Properties

Label 7360.2.a.bx.1.2
Level $7360$
Weight $2$
Character 7360.1
Self dual yes
Analytic conductor $58.770$
Analytic rank $1$
Dimension $3$
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: \(3\)
Coefficient field: 3.3.1573.1
Defining polynomial: \(x^{3} - x^{2} - 7 x + 2\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
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 1.2
Root \(0.277754\) of defining polynomial
Character \(\chi\) \(=\) 7360.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.277754 q^{3} -1.00000 q^{5} -1.27775 q^{7} -2.92285 q^{9} +O(q^{10})\) \(q-0.277754 q^{3} -1.00000 q^{5} -1.27775 q^{7} -2.92285 q^{9} -0.277754 q^{11} +3.92285 q^{13} +0.277754 q^{15} +5.47836 q^{17} -3.92285 q^{19} +0.354902 q^{21} -1.00000 q^{23} +1.00000 q^{25} +1.64510 q^{27} -0.799393 q^{29} -5.27775 q^{31} +0.0771475 q^{33} +1.27775 q^{35} +1.75612 q^{37} -1.08959 q^{39} +10.0339 q^{41} -4.00000 q^{43} +2.92285 q^{45} +8.95672 q^{47} -5.36734 q^{49} -1.52164 q^{51} -10.6451 q^{53} +0.277754 q^{55} +1.08959 q^{57} +8.08959 q^{59} -15.0124 q^{61} +3.73469 q^{63} -3.92285 q^{65} +12.6451 q^{67} +0.277754 q^{69} -9.32407 q^{71} +4.55551 q^{73} -0.277754 q^{75} +0.354902 q^{77} +8.00000 q^{79} +8.31162 q^{81} -2.64510 q^{83} -5.47836 q^{85} +0.222035 q^{87} +13.2902 q^{89} -5.01244 q^{91} +1.46592 q^{93} +3.92285 q^{95} +3.16674 q^{97} +0.811835 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{3} - 3 q^{5} - 4 q^{7} + 6 q^{9} + O(q^{10}) \) \( 3 q - q^{3} - 3 q^{5} - 4 q^{7} + 6 q^{9} - q^{11} - 3 q^{13} + q^{15} + 2 q^{17} + 3 q^{19} + 16 q^{21} - 3 q^{23} + 3 q^{25} - 10 q^{27} - 17 q^{29} - 16 q^{31} + 15 q^{33} + 4 q^{35} - 9 q^{37} + 12 q^{39} + 16 q^{41} - 12 q^{43} - 6 q^{45} - 2 q^{47} - q^{49} - 19 q^{51} - 17 q^{53} + q^{55} - 12 q^{57} + 9 q^{59} - 15 q^{61} - 19 q^{63} + 3 q^{65} + 23 q^{67} + q^{69} + 16 q^{71} + 14 q^{73} - q^{75} + 16 q^{77} + 24 q^{79} + 11 q^{81} + 7 q^{83} - 2 q^{85} + 2 q^{87} + 10 q^{89} + 15 q^{91} + 20 q^{93} - 3 q^{95} + 9 q^{97} - 13 q^{99} + O(q^{100}) \)

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
\(3\) −0.277754 −0.160362 −0.0801808 0.996780i \(-0.525550\pi\)
−0.0801808 + 0.996780i \(0.525550\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.27775 −0.482946 −0.241473 0.970408i \(-0.577630\pi\)
−0.241473 + 0.970408i \(0.577630\pi\)
\(8\) 0 0
\(9\) −2.92285 −0.974284
\(10\) 0 0
\(11\) −0.277754 −0.0837461 −0.0418730 0.999123i \(-0.513333\pi\)
−0.0418730 + 0.999123i \(0.513333\pi\)
\(12\) 0 0
\(13\) 3.92285 1.08800 0.544002 0.839084i \(-0.316908\pi\)
0.544002 + 0.839084i \(0.316908\pi\)
\(14\) 0 0
\(15\) 0.277754 0.0717159
\(16\) 0 0
\(17\) 5.47836 1.32870 0.664349 0.747423i \(-0.268709\pi\)
0.664349 + 0.747423i \(0.268709\pi\)
\(18\) 0 0
\(19\) −3.92285 −0.899964 −0.449982 0.893038i \(-0.648570\pi\)
−0.449982 + 0.893038i \(0.648570\pi\)
\(20\) 0 0
\(21\) 0.354902 0.0774459
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.64510 0.316599
\(28\) 0 0
\(29\) −0.799393 −0.148444 −0.0742218 0.997242i \(-0.523647\pi\)
−0.0742218 + 0.997242i \(0.523647\pi\)
\(30\) 0 0
\(31\) −5.27775 −0.947913 −0.473956 0.880548i \(-0.657175\pi\)
−0.473956 + 0.880548i \(0.657175\pi\)
\(32\) 0 0
\(33\) 0.0771475 0.0134297
\(34\) 0 0
\(35\) 1.27775 0.215980
\(36\) 0 0
\(37\) 1.75612 0.288704 0.144352 0.989526i \(-0.453890\pi\)
0.144352 + 0.989526i \(0.453890\pi\)
\(38\) 0 0
\(39\) −1.08959 −0.174474
\(40\) 0 0
\(41\) 10.0339 1.56703 0.783514 0.621375i \(-0.213425\pi\)
0.783514 + 0.621375i \(0.213425\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 2.92285 0.435713
\(46\) 0 0
\(47\) 8.95672 1.30647 0.653236 0.757154i \(-0.273411\pi\)
0.653236 + 0.757154i \(0.273411\pi\)
\(48\) 0 0
\(49\) −5.36734 −0.766763
\(50\) 0 0
\(51\) −1.52164 −0.213072
\(52\) 0 0
\(53\) −10.6451 −1.46222 −0.731108 0.682261i \(-0.760997\pi\)
−0.731108 + 0.682261i \(0.760997\pi\)
\(54\) 0 0
\(55\) 0.277754 0.0374524
\(56\) 0 0
\(57\) 1.08959 0.144320
\(58\) 0 0
\(59\) 8.08959 1.05317 0.526587 0.850121i \(-0.323471\pi\)
0.526587 + 0.850121i \(0.323471\pi\)
\(60\) 0 0
\(61\) −15.0124 −1.92215 −0.961073 0.276294i \(-0.910894\pi\)
−0.961073 + 0.276294i \(0.910894\pi\)
