Properties

Label 6008.2.a.b.1.8
Level 6008
Weight 2
Character 6008.1
Self dual yes
Analytic conductor 47.974
Analytic rank 1
Dimension 44
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(1\)
Dimension: \(44\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.32283 q^{3} +3.89591 q^{5} +0.0996640 q^{7} +2.39554 q^{9} +O(q^{10})\) \(q-2.32283 q^{3} +3.89591 q^{5} +0.0996640 q^{7} +2.39554 q^{9} -5.90464 q^{11} -0.114246 q^{13} -9.04954 q^{15} -0.599000 q^{17} -3.75876 q^{19} -0.231503 q^{21} +8.45024 q^{23} +10.1781 q^{25} +1.40405 q^{27} -4.82511 q^{29} -5.02204 q^{31} +13.7155 q^{33} +0.388282 q^{35} +4.30770 q^{37} +0.265374 q^{39} -1.72885 q^{41} +7.69072 q^{43} +9.33282 q^{45} +3.57421 q^{47} -6.99007 q^{49} +1.39138 q^{51} +8.09824 q^{53} -23.0040 q^{55} +8.73095 q^{57} -8.16867 q^{59} +12.5579 q^{61} +0.238749 q^{63} -0.445092 q^{65} +0.648145 q^{67} -19.6285 q^{69} -10.7524 q^{71} -16.5173 q^{73} -23.6420 q^{75} -0.588480 q^{77} -3.11173 q^{79} -10.4480 q^{81} -12.1879 q^{83} -2.33365 q^{85} +11.2079 q^{87} -4.53075 q^{89} -0.0113862 q^{91} +11.6654 q^{93} -14.6438 q^{95} -12.9395 q^{97} -14.1448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.32283 −1.34109 −0.670543 0.741870i \(-0.733939\pi\)
−0.670543 + 0.741870i \(0.733939\pi\)
\(4\) 0 0
\(5\) 3.89591 1.74230 0.871152 0.491013i \(-0.163373\pi\)
0.871152 + 0.491013i \(0.163373\pi\)
\(6\) 0 0
\(7\) 0.0996640 0.0376694 0.0188347 0.999823i \(-0.494004\pi\)
0.0188347 + 0.999823i \(0.494004\pi\)
\(8\) 0 0
\(9\) 2.39554 0.798514
\(10\) 0 0
\(11\) −5.90464 −1.78032 −0.890159 0.455651i \(-0.849407\pi\)
−0.890159 + 0.455651i \(0.849407\pi\)
\(12\) 0 0
\(13\) −0.114246 −0.0316861 −0.0158431 0.999874i \(-0.505043\pi\)
−0.0158431 + 0.999874i \(0.505043\pi\)
\(14\) 0 0
\(15\) −9.04954 −2.33658
\(16\) 0 0
\(17\) −0.599000 −0.145279 −0.0726394 0.997358i \(-0.523142\pi\)
−0.0726394 + 0.997358i \(0.523142\pi\)
\(18\) 0 0
\(19\) −3.75876 −0.862318 −0.431159 0.902276i \(-0.641895\pi\)
−0.431159 + 0.902276i \(0.641895\pi\)
\(20\) 0 0
\(21\) −0.231503 −0.0505180
\(22\) 0 0
\(23\) 8.45024 1.76200 0.880998 0.473119i \(-0.156872\pi\)
0.880998 + 0.473119i \(0.156872\pi\)
\(24\) 0 0
\(25\) 10.1781 2.03562
\(26\) 0 0
\(27\) 1.40405 0.270210
\(28\) 0 0
\(29\) −4.82511 −0.896001 −0.448001 0.894033i \(-0.647864\pi\)
−0.448001 + 0.894033i \(0.647864\pi\)
\(30\) 0 0
\(31\) −5.02204 −0.901986 −0.450993 0.892528i \(-0.648930\pi\)
−0.450993 + 0.892528i \(0.648930\pi\)
\(32\) 0 0
\(33\) 13.7155 2.38756
\(34\) 0 0
\(35\) 0.388282 0.0656316
\(36\) 0 0
\(37\) 4.30770 0.708181 0.354090 0.935211i \(-0.384791\pi\)
0.354090 + 0.935211i \(0.384791\pi\)
\(38\) 0 0
\(39\) 0.265374 0.0424938
\(40\) 0 0
\(41\) −1.72885 −0.270001 −0.135000 0.990846i \(-0.543104\pi\)
−0.135000 + 0.990846i \(0.543104\pi\)
\(42\) 0 0
\(43\) 7.69072 1.17282 0.586412 0.810013i \(-0.300540\pi\)
0.586412 + 0.810013i \(0.300540\pi\)
\(44\) 0 0
\(45\) 9.33282 1.39125
\(46\) 0 0
\(47\) 3.57421 0.521353 0.260676 0.965426i \(-0.416054\pi\)
0.260676 + 0.965426i \(0.416054\pi\)
\(48\) 0 0
\(49\) −6.99007 −0.998581
\(50\) 0 0
\(51\) 1.39138 0.194832
\(52\) 0 0
\(53\) 8.09824 1.11238 0.556189 0.831056i \(-0.312263\pi\)
0.556189 + 0.831056i \(0.312263\pi\)
\(54\) 0 0
\(55\) −23.0040 −3.10185
\(56\) 0 0
\(57\) 8.73095 1.15644
\(58\) 0 0
\(59\) −8.16867 −1.06347 −0.531735 0.846911i \(-0.678460\pi\)
−0.531735 + 0.846911i \(0.678460\pi\)
\(60\) 0 0
\(61\) 12.5579 1.60787 0.803937 0.594715i \(-0.202735\pi\)
0.803937 + 0.594715i \(0.202735\pi\)
\(62\) 0 0
\(63\) 0.238749 0.0300796
\(64\) 0 0
\(65\) −0.445092 −0.0552068
\(66\) 0 0
\(67\) 0.648145 0.0791835 0.0395917 0.999216i \(-0.487394\pi\)
0.0395917 + 0.999216i \(0.487394\pi\)
\(68\) 0 0
\(69\) −19.6285 −2.36299
\(70\) 0 0
\(71\) −10.7524 −1.27607 −0.638037 0.770006i \(-0.720253\pi\)
−0.638037 + 0.770006i \(0.720253\pi\)
\(72\) 0 0
\(73\) −16.5173 −1.93320 −0.966601 0.256286i \(-0.917501\pi\)
−0.966601 + 0.256286i \(0.917501\pi\)
\(74\) 0 0
\(75\) −23.6420 −2.72995
\(76\) 0 0
\(77\) −0.588480 −0.0670635
\(78\) 0 0
\(79\) −3.11173 −0.350097 −0.175049 0.984560i \(-0.556008\pi\)
