Properties

Label 2205.4.a.ca.1.4
Level $2205$
Weight $4$
Character 2205.1
Self dual yes
Analytic conductor $130.099$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2205.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(130.099211563\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.1163891200.1
Defining polynomial: \( x^{6} - 2x^{5} - 23x^{4} + 12x^{3} + 154x^{2} + 152x + 28 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2\cdot 7 \)
Twist minimal: no (minimal twist has level 245)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.04490\) of defining polynomial
Character \(\chi\) \(=\) 2205.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.369315 q^{2} -7.86361 q^{4} +5.00000 q^{5} -5.85867 q^{8} +O(q^{10})\) \(q+0.369315 q^{2} -7.86361 q^{4} +5.00000 q^{5} -5.85867 q^{8} +1.84657 q^{10} -30.6361 q^{11} -36.4622 q^{13} +60.7452 q^{16} -79.7341 q^{17} +152.418 q^{19} -39.3180 q^{20} -11.3144 q^{22} -22.2207 q^{23} +25.0000 q^{25} -13.4660 q^{26} -101.285 q^{29} -249.956 q^{31} +69.3034 q^{32} -29.4470 q^{34} +7.55765 q^{37} +56.2904 q^{38} -29.2933 q^{40} +142.280 q^{41} -237.530 q^{43} +240.910 q^{44} -8.20644 q^{46} -331.129 q^{47} +9.23287 q^{50} +286.725 q^{52} +487.337 q^{53} -153.180 q^{55} -37.4059 q^{58} -717.355 q^{59} -354.592 q^{61} -92.3126 q^{62} -460.367 q^{64} -182.311 q^{65} +57.5883 q^{67} +626.997 q^{68} +696.174 q^{71} +261.035 q^{73} +2.79115 q^{74} -1198.56 q^{76} +271.344 q^{79} +303.726 q^{80} +52.5460 q^{82} +681.441 q^{83} -398.670 q^{85} -87.7234 q^{86} +179.487 q^{88} +160.668 q^{89} +174.735 q^{92} -122.291 q^{94} +762.092 q^{95} +167.841 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{2} + 14 q^{4} + 30 q^{5} + 66 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{2} + 14 q^{4} + 30 q^{5} + 66 q^{8} + 10 q^{10} + 16 q^{11} + 168 q^{13} + 298 q^{16} + 4 q^{17} + 308 q^{19} + 70 q^{20} - 236 q^{22} + 336 q^{23} + 150 q^{25} - 56 q^{26} - 176 q^{29} + 392 q^{31} + 770 q^{32} + 812 q^{34} - 140 q^{37} - 20 q^{38} + 330 q^{40} - 656 q^{41} - 388 q^{43} + 160 q^{44} - 388 q^{46} - 628 q^{47} + 50 q^{50} + 1520 q^{52} + 676 q^{53} + 80 q^{55} - 2012 q^{58} - 996 q^{59} + 740 q^{61} + 364 q^{62} + 1426 q^{64} + 840 q^{65} + 1768 q^{67} + 2940 q^{68} + 224 q^{71} + 2640 q^{73} - 928 q^{74} - 1340 q^{76} + 1636 q^{79} + 1490 q^{80} - 1756 q^{82} - 140 q^{83} + 20 q^{85} - 1180 q^{86} - 5652 q^{88} + 1904 q^{89} + 1952 q^{92} - 3332 q^{94} + 1540 q^{95} + 516 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.369315 0.130573 0.0652863 0.997867i \(-0.479204\pi\)
0.0652863 + 0.997867i \(0.479204\pi\)
\(3\) 0 0
\(4\) −7.86361 −0.982951
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 0 0
\(8\) −5.85867 −0.258919
\(9\) 0 0
\(10\) 1.84657 0.0583938
\(11\) −30.6361 −0.839739 −0.419870 0.907584i \(-0.637924\pi\)
−0.419870 + 0.907584i \(0.637924\pi\)
\(12\) 0 0
\(13\) −36.4622 −0.777908 −0.388954 0.921257i \(-0.627164\pi\)
−0.388954 + 0.921257i \(0.627164\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 60.7452 0.949143
\(17\) −79.7341 −1.13755 −0.568775 0.822493i \(-0.692583\pi\)
−0.568775 + 0.822493i \(0.692583\pi\)
\(18\) 0 0
\(19\) 152.418 1.84038 0.920189 0.391474i \(-0.128035\pi\)
0.920189 + 0.391474i \(0.128035\pi\)
\(20\) −39.3180 −0.439589
\(21\) 0 0
\(22\) −11.3144 −0.109647
\(23\) −22.2207 −0.201450 −0.100725 0.994914i \(-0.532116\pi\)
−0.100725 + 0.994914i \(0.532116\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) −13.4660 −0.101573
\(27\) 0 0
\(28\) 0 0
\(29\) −101.285 −0.648555 −0.324278 0.945962i \(-0.605121\pi\)
−0.324278 + 0.945962i \(0.605121\pi\)
\(30\) 0 0
\(31\) −249.956 −1.44818 −0.724089 0.689707i \(-0.757739\pi\)
−0.724089 + 0.689707i \(0.757739\pi\)
\(32\) 69.3034 0.382851
\(33\) 0 0
\(34\) −29.4470 −0.148533
\(35\) 0 0
\(36\) 0 0
\(37\) 7.55765 0.0335803 0.0167901 0.999859i \(-0.494655\pi\)
0.0167901 + 0.999859i \(0.494655\pi\)
\(38\) 56.2904 0.240303
\(39\) 0 0
\(40\) −29.2933 −0.115792
\(41\) 142.280 0.541960 0.270980 0.962585i \(-0.412652\pi\)
0.270980 + 0.962585i \(0.412652\pi\)
\(42\) 0 0
\(43\) −237.530 −0.842396 −0.421198 0.906969i \(-0.638390\pi\)
−0.421198 + 0.906969i \(0.638390\pi\)
\(44\) 240.910 0.825422
\(45\) 0 0
\(46\) −8.20644 −0.0263038
\(47\) −331.129 −1.02766 −0.513830 0.857892i \(-0.671774\pi\)
−0.513830 + 0.857892i \(0.671774\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 9.23287 0.0261145
\(51\) 0 0
\(52\) 286.725 0.764645
\(53\) 487.337 1.26303 0.631517 0.775362i \(-0.282432\pi\)
