Properties

Label 4016.2.a.m.1.9
Level 4016
Weight 2
Character 4016.1
Self dual yes
Analytic conductor 32.068
Analytic rank 0
Dimension 23
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4016 = 2^{4} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0679214517\)
Analytic rank: \(0\)
Dimension: \(23\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 2008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.39383 q^{3} -3.54571 q^{5} +3.34862 q^{7} -1.05724 q^{9} +O(q^{10})\) \(q-1.39383 q^{3} -3.54571 q^{5} +3.34862 q^{7} -1.05724 q^{9} +1.30546 q^{11} -1.98436 q^{13} +4.94212 q^{15} +7.91610 q^{17} -4.46220 q^{19} -4.66741 q^{21} +1.70505 q^{23} +7.57207 q^{25} +5.65510 q^{27} +0.208137 q^{29} -9.03679 q^{31} -1.81960 q^{33} -11.8732 q^{35} -2.45973 q^{37} +2.76586 q^{39} -3.96457 q^{41} -0.799495 q^{43} +3.74865 q^{45} -10.8016 q^{47} +4.21324 q^{49} -11.0337 q^{51} +0.665446 q^{53} -4.62880 q^{55} +6.21956 q^{57} -12.7607 q^{59} -1.09665 q^{61} -3.54028 q^{63} +7.03597 q^{65} +14.2147 q^{67} -2.37655 q^{69} +3.44150 q^{71} +15.8322 q^{73} -10.5542 q^{75} +4.37150 q^{77} +8.66181 q^{79} -4.71055 q^{81} -13.1306 q^{83} -28.0682 q^{85} -0.290108 q^{87} -1.71867 q^{89} -6.64486 q^{91} +12.5958 q^{93} +15.8217 q^{95} +17.1470 q^{97} -1.38018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

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
\(3\) −1.39383 −0.804729 −0.402364 0.915480i \(-0.631811\pi\)
−0.402364 + 0.915480i \(0.631811\pi\)
\(4\) 0 0
\(5\) −3.54571 −1.58569 −0.792845 0.609423i \(-0.791401\pi\)
−0.792845 + 0.609423i \(0.791401\pi\)
\(6\) 0 0
\(7\) 3.34862 1.26566 0.632829 0.774291i \(-0.281893\pi\)
0.632829 + 0.774291i \(0.281893\pi\)
\(8\) 0 0
\(9\) −1.05724 −0.352412
\(10\) 0 0
\(11\) 1.30546 0.393612 0.196806 0.980442i \(-0.436943\pi\)
0.196806 + 0.980442i \(0.436943\pi\)
\(12\) 0 0
\(13\) −1.98436 −0.550362 −0.275181 0.961392i \(-0.588738\pi\)
−0.275181 + 0.961392i \(0.588738\pi\)
\(14\) 0 0
\(15\) 4.94212 1.27605
\(16\) 0 0
\(17\) 7.91610 1.91994 0.959968 0.280110i \(-0.0903710\pi\)
0.959968 + 0.280110i \(0.0903710\pi\)
\(18\) 0 0
\(19\) −4.46220 −1.02370 −0.511850 0.859075i \(-0.671040\pi\)
−0.511850 + 0.859075i \(0.671040\pi\)
\(20\) 0 0
\(21\) −4.66741 −1.01851
\(22\) 0 0
\(23\) 1.70505 0.355527 0.177764 0.984073i \(-0.443114\pi\)
0.177764 + 0.984073i \(0.443114\pi\)
\(24\) 0 0
\(25\) 7.57207 1.51441
\(26\) 0 0
\(27\) 5.65510 1.08832
\(28\) 0 0
\(29\) 0.208137 0.0386501 0.0193251 0.999813i \(-0.493848\pi\)
0.0193251 + 0.999813i \(0.493848\pi\)
\(30\) 0 0
\(31\) −9.03679 −1.62306 −0.811528 0.584314i \(-0.801364\pi\)
−0.811528 + 0.584314i \(0.801364\pi\)
\(32\) 0 0
\(33\) −1.81960 −0.316751
\(34\) 0 0
\(35\) −11.8732 −2.00694
\(36\) 0 0
\(37\) −2.45973 −0.404377 −0.202189 0.979347i \(-0.564805\pi\)
−0.202189 + 0.979347i \(0.564805\pi\)
\(38\) 0 0
\(39\) 2.76586 0.442892
\(40\) 0 0
\(41\) −3.96457 −0.619161 −0.309581 0.950873i \(-0.600189\pi\)
−0.309581 + 0.950873i \(0.600189\pi\)
\(42\) 0 0
\(43\) −0.799495 −0.121922 −0.0609609 0.998140i \(-0.519416\pi\)
−0.0609609 + 0.998140i \(0.519416\pi\)
\(44\) 0 0
\(45\) 3.74865 0.558816
\(46\) 0 0
\(47\) −10.8016 −1.57558 −0.787790 0.615943i \(-0.788775\pi\)
−0.787790 + 0.615943i \(0.788775\pi\)
\(48\) 0 0
\(49\) 4.21324 0.601892
\(50\) 0 0
\(51\) −11.0337 −1.54503
\(52\) 0 0
\(53\) 0.665446 0.0914060 0.0457030 0.998955i \(-0.485447\pi\)
0.0457030 + 0.998955i \(0.485447\pi\)
\(54\) 0 0
\(55\) −4.62880 −0.624147
\(56\) 0 0
\(57\) 6.21956 0.823801
\(58\) 0 0
\(59\) −12.7607 −1.66130 −0.830648 0.556798i \(-0.812030\pi\)
−0.830648 + 0.556798i \(0.812030\pi\)
\(60\) 0 0
\(61\) −1.09665 −0.140411 −0.0702056 0.997533i \(-0.522366\pi\)
−0.0702056 + 0.997533i \(0.522366\pi\)
\(62\) 0 0
\(63\) −3.54028 −0.446033
\(64\) 0 0
\(65\) 7.03597 0.872704
\(66\) 0 0
\(67\) 14.2147 1.73660 0.868301 0.496037i \(-0.165212\pi\)
0.868301 + 0.496037i \(0.165212\pi\)
\(68\) 0 0
\(69\) −2.37655 −0.286103
\(70\) 0 0
\(71\) 3.44150 0.408431 0.204216 0.978926i \(-0.434536\pi\)
0.204216 + 0.978926i \(0.434536\pi\)
\(72\) 0 0
\(73\) 15.8322 1.85302 0.926509 0.376273i \(-0.122795\pi\)
