Properties

Label 8464.2.a.bd.1.2
Level $8464$
Weight $2$
Character 8464.1
Self dual yes
Analytic conductor $67.585$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8464 = 2^{4} \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8464.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(67.5853802708\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \(x^{2} - x - 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 184)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.56155\) of defining polynomial
Character \(\chi\) \(=\) 8464.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.56155 q^{3} -2.00000 q^{5} +3.56155 q^{9} +O(q^{10})\) \(q+2.56155 q^{3} -2.00000 q^{5} +3.56155 q^{9} +5.12311 q^{11} +4.56155 q^{13} -5.12311 q^{15} +3.12311 q^{17} +5.12311 q^{19} -1.00000 q^{25} +1.43845 q^{27} -0.561553 q^{29} +6.56155 q^{31} +13.1231 q^{33} +8.24621 q^{37} +11.6847 q^{39} +10.8078 q^{41} -8.00000 q^{43} -7.12311 q^{45} -11.6847 q^{47} -7.00000 q^{49} +8.00000 q^{51} -2.00000 q^{53} -10.2462 q^{55} +13.1231 q^{57} +6.24621 q^{59} -12.2462 q^{61} -9.12311 q^{65} -5.12311 q^{67} -9.43845 q^{71} -2.31534 q^{73} -2.56155 q^{75} -5.12311 q^{79} -7.00000 q^{81} -2.24621 q^{83} -6.24621 q^{85} -1.43845 q^{87} +13.3693 q^{89} +16.8078 q^{93} -10.2462 q^{95} +13.3693 q^{97} +18.2462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} - 4 q^{5} + 3 q^{9} + O(q^{10}) \) \( 2 q + q^{3} - 4 q^{5} + 3 q^{9} + 2 q^{11} + 5 q^{13} - 2 q^{15} - 2 q^{17} + 2 q^{19} - 2 q^{25} + 7 q^{27} + 3 q^{29} + 9 q^{31} + 18 q^{33} + 11 q^{39} + q^{41} - 16 q^{43} - 6 q^{45} - 11 q^{47} - 14 q^{49} + 16 q^{51} - 4 q^{53} - 4 q^{55} + 18 q^{57} - 4 q^{59} - 8 q^{61} - 10 q^{65} - 2 q^{67} - 23 q^{71} - 17 q^{73} - q^{75} - 2 q^{79} - 14 q^{81} + 12 q^{83} + 4 q^{85} - 7 q^{87} + 2 q^{89} + 13 q^{93} - 4 q^{95} + 2 q^{97} + 20 q^{99} + O(q^{100}) \)

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
\(3\) 2.56155 1.47891 0.739457 0.673204i \(-0.235083\pi\)
0.739457 + 0.673204i \(0.235083\pi\)
\(4\) 0 0
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 3.56155 1.18718
\(10\) 0 0
\(11\) 5.12311 1.54467 0.772337 0.635213i \(-0.219088\pi\)
0.772337 + 0.635213i \(0.219088\pi\)
\(12\) 0 0
\(13\) 4.56155 1.26515 0.632574 0.774500i \(-0.281999\pi\)
0.632574 + 0.774500i \(0.281999\pi\)
\(14\) 0 0
\(15\) −5.12311 −1.32278
\(16\) 0 0
\(17\) 3.12311 0.757464 0.378732 0.925506i \(-0.376360\pi\)
0.378732 + 0.925506i \(0.376360\pi\)
\(18\) 0 0
\(19\) 5.12311 1.17532 0.587661 0.809108i \(-0.300049\pi\)
0.587661 + 0.809108i \(0.300049\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 1.43845 0.276829
\(28\) 0 0
\(29\) −0.561553 −0.104278 −0.0521389 0.998640i \(-0.516604\pi\)
−0.0521389 + 0.998640i \(0.516604\pi\)
\(30\) 0 0
\(31\) 6.56155 1.17849 0.589245 0.807955i \(-0.299425\pi\)
0.589245 + 0.807955i \(0.299425\pi\)
\(32\) 0 0
\(33\) 13.1231 2.28444
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 8.24621 1.35567 0.677834 0.735215i \(-0.262919\pi\)
0.677834 + 0.735215i \(0.262919\pi\)
\(38\) 0 0
\(39\) 11.6847 1.87104
\(40\) 0 0
\(41\) 10.8078 1.68789 0.843945 0.536430i \(-0.180228\pi\)
0.843945 + 0.536430i \(0.180228\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) −7.12311 −1.06185
\(46\) 0 0
\(47\) −11.6847 −1.70438 −0.852191 0.523230i \(-0.824727\pi\)
−0.852191 + 0.523230i \(0.824727\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 8.00000 1.12022
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) −10.2462 −1.38160
\(56\) 0 0
\(57\) 13.1231 1.73820
\(58\) 0 0
\(59\) 6.24621 0.813187 0.406594 0.913609i \(-0.366716\pi\)
0.406594 + 0.913609i \(0.366716\pi\)
\(60\) 0 0
\(61\) −12.2462 −1.56797 −0.783983 0.620782i \(-0.786815\pi\)
−0.783983 + 0.620782i \(0.786815\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −9.12311 −1.13158
\(66\) 0 0
\(67\) −5.12311 −0.625887 −0.312943 0.949772i \(-0.601315\pi\)
−0.312943 + 0.949772i \(0.601315\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −9.43845 −1.12014 −0.560069 0.828446i \(-0.689225\pi\)
−0.560069 + 0.828446i \(0.689225\pi\)
\(72\) 0 0
