Properties

Label 8004.2.a.i.1.6
Level $8004$
Weight $2$
Character 8004.1
Self dual yes
Analytic conductor $63.912$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8004.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 5 x^{15} - 43 x^{14} + 234 x^{13} + 634 x^{12} - 4048 x^{11} - 3483 x^{10} + 32512 x^{9} - 137 x^{8} - 121665 x^{7} + 60168 x^{6} + 172218 x^{5} - 138024 x^{4} - 17844 x^{3} + 14352 x^{2} + 72 x - 208\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-0.309856\) of defining polynomial
Character \(\chi\) \(=\) 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -0.309856 q^{5} -1.15608 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -0.309856 q^{5} -1.15608 q^{7} +1.00000 q^{9} +5.92157 q^{11} -4.60261 q^{13} +0.309856 q^{15} -7.33718 q^{17} -3.96569 q^{19} +1.15608 q^{21} +1.00000 q^{23} -4.90399 q^{25} -1.00000 q^{27} +1.00000 q^{29} +7.27559 q^{31} -5.92157 q^{33} +0.358219 q^{35} +2.80212 q^{37} +4.60261 q^{39} -4.27213 q^{41} +5.11611 q^{43} -0.309856 q^{45} +3.04361 q^{47} -5.66347 q^{49} +7.33718 q^{51} -13.6612 q^{53} -1.83483 q^{55} +3.96569 q^{57} -0.903422 q^{59} +11.0272 q^{61} -1.15608 q^{63} +1.42615 q^{65} +7.41964 q^{67} -1.00000 q^{69} +3.44912 q^{71} -4.89506 q^{73} +4.90399 q^{75} -6.84582 q^{77} +14.5506 q^{79} +1.00000 q^{81} -15.6780 q^{83} +2.27347 q^{85} -1.00000 q^{87} +5.84517 q^{89} +5.32099 q^{91} -7.27559 q^{93} +1.22879 q^{95} +5.92869 q^{97} +5.92157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{3} + 5q^{5} - 4q^{7} + 16q^{9} + O(q^{10}) \) \( 16q - 16q^{3} + 5q^{5} - 4q^{7} + 16q^{9} + 5q^{11} + 8q^{13} - 5q^{15} + 7q^{17} + q^{19} + 4q^{21} + 16q^{23} + 31q^{25} - 16q^{27} + 16q^{29} - 2q^{31} - 5q^{33} + 5q^{35} + 14q^{37} - 8q^{39} - q^{41} - 13q^{43} + 5q^{45} - 4q^{47} + 30q^{49} - 7q^{51} + 19q^{53} - 37q^{55} - q^{57} + 12q^{59} + 21q^{61} - 4q^{63} + 26q^{65} - 11q^{67} - 16q^{69} + 7q^{71} - 13q^{73} - 31q^{75} + 4q^{77} - 18q^{79} + 16q^{81} + 25q^{83} + 48q^{85} - 16q^{87} + 12q^{89} - 11q^{91} + 2q^{93} - q^{95} + 5q^{97} + 5q^{99} + O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −0.309856 −0.138572 −0.0692859 0.997597i \(-0.522072\pi\)
−0.0692859 + 0.997597i \(0.522072\pi\)
\(6\) 0 0
\(7\) −1.15608 −0.436958 −0.218479 0.975842i \(-0.570110\pi\)
−0.218479 + 0.975842i \(0.570110\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.92157 1.78542 0.892710 0.450632i \(-0.148802\pi\)
0.892710 + 0.450632i \(0.148802\pi\)
\(12\) 0 0
\(13\) −4.60261 −1.27653 −0.638267 0.769815i \(-0.720348\pi\)
−0.638267 + 0.769815i \(0.720348\pi\)
\(14\) 0 0
\(15\) 0.309856 0.0800045
\(16\) 0 0
\(17\) −7.33718 −1.77953 −0.889764 0.456421i \(-0.849131\pi\)
−0.889764 + 0.456421i \(0.849131\pi\)
\(18\) 0 0
\(19\) −3.96569 −0.909791 −0.454896 0.890545i \(-0.650323\pi\)
−0.454896 + 0.890545i \(0.650323\pi\)
\(20\) 0 0
\(21\) 1.15608 0.252278
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.90399 −0.980798
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 7.27559 1.30673 0.653367 0.757041i \(-0.273356\pi\)
0.653367 + 0.757041i \(0.273356\pi\)
\(32\) 0 0
\(33\) −5.92157 −1.03081
\(34\) 0 0
\(35\) 0.358219 0.0605501
\(36\) 0 0
\(37\) 2.80212 0.460666 0.230333 0.973112i \(-0.426018\pi\)
0.230333 + 0.973112i \(0.426018\pi\)
\(38\) 0 0
\(39\) 4.60261 0.737007
\(40\) 0 0
\(41\) −4.27213 −0.667194 −0.333597 0.942716i \(-0.608263\pi\)
−0.333597 + 0.942716i \(0.608263\pi\)
\(42\) 0 0
\(43\) 5.11611 0.780199 0.390100 0.920773i \(-0.372441\pi\)
0.390100 + 0.920773i \(0.372441\pi\)
\(44\) 0 0
\(45\) −0.309856 −0.0461906
\(46\) 0 0
\(47\) 3.04361 0.443956 0.221978 0.975052i \(-0.428749\pi\)
0.221978 + 0.975052i \(0.428749\pi\)
\(48\) 0 0
\(49\) −5.66347 −0.809068
\(50\) 0 0
\(51\) 7.33718 1.02741
\(52\) 0 0
\(53\) −13.6612 −1.87652 −0.938258 0.345936i \(-0.887561\pi\)
−0.938258 + 0.345936i \(0.887561\pi\)
\(54\) 0 0
\(55\) −1.83483 −0.247409
\(56\) 0 0
\(57\) 3.96569 0.525268
\(58\) 0 0
\(59\) −0.903422 −0.117615 −0.0588077 0.998269i \(-0.518730\pi\)
−0.0588077 + 0.998269i \(0.518730\pi\)
\(60\) 0 0
\(61\) 11.0272 1.41189 0.705946 0.708266i \(-0.250522\pi\)
0.705946 + 0.708266i \(0.250522\pi\)
\(62\) 0 0
