Properties

Label 2160.4.a.bo.1.3
Level $2160$
Weight $4$
Character 2160.1
Self dual yes
Analytic conductor $127.444$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2160.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(127.444125612\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.985.1
Defining polynomial: \( x^{3} - x^{2} - 6x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 1080)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-2.09376\) of defining polynomial
Character \(\chi\) \(=\) 2160.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.00000 q^{5} +12.8657 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} +12.8657 q^{7} -18.2595 q^{11} +20.2595 q^{13} +6.65336 q^{17} -150.972 q^{19} +88.1068 q^{23} +25.0000 q^{25} -201.867 q^{29} +268.330 q^{31} +64.3283 q^{35} -123.539 q^{37} +275.174 q^{41} -488.679 q^{43} -436.725 q^{47} -177.475 q^{49} +340.573 q^{53} -91.2975 q^{55} -548.360 q^{59} -206.793 q^{61} +101.298 q^{65} -499.621 q^{67} +460.900 q^{71} -416.818 q^{73} -234.921 q^{77} +289.912 q^{79} -909.471 q^{83} +33.2668 q^{85} +186.814 q^{89} +260.652 q^{91} -754.862 q^{95} +648.440 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 15 q^{5} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 15 q^{5} - 6 q^{7} - 12 q^{11} + 18 q^{13} - 21 q^{17} - 57 q^{19} - 87 q^{23} + 75 q^{25} + 138 q^{29} - 117 q^{31} - 30 q^{35} + 150 q^{37} - 180 q^{43} - 684 q^{47} - 81 q^{49} + 87 q^{53} - 60 q^{55} - 714 q^{59} - 513 q^{61} + 90 q^{65} + 174 q^{67} - 768 q^{71} - 252 q^{73} + 888 q^{77} - 207 q^{79} - 1689 q^{83} - 105 q^{85} + 312 q^{89} - 900 q^{91} - 285 q^{95} - 1080 q^{97}+O(q^{100}) \) 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 0
\(3\) 0 0
\(4\) 0 0
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 12.8657 0.694680 0.347340 0.937739i \(-0.387085\pi\)
0.347340 + 0.937739i \(0.387085\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −18.2595 −0.500495 −0.250248 0.968182i \(-0.580512\pi\)
−0.250248 + 0.968182i \(0.580512\pi\)
\(12\) 0 0
\(13\) 20.2595 0.432229 0.216114 0.976368i \(-0.430662\pi\)
0.216114 + 0.976368i \(0.430662\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.65336 0.0949222 0.0474611 0.998873i \(-0.484887\pi\)
0.0474611 + 0.998873i \(0.484887\pi\)
\(18\) 0 0
\(19\) −150.972 −1.82292 −0.911459 0.411390i \(-0.865043\pi\)
−0.911459 + 0.411390i \(0.865043\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 88.1068 0.798762 0.399381 0.916785i \(-0.369225\pi\)
0.399381 + 0.916785i \(0.369225\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −201.867 −1.29261 −0.646306 0.763078i \(-0.723687\pi\)
−0.646306 + 0.763078i \(0.723687\pi\)
\(30\) 0 0
\(31\) 268.330 1.55463 0.777313 0.629114i \(-0.216582\pi\)
0.777313 + 0.629114i \(0.216582\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 64.3283 0.310670
\(36\) 0 0
\(37\) −123.539 −0.548909 −0.274455 0.961600i \(-0.588497\pi\)
−0.274455 + 0.961600i \(0.588497\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 275.174 1.04817 0.524084 0.851666i \(-0.324408\pi\)
0.524084 + 0.851666i \(0.324408\pi\)
\(42\) 0 0
\(43\) −488.679 −1.73309 −0.866545 0.499098i \(-0.833665\pi\)
−0.866545 + 0.499098i \(0.833665\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −436.725 −1.35538 −0.677691 0.735347i \(-0.737019\pi\)
−0.677691 + 0.735347i \(0.737019\pi\)
\(48\) 0 0
\(49\) −177.475 −0.517420
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 340.573 0.882665 0.441332 0.897344i \(-0.354506\pi\)
0.441332 + 0.897344i \(0.354506\pi\)
\(54\) 0 0
\(55\) −91.2975 −0.223828
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −548.360 −1.21001 −0.605004 0.796223i \(-0.706828\pi\)
−0.605004 + 0.796223i \(0.706828\pi\)
\(60\) 0 0
\(61\) −206.793 −0.434051 −0.217025 0.976166i \(-0.569635\pi\)
−0.217025 + 0.976166i \(0.569635\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 101.298 0.193299
\(66\) 0 0
\(67\) −499.621 −0.911021 −0.455511 0.890230i \(-0.650543\pi\)
