Properties

Label 8004.2.a.i.1.11
Level $8004$
Weight $2$
Character 8004.1
Self dual yes
Analytic conductor $63.912$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8004.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 5 x^{15} - 43 x^{14} + 234 x^{13} + 634 x^{12} - 4048 x^{11} - 3483 x^{10} + 32512 x^{9} - 137 x^{8} - 121665 x^{7} + 60168 x^{6} + 172218 x^{5} - 138024 x^{4} - 17844 x^{3} + 14352 x^{2} + 72 x - 208\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(1.38601\) of defining polynomial
Character \(\chi\) \(=\) 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.38601 q^{5} -3.43605 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.38601 q^{5} -3.43605 q^{7} +1.00000 q^{9} +2.64786 q^{11} +3.17941 q^{13} -1.38601 q^{15} -7.44723 q^{17} +7.20390 q^{19} +3.43605 q^{21} +1.00000 q^{23} -3.07898 q^{25} -1.00000 q^{27} +1.00000 q^{29} -6.70556 q^{31} -2.64786 q^{33} -4.76239 q^{35} +2.03449 q^{37} -3.17941 q^{39} +7.14729 q^{41} -3.08585 q^{43} +1.38601 q^{45} +5.04741 q^{47} +4.80643 q^{49} +7.44723 q^{51} +9.24810 q^{53} +3.66995 q^{55} -7.20390 q^{57} +0.888525 q^{59} -0.116322 q^{61} -3.43605 q^{63} +4.40669 q^{65} -7.88452 q^{67} -1.00000 q^{69} -15.4402 q^{71} +8.68948 q^{73} +3.07898 q^{75} -9.09817 q^{77} +10.3464 q^{79} +1.00000 q^{81} +2.69423 q^{83} -10.3219 q^{85} -1.00000 q^{87} +15.8946 q^{89} -10.9246 q^{91} +6.70556 q^{93} +9.98468 q^{95} +8.50807 q^{97} +2.64786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{3} + 5q^{5} - 4q^{7} + 16q^{9} + O(q^{10}) \) \( 16q - 16q^{3} + 5q^{5} - 4q^{7} + 16q^{9} + 5q^{11} + 8q^{13} - 5q^{15} + 7q^{17} + q^{19} + 4q^{21} + 16q^{23} + 31q^{25} - 16q^{27} + 16q^{29} - 2q^{31} - 5q^{33} + 5q^{35} + 14q^{37} - 8q^{39} - q^{41} - 13q^{43} + 5q^{45} - 4q^{47} + 30q^{49} - 7q^{51} + 19q^{53} - 37q^{55} - q^{57} + 12q^{59} + 21q^{61} - 4q^{63} + 26q^{65} - 11q^{67} - 16q^{69} + 7q^{71} - 13q^{73} - 31q^{75} + 4q^{77} - 18q^{79} + 16q^{81} + 25q^{83} + 48q^{85} - 16q^{87} + 12q^{89} - 11q^{91} + 2q^{93} - q^{95} + 5q^{97} + 5q^{99} + O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.38601 0.619842 0.309921 0.950762i \(-0.399697\pi\)
0.309921 + 0.950762i \(0.399697\pi\)
\(6\) 0 0
\(7\) −3.43605 −1.29870 −0.649352 0.760488i \(-0.724960\pi\)
−0.649352 + 0.760488i \(0.724960\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.64786 0.798359 0.399180 0.916873i \(-0.369295\pi\)
0.399180 + 0.916873i \(0.369295\pi\)
\(12\) 0 0
\(13\) 3.17941 0.881810 0.440905 0.897554i \(-0.354658\pi\)
0.440905 + 0.897554i \(0.354658\pi\)
\(14\) 0 0
\(15\) −1.38601 −0.357866
\(16\) 0 0
\(17\) −7.44723 −1.80622 −0.903110 0.429410i \(-0.858721\pi\)
−0.903110 + 0.429410i \(0.858721\pi\)
\(18\) 0 0
\(19\) 7.20390 1.65269 0.826345 0.563165i \(-0.190416\pi\)
0.826345 + 0.563165i \(0.190416\pi\)
\(20\) 0 0
\(21\) 3.43605 0.749807
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −3.07898 −0.615796
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −6.70556 −1.20435 −0.602177 0.798363i \(-0.705700\pi\)
−0.602177 + 0.798363i \(0.705700\pi\)
\(32\) 0 0
\(33\) −2.64786 −0.460933
\(34\) 0 0
\(35\) −4.76239 −0.804991
\(36\) 0 0
\(37\) 2.03449 0.334468 0.167234 0.985917i \(-0.446517\pi\)
0.167234 + 0.985917i \(0.446517\pi\)
\(38\) 0 0
\(39\) −3.17941 −0.509113
\(40\) 0 0
\(41\) 7.14729 1.11622 0.558110 0.829767i \(-0.311527\pi\)
0.558110 + 0.829767i \(0.311527\pi\)
\(42\) 0 0
\(43\) −3.08585 −0.470587 −0.235294 0.971924i \(-0.575605\pi\)
−0.235294 + 0.971924i \(0.575605\pi\)
\(44\) 0 0
\(45\) 1.38601 0.206614
\(46\) 0 0
\(47\) 5.04741 0.736240 0.368120 0.929778i \(-0.380002\pi\)
0.368120 + 0.929778i \(0.380002\pi\)
\(48\) 0 0
\(49\) 4.80643 0.686633
\(50\) 0 0
\(51\) 7.44723 1.04282
\(52\) 0 0
\(53\) 9.24810 1.27032 0.635162 0.772379i \(-0.280933\pi\)
0.635162 + 0.772379i \(0.280933\pi\)
\(54\) 0 0
\(55\) 3.66995 0.494856
\(56\) 0 0
\(57\) −7.20390 −0.954181
\(58\) 0 0
\(59\) 0.888525 0.115676 0.0578381 0.998326i \(-0.481579\pi\)
0.0578381 + 0.998326i \(0.481579\pi\)
\(60\) 0 0
\(61\) −0.116322 −0.0148936 −0.00744678 0.999972i \(-0.502370\pi\)
−0.00744678 + 0.999972i \(0.502370\pi\)
\(62\) 0 0
\(63\) −3.43605 −0.432901
