LMFDB - Embedded newform 2009.4.a.m.1.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2009,4,Mod(1,2009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2009, 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("2009.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2009 = 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2009.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:	$118.534837202$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.34
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.18565 q^{2} -5.56348 q^{3} +2.14840 q^{4} -0.334741 q^{5} -17.7233 q^{6} -18.6412 q^{8} +3.95229 q^{9} +O(q^{10})$	\(q+3.18565 q^{2} -5.56348 q^{3} +2.14840 q^{4} -0.334741 q^{5} -17.7233 q^{6} -18.6412 q^{8} +3.95229 q^{9} -1.06637 q^{10} -38.4554 q^{11} -11.9526 q^{12} -84.0040 q^{13} +1.86233 q^{15} -76.5716 q^{16} -95.0435 q^{17} +12.5906 q^{18} -31.7289 q^{19} -0.719157 q^{20} -122.506 q^{22} +119.788 q^{23} +103.710 q^{24} -124.888 q^{25} -267.608 q^{26} +128.225 q^{27} -134.970 q^{29} +5.93273 q^{30} -320.716 q^{31} -94.8011 q^{32} +213.946 q^{33} -302.776 q^{34} +8.49108 q^{36} +347.490 q^{37} -101.077 q^{38} +467.355 q^{39} +6.23998 q^{40} +41.0000 q^{41} -253.641 q^{43} -82.6175 q^{44} -1.32299 q^{45} +381.603 q^{46} +30.5280 q^{47} +426.004 q^{48} -397.850 q^{50} +528.772 q^{51} -180.474 q^{52} +156.112 q^{53} +408.482 q^{54} +12.8726 q^{55} +176.523 q^{57} -429.968 q^{58} -710.575 q^{59} +4.00102 q^{60} -414.183 q^{61} -1021.69 q^{62} +310.569 q^{64} +28.1196 q^{65} +681.558 q^{66} +79.2811 q^{67} -204.191 q^{68} -666.437 q^{69} -227.985 q^{71} -73.6754 q^{72} +17.1435 q^{73} +1106.98 q^{74} +694.811 q^{75} -68.1662 q^{76} +1488.83 q^{78} -450.298 q^{79} +25.6317 q^{80} -820.091 q^{81} +130.612 q^{82} +350.037 q^{83} +31.8150 q^{85} -808.011 q^{86} +750.903 q^{87} +716.855 q^{88} -201.814 q^{89} -4.21460 q^{90} +257.352 q^{92} +1784.30 q^{93} +97.2518 q^{94} +10.6210 q^{95} +527.424 q^{96} -366.814 q^{97} -151.987 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} + 6 q^{3} + 213 q^{4} - 4 q^{5} + 12 q^{6} + 57 q^{8} + 452 q^{9}+O(q^{10}) $ 44 * q + 3 * q^2 + 6 * q^3 + 213 * q^4 - 4 * q^5 + 12 * q^6 + 57 * q^8 + 452 * q^9	\( 44 q + 3 q^{2} + 6 q^{3} + 213 q^{4} - 4 q^{5} + 12 q^{6} + 57 q^{8} + 452 q^{9} + 12 q^{10} + 124 q^{11} + 220 q^{12} - 96 q^{13} + 234 q^{15} + 1281 q^{16} + 2 q^{17} + 148 q^{18} + 58 q^{19} - 422 q^{20} + 270 q^{22} + 638 q^{23} - 106 q^{24} + 1570 q^{25} + 327 q^{26} - 48 q^{27} + 224 q^{29} + 1133 q^{30} + 4 q^{31} + 364 q^{32} + 254 q^{33} + 140 q^{34} + 2705 q^{36} + 410 q^{37} + 264 q^{38} + 1460 q^{39} + 26 q^{40} + 1804 q^{41} + 1476 q^{43} + 893 q^{44} - 1724 q^{45} + 1588 q^{46} + 430 q^{47} + 2210 q^{48} + 2710 q^{50} + 1460 q^{51} - 1811 q^{52} + 648 q^{53} + 540 q^{54} + 882 q^{55} + 3734 q^{57} + 1049 q^{58} - 1480 q^{59} + 1076 q^{60} - 1014 q^{61} + 2463 q^{62} + 7595 q^{64} + 468 q^{65} - 2864 q^{66} + 1852 q^{67} - 419 q^{68} + 3248 q^{69} + 4656 q^{71} + 151 q^{72} - 2488 q^{73} + 917 q^{74} - 1538 q^{75} + 987 q^{76} + 5488 q^{78} + 4730 q^{79} - 4484 q^{80} + 6116 q^{81} + 123 q^{82} + 2136 q^{83} + 5796 q^{85} + 646 q^{86} - 2988 q^{87} + 3160 q^{88} + 236 q^{89} + 7902 q^{90} + 4726 q^{92} + 1402 q^{93} + 2485 q^{94} + 5756 q^{95} - 9084 q^{96} + 362 q^{97} + 9816 q^{99}+O(q^{100}) \) 44 * q + 3 * q^2 + 6 * q^3 + 213 * q^4 - 4 * q^5 + 12 * q^6 + 57 * q^8 + 452 * q^9 + 12 * q^10 + 124 * q^11 + 220 * q^12 - 96 * q^13 + 234 * q^15 + 1281 * q^16 + 2 * q^17 + 148 * q^18 + 58 * q^19 - 422 * q^20 + 270 * q^22 + 638 * q^23 - 106 * q^24 + 1570 * q^25 + 327 * q^26 - 48 * q^27 + 224 * q^29 + 1133 * q^30 + 4 * q^31 + 364 * q^32 + 254 * q^33 + 140 * q^34 + 2705 * q^36 + 410 * q^37 + 264 * q^38 + 1460 * q^39 + 26 * q^40 + 1804 * q^41 + 1476 * q^43 + 893 * q^44 - 1724 * q^45 + 1588 * q^46 + 430 * q^47 + 2210 * q^48 + 2710 * q^50 + 1460 * q^51 - 1811 * q^52 + 648 * q^53 + 540 * q^54 + 882 * q^55 + 3734 * q^57 + 1049 * q^58 - 1480 * q^59 + 1076 * q^60 - 1014 * q^61 + 2463 * q^62 + 7595 * q^64 + 468 * q^65 - 2864 * q^66 + 1852 * q^67 - 419 * q^68 + 3248 * q^69 + 4656 * q^71 + 151 * q^72 - 2488 * q^73 + 917 * q^74 - 1538 * q^75 + 987 * q^76 + 5488 * q^78 + 4730 * q^79 - 4484 * q^80 + 6116 * q^81 + 123 * q^82 + 2136 * q^83 + 5796 * q^85 + 646 * q^86 - 2988 * q^87 + 3160 * q^88 + 236 * q^89 + 7902 * q^90 + 4726 * q^92 + 1402 * q^93 + 2485 * q^94 + 5756 * q^95 - 9084 * q^96 + 362 * q^97 + 9816 * 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 $

$2$	3.18565	1.12630	0.563150	−	0.826355i	$-0.309589\pi$
$2$	3.18565	1.12630	0.563150	+	0.826355i	$0.309589\pi$
$3$	−5.56348	−1.07069	−0.535346	−	0.844633i	$-0.679819\pi$
$3$	−5.56348	−1.07069	−0.535346	+	0.844633i	$0.679819\pi$
$4$	2.14840	0.268550
$5$	−0.334741	−0.0299402	−0.0149701	−	0.999888i	$-0.504765\pi$
$5$	−0.334741	−0.0299402	−0.0149701	+	0.999888i	$0.504765\pi$
$6$	−17.7233	−1.20592
$7$	0	0
$7$	0	0
$8$	−18.6412	−0.823832
$9$	3.95229	0.146381
$10$	−1.06637	−0.0337216
$11$	−38.4554	−1.05407	−0.527034	−	0.849844i	$-0.676696\pi$
$11$	−38.4554	−1.05407	−0.527034	+	0.849844i	$0.676696\pi$
$12$	−11.9526	−0.287534
$13$	−84.0040	−1.79219	−0.896097	−	0.443858i	$-0.853609\pi$
$13$	−84.0040	−1.79219	−0.896097	+	0.443858i	$0.853609\pi$
$14$	0	0
$15$	1.86233	0.0320567
$16$	−76.5716	−1.19643
$17$	−95.0435	−1.35597	−0.677983	−	0.735077i	$-0.737146\pi$
$17$	−95.0435	−1.35597	−0.677983	+	0.735077i	$0.737146\pi$
$18$	12.5906	0.164869
$19$	−31.7289	−0.383111	−0.191555	−	0.981482i	$-0.561353\pi$
$19$	−31.7289	−0.383111	−0.191555	+	0.981482i	$0.561353\pi$
$20$	−0.719157	−0.00804042
$21$	0	0
$22$	−122.506	−1.18720
$23$	119.788	1.08598	0.542989	−	0.839740i	$-0.317293\pi$
$23$	119.788	1.08598	0.542989	+	0.839740i	$0.317293\pi$
$24$	103.710	0.882070
$25$	−124.888	−0.999104
$26$	−267.608	−2.01855
$27$	128.225	0.913963
$28$	0	0
$29$	−134.970	−0.864252	−0.432126	−	0.901813i	$-0.642237\pi$
