Properties

Label 2166.4.a.p.1.2
Level $2166$
Weight $4$
Character 2166.1
Self dual yes
Analytic conductor $127.798$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2166.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(127.798137072\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \(x^{2} - x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 2166.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -0.909830 q^{5} +6.00000 q^{6} -16.3262 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -0.909830 q^{5} +6.00000 q^{6} -16.3262 q^{7} +8.00000 q^{8} +9.00000 q^{9} -1.81966 q^{10} -1.94427 q^{11} +12.0000 q^{12} +15.0902 q^{13} -32.6525 q^{14} -2.72949 q^{15} +16.0000 q^{16} +32.0132 q^{17} +18.0000 q^{18} -3.63932 q^{20} -48.9787 q^{21} -3.88854 q^{22} -44.8885 q^{23} +24.0000 q^{24} -124.172 q^{25} +30.1803 q^{26} +27.0000 q^{27} -65.3050 q^{28} +31.1509 q^{29} -5.45898 q^{30} -299.503 q^{31} +32.0000 q^{32} -5.83282 q^{33} +64.0263 q^{34} +14.8541 q^{35} +36.0000 q^{36} -252.885 q^{37} +45.2705 q^{39} -7.27864 q^{40} +81.6475 q^{41} -97.9574 q^{42} -217.095 q^{43} -7.77709 q^{44} -8.18847 q^{45} -89.7771 q^{46} +187.743 q^{47} +48.0000 q^{48} -76.4540 q^{49} -248.344 q^{50} +96.0395 q^{51} +60.3607 q^{52} -11.8127 q^{53} +54.0000 q^{54} +1.76896 q^{55} -130.610 q^{56} +62.3018 q^{58} +244.046 q^{59} -10.9180 q^{60} +526.508 q^{61} -599.007 q^{62} -146.936 q^{63} +64.0000 q^{64} -13.7295 q^{65} -11.6656 q^{66} -210.726 q^{67} +128.053 q^{68} -134.666 q^{69} +29.7082 q^{70} -503.418 q^{71} +72.0000 q^{72} +115.265 q^{73} -505.771 q^{74} -372.517 q^{75} +31.7426 q^{77} +90.5410 q^{78} +220.492 q^{79} -14.5573 q^{80} +81.0000 q^{81} +163.295 q^{82} +200.023 q^{83} -195.915 q^{84} -29.1265 q^{85} -434.190 q^{86} +93.4528 q^{87} -15.5542 q^{88} -174.091 q^{89} -16.3769 q^{90} -246.366 q^{91} -179.554 q^{92} -898.510 q^{93} +375.485 q^{94} +96.0000 q^{96} -1105.40 q^{97} -152.908 q^{98} -17.4984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} - 13 q^{5} + 12 q^{6} - 17 q^{7} + 16 q^{8} + 18 q^{9} + O(q^{10}) \) \( 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} - 13 q^{5} + 12 q^{6} - 17 q^{7} + 16 q^{8} + 18 q^{9} - 26 q^{10} + 14 q^{11} + 24 q^{12} + 19 q^{13} - 34 q^{14} - 39 q^{15} + 32 q^{16} - 12 q^{17} + 36 q^{18} - 52 q^{20} - 51 q^{21} + 28 q^{22} - 54 q^{23} + 48 q^{24} - 103 q^{25} + 38 q^{26} + 54 q^{27} - 68 q^{28} - 130 q^{29} - 78 q^{30} - 239 q^{31} + 64 q^{32} + 42 q^{33} - 24 q^{34} + 23 q^{35} + 72 q^{36} - 148 q^{37} + 57 q^{39} - 104 q^{40} + 331 q^{41} - 102 q^{42} - 224 q^{43} + 56 q^{44} - 117 q^{45} - 108 q^{46} + 333 q^{47} + 96 q^{48} - 419 q^{49} - 206 q^{50} - 36 q^{51} + 76 q^{52} - 766 q^{53} + 108 q^{54} - 191 q^{55} - 136 q^{56} - 260 q^{58} - 460 q^{59} - 156 q^{60} + 494 q^{61} - 478 q^{62} - 153 q^{63} + 128 q^{64} - 61 q^{65} + 84 q^{66} - 133 q^{67} - 48 q^{68} - 162 q^{69} + 46 q^{70} - 459 q^{71} + 144 q^{72} + 396 q^{73} - 296 q^{74} - 309 q^{75} + 21 q^{77} + 114 q^{78} + 1000 q^{79} - 208 q^{80} + 162 q^{81} + 662 q^{82} - 74 q^{83} - 204 q^{84} + 503 q^{85} - 448 q^{86} - 390 q^{87} + 112 q^{88} - 1180 q^{89} - 234 q^{90} - 249 q^{91} - 216 q^{92} - 717 q^{93} + 666 q^{94} + 192 q^{96} - 1938 q^{97} - 838 q^{98} + 126 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) 3.00000 0.577350
\(4\) 4.00000 0.500000
\(5\) −0.909830 −0.0813777 −0.0406888 0.999172i \(-0.512955\pi\)
−0.0406888 + 0.999172i \(0.512955\pi\)
\(6\) 6.00000 0.408248
\(7\) −16.3262 −0.881534 −0.440767 0.897622i \(-0.645293\pi\)
−0.440767 + 0.897622i \(0.645293\pi\)
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) −1.81966 −0.0575427
\(11\) −1.94427 −0.0532927 −0.0266464 0.999645i \(-0.508483\pi\)
−0.0266464 + 0.999645i \(0.508483\pi\)
\(12\) 12.0000 0.288675
\(13\) 15.0902 0.321943 0.160972 0.986959i \(-0.448537\pi\)
0.160972 + 0.986959i \(0.448537\pi\)
\(14\) −32.6525 −0.623339
\(15\) −2.72949 −0.0469834
\(16\) 16.0000 0.250000
\(17\) 32.0132 0.456725 0.228363 0.973576i \(-0.426663\pi\)
0.228363 + 0.973576i \(0.426663\pi\)
\(18\) 18.0000 0.235702
\(19\) 0 0
\(20\) −3.63932 −0.0406888
\(21\) −48.9787 −0.508954
\(22\) −3.88854 −0.0376837
\(23\) −44.8885 −0.406953 −0.203476 0.979080i \(-0.565224\pi\)
−0.203476 + 0.979080i \(0.565224\pi\)
\(24\) 24.0000 0.204124
\(25\) −124.172 −0.993378
\(26\) 30.1803 0.227648
\(27\) 27.0000 0.192450
\(28\) −65.3050 −0.440767
\(29\) 31.1509 0.199468 0.0997342 0.995014i \(-0.468201\pi\)
0.0997342 + 0.995014i \(0.468201\pi\)
\(30\) −5.45898 −0.0332223
\(31\) −299.503 −1.73524 −0.867620 0.497229i \(-0.834351\pi\)
−0.867620 + 0.497229i \(0.834351\pi\)
\(32\) 32.0000 0.176777
\(33\) −5.83282 −0.0307686
\(34\) 64.0263 0.322954
\(35\) 14.8541 0.0717372
\(36\) 36.0000 0.166667
\(37\) −252.885 −1.12362 −0.561812 0.827265i \(-0.689896\pi\)
−0.561812 + 0.827265i \(0.689896\pi\)
\(38\) 0 0
\(39\) 45.2705 0.185874
\(40\) −7.27864 −0.0287714
\(41\) 81.6475 0.311005 0.155502 0.987836i \(-0.450300\pi\)
0.155502 + 0.987836i \(0.450300\pi\)
\(42\) −97.9574 −0.359885
\(43\) −217.095 −0.769923 −0.384962 0.922933i \(-0.625785\pi\)
−0.384962 + 0.922933i \(0.625785\pi\)
\(44\) −7.77709 −0.0266464
