Properties

Label 966.4.a.f.1.3
Level $966$
Weight $4$
Character 966.1
Self dual yes
Analytic conductor $56.996$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 966.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.9958450655\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.12197.1
Defining polynomial: \( x^{3} - x^{2} - 15x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-3.24392\) of defining polynomial
Character \(\chi\) \(=\) 966.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +13.7318 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +13.7318 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +27.4635 q^{10} +45.9053 q^{11} -12.0000 q^{12} +5.45531 q^{13} +14.0000 q^{14} -41.1953 q^{15} +16.0000 q^{16} +39.2521 q^{17} +18.0000 q^{18} +27.3958 q^{19} +54.9270 q^{20} -21.0000 q^{21} +91.8107 q^{22} -23.0000 q^{23} -24.0000 q^{24} +63.5611 q^{25} +10.9106 q^{26} -27.0000 q^{27} +28.0000 q^{28} +9.12126 q^{29} -82.3905 q^{30} +29.6741 q^{31} +32.0000 q^{32} -137.716 q^{33} +78.5042 q^{34} +96.1223 q^{35} +36.0000 q^{36} +350.619 q^{37} +54.7916 q^{38} -16.3659 q^{39} +109.854 q^{40} -445.765 q^{41} -42.0000 q^{42} -447.238 q^{43} +183.621 q^{44} +123.586 q^{45} -46.0000 q^{46} +585.065 q^{47} -48.0000 q^{48} +49.0000 q^{49} +127.122 q^{50} -117.756 q^{51} +21.8212 q^{52} -595.290 q^{53} -54.0000 q^{54} +630.361 q^{55} +56.0000 q^{56} -82.1874 q^{57} +18.2425 q^{58} -365.737 q^{59} -164.781 q^{60} +629.292 q^{61} +59.3483 q^{62} +63.0000 q^{63} +64.0000 q^{64} +74.9110 q^{65} -275.432 q^{66} -150.031 q^{67} +157.008 q^{68} +69.0000 q^{69} +192.245 q^{70} -125.507 q^{71} +72.0000 q^{72} -702.089 q^{73} +701.238 q^{74} -190.683 q^{75} +109.583 q^{76} +321.337 q^{77} -32.7319 q^{78} +783.124 q^{79} +219.708 q^{80} +81.0000 q^{81} -891.530 q^{82} +744.142 q^{83} -84.0000 q^{84} +539.000 q^{85} -894.476 q^{86} -27.3638 q^{87} +367.243 q^{88} -40.6181 q^{89} +247.172 q^{90} +38.1872 q^{91} -92.0000 q^{92} -89.0224 q^{93} +1170.13 q^{94} +376.193 q^{95} -96.0000 q^{96} +394.706 q^{97} +98.0000 q^{98} +413.148 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 9 q^{5} - 18 q^{6} + 21 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 9 q^{5} - 18 q^{6} + 21 q^{7} + 24 q^{8} + 27 q^{9} + 18 q^{10} + 53 q^{11} - 36 q^{12} + 61 q^{13} + 42 q^{14} - 27 q^{15} + 48 q^{16} - 2 q^{17} + 54 q^{18} + 63 q^{19} + 36 q^{20} - 63 q^{21} + 106 q^{22} - 69 q^{23} - 72 q^{24} - 72 q^{25} + 122 q^{26} - 81 q^{27} + 84 q^{28} + 312 q^{29} - 54 q^{30} + 220 q^{31} + 96 q^{32} - 159 q^{33} - 4 q^{34} + 63 q^{35} + 108 q^{36} - 44 q^{37} + 126 q^{38} - 183 q^{39} + 72 q^{40} + 171 q^{41} - 126 q^{42} - 627 q^{43} + 212 q^{44} + 81 q^{45} - 138 q^{46} + 353 q^{47} - 144 q^{48} + 147 q^{49} - 144 q^{50} + 6 q^{51} + 244 q^{52} - 504 q^{53} - 162 q^{54} + 1181 q^{55} + 168 q^{56} - 189 q^{57} + 624 q^{58} + 538 q^{59} - 108 q^{60} + 256 q^{61} + 440 q^{62} + 189 q^{63} + 192 q^{64} + 244 q^{65} - 318 q^{66} + 1113 q^{67} - 8 q^{68} + 207 q^{69} + 126 q^{70} + 53 q^{71} + 216 q^{72} + 360 q^{73} - 88 q^{74} + 216 q^{75} + 252 q^{76} + 371 q^{77} - 366 q^{78} + 134 q^{79} + 144 q^{80} + 243 q^{81} + 342 q^{82} + 1506 q^{83} - 252 q^{84} + 577 q^{85} - 1254 q^{86} - 936 q^{87} + 424 q^{88} + 2381 q^{89} + 162 q^{90} + 427 q^{91} - 276 q^{92} - 660 q^{93} + 706 q^{94} + 945 q^{95} - 288 q^{96} - 88 q^{97} + 294 q^{98} + 477 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) −3.00000 −0.577350
\(4\) 4.00000 0.500000
\(5\) 13.7318 1.22821 0.614103 0.789226i \(-0.289518\pi\)
0.614103 + 0.789226i \(0.289518\pi\)
\(6\) −6.00000 −0.408248
\(7\) 7.00000 0.377964
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) 27.4635 0.868472
\(11\) 45.9053 1.25827 0.629135 0.777296i \(-0.283409\pi\)
0.629135 + 0.777296i \(0.283409\pi\)
\(12\) −12.0000 −0.288675
\(13\) 5.45531 0.116387 0.0581935 0.998305i \(-0.481466\pi\)
0.0581935 + 0.998305i \(0.481466\pi\)
\(14\) 14.0000 0.267261
\(15\) −41.1953 −0.709105
\(16\) 16.0000 0.250000
\(17\) 39.2521 0.560002 0.280001 0.960000i \(-0.409665\pi\)
0.280001 + 0.960000i \(0.409665\pi\)
\(18\) 18.0000 0.235702
\(19\) 27.3958 0.330791 0.165396 0.986227i \(-0.447110\pi\)
0.165396 + 0.986227i \(0.447110\pi\)
\(20\) 54.9270 0.614103
\(21\) −21.0000 −0.218218
\(22\) 91.8107 0.889732
\(23\) −23.0000 −0.208514
\(24\) −24.0000 −0.204124
\(25\) 63.5611 0.508489
\(26\) 10.9106 0.0822981
\(27\) −27.0000 −0.192450
\(28\) 28.0000 0.188982
\(29\) 9.12126 0.0584060 0.0292030 0.999574i \(-0.490703\pi\)
0.0292030 + 0.999574i \(0.490703\pi\)
\(30\) −82.3905 −0.501413
\(31\) 29.6741 0.171924 0.0859618 0.996298i \(-0.472604\pi\)
0.0859618 + 0.996298i \(0.472604\pi\)
\(32\) 32.0000 0.176777
\(33\) −137.716 −0.726463
\(34\) 78.5042 0.395981
\(35\) 96.1223 0.464218
\(36\) 36.0000 0.166667
\(37\) 350.619 1.55788 0.778938 0.627101i \(-0.215759\pi\)
0.778938 + 0.627101i \(0.215759\pi\)
\(38\) 54.7916 0.233905
\(39\) −16.3659 −0.0671961
\(40\) 109.854 0.434236
\(41\) −445.765 −1.69797 −0.848985 0.528417i \(-0.822786\pi\)
−0.848985 + 0.528417i \(0.822786\pi\)
\(42\) −42.0000 −0.154303
\(43\) −447.238 −1.58612 −0.793060 0.609144i \(-0.791513\pi\)
−0.793060 + 0.609144i \(0.791513\pi\)
\(44\) 183.621 0.629135
