Properties

Label 1849.4.a.j.1.46
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $50$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(109.094531601\)
Analytic rank: \(1\)
Dimension: \(50\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.46
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.85844 q^{2} +5.73018 q^{3} +15.6044 q^{4} -14.4569 q^{5} +27.8397 q^{6} +13.1859 q^{7} +36.9457 q^{8} +5.83494 q^{9} +O(q^{10})\) \(q+4.85844 q^{2} +5.73018 q^{3} +15.6044 q^{4} -14.4569 q^{5} +27.8397 q^{6} +13.1859 q^{7} +36.9457 q^{8} +5.83494 q^{9} -70.2380 q^{10} -56.6297 q^{11} +89.4162 q^{12} -68.5859 q^{13} +64.0631 q^{14} -82.8407 q^{15} +54.6629 q^{16} +23.3842 q^{17} +28.3487 q^{18} +119.755 q^{19} -225.592 q^{20} +75.5578 q^{21} -275.132 q^{22} -49.8515 q^{23} +211.705 q^{24} +84.0024 q^{25} -333.220 q^{26} -121.280 q^{27} +205.759 q^{28} -290.660 q^{29} -402.477 q^{30} +58.9050 q^{31} -29.9890 q^{32} -324.498 q^{33} +113.611 q^{34} -190.628 q^{35} +91.0510 q^{36} -147.330 q^{37} +581.820 q^{38} -393.009 q^{39} -534.121 q^{40} +216.626 q^{41} +367.093 q^{42} -883.674 q^{44} -84.3552 q^{45} -242.201 q^{46} -233.374 q^{47} +313.228 q^{48} -169.131 q^{49} +408.121 q^{50} +133.996 q^{51} -1070.24 q^{52} +712.940 q^{53} -589.229 q^{54} +818.690 q^{55} +487.164 q^{56} +686.215 q^{57} -1412.15 q^{58} +70.0677 q^{59} -1292.68 q^{60} -328.266 q^{61} +286.186 q^{62} +76.9392 q^{63} -583.003 q^{64} +991.541 q^{65} -1576.55 q^{66} +307.039 q^{67} +364.898 q^{68} -285.658 q^{69} -926.155 q^{70} -1135.63 q^{71} +215.576 q^{72} -203.220 q^{73} -715.792 q^{74} +481.349 q^{75} +1868.70 q^{76} -746.715 q^{77} -1909.41 q^{78} +255.296 q^{79} -790.257 q^{80} -852.497 q^{81} +1052.47 q^{82} +665.658 q^{83} +1179.04 q^{84} -338.064 q^{85} -1665.53 q^{87} -2092.22 q^{88} +834.098 q^{89} -409.835 q^{90} -904.369 q^{91} -777.905 q^{92} +337.536 q^{93} -1133.83 q^{94} -1731.28 q^{95} -171.842 q^{96} +817.923 q^{97} -821.713 q^{98} -330.431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} + 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} + 386q^{18} - 12q^{19} - 108q^{20} - 408q^{21} - 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} - 1493q^{26} - 10q^{27} + 242q^{28} - 208q^{29} + 48q^{30} - 932q^{31} + 1124q^{32} - 254q^{33} - 765q^{34} - 1452q^{35} + 747q^{36} + 90q^{37} - 1213q^{38} + 1610q^{39} - 1693q^{40} - 1354q^{41} + 16q^{42} - 2704q^{44} - 4508q^{45} - 233q^{46} - 3484q^{47} + 376q^{48} + 1324q^{49} + 408q^{50} - 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} + 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} - 1172q^{61} + 1546q^{62} + 3686q^{63} + 606q^{64} - 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} - 136q^{69} + 1310q^{70} - 162q^{71} + 5814q^{72} - 746q^{73} - 4332q^{74} - 236q^{75} - 1338q^{76} - 2024q^{77} - 2782q^{78} - 2656q^{79} + 5713q^{80} - 86q^{81} + 4168q^{82} - 3514q^{83} - 4269q^{84} + 7558q^{85} - 10278q^{87} - 11692q^{88} - 2640q^{89} - 8286q^{90} + 5946q^{91} - 4271q^{92} + 2q^{93} - 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} + 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.85844 1.71772 0.858859 0.512212i \(-0.171174\pi\)
0.858859 + 0.512212i \(0.171174\pi\)
\(3\) 5.73018 1.10277 0.551387 0.834250i \(-0.314099\pi\)
0.551387 + 0.834250i \(0.314099\pi\)
\(4\) 15.6044 1.95055
\(5\) −14.4569 −1.29307 −0.646533 0.762886i \(-0.723782\pi\)
−0.646533 + 0.762886i \(0.723782\pi\)
\(6\) 27.8397 1.89425
\(7\) 13.1859 0.711974 0.355987 0.934491i \(-0.384145\pi\)
0.355987 + 0.934491i \(0.384145\pi\)
\(8\) 36.9457 1.63278
\(9\) 5.83494 0.216109
\(10\) −70.2380 −2.22112
\(11\) −56.6297 −1.55223 −0.776113 0.630594i \(-0.782811\pi\)
−0.776113 + 0.630594i \(0.782811\pi\)
\(12\) 89.4162 2.15102
\(13\) −68.5859 −1.46325 −0.731627 0.681705i \(-0.761239\pi\)
−0.731627 + 0.681705i \(0.761239\pi\)
\(14\) 64.0631 1.22297
\(15\) −82.8407 −1.42596
\(16\) 54.6629 0.854108
\(17\) 23.3842 0.333618 0.166809 0.985989i \(-0.446654\pi\)
0.166809 + 0.985989i \(0.446654\pi\)
\(18\) 28.3487 0.371214
\(19\) 119.755 1.44598 0.722989 0.690859i \(-0.242768\pi\)
0.722989 + 0.690859i \(0.242768\pi\)
\(20\) −225.592 −2.52220
\(21\) 75.5578 0.785146
\(22\) −275.132 −2.66629
\(23\) −49.8515 −0.451946 −0.225973 0.974134i \(-0.572556\pi\)
−0.225973 + 0.974134i \(0.572556\pi\)
\(24\) 211.705 1.80059
\(25\) 84.0024 0.672019
\(26\) −333.220 −2.51346
\(27\) −121.280 −0.864454
\(28\) 205.759 1.38874
\(29\) −290.660 −1.86118 −0.930590 0.366064i \(-0.880705\pi\)
−0.930590 + 0.366064i \(0.880705\pi\)
\(30\) −402.477 −2.44939
\(31\) 58.9050 0.341279 0.170639 0.985334i \(-0.445417\pi\)
0.170639 + 0.985334i \(0.445417\pi\)
\(32\) −29.9890 −0.165667
\(33\) −324.498 −1.71175
\(34\) 113.611 0.573062
\(35\) −190.628 −0.920629
\(36\) 91.0510 0.421532
\(37\) −147.330 −0.654617 −0.327309 0.944918i \(-0.606142\pi\)
−0.327309 + 0.944918i \(0.606142\pi\)
\(38\) 581.820 2.48378
\(39\) −393.009 −1.61364
\(40\) −534.121 −2.11130
\(41\) 216.626 0.825154 0.412577 0.910923i \(-0.364629\pi\)
0.412577 + 0.910923i \(0.364629\pi\)
\(42\) 367.093 1.34866
\(43\) 0 0
\(44\) −883.674 −3.02770
\(45\) −84.3552 −0.279443