$29$	−134.970	−0.864252	−0.432126	+	0.901813i	$0.642237\pi$
$30$	5.93273	0.0361054
$31$	−320.716	−1.85814	−0.929070	−	0.369905i	$-0.879390\pi$
$31$	−320.716	−1.85814	−0.929070	+	0.369905i	$0.879390\pi$
$32$	−94.8011	−0.523707
$33$	213.946	1.12858
$34$	−302.776	−1.52722
$35$	0	0
$36$	8.49108	0.0393106
$37$	347.490	1.54397	0.771987	−	0.635639i	$-0.219263\pi$
$37$	347.490	1.54397	0.771987	+	0.635639i	$0.219263\pi$
$38$	−101.077	−0.431497
$39$	467.355	1.91889
$40$	6.23998	0.0246657
$41$	41.0000	0.156174
$41$	41.0000	0.156174
$42$	0	0
$43$	−253.641	−0.899531	−0.449765	−	0.893147i	$-0.648492\pi$
$43$	−253.641	−0.899531	−0.449765	+	0.893147i	$0.648492\pi$
$44$	−82.6175	−0.283070
$45$	−1.32299	−0.00438268
$46$	381.603	1.22314
$47$	30.5280	0.0947441	0.0473720	−	0.998877i	$-0.484915\pi$
$47$	30.5280	0.0947441	0.0473720	+	0.998877i	$0.484915\pi$
$48$	426.004	1.28101
$49$	0	0
$50$	−397.850	−1.12529
$51$	528.772	1.45182
$52$	−180.474	−0.481293
$53$	156.112	0.404596	0.202298	−	0.979324i	$-0.435159\pi$
$53$	156.112	0.404596	0.202298	+	0.979324i	$0.435159\pi$
$54$	408.482	1.02940
$55$	12.8726	0.0315590
$56$	0	0
$57$	176.523	0.410193
$58$	−429.968	−0.973407
$59$	−710.575	−1.56795	−0.783974	−	0.620793i	$-0.786811\pi$
$59$	−710.575	−1.56795	−0.783974	+	0.620793i	$0.786811\pi$
$60$	4.00102	0.00860882
$61$	−414.183	−0.869356	−0.434678	−	0.900586i	$-0.643138\pi$
$61$	−414.183	−0.869356	−0.434678	+	0.900586i	$0.643138\pi$
$62$	−1021.69	−2.09282
$63$	0	0
$64$	310.569	0.606580
$65$	28.1196	0.0536586
$66$	681.558	1.27112
$67$	79.2811	0.144563	0.0722816	−	0.997384i	$-0.476972\pi$
$67$	79.2811	0.144563	0.0722816	+	0.997384i	$0.476972\pi$
$68$	−204.191	−0.364144
$69$	−666.437	−1.16275
$70$	0	0
$71$	−227.985	−0.381083	−0.190541	−	0.981679i	$-0.561024\pi$
$71$	−227.985	−0.381083	−0.190541	+	0.981679i	$0.561024\pi$
$72$	−73.6754	−0.120593
$73$	17.1435	0.0274862	0.0137431	−	0.999906i	$-0.495625\pi$
$73$	17.1435	0.0274862	0.0137431	+	0.999906i	$0.495625\pi$
$74$	1106.98	1.73898
$75$	694.811	1.06973
$76$	−68.1662	−0.102884
$77$	0	0
$78$	1488.83	2.16124
$79$	−450.298	−0.641297	−0.320649	−	0.947198i	$-0.603901\pi$
$79$	−450.298	−0.641297	−0.320649	+	0.947198i	$0.603901\pi$
$80$	25.6317	0.0358214
$81$	−820.091	−1.12495
$82$	130.612	0.175898
$83$	350.037	0.462910	0.231455	−	0.972846i	$-0.425651\pi$
$83$	350.037	0.462910	0.231455	+	0.972846i	$0.425651\pi$
$84$	0	0
$85$	31.8150	0.0405979
$86$	−808.011	−1.01314
$87$	750.903	0.925348
$88$	716.855	0.868375
$89$	−201.814	−0.240362	−0.120181	−	0.992752i	$-0.538348\pi$
$89$	−201.814	−0.240362	−0.120181	+	0.992752i	$0.538348\pi$
$90$	−4.21460	−0.00493620
$91$	0	0
$92$	257.352	0.291639
$93$	1784.30	1.98949
$94$	97.2518	0.106710
$95$	10.6210	0.0114704
$96$	527.424	0.560729
$97$	−366.814	−0.383962	−0.191981	−	0.981399i	$-0.561491\pi$
$97$	−366.814	−0.383962	−0.191981	+	0.981399i	$0.561491\pi$
$98$	0	0
$99$	−151.987	−0.154296
$100$	−268.309	−0.268309
$101$	−617.231	−0.608087	−0.304043	−	0.952658i	$-0.598337\pi$
$101$	−617.231	−0.608087	−0.304043	+	0.952658i	$0.598337\pi$
$102$	1684.49	1.63519
$103$	−1763.38	−1.68690	−0.843452	−	0.537205i	$-0.819480\pi$
$103$	−1763.38	−1.68690	−0.843452	+	0.537205i	$0.819480\pi$
$104$	1565.93	1.47647
$105$	0	0
$106$	497.318	0.455696
$107$	1205.89	1.08951	0.544756	−	0.838595i	$-0.316622\pi$
$107$	1205.89	1.08951	0.544756	+	0.838595i	$0.316622\pi$
$108$	275.479	0.245444
$109$	1367.96	1.20208	0.601042	−	0.799217i	$-0.294752\pi$
$109$	1367.96	1.20208	0.601042	+	0.799217i	$0.294752\pi$
$110$	41.0078	0.0355449
$111$	−1933.25	−1.65312
$112$	0	0
$113$	1254.42	1.04430	0.522149	−	0.852855i	$-0.325131\pi$
$113$	1254.42	1.04430	0.522149	+	0.852855i	$0.325131\pi$
$114$	562.341	0.462000
$115$	−40.0980	−0.0325144
$116$	−289.969	−0.232095
$117$	−332.008	−0.262343
$118$	−2263.65	−1.76598
$119$	0	0
$120$	−34.7160	−0.0264093
$121$	147.821	0.111060
$122$	−1319.44	−0.979155
$123$	−228.103	−0.167214
$124$	−689.025	−0.499002
$125$	83.6479	0.0598535
$126$	0	0
$127$	−1594.98	−1.11443	−0.557213	−	0.830370i	$-0.688129\pi$
$127$	−1594.98	−1.11443	−0.557213	+	0.830370i	$0.688129\pi$
$128$	1747.77	1.20690
$129$	1411.12	0.963120
$130$	89.5794	0.0604357
$131$	−2879.80	−1.92068	−0.960340	−	0.278831i	$-0.910053\pi$
$131$	−2879.80	−1.92068	−0.960340	+	0.278831i	$0.910053\pi$
$132$	459.641	0.303080
$133$	0	0
$134$	252.562	0.162821
$135$	−42.9224	−0.0273642
$136$	1771.72	1.11709
$137$	1995.31	1.24431	0.622155	−	0.782894i	$-0.286257\pi$
$137$	1995.31	1.24431	0.622155	+	0.782894i	$0.286257\pi$
$138$	−2123.04	−1.30960
$139$	−2973.25	−1.81430	−0.907149	−	0.420809i	$-0.861746\pi$
$139$	−2973.25	−1.81430	−0.907149	+	0.420809i	$0.861746\pi$
$140$	0	0
$141$	−169.842	−0.101442
$142$	−726.282	−0.429213
$143$	3230.41	1.88910
$144$	−302.633	−0.175135
$145$	45.1801	0.0258759
$146$	54.6132	0.0309577
$147$	0	0
$148$	746.546	0.414633
$149$	−964.246	−0.530162	−0.265081	−	0.964226i	$-0.585399\pi$
$149$	−964.246	−0.530162	−0.265081	+	0.964226i	$0.585399\pi$
$150$	2213.43	1.20484
$151$	830.906	0.447802	0.223901	−	0.974612i	$-0.428121\pi$
$151$	830.906	0.447802	0.223901	+	0.974612i	$0.428121\pi$
$152$	591.464	0.315619
$153$	−375.639	−0.198488
$154$	0	0
$155$	107.357	0.0556330
$156$	1004.06	0.515317
$157$	1780.72	0.905203	0.452602	−	0.891713i	$-0.350496\pi$
$157$	1780.72	0.905203	0.452602	+	0.891713i	$0.350496\pi$
$158$	−1434.49	−0.722293
$159$	−868.524	−0.433198
$160$	31.7338	0.0156799
$161$	0	0
$162$	−2612.53	−1.26703
$163$	−619.337	−0.297609	−0.148804	−	0.988867i	$-0.547542\pi$
$163$	−619.337	−0.297609	−0.148804	+	0.988867i	$0.547542\pi$
$164$	88.0843	0.0419404
$165$	−71.6166	−0.0337900
$166$	1115.10	0.521375
$167$	3246.91	1.50451	0.752256	−	0.658870i	$-0.228965\pi$
$167$	3246.91	1.50451	0.752256	+	0.658870i	$0.228965\pi$
$168$	0	0
$169$	4859.68	2.21196
$170$	101.352	0.0457254
$171$	−125.402	−0.0560801
$172$	−544.920	−0.241569
$173$	1580.78	0.694707	0.347354	−	0.937734i	$-0.387080\pi$
