Properties

Label 1815.4.a.n.1.1
Level $1815$
Weight $4$
Character 1815.1
Self dual yes
Analytic conductor $107.088$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1815.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(107.088466660\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \(x^{2} - x - 4\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.56155\) of defining polynomial
Character \(\chi\) \(=\) 1815.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.56155 q^{2} +3.00000 q^{3} -5.56155 q^{4} -5.00000 q^{5} -4.68466 q^{6} +10.2462 q^{7} +21.1771 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-1.56155 q^{2} +3.00000 q^{3} -5.56155 q^{4} -5.00000 q^{5} -4.68466 q^{6} +10.2462 q^{7} +21.1771 q^{8} +9.00000 q^{9} +7.80776 q^{10} -16.6847 q^{12} +40.8769 q^{13} -16.0000 q^{14} -15.0000 q^{15} +11.4233 q^{16} +98.7083 q^{17} -14.0540 q^{18} +39.6458 q^{19} +27.8078 q^{20} +30.7386 q^{21} +61.6932 q^{23} +63.5312 q^{24} +25.0000 q^{25} -63.8314 q^{26} +27.0000 q^{27} -56.9848 q^{28} +149.093 q^{29} +23.4233 q^{30} +54.7386 q^{31} -187.255 q^{32} -154.138 q^{34} -51.2311 q^{35} -50.0540 q^{36} +44.8939 q^{37} -61.9091 q^{38} +122.631 q^{39} -105.885 q^{40} -336.479 q^{41} -48.0000 q^{42} +2.36745 q^{43} -45.0000 q^{45} -96.3371 q^{46} -333.295 q^{47} +34.2699 q^{48} -238.015 q^{49} -39.0388 q^{50} +296.125 q^{51} -227.339 q^{52} +640.064 q^{53} -42.1619 q^{54} +216.985 q^{56} +118.938 q^{57} -232.816 q^{58} -370.773 q^{59} +83.4233 q^{60} +714.405 q^{61} -85.4773 q^{62} +92.2159 q^{63} +201.022 q^{64} -204.384 q^{65} -404.985 q^{67} -548.972 q^{68} +185.080 q^{69} +80.0000 q^{70} +939.292 q^{71} +190.594 q^{72} +362.570 q^{73} -70.1042 q^{74} +75.0000 q^{75} -220.492 q^{76} -191.494 q^{78} -951.835 q^{79} -57.1165 q^{80} +81.0000 q^{81} +525.430 q^{82} -735.221 q^{83} -170.955 q^{84} -493.542 q^{85} -3.69690 q^{86} +447.278 q^{87} +385.879 q^{89} +70.2699 q^{90} +418.833 q^{91} -343.110 q^{92} +164.216 q^{93} +520.458 q^{94} -198.229 q^{95} -561.764 q^{96} -966.345 q^{97} +371.673 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + 6q^{3} - 7q^{4} - 10q^{5} + 3q^{6} + 4q^{7} - 3q^{8} + 18q^{9} + O(q^{10}) \) \( 2q + q^{2} + 6q^{3} - 7q^{4} - 10q^{5} + 3q^{6} + 4q^{7} - 3q^{8} + 18q^{9} - 5q^{10} - 21q^{12} + 90q^{13} - 32q^{14} - 30q^{15} - 39q^{16} + 16q^{17} + 9q^{18} + 170q^{19} + 35q^{20} + 12q^{21} - 124q^{23} - 9q^{24} + 50q^{25} + 62q^{26} + 54q^{27} - 48q^{28} + 158q^{29} - 15q^{30} + 60q^{31} - 123q^{32} - 366q^{34} - 20q^{35} - 63q^{36} - 372q^{37} + 272q^{38} + 270q^{39} + 15q^{40} - 38q^{41} - 96q^{42} + 516q^{43} - 90q^{45} - 572q^{46} + 224q^{47} - 117q^{48} - 542q^{49} + 25q^{50} + 48q^{51} - 298q^{52} + 472q^{53} + 27q^{54} + 368q^{56} + 510q^{57} - 210q^{58} + 248q^{59} + 105q^{60} - 72q^{61} - 72q^{62} + 36q^{63} + 769q^{64} - 450q^{65} - 744q^{67} - 430q^{68} - 372q^{69} + 160q^{70} + 2060q^{71} - 27q^{72} + 486q^{73} - 1138q^{74} + 150q^{75} - 408q^{76} + 186q^{78} - 642q^{79} + 195q^{80} + 162q^{81} + 1290q^{82} + 286q^{83} - 144q^{84} - 80q^{85} + 1312q^{86} + 474q^{87} + 244q^{89} - 45q^{90} + 112q^{91} - 76q^{92} + 180q^{93} + 1948q^{94} - 850q^{95} - 369q^{96} - 168q^{97} - 407q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.56155 −0.552092 −0.276046 0.961144i \(-0.589024\pi\)
−0.276046 + 0.961144i \(0.589024\pi\)
\(3\) 3.00000 0.577350
\(4\) −5.56155 −0.695194
\(5\) −5.00000 −0.447214
\(6\) −4.68466 −0.318751
\(7\) 10.2462 0.553243 0.276622 0.960979i \(-0.410785\pi\)
0.276622 + 0.960979i \(0.410785\pi\)
\(8\) 21.1771 0.935904
\(9\) 9.00000 0.333333
\(10\) 7.80776 0.246903
\(11\) 0 0
\(12\) −16.6847 −0.401371
\(13\) 40.8769 0.872093 0.436047 0.899924i \(-0.356378\pi\)
0.436047 + 0.899924i \(0.356378\pi\)
\(14\) −16.0000 −0.305441
\(15\) −15.0000 −0.258199
\(16\) 11.4233 0.178489
\(17\) 98.7083 1.40825 0.704126 0.710075i \(-0.251339\pi\)
0.704126 + 0.710075i \(0.251339\pi\)
\(18\) −14.0540 −0.184031
\(19\) 39.6458 0.478704 0.239352 0.970933i \(-0.423065\pi\)
0.239352 + 0.970933i \(0.423065\pi\)
\(20\) 27.8078 0.310900
\(21\) 30.7386 0.319415
\(22\) 0 0
\(23\) 61.6932 0.559301 0.279650 0.960102i \(-0.409781\pi\)
0.279650 + 0.960102i \(0.409781\pi\)
\(24\) 63.5312 0.540344
\(25\) 25.0000 0.200000
\(26\) −63.8314 −0.481476
\(27\) 27.0000 0.192450
\(28\) −56.9848 −0.384612
\(29\) 149.093 0.954684 0.477342 0.878718i \(-0.341600\pi\)
0.477342 + 0.878718i \(0.341600\pi\)
\(30\) 23.4233 0.142550
\(31\) 54.7386 0.317140 0.158570 0.987348i \(-0.449312\pi\)
0.158570 + 0.987348i \(0.449312\pi\)
\(32\) −187.255 −1.03445
\(33\) 0 0
\(34\) −154.138 −0.777485
\(35\) −51.2311 −0.247418
\(36\) −50.0540 −0.231731
\(37\) 44.8939 0.199473 0.0997367 0.995014i \(-0.468200\pi\)
0.0997367 + 0.995014i \(0.468200\pi\)
\(38\) −61.9091 −0.264289
\(39\) 122.631 0.503503
\(40\) −105.885 −0.418549
\(41\) −336.479 −1.28169 −0.640844 0.767671i \(-0.721415\pi\)
−0.640844 + 0.767671i \(0.721415\pi\)
\(42\) −48.0000 −0.176347
\(43\) 2.36745 0.00839611 0.00419806 0.999991i \(-0.498664\pi\)
0.00419806 + 0.999991i \(0.498664\pi\)
\(44\) 0 0
\(45\) −45.0000 −0.149071