\(63\) −1.15608 −0.145653
\(64\) 0 0
\(65\) 1.42615 0.176892
\(66\) 0 0
\(67\) 7.41964 0.906454 0.453227 0.891395i \(-0.350273\pi\)
0.453227 + 0.891395i \(0.350273\pi\)
\(68\) 0 0
\(69\) −1.00000 −0.120386
\(70\) 0 0
\(71\) 3.44912 0.409335 0.204667 0.978832i \(-0.434389\pi\)
0.204667 + 0.978832i \(0.434389\pi\)
\(72\) 0 0
\(73\) −4.89506 −0.572923 −0.286461 0.958092i \(-0.592479\pi\)
−0.286461 + 0.958092i \(0.592479\pi\)
\(74\) 0 0
\(75\) 4.90399 0.566264
\(76\) 0 0
\(77\) −6.84582 −0.780153
\(78\) 0 0
\(79\) 14.5506 1.63707 0.818535 0.574456i \(-0.194786\pi\)
0.818535 + 0.574456i \(0.194786\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −15.6780 −1.72088 −0.860441 0.509550i \(-0.829812\pi\)
−0.860441 + 0.509550i \(0.829812\pi\)
\(84\) 0 0
\(85\) 2.27347 0.246593
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) 5.84517 0.619586 0.309793 0.950804i \(-0.399740\pi\)
0.309793 + 0.950804i \(0.399740\pi\)
\(90\) 0 0
\(91\) 5.32099 0.557792
\(92\) 0 0
\(93\) −7.27559 −0.754443
\(94\) 0 0
\(95\) 1.22879 0.126071
\(96\) 0 0
\(97\) 5.92869 0.601967 0.300984 0.953629i \(-0.402685\pi\)
0.300984 + 0.953629i \(0.402685\pi\)
\(98\) 0 0
\(99\) 5.92157 0.595140
\(100\) 0 0
\(101\) 10.5052 1.04531 0.522655 0.852545i \(-0.324942\pi\)
0.522655 + 0.852545i \(0.324942\pi\)
\(102\) 0 0
\(103\) −4.57362 −0.450652 −0.225326 0.974283i \(-0.572345\pi\)
−0.225326 + 0.974283i \(0.572345\pi\)
\(104\) 0 0
\(105\) −0.358219 −0.0349586
\(106\) 0 0
\(107\) −6.80910 −0.658261 −0.329130 0.944284i \(-0.606756\pi\)
−0.329130 + 0.944284i \(0.606756\pi\)
\(108\) 0 0
\(109\) 2.49451 0.238931 0.119465 0.992838i \(-0.461882\pi\)
0.119465 + 0.992838i \(0.461882\pi\)
\(110\) 0 0
\(111\) −2.80212 −0.265966
\(112\) 0 0
\(113\) 9.51872 0.895446 0.447723 0.894172i \(-0.352235\pi\)
0.447723 + 0.894172i \(0.352235\pi\)
\(114\) 0 0
\(115\) −0.309856 −0.0288942
\(116\) 0 0
\(117\) −4.60261 −0.425511
\(118\) 0 0
\(119\) 8.48238 0.777579
\(120\) 0 0
\(121\) 24.0649 2.18772
\(122\) 0 0
\(123\) 4.27213 0.385205
\(124\) 0 0
\(125\) 3.06881 0.274483
\(126\) 0 0
\(127\) −17.2784 −1.53321 −0.766604 0.642120i \(-0.778055\pi\)
−0.766604 + 0.642120i \(0.778055\pi\)
\(128\) 0 0
\(129\) −5.11611 −0.450448
\(130\) 0 0
\(131\) 8.59137 0.750632 0.375316 0.926897i \(-0.377534\pi\)
0.375316 + 0.926897i \(0.377534\pi\)
\(132\) 0 0
\(133\) 4.58466 0.397540
\(134\) 0 0
\(135\) 0.309856 0.0266682
\(136\) 0 0
\(137\) 4.88945 0.417734 0.208867 0.977944i \(-0.433022\pi\)
0.208867 + 0.977944i \(0.433022\pi\)
\(138\) 0 0
\(139\) −20.2173 −1.71481 −0.857404 0.514644i \(-0.827924\pi\)
−0.857404 + 0.514644i \(0.827924\pi\)
\(140\) 0 0
\(141\) −3.04361 −0.256318
\(142\) 0 0
\(143\) −27.2547 −2.27915
\(144\) 0 0
\(145\) −0.309856 −0.0257322
\(146\) 0 0
\(147\) 5.66347 0.467115
\(148\) 0 0
\(149\) −12.2316 −1.00205 −0.501025 0.865433i \(-0.667043\pi\)
−0.501025 + 0.865433i \(0.667043\pi\)
\(150\) 0 0
\(151\) 13.3244 1.08433 0.542164 0.840273i \(-0.317605\pi\)
0.542164 + 0.840273i \(0.317605\pi\)
\(152\) 0 0
\(153\) −7.33718 −0.593176
\(154\) 0 0
\(155\) −2.25439 −0.181077
\(156\) 0 0
\(157\) 9.60039 0.766194 0.383097 0.923708i \(-0.374857\pi\)
0.383097 + 0.923708i \(0.374857\pi\)
\(158\) 0 0
\(159\) 13.6612 1.08341
\(160\) 0 0
\(161\) −1.15608 −0.0911120
\(162\) 0 0
\(163\) 10.2315 0.801396 0.400698 0.916210i \(-0.368768\pi\)
0.400698 + 0.916210i \(0.368768\pi\)
\(164\) 0 0
\(165\) 1.83483 0.142842
\(166\) 0 0
\(167\) 5.87711 0.454784 0.227392 0.973803i \(-0.426980\pi\)
0.227392 + 0.973803i \(0.426980\pi\)
\(168\) 0 0
\(169\) 8.18401 0.629539
\(170\) 0 0
\(171\) −3.96569 −0.303264
\(172\) 0 0
\(173\) 12.3777 0.941057 0.470529 0.882385i \(-0.344063\pi\)
0.470529 + 0.882385i \(0.344063\pi\)
\(174\) 0 0
\(175\) 5.66941 0.428567
\(176\) 0 0
\(177\) 0.903422 0.0679053
\(178\) 0 0
\(179\) −16.0178 −1.19722 −0.598612 0.801039i \(-0.704281\pi\)
−0.598612 + 0.801039i \(0.704281\pi\)
\(180\) 0 0
\(181\) −2.94379 −0.218810 −0.109405 0.993997i \(-0.534895\pi\)
−0.109405 + 0.993997i \(0.534895\pi\)
\(182\) 0 0
\(183\) −11.0272 −0.815156
\(184\) 0 0
\(185\) −0.868255 −0.0638354
\(186\) 0 0
\(187\) −43.4476 −3.17720
\(188\) 0 0
\(189\) 1.15608 0.0840926
\(190\) 0 0