\(45\) −8.18847 −0.0271259
\(46\) −89.7771 −0.287759
\(47\) 187.743 0.582661 0.291331 0.956622i \(-0.405902\pi\)
0.291331 + 0.956622i \(0.405902\pi\)
\(48\) 48.0000 0.144338
\(49\) −76.4540 −0.222898
\(50\) −248.344 −0.702424
\(51\) 96.0395 0.263690
\(52\) 60.3607 0.160972
\(53\) −11.8127 −0.0306151 −0.0153076 0.999883i \(-0.504873\pi\)
−0.0153076 + 0.999883i \(0.504873\pi\)
\(54\) 54.0000 0.136083
\(55\) 1.76896 0.00433684
\(56\) −130.610 −0.311669
\(57\) 0 0
\(58\) 62.3018 0.141045
\(59\) 244.046 0.538511 0.269255 0.963069i \(-0.413222\pi\)
0.269255 + 0.963069i \(0.413222\pi\)
\(60\) −10.9180 −0.0234917
\(61\) 526.508 1.10512 0.552562 0.833472i \(-0.313650\pi\)
0.552562 + 0.833472i \(0.313650\pi\)
\(62\) −599.007 −1.22700
\(63\) −146.936 −0.293845
\(64\) 64.0000 0.125000
\(65\) −13.7295 −0.0261990
\(66\) −11.6656 −0.0217567
\(67\) −210.726 −0.384244 −0.192122 0.981371i \(-0.561537\pi\)
−0.192122 + 0.981371i \(0.561537\pi\)
\(68\) 128.053 0.228363
\(69\) −134.666 −0.234954
\(70\) 29.7082 0.0507259
\(71\) −503.418 −0.841476 −0.420738 0.907182i \(-0.638229\pi\)
−0.420738 + 0.907182i \(0.638229\pi\)
\(72\) 72.0000 0.117851
\(73\) 115.265 0.184806 0.0924028 0.995722i \(-0.470545\pi\)
0.0924028 + 0.995722i \(0.470545\pi\)
\(74\) −505.771 −0.794523
\(75\) −372.517 −0.573527
\(76\) 0 0
\(77\) 31.7426 0.0469794
\(78\) 90.5410 0.131433
\(79\) 220.492 0.314016 0.157008 0.987597i \(-0.449815\pi\)
0.157008 + 0.987597i \(0.449815\pi\)
\(80\) −14.5573 −0.0203444
\(81\) 81.0000 0.111111
\(82\) 163.295 0.219913
\(83\) 200.023 0.264523 0.132261 0.991215i \(-0.457776\pi\)
0.132261 + 0.991215i \(0.457776\pi\)
\(84\) −195.915 −0.254477
\(85\) −29.1265 −0.0371672
\(86\) −434.190 −0.544418
\(87\) 93.4528 0.115163
\(88\) −15.5542 −0.0188418
\(89\) −174.091 −0.207344 −0.103672 0.994612i \(-0.533059\pi\)
−0.103672 + 0.994612i \(0.533059\pi\)
\(90\) −16.3769 −0.0191809
\(91\) −246.366 −0.283804
\(92\) −179.554 −0.203476
\(93\) −898.510 −1.00184
\(94\) 375.485 0.412004
\(95\) 0 0
\(96\) 96.0000 0.102062
\(97\) −1105.40 −1.15708 −0.578538 0.815655i \(-0.696377\pi\)
−0.578538 + 0.815655i \(0.696377\pi\)
\(98\) −152.908 −0.157613
\(99\) −17.4984 −0.0177642
\(100\) −496.689 −0.496689
\(101\) −896.371 −0.883092 −0.441546 0.897239i \(-0.645570\pi\)
−0.441546 + 0.897239i \(0.645570\pi\)
\(102\) 192.079 0.186457
\(103\) 161.160 0.154170 0.0770852 0.997025i \(-0.475439\pi\)
0.0770852 + 0.997025i \(0.475439\pi\)
\(104\) 120.721 0.113824
\(105\) 44.5623 0.0414175
\(106\) −23.6254 −0.0216482
\(107\) −1121.56 −1.01333 −0.506663 0.862144i \(-0.669121\pi\)
−0.506663 + 0.862144i \(0.669121\pi\)
\(108\) 108.000 0.0962250
\(109\) 983.166 0.863947 0.431973 0.901886i \(-0.357817\pi\)
0.431973 + 0.901886i \(0.357817\pi\)
\(110\) 3.53791 0.00306661
\(111\) −758.656 −0.648725
\(112\) −261.220 −0.220383
\(113\) −500.349 −0.416539 −0.208270 0.978071i \(-0.566783\pi\)
−0.208270 + 0.978071i \(0.566783\pi\)
\(114\) 0 0
\(115\) 40.8409 0.0331169
\(116\) 124.604 0.0997342
\(117\) 135.812 0.107314
\(118\) 488.093 0.380785
\(119\) −522.654 −0.402619
\(120\) −21.8359 −0.0166111
\(121\) −1327.22 −0.997160
\(122\) 1053.02 0.781440
\(123\) 244.942 0.179559
\(124\) −1198.01 −0.867620
\(125\) 226.704 0.162216
\(126\) −293.872 −0.207780
\(127\) −865.459 −0.604701 −0.302351 0.953197i \(-0.597771\pi\)
−0.302351 + 0.953197i \(0.597771\pi\)
\(128\) 128.000 0.0883883
\(129\) −651.286 −0.444515
\(130\) −27.4590 −0.0185255
\(131\) −2344.79 −1.56386 −0.781930 0.623366i \(-0.785765\pi\)
−0.781930 + 0.623366i \(0.785765\pi\)
\(132\) −23.3313 −0.0153843
\(133\) 0 0
\(134\) −421.453 −0.271701
\(135\) −24.5654 −0.0156611
\(136\) 256.105 0.161477
\(137\) 2071.28 1.29169 0.645843 0.763470i \(-0.276506\pi\)
0.645843 + 0.763470i \(0.276506\pi\)
\(138\) −269.331 −0.166138
\(139\) −1467.54 −0.895507 −0.447753 0.894157i \(-0.647776\pi\)
−0.447753 + 0.894157i \(0.647776\pi\)
\(140\) 59.4164 0.0358686
\(141\) 563.228 0.336400
\(142\) −1006.84 −0.595013
\(143\) −29.3394 −0.0171572
\(144\) 144.000 0.0833333
\(145\) −28.3420 −0.0162323
\(146\) 230.531 0.130677
\(147\) −229.362 −0.128690
\(148\) −1011.54 −0.561812
\(149\) −176.948 −0.0972895 −0.0486447 0.998816i \(-0.515490\pi\)
−0.0486447 + 0.998816i \(0.515490\pi\)
\(150\) −745.033 −0.405545
\(151\) −1138.74 −0.613706 −0.306853 0.951757i \(-0.599276\pi\)
−0.306853 + 0.951757i \(0.599276\pi\)
\(152\) 0 0
\(153\) 288.118 0.152242
\(154\) 63.4853 0.0332194
\(155\) 272.497 0.141210
\(156\) 181.082 0.0929370
\(157\) −1952.19 −0.992366 −0.496183 0.868218i \(-0.665266\pi\)
−0.496183 + 0.868218i \(0.665266\pi\)
\(158\) 440.983 0.222043
\(159\) −35.4381 −0.0176756
\(160\) −29.1146 −0.0143857
\(161\) 732.861 0.358742
\(162\) 162.000 0.0785674
\(163\) 385.974 0.185471 0.0927357 0.995691i \(-0.470439\pi\)
0.0927357 + 0.995691i \(0.470439\pi\)
\(164\) 326.590 0.155502
\(165\) 5.30687 0.00250387
\(166\) 400.046 0.187046
\(167\) −3206.11 −1.48561 −0.742803 0.669510i \(-0.766504\pi\)
−0.742803 + 0.669510i \(0.766504\pi\)
\(168\) −391.830 −0.179942
\(169\) −1969.29 −0.896353
\(170\) −58.2531 −0.0262812
\(171\) 0 0
\(172\) −868.381 −0.384962
\(173\) −3194.72 −1.40399 −0.701993 0.712184i \(-0.747706\pi\)
−0.701993 + 0.712184i \(0.747706\pi\)
