Properties

Label 1849.4.a.j.1.1
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 1.1
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.33237 q^{2} +5.38049 q^{3} +20.4342 q^{4} +1.13957 q^{5} -28.6907 q^{6} +19.4433 q^{7} -66.3036 q^{8} +1.94964 q^{9} +O(q^{10})\) \(q-5.33237 q^{2} +5.38049 q^{3} +20.4342 q^{4} +1.13957 q^{5} -28.6907 q^{6} +19.4433 q^{7} -66.3036 q^{8} +1.94964 q^{9} -6.07658 q^{10} +11.2409 q^{11} +109.946 q^{12} +82.3500 q^{13} -103.679 q^{14} +6.13142 q^{15} +190.082 q^{16} -132.630 q^{17} -10.3962 q^{18} +41.5526 q^{19} +23.2861 q^{20} +104.614 q^{21} -59.9405 q^{22} +97.0017 q^{23} -356.746 q^{24} -123.701 q^{25} -439.121 q^{26} -134.783 q^{27} +397.308 q^{28} -94.9288 q^{29} -32.6950 q^{30} -265.836 q^{31} -483.159 q^{32} +60.4813 q^{33} +707.235 q^{34} +22.1569 q^{35} +39.8392 q^{36} -70.0555 q^{37} -221.574 q^{38} +443.083 q^{39} -75.5573 q^{40} +30.4482 q^{41} -557.843 q^{42} +229.698 q^{44} +2.22174 q^{45} -517.249 q^{46} -418.189 q^{47} +1022.73 q^{48} +35.0417 q^{49} +659.622 q^{50} -713.617 q^{51} +1682.75 q^{52} -399.944 q^{53} +718.714 q^{54} +12.8097 q^{55} -1289.16 q^{56} +223.573 q^{57} +506.195 q^{58} -57.1424 q^{59} +125.290 q^{60} +331.172 q^{61} +1417.54 q^{62} +37.9074 q^{63} +1055.73 q^{64} +93.8432 q^{65} -322.509 q^{66} +156.263 q^{67} -2710.19 q^{68} +521.916 q^{69} -118.149 q^{70} -564.356 q^{71} -129.268 q^{72} +69.0808 q^{73} +373.562 q^{74} -665.574 q^{75} +849.093 q^{76} +218.559 q^{77} -2362.68 q^{78} -569.629 q^{79} +216.611 q^{80} -777.839 q^{81} -162.361 q^{82} -785.399 q^{83} +2137.71 q^{84} -151.141 q^{85} -510.763 q^{87} -745.310 q^{88} -429.427 q^{89} -11.8471 q^{90} +1601.15 q^{91} +1982.15 q^{92} -1430.33 q^{93} +2229.94 q^{94} +47.3519 q^{95} -2599.63 q^{96} -1161.42 q^{97} -186.855 q^{98} +21.9156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} + 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} + 386q^{18} - 12q^{19} - 108q^{20} - 408q^{21} - 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} - 1493q^{26} - 10q^{27} + 242q^{28} - 208q^{29} + 48q^{30} - 932q^{31} + 1124q^{32} - 254q^{33} - 765q^{34} - 1452q^{35} + 747q^{36} + 90q^{37} - 1213q^{38} + 1610q^{39} - 1693q^{40} - 1354q^{41} + 16q^{42} - 2704q^{44} - 4508q^{45} - 233q^{46} - 3484q^{47} + 376q^{48} + 1324q^{49} + 408q^{50} - 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} + 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} - 1172q^{61} + 1546q^{62} + 3686q^{63} + 606q^{64} - 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} - 136q^{69} + 1310q^{70} - 162q^{71} + 5814q^{72} - 746q^{73} - 4332q^{74} - 236q^{75} - 1338q^{76} - 2024q^{77} - 2782q^{78} - 2656q^{79} + 5713q^{80} - 86q^{81} + 4168q^{82} - 3514q^{83} - 4269q^{84} + 7558q^{85} - 10278q^{87} - 11692q^{88} - 2640q^{89} - 8286q^{90} + 5946q^{91} - 4271q^{92} + 2q^{93} - 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} + 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.33237 −1.88528 −0.942639 0.333814i \(-0.891664\pi\)
−0.942639 + 0.333814i \(0.891664\pi\)
\(3\) 5.38049 1.03548 0.517738 0.855539i \(-0.326774\pi\)
0.517738 + 0.855539i \(0.326774\pi\)
\(4\) 20.4342 2.55427
\(5\) 1.13957 0.101926 0.0509629 0.998701i \(-0.483771\pi\)
0.0509629 + 0.998701i \(0.483771\pi\)
\(6\) −28.6907 −1.95216
\(7\) 19.4433 1.04984 0.524920 0.851152i \(-0.324095\pi\)
0.524920 + 0.851152i \(0.324095\pi\)
\(8\) −66.3036 −2.93023
\(9\) 1.94964 0.0722088
\(10\) −6.07658 −0.192158
\(11\) 11.2409 0.308113 0.154057 0.988062i \(-0.450766\pi\)
0.154057 + 0.988062i \(0.450766\pi\)
\(12\) 109.946 2.64488
\(13\) 82.3500 1.75691 0.878453 0.477829i \(-0.158576\pi\)
0.878453 + 0.477829i \(0.158576\pi\)
\(14\) −103.679 −1.97924
\(15\) 6.13142 0.105542
\(16\) 190.082 2.97003
\(17\) −132.630 −1.89221 −0.946106 0.323856i \(-0.895021\pi\)
−0.946106 + 0.323856i \(0.895021\pi\)
\(18\) −10.3962 −0.136134
\(19\) 41.5526 0.501727 0.250864 0.968022i \(-0.419285\pi\)
0.250864 + 0.968022i \(0.419285\pi\)
\(20\) 23.2861 0.260346
\(21\) 104.614 1.08708
\(22\) −59.9405 −0.580879
\(23\) 97.0017 0.879402 0.439701 0.898144i \(-0.355084\pi\)
0.439701 + 0.898144i \(0.355084\pi\)
\(24\) −356.746 −3.03418
\(25\) −123.701 −0.989611
\(26\) −439.121 −3.31225
\(27\) −134.783 −0.960705
\(28\) 397.308 2.68157
\(29\) −94.9288 −0.607856 −0.303928 0.952695i \(-0.598298\pi\)
−0.303928 + 0.952695i \(0.598298\pi\)
\(30\) −32.6950 −0.198975
\(31\) −265.836 −1.54018 −0.770091 0.637935i \(-0.779789\pi\)
−0.770091 + 0.637935i \(0.779789\pi\)
\(32\) −483.159 −2.66910
\(33\) 60.4813 0.319044
\(34\) 707.235 3.56735
\(35\) 22.1569 0.107006
\(36\) 39.8392 0.184441
\(37\) −70.0555 −0.311272 −0.155636 0.987814i \(-0.549743\pi\)
−0.155636 + 0.987814i \(0.549743\pi\)
\(38\) −221.574 −0.945896
\(39\) 443.083 1.81923
\(40\) −75.5573 −0.298666
\(41\) 30.4482 0.115981 0.0579903 0.998317i \(-0.481531\pi\)
0.0579903 + 0.998317i \(0.481531\pi\)
\(42\) −557.843 −2.04945
\(43\) 0 0
\(44\) 229.698 0.787006
\(45\) 2.22174 0.00735994
\(46\) −517.249 −1.65792
\(47\) −418.189 −1.29785 −0.648927 0.760850i \(-0.724782\pi\)
−0.648927 + 0.760850i \(0.724782\pi\)
\(48\) 1022.73 3.07539
