Properties

Label 637.4.a.d.1.3
Level $637$
Weight $4$
Character 637.1
Self dual yes
Analytic conductor $37.584$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 637.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.5842166737\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.5364412.1
Defining polynomial: \( x^{4} - 27x^{2} - 24x + 76 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.32361\) of defining polynomial
Character \(\chi\) \(=\) 637.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.323612 q^{2} -1.75980 q^{3} -7.89528 q^{4} +5.91876 q^{5} -0.569491 q^{6} -5.14391 q^{8} -23.9031 q^{9} +O(q^{10})\) \(q+0.323612 q^{2} -1.75980 q^{3} -7.89528 q^{4} +5.91876 q^{5} -0.569491 q^{6} -5.14391 q^{8} -23.9031 q^{9} +1.91538 q^{10} -60.8448 q^{11} +13.8941 q^{12} +13.0000 q^{13} -10.4158 q^{15} +61.4976 q^{16} +1.36094 q^{17} -7.73534 q^{18} +4.20658 q^{19} -46.7303 q^{20} -19.6901 q^{22} -10.6695 q^{23} +9.05222 q^{24} -89.9682 q^{25} +4.20696 q^{26} +89.5791 q^{27} +124.031 q^{29} -3.37068 q^{30} -90.9367 q^{31} +61.0526 q^{32} +107.074 q^{33} +0.440417 q^{34} +188.722 q^{36} +101.085 q^{37} +1.36130 q^{38} -22.8773 q^{39} -30.4456 q^{40} -235.305 q^{41} +6.98363 q^{43} +480.386 q^{44} -141.477 q^{45} -3.45278 q^{46} +243.878 q^{47} -108.223 q^{48} -29.1148 q^{50} -2.39498 q^{51} -102.639 q^{52} -282.024 q^{53} +28.9889 q^{54} -360.126 q^{55} -7.40271 q^{57} +40.1380 q^{58} +675.683 q^{59} +82.2357 q^{60} -87.6018 q^{61} -29.4282 q^{62} -472.223 q^{64} +76.9439 q^{65} +34.6506 q^{66} +122.719 q^{67} -10.7450 q^{68} +18.7761 q^{69} +35.3966 q^{71} +122.955 q^{72} +1073.70 q^{73} +32.7124 q^{74} +158.326 q^{75} -33.2121 q^{76} -7.40339 q^{78} +811.612 q^{79} +363.990 q^{80} +487.743 q^{81} -76.1477 q^{82} +1102.66 q^{83} +8.05509 q^{85} +2.25999 q^{86} -218.269 q^{87} +312.980 q^{88} +1093.27 q^{89} -45.7837 q^{90} +84.2387 q^{92} +160.030 q^{93} +78.9220 q^{94} +24.8977 q^{95} -107.440 q^{96} -911.865 q^{97} +1454.38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 5 q^{3} + 26 q^{4} + 36 q^{5} + 45 q^{6} - 30 q^{8} + 21 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} + 5 q^{3} + 26 q^{4} + 36 q^{5} + 45 q^{6} - 30 q^{8} + 21 q^{9} + 44 q^{10} - 95 q^{11} + 17 q^{12} + 52 q^{13} - 16 q^{15} + 58 q^{16} + 146 q^{17} + 65 q^{18} + 48 q^{19} + 474 q^{20} - 143 q^{22} - 121 q^{23} + 469 q^{24} + 506 q^{25} - 52 q^{26} + 83 q^{27} - 440 q^{29} + 1548 q^{30} + 283 q^{31} - 114 q^{32} - 227 q^{33} - 1234 q^{34} + 755 q^{36} - 209 q^{37} - 440 q^{38} + 65 q^{39} - 754 q^{40} + 93 q^{41} + 526 q^{43} + 217 q^{44} + 768 q^{45} - 841 q^{46} + 783 q^{47} - 1407 q^{48} + 446 q^{50} - 672 q^{51} + 338 q^{52} - 340 q^{53} + 199 q^{54} - 756 q^{55} - 1014 q^{57} + 1916 q^{58} + 922 q^{59} - 396 q^{60} + 141 q^{61} - 1745 q^{62} - 1510 q^{64} + 468 q^{65} - 503 q^{66} - 523 q^{67} + 1710 q^{68} - 1595 q^{69} + 1468 q^{71} - 9 q^{72} + 47 q^{73} - 2249 q^{74} + 1547 q^{75} + 1382 q^{76} + 585 q^{78} + 1025 q^{79} + 2538 q^{80} - 1772 q^{81} + 1561 q^{82} + 1190 q^{83} - 568 q^{85} + 738 q^{86} - 720 q^{87} - 555 q^{88} + 2962 q^{89} + 1960 q^{90} - 599 q^{92} - 763 q^{93} - 317 q^{94} + 2082 q^{95} + 45 q^{96} - 2715 q^{97} + 586 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.323612 0.114414 0.0572071 0.998362i \(-0.481780\pi\)
0.0572071 + 0.998362i \(0.481780\pi\)
\(3\) −1.75980 −0.338673 −0.169336 0.985558i \(-0.554162\pi\)
−0.169336 + 0.985558i \(0.554162\pi\)
\(4\) −7.89528 −0.986909
\(5\) 5.91876 0.529390 0.264695 0.964332i \(-0.414729\pi\)
0.264695 + 0.964332i \(0.414729\pi\)
\(6\) −0.569491 −0.0387490
\(7\) 0 0
\(8\) −5.14391 −0.227331
\(9\) −23.9031 −0.885301
\(10\) 1.91538 0.0605698
\(11\) −60.8448 −1.66776 −0.833882 0.551943i \(-0.813886\pi\)
−0.833882 + 0.551943i \(0.813886\pi\)
\(12\) 13.8941 0.334239
\(13\) 13.0000 0.277350
\(14\) 0 0
\(15\) −10.4158 −0.179290
\(16\) 61.4976 0.960900
\(17\) 1.36094 0.0194163 0.00970813 0.999953i \(-0.496910\pi\)
0.00970813 + 0.999953i \(0.496910\pi\)
\(18\) −7.73534 −0.101291
\(19\) 4.20658 0.0507923 0.0253962 0.999677i \(-0.491915\pi\)
0.0253962 + 0.999677i \(0.491915\pi\)
\(20\) −46.7303 −0.522460
\(21\) 0 0
\(22\) −19.6901 −0.190816
\(23\) −10.6695 −0.0967281 −0.0483640 0.998830i \(-0.515401\pi\)
−0.0483640 + 0.998830i \(0.515401\pi\)
\(24\) 9.05222 0.0769907
\(25\) −89.9682 −0.719746
\(26\) 4.20696 0.0317328
\(27\) 89.5791 0.638500
\(28\) 0 0
\(29\) 124.031 0.794207 0.397103 0.917774i \(-0.370015\pi\)
0.397103 + 0.917774i \(0.370015\pi\)
\(30\) −3.37068 −0.0205133
\(31\) −90.9367 −0.526862 −0.263431 0.964678i \(-0.584854\pi\)
−0.263431 + 0.964678i \(0.584854\pi\)
\(32\) 61.0526 0.337271
\(33\) 107.074 0.564826
\(34\) 0.440417 0.00222150
\(35\) 0 0
\(36\) 188.722 0.873712
\(37\) 101.085 0.449143 0.224572 0.974458i \(-0.427902\pi\)
0.224572 + 0.974458i \(0.427902\pi\)
\(38\) 1.36130 0.00581137
\(39\) −22.8773 −0.0939309
\(40\) −30.4456 −0.120347
\(41\) −235.305 −0.896306 −0.448153 0.893957i \(-0.647918\pi\)
−0.448153 + 0.893957i \(0.647918\pi\)
\(42\) 0 0