−0.455511 + 0.890230i \(0.650543\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 460.900 0.770406 0.385203 0.922832i \(-0.374131\pi\)
0.385203 + 0.922832i \(0.374131\pi\)
\(72\) 0 0
\(73\) −416.818 −0.668285 −0.334143 0.942522i \(-0.608447\pi\)
−0.334143 + 0.942522i \(0.608447\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −234.921 −0.347684
\(78\) 0 0
\(79\) 289.912 0.412882 0.206441 0.978459i \(-0.433812\pi\)
0.206441 + 0.978459i \(0.433812\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −909.471 −1.20274 −0.601370 0.798971i \(-0.705378\pi\)
−0.601370 + 0.798971i \(0.705378\pi\)
\(84\) 0 0
\(85\) 33.2668 0.0424505
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 186.814 0.222497 0.111249 0.993793i \(-0.464515\pi\)
0.111249 + 0.993793i \(0.464515\pi\)
\(90\) 0 0
\(91\) 260.652 0.300261
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −754.862 −0.815234
\(96\) 0 0
\(97\) 648.440 0.678754 0.339377 0.940651i \(-0.389784\pi\)
0.339377 + 0.940651i \(0.389784\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1415.88 1.39490 0.697450 0.716634i \(-0.254318\pi\)
0.697450 + 0.716634i \(0.254318\pi\)
\(102\) 0 0
\(103\) 1199.94 1.14790 0.573949 0.818891i \(-0.305411\pi\)
0.573949 + 0.818891i \(0.305411\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1597.84 −1.44363 −0.721817 0.692084i \(-0.756693\pi\)
−0.721817 + 0.692084i \(0.756693\pi\)
\(108\) 0 0
\(109\) 1316.75 1.15708 0.578541 0.815653i \(-0.303622\pi\)
0.578541 + 0.815653i \(0.303622\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −806.519 −0.671425 −0.335712 0.941965i \(-0.608977\pi\)
−0.335712 + 0.941965i \(0.608977\pi\)
\(114\) 0 0
\(115\) 440.534 0.357217
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 85.5999 0.0659406
\(120\) 0 0
\(121\) −997.590 −0.749504
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1480.02 −1.03410 −0.517050 0.855955i \(-0.672970\pi\)
−0.517050 + 0.855955i \(0.672970\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 95.0432 0.0633890 0.0316945 0.999498i \(-0.489910\pi\)
0.0316945 + 0.999498i \(0.489910\pi\)
\(132\) 0 0
\(133\) −1942.36 −1.26635
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 793.417 0.494790 0.247395 0.968915i \(-0.420425\pi\)
0.247395 + 0.968915i \(0.420425\pi\)
\(138\) 0 0
\(139\) 24.6768 0.0150580 0.00752900 0.999972i \(-0.497603\pi\)
0.00752900 + 0.999972i \(0.497603\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −369.929 −0.216329
\(144\) 0 0
\(145\) −1009.33 −0.578074
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3092.28 1.70020 0.850098 0.526624i \(-0.176543\pi\)
0.850098 + 0.526624i \(0.176543\pi\)
\(150\) 0 0
\(151\) −2056.52 −1.10832 −0.554162 0.832409i \(-0.686961\pi\)
−0.554162 + 0.832409i \(0.686961\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1341.65 0.695250
\(156\) 0 0
\(157\) −649.944 −0.330390 −0.165195 0.986261i \(-0.552825\pi\)
−0.165195 + 0.986261i \(0.552825\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1133.55 0.554884
\(162\) 0 0
\(163\) −3183.46 −1.52974 −0.764870 0.644185i \(-0.777197\pi\)
−0.764870 + 0.644185i \(0.777197\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −743.307 −0.344424 −0.172212 0.985060i \(-0.555091\pi\)
−0.172212 + 0.985060i \(0.555091\pi\)
\(168\) 0 0
\(169\) −1786.55 −0.813178
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2152.84 0.946113 0.473057 0.881032i \(-0.343151\pi\)
0.473057 + 0.881032i \(0.343151\pi\)
\(174\) 0 0
\(175\) 321.641 0.138936
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 597.624 0.249545 0.124772 0.992185i \(-0.460180\pi\)
0.124772 + 0.992185i \(0.460180\pi\)
\(180\) 0 0
\(181\) −736.338 −0.302384 −0.151192 0.988504i \(-0.548311\pi\)
−0.151192 + 0.988504i \(0.548311\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −617.693 −0.245480
\(186\) 0 0
\(187\) −121.487 −0.0475081
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3355.19 −1.27106 −0.635531 0.772075i \(-0.719219\pi\)
−0.635531 + 0.772075i \(0.719219\pi\)
\(192\) 0 0
\(193\) 1521.54 0.567475 0.283737 0.958902i \(-0.408426\pi\)