\(73\) −2.31534 −0.270990 −0.135495 0.990778i \(-0.543263\pi\)
−0.135495 + 0.990778i \(0.543263\pi\)
\(74\) 0 0
\(75\) −2.56155 −0.295783
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −5.12311 −0.576394 −0.288197 0.957571i \(-0.593056\pi\)
−0.288197 + 0.957571i \(0.593056\pi\)
\(80\) 0 0
\(81\) −7.00000 −0.777778
\(82\) 0 0
\(83\) −2.24621 −0.246554 −0.123277 0.992372i \(-0.539340\pi\)
−0.123277 + 0.992372i \(0.539340\pi\)
\(84\) 0 0
\(85\) −6.24621 −0.677497
\(86\) 0 0
\(87\) −1.43845 −0.154218
\(88\) 0 0
\(89\) 13.3693 1.41714 0.708572 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 16.8078 1.74288
\(94\) 0 0
\(95\) −10.2462 −1.05124
\(96\) 0 0
\(97\) 13.3693 1.35745 0.678724 0.734393i \(-0.262533\pi\)
0.678724 + 0.734393i \(0.262533\pi\)
\(98\) 0 0
\(99\) 18.2462 1.83381
\(100\) 0 0
\(101\) −4.24621 −0.422514 −0.211257 0.977431i \(-0.567756\pi\)
−0.211257 + 0.977431i \(0.567756\pi\)
\(102\) 0 0
\(103\) 2.24621 0.221326 0.110663 0.993858i \(-0.464703\pi\)
0.110663 + 0.993858i \(0.464703\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.87689 0.278120 0.139060 0.990284i \(-0.455592\pi\)
0.139060 + 0.990284i \(0.455592\pi\)
\(108\) 0 0
\(109\) −4.87689 −0.467122 −0.233561 0.972342i \(-0.575038\pi\)
−0.233561 + 0.972342i \(0.575038\pi\)
\(110\) 0 0
\(111\) 21.1231 2.00492
\(112\) 0 0
\(113\) 11.1231 1.04637 0.523187 0.852218i \(-0.324743\pi\)
0.523187 + 0.852218i \(0.324743\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 16.2462 1.50196
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 15.2462 1.38602
\(122\) 0 0
\(123\) 27.6847 2.49624
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 11.6847 1.03685 0.518423 0.855124i \(-0.326519\pi\)
0.518423 + 0.855124i \(0.326519\pi\)
\(128\) 0 0
\(129\) −20.4924 −1.80426
\(130\) 0 0
\(131\) −15.6847 −1.37037 −0.685187 0.728367i \(-0.740280\pi\)
−0.685187 + 0.728367i \(0.740280\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −2.87689 −0.247604
\(136\) 0 0
\(137\) −15.1231 −1.29205 −0.646027 0.763315i \(-0.723571\pi\)
−0.646027 + 0.763315i \(0.723571\pi\)
\(138\) 0 0
\(139\) 15.6847 1.33036 0.665178 0.746685i \(-0.268356\pi\)
0.665178 + 0.746685i \(0.268356\pi\)
\(140\) 0 0
\(141\) −29.9309 −2.52063
\(142\) 0 0
\(143\) 23.3693 1.95424
\(144\) 0 0
\(145\) 1.12311 0.0932688
\(146\) 0 0
\(147\) −17.9309 −1.47891
\(148\) 0 0
\(149\) 3.75379 0.307522 0.153761 0.988108i \(-0.450861\pi\)
0.153761 + 0.988108i \(0.450861\pi\)
\(150\) 0 0
\(151\) 14.5616 1.18500 0.592501 0.805570i \(-0.298141\pi\)
0.592501 + 0.805570i \(0.298141\pi\)
\(152\) 0 0
\(153\) 11.1231 0.899250
\(154\) 0 0
\(155\) −13.1231 −1.05407
\(156\) 0 0
\(157\) −12.8769 −1.02769 −0.513844 0.857884i \(-0.671779\pi\)
−0.513844 + 0.857884i \(0.671779\pi\)
\(158\) 0 0
\(159\) −5.12311 −0.406289
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 9.93087 0.777846 0.388923 0.921270i \(-0.372847\pi\)
0.388923 + 0.921270i \(0.372847\pi\)
\(164\) 0 0
\(165\) −26.2462 −2.04326
\(166\) 0 0
\(167\) 16.0000 1.23812 0.619059 0.785345i \(-0.287514\pi\)
0.619059 + 0.785345i \(0.287514\pi\)
\(168\) 0 0
\(169\) 7.80776 0.600597
\(170\) 0 0
\(171\) 18.2462 1.39532
\(172\) 0 0
\(173\) −10.0000 −0.760286 −0.380143 0.924928i \(-0.624125\pi\)
−0.380143 + 0.924928i \(0.624125\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 16.0000 1.20263
\(178\) 0 0
\(179\) 15.6847 1.17233 0.586163 0.810193i \(-0.300638\pi\)
0.586163 + 0.810193i \(0.300638\pi\)
\(180\) 0 0
\(181\) −20.2462 −1.50489 −0.752445 0.658656i \(-0.771125\pi\)
−0.752445 + 0.658656i \(0.771125\pi\)
\(182\) 0 0
\(183\) −31.3693 −2.31889
\(184\) 0 0
\(185\) −16.4924 −1.21255
\(186\) 0 0
\(187\) 16.0000 1.17004
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0.630683 0.0456346 0.0228173 0.999740i \(-0.492736\pi\)
0.0228173 + 0.999740i \(0.492736\pi\)
\(192\) 0 0
\(193\) −4.56155 −0.328348 −0.164174 0.986431i \(-0.552496\pi\)
−0.164174 + 0.986431i \(0.552496\pi\)
\(194\) 0 0
\(195\) −23.3693 −1.67351
\(196\) 0 0
\(197\) 11.9309 0.850039 0.425020 0.905184i \(-0.360267\pi\)
0.425020 + 0.905184i \(0.360267\pi\)
\(198\) 0 0