−0.175049 + 0.984560i \(0.556008\pi\)
\(80\) 0 0
\(81\) −10.4480 −1.16089
\(82\) 0 0
\(83\) −12.1879 −1.33779 −0.668896 0.743356i \(-0.733233\pi\)
−0.668896 + 0.743356i \(0.733233\pi\)
\(84\) 0 0
\(85\) −2.33365 −0.253120
\(86\) 0 0
\(87\) 11.2079 1.20162
\(88\) 0 0
\(89\) −4.53075 −0.480258 −0.240129 0.970741i \(-0.577190\pi\)
−0.240129 + 0.970741i \(0.577190\pi\)
\(90\) 0 0
\(91\) −0.0113862 −0.00119360
\(92\) 0 0
\(93\) 11.6654 1.20964
\(94\) 0 0
\(95\) −14.6438 −1.50242
\(96\) 0 0
\(97\) −12.9395 −1.31381 −0.656904 0.753974i \(-0.728134\pi\)
−0.656904 + 0.753974i \(0.728134\pi\)
\(98\) 0 0
\(99\) −14.1448 −1.42161
\(100\) 0 0
\(101\) 10.0137 0.996398 0.498199 0.867063i \(-0.333995\pi\)
0.498199 + 0.867063i \(0.333995\pi\)
\(102\) 0 0
\(103\) −19.2251 −1.89430 −0.947152 0.320786i \(-0.896053\pi\)
−0.947152 + 0.320786i \(0.896053\pi\)
\(104\) 0 0
\(105\) −0.901913 −0.0880177
\(106\) 0 0
\(107\) 0.515605 0.0498454 0.0249227 0.999689i \(-0.492066\pi\)
0.0249227 + 0.999689i \(0.492066\pi\)
\(108\) 0 0
\(109\) 13.9042 1.33178 0.665892 0.746048i \(-0.268051\pi\)
0.665892 + 0.746048i \(0.268051\pi\)
\(110\) 0 0
\(111\) −10.0060 −0.949732
\(112\) 0 0
\(113\) 17.7994 1.67442 0.837212 0.546879i \(-0.184184\pi\)
0.837212 + 0.546879i \(0.184184\pi\)
\(114\) 0 0
\(115\) 32.9214 3.06993
\(116\) 0 0
\(117\) −0.273681 −0.0253018
\(118\) 0 0
\(119\) −0.0596987 −0.00547257
\(120\) 0 0
\(121\) 23.8648 2.16953
\(122\) 0 0
\(123\) 4.01583 0.362095
\(124\) 0 0
\(125\) 20.1735 1.80437
\(126\) 0 0
\(127\) 12.9798 1.15177 0.575883 0.817532i \(-0.304658\pi\)
0.575883 + 0.817532i \(0.304658\pi\)
\(128\) 0 0
\(129\) −17.8642 −1.57286
\(130\) 0 0
\(131\) −13.3554 −1.16687 −0.583435 0.812160i \(-0.698292\pi\)
−0.583435 + 0.812160i \(0.698292\pi\)
\(132\) 0 0
\(133\) −0.374612 −0.0324830
\(134\) 0 0
\(135\) 5.47006 0.470788
\(136\) 0 0
\(137\) −16.0945 −1.37505 −0.687523 0.726163i \(-0.741302\pi\)
−0.687523 + 0.726163i \(0.741302\pi\)
\(138\) 0 0
\(139\) −12.3178 −1.04478 −0.522390 0.852706i \(-0.674960\pi\)
−0.522390 + 0.852706i \(0.674960\pi\)
\(140\) 0 0
\(141\) −8.30230 −0.699179
\(142\) 0 0
\(143\) 0.674581 0.0564113
\(144\) 0 0
\(145\) −18.7982 −1.56111
\(146\) 0 0
\(147\) 16.2367 1.33918
\(148\) 0 0
\(149\) −11.6426 −0.953799 −0.476899 0.878958i \(-0.658239\pi\)
−0.476899 + 0.878958i \(0.658239\pi\)
\(150\) 0 0
\(151\) −17.7102 −1.44123 −0.720617 0.693334i \(-0.756141\pi\)
−0.720617 + 0.693334i \(0.756141\pi\)
\(152\) 0 0
\(153\) −1.43493 −0.116007
\(154\) 0 0
\(155\) −19.5654 −1.57153
\(156\) 0 0
\(157\) −10.6610 −0.850843 −0.425422 0.904995i \(-0.639874\pi\)
−0.425422 + 0.904995i \(0.639874\pi\)
\(158\) 0 0
\(159\) −18.8108 −1.49180
\(160\) 0 0
\(161\) 0.842184 0.0663734
\(162\) 0 0
\(163\) 24.7667 1.93988 0.969939 0.243347i \(-0.0782453\pi\)
0.969939 + 0.243347i \(0.0782453\pi\)
\(164\) 0 0
\(165\) 53.4343 4.15986
\(166\) 0 0
\(167\) 18.2172 1.40969 0.704845 0.709361i \(-0.251016\pi\)
0.704845 + 0.709361i \(0.251016\pi\)
\(168\) 0 0
\(169\) −12.9869 −0.998996
\(170\) 0 0
\(171\) −9.00426 −0.688573
\(172\) 0 0
\(173\) 9.92966 0.754938 0.377469 0.926022i \(-0.376794\pi\)
0.377469 + 0.926022i \(0.376794\pi\)
\(174\) 0 0
\(175\) 1.01439 0.0766808
\(176\) 0 0
\(177\) 18.9744 1.42621
\(178\) 0 0
\(179\) −0.765250 −0.0571975 −0.0285987 0.999591i \(-0.509104\pi\)
−0.0285987 + 0.999591i \(0.509104\pi\)
\(180\) 0 0
\(181\) −20.4570 −1.52055 −0.760277 0.649599i \(-0.774937\pi\)
−0.760277 + 0.649599i \(0.774937\pi\)
\(182\) 0 0
\(183\) −29.1699 −2.15630
\(184\) 0 0
\(185\) 16.7824 1.23387
\(186\) 0 0
\(187\) 3.53688 0.258642
\(188\) 0 0
\(189\) 0.139933 0.0101787
\(190\) 0 0
\(191\) 8.64057 0.625210 0.312605 0.949883i \(-0.398798\pi\)
0.312605 + 0.949883i \(0.398798\pi\)
\(192\) 0 0
\(193\) 27.0662 1.94827 0.974135 0.225968i \(-0.0725545\pi\)
0.974135 + 0.225968i \(0.0725545\pi\)
\(194\) 0 0
\(195\) 1.03387 0.0740371
\(196\) 0 0
\(197\) −20.1750 −1.43741 −0.718705 0.695315i \(-0.755265\pi\)
−0.718705 + 0.695315i \(0.755265\pi\)
\(198\) 0 0
\(199\) −5.33390 −0.378110 −0.189055 0.981966i \(-0.560543\pi\)