0.283737 + 0.958902i \(0.408426\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 364.341 0.131768 0.0658838 0.997827i \(-0.479013\pi\)
0.0658838 + 0.997827i \(0.479013\pi\)
\(198\) 0 0
\(199\) 171.730 0.0611738 0.0305869 0.999532i \(-0.490262\pi\)
0.0305869 + 0.999532i \(0.490262\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2597.15 −0.897952
\(204\) 0 0
\(205\) 1375.87 0.468755
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2756.68 0.912362
\(210\) 0 0
\(211\) −904.632 −0.295154 −0.147577 0.989051i \(-0.547147\pi\)
−0.147577 + 0.989051i \(0.547147\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2443.40 −0.775062
\(216\) 0 0
\(217\) 3452.24 1.07997
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 134.794 0.0410281
\(222\) 0 0
\(223\) −405.423 −0.121745 −0.0608724 0.998146i \(-0.519388\pi\)
−0.0608724 + 0.998146i \(0.519388\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −556.762 −0.162791 −0.0813956 0.996682i \(-0.525938\pi\)
−0.0813956 + 0.996682i \(0.525938\pi\)
\(228\) 0 0
\(229\) −4584.45 −1.32292 −0.661461 0.749979i \(-0.730063\pi\)
−0.661461 + 0.749979i \(0.730063\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4593.97 1.29168 0.645839 0.763473i \(-0.276508\pi\)
0.645839 + 0.763473i \(0.276508\pi\)
\(234\) 0 0
\(235\) −2183.63 −0.606145
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1754.22 −0.474775 −0.237387 0.971415i \(-0.576291\pi\)
−0.237387 + 0.971415i \(0.576291\pi\)
\(240\) 0 0
\(241\) −4394.90 −1.17469 −0.587346 0.809336i \(-0.699827\pi\)
−0.587346 + 0.809336i \(0.699827\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −887.375 −0.231397
\(246\) 0 0
\(247\) −3058.63 −0.787918
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2260.13 −0.568360 −0.284180 0.958771i \(-0.591721\pi\)
−0.284180 + 0.958771i \(0.591721\pi\)
\(252\) 0 0
\(253\) −1608.79 −0.399777
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −570.878 −0.138562 −0.0692809 0.997597i \(-0.522070\pi\)
−0.0692809 + 0.997597i \(0.522070\pi\)
\(258\) 0 0
\(259\) −1589.41 −0.381316
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6248.85 1.46510 0.732549 0.680715i \(-0.238331\pi\)
0.732549 + 0.680715i \(0.238331\pi\)
\(264\) 0 0
\(265\) 1702.86 0.394740
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1718.42 −0.389494 −0.194747 0.980853i \(-0.562389\pi\)
−0.194747 + 0.980853i \(0.562389\pi\)
\(270\) 0 0
\(271\) −883.253 −0.197985 −0.0989923 0.995088i \(-0.531562\pi\)
−0.0989923 + 0.995088i \(0.531562\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −456.488 −0.100099
\(276\) 0 0
\(277\) −4889.06 −1.06049 −0.530244 0.847845i \(-0.677900\pi\)
−0.530244 + 0.847845i \(0.677900\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3590.34 −0.762212 −0.381106 0.924531i \(-0.624457\pi\)
−0.381106 + 0.924531i \(0.624457\pi\)
\(282\) 0 0
\(283\) 2003.82 0.420900 0.210450 0.977605i \(-0.432507\pi\)
0.210450 + 0.977605i \(0.432507\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3540.29 0.728142
\(288\) 0 0
\(289\) −4868.73 −0.990990
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4348.62 0.867062 0.433531 0.901139i \(-0.357267\pi\)
0.433531 + 0.901139i \(0.357267\pi\)
\(294\) 0 0
\(295\) −2741.80 −0.541132
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1785.00 0.345248
\(300\) 0 0
\(301\) −6287.18 −1.20394
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1033.96 −0.194113
\(306\) 0 0
\(307\) −7513.36 −1.39678 −0.698388 0.715719i \(-0.746099\pi\)
−0.698388 + 0.715719i \(0.746099\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 624.265 0.113823 0.0569113 0.998379i \(-0.481875\pi\)
0.0569113 + 0.998379i \(0.481875\pi\)
\(312\) 0 0
\(313\) −1963.18 −0.354521 −0.177261 0.984164i \(-0.556724\pi\)
−0.177261 + 0.984164i \(0.556724\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2928.29 0.518829 0.259415 0.965766i \(-0.416470\pi\)
0.259415 + 0.965766i \(0.416470\pi\)
\(318\) 0 0
\(319\) 3685.99 0.646946
