Properties

Label 1232.4.a.s.1.2
Level $1232$
Weight $4$
Character 1232.1
Self dual yes
Analytic conductor $72.690$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1232.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.6903531271\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.522072.1
Defining polynomial: \( x^{4} - x^{3} - 12x^{2} + 5x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 77)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-3.20317\) of defining polynomial
Character \(\chi\) \(=\) 1232.1

$q$-expansion

\(f(q)\) \(=\) \(q-6.57251 q^{3} +15.5514 q^{5} +7.00000 q^{7} +16.1978 q^{9} +O(q^{10})\) \(q-6.57251 q^{3} +15.5514 q^{5} +7.00000 q^{7} +16.1978 q^{9} +11.0000 q^{11} +74.3459 q^{13} -102.211 q^{15} -94.0836 q^{17} -135.682 q^{19} -46.0075 q^{21} -81.1793 q^{23} +116.845 q^{25} +70.9972 q^{27} -53.4259 q^{29} +9.50536 q^{31} -72.2976 q^{33} +108.860 q^{35} -9.14224 q^{37} -488.639 q^{39} -339.461 q^{41} -433.078 q^{43} +251.899 q^{45} +54.4784 q^{47} +49.0000 q^{49} +618.365 q^{51} +123.830 q^{53} +171.065 q^{55} +891.773 q^{57} +534.396 q^{59} -358.624 q^{61} +113.385 q^{63} +1156.18 q^{65} +694.318 q^{67} +533.551 q^{69} +278.330 q^{71} -886.688 q^{73} -767.963 q^{75} +77.0000 q^{77} +185.631 q^{79} -903.972 q^{81} +122.624 q^{83} -1463.13 q^{85} +351.142 q^{87} -847.086 q^{89} +520.422 q^{91} -62.4740 q^{93} -2110.04 q^{95} +1002.49 q^{97} +178.176 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 14 q^{3} + 10 q^{5} + 28 q^{7} + 76 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 14 q^{3} + 10 q^{5} + 28 q^{7} + 76 q^{9} + 44 q^{11} + 58 q^{13} - 284 q^{15} + 4 q^{17} - 258 q^{19} - 98 q^{21} - 8 q^{23} + 80 q^{25} - 428 q^{27} - 396 q^{29} + 56 q^{31} - 154 q^{33} + 70 q^{35} + 84 q^{37} + 412 q^{39} + 52 q^{41} - 408 q^{43} + 826 q^{45} - 8 q^{47} + 196 q^{49} + 388 q^{51} + 624 q^{53} + 110 q^{55} + 48 q^{57} + 238 q^{59} - 162 q^{61} + 532 q^{63} - 32 q^{65} - 1340 q^{67} + 2416 q^{69} - 1788 q^{71} + 1456 q^{73} + 806 q^{75} + 308 q^{77} + 1324 q^{79} + 1444 q^{81} - 450 q^{83} - 1736 q^{85} - 588 q^{87} - 3072 q^{89} + 406 q^{91} - 1264 q^{93} - 24 q^{95} - 652 q^{97} + 836 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −6.57251 −1.26488 −0.632440 0.774610i \(-0.717946\pi\)
−0.632440 + 0.774610i \(0.717946\pi\)
\(4\) 0 0
\(5\) 15.5514 1.39096 0.695478 0.718547i \(-0.255193\pi\)
0.695478 + 0.718547i \(0.255193\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) 0 0
\(9\) 16.1978 0.599920
\(10\) 0 0
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) 74.3459 1.58614 0.793071 0.609129i \(-0.208481\pi\)
0.793071 + 0.609129i \(0.208481\pi\)
\(14\) 0 0
\(15\) −102.211 −1.75939
\(16\) 0 0
\(17\) −94.0836 −1.34227 −0.671136 0.741334i \(-0.734193\pi\)
−0.671136 + 0.741334i \(0.734193\pi\)
\(18\) 0 0
\(19\) −135.682 −1.63830 −0.819149 0.573581i \(-0.805554\pi\)
−0.819149 + 0.573581i \(0.805554\pi\)
\(20\) 0 0
\(21\) −46.0075 −0.478080
\(22\) 0 0
\(23\) −81.1793 −0.735959 −0.367979 0.929834i \(-0.619950\pi\)
−0.367979 + 0.929834i \(0.619950\pi\)
\(24\) 0 0
\(25\) 116.845 0.934758
\(26\) 0 0
\(27\) 70.9972 0.506053
\(28\) 0 0
\(29\) −53.4259 −0.342102 −0.171051 0.985262i \(-0.554716\pi\)
−0.171051 + 0.985262i \(0.554716\pi\)
\(30\) 0 0
\(31\) 9.50536 0.0550714 0.0275357 0.999621i \(-0.491234\pi\)
0.0275357 + 0.999621i \(0.491234\pi\)
\(32\) 0 0
\(33\) −72.2976 −0.381376
\(34\) 0 0
\(35\) 108.860 0.525732
\(36\) 0 0
\(37\) −9.14224 −0.0406209 −0.0203105 0.999794i \(-0.506465\pi\)
−0.0203105 + 0.999794i \(0.506465\pi\)
\(38\) 0 0
\(39\) −488.639 −2.00628
\(40\) 0 0
\(41\) −339.461 −1.29305 −0.646523 0.762894i \(-0.723778\pi\)
−0.646523 + 0.762894i \(0.723778\pi\)
\(42\) 0 0
\(43\) −433.078 −1.53590 −0.767950 0.640509i \(-0.778723\pi\)
−0.767950 + 0.640509i \(0.778723\pi\)
\(44\) 0 0
\(45\) 251.899 0.834463
\(46\) 0 0
\(47\) 54.4784 0.169074 0.0845371 0.996420i \(-0.473059\pi\)
0.0845371 + 0.996420i \(0.473059\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 618.365 1.69781
\(52\) 0 0
\(53\) 123.830 0.320932 0.160466 0.987041i \(-0.448700\pi\)
0.160466 + 0.987041i \(0.448700\pi\)
\(54\) 0 0
\(55\) 171.065 0.419389
\(56\) 0 0
\(57\) 891.773 2.07225
\(58\) 0 0
