Properties

Label 8016.2.a.be.1.4
Level 8016
Weight 2
Character 8016.1
Self dual yes
Analytic conductor 64.008
Analytic rank 0
Dimension 11
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - x^{10} - 33 x^{9} + 22 x^{8} + 417 x^{7} - 151 x^{6} - 2470 x^{5} + 272 x^{4} + 6584 x^{3} + 292 x^{2} - 5687 x + 242\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 4008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(2.38119\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -1.38119 q^{5} +0.260099 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -1.38119 q^{5} +0.260099 q^{7} +1.00000 q^{9} +3.57901 q^{11} -1.29974 q^{13} -1.38119 q^{15} -4.24502 q^{17} -5.37321 q^{19} +0.260099 q^{21} -5.60388 q^{23} -3.09232 q^{25} +1.00000 q^{27} +2.23067 q^{29} +9.62228 q^{31} +3.57901 q^{33} -0.359246 q^{35} +0.0808905 q^{37} -1.29974 q^{39} +4.29012 q^{41} +10.5096 q^{43} -1.38119 q^{45} +6.20376 q^{47} -6.93235 q^{49} -4.24502 q^{51} +12.3984 q^{53} -4.94329 q^{55} -5.37321 q^{57} -3.18358 q^{59} -6.40971 q^{61} +0.260099 q^{63} +1.79518 q^{65} -2.58992 q^{67} -5.60388 q^{69} -10.9927 q^{71} +11.2300 q^{73} -3.09232 q^{75} +0.930895 q^{77} +11.9509 q^{79} +1.00000 q^{81} -4.33550 q^{83} +5.86317 q^{85} +2.23067 q^{87} +8.61186 q^{89} -0.338060 q^{91} +9.62228 q^{93} +7.42142 q^{95} +0.0718231 q^{97} +3.57901 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q + 11q^{3} + 10q^{5} + q^{7} + 11q^{9} + O(q^{10}) \) \( 11q + 11q^{3} + 10q^{5} + q^{7} + 11q^{9} + q^{11} + 10q^{13} + 10q^{15} + 17q^{17} - 2q^{19} + q^{21} + 3q^{23} + 21q^{25} + 11q^{27} + 17q^{29} + 15q^{31} + q^{33} - 11q^{35} + 4q^{37} + 10q^{39} + 16q^{41} - 10q^{43} + 10q^{45} + 16q^{47} + 22q^{49} + 17q^{51} + 42q^{53} + 5q^{55} - 2q^{57} + 2q^{59} + 12q^{61} + q^{63} + 10q^{65} + q^{67} + 3q^{69} + 9q^{71} + 24q^{73} + 21q^{75} + 22q^{77} + 30q^{79} + 11q^{81} - 16q^{83} + 25q^{85} + 17q^{87} + 37q^{89} - q^{91} + 15q^{93} - 5q^{95} + 4q^{97} + q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −1.38119 −0.617687 −0.308843 0.951113i \(-0.599942\pi\)
−0.308843 + 0.951113i \(0.599942\pi\)
\(6\) 0 0
\(7\) 0.260099 0.0983081 0.0491540 0.998791i \(-0.484347\pi\)
0.0491540 + 0.998791i \(0.484347\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.57901 1.07911 0.539556 0.841950i \(-0.318592\pi\)
0.539556 + 0.841950i \(0.318592\pi\)
\(12\) 0 0
\(13\) −1.29974 −0.360482 −0.180241 0.983622i \(-0.557688\pi\)
−0.180241 + 0.983622i \(0.557688\pi\)
\(14\) 0 0
\(15\) −1.38119 −0.356621
\(16\) 0 0
\(17\) −4.24502 −1.02957 −0.514784 0.857320i \(-0.672128\pi\)
−0.514784 + 0.857320i \(0.672128\pi\)
\(18\) 0 0
\(19\) −5.37321 −1.23270 −0.616350 0.787473i \(-0.711389\pi\)
−0.616350 + 0.787473i \(0.711389\pi\)
\(20\) 0 0
\(21\) 0.260099 0.0567582
\(22\) 0 0
\(23\) −5.60388 −1.16849 −0.584245 0.811578i \(-0.698609\pi\)
−0.584245 + 0.811578i \(0.698609\pi\)
\(24\) 0 0
\(25\) −3.09232 −0.618463
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 2.23067 0.414224 0.207112 0.978317i \(-0.433594\pi\)
0.207112 + 0.978317i \(0.433594\pi\)
\(30\) 0 0
\(31\) 9.62228 1.72821 0.864106 0.503309i \(-0.167884\pi\)
0.864106 + 0.503309i \(0.167884\pi\)
\(32\) 0 0
\(33\) 3.57901 0.623025
\(34\) 0 0
\(35\) −0.359246 −0.0607236
\(36\) 0 0
\(37\) 0.0808905 0.0132983 0.00664916 0.999978i \(-0.497883\pi\)
0.00664916 + 0.999978i \(0.497883\pi\)
\(38\) 0 0
\(39\) −1.29974 −0.208125
\(40\) 0 0
\(41\) 4.29012 0.670005 0.335002 0.942217i \(-0.391263\pi\)
0.335002 + 0.942217i \(0.391263\pi\)
\(42\) 0 0
\(43\) 10.5096 1.60270 0.801352 0.598193i \(-0.204114\pi\)
0.801352 + 0.598193i \(0.204114\pi\)
\(44\) 0 0
\(45\) −1.38119 −0.205896
\(46\) 0 0
\(47\) 6.20376 0.904911 0.452455 0.891787i \(-0.350548\pi\)
0.452455 + 0.891787i \(0.350548\pi\)
\(48\) 0 0
\(49\) −6.93235 −0.990336
\(50\) 0 0
\(51\) −4.24502 −0.594421
\(52\) 0 0
\(53\) 12.3984 1.70305 0.851524 0.524316i \(-0.175679\pi\)
0.851524 + 0.524316i \(0.175679\pi\)
\(54\) 0 0
\(55\) −4.94329 −0.666553
\(56\) 0 0
\(57\) −5.37321 −0.711699
\(58\) 0 0
\(59\) −3.18358 −0.414467 −0.207234 0.978292i \(-0.566446\pi\)
−0.207234 + 0.978292i \(0.566446\pi\)
\(60\) 0 0
\(61\) −6.40971 −0.820679 −0.410339 0.911933i \(-0.634590\pi\)
