Properties

Label 4016.2.a.m.1.2
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 1.2
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.26165 q^{3} -4.10224 q^{5} +1.61221 q^{7} +7.63839 q^{9} +O(q^{10})\) \(q-3.26165 q^{3} -4.10224 q^{5} +1.61221 q^{7} +7.63839 q^{9} -5.52272 q^{11} +3.26255 q^{13} +13.3801 q^{15} -4.72190 q^{17} +3.75601 q^{19} -5.25848 q^{21} -4.65709 q^{23} +11.8284 q^{25} -15.1288 q^{27} -3.54583 q^{29} -5.76666 q^{31} +18.0132 q^{33} -6.61368 q^{35} -0.102706 q^{37} -10.6413 q^{39} +10.2306 q^{41} -2.60241 q^{43} -31.3345 q^{45} -6.85910 q^{47} -4.40077 q^{49} +15.4012 q^{51} +3.77385 q^{53} +22.6555 q^{55} -12.2508 q^{57} -5.75365 q^{59} -9.91122 q^{61} +12.3147 q^{63} -13.3838 q^{65} -13.8484 q^{67} +15.1898 q^{69} -15.0515 q^{71} -15.6479 q^{73} -38.5801 q^{75} -8.90380 q^{77} +6.36204 q^{79} +26.4298 q^{81} -10.9919 q^{83} +19.3704 q^{85} +11.5653 q^{87} +1.56890 q^{89} +5.25992 q^{91} +18.8088 q^{93} -15.4081 q^{95} -6.16465 q^{97} -42.1847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

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
\(3\) −3.26165 −1.88312 −0.941558 0.336850i \(-0.890639\pi\)
−0.941558 + 0.336850i \(0.890639\pi\)
\(4\) 0 0
\(5\) −4.10224 −1.83458 −0.917289 0.398222i \(-0.869627\pi\)
−0.917289 + 0.398222i \(0.869627\pi\)
\(6\) 0 0
\(7\) 1.61221 0.609359 0.304679 0.952455i \(-0.401451\pi\)
0.304679 + 0.952455i \(0.401451\pi\)
\(8\) 0 0
\(9\) 7.63839 2.54613
\(10\) 0 0
\(11\) −5.52272 −1.66516 −0.832582 0.553902i \(-0.813138\pi\)
−0.832582 + 0.553902i \(0.813138\pi\)
\(12\) 0 0
\(13\) 3.26255 0.904868 0.452434 0.891798i \(-0.350556\pi\)
0.452434 + 0.891798i \(0.350556\pi\)
\(14\) 0 0
\(15\) 13.3801 3.45473
\(16\) 0 0
\(17\) −4.72190 −1.14523 −0.572614 0.819825i \(-0.694071\pi\)
−0.572614 + 0.819825i \(0.694071\pi\)
\(18\) 0 0
\(19\) 3.75601 0.861688 0.430844 0.902426i \(-0.358216\pi\)
0.430844 + 0.902426i \(0.358216\pi\)
\(20\) 0 0
\(21\) −5.25848 −1.14749
\(22\) 0 0
\(23\) −4.65709 −0.971070 −0.485535 0.874217i \(-0.661375\pi\)
−0.485535 + 0.874217i \(0.661375\pi\)
\(24\) 0 0
\(25\) 11.8284 2.36568
\(26\) 0 0
\(27\) −15.1288 −2.91154
\(28\) 0 0
\(29\) −3.54583 −0.658443 −0.329222 0.944253i \(-0.606786\pi\)
−0.329222 + 0.944253i \(0.606786\pi\)
\(30\) 0 0
\(31\) −5.76666 −1.03572 −0.517861 0.855465i \(-0.673272\pi\)
−0.517861 + 0.855465i \(0.673272\pi\)
\(32\) 0 0
\(33\) 18.0132 3.13570
\(34\) 0 0
\(35\) −6.61368 −1.11792
\(36\) 0 0
\(37\) −0.102706 −0.0168847 −0.00844236 0.999964i \(-0.502687\pi\)
−0.00844236 + 0.999964i \(0.502687\pi\)
\(38\) 0 0
\(39\) −10.6413 −1.70397
\(40\) 0 0
\(41\) 10.2306 1.59776 0.798878 0.601493i \(-0.205427\pi\)
