Properties

Label 8008.2.a.j.1.5
Level 8008
Weight 2
Character 8008.1
Self dual yes
Analytic conductor 63.944
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.668973.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-1.26787\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.43421 q^{3} +1.30958 q^{5} +1.00000 q^{7} +2.92540 q^{9} +O(q^{10})\) \(q+2.43421 q^{3} +1.30958 q^{5} +1.00000 q^{7} +2.92540 q^{9} -1.00000 q^{11} -1.00000 q^{13} +3.18779 q^{15} +5.30958 q^{17} -1.44400 q^{19} +2.43421 q^{21} +8.93159 q^{23} -3.28500 q^{25} -0.181603 q^{27} -5.58176 q^{29} -6.13083 q^{31} -2.43421 q^{33} +1.30958 q^{35} +8.97877 q^{37} -2.43421 q^{39} -3.64943 q^{41} +6.67538 q^{43} +3.83103 q^{45} -2.40679 q^{47} +1.00000 q^{49} +12.9246 q^{51} +4.61582 q^{53} -1.30958 q^{55} -3.51501 q^{57} +14.3055 q^{59} +11.6220 q^{61} +2.92540 q^{63} -1.30958 q^{65} +0.118445 q^{67} +21.7414 q^{69} +10.5248 q^{71} +13.9976 q^{73} -7.99640 q^{75} -1.00000 q^{77} -11.0968 q^{79} -9.21825 q^{81} +14.3412 q^{83} +6.95331 q^{85} -13.5872 q^{87} -12.3124 q^{89} -1.00000 q^{91} -14.9237 q^{93} -1.89103 q^{95} +17.7254 q^{97} -2.92540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + q^{3} - q^{5} + 5q^{7} + 6q^{9} + O(q^{10}) \) \( 5q + q^{3} - q^{5} + 5q^{7} + 6q^{9} - 5q^{11} - 5q^{13} - 5q^{15} + 19q^{17} - 5q^{19} + q^{21} + 5q^{23} + 12q^{25} - 11q^{27} - 17q^{29} + 4q^{31} - q^{33} - q^{35} + 10q^{37} - q^{39} + 10q^{41} - 25q^{43} + q^{45} + 3q^{47} + 5q^{49} - q^{51} + 22q^{53} + q^{55} + 16q^{57} + 21q^{59} + 26q^{61} + 6q^{63} + q^{65} + 28q^{67} + 16q^{69} + 28q^{71} - 4q^{73} - 5q^{77} - 11q^{79} + 5q^{81} + 33q^{85} + 31q^{87} - 37q^{89} - 5q^{91} - 49q^{93} + 29q^{95} + 18q^{97} - 6q^{99} + O(q^{100}) \)

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
\(3\) 2.43421 1.40539 0.702697 0.711489i \(-0.251979\pi\)
0.702697 + 0.711489i \(0.251979\pi\)
\(4\) 0 0
\(5\) 1.30958 0.585661 0.292831 0.956164i \(-0.405403\pi\)
0.292831 + 0.956164i \(0.405403\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 2.92540 0.975132
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 3.18779 0.823085
\(16\) 0 0
\(17\) 5.30958 1.28776 0.643881 0.765126i \(-0.277323\pi\)
0.643881 + 0.765126i \(0.277323\pi\)
\(18\) 0 0
\(19\) −1.44400 −0.331277 −0.165638 0.986187i \(-0.552968\pi\)
−0.165638 + 0.986187i \(0.552968\pi\)
\(20\) 0 0
\(21\) 2.43421 0.531189
\(22\) 0 0
\(23\) 8.93159 1.86236 0.931182 0.364554i \(-0.118779\pi\)
0.931182 + 0.364554i \(0.118779\pi\)
\(24\) 0 0
\(25\) −3.28500 −0.657001
\(26\) 0 0
\(27\) −0.181603 −0.0349496
\(28\) 0 0
\(29\) −5.58176 −1.03651 −0.518254 0.855227i \(-0.673418\pi\)
−0.518254 + 0.855227i \(0.673418\pi\)
\(30\) 0 0
\(31\) −6.13083 −1.10113 −0.550564 0.834793i \(-0.685587\pi\)
−0.550564 + 0.834793i \(0.685587\pi\)
\(32\) 0 0
\(33\) −2.43421 −0.423742
\(34\) 0 0
\(35\) 1.30958 0.221359
\(36\) 0 0
\(37\) 8.97877 1.47610 0.738050 0.674746i \(-0.235747\pi\)
0.738050 + 0.674746i \(0.235747\pi\)
\(38\) 0 0
\(39\) −2.43421 −0.389786
\(40\) 0 0
\(41\) −3.64943 −0.569945 −0.284973 0.958536i \(-0.591985\pi\)
−0.284973 + 0.958536i \(0.591985\pi\)
\(42\) 0 0
\(43\) 6.67538 1.01799 0.508993 0.860771i \(-0.330018\pi\)
0.508993 + 0.860771i \(0.330018\pi\)
\(44\) 0 0
\(45\) 3.83103 0.571097
\(46\) 0 0
\(47\) −2.40679 −0.351066 −0.175533 0.984474i \(-0.556165\pi\)
−0.175533 + 0.984474i \(0.556165\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 12.9246 1.80981
\(52\) 0 0
\(53\) 4.61582 0.634031 0.317016 0.948420i \(-0.397319\pi\)
0.317016 + 0.948420i \(0.397319\pi\)
\(54\) 0 0
\(55\) −1.30958 −0.176584
\(56\) 0 0
\(57\) −3.51501 −0.465574
\(58\) 0 0
\(59\) 14.3055 1.86242 0.931208 0.364488i \(-0.118756\pi\)
0.931208 + 0.364488i \(0.118756\pi\)
\(60\) 0 0
\(61\) 11.6220 1.48805 0.744023 0.668154i \(-0.232915\pi\)
0.744023 + 0.668154i \(0.232915\pi\)
\(62\) 0 0
\(63\) 2.92540 0.368565
\(64\) 0 0
\(65\) −1.30958 −0.162433
\(66\) 0 0
\(67\) 0.118445 0.0144704 0.00723518 0.999974i \(-0.497697\pi\)
0.00723518 + 0.999974i \(0.497697\pi\)
\(68\) 0 0
\(69\) 21.7414 2.61736
\(70\) 0 0
\(71\) 10.5248 1.24906 0.624532 0.780999i \(-0.285290\pi\)
