LMFDB - Embedded newform 1859.4.a.q.1.42

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:	$0$
Dimension:	$51$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.42
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)

$f(q)$	$=$	$q+3.79290 q^{2} -5.52551 q^{3} +6.38608 q^{4} +13.9792 q^{5} -20.9577 q^{6} +15.0455 q^{7} -6.12143 q^{8} +3.53129 q^{9} +O(q^{10})$	\(q+3.79290 q^{2} -5.52551 q^{3} +6.38608 q^{4} +13.9792 q^{5} -20.9577 q^{6} +15.0455 q^{7} -6.12143 q^{8} +3.53129 q^{9} +53.0218 q^{10} +11.0000 q^{11} -35.2864 q^{12} +57.0659 q^{14} -77.2423 q^{15} -74.3066 q^{16} +30.2223 q^{17} +13.3938 q^{18} +25.3314 q^{19} +89.2724 q^{20} -83.1339 q^{21} +41.7219 q^{22} +140.864 q^{23} +33.8240 q^{24} +70.4186 q^{25} +129.677 q^{27} +96.0815 q^{28} -155.291 q^{29} -292.972 q^{30} -43.9418 q^{31} -232.866 q^{32} -60.7806 q^{33} +114.630 q^{34} +210.324 q^{35} +22.5511 q^{36} +276.238 q^{37} +96.0793 q^{38} -85.5728 q^{40} +82.5163 q^{41} -315.318 q^{42} +366.942 q^{43} +70.2469 q^{44} +49.3647 q^{45} +534.282 q^{46} -295.998 q^{47} +410.582 q^{48} -116.634 q^{49} +267.090 q^{50} -166.994 q^{51} -403.784 q^{53} +491.850 q^{54} +153.771 q^{55} -92.0997 q^{56} -139.969 q^{57} -589.003 q^{58} +145.614 q^{59} -493.276 q^{60} +634.677 q^{61} -166.667 q^{62} +53.1299 q^{63} -288.784 q^{64} -230.535 q^{66} +354.361 q^{67} +193.002 q^{68} -778.345 q^{69} +797.737 q^{70} -129.912 q^{71} -21.6165 q^{72} +1034.07 q^{73} +1047.74 q^{74} -389.099 q^{75} +161.768 q^{76} +165.500 q^{77} +230.441 q^{79} -1038.75 q^{80} -811.875 q^{81} +312.976 q^{82} +122.023 q^{83} -530.900 q^{84} +422.484 q^{85} +1391.77 q^{86} +858.063 q^{87} -67.3357 q^{88} +1168.25 q^{89} +187.235 q^{90} +899.568 q^{92} +242.801 q^{93} -1122.69 q^{94} +354.113 q^{95} +1286.70 q^{96} +1079.92 q^{97} -442.382 q^{98} +38.8442 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) $ 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * 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 $

$2$	3.79290	1.34099	0.670496	−	0.741913i	$-0.266081\pi$
$2$	3.79290	1.34099	0.670496	+	0.741913i	$0.266081\pi$
$3$	−5.52551	−1.06339	−0.531693	−	0.846937i	$-0.678444\pi$
$3$	−5.52551	−1.06339	−0.531693	+	0.846937i	$0.678444\pi$
$4$	6.38608	0.798260
$5$	13.9792	1.25034	0.625170	−	0.780489i	$-0.285030\pi$
$5$	13.9792	1.25034	0.625170	+	0.780489i	$0.285030\pi$
$6$	−20.9577	−1.42599
$7$	15.0455	0.812378	0.406189	−	0.913789i	$-0.366857\pi$
$7$	15.0455	0.812378	0.406189	+	0.913789i	$0.366857\pi$
$8$	−6.12143	−0.270531
$9$	3.53129	0.130788
$10$	53.0218	1.67670
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−35.2864	−0.848858
$13$	0	0
$13$	0	0
$14$	57.0659	1.08939
$15$	−77.2423	−1.32959
$16$	−74.3066	−1.16104
$17$	30.2223	0.431176	0.215588	−	0.976484i	$-0.430833\pi$
$17$	30.2223	0.431176	0.215588	+	0.976484i	$0.430833\pi$
$18$	13.3938	0.175386
$19$	25.3314	0.305864	0.152932	−	0.988237i	$-0.451128\pi$
$19$	25.3314	0.305864	0.152932	+	0.988237i	$0.451128\pi$
$20$	89.2724	0.998096
$21$	−83.1339	−0.863871
$22$	41.7219	0.404324
$23$	140.864	1.27705	0.638525	−	0.769601i	$-0.279545\pi$
$23$	140.864	1.27705	0.638525	+	0.769601i	$0.279545\pi$
$24$	33.8240	0.287679
$25$	70.4186	0.563348
$26$	0	0
$27$	129.677	0.924307
$28$	96.0815	0.648489
$29$	−155.291	−0.994373	−0.497187	−	0.867644i	$-0.665634\pi$
$29$	−155.291	−0.994373	−0.497187	+	0.867644i	$0.665634\pi$
$30$	−292.972	−1.78297
$31$	−43.9418	−0.254586	−0.127293	−	0.991865i	$-0.540629\pi$
$31$	−43.9418	−0.254586	−0.127293	+	0.991865i	$0.540629\pi$
$32$	−232.866	−1.28642
$33$	−60.7806	−0.320623
$34$	114.630	0.578203
$35$	210.324	1.01575
$36$	22.5511	0.104403
$37$	276.238	1.22739	0.613693	−	0.789545i	$-0.289683\pi$
$37$	276.238	1.22739	0.613693	+	0.789545i	$0.289683\pi$
$38$	96.0793	0.410161
$39$	0	0
$40$	−85.5728	−0.338256
$41$	82.5163	0.314314	0.157157	−	0.987574i	$-0.449767\pi$
$41$	82.5163	0.314314	0.157157	+	0.987574i	$0.449767\pi$
$42$	−315.318	−1.15844
$43$	366.942	1.30135	0.650676	−	0.759355i	$-0.274485\pi$
$43$	366.942	1.30135	0.650676	+	0.759355i	$0.274485\pi$
$44$	70.2469	0.240685
$45$	49.3647	0.163530
$46$	534.282	1.71251
$47$	−295.998	−0.918634	−0.459317	−	0.888272i	$-0.651906\pi$
$47$	−295.998	−0.918634	−0.459317	+	0.888272i	$0.651906\pi$
$48$	410.582	1.23463
$49$	−116.634	−0.340041
$50$	267.090	0.755446
$51$	−166.994	−0.458506
$52$	0	0
$53$	−403.784	−1.04649	−0.523245	−	0.852182i	$-0.675279\pi$
$53$	−403.784	−1.04649	−0.523245	+	0.852182i	$0.675279\pi$
$54$	491.850	1.23949
$55$	153.771	0.376991
$56$	−92.0997	−0.219774
$57$	−139.969	−0.325251
$58$	−589.003	−1.33345
$59$	145.614	0.321312	0.160656	−	0.987010i	$-0.448639\pi$
$59$	145.614	0.321312	0.160656	+	0.987010i	$0.448639\pi$
$60$	−493.276	−1.06136
$61$	634.677	1.33217	0.666083	−	0.745878i	$-0.267970\pi$
$61$	634.677	1.33217	0.666083	+	0.745878i	$0.267970\pi$
$62$	−166.667	−0.341398
$63$	53.1299	0.106250
$64$	−288.784	−0.564032
$65$	0	0
$66$	−230.535	−0.429953
$67$	354.361	0.646151	0.323076	−	0.946373i	$-0.395283\pi$
$67$	354.361	0.646151	0.323076	+	0.946373i	$0.395283\pi$
$68$	193.002	0.344190
$69$	−778.345	−1.35800
$70$	797.737	1.36211
$71$	−129.912	−0.217150	−0.108575	−	0.994088i	$-0.534629\pi$
$71$	−129.912	−0.217150	−0.108575	+	0.994088i	$0.534629\pi$
$72$	−21.6165	−0.0353824
$73$	1034.07	1.65793	0.828963	−	0.559304i	$-0.188932\pi$
