LMFDB - Embedded newform 1859.4.a.o.1.6

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			1.6
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)

$f(q)$	$=$	$q-3.79953 q^{2} +4.80997 q^{3} +6.43642 q^{4} +1.29866 q^{5} -18.2756 q^{6} -1.62019 q^{7} +5.94086 q^{8} -3.86420 q^{9} +O(q^{10})$	\(q-3.79953 q^{2} +4.80997 q^{3} +6.43642 q^{4} +1.29866 q^{5} -18.2756 q^{6} -1.62019 q^{7} +5.94086 q^{8} -3.86420 q^{9} -4.93429 q^{10} -11.0000 q^{11} +30.9590 q^{12} +6.15596 q^{14} +6.24650 q^{15} -74.0638 q^{16} +42.5920 q^{17} +14.6822 q^{18} +62.5307 q^{19} +8.35871 q^{20} -7.79306 q^{21} +41.7948 q^{22} -35.1144 q^{23} +28.5753 q^{24} -123.313 q^{25} -148.456 q^{27} -10.4282 q^{28} -43.3864 q^{29} -23.7338 q^{30} +216.323 q^{31} +233.881 q^{32} -52.9097 q^{33} -161.829 q^{34} -2.10407 q^{35} -24.8716 q^{36} +169.251 q^{37} -237.587 q^{38} +7.71514 q^{40} +89.5980 q^{41} +29.6100 q^{42} +38.3091 q^{43} -70.8007 q^{44} -5.01828 q^{45} +133.418 q^{46} -325.682 q^{47} -356.245 q^{48} -340.375 q^{49} +468.533 q^{50} +204.866 q^{51} +341.422 q^{53} +564.062 q^{54} -14.2852 q^{55} -9.62531 q^{56} +300.771 q^{57} +164.848 q^{58} -67.2154 q^{59} +40.2051 q^{60} +332.978 q^{61} -821.926 q^{62} +6.26074 q^{63} -296.127 q^{64} +201.032 q^{66} -253.227 q^{67} +274.140 q^{68} -168.899 q^{69} +7.99448 q^{70} +113.430 q^{71} -22.9567 q^{72} -638.923 q^{73} -643.074 q^{74} -593.134 q^{75} +402.474 q^{76} +17.8221 q^{77} -339.850 q^{79} -96.1836 q^{80} -609.734 q^{81} -340.430 q^{82} +884.850 q^{83} -50.1594 q^{84} +55.3124 q^{85} -145.557 q^{86} -208.687 q^{87} -65.3494 q^{88} -467.941 q^{89} +19.0671 q^{90} -226.011 q^{92} +1040.51 q^{93} +1237.44 q^{94} +81.2060 q^{95} +1124.96 q^{96} +661.757 q^{97} +1293.26 q^{98} +42.5062 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.79953	−1.34334	−0.671668	−	0.740852i	$-0.734422\pi$
$2$	−3.79953	−1.34334	−0.671668	+	0.740852i	$0.734422\pi$
$3$	4.80997	0.925679	0.462839	−	0.886442i	$-0.346831\pi$
$3$	4.80997	0.925679	0.462839	+	0.886442i	$0.346831\pi$
$4$	6.43642	0.804553
$5$	1.29866	0.116155	0.0580777	−	0.998312i	$-0.481503\pi$
$5$	1.29866	0.116155	0.0580777	+	0.998312i	$0.481503\pi$
$6$	−18.2756	−1.24350
$7$	−1.62019	−0.0874820	−0.0437410	−	0.999043i	$-0.513928\pi$
$7$	−1.62019	−0.0874820	−0.0437410	+	0.999043i	$0.513928\pi$
$8$	5.94086	0.262551
$9$	−3.86420	−0.143119
$10$	−4.93429	−0.156036
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	30.9590	0.744758
$13$	0	0
$13$	0	0
$14$	6.15596	0.117518
$15$	6.24650	0.107523
$16$	−74.0638	−1.15725
$17$	42.5920	0.607651	0.303826	−	0.952728i	$-0.401736\pi$
$17$	42.5920	0.607651	0.303826	+	0.952728i	$0.401736\pi$
$18$	14.6822	0.192256
$19$	62.5307	0.755028	0.377514	−	0.926004i	$-0.376779\pi$
$19$	62.5307	0.755028	0.377514	+	0.926004i	$0.376779\pi$
$20$	8.35871	0.0934532
$21$	−7.79306	−0.0809802
$22$	41.7948	0.405031
$23$	−35.1144	−0.318342	−0.159171	−	0.987251i	$-0.550882\pi$
$23$	−35.1144	−0.318342	−0.159171	+	0.987251i	$0.550882\pi$
$24$	28.5753	0.243038
$25$	−123.313	−0.986508
$26$	0	0
$27$	−148.456	−1.05816
$28$	−10.4282	−0.0703839
$29$	−43.3864	−0.277815	−0.138908	−	0.990305i	$-0.544359\pi$
$29$	−43.3864	−0.277815	−0.138908	+	0.990305i	$0.544359\pi$
$30$	−23.7338	−0.144439
$31$	216.323	1.25332	0.626658	−	0.779294i	$-0.284422\pi$
$31$	216.323	1.25332	0.626658	+	0.779294i	$0.284422\pi$
$32$	233.881	1.29202
$33$	−52.9097	−0.279103
$34$	−161.829	−0.816280
$35$	−2.10407	−0.0101615
$36$	−24.8716	−0.115147
$37$	169.251	0.752018	0.376009	−	0.926616i	$-0.377296\pi$
$37$	169.251	0.752018	0.376009	+	0.926616i	$0.377296\pi$
$38$	−237.587	−1.01426
$39$	0	0
$40$	7.71514	0.0304968
$41$	89.5980	0.341289	0.170645	−	0.985333i	$-0.445415\pi$
$41$	89.5980	0.341289	0.170645	+	0.985333i	$0.445415\pi$
$42$	29.6100	0.108784
$43$	38.3091	0.135862	0.0679312	−	0.997690i	$-0.478360\pi$
$43$	38.3091	0.135862	0.0679312	+	0.997690i	$0.478360\pi$
$44$	−70.8007	−0.242582
$45$	−5.01828	−0.0166240
$46$	133.418	0.427640
$47$	−325.682	−1.01076	−0.505379	−	0.862897i	$-0.668647\pi$
$47$	−325.682	−1.01076	−0.505379	+	0.862897i	$0.668647\pi$
$48$	−356.245	−1.07124
$49$	−340.375	−0.992347
$50$	468.533	1.32521
$51$	204.866	0.562490
$52$	0	0
$53$	341.422	0.884867	0.442434	−	0.896801i	$-0.354115\pi$
$53$	341.422	0.884867	0.442434	+	0.896801i	$0.354115\pi$
$54$	564.062	1.42147
$55$	−14.2852	−0.0350222
$56$	−9.62531	−0.0229685
$57$	300.771	0.698913
$58$	164.848	0.373200
$59$	−67.2154	−0.148317	−0.0741584	−	0.997246i	$-0.523627\pi$
$59$	−67.2154	−0.148317	−0.0741584	+	0.997246i	$0.523627\pi$
$60$	40.2051	0.0865077
$61$	332.978	0.698910	0.349455	−	0.936953i	$-0.386367\pi$
$61$	332.978	0.698910	0.349455	+	0.936953i	$0.386367\pi$
$62$	−821.926	−1.68362
$63$	6.26074	0.0125203
$64$	−296.127	−0.578372
$65$	0	0
$66$	201.032	0.374929
$67$	−253.227	−0.461741	−0.230871	−	0.972984i	$-0.574157\pi$
$67$	−253.227	−0.461741	−0.230871	+	0.972984i	$0.574157\pi$
$68$	274.140	0.488888
$69$	−168.899	−0.294682
$70$	7.99448	0.0136503
$71$	113.430	0.189601	0.0948007	−	0.995496i	$-0.469779\pi$
$71$	113.430	0.189601	0.0948007	+	0.995496i	$0.469779\pi$
$72$	−22.9567	−0.0375760
$73$	−638.923	−1.02439	−0.512193	−	0.858870i	$-0.671167\pi$
$73$	−638.923	−1.02439	−0.512193	+	0.858870i	$0.671167\pi$
$74$	−643.074	−1.01021
$75$	−593.134	−0.913190
$76$	402.474	0.607460
$77$	17.8221	0.0263768
$78$	0	0