\(64\) 0 0
\(65\) 4.40669 0.546583
\(66\) 0 0
\(67\) −7.88452 −0.963247 −0.481623 0.876378i \(-0.659953\pi\)
−0.481623 + 0.876378i \(0.659953\pi\)
\(68\) 0 0
\(69\) −1.00000 −0.120386
\(70\) 0 0
\(71\) −15.4402 −1.83241 −0.916205 0.400709i \(-0.868764\pi\)
−0.916205 + 0.400709i \(0.868764\pi\)
\(72\) 0 0
\(73\) 8.68948 1.01703 0.508513 0.861054i \(-0.330195\pi\)
0.508513 + 0.861054i \(0.330195\pi\)
\(74\) 0 0
\(75\) 3.07898 0.355530
\(76\) 0 0
\(77\) −9.09817 −1.03683
\(78\) 0 0
\(79\) 10.3464 1.16406 0.582030 0.813168i \(-0.302259\pi\)
0.582030 + 0.813168i \(0.302259\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 2.69423 0.295731 0.147865 0.989008i \(-0.452760\pi\)
0.147865 + 0.989008i \(0.452760\pi\)
\(84\) 0 0
\(85\) −10.3219 −1.11957
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) 15.8946 1.68483 0.842414 0.538831i \(-0.181134\pi\)
0.842414 + 0.538831i \(0.181134\pi\)
\(90\) 0 0
\(91\) −10.9246 −1.14521
\(92\) 0 0
\(93\) 6.70556 0.695334
\(94\) 0 0
\(95\) 9.98468 1.02441
\(96\) 0 0
\(97\) 8.50807 0.863863 0.431932 0.901906i \(-0.357832\pi\)
0.431932 + 0.901906i \(0.357832\pi\)
\(98\) 0 0
\(99\) 2.64786 0.266120
\(100\) 0 0
\(101\) −13.6985 −1.36305 −0.681526 0.731794i \(-0.738683\pi\)
−0.681526 + 0.731794i \(0.738683\pi\)
\(102\) 0 0
\(103\) 0.0167442 0.00164985 0.000824925 1.00000i \(-0.499737\pi\)
0.000824925 1.00000i \(0.499737\pi\)
\(104\) 0 0
\(105\) 4.76239 0.464762
\(106\) 0 0
\(107\) −11.9335 −1.15366 −0.576828 0.816866i \(-0.695710\pi\)
−0.576828 + 0.816866i \(0.695710\pi\)
\(108\) 0 0
\(109\) 2.32636 0.222825 0.111412 0.993774i \(-0.464463\pi\)
0.111412 + 0.993774i \(0.464463\pi\)
\(110\) 0 0
\(111\) −2.03449 −0.193105
\(112\) 0 0
\(113\) −4.35571 −0.409750 −0.204875 0.978788i \(-0.565679\pi\)
−0.204875 + 0.978788i \(0.565679\pi\)
\(114\) 0 0
\(115\) 1.38601 0.129246
\(116\) 0 0
\(117\) 3.17941 0.293937
\(118\) 0 0
\(119\) 25.5891 2.34574
\(120\) 0 0
\(121\) −3.98885 −0.362623
\(122\) 0 0
\(123\) −7.14729 −0.644450
\(124\) 0 0
\(125\) −11.1975 −1.00154
\(126\) 0 0
\(127\) −0.680671 −0.0603998 −0.0301999 0.999544i \(-0.509614\pi\)
−0.0301999 + 0.999544i \(0.509614\pi\)
\(128\) 0 0
\(129\) 3.08585 0.271694
\(130\) 0 0
\(131\) 3.31610 0.289729 0.144864 0.989452i \(-0.453725\pi\)
0.144864 + 0.989452i \(0.453725\pi\)
\(132\) 0 0
\(133\) −24.7530 −2.14635
\(134\) 0 0
\(135\) −1.38601 −0.119289
\(136\) 0 0
\(137\) −5.69652 −0.486686 −0.243343 0.969940i \(-0.578244\pi\)
−0.243343 + 0.969940i \(0.578244\pi\)
\(138\) 0 0
\(139\) 14.7590 1.25184 0.625920 0.779887i \(-0.284723\pi\)
0.625920 + 0.779887i \(0.284723\pi\)
\(140\) 0 0
\(141\) −5.04741 −0.425068
\(142\) 0 0
\(143\) 8.41863 0.704001
\(144\) 0 0
\(145\) 1.38601 0.115102
\(146\) 0 0
\(147\) −4.80643 −0.396428
\(148\) 0 0
\(149\) −0.160060 −0.0131126 −0.00655630 0.999979i \(-0.502087\pi\)
−0.00655630 + 0.999979i \(0.502087\pi\)
\(150\) 0 0
\(151\) 2.17562 0.177050 0.0885248 0.996074i \(-0.471785\pi\)
0.0885248 + 0.996074i \(0.471785\pi\)
\(152\) 0 0
\(153\) −7.44723 −0.602073
\(154\) 0 0
\(155\) −9.29396 −0.746509
\(156\) 0 0
\(157\) 12.7136 1.01466 0.507330 0.861752i \(-0.330633\pi\)
0.507330 + 0.861752i \(0.330633\pi\)
\(158\) 0 0
\(159\) −9.24810 −0.733422
\(160\) 0 0
\(161\) −3.43605 −0.270799
\(162\) 0 0
\(163\) −20.9400 −1.64014 −0.820072 0.572260i \(-0.806067\pi\)
−0.820072 + 0.572260i \(0.806067\pi\)
\(164\) 0 0
\(165\) −3.66995 −0.285705
\(166\) 0 0
\(167\) −2.32471 −0.179892 −0.0899459 0.995947i \(-0.528669\pi\)
−0.0899459 + 0.995947i \(0.528669\pi\)
\(168\) 0 0
\(169\) −2.89134 −0.222411
\(170\) 0 0
\(171\) 7.20390 0.550896
\(172\) 0 0
\(173\) 16.3745 1.24493 0.622464 0.782648i \(-0.286132\pi\)
0.622464 + 0.782648i \(0.286132\pi\)
\(174\) 0 0
\(175\) 10.5795 0.799737
\(176\) 0 0
\(177\) −0.888525 −0.0667856
\(178\) 0 0
\(179\) −1.66977 −0.124804 −0.0624022 0.998051i \(-0.519876\pi\)
−0.0624022 + 0.998051i \(0.519876\pi\)
\(180\) 0 0
\(181\) 8.94963 0.665221 0.332610 0.943064i \(-0.392071\pi\)
0.332610 + 0.943064i \(0.392071\pi\)
\(182\) 0 0
\(183\) 0.116322 0.00859880
\(184\) 0 0
\(185\) 2.81982 0.207317
\(186\) 0 0
\(187\) −19.7192 −1.44201
\(188\) 0 0
\(189\) 3.43605 0.249936