\(46\) −96.3371 −0.308786
\(47\) −333.295 −1.03439 −0.517193 0.855869i \(-0.673023\pi\)
−0.517193 + 0.855869i \(0.673023\pi\)
\(48\) 34.2699 0.103051
\(49\) −238.015 −0.693922
\(50\) −39.0388 −0.110418
\(51\) 296.125 0.813055
\(52\) −227.339 −0.606274
\(53\) 640.064 1.65886 0.829430 0.558610i \(-0.188665\pi\)
0.829430 + 0.558610i \(0.188665\pi\)
\(54\) −42.1619 −0.106250
\(55\) 0 0
\(56\) 216.985 0.517782
\(57\) 118.938 0.276380
\(58\) −232.816 −0.527074
\(59\) −370.773 −0.818144 −0.409072 0.912502i \(-0.634147\pi\)
−0.409072 + 0.912502i \(0.634147\pi\)
\(60\) 83.4233 0.179498
\(61\) 714.405 1.49951 0.749756 0.661715i \(-0.230171\pi\)
0.749756 + 0.661715i \(0.230171\pi\)
\(62\) −85.4773 −0.175091
\(63\) 92.2159 0.184414
\(64\) 201.022 0.392621
\(65\) −204.384 −0.390012
\(66\) 0 0
\(67\) −404.985 −0.738459 −0.369230 0.929338i \(-0.620378\pi\)
−0.369230 + 0.929338i \(0.620378\pi\)
\(68\) −548.972 −0.979009
\(69\) 185.080 0.322912
\(70\) 80.0000 0.136598
\(71\) 939.292 1.57005 0.785024 0.619465i \(-0.212651\pi\)
0.785024 + 0.619465i \(0.212651\pi\)
\(72\) 190.594 0.311968
\(73\) 362.570 0.581310 0.290655 0.956828i \(-0.406127\pi\)
0.290655 + 0.956828i \(0.406127\pi\)
\(74\) −70.1042 −0.110128
\(75\) 75.0000 0.115470
\(76\) −220.492 −0.332792
\(77\) 0 0
\(78\) −191.494 −0.277980
\(79\) −951.835 −1.35557 −0.677784 0.735261i \(-0.737059\pi\)
−0.677784 + 0.735261i \(0.737059\pi\)
\(80\) −57.1165 −0.0798227
\(81\) 81.0000 0.111111
\(82\) 525.430 0.707610
\(83\) −735.221 −0.972302 −0.486151 0.873875i \(-0.661599\pi\)
−0.486151 + 0.873875i \(0.661599\pi\)
\(84\) −170.955 −0.222056
\(85\) −493.542 −0.629789
\(86\) −3.69690 −0.00463543
\(87\) 447.278 0.551187
\(88\) 0 0
\(89\) 385.879 0.459585 0.229793 0.973240i \(-0.426195\pi\)
0.229793 + 0.973240i \(0.426195\pi\)
\(90\) 70.2699 0.0823011
\(91\) 418.833 0.482480
\(92\) −343.110 −0.388823
\(93\) 164.216 0.183101
\(94\) 520.458 0.571076
\(95\) −198.229 −0.214083
\(96\) −561.764 −0.597238
\(97\) −966.345 −1.01152 −0.505760 0.862674i \(-0.668788\pi\)
−0.505760 + 0.862674i \(0.668788\pi\)
\(98\) 371.673 0.383109
\(99\) 0 0
\(100\) −139.039 −0.139039
\(101\) −348.600 −0.343436 −0.171718 0.985146i \(-0.554932\pi\)
−0.171718 + 0.985146i \(0.554932\pi\)
\(102\) −462.415 −0.448881
\(103\) −1536.38 −1.46975 −0.734873 0.678204i \(-0.762758\pi\)
−0.734873 + 0.678204i \(0.762758\pi\)
\(104\) 865.653 0.816195
\(105\) −153.693 −0.142847
\(106\) −999.494 −0.915844
\(107\) 779.180 0.703983 0.351991 0.936003i \(-0.385505\pi\)
0.351991 + 0.936003i \(0.385505\pi\)
\(108\) −150.162 −0.133790
\(109\) 1501.79 1.31968 0.659842 0.751404i \(-0.270623\pi\)
0.659842 + 0.751404i \(0.270623\pi\)
\(110\) 0 0
\(111\) 134.682 0.115166
\(112\) 117.045 0.0987478
\(113\) 170.000 0.141524 0.0707622 0.997493i \(-0.477457\pi\)
0.0707622 + 0.997493i \(0.477457\pi\)
\(114\) −185.727 −0.152587
\(115\) −308.466 −0.250127
\(116\) −829.187 −0.663691
\(117\) 367.892 0.290698
\(118\) 578.981 0.451691
\(119\) 1011.39 0.779106
\(120\) −317.656 −0.241649
\(121\) 0 0
\(122\) −1115.58 −0.827869
\(123\) −1009.44 −0.739983
\(124\) −304.432 −0.220474
\(125\) −125.000 −0.0894427
\(126\) −144.000 −0.101814
\(127\) 1739.82 1.21562 0.607811 0.794082i \(-0.292048\pi\)
0.607811 + 0.794082i \(0.292048\pi\)
\(128\) 1184.13 0.817683
\(129\) 7.10235 0.00484750
\(130\) 319.157 0.215323
\(131\) −312.837 −0.208647 −0.104323 0.994543i \(-0.533268\pi\)
−0.104323 + 0.994543i \(0.533268\pi\)
\(132\) 0 0
\(133\) 406.220 0.264840
\(134\) 632.405 0.407698
\(135\) −135.000 −0.0860663
\(136\) 2090.35 1.31799
\(137\) −716.928 −0.447090 −0.223545 0.974694i \(-0.571763\pi\)
−0.223545 + 0.974694i \(0.571763\pi\)
\(138\) −289.011 −0.178277
\(139\) 876.483 0.534837 0.267418 0.963581i \(-0.413829\pi\)
0.267418 + 0.963581i \(0.413829\pi\)
\(140\) 284.924 0.172004
\(141\) −999.886 −0.597203
\(142\) −1466.75 −0.866811
\(143\) 0 0
\(144\) 102.810 0.0594963
\(145\) −745.464 −0.426948
\(146\) −566.172 −0.320937
\(147\) −714.045 −0.400636
\(148\) −249.680 −0.138673
\(149\) 2376.36 1.30657 0.653285 0.757112i \(-0.273390\pi\)
0.653285 + 0.757112i \(0.273390\pi\)
\(150\) −117.116 −0.0637501
\(151\) 92.8466 0.0500381 0.0250190 0.999687i \(-0.492035\pi\)
0.0250190 + 0.999687i \(0.492035\pi\)
\(152\) 839.583 0.448021
\(153\) 888.375 0.469417
\(154\) 0 0
\(155\) −273.693 −0.141829
\(156\) −682.017 −0.350032
\(157\) −1881.24 −0.956301 −0.478150 0.878278i \(-0.658693\pi\)
−0.478150 + 0.878278i \(0.658693\pi\)
\(158\) 1486.34 0.748398
\(159\) 1920.19 0.957743
\(160\) 936.274 0.462618
\(161\) 632.121 0.309429
\(162\) −126.486 −0.0613436
\(163\) −2465.49 −1.18474 −0.592369 0.805667i \(-0.701807\pi\)
−0.592369 + 0.805667i \(0.701807\pi\)
\(164\) 1871.35 0.891022
\(165\) 0 0
\(166\) 1148.09 0.536800
\(167\) 1254.30 0.581200 0.290600 0.956845i \(-0.406145\pi\)
0.290600 + 0.956845i \(0.406145\pi\)
\(168\) 650.955 0.298942
\(169\) −526.080 −0.239454
\(170\) 770.691 0.347702
\(171\) 356.813 0.159568
\(172\) −13.1667 −0.00583693
\(173\) 1206.71 0.530314 0.265157 0.964205i \(-0.414576\pi\)
0.265157 + 0.964205i \(0.414576\pi\)
\(174\) −698.449 −0.304306