$79$	−339.850	−0.484002	−0.242001	−	0.970276i	$-0.577804\pi$
$79$	−339.850	−0.484002	−0.242001	+	0.970276i	$0.577804\pi$
$80$	−96.1836	−0.134421
$81$	−609.734	−0.836398
$82$	−340.430	−0.458466
$83$	884.850	1.17018	0.585090	−	0.810969i	$-0.301059\pi$
$83$	884.850	1.17018	0.585090	+	0.810969i	$0.301059\pi$
$84$	−50.1594	−0.0651529
$85$	55.3124	0.0705820
$86$	−145.557	−0.182509
$87$	−208.687	−0.257168
$88$	−65.3494	−0.0791622
$89$	−467.941	−0.557322	−0.278661	−	0.960389i	$-0.589891\pi$
$89$	−467.941	−0.557322	−0.278661	+	0.960389i	$0.589891\pi$
$90$	19.0671	0.0223316
$91$	0	0
$92$	−226.011	−0.256123
$93$	1040.51	1.16017
$94$	1237.44	1.35779
$95$	81.2060	0.0877006
$96$	1124.96	1.19600
$97$	661.757	0.692693	0.346347	−	0.938107i	$-0.387422\pi$
$97$	661.757	0.692693	0.346347	+	0.938107i	$0.387422\pi$
$98$	1293.26	1.33306
$99$	42.5062	0.0431519
$100$	−793.698	−0.793698
$101$	−2016.44	−1.98656	−0.993282	−	0.115720i	$-0.963083\pi$
$101$	−2016.44	−1.98656	−0.993282	+	0.115720i	$0.963083\pi$
$102$	−778.395	−0.755613
$103$	689.014	0.659132	0.329566	−	0.944133i	$-0.393098\pi$
$103$	689.014	0.659132	0.329566	+	0.944133i	$0.393098\pi$
$104$	0	0
$105$	−10.1205	−0.00940630
$106$	−1297.24	−1.18867
$107$	−570.871	−0.515778	−0.257889	−	0.966175i	$-0.583027\pi$
$107$	−570.871	−0.515778	−0.257889	+	0.966175i	$0.583027\pi$
$108$	−955.525	−0.851346
$109$	−408.229	−0.358727	−0.179363	−	0.983783i	$-0.557404\pi$
$109$	−408.229	−0.358727	−0.179363	+	0.983783i	$0.557404\pi$
$110$	54.2772	0.0470466
$111$	814.091	0.696127
$112$	119.997	0.101238
$113$	−543.756	−0.452675	−0.226337	−	0.974049i	$-0.572675\pi$
$113$	−543.756	−0.452675	−0.226337	+	0.974049i	$0.572675\pi$
$114$	−1142.79	−0.938876
$115$	−45.6016	−0.0369772
$116$	−279.253	−0.223517
$117$	0	0
$118$	255.387	0.199239
$119$	−69.0070	−0.0531585
$120$	37.1096	0.0282302
$121$	121.000	0.0909091
$122$	−1265.16	−0.938871
$123$	430.964	0.315924
$124$	1392.35	1.00836
$125$	−322.474	−0.230744
$126$	−23.7879	−0.0168190
$127$	−1245.78	−0.870431	−0.435215	−	0.900326i	$-0.643328\pi$
$127$	−1245.78	−0.870431	−0.435215	+	0.900326i	$0.643328\pi$
$128$	−745.906	−0.515073
$129$	184.266	0.125765
$130$	0	0
$131$	−1092.78	−0.728826	−0.364413	−	0.931237i	$-0.618730\pi$
$131$	−1092.78	−0.728826	−0.364413	+	0.931237i	$0.618730\pi$
$132$	−340.549	−0.224553
$133$	−101.312	−0.0660513
$134$	962.145	0.620274
$135$	−192.793	−0.122911
$136$	253.033	0.159540
$137$	315.651	0.196846	0.0984230	−	0.995145i	$-0.468620\pi$
$137$	315.651	0.196846	0.0984230	+	0.995145i	$0.468620\pi$
$138$	641.738	0.395858
$139$	−1688.81	−1.03053	−0.515264	−	0.857032i	$-0.672306\pi$
$139$	−1688.81	−1.03053	−0.515264	+	0.857032i	$0.672306\pi$
$140$	−13.5427	−0.00817547
$141$	−1566.52	−0.935638
$142$	−430.982	−0.254698
$143$	0	0
$144$	286.198	0.165624
$145$	−56.3441	−0.0322698
$146$	2427.61	1.37610
$147$	−1637.19	−0.918595
$148$	1089.37	0.605038
$149$	2749.48	1.51172	0.755860	−	0.654733i	$-0.227219\pi$
$149$	2749.48	1.51172	0.755860	+	0.654733i	$0.227219\pi$
$150$	2253.63	1.22672
$151$	−1801.51	−0.970895	−0.485447	−	0.874266i	$-0.661343\pi$
$151$	−1801.51	−0.970895	−0.485447	+	0.874266i	$0.661343\pi$
$152$	371.486	0.198233
$153$	−164.584	−0.0869662
$154$	−67.7155	−0.0354329
$155$	280.930	0.145580
$156$	0	0
$157$	1850.87	0.940863	0.470432	−	0.882436i	$-0.344098\pi$
$157$	1850.87	0.940863	0.470432	+	0.882436i	$0.344098\pi$
$158$	1291.27	0.650177
$159$	1642.23	0.819103
$160$	303.731	0.150075
$161$	56.8920	0.0278492
$162$	2316.70	1.12356
$163$	551.212	0.264873	0.132436	−	0.991192i	$-0.457720\pi$
$163$	551.212	0.264873	0.132436	+	0.991192i	$0.457720\pi$
$164$	576.691	0.274585
$165$	−68.7115	−0.0324193
$166$	−3362.01	−1.57194
$167$	89.7313	0.0415785	0.0207893	−	0.999784i	$-0.493382\pi$
$167$	89.7313	0.0415785	0.0207893	+	0.999784i	$0.493382\pi$
$168$	−46.2974	−0.0212615
$169$	0	0
$170$	−210.161	−0.0948154
$171$	−241.631	−0.108059
$172$	246.574	0.109309
$173$	−2921.16	−1.28377	−0.641884	−	0.766801i	$-0.721847\pi$
$173$	−2921.16	−1.28377	−0.641884	+	0.766801i	$0.721847\pi$
$174$	792.913	0.345463
$175$	199.791	0.0863017
$176$	814.702	0.348923
$177$	−323.304	−0.137294
$178$	1777.96	0.748671
$179$	−1282.91	−0.535695	−0.267848	−	0.963461i	$-0.586312\pi$
$179$	−1282.91	−0.535695	−0.267848	+	0.963461i	$0.586312\pi$
$180$	−32.2998	−0.0133749
$181$	58.6272	0.0240758	0.0120379	−	0.999928i	$-0.496168\pi$
$181$	58.6272	0.0240758	0.0120379	+	0.999928i	$0.496168\pi$
$182$	0	0
$183$	1601.62	0.646966
$184$	−208.610	−0.0835811
$185$	219.799	0.0873510
$186$	−3953.44	−1.55850
$187$	−468.512	−0.183214
$188$	−2096.23	−0.813209
$189$	240.527	0.0925700
$190$	−308.545	−0.117811
$191$	1856.77	0.703408	0.351704	−	0.936111i	$-0.385602\pi$
$191$	1856.77	0.703408	0.351704	+	0.936111i	$0.385602\pi$
$192$	−1424.36	−0.535387
$193$	−3214.97	−1.19906	−0.599530	−	0.800352i	$-0.704646\pi$
$193$	−3214.97	−1.19906	−0.599530	+	0.800352i	$0.704646\pi$
$194$	−2514.36	−0.930520
$195$	0	0
$196$	−2190.80	−0.798396
$197$	1826.74	0.660660	0.330330	−	0.943865i	$-0.392840\pi$
$197$	1826.74	0.660660	0.330330	+	0.943865i	$0.392840\pi$
$198$	−161.504	−0.0579675
$199$	2856.48	1.01754	0.508770	−	0.860903i	$-0.330101\pi$
$199$	2856.48	1.01754	0.508770	+	0.860903i	$0.330101\pi$
$200$	−732.588	−0.259009
$201$	−1218.02	−0.427424
$202$	7661.51	2.66862
$203$	70.2941	0.0243038
$204$	1318.60	0.452553
$205$	116.357	0.0396426
$206$	−2617.93	−0.885436
$207$	135.689	0.0455606