\(49\) 35.0417 0.102162
\(50\) 659.622 1.86569
\(51\) −713.617 −1.95934
\(52\) 1682.75 4.48761
\(53\) −399.944 −1.03654 −0.518269 0.855218i \(-0.673423\pi\)
−0.518269 + 0.855218i \(0.673423\pi\)
\(54\) 718.714 1.81120
\(55\) 12.8097 0.0314047
\(56\) −1289.16 −3.07627
\(57\) 223.573 0.519526
\(58\) 506.195 1.14598
\(59\) −57.1424 −0.126090 −0.0630450 0.998011i \(-0.520081\pi\)
−0.0630450 + 0.998011i \(0.520081\pi\)
\(60\) 125.290 0.269582
\(61\) 331.172 0.695118 0.347559 0.937658i \(-0.387011\pi\)
0.347559 + 0.937658i \(0.387011\pi\)
\(62\) 1417.54 2.90367
\(63\) 37.9074 0.0758077
\(64\) 1055.73 2.06196
\(65\) 93.8432 0.179074
\(66\) −322.509 −0.601486
\(67\) 156.263 0.284934 0.142467 0.989800i \(-0.454496\pi\)
0.142467 + 0.989800i \(0.454496\pi\)
\(68\) −2710.19 −4.83322
\(69\) 521.916 0.910599
\(70\) −118.149 −0.201735
\(71\) −564.356 −0.943335 −0.471667 0.881777i \(-0.656348\pi\)
−0.471667 + 0.881777i \(0.656348\pi\)
\(72\) −129.268 −0.211589
\(73\) 69.0808 0.110758 0.0553788 0.998465i \(-0.482363\pi\)
0.0553788 + 0.998465i \(0.482363\pi\)
\(74\) 373.562 0.586834
\(75\) −665.574 −1.02472
\(76\) 849.093 1.28155
\(77\) 218.559 0.323470
\(78\) −2362.68 −3.42976
\(79\) −569.629 −0.811244 −0.405622 0.914041i \(-0.632945\pi\)
−0.405622 + 0.914041i \(0.632945\pi\)
\(80\) 216.611 0.302723
\(81\) −777.839 −1.06699
\(82\) −162.361 −0.218656
\(83\) −785.399 −1.03866 −0.519330 0.854574i \(-0.673818\pi\)
−0.519330 + 0.854574i \(0.673818\pi\)
\(84\) 2137.71 2.77670
\(85\) −151.141 −0.192865
\(86\) 0 0
\(87\) −510.763 −0.629420
\(88\) −745.310 −0.902844
\(89\) −429.427 −0.511451 −0.255726 0.966749i \(-0.582314\pi\)
−0.255726 + 0.966749i \(0.582314\pi\)
\(90\) −11.8471 −0.0138755
\(91\) 1601.15 1.84447
\(92\) 1982.15 2.24623
\(93\) −1430.33 −1.59482
\(94\) 2229.94 2.44682
\(95\) 47.3519 0.0511390
\(96\) −2599.63 −2.76379
\(97\) −1161.42 −1.21572 −0.607858 0.794046i \(-0.707971\pi\)
−0.607858 + 0.794046i \(0.707971\pi\)
\(98\) −186.855 −0.192604
\(99\) 21.9156 0.0222485
\(100\) −2527.74 −2.52774
\(101\) 190.011 0.187196 0.0935978 0.995610i \(-0.470163\pi\)
0.0935978 + 0.995610i \(0.470163\pi\)
\(102\) 3805.27 3.69390
\(103\) −552.932 −0.528952 −0.264476 0.964392i \(-0.585199\pi\)
−0.264476 + 0.964392i \(0.585199\pi\)
\(104\) −5460.10 −5.14814
\(105\) 119.215 0.110802
\(106\) 2132.65 1.95416
\(107\) −1660.97 −1.50067 −0.750336 0.661057i \(-0.770108\pi\)
−0.750336 + 0.661057i \(0.770108\pi\)
\(108\) −2754.18 −2.45390
\(109\) −851.383 −0.748144 −0.374072 0.927400i \(-0.622039\pi\)
−0.374072 + 0.927400i \(0.622039\pi\)
\(110\) −68.3061 −0.0592066
\(111\) −376.933 −0.322314
\(112\) 3695.82 3.11806
\(113\) 336.677 0.280282 0.140141 0.990132i \(-0.455244\pi\)
0.140141 + 0.990132i \(0.455244\pi\)
\(114\) −1192.18 −0.979451
\(115\) 110.540 0.0896337
\(116\) −1939.79 −1.55263
\(117\) 160.553 0.126864
\(118\) 304.705 0.237715
\(119\) −2578.77 −1.98652
\(120\) −406.535 −0.309262
\(121\) −1204.64 −0.905066
\(122\) −1765.93 −1.31049
\(123\) 163.826 0.120095
\(124\) −5432.15 −3.93404
\(125\) −283.411 −0.202793
\(126\) −202.136 −0.142918
\(127\) 1906.99 1.33242 0.666212 0.745762i \(-0.267914\pi\)
0.666212 + 0.745762i \(0.267914\pi\)
\(128\) −1764.25 −1.21827
\(129\) 0 0
\(130\) −500.407 −0.337604
\(131\) 1298.17 0.865815 0.432908 0.901438i \(-0.357488\pi\)
0.432908 + 0.901438i \(0.357488\pi\)
\(132\) 1235.89 0.814925
\(133\) 807.920 0.526733
\(134\) −833.253 −0.537180
\(135\) −153.594 −0.0979206
\(136\) 8793.88 5.54462
\(137\) −259.404 −0.161769 −0.0808847 0.996723i \(-0.525775\pi\)
−0.0808847 + 0.996723i \(0.525775\pi\)
\(138\) −2783.05 −1.71673
\(139\) −52.2455 −0.0318806 −0.0159403 0.999873i \(-0.505074\pi\)
−0.0159403 + 0.999873i \(0.505074\pi\)
\(140\) 452.758 0.273322
\(141\) −2250.06 −1.34390
\(142\) 3009.36 1.77845
\(143\) 925.685 0.541326
\(144\) 370.591 0.214462
\(145\) −108.178 −0.0619562
\(146\) −368.365 −0.208809
\(147\) 188.541 0.105787
\(148\) −1431.53 −0.795073
\(149\) −3239.65 −1.78123 −0.890613 0.454762i \(-0.849724\pi\)
−0.890613 + 0.454762i \(0.849724\pi\)
\(150\) 3549.09 1.93188
\(151\) 2294.66 1.23667 0.618334 0.785915i \(-0.287808\pi\)
0.618334 + 0.785915i \(0.287808\pi\)
\(152\) −2755.09 −1.47018
\(153\) −258.581 −0.136634
\(154\) −1165.44 −0.609830
\(155\) −302.938 −0.156984
\(156\) 9054.03 4.64681
\(157\) 3333.45 1.69451 0.847257 0.531184i \(-0.178253\pi\)
0.847257 + 0.531184i \(0.178253\pi\)
\(158\) 3037.47 1.52942
\(159\) −2151.89 −1.07331
\(160\) −550.591 −0.272050
\(161\) 1886.03 0.923231
\(162\) 4147.73 2.01158
\(163\) −1886.07 −0.906310 −0.453155 0.891432i \(-0.649702\pi\)
−0.453155 + 0.891432i \(0.649702\pi\)
\(164\) 622.183 0.296246
\(165\) 68.9224 0.0325188
\(166\) 4188.04 1.95816
\(167\) −628.615 −0.291280 −0.145640 0.989338i \(-0.546524\pi\)
−0.145640 + 0.989338i \(0.546524\pi\)
\(168\) −6936.31 −3.18541
\(169\) 4584.52 2.08672
\(170\) 805.940 0.363605
\(171\) 81.0126 0.0362292
\(172\) 0 0
\(173\) 2010.27 0.883456 0.441728 0.897149i \(-0.354366\pi\)
0.441728 + 0.897149i \(0.354366\pi\)
\(174\) 2723.58 1.18663
\(175\) −2405.16 −1.03893
\(176\) 2136.69 0.915107
\(177\) −307.454 −0.130563