0.798878 + 0.601493i \(0.205427\pi\)
\(42\) 0 0
\(43\) −2.60241 −0.396864 −0.198432 0.980115i \(-0.563585\pi\)
−0.198432 + 0.980115i \(0.563585\pi\)
\(44\) 0 0
\(45\) −31.3345 −4.67107
\(46\) 0 0
\(47\) −6.85910 −1.00050 −0.500251 0.865880i \(-0.666759\pi\)
−0.500251 + 0.865880i \(0.666759\pi\)
\(48\) 0 0
\(49\) −4.40077 −0.628682
\(50\) 0 0
\(51\) 15.4012 2.15660
\(52\) 0 0
\(53\) 3.77385 0.518378 0.259189 0.965827i \(-0.416545\pi\)
0.259189 + 0.965827i \(0.416545\pi\)
\(54\) 0 0
\(55\) 22.6555 3.05487
\(56\) 0 0
\(57\) −12.2508 −1.62266
\(58\) 0 0
\(59\) −5.75365 −0.749061 −0.374531 0.927215i \(-0.622196\pi\)
−0.374531 + 0.927215i \(0.622196\pi\)
\(60\) 0 0
\(61\) −9.91122 −1.26900 −0.634501 0.772922i \(-0.718794\pi\)
−0.634501 + 0.772922i \(0.718794\pi\)
\(62\) 0 0
\(63\) 12.3147 1.55151
\(64\) 0 0
\(65\) −13.3838 −1.66005
\(66\) 0 0
\(67\) −13.8484 −1.69186 −0.845928 0.533298i \(-0.820953\pi\)
−0.845928 + 0.533298i \(0.820953\pi\)
\(68\) 0 0
\(69\) 15.1898 1.82864
\(70\) 0 0
\(71\) −15.0515 −1.78629 −0.893145 0.449769i \(-0.851506\pi\)
−0.893145 + 0.449769i \(0.851506\pi\)
\(72\) 0 0
\(73\) −15.6479 −1.83145 −0.915723 0.401811i \(-0.868381\pi\)
−0.915723 + 0.401811i \(0.868381\pi\)
\(74\) 0 0
\(75\) −38.5801 −4.45485
\(76\) 0 0
\(77\) −8.90380 −1.01468
\(78\) 0 0
\(79\) 6.36204 0.715786 0.357893 0.933763i \(-0.383495\pi\)
0.357893 + 0.933763i \(0.383495\pi\)
\(80\) 0 0
\(81\) 26.4298 2.93664
\(82\) 0 0
\(83\) −10.9919 −1.20652 −0.603261 0.797544i \(-0.706132\pi\)
−0.603261 + 0.797544i \(0.706132\pi\)
\(84\) 0 0
\(85\) 19.3704 2.10101
\(86\) 0 0
\(87\) 11.5653 1.23993
\(88\) 0 0
\(89\) 1.56890 0.166303 0.0831517 0.996537i \(-0.473501\pi\)
0.0831517 + 0.996537i \(0.473501\pi\)
\(90\) 0 0
\(91\) 5.25992 0.551390
\(92\) 0 0
\(93\) 18.8088 1.95039
\(94\) 0 0
\(95\) −15.4081 −1.58083
\(96\) 0 0
\(97\) −6.16465 −0.625925 −0.312962 0.949765i \(-0.601321\pi\)
−0.312962 + 0.949765i \(0.601321\pi\)
\(98\) 0 0
\(99\) −42.1847 −4.23972
\(100\) 0 0
\(101\) 2.60250 0.258958 0.129479 0.991582i \(-0.458669\pi\)
0.129479 + 0.991582i \(0.458669\pi\)
\(102\) 0 0
\(103\) 0.121978 0.0120189 0.00600944 0.999982i \(-0.498087\pi\)
0.00600944 + 0.999982i \(0.498087\pi\)
\(104\) 0 0
\(105\) 21.5715 2.10517
\(106\) 0 0
\(107\) 16.5618 1.60109 0.800544 0.599274i \(-0.204544\pi\)
0.800544 + 0.599274i \(0.204544\pi\)
\(108\) 0 0
\(109\) −7.91023 −0.757662 −0.378831 0.925466i \(-0.623674\pi\)
−0.378831 + 0.925466i \(0.623674\pi\)
\(110\) 0 0
\(111\) 0.334990 0.0317959
\(112\) 0 0
\(113\) −7.99692 −0.752287 −0.376143 0.926561i \(-0.622750\pi\)
−0.376143 + 0.926561i \(0.622750\pi\)
\(114\) 0 0