0.624532 + 0.780999i \(0.285290\pi\)
\(72\) 0 0
\(73\) 13.9976 1.63829 0.819147 0.573583i \(-0.194447\pi\)
0.819147 + 0.573583i \(0.194447\pi\)
\(74\) 0 0
\(75\) −7.99640 −0.923345
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −11.0968 −1.24848 −0.624242 0.781231i \(-0.714592\pi\)
−0.624242 + 0.781231i \(0.714592\pi\)
\(80\) 0 0
\(81\) −9.21825 −1.02425
\(82\) 0 0
\(83\) 14.3412 1.57415 0.787077 0.616855i \(-0.211593\pi\)
0.787077 + 0.616855i \(0.211593\pi\)
\(84\) 0 0
\(85\) 6.95331 0.754192
\(86\) 0 0
\(87\) −13.5872 −1.45670
\(88\) 0 0
\(89\) −12.3124 −1.30511 −0.652557 0.757739i \(-0.726304\pi\)
−0.652557 + 0.757739i \(0.726304\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −14.9237 −1.54752
\(94\) 0 0
\(95\) −1.89103 −0.194016
\(96\) 0 0
\(97\) 17.7254 1.79974 0.899871 0.436156i \(-0.143660\pi\)
0.899871 + 0.436156i \(0.143660\pi\)
\(98\) 0 0
\(99\) −2.92540 −0.294013
\(100\) 0 0
\(101\) −5.64158 −0.561359 −0.280679 0.959802i \(-0.590560\pi\)
−0.280679 + 0.959802i \(0.590560\pi\)
\(102\) 0 0
\(103\) −2.83512 −0.279353 −0.139676 0.990197i \(-0.544606\pi\)
−0.139676 + 0.990197i \(0.544606\pi\)
\(104\) 0 0
\(105\) 3.18779 0.311097
\(106\) 0 0
\(107\) −3.21900 −0.311192 −0.155596 0.987821i \(-0.549730\pi\)
−0.155596 + 0.987821i \(0.549730\pi\)
\(108\) 0 0
\(109\) 16.5812 1.58819 0.794095 0.607793i \(-0.207945\pi\)
0.794095 + 0.607793i \(0.207945\pi\)
\(110\) 0 0
\(111\) 21.8562 2.07450
\(112\) 0 0
\(113\) 0.535512 0.0503767 0.0251884 0.999683i \(-0.491981\pi\)
0.0251884 + 0.999683i \(0.491981\pi\)
\(114\) 0 0
\(115\) 11.6966 1.09071
\(116\) 0 0
\(117\) −2.92540 −0.270453
\(118\) 0 0
\(119\) 5.30958 0.486728
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −8.88349 −0.800998
\(124\) 0 0
\(125\) −10.8499 −0.970441
\(126\) 0 0
\(127\) −14.1678 −1.25718 −0.628592 0.777735i \(-0.716369\pi\)
−0.628592 + 0.777735i \(0.716369\pi\)
\(128\) 0 0
\(129\) 16.2493 1.43067
\(130\) 0 0
\(131\) −20.0250 −1.74959 −0.874797 0.484490i \(-0.839005\pi\)
−0.874797 + 0.484490i \(0.839005\pi\)
\(132\) 0 0
\(133\) −1.44400 −0.125211
\(134\) 0 0
\(135\) −0.237824 −0.0204686
\(136\) 0 0
\(137\) −9.24445 −0.789807 −0.394903 0.918723i \(-0.629222\pi\)
−0.394903 + 0.918723i \(0.629222\pi\)
\(138\) 0 0
\(139\) 7.52314 0.638104 0.319052 0.947737i \(-0.396635\pi\)
0.319052 + 0.947737i \(0.396635\pi\)
\(140\) 0 0
\(141\) −5.85864 −0.493386
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −7.30976 −0.607042
\(146\) 0 0
\(147\) 2.43421 0.200771
\(148\) 0 0
\(149\) −16.7948 −1.37588 −0.687940 0.725768i \(-0.741485\pi\)
−0.687940 + 0.725768i \(0.741485\pi\)
\(150\) 0 0
\(151\) −2.11016 −0.171722 −0.0858611 0.996307i \(-0.527364\pi\)
−0.0858611 + 0.996307i \(0.527364\pi\)
\(152\) 0 0
\(153\) 15.5326 1.25574
\(154\) 0 0
\(155\) −8.02880 −0.644888
\(156\) 0 0
\(157\) −6.71425 −0.535855 −0.267928 0.963439i \(-0.586339\pi\)
−0.267928 + 0.963439i \(0.586339\pi\)
\(158\) 0 0
\(159\) 11.2359 0.891064
\(160\) 0 0
\(161\) 8.93159 0.703908
\(162\) 0 0
\(163\) −3.84582 −0.301228 −0.150614 0.988593i \(-0.548125\pi\)
−0.150614 + 0.988593i \(0.548125\pi\)
\(164\) 0 0
\(165\) −3.18779 −0.248169
\(166\) 0 0
\(167\) 0.452598 0.0350231 0.0175115 0.999847i \(-0.494426\pi\)
0.0175115 + 0.999847i \(0.494426\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −4.22428 −0.323038
\(172\) 0 0
\(173\) −7.14061 −0.542891 −0.271445 0.962454i \(-0.587502\pi\)
−0.271445 + 0.962454i \(0.587502\pi\)
\(174\) 0 0
\(175\) −3.28500 −0.248323
\(176\) 0 0
\(177\) 34.8226 2.61743
\(178\) 0 0
\(179\) −7.42940 −0.555299 −0.277650 0.960682i \(-0.589555\pi\)
−0.277650 + 0.960682i \(0.589555\pi\)
\(180\) 0 0
\(181\) 12.5572 0.933369 0.466684 0.884424i \(-0.345448\pi\)
0.466684 + 0.884424i \(0.345448\pi\)
\(182\) 0 0
\(183\) 28.2904 2.09129
\(184\) 0 0
\(185\) 11.7584 0.864495
\(186\) 0 0
\(187\) −5.30958 −0.388275
\(188\) 0 0
\(189\) −0.181603 −0.0132097
\(190\) 0 0
\(191\) 23.7540 1.71878 0.859390 0.511320i \(-0.170843\pi\)
0.859390 + 0.511320i \(0.170843\pi\)
\(192\) 0 0
\(193\) −3.35777 −0.241698 −0.120849 0.992671i \(-0.538562\pi\)
−0.120849 + 0.992671i \(0.538562\pi\)
