Properties

Label 1441.4.a.c.1.3
Level $1441$
Weight $4$
Character 1441.1
Self dual yes
Analytic conductor $85.022$
Analytic rank $0$
Dimension $84$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1441,4,Mod(1,1441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1441, 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("1441.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1441.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: \(85.0217523183\)
Analytic rank: \(0\)
Dimension: \(84\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 1441.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.25317 q^{2} -10.3044 q^{3} +19.5957 q^{4} -18.0312 q^{5} +54.1305 q^{6} -26.5546 q^{7} -60.9144 q^{8} +79.1798 q^{9} +O(q^{10})\) \(q-5.25317 q^{2} -10.3044 q^{3} +19.5957 q^{4} -18.0312 q^{5} +54.1305 q^{6} -26.5546 q^{7} -60.9144 q^{8} +79.1798 q^{9} +94.7210 q^{10} -11.0000 q^{11} -201.922 q^{12} -52.4375 q^{13} +139.496 q^{14} +185.800 q^{15} +163.227 q^{16} +46.2394 q^{17} -415.945 q^{18} -54.5775 q^{19} -353.335 q^{20} +273.628 q^{21} +57.7848 q^{22} +90.0293 q^{23} +627.684 q^{24} +200.125 q^{25} +275.463 q^{26} -537.679 q^{27} -520.357 q^{28} +1.18696 q^{29} -976.039 q^{30} +338.032 q^{31} -370.145 q^{32} +113.348 q^{33} -242.903 q^{34} +478.811 q^{35} +1551.59 q^{36} +41.2187 q^{37} +286.705 q^{38} +540.335 q^{39} +1098.36 q^{40} +118.700 q^{41} -1437.41 q^{42} -37.1665 q^{43} -215.553 q^{44} -1427.71 q^{45} -472.939 q^{46} -178.029 q^{47} -1681.95 q^{48} +362.145 q^{49} -1051.29 q^{50} -476.468 q^{51} -1027.55 q^{52} +400.501 q^{53} +2824.52 q^{54} +198.343 q^{55} +1617.55 q^{56} +562.386 q^{57} -6.23531 q^{58} +248.128 q^{59} +3640.89 q^{60} -821.226 q^{61} -1775.74 q^{62} -2102.59 q^{63} +638.615 q^{64} +945.512 q^{65} -595.436 q^{66} +1013.90 q^{67} +906.096 q^{68} -927.694 q^{69} -2515.27 q^{70} +1106.36 q^{71} -4823.19 q^{72} +135.623 q^{73} -216.529 q^{74} -2062.16 q^{75} -1069.49 q^{76} +292.100 q^{77} -2838.47 q^{78} -937.852 q^{79} -2943.19 q^{80} +3402.59 q^{81} -623.549 q^{82} +571.167 q^{83} +5361.94 q^{84} -833.753 q^{85} +195.242 q^{86} -12.2309 q^{87} +670.058 q^{88} -661.609 q^{89} +7499.99 q^{90} +1392.46 q^{91} +1764.19 q^{92} -3483.21 q^{93} +935.217 q^{94} +984.098 q^{95} +3814.11 q^{96} -1572.44 q^{97} -1902.41 q^{98} -870.978 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9} - 58 q^{10} - 924 q^{11} + 152 q^{12} - 202 q^{13} + 306 q^{14} + 630 q^{15} + 1720 q^{16} + 148 q^{17} + 251 q^{18} + 33 q^{19} + 510 q^{20} - 206 q^{21} - 132 q^{22} + 938 q^{23} + 518 q^{24} + 2288 q^{25} + 788 q^{26} + 506 q^{27} + 52 q^{28} + 197 q^{29} + 93 q^{30} + 1018 q^{31} + 1173 q^{32} - 154 q^{33} - 16 q^{34} + 1126 q^{35} + 6815 q^{36} + 1059 q^{37} + 3259 q^{38} + 1350 q^{39} + 2912 q^{40} + 523 q^{41} + 1171 q^{42} + 110 q^{43} - 4180 q^{44} + 572 q^{45} - 552 q^{46} + 3764 q^{47} + 6132 q^{48} + 6165 q^{49} + 2316 q^{50} + 1910 q^{51} + 137 q^{52} + 2586 q^{53} + 5126 q^{54} - 418 q^{55} + 3853 q^{56} + 1480 q^{57} + 2576 q^{58} + 5392 q^{59} + 10535 q^{60} - 3704 q^{61} + 3766 q^{62} + 1375 q^{63} + 7804 q^{64} + 3178 q^{65} - 649 q^{66} + 2095 q^{67} + 1751 q^{68} + 2690 q^{69} + 1475 q^{70} + 10220 q^{71} + 4930 q^{72} - 100 q^{73} + 4970 q^{74} + 312 q^{75} + 1005 q^{76} - 121 q^{77} + 2325 q^{78} + 810 q^{79} + 12763 q^{80} + 14368 q^{81} + 2363 q^{82} + 3097 q^{83} + 6017 q^{84} - 1102 q^{85} + 4884 q^{86} + 2552 q^{87} - 1782 q^{88} + 7493 q^{89} + 1052 q^{90} + 2238 q^{91} + 9134 q^{92} + 4776 q^{93} + 1885 q^{94} + 6782 q^{95} + 10849 q^{96} + 1180 q^{97} + 13073 q^{98} - 9416 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.25317 −1.85727 −0.928637 0.370989i \(-0.879019\pi\)
−0.928637 + 0.370989i \(0.879019\pi\)
\(3\) −10.3044 −1.98307 −0.991537 0.129822i \(-0.958560\pi\)
−0.991537 + 0.129822i \(0.958560\pi\)
\(4\) 19.5957 2.44947
\(5\) −18.0312 −1.61276 −0.806380 0.591397i \(-0.798577\pi\)
−0.806380 + 0.591397i \(0.798577\pi\)
\(6\) 54.1305 3.68311
\(7\) −26.5546 −1.43381 −0.716906 0.697170i \(-0.754442\pi\)
−0.716906 + 0.697170i \(0.754442\pi\)
\(8\) −60.9144 −2.69206
\(9\) 79.1798 2.93259
\(10\) 94.7210 2.99534
\(11\) −11.0000 −0.301511
\(12\) −201.922 −4.85748
\(13\) −52.4375 −1.11873 −0.559367 0.828920i \(-0.688956\pi\)
−0.559367 + 0.828920i \(0.688956\pi\)
\(14\) 139.496 2.66298
\(15\) 185.800 3.19823
\(16\) 163.227 2.55043
\(17\) 46.2394 0.659689 0.329844 0.944035i \(-0.393004\pi\)
0.329844 + 0.944035i \(0.393004\pi\)
\(18\) −415.945 −5.44662
\(19\) −54.5775 −0.658996 −0.329498 0.944156i \(-0.606880\pi\)
−0.329498 + 0.944156i \(0.606880\pi\)
\(20\) −353.335 −3.95041
\(21\) 273.628 2.84336
\(22\) 57.7848 0.559989
\(23\) 90.0293 0.816192 0.408096 0.912939i \(-0.366193\pi\)
0.408096 + 0.912939i \(0.366193\pi\)
\(24\) 627.684 5.33856
\(25\) 200.125 1.60100
\(26\) 275.463 2.07780
\(27\) −537.679 −3.83246
\(28\) −520.357 −3.51208
\(29\) 1.18696 0.00760046 0.00380023 0.999993i \(-0.498790\pi\)
0.00380023 + 0.999993i \(0.498790\pi\)
\(30\) −976.039 −5.93998
\(31\) 338.032 1.95846 0.979232 0.202741i \(-0.0649848\pi\)
0.979232 + 0.202741i \(0.0649848\pi\)
\(32\) −370.145 −2.04478
\(33\) 113.348 0.597920
\(34\) −242.903 −1.22522