\(115\) 19.1045 1.78150
\(116\) 0 0
\(117\) 24.9206 2.30391
\(118\) 0 0
\(119\) −7.61270 −0.697855
\(120\) 0 0
\(121\) 19.5005 1.77277
\(122\) 0 0
\(123\) −33.3688 −3.00876
\(124\) 0 0
\(125\) −28.0117 −2.50544
\(126\) 0 0
\(127\) 3.88187 0.344460 0.172230 0.985057i \(-0.444903\pi\)
0.172230 + 0.985057i \(0.444903\pi\)
\(128\) 0 0
\(129\) 8.48817 0.747341
\(130\) 0 0
\(131\) 11.7914 1.03022 0.515109 0.857125i \(-0.327752\pi\)
0.515109 + 0.857125i \(0.327752\pi\)
\(132\) 0 0
\(133\) 6.05549 0.525077
\(134\) 0 0
\(135\) 62.0620 5.34145
\(136\) 0 0
\(137\) 1.08131 0.0923824 0.0461912 0.998933i \(-0.485292\pi\)
0.0461912 + 0.998933i \(0.485292\pi\)
\(138\) 0 0
\(139\) −7.63350 −0.647465 −0.323733 0.946149i \(-0.604938\pi\)
−0.323733 + 0.946149i \(0.604938\pi\)
\(140\) 0 0
\(141\) 22.3720 1.88406
\(142\) 0 0
\(143\) −18.0182 −1.50675
\(144\) 0 0
\(145\) 14.5458 1.20797
\(146\) 0 0
\(147\) 14.3538 1.18388
\(148\) 0 0
\(149\) 7.96318 0.652369 0.326184 0.945306i \(-0.394237\pi\)
0.326184 + 0.945306i \(0.394237\pi\)
\(150\) 0 0
\(151\) 15.9239 1.29586 0.647932 0.761698i \(-0.275634\pi\)
0.647932 + 0.761698i \(0.275634\pi\)
\(152\) 0 0
\(153\) −36.0677 −2.91590
\(154\) 0 0
\(155\) 23.6562 1.90011
\(156\) 0 0
\(157\) 16.7099 1.33360 0.666798 0.745239i \(-0.267664\pi\)
0.666798 + 0.745239i \(0.267664\pi\)
\(158\) 0 0
\(159\) −12.3090 −0.976167
\(160\) 0 0
\(161\) −7.50822 −0.591730
\(162\) 0 0
\(163\) 7.33905 0.574839 0.287419 0.957805i \(-0.407203\pi\)
0.287419 + 0.957805i \(0.407203\pi\)
\(164\) 0 0
\(165\) −73.8945 −5.75268
\(166\) 0 0
\(167\) 10.0999 0.781554 0.390777 0.920485i \(-0.372206\pi\)
0.390777 + 0.920485i \(0.372206\pi\)
\(168\) 0 0
\(169\) −2.35577 −0.181213
\(170\) 0 0
\(171\) 28.6899 2.19397
\(172\) 0 0
\(173\) 1.69787 0.129087 0.0645434 0.997915i \(-0.479441\pi\)
0.0645434 + 0.997915i \(0.479441\pi\)
\(174\) 0 0
\(175\) 19.0699 1.44155
\(176\) 0 0
\(177\) 18.7664 1.41057
\(178\) 0 0
\(179\) −15.5898 −1.16523 −0.582617 0.812747i \(-0.697971\pi\)
−0.582617 + 0.812747i \(0.697971\pi\)
\(180\) 0 0
\(181\) 1.66228 0.123556 0.0617781 0.998090i \(-0.480323\pi\)
0.0617781 + 0.998090i \(0.480323\pi\)
\(182\) 0 0
\(183\) 32.3270 2.38968
\(184\) 0 0
\(185\) 0.421324 0.0309763
\(186\) 0 0
\(187\) 26.0777 1.90699
\(188\) 0 0
\(189\) −24.3909 −1.77417
\(190\) 0 0
\(191\) 11.7530 0.850420 0.425210 0.905095i \(-0.360200\pi\)
0.425210 + 0.905095i \(0.360200\pi\)
\(192\) 0 0
\(193\) 16.8485 1.21278 0.606392 0.795166i \(-0.292616\pi\)
0.606392 + 0.795166i \(0.292616\pi\)
\(194\) 0 0
\(195\) 43.6532 3.12607
\(196\) 0 0
\(197\) −17.7093 −1.26173 −0.630867 0.775891i \(-0.717301\pi\)
−0.630867 + 0.775891i \(0.717301\pi\)