\(194\) 0 0
\(195\) −3.18779 −0.228283
\(196\) 0 0
\(197\) 4.76640 0.339592 0.169796 0.985479i \(-0.445689\pi\)
0.169796 + 0.985479i \(0.445689\pi\)
\(198\) 0 0
\(199\) 1.11182 0.0788146 0.0394073 0.999223i \(-0.487453\pi\)
0.0394073 + 0.999223i \(0.487453\pi\)
\(200\) 0 0
\(201\) 0.288321 0.0203366
\(202\) 0 0
\(203\) −5.58176 −0.391763
\(204\) 0 0
\(205\) −4.77922 −0.333795
\(206\) 0 0
\(207\) 26.1284 1.81605
\(208\) 0 0
\(209\) 1.44400 0.0998837
\(210\) 0 0
\(211\) 19.4015 1.33566 0.667828 0.744315i \(-0.267224\pi\)
0.667828 + 0.744315i \(0.267224\pi\)
\(212\) 0 0
\(213\) 25.6196 1.75543
\(214\) 0 0
\(215\) 8.74193 0.596195
\(216\) 0 0
\(217\) −6.13083 −0.416188
\(218\) 0 0
\(219\) 34.0731 2.30245
\(220\) 0 0
\(221\) −5.30958 −0.357161
\(222\) 0 0
\(223\) 26.6327 1.78346 0.891729 0.452570i \(-0.149493\pi\)
0.891729 + 0.452570i \(0.149493\pi\)
\(224\) 0 0
\(225\) −9.60994 −0.640662
\(226\) 0 0
\(227\) −4.88683 −0.324351 −0.162175 0.986762i \(-0.551851\pi\)
−0.162175 + 0.986762i \(0.551851\pi\)
\(228\) 0 0
\(229\) 19.7445 1.30476 0.652378 0.757894i \(-0.273771\pi\)
0.652378 + 0.757894i \(0.273771\pi\)
\(230\) 0 0
\(231\) −2.43421 −0.160159
\(232\) 0 0
\(233\) −2.27887 −0.149293 −0.0746467 0.997210i \(-0.523783\pi\)
−0.0746467 + 0.997210i \(0.523783\pi\)
\(234\) 0 0
\(235\) −3.15188 −0.205606
\(236\) 0 0
\(237\) −27.0119 −1.75461
\(238\) 0 0
\(239\) −2.91921 −0.188828 −0.0944139 0.995533i \(-0.530098\pi\)
−0.0944139 + 0.995533i \(0.530098\pi\)
\(240\) 0 0
\(241\) −18.2628 −1.17641 −0.588207 0.808711i \(-0.700166\pi\)
−0.588207 + 0.808711i \(0.700166\pi\)
\(242\) 0 0
\(243\) −21.8944 −1.40452
\(244\) 0 0
\(245\) 1.30958 0.0836659
\(246\) 0 0
\(247\) 1.44400 0.0918796
\(248\) 0 0
\(249\) 34.9096 2.21231
\(250\) 0 0
\(251\) −22.7636 −1.43682 −0.718411 0.695618i \(-0.755130\pi\)
−0.718411 + 0.695618i \(0.755130\pi\)
\(252\) 0 0
\(253\) −8.93159 −0.561524
\(254\) 0 0
\(255\) 16.9258 1.05994
\(256\) 0 0
\(257\) 25.5863 1.59603 0.798015 0.602638i \(-0.205884\pi\)
0.798015 + 0.602638i \(0.205884\pi\)
\(258\) 0 0
\(259\) 8.97877 0.557913
\(260\) 0 0
\(261\) −16.3289 −1.01073
\(262\) 0 0
\(263\) −9.11200 −0.561870 −0.280935 0.959727i \(-0.590645\pi\)
−0.280935 + 0.959727i \(0.590645\pi\)
\(264\) 0 0
\(265\) 6.04477 0.371328
\(266\) 0 0
\(267\) −29.9711 −1.83420
\(268\) 0 0
\(269\) −1.12797 −0.0687738 −0.0343869 0.999409i \(-0.510948\pi\)
−0.0343869 + 0.999409i \(0.510948\pi\)
\(270\) 0 0
\(271\) 8.43287 0.512260 0.256130 0.966642i \(-0.417552\pi\)
0.256130 + 0.966642i \(0.417552\pi\)
\(272\) 0 0
\(273\) −2.43421 −0.147325
\(274\) 0 0
\(275\) 3.28500 0.198093
\(276\) 0 0
\(277\) −9.78523 −0.587937 −0.293969 0.955815i \(-0.594976\pi\)
−0.293969 + 0.955815i \(0.594976\pi\)
\(278\) 0 0
\(279\) −17.9351 −1.07375
\(280\) 0 0
\(281\) 5.05889 0.301788 0.150894 0.988550i \(-0.451785\pi\)
0.150894 + 0.988550i \(0.451785\pi\)
\(282\) 0 0
\(283\) −28.2306 −1.67814 −0.839068 0.544026i \(-0.816899\pi\)
−0.839068 + 0.544026i \(0.816899\pi\)
\(284\) 0 0
\(285\) −4.60318 −0.272669
\(286\) 0 0
\(287\) −3.64943 −0.215419
\(288\) 0 0
\(289\) 11.1916 0.658331
\(290\) 0 0
\(291\) 43.1474 2.52935
\(292\) 0 0
\(293\) −16.0621 −0.938358 −0.469179 0.883103i \(-0.655450\pi\)
−0.469179 + 0.883103i \(0.655450\pi\)
\(294\) 0 0
\(295\) 18.7342 1.09075
\(296\) 0 0
\(297\) 0.181603 0.0105377
\(298\) 0 0
\(299\) −8.93159 −0.516527
\(300\) 0 0
\(301\) 6.67538 0.384762
\(302\) 0 0
\(303\) −13.7328 −0.788930
\(304\) 0 0
\(305\) 15.2199 0.871491
\(306\) 0 0
\(307\) −31.4794 −1.79663 −0.898313 0.439356i \(-0.855207\pi\)
−0.898313 + 0.439356i \(0.855207\pi\)
\(308\) 0 0
\(309\) −6.90129 −0.392601
\(310\) 0 0
\(311\) −8.27672 −0.469330 −0.234665 0.972076i \(-0.575399\pi\)
−0.234665 + 0.972076i \(0.575399\pi\)
\(312\) 0 0
\(313\) −31.1040 −1.75810 −0.879052 0.476726i \(-0.841823\pi\)
−0.879052 + 0.476726i \(0.841823\pi\)
\(314\) 0 0
\(315\) 3.83103 0.215854
\(316\) 0 0
\(317\) 1.45211 0.0815585 0.0407793 0.999168i \(-0.487016\pi\)
0.0407793 + 0.999168i \(0.487016\pi\)
\(318\) 0 0
\(319\) 5.58176 0.312519
\(320\) 0 0
\(321\) −7.83572 −0.437347
\(322\) 0 0
\(323\) −7.66704 −0.426605