\(59\) 534.396 1.17919 0.589596 0.807698i \(-0.299287\pi\)
0.589596 + 0.807698i \(0.299287\pi\)
\(60\) 0 0
\(61\) −358.624 −0.752740 −0.376370 0.926469i \(-0.622828\pi\)
−0.376370 + 0.926469i \(0.622828\pi\)
\(62\) 0 0
\(63\) 113.385 0.226749
\(64\) 0 0
\(65\) 1156.18 2.20625
\(66\) 0 0
\(67\) 694.318 1.26604 0.633019 0.774137i \(-0.281816\pi\)
0.633019 + 0.774137i \(0.281816\pi\)
\(68\) 0 0
\(69\) 533.551 0.930899
\(70\) 0 0
\(71\) 278.330 0.465236 0.232618 0.972568i \(-0.425271\pi\)
0.232618 + 0.972568i \(0.425271\pi\)
\(72\) 0 0
\(73\) −886.688 −1.42163 −0.710815 0.703379i \(-0.751674\pi\)
−0.710815 + 0.703379i \(0.751674\pi\)
\(74\) 0 0
\(75\) −767.963 −1.18236
\(76\) 0 0
\(77\) 77.0000 0.113961
\(78\) 0 0
\(79\) 185.631 0.264369 0.132184 0.991225i \(-0.457801\pi\)
0.132184 + 0.991225i \(0.457801\pi\)
\(80\) 0 0
\(81\) −903.972 −1.24002
\(82\) 0 0
\(83\) 122.624 0.162166 0.0810830 0.996707i \(-0.474162\pi\)
0.0810830 + 0.996707i \(0.474162\pi\)
\(84\) 0 0
\(85\) −1463.13 −1.86704
\(86\) 0 0
\(87\) 351.142 0.432717
\(88\) 0 0
\(89\) −847.086 −1.00889 −0.504443 0.863445i \(-0.668302\pi\)
−0.504443 + 0.863445i \(0.668302\pi\)
\(90\) 0 0
\(91\) 520.422 0.599506
\(92\) 0 0
\(93\) −62.4740 −0.0696586
\(94\) 0 0
\(95\) −2110.04 −2.27880
\(96\) 0 0
\(97\) 1002.49 1.04935 0.524676 0.851302i \(-0.324186\pi\)
0.524676 + 0.851302i \(0.324186\pi\)
\(98\) 0 0
\(99\) 178.176 0.180883
\(100\) 0 0
\(101\) 1124.79 1.10812 0.554062 0.832476i \(-0.313077\pi\)
0.554062 + 0.832476i \(0.313077\pi\)
\(102\) 0 0
\(103\) −966.118 −0.924218 −0.462109 0.886823i \(-0.652907\pi\)
−0.462109 + 0.886823i \(0.652907\pi\)
\(104\) 0 0
\(105\) −715.480 −0.664988
\(106\) 0 0
\(107\) 144.202 0.130286 0.0651428 0.997876i \(-0.479250\pi\)
0.0651428 + 0.997876i \(0.479250\pi\)
\(108\) 0 0
\(109\) −1875.32 −1.64792 −0.823961 0.566647i \(-0.808240\pi\)
−0.823961 + 0.566647i \(0.808240\pi\)
\(110\) 0 0
\(111\) 60.0874 0.0513806
\(112\) 0 0
\(113\) 1207.46 1.00521 0.502603 0.864517i \(-0.332376\pi\)
0.502603 + 0.864517i \(0.332376\pi\)
\(114\) 0 0
\(115\) −1262.45 −1.02369
\(116\) 0 0
\(117\) 1204.24 0.951559
\(118\) 0 0
\(119\) −658.585 −0.507331
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 2231.11 1.63555
\(124\) 0 0
\(125\) −126.825 −0.0907483
\(126\) 0 0
\(127\) −1143.56 −0.799009 −0.399504 0.916731i \(-0.630818\pi\)
−0.399504 + 0.916731i \(0.630818\pi\)
\(128\) 0 0
\(129\) 2846.41 1.94273
\(130\) 0 0
\(131\) −2478.40 −1.65297 −0.826484 0.562961i \(-0.809662\pi\)
−0.826484 + 0.562961i \(0.809662\pi\)
\(132\) 0 0
\(133\) −949.776 −0.619218
\(134\) 0 0
\(135\) 1104.10 0.703897
\(136\) 0 0
\(137\) −835.661 −0.521134 −0.260567 0.965456i \(-0.583909\pi\)
−0.260567 + 0.965456i \(0.583909\pi\)
\(138\) 0 0
\(139\) 1726.99 1.05382 0.526912 0.849920i \(-0.323350\pi\)
0.526912 + 0.849920i \(0.323350\pi\)
\(140\) 0 0
\(141\) −358.060 −0.213859
\(142\) 0 0
\(143\) 817.805 0.478240
\(144\) 0 0
\(145\) −830.846 −0.475848
\(146\) 0 0
\(147\) −322.053 −0.180697
\(148\) 0 0
\(149\) −3454.95 −1.89960 −0.949799 0.312859i \(-0.898713\pi\)
−0.949799 + 0.312859i \(0.898713\pi\)
\(150\) 0 0
\(151\) 2468.17 1.33018 0.665089 0.746764i \(-0.268394\pi\)
0.665089 + 0.746764i \(0.268394\pi\)
\(152\) 0 0
\(153\) −1523.95 −0.805256
\(154\) 0 0
\(155\) 147.821 0.0766018
\(156\) 0 0
\(157\) −1561.27 −0.793649 −0.396824 0.917895i \(-0.629888\pi\)
−0.396824 + 0.917895i \(0.629888\pi\)
\(158\) 0 0
\(159\) −813.875 −0.405940
\(160\) 0 0
\(161\) −568.255 −0.278166
\(162\) 0 0
\(163\) −3458.59 −1.66195 −0.830973 0.556312i \(-0.812216\pi\)
−0.830973 + 0.556312i \(0.812216\pi\)
\(164\) 0 0
\(165\) −1124.33 −0.530477
\(166\) 0 0
\(167\) 972.527 0.450637 0.225319 0.974285i \(-0.427658\pi\)
0.225319 + 0.974285i \(0.427658\pi\)
\(168\) 0 0
\(169\) 3330.32 1.51585
\(170\) 0 0
\(171\) −2197.76 −0.982848
\(172\) 0 0
\(173\) −1154.18 −0.507230 −0.253615 0.967305i \(-0.581620\pi\)
−0.253615 + 0.967305i \(0.581620\pi\)
\(174\) 0 0
\(175\) 817.914 0.353305
\(176\) 0 0
\(177\) −3512.32 −1.49154
\(178\) 0 0
\(179\) −259.234 −0.108246 −0.0541231 0.998534i \(-0.517236\pi\)
−0.0541231 + 0.998534i \(0.517236\pi\)
\(180\) 0 0
\(181\) −2121.49 −0.871209 −0.435604 0.900138i \(-0.643465\pi\)
−0.435604 + 0.900138i \(0.643465\pi\)