−0.410339 + 0.911933i \(0.634590\pi\)
\(62\) 0 0
\(63\) 0.260099 0.0327694
\(64\) 0 0
\(65\) 1.79518 0.222665
\(66\) 0 0
\(67\) −2.58992 −0.316409 −0.158204 0.987406i \(-0.550570\pi\)
−0.158204 + 0.987406i \(0.550570\pi\)
\(68\) 0 0
\(69\) −5.60388 −0.674627
\(70\) 0 0
\(71\) −10.9927 −1.30460 −0.652298 0.757963i \(-0.726195\pi\)
−0.652298 + 0.757963i \(0.726195\pi\)
\(72\) 0 0
\(73\) 11.2300 1.31437 0.657185 0.753729i \(-0.271747\pi\)
0.657185 + 0.753729i \(0.271747\pi\)
\(74\) 0 0
\(75\) −3.09232 −0.357070
\(76\) 0 0
\(77\) 0.930895 0.106085
\(78\) 0 0
\(79\) 11.9509 1.34458 0.672290 0.740288i \(-0.265311\pi\)
0.672290 + 0.740288i \(0.265311\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −4.33550 −0.475883 −0.237941 0.971280i \(-0.576473\pi\)
−0.237941 + 0.971280i \(0.576473\pi\)
\(84\) 0 0
\(85\) 5.86317 0.635950
\(86\) 0 0
\(87\) 2.23067 0.239152
\(88\) 0 0
\(89\) 8.61186 0.912855 0.456428 0.889760i \(-0.349129\pi\)
0.456428 + 0.889760i \(0.349129\pi\)
\(90\) 0 0
\(91\) −0.338060 −0.0354383
\(92\) 0 0
\(93\) 9.62228 0.997784
\(94\) 0 0
\(95\) 7.42142 0.761422
\(96\) 0 0
\(97\) 0.0718231 0.00729253 0.00364627 0.999993i \(-0.498839\pi\)
0.00364627 + 0.999993i \(0.498839\pi\)
\(98\) 0 0
\(99\) 3.57901 0.359704
\(100\) 0 0
\(101\) 17.9592 1.78700 0.893501 0.449061i \(-0.148241\pi\)
0.893501 + 0.449061i \(0.148241\pi\)
\(102\) 0 0
\(103\) −0.277767 −0.0273692 −0.0136846 0.999906i \(-0.504356\pi\)
−0.0136846 + 0.999906i \(0.504356\pi\)
\(104\) 0 0
\(105\) −0.359246 −0.0350588
\(106\) 0 0
\(107\) 5.01695 0.485007 0.242504 0.970150i \(-0.422031\pi\)
0.242504 + 0.970150i \(0.422031\pi\)
\(108\) 0 0
\(109\) 15.0343 1.44002 0.720012 0.693962i \(-0.244136\pi\)
0.720012 + 0.693962i \(0.244136\pi\)
\(110\) 0 0
\(111\) 0.0808905 0.00767779
\(112\) 0 0
\(113\) 10.2708 0.966198 0.483099 0.875566i \(-0.339511\pi\)
0.483099 + 0.875566i \(0.339511\pi\)
\(114\) 0 0
\(115\) 7.74001 0.721760
\(116\) 0 0
\(117\) −1.29974 −0.120161
\(118\) 0 0
\(119\) −1.10412 −0.101215
\(120\) 0 0
\(121\) 1.80930 0.164481
\(122\) 0 0
\(123\) 4.29012 0.386827
\(124\) 0 0
\(125\) 11.1770 0.999703
\(126\) 0 0
\(127\) 3.02975 0.268847 0.134423 0.990924i \(-0.457082\pi\)
0.134423 + 0.990924i \(0.457082\pi\)
\(128\) 0 0
\(129\) 10.5096 0.925322
\(130\) 0 0
\(131\) 17.2097 1.50361 0.751807 0.659383i \(-0.229182\pi\)
0.751807 + 0.659383i \(0.229182\pi\)
\(132\) 0 0
\(133\) −1.39757 −0.121184
\(134\) 0 0
\(135\) −1.38119 −0.118874
\(136\) 0 0
\(137\) −7.36980 −0.629645 −0.314822 0.949151i \(-0.601945\pi\)
−0.314822 + 0.949151i \(0.601945\pi\)
\(138\) 0 0
\(139\) −15.4085 −1.30693 −0.653465 0.756957i \(-0.726685\pi\)
−0.653465 + 0.756957i \(0.726685\pi\)
\(140\) 0 0
\(141\) 6.20376 0.522450
\(142\) 0 0
\(143\) −4.65177 −0.389001
\(144\) 0 0
\(145\) −3.08097 −0.255861
\(146\) 0 0
\(147\) −6.93235 −0.571770
\(148\) 0 0
\(149\) −19.7078 −1.61452 −0.807261 0.590194i \(-0.799051\pi\)
−0.807261 + 0.590194i \(0.799051\pi\)
\(150\) 0 0
\(151\) 6.39372 0.520314 0.260157 0.965566i \(-0.416226\pi\)
0.260157 + 0.965566i \(0.416226\pi\)
\(152\) 0 0
\(153\) −4.24502 −0.343189
\(154\) 0 0
\(155\) −13.2902 −1.06749
\(156\) 0 0
\(157\) 11.6913 0.933070 0.466535 0.884503i \(-0.345502\pi\)
0.466535 + 0.884503i \(0.345502\pi\)
\(158\) 0 0
\(159\) 12.3984 0.983255
\(160\) 0 0
\(161\) −1.45756 −0.114872
\(162\) 0 0
\(163\) −9.58622 −0.750851 −0.375425 0.926853i \(-0.622503\pi\)
−0.375425 + 0.926853i \(0.622503\pi\)
\(164\) 0 0
\(165\) −4.94329 −0.384834
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −11.3107 −0.870052
\(170\) 0 0
\(171\) −5.37321 −0.410900
\(172\) 0 0
\(173\) 25.1843 1.91472 0.957362 0.288890i \(-0.0932860\pi\)
0.957362 + 0.288890i \(0.0932860\pi\)
\(174\) 0 0
\(175\) −0.804308 −0.0607999
\(176\) 0 0
\(177\) −3.18358 −0.239293
\(178\) 0 0
\(179\) 0.125279 0.00936380 0.00468190 0.999989i \(-0.498510\pi\)
0.00468190 + 0.999989i \(0.498510\pi\)
\(180\) 0 0
\(181\) −15.0014 −1.11504 −0.557522 0.830162i \(-0.688248\pi\)
−0.557522 + 0.830162i \(0.688248\pi\)
\(182\) 0 0
\(183\) −6.40971 −0.473819
\(184\) 0 0
\(185\) −0.111725 −0.00821419
\(186\) 0 0
\(187\) −15.1929 −1.11102
\(188\) 0 0
\(189\) 0.260099 0.0189194
\(190\) 0 0
