Properties

Label 8280.2.a.br.1.4
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $0$
Dimension $5$
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: \(5\)
Coefficient field: 5.5.20087896.1
Defining polynomial: \( x^{5} - x^{4} - 21x^{3} + 5x^{2} + 84x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 2760)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-3.43588\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} +2.62057 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} +2.62057 q^{7} +6.55627 q^{11} +7.06828 q^{13} -6.42405 q^{17} -1.80348 q^{19} +1.00000 q^{23} +1.00000 q^{25} +7.17684 q^{29} +4.10856 q^{31} -2.62057 q^{35} +4.62057 q^{37} -4.30508 q^{41} +6.87176 q^{43} -1.80348 q^{47} -0.132589 q^{49} +4.93606 q^{53} -6.55627 q^{55} +7.54623 q^{59} +2.70854 q^{61} -7.06828 q^{65} +7.37337 q^{67} -3.93569 q^{71} -5.04462 q^{73} +17.1812 q^{77} +6.11897 q^{79} +8.42405 q^{83} +6.42405 q^{85} -11.3838 q^{89} +18.5230 q^{91} +1.80348 q^{95} -17.9843 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 5 q^{5} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 5 q^{5} - 4 q^{7} + 4 q^{11} + 4 q^{13} - 10 q^{17} - 4 q^{19} + 5 q^{23} + 5 q^{25} - 10 q^{29} + 6 q^{31} + 4 q^{35} + 6 q^{37} - 12 q^{41} - 2 q^{43} - 4 q^{47} + 19 q^{49} - 4 q^{55} - 6 q^{59} + 16 q^{61} - 4 q^{65} - 4 q^{67} - 8 q^{71} + 14 q^{73} - 16 q^{77} + 18 q^{79} + 20 q^{83} + 10 q^{85} - 18 q^{89} + 20 q^{91} + 4 q^{95} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(7\) 2.62057 0.990484 0.495242 0.868755i \(-0.335079\pi\)
0.495242 + 0.868755i \(0.335079\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 6.55627 1.97679 0.988395 0.151907i \(-0.0485414\pi\)
0.988395 + 0.151907i \(0.0485414\pi\)
\(12\) 0 0
\(13\) 7.06828 1.96039 0.980195 0.198037i \(-0.0634565\pi\)
0.980195 + 0.198037i \(0.0634565\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.42405 −1.55806 −0.779030 0.626986i \(-0.784288\pi\)
−0.779030 + 0.626986i \(0.784288\pi\)
\(18\) 0 0
\(19\) −1.80348 −0.413746 −0.206873 0.978368i \(-0.566329\pi\)
−0.206873 + 0.978368i \(0.566329\pi\)
\(20\) 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
\(29\) 7.17684 1.33271 0.666353 0.745636i \(-0.267854\pi\)
0.666353 + 0.745636i \(0.267854\pi\)
\(30\) 0 0
\(31\) 4.10856 0.737919 0.368960 0.929445i \(-0.379714\pi\)
0.368960 + 0.929445i \(0.379714\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.62057 −0.442958
\(36\) 0 0
\(37\) 4.62057 0.759618 0.379809 0.925065i \(-0.375990\pi\)
0.379809 + 0.925065i \(0.375990\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.30508 −0.672341 −0.336171 0.941801i \(-0.609132\pi\)
−0.336171 + 0.941801i \(0.609132\pi\)
\(42\) 0 0
\(43\) 6.87176 1.04793 0.523967 0.851739i \(-0.324452\pi\)
0.523967 + 0.851739i \(0.324452\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.80348 −0.263064 −0.131532 0.991312i \(-0.541990\pi\)
−0.131532 + 0.991312i \(0.541990\pi\)
\(48\) 0 0
\(49\) −0.132589 −0.0189413
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.93606 0.678021 0.339010 0.940783i \(-0.389908\pi\)
0.339010 + 0.940783i \(0.389908\pi\)
\(54\) 0 0
\(55\) −6.55627 −0.884047
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 7.54623 0.982436 0.491218 0.871037i \(-0.336552\pi\)
0.491218 + 0.871037i \(0.336552\pi\)
\(60\) 0 0
\(61\) 2.70854 0.346793 0.173396 0.984852i \(-0.444526\pi\)
0.173396 + 0.984852i \(0.444526\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −7.06828 −0.876713
\(66\) 0 0
\(67\) 7.37337 0.900800 0.450400 0.892827i \(-0.351281\pi\)
0.450400 + 0.892827i \(0.351281\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −3.93569 −0.467081 −0.233541 0.972347i \(-0.575031\pi\)
−0.233541 + 0.972347i \(0.575031\pi\)
\(72\) 0 0
\(73\) −5.04462 −0.590429 −0.295214 0.955431i \(-0.595391\pi\)
−0.295214 + 0.955431i \(0.595391\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 17.1812 1.95798