\(182\) 0 0
\(183\) 2357.06 0.952126
\(184\) 0 0
\(185\) −142.174 −0.0565019
\(186\) 0 0
\(187\) −1034.92 −0.404710
\(188\) 0 0
\(189\) 496.981 0.191270
\(190\) 0 0
\(191\) −2918.27 −1.10554 −0.552772 0.833332i \(-0.686430\pi\)
−0.552772 + 0.833332i \(0.686430\pi\)
\(192\) 0 0
\(193\) 3757.48 1.40139 0.700697 0.713459i \(-0.252872\pi\)
0.700697 + 0.713459i \(0.252872\pi\)
\(194\) 0 0
\(195\) −7599.00 −2.79065
\(196\) 0 0
\(197\) 1608.39 0.581689 0.290845 0.956770i \(-0.406064\pi\)
0.290845 + 0.956770i \(0.406064\pi\)
\(198\) 0 0
\(199\) −2865.53 −1.02076 −0.510382 0.859948i \(-0.670496\pi\)
−0.510382 + 0.859948i \(0.670496\pi\)
\(200\) 0 0
\(201\) −4563.41 −1.60138
\(202\) 0 0
\(203\) −373.981 −0.129302
\(204\) 0 0
\(205\) −5279.08 −1.79857
\(206\) 0 0
\(207\) −1314.93 −0.441517
\(208\) 0 0
\(209\) −1492.50 −0.493965
\(210\) 0 0
\(211\) −821.996 −0.268192 −0.134096 0.990968i \(-0.542813\pi\)
−0.134096 + 0.990968i \(0.542813\pi\)
\(212\) 0 0
\(213\) −1829.33 −0.588467
\(214\) 0 0
\(215\) −6734.95 −2.13637
\(216\) 0 0
\(217\) 66.5375 0.0208150
\(218\) 0 0
\(219\) 5827.76 1.79819
\(220\) 0 0
\(221\) −6994.73 −2.12903
\(222\) 0 0
\(223\) −109.532 −0.0328916 −0.0164458 0.999865i \(-0.505235\pi\)
−0.0164458 + 0.999865i \(0.505235\pi\)
\(224\) 0 0
\(225\) 1892.63 0.560780
\(226\) 0 0
\(227\) −3023.03 −0.883900 −0.441950 0.897040i \(-0.645713\pi\)
−0.441950 + 0.897040i \(0.645713\pi\)
\(228\) 0 0
\(229\) −2278.75 −0.657571 −0.328786 0.944405i \(-0.606639\pi\)
−0.328786 + 0.944405i \(0.606639\pi\)
\(230\) 0 0
\(231\) −506.083 −0.144146
\(232\) 0 0
\(233\) −1864.08 −0.524121 −0.262061 0.965051i \(-0.584402\pi\)
−0.262061 + 0.965051i \(0.584402\pi\)
\(234\) 0 0
\(235\) 847.213 0.235175
\(236\) 0 0
\(237\) −1220.06 −0.334395
\(238\) 0 0
\(239\) −1404.69 −0.380174 −0.190087 0.981767i \(-0.560877\pi\)
−0.190087 + 0.981767i \(0.560877\pi\)
\(240\) 0 0
\(241\) 3879.32 1.03688 0.518442 0.855113i \(-0.326512\pi\)
0.518442 + 0.855113i \(0.326512\pi\)
\(242\) 0 0
\(243\) 4024.43 1.06242
\(244\) 0 0
\(245\) 762.017 0.198708
\(246\) 0 0
\(247\) −10087.4 −2.59857
\(248\) 0 0
\(249\) −805.950 −0.205121
\(250\) 0 0
\(251\) 2143.54 0.539040 0.269520 0.962995i \(-0.413135\pi\)
0.269520 + 0.962995i \(0.413135\pi\)
\(252\) 0 0
\(253\) −892.972 −0.221900
\(254\) 0 0
\(255\) 9616.42 2.36158
\(256\) 0 0
\(257\) 7288.62 1.76907 0.884537 0.466471i \(-0.154475\pi\)
0.884537 + 0.466471i \(0.154475\pi\)
\(258\) 0 0
\(259\) −63.9957 −0.0153533
\(260\) 0 0
\(261\) −865.385 −0.205234
\(262\) 0 0
\(263\) −2670.52 −0.626127 −0.313064 0.949732i \(-0.601355\pi\)
−0.313064 + 0.949732i \(0.601355\pi\)
\(264\) 0 0
\(265\) 1925.73 0.446402
\(266\) 0 0
\(267\) 5567.48 1.27612
\(268\) 0 0
\(269\) 1073.80 0.243387 0.121693 0.992568i \(-0.461168\pi\)
0.121693 + 0.992568i \(0.461168\pi\)
\(270\) 0 0
\(271\) −3624.88 −0.812530 −0.406265 0.913755i \(-0.633169\pi\)
−0.406265 + 0.913755i \(0.633169\pi\)
\(272\) 0 0
\(273\) −3420.47 −0.758302
\(274\) 0 0
\(275\) 1285.29 0.281840
\(276\) 0 0
\(277\) −4905.35 −1.06402 −0.532010 0.846738i \(-0.678563\pi\)
−0.532010 + 0.846738i \(0.678563\pi\)
\(278\) 0 0
\(279\) 153.966 0.0330384
\(280\) 0 0
\(281\) −2661.90 −0.565109 −0.282555 0.959251i \(-0.591182\pi\)
−0.282555 + 0.959251i \(0.591182\pi\)
\(282\) 0 0
\(283\) 4367.36 0.917359 0.458680 0.888602i \(-0.348323\pi\)
0.458680 + 0.888602i \(0.348323\pi\)
\(284\) 0 0
\(285\) 13868.3 2.88241
\(286\) 0 0
\(287\) −2376.23 −0.488726
\(288\) 0 0
\(289\) 3938.72 0.801693
\(290\) 0 0
\(291\) −6588.86 −1.32730
\(292\) 0 0
\(293\) 1992.30 0.397240 0.198620 0.980077i \(-0.436354\pi\)
0.198620 + 0.980077i \(0.436354\pi\)
\(294\) 0 0
\(295\) 8310.58 1.64021
\(296\) 0 0
\(297\) 780.969 0.152581
\(298\) 0 0
\(299\) −6035.35 −1.16734
\(300\) 0 0
\(301\) −3031.54 −0.580516
\(302\) 0 0
\(303\) −7392.67 −1.40164
\(304\) 0 0
\(305\) −5577.10 −1.04703
\(306\) 0 0
\(307\) −7633.53 −1.41912 −0.709558 0.704647i \(-0.751105\pi\)
−0.709558 + 0.704647i \(0.751105\pi\)
\(308\) 0 0
\(309\) 6349.82 1.16902
\(310\) 0 0
\(311\) −1453.52 −0.265020 −0.132510 0.991182i \(-0.542304\pi\)
−0.132510 + 0.991182i \(0.542304\pi\)
\(312\) 0 0
\(313\) 1936.27 0.349663 0.174831 0.984598i \(-0.444062\pi\)
0.174831 + 0.984598i \(0.444062\pi\)
