602646i	$-0.794113\pi$
$599$	−23397.9	−1.59602	−0.798008	+	0.602646i	$0.794113\pi$
$600$	−417.491	−0.0284067
$601$	−15297.0	−1.03823	−0.519117	−	0.854703i	$-0.673739\pi$
$601$	−15297.0	−1.03823	−0.519117	+	0.854703i	$0.673739\pi$
$602$	17527.3	1.18665
$603$	535.811	0.0361856
$604$	23104.9	1.55650
$605$	−206.520	−0.0138781
$606$	548.117	0.0367421
$607$	5905.91	0.394915	0.197458	−	0.980311i	$-0.436732\pi$
$607$	5905.91	0.394915	0.197458	+	0.980311i	$0.436732\pi$
$608$	−2786.41	−0.185861
$609$	−28042.2	−1.86589
$610$	−288.373	−0.0191408
$611$	0	0
$612$	−2801.83	−0.185061
$613$	12752.9	0.840267	0.420134	−	0.907462i	$-0.361983\pi$
$613$	12752.9	0.840267	0.420134	+	0.907462i	$0.361983\pi$
$614$	−17983.2	−1.18199
$615$	3002.03	0.196835
$616$	109.072	0.00713415
$617$	19445.0	1.26876	0.634380	−	0.773021i	$-0.281255\pi$
$617$	19445.0	1.26876	0.634380	+	0.773021i	$0.281255\pi$
$618$	4077.88	0.265431
$619$	−438.899	−0.0284990	−0.0142495	−	0.999898i	$-0.504536\pi$
$619$	−438.899	−0.0284990	−0.0142495	+	0.999898i	$0.504536\pi$
$620$	−1161.07	−0.0752094
$621$	−11889.6	−0.768301
$622$	−8340.63	−0.537667
$623$	20458.0	1.31562
$624$	0	0
$625$	14541.1	0.930629
$626$	28767.1	1.83668
$627$	−777.322	−0.0495108
$628$	15943.7	1.01309
$629$	−535.879	−0.0339696
$630$	1883.03	0.119082
$631$	21488.6	1.35570	0.677852	−	0.735198i	$-0.262911\pi$
$631$	21488.6	1.35570	0.677852	+	0.735198i	$0.262911\pi$
$632$	4.63497	0.000291724 0
$633$	−8055.62	−0.505817
$634$	21745.5	1.36218
$635$	2396.97	0.149797
$636$	−27174.4	−1.69424
$637$	0	0
$638$	10143.0	0.629410
$639$	−1344.72	−0.0832492
$640$	115.566	0.00713775
$641$	−8276.77	−0.510004	−0.255002	−	0.966940i	$-0.582076\pi$
$641$	−8276.77	−0.510004	−0.255002	+	0.966940i	$0.582076\pi$
$642$	11219.9	0.689742
$643$	−8237.69	−0.505230	−0.252615	−	0.967567i	$-0.581291\pi$
$643$	−8237.69	−0.505230	−0.252615	+	0.967567i	$0.581291\pi$
$644$	22191.5	1.35787
$645$	2590.00	0.158111
$646$	−1049.53	−0.0639211
$647$	−22717.4	−1.38039	−0.690196	−	0.723623i	$-0.742476\pi$
$647$	−22717.4	−1.38039	−0.690196	+	0.723623i	$0.742476\pi$
$648$	−481.242	−0.0291743
$649$	−7698.67	−0.465638
$650$	0	0
$651$	10475.0	0.630641
$652$	−15534.1	−0.933071
$653$	−14408.1	−0.863447	−0.431724	−	0.902006i	$-0.642094\pi$
$653$	−14408.1	−0.863447	−0.431724	+	0.902006i	$0.642094\pi$
$654$	31086.8	1.85870
$655$	−3534.98	−0.210875
$656$	17700.2	1.05347
$657$	−2624.96	−0.155874
$658$	−9566.52	−0.566781