\(174\) 186.906 0.0814326
\(175\) 2027.27 0.875696
\(176\) −31.1084 −0.0133232
\(177\) 732.139 0.310909
\(178\) −348.183 −0.146615
\(179\) 2449.26 1.02272 0.511358 0.859368i \(-0.329142\pi\)
0.511358 + 0.859368i \(0.329142\pi\)
\(180\) −32.7539 −0.0135629
\(181\) −2002.67 −0.822415 −0.411207 0.911542i \(-0.634893\pi\)
−0.411207 + 0.911542i \(0.634893\pi\)
\(182\) −492.731 −0.200680
\(183\) 1579.53 0.638043
\(184\) −359.108 −0.143879
\(185\) 230.083 0.0914380
\(186\) −1797.02 −0.708408
\(187\) −62.2423 −0.0243401
\(188\) 750.971 0.291331
\(189\) −440.808 −0.169651
\(190\) 0 0
\(191\) 4101.97 1.55397 0.776984 0.629520i \(-0.216749\pi\)
0.776984 + 0.629520i \(0.216749\pi\)
\(192\) 192.000 0.0721688
\(193\) 1756.55 0.655126 0.327563 0.944829i \(-0.393773\pi\)
0.327563 + 0.944829i \(0.393773\pi\)
\(194\) −2210.80 −0.818176
\(195\) −41.1885 −0.0151260
\(196\) −305.816 −0.111449
\(197\) 3670.57 1.32750 0.663750 0.747955i \(-0.268964\pi\)
0.663750 + 0.747955i \(0.268964\pi\)
\(198\) −34.9969 −0.0125612
\(199\) −2610.75 −0.930007 −0.465004 0.885309i \(-0.653947\pi\)
−0.465004 + 0.885309i \(0.653947\pi\)
\(200\) −993.378 −0.351212
\(201\) −632.179 −0.221843
\(202\) −1792.74 −0.624440
\(203\) −508.577 −0.175838
\(204\) 384.158 0.131845
\(205\) −74.2853 −0.0253088
\(206\) 322.320 0.109015
\(207\) −403.997 −0.135651
\(208\) 241.443 0.0804858
\(209\) 0 0
\(210\) 89.1246 0.0292866
\(211\) −3473.35 −1.13325 −0.566624 0.823976i \(-0.691751\pi\)
−0.566624 + 0.823976i \(0.691751\pi\)
\(212\) −47.2509 −0.0153076
\(213\) −1510.25 −0.485826
\(214\) −2243.13 −0.716529
\(215\) 197.520 0.0626546
\(216\) 216.000 0.0680414
\(217\) 4889.76 1.52967
\(218\) 1966.33 0.610903
\(219\) 345.796 0.106698
\(220\) 7.07583 0.00216842
\(221\) 483.084 0.147040
\(222\) −1517.31 −0.458718
\(223\) 2530.49 0.759885 0.379942 0.925010i \(-0.375944\pi\)
0.379942 + 0.925010i \(0.375944\pi\)
\(224\) −522.440 −0.155835
\(225\) −1117.55 −0.331126
\(226\) −1000.70 −0.294538
\(227\) −6734.59 −1.96912 −0.984560 0.175046i \(-0.943993\pi\)
−0.984560 + 0.175046i \(0.943993\pi\)
\(228\) 0 0
\(229\) −337.719 −0.0974546 −0.0487273 0.998812i \(-0.515517\pi\)
−0.0487273 + 0.998812i \(0.515517\pi\)
\(230\) 81.6819 0.0234172
\(231\) 95.2279 0.0271235
\(232\) 249.207 0.0705227
\(233\) −6311.26 −1.77452 −0.887262 0.461265i \(-0.847396\pi\)
−0.887262 + 0.461265i \(0.847396\pi\)
\(234\) 271.623 0.0758827
\(235\) −170.814 −0.0474156
\(236\) 976.186 0.269255
\(237\) 661.475 0.181297
\(238\) −1045.31 −0.284695
\(239\) −3275.56 −0.886519 −0.443260 0.896393i \(-0.646178\pi\)
−0.443260 + 0.896393i \(0.646178\pi\)
\(240\) −43.6718 −0.0117459
\(241\) 1668.27 0.445904 0.222952 0.974829i \(-0.428431\pi\)
0.222952 + 0.974829i \(0.428431\pi\)
\(242\) −2654.44 −0.705099
\(243\) 243.000 0.0641500
\(244\) 2106.03 0.552562
\(245\) 69.5601 0.0181389
\(246\) 489.885 0.126967
\(247\) 0 0
\(248\) −2396.03 −0.613500
\(249\) 600.070 0.152722
\(250\) 453.409 0.114704
\(251\) −2044.39 −0.514106 −0.257053 0.966397i \(-0.582751\pi\)
−0.257053 + 0.966397i \(0.582751\pi\)
\(252\) −587.745 −0.146922
\(253\) 87.2755 0.0216876
\(254\) −1730.92 −0.427588
\(255\) −87.3796 −0.0214585
\(256\) 256.000 0.0625000
\(257\) 5181.31 1.25759 0.628797 0.777570i \(-0.283548\pi\)
0.628797 + 0.777570i \(0.283548\pi\)
\(258\) −1302.57 −0.314320
\(259\) 4128.67 0.990513
\(260\) −54.9180 −0.0130995
\(261\) 280.358 0.0664894
\(262\) −4689.59 −1.10582
\(263\) 7137.93 1.67355 0.836774 0.547548i \(-0.184439\pi\)
0.836774 + 0.547548i \(0.184439\pi\)
\(264\) −46.6625 −0.0108783
\(265\) 10.7476 0.00249139
\(266\) 0 0
\(267\) −522.274 −0.119710
\(268\) −842.906 −0.192122
\(269\) 6395.52 1.44960 0.724798 0.688961i \(-0.241933\pi\)
0.724798 + 0.688961i \(0.241933\pi\)
\(270\) −49.1308 −0.0110741
\(271\) −6478.86 −1.45226 −0.726131 0.687556i \(-0.758683\pi\)
−0.726131 + 0.687556i \(0.758683\pi\)
\(272\) 512.210 0.114181
\(273\) −739.097 −0.163854
\(274\) 4142.55 0.913360
\(275\) 241.425 0.0529398
\(276\) −538.663 −0.117477
\(277\) 3501.93 0.759606 0.379803 0.925067i \(-0.375992\pi\)
0.379803 + 0.925067i \(0.375992\pi\)
\(278\) −2935.09 −0.633219
\(279\) −2695.53 −0.578413
\(280\) 118.833 0.0253629
\(281\) 1722.75 0.365731 0.182865 0.983138i \(-0.441463\pi\)
0.182865 + 0.983138i \(0.441463\pi\)
\(282\) 1126.46 0.237870
\(283\) −905.945 −0.190293 −0.0951464 0.995463i \(-0.530332\pi\)
−0.0951464 + 0.995463i \(0.530332\pi\)
\(284\) −2013.67 −0.420738
\(285\) 0 0
\(286\) −58.6788 −0.0121320
\(287\) −1333.00 −0.274161
\(288\) 288.000 0.0589256
\(289\) −3888.16 −0.791402
\(290\) −56.6841 −0.0114779
\(291\) −3316.20 −0.668038
\(292\) 461.062 0.0924028
\(293\) 6570.56 1.31009 0.655045 0.755590i \(-0.272650\pi\)
0.655045 + 0.755590i \(0.272650\pi\)
\(294\) −458.724 −0.0909977
\(295\) −222.041 −0.0438228
\(296\) −2023.08 −0.397261
\(297\) −52.4953 −0.0102562
\(298\) −353.896 −0.0687940
\(299\) −677.376 −0.131016
\(300\) −1490.07 −0.286763
\(301\) 3544.35 0.678714
\(302\) −2277.49 −0.433956
\(303\) −2689.11 −0.509853
\(304\) 0 0
\(305\) −479.033 −0.0899323
\(306\) 576.237 0.107651
\(307\) 566.581 0.105331 0.0526653 0.998612i \(-0.483228\pi\)
0.0526653 + 0.998612i \(0.483228\pi\)