\(62\) 0 0
\(63\) 3.73469 0.470526
\(64\) 0 0
\(65\) −3.92285 −0.486570
\(66\) 0 0
\(67\) 12.6451 1.54484 0.772422 0.635109i \(-0.219045\pi\)
0.772422 + 0.635109i \(0.219045\pi\)
\(68\) 0 0
\(69\) 0.277754 0.0334377
\(70\) 0 0
\(71\) −9.32407 −1.10656 −0.553282 0.832994i \(-0.686625\pi\)
−0.553282 + 0.832994i \(0.686625\pi\)
\(72\) 0 0
\(73\) 4.55551 0.533182 0.266591 0.963810i \(-0.414103\pi\)
0.266591 + 0.963810i \(0.414103\pi\)
\(74\) 0 0
\(75\) −0.277754 −0.0320723
\(76\) 0 0
\(77\) 0.354902 0.0404448
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) 8.31162 0.923514
\(82\) 0 0
\(83\) −2.64510 −0.290337 −0.145169 0.989407i \(-0.546372\pi\)
−0.145169 + 0.989407i \(0.546372\pi\)
\(84\) 0 0
\(85\) −5.47836 −0.594212
\(86\) 0 0
\(87\) 0.222035 0.0238046
\(88\) 0 0
\(89\) 13.2902 1.40876 0.704379 0.709824i \(-0.251226\pi\)
0.704379 + 0.709824i \(0.251226\pi\)
\(90\) 0 0
\(91\) −5.01244 −0.525447
\(92\) 0 0
\(93\) 1.46592 0.152009
\(94\) 0 0
\(95\) 3.92285 0.402476
\(96\) 0 0
\(97\) 3.16674 0.321533 0.160767 0.986992i \(-0.448603\pi\)
0.160767 + 0.986992i \(0.448603\pi\)
\(98\) 0 0
\(99\) 0.811835 0.0815925
\(100\) 0 0
\(101\) −5.60182 −0.557402 −0.278701 0.960378i \(-0.589904\pi\)
−0.278701 + 0.960378i \(0.589904\pi\)
\(102\) 0 0
\(103\) −2.83326 −0.279170 −0.139585 0.990210i \(-0.544577\pi\)
−0.139585 + 0.990210i \(0.544577\pi\)
\(104\) 0 0
\(105\) −0.354902 −0.0346349
\(106\) 0 0
\(107\) −19.2006 −1.85619 −0.928096 0.372340i \(-0.878556\pi\)
−0.928096 + 0.372340i \(0.878556\pi\)
\(108\) 0 0
\(109\) 4.07715 0.390520 0.195260 0.980752i \(-0.437445\pi\)
0.195260 + 0.980752i \(0.437445\pi\)
\(110\) 0 0
\(111\) −0.487769 −0.0462970
\(112\) 0 0
\(113\) 11.7561 1.10592 0.552961 0.833207i \(-0.313498\pi\)
0.552961 + 0.833207i \(0.313498\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) −11.4659 −1.06002
\(118\) 0 0
\(119\) −7.00000 −0.641689
\(120\) 0 0
\(121\) −10.9229 −0.992987
\(122\) 0 0
\(123\) −2.78695 −0.251291
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 17.8457 1.58355 0.791775 0.610813i \(-0.209157\pi\)
0.791775 + 0.610813i \(0.209157\pi\)
\(128\) 0 0
\(129\) 1.11102 0.0978196
\(130\) 0 0
\(131\) −12.4012 −1.08350 −0.541750 0.840540i \(-0.682238\pi\)
−0.541750 + 0.840540i \(0.682238\pi\)
\(132\) 0 0
\(133\) 5.01244 0.434634
\(134\) 0 0
\(135\) −1.64510 −0.141588
\(136\) 0 0
\(137\) 15.0339 1.28443 0.642215 0.766524i \(-0.278016\pi\)
0.642215 + 0.766524i \(0.278016\pi\)
\(138\) 0 0
\(139\) −18.0030 −1.52700 −0.763499 0.645809i \(-0.776520\pi\)
−0.763499 + 0.645809i \(0.776520\pi\)
\(140\) 0 0
\(141\) −2.48777 −0.209508
\(142\) 0 0
\(143\) −1.08959 −0.0911160
\(144\) 0 0
\(145\) 0.799393 0.0663860
\(146\) 0 0
\(147\) 1.49080 0.122959
\(148\) 0 0
\(149\) 14.3241 1.17347 0.586737 0.809778i \(-0.300412\pi\)
0.586737 + 0.809778i \(0.300412\pi\)
\(150\) 0 0
\(151\) −24.1912 −1.96865 −0.984326 0.176359i \(-0.943568\pi\)
−0.984326 + 0.176359i \(0.943568\pi\)
\(152\) 0 0
\(153\) −16.0124 −1.29453
\(154\) 0 0
\(155\) 5.27775 0.423919
\(156\) 0 0
\(157\) −12.7994 −1.02150 −0.510751 0.859728i \(-0.670633\pi\)
−0.510751 + 0.859728i \(0.670633\pi\)
\(158\) 0 0
\(159\) 2.95672 0.234483
\(160\) 0 0
\(161\) 1.27775 0.100701
\(162\) 0 0
\(163\) 19.4351 1.52227 0.761137 0.648592i \(-0.224642\pi\)
0.761137 + 0.648592i \(0.224642\pi\)
\(164\) 0 0
\(165\) −0.0771475 −0.00600592
\(166\) 0 0
\(167\) −24.8024 −1.91927 −0.959635 0.281249i \(-0.909251\pi\)
−0.959635 + 0.281249i \(0.909251\pi\)
\(168\) 0 0
\(169\) 2.38877 0.183752
\(170\) 0 0
\(171\) 11.4659 0.876821
\(172\) 0 0
\(173\) 12.6790 0.963964 0.481982 0.876181i \(-0.339917\pi\)
0.481982 + 0.876181i \(0.339917\pi\)
\(174\) 0 0
\(175\) −1.27775 −0.0965892
\(176\) 0 0
\(177\) −2.24692 −0.168889
\(178\) 0 0
\(179\) −0.154295 −0.0115325 −0.00576627 0.999983i \(-0.501835\pi\)
−0.00576627 + 0.999983i \(0.501835\pi\)
\(180\) 0 0
\(181\) −0.410621 −0.0305212 −0.0152606 0.999884i \(-0.504858\pi\)
−0.0152606 + 0.999884i \(0.504858\pi\)
\(182\) 0 0
\(183\) 4.16977 0.308238
\(184\) 0 0
\(185\) −1.75612 −0.129112
\(186\) 0 0
\(187\) −1.52164 −0.111273
\(188\) 0 0
\(189\) −2.10203 −0.152900
\(190\) 0 0
\(191\) 7.44449 0.538664 0.269332 0.963047i \(-0.413197\pi\)