\(178\) 2289.86 0.964228
\(179\) 1442.47 0.602320 0.301160 0.953574i \(-0.402626\pi\)
0.301160 + 0.953574i \(0.402626\pi\)
\(180\) 45.3994 0.0187993
\(181\) −1243.78 −0.510770 −0.255385 0.966839i \(-0.582202\pi\)
−0.255385 + 0.966839i \(0.582202\pi\)
\(182\) −8537.95 −3.47734
\(183\) 1781.86 0.719777
\(184\) −6431.56 −2.57685
\(185\) −79.8329 −0.0317266
\(186\) 7627.04 3.00668
\(187\) −1490.88 −0.583016
\(188\) −8545.35 −3.31507
\(189\) −2620.63 −1.00859
\(190\) −252.498 −0.0964112
\(191\) 3169.52 1.20072 0.600362 0.799728i \(-0.295023\pi\)
0.600362 + 0.799728i \(0.295023\pi\)
\(192\) 5680.32 2.13511
\(193\) −2034.25 −0.758698 −0.379349 0.925254i \(-0.623852\pi\)
−0.379349 + 0.925254i \(0.623852\pi\)
\(194\) 6193.13 2.29196
\(195\) 504.922 0.185427
\(196\) 716.048 0.260950
\(197\) 3188.91 1.15330 0.576650 0.816991i \(-0.304360\pi\)
0.576650 + 0.816991i \(0.304360\pi\)
\(198\) −116.862 −0.0419446
\(199\) −1546.27 −0.550814 −0.275407 0.961328i \(-0.588813\pi\)
−0.275407 + 0.961328i \(0.588813\pi\)
\(200\) 8201.85 2.89979
\(201\) 840.772 0.295042
\(202\) −1013.21 −0.352916
\(203\) −1845.73 −0.638151
\(204\) −14582.2 −5.00468
\(205\) 34.6977 0.0118214
\(206\) 2948.44 0.997221
\(207\) 189.118 0.0635006
\(208\) 15653.3 5.21807
\(209\) 467.087 0.154589
\(210\) −635.698 −0.208892
\(211\) 4947.03 1.61406 0.807032 0.590508i \(-0.201072\pi\)
0.807032 + 0.590508i \(0.201072\pi\)
\(212\) −8172.52 −2.64760
\(213\) −3036.51 −0.976800
\(214\) 8856.90 2.82918
\(215\) 0 0
\(216\) 8936.61 2.81509
\(217\) −5168.73 −1.61694
\(218\) 4539.89 1.41046
\(219\) 371.688 0.114687
\(220\) 261.756 0.0802162
\(221\) −10922.1 −3.32444
\(222\) 2009.95 0.607652
\(223\) −1020.68 −0.306501 −0.153251 0.988187i \(-0.548974\pi\)
−0.153251 + 0.988187i \(0.548974\pi\)
\(224\) −9394.20 −2.80213
\(225\) −241.173 −0.0714587
\(226\) −1795.29 −0.528410
\(227\) 1897.59 0.554836 0.277418 0.960749i \(-0.410521\pi\)
0.277418 + 0.960749i \(0.410521\pi\)
\(228\) 4568.53 1.32701
\(229\) 3784.45 1.09207 0.546034 0.837763i \(-0.316137\pi\)
0.546034 + 0.837763i \(0.316137\pi\)
\(230\) −589.439 −0.168984
\(231\) 1175.96 0.334945
\(232\) 6294.12 1.78116
\(233\) −5821.37 −1.63678 −0.818391 0.574661i \(-0.805134\pi\)
−0.818391 + 0.574661i \(0.805134\pi\)
\(234\) −856.126 −0.239174
\(235\) −476.554 −0.132285
\(236\) −1167.66 −0.322068
\(237\) −3064.88 −0.840023
\(238\) 13751.0 3.74514
\(239\) 3277.24 0.886975 0.443488 0.896280i \(-0.353741\pi\)
0.443488 + 0.896280i \(0.353741\pi\)
\(240\) 1165.47 0.313462
\(241\) −3524.53 −0.942054 −0.471027 0.882119i \(-0.656117\pi\)
−0.471027 + 0.882119i \(0.656117\pi\)
\(242\) 6423.60 1.70630
\(243\) −546.008 −0.144142
\(244\) 6767.22 1.77552
\(245\) 39.9323 0.0104130
\(246\) −873.581 −0.226413
\(247\) 3421.86 0.881488
\(248\) 17625.9 4.51309
\(249\) −4225.83 −1.07551
\(250\) 1511.25 0.382321
\(251\) 658.193 0.165517 0.0827585 0.996570i \(-0.473627\pi\)
0.0827585 + 0.996570i \(0.473627\pi\)
\(252\) 774.606 0.193633
\(253\) 1090.38 0.270956
\(254\) −10168.8 −2.51199
\(255\) −813.213 −0.199707
\(256\) 961.825 0.234821
\(257\) 4247.86 1.03103 0.515514 0.856881i \(-0.327601\pi\)
0.515514 + 0.856881i \(0.327601\pi\)
\(258\) 0 0
\(259\) −1362.11 −0.326785
\(260\) 1917.61 0.457404
\(261\) −185.077 −0.0438926
\(262\) −6922.33 −1.63230
\(263\) 2058.13 0.482547 0.241274 0.970457i \(-0.422435\pi\)
0.241274 + 0.970457i \(0.422435\pi\)
\(264\) −4010.13 −0.934873
\(265\) −455.762 −0.105650
\(266\) −4308.13 −0.993038
\(267\) −2310.53 −0.529595
\(268\) 3193.11 0.727799
\(269\) 4941.92 1.12013 0.560064 0.828450i \(-0.310777\pi\)
0.560064 + 0.828450i \(0.310777\pi\)
\(270\) 819.021 0.184608
\(271\) 7166.71 1.60644 0.803222 0.595679i \(-0.203117\pi\)
0.803222 + 0.595679i \(0.203117\pi\)
\(272\) −25210.7 −5.61993
\(273\) 8614.99 1.90990
\(274\) 1383.24 0.304980
\(275\) −1390.51 −0.304913
\(276\) 10664.9 2.32592
\(277\) −1097.77 −0.238118 −0.119059 0.992887i \(-0.537988\pi\)
−0.119059 + 0.992887i \(0.537988\pi\)
\(278\) 278.592 0.0601038
\(279\) −518.285 −0.111215
\(280\) −1469.08 −0.313552
\(281\) −3052.94 −0.648125 −0.324062 0.946036i \(-0.605049\pi\)
−0.324062 + 0.946036i \(0.605049\pi\)
\(282\) 11998.2 2.53362
\(283\) −3952.97 −0.830316 −0.415158 0.909749i \(-0.636274\pi\)
−0.415158 + 0.909749i \(0.636274\pi\)
\(284\) −11532.2 −2.40953
\(285\) 254.776 0.0529531
\(286\) −4936.10 −1.02055
\(287\) 592.013 0.121761
\(288\) −941.985 −0.192733
\(289\) 12677.8 2.58047
\(290\) 576.843 0.116805
\(291\) −6249.01 −1.25884
\(292\) 1411.61 0.282905
\(293\) −229.679 −0.0457953 −0.0228976 0.999738i \(-0.507289\pi\)
−0.0228976 + 0.999738i \(0.507289\pi\)
\(294\) −1005.37 −0.199437
\(295\) −65.1175 −0.0128518
\(296\) 4644.93 0.912099
\(297\) −1515.08 −0.296006
\(298\) 17275.0 3.35810
\(299\) 7988.08 1.54503
\(300\) −13600.4 −2.61741
\(301\) 0 0
\(302\) −12236.0 −2.33146
\(303\) 1022.35 0.193836
\(304\) 7898.40 1.49015
\(305\) 377.392 0.0708504
\(306\) 1378.85 0.257594
\(307\) 3264.44 0.606878 0.303439 0.952851i \(-0.401865\pi\)
0.303439 + 0.952851i \(0.401865\pi\)
\(308\) 4466.08 0.826229
\(309\) −2975.05 −0.547717
\(310\) 1615.38 0.295959
\(311\) 6556.37 1.19543 0.597713 0.801710i \(-0.296076\pi\)
