Properties

Label 2352.4.a.bn.1.1
Level $2352$
Weight $4$
Character 2352.1
Self dual yes
Analytic conductor $138.772$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2352.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(138.772492334\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Defining polynomial: \(x^{2} - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 7 \)
Twist minimal: no (minimal twist has level 294)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.41421\) of defining polynomial
Character \(\chi\) \(=\) 2352.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.00000 q^{3} -15.8995 q^{5} +9.00000 q^{9} +O(q^{10})\) \(q-3.00000 q^{3} -15.8995 q^{5} +9.00000 q^{9} -57.3970 q^{11} +5.69848 q^{13} +47.6985 q^{15} -51.8995 q^{17} -16.2010 q^{19} +213.397 q^{23} +127.794 q^{25} -27.0000 q^{27} -218.191 q^{29} +251.397 q^{31} +172.191 q^{33} +386.794 q^{37} -17.0955 q^{39} -328.503 q^{41} +37.5879 q^{43} -143.095 q^{45} +254.995 q^{47} +155.698 q^{51} +211.588 q^{53} +912.583 q^{55} +48.6030 q^{57} +412.201 q^{59} -836.693 q^{61} -90.6030 q^{65} +165.588 q^{67} -640.191 q^{69} +465.015 q^{71} +449.658 q^{73} -383.382 q^{75} +343.558 q^{79} +81.0000 q^{81} -1502.33 q^{83} +825.176 q^{85} +654.573 q^{87} -341.085 q^{89} -754.191 q^{93} +257.588 q^{95} -865.437 q^{97} -516.573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 6q^{3} - 12q^{5} + 18q^{9} + O(q^{10}) \) \( 2q - 6q^{3} - 12q^{5} + 18q^{9} + 4q^{11} - 48q^{13} + 36q^{15} - 84q^{17} - 72q^{19} + 308q^{23} + 18q^{25} - 54q^{27} - 80q^{29} + 384q^{31} - 12q^{33} + 536q^{37} + 144q^{39} - 756q^{41} - 400q^{43} - 108q^{45} + 312q^{47} + 252q^{51} - 52q^{53} + 1152q^{55} + 216q^{57} + 864q^{59} - 1416q^{61} - 300q^{65} - 144q^{67} - 924q^{69} + 1524q^{71} - 744q^{73} - 54q^{75} - 976q^{79} + 162q^{81} - 312q^{83} + 700q^{85} + 240q^{87} - 108q^{89} - 1152q^{93} + 40q^{95} + 744q^{97} + 36q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.00000 −0.577350
\(4\) 0 0
\(5\) −15.8995 −1.42209 −0.711047 0.703144i \(-0.751779\pi\)
−0.711047 + 0.703144i \(0.751779\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) −57.3970 −1.57326 −0.786629 0.617426i \(-0.788176\pi\)
−0.786629 + 0.617426i \(0.788176\pi\)
\(12\) 0 0
\(13\) 5.69848 0.121575 0.0607875 0.998151i \(-0.480639\pi\)
0.0607875 + 0.998151i \(0.480639\pi\)
\(14\) 0 0
\(15\) 47.6985 0.821046
\(16\) 0 0
\(17\) −51.8995 −0.740440 −0.370220 0.928944i \(-0.620718\pi\)
−0.370220 + 0.928944i \(0.620718\pi\)
\(18\) 0 0
\(19\) −16.2010 −0.195619 −0.0978096 0.995205i \(-0.531184\pi\)
−0.0978096 + 0.995205i \(0.531184\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 213.397 1.93462 0.967312 0.253590i \(-0.0816114\pi\)
0.967312 + 0.253590i \(0.0816114\pi\)
\(24\) 0 0
\(25\) 127.794 1.02235
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −218.191 −1.39714 −0.698570 0.715542i \(-0.746180\pi\)
−0.698570 + 0.715542i \(0.746180\pi\)
\(30\) 0 0
\(31\) 251.397 1.45652 0.728262 0.685299i \(-0.240329\pi\)
0.728262 + 0.685299i \(0.240329\pi\)
\(32\) 0 0
\(33\) 172.191 0.908321
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 386.794 1.71861 0.859304 0.511464i \(-0.170897\pi\)
0.859304 + 0.511464i \(0.170897\pi\)
\(38\) 0 0
\(39\) −17.0955 −0.0701914
\(40\) 0 0
\(41\) −328.503 −1.25130 −0.625652 0.780102i \(-0.715167\pi\)
−0.625652 + 0.780102i \(0.715167\pi\)
\(42\) 0 0
\(43\) 37.5879 0.133305 0.0666523 0.997776i \(-0.478768\pi\)
0.0666523 + 0.997776i \(0.478768\pi\)
\(44\) 0 0
\(45\) −143.095 −0.474031
\(46\) 0 0
\(47\) 254.995 0.791379 0.395690 0.918384i \(-0.370506\pi\)
0.395690 + 0.918384i \(0.370506\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 155.698 0.427493
\(52\) 0 0
\(53\) 211.588 0.548374 0.274187 0.961676i \(-0.411591\pi\)
0.274187 + 0.961676i \(0.411591\pi\)
\(54\) 0 0
\(55\) 912.583 2.23732
\(56\) 0 0
\(57\) 48.6030 0.112941
\(58\) 0 0
\(59\) 412.201 0.909559 0.454780 0.890604i \(-0.349718\pi\)
0.454780 + 0.890604i \(0.349718\pi\)
\(60\) 0 0
\(61\) −836.693 −1.75619 −0.878095 0.478486i \(-0.841186\pi\)
−0.878095 + 0.478486i \(0.841186\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −90.6030 −0.172891
\(66\) 0 0