\(35\) 478.811 2.31240
\(36\) 1551.59 7.18328
\(37\) 41.2187 0.183144 0.0915718 0.995798i \(-0.470811\pi\)
0.0915718 + 0.995798i \(0.470811\pi\)
\(38\) 286.705 1.22394
\(39\) 540.335 2.21853
\(40\) 1098.36 4.34165
\(41\) 118.700 0.452141 0.226071 0.974111i \(-0.427412\pi\)
0.226071 + 0.974111i \(0.427412\pi\)
\(42\) −1437.41 −5.28089
\(43\) −37.1665 −0.131810 −0.0659051 0.997826i \(-0.520993\pi\)
−0.0659051 + 0.997826i \(0.520993\pi\)
\(44\) −215.553 −0.738543
\(45\) −1427.71 −4.72956
\(46\) −472.939 −1.51589
\(47\) −178.029 −0.552515 −0.276258 0.961084i \(-0.589094\pi\)
−0.276258 + 0.961084i \(0.589094\pi\)
\(48\) −1681.95 −5.05769
\(49\) 362.145 1.05582
\(50\) −1051.29 −2.97349
\(51\) −476.468 −1.30821
\(52\) −1027.55 −2.74031
\(53\) 400.501 1.03798 0.518991 0.854779i \(-0.326308\pi\)
0.518991 + 0.854779i \(0.326308\pi\)
\(54\) 2824.52 7.11793
\(55\) 198.343 0.486266
\(56\) 1617.55 3.85991
\(57\) 562.386 1.30684
\(58\) −6.23531 −0.0141161
\(59\) 248.128 0.547516 0.273758 0.961799i \(-0.411733\pi\)
0.273758 + 0.961799i \(0.411733\pi\)
\(60\) 3640.89 7.83395
\(61\) −821.226 −1.72373 −0.861863 0.507142i \(-0.830702\pi\)
−0.861863 + 0.507142i \(0.830702\pi\)
\(62\) −1775.74 −3.63741
\(63\) −2102.59 −4.20478
\(64\) 638.615 1.24730
\(65\) 945.512 1.80425
\(66\) −595.436 −1.11050
\(67\) 1013.90 1.84878 0.924389 0.381450i \(-0.124575\pi\)
0.924389 + 0.381450i \(0.124575\pi\)
\(68\) 906.096 1.61589
\(69\) −927.694 −1.61857
\(70\) −2515.27 −4.29475
\(71\) 1106.36 1.84930 0.924650 0.380819i \(-0.124358\pi\)
0.924650 + 0.380819i \(0.124358\pi\)
\(72\) −4823.19 −7.89470
\(73\) 135.623 0.217445 0.108722 0.994072i \(-0.465324\pi\)
0.108722 + 0.994072i \(0.465324\pi\)
\(74\) −216.529 −0.340148
\(75\) −2062.16 −3.17490
\(76\) −1069.49 −1.61419
\(77\) 292.100 0.432311
\(78\) −2838.47 −4.12043
\(79\) −937.852 −1.33565 −0.667826 0.744317i \(-0.732775\pi\)
−0.667826 + 0.744317i \(0.732775\pi\)
\(80\) −2943.19 −4.11323
\(81\) 3402.59 4.66747
\(82\) −623.549 −0.839750
\(83\) 571.167 0.755347 0.377673 0.925939i \(-0.376724\pi\)
0.377673 + 0.925939i \(0.376724\pi\)
\(84\) 5361.94 6.96471
\(85\) −833.753 −1.06392
\(86\) 195.242 0.244808
\(87\) −12.2309 −0.0150723
\(88\) 670.058 0.811687
\(89\) −661.609 −0.787982 −0.393991 0.919114i \(-0.628906\pi\)
−0.393991 + 0.919114i \(0.628906\pi\)
\(90\) 7499.99 8.78409
\(91\) 1392.46 1.60406
\(92\) 1764.19 1.99924
\(93\) −3483.21 −3.88378
\(94\) 935.217 1.02617
\(95\) 984.098 1.06280
\(96\) 3814.11 4.05496
\(97\) −1572.44 −1.64595 −0.822975 0.568077i \(-0.807688\pi\)
−0.822975 + 0.568077i \(0.807688\pi\)
\(98\) −1902.41 −1.96094
\(99\) −870.978 −0.884208
\(100\) 3921.59 3.92159
\(101\) −288.683 −0.284407 −0.142203 0.989837i \(-0.545419\pi\)
−0.142203 + 0.989837i \(0.545419\pi\)
\(102\) 2502.96 2.42971
\(103\) 294.115 0.281359 0.140680 0.990055i \(-0.455071\pi\)
0.140680 + 0.990055i \(0.455071\pi\)
\(104\) 3194.20 3.01170
\(105\) −4933.84 −4.58565
\(106\) −2103.90 −1.92782
\(107\) −921.288 −0.832377 −0.416188 0.909278i \(-0.636634\pi\)
−0.416188 + 0.909278i \(0.636634\pi\)
\(108\) −10536.2 −9.38749
\(109\) −1495.06 −1.31376 −0.656882 0.753993i \(-0.728125\pi\)
−0.656882 + 0.753993i \(0.728125\pi\)
\(110\) −1041.93 −0.903129
\(111\) −424.732 −0.363187
\(112\) −4334.43 −3.65683
\(113\) −1330.59 −1.10771 −0.553854 0.832613i \(-0.686844\pi\)
−0.553854 + 0.832613i \(0.686844\pi\)
\(114\) −2954.31 −2.42716
\(115\) −1623.34 −1.31632
\(116\) 23.2594 0.0186171
\(117\) −4151.99 −3.28079
\(118\) −1303.46 −1.01689
\(119\) −1227.87 −0.945870
\(120\) −11317.9 −8.60982
\(121\) 121.000 0.0909091
\(122\) 4314.04 3.20143
\(123\) −1223.12 −0.896630
\(124\) 6624.00 4.79720
\(125\) −1354.59 −0.969265
\(126\) 11045.2 7.80942
\(127\) −2152.08 −1.50367 −0.751836 0.659350i \(-0.770831\pi\)
−0.751836 + 0.659350i \(0.770831\pi\)
\(128\) −393.590 −0.271787
\(129\) 382.977 0.261390
\(130\) −4966.93 −3.35099
\(131\) −131.000 −0.0873704
\(132\) 2221.14 1.46459
\(133\) 1449.28 0.944877
\(134\) −5326.21 −3.43369
\(135\) 9695.01 6.18084
\(136\) −2816.65 −1.77592
\(137\) −359.725 −0.224331 −0.112166 0.993690i \(-0.535779\pi\)
−0.112166 + 0.993690i \(0.535779\pi\)
\(138\) 4873.33 3.00613
\(139\) −331.298 −0.202160 −0.101080 0.994878i \(-0.532230\pi\)
−0.101080 + 0.994878i \(0.532230\pi\)
\(140\) 9382.66 5.66414
\(141\) 1834.48 1.09568
\(142\) −5811.87 −3.43466
\(143\) 576.813 0.337311
\(144\) 12924.3 7.47935
\(145\) −21.4024 −0.0122577
\(146\) −712.449 −0.403854
\(147\) −3731.67 −2.09376
\(148\) 807.711 0.448605
\(149\) 1458.87 0.802116 0.401058 0.916053i \(-0.368643\pi\)
0.401058 + 0.916053i \(0.368643\pi\)
\(150\) 10832.8 5.89666
\(151\) 1101.94 0.593870 0.296935 0.954898i \(-0.404035\pi\)
0.296935 + 0.954898i \(0.404035\pi\)
\(152\) 3324.55 1.77406
\(153\) 3661.23 1.93459
\(154\) −1534.45 −0.802919
\(155\) −6095.13 −3.15854
\(156\) 10588.3 5.43423
\(157\) −2392.66 −1.21627 −0.608136 0.793833i \(-0.708083\pi\)
−0.608136 + 0.793833i \(0.708083\pi\)
\(158\) 4926.69 2.48067
\(159\) −4126.91 −2.05840
\(160\) 6674.17 3.29775
\(161\) −2390.69 −1.17027
\(162\) −17874.4 −8.66878
\(163\) 1891.68 0.909003 0.454502 0.890746i \(-0.349817\pi\)
0.454502 + 0.890746i \(0.349817\pi\)
\(164\) 2326.01 1.10751
\(165\) −2043.80 −0.964301