\(43\) 6.98363 0.0247673 0.0123836 0.999923i \(-0.496058\pi\)
0.0123836 + 0.999923i \(0.496058\pi\)
\(44\) 480.386 1.64593
\(45\) −141.477 −0.468670
\(46\) −3.45278 −0.0110671
\(47\) 243.878 0.756879 0.378440 0.925626i \(-0.376461\pi\)
0.378440 + 0.925626i \(0.376461\pi\)
\(48\) −108.223 −0.325430
\(49\) 0 0
\(50\) −29.1148 −0.0823491
\(51\) −2.39498 −0.00657576
\(52\) −102.639 −0.273719
\(53\) −282.024 −0.730924 −0.365462 0.930826i \(-0.619089\pi\)
−0.365462 + 0.930826i \(0.619089\pi\)
\(54\) 28.9889 0.0730535
\(55\) −360.126 −0.882898
\(56\) 0 0
\(57\) −7.40271 −0.0172020
\(58\) 40.1380 0.0908685
\(59\) 675.683 1.49096 0.745479 0.666529i \(-0.232221\pi\)
0.745479 + 0.666529i \(0.232221\pi\)
\(60\) 82.2357 0.176943
\(61\) −87.6018 −0.183873 −0.0919365 0.995765i \(-0.529306\pi\)
−0.0919365 + 0.995765i \(0.529306\pi\)
\(62\) −29.4282 −0.0602805
\(63\) 0 0
\(64\) −472.223 −0.922311
\(65\) 76.9439 0.146826
\(66\) 34.6506 0.0646241
\(67\) 122.719 0.223768 0.111884 0.993721i \(-0.464311\pi\)
0.111884 + 0.993721i \(0.464311\pi\)
\(68\) −10.7450 −0.0191621
\(69\) 18.7761 0.0327592
\(70\) 0 0
\(71\) 35.3966 0.0591663 0.0295831 0.999562i \(-0.490582\pi\)
0.0295831 + 0.999562i \(0.490582\pi\)
\(72\) 122.955 0.201256
\(73\) 1073.70 1.72147 0.860733 0.509057i \(-0.170006\pi\)
0.860733 + 0.509057i \(0.170006\pi\)
\(74\) 32.7124 0.0513884
\(75\) 158.326 0.243758
\(76\) −33.2121 −0.0501274
\(77\) 0 0
\(78\) −7.40339 −0.0107470
\(79\) 811.612 1.15587 0.577934 0.816084i \(-0.303859\pi\)
0.577934 + 0.816084i \(0.303859\pi\)
\(80\) 363.990 0.508691
\(81\) 487.743 0.669058
\(82\) −76.1477 −0.102550
\(83\) 1102.66 1.45823 0.729116 0.684391i \(-0.239932\pi\)
0.729116 + 0.684391i \(0.239932\pi\)
\(84\) 0 0
\(85\) 8.05509 0.0102788
\(86\) 2.25999 0.00283373
\(87\) −218.269 −0.268976
\(88\) 312.980 0.379134
\(89\) 1093.27 1.30209 0.651044 0.759040i \(-0.274331\pi\)
0.651044 + 0.759040i \(0.274331\pi\)
\(90\) −45.7837 −0.0536225
\(91\) 0 0
\(92\) 84.2387 0.0954618
\(93\) 160.030 0.178434
\(94\) 78.9220 0.0865977
\(95\) 24.8977 0.0268890
\(96\) −107.440 −0.114225
\(97\) −911.865 −0.954494 −0.477247 0.878769i \(-0.658365\pi\)
−0.477247 + 0.878769i \(0.658365\pi\)
\(98\) 0 0
\(99\) 1454.38 1.47647
\(100\) 710.324 0.710324
\(101\) 1708.38 1.68307 0.841535 0.540202i \(-0.181652\pi\)
0.841535 + 0.540202i \(0.181652\pi\)
\(102\) −0.775044 −0.000752360 0
\(103\) 833.431 0.797285 0.398643 0.917106i \(-0.369481\pi\)
0.398643 + 0.917106i \(0.369481\pi\)
\(104\) −66.8708 −0.0630502
\(105\) 0 0
\(106\) −91.2664 −0.0836281
\(107\) 296.677 0.268045 0.134022 0.990978i \(-0.457211\pi\)
0.134022 + 0.990978i \(0.457211\pi\)
\(108\) −707.251 −0.630142
\(109\) −2012.35 −1.76833 −0.884166 0.467173i \(-0.845272\pi\)
−0.884166 + 0.467173i \(0.845272\pi\)
\(110\) −116.541 −0.101016
\(111\) −177.889 −0.152113
\(112\) 0 0
\(113\) −459.400 −0.382448 −0.191224 0.981546i \(-0.561246\pi\)
−0.191224 + 0.981546i \(0.561246\pi\)
\(114\) −2.39561 −0.00196815
\(115\) −63.1503 −0.0512069
\(116\) −979.259 −0.783810
\(117\) −310.741 −0.245538
\(118\) 218.659 0.170587
\(119\) 0 0
\(120\) 53.5780 0.0407581
\(121\) 2371.09 1.78143
\(122\) −28.3490 −0.0210377
\(123\) 414.089 0.303554
\(124\) 717.971 0.519965
\(125\) −1272.35 −0.910417
\(126\) 0 0
\(127\) 2573.78 1.79832 0.899158 0.437624i \(-0.144180\pi\)
0.899158 + 0.437624i \(0.144180\pi\)
\(128\) −641.238 −0.442797
\(129\) −12.2898 −0.00838801
\(130\) 24.9000 0.0167990
\(131\) −599.610 −0.399910 −0.199955 0.979805i \(-0.564080\pi\)
−0.199955 + 0.979805i \(0.564080\pi\)
\(132\) −845.382 −0.557432
\(133\) 0 0
\(134\) 39.7133 0.0256023
\(135\) 530.197 0.338016
\(136\) −7.00055 −0.00441391
\(137\) −1501.25 −0.936207 −0.468104 0.883674i \(-0.655063\pi\)
−0.468104 + 0.883674i \(0.655063\pi\)
\(138\) 6.07619 0.00374811
\(139\) −2652.59 −1.61863 −0.809316 0.587374i \(-0.800162\pi\)
−0.809316 + 0.587374i \(0.800162\pi\)
\(140\) 0 0
\(141\) −429.176 −0.256334
\(142\) 11.4548 0.00676946
\(143\) −790.982 −0.462554
\(144\) −1469.98 −0.850685
\(145\) 734.111 0.420445
\(146\) 347.462 0.196960
\(147\) 0 0
\(148\) −798.095 −0.443264
\(149\) 1316.52 0.723852 0.361926 0.932207i \(-0.382119\pi\)
0.361926 + 0.932207i \(0.382119\pi\)
\(150\) 51.2361 0.0278894
\(151\) 2051.26 1.10549 0.552744 0.833351i \(-0.313581\pi\)
0.552744 + 0.833351i \(0.313581\pi\)
\(152\) −21.6382 −0.0115467
\(153\) −32.5307 −0.0171892
\(154\) 0 0
\(155\) −538.233 −0.278916
\(156\) 180.623 0.0927013
\(157\) −1313.72 −0.667809 −0.333904 0.942607i \(-0.608366\pi\)
−0.333904 + 0.942607i \(0.608366\pi\)
\(158\) 262.648 0.132248
\(159\) 496.305 0.247544
\(160\) 361.356 0.178548
\(161\) 0 0
\(162\) 157.840 0.0765498
\(163\) −1850.44 −0.889190 −0.444595 0.895732i \(-0.646652\pi\)
−0.444595 + 0.895732i \(0.646652\pi\)
\(164\) 1857.80 0.884572
\(165\) 633.748 0.299013
\(166\) 356.836 0.166842
\(167\) 1090.13 0.505130 0.252565 0.967580i \(-0.418726\pi\)
0.252565 + 0.967580i \(0.418726\pi\)
\(168\) 0 0
\(169\) 169.000 0.0769231
\(170\) 2.60672 0.00117604
\(171\) −100.550 −0.0449665
\(172\) −55.1377 −0.0244431
