Properties

Label 1849.4.a.j.1.49
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 1.49
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.40604 q^{2} +2.51556 q^{3} +21.2252 q^{4} +3.24888 q^{5} +13.5992 q^{6} -35.6131 q^{7} +71.4960 q^{8} -20.6720 q^{9} +O(q^{10})\) \(q+5.40604 q^{2} +2.51556 q^{3} +21.2252 q^{4} +3.24888 q^{5} +13.5992 q^{6} -35.6131 q^{7} +71.4960 q^{8} -20.6720 q^{9} +17.5635 q^{10} -42.5559 q^{11} +53.3932 q^{12} +22.6295 q^{13} -192.525 q^{14} +8.17273 q^{15} +216.708 q^{16} -6.66526 q^{17} -111.753 q^{18} -14.7438 q^{19} +68.9581 q^{20} -89.5866 q^{21} -230.059 q^{22} -95.0580 q^{23} +179.852 q^{24} -114.445 q^{25} +122.336 q^{26} -119.922 q^{27} -755.895 q^{28} -125.391 q^{29} +44.1820 q^{30} +56.0788 q^{31} +599.564 q^{32} -107.052 q^{33} -36.0326 q^{34} -115.702 q^{35} -438.767 q^{36} -217.165 q^{37} -79.7056 q^{38} +56.9257 q^{39} +232.282 q^{40} +342.891 q^{41} -484.308 q^{42} -903.258 q^{44} -67.1607 q^{45} -513.887 q^{46} -399.043 q^{47} +545.141 q^{48} +925.290 q^{49} -618.693 q^{50} -16.7668 q^{51} +480.316 q^{52} +211.948 q^{53} -648.300 q^{54} -138.259 q^{55} -2546.19 q^{56} -37.0889 q^{57} -677.869 q^{58} -435.319 q^{59} +173.468 q^{60} +693.529 q^{61} +303.164 q^{62} +736.193 q^{63} +1507.60 q^{64} +73.5204 q^{65} -578.725 q^{66} -141.684 q^{67} -141.472 q^{68} -239.124 q^{69} -625.491 q^{70} -632.678 q^{71} -1477.96 q^{72} +736.909 q^{73} -1174.00 q^{74} -287.892 q^{75} -312.941 q^{76} +1515.55 q^{77} +307.743 q^{78} +165.173 q^{79} +704.058 q^{80} +256.474 q^{81} +1853.68 q^{82} -1207.11 q^{83} -1901.50 q^{84} -21.6546 q^{85} -315.428 q^{87} -3042.58 q^{88} -385.206 q^{89} -363.073 q^{90} -805.906 q^{91} -2017.63 q^{92} +141.069 q^{93} -2157.24 q^{94} -47.9008 q^{95} +1508.24 q^{96} +625.326 q^{97} +5002.15 q^{98} +879.715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} + 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} + 386q^{18} - 12q^{19} - 108q^{20} - 408q^{21} - 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} - 1493q^{26} - 10q^{27} + 242q^{28} - 208q^{29} + 48q^{30} - 932q^{31} + 1124q^{32} - 254q^{33} - 765q^{34} - 1452q^{35} + 747q^{36} + 90q^{37} - 1213q^{38} + 1610q^{39} - 1693q^{40} - 1354q^{41} + 16q^{42} - 2704q^{44} - 4508q^{45} - 233q^{46} - 3484q^{47} + 376q^{48} + 1324q^{49} + 408q^{50} - 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} + 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} - 1172q^{61} + 1546q^{62} + 3686q^{63} + 606q^{64} - 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} - 136q^{69} + 1310q^{70} - 162q^{71} + 5814q^{72} - 746q^{73} - 4332q^{74} - 236q^{75} - 1338q^{76} - 2024q^{77} - 2782q^{78} - 2656q^{79} + 5713q^{80} - 86q^{81} + 4168q^{82} - 3514q^{83} - 4269q^{84} + 7558q^{85} - 10278q^{87} - 11692q^{88} - 2640q^{89} - 8286q^{90} + 5946q^{91} - 4271q^{92} + 2q^{93} - 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} + 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.40604 1.91132 0.955661 0.294469i \(-0.0951428\pi\)
0.955661 + 0.294469i \(0.0951428\pi\)
\(3\) 2.51556 0.484119 0.242059 0.970261i \(-0.422177\pi\)
0.242059 + 0.970261i \(0.422177\pi\)
\(4\) 21.2252 2.65315
\(5\) 3.24888 0.290588 0.145294 0.989389i \(-0.453587\pi\)
0.145294 + 0.989389i \(0.453587\pi\)
\(6\) 13.5992 0.925307
\(7\) −35.6131 −1.92292 −0.961462 0.274937i \(-0.911343\pi\)
−0.961462 + 0.274937i \(0.911343\pi\)
\(8\) 71.4960 3.15971
\(9\) −20.6720 −0.765629
\(10\) 17.5635 0.555408
\(11\) −42.5559 −1.16646 −0.583231 0.812306i \(-0.698212\pi\)
−0.583231 + 0.812306i \(0.698212\pi\)
\(12\) 53.3932 1.28444
\(13\) 22.6295 0.482792 0.241396 0.970427i \(-0.422395\pi\)
0.241396 + 0.970427i \(0.422395\pi\)
\(14\) −192.525 −3.67533
\(15\) 8.17273 0.140679
\(16\) 216.708 3.38606
\(17\) −6.66526 −0.0950919 −0.0475460 0.998869i \(-0.515140\pi\)
−0.0475460 + 0.998869i \(0.515140\pi\)
\(18\) −111.753 −1.46336
\(19\) −14.7438 −0.178024 −0.0890122 0.996031i \(-0.528371\pi\)
−0.0890122 + 0.996031i \(0.528371\pi\)
\(20\) 68.9581 0.770975
\(21\) −89.5866 −0.930924
\(22\) −230.059 −2.22948
\(23\) −95.0580 −0.861781 −0.430891 0.902404i \(-0.641801\pi\)
−0.430891 + 0.902404i \(0.641801\pi\)
\(24\) 179.852 1.52967
\(25\) −114.445 −0.915558
\(26\) 122.336 0.922771
\(27\) −119.922 −0.854774
\(28\) −755.895 −5.10181
\(29\) −125.391 −0.802915 −0.401458 0.915878i \(-0.631496\pi\)
−0.401458 + 0.915878i \(0.631496\pi\)
\(30\) 44.1820 0.268883
\(31\) 56.0788 0.324905 0.162452 0.986716i \(-0.448060\pi\)
0.162452 + 0.986716i \(0.448060\pi\)
\(32\) 599.564 3.31215
\(33\) −107.052 −0.564706
\(34\) −36.0326 −0.181751
\(35\) −115.702 −0.558779
\(36\) −438.767 −2.03133
\(37\) −217.165 −0.964911 −0.482456 0.875920i \(-0.660255\pi\)
−0.482456 + 0.875920i \(0.660255\pi\)
\(38\) −79.7056 −0.340262
\(39\) 56.9257 0.233729
\(40\) 232.282 0.918174
\(41\) 342.891 1.30611 0.653055 0.757310i \(-0.273487\pi\)
0.653055 + 0.757310i \(0.273487\pi\)
\(42\) −484.308 −1.77930
\(43\) 0 0
\(44\) −903.258 −3.09480
\(45\) −67.1607 −0.222483
\(46\) −513.887 −1.64714
\(47\) −399.043 −1.23843 −0.619217 0.785220i \(-0.712550\pi\)
−0.619217 + 0.785220i \(0.712550\pi\)