\(46\) −242.201 −0.776316
\(47\) −233.374 −0.724277 −0.362139 0.932124i \(-0.617953\pi\)
−0.362139 + 0.932124i \(0.617953\pi\)
\(48\) 313.228 0.941888
\(49\) −169.131 −0.493093
\(50\) 408.121 1.15434
\(51\) 133.996 0.367905
\(52\) −1070.24 −2.85416
\(53\) 712.940 1.84773 0.923866 0.382716i \(-0.125011\pi\)
0.923866 + 0.382716i \(0.125011\pi\)
\(54\) −589.229 −1.48489
\(55\) 818.690 2.00713
\(56\) 487.164 1.16250
\(57\) 686.215 1.59459
\(58\) −1412.15 −3.19698
\(59\) 70.0677 0.154611 0.0773054 0.997007i \(-0.475368\pi\)
0.0773054 + 0.997007i \(0.475368\pi\)
\(60\) −1292.68 −2.78141
\(61\) −328.266 −0.689019 −0.344509 0.938783i \(-0.611955\pi\)
−0.344509 + 0.938783i \(0.611955\pi\)
\(62\) 286.186 0.586221
\(63\) 76.9392 0.153864
\(64\) −583.003 −1.13868
\(65\) 991.541 1.89208
\(66\) −1576.55 −2.94031
\(67\) 307.039 0.559863 0.279932 0.960020i \(-0.409688\pi\)
0.279932 + 0.960020i \(0.409688\pi\)
\(68\) 364.898 0.650740
\(69\) −285.658 −0.498394
\(70\) −926.155 −1.58138
\(71\) −1135.63 −1.89823 −0.949114 0.314933i \(-0.898018\pi\)
−0.949114 + 0.314933i \(0.898018\pi\)
\(72\) 215.576 0.352859
\(73\) −203.220 −0.325824 −0.162912 0.986641i \(-0.552089\pi\)
−0.162912 + 0.986641i \(0.552089\pi\)
\(74\) −715.792 −1.12445
\(75\) 481.349 0.741085
\(76\) 1868.70 2.82046
\(77\) −746.715 −1.10514
\(78\) −1909.41 −2.77177
\(79\) 255.296 0.363583 0.181791 0.983337i \(-0.441810\pi\)
0.181791 + 0.983337i \(0.441810\pi\)
\(80\) −790.257 −1.10442
\(81\) −852.497 −1.16941
\(82\) 1052.47 1.41738
\(83\) 665.658 0.880306 0.440153 0.897923i \(-0.354924\pi\)
0.440153 + 0.897923i \(0.354924\pi\)
\(84\) 1179.04 1.53147
\(85\) −338.064 −0.431390
\(86\) 0 0
\(87\) −1665.53 −2.05246
\(88\) −2092.22 −2.53445
\(89\) 834.098 0.993419 0.496709 0.867917i \(-0.334542\pi\)
0.496709 + 0.867917i \(0.334542\pi\)
\(90\) −409.835 −0.480004
\(91\) −904.369 −1.04180
\(92\) −777.905 −0.881545
\(93\) 337.536 0.376353
\(94\) −1133.83 −1.24410
\(95\) −1731.28 −1.86974
\(96\) −171.842 −0.182693
\(97\) 817.923 0.856160 0.428080 0.903741i \(-0.359190\pi\)
0.428080 + 0.903741i \(0.359190\pi\)
\(98\) −821.713 −0.846995
\(99\) −330.431 −0.335450
\(100\) 1310.81 1.31081
\(101\) −642.462 −0.632944 −0.316472 0.948602i \(-0.602498\pi\)
−0.316472 + 0.948602i \(0.602498\pi\)
\(102\) 651.010 0.631957
\(103\) 76.9496 0.0736123 0.0368062 0.999322i \(-0.488282\pi\)
0.0368062 + 0.999322i \(0.488282\pi\)
\(104\) −2533.95 −2.38918
\(105\) −1092.33 −1.01524
\(106\) 3463.77 3.17388
\(107\) −843.742 −0.762315 −0.381157 0.924510i \(-0.624474\pi\)
−0.381157 + 0.924510i \(0.624474\pi\)
\(108\) −1892.50 −1.68616
\(109\) −1162.50 −1.02154 −0.510769 0.859718i \(-0.670639\pi\)
−0.510769 + 0.859718i \(0.670639\pi\)
\(110\) 3977.56 3.44768
\(111\) −844.225 −0.721894
\(112\) 720.782 0.608103
\(113\) −884.391 −0.736252 −0.368126 0.929776i \(-0.620001\pi\)
−0.368126 + 0.929776i \(0.620001\pi\)
\(114\) 3333.93 2.73905
\(115\) 720.699 0.584396
\(116\) −4535.58 −3.63033
\(117\) −400.195 −0.316222
\(118\) 340.420 0.265578
\(119\) 308.343 0.237527
\(120\) −3060.61 −2.32828
\(121\) 1875.92 1.40941
\(122\) −1594.86 −1.18354
\(123\) 1241.31 0.909958
\(124\) 919.179 0.665683
\(125\) 592.699 0.424101
\(126\) 373.804 0.264295
\(127\) −582.571 −0.407046 −0.203523 0.979070i \(-0.565239\pi\)
−0.203523 + 0.979070i \(0.565239\pi\)
\(128\) −2592.57 −1.79026
\(129\) 0 0
\(130\) 4817.34 3.25007
\(131\) 903.044 0.602285 0.301142 0.953579i \(-0.402632\pi\)
0.301142 + 0.953579i \(0.402632\pi\)
\(132\) −5063.61 −3.33887
\(133\) 1579.08 1.02950
\(134\) 1491.73 0.961687
\(135\) 1753.33 1.11780
\(136\) 863.947 0.544727
\(137\) −2121.22 −1.32283 −0.661415 0.750020i \(-0.730044\pi\)
−0.661415 + 0.750020i \(0.730044\pi\)
\(138\) −1387.85 −0.856100
\(139\) 1042.17 0.635939 0.317970 0.948101i \(-0.396999\pi\)
0.317970 + 0.948101i \(0.396999\pi\)
\(140\) −2974.64 −1.79574
\(141\) −1337.27 −0.798713
\(142\) −5517.38 −3.26062
\(143\) 3884.00 2.27130
\(144\) 318.955 0.184580
\(145\) 4202.05 2.40663
\(146\) −987.334 −0.559673
\(147\) −969.151 −0.543770
\(148\) −2298.99 −1.27687
\(149\) 323.453 0.177841 0.0889205 0.996039i \(-0.471658\pi\)
0.0889205 + 0.996039i \(0.471658\pi\)
\(150\) 2338.60 1.27297
\(151\) 864.578 0.465949 0.232975 0.972483i \(-0.425154\pi\)
0.232975 + 0.972483i \(0.425154\pi\)
\(152\) 4424.42 2.36097
\(153\) 136.446 0.0720979
\(154\) −3627.87 −1.89833
\(155\) −851.584 −0.441296
\(156\) −6132.69 −3.14749
\(157\) 577.261 0.293442 0.146721 0.989178i \(-0.453128\pi\)
0.146721 + 0.989178i \(0.453128\pi\)
\(158\) 1240.34 0.624533
\(159\) 4085.27 2.03763
\(160\) 433.548 0.214219
\(161\) −657.339 −0.321774
\(162\) −4141.80 −2.00871
\(163\) 1803.66 0.866707 0.433353 0.901224i \(-0.357330\pi\)
0.433353 + 0.901224i \(0.357330\pi\)
\(164\) 3380.33 1.60951
\(165\) 4691.24 2.21341
\(166\) 3234.06 1.51212
\(167\) −2552.51 −1.18275 −0.591374 0.806397i \(-0.701414\pi\)
−0.591374 + 0.806397i \(0.701414\pi\)
\(168\) 2791.53 1.28197
\(169\) 2507.03 1.14111
\(170\) −1642.46 −0.741007
\(171\) 698.761 0.312489
\(172\) 0 0
\(173\) −676.365 −0.297243 −0.148622 0.988894i \(-0.547484\pi\)
−0.148622 + 0.988894i \(0.547484\pi\)