\(308\) 126.971 0.0234897
\(309\) 483.479 0.0890103
\(310\) 544.995 0.0998504
\(311\) 3507.55 0.639534 0.319767 0.947496i \(-0.396395\pi\)
0.319767 + 0.947496i \(0.396395\pi\)
\(312\) 362.164 0.0657164
\(313\) −321.768 −0.0581067 −0.0290534 0.999578i \(-0.509249\pi\)
−0.0290534 + 0.999578i \(0.509249\pi\)
\(314\) −3904.37 −0.701709
\(315\) 133.687 0.0239124
\(316\) 881.966 0.157008
\(317\) −3797.03 −0.672752 −0.336376 0.941728i \(-0.609201\pi\)
−0.336376 + 0.941728i \(0.609201\pi\)
\(318\) −70.8763 −0.0124986
\(319\) −60.5659 −0.0106302
\(320\) −58.2291 −0.0101722
\(321\) −3364.69 −0.585043
\(322\) 1465.72 0.253669
\(323\) 0 0
\(324\) 324.000 0.0555556
\(325\) −1873.78 −0.319811
\(326\) 771.948 0.131148
\(327\) 2949.50 0.498800
\(328\) 653.180 0.109957
\(329\) −3065.13 −0.513636
\(330\) 10.6137 0.00177051
\(331\) 9588.45 1.59223 0.796116 0.605144i \(-0.206885\pi\)
0.796116 + 0.605144i \(0.206885\pi\)
\(332\) 800.093 0.132261
\(333\) −2275.97 −0.374542
\(334\) −6412.22 −1.05048
\(335\) 191.725 0.0312689
\(336\) −783.659 −0.127238
\(337\) 9263.59 1.49739 0.748694 0.662916i \(-0.230681\pi\)
0.748694 + 0.662916i \(0.230681\pi\)
\(338\) −3938.57 −0.633817
\(339\) −1501.05 −0.240489
\(340\) −116.506 −0.0185836
\(341\) 582.316 0.0924756
\(342\) 0 0
\(343\) 6848.11 1.07803
\(344\) −1736.76 −0.272209
\(345\) 122.523 0.0191200
\(346\) −6389.43 −0.992768
\(347\) −3603.50 −0.557481 −0.278740 0.960367i \(-0.589917\pi\)
−0.278740 + 0.960367i \(0.589917\pi\)
\(348\) 373.811 0.0575815
\(349\) 3751.60 0.575411 0.287706 0.957719i \(-0.407108\pi\)
0.287706 + 0.957719i \(0.407108\pi\)
\(350\) 4054.53 0.619211
\(351\) 407.435 0.0619580
\(352\) −62.2167 −0.00942091
\(353\) −8836.39 −1.33233 −0.666166 0.745803i \(-0.732066\pi\)
−0.666166 + 0.745803i \(0.732066\pi\)
\(354\) 1464.28 0.219846
\(355\) 458.025 0.0684773
\(356\) −696.365 −0.103672
\(357\) −1567.96 −0.232452
\(358\) 4898.52 0.723170
\(359\) 7348.14 1.08028 0.540139 0.841576i \(-0.318371\pi\)
0.540139 + 0.841576i \(0.318371\pi\)
\(360\) −65.5078 −0.00959045
\(361\) 0 0
\(362\) −4005.33 −0.581535
\(363\) −3981.66 −0.575711
\(364\) −985.463 −0.141902
\(365\) −104.872 −0.0150390
\(366\) 3159.05 0.451165
\(367\) −10829.4 −1.54030 −0.770150 0.637862i \(-0.779819\pi\)
−0.770150 + 0.637862i \(0.779819\pi\)
\(368\) −718.217 −0.101738
\(369\) 734.827 0.103668
\(370\) 460.166 0.0646564
\(371\) 192.857 0.0269883
\(372\) −3594.04 −0.500920
\(373\) 10614.6 1.47347 0.736734 0.676183i \(-0.236367\pi\)
0.736734 + 0.676183i \(0.236367\pi\)
\(374\) −124.485 −0.0172111
\(375\) 680.113 0.0936557
\(376\) 1501.94 0.206002
\(377\) 470.073 0.0642174
\(378\) −881.617 −0.119962
\(379\) 3538.17 0.479535 0.239767 0.970830i \(-0.422929\pi\)
0.239767 + 0.970830i \(0.422929\pi\)
\(380\) 0 0
\(381\) −2596.38 −0.349124
\(382\) 8203.93 1.09882
\(383\) 13138.1 1.75280 0.876402 0.481581i \(-0.159937\pi\)
0.876402 + 0.481581i \(0.159937\pi\)
\(384\) 384.000 0.0510310
\(385\) −28.8804 −0.00382307
\(386\) 3513.10 0.463244
\(387\) −1953.86 −0.256641
\(388\) −4421.60 −0.578538
\(389\) 1058.46 0.137958 0.0689792 0.997618i \(-0.478026\pi\)
0.0689792 + 0.997618i \(0.478026\pi\)
\(390\) −82.3769 −0.0106957
\(391\) −1437.02 −0.185866
\(392\) −611.632 −0.0788063
\(393\) −7034.38 −0.902895
\(394\) 7341.14 0.938684
\(395\) −200.610 −0.0255539
\(396\) −69.9938 −0.00888212
\(397\) −15180.8 −1.91915 −0.959573 0.281461i \(-0.909181\pi\)
−0.959573 + 0.281461i \(0.909181\pi\)
\(398\) −5221.51 −0.657615
\(399\) 0 0
\(400\) −1986.76 −0.248344
\(401\) −1336.20 −0.166400 −0.0832002 0.996533i \(-0.526514\pi\)
−0.0832002 + 0.996533i \(0.526514\pi\)
\(402\) −1264.36 −0.156867
\(403\) −4519.56 −0.558648
\(404\) −3585.49 −0.441546
\(405\) −73.6962 −0.00904196
\(406\) −1017.15 −0.124336
\(407\) 491.678 0.0598810
\(408\) 768.316 0.0932287
\(409\) −1976.03 −0.238896 −0.119448 0.992840i \(-0.538112\pi\)
−0.119448 + 0.992840i \(0.538112\pi\)
\(410\) −148.571 −0.0178960
\(411\) 6213.83 0.745755
\(412\) 644.639 0.0770852
\(413\) −3984.36 −0.474716
\(414\) −807.994 −0.0959196
\(415\) −181.987 −0.0215263
\(416\) 482.885 0.0569120
\(417\) −4402.63 −0.517021
\(418\) 0 0
\(419\) 3242.90 0.378105 0.189052 0.981967i \(-0.439458\pi\)
0.189052 + 0.981967i \(0.439458\pi\)
\(420\) 178.249 0.0207087
\(421\) 11959.4 1.38448 0.692241 0.721667i \(-0.256624\pi\)
0.692241 + 0.721667i \(0.256624\pi\)
\(422\) −6946.71 −0.801328
\(423\) 1689.68 0.194220
\(424\) −94.5017 −0.0108241
\(425\) −3975.14 −0.453701
\(426\) −3020.51 −0.343531
\(427\) −8595.90 −0.974204
\(428\) −4486.26 −0.506663
\(429\) −88.0182 −0.00990573
\(430\) 395.039 0.0443035
\(431\) −7226.13 −0.807589 −0.403794 0.914850i \(-0.632309\pi\)
−0.403794 + 0.914850i \(0.632309\pi\)
\(432\) 432.000 0.0481125
\(433\) 9903.01 1.09909 0.549547 0.835462i \(-0.314800\pi\)
0.549547 + 0.835462i \(0.314800\pi\)
\(434\) 9779.53 1.08164
\(435\) −85.0261 −0.00937170
\(436\) 3932.66 0.431973
\(437\) 0 0
\(438\) 691.593 0.0754465
\(439\) 7077.97 0.769506 0.384753 0.923020i \(-0.374287\pi\)
0.384753 + 0.923020i \(0.374287\pi\)
\(440\) 14.1517 0.00153330
\(441\) −688.086 −0.0742993
\(442\) 966.168 0.103973
\(443\) −7730.58 −0.829099 −0.414550 0.910027i \(-0.636061\pi\)
