Properties

Label 8008.2.a.n.1.4
Level 8008
Weight 2
Character 8008.1
Self dual yes
Analytic conductor 63.944
Analytic rank 0
Dimension 9
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: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.21838\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.21838 q^{3} +2.90030 q^{5} -1.00000 q^{7} -1.51556 q^{9} +O(q^{10})\) \(q-1.21838 q^{3} +2.90030 q^{5} -1.00000 q^{7} -1.51556 q^{9} +1.00000 q^{11} -1.00000 q^{13} -3.53365 q^{15} +3.20996 q^{17} -0.338048 q^{19} +1.21838 q^{21} +7.17564 q^{23} +3.41172 q^{25} +5.50165 q^{27} +10.5557 q^{29} +1.34712 q^{31} -1.21838 q^{33} -2.90030 q^{35} +2.97901 q^{37} +1.21838 q^{39} -3.83082 q^{41} -2.40992 q^{43} -4.39557 q^{45} -12.1040 q^{47} +1.00000 q^{49} -3.91094 q^{51} +1.77133 q^{53} +2.90030 q^{55} +0.411870 q^{57} -6.34524 q^{59} -6.55153 q^{61} +1.51556 q^{63} -2.90030 q^{65} -0.479975 q^{67} -8.74263 q^{69} -7.64425 q^{71} -5.07758 q^{73} -4.15676 q^{75} -1.00000 q^{77} +1.11643 q^{79} -2.15641 q^{81} +7.65360 q^{83} +9.30983 q^{85} -12.8609 q^{87} +15.7332 q^{89} +1.00000 q^{91} -1.64130 q^{93} -0.980440 q^{95} +16.9715 q^{97} -1.51556 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + O(q^{10}) \) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + 9q^{11} - 9q^{13} + 11q^{15} + 7q^{17} - 17q^{19} + 3q^{21} + 11q^{23} + 18q^{25} - 9q^{27} + 9q^{29} - 8q^{31} - 3q^{33} - q^{35} + 2q^{37} + 3q^{39} + 18q^{41} + 7q^{43} + 5q^{45} + 15q^{47} + 9q^{49} - 7q^{51} - 4q^{53} + q^{55} + 22q^{57} - 23q^{59} + 12q^{61} - 12q^{63} - q^{65} - 16q^{67} - 32q^{69} - 6q^{71} + 4q^{73} - 14q^{75} - 9q^{77} + 21q^{79} + 5q^{81} - 16q^{83} + 53q^{85} + 41q^{87} + 5q^{89} + 9q^{91} + 29q^{93} + 19q^{95} + 18q^{97} + 12q^{99} + O(q^{100}) \)

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
\(3\) −1.21838 −0.703430 −0.351715 0.936107i \(-0.614401\pi\)
−0.351715 + 0.936107i \(0.614401\pi\)
\(4\) 0 0
\(5\) 2.90030 1.29705 0.648526 0.761193i \(-0.275386\pi\)
0.648526 + 0.761193i \(0.275386\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −1.51556 −0.505186
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −3.53365 −0.912385
\(16\) 0 0
\(17\) 3.20996 0.778529 0.389265 0.921126i \(-0.372729\pi\)
0.389265 + 0.921126i \(0.372729\pi\)
\(18\) 0 0
\(19\) −0.338048 −0.0775536 −0.0387768 0.999248i \(-0.512346\pi\)
−0.0387768 + 0.999248i \(0.512346\pi\)
\(20\) 0 0
\(21\) 1.21838 0.265872
\(22\) 0 0
\(23\) 7.17564 1.49622 0.748112 0.663573i \(-0.230961\pi\)
0.748112 + 0.663573i \(0.230961\pi\)
\(24\) 0 0
\(25\) 3.41172 0.682344
\(26\) 0 0
\(27\) 5.50165 1.05879
\(28\) 0 0
\(29\) 10.5557 1.96015 0.980075 0.198626i \(-0.0636479\pi\)
0.980075 + 0.198626i \(0.0636479\pi\)
\(30\) 0 0
\(31\) 1.34712 0.241950 0.120975 0.992656i \(-0.461398\pi\)
0.120975 + 0.992656i \(0.461398\pi\)
\(32\) 0 0
\(33\) −1.21838 −0.212092
\(34\) 0 0
\(35\) −2.90030 −0.490240
\(36\) 0 0
\(37\) 2.97901 0.489746 0.244873 0.969555i \(-0.421254\pi\)
0.244873 + 0.969555i \(0.421254\pi\)
\(38\) 0 0
\(39\) 1.21838 0.195096
\(40\) 0 0
\(41\) −3.83082 −0.598273 −0.299137 0.954210i \(-0.596699\pi\)
−0.299137 + 0.954210i \(0.596699\pi\)
\(42\) 0 0
\(43\) −2.40992 −0.367510 −0.183755 0.982972i \(-0.558825\pi\)
−0.183755 + 0.982972i \(0.558825\pi\)
\(44\) 0 0
\(45\) −4.39557 −0.655253
\(46\) 0 0
\(47\) −12.1040 −1.76555 −0.882777 0.469793i \(-0.844329\pi\)
−0.882777 + 0.469793i \(0.844329\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −3.91094 −0.547641
\(52\) 0 0
\(53\) 1.77133 0.243311 0.121656 0.992572i \(-0.461180\pi\)
0.121656 + 0.992572i \(0.461180\pi\)
\(54\) 0 0
\(55\) 2.90030 0.391076
\(56\) 0 0
\(57\) 0.411870 0.0545535
\(58\) 0 0
\(59\) −6.34524 −0.826080 −0.413040 0.910713i \(-0.635533\pi\)
−0.413040 + 0.910713i \(0.635533\pi\)
\(60\) 0 0
\(61\) −6.55153 −0.838837 −0.419419 0.907793i \(-0.637766\pi\)
−0.419419 + 0.907793i \(0.637766\pi\)
\(62\) 0 0
\(63\) 1.51556 0.190942
\(64\) 0 0
\(65\) −2.90030 −0.359737
\(66\) 0 0
\(67\) −0.479975 −0.0586383 −0.0293192 0.999570i \(-0.509334\pi\)
−0.0293192 + 0.999570i \(0.509334\pi\)
\(68\) 0 0
\(69\) −8.74263 −1.05249
\(70\) 0 0