\(174\) −8091.89 −3.52554
\(175\) 1107.65 0.478460
\(176\) −3095.54 −1.32577
\(177\) 401.500 0.170501
\(178\) 4052.42 1.70641
\(179\) 1530.14 0.638927 0.319464 0.947598i \(-0.396497\pi\)
0.319464 + 0.947598i \(0.396497\pi\)
\(180\) −1316.32 −0.545069
\(181\) 2614.23 1.07356 0.536780 0.843722i \(-0.319641\pi\)
0.536780 + 0.843722i \(0.319641\pi\)
\(182\) −4393.82 −1.78952
\(183\) −1881.02 −0.759832
\(184\) −1841.80 −0.737930
\(185\) 2129.93 0.846463
\(186\) 1639.90 0.646469
\(187\) −1324.24 −0.517851
\(188\) −3641.66 −1.41274
\(189\) −1599.18 −0.615469
\(190\) −8411.33 −3.21169
\(191\) 3942.47 1.49355 0.746773 0.665079i \(-0.231602\pi\)
0.746773 + 0.665079i \(0.231602\pi\)
\(192\) −3340.71 −1.25570
\(193\) −80.0135 −0.0298420 −0.0149210 0.999889i \(-0.504750\pi\)
−0.0149210 + 0.999889i \(0.504750\pi\)
\(194\) 3973.83 1.47064
\(195\) 5681.70 2.08654
\(196\) −2639.19 −0.961806
\(197\) 2777.66 1.00457 0.502284 0.864703i \(-0.332493\pi\)
0.502284 + 0.864703i \(0.332493\pi\)
\(198\) −1605.38 −0.576208
\(199\) −2219.08 −0.790484 −0.395242 0.918577i \(-0.629339\pi\)
−0.395242 + 0.918577i \(0.629339\pi\)
\(200\) 3103.53 1.09726
\(201\) 1759.39 0.617402
\(202\) −3121.36 −1.08722
\(203\) −3832.62 −1.32511
\(204\) 2090.93 0.717619
\(205\) −3131.75 −1.06698
\(206\) 373.855 0.126445
\(207\) −290.881 −0.0976696
\(208\) −3749.11 −1.24978
\(209\) −6781.66 −2.24449
\(210\) −5307.03 −1.74390
\(211\) 3231.50 1.05434 0.527169 0.849760i \(-0.323253\pi\)
0.527169 + 0.849760i \(0.323253\pi\)
\(212\) 11125.0 3.60410
\(213\) −6507.35 −2.09332
\(214\) −4099.27 −1.30944
\(215\) 0 0
\(216\) −4480.76 −1.41147
\(217\) 776.717 0.242982
\(218\) −5647.96 −1.75471
\(219\) −1164.49 −0.359310
\(220\) 12775.2 3.91502
\(221\) −1603.83 −0.488168
\(222\) −4101.61 −1.24001
\(223\) −2987.09 −0.896996 −0.448498 0.893784i \(-0.648041\pi\)
−0.448498 + 0.893784i \(0.648041\pi\)
\(224\) −395.433 −0.117951
\(225\) 490.149 0.145229
\(226\) −4296.76 −1.26467
\(227\) 2015.14 0.589206 0.294603 0.955620i \(-0.404813\pi\)
0.294603 + 0.955620i \(0.404813\pi\)
\(228\) 10708.0 3.11033
\(229\) −4594.18 −1.32573 −0.662865 0.748739i \(-0.730659\pi\)
−0.662865 + 0.748739i \(0.730659\pi\)
\(230\) 3501.47 1.00383
\(231\) −4278.81 −1.21872
\(232\) −10738.6 −3.03890
\(233\) −919.717 −0.258595 −0.129298 0.991606i \(-0.541272\pi\)
−0.129298 + 0.991606i \(0.541272\pi\)
\(234\) −1944.32 −0.543181
\(235\) 3373.86 0.936538
\(236\) 1093.37 0.301577
\(237\) 1462.89 0.400950
\(238\) 1498.07 0.408005
\(239\) 1476.81 0.399695 0.199847 0.979827i \(-0.435955\pi\)
0.199847 + 0.979827i \(0.435955\pi\)
\(240\) −4528.32 −1.21792
\(241\) 5049.60 1.34968 0.674841 0.737963i \(-0.264212\pi\)
0.674841 + 0.737963i \(0.264212\pi\)
\(242\) 9114.05 2.42096
\(243\) −1610.41 −0.425135
\(244\) −5122.41 −1.34397
\(245\) 2445.11 0.637602
\(246\) 6030.81 1.56305
\(247\) −8213.48 −2.11583
\(248\) 2176.28 0.557235
\(249\) 3814.34 0.970778
\(250\) 2879.59 0.728486
\(251\) −292.300 −0.0735052 −0.0367526 0.999324i \(-0.511701\pi\)
−0.0367526 + 0.999324i \(0.511701\pi\)
\(252\) 1200.59 0.300120
\(253\) 2823.08 0.701523
\(254\) −2830.39 −0.699190
\(255\) −1937.17 −0.475726
\(256\) −7931.84 −1.93648
\(257\) 4.22507 0.00102550 0.000512749 1.00000i \(-0.499837\pi\)
0.000512749 1.00000i \(0.499837\pi\)
\(258\) 0 0
\(259\) −1942.68 −0.466070
\(260\) 15472.4 3.69061
\(261\) −1695.98 −0.402217
\(262\) 4387.38 1.03456
\(263\) −8246.98 −1.93358 −0.966788 0.255580i \(-0.917733\pi\)
−0.966788 + 0.255580i \(0.917733\pi\)
\(264\) −11988.8 −2.79492
\(265\) −10306.9 −2.38924
\(266\) 7671.85 1.76839
\(267\) 4779.53 1.09552
\(268\) 4791.18 1.09204
\(269\) 3136.78 0.710976 0.355488 0.934681i \(-0.384315\pi\)
0.355488 + 0.934681i \(0.384315\pi\)
\(270\) 8518.44 1.92006
\(271\) −1246.03 −0.279303 −0.139652 0.990201i \(-0.544598\pi\)
−0.139652 + 0.990201i \(0.544598\pi\)
\(272\) 1278.25 0.284946
\(273\) −5182.20 −1.14887
\(274\) −10305.8 −2.27225
\(275\) −4757.03 −1.04313
\(276\) −4457.53 −0.972145
\(277\) −1353.84 −0.293662 −0.146831 0.989162i \(-0.546907\pi\)
−0.146831 + 0.989162i \(0.546907\pi\)
\(278\) 5063.31 1.09236
\(279\) 343.707 0.0737534
\(280\) −7042.88 −1.50319
\(281\) −5032.93 −1.06847 −0.534234 0.845337i \(-0.679400\pi\)
−0.534234 + 0.845337i \(0.679400\pi\)
\(282\) −6497.05 −1.37196
\(283\) −1540.76 −0.323636 −0.161818 0.986821i \(-0.551736\pi\)
−0.161818 + 0.986821i \(0.551736\pi\)
\(284\) −17720.8 −3.70260
\(285\) −9920.55 −2.06190
\(286\) 18870.2 3.90146
\(287\) 2856.42 0.587488
\(288\) −174.984 −0.0358022
\(289\) −4366.18 −0.888699
\(290\) 20415.4 4.13391
\(291\) 4686.85 0.944150
\(292\) −3171.14 −0.635537
\(293\) −2032.88 −0.405331 −0.202665 0.979248i \(-0.564960\pi\)
−0.202665 + 0.979248i \(0.564960\pi\)
\(294\) −4708.56 −0.934044
\(295\) −1012.96 −0.199922
\(296\) −5443.19 −1.06885
\(297\) 6868.02 1.34183
\(298\) 1571.48 0.305481
\(299\) 3419.11 0.661312
\(300\) 7511.17 1.44553
\(301\) 0 0
\(302\) 4200.50 0.800369
\(303\) −3681.42 −0.697994
\(304\) 6546.14 1.23502
\(305\) 4745.71 0.890947
\(306\) 662.913 0.123844
\(307\) −9698.57 −1.80302 −0.901509 0.432761i \(-0.857539\pi\)
−0.901509 + 0.432761i \(0.857539\pi\)