\(199\) 2.87689 0.203938 0.101969 0.994788i \(-0.467486\pi\)
0.101969 + 0.994788i \(0.467486\pi\)
\(200\) 0 0
\(201\) −13.1231 −0.925633
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −21.6155 −1.50969
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 26.2462 1.81549
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) −24.1771 −1.65659
\(214\) 0 0
\(215\) 16.0000 1.09119
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −5.93087 −0.400771
\(220\) 0 0
\(221\) 14.2462 0.958304
\(222\) 0 0
\(223\) −4.49242 −0.300835 −0.150417 0.988623i \(-0.548062\pi\)
−0.150417 + 0.988623i \(0.548062\pi\)
\(224\) 0 0
\(225\) −3.56155 −0.237437
\(226\) 0 0
\(227\) 10.2462 0.680065 0.340032 0.940414i \(-0.389562\pi\)
0.340032 + 0.940414i \(0.389562\pi\)
\(228\) 0 0
\(229\) −23.1231 −1.52802 −0.764009 0.645206i \(-0.776772\pi\)
−0.764009 + 0.645206i \(0.776772\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 21.0540 1.37929 0.689646 0.724147i \(-0.257766\pi\)
0.689646 + 0.724147i \(0.257766\pi\)
\(234\) 0 0
\(235\) 23.3693 1.52445
\(236\) 0 0
\(237\) −13.1231 −0.852437
\(238\) 0 0
\(239\) 11.0540 0.715022 0.357511 0.933909i \(-0.383625\pi\)
0.357511 + 0.933909i \(0.383625\pi\)
\(240\) 0 0
\(241\) 26.4924 1.70653 0.853263 0.521480i \(-0.174620\pi\)
0.853263 + 0.521480i \(0.174620\pi\)
\(242\) 0 0
\(243\) −22.2462 −1.42710
\(244\) 0 0
\(245\) 14.0000 0.894427
\(246\) 0 0
\(247\) 23.3693 1.48695
\(248\) 0 0
\(249\) −5.75379 −0.364632
\(250\) 0 0
\(251\) 10.2462 0.646735 0.323368 0.946273i \(-0.395185\pi\)
0.323368 + 0.946273i \(0.395185\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −16.0000 −1.00196
\(256\) 0 0
\(257\) −17.6847 −1.10314 −0.551569 0.834129i \(-0.685971\pi\)
−0.551569 + 0.834129i \(0.685971\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −2.00000 −0.123797
\(262\) 0 0
\(263\) −10.8769 −0.670698 −0.335349 0.942094i \(-0.608854\pi\)
−0.335349 + 0.942094i \(0.608854\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) 0 0
\(267\) 34.2462 2.09583
\(268\) 0 0
\(269\) 25.6847 1.56602 0.783011 0.622008i \(-0.213683\pi\)
0.783011 + 0.622008i \(0.213683\pi\)
\(270\) 0 0
\(271\) −24.0000 −1.45790 −0.728948 0.684569i \(-0.759990\pi\)
−0.728948 + 0.684569i \(0.759990\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.12311 −0.308935
\(276\) 0 0
\(277\) −2.80776 −0.168702 −0.0843511 0.996436i \(-0.526882\pi\)
−0.0843511 + 0.996436i \(0.526882\pi\)
\(278\) 0 0
\(279\) 23.3693 1.39908
\(280\) 0 0
\(281\) 3.12311 0.186309 0.0931544 0.995652i \(-0.470305\pi\)
0.0931544 + 0.995652i \(0.470305\pi\)
\(282\) 0 0
\(283\) −5.12311 −0.304537 −0.152269 0.988339i \(-0.548658\pi\)
−0.152269 + 0.988339i \(0.548658\pi\)
\(284\) 0 0
\(285\) −26.2462 −1.55469
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −7.24621 −0.426248
\(290\) 0 0
\(291\) 34.2462 2.00755
\(292\) 0 0
\(293\) −9.36932 −0.547361 −0.273681 0.961821i \(-0.588241\pi\)
−0.273681 + 0.961821i \(0.588241\pi\)
\(294\) 0 0
\(295\) −12.4924 −0.727337
\(296\) 0 0
\(297\) 7.36932 0.427611
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −10.8769 −0.624861
\(304\) 0 0
\(305\) 24.4924 1.40243
\(306\) 0 0
\(307\) 1.75379 0.100094 0.0500470 0.998747i \(-0.484063\pi\)
0.0500470 + 0.998747i \(0.484063\pi\)
\(308\) 0 0
\(309\) 5.75379 0.327322
\(310\) 0 0
\(311\) −1.43845 −0.0815669 −0.0407834 0.999168i \(-0.512985\pi\)
−0.0407834 + 0.999168i \(0.512985\pi\)
\(312\) 0 0
\(313\) −9.36932 −0.529585 −0.264793 0.964305i \(-0.585303\pi\)
−0.264793 + 0.964305i \(0.585303\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −20.2462 −1.13714 −0.568570 0.822635i \(-0.692503\pi\)
−0.568570 + 0.822635i \(0.692503\pi\)
\(318\) 0 0
\(319\) −2.87689 −0.161075
\(320\) 0 0
\(321\) 7.36932 0.411315
\(322\) 0 0
\(323\) 16.0000 0.890264
\(324\) 0 0
\(325\) −4.56155 −0.253029
\(326\) 0 0
\(327\) −12.4924 −0.690833
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 30.4233 1.67222 0.836108 0.548565i \(-0.184826\pi\)
0.836108 + 0.548565i \(0.184826\pi\)
\(332\) 0 0
\(333\) 29.3693 1.60943
\(334\) 0 0
\(335\) 10.2462 0.559810
\(336\) 0 0