0.926509 + 0.376273i \(0.122795\pi\)
\(74\) 0 0
\(75\) −10.5542 −1.21869
\(76\) 0 0
\(77\) 4.37150 0.498179
\(78\) 0 0
\(79\) 8.66181 0.974529 0.487265 0.873254i \(-0.337995\pi\)
0.487265 + 0.873254i \(0.337995\pi\)
\(80\) 0 0
\(81\) −4.71055 −0.523394
\(82\) 0 0
\(83\) −13.1306 −1.44128 −0.720638 0.693312i \(-0.756151\pi\)
−0.720638 + 0.693312i \(0.756151\pi\)
\(84\) 0 0
\(85\) −28.0682 −3.04442
\(86\) 0 0
\(87\) −0.290108 −0.0311029
\(88\) 0 0
\(89\) −1.71867 −0.182178 −0.0910892 0.995843i \(-0.529035\pi\)
−0.0910892 + 0.995843i \(0.529035\pi\)
\(90\) 0 0
\(91\) −6.64486 −0.696571
\(92\) 0 0
\(93\) 12.5958 1.30612
\(94\) 0 0
\(95\) 15.8217 1.62327
\(96\) 0 0
\(97\) 17.1470 1.74102 0.870508 0.492154i \(-0.163790\pi\)
0.870508 + 0.492154i \(0.163790\pi\)
\(98\) 0 0
\(99\) −1.38018 −0.138714
\(100\) 0 0
\(101\) 11.2421 1.11864 0.559318 0.828953i \(-0.311063\pi\)
0.559318 + 0.828953i \(0.311063\pi\)
\(102\) 0 0
\(103\) 4.36024 0.429627 0.214814 0.976655i \(-0.431086\pi\)
0.214814 + 0.976655i \(0.431086\pi\)
\(104\) 0 0
\(105\) 16.5493 1.61504
\(106\) 0 0
\(107\) 3.64445 0.352322 0.176161 0.984361i \(-0.443632\pi\)
0.176161 + 0.984361i \(0.443632\pi\)
\(108\) 0 0
\(109\) 7.47130 0.715621 0.357810 0.933794i \(-0.383523\pi\)
0.357810 + 0.933794i \(0.383523\pi\)
\(110\) 0 0
\(111\) 3.42845 0.325414
\(112\) 0 0
\(113\) −0.345864 −0.0325361 −0.0162681 0.999868i \(-0.505179\pi\)
−0.0162681 + 0.999868i \(0.505179\pi\)
\(114\) 0 0
\(115\) −6.04561 −0.563756
\(116\) 0 0
\(117\) 2.09794 0.193954
\(118\) 0 0
\(119\) 26.5080 2.42998
\(120\) 0 0
\(121\) −9.29576 −0.845069
\(122\) 0 0
\(123\) 5.52594 0.498257
\(124\) 0 0
\(125\) −9.11981 −0.815700
\(126\) 0 0
\(127\) 2.67106 0.237019 0.118509 0.992953i \(-0.462188\pi\)
0.118509 + 0.992953i \(0.462188\pi\)
\(128\) 0 0
\(129\) 1.11436 0.0981140
\(130\) 0 0
\(131\) 2.76355 0.241453 0.120726 0.992686i \(-0.461478\pi\)
0.120726 + 0.992686i \(0.461478\pi\)
\(132\) 0 0
\(133\) −14.9422 −1.29565
\(134\) 0 0
\(135\) −20.0514 −1.72575
\(136\) 0 0
\(137\) 0.0385432 0.00329297 0.00164648 0.999999i \(-0.499476\pi\)
0.00164648 + 0.999999i \(0.499476\pi\)
\(138\) 0 0
\(139\) 0.628671 0.0533232 0.0266616 0.999645i \(-0.491512\pi\)
0.0266616 + 0.999645i \(0.491512\pi\)
\(140\) 0 0
\(141\) 15.0557 1.26791
\(142\) 0 0
\(143\) −2.59051 −0.216630
\(144\) 0 0
\(145\) −0.737995 −0.0612871
\(146\) 0 0
\(147\) −5.87255 −0.484360
\(148\) 0 0
\(149\) −11.3639 −0.930968 −0.465484 0.885056i \(-0.654120\pi\)
−0.465484 + 0.885056i \(0.654120\pi\)
\(150\) 0 0
\(151\) −14.5798 −1.18649 −0.593245 0.805022i \(-0.702154\pi\)
−0.593245 + 0.805022i \(0.702154\pi\)
\(152\) 0 0
\(153\) −8.36918 −0.676608
\(154\) 0 0
\(155\) 32.0418 2.57366
\(156\) 0 0
\(157\) 10.7179 0.855385 0.427693 0.903924i \(-0.359327\pi\)
0.427693 + 0.903924i \(0.359327\pi\)
\(158\) 0 0
\(159\) −0.927519 −0.0735570
\(160\) 0 0
\(161\) 5.70955 0.449976
\(162\) 0 0
\(163\) 12.0147 0.941067 0.470534 0.882382i \(-0.344061\pi\)
0.470534 + 0.882382i \(0.344061\pi\)
\(164\) 0 0
\(165\) 6.45177 0.502269
\(166\) 0 0
\(167\) 5.47233 0.423462 0.211731 0.977328i \(-0.432090\pi\)
0.211731 + 0.977328i \(0.432090\pi\)
\(168\) 0 0
\(169\) −9.06232 −0.697101
\(170\) 0 0
\(171\) 4.71760 0.360764
\(172\) 0 0
\(173\) −2.60501 −0.198055 −0.0990277 0.995085i \(-0.531573\pi\)
−0.0990277 + 0.995085i \(0.531573\pi\)
\(174\) 0 0
\(175\) 25.3560 1.91673
\(176\) 0 0
\(177\) 17.7862 1.33689
\(178\) 0 0
\(179\) −9.95712 −0.744230 −0.372115 0.928187i \(-0.621367\pi\)
−0.372115 + 0.928187i \(0.621367\pi\)
\(180\) 0 0
\(181\) −10.4862 −0.779431 −0.389716 0.920935i \(-0.627427\pi\)
−0.389716 + 0.920935i \(0.627427\pi\)
\(182\) 0 0
\(183\) 1.52854 0.112993
\(184\) 0 0
\(185\) 8.72149 0.641217
\(186\) 0 0
\(187\) 10.3342 0.755711
\(188\) 0 0
\(189\) 18.9368 1.37745
\(190\) 0 0
\(191\) −4.51146 −0.326437 −0.163219 0.986590i \(-0.552188\pi\)
−0.163219 + 0.986590i \(0.552188\pi\)
\(192\) 0 0
\(193\) 22.8795 1.64690 0.823451 0.567387i \(-0.192046\pi\)
0.823451 + 0.567387i \(0.192046\pi\)
\(194\) 0 0
\(195\) −9.80695 −0.702290
\(196\) 0 0