\(78\) 0 0
\(79\) 6.11897 0.688437 0.344219 0.938889i \(-0.388144\pi\)
0.344219 + 0.938889i \(0.388144\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 8.42405 0.924660 0.462330 0.886708i \(-0.347014\pi\)
0.462330 + 0.886708i \(0.347014\pi\)
\(84\) 0 0
\(85\) 6.42405 0.696786
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −11.3838 −1.20668 −0.603339 0.797485i \(-0.706163\pi\)
−0.603339 + 0.797485i \(0.706163\pi\)
\(90\) 0 0
\(91\) 18.5230 1.94173
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.80348 0.185033
\(96\) 0 0
\(97\) −17.9843 −1.82603 −0.913014 0.407927i \(-0.866252\pi\)
−0.913014 + 0.407927i \(0.866252\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.67126 −0.166296 −0.0831481 0.996537i \(-0.526497\pi\)
−0.0831481 + 0.996537i \(0.526497\pi\)
\(102\) 0 0
\(103\) 6.72913 0.663041 0.331521 0.943448i \(-0.392438\pi\)
0.331521 + 0.943448i \(0.392438\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −17.9296 −1.73332 −0.866662 0.498896i \(-0.833739\pi\)
−0.866662 + 0.498896i \(0.833739\pi\)
\(108\) 0 0
\(109\) −12.6692 −1.21349 −0.606744 0.794898i \(-0.707525\pi\)
−0.606744 + 0.794898i \(0.707525\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −21.1708 −1.99158 −0.995790 0.0916634i \(-0.970782\pi\)
−0.995790 + 0.0916634i \(0.970782\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −16.8347 −1.54323
\(120\) 0 0
\(121\) 31.9847 2.90770
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −4.04425 −0.358870 −0.179435 0.983770i \(-0.557427\pi\)
−0.179435 + 0.983770i \(0.557427\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −4.72614 −0.409808
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.75316 −0.491526 −0.245763 0.969330i \(-0.579038\pi\)
−0.245763 + 0.969330i \(0.579038\pi\)
\(138\) 0 0
\(139\) 4.50161 0.381821 0.190911 0.981607i \(-0.438856\pi\)
0.190911 + 0.981607i \(0.438856\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 46.3416 3.87528
\(144\) 0 0
\(145\) −7.17684 −0.596004
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 14.1572 1.15980 0.579900 0.814688i \(-0.303092\pi\)
0.579900 + 0.814688i \(0.303092\pi\)
\(150\) 0 0
\(151\) −18.9847 −1.54495 −0.772475 0.635045i \(-0.780982\pi\)
−0.772475 + 0.635045i \(0.780982\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4.10856 −0.330007
\(156\) 0 0
\(157\) 8.22753 0.656628 0.328314 0.944569i \(-0.393520\pi\)
0.328314 + 0.944569i \(0.393520\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.62057 0.206530
\(162\) 0 0
\(163\) 0.264439 0.0207124 0.0103562 0.999946i \(-0.496703\pi\)
0.0103562 + 0.999946i \(0.496703\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −9.45775 −0.731862 −0.365931 0.930642i \(-0.619249\pi\)
−0.365931 + 0.930642i \(0.619249\pi\)
\(168\) 0 0
\(169\) 36.9606 2.84313
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.758851 0.0576944 0.0288472 0.999584i \(-0.490816\pi\)
0.0288472 + 0.999584i \(0.490816\pi\)
\(174\) 0 0
\(175\) 2.62057 0.198097
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −21.9606 −1.64142 −0.820708 0.571348i \(-0.806420\pi\)
−0.820708 + 0.571348i \(0.806420\pi\)
\(180\) 0 0
\(181\) −14.4727 −1.07574 −0.537872 0.843027i \(-0.680772\pi\)
−0.537872 + 0.843027i \(0.680772\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.62057 −0.339711
\(186\) 0 0
\(187\) −42.1178 −3.07996
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 11.9400 0.863951 0.431976 0.901885i \(-0.357817\pi\)
0.431976 + 0.901885i \(0.357817\pi\)
\(192\) 0 0
\(193\) 11.6342 0.837448 0.418724 0.908114i \(-0.362477\pi\)
0.418724 + 0.908114i \(0.362477\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −24.6181 −1.75397 −0.876984 0.480519i \(-0.840448\pi\)
−0.876984 + 0.480519i \(0.840448\pi\)
\(198\) 0 0
\(199\) 18.7291 1.32767 0.663837 0.747878i \(-0.268927\pi\)
0.663837 + 0.747878i \(0.268927\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 18.8075 1.32002