\(166\) −3000.44 −1.40289
\(167\) 1363.39 0.631751 0.315876 0.948801i \(-0.397702\pi\)
0.315876 + 0.948801i \(0.397702\pi\)
\(168\) −16667.9 −7.65449
\(169\) 552.694 0.251568
\(170\) 4379.84 1.97599
\(171\) −4321.43 −1.93256
\(172\) −728.306 −0.322865
\(173\) −2391.24 −1.05088 −0.525441 0.850830i \(-0.676100\pi\)
−0.525441 + 0.850830i \(0.676100\pi\)
\(174\) 64.2509 0.0279934
\(175\) −5314.22 −2.29553
\(176\) −1795.50 −0.768983
\(177\) −2556.80 −1.08577
\(178\) 3475.54 1.46350
\(179\) −2773.35 −1.15804 −0.579022 0.815312i \(-0.696566\pi\)
−0.579022 + 0.815312i \(0.696566\pi\)
\(180\) −27977.0 −11.5849
\(181\) 2734.39 1.12290 0.561452 0.827510i \(-0.310243\pi\)
0.561452 + 0.827510i \(0.310243\pi\)
\(182\) −7314.80 −2.97917
\(183\) 8462.21 3.41828
\(184\) −5484.08 −2.19724
\(185\) −743.223 −0.295367
\(186\) 18297.9 7.21325
\(187\) −508.634 −0.198904
\(188\) −3488.62 −1.35337
\(189\) 14277.8 5.49503
\(190\) −5169.63 −1.97392
\(191\) 1191.84 0.451511 0.225755 0.974184i \(-0.427515\pi\)
0.225755 + 0.974184i \(0.427515\pi\)
\(192\) −6580.52 −2.47348
\(193\) 1765.14 0.658330 0.329165 0.944273i \(-0.393233\pi\)
0.329165 + 0.944273i \(0.393233\pi\)
\(194\) 8260.29 3.05698
\(195\) −9742.90 −3.57797
\(196\) 7096.50 2.58619
\(197\) 912.644 0.330067 0.165033 0.986288i \(-0.447227\pi\)
0.165033 + 0.986288i \(0.447227\pi\)
\(198\) 4575.39 1.64222
\(199\) 896.640 0.319403 0.159701 0.987165i \(-0.448947\pi\)
0.159701 + 0.987165i \(0.448947\pi\)
\(200\) −12190.5 −4.30998
\(201\) −10447.6 −3.66627
\(202\) 1516.50 0.528221
\(203\) −31.5193 −0.0108976
\(204\) −9336.74 −3.20442
\(205\) −2140.30 −0.729195
\(206\) −1545.03 −0.522561
\(207\) 7128.50 2.39355
\(208\) −8559.24 −2.85325
\(209\) 600.352 0.198695
\(210\) 25918.3 8.51682
\(211\) −4030.23 −1.31494 −0.657471 0.753480i \(-0.728374\pi\)
−0.657471 + 0.753480i \(0.728374\pi\)
\(212\) 7848.12 2.54251
\(213\) −11400.3 −3.66730
\(214\) 4839.68 1.54595
\(215\) 670.157 0.212578
\(216\) 32752.4 10.3172
\(217\) −8976.30 −2.80807
\(218\) 7853.78 2.44002
\(219\) −1397.51 −0.431209
\(220\) 3886.69 1.19109
\(221\) −2424.68 −0.738017
\(222\) 2231.19 0.674539
\(223\) 1376.31 0.413294 0.206647 0.978416i \(-0.433745\pi\)
0.206647 + 0.978416i \(0.433745\pi\)
\(224\) 9829.04 2.93183
\(225\) 15845.8 4.69506
\(226\) 6989.79 2.05732
\(227\) 6010.26 1.75734 0.878668 0.477434i \(-0.158433\pi\)
0.878668 + 0.477434i \(0.158433\pi\)
\(228\) 11020.4 3.20106
\(229\) 950.777 0.274363 0.137182 0.990546i \(-0.456196\pi\)
0.137182 + 0.990546i \(0.456196\pi\)
\(230\) 8527.66 2.44477
\(231\) −3009.91 −0.857304
\(232\) −72.3031 −0.0204609
\(233\) 3643.61 1.02447 0.512233 0.858847i \(-0.328818\pi\)
0.512233 + 0.858847i \(0.328818\pi\)
\(234\) 21811.1 6.09332
\(235\) 3210.08 0.891075
\(236\) 4862.25 1.34112
\(237\) 9663.96 2.64870
\(238\) 6450.19 1.75674
\(239\) 4709.78 1.27469 0.637344 0.770580i \(-0.280033\pi\)
0.637344 + 0.770580i \(0.280033\pi\)
\(240\) 30327.7 8.15684
\(241\) −1340.56 −0.358312 −0.179156 0.983821i \(-0.557337\pi\)
−0.179156 + 0.983821i \(0.557337\pi\)
\(242\) −635.633 −0.168843
\(243\) −20544.1 −5.42348
\(244\) −16092.5 −4.22221
\(245\) −6529.91 −1.70278
\(246\) 6425.28 1.66529
\(247\) 2861.91 0.737242
\(248\) −20591.0 −5.27231
\(249\) −5885.51 −1.49791
\(250\) 7115.88 1.80019
\(251\) 7691.36 1.93416 0.967081 0.254470i \(-0.0819011\pi\)
0.967081 + 0.254470i \(0.0819011\pi\)
\(252\) −41201.7 −10.2995
\(253\) −990.322 −0.246091
\(254\) 11305.2 2.79273
\(255\) 8591.29 2.10983
\(256\) −3041.33 −0.742512
\(257\) 488.551 0.118580 0.0592898 0.998241i \(-0.481116\pi\)
0.0592898 + 0.998241i \(0.481116\pi\)
\(258\) −2011.84 −0.485472
\(259\) −1094.54 −0.262593
\(260\) 18528.0 4.41946
\(261\) 93.9835 0.0222890
\(262\) 688.165 0.162271
\(263\) 7447.01 1.74602 0.873008 0.487707i \(-0.162166\pi\)
0.873008 + 0.487707i \(0.162166\pi\)
\(264\) −6904.52 −1.60964
\(265\) −7221.53 −1.67402
\(266\) −7613.31 −1.75490
\(267\) 6817.45 1.56263
\(268\) 19868.2 4.52852
\(269\) −3643.94 −0.825928 −0.412964 0.910747i \(-0.635506\pi\)
−0.412964 + 0.910747i \(0.635506\pi\)
\(270\) −50929.5 −11.4795
\(271\) 1331.18 0.298388 0.149194 0.988808i \(-0.452332\pi\)
0.149194 + 0.988808i \(0.452332\pi\)
\(272\) 7547.54 1.68249
\(273\) −14348.4 −3.18096
\(274\) 1889.69 0.416644
\(275\) −2201.37 −0.482719
\(276\) −18178.9 −3.96463
\(277\) 1231.42 0.267108 0.133554 0.991042i \(-0.457361\pi\)
0.133554 + 0.991042i \(0.457361\pi\)
\(278\) 1740.36 0.375467
\(279\) 26765.3 5.74337
\(280\) −29166.5 −6.22511
\(281\) −1325.64 −0.281427 −0.140713 0.990050i \(-0.544940\pi\)
−0.140713 + 0.990050i \(0.544940\pi\)
\(282\) −9636.81 −2.03498
\(283\) −6903.64 −1.45010 −0.725051 0.688695i \(-0.758184\pi\)
−0.725051 + 0.688695i \(0.758184\pi\)
\(284\) 21679.9 4.52980
\(285\) −10140.5 −2.10762
\(286\) −3030.09 −0.626480
\(287\) −3152.02 −0.648285
\(288\) −29308.0 −5.99650
\(289\) −2774.91 −0.564811
\(290\) 112.430 0.0227660
\(291\) 16203.0 3.26404
\(292\) 2657.63 0.532624
\(293\) 6137.32 1.22371 0.611853 0.790972i \(-0.290424\pi\)
0.611853 + 0.790972i \(0.290424\pi\)
\(294\) 19603.1 3.88869
\(295\) −4474.04 −0.883013
\(296\) −2510.81 −0.493034
\(297\) 5914.47 1.15553
\(298\) −7663.68 −1.48975
\(299\) −4720.91 −0.913102