\(191\) 22.1472 1.60252 0.801259 0.598317i \(-0.204164\pi\)
0.801259 + 0.598317i \(0.204164\pi\)
\(192\) 0 0
\(193\) 9.91772 0.713893 0.356947 0.934125i \(-0.383818\pi\)
0.356947 + 0.934125i \(0.383818\pi\)
\(194\) 0 0
\(195\) −1.42615 −0.102128
\(196\) 0 0
\(197\) 2.07980 0.148179 0.0740897 0.997252i \(-0.476395\pi\)
0.0740897 + 0.997252i \(0.476395\pi\)
\(198\) 0 0
\(199\) −11.4598 −0.812361 −0.406181 0.913793i \(-0.633140\pi\)
−0.406181 + 0.913793i \(0.633140\pi\)
\(200\) 0 0
\(201\) −7.41964 −0.523341
\(202\) 0 0
\(203\) −1.15608 −0.0811411
\(204\) 0 0
\(205\) 1.32375 0.0924544
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) −23.4831 −1.62436
\(210\) 0 0
\(211\) −10.7296 −0.738659 −0.369329 0.929299i \(-0.620413\pi\)
−0.369329 + 0.929299i \(0.620413\pi\)
\(212\) 0 0
\(213\) −3.44912 −0.236330
\(214\) 0 0
\(215\) −1.58526 −0.108114
\(216\) 0 0
\(217\) −8.41118 −0.570988
\(218\) 0 0
\(219\) 4.89506 0.330777
\(220\) 0 0
\(221\) 33.7702 2.27163
\(222\) 0 0
\(223\) −6.24882 −0.418452 −0.209226 0.977867i \(-0.567094\pi\)
−0.209226 + 0.977867i \(0.567094\pi\)
\(224\) 0 0
\(225\) −4.90399 −0.326933
\(226\) 0 0
\(227\) 23.1179 1.53439 0.767196 0.641413i \(-0.221651\pi\)
0.767196 + 0.641413i \(0.221651\pi\)
\(228\) 0 0
\(229\) −6.58061 −0.434859 −0.217429 0.976076i \(-0.569767\pi\)
−0.217429 + 0.976076i \(0.569767\pi\)
\(230\) 0 0
\(231\) 6.84582 0.450422
\(232\) 0 0
\(233\) −16.8724 −1.10535 −0.552673 0.833398i \(-0.686392\pi\)
−0.552673 + 0.833398i \(0.686392\pi\)
\(234\) 0 0
\(235\) −0.943081 −0.0615198
\(236\) 0 0
\(237\) −14.5506 −0.945163
\(238\) 0 0
\(239\) 22.1356 1.43183 0.715915 0.698187i \(-0.246010\pi\)
0.715915 + 0.698187i \(0.246010\pi\)
\(240\) 0 0
\(241\) −4.15266 −0.267496 −0.133748 0.991015i \(-0.542701\pi\)
−0.133748 + 0.991015i \(0.542701\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 1.75486 0.112114
\(246\) 0 0
\(247\) 18.2525 1.16138
\(248\) 0 0
\(249\) 15.6780 0.993552
\(250\) 0 0
\(251\) 10.8013 0.681769 0.340885 0.940105i \(-0.389273\pi\)
0.340885 + 0.940105i \(0.389273\pi\)
\(252\) 0 0
\(253\) 5.92157 0.372286
\(254\) 0 0
\(255\) −2.27347 −0.142370
\(256\) 0 0
\(257\) 27.1696 1.69479 0.847397 0.530959i \(-0.178168\pi\)
0.847397 + 0.530959i \(0.178168\pi\)
\(258\) 0 0
\(259\) −3.23949 −0.201292
\(260\) 0 0
\(261\) 1.00000 0.0618984
\(262\) 0 0
\(263\) −17.0608 −1.05202 −0.526008 0.850480i \(-0.676312\pi\)
−0.526008 + 0.850480i \(0.676312\pi\)
\(264\) 0 0
\(265\) 4.23302 0.260032
\(266\) 0 0
\(267\) −5.84517 −0.357718
\(268\) 0 0
\(269\) −1.06857 −0.0651521 −0.0325761 0.999469i \(-0.510371\pi\)
−0.0325761 + 0.999469i \(0.510371\pi\)
\(270\) 0 0
\(271\) −29.0640 −1.76551 −0.882756 0.469832i \(-0.844314\pi\)
−0.882756 + 0.469832i \(0.844314\pi\)
\(272\) 0 0
\(273\) −5.32099 −0.322041
\(274\) 0 0
\(275\) −29.0393 −1.75114
\(276\) 0 0
\(277\) −19.3666 −1.16363 −0.581813 0.813323i \(-0.697656\pi\)
−0.581813 + 0.813323i \(0.697656\pi\)
\(278\) 0 0
\(279\) 7.27559 0.435578
\(280\) 0 0
\(281\) −10.4904 −0.625808 −0.312904 0.949785i \(-0.601302\pi\)
−0.312904 + 0.949785i \(0.601302\pi\)
\(282\) 0 0
\(283\) 5.42301 0.322364 0.161182 0.986925i \(-0.448469\pi\)
0.161182 + 0.986925i \(0.448469\pi\)
\(284\) 0 0
\(285\) −1.22879 −0.0727874
\(286\) 0 0
\(287\) 4.93893 0.291536
\(288\) 0 0
\(289\) 36.8342 2.16672
\(290\) 0 0
\(291\) −5.92869 −0.347546
\(292\) 0 0
\(293\) 9.55426 0.558166 0.279083 0.960267i \(-0.409970\pi\)
0.279083 + 0.960267i \(0.409970\pi\)
\(294\) 0 0
\(295\) 0.279931 0.0162982
\(296\) 0 0
\(297\) −5.92157 −0.343604
\(298\) 0 0
\(299\) −4.60261 −0.266176
\(300\) 0 0
\(301\) −5.91464 −0.340914
\(302\) 0 0
\(303\) −10.5052 −0.603510
\(304\) 0 0
\(305\) −3.41685 −0.195648
\(306\) 0 0
\(307\) −16.7330 −0.955004 −0.477502 0.878631i \(-0.658458\pi\)
−0.477502 + 0.878631i \(0.658458\pi\)
\(308\) 0 0
\(309\) 4.57362 0.260184
\(310\) 0 0
\(311\) 22.8155 1.29375 0.646873 0.762597i \(-0.276076\pi\)
0.646873 + 0.762597i \(0.276076\pi\)
\(312\) 0 0
\(313\) 2.54313 0.143746 0.0718730 0.997414i \(-0.477102\pi\)
0.0718730 + 0.997414i \(0.477102\pi\)
\(314\) 0 0
\(315\) 0.358219 0.0201834
\(316\) 0 0
\(317\) −16.4581 −0.924378 −0.462189 0.886781i \(-0.652936\pi\)
