LMFDB - Embedded newform 1859.4.a.p.1.10

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			1.10
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	$-0.733919\pi$
$2$	−3.79290	−1.34099	−0.670496	+	0.741913i	$0.733919\pi$
$3$	−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	$-0.714970\pi$
$5$	−13.9792	−1.25034	−0.625170	+	0.780489i	$0.714970\pi$
$6$	20.9577	1.42599
$7$	−15.0455	−0.812378	−0.406189	−	0.913789i	$-0.633143\pi$
$7$	−15.0455	−0.812378	−0.406189	+	0.913789i	$0.633143\pi$
$8$	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	$-0.548872\pi$
$19$	−25.3314	−0.305864	−0.152932	+	0.988237i	$0.548872\pi$
$20$	−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	$-0.459371\pi$
$31$	43.9418	0.254586	0.127293	+	0.991865i	$0.459371\pi$
$32$	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	$-0.710317\pi$
$37$	−276.238	−1.22739	−0.613693	+	0.789545i	$0.710317\pi$
$38$	96.0793	0.410161
$39$	0	0
$40$	−85.5728	−0.338256
$41$	−82.5163	−0.314314	−0.157157	−	0.987574i	$-0.550233\pi$
$41$	−82.5163	−0.314314	−0.157157	+	0.987574i	$0.550233\pi$
$42$	−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	$-0.348094\pi$
$47$	295.998	0.918634	0.459317	+	0.888272i	$0.348094\pi$
$48$	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	$-0.551361\pi$
$59$	−145.614	−0.321312	−0.160656	+	0.987010i	$0.551361\pi$
$60$	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	$-0.604717\pi$
$67$	−354.361	−0.646151	−0.323076	+	0.946373i	$0.604717\pi$
$68$	193.002	0.344190
$69$	−778.345	−1.35800
$70$	−797.737	−1.36211
$71$	129.912	0.217150	0.108575	−	0.994088i	$-0.465371\pi$
$71$	129.912	0.217150	0.108575	+	0.994088i	$0.465371\pi$
$72$	21.6165	0.0353824
$73$	−1034.07	−1.65793	−0.828963	−	0.559304i	$-0.811068\pi$
$73$	−1034.07	−1.65793	−0.828963	+	0.559304i	$0.811068\pi$
$74$	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	$-0.525711\pi$
$83$	−122.023	−0.161371	−0.0806854	+	0.996740i	$0.525711\pi$
$84$	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	$-0.744906\pi$
$89$	−1168.25	−1.39140	−0.695701	+	0.718332i	$0.744906\pi$
$90$	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	$-0.691203\pi$
$97$	−1079.92	−1.13041	−0.565204	+	0.824951i	$0.691203\pi$
$98$	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	$-0.413547\pi$
$109$	610.589	0.536549	0.268274	+	0.963343i	$0.413547\pi$
$110$	−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	$-0.462604\pi$
$137$	375.915	0.234428	0.117214	+	0.993107i	$0.462604\pi$
$138$	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	$-0.757732\pi$
$149$	−2633.86	−1.44815	−0.724074	+	0.689723i	$0.757732\pi$
$150$	1475.81	0.803330
$151$	−2201.86	−1.18665	−0.593327	−	0.804962i	$-0.702186\pi$
$151$	−2201.86	−1.18665	−0.593327	+	0.804962i	$0.702186\pi$
$152$	−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	$-0.640212\pi$
$163$	−1774.64	−0.852762	−0.426381	+	0.904544i	$0.640212\pi$
$164$	−526.956	−0.250905
$165$	−849.666	−0.400887
$166$	462.821	0.216397
$167$	−1910.22	−0.885133	−0.442567	−	0.896736i	$-0.645932\pi$
$167$	−1910.22	−0.885133	−0.442567	+	0.896736i	$0.645932\pi$
$168$	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	$-0.716476\pi$
$193$	−3372.22	−1.25771	−0.628854	+	0.777523i	$0.716476\pi$
$194$	4096.04	1.51587
$195$	0	0
$196$	−744.835	−0.271441
$197$	−5026.68	−1.81795	−0.908974	−	0.416852i	$-0.863133\pi$
$197$	−5026.68	−1.81795	−0.908974	+	0.416852i	$0.863133\pi$
$198$	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	$-0.727017\pi$
$223$	−4357.46	−1.30851	−0.654254	+	0.756275i	$0.727017\pi$
$224$	−3503.58	−1.04506
$225$	248.668	0.0736795