\(314\) 0 0
\(315\) 1763.29 0.315397
\(316\) 0 0
\(317\) −1534.36 −0.271856 −0.135928 0.990719i \(-0.543402\pi\)
−0.135928 + 0.990719i \(0.543402\pi\)
\(318\) 0 0
\(319\) −587.685 −0.103148
\(320\) 0 0
\(321\) −947.770 −0.164795
\(322\) 0 0
\(323\) 12765.5 2.19904
\(324\) 0 0
\(325\) 8686.94 1.48266
\(326\) 0 0
\(327\) 12325.6 2.08442
\(328\) 0 0
\(329\) 381.349 0.0639041
\(330\) 0 0
\(331\) −3807.42 −0.632251 −0.316125 0.948717i \(-0.602382\pi\)
−0.316125 + 0.948717i \(0.602382\pi\)
\(332\) 0 0
\(333\) −148.085 −0.0243693
\(334\) 0 0
\(335\) 10797.6 1.76100
\(336\) 0 0
\(337\) −4724.09 −0.763614 −0.381807 0.924242i \(-0.624698\pi\)
−0.381807 + 0.924242i \(0.624698\pi\)
\(338\) 0 0
\(339\) −7936.05 −1.27147
\(340\) 0 0
\(341\) 104.559 0.0166046
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 0 0
\(345\) 8297.45 1.29484
\(346\) 0 0
\(347\) −6122.41 −0.947171 −0.473586 0.880748i \(-0.657041\pi\)
−0.473586 + 0.880748i \(0.657041\pi\)
\(348\) 0 0
\(349\) 6778.93 1.03974 0.519868 0.854247i \(-0.325981\pi\)
0.519868 + 0.854247i \(0.325981\pi\)
\(350\) 0 0
\(351\) 5278.35 0.802672
\(352\) 0 0
\(353\) −3486.98 −0.525760 −0.262880 0.964829i \(-0.584672\pi\)
−0.262880 + 0.964829i \(0.584672\pi\)
\(354\) 0 0
\(355\) 4328.42 0.647123
\(356\) 0 0
\(357\) 4328.55 0.641713
\(358\) 0 0
\(359\) −3230.16 −0.474878 −0.237439 0.971402i \(-0.576308\pi\)
−0.237439 + 0.971402i \(0.576308\pi\)
\(360\) 0 0
\(361\) 11550.7 1.68402
\(362\) 0 0
\(363\) −795.273 −0.114989
\(364\) 0 0
\(365\) −13789.2 −1.97742
\(366\) 0 0
\(367\) 8190.16 1.16491 0.582456 0.812862i \(-0.302092\pi\)
0.582456 + 0.812862i \(0.302092\pi\)
\(368\) 0 0
\(369\) −5498.54 −0.775725
\(370\) 0 0
\(371\) 866.812 0.121301
\(372\) 0 0
\(373\) 5008.53 0.695260 0.347630 0.937632i \(-0.386987\pi\)
0.347630 + 0.937632i \(0.386987\pi\)
\(374\) 0 0
\(375\) 833.556 0.114786
\(376\) 0 0
\(377\) −3972.00 −0.542622
\(378\) 0 0
\(379\) −1522.26 −0.206314 −0.103157 0.994665i \(-0.532894\pi\)
−0.103157 + 0.994665i \(0.532894\pi\)
\(380\) 0 0
\(381\) 7516.02 1.01065
\(382\) 0 0
\(383\) −8520.08 −1.13670 −0.568349 0.822787i \(-0.692418\pi\)
−0.568349 + 0.822787i \(0.692418\pi\)
\(384\) 0 0
\(385\) 1197.45 0.158514
\(386\) 0 0
\(387\) −7014.93 −0.921418
\(388\) 0 0
\(389\) 1588.83 0.207088 0.103544 0.994625i \(-0.466982\pi\)
0.103544 + 0.994625i \(0.466982\pi\)
\(390\) 0 0
\(391\) 7637.64 0.987856
\(392\) 0 0
\(393\) 16289.3 2.09080
\(394\) 0 0
\(395\) 2886.82 0.367725
\(396\) 0 0
\(397\) −1483.46 −0.187539 −0.0937694 0.995594i \(-0.529892\pi\)
−0.0937694 + 0.995594i \(0.529892\pi\)
\(398\) 0 0
\(399\) 6242.41 0.783236
\(400\) 0 0
\(401\) 10189.5 1.26892 0.634460 0.772956i \(-0.281222\pi\)
0.634460 + 0.772956i \(0.281222\pi\)
\(402\) 0 0
\(403\) 706.685 0.0873510
\(404\) 0 0
\(405\) −14058.0 −1.72481
\(406\) 0 0
\(407\) −100.565 −0.0122477
\(408\) 0 0
\(409\) 3465.96 0.419024 0.209512 0.977806i \(-0.432812\pi\)
0.209512 + 0.977806i \(0.432812\pi\)
\(410\) 0 0
\(411\) 5492.39 0.659171
\(412\) 0 0
\(413\) 3740.77 0.445693
\(414\) 0 0
\(415\) 1906.98 0.225566
\(416\) 0 0
\(417\) −11350.7 −1.33296
\(418\) 0 0
\(419\) −2754.83 −0.321199 −0.160599 0.987020i \(-0.551343\pi\)
−0.160599 + 0.987020i \(0.551343\pi\)
\(420\) 0 0
\(421\) −3140.19 −0.363524 −0.181762 0.983343i \(-0.558180\pi\)
−0.181762 + 0.983343i \(0.558180\pi\)
\(422\) 0 0
\(423\) 882.433 0.101431
\(424\) 0 0
\(425\) −10993.2 −1.25470
\(426\) 0 0
\(427\) −2510.37 −0.284509
\(428\) 0 0
\(429\) −5375.03 −0.604916
\(430\) 0 0
\(431\) 4476.22 0.500260 0.250130 0.968212i \(-0.419527\pi\)
0.250130 + 0.968212i \(0.419527\pi\)
\(432\) 0 0
\(433\) 1646.00 0.182683 0.0913416 0.995820i \(-0.470884\pi\)
0.0913416 + 0.995820i \(0.470884\pi\)
\(434\) 0 0
\(435\) 5460.74 0.601891
\(436\) 0 0
\(437\) 11014.6 1.20572
\(438\) 0 0
\(439\) 7241.05 0.787236 0.393618 0.919274i \(-0.371223\pi\)
0.393618 + 0.919274i \(0.371223\pi\)
\(440\) 0 0
\(441\) 793.695 0.0857029
\(442\) 0 0
\(443\) −5887.27 −0.631405 −0.315703 0.948858i \(-0.602240\pi\)
−0.315703 + 0.948858i \(0.602240\pi\)
\(444\) 0 0
\(445\) −13173.3 −1.40332
\(446\) 0 0
\(447\) 22707.7 2.40276
\(448\) 0 0
\(449\) 6378.42 0.670415 0.335207 0.942144i \(-0.391194\pi\)
0.335207 + 0.942144i \(0.391194\pi\)
