Properties

Label 7360.2.a.bo.1.1
Level $7360$
Weight $2$
Character 7360.1
Self dual yes
Analytic conductor $58.770$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 7360 = 2^{6} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7360.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(58.7698958877\)
Analytic rank: \(0\)
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 460)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.56155\) of defining polynomial
Character \(\chi\) \(=\) 7360.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.56155 q^{3} -1.00000 q^{5} -2.56155 q^{7} -0.561553 q^{9} +O(q^{10})\) \(q-1.56155 q^{3} -1.00000 q^{5} -2.56155 q^{7} -0.561553 q^{9} +2.00000 q^{11} +3.56155 q^{13} +1.56155 q^{15} +2.56155 q^{17} +6.00000 q^{19} +4.00000 q^{21} -1.00000 q^{23} +1.00000 q^{25} +5.56155 q^{27} -6.12311 q^{29} -7.24621 q^{31} -3.12311 q^{33} +2.56155 q^{35} +4.56155 q^{37} -5.56155 q^{39} +4.12311 q^{41} +0.561553 q^{45} -4.68466 q^{47} -0.438447 q^{49} -4.00000 q^{51} +4.56155 q^{53} -2.00000 q^{55} -9.36932 q^{57} -3.68466 q^{59} +7.12311 q^{61} +1.43845 q^{63} -3.56155 q^{65} -8.56155 q^{67} +1.56155 q^{69} -10.1231 q^{71} -4.43845 q^{73} -1.56155 q^{75} -5.12311 q^{77} -4.87689 q^{79} -7.00000 q^{81} -13.9309 q^{83} -2.56155 q^{85} +9.56155 q^{87} +14.2462 q^{89} -9.12311 q^{91} +11.3153 q^{93} -6.00000 q^{95} -13.1231 q^{97} -1.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} - 2 q^{5} - q^{7} + 3 q^{9} + O(q^{10}) \) \( 2 q + q^{3} - 2 q^{5} - q^{7} + 3 q^{9} + 4 q^{11} + 3 q^{13} - q^{15} + q^{17} + 12 q^{19} + 8 q^{21} - 2 q^{23} + 2 q^{25} + 7 q^{27} - 4 q^{29} + 2 q^{31} + 2 q^{33} + q^{35} + 5 q^{37} - 7 q^{39} - 3 q^{45} + 3 q^{47} - 5 q^{49} - 8 q^{51} + 5 q^{53} - 4 q^{55} + 6 q^{57} + 5 q^{59} + 6 q^{61} + 7 q^{63} - 3 q^{65} - 13 q^{67} - q^{69} - 12 q^{71} - 13 q^{73} + q^{75} - 2 q^{77} - 18 q^{79} - 14 q^{81} + q^{83} - q^{85} + 15 q^{87} + 12 q^{89} - 10 q^{91} + 35 q^{93} - 12 q^{95} - 18 q^{97} + 6 q^{99} + O(q^{100}) \)

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
\(3\) −1.56155 −0.901563 −0.450781 0.892634i \(-0.648855\pi\)
−0.450781 + 0.892634i \(0.648855\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −2.56155 −0.968176 −0.484088 0.875019i \(-0.660849\pi\)
−0.484088 + 0.875019i \(0.660849\pi\)
\(8\) 0 0
\(9\) −0.561553 −0.187184
\(10\) 0 0
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) 3.56155 0.987797 0.493899 0.869520i \(-0.335571\pi\)
0.493899 + 0.869520i \(0.335571\pi\)
\(14\) 0 0
\(15\) 1.56155 0.403191
\(16\) 0 0
\(17\) 2.56155 0.621268 0.310634 0.950530i \(-0.399459\pi\)
0.310634 + 0.950530i \(0.399459\pi\)
\(18\) 0 0
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 0 0
\(21\) 4.00000 0.872872
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.56155 1.07032
\(28\) 0 0
\(29\) −6.12311 −1.13703 −0.568516 0.822672i \(-0.692482\pi\)
−0.568516 + 0.822672i \(0.692482\pi\)
\(30\) 0 0
\(31\) −7.24621 −1.30146 −0.650729 0.759310i \(-0.725537\pi\)
−0.650729 + 0.759310i \(0.725537\pi\)
\(32\) 0 0
\(33\) −3.12311 −0.543663
\(34\) 0 0
\(35\) 2.56155 0.432981
\(36\) 0 0
\(37\) 4.56155 0.749915 0.374957 0.927042i \(-0.377657\pi\)
0.374957 + 0.927042i \(0.377657\pi\)
\(38\) 0 0
\(39\) −5.56155 −0.890561
\(40\) 0 0
\(41\) 4.12311 0.643921 0.321960 0.946753i \(-0.395658\pi\)
0.321960 + 0.946753i \(0.395658\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0.561553 0.0837114
\(46\) 0 0
\(47\) −4.68466 −0.683328 −0.341664 0.939822i \(-0.610990\pi\)
−0.341664 + 0.939822i \(0.610990\pi\)
\(48\) 0 0
\(49\) −0.438447 −0.0626353
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) 0 0
\(53\) 4.56155 0.626577 0.313289 0.949658i \(-0.398569\pi\)
0.313289 + 0.949658i \(0.398569\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) −9.36932 −1.24100
\(58\) 0 0
\(59\) −3.68466 −0.479702 −0.239851 0.970810i \(-0.577099\pi\)
−0.239851 + 0.970810i \(0.577099\pi\)
\(60\) 0 0
\(61\) 7.12311 0.912020 0.456010 0.889975i \(-0.349278\pi\)
0.456010 + 0.889975i \(0.349278\pi\)
\(62\) 0 0
\(63\) 1.43845 0.181227
\(64\) 0 0
\(65\) −3.56155 −0.441756
\(66\) 0 0
\(67\) −8.56155 −1.04596 −0.522980 0.852345i \(-0.675180\pi\)