$208$	0	0
$209$	−687.838	−0.227649
$210$	38.4532	0.0126358
$211$	2705.92	0.882859	0.441430	−	0.897296i	$-0.354472\pi$
$211$	2705.92	0.882859	0.441430	+	0.897296i	$0.354472\pi$
$212$	2197.54	0.711922
$213$	545.596	0.175510
$214$	2169.04	0.692863
$215$	49.7504	0.0157812
$216$	−881.955	−0.277821
$217$	−350.484	−0.109643
$218$	1551.08	0.481891
$219$	−3073.20	−0.948253
$220$	−91.9458	−0.0281772
$221$	0	0
$222$	−3093.16	−0.935133
$223$	−4218.90	−1.26690	−0.633449	−	0.773784i	$-0.718361\pi$
$223$	−4218.90	−1.26690	−0.633449	+	0.773784i	$0.718361\pi$
$224$	−378.931	−0.113029
$225$	476.508	0.141188
$226$	2066.02	0.608095
$227$	−1887.07	−0.551758	−0.275879	−	0.961192i	$-0.588969\pi$
$227$	−1887.07	−0.551758	−0.275879	+	0.961192i	$0.588969\pi$
$228$	1935.89	0.562313
$229$	−1730.30	−0.499308	−0.249654	−	0.968335i	$-0.580317\pi$
$229$	−1730.30	−0.499308	−0.249654	+	0.968335i	$0.580317\pi$
$230$	173.265	0.0496728
$231$	85.7236	0.0244165
$232$	−257.752	−0.0729408
$233$	−2161.58	−0.607767	−0.303884	−	0.952709i	$-0.598283\pi$
$233$	−2161.58	−0.607767	−0.303884	+	0.952709i	$0.598283\pi$
$234$	0	0
$235$	−422.950	−0.117405
$236$	−432.626	−0.119329
$237$	−1634.67	−0.448030
$238$	262.194	0.0714098
$239$	2760.79	0.747198	0.373599	−	0.927590i	$-0.378124\pi$
$239$	2760.79	0.747198	0.373599	+	0.927590i	$0.378124\pi$
$240$	−462.640	−0.124430
$241$	2291.05	0.612364	0.306182	−	0.951973i	$-0.400948\pi$
$241$	2291.05	0.612364	0.306182	+	0.951973i	$0.400948\pi$
$242$	−459.743	−0.122121
$243$	1075.50	0.283924
$244$	2143.19	0.562310
$245$	−442.031	−0.115267
$246$	−1637.46	−0.424393
$247$	0	0
$248$	1285.14	0.329060
$249$	4256.10	1.08321
$250$	1225.25	0.309967
$251$	−751.912	−0.189085	−0.0945423	−	0.995521i	$-0.530139\pi$
$251$	−751.912	−0.189085	−0.0945423	+	0.995521i	$0.530139\pi$
$252$	40.2968	0.0100732
$253$	386.259	0.0959837
$254$	4733.36	1.16928
$255$	266.051	0.0653363
$256$	5203.10	1.27029
$257$	920.883	0.223514	0.111757	−	0.993736i	$-0.464352\pi$
$257$	920.883	0.223514	0.111757	+	0.993736i	$0.464352\pi$
$258$	−700.123	−0.168945
$259$	−274.218	−0.0657880
$260$	0	0
$261$	167.654	0.0397606
$262$	4152.03	0.979059
$263$	−5979.43	−1.40193	−0.700964	−	0.713196i	$-0.747247\pi$
$263$	−5979.43	−1.40193	−0.700964	+	0.713196i	$0.747247\pi$
$264$	−314.329	−0.0732788
$265$	443.391	0.102782
$266$	384.936	0.0887291
$267$	−2250.78	−0.515901
$268$	−1629.88	−0.371495
$269$	6780.92	1.53695	0.768476	−	0.639878i	$-0.221015\pi$
$269$	6780.92	1.53695	0.768476	+	0.639878i	$0.221015\pi$
$270$	732.524	0.165111
$271$	−2241.91	−0.502532	−0.251266	−	0.967918i	$-0.580847\pi$
$271$	−2241.91	−0.502532	−0.251266	+	0.967918i	$0.580847\pi$
$272$	−3154.53	−0.703203
$273$	0	0
$274$	−1199.33	−0.264430
$275$	1356.45	0.297443
$276$	−1087.11	−0.237088
$277$	4135.48	0.897028	0.448514	−	0.893776i	$-0.351953\pi$
$277$	4135.48	0.897028	0.448514	+	0.893776i	$0.351953\pi$
$278$	6416.70	1.38434
$279$	−835.917	−0.179373
$280$	−12.5000	−0.00266792
$281$	−2574.08	−0.546466	−0.273233	−	0.961948i	$-0.588093\pi$
$281$	−2574.08	−0.546466	−0.273233	+	0.961948i	$0.588093\pi$
$282$	5952.05	1.25688
$283$	3140.17	0.659589	0.329794	−	0.944053i	$-0.393021\pi$
$283$	3140.17	0.659589	0.329794	+	0.944053i	$0.393021\pi$
$284$	730.085	0.152544
$285$	390.598	0.0811826
$286$	0	0
$287$	−145.166	−0.0298567
$288$	−903.763	−0.184912
$289$	−3098.92	−0.630760
$290$	214.081	0.0433492
$291$	3183.03	0.641211
$292$	−4112.38	−0.824173
$293$	−36.1446	−0.00720679	−0.00360339	−	0.999994i	$-0.501147\pi$
$293$	−36.1446	−0.00720679	−0.00360339	+	0.999994i	$0.501147\pi$
$294$	6220.56	1.23398
$295$	−87.2897	−0.0172278
$296$	1005.49	0.197443
$297$	1633.01	0.319047
$298$	−10446.7	−2.03075
$299$	0	0
$300$	−3817.66	−0.734709
$301$	−62.0680	−0.0118855
$302$	6844.90	1.30424
$303$	−9699.00	−1.83892
$304$	−4631.26	−0.873754
$305$	432.425	0.0811822
$306$	625.342	0.116825
$307$	−6834.17	−1.27051	−0.635256	−	0.772302i	$-0.719105\pi$
$307$	−6834.17	−1.27051	−0.635256	+	0.772302i	$0.719105\pi$
$308$	114.710	0.0212215
$309$	3314.14	0.610145
$310$	−1067.40	−0.195562
$311$	−5088.06	−0.927709	−0.463855	−	0.885911i	$-0.653534\pi$
$311$	−5088.06	−0.927709	−0.463855	+	0.885911i	$0.653534\pi$
$312$	0	0
$313$	−5990.28	−1.08176	−0.540879	−	0.841100i	$-0.681908\pi$
$313$	−5990.28	−1.08176	−0.540879	+	0.841100i	$0.681908\pi$
$314$	−7032.44	−1.26390
$315$	8.13056	0.00145430
$316$	−2187.42	−0.389405
$317$	4293.56	0.760727	0.380364	−	0.924837i	$-0.375799\pi$
$317$	4293.56	0.760727	0.380364	+	0.924837i	$0.375799\pi$
$318$	−6239.70	−1.10033
$319$	477.250	0.0837645
$320$	−384.567	−0.0671811
$321$	−2745.87	−0.477445
$322$	−216.163	−0.0374108
$323$	2663.31	0.458794
$324$	−3924.51	−0.672927
$325$	0	0
$326$	−2094.34	−0.355813
$327$	−1963.57	−0.332066
$328$	532.289	0.0896059
$329$	527.667	0.0884232
$330$	261.072	0.0435500
$331$	3249.44	0.539593	0.269797	−	0.962917i	$-0.413044\pi$
$331$	3249.44	0.539593	0.269797	+	0.962917i	$0.413044\pi$
$332$	5695.27	0.941471
$333$	−654.020	−0.107628
$334$	−340.937	−0.0558540
$335$	−328.856	−0.0536338
$336$	577.184	0.0937142
$337$	−223.966	−0.0362023	−0.0181012	−	0.999836i	$-0.505762\pi$
$337$	−223.966	−0.0362023	−0.0181012	+	0.999836i	$0.505762\pi$
$338$	0	0
$339$	−2615.45	−0.419032
$340$	356.014	0.0567870
$341$	−2379.55	−0.377889
$342$	918.085	0.145159
$343$	1107.20	0.174294
$344$	227.589	0.0356708
$345$	−219.342	−0.0342290
$346$	11099.1	1.72453