−0.462189 + 0.886781i \(0.652936\pi\)
\(318\) 0 0
\(319\) 5.92157 0.331544
\(320\) 0 0
\(321\) 6.80910 0.380047
\(322\) 0 0
\(323\) 29.0970 1.61900
\(324\) 0 0
\(325\) 22.5711 1.25202
\(326\) 0 0
\(327\) −2.49451 −0.137947
\(328\) 0 0
\(329\) −3.51866 −0.193990
\(330\) 0 0
\(331\) 28.3233 1.55679 0.778394 0.627777i \(-0.216035\pi\)
0.778394 + 0.627777i \(0.216035\pi\)
\(332\) 0 0
\(333\) 2.80212 0.153555
\(334\) 0 0
\(335\) −2.29902 −0.125609
\(336\) 0 0
\(337\) 31.1542 1.69708 0.848539 0.529133i \(-0.177483\pi\)
0.848539 + 0.529133i \(0.177483\pi\)
\(338\) 0 0
\(339\) −9.51872 −0.516986
\(340\) 0 0
\(341\) 43.0829 2.33307
\(342\) 0 0
\(343\) 14.6400 0.790487
\(344\) 0 0
\(345\) 0.309856 0.0166821
\(346\) 0 0
\(347\) 25.8412 1.38723 0.693615 0.720346i \(-0.256017\pi\)
0.693615 + 0.720346i \(0.256017\pi\)
\(348\) 0 0
\(349\) 26.8116 1.43519 0.717596 0.696459i \(-0.245242\pi\)
0.717596 + 0.696459i \(0.245242\pi\)
\(350\) 0 0
\(351\) 4.60261 0.245669
\(352\) 0 0
\(353\) 32.1950 1.71357 0.856783 0.515678i \(-0.172460\pi\)
0.856783 + 0.515678i \(0.172460\pi\)
\(354\) 0 0
\(355\) −1.06873 −0.0567223
\(356\) 0 0
\(357\) −8.48238 −0.448935
\(358\) 0 0
\(359\) 17.4132 0.919035 0.459517 0.888169i \(-0.348022\pi\)
0.459517 + 0.888169i \(0.348022\pi\)
\(360\) 0 0
\(361\) −3.27332 −0.172280
\(362\) 0 0
\(363\) −24.0649 −1.26308
\(364\) 0 0
\(365\) 1.51676 0.0793910
\(366\) 0 0
\(367\) −2.75102 −0.143602 −0.0718010 0.997419i \(-0.522875\pi\)
−0.0718010 + 0.997419i \(0.522875\pi\)
\(368\) 0 0
\(369\) −4.27213 −0.222398
\(370\) 0 0
\(371\) 15.7935 0.819959
\(372\) 0 0
\(373\) −18.8136 −0.974131 −0.487066 0.873365i \(-0.661933\pi\)
−0.487066 + 0.873365i \(0.661933\pi\)
\(374\) 0 0
\(375\) −3.06881 −0.158473
\(376\) 0 0
\(377\) −4.60261 −0.237046
\(378\) 0 0
\(379\) 17.7700 0.912781 0.456391 0.889780i \(-0.349142\pi\)
0.456391 + 0.889780i \(0.349142\pi\)
\(380\) 0 0
\(381\) 17.2784 0.885198
\(382\) 0 0
\(383\) 14.2681 0.729068 0.364534 0.931190i \(-0.381228\pi\)
0.364534 + 0.931190i \(0.381228\pi\)
\(384\) 0 0
\(385\) 2.12122 0.108107
\(386\) 0 0
\(387\) 5.11611 0.260066
\(388\) 0 0
\(389\) 20.0206 1.01509 0.507543 0.861626i \(-0.330554\pi\)
0.507543 + 0.861626i \(0.330554\pi\)
\(390\) 0 0
\(391\) −7.33718 −0.371057
\(392\) 0 0
\(393\) −8.59137 −0.433378
\(394\) 0 0
\(395\) −4.50859 −0.226852
\(396\) 0 0
\(397\) 29.3789 1.47448 0.737242 0.675628i \(-0.236128\pi\)
0.737242 + 0.675628i \(0.236128\pi\)
\(398\) 0 0
\(399\) −4.58466 −0.229520
\(400\) 0 0
\(401\) −16.0068 −0.799342 −0.399671 0.916659i \(-0.630876\pi\)
−0.399671 + 0.916659i \(0.630876\pi\)
\(402\) 0 0
\(403\) −33.4867 −1.66809
\(404\) 0 0
\(405\) −0.309856 −0.0153969
\(406\) 0 0
\(407\) 16.5930 0.822482
\(408\) 0 0
\(409\) −13.7904 −0.681890 −0.340945 0.940083i \(-0.610747\pi\)
−0.340945 + 0.940083i \(0.610747\pi\)
\(410\) 0 0
\(411\) −4.88945 −0.241179
\(412\) 0 0
\(413\) 1.04443 0.0513930
\(414\) 0 0
\(415\) 4.85792 0.238466
\(416\) 0 0
\(417\) 20.2173 0.990045
\(418\) 0 0
\(419\) −16.2513 −0.793926 −0.396963 0.917835i \(-0.629936\pi\)
−0.396963 + 0.917835i \(0.629936\pi\)
\(420\) 0 0
\(421\) −1.53538 −0.0748296 −0.0374148 0.999300i \(-0.511912\pi\)
−0.0374148 + 0.999300i \(0.511912\pi\)
\(422\) 0 0
\(423\) 3.04361 0.147985
\(424\) 0 0
\(425\) 35.9815 1.74536
\(426\) 0 0
\(427\) −12.7484 −0.616937
\(428\) 0 0
\(429\) 27.2547 1.31587
\(430\) 0 0
\(431\) 10.1108 0.487022 0.243511 0.969898i \(-0.421701\pi\)
0.243511 + 0.969898i \(0.421701\pi\)
\(432\) 0 0
\(433\) 0.641277 0.0308178 0.0154089 0.999881i \(-0.495095\pi\)
0.0154089 + 0.999881i \(0.495095\pi\)
\(434\) 0 0
\(435\) 0.309856 0.0148565
\(436\) 0 0
\(437\) −3.96569 −0.189705
\(438\) 0 0
\(439\) −33.3571 −1.59205 −0.796025 0.605264i \(-0.793068\pi\)
−0.796025 + 0.605264i \(0.793068\pi\)
\(440\) 0 0
\(441\) −5.66347 −0.269689
\(442\) 0 0
\(443\) 30.6287 1.45522 0.727608 0.685993i \(-0.240632\pi\)
0.727608 + 0.685993i \(0.240632\pi\)
\(444\) 0 0
\(445\) −1.81116 −0.0858572
\(446\) 0 0
\(447\) 12.2316 0.578533
\(448\) 0 0
\(449\) 16.9021 0.797658 0.398829 0.917025i \(-0.369417\pi\)
0.398829 + 0.917025i \(0.369417\pi\)
\(450\) 0 0
\(451\) −25.2977 −1.19122
