Properties

Label 7360.2.a.cu.1.4
Level $7360$
Weight $2$
Character 7360.1
Self dual yes
Analytic conductor $58.770$
Analytic rank $1$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7360 = 2^{6} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7360.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(58.7698958877\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.255601784.1
Defining polynomial: \(x^{6} - x^{5} - 10 x^{4} + 5 x^{3} + 25 x^{2} - 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 3680)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.397065\) of defining polynomial
Character \(\chi\) \(=\) 7360.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.602935 q^{3} -1.00000 q^{5} +4.26364 q^{7} -2.63647 q^{9} +O(q^{10})\) \(q-0.602935 q^{3} -1.00000 q^{5} +4.26364 q^{7} -2.63647 q^{9} +3.63990 q^{11} -4.55951 q^{13} +0.602935 q^{15} -1.85371 q^{17} -1.23973 q^{19} -2.57070 q^{21} +1.00000 q^{23} +1.00000 q^{25} +3.39843 q^{27} -5.38880 q^{29} +4.49050 q^{31} -2.19462 q^{33} -4.26364 q^{35} +1.78619 q^{37} +2.74909 q^{39} -2.90043 q^{41} +0.649335 q^{43} +2.63647 q^{45} +5.27132 q^{47} +11.1786 q^{49} +1.11767 q^{51} -4.45826 q^{53} -3.63990 q^{55} +0.747474 q^{57} -4.22978 q^{59} -13.6015 q^{61} -11.2409 q^{63} +4.55951 q^{65} -8.69262 q^{67} -0.602935 q^{69} +0.430737 q^{71} -12.8339 q^{73} -0.602935 q^{75} +15.5192 q^{77} +11.7426 q^{79} +5.86038 q^{81} +1.77643 q^{83} +1.85371 q^{85} +3.24910 q^{87} -9.83271 q^{89} -19.4401 q^{91} -2.70748 q^{93} +1.23973 q^{95} +1.29912 q^{97} -9.59647 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 5 q^{3} - 6 q^{5} + 4 q^{7} + 7 q^{9} + O(q^{10}) \) \( 6 q - 5 q^{3} - 6 q^{5} + 4 q^{7} + 7 q^{9} - 7 q^{11} - q^{13} + 5 q^{15} - 5 q^{19} + 6 q^{23} + 6 q^{25} - 20 q^{27} + 3 q^{29} + 12 q^{31} - 3 q^{33} - 4 q^{35} - 7 q^{37} + 8 q^{39} + 8 q^{41} - 28 q^{43} - 7 q^{45} + 8 q^{47} + 6 q^{49} - 7 q^{51} + 5 q^{53} + 7 q^{55} + 18 q^{57} - 9 q^{59} + 3 q^{61} - 5 q^{63} + q^{65} - 27 q^{67} - 5 q^{69} - 2 q^{71} - 2 q^{73} - 5 q^{75} + 14 q^{77} + 4 q^{79} + 14 q^{81} - 23 q^{83} + 12 q^{87} - 4 q^{89} + q^{91} + 4 q^{93} + 5 q^{95} - q^{97} - q^{99} + O(q^{100}) \)

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
\(3\) −0.602935 −0.348105 −0.174052 0.984736i \(-0.555686\pi\)
−0.174052 + 0.984736i \(0.555686\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 4.26364 1.61150 0.805752 0.592253i \(-0.201762\pi\)
0.805752 + 0.592253i \(0.201762\pi\)
\(8\) 0 0
\(9\) −2.63647 −0.878823
\(10\) 0 0
\(11\) 3.63990 1.09747 0.548735 0.835996i \(-0.315110\pi\)
0.548735 + 0.835996i \(0.315110\pi\)
\(12\) 0 0
\(13\) −4.55951 −1.26458 −0.632291 0.774731i \(-0.717885\pi\)
−0.632291 + 0.774731i \(0.717885\pi\)
\(14\) 0 0
\(15\) 0.602935 0.155677
\(16\) 0 0
\(17\) −1.85371 −0.449590 −0.224795 0.974406i \(-0.572171\pi\)
−0.224795 + 0.974406i \(0.572171\pi\)
\(18\) 0 0
\(19\) −1.23973 −0.284412 −0.142206 0.989837i \(-0.545420\pi\)
−0.142206 + 0.989837i \(0.545420\pi\)
\(20\) 0 0
\(21\) −2.57070 −0.560972
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 3.39843 0.654027
\(28\) 0 0
\(29\) −5.38880 −1.00068 −0.500338 0.865830i \(-0.666791\pi\)
−0.500338 + 0.865830i \(0.666791\pi\)
\(30\) 0 0
\(31\) 4.49050 0.806517 0.403259 0.915086i \(-0.367878\pi\)
0.403259 + 0.915086i \(0.367878\pi\)
\(32\) 0 0
\(33\) −2.19462 −0.382035
\(34\) 0 0
\(35\) −4.26364 −0.720686
\(36\) 0 0
\(37\) 1.78619 0.293648 0.146824 0.989163i \(-0.453095\pi\)
0.146824 + 0.989163i \(0.453095\pi\)
\(38\) 0 0
\(39\) 2.74909 0.440207
\(40\) 0 0
\(41\) −2.90043 −0.452971 −0.226485 0.974015i \(-0.572724\pi\)
−0.226485 + 0.974015i \(0.572724\pi\)
\(42\) 0 0
\(43\) 0.649335 0.0990226 0.0495113 0.998774i \(-0.484234\pi\)
0.0495113 + 0.998774i \(0.484234\pi\)
\(44\) 0 0
\(45\) 2.63647 0.393022
\(46\) 0 0
\(47\) 5.27132 0.768901 0.384451 0.923146i \(-0.374391\pi\)
0.384451 + 0.923146i \(0.374391\pi\)
\(48\) 0 0
\(49\) 11.1786 1.59694
\(50\) 0 0
\(51\) 1.11767 0.156504
\(52\) 0 0
\(53\) −4.45826 −0.612389 −0.306194 0.951969i \(-0.599056\pi\)
−0.306194 + 0.951969i \(0.599056\pi\)
\(54\) 0 0
\(55\) −3.63990 −0.490803
\(56\) 0 0
\(57\) 0.747474 0.0990053
\(58\) 0 0
\(59\) −4.22978 −0.550671 −0.275335 0.961348i \(-0.588789\pi\)