−0.522980 + 0.852345i \(0.675180\pi\)
\(68\) 0 0
\(69\) 1.56155 0.187989
\(70\) 0 0
\(71\) −10.1231 −1.20139 −0.600696 0.799478i \(-0.705110\pi\)
−0.600696 + 0.799478i \(0.705110\pi\)
\(72\) 0 0
\(73\) −4.43845 −0.519481 −0.259740 0.965678i \(-0.583637\pi\)
−0.259740 + 0.965678i \(0.583637\pi\)
\(74\) 0 0
\(75\) −1.56155 −0.180313
\(76\) 0 0
\(77\) −5.12311 −0.583832
\(78\) 0 0
\(79\) −4.87689 −0.548693 −0.274347 0.961631i \(-0.588462\pi\)
−0.274347 + 0.961631i \(0.588462\pi\)
\(80\) 0 0
\(81\) −7.00000 −0.777778
\(82\) 0 0
\(83\) −13.9309 −1.52911 −0.764556 0.644558i \(-0.777042\pi\)
−0.764556 + 0.644558i \(0.777042\pi\)
\(84\) 0 0
\(85\) −2.56155 −0.277839
\(86\) 0 0
\(87\) 9.56155 1.02511
\(88\) 0 0
\(89\) 14.2462 1.51010 0.755048 0.655670i \(-0.227614\pi\)
0.755048 + 0.655670i \(0.227614\pi\)
\(90\) 0 0
\(91\) −9.12311 −0.956361
\(92\) 0 0
\(93\) 11.3153 1.17335
\(94\) 0 0
\(95\) −6.00000 −0.615587
\(96\) 0 0
\(97\) −13.1231 −1.33245 −0.666225 0.745751i \(-0.732091\pi\)
−0.666225 + 0.745751i \(0.732091\pi\)
\(98\) 0 0
\(99\) −1.12311 −0.112876
\(100\) 0 0
\(101\) 17.6847 1.75969 0.879845 0.475261i \(-0.157647\pi\)
0.879845 + 0.475261i \(0.157647\pi\)
\(102\) 0 0
\(103\) 16.0000 1.57653 0.788263 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) 0 0
\(105\) −4.00000 −0.390360
\(106\) 0 0
\(107\) 3.43845 0.332407 0.166204 0.986091i \(-0.446849\pi\)
0.166204 + 0.986091i \(0.446849\pi\)
\(108\) 0 0
\(109\) −15.3693 −1.47211 −0.736057 0.676920i \(-0.763314\pi\)
−0.736057 + 0.676920i \(0.763314\pi\)
\(110\) 0 0
\(111\) −7.12311 −0.676095
\(112\) 0 0
\(113\) 12.8078 1.20485 0.602427 0.798174i \(-0.294201\pi\)
0.602427 + 0.798174i \(0.294201\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) −2.00000 −0.184900
\(118\) 0 0
\(119\) −6.56155 −0.601497
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) −6.43845 −0.580535
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −7.80776 −0.692827 −0.346414 0.938082i \(-0.612601\pi\)
−0.346414 + 0.938082i \(0.612601\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.192236 0.0167957 0.00839787 0.999965i \(-0.497327\pi\)
0.00839787 + 0.999965i \(0.497327\pi\)
\(132\) 0 0
\(133\) −15.3693 −1.33269
\(134\) 0 0
\(135\) −5.56155 −0.478662
\(136\) 0 0
\(137\) 6.87689 0.587533 0.293766 0.955877i \(-0.405091\pi\)
0.293766 + 0.955877i \(0.405091\pi\)
\(138\) 0 0
\(139\) −11.2462 −0.953891 −0.476946 0.878933i \(-0.658256\pi\)
−0.476946 + 0.878933i \(0.658256\pi\)
\(140\) 0 0
\(141\) 7.31534 0.616063
\(142\) 0 0
\(143\) 7.12311 0.595664
\(144\) 0 0
\(145\) 6.12311 0.508496
\(146\) 0 0
\(147\) 0.684658 0.0564697
\(148\) 0 0
\(149\) 9.36932 0.767564 0.383782 0.923424i \(-0.374621\pi\)
0.383782 + 0.923424i \(0.374621\pi\)
\(150\) 0 0
\(151\) 14.0540 1.14370 0.571848 0.820359i \(-0.306227\pi\)
0.571848 + 0.820359i \(0.306227\pi\)
\(152\) 0 0
\(153\) −1.43845 −0.116292
\(154\) 0 0
\(155\) 7.24621 0.582030
\(156\) 0 0
\(157\) 4.31534 0.344402 0.172201 0.985062i \(-0.444912\pi\)
0.172201 + 0.985062i \(0.444912\pi\)
\(158\) 0 0
\(159\) −7.12311 −0.564899
\(160\) 0 0
\(161\) 2.56155 0.201879
\(162\) 0 0
\(163\) 16.9309 1.32613 0.663064 0.748563i \(-0.269256\pi\)
0.663064 + 0.748563i \(0.269256\pi\)
\(164\) 0 0
\(165\) 3.12311 0.243133
\(166\) 0 0
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) −0.315342 −0.0242570
\(170\) 0 0
\(171\) −3.36932 −0.257658
\(172\) 0 0
\(173\) −5.36932 −0.408222 −0.204111 0.978948i \(-0.565430\pi\)
−0.204111 + 0.978948i \(0.565430\pi\)
\(174\) 0 0
\(175\) −2.56155 −0.193635
\(176\) 0 0
\(177\) 5.75379 0.432481
\(178\) 0 0
\(179\) −6.93087 −0.518038 −0.259019 0.965872i \(-0.583399\pi\)
−0.259019 + 0.965872i \(0.583399\pi\)
\(180\) 0 0
\(181\) 5.36932 0.399098 0.199549 0.979888i \(-0.436052\pi\)
0.199549 + 0.979888i \(0.436052\pi\)
\(182\) 0 0
\(183\) −11.1231 −0.822244
\(184\) 0 0
\(185\) −4.56155 −0.335372
\(186\) 0 0
\(187\) 5.12311 0.374639
\(188\) 0 0
\(189\) −14.2462 −1.03626
\(190\) 0 0
\(191\) −17.3693 −1.25680 −0.628400 0.777891i \(-0.716290\pi\)
−0.628400 + 0.777891i \(0.716290\pi\)
\(192\) 0 0
\(193\) 2.43845 0.175523 0.0877616 0.996142i \(-0.472029\pi\)
0.0877616 + 0.996142i \(0.472029\pi\)