\(324\) 0 0
\(325\) 3.28500 0.182219
\(326\) 0 0
\(327\) 40.3622 2.23203
\(328\) 0 0
\(329\) −2.40679 −0.132691
\(330\) 0 0
\(331\) 6.13794 0.337372 0.168686 0.985670i \(-0.446048\pi\)
0.168686 + 0.985670i \(0.446048\pi\)
\(332\) 0 0
\(333\) 26.2664 1.43939
\(334\) 0 0
\(335\) 0.155113 0.00847473
\(336\) 0 0
\(337\) −25.7355 −1.40190 −0.700951 0.713209i \(-0.747241\pi\)
−0.700951 + 0.713209i \(0.747241\pi\)
\(338\) 0 0
\(339\) 1.30355 0.0707992
\(340\) 0 0
\(341\) 6.13083 0.332003
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 28.4720 1.53288
\(346\) 0 0
\(347\) 8.13009 0.436446 0.218223 0.975899i \(-0.429974\pi\)
0.218223 + 0.975899i \(0.429974\pi\)
\(348\) 0 0
\(349\) 17.5158 0.937597 0.468799 0.883305i \(-0.344687\pi\)
0.468799 + 0.883305i \(0.344687\pi\)
\(350\) 0 0
\(351\) 0.181603 0.00969328
\(352\) 0 0
\(353\) −5.48758 −0.292075 −0.146037 0.989279i \(-0.546652\pi\)
−0.146037 + 0.989279i \(0.546652\pi\)
\(354\) 0 0
\(355\) 13.7830 0.731528
\(356\) 0 0
\(357\) 12.9246 0.684045
\(358\) 0 0
\(359\) −15.1990 −0.802173 −0.401086 0.916040i \(-0.631367\pi\)
−0.401086 + 0.916040i \(0.631367\pi\)
\(360\) 0 0
\(361\) −16.9149 −0.890256
\(362\) 0 0
\(363\) 2.43421 0.127763
\(364\) 0 0
\(365\) 18.3309 0.959486
\(366\) 0 0
\(367\) 0.0566587 0.00295756 0.00147878 0.999999i \(-0.499529\pi\)
0.00147878 + 0.999999i \(0.499529\pi\)
\(368\) 0 0
\(369\) −10.6760 −0.555772
\(370\) 0 0
\(371\) 4.61582 0.239641
\(372\) 0 0
\(373\) −8.30927 −0.430238 −0.215119 0.976588i \(-0.569014\pi\)
−0.215119 + 0.976588i \(0.569014\pi\)
\(374\) 0 0
\(375\) −26.4109 −1.36385
\(376\) 0 0
\(377\) 5.58176 0.287476
\(378\) 0 0
\(379\) −30.8510 −1.58471 −0.792354 0.610061i \(-0.791145\pi\)
−0.792354 + 0.610061i \(0.791145\pi\)
\(380\) 0 0
\(381\) −34.4873 −1.76684
\(382\) 0 0
\(383\) 32.8915 1.68068 0.840338 0.542063i \(-0.182357\pi\)
0.840338 + 0.542063i \(0.182357\pi\)
\(384\) 0 0
\(385\) −1.30958 −0.0667423
\(386\) 0 0
\(387\) 19.5281 0.992670
\(388\) 0 0
\(389\) 1.09936 0.0557397 0.0278698 0.999612i \(-0.491128\pi\)
0.0278698 + 0.999612i \(0.491128\pi\)
\(390\) 0 0
\(391\) 47.4230 2.39828
\(392\) 0 0
\(393\) −48.7452 −2.45887
\(394\) 0 0
\(395\) −14.5321 −0.731189
\(396\) 0 0
\(397\) −27.4618 −1.37827 −0.689135 0.724633i \(-0.742009\pi\)
−0.689135 + 0.724633i \(0.742009\pi\)
\(398\) 0 0
\(399\) −3.51501 −0.175971
\(400\) 0 0
\(401\) 23.1990 1.15850 0.579251 0.815149i \(-0.303345\pi\)
0.579251 + 0.815149i \(0.303345\pi\)
\(402\) 0 0
\(403\) 6.13083 0.305398
\(404\) 0 0
\(405\) −12.0720 −0.599863
\(406\) 0 0
\(407\) −8.97877 −0.445061
\(408\) 0 0
\(409\) 5.56815 0.275327 0.137664 0.990479i \(-0.456041\pi\)
0.137664 + 0.990479i \(0.456041\pi\)
\(410\) 0 0
\(411\) −22.5030 −1.10999
\(412\) 0 0
\(413\) 14.3055 0.703927
\(414\) 0 0
\(415\) 18.7810 0.921921
\(416\) 0 0
\(417\) 18.3129 0.896788
\(418\) 0 0
\(419\) 3.09822 0.151358 0.0756790 0.997132i \(-0.475888\pi\)
0.0756790 + 0.997132i \(0.475888\pi\)
\(420\) 0 0
\(421\) 34.7521 1.69371 0.846857 0.531821i \(-0.178492\pi\)
0.846857 + 0.531821i \(0.178492\pi\)
\(422\) 0 0
\(423\) −7.04081 −0.342336
\(424\) 0 0
\(425\) −17.4420 −0.846061
\(426\) 0 0
\(427\) 11.6220 0.562428
\(428\) 0 0
\(429\) 2.43421 0.117525
\(430\) 0 0
\(431\) −36.5946 −1.76270 −0.881350 0.472465i \(-0.843364\pi\)
−0.881350 + 0.472465i \(0.843364\pi\)
\(432\) 0 0
\(433\) −27.9134 −1.34143 −0.670716 0.741714i \(-0.734013\pi\)
−0.670716 + 0.741714i \(0.734013\pi\)
\(434\) 0 0
\(435\) −17.7935 −0.853134
\(436\) 0 0
\(437\) −12.8972 −0.616958
\(438\) 0 0
\(439\) −37.7039 −1.79951 −0.899754 0.436398i \(-0.856254\pi\)
−0.899754 + 0.436398i \(0.856254\pi\)
\(440\) 0 0
\(441\) 2.92540 0.139305
\(442\) 0 0
\(443\) 3.03045 0.143981 0.0719906 0.997405i \(-0.477065\pi\)
0.0719906 + 0.997405i \(0.477065\pi\)
\(444\) 0 0
\(445\) −16.1241 −0.764355
\(446\) 0 0
\(447\) −40.8820 −1.93365
\(448\) 0 0
\(449\) 6.47823 0.305727 0.152863 0.988247i \(-0.451151\pi\)
0.152863 + 0.988247i \(0.451151\pi\)
\(450\) 0 0
\(451\) 3.64943 0.171845
\(452\) 0 0
\(453\) −5.13658 −0.241337
\(454\) 0 0
\(455\) −1.30958 −0.0613940
\(456\) 0 0
\(457\) 4.03690 0.188838 0.0944192 0.995533i \(-0.469901\pi\)