$347$	3954.54	0.611789	0.305895	−	0.952065i	$-0.401044\pi$
$347$	3954.54	0.611789	0.305895	+	0.952065i	$0.401044\pi$
$348$	−1343.20	−0.206905
$349$	−6151.61	−0.943519	−0.471759	−	0.881727i	$-0.656381\pi$
$349$	−6151.61	−0.943519	−0.471759	+	0.881727i	$0.656381\pi$
$350$	−759.112	−0.115932
$351$	0	0
$352$	−2572.69	−0.389559
$353$	−10687.8	−1.61149	−0.805746	−	0.592261i	$-0.798235\pi$
$353$	−10687.8	−1.61149	−0.805746	+	0.592261i	$0.798235\pi$
$354$	1228.40	0.184432
$355$	147.307	0.0220232
$356$	−3011.87	−0.448395
$357$	−331.922	−0.0492077
$358$	4874.47	0.719619
$359$	−6082.74	−0.894247	−0.447124	−	0.894472i	$-0.647552\pi$
$359$	−6082.74	−0.894247	−0.447124	+	0.894472i	$0.647552\pi$
$360$	−29.8129	−0.00436466
$361$	−2948.91	−0.429933
$362$	−222.756	−0.0323419
$363$	582.006	0.0841526
$364$	0	0
$365$	−829.742	−0.118988
$366$	−6085.38	−0.869093
$367$	−9224.66	−1.31205	−0.656026	−	0.754738i	$-0.727764\pi$
$367$	−9224.66	−1.31205	−0.656026	+	0.754738i	$0.727764\pi$
$368$	2600.71	0.368400
$369$	−346.225	−0.0488449
$370$	−835.133	−0.117342
$371$	−553.169	−0.0774099
$372$	6697.15	0.933416
$373$	−13664.5	−1.89684	−0.948419	−	0.317018i	$-0.897318\pi$
$373$	−13664.5	−1.89684	−0.948419	+	0.317018i	$0.897318\pi$
$374$	1780.12	0.246118
$375$	−1551.09	−0.213595
$376$	−1934.83	−0.265376
$377$	0	0
$378$	−913.888	−0.124353
$379$	−13259.5	−1.79708	−0.898542	−	0.438888i	$-0.855372\pi$
$379$	−13259.5	−1.79708	−0.898542	+	0.438888i	$0.855372\pi$
$380$	522.676	0.0705598
$381$	−5992.14	−0.805740
$382$	−7054.84	−0.944913
$383$	−12584.6	−1.67896	−0.839482	−	0.543388i	$-0.817141\pi$
$383$	−12584.6	−1.67896	−0.839482	+	0.543388i	$0.817141\pi$
$384$	−3587.78	−0.476792
$385$	23.1448	0.00306381
$386$	12215.4	1.61074
$387$	−148.034	−0.0194444
$388$	4259.35	0.557308
$389$	7210.38	0.939797	0.469898	−	0.882720i	$-0.344291\pi$
$389$	7210.38	0.939797	0.469898	+	0.882720i	$0.344291\pi$
$390$	0	0
$391$	−1495.59	−0.193441
$392$	−2022.12	−0.260542
$393$	−5256.22	−0.674659
$394$	−6940.76	−0.887489
$395$	−441.349	−0.0562195
$396$	273.588	0.0347180
$397$	−8393.51	−1.06110	−0.530552	−	0.847652i	$-0.678015\pi$
$397$	−8393.51	−1.06110	−0.530552	+	0.847652i	$0.678015\pi$
$398$	−10853.3	−1.36690
$399$	−487.305	−0.0611423
$400$	9133.07	1.14163
$401$	8267.45	1.02957	0.514784	−	0.857320i	$-0.327872\pi$
$401$	8267.45	1.02957	0.514784	+	0.857320i	$0.327872\pi$
$402$	4627.89	0.574174
$403$	0	0
$404$	−12978.6	−1.59830
$405$	−791.836	−0.0971523
$406$	−267.085	−0.0326482
$407$	−1861.76	−0.226742
$408$	1217.08	0.147682
$409$	−7210.94	−0.871780	−0.435890	−	0.900000i	$-0.643566\pi$
$409$	−7210.94	−0.871780	−0.435890	+	0.900000i	$0.643566\pi$
$410$	−442.103	−0.0532534
$411$	1518.27	0.182216
$412$	4434.79	0.530307
$413$	108.902	0.0129750
$414$	−515.555	−0.0612033
$415$	1149.12	0.135923
$416$	0	0
$417$	−8123.14	−0.953937
$418$	2613.46	0.305810
$419$	−6344.57	−0.739743	−0.369872	−	0.929083i	$-0.620598\pi$
$419$	−6344.57	−0.739743	−0.369872	+	0.929083i	$0.620598\pi$
$420$	−65.1399	−0.00756786
$421$	−66.2152	−0.00766540	−0.00383270	−	0.999993i	$-0.501220\pi$
$421$	−66.2152	−0.00766540	−0.00383270	+	0.999993i	$0.501220\pi$
$422$	−10281.2	−1.18598
$423$	1258.50	0.144658
$424$	2028.34	0.232323
$425$	−5252.17	−0.599453
$426$	−2073.01	−0.235769
$427$	−539.488	−0.0611420
$428$	−3674.37	−0.414971
$429$	0	0
$430$	−189.028	−0.0211994
$431$	−892.273	−0.0997200	−0.0498600	−	0.998756i	$-0.515878\pi$
$431$	−892.273	−0.0997200	−0.0498600	+	0.998756i	$0.515878\pi$
$432$	10995.2	1.22455
$433$	−17502.0	−1.94247	−0.971236	−	0.238119i	$-0.923469\pi$
$433$	−17502.0	−1.94247	−0.971236	+	0.238119i	$0.923469\pi$
$434$	1331.68	0.147287
$435$	−271.013	−0.0298715
$436$	−2627.53	−0.288615
$437$	−2195.73	−0.240357
$438$	11676.7	1.27382
$439$	5997.88	0.652080	0.326040	−	0.945356i	$-0.394286\pi$
$439$	5997.88	0.652080	0.326040	+	0.945356i	$0.394286\pi$
$440$	−84.8665	−0.00919512
$441$	1315.28	0.142023
$442$	0	0
$443$	5219.81	0.559821	0.279910	−	0.960026i	$-0.409695\pi$
$443$	5219.81	0.559821	0.279910	+	0.960026i	$0.409695\pi$
$444$	5239.84	0.560071
$445$	−607.696	−0.0647360
$446$	16029.8	1.70187
$447$	13224.9	1.39937
$448$	479.781	0.0505971
$449$	−8050.74	−0.846187	−0.423093	−	0.906086i	$-0.639056\pi$
$449$	−8050.74	−0.846187	−0.423093	+	0.906086i	$0.639056\pi$
$450$	−1810.51	−0.189663
$451$	−985.578	−0.102903
$452$	−3499.84	−0.364201
$453$	−8665.22	−0.898737
$454$	7169.97	0.741197
$455$	0	0
$456$	1786.84	0.183501
$457$	−18660.7	−1.91009	−0.955043	−	0.296468i	$-0.904191\pi$
$457$	−18660.7	−1.91009	−0.955043	+	0.296468i	$0.904191\pi$
$458$	6574.33	0.670739
$459$	−6323.03	−0.642993
$460$	−293.511	−0.0297501
$461$	−13917.5	−1.40608	−0.703040	−	0.711151i	$-0.748174\pi$
$461$	−13917.5	−1.40608	−0.703040	+	0.711151i	$0.748174\pi$
$462$	−325.709	−0.0327995
$463$	1262.35	0.126709	0.0633544	−	0.997991i	$-0.479820\pi$
$463$	1262.35	0.126709	0.0633544	+	0.997991i	$0.479820\pi$
$464$	3213.36	0.321501
$465$	1351.26	0.134760
$466$	8212.98	0.816436
$467$	−3161.82	−0.313301	−0.156650	−	0.987654i	$-0.550070\pi$
$467$	−3161.82	−0.313301	−0.156650	+	0.987654i	$0.550070\pi$
$468$	0	0
$469$	410.276	0.0403940
$470$	1607.01	0.157715
$471$	8902.63	0.870937
$472$	−399.317	−0.0389408
$473$	−421.400	−0.0409641
$474$	6210.97	0.601855
$475$	−7710.88	−0.744841
$476$	−444.159	−0.0427689
$477$	−1319.33	−0.126641
$478$	−10489.7	−1.00374