0.269332 + 0.963047i \(0.413197\pi\)
\(192\) 0 0
\(193\) −8.06774 −0.580729 −0.290364 0.956916i \(-0.593776\pi\)
−0.290364 + 0.956916i \(0.593776\pi\)
\(194\) 0 0
\(195\) 1.08959 0.0780271
\(196\) 0 0
\(197\) −18.4569 −1.31500 −0.657501 0.753454i \(-0.728386\pi\)
−0.657501 + 0.753454i \(0.728386\pi\)
\(198\) 0 0
\(199\) −3.29020 −0.233236 −0.116618 0.993177i \(-0.537205\pi\)
−0.116618 + 0.993177i \(0.537205\pi\)
\(200\) 0 0
\(201\) −3.51223 −0.247734
\(202\) 0 0
\(203\) 1.02143 0.0716902
\(204\) 0 0
\(205\) −10.0339 −0.700796
\(206\) 0 0
\(207\) 2.92285 0.203152
\(208\) 0 0
\(209\) 1.08959 0.0753685
\(210\) 0 0
\(211\) −26.3365 −1.81308 −0.906540 0.422120i \(-0.861286\pi\)
−0.906540 + 0.422120i \(0.861286\pi\)
\(212\) 0 0
\(213\) 2.58980 0.177450
\(214\) 0 0
\(215\) 4.00000 0.272798
\(216\) 0 0
\(217\) 6.74367 0.457790
\(218\) 0 0
\(219\) −1.26531 −0.0855019
\(220\) 0 0
\(221\) 21.4908 1.44563
\(222\) 0 0
\(223\) −25.9134 −1.73529 −0.867646 0.497182i \(-0.834368\pi\)
−0.867646 + 0.497182i \(0.834368\pi\)
\(224\) 0 0
\(225\) −2.92285 −0.194857
\(226\) 0 0
\(227\) −10.7347 −0.712486 −0.356243 0.934393i \(-0.615943\pi\)
−0.356243 + 0.934393i \(0.615943\pi\)
\(228\) 0 0
\(229\) −4.22203 −0.279000 −0.139500 0.990222i \(-0.544550\pi\)
−0.139500 + 0.990222i \(0.544550\pi\)
\(230\) 0 0
\(231\) −0.0985755 −0.00648579
\(232\) 0 0
\(233\) −4.55551 −0.298441 −0.149221 0.988804i \(-0.547676\pi\)
−0.149221 + 0.988804i \(0.547676\pi\)
\(234\) 0 0
\(235\) −8.95672 −0.584272
\(236\) 0 0
\(237\) −2.22203 −0.144337
\(238\) 0 0
\(239\) −24.3365 −1.57420 −0.787099 0.616827i \(-0.788418\pi\)
−0.787099 + 0.616827i \(0.788418\pi\)
\(240\) 0 0
\(241\) 15.6914 1.01077 0.505386 0.862893i \(-0.331350\pi\)
0.505386 + 0.862893i \(0.331350\pi\)
\(242\) 0 0
\(243\) −7.24388 −0.464695
\(244\) 0 0
\(245\) 5.36734 0.342907
\(246\) 0 0
\(247\) −15.3888 −0.979164
\(248\) 0 0
\(249\) 0.734688 0.0465589
\(250\) 0 0
\(251\) −30.6575 −1.93509 −0.967543 0.252705i \(-0.918680\pi\)
−0.967543 + 0.252705i \(0.918680\pi\)
\(252\) 0 0
\(253\) 0.277754 0.0174623
\(254\) 0 0
\(255\) 1.52164 0.0952887
\(256\) 0 0
\(257\) 4.24692 0.264916 0.132458 0.991189i \(-0.457713\pi\)
0.132458 + 0.991189i \(0.457713\pi\)
\(258\) 0 0
\(259\) −2.24388 −0.139428
\(260\) 0 0
\(261\) 2.33651 0.144626
\(262\) 0 0
\(263\) −20.2130 −1.24639 −0.623195 0.782066i \(-0.714166\pi\)
−0.623195 + 0.782066i \(0.714166\pi\)
\(264\) 0 0
\(265\) 10.6451 0.653923
\(266\) 0 0
\(267\) −3.69141 −0.225911
\(268\) 0 0
\(269\) −6.08959 −0.371289 −0.185644 0.982617i \(-0.559437\pi\)
−0.185644 + 0.982617i \(0.559437\pi\)
\(270\) 0 0
\(271\) −8.78999 −0.533954 −0.266977 0.963703i \(-0.586025\pi\)
−0.266977 + 0.963703i \(0.586025\pi\)
\(272\) 0 0
\(273\) 1.39223 0.0842614
\(274\) 0 0
\(275\) −0.277754 −0.0167492
\(276\) 0 0
\(277\) −22.8024 −1.37007 −0.685033 0.728512i \(-0.740212\pi\)
−0.685033 + 0.728512i \(0.740212\pi\)
\(278\) 0 0
\(279\) 15.4261 0.923536
\(280\) 0 0
\(281\) −23.3579 −1.39342 −0.696709 0.717354i \(-0.745353\pi\)
−0.696709 + 0.717354i \(0.745353\pi\)
\(282\) 0 0
\(283\) −12.2439 −0.727823 −0.363912 0.931433i \(-0.618559\pi\)
−0.363912 + 0.931433i \(0.618559\pi\)
\(284\) 0 0
\(285\) −1.08959 −0.0645417
\(286\) 0 0
\(287\) −12.8208 −0.756789
\(288\) 0 0
\(289\) 13.0124 0.765438
\(290\) 0 0
\(291\) −0.879575 −0.0515616
\(292\) 0 0
\(293\) −26.1573 −1.52813 −0.764064 0.645141i \(-0.776799\pi\)
−0.764064 + 0.645141i \(0.776799\pi\)
\(294\) 0 0
\(295\) −8.08959 −0.470994
\(296\) 0 0
\(297\) −0.456933 −0.0265140
\(298\) 0 0
\(299\) −3.92285 −0.226864
\(300\) 0 0
\(301\) 5.11102 0.294594
\(302\) 0 0
\(303\) 1.55593 0.0893859
\(304\) 0 0
\(305\) 15.0124 0.859610
\(306\) 0 0
\(307\) 5.38877 0.307553 0.153777 0.988106i \(-0.450856\pi\)
0.153777 + 0.988106i \(0.450856\pi\)
\(308\) 0 0
\(309\) 0.786951 0.0447681
\(310\) 0 0
\(311\) −26.5804 −1.50724 −0.753618 0.657313i \(-0.771693\pi\)
−0.753618 + 0.657313i \(0.771693\pi\)
\(312\) 0 0
\(313\) 25.1235 1.42006 0.710031 0.704170i \(-0.248681\pi\)
0.710031 + 0.704170i \(0.248681\pi\)
\(314\) 0 0
\(315\) −3.73469 −0.210426
\(316\) 0 0
\(317\) −19.5894 −1.10025 −0.550125 0.835083i \(-0.685420\pi\)