\(450\) 0 0
\(451\) −3734.07 −0.389868
\(452\) 0 0
\(453\) −16222.1 −1.68252
\(454\) 0 0
\(455\) 8093.26 0.833886
\(456\) 0 0
\(457\) −18368.0 −1.88013 −0.940064 0.340998i \(-0.889235\pi\)
−0.940064 + 0.340998i \(0.889235\pi\)
\(458\) 0 0
\(459\) −6679.67 −0.679260
\(460\) 0 0
\(461\) 17510.6 1.76909 0.884546 0.466453i \(-0.154468\pi\)
0.884546 + 0.466453i \(0.154468\pi\)
\(462\) 0 0
\(463\) 12732.5 1.27803 0.639016 0.769193i \(-0.279342\pi\)
0.639016 + 0.769193i \(0.279342\pi\)
\(464\) 0 0
\(465\) −971.556 −0.0968921
\(466\) 0 0
\(467\) 4997.23 0.495170 0.247585 0.968866i \(-0.420363\pi\)
0.247585 + 0.968866i \(0.420363\pi\)
\(468\) 0 0
\(469\) 4860.23 0.478517
\(470\) 0 0
\(471\) 10261.5 1.00387
\(472\) 0 0
\(473\) −4763.85 −0.463091
\(474\) 0 0
\(475\) −15853.8 −1.53141
\(476\) 0 0
\(477\) 2005.78 0.192534
\(478\) 0 0
\(479\) 9075.53 0.865703 0.432851 0.901465i \(-0.357507\pi\)
0.432851 + 0.901465i \(0.357507\pi\)
\(480\) 0 0
\(481\) −679.688 −0.0644306
\(482\) 0 0
\(483\) 3734.86 0.351847
\(484\) 0 0
\(485\) 15590.0 1.45960
\(486\) 0 0
\(487\) 3867.63 0.359875 0.179937 0.983678i \(-0.442410\pi\)
0.179937 + 0.983678i \(0.442410\pi\)
\(488\) 0 0
\(489\) 22731.6 2.10216
\(490\) 0 0
\(491\) −7334.24 −0.674113 −0.337057 0.941484i \(-0.609431\pi\)
−0.337057 + 0.941484i \(0.609431\pi\)
\(492\) 0 0
\(493\) 5026.50 0.459193
\(494\) 0 0
\(495\) 2770.88 0.251600
\(496\) 0 0
\(497\) 1948.31 0.175843
\(498\) 0 0
\(499\) 4365.93 0.391675 0.195838 0.980636i \(-0.437257\pi\)
0.195838 + 0.980636i \(0.437257\pi\)
\(500\) 0 0
\(501\) −6391.94 −0.570002
\(502\) 0 0
\(503\) 16352.6 1.44956 0.724779 0.688981i \(-0.241942\pi\)
0.724779 + 0.688981i \(0.241942\pi\)
\(504\) 0 0
\(505\) 17492.0 1.54135
\(506\) 0 0
\(507\) −21888.5 −1.91737
\(508\) 0 0
\(509\) −12108.2 −1.05440 −0.527199 0.849742i \(-0.676758\pi\)
−0.527199 + 0.849742i \(0.676758\pi\)
\(510\) 0 0
\(511\) −6206.82 −0.537326
\(512\) 0 0
\(513\) −9633.06 −0.829065
\(514\) 0 0
\(515\) −15024.4 −1.28555
\(516\) 0 0
\(517\) 599.262 0.0509778
\(518\) 0 0
\(519\) 7585.86 0.641584
\(520\) 0 0
\(521\) −5625.67 −0.473062 −0.236531 0.971624i \(-0.576010\pi\)
−0.236531 + 0.971624i \(0.576010\pi\)
\(522\) 0 0
\(523\) 3280.32 0.274261 0.137130 0.990553i \(-0.456212\pi\)
0.137130 + 0.990553i \(0.456212\pi\)
\(524\) 0 0
\(525\) −5375.74 −0.446889
\(526\) 0 0
\(527\) −894.298 −0.0739207
\(528\) 0 0
\(529\) −5576.93 −0.458365
\(530\) 0 0
\(531\) 8656.06 0.707422
\(532\) 0 0
\(533\) −25237.6 −2.05096
\(534\) 0 0
\(535\) 2242.54 0.181221
\(536\) 0 0
\(537\) 1703.82 0.136918
\(538\) 0 0
\(539\) 539.000 0.0430730
\(540\) 0 0
\(541\) −7772.10 −0.617650 −0.308825 0.951119i \(-0.599936\pi\)
−0.308825 + 0.951119i \(0.599936\pi\)
\(542\) 0 0
\(543\) 13943.5 1.10197
\(544\) 0 0
\(545\) −29163.8 −2.29219
\(546\) 0 0
\(547\) −10022.2 −0.783398 −0.391699 0.920094i \(-0.628112\pi\)
−0.391699 + 0.920094i \(0.628112\pi\)
\(548\) 0 0
\(549\) −5808.94 −0.451584
\(550\) 0 0
\(551\) 7248.95 0.560464
\(552\) 0 0
\(553\) 1299.42 0.0999220
\(554\) 0 0
\(555\) 934.441 0.0714681
\(556\) 0 0
\(557\) −10849.3 −0.825310 −0.412655 0.910887i \(-0.635399\pi\)
−0.412655 + 0.910887i \(0.635399\pi\)
\(558\) 0 0
\(559\) −32197.6 −2.43616
\(560\) 0 0
\(561\) 6802.01 0.511910
\(562\) 0 0
\(563\) −22019.9 −1.64836 −0.824180 0.566328i \(-0.808363\pi\)
−0.824180 + 0.566328i \(0.808363\pi\)
\(564\) 0 0
\(565\) 18777.7 1.39820
\(566\) 0 0
\(567\) −6327.80 −0.468682
\(568\) 0 0
\(569\) 13742.9 1.01253 0.506267 0.862377i \(-0.331025\pi\)
0.506267 + 0.862377i \(0.331025\pi\)
\(570\) 0 0
\(571\) −19382.4 −1.42054 −0.710269 0.703931i \(-0.751427\pi\)
−0.710269 + 0.703931i \(0.751427\pi\)
\(572\) 0 0
\(573\) 19180.4 1.39838
\(574\) 0 0
\(575\) −9485.37 −0.687943
\(576\) 0 0
\(577\) −565.348 −0.0407899 −0.0203949 0.999792i \(-0.506492\pi\)
−0.0203949 + 0.999792i \(0.506492\pi\)
\(578\) 0 0
\(579\) −24696.0 −1.77260
\(580\) 0 0
\(581\) 858.371 0.0612930
\(582\) 0 0
\(583\) 1362.13 0.0967646
\(584\) 0 0
\(585\) 18727.6 1.32358
\(586\) 0 0
\(587\) 20727.4 1.45743 0.728714 0.684818i \(-0.240118\pi\)
0.728714 + 0.684818i \(0.240118\pi\)
\(588\) 0 0
\(589\) −1289.71 −0.0902233
\(590\) 0 0
\(591\) −10571.1 −0.735767
\(592\) 0 0
\(593\) −2787.10 −0.193006 −0.0965030 0.995333i \(-0.530766\pi\)