\(190\) 0 0
\(191\) −9.07286 −0.656489 −0.328244 0.944593i \(-0.606457\pi\)
−0.328244 + 0.944593i \(0.606457\pi\)
\(192\) 0 0
\(193\) 9.95677 0.716704 0.358352 0.933587i \(-0.383339\pi\)
0.358352 + 0.933587i \(0.383339\pi\)
\(194\) 0 0
\(195\) −4.40669 −0.315570
\(196\) 0 0
\(197\) −4.20922 −0.299894 −0.149947 0.988694i \(-0.547910\pi\)
−0.149947 + 0.988694i \(0.547910\pi\)
\(198\) 0 0
\(199\) 13.5522 0.960689 0.480344 0.877080i \(-0.340512\pi\)
0.480344 + 0.877080i \(0.340512\pi\)
\(200\) 0 0
\(201\) 7.88452 0.556131
\(202\) 0 0
\(203\) −3.43605 −0.241163
\(204\) 0 0
\(205\) 9.90621 0.691880
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 19.0749 1.31944
\(210\) 0 0
\(211\) 7.74403 0.533121 0.266561 0.963818i \(-0.414113\pi\)
0.266561 + 0.963818i \(0.414113\pi\)
\(212\) 0 0
\(213\) 15.4402 1.05794
\(214\) 0 0
\(215\) −4.27701 −0.291690
\(216\) 0 0
\(217\) 23.0406 1.56410
\(218\) 0 0
\(219\) −8.68948 −0.587180
\(220\) 0 0
\(221\) −23.6778 −1.59274
\(222\) 0 0
\(223\) −14.9462 −1.00087 −0.500436 0.865774i \(-0.666827\pi\)
−0.500436 + 0.865774i \(0.666827\pi\)
\(224\) 0 0
\(225\) −3.07898 −0.205265
\(226\) 0 0
\(227\) 19.4919 1.29372 0.646861 0.762608i \(-0.276081\pi\)
0.646861 + 0.762608i \(0.276081\pi\)
\(228\) 0 0
\(229\) 12.4043 0.819697 0.409848 0.912154i \(-0.365582\pi\)
0.409848 + 0.912154i \(0.365582\pi\)
\(230\) 0 0
\(231\) 9.09817 0.598615
\(232\) 0 0
\(233\) 21.6702 1.41966 0.709830 0.704373i \(-0.248772\pi\)
0.709830 + 0.704373i \(0.248772\pi\)
\(234\) 0 0
\(235\) 6.99575 0.456352
\(236\) 0 0
\(237\) −10.3464 −0.672070
\(238\) 0 0
\(239\) −7.20633 −0.466139 −0.233069 0.972460i \(-0.574877\pi\)
−0.233069 + 0.972460i \(0.574877\pi\)
\(240\) 0 0
\(241\) 21.5021 1.38507 0.692536 0.721383i \(-0.256493\pi\)
0.692536 + 0.721383i \(0.256493\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 6.66176 0.425604
\(246\) 0 0
\(247\) 22.9042 1.45736
\(248\) 0 0
\(249\) −2.69423 −0.170740
\(250\) 0 0
\(251\) 2.47047 0.155934 0.0779672 0.996956i \(-0.475157\pi\)
0.0779672 + 0.996956i \(0.475157\pi\)
\(252\) 0 0
\(253\) 2.64786 0.166469
\(254\) 0 0
\(255\) 10.3219 0.646384
\(256\) 0 0
\(257\) 14.7725 0.921482 0.460741 0.887535i \(-0.347584\pi\)
0.460741 + 0.887535i \(0.347584\pi\)
\(258\) 0 0
\(259\) −6.99060 −0.434375
\(260\) 0 0
\(261\) 1.00000 0.0618984
\(262\) 0 0
\(263\) 15.8393 0.976694 0.488347 0.872649i \(-0.337600\pi\)
0.488347 + 0.872649i \(0.337600\pi\)
\(264\) 0 0
\(265\) 12.8179 0.787400
\(266\) 0 0
\(267\) −15.8946 −0.972736
\(268\) 0 0
\(269\) 9.31464 0.567924 0.283962 0.958836i \(-0.408351\pi\)
0.283962 + 0.958836i \(0.408351\pi\)
\(270\) 0 0
\(271\) 8.34005 0.506622 0.253311 0.967385i \(-0.418480\pi\)
0.253311 + 0.967385i \(0.418480\pi\)
\(272\) 0 0
\(273\) 10.9246 0.661188
\(274\) 0 0
\(275\) −8.15270 −0.491626
\(276\) 0 0
\(277\) 14.0290 0.842921 0.421461 0.906847i \(-0.361518\pi\)
0.421461 + 0.906847i \(0.361518\pi\)
\(278\) 0 0
\(279\) −6.70556 −0.401451
\(280\) 0 0
\(281\) 12.9642 0.773382 0.386691 0.922209i \(-0.373618\pi\)
0.386691 + 0.922209i \(0.373618\pi\)
\(282\) 0 0
\(283\) −32.1659 −1.91207 −0.956033 0.293260i \(-0.905260\pi\)
−0.956033 + 0.293260i \(0.905260\pi\)
\(284\) 0 0
\(285\) −9.98468 −0.591441
\(286\) 0 0
\(287\) −24.5584 −1.44964
\(288\) 0 0
\(289\) 38.4613 2.26243
\(290\) 0 0
\(291\) −8.50807 −0.498752
\(292\) 0 0
\(293\) −21.7425 −1.27021 −0.635104 0.772427i \(-0.719043\pi\)
−0.635104 + 0.772427i \(0.719043\pi\)
\(294\) 0 0
\(295\) 1.23150 0.0717009
\(296\) 0 0
\(297\) −2.64786 −0.153644
\(298\) 0 0
\(299\) 3.17941 0.183870
\(300\) 0 0
\(301\) 10.6031 0.611154
\(302\) 0 0
\(303\) 13.6985 0.786958
\(304\) 0 0
\(305\) −0.161224 −0.00923165
\(306\) 0 0
\(307\) 33.5501 1.91481 0.957403 0.288754i \(-0.0932409\pi\)
0.957403 + 0.288754i \(0.0932409\pi\)
\(308\) 0 0
\(309\) −0.0167442 −0.000952542 0
\(310\) 0 0
\(311\) 15.8244 0.897317 0.448658 0.893703i \(-0.351902\pi\)
0.448658 + 0.893703i \(0.351902\pi\)
\(312\) 0 0
\(313\) 0.361470 0.0204315 0.0102157 0.999948i \(-0.496748\pi\)
0.0102157 + 0.999948i \(0.496748\pi\)
\(314\) 0 0
\(315\) −4.76239 −0.268330
\(316\) 0 0
\(317\) 8.33691 0.468248 0.234124 0.972207i \(-0.424778\pi\)
