Properties

Label 1849.4.a.i.1.35
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 1.35
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.12255 q^{2} -9.87196 q^{3} -3.49478 q^{4} +15.5747 q^{5} -20.9537 q^{6} +16.3831 q^{7} -24.3983 q^{8} +70.4556 q^{9} +O(q^{10})\) \(q+2.12255 q^{2} -9.87196 q^{3} -3.49478 q^{4} +15.5747 q^{5} -20.9537 q^{6} +16.3831 q^{7} -24.3983 q^{8} +70.4556 q^{9} +33.0580 q^{10} +42.7049 q^{11} +34.5003 q^{12} -44.4137 q^{13} +34.7739 q^{14} -153.752 q^{15} -23.8283 q^{16} -80.6618 q^{17} +149.546 q^{18} -9.72641 q^{19} -54.4300 q^{20} -161.733 q^{21} +90.6434 q^{22} +81.9683 q^{23} +240.859 q^{24} +117.570 q^{25} -94.2703 q^{26} -428.992 q^{27} -57.2552 q^{28} -170.553 q^{29} -326.348 q^{30} -115.463 q^{31} +144.609 q^{32} -421.581 q^{33} -171.209 q^{34} +255.161 q^{35} -246.227 q^{36} -56.3932 q^{37} -20.6448 q^{38} +438.450 q^{39} -379.995 q^{40} +9.51295 q^{41} -343.287 q^{42} -149.244 q^{44} +1097.32 q^{45} +173.982 q^{46} +9.55328 q^{47} +235.232 q^{48} -74.5945 q^{49} +249.549 q^{50} +796.290 q^{51} +155.216 q^{52} +254.029 q^{53} -910.558 q^{54} +665.115 q^{55} -399.719 q^{56} +96.0187 q^{57} -362.007 q^{58} +288.741 q^{59} +537.331 q^{60} +67.9815 q^{61} -245.075 q^{62} +1154.28 q^{63} +497.567 q^{64} -691.728 q^{65} -894.828 q^{66} +273.745 q^{67} +281.895 q^{68} -809.187 q^{69} +541.592 q^{70} +113.470 q^{71} -1718.99 q^{72} +908.508 q^{73} -119.698 q^{74} -1160.65 q^{75} +33.9916 q^{76} +699.638 q^{77} +930.632 q^{78} -798.537 q^{79} -371.118 q^{80} +2332.69 q^{81} +20.1917 q^{82} -1273.00 q^{83} +565.221 q^{84} -1256.28 q^{85} +1683.69 q^{87} -1041.93 q^{88} -1394.34 q^{89} +2329.12 q^{90} -727.633 q^{91} -286.461 q^{92} +1139.84 q^{93} +20.2773 q^{94} -151.486 q^{95} -1427.58 q^{96} +253.183 q^{97} -158.331 q^{98} +3008.80 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} - 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} - 386q^{18} + 12q^{19} + 108q^{20} - 408q^{21} + 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} + 1493q^{26} + 10q^{27} - 242q^{28} + 208q^{29} - 48q^{30} - 932q^{31} - 1124q^{32} + 254q^{33} + 765q^{34} - 1452q^{35} + 747q^{36} - 90q^{37} - 1213q^{38} - 1610q^{39} - 1693q^{40} - 1354q^{41} - 16q^{42} - 2704q^{44} + 4508q^{45} + 233q^{46} - 3484q^{47} - 376q^{48} + 1324q^{49} - 408q^{50} + 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} - 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} + 1172q^{61} - 1546q^{62} - 3686q^{63} + 606q^{64} + 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} + 136q^{69} - 1310q^{70} + 162q^{71} - 5814q^{72} + 746q^{73} - 4332q^{74} + 236q^{75} + 1338q^{76} + 2024q^{77} - 2782q^{78} - 2656q^{79} - 5713q^{80} - 86q^{81} - 4168q^{82} - 3514q^{83} - 4269q^{84} - 7558q^{85} - 10278q^{87} + 11692q^{88} + 2640q^{89} - 8286q^{90} - 5946q^{91} - 4271q^{92} - 2q^{93} + 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} - 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.12255 0.750435 0.375218 0.926937i \(-0.377568\pi\)
0.375218 + 0.926937i \(0.377568\pi\)
\(3\) −9.87196 −1.89986 −0.949930 0.312463i \(-0.898846\pi\)
−0.949930 + 0.312463i \(0.898846\pi\)
\(4\) −3.49478 −0.436847
\(5\) 15.5747 1.39304 0.696520 0.717537i \(-0.254731\pi\)
0.696520 + 0.717537i \(0.254731\pi\)
\(6\) −20.9537 −1.42572
\(7\) 16.3831 0.884603 0.442302 0.896866i \(-0.354162\pi\)
0.442302 + 0.896866i \(0.354162\pi\)
\(8\) −24.3983 −1.07826
\(9\) 70.4556 2.60947
\(10\) 33.0580 1.04539
\(11\) 42.7049 1.17055 0.585274 0.810836i \(-0.300987\pi\)
0.585274 + 0.810836i \(0.300987\pi\)
\(12\) 34.5003 0.829948
\(13\) −44.4137 −0.947549 −0.473774 0.880646i \(-0.657109\pi\)
−0.473774 + 0.880646i \(0.657109\pi\)
\(14\) 34.7739 0.663837
\(15\) −153.752 −2.64658
\(16\) −23.8283 −0.372318
\(17\) −80.6618 −1.15079 −0.575393 0.817877i \(-0.695151\pi\)
−0.575393 + 0.817877i \(0.695151\pi\)
\(18\) 149.546 1.95824
\(19\) −9.72641 −0.117442 −0.0587208 0.998274i \(-0.518702\pi\)
−0.0587208 + 0.998274i \(0.518702\pi\)
\(20\) −54.4300 −0.608546
\(21\) −161.733 −1.68062
\(22\) 90.6434 0.878420
\(23\) 81.9683 0.743111 0.371556 0.928411i \(-0.378824\pi\)
0.371556 + 0.928411i \(0.378824\pi\)
\(24\) 240.859 2.04854
\(25\) 117.570 0.940562
\(26\) −94.2703 −0.711074
\(27\) −428.992 −3.05776
\(28\) −57.2552 −0.386436
\(29\) −170.553 −1.09210 −0.546049 0.837753i \(-0.683869\pi\)
−0.546049 + 0.837753i \(0.683869\pi\)
\(30\) −326.348 −1.98609
\(31\) −115.463 −0.668958 −0.334479 0.942403i \(-0.608560\pi\)
−0.334479 + 0.942403i \(0.608560\pi\)
\(32\) 144.609 0.798860
\(33\) −421.581 −2.22388
\(34\) −171.209 −0.863590
\(35\) 255.161 1.23229
\(36\) −246.227 −1.13994
\(37\) −56.3932 −0.250567 −0.125284 0.992121i \(-0.539984\pi\)
−0.125284 + 0.992121i \(0.539984\pi\)
\(38\) −20.6448 −0.0881323
\(39\) 438.450 1.80021
\(40\) −379.995 −1.50206
\(41\) 9.51295 0.0362359 0.0181180 0.999836i \(-0.494233\pi\)
0.0181180 + 0.999836i \(0.494233\pi\)
\(42\) −343.287 −1.26120
\(43\) 0 0
\(44\) −149.244 −0.511350
\(45\) 1097.32 3.63509
\(46\) 173.982 0.557657
\(47\) 9.55328 0.0296487 0.0148243 0.999890i \(-0.495281\pi\)
0.0148243 + 0.999890i \(0.495281\pi\)