−0.550125 + 0.835083i \(0.685420\pi\)
\(318\) 0 0
\(319\) 0.222035 0.0124316
\(320\) 0 0
\(321\) 5.33305 0.297662
\(322\) 0 0
\(323\) −21.4908 −1.19578
\(324\) 0 0
\(325\) 3.92285 0.217601
\(326\) 0 0
\(327\) −1.13245 −0.0626244
\(328\) 0 0
\(329\) −11.4445 −0.630955
\(330\) 0 0
\(331\) 31.1141 1.71018 0.855091 0.518477i \(-0.173501\pi\)
0.855091 + 0.518477i \(0.173501\pi\)
\(332\) 0 0
\(333\) −5.13287 −0.281279
\(334\) 0 0
\(335\) −12.6451 −0.690876
\(336\) 0 0
\(337\) 17.9229 0.976320 0.488160 0.872754i \(-0.337668\pi\)
0.488160 + 0.872754i \(0.337668\pi\)
\(338\) 0 0
\(339\) −3.26531 −0.177347
\(340\) 0 0
\(341\) 1.46592 0.0793840
\(342\) 0 0
\(343\) 15.8024 0.853251
\(344\) 0 0
\(345\) −0.277754 −0.0149538
\(346\) 0 0
\(347\) −7.16674 −0.384731 −0.192365 0.981323i \(-0.561616\pi\)
−0.192365 + 0.981323i \(0.561616\pi\)
\(348\) 0 0
\(349\) −7.93529 −0.424767 −0.212383 0.977186i \(-0.568123\pi\)
−0.212383 + 0.977186i \(0.568123\pi\)
\(350\) 0 0
\(351\) 6.45348 0.344461
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 9.32407 0.494870
\(356\) 0 0
\(357\) 1.94428 0.102902
\(358\) 0 0
\(359\) 27.6049 1.45693 0.728464 0.685084i \(-0.240234\pi\)
0.728464 + 0.685084i \(0.240234\pi\)
\(360\) 0 0
\(361\) −3.61123 −0.190065
\(362\) 0 0
\(363\) 3.03387 0.159237
\(364\) 0 0
\(365\) −4.55551 −0.238446
\(366\) 0 0
\(367\) 11.5341 0.602074 0.301037 0.953612i \(-0.402667\pi\)
0.301037 + 0.953612i \(0.402667\pi\)
\(368\) 0 0
\(369\) −29.3275 −1.52673
\(370\) 0 0
\(371\) 13.6018 0.706171
\(372\) 0 0
\(373\) 11.6237 0.601851 0.300925 0.953648i \(-0.402704\pi\)
0.300925 + 0.953648i \(0.402704\pi\)
\(374\) 0 0
\(375\) 0.277754 0.0143432
\(376\) 0 0
\(377\) −3.13590 −0.161507
\(378\) 0 0
\(379\) 12.2778 0.630666 0.315333 0.948981i \(-0.397884\pi\)
0.315333 + 0.948981i \(0.397884\pi\)
\(380\) 0 0
\(381\) −4.95672 −0.253941
\(382\) 0 0
\(383\) 4.64510 0.237353 0.118677 0.992933i \(-0.462135\pi\)
0.118677 + 0.992933i \(0.462135\pi\)
\(384\) 0 0
\(385\) −0.354902 −0.0180875
\(386\) 0 0
\(387\) 11.6914 0.594308
\(388\) 0 0
\(389\) 9.90142 0.502022 0.251011 0.967984i \(-0.419237\pi\)
0.251011 + 0.967984i \(0.419237\pi\)
\(390\) 0 0
\(391\) −5.47836 −0.277053
\(392\) 0 0
\(393\) 3.44449 0.173752
\(394\) 0 0
\(395\) −8.00000 −0.402524
\(396\) 0 0
\(397\) 6.34549 0.318471 0.159236 0.987241i \(-0.449097\pi\)
0.159236 + 0.987241i \(0.449097\pi\)
\(398\) 0 0
\(399\) −1.39223 −0.0696986
\(400\) 0 0
\(401\) −5.84571 −0.291921 −0.145960 0.989290i \(-0.546627\pi\)
−0.145960 + 0.989290i \(0.546627\pi\)
\(402\) 0 0
\(403\) −20.7039 −1.03133
\(404\) 0 0
\(405\) −8.31162 −0.413008
\(406\) 0 0
\(407\) −0.487769 −0.0241778
\(408\) 0 0
\(409\) 7.52467 0.372071 0.186036 0.982543i \(-0.440436\pi\)
0.186036 + 0.982543i \(0.440436\pi\)
\(410\) 0 0
\(411\) −4.17572 −0.205973
\(412\) 0 0
\(413\) −10.3365 −0.508626
\(414\) 0 0
\(415\) 2.64510 0.129843
\(416\) 0 0
\(417\) 5.00042 0.244872
\(418\) 0 0
\(419\) 14.4012 0.703545 0.351773 0.936085i \(-0.385579\pi\)
0.351773 + 0.936085i \(0.385579\pi\)
\(420\) 0 0
\(421\) 18.4784 0.900580 0.450290 0.892882i \(-0.351321\pi\)
0.450290 + 0.892882i \(0.351321\pi\)
\(422\) 0 0
\(423\) −26.1792 −1.27288
\(424\) 0 0
\(425\) 5.47836 0.265740
\(426\) 0 0
\(427\) 19.1822 0.928292
\(428\) 0 0
\(429\) 0.302638 0.0146115
\(430\) 0 0
\(431\) 13.1359 0.632734 0.316367 0.948637i \(-0.397537\pi\)
0.316367 + 0.948637i \(0.397537\pi\)
\(432\) 0 0
\(433\) −36.1479 −1.73716 −0.868579 0.495550i \(-0.834966\pi\)
−0.868579 + 0.495550i \(0.834966\pi\)
\(434\) 0 0
\(435\) −0.222035 −0.0106458
\(436\) 0 0
\(437\) 3.92285 0.187655
\(438\) 0 0
\(439\) 8.16977 0.389922 0.194961 0.980811i \(-0.437542\pi\)
0.194961 + 0.980811i \(0.437542\pi\)
\(440\) 0 0
\(441\) 15.6880 0.747045
\(442\) 0 0
\(443\) 1.36734 0.0649645 0.0324822 0.999472i \(-0.489659\pi\)
0.0324822 + 0.999472i \(0.489659\pi\)
\(444\) 0 0
\(445\) −13.2902 −0.630016
\(446\) 0 0
\(447\) −3.97857 −0.188180
\(448\) 0 0
\(449\) −0.944281 −0.0445634 −0.0222817 0.999752i \(-0.507093\pi\)
−0.0222817 + 0.999752i \(0.507093\pi\)
\(450\) 0 0
\(451\) −2.78695 −0.131232
\(452\) 0 0
\(453\) 6.71921 0.315696
\(454\) 0 0
\(455\) 5.01244 0.234987
\(456\) 0 0
\(457\) −7.75612 −0.362816 −0.181408 0.983408i \(-0.558065\pi\)
