Properties

Label 8280.2.a.bj.1.1
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(66.1161328736\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.2597.1
Defining polynomial: \(x^{3} - x^{2} - 9 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 920)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.07912\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} -2.07912 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} -2.07912 q^{7} -5.07912 q^{11} -3.48097 q^{13} -6.48097 q^{17} -7.48097 q^{19} -1.00000 q^{23} +1.00000 q^{25} +1.56009 q^{29} +0.0791189 q^{31} +2.07912 q^{35} -9.71833 q^{37} +0.480973 q^{41} +8.00000 q^{43} -6.96195 q^{47} -2.67726 q^{49} -11.7183 q^{53} +5.07912 q^{55} +11.5601 q^{59} +7.88283 q^{61} +3.48097 q^{65} -9.71833 q^{67} +9.67726 q^{71} -13.2784 q^{73} +10.5601 q^{77} -12.3165 q^{79} +4.59815 q^{83} +6.48097 q^{85} -8.31648 q^{89} +7.23736 q^{91} +7.48097 q^{95} +7.23736 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 3q^{5} + 2q^{7} + O(q^{10}) \) \( 3q - 3q^{5} + 2q^{7} - 7q^{11} - q^{13} - 10q^{17} - 13q^{19} - 3q^{23} + 3q^{25} - 13q^{29} - 8q^{31} - 2q^{35} + 5q^{37} - 8q^{41} + 24q^{43} - 2q^{47} - q^{49} - q^{53} + 7q^{55} + 17q^{59} + 13q^{61} + q^{65} + 5q^{67} + 22q^{71} + 12q^{73} + 14q^{77} - 4q^{79} + 15q^{83} + 10q^{85} + 8q^{89} - 3q^{91} + 13q^{95} - 3q^{97} + O(q^{100}) \)

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 0
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −2.07912 −0.785833 −0.392917 0.919574i \(-0.628534\pi\)
−0.392917 + 0.919574i \(0.628534\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −5.07912 −1.53141 −0.765706 0.643191i \(-0.777610\pi\)
−0.765706 + 0.643191i \(0.777610\pi\)
\(12\) 0 0
\(13\) −3.48097 −0.965448 −0.482724 0.875772i \(-0.660353\pi\)
−0.482724 + 0.875772i \(0.660353\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.48097 −1.57187 −0.785933 0.618311i \(-0.787817\pi\)
−0.785933 + 0.618311i \(0.787817\pi\)
\(18\) 0 0
\(19\) −7.48097 −1.71625 −0.858126 0.513438i \(-0.828371\pi\)
−0.858126 + 0.513438i \(0.828371\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.56009 0.289702 0.144851 0.989453i \(-0.453730\pi\)
0.144851 + 0.989453i \(0.453730\pi\)
\(30\) 0 0
\(31\) 0.0791189 0.0142102 0.00710508 0.999975i \(-0.497738\pi\)
0.00710508 + 0.999975i \(0.497738\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.07912 0.351435
\(36\) 0 0
\(37\) −9.71833 −1.59768 −0.798842 0.601541i \(-0.794554\pi\)
−0.798842 + 0.601541i \(0.794554\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.480973 0.0751154 0.0375577 0.999294i \(-0.488042\pi\)
0.0375577 + 0.999294i \(0.488042\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.96195 −1.01550 −0.507752 0.861503i \(-0.669523\pi\)
−0.507752 + 0.861503i \(0.669523\pi\)
\(48\) 0 0
\(49\) −2.67726 −0.382466
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −11.7183 −1.60964 −0.804818 0.593521i \(-0.797737\pi\)
−0.804818 + 0.593521i \(0.797737\pi\)
\(54\) 0 0
\(55\) 5.07912 0.684868
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 11.5601 1.50500 0.752498 0.658595i \(-0.228849\pi\)
0.752498 + 0.658595i \(0.228849\pi\)
\(60\) 0 0
\(61\) 7.88283 1.00929 0.504646 0.863326i \(-0.331623\pi\)
0.504646 + 0.863326i \(0.331623\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.48097 0.431762
\(66\) 0 0
\(67\) −9.71833 −1.18728 −0.593641 0.804730i \(-0.702310\pi\)
−0.593641 + 0.804730i \(0.702310\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 9.67726 1.14848 0.574240 0.818687i \(-0.305298\pi\)
0.574240 + 0.818687i \(0.305298\pi\)
\(72\) 0 0
\(73\) −13.2784 −1.55412 −0.777061 0.629425i \(-0.783290\pi\)
−0.777061 + 0.629425i \(0.783290\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 10.5601 1.20343
\(78\) 0 0
\(79\) −12.3165 −1.38571 −0.692856 0.721076i \(-0.743648\pi\)
−0.692856 + 0.721076i \(0.743648\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.59815 0.504712 0.252356 0.967634i \(-0.418795\pi\)