\(45\) 123.586 0.409402
\(46\) −46.0000 −0.147442
\(47\) 585.065 1.81576 0.907878 0.419235i \(-0.137702\pi\)
0.907878 + 0.419235i \(0.137702\pi\)
\(48\) −48.0000 −0.144338
\(49\) 49.0000 0.142857
\(50\) 127.122 0.359556
\(51\) −117.756 −0.323317
\(52\) 21.8212 0.0581935
\(53\) −595.290 −1.54282 −0.771409 0.636340i \(-0.780448\pi\)
−0.771409 + 0.636340i \(0.780448\pi\)
\(54\) −54.0000 −0.136083
\(55\) 630.361 1.54542
\(56\) 56.0000 0.133631
\(57\) −82.1874 −0.190982
\(58\) 18.2425 0.0412993
\(59\) −365.737 −0.807031 −0.403516 0.914973i \(-0.632212\pi\)
−0.403516 + 0.914973i \(0.632212\pi\)
\(60\) −164.781 −0.354552
\(61\) 629.292 1.32086 0.660431 0.750887i \(-0.270374\pi\)
0.660431 + 0.750887i \(0.270374\pi\)
\(62\) 59.3483 0.121568
\(63\) 63.0000 0.125988
\(64\) 64.0000 0.125000
\(65\) 74.9110 0.142947
\(66\) −275.432 −0.513687
\(67\) −150.031 −0.273569 −0.136785 0.990601i \(-0.543677\pi\)
−0.136785 + 0.990601i \(0.543677\pi\)
\(68\) 157.008 0.280001
\(69\) 69.0000 0.120386
\(70\) 192.245 0.328252
\(71\) −125.507 −0.209788 −0.104894 0.994483i \(-0.533450\pi\)
−0.104894 + 0.994483i \(0.533450\pi\)
\(72\) 72.0000 0.117851
\(73\) −702.089 −1.12566 −0.562831 0.826572i \(-0.690288\pi\)
−0.562831 + 0.826572i \(0.690288\pi\)
\(74\) 701.238 1.10158
\(75\) −190.683 −0.293576
\(76\) 109.583 0.165396
\(77\) 321.337 0.475582
\(78\) −32.7319 −0.0475148
\(79\) 783.124 1.11530 0.557648 0.830078i \(-0.311704\pi\)
0.557648 + 0.830078i \(0.311704\pi\)
\(80\) 219.708 0.307051
\(81\) 81.0000 0.111111
\(82\) −891.530 −1.20065
\(83\) 744.142 0.984098 0.492049 0.870567i \(-0.336248\pi\)
0.492049 + 0.870567i \(0.336248\pi\)
\(84\) −84.0000 −0.109109
\(85\) 539.000 0.687798
\(86\) −894.476 −1.12156
\(87\) −27.3638 −0.0337207
\(88\) 367.243 0.444866
\(89\) −40.6181 −0.0483766 −0.0241883 0.999707i \(-0.507700\pi\)
−0.0241883 + 0.999707i \(0.507700\pi\)
\(90\) 247.172 0.289491
\(91\) 38.1872 0.0439902
\(92\) −92.0000 −0.104257
\(93\) −89.0224 −0.0992602
\(94\) 1170.13 1.28393
\(95\) 376.193 0.406279
\(96\) −96.0000 −0.102062
\(97\) 394.706 0.413158 0.206579 0.978430i \(-0.433767\pi\)
0.206579 + 0.978430i \(0.433767\pi\)
\(98\) 98.0000 0.101015
\(99\) 413.148 0.419424
\(100\) 254.244 0.254244
\(101\) 749.885 0.738775 0.369388 0.929275i \(-0.379567\pi\)
0.369388 + 0.929275i \(0.379567\pi\)
\(102\) −235.513 −0.228620
\(103\) 332.501 0.318081 0.159040 0.987272i \(-0.449160\pi\)
0.159040 + 0.987272i \(0.449160\pi\)
\(104\) 43.6425 0.0411490
\(105\) −288.367 −0.268016
\(106\) −1190.58 −1.09094
\(107\) 1755.87 1.58641 0.793206 0.608954i \(-0.208411\pi\)
0.793206 + 0.608954i \(0.208411\pi\)
\(108\) −108.000 −0.0962250
\(109\) 798.305 0.701502 0.350751 0.936469i \(-0.385926\pi\)
0.350751 + 0.936469i \(0.385926\pi\)
\(110\) 1260.72 1.09277
\(111\) −1051.86 −0.899440
\(112\) 112.000 0.0944911
\(113\) −544.067 −0.452934 −0.226467 0.974019i \(-0.572717\pi\)
−0.226467 + 0.974019i \(0.572717\pi\)
\(114\) −164.375 −0.135045
\(115\) −315.830 −0.256099
\(116\) 36.4850 0.0292030
\(117\) 49.0978 0.0387957
\(118\) −731.473 −0.570657
\(119\) 274.765 0.211661
\(120\) −329.562 −0.250706
\(121\) 776.300 0.583246
\(122\) 1258.58 0.933990
\(123\) 1337.29 0.980324
\(124\) 118.697 0.0859618
\(125\) −843.664 −0.603677
\(126\) 126.000 0.0890871
\(127\) −1.40468 −0.000981457 0 −0.000490729 1.00000i \(-0.500156\pi\)
−0.000490729 1.00000i \(0.500156\pi\)
\(128\) 128.000 0.0883883
\(129\) 1341.71 0.915747
\(130\) 149.822 0.101079
\(131\) −2194.78 −1.46380 −0.731902 0.681410i \(-0.761367\pi\)
−0.731902 + 0.681410i \(0.761367\pi\)
\(132\) −550.864 −0.363232
\(133\) 191.771 0.125027
\(134\) −300.061 −0.193443
\(135\) −370.757 −0.236368
\(136\) 314.017 0.197991
\(137\) −1234.48 −0.769843 −0.384921 0.922949i \(-0.625771\pi\)
−0.384921 + 0.922949i \(0.625771\pi\)
\(138\) 138.000 0.0851257
\(139\) −838.469 −0.511640 −0.255820 0.966724i \(-0.582346\pi\)
−0.255820 + 0.966724i \(0.582346\pi\)
\(140\) 384.489 0.232109
\(141\) −1755.19 −1.04833
\(142\) −251.014 −0.148342
\(143\) 250.428 0.146446
\(144\) 144.000 0.0833333
\(145\) 125.251 0.0717346
\(146\) −1404.18 −0.795963
\(147\) −147.000 −0.0824786
\(148\) 1402.48 0.778938
\(149\) 609.791 0.335275 0.167638 0.985849i \(-0.446386\pi\)
0.167638 + 0.985849i \(0.446386\pi\)
\(150\) −381.366 −0.207590
\(151\) 2067.33 1.11415 0.557075 0.830462i \(-0.311924\pi\)
0.557075 + 0.830462i \(0.311924\pi\)
\(152\) 219.167 0.116952
\(153\) 353.269 0.186667
\(154\) 642.675 0.336287
\(155\) 407.478 0.211158
\(156\) −65.4637 −0.0335980
\(157\) 3476.30 1.76713 0.883563 0.468312i \(-0.155138\pi\)
0.883563 + 0.468312i \(0.155138\pi\)
\(158\) 1566.25 0.788633
\(159\) 1785.87 0.890746
\(160\) 439.416 0.217118
\(161\) −161.000 −0.0788110
\(162\) 162.000 0.0785674
\(163\) −1070.77 −0.514535 −0.257267 0.966340i \(-0.582822\pi\)
−0.257267 + 0.966340i \(0.582822\pi\)
\(164\) −1783.06 −0.848985
\(165\) −1891.08 −0.892246
\(166\) 1488.28 0.695863
\(167\) 2373.54 1.09982 0.549909 0.835224i \(-0.314662\pi\)
0.549909 + 0.835224i \(0.314662\pi\)
\(168\) −168.000 −0.0771517
\(169\) −2167.24 −0.986454
\(170\) 1078.00 0.486346
\(171\) 246.562 0.110264
\(172\) −1788.95 −0.793060
\(173\) 451.372 0.198365 0.0991825 0.995069i \(-0.468377\pi\)
0.0991825 + 0.995069i \(0.468377\pi\)