\(191\) 4.07344 0.294744 0.147372 0.989081i \(-0.452919\pi\)
0.147372 + 0.989081i \(0.452919\pi\)
\(192\) 0 0
\(193\) 11.2459 0.809496 0.404748 0.914428i \(-0.367359\pi\)
0.404748 + 0.914428i \(0.367359\pi\)
\(194\) 0 0
\(195\) 1.79518 0.128556
\(196\) 0 0
\(197\) −5.88075 −0.418986 −0.209493 0.977810i \(-0.567181\pi\)
−0.209493 + 0.977810i \(0.567181\pi\)
\(198\) 0 0
\(199\) −19.8895 −1.40993 −0.704963 0.709244i \(-0.749037\pi\)
−0.704963 + 0.709244i \(0.749037\pi\)
\(200\) 0 0
\(201\) −2.58992 −0.182679
\(202\) 0 0
\(203\) 0.580193 0.0407216
\(204\) 0 0
\(205\) −5.92547 −0.413853
\(206\) 0 0
\(207\) −5.60388 −0.389496
\(208\) 0 0
\(209\) −19.2308 −1.33022
\(210\) 0 0
\(211\) −14.3807 −0.990008 −0.495004 0.868891i \(-0.664833\pi\)
−0.495004 + 0.868891i \(0.664833\pi\)
\(212\) 0 0
\(213\) −10.9927 −0.753209
\(214\) 0 0
\(215\) −14.5158 −0.989969
\(216\) 0 0
\(217\) 2.50274 0.169897
\(218\) 0 0
\(219\) 11.2300 0.758852
\(220\) 0 0
\(221\) 5.51741 0.371141
\(222\) 0 0
\(223\) 28.9444 1.93826 0.969131 0.246546i \(-0.0792958\pi\)
0.969131 + 0.246546i \(0.0792958\pi\)
\(224\) 0 0
\(225\) −3.09232 −0.206154
\(226\) 0 0
\(227\) −20.1056 −1.33445 −0.667227 0.744855i \(-0.732519\pi\)
−0.667227 + 0.744855i \(0.732519\pi\)
\(228\) 0 0
\(229\) 26.3261 1.73968 0.869838 0.493337i \(-0.164223\pi\)
0.869838 + 0.493337i \(0.164223\pi\)
\(230\) 0 0
\(231\) 0.930895 0.0612484
\(232\) 0 0
\(233\) 8.10123 0.530729 0.265365 0.964148i \(-0.414508\pi\)
0.265365 + 0.964148i \(0.414508\pi\)
\(234\) 0 0
\(235\) −8.56856 −0.558951
\(236\) 0 0
\(237\) 11.9509 0.776294
\(238\) 0 0
\(239\) 13.5900 0.879062 0.439531 0.898227i \(-0.355145\pi\)
0.439531 + 0.898227i \(0.355145\pi\)
\(240\) 0 0
\(241\) 25.7782 1.66052 0.830261 0.557375i \(-0.188191\pi\)
0.830261 + 0.557375i \(0.188191\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 9.57488 0.611717
\(246\) 0 0
\(247\) 6.98377 0.444366
\(248\) 0 0
\(249\) −4.33550 −0.274751
\(250\) 0 0
\(251\) −11.4113 −0.720274 −0.360137 0.932899i \(-0.617270\pi\)
−0.360137 + 0.932899i \(0.617270\pi\)
\(252\) 0 0
\(253\) −20.0563 −1.26093
\(254\) 0 0
\(255\) 5.86317 0.367166
\(256\) 0 0
\(257\) 7.63267 0.476113 0.238056 0.971251i \(-0.423490\pi\)
0.238056 + 0.971251i \(0.423490\pi\)
\(258\) 0 0
\(259\) 0.0210395 0.00130733
\(260\) 0 0
\(261\) 2.23067 0.138075
\(262\) 0 0
\(263\) −12.6577 −0.780510 −0.390255 0.920707i \(-0.627613\pi\)
−0.390255 + 0.920707i \(0.627613\pi\)
\(264\) 0 0
\(265\) −17.1245 −1.05195
\(266\) 0 0
\(267\) 8.61186 0.527037
\(268\) 0 0
\(269\) −0.272939 −0.0166414 −0.00832070 0.999965i \(-0.502649\pi\)
−0.00832070 + 0.999965i \(0.502649\pi\)
\(270\) 0 0
\(271\) −3.48099 −0.211455 −0.105727 0.994395i \(-0.533717\pi\)
−0.105727 + 0.994395i \(0.533717\pi\)
\(272\) 0 0
\(273\) −0.338060 −0.0204603
\(274\) 0 0
\(275\) −11.0674 −0.667391
\(276\) 0 0
\(277\) 9.17422 0.551225 0.275613 0.961269i \(-0.411119\pi\)
0.275613 + 0.961269i \(0.411119\pi\)
\(278\) 0 0
\(279\) 9.62228 0.576071
\(280\) 0 0
\(281\) 27.2804 1.62741 0.813706 0.581277i \(-0.197447\pi\)
0.813706 + 0.581277i \(0.197447\pi\)
\(282\) 0 0
\(283\) −15.4054 −0.915759 −0.457879 0.889014i \(-0.651391\pi\)
−0.457879 + 0.889014i \(0.651391\pi\)
\(284\) 0 0
\(285\) 7.42142 0.439607
\(286\) 0 0
\(287\) 1.11586 0.0658669
\(288\) 0 0
\(289\) 1.02017 0.0600100
\(290\) 0 0
\(291\) 0.0718231 0.00421034
\(292\) 0 0
\(293\) 15.4315 0.901519 0.450759 0.892645i \(-0.351153\pi\)
0.450759 + 0.892645i \(0.351153\pi\)
\(294\) 0 0
\(295\) 4.39713 0.256011
\(296\) 0 0
\(297\) 3.57901 0.207675
\(298\) 0 0
\(299\) 7.28357 0.421220
\(300\) 0 0
\(301\) 2.73354 0.157559
\(302\) 0 0
\(303\) 17.9592 1.03173
\(304\) 0 0
\(305\) 8.85302 0.506922
\(306\) 0 0
\(307\) −8.51510 −0.485982 −0.242991 0.970029i \(-0.578129\pi\)
−0.242991 + 0.970029i \(0.578129\pi\)
\(308\) 0 0
\(309\) −0.277767 −0.0158016
\(310\) 0 0
\(311\) −23.1383 −1.31205 −0.656026 0.754739i \(-0.727764\pi\)
−0.656026 + 0.754739i \(0.727764\pi\)
\(312\) 0 0
\(313\) 16.5786 0.937079 0.468539 0.883443i \(-0.344780\pi\)
0.468539 + 0.883443i \(0.344780\pi\)
\(314\) 0 0
\(315\) −0.359246 −0.0202412
\(316\) 0 0
\(317\) 15.1097 0.848645 0.424322 0.905511i \(-0.360512\pi\)