0.597713 + 0.801710i \(0.296076\pi\)
\(312\) −29378.0 −5.33077
\(313\) −7030.21 −1.26956 −0.634778 0.772694i \(-0.718909\pi\)
−0.634778 + 0.772694i \(0.718909\pi\)
\(314\) −17775.2 −3.19463
\(315\) 43.1979 0.00772676
\(316\) −11639.9 −2.07214
\(317\) 6485.38 1.14907 0.574535 0.818480i \(-0.305183\pi\)
0.574535 + 0.818480i \(0.305183\pi\)
\(318\) 11474.7 2.02349
\(319\) −1067.08 −0.187289
\(320\) 1203.07 0.210167
\(321\) −8936.82 −1.55391
\(322\) −10057.0 −1.74055
\(323\) −5511.14 −0.949375
\(324\) −15894.5 −2.72539
\(325\) −10186.8 −1.73865
\(326\) 10057.2 1.70865
\(327\) −4580.85 −0.774684
\(328\) −2018.82 −0.339850
\(329\) −8130.98 −1.36254
\(330\) −367.520 −0.0613070
\(331\) −5097.58 −0.846490 −0.423245 0.906015i \(-0.639109\pi\)
−0.423245 + 0.906015i \(0.639109\pi\)
\(332\) −16049.0 −2.65302
\(333\) −136.583 −0.0224766
\(334\) 3352.01 0.549143
\(335\) 178.072 0.0290422
\(336\) 19885.3 3.22867
\(337\) −6280.94 −1.01527 −0.507633 0.861574i \(-0.669479\pi\)
−0.507633 + 0.861574i \(0.669479\pi\)
\(338\) −24446.4 −3.93404
\(339\) 1811.49 0.290225
\(340\) −3088.44 −0.492630
\(341\) −2988.23 −0.474551
\(342\) −431.989 −0.0683020
\(343\) −5987.72 −0.942585
\(344\) 0 0
\(345\) 594.757 0.0928135
\(346\) −10719.5 −1.66556
\(347\) −2180.02 −0.337261 −0.168631 0.985679i \(-0.553935\pi\)
−0.168631 + 0.985679i \(0.553935\pi\)
\(348\) −10437.0 −1.60771
\(349\) 9644.24 1.47921 0.739605 0.673041i \(-0.235012\pi\)
0.739605 + 0.673041i \(0.235012\pi\)
\(350\) 12825.2 1.95868
\(351\) −11099.4 −1.68787
\(352\) −5431.12 −0.822386
\(353\) −5127.42 −0.773103 −0.386551 0.922268i \(-0.626334\pi\)
−0.386551 + 0.922268i \(0.626334\pi\)
\(354\) 1639.46 0.246148
\(355\) −643.121 −0.0961502
\(356\) −8774.98 −1.30639
\(357\) −13875.1 −2.05699
\(358\) −7691.79 −1.13554
\(359\) −5232.56 −0.769259 −0.384629 0.923071i \(-0.625671\pi\)
−0.384629 + 0.923071i \(0.625671\pi\)
\(360\) −147.309 −0.0215664
\(361\) −5132.38 −0.748270
\(362\) 6632.30 0.962944
\(363\) −6481.57 −0.937173
\(364\) 32718.3 4.71127
\(365\) 78.7221 0.0112890
\(366\) −9501.56 −1.35698
\(367\) 5608.15 0.797666 0.398833 0.917024i \(-0.369415\pi\)
0.398833 + 0.917024i \(0.369415\pi\)
\(368\) 18438.3 2.61185
\(369\) 59.3629 0.00837483
\(370\) 425.698 0.0598135
\(371\) −7776.23 −1.08820
\(372\) −29227.6 −4.07360
\(373\) −5236.17 −0.726860 −0.363430 0.931621i \(-0.618394\pi\)
−0.363430 + 0.931621i \(0.618394\pi\)
\(374\) 7949.93 1.09915
\(375\) −1524.89 −0.209987
\(376\) 27727.5 3.80302
\(377\) −7817.38 −1.06795
\(378\) 13974.2 1.90146
\(379\) −3323.14 −0.450392 −0.225196 0.974314i \(-0.572302\pi\)
−0.225196 + 0.974314i \(0.572302\pi\)
\(380\) 967.597 0.130623
\(381\) 10260.5 1.37969
\(382\) −16901.0 −2.26370
\(383\) 7934.47 1.05857 0.529285 0.848444i \(-0.322460\pi\)
0.529285 + 0.848444i \(0.322460\pi\)
\(384\) −9492.52 −1.26149
\(385\) 249.063 0.0329699
\(386\) 10847.4 1.43036
\(387\) 0 0
\(388\) −23732.7 −3.10527
\(389\) 2071.19 0.269958 0.134979 0.990848i \(-0.456903\pi\)
0.134979 + 0.990848i \(0.456903\pi\)
\(390\) −2692.43 −0.349581
\(391\) −12865.4 −1.66402
\(392\) −2323.39 −0.299360
\(393\) 6984.80 0.896530
\(394\) −17004.4 −2.17429
\(395\) −649.129 −0.0826867
\(396\) 447.828 0.0568287
\(397\) 7588.62 0.959349 0.479675 0.877446i \(-0.340755\pi\)
0.479675 + 0.877446i \(0.340755\pi\)
\(398\) 8245.27 1.03844
\(399\) 4347.00 0.545419
\(400\) −23513.4 −2.93918
\(401\) −2081.48 −0.259212 −0.129606 0.991566i \(-0.541371\pi\)
−0.129606 + 0.991566i \(0.541371\pi\)
\(402\) −4483.31 −0.556237
\(403\) −21891.6 −2.70595
\(404\) 3882.71 0.478148
\(405\) −886.398 −0.108754
\(406\) 9842.11 1.20309
\(407\) −787.485 −0.0959071
\(408\) 47315.4 5.74132
\(409\) −3217.52 −0.388988 −0.194494 0.980904i \(-0.562306\pi\)
−0.194494 + 0.980904i \(0.562306\pi\)
\(410\) −185.021 −0.0222867
\(411\) −1395.72 −0.167508
\(412\) −11298.7 −1.35109
\(413\) −1111.04 −0.132374
\(414\) −1008.45 −0.119716
\(415\) −895.013 −0.105866
\(416\) −39788.1 −4.68936
\(417\) −281.106 −0.0330116
\(418\) −2490.68 −0.291443
\(419\) −7694.73 −0.897165 −0.448582 0.893741i \(-0.648071\pi\)
−0.448582 + 0.893741i \(0.648071\pi\)
\(420\) 2436.06 0.283018
\(421\) 1838.05 0.212781 0.106391 0.994324i \(-0.466071\pi\)
0.106391 + 0.994324i \(0.466071\pi\)
\(422\) −26379.4 −3.04296
\(423\) −815.318 −0.0937166
\(424\) 26517.7 3.03730
\(425\) 16406.6 1.87255
\(426\) 16191.8 1.84154
\(427\) 6439.07 0.729762
\(428\) −33940.5 −3.83312
\(429\) 4980.64 0.560530
\(430\) 0 0
\(431\) −4840.45 −0.540966 −0.270483 0.962725i \(-0.587183\pi\)
−0.270483 + 0.962725i \(0.587183\pi\)
\(432\) −25619.9 −2.85332
\(433\) −3091.82 −0.343148 −0.171574 0.985171i \(-0.554885\pi\)
−0.171574 + 0.985171i \(0.554885\pi\)
\(434\) 27561.6 3.04839
\(435\) −582.048 −0.0641541
\(436\) −17397.3 −1.91096
\(437\) 4030.67 0.441220
\(438\) −1981.98 −0.216216
\(439\) −8495.03 −0.923566 −0.461783 0.886993i \(-0.652790\pi\)
−0.461783 + 0.886993i \(0.652790\pi\)
\(440\) −849.329 −0.0920231
\(441\) 68.3186 0.00737702
\(442\) 58240.8 6.26749
\(443\) −7752.60 −0.831461 −0.415730 0.909488i \(-0.636474\pi\)
−0.415730 + 0.909488i \(0.636474\pi\)
\(444\) −7702.31 −0.823278