\(308\) −11652.1 −2.15564
\(309\) 440.935 0.0811777
\(310\) −4137.37 −0.758022
\(311\) −8337.39 −1.52016 −0.760081 0.649829i \(-0.774841\pi\)
−0.760081 + 0.649829i \(0.774841\pi\)
\(312\) −14520.0 −2.63472
\(313\) 9108.79 1.64492 0.822459 0.568825i \(-0.192602\pi\)
0.822459 + 0.568825i \(0.192602\pi\)
\(314\) 2804.59 0.504051
\(315\) −1112.30 −0.198956
\(316\) 3983.75 0.709188
\(317\) 3842.07 0.680733 0.340366 0.940293i \(-0.389449\pi\)
0.340366 + 0.940293i \(0.389449\pi\)
\(318\) 19848.0 3.50007
\(319\) 16460.0 2.88897
\(320\) 8428.43 1.47239
\(321\) −4834.79 −0.840660
\(322\) −3193.64 −0.552716
\(323\) 2800.37 0.482405
\(324\) −13302.7 −2.28099
\(325\) −5761.38 −0.983335
\(326\) 8762.95 1.48876
\(327\) −6661.36 −1.12653
\(328\) 8003.40 1.34730
\(329\) −3077.25 −0.515666
\(330\) 22792.1 3.80201
\(331\) −2360.71 −0.392014 −0.196007 0.980603i \(-0.562798\pi\)
−0.196007 + 0.980603i \(0.562798\pi\)
\(332\) 10387.2 1.71709
\(333\) −859.659 −0.141469
\(334\) −12401.2 −2.03163
\(335\) −4438.84 −0.723940
\(336\) 4130.21 0.670599
\(337\) −66.5688 −0.0107603 −0.00538017 0.999986i \(-0.501713\pi\)
−0.00538017 + 0.999986i \(0.501713\pi\)
\(338\) 12180.2 1.96011
\(339\) −5067.72 −0.811919
\(340\) −5275.29 −0.841450
\(341\) −3335.77 −0.529742
\(342\) 3394.89 0.536768
\(343\) −6752.93 −1.06304
\(344\) 0 0
\(345\) 4129.73 0.644456
\(346\) −3286.08 −0.510580
\(347\) 2886.72 0.446592 0.223296 0.974751i \(-0.428318\pi\)
0.223296 + 0.974751i \(0.428318\pi\)
\(348\) −25989.7 −4.00343
\(349\) 7743.50 1.18768 0.593840 0.804583i \(-0.297611\pi\)
0.593840 + 0.804583i \(0.297611\pi\)
\(350\) 5381.45 0.821859
\(351\) 8318.07 1.26492
\(352\) 1698.27 0.257153
\(353\) −2857.45 −0.430840 −0.215420 0.976521i \(-0.569112\pi\)
−0.215420 + 0.976521i \(0.569112\pi\)
\(354\) 1950.67 0.292872
\(355\) 16417.7 2.45453
\(356\) 13015.6 1.93772
\(357\) 1766.86 0.261939
\(358\) 7434.09 1.09750
\(359\) −2242.44 −0.329670 −0.164835 0.986321i \(-0.552709\pi\)
−0.164835 + 0.986321i \(0.552709\pi\)
\(360\) −3116.56 −0.456270
\(361\) 7482.16 1.09085
\(362\) 12701.1 1.84407
\(363\) 10749.4 1.55426
\(364\) −14112.2 −2.03208
\(365\) 2937.94 0.421312
\(366\) −9138.84 −1.30518
\(367\) 11678.8 1.66111 0.830557 0.556934i \(-0.188022\pi\)
0.830557 + 0.556934i \(0.188022\pi\)
\(368\) −2725.03 −0.386011
\(369\) 1264.00 0.178323
\(370\) 10348.1 1.45398
\(371\) 9400.78 1.31554
\(372\) 5267.06 0.734097
\(373\) −4698.81 −0.652266 −0.326133 0.945324i \(-0.605746\pi\)
−0.326133 + 0.945324i \(0.605746\pi\)
\(374\) −6433.75 −0.889522
\(375\) 3396.27 0.467687
\(376\) −8622.15 −1.18259
\(377\) 19935.2 2.72338
\(378\) −7769.54 −1.05720
\(379\) 9794.57 1.32748 0.663738 0.747965i \(-0.268969\pi\)
0.663738 + 0.747965i \(0.268969\pi\)
\(380\) −27015.7 −3.64704
\(381\) −3338.24 −0.448879
\(382\) 19154.3 2.56549
\(383\) −4659.25 −0.621610 −0.310805 0.950474i \(-0.600599\pi\)
−0.310805 + 0.950474i \(0.600599\pi\)
\(384\) −14855.9 −1.97425
\(385\) 10795.2 1.42902
\(386\) −388.741 −0.0512601
\(387\) 0 0
\(388\) 12763.2 1.66999
\(389\) −15017.9 −1.95743 −0.978713 0.205236i \(-0.934204\pi\)
−0.978713 + 0.205236i \(0.934204\pi\)
\(390\) 27604.2 3.58409
\(391\) −1165.74 −0.150777
\(392\) −6248.66 −0.805115
\(393\) 5174.60 0.664184
\(394\) 13495.1 1.72557
\(395\) −3690.79 −0.470137
\(396\) −5156.19 −0.654313
\(397\) 5330.02 0.673819 0.336909 0.941537i \(-0.390618\pi\)
0.336909 + 0.941537i \(0.390618\pi\)
\(398\) −10781.3 −1.35783
\(399\) 9048.39 1.13530
\(400\) 4591.82 0.573977
\(401\) 1881.10 0.234259 0.117130 0.993117i \(-0.462631\pi\)
0.117130 + 0.993117i \(0.462631\pi\)
\(402\) 8547.89 1.06052
\(403\) −4040.05 −0.499378
\(404\) −10025.3 −1.23459
\(405\) 12324.5 1.51212
\(406\) −18620.6 −2.27617
\(407\) 8343.23 1.01611
\(408\) 4950.57 0.600710
\(409\) −8907.66 −1.07691 −0.538454 0.842655i \(-0.680991\pi\)
−0.538454 + 0.842655i \(0.680991\pi\)
\(410\) −15215.4 −1.83277
\(411\) −12154.9 −1.45878
\(412\) 1200.76 0.143585
\(413\) 923.908 0.110079
\(414\) −1413.23 −0.167769
\(415\) −9623.36 −1.13829
\(416\) 2056.82 0.242413
\(417\) 5971.81 0.701297
\(418\) −32948.3 −3.85539
\(419\) 14129.0 1.64736 0.823682 0.567052i \(-0.191916\pi\)
0.823682 + 0.567052i \(0.191916\pi\)
\(420\) −17045.2 −1.98029
\(421\) −631.853 −0.0731464 −0.0365732 0.999331i \(-0.511644\pi\)
−0.0365732 + 0.999331i \(0.511644\pi\)
\(422\) 15700.0 1.81106
\(423\) −1361.72 −0.156523
\(424\) 26340.0 3.01695
\(425\) 1964.33 0.224198
\(426\) −31615.6 −3.59572
\(427\) −4328.50 −0.490563
\(428\) −13166.1 −1.48694
\(429\) 22256.0 2.50473
\(430\) 0 0
\(431\) −1391.25 −0.155485 −0.0777426 0.996973i \(-0.524771\pi\)
−0.0777426 + 0.996973i \(0.524771\pi\)
\(432\) −6629.50 −0.738337
\(433\) 11215.1 1.24472 0.622359 0.782732i \(-0.286175\pi\)
0.622359 + 0.782732i \(0.286175\pi\)
\(434\) 3773.63 0.417374
\(435\) 24078.5 2.65396
\(436\) −18140.2 −1.99257
\(437\) −5969.95 −0.653504
\(438\) −5657.60 −0.617193
\(439\) 4321.01 0.469774 0.234887 0.972023i \(-0.424528\pi\)
0.234887 + 0.972023i \(0.424528\pi\)
\(440\) 30247.1 3.27721
\(441\) −986.870 −0.106562
\(442\) −7792.10 −0.838535
\(443\) −10333.2 −1.10823 −0.554113 0.832441i \(-0.686943\pi\)