$73$	1034.07	1.65793	0.828963	+	0.559304i	$0.188932\pi$
$74$	1047.74	1.64591
$75$	−389.099	−0.599056
$76$	161.768	0.244159
$77$	165.500	0.244941
$78$	0	0
$79$	230.441	0.328185	0.164092	−	0.986445i	$-0.447530\pi$
$79$	230.441	0.328185	0.164092	+	0.986445i	$0.447530\pi$
$80$	−1038.75	−1.45170
$81$	−811.875	−1.11368
$82$	312.976	0.421493
$83$	122.023	0.161371	0.0806854	−	0.996740i	$-0.474289\pi$
$83$	122.023	0.161371	0.0806854	+	0.996740i	$0.474289\pi$
$84$	−530.900	−0.689594
$85$	422.484	0.539116
$86$	1391.77	1.74510
$87$	858.063	1.05740
$88$	−67.3357	−0.0815683
$89$	1168.25	1.39140	0.695701	−	0.718332i	$-0.255094\pi$
$89$	1168.25	1.39140	0.695701	+	0.718332i	$0.255094\pi$
$90$	187.235	0.219292
$91$	0	0
$92$	899.568	1.01942
$93$	242.801	0.270723
$94$	−1122.69	−1.23188
$95$	354.113	0.382434
$96$	1286.70	1.36796
$97$	1079.92	1.13041	0.565204	−	0.824951i	$-0.308797\pi$
$97$	1079.92	1.13041	0.565204	+	0.824951i	$0.308797\pi$
$98$	−442.382	−0.455993
$99$	38.8442	0.0394342
$100$	449.699	0.449699
$101$	−1817.96	−1.79103	−0.895514	−	0.445033i	$-0.853192\pi$
$101$	−1817.96	−1.79103	−0.895514	+	0.445033i	$0.853192\pi$
$102$	−633.391	−0.614853
$103$	−1234.65	−1.18110	−0.590552	−	0.807000i	$-0.701090\pi$
$103$	−1234.65	−1.18110	−0.590552	+	0.807000i	$0.701090\pi$
$104$	0	0
$105$	−1162.15	−1.08013
$106$	−1531.51	−1.40334
$107$	520.283	0.470071	0.235036	−	0.971987i	$-0.424479\pi$
$107$	520.283	0.470071	0.235036	+	0.971987i	$0.424479\pi$
$108$	828.126	0.737837
$109$	−610.589	−0.536549	−0.268274	−	0.963343i	$-0.586453\pi$
$109$	−610.589	−0.536549	−0.268274	+	0.963343i	$0.586453\pi$
$110$	583.239	0.505543
$111$	−1526.36	−1.30518
$112$	−1117.98	−0.943205
$113$	373.015	0.310534	0.155267	−	0.987873i	$-0.450376\pi$
$113$	373.015	0.310534	0.155267	+	0.987873i	$0.450376\pi$
$114$	−530.887	−0.436159
$115$	1969.17	1.59675
$116$	−991.702	−0.793769
$117$	0	0
$118$	552.301	0.430876
$119$	454.709	0.350278
$120$	472.834	0.359697
$121$	121.000	0.0909091
$122$	2407.27	1.78642
$123$	−455.945	−0.334237
$124$	−280.616	−0.203226
$125$	−763.006	−0.545963
$126$	201.516	0.142480
$127$	34.7410	0.0242738	0.0121369	−	0.999926i	$-0.496137\pi$
$127$	34.7410	0.0242738	0.0121369	+	0.999926i	$0.496137\pi$
$128$	767.598	0.530053
$129$	−2027.54	−1.38384
$130$	0	0
$131$	−2136.12	−1.42469	−0.712344	−	0.701831i	$-0.752366\pi$
$131$	−2136.12	−1.42469	−0.712344	+	0.701831i	$0.752366\pi$
$132$	−388.150	−0.255940
$133$	381.122	0.248477
$134$	1344.06	0.866484
$135$	1812.78	1.15570
$136$	−185.004	−0.116647
$137$	−375.915	−0.234428	−0.117214	−	0.993107i	$-0.537396\pi$
$137$	−375.915	−0.234428	−0.117214	+	0.993107i	$0.537396\pi$
$138$	−2952.18	−1.82106
$139$	145.327	0.0886796	0.0443398	−	0.999017i	$-0.485882\pi$
$139$	145.327	0.0886796	0.0443398	+	0.999017i	$0.485882\pi$
$140$	1343.14	0.810832
$141$	1635.54	0.976862
$142$	−492.742	−0.291197
$143$	0	0
$144$	−262.398	−0.151851
$145$	−2170.85	−1.24330
$146$	3922.12	2.22326
$147$	644.463	0.361595
$148$	1764.08	0.979773
$149$	2633.86	1.44815	0.724074	−	0.689723i	$-0.242268\pi$
$149$	2633.86	1.44815	0.724074	+	0.689723i	$0.242268\pi$
$150$	−1475.81	−0.803330
$151$	2201.86	1.18665	0.593327	−	0.804962i	$-0.297814\pi$
$151$	2201.86	1.18665	0.593327	+	0.804962i	$0.297814\pi$
$152$	−155.064	−0.0827458
$153$	106.724	0.0563928
$154$	627.725	0.328464
$155$	−614.271	−0.318319
$156$	0	0
$157$	2416.50	1.22840	0.614198	−	0.789152i	$-0.289480\pi$
$157$	2416.50	1.22840	0.614198	+	0.789152i	$0.289480\pi$
$158$	874.038	0.440093
$159$	2231.11	1.11282
$160$	−3255.29	−1.60846
$161$	2119.36	1.03745
$162$	−3079.36	−1.49344
$163$	1774.64	0.852762	0.426381	−	0.904544i	$-0.359788\pi$
$163$	1774.64	0.852762	0.426381	+	0.904544i	$0.359788\pi$
$164$	526.956	0.250905
$165$	−849.666	−0.400887
$166$	462.821	0.216397
$167$	1910.22	0.885133	0.442567	−	0.896736i	$-0.354068\pi$
$167$	1910.22	0.885133	0.442567	+	0.896736i	$0.354068\pi$
$168$	508.898	0.233704
$169$	0	0
$170$	1602.44	0.722950
$171$	89.4524	0.0400035
$172$	2343.32	1.03882
$173$	−305.524	−0.134269	−0.0671346	−	0.997744i	$-0.521386\pi$
$173$	−305.524	−0.134269	−0.0671346	+	0.997744i	$0.521386\pi$
$174$	3254.55	1.41797
$175$	1059.48	0.457652
$176$	−817.373	−0.350067
$177$	−804.594	−0.341678
$178$	4431.07	1.86586
$179$	4120.63	1.72062	0.860309	−	0.509773i	$-0.170271\pi$
$179$	4120.63	1.72062	0.860309	+	0.509773i	$0.170271\pi$
$180$	315.247	0.130539
$181$	−2255.78	−0.926356	−0.463178	−	0.886265i	$-0.653291\pi$
$181$	−2255.78	−0.926356	−0.463178	+	0.886265i	$0.653291\pi$
$182$	0	0
$183$	−3506.92	−1.41661
$184$	−862.288	−0.345482
$185$	3861.59	1.53465
$186$	920.919	0.363038
$187$	332.445	0.130004
$188$	−1890.27	−0.733309
$189$	1951.04	0.750887
$190$	1343.11	0.512841
$191$	−2154.05	−0.816028	−0.408014	−	0.912976i	$-0.633779\pi$
$191$	−2154.05	−0.816028	−0.408014	+	0.912976i	$0.633779\pi$
$192$	1595.68	0.599784
$193$	3372.22	1.25771	0.628854	−	0.777523i	$-0.283524\pi$
$193$	3372.22	1.25771	0.628854	+	0.777523i	$0.283524\pi$
$194$	4096.04	1.51587
$195$	0	0
$196$	−744.835	−0.271441
$197$	5026.68	1.81795	0.908974	−	0.416852i	$-0.136867\pi$
$197$	5026.68	1.81795	0.908974	+	0.416852i	$0.136867\pi$
$198$	147.332	0.0528810
$199$	2296.08	0.817914	0.408957	−	0.912554i	$-0.365893\pi$
$199$	2296.08	0.817914	0.408957	+	0.912554i	$0.365893\pi$
$200$	−431.062	−0.152403
$201$	−1958.03	−0.687108
$202$	−6895.34	−2.40175