$659$	2431.31	0.143719	0.0718593	−	0.997415i	$-0.477107\pi$
$659$	2431.31	0.143719	0.0718593	+	0.997415i	$0.477107\pi$
$660$	−954.690	−0.0563049
$661$	25011.0	1.47173	0.735865	−	0.677128i	$-0.236776\pi$
$661$	25011.0	1.47173	0.735865	+	0.677128i	$0.236776\pi$
$662$	18103.8	1.06288
$663$	0	0
$664$	265.917	0.0155415
$665$	349.726	0.0203936
$666$	−1308.95	−0.0761572
$667$	−34839.6	−2.02248
$668$	17285.8	1.00121
$669$	−30794.3	−1.77964
$670$	246.504	0.0142139
$671$	−466.574	−0.0268433
$672$	30874.5	1.77234
$673$	−17618.2	−1.00911	−0.504556	−	0.863379i	$-0.668344\pi$
$673$	−17618.2	−1.00911	−0.504556	+	0.863379i	$0.668344\pi$
$674$	36076.2	2.06173
$675$	9644.65	0.549960
$676$	0	0
$677$	−25675.0	−1.45756	−0.728782	−	0.684746i	$-0.759913\pi$
$677$	−25675.0	−1.45756	−0.728782	+	0.684746i	$0.759913\pi$
$678$	27379.2	1.55088
$679$	−11933.3	−0.674458
$680$	21.7616	0.00122723
$681$	17239.7	0.970086
$682$	−3788.84	−0.212731
$683$	−31774.8	−1.78013	−0.890066	−	0.455832i	$-0.849342\pi$
$683$	−31774.8	−1.78013	−0.890066	+	0.455832i	$0.849342\pi$
$684$	−1271.07	−0.0710532
$685$	3012.79	0.168048
$686$	24990.2	1.39086
$687$	18801.6	1.04414
$688$	15270.9	0.846215
$689$	0	0
$690$	6613.81	0.364903
$691$	−13634.9	−0.750648	−0.375324	−	0.926894i	$-0.622469\pi$
$691$	−13634.9	−0.750648	−0.375324	+	0.926894i	$0.622469\pi$
$692$	8692.29	0.477502
$693$	3046.65	0.167003
$694$	18756.6	1.02592
$695$	2355.65	0.128568
$696$	−791.590	−0.0431109
$697$	6558.04	0.356390
$698$	−1981.46	−0.107449
$699$	43132.5	2.33394
$700$	−18001.3	−0.971980
$701$	−6056.20	−0.326304	−0.163152	−	0.986601i	$-0.552166\pi$
$701$	−6056.20	−0.326304	−0.163152	+	0.986601i	$0.552166\pi$
$702$	0	0
$703$	−243.104	−0.0130425
$704$	−5443.47	−0.291418
$705$	−1413.64	−0.0755187
$706$	28460.9	1.51719
$707$	−398.994	−0.0212245
$708$	−35589.0	−1.88915
$709$	26265.1	1.39126	0.695632	−	0.718399i	$-0.255125\pi$
$709$	26265.1	1.39126	0.695632	+	0.718399i	$0.255125\pi$
$710$	−618.648	−0.0327006
$711$	129.466	0.00682893
$712$	577.499	0.0303971
$713$	13014.1	0.683567
$714$	11629.2	0.609538
$715$	0	0
$716$	−13842.2	−0.722495
$717$	37680.4	1.96262
$718$	−18845.1	−0.979516
$719$	4631.77	0.240245	0.120122	−	0.992759i	$-0.461671\pi$
$719$	4631.77	0.240245	0.120122	+	0.992759i	$0.461671\pi$
$720$	1640.61	0.0849191
$721$	−2968.43	−0.153329
$722$	26845.8	1.38379
$723$	−47287.6	−2.43243
$724$	34124.1	1.75167
$725$	28261.3	1.44772