\(173\) −2306.38 −1.01359 −0.506795 0.862066i \(-0.669170\pi\)
−0.506795 + 0.862066i \(0.669170\pi\)
\(174\) −70.6346 −0.0307747
\(175\) 0 0
\(176\) −3741.81 −1.60255
\(177\) −1189.06 −0.504947
\(178\) 353.794 0.148977
\(179\) −363.408 −0.151745 −0.0758726 0.997118i \(-0.524174\pi\)
−0.0758726 + 0.997118i \(0.524174\pi\)
\(180\) 1117.00 0.462535
\(181\) 3863.47 1.58657 0.793287 0.608848i \(-0.208368\pi\)
0.793287 + 0.608848i \(0.208368\pi\)
\(182\) 0 0
\(183\) 154.161 0.0622728
\(184\) 54.8829 0.0219893
\(185\) 598.299 0.237772
\(186\) 51.7877 0.0204154
\(187\) −82.8061 −0.0323817
\(188\) −1925.49 −0.746971
\(189\) 0 0
\(190\) 8.05721 0.00307648
\(191\) −1304.09 −0.494035 −0.247017 0.969011i \(-0.579450\pi\)
−0.247017 + 0.969011i \(0.579450\pi\)
\(192\) 831.016 0.312362
\(193\) −96.9311 −0.0361516 −0.0180758 0.999837i \(-0.505754\pi\)
−0.0180758 + 0.999837i \(0.505754\pi\)
\(194\) −295.091 −0.109208
\(195\) −135.406 −0.0497261
\(196\) 0 0
\(197\) −3135.09 −1.13384 −0.566919 0.823774i \(-0.691865\pi\)
−0.566919 + 0.823774i \(0.691865\pi\)
\(198\) 470.655 0.168929
\(199\) −3431.34 −1.22232 −0.611159 0.791508i \(-0.709296\pi\)
−0.611159 + 0.791508i \(0.709296\pi\)
\(200\) 462.788 0.163620
\(201\) −215.960 −0.0757842
\(202\) 552.853 0.192567
\(203\) 0 0
\(204\) 18.9090 0.00648968
\(205\) −1392.72 −0.474496
\(206\) 269.708 0.0912207
\(207\) 255.034 0.0856334
\(208\) 799.468 0.266506
\(209\) −255.948 −0.0847096
\(210\) 0 0
\(211\) 4599.00 1.50051 0.750256 0.661147i \(-0.229930\pi\)
0.750256 + 0.661147i \(0.229930\pi\)
\(212\) 2226.66 0.721356
\(213\) −62.2908 −0.0200380
\(214\) 96.0082 0.0306681
\(215\) 41.3345 0.0131116
\(216\) −460.786 −0.145151
\(217\) 0 0
\(218\) −651.221 −0.202322
\(219\) −1889.49 −0.583014
\(220\) 2843.29 0.871340
\(221\) 17.6922 0.00538510
\(222\) −57.5671 −0.0174038
\(223\) 4769.56 1.43226 0.716129 0.697968i \(-0.245912\pi\)
0.716129 + 0.697968i \(0.245912\pi\)
\(224\) 0 0
\(225\) 2150.52 0.637192
\(226\) −148.667 −0.0437575
\(227\) −5426.06 −1.58652 −0.793260 0.608883i \(-0.791618\pi\)
−0.793260 + 0.608883i \(0.791618\pi\)
\(228\) 58.4464 0.0169768
\(229\) 3946.45 1.13881 0.569407 0.822056i \(-0.307173\pi\)
0.569407 + 0.822056i \(0.307173\pi\)
\(230\) −20.4362 −0.00585880
\(231\) 0 0
\(232\) −638.004 −0.180547
\(233\) −4611.04 −1.29648 −0.648238 0.761437i \(-0.724494\pi\)
−0.648238 + 0.761437i \(0.724494\pi\)
\(234\) −100.559 −0.0280931
\(235\) 1443.46 0.400685
\(236\) −5334.71 −1.47144
\(237\) −1428.27 −0.391461
\(238\) 0 0
\(239\) −1663.03 −0.450094 −0.225047 0.974348i \(-0.572253\pi\)
−0.225047 + 0.974348i \(0.572253\pi\)
\(240\) −640.547 −0.172280
\(241\) −2964.29 −0.792311 −0.396156 0.918183i \(-0.629656\pi\)
−0.396156 + 0.918183i \(0.629656\pi\)
\(242\) 767.313 0.203821
\(243\) −3276.96 −0.865092
\(244\) 691.640 0.181466
\(245\) 0 0
\(246\) 134.004 0.0347309
\(247\) 54.6855 0.0140873
\(248\) 467.770 0.119772
\(249\) −1940.46 −0.493863
\(250\) −411.747 −0.104165
\(251\) 3483.07 0.875893 0.437947 0.899001i \(-0.355706\pi\)
0.437947 + 0.899001i \(0.355706\pi\)
\(252\) 0 0
\(253\) 649.184 0.161320
\(254\) 832.907 0.205753
\(255\) −14.1753 −0.00348114
\(256\) 3570.27 0.871649
\(257\) −4983.36 −1.20955 −0.604774 0.796397i \(-0.706736\pi\)
−0.604774 + 0.796397i \(0.706736\pi\)
\(258\) −3.97712 −0.000959707 0
\(259\) 0 0
\(260\) −607.494 −0.144904
\(261\) −2964.73 −0.703112
\(262\) −194.041 −0.0457553
\(263\) 7413.00 1.73804 0.869021 0.494776i \(-0.164750\pi\)
0.869021 + 0.494776i \(0.164750\pi\)
\(264\) −550.780 −0.128402
\(265\) −1669.23 −0.386944
\(266\) 0 0
\(267\) −1923.92 −0.440982
\(268\) −968.898 −0.220839
\(269\) 7815.61 1.77147 0.885736 0.464189i \(-0.153654\pi\)
0.885736 + 0.464189i \(0.153654\pi\)
\(270\) 171.578 0.0386738
\(271\) 940.210 0.210752 0.105376 0.994432i \(-0.466395\pi\)
0.105376 + 0.994432i \(0.466395\pi\)
\(272\) 83.6945 0.0186571
\(273\) 0 0
\(274\) −485.823 −0.107115
\(275\) 5474.10 1.20037
\(276\) −148.243 −0.0323303
\(277\) 1086.00 0.235565 0.117783 0.993039i \(-0.462421\pi\)
0.117783 + 0.993039i \(0.462421\pi\)
\(278\) −858.411 −0.185194
\(279\) 2173.67 0.466431
\(280\) 0 0
\(281\) 81.9702 0.0174019 0.00870095 0.999962i \(-0.497230\pi\)
0.00870095 + 0.999962i \(0.497230\pi\)
\(282\) −138.887 −0.0293283
\(283\) −8459.84 −1.77698 −0.888490 0.458896i \(-0.848245\pi\)
−0.888490 + 0.458896i \(0.848245\pi\)
\(284\) −279.466 −0.0583918
\(285\) −43.8149 −0.00910656
\(286\) −255.972 −0.0529228
\(287\) 0 0
\(288\) −1459.35 −0.298586
\(289\) −4911.15 −0.999623
\(290\) 237.567 0.0481049
\(291\) 1604.70 0.323261
\(292\) −8477.15 −1.69893
\(293\) 3439.10 0.685714 0.342857 0.939388i \(-0.388605\pi\)
0.342857 + 0.939388i \(0.388605\pi\)
\(294\) 0 0
\(295\) 3999.21 0.789298
\(296\) −519.973 −0.102104
\(297\) −5450.42 −1.06487
\(298\) 426.043 0.0828189
\(299\) −138.704 −0.0268275
\(300\) −1250.02 −0.240567
\(301\) 0 0
\(302\) 663.811 0.126484
\(303\) −3006.40 −0.570010
\(304\) 258.694 0.0488063
\(305\) −518.494 −0.0973406
\(306\) −10.5273 −0.00196669
\(307\) 1076.49 0.200126 0.100063 0.994981i \(-0.468096\pi\)