0.252356 + 0.967634i \(0.418795\pi\)
\(84\) 0 0
\(85\) 6.48097 0.702960
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −8.31648 −0.881545 −0.440772 0.897619i \(-0.645295\pi\)
−0.440772 + 0.897619i \(0.645295\pi\)
\(90\) 0 0
\(91\) 7.23736 0.758681
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 7.48097 0.767532
\(96\) 0 0
\(97\) 7.23736 0.734842 0.367421 0.930055i \(-0.380241\pi\)
0.367421 + 0.930055i \(0.380241\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.43991 −0.242780 −0.121390 0.992605i \(-0.538735\pi\)
−0.121390 + 0.992605i \(0.538735\pi\)
\(102\) 0 0
\(103\) 7.88283 0.776718 0.388359 0.921508i \(-0.373042\pi\)
0.388359 + 0.921508i \(0.373042\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.6803 1.61254 0.806272 0.591546i \(-0.201482\pi\)
0.806272 + 0.591546i \(0.201482\pi\)
\(108\) 0 0
\(109\) 5.32274 0.509826 0.254913 0.966964i \(-0.417953\pi\)
0.254913 + 0.966964i \(0.417953\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.20556 0.207482 0.103741 0.994604i \(-0.466919\pi\)
0.103741 + 0.994604i \(0.466919\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 13.4747 1.23522
\(120\) 0 0
\(121\) 14.7974 1.34522
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 6.15824 0.546455 0.273228 0.961949i \(-0.411909\pi\)
0.273228 + 0.961949i \(0.411909\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 7.19629 0.628743 0.314371 0.949300i \(-0.398206\pi\)
0.314371 + 0.949300i \(0.398206\pi\)
\(132\) 0 0
\(133\) 15.5538 1.34869
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −12.6012 −1.07659 −0.538295 0.842757i \(-0.680931\pi\)
−0.538295 + 0.842757i \(0.680931\pi\)
\(138\) 0 0
\(139\) −8.75638 −0.742707 −0.371353 0.928492i \(-0.621106\pi\)
−0.371353 + 0.928492i \(0.621106\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 17.6803 1.47850
\(144\) 0 0
\(145\) −1.56009 −0.129559
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.79745 −0.147253 −0.0736264 0.997286i \(-0.523457\pi\)
−0.0736264 + 0.997286i \(0.523457\pi\)
\(150\) 0 0
\(151\) −19.3956 −1.57839 −0.789196 0.614142i \(-0.789502\pi\)
−0.789196 + 0.614142i \(0.789502\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.0791189 −0.00635498
\(156\) 0 0
\(157\) 4.36380 0.348269 0.174135 0.984722i \(-0.444287\pi\)
0.174135 + 0.984722i \(0.444287\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.07912 0.163858
\(162\) 0 0
\(163\) 5.32274 0.416909 0.208454 0.978032i \(-0.433157\pi\)
0.208454 + 0.978032i \(0.433157\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) −0.882827 −0.0679098
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 9.23736 0.702303 0.351152 0.936319i \(-0.385790\pi\)
0.351152 + 0.936319i \(0.385790\pi\)
\(174\) 0 0
\(175\) −2.07912 −0.157167
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2.96195 −0.221386 −0.110693 0.993855i \(-0.535307\pi\)
−0.110693 + 0.993855i \(0.535307\pi\)
\(180\) 0 0
\(181\) 10.8355 0.805397 0.402698 0.915333i \(-0.368072\pi\)
0.402698 + 0.915333i \(0.368072\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 9.71833 0.714506
\(186\) 0 0
\(187\) 32.9176 2.40718
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −7.76565 −0.561903 −0.280952 0.959722i \(-0.590650\pi\)
−0.280952 + 0.959722i \(0.590650\pi\)
\(192\) 0 0
\(193\) −2.15824 −0.155353 −0.0776767 0.996979i \(-0.524750\pi\)
−0.0776767 + 0.996979i \(0.524750\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −12.0411 −0.857890 −0.428945 0.903331i \(-0.641115\pi\)
−0.428945 + 0.903331i \(0.641115\pi\)
\(198\) 0 0
\(199\) −14.0000 −0.992434 −0.496217 0.868199i \(-0.665278\pi\)
−0.496217 + 0.868199i \(0.665278\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.24362 −0.227657
\(204\) 0 0
\(205\) −0.480973 −0.0335926
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 37.9968 2.62829
\(210\) 0 0
\(211\) 3.40185 0.234193 0.117097 0.993121i \(-0.462641\pi\)