\(67\) 165.588 0.301937 0.150969 0.988539i \(-0.451761\pi\)
0.150969 + 0.988539i \(0.451761\pi\)
\(68\) 0 0
\(69\) −640.191 −1.11696
\(70\) 0 0
\(71\) 465.015 0.777284 0.388642 0.921389i \(-0.372944\pi\)
0.388642 + 0.921389i \(0.372944\pi\)
\(72\) 0 0
\(73\) 449.658 0.720938 0.360469 0.932771i \(-0.382617\pi\)
0.360469 + 0.932771i \(0.382617\pi\)
\(74\) 0 0
\(75\) −383.382 −0.590255
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 343.558 0.489282 0.244641 0.969614i \(-0.421330\pi\)
0.244641 + 0.969614i \(0.421330\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) −1502.33 −1.98677 −0.993387 0.114812i \(-0.963373\pi\)
−0.993387 + 0.114812i \(0.963373\pi\)
\(84\) 0 0
\(85\) 825.176 1.05298
\(86\) 0 0
\(87\) 654.573 0.806639
\(88\) 0 0
\(89\) −341.085 −0.406236 −0.203118 0.979154i \(-0.565107\pi\)
−0.203118 + 0.979154i \(0.565107\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −754.191 −0.840924
\(94\) 0 0
\(95\) 257.588 0.278189
\(96\) 0 0
\(97\) −865.437 −0.905895 −0.452947 0.891537i \(-0.649627\pi\)
−0.452947 + 0.891537i \(0.649627\pi\)
\(98\) 0 0
\(99\) −516.573 −0.524419
\(100\) 0 0
\(101\) −243.256 −0.239652 −0.119826 0.992795i \(-0.538234\pi\)
−0.119826 + 0.992795i \(0.538234\pi\)
\(102\) 0 0
\(103\) 953.346 0.912000 0.456000 0.889980i \(-0.349282\pi\)
0.456000 + 0.889980i \(0.349282\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1344.95 1.21516 0.607578 0.794260i \(-0.292141\pi\)
0.607578 + 0.794260i \(0.292141\pi\)
\(108\) 0 0
\(109\) 1734.35 1.52404 0.762022 0.647551i \(-0.224207\pi\)
0.762022 + 0.647551i \(0.224207\pi\)
\(110\) 0 0
\(111\) −1160.38 −0.992239
\(112\) 0 0
\(113\) 1441.18 1.19977 0.599887 0.800085i \(-0.295212\pi\)
0.599887 + 0.800085i \(0.295212\pi\)
\(114\) 0 0
\(115\) −3392.90 −2.75122
\(116\) 0 0
\(117\) 51.2864 0.0405250
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1963.41 1.47514
\(122\) 0 0
\(123\) 985.508 0.722441
\(124\) 0 0
\(125\) −44.4222 −0.0317860
\(126\) 0 0
\(127\) −1184.70 −0.827759 −0.413880 0.910332i \(-0.635827\pi\)
−0.413880 + 0.910332i \(0.635827\pi\)
\(128\) 0 0
\(129\) −112.764 −0.0769634
\(130\) 0 0
\(131\) −297.588 −0.198476 −0.0992381 0.995064i \(-0.531641\pi\)
−0.0992381 + 0.995064i \(0.531641\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 429.286 0.273682
\(136\) 0 0
\(137\) 620.985 0.387258 0.193629 0.981075i \(-0.437974\pi\)
0.193629 + 0.981075i \(0.437974\pi\)
\(138\) 0 0
\(139\) 898.754 0.548426 0.274213 0.961669i \(-0.411583\pi\)
0.274213 + 0.961669i \(0.411583\pi\)
\(140\) 0 0
\(141\) −764.985 −0.456903
\(142\) 0 0
\(143\) −327.076 −0.191269
\(144\) 0 0
\(145\) 3469.13 1.98686
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3054.70 −1.67954 −0.839769 0.542945i \(-0.817309\pi\)
−0.839769 + 0.542945i \(0.817309\pi\)
\(150\) 0 0
\(151\) 65.1455 0.0351090 0.0175545 0.999846i \(-0.494412\pi\)
0.0175545 + 0.999846i \(0.494412\pi\)
\(152\) 0 0
\(153\) −467.095 −0.246813
\(154\) 0 0
\(155\) −3997.08 −2.07131
\(156\) 0 0
\(157\) 1542.22 0.783966 0.391983 0.919973i \(-0.371789\pi\)
0.391983 + 0.919973i \(0.371789\pi\)
\(158\) 0 0
\(159\) −634.764 −0.316604
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2514.73 1.20840 0.604200 0.796833i \(-0.293493\pi\)
0.604200 + 0.796833i \(0.293493\pi\)
\(164\) 0 0
\(165\) −2737.75 −1.29172
\(166\) 0 0
\(167\) −528.643 −0.244956 −0.122478 0.992471i \(-0.539084\pi\)
−0.122478 + 0.992471i \(0.539084\pi\)
\(168\) 0 0
\(169\) −2164.53 −0.985220
\(170\) 0 0
\(171\) −145.809 −0.0652064
\(172\) 0 0
\(173\) 96.8439 0.0425602 0.0212801 0.999774i \(-0.493226\pi\)
0.0212801 + 0.999774i \(0.493226\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1236.60 −0.525134
\(178\) 0 0
\(179\) 534.542 0.223204 0.111602 0.993753i \(-0.464402\pi\)
0.111602 + 0.993753i \(0.464402\pi\)
\(180\) 0 0
\(181\) 2087.00 0.857049 0.428524 0.903530i \(-0.359034\pi\)
0.428524 + 0.903530i \(0.359034\pi\)
\(182\) 0 0
\(183\) 2510.08 1.01394
\(184\) 0 0
\(185\) −6149.83 −2.44402
\(186\) 0 0
\(187\) 2978.87 1.16490
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3387.69 −1.28337 −0.641687 0.766966i \(-0.721765\pi\)
−0.641687 + 0.766966i \(0.721765\pi\)
\(192\) 0 0
\(193\) −1908.35 −0.711742 −0.355871 0.934535i \(-0.615816\pi\)