\(452\) 0 0
\(453\) −13.3244 −0.626037
\(454\) 0 0
\(455\) −1.64874 −0.0772942
\(456\) 0 0
\(457\) 28.7154 1.34325 0.671624 0.740892i \(-0.265597\pi\)
0.671624 + 0.740892i \(0.265597\pi\)
\(458\) 0 0
\(459\) 7.33718 0.342470
\(460\) 0 0
\(461\) 7.39735 0.344529 0.172264 0.985051i \(-0.444892\pi\)
0.172264 + 0.985051i \(0.444892\pi\)
\(462\) 0 0
\(463\) −32.3696 −1.50434 −0.752172 0.658966i \(-0.770994\pi\)
−0.752172 + 0.658966i \(0.770994\pi\)
\(464\) 0 0
\(465\) 2.25439 0.104545
\(466\) 0 0
\(467\) −11.6083 −0.537168 −0.268584 0.963256i \(-0.586556\pi\)
−0.268584 + 0.963256i \(0.586556\pi\)
\(468\) 0 0
\(469\) −8.57772 −0.396082
\(470\) 0 0
\(471\) −9.60039 −0.442362
\(472\) 0 0
\(473\) 30.2954 1.39298
\(474\) 0 0
\(475\) 19.4477 0.892321
\(476\) 0 0
\(477\) −13.6612 −0.625505
\(478\) 0 0
\(479\) 28.3318 1.29451 0.647256 0.762272i \(-0.275916\pi\)
0.647256 + 0.762272i \(0.275916\pi\)
\(480\) 0 0
\(481\) −12.8971 −0.588056
\(482\) 0 0
\(483\) 1.15608 0.0526036
\(484\) 0 0
\(485\) −1.83704 −0.0834157
\(486\) 0 0
\(487\) 26.6567 1.20793 0.603964 0.797011i \(-0.293587\pi\)
0.603964 + 0.797011i \(0.293587\pi\)
\(488\) 0 0
\(489\) −10.2315 −0.462686
\(490\) 0 0
\(491\) 37.9235 1.71146 0.855732 0.517420i \(-0.173108\pi\)
0.855732 + 0.517420i \(0.173108\pi\)
\(492\) 0 0
\(493\) −7.33718 −0.330450
\(494\) 0 0
\(495\) −1.83483 −0.0824696
\(496\) 0 0
\(497\) −3.98746 −0.178862
\(498\) 0 0
\(499\) 8.59056 0.384566 0.192283 0.981339i \(-0.438411\pi\)
0.192283 + 0.981339i \(0.438411\pi\)
\(500\) 0 0
\(501\) −5.87711 −0.262570
\(502\) 0 0
\(503\) 1.87519 0.0836106 0.0418053 0.999126i \(-0.486689\pi\)
0.0418053 + 0.999126i \(0.486689\pi\)
\(504\) 0 0
\(505\) −3.25511 −0.144850
\(506\) 0 0
\(507\) −8.18401 −0.363465
\(508\) 0 0
\(509\) 42.0374 1.86328 0.931638 0.363387i \(-0.118380\pi\)
0.931638 + 0.363387i \(0.118380\pi\)
\(510\) 0 0
\(511\) 5.65909 0.250343
\(512\) 0 0
\(513\) 3.96569 0.175089
\(514\) 0 0
\(515\) 1.41716 0.0624477
\(516\) 0 0
\(517\) 18.0229 0.792648
\(518\) 0 0
\(519\) −12.3777 −0.543320
\(520\) 0 0
\(521\) 7.62850 0.334211 0.167105 0.985939i \(-0.446558\pi\)
0.167105 + 0.985939i \(0.446558\pi\)
\(522\) 0 0
\(523\) 28.1008 1.22876 0.614381 0.789009i \(-0.289406\pi\)
0.614381 + 0.789009i \(0.289406\pi\)
\(524\) 0 0
\(525\) −5.66941 −0.247434
\(526\) 0 0
\(527\) −53.3823 −2.32537
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −0.903422 −0.0392052
\(532\) 0 0
\(533\) 19.6629 0.851696
\(534\) 0 0
\(535\) 2.10984 0.0912164
\(536\) 0 0
\(537\) 16.0178 0.691218
\(538\) 0 0
\(539\) −33.5366 −1.44453
\(540\) 0 0
\(541\) 9.06933 0.389921 0.194960 0.980811i \(-0.437542\pi\)
0.194960 + 0.980811i \(0.437542\pi\)
\(542\) 0 0
\(543\) 2.94379 0.126330
\(544\) 0 0
\(545\) −0.772939 −0.0331091
\(546\) 0 0
\(547\) 14.1909 0.606759 0.303379 0.952870i \(-0.401885\pi\)
0.303379 + 0.952870i \(0.401885\pi\)
\(548\) 0 0
\(549\) 11.0272 0.470631
\(550\) 0 0
\(551\) −3.96569 −0.168944
\(552\) 0 0
\(553\) −16.8217 −0.715331
\(554\) 0 0
\(555\) 0.868255 0.0368554
\(556\) 0 0
\(557\) −7.80664 −0.330778 −0.165389 0.986228i \(-0.552888\pi\)
−0.165389 + 0.986228i \(0.552888\pi\)
\(558\) 0 0
\(559\) −23.5474 −0.995951
\(560\) 0 0
\(561\) 43.4476 1.83436
\(562\) 0 0
\(563\) −1.73244 −0.0730135 −0.0365068 0.999333i \(-0.511623\pi\)
−0.0365068 + 0.999333i \(0.511623\pi\)
\(564\) 0 0
\(565\) −2.94944 −0.124084
\(566\) 0 0
\(567\) −1.15608 −0.0485509
\(568\) 0 0
\(569\) 39.3501 1.64964 0.824821 0.565394i \(-0.191276\pi\)
0.824821 + 0.565394i \(0.191276\pi\)
\(570\) 0 0
\(571\) −16.2007 −0.677977 −0.338988 0.940791i \(-0.610085\pi\)
−0.338988 + 0.940791i \(0.610085\pi\)
\(572\) 0 0
\(573\) −22.1472 −0.925214
\(574\) 0 0
\(575\) −4.90399 −0.204510
\(576\) 0 0
\(577\) 31.6855 1.31908 0.659542 0.751668i \(-0.270750\pi\)
0.659542 + 0.751668i \(0.270750\pi\)
\(578\) 0 0
\(579\) −9.91772 −0.412166
\(580\) 0 0
\(581\) 18.1250 0.751953
\(582\) 0 0
\(583\) −80.8960 −3.35037
\(584\) 0 0
\(585\) 1.42615 0.0589639
\(586\) 0 0
\(587\) 34.4254 1.42089 0.710445 0.703753i \(-0.248494\pi\)
0.710445 + 0.703753i \(0.248494\pi\)
\(588\) 0 0
\(589\) −28.8527 −1.18886
\(590\) 0 0
\(591\) −2.07980 −0.0855514
\(592\) 0 0