\(445\) −489.360 −0.0521301
\(446\) 5442.64 0.577840
\(447\) −17430.9 −1.84441
\(448\) 20526.8 2.16473
\(449\) −2654.77 −0.279034 −0.139517 0.990220i \(-0.544555\pi\)
−0.139517 + 0.990220i \(0.544555\pi\)
\(450\) 1286.02 0.134719
\(451\) 342.264 0.0357352
\(452\) 6879.72 0.715917
\(453\) 12346.4 1.28054
\(454\) −10118.7 −1.04602
\(455\) 1824.62 0.187999
\(456\) −14823.7 −1.52233
\(457\) 1223.05 0.125190 0.0625952 0.998039i \(-0.480062\pi\)
0.0625952 + 0.998039i \(0.480062\pi\)
\(458\) −20180.1 −2.05885
\(459\) 17876.4 1.81786
\(460\) 2258.79 0.228949
\(461\) −15665.7 −1.58270 −0.791350 0.611364i \(-0.790621\pi\)
−0.791350 + 0.611364i \(0.790621\pi\)
\(462\) −6270.63 −0.631464
\(463\) −7084.10 −0.711072 −0.355536 0.934663i \(-0.615702\pi\)
−0.355536 + 0.934663i \(0.615702\pi\)
\(464\) −18044.3 −1.80535
\(465\) −1629.95 −0.162553
\(466\) 31041.7 3.08579
\(467\) 9122.22 0.903910 0.451955 0.892041i \(-0.350727\pi\)
0.451955 + 0.892041i \(0.350727\pi\)
\(468\) 3280.76 0.324045
\(469\) 3038.27 0.299135
\(470\) 2541.16 0.249394
\(471\) 17935.6 1.75463
\(472\) 3788.75 0.369473
\(473\) 0 0
\(474\) 16343.1 1.58368
\(475\) −5140.12 −0.496515
\(476\) −52695.1 −5.07411
\(477\) −779.746 −0.0748472
\(478\) −17475.5 −1.67219
\(479\) 5530.27 0.527525 0.263762 0.964588i \(-0.415037\pi\)
0.263762 + 0.964588i \(0.415037\pi\)
\(480\) −2962.45 −0.281701
\(481\) −5769.07 −0.546875
\(482\) 18794.1 1.77603
\(483\) 10147.8 0.955982
\(484\) −24615.9 −2.31178
\(485\) −1323.52 −0.123913
\(486\) 2911.52 0.271747
\(487\) 8915.86 0.829602 0.414801 0.909912i \(-0.363851\pi\)
0.414801 + 0.909912i \(0.363851\pi\)
\(488\) −21957.9 −2.03686
\(489\) −10148.0 −0.938462
\(490\) −212.934 −0.0196314
\(491\) −10178.5 −0.935535 −0.467767 0.883852i \(-0.654942\pi\)
−0.467767 + 0.883852i \(0.654942\pi\)
\(492\) 3347.65 0.306755
\(493\) 12590.4 1.15019
\(494\) −18246.6 −1.66185
\(495\) 24.9743 0.00226770
\(496\) −50530.7 −4.57439
\(497\) −10972.9 −0.990350
\(498\) 22533.7 2.02763
\(499\) −2520.11 −0.226083 −0.113042 0.993590i \(-0.536059\pi\)
−0.113042 + 0.993590i \(0.536059\pi\)
\(500\) −5791.28 −0.517988
\(501\) −3382.25 −0.301613
\(502\) −3509.73 −0.312045
\(503\) 13769.0 1.22053 0.610267 0.792196i \(-0.291062\pi\)
0.610267 + 0.792196i \(0.291062\pi\)
\(504\) −2513.40 −0.222134
\(505\) 216.529 0.0190801
\(506\) −5814.32 −0.510826
\(507\) 24666.9 2.16074
\(508\) 38967.7 3.40337
\(509\) −2487.17 −0.216585 −0.108292 0.994119i \(-0.534538\pi\)
−0.108292 + 0.994119i \(0.534538\pi\)
\(510\) 4336.35 0.376504
\(511\) 1343.16 0.116278
\(512\) 8985.19 0.775572
\(513\) −5600.59 −0.482012
\(514\) −22651.1 −1.94377
\(515\) −630.103 −0.0539139
\(516\) 0 0
\(517\) −4700.81 −0.399887
\(518\) 7263.28 0.616081
\(519\) 10816.2 0.914797
\(520\) −6222.14 −0.524729
\(521\) 10805.0 0.908594 0.454297 0.890850i \(-0.349891\pi\)
0.454297 + 0.890850i \(0.349891\pi\)
\(522\) 986.898 0.0827497
\(523\) 15831.2 1.32361 0.661805 0.749676i \(-0.269791\pi\)
0.661805 + 0.749676i \(0.269791\pi\)
\(524\) 26527.1 2.21153
\(525\) −12940.9 −1.07579
\(526\) −10974.7 −0.909736
\(527\) 35258.0 2.91435
\(528\) 11496.4 0.947570
\(529\) −2757.68 −0.226652
\(530\) 2430.29 0.199180
\(531\) −111.407 −0.00910481
\(532\) 16509.2 1.34542
\(533\) 2507.41 0.203767
\(534\) 12320.6 0.998434
\(535\) −1892.78 −0.152957
\(536\) −10360.8 −0.834924
\(537\) 7761.20 0.623688
\(538\) −26352.2 −2.11175
\(539\) 393.899 0.0314776
\(540\) −3138.57 −0.250116
\(541\) 6016.44 0.478128 0.239064 0.971004i \(-0.423159\pi\)
0.239064 + 0.971004i \(0.423159\pi\)
\(542\) −38215.5 −3.02859
\(543\) −6692.14 −0.528890
\(544\) 64081.6 5.05051
\(545\) −970.206 −0.0762552
\(546\) −45938.3 −3.60069
\(547\) 13119.1 1.02547 0.512734 0.858547i \(-0.328633\pi\)
0.512734 + 0.858547i \(0.328633\pi\)
\(548\) −5300.71 −0.413203
\(549\) 645.665 0.0501936
\(550\) 7414.72 0.574845
\(551\) −3944.54 −0.304978
\(552\) −34604.9 −2.66827
\(553\) −11075.5 −0.851676
\(554\) 5853.73 0.448919
\(555\) −429.540 −0.0328521
\(556\) −1067.59 −0.0814317
\(557\) −7200.35 −0.547736 −0.273868 0.961767i \(-0.588303\pi\)
−0.273868 + 0.961767i \(0.588303\pi\)
\(558\) 2763.69 0.209671
\(559\) 0 0
\(560\) 4211.63 0.317810
\(561\) −8021.67 −0.603699
\(562\) 16279.4 1.22189
\(563\) −22074.0 −1.65241 −0.826205 0.563369i \(-0.809505\pi\)
−0.826205 + 0.563369i \(0.809505\pi\)
\(564\) −45978.2 −3.43268
\(565\) 383.665 0.0285680
\(566\) 21078.7 1.56538
\(567\) −15123.8 −1.12017
\(568\) 37418.9 2.76419
\(569\) 13386.6 0.986286 0.493143 0.869948i \(-0.335848\pi\)
0.493143 + 0.869948i \(0.335848\pi\)
\(570\) −1358.56 −0.0998314
\(571\) −22610.4 −1.65712 −0.828561 0.559899i \(-0.810840\pi\)
−0.828561 + 0.559899i \(0.810840\pi\)
\(572\) 18915.6 1.38269
\(573\) 17053.6 1.24332
\(574\) −3156.83 −0.229553
\(575\) −11999.2 −0.870266
\(576\) 2058.28 0.148892
\(577\) 1067.23 0.0770006 0.0385003 0.999259i \(-0.487742\pi\)
0.0385003 + 0.999259i \(0.487742\pi\)
\(578\) −67603.0 −4.86490
\(579\) −10945.3 −0.785613
\(580\) −2210.52 −0.158253
\(581\) −15270.7 −1.09043
\(582\) 33322.0 2.37327
\(583\) −4495.72 −0.319371
\(584\) −4580.31 −0.324545
\(585\) 182.960 0.0129307
\(586\) 1224.74 0.0863368