\(337\) −19.6155 −1.06853 −0.534263 0.845318i \(-0.679411\pi\)
−0.534263 + 0.845318i \(0.679411\pi\)
\(338\) 0 0
\(339\) 28.4924 1.54750
\(340\) 0 0
\(341\) 33.6155 1.82038
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −16.4924 −0.885360 −0.442680 0.896680i \(-0.645972\pi\)
−0.442680 + 0.896680i \(0.645972\pi\)
\(348\) 0 0
\(349\) −22.3153 −1.19451 −0.597256 0.802050i \(-0.703743\pi\)
−0.597256 + 0.802050i \(0.703743\pi\)
\(350\) 0 0
\(351\) 6.56155 0.350230
\(352\) 0 0
\(353\) 11.4384 0.608807 0.304404 0.952543i \(-0.401543\pi\)
0.304404 + 0.952543i \(0.401543\pi\)
\(354\) 0 0
\(355\) 18.8769 1.00188
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 17.6155 0.929712 0.464856 0.885386i \(-0.346106\pi\)
0.464856 + 0.885386i \(0.346106\pi\)
\(360\) 0 0
\(361\) 7.24621 0.381380
\(362\) 0 0
\(363\) 39.0540 2.04980
\(364\) 0 0
\(365\) 4.63068 0.242381
\(366\) 0 0
\(367\) 2.24621 0.117251 0.0586256 0.998280i \(-0.481328\pi\)
0.0586256 + 0.998280i \(0.481328\pi\)
\(368\) 0 0
\(369\) 38.4924 2.00384
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −22.4924 −1.16461 −0.582307 0.812969i \(-0.697850\pi\)
−0.582307 + 0.812969i \(0.697850\pi\)
\(374\) 0 0
\(375\) 30.7386 1.58734
\(376\) 0 0
\(377\) −2.56155 −0.131927
\(378\) 0 0
\(379\) 20.4924 1.05263 0.526313 0.850291i \(-0.323574\pi\)
0.526313 + 0.850291i \(0.323574\pi\)
\(380\) 0 0
\(381\) 29.9309 1.53340
\(382\) 0 0
\(383\) 26.2462 1.34112 0.670559 0.741856i \(-0.266054\pi\)
0.670559 + 0.741856i \(0.266054\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −28.4924 −1.44835
\(388\) 0 0
\(389\) −1.36932 −0.0694271 −0.0347136 0.999397i \(-0.511052\pi\)
−0.0347136 + 0.999397i \(0.511052\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −40.1771 −2.02667
\(394\) 0 0
\(395\) 10.2462 0.515543
\(396\) 0 0
\(397\) 20.5616 1.03195 0.515977 0.856602i \(-0.327429\pi\)
0.515977 + 0.856602i \(0.327429\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 11.7538 0.586956 0.293478 0.955966i \(-0.405187\pi\)
0.293478 + 0.955966i \(0.405187\pi\)
\(402\) 0 0
\(403\) 29.9309 1.49096
\(404\) 0 0
\(405\) 14.0000 0.695666
\(406\) 0 0
\(407\) 42.2462 2.09407
\(408\) 0 0
\(409\) −27.3002 −1.34991 −0.674954 0.737860i \(-0.735836\pi\)
−0.674954 + 0.737860i \(0.735836\pi\)
\(410\) 0 0
\(411\) −38.7386 −1.91084
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 4.49242 0.220524
\(416\) 0 0
\(417\) 40.1771 1.96748
\(418\) 0 0
\(419\) −12.4924 −0.610295 −0.305147 0.952305i \(-0.598706\pi\)
−0.305147 + 0.952305i \(0.598706\pi\)
\(420\) 0 0
\(421\) 27.1231 1.32190 0.660950 0.750430i \(-0.270154\pi\)
0.660950 + 0.750430i \(0.270154\pi\)
\(422\) 0 0
\(423\) −41.6155 −2.02342
\(424\) 0 0
\(425\) −3.12311 −0.151493
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 59.8617 2.89015
\(430\) 0 0
\(431\) −28.4924 −1.37243 −0.686216 0.727398i \(-0.740729\pi\)
−0.686216 + 0.727398i \(0.740729\pi\)
\(432\) 0 0
\(433\) −24.7386 −1.18886 −0.594431 0.804146i \(-0.702623\pi\)
−0.594431 + 0.804146i \(0.702623\pi\)
\(434\) 0 0
\(435\) 2.87689 0.137937
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −11.0540 −0.527577 −0.263789 0.964580i \(-0.584972\pi\)
−0.263789 + 0.964580i \(0.584972\pi\)
\(440\) 0 0
\(441\) −24.9309 −1.18718
\(442\) 0 0
\(443\) 6.06913 0.288353 0.144177 0.989552i \(-0.453947\pi\)
0.144177 + 0.989552i \(0.453947\pi\)
\(444\) 0 0
\(445\) −26.7386 −1.26753
\(446\) 0 0
\(447\) 9.61553 0.454799
\(448\) 0 0
\(449\) −8.24621 −0.389163 −0.194581 0.980886i \(-0.562335\pi\)
−0.194581 + 0.980886i \(0.562335\pi\)
\(450\) 0 0
\(451\) 55.3693 2.60724
\(452\) 0 0
\(453\) 37.3002 1.75252
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 5.36932 0.251166 0.125583 0.992083i \(-0.459920\pi\)
0.125583 + 0.992083i \(0.459920\pi\)
\(458\) 0 0
\(459\) 4.49242 0.209688
\(460\) 0 0
\(461\) −10.8078 −0.503368 −0.251684 0.967809i \(-0.580984\pi\)
−0.251684 + 0.967809i \(0.580984\pi\)
\(462\) 0 0
\(463\) −12.4924 −0.580572 −0.290286 0.956940i \(-0.593750\pi\)
−0.290286 + 0.956940i \(0.593750\pi\)
\(464\) 0 0
\(465\) −33.6155 −1.55888
\(466\) 0 0
\(467\) −15.3693 −0.711207 −0.355604 0.934637i \(-0.615725\pi\)