−0.275335 + 0.961348i \(0.588789\pi\)
\(60\) 0 0
\(61\) −13.6015 −1.74150 −0.870748 0.491730i \(-0.836365\pi\)
−0.870748 + 0.491730i \(0.836365\pi\)
\(62\) 0 0
\(63\) −11.2409 −1.41623
\(64\) 0 0
\(65\) 4.55951 0.565538
\(66\) 0 0
\(67\) −8.69262 −1.06197 −0.530986 0.847380i \(-0.678178\pi\)
−0.530986 + 0.847380i \(0.678178\pi\)
\(68\) 0 0
\(69\) −0.602935 −0.0725849
\(70\) 0 0
\(71\) 0.430737 0.0511190 0.0255595 0.999673i \(-0.491863\pi\)
0.0255595 + 0.999673i \(0.491863\pi\)
\(72\) 0 0
\(73\) −12.8339 −1.50210 −0.751050 0.660246i \(-0.770452\pi\)
−0.751050 + 0.660246i \(0.770452\pi\)
\(74\) 0 0
\(75\) −0.602935 −0.0696210
\(76\) 0 0
\(77\) 15.5192 1.76858
\(78\) 0 0
\(79\) 11.7426 1.32115 0.660575 0.750760i \(-0.270313\pi\)
0.660575 + 0.750760i \(0.270313\pi\)
\(80\) 0 0
\(81\) 5.86038 0.651153
\(82\) 0 0
\(83\) 1.77643 0.194988 0.0974942 0.995236i \(-0.468917\pi\)
0.0974942 + 0.995236i \(0.468917\pi\)
\(84\) 0 0
\(85\) 1.85371 0.201063
\(86\) 0 0
\(87\) 3.24910 0.348340
\(88\) 0 0
\(89\) −9.83271 −1.04226 −0.521132 0.853476i \(-0.674490\pi\)
−0.521132 + 0.853476i \(0.674490\pi\)
\(90\) 0 0
\(91\) −19.4401 −2.03788
\(92\) 0 0
\(93\) −2.70748 −0.280752
\(94\) 0 0
\(95\) 1.23973 0.127193
\(96\) 0 0
\(97\) 1.29912 0.131906 0.0659528 0.997823i \(-0.478991\pi\)
0.0659528 + 0.997823i \(0.478991\pi\)
\(98\) 0 0
\(99\) −9.59647 −0.964482
\(100\) 0 0
\(101\) 4.07587 0.405564 0.202782 0.979224i \(-0.435002\pi\)
0.202782 + 0.979224i \(0.435002\pi\)
\(102\) 0 0
\(103\) −0.492251 −0.0485030 −0.0242515 0.999706i \(-0.507720\pi\)
−0.0242515 + 0.999706i \(0.507720\pi\)
\(104\) 0 0
\(105\) 2.57070 0.250874
\(106\) 0 0
\(107\) −15.4936 −1.49782 −0.748912 0.662670i \(-0.769423\pi\)
−0.748912 + 0.662670i \(0.769423\pi\)
\(108\) 0 0
\(109\) −0.397130 −0.0380381 −0.0190191 0.999819i \(-0.506054\pi\)
−0.0190191 + 0.999819i \(0.506054\pi\)
\(110\) 0 0
\(111\) −1.07696 −0.102220
\(112\) 0 0
\(113\) −0.288008 −0.0270935 −0.0135468 0.999908i \(-0.504312\pi\)
−0.0135468 + 0.999908i \(0.504312\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 12.0210 1.11134
\(118\) 0 0
\(119\) −7.90353 −0.724516
\(120\) 0 0
\(121\) 2.24884 0.204440
\(122\) 0 0
\(123\) 1.74877 0.157681
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 4.36489 0.387321 0.193661 0.981069i \(-0.437964\pi\)
0.193661 + 0.981069i \(0.437964\pi\)
\(128\) 0 0
\(129\) −0.391507 −0.0344703
\(130\) 0 0
\(131\) −12.7148 −1.11090 −0.555448 0.831551i \(-0.687453\pi\)
−0.555448 + 0.831551i \(0.687453\pi\)
\(132\) 0 0
\(133\) −5.28574 −0.458332
\(134\) 0 0
\(135\) −3.39843 −0.292490
\(136\) 0 0
\(137\) −14.8502 −1.26874 −0.634368 0.773031i \(-0.718739\pi\)
−0.634368 + 0.773031i \(0.718739\pi\)
\(138\) 0 0
\(139\) 20.0447 1.70017 0.850085 0.526645i \(-0.176550\pi\)
0.850085 + 0.526645i \(0.176550\pi\)
\(140\) 0 0
\(141\) −3.17827 −0.267658
\(142\) 0 0
\(143\) −16.5962 −1.38784
\(144\) 0 0
\(145\) 5.38880 0.447516
\(146\) 0 0
\(147\) −6.73997 −0.555904
\(148\) 0 0
\(149\) 5.95975 0.488242 0.244121 0.969745i \(-0.421501\pi\)
0.244121 + 0.969745i \(0.421501\pi\)
\(150\) 0 0
\(151\) −0.548585 −0.0446432 −0.0223216 0.999751i \(-0.507106\pi\)
−0.0223216 + 0.999751i \(0.507106\pi\)
\(152\) 0 0
\(153\) 4.88724 0.395110
\(154\) 0 0
\(155\) −4.49050 −0.360685
\(156\) 0 0
\(157\) 20.0659 1.60143 0.800715 0.599046i \(-0.204453\pi\)
0.800715 + 0.599046i \(0.204453\pi\)
\(158\) 0 0
\(159\) 2.68804 0.213176
\(160\) 0 0
\(161\) 4.26364 0.336022
\(162\) 0 0
\(163\) −12.2282 −0.957788 −0.478894 0.877873i \(-0.658962\pi\)
−0.478894 + 0.877873i \(0.658962\pi\)
\(164\) 0 0
\(165\) 2.19462 0.170851
\(166\) 0 0
\(167\) 9.75239 0.754663 0.377331 0.926078i \(-0.376842\pi\)
0.377331 + 0.926078i \(0.376842\pi\)
\(168\) 0 0
\(169\) 7.78916 0.599166
\(170\) 0 0
\(171\) 3.26850 0.249948
\(172\) 0 0
\(173\) 21.5206 1.63618 0.818089 0.575092i \(-0.195034\pi\)
0.818089 + 0.575092i \(0.195034\pi\)
\(174\) 0 0
\(175\) 4.26364 0.322301
\(176\) 0 0
\(177\) 2.55028 0.191691
\(178\) 0 0
\(179\) −5.19087 −0.387984 −0.193992 0.981003i \(-0.562144\pi\)
−0.193992 + 0.981003i \(0.562144\pi\)
\(180\) 0 0
\(181\) −13.5415 −1.00653 −0.503265 0.864132i \(-0.667868\pi\)
−0.503265 + 0.864132i \(0.667868\pi\)
\(182\) 0 0