0.631517 + 0.775362i \(0.282432\pi\)
\(54\) 0 0
\(55\) −153.180 −0.375543
\(56\) 0 0
\(57\) 0 0
\(58\) −37.4059 −0.0846835
\(59\) −717.355 −1.58291 −0.791454 0.611228i \(-0.790676\pi\)
−0.791454 + 0.611228i \(0.790676\pi\)
\(60\) 0 0
\(61\) −354.592 −0.744276 −0.372138 0.928177i \(-0.621375\pi\)
−0.372138 + 0.928177i \(0.621375\pi\)
\(62\) −92.3126 −0.189092
\(63\) 0 0
\(64\) −460.367 −0.899153
\(65\) −182.311 −0.347891
\(66\) 0 0
\(67\) 57.5883 0.105008 0.0525040 0.998621i \(-0.483280\pi\)
0.0525040 + 0.998621i \(0.483280\pi\)
\(68\) 626.997 1.11816
\(69\) 0 0
\(70\) 0 0
\(71\) 696.174 1.16367 0.581836 0.813306i \(-0.302335\pi\)
0.581836 + 0.813306i \(0.302335\pi\)
\(72\) 0 0
\(73\) 261.035 0.418518 0.209259 0.977860i \(-0.432895\pi\)
0.209259 + 0.977860i \(0.432895\pi\)
\(74\) 2.79115 0.00438466
\(75\) 0 0
\(76\) −1198.56 −1.80900
\(77\) 0 0
\(78\) 0 0
\(79\) 271.344 0.386438 0.193219 0.981156i \(-0.438107\pi\)
0.193219 + 0.981156i \(0.438107\pi\)
\(80\) 303.726 0.424470
\(81\) 0 0
\(82\) 52.5460 0.0707651
\(83\) 681.441 0.901179 0.450590 0.892731i \(-0.351214\pi\)
0.450590 + 0.892731i \(0.351214\pi\)
\(84\) 0 0
\(85\) −398.670 −0.508728
\(86\) −87.7234 −0.109994
\(87\) 0 0
\(88\) 179.487 0.217424
\(89\) 160.668 0.191357 0.0956784 0.995412i \(-0.469498\pi\)
0.0956784 + 0.995412i \(0.469498\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 174.735 0.198015
\(93\) 0 0
\(94\) −122.291 −0.134184
\(95\) 762.092 0.823042
\(96\) 0 0
\(97\) 167.841 0.175687 0.0878436 0.996134i \(-0.472002\pi\)
0.0878436 + 0.996134i \(0.472002\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −196.590 −0.196590
\(101\) −413.394 −0.407270 −0.203635 0.979047i \(-0.565276\pi\)
−0.203635 + 0.979047i \(0.565276\pi\)
\(102\) 0 0
\(103\) 1451.11 1.38817 0.694086 0.719892i \(-0.255809\pi\)
0.694086 + 0.719892i \(0.255809\pi\)
\(104\) 213.620 0.201415
\(105\) 0 0
\(106\) 179.981 0.164918
\(107\) 1780.63 1.60878 0.804391 0.594100i \(-0.202492\pi\)
0.804391 + 0.594100i \(0.202492\pi\)
\(108\) 0 0
\(109\) 37.8920 0.0332972 0.0166486 0.999861i \(-0.494700\pi\)
0.0166486 + 0.999861i \(0.494700\pi\)
\(110\) −56.5718 −0.0490356
\(111\) 0 0
\(112\) 0 0
\(113\) −457.320 −0.380717 −0.190359 0.981715i \(-0.560965\pi\)
−0.190359 + 0.981715i \(0.560965\pi\)
\(114\) 0 0
\(115\) −111.104 −0.0900910
\(116\) 796.463 0.637498
\(117\) 0 0
\(118\) −264.930 −0.206684
\(119\) 0 0
\(120\) 0 0
\(121\) −392.430 −0.294838
\(122\) −130.956 −0.0971820
\(123\) 0 0
\(124\) 1965.56 1.42349
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −2545.41 −1.77849 −0.889246 0.457429i \(-0.848771\pi\)
−0.889246 + 0.457429i \(0.848771\pi\)
\(128\) −724.447 −0.500256
\(129\) 0 0
\(130\) −67.3302 −0.0454250
\(131\) 970.873 0.647523 0.323762 0.946139i \(-0.395052\pi\)
0.323762 + 0.946139i \(0.395052\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 21.2682 0.0137112
\(135\) 0 0
\(136\) 467.135 0.294533
\(137\) −183.635 −0.114518 −0.0572592 0.998359i \(-0.518236\pi\)
−0.0572592 + 0.998359i \(0.518236\pi\)
\(138\) 0 0
\(139\) −1078.90 −0.658356 −0.329178 0.944268i \(-0.606772\pi\)
−0.329178 + 0.944268i \(0.606772\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 257.108 0.151944
\(143\) 1117.06 0.653240
\(144\) 0 0
\(145\) −506.424 −0.290043
\(146\) 96.4040 0.0546469
\(147\) 0 0
\(148\) −59.4304 −0.0330077
\(149\) −1211.24 −0.665962 −0.332981 0.942934i \(-0.608054\pi\)
−0.332981 + 0.942934i \(0.608054\pi\)
\(150\) 0 0
\(151\) −602.244 −0.324569 −0.162285 0.986744i \(-0.551886\pi\)
−0.162285 + 0.986744i \(0.551886\pi\)
\(152\) −892.969 −0.476509
\(153\) 0 0
\(154\) 0 0
\(155\) −1249.78 −0.647644
\(156\) 0 0
\(157\) 1602.07 0.814389 0.407195 0.913341i \(-0.366507\pi\)
0.407195 + 0.913341i \(0.366507\pi\)
\(158\) 100.212 0.0504582
\(159\) 0 0
\(160\) 346.517 0.171216
\(161\) 0 0
\(162\) 0 0
\(163\) −3091.61 −1.48561 −0.742803 0.669510i \(-0.766504\pi\)
−0.742803 + 0.669510i \(0.766504\pi\)
\(164\) −1118.83 −0.532720
\(165\) 0 0
\(166\) 251.666 0.117669
\(167\) 3251.19 1.50649 0.753247 0.657738i \(-0.228487\pi\)
0.753247 + 0.657738i \(0.228487\pi\)
\(168\) 0 0
\(169\) −867.505 −0.394859
\(170\) −147.235 −0.0664259
\(171\) 0 0
\(172\) 1867.84 0.828034
\(173\) −2254.55 −0.990809 −0.495405 0.868662i \(-0.664980\pi\)
−0.495405 + 0.868662i \(0.664980\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1860.99 −0.797033
\(177\) 0 0
\(178\) 59.3370 0.0249859
\(179\) 2685.46 1.12135 0.560673 0.828038i \(-0.310543\pi\)
0.560673 + 0.828038i \(0.310543\pi\)
\(180\) 0 0