\(175\) 256.155 0.110649
\(176\) 0 0
\(177\) −1112.32 −0.472356
\(178\) −602.570 −0.253733
\(179\) −1442.29 −0.602244 −0.301122 0.953586i \(-0.597361\pi\)
−0.301122 + 0.953586i \(0.597361\pi\)
\(180\) 250.270 0.103633
\(181\) 4261.81 1.75015 0.875076 0.483985i \(-0.160811\pi\)
0.875076 + 0.483985i \(0.160811\pi\)
\(182\) −654.030 −0.266373
\(183\) 2143.22 0.865744
\(184\) 1306.48 0.523451
\(185\) −224.470 −0.0892072
\(186\) −256.432 −0.101089
\(187\) 0 0
\(188\) 1853.64 0.719099
\(189\) 276.648 0.106472
\(190\) 309.545 0.118194
\(191\) −852.223 −0.322852 −0.161426 0.986885i \(-0.551609\pi\)
−0.161426 + 0.986885i \(0.551609\pi\)
\(192\) 603.065 0.226680
\(193\) 2459.95 0.917468 0.458734 0.888574i \(-0.348303\pi\)
0.458734 + 0.888574i \(0.348303\pi\)
\(194\) 1509.00 0.558452
\(195\) −613.153 −0.225173
\(196\) 1323.73 0.482410
\(197\) −3477.06 −1.25751 −0.628756 0.777602i \(-0.716436\pi\)
−0.628756 + 0.777602i \(0.716436\pi\)
\(198\) 0 0
\(199\) 3995.04 1.42312 0.711560 0.702626i \(-0.247989\pi\)
0.711560 + 0.702626i \(0.247989\pi\)
\(200\) 529.427 0.187181
\(201\) −1214.95 −0.426350
\(202\) 544.358 0.189608
\(203\) 1527.64 0.528173
\(204\) −1646.91 −0.565231
\(205\) 1682.40 0.573188
\(206\) 2399.14 0.811436
\(207\) 555.239 0.186434
\(208\) 466.949 0.155659
\(209\) 0 0
\(210\) 240.000 0.0788646
\(211\) −1046.13 −0.341319 −0.170660 0.985330i \(-0.554590\pi\)
−0.170660 + 0.985330i \(0.554590\pi\)
\(212\) −3559.75 −1.15323
\(213\) 2817.88 0.906468
\(214\) −1216.73 −0.388664
\(215\) −11.8373 −0.00375486
\(216\) 571.781 0.180115
\(217\) 560.864 0.175456
\(218\) −2345.13 −0.728587
\(219\) 1087.71 0.335619
\(220\) 0 0
\(221\) 4034.89 1.22813
\(222\) −210.313 −0.0635823
\(223\) −506.265 −0.152027 −0.0760135 0.997107i \(-0.524219\pi\)
−0.0760135 + 0.997107i \(0.524219\pi\)
\(224\) −1918.65 −0.572300
\(225\) 225.000 0.0666667
\(226\) −265.464 −0.0781345
\(227\) 4286.29 1.25326 0.626632 0.779315i \(-0.284433\pi\)
0.626632 + 0.779315i \(0.284433\pi\)
\(228\) −661.477 −0.192138
\(229\) 5709.37 1.64754 0.823769 0.566926i \(-0.191867\pi\)
0.823769 + 0.566926i \(0.191867\pi\)
\(230\) 481.686 0.138093
\(231\) 0 0
\(232\) 3157.35 0.893492
\(233\) −2946.09 −0.828348 −0.414174 0.910198i \(-0.635929\pi\)
−0.414174 + 0.910198i \(0.635929\pi\)
\(234\) −574.483 −0.160492
\(235\) 1666.48 0.462591
\(236\) 2062.07 0.568769
\(237\) −2855.51 −0.782637
\(238\) −1579.33 −0.430139
\(239\) 2078.89 0.562646 0.281323 0.959613i \(-0.409227\pi\)
0.281323 + 0.959613i \(0.409227\pi\)
\(240\) −171.349 −0.0460856
\(241\) −1853.37 −0.495378 −0.247689 0.968840i \(-0.579671\pi\)
−0.247689 + 0.968840i \(0.579671\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) −3973.20 −1.04245
\(245\) 1190.08 0.310331
\(246\) 1576.29 0.408539
\(247\) 1620.60 0.417475
\(248\) 1159.20 0.296813
\(249\) −2205.66 −0.561359
\(250\) 195.194 0.0493806
\(251\) −2358.39 −0.593068 −0.296534 0.955022i \(-0.595831\pi\)
−0.296534 + 0.955022i \(0.595831\pi\)
\(252\) −512.864 −0.128204
\(253\) 0 0
\(254\) −2716.82 −0.671135
\(255\) −1480.62 −0.363609
\(256\) −3457.26 −0.844057
\(257\) 5519.25 1.33962 0.669809 0.742534i \(-0.266376\pi\)
0.669809 + 0.742534i \(0.266376\pi\)
\(258\) −11.0907 −0.00267627
\(259\) 459.993 0.110357
\(260\) 1136.70 0.271134
\(261\) 1341.84 0.318228
\(262\) 488.512 0.115192
\(263\) −2259.65 −0.529795 −0.264898 0.964277i \(-0.585338\pi\)
−0.264898 + 0.964277i \(0.585338\pi\)
\(264\) 0 0
\(265\) −3200.32 −0.741865
\(266\) −634.333 −0.146216
\(267\) 1157.64 0.265342
\(268\) 2252.34 0.513373
\(269\) 7039.53 1.59557 0.797783 0.602944i \(-0.206006\pi\)
0.797783 + 0.602944i \(0.206006\pi\)
\(270\) 210.810 0.0475165
\(271\) −5155.08 −1.15553 −0.577765 0.816203i \(-0.696075\pi\)
−0.577765 + 0.816203i \(0.696075\pi\)
\(272\) 1127.57 0.251357
\(273\) 1256.50 0.278560
\(274\) 1119.52 0.246835
\(275\) 0 0
\(276\) −1029.33 −0.224487
\(277\) −9074.52 −1.96836 −0.984179 0.177175i \(-0.943304\pi\)
−0.984179 + 0.177175i \(0.943304\pi\)
\(278\) −1368.67 −0.295279
\(279\) 492.648 0.105713
\(280\) −1084.92 −0.231559
\(281\) 3407.79 0.723459 0.361729 0.932283i \(-0.382186\pi\)
0.361729 + 0.932283i \(0.382186\pi\)
\(282\) 1561.38 0.329711
\(283\) 8827.73 1.85425 0.927127 0.374746i \(-0.122270\pi\)
0.927127 + 0.374746i \(0.122270\pi\)
\(284\) −5223.92 −1.09149
\(285\) −594.688 −0.123601
\(286\) 0 0
\(287\) −3447.64 −0.709085
\(288\) −1685.29 −0.344815
\(289\) 4830.33 0.983174
\(290\) 1164.08 0.235715
\(291\) −2899.03 −0.584001
\(292\) −2016.45 −0.404123
\(293\) 4528.29 0.902886 0.451443 0.892300i \(-0.350909\pi\)
0.451443 + 0.892300i \(0.350909\pi\)
\(294\) 1115.02 0.221188
\(295\) 1853.86 0.365885
\(296\) 950.722 0.186688
\(297\) 0 0
\(298\) −3710.81 −0.721347
\(299\) 2521.83 0.487762
\(300\) −417.116 −0.0802741
\(301\) 24.2574 0.00464509
\(302\) −144.985 −0.0276256
\(303\) −1045.80 −0.198283
\(304\) 452.886 0.0854434
\(305\) −3572.03 −0.670602
\(306\) −1387.24 −0.259162
\(307\) −568.106 −0.105614 −0.0528071 0.998605i \(-0.516817\pi\)
−0.0528071 + 0.998605i \(0.516817\pi\)
\(308\) 0 0
\(309\) −4609.14 −0.848559
\(310\) 427.386 0.0783029