$226$	−1414.81	−0.416423
$227$	−1877.12	−0.548850	−0.274425	−	0.961609i	$-0.588487\pi$
$227$	−1877.12	−0.548850	−0.274425	+	0.961609i	$0.588487\pi$
$228$	893.852	0.259635
$229$	4608.22	1.32978	0.664890	−	0.746942i	$-0.268479\pi$
$229$	4608.22	1.32978	0.664890	+	0.746942i	$0.268479\pi$
$230$	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	$-0.846391\pi$
$239$	−6545.81	−1.77160	−0.885801	+	0.464065i	$0.846391\pi$
$240$	−5739.62	−1.54371
$241$	−1619.94	−0.432985	−0.216492	−	0.976284i	$-0.569462\pi$
$241$	−1619.94	−0.432985	−0.216492	+	0.976284i	$0.569462\pi$
$242$	−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	$-0.482920\pi$
$271$	478.527	0.107264	0.0536318	+	0.998561i	$0.482920\pi$
$272$	−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	$-0.231424\pi$
$281$	7038.72	1.49429	0.747144	+	0.664662i	$0.231424\pi$
$282$	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	$-0.520334\pi$
$293$	−640.326	−0.127673	−0.0638366	+	0.997960i	$0.520334\pi$
$294$	−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	$-0.334305\pi$
$307$	5350.62	0.994709	0.497355	+	0.867547i	$0.334305\pi$
$308$	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	$-0.546254\pi$
$317$	−1634.52	−0.289603	−0.144801	+	0.989461i	$0.546254\pi$
$318$	−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	$-0.403479\pi$
$331$	3596.41	0.597210	0.298605	+	0.954377i	$0.403479\pi$
$332$	−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	$-0.186856\pi$
$349$	10856.8	1.66518	0.832592	+	0.553886i	$0.186856\pi$
$350$	4018.50	0.613708
$351$	0	0
$352$	−2561.53	−0.387869
$353$	2346.38	0.353783	0.176891	−	0.984230i	$-0.443396\pi$
$353$	2346.38	0.353783	0.176891	+	0.984230i	$0.443396\pi$
$354$	−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	$-0.383116\pi$
$359$	4883.98	0.718013	0.359007	+	0.933335i	$0.383116\pi$
$360$	−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	$-0.405029\pi$
$379$	4337.76	0.587905	0.293952	+	0.955820i	$0.405029\pi$
$380$	2261.39	0.305282
$381$	−191.962	−0.0258124
$382$	8170.08	1.09429
$383$	5520.84	0.736558	0.368279	−	0.929715i	$-0.379947\pi$
$383$	5520.84	0.736558	0.368279	+	0.929715i	$0.379947\pi$
$384$	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	$-0.669759\pi$
$397$	−8042.88	−1.01678	−0.508388	+	0.861128i	$0.669759\pi$
$398$	−8708.80	−1.09682
$399$	−2105.89	−0.264227
$400$	−5232.56	−0.654071
$401$	−3609.51	−0.449502	−0.224751	−	0.974416i	$-0.572157\pi$
$401$	−3609.51	−0.449502	−0.224751	+	0.974416i	$0.572157\pi$
$402$	−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	$-0.500791\pi$
$409$	−41.1264	−0.00497206	−0.00248603	+	0.999997i	$0.500791\pi$
$410$	−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	$-0.365627\pi$
$421$	7078.46	0.819437	0.409718	+	0.912212i	$0.365627\pi$
$422$	−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	$-0.319121\pi$
$431$	9630.63	1.07631	0.538157	+	0.842845i	$0.319121\pi$
$432$	−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	$-0.385971\pi$
$449$	6671.71	0.701242	0.350621	+	0.936517i	$0.385971\pi$
$450$	−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	$-0.479984\pi$
$457$	1227.86	0.125682	0.0628410	+	0.998024i	$0.479984\pi$
$458$	−17478.5	−1.78322
$459$	3919.13	0.398539
$460$	−12575.3	−1.27462
$461$	−1567.28	−0.158341	−0.0791706	−	0.996861i	$-0.525227\pi$
$461$	−1567.28	−0.158341	−0.0791706	+	0.996861i	$0.525227\pi$
$462$	3468.50	0.349284
$463$	−18258.5	−1.83271	−0.916355	−	0.400367i	$-0.868883\pi$
$463$	−18258.5	−1.83271	−0.916355	+	0.400367i	$0.868883\pi$
$464$	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	$-0.503770\pi$