\(183\) 8.20083 0.606223
\(184\) 0 0
\(185\) −1.78619 −0.131323
\(186\) 0 0
\(187\) −6.74730 −0.493411
\(188\) 0 0
\(189\) 14.4897 1.05397
\(190\) 0 0
\(191\) −13.6811 −0.989927 −0.494963 0.868914i \(-0.664819\pi\)
−0.494963 + 0.868914i \(0.664819\pi\)
\(192\) 0 0
\(193\) 4.77913 0.344010 0.172005 0.985096i \(-0.444976\pi\)
0.172005 + 0.985096i \(0.444976\pi\)
\(194\) 0 0
\(195\) −2.74909 −0.196866
\(196\) 0 0
\(197\) 12.1724 0.867248 0.433624 0.901094i \(-0.357235\pi\)
0.433624 + 0.901094i \(0.357235\pi\)
\(198\) 0 0
\(199\) 15.0712 1.06837 0.534183 0.845369i \(-0.320619\pi\)
0.534183 + 0.845369i \(0.320619\pi\)
\(200\) 0 0
\(201\) 5.24109 0.369678
\(202\) 0 0
\(203\) −22.9759 −1.61259
\(204\) 0 0
\(205\) 2.90043 0.202575
\(206\) 0 0
\(207\) −2.63647 −0.183247
\(208\) 0 0
\(209\) −4.51247 −0.312134
\(210\) 0 0
\(211\) −26.1273 −1.79868 −0.899339 0.437253i \(-0.855951\pi\)
−0.899339 + 0.437253i \(0.855951\pi\)
\(212\) 0 0
\(213\) −0.259706 −0.0177948
\(214\) 0 0
\(215\) −0.649335 −0.0442843
\(216\) 0 0
\(217\) 19.1459 1.29970
\(218\) 0 0
\(219\) 7.73803 0.522888
\(220\) 0 0
\(221\) 8.45200 0.568543
\(222\) 0 0
\(223\) −24.1628 −1.61806 −0.809032 0.587765i \(-0.800008\pi\)
−0.809032 + 0.587765i \(0.800008\pi\)
\(224\) 0 0
\(225\) −2.63647 −0.175765
\(226\) 0 0
\(227\) 17.3473 1.15138 0.575691 0.817667i \(-0.304733\pi\)
0.575691 + 0.817667i \(0.304733\pi\)
\(228\) 0 0
\(229\) −7.10305 −0.469383 −0.234692 0.972070i \(-0.575408\pi\)
−0.234692 + 0.972070i \(0.575408\pi\)
\(230\) 0 0
\(231\) −9.35707 −0.615650
\(232\) 0 0
\(233\) −24.0724 −1.57704 −0.788518 0.615012i \(-0.789151\pi\)
−0.788518 + 0.615012i \(0.789151\pi\)
\(234\) 0 0
\(235\) −5.27132 −0.343863
\(236\) 0 0
\(237\) −7.08004 −0.459898
\(238\) 0 0
\(239\) −17.6977 −1.14477 −0.572385 0.819985i \(-0.693982\pi\)
−0.572385 + 0.819985i \(0.693982\pi\)
\(240\) 0 0
\(241\) 26.8297 1.72825 0.864126 0.503276i \(-0.167872\pi\)
0.864126 + 0.503276i \(0.167872\pi\)
\(242\) 0 0
\(243\) −13.7287 −0.880697
\(244\) 0 0
\(245\) −11.1786 −0.714175
\(246\) 0 0
\(247\) 5.65254 0.359663
\(248\) 0 0
\(249\) −1.07107 −0.0678764
\(250\) 0 0
\(251\) 3.95975 0.249937 0.124969 0.992161i \(-0.460117\pi\)
0.124969 + 0.992161i \(0.460117\pi\)
\(252\) 0 0
\(253\) 3.63990 0.228838
\(254\) 0 0
\(255\) −1.11767 −0.0699909
\(256\) 0 0
\(257\) 11.7963 0.735835 0.367917 0.929858i \(-0.380071\pi\)
0.367917 + 0.929858i \(0.380071\pi\)
\(258\) 0 0
\(259\) 7.61566 0.473214
\(260\) 0 0
\(261\) 14.2074 0.879417
\(262\) 0 0
\(263\) 6.34551 0.391281 0.195640 0.980676i \(-0.437321\pi\)
0.195640 + 0.980676i \(0.437321\pi\)
\(264\) 0 0
\(265\) 4.45826 0.273869
\(266\) 0 0
\(267\) 5.92849 0.362817
\(268\) 0 0
\(269\) −24.9417 −1.52072 −0.760360 0.649502i \(-0.774977\pi\)
−0.760360 + 0.649502i \(0.774977\pi\)
\(270\) 0 0
\(271\) 1.25103 0.0759945 0.0379973 0.999278i \(-0.487902\pi\)
0.0379973 + 0.999278i \(0.487902\pi\)
\(272\) 0 0
\(273\) 11.7211 0.709395
\(274\) 0 0
\(275\) 3.63990 0.219494
\(276\) 0 0
\(277\) −9.68726 −0.582051 −0.291026 0.956715i \(-0.593997\pi\)
−0.291026 + 0.956715i \(0.593997\pi\)
\(278\) 0 0
\(279\) −11.8391 −0.708786
\(280\) 0 0
\(281\) −25.3407 −1.51170 −0.755850 0.654744i \(-0.772776\pi\)
−0.755850 + 0.654744i \(0.772776\pi\)
\(282\) 0 0
\(283\) −10.2484 −0.609203 −0.304602 0.952480i \(-0.598523\pi\)
−0.304602 + 0.952480i \(0.598523\pi\)
\(284\) 0 0
\(285\) −0.747474 −0.0442765
\(286\) 0 0
\(287\) −12.3664 −0.729964
\(288\) 0 0
\(289\) −13.5638 −0.797869
\(290\) 0 0
\(291\) −0.783285 −0.0459170
\(292\) 0 0
\(293\) −21.4420 −1.25265 −0.626327 0.779561i \(-0.715442\pi\)
−0.626327 + 0.779561i \(0.715442\pi\)
\(294\) 0 0
\(295\) 4.22978 0.246267
\(296\) 0 0
\(297\) 12.3699 0.717775
\(298\) 0 0
\(299\) −4.55951 −0.263683
\(300\) 0 0
\(301\) 2.76853 0.159575
\(302\) 0 0
\(303\) −2.45749 −0.141179
\(304\) 0 0
\(305\) 13.6015 0.778821
\(306\) 0 0
\(307\) −33.8194 −1.93017 −0.965086 0.261932i \(-0.915640\pi\)
−0.965086 + 0.261932i \(0.915640\pi\)
\(308\) 0 0
\(309\) 0.296796 0.0168841
\(310\) 0 0
\(311\) 28.5617 1.61958 0.809792 0.586718i \(-0.199580\pi\)
0.809792 + 0.586718i \(0.199580\pi\)
\(312\) 0 0
\(313\) −5.61379 −0.317310 −0.158655 0.987334i \(-0.550716\pi\)
−0.158655 + 0.987334i \(0.550716\pi\)
\(314\) 0 0