\(197\) 23.6017 1.68155 0.840775 0.541384i \(-0.182099\pi\)
0.840775 + 0.541384i \(0.182099\pi\)
\(198\) 0 0
\(199\) 9.74219 0.690606 0.345303 0.938491i \(-0.387776\pi\)
0.345303 + 0.938491i \(0.387776\pi\)
\(200\) 0 0
\(201\) −19.8129 −1.39749
\(202\) 0 0
\(203\) 0.696972 0.0489179
\(204\) 0 0
\(205\) 14.0572 0.981798
\(206\) 0 0
\(207\) −1.80264 −0.125292
\(208\) 0 0
\(209\) −5.82525 −0.402941
\(210\) 0 0
\(211\) 16.0568 1.10540 0.552699 0.833381i \(-0.313598\pi\)
0.552699 + 0.833381i \(0.313598\pi\)
\(212\) 0 0
\(213\) −4.79687 −0.328676
\(214\) 0 0
\(215\) 2.83478 0.193330
\(216\) 0 0
\(217\) −30.2608 −2.05423
\(218\) 0 0
\(219\) −22.0674 −1.49118
\(220\) 0 0
\(221\) −15.7084 −1.05666
\(222\) 0 0
\(223\) 23.7488 1.59034 0.795169 0.606388i \(-0.207382\pi\)
0.795169 + 0.606388i \(0.207382\pi\)
\(224\) 0 0
\(225\) −8.00546 −0.533697
\(226\) 0 0
\(227\) 5.58879 0.370941 0.185471 0.982650i \(-0.440619\pi\)
0.185471 + 0.982650i \(0.440619\pi\)
\(228\) 0 0
\(229\) 2.15354 0.142310 0.0711549 0.997465i \(-0.477332\pi\)
0.0711549 + 0.997465i \(0.477332\pi\)
\(230\) 0 0
\(231\) −6.09314 −0.400899
\(232\) 0 0
\(233\) 7.54167 0.494071 0.247035 0.969006i \(-0.420544\pi\)
0.247035 + 0.969006i \(0.420544\pi\)
\(234\) 0 0
\(235\) 38.2995 2.49838
\(236\) 0 0
\(237\) −12.0731 −0.784232
\(238\) 0 0
\(239\) 2.69180 0.174118 0.0870590 0.996203i \(-0.472253\pi\)
0.0870590 + 0.996203i \(0.472253\pi\)
\(240\) 0 0
\(241\) −7.52116 −0.484481 −0.242240 0.970216i \(-0.577882\pi\)
−0.242240 + 0.970216i \(0.577882\pi\)
\(242\) 0 0
\(243\) −10.3996 −0.667134
\(244\) 0 0
\(245\) −14.9389 −0.954414
\(246\) 0 0
\(247\) 8.85462 0.563406
\(248\) 0 0
\(249\) 18.3019 1.15984
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) 2.22588 0.139940
\(254\) 0 0
\(255\) 39.1223 2.44993
\(256\) 0 0
\(257\) −2.05695 −0.128309 −0.0641545 0.997940i \(-0.520435\pi\)
−0.0641545 + 0.997940i \(0.520435\pi\)
\(258\) 0 0
\(259\) −8.23669 −0.511803
\(260\) 0 0
\(261\) −0.220050 −0.0136208
\(262\) 0 0
\(263\) −12.9847 −0.800670 −0.400335 0.916369i \(-0.631106\pi\)
−0.400335 + 0.916369i \(0.631106\pi\)
\(264\) 0 0
\(265\) −2.35948 −0.144942
\(266\) 0 0
\(267\) 2.39553 0.146604
\(268\) 0 0
\(269\) 25.6995 1.56693 0.783463 0.621438i \(-0.213451\pi\)
0.783463 + 0.621438i \(0.213451\pi\)
\(270\) 0 0
\(271\) −12.7065 −0.771863 −0.385931 0.922527i \(-0.626120\pi\)
−0.385931 + 0.922527i \(0.626120\pi\)
\(272\) 0 0
\(273\) 9.26182 0.560551
\(274\) 0 0
\(275\) 9.88507 0.596092
\(276\) 0 0
\(277\) 19.8677 1.19374 0.596868 0.802340i \(-0.296412\pi\)
0.596868 + 0.802340i \(0.296412\pi\)
\(278\) 0 0
\(279\) 9.55401 0.571984
\(280\) 0 0
\(281\) 30.8497 1.84034 0.920171 0.391518i \(-0.128050\pi\)
0.920171 + 0.391518i \(0.128050\pi\)
\(282\) 0 0
\(283\) 11.9389 0.709695 0.354848 0.934924i \(-0.384533\pi\)
0.354848 + 0.934924i \(0.384533\pi\)
\(284\) 0 0
\(285\) −22.0528 −1.30629
\(286\) 0 0
\(287\) −13.2758 −0.783647
\(288\) 0 0
\(289\) 45.6646 2.68615
\(290\) 0 0
\(291\) −23.9001 −1.40105
\(292\) 0 0
\(293\) −10.0471 −0.586961 −0.293480 0.955965i \(-0.594814\pi\)
−0.293480 + 0.955965i \(0.594814\pi\)
\(294\) 0 0
\(295\) 45.2456 2.63430
\(296\) 0 0
\(297\) 7.38253 0.428378
\(298\) 0 0
\(299\) −3.38343 −0.195669
\(300\) 0 0
\(301\) −2.67720 −0.154311
\(302\) 0 0
\(303\) −15.6696 −0.900198
\(304\) 0 0
\(305\) 3.88839 0.222649
\(306\) 0 0
\(307\) 25.1331 1.43442 0.717210 0.696858i \(-0.245419\pi\)
0.717210 + 0.696858i \(0.245419\pi\)
\(308\) 0 0
\(309\) −6.07744 −0.345733
\(310\) 0 0
\(311\) −23.3800 −1.32576 −0.662880 0.748725i \(-0.730666\pi\)
−0.662880 + 0.748725i \(0.730666\pi\)
\(312\) 0 0
\(313\) 32.8535 1.85699 0.928495 0.371344i \(-0.121103\pi\)
0.928495 + 0.371344i \(0.121103\pi\)
\(314\) 0 0
\(315\) 12.5528 0.707270
\(316\) 0 0
\(317\) 7.68671 0.431729 0.215864 0.976423i \(-0.430743\pi\)
0.215864 + 0.976423i \(0.430743\pi\)
\(318\) 0 0
\(319\) 0.271716 0.0152132
\(320\) 0 0
\(321\) −5.07974 −0.283524
\(322\) 0 0
\(323\) −35.3233 −1.96544
\(324\) 0 0
\(325\) −15.0257 −0.833476
\(326\) 0 0
\(327\) −10.4137 −0.575881
\(328\) 0 0
\(329\) −36.1706 −1.99415
\(330\) 0 0
\(331\) 3.62040 0.198995 0.0994976 0.995038i \(-0.468276\pi\)