\(48\) 545.141 1.63926
\(49\) 925.290 2.69764
\(50\) −618.693 −1.74993
\(51\) −16.7668 −0.0460358
\(52\) 480.316 1.28092
\(53\) 211.948 0.549307 0.274653 0.961543i \(-0.411437\pi\)
0.274653 + 0.961543i \(0.411437\pi\)
\(54\) −648.300 −1.63375
\(55\) −138.259 −0.338960
\(56\) −2546.19 −6.07588
\(57\) −37.0889 −0.0861850
\(58\) −677.869 −1.53463
\(59\) −435.319 −0.960572 −0.480286 0.877112i \(-0.659467\pi\)
−0.480286 + 0.877112i \(0.659467\pi\)
\(60\) 173.468 0.373243
\(61\) 693.529 1.45569 0.727847 0.685740i \(-0.240521\pi\)
0.727847 + 0.685740i \(0.240521\pi\)
\(62\) 303.164 0.620998
\(63\) 736.193 1.47225
\(64\) 1507.60 2.94453
\(65\) 73.5204 0.140294
\(66\) −578.725 −1.07934
\(67\) −141.684 −0.258351 −0.129175 0.991622i \(-0.541233\pi\)
−0.129175 + 0.991622i \(0.541233\pi\)
\(68\) −141.472 −0.252293
\(69\) −239.124 −0.417205
\(70\) −625.491 −1.06801
\(71\) −632.678 −1.05754 −0.528768 0.848766i \(-0.677346\pi\)
−0.528768 + 0.848766i \(0.677346\pi\)
\(72\) −1477.96 −2.41916
\(73\) 736.909 1.18149 0.590744 0.806859i \(-0.298834\pi\)
0.590744 + 0.806859i \(0.298834\pi\)
\(74\) −1174.00 −1.84426
\(75\) −287.892 −0.443239
\(76\) −312.941 −0.472326
\(77\) 1515.55 2.24302
\(78\) 307.743 0.446731
\(79\) 165.173 0.235233 0.117617 0.993059i \(-0.462475\pi\)
0.117617 + 0.993059i \(0.462475\pi\)
\(80\) 704.058 0.983951
\(81\) 256.474 0.351817
\(82\) 1853.68 2.49640
\(83\) −1207.11 −1.59635 −0.798177 0.602422i \(-0.794202\pi\)
−0.798177 + 0.602422i \(0.794202\pi\)
\(84\) −1901.50 −2.46988
\(85\) −21.6546 −0.0276326
\(86\) 0 0
\(87\) −315.428 −0.388706
\(88\) −3042.58 −3.68568
\(89\) −385.206 −0.458783 −0.229392 0.973334i \(-0.573674\pi\)
−0.229392 + 0.973334i \(0.573674\pi\)
\(90\) −363.073 −0.425236
\(91\) −805.906 −0.928372
\(92\) −2017.63 −2.28644
\(93\) 141.069 0.157293
\(94\) −2157.24 −2.36705
\(95\) −47.9008 −0.0517318
\(96\) 1508.24 1.60348
\(97\) 625.326 0.654559 0.327279 0.944928i \(-0.393868\pi\)
0.327279 + 0.944928i \(0.393868\pi\)
\(98\) 5002.15 5.15606
\(99\) 879.715 0.893077
\(100\) −2429.12 −2.42912
\(101\) −112.459 −0.110793 −0.0553965 0.998464i \(-0.517642\pi\)
−0.0553965 + 0.998464i \(0.517642\pi\)
\(102\) −90.6421 −0.0879892
\(103\) −1643.53 −1.57225 −0.786124 0.618068i \(-0.787916\pi\)
−0.786124 + 0.618068i \(0.787916\pi\)
\(104\) 1617.92 1.52548
\(105\) −291.056 −0.270516
\(106\) 1145.80 1.04990
\(107\) 865.531 0.782001 0.391000 0.920391i \(-0.372129\pi\)
0.391000 + 0.920391i \(0.372129\pi\)
\(108\) −2545.36 −2.26785
\(109\) 147.602 0.129703 0.0648517 0.997895i \(-0.479343\pi\)
0.0648517 + 0.997895i \(0.479343\pi\)
\(110\) −747.432 −0.647862
\(111\) −546.291 −0.467132
\(112\) −7717.64 −6.51115
\(113\) −1485.11 −1.23635 −0.618176 0.786040i \(-0.712128\pi\)
−0.618176 + 0.786040i \(0.712128\pi\)
\(114\) −200.504 −0.164727
\(115\) −308.832 −0.250424
\(116\) −2661.45 −2.13026
\(117\) −467.797 −0.369639
\(118\) −2353.35 −1.83596
\(119\) 237.370 0.182855
\(120\) 584.317 0.444505
\(121\) 480.004 0.360634
\(122\) 3749.24 2.78230
\(123\) 862.561 0.632313
\(124\) 1190.28 0.862022
\(125\) −777.926 −0.556639
\(126\) 3979.88 2.81394
\(127\) −24.8952 −0.0173944 −0.00869721 0.999962i \(-0.502768\pi\)
−0.00869721 + 0.999962i \(0.502768\pi\)
\(128\) 3353.62 2.31579
\(129\) 0 0
\(130\) 397.454 0.268146
\(131\) 1737.49 1.15882 0.579409 0.815037i \(-0.303284\pi\)
0.579409 + 0.815037i \(0.303284\pi\)
\(132\) −2272.20 −1.49825
\(133\) 525.073 0.342328
\(134\) −765.950 −0.493791
\(135\) −389.610 −0.248387
\(136\) −476.539 −0.300463
\(137\) 547.378 0.341355 0.170678 0.985327i \(-0.445404\pi\)
0.170678 + 0.985327i \(0.445404\pi\)
\(138\) −1292.71 −0.797412
\(139\) 2059.83 1.25692 0.628462 0.777840i \(-0.283685\pi\)
0.628462 + 0.777840i \(0.283685\pi\)
\(140\) −2455.81 −1.48253
\(141\) −1003.82 −0.599550
\(142\) −3420.28 −2.02129
\(143\) −963.018 −0.563158
\(144\) −4479.79 −2.59247
\(145\) −407.380 −0.233318
\(146\) 3983.75 2.25820
\(147\) 2327.62 1.30598
\(148\) −4609.38 −2.56006
\(149\) −581.330 −0.319627 −0.159814 0.987147i \(-0.551089\pi\)
−0.159814 + 0.987147i \(0.551089\pi\)
\(150\) −1556.36 −0.847173
\(151\) 291.912 0.157321 0.0786604 0.996901i \(-0.474936\pi\)
0.0786604 + 0.996901i \(0.474936\pi\)
\(152\) −1054.12 −0.562505
\(153\) 137.784 0.0728051
\(154\) 8193.09 4.28713
\(155\) 182.193 0.0944135
\(156\) 1208.26 0.620117
\(157\) 1119.70 0.569181 0.284591 0.958649i \(-0.408142\pi\)
0.284591 + 0.958649i \(0.408142\pi\)
\(158\) 892.932 0.449607
\(159\) 533.166 0.265930
\(160\) 1947.91 0.962473
\(161\) 3385.31 1.65714
\(162\) 1386.51 0.672435
\(163\) −1952.25 −0.938111 −0.469055 0.883169i \(-0.655406\pi\)
−0.469055 + 0.883169i \(0.655406\pi\)
\(164\) 7277.93 3.46531
\(165\) −347.798 −0.164097
\(166\) −6525.68 −3.05115
\(167\) 2143.75 0.993342 0.496671 0.867939i \(-0.334555\pi\)
0.496671 + 0.867939i \(0.334555\pi\)
\(168\) −6405.08 −2.94145
\(169\) −1684.91 −0.766912
\(170\) −117.066 −0.0528148
\(171\) 304.784 0.136301
\(172\) 0 0
\(173\) −414.204 −0.182031 −0.0910154 0.995849i \(-0.529011\pi\)
−0.0910154 + 0.995849i \(0.529011\pi\)
\(174\) −1705.22 −0.742943
\(175\) 4075.73 1.76055
\(176\) −9222.21 −3.94972