\(204\) 0 0
\(205\) 4.30508 0.300680
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −11.8241 −0.817888
\(210\) 0 0
\(211\) 3.49839 0.240839 0.120420 0.992723i \(-0.461576\pi\)
0.120420 + 0.992723i \(0.461576\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6.87176 −0.468650
\(216\) 0 0
\(217\) 10.7668 0.730897
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −45.4070 −3.05441
\(222\) 0 0
\(223\) −13.8477 −0.927313 −0.463656 0.886015i \(-0.653463\pi\)
−0.463656 + 0.886015i \(0.653463\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −19.5772 −1.29939 −0.649693 0.760196i \(-0.725103\pi\)
−0.649693 + 0.760196i \(0.725103\pi\)
\(228\) 0 0
\(229\) 25.4959 1.68482 0.842410 0.538838i \(-0.181136\pi\)
0.842410 + 0.538838i \(0.181136\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −16.9847 −1.11270 −0.556351 0.830947i \(-0.687799\pi\)
−0.556351 + 0.830947i \(0.687799\pi\)
\(234\) 0 0
\(235\) 1.80348 0.117646
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −16.5459 −1.07026 −0.535131 0.844769i \(-0.679738\pi\)
−0.535131 + 0.844769i \(0.679738\pi\)
\(240\) 0 0
\(241\) −10.1572 −0.654280 −0.327140 0.944976i \(-0.606085\pi\)
−0.327140 + 0.944976i \(0.606085\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.132589 0.00847081
\(246\) 0 0
\(247\) −12.7475 −0.811103
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5.72950 −0.361643 −0.180822 0.983516i \(-0.557876\pi\)
−0.180822 + 0.983516i \(0.557876\pi\)
\(252\) 0 0
\(253\) 6.55627 0.412189
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 19.5269 1.21806 0.609028 0.793149i \(-0.291560\pi\)
0.609028 + 0.793149i \(0.291560\pi\)
\(258\) 0 0
\(259\) 12.1086 0.752389
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 29.0726 1.79270 0.896348 0.443352i \(-0.146211\pi\)
0.896348 + 0.443352i \(0.146211\pi\)
\(264\) 0 0
\(265\) −4.93606 −0.303220
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −11.8078 −0.719936 −0.359968 0.932965i \(-0.617212\pi\)
−0.359968 + 0.932965i \(0.617212\pi\)
\(270\) 0 0
\(271\) 9.13259 0.554765 0.277383 0.960760i \(-0.410533\pi\)
0.277383 + 0.960760i \(0.410533\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6.55627 0.395358
\(276\) 0 0
\(277\) 27.8564 1.67373 0.836865 0.547409i \(-0.184386\pi\)
0.836865 + 0.547409i \(0.184386\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 11.9461 0.712645 0.356322 0.934363i \(-0.384031\pi\)
0.356322 + 0.934363i \(0.384031\pi\)
\(282\) 0 0
\(283\) −17.0076 −1.01099 −0.505497 0.862828i \(-0.668691\pi\)
−0.505497 + 0.862828i \(0.668691\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −11.2818 −0.665943
\(288\) 0 0
\(289\) 24.2684 1.42755
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 23.9472 1.39901 0.699506 0.714626i \(-0.253403\pi\)
0.699506 + 0.714626i \(0.253403\pi\)
\(294\) 0 0
\(295\) −7.54623 −0.439359
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7.06828 0.408769
\(300\) 0 0
\(301\) 18.0080 1.03796
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.70854 −0.155091
\(306\) 0 0
\(307\) 15.9400 0.909746 0.454873 0.890556i \(-0.349685\pi\)
0.454873 + 0.890556i \(0.349685\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −8.16023 −0.462724 −0.231362 0.972868i \(-0.574318\pi\)
−0.231362 + 0.972868i \(0.574318\pi\)
\(312\) 0 0
\(313\) 2.84375 0.160738 0.0803692 0.996765i \(-0.474390\pi\)
0.0803692 + 0.996765i \(0.474390\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 23.5269 1.32140 0.660702 0.750648i \(-0.270259\pi\)
0.660702 + 0.750648i \(0.270259\pi\)
\(318\) 0 0
\(319\) 47.0533 2.63448
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 11.5856 0.644641
\(324\) 0 0
\(325\) 7.06828 0.392078
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4.72614 −0.260561
\(330\) 0 0
\(331\) −11.9326 −0.655877 −0.327938 0.944699i \(-0.606354\pi\)
−0.327938 + 0.944699i \(0.606354\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −7.37337 −0.402850