0.0994976 + 0.995038i \(0.468276\pi\)
\(332\) 0 0
\(333\) 2.60051 0.142507
\(334\) 0 0
\(335\) −50.4012 −2.75371
\(336\) 0 0
\(337\) −7.27600 −0.396349 −0.198174 0.980167i \(-0.563501\pi\)
−0.198174 + 0.980167i \(0.563501\pi\)
\(338\) 0 0
\(339\) 0.482076 0.0261828
\(340\) 0 0
\(341\) −11.7972 −0.638855
\(342\) 0 0
\(343\) −9.33179 −0.503869
\(344\) 0 0
\(345\) 8.42656 0.453670
\(346\) 0 0
\(347\) 10.7648 0.577887 0.288943 0.957346i \(-0.406696\pi\)
0.288943 + 0.957346i \(0.406696\pi\)
\(348\) 0 0
\(349\) 19.7330 1.05628 0.528142 0.849156i \(-0.322889\pi\)
0.528142 + 0.849156i \(0.322889\pi\)
\(350\) 0 0
\(351\) −11.2218 −0.598973
\(352\) 0 0
\(353\) 29.8869 1.59072 0.795360 0.606137i \(-0.207282\pi\)
0.795360 + 0.606137i \(0.207282\pi\)
\(354\) 0 0
\(355\) −12.2026 −0.647646
\(356\) 0 0
\(357\) −36.9477 −1.95548
\(358\) 0 0
\(359\) −4.41597 −0.233066 −0.116533 0.993187i \(-0.537178\pi\)
−0.116533 + 0.993187i \(0.537178\pi\)
\(360\) 0 0
\(361\) 0.911272 0.0479617
\(362\) 0 0
\(363\) 12.9567 0.680051
\(364\) 0 0
\(365\) −56.1364 −2.93831
\(366\) 0 0
\(367\) 10.3648 0.541038 0.270519 0.962715i \(-0.412805\pi\)
0.270519 + 0.962715i \(0.412805\pi\)
\(368\) 0 0
\(369\) 4.19148 0.218200
\(370\) 0 0
\(371\) 2.22832 0.115689
\(372\) 0 0
\(373\) 27.5539 1.42669 0.713344 0.700814i \(-0.247180\pi\)
0.713344 + 0.700814i \(0.247180\pi\)
\(374\) 0 0
\(375\) 12.7115 0.656418
\(376\) 0 0
\(377\) −0.413019 −0.0212716
\(378\) 0 0
\(379\) −0.503584 −0.0258674 −0.0129337 0.999916i \(-0.504117\pi\)
−0.0129337 + 0.999916i \(0.504117\pi\)
\(380\) 0 0
\(381\) −3.72301 −0.190736
\(382\) 0 0
\(383\) −23.3960 −1.19548 −0.597741 0.801689i \(-0.703935\pi\)
−0.597741 + 0.801689i \(0.703935\pi\)
\(384\) 0 0
\(385\) −15.5001 −0.789958
\(386\) 0 0
\(387\) 0.845254 0.0429667
\(388\) 0 0
\(389\) 35.0778 1.77852 0.889258 0.457407i \(-0.151222\pi\)
0.889258 + 0.457407i \(0.151222\pi\)
\(390\) 0 0
\(391\) 13.4973 0.682589
\(392\) 0 0
\(393\) −3.85192 −0.194304
\(394\) 0 0
\(395\) −30.7123 −1.54530
\(396\) 0 0
\(397\) −30.3735 −1.52440 −0.762201 0.647341i \(-0.775881\pi\)
−0.762201 + 0.647341i \(0.775881\pi\)
\(398\) 0 0
\(399\) 20.8269 1.04265
\(400\) 0 0
\(401\) 11.5805 0.578302 0.289151 0.957283i \(-0.406627\pi\)
0.289151 + 0.957283i \(0.406627\pi\)
\(402\) 0 0
\(403\) 17.9322 0.893269
\(404\) 0 0
\(405\) 16.7022 0.829941
\(406\) 0 0
\(407\) −3.21109 −0.159168
\(408\) 0 0
\(409\) 10.0559 0.497234 0.248617 0.968602i \(-0.420024\pi\)
0.248617 + 0.968602i \(0.420024\pi\)
\(410\) 0 0
\(411\) −0.0537227 −0.00264995
\(412\) 0 0
\(413\) −42.7306 −2.10263
\(414\) 0 0
\(415\) 46.5575 2.28542
\(416\) 0 0
\(417\) −0.876262 −0.0429107
\(418\) 0 0
\(419\) 19.0038 0.928397 0.464198 0.885731i \(-0.346342\pi\)
0.464198 + 0.885731i \(0.346342\pi\)
\(420\) 0 0
\(421\) −22.8047 −1.11143 −0.555717 0.831371i \(-0.687556\pi\)
−0.555717 + 0.831371i \(0.687556\pi\)
\(422\) 0 0
\(423\) 11.4199 0.555253
\(424\) 0 0
\(425\) 59.9412 2.90758
\(426\) 0 0
\(427\) −3.67225 −0.177713
\(428\) 0 0
\(429\) 3.61074 0.174328
\(430\) 0 0
\(431\) 22.2844 1.07340 0.536702 0.843772i \(-0.319670\pi\)
0.536702 + 0.843772i \(0.319670\pi\)
\(432\) 0 0
\(433\) −26.4647 −1.27181 −0.635906 0.771766i \(-0.719373\pi\)
−0.635906 + 0.771766i \(0.719373\pi\)
\(434\) 0 0
\(435\) 1.02864 0.0493195
\(436\) 0 0
\(437\) −7.60827 −0.363953
\(438\) 0 0
\(439\) −10.9841 −0.524245 −0.262122 0.965035i \(-0.584422\pi\)
−0.262122 + 0.965035i \(0.584422\pi\)
\(440\) 0 0
\(441\) −4.45439 −0.212114
\(442\) 0 0
\(443\) 16.1484 0.767235 0.383618 0.923492i \(-0.374678\pi\)
0.383618 + 0.923492i \(0.374678\pi\)
\(444\) 0 0
\(445\) 6.09390 0.288878
\(446\) 0 0
\(447\) 15.8394 0.749176
\(448\) 0 0
\(449\) 26.6912 1.25963 0.629817 0.776743i \(-0.283130\pi\)
0.629817 + 0.776743i \(0.283130\pi\)
\(450\) 0 0
\(451\) −5.17560 −0.243710
\(452\) 0 0
\(453\) 20.3218 0.954803
\(454\) 0 0
\(455\) 23.5608 1.10455
\(456\) 0 0
\(457\) 11.3731 0.532013 0.266006 0.963971i \(-0.414296\pi\)
0.266006 + 0.963971i \(0.414296\pi\)
\(458\) 0 0
\(459\) 44.7663 2.08951
\(460\) 0 0
\(461\) −37.7563 −1.75848 −0.879242 0.476375i \(-0.841950\pi\)