\(48\) 235.232 0.707351
\(49\) −74.5945 −0.217477
\(50\) 249.549 0.705830
\(51\) 796.290 2.18633
\(52\) 155.216 0.413934
\(53\) 254.029 0.658370 0.329185 0.944265i \(-0.393226\pi\)
0.329185 + 0.944265i \(0.393226\pi\)
\(54\) −910.558 −2.29465
\(55\) 665.115 1.63062
\(56\) −399.719 −0.953833
\(57\) 96.0187 0.223123
\(58\) −362.007 −0.819549
\(59\) 288.741 0.637133 0.318566 0.947901i \(-0.396799\pi\)
0.318566 + 0.947901i \(0.396799\pi\)
\(60\) 537.331 1.15615
\(61\) 67.9815 0.142691 0.0713454 0.997452i \(-0.477271\pi\)
0.0713454 + 0.997452i \(0.477271\pi\)
\(62\) −245.075 −0.502009
\(63\) 1154.28 2.30834
\(64\) 497.567 0.971810
\(65\) −691.728 −1.31997
\(66\) −894.828 −1.66887
\(67\) 273.745 0.499153 0.249577 0.968355i \(-0.419709\pi\)
0.249577 + 0.968355i \(0.419709\pi\)
\(68\) 281.895 0.502717
\(69\) −809.187 −1.41181
\(70\) 541.592 0.924752
\(71\) 113.470 0.189668 0.0948339 0.995493i \(-0.469768\pi\)
0.0948339 + 0.995493i \(0.469768\pi\)
\(72\) −1718.99 −2.81369
\(73\) 908.508 1.45661 0.728307 0.685251i \(-0.240307\pi\)
0.728307 + 0.685251i \(0.240307\pi\)
\(74\) −119.698 −0.188035
\(75\) −1160.65 −1.78694
\(76\) 33.9916 0.0513040
\(77\) 699.638 1.03547
\(78\) 930.632 1.35094
\(79\) −798.537 −1.13725 −0.568623 0.822598i \(-0.692524\pi\)
−0.568623 + 0.822598i \(0.692524\pi\)
\(80\) −371.118 −0.518653
\(81\) 2332.69 3.19985
\(82\) 20.1917 0.0271927
\(83\) −1273.00 −1.68349 −0.841744 0.539878i \(-0.818471\pi\)
−0.841744 + 0.539878i \(0.818471\pi\)
\(84\) 565.221 0.734175
\(85\) −1256.28 −1.60309
\(86\) 0 0
\(87\) 1683.69 2.07483
\(88\) −1041.93 −1.26215
\(89\) −1394.34 −1.66067 −0.830335 0.557265i \(-0.811851\pi\)
−0.830335 + 0.557265i \(0.811851\pi\)
\(90\) 2329.12 2.72790
\(91\) −727.633 −0.838205
\(92\) −286.461 −0.324626
\(93\) 1139.84 1.27093
\(94\) 20.2773 0.0222494
\(95\) −151.486 −0.163601
\(96\) −1427.58 −1.51772
\(97\) 253.183 0.265018 0.132509 0.991182i \(-0.457697\pi\)
0.132509 + 0.991182i \(0.457697\pi\)
\(98\) −158.331 −0.163202
\(99\) 3008.80 3.05450
\(100\) −410.882 −0.410882
\(101\) 623.621 0.614383 0.307191 0.951648i \(-0.400611\pi\)
0.307191 + 0.951648i \(0.400611\pi\)
\(102\) 1690.17 1.64070
\(103\) −1534.71 −1.46815 −0.734076 0.679067i \(-0.762385\pi\)
−0.734076 + 0.679067i \(0.762385\pi\)
\(104\) 1083.62 1.02170
\(105\) −2518.94 −2.34117
\(106\) 539.190 0.494064
\(107\) 978.902 0.884430 0.442215 0.896909i \(-0.354193\pi\)
0.442215 + 0.896909i \(0.354193\pi\)
\(108\) 1499.23 1.33577
\(109\) −615.263 −0.540656 −0.270328 0.962768i \(-0.587132\pi\)
−0.270328 + 0.962768i \(0.587132\pi\)
\(110\) 1411.74 1.22367
\(111\) 556.712 0.476043
\(112\) −390.381 −0.329353
\(113\) 1889.47 1.57298 0.786488 0.617605i \(-0.211897\pi\)
0.786488 + 0.617605i \(0.211897\pi\)
\(114\) 203.805 0.167439
\(115\) 1276.63 1.03518
\(116\) 596.044 0.477080
\(117\) −3129.19 −2.47260
\(118\) 612.867 0.478127
\(119\) −1321.49 −1.01799
\(120\) 3751.29 2.85370
\(121\) 492.710 0.370181
\(122\) 144.294 0.107080
\(123\) −93.9115 −0.0688432
\(124\) 403.516 0.292232
\(125\) −115.717 −0.0828002
\(126\) 2450.02 1.73226
\(127\) −333.272 −0.232859 −0.116430 0.993199i \(-0.537145\pi\)
−0.116430 + 0.993199i \(0.537145\pi\)
\(128\) −100.762 −0.0695797
\(129\) 0 0
\(130\) −1468.23 −0.990554
\(131\) 1298.39 0.865959 0.432979 0.901404i \(-0.357462\pi\)
0.432979 + 0.901404i \(0.357462\pi\)
\(132\) 1473.33 0.971493
\(133\) −159.349 −0.103889
\(134\) 581.038 0.374582
\(135\) −6681.41 −4.25959
\(136\) 1968.01 1.24085
\(137\) −1989.18 −1.24049 −0.620245 0.784408i \(-0.712967\pi\)
−0.620245 + 0.784408i \(0.712967\pi\)
\(138\) −1717.54 −1.05947
\(139\) −1554.18 −0.948374 −0.474187 0.880424i \(-0.657258\pi\)
−0.474187 + 0.880424i \(0.657258\pi\)
\(140\) −891.731 −0.538322
\(141\) −94.3096 −0.0563284
\(142\) 240.846 0.142333
\(143\) −1896.68 −1.10915
\(144\) −1678.84 −0.971550
\(145\) −2656.30 −1.52134
\(146\) 1928.36 1.09309
\(147\) 736.394 0.413175
\(148\) 197.082 0.109460
\(149\) 2018.71 1.10993 0.554964 0.831875i \(-0.312732\pi\)
0.554964 + 0.831875i \(0.312732\pi\)
\(150\) −2463.54 −1.34098
\(151\) −219.429 −0.118258 −0.0591289 0.998250i \(-0.518832\pi\)
−0.0591289 + 0.998250i \(0.518832\pi\)
\(152\) 237.307 0.126633
\(153\) −5683.08 −3.00294
\(154\) 1485.02 0.777053
\(155\) −1798.29 −0.931885
\(156\) −1532.28 −0.786416
\(157\) 2441.15 1.24092 0.620462 0.784236i \(-0.286945\pi\)
0.620462 + 0.784236i \(0.286945\pi\)
\(158\) −1694.94 −0.853430
\(159\) −2507.77 −1.25081
\(160\) 2252.24 1.11284
\(161\) 1342.89 0.657359
\(162\) 4951.26 2.40128
\(163\) −2934.10 −1.40992 −0.704959 0.709248i \(-0.749035\pi\)
−0.704959 + 0.709248i \(0.749035\pi\)
\(164\) −33.2456 −0.0158296
\(165\) −6565.99 −3.09795
\(166\) −2702.00 −1.26335
\(167\) −4127.64 −1.91261 −0.956306 0.292368i \(-0.905557\pi\)
−0.956306 + 0.292368i \(0.905557\pi\)
\(168\) 3946.01 1.81215
\(169\) −224.427 −0.102152
\(170\) −2666.52 −1.20302
\(171\) −685.280 −0.306460
\(172\) 0 0
\(173\) −803.747 −0.353224 −0.176612 0.984281i \(-0.556514\pi\)
−0.176612 + 0.984281i \(0.556514\pi\)
\(174\) 3573.72 1.55703
\(175\) 1926.16 0.832024
\(176\) −1017.59 −0.435815
\(177\) −2850.44 −1.21046
\(178\) −2959.55 −1.24622