$726$	−3115.36	−0.159259
$727$	22011.8	1.12293	0.561466	−	0.827500i	$-0.310238\pi$
$727$	22011.8	1.12293	0.561466	+	0.827500i	$0.310238\pi$
$728$	0	0
$729$	344.253	0.0174899
$730$	−1207.63	−0.0612281
$731$	5657.95	0.286274
$732$	−2156.85	−0.108907
$733$	−7035.82	−0.354535	−0.177267	−	0.984163i	$-0.556726\pi$
$733$	−7035.82	−0.354535	−0.177267	+	0.984163i	$0.556726\pi$
$734$	−8115.05	−0.408082
$735$	−91.1560	−0.00457461
$736$	38358.5	1.92108
$737$	398.832	0.0199338
$738$	16018.8	0.798997
$739$	15949.5	0.793926	0.396963	−	0.917835i	$-0.370064\pi$
$739$	15949.5	0.793926	0.396963	+	0.917835i	$0.370064\pi$
$740$	−298.575	−0.0148322
$741$	0	0
$742$	39896.4	1.97391
$743$	−28032.2	−1.38412	−0.692061	−	0.721839i	$-0.743297\pi$
$743$	−28032.2	−1.38412	−0.692061	+	0.721839i	$0.743297\pi$
$744$	295.694	0.0145708
$745$	2286.62	0.112450
$746$	34929.2	1.71427
$747$	7427.72	0.363810
$748$	−2085.55	−0.101946
$749$	−8167.36	−0.398436
$750$	−10858.0	−0.528638
$751$	−2102.60	−0.102164	−0.0510819	−	0.998694i	$-0.516267\pi$
$751$	−2102.60	−0.102164	−0.0510819	+	0.998694i	$0.516267\pi$
$752$	−8334.91	−0.404179
$753$	−18632.4	−0.901728
$754$	0	0
$755$	−5012.57	−0.241624
$756$	−11648.0	−0.560364
$757$	−1337.57	−0.0642202	−0.0321101	−	0.999484i	$-0.510223\pi$
$757$	−1337.57	−0.0642202	−0.0321101	+	0.999484i	$0.510223\pi$
$758$	20939.2	1.00336
$759$	10700.8	0.511747
$760$	9.87224	0.000471189 0
$761$	5825.13	0.277478	0.138739	−	0.990329i	$-0.455695\pi$
$761$	5825.13	0.277478	0.138739	+	0.990329i	$0.455695\pi$
$762$	36158.5	1.71901
$763$	−22629.1	−1.07370
$764$	−26302.1	−1.24552
$765$	607.854	0.0287281
$766$	−17482.3	−0.824624
$767$	0	0
$768$	27331.9	1.28419
$769$	24385.5	1.14352	0.571758	−	0.820422i	$-0.306261\pi$
$769$	24385.5	1.14352	0.571758	+	0.820422i	$0.306261\pi$
$770$	1401.64	0.0655993
$771$	46176.8	2.15696
$772$	−4054.95	−0.189042
$773$	−32301.2	−1.50297	−0.751483	−	0.659752i	$-0.770661\pi$
$773$	−32301.2	−1.50297	−0.751483	+	0.659752i	$0.770661\pi$
$774$	13820.2	0.641805
$775$	−10556.8	−0.489306
$776$	−336.859	−0.0155832
$777$	2693.69	0.124370
$778$	49837.3	2.29660
$779$	2975.09	0.136834
$780$	0	0
$781$	−1000.94	−0.0458599
$782$	14448.1	0.660693
$783$	18286.9	0.834636
$784$	−537.462	−0.0244835
$785$	−3458.97	−0.157269
$786$	−53325.4	−2.41992
$787$	13567.4	0.614517	0.307258	−	0.951626i	$-0.400588\pi$
$787$	13567.4	0.614517	0.307258	+	0.951626i	$0.400588\pi$
$788$	22364.9	1.01106