\(587\) 6633.97 0.466462 0.233231 0.972421i \(-0.425070\pi\)
0.233231 + 0.972421i \(0.425070\pi\)
\(588\) 3852.69 0.270208
\(589\) −11046.2 −0.772751
\(590\) 347.231 0.0242293
\(591\) 17157.9 1.19421
\(592\) −13316.3 −0.924487
\(593\) −20524.6 −1.42133 −0.710663 0.703533i \(-0.751605\pi\)
−0.710663 + 0.703533i \(0.751605\pi\)
\(594\) 8078.96 0.558054
\(595\) −2938.68 −0.202478
\(596\) −66199.6 −4.54973
\(597\) −8319.68 −0.570355
\(598\) −42595.4 −2.91280
\(599\) 4328.83 0.295277 0.147639 0.989041i \(-0.452833\pi\)
0.147639 + 0.989041i \(0.452833\pi\)
\(600\) 44129.9 3.00266
\(601\) −22901.3 −1.55435 −0.777174 0.629286i \(-0.783348\pi\)
−0.777174 + 0.629286i \(0.783348\pi\)
\(602\) 0 0
\(603\) 304.657 0.0205748
\(604\) 46889.5 3.15879
\(605\) −1372.77 −0.0922496
\(606\) −5451.54 −0.365435
\(607\) −3876.30 −0.259199 −0.129600 0.991566i \(-0.541369\pi\)
−0.129600 + 0.991566i \(0.541369\pi\)
\(608\) −20076.5 −1.33916
\(609\) −9930.92 −0.660790
\(610\) −2012.39 −0.133573
\(611\) −34437.9 −2.28021
\(612\) −5283.90 −0.349002
\(613\) 26240.8 1.72897 0.864484 0.502660i \(-0.167645\pi\)
0.864484 + 0.502660i \(0.167645\pi\)
\(614\) −17407.2 −1.14413
\(615\) 186.690 0.0122408
\(616\) −14491.3 −0.947841
\(617\) 29037.2 1.89464 0.947321 0.320286i \(-0.103779\pi\)
0.947321 + 0.320286i \(0.103779\pi\)
\(618\) 15864.0 1.03260
\(619\) 951.665 0.0617942 0.0308971 0.999523i \(-0.490164\pi\)
0.0308971 + 0.999523i \(0.490164\pi\)
\(620\) −6190.28 −0.400980
\(621\) −13074.2 −0.844846
\(622\) −34961.0 −2.25371
\(623\) −8349.47 −0.536942
\(624\) 84222.1 5.40318
\(625\) 15139.7 0.968941
\(626\) 37487.7 2.39347
\(627\) 2513.16 0.160073
\(628\) 68116.4 4.32825
\(629\) 9291.50 0.588993
\(630\) −230.347 −0.0145671
\(631\) 7974.08 0.503079 0.251540 0.967847i \(-0.419063\pi\)
0.251540 + 0.967847i \(0.419063\pi\)
\(632\) 37768.5 2.37713
\(633\) 26617.4 1.67132
\(634\) −34582.5 −2.16632
\(635\) 2173.14 0.135808
\(636\) −43972.2 −2.74152
\(637\) 2885.68 0.179490
\(638\) 5690.07 0.353091
\(639\) −1100.29 −0.0681171
\(640\) −2010.48 −0.124174
\(641\) −25568.9 −1.57552 −0.787761 0.615981i \(-0.788760\pi\)
−0.787761 + 0.615981i \(0.788760\pi\)
\(642\) 47654.4 2.92955
\(643\) −14114.5 −0.865663 −0.432832 0.901475i \(-0.642486\pi\)
−0.432832 + 0.901475i \(0.642486\pi\)
\(644\) 38539.5 2.35818
\(645\) 0 0
\(646\) 29387.5 1.78984
\(647\) 4730.36 0.287434 0.143717 0.989619i \(-0.454095\pi\)
0.143717 + 0.989619i \(0.454095\pi\)
\(648\) 51573.5 3.12654
\(649\) −642.330 −0.0388500
\(650\) 54319.8 3.27784
\(651\) −27810.3 −1.67430
\(652\) −38540.3 −2.31496
\(653\) −1693.66 −0.101498 −0.0507490 0.998711i \(-0.516161\pi\)
−0.0507490 + 0.998711i \(0.516161\pi\)
\(654\) 24426.8 1.46050
\(655\) 1479.35 0.0882489
\(656\) 5787.65 0.344466
\(657\) 134.683 0.00799767
\(658\) 43357.4 2.56876
\(659\) −8066.13 −0.476801 −0.238400 0.971167i \(-0.576623\pi\)
−0.238400 + 0.971167i \(0.576623\pi\)
\(660\) 1408.37 0.0830619
\(661\) −226.554 −0.0133312 −0.00666560 0.999978i \(-0.502122\pi\)
−0.00666560 + 0.999978i \(0.502122\pi\)
\(662\) 27182.2 1.59587
\(663\) −58766.3 −3.44237
\(664\) 52074.8 3.04351
\(665\) 920.677 0.0536877
\(666\) 728.311 0.0423746
\(667\) −9208.25 −0.534550
\(668\) −12845.2 −0.744007
\(669\) −5491.75 −0.317374
\(670\) −949.547 −0.0547525
\(671\) 3722.65 0.214175
\(672\) −50545.4 −2.90153
\(673\) −7867.98 −0.450651 −0.225326 0.974284i \(-0.572345\pi\)
−0.225326 + 0.974284i \(0.572345\pi\)
\(674\) 33492.3 1.91406
\(675\) 16672.9 0.950724
\(676\) 93680.8 5.33004
\(677\) −20935.2 −1.18848 −0.594242 0.804287i \(-0.702548\pi\)
−0.594242 + 0.804287i \(0.702548\pi\)
\(678\) −9659.52 −0.547156
\(679\) −22581.9 −1.27631
\(680\) 10021.2 0.565140
\(681\) 10210.0 0.574519
\(682\) 15934.4 0.894660
\(683\) 13418.1 0.751726 0.375863 0.926675i \(-0.377346\pi\)
0.375863 + 0.926675i \(0.377346\pi\)
\(684\) 1655.42 0.0925391
\(685\) −295.608 −0.0164885
\(686\) 31928.8 1.77703
\(687\) 20362.2 1.13081
\(688\) 0 0
\(689\) −32935.4 −1.82110
\(690\) −3171.47 −0.174979
\(691\) 28272.5 1.55649 0.778246 0.627960i \(-0.216110\pi\)
0.778246 + 0.627960i \(0.216110\pi\)
\(692\) 41078.2 2.25659
\(693\) 426.112 0.0233574
\(694\) 11624.7 0.635831
\(695\) −59.5371 −0.00324946
\(696\) 33865.4 1.84435
\(697\) −4038.36 −0.219460
\(698\) −51426.6 −2.78872
\(699\) −31321.8 −1.69485
\(700\) −49147.5 −2.65372
\(701\) −8270.14 −0.445590 −0.222795 0.974865i \(-0.571518\pi\)
−0.222795 + 0.974865i \(0.571518\pi\)
\(702\) 59186.0 3.18210
\(703\) −2910.99 −0.156174
\(704\) 11867.3 0.635319
\(705\) −2564.09 −0.136978
\(706\) 27341.3 1.45751
\(707\) 3694.43 0.196525
\(708\) −6282.57 −0.333493
\(709\) −18435.9 −0.976549 −0.488274 0.872690i \(-0.662373\pi\)
−0.488274 + 0.872690i \(0.662373\pi\)
\(710\) 3429.36 0.181270
\(711\) −1110.57 −0.0585790
\(712\) 28472.6 1.49867
\(713\) −25786.6 −1.35444
\(714\) 73986.9 3.87800
\(715\) 1054.88 0.0551751
\(716\) 29475.7 1.53849
\(717\) 17633.2 0.918441
\(718\) 27901.9 1.45027
\(719\) 807.291 0.0418733 0.0209366 0.999781i \(-0.493335\pi\)
0.0209366 + 0.999781i \(0.493335\pi\)
\(720\) 422.313 0.0218593
\(721\) −10750.8 −0.555314
\(722\) 27367.8 1.41070