\(336\) 0 0
\(337\) 12.6073 0.686765 0.343382 0.939196i \(-0.388427\pi\)
0.343382 + 0.939196i \(0.388427\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 26.9368 1.45871
\(342\) 0 0
\(343\) −18.6915 −1.00925
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5.85132 0.314115 0.157058 0.987589i \(-0.449799\pi\)
0.157058 + 0.987589i \(0.449799\pi\)
\(348\) 0 0
\(349\) −29.7034 −1.58999 −0.794993 0.606618i \(-0.792526\pi\)
−0.794993 + 0.606618i \(0.792526\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.1160 0.538419 0.269209 0.963082i \(-0.413238\pi\)
0.269209 + 0.963082i \(0.413238\pi\)
\(354\) 0 0
\(355\) 3.93569 0.208885
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.45775 −0.0769369 −0.0384684 0.999260i \(-0.512248\pi\)
−0.0384684 + 0.999260i \(0.512248\pi\)
\(360\) 0 0
\(361\) −15.7475 −0.828815
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5.04462 0.264048
\(366\) 0 0
\(367\) 1.98959 0.103856 0.0519280 0.998651i \(-0.483463\pi\)
0.0519280 + 0.998651i \(0.483463\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 12.9353 0.671569
\(372\) 0 0
\(373\) 5.12218 0.265217 0.132608 0.991169i \(-0.457665\pi\)
0.132608 + 0.991169i \(0.457665\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 50.7280 2.61262
\(378\) 0 0
\(379\) −9.79084 −0.502922 −0.251461 0.967867i \(-0.580911\pi\)
−0.251461 + 0.967867i \(0.580911\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −15.4176 −0.787804 −0.393902 0.919152i \(-0.628875\pi\)
−0.393902 + 0.919152i \(0.628875\pi\)
\(384\) 0 0
\(385\) −17.1812 −0.875635
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 38.3616 1.94501 0.972506 0.232877i \(-0.0748138\pi\)
0.972506 + 0.232877i \(0.0748138\pi\)
\(390\) 0 0
\(391\) −6.42405 −0.324878
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6.11897 −0.307879
\(396\) 0 0
\(397\) 2.87102 0.144092 0.0720462 0.997401i \(-0.477047\pi\)
0.0720462 + 0.997401i \(0.477047\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 29.8453 1.49040 0.745201 0.666840i \(-0.232354\pi\)
0.745201 + 0.666840i \(0.232354\pi\)
\(402\) 0 0
\(403\) 29.0405 1.44661
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 30.2937 1.50160
\(408\) 0 0
\(409\) −6.21788 −0.307454 −0.153727 0.988113i \(-0.549128\pi\)
−0.153727 + 0.988113i \(0.549128\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 19.7755 0.973087
\(414\) 0 0
\(415\) −8.42405 −0.413520
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 33.6695 1.64487 0.822433 0.568863i \(-0.192616\pi\)
0.822433 + 0.568863i \(0.192616\pi\)
\(420\) 0 0
\(421\) 17.0149 0.829256 0.414628 0.909991i \(-0.363912\pi\)
0.414628 + 0.909991i \(0.363912\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −6.42405 −0.311612
\(426\) 0 0
\(427\) 7.09793 0.343493
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −19.6422 −0.946129 −0.473065 0.881028i \(-0.656852\pi\)
−0.473065 + 0.881028i \(0.656852\pi\)
\(432\) 0 0
\(433\) −5.24476 −0.252047 −0.126023 0.992027i \(-0.540221\pi\)
−0.126023 + 0.992027i \(0.540221\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.80348 −0.0862719
\(438\) 0 0
\(439\) 17.9194 0.855249 0.427624 0.903957i \(-0.359351\pi\)
0.427624 + 0.903957i \(0.359351\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9.75616 0.463529 0.231764 0.972772i \(-0.425550\pi\)
0.231764 + 0.972772i \(0.425550\pi\)
\(444\) 0 0
\(445\) 11.3838 0.539643
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 34.5703 1.63147 0.815736 0.578425i \(-0.196332\pi\)
0.815736 + 0.578425i \(0.196332\pi\)
\(450\) 0 0
\(451\) −28.2253 −1.32908
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −18.5230 −0.868370
\(456\) 0 0
\(457\) 30.0455 1.40547 0.702736 0.711451i \(-0.251962\pi\)
0.702736 + 0.711451i \(0.251962\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 15.2849 0.711888 0.355944 0.934507i \(-0.384159\pi\)
0.355944 + 0.934507i \(0.384159\pi\)