−0.414550 + 0.910027i \(0.636061\pi\)
\(444\) −3034.63 −0.324362
\(445\) 158.394 0.0168732
\(446\) 5060.98 0.537320
\(447\) −530.843 −0.0561701
\(448\) −1044.88 −0.110192
\(449\) 2353.41 0.247359 0.123679 0.992322i \(-0.460531\pi\)
0.123679 + 0.992322i \(0.460531\pi\)
\(450\) −2235.10 −0.234141
\(451\) −158.745 −0.0165743
\(452\) −2001.40 −0.208270
\(453\) −3416.23 −0.354323
\(454\) −13469.2 −1.39238
\(455\) 224.151 0.0230953
\(456\) 0 0
\(457\) 8420.95 0.861959 0.430980 0.902362i \(-0.358168\pi\)
0.430980 + 0.902362i \(0.358168\pi\)
\(458\) −675.438 −0.0689108
\(459\) 864.355 0.0878968
\(460\) 163.364 0.0165584
\(461\) −669.622 −0.0676517 −0.0338258 0.999428i \(-0.510769\pi\)
−0.0338258 + 0.999428i \(0.510769\pi\)
\(462\) 190.456 0.0191792
\(463\) 5570.89 0.559182 0.279591 0.960119i \(-0.409801\pi\)
0.279591 + 0.960119i \(0.409801\pi\)
\(464\) 498.415 0.0498671
\(465\) 817.492 0.0815275
\(466\) −12622.5 −1.25478
\(467\) −10869.8 −1.07707 −0.538537 0.842602i \(-0.681023\pi\)
−0.538537 + 0.842602i \(0.681023\pi\)
\(468\) 543.246 0.0536572
\(469\) 3440.37 0.338724
\(470\) −341.628 −0.0335279
\(471\) −5856.56 −0.572943
\(472\) 1952.37 0.190392
\(473\) 422.092 0.0410313
\(474\) 1322.95 0.128196
\(475\) 0 0
\(476\) −2090.62 −0.201309
\(477\) −106.314 −0.0102050
\(478\) −6551.11 −0.626864
\(479\) −2435.33 −0.232303 −0.116151 0.993232i \(-0.537056\pi\)
−0.116151 + 0.993232i \(0.537056\pi\)
\(480\) −87.3437 −0.00830557
\(481\) −3816.08 −0.361743
\(482\) 3336.55 0.315302
\(483\) 2198.58 0.207120
\(484\) −5308.88 −0.498580
\(485\) 1005.73 0.0941602
\(486\) 486.000 0.0453609
\(487\) 10685.2 0.994233 0.497116 0.867684i \(-0.334392\pi\)
0.497116 + 0.867684i \(0.334392\pi\)
\(488\) 4212.07 0.390720
\(489\) 1157.92 0.107082
\(490\) 139.120 0.0128261
\(491\) −9068.91 −0.833552 −0.416776 0.909009i \(-0.636840\pi\)
−0.416776 + 0.909009i \(0.636840\pi\)
\(492\) 979.769 0.0897793
\(493\) 997.239 0.0911022
\(494\) 0 0
\(495\) 15.9206 0.00144561
\(496\) −4792.06 −0.433810
\(497\) 8218.93 0.741789
\(498\) 1200.14 0.107991
\(499\) −9085.54 −0.815080 −0.407540 0.913187i \(-0.633613\pi\)
−0.407540 + 0.913187i \(0.633613\pi\)
\(500\) 906.817 0.0811082
\(501\) −9618.33 −0.857716
\(502\) −4088.77 −0.363528
\(503\) −229.914 −0.0203804 −0.0101902 0.999948i \(-0.503244\pi\)
−0.0101902 + 0.999948i \(0.503244\pi\)
\(504\) −1175.49 −0.103890
\(505\) 815.546 0.0718640
\(506\) 174.551 0.0153355
\(507\) −5907.86 −0.517509
\(508\) −3461.84 −0.302351
\(509\) 9812.78 0.854507 0.427253 0.904132i \(-0.359481\pi\)
0.427253 + 0.904132i \(0.359481\pi\)
\(510\) −174.759 −0.0151735
\(511\) −1881.85 −0.162912
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 10362.6 0.889253
\(515\) −146.628 −0.0125460
\(516\) −2605.14 −0.222258
\(517\) −365.023 −0.0310516
\(518\) 8257.34 0.700399
\(519\) −9584.15 −0.810592
\(520\) −109.836 −0.00926274
\(521\) 8772.27 0.737658 0.368829 0.929497i \(-0.379759\pi\)
0.368829 + 0.929497i \(0.379759\pi\)
\(522\) 560.717 0.0470151
\(523\) −4563.38 −0.381535 −0.190767 0.981635i \(-0.561098\pi\)
−0.190767 + 0.981635i \(0.561098\pi\)
\(524\) −9379.18 −0.781930
\(525\) 6081.80 0.505583
\(526\) 14275.9 1.18338
\(527\) −9588.05 −0.792528
\(528\) −93.3251 −0.00769214
\(529\) −10152.0 −0.834390
\(530\) 21.4951 0.00176168
\(531\) 2196.42 0.179504
\(532\) 0 0
\(533\) 1232.07 0.100126
\(534\) −1044.55 −0.0846480
\(535\) 1020.43 0.0824620
\(536\) −1685.81 −0.135851
\(537\) 7347.78 0.590466
\(538\) 12791.0 1.02502
\(539\) 148.647 0.0118788
\(540\) −98.2616 −0.00783057
\(541\) −5541.69 −0.440399 −0.220200 0.975455i \(-0.570671\pi\)
−0.220200 + 0.975455i \(0.570671\pi\)
\(542\) −12957.7 −1.02690
\(543\) −6008.00 −0.474821
\(544\) 1024.42 0.0807384
\(545\) −894.514 −0.0703060
\(546\) −1478.19 −0.115862
\(547\) 482.902 0.0377466 0.0188733 0.999822i \(-0.493992\pi\)
0.0188733 + 0.999822i \(0.493992\pi\)
\(548\) 8285.10 0.645843
\(549\) 4738.58 0.368374
\(550\) 482.849 0.0374341
\(551\) 0 0
\(552\) −1077.33 −0.0830688
\(553\) −3599.80 −0.276815
\(554\) 7003.87 0.537123
\(555\) 690.248 0.0527917
\(556\) −5870.18 −0.447753
\(557\) −9850.15 −0.749308 −0.374654 0.927165i \(-0.622238\pi\)
−0.374654 + 0.927165i \(0.622238\pi\)
\(558\) −5391.06 −0.409000
\(559\) −3276.00 −0.247872
\(560\) 237.666 0.0179343
\(561\) −186.727 −0.0140528
\(562\) 3445.49 0.258611
\(563\) −15083.7 −1.12913 −0.564567 0.825387i \(-0.690957\pi\)
−0.564567 + 0.825387i \(0.690957\pi\)
\(564\) 2252.91 0.168200
\(565\) 455.233 0.0338970
\(566\) −1811.89 −0.134557
\(567\) −1322.43 −0.0979482
\(568\) −4027.35 −0.297507
\(569\) 354.846 0.0261439 0.0130720 0.999915i \(-0.495839\pi\)
0.0130720 + 0.999915i \(0.495839\pi\)
\(570\) 0 0
\(571\) 10394.6 0.761821 0.380910 0.924612i \(-0.375611\pi\)
0.380910 + 0.924612i \(0.375611\pi\)
\(572\) −117.358 −0.00857861
\(573\) 12305.9 0.897184
\(574\) −2665.99 −0.193861
\(575\) 5573.91 0.404258
\(576\) 576.000 0.0416667
\(577\) 1289.40 0.0930303 0.0465151 0.998918i \(-0.485188\pi\)
0.0465151 + 0.998918i \(0.485188\pi\)
\(578\) −7776.32 −0.559606
\(579\) 5269.65 0.378237
\(580\) −113.368 −0.00811613
\(581\) −3265.63 −0.233186
\(582\) −6632.40 −0.472374
\(583\) 22.9671 0.00163156
\(584\) 922.124 0.0653386