−0.355871 + 0.934535i \(0.615816\pi\)
\(194\) 0 0
\(195\) 271.809 0.0998187
\(196\) 0 0
\(197\) −2061.88 −0.745699 −0.372850 0.927892i \(-0.621619\pi\)
−0.372850 + 0.927892i \(0.621619\pi\)
\(198\) 0 0
\(199\) −3171.50 −1.12976 −0.564878 0.825174i \(-0.691077\pi\)
−0.564878 + 0.825174i \(0.691077\pi\)
\(200\) 0 0
\(201\) −496.764 −0.174323
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 5223.02 1.77947
\(206\) 0 0
\(207\) 1920.57 0.644875
\(208\) 0 0
\(209\) 929.889 0.307760
\(210\) 0 0
\(211\) −1349.97 −0.440454 −0.220227 0.975449i \(-0.570680\pi\)
−0.220227 + 0.975449i \(0.570680\pi\)
\(212\) 0 0
\(213\) −1395.05 −0.448765
\(214\) 0 0
\(215\) −597.628 −0.189572
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1348.97 −0.416234
\(220\) 0 0
\(221\) −295.748 −0.0900190
\(222\) 0 0
\(223\) 1361.85 0.408951 0.204476 0.978872i \(-0.434451\pi\)
0.204476 + 0.978872i \(0.434451\pi\)
\(224\) 0 0
\(225\) 1150.15 0.340784
\(226\) 0 0
\(227\) −1861.81 −0.544373 −0.272186 0.962245i \(-0.587747\pi\)
−0.272186 + 0.962245i \(0.587747\pi\)
\(228\) 0 0
\(229\) −5358.78 −1.54637 −0.773184 0.634181i \(-0.781337\pi\)
−0.773184 + 0.634181i \(0.781337\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5441.12 1.52987 0.764935 0.644107i \(-0.222771\pi\)
0.764935 + 0.644107i \(0.222771\pi\)
\(234\) 0 0
\(235\) −4054.29 −1.12542
\(236\) 0 0
\(237\) −1030.67 −0.282487
\(238\) 0 0
\(239\) 1157.28 0.313213 0.156607 0.987661i \(-0.449945\pi\)
0.156607 + 0.987661i \(0.449945\pi\)
\(240\) 0 0
\(241\) −3969.38 −1.06095 −0.530477 0.847699i \(-0.677987\pi\)
−0.530477 + 0.847699i \(0.677987\pi\)
\(242\) 0 0
\(243\) −243.000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −92.3212 −0.0237824
\(248\) 0 0
\(249\) 4506.99 1.14706
\(250\) 0 0
\(251\) −5978.75 −1.50349 −0.751744 0.659455i \(-0.770787\pi\)
−0.751744 + 0.659455i \(0.770787\pi\)
\(252\) 0 0
\(253\) −12248.3 −3.04366
\(254\) 0 0
\(255\) −2475.53 −0.607935
\(256\) 0 0
\(257\) 4650.15 1.12867 0.564335 0.825546i \(-0.309132\pi\)
0.564335 + 0.825546i \(0.309132\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −1963.72 −0.465713
\(262\) 0 0
\(263\) −3695.37 −0.866411 −0.433205 0.901295i \(-0.642618\pi\)
−0.433205 + 0.901295i \(0.642618\pi\)
\(264\) 0 0
\(265\) −3364.14 −0.779840
\(266\) 0 0
\(267\) 1023.26 0.234540
\(268\) 0 0
\(269\) −7157.69 −1.62235 −0.811175 0.584804i \(-0.801171\pi\)
−0.811175 + 0.584804i \(0.801171\pi\)
\(270\) 0 0
\(271\) −4038.37 −0.905216 −0.452608 0.891710i \(-0.649506\pi\)
−0.452608 + 0.891710i \(0.649506\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −7334.98 −1.60842
\(276\) 0 0
\(277\) −2754.82 −0.597550 −0.298775 0.954324i \(-0.596578\pi\)
−0.298775 + 0.954324i \(0.596578\pi\)
\(278\) 0 0
\(279\) 2262.57 0.485508
\(280\) 0 0
\(281\) −772.742 −0.164050 −0.0820248 0.996630i \(-0.526139\pi\)
−0.0820248 + 0.996630i \(0.526139\pi\)
\(282\) 0 0
\(283\) 6745.49 1.41688 0.708441 0.705770i \(-0.249399\pi\)
0.708441 + 0.705770i \(0.249399\pi\)
\(284\) 0 0
\(285\) −772.764 −0.160613
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −2219.44 −0.451749
\(290\) 0 0
\(291\) 2596.31 0.523019
\(292\) 0 0
\(293\) 1922.69 0.383362 0.191681 0.981457i \(-0.438606\pi\)
0.191681 + 0.981457i \(0.438606\pi\)
\(294\) 0 0
\(295\) −6553.79 −1.29348
\(296\) 0 0
\(297\) 1549.72 0.302774
\(298\) 0 0
\(299\) 1216.04 0.235202
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 729.768 0.138363
\(304\) 0 0
\(305\) 13303.0 2.49747
\(306\) 0 0
\(307\) −2016.68 −0.374913 −0.187456 0.982273i \(-0.560024\pi\)
−0.187456 + 0.982273i \(0.560024\pi\)
\(308\) 0 0
\(309\) −2860.04 −0.526544
\(310\) 0 0
\(311\) −7149.99 −1.30366 −0.651831 0.758365i \(-0.725999\pi\)
−0.651831 + 0.758365i \(0.725999\pi\)
\(312\) 0 0
\(313\) 8596.49 1.55240 0.776202 0.630484i \(-0.217144\pi\)
0.776202 + 0.630484i \(0.217144\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2853.24 −0.505532 −0.252766 0.967527i \(-0.581340\pi\)
−0.252766 + 0.967527i \(0.581340\pi\)
\(318\) 0 0
\(319\) 12523.5 2.19806
\(320\) 0 0
\(321\) −4034.86 −0.701570
\(322\) 0 0
\(323\) 840.824 0.144844
\(324\) 0 0
\(325\) 728.232 0.124292
\(326\) 0 0
\(327\) −5203.05 −0.879907