\(179\) −3352.74 −1.39998 −0.699988 0.714155i \(-0.746811\pi\)
−0.699988 + 0.714155i \(0.746811\pi\)
\(180\) −3834.90 −1.58798
\(181\) −4226.02 −1.73546 −0.867728 0.497040i \(-0.834420\pi\)
−0.867728 + 0.497040i \(0.834420\pi\)
\(182\) −1544.44 −0.629018
\(183\) −671.111 −0.271093
\(184\) −1999.88 −0.801268
\(185\) −878.306 −0.349050
\(186\) 2419.37 0.953748
\(187\) −3444.66 −1.34705
\(188\) −33.3866 −0.0129519
\(189\) −7028.21 −2.70491
\(190\) −321.536 −0.122772
\(191\) 3645.85 1.38118 0.690588 0.723249i \(-0.257352\pi\)
0.690588 + 0.723249i \(0.257352\pi\)
\(192\) −4911.96 −1.84630
\(193\) 3201.57 1.19406 0.597032 0.802218i \(-0.296347\pi\)
0.597032 + 0.802218i \(0.296347\pi\)
\(194\) 537.393 0.198879
\(195\) 6828.71 2.50776
\(196\) 260.691 0.0950041
\(197\) 92.9451 0.0336145 0.0168073 0.999859i \(-0.494650\pi\)
0.0168073 + 0.999859i \(0.494650\pi\)
\(198\) 6386.33 2.29221
\(199\) 97.0214 0.0345611 0.0172806 0.999851i \(-0.494499\pi\)
0.0172806 + 0.999851i \(0.494499\pi\)
\(200\) −2868.51 −1.01417
\(201\) −2702.40 −0.948321
\(202\) 1323.67 0.461054
\(203\) −2794.18 −0.966074
\(204\) −2782.86 −0.955093
\(205\) 148.161 0.0504781
\(206\) −3257.51 −1.10175
\(207\) 5775.12 1.93912
\(208\) 1058.30 0.352789
\(209\) −415.365 −0.137471
\(210\) −5346.58 −1.75690
\(211\) −106.820 −0.0348522 −0.0174261 0.999848i \(-0.505547\pi\)
−0.0174261 + 0.999848i \(0.505547\pi\)
\(212\) −887.776 −0.287607
\(213\) −1120.17 −0.360342
\(214\) 2077.77 0.663708
\(215\) 0 0
\(216\) 10466.7 3.29706
\(217\) −1891.63 −0.591762
\(218\) −1305.93 −0.405727
\(219\) −8968.76 −2.76736
\(220\) −2324.43 −0.712331
\(221\) 3582.48 1.09043
\(222\) 1181.65 0.357239
\(223\) 3792.84 1.13896 0.569478 0.822006i \(-0.307145\pi\)
0.569478 + 0.822006i \(0.307145\pi\)
\(224\) 2369.14 0.706675
\(225\) 8283.48 2.45436
\(226\) 4010.50 1.18042
\(227\) −2142.14 −0.626339 −0.313170 0.949697i \(-0.601391\pi\)
−0.313170 + 0.949697i \(0.601391\pi\)
\(228\) −335.564 −0.0974705
\(229\) −866.711 −0.250104 −0.125052 0.992150i \(-0.539910\pi\)
−0.125052 + 0.992150i \(0.539910\pi\)
\(230\) 2709.71 0.776839
\(231\) −6906.80 −1.96725
\(232\) 4161.19 1.17757
\(233\) −2698.47 −0.758724 −0.379362 0.925248i \(-0.623856\pi\)
−0.379362 + 0.925248i \(0.623856\pi\)
\(234\) −6641.87 −1.85552
\(235\) 148.789 0.0413018
\(236\) −1009.08 −0.278330
\(237\) 7883.13 2.16061
\(238\) −2804.93 −0.763935
\(239\) −1856.90 −0.502564 −0.251282 0.967914i \(-0.580852\pi\)
−0.251282 + 0.967914i \(0.580852\pi\)
\(240\) 3663.66 0.985369
\(241\) 4891.12 1.30732 0.653661 0.756788i \(-0.273232\pi\)
0.653661 + 0.756788i \(0.273232\pi\)
\(242\) 1045.80 0.277796
\(243\) −11445.5 −3.02151
\(244\) −237.580 −0.0623341
\(245\) −1161.78 −0.302954
\(246\) −199.332 −0.0516623
\(247\) 431.985 0.111282
\(248\) 2817.09 0.721311
\(249\) 12567.0 3.19839
\(250\) −245.615 −0.0621362
\(251\) −5679.81 −1.42831 −0.714156 0.699987i \(-0.753189\pi\)
−0.714156 + 0.699987i \(0.753189\pi\)
\(252\) −4033.95 −1.00839
\(253\) 3500.45 0.869847
\(254\) −707.387 −0.174746
\(255\) 12402.0 3.04565
\(256\) −4194.41 −1.02403
\(257\) 3095.65 0.751366 0.375683 0.926748i \(-0.377408\pi\)
0.375683 + 0.926748i \(0.377408\pi\)
\(258\) 0 0
\(259\) −923.895 −0.221653
\(260\) 2417.43 0.576627
\(261\) −12016.4 −2.84980
\(262\) 2755.89 0.649846
\(263\) −2790.13 −0.654170 −0.327085 0.944995i \(-0.606066\pi\)
−0.327085 + 0.944995i \(0.606066\pi\)
\(264\) 10285.8 2.39792
\(265\) 3956.42 0.917136
\(266\) −338.225 −0.0779622
\(267\) 13764.9 3.15504
\(268\) −956.678 −0.218054
\(269\) −8193.14 −1.85704 −0.928521 0.371279i \(-0.878919\pi\)
−0.928521 + 0.371279i \(0.878919\pi\)
\(270\) −14181.6 −3.19654
\(271\) −4239.14 −0.950218 −0.475109 0.879927i \(-0.657591\pi\)
−0.475109 + 0.879927i \(0.657591\pi\)
\(272\) 1922.04 0.428458
\(273\) 7183.16 1.59247
\(274\) −4222.14 −0.930907
\(275\) 5020.83 1.10097
\(276\) 2827.93 0.616744
\(277\) 8528.69 1.84996 0.924981 0.380014i \(-0.124081\pi\)
0.924981 + 0.380014i \(0.124081\pi\)
\(278\) −3298.83 −0.711693
\(279\) −8134.99 −1.74562
\(280\) −6225.48 −1.32873
\(281\) −1287.15 −0.273257 −0.136628 0.990622i \(-0.543627\pi\)
−0.136628 + 0.990622i \(0.543627\pi\)
\(282\) −200.177 −0.0422708
\(283\) −8974.14 −1.88501 −0.942504 0.334194i \(-0.891536\pi\)
−0.942504 + 0.334194i \(0.891536\pi\)
\(284\) −396.552 −0.0828558
\(285\) 1495.46 0.310819
\(286\) −4025.80 −0.832345
\(287\) 155.851 0.0320544
\(288\) 10188.5 2.08460
\(289\) 1593.32 0.324308
\(290\) −5638.14 −1.14167
\(291\) −2499.41 −0.503498
\(292\) −3175.03 −0.636318
\(293\) 1173.60 0.234002 0.117001 0.993132i \(-0.462672\pi\)
0.117001 + 0.993132i \(0.462672\pi\)
\(294\) 1563.03 0.310061
\(295\) 4497.04 0.887552
\(296\) 1375.90 0.270177
\(297\) −18320.1 −3.57925
\(298\) 4284.81 0.832928
\(299\) −3640.51 −0.704134
\(300\) 4056.21 0.780617
\(301\) 0 0
\(302\) −465.750 −0.0887447
\(303\) −6156.37 −1.16724
\(304\) 231.764 0.0437256
\(305\) 1058.79 0.198774
\(306\) −12062.6 −2.25351
\(307\) −8027.77 −1.49241 −0.746204 0.665718i \(-0.768126\pi\)
−0.746204 + 0.665718i \(0.768126\pi\)
\(308\) −2445.08 −0.452342
\(309\) 15150.6 2.78928
\(310\) −3816.97 −0.699320