−0.181408 + 0.983408i \(0.558065\pi\)
\(458\) 0 0
\(459\) 9.01244 0.420665
\(460\) 0 0
\(461\) −9.84571 −0.458560 −0.229280 0.973360i \(-0.573637\pi\)
−0.229280 + 0.973360i \(0.573637\pi\)
\(462\) 0 0
\(463\) −7.29020 −0.338804 −0.169402 0.985547i \(-0.554184\pi\)
−0.169402 + 0.985547i \(0.554184\pi\)
\(464\) 0 0
\(465\) −1.46592 −0.0679804
\(466\) 0 0
\(467\) −37.5153 −1.73600 −0.868000 0.496565i \(-0.834595\pi\)
−0.868000 + 0.496565i \(0.834595\pi\)
\(468\) 0 0
\(469\) −16.1573 −0.746076
\(470\) 0 0
\(471\) 3.55509 0.163810
\(472\) 0 0
\(473\) 1.11102 0.0510846
\(474\) 0 0
\(475\) −3.92285 −0.179993
\(476\) 0 0
\(477\) 31.1141 1.42461
\(478\) 0 0
\(479\) 26.1792 1.19616 0.598079 0.801437i \(-0.295931\pi\)
0.598079 + 0.801437i \(0.295931\pi\)
\(480\) 0 0
\(481\) 6.88898 0.314111
\(482\) 0 0
\(483\) −0.354902 −0.0161486
\(484\) 0 0
\(485\) −3.16674 −0.143794
\(486\) 0 0
\(487\) 10.9567 0.496496 0.248248 0.968696i \(-0.420145\pi\)
0.248248 + 0.968696i \(0.420145\pi\)
\(488\) 0 0
\(489\) −5.39818 −0.244114
\(490\) 0 0
\(491\) −19.6884 −0.888524 −0.444262 0.895897i \(-0.646534\pi\)
−0.444262 + 0.895897i \(0.646534\pi\)
\(492\) 0 0
\(493\) −4.37936 −0.197237
\(494\) 0 0
\(495\) −0.811835 −0.0364893
\(496\) 0 0
\(497\) 11.9139 0.534410
\(498\) 0 0
\(499\) 32.8243 1.46942 0.734708 0.678383i \(-0.237319\pi\)
0.734708 + 0.678383i \(0.237319\pi\)
\(500\) 0 0
\(501\) 6.88898 0.307777
\(502\) 0 0
\(503\) −17.9010 −0.798166 −0.399083 0.916915i \(-0.630672\pi\)
−0.399083 + 0.916915i \(0.630672\pi\)
\(504\) 0 0
\(505\) 5.60182 0.249278
\(506\) 0 0
\(507\) −0.663492 −0.0294667
\(508\) 0 0
\(509\) 43.3579 1.92181 0.960903 0.276884i \(-0.0893018\pi\)
0.960903 + 0.276884i \(0.0893018\pi\)
\(510\) 0 0
\(511\) −5.82082 −0.257498
\(512\) 0 0
\(513\) −6.45348 −0.284928
\(514\) 0 0
\(515\) 2.83326 0.124848
\(516\) 0 0
\(517\) −2.48777 −0.109412
\(518\) 0 0
\(519\) −3.52164 −0.154583
\(520\) 0 0
\(521\) −25.5122 −1.11771 −0.558856 0.829265i \(-0.688759\pi\)
−0.558856 + 0.829265i \(0.688759\pi\)
\(522\) 0 0
\(523\) −24.4012 −1.06699 −0.533495 0.845803i \(-0.679122\pi\)
−0.533495 + 0.845803i \(0.679122\pi\)
\(524\) 0 0
\(525\) 0.354902 0.0154892
\(526\) 0 0
\(527\) −28.9134 −1.25949
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −23.6447 −1.02609
\(532\) 0 0
\(533\) 39.3614 1.70493
\(534\) 0 0
\(535\) 19.2006 0.830115
\(536\) 0 0
\(537\) 0.0428561 0.00184938
\(538\) 0 0
\(539\) 1.49080 0.0642134
\(540\) 0 0
\(541\) 16.3147 0.701422 0.350711 0.936484i \(-0.385940\pi\)
0.350711 + 0.936484i \(0.385940\pi\)
\(542\) 0 0
\(543\) 0.114052 0.00489443
\(544\) 0 0
\(545\) −4.07715 −0.174646
\(546\) 0 0
\(547\) 11.1016 0.474671 0.237335 0.971428i \(-0.423726\pi\)
0.237335 + 0.971428i \(0.423726\pi\)
\(548\) 0 0
\(549\) 43.8792 1.87272
\(550\) 0 0
\(551\) 3.13590 0.133594
\(552\) 0 0
\(553\) −10.2220 −0.434685
\(554\) 0 0
\(555\) 0.487769 0.0207046
\(556\) 0 0
\(557\) −39.8487 −1.68845 −0.844223 0.535993i \(-0.819937\pi\)
−0.844223 + 0.535993i \(0.819937\pi\)
\(558\) 0 0
\(559\) −15.6914 −0.663676
\(560\) 0 0
\(561\) 0.422642 0.0178440
\(562\) 0 0
\(563\) 11.0463 0.465547 0.232773 0.972531i \(-0.425220\pi\)
0.232773 + 0.972531i \(0.425220\pi\)
\(564\) 0 0
\(565\) −11.7561 −0.494584
\(566\) 0 0
\(567\) −10.6202 −0.446007
\(568\) 0 0
\(569\) −38.4938 −1.61375 −0.806873 0.590725i \(-0.798842\pi\)
−0.806873 + 0.590725i \(0.798842\pi\)
\(570\) 0 0
\(571\) −20.2778 −0.848598 −0.424299 0.905522i \(-0.639479\pi\)
−0.424299 + 0.905522i \(0.639479\pi\)
\(572\) 0 0
\(573\) −2.06774 −0.0863811
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −14.8024 −0.616233 −0.308117 0.951349i \(-0.599699\pi\)
−0.308117 + 0.951349i \(0.599699\pi\)
\(578\) 0 0
\(579\) 2.24085 0.0931265
\(580\) 0 0
\(581\) 3.37979 0.140217
\(582\) 0 0
\(583\) 2.95672 0.122455
\(584\) 0 0
\(585\) 11.4659 0.474057
\(586\) 0 0
\(587\) −36.7716 −1.51773 −0.758863 0.651250i \(-0.774245\pi\)
−0.758863 + 0.651250i \(0.774245\pi\)
\(588\) 0 0
\(589\) 20.7039 0.853087
\(590\) 0 0
\(591\) 5.12649 0.210876
\(592\) 0 0
\(593\) −8.73469 −0.358691 −0.179345 0.983786i \(-0.557398\pi\)
−0.179345 + 0.983786i \(0.557398\pi\)
\(594\) 0 0