\(311\) −6853.59 −1.24962 −0.624809 0.780778i \(-0.714823\pi\)
−0.624809 + 0.780778i \(0.714823\pi\)
\(312\) 2596.96 0.471230
\(313\) −1138.92 −0.205673 −0.102837 0.994698i \(-0.532792\pi\)
−0.102837 + 0.994698i \(0.532792\pi\)
\(314\) 2937.65 0.527966
\(315\) −461.080 −0.0824727
\(316\) 5293.68 0.942382
\(317\) 3207.48 0.568297 0.284148 0.958780i \(-0.408289\pi\)
0.284148 + 0.958780i \(0.408289\pi\)
\(318\) −2998.48 −0.528763
\(319\) 0 0
\(320\) −1005.11 −0.175585
\(321\) 2337.54 0.406445
\(322\) −987.091 −0.170834
\(323\) 3913.37 0.674136
\(324\) −450.486 −0.0772438
\(325\) 1021.92 0.174419
\(326\) 3850.00 0.654085
\(327\) 4505.37 0.761920
\(328\) −7125.65 −1.19954
\(329\) −3415.02 −0.572267
\(330\) 0 0
\(331\) −9135.12 −1.51695 −0.758477 0.651700i \(-0.774056\pi\)
−0.758477 + 0.651700i \(0.774056\pi\)
\(332\) 4088.97 0.675938
\(333\) 404.045 0.0664911
\(334\) −1958.65 −0.320876
\(335\) 2024.92 0.330249
\(336\) 351.136 0.0570121
\(337\) 3470.05 0.560907 0.280453 0.959868i \(-0.409515\pi\)
0.280453 + 0.959868i \(0.409515\pi\)
\(338\) 821.501 0.132200
\(339\) 510.000 0.0817091
\(340\) 2744.86 0.437826
\(341\) 0 0
\(342\) −557.182 −0.0880963
\(343\) −5953.20 −0.937151
\(344\) 50.1357 0.00785795
\(345\) −925.398 −0.144411
\(346\) −1884.34 −0.292782
\(347\) 89.3315 0.0138201 0.00691004 0.999976i \(-0.497800\pi\)
0.00691004 + 0.999976i \(0.497800\pi\)
\(348\) −2487.56 −0.383182
\(349\) 149.375 0.0229107 0.0114554 0.999934i \(-0.496354\pi\)
0.0114554 + 0.999934i \(0.496354\pi\)
\(350\) −400.000 −0.0610883
\(351\) 1103.68 0.167834
\(352\) 0 0
\(353\) 7867.64 1.18627 0.593133 0.805104i \(-0.297891\pi\)
0.593133 + 0.805104i \(0.297891\pi\)
\(354\) 1736.94 0.260784
\(355\) −4696.46 −0.702147
\(356\) −2146.09 −0.319501
\(357\) 3034.16 0.449817
\(358\) 2252.21 0.332494
\(359\) −4974.22 −0.731279 −0.365639 0.930757i \(-0.619150\pi\)
−0.365639 + 0.930757i \(0.619150\pi\)
\(360\) −952.969 −0.139516
\(361\) −5287.21 −0.770842
\(362\) −6655.04 −0.966246
\(363\) 0 0
\(364\) −2329.36 −0.335417
\(365\) −1812.85 −0.259970
\(366\) −3346.74 −0.477970
\(367\) −13266.7 −1.88696 −0.943479 0.331433i \(-0.892468\pi\)
−0.943479 + 0.331433i \(0.892468\pi\)
\(368\) 704.739 0.0998290
\(369\) −3028.31 −0.427229
\(370\) 350.521 0.0492506
\(371\) 6558.23 0.917754
\(372\) −913.295 −0.127291
\(373\) 4632.77 0.643099 0.321549 0.946893i \(-0.395796\pi\)
0.321549 + 0.946893i \(0.395796\pi\)
\(374\) 0 0
\(375\) −375.000 −0.0516398
\(376\) −7058.22 −0.968085
\(377\) 6094.45 0.832573
\(378\) −432.000 −0.0587822
\(379\) 6503.31 0.881406 0.440703 0.897653i \(-0.354729\pi\)
0.440703 + 0.897653i \(0.354729\pi\)
\(380\) 1102.46 0.148829
\(381\) 5219.45 0.701839
\(382\) 1330.79 0.178244
\(383\) 12734.5 1.69897 0.849484 0.527614i \(-0.176913\pi\)
0.849484 + 0.527614i \(0.176913\pi\)
\(384\) 3552.39 0.472090
\(385\) 0 0
\(386\) −3841.35 −0.506527
\(387\) 21.3071 0.00279870
\(388\) 5374.38 0.703203
\(389\) 12024.6 1.56728 0.783639 0.621216i \(-0.213361\pi\)
0.783639 + 0.621216i \(0.213361\pi\)
\(390\) 957.471 0.124317
\(391\) 6089.63 0.787636
\(392\) −5040.47 −0.649444
\(393\) −938.511 −0.120462
\(394\) 5429.61 0.694263
\(395\) 4759.18 0.606228
\(396\) 0 0
\(397\) −5223.65 −0.660371 −0.330186 0.943916i \(-0.607111\pi\)
−0.330186 + 0.943916i \(0.607111\pi\)
\(398\) −6238.46 −0.785693
\(399\) 1218.66 0.152905
\(400\) 285.582 0.0356978
\(401\) 9648.18 1.20151 0.600757 0.799432i \(-0.294866\pi\)
0.600757 + 0.799432i \(0.294866\pi\)
\(402\) 1897.22 0.235384
\(403\) 2237.55 0.276576
\(404\) 1938.76 0.238755
\(405\) −405.000 −0.0496904
\(406\) −2385.48 −0.291600
\(407\) 0 0
\(408\) 6271.06 0.760941
\(409\) 2010.47 0.243060 0.121530 0.992588i \(-0.461220\pi\)
0.121530 + 0.992588i \(0.461220\pi\)
\(410\) −2627.15 −0.316453
\(411\) −2150.78 −0.258127
\(412\) 8544.65 1.02176
\(413\) −3799.02 −0.452633
\(414\) −867.034 −0.102929
\(415\) 3676.11 0.434827
\(416\) −7654.39 −0.902133
\(417\) 2629.45 0.308788
\(418\) 0 0
\(419\) 4435.27 0.517129 0.258565 0.965994i \(-0.416750\pi\)
0.258565 + 0.965994i \(0.416750\pi\)
\(420\) 854.773 0.0993063
\(421\) 15217.9 1.76170 0.880852 0.473392i \(-0.156971\pi\)
0.880852 + 0.473392i \(0.156971\pi\)
\(422\) 1633.58 0.188440
\(423\) −2999.66 −0.344795
\(424\) 13554.7 1.55253
\(425\) 2467.71 0.281650
\(426\) −4400.26 −0.500454
\(427\) 7319.95 0.829595
\(428\) −4333.45 −0.489405
\(429\) 0 0
\(430\) 18.4845 0.00207303
\(431\) 5622.11 0.628324 0.314162 0.949369i \(-0.398277\pi\)
0.314162 + 0.949369i \(0.398277\pi\)
\(432\) 308.429 0.0343502
\(433\) −14306.3 −1.58780 −0.793898 0.608051i \(-0.791951\pi\)
−0.793898 + 0.608051i \(0.791951\pi\)
\(434\) −875.818 −0.0968678
\(435\) −2236.39 −0.246498
\(436\) −8352.29 −0.917436
\(437\) 2445.88 0.267740
\(438\) −1698.52 −0.185293
\(439\) −4384.20 −0.476643 −0.238322 0.971186i \(-0.576597\pi\)
−0.238322 + 0.971186i \(0.576597\pi\)
\(440\) 0 0
\(441\) −2142.14 −0.231307
\(442\) −6300.69 −0.678039
\(443\) −10090.0 −1.08214 −0.541071 0.840977i \(-0.681981\pi\)
−0.541071 + 0.840977i \(0.681981\pi\)
\(444\) −749.040 −0.0800627
\(445\) −1929.39 −0.205533
\(446\) 790.560 0.0839330