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1004.47 −0.173035
\(324\) 0 0
\(325\) 506.488 0.0864458
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −5618.76 −0.941556
\(330\) 0 0
\(331\) −3619.06 −0.600972 −0.300486 0.953786i \(-0.597149\pi\)
−0.300486 + 0.953786i \(0.597149\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2498.11 −0.407421
\(336\) 0 0
\(337\) −9440.02 −1.52591 −0.762954 0.646453i \(-0.776251\pi\)
−0.762954 + 0.646453i \(0.776251\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4899.57 −0.778083
\(342\) 0 0
\(343\) −6696.25 −1.05412
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1657.99 −0.256500 −0.128250 0.991742i \(-0.540936\pi\)
−0.128250 + 0.991742i \(0.540936\pi\)
\(348\) 0 0
\(349\) −4537.03 −0.695879 −0.347939 0.937517i \(-0.613119\pi\)
−0.347939 + 0.937517i \(0.613119\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −8627.43 −1.30083 −0.650413 0.759580i \(-0.725404\pi\)
−0.650413 + 0.759580i \(0.725404\pi\)
\(354\) 0 0
\(355\) 2304.50 0.344536
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10116.5 −1.48726 −0.743631 0.668590i \(-0.766898\pi\)
−0.743631 + 0.668590i \(0.766898\pi\)
\(360\) 0 0
\(361\) 15933.7 2.32303
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2084.09 −0.298866
\(366\) 0 0
\(367\) −4707.74 −0.669597 −0.334798 0.942290i \(-0.608668\pi\)
−0.334798 + 0.942290i \(0.608668\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4381.69 0.613170
\(372\) 0 0
\(373\) −14191.2 −1.96995 −0.984973 0.172706i \(-0.944749\pi\)
−0.984973 + 0.172706i \(0.944749\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4089.73 −0.558704
\(378\) 0 0
\(379\) −8841.08 −1.19825 −0.599124 0.800656i \(-0.704484\pi\)
−0.599124 + 0.800656i \(0.704484\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 6225.37 0.830553 0.415276 0.909695i \(-0.363685\pi\)
0.415276 + 0.909695i \(0.363685\pi\)
\(384\) 0 0
\(385\) −1174.60 −0.155489
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3967.13 0.517074 0.258537 0.966001i \(-0.416760\pi\)
0.258537 + 0.966001i \(0.416760\pi\)
\(390\) 0 0
\(391\) 586.206 0.0758203
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1449.56 0.184646
\(396\) 0 0
\(397\) 10510.6 1.32875 0.664375 0.747399i \(-0.268698\pi\)
0.664375 + 0.747399i \(0.268698\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6440.92 0.802105 0.401052 0.916055i \(-0.368645\pi\)
0.401052 + 0.916055i \(0.368645\pi\)
\(402\) 0 0
\(403\) 5436.22 0.671954
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2255.76 0.274726
\(408\) 0 0
\(409\) −4820.75 −0.582813 −0.291407 0.956599i \(-0.594123\pi\)
−0.291407 + 0.956599i \(0.594123\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −7055.01 −0.840568
\(414\) 0 0
\(415\) −4547.36 −0.537882
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 17003.8 1.98255 0.991276 0.131803i \(-0.0420767\pi\)
0.991276 + 0.131803i \(0.0420767\pi\)
\(420\) 0 0
\(421\) 1582.86 0.183239 0.0916197 0.995794i \(-0.470796\pi\)
0.0916197 + 0.995794i \(0.470796\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 166.334 0.0189844
\(426\) 0 0
\(427\) −2660.52 −0.301526
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 10518.7 1.17557 0.587784 0.809018i \(-0.300001\pi\)
0.587784 + 0.809018i \(0.300001\pi\)
\(432\) 0 0
\(433\) −5469.93 −0.607086 −0.303543 0.952818i \(-0.598170\pi\)
−0.303543 + 0.952818i \(0.598170\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −13301.7 −1.45608
\(438\) 0 0
\(439\) 12068.3 1.31205 0.656024 0.754740i \(-0.272237\pi\)
0.656024 + 0.754740i \(0.272237\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9948.23 1.06694 0.533470 0.845819i \(-0.320888\pi\)
0.533470 + 0.845819i \(0.320888\pi\)
\(444\) 0 0
\(445\) 934.071 0.0995039
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −12449.4 −1.30852 −0.654258 0.756271i \(-0.727019\pi\)
−0.654258 + 0.756271i \(0.727019\pi\)
\(450\) 0 0
\(451\) −5024.54 −0.524603
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1303.26 0.134281
\(456\) 0 0
\(457\) 15270.3 1.56305 0.781524 0.623875i \(-0.214442\pi\)