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1619.12 −0.268866 −0.134433 0.990923i \(-0.542921\pi\)
−0.134433 + 0.990923i \(0.542921\pi\)
\(332\) 0 0
\(333\) 3481.15 0.572870
\(334\) 0 0
\(335\) −2632.76 −0.429383
\(336\) 0 0
\(337\) −3278.67 −0.529972 −0.264986 0.964252i \(-0.585367\pi\)
−0.264986 + 0.964252i \(0.585367\pi\)
\(338\) 0 0
\(339\) −4323.53 −0.692690
\(340\) 0 0
\(341\) −14429.4 −2.29149
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 10178.7 1.58842
\(346\) 0 0
\(347\) 2850.30 0.440957 0.220479 0.975392i \(-0.429238\pi\)
0.220479 + 0.975392i \(0.429238\pi\)
\(348\) 0 0
\(349\) −4725.32 −0.724758 −0.362379 0.932031i \(-0.618035\pi\)
−0.362379 + 0.932031i \(0.618035\pi\)
\(350\) 0 0
\(351\) −153.859 −0.0233971
\(352\) 0 0
\(353\) 6727.44 1.01435 0.507175 0.861843i \(-0.330690\pi\)
0.507175 + 0.861843i \(0.330690\pi\)
\(354\) 0 0
\(355\) −7393.51 −1.10537
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7331.89 1.07789 0.538945 0.842341i \(-0.318823\pi\)
0.538945 + 0.842341i \(0.318823\pi\)
\(360\) 0 0
\(361\) −6596.53 −0.961733
\(362\) 0 0
\(363\) −5890.24 −0.851673
\(364\) 0 0
\(365\) −7149.34 −1.02524
\(366\) 0 0
\(367\) −2774.43 −0.394616 −0.197308 0.980342i \(-0.563220\pi\)
−0.197308 + 0.980342i \(0.563220\pi\)
\(368\) 0 0
\(369\) −2956.52 −0.417101
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 2527.35 0.350834 0.175417 0.984494i \(-0.443873\pi\)
0.175417 + 0.984494i \(0.443873\pi\)
\(374\) 0 0
\(375\) 133.267 0.0183516
\(376\) 0 0
\(377\) −1243.36 −0.169857
\(378\) 0 0
\(379\) −3116.40 −0.422371 −0.211186 0.977446i \(-0.567732\pi\)
−0.211186 + 0.977446i \(0.567732\pi\)
\(380\) 0 0
\(381\) 3554.11 0.477907
\(382\) 0 0
\(383\) −1518.07 −0.202532 −0.101266 0.994859i \(-0.532289\pi\)
−0.101266 + 0.994859i \(0.532289\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 338.291 0.0444349
\(388\) 0 0
\(389\) −3246.77 −0.423182 −0.211591 0.977358i \(-0.567865\pi\)
−0.211591 + 0.977358i \(0.567865\pi\)
\(390\) 0 0
\(391\) −11075.2 −1.43247
\(392\) 0 0
\(393\) 892.764 0.114590
\(394\) 0 0
\(395\) −5462.39 −0.695804
\(396\) 0 0
\(397\) −1830.62 −0.231427 −0.115713 0.993283i \(-0.536915\pi\)
−0.115713 + 0.993283i \(0.536915\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3385.81 −0.421644 −0.210822 0.977524i \(-0.567614\pi\)
−0.210822 + 0.977524i \(0.567614\pi\)
\(402\) 0 0
\(403\) 1432.58 0.177077
\(404\) 0 0
\(405\) −1287.86 −0.158010
\(406\) 0 0
\(407\) −22200.8 −2.70382
\(408\) 0 0
\(409\) −9253.17 −1.11868 −0.559340 0.828938i \(-0.688945\pi\)
−0.559340 + 0.828938i \(0.688945\pi\)
\(410\) 0 0
\(411\) −1862.95 −0.223583
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 23886.3 2.82538
\(416\) 0 0
\(417\) −2696.26 −0.316634
\(418\) 0 0
\(419\) 3547.52 0.413622 0.206811 0.978381i \(-0.433692\pi\)
0.206811 + 0.978381i \(0.433692\pi\)
\(420\) 0 0
\(421\) 7848.87 0.908624 0.454312 0.890843i \(-0.349885\pi\)
0.454312 + 0.890843i \(0.349885\pi\)
\(422\) 0 0
\(423\) 2294.95 0.263793
\(424\) 0 0
\(425\) −6632.44 −0.756990
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 981.227 0.110429
\(430\) 0 0
\(431\) 4447.32 0.497030 0.248515 0.968628i \(-0.420057\pi\)
0.248515 + 0.968628i \(0.420057\pi\)
\(432\) 0 0
\(433\) 6994.82 0.776327 0.388164 0.921590i \(-0.373110\pi\)
0.388164 + 0.921590i \(0.373110\pi\)
\(434\) 0 0
\(435\) −10407.4 −1.14712
\(436\) 0 0
\(437\) −3457.25 −0.378450
\(438\) 0 0
\(439\) 636.182 0.0691647 0.0345823 0.999402i \(-0.488990\pi\)
0.0345823 + 0.999402i \(0.488990\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4474.24 0.479859 0.239929 0.970790i \(-0.422876\pi\)
0.239929 + 0.970790i \(0.422876\pi\)
\(444\) 0 0
\(445\) 5423.08 0.577705
\(446\) 0 0
\(447\) 9164.11 0.969681
\(448\) 0 0
\(449\) −2389.42 −0.251144 −0.125572 0.992085i \(-0.540077\pi\)
−0.125572 + 0.992085i \(0.540077\pi\)
\(450\) 0 0
\(451\) 18855.0 1.96862
\(452\) 0 0
\(453\) −195.436 −0.0202702
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −4438.34 −0.454304 −0.227152 0.973859i \(-0.572941\pi\)
−0.227152 + 0.973859i \(0.572941\pi\)
\(458\) 0 0
\(459\) 1401.29 0.142498
\(460\) 0 0
\(461\) 14079.8 1.42248 0.711240 0.702949i \(-0.248134\pi\)
0.711240 + 0.702949i \(0.248134\pi\)
\(462\) 0 0