0.100063 + 0.994981i \(0.468096\pi\)
\(308\) 0 0
\(309\) −1466.67 −0.270019
\(310\) −174.179 −0.0319119
\(311\) 7001.34 1.27656 0.638279 0.769805i \(-0.279647\pi\)
0.638279 + 0.769805i \(0.279647\pi\)
\(312\) 117.679 0.0213534
\(313\) 7431.60 1.34204 0.671020 0.741439i \(-0.265856\pi\)
0.671020 + 0.741439i \(0.265856\pi\)
\(314\) −425.135 −0.0764068
\(315\) 0 0
\(316\) −6407.90 −1.14074
\(317\) −7181.40 −1.27239 −0.636195 0.771528i \(-0.719493\pi\)
−0.636195 + 0.771528i \(0.719493\pi\)
\(318\) 160.610 0.0283226
\(319\) −7546.64 −1.32455
\(320\) −2794.98 −0.488263
\(321\) −522.090 −0.0907795
\(322\) 0 0
\(323\) 5.72490 0.000986198 0
\(324\) −3850.87 −0.660300
\(325\) −1169.59 −0.199622
\(326\) −598.826 −0.101736
\(327\) 3541.32 0.598886
\(328\) 1210.39 0.203758
\(329\) 0 0
\(330\) 205.089 0.0342114
\(331\) −3742.93 −0.621540 −0.310770 0.950485i \(-0.600587\pi\)
−0.310770 + 0.950485i \(0.600587\pi\)
\(332\) −8705.84 −1.43914
\(333\) −2416.25 −0.397627
\(334\) 352.779 0.0577940
\(335\) 726.343 0.118461
\(336\) 0 0
\(337\) 10859.5 1.75535 0.877674 0.479258i \(-0.159094\pi\)
0.877674 + 0.479258i \(0.159094\pi\)
\(338\) 54.6905 0.00880109
\(339\) 808.449 0.129525
\(340\) −63.5971 −0.0101442
\(341\) 5533.03 0.878681
\(342\) −32.5393 −0.00514481
\(343\) 0 0
\(344\) −35.9231 −0.00563037
\(345\) 111.132 0.0173424
\(346\) −746.374 −0.115969
\(347\) 267.989 0.0414594 0.0207297 0.999785i \(-0.493401\pi\)
0.0207297 + 0.999785i \(0.493401\pi\)
\(348\) 1723.30 0.265455
\(349\) 5082.15 0.779488 0.389744 0.920923i \(-0.372563\pi\)
0.389744 + 0.920923i \(0.372563\pi\)
\(350\) 0 0
\(351\) 1164.53 0.177088
\(352\) −3714.73 −0.562489
\(353\) −9356.72 −1.41079 −0.705394 0.708815i \(-0.749230\pi\)
−0.705394 + 0.708815i \(0.749230\pi\)
\(354\) −384.796 −0.0577731
\(355\) 209.504 0.0313221
\(356\) −8631.63 −1.28504
\(357\) 0 0
\(358\) −117.603 −0.0173618
\(359\) −499.977 −0.0735036 −0.0367518 0.999324i \(-0.511701\pi\)
−0.0367518 + 0.999324i \(0.511701\pi\)
\(360\) 727.744 0.106543
\(361\) −6841.30 −0.997420
\(362\) 1250.27 0.181527
\(363\) −4172.63 −0.603323
\(364\) 0 0
\(365\) 6354.97 0.911327
\(366\) 49.8884 0.00712489
\(367\) 2754.73 0.391814 0.195907 0.980622i \(-0.437235\pi\)
0.195907 + 0.980622i \(0.437235\pi\)
\(368\) −656.149 −0.0929460
\(369\) 5624.53 0.793500
\(370\) 193.617 0.0272045
\(371\) 0 0
\(372\) −1263.48 −0.176098
\(373\) −9414.45 −1.30687 −0.653434 0.756984i \(-0.726672\pi\)
−0.653434 + 0.756984i \(0.726672\pi\)
\(374\) −26.7971 −0.00370493
\(375\) 2239.07 0.308333
\(376\) −1254.49 −0.172062
\(377\) 1612.40 0.220273
\(378\) 0 0
\(379\) −11295.5 −1.53090 −0.765451 0.643494i \(-0.777484\pi\)
−0.765451 + 0.643494i \(0.777484\pi\)
\(380\) −196.574 −0.0265370
\(381\) −4529.33 −0.609041
\(382\) −422.019 −0.0565246
\(383\) −265.629 −0.0354386 −0.0177193 0.999843i \(-0.505641\pi\)
−0.0177193 + 0.999843i \(0.505641\pi\)
\(384\) 1128.45 0.149963
\(385\) 0 0
\(386\) −31.3681 −0.00413625
\(387\) −166.931 −0.0219265
\(388\) 7199.43 0.941999
\(389\) 11601.0 1.51207 0.756037 0.654529i \(-0.227133\pi\)
0.756037 + 0.654529i \(0.227133\pi\)
\(390\) −43.8189 −0.00568937
\(391\) −14.5206 −0.00187810
\(392\) 0 0
\(393\) 1055.19 0.135438
\(394\) −1014.55 −0.129727
\(395\) 4803.74 0.611905
\(396\) −11482.7 −1.45714
\(397\) −6664.32 −0.842501 −0.421250 0.906944i \(-0.638409\pi\)
−0.421250 + 0.906944i \(0.638409\pi\)
\(398\) −1110.42 −0.139851
\(399\) 0 0
\(400\) −5532.83 −0.691603
\(401\) 7874.09 0.980582 0.490291 0.871559i \(-0.336891\pi\)
0.490291 + 0.871559i \(0.336891\pi\)
\(402\) −69.8872 −0.00867079
\(403\) −1182.18 −0.146125
\(404\) −13488.1 −1.66104
\(405\) 2886.84 0.354193
\(406\) 0 0
\(407\) −6150.51 −0.749065
\(408\) 12.3195 0.00149487
\(409\) 2311.74 0.279483 0.139741 0.990188i \(-0.455373\pi\)
0.139741 + 0.990188i \(0.455373\pi\)
\(410\) −450.700 −0.0542890
\(411\) 2641.89 0.317068
\(412\) −6580.16 −0.786848
\(413\) 0 0
\(414\) 82.5323 0.00979768
\(415\) 6526.41 0.771973
\(416\) 793.684 0.0935422
\(417\) 4668.02 0.548186
\(418\) −82.8280 −0.00969198
\(419\) 3945.48 0.460023 0.230011 0.973188i \(-0.426124\pi\)
0.230011 + 0.973188i \(0.426124\pi\)
\(420\) 0 0
\(421\) −699.284 −0.0809526 −0.0404763 0.999180i \(-0.512888\pi\)
−0.0404763 + 0.999180i \(0.512888\pi\)
\(422\) 1488.29 0.171680
\(423\) −5829.46 −0.670066
\(424\) 1450.70 0.166161
\(425\) −122.441 −0.0139748
\(426\) −20.1581 −0.00229263
\(427\) 0 0
\(428\) −2342.34 −0.264536
\(429\) 1391.97 0.156655
\(430\) 13.3763 0.00150015
\(431\) 14778.0 1.65158 0.825789 0.563980i \(-0.190730\pi\)
0.825789 + 0.563980i \(0.190730\pi\)
\(432\) 5508.89 0.613534
\(433\) −4217.17 −0.468046 −0.234023 0.972231i \(-0.575189\pi\)
−0.234023 + 0.972231i \(0.575189\pi\)
\(434\) 0 0
\(435\) −1291.88 −0.142393
\(436\) 15888.1 1.74518
\(437\) −44.8821 −0.00491305
\(438\) −611.462 −0.0667050
\(439\) −6372.34 −0.692791 −0.346395 0.938089i \(-0.612594\pi\)
−0.346395 + 0.938089i \(0.612594\pi\)
\(440\) 1852.45 0.200710
\(441\) 0 0
\(442\) 5.72542 0.000616132 0
\(443\) 7824.17 0.839137 0.419568 0.907724i \(-0.362181\pi\)