\(593\) −38.7103 −1.58964 −0.794821 0.606844i \(-0.792435\pi\)
−0.794821 + 0.606844i \(0.792435\pi\)
\(594\) 0 0
\(595\) −2.62832 −0.107751
\(596\) 0 0
\(597\) 11.4598 0.469017
\(598\) 0 0
\(599\) −26.7623 −1.09348 −0.546739 0.837303i \(-0.684131\pi\)
−0.546739 + 0.837303i \(0.684131\pi\)
\(600\) 0 0
\(601\) −5.97759 −0.243831 −0.121915 0.992540i \(-0.538904\pi\)
−0.121915 + 0.992540i \(0.538904\pi\)
\(602\) 0 0
\(603\) 7.41964 0.302151
\(604\) 0 0
\(605\) −7.45667 −0.303157
\(606\) 0 0
\(607\) 27.0115 1.09636 0.548182 0.836359i \(-0.315320\pi\)
0.548182 + 0.836359i \(0.315320\pi\)
\(608\) 0 0
\(609\) 1.15608 0.0468468
\(610\) 0 0
\(611\) −14.0085 −0.566725
\(612\) 0 0
\(613\) 19.8569 0.802014 0.401007 0.916075i \(-0.368660\pi\)
0.401007 + 0.916075i \(0.368660\pi\)
\(614\) 0 0
\(615\) −1.32375 −0.0533786
\(616\) 0 0
\(617\) −1.56892 −0.0631622 −0.0315811 0.999501i \(-0.510054\pi\)
−0.0315811 + 0.999501i \(0.510054\pi\)
\(618\) 0 0
\(619\) 40.2654 1.61840 0.809201 0.587532i \(-0.199900\pi\)
0.809201 + 0.587532i \(0.199900\pi\)
\(620\) 0 0
\(621\) −1.00000 −0.0401286
\(622\) 0 0
\(623\) −6.75749 −0.270733
\(624\) 0 0
\(625\) 23.5691 0.942762
\(626\) 0 0
\(627\) 23.4831 0.937824
\(628\) 0 0
\(629\) −20.5597 −0.819769
\(630\) 0 0
\(631\) 7.30495 0.290805 0.145403 0.989373i \(-0.453552\pi\)
0.145403 + 0.989373i \(0.453552\pi\)
\(632\) 0 0
\(633\) 10.7296 0.426465
\(634\) 0 0
\(635\) 5.35381 0.212460
\(636\) 0 0
\(637\) 26.0668 1.03280
\(638\) 0 0
\(639\) 3.44912 0.136445
\(640\) 0 0
\(641\) −2.70083 −0.106676 −0.0533381 0.998577i \(-0.516986\pi\)
−0.0533381 + 0.998577i \(0.516986\pi\)
\(642\) 0 0
\(643\) −42.7930 −1.68759 −0.843796 0.536664i \(-0.819684\pi\)
−0.843796 + 0.536664i \(0.819684\pi\)
\(644\) 0 0
\(645\) 1.58526 0.0624194
\(646\) 0 0
\(647\) −44.4022 −1.74563 −0.872815 0.488051i \(-0.837708\pi\)
−0.872815 + 0.488051i \(0.837708\pi\)
\(648\) 0 0
\(649\) −5.34967 −0.209993
\(650\) 0 0
\(651\) 8.41118 0.329660
\(652\) 0 0
\(653\) −8.71982 −0.341233 −0.170617 0.985338i \(-0.554576\pi\)
−0.170617 + 0.985338i \(0.554576\pi\)
\(654\) 0 0
\(655\) −2.66209 −0.104016
\(656\) 0 0
\(657\) −4.89506 −0.190974
\(658\) 0 0
\(659\) 42.7102 1.66375 0.831876 0.554961i \(-0.187267\pi\)
0.831876 + 0.554961i \(0.187267\pi\)
\(660\) 0 0
\(661\) −28.8654 −1.12273 −0.561366 0.827568i \(-0.689724\pi\)
−0.561366 + 0.827568i \(0.689724\pi\)
\(662\) 0 0
\(663\) −33.7702 −1.31153
\(664\) 0 0
\(665\) −1.42059 −0.0550879
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 0 0
\(669\) 6.24882 0.241593
\(670\) 0 0
\(671\) 65.2984 2.52082
\(672\) 0 0
\(673\) −35.2189 −1.35759 −0.678794 0.734329i \(-0.737497\pi\)
−0.678794 + 0.734329i \(0.737497\pi\)
\(674\) 0 0
\(675\) 4.90399 0.188755
\(676\) 0 0
\(677\) −22.7503 −0.874366 −0.437183 0.899373i \(-0.644024\pi\)
−0.437183 + 0.899373i \(0.644024\pi\)
\(678\) 0 0
\(679\) −6.85405 −0.263034
\(680\) 0 0
\(681\) −23.1179 −0.885882
\(682\) 0 0
\(683\) 24.2731 0.928785 0.464392 0.885630i \(-0.346273\pi\)
0.464392 + 0.885630i \(0.346273\pi\)
\(684\) 0 0
\(685\) −1.51503 −0.0578862
\(686\) 0 0
\(687\) 6.58061 0.251066
\(688\) 0 0
\(689\) 62.8774 2.39544
\(690\) 0 0
\(691\) 1.94632 0.0740417 0.0370208 0.999314i \(-0.488213\pi\)
0.0370208 + 0.999314i \(0.488213\pi\)
\(692\) 0 0
\(693\) −6.84582 −0.260051
\(694\) 0 0
\(695\) 6.26445 0.237624
\(696\) 0 0
\(697\) 31.3454 1.18729
\(698\) 0 0
\(699\) 16.8724 0.638171
\(700\) 0 0
\(701\) −40.3281 −1.52317 −0.761586 0.648064i \(-0.775579\pi\)
−0.761586 + 0.648064i \(0.775579\pi\)
\(702\) 0 0
\(703\) −11.1123 −0.419110
\(704\) 0 0
\(705\) 0.943081 0.0355185
\(706\) 0 0
\(707\) −12.1449 −0.456756
\(708\) 0 0
\(709\) −44.4185 −1.66817 −0.834085 0.551636i \(-0.814004\pi\)
−0.834085 + 0.551636i \(0.814004\pi\)
\(710\) 0 0
\(711\) 14.5506 0.545690
\(712\) 0 0
\(713\) 7.27559 0.272473
\(714\) 0 0
\(715\) 8.44502 0.315826
\(716\) 0 0
\(717\) −22.1356 −0.826668
\(718\) 0 0
\(719\) −41.9951 −1.56615 −0.783076 0.621926i \(-0.786350\pi\)
−0.783076 + 0.621926i \(0.786350\pi\)
\(720\) 0 0
\(721\) 5.28748 0.196916
\(722\) 0 0
\(723\) 4.15266 0.154439
\(724\) 0 0
\(725\) −4.90399 −0.182130
\(726\) 0 0