\(71\) −7.64425 −0.907205 −0.453603 0.891204i \(-0.649861\pi\)
−0.453603 + 0.891204i \(0.649861\pi\)
\(72\) 0 0
\(73\) −5.07758 −0.594286 −0.297143 0.954833i \(-0.596034\pi\)
−0.297143 + 0.954833i \(0.596034\pi\)
\(74\) 0 0
\(75\) −4.15676 −0.479981
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 1.11643 0.125608 0.0628038 0.998026i \(-0.479996\pi\)
0.0628038 + 0.998026i \(0.479996\pi\)
\(80\) 0 0
\(81\) −2.15641 −0.239601
\(82\) 0 0
\(83\) 7.65360 0.840092 0.420046 0.907503i \(-0.362014\pi\)
0.420046 + 0.907503i \(0.362014\pi\)
\(84\) 0 0
\(85\) 9.30983 1.00979
\(86\) 0 0
\(87\) −12.8609 −1.37883
\(88\) 0 0
\(89\) 15.7332 1.66771 0.833856 0.551983i \(-0.186129\pi\)
0.833856 + 0.551983i \(0.186129\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −1.64130 −0.170195
\(94\) 0 0
\(95\) −0.980440 −0.100591
\(96\) 0 0
\(97\) 16.9715 1.72320 0.861598 0.507591i \(-0.169464\pi\)
0.861598 + 0.507591i \(0.169464\pi\)
\(98\) 0 0
\(99\) −1.51556 −0.152319
\(100\) 0 0
\(101\) 8.90578 0.886159 0.443079 0.896482i \(-0.353886\pi\)
0.443079 + 0.896482i \(0.353886\pi\)
\(102\) 0 0
\(103\) −12.8118 −1.26238 −0.631191 0.775628i \(-0.717434\pi\)
−0.631191 + 0.775628i \(0.717434\pi\)
\(104\) 0 0
\(105\) 3.53365 0.344849
\(106\) 0 0
\(107\) −9.75077 −0.942642 −0.471321 0.881962i \(-0.656223\pi\)
−0.471321 + 0.881962i \(0.656223\pi\)
\(108\) 0 0
\(109\) 4.90638 0.469946 0.234973 0.972002i \(-0.424500\pi\)
0.234973 + 0.972002i \(0.424500\pi\)
\(110\) 0 0
\(111\) −3.62955 −0.344502
\(112\) 0 0
\(113\) −13.2893 −1.25015 −0.625077 0.780563i \(-0.714933\pi\)
−0.625077 + 0.780563i \(0.714933\pi\)
\(114\) 0 0
\(115\) 20.8115 1.94068
\(116\) 0 0
\(117\) 1.51556 0.140113
\(118\) 0 0
\(119\) −3.20996 −0.294256
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 4.66738 0.420844
\(124\) 0 0
\(125\) −4.60649 −0.412017
\(126\) 0 0
\(127\) 6.66573 0.591488 0.295744 0.955267i \(-0.404432\pi\)
0.295744 + 0.955267i \(0.404432\pi\)
\(128\) 0 0
\(129\) 2.93619 0.258517
\(130\) 0 0
\(131\) 8.77634 0.766792 0.383396 0.923584i \(-0.374754\pi\)
0.383396 + 0.923584i \(0.374754\pi\)
\(132\) 0 0
\(133\) 0.338048 0.0293125
\(134\) 0 0
\(135\) 15.9564 1.37331
\(136\) 0 0
\(137\) 9.29231 0.793896 0.396948 0.917841i \(-0.370069\pi\)
0.396948 + 0.917841i \(0.370069\pi\)
\(138\) 0 0
\(139\) −5.54313 −0.470162 −0.235081 0.971976i \(-0.575536\pi\)
−0.235081 + 0.971976i \(0.575536\pi\)
\(140\) 0 0
\(141\) 14.7473 1.24194
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 30.6148 2.54242
\(146\) 0 0
\(147\) −1.21838 −0.100490
\(148\) 0 0
\(149\) −3.44869 −0.282528 −0.141264 0.989972i \(-0.545117\pi\)
−0.141264 + 0.989972i \(0.545117\pi\)
\(150\) 0 0
\(151\) 20.3094 1.65275 0.826377 0.563117i \(-0.190398\pi\)
0.826377 + 0.563117i \(0.190398\pi\)
\(152\) 0 0
\(153\) −4.86488 −0.393302
\(154\) 0 0
\(155\) 3.90704 0.313821
\(156\) 0 0
\(157\) 14.0052 1.11774 0.558869 0.829256i \(-0.311236\pi\)
0.558869 + 0.829256i \(0.311236\pi\)
\(158\) 0 0
\(159\) −2.15815 −0.171152
\(160\) 0 0
\(161\) −7.17564 −0.565519
\(162\) 0 0
\(163\) 23.2055 1.81760 0.908799 0.417235i \(-0.137001\pi\)
0.908799 + 0.417235i \(0.137001\pi\)
\(164\) 0 0
\(165\) −3.53365 −0.275095
\(166\) 0 0
\(167\) −19.4507 −1.50514 −0.752569 0.658514i \(-0.771185\pi\)
−0.752569 + 0.658514i \(0.771185\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0.512332 0.0391790
\(172\) 0 0
\(173\) 13.3217 1.01283 0.506416 0.862289i \(-0.330970\pi\)
0.506416 + 0.862289i \(0.330970\pi\)
\(174\) 0 0
\(175\) −3.41172 −0.257902
\(176\) 0 0
\(177\) 7.73090 0.581090
\(178\) 0 0
\(179\) −15.7801 −1.17946 −0.589731 0.807600i \(-0.700766\pi\)
−0.589731 + 0.807600i \(0.700766\pi\)
\(180\) 0 0
\(181\) −2.04562 −0.152050 −0.0760251 0.997106i \(-0.524223\pi\)
−0.0760251 + 0.997106i \(0.524223\pi\)
\(182\) 0 0
\(183\) 7.98223 0.590063
\(184\) 0 0
\(185\) 8.64000 0.635226
\(186\) 0 0
\(187\) 3.20996 0.234735
\(188\) 0 0
\(189\) −5.50165 −0.400186
\(190\) 0 0
\(191\) 19.8934 1.43944 0.719718 0.694267i \(-0.244271\pi\)
0.719718 + 0.694267i \(0.244271\pi\)
\(192\) 0 0
\(193\) 2.68351 0.193163 0.0965817 0.995325i \(-0.469209\pi\)