$789$	41254.9	1.86149
$790$	59.5620	0.00268243
$791$	−19930.3	−0.895879
$792$	86.0026	0.00385855
$793$	0	0
$794$	−38245.3	−1.70941
$795$	5895.46	0.263007
$796$	11678.7	0.520025
$797$	22776.3	1.01227	0.506135	−	0.862454i	$-0.331074\pi$
$797$	22776.3	1.01227	0.506135	+	0.862454i	$0.331074\pi$
$798$	5275.63	0.234029
$799$	−3088.14	−0.136734
$800$	−31115.7	−1.37513
$801$	16131.0	0.711561
$802$	−26397.0	−1.16223
$803$	−1953.90	−0.0858674
$804$	1843.70	0.0808735
$805$	−4814.42	−0.210790
$806$	0	0
$807$	36132.0	1.57609
$808$	−11.2630	−0.000490385 0
$809$	−21902.3	−0.951846	−0.475923	−	0.879487i	$-0.657886\pi$
$809$	−21902.3	−0.951846	−0.475923	+	0.879487i	$0.657886\pi$
$810$	−6184.22	−0.268261
$811$	−10007.8	−0.433318	−0.216659	−	0.976247i	$-0.569516\pi$
$811$	−10007.8	−0.433318	−0.216659	+	0.976247i	$0.569516\pi$
$812$	−34131.7	−1.47511
$813$	−11158.0	−0.481338
$814$	−974.318	−0.0419531
$815$	3370.11	0.144846
$816$	10132.0	0.434671
$817$	2566.76	0.109914
$818$	−14556.4	−0.622192
$819$	0	0
$820$	3653.94	0.155611
$821$	22851.7	0.971412	0.485706	−	0.874122i	$-0.338563\pi$
$821$	22851.7	0.971412	0.485706	+	0.874122i	$0.338563\pi$
$822$	45448.1	1.92845
$823$	−29956.1	−1.26878	−0.634388	−	0.773015i	$-0.718748\pi$
$823$	−29956.1	−1.26878	−0.634388	+	0.773015i	$0.718748\pi$
$824$	−83.7945	−0.00354262
$825$	−8680.31	−0.366315
$826$	52250.3	2.20099
$827$	33889.4	1.42497	0.712485	−	0.701688i	$-0.247570\pi$
$827$	33889.4	1.42497	0.712485	+	0.701688i	$0.247570\pi$
$828$	17497.9	0.734411
$829$	806.178	0.0337753	0.0168877	−	0.999857i	$-0.494624\pi$
$829$	806.178	0.0337753	0.0168877	+	0.999857i	$0.494624\pi$
$830$	3417.18	0.142906
$831$	−38292.0	−1.59848
$832$	0	0
$833$	−199.133	−0.00828278
$834$	35535.2	1.47540
$835$	−3750.14	−0.155424
$836$	−946.121	−0.0391415
$837$	−6830.96	−0.282094
$838$	−9020.10	−0.371831
$839$	18309.3	0.753406	0.376703	−	0.926334i	$-0.377058\pi$
$839$	18309.3	0.753406	0.376703	+	0.926334i	$0.377058\pi$
$840$	−109.388	−0.00449316
$841$	29196.2	1.19710
$842$	60358.7	2.47043
$843$	22378.4	0.914297
$844$	−9804.93	−0.399881
$845$	0	0
$846$	−7543.13	−0.306546
$847$	2267.78	0.0919976
$848$	34760.1	1.40762
$849$	813.126	0.0328697
$850$	−11720.0	−0.472933
$851$	3346.64	0.134808
$852$	−4627.11	−0.186059
$853$	−7683.10	−0.308399	−0.154200	−	0.988040i	$-0.549280\pi$
$853$	−7683.10	−0.308399	−0.154200	+	0.988040i	$0.549280\pi$
$854$	3166.60	0.126884
$855$	275.756	0.0110300