\(177\) −1095.07 −0.465031
\(178\) −2082.44 −0.876883
\(179\) 399.199 0.166690 0.0833450 0.996521i \(-0.473440\pi\)
0.0833450 + 0.996521i \(0.473440\pi\)
\(180\) −1425.50 −0.590281
\(181\) 848.060 0.348264 0.174132 0.984722i \(-0.444288\pi\)
0.174132 + 0.984722i \(0.444288\pi\)
\(182\) −4356.75 −1.77442
\(183\) 1744.61 0.704729
\(184\) −6796.27 −2.72298
\(185\) −705.542 −0.280392
\(186\) 762.626 0.300637
\(187\) 283.646 0.110921
\(188\) −8469.78 −3.28576
\(189\) 4270.77 1.64367
\(190\) −258.954 −0.0988762
\(191\) −2352.82 −0.891332 −0.445666 0.895199i \(-0.647033\pi\)
−0.445666 + 0.895199i \(0.647033\pi\)
\(192\) 3792.45 1.42550
\(193\) 4800.09 1.79025 0.895125 0.445816i \(-0.147086\pi\)
0.895125 + 0.445816i \(0.147086\pi\)
\(194\) 3380.53 1.25107
\(195\) 184.945 0.0679188
\(196\) 19639.5 7.15725
\(197\) −1982.45 −0.716974 −0.358487 0.933535i \(-0.616707\pi\)
−0.358487 + 0.933535i \(0.616707\pi\)
\(198\) 4755.77 1.70696
\(199\) 2500.62 0.890774 0.445387 0.895338i \(-0.353066\pi\)
0.445387 + 0.895338i \(0.353066\pi\)
\(200\) −8182.34 −2.89290
\(201\) −356.415 −0.125072
\(202\) −607.957 −0.211761
\(203\) 4465.56 1.54395
\(204\) −355.880 −0.122140
\(205\) 1114.01 0.379540
\(206\) −8884.97 −3.00507
\(207\) 1965.04 0.659805
\(208\) 4904.00 1.63476
\(209\) 627.436 0.207659
\(210\) −1573.46 −0.517042
\(211\) −5317.49 −1.73493 −0.867466 0.497496i \(-0.834253\pi\)
−0.867466 + 0.497496i \(0.834253\pi\)
\(212\) 4498.64 1.45739
\(213\) −1591.54 −0.511973
\(214\) 4679.09 1.49466
\(215\) 0 0
\(216\) −8573.91 −2.70084
\(217\) −1997.14 −0.624767
\(218\) 797.940 0.247905
\(219\) 1853.73 0.571981
\(220\) −2934.57 −0.899313
\(221\) −150.831 −0.0459096
\(222\) −2953.27 −0.892839
\(223\) 6017.56 1.80702 0.903511 0.428566i \(-0.140981\pi\)
0.903511 + 0.428566i \(0.140981\pi\)
\(224\) −21352.3 −6.36902
\(225\) 2365.80 0.700978
\(226\) −8028.58 −2.36307
\(227\) 1324.60 0.387298 0.193649 0.981071i \(-0.437968\pi\)
0.193649 + 0.981071i \(0.437968\pi\)
\(228\) −787.220 −0.228662
\(229\) −2621.79 −0.756561 −0.378281 0.925691i \(-0.623485\pi\)
−0.378281 + 0.925691i \(0.623485\pi\)
\(230\) −1669.56 −0.478640
\(231\) 3812.44 1.08589
\(232\) −8964.96 −2.53698
\(233\) −5136.07 −1.44410 −0.722050 0.691841i \(-0.756800\pi\)
−0.722050 + 0.691841i \(0.756800\pi\)
\(234\) −2528.92 −0.706500
\(235\) −1296.44 −0.359875
\(236\) −9239.75 −2.54854
\(237\) 415.502 0.113881
\(238\) 1283.23 0.349494
\(239\) −3084.80 −0.834893 −0.417446 0.908702i \(-0.637075\pi\)
−0.417446 + 0.908702i \(0.637075\pi\)
\(240\) 1771.10 0.476349
\(241\) 2349.42 0.627966 0.313983 0.949429i \(-0.398337\pi\)
0.313983 + 0.949429i \(0.398337\pi\)
\(242\) 2594.92 0.689288
\(243\) 3883.06 1.02510
\(244\) 14720.3 3.86218
\(245\) 3006.15 0.783902
\(246\) 4663.03 1.20855
\(247\) −333.645 −0.0859487
\(248\) 4009.41 1.02660
\(249\) −3036.55 −0.772825
\(250\) −4205.50 −1.06392
\(251\) −2635.49 −0.662751 −0.331376 0.943499i \(-0.607513\pi\)
−0.331376 + 0.943499i \(0.607513\pi\)
\(252\) 15625.8 3.90609
\(253\) 4045.28 1.00524
\(254\) −134.584 −0.0332463
\(255\) −54.4734 −0.0133775
\(256\) 6068.99 1.48169
\(257\) 2469.84 0.599472 0.299736 0.954022i \(-0.403101\pi\)
0.299736 + 0.954022i \(0.403101\pi\)
\(258\) 0 0
\(259\) 7733.91 1.85545
\(260\) 1560.49 0.372220
\(261\) 2592.08 0.614735
\(262\) 9392.93 2.21487
\(263\) −1293.67 −0.303313 −0.151656 0.988433i \(-0.548461\pi\)
−0.151656 + 0.988433i \(0.548461\pi\)
\(264\) −7653.77 −1.78431
\(265\) 688.592 0.159622
\(266\) 2838.56 0.654298
\(267\) −969.006 −0.222106
\(268\) −3007.28 −0.685443
\(269\) −3344.50 −0.758060 −0.379030 0.925384i \(-0.623742\pi\)
−0.379030 + 0.925384i \(0.623742\pi\)
\(270\) −2106.25 −0.474748
\(271\) 1532.27 0.343465 0.171732 0.985144i \(-0.445064\pi\)
0.171732 + 0.985144i \(0.445064\pi\)
\(272\) −1444.42 −0.321987
\(273\) −2027.30 −0.449442
\(274\) 2959.15 0.652440
\(275\) 4870.30 1.06796
\(276\) −5075.45 −1.10691
\(277\) 6489.77 1.40770 0.703849 0.710350i \(-0.251463\pi\)
0.703849 + 0.710350i \(0.251463\pi\)
\(278\) 11135.5 2.40239
\(279\) −1159.26 −0.248757
\(280\) −8272.26 −1.76558
\(281\) −2862.27 −0.607648 −0.303824 0.952728i \(-0.598263\pi\)
−0.303824 + 0.952728i \(0.598263\pi\)
\(282\) −5426.66 −1.14593
\(283\) 5939.25 1.24753 0.623767 0.781611i \(-0.285602\pi\)
0.623767 + 0.781611i \(0.285602\pi\)
\(284\) −13428.7 −2.80580
\(285\) −120.497 −0.0250443
\(286\) −5206.11 −1.07638
\(287\) −12211.4 −2.51155
\(288\) −12394.2 −2.53588
\(289\) −4868.57 −0.990958
\(290\) −2202.31 −0.445945
\(291\) 1573.04 0.316884
\(292\) 15641.0 3.13467
\(293\) 7464.27 1.48828 0.744142 0.668022i \(-0.232859\pi\)
0.744142 + 0.668022i \(0.232859\pi\)
\(294\) 12583.2 2.49614
\(295\) −1414.30 −0.279131
\(296\) −15526.4 −3.04884
\(297\) 5103.37 0.997062
\(298\) −3142.69 −0.610910
\(299\) −2151.12 −0.416061
\(300\) −6110.57 −1.17598
\(301\) 0 0
\(302\) 1578.08 0.300691
\(303\) −282.897 −0.0536370
\(304\) −3195.11 −0.602802
\(305\) 2253.19 0.423007
\(306\) 744.866 0.139154
\(307\) −1428.88 −0.265637 −0.132818 0.991140i \(-0.542403\pi\)
−0.132818 + 0.991140i \(0.542403\pi\)
\(308\) 32167.8 5.95107
\(309\) −4134.39 −0.761155
\(310\) 984.942 0.180455