\(311\) 5900.91 1.07592 0.537958 0.842972i \(-0.319196\pi\)
0.537958 + 0.842972i \(0.319196\pi\)
\(312\) −10697.4 −1.94109
\(313\) −7645.72 −1.38071 −0.690354 0.723471i \(-0.742545\pi\)
−0.690354 + 0.723471i \(0.742545\pi\)
\(314\) 5181.47 0.931234
\(315\) 17977.5 3.21562
\(316\) 2790.71 0.496803
\(317\) 8873.30 1.57216 0.786079 0.618126i \(-0.212108\pi\)
0.786079 + 0.618126i \(0.212108\pi\)
\(318\) −5322.87 −0.938653
\(319\) −7283.45 −1.27835
\(320\) 7749.44 1.35377
\(321\) −9663.68 −1.68029
\(322\) 2850.36 0.493305
\(323\) 784.549 0.135150
\(324\) −8152.24 −1.39785
\(325\) −5221.72 −0.891228
\(326\) −6227.78 −1.05805
\(327\) 6073.85 1.02717
\(328\) −232.099 −0.0390718
\(329\) 156.512 0.0262273
\(330\) −13936.6 −2.32481
\(331\) −3998.27 −0.663943 −0.331971 0.943289i \(-0.607714\pi\)
−0.331971 + 0.943289i \(0.607714\pi\)
\(332\) 4448.84 0.735426
\(333\) −3973.22 −0.653847
\(334\) −8761.12 −1.43529
\(335\) 4263.49 0.695341
\(336\) 3853.83 0.625725
\(337\) 3151.54 0.509423 0.254711 0.967017i \(-0.418020\pi\)
0.254711 + 0.967017i \(0.418020\pi\)
\(338\) −476.359 −0.0766583
\(339\) −18652.8 −2.98844
\(340\) 4390.42 0.700306
\(341\) −4930.82 −0.783047
\(342\) −1454.54 −0.229978
\(343\) −6841.49 −1.07698
\(344\) 0 0
\(345\) −12602.8 −1.96670
\(346\) −1705.99 −0.265072
\(347\) 2639.21 0.408300 0.204150 0.978940i \(-0.434557\pi\)
0.204150 + 0.978940i \(0.434557\pi\)
\(348\) −5884.12 −0.906386
\(349\) −8673.47 −1.33032 −0.665158 0.746702i \(-0.731636\pi\)
−0.665158 + 0.746702i \(0.731636\pi\)
\(350\) 4088.38 0.624380
\(351\) 19053.1 2.89738
\(352\) 6175.52 0.935104
\(353\) −799.760 −0.120586 −0.0602931 0.998181i \(-0.519204\pi\)
−0.0602931 + 0.998181i \(0.519204\pi\)
\(354\) −6050.20 −0.908374
\(355\) 1767.26 0.264215
\(356\) 4872.90 0.725459
\(357\) 13045.7 1.93404
\(358\) −7116.36 −1.05059
\(359\) −6892.85 −1.01334 −0.506672 0.862139i \(-0.669125\pi\)
−0.506672 + 0.862139i \(0.669125\pi\)
\(360\) −26772.8 −3.91958
\(361\) −6764.40 −0.986207
\(362\) −8969.94 −1.30235
\(363\) −4864.02 −0.703291
\(364\) 2542.91 0.366167
\(365\) 14149.7 2.02912
\(366\) −1424.47 −0.203437
\(367\) 10785.9 1.53412 0.767058 0.641578i \(-0.221720\pi\)
0.767058 + 0.641578i \(0.221720\pi\)
\(368\) −1953.17 −0.276673
\(369\) 670.241 0.0945565
\(370\) −1864.25 −0.261940
\(371\) 4161.79 0.582397
\(372\) −3983.49 −0.555200
\(373\) 2319.02 0.321916 0.160958 0.986961i \(-0.448542\pi\)
0.160958 + 0.986961i \(0.448542\pi\)
\(374\) −7311.46 −1.01087
\(375\) 1142.35 0.157309
\(376\) −233.083 −0.0319690
\(377\) 7574.88 1.03482
\(378\) −14917.7 −2.02986
\(379\) −9170.77 −1.24293 −0.621466 0.783441i \(-0.713462\pi\)
−0.621466 + 0.783441i \(0.713462\pi\)
\(380\) 529.408 0.0714686
\(381\) 3290.05 0.442400
\(382\) 7738.50 1.03648
\(383\) 6403.02 0.854253 0.427127 0.904192i \(-0.359526\pi\)
0.427127 + 0.904192i \(0.359526\pi\)
\(384\) 994.720 0.132192
\(385\) 10896.6 1.44245
\(386\) 6795.50 0.896067
\(387\) 0 0
\(388\) −884.817 −0.115773
\(389\) 7196.53 0.937991 0.468995 0.883201i \(-0.344616\pi\)
0.468995 + 0.883201i \(0.344616\pi\)
\(390\) 14494.3 1.88191
\(391\) −6611.71 −0.855162
\(392\) 1819.98 0.234497
\(393\) −12817.6 −1.64520
\(394\) 197.281 0.0252255
\(395\) −12436.9 −1.58423
\(396\) −10515.1 −1.33435
\(397\) 10186.1 1.28773 0.643863 0.765141i \(-0.277331\pi\)
0.643863 + 0.765141i \(0.277331\pi\)
\(398\) 205.933 0.0259359
\(399\) 1573.08 0.197375
\(400\) −2801.50 −0.350188
\(401\) 4639.83 0.577810 0.288905 0.957358i \(-0.406709\pi\)
0.288905 + 0.957358i \(0.406709\pi\)
\(402\) −5735.98 −0.711654
\(403\) 5128.12 0.633870
\(404\) −2179.42 −0.268391
\(405\) 36330.9 4.45752
\(406\) −5930.79 −0.724976
\(407\) −2408.27 −0.293301
\(408\) −19428.1 −2.35743
\(409\) −9793.28 −1.18398 −0.591988 0.805947i \(-0.701657\pi\)
−0.591988 + 0.805947i \(0.701657\pi\)
\(410\) 314.479 0.0378806
\(411\) 19637.1 2.35676
\(412\) 5363.48 0.641358
\(413\) 4730.46 0.563610
\(414\) 12258.0 1.45519
\(415\) −19826.5 −2.34517
\(416\) −6422.62 −0.756959
\(417\) 15342.8 1.80178
\(418\) −881.635 −0.103163
\(419\) 10390.7 1.21150 0.605748 0.795657i \(-0.292874\pi\)
0.605748 + 0.795657i \(0.292874\pi\)
\(420\) 8803.13 1.02274
\(421\) 1278.81 0.148041 0.0740206 0.997257i \(-0.476417\pi\)
0.0740206 + 0.997257i \(0.476417\pi\)
\(422\) −226.732 −0.0261543
\(423\) 673.082 0.0773673
\(424\) −6197.87 −0.709895
\(425\) −9483.42 −1.08238
\(426\) −2377.62 −0.270414
\(427\) 1113.75 0.126225
\(428\) −3421.04 −0.386361
\(429\) 18724.0 2.10723
\(430\) 0 0
\(431\) −8345.12 −0.932646 −0.466323 0.884615i \(-0.654422\pi\)
−0.466323 + 0.884615i \(0.654422\pi\)
\(432\) 10222.2 1.13846
\(433\) 8533.68 0.947119 0.473560 0.880762i \(-0.342969\pi\)
0.473560 + 0.880762i \(0.342969\pi\)
\(434\) −4015.09 −0.444079
\(435\) 26222.9 2.89033
\(436\) 2150.21 0.236184
\(437\) −797.257 −0.0872722
\(438\) −19036.6 −2.07673
\(439\) −14123.5 −1.53549 −0.767744 0.640756i \(-0.778621\pi\)
−0.767744 + 0.640756i \(0.778621\pi\)
\(440\) −16227.6 −1.75823
\(441\) −5255.60 −0.567499
\(442\) 7604.01 0.818293
\(443\) 6033.41 0.647079 0.323539 0.946215i \(-0.395127\pi\)
0.323539 + 0.946215i \(0.395127\pi\)
\(444\) −1945.58 −0.207958