0.234124 + 0.972207i \(0.424778\pi\)
\(318\) 0 0
\(319\) 2.64786 0.148252
\(320\) 0 0
\(321\) 11.9335 0.666064
\(322\) 0 0
\(323\) −53.6492 −2.98512
\(324\) 0 0
\(325\) −9.78934 −0.543015
\(326\) 0 0
\(327\) −2.32636 −0.128648
\(328\) 0 0
\(329\) −17.3431 −0.956158
\(330\) 0 0
\(331\) −15.6444 −0.859894 −0.429947 0.902854i \(-0.641468\pi\)
−0.429947 + 0.902854i \(0.641468\pi\)
\(332\) 0 0
\(333\) 2.03449 0.111489
\(334\) 0 0
\(335\) −10.9280 −0.597061
\(336\) 0 0
\(337\) −1.64739 −0.0897390 −0.0448695 0.998993i \(-0.514287\pi\)
−0.0448695 + 0.998993i \(0.514287\pi\)
\(338\) 0 0
\(339\) 4.35571 0.236569
\(340\) 0 0
\(341\) −17.7554 −0.961507
\(342\) 0 0
\(343\) 7.53721 0.406971
\(344\) 0 0
\(345\) −1.38601 −0.0746202
\(346\) 0 0
\(347\) 33.2002 1.78228 0.891141 0.453727i \(-0.149906\pi\)
0.891141 + 0.453727i \(0.149906\pi\)
\(348\) 0 0
\(349\) 8.30391 0.444498 0.222249 0.974990i \(-0.428660\pi\)
0.222249 + 0.974990i \(0.428660\pi\)
\(350\) 0 0
\(351\) −3.17941 −0.169704
\(352\) 0 0
\(353\) −18.7231 −0.996532 −0.498266 0.867024i \(-0.666030\pi\)
−0.498266 + 0.867024i \(0.666030\pi\)
\(354\) 0 0
\(355\) −21.4002 −1.13580
\(356\) 0 0
\(357\) −25.5891 −1.35432
\(358\) 0 0
\(359\) 33.7762 1.78264 0.891319 0.453376i \(-0.149780\pi\)
0.891319 + 0.453376i \(0.149780\pi\)
\(360\) 0 0
\(361\) 32.8962 1.73138
\(362\) 0 0
\(363\) 3.98885 0.209360
\(364\) 0 0
\(365\) 12.0437 0.630395
\(366\) 0 0
\(367\) −18.5205 −0.966761 −0.483381 0.875410i \(-0.660591\pi\)
−0.483381 + 0.875410i \(0.660591\pi\)
\(368\) 0 0
\(369\) 7.14729 0.372073
\(370\) 0 0
\(371\) −31.7769 −1.64978
\(372\) 0 0
\(373\) 2.87668 0.148949 0.0744744 0.997223i \(-0.476272\pi\)
0.0744744 + 0.997223i \(0.476272\pi\)
\(374\) 0 0
\(375\) 11.1975 0.578238
\(376\) 0 0
\(377\) 3.17941 0.163748
\(378\) 0 0
\(379\) −35.1025 −1.80309 −0.901546 0.432684i \(-0.857567\pi\)
−0.901546 + 0.432684i \(0.857567\pi\)
\(380\) 0 0
\(381\) 0.680671 0.0348718
\(382\) 0 0
\(383\) −18.5022 −0.945419 −0.472710 0.881218i \(-0.656724\pi\)
−0.472710 + 0.881218i \(0.656724\pi\)
\(384\) 0 0
\(385\) −12.6101 −0.642672
\(386\) 0 0
\(387\) −3.08585 −0.156862
\(388\) 0 0
\(389\) 28.8868 1.46462 0.732311 0.680971i \(-0.238442\pi\)
0.732311 + 0.680971i \(0.238442\pi\)
\(390\) 0 0
\(391\) −7.44723 −0.376623
\(392\) 0 0
\(393\) −3.31610 −0.167275
\(394\) 0 0
\(395\) 14.3402 0.721533
\(396\) 0 0
\(397\) 1.98400 0.0995742 0.0497871 0.998760i \(-0.484146\pi\)
0.0497871 + 0.998760i \(0.484146\pi\)
\(398\) 0 0
\(399\) 24.7530 1.23920
\(400\) 0 0
\(401\) 15.3643 0.767255 0.383628 0.923488i \(-0.374675\pi\)
0.383628 + 0.923488i \(0.374675\pi\)
\(402\) 0 0
\(403\) −21.3197 −1.06201
\(404\) 0 0
\(405\) 1.38601 0.0688713
\(406\) 0 0
\(407\) 5.38703 0.267025
\(408\) 0 0
\(409\) −12.0754 −0.597090 −0.298545 0.954396i \(-0.596501\pi\)
−0.298545 + 0.954396i \(0.596501\pi\)
\(410\) 0 0
\(411\) 5.69652 0.280989
\(412\) 0 0
\(413\) −3.05302 −0.150229
\(414\) 0 0
\(415\) 3.73423 0.183306
\(416\) 0 0
\(417\) −14.7590 −0.722751
\(418\) 0 0
\(419\) 10.9620 0.535529 0.267764 0.963484i \(-0.413715\pi\)
0.267764 + 0.963484i \(0.413715\pi\)
\(420\) 0 0
\(421\) 1.61154 0.0785419 0.0392709 0.999229i \(-0.487496\pi\)
0.0392709 + 0.999229i \(0.487496\pi\)
\(422\) 0 0
\(423\) 5.04741 0.245413
\(424\) 0 0
\(425\) 22.9299 1.11226
\(426\) 0 0
\(427\) 0.399689 0.0193423
\(428\) 0 0
\(429\) −8.41863 −0.406455
\(430\) 0 0
\(431\) 14.7932 0.712566 0.356283 0.934378i \(-0.384044\pi\)
0.356283 + 0.934378i \(0.384044\pi\)
\(432\) 0 0
\(433\) 26.8890 1.29220 0.646101 0.763252i \(-0.276399\pi\)
0.646101 + 0.763252i \(0.276399\pi\)
\(434\) 0 0
\(435\) −1.38601 −0.0664540
\(436\) 0 0
\(437\) 7.20390 0.344610
\(438\) 0 0
\(439\) −6.15227 −0.293632 −0.146816 0.989164i \(-0.546902\pi\)
−0.146816 + 0.989164i \(0.546902\pi\)
\(440\) 0 0
\(441\) 4.80643 0.228878
\(442\) 0 0
\(443\) 9.14045 0.434276 0.217138 0.976141i \(-0.430328\pi\)
0.217138 + 0.976141i \(0.430328\pi\)
\(444\) 0 0
\(445\) 22.0301 1.04433
\(446\) 0 0
\(447\) 0.160060 0.00757057
\(448\) 0 0
\(449\) −12.0735 −0.569782 −0.284891 0.958560i \(-0.591957\pi\)
−0.284891 + 0.958560i \(0.591957\pi\)
\(450\) 0 0
\(451\) 18.9250 0.891144
\(452\) 0 0