0.781524 + 0.623875i \(0.214442\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11670.3 1.17905 0.589524 0.807751i \(-0.299315\pi\)
0.589524 + 0.807751i \(0.299315\pi\)
\(462\) 0 0
\(463\) 9205.75 0.924033 0.462017 0.886871i \(-0.347126\pi\)
0.462017 + 0.886871i \(0.347126\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −12090.0 −1.19799 −0.598994 0.800754i \(-0.704433\pi\)
−0.598994 + 0.800754i \(0.704433\pi\)
\(468\) 0 0
\(469\) −6427.95 −0.632868
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8923.04 0.867404
\(474\) 0 0
\(475\) −3774.31 −0.364584
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3804.88 −0.362942 −0.181471 0.983396i \(-0.558086\pi\)
−0.181471 + 0.983396i \(0.558086\pi\)
\(480\) 0 0
\(481\) −2502.83 −0.237254
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3242.20 0.303548
\(486\) 0 0
\(487\) −5679.19 −0.528437 −0.264218 0.964463i \(-0.585114\pi\)
−0.264218 + 0.964463i \(0.585114\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7710.36 −0.708684 −0.354342 0.935116i \(-0.615295\pi\)
−0.354342 + 0.935116i \(0.615295\pi\)
\(492\) 0 0
\(493\) −1343.09 −0.122698
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5929.78 0.535185
\(498\) 0 0
\(499\) 7766.60 0.696755 0.348378 0.937354i \(-0.386733\pi\)
0.348378 + 0.937354i \(0.386733\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −8393.87 −0.744064 −0.372032 0.928220i \(-0.621339\pi\)
−0.372032 + 0.928220i \(0.621339\pi\)
\(504\) 0 0
\(505\) 7079.38 0.623818
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −14775.6 −1.28667 −0.643337 0.765583i \(-0.722451\pi\)
−0.643337 + 0.765583i \(0.722451\pi\)
\(510\) 0 0
\(511\) −5362.63 −0.464245
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5999.70 0.513356
\(516\) 0 0
\(517\) 7974.39 0.678362
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −21089.0 −1.77337 −0.886684 0.462376i \(-0.846997\pi\)
−0.886684 + 0.462376i \(0.846997\pi\)
\(522\) 0 0
\(523\) −860.536 −0.0719476 −0.0359738 0.999353i \(-0.511453\pi\)
−0.0359738 + 0.999353i \(0.511453\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1785.29 0.147569
\(528\) 0 0
\(529\) −4404.19 −0.361979
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5574.88 0.453049
\(534\) 0 0
\(535\) −7989.19 −0.645613
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3240.61 0.258966
\(540\) 0 0
\(541\) −23226.2 −1.84579 −0.922895 0.385051i \(-0.874184\pi\)
−0.922895 + 0.385051i \(0.874184\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 6583.76 0.517463
\(546\) 0 0
\(547\) −11800.1 −0.922371 −0.461185 0.887304i \(-0.652576\pi\)
−0.461185 + 0.887304i \(0.652576\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 30476.3 2.35633
\(552\) 0 0
\(553\) 3729.91 0.286821
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −13654.7 −1.03872 −0.519361 0.854555i \(-0.673830\pi\)
−0.519361 + 0.854555i \(0.673830\pi\)
\(558\) 0 0
\(559\) −9900.40 −0.749092
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 12390.2 0.927502 0.463751 0.885966i \(-0.346503\pi\)
0.463751 + 0.885966i \(0.346503\pi\)
\(564\) 0 0
\(565\) −4032.60 −0.300270
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −12361.4 −0.910753 −0.455376 0.890299i \(-0.650495\pi\)
−0.455376 + 0.890299i \(0.650495\pi\)
\(570\) 0 0
\(571\) 20577.3 1.50812 0.754058 0.656807i \(-0.228094\pi\)
0.754058 + 0.656807i \(0.228094\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2202.67 0.159752
\(576\) 0 0
\(577\) 18345.2 1.32361 0.661803 0.749678i \(-0.269791\pi\)
0.661803 + 0.749678i \(0.269791\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −11700.9 −0.835520
\(582\) 0 0
\(583\) −6218.69 −0.441770
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 19713.9 1.38617 0.693085 0.720856i \(-0.256251\pi\)
0.693085 + 0.720856i \(0.256251\pi\)
\(588\) 0 0
\(589\) −40510.4 −2.83396
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −6553.49 −0.453827 −0.226914 0.973915i \(-0.572864\pi\)
−0.226914 + 0.973915i \(0.572864\pi\)