$173$	1580.78	0.694707	0.347354	+	0.937734i	$0.387080\pi$
$174$	2392.12	1.04222
$175$	0	0
$176$	2944.59	1.26112
$177$	3953.27	1.67879
$178$	−642.910	−0.270720
$179$	1744.65	0.728500	0.364250	−	0.931301i	$-0.381325\pi$
$179$	1744.65	0.728500	0.364250	+	0.931301i	$0.381325\pi$
$180$	−2.84232	−0.00117697
$181$	−3300.30	−1.35530	−0.677650	−	0.735385i	$-0.737001\pi$
$181$	−3300.30	−1.35530	−0.677650	+	0.735385i	$0.737001\pi$
$182$	0	0
$183$	2304.30	0.930812
$184$	−2232.99	−0.894663
$185$	−116.319	−0.0462268
$186$	5684.15	2.24077
$187$	3654.94	1.42928
$188$	65.5863	0.0254435
$189$	0	0
$190$	33.8347	0.0129191
$191$	−344.459	−0.130493	−0.0652466	−	0.997869i	$-0.520783\pi$
$191$	−344.459	−0.130493	−0.0652466	+	0.997869i	$0.520783\pi$
$192$	−1727.84	−0.649460
$193$	−4943.31	−1.84366	−0.921832	−	0.387589i	$-0.873308\pi$
$193$	−4943.31	−1.84366	−0.921832	+	0.387589i	$0.873308\pi$
$194$	−1168.54	−0.432456
$195$	−156.443	−0.0574519
$196$	0	0
$197$	−4236.61	−1.53221	−0.766106	−	0.642714i	$-0.777808\pi$
$197$	−4236.61	−1.53221	−0.766106	+	0.642714i	$0.777808\pi$
$198$	−484.178	−0.173783
$199$	5314.50	1.89314	0.946570	−	0.322499i	$-0.104523\pi$
$199$	5314.50	1.89314	0.946570	+	0.322499i	$0.104523\pi$
$200$	2328.06	0.823093
$201$	−441.079	−0.154783
$202$	−1966.28	−0.684887
$203$	0	0
$204$	1136.01	0.389886
$205$	−13.7244	−0.00467587
$206$	−5617.52	−1.89996
$207$	473.436	0.158967
$208$	6432.32	2.14424
$209$	1220.15	0.403825
$210$	0	0
$211$	−2434.28	−0.794232	−0.397116	−	0.917768i	$-0.629989\pi$
$211$	−2434.28	−0.794232	−0.397116	+	0.917768i	$0.629989\pi$
$212$	335.390	0.108654
$213$	1268.39	0.408022
$214$	3841.55	1.22712
$215$	84.9040	0.0269321
$216$	−2390.27	−0.752952
$217$	0	0
$218$	4357.86	1.35391
$219$	−95.3774	−0.0294293
$220$	27.6555	0.00847516
$221$	7984.04	2.43016
$222$	−6158.68	−1.86191
$223$	3471.06	1.04233	0.521164	−	0.853457i	$-0.325498\pi$
$223$	3471.06	1.04233	0.521164	+	0.853457i	$0.325498\pi$
$224$	0	0
$225$	−493.593	−0.146250
$226$	3996.14	1.17619
$227$	3789.52	1.10802	0.554008	−	0.832511i	$-0.313098\pi$
$227$	3789.52	1.10802	0.554008	+	0.832511i	$0.313098\pi$
$228$	379.241	0.110157
$229$	2395.61	0.691295	0.345647	−	0.938364i	$-0.387659\pi$
$229$	2395.61	0.691295	0.345647	+	0.938364i	$0.387659\pi$
$230$	−127.738	−0.0366209
$231$	0	0
$232$	2516.00	0.711999
$233$	−1024.74	−0.288124	−0.144062	−	0.989569i	$-0.546016\pi$
$233$	−1024.74	−0.288124	−0.144062	+	0.989569i	$0.546016\pi$
$234$	−1057.66	−0.295477
$235$	−10.2190	−0.00283665
$236$	−1526.60	−0.421072
$237$	2505.22	0.686632
$238$	0	0
$239$	−3485.78	−0.943417	−0.471709	−	0.881755i	$-0.656363\pi$
$239$	−3485.78	−0.943417	−0.471709	+	0.881755i	$0.656363\pi$
$240$	−142.601	−0.0383536
$241$	−1096.77	−0.293149	−0.146574	−	0.989200i	$-0.546825\pi$
$241$	−1096.77	−0.293149	−0.146574	+	0.989200i	$0.546825\pi$
$242$	470.907	0.125087
$243$	1100.47	0.290516
$244$	−889.830	−0.233465
$245$	0	0
$246$	−726.656	−0.188333
$247$	2665.35	0.686608
$248$	5978.53	1.53079
$249$	−1947.42	−0.495634
$250$	266.473	0.0674130
$251$	−2249.47	−0.565679	−0.282839	−	0.959167i	$-0.591276\pi$
$251$	−2249.47	−0.565679	−0.282839	+	0.959167i	$0.591276\pi$
$252$	0	0
$253$	−4606.50	−1.14470
$254$	−5081.07	−1.25518
$255$	−177.002	−0.0434678
$256$	3083.25	0.752747
$257$	3910.19	0.949071	0.474535	−	0.880236i	$-0.342616\pi$
$257$	3910.19	0.949071	0.474535	+	0.880236i	$0.342616\pi$
$258$	4495.35	1.08476
$259$	0	0
$260$	60.4121	0.0144100
$261$	−533.441	−0.126510
$262$	−9174.04	−2.16326
$263$	−2775.19	−0.650668	−0.325334	−	0.945599i	$-0.605477\pi$
$263$	−2775.19	−0.650668	−0.325334	+	0.945599i	$0.605477\pi$
$264$	−3988.21	−0.929762
$265$	−52.2571	−0.0121137
$266$	0	0
$267$	1122.79	0.257354
$268$	170.327	0.0388224
$269$	−4768.24	−1.08076	−0.540381	−	0.841420i	$-0.681720\pi$
$269$	−4768.24	−1.08076	−0.540381	+	0.841420i	$0.681720\pi$
$270$	−136.736	−0.0308203
$271$	−3104.12	−0.695800	−0.347900	−	0.937532i	$-0.613105\pi$
$271$	−3104.12	−0.695800	−0.347900	+	0.937532i	$0.613105\pi$
$272$	7277.63	1.62232
$273$	0	0
$274$	6356.36	1.40147
$275$	4802.62	1.05312
$276$	−1431.77	−0.312255
$277$	519.963	0.112785	0.0563927	−	0.998409i	$-0.482040\pi$
$277$	519.963	0.112785	0.0563927	+	0.998409i	$0.482040\pi$
$278$	−9471.74	−2.04344
$279$	−1267.56	−0.271996
$280$	0	0
$281$	−5250.42	−1.11464	−0.557320	−	0.830298i	$-0.688170\pi$
$281$	−5250.42	−1.11464	−0.557320	+	0.830298i	$0.688170\pi$
$282$	−541.058	−0.114254
$283$	−1231.10	−0.258591	−0.129295	−	0.991606i	$-0.541272\pi$
$283$	−1231.10	−0.258591	−0.129295	+	0.991606i	$0.541272\pi$
$284$	−489.803	−0.102340
$285$	−59.0895	−0.0122813
$286$	10291.0	2.12769
$287$	0	0
$288$	−374.681	−0.0766608
$289$	4120.26	0.838645
$290$	143.928	0.0291440
$291$	2040.76	0.411105
$292$	36.8310	0.00738141
$293$	8826.81	1.75996	0.879979	−	0.475012i	$-0.157556\pi$
$293$	8826.81	1.75996	0.879979	+	0.475012i	$0.157556\pi$
$294$	0	0
$295$	237.859	0.0469447
$296$	−6477.63	−1.27197
$297$	−4930.97	−0.963379
$298$	−3071.75	−0.597121
$299$	−10062.7	−1.94628
$300$	1492.73	0.287276
$301$	0	0
$302$	2646.98	0.504359
$303$	3433.95	0.651073
$304$	2429.53	0.458365
$305$	138.644	0.0260287
$306$	−1196.66	−0.223557
$307$	−7650.76	−1.42232	−0.711160	−	0.703031i	$-0.751830\pi$
$307$	−7650.76	−1.42232	−0.711160	+	0.703031i	$0.751830\pi$
$308$	0	0
$309$	9810.53	1.80615
$310$	342.002	0.0626594
$311$	3281.49	0.598316	0.299158	−	0.954204i	$-0.403294\pi$
$311$	3281.49	0.598316	0.299158	+	0.954204i	$0.403294\pi$
$312$	−8712.04	−1.58084
$313$	1642.86	0.296677	0.148338	−	0.988937i	$-0.452608\pi$
$313$	1642.86	0.296677	0.148338	+	0.988937i	$0.452608\pi$
$314$	5672.76	1.01953
$315$	0	0
$316$	−967.419	−0.172220
$317$	6739.27	1.19405	0.597027	−	0.802221i	$-0.296349\pi$
$317$	6739.27	1.19405	0.597027	+	0.802221i	$0.296349\pi$
$318$	−2766.82	−0.487910
$319$	5190.34	0.910981
$320$	−103.960	−0.0181611
$321$	−6708.94	−1.16653
$322$	0	0
$323$	3015.62	0.519485