\(453\) −2.17562 −0.102220
\(454\) 0 0
\(455\) −15.1416 −0.709850
\(456\) 0 0
\(457\) 39.8810 1.86555 0.932776 0.360456i \(-0.117379\pi\)
0.932776 + 0.360456i \(0.117379\pi\)
\(458\) 0 0
\(459\) 7.44723 0.347607
\(460\) 0 0
\(461\) −7.10698 −0.331005 −0.165502 0.986209i \(-0.552925\pi\)
−0.165502 + 0.986209i \(0.552925\pi\)
\(462\) 0 0
\(463\) 15.7900 0.733821 0.366911 0.930256i \(-0.380415\pi\)
0.366911 + 0.930256i \(0.380415\pi\)
\(464\) 0 0
\(465\) 9.29396 0.430997
\(466\) 0 0
\(467\) −30.7866 −1.42463 −0.712316 0.701859i \(-0.752354\pi\)
−0.712316 + 0.701859i \(0.752354\pi\)
\(468\) 0 0
\(469\) 27.0916 1.25097
\(470\) 0 0
\(471\) −12.7136 −0.585814
\(472\) 0 0
\(473\) −8.17088 −0.375698
\(474\) 0 0
\(475\) −22.1807 −1.01772
\(476\) 0 0
\(477\) 9.24810 0.423441
\(478\) 0 0
\(479\) 25.9678 1.18650 0.593249 0.805019i \(-0.297845\pi\)
0.593249 + 0.805019i \(0.297845\pi\)
\(480\) 0 0
\(481\) 6.46847 0.294937
\(482\) 0 0
\(483\) 3.43605 0.156346
\(484\) 0 0
\(485\) 11.7923 0.535459
\(486\) 0 0
\(487\) 23.8307 1.07987 0.539936 0.841706i \(-0.318448\pi\)
0.539936 + 0.841706i \(0.318448\pi\)
\(488\) 0 0
\(489\) 20.9400 0.946938
\(490\) 0 0
\(491\) 23.1326 1.04396 0.521981 0.852957i \(-0.325193\pi\)
0.521981 + 0.852957i \(0.325193\pi\)
\(492\) 0 0
\(493\) −7.44723 −0.335406
\(494\) 0 0
\(495\) 3.66995 0.164952
\(496\) 0 0
\(497\) 53.0532 2.37976
\(498\) 0 0
\(499\) −27.2255 −1.21878 −0.609389 0.792871i \(-0.708585\pi\)
−0.609389 + 0.792871i \(0.708585\pi\)
\(500\) 0 0
\(501\) 2.32471 0.103861
\(502\) 0 0
\(503\) −29.0909 −1.29710 −0.648550 0.761172i \(-0.724624\pi\)
−0.648550 + 0.761172i \(0.724624\pi\)
\(504\) 0 0
\(505\) −18.9862 −0.844877
\(506\) 0 0
\(507\) 2.89134 0.128409
\(508\) 0 0
\(509\) 5.92211 0.262493 0.131246 0.991350i \(-0.458102\pi\)
0.131246 + 0.991350i \(0.458102\pi\)
\(510\) 0 0
\(511\) −29.8575 −1.32082
\(512\) 0 0
\(513\) −7.20390 −0.318060
\(514\) 0 0
\(515\) 0.0232075 0.00102265
\(516\) 0 0
\(517\) 13.3648 0.587784
\(518\) 0 0
\(519\) −16.3745 −0.718760
\(520\) 0 0
\(521\) 35.4649 1.55375 0.776873 0.629658i \(-0.216805\pi\)
0.776873 + 0.629658i \(0.216805\pi\)
\(522\) 0 0
\(523\) −38.7489 −1.69437 −0.847186 0.531296i \(-0.821705\pi\)
−0.847186 + 0.531296i \(0.821705\pi\)
\(524\) 0 0
\(525\) −10.5795 −0.461728
\(526\) 0 0
\(527\) 49.9379 2.17533
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0.888525 0.0385587
\(532\) 0 0
\(533\) 22.7242 0.984294
\(534\) 0 0
\(535\) −16.5399 −0.715084
\(536\) 0 0
\(537\) 1.66977 0.0720559
\(538\) 0 0
\(539\) 12.7267 0.548180
\(540\) 0 0
\(541\) 29.2132 1.25598 0.627988 0.778223i \(-0.283879\pi\)
0.627988 + 0.778223i \(0.283879\pi\)
\(542\) 0 0
\(543\) −8.94963 −0.384065
\(544\) 0 0
\(545\) 3.22435 0.138116
\(546\) 0 0
\(547\) −32.1886 −1.37629 −0.688143 0.725575i \(-0.741574\pi\)
−0.688143 + 0.725575i \(0.741574\pi\)
\(548\) 0 0
\(549\) −0.116322 −0.00496452
\(550\) 0 0
\(551\) 7.20390 0.306897
\(552\) 0 0
\(553\) −35.5507 −1.51177
\(554\) 0 0
\(555\) −2.81982 −0.119695
\(556\) 0 0
\(557\) 30.0309 1.27245 0.636226 0.771503i \(-0.280495\pi\)
0.636226 + 0.771503i \(0.280495\pi\)
\(558\) 0 0
\(559\) −9.81118 −0.414969
\(560\) 0 0
\(561\) 19.7192 0.832546
\(562\) 0 0
\(563\) −3.77593 −0.159137 −0.0795683 0.996829i \(-0.525354\pi\)
−0.0795683 + 0.996829i \(0.525354\pi\)
\(564\) 0 0
\(565\) −6.03705 −0.253980
\(566\) 0 0
\(567\) −3.43605 −0.144300
\(568\) 0 0
\(569\) −10.4927 −0.439878 −0.219939 0.975514i \(-0.570586\pi\)
−0.219939 + 0.975514i \(0.570586\pi\)
\(570\) 0 0
\(571\) −0.129941 −0.00543785 −0.00271893 0.999996i \(-0.500865\pi\)
−0.00271893 + 0.999996i \(0.500865\pi\)
\(572\) 0 0
\(573\) 9.07286 0.379024
\(574\) 0 0
\(575\) −3.07898 −0.128402
\(576\) 0 0
\(577\) −20.0833 −0.836080 −0.418040 0.908429i \(-0.637283\pi\)
−0.418040 + 0.908429i \(0.637283\pi\)
\(578\) 0 0
\(579\) −9.95677 −0.413789
\(580\) 0 0
\(581\) −9.25752 −0.384067
\(582\) 0 0
\(583\) 24.4877 1.01417
\(584\) 0 0
\(585\) 4.40669 0.182194
\(586\) 0 0
\(587\) 30.5687 1.26170 0.630852 0.775903i \(-0.282705\pi\)
0.630852 + 0.775903i \(0.282705\pi\)
\(588\) 0 0
\(589\) −48.3062 −1.99042
\(590\) 0 0
\(591\) 4.20922 0.173144
\(592\) 0 0