$479$	−248.305	−0.0236855	−0.0118428	+	0.999930i	$0.503770\pi$
$480$	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	$-0.356391\pi$
$487$	9371.73	0.872019	0.436010	+	0.899942i	$0.356391\pi$
$488$	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	$-0.400602\pi$
$499$	6848.99	0.614434	0.307217	+	0.951639i	$0.400602\pi$
$500$	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	$-0.251525\pi$
$509$	16162.2	1.40742	0.703711	+	0.710486i	$0.251525\pi$
$510$	−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	$-0.344446\pi$
$541$	11815.0	0.938936	0.469468	+	0.882949i	$0.344446\pi$
$542$	−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	$-0.501561\pi$
$557$	−128.957	−0.00980982	−0.00490491	+	0.999988i	$0.501561\pi$
$558$	−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	$-0.740004\pi$
$577$	−18976.0	−1.36911	−0.684557	+	0.728959i	$0.740004\pi$
$578$	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	$-0.588882\pi$
$587$	−7839.55	−0.551231	−0.275616	+	0.961268i	$0.588882\pi$
$588$	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	$-0.737926\pi$
$593$	−19632.8	−1.35956	−0.679782	+	0.733414i	$0.737926\pi$
$594$	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	$-0.504597\pi$
$613$	−438.335	−0.0288812	−0.0144406	+	0.999896i	$0.504597\pi$
$614$	−20294.3	−1.33390
$615$	−6373.75	−0.417910
$616$	1013.10	0.0662643
$617$	−6592.88	−0.430177	−0.215089	−	0.976595i	$-0.569004\pi$
$617$	−6592.88	−0.430177	−0.215089	+	0.976595i	$0.569004\pi$
$618$	−25875.4	−1.68424
$619$	28094.7	1.82427	0.912134	−	0.409891i	$-0.134433\pi$
$619$	28094.7	1.82427	0.912134	+	0.409891i	$0.134433\pi$
$620$	−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	$-0.506015\pi$
$631$	−598.987	−0.0377897	−0.0188948	+	0.999821i	$0.506015\pi$
$632$	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	$-0.148761\pi$
$643$	29112.9	1.78553	0.892767	+	0.450518i	$0.148761\pi$
$644$	−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	$-0.773094\pi$
$661$	−25712.4	−1.51301	−0.756503	+	0.653990i	$0.773094\pi$
$662$	−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	$-0.776019\pi$
$683$	−27220.2	−1.52496	−0.762482	+	0.647009i	$0.776019\pi$
$684$	−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	$-0.484964\pi$
$691$	1715.43	0.0944398	0.0472199	+	0.998885i	$0.484964\pi$
$692$	−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	$-0.741255\pi$
$709$	−25954.9	−1.37483	−0.687416	+	0.726264i	$0.741255\pi$
$710$	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	$-0.544088\pi$
$733$	−5479.83	−0.276129	−0.138064	+	0.990423i	$0.544088\pi$
$734$	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	$-0.369863\pi$
$739$	15972.7	0.795083	0.397542	+	0.917584i	$0.369863\pi$
$740$	24660.4	1.22505
$741$	0	0
$742$	−23042.3	−1.14004
$743$	−29476.9	−1.45546	−0.727728	−	0.685866i	$-0.759424\pi$
$743$	−29476.9	−1.45546	−0.727728	+	0.685866i	$0.759424\pi$
$744$	−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	$-0.715170\pi$
$761$	−26269.0	−1.25132	−0.625658	+	0.780097i	$0.715170\pi$
$762$	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	$-0.545751\pi$
$769$	−6109.01	−0.286471	−0.143236	+	0.989689i	$0.545751\pi$
$770$	8775.10	0.410692
$771$	−6728.48	−0.314294
$772$	−21535.3	−1.00398
$773$	−20084.9	−0.934546	−0.467273	−	0.884113i	$-0.654763\pi$
$773$	−20084.9	−0.934546	−0.467273	+	0.884113i	$0.654763\pi$
$774$	−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	$-0.559091\pi$
$787$	−8150.10	−0.369148	−0.184574	+	0.982819i	$0.559091\pi$
$788$	−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	$-0.272305\pi$