\(315\) 11.2409 0.633356
\(316\) 0 0
\(317\) −19.4931 −1.09484 −0.547421 0.836857i \(-0.684390\pi\)
−0.547421 + 0.836857i \(0.684390\pi\)
\(318\) 0 0
\(319\) −19.6147 −1.09821
\(320\) 0 0
\(321\) 9.34164 0.521399
\(322\) 0 0
\(323\) 2.29809 0.127869
\(324\) 0 0
\(325\) −4.55951 −0.252916
\(326\) 0 0
\(327\) 0.239444 0.0132413
\(328\) 0 0
\(329\) 22.4750 1.23909
\(330\) 0 0
\(331\) 21.7710 1.19664 0.598321 0.801256i \(-0.295835\pi\)
0.598321 + 0.801256i \(0.295835\pi\)
\(332\) 0 0
\(333\) −4.70923 −0.258064
\(334\) 0 0
\(335\) 8.69262 0.474929
\(336\) 0 0
\(337\) 14.2835 0.778074 0.389037 0.921222i \(-0.372808\pi\)
0.389037 + 0.921222i \(0.372808\pi\)
\(338\) 0 0
\(339\) 0.173650 0.00943138
\(340\) 0 0
\(341\) 16.3449 0.885128
\(342\) 0 0
\(343\) 17.8160 0.961976
\(344\) 0 0
\(345\) 0.602935 0.0324609
\(346\) 0 0
\(347\) −24.2248 −1.30045 −0.650226 0.759740i \(-0.725326\pi\)
−0.650226 + 0.759740i \(0.725326\pi\)
\(348\) 0 0
\(349\) 12.7265 0.681232 0.340616 0.940203i \(-0.389364\pi\)
0.340616 + 0.940203i \(0.389364\pi\)
\(350\) 0 0
\(351\) −15.4952 −0.827071
\(352\) 0 0
\(353\) −26.6419 −1.41801 −0.709003 0.705205i \(-0.750855\pi\)
−0.709003 + 0.705205i \(0.750855\pi\)
\(354\) 0 0
\(355\) −0.430737 −0.0228611
\(356\) 0 0
\(357\) 4.76532 0.252207
\(358\) 0 0
\(359\) −17.4725 −0.922165 −0.461083 0.887357i \(-0.652539\pi\)
−0.461083 + 0.887357i \(0.652539\pi\)
\(360\) 0 0
\(361\) −17.4631 −0.919110
\(362\) 0 0
\(363\) −1.35591 −0.0711666
\(364\) 0 0
\(365\) 12.8339 0.671759
\(366\) 0 0
\(367\) 32.1078 1.67601 0.838007 0.545660i \(-0.183721\pi\)
0.838007 + 0.545660i \(0.183721\pi\)
\(368\) 0 0
\(369\) 7.64689 0.398081
\(370\) 0 0
\(371\) −19.0084 −0.986867
\(372\) 0 0
\(373\) 0.273085 0.0141398 0.00706991 0.999975i \(-0.497750\pi\)
0.00706991 + 0.999975i \(0.497750\pi\)
\(374\) 0 0
\(375\) 0.602935 0.0311354
\(376\) 0 0
\(377\) 24.5703 1.26544
\(378\) 0 0
\(379\) 25.1573 1.29224 0.646121 0.763235i \(-0.276390\pi\)
0.646121 + 0.763235i \(0.276390\pi\)
\(380\) 0 0
\(381\) −2.63175 −0.134828
\(382\) 0 0
\(383\) 23.5544 1.20357 0.601786 0.798657i \(-0.294456\pi\)
0.601786 + 0.798657i \(0.294456\pi\)
\(384\) 0 0
\(385\) −15.5192 −0.790931
\(386\) 0 0
\(387\) −1.71195 −0.0870234
\(388\) 0 0
\(389\) −4.09913 −0.207834 −0.103917 0.994586i \(-0.533138\pi\)
−0.103917 + 0.994586i \(0.533138\pi\)
\(390\) 0 0
\(391\) −1.85371 −0.0937460
\(392\) 0 0
\(393\) 7.66619 0.386708
\(394\) 0 0
\(395\) −11.7426 −0.590836
\(396\) 0 0
\(397\) −23.3298 −1.17089 −0.585444 0.810713i \(-0.699080\pi\)
−0.585444 + 0.810713i \(0.699080\pi\)
\(398\) 0 0
\(399\) 3.18696 0.159547
\(400\) 0 0
\(401\) −0.820503 −0.0409740 −0.0204870 0.999790i \(-0.506522\pi\)
−0.0204870 + 0.999790i \(0.506522\pi\)
\(402\) 0 0
\(403\) −20.4745 −1.01991
\(404\) 0 0
\(405\) −5.86038 −0.291204
\(406\) 0 0
\(407\) 6.50154 0.322270
\(408\) 0 0
\(409\) −33.5791 −1.66038 −0.830190 0.557481i \(-0.811768\pi\)
−0.830190 + 0.557481i \(0.811768\pi\)
\(410\) 0 0
\(411\) 8.95369 0.441653
\(412\) 0 0
\(413\) −18.0343 −0.887408
\(414\) 0 0
\(415\) −1.77643 −0.0872015
\(416\) 0 0
\(417\) −12.0857 −0.591838
\(418\) 0 0
\(419\) 23.5624 1.15110 0.575548 0.817768i \(-0.304789\pi\)
0.575548 + 0.817768i \(0.304789\pi\)
\(420\) 0 0
\(421\) −0.354746 −0.0172893 −0.00864463 0.999963i \(-0.502752\pi\)
−0.00864463 + 0.999963i \(0.502752\pi\)
\(422\) 0 0
\(423\) −13.8977 −0.675728
\(424\) 0 0
\(425\) −1.85371 −0.0899180
\(426\) 0 0
\(427\) −57.9919 −2.80643
\(428\) 0 0
\(429\) 10.0064 0.483114
\(430\) 0 0
\(431\) −8.67271 −0.417750 −0.208875 0.977942i \(-0.566980\pi\)
−0.208875 + 0.977942i \(0.566980\pi\)
\(432\) 0 0
\(433\) −40.3628 −1.93971 −0.969857 0.243675i \(-0.921647\pi\)
−0.969857 + 0.243675i \(0.921647\pi\)
\(434\) 0 0
\(435\) −3.24910 −0.155782
\(436\) 0 0
\(437\) −1.23973 −0.0593041
\(438\) 0 0
\(439\) 8.63987 0.412359 0.206179 0.978514i \(-0.433897\pi\)
0.206179 + 0.978514i \(0.433897\pi\)
\(440\) 0 0
\(441\) −29.4720 −1.40343
\(442\) 0 0
\(443\) −1.56964 −0.0745757 −0.0372879 0.999305i \(-0.511872\pi\)
−0.0372879 + 0.999305i \(0.511872\pi\)
\(444\) 0 0
\(445\) 9.83271 0.466115
\(446\) 0 0
\(447\) −3.59334 −0.169959
\(448\) 0 0
\(449\) −33.4502 −1.57861 −0.789306 0.614000i \(-0.789559\pi\)