$479$	11469.9	1.09410	0.547049	−	0.837100i	$-0.315751\pi$
$479$	11469.9	1.09410	0.547049	+	0.837100i	$0.315751\pi$
$480$	1460.94	0.138922
$481$	0	0
$482$	−8704.92	−0.822611
$483$	273.649	0.0257794
$484$	778.807	0.0731412
$485$	859.396	0.0804601
$486$	−4086.41	−0.381406
$487$	−6505.89	−0.605360	−0.302680	−	0.953092i	$-0.597881\pi$
$487$	−6505.89	−0.605360	−0.302680	+	0.953092i	$0.597881\pi$
$488$	1978.18	0.183500
$489$	2651.31	0.245187
$490$	1679.51	0.154842
$491$	7742.24	0.711614	0.355807	−	0.934559i	$-0.384206\pi$
$491$	7742.24	0.711614	0.355807	+	0.934559i	$0.384206\pi$
$492$	2773.86	0.254178
$493$	−1847.91	−0.168815
$494$	0	0
$495$	55.2011	0.00501233
$496$	−16021.7	−1.45040
$497$	−183.778	−0.0165867
$498$	−16171.2	−1.45512
$499$	−4385.54	−0.393435	−0.196717	−	0.980460i	$-0.563028\pi$
$499$	−4385.54	−0.393435	−0.196717	+	0.980460i	$0.563028\pi$
$500$	−2075.58	−0.185646
$501$	431.605	0.0384884
$502$	2856.91	0.254004
$503$	−15340.1	−1.35980	−0.679901	−	0.733304i	$-0.737977\pi$
$503$	−15340.1	−1.35980	−0.679901	+	0.733304i	$0.737977\pi$
$504$	37.1942	0.00328722
$505$	−2618.66	−0.230750
$506$	−1467.60	−0.128938
$507$	0	0
$508$	−8018.34	−0.700308
$509$	5860.56	0.510343	0.255172	−	0.966896i	$-0.417868\pi$
$509$	5860.56	0.510343	0.255172	+	0.966896i	$0.417868\pi$
$510$	−1010.87	−0.0877686
$511$	1035.18	0.0896154
$512$	−13802.1	−1.19135
$513$	−9283.05	−0.798941
$514$	−3498.92	−0.300255
$515$	894.794	0.0765618
$516$	1186.01	0.101185
$517$	3582.51	0.304755
$518$	1041.90	0.0883755
$519$	−14050.7	−1.18836
$520$	0	0
$521$	8279.11	0.696189	0.348095	−	0.937459i	$-0.386829\pi$
$521$	8279.11	0.696189	0.348095	+	0.937459i	$0.386829\pi$
$522$	−637.005	−0.0534118
$523$	−11446.6	−0.957025	−0.478512	−	0.878081i	$-0.658824\pi$
$523$	−11446.6	−0.957025	−0.478512	+	0.878081i	$0.658824\pi$
$524$	−7033.57	−0.586379
$525$	960.989	0.0798876
$526$	22719.0	1.88326
$527$	9213.63	0.761579
$528$	3918.69	0.322991
$529$	−10934.0	−0.898658
$530$	−1684.68	−0.138071
$531$	259.734	0.0212269
$532$	−652.084	−0.0531418
$533$	0	0
$534$	8551.92	0.693029
$535$	−741.367	−0.0599104
$536$	−1504.39	−0.121231
$537$	−6170.77	−0.495882
$538$	−25764.3	−2.06464
$539$	3744.12	0.299204
$540$	−1240.90	−0.0988885
$541$	1021.06	0.0811439	0.0405719	−	0.999177i	$-0.487082\pi$
$541$	1021.06	0.0811439	0.0405719	+	0.999177i	$0.487082\pi$
$542$	8518.19	0.675070
$543$	281.995	0.0222865
$544$	9961.45	0.785099
$545$	−530.150	−0.0416681
$546$	0	0
$547$	−19405.8	−1.51688	−0.758438	−	0.651746i	$-0.774037\pi$
$547$	−19405.8	−1.51688	−0.758438	+	0.651746i	$0.774037\pi$
$548$	2031.66	0.158373
$549$	−1286.70	−0.100027
$550$	−5153.87	−0.399566
$551$	−2712.98	−0.209758
$552$	−1003.41	−0.0773692
$553$	550.622	0.0423414
$554$	−15712.9	−1.20501
$555$	1057.23	0.0808590
$556$	−10869.9	−0.829114
$557$	1980.10	0.150627	0.0753136	−	0.997160i	$-0.476004\pi$
$557$	1980.10	0.150627	0.0753136	+	0.997160i	$0.476004\pi$
$558$	3176.09	0.240958
$559$	0	0
$560$	155.836	0.0117594
$561$	−2253.53	−0.169597
$562$	9780.30	0.734087
$563$	1526.82	0.114294	0.0571471	−	0.998366i	$-0.481800\pi$
$563$	1526.82	0.114294	0.0571471	+	0.998366i	$0.481800\pi$
$564$	−10082.8	−0.752770
$565$	−706.153	−0.0525807
$566$	−11931.2	−0.886050
$567$	987.885	0.0731698
$568$	673.873	0.0497801
$569$	13753.6	1.01333	0.506663	−	0.862144i	$-0.330879\pi$
$569$	13753.6	1.01333	0.506663	+	0.862144i	$0.330879\pi$
$570$	−1484.09	−0.109056
$571$	−21668.9	−1.58812	−0.794059	−	0.607841i	$-0.792036\pi$
$571$	−21668.9	−1.58812	−0.794059	+	0.607841i	$0.792036\pi$
$572$	0	0
$573$	8930.98	0.651130
$574$	551.561	0.0401075
$575$	4330.08	0.314047
$576$	1144.29	0.0827758
$577$	11200.1	0.808086	0.404043	−	0.914740i	$-0.367605\pi$
$577$	11200.1	0.808086	0.404043	+	0.914740i	$0.367605\pi$
$578$	11774.5	0.847323
$579$	−15463.9	−1.10995
$580$	−362.654	−0.0259628
$581$	−1433.62	−0.102370
$582$	−12094.0	−0.861363
$583$	−3755.65	−0.266797
$584$	−3795.75	−0.268954
$585$	0	0
$586$	137.332	0.00968114
$587$	19830.4	1.39436	0.697181	−	0.716895i	$-0.254438\pi$
$587$	19830.4	1.39436	0.697181	+	0.716895i	$0.254438\pi$
$588$	−10537.7	−0.739058
$589$	13526.8	0.946288
$590$	331.660	0.0231428
$591$	8786.58	0.611559
$592$	−12535.4	−0.870271
$593$	−24271.4	−1.68079	−0.840395	−	0.541975i	$-0.817677\pi$
$593$	−24271.4	−1.68079	−0.840395	+	0.541975i	$0.817677\pi$
$594$	−6204.69	−0.428588
$595$	−89.6165	−0.00617466
$596$	17696.8	1.21626
$597$	13739.6	0.941914
$598$	0	0
$599$	27754.4	1.89318	0.946589	−	0.322443i	$-0.104504\pi$
$599$	27754.4	1.89318	0.946589	+	0.322443i	$0.104504\pi$
$600$	−3523.72	−0.239759
$601$	13670.1	0.927813	0.463906	−	0.885884i	$-0.346447\pi$
$601$	13670.1	0.927813	0.463906	+	0.885884i	$0.346447\pi$
$602$	235.829	0.0159662
$603$	978.522	0.0660838
$604$	−11595.3	−0.781136
$605$	157.138	0.0105596
$606$	36851.6	2.47029
$607$	−20558.4	−1.37470	−0.687348	−	0.726328i	$-0.741225\pi$
$607$	−20558.4	−1.37470	−0.687348	+	0.726328i	$0.741225\pi$
$608$	14624.7	0.975512
$609$	338.113	0.0224976
$610$	−1643.01	−0.109055
$611$	0	0
$612$	−1059.33	−0.0699689
$613$	6803.68	0.448284	0.224142	−	0.974557i	$-0.428042\pi$
$613$	6803.68	0.448284	0.224142	+	0.974557i	$0.428042\pi$
$614$	25966.6	1.70672
$615$	559.674	0.0366963
$616$	105.878	0.00692526
$617$	29749.4	1.94111	0.970555	−	0.240880i	$-0.0774362\pi$
$617$	29749.4	1.94111	0.970555	+	0.240880i	$0.0774362\pi$
$618$	−12592.2	−0.819630
$619$	−124.952	−0.00811351	−0.00405676	−	0.999992i	$-0.501291\pi$