0.419568 + 0.907724i \(0.362181\pi\)
\(444\) 1404.48 0.150121
\(445\) 6470.78 0.689313
\(446\) 1543.49 0.163871
\(447\) −2316.81 −0.245149
\(448\) 0 0
\(449\) 3132.31 0.329226 0.164613 0.986358i \(-0.447362\pi\)
0.164613 + 0.986358i \(0.447362\pi\)
\(450\) 695.935 0.0729038
\(451\) 14317.1 1.49483
\(452\) 3627.09 0.377442
\(453\) −3609.79 −0.374399
\(454\) −1755.94 −0.181520
\(455\) 0 0
\(456\) 38.0788 0.00391054
\(457\) 2253.14 0.230629 0.115314 0.993329i \(-0.463212\pi\)
0.115314 + 0.993329i \(0.463212\pi\)
\(458\) 1277.12 0.130297
\(459\) 121.912 0.0123973
\(460\) 498.589 0.0505366
\(461\) 9164.98 0.925934 0.462967 0.886375i \(-0.346785\pi\)
0.462967 + 0.886375i \(0.346785\pi\)
\(462\) 0 0
\(463\) 7086.00 0.711263 0.355631 0.934626i \(-0.384266\pi\)
0.355631 + 0.934626i \(0.384266\pi\)
\(464\) 7627.61 0.763153
\(465\) 947.180 0.0944611
\(466\) −1492.19 −0.148335
\(467\) −11174.0 −1.10721 −0.553607 0.832778i \(-0.686749\pi\)
−0.553607 + 0.832778i \(0.686749\pi\)
\(468\) 2453.38 0.242324
\(469\) 0 0
\(470\) 467.121 0.0458440
\(471\) 2311.87 0.226169
\(472\) −3475.65 −0.338940
\(473\) −424.918 −0.0413060
\(474\) −462.206 −0.0447887
\(475\) −378.458 −0.0365576
\(476\) 0 0
\(477\) 6741.25 0.647088
\(478\) −538.176 −0.0514971
\(479\) −8240.34 −0.786035 −0.393018 0.919531i \(-0.628569\pi\)
−0.393018 + 0.919531i \(0.628569\pi\)
\(480\) −635.913 −0.0604694
\(481\) 1314.11 0.124570
\(482\) −959.282 −0.0906517
\(483\) 0 0
\(484\) −18720.4 −1.75811
\(485\) −5397.12 −0.505300
\(486\) −1060.47 −0.0989788
\(487\) −9967.60 −0.927464 −0.463732 0.885975i \(-0.653490\pi\)
−0.463732 + 0.885975i \(0.653490\pi\)
\(488\) 450.615 0.0418000
\(489\) 3256.40 0.301144
\(490\) 0 0
\(491\) 11339.8 1.04228 0.521138 0.853473i \(-0.325508\pi\)
0.521138 + 0.853473i \(0.325508\pi\)
\(492\) −3269.35 −0.299581
\(493\) 168.799 0.0154205
\(494\) 17.6969 0.00161178
\(495\) 8608.14 0.781630
\(496\) −5592.39 −0.506261
\(497\) 0 0
\(498\) −627.958 −0.0565050
\(499\) 8011.01 0.718682 0.359341 0.933206i \(-0.383002\pi\)
0.359341 + 0.933206i \(0.383002\pi\)
\(500\) 10045.5 0.898499
\(501\) −1918.40 −0.171074
\(502\) 1127.16 0.100215
\(503\) 17925.8 1.58901 0.794503 0.607260i \(-0.207731\pi\)
0.794503 + 0.607260i \(0.207731\pi\)
\(504\) 0 0
\(505\) 10111.5 0.891001
\(506\) 210.084 0.0184572
\(507\) −297.405 −0.0260517
\(508\) −20320.7 −1.77477
\(509\) 13744.2 1.19686 0.598429 0.801176i \(-0.295792\pi\)
0.598429 + 0.801176i \(0.295792\pi\)
\(510\) −4.58730 −0.000398292 0
\(511\) 0 0
\(512\) 6285.29 0.542526
\(513\) 376.821 0.0324309
\(514\) −1612.68 −0.138389
\(515\) 4932.88 0.422075
\(516\) 97.0310 0.00827820
\(517\) −14838.7 −1.26230
\(518\) 0 0
\(519\) 4058.77 0.343276
\(520\) −395.792 −0.0333782
\(521\) −2637.79 −0.221811 −0.110906 0.993831i \(-0.535375\pi\)
−0.110906 + 0.993831i \(0.535375\pi\)
\(522\) −959.423 −0.0804460
\(523\) 16059.6 1.34271 0.671353 0.741138i \(-0.265713\pi\)
0.671353 + 0.741138i \(0.265713\pi\)
\(524\) 4734.08 0.394674
\(525\) 0 0
\(526\) 2398.94 0.198857
\(527\) −123.759 −0.0102297
\(528\) 6584.81 0.542741
\(529\) −12053.2 −0.990644
\(530\) −540.184 −0.0442719
\(531\) −16150.9 −1.31995
\(532\) 0 0
\(533\) −3058.97 −0.248590
\(534\) −622.605 −0.0504546
\(535\) 1755.96 0.141900
\(536\) −631.253 −0.0508694
\(537\) 639.524 0.0513920
\(538\) 2529.23 0.202682
\(539\) 0 0
\(540\) −4186.05 −0.333591
\(541\) 10315.9 0.819804 0.409902 0.912130i \(-0.365563\pi\)
0.409902 + 0.912130i \(0.365563\pi\)
\(542\) 304.263 0.0241130
\(543\) −6798.92 −0.537329
\(544\) 83.0890 0.00654855
\(545\) −11910.6 −0.936138
\(546\) 0 0
\(547\) −5327.06 −0.416396 −0.208198 0.978087i \(-0.566760\pi\)
−0.208198 + 0.978087i \(0.566760\pi\)
\(548\) 11852.8 0.923952
\(549\) 2093.96 0.162783
\(550\) 1771.49 0.137339
\(551\) 521.746 0.0403396
\(552\) −96.5827 −0.00744716
\(553\) 0 0
\(554\) 351.444 0.0269520
\(555\) −1052.88 −0.0805270
\(556\) 20942.9 1.59744
\(557\) 11816.4 0.898884 0.449442 0.893310i \(-0.351623\pi\)
0.449442 + 0.893310i \(0.351623\pi\)
\(558\) 703.427 0.0533664
\(559\) 90.7872 0.00686921
\(560\) 0 0
\(561\) 145.722 0.0109668
\(562\) 26.5266 0.00199102
\(563\) 20627.2 1.54411 0.772054 0.635557i \(-0.219230\pi\)
0.772054 + 0.635557i \(0.219230\pi\)
\(564\) 3388.46 0.252979
\(565\) −2719.08 −0.202465
\(566\) −2737.71 −0.203312
\(567\) 0 0
\(568\) −182.077 −0.0134503
\(569\) −13529.3 −0.996798 −0.498399 0.866948i \(-0.666078\pi\)
−0.498399 + 0.866948i \(0.666078\pi\)
\(570\) −14.1790 −0.00104192
\(571\) −13230.8 −0.969690 −0.484845 0.874600i \(-0.661124\pi\)
−0.484845 + 0.874600i \(0.661124\pi\)
\(572\) 6245.02 0.456499
\(573\) 2294.93 0.167316
\(574\) 0 0
\(575\) 959.917 0.0696196
\(576\) 11287.6 0.816523
\(577\) −21279.3 −1.53530 −0.767650 0.640870i \(-0.778574\pi\)
−0.767650 + 0.640870i \(0.778574\pi\)
\(578\) −1589.31 −0.114371
\(579\) 170.579 0.0122435
\(580\) −5796.00 −0.414941
\(581\) 0 0
\(582\) 519.299 0.0369857
\(583\) 17159.7 1.21901
\(584\) −5523.01 −0.391342
\(585\) −1839.20 −0.129986
\(586\) 1112.93 0.0784555
\(587\) 13737.6 0.965945 0.482972 0.875636i \(-0.339557\pi\)