−0.189055 + 0.981966i \(0.560543\pi\)
\(200\) 0 0
\(201\) −1.50553 −0.106192
\(202\) 0 0
\(203\) −0.480890 −0.0337519
\(204\) 0 0
\(205\) −6.73544 −0.470424
\(206\) 0 0
\(207\) 20.2429 1.40698
\(208\) 0 0
\(209\) 22.1941 1.53520
\(210\) 0 0
\(211\) 6.74619 0.464427 0.232213 0.972665i \(-0.425403\pi\)
0.232213 + 0.972665i \(0.425403\pi\)
\(212\) 0 0
\(213\) 24.9760 1.71133
\(214\) 0 0
\(215\) 29.9624 2.04342
\(216\) 0 0
\(217\) −0.500517 −0.0339773
\(218\) 0 0
\(219\) 38.3669 2.59259
\(220\) 0 0
\(221\) 0.0684333 0.00460332
\(222\) 0 0
\(223\) −22.0288 −1.47516 −0.737580 0.675260i \(-0.764032\pi\)
−0.737580 + 0.675260i \(0.764032\pi\)
\(224\) 0 0
\(225\) 24.3821 1.62547
\(226\) 0 0
\(227\) −14.3582 −0.952990 −0.476495 0.879177i \(-0.658093\pi\)
−0.476495 + 0.879177i \(0.658093\pi\)
\(228\) 0 0
\(229\) −9.58291 −0.633256 −0.316628 0.948550i \(-0.602551\pi\)
−0.316628 + 0.948550i \(0.602551\pi\)
\(230\) 0 0
\(231\) 1.36694 0.0899380
\(232\) 0 0
\(233\) −18.0682 −1.18369 −0.591844 0.806053i \(-0.701600\pi\)
−0.591844 + 0.806053i \(0.701600\pi\)
\(234\) 0 0
\(235\) 13.9248 0.908355
\(236\) 0 0
\(237\) 7.22803 0.469511
\(238\) 0 0
\(239\) −14.7459 −0.953832 −0.476916 0.878949i \(-0.658245\pi\)
−0.476916 + 0.878949i \(0.658245\pi\)
\(240\) 0 0
\(241\) −14.2052 −0.915038 −0.457519 0.889200i \(-0.651262\pi\)
−0.457519 + 0.889200i \(0.651262\pi\)
\(242\) 0 0
\(243\) 20.0568 1.28664
\(244\) 0 0
\(245\) −27.2327 −1.73983
\(246\) 0 0
\(247\) 0.429422 0.0273235
\(248\) 0 0
\(249\) 28.3103 1.79409
\(250\) 0 0
\(251\) 22.0204 1.38991 0.694956 0.719052i \(-0.255424\pi\)
0.694956 + 0.719052i \(0.255424\pi\)
\(252\) 0 0
\(253\) −49.8957 −3.13691
\(254\) 0 0
\(255\) 5.42067 0.339456
\(256\) 0 0
\(257\) −11.2542 −0.702016 −0.351008 0.936373i \(-0.614161\pi\)
−0.351008 + 0.936373i \(0.614161\pi\)
\(258\) 0 0
\(259\) 0.429322 0.0266768
\(260\) 0 0
\(261\) −11.5588 −0.715470
\(262\) 0 0
\(263\) 10.2942 0.634766 0.317383 0.948297i \(-0.397196\pi\)
0.317383 + 0.948297i \(0.397196\pi\)
\(264\) 0 0
\(265\) 31.5500 1.93810
\(266\) 0 0
\(267\) 10.5242 0.644068
\(268\) 0 0
\(269\) 11.6473 0.710151 0.355076 0.934838i \(-0.384455\pi\)
0.355076 + 0.934838i \(0.384455\pi\)
\(270\) 0 0
\(271\) −2.40010 −0.145796 −0.0728978 0.997339i \(-0.523225\pi\)
−0.0728978 + 0.997339i \(0.523225\pi\)
\(272\) 0 0
\(273\) 0.0264482 0.00160072
\(274\) 0 0
\(275\) −60.0982 −3.62405
\(276\) 0 0
\(277\) −4.93482 −0.296504 −0.148252 0.988950i \(-0.547365\pi\)
−0.148252 + 0.988950i \(0.547365\pi\)
\(278\) 0 0
\(279\) −12.0305 −0.720248
\(280\) 0 0
\(281\) −14.2937 −0.852693 −0.426346 0.904560i \(-0.640200\pi\)
−0.426346 + 0.904560i \(0.640200\pi\)
\(282\) 0 0
\(283\) 14.1385 0.840448 0.420224 0.907420i \(-0.361951\pi\)
0.420224 + 0.907420i \(0.361951\pi\)
\(284\) 0 0
\(285\) 34.0150 2.01488
\(286\) 0 0
\(287\) −0.172304 −0.0101708
\(288\) 0 0
\(289\) −16.6412 −0.978894
\(290\) 0 0
\(291\) 30.0563 1.76193
\(292\) 0 0
\(293\) −16.6522 −0.972830 −0.486415 0.873728i \(-0.661696\pi\)
−0.486415 + 0.873728i \(0.661696\pi\)
\(294\) 0 0
\(295\) −31.8244 −1.85289
\(296\) 0 0
\(297\) −8.29043 −0.481059
\(298\) 0 0
\(299\) −0.965405 −0.0558308
\(300\) 0 0
\(301\) 0.766488 0.0441796
\(302\) 0 0
\(303\) −23.2601 −1.33626
\(304\) 0 0
\(305\) 48.9244 2.80140
\(306\) 0 0
\(307\) 5.76420 0.328980 0.164490 0.986379i \(-0.447402\pi\)
0.164490 + 0.986379i \(0.447402\pi\)
\(308\) 0 0
\(309\) 44.6566 2.54043
\(310\) 0 0
\(311\) −26.5164 −1.50361 −0.751803 0.659388i \(-0.770816\pi\)
−0.751803 + 0.659388i \(0.770816\pi\)
\(312\) 0 0
\(313\) −25.4430 −1.43813 −0.719063 0.694945i \(-0.755429\pi\)
−0.719063 + 0.694945i \(0.755429\pi\)
\(314\) 0 0
\(315\) 0.930146 0.0524078
\(316\) 0 0
\(317\) 6.15542 0.345723 0.172861 0.984946i \(-0.444699\pi\)
0.172861 + 0.984946i \(0.444699\pi\)
\(318\) 0 0
\(319\) 28.4906 1.59517
\(320\) 0 0
\(321\) −1.19766 −0.0668470
\(322\) 0 0
\(323\) 2.25149 0.125276
\(324\) 0 0
\(325\) −1.16281 −0.0645010
\(326\) 0 0
\(327\) −32.2972 −1.78604
\(328\) 0 0
\(329\) 0.356220 0.0196391
\(330\) 0 0
\(331\) −19.3803 −1.06524 −0.532619 0.846355i \(-0.678792\pi\)