0.424322 + 0.905511i \(0.360512\pi\)
\(318\) 0 0
\(319\) 7.98357 0.446994
\(320\) 0 0
\(321\) 5.01695 0.280019
\(322\) 0 0
\(323\) 22.8094 1.26915
\(324\) 0 0
\(325\) 4.01920 0.222945
\(326\) 0 0
\(327\) 15.0343 0.831398
\(328\) 0 0
\(329\) 1.61359 0.0889600
\(330\) 0 0
\(331\) −21.7163 −1.19364 −0.596818 0.802377i \(-0.703568\pi\)
−0.596818 + 0.802377i \(0.703568\pi\)
\(332\) 0 0
\(333\) 0.0808905 0.00443277
\(334\) 0 0
\(335\) 3.57716 0.195441
\(336\) 0 0
\(337\) −31.3088 −1.70550 −0.852750 0.522319i \(-0.825067\pi\)
−0.852750 + 0.522319i \(0.825067\pi\)
\(338\) 0 0
\(339\) 10.2708 0.557835
\(340\) 0 0
\(341\) 34.4382 1.86493
\(342\) 0 0
\(343\) −3.62379 −0.195666
\(344\) 0 0
\(345\) 7.74001 0.416708
\(346\) 0 0
\(347\) 1.35131 0.0725419 0.0362710 0.999342i \(-0.488452\pi\)
0.0362710 + 0.999342i \(0.488452\pi\)
\(348\) 0 0
\(349\) −0.0510230 −0.00273120 −0.00136560 0.999999i \(-0.500435\pi\)
−0.00136560 + 0.999999i \(0.500435\pi\)
\(350\) 0 0
\(351\) −1.29974 −0.0693749
\(352\) 0 0
\(353\) 19.0639 1.01467 0.507334 0.861749i \(-0.330631\pi\)
0.507334 + 0.861749i \(0.330631\pi\)
\(354\) 0 0
\(355\) 15.1830 0.805831
\(356\) 0 0
\(357\) −1.10412 −0.0584364
\(358\) 0 0
\(359\) 20.9791 1.10724 0.553618 0.832771i \(-0.313247\pi\)
0.553618 + 0.832771i \(0.313247\pi\)
\(360\) 0 0
\(361\) 9.87140 0.519547
\(362\) 0 0
\(363\) 1.80930 0.0949634
\(364\) 0 0
\(365\) −15.5107 −0.811869
\(366\) 0 0
\(367\) 21.3923 1.11667 0.558335 0.829616i \(-0.311440\pi\)
0.558335 + 0.829616i \(0.311440\pi\)
\(368\) 0 0
\(369\) 4.29012 0.223335
\(370\) 0 0
\(371\) 3.22480 0.167423
\(372\) 0 0
\(373\) 35.6765 1.84726 0.923628 0.383289i \(-0.125209\pi\)
0.923628 + 0.383289i \(0.125209\pi\)
\(374\) 0 0
\(375\) 11.1770 0.577179
\(376\) 0 0
\(377\) −2.89928 −0.149321
\(378\) 0 0
\(379\) −2.77234 −0.142405 −0.0712027 0.997462i \(-0.522684\pi\)
−0.0712027 + 0.997462i \(0.522684\pi\)
\(380\) 0 0
\(381\) 3.02975 0.155219
\(382\) 0 0
\(383\) −22.0347 −1.12592 −0.562960 0.826484i \(-0.690337\pi\)
−0.562960 + 0.826484i \(0.690337\pi\)
\(384\) 0 0
\(385\) −1.28574 −0.0655275
\(386\) 0 0
\(387\) 10.5096 0.534235
\(388\) 0 0
\(389\) 17.7239 0.898635 0.449318 0.893372i \(-0.351667\pi\)
0.449318 + 0.893372i \(0.351667\pi\)
\(390\) 0 0
\(391\) 23.7886 1.20304
\(392\) 0 0
\(393\) 17.2097 0.868112
\(394\) 0 0
\(395\) −16.5064 −0.830529
\(396\) 0 0
\(397\) −24.1866 −1.21389 −0.606944 0.794744i \(-0.707605\pi\)
−0.606944 + 0.794744i \(0.707605\pi\)
\(398\) 0 0
\(399\) −1.39757 −0.0699658
\(400\) 0 0
\(401\) −14.3128 −0.714748 −0.357374 0.933961i \(-0.616328\pi\)
−0.357374 + 0.933961i \(0.616328\pi\)
\(402\) 0 0
\(403\) −12.5064 −0.622990
\(404\) 0 0
\(405\) −1.38119 −0.0686318
\(406\) 0 0
\(407\) 0.289508 0.0143504
\(408\) 0 0
\(409\) −21.1631 −1.04645 −0.523223 0.852196i \(-0.675271\pi\)
−0.523223 + 0.852196i \(0.675271\pi\)
\(410\) 0 0
\(411\) −7.36980 −0.363526
\(412\) 0 0
\(413\) −0.828046 −0.0407455
\(414\) 0 0
\(415\) 5.98814 0.293946
\(416\) 0 0
\(417\) −15.4085 −0.754556
\(418\) 0 0
\(419\) 19.8760 0.971004 0.485502 0.874235i \(-0.338637\pi\)
0.485502 + 0.874235i \(0.338637\pi\)
\(420\) 0 0
\(421\) −31.1319 −1.51728 −0.758639 0.651511i \(-0.774135\pi\)
−0.758639 + 0.651511i \(0.774135\pi\)
\(422\) 0 0
\(423\) 6.20376 0.301637
\(424\) 0 0
\(425\) 13.1269 0.636750
\(426\) 0 0
\(427\) −1.66716 −0.0806794
\(428\) 0 0
\(429\) −4.65177 −0.224590
\(430\) 0 0
\(431\) 21.1346 1.01802 0.509008 0.860762i \(-0.330012\pi\)
0.509008 + 0.860762i \(0.330012\pi\)
\(432\) 0 0
\(433\) −28.1322 −1.35195 −0.675974 0.736926i \(-0.736277\pi\)
−0.675974 + 0.736926i \(0.736277\pi\)
\(434\) 0 0
\(435\) −3.08097 −0.147721
\(436\) 0 0
\(437\) 30.1108 1.44040
\(438\) 0 0
\(439\) 29.5191 1.40887 0.704435 0.709769i \(-0.251201\pi\)
0.704435 + 0.709769i \(0.251201\pi\)
\(440\) 0 0
\(441\) −6.93235 −0.330112
\(442\) 0 0
\(443\) 29.2445 1.38945 0.694724 0.719276i \(-0.255526\pi\)
0.694724 + 0.719276i \(0.255526\pi\)
\(444\) 0 0
\(445\) −11.8946 −0.563859
\(446\) 0 0
\(447\) −19.7078 −0.932145
\(448\) 0 0
\(449\) 31.0316 1.46447 0.732236 0.681051i \(-0.238477\pi\)
0.732236 + 0.681051i \(0.238477\pi\)
\(450\) 0 0
\(451\) 15.3544 0.723010
\(452\) 0 0
\(453\) 6.39372 0.300403