−0.789306 + 0.614000i \(0.789559\pi\)
\(450\) 0 0
\(451\) −10.5573 −0.497122
\(452\) 0 0
\(453\) 0.330761 0.0155405
\(454\) 0 0
\(455\) 19.4401 0.911366
\(456\) 0 0
\(457\) −13.4322 −0.628330 −0.314165 0.949368i \(-0.601725\pi\)
−0.314165 + 0.949368i \(0.601725\pi\)
\(458\) 0 0
\(459\) −6.29968 −0.294044
\(460\) 0 0
\(461\) 22.2689 1.03717 0.518583 0.855027i \(-0.326460\pi\)
0.518583 + 0.855027i \(0.326460\pi\)
\(462\) 0 0
\(463\) −38.7201 −1.79948 −0.899738 0.436431i \(-0.856242\pi\)
−0.899738 + 0.436431i \(0.856242\pi\)
\(464\) 0 0
\(465\) 2.70748 0.125556
\(466\) 0 0
\(467\) 1.55132 0.0717864 0.0358932 0.999356i \(-0.488572\pi\)
0.0358932 + 0.999356i \(0.488572\pi\)
\(468\) 0 0
\(469\) −37.0622 −1.71137
\(470\) 0 0
\(471\) −12.0984 −0.557465
\(472\) 0 0
\(473\) 2.36351 0.108674
\(474\) 0 0
\(475\) −1.23973 −0.0568825
\(476\) 0 0
\(477\) 11.7541 0.538182
\(478\) 0 0
\(479\) −12.5953 −0.575492 −0.287746 0.957707i \(-0.592906\pi\)
−0.287746 + 0.957707i \(0.592906\pi\)
\(480\) 0 0
\(481\) −8.14415 −0.371341
\(482\) 0 0
\(483\) −2.57070 −0.116971
\(484\) 0 0
\(485\) −1.29912 −0.0589900
\(486\) 0 0
\(487\) −17.2243 −0.780507 −0.390253 0.920708i \(-0.627613\pi\)
−0.390253 + 0.920708i \(0.627613\pi\)
\(488\) 0 0
\(489\) 7.37282 0.333411
\(490\) 0 0
\(491\) −19.0641 −0.860351 −0.430176 0.902745i \(-0.641548\pi\)
−0.430176 + 0.902745i \(0.641548\pi\)
\(492\) 0 0
\(493\) 9.98926 0.449894
\(494\) 0 0
\(495\) 9.59647 0.431329
\(496\) 0 0
\(497\) 1.83650 0.0823785
\(498\) 0 0
\(499\) −3.60752 −0.161495 −0.0807474 0.996735i \(-0.525731\pi\)
−0.0807474 + 0.996735i \(0.525731\pi\)
\(500\) 0 0
\(501\) −5.88006 −0.262702
\(502\) 0 0
\(503\) −16.2314 −0.723721 −0.361861 0.932232i \(-0.617858\pi\)
−0.361861 + 0.932232i \(0.617858\pi\)
\(504\) 0 0
\(505\) −4.07587 −0.181374
\(506\) 0 0
\(507\) −4.69636 −0.208573
\(508\) 0 0
\(509\) −42.6827 −1.89188 −0.945939 0.324345i \(-0.894856\pi\)
−0.945939 + 0.324345i \(0.894856\pi\)
\(510\) 0 0
\(511\) −54.7193 −2.42064
\(512\) 0 0
\(513\) −4.21311 −0.186014
\(514\) 0 0
\(515\) 0.492251 0.0216912
\(516\) 0 0
\(517\) 19.1871 0.843846
\(518\) 0 0
\(519\) −12.9755 −0.569561
\(520\) 0 0
\(521\) −20.5335 −0.899588 −0.449794 0.893132i \(-0.648503\pi\)
−0.449794 + 0.893132i \(0.648503\pi\)
\(522\) 0 0
\(523\) −5.54661 −0.242536 −0.121268 0.992620i \(-0.538696\pi\)
−0.121268 + 0.992620i \(0.538696\pi\)
\(524\) 0 0
\(525\) −2.57070 −0.112194
\(526\) 0 0
\(527\) −8.32406 −0.362602
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 11.1517 0.483942
\(532\) 0 0
\(533\) 13.2245 0.572818
\(534\) 0 0
\(535\) 15.4936 0.669847
\(536\) 0 0
\(537\) 3.12976 0.135059
\(538\) 0 0
\(539\) 40.6890 1.75260
\(540\) 0 0
\(541\) 6.16238 0.264942 0.132471 0.991187i \(-0.457709\pi\)
0.132471 + 0.991187i \(0.457709\pi\)
\(542\) 0 0
\(543\) 8.16464 0.350378
\(544\) 0 0
\(545\) 0.397130 0.0170112
\(546\) 0 0
\(547\) 23.5084 1.00515 0.502574 0.864534i \(-0.332386\pi\)
0.502574 + 0.864534i \(0.332386\pi\)
\(548\) 0 0
\(549\) 35.8600 1.53047
\(550\) 0 0
\(551\) 6.68064 0.284605
\(552\) 0 0
\(553\) 50.0663 2.12904
\(554\) 0 0
\(555\) 1.07696 0.0457143
\(556\) 0 0
\(557\) −1.79332 −0.0759853 −0.0379927 0.999278i \(-0.512096\pi\)
−0.0379927 + 0.999278i \(0.512096\pi\)
\(558\) 0 0
\(559\) −2.96065 −0.125222
\(560\) 0 0
\(561\) 4.06818 0.171759
\(562\) 0 0
\(563\) 16.1239 0.679543 0.339771 0.940508i \(-0.389650\pi\)
0.339771 + 0.940508i \(0.389650\pi\)
\(564\) 0 0
\(565\) 0.288008 0.0121166
\(566\) 0 0
\(567\) 24.9865 1.04934
\(568\) 0 0
\(569\) 12.0589 0.505536 0.252768 0.967527i \(-0.418659\pi\)
0.252768 + 0.967527i \(0.418659\pi\)
\(570\) 0 0
\(571\) 23.9032 1.00032 0.500159 0.865934i \(-0.333275\pi\)
0.500159 + 0.865934i \(0.333275\pi\)
\(572\) 0 0
\(573\) 8.24879 0.344598
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 6.96576 0.289988 0.144994 0.989433i \(-0.453684\pi\)
0.144994 + 0.989433i \(0.453684\pi\)
\(578\) 0 0
\(579\) −2.88151 −0.119751
\(580\) 0 0
\(581\) 7.57405 0.314225
\(582\) 0 0
\(583\) −16.2276 −0.672078
\(584\) 0 0
\(585\) −12.0210 −0.497008
\(586\) 0 0
\(587\) 3.60990 0.148996 0.0744982 0.997221i \(-0.476264\pi\)
0.0744982 + 0.997221i \(0.476264\pi\)
\(588\) 0 0
\(589\) −5.56698 −0.229384
\(590\) 0 0
\(591\) −7.33917 −0.301893