\(174\) −54.7275 −0.0238442
\(175\) 444.928 0.192191
\(176\) 734.485 0.314568
\(177\) 1097.21 0.465940
\(178\) −81.2363 −0.0342074
\(179\) 1.91608 0.000800081 0 0.000400041 1.00000i \(-0.499873\pi\)
0.000400041 1.00000i \(0.499873\pi\)
\(180\) 494.343 0.204701
\(181\) 3796.95 1.55925 0.779627 0.626245i \(-0.215409\pi\)
0.779627 + 0.626245i \(0.215409\pi\)
\(182\) 76.3744 0.0311057
\(183\) −1887.88 −0.762600
\(184\) −184.000 −0.0737210
\(185\) 4814.61 1.91339
\(186\) −178.045 −0.0701875
\(187\) 1801.88 0.704634
\(188\) 2340.26 0.907878
\(189\) −189.000 −0.0727393
\(190\) 752.385 0.287283
\(191\) 3450.82 1.30729 0.653646 0.756800i \(-0.273238\pi\)
0.653646 + 0.756800i \(0.273238\pi\)
\(192\) −192.000 −0.0721688
\(193\) −3555.01 −1.32588 −0.662941 0.748672i \(-0.730692\pi\)
−0.662941 + 0.748672i \(0.730692\pi\)
\(194\) 789.411 0.292146
\(195\) −224.733 −0.0825306
\(196\) 196.000 0.0714286
\(197\) −1324.72 −0.479098 −0.239549 0.970884i \(-0.577000\pi\)
−0.239549 + 0.970884i \(0.577000\pi\)
\(198\) 826.296 0.296577
\(199\) −1475.79 −0.525708 −0.262854 0.964836i \(-0.584664\pi\)
−0.262854 + 0.964836i \(0.584664\pi\)
\(200\) 508.489 0.179778
\(201\) 450.092 0.157945
\(202\) 1499.77 0.522393
\(203\) 63.8488 0.0220754
\(204\) −471.025 −0.161659
\(205\) −6121.13 −2.08546
\(206\) 665.003 0.224917
\(207\) −207.000 −0.0695048
\(208\) 87.2850 0.0290968
\(209\) 1257.61 0.416225
\(210\) −576.734 −0.189516
\(211\) 585.617 0.191069 0.0955345 0.995426i \(-0.469544\pi\)
0.0955345 + 0.995426i \(0.469544\pi\)
\(212\) −2381.16 −0.771409
\(213\) 376.521 0.121121
\(214\) 3511.73 1.12176
\(215\) −6141.36 −1.94808
\(216\) −216.000 −0.0680414
\(217\) 207.719 0.0649810
\(218\) 1596.61 0.496037
\(219\) 2106.27 0.649901
\(220\) 2521.44 0.772708
\(221\) 214.133 0.0651770
\(222\) −2103.71 −0.636000
\(223\) 3068.81 0.921536 0.460768 0.887521i \(-0.347574\pi\)
0.460768 + 0.887521i \(0.347574\pi\)
\(224\) 224.000 0.0668153
\(225\) 572.050 0.169496
\(226\) −1088.13 −0.320272
\(227\) 4555.53 1.33199 0.665994 0.745957i \(-0.268008\pi\)
0.665994 + 0.745957i \(0.268008\pi\)
\(228\) −328.750 −0.0954912
\(229\) −3835.82 −1.10689 −0.553446 0.832885i \(-0.686688\pi\)
−0.553446 + 0.832885i \(0.686688\pi\)
\(230\) −631.661 −0.181089
\(231\) −964.012 −0.274577
\(232\) 72.9700 0.0206496
\(233\) −544.549 −0.153110 −0.0765549 0.997065i \(-0.524392\pi\)
−0.0765549 + 0.997065i \(0.524392\pi\)
\(234\) 98.1956 0.0274327
\(235\) 8033.97 2.23012
\(236\) −1462.95 −0.403516
\(237\) −2349.37 −0.643916
\(238\) 549.530 0.149667
\(239\) −6593.05 −1.78439 −0.892194 0.451652i \(-0.850835\pi\)
−0.892194 + 0.451652i \(0.850835\pi\)
\(240\) −659.124 −0.177276
\(241\) −742.035 −0.198335 −0.0991674 0.995071i \(-0.531618\pi\)
−0.0991674 + 0.995071i \(0.531618\pi\)
\(242\) 1552.60 0.412417
\(243\) −243.000 −0.0641500
\(244\) 2517.17 0.660431
\(245\) 672.856 0.175458
\(246\) 2674.59 0.693194
\(247\) 149.453 0.0384998
\(248\) 237.393 0.0607842
\(249\) −2232.42 −0.568169
\(250\) −1687.33 −0.426864
\(251\) 3887.66 0.977638 0.488819 0.872385i \(-0.337428\pi\)
0.488819 + 0.872385i \(0.337428\pi\)
\(252\) 252.000 0.0629941
\(253\) −1055.82 −0.262368
\(254\) −2.80936 −0.000693995 0
\(255\) −1617.00 −0.397100
\(256\) 256.000 0.0625000
\(257\) −5919.83 −1.43684 −0.718422 0.695607i \(-0.755135\pi\)
−0.718422 + 0.695607i \(0.755135\pi\)
\(258\) 2683.43 0.647531
\(259\) 2454.33 0.588821
\(260\) 299.644 0.0714736
\(261\) 82.0913 0.0194687
\(262\) −4389.55 −1.03507
\(263\) −5378.10 −1.26094 −0.630471 0.776213i \(-0.717138\pi\)
−0.630471 + 0.776213i \(0.717138\pi\)
\(264\) −1101.73 −0.256843
\(265\) −8174.37 −1.89490
\(266\) 383.541 0.0884076
\(267\) 121.854 0.0279302
\(268\) −600.122 −0.136785
\(269\) 563.438 0.127708 0.0638539 0.997959i \(-0.479661\pi\)
0.0638539 + 0.997959i \(0.479661\pi\)
\(270\) −741.515 −0.167138
\(271\) −8229.05 −1.84457 −0.922286 0.386507i \(-0.873681\pi\)
−0.922286 + 0.386507i \(0.873681\pi\)
\(272\) 628.034 0.140001
\(273\) −114.562 −0.0253977
\(274\) −2468.95 −0.544361
\(275\) 2917.79 0.639816
\(276\) 276.000 0.0601929
\(277\) −7056.39 −1.53060 −0.765302 0.643671i \(-0.777410\pi\)
−0.765302 + 0.643671i \(0.777410\pi\)
\(278\) −1676.94 −0.361784
\(279\) 267.067 0.0573079
\(280\) 768.978 0.164126
\(281\) 2775.63 0.589252 0.294626 0.955613i \(-0.404805\pi\)
0.294626 + 0.955613i \(0.404805\pi\)
\(282\) −3510.39 −0.741279
\(283\) −2283.10 −0.479562 −0.239781 0.970827i \(-0.577076\pi\)
−0.239781 + 0.970827i \(0.577076\pi\)
\(284\) −502.028 −0.104894
\(285\) −1128.58 −0.234566
\(286\) 500.856 0.103553
\(287\) −3120.35 −0.641773
\(288\) 288.000 0.0589256
\(289\) −3372.27 −0.686398
\(290\) 250.502 0.0507240
\(291\) −1184.12 −0.238537
\(292\) −2808.35 −0.562831
\(293\) −1830.89 −0.365056 −0.182528 0.983201i \(-0.558428\pi\)
−0.182528 + 0.983201i \(0.558428\pi\)
\(294\) −294.000 −0.0583212
\(295\) −5022.21 −0.991200
\(296\) 2804.95 0.550792
\(297\) −1239.44 −0.242154
\(298\) 1219.58 0.237075
\(299\) −125.472 −0.0242684
\(300\) −762.733 −0.146788
\(301\) −3130.67 −0.599497
\(302\) 4134.65 0.787823
\(303\) −2249.65 −0.426532
\(304\) 438.333 0.0826978
\(305\) 8641.28 1.62229
\(306\) 706.538 0.131994
\(307\) −52.1972 −0.00970375 −0.00485187 0.999988i \(-0.501544\pi\)