−0.355604 + 0.934637i \(0.615725\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −32.9848 −1.51986
\(472\) 0 0
\(473\) −40.9848 −1.88449
\(474\) 0 0
\(475\) −5.12311 −0.235064
\(476\) 0 0
\(477\) −7.12311 −0.326145
\(478\) 0 0
\(479\) 10.2462 0.468161 0.234081 0.972217i \(-0.424792\pi\)
0.234081 + 0.972217i \(0.424792\pi\)
\(480\) 0 0
\(481\) 37.6155 1.71512
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −26.7386 −1.21414
\(486\) 0 0
\(487\) −12.3153 −0.558061 −0.279031 0.960282i \(-0.590013\pi\)
−0.279031 + 0.960282i \(0.590013\pi\)
\(488\) 0 0
\(489\) 25.4384 1.15037
\(490\) 0 0
\(491\) −12.8078 −0.578006 −0.289003 0.957328i \(-0.593324\pi\)
−0.289003 + 0.957328i \(0.593324\pi\)
\(492\) 0 0
\(493\) −1.75379 −0.0789867
\(494\) 0 0
\(495\) −36.4924 −1.64021
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 23.0540 1.03204 0.516019 0.856577i \(-0.327413\pi\)
0.516019 + 0.856577i \(0.327413\pi\)
\(500\) 0 0
\(501\) 40.9848 1.83107
\(502\) 0 0
\(503\) 7.36932 0.328582 0.164291 0.986412i \(-0.447466\pi\)
0.164291 + 0.986412i \(0.447466\pi\)
\(504\) 0 0
\(505\) 8.49242 0.377908
\(506\) 0 0
\(507\) 20.0000 0.888231
\(508\) 0 0
\(509\) −15.3002 −0.678169 −0.339084 0.940756i \(-0.610117\pi\)
−0.339084 + 0.940756i \(0.610117\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 7.36932 0.325363
\(514\) 0 0
\(515\) −4.49242 −0.197960
\(516\) 0 0
\(517\) −59.8617 −2.63272
\(518\) 0 0
\(519\) −25.6155 −1.12440
\(520\) 0 0
\(521\) −19.6155 −0.859372 −0.429686 0.902978i \(-0.641376\pi\)
−0.429686 + 0.902978i \(0.641376\pi\)
\(522\) 0 0
\(523\) 5.75379 0.251596 0.125798 0.992056i \(-0.459851\pi\)
0.125798 + 0.992056i \(0.459851\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 20.4924 0.892664
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 22.2462 0.965403
\(532\) 0 0
\(533\) 49.3002 2.13543
\(534\) 0 0
\(535\) −5.75379 −0.248758
\(536\) 0 0
\(537\) 40.1771 1.73377
\(538\) 0 0
\(539\) −35.8617 −1.54467
\(540\) 0 0
\(541\) 35.9309 1.54479 0.772394 0.635143i \(-0.219059\pi\)
0.772394 + 0.635143i \(0.219059\pi\)
\(542\) 0 0
\(543\) −51.8617 −2.22560
\(544\) 0 0
\(545\) 9.75379 0.417806
\(546\) 0 0
\(547\) −43.5464 −1.86191 −0.930955 0.365135i \(-0.881023\pi\)
−0.930955 + 0.365135i \(0.881023\pi\)
\(548\) 0 0
\(549\) −43.6155 −1.86147
\(550\) 0 0
\(551\) −2.87689 −0.122560
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −42.2462 −1.79325
\(556\) 0 0
\(557\) 0.876894 0.0371552 0.0185776 0.999827i \(-0.494086\pi\)
0.0185776 + 0.999827i \(0.494086\pi\)
\(558\) 0 0
\(559\) −36.4924 −1.54347
\(560\) 0 0
\(561\) 40.9848 1.73038
\(562\) 0 0
\(563\) 5.75379 0.242493 0.121247 0.992622i \(-0.461311\pi\)
0.121247 + 0.992622i \(0.461311\pi\)
\(564\) 0 0
\(565\) −22.2462 −0.935905
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.24621 0.345699 0.172850 0.984948i \(-0.444703\pi\)
0.172850 + 0.984948i \(0.444703\pi\)
\(570\) 0 0
\(571\) −11.5076 −0.481577 −0.240789 0.970578i \(-0.577406\pi\)
−0.240789 + 0.970578i \(0.577406\pi\)
\(572\) 0 0
\(573\) 1.61553 0.0674897
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 15.9309 0.663211 0.331605 0.943418i \(-0.392410\pi\)
0.331605 + 0.943418i \(0.392410\pi\)
\(578\) 0 0
\(579\) −11.6847 −0.485598
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −10.2462 −0.424355
\(584\) 0 0
\(585\) −32.4924 −1.34340
\(586\) 0 0
\(587\) 23.0540 0.951539 0.475770 0.879570i \(-0.342170\pi\)
0.475770 + 0.879570i \(0.342170\pi\)
\(588\) 0 0
\(589\) 33.6155 1.38510
\(590\) 0 0
\(591\) 30.5616 1.25713
\(592\) 0 0
\(593\) −44.7386 −1.83720 −0.918598 0.395194i \(-0.870677\pi\)
−0.918598 + 0.395194i \(0.870677\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 7.36932 0.301606
\(598\) 0 0
\(599\) −8.00000 −0.326871 −0.163436 0.986554i \(-0.552258\pi\)
−0.163436 + 0.986554i \(0.552258\pi\)
\(600\) 0 0
\(601\) −38.8078 −1.58300 −0.791501 0.611168i \(-0.790700\pi\)
−0.791501 + 0.611168i \(0.790700\pi\)
\(602\) 0 0
\(603\) −18.2462 −0.743043
\(604\) 0 0
\(605\) −30.4924 −1.23969
\(606\) 0 0
\(607\) 14.7386 0.598223 0.299111 0.954218i \(-0.403310\pi\)