\(593\) 4.39665 0.180549 0.0902744 0.995917i \(-0.471226\pi\)
0.0902744 + 0.995917i \(0.471226\pi\)
\(594\) 0 0
\(595\) 35.4667 1.45399
\(596\) 0 0
\(597\) −13.5522 −0.554654
\(598\) 0 0
\(599\) 32.6995 1.33607 0.668033 0.744132i \(-0.267137\pi\)
0.668033 + 0.744132i \(0.267137\pi\)
\(600\) 0 0
\(601\) −9.56886 −0.390322 −0.195161 0.980771i \(-0.562523\pi\)
−0.195161 + 0.980771i \(0.562523\pi\)
\(602\) 0 0
\(603\) −7.88452 −0.321082
\(604\) 0 0
\(605\) −5.52858 −0.224769
\(606\) 0 0
\(607\) −44.1392 −1.79155 −0.895777 0.444504i \(-0.853380\pi\)
−0.895777 + 0.444504i \(0.853380\pi\)
\(608\) 0 0
\(609\) 3.43605 0.139236
\(610\) 0 0
\(611\) 16.0478 0.649224
\(612\) 0 0
\(613\) 40.3468 1.62959 0.814796 0.579748i \(-0.196849\pi\)
0.814796 + 0.579748i \(0.196849\pi\)
\(614\) 0 0
\(615\) −9.90621 −0.399457
\(616\) 0 0
\(617\) −1.67027 −0.0672427 −0.0336213 0.999435i \(-0.510704\pi\)
−0.0336213 + 0.999435i \(0.510704\pi\)
\(618\) 0 0
\(619\) 18.2055 0.731740 0.365870 0.930666i \(-0.380771\pi\)
0.365870 + 0.930666i \(0.380771\pi\)
\(620\) 0 0
\(621\) −1.00000 −0.0401286
\(622\) 0 0
\(623\) −54.6147 −2.18809
\(624\) 0 0
\(625\) −0.124984 −0.00499936
\(626\) 0 0
\(627\) −19.0749 −0.761779
\(628\) 0 0
\(629\) −15.1513 −0.604122
\(630\) 0 0
\(631\) −26.8565 −1.06914 −0.534569 0.845125i \(-0.679526\pi\)
−0.534569 + 0.845125i \(0.679526\pi\)
\(632\) 0 0
\(633\) −7.74403 −0.307798
\(634\) 0 0
\(635\) −0.943416 −0.0374383
\(636\) 0 0
\(637\) 15.2816 0.605480
\(638\) 0 0
\(639\) −15.4402 −0.610803
\(640\) 0 0
\(641\) 49.0780 1.93846 0.969232 0.246151i \(-0.0791658\pi\)
0.969232 + 0.246151i \(0.0791658\pi\)
\(642\) 0 0
\(643\) −20.7188 −0.817070 −0.408535 0.912743i \(-0.633960\pi\)
−0.408535 + 0.912743i \(0.633960\pi\)
\(644\) 0 0
\(645\) 4.27701 0.168407
\(646\) 0 0
\(647\) −17.3265 −0.681176 −0.340588 0.940213i \(-0.610626\pi\)
−0.340588 + 0.940213i \(0.610626\pi\)
\(648\) 0 0
\(649\) 2.35269 0.0923511
\(650\) 0 0
\(651\) −23.0406 −0.903033
\(652\) 0 0
\(653\) −6.74821 −0.264078 −0.132039 0.991245i \(-0.542152\pi\)
−0.132039 + 0.991245i \(0.542152\pi\)
\(654\) 0 0
\(655\) 4.59614 0.179586
\(656\) 0 0
\(657\) 8.68948 0.339009
\(658\) 0 0
\(659\) 48.8832 1.90422 0.952110 0.305757i \(-0.0989094\pi\)
0.952110 + 0.305757i \(0.0989094\pi\)
\(660\) 0 0
\(661\) −30.5438 −1.18802 −0.594009 0.804458i \(-0.702456\pi\)
−0.594009 + 0.804458i \(0.702456\pi\)
\(662\) 0 0
\(663\) 23.6778 0.919570
\(664\) 0 0
\(665\) −34.3078 −1.33040
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 0 0
\(669\) 14.9462 0.577854
\(670\) 0 0
\(671\) −0.308005 −0.0118904
\(672\) 0 0
\(673\) −22.5888 −0.870736 −0.435368 0.900253i \(-0.643382\pi\)
−0.435368 + 0.900253i \(0.643382\pi\)
\(674\) 0 0
\(675\) 3.07898 0.118510
\(676\) 0 0
\(677\) −48.9364 −1.88078 −0.940389 0.340100i \(-0.889539\pi\)
−0.940389 + 0.340100i \(0.889539\pi\)
\(678\) 0 0
\(679\) −29.2341 −1.12190
\(680\) 0 0
\(681\) −19.4919 −0.746931
\(682\) 0 0
\(683\) 35.1962 1.34675 0.673373 0.739303i \(-0.264845\pi\)
0.673373 + 0.739303i \(0.264845\pi\)
\(684\) 0 0
\(685\) −7.89542 −0.301669
\(686\) 0 0
\(687\) −12.4043 −0.473252
\(688\) 0 0
\(689\) 29.4035 1.12018
\(690\) 0 0
\(691\) 35.9630 1.36810 0.684049 0.729436i \(-0.260217\pi\)
0.684049 + 0.729436i \(0.260217\pi\)
\(692\) 0 0
\(693\) −9.09817 −0.345611
\(694\) 0 0
\(695\) 20.4561 0.775943
\(696\) 0 0
\(697\) −53.2275 −2.01614
\(698\) 0 0
\(699\) −21.6702 −0.819641
\(700\) 0 0
\(701\) 2.71185 0.102425 0.0512126 0.998688i \(-0.483691\pi\)
0.0512126 + 0.998688i \(0.483691\pi\)
\(702\) 0 0
\(703\) 14.6563 0.552771
\(704\) 0 0
\(705\) −6.99575 −0.263475
\(706\) 0 0
\(707\) 47.0687 1.77020
\(708\) 0 0
\(709\) 45.8632 1.72243 0.861214 0.508243i \(-0.169705\pi\)
0.861214 + 0.508243i \(0.169705\pi\)
\(710\) 0 0
\(711\) 10.3464 0.388020
\(712\) 0 0
\(713\) −6.70556 −0.251125
\(714\) 0 0
\(715\) 11.6683 0.436369
\(716\) 0 0
\(717\) 7.20633 0.269125
\(718\) 0 0
\(719\) 18.9186 0.705546 0.352773 0.935709i \(-0.385239\pi\)
0.352773 + 0.935709i \(0.385239\pi\)
\(720\) 0 0
\(721\) −0.0575337 −0.00214267
\(722\) 0 0
\(723\) −21.5021 −0.799672
\(724\) 0 0
\(725\) −3.07898 −0.114350
\(726\) 0 0