\(300\) −40409.5 −7.77681
\(301\) 986.941 0.188991
\(302\) −5788.66 −1.10298
\(303\) 2974.70 0.564000
\(304\) −8908.54 −1.68072
\(305\) 14807.7 2.77996
\(306\) −19233.0 −3.59307
\(307\) −7323.78 −1.36153 −0.680765 0.732502i \(-0.738353\pi\)
−0.680765 + 0.732502i \(0.738353\pi\)
\(308\) 5723.92 1.05893
\(309\) −3030.66 −0.557956
\(310\) 32018.8 5.86627
\(311\) 144.219 0.0262955 0.0131478 0.999914i \(-0.495815\pi\)
0.0131478 + 0.999914i \(0.495815\pi\)
\(312\) −32914.2 −5.97243
\(313\) −311.122 −0.0561841 −0.0280921 0.999605i \(-0.508943\pi\)
−0.0280921 + 0.999605i \(0.508943\pi\)
\(314\) 12569.0 2.25895
\(315\) 37912.2 6.78130
\(316\) −18377.9 −3.27164
\(317\) −36.5280 −0.00647198 −0.00323599 0.999995i \(-0.501030\pi\)
−0.00323599 + 0.999995i \(0.501030\pi\)
\(318\) 21679.3 3.82301
\(319\) −13.0566 −0.00229163
\(320\) −11515.0 −2.01159
\(321\) 9493.28 1.65067
\(322\) 12558.7 2.17350
\(323\) −2523.63 −0.434733
\(324\) 66676.2 11.4328
\(325\) −10494.0 −1.79109
\(326\) −9937.29 −1.68827
\(327\) 15405.6 2.60529
\(328\) −7230.52 −1.21719
\(329\) 4727.49 0.792203
\(330\) 10736.4 1.79097
\(331\) −448.958 −0.0745528 −0.0372764 0.999305i \(-0.511868\pi\)
−0.0372764 + 0.999305i \(0.511868\pi\)
\(332\) 11192.5 1.85020
\(333\) 3263.69 0.537084
\(334\) −7162.12 −1.17334
\(335\) −18281.9 −2.98164
\(336\) 44663.5 7.25177
\(337\) 383.787 0.0620363 0.0310181 0.999519i \(-0.490125\pi\)
0.0310181 + 0.999519i \(0.490125\pi\)
\(338\) −2903.39 −0.467230
\(339\) 13710.8 2.19667
\(340\) −16338.0 −2.60604
\(341\) −3718.36 −0.590499
\(342\) 22701.2 3.58930
\(343\) −508.388 −0.0800302
\(344\) 2263.97 0.354841
\(345\) 16727.5 2.61036
\(346\) 12561.6 1.95178
\(347\) 1808.94 0.279852 0.139926 0.990162i \(-0.455313\pi\)
0.139926 + 0.990162i \(0.455313\pi\)
\(348\) −239.673 −0.0369191
\(349\) −6265.06 −0.960920 −0.480460 0.877017i \(-0.659530\pi\)
−0.480460 + 0.877017i \(0.659530\pi\)
\(350\) 27916.5 4.26343
\(351\) 28194.6 4.28751
\(352\) 4071.60 0.616525
\(353\) −6086.08 −0.917647 −0.458823 0.888528i \(-0.651729\pi\)
−0.458823 + 0.888528i \(0.651729\pi\)
\(354\) 13431.3 2.01657
\(355\) −19948.9 −2.98248
\(356\) −12964.7 −1.93014
\(357\) 12652.4 1.87573
\(358\) 14568.9 2.15081
\(359\) −2719.51 −0.399805 −0.199903 0.979816i \(-0.564063\pi\)
−0.199903 + 0.979816i \(0.564063\pi\)
\(360\) 86968.0 12.7323
\(361\) −3880.30 −0.565724
\(362\) −14364.2 −2.08554
\(363\) −1246.83 −0.180280
\(364\) 27286.2 3.92908
\(365\) −2445.44 −0.350686
\(366\) −44453.4 −6.34868
\(367\) 1885.98 0.268249 0.134124 0.990965i \(-0.457178\pi\)
0.134124 + 0.990965i \(0.457178\pi\)
\(368\) 14695.2 2.08164
\(369\) 9398.62 1.32594
\(370\) 3904.28 0.548577
\(371\) −10635.1 −1.48827
\(372\) −68256.0 −9.51320
\(373\) 8088.95 1.12287 0.561434 0.827521i \(-0.310250\pi\)
0.561434 + 0.827521i \(0.310250\pi\)
\(374\) 2671.94 0.369419
\(375\) 13958.2 1.92213
\(376\) 10844.5 1.48741
\(377\) −62.2414 −0.00850290
\(378\) −75003.9 −10.2058
\(379\) 1700.65 0.230491 0.115246 0.993337i \(-0.463234\pi\)
0.115246 + 0.993337i \(0.463234\pi\)
\(380\) 19284.1 2.60330
\(381\) 22175.8 2.98189
\(382\) −6260.93 −0.838579
\(383\) −3374.25 −0.450173 −0.225087 0.974339i \(-0.572266\pi\)
−0.225087 + 0.974339i \(0.572266\pi\)
\(384\) 4055.69 0.538974
\(385\) −5266.92 −0.697213
\(386\) −9272.58 −1.22270
\(387\) −2942.84 −0.386545
\(388\) −30813.2 −4.03170
\(389\) 3288.47 0.428617 0.214308 0.976766i \(-0.431250\pi\)
0.214308 + 0.976766i \(0.431250\pi\)
\(390\) 51181.1 6.64527
\(391\) 4162.90 0.538432
\(392\) −22059.8 −2.84232
\(393\) 1349.87 0.173262
\(394\) −4794.27 −0.613025
\(395\) 16910.6 2.15409
\(396\) −17067.5 −2.16584
\(397\) −5625.62 −0.711189 −0.355594 0.934640i \(-0.615722\pi\)
−0.355594 + 0.934640i \(0.615722\pi\)
\(398\) −4710.20 −0.593219
\(399\) −14933.9 −1.87376
\(400\) 32665.8 4.08323
\(401\) −4724.62 −0.588370 −0.294185 0.955748i \(-0.595048\pi\)
−0.294185 + 0.955748i \(0.595048\pi\)
\(402\) 54883.2 6.80926
\(403\) −17725.6 −2.19100
\(404\) −5656.97 −0.696645
\(405\) −61352.8 −7.52752
\(406\) 165.576 0.0202399
\(407\) −453.406 −0.0552199
\(408\) 29023.7 3.52179
\(409\) 15299.5 1.84966 0.924831 0.380379i \(-0.124207\pi\)
0.924831 + 0.380379i \(0.124207\pi\)
\(410\) 11243.4 1.35432
\(411\) 3706.73 0.444865
\(412\) 5763.40 0.689180
\(413\) −6588.92 −0.785036
\(414\) −37447.2 −4.44548
\(415\) −10298.8 −1.21819
\(416\) 19409.5 2.28757
\(417\) 3413.81 0.400899
\(418\) −3153.75 −0.369031
\(419\) −9422.96 −1.09867 −0.549334 0.835603i \(-0.685118\pi\)
−0.549334 + 0.835603i \(0.685118\pi\)
\(420\) −96682.3 −11.2324
\(421\) −9248.30 −1.07063 −0.535314 0.844653i \(-0.679807\pi\)
−0.535314 + 0.844653i \(0.679807\pi\)
\(422\) 21171.5 2.44221
\(423\) −14096.3 −1.62030
\(424\) −24396.3 −2.79431
\(425\) 9253.65 1.05616
\(426\) 59887.6 6.81118
\(427\) 21807.3 2.47150
\(428\) −18053.3 −2.03888
\(429\) −5943.69 −0.668913
\(430\) −3520.45 −0.394816
\(431\) −2945.15 −0.329149 −0.164574 0.986365i \(-0.552625\pi\)
−0.164574 + 0.986365i \(0.552625\pi\)
\(432\) −87764.0 −9.77441
\(433\) −761.565 −0.0845231 −0.0422615 0.999107i \(-0.513456\pi\)
−0.0422615 + 0.999107i \(0.513456\pi\)
\(434\) 47154.0 5.21536
\(435\) 220.538 0.0243080
\(436\) −29296.7 −3.21803
\(437\) −4913.57 −0.537867