0.117097 + 0.993121i \(0.462641\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) −0.164498 −0.0111668
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 22.5601 1.51756
\(222\) 0 0
\(223\) 5.19629 0.347969 0.173985 0.984748i \(-0.444336\pi\)
0.173985 + 0.984748i \(0.444336\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.35453 −0.355393 −0.177696 0.984085i \(-0.556864\pi\)
−0.177696 + 0.984085i \(0.556864\pi\)
\(228\) 0 0
\(229\) −0.803708 −0.0531105 −0.0265553 0.999647i \(-0.508454\pi\)
−0.0265553 + 0.999647i \(0.508454\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −14.1582 −0.927537 −0.463768 0.885956i \(-0.653503\pi\)
−0.463768 + 0.885956i \(0.653503\pi\)
\(234\) 0 0
\(235\) 6.96195 0.454147
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −10.9146 −0.706008 −0.353004 0.935622i \(-0.614840\pi\)
−0.353004 + 0.935622i \(0.614840\pi\)
\(240\) 0 0
\(241\) −27.4367 −1.76735 −0.883675 0.468100i \(-0.844939\pi\)
−0.883675 + 0.468100i \(0.844939\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.67726 0.171044
\(246\) 0 0
\(247\) 26.0411 1.65695
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 16.5190 1.04267 0.521336 0.853352i \(-0.325434\pi\)
0.521336 + 0.853352i \(0.325434\pi\)
\(252\) 0 0
\(253\) 5.07912 0.319321
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −19.7657 −1.23295 −0.616474 0.787375i \(-0.711439\pi\)
−0.616474 + 0.787375i \(0.711439\pi\)
\(258\) 0 0
\(259\) 20.2056 1.25551
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −7.44292 −0.458950 −0.229475 0.973315i \(-0.573701\pi\)
−0.229475 + 0.973315i \(0.573701\pi\)
\(264\) 0 0
\(265\) 11.7183 0.719851
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 22.7564 1.38748 0.693741 0.720225i \(-0.255961\pi\)
0.693741 + 0.720225i \(0.255961\pi\)
\(270\) 0 0
\(271\) −19.0411 −1.15666 −0.578331 0.815802i \(-0.696296\pi\)
−0.578331 + 0.815802i \(0.696296\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.07912 −0.306282
\(276\) 0 0
\(277\) −18.3165 −1.10053 −0.550265 0.834990i \(-0.685473\pi\)
−0.550265 + 0.834990i \(0.685473\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −26.0821 −1.55593 −0.777965 0.628308i \(-0.783748\pi\)
−0.777965 + 0.628308i \(0.783748\pi\)
\(282\) 0 0
\(283\) −25.6422 −1.52427 −0.762136 0.647417i \(-0.775849\pi\)
−0.762136 + 0.647417i \(0.775849\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.00000 −0.0590281
\(288\) 0 0
\(289\) 25.0030 1.47077
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −30.8385 −1.80161 −0.900803 0.434229i \(-0.857021\pi\)
−0.900803 + 0.434229i \(0.857021\pi\)
\(294\) 0 0
\(295\) −11.5601 −0.673055
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.48097 0.201310
\(300\) 0 0
\(301\) −16.6330 −0.958707
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −7.88283 −0.451369
\(306\) 0 0
\(307\) −1.88283 −0.107459 −0.0537293 0.998556i \(-0.517111\pi\)
−0.0537293 + 0.998556i \(0.517111\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.60742 −0.0911482 −0.0455741 0.998961i \(-0.514512\pi\)
−0.0455741 + 0.998961i \(0.514512\pi\)
\(312\) 0 0
\(313\) −1.68654 −0.0953286 −0.0476643 0.998863i \(-0.515178\pi\)
−0.0476643 + 0.998863i \(0.515178\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 12.6773 0.712026 0.356013 0.934481i \(-0.384136\pi\)
0.356013 + 0.934481i \(0.384136\pi\)
\(318\) 0 0
\(319\) −7.92389 −0.443653
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 48.4840 2.69772
\(324\) 0 0
\(325\) −3.48097 −0.193090
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 14.4747 0.798017
\(330\) 0 0
\(331\) 33.3893 1.83524 0.917622 0.397454i \(-0.130106\pi\)
0.917622 + 0.397454i \(0.130106\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 9.71833 0.530969
\(336\) 0 0
\(337\) −17.6392 −0.960869 −0.480435 0.877031i \(-0.659521\pi\)
−0.480435 + 0.877031i \(0.659521\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −0.401854 −0.0217616
\(342\) 0 0