\(592\) 0 0
\(593\) −7.74967 −0.318241 −0.159120 0.987259i \(-0.550866\pi\)
−0.159120 + 0.987259i \(0.550866\pi\)
\(594\) 0 0
\(595\) 7.90353 0.324013
\(596\) 0 0
\(597\) −9.08693 −0.371903
\(598\) 0 0
\(599\) 19.1300 0.781631 0.390816 0.920469i \(-0.372193\pi\)
0.390816 + 0.920469i \(0.372193\pi\)
\(600\) 0 0
\(601\) 5.55815 0.226722 0.113361 0.993554i \(-0.463838\pi\)
0.113361 + 0.993554i \(0.463838\pi\)
\(602\) 0 0
\(603\) 22.9178 0.933286
\(604\) 0 0
\(605\) −2.24884 −0.0914285
\(606\) 0 0
\(607\) −2.45607 −0.0996890 −0.0498445 0.998757i \(-0.515873\pi\)
−0.0498445 + 0.998757i \(0.515873\pi\)
\(608\) 0 0
\(609\) 13.8530 0.561351
\(610\) 0 0
\(611\) −24.0347 −0.972338
\(612\) 0 0
\(613\) 8.75548 0.353630 0.176815 0.984244i \(-0.443421\pi\)
0.176815 + 0.984244i \(0.443421\pi\)
\(614\) 0 0
\(615\) −1.74877 −0.0705172
\(616\) 0 0
\(617\) −23.4835 −0.945411 −0.472706 0.881220i \(-0.656723\pi\)
−0.472706 + 0.881220i \(0.656723\pi\)
\(618\) 0 0
\(619\) 20.3874 0.819438 0.409719 0.912212i \(-0.365627\pi\)
0.409719 + 0.912212i \(0.365627\pi\)
\(620\) 0 0
\(621\) 3.39843 0.136374
\(622\) 0 0
\(623\) −41.9231 −1.67961
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 2.72073 0.108655
\(628\) 0 0
\(629\) −3.31107 −0.132021
\(630\) 0 0
\(631\) −39.7165 −1.58109 −0.790545 0.612403i \(-0.790203\pi\)
−0.790545 + 0.612403i \(0.790203\pi\)
\(632\) 0 0
\(633\) 15.7531 0.626128
\(634\) 0 0
\(635\) −4.36489 −0.173215
\(636\) 0 0
\(637\) −50.9690 −2.01946
\(638\) 0 0
\(639\) −1.13562 −0.0449246
\(640\) 0 0
\(641\) 3.49864 0.138188 0.0690940 0.997610i \(-0.477989\pi\)
0.0690940 + 0.997610i \(0.477989\pi\)
\(642\) 0 0
\(643\) 33.9716 1.33971 0.669855 0.742492i \(-0.266356\pi\)
0.669855 + 0.742492i \(0.266356\pi\)
\(644\) 0 0
\(645\) 0.391507 0.0154156
\(646\) 0 0
\(647\) −21.0113 −0.826039 −0.413020 0.910722i \(-0.635526\pi\)
−0.413020 + 0.910722i \(0.635526\pi\)
\(648\) 0 0
\(649\) −15.3960 −0.604345
\(650\) 0 0
\(651\) −11.5437 −0.452434
\(652\) 0 0
\(653\) −6.94516 −0.271785 −0.135892 0.990724i \(-0.543390\pi\)
−0.135892 + 0.990724i \(0.543390\pi\)
\(654\) 0 0
\(655\) 12.7148 0.496808
\(656\) 0 0
\(657\) 33.8363 1.32008
\(658\) 0 0
\(659\) −10.5141 −0.409572 −0.204786 0.978807i \(-0.565650\pi\)
−0.204786 + 0.978807i \(0.565650\pi\)
\(660\) 0 0
\(661\) 33.7748 1.31369 0.656843 0.754027i \(-0.271891\pi\)
0.656843 + 0.754027i \(0.271891\pi\)
\(662\) 0 0
\(663\) −5.09601 −0.197913
\(664\) 0 0
\(665\) 5.28574 0.204972
\(666\) 0 0
\(667\) −5.38880 −0.208655
\(668\) 0 0
\(669\) 14.5686 0.563256
\(670\) 0 0
\(671\) −49.5081 −1.91124
\(672\) 0 0
\(673\) −17.3866 −0.670203 −0.335102 0.942182i \(-0.608771\pi\)
−0.335102 + 0.942182i \(0.608771\pi\)
\(674\) 0 0
\(675\) 3.39843 0.130805
\(676\) 0 0
\(677\) −3.84504 −0.147777 −0.0738884 0.997267i \(-0.523541\pi\)
−0.0738884 + 0.997267i \(0.523541\pi\)
\(678\) 0 0
\(679\) 5.53897 0.212566
\(680\) 0 0
\(681\) −10.4593 −0.400802
\(682\) 0 0
\(683\) 24.0383 0.919799 0.459900 0.887971i \(-0.347885\pi\)
0.459900 + 0.887971i \(0.347885\pi\)
\(684\) 0 0
\(685\) 14.8502 0.567396
\(686\) 0 0
\(687\) 4.28268 0.163394
\(688\) 0 0
\(689\) 20.3275 0.774416
\(690\) 0 0
\(691\) 27.2386 1.03621 0.518103 0.855319i \(-0.326639\pi\)
0.518103 + 0.855319i \(0.326639\pi\)
\(692\) 0 0
\(693\) −40.9159 −1.55427
\(694\) 0 0
\(695\) −20.0447 −0.760339
\(696\) 0 0
\(697\) 5.37654 0.203651
\(698\) 0 0
\(699\) 14.5141 0.548973
\(700\) 0 0
\(701\) −21.1776 −0.799867 −0.399934 0.916544i \(-0.630967\pi\)
−0.399934 + 0.916544i \(0.630967\pi\)
\(702\) 0 0
\(703\) −2.21438 −0.0835171
\(704\) 0 0
\(705\) 3.17827 0.119700
\(706\) 0 0
\(707\) 17.3780 0.653568
\(708\) 0 0
\(709\) −33.7589 −1.26784 −0.633922 0.773397i \(-0.718556\pi\)
−0.633922 + 0.773397i \(0.718556\pi\)
\(710\) 0 0
\(711\) −30.9591 −1.16106
\(712\) 0 0
\(713\) 4.49050 0.168170
\(714\) 0 0
\(715\) 16.5962 0.620661
\(716\) 0 0
\(717\) 10.6706 0.398500
\(718\) 0 0
\(719\) −14.3506 −0.535186 −0.267593 0.963532i \(-0.586228\pi\)
−0.267593 + 0.963532i \(0.586228\pi\)
\(720\) 0 0
\(721\) −2.09878 −0.0781627
\(722\) 0 0
\(723\) −16.1766 −0.601612
\(724\) 0 0
\(725\) −5.38880 −0.200135
\(726\) 0 0
\(727\) 23.1234 0.857600 0.428800 0.903399i \(-0.358937\pi\)
0.428800 + 0.903399i \(0.358937\pi\)