\(463\) −4687.50 −0.470511 −0.235255 0.971934i \(-0.575593\pi\)
−0.235255 + 0.971934i \(0.575593\pi\)
\(464\) 0 0
\(465\) 11991.3 1.19587
\(466\) 0 0
\(467\) 8447.26 0.837029 0.418514 0.908210i \(-0.362551\pi\)
0.418514 + 0.908210i \(0.362551\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −4626.66 −0.452623
\(472\) 0 0
\(473\) −2157.43 −0.209723
\(474\) 0 0
\(475\) −2070.39 −0.199992
\(476\) 0 0
\(477\) 1904.29 0.182791
\(478\) 0 0
\(479\) −4369.41 −0.416792 −0.208396 0.978045i \(-0.566824\pi\)
−0.208396 + 0.978045i \(0.566824\pi\)
\(480\) 0 0
\(481\) 2204.14 0.208940
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 13760.0 1.28827
\(486\) 0 0
\(487\) 14477.7 1.34712 0.673561 0.739132i \(-0.264764\pi\)
0.673561 + 0.739132i \(0.264764\pi\)
\(488\) 0 0
\(489\) −7544.20 −0.697670
\(490\) 0 0
\(491\) −9306.12 −0.855355 −0.427677 0.903931i \(-0.640668\pi\)
−0.427677 + 0.903931i \(0.640668\pi\)
\(492\) 0 0
\(493\) 11324.0 1.03450
\(494\) 0 0
\(495\) 8213.25 0.745774
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 12237.5 1.09785 0.548926 0.835871i \(-0.315037\pi\)
0.548926 + 0.835871i \(0.315037\pi\)
\(500\) 0 0
\(501\) 1585.93 0.141425
\(502\) 0 0
\(503\) 5524.30 0.489694 0.244847 0.969562i \(-0.421262\pi\)
0.244847 + 0.969562i \(0.421262\pi\)
\(504\) 0 0
\(505\) 3867.65 0.340808
\(506\) 0 0
\(507\) 6493.58 0.568817
\(508\) 0 0
\(509\) 10079.6 0.877743 0.438871 0.898550i \(-0.355378\pi\)
0.438871 + 0.898550i \(0.355378\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 437.427 0.0376470
\(514\) 0 0
\(515\) −15157.7 −1.29695
\(516\) 0 0
\(517\) −14635.9 −1.24504
\(518\) 0 0
\(519\) −290.532 −0.0245721
\(520\) 0 0
\(521\) −5706.61 −0.479868 −0.239934 0.970789i \(-0.577126\pi\)
−0.239934 + 0.970789i \(0.577126\pi\)
\(522\) 0 0
\(523\) −10657.3 −0.891032 −0.445516 0.895274i \(-0.646980\pi\)
−0.445516 + 0.895274i \(0.646980\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −13047.4 −1.07847
\(528\) 0 0
\(529\) 33371.3 2.74277
\(530\) 0 0
\(531\) 3709.81 0.303186
\(532\) 0 0
\(533\) −1871.97 −0.152127
\(534\) 0 0
\(535\) −21384.1 −1.72807
\(536\) 0 0
\(537\) −1603.63 −0.128867
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −4010.48 −0.318714 −0.159357 0.987221i \(-0.550942\pi\)
−0.159357 + 0.987221i \(0.550942\pi\)
\(542\) 0 0
\(543\) −6261.01 −0.494817
\(544\) 0 0
\(545\) −27575.3 −2.16733
\(546\) 0 0
\(547\) 17619.8 1.37728 0.688638 0.725105i \(-0.258209\pi\)
0.688638 + 0.725105i \(0.258209\pi\)
\(548\) 0 0
\(549\) −7530.24 −0.585397
\(550\) 0 0
\(551\) 3534.91 0.273307
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 18449.5 1.41106
\(556\) 0 0
\(557\) −10337.7 −0.786395 −0.393198 0.919454i \(-0.628631\pi\)
−0.393198 + 0.919454i \(0.628631\pi\)
\(558\) 0 0
\(559\) 214.194 0.0162065
\(560\) 0 0
\(561\) −8936.62 −0.672557
\(562\) 0 0
\(563\) −24023.7 −1.79836 −0.899180 0.437580i \(-0.855836\pi\)
−0.899180 + 0.437580i \(0.855836\pi\)
\(564\) 0 0
\(565\) −22914.0 −1.70619
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −13179.2 −0.971001 −0.485501 0.874236i \(-0.661363\pi\)
−0.485501 + 0.874236i \(0.661363\pi\)
\(570\) 0 0
\(571\) −7776.26 −0.569924 −0.284962 0.958539i \(-0.591981\pi\)
−0.284962 + 0.958539i \(0.591981\pi\)
\(572\) 0 0
\(573\) 10163.1 0.740956
\(574\) 0 0
\(575\) 27270.8 1.97787
\(576\) 0 0
\(577\) −20167.0 −1.45505 −0.727525 0.686081i \(-0.759330\pi\)
−0.727525 + 0.686081i \(0.759330\pi\)
\(578\) 0 0
\(579\) 5725.05 0.410924
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −12144.5 −0.862734
\(584\) 0 0
\(585\) −815.427 −0.0576304
\(586\) 0 0
\(587\) −8365.08 −0.588184 −0.294092 0.955777i \(-0.595017\pi\)
−0.294092 + 0.955777i \(0.595017\pi\)
\(588\) 0 0
\(589\) −4072.88 −0.284924
\(590\) 0 0
\(591\) 6185.64 0.430530
\(592\) 0 0
\(593\) 27621.9 1.91281 0.956403 0.292050i \(-0.0943373\pi\)
0.956403 + 0.292050i \(0.0943373\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 9514.49 0.652265
\(598\) 0 0
\(599\) −538.318 −0.0367197 −0.0183598 0.999831i \(-0.505844\pi\)
−0.0183598 + 0.999831i \(0.505844\pi\)
\(600\) 0 0
\(601\) −6958.64 −0.472294 −0.236147 0.971717i \(-0.575885\pi\)
−0.236147 + 0.971717i \(0.575885\pi\)
\(602\) 0 0
\(603\) 1490.29 0.100646