\(194\) 0 0
\(195\) 5.56155 0.398271
\(196\) 0 0
\(197\) 18.6847 1.33123 0.665613 0.746297i \(-0.268170\pi\)
0.665613 + 0.746297i \(0.268170\pi\)
\(198\) 0 0
\(199\) 10.0000 0.708881 0.354441 0.935079i \(-0.384671\pi\)
0.354441 + 0.935079i \(0.384671\pi\)
\(200\) 0 0
\(201\) 13.3693 0.942999
\(202\) 0 0
\(203\) 15.6847 1.10085
\(204\) 0 0
\(205\) −4.12311 −0.287970
\(206\) 0 0
\(207\) 0.561553 0.0390306
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 0.315342 0.0217090 0.0108545 0.999941i \(-0.496545\pi\)
0.0108545 + 0.999941i \(0.496545\pi\)
\(212\) 0 0
\(213\) 15.8078 1.08313
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 18.5616 1.26004
\(218\) 0 0
\(219\) 6.93087 0.468345
\(220\) 0 0
\(221\) 9.12311 0.613686
\(222\) 0 0
\(223\) 17.6155 1.17962 0.589812 0.807541i \(-0.299202\pi\)
0.589812 + 0.807541i \(0.299202\pi\)
\(224\) 0 0
\(225\) −0.561553 −0.0374369
\(226\) 0 0
\(227\) 26.2462 1.74202 0.871011 0.491263i \(-0.163465\pi\)
0.871011 + 0.491263i \(0.163465\pi\)
\(228\) 0 0
\(229\) 26.7386 1.76694 0.883469 0.468489i \(-0.155201\pi\)
0.883469 + 0.468489i \(0.155201\pi\)
\(230\) 0 0
\(231\) 8.00000 0.526361
\(232\) 0 0
\(233\) −0.684658 −0.0448535 −0.0224267 0.999748i \(-0.507139\pi\)
−0.0224267 + 0.999748i \(0.507139\pi\)
\(234\) 0 0
\(235\) 4.68466 0.305593
\(236\) 0 0
\(237\) 7.61553 0.494682
\(238\) 0 0
\(239\) −2.75379 −0.178128 −0.0890639 0.996026i \(-0.528388\pi\)
−0.0890639 + 0.996026i \(0.528388\pi\)
\(240\) 0 0
\(241\) 6.00000 0.386494 0.193247 0.981150i \(-0.438098\pi\)
0.193247 + 0.981150i \(0.438098\pi\)
\(242\) 0 0
\(243\) −5.75379 −0.369106
\(244\) 0 0
\(245\) 0.438447 0.0280114
\(246\) 0 0
\(247\) 21.3693 1.35970
\(248\) 0 0
\(249\) 21.7538 1.37859
\(250\) 0 0
\(251\) −7.36932 −0.465147 −0.232574 0.972579i \(-0.574715\pi\)
−0.232574 + 0.972579i \(0.574715\pi\)
\(252\) 0 0
\(253\) −2.00000 −0.125739
\(254\) 0 0
\(255\) 4.00000 0.250490
\(256\) 0 0
\(257\) 31.8078 1.98411 0.992057 0.125790i \(-0.0401465\pi\)
0.992057 + 0.125790i \(0.0401465\pi\)
\(258\) 0 0
\(259\) −11.6847 −0.726049
\(260\) 0 0
\(261\) 3.43845 0.212835
\(262\) 0 0
\(263\) −0.0691303 −0.00426276 −0.00213138 0.999998i \(-0.500678\pi\)
−0.00213138 + 0.999998i \(0.500678\pi\)
\(264\) 0 0
\(265\) −4.56155 −0.280214
\(266\) 0 0
\(267\) −22.2462 −1.36145
\(268\) 0 0
\(269\) −23.2462 −1.41735 −0.708673 0.705537i \(-0.750706\pi\)
−0.708673 + 0.705537i \(0.750706\pi\)
\(270\) 0 0
\(271\) −21.9309 −1.33221 −0.666103 0.745860i \(-0.732039\pi\)
−0.666103 + 0.745860i \(0.732039\pi\)
\(272\) 0 0
\(273\) 14.2462 0.862220
\(274\) 0 0
\(275\) 2.00000 0.120605
\(276\) 0 0
\(277\) 6.68466 0.401642 0.200821 0.979628i \(-0.435639\pi\)
0.200821 + 0.979628i \(0.435639\pi\)
\(278\) 0 0
\(279\) 4.06913 0.243612
\(280\) 0 0
\(281\) −6.87689 −0.410241 −0.205121 0.978737i \(-0.565759\pi\)
−0.205121 + 0.978737i \(0.565759\pi\)
\(282\) 0 0
\(283\) 14.8078 0.880230 0.440115 0.897941i \(-0.354938\pi\)
0.440115 + 0.897941i \(0.354938\pi\)
\(284\) 0 0
\(285\) 9.36932 0.554990
\(286\) 0 0
\(287\) −10.5616 −0.623429
\(288\) 0 0
\(289\) −10.4384 −0.614026
\(290\) 0 0
\(291\) 20.4924 1.20129
\(292\) 0 0
\(293\) 16.8078 0.981920 0.490960 0.871182i \(-0.336646\pi\)
0.490960 + 0.871182i \(0.336646\pi\)
\(294\) 0 0
\(295\) 3.68466 0.214529
\(296\) 0 0
\(297\) 11.1231 0.645428
\(298\) 0 0
\(299\) −3.56155 −0.205970
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −27.6155 −1.58647
\(304\) 0 0
\(305\) −7.12311 −0.407868
\(306\) 0 0
\(307\) −21.1231 −1.20556 −0.602780 0.797908i \(-0.705940\pi\)
−0.602780 + 0.797908i \(0.705940\pi\)
\(308\) 0 0
\(309\) −24.9848 −1.42134
\(310\) 0 0
\(311\) −8.68466 −0.492462 −0.246231 0.969211i \(-0.579192\pi\)
−0.246231 + 0.969211i \(0.579192\pi\)
\(312\) 0 0
\(313\) −0.807764 −0.0456575 −0.0228288 0.999739i \(-0.507267\pi\)
−0.0228288 + 0.999739i \(0.507267\pi\)
\(314\) 0 0
\(315\) −1.43845 −0.0810473
\(316\) 0 0
\(317\) −15.1231 −0.849398 −0.424699 0.905335i \(-0.639620\pi\)
−0.424699 + 0.905335i \(0.639620\pi\)
\(318\) 0 0
\(319\) −12.2462 −0.685656
\(320\) 0 0
\(321\) −5.36932 −0.299686
\(322\) 0 0
\(323\) 15.3693 0.855172
\(324\) 0 0
\(325\) 3.56155 0.197559
\(326\) 0 0
\(327\) 24.0000 1.32720