$811$	30295.2	1.31173	0.655863	+	0.754880i	$0.272305\pi$
$812$	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	$-0.352978\pi$
$821$	20966.4	0.891271	0.445635	+	0.895215i	$0.352978\pi$
$822$	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	$-0.525555\pi$
$827$	−3814.63	−0.160396	−0.0801982	+	0.996779i	$0.525555\pi$
$828$	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	$-0.389923\pi$
$839$	16475.1	0.677932	0.338966	+	0.940799i	$0.389923\pi$
$840$	−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	$-0.697430\pi$
$853$	−28960.5	−1.16247	−0.581235	+	0.813736i	$0.697430\pi$
$854$	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	$-0.762908\pi$
$863$	−37277.6	−1.47039	−0.735193	+	0.677858i	$0.762908\pi$
$864$	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	$-0.645481\pi$
$877$	−22922.4	−0.882593	−0.441296	+	0.897361i	$0.645481\pi$
$878$	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	$-0.664243\pi$
$929$	−27941.3	−0.986785	−0.493393	+	0.869807i	$0.664243\pi$
$930$	−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	$-0.494476\pi$
$941$	1001.77	0.0347045	0.0173522	+	0.999849i	$0.494476\pi$
$942$	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	$-0.420144\pi$
$947$	14469.2	0.496501	0.248251	+	0.968696i	$0.420144\pi$
$948$	−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	$-0.416529\pi$
$967$	15590.7	0.518473	0.259237	+	0.965814i	$0.416529\pi$
$968$	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	$-0.147013\pi$
$977$	54677.1	1.79046	0.895228	+	0.445608i	$0.147013\pi$
$978$	−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	$-0.515022\pi$
$983$	−2907.79	−0.0943479	−0.0471740	+	0.998887i	$0.515022\pi$
$984$	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.p.1.10	✓	51
13.12	even	2		1859.4.a.q.1.42	yes	51

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-3.79290 q^{2} -5.52551 q^{3} +6.38608 q^{4} -13.9792 q^{5} +20.9577 q^{6} -15.0455 q^{7} +6.12143 q^{8} +3.53129 q^{9} +O(q^{10})\)	\(q-3.79290 q^{2} -5.52551 q^{3} +6.38608 q^{4} -13.9792 q^{5} +20.9577 q^{6} -15.0455 q^{7} +6.12143 q^{8} +3.53129 q^{9} +53.0218 q^{10} -11.0000 q^{11} -35.2864 q^{12} +57.0659 q^{14} +77.2423 q^{15} -74.3066 q^{16} +30.2223 q^{17} -13.3938 q^{18} -25.3314 q^{19} -89.2724 q^{20} +83.1339 q^{21} +41.7219 q^{22} +140.864 q^{23} -33.8240 q^{24} +70.4186 q^{25} +129.677 q^{27} -96.0815 q^{28} -155.291 q^{29} -292.972 q^{30} +43.9418 q^{31} +232.866 q^{32} +60.7806 q^{33} -114.630 q^{34} +210.324 q^{35} +22.5511 q^{36} -276.238 q^{37} +96.0793 q^{38} -85.5728 q^{40} -82.5163 q^{41} -315.318 q^{42} +366.942 q^{43} -70.2469 q^{44} -49.3647 q^{45} -534.282 q^{46} +295.998 q^{47} +410.582 q^{48} -116.634 q^{49} -267.090 q^{50} -166.994 q^{51} -403.784 q^{53} -491.850 q^{54} +153.771 q^{55} -92.0997 q^{56} +139.969 q^{57} +589.003 q^{58} -145.614 q^{59} +493.276 q^{60} +634.677 q^{61} -166.667 q^{62} -53.1299 q^{63} -288.784 q^{64} -230.535 q^{66} -354.361 q^{67} +193.002 q^{68} -778.345 q^{69} -797.737 q^{70} +129.912 q^{71} +21.6165 q^{72} -1034.07 q^{73} +1047.74 q^{74} -389.099 q^{75} -161.768 q^{76} +165.500 q^{77} +230.441 q^{79} +1038.75 q^{80} -811.875 q^{81} +312.976 q^{82} -122.023 q^{83} +530.900 q^{84} -422.484 q^{85} -1391.77 q^{86} +858.063 q^{87} -67.3357 q^{88} -1168.25 q^{89} +187.235 q^{90} +899.568 q^{92} -242.801 q^{93} -1122.69 q^{94} +354.113 q^{95} -1286.70 q^{96} -1079.92 q^{97} +442.382 q^{98} -38.8442 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9}+O(q^{10}) \) 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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