−0.00485187 + 0.999988i \(0.501544\pi\)
\(308\) 1285.35 0.237791
\(309\) −997.504 −0.183644
\(310\) 814.956 0.149311
\(311\) 5264.42 0.959864 0.479932 0.877306i \(-0.340661\pi\)
0.479932 + 0.877306i \(0.340661\pi\)
\(312\) −130.927 −0.0237574
\(313\) 3816.63 0.689230 0.344615 0.938744i \(-0.388010\pi\)
0.344615 + 0.938744i \(0.388010\pi\)
\(314\) 6952.60 1.24955
\(315\) 865.101 0.154739
\(316\) 3132.50 0.557648
\(317\) −11060.4 −1.95966 −0.979831 0.199827i \(-0.935962\pi\)
−0.979831 + 0.199827i \(0.935962\pi\)
\(318\) 3571.74 0.629853
\(319\) 418.714 0.0734906
\(320\) 878.832 0.153526
\(321\) −5267.60 −0.915915
\(322\) −322.000 −0.0557278
\(323\) 1075.34 0.185244
\(324\) 324.000 0.0555556
\(325\) 346.746 0.0591815
\(326\) −2141.54 −0.363831
\(327\) −2394.91 −0.405012
\(328\) −3566.12 −0.600323
\(329\) 4095.45 0.686291
\(330\) −3782.16 −0.630913
\(331\) 6972.73 1.15787 0.578936 0.815373i \(-0.303468\pi\)
0.578936 + 0.815373i \(0.303468\pi\)
\(332\) 2976.57 0.492049
\(333\) 3155.57 0.519292
\(334\) 4747.07 0.777689
\(335\) −2060.18 −0.335999
\(336\) −336.000 −0.0545545
\(337\) −9451.07 −1.52769 −0.763846 0.645398i \(-0.776692\pi\)
−0.763846 + 0.645398i \(0.776692\pi\)
\(338\) −4334.48 −0.697528
\(339\) 1632.20 0.261501
\(340\) 2156.00 0.343899
\(341\) 1362.20 0.216327
\(342\) 493.125 0.0779682
\(343\) 343.000 0.0539949
\(344\) −3577.90 −0.560778
\(345\) 947.491 0.147859
\(346\) 902.743 0.140265
\(347\) 1404.40 0.217269 0.108634 0.994082i \(-0.465352\pi\)
0.108634 + 0.994082i \(0.465352\pi\)
\(348\) −109.455 −0.0168604
\(349\) −4669.60 −0.716211 −0.358106 0.933681i \(-0.616577\pi\)
−0.358106 + 0.933681i \(0.616577\pi\)
\(350\) 889.855 0.135899
\(351\) −147.293 −0.0223987
\(352\) 1468.97 0.222433
\(353\) −6282.45 −0.947255 −0.473627 0.880725i \(-0.657056\pi\)
−0.473627 + 0.880725i \(0.657056\pi\)
\(354\) 2194.42 0.329469
\(355\) −1723.43 −0.257663
\(356\) −162.473 −0.0241883
\(357\) −824.294 −0.122202
\(358\) 3.83216 0.000565743 0
\(359\) −8274.06 −1.21640 −0.608200 0.793783i \(-0.708108\pi\)
−0.608200 + 0.793783i \(0.708108\pi\)
\(360\) 988.686 0.144745
\(361\) −6108.47 −0.890577
\(362\) 7593.89 1.10256
\(363\) −2328.90 −0.336737
\(364\) 152.749 0.0219951
\(365\) −9640.91 −1.38254
\(366\) −3775.75 −0.539239
\(367\) −205.888 −0.0292841 −0.0146421 0.999893i \(-0.504661\pi\)
−0.0146421 + 0.999893i \(0.504661\pi\)
\(368\) −368.000 −0.0521286
\(369\) −4011.88 −0.565990
\(370\) 9629.22 1.35297
\(371\) −4167.03 −0.583130
\(372\) −356.090 −0.0496301
\(373\) 152.876 0.0212215 0.0106107 0.999944i \(-0.496622\pi\)
0.0106107 + 0.999944i \(0.496622\pi\)
\(374\) 3603.76 0.498252
\(375\) 2530.99 0.348533
\(376\) 4680.52 0.641966
\(377\) 49.7593 0.00679770
\(378\) −378.000 −0.0514344
\(379\) −11194.5 −1.51721 −0.758603 0.651553i \(-0.774118\pi\)
−0.758603 + 0.651553i \(0.774118\pi\)
\(380\) 1504.77 0.203140
\(381\) 4.21404 0.000566645 0
\(382\) 6901.65 0.924395
\(383\) 3885.85 0.518427 0.259214 0.965820i \(-0.416537\pi\)
0.259214 + 0.965820i \(0.416537\pi\)
\(384\) −384.000 −0.0510310
\(385\) 4412.53 0.584112
\(386\) −7110.02 −0.937540
\(387\) −4025.14 −0.528707
\(388\) 1578.82 0.206579
\(389\) 6311.77 0.822671 0.411336 0.911484i \(-0.365062\pi\)
0.411336 + 0.911484i \(0.365062\pi\)
\(390\) −449.466 −0.0583579
\(391\) −902.799 −0.116769
\(392\) 392.000 0.0505076
\(393\) 6584.33 0.845128
\(394\) −2649.44 −0.338773
\(395\) 10753.7 1.36981
\(396\) 1652.59 0.209712
\(397\) −8255.41 −1.04365 −0.521823 0.853054i \(-0.674748\pi\)
−0.521823 + 0.853054i \(0.674748\pi\)
\(398\) −2951.58 −0.371732
\(399\) −575.312 −0.0721845
\(400\) 1016.98 0.127122
\(401\) −12951.5 −1.61288 −0.806441 0.591315i \(-0.798609\pi\)
−0.806441 + 0.591315i \(0.798609\pi\)
\(402\) 900.183 0.111684
\(403\) 161.882 0.0200097
\(404\) 2999.54 0.369388
\(405\) 1112.27 0.136467
\(406\) 127.698 0.0156097
\(407\) 16095.3 1.96023
\(408\) −942.051 −0.114310
\(409\) 3097.26 0.374449 0.187225 0.982317i \(-0.440051\pi\)
0.187225 + 0.982317i \(0.440051\pi\)
\(410\) −12242.3 −1.47464
\(411\) 3703.43 0.444469
\(412\) 1330.01 0.159040
\(413\) −2560.16 −0.305029
\(414\) −414.000 −0.0491473
\(415\) 10218.4 1.20867
\(416\) 174.570 0.0205745
\(417\) 2515.41 0.295396
\(418\) 2515.23 0.294315
\(419\) 6368.21 0.742500 0.371250 0.928533i \(-0.378929\pi\)
0.371250 + 0.928533i \(0.378929\pi\)
\(420\) −1153.47 −0.134008
\(421\) 284.879 0.0329790 0.0164895 0.999864i \(-0.494751\pi\)
0.0164895 + 0.999864i \(0.494751\pi\)
\(422\) 1171.23 0.135106
\(423\) 5265.58 0.605252
\(424\) −4762.32 −0.545468
\(425\) 2494.91 0.284755
\(426\) 753.042 0.0856456
\(427\) 4405.04 0.499239
\(428\) 7023.47 0.793206
\(429\) −751.284 −0.0845509
\(430\) −12282.7 −1.37750
\(431\) 6676.27 0.746136 0.373068 0.927804i \(-0.378306\pi\)
0.373068 + 0.927804i \(0.378306\pi\)
\(432\) −432.000 −0.0481125
\(433\) −6732.35 −0.747197 −0.373598 0.927591i \(-0.621876\pi\)
−0.373598 + 0.927591i \(0.621876\pi\)
\(434\) 415.438 0.0459485
\(435\) −375.753 −0.0414160
\(436\) 3193.22 0.350751
\(437\) −630.104 −0.0689747
\(438\) 4212.53 0.459549
\(439\) 6792.07 0.738424 0.369212 0.929345i \(-0.379628\pi\)
0.369212 + 0.929345i \(0.379628\pi\)
\(440\) 5042.89 0.546387
\(441\) 441.000 0.0476190
\(442\) 428.265 0.0460871