−0.879242 + 0.476375i \(0.841950\pi\)
\(462\) 0 0
\(463\) −24.4504 −1.13631 −0.568154 0.822922i \(-0.692342\pi\)
−0.568154 + 0.822922i \(0.692342\pi\)
\(464\) 0 0
\(465\) −44.6609 −2.07110
\(466\) 0 0
\(467\) −13.3351 −0.617073 −0.308536 0.951213i \(-0.599839\pi\)
−0.308536 + 0.951213i \(0.599839\pi\)
\(468\) 0 0
\(469\) 47.5996 2.19795
\(470\) 0 0
\(471\) −14.9390 −0.688353
\(472\) 0 0
\(473\) −1.04371 −0.0479899
\(474\) 0 0
\(475\) −33.7881 −1.55031
\(476\) 0 0
\(477\) −0.703533 −0.0322126
\(478\) 0 0
\(479\) −16.5168 −0.754672 −0.377336 0.926076i \(-0.623160\pi\)
−0.377336 + 0.926076i \(0.623160\pi\)
\(480\) 0 0
\(481\) 4.88099 0.222554
\(482\) 0 0
\(483\) −7.95815 −0.362109
\(484\) 0 0
\(485\) −60.7984 −2.76071
\(486\) 0 0
\(487\) 29.5815 1.34047 0.670233 0.742151i \(-0.266194\pi\)
0.670233 + 0.742151i \(0.266194\pi\)
\(488\) 0 0
\(489\) −16.7465 −0.757304
\(490\) 0 0
\(491\) −31.0452 −1.40105 −0.700525 0.713628i \(-0.747051\pi\)
−0.700525 + 0.713628i \(0.747051\pi\)
\(492\) 0 0
\(493\) 1.64764 0.0742058
\(494\) 0 0
\(495\) 4.89373 0.219957
\(496\) 0 0
\(497\) 11.5243 0.516935
\(498\) 0 0
\(499\) −12.5466 −0.561661 −0.280831 0.959757i \(-0.590610\pi\)
−0.280831 + 0.959757i \(0.590610\pi\)
\(500\) 0 0
\(501\) −7.62750 −0.340772
\(502\) 0 0
\(503\) −35.8802 −1.59982 −0.799910 0.600119i \(-0.795120\pi\)
−0.799910 + 0.600119i \(0.795120\pi\)
\(504\) 0 0
\(505\) −39.8614 −1.77381
\(506\) 0 0
\(507\) 12.6313 0.560977
\(508\) 0 0
\(509\) −25.7570 −1.14166 −0.570830 0.821068i \(-0.693378\pi\)
−0.570830 + 0.821068i \(0.693378\pi\)
\(510\) 0 0
\(511\) 53.0159 2.34529
\(512\) 0 0
\(513\) −25.2342 −1.11412
\(514\) 0 0
\(515\) −15.4602 −0.681256
\(516\) 0 0
\(517\) −14.1012 −0.620168
\(518\) 0 0
\(519\) 3.63095 0.159381
\(520\) 0 0
\(521\) −23.6115 −1.03444 −0.517219 0.855853i \(-0.673033\pi\)
−0.517219 + 0.855853i \(0.673033\pi\)
\(522\) 0 0
\(523\) 43.6381 1.90816 0.954080 0.299551i \(-0.0968367\pi\)
0.954080 + 0.299551i \(0.0968367\pi\)
\(524\) 0 0
\(525\) −35.3419 −1.54245
\(526\) 0 0
\(527\) −71.5361 −3.11616
\(528\) 0 0
\(529\) −20.0928 −0.873600
\(530\) 0 0
\(531\) 13.4910 0.585460
\(532\) 0 0
\(533\) 7.86713 0.340763
\(534\) 0 0
\(535\) −12.9222 −0.558674
\(536\) 0 0
\(537\) 13.8785 0.598904
\(538\) 0 0
\(539\) 5.50024 0.236912
\(540\) 0 0
\(541\) −30.1373 −1.29570 −0.647852 0.761766i \(-0.724332\pi\)
−0.647852 + 0.761766i \(0.724332\pi\)
\(542\) 0 0
\(543\) 14.6160 0.627231
\(544\) 0 0
\(545\) −26.4911 −1.13475
\(546\) 0 0
\(547\) −22.9197 −0.979974 −0.489987 0.871730i \(-0.662998\pi\)
−0.489987 + 0.871730i \(0.662998\pi\)
\(548\) 0 0
\(549\) 1.15941 0.0494825
\(550\) 0 0
\(551\) −0.928751 −0.0395661
\(552\) 0 0
\(553\) 29.0051 1.23342
\(554\) 0 0
\(555\) −12.1563 −0.516005
\(556\) 0 0
\(557\) 31.8431 1.34923 0.674617 0.738168i \(-0.264309\pi\)
0.674617 + 0.738168i \(0.264309\pi\)
\(558\) 0 0
\(559\) 1.58649 0.0671012
\(560\) 0 0
\(561\) −14.4041 −0.608142
\(562\) 0 0
\(563\) −7.47665 −0.315103 −0.157552 0.987511i \(-0.550360\pi\)
−0.157552 + 0.987511i \(0.550360\pi\)
\(564\) 0 0
\(565\) 1.22633 0.0515922
\(566\) 0 0
\(567\) −15.7738 −0.662438
\(568\) 0 0
\(569\) 1.33344 0.0559005 0.0279503 0.999609i \(-0.491102\pi\)
0.0279503 + 0.999609i \(0.491102\pi\)
\(570\) 0 0
\(571\) 38.2509 1.60075 0.800375 0.599500i \(-0.204634\pi\)
0.800375 + 0.599500i \(0.204634\pi\)
\(572\) 0 0
\(573\) 6.28821 0.262694
\(574\) 0 0
\(575\) 12.9107 0.538415
\(576\) 0 0
\(577\) 6.83043 0.284354 0.142177 0.989841i \(-0.454590\pi\)
0.142177 + 0.989841i \(0.454590\pi\)
\(578\) 0 0
\(579\) −31.8901 −1.32531
\(580\) 0 0
\(581\) −43.9695 −1.82416
\(582\) 0 0
\(583\) 0.868716 0.0359786
\(584\) 0 0
\(585\) −7.43867 −0.307551
\(586\) 0 0
\(587\) −28.2880 −1.16757 −0.583784 0.811909i \(-0.698429\pi\)
−0.583784 + 0.811909i \(0.698429\pi\)
\(588\) 0 0
\(589\) 40.3240 1.66152
\(590\) 0 0
\(591\) −32.8968 −1.35319
\(592\) 0 0
\(593\) −7.03794 −0.289014 −0.144507 0.989504i \(-0.546160\pi\)
−0.144507 + 0.989504i \(0.546160\pi\)
\(594\) 0 0
\(595\) −93.9897 −3.85320
\(596\) 0 0
\(597\) −13.5790 −0.555750
\(598\) 0 0