$619$	−124.952	−0.00811351	−0.00405676	+	0.999992i	$0.501291\pi$
$620$	1808.18	0.117126
$621$	5212.94	0.336857
$622$	19332.2	1.24623
$623$	758.153	0.0487557
$624$	0	0
$625$	14995.4	0.959706
$626$	22760.2	1.45317
$627$	−3308.48	−0.210730
$628$	11913.0	0.756974
$629$	7208.73	0.456965
$630$	−30.8923	−0.00195362
$631$	24670.9	1.55647	0.778237	−	0.627971i	$-0.216114\pi$
$631$	24670.9	1.55647	0.778237	+	0.627971i	$0.216114\pi$
$632$	−2019.00	−0.127075
$633$	13015.4	0.817244
$634$	−16313.5	−1.02191
$635$	−1617.84	−0.101105
$636$	10570.1	0.659012
$637$	0	0
$638$	−1813.33	−0.112524
$639$	−438.318	−0.0271355
$640$	−968.676	−0.0598286
$641$	−964.516	−0.0594323	−0.0297161	−	0.999558i	$-0.509460\pi$
$641$	−964.516	−0.0594323	−0.0297161	+	0.999558i	$0.509460\pi$
$642$	10433.0	0.641369
$643$	25364.2	1.55562	0.777811	−	0.628499i	$-0.216330\pi$
$643$	25364.2	1.55562	0.777811	+	0.628499i	$0.216330\pi$
$644$	366.181	0.0224061
$645$	239.298	0.0146083
$646$	−10119.3	−0.616314
$647$	17180.8	1.04397	0.521984	−	0.852955i	$-0.325192\pi$
$647$	17180.8	1.04397	0.521984	+	0.852955i	$0.325192\pi$
$648$	−3622.35	−0.219597
$649$	739.369	0.0447192
$650$	0	0
$651$	−1685.82	−0.101494
$652$	3547.83	0.213104
$653$	−29381.5	−1.76078	−0.880388	−	0.474255i	$-0.842718\pi$
$653$	−29381.5	−1.76078	−0.880388	+	0.474255i	$0.842718\pi$
$654$	7460.63	0.446076
$655$	−1419.14	−0.0846572
$656$	−6635.97	−0.394956
$657$	2468.93	0.146609
$658$	−2004.89	−0.118782
$659$	−11890.6	−0.702872	−0.351436	−	0.936212i	$-0.614306\pi$
$659$	−11890.6	−0.702872	−0.351436	+	0.936212i	$0.614306\pi$
$660$	−442.257	−0.0260830
$661$	7083.25	0.416803	0.208401	−	0.978043i	$-0.433174\pi$
$661$	7083.25	0.416803	0.208401	+	0.978043i	$0.433174\pi$
$662$	−12346.3	−0.724855
$663$	0	0
$664$	5256.77	0.307232
$665$	−131.569	−0.00767222
$666$	2484.97	0.144580
$667$	1523.49	0.0884403
$668$	577.549	0.0334521
$669$	−20292.8	−1.17274
$670$	1249.50	0.0720482
$671$	−3662.76	−0.210729
$672$	−1822.65	−0.104628
$673$	7492.85	0.429165	0.214583	−	0.976706i	$-0.431161\pi$
$673$	7492.85	0.429165	0.214583	+	0.976706i	$0.431161\pi$
$674$	850.964	0.0486319
$675$	18306.6	1.04388
$676$	0	0
$677$	21186.3	1.20274	0.601370	−	0.798971i	$-0.294622\pi$
$677$	21186.3	1.20274	0.601370	+	0.798971i	$0.294622\pi$
$678$	9937.48	0.562900
$679$	−1072.17	−0.0605982
$680$	328.603	0.0185314
$681$	−9076.74	−0.510751
$682$	9041.19	0.507632
$683$	11337.7	0.635176	0.317588	−	0.948229i	$-0.397127\pi$
$683$	11337.7	0.635176	0.317588	+	0.948229i	$0.397127\pi$
$684$	−1555.24	−0.0869388
$685$	409.923	0.0228647
$686$	−4206.83	−0.234136
$687$	−8322.70	−0.462199
$688$	−2837.32	−0.157226
$689$	0	0
$690$	833.398	0.0459810
$691$	10680.7	0.588005	0.294002	−	0.955805i	$-0.405013\pi$
$691$	10680.7	0.588005	0.294002	+	0.955805i	$0.405013\pi$
$692$	−18801.9	−1.03286
$693$	−68.8681	−0.00377501
$694$	−15025.4	−0.821839
$695$	−2193.19	−0.119701
$696$	−1239.78	−0.0675197
$697$	3816.16	0.207385
$698$	23373.2	1.26746
$699$	−10397.1	−0.562597
$700$	1285.94	0.0694342
$701$	−8351.67	−0.449983	−0.224992	−	0.974361i	$-0.572236\pi$
$701$	−8351.67	−0.449983	−0.224992	+	0.974361i	$0.572236\pi$
$702$	0	0
$703$	10583.4	0.567794
$704$	3257.39	0.174386
$705$	−2034.38	−0.108680
$706$	40608.8	2.16478
$707$	3267.01	0.173789
$708$	−2080.92	−0.110460
$709$	−17277.7	−0.915201	−0.457601	−	0.889158i	$-0.651291\pi$
$709$	−17277.7	−0.915201	−0.457601	+	0.889158i	$0.651291\pi$
$710$	−559.698	−0.0295846
$711$	1313.25	0.0692697
$712$	−2779.97	−0.146326
$713$	−7596.06	−0.398983
$714$	1261.15	0.0661025
$715$	0	0
$716$	−8257.37	−0.430995
$717$	13279.3	0.691666
$718$	23111.5	1.20127
$719$	−21149.6	−1.09700	−0.548502	−	0.836149i	$-0.684802\pi$
$719$	−21149.6	−1.09700	−0.548502	+	0.836149i	$0.684802\pi$
$720$	371.673	0.0192381
$721$	−1116.33	−0.0576622
$722$	11204.5	0.577545
$723$	11019.9	0.566852
$724$	377.349	0.0193703
$725$	5350.13	0.274067
$726$	−2211.35	−0.113045
$727$	5227.37	0.266675	0.133337	−	0.991071i	$-0.457431\pi$
$727$	5227.37	0.266675	0.133337	+	0.991071i	$0.457431\pi$
$728$	0	0
$729$	21636.0	1.09922
$730$	3152.63	0.159841
$731$	1631.66	0.0825570
$732$	10308.7	0.520518
$733$	−6152.37	−0.310018	−0.155009	−	0.987913i	$-0.549541\pi$
$733$	−6152.37	−0.310018	−0.155009	+	0.987913i	$0.549541\pi$
$734$	35049.4	1.76253
$735$	−2126.15	−0.106700
$736$	−8212.59	−0.411305
$737$	2785.50	0.139220
$738$	1315.49	0.0656151
$739$	−31210.2	−1.55356	−0.776782	−	0.629769i	$-0.783149\pi$
$739$	−31210.2	−1.55356	−0.776782	+	0.629769i	$0.783149\pi$
$740$	1414.72	0.0702785
$741$	0	0
$742$	2101.78	0.103988
$743$	8135.91	0.401719	0.200860	−	0.979620i	$-0.435626\pi$
$743$	8135.91	0.401719	0.200860	+	0.979620i	$0.435626\pi$
$744$	6181.51	0.304604
$745$	3570.64	0.175595
$746$	51918.7	2.54809
$747$	−3419.24	−0.167474
$748$	−3015.54	−0.147405
$749$	924.920	0.0451213
$750$	5893.42	0.286930
$751$	−19772.7	−0.960739	−0.480369	−	0.877066i	$-0.659497\pi$
$751$	−19772.7	−0.960739	−0.480369	+	0.877066i	$0.659497\pi$
$752$	24121.3	1.16970
$753$	−3616.67	−0.175032
$754$	0	0
$755$	−2339.55	−0.112775
$756$	1548.13	0.0744775
$757$	−451.352	−0.0216706	−0.0108353	−	0.999941i	$-0.503449\pi$
$757$	−451.352	−0.0216706	−0.0108353	+	0.999941i	$0.503449\pi$
$758$	50379.8	2.41409
$759$	1857.89	0.0888501
$760$	482.433	0.0230259
$761$	−9138.05	−0.435288	−0.217644	−	0.976028i	$-0.569837\pi$
