Properties

Label 1849.4.a.i.1.6
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 1.6
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.80125 q^{2} -5.52870 q^{3} +15.0520 q^{4} +18.8098 q^{5} +26.5447 q^{6} +0.563586 q^{7} -33.8585 q^{8} +3.56656 q^{9} +O(q^{10})\) \(q-4.80125 q^{2} -5.52870 q^{3} +15.0520 q^{4} +18.8098 q^{5} +26.5447 q^{6} +0.563586 q^{7} -33.8585 q^{8} +3.56656 q^{9} -90.3106 q^{10} -21.9318 q^{11} -83.2181 q^{12} +90.1443 q^{13} -2.70592 q^{14} -103.994 q^{15} +42.1470 q^{16} -68.5734 q^{17} -17.1239 q^{18} +29.2074 q^{19} +283.125 q^{20} -3.11590 q^{21} +105.300 q^{22} -171.303 q^{23} +187.194 q^{24} +228.809 q^{25} -432.806 q^{26} +129.557 q^{27} +8.48310 q^{28} +9.36853 q^{29} +499.300 q^{30} +244.427 q^{31} +68.5095 q^{32} +121.255 q^{33} +329.238 q^{34} +10.6009 q^{35} +53.6839 q^{36} +213.593 q^{37} -140.232 q^{38} -498.381 q^{39} -636.872 q^{40} -191.608 q^{41} +14.9602 q^{42} -330.118 q^{44} +67.0863 q^{45} +822.469 q^{46} -341.454 q^{47} -233.018 q^{48} -342.682 q^{49} -1098.57 q^{50} +379.122 q^{51} +1356.85 q^{52} -488.826 q^{53} -622.034 q^{54} -412.533 q^{55} -19.0822 q^{56} -161.479 q^{57} -44.9807 q^{58} +319.938 q^{59} -1565.32 q^{60} -51.1903 q^{61} -1173.56 q^{62} +2.01006 q^{63} -666.107 q^{64} +1695.60 q^{65} -582.173 q^{66} -733.622 q^{67} -1032.17 q^{68} +947.083 q^{69} -50.8978 q^{70} -417.297 q^{71} -120.758 q^{72} +35.6291 q^{73} -1025.51 q^{74} -1265.01 q^{75} +439.630 q^{76} -12.3605 q^{77} +2392.85 q^{78} +32.5557 q^{79} +792.777 q^{80} -812.577 q^{81} +919.957 q^{82} -73.6881 q^{83} -46.9006 q^{84} -1289.85 q^{85} -51.7958 q^{87} +742.578 q^{88} -1128.32 q^{89} -322.098 q^{90} +50.8041 q^{91} -2578.45 q^{92} -1351.37 q^{93} +1639.41 q^{94} +549.385 q^{95} -378.768 q^{96} -309.477 q^{97} +1645.30 q^{98} -78.2211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} - 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} - 386q^{18} + 12q^{19} + 108q^{20} - 408q^{21} + 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} + 1493q^{26} + 10q^{27} - 242q^{28} + 208q^{29} - 48q^{30} - 932q^{31} - 1124q^{32} + 254q^{33} + 765q^{34} - 1452q^{35} + 747q^{36} - 90q^{37} - 1213q^{38} - 1610q^{39} - 1693q^{40} - 1354q^{41} - 16q^{42} - 2704q^{44} + 4508q^{45} + 233q^{46} - 3484q^{47} - 376q^{48} + 1324q^{49} - 408q^{50} + 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} - 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} + 1172q^{61} - 1546q^{62} - 3686q^{63} + 606q^{64} + 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} + 136q^{69} - 1310q^{70} + 162q^{71} - 5814q^{72} + 746q^{73} - 4332q^{74} + 236q^{75} + 1338q^{76} + 2024q^{77} - 2782q^{78} - 2656q^{79} - 5713q^{80} - 86q^{81} - 4168q^{82} - 3514q^{83} - 4269q^{84} - 7558q^{85} - 10278q^{87} + 11692q^{88} + 2640q^{89} - 8286q^{90} - 5946q^{91} - 4271q^{92} - 2q^{93} + 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} - 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.80125 −1.69750 −0.848749 0.528795i \(-0.822644\pi\)
−0.848749 + 0.528795i \(0.822644\pi\)
\(3\) −5.52870 −1.06400 −0.532000 0.846745i \(-0.678559\pi\)
−0.532000 + 0.846745i \(0.678559\pi\)
\(4\) 15.0520 1.88150
\(5\) 18.8098 1.68240 0.841200 0.540724i \(-0.181850\pi\)
0.841200 + 0.540724i \(0.181850\pi\)
\(6\) 26.5447 1.80614
\(7\) 0.563586 0.0304308 0.0152154 0.999884i \(-0.495157\pi\)
0.0152154 + 0.999884i \(0.495157\pi\)
\(8\) −33.8585 −1.49635
\(9\) 3.56656 0.132095
\(10\) −90.3106 −2.85587
\(11\) −21.9318 −0.601154 −0.300577 0.953758i \(-0.597179\pi\)
−0.300577 + 0.953758i \(0.597179\pi\)
\(12\) −83.2181 −2.00192
\(13\) 90.1443 1.92320 0.961598 0.274463i \(-0.0885001\pi\)
0.961598 + 0.274463i \(0.0885001\pi\)
\(14\) −2.70592 −0.0516562
\(15\) −103.994 −1.79007
\(16\) 42.1470 0.658547
\(17\) −68.5734 −0.978323 −0.489161 0.872193i \(-0.662697\pi\)
−0.489161 + 0.872193i \(0.662697\pi\)
\(18\) −17.1239 −0.224231
\(19\) 29.2074 0.352665 0.176332 0.984331i \(-0.443577\pi\)
0.176332 + 0.984331i \(0.443577\pi\)
\(20\) 283.125 3.16544
\(21\) −3.11590 −0.0323783
\(22\) 105.300 1.02046
\(23\) −171.303 −1.55301 −0.776503 0.630114i \(-0.783008\pi\)
−0.776503 + 0.630114i \(0.783008\pi\)
\(24\) 187.194 1.59211
\(25\) 228.809 1.83047
\(26\) −432.806 −3.26462
\(27\) 129.557 0.923451
\(28\) 8.48310 0.0572556
\(29\) 9.36853 0.0599894 0.0299947 0.999550i \(-0.490451\pi\)
0.0299947 + 0.999550i \(0.490451\pi\)
\(30\) 499.300 3.03865
\(31\) 244.427 1.41614 0.708071 0.706141i \(-0.249565\pi\)
0.708071 + 0.706141i \(0.249565\pi\)
\(32\) 68.5095 0.378465
\(33\) 121.255 0.639627
\(34\) 329.238 1.66070
\(35\) 10.6009 0.0511967
\(36\) 53.6839 0.248537
\(37\) 213.593 0.949041 0.474520 0.880245i \(-0.342622\pi\)
0.474520 + 0.880245i \(0.342622\pi\)
\(38\) −140.232 −0.598648
\(39\) −498.381 −2.04628
\(40\) −636.872 −2.51746
\(41\) −191.608 −0.729856 −0.364928 0.931036i \(-0.618906\pi\)
−0.364928 + 0.931036i \(0.618906\pi\)
\(42\) 14.9602 0.0549622
\(43\) 0 0
\(44\) −330.118 −1.13107
\(45\) 67.0863 0.222236
\(46\) 822.469 2.63623
\(47\) −341.454 −1.05971 −0.529853 0.848089i \(-0.677753\pi\)
−0.529853 + 0.848089i \(0.677753\pi\)
\(48\) −233.018 −0.700694