\(462\) 0 0
\(463\) 4.89235 0.227367 0.113684 0.993517i \(-0.463735\pi\)
0.113684 + 0.993517i \(0.463735\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 35.4972 1.64262 0.821308 0.570485i \(-0.193245\pi\)
0.821308 + 0.570485i \(0.193245\pi\)
\(468\) 0 0
\(469\) 19.3225 0.892228
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 45.0531 2.07154
\(474\) 0 0
\(475\) −1.80348 −0.0827491
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7.80421 −0.356584 −0.178292 0.983978i \(-0.557057\pi\)
−0.178292 + 0.983978i \(0.557057\pi\)
\(480\) 0 0
\(481\) 32.6595 1.48915
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 17.9843 0.816625
\(486\) 0 0
\(487\) −21.5498 −0.976517 −0.488258 0.872699i \(-0.662368\pi\)
−0.488258 + 0.872699i \(0.662368\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 15.8315 0.714465 0.357232 0.934016i \(-0.383720\pi\)
0.357232 + 0.934016i \(0.383720\pi\)
\(492\) 0 0
\(493\) −46.1044 −2.07644
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −10.3138 −0.462636
\(498\) 0 0
\(499\) −5.76357 −0.258013 −0.129006 0.991644i \(-0.541179\pi\)
−0.129006 + 0.991644i \(0.541179\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 18.8075 0.838583 0.419291 0.907852i \(-0.362279\pi\)
0.419291 + 0.907852i \(0.362279\pi\)
\(504\) 0 0
\(505\) 1.67126 0.0743699
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3.21675 −0.142580 −0.0712900 0.997456i \(-0.522712\pi\)
−0.0712900 + 0.997456i \(0.522712\pi\)
\(510\) 0 0
\(511\) −13.2198 −0.584810
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −6.72913 −0.296521
\(516\) 0 0
\(517\) −11.8241 −0.520022
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −14.9100 −0.653217 −0.326609 0.945160i \(-0.605906\pi\)
−0.326609 + 0.945160i \(0.605906\pi\)
\(522\) 0 0
\(523\) 12.3982 0.542134 0.271067 0.962561i \(-0.412624\pi\)
0.271067 + 0.962561i \(0.412624\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −26.3936 −1.14972
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −30.4296 −1.31805
\(534\) 0 0
\(535\) 17.9296 0.775166
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.869290 −0.0374430
\(540\) 0 0
\(541\) −30.8954 −1.32830 −0.664149 0.747600i \(-0.731206\pi\)
−0.664149 + 0.747600i \(0.731206\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 12.6692 0.542688
\(546\) 0 0
\(547\) 14.2251 0.608220 0.304110 0.952637i \(-0.401641\pi\)
0.304110 + 0.952637i \(0.401641\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −12.9433 −0.551401
\(552\) 0 0
\(553\) 16.0352 0.681886
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14.6989 0.622811 0.311406 0.950277i \(-0.399200\pi\)
0.311406 + 0.950277i \(0.399200\pi\)
\(558\) 0 0
\(559\) 48.5715 2.05436
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −19.4972 −0.821710 −0.410855 0.911701i \(-0.634770\pi\)
−0.410855 + 0.911701i \(0.634770\pi\)
\(564\) 0 0
\(565\) 21.1708 0.890662
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 17.8854 0.749795 0.374898 0.927066i \(-0.377678\pi\)
0.374898 + 0.927066i \(0.377678\pi\)
\(570\) 0 0
\(571\) −23.3904 −0.978856 −0.489428 0.872044i \(-0.662794\pi\)
−0.489428 + 0.872044i \(0.662794\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) −45.7515 −1.90466 −0.952329 0.305072i \(-0.901320\pi\)
−0.952329 + 0.305072i \(0.901320\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 22.0759 0.915861
\(582\) 0 0
\(583\) 32.3622 1.34030
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −24.9839 −1.03120 −0.515599 0.856830i \(-0.672430\pi\)
−0.515599 + 0.856830i \(0.672430\pi\)
\(588\) 0 0
\(589\) −7.40969 −0.305311
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −25.3178 −1.03968 −0.519838 0.854265i \(-0.674008\pi\)
−0.519838 + 0.854265i \(0.674008\pi\)
\(594\) 0 0
\(595\) 16.8347 0.690155
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −5.23756 −0.214001 −0.107000 0.994259i \(-0.534125\pi\)
−0.107000 + 0.994259i \(0.534125\pi\)