\(454\) 0 0
\(455\) 0.466925 0.0218898
\(456\) 0 0
\(457\) −1.48784 −0.0695981 −0.0347991 0.999394i \(-0.511079\pi\)
−0.0347991 + 0.999394i \(0.511079\pi\)
\(458\) 0 0
\(459\) −4.24502 −0.198140
\(460\) 0 0
\(461\) −5.65328 −0.263299 −0.131650 0.991296i \(-0.542027\pi\)
−0.131650 + 0.991296i \(0.542027\pi\)
\(462\) 0 0
\(463\) −10.1653 −0.472421 −0.236210 0.971702i \(-0.575905\pi\)
−0.236210 + 0.971702i \(0.575905\pi\)
\(464\) 0 0
\(465\) −13.2902 −0.616318
\(466\) 0 0
\(467\) 17.3327 0.802062 0.401031 0.916064i \(-0.368652\pi\)
0.401031 + 0.916064i \(0.368652\pi\)
\(468\) 0 0
\(469\) −0.673634 −0.0311055
\(470\) 0 0
\(471\) 11.6913 0.538708
\(472\) 0 0
\(473\) 37.6141 1.72950
\(474\) 0 0
\(475\) 16.6157 0.762379
\(476\) 0 0
\(477\) 12.3984 0.567683
\(478\) 0 0
\(479\) 32.5368 1.48664 0.743322 0.668934i \(-0.233249\pi\)
0.743322 + 0.668934i \(0.233249\pi\)
\(480\) 0 0
\(481\) −0.105136 −0.00479381
\(482\) 0 0
\(483\) −1.45756 −0.0663213
\(484\) 0 0
\(485\) −0.0992013 −0.00450450
\(486\) 0 0
\(487\) −20.4665 −0.927426 −0.463713 0.885985i \(-0.653483\pi\)
−0.463713 + 0.885985i \(0.653483\pi\)
\(488\) 0 0
\(489\) −9.58622 −0.433504
\(490\) 0 0
\(491\) 34.2008 1.54346 0.771730 0.635951i \(-0.219392\pi\)
0.771730 + 0.635951i \(0.219392\pi\)
\(492\) 0 0
\(493\) −9.46921 −0.426472
\(494\) 0 0
\(495\) −4.94329 −0.222184
\(496\) 0 0
\(497\) −2.85919 −0.128252
\(498\) 0 0
\(499\) −19.6637 −0.880269 −0.440134 0.897932i \(-0.645069\pi\)
−0.440134 + 0.897932i \(0.645069\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 38.2959 1.70753 0.853764 0.520660i \(-0.174314\pi\)
0.853764 + 0.520660i \(0.174314\pi\)
\(504\) 0 0
\(505\) −24.8050 −1.10381
\(506\) 0 0
\(507\) −11.3107 −0.502325
\(508\) 0 0
\(509\) 27.9600 1.23931 0.619653 0.784876i \(-0.287273\pi\)
0.619653 + 0.784876i \(0.287273\pi\)
\(510\) 0 0
\(511\) 2.92091 0.129213
\(512\) 0 0
\(513\) −5.37321 −0.237233
\(514\) 0 0
\(515\) 0.383648 0.0169056
\(516\) 0 0
\(517\) 22.2033 0.976499
\(518\) 0 0
\(519\) 25.1843 1.10547
\(520\) 0 0
\(521\) −4.32725 −0.189580 −0.0947900 0.995497i \(-0.530218\pi\)
−0.0947900 + 0.995497i \(0.530218\pi\)
\(522\) 0 0
\(523\) −4.71291 −0.206081 −0.103041 0.994677i \(-0.532857\pi\)
−0.103041 + 0.994677i \(0.532857\pi\)
\(524\) 0 0
\(525\) −0.804308 −0.0351029
\(526\) 0 0
\(527\) −40.8467 −1.77931
\(528\) 0 0
\(529\) 8.40344 0.365367
\(530\) 0 0
\(531\) −3.18358 −0.138156
\(532\) 0 0
\(533\) −5.57604 −0.241525
\(534\) 0 0
\(535\) −6.92936 −0.299582
\(536\) 0 0
\(537\) 0.125279 0.00540619
\(538\) 0 0
\(539\) −24.8109 −1.06868
\(540\) 0 0
\(541\) −24.6119 −1.05815 −0.529075 0.848575i \(-0.677461\pi\)
−0.529075 + 0.848575i \(0.677461\pi\)
\(542\) 0 0
\(543\) −15.0014 −0.643771
\(544\) 0 0
\(545\) −20.7652 −0.889483
\(546\) 0 0
\(547\) −29.3102 −1.25321 −0.626607 0.779335i \(-0.715557\pi\)
−0.626607 + 0.779335i \(0.715557\pi\)
\(548\) 0 0
\(549\) −6.40971 −0.273560
\(550\) 0 0
\(551\) −11.9858 −0.510614
\(552\) 0 0
\(553\) 3.10841 0.132183
\(554\) 0 0
\(555\) −0.111725 −0.00474247
\(556\) 0 0
\(557\) −32.1370 −1.36169 −0.680844 0.732428i \(-0.738387\pi\)
−0.680844 + 0.732428i \(0.738387\pi\)
\(558\) 0 0
\(559\) −13.6598 −0.577747
\(560\) 0 0
\(561\) −15.1929 −0.641447
\(562\) 0 0
\(563\) −36.8692 −1.55385 −0.776926 0.629591i \(-0.783222\pi\)
−0.776926 + 0.629591i \(0.783222\pi\)
\(564\) 0 0
\(565\) −14.1860 −0.596808
\(566\) 0 0
\(567\) 0.260099 0.0109231
\(568\) 0 0
\(569\) 39.4146 1.65234 0.826172 0.563418i \(-0.190514\pi\)
0.826172 + 0.563418i \(0.190514\pi\)
\(570\) 0 0
\(571\) −21.3581 −0.893809 −0.446905 0.894582i \(-0.647474\pi\)
−0.446905 + 0.894582i \(0.647474\pi\)
\(572\) 0 0
\(573\) 4.07344 0.170170
\(574\) 0 0
\(575\) 17.3290 0.722668
\(576\) 0 0
\(577\) 36.0651 1.50141 0.750704 0.660639i \(-0.229714\pi\)
0.750704 + 0.660639i \(0.229714\pi\)
\(578\) 0 0
\(579\) 11.2459 0.467363
\(580\) 0 0
\(581\) −1.12766 −0.0467831
\(582\) 0 0
\(583\) 44.3739 1.83778
\(584\) 0 0
\(585\) 1.79518 0.0742217
\(586\) 0 0
\(587\) −6.65047 −0.274494 −0.137247 0.990537i \(-0.543825\pi\)
−0.137247 + 0.990537i \(0.543825\pi\)
\(588\) 0 0
\(589\) −51.7025 −2.13037
\(590\) 0 0
\(591\) −5.88075 −0.241902
\(592\) 0 0