−0.0965030 + 0.995333i \(0.530766\pi\)
\(594\) 0 0
\(595\) −10241.9 −0.705675
\(596\) 0 0
\(597\) 18833.7 1.29114
\(598\) 0 0
\(599\) −18935.5 −1.29162 −0.645812 0.763497i \(-0.723481\pi\)
−0.645812 + 0.763497i \(0.723481\pi\)
\(600\) 0 0
\(601\) 15821.3 1.07382 0.536908 0.843641i \(-0.319592\pi\)
0.536908 + 0.843641i \(0.319592\pi\)
\(602\) 0 0
\(603\) 11246.5 0.759521
\(604\) 0 0
\(605\) 1881.71 0.126451
\(606\) 0 0
\(607\) 2084.63 0.139394 0.0696972 0.997568i \(-0.477797\pi\)
0.0696972 + 0.997568i \(0.477797\pi\)
\(608\) 0 0
\(609\) 2458.00 0.163552
\(610\) 0 0
\(611\) 4050.25 0.268176
\(612\) 0 0
\(613\) −4395.15 −0.289590 −0.144795 0.989462i \(-0.546252\pi\)
−0.144795 + 0.989462i \(0.546252\pi\)
\(614\) 0 0
\(615\) 34696.8 2.27498
\(616\) 0 0
\(617\) −98.5856 −0.00643259 −0.00321629 0.999995i \(-0.501024\pi\)
−0.00321629 + 0.999995i \(0.501024\pi\)
\(618\) 0 0
\(619\) 16533.9 1.07359 0.536796 0.843712i \(-0.319634\pi\)
0.536796 + 0.843712i \(0.319634\pi\)
\(620\) 0 0
\(621\) −5763.50 −0.372434
\(622\) 0 0
\(623\) −5929.60 −0.381323
\(624\) 0 0
\(625\) −16577.9 −1.06099
\(626\) 0 0
\(627\) 9809.50 0.624806
\(628\) 0 0
\(629\) 860.135 0.0545243
\(630\) 0 0
\(631\) −22032.9 −1.39004 −0.695022 0.718989i \(-0.744605\pi\)
−0.695022 + 0.718989i \(0.744605\pi\)
\(632\) 0 0
\(633\) 5402.57 0.339231
\(634\) 0 0
\(635\) −17783.8 −1.11139
\(636\) 0 0
\(637\) 3642.95 0.226592
\(638\) 0 0
\(639\) 4508.35 0.279104
\(640\) 0 0
\(641\) 434.281 0.0267598 0.0133799 0.999910i \(-0.495741\pi\)
0.0133799 + 0.999910i \(0.495741\pi\)
\(642\) 0 0
\(643\) −10963.1 −0.672381 −0.336190 0.941794i \(-0.609139\pi\)
−0.336190 + 0.941794i \(0.609139\pi\)
\(644\) 0 0
\(645\) 44265.5 2.70225
\(646\) 0 0
\(647\) 452.083 0.0274702 0.0137351 0.999906i \(-0.495628\pi\)
0.0137351 + 0.999906i \(0.495628\pi\)
\(648\) 0 0
\(649\) 5878.35 0.355540
\(650\) 0 0
\(651\) −437.318 −0.0263285
\(652\) 0 0
\(653\) −10438.7 −0.625572 −0.312786 0.949824i \(-0.601262\pi\)
−0.312786 + 0.949824i \(0.601262\pi\)
\(654\) 0 0
\(655\) −38542.5 −2.29920
\(656\) 0 0
\(657\) −14362.4 −0.852865
\(658\) 0 0
\(659\) 8738.79 0.516563 0.258281 0.966070i \(-0.416844\pi\)
0.258281 + 0.966070i \(0.416844\pi\)
\(660\) 0 0
\(661\) 12849.4 0.756102 0.378051 0.925785i \(-0.376594\pi\)
0.378051 + 0.925785i \(0.376594\pi\)
\(662\) 0 0
\(663\) 45972.9 2.69297
\(664\) 0 0
\(665\) −14770.3 −0.861305
\(666\) 0 0
\(667\) 4337.08 0.251773
\(668\) 0 0
\(669\) 719.903 0.0416040
\(670\) 0 0
\(671\) −3944.87 −0.226960
\(672\) 0 0
\(673\) −22926.5 −1.31315 −0.656577 0.754259i \(-0.727996\pi\)
−0.656577 + 0.754259i \(0.727996\pi\)
\(674\) 0 0
\(675\) 8295.66 0.473037
\(676\) 0 0
\(677\) 13633.4 0.773965 0.386983 0.922087i \(-0.373517\pi\)
0.386983 + 0.922087i \(0.373517\pi\)
\(678\) 0 0
\(679\) 7017.41 0.396618
\(680\) 0 0
\(681\) 19868.9 1.11803
\(682\) 0 0
\(683\) −33307.5 −1.86600 −0.932998 0.359882i \(-0.882817\pi\)
−0.932998 + 0.359882i \(0.882817\pi\)
\(684\) 0 0
\(685\) −12995.7 −0.724874
\(686\) 0 0
\(687\) 14977.1 0.831748
\(688\) 0 0
\(689\) 9206.28 0.509044
\(690\) 0 0
\(691\) 10077.3 0.554786 0.277393 0.960757i \(-0.410530\pi\)
0.277393 + 0.960757i \(0.410530\pi\)
\(692\) 0 0
\(693\) 1247.23 0.0683673
\(694\) 0 0
\(695\) 26857.1 1.46582
\(696\) 0 0
\(697\) 31937.7 1.73562
\(698\) 0 0
\(699\) 12251.7 0.662950
\(700\) 0 0
\(701\) −4621.74 −0.249017 −0.124508 0.992219i \(-0.539735\pi\)
−0.124508 + 0.992219i \(0.539735\pi\)
\(702\) 0 0
\(703\) 1240.44 0.0665492
\(704\) 0 0
\(705\) −5568.31 −0.297468
\(706\) 0 0
\(707\) 7873.51 0.418831
\(708\) 0 0
\(709\) 17746.6 0.940038 0.470019 0.882656i \(-0.344247\pi\)
0.470019 + 0.882656i \(0.344247\pi\)
\(710\) 0 0
\(711\) 3006.82 0.158600
\(712\) 0 0
\(713\) −771.638 −0.0405302
\(714\) 0 0
\(715\) 12718.0 0.665211
\(716\) 0 0
\(717\) 9232.31 0.480875
\(718\) 0 0
\(719\) 31652.1 1.64176 0.820879 0.571103i \(-0.193484\pi\)
0.820879 + 0.571103i \(0.193484\pi\)
\(720\) 0 0
\(721\) −6762.83 −0.349322
\(722\) 0 0
\(723\) −25496.9 −1.31153
\(724\) 0 0
\(725\) −6242.54 −0.319782
\(726\) 0 0
\(727\) −21610.8 −1.10248 −0.551239 0.834348i \(-0.685845\pi\)
−0.551239 + 0.834348i \(0.685845\pi\)
\(728\) 0 0
\(729\) −2043.39 −0.103815
\(730\) 0 0