0.0965817 + 0.995325i \(0.469209\pi\)
\(194\) 0 0
\(195\) 3.53365 0.253050
\(196\) 0 0
\(197\) 11.8597 0.844968 0.422484 0.906370i \(-0.361158\pi\)
0.422484 + 0.906370i \(0.361158\pi\)
\(198\) 0 0
\(199\) −16.0890 −1.14052 −0.570261 0.821463i \(-0.693158\pi\)
−0.570261 + 0.821463i \(0.693158\pi\)
\(200\) 0 0
\(201\) 0.584791 0.0412480
\(202\) 0 0
\(203\) −10.5557 −0.740867
\(204\) 0 0
\(205\) −11.1105 −0.775992
\(206\) 0 0
\(207\) −10.8751 −0.755872
\(208\) 0 0
\(209\) −0.338048 −0.0233833
\(210\) 0 0
\(211\) −8.95441 −0.616447 −0.308224 0.951314i \(-0.599734\pi\)
−0.308224 + 0.951314i \(0.599734\pi\)
\(212\) 0 0
\(213\) 9.31357 0.638155
\(214\) 0 0
\(215\) −6.98949 −0.476679
\(216\) 0 0
\(217\) −1.34712 −0.0914483
\(218\) 0 0
\(219\) 6.18641 0.418039
\(220\) 0 0
\(221\) −3.20996 −0.215925
\(222\) 0 0
\(223\) 8.41486 0.563501 0.281750 0.959488i \(-0.409085\pi\)
0.281750 + 0.959488i \(0.409085\pi\)
\(224\) 0 0
\(225\) −5.17066 −0.344711
\(226\) 0 0
\(227\) 10.9637 0.727687 0.363844 0.931460i \(-0.381464\pi\)
0.363844 + 0.931460i \(0.381464\pi\)
\(228\) 0 0
\(229\) 13.4275 0.887315 0.443658 0.896196i \(-0.353681\pi\)
0.443658 + 0.896196i \(0.353681\pi\)
\(230\) 0 0
\(231\) 1.21838 0.0801633
\(232\) 0 0
\(233\) 18.8452 1.23459 0.617294 0.786732i \(-0.288229\pi\)
0.617294 + 0.786732i \(0.288229\pi\)
\(234\) 0 0
\(235\) −35.1053 −2.29001
\(236\) 0 0
\(237\) −1.36023 −0.0883562
\(238\) 0 0
\(239\) −26.9165 −1.74109 −0.870543 0.492093i \(-0.836232\pi\)
−0.870543 + 0.492093i \(0.836232\pi\)
\(240\) 0 0
\(241\) 17.9783 1.15809 0.579043 0.815297i \(-0.303426\pi\)
0.579043 + 0.815297i \(0.303426\pi\)
\(242\) 0 0
\(243\) −13.8776 −0.890251
\(244\) 0 0
\(245\) 2.90030 0.185293
\(246\) 0 0
\(247\) 0.338048 0.0215095
\(248\) 0 0
\(249\) −9.32497 −0.590946
\(250\) 0 0
\(251\) 17.4480 1.10131 0.550653 0.834734i \(-0.314379\pi\)
0.550653 + 0.834734i \(0.314379\pi\)
\(252\) 0 0
\(253\) 7.17564 0.451128
\(254\) 0 0
\(255\) −11.3429 −0.710318
\(256\) 0 0
\(257\) −16.0870 −1.00348 −0.501740 0.865019i \(-0.667307\pi\)
−0.501740 + 0.865019i \(0.667307\pi\)
\(258\) 0 0
\(259\) −2.97901 −0.185107
\(260\) 0 0
\(261\) −15.9978 −0.990241
\(262\) 0 0
\(263\) −8.61980 −0.531520 −0.265760 0.964039i \(-0.585623\pi\)
−0.265760 + 0.964039i \(0.585623\pi\)
\(264\) 0 0
\(265\) 5.13738 0.315587
\(266\) 0 0
\(267\) −19.1689 −1.17312
\(268\) 0 0
\(269\) 7.93841 0.484013 0.242007 0.970275i \(-0.422194\pi\)
0.242007 + 0.970275i \(0.422194\pi\)
\(270\) 0 0
\(271\) 27.9301 1.69663 0.848315 0.529492i \(-0.177617\pi\)
0.848315 + 0.529492i \(0.177617\pi\)
\(272\) 0 0
\(273\) −1.21838 −0.0737395
\(274\) 0 0
\(275\) 3.41172 0.205734
\(276\) 0 0
\(277\) 18.6275 1.11922 0.559609 0.828757i \(-0.310951\pi\)
0.559609 + 0.828757i \(0.310951\pi\)
\(278\) 0 0
\(279\) −2.04164 −0.122230
\(280\) 0 0
\(281\) 15.9773 0.953124 0.476562 0.879141i \(-0.341883\pi\)
0.476562 + 0.879141i \(0.341883\pi\)
\(282\) 0 0
\(283\) 28.0250 1.66592 0.832958 0.553336i \(-0.186646\pi\)
0.832958 + 0.553336i \(0.186646\pi\)
\(284\) 0 0
\(285\) 1.19454 0.0707587
\(286\) 0 0
\(287\) 3.83082 0.226126
\(288\) 0 0
\(289\) −6.69617 −0.393893
\(290\) 0 0
\(291\) −20.6777 −1.21215
\(292\) 0 0
\(293\) 1.21281 0.0708530 0.0354265 0.999372i \(-0.488721\pi\)
0.0354265 + 0.999372i \(0.488721\pi\)
\(294\) 0 0
\(295\) −18.4031 −1.07147
\(296\) 0 0
\(297\) 5.50165 0.319238
\(298\) 0 0
\(299\) −7.17564 −0.414978
\(300\) 0 0
\(301\) 2.40992 0.138906
\(302\) 0 0
\(303\) −10.8506 −0.623351
\(304\) 0 0
\(305\) −19.0014 −1.08802
\(306\) 0 0
\(307\) −15.8553 −0.904910 −0.452455 0.891787i \(-0.649452\pi\)
−0.452455 + 0.891787i \(0.649452\pi\)
\(308\) 0 0
\(309\) 15.6096 0.887997
\(310\) 0 0
\(311\) −23.4291 −1.32854 −0.664271 0.747492i \(-0.731258\pi\)
−0.664271 + 0.747492i \(0.731258\pi\)
\(312\) 0 0
\(313\) −29.3280 −1.65772 −0.828859 0.559458i \(-0.811009\pi\)
−0.828859 + 0.559458i \(0.811009\pi\)
\(314\) 0 0
\(315\) 4.39557 0.247662
\(316\) 0 0
\(317\) −7.88166 −0.442678 −0.221339 0.975197i \(-0.571043\pi\)
−0.221339 + 0.975197i \(0.571043\pi\)
\(318\) 0 0
\(319\) 10.5557 0.591008
\(320\) 0 0
\(321\) 11.8801 0.663083
\(322\) 0 0