\(599\) 30.4870 1.24567 0.622833 0.782355i \(-0.285982\pi\)
0.622833 + 0.782355i \(0.285982\pi\)
\(600\) 0 0
\(601\) 7.23286 0.295035 0.147517 0.989059i \(-0.452872\pi\)
0.147517 + 0.989059i \(0.452872\pi\)
\(602\) 0 0
\(603\) −15.0283 −0.611999
\(604\) 0 0
\(605\) 32.9601 1.34002
\(606\) 0 0
\(607\) 22.0128 0.893471 0.446736 0.894666i \(-0.352586\pi\)
0.446736 + 0.894666i \(0.352586\pi\)
\(608\) 0 0
\(609\) −0.971462 −0.0393656
\(610\) 0 0
\(611\) 21.4343 0.867141
\(612\) 0 0
\(613\) −14.1465 −0.571372 −0.285686 0.958323i \(-0.592221\pi\)
−0.285686 + 0.958323i \(0.592221\pi\)
\(614\) 0 0
\(615\) −19.5934 −0.790081
\(616\) 0 0
\(617\) −36.2883 −1.46091 −0.730456 0.682960i \(-0.760692\pi\)
−0.730456 + 0.682960i \(0.760692\pi\)
\(618\) 0 0
\(619\) −2.67210 −0.107401 −0.0537005 0.998557i \(-0.517102\pi\)
−0.0537005 + 0.998557i \(0.517102\pi\)
\(620\) 0 0
\(621\) 9.64222 0.386929
\(622\) 0 0
\(623\) −5.75516 −0.230576
\(624\) 0 0
\(625\) −5.52413 −0.220965
\(626\) 0 0
\(627\) 8.11942 0.324258
\(628\) 0 0
\(629\) −19.4715 −0.776378
\(630\) 0 0
\(631\) −41.5356 −1.65351 −0.826753 0.562565i \(-0.809815\pi\)
−0.826753 + 0.562565i \(0.809815\pi\)
\(632\) 0 0
\(633\) −22.3805 −0.889546
\(634\) 0 0
\(635\) −9.47082 −0.375838
\(636\) 0 0
\(637\) −8.36059 −0.331259
\(638\) 0 0
\(639\) −3.63848 −0.143936
\(640\) 0 0
\(641\) −38.6560 −1.52682 −0.763410 0.645914i \(-0.776476\pi\)
−0.763410 + 0.645914i \(0.776476\pi\)
\(642\) 0 0
\(643\) −27.1319 −1.06998 −0.534989 0.844859i \(-0.679684\pi\)
−0.534989 + 0.844859i \(0.679684\pi\)
\(644\) 0 0
\(645\) −3.95120 −0.155578
\(646\) 0 0
\(647\) −1.46110 −0.0574419 −0.0287209 0.999587i \(-0.509143\pi\)
−0.0287209 + 0.999587i \(0.509143\pi\)
\(648\) 0 0
\(649\) −16.6586 −0.653907
\(650\) 0 0
\(651\) 42.1784 1.65310
\(652\) 0 0
\(653\) −22.2501 −0.870714 −0.435357 0.900258i \(-0.643378\pi\)
−0.435357 + 0.900258i \(0.643378\pi\)
\(654\) 0 0
\(655\) −9.79876 −0.382869
\(656\) 0 0
\(657\) −16.7383 −0.653025
\(658\) 0 0
\(659\) 32.1491 1.25235 0.626176 0.779682i \(-0.284619\pi\)
0.626176 + 0.779682i \(0.284619\pi\)
\(660\) 0 0
\(661\) −43.9293 −1.70865 −0.854326 0.519738i \(-0.826030\pi\)
−0.854326 + 0.519738i \(0.826030\pi\)
\(662\) 0 0
\(663\) 21.8948 0.850325
\(664\) 0 0
\(665\) 52.9808 2.05451
\(666\) 0 0
\(667\) 0.354884 0.0137412
\(668\) 0 0
\(669\) −33.1018 −1.27979
\(670\) 0 0
\(671\) −1.43163 −0.0552676
\(672\) 0 0
\(673\) 38.8748 1.49851 0.749257 0.662279i \(-0.230411\pi\)
0.749257 + 0.662279i \(0.230411\pi\)
\(674\) 0 0
\(675\) 42.8208 1.64817
\(676\) 0 0
\(677\) 0.347985 0.0133742 0.00668708 0.999978i \(-0.497871\pi\)
0.00668708 + 0.999978i \(0.497871\pi\)
\(678\) 0 0
\(679\) 57.4188 2.20353
\(680\) 0 0
\(681\) −7.78983 −0.298507
\(682\) 0 0
\(683\) −1.74287 −0.0666891 −0.0333445 0.999444i \(-0.510616\pi\)
−0.0333445 + 0.999444i \(0.510616\pi\)
\(684\) 0 0
\(685\) −0.136663 −0.00522163
\(686\) 0 0
\(687\) −3.00167 −0.114521
\(688\) 0 0
\(689\) −1.32048 −0.0503064
\(690\) 0 0
\(691\) 11.7853 0.448335 0.224168 0.974551i \(-0.428034\pi\)
0.224168 + 0.974551i \(0.428034\pi\)
\(692\) 0 0
\(693\) −4.62171 −0.175564
\(694\) 0 0
\(695\) −2.22909 −0.0845541
\(696\) 0 0
\(697\) −31.3839 −1.18875
\(698\) 0 0
\(699\) −10.5118 −0.397593
\(700\) 0 0
\(701\) 33.1814 1.25325 0.626623 0.779323i \(-0.284437\pi\)
0.626623 + 0.779323i \(0.284437\pi\)
\(702\) 0 0
\(703\) 10.9758 0.413961
\(704\) 0 0
\(705\) −53.3830 −2.01052
\(706\) 0 0
\(707\) 37.6456 1.41581
\(708\) 0 0
\(709\) 45.6003 1.71255 0.856277 0.516516i \(-0.172771\pi\)
0.856277 + 0.516516i \(0.172771\pi\)
\(710\) 0 0
\(711\) −9.15757 −0.343436
\(712\) 0 0
\(713\) −15.4082 −0.577040
\(714\) 0 0
\(715\) 9.18521 0.343507
\(716\) 0 0
\(717\) −3.75191 −0.140118
\(718\) 0 0
\(719\) −22.6657 −0.845288 −0.422644 0.906296i \(-0.638898\pi\)
−0.422644 + 0.906296i \(0.638898\pi\)
\(720\) 0 0
\(721\) 14.6008 0.543762
\(722\) 0 0
\(723\) 10.4832 0.389875
\(724\) 0 0
\(725\) 1.57603 0.0585323
\(726\) 0 0
\(727\) 11.2007 0.415410 0.207705 0.978191i \(-0.433401\pi\)
0.207705 + 0.978191i \(0.433401\pi\)
\(728\) 0 0
\(729\) 28.6269 1.06026
\(730\) 0 0