\(595\) 7.00000 0.286972
\(596\) 0 0
\(597\) 0.913866 0.0374021
\(598\) 0 0
\(599\) 20.8581 0.852241 0.426120 0.904666i \(-0.359880\pi\)
0.426120 + 0.904666i \(0.359880\pi\)
\(600\) 0 0
\(601\) 42.7283 1.74292 0.871462 0.490463i \(-0.163172\pi\)
0.871462 + 0.490463i \(0.163172\pi\)
\(602\) 0 0
\(603\) −36.9598 −1.50512
\(604\) 0 0
\(605\) 10.9229 0.444077
\(606\) 0 0
\(607\) −1.29020 −0.0523675 −0.0261837 0.999657i \(-0.508335\pi\)
−0.0261837 + 0.999657i \(0.508335\pi\)
\(608\) 0 0
\(609\) −0.283706 −0.0114964
\(610\) 0 0
\(611\) 35.1359 1.42145
\(612\) 0 0
\(613\) −42.4938 −1.71631 −0.858155 0.513391i \(-0.828389\pi\)
−0.858155 + 0.513391i \(0.828389\pi\)
\(614\) 0 0
\(615\) 2.78695 0.112381
\(616\) 0 0
\(617\) −6.34246 −0.255338 −0.127669 0.991817i \(-0.540749\pi\)
−0.127669 + 0.991817i \(0.540749\pi\)
\(618\) 0 0
\(619\) 22.3241 0.897280 0.448640 0.893713i \(-0.351909\pi\)
0.448640 + 0.893713i \(0.351909\pi\)
\(620\) 0 0
\(621\) −1.64510 −0.0660155
\(622\) 0 0
\(623\) −16.9816 −0.680354
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −0.302638 −0.0120862
\(628\) 0 0
\(629\) 9.62064 0.383600
\(630\) 0 0
\(631\) 30.6481 1.22008 0.610041 0.792370i \(-0.291153\pi\)
0.610041 + 0.792370i \(0.291153\pi\)
\(632\) 0 0
\(633\) 7.31508 0.290748
\(634\) 0 0
\(635\) −17.8457 −0.708185
\(636\) 0 0
\(637\) −21.0553 −0.834241
\(638\) 0 0
\(639\) 27.2529 1.07811
\(640\) 0 0
\(641\) −24.3147 −0.960371 −0.480186 0.877167i \(-0.659431\pi\)
−0.480186 + 0.877167i \(0.659431\pi\)
\(642\) 0 0
\(643\) −23.6944 −0.934418 −0.467209 0.884147i \(-0.654740\pi\)
−0.467209 + 0.884147i \(0.654740\pi\)
\(644\) 0 0
\(645\) −1.11102 −0.0437463
\(646\) 0 0
\(647\) −32.8951 −1.29324 −0.646619 0.762813i \(-0.723818\pi\)
−0.646619 + 0.762813i \(0.723818\pi\)
\(648\) 0 0
\(649\) −2.24692 −0.0881993
\(650\) 0 0
\(651\) −1.87308 −0.0734120
\(652\) 0 0
\(653\) 48.9045 1.91378 0.956890 0.290452i \(-0.0938055\pi\)
0.956890 + 0.290452i \(0.0938055\pi\)
\(654\) 0 0
\(655\) 12.4012 0.484556
\(656\) 0 0
\(657\) −13.3151 −0.519471
\(658\) 0 0
\(659\) 21.9134 0.853627 0.426813 0.904340i \(-0.359636\pi\)
0.426813 + 0.904340i \(0.359636\pi\)
\(660\) 0 0
\(661\) −6.34549 −0.246811 −0.123406 0.992356i \(-0.539382\pi\)
−0.123406 + 0.992356i \(0.539382\pi\)
\(662\) 0 0
\(663\) −5.96916 −0.231823
\(664\) 0 0
\(665\) −5.01244 −0.194374
\(666\) 0 0
\(667\) 0.799393 0.0309526
\(668\) 0 0
\(669\) 7.19757 0.278274
\(670\) 0 0
\(671\) 4.16977 0.160972
\(672\) 0 0
\(673\) 22.9816 0.885876 0.442938 0.896552i \(-0.353936\pi\)
0.442938 + 0.896552i \(0.353936\pi\)
\(674\) 0 0
\(675\) 1.64510 0.0633199
\(676\) 0 0
\(677\) 9.97815 0.383491 0.191746 0.981445i \(-0.438585\pi\)
0.191746 + 0.981445i \(0.438585\pi\)
\(678\) 0 0
\(679\) −4.04631 −0.155283
\(680\) 0 0
\(681\) 2.98161 0.114255
\(682\) 0 0
\(683\) 15.1265 0.578799 0.289400 0.957208i \(-0.406544\pi\)
0.289400 + 0.957208i \(0.406544\pi\)
\(684\) 0 0
\(685\) −15.0339 −0.574415
\(686\) 0 0
\(687\) 1.17269 0.0447409
\(688\) 0 0
\(689\) −41.7592 −1.59090
\(690\) 0 0
\(691\) 35.8457 1.36363 0.681817 0.731522i \(-0.261190\pi\)
0.681817 + 0.731522i \(0.261190\pi\)
\(692\) 0 0
\(693\) −1.03733 −0.0394047
\(694\) 0 0
\(695\) 18.0030 0.682894
\(696\) 0 0
\(697\) 54.9692 2.08211
\(698\) 0 0
\(699\) 1.26531 0.0478585
\(700\) 0 0
\(701\) 13.0339 0.492282 0.246141 0.969234i \(-0.420837\pi\)
0.246141 + 0.969234i \(0.420837\pi\)
\(702\) 0 0
\(703\) −6.88898 −0.259823
\(704\) 0 0
\(705\) 2.48777 0.0936948
\(706\) 0 0
\(707\) 7.15775 0.269195
\(708\) 0 0
\(709\) 2.21001 0.0829988 0.0414994 0.999139i \(-0.486787\pi\)
0.0414994 + 0.999139i \(0.486787\pi\)
\(710\) 0 0
\(711\) −23.3828 −0.876924
\(712\) 0 0
\(713\) 5.27775 0.197653
\(714\) 0 0
\(715\) 1.08959 0.0407483
\(716\) 0 0
\(717\) 6.75957 0.252441
\(718\) 0 0
\(719\) −37.9259 −1.41440 −0.707198 0.707015i \(-0.750041\pi\)
−0.707198 + 0.707015i \(0.750041\pi\)
\(720\) 0 0
\(721\) 3.62021 0.134824
\(722\) 0 0
\(723\) −4.35836 −0.162089
\(724\) 0 0
\(725\) −0.799393 −0.0296887
\(726\) 0 0
\(727\) −26.5465 −0.984556 −0.492278 0.870438i \(-0.663836\pi\)
−0.492278 + 0.870438i \(0.663836\pi\)
\(728\) 0 0
\(729\) −22.9229 −0.848995
\(730\) 0 0
\(731\) −21.9134 −0.810498
\(732\) 0 0