\(181\) 1293.25 0.531087 0.265543 0.964099i \(-0.414449\pi\)
0.265543 + 0.964099i \(0.414449\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 130.184 0.0521591
\(185\) 37.7882 0.0150175
\(186\) 0 0
\(187\) 2442.74 0.955245
\(188\) 2603.86 1.01014
\(189\) 0 0
\(190\) 281.452 0.107467
\(191\) 139.878 0.0529905 0.0264953 0.999649i \(-0.491565\pi\)
0.0264953 + 0.999649i \(0.491565\pi\)
\(192\) 0 0
\(193\) 2384.81 0.889442 0.444721 0.895669i \(-0.353303\pi\)
0.444721 + 0.895669i \(0.353303\pi\)
\(194\) 61.9861 0.0229399
\(195\) 0 0
\(196\) 0 0
\(197\) 1008.67 0.364797 0.182399 0.983225i \(-0.441614\pi\)
0.182399 + 0.983225i \(0.441614\pi\)
\(198\) 0 0
\(199\) 995.036 0.354453 0.177227 0.984170i \(-0.443287\pi\)
0.177227 + 0.984170i \(0.443287\pi\)
\(200\) −146.467 −0.0517838
\(201\) 0 0
\(202\) −152.672 −0.0531782
\(203\) 0 0
\(204\) 0 0
\(205\) 711.399 0.242372
\(206\) 535.915 0.181257
\(207\) 0 0
\(208\) −2214.90 −0.738346
\(209\) −4669.51 −1.54544
\(210\) 0 0
\(211\) 2307.30 0.752802 0.376401 0.926457i \(-0.377161\pi\)
0.376401 + 0.926457i \(0.377161\pi\)
\(212\) −3832.22 −1.24150
\(213\) 0 0
\(214\) 657.612 0.210063
\(215\) −1187.65 −0.376731
\(216\) 0 0
\(217\) 0 0
\(218\) 13.9941 0.00434770
\(219\) 0 0
\(220\) 1204.55 0.369140
\(221\) 2907.28 0.884910
\(222\) 0 0
\(223\) 1629.00 0.489173 0.244587 0.969627i \(-0.421348\pi\)
0.244587 + 0.969627i \(0.421348\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −168.895 −0.0497112
\(227\) 2410.92 0.704926 0.352463 0.935826i \(-0.385344\pi\)
0.352463 + 0.935826i \(0.385344\pi\)
\(228\) 0 0
\(229\) 3666.59 1.05806 0.529028 0.848604i \(-0.322557\pi\)
0.529028 + 0.848604i \(0.322557\pi\)
\(230\) −41.0322 −0.0117634
\(231\) 0 0
\(232\) 593.393 0.167923
\(233\) 3018.33 0.848658 0.424329 0.905508i \(-0.360510\pi\)
0.424329 + 0.905508i \(0.360510\pi\)
\(234\) 0 0
\(235\) −1655.64 −0.459584
\(236\) 5640.99 1.55592
\(237\) 0 0
\(238\) 0 0
\(239\) 546.873 0.148010 0.0740048 0.997258i \(-0.476422\pi\)
0.0740048 + 0.997258i \(0.476422\pi\)
\(240\) 0 0
\(241\) 3135.27 0.838010 0.419005 0.907984i \(-0.362379\pi\)
0.419005 + 0.907984i \(0.362379\pi\)
\(242\) −144.930 −0.0384978
\(243\) 0 0
\(244\) 2788.37 0.731587
\(245\) 0 0
\(246\) 0 0
\(247\) −5557.52 −1.43165
\(248\) 1464.41 0.374960
\(249\) 0 0
\(250\) 46.1644 0.0116788
\(251\) 914.967 0.230088 0.115044 0.993360i \(-0.463299\pi\)
0.115044 + 0.993360i \(0.463299\pi\)
\(252\) 0 0
\(253\) 680.756 0.169165
\(254\) −940.058 −0.232222
\(255\) 0 0
\(256\) 3415.38 0.833834
\(257\) 6334.18 1.53741 0.768707 0.639602i \(-0.220901\pi\)
0.768707 + 0.639602i \(0.220901\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1433.62 0.341960
\(261\) 0 0
\(262\) 358.558 0.0845487
\(263\) −4126.75 −0.967553 −0.483777 0.875191i \(-0.660735\pi\)
−0.483777 + 0.875191i \(0.660735\pi\)
\(264\) 0 0
\(265\) 2436.68 0.564846
\(266\) 0 0
\(267\) 0 0
\(268\) −452.852 −0.103218
\(269\) 5887.07 1.33435 0.667176 0.744900i \(-0.267503\pi\)
0.667176 + 0.744900i \(0.267503\pi\)
\(270\) 0 0
\(271\) 7237.72 1.62236 0.811181 0.584795i \(-0.198825\pi\)
0.811181 + 0.584795i \(0.198825\pi\)
\(272\) −4843.46 −1.07970
\(273\) 0 0
\(274\) −67.8192 −0.0149530
\(275\) −765.902 −0.167948
\(276\) 0 0
\(277\) 5640.17 1.22341 0.611705 0.791086i \(-0.290484\pi\)
0.611705 + 0.791086i \(0.290484\pi\)
\(278\) −398.456 −0.0859632
\(279\) 0 0
\(280\) 0 0
\(281\) 2593.05 0.550492 0.275246 0.961374i \(-0.411241\pi\)
0.275246 + 0.961374i \(0.411241\pi\)
\(282\) 0 0
\(283\) 2533.26 0.532109 0.266054 0.963958i \(-0.414280\pi\)
0.266054 + 0.963958i \(0.414280\pi\)
\(284\) −5474.44 −1.14383
\(285\) 0 0
\(286\) 412.547 0.0852952
\(287\) 0 0
\(288\) 0 0
\(289\) 1444.52 0.294021
\(290\) −187.030 −0.0378716
\(291\) 0 0
\(292\) −2052.67 −0.411382
\(293\) 589.215 0.117482 0.0587411 0.998273i \(-0.481291\pi\)
0.0587411 + 0.998273i \(0.481291\pi\)
\(294\) 0 0
\(295\) −3586.77 −0.707898
\(296\) −44.2777 −0.00869456
\(297\) 0 0
\(298\) −447.327 −0.0869563
\(299\) 810.217 0.156709
\(300\) 0 0
\(301\) 0 0
\(302\) −222.418 −0.0423798
\(303\) 0 0
\(304\) 9258.68 1.74678
\(305\) −1772.96 −0.332851
\(306\) 0 0
\(307\) 5273.75 0.980420 0.490210 0.871604i \(-0.336920\pi\)
0.490210 + 0.871604i \(0.336920\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −461.563 −0.0845646
\(311\) 3295.08 0.600795 0.300397 0.953814i \(-0.402881\pi\)
0.300397 + 0.953814i \(0.402881\pi\)
\(312\) 0 0
\(313\) −1819.37 −0.328553 −0.164276 0.986414i \(-0.552529\pi\)
−0.164276 + 0.986414i \(0.552529\pi\)