\(600\) 0 0
\(601\) −26.1173 −1.06535 −0.532673 0.846321i \(-0.678812\pi\)
−0.532673 + 0.846321i \(0.678812\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −31.9847 −1.30036
\(606\) 0 0
\(607\) −24.6631 −1.00105 −0.500523 0.865723i \(-0.666859\pi\)
−0.500523 + 0.865723i \(0.666859\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −12.7475 −0.515708
\(612\) 0 0
\(613\) −4.60052 −0.185813 −0.0929067 0.995675i \(-0.529616\pi\)
−0.0929067 + 0.995675i \(0.529616\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −18.9143 −0.761461 −0.380731 0.924686i \(-0.624327\pi\)
−0.380731 + 0.924686i \(0.624327\pi\)
\(618\) 0 0
\(619\) −47.9686 −1.92802 −0.964010 0.265865i \(-0.914343\pi\)
−0.964010 + 0.265865i \(0.914343\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −29.8320 −1.19519
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −29.6828 −1.18353
\(630\) 0 0
\(631\) −29.5445 −1.17615 −0.588074 0.808807i \(-0.700114\pi\)
−0.588074 + 0.808807i \(0.700114\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.04425 0.160491
\(636\) 0 0
\(637\) −0.937178 −0.0371323
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 43.2557 1.70850 0.854248 0.519865i \(-0.174018\pi\)
0.854248 + 0.519865i \(0.174018\pi\)
\(642\) 0 0
\(643\) −37.2455 −1.46882 −0.734410 0.678707i \(-0.762541\pi\)
−0.734410 + 0.678707i \(0.762541\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −41.9007 −1.64729 −0.823643 0.567109i \(-0.808062\pi\)
−0.823643 + 0.567109i \(0.808062\pi\)
\(648\) 0 0
\(649\) 49.4751 1.94207
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −36.4697 −1.42717 −0.713584 0.700570i \(-0.752929\pi\)
−0.713584 + 0.700570i \(0.752929\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 17.8247 0.694350 0.347175 0.937800i \(-0.387141\pi\)
0.347175 + 0.937800i \(0.387141\pi\)
\(660\) 0 0
\(661\) −2.70189 −0.105091 −0.0525456 0.998619i \(-0.516733\pi\)
−0.0525456 + 0.998619i \(0.516733\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.72614 0.183272
\(666\) 0 0
\(667\) 7.17684 0.277889
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 17.7579 0.685537
\(672\) 0 0
\(673\) 8.19652 0.315953 0.157976 0.987443i \(-0.449503\pi\)
0.157976 + 0.987443i \(0.449503\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −26.8759 −1.03292 −0.516462 0.856310i \(-0.672751\pi\)
−0.516462 + 0.856310i \(0.672751\pi\)
\(678\) 0 0
\(679\) −47.1292 −1.80865
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 17.1252 0.655277 0.327638 0.944803i \(-0.393747\pi\)
0.327638 + 0.944803i \(0.393747\pi\)
\(684\) 0 0
\(685\) 5.75316 0.219817
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 34.8895 1.32918
\(690\) 0 0
\(691\) 15.7042 0.597414 0.298707 0.954345i \(-0.403445\pi\)
0.298707 + 0.954345i \(0.403445\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4.50161 −0.170756
\(696\) 0 0
\(697\) 27.6561 1.04755
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 6.81955 0.257571 0.128785 0.991672i \(-0.458892\pi\)
0.128785 + 0.991672i \(0.458892\pi\)
\(702\) 0 0
\(703\) −8.33309 −0.314289
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.37965 −0.164714
\(708\) 0 0
\(709\) 23.0955 0.867368 0.433684 0.901065i \(-0.357213\pi\)
0.433684 + 0.901065i \(0.357213\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.10856 0.153867
\(714\) 0 0
\(715\) −46.3416 −1.73308
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 22.5152 0.839675 0.419838 0.907599i \(-0.362087\pi\)
0.419838 + 0.907599i \(0.362087\pi\)
\(720\) 0 0
\(721\) 17.6342 0.656732
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 7.17684 0.266541
\(726\) 0 0
\(727\) −3.45998 −0.128323 −0.0641617 0.997940i \(-0.520437\pi\)
−0.0641617 + 0.997940i \(0.520437\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −44.1445 −1.63274
\(732\) 0 0
\(733\) −16.2835 −0.601446 −0.300723 0.953711i \(-0.597228\pi\)
−0.300723 + 0.953711i \(0.597228\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 48.3418 1.78069