\(594\) 0 0
\(595\) 427.999 0.0294895
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −15005.2 −1.02354 −0.511768 0.859124i \(-0.671009\pi\)
−0.511768 + 0.859124i \(0.671009\pi\)
\(600\) 0 0
\(601\) −20290.4 −1.37714 −0.688572 0.725168i \(-0.741762\pi\)
−0.688572 + 0.725168i \(0.741762\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4987.95 −0.335189
\(606\) 0 0
\(607\) −11867.6 −0.793563 −0.396781 0.917913i \(-0.629873\pi\)
−0.396781 + 0.917913i \(0.629873\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −8847.84 −0.585835
\(612\) 0 0
\(613\) 27850.2 1.83501 0.917503 0.397730i \(-0.130202\pi\)
0.917503 + 0.397730i \(0.130202\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4116.33 0.268586 0.134293 0.990942i \(-0.457124\pi\)
0.134293 + 0.990942i \(0.457124\pi\)
\(618\) 0 0
\(619\) 25022.4 1.62478 0.812388 0.583117i \(-0.198167\pi\)
0.812388 + 0.583117i \(0.198167\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2403.49 0.154565
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −821.948 −0.0521037
\(630\) 0 0
\(631\) −17801.6 −1.12309 −0.561545 0.827446i \(-0.689793\pi\)
−0.561545 + 0.827446i \(0.689793\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −7400.10 −0.462463
\(636\) 0 0
\(637\) −3595.56 −0.223644
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 19325.4 1.19081 0.595405 0.803426i \(-0.296992\pi\)
0.595405 + 0.803426i \(0.296992\pi\)
\(642\) 0 0
\(643\) −267.444 −0.0164028 −0.00820138 0.999966i \(-0.502611\pi\)
−0.00820138 + 0.999966i \(0.502611\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 18749.2 1.13927 0.569634 0.821898i \(-0.307085\pi\)
0.569634 + 0.821898i \(0.307085\pi\)
\(648\) 0 0
\(649\) 10012.8 0.605603
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −14996.0 −0.898684 −0.449342 0.893360i \(-0.648341\pi\)
−0.449342 + 0.893360i \(0.648341\pi\)
\(654\) 0 0
\(655\) 475.216 0.0283484
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −19249.4 −1.13786 −0.568929 0.822386i \(-0.692642\pi\)
−0.568929 + 0.822386i \(0.692642\pi\)
\(660\) 0 0
\(661\) 12989.7 0.764357 0.382178 0.924089i \(-0.375174\pi\)
0.382178 + 0.924089i \(0.375174\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −9711.80 −0.566327
\(666\) 0 0
\(667\) −17785.8 −1.03249
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3775.93 0.217240
\(672\) 0 0
\(673\) −5909.54 −0.338478 −0.169239 0.985575i \(-0.554131\pi\)
−0.169239 + 0.985575i \(0.554131\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 23548.5 1.33684 0.668420 0.743784i \(-0.266971\pi\)
0.668420 + 0.743784i \(0.266971\pi\)
\(678\) 0 0
\(679\) 8342.60 0.471516
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 10065.3 0.563890 0.281945 0.959431i \(-0.409020\pi\)
0.281945 + 0.959431i \(0.409020\pi\)
\(684\) 0 0
\(685\) 3967.09 0.221277
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 6899.83 0.381513
\(690\) 0 0
\(691\) 28648.5 1.57720 0.788598 0.614910i \(-0.210807\pi\)
0.788598 + 0.614910i \(0.210807\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 123.384 0.00673414
\(696\) 0 0
\(697\) 1830.83 0.0994945
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 30910.9 1.66546 0.832730 0.553679i \(-0.186777\pi\)
0.832730 + 0.553679i \(0.186777\pi\)
\(702\) 0 0
\(703\) 18650.9 1.00062
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 18216.2 0.969009
\(708\) 0 0
\(709\) 11680.0 0.618691 0.309345 0.950950i \(-0.399890\pi\)
0.309345 + 0.950950i \(0.399890\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 23641.7 1.24178
\(714\) 0 0
\(715\) −1849.64 −0.0967451
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −9205.71 −0.477489 −0.238745 0.971082i \(-0.576736\pi\)
−0.238745 + 0.971082i \(0.576736\pi\)
\(720\) 0 0
\(721\) 15438.0 0.797422
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −5046.67 −0.258522
\(726\) 0 0
\(727\) −8102.51 −0.413350 −0.206675 0.978410i \(-0.566264\pi\)
−0.206675 + 0.978410i \(0.566264\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3251.36 −0.164509
\(732\) 0 0