\(443\) −11163.4 −1.19726 −0.598631 0.801025i \(-0.704289\pi\)
−0.598631 + 0.801025i \(0.704289\pi\)
\(444\) −4207.43 −0.449720
\(445\) −557.758 −0.0594164
\(446\) 6137.61 0.651624
\(447\) −1829.37 −0.193571
\(448\) 448.000 0.0472456
\(449\) 9879.67 1.03842 0.519210 0.854647i \(-0.326226\pi\)
0.519210 + 0.854647i \(0.326226\pi\)
\(450\) 1144.10 0.119852
\(451\) −20463.0 −2.13651
\(452\) −2176.27 −0.226467
\(453\) −6201.98 −0.643254
\(454\) 9111.07 0.941858
\(455\) 524.377 0.0540290
\(456\) −657.500 −0.0675225
\(457\) −6171.28 −0.631686 −0.315843 0.948812i \(-0.602287\pi\)
−0.315843 + 0.948812i \(0.602287\pi\)
\(458\) −7671.65 −0.782691
\(459\) −1059.81 −0.107772
\(460\) −1263.32 −0.128049
\(461\) 3077.14 0.310883 0.155441 0.987845i \(-0.450320\pi\)
0.155441 + 0.987845i \(0.450320\pi\)
\(462\) −1928.02 −0.194155
\(463\) −7010.22 −0.703656 −0.351828 0.936065i \(-0.614440\pi\)
−0.351828 + 0.936065i \(0.614440\pi\)
\(464\) 145.940 0.0146015
\(465\) −1222.43 −0.121912
\(466\) −1089.10 −0.108265
\(467\) 3695.28 0.366161 0.183081 0.983098i \(-0.441393\pi\)
0.183081 + 0.983098i \(0.441393\pi\)
\(468\) 196.391 0.0193978
\(469\) −1050.21 −0.103400
\(470\) 16067.9 1.57693
\(471\) −10428.9 −1.02025
\(472\) −2925.89 −0.285329
\(473\) −20530.6 −1.99577
\(474\) −4698.75 −0.455318
\(475\) 1741.31 0.168204
\(476\) 1099.06 0.105830
\(477\) −5357.61 −0.514273
\(478\) −13186.1 −1.26175
\(479\) 15333.3 1.46263 0.731313 0.682042i \(-0.238908\pi\)
0.731313 + 0.682042i \(0.238908\pi\)
\(480\) −1318.25 −0.125353
\(481\) 1912.74 0.181316
\(482\) −1484.07 −0.140244
\(483\) 483.000 0.0455016
\(484\) 3105.20 0.291623
\(485\) 5420.00 0.507442
\(486\) −486.000 −0.0453609
\(487\) −9095.79 −0.846344 −0.423172 0.906049i \(-0.639083\pi\)
−0.423172 + 0.906049i \(0.639083\pi\)
\(488\) 5034.33 0.466995
\(489\) 3212.31 0.297067
\(490\) 1345.71 0.124067
\(491\) 14841.7 1.36415 0.682073 0.731284i \(-0.261078\pi\)
0.682073 + 0.731284i \(0.261078\pi\)
\(492\) 5349.18 0.490162
\(493\) 358.029 0.0327075
\(494\) 298.905 0.0272235
\(495\) 5673.25 0.515138
\(496\) 474.786 0.0429809
\(497\) −878.549 −0.0792924
\(498\) −4464.85 −0.401756
\(499\) 6799.26 0.609974 0.304987 0.952357i \(-0.401348\pi\)
0.304987 + 0.952357i \(0.401348\pi\)
\(500\) −3374.66 −0.301838
\(501\) −7120.61 −0.634981
\(502\) 7775.32 0.691294
\(503\) 10513.9 0.931995 0.465997 0.884786i \(-0.345696\pi\)
0.465997 + 0.884786i \(0.345696\pi\)
\(504\) 504.000 0.0445435
\(505\) 10297.2 0.907368
\(506\) −2111.65 −0.185522
\(507\) 6501.72 0.569530
\(508\) −5.61871 −0.000490729 0
\(509\) −5087.78 −0.443049 −0.221525 0.975155i \(-0.571103\pi\)
−0.221525 + 0.975155i \(0.571103\pi\)
\(510\) −3234.00 −0.280792
\(511\) −4914.62 −0.425460
\(512\) 512.000 0.0441942
\(513\) −739.687 −0.0636608
\(514\) −11839.7 −1.01600
\(515\) 4565.83 0.390669
\(516\) 5366.86 0.457873
\(517\) 26857.6 2.28471
\(518\) 4908.66 0.416360
\(519\) −1354.12 −0.114526
\(520\) 599.288 0.0505395
\(521\) −1548.83 −0.130241 −0.0651205 0.997877i \(-0.520743\pi\)
−0.0651205 + 0.997877i \(0.520743\pi\)
\(522\) 164.183 0.0137664
\(523\) 10212.0 0.853806 0.426903 0.904297i \(-0.359605\pi\)
0.426903 + 0.904297i \(0.359605\pi\)
\(524\) −8779.10 −0.731902
\(525\) −1334.78 −0.110961
\(526\) −10756.2 −0.891621
\(527\) 1164.77 0.0962776
\(528\) −2203.46 −0.181616
\(529\) 529.000 0.0434783
\(530\) −16348.7 −1.33989
\(531\) −3291.63 −0.269010
\(532\) 767.083 0.0625136
\(533\) −2431.79 −0.197622
\(534\) 243.709 0.0197496
\(535\) 24111.1 1.94844
\(536\) −1200.24 −0.0967214
\(537\) −5.74824 −0.000461927 0
\(538\) 1126.88 0.0903031
\(539\) 2249.36 0.179753
\(540\) −1483.03 −0.118184
\(541\) −5217.67 −0.414649 −0.207325 0.978272i \(-0.566476\pi\)
−0.207325 + 0.978272i \(0.566476\pi\)
\(542\) −16458.1 −1.30431
\(543\) −11390.8 −0.900235
\(544\) 1256.07 0.0989953
\(545\) 10962.1 0.861588
\(546\) −229.123 −0.0179589
\(547\) −17929.1 −1.40145 −0.700726 0.713430i \(-0.747140\pi\)
−0.700726 + 0.713430i \(0.747140\pi\)
\(548\) −4937.91 −0.384921
\(549\) 5663.63 0.440287
\(550\) 5835.59 0.452419
\(551\) 249.884 0.0193202
\(552\) 552.000 0.0425628
\(553\) 5481.87 0.421542
\(554\) −14112.8 −1.08230
\(555\) −14443.8 −1.10470
\(556\) −3353.88 −0.255820
\(557\) 10493.0 0.798208 0.399104 0.916906i \(-0.369321\pi\)
0.399104 + 0.916906i \(0.369321\pi\)
\(558\) 534.135 0.0405228
\(559\) −2439.82 −0.184604
\(560\) 1537.96 0.116055
\(561\) −5405.64 −0.406821
\(562\) 5551.25 0.416664
\(563\) 14588.7 1.09208 0.546040 0.837759i \(-0.316135\pi\)
0.546040 + 0.837759i \(0.316135\pi\)
\(564\) −7020.78 −0.524163
\(565\) −7470.99 −0.556296
\(566\) −4566.20 −0.339102
\(567\) 567.000 0.0419961
\(568\) −1004.06 −0.0741712
\(569\) 8804.22 0.648668 0.324334 0.945943i \(-0.394860\pi\)
0.324334 + 0.945943i \(0.394860\pi\)
\(570\) −2257.16 −0.165863
\(571\) −12325.9 −0.903369 −0.451685 0.892178i \(-0.649177\pi\)
−0.451685 + 0.892178i \(0.649177\pi\)
\(572\) 1001.71 0.0732232
\(573\) −10352.5 −0.754766
\(574\) −6240.71 −0.453802
\(575\) −1461.90 −0.106027
\(576\) 576.000 0.0416667
\(577\) 9189.41 0.663016 0.331508 0.943452i \(-0.392443\pi\)
0.331508 + 0.943452i \(0.392443\pi\)
\(578\) −6744.54 −0.485356
\(579\) 10665.0 0.765498
\(580\) 501.003 0.0358673
\(581\) 5208.99 0.371954
\(582\) −2368.23 −0.168671