\(738\) 0 0
\(739\) 24.2459 0.891899 0.445949 0.895058i \(-0.352866\pi\)
0.445949 + 0.895058i \(0.352866\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −30.7202 −1.12702 −0.563508 0.826111i \(-0.690549\pi\)
−0.563508 + 0.826111i \(0.690549\pi\)
\(744\) 0 0
\(745\) −14.1572 −0.518678
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −46.9860 −1.71683
\(750\) 0 0
\(751\) −37.3493 −1.36290 −0.681448 0.731867i \(-0.738649\pi\)
−0.681448 + 0.731867i \(0.738649\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 18.9847 0.690923
\(756\) 0 0
\(757\) 18.8930 0.686677 0.343338 0.939212i \(-0.388442\pi\)
0.343338 + 0.939212i \(0.388442\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 37.5549 1.36137 0.680683 0.732578i \(-0.261683\pi\)
0.680683 + 0.732578i \(0.261683\pi\)
\(762\) 0 0
\(763\) −33.2005 −1.20194
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 53.3389 1.92596
\(768\) 0 0
\(769\) −35.8799 −1.29386 −0.646931 0.762549i \(-0.723948\pi\)
−0.646931 + 0.762549i \(0.723948\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 32.3745 1.16443 0.582215 0.813035i \(-0.302186\pi\)
0.582215 + 0.813035i \(0.302186\pi\)
\(774\) 0 0
\(775\) 4.10856 0.147584
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7.76411 0.278178
\(780\) 0 0
\(781\) −25.8035 −0.923321
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −8.22753 −0.293653
\(786\) 0 0
\(787\) −47.7278 −1.70131 −0.850656 0.525723i \(-0.823795\pi\)
−0.850656 + 0.525723i \(0.823795\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −55.4796 −1.97263
\(792\) 0 0
\(793\) 19.1447 0.679849
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 12.8427 0.454910 0.227455 0.973789i \(-0.426959\pi\)
0.227455 + 0.973789i \(0.426959\pi\)
\(798\) 0 0
\(799\) 11.5856 0.409870
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −33.0739 −1.16715
\(804\) 0 0
\(805\) −2.62057 −0.0923631
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −8.84864 −0.311102 −0.155551 0.987828i \(-0.549715\pi\)
−0.155551 + 0.987828i \(0.549715\pi\)
\(810\) 0 0
\(811\) 30.4149 1.06801 0.534006 0.845480i \(-0.320686\pi\)
0.534006 + 0.845480i \(0.320686\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −0.264439 −0.00926289
\(816\) 0 0
\(817\) −12.3930 −0.433578
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −31.2463 −1.09050 −0.545251 0.838273i \(-0.683566\pi\)
−0.545251 + 0.838273i \(0.683566\pi\)
\(822\) 0 0
\(823\) −50.6232 −1.76462 −0.882308 0.470673i \(-0.844011\pi\)
−0.882308 + 0.470673i \(0.844011\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 32.5478 1.13180 0.565898 0.824475i \(-0.308529\pi\)
0.565898 + 0.824475i \(0.308529\pi\)
\(828\) 0 0
\(829\) −29.0119 −1.00763 −0.503813 0.863813i \(-0.668070\pi\)
−0.503813 + 0.863813i \(0.668070\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0.851759 0.0295117
\(834\) 0 0
\(835\) 9.45775 0.327299
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1.97993 0.0683547 0.0341774 0.999416i \(-0.489119\pi\)
0.0341774 + 0.999416i \(0.489119\pi\)
\(840\) 0 0
\(841\) 22.5071 0.776106
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −36.9606 −1.27148
\(846\) 0 0
\(847\) 83.8182 2.88003
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4.62057 0.158391
\(852\) 0 0
\(853\) −11.1781 −0.382732 −0.191366 0.981519i \(-0.561292\pi\)
−0.191366 + 0.981519i \(0.561292\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −29.2491 −0.999130 −0.499565 0.866276i \(-0.666507\pi\)
−0.499565 + 0.866276i \(0.666507\pi\)
\(858\) 0 0
\(859\) 47.5143 1.62117 0.810584 0.585623i \(-0.199150\pi\)
0.810584 + 0.585623i \(0.199150\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 16.5628 0.563806 0.281903 0.959443i \(-0.409034\pi\)
0.281903 + 0.959443i \(0.409034\pi\)
\(864\) 0 0
\(865\) −0.758851 −0.0258017
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 40.1176 1.36090