\(445\) −21716.4 −2.31338
\(446\) 8050.49 0.854713
\(447\) −19928.6 −2.10871
\(448\) 8151.68 0.859667
\(449\) −15345.6 −1.61293 −0.806464 0.591284i \(-0.798621\pi\)
−0.806464 + 0.591284i \(0.798621\pi\)
\(450\) 17582.1 1.84184
\(451\) 406.250 0.0424159
\(452\) −6603.28 −0.687150
\(453\) 2166.20 0.224673
\(454\) −4546.81 −0.470027
\(455\) −11332.6 −1.16765
\(456\) −2342.69 −0.240584
\(457\) −16460.5 −1.68488 −0.842439 0.538792i \(-0.818881\pi\)
−0.842439 + 0.538792i \(0.818881\pi\)
\(458\) −1839.64 −0.187687
\(459\) 34603.3 3.51883
\(460\) −4461.53 −0.452217
\(461\) −1574.00 −0.159021 −0.0795103 0.996834i \(-0.525336\pi\)
−0.0795103 + 0.996834i \(0.525336\pi\)
\(462\) −14660.0 −1.47629
\(463\) −10676.6 −1.07167 −0.535834 0.844323i \(-0.680003\pi\)
−0.535834 + 0.844323i \(0.680003\pi\)
\(464\) 4063.99 0.406608
\(465\) 17752.7 1.77045
\(466\) −5727.64 −0.569373
\(467\) −6834.42 −0.677215 −0.338607 0.940928i \(-0.609956\pi\)
−0.338607 + 0.940928i \(0.609956\pi\)
\(468\) 10935.8 1.08015
\(469\) 4484.79 0.441553
\(470\) 315.812 0.0309943
\(471\) −24099.0 −2.35758
\(472\) −7044.77 −0.686995
\(473\) 0 0
\(474\) 16732.3 1.62140
\(475\) −1143.54 −0.110461
\(476\) 4618.31 0.444706
\(477\) 17897.8 1.71800
\(478\) −3941.36 −0.377142
\(479\) −3790.83 −0.361602 −0.180801 0.983520i \(-0.557869\pi\)
−0.180801 + 0.983520i \(0.557869\pi\)
\(480\) −22234.0 −2.11425
\(481\) 2504.63 0.237425
\(482\) 10381.6 0.981060
\(483\) −13257.0 −1.24889
\(484\) −1721.91 −0.161712
\(485\) 3943.23 0.369181
\(486\) −24293.6 −2.26745
\(487\) 6937.25 0.645497 0.322748 0.946485i \(-0.395393\pi\)
0.322748 + 0.946485i \(0.395393\pi\)
\(488\) −1658.63 −0.153858
\(489\) 28965.4 2.67865
\(490\) −2465.95 −0.227347
\(491\) −3418.47 −0.314203 −0.157101 0.987582i \(-0.550215\pi\)
−0.157101 + 0.987582i \(0.550215\pi\)
\(492\) 328.200 0.0300739
\(493\) 13757.1 1.25677
\(494\) 916.911 0.0835097
\(495\) 46861.1 4.25505
\(496\) 2751.28 0.249065
\(497\) 1858.99 0.167781
\(498\) 26674.0 2.40018
\(499\) 8330.03 0.747301 0.373651 0.927570i \(-0.378106\pi\)
0.373651 + 0.927570i \(0.378106\pi\)
\(500\) 404.404 0.0361710
\(501\) 40747.9 3.63369
\(502\) −12055.7 −1.07186
\(503\) −1435.22 −0.127223 −0.0636116 0.997975i \(-0.520262\pi\)
−0.0636116 + 0.997975i \(0.520262\pi\)
\(504\) −28162.4 −2.48900
\(505\) 9712.69 0.855860
\(506\) 7429.88 0.652764
\(507\) 2215.54 0.194074
\(508\) 1164.71 0.101724
\(509\) −1358.45 −0.118295 −0.0591477 0.998249i \(-0.518838\pi\)
−0.0591477 + 0.998249i \(0.518838\pi\)
\(510\) 26323.8 2.28556
\(511\) 14884.2 1.28853
\(512\) −8096.75 −0.698885
\(513\) 4172.55 0.359109
\(514\) 6570.67 0.563851
\(515\) −23902.6 −2.04520
\(516\) 0 0
\(517\) 407.972 0.0347052
\(518\) −1961.02 −0.166336
\(519\) 7934.56 0.671076
\(520\) 16876.9 1.42328
\(521\) 852.637 0.0716981 0.0358490 0.999357i \(-0.488586\pi\)
0.0358490 + 0.999357i \(0.488586\pi\)
\(522\) −25505.4 −2.13859
\(523\) −9749.01 −0.815094 −0.407547 0.913184i \(-0.633616\pi\)
−0.407547 + 0.913184i \(0.633616\pi\)
\(524\) −4537.57 −0.378292
\(525\) −19015.0 −1.58073
\(526\) −5922.19 −0.490912
\(527\) 9313.42 0.769827
\(528\) 10045.6 0.827988
\(529\) −5448.21 −0.447785
\(530\) 8397.71 0.688251
\(531\) 20343.4 1.66258
\(532\) 556.888 0.0453837
\(533\) −422.505 −0.0343353
\(534\) 29216.6 2.36765
\(535\) 15246.1 1.23205
\(536\) −6678.90 −0.538217
\(537\) 33098.1 2.65976
\(538\) −17390.4 −1.39359
\(539\) −3185.55 −0.254567
\(540\) 23350.0 1.86079
\(541\) 4019.47 0.319428 0.159714 0.987163i \(-0.448943\pi\)
0.159714 + 0.987163i \(0.448943\pi\)
\(542\) −8997.78 −0.713077
\(543\) 41719.1 3.29712
\(544\) −11664.4 −0.919317
\(545\) −9582.52 −0.753156
\(546\) 15246.6 1.19505
\(547\) 4687.88 0.366434 0.183217 0.983073i \(-0.441349\pi\)
0.183217 + 0.983073i \(0.441349\pi\)
\(548\) 6951.74 0.541904
\(549\) 4789.68 0.372347
\(550\) 10657.0 0.826208
\(551\) 1658.87 0.128258
\(552\) 19742.8 1.52230
\(553\) −13082.5 −1.00601
\(554\) 18102.6 1.38828
\(555\) 8670.60 0.663147
\(556\) 5431.52 0.414294
\(557\) 8917.98 0.678397 0.339198 0.940715i \(-0.389844\pi\)
0.339198 + 0.940715i \(0.389844\pi\)
\(558\) −17266.9 −1.30998
\(559\) 0 0
\(560\) −6080.06 −0.458803
\(561\) 34005.5 2.55920
\(562\) −2732.05 −0.205061
\(563\) 4096.21 0.306634 0.153317 0.988177i \(-0.451004\pi\)
0.153317 + 0.988177i \(0.451004\pi\)
\(564\) 329.591 0.0246069
\(565\) 29427.9 2.19122
\(566\) −19048.1 −1.41458
\(567\) 38216.7 2.83060
\(568\) −2768.47 −0.204511
\(569\) 2683.32 0.197699 0.0988495 0.995102i \(-0.468484\pi\)
0.0988495 + 0.995102i \(0.468484\pi\)
\(570\) 3174.19 0.233249
\(571\) 10667.4 0.781815 0.390908 0.920430i \(-0.372161\pi\)
0.390908 + 0.920430i \(0.372161\pi\)
\(572\) 6628.48 0.484529
\(573\) −35991.7 −2.62404
\(574\) 330.803 0.0240548
\(575\) 9637.02 0.698942
\(576\) 35056.4 2.53591
\(577\) −21766.6 −1.57046 −0.785230 0.619205i \(-0.787455\pi\)
−0.785230 + 0.619205i \(0.787455\pi\)
\(578\) 3381.91 0.243372
\(579\) −31605.8 −2.26855
\(580\) 9283.19 0.664592
\(581\) −20855.6 −1.48922
\(582\) −5305.12 −0.377843
\(583\) 10848.3 0.770653
\(584\) −22166.0 −1.57061
\(585\) −48736.1 −3.44443
\(586\) 2491.04 0.175604