\(733\) 8.37936 0.309499 0.154749 0.987954i \(-0.450543\pi\)
0.154749 + 0.987954i \(0.450543\pi\)
\(734\) 0 0
\(735\) −1.49080 −0.0549891
\(736\) 0 0
\(737\) −3.51223 −0.129375
\(738\) 0 0
\(739\) −23.4904 −0.864108 −0.432054 0.901848i \(-0.642211\pi\)
−0.432054 + 0.901848i \(0.642211\pi\)
\(740\) 0 0
\(741\) 4.27430 0.157020
\(742\) 0 0
\(743\) −28.7681 −1.05540 −0.527700 0.849431i \(-0.676946\pi\)
−0.527700 + 0.849431i \(0.676946\pi\)
\(744\) 0 0
\(745\) −14.3241 −0.524793
\(746\) 0 0
\(747\) 7.73123 0.282871
\(748\) 0 0
\(749\) 24.5337 0.896440
\(750\) 0 0
\(751\) 3.13590 0.114431 0.0572153 0.998362i \(-0.481778\pi\)
0.0572153 + 0.998362i \(0.481778\pi\)
\(752\) 0 0
\(753\) 8.51527 0.310314
\(754\) 0 0
\(755\) 24.1912 0.880408
\(756\) 0 0
\(757\) 0.0218495 0.000794132 0 0.000397066 1.00000i \(-0.499874\pi\)
0.000397066 1.00000i \(0.499874\pi\)
\(758\) 0 0
\(759\) −0.0771475 −0.00280028
\(760\) 0 0
\(761\) −8.83368 −0.320221 −0.160110 0.987099i \(-0.551185\pi\)
−0.160110 + 0.987099i \(0.551185\pi\)
\(762\) 0 0
\(763\) −5.20959 −0.188600
\(764\) 0 0
\(765\) 16.0124 0.578931
\(766\) 0 0
\(767\) 31.7343 1.14586
\(768\) 0 0
\(769\) −53.2036 −1.91857 −0.959286 0.282436i \(-0.908858\pi\)
−0.959286 + 0.282436i \(0.908858\pi\)
\(770\) 0 0
\(771\) −1.17960 −0.0424823
\(772\) 0 0
\(773\) 15.3768 0.553063 0.276532 0.961005i \(-0.410815\pi\)
0.276532 + 0.961005i \(0.410815\pi\)
\(774\) 0 0
\(775\) −5.27775 −0.189583
\(776\) 0 0
\(777\) 0.623249 0.0223589
\(778\) 0 0
\(779\) −39.3614 −1.41027
\(780\) 0 0
\(781\) 2.58980 0.0926703
\(782\) 0 0
\(783\) −1.31508 −0.0469971
\(784\) 0 0
\(785\) 12.7994 0.456830
\(786\) 0 0
\(787\) −36.0957 −1.28667 −0.643336 0.765584i \(-0.722450\pi\)
−0.643336 + 0.765584i \(0.722450\pi\)
\(788\) 0 0
\(789\) 5.61426 0.199873
\(790\) 0 0
\(791\) −15.0214 −0.534100
\(792\) 0 0
\(793\) −58.8916 −2.09130
\(794\) 0 0
\(795\) −2.95672 −0.104864
\(796\) 0 0
\(797\) 6.13245 0.217222 0.108611 0.994084i \(-0.465360\pi\)
0.108611 + 0.994084i \(0.465360\pi\)
\(798\) 0 0
\(799\) 49.0682 1.73591
\(800\) 0 0
\(801\) −38.8453 −1.37253
\(802\) 0 0
\(803\) −1.26531 −0.0446519
\(804\) 0 0
\(805\) −1.27775 −0.0450349
\(806\) 0 0
\(807\) 1.69141 0.0595405
\(808\) 0 0
\(809\) −30.7008 −1.07938 −0.539692 0.841863i \(-0.681459\pi\)
−0.539692 + 0.841863i \(0.681459\pi\)
\(810\) 0 0
\(811\) 0.490803 0.0172344 0.00861722 0.999963i \(-0.497257\pi\)
0.00861722 + 0.999963i \(0.497257\pi\)
\(812\) 0 0
\(813\) 2.44146 0.0856256
\(814\) 0 0
\(815\) −19.4351 −0.680781
\(816\) 0 0
\(817\) 15.6914 0.548973
\(818\) 0 0
\(819\) 14.6506 0.511934
\(820\) 0 0
\(821\) 18.8024 0.656209 0.328105 0.944641i \(-0.393590\pi\)
0.328105 + 0.944641i \(0.393590\pi\)
\(822\) 0 0
\(823\) −36.2718 −1.26436 −0.632178 0.774823i \(-0.717839\pi\)
−0.632178 + 0.774823i \(0.717839\pi\)
\(824\) 0 0
\(825\) 0.0771475 0.00268593
\(826\) 0 0
\(827\) 51.6018 1.79437 0.897186 0.441654i \(-0.145608\pi\)
0.897186 + 0.441654i \(0.145608\pi\)
\(828\) 0 0
\(829\) −17.2255 −0.598266 −0.299133 0.954211i \(-0.596697\pi\)
−0.299133 + 0.954211i \(0.596697\pi\)
\(830\) 0 0
\(831\) 6.33347 0.219706
\(832\) 0 0
\(833\) −29.4042 −1.01880
\(834\) 0 0
\(835\) 24.8024 0.858323
\(836\) 0 0
\(837\) −8.68242 −0.300108
\(838\) 0 0
\(839\) −13.7592 −0.475019 −0.237509 0.971385i \(-0.576331\pi\)
−0.237509 + 0.971385i \(0.576331\pi\)
\(840\) 0 0
\(841\) −28.3610 −0.977965
\(842\) 0 0
\(843\) 6.48777 0.223451
\(844\) 0 0
\(845\) −2.38877 −0.0821762
\(846\) 0 0
\(847\) 13.9567 0.479559
\(848\) 0 0
\(849\) 3.40079 0.116715
\(850\) 0 0
\(851\) −1.75612 −0.0601989
\(852\) 0 0
\(853\) 22.3490 0.765213 0.382607 0.923911i \(-0.375026\pi\)
0.382607 + 0.923911i \(0.375026\pi\)
\(854\) 0 0
\(855\) −11.4659 −0.392126
\(856\) 0 0
\(857\) 35.9134 1.22678 0.613390 0.789780i \(-0.289805\pi\)
0.613390 + 0.789780i \(0.289805\pi\)
\(858\) 0 0
\(859\) −5.64552 −0.192623 −0.0963113 0.995351i \(-0.530704\pi\)
−0.0963113 + 0.995351i \(0.530704\pi\)
\(860\) 0 0
\(861\) 3.56104 0.121360
\(862\) 0 0
\(863\) 36.5616 1.24457 0.622285 0.782791i \(-0.286204\pi\)
0.622285 + 0.782791i \(0.286204\pi\)
\(864\) 0 0
\(865\) −12.6790 −0.431098
\(866\) 0 0
\(867\) −3.61426 −0.122747
\(868\) 0 0