\(323\) −1.08512 −0.0603777
\(324\) 0 0
\(325\) −3.41172 −0.189248
\(326\) 0 0
\(327\) −5.97782 −0.330574
\(328\) 0 0
\(329\) 12.1040 0.667316
\(330\) 0 0
\(331\) 10.0779 0.553930 0.276965 0.960880i \(-0.410671\pi\)
0.276965 + 0.960880i \(0.410671\pi\)
\(332\) 0 0
\(333\) −4.51486 −0.247413
\(334\) 0 0
\(335\) −1.39207 −0.0760570
\(336\) 0 0
\(337\) −18.8753 −1.02820 −0.514102 0.857729i \(-0.671875\pi\)
−0.514102 + 0.857729i \(0.671875\pi\)
\(338\) 0 0
\(339\) 16.1914 0.879396
\(340\) 0 0
\(341\) 1.34712 0.0729505
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −25.3562 −1.36513
\(346\) 0 0
\(347\) 18.3631 0.985784 0.492892 0.870091i \(-0.335940\pi\)
0.492892 + 0.870091i \(0.335940\pi\)
\(348\) 0 0
\(349\) −2.22415 −0.119056 −0.0595281 0.998227i \(-0.518960\pi\)
−0.0595281 + 0.998227i \(0.518960\pi\)
\(350\) 0 0
\(351\) −5.50165 −0.293656
\(352\) 0 0
\(353\) 5.40051 0.287440 0.143720 0.989618i \(-0.454093\pi\)
0.143720 + 0.989618i \(0.454093\pi\)
\(354\) 0 0
\(355\) −22.1706 −1.17669
\(356\) 0 0
\(357\) 3.91094 0.206989
\(358\) 0 0
\(359\) −24.5262 −1.29444 −0.647222 0.762302i \(-0.724069\pi\)
−0.647222 + 0.762302i \(0.724069\pi\)
\(360\) 0 0
\(361\) −18.8857 −0.993985
\(362\) 0 0
\(363\) −1.21838 −0.0639482
\(364\) 0 0
\(365\) −14.7265 −0.770820
\(366\) 0 0
\(367\) 29.7524 1.55306 0.776532 0.630077i \(-0.216977\pi\)
0.776532 + 0.630077i \(0.216977\pi\)
\(368\) 0 0
\(369\) 5.80583 0.302240
\(370\) 0 0
\(371\) −1.77133 −0.0919629
\(372\) 0 0
\(373\) 25.3278 1.31142 0.655711 0.755012i \(-0.272369\pi\)
0.655711 + 0.755012i \(0.272369\pi\)
\(374\) 0 0
\(375\) 5.61244 0.289825
\(376\) 0 0
\(377\) −10.5557 −0.543648
\(378\) 0 0
\(379\) −12.3986 −0.636872 −0.318436 0.947944i \(-0.603158\pi\)
−0.318436 + 0.947944i \(0.603158\pi\)
\(380\) 0 0
\(381\) −8.12137 −0.416070
\(382\) 0 0
\(383\) 19.6711 1.00515 0.502574 0.864534i \(-0.332387\pi\)
0.502574 + 0.864534i \(0.332387\pi\)
\(384\) 0 0
\(385\) −2.90030 −0.147813
\(386\) 0 0
\(387\) 3.65238 0.185661
\(388\) 0 0
\(389\) 9.16212 0.464538 0.232269 0.972652i \(-0.425385\pi\)
0.232269 + 0.972652i \(0.425385\pi\)
\(390\) 0 0
\(391\) 23.0335 1.16485
\(392\) 0 0
\(393\) −10.6929 −0.539385
\(394\) 0 0
\(395\) 3.23796 0.162920
\(396\) 0 0
\(397\) 11.0924 0.556713 0.278357 0.960478i \(-0.410210\pi\)
0.278357 + 0.960478i \(0.410210\pi\)
\(398\) 0 0
\(399\) −0.411870 −0.0206193
\(400\) 0 0
\(401\) 21.1617 1.05676 0.528382 0.849006i \(-0.322799\pi\)
0.528382 + 0.849006i \(0.322799\pi\)
\(402\) 0 0
\(403\) −1.34712 −0.0671047
\(404\) 0 0
\(405\) −6.25422 −0.310775
\(406\) 0 0
\(407\) 2.97901 0.147664
\(408\) 0 0
\(409\) 39.4751 1.95192 0.975959 0.217955i \(-0.0699385\pi\)
0.975959 + 0.217955i \(0.0699385\pi\)
\(410\) 0 0
\(411\) −11.3215 −0.558450
\(412\) 0 0
\(413\) 6.34524 0.312229
\(414\) 0 0
\(415\) 22.1977 1.08964
\(416\) 0 0
\(417\) 6.75362 0.330726
\(418\) 0 0
\(419\) 27.8391 1.36003 0.680016 0.733198i \(-0.261973\pi\)
0.680016 + 0.733198i \(0.261973\pi\)
\(420\) 0 0
\(421\) 19.0248 0.927211 0.463606 0.886042i \(-0.346555\pi\)
0.463606 + 0.886042i \(0.346555\pi\)
\(422\) 0 0
\(423\) 18.3444 0.891933
\(424\) 0 0
\(425\) 10.9515 0.531224
\(426\) 0 0
\(427\) 6.55153 0.317051
\(428\) 0 0
\(429\) 1.21838 0.0588238
\(430\) 0 0
\(431\) −5.54985 −0.267327 −0.133664 0.991027i \(-0.542674\pi\)
−0.133664 + 0.991027i \(0.542674\pi\)
\(432\) 0 0
\(433\) 15.7316 0.756010 0.378005 0.925803i \(-0.376610\pi\)
0.378005 + 0.925803i \(0.376610\pi\)
\(434\) 0 0
\(435\) −37.3003 −1.78841
\(436\) 0 0
\(437\) −2.42571 −0.116037
\(438\) 0 0
\(439\) 8.98296 0.428733 0.214367 0.976753i \(-0.431231\pi\)
0.214367 + 0.976753i \(0.431231\pi\)
\(440\) 0 0
\(441\) −1.51556 −0.0721695
\(442\) 0 0
\(443\) −4.35431 −0.206879 −0.103440 0.994636i \(-0.532985\pi\)
−0.103440 + 0.994636i \(0.532985\pi\)
\(444\) 0 0
\(445\) 45.6308 2.16311
\(446\) 0 0
\(447\) 4.20181 0.198739
\(448\) 0 0
\(449\) 24.4540 1.15406 0.577028 0.816724i \(-0.304212\pi\)
0.577028 + 0.816724i \(0.304212\pi\)
\(450\) 0 0
\(451\) −3.83082 −0.180386
\(452\) 0 0
\(453\) −24.7445 −1.16260
\(454\) 0 0
\(455\) 2.90030 0.135968
\(456\) 0 0