$856$	−230.553	−0.00920576
$857$	49018.8	1.95385	0.976926	−	0.213578i	$-0.0685118\pi$
$857$	49018.8	1.95385	0.976926	+	0.213578i	$0.0685118\pi$
$858$	0	0
$859$	−7148.30	−0.283931	−0.141965	−	0.989872i	$-0.545342\pi$
$859$	−7148.30	−0.283931	−0.141965	+	0.989872i	$0.545342\pi$
$860$	3152.43	0.124997
$861$	−32965.2	−1.30482
$862$	22649.9	0.894964
$863$	24806.1	0.978457	0.489229	−	0.872156i	$-0.337278\pi$
$863$	24806.1	0.978457	0.489229	+	0.872156i	$0.337278\pi$
$864$	−20133.9	−0.792788
$865$	−1885.78	−0.0741255
$866$	9746.57	0.382450
$867$	−28001.6	−1.09687
$868$	12749.7	0.498563
$869$	96.3686	0.00376189
$870$	−10172.4	−0.396409
$871$	0	0
$872$	−638.788	−0.0248074
$873$	−9409.31	−0.364785
$874$	6554.44	0.253670
$875$	7903.92	0.305373
$876$	−9032.37	−0.348374
$877$	−11908.2	−0.458508	−0.229254	−	0.973367i	$-0.573629\pi$
$877$	−11908.2	−0.458508	−0.229254	+	0.973367i	$0.573629\pi$
$878$	−27135.2	−1.04302
$879$	−39617.7	−1.52022
$880$	1221.19	0.0467798
$881$	30630.9	1.17138	0.585688	−	0.810536i	$-0.300824\pi$
$881$	30630.9	1.17138	0.585688	+	0.810536i	$0.300824\pi$
$882$	−486.406	−0.0185693
$883$	21633.3	0.824483	0.412241	−	0.911075i	$-0.364746\pi$
$883$	21633.3	0.824483	0.412241	+	0.911075i	$0.364746\pi$
$884$	0	0
$885$	7720.99	0.293264
$886$	73757.3	2.79675
$887$	−9515.97	−0.360220	−0.180110	−	0.983646i	$-0.557645\pi$
$887$	−9515.97	−0.360220	−0.180110	+	0.983646i	$0.557645\pi$
$888$	76.0390	0.00287354
$889$	−26321.0	−0.993002
$890$	7421.19	0.279504
$891$	−10005.8	−0.376214
$892$	−37481.5	−1.40692
$893$	−1400.95	−0.0524983
$894$	34493.8	1.29043
$895$	3003.05	0.112157
$896$	−1269.03	−0.0473161
$897$	0	0
$898$	43420.9	1.61356
$899$	−20016.4	−0.742586
$900$	−14193.9	−0.525701
$901$	12878.8	0.476199
$902$	11923.6	0.440148
$903$	−28440.7	−1.04811
$904$	−562.604	−0.0206990
$905$	−7403.18	−0.271923
$906$	−75614.9	−2.77278
$907$	−25347.2	−0.927940	−0.463970	−	0.885851i	$-0.653575\pi$
$907$	−25347.2	−0.927940	−0.463970	+	0.885851i	$0.653575\pi$
$908$	20983.4	0.766916
$909$	−314.604	−0.0114794
$910$	0	0
$911$	23079.5	0.839359	0.419680	−	0.907672i	$-0.362142\pi$
$911$	23079.5	0.839359	0.419680	+	0.907672i	$0.362142\pi$
$912$	4596.44	0.166890
$913$	5528.84	0.200414
$914$	8895.02	0.321905
$915$	467.927	0.0169062
$916$	22884.4	0.825461
$917$	38817.4	1.39789
$918$	−7583.61	−0.272654
$919$	−44847.1	−1.60976	−0.804881	−	0.593436i	$-0.797771\pi$
$919$	−44847.1	−1.60976	−0.804881	+	0.593436i	$0.797771\pi$