\(447\) 7129.07 0.754348
\(448\) 2059.71 0.217215
\(449\) 9582.52 1.00719 0.503594 0.863941i \(-0.332011\pi\)
0.503594 + 0.863941i \(0.332011\pi\)
\(450\) −351.349 −0.0368062
\(451\) 0 0
\(452\) −945.464 −0.0983869
\(453\) 278.540 0.0288895
\(454\) −6693.27 −0.691918
\(455\) −2094.17 −0.215772
\(456\) 2518.75 0.258665
\(457\) −9999.34 −1.02352 −0.511761 0.859128i \(-0.671007\pi\)
−0.511761 + 0.859128i \(0.671007\pi\)
\(458\) −8915.49 −0.909593
\(459\) 2665.12 0.271018
\(460\) 1715.55 0.173887
\(461\) 11115.8 1.12302 0.561512 0.827468i \(-0.310220\pi\)
0.561512 + 0.827468i \(0.310220\pi\)
\(462\) 0 0
\(463\) −1567.16 −0.157305 −0.0786524 0.996902i \(-0.525062\pi\)
−0.0786524 + 0.996902i \(0.525062\pi\)
\(464\) 1703.13 0.170401
\(465\) −821.080 −0.0818853
\(466\) 4600.48 0.457325
\(467\) 12648.8 1.25335 0.626675 0.779281i \(-0.284415\pi\)
0.626675 + 0.779281i \(0.284415\pi\)
\(468\) −2046.05 −0.202091
\(469\) −4149.56 −0.408548
\(470\) −2602.29 −0.255393
\(471\) −5643.72 −0.552120
\(472\) −7851.88 −0.765704
\(473\) 0 0
\(474\) 4459.02 0.432088
\(475\) 991.146 0.0957408
\(476\) −5624.88 −0.541630
\(477\) 5760.58 0.552953
\(478\) −3246.30 −0.310633
\(479\) 10719.2 1.02249 0.511247 0.859434i \(-0.329184\pi\)
0.511247 + 0.859434i \(0.329184\pi\)
\(480\) 2808.82 0.267093
\(481\) 1835.12 0.173959
\(482\) 2894.14 0.273494
\(483\) 1896.36 0.178649
\(484\) 0 0
\(485\) 4831.72 0.452365
\(486\) −379.457 −0.0354167
\(487\) 7161.20 0.666335 0.333167 0.942868i \(-0.391883\pi\)
0.333167 + 0.942868i \(0.391883\pi\)
\(488\) 15129.0 1.40340
\(489\) −7396.48 −0.684009
\(490\) −1858.37 −0.171331
\(491\) −14567.3 −1.33893 −0.669463 0.742845i \(-0.733476\pi\)
−0.669463 + 0.742845i \(0.733476\pi\)
\(492\) 5614.04 0.514432
\(493\) 14716.7 1.34444
\(494\) −2530.65 −0.230485
\(495\) 0 0
\(496\) 625.295 0.0566060
\(497\) 9624.18 0.868619
\(498\) 3444.26 0.309922
\(499\) −4638.99 −0.416172 −0.208086 0.978111i \(-0.566723\pi\)
−0.208086 + 0.978111i \(0.566723\pi\)
\(500\) 695.194 0.0621801
\(501\) 3762.89 0.335556
\(502\) 3682.75 0.327428
\(503\) 12206.3 1.08201 0.541006 0.841019i \(-0.318044\pi\)
0.541006 + 0.841019i \(0.318044\pi\)
\(504\) 1952.86 0.172594
\(505\) 1743.00 0.153589
\(506\) 0 0
\(507\) −1578.24 −0.138249
\(508\) −9676.09 −0.845093
\(509\) 10018.6 0.872427 0.436214 0.899843i \(-0.356319\pi\)
0.436214 + 0.899843i \(0.356319\pi\)
\(510\) 2312.07 0.200746
\(511\) 3714.97 0.321606
\(512\) −4074.36 −0.351686
\(513\) 1070.44 0.0921267
\(514\) −8618.61 −0.739592
\(515\) 7681.89 0.657291
\(516\) −39.5001 −0.00336995
\(517\) 0 0
\(518\) −718.303 −0.0609274
\(519\) 3620.12 0.306177
\(520\) −4328.27 −0.365014
\(521\) 1054.72 0.0886916 0.0443458 0.999016i \(-0.485880\pi\)
0.0443458 + 0.999016i \(0.485880\pi\)
\(522\) −2095.35 −0.175691
\(523\) 16234.2 1.35730 0.678652 0.734460i \(-0.262564\pi\)
0.678652 + 0.734460i \(0.262564\pi\)
\(524\) 1739.86 0.145050
\(525\) 768.466 0.0638830
\(526\) 3528.57 0.292496
\(527\) 5403.16 0.446613
\(528\) 0 0
\(529\) −8360.95 −0.687183
\(530\) 4997.47 0.409578
\(531\) −3336.95 −0.272715
\(532\) −2259.21 −0.184115
\(533\) −13754.2 −1.11775
\(534\) −1807.71 −0.146493
\(535\) −3895.90 −0.314831
\(536\) −8576.40 −0.691127
\(537\) −4326.86 −0.347706
\(538\) −10992.6 −0.880900
\(539\) 0 0
\(540\) 750.810 0.0598328
\(541\) −675.936 −0.0537167 −0.0268584 0.999639i \(-0.508550\pi\)
−0.0268584 + 0.999639i \(0.508550\pi\)
\(542\) 8049.93 0.637960
\(543\) 12785.4 1.01045
\(544\) −18483.6 −1.45676
\(545\) −7508.96 −0.590181
\(546\) −1962.09 −0.153791
\(547\) −13058.2 −1.02071 −0.510355 0.859964i \(-0.670486\pi\)
−0.510355 + 0.859964i \(0.670486\pi\)
\(548\) 3987.23 0.310814
\(549\) 6429.65 0.499837
\(550\) 0 0
\(551\) 5910.91 0.457011
\(552\) 3919.44 0.302215
\(553\) −9752.70 −0.749959
\(554\) 14170.3 1.08672
\(555\) −673.409 −0.0515038
\(556\) −4874.61 −0.371815
\(557\) 6710.48 0.510471 0.255236 0.966879i \(-0.417847\pi\)
0.255236 + 0.966879i \(0.417847\pi\)
\(558\) −769.295 −0.0583636
\(559\) 96.7741 0.00732219
\(560\) −585.227 −0.0441614
\(561\) 0 0
\(562\) −5321.45 −0.399416
\(563\) 20820.5 1.55858 0.779288 0.626666i \(-0.215581\pi\)
0.779288 + 0.626666i \(0.215581\pi\)
\(564\) 5560.92 0.415172
\(565\) −850.000 −0.0632916
\(566\) −13785.0 −1.02372
\(567\) 829.943 0.0614715
\(568\) 19891.5 1.46941
\(569\) −3251.08 −0.239530 −0.119765 0.992802i \(-0.538214\pi\)
−0.119765 + 0.992802i \(0.538214\pi\)
\(570\) 928.636 0.0682391
\(571\) 4637.50 0.339883 0.169941 0.985454i \(-0.445642\pi\)
0.169941 + 0.985454i \(0.445642\pi\)
\(572\) 0 0
\(573\) −2556.67 −0.186399
\(574\) 5383.67 0.391481
\(575\) 1542.33 0.111860
\(576\) 1809.20 0.130874
\(577\) 14462.4 1.04346 0.521730 0.853111i \(-0.325287\pi\)
0.521730 + 0.853111i \(0.325287\pi\)
\(578\) −7542.82 −0.542803
\(579\) 7379.86 0.529700
\(580\) 4145.94 0.296812
\(581\) −7533.23 −0.537920
\(582\) 4526.99 0.322423
\(583\) 0 0
\(584\) 7678.18 0.544050
\(585\) −1839.46 −0.130004
\(586\) −7071.17 −0.498476
\(587\) −22759.7 −1.60033 −0.800166 0.599779i \(-0.795255\pi\)
−0.800166 + 0.599779i \(0.795255\pi\)
\(588\) 3971.20 0.278520
\(589\) 2170.16 0.151816