−0.532619 + 0.846355i \(0.678792\pi\)
\(332\) 0 0
\(333\) 10.3193 0.565492
\(334\) 0 0
\(335\) 2.52511 0.137962
\(336\) 0 0
\(337\) 25.2283 1.37427 0.687136 0.726529i \(-0.258868\pi\)
0.687136 + 0.726529i \(0.258868\pi\)
\(338\) 0 0
\(339\) −41.3449 −2.24555
\(340\) 0 0
\(341\) 29.6534 1.60582
\(342\) 0 0
\(343\) −1.39431 −0.0752854
\(344\) 0 0
\(345\) −76.4708 −4.11705
\(346\) 0 0
\(347\) 10.3526 0.555757 0.277879 0.960616i \(-0.410369\pi\)
0.277879 + 0.960616i \(0.410369\pi\)
\(348\) 0 0
\(349\) −10.1171 −0.541555 −0.270778 0.962642i \(-0.587281\pi\)
−0.270778 + 0.962642i \(0.587281\pi\)
\(350\) 0 0
\(351\) −0.160407 −0.00856190
\(352\) 0 0
\(353\) 5.85827 0.311804 0.155902 0.987773i \(-0.450172\pi\)
0.155902 + 0.987773i \(0.450172\pi\)
\(354\) 0 0
\(355\) −41.8903 −2.22331
\(356\) 0 0
\(357\) 0.138670 0.00733919
\(358\) 0 0
\(359\) 22.3184 1.17792 0.588959 0.808163i \(-0.299538\pi\)
0.588959 + 0.808163i \(0.299538\pi\)
\(360\) 0 0
\(361\) −4.87176 −0.256408
\(362\) 0 0
\(363\) −55.4339 −2.90953
\(364\) 0 0
\(365\) −64.3499 −3.36823
\(366\) 0 0
\(367\) 17.9832 0.938717 0.469358 0.883008i \(-0.344485\pi\)
0.469358 + 0.883008i \(0.344485\pi\)
\(368\) 0 0
\(369\) −4.14153 −0.215600
\(370\) 0 0
\(371\) 0.807102 0.0419027
\(372\) 0 0
\(373\) −13.1695 −0.681893 −0.340946 0.940083i \(-0.610747\pi\)
−0.340946 + 0.940083i \(0.610747\pi\)
\(374\) 0 0
\(375\) −46.8596 −2.41982
\(376\) 0 0
\(377\) 0.551249 0.0283908
\(378\) 0 0
\(379\) 16.7348 0.859610 0.429805 0.902922i \(-0.358582\pi\)
0.429805 + 0.902922i \(0.358582\pi\)
\(380\) 0 0
\(381\) −30.1498 −1.54462
\(382\) 0 0
\(383\) −20.0825 −1.02617 −0.513084 0.858338i \(-0.671497\pi\)
−0.513084 + 0.858338i \(0.671497\pi\)
\(384\) 0 0
\(385\) −2.29267 −0.116845
\(386\) 0 0
\(387\) 18.4235 0.936517
\(388\) 0 0
\(389\) −33.8905 −1.71832 −0.859158 0.511710i \(-0.829012\pi\)
−0.859158 + 0.511710i \(0.829012\pi\)
\(390\) 0 0
\(391\) −5.06169 −0.255981
\(392\) 0 0
\(393\) 31.0224 1.56488
\(394\) 0 0
\(395\) −12.1230 −0.609976
\(396\) 0 0
\(397\) 28.1181 1.41121 0.705605 0.708606i \(-0.250676\pi\)
0.705605 + 0.708606i \(0.250676\pi\)
\(398\) 0 0
\(399\) 0.870161 0.0435626
\(400\) 0 0
\(401\) −5.63888 −0.281592 −0.140796 0.990039i \(-0.544966\pi\)
−0.140796 + 0.990039i \(0.544966\pi\)
\(402\) 0 0
\(403\) 0.573748 0.0285804
\(404\) 0 0
\(405\) −40.7045 −2.02262
\(406\) 0 0
\(407\) −25.4354 −1.26079
\(408\) 0 0
\(409\) 17.2320 0.852067 0.426033 0.904707i \(-0.359911\pi\)
0.426033 + 0.904707i \(0.359911\pi\)
\(410\) 0 0
\(411\) 37.3848 1.84406
\(412\) 0 0
\(413\) −0.814122 −0.0400603
\(414\) 0 0
\(415\) −47.4828 −2.33084
\(416\) 0 0
\(417\) 28.6121 1.40114
\(418\) 0 0
\(419\) 3.82680 0.186951 0.0934756 0.995622i \(-0.470202\pi\)
0.0934756 + 0.995622i \(0.470202\pi\)
\(420\) 0 0
\(421\) −20.7975 −1.01361 −0.506804 0.862061i \(-0.669173\pi\)
−0.506804 + 0.862061i \(0.669173\pi\)
\(422\) 0 0
\(423\) 8.56218 0.416308
\(424\) 0 0
\(425\) −6.09669 −0.295733
\(426\) 0 0
\(427\) 1.25157 0.0605677
\(428\) 0 0
\(429\) −1.56694 −0.0756525
\(430\) 0 0
\(431\) −29.9927 −1.44470 −0.722348 0.691530i \(-0.756937\pi\)
−0.722348 + 0.691530i \(0.756937\pi\)
\(432\) 0 0
\(433\) −23.7873 −1.14314 −0.571571 0.820552i \(-0.693666\pi\)
−0.571571 + 0.820552i \(0.693666\pi\)
\(434\) 0 0
\(435\) 43.6651 2.09358
\(436\) 0 0
\(437\) −31.7624 −1.51940
\(438\) 0 0
\(439\) −8.55479 −0.408298 −0.204149 0.978940i \(-0.565443\pi\)
−0.204149 + 0.978940i \(0.565443\pi\)
\(440\) 0 0
\(441\) −16.7450 −0.797381
\(442\) 0 0
\(443\) 27.6606 1.31420 0.657098 0.753806i \(-0.271784\pi\)
0.657098 + 0.753806i \(0.271784\pi\)
\(444\) 0 0
\(445\) −17.6514 −0.836756
\(446\) 0 0
\(447\) 27.0438 1.27913
\(448\) 0 0
\(449\) 6.96415 0.328659 0.164329 0.986406i \(-0.447454\pi\)
0.164329 + 0.986406i \(0.447454\pi\)
\(450\) 0 0
\(451\) 10.2082 0.480687
\(452\) 0 0
\(453\) 41.1377 1.93282
\(454\) 0 0
\(455\) −0.0443596 −0.00207961
\(456\) 0 0
\(457\) 30.2530 1.41517 0.707587 0.706626i \(-0.249784\pi\)
0.707587 + 0.706626i \(0.249784\pi\)
\(458\) 0 0
\(459\) −0.841027 −0.0392558
\(460\) 0 0