\(723\) −18963.7 −0.975474
\(724\) −25415.6 −1.30465
\(725\) 11742.8 0.601541
\(726\) 34562.1 1.76683
\(727\) 6429.96 0.328025 0.164012 0.986458i \(-0.447556\pi\)
0.164012 + 0.986458i \(0.447556\pi\)
\(728\) −106162. −5.40472
\(729\) 18063.9 0.917739
\(730\) −419.775 −0.0212830
\(731\) 0 0
\(732\) 36410.9 1.83851
\(733\) −21819.9 −1.09951 −0.549753 0.835327i \(-0.685278\pi\)
−0.549753 + 0.835327i \(0.685278\pi\)
\(734\) −29904.8 −1.50382
\(735\) 214.855 0.0107824
\(736\) −46867.2 −2.34721
\(737\) 1756.53 0.0877921
\(738\) −316.545 −0.0157889
\(739\) 19531.5 0.972228 0.486114 0.873896i \(-0.338414\pi\)
0.486114 + 0.873896i \(0.338414\pi\)
\(740\) −1631.32 −0.0810384
\(741\) 18411.3 0.912759
\(742\) 41465.7 2.05156
\(743\) 24083.9 1.18917 0.594585 0.804033i \(-0.297316\pi\)
0.594585 + 0.804033i \(0.297316\pi\)
\(744\) 94836.0 4.67319
\(745\) −3691.79 −0.181553
\(746\) 27921.2 1.37033
\(747\) −1531.24 −0.0750004
\(748\) −30464.9 −1.48918
\(749\) −32294.7 −1.57546
\(750\) 8131.29 0.395883
\(751\) −12480.5 −0.606417 −0.303209 0.952924i \(-0.598058\pi\)
−0.303209 + 0.952924i \(0.598058\pi\)
\(752\) −79490.3 −3.85467
\(753\) 3541.40 0.171389
\(754\) 41685.2 2.01337
\(755\) 2614.92 0.126048
\(756\) −53550.4 −2.57620
\(757\) −37150.9 −1.78372 −0.891858 0.452315i \(-0.850598\pi\)
−0.891858 + 0.452315i \(0.850598\pi\)
\(758\) 17720.2 0.849113
\(759\) 5866.79 0.280568
\(760\) −3139.60 −0.149849
\(761\) −32130.3 −1.53052 −0.765258 0.643724i \(-0.777388\pi\)
−0.765258 + 0.643724i \(0.777388\pi\)
\(762\) −54712.9 −2.60110
\(763\) −16553.7 −0.785431
\(764\) 64766.5 3.06698
\(765\) −294.670 −0.0139266
\(766\) −42309.5 −1.99570
\(767\) −4705.68 −0.221528
\(768\) 5175.09 0.243151
\(769\) −19725.3 −0.924984 −0.462492 0.886624i \(-0.653045\pi\)
−0.462492 + 0.886624i \(0.653045\pi\)
\(770\) −1328.09 −0.0621574
\(771\) 22855.5 1.06760
\(772\) −41568.3 −1.93792
\(773\) −4215.71 −0.196156 −0.0980780 0.995179i \(-0.531269\pi\)
−0.0980780 + 0.995179i \(0.531269\pi\)
\(774\) 0 0
\(775\) 32884.3 1.52418
\(776\) 77006.4 3.56233
\(777\) −7328.82 −0.338378
\(778\) −11044.4 −0.508945
\(779\) 1265.20 0.0581907
\(780\) 10317.7 0.473630
\(781\) −6343.85 −0.290654
\(782\) 68602.9 3.13713
\(783\) 12794.8 0.583970
\(784\) 6660.79 0.303425
\(785\) 3798.69 0.172715
\(786\) −37245.5 −1.69021
\(787\) −35244.1 −1.59634 −0.798169 0.602434i \(-0.794198\pi\)
−0.798169 + 0.602434i \(0.794198\pi\)
\(788\) 65162.6 2.94584
\(789\) 11073.8 0.499666
\(790\) 3461.40 0.155887
\(791\) 6546.11 0.294251
\(792\) −1453.08 −0.0651933
\(793\) 27272.0 1.22126
\(794\) −40465.3 −1.80864
\(795\) −2452.22 −0.109398
\(796\) −31596.7 −1.40693
\(797\) 17073.8 0.758828 0.379414 0.925227i \(-0.376126\pi\)
0.379414 + 0.925227i \(0.376126\pi\)
\(798\) −23179.8 −1.02827
\(799\) 55464.7 2.45582
\(800\) 59767.4 2.64137
\(801\) −837.227 −0.0369313
\(802\) 11099.2 0.488687
\(803\) 776.528 0.0341259
\(804\) 17180.5 0.753618
\(805\) 2149.26 0.0941010
\(806\) 116734. 5.10147
\(807\) 26589.9 1.15986
\(808\) −12598.4 −0.548527
\(809\) 12016.0 0.522202 0.261101 0.965312i \(-0.415914\pi\)
0.261101 + 0.965312i \(0.415914\pi\)
\(810\) 4726.60 0.205032
\(811\) 41834.3 1.81135 0.905673 0.423976i \(-0.139366\pi\)
0.905673 + 0.423976i \(0.139366\pi\)
\(812\) −37715.9 −1.63001
\(813\) 38560.4 1.66343
\(814\) 4199.16 0.180811
\(815\) −2149.30 −0.0923764
\(816\) −135646. −5.81930
\(817\) 0 0
\(818\) 17157.0 0.733350
\(819\) 3121.67 0.133187
\(820\) 709.018 0.0301951
\(821\) 26438.7 1.12389 0.561947 0.827173i \(-0.310052\pi\)
0.561947 + 0.827173i \(0.310052\pi\)
\(822\) 7442.50 0.315799
\(823\) 16854.2 0.713853 0.356926 0.934132i \(-0.383825\pi\)
0.356926 + 0.934132i \(0.383825\pi\)
\(824\) 36661.4 1.54995
\(825\) −7481.62 −0.315729
\(826\) 5924.46 0.249562
\(827\) −20262.0 −0.851970 −0.425985 0.904730i \(-0.640072\pi\)
−0.425985 + 0.904730i \(0.640072\pi\)
\(828\) 3864.47 0.162198
\(829\) −15273.0 −0.639869 −0.319935 0.947440i \(-0.603661\pi\)
−0.319935 + 0.947440i \(0.603661\pi\)
\(830\) 4772.54 0.199587
\(831\) −5906.55 −0.246566
\(832\) 86939.0 3.62268
\(833\) −4647.60 −0.193313
\(834\) 1498.96 0.0622360
\(835\) −716.348 −0.0296889
\(836\) 9544.54 0.394862
\(837\) 35830.3 1.47966
\(838\) 41031.1 1.69140
\(839\) 38209.7 1.57228 0.786142 0.618046i \(-0.212076\pi\)
0.786142 + 0.618046i \(0.212076\pi\)
\(840\) −7904.38 −0.324675
\(841\) −15377.5 −0.630511
\(842\) −9801.15 −0.401152
\(843\) −16426.3 −0.671117
\(844\) 101088. 4.12276
\(845\) 5224.36 0.212690
\(846\) 4347.58 0.176682
\(847\) −23422.2 −0.950174
\(848\) −76022.2 −3.07855
\(849\) −21268.9 −0.859772
\(850\) −87485.9 −3.53029
\(851\) −6795.50 −0.273733
\(852\) −62048.6 −2.49501
\(853\) −37931.9 −1.52258 −0.761292 0.648409i \(-0.775435\pi\)
−0.761292 + 0.648409i \(0.775435\pi\)
\(854\) −34335.5 −1.37580
\(855\) 92.3191 0.00369269
\(856\) 110128. 4.39732
\(857\) 13948.7 0.555984 0.277992 0.960583i \(-0.410331\pi\)
0.277992 + 0.960583i \(0.410331\pi\)
\(858\) −26558.6 −1.05675
\(859\) 15379.3 0.610869 0.305434 0.952213i \(-0.401198\pi\)
0.305434 + 0.952213i \(0.401198\pi\)
\(860\) 0 0
\(861\) 3185.32 0.126081
\(862\) 25811.1 1.01987