\(593\) 0.0351096 0.00144178 0.000720889 1.00000i \(-0.499771\pi\)
0.000720889 1.00000i \(0.499771\pi\)
\(594\) 0 0
\(595\) 1.52500 0.0625190
\(596\) 0 0
\(597\) −19.8895 −0.814022
\(598\) 0 0
\(599\) 29.1516 1.19110 0.595550 0.803318i \(-0.296934\pi\)
0.595550 + 0.803318i \(0.296934\pi\)
\(600\) 0 0
\(601\) 41.1130 1.67703 0.838517 0.544876i \(-0.183423\pi\)
0.838517 + 0.544876i \(0.183423\pi\)
\(602\) 0 0
\(603\) −2.58992 −0.105470
\(604\) 0 0
\(605\) −2.49898 −0.101598
\(606\) 0 0
\(607\) −5.72077 −0.232199 −0.116099 0.993238i \(-0.537039\pi\)
−0.116099 + 0.993238i \(0.537039\pi\)
\(608\) 0 0
\(609\) 0.580193 0.0235106
\(610\) 0 0
\(611\) −8.06326 −0.326204
\(612\) 0 0
\(613\) 5.16466 0.208599 0.104299 0.994546i \(-0.466740\pi\)
0.104299 + 0.994546i \(0.466740\pi\)
\(614\) 0 0
\(615\) −5.92547 −0.238938
\(616\) 0 0
\(617\) −35.1409 −1.41472 −0.707360 0.706854i \(-0.750114\pi\)
−0.707360 + 0.706854i \(0.750114\pi\)
\(618\) 0 0
\(619\) 22.6982 0.912318 0.456159 0.889898i \(-0.349225\pi\)
0.456159 + 0.889898i \(0.349225\pi\)
\(620\) 0 0
\(621\) −5.60388 −0.224876
\(622\) 0 0
\(623\) 2.23993 0.0897411
\(624\) 0 0
\(625\) 0.0240062 0.000960247 0
\(626\) 0 0
\(627\) −19.2308 −0.768003
\(628\) 0 0
\(629\) −0.343382 −0.0136915
\(630\) 0 0
\(631\) 35.0964 1.39717 0.698583 0.715529i \(-0.253814\pi\)
0.698583 + 0.715529i \(0.253814\pi\)
\(632\) 0 0
\(633\) −14.3807 −0.571581
\(634\) 0 0
\(635\) −4.18465 −0.166063
\(636\) 0 0
\(637\) 9.01024 0.356999
\(638\) 0 0
\(639\) −10.9927 −0.434865
\(640\) 0 0
\(641\) 5.49562 0.217064 0.108532 0.994093i \(-0.465385\pi\)
0.108532 + 0.994093i \(0.465385\pi\)
\(642\) 0 0
\(643\) 30.9837 1.22188 0.610940 0.791677i \(-0.290792\pi\)
0.610940 + 0.791677i \(0.290792\pi\)
\(644\) 0 0
\(645\) −14.5158 −0.571559
\(646\) 0 0
\(647\) −15.3651 −0.604065 −0.302033 0.953298i \(-0.597665\pi\)
−0.302033 + 0.953298i \(0.597665\pi\)
\(648\) 0 0
\(649\) −11.3941 −0.447256
\(650\) 0 0
\(651\) 2.50274 0.0980902
\(652\) 0 0
\(653\) −49.3594 −1.93158 −0.965791 0.259321i \(-0.916501\pi\)
−0.965791 + 0.259321i \(0.916501\pi\)
\(654\) 0 0
\(655\) −23.7698 −0.928762
\(656\) 0 0
\(657\) 11.2300 0.438124
\(658\) 0 0
\(659\) 18.8524 0.734385 0.367192 0.930145i \(-0.380319\pi\)
0.367192 + 0.930145i \(0.380319\pi\)
\(660\) 0 0
\(661\) −36.9080 −1.43556 −0.717778 0.696272i \(-0.754841\pi\)
−0.717778 + 0.696272i \(0.754841\pi\)
\(662\) 0 0
\(663\) 5.51741 0.214278
\(664\) 0 0
\(665\) 1.93030 0.0748539
\(666\) 0 0
\(667\) −12.5004 −0.484017
\(668\) 0 0
\(669\) 28.9444 1.11906
\(670\) 0 0
\(671\) −22.9404 −0.885604
\(672\) 0 0
\(673\) −4.15105 −0.160011 −0.0800057 0.996794i \(-0.525494\pi\)
−0.0800057 + 0.996794i \(0.525494\pi\)
\(674\) 0 0
\(675\) −3.09232 −0.119023
\(676\) 0 0
\(677\) −45.6659 −1.75508 −0.877541 0.479502i \(-0.840817\pi\)
−0.877541 + 0.479502i \(0.840817\pi\)
\(678\) 0 0
\(679\) 0.0186811 0.000716915 0
\(680\) 0 0
\(681\) −20.1056 −0.770447
\(682\) 0 0
\(683\) −34.4197 −1.31704 −0.658518 0.752565i \(-0.728816\pi\)
−0.658518 + 0.752565i \(0.728816\pi\)
\(684\) 0 0
\(685\) 10.1791 0.388923
\(686\) 0 0
\(687\) 26.3261 1.00440
\(688\) 0 0
\(689\) −16.1146 −0.613919
\(690\) 0 0
\(691\) 28.3874 1.07991 0.539954 0.841694i \(-0.318441\pi\)
0.539954 + 0.841694i \(0.318441\pi\)
\(692\) 0 0
\(693\) 0.930895 0.0353618
\(694\) 0 0
\(695\) 21.2820 0.807273
\(696\) 0 0
\(697\) −18.2117 −0.689815
\(698\) 0 0
\(699\) 8.10123 0.306417
\(700\) 0 0
\(701\) 20.7096 0.782189 0.391095 0.920350i \(-0.372096\pi\)
0.391095 + 0.920350i \(0.372096\pi\)
\(702\) 0 0
\(703\) −0.434642 −0.0163928
\(704\) 0 0
\(705\) −8.56856 −0.322711
\(706\) 0 0
\(707\) 4.67115 0.175677
\(708\) 0 0
\(709\) 12.3505 0.463833 0.231917 0.972736i \(-0.425500\pi\)
0.231917 + 0.972736i \(0.425500\pi\)
\(710\) 0 0
\(711\) 11.9509 0.448193
\(712\) 0 0
\(713\) −53.9221 −2.01940
\(714\) 0 0
\(715\) 6.42498 0.240281
\(716\) 0 0
\(717\) 13.5900 0.507527
\(718\) 0 0
\(719\) 40.7997 1.52157 0.760786 0.649003i \(-0.224814\pi\)
0.760786 + 0.649003i \(0.224814\pi\)
\(720\) 0 0
\(721\) −0.0722468 −0.00269061
\(722\) 0 0
\(723\) 25.7782 0.958703
\(724\) 0 0
\(725\) −6.89793 −0.256183
\(726\) 0 0
\(727\) −25.3456 −0.940015 −0.470007 0.882662i \(-0.655749\pi\)