\(727\) −46.4995 −1.72457 −0.862285 0.506424i \(-0.830967\pi\)
−0.862285 + 0.506424i \(0.830967\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −37.5378 −1.38839
\(732\) 0 0
\(733\) 27.7531 1.02508 0.512542 0.858662i \(-0.328704\pi\)
0.512542 + 0.858662i \(0.328704\pi\)
\(734\) 0 0
\(735\) −1.75486 −0.0647291
\(736\) 0 0
\(737\) 43.9359 1.61840
\(738\) 0 0
\(739\) −21.0418 −0.774034 −0.387017 0.922073i \(-0.626495\pi\)
−0.387017 + 0.922073i \(0.626495\pi\)
\(740\) 0 0
\(741\) −18.2525 −0.670523
\(742\) 0 0
\(743\) −6.20977 −0.227814 −0.113907 0.993491i \(-0.536337\pi\)
−0.113907 + 0.993491i \(0.536337\pi\)
\(744\) 0 0
\(745\) 3.79003 0.138856
\(746\) 0 0
\(747\) −15.6780 −0.573627
\(748\) 0 0
\(749\) 7.87188 0.287632
\(750\) 0 0
\(751\) −35.9054 −1.31021 −0.655103 0.755540i \(-0.727375\pi\)
−0.655103 + 0.755540i \(0.727375\pi\)
\(752\) 0 0
\(753\) −10.8013 −0.393620
\(754\) 0 0
\(755\) −4.12866 −0.150257
\(756\) 0 0
\(757\) 42.7030 1.55207 0.776033 0.630692i \(-0.217229\pi\)
0.776033 + 0.630692i \(0.217229\pi\)
\(758\) 0 0
\(759\) −5.92157 −0.214939
\(760\) 0 0
\(761\) −11.0786 −0.401599 −0.200799 0.979632i \(-0.564354\pi\)
−0.200799 + 0.979632i \(0.564354\pi\)
\(762\) 0 0
\(763\) −2.88386 −0.104403
\(764\) 0 0
\(765\) 2.27347 0.0821975
\(766\) 0 0
\(767\) 4.15810 0.150140
\(768\) 0 0
\(769\) 22.8258 0.823121 0.411561 0.911382i \(-0.364984\pi\)
0.411561 + 0.911382i \(0.364984\pi\)
\(770\) 0 0
\(771\) −27.1696 −0.978490
\(772\) 0 0
\(773\) −27.8064 −1.00013 −0.500063 0.865989i \(-0.666690\pi\)
−0.500063 + 0.865989i \(0.666690\pi\)
\(774\) 0 0
\(775\) −35.6794 −1.28164
\(776\) 0 0
\(777\) 3.23949 0.116216
\(778\) 0 0
\(779\) 16.9419 0.607007
\(780\) 0 0
\(781\) 20.4242 0.730834
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) −2.97474 −0.106173
\(786\) 0 0
\(787\) −27.9091 −0.994853 −0.497426 0.867506i \(-0.665722\pi\)
−0.497426 + 0.867506i \(0.665722\pi\)
\(788\) 0 0
\(789\) 17.0608 0.607382
\(790\) 0 0
\(791\) −11.0044 −0.391272
\(792\) 0 0
\(793\) −50.7540 −1.80233
\(794\) 0 0
\(795\) −4.23302 −0.150130
\(796\) 0 0
\(797\) −26.2558 −0.930028 −0.465014 0.885303i \(-0.653951\pi\)
−0.465014 + 0.885303i \(0.653951\pi\)
\(798\) 0 0
\(799\) −22.3315 −0.790032
\(800\) 0 0
\(801\) 5.84517 0.206529
\(802\) 0 0
\(803\) −28.9864 −1.02291
\(804\) 0 0
\(805\) 0.358219 0.0126256
\(806\) 0 0
\(807\) 1.06857 0.0376156
\(808\) 0 0
\(809\) −35.1355 −1.23530 −0.617649 0.786454i \(-0.711915\pi\)
−0.617649 + 0.786454i \(0.711915\pi\)
\(810\) 0 0
\(811\) −31.0505 −1.09033 −0.545165 0.838329i \(-0.683533\pi\)
−0.545165 + 0.838329i \(0.683533\pi\)
\(812\) 0 0
\(813\) 29.0640 1.01932
\(814\) 0 0
\(815\) −3.17031 −0.111051
\(816\) 0 0
\(817\) −20.2889 −0.709818
\(818\) 0 0
\(819\) 5.32099 0.185931
\(820\) 0 0
\(821\) 34.0706 1.18907 0.594536 0.804069i \(-0.297336\pi\)
0.594536 + 0.804069i \(0.297336\pi\)
\(822\) 0 0
\(823\) −31.8488 −1.11018 −0.555090 0.831790i \(-0.687316\pi\)
−0.555090 + 0.831790i \(0.687316\pi\)
\(824\) 0 0
\(825\) 29.0393 1.01102
\(826\) 0 0
\(827\) 8.76305 0.304721 0.152361 0.988325i \(-0.451313\pi\)
0.152361 + 0.988325i \(0.451313\pi\)
\(828\) 0 0
\(829\) −17.2199 −0.598073 −0.299037 0.954242i \(-0.596665\pi\)
−0.299037 + 0.954242i \(0.596665\pi\)
\(830\) 0 0
\(831\) 19.3666 0.671820
\(832\) 0 0
\(833\) 41.5539 1.43976
\(834\) 0 0
\(835\) −1.82106 −0.0630203
\(836\) 0 0
\(837\) −7.27559 −0.251481
\(838\) 0 0
\(839\) −11.2209 −0.387389 −0.193694 0.981062i \(-0.562047\pi\)
−0.193694 + 0.981062i \(0.562047\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) 10.4904 0.361310
\(844\) 0 0
\(845\) −2.53587 −0.0872364
\(846\) 0 0
\(847\) −27.8210 −0.955942
\(848\) 0 0
\(849\) −5.42301 −0.186117
\(850\) 0 0
\(851\) 2.80212 0.0960556
\(852\) 0 0
\(853\) −18.2145 −0.623654 −0.311827 0.950139i \(-0.600941\pi\)
−0.311827 + 0.950139i \(0.600941\pi\)
\(854\) 0 0
\(855\) 1.22879 0.0420238
\(856\) 0 0
\(857\) 23.0162 0.786218 0.393109 0.919492i \(-0.371400\pi\)
0.393109 + 0.919492i \(0.371400\pi\)
\(858\) 0 0
\(859\) 50.4794 1.72233 0.861167 0.508322i \(-0.169734\pi\)
0.861167 + 0.508322i \(0.169734\pi\)
\(860\) 0 0
\(861\) −4.93893 −0.168318
\(862\) 0 0
\(863\) 27.9165 0.950288 0.475144 0.879908i \(-0.342396\pi\)