\(728\) 0 0
\(729\) −9.30361 −0.344578
\(730\) 0 0
\(731\) −1.20368 −0.0445196
\(732\) 0 0
\(733\) 9.30758 0.343783 0.171892 0.985116i \(-0.445012\pi\)
0.171892 + 0.985116i \(0.445012\pi\)
\(734\) 0 0
\(735\) 6.73997 0.248608
\(736\) 0 0
\(737\) −31.6402 −1.16548
\(738\) 0 0
\(739\) 29.8573 1.09832 0.549160 0.835717i \(-0.314948\pi\)
0.549160 + 0.835717i \(0.314948\pi\)
\(740\) 0 0
\(741\) −3.40812 −0.125200
\(742\) 0 0
\(743\) −35.3524 −1.29695 −0.648476 0.761235i \(-0.724593\pi\)
−0.648476 + 0.761235i \(0.724593\pi\)
\(744\) 0 0
\(745\) −5.95975 −0.218348
\(746\) 0 0
\(747\) −4.68350 −0.171360
\(748\) 0 0
\(749\) −66.0591 −2.41375
\(750\) 0 0
\(751\) 49.2370 1.79668 0.898342 0.439298i \(-0.144773\pi\)
0.898342 + 0.439298i \(0.144773\pi\)
\(752\) 0 0
\(753\) −2.38747 −0.0870043
\(754\) 0 0
\(755\) 0.548585 0.0199650
\(756\) 0 0
\(757\) 12.1108 0.440175 0.220087 0.975480i \(-0.429366\pi\)
0.220087 + 0.975480i \(0.429366\pi\)
\(758\) 0 0
\(759\) −2.19462 −0.0796597
\(760\) 0 0
\(761\) 47.4310 1.71937 0.859686 0.510822i \(-0.170659\pi\)
0.859686 + 0.510822i \(0.170659\pi\)
\(762\) 0 0
\(763\) −1.69322 −0.0612986
\(764\) 0 0
\(765\) −4.88724 −0.176699
\(766\) 0 0
\(767\) 19.2857 0.696368
\(768\) 0 0
\(769\) 5.63608 0.203242 0.101621 0.994823i \(-0.467597\pi\)
0.101621 + 0.994823i \(0.467597\pi\)
\(770\) 0 0
\(771\) −7.11242 −0.256148
\(772\) 0 0
\(773\) −20.4841 −0.736760 −0.368380 0.929675i \(-0.620087\pi\)
−0.368380 + 0.929675i \(0.620087\pi\)
\(774\) 0 0
\(775\) 4.49050 0.161303
\(776\) 0 0
\(777\) −4.59175 −0.164728
\(778\) 0 0
\(779\) 3.59573 0.128831
\(780\) 0 0
\(781\) 1.56784 0.0561016
\(782\) 0 0
\(783\) −18.3134 −0.654469
\(784\) 0 0
\(785\) −20.0659 −0.716181
\(786\) 0 0
\(787\) −43.2633 −1.54217 −0.771084 0.636733i \(-0.780285\pi\)
−0.771084 + 0.636733i \(0.780285\pi\)
\(788\) 0 0
\(789\) −3.82593 −0.136207
\(790\) 0 0
\(791\) −1.22796 −0.0436613
\(792\) 0 0
\(793\) 62.0163 2.20226
\(794\) 0 0
\(795\) −2.68804 −0.0953350
\(796\) 0 0
\(797\) −27.9666 −0.990628 −0.495314 0.868714i \(-0.664947\pi\)
−0.495314 + 0.868714i \(0.664947\pi\)
\(798\) 0 0
\(799\) −9.77148 −0.345690
\(800\) 0 0
\(801\) 25.9236 0.915966
\(802\) 0 0
\(803\) −46.7142 −1.64851
\(804\) 0 0
\(805\) −4.26364 −0.150273
\(806\) 0 0
\(807\) 15.0382 0.529370
\(808\) 0 0
\(809\) 31.5540 1.10938 0.554691 0.832057i \(-0.312837\pi\)
0.554691 + 0.832057i \(0.312837\pi\)
\(810\) 0 0
\(811\) 8.46732 0.297328 0.148664 0.988888i \(-0.452503\pi\)
0.148664 + 0.988888i \(0.452503\pi\)
\(812\) 0 0
\(813\) −0.754289 −0.0264541
\(814\) 0 0
\(815\) 12.2282 0.428336
\(816\) 0 0
\(817\) −0.804997 −0.0281633
\(818\) 0 0
\(819\) 51.2532 1.79093
\(820\) 0 0
\(821\) −0.659828 −0.0230281 −0.0115141 0.999934i \(-0.503665\pi\)
−0.0115141 + 0.999934i \(0.503665\pi\)
\(822\) 0 0
\(823\) 42.9987 1.49884 0.749419 0.662096i \(-0.230333\pi\)
0.749419 + 0.662096i \(0.230333\pi\)
\(824\) 0 0
\(825\) −2.19462 −0.0764069
\(826\) 0 0
\(827\) −9.52132 −0.331089 −0.165544 0.986202i \(-0.552938\pi\)
−0.165544 + 0.986202i \(0.552938\pi\)
\(828\) 0 0
\(829\) 46.3024 1.60815 0.804074 0.594529i \(-0.202661\pi\)
0.804074 + 0.594529i \(0.202661\pi\)
\(830\) 0 0
\(831\) 5.84079 0.202615
\(832\) 0 0
\(833\) −20.7219 −0.717970
\(834\) 0 0
\(835\) −9.75239 −0.337495
\(836\) 0 0
\(837\) 15.2606 0.527484
\(838\) 0 0
\(839\) 1.55100 0.0535465 0.0267732 0.999642i \(-0.491477\pi\)
0.0267732 + 0.999642i \(0.491477\pi\)
\(840\) 0 0
\(841\) 0.0392028 0.00135182
\(842\) 0 0
\(843\) 15.2788 0.526230
\(844\) 0 0
\(845\) −7.78916 −0.267955
\(846\) 0 0
\(847\) 9.58825 0.329456
\(848\) 0 0
\(849\) 6.17911 0.212067
\(850\) 0 0
\(851\) 1.78619 0.0612298
\(852\) 0 0
\(853\) −7.61471 −0.260723 −0.130361 0.991467i \(-0.541614\pi\)
−0.130361 + 0.991467i \(0.541614\pi\)
\(854\) 0 0
\(855\) −3.26850 −0.111780
\(856\) 0 0
\(857\) 13.0077 0.444336 0.222168 0.975008i \(-0.428687\pi\)
0.222168 + 0.975008i \(0.428687\pi\)
\(858\) 0 0
\(859\) 14.1260 0.481973 0.240987 0.970528i \(-0.422529\pi\)
0.240987 + 0.970528i \(0.422529\pi\)
\(860\) 0 0
\(861\) 7.45612 0.254104
\(862\) 0 0
\(863\) −49.0516 −1.66974 −0.834868 0.550450i \(-0.814456\pi\)
−0.834868 + 0.550450i \(0.814456\pi\)
\(864\) 0 0
\(865\) −21.5206 −0.731721
\(866\) 0 0