$920$	−135.904	−0.00487025
$921$	29180.3	1.04400
$922$	−45459.8	−1.62379
$923$	0	0
$924$	10483.4	0.373245
$925$	−2714.73	−0.0964971
$926$	71309.0	2.53063
$927$	−2340.59	−0.0829288
$928$	−58997.3	−2.08694
$929$	−42164.9	−1.48911	−0.744555	−	0.667561i	$-0.767339\pi$
$929$	−42164.9	−1.48911	−0.744555	+	0.667561i	$0.767339\pi$
$930$	3799.83	0.133980
$931$	−90.3378	−0.00318013
$932$	52498.9	1.84513
$933$	13533.9	0.474898
$934$	64259.5	2.25121
$935$	452.458	0.0158256
$936$	0	0
$937$	30667.3	1.06922	0.534609	−	0.845100i	$-0.320459\pi$
$937$	30667.3	1.06922	0.534609	+	0.845100i	$0.320459\pi$
$938$	−2706.85	−0.0942236
$939$	−46678.8	−1.62226
$940$	−1720.61	−0.0597024
$941$	7845.31	0.271785	0.135893	−	0.990724i	$-0.456610\pi$
$941$	7845.31	0.271785	0.135893	+	0.990724i	$0.456610\pi$
$942$	−52178.7	−1.80475
$943$	−40955.9	−1.41433
$944$	45523.6	1.56956
$945$	2527.03	0.0869887
$946$	10287.1	0.353554
$947$	29771.9	1.02160	0.510801	−	0.859699i	$-0.329349\pi$
$947$	29771.9	1.02160	0.510801	+	0.859699i	$0.329349\pi$
$948$	445.487	0.0152624
$949$	0	0
$950$	−5316.84	−0.181580
$951$	−35285.2	−1.20316
$952$	−238.962	−0.00813531
$953$	−46696.6	−1.58725	−0.793626	−	0.608406i	$-0.791809\pi$
$953$	−46696.6	−1.58725	−0.793626	+	0.608406i	$0.791809\pi$
$954$	31458.0	1.06760
$955$	5706.21	0.193350
$956$	45862.9	1.55158
$957$	−16458.4	−0.555931
$958$	−72601.2	−2.44848
$959$	−33083.3	−1.11399
$960$	5459.25	0.183538
$961$	−22314.0	−0.749018
$962$	0	0
$963$	−6439.91	−0.215497
$964$	−57556.4	−1.92299
$965$	879.716	0.0293462
$966$	−72625.8	−2.41894
$967$	−3761.36	−0.125085	−0.0625425	−	0.998042i	$-0.519921\pi$
$967$	−3761.36	−0.125085	−0.0625425	+	0.998042i	$0.519921\pi$
$968$	64.0162	0.00212558
$969$	1703.01	0.0564587
$970$	−4328.83	−0.143289
$971$	−22659.9	−0.748908	−0.374454	−	0.927245i	$-0.622170\pi$
$971$	−22659.9	−0.748908	−0.374454	+	0.927245i	$0.622170\pi$
$972$	−29473.9	−0.972608
$973$	−25867.3	−0.852279
$974$	23045.5	0.758136
$975$	0	0
$976$	2758.93	0.0904829
$977$	−4084.89	−0.133764	−0.0668820	−	0.997761i	$-0.521305\pi$
$977$	−4084.89	−0.133764	−0.0668820	+	0.997761i	$0.521305\pi$
$978$	50838.2	1.66220
$979$	12007.1	0.391981
$980$	−110.951	−0.00361653
$981$	−17842.9	−0.580714
$982$	38519.8	1.25175
$983$	1217.14	0.0394923	0.0197461	−	0.999805i	$-0.493714\pi$
$983$	1217.14	0.0394923	0.0197461	+	0.999805i	$0.493714\pi$
$984$	−930.559	−0.0301475
$985$	−4852.05	−0.156953