$324$	−1761.88	−0.302106
$325$	10491.1	1.79059
$326$	−1973.00	−0.335197
$327$	−7610.64	−1.28706
$328$	−764.289	−0.128661
$329$	0	0
$330$	−228.146	−0.0380576
$331$	10497.7	1.74322	0.871612	−	0.490197i	$-0.163075\pi$
$331$	10497.7	1.74322	0.871612	+	0.490197i	$0.163075\pi$
$332$	752.018	0.124314
$333$	1373.38	0.226008
$334$	10343.5	1.69453
$335$	−26.5387	−0.00432825
$336$	0	0
$337$	−2807.64	−0.453834	−0.226917	−	0.973914i	$-0.572865\pi$
$337$	−2807.64	−0.453834	−0.226917	+	0.973914i	$0.572865\pi$
$338$	15481.2	2.49133
$339$	−6978.92	−1.11812
$340$	68.3512	0.0109025
$341$	12333.3	1.95861
$342$	−399.486	−0.0631630
$343$	0	0
$344$	4728.16	0.741062
$345$	223.084	0.0348129
$346$	5035.81	0.782448
$347$	−5630.87	−0.871126	−0.435563	−	0.900158i	$-0.643451\pi$
$347$	−5630.87	−0.871126	−0.435563	+	0.900158i	$0.643451\pi$
$348$	1613.24	0.248502
$349$	325.221	0.0498817	0.0249408	−	0.999689i	$-0.492060\pi$
$349$	325.221	0.0498817	0.0249408	+	0.999689i	$0.492060\pi$
$350$	0	0
$351$	−10771.5	−1.63800
$352$	3645.62	0.552023
$353$	−480.480	−0.0724458	−0.0362229	−	0.999344i	$-0.511533\pi$
$353$	−480.480	−0.0724458	−0.0362229	+	0.999344i	$0.511533\pi$
$354$	12593.7	1.89082
$355$	76.3161	0.0114097
$356$	−433.577	−0.0645492
$357$	0	0
$358$	5557.86	0.820509
$359$	−11037.5	−1.62266	−0.811332	−	0.584585i	$-0.801257\pi$
$359$	−11037.5	−1.62266	−0.811332	+	0.584585i	$0.801257\pi$
$360$	24.6622	0.00361059
$361$	−5852.28	−0.853226
$362$	−10513.6	−1.52647
$363$	−822.399	−0.118911
$364$	0	0
$365$	−5.73864	−0.000822942 0
$366$	7340.70	1.04837
$367$	−7472.00	−1.06277	−0.531383	−	0.847132i	$-0.678327\pi$
$367$	−7472.00	−1.06277	−0.531383	+	0.847132i	$0.678327\pi$
$368$	−9172.34	−1.29930
$369$	162.044	0.0228609
$370$	−370.553	−0.0520653
$371$	0	0
$372$	3833.38	0.534278
$373$	−6358.92	−0.882715	−0.441357	−	0.897331i	$-0.645503\pi$
$373$	−6358.92	−0.882715	−0.441357	+	0.897331i	$0.645503\pi$
$374$	11643.4	1.60980
$375$	−465.373	−0.0640847
$376$	−569.079	−0.0780532
$377$	11338.0	1.54891
$378$	0	0
$379$	8642.35	1.17131	0.585656	−	0.810559i	$-0.300837\pi$
$379$	8642.35	1.17131	0.585656	+	0.810559i	$0.300837\pi$
$380$	22.8180	0.00308037
$381$	8873.66	1.19321
$382$	−1097.33	−0.146974
$383$	−1494.74	−0.199419	−0.0997095	−	0.995017i	$-0.531791\pi$
$383$	−1494.74	−0.199419	−0.0997095	+	0.995017i	$0.531791\pi$
$384$	−9723.70	−1.29222
$385$	0	0
$386$	−15747.7	−2.07652
$387$	−1002.46	−0.131674
$388$	−788.062	−0.103113
$389$	−12987.4	−1.69277	−0.846383	−	0.532574i	$-0.821225\pi$
$389$	−12987.4	−1.69277	−0.846383	+	0.532574i	$0.821225\pi$
$390$	−498.373	−0.0647080
$391$	−11385.1	−1.47255
$392$	0	0
$393$	16021.7	2.05646
$394$	−13496.4	−1.72573
$395$	150.733	0.0192006
$396$	−326.528	−0.0414360
$397$	−5665.16	−0.716187	−0.358093	−	0.933686i	$-0.616573\pi$
$397$	−5665.16	−0.716187	−0.358093	+	0.933686i	$0.616573\pi$
$398$	16930.2	2.13224
$399$	0	0
$400$	9562.87	1.19536
$401$	−14464.0	−1.80124	−0.900619	−	0.434609i	$-0.856887\pi$
$401$	−14464.0	−1.80124	−0.900619	+	0.434609i	$0.856887\pi$
$402$	−1405.12	−0.174331
$403$	26941.4	3.33015
$404$	−1326.06	−0.163301
$405$	274.519	0.0336813
$406$	0	0
$407$	−13362.9	−1.62745
$408$	−9856.95	−1.19606
$409$	−9111.03	−1.10149	−0.550747	−	0.834672i	$-0.685657\pi$
$409$	−9111.03	−1.10149	−0.550747	+	0.834672i	$0.685657\pi$
$410$	−43.7212	−0.00526643
$411$	−11100.8	−1.33227
$412$	−3788.44	−0.453017
$413$	0	0
$414$	1508.20	0.179044
$415$	−117.172	−0.0138596
$416$	7963.67	0.938584
$417$	16541.6	1.94255
$418$	3886.97	0.454827
$419$	1605.47	0.187189	0.0935945	−	0.995610i	$-0.470164\pi$
$419$	1605.47	0.187189	0.0935945	+	0.995610i	$0.470164\pi$
$420$	0	0
$421$	−6930.23	−0.802277	−0.401138	−	0.916017i	$-0.631385\pi$
$421$	−6930.23	−0.802277	−0.401138	+	0.916017i	$0.631385\pi$
$422$	−7754.79	−0.894543
$423$	120.656	0.0138687
$424$	−2910.11	−0.333319
$425$	11869.8	1.35475
$426$	4040.66	0.459555
$427$	0	0
$428$	2590.73	0.292588
$429$	−17972.3	−2.02264
$430$	270.475	0.0303336
$431$	−374.715	−0.0418780	−0.0209390	−	0.999781i	$-0.506666\pi$
$431$	−374.715	−0.0418780	−0.0209390	+	0.999781i	$0.506666\pi$
$432$	−9818.42	−1.09349
$433$	8798.22	0.976479	0.488240	−	0.872710i	$-0.337639\pi$
$433$	8798.22	0.976479	0.488240	+	0.872710i	$0.337639\pi$
$434$	0	0
$435$	−251.358	−0.0277051
$436$	2938.93	0.322819
$437$	−3800.73	−0.416050
$438$	−303.840	−0.0331462
$439$	−6402.67	−0.696088	−0.348044	−	0.937478i	$-0.613154\pi$
$439$	−6402.67	−0.696088	−0.348044	+	0.937478i	$0.613154\pi$
$440$	−239.961	−0.0259993
$441$	0	0
$442$	25434.4	2.73708
$443$	−432.334	−0.0463675	−0.0231838	−	0.999731i	$-0.507380\pi$
$443$	−432.334	−0.0463675	−0.0231838	+	0.999731i	$0.507380\pi$
$444$	−4153.39	−0.443945
$445$	67.5555	0.00719649
$446$	11057.6	1.17397
$447$	5364.56	0.567640
$448$	0	0
$449$	2840.47	0.298553	0.149276	−	0.988796i	$-0.452306\pi$
$449$	2840.47	0.298553	0.149276	+	0.988796i	$0.452306\pi$
$450$	−1572.42	−0.164721
$451$	−1576.67	−0.164618
$452$	2694.98	0.280446
$453$	−4622.73	−0.479458
$454$	12072.1	1.24796
$455$	0	0
$456$	−3290.60	−0.337930
$457$	1239.04	0.126827	0.0634133	−	0.997987i	$-0.479801\pi$
$457$	1239.04	0.126827	0.0634133	+	0.997987i	$0.479801\pi$
$458$	7631.60	0.778605
$459$	−12187.0	−1.23930
$460$	−86.1463	−0.00873173
$461$	−2295.98	−0.231962	−0.115981	−	0.993251i	$-0.537001\pi$
$461$	−2295.98	−0.231962	−0.115981	+	0.993251i	$0.537001\pi$
$462$	0	0
$463$	12105.9	1.21513	0.607567	−	0.794268i	$-0.292146\pi$
$463$	12105.9	1.21513	0.607567	+	0.794268i	$0.292146\pi$
$464$	10334.9	1.03402
$465$	−597.278	−0.0595658
$466$	−3264.46	−0.324514
$467$	−1050.00	−0.104043	−0.0520215	−	0.998646i	$-0.516566\pi$
$467$	−1050.00	−0.104043	−0.0520215	+	0.998646i	$0.516566\pi$
$468$	−713.285	−0.0704522
$469$	0	0
$470$	−32.5542	−0.00319492
$471$	−9906.99	−0.969194
$472$	13246.0	1.29173
$473$	9753.86	0.948167
$474$	7980.78	0.773353
$475$	3962.55	0.382767
$476$	0	0
$477$	616.999	0.0592252
$478$	−11104.5	−1.06257