\(49\) −342.682 −0.999074
\(50\) −1098.57 −3.10722
\(51\) 379.122 1.04093
\(52\) 1356.85 3.61850
\(53\) −488.826 −1.26690 −0.633448 0.773785i \(-0.718361\pi\)
−0.633448 + 0.773785i \(0.718361\pi\)
\(54\) −622.034 −1.56756
\(55\) −412.533 −1.01138
\(56\) −19.0822 −0.0455350
\(57\) −161.479 −0.375235
\(58\) −44.9807 −0.101832
\(59\) 319.938 0.705972 0.352986 0.935629i \(-0.385166\pi\)
0.352986 + 0.935629i \(0.385166\pi\)
\(60\) −1565.32 −3.36802
\(61\) −51.1903 −0.107447 −0.0537234 0.998556i \(-0.517109\pi\)
−0.0537234 + 0.998556i \(0.517109\pi\)
\(62\) −1173.56 −2.40390
\(63\) 2.01006 0.00401975
\(64\) −666.107 −1.30099
\(65\) 1695.60 3.23558
\(66\) −582.173 −1.08577
\(67\) −733.622 −1.33771 −0.668853 0.743395i \(-0.733214\pi\)
−0.668853 + 0.743395i \(0.733214\pi\)
\(68\) −1032.17 −1.84072
\(69\) 947.083 1.65240
\(70\) −50.8978 −0.0869064
\(71\) −417.297 −0.697522 −0.348761 0.937212i \(-0.613398\pi\)
−0.348761 + 0.937212i \(0.613398\pi\)
\(72\) −120.758 −0.197660
\(73\) 35.6291 0.0571243 0.0285621 0.999592i \(-0.490907\pi\)
0.0285621 + 0.999592i \(0.490907\pi\)
\(74\) −1025.51 −1.61100
\(75\) −1265.01 −1.94762
\(76\) 439.630 0.663539
\(77\) −12.3605 −0.0182936
\(78\) 2392.85 3.47356
\(79\) 32.5557 0.0463645 0.0231823 0.999731i \(-0.492620\pi\)
0.0231823 + 0.999731i \(0.492620\pi\)
\(80\) 792.777 1.10794
\(81\) −812.577 −1.11465
\(82\) 919.957 1.23893
\(83\) −73.6881 −0.0974497 −0.0487248 0.998812i \(-0.515516\pi\)
−0.0487248 + 0.998812i \(0.515516\pi\)
\(84\) −46.9006 −0.0609199
\(85\) −1289.85 −1.64593
\(86\) 0 0
\(87\) −51.7958 −0.0638287
\(88\) 742.578 0.899536
\(89\) −1128.32 −1.34384 −0.671918 0.740626i \(-0.734529\pi\)
−0.671918 + 0.740626i \(0.734529\pi\)
\(90\) −322.098 −0.377246
\(91\) 50.8041 0.0585243
\(92\) −2578.45 −2.92198
\(93\) −1351.37 −1.50678
\(94\) 1639.41 1.79885
\(95\) 549.385 0.593323
\(96\) −378.768 −0.402686
\(97\) −309.477 −0.323944 −0.161972 0.986795i \(-0.551785\pi\)
−0.161972 + 0.986795i \(0.551785\pi\)
\(98\) 1645.30 1.69593
\(99\) −78.2211 −0.0794093
\(100\) 3444.03 3.44403
\(101\) 331.449 0.326538 0.163269 0.986582i \(-0.447796\pi\)
0.163269 + 0.986582i \(0.447796\pi\)
\(102\) −1820.26 −1.76699
\(103\) 132.978 0.127211 0.0636053 0.997975i \(-0.479740\pi\)
0.0636053 + 0.997975i \(0.479740\pi\)
\(104\) −3052.15 −2.87777
\(105\) −58.6094 −0.0544733
\(106\) 2346.98 2.15055
\(107\) −273.667 −0.247256 −0.123628 0.992329i \(-0.539453\pi\)
−0.123628 + 0.992329i \(0.539453\pi\)
\(108\) 1950.09 1.73747
\(109\) 1590.63 1.39775 0.698874 0.715245i \(-0.253685\pi\)
0.698874 + 0.715245i \(0.253685\pi\)
\(110\) 1980.68 1.71682
\(111\) −1180.89 −1.00978
\(112\) 23.7535 0.0200401
\(113\) 484.817 0.403608 0.201804 0.979426i \(-0.435320\pi\)
0.201804 + 0.979426i \(0.435320\pi\)
\(114\) 775.300 0.636961
\(115\) −3222.17 −2.61278
\(116\) 141.015 0.112870
\(117\) 321.505 0.254044
\(118\) −1536.10 −1.19839
\(119\) −38.6470 −0.0297711
\(120\) 3521.07 2.67857
\(121\) −849.995 −0.638614
\(122\) 245.778 0.182391
\(123\) 1059.34 0.776566
\(124\) 3679.12 2.66448
\(125\) 1952.62 1.39718
\(126\) −9.65081 −0.00682351
\(127\) 401.864 0.280785 0.140392 0.990096i \(-0.455164\pi\)
0.140392 + 0.990096i \(0.455164\pi\)
\(128\) 2650.07 1.82997
\(129\) 0 0
\(130\) −8140.99 −5.49240
\(131\) −2186.29 −1.45815 −0.729073 0.684436i \(-0.760049\pi\)
−0.729073 + 0.684436i \(0.760049\pi\)
\(132\) 1825.12 1.20346
\(133\) 16.4609 0.0107319
\(134\) 3522.31 2.27075
\(135\) 2436.93 1.55361
\(136\) 2321.79 1.46391
\(137\) 830.062 0.517642 0.258821 0.965925i \(-0.416666\pi\)
0.258821 + 0.965925i \(0.416666\pi\)
\(138\) −4547.18 −2.80494
\(139\) −1919.05 −1.17102 −0.585511 0.810664i \(-0.699106\pi\)
−0.585511 + 0.810664i \(0.699106\pi\)
\(140\) 159.565 0.0963267
\(141\) 1887.80 1.12753
\(142\) 2003.55 1.18404
\(143\) −1977.03 −1.15614
\(144\) 150.320 0.0869907
\(145\) 176.220 0.100926
\(146\) −171.064 −0.0969684
\(147\) 1894.59 1.06301
\(148\) 3215.01 1.78562
\(149\) 1690.89 0.929686 0.464843 0.885393i \(-0.346111\pi\)
0.464843 + 0.885393i \(0.346111\pi\)
\(150\) 6073.65 3.30608
\(151\) 1011.84 0.545311 0.272656 0.962112i \(-0.412098\pi\)
0.272656 + 0.962112i \(0.412098\pi\)
\(152\) −988.917 −0.527709
\(153\) −244.571 −0.129231
\(154\) 59.3457 0.0310533
\(155\) 4597.63 2.38252
\(156\) −7501.64 −3.85008
\(157\) −1236.95 −0.628786 −0.314393 0.949293i \(-0.601801\pi\)
−0.314393 + 0.949293i \(0.601801\pi\)
\(158\) −156.308 −0.0787037
\(159\) 2702.58 1.34798
\(160\) 1288.65 0.636729
\(161\) −96.5439 −0.0472592
\(162\) 3901.39 1.89211
\(163\) 1060.28 0.509495 0.254747 0.967008i \(-0.418008\pi\)
0.254747 + 0.967008i \(0.418008\pi\)
\(164\) −2884.08 −1.37323
\(165\) 2280.77 1.07611
\(166\) 353.795 0.165421
\(167\) −1645.91 −0.762660 −0.381330 0.924439i \(-0.624534\pi\)
−0.381330 + 0.924439i \(0.624534\pi\)
\(168\) 105.500 0.0484493
\(169\) 5929.00 2.69868
\(170\) 6192.90 2.79396
\(171\) 104.170 0.0465852
\(172\) 0 0
\(173\) 2977.10 1.30835 0.654176 0.756342i \(-0.273015\pi\)
0.654176 + 0.756342i \(0.273015\pi\)
\(174\) 248.685 0.108349
\(175\) 128.953 0.0557026
\(176\) −924.361 −0.395888
\(177\) −1768.84 −0.751154
\(178\) 5417.33 2.28116