\(438\) 7341.33 0.800873
\(439\) −7594.12 −0.825621 −0.412810 0.910817i \(-0.635453\pi\)
−0.412810 + 0.910817i \(0.635453\pi\)
\(440\) −12082.0 −1.30906
\(441\) 28674.6 3.09627
\(442\) 12737.3 1.37070
\(443\) −15935.7 −1.70909 −0.854547 0.519375i \(-0.826165\pi\)
−0.854547 + 0.519375i \(0.826165\pi\)
\(444\) −8322.95 −0.889616
\(445\) 11929.6 1.27083
\(446\) −7229.99 −0.767601
\(447\) −15032.7 −1.59066
\(448\) −16958.1 −1.78839
\(449\) 2666.73 0.280291 0.140145 0.990131i \(-0.455243\pi\)
0.140145 + 0.990131i \(0.455243\pi\)
\(450\) −83240.8 −8.72002
\(451\) −1305.70 −0.136326
\(452\) −26073.9 −2.71330
\(453\) −11354.8 −1.17769
\(454\) −31572.9 −3.26385
\(455\) −25107.7 −2.58696
\(456\) −34257.4 −3.51809
\(457\) 12124.3 1.24103 0.620514 0.784196i \(-0.286924\pi\)
0.620514 + 0.784196i \(0.286924\pi\)
\(458\) −4994.59 −0.509567
\(459\) −24862.0 −2.52823
\(460\) −31810.5 −3.22429
\(461\) 2888.14 0.291788 0.145894 0.989300i \(-0.453394\pi\)
0.145894 + 0.989300i \(0.453394\pi\)
\(462\) 15811.5 1.59225
\(463\) −3588.29 −0.360177 −0.180089 0.983650i \(-0.557638\pi\)
−0.180089 + 0.983650i \(0.557638\pi\)
\(464\) 193.745 0.0193844
\(465\) 62806.5 6.26361
\(466\) −19140.5 −1.90271
\(467\) −9595.62 −0.950819 −0.475409 0.879765i \(-0.657700\pi\)
−0.475409 + 0.879765i \(0.657700\pi\)
\(468\) −81361.4 −8.03618
\(469\) −26923.8 −2.65080
\(470\) −16863.1 −1.65497
\(471\) 24654.8 2.41196
\(472\) −15114.5 −1.47395
\(473\) 408.832 0.0397423
\(474\) −50766.4 −4.91936
\(475\) −10922.3 −1.05505
\(476\) −24061.0 −2.31688
\(477\) 31711.6 3.04397
\(478\) −24741.2 −2.36744
\(479\) −598.125 −0.0570544 −0.0285272 0.999593i \(-0.509082\pi\)
−0.0285272 + 0.999593i \(0.509082\pi\)
\(480\) −68773.0 −6.53967
\(481\) −2161.41 −0.204889
\(482\) 7042.20 0.665484
\(483\) 24634.5 2.32072
\(484\) 2371.09 0.222679
\(485\) 28353.0 2.65452
\(486\) 107922. 10.0729
\(487\) 19555.6 1.81961 0.909803 0.415040i \(-0.136232\pi\)
0.909803 + 0.415040i \(0.136232\pi\)
\(488\) 50024.5 4.64037
\(489\) −19492.5 −1.80262
\(490\) 34302.7 3.16253
\(491\) 2751.54 0.252903 0.126451 0.991973i \(-0.459641\pi\)
0.126451 + 0.991973i \(0.459641\pi\)
\(492\) −23968.0 −2.19627
\(493\) 54.8845 0.00501394
\(494\) −15034.1 −1.36926
\(495\) 15704.8 1.42602
\(496\) 55176.1 4.99492
\(497\) −29378.8 −2.65155
\(498\) 30917.6 2.78203
\(499\) −6253.61 −0.561022 −0.280511 0.959851i \(-0.590504\pi\)
−0.280511 + 0.959851i \(0.590504\pi\)
\(500\) −26544.2 −2.37418
\(501\) −14048.9 −1.25281
\(502\) −40404.0 −3.59227
\(503\) −13371.7 −1.18532 −0.592660 0.805453i \(-0.701922\pi\)
−0.592660 + 0.805453i \(0.701922\pi\)
\(504\) 128078. 11.3195
\(505\) 5205.31 0.458680
\(506\) 5202.33 0.457059
\(507\) −5695.16 −0.498878
\(508\) −42171.6 −3.68320
\(509\) 3054.44 0.265984 0.132992 0.991117i \(-0.457542\pi\)
0.132992 + 0.991117i \(0.457542\pi\)
\(510\) −45131.5 −3.91854
\(511\) −3601.41 −0.311775
\(512\) 19125.3 1.65084
\(513\) 29345.2 2.52558
\(514\) −2566.44 −0.220235
\(515\) −5303.25 −0.453765
\(516\) 7504.72 0.640265
\(517\) 1958.32 0.166590
\(518\) 5749.83 0.487708
\(519\) 24640.2 2.08398
\(520\) −57595.3 −4.85716
\(521\) −7104.61 −0.597426 −0.298713 0.954343i \(-0.596557\pi\)
−0.298713 + 0.954343i \(0.596557\pi\)
\(522\) −493.711 −0.0413968
\(523\) 13914.0 1.16332 0.581659 0.813432i \(-0.302404\pi\)
0.581659 + 0.813432i \(0.302404\pi\)
\(524\) −2567.04 −0.214011
\(525\) 54759.7 4.55221
\(526\) −39120.4 −3.24283
\(527\) 15630.4 1.29198
\(528\) 18501.5 1.52495
\(529\) −4061.73 −0.333831
\(530\) 37935.9 3.10911
\(531\) 19646.7 1.60564
\(532\) 28399.8 2.31445
\(533\) −6224.32 −0.505826
\(534\) −35813.2 −2.90223
\(535\) 16611.9 1.34242
\(536\) −61761.4 −4.97702
\(537\) 28577.6 2.29649
\(538\) 19142.2 1.53398
\(539\) −3983.60 −0.318341
\(540\) 189981. 15.1398
\(541\) −11856.1 −0.942204 −0.471102 0.882079i \(-0.656144\pi\)
−0.471102 + 0.882079i \(0.656144\pi\)
\(542\) −6992.90 −0.554189
\(543\) −28176.1 −2.22680
\(544\) −17115.3 −1.34892
\(545\) 26957.7 2.11879
\(546\) 75374.3 5.90792
\(547\) 17085.6 1.33552 0.667759 0.744377i \(-0.267254\pi\)
0.667759 + 0.744377i \(0.267254\pi\)
\(548\) −7049.07 −0.549492
\(549\) −65024.5 −5.05497
\(550\) 11564.2 0.896541
\(551\) −64.7814 −0.00500868
\(552\) 56509.9 4.35729
\(553\) 24904.2 1.91507
\(554\) −6468.85 −0.496093
\(555\) 7658.44 0.585735
\(556\) −6492.02 −0.495185
\(557\) −5297.40 −0.402977 −0.201488 0.979491i \(-0.564578\pi\)
−0.201488 + 0.979491i \(0.564578\pi\)
\(558\) −140603. −10.6670
\(559\) 1948.92 0.147461
\(560\) 78155.1 5.89760
\(561\) 5241.14 0.394441
\(562\) 6963.79 0.522686
\(563\) −8731.83 −0.653646 −0.326823 0.945086i \(-0.605978\pi\)
−0.326823 + 0.945086i \(0.605978\pi\)
\(564\) 35947.9 2.68383
\(565\) 23992.1 1.78647
\(566\) 36266.0 2.69324
\(567\) −90354.2 −6.69228
\(568\) −67393.0 −4.97843
\(569\) −19113.1 −1.40819 −0.704097 0.710104i \(-0.748648\pi\)
−0.704097 + 0.710104i \(0.748648\pi\)
\(570\) 53269.7 3.91443
\(571\) −6190.18 −0.453679 −0.226840 0.973932i \(-0.572839\pi\)
−0.226840 + 0.973932i \(0.572839\pi\)
\(572\) 11303.1 0.826233
\(573\) −12281.1 −0.895379
\(574\) 16558.1 1.20404
\(575\) 18017.1 1.30672
\(576\) 50565.4 3.65780
\(577\) −16328.4 −1.17810 −0.589048 0.808098i \(-0.700497\pi\)