$986$	−22221.9	−0.717737
$987$	15523.1	0.500613
$988$	0	0
$989$	−35334.7	−1.13608
$990$	1105.18	0.0354798
$991$	8266.62	0.264983	0.132491	−	0.991184i	$-0.457702\pi$
$991$	8266.62	0.264983	0.132491	+	0.991184i	$0.457702\pi$
$992$	22038.1	0.705353
$993$	−29376.1	−0.938793
$994$	6793.34	0.216772
$995$	−2533.68	−0.0807266
$996$	25558.4	0.813102
$997$	33871.5	1.07595	0.537974	−	0.842961i	$-0.319190\pi$
$997$	33871.5	1.07595	0.537974	+	0.842961i	$0.319190\pi$
$998$	46523.1	1.47561
$999$	−1756.61	−0.0556323

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.n.1.8	✓	39
13.12	even	2		1859.4.a.o.1.32	yes	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.n.1.8	✓	39	1.1	even	1	trivial
1859.4.a.o.1.32	yes	39	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-3.98336 q^{2} +6.46359 q^{3} +7.86718 q^{4} -1.70678 q^{5} -25.7468 q^{6} +18.7420 q^{7} +0.529060 q^{8} +14.7780 q^{9} +O(q^{10})\)	\(q-3.98336 q^{2} +6.46359 q^{3} +7.86718 q^{4} -1.70678 q^{5} -25.7468 q^{6} +18.7420 q^{7} +0.529060 q^{8} +14.7780 q^{9} +6.79871 q^{10} +11.0000 q^{11} +50.8502 q^{12} -74.6562 q^{14} -11.0319 q^{15} -65.0449 q^{16} -24.0995 q^{17} -58.8660 q^{18} -10.9329 q^{19} -13.4275 q^{20} +121.141 q^{21} -43.8170 q^{22} +150.505 q^{23} +3.41962 q^{24} -122.087 q^{25} -78.9983 q^{27} +147.447 q^{28} -231.485 q^{29} +43.9441 q^{30} +86.4697 q^{31} +254.865 q^{32} +71.0995 q^{33} +95.9972 q^{34} -31.9884 q^{35} +116.261 q^{36} +22.2361 q^{37} +43.5496 q^{38} -0.902987 q^{40} -272.123 q^{41} -482.547 q^{42} -234.774 q^{43} +86.5390 q^{44} -25.2227 q^{45} -599.517 q^{46} +128.141 q^{47} -420.423 q^{48} +8.26294 q^{49} +486.317 q^{50} -155.769 q^{51} -534.401 q^{53} +314.679 q^{54} -18.7745 q^{55} +9.91564 q^{56} -70.6656 q^{57} +922.088 q^{58} -699.879 q^{59} -86.7900 q^{60} -42.4158 q^{61} -344.440 q^{62} +276.969 q^{63} -494.861 q^{64} -283.215 q^{66} +36.2575 q^{67} -189.595 q^{68} +972.803 q^{69} +127.422 q^{70} -90.9950 q^{71} +7.81842 q^{72} -177.627 q^{73} -88.5743 q^{74} -789.119 q^{75} -86.0110 q^{76} +206.162 q^{77} +8.76078 q^{79} +111.017 q^{80} -909.617 q^{81} +1083.97 q^{82} +502.622 q^{83} +953.035 q^{84} +41.1325 q^{85} +935.190 q^{86} -1496.22 q^{87} +5.81966 q^{88} +1091.56 q^{89} +100.471 q^{90} +1184.05 q^{92} +558.904 q^{93} -510.432 q^{94} +18.6600 q^{95} +1647.34 q^{96} -636.713 q^{97} -32.9143 q^{98} +162.557 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9}+O(q^{10}) \) 