\(179\) 4.36944 0.00182451 0.000912256 1.00000i \(-0.499710\pi\)
0.000912256 1.00000i \(0.499710\pi\)
\(180\) 1009.78 0.418138
\(181\) 1585.58 0.651134 0.325567 0.945519i \(-0.394445\pi\)
0.325567 + 0.945519i \(0.394445\pi\)
\(182\) −243.923 −0.0993450
\(183\) 283.016 0.114323
\(184\) 5800.06 2.32384
\(185\) 4017.65 1.59667
\(186\) 6488.25 2.55775
\(187\) 1503.94 0.588122
\(188\) −5139.57 −1.99384
\(189\) 73.0162 0.0281013
\(190\) −2637.73 −1.00716
\(191\) 632.532 0.239625 0.119813 0.992797i \(-0.461771\pi\)
0.119813 + 0.992797i \(0.461771\pi\)
\(192\) 3682.71 1.38425
\(193\) 2150.82 0.802174 0.401087 0.916040i \(-0.368633\pi\)
0.401087 + 0.916040i \(0.368633\pi\)
\(194\) 1485.88 0.549895
\(195\) −9374.45 −3.44266
\(196\) −5158.06 −1.87976
\(197\) −865.753 −0.313109 −0.156554 0.987669i \(-0.550039\pi\)
−0.156554 + 0.987669i \(0.550039\pi\)
\(198\) 375.559 0.134797
\(199\) −4687.11 −1.66965 −0.834825 0.550516i \(-0.814431\pi\)
−0.834825 + 0.550516i \(0.814431\pi\)
\(200\) −7747.11 −2.73902
\(201\) 4055.98 1.42332
\(202\) −1591.37 −0.554298
\(203\) 5.27997 0.00182552
\(204\) 5706.55 1.95852
\(205\) −3604.10 −1.22791
\(206\) −638.460 −0.215940
\(207\) −610.962 −0.205144
\(208\) 3799.32 1.26652
\(209\) −640.571 −0.212006
\(210\) 281.399 0.0924683
\(211\) −1447.08 −0.472138 −0.236069 0.971736i \(-0.575859\pi\)
−0.236069 + 0.971736i \(0.575859\pi\)
\(212\) −7357.82 −2.38367
\(213\) 2307.11 0.742163
\(214\) 1313.94 0.419717
\(215\) 0 0
\(216\) −4386.59 −1.38180
\(217\) 137.756 0.0430943
\(218\) −7637.00 −2.37267
\(219\) −196.983 −0.0607802
\(220\) −6209.45 −1.90292
\(221\) −6181.50 −1.88151
\(222\) 5669.77 1.71410
\(223\) −5483.79 −1.64673 −0.823367 0.567510i \(-0.807907\pi\)
−0.823367 + 0.567510i \(0.807907\pi\)
\(224\) 38.6110 0.0115170
\(225\) 816.059 0.241795
\(226\) −2327.73 −0.685125
\(227\) 6340.18 1.85380 0.926900 0.375309i \(-0.122463\pi\)
0.926900 + 0.375309i \(0.122463\pi\)
\(228\) −2430.58 −0.706005
\(229\) −5138.02 −1.48266 −0.741332 0.671139i \(-0.765805\pi\)
−0.741332 + 0.671139i \(0.765805\pi\)
\(230\) 15470.5 4.43518
\(231\) 68.3373 0.0194644
\(232\) −317.204 −0.0897650
\(233\) −3941.80 −1.10831 −0.554154 0.832414i \(-0.686958\pi\)
−0.554154 + 0.832414i \(0.686958\pi\)
\(234\) −1543.63 −0.431239
\(235\) −6422.68 −1.78285
\(236\) 4815.71 1.32829
\(237\) −179.991 −0.0493318
\(238\) 185.554 0.0505364
\(239\) −367.931 −0.0995794 −0.0497897 0.998760i \(-0.515855\pi\)
−0.0497897 + 0.998760i \(0.515855\pi\)
\(240\) −4383.03 −1.17885
\(241\) 812.124 0.217068 0.108534 0.994093i \(-0.465384\pi\)
0.108534 + 0.994093i \(0.465384\pi\)
\(242\) 4081.04 1.08405
\(243\) 994.469 0.262532
\(244\) −770.518 −0.202161
\(245\) −6445.79 −1.68084
\(246\) −5086.17 −1.31822
\(247\) 2632.88 0.678243
\(248\) −8275.94 −2.11904
\(249\) 407.400 0.103686
\(250\) −9375.01 −2.37171
\(251\) −3984.26 −1.00193 −0.500964 0.865468i \(-0.667021\pi\)
−0.500964 + 0.865468i \(0.667021\pi\)
\(252\) 30.2555 0.00756316
\(253\) 3756.99 0.933595
\(254\) −1929.45 −0.476631
\(255\) 7131.20 1.75127
\(256\) −7394.81 −1.80537
\(257\) 2945.96 0.715034 0.357517 0.933907i \(-0.383623\pi\)
0.357517 + 0.933907i \(0.383623\pi\)
\(258\) 0 0
\(259\) 120.378 0.0288800
\(260\) 25522.1 6.08776
\(261\) 33.4134 0.00792429
\(262\) 10496.9 2.47520
\(263\) −1825.81 −0.428076 −0.214038 0.976825i \(-0.568662\pi\)
−0.214038 + 0.976825i \(0.568662\pi\)
\(264\) −4105.50 −0.957105
\(265\) −9194.72 −2.13142
\(266\) −79.0327 −0.0182173
\(267\) 6238.13 1.42984
\(268\) −11042.5 −2.51689
\(269\) 3509.27 0.795404 0.397702 0.917515i \(-0.369808\pi\)
0.397702 + 0.917515i \(0.369808\pi\)
\(270\) −11700.3 −2.63726
\(271\) −8225.07 −1.84368 −0.921840 0.387571i \(-0.873314\pi\)
−0.921840 + 0.387571i \(0.873314\pi\)
\(272\) −2890.16 −0.644272
\(273\) −280.881 −0.0622698
\(274\) −3985.34 −0.878697
\(275\) −5018.19 −1.10039
\(276\) 14255.5 3.10899
\(277\) −1286.60 −0.279076 −0.139538 0.990217i \(-0.544562\pi\)
−0.139538 + 0.990217i \(0.544562\pi\)
\(278\) 9213.87 1.98781
\(279\) 871.764 0.187065
\(280\) −358.932 −0.0766081
\(281\) 4799.08 1.01882 0.509411 0.860523i \(-0.329863\pi\)
0.509411 + 0.860523i \(0.329863\pi\)
\(282\) −9063.80 −1.91398
\(283\) 792.682 0.166502 0.0832510 0.996529i \(-0.473470\pi\)
0.0832510 + 0.996529i \(0.473470\pi\)
\(284\) −6281.17 −1.31239
\(285\) −3037.38 −0.631295
\(286\) 9492.21 1.96254
\(287\) −107.987 −0.0222101
\(288\) 244.343 0.0499932
\(289\) −210.694 −0.0428850
\(290\) −846.077 −0.171322
\(291\) 1711.01 0.344677
\(292\) 536.290 0.107479
\(293\) 5226.15 1.04203 0.521015 0.853547i \(-0.325553\pi\)
0.521015 + 0.853547i \(0.325553\pi\)
\(294\) −9096.40 −1.80447
\(295\) 6017.97 1.18773
\(296\) −7231.95 −1.42010
\(297\) −2841.41 −0.555136
\(298\) −8118.39 −1.57814
\(299\) −15442.0 −2.98673
\(300\) −19041.0 −3.66445
\(301\) 0 0
\(302\) −4858.08 −0.925665
\(303\) −1832.48 −0.347437
\(304\) 1231.00 0.232246
\(305\) −962.880 −0.180768
\(306\) 1174.25 0.219370
\(307\) 5434.88 1.01037 0.505187 0.863010i \(-0.331423\pi\)
0.505187 + 0.863010i \(0.331423\pi\)
\(308\) −186.050 −0.0344194
\(309\) −735.195 −0.135352
\(310\) −22074.4 −4.04432