\(585\) −123.565 −0.00873299
\(586\) 13141.1 0.926373
\(587\) 19612.9 1.37906 0.689531 0.724256i \(-0.257817\pi\)
0.689531 + 0.724256i \(0.257817\pi\)
\(588\) −917.447 −0.0643451
\(589\) 0 0
\(590\) −444.082 −0.0309874
\(591\) 11011.7 0.766432
\(592\) −4046.17 −0.280906
\(593\) 7358.41 0.509568 0.254784 0.966998i \(-0.417996\pi\)
0.254784 + 0.966998i \(0.417996\pi\)
\(594\) −104.991 −0.00725222
\(595\) 475.527 0.0327642
\(596\) −707.791 −0.0486447
\(597\) −7832.26 −0.536940
\(598\) −1354.75 −0.0926420
\(599\) 16712.6 1.13999 0.569997 0.821647i \(-0.306944\pi\)
0.569997 + 0.821647i \(0.306944\pi\)
\(600\) −2980.13 −0.202772
\(601\) 8181.83 0.555314 0.277657 0.960680i \(-0.410442\pi\)
0.277657 + 0.960680i \(0.410442\pi\)
\(602\) 7088.70 0.479923
\(603\) −1896.54 −0.128081
\(604\) −4554.97 −0.306853
\(605\) 1207.54 0.0811466
\(606\) −5378.23 −0.360521
\(607\) 19171.1 1.28193 0.640966 0.767569i \(-0.278534\pi\)
0.640966 + 0.767569i \(0.278534\pi\)
\(608\) 0 0
\(609\) −1525.73 −0.101520
\(610\) −958.067 −0.0635918
\(611\) 2833.07 0.187584
\(612\) 1152.47 0.0761209
\(613\) −23387.4 −1.54096 −0.770481 0.637463i \(-0.779984\pi\)
−0.770481 + 0.637463i \(0.779984\pi\)
\(614\) 1133.16 0.0744800
\(615\) −222.856 −0.0146121
\(616\) 253.941 0.0166097
\(617\) 29646.2 1.93438 0.967189 0.254056i \(-0.0817649\pi\)
0.967189 + 0.254056i \(0.0817649\pi\)
\(618\) 966.959 0.0629398
\(619\) 17042.8 1.10663 0.553317 0.832971i \(-0.313362\pi\)
0.553317 + 0.832971i \(0.313362\pi\)
\(620\) 1089.99 0.0706049
\(621\) −1211.99 −0.0783181
\(622\) 7015.11 0.452219
\(623\) 2842.26 0.182781
\(624\) 724.328 0.0464685
\(625\) 15315.3 0.980177
\(626\) −643.536 −0.0410876
\(627\) 0 0
\(628\) −7808.75 −0.496183
\(629\) −8095.66 −0.513188
\(630\) 267.374 0.0169086
\(631\) −12936.7 −0.816170 −0.408085 0.912944i \(-0.633803\pi\)
−0.408085 + 0.912944i \(0.633803\pi\)
\(632\) 1763.93 0.111021
\(633\) −10420.1 −0.654282
\(634\) −7594.05 −0.475707
\(635\) 787.421 0.0492092
\(636\) −141.753 −0.00883782
\(637\) −1153.70 −0.0717604
\(638\) −121.132 −0.00751669
\(639\) −4530.76 −0.280492
\(640\) −116.458 −0.00719284
\(641\) −30925.1 −1.90557 −0.952783 0.303650i \(-0.901794\pi\)
−0.952783 + 0.303650i \(0.901794\pi\)
\(642\) −6729.39 −0.413688
\(643\) −2848.23 −0.174686 −0.0873430 0.996178i \(-0.527838\pi\)
−0.0873430 + 0.996178i \(0.527838\pi\)
\(644\) 2931.44 0.179371
\(645\) 592.559 0.0361736
\(646\) 0 0
\(647\) 14856.5 0.902733 0.451367 0.892339i \(-0.350937\pi\)
0.451367 + 0.892339i \(0.350937\pi\)
\(648\) 648.000 0.0392837
\(649\) −474.493 −0.0286987
\(650\) −3747.56 −0.226141
\(651\) 14669.3 0.883157
\(652\) 1543.90 0.0927357
\(653\) −697.326 −0.0417894 −0.0208947 0.999782i \(-0.506651\pi\)
−0.0208947 + 0.999782i \(0.506651\pi\)
\(654\) 5898.99 0.352705
\(655\) 2133.36 0.127263
\(656\) 1306.36 0.0777512
\(657\) 1037.39 0.0616018
\(658\) −6130.26 −0.363195
\(659\) −2792.41 −0.165064 −0.0825319 0.996588i \(-0.526301\pi\)
−0.0825319 + 0.996588i \(0.526301\pi\)
\(660\) 21.2275 0.00125194
\(661\) 28297.2 1.66510 0.832551 0.553949i \(-0.186880\pi\)
0.832551 + 0.553949i \(0.186880\pi\)
\(662\) 19176.9 1.12588
\(663\) 1449.25 0.0848933
\(664\) 1600.19 0.0935230
\(665\) 0 0
\(666\) −4551.94 −0.264841
\(667\) −1398.32 −0.0811741
\(668\) −12824.4 −0.742803
\(669\) 7591.48 0.438720
\(670\) 383.450 0.0221104
\(671\) −1023.68 −0.0588950
\(672\) −1567.32 −0.0899712
\(673\) −19162.8 −1.09758 −0.548790 0.835960i \(-0.684911\pi\)
−0.548790 + 0.835960i \(0.684911\pi\)
\(674\) 18527.2 1.05881
\(675\) −3352.65 −0.191176
\(676\) −7877.15 −0.448176
\(677\) −14029.7 −0.796463 −0.398232 0.917285i \(-0.630376\pi\)
−0.398232 + 0.917285i \(0.630376\pi\)
\(678\) −3002.10 −0.170051
\(679\) 18047.0 1.02000
\(680\) −233.012 −0.0131406
\(681\) −20203.8 −1.13687
\(682\) 1164.63 0.0653901
\(683\) −6578.33 −0.368540 −0.184270 0.982876i \(-0.558992\pi\)
−0.184270 + 0.982876i \(0.558992\pi\)
\(684\) 0 0
\(685\) −1884.51 −0.105114
\(686\) 13696.2 0.762279
\(687\) −1013.16 −0.0562654
\(688\) −3473.52 −0.192481
\(689\) −178.256 −0.00985633
\(690\) 245.046 0.0135199
\(691\) 28001.9 1.54159 0.770797 0.637080i \(-0.219858\pi\)
0.770797 + 0.637080i \(0.219858\pi\)
\(692\) −12778.9 −0.701993
\(693\) 285.684 0.0156598
\(694\) −7206.99 −0.394198
\(695\) 1335.22 0.0728743
\(696\) 747.622 0.0407163
\(697\) 2613.79 0.142044
\(698\) 7503.20 0.406877
\(699\) −18933.8 −1.02452
\(700\) 8109.06 0.437848
\(701\) 1649.54 0.0888762 0.0444381 0.999012i \(-0.485850\pi\)
0.0444381 + 0.999012i \(0.485850\pi\)
\(702\) 814.869 0.0438109
\(703\) 0 0
\(704\) −124.433 −0.00666159
\(705\) −512.442 −0.0273754
\(706\) −17672.8 −0.942102
\(707\) 14634.4 0.778476
\(708\) 2928.56 0.155455
\(709\) 12138.8 0.642993 0.321496 0.946911i \(-0.395814\pi\)
0.321496 + 0.946911i \(0.395814\pi\)
\(710\) 916.050 0.0484208
\(711\) 1984.42 0.104672
\(712\) −1392.73 −0.0733073
\(713\) 13444.3 0.706160
\(714\) −3135.93 −0.164368
\(715\) 26.6939 0.00139622
\(716\) 9797.04 0.511358
\(717\) −9826.67 −0.511832
\(718\) 14696.3 0.763872
\(719\) −17081.4 −0.885994 −0.442997 0.896523i \(-0.646085\pi\)
−0.442997 + 0.896523i \(0.646085\pi\)
\(720\) −131.016 −0.00678147
\(721\) −2631.13 −0.135906