$479$	8044.42	0.767347	0.383673	−	0.923469i	$-0.374659\pi$
$479$	8044.42	0.767347	0.383673	+	0.923469i	$0.374659\pi$
$480$	−176.551	−0.0167883
$481$	−29190.6	−2.76710
$482$	−3493.92	−0.330173
$483$	0	0
$484$	317.578	0.0298252
$485$	122.788	0.0114959
$486$	3505.73	0.327208
$487$	−5873.37	−0.546505	−0.273252	−	0.961942i	$-0.588099\pi$
$487$	−5873.37	−0.546505	−0.273252	+	0.961942i	$0.588099\pi$
$488$	7720.86	0.716203
$489$	3445.67	0.318647
$490$	0	0
$491$	2136.28	0.196352	0.0981762	−	0.995169i	$-0.468699\pi$
$491$	2136.28	0.196352	0.0981762	+	0.995169i	$0.468699\pi$
$492$	−490.055	−0.0449052
$493$	12828.0	1.17190
$494$	8490.89	0.773326
$495$	50.8764	0.00461964
$496$	24557.7	2.22313
$497$	0	0
$498$	−6203.81	−0.558232
$499$	11060.7	0.992274	0.496137	−	0.868244i	$-0.334751\pi$
$499$	11060.7	0.992274	0.496137	+	0.868244i	$0.334751\pi$
$500$	179.709	0.0160736
$501$	−18064.1	−1.61087
$502$	−7166.04	−0.637123
$503$	−14041.1	−1.24465	−0.622326	−	0.782758i	$-0.713812\pi$
$503$	−14041.1	−1.24465	−0.622326	+	0.782758i	$0.713812\pi$
$504$	0	0
$505$	206.613	0.0182062
$506$	−14674.7	−1.28927
$507$	−27036.7	−2.36833
$508$	−3426.66	−0.299278
$509$	−13576.2	−1.18223	−0.591115	−	0.806587i	$-0.701312\pi$
$509$	−13576.2	−1.18223	−0.591115	+	0.806587i	$0.701312\pi$
$510$	−563.867	−0.0489578
$511$	0	0
$512$	−4160.01	−0.359079
$513$	−4068.45	−0.350149
$514$	12456.5	1.06894
$515$	590.277	0.0505062
$516$	3031.65	0.258646
$517$	−1173.97	−0.0998667
$518$	0	0
$519$	−8794.62	−0.743817
$520$	−524.183	−0.0442057
$521$	3978.01	0.334510	0.167255	−	0.985914i	$-0.446510\pi$
$521$	3978.01	0.334510	0.167255	+	0.985914i	$0.446510\pi$
$522$	−1699.36	−0.142488
$523$	16138.4	1.34930	0.674650	−	0.738138i	$-0.264295\pi$
$523$	16138.4	1.34930	0.674650	+	0.738138i	$0.264295\pi$
$524$	−6186.95	−0.515798
$525$	0	0
$526$	−8840.81	−0.732847
$527$	30482.0	2.51957
$528$	−16382.2	−1.35027
$529$	2182.13	0.179348
$530$	−166.473	−0.0136436
$531$	−2808.40	−0.229518
$532$	0	0
$533$	−3444.16	−0.279894
$534$	3576.82	0.289858
$535$	−403.661	−0.0326202
$536$	−1477.89	−0.119096
$537$	−9706.34	−0.779999
$538$	−15190.0	−1.21726
$539$	0	0
$540$	−92.2143	−0.00734865
$541$	−7125.75	−0.566284	−0.283142	−	0.959078i	$-0.591377\pi$
$541$	−7125.75	−0.566284	−0.283142	+	0.959078i	$0.591377\pi$
$542$	−9888.65	−0.783679
$543$	18361.1	1.45111
$544$	9010.22	0.710129
$545$	−457.914	−0.0359906
$546$	0	0
$547$	−13164.9	−1.02905	−0.514524	−	0.857476i	$-0.672031\pi$
$547$	−13164.9	−1.02905	−0.514524	+	0.857476i	$0.672031\pi$
$548$	4286.71	0.334159
$549$	−1636.97	−0.127257
$550$	15299.5	1.18613
$551$	4282.45	0.331104
$552$	12423.2	0.957909
$553$	0	0
$554$	1656.42	0.127030
$555$	647.140	0.0494947
$556$	−6387.71	−0.487229
$557$	−19798.1	−1.50606	−0.753028	−	0.657989i	$-0.771407\pi$
$557$	−19798.1	−1.50606	−0.753028	+	0.657989i	$0.771407\pi$
$558$	−4038.02	−0.306349
$559$	21306.8	1.61213
$560$	0	0
$561$	−20334.2	−1.53032
$562$	−16726.0	−1.25542
$563$	−6539.11	−0.489504	−0.244752	−	0.969586i	$-0.578707\pi$
$563$	−6539.11	−0.489504	−0.244752	+	0.969586i	$0.578707\pi$
$564$	−364.888	−0.0272421
$565$	−419.905	−0.0312665
$566$	−3921.85	−0.291250
$567$	0	0
$568$	4249.92	0.313948
$569$	4152.49	0.305943	0.152971	−	0.988231i	$-0.451116\pi$
$569$	4152.49	0.305943	0.152971	+	0.988231i	$0.451116\pi$
$570$	−188.239	−0.0138324
$571$	−16030.8	−1.17490	−0.587451	−	0.809260i	$-0.699868\pi$
$571$	−16030.8	−1.17490	−0.587451	+	0.809260i	$0.699868\pi$
$572$	6940.21	0.507316
$573$	1916.39	0.139718
$574$	0	0
$575$	−14960.1	−1.08500
$576$	1227.46	0.0887918
$577$	−16743.8	−1.20807	−0.604033	−	0.796960i	$-0.706440\pi$
$577$	−16743.8	−1.20807	−0.604033	+	0.796960i	$0.706440\pi$
$578$	13125.7	0.944565
$579$	27502.0	1.97400
$580$	97.0648	0.00694896
$581$	0	0
$582$	6501.16	0.463027
$583$	−6003.34	−0.426472
$584$	−319.575	−0.0226440
$585$	111.137	0.00785461
$586$	28119.2	1.98224
$587$	−20200.5	−1.42038	−0.710190	−	0.704010i	$-0.751391\pi$
$587$	−20200.5	−1.42038	−0.710190	+	0.704010i	$0.751391\pi$
$588$	0	0
$589$	10176.0	0.711873
$590$	757.736	0.0528737
$591$	23570.3	1.64053
$592$	−26607.9	−1.84726
$593$	−15556.5	−1.07728	−0.538642	−	0.842535i	$-0.681062\pi$
$593$	−15556.5	−1.07728	−0.538642	+	0.842535i	$0.681062\pi$
$594$	−15708.4	−1.08505
$595$	0	0
$596$	−2071.58	−0.142375
$597$	−29567.1	−2.02697
$598$	−32056.2	−2.19210
$599$	25922.9	1.76825	0.884125	−	0.467250i	$-0.154755\pi$
$599$	25922.9	1.76825	0.884125	+	0.467250i	$0.154755\pi$
$600$	−12952.1	−0.881279
$601$	−16623.4	−1.12826	−0.564128	−	0.825687i	$-0.690788\pi$
$601$	−16623.4	−1.12826	−0.564128	+	0.825687i	$0.690788\pi$
$602$	0	0
$603$	313.342	0.0211613
$604$	1785.12	0.120257
$605$	−49.4818	−0.00332516
$606$	10939.4	0.733303
$607$	−8474.16	−0.566649	−0.283324	−	0.959024i	$-0.591437\pi$
$607$	−8474.16	−0.566649	−0.283324	+	0.959024i	$0.591437\pi$
$608$	3007.93	0.200638
$609$	0	0
$610$	441.673	0.0293161
$611$	−2564.48	−0.169800
$612$	−807.022	−0.0533038
$613$	−29418.5	−1.93834	−0.969169	−	0.246395i	$-0.920754\pi$
$613$	−29418.5	−1.93834	−0.969169	+	0.246395i	$0.920754\pi$
$614$	−24372.7	−1.60196
$615$	76.3554	0.00500642
$616$	0	0
$617$	722.623	0.0471503	0.0235751	−	0.999722i	$-0.492495\pi$
$617$	722.623	0.0471503	0.0235751	+	0.999722i	$0.492495\pi$
$618$	31253.0	2.03427
$619$	−12086.3	−0.784799	−0.392399	−	0.919795i	$-0.628355\pi$
$619$	−12086.3	−0.784799	−0.392399	+	0.919795i	$0.628355\pi$
$620$	230.645	0.0149402
$621$	15359.9	0.992544
$622$	10453.7	0.673883
$623$	0	0
$624$	−35786.1	−2.29582
$625$	15583.0	0.997312
$626$	5233.58	0.334147
$627$	−6788.26	−0.432372
$628$	3825.69	0.243092
$629$	−33026.7	−2.09358
$630$	0	0
$631$	15819.6	0.998047	0.499023	−	0.866588i	$-0.333692\pi$
$631$	15819.6	0.998047	0.499023	+	0.866588i	$0.333692\pi$
$632$	8394.09	0.528321
$633$	13543.1	0.850378
$634$	21469.0	1.34486
$635$	533.908	0.0333661
$636$	−1865.93	−0.116335
$637$	0	0
$638$	16534.6	1.02604
$639$	−901.064	−0.0557833