\(311\) 434.161 0.0791608 0.0395804 0.999216i \(-0.487398\pi\)
0.0395804 + 0.999216i \(0.487398\pi\)
\(312\) 16874.4 3.06195
\(313\) 7130.42 1.28765 0.643826 0.765172i \(-0.277346\pi\)
0.643826 + 0.765172i \(0.277346\pi\)
\(314\) 5938.91 1.06736
\(315\) 37.8089 0.00676282
\(316\) 490.028 0.0872350
\(317\) −3967.42 −0.702942 −0.351471 0.936199i \(-0.614318\pi\)
−0.351471 + 0.936199i \(0.614318\pi\)
\(318\) −12975.7 −2.28819
\(319\) −205.469 −0.0360629
\(320\) −12529.3 −2.18879
\(321\) 1513.02 0.263080
\(322\) 463.532 0.0802224
\(323\) −2002.85 −0.345020
\(324\) −12230.9 −2.09721
\(325\) 20625.8 3.52035
\(326\) −5090.68 −0.864867
\(327\) −8794.11 −1.48720
\(328\) 6487.55 1.09212
\(329\) −192.439 −0.0322477
\(330\) −10950.6 −1.82669
\(331\) −2977.86 −0.494495 −0.247248 0.968952i \(-0.579526\pi\)
−0.247248 + 0.968952i \(0.579526\pi\)
\(332\) −1109.15 −0.183352
\(333\) 761.793 0.125363
\(334\) 7902.43 1.29462
\(335\) −13799.3 −2.25055
\(336\) −131.326 −0.0213227
\(337\) 3415.37 0.552069 0.276035 0.961148i \(-0.410980\pi\)
0.276035 + 0.961148i \(0.410980\pi\)
\(338\) −28466.6 −4.58101
\(339\) −2680.41 −0.429439
\(340\) −19414.9 −3.09682
\(341\) −5360.73 −0.851320
\(342\) −500.145 −0.0790782
\(343\) −386.441 −0.0608334
\(344\) 0 0
\(345\) 17814.4 2.77999
\(346\) −14293.8 −2.22093
\(347\) −4500.31 −0.696222 −0.348111 0.937453i \(-0.613177\pi\)
−0.348111 + 0.937453i \(0.613177\pi\)
\(348\) −779.632 −0.120094
\(349\) −746.598 −0.114511 −0.0572557 0.998360i \(-0.518235\pi\)
−0.0572557 + 0.998360i \(0.518235\pi\)
\(350\) −619.137 −0.0945550
\(351\) 11678.8 1.77598
\(352\) −1502.54 −0.227516
\(353\) 8674.41 1.30791 0.653955 0.756533i \(-0.273108\pi\)
0.653955 + 0.756533i \(0.273108\pi\)
\(354\) 8492.65 1.27508
\(355\) −7849.28 −1.17351
\(356\) −16983.4 −2.52843
\(357\) 213.668 0.0316764
\(358\) −20.9788 −0.00309711
\(359\) −6602.33 −0.970634 −0.485317 0.874338i \(-0.661296\pi\)
−0.485317 + 0.874338i \(0.661296\pi\)
\(360\) −2271.44 −0.332543
\(361\) −6005.93 −0.875628
\(362\) −7612.77 −1.10530
\(363\) 4699.37 0.679485
\(364\) 764.704 0.110114
\(365\) 670.177 0.0961059
\(366\) −1358.83 −0.194064
\(367\) 6165.86 0.876990 0.438495 0.898734i \(-0.355512\pi\)
0.438495 + 0.898734i \(0.355512\pi\)
\(368\) −7219.91 −1.02273
\(369\) −683.380 −0.0964102
\(370\) −19289.7 −2.71034
\(371\) −275.496 −0.0385526
\(372\) −20340.8 −2.83500
\(373\) −13214.6 −1.83438 −0.917191 0.398447i \(-0.869549\pi\)
−0.917191 + 0.398447i \(0.869549\pi\)
\(374\) −7220.79 −0.998337
\(375\) −10795.4 −1.48660
\(376\) 11561.1 1.58569
\(377\) 844.520 0.115371
\(378\) −350.569 −0.0477020
\(379\) −3031.81 −0.410907 −0.205453 0.978667i \(-0.565867\pi\)
−0.205453 + 0.978667i \(0.565867\pi\)
\(380\) 8269.35 1.11634
\(381\) −2221.78 −0.298755
\(382\) −3036.94 −0.406763
\(383\) −345.297 −0.0460675 −0.0230337 0.999735i \(-0.507333\pi\)
−0.0230337 + 0.999735i \(0.507333\pi\)
\(384\) −14651.5 −1.94708
\(385\) −232.498 −0.0307771
\(386\) −10326.6 −1.36169
\(387\) 0 0
\(388\) −4658.25 −0.609502
\(389\) 1815.47 0.236628 0.118314 0.992976i \(-0.462251\pi\)
0.118314 + 0.992976i \(0.462251\pi\)
\(390\) 45009.1 5.84391
\(391\) 11746.8 1.51934
\(392\) 11602.7 1.49496
\(393\) 12087.4 1.55147
\(394\) 4156.70 0.531501
\(395\) 612.365 0.0780037
\(396\) −1177.39 −0.149409
\(397\) 13316.0 1.68341 0.841704 0.539939i \(-0.181553\pi\)
0.841704 + 0.539939i \(0.181553\pi\)
\(398\) 22504.0 2.83423
\(399\) −91.0072 −0.0114187
\(400\) 9643.60 1.20545
\(401\) 3895.31 0.485094 0.242547 0.970140i \(-0.422017\pi\)
0.242547 + 0.970140i \(0.422017\pi\)
\(402\) −19473.8 −2.41608
\(403\) 22033.7 2.72352
\(404\) 4988.97 0.614383
\(405\) −15284.4 −1.87528
\(406\) −25.3505 −0.00309882
\(407\) −4684.49 −0.570520
\(408\) −12836.5 −1.55760
\(409\) 7160.50 0.865682 0.432841 0.901470i \(-0.357511\pi\)
0.432841 + 0.901470i \(0.357511\pi\)
\(410\) 17304.2 2.08437
\(411\) −4589.17 −0.550771
\(412\) 2001.58 0.239347
\(413\) 180.312 0.0214833
\(414\) 2933.38 0.348232
\(415\) −1386.06 −0.163949
\(416\) 6175.74 0.727862
\(417\) 10609.9 1.24597
\(418\) 3075.54 0.359879
\(419\) −8139.57 −0.949032 −0.474516 0.880247i \(-0.657377\pi\)
−0.474516 + 0.880247i \(0.657377\pi\)
\(420\) −882.190 −0.102492
\(421\) 4012.83 0.464545 0.232272 0.972651i \(-0.425384\pi\)
0.232272 + 0.972651i \(0.425384\pi\)
\(422\) 6947.80 0.801454
\(423\) −1217.82 −0.139982
\(424\) 16550.9 1.89572
\(425\) −15690.2 −1.79079
\(426\) −11077.0 −1.25982
\(427\) −28.8501 −0.00326969
\(428\) −4119.24 −0.465212
\(429\) 10930.4 1.23013
\(430\) 0 0
\(431\) 4194.35 0.468758 0.234379 0.972145i \(-0.424694\pi\)
0.234379 + 0.972145i \(0.424694\pi\)
\(432\) 5460.42 0.608136
\(433\) 7807.78 0.866555 0.433277 0.901261i \(-0.357357\pi\)
0.433277 + 0.901261i \(0.357357\pi\)
\(434\) −661.400 −0.0731526
\(435\) −974.269 −0.107385
\(436\) 23942.2 2.62986
\(437\) −5003.31 −0.547690
\(438\) 945.764 0.103174
\(439\) −16558.6 −1.80022 −0.900112 0.435660i \(-0.856515\pi\)
−0.900112 + 0.435660i \(0.856515\pi\)
\(440\) 13967.8 1.51338
\(441\) −1222.20 −0.131972
\(442\) 29678.9 3.19385
\(443\) −13329.5 −1.42958 −0.714788 0.699341i \(-0.753477\pi\)
−0.714788 + 0.699341i \(0.753477\pi\)
\(444\) −17774.8 −1.89990