\(604\) 0 0
\(605\) −31217.3 −2.09779
\(606\) 0 0
\(607\) −17297.6 −1.15665 −0.578326 0.815806i \(-0.696294\pi\)
−0.578326 + 0.815806i \(0.696294\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1453.08 0.0962120
\(612\) 0 0
\(613\) −839.158 −0.0552908 −0.0276454 0.999618i \(-0.508801\pi\)
−0.0276454 + 0.999618i \(0.508801\pi\)
\(614\) 0 0
\(615\) −15669.1 −1.02738
\(616\) 0 0
\(617\) −16040.0 −1.04659 −0.523295 0.852152i \(-0.675297\pi\)
−0.523295 + 0.852152i \(0.675297\pi\)
\(618\) 0 0
\(619\) −5429.28 −0.352538 −0.176269 0.984342i \(-0.556403\pi\)
−0.176269 + 0.984342i \(0.556403\pi\)
\(620\) 0 0
\(621\) −5761.72 −0.372318
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −15268.0 −0.977149
\(626\) 0 0
\(627\) −2789.67 −0.177685
\(628\) 0 0
\(629\) −20074.4 −1.27253
\(630\) 0 0
\(631\) 1807.86 0.114057 0.0570284 0.998373i \(-0.481837\pi\)
0.0570284 + 0.998373i \(0.481837\pi\)
\(632\) 0 0
\(633\) 4049.91 0.254296
\(634\) 0 0
\(635\) 18836.2 1.17715
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 4185.14 0.259095
\(640\) 0 0
\(641\) −5904.56 −0.363832 −0.181916 0.983314i \(-0.558230\pi\)
−0.181916 + 0.983314i \(0.558230\pi\)
\(642\) 0 0
\(643\) 8092.42 0.496320 0.248160 0.968719i \(-0.420174\pi\)
0.248160 + 0.968719i \(0.420174\pi\)
\(644\) 0 0
\(645\) 1792.88 0.109449
\(646\) 0 0
\(647\) 20192.7 1.22698 0.613490 0.789702i \(-0.289765\pi\)
0.613490 + 0.789702i \(0.289765\pi\)
\(648\) 0 0
\(649\) −23659.1 −1.43097
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −21180.8 −1.26933 −0.634664 0.772789i \(-0.718861\pi\)
−0.634664 + 0.772789i \(0.718861\pi\)
\(654\) 0 0
\(655\) 4731.50 0.282252
\(656\) 0 0
\(657\) 4046.92 0.240313
\(658\) 0 0
\(659\) −28411.3 −1.67944 −0.839718 0.543023i \(-0.817280\pi\)
−0.839718 + 0.543023i \(0.817280\pi\)
\(660\) 0 0
\(661\) −16704.9 −0.982975 −0.491488 0.870885i \(-0.663547\pi\)
−0.491488 + 0.870885i \(0.663547\pi\)
\(662\) 0 0
\(663\) 887.245 0.0519725
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −46561.3 −2.70294
\(668\) 0 0
\(669\) −4085.55 −0.236108
\(670\) 0 0
\(671\) 48023.7 2.76294
\(672\) 0 0
\(673\) −9047.09 −0.518187 −0.259093 0.965852i \(-0.583424\pi\)
−0.259093 + 0.965852i \(0.583424\pi\)
\(674\) 0 0
\(675\) −3450.44 −0.196752
\(676\) 0 0
\(677\) 7844.26 0.445316 0.222658 0.974897i \(-0.428527\pi\)
0.222658 + 0.974897i \(0.428527\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 5585.43 0.314294
\(682\) 0 0
\(683\) −25766.1 −1.44350 −0.721751 0.692153i \(-0.756662\pi\)
−0.721751 + 0.692153i \(0.756662\pi\)
\(684\) 0 0
\(685\) −9873.35 −0.550717
\(686\) 0 0
\(687\) 16076.3 0.892796
\(688\) 0 0
\(689\) 1205.73 0.0666686
\(690\) 0 0
\(691\) 24674.1 1.35839 0.679195 0.733958i \(-0.262329\pi\)
0.679195 + 0.733958i \(0.262329\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −14289.7 −0.779914
\(696\) 0 0
\(697\) 17049.1 0.926515
\(698\) 0 0
\(699\) −16323.4 −0.883271
\(700\) 0 0
\(701\) 29377.9 1.58286 0.791431 0.611258i \(-0.209336\pi\)
0.791431 + 0.611258i \(0.209336\pi\)
\(702\) 0 0
\(703\) −6266.45 −0.336193
\(704\) 0 0
\(705\) 12162.9 0.649759
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 30594.3 1.62058 0.810291 0.586028i \(-0.199309\pi\)
0.810291 + 0.586028i \(0.199309\pi\)
\(710\) 0 0
\(711\) 3092.02 0.163094
\(712\) 0 0
\(713\) 53647.4 2.81782
\(714\) 0 0
\(715\) 5200.34 0.272002
\(716\) 0 0
\(717\) −3471.83 −0.180834
\(718\) 0 0
\(719\) 1946.94 0.100985 0.0504927 0.998724i \(-0.483921\pi\)
0.0504927 + 0.998724i \(0.483921\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 11908.1 0.612542
\(724\) 0 0
\(725\) −27883.5 −1.42837
\(726\) 0 0
\(727\) −15750.6 −0.803518 −0.401759 0.915745i \(-0.631601\pi\)
−0.401759 + 0.915745i \(0.631601\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −1950.79 −0.0987040
\(732\) 0 0
\(733\) 14349.6 0.723074 0.361537 0.932358i \(-0.382252\pi\)
0.361537 + 0.932358i \(0.382252\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −9504.24 −0.475025
\(738\) 0 0
\(739\) 17758.1 0.883953 0.441976 0.897027i \(-0.354278\pi\)
0.441976 + 0.897027i \(0.354278\pi\)
\(740\) 0 0
\(741\) 276.964 0.0137308
\(742\) 0 0
\(743\) 29187.6 1.44117 0.720586 0.693366i \(-0.243873\pi\)