\(731\) −6.32888 −0.234082
\(732\) 0 0
\(733\) 43.9473 1.62323 0.811615 0.584193i \(-0.198589\pi\)
0.811615 + 0.584193i \(0.198589\pi\)
\(734\) 0 0
\(735\) 20.8224 0.768044
\(736\) 0 0
\(737\) 18.5568 0.683549
\(738\) 0 0
\(739\) −37.1650 −1.36714 −0.683569 0.729886i \(-0.739573\pi\)
−0.683569 + 0.729886i \(0.739573\pi\)
\(740\) 0 0
\(741\) −12.3418 −0.453389
\(742\) 0 0
\(743\) −3.57194 −0.131042 −0.0655208 0.997851i \(-0.520871\pi\)
−0.0655208 + 0.997851i \(0.520871\pi\)
\(744\) 0 0
\(745\) 40.2931 1.47623
\(746\) 0 0
\(747\) 13.8822 0.507923
\(748\) 0 0
\(749\) 12.2039 0.445919
\(750\) 0 0
\(751\) 49.2531 1.79727 0.898636 0.438695i \(-0.144559\pi\)
0.898636 + 0.438695i \(0.144559\pi\)
\(752\) 0 0
\(753\) −1.39383 −0.0507940
\(754\) 0 0
\(755\) 51.6959 1.88141
\(756\) 0 0
\(757\) 5.68995 0.206805 0.103402 0.994640i \(-0.467027\pi\)
0.103402 + 0.994640i \(0.467027\pi\)
\(758\) 0 0
\(759\) −3.10250 −0.112614
\(760\) 0 0
\(761\) −13.0205 −0.471993 −0.235997 0.971754i \(-0.575835\pi\)
−0.235997 + 0.971754i \(0.575835\pi\)
\(762\) 0 0
\(763\) 25.0185 0.905732
\(764\) 0 0
\(765\) 29.6747 1.07289
\(766\) 0 0
\(767\) 25.3217 0.914315
\(768\) 0 0
\(769\) 52.3974 1.88950 0.944749 0.327793i \(-0.106305\pi\)
0.944749 + 0.327793i \(0.106305\pi\)
\(770\) 0 0
\(771\) 2.86704 0.103254
\(772\) 0 0
\(773\) 35.0533 1.26078 0.630389 0.776279i \(-0.282895\pi\)
0.630389 + 0.776279i \(0.282895\pi\)
\(774\) 0 0
\(775\) −68.4272 −2.45798
\(776\) 0 0
\(777\) 11.4806 0.411863
\(778\) 0 0
\(779\) 17.6907 0.633835
\(780\) 0 0
\(781\) 4.49276 0.160764
\(782\) 0 0
\(783\) 1.17704 0.0420639
\(784\) 0 0
\(785\) −38.0027 −1.35638
\(786\) 0 0
\(787\) 29.7824 1.06163 0.530814 0.847489i \(-0.321886\pi\)
0.530814 + 0.847489i \(0.321886\pi\)
\(788\) 0 0
\(789\) 18.0984 0.644322
\(790\) 0 0
\(791\) −1.15817 −0.0411796
\(792\) 0 0
\(793\) 2.17614 0.0772770
\(794\) 0 0
\(795\) 3.28871 0.116639
\(796\) 0 0
\(797\) 17.9195 0.634742 0.317371 0.948301i \(-0.397200\pi\)
0.317371 + 0.948301i \(0.397200\pi\)
\(798\) 0 0
\(799\) −85.5068 −3.02501
\(800\) 0 0
\(801\) 1.81704 0.0642018
\(802\) 0 0
\(803\) 20.6684 0.729371
\(804\) 0 0
\(805\) −20.2444 −0.713522
\(806\) 0 0
\(807\) −35.8208 −1.26095
\(808\) 0 0
\(809\) 19.1408 0.672954 0.336477 0.941692i \(-0.390765\pi\)
0.336477 + 0.941692i \(0.390765\pi\)
\(810\) 0 0
\(811\) 40.8997 1.43618 0.718091 0.695949i \(-0.245016\pi\)
0.718091 + 0.695949i \(0.245016\pi\)
\(812\) 0 0
\(813\) 17.7107 0.621140
\(814\) 0 0
\(815\) −42.6008 −1.49224
\(816\) 0 0
\(817\) 3.56751 0.124811
\(818\) 0 0
\(819\) 7.02519 0.245480
\(820\) 0 0
\(821\) 10.4630 0.365160 0.182580 0.983191i \(-0.441555\pi\)
0.182580 + 0.983191i \(0.441555\pi\)
\(822\) 0 0
\(823\) 41.3018 1.43969 0.719846 0.694134i \(-0.244213\pi\)
0.719846 + 0.694134i \(0.244213\pi\)
\(824\) 0 0
\(825\) −13.7781 −0.479692
\(826\) 0 0
\(827\) −29.3280 −1.01983 −0.509917 0.860224i \(-0.670324\pi\)
−0.509917 + 0.860224i \(0.670324\pi\)
\(828\) 0 0
\(829\) 30.6086 1.06308 0.531540 0.847033i \(-0.321614\pi\)
0.531540 + 0.847033i \(0.321614\pi\)
\(830\) 0 0
\(831\) −27.6922 −0.960633
\(832\) 0 0
\(833\) 33.3524 1.15559
\(834\) 0 0
\(835\) −19.4033 −0.671479
\(836\) 0 0
\(837\) −51.1039 −1.76641
\(838\) 0 0
\(839\) −1.83313 −0.0632867 −0.0316434 0.999499i \(-0.510074\pi\)
−0.0316434 + 0.999499i \(0.510074\pi\)
\(840\) 0 0
\(841\) −28.9567 −0.998506
\(842\) 0 0
\(843\) −42.9993 −1.48098
\(844\) 0 0
\(845\) 32.1324 1.10539
\(846\) 0 0
\(847\) −31.1280 −1.06957
\(848\) 0 0
\(849\) −16.6408 −0.571112
\(850\) 0 0
\(851\) −4.19396 −0.143767
\(852\) 0 0
\(853\) 11.8480 0.405669 0.202835 0.979213i \(-0.434985\pi\)
0.202835 + 0.979213i \(0.434985\pi\)
\(854\) 0 0
\(855\) −16.7273 −0.572060
\(856\) 0 0
\(857\) 17.1219 0.584873 0.292436 0.956285i \(-0.405534\pi\)
0.292436 + 0.956285i \(0.405534\pi\)
\(858\) 0 0
\(859\) 24.0843 0.821745 0.410873 0.911693i \(-0.365224\pi\)
0.410873 + 0.911693i \(0.365224\pi\)
\(860\) 0 0
\(861\) 18.5042 0.630623
\(862\) 0 0
\(863\) −27.6792 −0.942211 −0.471106 0.882077i \(-0.656145\pi\)
−0.471106 + 0.882077i \(0.656145\pi\)
\(864\) 0 0
\(865\) 9.23662 0.314054