\(445\) −21223.4 −2.26087
\(446\) 26329.0 2.79533
\(447\) −9348.44 −0.989185
\(448\) −375.409 −0.0395902
\(449\) −2475.47 −0.260189 −0.130094 0.991502i \(-0.541528\pi\)
−0.130094 + 0.991502i \(0.541528\pi\)
\(450\) −3918.10 −0.410447
\(451\) 4202.31 0.438756
\(452\) 7297.47 0.759390
\(453\) −5594.14 −0.580211
\(454\) −30440.8 −3.14682
\(455\) 955.614 0.0984613
\(456\) 5467.43 0.561482
\(457\) 11342.0 1.16095 0.580477 0.814276i \(-0.302866\pi\)
0.580477 + 0.814276i \(0.302866\pi\)
\(458\) 24668.9 2.51682
\(459\) −8884.13 −0.903433
\(460\) −48500.2 −4.91594
\(461\) −5072.43 −0.512465 −0.256233 0.966615i \(-0.582481\pi\)
−0.256233 + 0.966615i \(0.582481\pi\)
\(462\) −328.105 −0.0330407
\(463\) −13775.2 −1.38269 −0.691346 0.722524i \(-0.742982\pi\)
−0.691346 + 0.722524i \(0.742982\pi\)
\(464\) 394.856 0.0395059
\(465\) −25418.9 −2.53500
\(466\) 18925.6 1.88135
\(467\) 11957.0 1.18481 0.592403 0.805642i \(-0.298179\pi\)
0.592403 + 0.805642i \(0.298179\pi\)
\(468\) 4839.30 0.477984
\(469\) −413.459 −0.0407074
\(470\) 30836.9 3.02639
\(471\) 6838.73 0.669028
\(472\) −10832.6 −1.05638
\(473\) 0 0
\(474\) 864.180 0.0837407
\(475\) 6682.89 0.645541
\(476\) −581.715 −0.0560144
\(477\) −1743.43 −0.167350
\(478\) 1766.53 0.169036
\(479\) −15782.6 −1.50548 −0.752739 0.658319i \(-0.771268\pi\)
−0.752739 + 0.658319i \(0.771268\pi\)
\(480\) −7124.56 −0.677479
\(481\) 19254.2 1.82519
\(482\) −3899.21 −0.368473
\(483\) 533.763 0.0502837
\(484\) −12794.1 −1.20155
\(485\) −5821.20 −0.545004
\(486\) −4774.70 −0.445647
\(487\) 2228.11 0.207321 0.103661 0.994613i \(-0.466944\pi\)
0.103661 + 0.994613i \(0.466944\pi\)
\(488\) 1733.23 0.160778
\(489\) −5861.98 −0.542102
\(490\) 30947.8 2.85323
\(491\) −8782.43 −0.807221 −0.403611 0.914931i \(-0.632245\pi\)
−0.403611 + 0.914931i \(0.632245\pi\)
\(492\) 15945.2 1.46111
\(493\) −642.432 −0.0586890
\(494\) −12641.1 −1.15132
\(495\) −1471.32 −0.133598
\(496\) 10301.9 0.932597
\(497\) −235.183 −0.0212261
\(498\) −1956.03 −0.176008
\(499\) 680.761 0.0610722 0.0305361 0.999534i \(-0.490279\pi\)
0.0305361 + 0.999534i \(0.490279\pi\)
\(500\) 29390.8 2.62880
\(501\) 9099.74 0.811470
\(502\) 19129.4 1.70077
\(503\) 5406.14 0.479220 0.239610 0.970869i \(-0.422980\pi\)
0.239610 + 0.970869i \(0.422980\pi\)
\(504\) −68.0577 −0.00601494
\(505\) 6234.48 0.549368
\(506\) −18038.2 −1.58478
\(507\) −32779.7 −2.87139
\(508\) 6048.86 0.528297
\(509\) −21162.7 −1.84286 −0.921432 0.388539i \(-0.872980\pi\)
−0.921432 + 0.388539i \(0.872980\pi\)
\(510\) −34238.7 −2.97278
\(511\) 20.0801 0.00173834
\(512\) 14303.8 1.23465
\(513\) 3784.00 0.325668
\(514\) −14144.3 −1.21377
\(515\) 2501.29 0.214019
\(516\) 0 0
\(517\) 7488.71 0.637047
\(518\) −577.966 −0.0490238
\(519\) −16459.5 −1.39209
\(520\) −57410.4 −4.84156
\(521\) 172.007 0.0144641 0.00723203 0.999974i \(-0.497698\pi\)
0.00723203 + 0.999974i \(0.497698\pi\)
\(522\) −160.426 −0.0134515
\(523\) 6460.04 0.540111 0.270055 0.962845i \(-0.412958\pi\)
0.270055 + 0.962845i \(0.412958\pi\)
\(524\) −32908.1 −2.74351
\(525\) −712.944 −0.0592675
\(526\) 8766.15 0.726658
\(527\) −16761.2 −1.38544
\(528\) 5110.52 0.421225
\(529\) 17177.7 1.41183
\(530\) 44146.2 3.61809
\(531\) 1141.08 0.0932552
\(532\) 247.769 0.0201920
\(533\) −17272.3 −1.40366
\(534\) −29950.8 −2.42715
\(535\) −5147.62 −0.415983
\(536\) 24839.4 2.00167
\(537\) −24.1574 −0.00194128
\(538\) −16848.9 −1.35020
\(539\) 7515.65 0.600597
\(540\) 36680.7 2.92313
\(541\) −8894.36 −0.706837 −0.353418 0.935465i \(-0.614981\pi\)
−0.353418 + 0.935465i \(0.614981\pi\)
\(542\) 39490.6 3.12964
\(543\) −8766.21 −0.692806
\(544\) −4697.92 −0.370261
\(545\) 29919.4 2.35157
\(546\) 1348.58 0.105703
\(547\) 7309.10 0.571325 0.285662 0.958330i \(-0.407786\pi\)
0.285662 + 0.958330i \(0.407786\pi\)
\(548\) 12494.1 0.973945
\(549\) −182.573 −0.0141932
\(550\) 24093.6 1.86792
\(551\) 273.630 0.0211561
\(552\) −32066.8 −2.47256
\(553\) 18.3479 0.00141091
\(554\) 6177.27 0.473731
\(555\) −22212.4 −1.69885
\(556\) −28885.6 −2.20328
\(557\) −20239.8 −1.53965 −0.769826 0.638254i \(-0.779657\pi\)
−0.769826 + 0.638254i \(0.779657\pi\)
\(558\) −4185.56 −0.317543
\(559\) 0 0
\(560\) 446.798 0.0337155
\(561\) −8314.83 −0.625762
\(562\) −23041.6 −1.72945
\(563\) 4935.99 0.369498 0.184749 0.982786i \(-0.440853\pi\)
0.184749 + 0.982786i \(0.440853\pi\)
\(564\) 28415.2 2.12144
\(565\) 9119.31 0.679031
\(566\) −3805.87 −0.282637
\(567\) −457.957 −0.0339195
\(568\) 14129.1 1.04374
\(569\) 10385.0 0.765132 0.382566 0.923928i \(-0.375040\pi\)
0.382566 + 0.923928i \(0.375040\pi\)
\(570\) 14583.2 1.07162
\(571\) −8599.14 −0.630232 −0.315116 0.949053i \(-0.602043\pi\)
−0.315116 + 0.949053i \(0.602043\pi\)
\(572\) −29758.3 −2.17527
\(573\) −3497.08 −0.254961
\(574\) 518.475 0.0377016
\(575\) −39195.6 −2.84273
\(576\) −2375.71 −0.171854
\(577\) 14110.2 1.01805 0.509026 0.860751i \(-0.330006\pi\)
0.509026 + 0.860751i \(0.330006\pi\)
\(578\) 1011.59 0.0727972
\(579\) −11891.3 −0.853513
\(580\) 2652.47 0.189893
\(581\) −41.5296 −0.00296547
\(582\) −8214.97 −0.585088
\(583\) 10720.9 0.761599
\(584\) −1206.35 −0.0854778
\(585\) 6047.45 0.427404