\(328\) 0 0
\(329\) 12.0000 0.661581
\(330\) 0 0
\(331\) 28.6155 1.57285 0.786426 0.617685i \(-0.211929\pi\)
0.786426 + 0.617685i \(0.211929\pi\)
\(332\) 0 0
\(333\) −2.56155 −0.140372
\(334\) 0 0
\(335\) 8.56155 0.467768
\(336\) 0 0
\(337\) 13.6155 0.741685 0.370843 0.928696i \(-0.379069\pi\)
0.370843 + 0.928696i \(0.379069\pi\)
\(338\) 0 0
\(339\) −20.0000 −1.08625
\(340\) 0 0
\(341\) −14.4924 −0.784809
\(342\) 0 0
\(343\) 19.0540 1.02882
\(344\) 0 0
\(345\) −1.56155 −0.0840712
\(346\) 0 0
\(347\) 16.4924 0.885360 0.442680 0.896680i \(-0.354028\pi\)
0.442680 + 0.896680i \(0.354028\pi\)
\(348\) 0 0
\(349\) 26.3693 1.41152 0.705759 0.708452i \(-0.250606\pi\)
0.705759 + 0.708452i \(0.250606\pi\)
\(350\) 0 0
\(351\) 19.8078 1.05726
\(352\) 0 0
\(353\) −2.05398 −0.109322 −0.0546610 0.998505i \(-0.517408\pi\)
−0.0546610 + 0.998505i \(0.517408\pi\)
\(354\) 0 0
\(355\) 10.1231 0.537279
\(356\) 0 0
\(357\) 10.2462 0.542287
\(358\) 0 0
\(359\) −15.6155 −0.824156 −0.412078 0.911149i \(-0.635197\pi\)
−0.412078 + 0.911149i \(0.635197\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 0 0
\(363\) 10.9309 0.573722
\(364\) 0 0
\(365\) 4.43845 0.232319
\(366\) 0 0
\(367\) 22.5616 1.17770 0.588852 0.808241i \(-0.299580\pi\)
0.588852 + 0.808241i \(0.299580\pi\)
\(368\) 0 0
\(369\) −2.31534 −0.120532
\(370\) 0 0
\(371\) −11.6847 −0.606637
\(372\) 0 0
\(373\) 20.2462 1.04831 0.524155 0.851623i \(-0.324381\pi\)
0.524155 + 0.851623i \(0.324381\pi\)
\(374\) 0 0
\(375\) 1.56155 0.0806382
\(376\) 0 0
\(377\) −21.8078 −1.12316
\(378\) 0 0
\(379\) −36.4924 −1.87449 −0.937245 0.348672i \(-0.886633\pi\)
−0.937245 + 0.348672i \(0.886633\pi\)
\(380\) 0 0
\(381\) 12.1922 0.624627
\(382\) 0 0
\(383\) −3.19224 −0.163116 −0.0815578 0.996669i \(-0.525990\pi\)
−0.0815578 + 0.996669i \(0.525990\pi\)
\(384\) 0 0
\(385\) 5.12311 0.261098
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 10.8769 0.551480 0.275740 0.961232i \(-0.411077\pi\)
0.275740 + 0.961232i \(0.411077\pi\)
\(390\) 0 0
\(391\) −2.56155 −0.129543
\(392\) 0 0
\(393\) −0.300187 −0.0151424
\(394\) 0 0
\(395\) 4.87689 0.245383
\(396\) 0 0
\(397\) −34.5464 −1.73383 −0.866917 0.498453i \(-0.833902\pi\)
−0.866917 + 0.498453i \(0.833902\pi\)
\(398\) 0 0
\(399\) 24.0000 1.20150
\(400\) 0 0
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) 0 0
\(403\) −25.8078 −1.28558
\(404\) 0 0
\(405\) 7.00000 0.347833
\(406\) 0 0
\(407\) 9.12311 0.452216
\(408\) 0 0
\(409\) −35.9848 −1.77934 −0.889668 0.456608i \(-0.849064\pi\)
−0.889668 + 0.456608i \(0.849064\pi\)
\(410\) 0 0
\(411\) −10.7386 −0.529698
\(412\) 0 0
\(413\) 9.43845 0.464436
\(414\) 0 0
\(415\) 13.9309 0.683839
\(416\) 0 0
\(417\) 17.5616 0.859993
\(418\) 0 0
\(419\) −18.8769 −0.922197 −0.461098 0.887349i \(-0.652544\pi\)
−0.461098 + 0.887349i \(0.652544\pi\)
\(420\) 0 0
\(421\) −25.1231 −1.22443 −0.612213 0.790693i \(-0.709720\pi\)
−0.612213 + 0.790693i \(0.709720\pi\)
\(422\) 0 0
\(423\) 2.63068 0.127908
\(424\) 0 0
\(425\) 2.56155 0.124254
\(426\) 0 0
\(427\) −18.2462 −0.882996
\(428\) 0 0
\(429\) −11.1231 −0.537029
\(430\) 0 0
\(431\) 10.2462 0.493543 0.246771 0.969074i \(-0.420630\pi\)
0.246771 + 0.969074i \(0.420630\pi\)
\(432\) 0 0
\(433\) 39.9309 1.91896 0.959478 0.281785i \(-0.0909265\pi\)
0.959478 + 0.281785i \(0.0909265\pi\)
\(434\) 0 0
\(435\) −9.56155 −0.458441
\(436\) 0 0
\(437\) −6.00000 −0.287019
\(438\) 0 0
\(439\) −19.8078 −0.945373 −0.472686 0.881231i \(-0.656716\pi\)
−0.472686 + 0.881231i \(0.656716\pi\)
\(440\) 0 0
\(441\) 0.246211 0.0117243
\(442\) 0 0
\(443\) −11.8078 −0.561004 −0.280502 0.959853i \(-0.590501\pi\)
−0.280502 + 0.959853i \(0.590501\pi\)
\(444\) 0 0
\(445\) −14.2462 −0.675335
\(446\) 0 0
\(447\) −14.6307 −0.692008
\(448\) 0 0
\(449\) −21.6847 −1.02336 −0.511681 0.859175i \(-0.670977\pi\)
−0.511681 + 0.859175i \(0.670977\pi\)
\(450\) 0 0
\(451\) 8.24621 0.388299
\(452\) 0 0
\(453\) −21.9460 −1.03111
\(454\) 0 0
\(455\) 9.12311 0.427698
\(456\) 0 0
\(457\) 9.43845 0.441512 0.220756 0.975329i \(-0.429148\pi\)
0.220756 + 0.975329i \(0.429148\pi\)
\(458\) 0 0
\(459\) 14.2462 0.664956
\(460\) 0 0
\(461\) 40.9309 1.90634 0.953170 0.302434i \(-0.0977992\pi\)