0.299111 + 0.954218i \(0.403310\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −53.3002 −2.15629
\(612\) 0 0
\(613\) 28.1080 1.13527 0.567635 0.823281i \(-0.307859\pi\)
0.567635 + 0.823281i \(0.307859\pi\)
\(614\) 0 0
\(615\) −55.3693 −2.23271
\(616\) 0 0
\(617\) −34.9848 −1.40844 −0.704218 0.709983i \(-0.748702\pi\)
−0.704218 + 0.709983i \(0.748702\pi\)
\(618\) 0 0
\(619\) 28.4924 1.14521 0.572604 0.819832i \(-0.305933\pi\)
0.572604 + 0.819832i \(0.305933\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 0 0
\(627\) 67.2311 2.68495
\(628\) 0 0
\(629\) 25.7538 1.02687
\(630\) 0 0
\(631\) −6.73863 −0.268261 −0.134130 0.990964i \(-0.542824\pi\)
−0.134130 + 0.990964i \(0.542824\pi\)
\(632\) 0 0
\(633\) 10.2462 0.407250
\(634\) 0 0
\(635\) −23.3693 −0.927383
\(636\) 0 0
\(637\) −31.9309 −1.26515
\(638\) 0 0
\(639\) −33.6155 −1.32981
\(640\) 0 0
\(641\) 13.3693 0.528056 0.264028 0.964515i \(-0.414949\pi\)
0.264028 + 0.964515i \(0.414949\pi\)
\(642\) 0 0
\(643\) −23.3693 −0.921596 −0.460798 0.887505i \(-0.652437\pi\)
−0.460798 + 0.887505i \(0.652437\pi\)
\(644\) 0 0
\(645\) 40.9848 1.61378
\(646\) 0 0
\(647\) 29.3002 1.15191 0.575955 0.817482i \(-0.304630\pi\)
0.575955 + 0.817482i \(0.304630\pi\)
\(648\) 0 0
\(649\) 32.0000 1.25611
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 25.0540 0.980438 0.490219 0.871599i \(-0.336917\pi\)
0.490219 + 0.871599i \(0.336917\pi\)
\(654\) 0 0
\(655\) 31.3693 1.22570
\(656\) 0 0
\(657\) −8.24621 −0.321715
\(658\) 0 0
\(659\) 2.24621 0.0875000 0.0437500 0.999043i \(-0.486070\pi\)
0.0437500 + 0.999043i \(0.486070\pi\)
\(660\) 0 0
\(661\) 0.246211 0.00957651 0.00478825 0.999989i \(-0.498476\pi\)
0.00478825 + 0.999989i \(0.498476\pi\)
\(662\) 0 0
\(663\) 36.4924 1.41725
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −11.5076 −0.444909
\(670\) 0 0
\(671\) −62.7386 −2.42200
\(672\) 0 0
\(673\) −2.94602 −0.113561 −0.0567805 0.998387i \(-0.518084\pi\)
−0.0567805 + 0.998387i \(0.518084\pi\)
\(674\) 0 0
\(675\) −1.43845 −0.0553659
\(676\) 0 0
\(677\) 38.9848 1.49831 0.749155 0.662395i \(-0.230460\pi\)
0.749155 + 0.662395i \(0.230460\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 26.2462 1.00576
\(682\) 0 0
\(683\) −16.3153 −0.624289 −0.312145 0.950035i \(-0.601047\pi\)
−0.312145 + 0.950035i \(0.601047\pi\)
\(684\) 0 0
\(685\) 30.2462 1.15565
\(686\) 0 0
\(687\) −59.2311 −2.25981
\(688\) 0 0
\(689\) −9.12311 −0.347563
\(690\) 0 0
\(691\) −20.9848 −0.798301 −0.399151 0.916885i \(-0.630695\pi\)
−0.399151 + 0.916885i \(0.630695\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −31.3693 −1.18991
\(696\) 0 0
\(697\) 33.7538 1.27852
\(698\) 0 0
\(699\) 53.9309 2.03985
\(700\) 0 0
\(701\) −29.8617 −1.12786 −0.563931 0.825822i \(-0.690712\pi\)
−0.563931 + 0.825822i \(0.690712\pi\)
\(702\) 0 0
\(703\) 42.2462 1.59335
\(704\) 0 0
\(705\) 59.8617 2.25452
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 37.3693 1.40343 0.701717 0.712456i \(-0.252417\pi\)
0.701717 + 0.712456i \(0.252417\pi\)
\(710\) 0 0
\(711\) −18.2462 −0.684286
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −46.7386 −1.74793
\(716\) 0 0
\(717\) 28.3153 1.05746
\(718\) 0 0
\(719\) −4.49242 −0.167539 −0.0837695 0.996485i \(-0.526696\pi\)
−0.0837695 + 0.996485i \(0.526696\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 67.8617 2.52381
\(724\) 0 0
\(725\) 0.561553 0.0208555
\(726\) 0 0
\(727\) −39.3693 −1.46013 −0.730064 0.683379i \(-0.760510\pi\)
−0.730064 + 0.683379i \(0.760510\pi\)
\(728\) 0 0
\(729\) −35.9848 −1.33277
\(730\) 0 0
\(731\) −24.9848 −0.924098
\(732\) 0 0
\(733\) −49.3693 −1.82350 −0.911749 0.410749i \(-0.865267\pi\)
−0.911749 + 0.410749i \(0.865267\pi\)
\(734\) 0 0
\(735\) 35.8617 1.32278
\(736\) 0 0
\(737\) −26.2462 −0.966792
\(738\) 0 0
\(739\) −0.315342 −0.0116000 −0.00580001 0.999983i \(-0.501846\pi\)
−0.00580001 + 0.999983i \(0.501846\pi\)
\(740\) 0 0
\(741\) 59.8617 2.19908
\(742\) 0 0
\(743\) 34.2462 1.25637 0.628186 0.778063i \(-0.283798\pi\)
0.628186 + 0.778063i \(0.283798\pi\)
\(744\) 0 0
\(745\) −7.50758 −0.275056
\(746\) 0 0
\(747\) −8.00000 −0.292705