−0.589048 + 0.808098i \(0.700497\pi\)
\(578\) 14577.1 1.04901
\(579\) −18188.6 −1.30552
\(580\) −419.396 −0.0300249
\(581\) −15167.1 −1.08302
\(582\) −85117.0 −6.06222
\(583\) −4405.52 −0.312964
\(584\) −8261.38 −0.585374
\(585\) 74865.5 5.29112
\(586\) −32240.3 −2.27276
\(587\) 6242.77 0.438955 0.219478 0.975618i \(-0.429565\pi\)
0.219478 + 0.975618i \(0.429565\pi\)
\(588\) −73124.9 −5.12861
\(589\) −18449.0 −1.29062
\(590\) 23502.9 1.64000
\(591\) −9404.21 −0.654547
\(592\) 6728.02 0.467094
\(593\) −3872.35 −0.268159 −0.134080 0.990971i \(-0.542808\pi\)
−0.134080 + 0.990971i \(0.542808\pi\)
\(594\) −31069.7 −2.14614
\(595\) 22140.0 1.52546
\(596\) 28587.6 1.96476
\(597\) −9239.30 −0.633400
\(598\) 24799.7 1.69588
\(599\) 16072.9 1.09636 0.548181 0.836360i \(-0.315321\pi\)
0.548181 + 0.836360i \(0.315321\pi\)
\(600\) 125615. 8.54702
\(601\) −8869.90 −0.602014 −0.301007 0.953622i \(-0.597323\pi\)
−0.301007 + 0.953622i \(0.597323\pi\)
\(602\) −5184.56 −0.351008
\(603\) 80280.8 5.42170
\(604\) 21593.3 1.45467
\(605\) −2181.78 −0.146615
\(606\) −15626.6 −1.04750
\(607\) 18799.9 1.25711 0.628555 0.777765i \(-0.283647\pi\)
0.628555 + 0.777765i \(0.283647\pi\)
\(608\) 20201.6 1.34750
\(609\) 324.786 0.0216108
\(610\) −77787.3 −5.16314
\(611\) 9335.41 0.618118
\(612\) 71744.5 4.73873
\(613\) −8847.63 −0.582956 −0.291478 0.956577i \(-0.594147\pi\)
−0.291478 + 0.956577i \(0.594147\pi\)
\(614\) 38473.0 2.52874
\(615\) 22054.4 1.44605
\(616\) −17793.1 −1.16381
\(617\) −23869.9 −1.55748 −0.778742 0.627345i \(-0.784142\pi\)
−0.778742 + 0.627345i \(0.784142\pi\)
\(618\) 15920.6 1.03628
\(619\) 3144.64 0.204190 0.102095 0.994775i \(-0.467445\pi\)
0.102095 + 0.994775i \(0.467445\pi\)
\(620\) −119439. −7.73673
\(621\) −48406.9 −3.12802
\(622\) −757.606 −0.0488380
\(623\) 17568.7 1.12982
\(624\) 88197.5 5.65821
\(625\) −590.697 −0.0378046
\(626\) 1634.37 0.104349
\(627\) −6186.25 −0.394027
\(628\) −46885.9 −2.97922
\(629\) 1905.93 0.120818
\(630\) −199159. −12.5947
\(631\) 2817.93 0.177781 0.0888906 0.996041i \(-0.471668\pi\)
0.0888906 + 0.996041i \(0.471668\pi\)
\(632\) 57128.6 3.59566
\(633\) 41529.0 2.60763
\(634\) 191.888 0.0120202
\(635\) 38804.6 2.42506
\(636\) −80869.9 −5.04198
\(637\) −18990.0 −1.18118
\(638\) 68.5884 0.00425618
\(639\) 87601.0 5.42323
\(640\) 7096.90 0.438327
\(641\) 8231.21 0.507197 0.253598 0.967310i \(-0.418386\pi\)
0.253598 + 0.967310i \(0.418386\pi\)
\(642\) −49869.8 −3.06574
\(643\) −19131.1 −1.17334 −0.586669 0.809827i \(-0.699561\pi\)
−0.586669 + 0.809827i \(0.699561\pi\)
\(644\) −46847.3 −2.86653
\(645\) −6905.54 −0.421559
\(646\) 13257.1 0.807418
\(647\) −14599.5 −0.887118 −0.443559 0.896245i \(-0.646284\pi\)
−0.443559 + 0.896245i \(0.646284\pi\)
\(648\) −207266. −12.5651
\(649\) −2729.40 −0.165082
\(650\) 55126.9 3.32655
\(651\) 92495.1 5.56861
\(652\) 37068.8 2.22657
\(653\) 17773.9 1.06516 0.532579 0.846380i \(-0.321223\pi\)
0.532579 + 0.846380i \(0.321223\pi\)
\(654\) −80928.1 −4.83875
\(655\) 2362.09 0.140908
\(656\) 19375.0 1.15315
\(657\) 10738.6 0.637675
\(658\) −24834.3 −1.47134
\(659\) 1956.76 0.115667 0.0578334 0.998326i \(-0.481581\pi\)
0.0578334 + 0.998326i \(0.481581\pi\)
\(660\) −40049.8 −2.36203
\(661\) 19708.5 1.15971 0.579856 0.814719i \(-0.303109\pi\)
0.579856 + 0.814719i \(0.303109\pi\)
\(662\) 2358.45 0.138465
\(663\) 24984.8 1.46354
\(664\) −34792.3 −2.03344
\(665\) −26132.3 −1.52386
\(666\) −17144.7 −0.997513
\(667\) 106.861 0.00620343
\(668\) 26716.7 1.54745
\(669\) −14182.0 −0.819594
\(670\) 96038.0 5.53772
\(671\) 9033.49 0.519723
\(672\) −101282. −5.81404
\(673\) 28994.4 1.66070 0.830350 0.557243i \(-0.188141\pi\)
0.830350 + 0.557243i \(0.188141\pi\)
\(674\) −2016.10 −0.115218
\(675\) −107603. −6.13576
\(676\) 10830.5 0.616207
\(677\) 18754.0 1.06466 0.532331 0.846536i \(-0.321316\pi\)
0.532331 + 0.846536i \(0.321316\pi\)
\(678\) −72025.4 −4.07982
\(679\) 41755.5 2.35998
\(680\) 50787.6 2.86414
\(681\) −61931.9 −3.48493
\(682\) 19533.1 1.09672
\(683\) 28623.5 1.60358 0.801792 0.597603i \(-0.203880\pi\)
0.801792 + 0.597603i \(0.203880\pi\)
\(684\) −84681.7 −4.73375
\(685\) 6486.27 0.361792
\(686\) 2670.65 0.148638
\(687\) −9797.15 −0.544082
\(688\) −6066.59 −0.336172
\(689\) −21001.3 −1.16123
\(690\) −87872.1 −4.84816
\(691\) 11584.4 0.637760 0.318880 0.947795i \(-0.396693\pi\)
0.318880 + 0.947795i \(0.396693\pi\)
\(692\) −46858.1 −2.57410
\(693\) 23128.4 1.26779
\(694\) −9502.64 −0.519763
\(695\) 5973.70 0.326036
\(696\) 745.037 0.0405755
\(697\) 5488.61 0.298272
\(698\) 32911.4 1.78469
\(699\) −37545.0 −2.03159
\(700\) −104136. −5.62283
\(701\) −2377.63 −0.128106 −0.0640528 0.997947i \(-0.520403\pi\)
−0.0640528 + 0.997947i \(0.520403\pi\)
\(702\) −148111. −7.96308
\(703\) −2249.61 −0.120691
\(704\) −7024.77 −0.376074
\(705\) −33077.8 −1.76707
\(706\) 31971.2 1.70432
\(707\) 7665.86 0.407786
\(708\) −50102.3 −2.65955
\(709\) 23464.5 1.24292 0.621459 0.783447i \(-0.286540\pi\)
0.621459 + 0.783447i \(0.286540\pi\)
\(710\) 104795. 5.53928
\(711\) −74258.9 −3.91691
\(712\) 40301.5 2.12129
\(713\) 30432.8 1.59848
\(714\) −66465.1 −3.48375
\(715\) −10400.6 −0.544002
\(716\) −54345.9 −2.83659
\(717\) −48531.3 −2.52780
\(718\) 14286.0 0.742548