\(311\) −6168.29 −1.12467 −0.562334 0.826910i \(-0.690096\pi\)
−0.562334 + 0.826910i \(0.690096\pi\)
\(312\) 4069.96 0.738514
\(313\) −208.901 −0.0377245 −0.0188623 0.999822i \(-0.506004\pi\)
−0.0188623 + 0.999822i \(0.506004\pi\)
\(314\) 6053.11 1.08789
\(315\) 2391.80 0.427818
\(316\) 3505.84 0.624110
\(317\) −392.532 −0.0695483 −0.0347741 0.999395i \(-0.511071\pi\)
−0.0347741 + 0.999395i \(0.511071\pi\)
\(318\) 2882.32 0.508277
\(319\) 5336.13 0.936570
\(320\) 4898.00 0.855645
\(321\) 2177.29 0.378581
\(322\) 18301.1 3.16733
\(323\) 98.2714 0.0169287
\(324\) 5443.72 0.933423
\(325\) −2589.83 −0.442024
\(326\) −10553.9 −1.79303
\(327\) 371.300 0.0627919
\(328\) 24515.3 4.12693
\(329\) 14211.2 2.38142
\(330\) −1880.21 −0.313642
\(331\) −1850.13 −0.307228 −0.153614 0.988131i \(-0.549091\pi\)
−0.153614 + 0.988131i \(0.549091\pi\)
\(332\) −25621.2 −4.23537
\(333\) 4489.23 0.738764
\(334\) 11589.2 1.89860
\(335\) −460.315 −0.0750736
\(336\) −19414.1 −3.15217
\(337\) −2895.95 −0.468109 −0.234054 0.972224i \(-0.575199\pi\)
−0.234054 + 0.972224i \(0.575199\pi\)
\(338\) −9108.66 −1.46582
\(339\) −3735.89 −0.598541
\(340\) −459.624 −0.0733135
\(341\) −2386.48 −0.378989
\(342\) 1647.67 0.260514
\(343\) −20737.1 −3.26443
\(344\) 0 0
\(345\) −776.883 −0.121235
\(346\) −2239.20 −0.347919
\(347\) −9809.84 −1.51764 −0.758818 0.651303i \(-0.774223\pi\)
−0.758818 + 0.651303i \(0.774223\pi\)
\(348\) −6695.03 −1.03130
\(349\) −3828.19 −0.587158 −0.293579 0.955935i \(-0.594846\pi\)
−0.293579 + 0.955935i \(0.594846\pi\)
\(350\) 22033.5 3.36498
\(351\) −2713.76 −0.412678
\(352\) −25515.0 −3.86350
\(353\) 7778.32 1.17280 0.586399 0.810022i \(-0.300545\pi\)
0.586399 + 0.810022i \(0.300545\pi\)
\(354\) −5919.99 −0.888824
\(355\) −2055.49 −0.307307
\(356\) −8176.07 −1.21722
\(357\) 597.118 0.0885234
\(358\) 2158.08 0.318598
\(359\) 2684.71 0.394689 0.197345 0.980334i \(-0.436768\pi\)
0.197345 + 0.980334i \(0.436768\pi\)
\(360\) −4801.72 −0.702980
\(361\) −6641.62 −0.968307
\(362\) 4584.64 0.665645
\(363\) 1207.48 0.174590
\(364\) −17105.5 −2.46311
\(365\) 2394.12 0.343327
\(366\) 9431.43 1.34696
\(367\) −10736.5 −1.52709 −0.763545 0.645754i \(-0.776543\pi\)
−0.763545 + 0.645754i \(0.776543\pi\)
\(368\) −20599.8 −2.91805
\(369\) −7088.23 −0.999996
\(370\) −3814.19 −0.535919
\(371\) −7548.11 −1.05628
\(372\) 2994.23 0.417321
\(373\) −2293.02 −0.318306 −0.159153 0.987254i \(-0.550876\pi\)
−0.159153 + 0.987254i \(0.550876\pi\)
\(374\) 1533.40 0.212006
\(375\) −1956.92 −0.269479
\(376\) −28530.0 −3.91309
\(377\) −2837.54 −0.387641
\(378\) 23087.9 3.14158
\(379\) 427.679 0.0579641 0.0289820 0.999580i \(-0.490773\pi\)
0.0289820 + 0.999580i \(0.490773\pi\)
\(380\) −1016.71 −0.137252
\(381\) −62.6252 −0.00842097
\(382\) −12719.4 −1.70362
\(383\) 2449.51 0.326800 0.163400 0.986560i \(-0.447754\pi\)
0.163400 + 0.986560i \(0.447754\pi\)
\(384\) 8436.21 1.12112
\(385\) 4923.82 0.651795
\(386\) 25949.5 3.42174
\(387\) 0 0
\(388\) 13272.7 1.73664
\(389\) 6014.07 0.783871 0.391935 0.919993i \(-0.371806\pi\)
0.391935 + 0.919993i \(0.371806\pi\)
\(390\) 999.817 0.129815
\(391\) 633.587 0.0819485
\(392\) 66154.5 8.52375
\(393\) 4370.75 0.561005
\(394\) −10717.2 −1.37037
\(395\) 536.627 0.0683560
\(396\) 18672.1 2.36947
\(397\) −6215.54 −0.785766 −0.392883 0.919588i \(-0.628522\pi\)
−0.392883 + 0.919588i \(0.628522\pi\)
\(398\) 13518.4 1.70256
\(399\) 1320.85 0.165727
\(400\) −24801.1 −3.10014
\(401\) −10720.5 −1.33505 −0.667525 0.744587i \(-0.732646\pi\)
−0.667525 + 0.744587i \(0.732646\pi\)
\(402\) −1926.79 −0.239054
\(403\) 1269.03 0.156861
\(404\) −2386.97 −0.293951
\(405\) 833.253 0.102234
\(406\) 24141.0 2.95098
\(407\) 9241.65 1.12553
\(408\) −1198.76 −0.145460
\(409\) 7818.02 0.945174 0.472587 0.881284i \(-0.343320\pi\)
0.472587 + 0.881284i \(0.343320\pi\)
\(410\) 6022.37 0.725424
\(411\) 1376.96 0.165257
\(412\) −34884.2 −4.17142
\(413\) 15503.1 1.84711
\(414\) 10623.1 1.26110
\(415\) −3921.75 −0.463882
\(416\) 13567.8 1.59908
\(417\) 5181.62 0.608501
\(418\) 3391.94 0.396903
\(419\) −11145.2 −1.29947 −0.649734 0.760162i \(-0.725120\pi\)
−0.649734 + 0.760162i \(0.725120\pi\)
\(420\) −6177.72 −0.717719
\(421\) 2337.34 0.270582 0.135291 0.990806i \(-0.456803\pi\)
0.135291 + 0.990806i \(0.456803\pi\)
\(422\) −28746.5 −3.31602
\(423\) 8249.01 0.948182
\(424\) 15153.4 1.73565
\(425\) 762.804 0.0870622
\(426\) −8603.90 −0.978545
\(427\) −24698.7 −2.79919
\(428\) 18371.1 2.07477
\(429\) −2422.53 −0.272636
\(430\) 0 0
\(431\) −14704.4 −1.64335 −0.821675 0.569956i \(-0.806960\pi\)
−0.821675 + 0.569956i \(0.806960\pi\)
\(432\) −25988.0 −2.89432
\(433\) 10162.1 1.12785 0.563927 0.825824i \(-0.309290\pi\)
0.563927 + 0.825824i \(0.309290\pi\)
\(434\) −10796.6 −1.19413
\(435\) −1024.79 −0.112954
\(436\) 3132.88 0.344123
\(437\) 1401.52 0.153418
\(438\) 10021.4 1.09324
\(439\) 1142.15 0.124173 0.0620865 0.998071i \(-0.480225\pi\)
0.0620865 + 0.998071i \(0.480225\pi\)
\(440\) −9884.95 −1.07101
\(441\) −19127.6 −2.06539
\(442\) −815.400 −0.0877480
\(443\) 4576.56 0.490832 0.245416 0.969418i \(-0.421075\pi\)
0.245416 + 0.969418i \(0.421075\pi\)