\(314\) 591.668 0.106337
\(315\) 0 0
\(316\) −2133.75 −0.379850
\(317\) −1887.91 −0.334496 −0.167248 0.985915i \(-0.553488\pi\)
−0.167248 + 0.985915i \(0.553488\pi\)
\(318\) 0 0
\(319\) 3102.97 0.544617
\(320\) −2301.83 −0.402114
\(321\) 0 0
\(322\) 0 0
\(323\) −12152.9 −2.09352
\(324\) 0 0
\(325\) −911.556 −0.155582
\(326\) −1141.78 −0.193979
\(327\) 0 0
\(328\) −833.569 −0.140324
\(329\) 0 0
\(330\) 0 0
\(331\) −456.387 −0.0757863 −0.0378932 0.999282i \(-0.512065\pi\)
−0.0378932 + 0.999282i \(0.512065\pi\)
\(332\) −5358.58 −0.885815
\(333\) 0 0
\(334\) 1200.71 0.196707
\(335\) 287.942 0.0469610
\(336\) 0 0
\(337\) 8174.42 1.32133 0.660666 0.750680i \(-0.270274\pi\)
0.660666 + 0.750680i \(0.270274\pi\)
\(338\) −320.383 −0.0515577
\(339\) 0 0
\(340\) 3134.99 0.500055
\(341\) 7657.69 1.21609
\(342\) 0 0
\(343\) 0 0
\(344\) 1391.61 0.218112
\(345\) 0 0
\(346\) −832.637 −0.129372
\(347\) 7935.70 1.22770 0.613849 0.789424i \(-0.289621\pi\)
0.613849 + 0.789424i \(0.289621\pi\)
\(348\) 0 0
\(349\) 8649.40 1.32662 0.663312 0.748343i \(-0.269150\pi\)
0.663312 + 0.748343i \(0.269150\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2123.19 −0.321495
\(353\) 4931.06 0.743495 0.371747 0.928334i \(-0.378759\pi\)
0.371747 + 0.928334i \(0.378759\pi\)
\(354\) 0 0
\(355\) 3480.87 0.520410
\(356\) −1263.43 −0.188094
\(357\) 0 0
\(358\) 991.781 0.146417
\(359\) −8243.64 −1.21193 −0.605965 0.795491i \(-0.707213\pi\)
−0.605965 + 0.795491i \(0.707213\pi\)
\(360\) 0 0
\(361\) 16372.4 2.38699
\(362\) 477.617 0.0693453
\(363\) 0 0
\(364\) 0 0
\(365\) 1305.17 0.187167
\(366\) 0 0
\(367\) −8179.11 −1.16334 −0.581670 0.813425i \(-0.697601\pi\)
−0.581670 + 0.813425i \(0.697601\pi\)
\(368\) −1349.80 −0.191204
\(369\) 0 0
\(370\) 13.9558 0.00196088
\(371\) 0 0
\(372\) 0 0
\(373\) −12795.5 −1.77620 −0.888102 0.459646i \(-0.847976\pi\)
−0.888102 + 0.459646i \(0.847976\pi\)
\(374\) 902.140 0.124729
\(375\) 0 0
\(376\) 1939.97 0.266081
\(377\) 3693.07 0.504516
\(378\) 0 0
\(379\) −5735.40 −0.777329 −0.388664 0.921379i \(-0.627063\pi\)
−0.388664 + 0.921379i \(0.627063\pi\)
\(380\) −5992.79 −0.809010
\(381\) 0 0
\(382\) 51.6589 0.00691910
\(383\) −737.841 −0.0984384 −0.0492192 0.998788i \(-0.515673\pi\)
−0.0492192 + 0.998788i \(0.515673\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 880.745 0.116137
\(387\) 0 0
\(388\) −1319.83 −0.172692
\(389\) 13034.0 1.69884 0.849419 0.527718i \(-0.176952\pi\)
0.849419 + 0.527718i \(0.176952\pi\)
\(390\) 0 0
\(391\) 1771.75 0.229159
\(392\) 0 0
\(393\) 0 0
\(394\) 372.518 0.0476325
\(395\) 1356.72 0.172821
\(396\) 0 0
\(397\) 8313.64 1.05101 0.525503 0.850792i \(-0.323877\pi\)
0.525503 + 0.850792i \(0.323877\pi\)
\(398\) 367.481 0.0462819
\(399\) 0 0
\(400\) 1518.63 0.189829
\(401\) 14341.4 1.78598 0.892988 0.450080i \(-0.148604\pi\)
0.892988 + 0.450080i \(0.148604\pi\)
\(402\) 0 0
\(403\) 9113.97 1.12655
\(404\) 3250.77 0.400326
\(405\) 0 0
\(406\) 0 0
\(407\) −231.537 −0.0281987
\(408\) 0 0
\(409\) −6282.35 −0.759517 −0.379758 0.925086i \(-0.623993\pi\)
−0.379758 + 0.925086i \(0.623993\pi\)
\(410\) 262.730 0.0316471
\(411\) 0 0
\(412\) −11410.9 −1.36450
\(413\) 0 0
\(414\) 0 0
\(415\) 3407.21 0.403020
\(416\) −2526.96 −0.297823
\(417\) 0 0
\(418\) −1724.52 −0.201792
\(419\) −15226.1 −1.77528 −0.887640 0.460538i \(-0.847656\pi\)
−0.887640 + 0.460538i \(0.847656\pi\)
\(420\) 0 0
\(421\) −2026.55 −0.234603 −0.117302 0.993096i \(-0.537424\pi\)
−0.117302 + 0.993096i \(0.537424\pi\)
\(422\) 852.121 0.0982953
\(423\) 0 0
\(424\) −2855.14 −0.327024
\(425\) −1993.35 −0.227510
\(426\) 0 0
\(427\) 0 0
\(428\) −14002.2 −1.58135
\(429\) 0 0
\(430\) −438.617 −0.0491907
\(431\) −8983.56 −1.00400 −0.501999 0.864868i \(-0.667402\pi\)
−0.501999 + 0.864868i \(0.667402\pi\)
\(432\) 0 0
\(433\) −6836.59 −0.758766 −0.379383 0.925240i \(-0.623864\pi\)
−0.379383 + 0.925240i \(0.623864\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −297.968 −0.0327295
\(437\) −3386.85 −0.370743
\(438\) 0 0
\(439\) 7802.96 0.848325 0.424163 0.905586i \(-0.360568\pi\)
0.424163 + 0.905586i \(0.360568\pi\)
\(440\) 897.433 0.0972351
\(441\) 0 0
\(442\) 1073.70 0.115545
\(443\) −5184.37 −0.556020 −0.278010 0.960578i \(-0.589675\pi\)
−0.278010 + 0.960578i \(0.589675\pi\)
\(444\) 0 0
\(445\) 803.339 0.0855773
\(446\) 601.612 0.0638726
\(447\) 0 0
\(448\) 0 0
\(449\) 772.951 0.0812424 0.0406212 0.999175i \(-0.487066\pi\)
0.0406212 + 0.999175i \(0.487066\pi\)
\(450\) 0 0
\(451\) −4358.90 −0.455105
\(452\) 3596.18 0.374226