\(731\) 40745.5 2.06160
\(732\) 0 0
\(733\) −7665.43 −0.386261 −0.193130 0.981173i \(-0.561864\pi\)
−0.193130 + 0.981173i \(0.561864\pi\)
\(734\) 0 0
\(735\) −5008.36 −0.251342
\(736\) 0 0
\(737\) 7637.50 0.381725
\(738\) 0 0
\(739\) 13841.5 0.688996 0.344498 0.938787i \(-0.388049\pi\)
0.344498 + 0.938787i \(0.388049\pi\)
\(740\) 0 0
\(741\) 66299.7 3.28688
\(742\) 0 0
\(743\) 12136.3 0.599243 0.299621 0.954058i \(-0.403140\pi\)
0.299621 + 0.954058i \(0.403140\pi\)
\(744\) 0 0
\(745\) −53729.1 −2.64226
\(746\) 0 0
\(747\) 1986.25 0.0972867
\(748\) 0 0
\(749\) 1009.42 0.0492433
\(750\) 0 0
\(751\) −28866.7 −1.40261 −0.701305 0.712861i \(-0.747399\pi\)
−0.701305 + 0.712861i \(0.747399\pi\)
\(752\) 0 0
\(753\) −14088.4 −0.681820
\(754\) 0 0
\(755\) 38383.4 1.85022
\(756\) 0 0
\(757\) 8370.48 0.401889 0.200945 0.979603i \(-0.435599\pi\)
0.200945 + 0.979603i \(0.435599\pi\)
\(758\) 0 0
\(759\) 5869.06 0.280677
\(760\) 0 0
\(761\) 30458.1 1.45086 0.725430 0.688296i \(-0.241641\pi\)
0.725430 + 0.688296i \(0.241641\pi\)
\(762\) 0 0
\(763\) −13127.3 −0.622856
\(764\) 0 0
\(765\) −23699.5 −1.12008
\(766\) 0 0
\(767\) 39730.1 1.87037
\(768\) 0 0
\(769\) −32239.5 −1.51182 −0.755908 0.654678i \(-0.772804\pi\)
−0.755908 + 0.654678i \(0.772804\pi\)
\(770\) 0 0
\(771\) −47904.5 −2.23766
\(772\) 0 0
\(773\) −7524.47 −0.350112 −0.175056 0.984559i \(-0.556011\pi\)
−0.175056 + 0.984559i \(0.556011\pi\)
\(774\) 0 0
\(775\) 1110.65 0.0514784
\(776\) 0 0
\(777\) 420.612 0.0194200
\(778\) 0 0
\(779\) 46058.8 2.11839
\(780\) 0 0
\(781\) 3061.63 0.140274
\(782\) 0 0
\(783\) −3793.09 −0.173121
\(784\) 0 0
\(785\) −24279.9 −1.10393
\(786\) 0 0
\(787\) −33196.6 −1.50360 −0.751798 0.659394i \(-0.770813\pi\)
−0.751798 + 0.659394i \(0.770813\pi\)
\(788\) 0 0
\(789\) 17552.0 0.791976
\(790\) 0 0
\(791\) 8452.23 0.379932
\(792\) 0 0
\(793\) −26662.3 −1.19395
\(794\) 0 0
\(795\) −12656.9 −0.564645
\(796\) 0 0
\(797\) 8817.06 0.391865 0.195932 0.980617i \(-0.437227\pi\)
0.195932 + 0.980617i \(0.437227\pi\)
\(798\) 0 0
\(799\) −5125.52 −0.226944
\(800\) 0 0
\(801\) −13721.0 −0.605252
\(802\) 0 0
\(803\) −9753.57 −0.428638
\(804\) 0 0
\(805\) −8837.14 −0.386917
\(806\) 0 0
\(807\) −7057.59 −0.307855
\(808\) 0 0
\(809\) −28930.3 −1.25727 −0.628637 0.777699i \(-0.716387\pi\)
−0.628637 + 0.777699i \(0.716387\pi\)
\(810\) 0 0
\(811\) 45923.3 1.98839 0.994195 0.107594i \(-0.0343146\pi\)
0.994195 + 0.107594i \(0.0343146\pi\)
\(812\) 0 0
\(813\) 23824.5 1.02775
\(814\) 0 0
\(815\) −53785.7 −2.31169
\(816\) 0 0
\(817\) 58761.0 2.51626
\(818\) 0 0
\(819\) 8429.71 0.359656
\(820\) 0 0
\(821\) 16382.8 0.696423 0.348211 0.937416i \(-0.386789\pi\)
0.348211 + 0.937416i \(0.386789\pi\)
\(822\) 0 0
\(823\) 32395.3 1.37209 0.686045 0.727559i \(-0.259345\pi\)
0.686045 + 0.727559i \(0.259345\pi\)
\(824\) 0 0
\(825\) −8447.60 −0.356494
\(826\) 0 0
\(827\) 14329.2 0.602508 0.301254 0.953544i \(-0.402595\pi\)
0.301254 + 0.953544i \(0.402595\pi\)
\(828\) 0 0
\(829\) 16445.8 0.689005 0.344503 0.938785i \(-0.388048\pi\)
0.344503 + 0.938785i \(0.388048\pi\)
\(830\) 0 0
\(831\) 32240.4 1.34586
\(832\) 0 0
\(833\) −4610.10 −0.191753
\(834\) 0 0
\(835\) 15124.1 0.626816
\(836\) 0 0
\(837\) 674.854 0.0278690
\(838\) 0 0
\(839\) −40514.7 −1.66713 −0.833565 0.552422i \(-0.813704\pi\)
−0.833565 + 0.552422i \(0.813704\pi\)
\(840\) 0 0
\(841\) −21534.7 −0.882967
\(842\) 0 0
\(843\) 17495.4 0.714795
\(844\) 0 0
\(845\) 51791.0 2.10848
\(846\) 0 0
\(847\) 847.000 0.0343604
\(848\) 0 0
\(849\) −28704.5 −1.16035
\(850\) 0 0
\(851\) 742.160 0.0298953
\(852\) 0 0
\(853\) −27962.7 −1.12242 −0.561211 0.827673i \(-0.689664\pi\)
−0.561211 + 0.827673i \(0.689664\pi\)
\(854\) 0 0
\(855\) −34178.2 −1.36710
\(856\) 0 0
\(857\) −4639.52 −0.184928 −0.0924639 0.995716i \(-0.529474\pi\)
−0.0924639 + 0.995716i \(0.529474\pi\)
\(858\) 0 0
\(859\) −18521.2 −0.735663 −0.367831 0.929892i \(-0.619900\pi\)
−0.367831 + 0.929892i \(0.619900\pi\)
\(860\) 0 0
\(861\) 15617.8 0.618179
\(862\) 0 0
\(863\) −40491.4 −1.59715 −0.798577 0.601893i \(-0.794413\pi\)
−0.798577 + 0.601893i \(0.794413\pi\)
\(864\) 0 0
\(865\) −17949.1 −0.705534
\(866\) 0 0
\(867\) −25887.3 −1.01405
\(868\) 0 0
\(869\) 2041.94 0.0797102
\(870\) 0 0
\(871\) 51619.8 2.00812