\(444\) −11595.1 −1.23937
\(445\) −1251.49 −0.133317
\(446\) 32531.1 3.45380
\(447\) −1462.37 −0.154738
\(448\) −53690.2 −5.66210
\(449\) −4519.77 −0.475058 −0.237529 0.971380i \(-0.576337\pi\)
−0.237529 + 0.971380i \(0.576337\pi\)
\(450\) 12789.6 1.33979
\(451\) −14592.0 −1.52353
\(452\) −31521.9 −3.28023
\(453\) 734.320 0.0761619
\(454\) 7160.82 0.740251
\(455\) −2618.29 −0.269774
\(456\) −2651.71 −0.272319
\(457\) −12268.8 −1.25582 −0.627911 0.778285i \(-0.716090\pi\)
−0.627911 + 0.778285i \(0.716090\pi\)
\(458\) −14173.5 −1.44603
\(459\) 799.308 0.0812821
\(460\) −6555.02 −0.664412
\(461\) −17870.5 −1.80545 −0.902725 0.430219i \(-0.858436\pi\)
−0.902725 + 0.430219i \(0.858436\pi\)
\(462\) 20610.2 2.07548
\(463\) 12183.2 1.22289 0.611447 0.791285i \(-0.290588\pi\)
0.611447 + 0.791285i \(0.290588\pi\)
\(464\) −27173.3 −2.71872
\(465\) 458.317 0.0457074
\(466\) −27765.8 −2.76014
\(467\) −2853.02 −0.282703 −0.141351 0.989959i \(-0.545145\pi\)
−0.141351 + 0.989959i \(0.545145\pi\)
\(468\) −9929.08 −0.980709
\(469\) 5045.81 0.496789
\(470\) −7008.61 −0.687836
\(471\) 2816.66 0.275551
\(472\) −31123.6 −3.03513
\(473\) 0 0
\(474\) 2246.22 0.217663
\(475\) 1687.35 0.162992
\(476\) 5038.24 0.485141
\(477\) −4381.38 −0.420565
\(478\) −16676.6 −1.59575
\(479\) −9303.99 −0.887495 −0.443748 0.896152i \(-0.646351\pi\)
−0.443748 + 0.896152i \(0.646351\pi\)
\(480\) 4900.07 0.465951
\(481\) −4914.34 −0.465851
\(482\) 12701.1 1.20024
\(483\) 8515.93 0.802253
\(484\) 10188.2 0.956817
\(485\) 2031.61 0.190207
\(486\) 20991.9 1.95929
\(487\) −15240.7 −1.41811 −0.709057 0.705151i \(-0.750879\pi\)
−0.709057 + 0.705151i \(0.750879\pi\)
\(488\) 49584.5 4.59956
\(489\) −4910.99 −0.454157
\(490\) 16251.4 1.49829
\(491\) 13785.4 1.26706 0.633531 0.773717i \(-0.281605\pi\)
0.633531 + 0.773717i \(0.281605\pi\)
\(492\) 18308.0 1.67762
\(493\) 835.764 0.0763508
\(494\) −1803.70 −0.164276
\(495\) 2858.08 0.259518
\(496\) 12152.7 1.10015
\(497\) 22531.6 2.03356
\(498\) −16415.7 −1.47712
\(499\) 19041.0 1.70820 0.854100 0.520110i \(-0.174109\pi\)
0.854100 + 0.520110i \(0.174109\pi\)
\(500\) −16511.7 −1.47685
\(501\) 5392.72 0.480896
\(502\) −14247.5 −1.26673
\(503\) 1851.16 0.164094 0.0820470 0.996628i \(-0.473854\pi\)
0.0820470 + 0.996628i \(0.473854\pi\)
\(504\) 52634.8 4.65187
\(505\) −365.365 −0.0321951
\(506\) 21868.9 1.92133
\(507\) −4238.47 −0.371277
\(508\) −528.406 −0.0461500
\(509\) 4035.03 0.351374 0.175687 0.984446i \(-0.443785\pi\)
0.175687 + 0.984446i \(0.443785\pi\)
\(510\) −294.485 −0.0255686
\(511\) −26243.6 −2.27191
\(512\) 5980.24 0.516194
\(513\) 1768.10 0.152171
\(514\) 13352.0 1.14578
\(515\) −5339.62 −0.456877
\(516\) 0 0
\(517\) 16981.6 1.44459
\(518\) 41809.8 3.54637
\(519\) −1041.95 −0.0881245
\(520\) 5256.42 0.443287
\(521\) −10876.5 −0.914602 −0.457301 0.889312i \(-0.651184\pi\)
−0.457301 + 0.889312i \(0.651184\pi\)
\(522\) 14012.9 1.17496
\(523\) −7571.06 −0.633001 −0.316500 0.948592i \(-0.602508\pi\)
−0.316500 + 0.948592i \(0.602508\pi\)
\(524\) 36878.6 3.07452
\(525\) 10252.7 0.852315
\(526\) −6993.64 −0.579728
\(527\) −373.780 −0.0308958
\(528\) −23199.0 −1.91213
\(529\) −3130.97 −0.257333
\(530\) 3722.55 0.305089
\(531\) 8998.92 0.735442
\(532\) 11144.8 0.908247
\(533\) 7759.44 0.630579
\(534\) −5238.48 −0.424515
\(535\) 2812.00 0.227240
\(536\) −10129.9 −0.816312
\(537\) 1004.21 0.0806978
\(538\) −18080.5 −1.44890
\(539\) −39376.5 −3.14669
\(540\) −8269.56 −0.659010
\(541\) 9311.57 0.739992 0.369996 0.929033i \(-0.379359\pi\)
0.369996 + 0.929033i \(0.379359\pi\)
\(542\) 8283.52 0.656472
\(543\) 2133.34 0.168601
\(544\) −3996.25 −0.314959
\(545\) 479.539 0.0376903
\(546\) −10959.7 −0.859029
\(547\) 19005.3 1.48557 0.742787 0.669528i \(-0.233504\pi\)
0.742787 + 0.669528i \(0.233504\pi\)
\(548\) 11618.2 0.905667
\(549\) −14336.6 −1.11452
\(550\) 26329.0 2.04122
\(551\) 1848.74 0.142939
\(552\) −17096.4 −1.31824
\(553\) −5882.32 −0.452336
\(554\) 35083.9 2.69056
\(555\) −1774.83 −0.135743
\(556\) 43720.3 3.33481
\(557\) 20799.6 1.58224 0.791122 0.611659i \(-0.209498\pi\)
0.791122 + 0.611659i \(0.209498\pi\)
\(558\) −6267.00 −0.475454
\(559\) 0 0
\(560\) −25073.7 −1.89206
\(561\) 713.527 0.0536990
\(562\) −15473.6 −1.16141
\(563\) 16633.6 1.24516 0.622580 0.782556i \(-0.286085\pi\)
0.622580 + 0.782556i \(0.286085\pi\)
\(564\) −21306.2 −1.59070
\(565\) −4824.95 −0.359269
\(566\) 32107.8 2.38444
\(567\) −9133.84 −0.676517
\(568\) −45233.9 −3.34150
\(569\) −15215.4 −1.12102 −0.560511 0.828147i \(-0.689395\pi\)
−0.560511 + 0.828147i \(0.689395\pi\)
\(570\) −651.412 −0.0478678
\(571\) 4026.41 0.295096 0.147548 0.989055i \(-0.452862\pi\)
0.147548 + 0.989055i \(0.452862\pi\)
\(572\) −20440.3 −1.49414
\(573\) −5918.66 −0.431510
\(574\) −66015.2 −4.80039
\(575\) 10878.9 0.789011
\(576\) −31165.0 −2.25442
\(577\) 15767.5 1.13762 0.568811 0.822468i \(-0.307404\pi\)
0.568811 + 0.822468i \(0.307404\pi\)
\(578\) −26319.7 −1.89404
\(579\) 12074.9 0.866693
\(580\) −8646.73 −0.619028
\(581\) 42988.9 3.06967
\(582\) 8503.91 0.605668
\(583\) −9019.62 −0.640746
\(584\) 52686.0 3.73316
\(585\) −1519.81 −0.107413
\(586\) 40352.1 2.84459