0.482972 + 0.875636i \(0.339557\pi\)
\(588\) 0 0
\(589\) −382.532 −0.0267606
\(590\) 1294.19 0.0903070
\(591\) 5517.12 0.384000
\(592\) 6216.49 0.431582
\(593\) 22012.2 1.52434 0.762169 0.647379i \(-0.224135\pi\)
0.762169 + 0.647379i \(0.224135\pi\)
\(594\) −1763.82 −0.121836
\(595\) 0 0
\(596\) −10394.3 −0.714376
\(597\) 6038.46 0.413966
\(598\) −44.8862 −0.00306945
\(599\) 3333.73 0.227400 0.113700 0.993515i \(-0.463730\pi\)
0.113700 + 0.993515i \(0.463730\pi\)
\(600\) −814.412 −0.0554137
\(601\) −17140.5 −1.16336 −0.581678 0.813419i \(-0.697604\pi\)
−0.581678 + 0.813419i \(0.697604\pi\)
\(602\) 0 0
\(603\) −2933.36 −0.198102
\(604\) −16195.2 −1.09102
\(605\) 14033.9 0.943074
\(606\) −972.907 −0.0652173
\(607\) 2365.32 0.158164 0.0790818 0.996868i \(-0.474801\pi\)
0.0790818 + 0.996868i \(0.474801\pi\)
\(608\) 256.822 0.0171308
\(609\) 0 0
\(610\) −167.791 −0.0111372
\(611\) 3170.42 0.209921
\(612\) 256.839 0.0169642
\(613\) −165.695 −0.0109174 −0.00545869 0.999985i \(-0.501738\pi\)
−0.00545869 + 0.999985i \(0.501738\pi\)
\(614\) 348.367 0.0228973
\(615\) 2450.90 0.160699
\(616\) 0 0
\(617\) 5993.71 0.391082 0.195541 0.980696i \(-0.437354\pi\)
0.195541 + 0.980696i \(0.437354\pi\)
\(618\) −474.632 −0.0308940
\(619\) 7157.52 0.464758 0.232379 0.972625i \(-0.425349\pi\)
0.232379 + 0.972625i \(0.425349\pi\)
\(620\) 4249.50 0.275264
\(621\) −955.764 −0.0617609
\(622\) 2265.72 0.146056
\(623\) 0 0
\(624\) −1406.90 −0.0902582
\(625\) 3715.31 0.237780
\(626\) 2404.96 0.153549
\(627\) 450.416 0.0286888
\(628\) 10372.2 0.659067
\(629\) 137.571 0.00872069
\(630\) 0 0
\(631\) 25765.6 1.62554 0.812769 0.582586i \(-0.197959\pi\)
0.812769 + 0.582586i \(0.197959\pi\)
\(632\) −4174.86 −0.262764
\(633\) −8093.30 −0.508183
\(634\) −2323.99 −0.145580
\(635\) 15233.6 0.952011
\(636\) −3918.46 −0.244304
\(637\) 0 0
\(638\) −2442.19 −0.151547
\(639\) −846.090 −0.0523800
\(640\) −3795.34 −0.234412
\(641\) −20628.0 −1.27107 −0.635536 0.772072i \(-0.719221\pi\)
−0.635536 + 0.772072i \(0.719221\pi\)
\(642\) −168.955 −0.0103865
\(643\) −25301.9 −1.55180 −0.775901 0.630854i \(-0.782704\pi\)
−0.775901 + 0.630854i \(0.782704\pi\)
\(644\) 0 0
\(645\) −72.7402 −0.00444053
\(646\) 1.85265 0.000112835 0
\(647\) 14852.8 0.902508 0.451254 0.892396i \(-0.350977\pi\)
0.451254 + 0.892396i \(0.350977\pi\)
\(648\) −2508.91 −0.152097
\(649\) −41111.8 −2.48656
\(650\) −378.493 −0.0228395
\(651\) 0 0
\(652\) 14609.8 0.877550
\(653\) 25682.0 1.53907 0.769537 0.638602i \(-0.220487\pi\)
0.769537 + 0.638602i \(0.220487\pi\)
\(654\) 1146.02 0.0685210
\(655\) −3548.95 −0.211708
\(656\) −14470.7 −0.861260
\(657\) −25664.8 −1.52402
\(658\) 0 0
\(659\) −7290.57 −0.430956 −0.215478 0.976509i \(-0.569131\pi\)
−0.215478 + 0.976509i \(0.569131\pi\)
\(660\) −5003.61 −0.295099
\(661\) −16930.0 −0.996222 −0.498111 0.867113i \(-0.665973\pi\)
−0.498111 + 0.867113i \(0.665973\pi\)
\(662\) −1211.26 −0.0711131
\(663\) −31.1347 −0.00182379
\(664\) −5672.00 −0.331501
\(665\) 0 0
\(666\) −781.929 −0.0454942
\(667\) −1323.35 −0.0768221
\(668\) −8606.87 −0.498517
\(669\) −8393.45 −0.485067
\(670\) 235.053 0.0135536
\(671\) 5330.11 0.306657
\(672\) 0 0
\(673\) 16730.2 0.958249 0.479125 0.877747i \(-0.340954\pi\)
0.479125 + 0.877747i \(0.340954\pi\)
\(674\) 3514.25 0.200837
\(675\) −8059.27 −0.459558
\(676\) −1334.30 −0.0759161
\(677\) 5093.48 0.289156 0.144578 0.989493i \(-0.453818\pi\)
0.144578 + 0.989493i \(0.453818\pi\)
\(678\) 261.624 0.0148195
\(679\) 0 0
\(680\) −41.4346 −0.00233668
\(681\) 9548.75 0.537311
\(682\) 1790.56 0.100534
\(683\) 25619.5 1.43529 0.717645 0.696409i \(-0.245220\pi\)
0.717645 + 0.696409i \(0.245220\pi\)
\(684\) 793.872 0.0443779
\(685\) −8885.54 −0.495619
\(686\) 0 0
\(687\) −6944.94 −0.385685
\(688\) 429.476 0.0237989
\(689\) −3666.31 −0.202722
\(690\) 35.9635 0.00198422
\(691\) 31693.2 1.74482 0.872408 0.488778i \(-0.162557\pi\)
0.872408 + 0.488778i \(0.162557\pi\)
\(692\) 18209.5 1.00032
\(693\) 0 0
\(694\) 86.7245 0.00474354
\(695\) −15700.1 −0.856888
\(696\) 1122.76 0.0611465
\(697\) −320.237 −0.0174029
\(698\) 1644.65 0.0891845
\(699\) 8114.48 0.439081
\(700\) 0 0
\(701\) 2661.14 0.143381 0.0716905 0.997427i \(-0.477161\pi\)
0.0716905 + 0.997427i \(0.477161\pi\)
\(702\) 376.855 0.0202614
\(703\) 425.223 0.0228130
\(704\) 28732.3 1.53820
\(705\) −2540.19 −0.135701
\(706\) −3027.95 −0.161414
\(707\) 0 0
\(708\) 9387.99 0.498337
\(709\) −16745.3 −0.887000 −0.443500 0.896274i \(-0.646263\pi\)
−0.443500 + 0.896274i \(0.646263\pi\)
\(710\) 67.7981 0.00358369
\(711\) −19400.1 −1.02329
\(712\) −5623.65 −0.296005
\(713\) 970.250 0.0509623
\(714\) 0 0
\(715\) −4681.64 −0.244872
\(716\) 2869.21 0.149759
\(717\) 2926.59 0.152434
\(718\) −161.799 −0.00840986
\(719\) −7621.40 −0.395313 −0.197657 0.980271i \(-0.563333\pi\)
−0.197657 + 0.980271i \(0.563333\pi\)
\(720\) −8700.49 −0.450344
\(721\) 0 0
\(722\) −2213.93 −0.114119
\(723\) 5216.55 0.268334
\(724\) −30503.2 −1.56580
\(725\) −11158.9 −0.571627
\(726\) −1350.31 −0.0690287