$640$	−585.052	−0.0361347
$641$	15252.1	0.939812	0.469906	−	0.882716i	$-0.344288\pi$
$641$	15252.1	0.939812	0.469906	+	0.882716i	$0.344288\pi$
$642$	−21372.4	−1.31386
$643$	−8815.11	−0.540644	−0.270322	−	0.962770i	$-0.587130\pi$
$643$	−8815.11	−0.540644	−0.270322	+	0.962770i	$0.587130\pi$
$644$	0	0
$645$	−472.361	−0.0288360
$646$	9606.73	0.585096
$647$	598.573	0.0363714	0.0181857	−	0.999835i	$-0.494211\pi$
$647$	598.573	0.0363714	0.0181857	+	0.999835i	$0.494211\pi$
$648$	15287.5	0.926773
$649$	27325.5	1.65273
$650$	33421.0	2.01674
$651$	0	0
$652$	−1330.58	−0.0799227
$653$	−2615.66	−0.156751	−0.0783757	−	0.996924i	$-0.524973\pi$
$653$	−2615.66	−0.156751	−0.0783757	+	0.996924i	$0.524973\pi$
$654$	−24244.9	−1.44962
$655$	963.988	0.0575055
$656$	−3139.43	−0.186851
$657$	67.7560	0.00402346
$658$	0	0
$659$	11736.3	0.693748	0.346874	−	0.937912i	$-0.387243\pi$
$659$	11736.3	0.693748	0.346874	+	0.937912i	$0.387243\pi$
$660$	−153.861	−0.00907428
$661$	−23690.7	−1.39404	−0.697020	−	0.717051i	$-0.745491\pi$
$661$	−23690.7	−1.39404	−0.697020	+	0.717051i	$0.745491\pi$
$662$	33442.1	1.96339
$663$	−44419.0	−2.60195
$664$	−6525.10	−0.381360
$665$	0	0
$666$	4375.12	0.254553
$667$	−16167.8	−0.938559
$668$	6975.66	0.404036
$669$	−19311.1	−1.11601
$670$	−84.5431	−0.00487490
$671$	15927.6	0.916361
$672$	0	0
$673$	−15904.6	−0.910961	−0.455481	−	0.890246i	$-0.650533\pi$
$673$	−15904.6	−0.910961	−0.455481	+	0.890246i	$0.650533\pi$
$674$	−8944.18	−0.511153
$675$	−16013.8	−0.913144
$676$	10440.5	0.594021
$677$	−11161.5	−0.633638	−0.316819	−	0.948486i	$-0.602615\pi$
$677$	−11161.5	−0.633638	−0.316819	+	0.948486i	$0.602615\pi$
$678$	−22232.4	−1.25934
$679$	0	0
$680$	−593.069	−0.0334458
$681$	−21082.9	−1.18634
$682$	39289.6	2.20598
$683$	−25946.3	−1.45360	−0.726800	−	0.686849i	$-0.758993\pi$
$683$	−25946.3	−1.45360	−0.726800	+	0.686849i	$0.758993\pi$
$684$	−269.412	−0.0150603
$685$	−667.912	−0.0372549
$686$	0	0
$687$	−13327.9	−0.740164
$688$	19421.7	1.07623
$689$	−13114.0	−0.725115
$690$	710.669	0.0392097
$691$	7479.42	0.411766	0.205883	−	0.978577i	$-0.433993\pi$
$691$	7479.42	0.411766	0.205883	+	0.978577i	$0.433993\pi$
$692$	3396.14	0.186563
$693$	0	0
$694$	−17938.0	−0.981149
$695$	995.269	0.0543204
$696$	−13997.7	−0.762331
$697$	−3896.78	−0.211766
$698$	1036.04	0.0561817
$699$	5701.11	0.308492
$700$	0	0
$701$	6592.06	0.355176	0.177588	−	0.984105i	$-0.443170\pi$
$701$	6592.06	0.355176	0.177588	+	0.984105i	$0.443170\pi$
$702$	−34314.1	−1.84488
$703$	−11025.5	−0.591512
$704$	−11943.1	−0.639377
$705$	56.8532	0.00303718
$706$	−1530.64	−0.0815956
$707$	0	0
$708$	8493.19	0.450838
$709$	−5097.27	−0.270003	−0.135001	−	0.990845i	$-0.543104\pi$
$709$	−5097.27	−0.270003	−0.135001	+	0.990845i	$0.543104\pi$
$710$	243.117	0.0128507
$711$	−1779.71	−0.0938738
$712$	3762.05	0.198018
$713$	−38417.9	−2.01790
$714$	0	0
$715$	−1081.35	−0.0565599
$716$	3748.21	0.195638
$717$	19393.1	1.01011
$718$	−35161.6	−1.82761
$719$	−9877.35	−0.512327	−0.256163	−	0.966633i	$-0.582459\pi$
$719$	−9877.35	−0.512327	−0.256163	+	0.966633i	$0.582459\pi$
$720$	101.304	0.00524357
$721$	0	0
$722$	−18643.3	−0.960988
$723$	6101.83	0.313872
$724$	−7090.35	−0.363965
$725$	16856.1	0.863478
$726$	−2619.88	−0.133930
$727$	19002.3	0.969405	0.484703	−	0.874679i	$-0.338928\pi$
$727$	19002.3	0.969405	0.484703	+	0.874679i	$0.338928\pi$
$728$	0	0
$729$	16020.0	0.813901
$730$	−18.2813	−0.000926879 0
$731$	24106.9	1.21973
$732$	4950.55	0.249969
$733$	−4605.75	−0.232083	−0.116042	−	0.993244i	$-0.537021\pi$
$733$	−4605.75	−0.232083	−0.116042	+	0.993244i	$0.537021\pi$
$734$	−23803.2	−1.19699
$735$	0	0
$736$	−11356.0	−0.568734
$737$	−3048.79	−0.152379
$738$	516.216	0.0257482
$739$	15279.3	0.760566	0.380283	−	0.924870i	$-0.375827\pi$
$739$	15279.3	0.760566	0.380283	+	0.924870i	$0.375827\pi$
$740$	−249.900	−0.0124142
$741$	−14828.6	−0.735146
$742$	0	0
$743$	−36053.8	−1.78020	−0.890098	−	0.455769i	$-0.849364\pi$
$743$	−36053.8	−1.78020	−0.890098	+	0.455769i	$0.849364\pi$
$744$	−33261.4	−1.63901
$745$	322.773	0.0158731
$746$	−20257.3	−0.994201
$747$	1383.45	0.0677612
$748$	7852.26	0.383833
$749$	0	0
$750$	−1482.52	−0.0721785
$751$	6492.85	0.315482	0.157741	−	0.987480i	$-0.449579\pi$
$751$	6492.85	0.315482	0.157741	+	0.987480i	$0.449579\pi$
$752$	−2337.58	−0.113355
$753$	12514.9	0.605668
$754$	36119.1	1.74453
$755$	−278.139	−0.0134073
$756$	0	0
$757$	−10407.2	−0.499680	−0.249840	−	0.968287i	$-0.580378\pi$
$757$	−10407.2	−0.499680	−0.249840	+	0.968287i	$0.580378\pi$
$758$	27531.5	1.31925
$759$	25628.1	1.22562
$760$	−197.987	−0.00944968
$761$	36057.9	1.71761	0.858803	−	0.512306i	$-0.171209\pi$
$761$	36057.9	1.71761	0.858803	+	0.512306i	$0.171209\pi$
$762$	28268.4	1.34391
$763$	0	0
$764$	−740.035	−0.0350439
$765$	125.742	0.00594276
$766$	−4761.72	−0.224606
$767$	59691.2	2.81007
$768$	−17153.6	−0.805961
$769$	−11977.1	−0.561645	−0.280823	−	0.959760i	$-0.590607\pi$
$769$	−11977.1	−0.561645	−0.280823	+	0.959760i	$0.590607\pi$
$770$	0	0
$771$	−21754.3	−1.01616
$772$	−10620.2	−0.495115
$773$	14624.3	0.680465	0.340232	−	0.940341i	$-0.389494\pi$
$773$	14624.3	0.680465	0.340232	+	0.940341i	$0.389494\pi$
$774$	−3193.49	−0.148305
$775$	40053.6	1.85647
$776$	6837.85	0.316320
$777$	0	0
$778$	−41373.3	−1.90656
$779$	−1300.88	−0.0598318
$780$	−336.101	−0.0154287
$781$	8767.28	0.401687
$782$	−36268.9	−1.65853
$783$	−17306.6	−0.789895
$784$	0	0
$785$	−596.081	−0.0271020
$786$	51039.6	2.31619
$787$	16830.0	0.762292	0.381146	−	0.924515i	$-0.375529\pi$
$787$	16830.0	0.762292	0.381146	+	0.924515i	$0.375529\pi$
$788$	−9101.91	−0.411475
$789$	15439.7	0.696665
$790$	480.185	0.0216256
$791$	0	0
$792$	2833.22	0.127114
$793$	34793.0	1.55805
$794$	−18047.2	−0.806641
$795$	290.731	0.0129700
$796$	11417.7	0.508402
$797$	−20542.8	−0.913004	−0.456502	−	0.889722i	$-0.650898\pi$
$797$	−20542.8	−0.913004	−0.456502	+	0.889722i	$0.650898\pi$
$798$	0	0
$799$	−2901.49	−0.128470
$800$	11839.5	0.523237