\(457\) 23.9544 1.12054 0.560269 0.828311i \(-0.310698\pi\)
0.560269 + 0.828311i \(0.310698\pi\)
\(458\) 0 0
\(459\) 17.6601 0.824301
\(460\) 0 0
\(461\) −40.4206 −1.88257 −0.941287 0.337608i \(-0.890382\pi\)
−0.941287 + 0.337608i \(0.890382\pi\)
\(462\) 0 0
\(463\) 13.9033 0.646141 0.323071 0.946375i \(-0.395285\pi\)
0.323071 + 0.946375i \(0.395285\pi\)
\(464\) 0 0
\(465\) −4.76025 −0.220751
\(466\) 0 0
\(467\) 3.41389 0.157976 0.0789880 0.996876i \(-0.474831\pi\)
0.0789880 + 0.996876i \(0.474831\pi\)
\(468\) 0 0
\(469\) 0.479975 0.0221632
\(470\) 0 0
\(471\) −17.0636 −0.786250
\(472\) 0 0
\(473\) −2.40992 −0.110808
\(474\) 0 0
\(475\) −1.15332 −0.0529182
\(476\) 0 0
\(477\) −2.68456 −0.122917
\(478\) 0 0
\(479\) 29.0810 1.32874 0.664371 0.747403i \(-0.268699\pi\)
0.664371 + 0.747403i \(0.268699\pi\)
\(480\) 0 0
\(481\) −2.97901 −0.135831
\(482\) 0 0
\(483\) 8.74263 0.397803
\(484\) 0 0
\(485\) 49.2224 2.23507
\(486\) 0 0
\(487\) −40.9117 −1.85389 −0.926944 0.375201i \(-0.877574\pi\)
−0.926944 + 0.375201i \(0.877574\pi\)
\(488\) 0 0
\(489\) −28.2731 −1.27855
\(490\) 0 0
\(491\) 21.8139 0.984447 0.492223 0.870469i \(-0.336184\pi\)
0.492223 + 0.870469i \(0.336184\pi\)
\(492\) 0 0
\(493\) 33.8835 1.52603
\(494\) 0 0
\(495\) −4.39557 −0.197566
\(496\) 0 0
\(497\) 7.64425 0.342891
\(498\) 0 0
\(499\) 3.60399 0.161337 0.0806684 0.996741i \(-0.474295\pi\)
0.0806684 + 0.996741i \(0.474295\pi\)
\(500\) 0 0
\(501\) 23.6982 1.05876
\(502\) 0 0
\(503\) −40.9551 −1.82610 −0.913049 0.407850i \(-0.866279\pi\)
−0.913049 + 0.407850i \(0.866279\pi\)
\(504\) 0 0
\(505\) 25.8294 1.14939
\(506\) 0 0
\(507\) −1.21838 −0.0541100
\(508\) 0 0
\(509\) −25.9845 −1.15174 −0.575872 0.817540i \(-0.695337\pi\)
−0.575872 + 0.817540i \(0.695337\pi\)
\(510\) 0 0
\(511\) 5.07758 0.224619
\(512\) 0 0
\(513\) −1.85982 −0.0821132
\(514\) 0 0
\(515\) −37.1579 −1.63737
\(516\) 0 0
\(517\) −12.1040 −0.532334
\(518\) 0 0
\(519\) −16.2309 −0.712456
\(520\) 0 0
\(521\) 4.37871 0.191835 0.0959173 0.995389i \(-0.469422\pi\)
0.0959173 + 0.995389i \(0.469422\pi\)
\(522\) 0 0
\(523\) −39.8178 −1.74111 −0.870556 0.492070i \(-0.836240\pi\)
−0.870556 + 0.492070i \(0.836240\pi\)
\(524\) 0 0
\(525\) 4.15676 0.181416
\(526\) 0 0
\(527\) 4.32419 0.188365
\(528\) 0 0
\(529\) 28.4898 1.23869
\(530\) 0 0
\(531\) 9.61659 0.417324
\(532\) 0 0
\(533\) 3.83082 0.165931
\(534\) 0 0
\(535\) −28.2801 −1.22266
\(536\) 0 0
\(537\) 19.2261 0.829669
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 10.7361 0.461581 0.230790 0.973003i \(-0.425869\pi\)
0.230790 + 0.973003i \(0.425869\pi\)
\(542\) 0 0
\(543\) 2.49234 0.106957
\(544\) 0 0
\(545\) 14.2299 0.609544
\(546\) 0 0
\(547\) 32.5328 1.39100 0.695500 0.718526i \(-0.255183\pi\)
0.695500 + 0.718526i \(0.255183\pi\)
\(548\) 0 0
\(549\) 9.92923 0.423769
\(550\) 0 0
\(551\) −3.56835 −0.152017
\(552\) 0 0
\(553\) −1.11643 −0.0474752
\(554\) 0 0
\(555\) −10.5268 −0.446837
\(556\) 0 0
\(557\) −14.5348 −0.615859 −0.307930 0.951409i \(-0.599636\pi\)
−0.307930 + 0.951409i \(0.599636\pi\)
\(558\) 0 0
\(559\) 2.40992 0.101929
\(560\) 0 0
\(561\) −3.91094 −0.165120
\(562\) 0 0
\(563\) 10.6786 0.450050 0.225025 0.974353i \(-0.427754\pi\)
0.225025 + 0.974353i \(0.427754\pi\)
\(564\) 0 0
\(565\) −38.5430 −1.62152
\(566\) 0 0
\(567\) 2.15641 0.0905605
\(568\) 0 0
\(569\) 10.7695 0.451481 0.225740 0.974187i \(-0.427520\pi\)
0.225740 + 0.974187i \(0.427520\pi\)
\(570\) 0 0
\(571\) −18.0492 −0.755334 −0.377667 0.925941i \(-0.623274\pi\)
−0.377667 + 0.925941i \(0.623274\pi\)
\(572\) 0 0
\(573\) −24.2376 −1.01254
\(574\) 0 0
\(575\) 24.4813 1.02094
\(576\) 0 0
\(577\) −17.9289 −0.746388 −0.373194 0.927753i \(-0.621737\pi\)
−0.373194 + 0.927753i \(0.621737\pi\)
\(578\) 0 0
\(579\) −3.26953 −0.135877
\(580\) 0 0
\(581\) −7.65360 −0.317525
\(582\) 0 0
\(583\) 1.77133 0.0733610
\(584\) 0 0
\(585\) 4.39557 0.181734
\(586\) 0 0
\(587\) −20.0383 −0.827069 −0.413534 0.910488i \(-0.635706\pi\)
−0.413534 + 0.910488i \(0.635706\pi\)
\(588\) 0 0
\(589\) −0.455391 −0.0187640
\(590\) 0 0
\(591\) −14.4496 −0.594376
\(592\) 0 0
\(593\) −24.5002 −1.00610 −0.503050 0.864257i \(-0.667789\pi\)