\(587\) 24126.0 1.69640 0.848201 0.529675i \(-0.177686\pi\)
0.848201 + 0.529675i \(0.177686\pi\)
\(588\) −2573.53 −0.180494
\(589\) 1123.04 0.0785635
\(590\) 9545.20 0.666050
\(591\) −917.551 −0.0638629
\(592\) 1343.76 0.0932906
\(593\) 23547.7 1.63067 0.815337 0.578987i \(-0.196552\pi\)
0.815337 + 0.578987i \(0.196552\pi\)
\(594\) −38885.3 −2.68600
\(595\) −20581.7 −1.41810
\(596\) −7054.94 −0.484868
\(597\) −957.791 −0.0656613
\(598\) −7727.17 −0.528407
\(599\) −10000.3 −0.682139 −0.341070 0.940038i \(-0.610789\pi\)
−0.341070 + 0.940038i \(0.610789\pi\)
\(600\) 28317.8 1.92678
\(601\) −4062.49 −0.275728 −0.137864 0.990451i \(-0.544024\pi\)
−0.137864 + 0.990451i \(0.544024\pi\)
\(602\) 0 0
\(603\) 19286.9 1.30252
\(604\) 766.857 0.0516605
\(605\) 7673.80 0.515676
\(606\) −13067.2 −0.875939
\(607\) −12695.2 −0.848902 −0.424451 0.905451i \(-0.639533\pi\)
−0.424451 + 0.905451i \(0.639533\pi\)
\(608\) −1406.53 −0.0938195
\(609\) 27584.1 1.83541
\(610\) 2247.34 0.149167
\(611\) −424.296 −0.0280936
\(612\) 19861.1 1.31182
\(613\) −4025.43 −0.265230 −0.132615 0.991168i \(-0.542337\pi\)
−0.132615 + 0.991168i \(0.542337\pi\)
\(614\) −17039.4 −1.11996
\(615\) −1462.64 −0.0959013
\(616\) −17070.0 −1.11651
\(617\) −21979.7 −1.43415 −0.717074 0.696997i \(-0.754519\pi\)
−0.717074 + 0.696997i \(0.754519\pi\)
\(618\) 32158.0 2.09318
\(619\) 3508.41 0.227811 0.113906 0.993492i \(-0.463664\pi\)
0.113906 + 0.993492i \(0.463664\pi\)
\(620\) 6284.63 0.407091
\(621\) −35163.7 −2.27226
\(622\) 12525.0 0.807405
\(623\) −22843.6 −1.46903
\(624\) −10447.5 −0.670250
\(625\) −16498.5 −1.05591
\(626\) −16228.4 −1.03613
\(627\) 4100.47 0.261176
\(628\) −8531.28 −0.542094
\(629\) 4548.78 0.288349
\(630\) 38158.2 2.41311
\(631\) −12163.9 −0.767412 −0.383706 0.923455i \(-0.625352\pi\)
−0.383706 + 0.923455i \(0.625352\pi\)
\(632\) 19482.9 1.22625
\(633\) 1054.53 0.0662143
\(634\) 18834.0 1.17980
\(635\) −5190.60 −0.324382
\(636\) 8764.09 0.546413
\(637\) 3313.02 0.206070
\(638\) −15459.5 −0.959321
\(639\) 7994.60 0.494932
\(640\) −1569.34 −0.0969273
\(641\) 19508.5 1.20209 0.601045 0.799216i \(-0.294751\pi\)
0.601045 + 0.799216i \(0.294751\pi\)
\(642\) −20511.7 −1.26095
\(643\) 8349.25 0.512072 0.256036 0.966667i \(-0.417583\pi\)
0.256036 + 0.966667i \(0.417583\pi\)
\(644\) −4693.11 −0.287165
\(645\) 0 0
\(646\) 1665.25 0.101421
\(647\) −24420.9 −1.48390 −0.741952 0.670453i \(-0.766100\pi\)
−0.741952 + 0.670453i \(0.766100\pi\)
\(648\) −56913.6 −3.45027
\(649\) 12330.6 0.745794
\(650\) −11083.4 −0.668809
\(651\) 18674.1 1.12427
\(652\) 10254.0 0.615919
\(653\) 17813.5 1.06753 0.533763 0.845634i \(-0.320777\pi\)
0.533763 + 0.845634i \(0.320777\pi\)
\(654\) 12892.1 0.770825
\(655\) 20221.9 1.20632
\(656\) −226.678 −0.0134913
\(657\) 64009.5 3.80099
\(658\) 332.205 0.0196819
\(659\) −10172.2 −0.601294 −0.300647 0.953735i \(-0.597203\pi\)
−0.300647 + 0.953735i \(0.597203\pi\)
\(660\) 22946.7 1.35333
\(661\) −10378.7 −0.610716 −0.305358 0.952238i \(-0.598776\pi\)
−0.305358 + 0.952238i \(0.598776\pi\)
\(662\) −8486.54 −0.498246
\(663\) −35366.1 −2.07166
\(664\) 31058.9 1.81524
\(665\) −2481.80 −0.144722
\(666\) −8433.36 −0.490670
\(667\) −13979.9 −0.811551
\(668\) 14425.2 0.835519
\(669\) −37442.8 −2.16386
\(670\) 9049.47 0.521808
\(671\) 2903.15 0.167026
\(672\) −23388.1 −1.34258
\(673\) −20924.5 −1.19849 −0.599243 0.800567i \(-0.704532\pi\)
−0.599243 + 0.800567i \(0.704532\pi\)
\(674\) 6689.31 0.382289
\(675\) −50436.7 −2.87601
\(676\) 784.324 0.0446247
\(677\) −9393.92 −0.533290 −0.266645 0.963795i \(-0.585915\pi\)
−0.266645 + 0.963795i \(0.585915\pi\)
\(678\) −39591.5 −2.24263
\(679\) 4147.91 0.234436
\(680\) 30651.0 1.72855
\(681\) 21147.1 1.18996
\(682\) −10465.9 −0.587626
\(683\) −4288.63 −0.240263 −0.120132 0.992758i \(-0.538332\pi\)
−0.120132 + 0.992758i \(0.538332\pi\)
\(684\) 2394.90 0.133876
\(685\) −30980.8 −1.72805
\(686\) −14521.4 −0.808207
\(687\) 8556.14 0.475163
\(688\) 0 0
\(689\) −11282.4 −0.623838
\(690\) −26750.1 −1.47588
\(691\) −6084.89 −0.334993 −0.167496 0.985873i \(-0.553568\pi\)
−0.167496 + 0.985873i \(0.553568\pi\)
\(692\) 2808.92 0.154305
\(693\) 49293.4 2.70202
\(694\) 5601.86 0.306403
\(695\) −24205.9 −1.32112
\(696\) −41079.1 −2.23721
\(697\) −767.332 −0.0416998
\(698\) −18409.9 −0.998316
\(699\) 26639.2 1.44147
\(700\) −6731.51 −0.363467
\(701\) 19240.3 1.03666 0.518329 0.855182i \(-0.326554\pi\)
0.518329 + 0.855182i \(0.326554\pi\)
\(702\) 40441.2 2.17429
\(703\) 548.504 0.0294270
\(704\) 21248.6 1.13755
\(705\) −1468.84 −0.0784677
\(706\) −1697.53 −0.0904922
\(707\) 10216.8 0.543485
\(708\) 9961.64 0.528787
\(709\) −22023.7 −1.16660 −0.583299 0.812258i \(-0.698238\pi\)
−0.583299 + 0.812258i \(0.698238\pi\)
\(710\) 3751.10 0.198276
\(711\) −56261.4 −2.96761
\(712\) 34019.4 1.79063
\(713\) −9464.27 −0.497110
\(714\) 27690.1 1.45137
\(715\) −29540.2 −1.54509
\(716\) 11717.1 0.611575
\(717\) 18331.2 0.954801
\(718\) −14630.4 −0.760449
\(719\) −9873.52 −0.512128 −0.256064 0.966660i \(-0.582426\pi\)
−0.256064 + 0.966660i \(0.582426\pi\)
\(720\) −26147.4 −1.35341
\(721\) −25143.3 −1.29873
\(722\) −14357.8 −0.740085
\(723\) −48284.9 −2.48373