\(583\) −27327.0 −1.94128
\(584\) −5616.71 −0.397981
\(585\) 674.199 0.0476491
\(586\) −3661.77 −0.258134
\(587\) −25329.9 −1.78105 −0.890525 0.454935i \(-0.849663\pi\)
−0.890525 + 0.454935i \(0.849663\pi\)
\(588\) −588.000 −0.0412393
\(589\) 812.947 0.0568708
\(590\) −10044.4 −0.700884
\(591\) 3974.16 0.276607
\(592\) 5609.90 0.389469
\(593\) 5725.34 0.396478 0.198239 0.980154i \(-0.436478\pi\)
0.198239 + 0.980154i \(0.436478\pi\)
\(594\) −2478.89 −0.171229
\(595\) 3773.00 0.259963
\(596\) 2439.16 0.167638
\(597\) 4427.37 0.303518
\(598\) −250.944 −0.0171603
\(599\) −16336.7 −1.11436 −0.557178 0.830393i \(-0.688116\pi\)
−0.557178 + 0.830393i \(0.688116\pi\)
\(600\) −1525.47 −0.103795
\(601\) −19204.7 −1.30346 −0.651728 0.758453i \(-0.725956\pi\)
−0.651728 + 0.758453i \(0.725956\pi\)
\(602\) −6261.33 −0.423908
\(603\) −1350.27 −0.0911898
\(604\) 8269.30 0.557075
\(605\) 10660.0 0.716345
\(606\) −4499.31 −0.301604
\(607\) 6344.20 0.424223 0.212111 0.977246i \(-0.431966\pi\)
0.212111 + 0.977246i \(0.431966\pi\)
\(608\) 876.666 0.0584762
\(609\) −191.546 −0.0127452
\(610\) 17282.6 1.14713
\(611\) 3191.71 0.211330
\(612\) 1413.08 0.0933337
\(613\) −25232.0 −1.66250 −0.831248 0.555902i \(-0.812373\pi\)
−0.831248 + 0.555902i \(0.812373\pi\)
\(614\) −104.394 −0.00686158
\(615\) 18363.4 1.20404
\(616\) 2570.70 0.168144
\(617\) −1164.73 −0.0759969 −0.0379984 0.999278i \(-0.512098\pi\)
−0.0379984 + 0.999278i \(0.512098\pi\)
\(618\) −1995.01 −0.129856
\(619\) −3604.47 −0.234048 −0.117024 0.993129i \(-0.537336\pi\)
−0.117024 + 0.993129i \(0.537336\pi\)
\(620\) 1629.91 0.105579
\(621\) 621.000 0.0401286
\(622\) 10528.8 0.678726
\(623\) −284.327 −0.0182846
\(624\) −261.855 −0.0167990
\(625\) −19530.1 −1.24993
\(626\) 7633.27 0.487359
\(627\) −3772.84 −0.240308
\(628\) 13905.2 0.883563
\(629\) 13762.5 0.872413
\(630\) 1730.20 0.109417
\(631\) 2059.95 0.129961 0.0649803 0.997887i \(-0.479302\pi\)
0.0649803 + 0.997887i \(0.479302\pi\)
\(632\) 6264.99 0.394317
\(633\) −1756.85 −0.110314
\(634\) −22120.8 −1.38569
\(635\) −19.2887 −0.00120543
\(636\) 7143.48 0.445373
\(637\) 267.310 0.0166267
\(638\) 837.429 0.0519657
\(639\) −1129.56 −0.0699293
\(640\) 1757.66 0.108559
\(641\) 20939.2 1.29025 0.645125 0.764077i \(-0.276805\pi\)
0.645125 + 0.764077i \(0.276805\pi\)
\(642\) −10535.2 −0.647650
\(643\) −23140.6 −1.41925 −0.709624 0.704581i \(-0.751135\pi\)
−0.709624 + 0.704581i \(0.751135\pi\)
\(644\) −644.000 −0.0394055
\(645\) 18424.1 1.12473
\(646\) 2150.69 0.130987
\(647\) 4123.48 0.250558 0.125279 0.992122i \(-0.460017\pi\)
0.125279 + 0.992122i \(0.460017\pi\)
\(648\) 648.000 0.0392837
\(649\) −16789.3 −1.01546
\(650\) 693.491 0.0418476
\(651\) −623.157 −0.0375168
\(652\) −4283.08 −0.257267
\(653\) 7934.30 0.475487 0.237744 0.971328i \(-0.423592\pi\)
0.237744 + 0.971328i \(0.423592\pi\)
\(654\) −4789.83 −0.286387
\(655\) −30138.1 −1.79785
\(656\) −7132.24 −0.424493
\(657\) −6318.80 −0.375220
\(658\) 8190.91 0.485281
\(659\) −15803.7 −0.934181 −0.467091 0.884209i \(-0.654698\pi\)
−0.467091 + 0.884209i \(0.654698\pi\)
\(660\) −7564.33 −0.446123
\(661\) −5586.17 −0.328709 −0.164355 0.986401i \(-0.552554\pi\)
−0.164355 + 0.986401i \(0.552554\pi\)
\(662\) 13945.5 0.818739
\(663\) −642.398 −0.0376299
\(664\) 5953.13 0.347931
\(665\) 2633.35 0.153559
\(666\) 6311.14 0.367195
\(667\) −209.789 −0.0121785
\(668\) 9494.14 0.549909
\(669\) −9206.42 −0.532049
\(670\) −4120.37 −0.237587
\(671\) 28887.8 1.66200
\(672\) −672.000 −0.0385758
\(673\) −20234.7 −1.15897 −0.579487 0.814981i \(-0.696747\pi\)
−0.579487 + 0.814981i \(0.696747\pi\)
\(674\) −18902.1 −1.08024
\(675\) −1716.15 −0.0978587
\(676\) −8668.96 −0.493227
\(677\) −7512.52 −0.426484 −0.213242 0.976999i \(-0.568402\pi\)
−0.213242 + 0.976999i \(0.568402\pi\)
\(678\) 3264.40 0.184909
\(679\) 2762.94 0.156159
\(680\) 4312.00 0.243173
\(681\) −13666.6 −0.769024
\(682\) 2724.40 0.152966
\(683\) −16956.8 −0.949975 −0.474987 0.879993i \(-0.657547\pi\)
−0.474987 + 0.879993i \(0.657547\pi\)
\(684\) 986.249 0.0551319
\(685\) −16951.5 −0.945525
\(686\) 686.000 0.0381802
\(687\) 11507.5 0.639065
\(688\) −7155.81 −0.396530
\(689\) −3247.49 −0.179564
\(690\) 1894.98 0.104552
\(691\) 22505.5 1.23900 0.619500 0.784997i \(-0.287336\pi\)
0.619500 + 0.784997i \(0.287336\pi\)
\(692\) 1805.49 0.0991825
\(693\) 2892.04 0.158527
\(694\) 2808.80 0.153632
\(695\) −11513.7 −0.628399
\(696\) −218.910 −0.0119221
\(697\) −17497.2 −0.950867
\(698\) −9339.19 −0.506438
\(699\) 1633.65 0.0883980
\(700\) 1779.71 0.0960953
\(701\) 32977.4 1.77680 0.888402 0.459067i \(-0.151816\pi\)
0.888402 + 0.459067i \(0.151816\pi\)
\(702\) −294.587 −0.0158383
\(703\) 9605.49 0.515331
\(704\) 2937.94 0.157284
\(705\) −24101.9 −1.28756
\(706\) −12564.9 −0.669810
\(707\) 5249.19 0.279231
\(708\) 4388.84 0.232970
\(709\) 3887.13 0.205902 0.102951 0.994686i \(-0.467172\pi\)
0.102951 + 0.994686i \(0.467172\pi\)
\(710\) −3446.86 −0.182195
\(711\) 7048.12 0.371765
\(712\) −324.945 −0.0171037
\(713\) −682.505 −0.0358486
\(714\) −1648.59 −0.0864102
\(715\) 3438.81 0.179866
\(716\) 7.66432 0.000400041 0
\(717\) 19779.1 1.03022
\(718\) −16548.1 −0.860125
\(719\) 6960.02 0.361008 0.180504 0.983574i \(-0.442227\pi\)
0.180504 + 0.983574i \(0.442227\pi\)