−0.503050 + 0.864257i \(0.667789\pi\)
\(594\) 0 0
\(595\) −9.30983 −0.381666
\(596\) 0 0
\(597\) 19.6025 0.802278
\(598\) 0 0
\(599\) 12.6370 0.516335 0.258168 0.966100i \(-0.416881\pi\)
0.258168 + 0.966100i \(0.416881\pi\)
\(600\) 0 0
\(601\) 1.87669 0.0765517 0.0382759 0.999267i \(-0.487813\pi\)
0.0382759 + 0.999267i \(0.487813\pi\)
\(602\) 0 0
\(603\) 0.727431 0.0296233
\(604\) 0 0
\(605\) 2.90030 0.117914
\(606\) 0 0
\(607\) 25.9699 1.05408 0.527042 0.849839i \(-0.323301\pi\)
0.527042 + 0.849839i \(0.323301\pi\)
\(608\) 0 0
\(609\) 12.8609 0.521148
\(610\) 0 0
\(611\) 12.1040 0.489676
\(612\) 0 0
\(613\) −23.2858 −0.940505 −0.470252 0.882532i \(-0.655837\pi\)
−0.470252 + 0.882532i \(0.655837\pi\)
\(614\) 0 0
\(615\) 13.5368 0.545856
\(616\) 0 0
\(617\) 14.2406 0.573306 0.286653 0.958034i \(-0.407457\pi\)
0.286653 + 0.958034i \(0.407457\pi\)
\(618\) 0 0
\(619\) 30.9387 1.24353 0.621766 0.783203i \(-0.286416\pi\)
0.621766 + 0.783203i \(0.286416\pi\)
\(620\) 0 0
\(621\) 39.4778 1.58419
\(622\) 0 0
\(623\) −15.7332 −0.630336
\(624\) 0 0
\(625\) −30.4188 −1.21675
\(626\) 0 0
\(627\) 0.411870 0.0164485
\(628\) 0 0
\(629\) 9.56249 0.381281
\(630\) 0 0
\(631\) −2.77785 −0.110585 −0.0552923 0.998470i \(-0.517609\pi\)
−0.0552923 + 0.998470i \(0.517609\pi\)
\(632\) 0 0
\(633\) 10.9098 0.433627
\(634\) 0 0
\(635\) 19.3326 0.767191
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 11.5853 0.458308
\(640\) 0 0
\(641\) −27.1749 −1.07335 −0.536673 0.843790i \(-0.680319\pi\)
−0.536673 + 0.843790i \(0.680319\pi\)
\(642\) 0 0
\(643\) 4.95387 0.195362 0.0976808 0.995218i \(-0.468858\pi\)
0.0976808 + 0.995218i \(0.468858\pi\)
\(644\) 0 0
\(645\) 8.51583 0.335311
\(646\) 0 0
\(647\) 32.6204 1.28244 0.641220 0.767357i \(-0.278429\pi\)
0.641220 + 0.767357i \(0.278429\pi\)
\(648\) 0 0
\(649\) −6.34524 −0.249073
\(650\) 0 0
\(651\) 1.64130 0.0643275
\(652\) 0 0
\(653\) −2.88950 −0.113075 −0.0565374 0.998400i \(-0.518006\pi\)
−0.0565374 + 0.998400i \(0.518006\pi\)
\(654\) 0 0
\(655\) 25.4540 0.994569
\(656\) 0 0
\(657\) 7.69537 0.300225
\(658\) 0 0
\(659\) −2.94885 −0.114871 −0.0574355 0.998349i \(-0.518292\pi\)
−0.0574355 + 0.998349i \(0.518292\pi\)
\(660\) 0 0
\(661\) −28.9628 −1.12652 −0.563261 0.826279i \(-0.690454\pi\)
−0.563261 + 0.826279i \(0.690454\pi\)
\(662\) 0 0
\(663\) 3.91094 0.151888
\(664\) 0 0
\(665\) 0.980440 0.0380198
\(666\) 0 0
\(667\) 75.7441 2.93282
\(668\) 0 0
\(669\) −10.2525 −0.396383
\(670\) 0 0
\(671\) −6.55153 −0.252919
\(672\) 0 0
\(673\) 4.52456 0.174409 0.0872045 0.996190i \(-0.472207\pi\)
0.0872045 + 0.996190i \(0.472207\pi\)
\(674\) 0 0
\(675\) 18.7701 0.722461
\(676\) 0 0
\(677\) −9.94320 −0.382148 −0.191074 0.981576i \(-0.561197\pi\)
−0.191074 + 0.981576i \(0.561197\pi\)
\(678\) 0 0
\(679\) −16.9715 −0.651307
\(680\) 0 0
\(681\) −13.3579 −0.511877
\(682\) 0 0
\(683\) 36.2544 1.38723 0.693617 0.720344i \(-0.256016\pi\)
0.693617 + 0.720344i \(0.256016\pi\)
\(684\) 0 0
\(685\) 26.9504 1.02972
\(686\) 0 0
\(687\) −16.3598 −0.624164
\(688\) 0 0
\(689\) −1.77133 −0.0674823
\(690\) 0 0
\(691\) −45.4198 −1.72785 −0.863926 0.503619i \(-0.832002\pi\)
−0.863926 + 0.503619i \(0.832002\pi\)
\(692\) 0 0
\(693\) 1.51556 0.0575713
\(694\) 0 0
\(695\) −16.0767 −0.609825
\(696\) 0 0
\(697\) −12.2968 −0.465773
\(698\) 0 0
\(699\) −22.9605 −0.868447
\(700\) 0 0
\(701\) −25.0214 −0.945045 −0.472523 0.881319i \(-0.656657\pi\)
−0.472523 + 0.881319i \(0.656657\pi\)
\(702\) 0 0
\(703\) −1.00705 −0.0379815
\(704\) 0 0
\(705\) 42.7714 1.61086
\(706\) 0 0
\(707\) −8.90578 −0.334936
\(708\) 0 0
\(709\) −49.3904 −1.85490 −0.927448 0.373952i \(-0.878003\pi\)
−0.927448 + 0.373952i \(0.878003\pi\)
\(710\) 0 0
\(711\) −1.69201 −0.0634552
\(712\) 0 0
\(713\) 9.66643 0.362011
\(714\) 0 0
\(715\) −2.90030 −0.108465
\(716\) 0 0
\(717\) 32.7945 1.22473
\(718\) 0 0
\(719\) 0.951868 0.0354987 0.0177493 0.999842i \(-0.494350\pi\)
0.0177493 + 0.999842i \(0.494350\pi\)
\(720\) 0 0
\(721\) 12.8118 0.477135
\(722\) 0 0
\(723\) −21.9044 −0.814633
\(724\) 0 0
\(725\) 36.0132 1.33750
\(726\) 0 0
\(727\) −22.3584 −0.829229 −0.414614 0.909997i \(-0.636083\pi\)