−0.470007 + 0.882662i \(0.655749\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −44.6136 −1.65009
\(732\) 0 0
\(733\) −2.51219 −0.0927899 −0.0463949 0.998923i \(-0.514773\pi\)
−0.0463949 + 0.998923i \(0.514773\pi\)
\(734\) 0 0
\(735\) 9.57488 0.353175
\(736\) 0 0
\(737\) −9.26933 −0.341440
\(738\) 0 0
\(739\) −35.0409 −1.28900 −0.644499 0.764605i \(-0.722934\pi\)
−0.644499 + 0.764605i \(0.722934\pi\)
\(740\) 0 0
\(741\) 6.98377 0.256555
\(742\) 0 0
\(743\) −11.5421 −0.423440 −0.211720 0.977330i \(-0.567906\pi\)
−0.211720 + 0.977330i \(0.567906\pi\)
\(744\) 0 0
\(745\) 27.2201 0.997269
\(746\) 0 0
\(747\) −4.33550 −0.158628
\(748\) 0 0
\(749\) 1.30490 0.0476801
\(750\) 0 0
\(751\) 37.9598 1.38517 0.692586 0.721336i \(-0.256471\pi\)
0.692586 + 0.721336i \(0.256471\pi\)
\(752\) 0 0
\(753\) −11.4113 −0.415851
\(754\) 0 0
\(755\) −8.83094 −0.321391
\(756\) 0 0
\(757\) 8.58630 0.312074 0.156037 0.987751i \(-0.450128\pi\)
0.156037 + 0.987751i \(0.450128\pi\)
\(758\) 0 0
\(759\) −20.0563 −0.727998
\(760\) 0 0
\(761\) −1.05601 −0.0382802 −0.0191401 0.999817i \(-0.506093\pi\)
−0.0191401 + 0.999817i \(0.506093\pi\)
\(762\) 0 0
\(763\) 3.91040 0.141566
\(764\) 0 0
\(765\) 5.86317 0.211983
\(766\) 0 0
\(767\) 4.13782 0.149408
\(768\) 0 0
\(769\) 42.6410 1.53767 0.768836 0.639446i \(-0.220836\pi\)
0.768836 + 0.639446i \(0.220836\pi\)
\(770\) 0 0
\(771\) 7.63267 0.274884
\(772\) 0 0
\(773\) 32.7347 1.17738 0.588692 0.808357i \(-0.299643\pi\)
0.588692 + 0.808357i \(0.299643\pi\)
\(774\) 0 0
\(775\) −29.7551 −1.06884
\(776\) 0 0
\(777\) 0.0210395 0.000754789 0
\(778\) 0 0
\(779\) −23.0517 −0.825914
\(780\) 0 0
\(781\) −39.3430 −1.40780
\(782\) 0 0
\(783\) 2.23067 0.0797175
\(784\) 0 0
\(785\) −16.1479 −0.576345
\(786\) 0 0
\(787\) −38.4271 −1.36978 −0.684890 0.728647i \(-0.740150\pi\)
−0.684890 + 0.728647i \(0.740150\pi\)
\(788\) 0 0
\(789\) −12.6577 −0.450627
\(790\) 0 0
\(791\) 2.67143 0.0949851
\(792\) 0 0
\(793\) 8.33094 0.295840
\(794\) 0 0
\(795\) −17.1245 −0.607344
\(796\) 0 0
\(797\) 46.5485 1.64883 0.824416 0.565985i \(-0.191504\pi\)
0.824416 + 0.565985i \(0.191504\pi\)
\(798\) 0 0
\(799\) −26.3350 −0.931667
\(800\) 0 0
\(801\) 8.61186 0.304285
\(802\) 0 0
\(803\) 40.1922 1.41835
\(804\) 0 0
\(805\) 2.01317 0.0709548
\(806\) 0 0
\(807\) −0.272939 −0.00960791
\(808\) 0 0
\(809\) 38.3586 1.34862 0.674308 0.738450i \(-0.264442\pi\)
0.674308 + 0.738450i \(0.264442\pi\)
\(810\) 0 0
\(811\) 35.3307 1.24063 0.620314 0.784354i \(-0.287005\pi\)
0.620314 + 0.784354i \(0.287005\pi\)
\(812\) 0 0
\(813\) −3.48099 −0.122084
\(814\) 0 0
\(815\) 13.2404 0.463790
\(816\) 0 0
\(817\) −56.4705 −1.97565
\(818\) 0 0
\(819\) −0.338060 −0.0118128
\(820\) 0 0
\(821\) −6.32816 −0.220854 −0.110427 0.993884i \(-0.535222\pi\)
−0.110427 + 0.993884i \(0.535222\pi\)
\(822\) 0 0
\(823\) −13.5763 −0.473239 −0.236620 0.971602i \(-0.576040\pi\)
−0.236620 + 0.971602i \(0.576040\pi\)
\(824\) 0 0
\(825\) −11.0674 −0.385318
\(826\) 0 0
\(827\) 9.00252 0.313048 0.156524 0.987674i \(-0.449971\pi\)
0.156524 + 0.987674i \(0.449971\pi\)
\(828\) 0 0
\(829\) 26.7081 0.927610 0.463805 0.885937i \(-0.346484\pi\)
0.463805 + 0.885937i \(0.346484\pi\)
\(830\) 0 0
\(831\) 9.17422 0.318250
\(832\) 0 0
\(833\) 29.4279 1.01962
\(834\) 0 0
\(835\) 1.38119 0.0477980
\(836\) 0 0
\(837\) 9.62228 0.332595
\(838\) 0 0
\(839\) −38.2297 −1.31983 −0.659917 0.751338i \(-0.729409\pi\)
−0.659917 + 0.751338i \(0.729409\pi\)
\(840\) 0 0
\(841\) −24.0241 −0.828418
\(842\) 0 0
\(843\) 27.2804 0.939587
\(844\) 0 0
\(845\) 15.6222 0.537420
\(846\) 0 0
\(847\) 0.470595 0.0161699
\(848\) 0 0
\(849\) −15.4054 −0.528713
\(850\) 0 0
\(851\) −0.453301 −0.0155389
\(852\) 0 0
\(853\) −27.6328 −0.946129 −0.473065 0.881028i \(-0.656852\pi\)
−0.473065 + 0.881028i \(0.656852\pi\)
\(854\) 0 0
\(855\) 7.42142 0.253807
\(856\) 0 0
\(857\) −47.1251 −1.60976 −0.804882 0.593436i \(-0.797771\pi\)
−0.804882 + 0.593436i \(0.797771\pi\)
\(858\) 0 0
\(859\) 49.2154 1.67921 0.839604 0.543199i \(-0.182787\pi\)
0.839604 + 0.543199i \(0.182787\pi\)
\(860\) 0 0
\(861\) 1.11586 0.0380283
\(862\) 0 0
\(863\) −23.9655 −0.815795 −0.407897 0.913028i \(-0.633738\pi\)
−0.407897 + 0.913028i \(0.633738\pi\)