$203$	−2336.43	−0.807808
$204$	−1066.44	−0.366007
$205$	1153.51	0.392999
$206$	−4682.90	−1.58385
$207$	497.431	0.167023
$208$	0	0
$209$	278.645	0.0922214
$210$	−4407.90	−1.44845
$211$	1846.27	0.602382	0.301191	−	0.953564i	$-0.402616\pi$
$211$	1846.27	0.602382	0.301191	+	0.953564i	$0.402616\pi$
$212$	−2578.60	−0.835372
$213$	717.828	0.230914
$214$	1973.38	0.630362
$215$	5129.57	1.62713
$216$	−793.806	−0.250054
$217$	−661.124	−0.206820
$218$	−2315.90	−0.719508
$219$	−5713.76	−1.76301
$220$	981.997	0.300937
$221$	0	0
$222$	−5789.32	−1.75024
$223$	4357.46	1.30851	0.654254	−	0.756275i	$-0.272983\pi$
$223$	4357.46	1.30851	0.654254	+	0.756275i	$0.272983\pi$
$224$	−3503.58	−1.04506
$225$	248.668	0.0736795
$226$	1414.81	0.416423
$227$	1877.12	0.548850	0.274425	−	0.961609i	$-0.411513\pi$
$227$	1877.12	0.548850	0.274425	+	0.961609i	$0.411513\pi$
$228$	−893.852	−0.259635
$229$	−4608.22	−1.32978	−0.664890	−	0.746942i	$-0.731521\pi$
$229$	−4608.22	−1.32978	−0.664890	+	0.746942i	$0.731521\pi$
$230$	7468.85	2.14122
$231$	−914.473	−0.260467
$232$	950.603	0.269009
$233$	−4934.53	−1.38743	−0.693716	−	0.720249i	$-0.744028\pi$
$233$	−4934.53	−1.38743	−0.693716	+	0.720249i	$0.744028\pi$
$234$	0	0
$235$	−4137.83	−1.14860
$236$	929.906	0.256490
$237$	−1273.30	−0.348987
$238$	1724.66	0.469720
$239$	6545.81	1.77160	0.885801	−	0.464065i	$-0.153609\pi$
$239$	6545.81	1.77160	0.885801	+	0.464065i	$0.153609\pi$
$240$	5739.62	1.54371
$241$	1619.94	0.432985	0.216492	−	0.976284i	$-0.430538\pi$
$241$	1619.94	0.432985	0.216492	+	0.976284i	$0.430538\pi$
$242$	458.941	0.121908
$243$	984.755	0.259967
$244$	4053.10	1.06341
$245$	−1630.45	−0.425167
$246$	−1729.35	−0.448209
$247$	0	0
$248$	268.986	0.0688736
$249$	−674.240	−0.171599
$250$	−2894.00	−0.732132
$251$	1756.49	0.441707	0.220854	−	0.975307i	$-0.429116\pi$
$251$	1756.49	0.441707	0.220854	+	0.975307i	$0.429116\pi$
$252$	339.292	0.0848149
$253$	1549.50	0.385045
$254$	131.769	0.0325509
$255$	−2334.44	−0.573288
$256$	5221.70	1.27483
$257$	1217.71	0.295559	0.147780	−	0.989020i	$-0.452787\pi$
$257$	1217.71	0.295559	0.147780	+	0.989020i	$0.452787\pi$
$258$	−7690.27	−1.85572
$259$	4156.13	0.997101
$260$	0	0
$261$	−548.378	−0.130053
$262$	−8102.10	−1.91049
$263$	−1648.88	−0.386595	−0.193297	−	0.981140i	$-0.561918\pi$
$263$	−1648.88	−0.386595	−0.193297	+	0.981140i	$0.561918\pi$
$264$	372.064	0.0867385
$265$	−5644.59	−1.30847
$266$	1445.56	0.333206
$267$	−6455.20	−1.47960
$268$	2262.98	0.515797
$269$	2031.77	0.460517	0.230259	−	0.973129i	$-0.426043\pi$
$269$	2031.77	0.460517	0.230259	+	0.973129i	$0.426043\pi$
$270$	6875.68	1.54978
$271$	−478.527	−0.107264	−0.0536318	−	0.998561i	$-0.517080\pi$
$271$	−478.527	−0.107264	−0.0536318	+	0.998561i	$0.517080\pi$
$272$	−2245.72	−0.500613
$273$	0	0
$274$	−1425.81	−0.314366
$275$	774.604	0.169856
$276$	−4970.58	−1.08403
$277$	7070.18	1.53360	0.766798	−	0.641889i	$-0.221849\pi$
$277$	7070.18	1.53360	0.766798	+	0.641889i	$0.221849\pi$
$278$	551.210	0.118919
$279$	−155.171	−0.0332969
$280$	−1287.48	−0.274792
$281$	−7038.72	−1.49429	−0.747144	−	0.664662i	$-0.768576\pi$
$281$	−7038.72	−1.49429	−0.747144	+	0.664662i	$0.768576\pi$
$282$	6203.45	1.30996
$283$	−193.865	−0.0407210	−0.0203605	−	0.999793i	$-0.506481\pi$
$283$	−193.865	−0.0407210	−0.0203605	+	0.999793i	$0.506481\pi$
$284$	−829.626	−0.173342
$285$	−1956.65	−0.406674
$286$	0	0
$287$	1241.50	0.255342
$288$	−822.317	−0.168248
$289$	−3999.61	−0.814087
$290$	−8233.81	−1.66726
$291$	−5967.13	−1.20206
$292$	6603.64	1.32346
$293$	640.326	0.127673	0.0638366	−	0.997960i	$-0.479666\pi$
$293$	640.326	0.127673	0.0638366	+	0.997960i	$0.479666\pi$
$294$	2444.38	0.484896
$295$	2035.58	0.401749
$296$	−1690.97	−0.332046
$297$	1426.44	0.278689
$298$	9989.95	1.94195
$299$	0	0
$300$	−2484.82	−0.478203
$301$	5520.81	1.05719
$302$	8351.43	1.59129
$303$	10045.2	1.90455
$304$	−1882.29	−0.355120
$305$	8872.29	1.66566
$306$	404.792	0.0756223
$307$	−5350.62	−0.994709	−0.497355	−	0.867547i	$-0.665695\pi$
$307$	−5350.62	−0.994709	−0.497355	+	0.867547i	$0.665695\pi$
$308$	1056.90	0.195527
$309$	6822.07	1.25597
$310$	−2329.87	−0.426864
$311$	−5277.61	−0.962269	−0.481135	−	0.876647i	$-0.659775\pi$
$311$	−5277.61	−0.962269	−0.481135	+	0.876647i	$0.659775\pi$
$312$	0	0
$313$	9770.61	1.76443	0.882217	−	0.470843i	$-0.156050\pi$
$313$	9770.61	1.76443	0.882217	+	0.470843i	$0.156050\pi$
$314$	9165.56	1.64727
$315$	742.714	0.132848
$316$	1471.61	0.261977
$317$	1634.52	0.289603	0.144801	−	0.989461i	$-0.453746\pi$
$317$	1634.52	0.289603	0.144801	+	0.989461i	$0.453746\pi$
$318$	8462.39	1.49229
$319$	−1708.20	−0.299815
$320$	−4036.98	−0.705232
$321$	−2874.83	−0.499867
$322$	8038.53	1.39121
$323$	765.572	0.131881
$324$	−5184.70	−0.889009
$325$	0	0
$326$	6731.01	1.14355
$327$	3373.82	0.570558
$328$	−505.118	−0.0850319
$329$	−4453.43	−0.746279
$330$	−3222.70	−0.537587
$331$	−3596.41	−0.597210	−0.298605	−	0.954377i	$-0.596521\pi$
$331$	−3596.41	−0.597210	−0.298605	+	0.954377i	$0.596521\pi$
$332$	779.249	0.128816
$333$	975.476	0.160528
$334$	7245.27	1.18696
$335$	4953.70	0.807908
$336$	6177.40	1.00299
$337$	9503.26	1.53613	0.768065	−	0.640372i	$-0.221220\pi$
$337$	9503.26	1.53613	0.768065	+	0.640372i	$0.221220\pi$
$338$	0	0
$339$	−2061.10	−0.330217
$340$	2698.02	0.430355
$341$	−483.359	−0.0767606
$342$	339.284	0.0536443
$343$	−6915.41	−1.08862