\(719\) 14661.0 0.760450 0.380225 0.924894i \(-0.375847\pi\)
0.380225 + 0.924894i \(0.375847\pi\)
\(720\) −233041. −12.0624
\(721\) −7810.09 −0.403416
\(722\) 20383.9 1.05070
\(723\) 13813.6 0.710560
\(724\) 53582.4 2.75052
\(725\) 237.540 0.0121683
\(726\) 6549.79 0.334829
\(727\) −6763.57 −0.345044 −0.172522 0.985006i \(-0.555192\pi\)
−0.172522 + 0.985006i \(0.555192\pi\)
\(728\) −84820.6 −4.31821
\(729\) 119824. 6.08770
\(730\) 12846.3 0.651320
\(731\) −1718.56 −0.0869537
\(732\) 165823. 8.37296
\(733\) −5061.03 −0.255025 −0.127513 0.991837i \(-0.540699\pi\)
−0.127513 + 0.991837i \(0.540699\pi\)
\(734\) −9907.36 −0.498212
\(735\) 67286.6 3.37674
\(736\) −33323.9 −1.66893
\(737\) −11153.0 −0.557428
\(738\) −49372.5 −2.46264
\(739\) 810.711 0.0403552 0.0201776 0.999796i \(-0.493577\pi\)
0.0201776 + 0.999796i \(0.493577\pi\)
\(740\) −14564.0 −0.723492
\(741\) −29490.1 −1.46201
\(742\) 55868.2 2.76413
\(743\) −26504.2 −1.30868 −0.654338 0.756202i \(-0.727053\pi\)
−0.654338 + 0.756202i \(0.727053\pi\)
\(744\) 212177. 10.4554
\(745\) −26305.2 −1.29362
\(746\) −42492.6 −2.08548
\(747\) 45224.9 2.21512
\(748\) −9967.06 −0.487208
\(749\) 24464.4 1.19347
\(750\) −73324.6 −3.56991
\(751\) −23325.4 −1.13336 −0.566681 0.823937i \(-0.691773\pi\)
−0.566681 + 0.823937i \(0.691773\pi\)
\(752\) −29059.2 −1.40915
\(753\) −79254.6 −3.83559
\(754\) 326.964 0.0157922
\(755\) −19869.3 −0.957771
\(756\) 279785. 13.4599
\(757\) −10859.7 −0.521404 −0.260702 0.965419i \(-0.583954\pi\)
−0.260702 + 0.965419i \(0.583954\pi\)
\(758\) −8933.77 −0.428086
\(759\) 10204.6 0.488017
\(760\) −59945.7 −2.86113
\(761\) −20851.8 −0.993268 −0.496634 0.867960i \(-0.665431\pi\)
−0.496634 + 0.867960i \(0.665431\pi\)
\(762\) −116493. −5.53819
\(763\) 39700.6 1.88369
\(764\) 23355.0 1.10596
\(765\) −66016.4 −3.12004
\(766\) 17725.5 0.836095
\(767\) −13011.2 −0.612526
\(768\) 31339.0 1.47246
\(769\) 676.476 0.0317222 0.0158611 0.999874i \(-0.494951\pi\)
0.0158611 + 0.999874i \(0.494951\pi\)
\(770\) 27668.0 1.29492
\(771\) −5034.20 −0.235152
\(772\) 34589.2 1.61256
\(773\) −2661.71 −0.123849 −0.0619243 0.998081i \(-0.519724\pi\)
−0.0619243 + 0.998081i \(0.519724\pi\)
\(774\) 15459.2 0.717920
\(775\) 67648.6 3.13550
\(776\) 95784.3 4.43100
\(777\) 11278.6 0.520743
\(778\) −17274.9 −0.796059
\(779\) −6478.33 −0.297959
\(780\) −190919. −8.76412
\(781\) −12169.9 −0.557585
\(782\) −21868.4 −1.00002
\(783\) −638.205 −0.0291285
\(784\) 59112.0 2.69278
\(785\) 43142.5 1.96156
\(786\) −7091.10 −0.321795
\(787\) −34881.3 −1.57991 −0.789953 0.613168i \(-0.789895\pi\)
−0.789953 + 0.613168i \(0.789895\pi\)
\(788\) 17883.9 0.808489
\(789\) −76736.6 −3.46248
\(790\) −88834.2 −4.00073
\(791\) 35333.2 1.58825
\(792\) 53055.1 2.38034
\(793\) 43063.1 1.92839
\(794\) 29552.3 1.32087
\(795\) 74413.2 3.31970
\(796\) 17570.3 0.782367
\(797\) 24661.6 1.09606 0.548029 0.836460i \(-0.315378\pi\)
0.548029 + 0.836460i \(0.315378\pi\)
\(798\) 78450.3 3.48009
\(799\) −8231.97 −0.364488
\(800\) −74075.2 −3.27369
\(801\) −52386.0 −2.31082
\(802\) 24819.2 1.09277
\(803\) −1491.85 −0.0655620
\(804\) −204729. −8.98040
\(805\) 43107.0 1.88736
\(806\) 93115.4 4.06929
\(807\) 37548.4 1.63788
\(808\) 17585.0 0.765640
\(809\) −4938.85 −0.214636 −0.107318 0.994225i \(-0.534226\pi\)
−0.107318 + 0.994225i \(0.534226\pi\)
\(810\) 322296. 13.9807
\(811\) −8438.73 −0.365381 −0.182691 0.983170i \(-0.558481\pi\)
−0.182691 + 0.983170i \(0.558481\pi\)
\(812\) −617.644 −0.0266934
\(813\) −13716.9 −0.591727
\(814\) 2381.82 0.102558
\(815\) −34109.2 −1.46600
\(816\) −77772.6 −3.33650
\(817\) 2028.45 0.0868625
\(818\) −80370.8 −3.43533
\(819\) 110254. 4.70403
\(820\) −41940.8 −1.78614
\(821\) −45452.7 −1.93217 −0.966085 0.258226i \(-0.916862\pi\)
−0.966085 + 0.258226i \(0.916862\pi\)
\(822\) −19472.1 −0.826237
\(823\) −7760.32 −0.328685 −0.164343 0.986403i \(-0.552550\pi\)
−0.164343 + 0.986403i \(0.552550\pi\)
\(824\) −17915.8 −0.757436
\(825\) 22683.7 0.957268
\(826\) 34612.7 1.45803
\(827\) −22977.0 −0.966128 −0.483064 0.875585i \(-0.660476\pi\)
−0.483064 + 0.875585i \(0.660476\pi\)
\(828\) 139688. 5.86293
\(829\) −18121.6 −0.759215 −0.379608 0.925148i \(-0.623941\pi\)
−0.379608 + 0.925148i \(0.623941\pi\)
\(830\) 54101.5 2.26252
\(831\) −12689.0 −0.529695
\(832\) −33487.4 −1.39539
\(833\) 16745.4 0.696510
\(834\) −17933.3 −0.744580
\(835\) −24583.6 −1.01886
\(836\) 11764.4 0.486697
\(837\) −181753. −7.50574
\(838\) 49500.4 2.04053
\(839\) −9255.04 −0.380834 −0.190417 0.981703i \(-0.560984\pi\)
−0.190417 + 0.981703i \(0.560984\pi\)
\(840\) 300542. 12.3449
\(841\) −24387.6 −0.999942
\(842\) 48582.9 1.98845
\(843\) 13659.8 0.558090
\(844\) −78975.5 −3.22091
\(845\) −9965.75 −0.405719
\(846\) 74050.3 3.00934
\(847\) −3213.10 −0.130347
\(848\) 65372.8 2.64730
\(849\) 71137.6 2.87566
\(850\) −48611.0 −1.96158
\(851\) 3710.89 0.149480
\(852\) −223397. −8.98293
\(853\) −44511.4 −1.78668 −0.893341 0.449379i \(-0.851645\pi\)
−0.893341 + 0.449379i \(0.851645\pi\)
\(854\) −114557. −4.59025
\(855\) 77920.7 3.11676
\(856\) 56119.7 2.24081
\(857\) −37149.7 −1.48076 −0.740379 0.672190i \(-0.765354\pi\)
−0.740379 + 0.672190i \(0.765354\pi\)
\(858\) 31223.2 1.24236