0.953170 + 0.302434i \(0.0977992\pi\)
\(462\) 0 0
\(463\) 31.3693 1.45786 0.728928 0.684590i \(-0.240019\pi\)
0.728928 + 0.684590i \(0.240019\pi\)
\(464\) 0 0
\(465\) −11.3153 −0.524736
\(466\) 0 0
\(467\) −22.3153 −1.03263 −0.516315 0.856398i \(-0.672697\pi\)
−0.516315 + 0.856398i \(0.672697\pi\)
\(468\) 0 0
\(469\) 21.9309 1.01267
\(470\) 0 0
\(471\) −6.73863 −0.310500
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 6.00000 0.275299
\(476\) 0 0
\(477\) −2.56155 −0.117285
\(478\) 0 0
\(479\) 43.2311 1.97528 0.987639 0.156748i \(-0.0501009\pi\)
0.987639 + 0.156748i \(0.0501009\pi\)
\(480\) 0 0
\(481\) 16.2462 0.740763
\(482\) 0 0
\(483\) −4.00000 −0.182006
\(484\) 0 0
\(485\) 13.1231 0.595890
\(486\) 0 0
\(487\) −7.80776 −0.353804 −0.176902 0.984229i \(-0.556607\pi\)
−0.176902 + 0.984229i \(0.556607\pi\)
\(488\) 0 0
\(489\) −26.4384 −1.19559
\(490\) 0 0
\(491\) 11.4924 0.518646 0.259323 0.965791i \(-0.416501\pi\)
0.259323 + 0.965791i \(0.416501\pi\)
\(492\) 0 0
\(493\) −15.6847 −0.706401
\(494\) 0 0
\(495\) 1.12311 0.0504798
\(496\) 0 0
\(497\) 25.9309 1.16316
\(498\) 0 0
\(499\) 22.6155 1.01241 0.506205 0.862413i \(-0.331048\pi\)
0.506205 + 0.862413i \(0.331048\pi\)
\(500\) 0 0
\(501\) −12.4924 −0.558120
\(502\) 0 0
\(503\) 3.93087 0.175269 0.0876344 0.996153i \(-0.472069\pi\)
0.0876344 + 0.996153i \(0.472069\pi\)
\(504\) 0 0
\(505\) −17.6847 −0.786957
\(506\) 0 0
\(507\) 0.492423 0.0218693
\(508\) 0 0
\(509\) 27.1771 1.20460 0.602301 0.798269i \(-0.294251\pi\)
0.602301 + 0.798269i \(0.294251\pi\)
\(510\) 0 0
\(511\) 11.3693 0.502949
\(512\) 0 0
\(513\) 33.3693 1.47329
\(514\) 0 0
\(515\) −16.0000 −0.705044
\(516\) 0 0
\(517\) −9.36932 −0.412062
\(518\) 0 0
\(519\) 8.38447 0.368037
\(520\) 0 0
\(521\) −13.6155 −0.596507 −0.298254 0.954487i \(-0.596404\pi\)
−0.298254 + 0.954487i \(0.596404\pi\)
\(522\) 0 0
\(523\) −14.7386 −0.644475 −0.322238 0.946659i \(-0.604435\pi\)
−0.322238 + 0.946659i \(0.604435\pi\)
\(524\) 0 0
\(525\) 4.00000 0.174574
\(526\) 0 0
\(527\) −18.5616 −0.808554
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 2.06913 0.0897926
\(532\) 0 0
\(533\) 14.6847 0.636063
\(534\) 0 0
\(535\) −3.43845 −0.148657
\(536\) 0 0
\(537\) 10.8229 0.467043
\(538\) 0 0
\(539\) −0.876894 −0.0377705
\(540\) 0 0
\(541\) 2.68466 0.115422 0.0577112 0.998333i \(-0.481620\pi\)
0.0577112 + 0.998333i \(0.481620\pi\)
\(542\) 0 0
\(543\) −8.38447 −0.359812
\(544\) 0 0
\(545\) 15.3693 0.658349
\(546\) 0 0
\(547\) −21.1771 −0.905467 −0.452733 0.891646i \(-0.649551\pi\)
−0.452733 + 0.891646i \(0.649551\pi\)
\(548\) 0 0
\(549\) −4.00000 −0.170716
\(550\) 0 0
\(551\) −36.7386 −1.56512
\(552\) 0 0
\(553\) 12.4924 0.531232
\(554\) 0 0
\(555\) 7.12311 0.302359
\(556\) 0 0
\(557\) 15.6847 0.664580 0.332290 0.943177i \(-0.392179\pi\)
0.332290 + 0.943177i \(0.392179\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −8.00000 −0.337760
\(562\) 0 0
\(563\) 32.6695 1.37686 0.688428 0.725305i \(-0.258301\pi\)
0.688428 + 0.725305i \(0.258301\pi\)
\(564\) 0 0
\(565\) −12.8078 −0.538827
\(566\) 0 0
\(567\) 17.9309 0.753026
\(568\) 0 0
\(569\) 16.7386 0.701720 0.350860 0.936428i \(-0.385889\pi\)
0.350860 + 0.936428i \(0.385889\pi\)
\(570\) 0 0
\(571\) 36.0000 1.50655 0.753277 0.657704i \(-0.228472\pi\)
0.753277 + 0.657704i \(0.228472\pi\)
\(572\) 0 0
\(573\) 27.1231 1.13308
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −29.5616 −1.23066 −0.615332 0.788268i \(-0.710978\pi\)
−0.615332 + 0.788268i \(0.710978\pi\)
\(578\) 0 0
\(579\) −3.80776 −0.158245
\(580\) 0 0
\(581\) 35.6847 1.48045
\(582\) 0 0
\(583\) 9.12311 0.377840
\(584\) 0 0
\(585\) 2.00000 0.0826898
\(586\) 0 0
\(587\) 7.06913 0.291774 0.145887 0.989301i \(-0.453396\pi\)
0.145887 + 0.989301i \(0.453396\pi\)
\(588\) 0 0
\(589\) −43.4773 −1.79145
\(590\) 0 0
\(591\) −29.1771 −1.20018
\(592\) 0 0
\(593\) 15.6155 0.641253 0.320626 0.947206i \(-0.396107\pi\)
0.320626 + 0.947206i \(0.396107\pi\)
\(594\) 0 0
\(595\) 6.56155 0.268997
\(596\) 0 0
\(597\) −15.6155 −0.639101
\(598\) 0 0
\(599\) 32.9848 1.34772 0.673862 0.738857i \(-0.264634\pi\)
0.673862 + 0.738857i \(0.264634\pi\)
\(600\) 0 0
\(601\) 36.3693 1.48354 0.741768 0.670657i \(-0.233988\pi\)