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 40.9848 1.49556 0.747779 0.663948i \(-0.231120\pi\)
0.747779 + 0.663948i \(0.231120\pi\)
\(752\) 0 0
\(753\) 26.2462 0.956465
\(754\) 0 0
\(755\) −29.1231 −1.05990
\(756\) 0 0
\(757\) 1.50758 0.0547938 0.0273969 0.999625i \(-0.491278\pi\)
0.0273969 + 0.999625i \(0.491278\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −18.3153 −0.663931 −0.331965 0.943292i \(-0.607712\pi\)
−0.331965 + 0.943292i \(0.607712\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −22.2462 −0.804313
\(766\) 0 0
\(767\) 28.4924 1.02880
\(768\) 0 0
\(769\) 6.00000 0.216366 0.108183 0.994131i \(-0.465497\pi\)
0.108183 + 0.994131i \(0.465497\pi\)
\(770\) 0 0
\(771\) −45.3002 −1.63145
\(772\) 0 0
\(773\) −2.63068 −0.0946191 −0.0473095 0.998880i \(-0.515065\pi\)
−0.0473095 + 0.998880i \(0.515065\pi\)
\(774\) 0 0
\(775\) −6.56155 −0.235698
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 55.3693 1.98381
\(780\) 0 0
\(781\) −48.3542 −1.73025
\(782\) 0 0
\(783\) −0.807764 −0.0288671
\(784\) 0 0
\(785\) 25.7538 0.919192
\(786\) 0 0
\(787\) −26.2462 −0.935576 −0.467788 0.883841i \(-0.654949\pi\)
−0.467788 + 0.883841i \(0.654949\pi\)
\(788\) 0 0
\(789\) −27.8617 −0.991904
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −55.8617 −1.98371
\(794\) 0 0
\(795\) 10.2462 0.363396
\(796\) 0 0
\(797\) −12.2462 −0.433783 −0.216892 0.976196i \(-0.569592\pi\)
−0.216892 + 0.976196i \(0.569592\pi\)
\(798\) 0 0
\(799\) −36.4924 −1.29101
\(800\) 0 0
\(801\) 47.6155 1.68241
\(802\) 0 0
\(803\) −11.8617 −0.418592
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 65.7926 2.31601
\(808\) 0 0
\(809\) 26.0000 0.914111 0.457056 0.889438i \(-0.348904\pi\)
0.457056 + 0.889438i \(0.348904\pi\)
\(810\) 0 0
\(811\) −33.9309 −1.19147 −0.595737 0.803180i \(-0.703140\pi\)
−0.595737 + 0.803180i \(0.703140\pi\)
\(812\) 0 0
\(813\) −61.4773 −2.15610
\(814\) 0 0
\(815\) −19.8617 −0.695726
\(816\) 0 0
\(817\) −40.9848 −1.43388
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −24.7386 −0.863384 −0.431692 0.902021i \(-0.642083\pi\)
−0.431692 + 0.902021i \(0.642083\pi\)
\(822\) 0 0
\(823\) −49.4384 −1.72332 −0.861658 0.507489i \(-0.830574\pi\)
−0.861658 + 0.507489i \(0.830574\pi\)
\(824\) 0 0
\(825\) −13.1231 −0.456888
\(826\) 0 0
\(827\) 4.49242 0.156217 0.0781084 0.996945i \(-0.475112\pi\)
0.0781084 + 0.996945i \(0.475112\pi\)
\(828\) 0 0
\(829\) −20.2462 −0.703180 −0.351590 0.936154i \(-0.614359\pi\)
−0.351590 + 0.936154i \(0.614359\pi\)
\(830\) 0 0
\(831\) −7.19224 −0.249496
\(832\) 0 0
\(833\) −21.8617 −0.757464
\(834\) 0 0
\(835\) −32.0000 −1.10741
\(836\) 0 0
\(837\) 9.43845 0.326240
\(838\) 0 0
\(839\) 50.2462 1.73469 0.867346 0.497706i \(-0.165824\pi\)
0.867346 + 0.497706i \(0.165824\pi\)
\(840\) 0 0
\(841\) −28.6847 −0.989126
\(842\) 0 0
\(843\) 8.00000 0.275535
\(844\) 0 0
\(845\) −15.6155 −0.537190
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −13.1231 −0.450384
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −34.9848 −1.19786 −0.598929 0.800802i \(-0.704407\pi\)
−0.598929 + 0.800802i \(0.704407\pi\)
\(854\) 0 0
\(855\) −36.4924 −1.24801
\(856\) 0 0
\(857\) 16.5616 0.565732 0.282866 0.959159i \(-0.408715\pi\)
0.282866 + 0.959159i \(0.408715\pi\)
\(858\) 0 0
\(859\) −16.9460 −0.578191 −0.289095 0.957300i \(-0.593354\pi\)
−0.289095 + 0.957300i \(0.593354\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 8.17708 0.278351 0.139176 0.990268i \(-0.455555\pi\)
0.139176 + 0.990268i \(0.455555\pi\)
\(864\) 0 0
\(865\) 20.0000 0.680020
\(866\) 0 0
\(867\) −18.5616 −0.630383
\(868\) 0 0
\(869\) −26.2462 −0.890342
\(870\) 0 0
\(871\) −23.3693 −0.791839
\(872\) 0 0
\(873\) 47.6155 1.61154
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 30.9848 1.04628 0.523142 0.852246i \(-0.324760\pi\)
0.523142 + 0.852246i \(0.324760\pi\)
\(878\) 0 0
\(879\) −24.0000 −0.809500
\(880\) 0 0
\(881\) −4.87689 −0.164307 −0.0821534 0.996620i \(-0.526180\pi\)
−0.0821534 + 0.996620i \(0.526180\pi\)
\(882\) 0 0
\(883\) −36.9848 −1.24464 −0.622320 0.782763i \(-0.713810\pi\)
−0.622320 + 0.782763i \(0.713810\pi\)