\(343\) 20.1202 1.08639
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −19.7121 −1.05820 −0.529100 0.848560i \(-0.677470\pi\)
−0.529100 + 0.848560i \(0.677470\pi\)
\(348\) 0 0
\(349\) −16.0348 −0.858323 −0.429162 0.903228i \(-0.641191\pi\)
−0.429162 + 0.903228i \(0.641191\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8.00000 0.425797 0.212899 0.977074i \(-0.431710\pi\)
0.212899 + 0.977074i \(0.431710\pi\)
\(354\) 0 0
\(355\) −9.67726 −0.513616
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 13.1202 0.692457 0.346228 0.938150i \(-0.387462\pi\)
0.346228 + 0.938150i \(0.387462\pi\)
\(360\) 0 0
\(361\) 36.9650 1.94552
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 13.2784 0.695024
\(366\) 0 0
\(367\) 3.47796 0.181548 0.0907741 0.995872i \(-0.471066\pi\)
0.0907741 + 0.995872i \(0.471066\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 24.3638 1.26491
\(372\) 0 0
\(373\) 21.5949 1.11814 0.559071 0.829120i \(-0.311158\pi\)
0.559071 + 0.829120i \(0.311158\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.43064 −0.279692
\(378\) 0 0
\(379\) 7.80070 0.400695 0.200347 0.979725i \(-0.435793\pi\)
0.200347 + 0.979725i \(0.435793\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −32.4274 −1.65696 −0.828481 0.560017i \(-0.810795\pi\)
−0.828481 + 0.560017i \(0.810795\pi\)
\(384\) 0 0
\(385\) −10.5601 −0.538192
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −23.5538 −1.19423 −0.597113 0.802157i \(-0.703686\pi\)
−0.597113 + 0.802157i \(0.703686\pi\)
\(390\) 0 0
\(391\) 6.48097 0.327757
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 12.3165 0.619709
\(396\) 0 0
\(397\) −0.370060 −0.0185728 −0.00928639 0.999957i \(-0.502956\pi\)
−0.00928639 + 0.999957i \(0.502956\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11.3545 −0.567018 −0.283509 0.958970i \(-0.591499\pi\)
−0.283509 + 0.958970i \(0.591499\pi\)
\(402\) 0 0
\(403\) −0.275411 −0.0137192
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 49.3606 2.44671
\(408\) 0 0
\(409\) 4.88283 0.241440 0.120720 0.992687i \(-0.461480\pi\)
0.120720 + 0.992687i \(0.461480\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −24.0348 −1.18268
\(414\) 0 0
\(415\) −4.59815 −0.225714
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.51277 −0.0739035 −0.0369518 0.999317i \(-0.511765\pi\)
−0.0369518 + 0.999317i \(0.511765\pi\)
\(420\) 0 0
\(421\) 22.2722 1.08548 0.542739 0.839901i \(-0.317387\pi\)
0.542739 + 0.839901i \(0.317387\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −6.48097 −0.314373
\(426\) 0 0
\(427\) −16.3893 −0.793135
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 16.8858 0.813362 0.406681 0.913570i \(-0.366686\pi\)
0.406681 + 0.913570i \(0.366686\pi\)
\(432\) 0 0
\(433\) 24.3956 1.17238 0.586189 0.810175i \(-0.300628\pi\)
0.586189 + 0.810175i \(0.300628\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.48097 0.357863
\(438\) 0 0
\(439\) 40.0378 1.91090 0.955450 0.295152i \(-0.0953703\pi\)
0.955450 + 0.295152i \(0.0953703\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.22809 0.248394 0.124197 0.992258i \(-0.460365\pi\)
0.124197 + 0.992258i \(0.460365\pi\)
\(444\) 0 0
\(445\) 8.31648 0.394239
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −4.72459 −0.222967 −0.111484 0.993766i \(-0.535560\pi\)
−0.111484 + 0.993766i \(0.535560\pi\)
\(450\) 0 0
\(451\) −2.44292 −0.115033
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −7.23736 −0.339293
\(456\) 0 0
\(457\) 33.2311 1.55449 0.777243 0.629201i \(-0.216618\pi\)
0.777243 + 0.629201i \(0.216618\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 28.9619 1.34889 0.674446 0.738324i \(-0.264382\pi\)
0.674446 + 0.738324i \(0.264382\pi\)
\(462\) 0 0
\(463\) 4.39258 0.204141 0.102070 0.994777i \(-0.467453\pi\)
0.102070 + 0.994777i \(0.467453\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −17.0729 −0.790038 −0.395019 0.918673i \(-0.629262\pi\)
−0.395019 + 0.918673i \(0.629262\pi\)