$344$	−2246.21	−0.352057
$345$	−10880.7	−1.69796
$346$	−1158.82	−0.180054
$347$	−10682.2	−1.65260	−0.826298	−	0.563234i	$-0.809557\pi$
$347$	−10682.2	−1.65260	−0.826298	+	0.563234i	$0.809557\pi$
$348$	5479.66	0.844082
$349$	−10856.8	−1.66518	−0.832592	−	0.553886i	$-0.813144\pi$
$349$	−10856.8	−1.66518	−0.832592	+	0.553886i	$0.813144\pi$
$350$	4018.50	0.613708
$351$	0	0
$352$	−2561.53	−0.387869
$353$	−2346.38	−0.353783	−0.176891	−	0.984230i	$-0.556604\pi$
$353$	−2346.38	−0.353783	−0.176891	+	0.984230i	$0.556604\pi$
$354$	−3051.75	−0.458188
$355$	−1816.06	−0.271512
$356$	7460.57	1.11070
$357$	−2512.50	−0.372480
$358$	15629.1	2.30734
$359$	−4883.98	−0.718013	−0.359007	−	0.933335i	$-0.616884\pi$
$359$	−4883.98	−0.718013	−0.359007	+	0.933335i	$0.616884\pi$
$360$	−302.182	−0.0442400
$361$	−6217.32	−0.906447
$362$	−8555.93	−1.24224
$363$	−668.587	−0.0966714
$364$	0	0
$365$	14455.5	2.07297
$366$	−13301.4	−1.89966
$367$	−11470.0	−1.63142	−0.815711	−	0.578460i	$-0.803654\pi$
$367$	−11470.0	−1.63142	−0.815711	+	0.578460i	$0.803654\pi$
$368$	−10467.1	−1.48271
$369$	291.389	0.0411087
$370$	14646.6	2.05795
$371$	−6075.12	−0.850147
$372$	1550.55	0.216108
$373$	3115.05	0.432417	0.216208	−	0.976347i	$-0.430631\pi$
$373$	3115.05	0.432417	0.216208	+	0.976347i	$0.430631\pi$
$374$	1260.93	0.174335
$375$	4216.00	0.580569
$376$	1811.93	0.248519
$377$	0	0
$378$	7400.12	1.00693
$379$	−4337.76	−0.587905	−0.293952	−	0.955820i	$-0.594971\pi$
$379$	−4337.76	−0.587905	−0.293952	+	0.955820i	$0.594971\pi$
$380$	2261.39	0.305282
$381$	−191.962	−0.0258124
$382$	−8170.08	−1.09429
$383$	−5520.84	−0.736558	−0.368279	−	0.929715i	$-0.620053\pi$
$383$	−5520.84	−0.736558	−0.368279	+	0.929715i	$0.620053\pi$
$384$	−4241.37	−0.563650
$385$	2313.56	0.306260
$386$	12790.5	1.68658
$387$	1295.78	0.170202
$388$	6896.48	0.902360
$389$	−12876.4	−1.67831	−0.839153	−	0.543895i	$-0.816949\pi$
$389$	−12876.4	−1.67831	−0.839153	+	0.543895i	$0.816949\pi$
$390$	0	0
$391$	4257.23	0.550633
$392$	713.968	0.0919919
$393$	11803.2	1.51499
$394$	19065.7	2.43786
$395$	3221.38	0.410342
$396$	248.062	0.0314788
$397$	8042.88	1.01678	0.508388	−	0.861128i	$-0.330241\pi$
$397$	8042.88	1.01678	0.508388	+	0.861128i	$0.330241\pi$
$398$	8708.80	1.09682
$399$	−2105.89	−0.264227
$400$	−5232.56	−0.654071
$401$	3609.51	0.449502	0.224751	−	0.974416i	$-0.427843\pi$
$401$	3609.51	0.449502	0.224751	+	0.974416i	$0.427843\pi$
$402$	−7426.60	−0.921406
$403$	0	0
$404$	−11609.6	−1.42971
$405$	−11349.4	−1.39248
$406$	−8861.83	−1.08326
$407$	3038.62	0.370071
$408$	1022.24	0.124040
$409$	41.1264	0.00497206	0.00248603	−	0.999997i	$-0.499209\pi$
$409$	41.1264	0.00497206	0.00248603	+	0.999997i	$0.499209\pi$
$410$	4375.16	0.527009
$411$	2077.13	0.249287
$412$	−7884.57	−0.942828
$413$	2190.84	0.261027
$414$	1886.71	0.223977
$415$	1705.79	0.201768
$416$	0	0
$417$	−803.005	−0.0943006
$418$	1056.87	0.123668
$419$	7436.09	0.867009	0.433504	−	0.901151i	$-0.357277\pi$
$419$	7436.09	0.867009	0.433504	+	0.901151i	$0.357277\pi$
$420$	−7421.56	−0.862227
$421$	−7078.46	−0.819437	−0.409718	−	0.912212i	$-0.634373\pi$
$421$	−7078.46	−0.819437	−0.409718	+	0.912212i	$0.634373\pi$
$422$	7002.72	0.807790
$423$	−1045.26	−0.120147
$424$	2471.74	0.283109
$425$	2128.21	0.242902
$426$	2722.65	0.309654
$427$	9549.01	1.08222
$428$	3322.57	0.375239
$429$	0	0
$430$	19455.9	2.18197
$431$	−9630.63	−1.07631	−0.538157	−	0.842845i	$-0.680879\pi$
$431$	−9630.63	−1.07631	−0.538157	+	0.842845i	$0.680879\pi$
$432$	−9635.83	−1.07316
$433$	10351.6	1.14889	0.574443	−	0.818545i	$-0.305219\pi$
$433$	10351.6	1.14889	0.574443	+	0.818545i	$0.305219\pi$
$434$	−2507.58	−0.277345
$435$	11995.0	1.32211
$436$	−3899.27	−0.428306
$437$	3568.27	0.390603
$438$	−21671.7	−2.36419
$439$	−13811.5	−1.50156	−0.750782	−	0.660550i	$-0.770323\pi$
$439$	−13811.5	−1.50156	−0.750782	+	0.660550i	$0.770323\pi$
$440$	−941.301	−0.101988
$441$	−411.869	−0.0444735
$442$	0	0
$443$	11456.8	1.22873	0.614366	−	0.789021i	$-0.289412\pi$
$443$	11456.8	1.22873	0.614366	+	0.789021i	$0.289412\pi$
$444$	−9747.44	−1.04188
$445$	16331.3	1.73972
$446$	16527.4	1.75470
$447$	−14553.4	−1.53994
$448$	−4344.89	−0.458208
$449$	−6671.71	−0.701242	−0.350621	−	0.936517i	$-0.614029\pi$
$449$	−6671.71	−0.701242	−0.350621	+	0.936517i	$0.614029\pi$
$450$	943.174	0.0988036
$451$	907.679	0.0947693
$452$	2382.10	0.247887
$453$	−12166.4	−1.26187
$454$	7119.73	0.736003
$455$	0	0
$456$	856.809	0.0879907
$457$	−1227.86	−0.125682	−0.0628410	−	0.998024i	$-0.520016\pi$
$457$	−1227.86	−0.125682	−0.0628410	+	0.998024i	$0.520016\pi$
$458$	−17478.5	−1.78322
$459$	3919.13	0.398539
$460$	12575.3	1.27462
$461$	1567.28	0.158341	0.0791706	−	0.996861i	$-0.474773\pi$
$461$	1567.28	0.158341	0.0791706	+	0.996861i	$0.474773\pi$
$462$	−3468.50	−0.349284
$463$	18258.5	1.83271	0.916355	−	0.400367i	$-0.131117\pi$
$463$	18258.5	1.83271	0.916355	+	0.400367i	$0.131117\pi$
$464$	11539.2	1.15451
$465$	3394.16	0.338496
$466$	−18716.2	−1.86054
$467$	−16270.0	−1.61217	−0.806086	−	0.591799i	$-0.798418\pi$
$467$	−16270.0	−1.61217	−0.806086	+	0.591799i	$0.798418\pi$
$468$	0	0
$469$	5331.53	0.524919
$470$	−15694.4	−1.54027
$471$	−13352.4	−1.30626
$472$	−891.368	−0.0869249
$473$	4036.36	0.392373
$474$	−4829.51	−0.467989
$475$	1783.80	0.172308
$476$	2903.81	0.279613
$477$	−1425.88	−0.136869
$478$	24827.6	2.37571