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9} - 158 q^{10} + 429 q^{11} - 351 q^{12} - 176 q^{14} - 30 q^{15} + 230 q^{16} - 244 q^{17} - 21 q^{18} + 70 q^{19} - 366 q^{20} + 142 q^{21} - 47 q^{23} - 846 q^{24} + 322 q^{25} - 416 q^{27} - 1131 q^{28} - 838 q^{29} - 293 q^{30} - 507 q^{31} + 1433 q^{32} - 253 q^{33} - 166 q^{34} - 498 q^{35} + 815 q^{36} - 89 q^{37} + 81 q^{38} - 2917 q^{40} - 618 q^{41} - 318 q^{42} - 1064 q^{43} + 1254 q^{44} - 238 q^{45} + 1331 q^{46} - 1499 q^{47} - 1460 q^{48} - 413 q^{49} + 2459 q^{50} - 2350 q^{51} - 2745 q^{53} + 845 q^{54} - 253 q^{55} - 2904 q^{56} - 1450 q^{57} + 2509 q^{58} - 2285 q^{59} + 3566 q^{60} - 6218 q^{61} - 911 q^{62} + 1930 q^{63} + 67 q^{64} - 847 q^{66} - 546 q^{67} - 170 q^{68} - 5254 q^{69} + 2195 q^{70} + 263 q^{71} + 2393 q^{72} + 1148 q^{73} + 775 q^{74} - 5385 q^{75} + 7247 q^{76} + 44 q^{77} - 3666 q^{79} - 5594 q^{80} - 1901 q^{81} - 4414 q^{82} - 2722 q^{83} + 9971 q^{84} - 1858 q^{85} - 2478 q^{86} - 2284 q^{87} + 231 q^{88} - 13 q^{89} - 6771 q^{90} - 2232 q^{92} + 1082 q^{93} - 7330 q^{94} - 2352 q^{95} - 5770 q^{96} + 1197 q^{97} - 6813 q^{98} + 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9 - 158 * q^10 + 429 * q^11 - 351 * q^12 - 176 * q^14 - 30 * q^15 + 230 * q^16 - 244 * q^17 - 21 * q^18 + 70 * q^19 - 366 * q^20 + 142 * q^21 - 47 * q^23 - 846 * q^24 + 322 * q^25 - 416 * q^27 - 1131 * q^28 - 838 * q^29 - 293 * q^30 - 507 * q^31 + 1433 * q^32 - 253 * q^33 - 166 * q^34 - 498 * q^35 + 815 * q^36 - 89 * q^37 + 81 * q^38 - 2917 * q^40 - 618 * q^41 - 318 * q^42 - 1064 * q^43 + 1254 * q^44 - 238 * q^45 + 1331 * q^46 - 1499 * q^47 - 1460 * q^48 - 413 * q^49 + 2459 * q^50 - 2350 * q^51 - 2745 * q^53 + 845 * q^54 - 253 * q^55 - 2904 * q^56 - 1450 * q^57 + 2509 * q^58 - 2285 * q^59 + 3566 * q^60 - 6218 * q^61 - 911 * q^62 + 1930 * q^63 + 67 * q^64 - 847 * q^66 - 546 * q^67 - 170 * q^68 - 5254 * q^69 + 2195 * q^70 + 263 * q^71 + 2393 * q^72 + 1148 * q^73 + 775 * q^74 - 5385 * q^75 + 7247 * q^76 + 44 * q^77 - 3666 * q^79 - 5594 * q^80 - 1901 * q^81 - 4414 * q^82 - 2722 * q^83 + 9971 * q^84 - 1858 * q^85 - 2478 * q^86 - 2284 * q^87 + 231 * q^88 - 13 * q^89 - 6771 * q^90 - 2232 * q^92 + 1082 * q^93 - 7330 * q^94 - 2352 * q^95 - 5770 * q^96 + 1197 * q^97 - 6813 * q^98 + 2860 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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