$801$	−797.628	−0.0351845
$802$	−46077.2	−2.02873
$803$	−659.260	−0.0289723
$804$	−947.612	−0.0415668
$805$	0	0
$806$	85826.1	3.75074
$807$	26528.0	1.15716
$808$	11505.9	0.500961
$809$	−35693.0	−1.55117	−0.775587	−	0.631240i	$-0.782546\pi$
$809$	−35693.0	−1.55117	−0.775587	+	0.631240i	$0.782546\pi$
$810$	874.521	0.0379352
$811$	5527.05	0.239311	0.119655	−	0.992815i	$-0.461821\pi$
$811$	5527.05	0.239311	0.119655	+	0.992815i	$0.461821\pi$
$812$	0	0
$813$	17269.7	0.744988
$814$	−42569.5	−1.83300
$815$	207.318	0.00891047
$816$	−40488.9	−1.73700
$817$	8047.72	0.344620
$818$	−29024.6	−1.24061
$819$	0	0
$820$	−29.4855	−0.00125570
$821$	6140.52	0.261030	0.130515	−	0.991446i	$-0.458337\pi$
$821$	6140.52	0.261030	0.130515	+	0.991446i	$0.458337\pi$
$822$	−35363.5	−1.50054
$823$	36144.8	1.53090	0.765450	−	0.643496i	$-0.222517\pi$
$823$	36144.8	1.53090	0.765450	+	0.643496i	$0.222517\pi$
$824$	32871.5	1.38973
$825$	−26719.3	−1.12757
$826$	0	0
$827$	12049.0	0.506633	0.253316	−	0.967383i	$-0.418479\pi$
$827$	12049.0	0.506633	0.253316	+	0.967383i	$0.418479\pi$
$828$	1017.13	0.0426904
$829$	9448.89	0.395867	0.197933	−	0.980215i	$-0.436577\pi$
$829$	9448.89	0.395867	0.197933	+	0.980215i	$0.436577\pi$
$830$	−373.269	−0.0156101
$831$	−2892.80	−0.120758
$832$	−26089.0	−1.08711
$833$	0	0
$834$	52695.8	2.18790
$835$	−1086.88	−0.0450454
$836$	2621.36	0.108447
$837$	−41124.0	−1.69827
$838$	5114.46	0.210831
$839$	26070.9	1.07279	0.536393	−	0.843968i	$-0.319786\pi$
$839$	26070.9	1.07279	0.536393	+	0.843968i	$0.319786\pi$
$840$	0	0
$841$	−6172.07	−0.253068
$842$	−22077.3	−0.903604
$843$	29210.6	1.19344
$844$	−5229.81	−0.213291
$845$	−1626.73	−0.0662265
$846$	384.367	0.0156203
$847$	0	0
$848$	−11953.7	−0.484071
$849$	6849.18	0.276871
$850$	37813.0	1.52585
$851$	41625.1	1.67672
$852$	2725.01	0.109574
$853$	258.991	0.0103959	0.00519794	−	0.999986i	$-0.498345\pi$
$853$	258.991	0.0103959	0.00519794	+	0.999986i	$0.498345\pi$
$854$	0	0
$855$	41.9771	0.00167905
$856$	−22479.2	−0.897575
$857$	37899.8	1.51066	0.755329	−	0.655346i	$-0.227477\pi$
$857$	37899.8	1.51066	0.755329	+	0.655346i	$0.227477\pi$
$858$	−57253.6	−2.27810
$859$	30576.7	1.21451	0.607254	−	0.794508i	$-0.292271\pi$
$859$	30576.7	1.21451	0.607254	+	0.794508i	$0.292271\pi$
$860$	182.407	0.00723261
$861$	0	0
$862$	−1193.71	−0.0471671
$863$	19691.6	0.776721	0.388360	−	0.921508i	$-0.373042\pi$
$863$	19691.6	0.776721	0.388360	+	0.921508i	$0.373042\pi$
$864$	−12155.9	−0.478649
$865$	−529.152	−0.0207997
$866$	28028.1	1.09981
$867$	−22923.0	−0.897931
$868$	0	0
$869$	17316.4	0.675971
$870$	−800.741	−0.0312042
$871$	−6659.93	−0.259085
$872$	−25500.5	−0.990315
$873$	−1449.76	−0.0562048
$874$	−12107.8	−0.468596
$875$	0	0
$876$	−204.909	−0.00790322
$877$	26049.7	1.00301	0.501503	−	0.865156i	$-0.332780\pi$
$877$	26049.7	1.00301	0.501503	+	0.865156i	$0.332780\pi$
$878$	−20396.7	−0.784004
$879$	−49107.8	−1.88437
$880$	−985.677	−0.0377582
$881$	−3519.60	−0.134595	−0.0672976	−	0.997733i	$-0.521438\pi$
$881$	−3519.60	−0.134595	−0.0672976	+	0.997733i	$0.521438\pi$
$882$	0	0
$883$	6444.89	0.245626	0.122813	−	0.992430i	$-0.460808\pi$
$883$	6444.89	0.245626	0.122813	+	0.992430i	$0.460808\pi$
$884$	17152.9	0.652617
$885$	−1323.32	−0.0502633
$886$	−1377.27	−0.0522237
$887$	5990.84	0.226779	0.113389	−	0.993551i	$-0.463829\pi$
$887$	5990.84	0.226779	0.113389	+	0.993551i	$0.463829\pi$
$888$	36038.1	1.36189
$889$	0	0
$890$	215.209	0.00810540
$891$	31537.0	1.18578
$892$	7457.21	0.279917
$893$	−968.620	−0.0362974
$894$	17089.6	0.639332
$895$	−584.008	−0.0218114
$896$	0	0
$897$	55983.4	2.08387
$898$	9048.76	0.336260
$899$	43287.1	1.60590
$900$	−1060.43	−0.0392753
$901$	−14837.4	−0.548619
$902$	−5022.74	−0.185409
$903$	0	0
$904$	−23383.8	−0.860325
$905$	1104.75	0.0405779
$906$	−14726.4	−0.540013
$907$	−32147.6	−1.17690	−0.588448	−	0.808535i	$-0.700261\pi$
$907$	−32147.6	−1.17690	−0.588448	+	0.808535i	$0.700261\pi$
$908$	8141.40	0.297557
$909$	−2439.47	−0.0890124
$910$	0	0
$911$	21326.8	0.775620	0.387810	−	0.921739i	$-0.373232\pi$
$911$	21326.8	0.775620	0.387810	+	0.921739i	$0.373232\pi$
$912$	−13516.6	−0.490768
$913$	−13460.8	−0.487939
$914$	3947.15	0.142845
$915$	−771.344	−0.0278687
$916$	5146.73	0.185647
$917$	0	0
$918$	−38823.6	−1.39583
$919$	41696.0	1.49665	0.748326	−	0.663331i	$-0.230858\pi$
$919$	41696.0	1.49665	0.748326	+	0.663331i	$0.230858\pi$
$920$	747.474	0.0267864
$921$	42564.8	1.52287
$922$	−7314.19	−0.261258
$923$	19151.7	0.682974
$924$	0	0
$925$	−43397.3	−1.54259
$926$	38565.1	1.36860
$927$	−6969.39	−0.246931
$928$	12795.3	0.452615
$929$	5066.09	0.178916	0.0894581	−	0.995991i	$-0.471486\pi$
$929$	5066.09	0.178916	0.0894581	+	0.995991i	$0.471486\pi$
$930$	−1902.72	−0.0670889
$931$	0	0
$932$	−2201.54	−0.0773755
$933$	−18256.5	−0.640612
$934$	−3344.93	−0.117183
$935$	−1223.46	−0.0427930
$936$	6189.03	0.216127
$937$	−17184.7	−0.599147	−0.299573	−	0.954073i	$-0.596844\pi$
$937$	−17184.7	−0.599147	−0.299573	+	0.954073i	$0.596844\pi$
$938$	0	0
$939$	−9140.01	−0.317649
$940$	−21.9545	−0.000761782 0
$941$	−5988.82	−0.207471	−0.103735	−	0.994605i	$-0.533079\pi$
$941$	−5988.82	−0.207471	−0.103735	+	0.994605i	$0.533079\pi$
$942$	−31560.3	−1.09160
$943$	4911.30	0.169601
$944$	54409.8	1.87594
$945$	0	0
$946$	31072.4	1.06792
$947$	−15936.9	−0.546863	−0.273432	−	0.961891i	$-0.588159\pi$
$947$	−15936.9	−0.546863	−0.273432	+	0.961891i	$0.588159\pi$
$948$	5382.21	0.184395
$949$	−1440.12	−0.0492606
$950$	12623.3	0.431110
$951$	−37493.8	−1.27846
$952$	0	0
$953$	11105.9	0.377499	0.188750	−	0.982025i	$-0.439557\pi$
$953$	11105.9	0.377499	0.188750	+	0.982025i	$0.439557\pi$
$954$	1965.54	0.0667053
$955$	115.305	0.00390699
$956$	−7488.85	−0.253354
$957$	−28876.3	−0.975380
$958$	25626.8	0.864262
$959$	0	0
$960$	578.381	0.0194450
$961$	73067.8	2.45268
$962$	−92991.1	−3.11658
$963$	4766.02	0.159484
$964$	−2356.29	−0.0787250
$965$	1654.73	0.0551997
$966$	0	0