\(461\) −25.3323 −1.17984 −0.589922 0.807460i \(-0.700841\pi\)
−0.589922 + 0.807460i \(0.700841\pi\)
\(462\) 0 0
\(463\) 25.7879 1.19847 0.599233 0.800575i \(-0.295472\pi\)
0.599233 + 0.800575i \(0.295472\pi\)
\(464\) 0 0
\(465\) 45.4472 2.10756
\(466\) 0 0
\(467\) −3.68313 −0.170435 −0.0852174 0.996362i \(-0.527158\pi\)
−0.0852174 + 0.996362i \(0.527158\pi\)
\(468\) 0 0
\(469\) 0.0645967 0.00298280
\(470\) 0 0
\(471\) 24.7638 1.14106
\(472\) 0 0
\(473\) −45.4110 −2.08800
\(474\) 0 0
\(475\) −38.2570 −1.75535
\(476\) 0 0
\(477\) 19.3997 0.888250
\(478\) 0 0
\(479\) 3.25673 0.148804 0.0744020 0.997228i \(-0.476295\pi\)
0.0744020 + 0.997228i \(0.476295\pi\)
\(480\) 0 0
\(481\) −0.492136 −0.0224395
\(482\) 0 0
\(483\) −1.95625 −0.0890125
\(484\) 0 0
\(485\) −50.4112 −2.28905
\(486\) 0 0
\(487\) −21.5037 −0.974427 −0.487214 0.873283i \(-0.661987\pi\)
−0.487214 + 0.873283i \(0.661987\pi\)
\(488\) 0 0
\(489\) −57.5289 −2.60155
\(490\) 0 0
\(491\) −30.7292 −1.38679 −0.693395 0.720558i \(-0.743886\pi\)
−0.693395 + 0.720558i \(0.743886\pi\)
\(492\) 0 0
\(493\) 2.89024 0.130170
\(494\) 0 0
\(495\) −55.1070 −2.47687
\(496\) 0 0
\(497\) −1.07163 −0.0480690
\(498\) 0 0
\(499\) −39.5918 −1.77237 −0.886187 0.463327i \(-0.846655\pi\)
−0.886187 + 0.463327i \(0.846655\pi\)
\(500\) 0 0
\(501\) −42.3155 −1.89052
\(502\) 0 0
\(503\) −5.51630 −0.245960 −0.122980 0.992409i \(-0.539245\pi\)
−0.122980 + 0.992409i \(0.539245\pi\)
\(504\) 0 0
\(505\) 39.0124 1.73603
\(506\) 0 0
\(507\) 30.1665 1.33974
\(508\) 0 0
\(509\) −19.4619 −0.862634 −0.431317 0.902201i \(-0.641951\pi\)
−0.431317 + 0.902201i \(0.641951\pi\)
\(510\) 0 0
\(511\) −1.64618 −0.0728226
\(512\) 0 0
\(513\) −5.27749 −0.233007
\(514\) 0 0
\(515\) −74.8992 −3.30045
\(516\) 0 0
\(517\) −21.1045 −0.928173
\(518\) 0 0
\(519\) −23.0649 −1.01244
\(520\) 0 0
\(521\) −7.94769 −0.348195 −0.174097 0.984728i \(-0.555701\pi\)
−0.174097 + 0.984728i \(0.555701\pi\)
\(522\) 0 0
\(523\) −31.6974 −1.38603 −0.693016 0.720922i \(-0.743719\pi\)
−0.693016 + 0.720922i \(0.743719\pi\)
\(524\) 0 0
\(525\) −2.35626 −0.102836
\(526\) 0 0
\(527\) 3.00820 0.131039
\(528\) 0 0
\(529\) 48.4066 2.10463
\(530\) 0 0
\(531\) −19.5684 −0.849196
\(532\) 0 0
\(533\) 0.197514 0.00855528
\(534\) 0 0
\(535\) 2.00875 0.0868458
\(536\) 0 0
\(537\) 1.77755 0.0767068
\(538\) 0 0
\(539\) 41.2739 1.77779
\(540\) 0 0
\(541\) 19.7350 0.848475 0.424237 0.905551i \(-0.360542\pi\)
0.424237 + 0.905551i \(0.360542\pi\)
\(542\) 0 0
\(543\) 47.5181 2.03920
\(544\) 0 0
\(545\) 54.1697 2.32037
\(546\) 0 0
\(547\) −15.3389 −0.655845 −0.327923 0.944705i \(-0.606349\pi\)
−0.327923 + 0.944705i \(0.606349\pi\)
\(548\) 0 0
\(549\) 30.0830 1.28391
\(550\) 0 0
\(551\) 18.1364 0.772638
\(552\) 0 0
\(553\) −0.310128 −0.0131880
\(554\) 0 0
\(555\) −38.9827 −1.65472
\(556\) 0 0
\(557\) 27.1757 1.15147 0.575736 0.817636i \(-0.304716\pi\)
0.575736 + 0.817636i \(0.304716\pi\)
\(558\) 0 0
\(559\) −0.878633 −0.0371622
\(560\) 0 0
\(561\) −8.21558 −0.346862
\(562\) 0 0
\(563\) 24.4502 1.03045 0.515227 0.857054i \(-0.327708\pi\)
0.515227 + 0.857054i \(0.327708\pi\)
\(564\) 0 0
\(565\) 69.3447 2.91735
\(566\) 0 0
\(567\) −1.04129 −0.0437300
\(568\) 0 0
\(569\) 6.17990 0.259075 0.129537 0.991575i \(-0.458651\pi\)
0.129537 + 0.991575i \(0.458651\pi\)
\(570\) 0 0
\(571\) 14.8635 0.622019 0.311009 0.950407i \(-0.399333\pi\)
0.311009 + 0.950407i \(0.399333\pi\)
\(572\) 0 0
\(573\) −20.0706 −0.838461
\(574\) 0 0
\(575\) 86.0075 3.58676
\(576\) 0 0
\(577\) −19.4466 −0.809572 −0.404786 0.914411i \(-0.632654\pi\)
−0.404786 + 0.914411i \(0.632654\pi\)
\(578\) 0 0
\(579\) −62.8703 −2.61280
\(580\) 0 0
\(581\) −1.21469 −0.0503938
\(582\) 0 0
\(583\) −47.8172 −1.98039
\(584\) 0 0
\(585\) −1.06624 −0.0440834
\(586\) 0 0
\(587\) 14.6478 0.604578 0.302289 0.953216i \(-0.402249\pi\)
0.302289 + 0.953216i \(0.402249\pi\)
\(588\) 0 0
\(589\) 18.8766 0.777798
\(590\) 0 0
\(591\) 46.8632 1.92769
\(592\) 0 0
\(593\) 26.0984 1.07173 0.535867 0.844303i \(-0.319985\pi\)
0.535867 + 0.844303i \(0.319985\pi\)
\(594\) 0 0
\(595\) −0.232581 −0.00953488
\(596\) 0 0