$761$	−9138.05	−0.435288	−0.217644	+	0.976028i	$0.569837\pi$
$762$	22767.3	1.08238
$763$	661.408	0.0313821
$764$	11950.9	0.565929
$765$	−213.738	−0.0101016
$766$	47815.6	2.25541
$767$	0	0
$768$	25026.8	1.17588
$769$	22827.4	1.07045	0.535225	−	0.844710i	$-0.320227\pi$
$769$	22827.4	1.07045	0.535225	+	0.844710i	$0.320227\pi$
$770$	−87.9393	−0.00411573
$771$	4429.42	0.206902
$772$	−20692.9	−0.964708
$773$	3026.40	0.140818	0.0704088	−	0.997518i	$-0.477570\pi$
$773$	3026.40	0.140818	0.0704088	+	0.997518i	$0.477570\pi$
$774$	562.460	0.0261204
$775$	−26675.6	−1.23641
$776$	3931.40	0.181867
$777$	−1318.98	−0.0608986
$778$	−27396.1	−1.26246
$779$	5602.63	0.257683
$780$	0	0
$781$	−1247.73	−0.0571670
$782$	5682.55	0.259856
$783$	6440.96	0.293973
$784$	25209.5	1.14839
$785$	2403.65	0.109286
$786$	19971.1	0.906294
$787$	38985.6	1.76580	0.882901	−	0.469560i	$-0.155587\pi$
$787$	38985.6	1.76580	0.882901	+	0.469560i	$0.155587\pi$
$788$	11757.7	0.531536
$789$	−28760.9	−1.29774
$790$	1676.92	0.0755217
$791$	880.988	0.0396009
$792$	252.523	0.0113296
$793$	0	0
$794$	31891.4	1.42542
$795$	2132.70	0.0951433
$796$	18385.5	0.818664
$797$	3263.88	0.145060	0.0725299	−	0.997366i	$-0.476893\pi$
$797$	3263.88	0.145060	0.0725299	+	0.997366i	$0.476893\pi$
$798$	1851.53	0.0821347
$799$	−13871.5	−0.614189
$800$	−28840.7	−1.27459
$801$	1808.22	0.0797632
$802$	−31412.4	−1.38306
$803$	7028.15	0.308864
$804$	−7839.67	−0.343885
$805$	73.8832	0.00323483
$806$	0	0
$807$	32616.0	1.42272
$808$	−11979.4	−0.521575
$809$	−19749.4	−0.858282	−0.429141	−	0.903237i	$-0.641184\pi$
$809$	−19749.4	−0.858282	−0.429141	+	0.903237i	$0.641184\pi$
$810$	3008.61	0.130508
$811$	−19881.6	−0.860836	−0.430418	−	0.902630i	$-0.641634\pi$
$811$	−19881.6	−0.860836	−0.430418	+	0.902630i	$0.641634\pi$
$812$	452.443	0.0195537
$813$	−10783.5	−0.465183
$814$	7073.81	0.304591
$815$	715.835	0.0307664
$816$	−15173.2	−0.650940
$817$	2395.50	0.102580
$818$	27398.2	1.17109
$819$	0	0
$820$	748.924	0.0318946
$821$	32107.5	1.36487	0.682436	−	0.730945i	$-0.260920\pi$
$821$	32107.5	1.36487	0.682436	+	0.730945i	$0.260920\pi$
$822$	−5768.72	−0.244778
$823$	−39149.9	−1.65818	−0.829089	−	0.559117i	$-0.811140\pi$
$823$	−39149.9	−1.65818	−0.829089	+	0.559117i	$0.811140\pi$
$824$	4093.34	0.173056
$825$	6524.47	0.275337
$826$	−413.775	−0.0174299
$827$	−25509.4	−1.07261	−0.536306	−	0.844024i	$-0.680181\pi$
$827$	−25509.4	−1.07261	−0.536306	+	0.844024i	$0.680181\pi$
$828$	873.353	0.0366560
$829$	8456.68	0.354298	0.177149	−	0.984184i	$-0.443313\pi$
$829$	8456.68	0.354298	0.177149	+	0.984184i	$0.443313\pi$
$830$	−4366.10	−0.182590
$831$	19891.5	0.830360
$832$	0	0
$833$	−14497.2	−0.603001
$834$	30864.1	1.28146
$835$	116.530	0.00482958
$836$	−4427.21	−0.183156
$837$	−32114.4	−1.32621
$838$	24106.4	0.993724
$839$	1705.10	0.0701628	0.0350814	−	0.999384i	$-0.488831\pi$
$839$	1705.10	0.0701628	0.0350814	+	0.999384i	$0.488831\pi$
$840$	−60.1245	−0.00246964
$841$	−22506.6	−0.922819
$842$	251.587	0.0102972
$843$	−12381.3	−0.505852
$844$	17416.5	0.710307
$845$	0	0
$846$	−4781.72	−0.194325
$847$	−196.043	−0.00795291
$848$	−25287.0	−1.02401
$849$	15104.1	0.610567
$850$	19955.8	0.805267
$851$	−5943.14	−0.239399
$852$	3511.69	0.141207
$853$	10491.0	0.421108	0.210554	−	0.977582i	$-0.432473\pi$
$853$	10491.0	0.421108	0.210554	+	0.977582i	$0.432473\pi$
$854$	2049.80	0.0821343
$855$	−313.796	−0.0125516
$856$	−3391.47	−0.135418
$857$	28256.3	1.12627	0.563136	−	0.826364i	$-0.309595\pi$
$857$	28256.3	1.12627	0.563136	+	0.826364i	$0.309595\pi$
$858$	0	0
$859$	−22451.2	−0.891764	−0.445882	−	0.895092i	$-0.647110\pi$
$859$	−22451.2	−0.891764	−0.445882	+	0.895092i	$0.647110\pi$
$860$	320.215	0.0126968
$861$	−698.243	−0.0276377
$862$	3390.22	0.133957
$863$	25472.8	1.00476	0.502378	−	0.864648i	$-0.332459\pi$
$863$	25472.8	1.00476	0.502378	+	0.864648i	$0.332459\pi$
$864$	−34721.0	−1.36717
$865$	−3793.59	−0.149117
$866$	66499.2	2.60939
$867$	−14905.7	−0.583881
$868$	−2255.87	−0.0882132
$869$	3738.35	0.145932
$870$	1029.72	0.0401274
$871$	0	0
$872$	−2425.23	−0.0941842
$873$	−2557.16	−0.0991373
$874$	8342.74	0.322880
$875$	522.469	0.0201859
$876$	−19780.4	−0.762920
$877$	43584.1	1.67814	0.839070	−	0.544023i	$-0.183100\pi$
$877$	43584.1	1.67814	0.839070	+	0.544023i	$0.183100\pi$
$878$	−22789.1	−0.875963
$879$	−173.854	−0.00667117
$880$	1058.02	0.0405294
$881$	−15725.7	−0.601374	−0.300687	−	0.953723i	$-0.597216\pi$
$881$	−15725.7	−0.601374	−0.300687	+	0.953723i	$0.597216\pi$
$882$	−4997.44	−0.190785
$883$	29859.6	1.13800	0.569000	−	0.822338i	$-0.307330\pi$
$883$	29859.6	1.13800	0.569000	+	0.822338i	$0.307330\pi$
$884$	0	0
$885$	−419.861	−0.0159474
$886$	−19832.8	−0.752028
$887$	32321.3	1.22350	0.611749	−	0.791052i	$-0.290466\pi$
$887$	32321.3	1.22350	0.611749	+	0.791052i	$0.290466\pi$
$888$	4836.40	0.182769
$889$	2018.39	0.0761470
$890$	2308.96	0.0869623
$891$	6707.08	0.252184
$892$	−27154.6	−1.01929
$893$	−20365.2	−0.763151
$894$	−50248.5	−1.87982
$895$	−1666.07	−0.0622239
$896$	1208.51	0.0450596
$897$	0	0
$898$	30589.0	1.13671
$899$	−9385.48	−0.348190
$900$	3067.01	0.113593
$901$	14541.9	0.537691
$902$	3744.73	0.138233
$903$	−298.545	−0.0110022
$904$	−3230.38	−0.118850
$905$	76.1366	0.00279654
$906$	32923.8	1.20731
$907$	8207.50	0.300469	0.150235	−	0.988650i	$-0.451997\pi$
$907$	8207.50	0.300469	0.150235	+	0.988650i	$0.451997\pi$
$908$	−12146.0	−0.443919
$909$	7791.92	0.284314
$910$	0	0