\(587\) 19862.5 1.39661 0.698307 0.715798i \(-0.253937\pi\)
0.698307 + 0.715798i \(0.253937\pi\)
\(588\) 49404.2 3.46496
\(589\) −826.816 −0.0578410
\(590\) −7645.75 −0.533509
\(591\) −4986.97 −0.347100
\(592\) −47061.4 −3.26725
\(593\) −23932.8 −1.65734 −0.828670 0.559738i \(-0.810902\pi\)
−0.828670 + 0.559738i \(0.810902\pi\)
\(594\) 27589.0 1.90571
\(595\) 771.187 0.0531354
\(596\) −12338.9 −0.848020
\(597\) 6290.44 0.431241
\(598\) −11629.0 −0.795226
\(599\) −14604.5 −0.996202 −0.498101 0.867119i \(-0.665969\pi\)
−0.498101 + 0.867119i \(0.665969\pi\)
\(600\) −20583.1 −1.40051
\(601\) 52.6820 0.00357561 0.00178781 0.999998i \(-0.499431\pi\)
0.00178781 + 0.999998i \(0.499431\pi\)
\(602\) 0 0
\(603\) 2928.89 0.197801
\(604\) 6195.89 0.417396
\(605\) 1559.47 0.104796
\(606\) −1529.35 −0.102518
\(607\) 9852.75 0.658832 0.329416 0.944185i \(-0.393148\pi\)
0.329416 + 0.944185i \(0.393148\pi\)
\(608\) −8839.86 −0.589644
\(609\) 11233.4 0.747453
\(610\) 12180.8 0.808503
\(611\) −9030.15 −0.597906
\(612\) 2924.50 0.193163
\(613\) −12503.9 −0.823861 −0.411930 0.911215i \(-0.635145\pi\)
−0.411930 + 0.911215i \(0.635145\pi\)
\(614\) −7724.57 −0.507717
\(615\) 2802.35 0.183743
\(616\) 108355. 7.08728
\(617\) 2356.04 0.153729 0.0768644 0.997042i \(-0.475509\pi\)
0.0768644 + 0.997042i \(0.475509\pi\)
\(618\) −22350.6 −1.45481
\(619\) −5749.87 −0.373355 −0.186678 0.982421i \(-0.559772\pi\)
−0.186678 + 0.982421i \(0.559772\pi\)
\(620\) 3867.09 0.250493
\(621\) 11399.5 0.736629
\(622\) −33346.0 −2.14960
\(623\) 13718.4 0.882206
\(624\) 12336.3 0.791420
\(625\) 11778.2 0.753806
\(626\) −1129.33 −0.0721038
\(627\) 1578.35 0.100532
\(628\) 23765.8 1.51012
\(629\) 1447.46 0.0917553
\(630\) 12930.1 0.817697
\(631\) −23912.8 −1.50864 −0.754322 0.656505i \(-0.772034\pi\)
−0.754322 + 0.656505i \(0.772034\pi\)
\(632\) 11809.2 0.743268
\(633\) −13376.4 −0.839914
\(634\) −2122.04 −0.132929
\(635\) −80.8814 −0.00505461
\(636\) 11316.6 0.705552
\(637\) 20938.8 1.30240
\(638\) 28847.3 1.79009
\(639\) 13078.7 0.809680
\(640\) 10895.5 0.672940
\(641\) 4628.89 0.285226 0.142613 0.989778i \(-0.454449\pi\)
0.142613 + 0.989778i \(0.454449\pi\)
\(642\) 11770.5 0.723591
\(643\) −30231.9 −1.85417 −0.927085 0.374852i \(-0.877693\pi\)
−0.927085 + 0.374852i \(0.877693\pi\)
\(644\) 71853.9 4.39665
\(645\) 0 0
\(646\) 531.259 0.0323562
\(647\) −6207.36 −0.377181 −0.188591 0.982056i \(-0.560392\pi\)
−0.188591 + 0.982056i \(0.560392\pi\)
\(648\) 18336.9 1.11164
\(649\) 18525.4 1.12047
\(650\) −14000.7 −0.844850
\(651\) −5023.91 −0.302462
\(652\) −41436.9 −2.48895
\(653\) −2288.32 −0.137135 −0.0685674 0.997646i \(-0.521843\pi\)
−0.0685674 + 0.997646i \(0.521843\pi\)
\(654\) 2007.26 0.120015
\(655\) 5644.89 0.336739
\(656\) 74307.2 4.42257
\(657\) −15233.4 −0.904581
\(658\) 76826.0 4.55165
\(659\) 2633.73 0.155684 0.0778419 0.996966i \(-0.475197\pi\)
0.0778419 + 0.996966i \(0.475197\pi\)
\(660\) −7382.08 −0.435374
\(661\) −26447.4 −1.55625 −0.778127 0.628107i \(-0.783830\pi\)
−0.778127 + 0.628107i \(0.783830\pi\)
\(662\) −10001.9 −0.587212
\(663\) −379.425 −0.0222257
\(664\) −86303.5 −5.04401
\(665\) 1705.90 0.0994764
\(666\) 24268.9 1.41202
\(667\) 11919.4 0.691938
\(668\) 45501.5 2.63549
\(669\) 15137.5 0.874813
\(670\) −2488.48 −0.143490
\(671\) −29513.7 −1.69801
\(672\) −53712.9 −3.08336
\(673\) 18756.0 1.07428 0.537141 0.843493i \(-0.319504\pi\)
0.537141 + 0.843493i \(0.319504\pi\)
\(674\) −15655.6 −0.894706
\(675\) 13724.4 0.782596
\(676\) −35762.5 −2.03473
\(677\) 18144.7 1.03007 0.515034 0.857170i \(-0.327779\pi\)
0.515034 + 0.857170i \(0.327779\pi\)
\(678\) −20196.3 −1.14401
\(679\) −22269.8 −1.25867
\(680\) −1548.22 −0.0873109
\(681\) 3332.10 0.187498
\(682\) −12901.4 −0.724370
\(683\) 15347.3 0.859807 0.429904 0.902875i \(-0.358548\pi\)
0.429904 + 0.902875i \(0.358548\pi\)
\(684\) 6469.11 0.361626
\(685\) 1778.36 0.0991938
\(686\) −112106. −6.23938
\(687\) −6595.25 −0.366266
\(688\) 0 0
\(689\) 4796.27 0.265201
\(690\) −4199.86 −0.231719
\(691\) 7277.80 0.400667 0.200333 0.979728i \(-0.435797\pi\)
0.200333 + 0.979728i \(0.435797\pi\)
\(692\) −8791.56 −0.482955
\(693\) −31329.3 −1.71732
\(694\) −53032.3 −2.90069
\(695\) 6692.13 0.365248
\(696\) −22551.9 −1.22820
\(697\) −2285.46 −0.124201
\(698\) −20695.3 −1.12225
\(699\) −12920.1 −0.699116
\(700\) 86508.2 4.67101
\(701\) −1386.84 −0.0747223 −0.0373612 0.999302i \(-0.511895\pi\)
−0.0373612 + 0.999302i \(0.511895\pi\)
\(702\) −14670.7 −0.788760
\(703\) 3201.84 0.171778
\(704\) −64157.2 −3.43468
\(705\) −3261.27 −0.174222
\(706\) 42049.8 2.24160
\(707\) 4005.01 0.213047
\(708\) −23243.1 −1.23380
\(709\) 26596.1 1.40880 0.704399 0.709804i \(-0.251217\pi\)
0.704399 + 0.709804i \(0.251217\pi\)
\(710\) −11112.1 −0.587364
\(711\) −3414.46 −0.180101
\(712\) −27540.7 −1.44962
\(713\) −5330.74 −0.279997
\(714\) 3228.04 0.169197
\(715\) −3128.73 −0.163647
\(716\) 8473.08 0.442254
\(717\) −7759.99 −0.404187
\(718\) 14513.6 0.754379
\(719\) 22649.9 1.17482 0.587412 0.809288i \(-0.300147\pi\)
0.587412 + 0.809288i \(0.300147\pi\)
\(720\) −14554.3 −0.753341
\(721\) 58531.1 3.02332
\(722\) −35904.8 −1.85075