$479$	248.305	0.0236855	0.0118428	−	0.999930i	$-0.496230\pi$
$479$	248.305	0.0236855	0.0118428	+	0.999930i	$0.496230\pi$
$480$	17987.1	1.71041
$481$	0	0
$482$	6144.26	0.580629
$483$	−11710.6	−1.10321
$484$	772.716	0.0725691
$485$	15096.5	1.41339
$486$	3735.07	0.348614
$487$	−9371.73	−0.872019	−0.436010	−	0.899942i	$-0.643609\pi$
$487$	−9371.73	−0.872019	−0.436010	+	0.899942i	$0.643609\pi$
$488$	−3885.13	−0.360393
$489$	−9805.77	−0.906815
$490$	−6184.15	−0.570146
$491$	−9235.79	−0.848891	−0.424446	−	0.905453i	$-0.639531\pi$
$491$	−9235.79	−0.848891	−0.424446	+	0.905453i	$0.639531\pi$
$492$	−2911.70	−0.266808
$493$	−4693.26	−0.428750
$494$	0	0
$495$	543.011	0.0493061
$496$	3265.16	0.295585
$497$	−1954.58	−0.176408
$498$	−2557.32	−0.230113
$499$	−6848.99	−0.614434	−0.307217	−	0.951639i	$-0.599398\pi$
$499$	−6848.99	−0.614434	−0.307217	+	0.951639i	$0.599398\pi$
$500$	−4872.62	−0.435820
$501$	−10554.9	−0.941238
$502$	6662.18	0.592326
$503$	−4018.75	−0.356237	−0.178118	−	0.984009i	$-0.557001\pi$
$503$	−4018.75	−0.356237	−0.178118	+	0.984009i	$0.557001\pi$
$504$	−325.231	−0.0287439
$505$	−25413.7	−2.23939
$506$	5877.11	0.516342
$507$	0	0
$508$	221.859	0.0193768
$509$	−16162.2	−1.40742	−0.703711	−	0.710486i	$-0.748475\pi$
$509$	−16162.2	−1.40742	−0.703711	+	0.710486i	$0.748475\pi$
$510$	−8854.30	−0.768775
$511$	15558.0	1.34686
$512$	13664.6	1.17948
$513$	3284.89	0.282712
$514$	4618.66	0.396343
$515$	−17259.4	−1.47678
$516$	−12948.1	−1.10466
$517$	−3255.98	−0.276979
$518$	15763.8	1.33711
$519$	1688.18	0.142780
$520$	0	0
$521$	−8997.72	−0.756617	−0.378309	−	0.925680i	$-0.623494\pi$
$521$	−8997.72	−0.756617	−0.378309	+	0.925680i	$0.623494\pi$
$522$	−2079.94	−0.174400
$523$	1882.73	0.157411	0.0787054	−	0.996898i	$-0.474921\pi$
$523$	1882.73	0.157411	0.0787054	+	0.996898i	$0.474921\pi$
$524$	−13641.5	−1.13727
$525$	−5854.17	−0.486661
$526$	−6254.04	−0.518420
$527$	−1328.02	−0.109771
$528$	4516.40	0.372256
$529$	7675.63	0.630857
$530$	−21409.3	−1.75465
$531$	514.207	0.0420239
$532$	2433.88	0.198349
$533$	0	0
$534$	−24483.9	−1.98413
$535$	7273.15	0.587749
$536$	−2169.20	−0.174804
$537$	−22768.6	−1.82968
$538$	7706.30	0.617550
$539$	−1282.98	−0.102526
$540$	11576.6	0.922547
$541$	−11815.0	−0.938936	−0.469468	−	0.882949i	$-0.655554\pi$
$541$	−11815.0	−0.938936	−0.469468	+	0.882949i	$0.655554\pi$
$542$	−1815.00	−0.143840
$543$	12464.3	0.985074
$544$	−7037.75	−0.554671
$545$	−8535.56	−0.670868
$546$	0	0
$547$	−22530.8	−1.76115	−0.880574	−	0.473908i	$-0.842843\pi$
$547$	−22530.8	−1.76115	−0.880574	+	0.473908i	$0.842843\pi$
$548$	−2400.63	−0.187135
$549$	2241.23	0.174232
$550$	2938.00	0.227776
$551$	−3933.74	−0.304143
$552$	4764.58	0.367381
$553$	3467.09	0.266610
$554$	26816.5	2.05654
$555$	−21337.3	−1.63192
$556$	928.069	0.0707894
$557$	128.957	0.00980982	0.00490491	−	0.999988i	$-0.498439\pi$
$557$	128.957	0.00980982	0.00490491	+	0.999988i	$0.498439\pi$
$558$	−588.548	−0.0446509
$559$	0	0
$560$	−15628.4	−1.17933
$561$	−1836.93	−0.138245
$562$	−26697.2	−2.00383
$563$	−22186.6	−1.66084	−0.830422	−	0.557135i	$-0.811901\pi$
$563$	−22186.6	−1.66084	−0.830422	+	0.557135i	$0.811901\pi$
$564$	10444.7	0.779790
$565$	5214.46	0.388272
$566$	−735.309	−0.0546066
$567$	−12215.0	−0.904732
$568$	795.245	0.0587460
$569$	−6077.45	−0.447768	−0.223884	−	0.974616i	$-0.571874\pi$
$569$	−6077.45	−0.447768	−0.223884	+	0.974616i	$0.571874\pi$
$570$	−7421.39	−0.545347
$571$	−22438.3	−1.64451	−0.822255	−	0.569119i	$-0.807284\pi$
$571$	−22438.3	−1.64451	−0.822255	+	0.569119i	$0.807284\pi$
$572$	0	0
$573$	11902.2	0.867752
$574$	4708.87	0.342412
$575$	9919.43	0.719424
$576$	−1019.78	−0.0737689
$577$	18976.0	1.36911	0.684557	−	0.728959i	$-0.259996\pi$
$577$	18976.0	1.36911	0.684557	+	0.728959i	$0.259996\pi$
$578$	−15170.1	−1.09168
$579$	−18633.2	−1.33743
$580$	−13863.2	−0.992480
$581$	1835.89	0.131094
$582$	−22632.7	−1.61195
$583$	−4441.63	−0.315529
$584$	−6329.97	−0.448521
$585$	0	0
$586$	2428.69	0.171209
$587$	7839.55	0.551231	0.275616	−	0.961268i	$-0.411118\pi$
$587$	7839.55	0.551231	0.275616	+	0.961268i	$0.411118\pi$
$588$	4115.60	0.288647
$589$	−1113.10	−0.0778687
$590$	7720.73	0.538742
$591$	−27775.0	−1.93318
$592$	−20526.3	−1.42504
$593$	19632.8	1.35956	0.679782	−	0.733414i	$-0.262074\pi$
$593$	19632.8	1.35956	0.679782	+	0.733414i	$0.262074\pi$
$594$	5410.35	0.373720
$595$	6356.47	0.437966
$596$	16820.0	1.15600
$597$	−12687.0	−0.869757
$598$	0	0
$599$	−6058.06	−0.413232	−0.206616	−	0.978422i	$-0.566245\pi$
$599$	−6058.06	−0.413232	−0.206616	+	0.978422i	$0.566245\pi$
$600$	2381.84	0.162064
$601$	8980.53	0.609523	0.304762	−	0.952429i	$-0.401423\pi$
$601$	8980.53	0.609523	0.304762	+	0.952429i	$0.401423\pi$
$602$	20939.9	1.41768
$603$	1251.35	0.0845091
$604$	14061.2	0.947258
$605$	1691.49	0.113667
$606$	38100.3	2.55399
$607$	−5410.38	−0.361780	−0.180890	−	0.983503i	$-0.557898\pi$
$607$	−5410.38	−0.361780	−0.180890	+	0.983503i	$0.557898\pi$
$608$	−5898.81	−0.393468
$609$	12909.9	0.859011
$610$	33651.7	2.23364
$611$	0	0
$612$	681.546	0.0450161
$613$	438.335	0.0288812	0.0144406	−	0.999896i	$-0.495403\pi$
$613$	438.335	0.0288812	0.0144406	+	0.999896i	$0.495403\pi$
$614$	−20294.3	−1.33390
$615$	−6373.75	−0.417910
$616$	−1013.10	−0.0662643
$617$	6592.88	0.430177	0.215089	−	0.976595i	$-0.430996\pi$
$617$	6592.88	0.430177	0.215089	+	0.976595i	$0.430996\pi$