−0.554113 + 0.832441i \(0.686943\pi\)
\(444\) −13173.6 −1.40809
\(445\) −12058.5 −1.28456
\(446\) −14512.6 −1.54079
\(447\) 1853.44 0.196118
\(448\) −7687.44 −0.810709
\(449\) −8737.55 −0.918375 −0.459188 0.888339i \(-0.651859\pi\)
−0.459188 + 0.888339i \(0.651859\pi\)
\(450\) 2381.36 0.249463
\(451\) −12267.5 −1.28083
\(452\) −13800.4 −1.43610
\(453\) 4954.18 0.513836
\(454\) 9790.45 1.01209
\(455\) 13074.4 1.34711
\(456\) 25352.7 2.60362
\(457\) −11206.6 −1.14709 −0.573545 0.819174i \(-0.694432\pi\)
−0.573545 + 0.819174i \(0.694432\pi\)
\(458\) −22320.5 −2.27723
\(459\) −2836.03 −0.288398
\(460\) 11246.1 1.13990
\(461\) −14525.7 −1.46752 −0.733762 0.679407i \(-0.762237\pi\)
−0.733762 + 0.679407i \(0.762237\pi\)
\(462\) −20788.4 −2.09342
\(463\) −4930.50 −0.494903 −0.247451 0.968900i \(-0.579593\pi\)
−0.247451 + 0.968900i \(0.579593\pi\)
\(464\) −15888.3 −1.58965
\(465\) −4879.73 −0.486649
\(466\) −4468.39 −0.444193
\(467\) −6108.04 −0.605238 −0.302619 0.953112i \(-0.597861\pi\)
−0.302619 + 0.953112i \(0.597861\pi\)
\(468\) −6244.81 −0.616809
\(469\) 4048.60 0.398608
\(470\) 16391.7 1.60871
\(471\) 3307.81 0.323600
\(472\) 2588.70 0.252446
\(473\) 0 0
\(474\) 7107.37 0.688718
\(475\) 10059.7 0.971725
\(476\) 4811.52 0.463310
\(477\) 4159.96 0.399311
\(478\) 7175.00 0.686563
\(479\) −10162.4 −0.969382 −0.484691 0.874685i \(-0.661068\pi\)
−0.484691 + 0.874685i \(0.661068\pi\)
\(480\) 2484.31 0.236235
\(481\) 10104.7 0.957871
\(482\) 24533.2 2.31837
\(483\) −3766.67 −0.354843
\(484\) 29272.7 2.74912
\(485\) −11824.6 −1.10707
\(486\) −7824.08 −0.730263
\(487\) 13884.5 1.29192 0.645961 0.763371i \(-0.276457\pi\)
0.645961 + 0.763371i \(0.276457\pi\)
\(488\) −12128.0 −1.12502
\(489\) 10335.3 0.955781
\(490\) 11879.4 1.09522
\(491\) −14658.8 −1.34733 −0.673667 0.739035i \(-0.735282\pi\)
−0.673667 + 0.739035i \(0.735282\pi\)
\(492\) 19369.9 1.77492
\(493\) −6796.86 −0.620923
\(494\) −39904.7 −3.63441
\(495\) 4777.01 0.433759
\(496\) 3219.92 0.291489
\(497\) −14974.3 −1.35149
\(498\) 18531.7 1.66752
\(499\) −15383.3 −1.38006 −0.690029 0.723782i \(-0.742402\pi\)
−0.690029 + 0.723782i \(0.742402\pi\)
\(500\) 9248.73 0.827232
\(501\) −14626.3 −1.30430
\(502\) −1420.12 −0.126261
\(503\) 12847.1 1.13882 0.569409 0.822054i \(-0.307172\pi\)
0.569409 + 0.822054i \(0.307172\pi\)
\(504\) 2842.57 0.251227
\(505\) 9288.02 0.818438
\(506\) 13715.7 1.20502
\(507\) 14365.7 1.25839
\(508\) −9090.69 −0.793965
\(509\) −14988.6 −1.30522 −0.652611 0.757693i \(-0.726326\pi\)
−0.652611 + 0.757693i \(0.726326\pi\)
\(510\) −9411.60 −0.817162
\(511\) −2679.65 −0.231978
\(512\) −17795.8 −1.53607
\(513\) −14523.8 −1.24998
\(514\) 20.5273 0.00176151
\(515\) −1112.45 −0.0951856
\(516\) 0 0
\(517\) 13215.9 1.12424
\(518\) −9438.39 −0.800577
\(519\) −3875.69 −0.327792
\(520\) 36633.2 3.08937
\(521\) −10203.3 −0.857997 −0.428998 0.903305i \(-0.641133\pi\)
−0.428998 + 0.903305i \(0.641133\pi\)
\(522\) −8239.83 −0.690896
\(523\) −5487.11 −0.458766 −0.229383 0.973336i \(-0.573671\pi\)
−0.229383 + 0.973336i \(0.573671\pi\)
\(524\) 14091.5 1.17479
\(525\) 6347.03 0.527633
\(526\) −40067.4 −3.32134
\(527\) 1377.45 0.113857
\(528\) −17738.0 −1.46202
\(529\) −9681.83 −0.795745
\(530\) −50075.5 −4.10404
\(531\) 408.841 0.0334128
\(532\) 24640.6 2.00809
\(533\) −14857.5 −1.20741
\(534\) 23221.1 1.88179
\(535\) 12197.9 0.985723
\(536\) 11343.8 0.914136
\(537\) 8767.97 0.704592
\(538\) 15239.8 1.22126
\(539\) 9577.84 0.765393
\(540\) 27359.7 2.18032
\(541\) 13269.0 1.05449 0.527245 0.849713i \(-0.323225\pi\)
0.527245 + 0.849713i \(0.323225\pi\)
\(542\) −6053.78 −0.479764
\(543\) 14980.0 1.18389
\(544\) −701.269 −0.0552696
\(545\) 16806.2 1.32092
\(546\) −25177.4 −1.97343
\(547\) 9377.89 0.733034 0.366517 0.930411i \(-0.380550\pi\)
0.366517 + 0.930411i \(0.380550\pi\)
\(548\) −33100.4 −2.58025
\(549\) −1915.41 −0.148903
\(550\) −23111.7 −1.79180
\(551\) −34807.9 −2.69122
\(552\) −10553.8 −0.813770
\(553\) 3366.32 0.258861
\(554\) −6577.55 −0.504429
\(555\) 12204.9 0.933457
\(556\) 16262.4 1.24043
\(557\) 10526.2 0.800735 0.400368 0.916355i \(-0.368882\pi\)
0.400368 + 0.916355i \(0.368882\pi\)
\(558\) 1669.88 0.126688
\(559\) 0 0
\(560\) −10420.3 −0.786317
\(561\) −7588.14 −0.571072
\(562\) −24452.2 −1.83533
\(563\) 20928.1 1.56663 0.783315 0.621625i \(-0.213527\pi\)
0.783315 + 0.621625i \(0.213527\pi\)
\(564\) −20867.4 −1.55793
\(565\) 12785.6 0.952022
\(566\) −7485.71 −0.555915
\(567\) −11241.0 −0.832586
\(568\) −41956.5 −3.09940
\(569\) −16353.3 −1.20486 −0.602431 0.798171i \(-0.705801\pi\)
−0.602431 + 0.798171i \(0.705801\pi\)
\(570\) −48198.4 −3.54177
\(571\) 4027.42 0.295171 0.147585 0.989049i \(-0.452850\pi\)
0.147585 + 0.989049i \(0.452850\pi\)
\(572\) 60607.6 4.43030
\(573\) 22591.1 1.64704
\(574\) 13877.7 1.00914
\(575\) −4187.65 −0.303716
\(576\) −3401.79 −0.246078
\(577\) −18455.6 −1.33157 −0.665786 0.746143i \(-0.731904\pi\)
−0.665786 + 0.746143i \(0.731904\pi\)
\(578\) −21212.8 −1.52653
\(579\) −458.492 −0.0329089
\(580\) 65570.6 4.69426
\(581\) 8777.32 0.626755
\(582\) 22770.8 1.62178
\(583\) −40373.5 −2.86810
\(584\) −7508.12 −0.532000
\(585\) 5785.58 0.408896