\(722\) 0 0
\(723\) 5004.82 0.257443
\(724\) −8010.67 −0.411207
\(725\) −3868.08 −0.198147
\(726\) −7963.32 −0.407089
\(727\) −8523.48 −0.434826 −0.217413 0.976080i \(-0.569762\pi\)
−0.217413 + 0.976080i \(0.569762\pi\)
\(728\) −1970.93 −0.100340
\(729\) 729.000 0.0370370
\(730\) −209.744 −0.0106342
\(731\) −6949.90 −0.351644
\(732\) 6318.10 0.319022
\(733\) 19655.2 0.990425 0.495212 0.868772i \(-0.335090\pi\)
0.495212 + 0.868772i \(0.335090\pi\)
\(734\) −21658.8 −1.08916
\(735\) 208.680 0.0104725
\(736\) −1436.43 −0.0719397
\(737\) 409.709 0.0204774
\(738\) 1469.65 0.0733045
\(739\) −844.721 −0.0420481 −0.0210241 0.999779i \(-0.506693\pi\)
−0.0210241 + 0.999779i \(0.506693\pi\)
\(740\) 920.331 0.0457190
\(741\) 0 0
\(742\) 385.714 0.0190836
\(743\) −23692.3 −1.16983 −0.584916 0.811094i \(-0.698873\pi\)
−0.584916 + 0.811094i \(0.698873\pi\)
\(744\) −7188.08 −0.354204
\(745\) 160.992 0.00791719
\(746\) 21229.2 1.04190
\(747\) 1800.21 0.0881743
\(748\) −248.969 −0.0121701
\(749\) 18310.9 0.893280
\(750\) 1360.23 0.0662246
\(751\) −8581.33 −0.416960 −0.208480 0.978027i \(-0.566852\pi\)
−0.208480 + 0.978027i \(0.566852\pi\)
\(752\) 3003.88 0.145665
\(753\) −6133.16 −0.296819
\(754\) 940.145 0.0454086
\(755\) 1036.06 0.0499420
\(756\) −1763.23 −0.0848256
\(757\) −19326.7 −0.927926 −0.463963 0.885855i \(-0.653573\pi\)
−0.463963 + 0.885855i \(0.653573\pi\)
\(758\) 7076.34 0.339082
\(759\) 261.827 0.0125213
\(760\) 0 0
\(761\) −26601.6 −1.26716 −0.633580 0.773677i \(-0.718415\pi\)
−0.633580 + 0.773677i \(0.718415\pi\)
\(762\) −5192.75 −0.246868
\(763\) −16051.4 −0.761598
\(764\) 16407.9 0.776984
\(765\) −262.139 −0.0123891
\(766\) 26276.1 1.23942
\(767\) 3682.70 0.173370
\(768\) 768.000 0.0360844
\(769\) −24235.8 −1.13650 −0.568248 0.822857i \(-0.692379\pi\)
−0.568248 + 0.822857i \(0.692379\pi\)
\(770\) −57.7608 −0.00270332
\(771\) 15543.9 0.726072
\(772\) 7026.20 0.327563
\(773\) −11054.8 −0.514377 −0.257188 0.966361i \(-0.582796\pi\)
−0.257188 + 0.966361i \(0.582796\pi\)
\(774\) −3907.71 −0.181473
\(775\) 37190.0 1.72375
\(776\) −8843.20 −0.409088
\(777\) 12386.0 0.571873
\(778\) 2116.91 0.0975514
\(779\) 0 0
\(780\) −164.754 −0.00756299
\(781\) 978.782 0.0448445
\(782\) −2874.05 −0.131427
\(783\) 841.075 0.0383877
\(784\) −1223.26 −0.0557245
\(785\) 1776.16 0.0807565
\(786\) −14068.8 −0.638443
\(787\) −34632.5 −1.56863 −0.784316 0.620361i \(-0.786986\pi\)
−0.784316 + 0.620361i \(0.786986\pi\)
\(788\) 14682.3 0.663750
\(789\) 21413.8 0.966224
\(790\) −401.220 −0.0180693
\(791\) 8168.82 0.367193
\(792\) −139.988 −0.00628061
\(793\) 7945.10 0.355787
\(794\) −30361.5 −1.35704
\(795\) 32.2427 0.00143840
\(796\) −10443.0 −0.465004
\(797\) 21904.6 0.973526 0.486763 0.873534i \(-0.338178\pi\)
0.486763 + 0.873534i \(0.338178\pi\)
\(798\) 0 0
\(799\) 6010.23 0.266116
\(800\) −3973.51 −0.175606
\(801\) −1566.82 −0.0691148
\(802\) −2672.40 −0.117663
\(803\) −224.107 −0.00984879
\(804\) −2528.72 −0.110922
\(805\) −666.779 −0.0291936
\(806\) −9039.12 −0.395024
\(807\) 19186.6 0.836925
\(808\) −7170.97 −0.312220
\(809\) 33327.8 1.44838 0.724192 0.689598i \(-0.242213\pi\)
0.724192 + 0.689598i \(0.242213\pi\)
\(810\) −147.392 −0.00639363
\(811\) 1389.76 0.0601738 0.0300869 0.999547i \(-0.490422\pi\)
0.0300869 + 0.999547i \(0.490422\pi\)
\(812\) −2034.31 −0.0879191
\(813\) −19436.6 −0.838464
\(814\) 983.356 0.0423423
\(815\) −351.171 −0.0150932
\(816\) 1536.63 0.0659226
\(817\) 0 0
\(818\) −3952.06 −0.168925
\(819\) −2217.29 −0.0946013
\(820\) −297.141 −0.0126544
\(821\) −11572.6 −0.491943 −0.245972 0.969277i \(-0.579107\pi\)
−0.245972 + 0.969277i \(0.579107\pi\)
\(822\) 12427.7 0.527329
\(823\) 26073.3 1.10432 0.552162 0.833737i \(-0.313803\pi\)
0.552162 + 0.833737i \(0.313803\pi\)
\(824\) 1289.28 0.0545074
\(825\) 724.274 0.0305648
\(826\) −7968.72 −0.335675
\(827\) 44795.6 1.88355 0.941775 0.336245i \(-0.109157\pi\)
0.941775 + 0.336245i \(0.109157\pi\)
\(828\) −1615.99 −0.0678254
\(829\) 12346.2 0.517250 0.258625 0.965978i \(-0.416731\pi\)
0.258625 + 0.965978i \(0.416731\pi\)
\(830\) −363.974 −0.0152214
\(831\) 10505.8 0.438559
\(832\) 965.771 0.0402429
\(833\) −2447.53 −0.101803
\(834\) −8805.26 −0.365589
\(835\) 2917.02 0.120895
\(836\) 0 0
\(837\) −8086.59 −0.333947
\(838\) 6485.79 0.267360
\(839\) −7050.38 −0.290115 −0.145057 0.989423i \(-0.546337\pi\)
−0.145057 + 0.989423i \(0.546337\pi\)
\(840\) 356.498 0.0146433
\(841\) −23418.6 −0.960212
\(842\) 23918.8 0.978976
\(843\) 5168.24 0.211155
\(844\) −13893.4 −0.566624
\(845\) 1791.72 0.0729431
\(846\) 3379.37 0.137335
\(847\) 21668.5 0.879030
\(848\) −189.003 −0.00765378
\(849\) −2717.84 −0.109866
\(850\) −7950.29 −0.320815
\(851\) 11351.7 0.457262
\(852\) −6041.02 −0.242913
\(853\) 6590.63 0.264547 0.132274 0.991213i \(-0.457772\pi\)
0.132274 + 0.991213i \(0.457772\pi\)
\(854\) −17191.8 −0.688866
\(855\) 0 0
\(856\) −8972.52 −0.358264
\(857\) 41470.4 1.65298 0.826489 0.562954i \(-0.190335\pi\)
0.826489 + 0.562954i \(0.190335\pi\)
\(858\) −176.036 −0.00700441
\(859\) 33928.2 1.34763 0.673816 0.738899i \(-0.264654\pi\)
0.673816 + 0.738899i \(0.264654\pi\)
\(860\) 790.079 0.0313273
\(861\) −3998.99 −0.158287
\(862\) −14452.3 −0.571051