$618$	25875.4	1.68424
$619$	−28094.7	−1.82427	−0.912134	−	0.409891i	$-0.865567\pi$
$619$	−28094.7	−1.82427	−0.912134	+	0.409891i	$0.865567\pi$
$620$	−3922.79	−0.254102
$621$	18266.8	1.18039
$622$	−20017.4	−1.29040
$623$	17576.9	1.13034
$624$	0	0
$625$	−19468.5	−1.24599
$626$	37059.0	2.36609
$627$	−1539.66	−0.0980669
$628$	15432.0	0.980579
$629$	8348.55	0.529219
$630$	2817.04	0.178148
$631$	598.987	0.0377897	0.0188948	−	0.999821i	$-0.493985\pi$
$631$	598.987	0.0377897	0.0188948	+	0.999821i	$0.493985\pi$
$632$	−1410.63	−0.0887843
$633$	−10201.6	−0.640564
$634$	6199.58	0.388355
$635$	485.652	0.0303504
$636$	14248.1	0.888322
$637$	0	0
$638$	−6479.04	−0.402049
$639$	−458.755	−0.0284008
$640$	10730.4	0.662746
$641$	−23047.3	−1.42015	−0.710074	−	0.704127i	$-0.751339\pi$
$641$	−23047.3	−1.42015	−0.710074	+	0.704127i	$0.751339\pi$
$642$	−10903.9	−0.670318
$643$	−29112.9	−1.78553	−0.892767	−	0.450518i	$-0.851239\pi$
$643$	−29112.9	−1.78553	−0.892767	+	0.450518i	$0.851239\pi$
$644$	13534.4	0.828153
$645$	−28343.5	−1.73027
$646$	2903.74	0.176852
$647$	−10552.6	−0.641214	−0.320607	−	0.947212i	$-0.603887\pi$
$647$	−10552.6	−0.641214	−0.320607	+	0.947212i	$0.603887\pi$
$648$	4969.83	0.301286
$649$	1601.76	0.0968791
$650$	0	0
$651$	3653.05	0.219930
$652$	11333.0	0.680726
$653$	−15769.3	−0.945024	−0.472512	−	0.881324i	$-0.656653\pi$
$653$	−15769.3	−0.945024	−0.472512	+	0.881324i	$0.656653\pi$
$654$	12796.6	0.765114
$655$	−29861.4	−1.78134
$656$	−6131.51	−0.364932
$657$	3651.59	0.216838
$658$	−16891.4	−1.00075
$659$	12016.8	0.710333	0.355167	−	0.934803i	$-0.384424\pi$
$659$	12016.8	0.710333	0.355167	+	0.934803i	$0.384424\pi$
$660$	−5426.04	−0.320012
$661$	25712.4	1.51301	0.756503	−	0.653990i	$-0.226906\pi$
$661$	25712.4	1.51301	0.756503	+	0.653990i	$0.226906\pi$
$662$	−13640.8	−0.800854
$663$	0	0
$664$	−746.955	−0.0436559
$665$	5327.79	0.310681
$666$	3699.88	0.215267
$667$	−21874.9	−1.26986
$668$	12198.8	0.706567
$669$	−24077.2	−1.39145
$670$	18788.9	1.08340
$671$	6981.45	0.401663
$672$	19359.1	1.11130
$673$	−20750.3	−1.18851	−0.594253	−	0.804278i	$-0.702552\pi$
$673$	−20750.3	−1.18851	−0.594253	+	0.804278i	$0.702552\pi$
$674$	36044.9	2.05994
$675$	9131.64	0.520707
$676$	0	0
$677$	21048.4	1.19492	0.597458	−	0.801901i	$-0.296178\pi$
$677$	21048.4	1.19492	0.597458	+	0.801901i	$0.296178\pi$
$678$	−7817.54	−0.442818
$679$	16248.0	0.918320
$680$	−2586.21	−0.145848
$681$	−10372.1	−0.583639
$682$	−1833.33	−0.102935
$683$	27220.2	1.52496	0.762482	−	0.647009i	$-0.223981\pi$
$683$	27220.2	1.52496	0.762482	+	0.647009i	$0.223981\pi$
$684$	571.250	0.0319332
$685$	−5255.00	−0.293114
$686$	−26229.4	−1.45983
$687$	25462.8	1.41407
$688$	−27266.2	−1.51092
$689$	0	0
$690$	−41269.2	−2.27695
$691$	−1715.43	−0.0944398	−0.0472199	−	0.998885i	$-0.515036\pi$
$691$	−1715.43	−0.0944398	−0.0472199	+	0.998885i	$0.515036\pi$
$692$	−1951.10	−0.107182
$693$	584.429	0.0320355
$694$	−40516.5	−2.21612
$695$	2031.56	0.110880
$696$	−5252.57	−0.286061
$697$	2493.83	0.135525
$698$	−41178.6	−2.23300
$699$	27265.8	1.47537
$700$	6765.92	0.365325
$701$	−2274.13	−0.122529	−0.0612645	−	0.998122i	$-0.519513\pi$
$701$	−2274.13	−0.122529	−0.0612645	+	0.998122i	$0.519513\pi$
$702$	0	0
$703$	6997.49	0.375413
$704$	−3176.63	−0.170062
$705$	22863.6	1.22141
$706$	−8899.59	−0.474420
$707$	−27352.1	−1.45499
$708$	−5138.21	−0.272748
$709$	25954.9	1.37483	0.687416	−	0.726264i	$-0.258745\pi$
$709$	25954.9	1.37483	0.687416	+	0.726264i	$0.258745\pi$
$710$	−6888.14	−0.364095
$711$	813.753	0.0429228
$712$	−7151.38	−0.376418
$713$	−6189.81	−0.325119
$714$	−9529.65	−0.499493
$715$	0	0
$716$	26314.7	1.37350
$717$	−36168.9	−1.88390
$718$	−18524.5	−0.962850
$719$	10799.5	0.560159	0.280079	−	0.959977i	$-0.409639\pi$
$719$	10799.5	0.560159	0.280079	+	0.959977i	$0.409639\pi$
$720$	−3668.12	−0.189865
$721$	−18575.9	−0.959503
$722$	−23581.7	−1.21554
$723$	−8950.98	−0.460429
$724$	−14405.6	−0.739473
$725$	−10935.4	−0.560179
$726$	−2535.88	−0.129636
$727$	−22765.0	−1.16136	−0.580680	−	0.814132i	$-0.697213\pi$
$727$	−22765.0	−1.16136	−0.580680	+	0.814132i	$0.697213\pi$
$728$	0	0
$729$	16479.3	0.837237
$730$	54828.1	2.77984
$731$	11089.8	0.561112
$732$	−22395.5	−1.13082
$733$	5479.83	0.276129	0.138064	−	0.990423i	$-0.455912\pi$
$733$	5479.83	0.276129	0.138064	+	0.990423i	$0.455912\pi$
$734$	−43504.7	−2.18772
$735$	9009.10	0.452116
$736$	−32802.4	−1.64282
$737$	3897.98	0.194822
$738$	1105.21	0.0551264
$739$	−15972.7	−0.795083	−0.397542	−	0.917584i	$-0.630137\pi$
$739$	−15972.7	−0.795083	−0.397542	+	0.917584i	$0.630137\pi$
$740$	24660.4	1.22505
$741$	0	0
$742$	−23042.3	−1.14004
$743$	29476.9	1.45546	0.727728	−	0.685866i	$-0.240576\pi$
$743$	29476.9	1.45546	0.727728	+	0.685866i	$0.240576\pi$
$744$	−1486.29	−0.0732392
$745$	36819.3	1.81068
$746$	11815.1	0.579867
$747$	430.899	0.0211054
$748$	2123.02	0.103777
$749$	7827.89	0.381876
$750$	15990.9	0.778538
$751$	14783.2	0.718307	0.359153	−	0.933279i	$-0.383065\pi$
$751$	14783.2	0.718307	0.359153	+	0.933279i	$0.383065\pi$
$752$	21994.6	1.06657
$753$	−9705.49	−0.469705
$754$	0	0
$755$	30780.3	1.48372
$756$	12459.5	0.599403
$757$	33928.5	1.62900	0.814498	−	0.580166i	$-0.197012\pi$
$757$	33928.5	1.62900	0.814498	+	0.580166i	$0.197012\pi$
$758$	−16452.7	−0.788376
$759$	−8561.80	−0.409451
$760$	−2167.68	−0.103460
$761$	26269.0	1.25132	0.625658	−	0.780097i	$-0.284830\pi$