\(733\) −33738.0 −1.70006 −0.850028 0.526737i \(-0.823415\pi\)
−0.850028 + 0.526737i \(0.823415\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9122.84 0.455962
\(738\) 0 0
\(739\) 28667.6 1.42700 0.713502 0.700653i \(-0.247108\pi\)
0.713502 + 0.700653i \(0.247108\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2344.60 −0.115767 −0.0578837 0.998323i \(-0.518435\pi\)
−0.0578837 + 0.998323i \(0.518435\pi\)
\(744\) 0 0
\(745\) 15461.4 0.760351
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −20557.2 −1.00286
\(750\) 0 0
\(751\) 23466.1 1.14020 0.570101 0.821575i \(-0.306904\pi\)
0.570101 + 0.821575i \(0.306904\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −10282.6 −0.495658
\(756\) 0 0
\(757\) 5711.42 0.274221 0.137110 0.990556i \(-0.456219\pi\)
0.137110 + 0.990556i \(0.456219\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 8101.10 0.385893 0.192947 0.981209i \(-0.438196\pi\)
0.192947 + 0.981209i \(0.438196\pi\)
\(762\) 0 0
\(763\) 16940.9 0.803802
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −11109.5 −0.523000
\(768\) 0 0
\(769\) 19468.4 0.912937 0.456468 0.889740i \(-0.349114\pi\)
0.456468 + 0.889740i \(0.349114\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 9632.96 0.448219 0.224110 0.974564i \(-0.428053\pi\)
0.224110 + 0.974564i \(0.428053\pi\)
\(774\) 0 0
\(775\) 6708.24 0.310925
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −41543.6 −1.91073
\(780\) 0 0
\(781\) −8415.81 −0.385584
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3249.72 −0.147755
\(786\) 0 0
\(787\) −38781.5 −1.75656 −0.878278 0.478150i \(-0.841308\pi\)
−0.878278 + 0.478150i \(0.841308\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −10376.4 −0.466425
\(792\) 0 0
\(793\) −4189.52 −0.187609
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 7148.58 0.317711 0.158856 0.987302i \(-0.449220\pi\)
0.158856 + 0.987302i \(0.449220\pi\)
\(798\) 0 0
\(799\) −2905.69 −0.128656
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 7610.89 0.334474
\(804\) 0 0
\(805\) 5667.76 0.248152
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −9156.29 −0.397921 −0.198960 0.980008i \(-0.563757\pi\)
−0.198960 + 0.980008i \(0.563757\pi\)
\(810\) 0 0
\(811\) −21877.2 −0.947241 −0.473621 0.880729i \(-0.657053\pi\)
−0.473621 + 0.880729i \(0.657053\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −15917.3 −0.684120
\(816\) 0 0
\(817\) 73777.1 3.15928
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −33923.3 −1.44206 −0.721030 0.692903i \(-0.756331\pi\)
−0.721030 + 0.692903i \(0.756331\pi\)
\(822\) 0 0
\(823\) 6357.76 0.269280 0.134640 0.990895i \(-0.457012\pi\)
0.134640 + 0.990895i \(0.457012\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −8059.61 −0.338887 −0.169444 0.985540i \(-0.554197\pi\)
−0.169444 + 0.985540i \(0.554197\pi\)
\(828\) 0 0
\(829\) −25496.5 −1.06819 −0.534095 0.845425i \(-0.679347\pi\)
−0.534095 + 0.845425i \(0.679347\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1180.81 −0.0491146
\(834\) 0 0
\(835\) −3716.54 −0.154031
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 31917.6 1.31337 0.656686 0.754164i \(-0.271958\pi\)
0.656686 + 0.754164i \(0.271958\pi\)
\(840\) 0 0
\(841\) 16361.3 0.670846
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −8932.76 −0.363664
\(846\) 0 0
\(847\) −12834.7 −0.520666
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −10884.6 −0.438448
\(852\) 0 0
\(853\) −28295.7 −1.13579 −0.567893 0.823102i \(-0.692241\pi\)
−0.567893 + 0.823102i \(0.692241\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 41896.2 1.66995 0.834975 0.550288i \(-0.185482\pi\)
0.834975 + 0.550288i \(0.185482\pi\)
\(858\) 0 0
\(859\) 18124.5 0.719907 0.359953 0.932970i \(-0.382793\pi\)
0.359953 + 0.932970i \(0.382793\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −25361.4 −1.00036 −0.500182 0.865921i \(-0.666733\pi\)
−0.500182 + 0.865921i \(0.666733\pi\)
\(864\) 0 0
\(865\) 10764.2 0.423115
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −5293.66 −0.206646