\(863\) −4157.99 −0.164009 −0.0820043 0.996632i \(-0.526132\pi\)
−0.0820043 + 0.996632i \(0.526132\pi\)
\(864\) 65121.7 2.56422
\(865\) 2290.83 0.0900470
\(866\) 16486.7 0.646930
\(867\) 68213.0 2.67201
\(868\) −105619. −4.13011
\(869\) −6403.12 −0.249955
\(870\) 3103.69 0.120948
\(871\) 12868.3 0.500603
\(872\) 56449.8 2.19224
\(873\) −2264.35 −0.0877854
\(874\) −21493.0 −0.831822
\(875\) −5510.45 −0.212900
\(876\) 7595.15 0.292941
\(877\) −38274.3 −1.47370 −0.736848 0.676059i \(-0.763687\pi\)
−0.736848 + 0.676059i \(0.763687\pi\)
\(878\) 45298.6 1.74118
\(879\) −1235.79 −0.0474199
\(880\) 2434.89 0.0932730
\(881\) −16695.5 −0.638462 −0.319231 0.947677i \(-0.603425\pi\)
−0.319231 + 0.947677i \(0.603425\pi\)
\(882\) −364.300 −0.0139077
\(883\) −45928.1 −1.75040 −0.875200 0.483762i \(-0.839270\pi\)
−0.875200 + 0.483762i \(0.839270\pi\)
\(884\) −223184. −8.49152
\(885\) −350.364 −0.0133077
\(886\) 41339.7 1.56753
\(887\) −14180.1 −0.536779 −0.268389 0.963311i \(-0.586491\pi\)
−0.268389 + 0.963311i \(0.586491\pi\)
\(888\) 24992.0 0.944456
\(889\) 37078.2 1.39883
\(890\) 2609.45 0.0982797
\(891\) −8743.58 −0.328755
\(892\) −20856.7 −0.782887
\(893\) −17376.9 −0.651170
\(894\) 92948.0 3.47723
\(895\) 1643.79 0.0613920
\(896\) −34302.8 −1.27899
\(897\) 42979.8 1.59984
\(898\) 14156.2 0.526057
\(899\) 25235.5 0.936209
\(900\) −4928.17 −0.182525
\(901\) 53044.8 1.96135
\(902\) −1825.08 −0.0673708
\(903\) 0 0
\(904\) −22322.9 −0.821293
\(905\) −1417.37 −0.0520607
\(906\) −65835.5 −2.41417
\(907\) 23302.1 0.853071 0.426535 0.904471i \(-0.359734\pi\)
0.426535 + 0.904471i \(0.359734\pi\)
\(908\) 38775.8 1.41720
\(909\) 370.452 0.0135172
\(910\) −9729.55 −0.354430
\(911\) −26596.3 −0.967260 −0.483630 0.875273i \(-0.660682\pi\)
−0.483630 + 0.875273i \(0.660682\pi\)
\(912\) 42497.3 1.54301
\(913\) −8828.56 −0.320025
\(914\) −6521.77 −0.236019
\(915\) 2030.55 0.0733639
\(916\) 77332.2 2.78944
\(917\) 25240.7 0.908967
\(918\) −95323.3 −3.42717
\(919\) 40133.3 1.44056 0.720281 0.693683i \(-0.244013\pi\)
0.720281 + 0.693683i \(0.244013\pi\)
\(920\) −7329.18 −0.262648
\(921\) 17564.3 0.628407
\(922\) 83535.3 2.98383
\(923\) −46474.7 −1.65735
\(924\) 24029.7 0.855540
\(925\) 8665.97 0.308038
\(926\) 37775.1 1.34057
\(927\) −1078.02 −0.0381950
\(928\) 45865.7 1.62243
\(929\) −8697.44 −0.307162 −0.153581 0.988136i \(-0.549081\pi\)
−0.153581 + 0.988136i \(0.549081\pi\)
\(930\) 8691.51 0.306458
\(931\) 1456.07 0.0512577
\(932\) −118955. −4.18079
\(933\) 35276.5 1.23783
\(934\) −48643.0 −1.70412
\(935\) −1698.96 −0.0594244
\(936\) −10645.2 −0.371741
\(937\) 33520.7 1.16870 0.584351 0.811501i \(-0.301349\pi\)
0.584351 + 0.811501i \(0.301349\pi\)
\(938\) −16201.2 −0.563953
\(939\) −37826.0 −1.31459
\(940\) −9737.99 −0.337892
\(941\) −24899.8 −0.862604 −0.431302 0.902208i \(-0.641946\pi\)
−0.431302 + 0.902208i \(0.641946\pi\)
\(942\) −95639.3 −3.30796
\(943\) 2953.52 0.101994
\(944\) −10861.7 −0.374491
\(945\) −2986.38 −0.102801
\(946\) 0 0
\(947\) −22969.3 −0.788175 −0.394087 0.919073i \(-0.628939\pi\)
−0.394087 + 0.919073i \(0.628939\pi\)
\(948\) −62628.3 −2.14565
\(949\) 5688.80 0.194591
\(950\) 27409.0 0.936069
\(951\) 34894.5 1.18983
\(952\) 170982. 5.82096
\(953\) −23618.2 −0.802799 −0.401399 0.915903i \(-0.631476\pi\)
−0.401399 + 0.915903i \(0.631476\pi\)
\(954\) 4157.89 0.141108
\(955\) 3611.87 0.122385
\(956\) 66967.7 2.26558
\(957\) −5741.42 −0.193933
\(958\) −29489.4 −0.994531
\(959\) −5043.67 −0.169832
\(960\) 6473.09 0.217623
\(961\) 40878.0 1.37216
\(962\) 30762.8 1.03101
\(963\) −3238.29 −0.108362
\(964\) −72020.9 −2.40626
\(965\) −2318.17 −0.0773310
\(966\) −54111.7 −1.80229
\(967\) 41439.3 1.37807 0.689036 0.724727i \(-0.258034\pi\)
0.689036 + 0.724727i \(0.258034\pi\)
\(968\) 79872.2 2.65205
\(969\) −29652.6 −0.983054
\(970\) 7057.47 0.233610
\(971\) −47537.5 −1.57111 −0.785557 0.618790i \(-0.787623\pi\)
−0.785557 + 0.618790i \(0.787623\pi\)
\(972\) −11157.2 −0.368177
\(973\) −1015.82 −0.0334695
\(974\) −47542.7 −1.56403
\(975\) −54810.0 −1.80033
\(976\) 62949.8 2.06452
\(977\) −46979.4 −1.53839 −0.769194 0.639016i \(-0.779342\pi\)
−0.769194 + 0.639016i \(0.779342\pi\)
\(978\) 54112.8 1.76926
\(979\) −4827.13 −0.157585
\(980\) 815.983 0.0265976
\(981\) −1659.89 −0.0540226
\(982\) 54275.3 1.76374
\(983\) −6249.99 −0.202791 −0.101396 0.994846i \(-0.532331\pi\)
−0.101396 + 0.994846i \(0.532331\pi\)
\(984\) −10862.3 −0.351907
\(985\) 3633.97 0.117551
\(986\) −67136.9 −2.16843
\(987\) −43748.6 −1.41088
\(988\) 69922.8 2.25156
\(989\) 0 0
\(990\) −133.172 −0.00427524
\(991\) 9689.00 0.310576 0.155288 0.987869i \(-0.450369\pi\)
0.155288 + 0.987869i \(0.450369\pi\)
\(992\) 128441. 4.11090
\(993\) −27427.5 −0.876519
\(994\) 58511.8 1.86708
\(995\) −1762.07 −0.0561422
\(996\) −86351.3 −2.74713
\(997\) −26955.2 −0.856247 −0.428124 0.903720i \(-0.640825\pi\)
−0.428124 + 0.903720i \(0.640825\pi\)
\(998\) 13438.1 0.426229
\(999\) 9442.30 0.299040
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.1.1 yes 50
43.42 odd 2 1849.4.a.i.1.50 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.50 50 43.42 odd 2
1849.4.a.j.1.1 yes 50 1.1 even 1 trivial