\(586\) −9876.61 −0.696244
\(587\) 12216.2 0.858974 0.429487 0.903073i \(-0.358694\pi\)
0.429487 + 0.903073i \(0.358694\pi\)
\(588\) −15123.1 −1.06065
\(589\) 7054.14 0.493482
\(590\) −4921.42 −0.343409
\(591\) 15916.5 1.10781
\(592\) −8053.47 −0.559114
\(593\) −15656.9 −1.08424 −0.542118 0.840302i \(-0.682378\pi\)
−0.542118 + 0.840302i \(0.682378\pi\)
\(594\) 33367.9 2.30488
\(595\) −4457.69 −0.307138
\(596\) 5047.31 0.346889
\(597\) −12715.7 −0.871724
\(598\) 16611.5 1.13595
\(599\) −7086.75 −0.483400 −0.241700 0.970351i \(-0.577705\pi\)
−0.241700 + 0.970351i \(0.577705\pi\)
\(600\) 17783.8 1.21003
\(601\) 4349.45 0.295204 0.147602 0.989047i \(-0.452845\pi\)
0.147602 + 0.989047i \(0.452845\pi\)
\(602\) 0 0
\(603\) 1791.56 0.120991
\(604\) 13491.2 0.908859
\(605\) −27120.0 −1.82246
\(606\) −17886.0 −1.19896
\(607\) −11528.1 −0.770860 −0.385430 0.922737i \(-0.625947\pi\)
−0.385430 + 0.922737i \(0.625947\pi\)
\(608\) −3591.32 −0.239551
\(609\) −21961.6 −1.46130
\(610\) 23056.8 1.53040
\(611\) 16006.1 1.05980
\(612\) 2129.16 0.140631
\(613\) 19355.5 1.27530 0.637652 0.770324i \(-0.279906\pi\)
0.637652 + 0.770324i \(0.279906\pi\)
\(614\) −47119.9 −3.09708
\(615\) −17945.5 −1.17664
\(616\) −27587.9 −1.80446
\(617\) −13935.0 −0.909238 −0.454619 0.890686i \(-0.650225\pi\)
−0.454619 + 0.890686i \(0.650225\pi\)
\(618\) 2142.26 0.139440
\(619\) 15495.3 1.00615 0.503075 0.864243i \(-0.332202\pi\)
0.503075 + 0.864243i \(0.332202\pi\)
\(620\) −13288.5 −0.860772
\(621\) 6045.97 0.390687
\(622\) −40506.7 −2.61121
\(623\) 10998.4 0.707288
\(624\) −21483.0 −1.37822
\(625\) −19068.9 −1.22041
\(626\) 44254.5 2.82550
\(627\) −38860.1 −2.47516
\(628\) 9007.83 0.572375
\(629\) −3445.19 −0.218392
\(630\) −5404.06 −0.341750
\(631\) −13393.6 −0.844993 −0.422496 0.906365i \(-0.638846\pi\)
−0.422496 + 0.906365i \(0.638846\pi\)
\(632\) 9432.09 0.593652
\(633\) 18517.0 1.16270
\(634\) 18666.5 1.16931
\(635\) 8422.18 0.526337
\(636\) 63748.3 3.97451
\(637\) 11600.0 0.721521
\(638\) 79969.8 4.96244
\(639\) −6626.32 −0.410224
\(640\) 37480.6 2.31492
\(641\) 2195.86 0.135306 0.0676530 0.997709i \(-0.478449\pi\)
0.0676530 + 0.997709i \(0.478449\pi\)
\(642\) −23489.6 −1.44402
\(643\) −19987.0 −1.22583 −0.612915 0.790149i \(-0.710003\pi\)
−0.612915 + 0.790149i \(0.710003\pi\)
\(644\) −10257.4 −0.627637
\(645\) 0 0
\(646\) 13605.4 0.828635
\(647\) 27112.0 1.64743 0.823713 0.567008i \(-0.191899\pi\)
0.823713 + 0.567008i \(0.191899\pi\)
\(648\) −31496.1 −1.90939
\(649\) −3967.91 −0.239991
\(650\) −27991.3 −1.68909
\(651\) 4450.73 0.267954
\(652\) 28145.0 1.69056
\(653\) 15361.6 0.920591 0.460296 0.887766i \(-0.347743\pi\)
0.460296 + 0.887766i \(0.347743\pi\)
\(654\) −32363.8 −1.93505
\(655\) −13055.2 −0.778794
\(656\) 11841.4 0.704771
\(657\) −1185.78 −0.0704134
\(658\) −14950.6 −0.885769
\(659\) −276.285 −0.0163316 −0.00816580 0.999967i \(-0.502599\pi\)
−0.00816580 + 0.999967i \(0.502599\pi\)
\(660\) 73204.2 4.31738
\(661\) 1668.69 0.0981916 0.0490958 0.998794i \(-0.484366\pi\)
0.0490958 + 0.998794i \(0.484366\pi\)
\(662\) −11469.4 −0.673369
\(663\) −9190.22 −0.538339
\(664\) 24593.2 1.43735
\(665\) −22828.6 −1.33121
\(666\) −4176.60 −0.243003
\(667\) 14489.8 0.841153
\(668\) −39830.4 −2.30701
\(669\) −17116.5 −0.989184
\(670\) −21565.9 −1.24352
\(671\) 18589.6 1.06951
\(672\) −2265.90 −0.130073
\(673\) −188.158 −0.0107770 −0.00538851 0.999985i \(-0.501715\pi\)
−0.00538851 + 0.999985i \(0.501715\pi\)
\(674\) −323.421 −0.0184832
\(675\) −10187.8 −0.580930
\(676\) 39120.7 2.22580
\(677\) 15768.2 0.895154 0.447577 0.894245i \(-0.352287\pi\)
0.447577 + 0.894245i \(0.352287\pi\)
\(678\) −24621.2 −1.39465
\(679\) 10785.1 0.609563
\(680\) −12490.0 −0.704367
\(681\) 11547.1 0.649761
\(682\) −16206.6 −0.909947
\(683\) 7660.10 0.429144 0.214572 0.976708i \(-0.431164\pi\)
0.214572 + 0.976708i \(0.431164\pi\)
\(684\) 10903.8 0.609526
\(685\) 30666.2 1.71051
\(686\) −32808.7 −1.82601
\(687\) −26325.5 −1.46198
\(688\) 0 0
\(689\) −48897.6 −2.70370
\(690\) 20064.1 1.10699
\(691\) −5645.69 −0.310814 −0.155407 0.987851i \(-0.549669\pi\)
−0.155407 + 0.987851i \(0.549669\pi\)
\(692\) −10554.3 −0.579789
\(693\) −4357.04 −0.238832
\(694\) 14025.0 0.767118
\(695\) −15066.5 −0.822311
\(696\) −61534.3 −3.35122
\(697\) 5065.64 0.275286
\(698\) 37621.3 2.04010
\(699\) −5270.14 −0.285172
\(700\) 17284.3 0.933262
\(701\) −16807.3 −0.905568 −0.452784 0.891620i \(-0.649569\pi\)
−0.452784 + 0.891620i \(0.649569\pi\)
\(702\) 40412.8 2.17277
\(703\) −17643.4 −0.946562
\(704\) 33015.3 1.76749
\(705\) 19332.8 1.03279
\(706\) −13882.7 −0.740062
\(707\) −8471.46 −0.450640
\(708\) 6265.19 0.332571
\(709\) 2473.18 0.131005 0.0655023 0.997852i \(-0.479135\pi\)
0.0655023 + 0.997852i \(0.479135\pi\)
\(710\) 79764.3 4.21620
\(711\) 1489.64 0.0785735
\(712\) 30816.3 1.62204
\(713\) −2936.50 −0.154240
\(714\) 8584.18 0.449937
\(715\) −56150.6 −2.93694
\(716\) 23877.0 1.24626
\(717\) 8462.39 0.440773
\(718\) −10894.8 −0.566280
\(719\) 1318.06 0.0683664 0.0341832 0.999416i \(-0.489117\pi\)
0.0341832 + 0.999416i \(0.489117\pi\)
\(720\) −4611.10 −0.238675
\(721\) 1014.65 0.0524100
\(722\) 36351.6 1.87378