0.741768 + 0.670657i \(0.233988\pi\)
\(602\) 0 0
\(603\) 4.80776 0.195787
\(604\) 0 0
\(605\) 7.00000 0.284590
\(606\) 0 0
\(607\) −8.49242 −0.344697 −0.172348 0.985036i \(-0.555135\pi\)
−0.172348 + 0.985036i \(0.555135\pi\)
\(608\) 0 0
\(609\) −24.4924 −0.992483
\(610\) 0 0
\(611\) −16.6847 −0.674989
\(612\) 0 0
\(613\) 5.61553 0.226809 0.113405 0.993549i \(-0.463824\pi\)
0.113405 + 0.993549i \(0.463824\pi\)
\(614\) 0 0
\(615\) 6.43845 0.259623
\(616\) 0 0
\(617\) 0.561553 0.0226073 0.0113036 0.999936i \(-0.496402\pi\)
0.0113036 + 0.999936i \(0.496402\pi\)
\(618\) 0 0
\(619\) 12.4924 0.502113 0.251056 0.967972i \(-0.419222\pi\)
0.251056 + 0.967972i \(0.419222\pi\)
\(620\) 0 0
\(621\) −5.56155 −0.223177
\(622\) 0 0
\(623\) −36.4924 −1.46204
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −18.7386 −0.748349
\(628\) 0 0
\(629\) 11.6847 0.465898
\(630\) 0 0
\(631\) −30.2462 −1.20408 −0.602041 0.798465i \(-0.705646\pi\)
−0.602041 + 0.798465i \(0.705646\pi\)
\(632\) 0 0
\(633\) −0.492423 −0.0195720
\(634\) 0 0
\(635\) 7.80776 0.309842
\(636\) 0 0
\(637\) −1.56155 −0.0618710
\(638\) 0 0
\(639\) 5.68466 0.224882
\(640\) 0 0
\(641\) 6.87689 0.271621 0.135810 0.990735i \(-0.456636\pi\)
0.135810 + 0.990735i \(0.456636\pi\)
\(642\) 0 0
\(643\) 20.4233 0.805416 0.402708 0.915328i \(-0.368069\pi\)
0.402708 + 0.915328i \(0.368069\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5.31534 −0.208968 −0.104484 0.994527i \(-0.533319\pi\)
−0.104484 + 0.994527i \(0.533319\pi\)
\(648\) 0 0
\(649\) −7.36932 −0.289271
\(650\) 0 0
\(651\) −28.9848 −1.13601
\(652\) 0 0
\(653\) −39.6695 −1.55239 −0.776194 0.630494i \(-0.782852\pi\)
−0.776194 + 0.630494i \(0.782852\pi\)
\(654\) 0 0
\(655\) −0.192236 −0.00751128
\(656\) 0 0
\(657\) 2.49242 0.0972387
\(658\) 0 0
\(659\) 15.3693 0.598704 0.299352 0.954143i \(-0.403230\pi\)
0.299352 + 0.954143i \(0.403230\pi\)
\(660\) 0 0
\(661\) 6.49242 0.252526 0.126263 0.991997i \(-0.459702\pi\)
0.126263 + 0.991997i \(0.459702\pi\)
\(662\) 0 0
\(663\) −14.2462 −0.553277
\(664\) 0 0
\(665\) 15.3693 0.595997
\(666\) 0 0
\(667\) 6.12311 0.237088
\(668\) 0 0
\(669\) −27.5076 −1.06350
\(670\) 0 0
\(671\) 14.2462 0.549969
\(672\) 0 0
\(673\) 34.5464 1.33167 0.665833 0.746101i \(-0.268076\pi\)
0.665833 + 0.746101i \(0.268076\pi\)
\(674\) 0 0
\(675\) 5.56155 0.214064
\(676\) 0 0
\(677\) −26.8078 −1.03031 −0.515153 0.857098i \(-0.672265\pi\)
−0.515153 + 0.857098i \(0.672265\pi\)
\(678\) 0 0
\(679\) 33.6155 1.29005
\(680\) 0 0
\(681\) −40.9848 −1.57054
\(682\) 0 0
\(683\) 42.0540 1.60915 0.804575 0.593851i \(-0.202393\pi\)
0.804575 + 0.593851i \(0.202393\pi\)
\(684\) 0 0
\(685\) −6.87689 −0.262753
\(686\) 0 0
\(687\) −41.7538 −1.59301
\(688\) 0 0
\(689\) 16.2462 0.618931
\(690\) 0 0
\(691\) 16.4924 0.627401 0.313701 0.949522i \(-0.398431\pi\)
0.313701 + 0.949522i \(0.398431\pi\)
\(692\) 0 0
\(693\) 2.87689 0.109284
\(694\) 0 0
\(695\) 11.2462 0.426593
\(696\) 0 0
\(697\) 10.5616 0.400047
\(698\) 0 0
\(699\) 1.06913 0.0404382
\(700\) 0 0
\(701\) 1.75379 0.0662397 0.0331198 0.999451i \(-0.489456\pi\)
0.0331198 + 0.999451i \(0.489456\pi\)
\(702\) 0 0
\(703\) 27.3693 1.03225
\(704\) 0 0
\(705\) −7.31534 −0.275512
\(706\) 0 0
\(707\) −45.3002 −1.70369
\(708\) 0 0
\(709\) −29.7538 −1.11743 −0.558713 0.829361i \(-0.688705\pi\)
−0.558713 + 0.829361i \(0.688705\pi\)
\(710\) 0 0
\(711\) 2.73863 0.102707
\(712\) 0 0
\(713\) 7.24621 0.271373
\(714\) 0 0
\(715\) −7.12311 −0.266389
\(716\) 0 0
\(717\) 4.30019 0.160593
\(718\) 0 0
\(719\) −19.0540 −0.710593 −0.355297 0.934754i \(-0.615620\pi\)
−0.355297 + 0.934754i \(0.615620\pi\)
\(720\) 0 0
\(721\) −40.9848 −1.52636
\(722\) 0 0
\(723\) −9.36932 −0.348449
\(724\) 0 0
\(725\) −6.12311 −0.227406
\(726\) 0 0
\(727\) 21.1922 0.785977 0.392988 0.919543i \(-0.371441\pi\)
0.392988 + 0.919543i \(0.371441\pi\)
\(728\) 0 0
\(729\) 29.9848 1.11055
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.315342 −0.0116474 −0.00582370 0.999983i \(-0.501854\pi\)
−0.00582370 + 0.999983i \(0.501854\pi\)
\(734\) 0 0
\(735\) −0.684658 −0.0252540
\(736\) 0 0
\(737\) −17.1231 −0.630738
\(738\) 0 0
\(739\) 0.615528 0.0226426 0.0113213 0.999936i \(-0.496396\pi\)