\(468\) 0 0
\(469\) 20.2056 0.933006
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −40.6330 −1.86831
\(474\) 0 0
\(475\) −7.48097 −0.343251
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −27.0441 −1.23568 −0.617838 0.786306i \(-0.711991\pi\)
−0.617838 + 0.786306i \(0.711991\pi\)
\(480\) 0 0
\(481\) 33.8292 1.54248
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7.23736 −0.328631
\(486\) 0 0
\(487\) −28.0821 −1.27252 −0.636261 0.771474i \(-0.719520\pi\)
−0.636261 + 0.771474i \(0.719520\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7.48398 0.337747 0.168874 0.985638i \(-0.445987\pi\)
0.168874 + 0.985638i \(0.445987\pi\)
\(492\) 0 0
\(493\) −10.1109 −0.455373
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −20.1202 −0.902514
\(498\) 0 0
\(499\) 21.7183 0.972246 0.486123 0.873890i \(-0.338411\pi\)
0.486123 + 0.873890i \(0.338411\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7.27541 0.324395 0.162197 0.986758i \(-0.448142\pi\)
0.162197 + 0.986758i \(0.448142\pi\)
\(504\) 0 0
\(505\) 2.43991 0.108574
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −22.7151 −1.00683 −0.503414 0.864045i \(-0.667923\pi\)
−0.503414 + 0.864045i \(0.667923\pi\)
\(510\) 0 0
\(511\) 27.6074 1.22128
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −7.88283 −0.347359
\(516\) 0 0
\(517\) 35.3606 1.55516
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 16.5568 0.725368 0.362684 0.931912i \(-0.381860\pi\)
0.362684 + 0.931912i \(0.381860\pi\)
\(522\) 0 0
\(523\) 24.8037 1.08459 0.542295 0.840188i \(-0.317555\pi\)
0.542295 + 0.840188i \(0.317555\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.512767 −0.0223365
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.67425 −0.0725200
\(534\) 0 0
\(535\) −16.6803 −0.721151
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 13.5981 0.585714
\(540\) 0 0
\(541\) −21.8292 −0.938512 −0.469256 0.883062i \(-0.655478\pi\)
−0.469256 + 0.883062i \(0.655478\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5.32274 −0.228001
\(546\) 0 0
\(547\) −29.0759 −1.24319 −0.621597 0.783337i \(-0.713516\pi\)
−0.621597 + 0.783337i \(0.713516\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −11.6710 −0.497202
\(552\) 0 0
\(553\) 25.6074 1.08894
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.0348 0.933645 0.466822 0.884351i \(-0.345399\pi\)
0.466822 + 0.884351i \(0.345399\pi\)
\(558\) 0 0
\(559\) −27.8478 −1.17784
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.40185 −0.0590811 −0.0295406 0.999564i \(-0.509404\pi\)
−0.0295406 + 0.999564i \(0.509404\pi\)
\(564\) 0 0
\(565\) −2.20556 −0.0927887
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) −18.3575 −0.768239 −0.384120 0.923283i \(-0.625495\pi\)
−0.384120 + 0.923283i \(0.625495\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −11.5128 −0.479283 −0.239641 0.970861i \(-0.577030\pi\)
−0.239641 + 0.970861i \(0.577030\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −9.56009 −0.396619
\(582\) 0 0
\(583\) 59.5188 2.46502
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −40.1232 −1.65606 −0.828031 0.560683i \(-0.810539\pi\)
−0.828031 + 0.560683i \(0.810539\pi\)
\(588\) 0 0
\(589\) −0.591886 −0.0243882
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −18.7912 −0.771662 −0.385831 0.922570i \(-0.626085\pi\)
−0.385831 + 0.922570i \(0.626085\pi\)
\(594\) 0 0
\(595\) −13.4747 −0.552409
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 27.4777 1.12271 0.561355 0.827575i \(-0.310280\pi\)
0.561355 + 0.827575i \(0.310280\pi\)
\(600\) 0 0
\(601\) −19.5283 −0.796576 −0.398288 0.917260i \(-0.630396\pi\)
−0.398288 + 0.917260i \(0.630396\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −14.7974 −0.601602
\(606\) 0 0
\(607\) 45.9239 1.86399 0.931997 0.362467i \(-0.118065\pi\)
0.931997 + 0.362467i \(0.118065\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 24.2343 0.980417
\(612\) 0 0