\(586\) −25092.1 −1.76885
\(587\) 5528.80 0.388753 0.194376 0.980927i \(-0.437732\pi\)
0.194376 + 0.980927i \(0.437732\pi\)
\(588\) 28517.4 2.00006
\(589\) 7139.07 0.499423
\(590\) −28893.8 −2.01617
\(591\) 4786.49 0.333147
\(592\) 9002.32 0.624988
\(593\) −14338.2 −0.992918 −0.496459 0.868060i \(-0.665367\pi\)
−0.496459 + 0.868060i \(0.665367\pi\)
\(594\) 13642.3 0.942343
\(595\) −726.942 −0.0500869
\(596\) 25451.3 1.74921
\(597\) 25913.6 1.77651
\(598\) 74140.9 5.06998
\(599\) 17319.7 1.18141 0.590705 0.806888i \(-0.298850\pi\)
0.590705 + 0.806888i \(0.298850\pi\)
\(600\) 42831.5 2.91431
\(601\) 28433.6 1.92984 0.964918 0.262550i \(-0.0845633\pi\)
0.964918 + 0.262550i \(0.0845633\pi\)
\(602\) 0 0
\(603\) −2616.51 −0.176704
\(604\) 15230.2 1.02600
\(605\) −15988.2 −1.07440
\(606\) 8798.20 0.589773
\(607\) 6746.30 0.451110 0.225555 0.974230i \(-0.427580\pi\)
0.225555 + 0.974230i \(0.427580\pi\)
\(608\) 2000.98 0.133471
\(609\) −29.1914 −0.00194236
\(610\) 4623.03 0.306854
\(611\) −30780.2 −2.03802
\(612\) −3681.29 −0.243149
\(613\) −4756.54 −0.313401 −0.156701 0.987646i \(-0.550086\pi\)
−0.156701 + 0.987646i \(0.550086\pi\)
\(614\) −26094.2 −1.71511
\(615\) 19926.0 1.30649
\(616\) 418.507 0.0273736
\(617\) −13947.4 −0.910051 −0.455026 0.890478i \(-0.650370\pi\)
−0.455026 + 0.890478i \(0.650370\pi\)
\(618\) 3529.86 0.229760
\(619\) 10744.9 0.697699 0.348849 0.937179i \(-0.386572\pi\)
0.348849 + 0.937179i \(0.386572\pi\)
\(620\) 69203.5 4.48271
\(621\) −22193.4 −1.43412
\(622\) −2084.52 −0.134375
\(623\) −635.903 −0.0408939
\(624\) −21005.3 −1.34757
\(625\) 8127.28 0.520146
\(626\) −34234.9 −2.18579
\(627\) 3541.52 0.225574
\(628\) −18618.6 −1.18306
\(629\) −14646.8 −0.928468
\(630\) −181.530 −0.0114799
\(631\) −8390.63 −0.529360 −0.264680 0.964336i \(-0.585266\pi\)
−0.264680 + 0.964336i \(0.585266\pi\)
\(632\) −1102.29 −0.0693775
\(633\) 8000.48 0.502355
\(634\) 19048.6 1.19324
\(635\) 7558.97 0.472392
\(636\) 40679.2 2.53622
\(637\) −30890.9 −1.92141
\(638\) 986.508 0.0612167
\(639\) −1488.32 −0.0921390
\(640\) 49847.3 3.07873
\(641\) −6432.67 −0.396373 −0.198187 0.980164i \(-0.563505\pi\)
−0.198187 + 0.980164i \(0.563505\pi\)
\(642\) −7264.41 −0.446578
\(643\) 6600.52 0.404820 0.202410 0.979301i \(-0.435123\pi\)
0.202410 + 0.979301i \(0.435123\pi\)
\(644\) −1453.18 −0.0889182
\(645\) 0 0
\(646\) 9616.17 0.585671
\(647\) 16454.6 0.999839 0.499920 0.866072i \(-0.333363\pi\)
0.499920 + 0.866072i \(0.333363\pi\)
\(648\) 27512.6 1.66790
\(649\) −7016.82 −0.424398
\(650\) −99029.6 −5.97579
\(651\) −761.610 −0.0458523
\(652\) 15959.4 0.958615
\(653\) 22219.0 1.33154 0.665771 0.746156i \(-0.268103\pi\)
0.665771 + 0.746156i \(0.268103\pi\)
\(654\) 42222.7 2.52452
\(655\) −41123.7 −2.45318
\(656\) −8075.70 −0.480645
\(657\) 127.073 0.00754582
\(658\) 923.947 0.0547404
\(659\) −29368.5 −1.73601 −0.868007 0.496551i \(-0.834599\pi\)
−0.868007 + 0.496551i \(0.834599\pi\)
\(660\) 34330.2 2.02470
\(661\) −16178.2 −0.951981 −0.475990 0.879451i \(-0.657910\pi\)
−0.475990 + 0.879451i \(0.657910\pi\)
\(662\) 14297.4 0.839405
\(663\) 34175.7 2.00192
\(664\) 2494.97 0.145819
\(665\) 309.625 0.0180553
\(666\) −3657.56 −0.212804
\(667\) −1604.86 −0.0931639
\(668\) −24774.3 −1.43495
\(669\) 30318.2 1.75212
\(670\) 66253.9 3.82031
\(671\) 1122.70 0.0645920
\(672\) −213.469 −0.0122541
\(673\) −30064.0 −1.72197 −0.860983 0.508634i \(-0.830151\pi\)
−0.860983 + 0.508634i \(0.830151\pi\)
\(674\) −16398.1 −0.937136
\(675\) 29643.6 1.69035
\(676\) 89243.4 5.07757
\(677\) −27396.2 −1.55528 −0.777638 0.628713i \(-0.783582\pi\)
−0.777638 + 0.628713i \(0.783582\pi\)
\(678\) 12869.3 0.728972
\(679\) −174.417 −0.00985788
\(680\) 43672.4 2.46288
\(681\) −35053.0 −1.97244
\(682\) 25738.2 1.44511
\(683\) −27000.7 −1.51267 −0.756335 0.654185i \(-0.773012\pi\)
−0.756335 + 0.654185i \(0.773012\pi\)
\(684\) 1567.97 0.0876501
\(685\) 15613.3 0.870881
\(686\) 1855.40 0.103265
\(687\) 28406.6 1.57755
\(688\) 0 0
\(689\) −44064.9 −2.43649
\(690\) −85531.6 −4.71903
\(691\) −20353.7 −1.12054 −0.560270 0.828310i \(-0.689303\pi\)
−0.560270 + 0.828310i \(0.689303\pi\)
\(692\) 44811.4 2.46167
\(693\) −44.0843 −0.00241649
\(694\) 21607.1 1.18184
\(695\) −36097.0 −1.97013
\(696\) 1753.73 0.0955100
\(697\) 13139.2 0.714035
\(698\) 3584.61 0.194383
\(699\) 21793.0 1.17924
\(700\) 1941.01 0.104804
\(701\) −12725.1 −0.685622 −0.342811 0.939404i \(-0.611379\pi\)
−0.342811 + 0.939404i \(0.611379\pi\)
\(702\) −56072.8 −3.01472
\(703\) 6238.49 0.334693
\(704\) 14608.9 0.782096
\(705\) 35509.1 1.89695
\(706\) −41648.0 −2.22018
\(707\) 186.800 0.00993681
\(708\) −26624.6 −1.41330
\(709\) −29784.5 −1.57769 −0.788843 0.614595i \(-0.789320\pi\)
−0.788843 + 0.614595i \(0.789320\pi\)
\(710\) 37686.4 1.99203
\(711\) 116.112 0.00612451
\(712\) 38203.1 2.01085
\(713\) −41871.1 −2.19928
\(714\) −1025.87 −0.0537707
\(715\) −37187.5 −1.94508
\(716\) 65.7689 0.00343282
\(717\) 2034.18 0.105952
\(718\) 31699.4 1.64765
\(719\) −26156.8 −1.35673 −0.678363 0.734727i \(-0.737310\pi\)
−0.678363 + 0.734727i \(0.737310\pi\)
\(720\) 2827.49 0.146353
\(721\) 74.9444 0.00387112
\(722\) 28836.0 1.48638