$967$	−24762.2	−0.823473	−0.411736	−	0.911303i	$-0.635078\pi$
$967$	−24762.2	−0.823473	−0.411736	+	0.911303i	$0.635078\pi$
$968$	−2755.56	−0.0914949
$969$	−16777.3	−0.556208
$970$	391.160	0.0129478
$971$	17148.7	0.566763	0.283382	−	0.959007i	$-0.408544\pi$
$971$	17148.7	0.566763	0.283382	+	0.959007i	$0.408544\pi$
$972$	2364.25	0.0780179
$973$	0	0
$974$	−18710.5	−0.615528
$975$	−58366.9	−1.91717
$976$	31714.6	1.04012
$977$	11486.5	0.376138	0.188069	−	0.982156i	$-0.439777\pi$
$977$	11486.5	0.376138	0.188069	+	0.982156i	$0.439777\pi$
$978$	10976.7	0.358892
$979$	7760.85	0.253358
$980$	0	0
$981$	5406.59	0.175962
$982$	6805.45	0.221151
$983$	27252.6	0.884255	0.442128	−	0.896952i	$-0.354224\pi$
$983$	27252.6	0.884255	0.442128	+	0.896952i	$0.354224\pi$
$984$	4252.10	0.137756
$985$	1418.17	0.0458747
$986$	40865.7	1.31991
$987$	0	0
$988$	5726.23	0.184388
$989$	−30383.1	−0.976870
$990$	162.074	0.00520310
$991$	−58095.0	−1.86221	−0.931104	−	0.364754i	$-0.881153\pi$
$991$	−58095.0	−1.86221	−0.931104	+	0.364754i	$0.881153\pi$
$992$	30404.2	0.973120
$993$	−58403.9	−1.86646
$994$	0	0
$995$	−1778.98	−0.0566810
$996$	−4183.83	−0.133102
$997$	−16161.0	−0.513363	−0.256681	−	0.966496i	$-0.582629\pi$
$997$	−16161.0	−0.513363	−0.256681	+	0.966496i	$0.582629\pi$
$998$	35235.6	1.11760
$999$	44557.1	1.41113

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.4.a.m.1.34		44
7.3	odd	6		287.4.e.b.247.11	yes	88
7.5	odd	6		287.4.e.b.165.11	✓	88
7.6	odd	2		2009.4.a.l.1.34		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.4.e.b.165.11	✓	88	7.5	odd	6
287.4.e.b.247.11	yes	88	7.3	odd	6
2009.4.a.l.1.34		44	7.6	odd	2
2009.4.a.m.1.34		44	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:	\( N \)	\(=\)	\( 2009 = 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2009.a (trivial)

\(f(q)\)	\(=\)	\(q+3.18565 q^{2} -5.56348 q^{3} +2.14840 q^{4} -0.334741 q^{5} -17.7233 q^{6} -18.6412 q^{8} +3.95229 q^{9} +O(q^{10})\)	\(q+3.18565 q^{2} -5.56348 q^{3} +2.14840 q^{4} -0.334741 q^{5} -17.7233 q^{6} -18.6412 q^{8} +3.95229 q^{9} -1.06637 q^{10} -38.4554 q^{11} -11.9526 q^{12} -84.0040 q^{13} +1.86233 q^{15} -76.5716 q^{16} -95.0435 q^{17} +12.5906 q^{18} -31.7289 q^{19} -0.719157 q^{20} -122.506 q^{22} +119.788 q^{23} +103.710 q^{24} -124.888 q^{25} -267.608 q^{26} +128.225 q^{27} -134.970 q^{29} +5.93273 q^{30} -320.716 q^{31} -94.8011 q^{32} +213.946 q^{33} -302.776 q^{34} +8.49108 q^{36} +347.490 q^{37} -101.077 q^{38} +467.355 q^{39} +6.23998 q^{40} +41.0000 q^{41} -253.641 q^{43} -82.6175 q^{44} -1.32299 q^{45} +381.603 q^{46} +30.5280 q^{47} +426.004 q^{48} -397.850 q^{50} +528.772 q^{51} -180.474 q^{52} +156.112 q^{53} +408.482 q^{54} +12.8726 q^{55} +176.523 q^{57} -429.968 q^{58} -710.575 q^{59} +4.00102 q^{60} -414.183 q^{61} -1021.69 q^{62} +310.569 q^{64} +28.1196 q^{65} +681.558 q^{66} +79.2811 q^{67} -204.191 q^{68} -666.437 q^{69} -227.985 q^{71} -73.6754 q^{72} +17.1435 q^{73} +1106.98 q^{74} +694.811 q^{75} -68.1662 q^{76} +1488.83 q^{78} -450.298 q^{79} +25.6317 q^{80} -820.091 q^{81} +130.612 q^{82} +350.037 q^{83} +31.8150 q^{85} -808.011 q^{86} +750.903 q^{87} +716.855 q^{88} -201.814 q^{89} -4.21460 q^{90} +257.352 q^{92} +1784.30 q^{93} +97.2518 q^{94} +10.6210 q^{95} +527.424 q^{96} -366.814 q^{97} -151.987 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} + 6 q^{3} + 213 q^{4} - 4 q^{5} + 12 q^{6} + 57 q^{8} + 452 q^{9}+O(q^{10}) \) 44 * q + 3 * q^2 + 6 * q^3 + 213 * q^4 - 4 * q^5 + 12 * q^6 + 57 * q^8 + 452 * q^9	\( 44 q + 3 q^{2} + 6 q^{3} + 213 q^{4} - 4 q^{5} + 12 q^{6} + 57 q^{8} + 452 q^{9} + 12 q^{10} + 124 q^{11} + 220 q^{12} - 96 q^{13} + 234 q^{15} + 1281 q^{16} + 2 q^{17} + 148 q^{18} + 58 q^{19} - 422 q^{20} + 270 q^{22} + 638 q^{23} - 106 q^{24} + 1570 q^{25} + 327 q^{26} - 48 q^{27} + 224 q^{29} + 1133 q^{30} + 4 q^{31} + 364 q^{32} + 254 q^{33} + 140 q^{34} + 2705 q^{36} + 410 q^{37} + 264 q^{38} + 1460 q^{39} + 26 q^{40} + 1804 q^{41} + 1476 q^{43} + 893 q^{44} - 1724 q^{45} + 1588 q^{46} + 430 q^{47} + 2210 q^{48} + 2710 q^{50} + 1460 q^{51} - 1811 q^{52} + 648 q^{53} + 540 q^{54} + 882 q^{55} + 3734 q^{57} + 1049 q^{58} - 1480 q^{59} + 1076 q^{60} - 1014 q^{61} + 2463 q^{62} + 7595 q^{64} + 468 q^{65} - 2864 q^{66} + 1852 q^{67} - 419 q^{68} + 3248 q^{69} + 4656 q^{71} + 151 q^{72} - 2488 q^{73} + 917 q^{74} - 1538 q^{75} + 987 q^{76} + 5488 q^{78} + 4730 q^{79} - 4484 q^{80} + 6116 q^{81} + 123 q^{82} + 2136 q^{83} + 5796 q^{85} + 646 q^{86} - 2988 q^{87} + 3160 q^{88} + 236 q^{89} + 7902 q^{90} + 4726 q^{92} + 1402 q^{93} + 2485 q^{94} + 5756 q^{95} - 9084 q^{96} + 362 q^{97} + 9816 q^{99}+O(q^{100}) \) 44 * q + 3 * q^2 + 6 * q^3 + 213 * q^4 - 4 * q^5 + 12 * q^6 + 57 * q^8 + 452 * q^9 + 12 * q^10 + 124 * q^11 + 220 * q^12 - 96 * q^13 + 234 * q^15 + 1281 * q^16 + 2 * q^17 + 148 * q^18 + 58 * q^19 - 422 * q^20 + 270 * q^22 + 638 * q^23 - 106 * q^24 + 1570 * q^25 + 327 * q^26 - 48 * q^27 + 224 * q^29 + 1133 * q^30 + 4 * q^31 + 364 * q^32 + 254 * q^33 + 140 * q^34 + 2705 * q^36 + 410 * q^37 + 264 * q^38 + 1460 * q^39 + 26 * q^40 + 1804 * q^41 + 1476 * q^43 + 893 * q^44 - 1724 * q^45 + 1588 * q^46 + 430 * q^47 + 2210 * q^48 + 2710 * q^50 + 1460 * q^51 - 1811 * q^52 + 648 * q^53 + 540 * q^54 + 882 * q^55 + 3734 * q^57 + 1049 * q^58 - 1480 * q^59 + 1076 * q^60 - 1014 * q^61 + 2463 * q^62 + 7595 * q^64 + 468 * q^65 - 2864 * q^66 + 1852 * q^67 - 419 * q^68 + 3248 * q^69 + 4656 * q^71 + 151 * q^72 - 2488 * q^73 + 917 * q^74 - 1538 * q^75 + 987 * q^76 + 5488 * q^78 + 4730 * q^79 - 4484 * q^80 + 6116 * q^81 + 123 * q^82 + 2136 * q^83 + 5796 * q^85 + 646 * q^86 - 2988 * q^87 + 3160 * q^88 + 236 * q^89 + 7902 * q^90 + 4726 * q^92 + 1402 * q^93 + 2485 * q^94 + 5756 * q^95 - 9084 * q^96 + 362 * q^97 + 9816 * q^99

Introduction

L-functions

Modular forms

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Database

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