\(613\) 12.7091 0.513314 0.256657 0.966503i \(-0.417379\pi\)
0.256657 + 0.966503i \(0.417379\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −48.3102 −1.94490 −0.972448 0.233120i \(-0.925107\pi\)
−0.972448 + 0.233120i \(0.925107\pi\)
\(618\) 0 0
\(619\) 0.677265 0.0272216 0.0136108 0.999907i \(-0.495667\pi\)
0.0136108 + 0.999907i \(0.495667\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 17.2909 0.692747
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 62.9842 2.51135
\(630\) 0 0
\(631\) 44.3986 1.76748 0.883740 0.467978i \(-0.155017\pi\)
0.883740 + 0.467978i \(0.155017\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.15824 −0.244382
\(636\) 0 0
\(637\) 9.31949 0.369251
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −16.8798 −0.666713 −0.333356 0.942801i \(-0.608181\pi\)
−0.333356 + 0.942801i \(0.608181\pi\)
\(642\) 0 0
\(643\) −26.7564 −1.05517 −0.527584 0.849503i \(-0.676902\pi\)
−0.527584 + 0.849503i \(0.676902\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −32.5568 −1.27994 −0.639971 0.768399i \(-0.721054\pi\)
−0.639971 + 0.768399i \(0.721054\pi\)
\(648\) 0 0
\(649\) −58.7151 −2.30477
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.87356 0.386382 0.193191 0.981161i \(-0.438116\pi\)
0.193191 + 0.981161i \(0.438116\pi\)
\(654\) 0 0
\(655\) −7.19629 −0.281182
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 13.5128 0.526383 0.263191 0.964744i \(-0.415225\pi\)
0.263191 + 0.964744i \(0.415225\pi\)
\(660\) 0 0
\(661\) −26.7687 −1.04118 −0.520590 0.853807i \(-0.674288\pi\)
−0.520590 + 0.853807i \(0.674288\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −15.5538 −0.603152
\(666\) 0 0
\(667\) −1.56009 −0.0604070
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −40.0378 −1.54564
\(672\) 0 0
\(673\) −0.803708 −0.0309807 −0.0154903 0.999880i \(-0.504931\pi\)
−0.0154903 + 0.999880i \(0.504931\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 33.6422 1.29298 0.646488 0.762924i \(-0.276237\pi\)
0.646488 + 0.762924i \(0.276237\pi\)
\(678\) 0 0
\(679\) −15.0473 −0.577463
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 11.8736 0.454329 0.227165 0.973856i \(-0.427054\pi\)
0.227165 + 0.973856i \(0.427054\pi\)
\(684\) 0 0
\(685\) 12.6012 0.481465
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 40.7912 1.55402
\(690\) 0 0
\(691\) 27.9114 1.06180 0.530899 0.847435i \(-0.321854\pi\)
0.530899 + 0.847435i \(0.321854\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 8.75638 0.332149
\(696\) 0 0
\(697\) −3.11717 −0.118071
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 26.3668 0.995861 0.497930 0.867217i \(-0.334094\pi\)
0.497930 + 0.867217i \(0.334094\pi\)
\(702\) 0 0
\(703\) 72.7026 2.74203
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 5.07286 0.190785
\(708\) 0 0
\(709\) 11.8007 0.443184 0.221592 0.975139i \(-0.428875\pi\)
0.221592 + 0.975139i \(0.428875\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.0791189 −0.00296302
\(714\) 0 0
\(715\) −17.6803 −0.661205
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 12.9589 0.483287 0.241643 0.970365i \(-0.422314\pi\)
0.241643 + 0.970365i \(0.422314\pi\)
\(720\) 0 0
\(721\) −16.3893 −0.610371
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.56009 0.0579404
\(726\) 0 0
\(727\) −19.0318 −0.705850 −0.352925 0.935652i \(-0.614813\pi\)
−0.352925 + 0.935652i \(0.614813\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −51.8478 −1.91766
\(732\) 0 0
\(733\) −30.5220 −1.12736 −0.563679 0.825994i \(-0.690614\pi\)
−0.563679 + 0.825994i \(0.690614\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 49.3606 1.81822
\(738\) 0 0
\(739\) −6.18702 −0.227593 −0.113797 0.993504i \(-0.536301\pi\)
−0.113797 + 0.993504i \(0.536301\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −16.2722 −0.596968 −0.298484 0.954415i \(-0.596481\pi\)
−0.298484 + 0.954415i \(0.596481\pi\)
\(744\) 0 0
\(745\) 1.79745 0.0658534