$761$	26269.0	1.25132	0.625658	+	0.780097i	$0.284830\pi$
$762$	−728.092	−0.0346142
$763$	−9186.59	−0.435881
$764$	−13755.9	−0.651403
$765$	1491.91	0.0705102
$766$	−20940.0	−0.987719
$767$	0	0
$768$	−28852.6	−1.35563
$769$	6109.01	0.286471	0.143236	−	0.989689i	$-0.454249\pi$
$769$	6109.01	0.286471	0.143236	+	0.989689i	$0.454249\pi$
$770$	8775.10	0.410692
$771$	−6728.48	−0.314294
$772$	21535.3	1.00398
$773$	20084.9	0.934546	0.467273	−	0.884113i	$-0.345237\pi$
$773$	20084.9	0.934546	0.467273	+	0.884113i	$0.345237\pi$
$774$	4914.76	0.228239
$775$	−3094.32	−0.143421
$776$	−6610.68	−0.305811
$777$	−22964.7	−1.06030
$778$	−48839.0	−2.25060
$779$	2090.25	0.0961374
$780$	0	0
$781$	−1429.03	−0.0654733
$782$	16147.3	0.738395
$783$	−20137.6	−0.919106
$784$	8666.69	0.394802
$785$	33780.8	1.53591
$786$	44768.3	2.03159
$787$	8150.10	0.369148	0.184574	−	0.982819i	$-0.440909\pi$
$787$	8150.10	0.369148	0.184574	+	0.982819i	$0.440909\pi$
$788$	32100.8	1.45120
$789$	9110.91	0.411099
$790$	12218.4	0.550266
$791$	5612.18	0.252271
$792$	−237.782	−0.0106682
$793$	0	0
$794$	30505.8	1.36349
$795$	31189.2	1.39141
$796$	14663.0	0.652908
$797$	−8487.68	−0.377226	−0.188613	−	0.982052i	$-0.560399\pi$
$797$	−8487.68	−0.377226	−0.188613	+	0.982052i	$0.560399\pi$
$798$	−7987.44	−0.354326
$799$	−8945.76	−0.396093
$800$	−16398.1	−0.724700
$801$	4125.44	0.181979
$802$	13690.5	0.602779
$803$	11374.8	0.499883
$804$	−12504.1	−0.548491
$805$	29627.0	1.29716
$806$	0	0
$807$	−11226.6	−0.489707
$808$	11128.5	0.484529
$809$	31492.5	1.36863	0.684313	−	0.729189i	$-0.260102\pi$
$809$	31492.5	1.36863	0.684313	+	0.729189i	$0.260102\pi$
$810$	−43047.0	−1.86731
$811$	−30295.2	−1.31173	−0.655863	−	0.754880i	$-0.727695\pi$
$811$	−30295.2	−1.31173	−0.655863	+	0.754880i	$0.727695\pi$
$812$	−14920.6	−0.644841
$813$	2644.11	0.114063
$814$	11525.2	0.496262
$815$	24808.0	1.06624
$816$	12408.7	0.532344
$817$	9295.15	0.398037
$818$	155.988	0.00666749
$819$	0	0
$820$	7366.43	0.313716
$821$	−20966.4	−0.891271	−0.445635	−	0.895215i	$-0.647022\pi$
$821$	−20966.4	−0.891271	−0.445635	+	0.895215i	$0.647022\pi$
$822$	7878.33	0.334292
$823$	−41378.3	−1.75256	−0.876280	−	0.481802i	$-0.839982\pi$
$823$	−41378.3	−1.75256	−0.876280	+	0.481802i	$0.839982\pi$
$824$	7557.82	0.319526
$825$	−4280.08	−0.180622
$826$	8309.62	0.350035
$827$	3814.63	0.160396	0.0801982	−	0.996779i	$-0.474445\pi$
$827$	3814.63	0.160396	0.0801982	+	0.996779i	$0.474445\pi$
$828$	3176.64	0.133328
$829$	−25284.9	−1.05933	−0.529663	−	0.848208i	$-0.677682\pi$
$829$	−25284.9	−1.05933	−0.529663	+	0.848208i	$0.677682\pi$
$830$	6469.88	0.270570
$831$	−39066.4	−1.63080
$832$	0	0
$833$	−3524.95	−0.146618
$834$	−3045.72	−0.126456
$835$	26703.4	1.10672
$836$	1779.45	0.0736167
$837$	−5698.22	−0.235316
$838$	28204.3	1.16265
$839$	−16475.1	−0.677932	−0.338966	−	0.940799i	$-0.610077\pi$
$839$	−16475.1	−0.677932	−0.338966	+	0.940799i	$0.610077\pi$
$840$	7114.00	0.292210
$841$	−273.679	−0.0112214
$842$	−26847.9	−1.09886
$843$	38892.6	1.58900
$844$	11790.4	0.480858
$845$	0	0
$846$	−3964.55	−0.161116
$847$	1820.50	0.0738526
$848$	30003.8	1.21502
$849$	1071.20	0.0433022
$850$	8072.09	0.325730
$851$	38912.0	1.56743
$852$	4584.11	0.184330
$853$	28960.5	1.16247	0.581235	−	0.813736i	$-0.302570\pi$
$853$	28960.5	1.16247	0.581235	+	0.813736i	$0.302570\pi$
$854$	36218.4	1.45125
$855$	1250.47	0.0500179
$856$	−3184.87	−0.127169
$857$	19511.8	0.777726	0.388863	−	0.921296i	$-0.372868\pi$
$857$	19511.8	0.777726	0.388863	+	0.921296i	$0.372868\pi$
$858$	0	0
$859$	4263.10	0.169331	0.0846653	−	0.996409i	$-0.473018\pi$
$859$	4263.10	0.169331	0.0846653	+	0.996409i	$0.473018\pi$
$860$	32757.8	1.29887
$861$	−6859.90	−0.271527
$862$	−36528.0	−1.44333
$863$	37277.6	1.47039	0.735193	−	0.677858i	$-0.237092\pi$
$863$	37277.6	1.47039	0.735193	+	0.677858i	$0.237092\pi$
$864$	−30197.3	−1.18904
$865$	−4270.99	−0.167882
$866$	39262.7	1.54065
$867$	22099.9	0.865689
$868$	−4221.99	−0.165096
$869$	2534.85	0.0989514
$870$	45496.0	1.77294
$871$	0	0
$872$	3737.68	0.145153
$873$	3813.52	0.147844
$874$	13534.1	0.523796
$875$	−11479.8	−0.443528
$876$	−36488.5	−1.40734
$877$	22922.4	0.882593	0.441296	−	0.897361i	$-0.354519\pi$
$877$	22922.4	0.882593	0.441296	+	0.897361i	$0.354519\pi$
$878$	−52385.6	−2.01359
$879$	−3538.13	−0.135766
$880$	−11426.2	−0.437703
$881$	−32641.7	−1.24827	−0.624136	−	0.781315i	$-0.714549\pi$
$881$	−32641.7	−1.24827	−0.624136	+	0.781315i	$0.714549\pi$
$882$	−1562.18	−0.0596386
$883$	50121.7	1.91023	0.955113	−	0.296241i	$-0.0957331\pi$
$883$	50121.7	1.91023	0.955113	+	0.296241i	$0.0957331\pi$
$884$	0	0
$885$	−11247.6	−0.427214
$886$	43454.4	1.64772
$887$	−8190.72	−0.310054	−0.155027	−	0.987910i	$-0.549546\pi$
$887$	−8190.72	−0.310054	−0.155027	+	0.987910i	$0.549546\pi$
$888$	9343.48	0.353093
$889$	522.695	0.0197195
$890$	61942.9	2.33296
$891$	−8930.62	−0.335788
$892$	27827.1	1.04453
$893$	−7498.04	−0.280977
$894$	−55199.6	−2.06505
$895$	57603.2	2.15136
$896$	11548.9	0.430603
$897$	0	0
$898$	−25305.1	−0.940360
$899$	6823.76	0.253154
$900$	1588.02	0.0588154
$901$	−12203.3	−0.451222
$902$	3442.74	0.127085
$903$	−30505.3	−1.12420
$904$	−2283.38	−0.0840091
$905$	−31534.0	−1.15826
$906$	−46145.9	−1.69216
$907$	−45394.9	−1.66187	−0.830934	−	0.556371i	$-0.812193\pi$
$907$	−45394.9	−1.66187	−0.830934	+	0.556371i	$0.812193\pi$