\(723\) 5910.11 0.304010
\(724\) 18000.3 0.923998
\(725\) 14350.4 0.735116
\(726\) 6527.66 0.333697
\(727\) −35825.5 −1.82764 −0.913821 0.406117i \(-0.866883\pi\)
−0.913821 + 0.406117i \(0.866883\pi\)
\(728\) −57619.0 −2.93338
\(729\) 2843.23 0.144451
\(730\) 12942.7 0.656208
\(731\) 0 0
\(732\) 37029.7 1.86975
\(733\) −34195.3 −1.72310 −0.861549 0.507674i \(-0.830505\pi\)
−0.861549 + 0.507674i \(0.830505\pi\)
\(734\) −58042.1 −2.91876
\(735\) 7562.14 0.379502
\(736\) −56993.4 −2.85435
\(737\) 6029.50 0.301356
\(738\) −38319.2 −1.91131
\(739\) 28264.3 1.40693 0.703464 0.710731i \(-0.251636\pi\)
0.703464 + 0.710731i \(0.251636\pi\)
\(740\) −14975.3 −0.743922
\(741\) −839.303 −0.0416094
\(742\) −40805.3 −2.01888
\(743\) 12755.5 0.629815 0.314908 0.949122i \(-0.398026\pi\)
0.314908 + 0.949122i \(0.398026\pi\)
\(744\) 10085.9 0.496998
\(745\) −1888.67 −0.0928799
\(746\) −12396.2 −0.608385
\(747\) 24953.3 1.22222
\(748\) 6020.45 0.294291
\(749\) −30824.2 −1.50373
\(750\) −10579.2 −0.515062
\(751\) 22857.6 1.11064 0.555318 0.831638i \(-0.312597\pi\)
0.555318 + 0.831638i \(0.312597\pi\)
\(752\) −86475.9 −4.19342
\(753\) −6629.71 −0.320850
\(754\) −15339.8 −0.740907
\(755\) 948.385 0.0457156
\(756\) 90648.1 4.36090
\(757\) −6240.07 −0.299603 −0.149801 0.988716i \(-0.547863\pi\)
−0.149801 + 0.988716i \(0.547863\pi\)
\(758\) 2312.05 0.110788
\(759\) 10176.1 0.486653
\(760\) −3424.72 −0.163457
\(761\) 13726.9 0.653875 0.326938 0.945046i \(-0.393983\pi\)
0.326938 + 0.945046i \(0.393983\pi\)
\(762\) −338.554 −0.0160952
\(763\) −5256.55 −0.249410
\(764\) −49939.2 −2.36484
\(765\) 447.644 0.0211563
\(766\) 13242.2 0.624619
\(767\) −9851.06 −0.463756
\(768\) 15266.9 0.717313
\(769\) 5526.73 0.259167 0.129583 0.991569i \(-0.458636\pi\)
0.129583 + 0.991569i \(0.458636\pi\)
\(770\) 26618.3 1.24579
\(771\) 6213.02 0.290216
\(772\) 101883. 4.74980
\(773\) 25950.2 1.20746 0.603728 0.797191i \(-0.293681\pi\)
0.603728 + 0.797191i \(0.293681\pi\)
\(774\) 0 0
\(775\) −6417.93 −0.297469
\(776\) 44708.3 2.06821
\(777\) 19455.1 0.898259
\(778\) 32512.3 1.49823
\(779\) −5055.52 −0.232520
\(780\) 3925.49 0.180199
\(781\) 26924.2 1.23358
\(782\) 3425.19 0.156630
\(783\) 15037.1 0.686311
\(784\) 200518. 9.13438
\(785\) 3637.75 0.165397
\(786\) 23628.4 1.07226
\(787\) −29492.7 −1.33583 −0.667917 0.744235i \(-0.732814\pi\)
−0.667917 + 0.744235i \(0.732814\pi\)
\(788\) −42078.0 −1.90224
\(789\) −3254.30 −0.146839
\(790\) 2901.02 0.130650
\(791\) 52889.5 2.37741
\(792\) 62896.1 2.82186
\(793\) 15694.2 0.702797
\(794\) −33601.4 −1.50185
\(795\) 1732.19 0.0772761
\(796\) 53076.2 2.36336
\(797\) −34997.7 −1.55543 −0.777717 0.628614i \(-0.783622\pi\)
−0.777717 + 0.628614i \(0.783622\pi\)
\(798\) 7140.56 0.316758
\(799\) 2659.73 0.117765
\(800\) −68617.0 −3.03247
\(801\) 7962.96 0.351258
\(802\) −57955.3 −2.55171
\(803\) −31359.8 −1.37816
\(804\) −7564.98 −0.331836
\(805\) 10998.4 0.481546
\(806\) 6860.45 0.299813
\(807\) −8413.29 −0.366991
\(808\) −8040.37 −0.350073
\(809\) 32571.8 1.41553 0.707766 0.706447i \(-0.249703\pi\)
0.707766 + 0.706447i \(0.249703\pi\)
\(810\) 4504.60 0.195402
\(811\) 28857.9 1.24949 0.624747 0.780828i \(-0.285202\pi\)
0.624747 + 0.780828i \(0.285202\pi\)
\(812\) 94782.5 4.09632
\(813\) 3854.52 0.166278
\(814\) 49960.7 2.15126
\(815\) −6342.62 −0.272604
\(816\) −3633.51 −0.155880
\(817\) 0 0
\(818\) 42264.5 1.80653
\(819\) 16659.7 0.710789
\(820\) 23645.1 1.00698
\(821\) −12710.1 −0.540300 −0.270150 0.962818i \(-0.587073\pi\)
−0.270150 + 0.962818i \(0.587073\pi\)
\(822\) 7443.89 0.315858
\(823\) −8447.81 −0.357803 −0.178902 0.983867i \(-0.557254\pi\)
−0.178902 + 0.983867i \(0.557254\pi\)
\(824\) −117506. −4.96784
\(825\) 12251.5 0.517022
\(826\) 83810.1 3.53042
\(827\) −8494.53 −0.357175 −0.178588 0.983924i \(-0.557153\pi\)
−0.178588 + 0.983924i \(0.557153\pi\)
\(828\) 41708.4 1.75056
\(829\) −28640.7 −1.19992 −0.599959 0.800031i \(-0.704816\pi\)
−0.599959 + 0.800031i \(0.704816\pi\)
\(830\) −21201.1 −0.886628
\(831\) 16325.4 0.681493
\(832\) 34116.2 1.42159
\(833\) −6167.30 −0.256524
\(834\) 28012.0 1.16304
\(835\) 6964.77 0.288654
\(836\) 13317.5 0.550950
\(837\) −6725.05 −0.277720
\(838\) −60251.2 −2.48370
\(839\) −20471.9 −0.842393 −0.421196 0.906969i \(-0.638390\pi\)
−0.421196 + 0.906969i \(0.638390\pi\)
\(840\) −20809.3 −0.854750
\(841\) −8666.07 −0.355327
\(842\) 12635.7 0.517169
\(843\) −7200.21 −0.294174
\(844\) −112865. −4.60304
\(845\) −5474.05 −0.222856
\(846\) 44594.5 1.81228
\(847\) −17094.4 −0.693472
\(848\) 45930.8 1.85999
\(849\) 14940.5 0.603954
\(850\) 4123.75 0.166404
\(851\) 20643.3 0.831543
\(852\) −33780.7 −1.35834
\(853\) −32548.6 −1.30650 −0.653249 0.757143i \(-0.726595\pi\)
−0.653249 + 0.757143i \(0.726595\pi\)
\(854\) −133522. −5.35015
\(855\) 990.205 0.0396074
\(856\) 61882.0 2.47089
\(857\) −19607.8 −0.781553 −0.390776 0.920486i \(-0.627793\pi\)
−0.390776 + 0.920486i \(0.627793\pi\)
\(858\) −13096.3 −0.521094
\(859\) −36871.0 −1.46452 −0.732259 0.681026i \(-0.761534\pi\)
−0.732259 + 0.681026i \(0.761534\pi\)
\(860\) 0 0
\(861\) −30718.4 −1.21589
\(862\) −79492.3 −3.14097