\(590\) −2894.91 −0.202002
\(591\) −10431.2 −0.726025
\(592\) 512.836 0.0356038
\(593\) 14956.4 1.03573 0.517864 0.855463i \(-0.326727\pi\)
0.517864 + 0.855463i \(0.326727\pi\)
\(594\) 0 0
\(595\) −5056.93 −0.348427
\(596\) −13216.2 −0.908319
\(597\) 11985.1 0.821638
\(598\) −3937.96 −0.269290
\(599\) 2150.77 0.146708 0.0733539 0.997306i \(-0.476630\pi\)
0.0733539 + 0.997306i \(0.476630\pi\)
\(600\) 1588.28 0.108069
\(601\) −27759.8 −1.88410 −0.942050 0.335472i \(-0.891104\pi\)
−0.942050 + 0.335472i \(0.891104\pi\)
\(602\) −37.8792 −0.00256452
\(603\) −3644.86 −0.246153
\(604\) −516.371 −0.0347862
\(605\) 0 0
\(606\) 1633.07 0.109470
\(607\) 10991.5 0.734974 0.367487 0.930029i \(-0.380218\pi\)
0.367487 + 0.930029i \(0.380218\pi\)
\(608\) −7423.87 −0.495194
\(609\) 4582.91 0.304941
\(610\) 5577.91 0.370234
\(611\) −13624.1 −0.902081
\(612\) −4940.74 −0.326336
\(613\) −10646.1 −0.701457 −0.350728 0.936477i \(-0.614066\pi\)
−0.350728 + 0.936477i \(0.614066\pi\)
\(614\) 887.128 0.0583088
\(615\) 5047.19 0.330930
\(616\) 0 0
\(617\) 7199.92 0.469786 0.234893 0.972021i \(-0.424526\pi\)
0.234893 + 0.972021i \(0.424526\pi\)
\(618\) 7197.41 0.468483
\(619\) 12186.9 0.791332 0.395666 0.918395i \(-0.370514\pi\)
0.395666 + 0.918395i \(0.370514\pi\)
\(620\) 1522.16 0.0985990
\(621\) 1665.72 0.107637
\(622\) 10702.2 0.689905
\(623\) 3953.80 0.254262
\(624\) 1400.85 0.0898698
\(625\) 625.000 0.0400000
\(626\) 1778.49 0.113551
\(627\) 0 0
\(628\) 10462.6 0.664814
\(629\) 4431.40 0.280909
\(630\) 720.000 0.0455325
\(631\) 7370.64 0.465009 0.232505 0.972595i \(-0.425308\pi\)
0.232505 + 0.972595i \(0.425308\pi\)
\(632\) −20157.1 −1.26868
\(633\) −3138.38 −0.197061
\(634\) −5008.65 −0.313752
\(635\) −8699.09 −0.543642
\(636\) −10679.3 −0.665818
\(637\) −9729.32 −0.605164
\(638\) 0 0
\(639\) 8453.63 0.523349
\(640\) −5920.66 −0.365679
\(641\) −25014.9 −1.54139 −0.770693 0.637207i \(-0.780090\pi\)
−0.770693 + 0.637207i \(0.780090\pi\)
\(642\) −3650.19 −0.224395
\(643\) −21668.2 −1.32894 −0.664472 0.747313i \(-0.731343\pi\)
−0.664472 + 0.747313i \(0.731343\pi\)
\(644\) −3515.58 −0.215113
\(645\) −35.5118 −0.00216787
\(646\) −6110.94 −0.372185
\(647\) −27625.3 −1.67861 −0.839305 0.543661i \(-0.817038\pi\)
−0.839305 + 0.543661i \(0.817038\pi\)
\(648\) 1715.34 0.103989
\(649\) 0 0
\(650\) −1595.79 −0.0962952
\(651\) 1682.59 0.101299
\(652\) 13712.0 0.823623
\(653\) −14314.0 −0.857810 −0.428905 0.903350i \(-0.641101\pi\)
−0.428905 + 0.903350i \(0.641101\pi\)
\(654\) −7035.38 −0.420650
\(655\) 1564.19 0.0933096
\(656\) −3843.70 −0.228767
\(657\) 3263.13 0.193770
\(658\) 5332.73 0.315944
\(659\) 28327.8 1.67450 0.837249 0.546822i \(-0.184163\pi\)
0.837249 + 0.546822i \(0.184163\pi\)
\(660\) 0 0
\(661\) −32190.9 −1.89422 −0.947112 0.320905i \(-0.896013\pi\)
−0.947112 + 0.320905i \(0.896013\pi\)
\(662\) 14265.0 0.837498
\(663\) 12104.7 0.709059
\(664\) −15569.8 −0.909981
\(665\) −2031.10 −0.118440
\(666\) −630.938 −0.0367092
\(667\) 9198.01 0.533955
\(668\) −6975.84 −0.404047
\(669\) −1518.80 −0.0877729
\(670\) −3162.03 −0.182328
\(671\) 0 0
\(672\) −5755.95 −0.330418
\(673\) 6207.38 0.355538 0.177769 0.984072i \(-0.443112\pi\)
0.177769 + 0.984072i \(0.443112\pi\)
\(674\) −5418.66 −0.309672
\(675\) 675.000 0.0384900
\(676\) 2925.82 0.166467
\(677\) −28831.1 −1.63674 −0.818368 0.574695i \(-0.805121\pi\)
−0.818368 + 0.574695i \(0.805121\pi\)
\(678\) −796.392 −0.0451110
\(679\) −9901.37 −0.559617
\(680\) −10451.8 −0.589422
\(681\) 12858.9 0.723573
\(682\) 0 0
\(683\) 3193.10 0.178888 0.0894441 0.995992i \(-0.471491\pi\)
0.0894441 + 0.995992i \(0.471491\pi\)
\(684\) −1984.43 −0.110931
\(685\) 3584.64 0.199945
\(686\) 9296.24 0.517394
\(687\) 17128.1 0.951206
\(688\) 27.0441 0.00149861
\(689\) 26163.8 1.44668
\(690\) 1445.06 0.0797281
\(691\) 7682.49 0.422946 0.211473 0.977384i \(-0.432174\pi\)
0.211473 + 0.977384i \(0.432174\pi\)
\(692\) −6711.17 −0.368671
\(693\) 0 0
\(694\) −139.496 −0.00762996
\(695\) −4382.41 −0.239186
\(696\) 9472.05 0.515858
\(697\) −33213.3 −1.80494
\(698\) −233.256 −0.0126488
\(699\) −8838.28 −0.478247
\(700\) −1424.62 −0.0769223
\(701\) −26551.6 −1.43058 −0.715292 0.698825i \(-0.753707\pi\)
−0.715292 + 0.698825i \(0.753707\pi\)
\(702\) −1723.45 −0.0926601
\(703\) 1779.86 0.0954887
\(704\) 0 0
\(705\) 4999.43 0.267077
\(706\) −12285.7 −0.654928
\(707\) −3571.83 −0.190004
\(708\) 6186.22 0.328379
\(709\) −16304.6 −0.863655 −0.431828 0.901956i \(-0.642131\pi\)
−0.431828 + 0.901956i \(0.642131\pi\)
\(710\) 7333.77 0.387650
\(711\) −8566.52 −0.451856
\(712\) 8171.79 0.430127
\(713\) 3377.00 0.177377
\(714\) −4738.00 −0.248341
\(715\) 0 0
\(716\) 8021.36 0.418676
\(717\) 6236.68 0.324844
\(718\) 7767.50 0.403733
\(719\) −3973.62 −0.206107 −0.103053 0.994676i \(-0.532861\pi\)
−0.103053 + 0.994676i \(0.532861\pi\)
\(720\) −514.048 −0.0266076
\(721\) −15742.1 −0.813128
\(722\) 8256.25 0.425576
\(723\) −5560.11 −0.286007
\(724\) −23702.3 −1.21670
\(725\) 3727.32 0.190937
\(726\) 0 0
\(727\) −10780.4 −0.549961 −0.274980 0.961450i \(-0.588671\pi\)
−0.274980 + 0.961450i \(0.588671\pi\)