\(863\) −6042.42 −0.238339 −0.119169 0.992874i \(-0.538023\pi\)
−0.119169 + 0.992874i \(0.538023\pi\)
\(864\) 864.000 0.0340207
\(865\) 2906.65 0.114253
\(866\) 19806.0 0.777177
\(867\) −11664.5 −0.456916
\(868\) 19559.1 0.764836
\(869\) −428.695 −0.0167347
\(870\) −170.052 −0.00662680
\(871\) −3179.90 −0.123705
\(872\) 7865.32 0.305451
\(873\) −9948.60 −0.385692
\(874\) 0 0
\(875\) −3701.23 −0.142999
\(876\) 1383.19 0.0533488
\(877\) −23546.2 −0.906611 −0.453306 0.891355i \(-0.649755\pi\)
−0.453306 + 0.891355i \(0.649755\pi\)
\(878\) 14155.9 0.544123
\(879\) 19711.7 0.756381
\(880\) 28.3033 0.00108421
\(881\) −39700.3 −1.51820 −0.759101 0.650973i \(-0.774361\pi\)
−0.759101 + 0.650973i \(0.774361\pi\)
\(882\) −1376.17 −0.0525375
\(883\) −41792.3 −1.59278 −0.796389 0.604785i \(-0.793259\pi\)
−0.796389 + 0.604785i \(0.793259\pi\)
\(884\) 1932.34 0.0735198
\(885\) −666.122 −0.0253011
\(886\) −15461.2 −0.586262
\(887\) −3207.98 −0.121435 −0.0607177 0.998155i \(-0.519339\pi\)
−0.0607177 + 0.998155i \(0.519339\pi\)
\(888\) −6069.25 −0.229359
\(889\) 14129.7 0.533065
\(890\) 316.787 0.0119312
\(891\) −157.486 −0.00592141
\(892\) 10122.0 0.379942
\(893\) 0 0
\(894\) −1061.69 −0.0397183
\(895\) −2228.41 −0.0832263
\(896\) −2089.76 −0.0779173
\(897\) −2032.13 −0.0756419
\(898\) 4706.81 0.174909
\(899\) −9329.81 −0.346125
\(900\) −4470.20 −0.165563
\(901\) −378.162 −0.0139827
\(902\) −317.490 −0.0117198
\(903\) 10633.0 0.391856
\(904\) −4002.80 −0.147269
\(905\) 1822.09 0.0669262
\(906\) −6832.46 −0.250544
\(907\) 51184.8 1.87383 0.936915 0.349558i \(-0.113668\pi\)
0.936915 + 0.349558i \(0.113668\pi\)
\(908\) −26938.4 −0.984560
\(909\) −8067.34 −0.294364
\(910\) 448.302 0.0163308
\(911\) 15160.8 0.551372 0.275686 0.961248i \(-0.411095\pi\)
0.275686 + 0.961248i \(0.411095\pi\)
\(912\) 0 0
\(913\) −388.900 −0.0140971
\(914\) 16841.9 0.609497
\(915\) −1437.10 −0.0519225
\(916\) −1350.88 −0.0487273
\(917\) 38281.7 1.37860
\(918\) 1728.71 0.0621524
\(919\) 33318.2 1.19594 0.597969 0.801519i \(-0.295974\pi\)
0.597969 + 0.801519i \(0.295974\pi\)
\(920\) 326.728 0.0117086
\(921\) 1699.74 0.0608127
\(922\) −1339.24 −0.0478369
\(923\) −7596.67 −0.270907
\(924\) 380.912 0.0135618
\(925\) 31401.3 1.11618
\(926\) 11141.8 0.395401
\(927\) 1450.44 0.0513901
\(928\) 996.830 0.0352613
\(929\) 14464.8 0.510843 0.255421 0.966830i \(-0.417786\pi\)
0.255421 + 0.966830i \(0.417786\pi\)
\(930\) 1634.98 0.0576486
\(931\) 0 0
\(932\) −25245.0 −0.887262
\(933\) 10522.7 0.369235
\(934\) −21739.6 −0.761606
\(935\) 56.6299 0.00198074
\(936\) 1086.49 0.0379414
\(937\) 16046.8 0.559475 0.279737 0.960077i \(-0.409753\pi\)
0.279737 + 0.960077i \(0.409753\pi\)
\(938\) 6880.74 0.239514
\(939\) −965.304 −0.0335479
\(940\) −683.256 −0.0237078
\(941\) 19129.4 0.662700 0.331350 0.943508i \(-0.392496\pi\)
0.331350 + 0.943508i \(0.392496\pi\)
\(942\) −11713.1 −0.405132
\(943\) −3665.04 −0.126564
\(944\) 3904.74 0.134628
\(945\) 401.061 0.0138058
\(946\) 844.184 0.0290135
\(947\) −41617.7 −1.42808 −0.714041 0.700104i \(-0.753137\pi\)
−0.714041 + 0.700104i \(0.753137\pi\)
\(948\) 2645.90 0.0906485
\(949\) 1739.38 0.0594969
\(950\) 0 0
\(951\) −11391.1 −0.388413
\(952\) −4181.24 −0.142347
\(953\) −36269.8 −1.23284 −0.616419 0.787419i \(-0.711417\pi\)
−0.616419 + 0.787419i \(0.711417\pi\)
\(954\) −212.629 −0.00721605
\(955\) −3732.09 −0.126458
\(956\) −13102.2 −0.443260
\(957\) −181.698 −0.00613736
\(958\) −4870.66 −0.164263
\(959\) −33816.1 −1.13867
\(960\) −174.687 −0.00587293
\(961\) 59911.3 2.01105
\(962\) −7632.17 −0.255791
\(963\) −10094.1 −0.337775
\(964\) 6673.09 0.222952
\(965\) −1598.16 −0.0533126
\(966\) 4397.17 0.146456
\(967\) 28249.4 0.939442 0.469721 0.882815i \(-0.344354\pi\)
0.469721 + 0.882815i \(0.344354\pi\)
\(968\) −10617.8 −0.352549
\(969\) 0 0
\(970\) 2011.45 0.0665813
\(971\) −11234.1 −0.371285 −0.185643 0.982617i \(-0.559437\pi\)
−0.185643 + 0.982617i \(0.559437\pi\)
\(972\) 972.000 0.0320750
\(973\) 23959.5 0.789420
\(974\) 21370.3 0.703029
\(975\) −5621.34 −0.184643
\(976\) 8424.14 0.276281
\(977\) −10338.6 −0.338547 −0.169273 0.985569i \(-0.554142\pi\)
−0.169273 + 0.985569i \(0.554142\pi\)
\(978\) 2315.84 0.0757184
\(979\) 338.481 0.0110499
\(980\) 278.240 0.00906945
\(981\) 8848.49 0.287982
\(982\) −18137.8 −0.589410
\(983\) −35054.0 −1.13739 −0.568693 0.822550i \(-0.692551\pi\)
−0.568693 + 0.822550i \(0.692551\pi\)
\(984\) 1959.54 0.0634836
\(985\) −3339.60 −0.108029
\(986\) 1994.48 0.0644190
\(987\) −9195.39 −0.296548
\(988\) 0 0
\(989\) 9745.09 0.313322
\(990\) 31.8412 0.00102220
\(991\) −25256.8 −0.809595 −0.404798 0.914406i \(-0.632658\pi\)
−0.404798 + 0.914406i \(0.632658\pi\)
\(992\) −9584.11 −0.306750
\(993\) 28765.3 0.919275
\(994\) 16437.9 0.524524
\(995\) 2375.34 0.0756818
\(996\) 2400.28 0.0763612
\(997\) −39035.2 −1.23998 −0.619989 0.784611i \(-0.712863\pi\)
−0.619989 + 0.784611i \(0.712863\pi\)
\(998\) −18171.1 −0.576348
\(999\) −6827.91 −0.216242
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 2166.4.a.p.1.2 yes 2
19.18 odd 2 2166.4.a.j.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2166.4.a.j.1.2 2 19.18 odd 2
2166.4.a.p.1.2 yes 2 1.1 even 1 trivial