\(453\) 0 0
\(454\) 890.387 0.0920439
\(455\) 0 0
\(456\) 0 0
\(457\) 11532.7 1.18048 0.590239 0.807228i \(-0.299033\pi\)
0.590239 + 0.807228i \(0.299033\pi\)
\(458\) 1354.13 0.138153
\(459\) 0 0
\(460\) 873.675 0.0885550
\(461\) −10400.7 −1.05078 −0.525391 0.850861i \(-0.676081\pi\)
−0.525391 + 0.850861i \(0.676081\pi\)
\(462\) 0 0
\(463\) −13855.4 −1.39075 −0.695374 0.718648i \(-0.744761\pi\)
−0.695374 + 0.718648i \(0.744761\pi\)
\(464\) −6152.56 −0.615572
\(465\) 0 0
\(466\) 1114.71 0.110811
\(467\) 14734.5 1.46002 0.730011 0.683435i \(-0.239515\pi\)
0.730011 + 0.683435i \(0.239515\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −611.453 −0.0600090
\(471\) 0 0
\(472\) 4202.74 0.409845
\(473\) 7277.00 0.707393
\(474\) 0 0
\(475\) 3810.46 0.368076
\(476\) 0 0
\(477\) 0 0
\(478\) 201.968 0.0193260
\(479\) 1471.23 0.140338 0.0701691 0.997535i \(-0.477646\pi\)
0.0701691 + 0.997535i \(0.477646\pi\)
\(480\) 0 0
\(481\) −275.569 −0.0261224
\(482\) 1157.90 0.109421
\(483\) 0 0
\(484\) 3085.91 0.289812
\(485\) 839.204 0.0785697
\(486\) 0 0
\(487\) 5610.00 0.521998 0.260999 0.965339i \(-0.415948\pi\)
0.260999 + 0.965339i \(0.415948\pi\)
\(488\) 2077.44 0.192707
\(489\) 0 0
\(490\) 0 0
\(491\) 3193.98 0.293569 0.146784 0.989169i \(-0.453108\pi\)
0.146784 + 0.989169i \(0.453108\pi\)
\(492\) 0 0
\(493\) 8075.85 0.737764
\(494\) −2052.47 −0.186933
\(495\) 0 0
\(496\) −15183.6 −1.37453
\(497\) 0 0
\(498\) 0 0
\(499\) 8724.32 0.782673 0.391337 0.920248i \(-0.372013\pi\)
0.391337 + 0.920248i \(0.372013\pi\)
\(500\) −982.951 −0.0879178
\(501\) 0 0
\(502\) 337.911 0.0300432
\(503\) 14636.7 1.29745 0.648726 0.761022i \(-0.275302\pi\)
0.648726 + 0.761022i \(0.275302\pi\)
\(504\) 0 0
\(505\) −2066.97 −0.182136
\(506\) 251.413 0.0220883
\(507\) 0 0
\(508\) 20016.1 1.74817
\(509\) −8530.56 −0.742850 −0.371425 0.928463i \(-0.621131\pi\)
−0.371425 + 0.928463i \(0.621131\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 7056.93 0.609131
\(513\) 0 0
\(514\) 2339.31 0.200744
\(515\) 7255.53 0.620809
\(516\) 0 0
\(517\) 10144.5 0.862967
\(518\) 0 0
\(519\) 0 0
\(520\) 1068.10 0.0900756
\(521\) −13743.0 −1.15564 −0.577822 0.816163i \(-0.696097\pi\)
−0.577822 + 0.816163i \(0.696097\pi\)
\(522\) 0 0
\(523\) −2236.17 −0.186961 −0.0934806 0.995621i \(-0.529799\pi\)
−0.0934806 + 0.995621i \(0.529799\pi\)
\(524\) −7634.56 −0.636483
\(525\) 0 0
\(526\) −1524.07 −0.126336
\(527\) 19930.0 1.64737
\(528\) 0 0
\(529\) −11673.2 −0.959418
\(530\) 899.903 0.0737534
\(531\) 0 0
\(532\) 0 0
\(533\) −5187.84 −0.421595
\(534\) 0 0
\(535\) 8903.14 0.719470
\(536\) −337.391 −0.0271885
\(537\) 0 0
\(538\) 2174.18 0.174230
\(539\) 0 0
\(540\) 0 0
\(541\) −19487.9 −1.54870 −0.774352 0.632755i \(-0.781924\pi\)
−0.774352 + 0.632755i \(0.781924\pi\)
\(542\) 2673.00 0.211836
\(543\) 0 0
\(544\) −5525.84 −0.435512
\(545\) 189.460 0.0148910
\(546\) 0 0
\(547\) −15949.3 −1.24670 −0.623349 0.781944i \(-0.714228\pi\)
−0.623349 + 0.781944i \(0.714228\pi\)
\(548\) 1444.04 0.112566
\(549\) 0 0
\(550\) −282.859 −0.0219294
\(551\) −15437.7 −1.19359
\(552\) 0 0
\(553\) 0 0
\(554\) 2083.00 0.159744
\(555\) 0 0
\(556\) 8484.08 0.647132
\(557\) 6349.74 0.483029 0.241514 0.970397i \(-0.422356\pi\)
0.241514 + 0.970397i \(0.422356\pi\)
\(558\) 0 0
\(559\) 8660.88 0.655306
\(560\) 0 0
\(561\) 0 0
\(562\) 957.651 0.0718791
\(563\) 14805.0 1.10827 0.554135 0.832427i \(-0.313049\pi\)
0.554135 + 0.832427i \(0.313049\pi\)
\(564\) 0 0
\(565\) −2286.60 −0.170262
\(566\) 935.571 0.0694788
\(567\) 0 0
\(568\) −4078.65 −0.301297
\(569\) −24578.7 −1.81088 −0.905442 0.424469i \(-0.860461\pi\)
−0.905442 + 0.424469i \(0.860461\pi\)
\(570\) 0 0
\(571\) −15609.9 −1.14405 −0.572027 0.820235i \(-0.693843\pi\)
−0.572027 + 0.820235i \(0.693843\pi\)
\(572\) −8784.12 −0.642103
\(573\) 0 0
\(574\) 0 0
\(575\) −555.518 −0.0402899
\(576\) 0 0
\(577\) −15111.3 −1.09028 −0.545141 0.838344i \(-0.683524\pi\)
−0.545141 + 0.838344i \(0.683524\pi\)
\(578\) 533.484 0.0383910
\(579\) 0 0
\(580\) 3982.32 0.285098
\(581\) 0 0
\(582\) 0 0
\(583\) −14930.1 −1.06062
\(584\) −1529.31 −0.108362
\(585\) 0 0
\(586\) 217.606 0.0153399
\(587\) 14983.2 1.05353 0.526766 0.850010i \(-0.323404\pi\)
0.526766 + 0.850010i \(0.323404\pi\)
\(588\) 0 0
\(589\) −38098.0 −2.66519
\(590\) −1324.65 −0.0924320
\(591\) 0 0
\(592\) 459.090 0.0318725
\(593\) 6931.01 0.479971 0.239985 0.970777i \(-0.422857\pi\)
0.239985 + 0.970777i \(0.422857\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9524.68 0.654608
\(597\) 0 0