0.0944192 + 0.995533i \(0.469901\pi\)
\(458\) 0 0
\(459\) −0.964238 −0.0450068
\(460\) 0 0
\(461\) −12.3352 −0.574509 −0.287254 0.957854i \(-0.592742\pi\)
−0.287254 + 0.957854i \(0.592742\pi\)
\(462\) 0 0
\(463\) −14.9993 −0.697074 −0.348537 0.937295i \(-0.613321\pi\)
−0.348537 + 0.937295i \(0.613321\pi\)
\(464\) 0 0
\(465\) −19.5438 −0.906322
\(466\) 0 0
\(467\) −7.14272 −0.330525 −0.165263 0.986250i \(-0.552847\pi\)
−0.165263 + 0.986250i \(0.552847\pi\)
\(468\) 0 0
\(469\) 0.118445 0.00546929
\(470\) 0 0
\(471\) −16.3439 −0.753088
\(472\) 0 0
\(473\) −6.67538 −0.306934
\(474\) 0 0
\(475\) 4.74355 0.217649
\(476\) 0 0
\(477\) 13.5031 0.618264
\(478\) 0 0
\(479\) 16.7466 0.765174 0.382587 0.923920i \(-0.375033\pi\)
0.382587 + 0.923920i \(0.375033\pi\)
\(480\) 0 0
\(481\) −8.97877 −0.409396
\(482\) 0 0
\(483\) 21.7414 0.989267
\(484\) 0 0
\(485\) 23.2128 1.05404
\(486\) 0 0
\(487\) 30.3938 1.37728 0.688638 0.725105i \(-0.258209\pi\)
0.688638 + 0.725105i \(0.258209\pi\)
\(488\) 0 0
\(489\) −9.36155 −0.423344
\(490\) 0 0
\(491\) 7.26242 0.327749 0.163874 0.986481i \(-0.447601\pi\)
0.163874 + 0.986481i \(0.447601\pi\)
\(492\) 0 0
\(493\) −29.6368 −1.33478
\(494\) 0 0
\(495\) −3.83103 −0.172192
\(496\) 0 0
\(497\) 10.5248 0.472102
\(498\) 0 0
\(499\) −33.4915 −1.49929 −0.749643 0.661843i \(-0.769775\pi\)
−0.749643 + 0.661843i \(0.769775\pi\)
\(500\) 0 0
\(501\) 1.10172 0.0492212
\(502\) 0 0
\(503\) 26.2830 1.17190 0.585951 0.810346i \(-0.300721\pi\)
0.585951 + 0.810346i \(0.300721\pi\)
\(504\) 0 0
\(505\) −7.38810 −0.328766
\(506\) 0 0
\(507\) 2.43421 0.108107
\(508\) 0 0
\(509\) 26.6308 1.18039 0.590194 0.807262i \(-0.299051\pi\)
0.590194 + 0.807262i \(0.299051\pi\)
\(510\) 0 0
\(511\) 13.9976 0.619217
\(512\) 0 0
\(513\) 0.262236 0.0115780
\(514\) 0 0
\(515\) −3.71282 −0.163606
\(516\) 0 0
\(517\) 2.40679 0.105850
\(518\) 0 0
\(519\) −17.3818 −0.762975
\(520\) 0 0
\(521\) 15.8034 0.692357 0.346179 0.938169i \(-0.387479\pi\)
0.346179 + 0.938169i \(0.387479\pi\)
\(522\) 0 0
\(523\) 30.1601 1.31881 0.659405 0.751788i \(-0.270808\pi\)
0.659405 + 0.751788i \(0.270808\pi\)
\(524\) 0 0
\(525\) −7.99640 −0.348992
\(526\) 0 0
\(527\) −32.5521 −1.41799
\(528\) 0 0
\(529\) 56.7732 2.46840
\(530\) 0 0
\(531\) 41.8492 1.81610
\(532\) 0 0
\(533\) 3.64943 0.158074
\(534\) 0 0
\(535\) −4.21553 −0.182253
\(536\) 0 0
\(537\) −18.0847 −0.780414
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 37.4540 1.61027 0.805136 0.593090i \(-0.202092\pi\)
0.805136 + 0.593090i \(0.202092\pi\)
\(542\) 0 0
\(543\) 30.5669 1.31175
\(544\) 0 0
\(545\) 21.7144 0.930142
\(546\) 0 0
\(547\) 17.3336 0.741132 0.370566 0.928806i \(-0.379164\pi\)
0.370566 + 0.928806i \(0.379164\pi\)
\(548\) 0 0
\(549\) 33.9990 1.45104
\(550\) 0 0
\(551\) 8.06008 0.343371
\(552\) 0 0
\(553\) −11.0968 −0.471883
\(554\) 0 0
\(555\) 28.6225 1.21496
\(556\) 0 0
\(557\) −4.80454 −0.203575 −0.101787 0.994806i \(-0.532456\pi\)
−0.101787 + 0.994806i \(0.532456\pi\)
\(558\) 0 0
\(559\) −6.67538 −0.282338
\(560\) 0 0
\(561\) −12.9246 −0.545679
\(562\) 0 0
\(563\) 8.15734 0.343791 0.171895 0.985115i \(-0.445011\pi\)
0.171895 + 0.985115i \(0.445011\pi\)
\(564\) 0 0
\(565\) 0.701295 0.0295037
\(566\) 0 0
\(567\) −9.21825 −0.387130
\(568\) 0 0
\(569\) −36.6773 −1.53759 −0.768797 0.639493i \(-0.779144\pi\)
−0.768797 + 0.639493i \(0.779144\pi\)
\(570\) 0 0
\(571\) 5.57563 0.233333 0.116666 0.993171i \(-0.462779\pi\)
0.116666 + 0.993171i \(0.462779\pi\)
\(572\) 0 0
\(573\) 57.8224 2.41556
\(574\) 0 0
\(575\) −29.3403 −1.22357
\(576\) 0 0
\(577\) −43.0825 −1.79355 −0.896774 0.442490i \(-0.854095\pi\)
−0.896774 + 0.442490i \(0.854095\pi\)
\(578\) 0 0
\(579\) −8.17353 −0.339680
\(580\) 0 0
\(581\) 14.3412 0.594974
\(582\) 0 0
\(583\) −4.61582 −0.191168
\(584\) 0 0
\(585\) −3.83103 −0.158394
\(586\) 0 0
\(587\) −23.3648 −0.964368 −0.482184 0.876070i \(-0.660156\pi\)
−0.482184 + 0.876070i \(0.660156\pi\)
\(588\) 0 0
\(589\) 8.85292 0.364778
\(590\) 0 0
\(591\) 11.6024 0.477260
\(592\) 0 0
\(593\) −28.2788 −1.16127 −0.580636 0.814163i \(-0.697196\pi\)
−0.580636 + 0.814163i \(0.697196\pi\)