\(724\) 14769.0 0.758129
\(725\) −20051.9 −1.02719
\(726\) −10324.1 −0.527774
\(727\) −22548.2 −1.15030 −0.575150 0.818048i \(-0.695056\pi\)
−0.575150 + 0.818048i \(0.695056\pi\)
\(728\) 17753.0 0.903803
\(729\) 50006.4 2.54059
\(730\) 30033.5 1.52272
\(731\) 0 0
\(732\) 2345.38 0.118426
\(733\) 23342.2 1.17621 0.588106 0.808784i \(-0.299874\pi\)
0.588106 + 0.808784i \(0.299874\pi\)
\(734\) 22893.7 1.15125
\(735\) 11469.1 0.575570
\(736\) 11853.4 0.593642
\(737\) 11690.3 0.584282
\(738\) 1422.62 0.0709585
\(739\) 2588.54 0.128851 0.0644255 0.997923i \(-0.479479\pi\)
0.0644255 + 0.997923i \(0.479479\pi\)
\(740\) 3069.48 0.152482
\(741\) −4264.54 −0.211420
\(742\) 8833.60 0.437051
\(743\) −8452.43 −0.417348 −0.208674 0.977985i \(-0.566915\pi\)
−0.208674 + 0.977985i \(0.566915\pi\)
\(744\) −27810.2 −1.37039
\(745\) 31440.7 1.54617
\(746\) 4922.25 0.241577
\(747\) −89689.7 −4.39300
\(748\) 12038.3 0.588454
\(749\) 16037.4 0.782370
\(750\) 2424.70 0.118050
\(751\) −3358.11 −0.163168 −0.0815841 0.996666i \(-0.525998\pi\)
−0.0815841 + 0.996666i \(0.525998\pi\)
\(752\) −227.639 −0.0110387
\(753\) 56070.8 2.71359
\(754\) 16078.1 0.776563
\(755\) −3417.54 −0.164738
\(756\) 24562.0 1.18163
\(757\) −14867.1 −0.713810 −0.356905 0.934141i \(-0.616168\pi\)
−0.356905 + 0.934141i \(0.616168\pi\)
\(758\) −19465.4 −0.932739
\(759\) −34556.3 −1.65259
\(760\) 3695.98 0.176404
\(761\) 1721.42 0.0819991 0.0409995 0.999159i \(-0.486946\pi\)
0.0409995 + 0.999159i \(0.486946\pi\)
\(762\) 6983.30 0.331992
\(763\) −10079.9 −0.478266
\(764\) −12741.4 −0.603362
\(765\) −88512.0 −4.18321
\(766\) 13590.7 0.641062
\(767\) −12824.0 −0.603714
\(768\) 41407.0 1.94550
\(769\) 13213.3 0.619616 0.309808 0.950799i \(-0.399735\pi\)
0.309808 + 0.950799i \(0.399735\pi\)
\(770\) 23128.7 1.08247
\(771\) −30560.1 −1.42749
\(772\) −11188.8 −0.521623
\(773\) 26452.9 1.23085 0.615424 0.788196i \(-0.288985\pi\)
0.615424 + 0.788196i \(0.288985\pi\)
\(774\) 0 0
\(775\) −13575.0 −0.629196
\(776\) −6177.21 −0.285759
\(777\) 9120.66 0.421109
\(778\) 15275.0 0.703901
\(779\) −92.5268 −0.00425561
\(780\) −23864.8 −1.09551
\(781\) 4845.73 0.222015
\(782\) −14033.7 −0.641744
\(783\) 73165.8 3.33938
\(784\) 1777.46 0.0809704
\(785\) 38020.1 1.72866
\(786\) −27206.1 −1.23462
\(787\) 22609.2 1.02405 0.512027 0.858970i \(-0.328895\pi\)
0.512027 + 0.858970i \(0.328895\pi\)
\(788\) −324.822 −0.0146844
\(789\) 27544.0 1.24283
\(790\) −26398.1 −1.18886
\(791\) 30955.3 1.39146
\(792\) −73409.5 −3.29355
\(793\) −3019.31 −0.135207
\(794\) 21620.6 0.966355
\(795\) −39057.7 −1.74243
\(796\) −339.068 −0.0150979
\(797\) 16151.3 0.717829 0.358915 0.933370i \(-0.383147\pi\)
0.358915 + 0.933370i \(0.383147\pi\)
\(798\) 3338.95 0.148117
\(799\) −770.584 −0.0341193
\(800\) 17001.7 0.751377
\(801\) −98239.0 −4.33346
\(802\) 9848.27 0.433609
\(803\) 38797.8 1.70504
\(804\) 9444.28 0.414271
\(805\) 20915.1 0.915727
\(806\) 10884.7 0.475678
\(807\) 80882.4 3.52812
\(808\) −15215.3 −0.662465
\(809\) 8389.19 0.364584 0.182292 0.983244i \(-0.441648\pi\)
0.182292 + 0.983244i \(0.441648\pi\)
\(810\) 77114.2 3.34508
\(811\) −687.716 −0.0297768 −0.0148884 0.999889i \(-0.504739\pi\)
−0.0148884 + 0.999889i \(0.504739\pi\)
\(812\) 9765.04 0.422027
\(813\) 41848.6 1.80528
\(814\) −5111.67 −0.220103
\(815\) −45697.7 −1.96407
\(816\) −18974.3 −0.814010
\(817\) 0 0
\(818\) −20786.7 −0.888498
\(819\) −51265.8 −2.18727
\(820\) −517.790 −0.0220512
\(821\) −36524.3 −1.55263 −0.776313 0.630348i \(-0.782912\pi\)
−0.776313 + 0.630348i \(0.782912\pi\)
\(822\) 41680.8 1.76859
\(823\) −2950.87 −0.124983 −0.0624915 0.998045i \(-0.519905\pi\)
−0.0624915 + 0.998045i \(0.519905\pi\)
\(824\) 37444.3 1.58305
\(825\) −49565.4 −2.09169
\(826\) 10040.6 0.422953
\(827\) −7907.73 −0.332501 −0.166251 0.986084i \(-0.553166\pi\)
−0.166251 + 0.986084i \(0.553166\pi\)
\(828\) −20182.8 −0.847101
\(829\) −36919.5 −1.54677 −0.773383 0.633939i \(-0.781437\pi\)
−0.773383 + 0.633939i \(0.781437\pi\)
\(830\) −42082.7 −1.75989
\(831\) −84194.9 −3.51467
\(832\) −22098.8 −0.920838
\(833\) 6016.93 0.250269
\(834\) 32565.9 1.35212
\(835\) −64286.6 −2.66435
\(836\) 1451.61 0.0600538
\(837\) 49532.5 2.04551
\(838\) 22054.7 0.909149
\(839\) −21841.4 −0.898747 −0.449373 0.893344i \(-0.648353\pi\)
−0.449373 + 0.893344i \(0.648353\pi\)
\(840\) 61457.7 2.52440
\(841\) 4699.28 0.192680
\(842\) 2714.34 0.111095
\(843\) 12706.7 0.519149
\(844\) 373.313 0.0152251
\(845\) −3495.38 −0.142302
\(846\) 1428.65 0.0580591
\(847\) 8072.11 0.327463
\(848\) −6053.10 −0.245123
\(849\) 88592.4 3.58125
\(850\) −20129.0 −0.812260
\(851\) −4622.46 −0.186199
\(852\) 3914.75 0.157414
\(853\) −43215.2 −1.73466 −0.867328 0.497737i \(-0.834165\pi\)
−0.867328 + 0.497737i \(0.834165\pi\)
\(854\) 2363.99 0.0947236
\(855\) −10673.0 −0.426911
\(856\) −23883.5 −0.953646
\(857\) 14793.5 0.589657 0.294828 0.955550i \(-0.404738\pi\)
0.294828 + 0.955550i \(0.404738\pi\)
\(858\) 39742.6 1.58134
\(859\) 16459.1 0.653758 0.326879 0.945066i \(-0.394003\pi\)
0.326879 + 0.945066i \(0.394003\pi\)
\(860\) 0 0
\(861\) −1538.56 −0.0608989
\(862\) −17712.9 −0.699890