\(727\) 8.18289 0.303487 0.151743 0.988420i \(-0.451511\pi\)
0.151743 + 0.988420i \(0.451511\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 22.9810 0.849984
\(732\) 0 0
\(733\) −37.2184 −1.37469 −0.687347 0.726329i \(-0.741225\pi\)
−0.687347 + 0.726329i \(0.741225\pi\)
\(734\) 0 0
\(735\) −6.66176 −0.245723
\(736\) 0 0
\(737\) −20.8771 −0.769017
\(738\) 0 0
\(739\) 10.4788 0.385468 0.192734 0.981251i \(-0.438265\pi\)
0.192734 + 0.981251i \(0.438265\pi\)
\(740\) 0 0
\(741\) −22.9042 −0.841406
\(742\) 0 0
\(743\) −32.5439 −1.19392 −0.596959 0.802272i \(-0.703625\pi\)
−0.596959 + 0.802272i \(0.703625\pi\)
\(744\) 0 0
\(745\) −0.221844 −0.00812774
\(746\) 0 0
\(747\) 2.69423 0.0985769
\(748\) 0 0
\(749\) 41.0041 1.49826
\(750\) 0 0
\(751\) −15.1513 −0.552878 −0.276439 0.961031i \(-0.589154\pi\)
−0.276439 + 0.961031i \(0.589154\pi\)
\(752\) 0 0
\(753\) −2.47047 −0.0900288
\(754\) 0 0
\(755\) 3.01543 0.109743
\(756\) 0 0
\(757\) −51.6875 −1.87861 −0.939307 0.343079i \(-0.888530\pi\)
−0.939307 + 0.343079i \(0.888530\pi\)
\(758\) 0 0
\(759\) −2.64786 −0.0961111
\(760\) 0 0
\(761\) 5.36043 0.194316 0.0971578 0.995269i \(-0.469025\pi\)
0.0971578 + 0.995269i \(0.469025\pi\)
\(762\) 0 0
\(763\) −7.99348 −0.289384
\(764\) 0 0
\(765\) −10.3219 −0.373190
\(766\) 0 0
\(767\) 2.82499 0.102004
\(768\) 0 0
\(769\) −13.3418 −0.481117 −0.240559 0.970635i \(-0.577331\pi\)
−0.240559 + 0.970635i \(0.577331\pi\)
\(770\) 0 0
\(771\) −14.7725 −0.532018
\(772\) 0 0
\(773\) 49.0812 1.76533 0.882665 0.470003i \(-0.155747\pi\)
0.882665 + 0.470003i \(0.155747\pi\)
\(774\) 0 0
\(775\) 20.6463 0.741636
\(776\) 0 0
\(777\) 6.99060 0.250786
\(778\) 0 0
\(779\) 51.4884 1.84476
\(780\) 0 0
\(781\) −40.8834 −1.46292
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) 17.6212 0.628928
\(786\) 0 0
\(787\) −17.5113 −0.624211 −0.312106 0.950047i \(-0.601034\pi\)
−0.312106 + 0.950047i \(0.601034\pi\)
\(788\) 0 0
\(789\) −15.8393 −0.563895
\(790\) 0 0
\(791\) 14.9664 0.532145
\(792\) 0 0
\(793\) −0.369837 −0.0131333
\(794\) 0 0
\(795\) −12.8179 −0.454606
\(796\) 0 0
\(797\) −34.3432 −1.21650 −0.608248 0.793747i \(-0.708128\pi\)
−0.608248 + 0.793747i \(0.708128\pi\)
\(798\) 0 0
\(799\) −37.5892 −1.32981
\(800\) 0 0
\(801\) 15.8946 0.561609
\(802\) 0 0
\(803\) 23.0085 0.811952
\(804\) 0 0
\(805\) −4.76239 −0.167852
\(806\) 0 0
\(807\) −9.31464 −0.327891
\(808\) 0 0
\(809\) −23.6894 −0.832874 −0.416437 0.909165i \(-0.636721\pi\)
−0.416437 + 0.909165i \(0.636721\pi\)
\(810\) 0 0
\(811\) 47.4858 1.66745 0.833727 0.552177i \(-0.186203\pi\)
0.833727 + 0.552177i \(0.186203\pi\)
\(812\) 0 0
\(813\) −8.34005 −0.292498
\(814\) 0 0
\(815\) −29.0230 −1.01663
\(816\) 0 0
\(817\) −22.2302 −0.777735
\(818\) 0 0
\(819\) −10.9246 −0.381737
\(820\) 0 0
\(821\) −13.3373 −0.465474 −0.232737 0.972540i \(-0.574768\pi\)
−0.232737 + 0.972540i \(0.574768\pi\)
\(822\) 0 0
\(823\) −9.97366 −0.347660 −0.173830 0.984776i \(-0.555614\pi\)
−0.173830 + 0.984776i \(0.555614\pi\)
\(824\) 0 0
\(825\) 8.15270 0.283841
\(826\) 0 0
\(827\) 32.4815 1.12949 0.564746 0.825265i \(-0.308974\pi\)
0.564746 + 0.825265i \(0.308974\pi\)
\(828\) 0 0
\(829\) 39.4553 1.37034 0.685170 0.728383i \(-0.259728\pi\)
0.685170 + 0.728383i \(0.259728\pi\)
\(830\) 0 0
\(831\) −14.0290 −0.486661
\(832\) 0 0
\(833\) −35.7946 −1.24021
\(834\) 0 0
\(835\) −3.22207 −0.111504
\(836\) 0 0
\(837\) 6.70556 0.231778
\(838\) 0 0
\(839\) −10.7235 −0.370218 −0.185109 0.982718i \(-0.559264\pi\)
−0.185109 + 0.982718i \(0.559264\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −12.9642 −0.446512
\(844\) 0 0
\(845\) −4.00743 −0.137860
\(846\) 0 0
\(847\) 13.7059 0.470940
\(848\) 0 0
\(849\) 32.1659 1.10393
\(850\) 0 0
\(851\) 2.03449 0.0697413
\(852\) 0 0
\(853\) 18.1546 0.621602 0.310801 0.950475i \(-0.399403\pi\)
0.310801 + 0.950475i \(0.399403\pi\)
\(854\) 0 0
\(855\) 9.98468 0.341469
\(856\) 0 0
\(857\) 0.491319 0.0167831 0.00839156 0.999965i \(-0.497329\pi\)
0.00839156 + 0.999965i \(0.497329\pi\)
\(858\) 0 0
\(859\) 13.4023 0.457281 0.228641 0.973511i \(-0.426572\pi\)
0.228641 + 0.973511i \(0.426572\pi\)
\(860\) 0 0
\(861\) 24.5584 0.836949
\(862\) 0 0
\(863\) −7.60501 −0.258877 −0.129439 0.991587i \(-0.541318\pi\)