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −34.6803 −1.26719
\(750\) 0 0
\(751\) −17.5949 −0.642047 −0.321023 0.947071i \(-0.604027\pi\)
−0.321023 + 0.947071i \(0.604027\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 19.3956 0.705878
\(756\) 0 0
\(757\) 41.2496 1.49924 0.749622 0.661866i \(-0.230235\pi\)
0.749622 + 0.661866i \(0.230235\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −26.8067 −0.971743 −0.485871 0.874030i \(-0.661498\pi\)
−0.485871 + 0.874030i \(0.661498\pi\)
\(762\) 0 0
\(763\) −11.0666 −0.400638
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −40.2404 −1.45300
\(768\) 0 0
\(769\) −26.8798 −0.969311 −0.484655 0.874705i \(-0.661055\pi\)
−0.484655 + 0.874705i \(0.661055\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −41.0441 −1.47625 −0.738126 0.674662i \(-0.764289\pi\)
−0.738126 + 0.674662i \(0.764289\pi\)
\(774\) 0 0
\(775\) 0.0791189 0.00284203
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.59815 −0.128917
\(780\) 0 0
\(781\) −49.1520 −1.75880
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.36380 −0.155751
\(786\) 0 0
\(787\) −21.4840 −0.765821 −0.382911 0.923785i \(-0.625078\pi\)
−0.382911 + 0.923785i \(0.625078\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4.58563 −0.163046
\(792\) 0 0
\(793\) −27.4399 −0.974420
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −38.2692 −1.35556 −0.677781 0.735263i \(-0.737058\pi\)
−0.677781 + 0.735263i \(0.737058\pi\)
\(798\) 0 0
\(799\) 45.1202 1.59624
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 67.4427 2.38000
\(804\) 0 0
\(805\) −2.07912 −0.0732793
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 27.2026 0.956391 0.478195 0.878253i \(-0.341291\pi\)
0.478195 + 0.878253i \(0.341291\pi\)
\(810\) 0 0
\(811\) 38.5095 1.35225 0.676126 0.736786i \(-0.263657\pi\)
0.676126 + 0.736786i \(0.263657\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −5.32274 −0.186447
\(816\) 0 0
\(817\) −59.8478 −2.09381
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −10.0000 −0.349002 −0.174501 0.984657i \(-0.555831\pi\)
−0.174501 + 0.984657i \(0.555831\pi\)
\(822\) 0 0
\(823\) 40.1457 1.39939 0.699696 0.714441i \(-0.253319\pi\)
0.699696 + 0.714441i \(0.253319\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −0.851033 −0.0295933 −0.0147967 0.999891i \(-0.504710\pi\)
−0.0147967 + 0.999891i \(0.504710\pi\)
\(828\) 0 0
\(829\) −2.83851 −0.0985856 −0.0492928 0.998784i \(-0.515697\pi\)
−0.0492928 + 0.998784i \(0.515697\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 17.3513 0.601186
\(834\) 0 0
\(835\) −8.00000 −0.276851
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 10.2343 0.353329 0.176664 0.984271i \(-0.443469\pi\)
0.176664 + 0.984271i \(0.443469\pi\)
\(840\) 0 0
\(841\) −26.5661 −0.916073
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0.882827 0.0303702
\(846\) 0 0
\(847\) −30.7657 −1.05712
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 9.71833 0.333140
\(852\) 0 0
\(853\) 17.7213 0.606767 0.303384 0.952869i \(-0.401884\pi\)
0.303384 + 0.952869i \(0.401884\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −17.6835 −0.604058 −0.302029 0.953299i \(-0.597664\pi\)
−0.302029 + 0.953299i \(0.597664\pi\)
\(858\) 0 0
\(859\) −26.6042 −0.907722 −0.453861 0.891072i \(-0.649954\pi\)
−0.453861 + 0.891072i \(0.649954\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 53.5949 1.82439 0.912196 0.409755i \(-0.134386\pi\)
0.912196 + 0.409755i \(0.134386\pi\)
\(864\) 0 0
\(865\) −9.23736 −0.314080
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 62.5568 2.12210
\(870\) 0 0
\(871\) 33.8292 1.14626
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2.07912 0.0702870
\(876\) 0 0
\(877\) 25.9650 0.876774 0.438387 0.898786i \(-0.355550\pi\)
0.438387 + 0.898786i \(0.355550\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −29.9239 −1.00816 −0.504081 0.863657i \(-0.668169\pi\)
−0.504081 + 0.863657i \(0.668169\pi\)