\(598\) 299.225 0.0204619
\(599\) −12309.2 −0.839632 −0.419816 0.907609i \(-0.637905\pi\)
−0.419816 + 0.907609i \(0.637905\pi\)
\(600\) 0 0
\(601\) −15293.6 −1.03800 −0.519001 0.854774i \(-0.673696\pi\)
−0.519001 + 0.854774i \(0.673696\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4735.81 0.319036
\(605\) −1962.15 −0.131856
\(606\) 0 0
\(607\) 5338.80 0.356994 0.178497 0.983940i \(-0.442877\pi\)
0.178497 + 0.983940i \(0.442877\pi\)
\(608\) 10563.1 0.704590
\(609\) 0 0
\(610\) −654.780 −0.0434611
\(611\) 12073.7 0.799426
\(612\) 0 0
\(613\) −28848.6 −1.90079 −0.950396 0.311043i \(-0.899322\pi\)
−0.950396 + 0.311043i \(0.899322\pi\)
\(614\) 1947.68 0.128016
\(615\) 0 0
\(616\) 0 0
\(617\) 12346.6 0.805602 0.402801 0.915287i \(-0.368037\pi\)
0.402801 + 0.915287i \(0.368037\pi\)
\(618\) 0 0
\(619\) 6383.16 0.414477 0.207238 0.978290i \(-0.433552\pi\)
0.207238 + 0.978290i \(0.433552\pi\)
\(620\) 9827.79 0.636603
\(621\) 0 0
\(622\) 1216.92 0.0784473
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) −671.921 −0.0429000
\(627\) 0 0
\(628\) −12598.1 −0.800505
\(629\) −602.602 −0.0381992
\(630\) 0 0
\(631\) 25708.6 1.62194 0.810969 0.585090i \(-0.198941\pi\)
0.810969 + 0.585090i \(0.198941\pi\)
\(632\) −1589.72 −0.100056
\(633\) 0 0
\(634\) −697.232 −0.0436760
\(635\) −12727.0 −0.795366
\(636\) 0 0
\(637\) 0 0
\(638\) 1145.97 0.0711120
\(639\) 0 0
\(640\) −3622.24 −0.223721
\(641\) 18617.5 1.14719 0.573594 0.819139i \(-0.305549\pi\)
0.573594 + 0.819139i \(0.305549\pi\)
\(642\) 0 0
\(643\) −21168.8 −1.29832 −0.649158 0.760654i \(-0.724879\pi\)
−0.649158 + 0.760654i \(0.724879\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −4488.26 −0.273357
\(647\) 5952.47 0.361693 0.180847 0.983511i \(-0.442116\pi\)
0.180847 + 0.983511i \(0.442116\pi\)
\(648\) 0 0
\(649\) 21976.9 1.32923
\(650\) −336.651 −0.0203147
\(651\) 0 0
\(652\) 24311.2 1.46028
\(653\) 3040.63 0.182219 0.0911096 0.995841i \(-0.470959\pi\)
0.0911096 + 0.995841i \(0.470959\pi\)
\(654\) 0 0
\(655\) 4854.36 0.289581
\(656\) 8642.81 0.514398
\(657\) 0 0
\(658\) 0 0
\(659\) 3335.95 0.197193 0.0985966 0.995127i \(-0.468565\pi\)
0.0985966 + 0.995127i \(0.468565\pi\)
\(660\) 0 0
\(661\) −1547.90 −0.0910838 −0.0455419 0.998962i \(-0.514501\pi\)
−0.0455419 + 0.998962i \(0.514501\pi\)
\(662\) −168.550 −0.00989561
\(663\) 0 0
\(664\) −3992.34 −0.233332
\(665\) 0 0
\(666\) 0 0
\(667\) 2250.62 0.130651
\(668\) −25566.0 −1.48081
\(669\) 0 0
\(670\) 106.341 0.00613181
\(671\) 10863.3 0.624998
\(672\) 0 0
\(673\) 19632.4 1.12448 0.562239 0.826975i \(-0.309940\pi\)
0.562239 + 0.826975i \(0.309940\pi\)
\(674\) 3018.94 0.172530
\(675\) 0 0
\(676\) 6821.72 0.388127
\(677\) −30318.2 −1.72116 −0.860579 0.509317i \(-0.829898\pi\)
−0.860579 + 0.509317i \(0.829898\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 2335.68 0.131719
\(681\) 0 0
\(682\) 2828.10 0.158788
\(683\) −28970.8 −1.62304 −0.811520 0.584325i \(-0.801359\pi\)
−0.811520 + 0.584325i \(0.801359\pi\)
\(684\) 0 0
\(685\) −918.176 −0.0512142
\(686\) 0 0
\(687\) 0 0
\(688\) −14428.8 −0.799554
\(689\) −17769.4 −0.982525
\(690\) 0 0
\(691\) −3434.91 −0.189103 −0.0945514 0.995520i \(-0.530142\pi\)
−0.0945514 + 0.995520i \(0.530142\pi\)
\(692\) 17728.9 0.973917
\(693\) 0 0
\(694\) 2930.77 0.160304
\(695\) −5394.52 −0.294426
\(696\) 0 0
\(697\) −11344.5 −0.616507
\(698\) 3194.35 0.173221
\(699\) 0 0
\(700\) 0 0
\(701\) −16304.4 −0.878471 −0.439235 0.898372i \(-0.644751\pi\)
−0.439235 + 0.898372i \(0.644751\pi\)
\(702\) 0 0
\(703\) 1151.92 0.0618004
\(704\) 14103.8 0.755054
\(705\) 0 0
\(706\) 1821.11 0.0970800
\(707\) 0 0
\(708\) 0 0
\(709\) 16094.4 0.852519 0.426260 0.904601i \(-0.359831\pi\)
0.426260 + 0.904601i \(0.359831\pi\)
\(710\) 1285.54 0.0679512
\(711\) 0 0
\(712\) −941.299 −0.0495459
\(713\) 5554.21 0.291735
\(714\) 0 0
\(715\) 5585.30 0.292138
\(716\) −21117.4 −1.10223
\(717\) 0 0
\(718\) −3044.50 −0.158245
\(719\) −8651.93 −0.448766 −0.224383 0.974501i \(-0.572037\pi\)
−0.224383 + 0.974501i \(0.572037\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 6046.56 0.311676
\(723\) 0 0
\(724\) −10169.6 −0.522032
\(725\) −2532.12 −0.129711
\(726\) 0 0
\(727\) −6999.43 −0.357076 −0.178538 0.983933i \(-0.557137\pi\)
−0.178538 + 0.983933i \(0.557137\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 482.020 0.0244388
\(731\) 18939.3 0.958268
\(732\) 0 0
\(733\) 5167.74 0.260402 0.130201 0.991488i \(-0.458438\pi\)
0.130201 + 0.991488i \(0.458438\pi\)
\(734\) −3020.67 −0.151900
\(735\) 0 0