\(594\) 0 0
\(595\) 6.95331 0.285058
\(596\) 0 0
\(597\) 2.70640 0.110766
\(598\) 0 0
\(599\) 26.9244 1.10010 0.550051 0.835131i \(-0.314608\pi\)
0.550051 + 0.835131i \(0.314608\pi\)
\(600\) 0 0
\(601\) 20.6556 0.842561 0.421281 0.906930i \(-0.361581\pi\)
0.421281 + 0.906930i \(0.361581\pi\)
\(602\) 0 0
\(603\) 0.346499 0.0141105
\(604\) 0 0
\(605\) 1.30958 0.0532419
\(606\) 0 0
\(607\) −17.1738 −0.697061 −0.348531 0.937297i \(-0.613319\pi\)
−0.348531 + 0.937297i \(0.613319\pi\)
\(608\) 0 0
\(609\) −13.5872 −0.550581
\(610\) 0 0
\(611\) 2.40679 0.0973683
\(612\) 0 0
\(613\) 8.19637 0.331048 0.165524 0.986206i \(-0.447068\pi\)
0.165524 + 0.986206i \(0.447068\pi\)
\(614\) 0 0
\(615\) −11.6336 −0.469113
\(616\) 0 0
\(617\) 19.2026 0.773067 0.386533 0.922275i \(-0.373672\pi\)
0.386533 + 0.922275i \(0.373672\pi\)
\(618\) 0 0
\(619\) 31.0776 1.24911 0.624557 0.780979i \(-0.285280\pi\)
0.624557 + 0.780979i \(0.285280\pi\)
\(620\) 0 0
\(621\) −1.62201 −0.0650889
\(622\) 0 0
\(623\) −12.3124 −0.493287
\(624\) 0 0
\(625\) 2.21628 0.0886510
\(626\) 0 0
\(627\) 3.51501 0.140376
\(628\) 0 0
\(629\) 47.6735 1.90087
\(630\) 0 0
\(631\) −42.8626 −1.70633 −0.853166 0.521640i \(-0.825320\pi\)
−0.853166 + 0.521640i \(0.825320\pi\)
\(632\) 0 0
\(633\) 47.2275 1.87712
\(634\) 0 0
\(635\) −18.5538 −0.736284
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 30.7892 1.21800
\(640\) 0 0
\(641\) 31.8047 1.25621 0.628106 0.778128i \(-0.283831\pi\)
0.628106 + 0.778128i \(0.283831\pi\)
\(642\) 0 0
\(643\) −46.9897 −1.85309 −0.926545 0.376183i \(-0.877236\pi\)
−0.926545 + 0.376183i \(0.877236\pi\)
\(644\) 0 0
\(645\) 21.2797 0.837888
\(646\) 0 0
\(647\) −7.71409 −0.303272 −0.151636 0.988436i \(-0.548454\pi\)
−0.151636 + 0.988436i \(0.548454\pi\)
\(648\) 0 0
\(649\) −14.3055 −0.561540
\(650\) 0 0
\(651\) −14.9237 −0.584907
\(652\) 0 0
\(653\) −28.6944 −1.12290 −0.561449 0.827511i \(-0.689756\pi\)
−0.561449 + 0.827511i \(0.689756\pi\)
\(654\) 0 0
\(655\) −26.2243 −1.02467
\(656\) 0 0
\(657\) 40.9485 1.59755
\(658\) 0 0
\(659\) −37.2716 −1.45189 −0.725947 0.687750i \(-0.758598\pi\)
−0.725947 + 0.687750i \(0.758598\pi\)
\(660\) 0 0
\(661\) 21.1393 0.822223 0.411112 0.911585i \(-0.365141\pi\)
0.411112 + 0.911585i \(0.365141\pi\)
\(662\) 0 0
\(663\) −12.9246 −0.501952
\(664\) 0 0
\(665\) −1.89103 −0.0733311
\(666\) 0 0
\(667\) −49.8540 −1.93035
\(668\) 0 0
\(669\) 64.8297 2.50646
\(670\) 0 0
\(671\) −11.6220 −0.448663
\(672\) 0 0
\(673\) 15.6947 0.604985 0.302492 0.953152i \(-0.402181\pi\)
0.302492 + 0.953152i \(0.402181\pi\)
\(674\) 0 0
\(675\) 0.596568 0.0229619
\(676\) 0 0
\(677\) 2.89450 0.111245 0.0556224 0.998452i \(-0.482286\pi\)
0.0556224 + 0.998452i \(0.482286\pi\)
\(678\) 0 0
\(679\) 17.7254 0.680239
\(680\) 0 0
\(681\) −11.8956 −0.455840
\(682\) 0 0
\(683\) −29.7398 −1.13796 −0.568980 0.822351i \(-0.692662\pi\)
−0.568980 + 0.822351i \(0.692662\pi\)
\(684\) 0 0
\(685\) −12.1063 −0.462559
\(686\) 0 0
\(687\) 48.0624 1.83370
\(688\) 0 0
\(689\) −4.61582 −0.175849
\(690\) 0 0
\(691\) −25.6734 −0.976663 −0.488331 0.872658i \(-0.662394\pi\)
−0.488331 + 0.872658i \(0.662394\pi\)
\(692\) 0 0
\(693\) −2.92540 −0.111127
\(694\) 0 0
\(695\) 9.85214 0.373713
\(696\) 0 0
\(697\) −19.3769 −0.733954
\(698\) 0 0
\(699\) −5.54725 −0.209816
\(700\) 0 0
\(701\) 2.85211 0.107723 0.0538614 0.998548i \(-0.482847\pi\)
0.0538614 + 0.998548i \(0.482847\pi\)
\(702\) 0 0
\(703\) −12.9654 −0.488998
\(704\) 0 0
\(705\) −7.67235 −0.288957
\(706\) 0 0
\(707\) −5.64158 −0.212174
\(708\) 0 0
\(709\) 14.6803 0.551331 0.275666 0.961254i \(-0.411102\pi\)
0.275666 + 0.961254i \(0.411102\pi\)
\(710\) 0 0
\(711\) −32.4624 −1.21744
\(712\) 0 0
\(713\) −54.7580 −2.05070
\(714\) 0 0
\(715\) 1.30958 0.0489755
\(716\) 0 0
\(717\) −7.10597 −0.265377
\(718\) 0 0
\(719\) 26.4770 0.987427 0.493714 0.869625i \(-0.335639\pi\)
0.493714 + 0.869625i \(0.335639\pi\)
\(720\) 0 0
\(721\) −2.83512 −0.105585
\(722\) 0 0
\(723\) −44.4557 −1.65332
\(724\) 0 0
\(725\) 18.3361 0.680986
\(726\) 0 0
\(727\) 9.34346 0.346530 0.173265 0.984875i \(-0.444568\pi\)
0.173265 + 0.984875i \(0.444568\pi\)
\(728\) 0 0