\(884\) 0 0
\(885\) −32.0000 −1.07567
\(886\) 0 0
\(887\) −19.6847 −0.660946 −0.330473 0.943815i \(-0.607208\pi\)
−0.330473 + 0.943815i \(0.607208\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −35.8617 −1.20141
\(892\) 0 0
\(893\) −59.8617 −2.00320
\(894\) 0 0
\(895\) −31.3693 −1.04856
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −3.68466 −0.122890
\(900\) 0 0
\(901\) −6.24621 −0.208091
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 40.4924 1.34601
\(906\) 0 0
\(907\) 42.8769 1.42370 0.711852 0.702330i \(-0.247857\pi\)
0.711852 + 0.702330i \(0.247857\pi\)
\(908\) 0 0
\(909\) −15.1231 −0.501602
\(910\) 0 0
\(911\) −37.1231 −1.22994 −0.614972 0.788549i \(-0.710833\pi\)
−0.614972 + 0.788549i \(0.710833\pi\)
\(912\) 0 0
\(913\) −11.5076 −0.380845
\(914\) 0 0
\(915\) 62.7386 2.07408
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 37.7538 1.24538 0.622691 0.782468i \(-0.286039\pi\)
0.622691 + 0.782468i \(0.286039\pi\)
\(920\) 0 0
\(921\) 4.49242 0.148030
\(922\) 0 0
\(923\) −43.0540 −1.41714
\(924\) 0 0
\(925\) −8.24621 −0.271134
\(926\) 0 0
\(927\) 8.00000 0.262754
\(928\) 0 0
\(929\) 34.8078 1.14201 0.571003 0.820948i \(-0.306555\pi\)
0.571003 + 0.820948i \(0.306555\pi\)
\(930\) 0 0
\(931\) −35.8617 −1.17532
\(932\) 0 0
\(933\) −3.68466 −0.120630
\(934\) 0 0
\(935\) −32.0000 −1.04651
\(936\) 0 0
\(937\) −15.7538 −0.514654 −0.257327 0.966324i \(-0.582842\pi\)
−0.257327 + 0.966324i \(0.582842\pi\)
\(938\) 0 0
\(939\) −24.0000 −0.783210
\(940\) 0 0
\(941\) −39.1231 −1.27538 −0.637688 0.770294i \(-0.720109\pi\)
−0.637688 + 0.770294i \(0.720109\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.56155 0.0832393 0.0416196 0.999134i \(-0.486748\pi\)
0.0416196 + 0.999134i \(0.486748\pi\)
\(948\) 0 0
\(949\) −10.5616 −0.342843
\(950\) 0 0
\(951\) −51.8617 −1.68173
\(952\) 0 0
\(953\) −44.2462 −1.43328 −0.716638 0.697446i \(-0.754320\pi\)
−0.716638 + 0.697446i \(0.754320\pi\)
\(954\) 0 0
\(955\) −1.26137 −0.0408169
\(956\) 0 0
\(957\) −7.36932 −0.238216
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 12.0540 0.388838
\(962\) 0 0
\(963\) 10.2462 0.330180
\(964\) 0 0
\(965\) 9.12311 0.293683
\(966\) 0 0
\(967\) −35.0540 −1.12726 −0.563630 0.826027i \(-0.690596\pi\)
−0.563630 + 0.826027i \(0.690596\pi\)
\(968\) 0 0
\(969\) 40.9848 1.31662
\(970\) 0 0
\(971\) 31.3693 1.00669 0.503345 0.864086i \(-0.332103\pi\)
0.503345 + 0.864086i \(0.332103\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −11.6847 −0.374209
\(976\) 0 0
\(977\) 57.2311 1.83098 0.915492 0.402337i \(-0.131802\pi\)
0.915492 + 0.402337i \(0.131802\pi\)
\(978\) 0 0
\(979\) 68.4924 2.18903
\(980\) 0 0
\(981\) −17.3693 −0.554560
\(982\) 0 0
\(983\) 22.1080 0.705134 0.352567 0.935787i \(-0.385309\pi\)
0.352567 + 0.935787i \(0.385309\pi\)
\(984\) 0 0
\(985\) −23.8617 −0.760298
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −8.98485 −0.285413 −0.142707 0.989765i \(-0.545581\pi\)
−0.142707 + 0.989765i \(0.545581\pi\)
\(992\) 0 0
\(993\) 77.9309 2.47306
\(994\) 0 0
\(995\) −5.75379 −0.182407
\(996\) 0 0
\(997\) 14.0000 0.443384 0.221692 0.975117i \(-0.428842\pi\)
0.221692 + 0.975117i \(0.428842\pi\)
\(998\) 0 0
\(999\) 11.8617 0.375289
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 8464.2.a.bd.1.2 2
4.3 odd 2 4232.2.a.o.1.1 2
23.22 odd 2 368.2.a.i.1.2 2
69.68 even 2 3312.2.a.t.1.2 2
92.91 even 2 184.2.a.e.1.1 2
115.114 odd 2 9200.2.a.br.1.1 2
184.45 odd 2 1472.2.a.p.1.1 2
184.91 even 2 1472.2.a.u.1.2 2
276.275 odd 2 1656.2.a.j.1.1 2
460.183 odd 4 4600.2.e.o.4049.1 4
460.367 odd 4 4600.2.e.o.4049.4 4
460.459 even 2 4600.2.a.s.1.2 2
644.643 odd 2 9016.2.a.w.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
184.2.a.e.1.1 2 92.91 even 2
368.2.a.i.1.2 2 23.22 odd 2
1472.2.a.p.1.1 2 184.45 odd 2
1472.2.a.u.1.2 2 184.91 even 2
1656.2.a.j.1.1 2 276.275 odd 2
3312.2.a.t.1.2 2 69.68 even 2
4232.2.a.o.1.1 2 4.3 odd 2
4600.2.a.s.1.2 2 460.459 even 2
4600.2.e.o.4049.1 4 460.183 odd 4
4600.2.e.o.4049.4 4 460.367 odd 4
8464.2.a.bd.1.2 2 1.1 even 1 trivial
9016.2.a.w.1.2 2 644.643 odd 2
9200.2.a.br.1.1 2 115.114 odd 2