\(859\) 27146.6 1.07827 0.539133 0.842220i \(-0.318752\pi\)
0.539133 + 0.842220i \(0.318752\pi\)
\(860\) 13132.2 0.520704
\(861\) 32479.5 1.28560
\(862\) 15471.4 0.611320
\(863\) 16993.5 0.670296 0.335148 0.942166i \(-0.391214\pi\)
0.335148 + 0.942166i \(0.391214\pi\)
\(864\) 199019. 7.83655
\(865\) 43117.0 1.69482
\(866\) 4000.63 0.156983
\(867\) 28593.7 1.12006
\(868\) −175897. −6.87828
\(869\) 10316.4 0.402714
\(870\) −1158.52 −0.0451466
\(871\) −53166.7 −2.06829
\(872\) 91070.4 3.53673
\(873\) −124506. −4.82689
\(874\) 25811.8 0.998967
\(875\) 35970.5 1.38974
\(876\) −27385.2 −1.05623
\(877\) 39952.2 1.53830 0.769150 0.639068i \(-0.220680\pi\)
0.769150 + 0.639068i \(0.220680\pi\)
\(878\) 39893.2 1.53340
\(879\) −63241.1 −2.42670
\(880\) 32375.1 1.24019
\(881\) 40344.2 1.54283 0.771414 0.636334i \(-0.219550\pi\)
0.771414 + 0.636334i \(0.219550\pi\)
\(882\) −150632. −5.75063
\(883\) 5405.53 0.206014 0.103007 0.994681i \(-0.467154\pi\)
0.103007 + 0.994681i \(0.467154\pi\)
\(884\) −47513.4 −1.80775
\(885\) 46102.1 1.75108
\(886\) 83712.9 3.17426
\(887\) −12719.4 −0.481482 −0.240741 0.970589i \(-0.577390\pi\)
−0.240741 + 0.970589i \(0.577390\pi\)
\(888\) 25872.3 0.977723
\(889\) 57147.6 2.15598
\(890\) −62668.2 −2.36027
\(891\) −37428.5 −1.40730
\(892\) 26969.9 1.01235
\(893\) 9716.39 0.364106
\(894\) 78969.3 2.95428
\(895\) 50006.9 1.86765
\(896\) 10451.6 0.389691
\(897\) 48646.0 1.81075
\(898\) −14008.8 −0.520577
\(899\) 401.232 0.0148852
\(900\) 310511. 11.5004
\(901\) 18519.0 0.684746
\(902\) 6859.04 0.253194
\(903\) −10169.8 −0.374783
\(904\) 81051.9 2.98202
\(905\) −49304.3 −1.81097
\(906\) 59648.4 2.18729
\(907\) 25564.8 0.935903 0.467951 0.883754i \(-0.344992\pi\)
0.467951 + 0.883754i \(0.344992\pi\)
\(908\) 117776. 4.30454
\(909\) −22857.9 −0.834047
\(910\) 131895. 4.80469
\(911\) −29932.0 −1.08857 −0.544287 0.838899i \(-0.683200\pi\)
−0.544287 + 0.838899i \(0.683200\pi\)
\(912\) 91796.8 3.33300
\(913\) −6282.84 −0.227746
\(914\) −63690.8 −2.30493
\(915\) −152584. −5.51286
\(916\) 18631.2 0.672044
\(917\) 3478.65 0.125273
\(918\) 130604. 4.69562
\(919\) 2575.54 0.0924473 0.0462237 0.998931i \(-0.485281\pi\)
0.0462237 + 0.998931i \(0.485281\pi\)
\(920\) 98884.6 3.54362
\(921\) 75466.8 2.70002
\(922\) −15171.9 −0.541930
\(923\) −58014.6 −2.06888
\(924\) −58981.3 −2.09994
\(925\) 8248.88 0.293212
\(926\) 18849.9 0.668948
\(927\) 23288.0 0.825110
\(928\) −439.348 −0.0155413
\(929\) −51485.6 −1.81829 −0.909143 0.416484i \(-0.863262\pi\)
−0.909143 + 0.416484i \(0.863262\pi\)
\(930\) −329933. −11.6332
\(931\) −19765.0 −0.695779
\(932\) 71399.2 2.50940
\(933\) −1486.08 −0.0521460
\(934\) 50407.4 1.76593
\(935\) 9171.28 0.320784
\(936\) 252916. 8.83207
\(937\) 8752.34 0.305151 0.152576 0.988292i \(-0.451243\pi\)
0.152576 + 0.988292i \(0.451243\pi\)
\(938\) 141435. 4.92326
\(939\) 3205.91 0.111417
\(940\) 62904.0 2.18266
\(941\) 3020.57 0.104642 0.0523209 0.998630i \(-0.483338\pi\)
0.0523209 + 0.998630i \(0.483338\pi\)
\(942\) −129516. −4.47967
\(943\) 10686.5 0.369034
\(944\) 40501.2 1.39640
\(945\) −257447. −8.86217
\(946\) −2147.66 −0.0738123
\(947\) 46077.2 1.58111 0.790554 0.612393i \(-0.209793\pi\)
0.790554 + 0.612393i \(0.209793\pi\)
\(948\) 189372. 6.48790
\(949\) −7111.73 −0.243263
\(950\) 57376.7 1.95952
\(951\) 376.398 0.0128344
\(952\) 74794.8 2.54634
\(953\) −36480.0 −1.23998 −0.619992 0.784608i \(-0.712864\pi\)
−0.619992 + 0.784608i \(0.712864\pi\)
\(954\) −166586. −5.65349
\(955\) −21490.3 −0.728179
\(956\) 92291.6 3.12231
\(957\) 134.540 0.00454446
\(958\) 3142.05 0.105966
\(959\) 9552.33 0.321648
\(960\) 118655. 3.98913
\(961\) 84474.9 2.83558
\(962\) 11354.2 0.380535
\(963\) −72947.4 −2.44102
\(964\) −26269.3 −0.877675
\(965\) −31827.6 −1.06173
\(966\) −129409. −4.31022
\(967\) −41754.4 −1.38855 −0.694276 0.719709i \(-0.744275\pi\)
−0.694276 + 0.719709i \(0.744275\pi\)
\(968\) −7370.64 −0.244733
\(969\) 26004.4 0.862107
\(970\) −148943. −4.93018
\(971\) −48507.4 −1.60317 −0.801584 0.597883i \(-0.796009\pi\)
−0.801584 + 0.597883i \(0.796009\pi\)
\(972\) −402578. −13.2847
\(973\) 8797.46 0.289860
\(974\) −102729. −3.37951
\(975\) 108134. 3.55187
\(976\) −134047. −4.39624
\(977\) −39888.5 −1.30619 −0.653095 0.757276i \(-0.726530\pi\)
−0.653095 + 0.757276i \(0.726530\pi\)
\(978\) 102397. 3.34796
\(979\) 7277.70 0.237585
\(980\) −127959. −4.17090
\(981\) −118378. −3.85273
\(982\) −14454.3 −0.469709
\(983\) 18002.1 0.584108 0.292054 0.956402i \(-0.405661\pi\)
0.292054 + 0.956402i \(0.405661\pi\)
\(984\) 74505.9 2.41378
\(985\) −16456.1 −0.532319
\(986\) −288.317 −0.00931226
\(987\) −48713.7 −1.57100
\(988\) 56081.2 1.80585
\(989\) −3346.07 −0.107582
\(990\) −82499.9 −2.64850
\(991\) 3175.07 0.101775 0.0508877 0.998704i \(-0.483795\pi\)
0.0508877 + 0.998704i \(0.483795\pi\)
\(992\) −125121. −4.00463
\(993\) 4626.23 0.147844
\(994\) 154332. 4.92465
\(995\) −16167.5 −0.515120
\(996\) −115331. −3.66908
\(997\) 33079.8 1.05080 0.525400 0.850856i \(-0.323916\pi\)
0.525400 + 0.850856i \(0.323916\pi\)
\(998\) 32851.2 1.04197
\(999\) −22162.5 −0.701891
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1441.4.a.c.1.3 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.4.a.c.1.3 84 1.1 even 1 trivial