$908$	11987.4	0.438125
$909$	−6419.74	−0.234246
$910$	0	0
$911$	15467.7	0.562534	0.281267	−	0.959630i	$-0.409245\pi$
$911$	15467.7	0.562534	0.281267	+	0.959630i	$0.409245\pi$
$912$	10400.6	0.377630
$913$	1342.25	0.0486551
$914$	−4657.14	−0.168539
$915$	−49024.0	−1.77124
$916$	−29428.4	−1.06151
$917$	−32139.0	−1.15739
$918$	14864.9	0.534437
$919$	17923.7	0.643359	0.321680	−	0.946849i	$-0.395753\pi$
$919$	17923.7	0.643359	0.321680	+	0.946849i	$0.395753\pi$
$920$	−12054.1	−0.431970
$921$	29564.9	1.05776
$922$	5944.52	0.212334
$923$	0	0
$924$	−5839.90	−0.207920
$925$	19452.3	0.691446
$926$	69252.7	2.45765
$927$	−4359.90	−0.154475
$928$	36162.0	1.27918
$929$	27941.3	0.986785	0.493393	−	0.869807i	$-0.335757\pi$
$929$	27941.3	0.986785	0.493393	+	0.869807i	$0.335757\pi$
$930$	12873.7	0.453920
$931$	−2954.50	−0.104006
$932$	−31512.3	−1.10753
$933$	29161.5	1.02326
$934$	−61710.3	−2.16191
$935$	4647.33	0.162550
$936$	0	0
$937$	3357.31	0.117053	0.0585264	−	0.998286i	$-0.481360\pi$
$937$	3357.31	0.117053	0.0585264	+	0.998286i	$0.481360\pi$
$938$	20222.0	0.703913
$939$	−53987.6	−1.87627
$940$	−26424.5	−0.916885
$941$	−1001.77	−0.0347045	−0.0173522	−	0.999849i	$-0.505524\pi$
$941$	−1001.77	−0.0347045	−0.0173522	+	0.999849i	$0.505524\pi$
$942$	−50644.4	−1.75168
$943$	11623.6	0.401395
$944$	−10820.1	−0.373056
$945$	27274.1	0.938863
$946$	15309.5	0.526169
$947$	−14469.2	−0.496501	−0.248251	−	0.968696i	$-0.579856\pi$
$947$	−14469.2	−0.496501	−0.248251	+	0.968696i	$0.579856\pi$
$948$	−8131.41	−0.278582
$949$	0	0
$950$	6765.77	0.231064
$951$	−9031.58	−0.307959
$952$	−2783.47	−0.0947612
$953$	655.844	0.0222926	0.0111463	−	0.999938i	$-0.496452\pi$
$953$	655.844	0.0222926	0.0111463	+	0.999938i	$0.496452\pi$
$954$	−5408.21	−0.183540
$955$	−30111.9	−1.02031
$956$	41802.1	1.41420
$957$	9438.69	0.318819
$958$	941.798	0.0317621
$959$	−5655.82	−0.190444
$960$	22306.4	0.749933
$961$	−27860.1	−0.935186
$962$	0	0
$963$	1837.27	0.0614799
$964$	10345.0	0.345634
$965$	47141.0	1.57256
$966$	−44417.0	−1.47939
$967$	−15590.7	−0.518473	−0.259237	−	0.965814i	$-0.583471\pi$
$967$	−15590.7	−0.518473	−0.259237	+	0.965814i	$0.583471\pi$
$968$	−740.693	−0.0245938
$969$	−4230.18	−0.140240
$970$	57259.5	1.89535
$971$	−36210.2	−1.19675	−0.598374	−	0.801217i	$-0.704186\pi$
$971$	−36210.2	−1.19675	−0.598374	+	0.801217i	$0.704186\pi$
$972$	6288.72	0.207522
$973$	2186.51	0.0720414
$974$	−35546.0	−1.16937
$975$	0	0
$976$	−47160.7	−1.54670
$977$	−54677.1	−1.79046	−0.895228	−	0.445608i	$-0.852987\pi$
$977$	−54677.1	−1.79046	−0.895228	+	0.445608i	$0.852987\pi$
$978$	−37192.3	−1.21603
$979$	12850.8	0.419523
$980$	−10412.2	−0.339394
$981$	−2156.17	−0.0701744
$982$	−35030.4	−1.13836
$983$	2907.79	0.0943479	0.0471740	−	0.998887i	$-0.484978\pi$
$983$	2907.79	0.0943479	0.0471740	+	0.998887i	$0.484978\pi$
$984$	2791.03	0.0904217
$985$	70269.0	2.27305
$986$	−17801.0	−0.574950
$987$	24607.5	0.793582
$988$	0	0
$989$	51688.9	1.66189
$990$	2059.59	0.0661192
$991$	27530.2	0.882467	0.441234	−	0.897392i	$-0.354541\pi$
$991$	27530.2	0.882467	0.441234	+	0.897392i	$0.354541\pi$
$992$	10232.5	0.327504
$993$	19872.0	0.635064
$994$	−7413.52	−0.236562
$995$	32097.4	1.02267
$996$	−4305.75	−0.136981
$997$	−16719.0	−0.531089	−0.265545	−	0.964099i	$-0.585552\pi$
$997$	−16719.0	−0.531089	−0.265545	+	0.964099i	$0.585552\pi$
$998$	−25977.5	−0.823952
$999$	35821.6	1.13448

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.q.1.42	yes	51
13.12	even	2		1859.4.a.p.1.10	✓	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.10	✓	51	13.12	even	2
1859.4.a.q.1.42	yes	51	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)

\(f(q)\)	\(=\)	\(q+3.79290 q^{2} -5.52551 q^{3} +6.38608 q^{4} +13.9792 q^{5} -20.9577 q^{6} +15.0455 q^{7} -6.12143 q^{8} +3.53129 q^{9} +O(q^{10})\)	\(q+3.79290 q^{2} -5.52551 q^{3} +6.38608 q^{4} +13.9792 q^{5} -20.9577 q^{6} +15.0455 q^{7} -6.12143 q^{8} +3.53129 q^{9} +53.0218 q^{10} +11.0000 q^{11} -35.2864 q^{12} +57.0659 q^{14} -77.2423 q^{15} -74.3066 q^{16} +30.2223 q^{17} +13.3938 q^{18} +25.3314 q^{19} +89.2724 q^{20} -83.1339 q^{21} +41.7219 q^{22} +140.864 q^{23} +33.8240 q^{24} +70.4186 q^{25} +129.677 q^{27} +96.0815 q^{28} -155.291 q^{29} -292.972 q^{30} -43.9418 q^{31} -232.866 q^{32} -60.7806 q^{33} +114.630 q^{34} +210.324 q^{35} +22.5511 q^{36} +276.238 q^{37} +96.0793 q^{38} -85.5728 q^{40} +82.5163 q^{41} -315.318 q^{42} +366.942 q^{43} +70.2469 q^{44} +49.3647 q^{45} +534.282 q^{46} -295.998 q^{47} +410.582 q^{48} -116.634 q^{49} +267.090 q^{50} -166.994 q^{51} -403.784 q^{53} +491.850 q^{54} +153.771 q^{55} -92.0997 q^{56} -139.969 q^{57} -589.003 q^{58} +145.614 q^{59} -493.276 q^{60} +634.677 q^{61} -166.667 q^{62} +53.1299 q^{63} -288.784 q^{64} -230.535 q^{66} +354.361 q^{67} +193.002 q^{68} -778.345 q^{69} +797.737 q^{70} -129.912 q^{71} -21.6165 q^{72} +1034.07 q^{73} +1047.74 q^{74} -389.099 q^{75} +161.768 q^{76} +165.500 q^{77} +230.441 q^{79} -1038.75 q^{80} -811.875 q^{81} +312.976 q^{82} +122.023 q^{83} -530.900 q^{84} +422.484 q^{85} +1391.77 q^{86} +858.063 q^{87} -67.3357 q^{88} +1168.25 q^{89} +187.235 q^{90} +899.568 q^{92} +242.801 q^{93} -1122.69 q^{94} +354.113 q^{95} +1286.70 q^{96} +1079.92 q^{97} -442.382 q^{98} +38.8442 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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