\(727\) 33363.8 1.70206 0.851028 0.525120i \(-0.175979\pi\)
0.851028 + 0.525120i \(0.175979\pi\)
\(728\) 0 0
\(729\) −7402.29 −0.376075
\(730\) 2056.55 0.104269
\(731\) 9.50431 0.000480888 0
\(732\) −1217.14 −0.0614576
\(733\) 10628.8 0.535583 0.267791 0.963477i \(-0.413706\pi\)
0.267791 + 0.963477i \(0.413706\pi\)
\(734\) 891.465 0.0448291
\(735\) 0 0
\(736\) −651.401 −0.0326236
\(737\) −7466.79 −0.373192
\(738\) 1820.17 0.0907877
\(739\) 13321.7 0.663120 0.331560 0.943434i \(-0.392425\pi\)
0.331560 + 0.943434i \(0.392425\pi\)
\(740\) −4723.74 −0.234660
\(741\) −96.2352 −0.00477097
\(742\) 0 0
\(743\) −1456.36 −0.0719092 −0.0359546 0.999353i \(-0.511447\pi\)
−0.0359546 + 0.999353i \(0.511447\pi\)
\(744\) −823.179 −0.0405635
\(745\) 7792.20 0.383200
\(746\) −3046.63 −0.149524
\(747\) −26357.1 −1.29097
\(748\) 653.777 0.0319578
\(749\) 0 0
\(750\) 724.590 0.0352777
\(751\) −3929.23 −0.190918 −0.0954591 0.995433i \(-0.530432\pi\)
−0.0954591 + 0.995433i \(0.530432\pi\)
\(752\) 14997.9 0.727285
\(753\) −6129.48 −0.296641
\(754\) 521.794 0.0252024
\(755\) 12140.9 0.585235
\(756\) 0 0
\(757\) −27434.8 −1.31722 −0.658610 0.752484i \(-0.728855\pi\)
−0.658610 + 0.752484i \(0.728855\pi\)
\(758\) −3655.37 −0.175157
\(759\) −1142.43 −0.0546345
\(760\) −128.072 −0.00611269
\(761\) 19994.8 0.952445 0.476222 0.879325i \(-0.342006\pi\)
0.476222 + 0.879325i \(0.342006\pi\)
\(762\) −1465.75 −0.0696829
\(763\) 0 0
\(764\) 10296.1 0.487567
\(765\) −192.542 −0.00909982
\(766\) −85.9607 −0.00405468
\(767\) 8783.88 0.413517
\(768\) −6282.95 −0.295204
\(769\) 7948.30 0.372722 0.186361 0.982481i \(-0.440331\pi\)
0.186361 + 0.982481i \(0.440331\pi\)
\(770\) 0 0
\(771\) 8769.70 0.409641
\(772\) 765.297 0.0356783
\(773\) 21350.2 0.993418 0.496709 0.867917i \(-0.334542\pi\)
0.496709 + 0.867917i \(0.334542\pi\)
\(774\) −54.0208 −0.00250870
\(775\) 8181.42 0.379207
\(776\) 4690.55 0.216986
\(777\) 0 0
\(778\) 3754.24 0.173003
\(779\) −989.830 −0.0455255
\(780\) 1069.06 0.0490752
\(781\) −2153.70 −0.0986754
\(782\) −4.69903 −0.000214881 0
\(783\) 11110.6 0.507101
\(784\) 0 0
\(785\) −7775.58 −0.353532
\(786\) 341.473 0.0154961
\(787\) 20880.3 0.945744 0.472872 0.881131i \(-0.343217\pi\)
0.472872 + 0.881131i \(0.343217\pi\)
\(788\) 24752.4 1.11900
\(789\) −13045.4 −0.588627
\(790\) 1554.55 0.0700106
\(791\) 0 0
\(792\) −7481.20 −0.335647
\(793\) −1138.82 −0.0509972
\(794\) −2156.66 −0.0963941
\(795\) 2937.51 0.131047
\(796\) 27091.4 1.20632
\(797\) 40432.4 1.79697 0.898487 0.439001i \(-0.144668\pi\)
0.898487 + 0.439001i \(0.144668\pi\)
\(798\) 0 0
\(799\) 331.904 0.0146958
\(800\) −5492.80 −0.242750
\(801\) −26132.4 −1.15274
\(802\) 2548.15 0.112192
\(803\) −65329.0 −2.87100
\(804\) 1705.06 0.0747921
\(805\) 0 0
\(806\) −382.567 −0.0167188
\(807\) −13753.9 −0.599950
\(808\) −8787.74 −0.382614
\(809\) 19268.3 0.837376 0.418688 0.908130i \(-0.362490\pi\)
0.418688 + 0.908130i \(0.362490\pi\)
\(810\) 934.216 0.0405247
\(811\) 37223.2 1.61169 0.805846 0.592125i \(-0.201711\pi\)
0.805846 + 0.592125i \(0.201711\pi\)
\(812\) 0 0
\(813\) −1654.58 −0.0713758
\(814\) −1990.38 −0.0857037
\(815\) −10952.3 −0.470729
\(816\) −147.285 −0.00631864
\(817\) 29.3772 0.00125799
\(818\) 748.109 0.0319768
\(819\) 0 0
\(820\) 10995.9 0.468284
\(821\) −883.967 −0.0375769 −0.0187885 0.999823i \(-0.505981\pi\)
−0.0187885 + 0.999823i \(0.505981\pi\)
\(822\) 854.949 0.0362771
\(823\) 41410.5 1.75392 0.876961 0.480561i \(-0.159567\pi\)
0.876961 + 0.480561i \(0.159567\pi\)
\(824\) −4287.09 −0.181247
\(825\) −9633.29 −0.406531
\(826\) 0 0
\(827\) −37881.9 −1.59285 −0.796423 0.604739i \(-0.793277\pi\)
−0.796423 + 0.604739i \(0.793277\pi\)
\(828\) −2013.57 −0.0845124
\(829\) 4896.97 0.205161 0.102581 0.994725i \(-0.467290\pi\)
0.102581 + 0.994725i \(0.467290\pi\)
\(830\) 2112.03 0.0883247
\(831\) −1911.14 −0.0797795
\(832\) −6138.90 −0.255803
\(833\) 0 0
\(834\) 1510.63 0.0627203
\(835\) 6452.21 0.267411
\(836\) 2020.78 0.0836007
\(837\) −8146.03 −0.336401
\(838\) 1276.81 0.0526331
\(839\) −93.0019 −0.00382692 −0.00191346 0.999998i \(-0.500609\pi\)
−0.00191346 + 0.999998i \(0.500609\pi\)
\(840\) 0 0
\(841\) −9005.30 −0.369236
\(842\) −226.297 −0.00926212
\(843\) −144.251 −0.00589355
\(844\) −36310.4 −1.48087
\(845\) 1000.27 0.0407223
\(846\) −1886.48 −0.0766650
\(847\) 0 0
\(848\) −17343.8 −0.702345
\(849\) 14887.6 0.601815
\(850\) −39.6235 −0.00159891
\(851\) −1078.53 −0.0434448
\(852\) 491.803 0.0197757
\(853\) 8325.23 0.334174 0.167087 0.985942i \(-0.446564\pi\)
0.167087 + 0.985942i \(0.446564\pi\)
\(854\) 0 0
\(855\) −595.133 −0.0238048
\(856\) −1526.08 −0.0609348
\(857\) 3891.72 0.155121 0.0775606 0.996988i \(-0.475287\pi\)
0.0775606 + 0.996988i \(0.475287\pi\)
\(858\) 450.458 0.0179235
\(859\) −35346.9 −1.40398 −0.701991 0.712186i \(-0.747705\pi\)
−0.701991 + 0.712186i \(0.747705\pi\)
\(860\) −326.347 −0.0129399
\(861\) 0 0
\(862\) 4782.33 0.188964
\(863\) −21075.1 −0.831290 −0.415645 0.909527i \(-0.636444\pi\)
−0.415645 + 0.909527i \(0.636444\pi\)
\(864\) 5469.04 0.215348
\(865\) −13650.9 −0.536585
\(866\) −1364.73 −0.0535512