\(729\) −25.6408 −0.949661
\(730\) 0 0
\(731\) 35.4434 1.31092
\(732\) 0 0
\(733\) −14.3676 −0.530678 −0.265339 0.964155i \(-0.585484\pi\)
−0.265339 + 0.964155i \(0.585484\pi\)
\(734\) 0 0
\(735\) 3.18779 0.117584
\(736\) 0 0
\(737\) −0.118445 −0.00436298
\(738\) 0 0
\(739\) −14.5720 −0.536038 −0.268019 0.963414i \(-0.586369\pi\)
−0.268019 + 0.963414i \(0.586369\pi\)
\(740\) 0 0
\(741\) 3.51501 0.129127
\(742\) 0 0
\(743\) −9.45395 −0.346832 −0.173416 0.984849i \(-0.555480\pi\)
−0.173416 + 0.984849i \(0.555480\pi\)
\(744\) 0 0
\(745\) −21.9941 −0.805800
\(746\) 0 0
\(747\) 41.9538 1.53501
\(748\) 0 0
\(749\) −3.21900 −0.117620
\(750\) 0 0
\(751\) 23.0879 0.842491 0.421245 0.906947i \(-0.361593\pi\)
0.421245 + 0.906947i \(0.361593\pi\)
\(752\) 0 0
\(753\) −55.4114 −2.01930
\(754\) 0 0
\(755\) −2.76342 −0.100571
\(756\) 0 0
\(757\) −1.63004 −0.0592446 −0.0296223 0.999561i \(-0.509430\pi\)
−0.0296223 + 0.999561i \(0.509430\pi\)
\(758\) 0 0
\(759\) −21.7414 −0.789162
\(760\) 0 0
\(761\) 21.3870 0.775280 0.387640 0.921811i \(-0.373290\pi\)
0.387640 + 0.921811i \(0.373290\pi\)
\(762\) 0 0
\(763\) 16.5812 0.600280
\(764\) 0 0
\(765\) 20.3412 0.735437
\(766\) 0 0
\(767\) −14.3055 −0.516541
\(768\) 0 0
\(769\) 20.2435 0.730000 0.365000 0.931007i \(-0.381069\pi\)
0.365000 + 0.931007i \(0.381069\pi\)
\(770\) 0 0
\(771\) 62.2825 2.24305
\(772\) 0 0
\(773\) 35.3131 1.27013 0.635063 0.772461i \(-0.280974\pi\)
0.635063 + 0.772461i \(0.280974\pi\)
\(774\) 0 0
\(775\) 20.1398 0.723443
\(776\) 0 0
\(777\) 21.8562 0.784088
\(778\) 0 0
\(779\) 5.26978 0.188810
\(780\) 0 0
\(781\) −10.5248 −0.376607
\(782\) 0 0
\(783\) 1.01367 0.0362255
\(784\) 0 0
\(785\) −8.79283 −0.313830
\(786\) 0 0
\(787\) −18.0870 −0.644731 −0.322365 0.946615i \(-0.604478\pi\)
−0.322365 + 0.946615i \(0.604478\pi\)
\(788\) 0 0
\(789\) −22.1805 −0.789648
\(790\) 0 0
\(791\) 0.535512 0.0190406
\(792\) 0 0
\(793\) −11.6220 −0.412710
\(794\) 0 0
\(795\) 14.7143 0.521861
\(796\) 0 0
\(797\) 32.5035 1.15133 0.575666 0.817685i \(-0.304743\pi\)
0.575666 + 0.817685i \(0.304743\pi\)
\(798\) 0 0
\(799\) −12.7790 −0.452090
\(800\) 0 0
\(801\) −36.0187 −1.27266
\(802\) 0 0
\(803\) −13.9976 −0.493964
\(804\) 0 0
\(805\) 11.6966 0.412251
\(806\) 0 0
\(807\) −2.74573 −0.0966543
\(808\) 0 0
\(809\) 40.2892 1.41649 0.708247 0.705965i \(-0.249486\pi\)
0.708247 + 0.705965i \(0.249486\pi\)
\(810\) 0 0
\(811\) −53.3286 −1.87262 −0.936310 0.351175i \(-0.885782\pi\)
−0.936310 + 0.351175i \(0.885782\pi\)
\(812\) 0 0
\(813\) 20.5274 0.719927
\(814\) 0 0
\(815\) −5.03640 −0.176418
\(816\) 0 0
\(817\) −9.63926 −0.337235
\(818\) 0 0
\(819\) −2.92540 −0.102222
\(820\) 0 0
\(821\) −5.40557 −0.188656 −0.0943278 0.995541i \(-0.530070\pi\)
−0.0943278 + 0.995541i \(0.530070\pi\)
\(822\) 0 0
\(823\) −55.1841 −1.92360 −0.961798 0.273759i \(-0.911733\pi\)
−0.961798 + 0.273759i \(0.911733\pi\)
\(824\) 0 0
\(825\) 7.99640 0.278399
\(826\) 0 0
\(827\) −40.4077 −1.40511 −0.702557 0.711628i \(-0.747958\pi\)
−0.702557 + 0.711628i \(0.747958\pi\)
\(828\) 0 0
\(829\) −55.2329 −1.91832 −0.959159 0.282867i \(-0.908714\pi\)
−0.959159 + 0.282867i \(0.908714\pi\)
\(830\) 0 0
\(831\) −23.8193 −0.826283
\(832\) 0 0
\(833\) 5.30958 0.183966
\(834\) 0 0
\(835\) 0.592712 0.0205116
\(836\) 0 0
\(837\) 1.11338 0.0384840
\(838\) 0 0
\(839\) −3.06303 −0.105747 −0.0528737 0.998601i \(-0.516838\pi\)
−0.0528737 + 0.998601i \(0.516838\pi\)
\(840\) 0 0
\(841\) 2.15610 0.0743481
\(842\) 0 0
\(843\) 12.3144 0.424131
\(844\) 0 0
\(845\) 1.30958 0.0450509
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) −68.7194 −2.35844
\(850\) 0 0
\(851\) 80.1946 2.74904
\(852\) 0 0
\(853\) 19.0017 0.650606 0.325303 0.945610i \(-0.394534\pi\)
0.325303 + 0.945610i \(0.394534\pi\)
\(854\) 0 0
\(855\) −5.53202 −0.189191
\(856\) 0 0
\(857\) −33.1025 −1.13076 −0.565380 0.824830i \(-0.691271\pi\)
−0.565380 + 0.824830i \(0.691271\pi\)
\(858\) 0 0
\(859\) −14.0693 −0.480038 −0.240019 0.970768i \(-0.577154\pi\)
−0.240019 + 0.970768i \(0.577154\pi\)
\(860\) 0 0
\(861\) −8.88349 −0.302749
\(862\) 0 0
\(863\) 52.3893 1.78335 0.891677 0.452672i \(-0.149529\pi\)