$911$	−11642.2	−0.423405	−0.211702	−	0.977334i	$-0.567901\pi$
$911$	−11642.2	−0.423405	−0.211702	+	0.977334i	$0.567901\pi$
$912$	−22276.2	−0.808816
$913$	−9733.35	−0.352822
$914$	70901.7	2.56589
$915$	2079.95	0.0751487
$916$	−11137.0	−0.401720
$917$	1770.50	0.0637592
$918$	24024.5	0.863756
$919$	−32053.4	−1.15054	−0.575269	−	0.817964i	$-0.695103\pi$
$919$	−32053.4	−1.15054	−0.575269	+	0.817964i	$0.695103\pi$
$920$	−270.913	−0.00970840
$921$	−32872.2	−1.17609
$922$	52880.0	1.88884
$923$	0	0
$924$	551.754	0.0196443
$925$	−20870.9	−0.741872
$926$	−4796.32	−0.170212
$927$	−2662.49	−0.0943341
$928$	−10147.2	−0.358944
$929$	−556.250	−0.0196447	−0.00982237	−	0.999952i	$-0.503127\pi$
$929$	−556.250	−0.0196447	−0.00982237	+	0.999952i	$0.503127\pi$
$930$	−5134.17	−0.181028
$931$	−21283.9	−0.749249
$932$	−13912.8	−0.488981
$933$	−24473.4	−0.858761
$934$	12013.4	0.420868
$935$	−608.436	−0.0212813
$936$	0	0
$937$	−18812.9	−0.655913	−0.327957	−	0.944693i	$-0.606360\pi$
$937$	−18812.9	−0.655913	−0.327957	+	0.944693i	$0.606360\pi$
$938$	−1558.86	−0.0542628
$939$	−28813.0	−1.00136
$940$	−2722.29	−0.0944587
$941$	−12297.7	−0.426029	−0.213015	−	0.977049i	$-0.568328\pi$
$941$	−12297.7	−0.426029	−0.213015	+	0.977049i	$0.568328\pi$
$942$	−33825.8	−1.16996
$943$	−3146.18	−0.108647
$944$	4978.23	0.171639
$945$	312.362	0.0107525
$946$	1601.12	0.0550285
$947$	−21301.5	−0.730946	−0.365473	−	0.930822i	$-0.619093\pi$
$947$	−21301.5	−0.730946	−0.365473	+	0.930822i	$0.619093\pi$
$948$	−10521.4	−0.360464
$949$	0	0
$950$	29297.7	1.00057
$951$	20651.9	0.704189
$952$	−409.961	−0.0139568
$953$	−1006.35	−0.0342067	−0.0171033	−	0.999854i	$-0.505444\pi$
$953$	−1006.35	−0.0342067	−0.0171033	+	0.999854i	$0.505444\pi$
$954$	5012.81	0.170121
$955$	2411.30	0.0817047
$956$	17769.6	0.601161
$957$	2295.56	0.0775390
$958$	−43580.2	−1.46974
$959$	−511.415	−0.0172205
$960$	−1849.76	−0.0621881
$961$	17004.7	0.570800
$962$	0	0
$963$	2205.96	0.0738174
$964$	14746.2	0.492679
$965$	−4175.15	−0.139278
$966$	−1039.74	−0.0346304
$967$	−10139.9	−0.337205	−0.168602	−	0.985684i	$-0.553925\pi$
$967$	−10139.9	−0.337205	−0.168602	+	0.985684i	$0.553925\pi$
$968$	718.844	0.0238683
$969$	12810.4	0.424696
$970$	−3265.30	−0.108085
$971$	40199.7	1.32860	0.664299	−	0.747467i	$-0.268730\pi$
$971$	40199.7	1.32860	0.664299	+	0.747467i	$0.268730\pi$
$972$	6922.40	0.228432
$973$	2736.20	0.0901526
$974$	24719.3	0.813202
$975$	0	0
$976$	−24661.7	−0.808812
$977$	49085.4	1.60735	0.803675	−	0.595068i	$-0.202875\pi$
$977$	49085.4	1.60735	0.803675	+	0.595068i	$0.202875\pi$
$978$	−10073.7	−0.329368
$979$	5147.35	0.168039
$980$	−2845.10	−0.0927380
$981$	1577.48	0.0513405
$982$	−29416.9	−0.955937
$983$	−33803.0	−1.09680	−0.548398	−	0.836218i	$-0.684762\pi$
$983$	−33803.0	−1.09680	−0.548398	+	0.836218i	$0.684762\pi$
$984$	2560.29	0.0829463
$985$	2372.31	0.0767393
$986$	7021.19	0.226775
$987$	2538.06	0.0818515
$988$	0	0
$989$	−1345.20	−0.0432507
$990$	−209.738	−0.00673324
$991$	−51713.3	−1.65764	−0.828822	−	0.559512i	$-0.810989\pi$
$991$	−51713.3	−1.65764	−0.828822	+	0.559512i	$0.810989\pi$
$992$	50593.9	1.61931
$993$	15629.7	0.499490
$994$	698.272	0.0222815
$995$	3709.59	0.118193
$996$	27394.1	0.871500
$997$	−3230.85	−0.102630	−0.0513150	−	0.998683i	$-0.516341\pi$
$997$	−3230.85	−0.102630	−0.0513150	+	0.998683i	$0.516341\pi$
$998$	16663.0	0.528515
$999$	−25126.3	−0.795756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.o.1.6	yes	39
13.12	even	2		1859.4.a.n.1.34	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.n.1.34	✓	39	13.12	even	2
1859.4.a.o.1.6	yes	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-3.79953 q^{2} +4.80997 q^{3} +6.43642 q^{4} +1.29866 q^{5} -18.2756 q^{6} -1.62019 q^{7} +5.94086 q^{8} -3.86420 q^{9} +O(q^{10})\)	\(q-3.79953 q^{2} +4.80997 q^{3} +6.43642 q^{4} +1.29866 q^{5} -18.2756 q^{6} -1.62019 q^{7} +5.94086 q^{8} -3.86420 q^{9} -4.93429 q^{10} -11.0000 q^{11} +30.9590 q^{12} +6.15596 q^{14} +6.24650 q^{15} -74.0638 q^{16} +42.5920 q^{17} +14.6822 q^{18} +62.5307 q^{19} +8.35871 q^{20} -7.79306 q^{21} +41.7948 q^{22} -35.1144 q^{23} +28.5753 q^{24} -123.313 q^{25} -148.456 q^{27} -10.4282 q^{28} -43.3864 q^{29} -23.7338 q^{30} +216.323 q^{31} +233.881 q^{32} -52.9097 q^{33} -161.829 q^{34} -2.10407 q^{35} -24.8716 q^{36} +169.251 q^{37} -237.587 q^{38} +7.71514 q^{40} +89.5980 q^{41} +29.6100 q^{42} +38.3091 q^{43} -70.8007 q^{44} -5.01828 q^{45} +133.418 q^{46} -325.682 q^{47} -356.245 q^{48} -340.375 q^{49} +468.533 q^{50} +204.866 q^{51} +341.422 q^{53} +564.062 q^{54} -14.2852 q^{55} -9.62531 q^{56} +300.771 q^{57} +164.848 q^{58} -67.2154 q^{59} +40.2051 q^{60} +332.978 q^{61} -821.926 q^{62} +6.26074 q^{63} -296.127 q^{64} +201.032 q^{66} -253.227 q^{67} +274.140 q^{68} -168.899 q^{69} +7.99448 q^{70} +113.430 q^{71} -22.9567 q^{72} -638.923 q^{73} -643.074 q^{74} -593.134 q^{75} +402.474 q^{76} +17.8221 q^{77} -339.850 q^{79} -96.1836 q^{80} -609.734 q^{81} -340.430 q^{82} +884.850 q^{83} -50.1594 q^{84} +55.3124 q^{85} -145.557 q^{86} -208.687 q^{87} -65.3494 q^{88} -467.941 q^{89} +19.0671 q^{90} -226.011 q^{92} +1040.51 q^{93} +1237.44 q^{94} +81.2060 q^{95} +1124.96 q^{96} +661.757 q^{97} +1293.26 q^{98} +42.5062 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) \) 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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