\(863\) 21302.4 0.840259 0.420130 0.907464i \(-0.361985\pi\)
0.420130 + 0.907464i \(0.361985\pi\)
\(864\) −71900.6 −2.83114
\(865\) −1345.70 −0.0528960
\(866\) 54936.9 2.15569
\(867\) −12247.2 −0.479741
\(868\) −42389.7 −1.65760
\(869\) −7029.09 −0.274391
\(870\) −5540.04 −0.215891
\(871\) −3206.24 −0.124730
\(872\) 10552.9 0.409825
\(873\) −12926.7 −0.501149
\(874\) 7576.66 0.293232
\(875\) 27704.3 1.07037
\(876\) 39345.9 1.51755
\(877\) −1799.88 −0.0693016 −0.0346508 0.999399i \(-0.511032\pi\)
−0.0346508 + 0.999399i \(0.511032\pi\)
\(878\) 6174.52 0.237335
\(879\) 18776.8 0.720506
\(880\) −29961.8 −1.14774
\(881\) −7632.90 −0.291894 −0.145947 0.989292i \(-0.546623\pi\)
−0.145947 + 0.989292i \(0.546623\pi\)
\(882\) −103404. −3.94763
\(883\) −7483.72 −0.285218 −0.142609 0.989779i \(-0.545549\pi\)
−0.142609 + 0.989779i \(0.545549\pi\)
\(884\) −3201.43 −0.121805
\(885\) −3557.75 −0.135133
\(886\) 24741.0 0.938139
\(887\) 16767.7 0.634728 0.317364 0.948304i \(-0.397202\pi\)
0.317364 + 0.948304i \(0.397202\pi\)
\(888\) −39057.6 −1.47600
\(889\) 886.594 0.0334482
\(890\) −6765.57 −0.254812
\(891\) −10914.5 −0.410381
\(892\) 127724. 4.79430
\(893\) 5883.42 0.220472
\(894\) −7905.62 −0.295753
\(895\) 1296.95 0.0484382
\(896\) −119433. −4.45308
\(897\) −5411.25 −0.201423
\(898\) −24434.0 −0.907989
\(899\) −7031.78 −0.260871
\(900\) 50214.6 1.85980
\(901\) −1412.69 −0.0522347
\(902\) −78885.0 −2.91195
\(903\) 0 0
\(904\) −106180. −3.90651
\(905\) 2755.24 0.101201
\(906\) 3969.76 0.145570
\(907\) −42555.8 −1.55793 −0.778965 0.627068i \(-0.784255\pi\)
−0.778965 + 0.627068i \(0.784255\pi\)
\(908\) 28114.9 1.02756
\(909\) 2324.75 0.0848263
\(910\) −14154.6 −0.515625
\(911\) −24280.3 −0.883031 −0.441516 0.897254i \(-0.645559\pi\)
−0.441516 + 0.897254i \(0.645559\pi\)
\(912\) −8037.46 −0.291828
\(913\) 51369.6 1.86209
\(914\) −66325.6 −2.40028
\(915\) 5668.02 0.204786
\(916\) −55648.0 −2.00727
\(917\) −61877.3 −2.22832
\(918\) 4321.09 0.155356
\(919\) 11725.6 0.420883 0.210441 0.977606i \(-0.432510\pi\)
0.210441 + 0.977606i \(0.432510\pi\)
\(920\) −22080.2 −0.791265
\(921\) −3594.42 −0.128600
\(922\) −96608.6 −3.45080
\(923\) −14317.2 −0.510570
\(924\) 80919.8 2.88102
\(925\) 24853.4 0.883433
\(926\) 65862.6 2.33734
\(927\) 33975.0 1.20376
\(928\) −75180.0 −2.65938
\(929\) 2787.61 0.0984484 0.0492242 0.998788i \(-0.484325\pi\)
0.0492242 + 0.998788i \(0.484325\pi\)
\(930\) 2477.68 0.0873615
\(931\) −13642.3 −0.480246
\(932\) −109014. −3.83141
\(933\) −15516.7 −0.544473
\(934\) −15423.5 −0.540336
\(935\) 921.531 0.0322324
\(936\) −33445.6 −1.16795
\(937\) 9008.26 0.314074 0.157037 0.987593i \(-0.449806\pi\)
0.157037 + 0.987593i \(0.449806\pi\)
\(938\) 27277.8 0.949523
\(939\) −525.502 −0.0182632
\(940\) −27517.3 −0.954802
\(941\) −22821.0 −0.790586 −0.395293 0.918555i \(-0.629357\pi\)
−0.395293 + 0.918555i \(0.629357\pi\)
\(942\) 15226.9 0.526667
\(943\) −32594.5 −1.12558
\(944\) −94337.2 −3.25256
\(945\) 13875.2 0.477630
\(946\) 0 0
\(947\) −22989.4 −0.788864 −0.394432 0.918925i \(-0.629059\pi\)
−0.394432 + 0.918925i \(0.629059\pi\)
\(948\) 8819.12 0.302143
\(949\) 16675.9 0.570413
\(950\) 9121.89 0.311530
\(951\) −987.436 −0.0336696
\(952\) 16971.0 0.577767
\(953\) −40326.5 −1.37073 −0.685364 0.728201i \(-0.740357\pi\)
−0.685364 + 0.728201i \(0.740357\pi\)
\(954\) −23685.9 −0.803836
\(955\) −7644.03 −0.259011
\(956\) −65475.6 −2.21510
\(957\) 13423.3 0.453411
\(958\) −50297.7 −1.69629
\(959\) −19493.8 −0.656400
\(960\) 12321.2 0.414234
\(961\) −26646.2 −0.894437
\(962\) −26567.1 −0.890392
\(963\) −17892.3 −0.598722
\(964\) 49867.0 1.66609
\(965\) 15594.9 0.520226
\(966\) 46037.4 1.53336
\(967\) 17638.8 0.586581 0.293291 0.956023i \(-0.405250\pi\)
0.293291 + 0.956023i \(0.405250\pi\)
\(968\) 34318.3 1.13950
\(969\) 247.207 0.00819550
\(970\) 10982.9 0.363547
\(971\) −27474.1 −0.908019 −0.454010 0.890997i \(-0.650007\pi\)
−0.454010 + 0.890997i \(0.650007\pi\)
\(972\) 82418.7 2.71973
\(973\) −73356.9 −2.41697
\(974\) −82391.7 −2.71047
\(975\) −6514.86 −0.213992
\(976\) 150293. 4.92907
\(977\) −35587.3 −1.16534 −0.582671 0.812708i \(-0.697992\pi\)
−0.582671 + 0.812708i \(0.697992\pi\)
\(978\) −26549.0 −0.868040
\(979\) 16392.8 0.535153
\(980\) 63806.2 2.07981
\(981\) −3051.22 −0.0993047
\(982\) 74524.5 2.42176
\(983\) 16027.0 0.520023 0.260012 0.965605i \(-0.416274\pi\)
0.260012 + 0.965605i \(0.416274\pi\)
\(984\) 61669.6 1.99792
\(985\) −6440.74 −0.208344
\(986\) 4518.17 0.145931
\(987\) 35748.9 1.15289
\(988\) −7081.69 −0.228035
\(989\) 0 0
\(990\) 15450.9 0.496022
\(991\) −8618.18 −0.276252 −0.138126 0.990415i \(-0.544108\pi\)
−0.138126 + 0.990415i \(0.544108\pi\)
\(992\) 33622.8 1.07613
\(993\) −4654.11 −0.148735
\(994\) 121807. 3.88679
\(995\) 8124.20 0.258849
\(996\) −64451.4 −2.05042
\(997\) 30698.8 0.975166 0.487583 0.873077i \(-0.337879\pi\)
0.487583 + 0.873077i \(0.337879\pi\)
\(998\) 102936. 3.26492
\(999\) 26042.8 0.824781
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.1.49 yes 50
43.42 odd 2 1849.4.a.i.1.2 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.2 50 43.42 odd 2
1849.4.a.j.1.49 yes 50 1.1 even 1 trivial