0.891677 + 0.452672i \(0.149529\pi\)
\(864\) 0 0
\(865\) −9.35119 −0.317950
\(866\) 0 0
\(867\) 27.2428 0.925214
\(868\) 0 0
\(869\) 11.0968 0.376432
\(870\) 0 0
\(871\) −0.118445 −0.00401336
\(872\) 0 0
\(873\) 51.8538 1.75499
\(874\) 0 0
\(875\) −10.8499 −0.366792
\(876\) 0 0
\(877\) −1.86423 −0.0629505 −0.0314753 0.999505i \(-0.510021\pi\)
−0.0314753 + 0.999505i \(0.510021\pi\)
\(878\) 0 0
\(879\) −39.0986 −1.31876
\(880\) 0 0
\(881\) −22.4824 −0.757451 −0.378726 0.925509i \(-0.623638\pi\)
−0.378726 + 0.925509i \(0.623638\pi\)
\(882\) 0 0
\(883\) −36.4502 −1.22665 −0.613323 0.789832i \(-0.710168\pi\)
−0.613323 + 0.789832i \(0.710168\pi\)
\(884\) 0 0
\(885\) 45.6030 1.53293
\(886\) 0 0
\(887\) 19.8258 0.665684 0.332842 0.942983i \(-0.391992\pi\)
0.332842 + 0.942983i \(0.391992\pi\)
\(888\) 0 0
\(889\) −14.1678 −0.475171
\(890\) 0 0
\(891\) 9.21825 0.308823
\(892\) 0 0
\(893\) 3.47541 0.116300
\(894\) 0 0
\(895\) −9.72938 −0.325217
\(896\) 0 0
\(897\) −21.7414 −0.725924
\(898\) 0 0
\(899\) 34.2208 1.14133
\(900\) 0 0
\(901\) 24.5080 0.816481
\(902\) 0 0
\(903\) 16.2493 0.540743
\(904\) 0 0
\(905\) 16.4446 0.546638
\(906\) 0 0
\(907\) −8.72419 −0.289682 −0.144841 0.989455i \(-0.546267\pi\)
−0.144841 + 0.989455i \(0.546267\pi\)
\(908\) 0 0
\(909\) −16.5039 −0.547399
\(910\) 0 0
\(911\) −46.6394 −1.54523 −0.772616 0.634874i \(-0.781052\pi\)
−0.772616 + 0.634874i \(0.781052\pi\)
\(912\) 0 0
\(913\) −14.3412 −0.474625
\(914\) 0 0
\(915\) 37.0486 1.22479
\(916\) 0 0
\(917\) −20.0250 −0.661284
\(918\) 0 0
\(919\) −43.1913 −1.42475 −0.712375 0.701799i \(-0.752380\pi\)
−0.712375 + 0.701799i \(0.752380\pi\)
\(920\) 0 0
\(921\) −76.6277 −2.52497
\(922\) 0 0
\(923\) −10.5248 −0.346428
\(924\) 0 0
\(925\) −29.4953 −0.969799
\(926\) 0 0
\(927\) −8.29385 −0.272406
\(928\) 0 0
\(929\) 38.9013 1.27631 0.638155 0.769908i \(-0.279698\pi\)
0.638155 + 0.769908i \(0.279698\pi\)
\(930\) 0 0
\(931\) −1.44400 −0.0473252
\(932\) 0 0
\(933\) −20.1473 −0.659593
\(934\) 0 0
\(935\) −6.95331 −0.227398
\(936\) 0 0
\(937\) 27.9816 0.914120 0.457060 0.889436i \(-0.348903\pi\)
0.457060 + 0.889436i \(0.348903\pi\)
\(938\) 0 0
\(939\) −75.7138 −2.47083
\(940\) 0 0
\(941\) 17.9977 0.586707 0.293354 0.956004i \(-0.405229\pi\)
0.293354 + 0.956004i \(0.405229\pi\)
\(942\) 0 0
\(943\) −32.5952 −1.06145
\(944\) 0 0
\(945\) −0.237824 −0.00773642
\(946\) 0 0
\(947\) 13.5523 0.440390 0.220195 0.975456i \(-0.429331\pi\)
0.220195 + 0.975456i \(0.429331\pi\)
\(948\) 0 0
\(949\) −13.9976 −0.454381
\(950\) 0 0
\(951\) 3.53474 0.114622
\(952\) 0 0
\(953\) −5.56431 −0.180246 −0.0901229 0.995931i \(-0.528726\pi\)
−0.0901229 + 0.995931i \(0.528726\pi\)
\(954\) 0 0
\(955\) 31.1078 1.00662
\(956\) 0 0
\(957\) 13.5872 0.439212
\(958\) 0 0
\(959\) −9.24445 −0.298519
\(960\) 0 0
\(961\) 6.58702 0.212484
\(962\) 0 0
\(963\) −9.41684 −0.303453
\(964\) 0 0
\(965\) −4.39726 −0.141553
\(966\) 0 0
\(967\) 19.6187 0.630895 0.315447 0.948943i \(-0.397845\pi\)
0.315447 + 0.948943i \(0.397845\pi\)
\(968\) 0 0
\(969\) −18.6632 −0.599549
\(970\) 0 0
\(971\) 30.1798 0.968516 0.484258 0.874925i \(-0.339090\pi\)
0.484258 + 0.874925i \(0.339090\pi\)
\(972\) 0 0
\(973\) 7.52314 0.241181
\(974\) 0 0
\(975\) 7.99640 0.256090
\(976\) 0 0
\(977\) 11.1444 0.356541 0.178270 0.983982i \(-0.442950\pi\)
0.178270 + 0.983982i \(0.442950\pi\)
\(978\) 0 0
\(979\) 12.3124 0.393507
\(980\) 0 0
\(981\) 48.5066 1.54870
\(982\) 0 0
\(983\) 40.0228 1.27653 0.638264 0.769817i \(-0.279653\pi\)
0.638264 + 0.769817i \(0.279653\pi\)
\(984\) 0 0
\(985\) 6.24197 0.198886
\(986\) 0 0
\(987\) −5.85864 −0.186483
\(988\) 0 0
\(989\) 59.6217 1.89586
\(990\) 0 0
\(991\) −18.5061 −0.587866 −0.293933 0.955826i \(-0.594964\pi\)
−0.293933 + 0.955826i \(0.594964\pi\)
\(992\) 0 0
\(993\) 14.9411 0.474140
\(994\) 0 0
\(995\) 1.45601 0.0461587
\(996\) 0 0
\(997\) −50.3183 −1.59360 −0.796798 0.604245i \(-0.793475\pi\)
−0.796798 + 0.604245i \(0.793475\pi\)
\(998\) 0 0
\(999\) −1.63058 −0.0515891
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 8008.2.a.j.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8008.2.a.j.1.5 5 1.1 even 1 trivial