\(870\) 0 0
\(871\) 52.1171 1.76592
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2.62057 −0.0885916
\(876\) 0 0
\(877\) −4.80976 −0.162414 −0.0812070 0.996697i \(-0.525877\pi\)
−0.0812070 + 0.996697i \(0.525877\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −29.8046 −1.00414 −0.502072 0.864826i \(-0.667429\pi\)
−0.502072 + 0.864826i \(0.667429\pi\)
\(882\) 0 0
\(883\) −22.1579 −0.745673 −0.372836 0.927897i \(-0.621615\pi\)
−0.372836 + 0.927897i \(0.621615\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −31.3425 −1.05238 −0.526189 0.850367i \(-0.676380\pi\)
−0.526189 + 0.850367i \(0.676380\pi\)
\(888\) 0 0
\(889\) −10.5983 −0.355455
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 3.25252 0.108842
\(894\) 0 0
\(895\) 21.9606 0.734063
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 29.4865 0.983430
\(900\) 0 0
\(901\) −31.7095 −1.05640
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 14.4727 0.481087
\(906\) 0 0
\(907\) 11.3541 0.377006 0.188503 0.982073i \(-0.439636\pi\)
0.188503 + 0.982073i \(0.439636\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −5.23245 −0.173359 −0.0866794 0.996236i \(-0.527626\pi\)
−0.0866794 + 0.996236i \(0.527626\pi\)
\(912\) 0 0
\(913\) 55.2303 1.82786
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 58.1349 1.91769 0.958846 0.283925i \(-0.0916368\pi\)
0.958846 + 0.283925i \(0.0916368\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −27.8186 −0.915661
\(924\) 0 0
\(925\) 4.62057 0.151924
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 31.9681 1.04884 0.524419 0.851460i \(-0.324283\pi\)
0.524419 + 0.851460i \(0.324283\pi\)
\(930\) 0 0
\(931\) 0.239121 0.00783688
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 42.1178 1.37740
\(936\) 0 0
\(937\) 44.2567 1.44580 0.722902 0.690951i \(-0.242808\pi\)
0.722902 + 0.690951i \(0.242808\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −18.4144 −0.600292 −0.300146 0.953893i \(-0.597035\pi\)
−0.300146 + 0.953893i \(0.597035\pi\)
\(942\) 0 0
\(943\) −4.30508 −0.140193
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −48.8625 −1.58782 −0.793909 0.608037i \(-0.791957\pi\)
−0.793909 + 0.608037i \(0.791957\pi\)
\(948\) 0 0
\(949\) −35.6568 −1.15747
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 49.0643 1.58935 0.794674 0.607037i \(-0.207642\pi\)
0.794674 + 0.607037i \(0.207642\pi\)
\(954\) 0 0
\(955\) −11.9400 −0.386371
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −15.0766 −0.486849
\(960\) 0 0
\(961\) −14.1197 −0.455475
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −11.6342 −0.374518
\(966\) 0 0
\(967\) −20.4921 −0.658981 −0.329491 0.944159i \(-0.606877\pi\)
−0.329491 + 0.944159i \(0.606877\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 13.8581 0.444728 0.222364 0.974964i \(-0.428623\pi\)
0.222364 + 0.974964i \(0.428623\pi\)
\(972\) 0 0
\(973\) 11.7968 0.378188
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 10.1668 0.325266 0.162633 0.986687i \(-0.448001\pi\)
0.162633 + 0.986687i \(0.448001\pi\)
\(978\) 0 0
\(979\) −74.6351 −2.38535
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −50.6875 −1.61668 −0.808341 0.588715i \(-0.799634\pi\)
−0.808341 + 0.588715i \(0.799634\pi\)
\(984\) 0 0
\(985\) 24.6181 0.784399
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 6.87176 0.218509
\(990\) 0 0
\(991\) 19.9799 0.634684 0.317342 0.948311i \(-0.397210\pi\)
0.317342 + 0.948311i \(0.397210\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −18.7291 −0.593753
\(996\) 0 0
\(997\) −7.41454 −0.234821 −0.117410 0.993083i \(-0.537459\pi\)
−0.117410 + 0.993083i \(0.537459\pi\)
\(998\) 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.br.1.4 5
3.2 odd 2 2760.2.a.w.1.4 5
12.11 even 2 5520.2.a.cc.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2760.2.a.w.1.4 5 3.2 odd 2
5520.2.a.cc.1.2 5 12.11 even 2
8280.2.a.br.1.4 5 1.1 even 1 trivial