\(597\) 12.3898 0.507079
\(598\) 0 0
\(599\) −30.8440 −1.26025 −0.630126 0.776493i \(-0.716997\pi\)
−0.630126 + 0.776493i \(0.716997\pi\)
\(600\) 0 0
\(601\) −10.3212 −0.421008 −0.210504 0.977593i \(-0.567511\pi\)
−0.210504 + 0.977593i \(0.567511\pi\)
\(602\) 0 0
\(603\) 1.55266 0.0632291
\(604\) 0 0
\(605\) 92.9752 3.77998
\(606\) 0 0
\(607\) 2.14177 0.0869318 0.0434659 0.999055i \(-0.486160\pi\)
0.0434659 + 0.999055i \(0.486160\pi\)
\(608\) 0 0
\(609\) 1.11703 0.0452642
\(610\) 0 0
\(611\) −0.408339 −0.0165196
\(612\) 0 0
\(613\) 0.807877 0.0326298 0.0163149 0.999867i \(-0.494807\pi\)
0.0163149 + 0.999867i \(0.494807\pi\)
\(614\) 0 0
\(615\) 15.6453 0.630879
\(616\) 0 0
\(617\) −47.2375 −1.90171 −0.950855 0.309637i \(-0.899792\pi\)
−0.950855 + 0.309637i \(0.899792\pi\)
\(618\) 0 0
\(619\) 46.6928 1.87674 0.938371 0.345628i \(-0.112334\pi\)
0.938371 + 0.345628i \(0.112334\pi\)
\(620\) 0 0
\(621\) 11.8646 0.476109
\(622\) 0 0
\(623\) −0.451552 −0.0180911
\(624\) 0 0
\(625\) 27.7035 1.10814
\(626\) 0 0
\(627\) −51.5532 −2.05884
\(628\) 0 0
\(629\) −2.58031 −0.102884
\(630\) 0 0
\(631\) 13.5243 0.538392 0.269196 0.963085i \(-0.413242\pi\)
0.269196 + 0.963085i \(0.413242\pi\)
\(632\) 0 0
\(633\) −15.6703 −0.622837
\(634\) 0 0
\(635\) 50.5680 2.00673
\(636\) 0 0
\(637\) 0.798586 0.0316411
\(638\) 0 0
\(639\) −25.7578 −1.01896
\(640\) 0 0
\(641\) −22.1372 −0.874368 −0.437184 0.899372i \(-0.644024\pi\)
−0.437184 + 0.899372i \(0.644024\pi\)
\(642\) 0 0
\(643\) 21.1941 0.835815 0.417907 0.908490i \(-0.362764\pi\)
0.417907 + 0.908490i \(0.362764\pi\)
\(644\) 0 0
\(645\) −69.5975 −2.74040
\(646\) 0 0
\(647\) 13.0194 0.511846 0.255923 0.966697i \(-0.417621\pi\)
0.255923 + 0.966697i \(0.417621\pi\)
\(648\) 0 0
\(649\) 48.2331 1.89331
\(650\) 0 0
\(651\) 1.16262 0.0455665
\(652\) 0 0
\(653\) −3.73363 −0.146108 −0.0730542 0.997328i \(-0.523275\pi\)
−0.0730542 + 0.997328i \(0.523275\pi\)
\(654\) 0 0
\(655\) −52.0316 −2.03304
\(656\) 0 0
\(657\) −39.5679 −1.54369
\(658\) 0 0
\(659\) 30.5240 1.18905 0.594524 0.804078i \(-0.297341\pi\)
0.594524 + 0.804078i \(0.297341\pi\)
\(660\) 0 0
\(661\) −15.6436 −0.608464 −0.304232 0.952598i \(-0.598400\pi\)
−0.304232 + 0.952598i \(0.598400\pi\)
\(662\) 0 0
\(663\) −0.158959 −0.00617345
\(664\) 0 0
\(665\) −1.45946 −0.0565953
\(666\) 0 0
\(667\) −40.7734 −1.57875
\(668\) 0 0
\(669\) 51.1693 1.97832
\(670\) 0 0
\(671\) −74.1499 −2.86252
\(672\) 0 0
\(673\) −11.1808 −0.430989 −0.215495 0.976505i \(-0.569136\pi\)
−0.215495 + 0.976505i \(0.569136\pi\)
\(674\) 0 0
\(675\) 14.2906 0.550046
\(676\) 0 0
\(677\) −36.4148 −1.39954 −0.699768 0.714371i \(-0.746713\pi\)
−0.699768 + 0.714371i \(0.746713\pi\)
\(678\) 0 0
\(679\) −1.28960 −0.0494904
\(680\) 0 0
\(681\) 33.3518 1.27804
\(682\) 0 0
\(683\) 7.27488 0.278365 0.139183 0.990267i \(-0.455552\pi\)
0.139183 + 0.990267i \(0.455552\pi\)
\(684\) 0 0
\(685\) −62.7027 −2.39575
\(686\) 0 0
\(687\) 22.2595 0.849252
\(688\) 0 0
\(689\) −0.925190 −0.0352469
\(690\) 0 0
\(691\) −2.68549 −0.102161 −0.0510804 0.998695i \(-0.516266\pi\)
−0.0510804 + 0.998695i \(0.516266\pi\)
\(692\) 0 0
\(693\) −1.40973 −0.0535512
\(694\) 0 0
\(695\) −47.9890 −1.82033
\(696\) 0 0
\(697\) 1.03558 0.0392254
\(698\) 0 0
\(699\) 41.9694 1.58743
\(700\) 0 0
\(701\) 13.5715 0.512588 0.256294 0.966599i \(-0.417498\pi\)
0.256294 + 0.966599i \(0.417498\pi\)
\(702\) 0 0
\(703\) −16.1916 −0.610677
\(704\) 0 0
\(705\) −32.3450 −1.21818
\(706\) 0 0
\(707\) 0.998002 0.0375337
\(708\) 0 0
\(709\) 12.5915 0.472884 0.236442 0.971646i \(-0.424019\pi\)
0.236442 + 0.971646i \(0.424019\pi\)
\(710\) 0 0
\(711\) −7.45429 −0.279558
\(712\) 0 0
\(713\) −42.4375 −1.58930
\(714\) 0 0
\(715\) 2.62811 0.0982857
\(716\) 0 0
\(717\) 34.2522 1.27917
\(718\) 0 0
\(719\) 25.8803 0.965172 0.482586 0.875849i \(-0.339698\pi\)
0.482586 + 0.875849i \(0.339698\pi\)
\(720\) 0 0
\(721\) −1.91605 −0.0713573
\(722\) 0 0
\(723\) 32.9963 1.22715
\(724\) 0 0
\(725\) −49.1106 −1.82392
\(726\) 0 0
\(727\) −18.8980 −0.700889 −0.350445 0.936583i \(-0.613970\pi\)
−0.350445 + 0.936583i \(0.613970\pi\)