\(867\) 8.17807 0.277742
\(868\) 0 0
\(869\) 42.7419 1.44992
\(870\) 0 0
\(871\) 39.6341 1.34295
\(872\) 0 0
\(873\) −3.42509 −0.115922
\(874\) 0 0
\(875\) −4.26364 −0.144137
\(876\) 0 0
\(877\) 2.02340 0.0683255 0.0341628 0.999416i \(-0.489124\pi\)
0.0341628 + 0.999416i \(0.489124\pi\)
\(878\) 0 0
\(879\) 12.9281 0.436055
\(880\) 0 0
\(881\) −2.62923 −0.0885810 −0.0442905 0.999019i \(-0.514103\pi\)
−0.0442905 + 0.999019i \(0.514103\pi\)
\(882\) 0 0
\(883\) 54.1687 1.82292 0.911462 0.411385i \(-0.134955\pi\)
0.911462 + 0.411385i \(0.134955\pi\)
\(884\) 0 0
\(885\) −2.55028 −0.0857269
\(886\) 0 0
\(887\) −49.2234 −1.65276 −0.826380 0.563112i \(-0.809604\pi\)
−0.826380 + 0.563112i \(0.809604\pi\)
\(888\) 0 0
\(889\) 18.6103 0.624170
\(890\) 0 0
\(891\) 21.3312 0.714621
\(892\) 0 0
\(893\) −6.53499 −0.218685
\(894\) 0 0
\(895\) 5.19087 0.173512
\(896\) 0 0
\(897\) 2.74909 0.0917895
\(898\) 0 0
\(899\) −24.1984 −0.807062
\(900\) 0 0
\(901\) 8.26430 0.275324
\(902\) 0 0
\(903\) −1.66924 −0.0555489
\(904\) 0 0
\(905\) 13.5415 0.450134
\(906\) 0 0
\(907\) −5.30775 −0.176241 −0.0881204 0.996110i \(-0.528086\pi\)
−0.0881204 + 0.996110i \(0.528086\pi\)
\(908\) 0 0
\(909\) −10.7459 −0.356419
\(910\) 0 0
\(911\) 4.02578 0.133380 0.0666901 0.997774i \(-0.478756\pi\)
0.0666901 + 0.997774i \(0.478756\pi\)
\(912\) 0 0
\(913\) 6.46602 0.213994
\(914\) 0 0
\(915\) −8.20083 −0.271111
\(916\) 0 0
\(917\) −54.2112 −1.79021
\(918\) 0 0
\(919\) 44.4178 1.46521 0.732604 0.680655i \(-0.238305\pi\)
0.732604 + 0.680655i \(0.238305\pi\)
\(920\) 0 0
\(921\) 20.3909 0.671902
\(922\) 0 0
\(923\) −1.96395 −0.0646442
\(924\) 0 0
\(925\) 1.78619 0.0587295
\(926\) 0 0
\(927\) 1.29781 0.0426255
\(928\) 0 0
\(929\) 0.622945 0.0204382 0.0102191 0.999948i \(-0.496747\pi\)
0.0102191 + 0.999948i \(0.496747\pi\)
\(930\) 0 0
\(931\) −13.8584 −0.454191
\(932\) 0 0
\(933\) −17.2208 −0.563785
\(934\) 0 0
\(935\) 6.74730 0.220660
\(936\) 0 0
\(937\) −42.5551 −1.39021 −0.695107 0.718906i \(-0.744643\pi\)
−0.695107 + 0.718906i \(0.744643\pi\)
\(938\) 0 0
\(939\) 3.38475 0.110457
\(940\) 0 0
\(941\) −4.54974 −0.148317 −0.0741587 0.997246i \(-0.523627\pi\)
−0.0741587 + 0.997246i \(0.523627\pi\)
\(942\) 0 0
\(943\) −2.90043 −0.0944509
\(944\) 0 0
\(945\) −14.4897 −0.471348
\(946\) 0 0
\(947\) −7.65595 −0.248785 −0.124392 0.992233i \(-0.539698\pi\)
−0.124392 + 0.992233i \(0.539698\pi\)
\(948\) 0 0
\(949\) 58.5165 1.89953
\(950\) 0 0
\(951\) 11.7531 0.381120
\(952\) 0 0
\(953\) 29.2923 0.948872 0.474436 0.880290i \(-0.342652\pi\)
0.474436 + 0.880290i \(0.342652\pi\)
\(954\) 0 0
\(955\) 13.6811 0.442709
\(956\) 0 0
\(957\) 11.8264 0.382293
\(958\) 0 0
\(959\) −63.3157 −2.04457
\(960\) 0 0
\(961\) −10.8354 −0.349530
\(962\) 0 0
\(963\) 40.8484 1.31632
\(964\) 0 0
\(965\) −4.77913 −0.153846
\(966\) 0 0
\(967\) 20.0342 0.644256 0.322128 0.946696i \(-0.395602\pi\)
0.322128 + 0.946696i \(0.395602\pi\)
\(968\) 0 0
\(969\) −1.38560 −0.0445118
\(970\) 0 0
\(971\) 29.6018 0.949968 0.474984 0.879994i \(-0.342454\pi\)
0.474984 + 0.879994i \(0.342454\pi\)
\(972\) 0 0
\(973\) 85.4634 2.73983
\(974\) 0 0
\(975\) 2.74909 0.0880414
\(976\) 0 0
\(977\) 2.22512 0.0711878 0.0355939 0.999366i \(-0.488668\pi\)
0.0355939 + 0.999366i \(0.488668\pi\)
\(978\) 0 0
\(979\) −35.7900 −1.14385
\(980\) 0 0
\(981\) 1.04702 0.0334288
\(982\) 0 0
\(983\) 8.94663 0.285353 0.142677 0.989769i \(-0.454429\pi\)
0.142677 + 0.989769i \(0.454429\pi\)
\(984\) 0 0
\(985\) −12.1724 −0.387845
\(986\) 0 0
\(987\) −13.5510 −0.431332
\(988\) 0 0
\(989\) 0.649335 0.0206476
\(990\) 0 0
\(991\) 38.6304 1.22714 0.613568 0.789642i \(-0.289734\pi\)
0.613568 + 0.789642i \(0.289734\pi\)
\(992\) 0 0
\(993\) −13.1265 −0.416557
\(994\) 0 0
\(995\) −15.0712 −0.477788
\(996\) 0 0
\(997\) 40.9937 1.29828 0.649141 0.760668i \(-0.275128\pi\)
0.649141 + 0.760668i \(0.275128\pi\)
\(998\) 0 0
\(999\) 6.07023 0.192054
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 7360.2.a.cu.1.4 6
4.3 odd 2 7360.2.a.cv.1.3 6
8.3 odd 2 3680.2.a.bc.1.4 6
8.5 even 2 3680.2.a.bd.1.3 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3680.2.a.bc.1.4 6 8.3 odd 2
3680.2.a.bd.1.3 yes 6 8.5 even 2
7360.2.a.cu.1.4 6 1.1 even 1 trivial
7360.2.a.cv.1.3 6 4.3 odd 2