\(723\) −4489.99 −0.230961
\(724\) 23866.2 1.22511
\(725\) 2143.60 0.109809
\(726\) −22562.9 −1.15342
\(727\) −13708.6 −0.699346 −0.349673 0.936872i \(-0.613707\pi\)
−0.349673 + 0.936872i \(0.613707\pi\)
\(728\) −1720.15 −0.0875728
\(729\) 16441.4 0.835312
\(730\) −3217.69 −0.163140
\(731\) 0 0
\(732\) 4259.96 0.215099
\(733\) −19482.8 −0.981736 −0.490868 0.871234i \(-0.663320\pi\)
−0.490868 + 0.871234i \(0.663320\pi\)
\(734\) −29603.8 −1.48869
\(735\) 35636.8 1.78841
\(736\) −11735.9 −0.587758
\(737\) 16089.7 0.804167
\(738\) 3281.08 0.163656
\(739\) 9397.10 0.467764 0.233882 0.972265i \(-0.424857\pi\)
0.233882 + 0.972265i \(0.424857\pi\)
\(740\) 60473.7 3.00413
\(741\) −14556.4 −0.721650
\(742\) 1322.72 0.0654430
\(743\) 21996.2 1.08609 0.543044 0.839705i \(-0.317272\pi\)
0.543044 + 0.839705i \(0.317272\pi\)
\(744\) 45755.2 2.25466
\(745\) 31805.3 1.56410
\(746\) 63446.5 3.11386
\(747\) −262.813 −0.0128726
\(748\) 22637.3 1.10655
\(749\) −154.235 −0.00752419
\(750\) 51831.6 2.52350
\(751\) 26869.9 1.30559 0.652795 0.757534i \(-0.273596\pi\)
0.652795 + 0.757534i \(0.273596\pi\)
\(752\) −14391.3 −0.697867
\(753\) 22027.8 1.06605
\(754\) −4054.75 −0.195843
\(755\) 19032.4 0.917431
\(756\) 1099.04 0.0528727
\(757\) −1187.31 −0.0570058 −0.0285029 0.999594i \(-0.509074\pi\)
−0.0285029 + 0.999594i \(0.509074\pi\)
\(758\) 14556.5 0.697514
\(759\) −20771.3 −0.993345
\(760\) −18601.3 −0.887818
\(761\) −3960.08 −0.188637 −0.0943185 0.995542i \(-0.530067\pi\)
−0.0943185 + 0.995542i \(0.530067\pi\)
\(762\) 10667.3 0.507135
\(763\) 896.455 0.0425345
\(764\) 9520.88 0.450855
\(765\) −4600.33 −0.217419
\(766\) 1657.86 0.0781995
\(767\) 28840.6 1.35772
\(768\) 40883.7 1.92092
\(769\) −18342.9 −0.860157 −0.430079 0.902791i \(-0.641514\pi\)
−0.430079 + 0.902791i \(0.641514\pi\)
\(770\) 1116.28 0.0522441
\(771\) −16287.3 −0.760796
\(772\) 32374.2 1.50929
\(773\) 10523.7 0.489667 0.244834 0.969565i \(-0.421267\pi\)
0.244834 + 0.969565i \(0.421267\pi\)
\(774\) 0 0
\(775\) 55927.0 2.59220
\(776\) 10478.4 0.484734
\(777\) −665.535 −0.0307284
\(778\) −8716.55 −0.401675
\(779\) −5596.36 −0.257394
\(780\) −141104. −6.47737
\(781\) 9152.09 0.419318
\(782\) −56399.4 −2.57908
\(783\) 1213.75 0.0553973
\(784\) −14443.0 −0.657938
\(785\) −23266.8 −1.05787
\(786\) −58034.4 −2.63361
\(787\) 1362.84 0.0617281 0.0308641 0.999524i \(-0.490174\pi\)
0.0308641 + 0.999524i \(0.490174\pi\)
\(788\) −13031.3 −0.589114
\(789\) 10094.3 0.455473
\(790\) −2940.12 −0.132411
\(791\) 273.236 0.0122821
\(792\) 2648.45 0.118824
\(793\) −4614.52 −0.206641
\(794\) −63933.7 −2.85758
\(795\) 50834.9 2.26783
\(796\) −70550.4 −3.14145
\(797\) −30311.6 −1.34717 −0.673584 0.739111i \(-0.735246\pi\)
−0.673584 + 0.739111i \(0.735246\pi\)
\(798\) 436.948 0.0193832
\(799\) 23414.7 1.03673
\(800\) 15675.5 0.692768
\(801\) −4024.21 −0.177514
\(802\) −18702.4 −0.823446
\(803\) −781.411 −0.0343405
\(804\) 61050.7 2.67797
\(805\) −1815.97 −0.0795088
\(806\) −105789. −4.62317
\(807\) −19401.7 −0.846309
\(808\) −11222.4 −0.488615
\(809\) 39233.5 1.70504 0.852520 0.522694i \(-0.175073\pi\)
0.852520 + 0.522694i \(0.175073\pi\)
\(810\) 73384.3 3.18328
\(811\) −43510.5 −1.88392 −0.941961 0.335723i \(-0.891019\pi\)
−0.941961 + 0.335723i \(0.891019\pi\)
\(812\) 79.4742 0.00343473
\(813\) 45473.9 1.96167
\(814\) 22491.4 0.968456
\(815\) 19943.7 0.857174
\(816\) 15978.9 0.685505
\(817\) 0 0
\(818\) −34379.4 −1.46949
\(819\) 181.196 0.00773076
\(820\) −54249.0 −2.31031
\(821\) −20770.7 −0.882951 −0.441475 0.897273i \(-0.645545\pi\)
−0.441475 + 0.897273i \(0.645545\pi\)
\(822\) 22033.7 0.934933
\(823\) −15244.0 −0.645652 −0.322826 0.946458i \(-0.604633\pi\)
−0.322826 + 0.946458i \(0.604633\pi\)
\(824\) −4502.43 −0.190351
\(825\) 27744.1 1.17082
\(826\) −865.725 −0.0364678
\(827\) −32831.8 −1.38050 −0.690251 0.723570i \(-0.742500\pi\)
−0.690251 + 0.723570i \(0.742500\pi\)
\(828\) −9196.21 −0.385979
\(829\) 20720.4 0.868092 0.434046 0.900891i \(-0.357086\pi\)
0.434046 + 0.900891i \(0.357086\pi\)
\(830\) 6654.82 0.278304
\(831\) 7113.21 0.296937
\(832\) −60045.8 −2.50206
\(833\) 23498.9 0.977417
\(834\) −50940.7 −2.11503
\(835\) −30959.2 −1.28310
\(836\) −9641.88 −0.398889
\(837\) 31667.1 1.30774
\(838\) 39080.1 1.61098
\(839\) −45367.8 −1.86683 −0.933415 0.358799i \(-0.883186\pi\)
−0.933415 + 0.358799i \(0.883186\pi\)
\(840\) 1984.43 0.0815110
\(841\) −24301.2 −0.996401
\(842\) −19266.6 −0.788564
\(843\) −26532.7 −1.08403
\(844\) −21781.5 −0.888329
\(845\) 111523. 4.54026
\(846\) 5847.04 0.237619
\(847\) −479.045 −0.0194335
\(848\) −20602.6 −0.834311
\(849\) −4382.50 −0.177158
\(850\) 75332.5 3.03986
\(851\) −36589.1 −1.47387
\(852\) 34726.7 1.39638
\(853\) 9272.95 0.372216 0.186108 0.982529i \(-0.440413\pi\)
0.186108 + 0.982529i \(0.440413\pi\)
\(854\) 138.517 0.00555029
\(855\) 1959.41 0.0783748
\(856\) 9265.95 0.369981
\(857\) 8958.78 0.357090 0.178545 0.983932i \(-0.442861\pi\)
0.178545 + 0.983932i \(0.442861\pi\)
\(858\) −52479.6 −2.08814
\(859\) −3992.34 −0.158576 −0.0792880 0.996852i \(-0.525265\pi\)
−0.0792880 + 0.996852i \(0.525265\pi\)
\(860\) 0 0
\(861\) 597.030 0.0236315
\(862\) −20138.1 −0.795717