0.475144 + 0.879908i \(0.342396\pi\)
\(864\) 0 0
\(865\) −3.83530 −0.130404
\(866\) 0 0
\(867\) −36.8342 −1.25096
\(868\) 0 0
\(869\) 86.1624 2.92286
\(870\) 0 0
\(871\) −34.1497 −1.15712
\(872\) 0 0
\(873\) 5.92869 0.200656
\(874\) 0 0
\(875\) −3.54780 −0.119937
\(876\) 0 0
\(877\) 16.9914 0.573757 0.286879 0.957967i \(-0.407382\pi\)
0.286879 + 0.957967i \(0.407382\pi\)
\(878\) 0 0
\(879\) −9.55426 −0.322257
\(880\) 0 0
\(881\) 17.4171 0.586796 0.293398 0.955990i \(-0.405214\pi\)
0.293398 + 0.955990i \(0.405214\pi\)
\(882\) 0 0
\(883\) 50.7274 1.70711 0.853556 0.521001i \(-0.174441\pi\)
0.853556 + 0.521001i \(0.174441\pi\)
\(884\) 0 0
\(885\) −0.279931 −0.00940977
\(886\) 0 0
\(887\) −18.3574 −0.616382 −0.308191 0.951325i \(-0.599724\pi\)
−0.308191 + 0.951325i \(0.599724\pi\)
\(888\) 0 0
\(889\) 19.9752 0.669948
\(890\) 0 0
\(891\) 5.92157 0.198380
\(892\) 0 0
\(893\) −12.0700 −0.403907
\(894\) 0 0
\(895\) 4.96320 0.165902
\(896\) 0 0
\(897\) 4.60261 0.153677
\(898\) 0 0
\(899\) 7.27559 0.242654
\(900\) 0 0
\(901\) 100.235 3.33931
\(902\) 0 0
\(903\) 5.91464 0.196827
\(904\) 0 0
\(905\) 0.912152 0.0303210
\(906\) 0 0
\(907\) 40.0700 1.33050 0.665250 0.746620i \(-0.268325\pi\)
0.665250 + 0.746620i \(0.268325\pi\)
\(908\) 0 0
\(909\) 10.5052 0.348436
\(910\) 0 0
\(911\) 28.0643 0.929813 0.464906 0.885360i \(-0.346088\pi\)
0.464906 + 0.885360i \(0.346088\pi\)
\(912\) 0 0
\(913\) −92.8382 −3.07250
\(914\) 0 0
\(915\) 3.41685 0.112958
\(916\) 0 0
\(917\) −9.93233 −0.327995
\(918\) 0 0
\(919\) 16.9774 0.560033 0.280016 0.959995i \(-0.409660\pi\)
0.280016 + 0.959995i \(0.409660\pi\)
\(920\) 0 0
\(921\) 16.7330 0.551372
\(922\) 0 0
\(923\) −15.8749 −0.522530
\(924\) 0 0
\(925\) −13.7416 −0.451821
\(926\) 0 0
\(927\) −4.57362 −0.150217
\(928\) 0 0
\(929\) −21.0340 −0.690104 −0.345052 0.938584i \(-0.612139\pi\)
−0.345052 + 0.938584i \(0.612139\pi\)
\(930\) 0 0
\(931\) 22.4596 0.736083
\(932\) 0 0
\(933\) −22.8155 −0.746945
\(934\) 0 0
\(935\) 13.4625 0.440271
\(936\) 0 0
\(937\) 26.9518 0.880476 0.440238 0.897881i \(-0.354894\pi\)
0.440238 + 0.897881i \(0.354894\pi\)
\(938\) 0 0
\(939\) −2.54313 −0.0829918
\(940\) 0 0
\(941\) −54.3406 −1.77145 −0.885726 0.464209i \(-0.846339\pi\)
−0.885726 + 0.464209i \(0.846339\pi\)
\(942\) 0 0
\(943\) −4.27213 −0.139120
\(944\) 0 0
\(945\) −0.358219 −0.0116529
\(946\) 0 0
\(947\) 17.3397 0.563465 0.281733 0.959493i \(-0.409091\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(948\) 0 0
\(949\) 22.5300 0.731356
\(950\) 0 0
\(951\) 16.4581 0.533690
\(952\) 0 0
\(953\) −27.6489 −0.895635 −0.447818 0.894125i \(-0.647799\pi\)
−0.447818 + 0.894125i \(0.647799\pi\)
\(954\) 0 0
\(955\) −6.86246 −0.222064
\(956\) 0 0
\(957\) −5.92157 −0.191417
\(958\) 0 0
\(959\) −5.65261 −0.182532
\(960\) 0 0
\(961\) 21.9342 0.707555
\(962\) 0 0
\(963\) −6.80910 −0.219420
\(964\) 0 0
\(965\) −3.07307 −0.0989255
\(966\) 0 0
\(967\) −19.4879 −0.626688 −0.313344 0.949640i \(-0.601449\pi\)
−0.313344 + 0.949640i \(0.601449\pi\)
\(968\) 0 0
\(969\) −29.0970 −0.934729
\(970\) 0 0
\(971\) −18.9686 −0.608730 −0.304365 0.952555i \(-0.598444\pi\)
−0.304365 + 0.952555i \(0.598444\pi\)
\(972\) 0 0
\(973\) 23.3728 0.749299
\(974\) 0 0
\(975\) −22.5711 −0.722855
\(976\) 0 0
\(977\) 12.5571 0.401738 0.200869 0.979618i \(-0.435623\pi\)
0.200869 + 0.979618i \(0.435623\pi\)
\(978\) 0 0
\(979\) 34.6125 1.10622
\(980\) 0 0
\(981\) 2.49451 0.0796436
\(982\) 0 0
\(983\) 19.9515 0.636353 0.318176 0.948032i \(-0.396930\pi\)
0.318176 + 0.948032i \(0.396930\pi\)
\(984\) 0 0
\(985\) −0.644438 −0.0205335
\(986\) 0 0
\(987\) 3.51866 0.112000
\(988\) 0 0
\(989\) 5.11611 0.162683
\(990\) 0 0
\(991\) −44.7719 −1.42223 −0.711113 0.703078i \(-0.751809\pi\)
−0.711113 + 0.703078i \(0.751809\pi\)
\(992\) 0 0
\(993\) −28.3233 −0.898812
\(994\) 0 0
\(995\) 3.55088 0.112570
\(996\) 0 0
\(997\) −29.2775 −0.927228 −0.463614 0.886037i \(-0.653448\pi\)
−0.463614 + 0.886037i \(0.653448\pi\)
\(998\) 0 0
\(999\) −2.80212 −0.0886553
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 8004.2.a.i.1.6 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8004.2.a.i.1.6 16 1.1 even 1 trivial