\(869\) −2.22203 −0.0753774
\(870\) 0 0
\(871\) 49.6049 1.68080
\(872\) 0 0
\(873\) −9.25590 −0.313265
\(874\) 0 0
\(875\) 1.27775 0.0431960
\(876\) 0 0
\(877\) −6.45693 −0.218035 −0.109018 0.994040i \(-0.534770\pi\)
−0.109018 + 0.994040i \(0.534770\pi\)
\(878\) 0 0
\(879\) 7.26531 0.245053
\(880\) 0 0
\(881\) 12.3147 0.414891 0.207446 0.978247i \(-0.433485\pi\)
0.207446 + 0.978247i \(0.433485\pi\)
\(882\) 0 0
\(883\) −7.43508 −0.250210 −0.125105 0.992143i \(-0.539927\pi\)
−0.125105 + 0.992143i \(0.539927\pi\)
\(884\) 0 0
\(885\) 2.24692 0.0755293
\(886\) 0 0
\(887\) −23.6914 −0.795480 −0.397740 0.917498i \(-0.630205\pi\)
−0.397740 + 0.917498i \(0.630205\pi\)
\(888\) 0 0
\(889\) −22.8024 −0.764769
\(890\) 0 0
\(891\) −2.30859 −0.0773407
\(892\) 0 0
\(893\) −35.1359 −1.17578
\(894\) 0 0
\(895\) 0.154295 0.00515751
\(896\) 0 0
\(897\) 1.08959 0.0363803
\(898\) 0 0
\(899\) 4.21900 0.140712
\(900\) 0 0
\(901\) −58.3177 −1.94284
\(902\) 0 0
\(903\) −1.41961 −0.0472416
\(904\) 0 0
\(905\) 0.410621 0.0136495
\(906\) 0 0
\(907\) −10.5337 −0.349764 −0.174882 0.984589i \(-0.555954\pi\)
−0.174882 + 0.984589i \(0.555954\pi\)
\(908\) 0 0
\(909\) 16.3733 0.543068
\(910\) 0 0
\(911\) −37.9383 −1.25695 −0.628476 0.777829i \(-0.716321\pi\)
−0.628476 + 0.777829i \(0.716321\pi\)
\(912\) 0 0
\(913\) 0.734688 0.0243146
\(914\) 0 0
\(915\) −4.16977 −0.137848
\(916\) 0 0
\(917\) 15.8457 0.523271
\(918\) 0 0
\(919\) −27.2036 −0.897365 −0.448683 0.893691i \(-0.648107\pi\)
−0.448683 + 0.893691i \(0.648107\pi\)
\(920\) 0 0
\(921\) −1.49675 −0.0493198
\(922\) 0 0
\(923\) −36.5769 −1.20394
\(924\) 0 0
\(925\) 1.75612 0.0577407
\(926\) 0 0
\(927\) 8.28121 0.271991
\(928\) 0 0
\(929\) 1.84874 0.0606552 0.0303276 0.999540i \(-0.490345\pi\)
0.0303276 + 0.999540i \(0.490345\pi\)
\(930\) 0 0
\(931\) 21.0553 0.690060
\(932\) 0 0
\(933\) 7.38282 0.241703
\(934\) 0 0
\(935\) 1.52164 0.0497629
\(936\) 0 0
\(937\) 51.8363 1.69342 0.846709 0.532056i \(-0.178581\pi\)
0.846709 + 0.532056i \(0.178581\pi\)
\(938\) 0 0
\(939\) −6.97815 −0.227723
\(940\) 0 0
\(941\) 30.4569 0.992868 0.496434 0.868075i \(-0.334643\pi\)
0.496434 + 0.868075i \(0.334643\pi\)
\(942\) 0 0
\(943\) −10.0339 −0.326748
\(944\) 0 0
\(945\) 2.10203 0.0683791
\(946\) 0 0
\(947\) −38.8118 −1.26122 −0.630608 0.776102i \(-0.717194\pi\)
−0.630608 + 0.776102i \(0.717194\pi\)
\(948\) 0 0
\(949\) 17.8706 0.580104
\(950\) 0 0
\(951\) 5.44104 0.176438
\(952\) 0 0
\(953\) 2.49979 0.0809761 0.0404881 0.999180i \(-0.487109\pi\)
0.0404881 + 0.999180i \(0.487109\pi\)
\(954\) 0 0
\(955\) −7.44449 −0.240898
\(956\) 0 0
\(957\) −0.0616712 −0.00199355
\(958\) 0 0
\(959\) −19.2096 −0.620310
\(960\) 0 0
\(961\) −3.14531 −0.101462
\(962\) 0 0
\(963\) 56.1205 1.80846
\(964\) 0 0
\(965\) 8.06774 0.259710
\(966\) 0 0
\(967\) −1.35794 −0.0436683 −0.0218341 0.999762i \(-0.506951\pi\)
−0.0218341 + 0.999762i \(0.506951\pi\)
\(968\) 0 0
\(969\) 5.96916 0.191757
\(970\) 0 0
\(971\) 4.59241 0.147378 0.0736888 0.997281i \(-0.476523\pi\)
0.0736888 + 0.997281i \(0.476523\pi\)
\(972\) 0 0
\(973\) 23.0035 0.737457
\(974\) 0 0
\(975\) −1.08959 −0.0348948
\(976\) 0 0
\(977\) −9.45693 −0.302554 −0.151277 0.988491i \(-0.548339\pi\)
−0.151277 + 0.988491i \(0.548339\pi\)
\(978\) 0 0
\(979\) −3.69141 −0.117978
\(980\) 0 0
\(981\) −11.9169 −0.380477
\(982\) 0 0
\(983\) 24.6571 0.786440 0.393220 0.919444i \(-0.371361\pi\)
0.393220 + 0.919444i \(0.371361\pi\)
\(984\) 0 0
\(985\) 18.4569 0.588087
\(986\) 0 0
\(987\) 3.17876 0.101181
\(988\) 0 0
\(989\) 4.00000 0.127193
\(990\) 0 0
\(991\) 18.7437 0.595412 0.297706 0.954658i \(-0.403778\pi\)
0.297706 + 0.954658i \(0.403778\pi\)
\(992\) 0 0
\(993\) −8.64206 −0.274248
\(994\) 0 0
\(995\) 3.29020 0.104306
\(996\) 0 0
\(997\) −17.0682 −0.540554 −0.270277 0.962783i \(-0.587115\pi\)
−0.270277 + 0.962783i \(0.587115\pi\)
\(998\) 0 0
\(999\) 2.88898 0.0914034
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.bx.1.2 3
4.3 odd 2 7360.2.a.cd.1.2 3
8.3 odd 2 3680.2.a.q.1.2 3
8.5 even 2 3680.2.a.r.1.2 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3680.2.a.q.1.2 3 8.3 odd 2
3680.2.a.r.1.2 yes 3 8.5 even 2
7360.2.a.bx.1.2 3 1.1 even 1 trivial
7360.2.a.cd.1.2 3 4.3 odd 2