−0.414614 + 0.909997i \(0.636083\pi\)
\(728\) 0 0
\(729\) 23.3774 0.865830
\(730\) 0 0
\(731\) −7.73575 −0.286117
\(732\) 0 0
\(733\) −33.9992 −1.25579 −0.627895 0.778298i \(-0.716083\pi\)
−0.627895 + 0.778298i \(0.716083\pi\)
\(734\) 0 0
\(735\) −3.53365 −0.130341
\(736\) 0 0
\(737\) −0.479975 −0.0176801
\(738\) 0 0
\(739\) 33.6754 1.23877 0.619384 0.785088i \(-0.287382\pi\)
0.619384 + 0.785088i \(0.287382\pi\)
\(740\) 0 0
\(741\) −0.411870 −0.0151304
\(742\) 0 0
\(743\) 21.7180 0.796755 0.398378 0.917221i \(-0.369573\pi\)
0.398378 + 0.917221i \(0.369573\pi\)
\(744\) 0 0
\(745\) −10.0022 −0.366453
\(746\) 0 0
\(747\) −11.5995 −0.424403
\(748\) 0 0
\(749\) 9.75077 0.356285
\(750\) 0 0
\(751\) 1.64775 0.0601272 0.0300636 0.999548i \(-0.490429\pi\)
0.0300636 + 0.999548i \(0.490429\pi\)
\(752\) 0 0
\(753\) −21.2582 −0.774692
\(754\) 0 0
\(755\) 58.9033 2.14371
\(756\) 0 0
\(757\) −7.58858 −0.275812 −0.137906 0.990445i \(-0.544037\pi\)
−0.137906 + 0.990445i \(0.544037\pi\)
\(758\) 0 0
\(759\) −8.74263 −0.317337
\(760\) 0 0
\(761\) −0.206389 −0.00748159 −0.00374079 0.999993i \(-0.501191\pi\)
−0.00374079 + 0.999993i \(0.501191\pi\)
\(762\) 0 0
\(763\) −4.90638 −0.177623
\(764\) 0 0
\(765\) −14.1096 −0.510133
\(766\) 0 0
\(767\) 6.34524 0.229113
\(768\) 0 0
\(769\) 12.1132 0.436812 0.218406 0.975858i \(-0.429914\pi\)
0.218406 + 0.975858i \(0.429914\pi\)
\(770\) 0 0
\(771\) 19.6000 0.705878
\(772\) 0 0
\(773\) 44.7549 1.60972 0.804862 0.593462i \(-0.202239\pi\)
0.804862 + 0.593462i \(0.202239\pi\)
\(774\) 0 0
\(775\) 4.59599 0.165093
\(776\) 0 0
\(777\) 3.62955 0.130209
\(778\) 0 0
\(779\) 1.29500 0.0463982
\(780\) 0 0
\(781\) −7.64425 −0.273533
\(782\) 0 0
\(783\) 58.0740 2.07539
\(784\) 0 0
\(785\) 40.6193 1.44976
\(786\) 0 0
\(787\) 27.7427 0.988919 0.494460 0.869201i \(-0.335366\pi\)
0.494460 + 0.869201i \(0.335366\pi\)
\(788\) 0 0
\(789\) 10.5022 0.373887
\(790\) 0 0
\(791\) 13.2893 0.472514
\(792\) 0 0
\(793\) 6.55153 0.232652
\(794\) 0 0
\(795\) −6.25927 −0.221993
\(796\) 0 0
\(797\) −31.1866 −1.10469 −0.552343 0.833617i \(-0.686266\pi\)
−0.552343 + 0.833617i \(0.686266\pi\)
\(798\) 0 0
\(799\) −38.8534 −1.37453
\(800\) 0 0
\(801\) −23.8445 −0.842505
\(802\) 0 0
\(803\) −5.07758 −0.179184
\(804\) 0 0
\(805\) −20.8115 −0.733508
\(806\) 0 0
\(807\) −9.67197 −0.340469
\(808\) 0 0
\(809\) 47.8068 1.68080 0.840399 0.541969i \(-0.182321\pi\)
0.840399 + 0.541969i \(0.182321\pi\)
\(810\) 0 0
\(811\) −40.5500 −1.42390 −0.711951 0.702229i \(-0.752188\pi\)
−0.711951 + 0.702229i \(0.752188\pi\)
\(812\) 0 0
\(813\) −34.0293 −1.19346
\(814\) 0 0
\(815\) 67.3029 2.35752
\(816\) 0 0
\(817\) 0.814670 0.0285017
\(818\) 0 0
\(819\) −1.51556 −0.0529579
\(820\) 0 0
\(821\) 20.5251 0.716329 0.358165 0.933658i \(-0.383403\pi\)
0.358165 + 0.933658i \(0.383403\pi\)
\(822\) 0 0
\(823\) −47.5837 −1.65866 −0.829332 0.558757i \(-0.811279\pi\)
−0.829332 + 0.558757i \(0.811279\pi\)
\(824\) 0 0
\(825\) −4.15676 −0.144720
\(826\) 0 0
\(827\) 10.2056 0.354882 0.177441 0.984131i \(-0.443218\pi\)
0.177441 + 0.984131i \(0.443218\pi\)
\(828\) 0 0
\(829\) −36.1405 −1.25521 −0.627606 0.778531i \(-0.715965\pi\)
−0.627606 + 0.778531i \(0.715965\pi\)
\(830\) 0 0
\(831\) −22.6953 −0.787291
\(832\) 0 0
\(833\) 3.20996 0.111218
\(834\) 0 0
\(835\) −56.4127 −1.95224
\(836\) 0 0
\(837\) 7.41137 0.256175
\(838\) 0 0
\(839\) 10.5312 0.363576 0.181788 0.983338i \(-0.441812\pi\)
0.181788 + 0.983338i \(0.441812\pi\)
\(840\) 0 0
\(841\) 82.4235 2.84219
\(842\) 0 0
\(843\) −19.4663 −0.670456
\(844\) 0 0
\(845\) 2.90030 0.0997732
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −34.1451 −1.17186
\(850\) 0 0
\(851\) 21.3763 0.732769
\(852\) 0 0
\(853\) −33.2746 −1.13930 −0.569651 0.821887i \(-0.692922\pi\)
−0.569651 + 0.821887i \(0.692922\pi\)
\(854\) 0 0
\(855\) 1.48591 0.0508172
\(856\) 0 0
\(857\) −32.9235 −1.12465 −0.562323 0.826917i \(-0.690092\pi\)
−0.562323 + 0.826917i \(0.690092\pi\)
\(858\) 0 0
\(859\) −33.8803 −1.15598 −0.577991 0.816043i \(-0.696163\pi\)
−0.577991 + 0.816043i \(0.696163\pi\)
\(860\) 0 0
\(861\) −4.66738 −0.159064
\(862\) 0 0
\(863\) −11.6252 −0.395727 −0.197864 0.980230i \(-0.563400\pi\)