\(728\) 8869.67 0.451555
\(729\) 729.000 0.0370370
\(730\) 2830.86 0.143527
\(731\) 233.687 0.0118238
\(732\) −11919.6 −0.601860
\(733\) 9211.46 0.464165 0.232083 0.972696i \(-0.425446\pi\)
0.232083 + 0.972696i \(0.425446\pi\)
\(734\) 20716.6 1.04177
\(735\) 3570.23 0.179170
\(736\) −11552.3 −0.578566
\(737\) 0 0
\(738\) 4728.87 0.235870
\(739\) −11084.7 −0.551768 −0.275884 0.961191i \(-0.588971\pi\)
−0.275884 + 0.961191i \(0.588971\pi\)
\(740\) 1248.40 0.0620163
\(741\) 4861.80 0.241029
\(742\) −10241.0 −0.506685
\(743\) 27420.4 1.35391 0.676955 0.736024i \(-0.263299\pi\)
0.676955 + 0.736024i \(0.263299\pi\)
\(744\) 3477.61 0.171365
\(745\) −11881.8 −0.584316
\(746\) −7234.32 −0.355050
\(747\) −6616.99 −0.324101
\(748\) 0 0
\(749\) 7983.64 0.389474
\(750\) 585.582 0.0285099
\(751\) −11290.8 −0.548614 −0.274307 0.961642i \(-0.588448\pi\)
−0.274307 + 0.961642i \(0.588448\pi\)
\(752\) −3807.33 −0.184626
\(753\) −7075.16 −0.342408
\(754\) −9516.81 −0.459657
\(755\) −464.233 −0.0223777
\(756\) −1538.59 −0.0740185
\(757\) 3739.19 0.179528 0.0897642 0.995963i \(-0.471389\pi\)
0.0897642 + 0.995963i \(0.471389\pi\)
\(758\) −10155.3 −0.486617
\(759\) 0 0
\(760\) −4197.92 −0.200361
\(761\) 15621.1 0.744107 0.372053 0.928211i \(-0.378654\pi\)
0.372053 + 0.928211i \(0.378654\pi\)
\(762\) −8150.45 −0.387480
\(763\) 15387.7 0.730106
\(764\) 4739.69 0.224445
\(765\) −4441.87 −0.209930
\(766\) −19885.7 −0.937987
\(767\) −15156.0 −0.713498
\(768\) −10371.8 −0.487317
\(769\) −40241.7 −1.88706 −0.943531 0.331284i \(-0.892518\pi\)
−0.943531 + 0.331284i \(0.892518\pi\)
\(770\) 0 0
\(771\) 16557.8 0.773428
\(772\) −13681.2 −0.637818
\(773\) 22821.4 1.06187 0.530936 0.847412i \(-0.321840\pi\)
0.530936 + 0.847412i \(0.321840\pi\)
\(774\) −33.2721 −0.00154514
\(775\) 1368.47 0.0634281
\(776\) −20464.4 −0.946685
\(777\) 1379.98 0.0637148
\(778\) −18777.0 −0.865282
\(779\) −13340.0 −0.613549
\(780\) 3410.09 0.156539
\(781\) 0 0
\(782\) −9509.28 −0.434848
\(783\) 4025.51 0.183729
\(784\) −2718.92 −0.123857
\(785\) 9406.19 0.427671
\(786\) 1465.53 0.0665062
\(787\) 29454.3 1.33410 0.667048 0.745015i \(-0.267558\pi\)
0.667048 + 0.745015i \(0.267558\pi\)
\(788\) 19337.8 0.874216
\(789\) −6778.96 −0.305878
\(790\) −7431.70 −0.334694
\(791\) 1741.86 0.0782974
\(792\) 0 0
\(793\) 29202.7 1.30771
\(794\) 8157.00 0.364586
\(795\) −9600.97 −0.428316
\(796\) −22218.6 −0.989344
\(797\) −27440.3 −1.21955 −0.609777 0.792573i \(-0.708741\pi\)
−0.609777 + 0.792573i \(0.708741\pi\)
\(798\) −1903.00 −0.0844179
\(799\) −32899.0 −1.45668
\(800\) −4681.37 −0.206889
\(801\) 3472.91 0.153195
\(802\) −15066.1 −0.663346
\(803\) 0 0
\(804\) 6757.03 0.296396
\(805\) −3160.61 −0.138381
\(806\) −3494.05 −0.152695
\(807\) 21118.6 0.921201
\(808\) −7382.34 −0.321423
\(809\) 5060.18 0.219909 0.109954 0.993937i \(-0.464930\pi\)
0.109954 + 0.993937i \(0.464930\pi\)
\(810\) 632.429 0.0274337
\(811\) −30480.1 −1.31973 −0.659865 0.751384i \(-0.729387\pi\)
−0.659865 + 0.751384i \(0.729387\pi\)
\(812\) −8496.03 −0.367183
\(813\) −15465.2 −0.667146
\(814\) 0 0
\(815\) 12327.5 0.529831
\(816\) 3382.72 0.145121
\(817\) 93.8596 0.00401925
\(818\) −3139.46 −0.134192
\(819\) 3769.50 0.160827
\(820\) −9356.73 −0.398477
\(821\) −37909.0 −1.61149 −0.805745 0.592263i \(-0.798235\pi\)
−0.805745 + 0.592263i \(0.798235\pi\)
\(822\) 3358.56 0.142510
\(823\) 23636.0 1.00109 0.500546 0.865710i \(-0.333133\pi\)
0.500546 + 0.865710i \(0.333133\pi\)
\(824\) −32536.0 −1.37554
\(825\) 0 0
\(826\) 5932.36 0.249895
\(827\) 42634.3 1.79267 0.896336 0.443376i \(-0.146219\pi\)
0.896336 + 0.443376i \(0.146219\pi\)
\(828\) −3087.99 −0.129608
\(829\) −45152.5 −1.89169 −0.945845 0.324619i \(-0.894764\pi\)
−0.945845 + 0.324619i \(0.894764\pi\)
\(830\) −5740.44 −0.240064
\(831\) −27223.6 −1.13643
\(832\) 8217.15 0.342402
\(833\) −23494.1 −0.977217
\(834\) −4106.02 −0.170480
\(835\) −6271.49 −0.259921
\(836\) 0 0
\(837\) 1477.94 0.0610337
\(838\) −6925.91 −0.285503
\(839\) 30431.5 1.25222 0.626110 0.779734i \(-0.284646\pi\)
0.626110 + 0.779734i \(0.284646\pi\)
\(840\) −3254.77 −0.133691
\(841\) −2160.34 −0.0885784
\(842\) −23763.6 −0.972623
\(843\) 10223.4 0.417689
\(844\) 5818.09 0.237283
\(845\) 2630.40 0.107087
\(846\) 4684.13 0.190359
\(847\) 0 0
\(848\) 7311.64 0.296088
\(849\) 26483.2 1.07055
\(850\) −3853.46 −0.155497
\(851\) 2769.65 0.111566
\(852\) −15671.8 −0.630171
\(853\) −10367.2 −0.416139 −0.208070 0.978114i \(-0.566718\pi\)
−0.208070 + 0.978114i \(0.566718\pi\)
\(854\) −11430.5 −0.458013
\(855\) −1784.06 −0.0713610
\(856\) 16500.8 0.658860
\(857\) −12947.1 −0.516063 −0.258032 0.966136i \(-0.583074\pi\)
−0.258032 + 0.966136i \(0.583074\pi\)
\(858\) 0 0
\(859\) −20383.5 −0.809636 −0.404818 0.914397i \(-0.632665\pi\)
−0.404818 + 0.914397i \(0.632665\pi\)
\(860\) 65.8335 0.00261035
\(861\) −10342.9 −0.409391
\(862\) −8779.22 −0.346893
\(863\) 9056.42 0.357224 0.178612 0.983920i \(-0.442839\pi\)
0.178612 + 0.983920i \(0.442839\pi\)
\(864\) −5055.88 −0.199079
\(865\) −6033.54 −0.237164
\(866\) 22340.0 0.876610
\(867\) 14491.0 0.567636
\(868\) −3119.27 −0.121976
\(869\) 0 0