\(867\) 8642.61 0.338545
\(868\) 0 0
\(869\) −49382.4 −1.92771
\(870\) −418.070 −0.0162918
\(871\) 1595.34 0.0620621
\(872\) 10351.3 0.401996
\(873\) 21796.4 0.845014
\(874\) −14.5244 −0.000562122 0
\(875\) 0 0
\(876\) 14918.1 0.575382
\(877\) −47944.7 −1.84604 −0.923021 0.384751i \(-0.874287\pi\)
−0.923021 + 0.384751i \(0.874287\pi\)
\(878\) −2062.17 −0.0792651
\(879\) −6052.11 −0.232233
\(880\) −22146.9 −0.848376
\(881\) −37133.6 −1.42005 −0.710024 0.704178i \(-0.751316\pi\)
−0.710024 + 0.704178i \(0.751316\pi\)
\(882\) 0 0
\(883\) 1686.40 0.0642715 0.0321358 0.999484i \(-0.489769\pi\)
0.0321358 + 0.999484i \(0.489769\pi\)
\(884\) −139.685 −0.00531461
\(885\) −7037.79 −0.267314
\(886\) 2532.00 0.0960092
\(887\) −11389.6 −0.431146 −0.215573 0.976488i \(-0.569162\pi\)
−0.215573 + 0.976488i \(0.569162\pi\)
\(888\) 915.046 0.0345799
\(889\) 0 0
\(890\) 2094.02 0.0788672
\(891\) −29676.7 −1.11583
\(892\) −37657.0 −1.41351
\(893\) 1025.89 0.0384437
\(894\) −749.749 −0.0280485
\(895\) −2150.93 −0.0803325
\(896\) 0 0
\(897\) 244.090 0.00908576
\(898\) 1013.65 0.0376682
\(899\) −11279.0 −0.418437
\(900\) −16979.0 −0.628850
\(901\) −383.818 −0.0141918
\(902\) 4633.19 0.171029
\(903\) 0 0
\(904\) 2363.11 0.0869423
\(905\) 22867.0 0.839917
\(906\) −1168.17 −0.0428366
\(907\) −29663.9 −1.08597 −0.542985 0.839743i \(-0.682706\pi\)
−0.542985 + 0.839743i \(0.682706\pi\)
\(908\) 42840.2 1.56575
\(909\) −40835.6 −1.49002
\(910\) 0 0
\(911\) 16210.3 0.589541 0.294770 0.955568i \(-0.404757\pi\)
0.294770 + 0.955568i \(0.404757\pi\)
\(912\) −455.249 −0.0165294
\(913\) −67091.4 −2.43198
\(914\) 729.143 0.0263872
\(915\) 912.444 0.0329666
\(916\) −31158.3 −1.12391
\(917\) 0 0
\(918\) 39.4521 0.00141843
\(919\) −13025.5 −0.467542 −0.233771 0.972292i \(-0.575107\pi\)
−0.233771 + 0.972292i \(0.575107\pi\)
\(920\) 324.839 0.0116409
\(921\) −1894.41 −0.0677773
\(922\) 2965.90 0.105940
\(923\) 460.156 0.0164098
\(924\) 0 0
\(925\) −9094.46 −0.323269
\(926\) 2293.12 0.0813785
\(927\) −19921.6 −0.705837
\(928\) 7572.42 0.267863
\(929\) −46834.2 −1.65401 −0.827007 0.562192i \(-0.809958\pi\)
−0.827007 + 0.562192i \(0.809958\pi\)
\(930\) 306.519 0.0108077
\(931\) 0 0
\(932\) 36405.4 1.27951
\(933\) −12320.9 −0.432335
\(934\) −3616.03 −0.126681
\(935\) −490.110 −0.0171426
\(936\) 1598.42 0.0558184
\(937\) −24171.1 −0.842727 −0.421363 0.906892i \(-0.638448\pi\)
−0.421363 + 0.906892i \(0.638448\pi\)
\(938\) 0 0
\(939\) −13078.1 −0.454513
\(940\) −11396.5 −0.395439
\(941\) 32410.4 1.12279 0.561397 0.827547i \(-0.310264\pi\)
0.561397 + 0.827547i \(0.310264\pi\)
\(942\) 748.150 0.0258769
\(943\) 2510.59 0.0866979
\(944\) 41552.9 1.43266
\(945\) 0 0
\(946\) −137.509 −0.00472599
\(947\) −36285.0 −1.24509 −0.622547 0.782582i \(-0.713902\pi\)
−0.622547 + 0.782582i \(0.713902\pi\)
\(948\) 11276.6 0.386336
\(949\) 13958.1 0.477449
\(950\) −122.474 −0.00418271
\(951\) 12637.8 0.430924
\(952\) 0 0
\(953\) 31851.1 1.08264 0.541321 0.840816i \(-0.317924\pi\)
0.541321 + 0.840816i \(0.317924\pi\)
\(954\) 2181.55 0.0740360
\(955\) −7718.60 −0.261537
\(956\) 13130.1 0.444202
\(957\) 13280.5 0.448588
\(958\) −2666.68 −0.0899336
\(959\) 0 0
\(960\) 4918.59 0.165361
\(961\) −21521.5 −0.722416
\(962\) 425.261 0.0142526
\(963\) −7091.50 −0.237300
\(964\) 23403.9 0.781939
\(965\) −573.712 −0.0191383
\(966\) 0 0
\(967\) 455.696 0.0151543 0.00757714 0.999971i \(-0.497588\pi\)
0.00757714 + 0.999971i \(0.497588\pi\)
\(968\) −12196.7 −0.404975
\(969\) −10.0746 −0.000333998 0
\(970\) −1746.57 −0.0578135
\(971\) −10641.2 −0.351690 −0.175845 0.984418i \(-0.556266\pi\)
−0.175845 + 0.984418i \(0.556266\pi\)
\(972\) 25872.5 0.853767
\(973\) 0 0
\(974\) −3225.64 −0.106115
\(975\) 2058.23 0.0676064
\(976\) −5387.30 −0.176684
\(977\) 19412.9 0.635694 0.317847 0.948142i \(-0.397040\pi\)
0.317847 + 0.948142i \(0.397040\pi\)
\(978\) 1053.81 0.0344552
\(979\) −66519.5 −2.17158
\(980\) 0 0
\(981\) 48101.4 1.56551
\(982\) 3669.69 0.119251
\(983\) −44913.0 −1.45728 −0.728639 0.684898i \(-0.759847\pi\)
−0.728639 + 0.684898i \(0.759847\pi\)
\(984\) −2130.04 −0.0690072
\(985\) −18555.9 −0.600243
\(986\) 54.6254 0.00176433
\(987\) 0 0
\(988\) −431.757 −0.0139029
\(989\) −74.5119 −0.00239569
\(990\) 2785.70 0.0894296
\(991\) 36377.2 1.16605 0.583027 0.812453i \(-0.301868\pi\)
0.583027 + 0.812453i \(0.301868\pi\)
\(992\) −5551.93 −0.177695
\(993\) 6586.79 0.210499
\(994\) 0 0
\(995\) −20309.3 −0.647083
\(996\) 15320.5 0.487398
\(997\) −6366.39 −0.202232 −0.101116 0.994875i \(-0.532241\pi\)
−0.101116 + 0.994875i \(0.532241\pi\)
\(998\) 2592.46 0.0822274
\(999\) 9055.12 0.286778
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 637.4.a.d.1.3 4
7.6 odd 2 91.4.a.b.1.3 4
21.20 even 2 819.4.a.h.1.2 4
28.27 even 2 1456.4.a.s.1.2 4
35.34 odd 2 2275.4.a.h.1.2 4
91.90 odd 2 1183.4.a.e.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.4.a.b.1.3 4 7.6 odd 2
637.4.a.d.1.3 4 1.1 even 1 trivial
819.4.a.h.1.2 4 21.20 even 2
1183.4.a.e.1.2 4 91.90 odd 2
1456.4.a.s.1.2 4 28.27 even 2
2275.4.a.h.1.2 4 35.34 odd 2