\(720\) 1977.37 0.102350
\(721\) 2327.51 0.120223
\(722\) −12216.9 −0.629733
\(723\) 2226.11 0.114509
\(724\) 15187.8 0.779627
\(725\) 579.757 0.0296988
\(726\) −4657.80 −0.238109
\(727\) 9562.26 0.487819 0.243910 0.969798i \(-0.421570\pi\)
0.243910 + 0.969798i \(0.421570\pi\)
\(728\) 305.497 0.0155529
\(729\) 729.000 0.0370370
\(730\) −19281.8 −0.977606
\(731\) −17555.0 −0.888231
\(732\) −7551.50 −0.381300
\(733\) 35530.2 1.79037 0.895183 0.445699i \(-0.147045\pi\)
0.895183 + 0.445699i \(0.147045\pi\)
\(734\) −411.776 −0.0207070
\(735\) −2018.57 −0.101301
\(736\) −736.000 −0.0368605
\(737\) −6887.20 −0.344224
\(738\) −8023.77 −0.400215
\(739\) 26209.5 1.30464 0.652322 0.757942i \(-0.273795\pi\)
0.652322 + 0.757942i \(0.273795\pi\)
\(740\) 19258.4 0.956695
\(741\) −448.358 −0.0222279
\(742\) −8334.06 −0.412335
\(743\) 31885.1 1.57436 0.787181 0.616721i \(-0.211539\pi\)
0.787181 + 0.616721i \(0.211539\pi\)
\(744\) −712.179 −0.0350938
\(745\) 8373.50 0.411787
\(746\) 305.752 0.0150058
\(747\) 6697.27 0.328033
\(748\) 7207.53 0.352317
\(749\) 12291.1 0.599607
\(750\) 5061.98 0.246450
\(751\) −16826.8 −0.817600 −0.408800 0.912624i \(-0.634053\pi\)
−0.408800 + 0.912624i \(0.634053\pi\)
\(752\) 9361.04 0.453939
\(753\) −11663.0 −0.564439
\(754\) 99.5186 0.00480670
\(755\) 28388.0 1.36840
\(756\) −756.000 −0.0363696
\(757\) 11050.1 0.530545 0.265273 0.964173i \(-0.414538\pi\)
0.265273 + 0.964173i \(0.414538\pi\)
\(758\) −22388.9 −1.07283
\(759\) 3167.47 0.151478
\(760\) 3009.54 0.143641
\(761\) −25066.2 −1.19402 −0.597010 0.802234i \(-0.703645\pi\)
−0.597010 + 0.802234i \(0.703645\pi\)
\(762\) 8.42807 0.000400678 0
\(763\) 5588.13 0.265143
\(764\) 13803.3 0.653646
\(765\) 4851.00 0.229266
\(766\) 7771.70 0.366583
\(767\) −1995.21 −0.0939280
\(768\) −768.000 −0.0360844
\(769\) −39352.7 −1.84538 −0.922688 0.385547i \(-0.874013\pi\)
−0.922688 + 0.385547i \(0.874013\pi\)
\(770\) 8825.05 0.413030
\(771\) 17759.5 0.829563
\(772\) −14220.0 −0.662941
\(773\) 30740.7 1.43036 0.715179 0.698942i \(-0.246345\pi\)
0.715179 + 0.698942i \(0.246345\pi\)
\(774\) −8050.28 −0.373852
\(775\) 1886.12 0.0874212
\(776\) 3157.64 0.146073
\(777\) −7363.00 −0.339956
\(778\) 12623.5 0.581717
\(779\) −12212.1 −0.561674
\(780\) −898.932 −0.0412653
\(781\) −5761.44 −0.263970
\(782\) −1805.60 −0.0825678
\(783\) −246.274 −0.0112402
\(784\) 784.000 0.0357143
\(785\) 47735.7 2.17039
\(786\) 13168.7 0.597596
\(787\) −11194.1 −0.507021 −0.253511 0.967333i \(-0.581585\pi\)
−0.253511 + 0.967333i \(0.581585\pi\)
\(788\) −5298.88 −0.239549
\(789\) 16134.3 0.728005
\(790\) 21507.3 0.968604
\(791\) −3808.47 −0.171193
\(792\) 3305.18 0.148289
\(793\) 3432.98 0.153731
\(794\) −16510.8 −0.737969
\(795\) 24523.1 1.09402
\(796\) −5903.15 −0.262854
\(797\) 19455.8 0.864694 0.432347 0.901707i \(-0.357686\pi\)
0.432347 + 0.901707i \(0.357686\pi\)
\(798\) −1150.62 −0.0510422
\(799\) 22965.0 1.01683
\(800\) 2033.95 0.0898889
\(801\) −365.563 −0.0161255
\(802\) −25902.9 −1.14048
\(803\) −32229.6 −1.41639
\(804\) 1800.37 0.0789727
\(805\) −2210.81 −0.0967962
\(806\) 323.763 0.0141490
\(807\) −1690.31 −0.0737322
\(808\) 5999.08 0.261196
\(809\) 29099.7 1.26464 0.632319 0.774708i \(-0.282103\pi\)
0.632319 + 0.774708i \(0.282103\pi\)
\(810\) 2224.54 0.0964969
\(811\) −6804.12 −0.294605 −0.147303 0.989091i \(-0.547059\pi\)
−0.147303 + 0.989091i \(0.547059\pi\)
\(812\) 255.395 0.0110377
\(813\) 24687.2 1.06496
\(814\) 32190.6 1.38609
\(815\) −14703.5 −0.631954
\(816\) −1884.10 −0.0808293
\(817\) −12252.5 −0.524674
\(818\) 6194.52 0.264776
\(819\) 343.685 0.0146634
\(820\) −24484.5 −1.04273
\(821\) −35218.9 −1.49713 −0.748567 0.663059i \(-0.769258\pi\)
−0.748567 + 0.663059i \(0.769258\pi\)
\(822\) 7406.86 0.314287
\(823\) −36151.1 −1.53117 −0.765583 0.643337i \(-0.777549\pi\)
−0.765583 + 0.643337i \(0.777549\pi\)
\(824\) 2660.01 0.112459
\(825\) −8753.38 −0.369398
\(826\) −5120.31 −0.215688
\(827\) −5471.38 −0.230059 −0.115029 0.993362i \(-0.536696\pi\)
−0.115029 + 0.993362i \(0.536696\pi\)
\(828\) −828.000 −0.0347524
\(829\) 19839.0 0.831167 0.415583 0.909555i \(-0.363577\pi\)
0.415583 + 0.909555i \(0.363577\pi\)
\(830\) 20436.7 0.854662
\(831\) 21169.2 0.883695
\(832\) 349.140 0.0145484
\(833\) 1923.35 0.0800003
\(834\) 5030.81 0.208876
\(835\) 32592.8 1.35080
\(836\) 5030.46 0.208112
\(837\) −801.202 −0.0330867
\(838\) 12736.4 0.525027
\(839\) 24653.2 1.01445 0.507225 0.861813i \(-0.330671\pi\)
0.507225 + 0.861813i \(0.330671\pi\)
\(840\) −2306.93 −0.0947581
\(841\) −24305.8 −0.996589
\(842\) 569.757 0.0233196
\(843\) −8326.88 −0.340205
\(844\) 2342.47 0.0955345
\(845\) −29760.0 −1.21157
\(846\) 10531.2 0.427978
\(847\) 5434.10 0.220446
\(848\) −9524.64 −0.385704
\(849\) 6849.30 0.276875
\(850\) 4989.81 0.201352
\(851\) −8064.23 −0.324839
\(852\) 1506.08 0.0605606
\(853\) −27717.8 −1.11259 −0.556296 0.830984i \(-0.687778\pi\)
−0.556296 + 0.830984i \(0.687778\pi\)
\(854\) 8810.08 0.353015
\(855\) 3385.73 0.135426
\(856\) 14046.9 0.560881
\(857\) 31543.3 1.25729 0.628645 0.777693i \(-0.283610\pi\)
0.628645 + 0.777693i \(0.283610\pi\)
\(858\) −1502.57 −0.0597865
\(859\) 16748.0 0.665234 0.332617 0.943062i \(-0.392068\pi\)
0.332617 + 0.943062i \(0.392068\pi\)
\(860\) −24565.5 −0.974041