−0.129439 + 0.991587i \(0.541318\pi\)
\(864\) 0 0
\(865\) 22.6952 0.771659
\(866\) 0 0
\(867\) −38.4613 −1.30621
\(868\) 0 0
\(869\) 27.3958 0.929337
\(870\) 0 0
\(871\) −25.0681 −0.849401
\(872\) 0 0
\(873\) 8.50807 0.287954
\(874\) 0 0
\(875\) 38.4753 1.30070
\(876\) 0 0
\(877\) −24.4204 −0.824617 −0.412309 0.911044i \(-0.635277\pi\)
−0.412309 + 0.911044i \(0.635277\pi\)
\(878\) 0 0
\(879\) 21.7425 0.733355
\(880\) 0 0
\(881\) 23.8176 0.802436 0.401218 0.915983i \(-0.368587\pi\)
0.401218 + 0.915983i \(0.368587\pi\)
\(882\) 0 0
\(883\) 36.3543 1.22342 0.611709 0.791083i \(-0.290482\pi\)
0.611709 + 0.791083i \(0.290482\pi\)
\(884\) 0 0
\(885\) −1.23150 −0.0413965
\(886\) 0 0
\(887\) 24.1787 0.811840 0.405920 0.913909i \(-0.366951\pi\)
0.405920 + 0.913909i \(0.366951\pi\)
\(888\) 0 0
\(889\) 2.33882 0.0784415
\(890\) 0 0
\(891\) 2.64786 0.0887066
\(892\) 0 0
\(893\) 36.3610 1.21678
\(894\) 0 0
\(895\) −2.31431 −0.0773590
\(896\) 0 0
\(897\) −3.17941 −0.106157
\(898\) 0 0
\(899\) −6.70556 −0.223643
\(900\) 0 0
\(901\) −68.8728 −2.29448
\(902\) 0 0
\(903\) −10.6031 −0.352850
\(904\) 0 0
\(905\) 12.4043 0.412332
\(906\) 0 0
\(907\) −52.8003 −1.75320 −0.876602 0.481216i \(-0.840195\pi\)
−0.876602 + 0.481216i \(0.840195\pi\)
\(908\) 0 0
\(909\) −13.6985 −0.454351
\(910\) 0 0
\(911\) 20.9718 0.694827 0.347414 0.937712i \(-0.387060\pi\)
0.347414 + 0.937712i \(0.387060\pi\)
\(912\) 0 0
\(913\) 7.13395 0.236099
\(914\) 0 0
\(915\) 0.161224 0.00532990
\(916\) 0 0
\(917\) −11.3943 −0.376272
\(918\) 0 0
\(919\) −50.6431 −1.67056 −0.835282 0.549822i \(-0.814695\pi\)
−0.835282 + 0.549822i \(0.814695\pi\)
\(920\) 0 0
\(921\) −33.5501 −1.10551
\(922\) 0 0
\(923\) −49.0906 −1.61584
\(924\) 0 0
\(925\) −6.26415 −0.205964
\(926\) 0 0
\(927\) 0.0167442 0.000549950 0
\(928\) 0 0
\(929\) 51.3435 1.68452 0.842262 0.539068i \(-0.181224\pi\)
0.842262 + 0.539068i \(0.181224\pi\)
\(930\) 0 0
\(931\) 34.6251 1.13479
\(932\) 0 0
\(933\) −15.8244 −0.518066
\(934\) 0 0
\(935\) −27.3310 −0.893819
\(936\) 0 0
\(937\) −38.6986 −1.26423 −0.632114 0.774876i \(-0.717812\pi\)
−0.632114 + 0.774876i \(0.717812\pi\)
\(938\) 0 0
\(939\) −0.361470 −0.0117961
\(940\) 0 0
\(941\) 14.1476 0.461198 0.230599 0.973049i \(-0.425931\pi\)
0.230599 + 0.973049i \(0.425931\pi\)
\(942\) 0 0
\(943\) 7.14729 0.232748
\(944\) 0 0
\(945\) 4.76239 0.154921
\(946\) 0 0
\(947\) 18.4717 0.600248 0.300124 0.953900i \(-0.402972\pi\)
0.300124 + 0.953900i \(0.402972\pi\)
\(948\) 0 0
\(949\) 27.6274 0.896824
\(950\) 0 0
\(951\) −8.33691 −0.270343
\(952\) 0 0
\(953\) 35.7365 1.15762 0.578810 0.815462i \(-0.303517\pi\)
0.578810 + 0.815462i \(0.303517\pi\)
\(954\) 0 0
\(955\) −12.5751 −0.406919
\(956\) 0 0
\(957\) −2.64786 −0.0855931
\(958\) 0 0
\(959\) 19.5735 0.632062
\(960\) 0 0
\(961\) 13.9645 0.450468
\(962\) 0 0
\(963\) −11.9335 −0.384552
\(964\) 0 0
\(965\) 13.8002 0.444243
\(966\) 0 0
\(967\) 12.4558 0.400551 0.200275 0.979740i \(-0.435816\pi\)
0.200275 + 0.979740i \(0.435816\pi\)
\(968\) 0 0
\(969\) 53.6492 1.72346
\(970\) 0 0
\(971\) 33.1287 1.06315 0.531576 0.847011i \(-0.321600\pi\)
0.531576 + 0.847011i \(0.321600\pi\)
\(972\) 0 0
\(973\) −50.7126 −1.62577
\(974\) 0 0
\(975\) 9.78934 0.313510
\(976\) 0 0
\(977\) −50.0824 −1.60228 −0.801140 0.598478i \(-0.795773\pi\)
−0.801140 + 0.598478i \(0.795773\pi\)
\(978\) 0 0
\(979\) 42.0867 1.34510
\(980\) 0 0
\(981\) 2.32636 0.0742749
\(982\) 0 0
\(983\) −1.89456 −0.0604271 −0.0302136 0.999543i \(-0.509619\pi\)
−0.0302136 + 0.999543i \(0.509619\pi\)
\(984\) 0 0
\(985\) −5.83401 −0.185887
\(986\) 0 0
\(987\) 17.3431 0.552038
\(988\) 0 0
\(989\) −3.08585 −0.0981243
\(990\) 0 0
\(991\) 29.7752 0.945841 0.472921 0.881105i \(-0.343200\pi\)
0.472921 + 0.881105i \(0.343200\pi\)
\(992\) 0 0
\(993\) 15.6444 0.496460
\(994\) 0 0
\(995\) 18.7834 0.595475
\(996\) 0 0
\(997\) −0.654663 −0.0207334 −0.0103667 0.999946i \(-0.503300\pi\)
−0.0103667 + 0.999946i \(0.503300\pi\)
\(998\) 0 0
\(999\) −2.03449 −0.0643683
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 8004.2.a.i.1.11 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8004.2.a.i.1.11 16 1.1 even 1 trivial