\(882\) 0 0
\(883\) −4.75939 −0.160166 −0.0800832 0.996788i \(-0.525519\pi\)
−0.0800832 + 0.996788i \(0.525519\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −38.8037 −1.30290 −0.651451 0.758691i \(-0.725839\pi\)
−0.651451 + 0.758691i \(0.725839\pi\)
\(888\) 0 0
\(889\) −12.8037 −0.429423
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 52.0821 1.74286
\(894\) 0 0
\(895\) 2.96195 0.0990069
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0.123433 0.00411671
\(900\) 0 0
\(901\) 75.9462 2.53013
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −10.8355 −0.360184
\(906\) 0 0
\(907\) −51.0729 −1.69585 −0.847923 0.530119i \(-0.822147\pi\)
−0.847923 + 0.530119i \(0.822147\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 30.4933 1.01029 0.505143 0.863035i \(-0.331440\pi\)
0.505143 + 0.863035i \(0.331440\pi\)
\(912\) 0 0
\(913\) −23.3545 −0.772922
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −14.9619 −0.494087
\(918\) 0 0
\(919\) 8.00000 0.263896 0.131948 0.991257i \(-0.457877\pi\)
0.131948 + 0.991257i \(0.457877\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −33.6863 −1.10880
\(924\) 0 0
\(925\) −9.71833 −0.319537
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 17.3257 0.568439 0.284220 0.958759i \(-0.408266\pi\)
0.284220 + 0.958759i \(0.408266\pi\)
\(930\) 0 0
\(931\) 20.0285 0.656409
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −32.9176 −1.07652
\(936\) 0 0
\(937\) −47.5631 −1.55382 −0.776909 0.629612i \(-0.783214\pi\)
−0.776909 + 0.629612i \(0.783214\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −14.2754 −0.465365 −0.232683 0.972553i \(-0.574750\pi\)
−0.232683 + 0.972553i \(0.574750\pi\)
\(942\) 0 0
\(943\) −0.480973 −0.0156626
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −36.1900 −1.17602 −0.588009 0.808854i \(-0.700088\pi\)
−0.588009 + 0.808854i \(0.700088\pi\)
\(948\) 0 0
\(949\) 46.2218 1.50042
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −37.7942 −1.22427 −0.612137 0.790752i \(-0.709690\pi\)
−0.612137 + 0.790752i \(0.709690\pi\)
\(954\) 0 0
\(955\) 7.76565 0.251291
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 26.1993 0.846020
\(960\) 0 0
\(961\) −30.9937 −0.999798
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 2.15824 0.0694761
\(966\) 0 0
\(967\) 50.6390 1.62844 0.814220 0.580557i \(-0.197165\pi\)
0.814220 + 0.580557i \(0.197165\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −2.82623 −0.0906981 −0.0453490 0.998971i \(-0.514440\pi\)
−0.0453490 + 0.998971i \(0.514440\pi\)
\(972\) 0 0
\(973\) 18.2056 0.583644
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −25.8448 −0.826848 −0.413424 0.910539i \(-0.635667\pi\)
−0.413424 + 0.910539i \(0.635667\pi\)
\(978\) 0 0
\(979\) 42.2404 1.35001
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 41.3668 1.31940 0.659698 0.751531i \(-0.270684\pi\)
0.659698 + 0.751531i \(0.270684\pi\)
\(984\) 0 0
\(985\) 12.0411 0.383660
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −8.00000 −0.254385
\(990\) 0 0
\(991\) 54.4745 1.73044 0.865219 0.501394i \(-0.167179\pi\)
0.865219 + 0.501394i \(0.167179\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 14.0000 0.443830
\(996\) 0 0
\(997\) −15.5128 −0.491294 −0.245647 0.969359i \(-0.579000\pi\)
−0.245647 + 0.969359i \(0.579000\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8280.2.a.bj.1.1 3
3.2 odd 2 920.2.a.h.1.3 3
12.11 even 2 1840.2.a.s.1.1 3
15.2 even 4 4600.2.e.p.4049.1 6
15.8 even 4 4600.2.e.p.4049.6 6
15.14 odd 2 4600.2.a.x.1.1 3
24.5 odd 2 7360.2.a.by.1.1 3
24.11 even 2 7360.2.a.cc.1.3 3
60.59 even 2 9200.2.a.ce.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.a.h.1.3 3 3.2 odd 2
1840.2.a.s.1.1 3 12.11 even 2
4600.2.a.x.1.1 3 15.14 odd 2
4600.2.e.p.4049.1 6 15.2 even 4
4600.2.e.p.4049.6 6 15.8 even 4
7360.2.a.by.1.1 3 24.5 odd 2
7360.2.a.cc.1.3 3 24.11 even 2
8280.2.a.bj.1.1 3 1.1 even 1 trivial
9200.2.a.ce.1.3 3 60.59 even 2