\(723\) 28935.1 1.48839
\(724\) 40793.6 2.09404
\(725\) −24416.1 −1.25075
\(726\) 52225.1 2.66977
\(727\) 29579.7 1.50901 0.754505 0.656294i \(-0.227877\pi\)
0.754505 + 0.656294i \(0.227877\pi\)
\(728\) −33412.6 −1.70103
\(729\) 13789.5 0.700578
\(730\) 14273.8 0.723695
\(731\) 0 0
\(732\) −29352.3 −1.48209
\(733\) −20648.4 −1.04047 −0.520237 0.854022i \(-0.674156\pi\)
−0.520237 + 0.854022i \(0.674156\pi\)
\(734\) 56740.8 2.85332
\(735\) 14010.9 0.703131
\(736\) 1495.00 0.0748727
\(737\) −17387.5 −0.869035
\(738\) 6141.07 0.306309
\(739\) −412.419 −0.0205292 −0.0102646 0.999947i \(-0.503267\pi\)
−0.0102646 + 0.999947i \(0.503267\pi\)
\(740\) 33236.4 1.65107
\(741\) −47064.7 −2.33328
\(742\) 45673.1 2.25972
\(743\) 5178.96 0.255717 0.127858 0.991792i \(-0.459190\pi\)
0.127858 + 0.991792i \(0.459190\pi\)
\(744\) 12470.5 0.614504
\(745\) −4676.14 −0.229960
\(746\) −22828.9 −1.12041
\(747\) 3884.07 0.190242
\(748\) −20664.0 −1.01010
\(749\) −11125.5 −0.542748
\(750\) 16500.6 0.803355
\(751\) 34622.1 1.68226 0.841132 0.540831i \(-0.181890\pi\)
0.841132 + 0.540831i \(0.181890\pi\)
\(752\) −12756.9 −0.618611
\(753\) −1674.93 −0.0810596
\(754\) 96853.8 4.67800
\(755\) −12499.1 −0.602503
\(756\) −24954.4 −1.20051
\(757\) 18507.3 0.888585 0.444292 0.895882i \(-0.353455\pi\)
0.444292 + 0.895882i \(0.353455\pi\)
\(758\) 47586.4 2.28023
\(759\) 16176.7 0.773620
\(760\) −63963.4 −3.05289
\(761\) 20023.6 0.953817 0.476909 0.878953i \(-0.341757\pi\)
0.476909 + 0.878953i \(0.341757\pi\)
\(762\) −16218.6 −0.771048
\(763\) −15328.7 −0.727309
\(764\) 61520.0 2.91324
\(765\) −1972.58 −0.0932273
\(766\) −22636.7 −1.06775
\(767\) −4805.66 −0.226235
\(768\) −45450.8 −2.13550
\(769\) −16391.2 −0.768636 −0.384318 0.923201i \(-0.625563\pi\)
−0.384318 + 0.923201i \(0.625563\pi\)
\(770\) 52447.8 2.45466
\(771\) 24.2104 0.00113089
\(772\) −1248.57 −0.0582084
\(773\) −21244.9 −0.988519 −0.494260 0.869314i \(-0.664561\pi\)
−0.494260 + 0.869314i \(0.664561\pi\)
\(774\) 0 0
\(775\) 4948.16 0.229346
\(776\) 30218.7 1.39792
\(777\) −11131.9 −0.513970
\(778\) −72963.6 −3.36230
\(779\) 25942.0 1.19315
\(780\) 88659.8 4.06991
\(781\) 64310.2 2.94648
\(782\) −5663.67 −0.258993
\(783\) 35251.1 1.60890
\(784\) −9245.20 −0.421155
\(785\) −8345.41 −0.379440
\(786\) 25140.5 1.14088
\(787\) 2206.07 0.0999212 0.0499606 0.998751i \(-0.484090\pi\)
0.0499606 + 0.998751i \(0.484090\pi\)
\(788\) 43343.8 1.95947
\(789\) −47256.6 −2.13230
\(790\) −17931.5 −0.807562
\(791\) −11661.5 −0.524192
\(792\) −12208.0 −0.547717
\(793\) 22514.4 1.00821
\(794\) 25895.6 1.15743
\(795\) −59060.4 −2.63479
\(796\) −34627.5 −1.54188
\(797\) −39524.6 −1.75663 −0.878314 0.478085i \(-0.841331\pi\)
−0.878314 + 0.478085i \(0.841331\pi\)
\(798\) 43961.1 1.95013
\(799\) −5457.26 −0.241632
\(800\) −2519.15 −0.111332
\(801\) 4866.92 0.214687
\(802\) 9139.23 0.402391
\(803\) 11508.3 0.505752
\(804\) 27454.3 1.20428
\(805\) 9503.09 0.416075
\(806\) −19628.3 −0.857790
\(807\) 17974.3 0.784046
\(808\) −23736.2 −1.03346
\(809\) −39225.2 −1.70468 −0.852339 0.522990i \(-0.824816\pi\)
−0.852339 + 0.522990i \(0.824816\pi\)
\(810\) 59877.7 2.59739
\(811\) 10801.0 0.467664 0.233832 0.972277i \(-0.424873\pi\)
0.233832 + 0.972277i \(0.424873\pi\)
\(812\) −59805.9 −2.58470
\(813\) −7139.99 −0.308008
\(814\) 40535.1 1.74540
\(815\) −26075.3 −1.12071
\(816\) 7324.60 0.314231
\(817\) 0 0
\(818\) −43277.3 −1.84982
\(819\) −5276.94 −0.225142
\(820\) −48869.1 −2.08120
\(821\) 25868.4 1.09965 0.549826 0.835279i \(-0.314694\pi\)
0.549826 + 0.835279i \(0.314694\pi\)
\(822\) −59054.0 −2.50577
\(823\) 45014.4 1.90657 0.953283 0.302079i \(-0.0976806\pi\)
0.953283 + 0.302079i \(0.0976806\pi\)
\(824\) 2842.96 0.120193
\(825\) −27258.6 −1.15033
\(826\) 4488.75 0.189084
\(827\) 46882.2 1.97129 0.985644 0.168839i \(-0.0540017\pi\)
0.985644 + 0.168839i \(0.0540017\pi\)
\(828\) −4539.03 −0.190510
\(829\) −26628.6 −1.11562 −0.557810 0.829969i \(-0.688358\pi\)
−0.557810 + 0.829969i \(0.688358\pi\)
\(830\) −46754.5 −1.95527
\(831\) −7757.75 −0.323843
\(832\) 39985.8 1.66618
\(833\) −3955.00 −0.164505
\(834\) 29013.7 1.20463
\(835\) 36901.4 1.52937
\(836\) −105824. −4.37799
\(837\) −7143.97 −0.295020
\(838\) 68644.8 2.82971
\(839\) −23832.3 −0.980670 −0.490335 0.871534i \(-0.663126\pi\)
−0.490335 + 0.871534i \(0.663126\pi\)
\(840\) −40357.0 −1.65768
\(841\) 60094.2 2.46399
\(842\) −3069.82 −0.125645
\(843\) −28839.6 −1.17828
\(844\) 50425.7 2.05654
\(845\) −36243.9 −1.47553
\(846\) −6615.84 −0.268862
\(847\) 24735.8 1.00346
\(848\) 38971.4 1.57816
\(849\) −8828.85 −0.356897
\(850\) 9543.58 0.385108
\(851\) 7344.60 0.295852
\(852\) −101543. −4.08313
\(853\) −8283.40 −0.332495 −0.166248 0.986084i \(-0.553165\pi\)
−0.166248 + 0.986084i \(0.553165\pi\)
\(854\) −21029.7 −0.842649
\(855\) −10101.9 −0.404069
\(856\) −31172.6 −1.24470
\(857\) −16912.0 −0.674098 −0.337049 0.941487i \(-0.609429\pi\)
−0.337049 + 0.941487i \(0.609429\pi\)
\(858\) 108129. 4.30242
\(859\) 35911.2 1.42640 0.713199 0.700962i \(-0.247246\pi\)
0.713199 + 0.700962i \(0.247246\pi\)
\(860\) 0 0
\(861\) 16367.8 0.647866
\(862\) −6759.30 −0.267080