\(736\) −1539.97 −0.0771251
\(737\) −1764.28 −0.0881793
\(738\) 0 0
\(739\) −12319.1 −0.613214 −0.306607 0.951836i \(-0.599194\pi\)
−0.306607 + 0.951836i \(0.599194\pi\)
\(740\) −297.152 −0.0147615
\(741\) 0 0
\(742\) 0 0
\(743\) −16942.4 −0.836548 −0.418274 0.908321i \(-0.637365\pi\)
−0.418274 + 0.908321i \(0.637365\pi\)
\(744\) 0 0
\(745\) −6056.18 −0.297827
\(746\) −4725.56 −0.231923
\(747\) 0 0
\(748\) −19208.8 −0.938959
\(749\) 0 0
\(750\) 0 0
\(751\) 32917.9 1.59946 0.799728 0.600363i \(-0.204977\pi\)
0.799728 + 0.600363i \(0.204977\pi\)
\(752\) −20114.5 −0.975397
\(753\) 0 0
\(754\) 1363.90 0.0658760
\(755\) −3011.22 −0.145152
\(756\) 0 0
\(757\) −9433.45 −0.452926 −0.226463 0.974020i \(-0.572716\pi\)
−0.226463 + 0.974020i \(0.572716\pi\)
\(758\) −2118.17 −0.101498
\(759\) 0 0
\(760\) −4464.84 −0.213101
\(761\) 34551.0 1.64582 0.822912 0.568170i \(-0.192348\pi\)
0.822912 + 0.568170i \(0.192348\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1099.94 −0.0520871
\(765\) 0 0
\(766\) −272.495 −0.0128533
\(767\) 26156.4 1.23136
\(768\) 0 0
\(769\) −348.011 −0.0163194 −0.00815970 0.999967i \(-0.502597\pi\)
−0.00815970 + 0.999967i \(0.502597\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −18753.2 −0.874277
\(773\) 30083.9 1.39979 0.699897 0.714243i \(-0.253229\pi\)
0.699897 + 0.714243i \(0.253229\pi\)
\(774\) 0 0
\(775\) −6248.91 −0.289635
\(776\) −983.323 −0.0454887
\(777\) 0 0
\(778\) 4813.64 0.221822
\(779\) 21686.1 0.997412
\(780\) 0 0
\(781\) −21328.1 −0.977181
\(782\) 654.333 0.0299219
\(783\) 0 0
\(784\) 0 0
\(785\) 8010.35 0.364206
\(786\) 0 0
\(787\) 31958.4 1.44751 0.723757 0.690055i \(-0.242413\pi\)
0.723757 + 0.690055i \(0.242413\pi\)
\(788\) −7931.81 −0.358578
\(789\) 0 0
\(790\) 501.058 0.0225656
\(791\) 0 0
\(792\) 0 0
\(793\) 12929.2 0.578979
\(794\) 3070.35 0.137233
\(795\) 0 0
\(796\) −7824.57 −0.348410
\(797\) 364.165 0.0161849 0.00809247 0.999967i \(-0.497424\pi\)
0.00809247 + 0.999967i \(0.497424\pi\)
\(798\) 0 0
\(799\) 26402.2 1.16902
\(800\) 1732.59 0.0765702
\(801\) 0 0
\(802\) 5296.50 0.233199
\(803\) −7997.08 −0.351446
\(804\) 0 0
\(805\) 0 0
\(806\) 3365.92 0.147096
\(807\) 0 0
\(808\) 2421.94 0.105450
\(809\) −30714.8 −1.33482 −0.667412 0.744688i \(-0.732598\pi\)
−0.667412 + 0.744688i \(0.732598\pi\)
\(810\) 0 0
\(811\) 18967.6 0.821260 0.410630 0.911802i \(-0.365309\pi\)
0.410630 + 0.911802i \(0.365309\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −85.5100 −0.00368197
\(815\) −15458.1 −0.664383
\(816\) 0 0
\(817\) −36204.0 −1.55033
\(818\) −2320.17 −0.0991720
\(819\) 0 0
\(820\) −5594.16 −0.238240
\(821\) 14817.0 0.629860 0.314930 0.949115i \(-0.398019\pi\)
0.314930 + 0.949115i \(0.398019\pi\)
\(822\) 0 0
\(823\) −26588.1 −1.12613 −0.563063 0.826414i \(-0.690377\pi\)
−0.563063 + 0.826414i \(0.690377\pi\)
\(824\) −8501.54 −0.359424
\(825\) 0 0
\(826\) 0 0
\(827\) 11287.0 0.474592 0.237296 0.971437i \(-0.423739\pi\)
0.237296 + 0.971437i \(0.423739\pi\)
\(828\) 0 0
\(829\) 14448.6 0.605332 0.302666 0.953097i \(-0.402123\pi\)
0.302666 + 0.953097i \(0.402123\pi\)
\(830\) 1258.33 0.0526233
\(831\) 0 0
\(832\) 16786.0 0.699459
\(833\) 0 0
\(834\) 0 0
\(835\) 16255.9 0.673724
\(836\) 36719.2 1.51909
\(837\) 0 0
\(838\) −5623.21 −0.231803
\(839\) −40032.0 −1.64727 −0.823635 0.567120i \(-0.808057\pi\)
−0.823635 + 0.567120i \(0.808057\pi\)
\(840\) 0 0
\(841\) −14130.4 −0.579376
\(842\) −748.434 −0.0306327
\(843\) 0 0
\(844\) −18143.7 −0.739967
\(845\) −4337.53 −0.176586
\(846\) 0 0
\(847\) 0 0
\(848\) 29603.3 1.19880
\(849\) 0 0
\(850\) −736.175 −0.0297066
\(851\) −167.936 −0.00676473
\(852\) 0 0
\(853\) 10864.4 0.436098 0.218049 0.975938i \(-0.430031\pi\)
0.218049 + 0.975938i \(0.430031\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −10432.1 −0.416544
\(857\) −42013.7 −1.67463 −0.837316 0.546719i \(-0.815877\pi\)
−0.837316 + 0.546719i \(0.815877\pi\)
\(858\) 0 0
\(859\) 16135.6 0.640908 0.320454 0.947264i \(-0.396165\pi\)
0.320454 + 0.947264i \(0.396165\pi\)
\(860\) 9339.22 0.370308
\(861\) 0 0
\(862\) −3317.76 −0.131094
\(863\) 46246.8 1.82417 0.912086 0.409998i \(-0.134471\pi\)
0.912086 + 0.409998i \(0.134471\pi\)
\(864\) 0 0
\(865\) −11272.7 −0.443103
\(866\) −2524.85 −0.0990739
\(867\) 0 0
\(868\) 0 0
\(869\) −8312.93 −0.324507
\(870\) 0 0
\(871\) −2099.80 −0.0816865
\(872\) −221.996 −0.00862127
\(873\) 0 0
\(874\) −1250.81 −0.0484089
\(875\) 0 0
\(876\) 0 0
\(877\) −25094.1 −0.966212 −0.483106 0.875562i \(-0.660491\pi\)
−0.483106 + 0.875562i \(0.660491\pi\)