\(866\) 0 0
\(867\) −63.6487 −2.16162
\(868\) 0 0
\(869\) 11.3077 0.383587
\(870\) 0 0
\(871\) −28.2071 −0.955761
\(872\) 0 0
\(873\) −18.1284 −0.613555
\(874\) 0 0
\(875\) −30.5388 −1.03240
\(876\) 0 0
\(877\) −6.95777 −0.234947 −0.117474 0.993076i \(-0.537480\pi\)
−0.117474 + 0.993076i \(0.537480\pi\)
\(878\) 0 0
\(879\) 14.0040 0.472344
\(880\) 0 0
\(881\) 8.74633 0.294671 0.147336 0.989087i \(-0.452930\pi\)
0.147336 + 0.989087i \(0.452930\pi\)
\(882\) 0 0
\(883\) −12.9680 −0.436407 −0.218203 0.975903i \(-0.570020\pi\)
−0.218203 + 0.975903i \(0.570020\pi\)
\(884\) 0 0
\(885\) −63.0647 −2.11990
\(886\) 0 0
\(887\) −42.5491 −1.42866 −0.714330 0.699810i \(-0.753268\pi\)
−0.714330 + 0.699810i \(0.753268\pi\)
\(888\) 0 0
\(889\) 8.94437 0.299985
\(890\) 0 0
\(891\) −6.14945 −0.206014
\(892\) 0 0
\(893\) 48.1991 1.61292
\(894\) 0 0
\(895\) 35.3051 1.18012
\(896\) 0 0
\(897\) 4.71593 0.157460
\(898\) 0 0
\(899\) −1.88089 −0.0627313
\(900\) 0 0
\(901\) 5.26774 0.175494
\(902\) 0 0
\(903\) 3.73157 0.124179
\(904\) 0 0
\(905\) 37.1810 1.23594
\(906\) 0 0
\(907\) 12.5298 0.416044 0.208022 0.978124i \(-0.433297\pi\)
0.208022 + 0.978124i \(0.433297\pi\)
\(908\) 0 0
\(909\) −11.8856 −0.394220
\(910\) 0 0
\(911\) −6.34964 −0.210373 −0.105187 0.994453i \(-0.533544\pi\)
−0.105187 + 0.994453i \(0.533544\pi\)
\(912\) 0 0
\(913\) −17.1416 −0.567304
\(914\) 0 0
\(915\) −5.41976 −0.179172
\(916\) 0 0
\(917\) 9.25408 0.305597
\(918\) 0 0
\(919\) −2.92243 −0.0964020 −0.0482010 0.998838i \(-0.515349\pi\)
−0.0482010 + 0.998838i \(0.515349\pi\)
\(920\) 0 0
\(921\) −35.0312 −1.15432
\(922\) 0 0
\(923\) −6.82918 −0.224785
\(924\) 0 0
\(925\) −18.6252 −0.612394
\(926\) 0 0
\(927\) −4.60980 −0.151406
\(928\) 0 0
\(929\) 28.8491 0.946509 0.473254 0.880926i \(-0.343079\pi\)
0.473254 + 0.880926i \(0.343079\pi\)
\(930\) 0 0
\(931\) −18.8004 −0.616157
\(932\) 0 0
\(933\) 32.5878 1.06688
\(934\) 0 0
\(935\) −36.6420 −1.19832
\(936\) 0 0
\(937\) 21.5329 0.703448 0.351724 0.936104i \(-0.385595\pi\)
0.351724 + 0.936104i \(0.385595\pi\)
\(938\) 0 0
\(939\) −45.7922 −1.49437
\(940\) 0 0
\(941\) −34.9091 −1.13800 −0.569001 0.822337i \(-0.692670\pi\)
−0.569001 + 0.822337i \(0.692670\pi\)
\(942\) 0 0
\(943\) −6.75978 −0.220129
\(944\) 0 0
\(945\) −67.1443 −2.18420
\(946\) 0 0
\(947\) −16.5194 −0.536807 −0.268404 0.963307i \(-0.586496\pi\)
−0.268404 + 0.963307i \(0.586496\pi\)
\(948\) 0 0
\(949\) −31.4168 −1.01983
\(950\) 0 0
\(951\) −10.7140 −0.347425
\(952\) 0 0
\(953\) 14.2567 0.461820 0.230910 0.972975i \(-0.425830\pi\)
0.230910 + 0.972975i \(0.425830\pi\)
\(954\) 0 0
\(955\) 15.9963 0.517629
\(956\) 0 0
\(957\) −0.378726 −0.0122425
\(958\) 0 0
\(959\) 0.129066 0.00416777
\(960\) 0 0
\(961\) 50.6636 1.63431
\(962\) 0 0
\(963\) −3.85304 −0.124162
\(964\) 0 0
\(965\) −81.1241 −2.61148
\(966\) 0 0
\(967\) 0.743063 0.0238953 0.0119476 0.999929i \(-0.496197\pi\)
0.0119476 + 0.999929i \(0.496197\pi\)
\(968\) 0 0
\(969\) 49.2346 1.58164
\(970\) 0 0
\(971\) 57.8801 1.85746 0.928730 0.370757i \(-0.120902\pi\)
0.928730 + 0.370757i \(0.120902\pi\)
\(972\) 0 0
\(973\) 2.10518 0.0674890
\(974\) 0 0
\(975\) 20.9433 0.670722
\(976\) 0 0
\(977\) 34.4797 1.10310 0.551552 0.834140i \(-0.314036\pi\)
0.551552 + 0.834140i \(0.314036\pi\)
\(978\) 0 0
\(979\) −2.24366 −0.0717077
\(980\) 0 0
\(981\) −7.89892 −0.252193
\(982\) 0 0
\(983\) 24.6634 0.786641 0.393320 0.919401i \(-0.371326\pi\)
0.393320 + 0.919401i \(0.371326\pi\)
\(984\) 0 0
\(985\) −83.6848 −2.66642
\(986\) 0 0
\(987\) 50.4156 1.60475
\(988\) 0 0
\(989\) −1.36318 −0.0433465
\(990\) 0 0
\(991\) −40.7214 −1.29356 −0.646779 0.762677i \(-0.723885\pi\)
−0.646779 + 0.762677i \(0.723885\pi\)
\(992\) 0 0
\(993\) −5.04623 −0.160137
\(994\) 0 0
\(995\) −34.5430 −1.09509
\(996\) 0 0
\(997\) −29.7702 −0.942833 −0.471417 0.881911i \(-0.656257\pi\)
−0.471417 + 0.881911i \(0.656257\pi\)
\(998\) 0 0
\(999\) −13.9100 −0.440093
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 4016.2.a.m.1.9 23
4.3 odd 2 2008.2.a.d.1.15 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.15 23 4.3 odd 2
4016.2.a.m.1.9 23 1.1 even 1 trivial