\(864\) 0 0
\(865\) −34.7842 −1.18270
\(866\) 0 0
\(867\) 1.02017 0.0346468
\(868\) 0 0
\(869\) 42.7723 1.45095
\(870\) 0 0
\(871\) 3.36621 0.114060
\(872\) 0 0
\(873\) 0.0718231 0.00243084
\(874\) 0 0
\(875\) 2.90713 0.0982789
\(876\) 0 0
\(877\) 6.72694 0.227152 0.113576 0.993529i \(-0.463769\pi\)
0.113576 + 0.993529i \(0.463769\pi\)
\(878\) 0 0
\(879\) 15.4315 0.520492
\(880\) 0 0
\(881\) −2.21204 −0.0745254 −0.0372627 0.999306i \(-0.511864\pi\)
−0.0372627 + 0.999306i \(0.511864\pi\)
\(882\) 0 0
\(883\) −40.9253 −1.37725 −0.688623 0.725119i \(-0.741785\pi\)
−0.688623 + 0.725119i \(0.741785\pi\)
\(884\) 0 0
\(885\) 4.39713 0.147808
\(886\) 0 0
\(887\) 2.67010 0.0896532 0.0448266 0.998995i \(-0.485726\pi\)
0.0448266 + 0.998995i \(0.485726\pi\)
\(888\) 0 0
\(889\) 0.788033 0.0264298
\(890\) 0 0
\(891\) 3.57901 0.119901
\(892\) 0 0
\(893\) −33.3341 −1.11548
\(894\) 0 0
\(895\) −0.173034 −0.00578389
\(896\) 0 0
\(897\) 7.28357 0.243191
\(898\) 0 0
\(899\) 21.4641 0.715868
\(900\) 0 0
\(901\) −52.6313 −1.75340
\(902\) 0 0
\(903\) 2.73354 0.0909666
\(904\) 0 0
\(905\) 20.7198 0.688748
\(906\) 0 0
\(907\) 31.5598 1.04793 0.523963 0.851741i \(-0.324453\pi\)
0.523963 + 0.851741i \(0.324453\pi\)
\(908\) 0 0
\(909\) 17.9592 0.595667
\(910\) 0 0
\(911\) −1.18983 −0.0394210 −0.0197105 0.999806i \(-0.506274\pi\)
−0.0197105 + 0.999806i \(0.506274\pi\)
\(912\) 0 0
\(913\) −15.5168 −0.513530
\(914\) 0 0
\(915\) 8.85302 0.292672
\(916\) 0 0
\(917\) 4.47621 0.147817
\(918\) 0 0
\(919\) 18.7543 0.618648 0.309324 0.950957i \(-0.399897\pi\)
0.309324 + 0.950957i \(0.399897\pi\)
\(920\) 0 0
\(921\) −8.51510 −0.280582
\(922\) 0 0
\(923\) 14.2877 0.470284
\(924\) 0 0
\(925\) −0.250139 −0.00822452
\(926\) 0 0
\(927\) −0.277767 −0.00912306
\(928\) 0 0
\(929\) 17.6507 0.579102 0.289551 0.957163i \(-0.406494\pi\)
0.289551 + 0.957163i \(0.406494\pi\)
\(930\) 0 0
\(931\) 37.2490 1.22079
\(932\) 0 0
\(933\) −23.1383 −0.757513
\(934\) 0 0
\(935\) 20.9843 0.686261
\(936\) 0 0
\(937\) −48.8423 −1.59561 −0.797805 0.602916i \(-0.794005\pi\)
−0.797805 + 0.602916i \(0.794005\pi\)
\(938\) 0 0
\(939\) 16.5786 0.541023
\(940\) 0 0
\(941\) −3.14208 −0.102429 −0.0512145 0.998688i \(-0.516309\pi\)
−0.0512145 + 0.998688i \(0.516309\pi\)
\(942\) 0 0
\(943\) −24.0413 −0.782893
\(944\) 0 0
\(945\) −0.359246 −0.0116863
\(946\) 0 0
\(947\) −10.0506 −0.326602 −0.163301 0.986576i \(-0.552214\pi\)
−0.163301 + 0.986576i \(0.552214\pi\)
\(948\) 0 0
\(949\) −14.5960 −0.473808
\(950\) 0 0
\(951\) 15.1097 0.489965
\(952\) 0 0
\(953\) −7.69926 −0.249403 −0.124702 0.992194i \(-0.539797\pi\)
−0.124702 + 0.992194i \(0.539797\pi\)
\(954\) 0 0
\(955\) −5.62619 −0.182059
\(956\) 0 0
\(957\) 7.98357 0.258072
\(958\) 0 0
\(959\) −1.91688 −0.0618992
\(960\) 0 0
\(961\) 61.5883 1.98672
\(962\) 0 0
\(963\) 5.01695 0.161669
\(964\) 0 0
\(965\) −15.5327 −0.500015
\(966\) 0 0
\(967\) −26.5188 −0.852789 −0.426394 0.904537i \(-0.640216\pi\)
−0.426394 + 0.904537i \(0.640216\pi\)
\(968\) 0 0
\(969\) 22.8094 0.732743
\(970\) 0 0
\(971\) −47.1360 −1.51267 −0.756333 0.654187i \(-0.773011\pi\)
−0.756333 + 0.654187i \(0.773011\pi\)
\(972\) 0 0
\(973\) −4.00773 −0.128482
\(974\) 0 0
\(975\) 4.01920 0.128717
\(976\) 0 0
\(977\) 1.34004 0.0428718 0.0214359 0.999770i \(-0.493176\pi\)
0.0214359 + 0.999770i \(0.493176\pi\)
\(978\) 0 0
\(979\) 30.8219 0.985073
\(980\) 0 0
\(981\) 15.0343 0.480008
\(982\) 0 0
\(983\) 18.9209 0.603485 0.301742 0.953390i \(-0.402432\pi\)
0.301742 + 0.953390i \(0.402432\pi\)
\(984\) 0 0
\(985\) 8.12242 0.258802
\(986\) 0 0
\(987\) 1.61359 0.0513611
\(988\) 0 0
\(989\) −58.8947 −1.87274
\(990\) 0 0
\(991\) −53.1851 −1.68948 −0.844740 0.535178i \(-0.820245\pi\)
−0.844740 + 0.535178i \(0.820245\pi\)
\(992\) 0 0
\(993\) −21.7163 −0.689146
\(994\) 0 0
\(995\) 27.4711 0.870893
\(996\) 0 0
\(997\) 5.58170 0.176774 0.0883870 0.996086i \(-0.471829\pi\)
0.0883870 + 0.996086i \(0.471829\pi\)
\(998\) 0 0
\(999\) 0.0808905 0.00255926
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 8016.2.a.be.1.4 11
4.3 odd 2 4008.2.a.k.1.4 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4008.2.a.k.1.4 11 4.3 odd 2
8016.2.a.be.1.4 11 1.1 even 1 trivial