\(863\) −32877.1 −1.29681 −0.648406 0.761295i \(-0.724564\pi\)
−0.648406 + 0.761295i \(0.724564\pi\)
\(864\) −62036.2 −2.44272
\(865\) −12518.1 −0.492055
\(866\) 18113.2 0.710752
\(867\) −15729.2 −0.616139
\(868\) 6610.84 0.258510
\(869\) −34101.5 −1.33120
\(870\) 55659.5 2.16900
\(871\) −12158.0 −0.472972
\(872\) 15011.3 0.582968
\(873\) 17838.1 0.691557
\(874\) −1692.22 −0.0654921
\(875\) −1895.80 −0.0732453
\(876\) 31343.8 1.20891
\(877\) −13873.2 −0.534168 −0.267084 0.963673i \(-0.586060\pi\)
−0.267084 + 0.963673i \(0.586060\pi\)
\(878\) −29977.9 −1.15228
\(879\) −11585.8 −0.444572
\(880\) −15848.6 −0.607108
\(881\) 36781.0 1.40657 0.703283 0.710910i \(-0.251717\pi\)
0.703283 + 0.710910i \(0.251717\pi\)
\(882\) −11155.3 −0.425871
\(883\) 14471.7 0.551542 0.275771 0.961223i \(-0.411067\pi\)
0.275771 + 0.961223i \(0.411067\pi\)
\(884\) −12520.0 −0.476349
\(885\) −44394.6 −1.68622
\(886\) 12806.2 0.485591
\(887\) 29063.0 1.10016 0.550080 0.835112i \(-0.314597\pi\)
0.550080 + 0.835112i \(0.314597\pi\)
\(888\) −13582.8 −0.513298
\(889\) −5460.03 −0.205988
\(890\) −46094.1 −1.73604
\(891\) 99617.4 3.74558
\(892\) −13255.1 −0.497550
\(893\) −92.9191 −0.00348199
\(894\) −42299.5 −1.58245
\(895\) −52217.8 −1.95022
\(896\) −1650.79 −0.0615504
\(897\) 35939.0 1.33776
\(898\) −32571.8 −1.21040
\(899\) 19692.5 0.730568
\(900\) −28948.9 −1.07218
\(901\) −20490.5 −0.757643
\(902\) 862.286 0.0318304
\(903\) 0 0
\(904\) −46099.8 −1.69608
\(905\) −65818.8 −2.41756
\(906\) 4597.87 0.168603
\(907\) −5383.63 −0.197090 −0.0985450 0.995133i \(-0.531419\pi\)
−0.0985450 + 0.995133i \(0.531419\pi\)
\(908\) 7486.31 0.273614
\(909\) 43937.6 1.60321
\(910\) −24054.1 −0.876248
\(911\) −11716.3 −0.426100 −0.213050 0.977041i \(-0.568340\pi\)
−0.213050 + 0.977041i \(0.568340\pi\)
\(912\) −2287.97 −0.0830725
\(913\) −54363.2 −1.97060
\(914\) −34938.2 −1.26439
\(915\) −10452.3 −0.377643
\(916\) 3028.96 0.109257
\(917\) 21271.6 0.766030
\(918\) 73447.2 2.64065
\(919\) 18077.4 0.648879 0.324439 0.945906i \(-0.394824\pi\)
0.324439 + 0.945906i \(0.394824\pi\)
\(920\) −31147.5 −1.11620
\(921\) 79249.8 2.83537
\(922\) −3340.90 −0.119335
\(923\) −5039.62 −0.179719
\(924\) 24137.7 0.859386
\(925\) −6630.16 −0.235674
\(926\) −22661.6 −0.804217
\(927\) −108129. −3.83110
\(928\) −24663.5 −0.872435
\(929\) 2703.22 0.0954680 0.0477340 0.998860i \(-0.484800\pi\)
0.0477340 + 0.998860i \(0.484800\pi\)
\(930\) 37680.9 1.32861
\(931\) 725.537 0.0255408
\(932\) 9430.55 0.331446
\(933\) −58253.6 −2.04409
\(934\) −14506.4 −0.508206
\(935\) −53649.4 −1.87649
\(936\) 76346.8 2.66610
\(937\) 5610.28 0.195603 0.0978015 0.995206i \(-0.468819\pi\)
0.0978015 + 0.995206i \(0.468819\pi\)
\(938\) 9519.19 0.331357
\(939\) 75478.3 2.62315
\(940\) −519.985 −0.0180426
\(941\) −1782.55 −0.0617528 −0.0308764 0.999523i \(-0.509830\pi\)
−0.0308764 + 0.999523i \(0.509830\pi\)
\(942\) −51151.3 −1.76921
\(943\) 779.760 0.0269273
\(944\) −6880.21 −0.237216
\(945\) −109462. −3.76804
\(946\) 0 0
\(947\) −17721.3 −0.608094 −0.304047 0.952657i \(-0.598338\pi\)
−0.304047 + 0.952657i \(0.598338\pi\)
\(948\) −27549.8 −0.943855
\(949\) −40350.2 −1.38021
\(950\) −2427.21 −0.0828939
\(951\) −87596.9 −2.98688
\(952\) 32242.0 1.09766
\(953\) −12699.3 −0.431658 −0.215829 0.976431i \(-0.569245\pi\)
−0.215829 + 0.976431i \(0.569245\pi\)
\(954\) 37989.0 1.28924
\(955\) 56782.9 1.92403
\(956\) 6489.45 0.219544
\(957\) 71901.9 2.42869
\(958\) −8046.22 −0.271359
\(959\) −32588.9 −1.09734
\(960\) −76502.2 −2.57198
\(961\) −16459.4 −0.552495
\(962\) 5316.21 0.178172
\(963\) 68969.1 2.30789
\(964\) −17093.4 −0.571100
\(965\) 49863.4 1.66338
\(966\) −28138.6 −0.937211
\(967\) 30667.6 1.01986 0.509929 0.860216i \(-0.329671\pi\)
0.509929 + 0.860216i \(0.329671\pi\)
\(968\) −12021.3 −0.399151
\(969\) −7745.04 −0.256766
\(970\) 8369.71 0.277047
\(971\) 38789.5 1.28199 0.640996 0.767544i \(-0.278521\pi\)
0.640996 + 0.767544i \(0.278521\pi\)
\(972\) 39999.3 1.31994
\(973\) −25462.3 −0.838935
\(974\) 14724.7 0.484404
\(975\) 51548.6 1.69321
\(976\) −1619.89 −0.0531263
\(977\) 34788.6 1.13919 0.569594 0.821926i \(-0.307101\pi\)
0.569594 + 0.821926i \(0.307101\pi\)
\(978\) 61480.4 2.01015
\(979\) −59545.1 −1.94389
\(980\) 4060.18 0.132345
\(981\) −43348.7 −1.41082
\(982\) −7255.89 −0.235789
\(983\) −34284.6 −1.11242 −0.556210 0.831042i \(-0.687745\pi\)
−0.556210 + 0.831042i \(0.687745\pi\)
\(984\) 2291.28 0.0742309
\(985\) 1447.59 0.0468264
\(986\) 29200.1 0.943126
\(987\) −1545.08 −0.0498283
\(988\) −1509.69 −0.0486131
\(989\) 0 0
\(990\) 99465.0 3.19314
\(991\) −6213.41 −0.199168 −0.0995840 0.995029i \(-0.531751\pi\)
−0.0995840 + 0.995029i \(0.531751\pi\)
\(992\) −16697.0 −0.534404
\(993\) 39470.8 1.26140
\(994\) 3945.80 0.125909
\(995\) 1511.08 0.0481450
\(996\) −43918.7 −1.39721
\(997\) −38148.6 −1.21181 −0.605907 0.795535i \(-0.707190\pi\)
−0.605907 + 0.795535i \(0.707190\pi\)
\(998\) 17680.9 0.560801
\(999\) 24192.3 0.766175
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.1.35 50
43.42 odd 2 1849.4.a.j.1.16 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.35 50 1.1 even 1 trivial
1849.4.a.j.1.16 yes 50 43.42 odd 2