0.720586 + 0.693366i \(0.243873\pi\)
\(744\) 0 0
\(745\) 48568.2 2.38846
\(746\) 0 0
\(747\) −13521.0 −0.662258
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −13781.9 −0.669654 −0.334827 0.942280i \(-0.608678\pi\)
−0.334827 + 0.942280i \(0.608678\pi\)
\(752\) 0 0
\(753\) 17936.3 0.868039
\(754\) 0 0
\(755\) −1035.78 −0.0499283
\(756\) 0 0
\(757\) 36952.7 1.77420 0.887099 0.461579i \(-0.152717\pi\)
0.887099 + 0.461579i \(0.152717\pi\)
\(758\) 0 0
\(759\) 36745.0 1.75726
\(760\) 0 0
\(761\) 28816.5 1.37266 0.686332 0.727288i \(-0.259220\pi\)
0.686332 + 0.727288i \(0.259220\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 7426.58 0.350992
\(766\) 0 0
\(767\) 2348.92 0.110580
\(768\) 0 0
\(769\) 25285.2 1.18571 0.592854 0.805310i \(-0.298001\pi\)
0.592854 + 0.805310i \(0.298001\pi\)
\(770\) 0 0
\(771\) −13950.4 −0.651638
\(772\) 0 0
\(773\) −18418.2 −0.856995 −0.428497 0.903543i \(-0.640957\pi\)
−0.428497 + 0.903543i \(0.640957\pi\)
\(774\) 0 0
\(775\) 32127.0 1.48908
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5322.07 0.244779
\(780\) 0 0
\(781\) −26690.5 −1.22287
\(782\) 0 0
\(783\) 5891.15 0.268880
\(784\) 0 0
\(785\) −24520.5 −1.11487
\(786\) 0 0
\(787\) 11075.8 0.501664 0.250832 0.968031i \(-0.419296\pi\)
0.250832 + 0.968031i \(0.419296\pi\)
\(788\) 0 0
\(789\) 11086.1 0.500223
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −4767.88 −0.213509
\(794\) 0 0
\(795\) 10092.4 0.450241
\(796\) 0 0
\(797\) −4838.83 −0.215057 −0.107528 0.994202i \(-0.534294\pi\)
−0.107528 + 0.994202i \(0.534294\pi\)
\(798\) 0 0
\(799\) −13234.1 −0.585969
\(800\) 0 0
\(801\) −3069.77 −0.135412
\(802\) 0 0
\(803\) −25809.0 −1.13422
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 21473.1 0.936664
\(808\) 0 0
\(809\) −31509.9 −1.36938 −0.684690 0.728834i \(-0.740062\pi\)
−0.684690 + 0.728834i \(0.740062\pi\)
\(810\) 0 0
\(811\) −29463.3 −1.27570 −0.637851 0.770160i \(-0.720177\pi\)
−0.637851 + 0.770160i \(0.720177\pi\)
\(812\) 0 0
\(813\) 12115.1 0.522627
\(814\) 0 0
\(815\) −39983.0 −1.71846
\(816\) 0 0
\(817\) −608.962 −0.0260770
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 3502.22 0.148877 0.0744386 0.997226i \(-0.476284\pi\)
0.0744386 + 0.997226i \(0.476284\pi\)
\(822\) 0 0
\(823\) −39993.0 −1.69389 −0.846943 0.531684i \(-0.821560\pi\)
−0.846943 + 0.531684i \(0.821560\pi\)
\(824\) 0 0
\(825\) 22005.0 0.928623
\(826\) 0 0
\(827\) 10733.6 0.451322 0.225661 0.974206i \(-0.427546\pi\)
0.225661 + 0.974206i \(0.427546\pi\)
\(828\) 0 0
\(829\) 14537.5 0.609056 0.304528 0.952503i \(-0.401501\pi\)
0.304528 + 0.952503i \(0.401501\pi\)
\(830\) 0 0
\(831\) 8264.47 0.344996
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 8405.16 0.348351
\(836\) 0 0
\(837\) −6787.72 −0.280308
\(838\) 0 0
\(839\) 7353.57 0.302591 0.151295 0.988489i \(-0.451656\pi\)
0.151295 + 0.988489i \(0.451656\pi\)
\(840\) 0 0
\(841\) 23218.3 0.951998
\(842\) 0 0
\(843\) 2318.23 0.0947141
\(844\) 0 0
\(845\) 34414.9 1.40107
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −20236.5 −0.818037
\(850\) 0 0
\(851\) 82540.7 3.32486
\(852\) 0 0
\(853\) −19293.6 −0.774442 −0.387221 0.921987i \(-0.626565\pi\)
−0.387221 + 0.921987i \(0.626565\pi\)
\(854\) 0 0
\(855\) 2318.29 0.0927297
\(856\) 0 0
\(857\) 14161.6 0.564468 0.282234 0.959346i \(-0.408924\pi\)
0.282234 + 0.959346i \(0.408924\pi\)
\(858\) 0 0
\(859\) 8219.13 0.326465 0.163232 0.986588i \(-0.447808\pi\)
0.163232 + 0.986588i \(0.447808\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2574.95 −0.101567 −0.0507835 0.998710i \(-0.516172\pi\)
−0.0507835 + 0.998710i \(0.516172\pi\)
\(864\) 0 0
\(865\) −1539.77 −0.0605246
\(866\) 0 0
\(867\) 6658.33 0.260817
\(868\) 0 0
\(869\) −19719.2 −0.769766
\(870\) 0 0
\(871\) 943.600 0.0367080
\(872\) 0 0
\(873\) −7788.93 −0.301965
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 30981.1 1.19288 0.596442 0.802656i \(-0.296581\pi\)
0.596442 + 0.802656i \(0.296581\pi\)
\(878\) 0 0
\(879\) −5768.08 −0.221334
\(880\) 0 0
\(881\) 41781.8 1.59780 0.798902 0.601461i \(-0.205415\pi\)
0.798902 + 0.601461i \(0.205415\pi\)
\(882\) 0 0
\(883\) 39289.6 1.49740 0.748699 0.662911i \(-0.230679\pi\)
0.748699 + 0.662911i \(0.230679\pi\)
\(884\) 0 0