\(863\) −12877.6 −0.507949 −0.253975 0.967211i \(-0.581738\pi\)
−0.253975 + 0.967211i \(0.581738\pi\)
\(864\) 3637.05 0.143212
\(865\) 9778.15 0.384355
\(866\) 54487.8 2.13807
\(867\) −25019.0 −0.980033
\(868\) 12120.2 0.473949
\(869\) −14457.3 −0.564363
\(870\) 116984. 4.55876
\(871\) −21058.6 −0.819222
\(872\) −42949.5 −1.66795
\(873\) 4772.53 0.185024
\(874\) −29004.6 −1.12254
\(875\) 7815.29 0.301949
\(876\) −18171.2 −0.700853
\(877\) −40122.1 −1.54484 −0.772421 0.635110i \(-0.780955\pi\)
−0.772421 + 0.635110i \(0.780955\pi\)
\(878\) 20993.4 0.806939
\(879\) −11648.7 −0.446988
\(880\) 44752.0 1.71431
\(881\) −32354.6 −1.23729 −0.618646 0.785670i \(-0.712318\pi\)
−0.618646 + 0.785670i \(0.712318\pi\)
\(882\) −4794.65 −0.183043
\(883\) 2575.95 0.0981741 0.0490870 0.998795i \(-0.484369\pi\)
0.0490870 + 0.998795i \(0.484369\pi\)
\(884\) −25026.8 −0.952199
\(885\) −5804.46 −0.220469
\(886\) −50203.2 −1.90362
\(887\) −171.714 −0.00650009 −0.00325004 0.999995i \(-0.501035\pi\)
−0.00325004 + 0.999995i \(0.501035\pi\)
\(888\) −31190.5 −1.17870
\(889\) −7681.75 −0.289806
\(890\) −58585.4 −2.20650
\(891\) 48276.6 1.81518
\(892\) −46611.8 −1.74964
\(893\) −27947.5 −1.04729
\(894\) 9004.85 0.336876
\(895\) −22121.1 −0.826175
\(896\) −34185.5 −1.27462
\(897\) 19592.1 0.729277
\(898\) −42450.9 −1.57751
\(899\) −17121.3 −0.635181
\(900\) 7648.50 0.283278
\(901\) 16671.5 0.616437
\(902\) −59600.8 −2.20010
\(903\) 0 0
\(904\) −32674.4 −1.20214
\(905\) −37793.7 −1.38818
\(906\) 24069.6 0.882626
\(907\) 6826.29 0.249904 0.124952 0.992163i \(-0.460122\pi\)
0.124952 + 0.992163i \(0.460122\pi\)
\(908\) 31445.2 1.14928
\(909\) −3748.73 −0.136785
\(910\) 63521.1 2.31396
\(911\) −2888.99 −0.105067 −0.0525337 0.998619i \(-0.516730\pi\)
−0.0525337 + 0.998619i \(0.516730\pi\)
\(912\) 37510.5 1.36195
\(913\) −37696.0 −1.36643
\(914\) −54446.4 −1.97038
\(915\) 27193.8 0.982512
\(916\) −71689.6 −2.58591
\(917\) 11907.5 0.428811
\(918\) −13778.7 −0.495386
\(919\) 16257.1 0.583539 0.291770 0.956489i \(-0.405756\pi\)
0.291770 + 0.956489i \(0.405756\pi\)
\(920\) 26626.7 0.954193
\(921\) −55574.5 −1.98832
\(922\) −70572.1 −2.52079
\(923\) 77888.0 2.77759
\(924\) −66768.5 −2.37719
\(925\) −12376.0 −0.439915
\(926\) −23954.6 −0.850103
\(927\) 448.996 0.0159083
\(928\) 8716.60 0.308337
\(929\) −46132.6 −1.62924 −0.814618 0.579998i \(-0.803053\pi\)
−0.814618 + 0.579998i \(0.803053\pi\)
\(930\) −23707.9 −0.835926
\(931\) −20254.2 −0.713002
\(932\) −14351.7 −0.504404
\(933\) −47774.7 −1.67639
\(934\) −29675.5 −1.03963
\(935\) 19144.4 0.669615
\(936\) −14785.5 −0.516323
\(937\) 14113.4 0.492066 0.246033 0.969262i \(-0.420873\pi\)
0.246033 + 0.969262i \(0.420873\pi\)
\(938\) 19669.9 0.684696
\(939\) 52195.0 1.81397
\(940\) 52647.2 1.82677
\(941\) −27642.6 −0.957622 −0.478811 0.877918i \(-0.658932\pi\)
−0.478811 + 0.877918i \(0.658932\pi\)
\(942\) 16070.8 0.555854
\(943\) −10799.1 −0.372925
\(944\) 3830.11 0.132054
\(945\) 23119.3 0.795841
\(946\) 0 0
\(947\) 15987.3 0.548592 0.274296 0.961645i \(-0.411555\pi\)
0.274296 + 0.961645i \(0.411555\pi\)
\(948\) 22827.6 0.782074
\(949\) 13938.0 0.476763
\(950\) 48874.3 1.66915
\(951\) 22015.8 0.750694
\(952\) 11391.9 0.387831
\(953\) −44654.8 −1.51785 −0.758925 0.651178i \(-0.774275\pi\)
−0.758925 + 0.651178i \(0.774275\pi\)
\(954\) 20210.9 0.685904
\(955\) −56996.0 −1.93125
\(956\) 23044.8 0.779626
\(957\) 94318.6 3.18588
\(958\) −49373.6 −1.66512
\(959\) −27970.2 −0.941820
\(960\) 48296.4 1.62371
\(961\) −26321.2 −0.883529
\(962\) 49093.2 1.64535
\(963\) −4923.19 −0.164743
\(964\) 78796.2 2.63263
\(965\) 1156.75 0.0385876
\(966\) −18300.1 −0.609521
\(967\) −27849.4 −0.926140 −0.463070 0.886322i \(-0.653252\pi\)
−0.463070 + 0.886322i \(0.653252\pi\)
\(968\) 69307.2 2.30126
\(969\) 16046.6 0.531983
\(970\) −57449.3 −1.90164
\(971\) 25393.9 0.839268 0.419634 0.907694i \(-0.362159\pi\)
0.419634 + 0.907694i \(0.362159\pi\)
\(972\) −25129.6 −0.829250
\(973\) 13742.0 0.452772
\(974\) 67456.9 2.21916
\(975\) −33013.7 −1.08440
\(976\) −17944.0 −0.588497
\(977\) −45241.2 −1.48147 −0.740734 0.671798i \(-0.765522\pi\)
−0.740734 + 0.671798i \(0.765522\pi\)
\(978\) 50213.3 1.64176
\(979\) −47234.7 −1.54201
\(980\) 38154.6 1.24368
\(981\) −6783.14 −0.220764
\(982\) −71218.7 −2.31434
\(983\) −28920.1 −0.938361 −0.469180 0.883102i \(-0.655451\pi\)
−0.469180 + 0.883102i \(0.655451\pi\)
\(984\) 45860.9 1.48577
\(985\) −40156.4 −1.29897
\(986\) −33022.1 −1.06657
\(987\) −17633.2 −0.568663
\(988\) −128167. −4.12705
\(989\) 0 0
\(990\) 23208.8 0.745075
\(991\) −483.939 −0.0155124 −0.00775622 0.999970i \(-0.502469\pi\)
−0.00775622 + 0.999970i \(0.502469\pi\)
\(992\) −1766.50 −0.0565388
\(993\) −13527.3 −0.432302
\(994\) −72751.8 −2.32148
\(995\) 32081.0 1.02215
\(996\) 59520.6 1.89356
\(997\) −35131.0 −1.11596 −0.557978 0.829856i \(-0.688423\pi\)
−0.557978 + 0.829856i \(0.688423\pi\)
\(998\) −74738.6 −2.37055
\(999\) 17868.1 0.565886
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 1849.4.a.j.1.46 yes 50
43.42 odd 2 1849.4.a.i.1.5 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.5 50 43.42 odd 2
1849.4.a.j.1.46 yes 50 1.1 even 1 trivial