\(863\) 25382.8 1.00121 0.500603 0.865677i \(-0.333112\pi\)
0.500603 + 0.865677i \(0.333112\pi\)
\(864\) 8875.85 0.349494
\(865\) 55998.7 2.20117
\(866\) −37487.1 −1.47098
\(867\) 1164.86 0.0456296
\(868\) 2073.50 0.0810820
\(869\) −714.005 −0.0278722
\(870\) 4677.71 0.182287
\(871\) −66131.9 −2.57267
\(872\) −53856.3 −2.09152
\(873\) −1103.77 −0.0427914
\(874\) 24022.1 0.929704
\(875\) 1100.47 0.0425172
\(876\) −2964.99 −0.114358
\(877\) −34007.1 −1.30940 −0.654698 0.755891i \(-0.727204\pi\)
−0.654698 + 0.755891i \(0.727204\pi\)
\(878\) 79501.9 3.05588
\(879\) −28893.8 −1.10872
\(880\) −17387.0 −0.666042
\(881\) −34430.4 −1.31667 −0.658337 0.752723i \(-0.728740\pi\)
−0.658337 + 0.752723i \(0.728740\pi\)
\(882\) 5868.07 0.224023
\(883\) −4762.11 −0.181492 −0.0907461 0.995874i \(-0.528925\pi\)
−0.0907461 + 0.995874i \(0.528925\pi\)
\(884\) −93044.0 −3.54006
\(885\) −33271.6 −1.26374
\(886\) 63998.2 2.42670
\(887\) 42087.0 1.59317 0.796587 0.604524i \(-0.206637\pi\)
0.796587 + 0.604524i \(0.206637\pi\)
\(888\) 39983.3 1.51098
\(889\) 226.485 0.00854449
\(890\) 101899. 3.83782
\(891\) 17821.3 0.670074
\(892\) −82542.1 −3.09833
\(893\) −9972.97 −0.373721
\(894\) 44884.2 1.67914
\(895\) 82.1884 0.00306956
\(896\) 1493.54 0.0556873
\(897\) 85374.2 3.17788
\(898\) 11885.4 0.441670
\(899\) 2289.92 0.0849536
\(900\) 12283.3 0.454938
\(901\) 33520.5 1.23943
\(902\) −20176.3 −0.744787
\(903\) 0 0
\(904\) −16415.2 −0.603939
\(905\) 29824.5 1.09547
\(906\) 26858.9 0.984907
\(907\) −25450.7 −0.931726 −0.465863 0.884857i \(-0.654256\pi\)
−0.465863 + 0.884857i \(0.654256\pi\)
\(908\) 95432.5 3.48793
\(909\) 1182.13 0.0431340
\(910\) −4588.14 −0.167138
\(911\) 19434.6 0.706804 0.353402 0.935472i \(-0.385025\pi\)
0.353402 + 0.935472i \(0.385025\pi\)
\(912\) −6805.85 −0.247110
\(913\) 1616.11 0.0585822
\(914\) −54455.8 −1.97072
\(915\) 5323.48 0.192337
\(916\) −77337.6 −2.78963
\(917\) −1232.16 −0.0443725
\(918\) 42654.9 1.53358
\(919\) 479.135 0.0171983 0.00859913 0.999963i \(-0.497263\pi\)
0.00859913 + 0.999963i \(0.497263\pi\)
\(920\) 109098. 3.90962
\(921\) −30047.8 −1.07504
\(922\) 24354.0 0.869909
\(923\) −37617.0 −1.34147
\(924\) 1028.61 0.0366222
\(925\) 48872.0 1.73719
\(926\) 66138.0 2.34712
\(927\) 474.273 0.0168039
\(928\) 641.833 0.0227039
\(929\) −8375.21 −0.295782 −0.147891 0.989004i \(-0.547249\pi\)
−0.147891 + 0.989004i \(0.547249\pi\)
\(930\) 122043. 4.30316
\(931\) −10008.8 −0.352338
\(932\) −59332.1 −2.08529
\(933\) −2400.35 −0.0842271
\(934\) −57408.6 −2.01121
\(935\) 28288.8 0.989457
\(936\) −10885.7 −0.380138
\(937\) −15853.9 −0.552746 −0.276373 0.961050i \(-0.589133\pi\)
−0.276373 + 0.961050i \(0.589133\pi\)
\(938\) 1985.12 0.0691008
\(939\) −39422.0 −1.37006
\(940\) −96674.3 −3.35444
\(941\) −2647.73 −0.0917253 −0.0458626 0.998948i \(-0.514604\pi\)
−0.0458626 + 0.998948i \(0.514604\pi\)
\(942\) −32834.5 −1.13567
\(943\) 32823.0 1.13347
\(944\) 13484.4 0.464916
\(945\) 1373.42 0.0472776
\(946\) 0 0
\(947\) −27521.2 −0.944369 −0.472185 0.881500i \(-0.656534\pi\)
−0.472185 + 0.881500i \(0.656534\pi\)
\(948\) −2709.22 −0.0928179
\(949\) 3211.76 0.109861
\(950\) −32086.3 −1.09581
\(951\) 21934.7 0.747930
\(952\) 1308.53 0.0445480
\(953\) −49753.8 −1.69117 −0.845585 0.533842i \(-0.820748\pi\)
−0.845585 + 0.533842i \(0.820748\pi\)
\(954\) 8370.64 0.284077
\(955\) 11897.8 0.403145
\(956\) −5538.11 −0.187359
\(957\) 1135.98 0.0383709
\(958\) 75776.1 2.55555
\(959\) 467.811 0.0157523
\(960\) 69271.0 2.32887
\(961\) 29953.7 1.00546
\(962\) −92444.3 −3.09826
\(963\) −976.049 −0.0326612
\(964\) 12224.1 0.408415
\(965\) 40456.5 1.34958
\(966\) −2562.73 −0.0853566
\(967\) 52924.4 1.76002 0.880008 0.474960i \(-0.157537\pi\)
0.880008 + 0.474960i \(0.157537\pi\)
\(968\) 28779.6 0.955589
\(969\) 11073.1 0.367101
\(970\) 27949.0 0.925144
\(971\) 40927.9 1.35267 0.676333 0.736596i \(-0.263568\pi\)
0.676333 + 0.736596i \(0.263568\pi\)
\(972\) 14968.8 0.493954
\(973\) −1081.55 −0.0356351
\(974\) −10697.7 −0.351928
\(975\) −114034. −3.74565
\(976\) −2157.52 −0.0707588
\(977\) 43543.0 1.42586 0.712930 0.701236i \(-0.247368\pi\)
0.712930 + 0.701236i \(0.247368\pi\)
\(978\) 28144.8 0.920218
\(979\) 24746.0 0.807852
\(980\) −97022.1 −3.16251
\(981\) 5673.07 0.184635
\(982\) 42166.7 1.37026
\(983\) −46016.6 −1.49309 −0.746543 0.665337i \(-0.768288\pi\)
−0.746543 + 0.665337i \(0.768288\pi\)
\(984\) −35867.7 −1.16201
\(985\) −16284.6 −0.526774
\(986\) 3084.48 0.0996245
\(987\) 1063.94 0.0343115
\(988\) 39630.1 1.27612
\(989\) 0 0
\(990\) 7064.19 0.226783
\(991\) −42967.2 −1.37729 −0.688646 0.725098i \(-0.741795\pi\)
−0.688646 + 0.725098i \(0.741795\pi\)
\(992\) 16745.6 0.535960
\(993\) 16463.7 0.526143
\(994\) 1129.17 0.0360313
\(995\) −88163.5 −2.80902
\(996\) 6132.19 0.195086
\(997\) −43345.3 −1.37689 −0.688445 0.725288i \(-0.741706\pi\)
−0.688445 + 0.725288i \(0.741706\pi\)
\(998\) −3268.50 −0.103670
\(999\) 27672.4 0.876392
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.i.1.6 50
43.42 odd 2 1849.4.a.j.1.45 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.6 50 1.1 even 1 trivial
1849.4.a.j.1.45 yes 50 43.42 odd 2