\(728\) 0 0
\(729\) −15.2445 −0.564612
\(730\) 0 0
\(731\) −4.60674 −0.170387
\(732\) 0 0
\(733\) −6.61256 −0.244240 −0.122120 0.992515i \(-0.538969\pi\)
−0.122120 + 0.992515i \(0.538969\pi\)
\(734\) 0 0
\(735\) 63.2569 2.33327
\(736\) 0 0
\(737\) −3.82706 −0.140972
\(738\) 0 0
\(739\) −2.28543 −0.0840709 −0.0420354 0.999116i \(-0.513384\pi\)
−0.0420354 + 0.999116i \(0.513384\pi\)
\(740\) 0 0
\(741\) −0.997475 −0.0366432
\(742\) 0 0
\(743\) −33.3889 −1.22492 −0.612460 0.790502i \(-0.709820\pi\)
−0.612460 + 0.790502i \(0.709820\pi\)
\(744\) 0 0
\(745\) −45.3585 −1.66181
\(746\) 0 0
\(747\) −29.1965 −1.06825
\(748\) 0 0
\(749\) 0.0513872 0.00187765
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −51.1496 −1.86399
\(754\) 0 0
\(755\) −68.9972 −2.51107
\(756\) 0 0
\(757\) −26.3287 −0.956932 −0.478466 0.878106i \(-0.658807\pi\)
−0.478466 + 0.878106i \(0.658807\pi\)
\(758\) 0 0
\(759\) 115.899 4.20687
\(760\) 0 0
\(761\) 38.0302 1.37859 0.689297 0.724479i \(-0.257920\pi\)
0.689297 + 0.724479i \(0.257920\pi\)
\(762\) 0 0
\(763\) 1.38575 0.0501676
\(764\) 0 0
\(765\) −5.59036 −0.202120
\(766\) 0 0
\(767\) 0.933237 0.0336972
\(768\) 0 0
\(769\) 7.02534 0.253340 0.126670 0.991945i \(-0.459571\pi\)
0.126670 + 0.991945i \(0.459571\pi\)
\(770\) 0 0
\(771\) 26.1415 0.941464
\(772\) 0 0
\(773\) −29.4211 −1.05820 −0.529102 0.848558i \(-0.677471\pi\)
−0.529102 + 0.848558i \(0.677471\pi\)
\(774\) 0 0
\(775\) −51.1149 −1.83610
\(776\) 0 0
\(777\) −0.997242 −0.0357759
\(778\) 0 0
\(779\) 6.49832 0.232827
\(780\) 0 0
\(781\) 63.4890 2.27182
\(782\) 0 0
\(783\) −6.77471 −0.242108
\(784\) 0 0
\(785\) −41.5344 −1.48243
\(786\) 0 0
\(787\) 10.5990 0.377812 0.188906 0.981995i \(-0.439506\pi\)
0.188906 + 0.981995i \(0.439506\pi\)
\(788\) 0 0
\(789\) −23.9116 −0.851277
\(790\) 0 0
\(791\) 1.77396 0.0630746
\(792\) 0 0
\(793\) −1.43469 −0.0509472
\(794\) 0 0
\(795\) −73.2853 −2.59916
\(796\) 0 0
\(797\) 31.3456 1.11032 0.555158 0.831745i \(-0.312658\pi\)
0.555158 + 0.831745i \(0.312658\pi\)
\(798\) 0 0
\(799\) −2.14095 −0.0757415
\(800\) 0 0
\(801\) −10.8536 −0.383493
\(802\) 0 0
\(803\) 97.5287 3.44171
\(804\) 0 0
\(805\) 3.28107 0.115643
\(806\) 0 0
\(807\) −27.0548 −0.952375
\(808\) 0 0
\(809\) −7.02698 −0.247056 −0.123528 0.992341i \(-0.539421\pi\)
−0.123528 + 0.992341i \(0.539421\pi\)
\(810\) 0 0
\(811\) 20.0298 0.703342 0.351671 0.936124i \(-0.385614\pi\)
0.351671 + 0.936124i \(0.385614\pi\)
\(812\) 0 0
\(813\) 5.57502 0.195525
\(814\) 0 0
\(815\) 96.4889 3.37986
\(816\) 0 0
\(817\) −28.9075 −1.01135
\(818\) 0 0
\(819\) −0.0272761 −0.000953105 0
\(820\) 0 0
\(821\) 14.4064 0.502786 0.251393 0.967885i \(-0.419111\pi\)
0.251393 + 0.967885i \(0.419111\pi\)
\(822\) 0 0
\(823\) 21.7218 0.757175 0.378587 0.925566i \(-0.376410\pi\)
0.378587 + 0.925566i \(0.376410\pi\)
\(824\) 0 0
\(825\) 139.598 4.86017
\(826\) 0 0
\(827\) −3.99954 −0.139078 −0.0695388 0.997579i \(-0.522153\pi\)
−0.0695388 + 0.997579i \(0.522153\pi\)
\(828\) 0 0
\(829\) 34.3387 1.19263 0.596317 0.802749i \(-0.296630\pi\)
0.596317 + 0.802749i \(0.296630\pi\)
\(830\) 0 0
\(831\) 11.4627 0.397638
\(832\) 0 0
\(833\) 4.18705 0.145073
\(834\) 0 0
\(835\) 70.9727 2.45611
\(836\) 0 0
\(837\) −7.05121 −0.243725
\(838\) 0 0
\(839\) 1.38671 0.0478744 0.0239372 0.999713i \(-0.492380\pi\)
0.0239372 + 0.999713i \(0.492380\pi\)
\(840\) 0 0
\(841\) −5.71827 −0.197182
\(842\) 0 0
\(843\) 33.2019 1.14354
\(844\) 0 0
\(845\) −50.5960 −1.74055
\(846\) 0 0
\(847\) 2.37846 0.0817250
\(848\) 0 0
\(849\) −32.8414 −1.12711
\(850\) 0 0
\(851\) 36.4011 1.24781
\(852\) 0 0
\(853\) −32.3362 −1.10717 −0.553584 0.832793i \(-0.686740\pi\)
−0.553584 + 0.832793i \(0.686740\pi\)
\(854\) 0 0
\(855\) −35.0798 −1.19970
\(856\) 0 0
\(857\) −53.7240 −1.83518 −0.917588 0.397532i \(-0.869867\pi\)
−0.917588 + 0.397532i \(0.869867\pi\)
\(858\) 0 0
\(859\) 42.4809 1.44943 0.724715 0.689049i \(-0.241972\pi\)
0.724715 + 0.689049i \(0.241972\pi\)
\(860\) 0 0
\(861\) 0.400233 0.0136399
\(862\) 0 0
\(863\) 39.5249 1.34544 0.672722 0.739895i \(-0.265125\pi\)
0.672722 + 0.739895i \(0.265125\pi\)