0.0113213 + 0.999936i \(0.496396\pi\)
\(740\) 0 0
\(741\) −33.3693 −1.22585
\(742\) 0 0
\(743\) −3.50758 −0.128681 −0.0643403 0.997928i \(-0.520494\pi\)
−0.0643403 + 0.997928i \(0.520494\pi\)
\(744\) 0 0
\(745\) −9.36932 −0.343265
\(746\) 0 0
\(747\) 7.82292 0.286226
\(748\) 0 0
\(749\) −8.80776 −0.321829
\(750\) 0 0
\(751\) 13.1231 0.478869 0.239434 0.970913i \(-0.423038\pi\)
0.239434 + 0.970913i \(0.423038\pi\)
\(752\) 0 0
\(753\) 11.5076 0.419359
\(754\) 0 0
\(755\) −14.0540 −0.511477
\(756\) 0 0
\(757\) −12.5616 −0.456557 −0.228279 0.973596i \(-0.573310\pi\)
−0.228279 + 0.973596i \(0.573310\pi\)
\(758\) 0 0
\(759\) 3.12311 0.113362
\(760\) 0 0
\(761\) −43.9848 −1.59445 −0.797225 0.603683i \(-0.793699\pi\)
−0.797225 + 0.603683i \(0.793699\pi\)
\(762\) 0 0
\(763\) 39.3693 1.42526
\(764\) 0 0
\(765\) 1.43845 0.0520072
\(766\) 0 0
\(767\) −13.1231 −0.473848
\(768\) 0 0
\(769\) −10.6307 −0.383352 −0.191676 0.981458i \(-0.561392\pi\)
−0.191676 + 0.981458i \(0.561392\pi\)
\(770\) 0 0
\(771\) −49.6695 −1.78880
\(772\) 0 0
\(773\) 41.1231 1.47910 0.739548 0.673104i \(-0.235039\pi\)
0.739548 + 0.673104i \(0.235039\pi\)
\(774\) 0 0
\(775\) −7.24621 −0.260292
\(776\) 0 0
\(777\) 18.2462 0.654579
\(778\) 0 0
\(779\) 24.7386 0.886354
\(780\) 0 0
\(781\) −20.2462 −0.724466
\(782\) 0 0
\(783\) −34.0540 −1.21699
\(784\) 0 0
\(785\) −4.31534 −0.154021
\(786\) 0 0
\(787\) −39.6847 −1.41461 −0.707303 0.706911i \(-0.750088\pi\)
−0.707303 + 0.706911i \(0.750088\pi\)
\(788\) 0 0
\(789\) 0.107951 0.00384314
\(790\) 0 0
\(791\) −32.8078 −1.16651
\(792\) 0 0
\(793\) 25.3693 0.900891
\(794\) 0 0
\(795\) 7.12311 0.252631
\(796\) 0 0
\(797\) 52.4233 1.85693 0.928464 0.371422i \(-0.121130\pi\)
0.928464 + 0.371422i \(0.121130\pi\)
\(798\) 0 0
\(799\) −12.0000 −0.424529
\(800\) 0 0
\(801\) −8.00000 −0.282666
\(802\) 0 0
\(803\) −8.87689 −0.313259
\(804\) 0 0
\(805\) −2.56155 −0.0902829
\(806\) 0 0
\(807\) 36.3002 1.27783
\(808\) 0 0
\(809\) −54.1771 −1.90476 −0.952382 0.304906i \(-0.901375\pi\)
−0.952382 + 0.304906i \(0.901375\pi\)
\(810\) 0 0
\(811\) 47.2462 1.65904 0.829519 0.558478i \(-0.188614\pi\)
0.829519 + 0.558478i \(0.188614\pi\)
\(812\) 0 0
\(813\) 34.2462 1.20107
\(814\) 0 0
\(815\) −16.9309 −0.593062
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 5.12311 0.179016
\(820\) 0 0
\(821\) 34.4924 1.20379 0.601897 0.798574i \(-0.294412\pi\)
0.601897 + 0.798574i \(0.294412\pi\)
\(822\) 0 0
\(823\) 38.0540 1.32648 0.663239 0.748408i \(-0.269181\pi\)
0.663239 + 0.748408i \(0.269181\pi\)
\(824\) 0 0
\(825\) −3.12311 −0.108733
\(826\) 0 0
\(827\) 19.6847 0.684503 0.342251 0.939608i \(-0.388811\pi\)
0.342251 + 0.939608i \(0.388811\pi\)
\(828\) 0 0
\(829\) 29.5464 1.02619 0.513094 0.858332i \(-0.328499\pi\)
0.513094 + 0.858332i \(0.328499\pi\)
\(830\) 0 0
\(831\) −10.4384 −0.362106
\(832\) 0 0
\(833\) −1.12311 −0.0389133
\(834\) 0 0
\(835\) −8.00000 −0.276851
\(836\) 0 0
\(837\) −40.3002 −1.39298
\(838\) 0 0
\(839\) 42.8769 1.48027 0.740137 0.672456i \(-0.234760\pi\)
0.740137 + 0.672456i \(0.234760\pi\)
\(840\) 0 0
\(841\) 8.49242 0.292842
\(842\) 0 0
\(843\) 10.7386 0.369858
\(844\) 0 0
\(845\) 0.315342 0.0108481
\(846\) 0 0
\(847\) 17.9309 0.616112
\(848\) 0 0
\(849\) −23.1231 −0.793583
\(850\) 0 0
\(851\) −4.56155 −0.156368
\(852\) 0 0
\(853\) 20.2462 0.693217 0.346609 0.938010i \(-0.387333\pi\)
0.346609 + 0.938010i \(0.387333\pi\)
\(854\) 0 0
\(855\) 3.36932 0.115228
\(856\) 0 0
\(857\) −33.3153 −1.13803 −0.569015 0.822327i \(-0.692675\pi\)
−0.569015 + 0.822327i \(0.692675\pi\)
\(858\) 0 0
\(859\) −14.5076 −0.494992 −0.247496 0.968889i \(-0.579608\pi\)
−0.247496 + 0.968889i \(0.579608\pi\)
\(860\) 0 0
\(861\) 16.4924 0.562060
\(862\) 0 0
\(863\) 7.56155 0.257398 0.128699 0.991684i \(-0.458920\pi\)
0.128699 + 0.991684i \(0.458920\pi\)
\(864\) 0 0
\(865\) 5.36932 0.182562
\(866\) 0 0
\(867\) 16.3002 0.553583
\(868\) 0 0
\(869\) −9.75379 −0.330875
\(870\) 0 0
\(871\) −30.4924 −1.03320
\(872\) 0 0
\(873\) 7.36932 0.249414
\(874\) 0 0
\(875\) 2.56155 0.0865963
\(876\) 0 0
\(877\) 18.9848 0.641073 0.320536 0.947236i \(-0.396137\pi\)
0.320536 + 0.947236i \(0.396137\pi\)
\(878\) 0 0
\(879\) −26.2462 −0.885263