\(870\) 3492.24 0.136090
\(871\) −16554.5 −0.644005
\(872\) 31803.6 1.23510
\(873\) −8697.10 −0.337173
\(874\) −3819.37 −0.147817
\(875\) −1280.78 −0.0494836
\(876\) −6049.36 −0.233321
\(877\) 2867.88 0.110424 0.0552118 0.998475i \(-0.482417\pi\)
0.0552118 + 0.998475i \(0.482417\pi\)
\(878\) 6846.16 0.263151
\(879\) 13584.9 0.521281
\(880\) 0 0
\(881\) −11862.5 −0.453640 −0.226820 0.973937i \(-0.572833\pi\)
−0.226820 + 0.973937i \(0.572833\pi\)
\(882\) 3345.06 0.127703
\(883\) 33463.8 1.27537 0.637683 0.770299i \(-0.279893\pi\)
0.637683 + 0.770299i \(0.279893\pi\)
\(884\) −22440.3 −0.853787
\(885\) 5561.59 0.211244
\(886\) 15756.0 0.597442
\(887\) −2420.75 −0.0916357 −0.0458178 0.998950i \(-0.514589\pi\)
−0.0458178 + 0.998950i \(0.514589\pi\)
\(888\) 2852.17 0.107784
\(889\) 17826.5 0.672534
\(890\) 3012.85 0.113473
\(891\) 0 0
\(892\) 2815.62 0.105688
\(893\) −13213.8 −0.495165
\(894\) −11132.4 −0.416470
\(895\) 7211.44 0.269332
\(896\) 12132.9 0.452378
\(897\) 7565.48 0.281610
\(898\) −14963.6 −0.556060
\(899\) 8161.14 0.302769
\(900\) −1251.35 −0.0463463
\(901\) 63179.7 2.33609
\(902\) 0 0
\(903\) 72.7722 0.00268185
\(904\) 3600.10 0.132453
\(905\) −21309.0 −0.782692
\(906\) −434.955 −0.0159497
\(907\) −38154.1 −1.39679 −0.698393 0.715714i \(-0.746101\pi\)
−0.698393 + 0.715714i \(0.746101\pi\)
\(908\) −23838.4 −0.871262
\(909\) −3137.40 −0.114479
\(910\) 3270.15 0.119126
\(911\) −35758.0 −1.30045 −0.650227 0.759740i \(-0.725326\pi\)
−0.650227 + 0.759740i \(0.725326\pi\)
\(912\) 1358.66 0.0493308
\(913\) 0 0
\(914\) 15614.5 0.565079
\(915\) −10716.1 −0.387172
\(916\) −31753.0 −1.14536
\(917\) −3205.39 −0.115432
\(918\) −4161.73 −0.149627
\(919\) −17387.5 −0.624115 −0.312058 0.950063i \(-0.601018\pi\)
−0.312058 + 0.950063i \(0.601018\pi\)
\(920\) −6532.41 −0.234095
\(921\) −1704.32 −0.0609764
\(922\) −17357.9 −0.620013
\(923\) 38395.3 1.36923
\(924\) 0 0
\(925\) 1122.35 0.0398947
\(926\) 2447.20 0.0868467
\(927\) −13827.4 −0.489915
\(928\) −27918.3 −0.987569
\(929\) 6955.93 0.245658 0.122829 0.992428i \(-0.460803\pi\)
0.122829 + 0.992428i \(0.460803\pi\)
\(930\) 1282.16 0.0452082
\(931\) −9436.31 −0.332183
\(932\) 16384.9 0.575863
\(933\) −20560.8 −0.721467
\(934\) −19751.7 −0.691965
\(935\) 0 0
\(936\) 7790.88 0.272065
\(937\) 16074.5 0.560438 0.280219 0.959936i \(-0.409593\pi\)
0.280219 + 0.959936i \(0.409593\pi\)
\(938\) 6479.76 0.225556
\(939\) −3416.77 −0.118746
\(940\) −9268.20 −0.321591
\(941\) 687.126 0.0238041 0.0119021 0.999929i \(-0.496211\pi\)
0.0119021 + 0.999929i \(0.496211\pi\)
\(942\) 8812.96 0.304821
\(943\) −20758.5 −0.716849
\(944\) −4235.44 −0.146030
\(945\) −1383.24 −0.0476156
\(946\) 0 0
\(947\) 35352.0 1.21308 0.606540 0.795053i \(-0.292557\pi\)
0.606540 + 0.795053i \(0.292557\pi\)
\(948\) 15881.0 0.544085
\(949\) 14820.7 0.506956
\(950\) −1547.73 −0.0528578
\(951\) 9622.44 0.328106
\(952\) 21418.2 0.729168
\(953\) 19390.7 0.659103 0.329552 0.944138i \(-0.393102\pi\)
0.329552 + 0.944138i \(0.393102\pi\)
\(954\) −8995.45 −0.305281
\(955\) 4261.12 0.144384
\(956\) −11561.9 −0.391148
\(957\) 0 0
\(958\) −16738.7 −0.564511
\(959\) −7345.80 −0.247349
\(960\) −3015.33 −0.101374
\(961\) −26794.7 −0.899422
\(962\) −2865.64 −0.0960416
\(963\) 7012.62 0.234661
\(964\) 10307.6 0.344384
\(965\) −12299.8 −0.410304
\(966\) −2961.27 −0.0986308
\(967\) −28643.6 −0.952551 −0.476275 0.879296i \(-0.658013\pi\)
−0.476275 + 0.879296i \(0.658013\pi\)
\(968\) 0 0
\(969\) 11740.1 0.389213
\(970\) −7544.99 −0.249747
\(971\) −19574.8 −0.646946 −0.323473 0.946237i \(-0.604851\pi\)
−0.323473 + 0.946237i \(0.604851\pi\)
\(972\) −1351.46 −0.0445967
\(973\) 8980.63 0.295895
\(974\) −11182.6 −0.367878
\(975\) 3065.77 0.100701
\(976\) 8160.86 0.267646
\(977\) 50095.5 1.64043 0.820213 0.572058i \(-0.193855\pi\)
0.820213 + 0.572058i \(0.193855\pi\)
\(978\) 11550.0 0.377636
\(979\) 0 0
\(980\) −6618.67 −0.215740
\(981\) 13516.1 0.439895
\(982\) 22747.6 0.739211
\(983\) 14445.4 0.468706 0.234353 0.972152i \(-0.424703\pi\)
0.234353 + 0.972152i \(0.424703\pi\)
\(984\) −21376.9 −0.692553
\(985\) 17385.3 0.562377
\(986\) −22980.9 −0.742253
\(987\) −10245.0 −0.330399
\(988\) −9013.05 −0.290226
\(989\) 146.056 0.00469595
\(990\) 0 0
\(991\) 29120.1 0.933430 0.466715 0.884408i \(-0.345437\pi\)
0.466715 + 0.884408i \(0.345437\pi\)
\(992\) −10250.1 −0.328064
\(993\) −27405.4 −0.875814
\(994\) −15028.7 −0.479558
\(995\) −19975.2 −0.636438
\(996\) 12266.9 0.390253
\(997\) 9137.45 0.290257 0.145128 0.989413i \(-0.453640\pi\)
0.145128 + 0.989413i \(0.453640\pi\)
\(998\) 7244.03 0.229765
\(999\) 1212.14 0.0383887
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 1815.4.a.n.1.1 2
11.10 odd 2 165.4.a.c.1.2 2
33.32 even 2 495.4.a.d.1.1 2
55.32 even 4 825.4.c.j.199.3 4
55.43 even 4 825.4.c.j.199.2 4
55.54 odd 2 825.4.a.m.1.1 2
165.164 even 2 2475.4.a.n.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.4.a.c.1.2 2 11.10 odd 2
495.4.a.d.1.1 2 33.32 even 2
825.4.a.m.1.1 2 55.54 odd 2
825.4.c.j.199.2 4 55.43 even 4
825.4.c.j.199.3 4 55.32 even 4
1815.4.a.n.1.1 2 1.1 even 1 trivial
2475.4.a.n.1.2 2 165.164 even 2