\(861\) 9361.06 0.370528
\(862\) 13352.5 0.527598
\(863\) 39073.8 1.54124 0.770619 0.637296i \(-0.219947\pi\)
0.770619 + 0.637296i \(0.219947\pi\)
\(864\) −864.000 −0.0340207
\(865\) 6198.13 0.243633
\(866\) −13464.7 −0.528348
\(867\) 10116.8 0.396292
\(868\) 830.876 0.0324905
\(869\) 35949.6 1.40334
\(870\) −751.505 −0.0292855
\(871\) −818.463 −0.0318399
\(872\) 6386.44 0.248018
\(873\) 3552.35 0.137719
\(874\) −1260.21 −0.0487725
\(875\) −5905.65 −0.228168
\(876\) 8425.06 0.324950
\(877\) 11372.9 0.437896 0.218948 0.975737i \(-0.429738\pi\)
0.218948 + 0.975737i \(0.429738\pi\)
\(878\) 13584.1 0.522144
\(879\) 5492.66 0.210765
\(880\) 10085.8 0.386354
\(881\) 13707.3 0.524189 0.262095 0.965042i \(-0.415587\pi\)
0.262095 + 0.965042i \(0.415587\pi\)
\(882\) 882.000 0.0336718
\(883\) −7930.53 −0.302246 −0.151123 0.988515i \(-0.548289\pi\)
−0.151123 + 0.988515i \(0.548289\pi\)
\(884\) 856.530 0.0325885
\(885\) 15066.6 0.572270
\(886\) −22326.7 −0.846592
\(887\) −3379.90 −0.127943 −0.0639717 0.997952i \(-0.520377\pi\)
−0.0639717 + 0.997952i \(0.520377\pi\)
\(888\) −8414.85 −0.318000
\(889\) −9.83275 −0.000370956 0
\(890\) −1115.52 −0.0420137
\(891\) 3718.33 0.139808
\(892\) 12275.2 0.460768
\(893\) 16028.3 0.600636
\(894\) −3658.75 −0.136876
\(895\) 26.3111 0.000982664 0
\(896\) 896.000 0.0334077
\(897\) 376.417 0.0140114
\(898\) 19759.3 0.734273
\(899\) 270.665 0.0100414
\(900\) 2288.20 0.0847481
\(901\) −23366.4 −0.863981
\(902\) −40926.0 −1.51074
\(903\) 9392.00 0.346120
\(904\) −4352.53 −0.160136
\(905\) 52138.7 1.91508
\(906\) −12404.0 −0.454850
\(907\) −27965.5 −1.02379 −0.511896 0.859048i \(-0.671057\pi\)
−0.511896 + 0.859048i \(0.671057\pi\)
\(908\) 18222.1 0.665994
\(909\) 6748.96 0.246258
\(910\) 1048.75 0.0382042
\(911\) −1357.11 −0.0493557 −0.0246779 0.999695i \(-0.507856\pi\)
−0.0246779 + 0.999695i \(0.507856\pi\)
\(912\) −1315.00 −0.0477456
\(913\) 34160.1 1.23826
\(914\) −12342.6 −0.446669
\(915\) −25923.8 −0.936629
\(916\) −15343.3 −0.553446
\(917\) −15363.4 −0.553266
\(918\) −2119.61 −0.0762066
\(919\) −31780.9 −1.14076 −0.570379 0.821382i \(-0.693204\pi\)
−0.570379 + 0.821382i \(0.693204\pi\)
\(920\) −2526.64 −0.0905445
\(921\) 156.592 0.00560246
\(922\) 6154.29 0.219827
\(923\) −684.680 −0.0244166
\(924\) −3856.05 −0.137289
\(925\) 22285.7 0.792162
\(926\) −14020.4 −0.497560
\(927\) 2992.51 0.106027
\(928\) 291.880 0.0103248
\(929\) −37901.2 −1.33853 −0.669266 0.743023i \(-0.733391\pi\)
−0.669266 + 0.743023i \(0.733391\pi\)
\(930\) −2444.87 −0.0862047
\(931\) 1342.39 0.0472559
\(932\) −2178.20 −0.0765549
\(933\) −15793.3 −0.554178
\(934\) 7390.56 0.258915
\(935\) 24743.0 0.865436
\(936\) 392.782 0.0137163
\(937\) 41733.1 1.45503 0.727514 0.686093i \(-0.240676\pi\)
0.727514 + 0.686093i \(0.240676\pi\)
\(938\) −2100.43 −0.0731145
\(939\) −11449.9 −0.397927
\(940\) 32135.9 1.11506
\(941\) 6773.55 0.234656 0.117328 0.993093i \(-0.462567\pi\)
0.117328 + 0.993093i \(0.462567\pi\)
\(942\) −20857.8 −0.721426
\(943\) 10252.6 0.354051
\(944\) −5851.79 −0.201758
\(945\) −2595.30 −0.0893388
\(946\) −41061.2 −1.41122
\(947\) 32914.3 1.12943 0.564715 0.825286i \(-0.308986\pi\)
0.564715 + 0.825286i \(0.308986\pi\)
\(948\) −9397.49 −0.321958
\(949\) −3830.11 −0.131012
\(950\) 3482.62 0.118938
\(951\) 33181.2 1.13141
\(952\) 2198.12 0.0748334
\(953\) −25158.6 −0.855160 −0.427580 0.903978i \(-0.640634\pi\)
−0.427580 + 0.903978i \(0.640634\pi\)
\(954\) −10715.2 −0.363646
\(955\) 47385.9 1.60562
\(956\) −26372.2 −0.892194
\(957\) −1256.14 −0.0424298
\(958\) 30666.7 1.03423
\(959\) −8641.34 −0.290973
\(960\) −2636.50 −0.0886381
\(961\) −28910.4 −0.970442
\(962\) 3825.47 0.128210
\(963\) 15802.8 0.528804
\(964\) −2968.14 −0.0991674
\(965\) −48816.5 −1.62846
\(966\) 966.000 0.0321745
\(967\) 25734.2 0.855799 0.427899 0.903826i \(-0.359254\pi\)
0.427899 + 0.903826i \(0.359254\pi\)
\(968\) 6210.40 0.206208
\(969\) −3226.03 −0.106951
\(970\) 10840.0 0.358816
\(971\) −16969.6 −0.560846 −0.280423 0.959876i \(-0.590475\pi\)
−0.280423 + 0.959876i \(0.590475\pi\)
\(972\) −972.000 −0.0320750
\(973\) −5869.28 −0.193382
\(974\) −18191.6 −0.598455
\(975\) −1040.24 −0.0341684
\(976\) 10068.7 0.330215
\(977\) 47396.8 1.55205 0.776027 0.630700i \(-0.217232\pi\)
0.776027 + 0.630700i \(0.217232\pi\)
\(978\) 6424.62 0.210058
\(979\) −1864.59 −0.0608708
\(980\) 2691.42 0.0877290
\(981\) 7184.74 0.233834
\(982\) 29683.4 0.964597
\(983\) −40149.7 −1.30272 −0.651361 0.758768i \(-0.725802\pi\)
−0.651361 + 0.758768i \(0.725802\pi\)
\(984\) 10698.4 0.346597
\(985\) −18190.7 −0.588431
\(986\) 716.057 0.0231277
\(987\) −12286.4 −0.396230
\(988\) 597.811 0.0192499
\(989\) 10286.5 0.330729
\(990\) 11346.5 0.364258
\(991\) 24954.5 0.799906 0.399953 0.916536i \(-0.369026\pi\)
0.399953 + 0.916536i \(0.369026\pi\)
\(992\) 949.572 0.0303921
\(993\) −20918.2 −0.668498
\(994\) −1757.10 −0.0560682
\(995\) −20265.2 −0.645677
\(996\) −8929.70 −0.284085
\(997\) 14637.0 0.464952 0.232476 0.972602i \(-0.425317\pi\)
0.232476 + 0.972602i \(0.425317\pi\)
\(998\) 13598.5 0.431316
\(999\) −9466.71 −0.299813
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 966.4.a.f.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.4.a.f.1.3 3 1.1 even 1 trivial