\(872\) 0 0
\(873\) 16238.1 0.629528
\(874\) 0 0
\(875\) −887.772 −0.0342996
\(876\) 0 0
\(877\) −48530.3 −1.86859 −0.934295 0.356502i \(-0.883969\pi\)
−0.934295 + 0.356502i \(0.883969\pi\)
\(878\) 0 0
\(879\) −13094.4 −0.502461
\(880\) 0 0
\(881\) −11590.0 −0.443219 −0.221609 0.975135i \(-0.571131\pi\)
−0.221609 + 0.975135i \(0.571131\pi\)
\(882\) 0 0
\(883\) −41900.7 −1.59691 −0.798455 0.602054i \(-0.794349\pi\)
−0.798455 + 0.602054i \(0.794349\pi\)
\(884\) 0 0
\(885\) −54621.3 −2.07466
\(886\) 0 0
\(887\) 17136.8 0.648700 0.324350 0.945937i \(-0.394854\pi\)
0.324350 + 0.945937i \(0.394854\pi\)
\(888\) 0 0
\(889\) −8004.89 −0.301997
\(890\) 0 0
\(891\) −9943.69 −0.373879
\(892\) 0 0
\(893\) −7391.75 −0.276994
\(894\) 0 0
\(895\) −4031.44 −0.150566
\(896\) 0 0
\(897\) 39667.4 1.47654
\(898\) 0 0
\(899\) −507.832 −0.0188400
\(900\) 0 0
\(901\) −11650.4 −0.430778
\(902\) 0 0
\(903\) 19924.8 0.734283
\(904\) 0 0
\(905\) −32992.0 −1.21181
\(906\) 0 0
\(907\) −40350.7 −1.47720 −0.738601 0.674143i \(-0.764513\pi\)
−0.738601 + 0.674143i \(0.764513\pi\)
\(908\) 0 0
\(909\) 18219.1 0.664786
\(910\) 0 0
\(911\) 32322.7 1.17552 0.587760 0.809035i \(-0.300010\pi\)
0.587760 + 0.809035i \(0.300010\pi\)
\(912\) 0 0
\(913\) 1348.87 0.0488949
\(914\) 0 0
\(915\) 36655.5 1.32437
\(916\) 0 0
\(917\) −17348.8 −0.624763
\(918\) 0 0
\(919\) −2431.28 −0.0872694 −0.0436347 0.999048i \(-0.513894\pi\)
−0.0436347 + 0.999048i \(0.513894\pi\)
\(920\) 0 0
\(921\) 50171.4 1.79501
\(922\) 0 0
\(923\) 20692.7 0.737930
\(924\) 0 0
\(925\) −1068.22 −0.0379708
\(926\) 0 0
\(927\) −15649.0 −0.554457
\(928\) 0 0
\(929\) 40221.0 1.42046 0.710230 0.703970i \(-0.248591\pi\)
0.710230 + 0.703970i \(0.248591\pi\)
\(930\) 0 0
\(931\) −6648.43 −0.234042
\(932\) 0 0
\(933\) 9553.25 0.335219
\(934\) 0 0
\(935\) −16094.4 −0.562934
\(936\) 0 0
\(937\) 41503.4 1.44702 0.723510 0.690314i \(-0.242528\pi\)
0.723510 + 0.690314i \(0.242528\pi\)
\(938\) 0 0
\(939\) −12726.2 −0.442282
\(940\) 0 0
\(941\) −9032.78 −0.312923 −0.156461 0.987684i \(-0.550009\pi\)
−0.156461 + 0.987684i \(0.550009\pi\)
\(942\) 0 0
\(943\) 27557.2 0.951629
\(944\) 0 0
\(945\) 7728.72 0.266048
\(946\) 0 0
\(947\) −5565.96 −0.190992 −0.0954960 0.995430i \(-0.530444\pi\)
−0.0954960 + 0.995430i \(0.530444\pi\)
\(948\) 0 0
\(949\) −65921.7 −2.25491
\(950\) 0 0
\(951\) 10084.6 0.343865
\(952\) 0 0
\(953\) 32657.4 1.11005 0.555024 0.831834i \(-0.312709\pi\)
0.555024 + 0.831834i \(0.312709\pi\)
\(954\) 0 0
\(955\) −45383.1 −1.53776
\(956\) 0 0
\(957\) 3862.56 0.130469
\(958\) 0 0
\(959\) −5849.63 −0.196970
\(960\) 0 0
\(961\) −29700.6 −0.996967
\(962\) 0 0
\(963\) 2335.76 0.0781609
\(964\) 0 0
\(965\) 58433.9 1.94928
\(966\) 0 0
\(967\) 610.079 0.0202883 0.0101442 0.999949i \(-0.496771\pi\)
0.0101442 + 0.999949i \(0.496771\pi\)
\(968\) 0 0
\(969\) −83901.2 −2.78152
\(970\) 0 0
\(971\) 45371.4 1.49952 0.749762 0.661708i \(-0.230168\pi\)
0.749762 + 0.661708i \(0.230168\pi\)
\(972\) 0 0
\(973\) 12088.9 0.398308
\(974\) 0 0
\(975\) −57094.9 −1.87539
\(976\) 0 0
\(977\) 27229.0 0.891639 0.445820 0.895123i \(-0.352912\pi\)
0.445820 + 0.895123i \(0.352912\pi\)
\(978\) 0 0
\(979\) −9317.94 −0.304191
\(980\) 0 0
\(981\) −30376.2 −0.988622
\(982\) 0 0
\(983\) −7458.49 −0.242003 −0.121002 0.992652i \(-0.538611\pi\)
−0.121002 + 0.992652i \(0.538611\pi\)
\(984\) 0 0
\(985\) 25012.6 0.809104
\(986\) 0 0
\(987\) −2506.42 −0.0808310
\(988\) 0 0
\(989\) 35156.9 1.13036
\(990\) 0 0
\(991\) 24357.8 0.780778 0.390389 0.920650i \(-0.372340\pi\)
0.390389 + 0.920650i \(0.372340\pi\)
\(992\) 0 0
\(993\) 25024.3 0.799721
\(994\) 0 0
\(995\) −44562.9 −1.41984
\(996\) 0 0
\(997\) 19954.3 0.633862 0.316931 0.948449i \(-0.397348\pi\)
0.316931 + 0.948449i \(0.397348\pi\)
\(998\) 0 0
\(999\) −649.074 −0.0205563
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 1232.4.a.s.1.2 4
4.3 odd 2 77.4.a.d.1.1 4
12.11 even 2 693.4.a.l.1.4 4
20.19 odd 2 1925.4.a.p.1.4 4
28.27 even 2 539.4.a.g.1.1 4
44.43 even 2 847.4.a.d.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.4.a.d.1.1 4 4.3 odd 2
539.4.a.g.1.1 4 28.27 even 2
693.4.a.l.1.4 4 12.11 even 2
847.4.a.d.1.4 4 44.43 even 2
1232.4.a.s.1.2 4 1.1 even 1 trivial
1925.4.a.p.1.4 4 20.19 odd 2