\(864\) 0 0
\(865\) 38.6851 1.31533
\(866\) 0 0
\(867\) 38.6547 1.31278
\(868\) 0 0
\(869\) 18.3737 0.623284
\(870\) 0 0
\(871\) −0.0740479 −0.00250902
\(872\) 0 0
\(873\) −30.9972 −1.04909
\(874\) 0 0
\(875\) 2.01057 0.0679696
\(876\) 0 0
\(877\) −36.0978 −1.21894 −0.609468 0.792811i \(-0.708617\pi\)
−0.609468 + 0.792811i \(0.708617\pi\)
\(878\) 0 0
\(879\) 38.6802 1.30465
\(880\) 0 0
\(881\) 40.9091 1.37826 0.689131 0.724637i \(-0.257992\pi\)
0.689131 + 0.724637i \(0.257992\pi\)
\(882\) 0 0
\(883\) −20.3239 −0.683953 −0.341976 0.939709i \(-0.611096\pi\)
−0.341976 + 0.939709i \(0.611096\pi\)
\(884\) 0 0
\(885\) 73.9227 2.48488
\(886\) 0 0
\(887\) 1.44332 0.0484618 0.0242309 0.999706i \(-0.492286\pi\)
0.0242309 + 0.999706i \(0.492286\pi\)
\(888\) 0 0
\(889\) 1.29361 0.0433864
\(890\) 0 0
\(891\) 61.6917 2.06675
\(892\) 0 0
\(893\) −13.4346 −0.449572
\(894\) 0 0
\(895\) −2.98134 −0.0996554
\(896\) 0 0
\(897\) 2.24247 0.0748740
\(898\) 0 0
\(899\) 24.2319 0.808180
\(900\) 0 0
\(901\) −4.85084 −0.161605
\(902\) 0 0
\(903\) −1.78042 −0.0592487
\(904\) 0 0
\(905\) −79.6985 −2.64927
\(906\) 0 0
\(907\) −29.2840 −0.972359 −0.486180 0.873859i \(-0.661610\pi\)
−0.486180 + 0.873859i \(0.661610\pi\)
\(908\) 0 0
\(909\) 23.9882 0.795638
\(910\) 0 0
\(911\) −41.0149 −1.35888 −0.679441 0.733730i \(-0.737778\pi\)
−0.679441 + 0.733730i \(0.737778\pi\)
\(912\) 0 0
\(913\) 71.9650 2.38169
\(914\) 0 0
\(915\) −113.643 −3.75693
\(916\) 0 0
\(917\) −1.33106 −0.0439554
\(918\) 0 0
\(919\) −17.8345 −0.588306 −0.294153 0.955758i \(-0.595038\pi\)
−0.294153 + 0.955758i \(0.595038\pi\)
\(920\) 0 0
\(921\) −13.3893 −0.441191
\(922\) 0 0
\(923\) 1.22842 0.0404338
\(924\) 0 0
\(925\) 43.8442 1.44159
\(926\) 0 0
\(927\) −46.0545 −1.51263
\(928\) 0 0
\(929\) −53.9029 −1.76850 −0.884248 0.467018i \(-0.845328\pi\)
−0.884248 + 0.467018i \(0.845328\pi\)
\(930\) 0 0
\(931\) 26.2740 0.861094
\(932\) 0 0
\(933\) 61.5931 2.01647
\(934\) 0 0
\(935\) 13.7794 0.450634
\(936\) 0 0
\(937\) −41.8413 −1.36690 −0.683448 0.729999i \(-0.739521\pi\)
−0.683448 + 0.729999i \(0.739521\pi\)
\(938\) 0 0
\(939\) 59.0999 1.92865
\(940\) 0 0
\(941\) 18.0296 0.587749 0.293875 0.955844i \(-0.405055\pi\)
0.293875 + 0.955844i \(0.405055\pi\)
\(942\) 0 0
\(943\) −14.6092 −0.475741
\(944\) 0 0
\(945\) 0.545168 0.0177343
\(946\) 0 0
\(947\) 46.0916 1.49778 0.748889 0.662696i \(-0.230588\pi\)
0.748889 + 0.662696i \(0.230588\pi\)
\(948\) 0 0
\(949\) 1.88703 0.0612556
\(950\) 0 0
\(951\) −14.2980 −0.463644
\(952\) 0 0
\(953\) −16.9333 −0.548525 −0.274262 0.961655i \(-0.588434\pi\)
−0.274262 + 0.961655i \(0.588434\pi\)
\(954\) 0 0
\(955\) 33.6629 1.08931
\(956\) 0 0
\(957\) −66.1788 −2.13926
\(958\) 0 0
\(959\) −1.60404 −0.0517972
\(960\) 0 0
\(961\) −5.77908 −0.186422
\(962\) 0 0
\(963\) 1.23515 0.0398022
\(964\) 0 0
\(965\) 105.448 3.39448
\(966\) 0 0
\(967\) 8.61718 0.277110 0.138555 0.990355i \(-0.455754\pi\)
0.138555 + 0.990355i \(0.455754\pi\)
\(968\) 0 0
\(969\) −5.22984 −0.168007
\(970\) 0 0
\(971\) −14.5073 −0.465562 −0.232781 0.972529i \(-0.574782\pi\)
−0.232781 + 0.972529i \(0.574782\pi\)
\(972\) 0 0
\(973\) −1.22764 −0.0393563
\(974\) 0 0
\(975\) 2.70101 0.0865014
\(976\) 0 0
\(977\) 45.2892 1.44893 0.724465 0.689312i \(-0.242087\pi\)
0.724465 + 0.689312i \(0.242087\pi\)
\(978\) 0 0
\(979\) 26.7525 0.855012
\(980\) 0 0
\(981\) 33.3082 1.06345
\(982\) 0 0
\(983\) −46.2655 −1.47564 −0.737819 0.674998i \(-0.764144\pi\)
−0.737819 + 0.674998i \(0.764144\pi\)
\(984\) 0 0
\(985\) −78.6001 −2.50441
\(986\) 0 0
\(987\) −0.827440 −0.0263377
\(988\) 0 0
\(989\) 64.9885 2.06651
\(990\) 0 0
\(991\) −33.2575 −1.05646 −0.528229 0.849102i \(-0.677144\pi\)
−0.528229 + 0.849102i \(0.677144\pi\)
\(992\) 0 0
\(993\) 45.0172 1.42858
\(994\) 0 0
\(995\) −20.7804 −0.658783
\(996\) 0 0
\(997\) −17.5830 −0.556858 −0.278429 0.960457i \(-0.589814\pi\)
−0.278429 + 0.960457i \(0.589814\pi\)
\(998\) 0 0
\(999\) 6.04823 0.191357
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 6008.2.a.b.1.8 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.8 44 1.1 even 1 trivial