−0.197864 + 0.980230i \(0.563400\pi\)
\(864\) 0 0
\(865\) 38.6369 1.31370
\(866\) 0 0
\(867\) 8.15846 0.277076
\(868\) 0 0
\(869\) 1.11643 0.0378721
\(870\) 0 0
\(871\) 0.479975 0.0162633
\(872\) 0 0
\(873\) −25.7213 −0.870535
\(874\) 0 0
\(875\) 4.60649 0.155728
\(876\) 0 0
\(877\) 50.0458 1.68993 0.844964 0.534823i \(-0.179622\pi\)
0.844964 + 0.534823i \(0.179622\pi\)
\(878\) 0 0
\(879\) −1.47766 −0.0498402
\(880\) 0 0
\(881\) −28.0109 −0.943710 −0.471855 0.881676i \(-0.656415\pi\)
−0.471855 + 0.881676i \(0.656415\pi\)
\(882\) 0 0
\(883\) 13.6504 0.459373 0.229686 0.973265i \(-0.426230\pi\)
0.229686 + 0.973265i \(0.426230\pi\)
\(884\) 0 0
\(885\) 22.4219 0.753704
\(886\) 0 0
\(887\) −10.9354 −0.367173 −0.183587 0.983004i \(-0.558771\pi\)
−0.183587 + 0.983004i \(0.558771\pi\)
\(888\) 0 0
\(889\) −6.66573 −0.223561
\(890\) 0 0
\(891\) −2.15641 −0.0722423
\(892\) 0 0
\(893\) 4.09174 0.136925
\(894\) 0 0
\(895\) −45.7670 −1.52982
\(896\) 0 0
\(897\) 8.74263 0.291908
\(898\) 0 0
\(899\) 14.2198 0.474258
\(900\) 0 0
\(901\) 5.68590 0.189425
\(902\) 0 0
\(903\) −2.93619 −0.0977104
\(904\) 0 0
\(905\) −5.93292 −0.197217
\(906\) 0 0
\(907\) 25.9696 0.862305 0.431152 0.902279i \(-0.358107\pi\)
0.431152 + 0.902279i \(0.358107\pi\)
\(908\) 0 0
\(909\) −13.4972 −0.447675
\(910\) 0 0
\(911\) −22.7039 −0.752213 −0.376106 0.926576i \(-0.622737\pi\)
−0.376106 + 0.926576i \(0.622737\pi\)
\(912\) 0 0
\(913\) 7.65360 0.253297
\(914\) 0 0
\(915\) 23.1508 0.765343
\(916\) 0 0
\(917\) −8.77634 −0.289820
\(918\) 0 0
\(919\) 35.0952 1.15768 0.578841 0.815440i \(-0.303505\pi\)
0.578841 + 0.815440i \(0.303505\pi\)
\(920\) 0 0
\(921\) 19.3177 0.636541
\(922\) 0 0
\(923\) 7.64425 0.251613
\(924\) 0 0
\(925\) 10.1635 0.334175
\(926\) 0 0
\(927\) 19.4170 0.637738
\(928\) 0 0
\(929\) −49.6592 −1.62927 −0.814633 0.579977i \(-0.803062\pi\)
−0.814633 + 0.579977i \(0.803062\pi\)
\(930\) 0 0
\(931\) −0.338048 −0.0110791
\(932\) 0 0
\(933\) 28.5455 0.934537
\(934\) 0 0
\(935\) 9.30983 0.304464
\(936\) 0 0
\(937\) −10.6784 −0.348847 −0.174423 0.984671i \(-0.555806\pi\)
−0.174423 + 0.984671i \(0.555806\pi\)
\(938\) 0 0
\(939\) 35.7326 1.16609
\(940\) 0 0
\(941\) 46.1623 1.50485 0.752424 0.658679i \(-0.228885\pi\)
0.752424 + 0.658679i \(0.228885\pi\)
\(942\) 0 0
\(943\) −27.4886 −0.895151
\(944\) 0 0
\(945\) −15.9564 −0.519062
\(946\) 0 0
\(947\) 15.5959 0.506799 0.253400 0.967362i \(-0.418451\pi\)
0.253400 + 0.967362i \(0.418451\pi\)
\(948\) 0 0
\(949\) 5.07758 0.164825
\(950\) 0 0
\(951\) 9.60283 0.311393
\(952\) 0 0
\(953\) −13.3604 −0.432786 −0.216393 0.976306i \(-0.569429\pi\)
−0.216393 + 0.976306i \(0.569429\pi\)
\(954\) 0 0
\(955\) 57.6967 1.86702
\(956\) 0 0
\(957\) −12.8609 −0.415733
\(958\) 0 0
\(959\) −9.29231 −0.300064
\(960\) 0 0
\(961\) −29.1853 −0.941460
\(962\) 0 0
\(963\) 14.7779 0.476210
\(964\) 0 0
\(965\) 7.78298 0.250543
\(966\) 0 0
\(967\) 23.8066 0.765569 0.382785 0.923838i \(-0.374965\pi\)
0.382785 + 0.923838i \(0.374965\pi\)
\(968\) 0 0
\(969\) 1.32208 0.0424715
\(970\) 0 0
\(971\) −6.72845 −0.215926 −0.107963 0.994155i \(-0.534433\pi\)
−0.107963 + 0.994155i \(0.534433\pi\)
\(972\) 0 0
\(973\) 5.54313 0.177705
\(974\) 0 0
\(975\) 4.15676 0.133123
\(976\) 0 0
\(977\) 39.2128 1.25453 0.627265 0.778806i \(-0.284174\pi\)
0.627265 + 0.778806i \(0.284174\pi\)
\(978\) 0 0
\(979\) 15.7332 0.502834
\(980\) 0 0
\(981\) −7.43590 −0.237410
\(982\) 0 0
\(983\) 18.3795 0.586214 0.293107 0.956080i \(-0.405311\pi\)
0.293107 + 0.956080i \(0.405311\pi\)
\(984\) 0 0
\(985\) 34.3966 1.09597
\(986\) 0 0
\(987\) −14.7473 −0.469410
\(988\) 0 0
\(989\) −17.2927 −0.549877
\(990\) 0 0
\(991\) 27.3735 0.869549 0.434775 0.900539i \(-0.356828\pi\)
0.434775 + 0.900539i \(0.356828\pi\)
\(992\) 0 0
\(993\) −12.2787 −0.389651
\(994\) 0 0
\(995\) −46.6630 −1.47932
\(996\) 0 0
\(997\) 56.7976 1.79880 0.899399 0.437129i \(-0.144005\pi\)
0.899399 + 0.437129i \(0.144005\pi\)
\(998\) 0 0
\(999\) 16.3895 0.518540
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.n.1.4 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8008.2.a.n.1.4 9 1.1 even 1 trivial