\(878\) 2881.75 0.110768
\(879\) 0 0
\(880\) −9304.97 −0.356444
\(881\) 27546.6 1.05342 0.526712 0.850044i \(-0.323424\pi\)
0.526712 + 0.850044i \(0.323424\pi\)
\(882\) 0 0
\(883\) 5825.31 0.222013 0.111006 0.993820i \(-0.464593\pi\)
0.111006 + 0.993820i \(0.464593\pi\)
\(884\) −22861.7 −0.869823
\(885\) 0 0
\(886\) −1914.67 −0.0726010
\(887\) −6214.29 −0.235237 −0.117619 0.993059i \(-0.537526\pi\)
−0.117619 + 0.993059i \(0.537526\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 296.685 0.0111740
\(891\) 0 0
\(892\) −12809.8 −0.480833
\(893\) −50470.1 −1.89128
\(894\) 0 0
\(895\) 13427.3 0.501481
\(896\) 0 0
\(897\) 0 0
\(898\) 285.462 0.0106080
\(899\) 25316.8 0.939223
\(900\) 0 0
\(901\) −38857.3 −1.43677
\(902\) −1609.80 −0.0594242
\(903\) 0 0
\(904\) 2679.28 0.0985748
\(905\) 6466.26 0.237509
\(906\) 0 0
\(907\) 24415.9 0.893845 0.446923 0.894573i \(-0.352520\pi\)
0.446923 + 0.894573i \(0.352520\pi\)
\(908\) −18958.5 −0.692907
\(909\) 0 0
\(910\) 0 0
\(911\) 3493.35 0.127047 0.0635236 0.997980i \(-0.479766\pi\)
0.0635236 + 0.997980i \(0.479766\pi\)
\(912\) 0 0
\(913\) −20876.7 −0.756755
\(914\) 4259.21 0.154138
\(915\) 0 0
\(916\) −28832.6 −1.04002
\(917\) 0 0
\(918\) 0 0
\(919\) 15656.7 0.561989 0.280995 0.959709i \(-0.409336\pi\)
0.280995 + 0.959709i \(0.409336\pi\)
\(920\) 650.919 0.0233263
\(921\) 0 0
\(922\) −3841.14 −0.137203
\(923\) −25384.1 −0.905230
\(924\) 0 0
\(925\) 188.941 0.00671605
\(926\) −5117.02 −0.181594
\(927\) 0 0
\(928\) −7019.38 −0.248300
\(929\) 30504.5 1.07731 0.538654 0.842527i \(-0.318933\pi\)
0.538654 + 0.842527i \(0.318933\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −23735.0 −0.834189
\(933\) 0 0
\(934\) 5441.66 0.190639
\(935\) 12213.7 0.427199
\(936\) 0 0
\(937\) 50290.7 1.75339 0.876694 0.481049i \(-0.159744\pi\)
0.876694 + 0.481049i \(0.159744\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 13019.3 0.451748
\(941\) −18681.7 −0.647189 −0.323595 0.946196i \(-0.604891\pi\)
−0.323595 + 0.946196i \(0.604891\pi\)
\(942\) 0 0
\(943\) −3161.56 −0.109178
\(944\) −43575.8 −1.50241
\(945\) 0 0
\(946\) 2687.50 0.0923660
\(947\) −16332.6 −0.560440 −0.280220 0.959936i \(-0.590407\pi\)
−0.280220 + 0.959936i \(0.590407\pi\)
\(948\) 0 0
\(949\) −9517.91 −0.325568
\(950\) 1407.26 0.0480606
\(951\) 0 0
\(952\) 0 0
\(953\) 34233.6 1.16362 0.581812 0.813323i \(-0.302344\pi\)
0.581812 + 0.813323i \(0.302344\pi\)
\(954\) 0 0
\(955\) 699.388 0.0236981
\(956\) −4300.40 −0.145486
\(957\) 0 0
\(958\) 543.345 0.0183243
\(959\) 0 0
\(960\) 0 0
\(961\) 32687.2 1.09722
\(962\) −101.772 −0.00341086
\(963\) 0 0
\(964\) −24654.5 −0.823723
\(965\) 11924.0 0.397770
\(966\) 0 0
\(967\) 53792.0 1.78887 0.894434 0.447200i \(-0.147579\pi\)
0.894434 + 0.447200i \(0.147579\pi\)
\(968\) 2299.11 0.0763392
\(969\) 0 0
\(970\) 309.931 0.0102590
\(971\) −826.331 −0.0273102 −0.0136551 0.999907i \(-0.504347\pi\)
−0.0136551 + 0.999907i \(0.504347\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 2071.85 0.0681586
\(975\) 0 0
\(976\) −21539.8 −0.706425
\(977\) −8703.52 −0.285005 −0.142503 0.989794i \(-0.545515\pi\)
−0.142503 + 0.989794i \(0.545515\pi\)
\(978\) 0 0
\(979\) −4922.23 −0.160690
\(980\) 0 0
\(981\) 0 0
\(982\) 1179.58 0.0383320
\(983\) −41000.9 −1.33034 −0.665170 0.746692i \(-0.731641\pi\)
−0.665170 + 0.746692i \(0.731641\pi\)
\(984\) 0 0
\(985\) 5043.37 0.163142
\(986\) 2982.53 0.0963317
\(987\) 0 0
\(988\) 43702.1 1.40724
\(989\) 5278.09 0.169700
\(990\) 0 0
\(991\) −18341.0 −0.587912 −0.293956 0.955819i \(-0.594972\pi\)
−0.293956 + 0.955819i \(0.594972\pi\)
\(992\) −17322.8 −0.554436
\(993\) 0 0
\(994\) 0 0
\(995\) 4975.18 0.158516
\(996\) 0 0
\(997\) −57335.4 −1.82129 −0.910646 0.413187i \(-0.864416\pi\)
−0.910646 + 0.413187i \(0.864416\pi\)
\(998\) 3222.02 0.102196
\(999\) 0 0
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 2205.4.a.ca.1.4 6
3.2 odd 2 245.4.a.p.1.3 yes 6
7.6 odd 2 2205.4.a.bz.1.4 6
15.14 odd 2 1225.4.a.bi.1.4 6
21.2 odd 6 245.4.e.p.116.4 12
21.5 even 6 245.4.e.q.116.4 12
21.11 odd 6 245.4.e.p.226.4 12
21.17 even 6 245.4.e.q.226.4 12
21.20 even 2 245.4.a.o.1.3 6
105.104 even 2 1225.4.a.bj.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.4.a.o.1.3 6 21.20 even 2
245.4.a.p.1.3 yes 6 3.2 odd 2
245.4.e.p.116.4 12 21.2 odd 6
245.4.e.p.226.4 12 21.11 odd 6
245.4.e.q.116.4 12 21.5 even 6
245.4.e.q.226.4 12 21.17 even 6
1225.4.a.bi.1.4 6 15.14 odd 2
1225.4.a.bj.1.4 6 105.104 even 2
2205.4.a.bz.1.4 6 7.6 odd 2
2205.4.a.ca.1.4 6 1.1 even 1 trivial