\(880\) 0 0
\(881\) 41.4773 1.39740 0.698702 0.715413i \(-0.253761\pi\)
0.698702 + 0.715413i \(0.253761\pi\)
\(882\) 0 0
\(883\) 10.7386 0.361384 0.180692 0.983540i \(-0.442166\pi\)
0.180692 + 0.983540i \(0.442166\pi\)
\(884\) 0 0
\(885\) −5.75379 −0.193411
\(886\) 0 0
\(887\) −42.7926 −1.43684 −0.718418 0.695612i \(-0.755133\pi\)
−0.718418 + 0.695612i \(0.755133\pi\)
\(888\) 0 0
\(889\) 20.0000 0.670778
\(890\) 0 0
\(891\) −14.0000 −0.469018
\(892\) 0 0
\(893\) −28.1080 −0.940597
\(894\) 0 0
\(895\) 6.93087 0.231673
\(896\) 0 0
\(897\) 5.56155 0.185695
\(898\) 0 0
\(899\) 44.3693 1.47980
\(900\) 0 0
\(901\) 11.6847 0.389272
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −5.36932 −0.178482
\(906\) 0 0
\(907\) 21.6847 0.720027 0.360014 0.932947i \(-0.382772\pi\)
0.360014 + 0.932947i \(0.382772\pi\)
\(908\) 0 0
\(909\) −9.93087 −0.329386
\(910\) 0 0
\(911\) 3.12311 0.103473 0.0517366 0.998661i \(-0.483524\pi\)
0.0517366 + 0.998661i \(0.483524\pi\)
\(912\) 0 0
\(913\) −27.8617 −0.922089
\(914\) 0 0
\(915\) 11.1231 0.367719
\(916\) 0 0
\(917\) −0.492423 −0.0162612
\(918\) 0 0
\(919\) −46.7386 −1.54177 −0.770883 0.636977i \(-0.780185\pi\)
−0.770883 + 0.636977i \(0.780185\pi\)
\(920\) 0 0
\(921\) 32.9848 1.08689
\(922\) 0 0
\(923\) −36.0540 −1.18673
\(924\) 0 0
\(925\) 4.56155 0.149983
\(926\) 0 0
\(927\) −8.98485 −0.295101
\(928\) 0 0
\(929\) −56.7235 −1.86104 −0.930518 0.366245i \(-0.880643\pi\)
−0.930518 + 0.366245i \(0.880643\pi\)
\(930\) 0 0
\(931\) −2.63068 −0.0862172
\(932\) 0 0
\(933\) 13.5616 0.443985
\(934\) 0 0
\(935\) −5.12311 −0.167543
\(936\) 0 0
\(937\) −16.2462 −0.530741 −0.265370 0.964147i \(-0.585494\pi\)
−0.265370 + 0.964147i \(0.585494\pi\)
\(938\) 0 0
\(939\) 1.26137 0.0411631
\(940\) 0 0
\(941\) 37.7538 1.23074 0.615369 0.788239i \(-0.289007\pi\)
0.615369 + 0.788239i \(0.289007\pi\)
\(942\) 0 0
\(943\) −4.12311 −0.134267
\(944\) 0 0
\(945\) 14.2462 0.463429
\(946\) 0 0
\(947\) 56.6847 1.84200 0.921002 0.389558i \(-0.127372\pi\)
0.921002 + 0.389558i \(0.127372\pi\)
\(948\) 0 0
\(949\) −15.8078 −0.513142
\(950\) 0 0
\(951\) 23.6155 0.765786
\(952\) 0 0
\(953\) −38.4924 −1.24689 −0.623446 0.781866i \(-0.714268\pi\)
−0.623446 + 0.781866i \(0.714268\pi\)
\(954\) 0 0
\(955\) 17.3693 0.562058
\(956\) 0 0
\(957\) 19.1231 0.618162
\(958\) 0 0
\(959\) −17.6155 −0.568835
\(960\) 0 0
\(961\) 21.5076 0.693793
\(962\) 0 0
\(963\) −1.93087 −0.0622214
\(964\) 0 0
\(965\) −2.43845 −0.0784964
\(966\) 0 0
\(967\) 56.6847 1.82286 0.911428 0.411460i \(-0.134981\pi\)
0.911428 + 0.411460i \(0.134981\pi\)
\(968\) 0 0
\(969\) −24.0000 −0.770991
\(970\) 0 0
\(971\) −22.6307 −0.726253 −0.363127 0.931740i \(-0.618291\pi\)
−0.363127 + 0.931740i \(0.618291\pi\)
\(972\) 0 0
\(973\) 28.8078 0.923535
\(974\) 0 0
\(975\) −5.56155 −0.178112
\(976\) 0 0
\(977\) 59.7926 1.91294 0.956468 0.291839i \(-0.0942671\pi\)
0.956468 + 0.291839i \(0.0942671\pi\)
\(978\) 0 0
\(979\) 28.4924 0.910622
\(980\) 0 0
\(981\) 8.63068 0.275557
\(982\) 0 0
\(983\) 37.0540 1.18184 0.590919 0.806731i \(-0.298765\pi\)
0.590919 + 0.806731i \(0.298765\pi\)
\(984\) 0 0
\(985\) −18.6847 −0.595343
\(986\) 0 0
\(987\) −18.7386 −0.596457
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −53.3002 −1.69314 −0.846568 0.532280i \(-0.821335\pi\)
−0.846568 + 0.532280i \(0.821335\pi\)
\(992\) 0 0
\(993\) −44.6847 −1.41802
\(994\) 0 0
\(995\) −10.0000 −0.317021
\(996\) 0 0
\(997\) −55.6155 −1.76136 −0.880681 0.473710i \(-0.842914\pi\)
−0.880681 + 0.473710i \(0.842914\pi\)
\(998\) 0 0
\(999\) 25.3693 0.802650
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 7360.2.a.bo.1.1 2
4.3 odd 2 7360.2.a.bi.1.2 2
8.3 odd 2 460.2.a.e.1.1 2
8.5 even 2 1840.2.a.m.1.2 2
24.11 even 2 4140.2.a.m.1.2 2
40.3 even 4 2300.2.c.h.1749.2 4
40.19 odd 2 2300.2.a.i.1.2 2
40.27 even 4 2300.2.c.h.1749.3 4
40.29 even 2 9200.2.a.bv.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.a.e.1.1 2 8.3 odd 2
1840.2.a.m.1.2 2 8.5 even 2
2300.2.a.i.1.2 2 40.19 odd 2
2300.2.c.h.1749.2 4 40.3 even 4
2300.2.c.h.1749.3 4 40.27 even 4
4140.2.a.m.1.2 2 24.11 even 2
7360.2.a.bi.1.2 2 4.3 odd 2
7360.2.a.bo.1.1 2 1.1 even 1 trivial
9200.2.a.bv.1.1 2 40.29 even 2