\(885\) 19661.4 0.746790
\(886\) 0 0
\(887\) 5832.44 0.220783 0.110391 0.993888i \(-0.464790\pi\)
0.110391 + 0.993888i \(0.464790\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −4649.15 −0.174806
\(892\) 0 0
\(893\) −4131.18 −0.154809
\(894\) 0 0
\(895\) −8498.95 −0.317418
\(896\) 0 0
\(897\) −3648.12 −0.135794
\(898\) 0 0
\(899\) −54852.5 −2.03497
\(900\) 0 0
\(901\) −10981.3 −0.406038
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −33182.3 −1.21880
\(906\) 0 0
\(907\) −42387.9 −1.55178 −0.775892 0.630866i \(-0.782700\pi\)
−0.775892 + 0.630866i \(0.782700\pi\)
\(908\) 0 0
\(909\) −2189.30 −0.0798841
\(910\) 0 0
\(911\) −2275.12 −0.0827423 −0.0413711 0.999144i \(-0.513173\pi\)
−0.0413711 + 0.999144i \(0.513173\pi\)
\(912\) 0 0
\(913\) 86229.3 3.12571
\(914\) 0 0
\(915\) −39909.0 −1.44191
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 31284.3 1.12293 0.561465 0.827500i \(-0.310238\pi\)
0.561465 + 0.827500i \(0.310238\pi\)
\(920\) 0 0
\(921\) 6050.05 0.216456
\(922\) 0 0
\(923\) 2649.88 0.0944983
\(924\) 0 0
\(925\) 49429.9 1.75702
\(926\) 0 0
\(927\) 8580.12 0.304000
\(928\) 0 0
\(929\) −32196.6 −1.13707 −0.568535 0.822659i \(-0.692489\pi\)
−0.568535 + 0.822659i \(0.692489\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 21450.0 0.752669
\(934\) 0 0
\(935\) −47362.6 −1.65660
\(936\) 0 0
\(937\) −22293.6 −0.777269 −0.388635 0.921392i \(-0.627053\pi\)
−0.388635 + 0.921392i \(0.627053\pi\)
\(938\) 0 0
\(939\) −25789.5 −0.896281
\(940\) 0 0
\(941\) 31809.7 1.10198 0.550991 0.834511i \(-0.314250\pi\)
0.550991 + 0.834511i \(0.314250\pi\)
\(942\) 0 0
\(943\) −70101.4 −2.42080
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −18982.6 −0.651376 −0.325688 0.945477i \(-0.605596\pi\)
−0.325688 + 0.945477i \(0.605596\pi\)
\(948\) 0 0
\(949\) 2562.37 0.0876481
\(950\) 0 0
\(951\) 8559.71 0.291869
\(952\) 0 0
\(953\) 9254.58 0.314570 0.157285 0.987553i \(-0.449726\pi\)
0.157285 + 0.987553i \(0.449726\pi\)
\(954\) 0 0
\(955\) 53862.5 1.82508
\(956\) 0 0
\(957\) −37570.5 −1.26905
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 33409.4 1.12146
\(962\) 0 0
\(963\) 12104.6 0.405052
\(964\) 0 0
\(965\) 30341.8 1.01216
\(966\) 0 0
\(967\) −15317.5 −0.509387 −0.254694 0.967022i \(-0.581975\pi\)
−0.254694 + 0.967022i \(0.581975\pi\)
\(968\) 0 0
\(969\) −2522.47 −0.0836259
\(970\) 0 0
\(971\) 22432.6 0.741398 0.370699 0.928753i \(-0.379118\pi\)
0.370699 + 0.928753i \(0.379118\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −2184.70 −0.0717603
\(976\) 0 0
\(977\) −627.864 −0.0205600 −0.0102800 0.999947i \(-0.503272\pi\)
−0.0102800 + 0.999947i \(0.503272\pi\)
\(978\) 0 0
\(979\) 19577.3 0.639114
\(980\) 0 0
\(981\) 15609.2 0.508015
\(982\) 0 0
\(983\) 45032.6 1.46116 0.730579 0.682828i \(-0.239250\pi\)
0.730579 + 0.682828i \(0.239250\pi\)
\(984\) 0 0
\(985\) 32782.8 1.06045
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 8021.14 0.257894
\(990\) 0 0
\(991\) 31981.0 1.02514 0.512569 0.858646i \(-0.328694\pi\)
0.512569 + 0.858646i \(0.328694\pi\)
\(992\) 0 0
\(993\) 4857.35 0.155230
\(994\) 0 0
\(995\) 50425.2 1.60662
\(996\) 0 0
\(997\) −12378.8 −0.393221 −0.196611 0.980482i \(-0.562993\pi\)
−0.196611 + 0.980482i \(0.562993\pi\)
\(998\) 0 0
\(999\) −10443.4 −0.330746
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 2352.4.a.bn.1.1 2
4.3 odd 2 294.4.a.k.1.1 yes 2
7.6 odd 2 2352.4.a.cd.1.2 2
12.11 even 2 882.4.a.bi.1.2 2
28.3 even 6 294.4.e.o.79.1 4
28.11 odd 6 294.4.e.n.79.2 4
28.19 even 6 294.4.e.o.67.1 4
28.23 odd 6 294.4.e.n.67.2 4
28.27 even 2 294.4.a.j.1.2 2
84.11 even 6 882.4.g.y.667.1 4
84.23 even 6 882.4.g.y.361.1 4
84.47 odd 6 882.4.g.bd.361.2 4
84.59 odd 6 882.4.g.bd.667.2 4
84.83 odd 2 882.4.a.bc.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
294.4.a.j.1.2 2 28.27 even 2
294.4.a.k.1.1 yes 2 4.3 odd 2
294.4.e.n.67.2 4 28.23 odd 6
294.4.e.n.79.2 4 28.11 odd 6
294.4.e.o.67.1 4 28.19 even 6
294.4.e.o.79.1 4 28.3 even 6
882.4.a.bc.1.1 2 84.83 odd 2
882.4.a.bi.1.2 2 12.11 even 2
882.4.g.y.361.1 4 84.23 even 6
882.4.g.y.667.1 4 84.11 even 6
882.4.g.bd.361.2 4 84.47 odd 6
882.4.g.bd.667.2 4 84.59 odd 6
2352.4.a.bn.1.1 2 1.1 even 1 trivial
2352.4.a.cd.1.2 2 7.6 odd 2