\(870\) 0 0
\(871\) −10122.1 −0.393770
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1608.21 0.0621341
\(876\) 0 0
\(877\) 28128.7 1.08306 0.541528 0.840683i \(-0.317846\pi\)
0.541528 + 0.840683i \(0.317846\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −12198.2 −0.466481 −0.233240 0.972419i \(-0.574933\pi\)
−0.233240 + 0.972419i \(0.574933\pi\)
\(882\) 0 0
\(883\) 15725.2 0.599317 0.299658 0.954047i \(-0.403127\pi\)
0.299658 + 0.954047i \(0.403127\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −3176.83 −0.120257 −0.0601283 0.998191i \(-0.519151\pi\)
−0.0601283 + 0.998191i \(0.519151\pi\)
\(888\) 0 0
\(889\) −19041.4 −0.718368
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 65933.5 2.47075
\(894\) 0 0
\(895\) 2988.12 0.111600
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −54166.9 −2.00953
\(900\) 0 0
\(901\) 2265.95 0.0837845
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −3681.69 −0.135230
\(906\) 0 0
\(907\) 11400.8 0.417374 0.208687 0.977982i \(-0.433081\pi\)
0.208687 + 0.977982i \(0.433081\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 9547.78 0.347236 0.173618 0.984813i \(-0.444454\pi\)
0.173618 + 0.984813i \(0.444454\pi\)
\(912\) 0 0
\(913\) 16606.5 0.601966
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1222.79 0.0440351
\(918\) 0 0
\(919\) 47127.5 1.69161 0.845807 0.533488i \(-0.179119\pi\)
0.845807 + 0.533488i \(0.179119\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 9337.61 0.332992
\(924\) 0 0
\(925\) −3088.47 −0.109782
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 25591.7 0.903807 0.451904 0.892067i \(-0.350745\pi\)
0.451904 + 0.892067i \(0.350745\pi\)
\(930\) 0 0
\(931\) 26793.8 0.943214
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −607.436 −0.0212463
\(936\) 0 0
\(937\) 47575.6 1.65873 0.829364 0.558709i \(-0.188703\pi\)
0.829364 + 0.558709i \(0.188703\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 42722.0 1.48002 0.740009 0.672597i \(-0.234821\pi\)
0.740009 + 0.672597i \(0.234821\pi\)
\(942\) 0 0
\(943\) 24244.7 0.837238
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 19523.9 0.669948 0.334974 0.942227i \(-0.391272\pi\)
0.334974 + 0.942227i \(0.391272\pi\)
\(948\) 0 0
\(949\) −8444.52 −0.288852
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 6129.73 0.208354 0.104177 0.994559i \(-0.466779\pi\)
0.104177 + 0.994559i \(0.466779\pi\)
\(954\) 0 0
\(955\) −16775.9 −0.568436
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 10207.8 0.343721
\(960\) 0 0
\(961\) 42209.8 1.41686
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 7607.68 0.253782
\(966\) 0 0
\(967\) 33974.3 1.12982 0.564912 0.825151i \(-0.308910\pi\)
0.564912 + 0.825151i \(0.308910\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −28328.7 −0.936262 −0.468131 0.883659i \(-0.655072\pi\)
−0.468131 + 0.883659i \(0.655072\pi\)
\(972\) 0 0
\(973\) 317.484 0.0104605
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −37587.6 −1.23084 −0.615421 0.788198i \(-0.711014\pi\)
−0.615421 + 0.788198i \(0.711014\pi\)
\(978\) 0 0
\(979\) −3411.14 −0.111359
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 5777.92 0.187474 0.0937371 0.995597i \(-0.470119\pi\)
0.0937371 + 0.995597i \(0.470119\pi\)
\(984\) 0 0
\(985\) 1821.71 0.0589283
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −43056.0 −1.38433
\(990\) 0 0
\(991\) 45377.5 1.45455 0.727277 0.686344i \(-0.240785\pi\)
0.727277 + 0.686344i \(0.240785\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 858.648 0.0273578
\(996\) 0 0
\(997\) −6994.90 −0.222197 −0.111099 0.993809i \(-0.535437\pi\)
−0.111099 + 0.993809i \(0.535437\pi\)
\(998\) 0 0
\(999\) 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 2160.4.a.bo.1.3 3
3.2 odd 2 2160.4.a.bg.1.3 3
4.3 odd 2 1080.4.a.m.1.1 yes 3
12.11 even 2 1080.4.a.g.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1080.4.a.g.1.1 3 12.11 even 2
1080.4.a.m.1.1 yes 3 4.3 odd 2
2160.4.a.bg.1.3 3 3.2 odd 2
2160.4.a.bo.1.3 3 1.1 even 1 trivial