\(198\) 0 0
\(199\) 3.85488 0.273265 0.136632 0.990622i \(-0.456372\pi\)
0.136632 + 0.990622i \(0.456372\pi\)
\(200\) 0 0
\(201\) 45.1688 3.18596
\(202\) 0 0
\(203\) −5.71662 −0.401228
\(204\) 0 0
\(205\) −41.9685 −2.93121
\(206\) 0 0
\(207\) −35.5726 −2.47247
\(208\) 0 0
\(209\) −20.7434 −1.43485
\(210\) 0 0
\(211\) 14.4082 0.991899 0.495949 0.868351i \(-0.334820\pi\)
0.495949 + 0.868351i \(0.334820\pi\)
\(212\) 0 0
\(213\) 49.0929 3.36379
\(214\) 0 0
\(215\) 10.6757 0.728078
\(216\) 0 0
\(217\) −9.29708 −0.631127
\(218\) 0 0
\(219\) 51.0380 3.44883
\(220\) 0 0
\(221\) −15.4054 −1.03628
\(222\) 0 0
\(223\) −16.5318 −1.10705 −0.553525 0.832832i \(-0.686718\pi\)
−0.553525 + 0.832832i \(0.686718\pi\)
\(224\) 0 0
\(225\) 90.3498 6.02332
\(226\) 0 0
\(227\) −5.18928 −0.344425 −0.172212 0.985060i \(-0.555092\pi\)
−0.172212 + 0.985060i \(0.555092\pi\)
\(228\) 0 0
\(229\) −16.4771 −1.08884 −0.544420 0.838813i \(-0.683250\pi\)
−0.544420 + 0.838813i \(0.683250\pi\)
\(230\) 0 0
\(231\) 29.0411 1.91076
\(232\) 0 0
\(233\) 16.8186 1.10182 0.550911 0.834564i \(-0.314280\pi\)
0.550911 + 0.834564i \(0.314280\pi\)
\(234\) 0 0
\(235\) 28.1377 1.83550
\(236\) 0 0
\(237\) −20.7508 −1.34791
\(238\) 0 0
\(239\) 10.9090 0.705646 0.352823 0.935690i \(-0.385222\pi\)
0.352823 + 0.935690i \(0.385222\pi\)
\(240\) 0 0
\(241\) −3.58735 −0.231081 −0.115541 0.993303i \(-0.536860\pi\)
−0.115541 + 0.993303i \(0.536860\pi\)
\(242\) 0 0
\(243\) −40.8184 −2.61850
\(244\) 0 0
\(245\) 18.0530 1.15337
\(246\) 0 0
\(247\) 12.2542 0.779714
\(248\) 0 0
\(249\) 35.8519 2.27202
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) 25.7198 1.61699
\(254\) 0 0
\(255\) −63.1794 −3.95645
\(256\) 0 0
\(257\) −17.9081 −1.11708 −0.558539 0.829478i \(-0.688638\pi\)
−0.558539 + 0.829478i \(0.688638\pi\)
\(258\) 0 0
\(259\) −0.165583 −0.0102888
\(260\) 0 0
\(261\) −27.0844 −1.67648
\(262\) 0 0
\(263\) 5.39226 0.332501 0.166251 0.986084i \(-0.446834\pi\)
0.166251 + 0.986084i \(0.446834\pi\)
\(264\) 0 0
\(265\) −15.4812 −0.951005
\(266\) 0 0
\(267\) −5.11722 −0.313169
\(268\) 0 0
\(269\) −20.7985 −1.26811 −0.634054 0.773289i \(-0.718610\pi\)
−0.634054 + 0.773289i \(0.718610\pi\)
\(270\) 0 0
\(271\) −23.8707 −1.45004 −0.725020 0.688728i \(-0.758169\pi\)
−0.725020 + 0.688728i \(0.758169\pi\)
\(272\) 0 0
\(273\) −17.1560 −1.03833
\(274\) 0 0
\(275\) −65.3249 −3.93924
\(276\) 0 0
\(277\) −8.62585 −0.518277 −0.259139 0.965840i \(-0.583439\pi\)
−0.259139 + 0.965840i \(0.583439\pi\)
\(278\) 0 0
\(279\) −44.0480 −2.63708
\(280\) 0 0
\(281\) 3.66452 0.218607 0.109303 0.994008i \(-0.465138\pi\)
0.109303 + 0.994008i \(0.465138\pi\)
\(282\) 0 0
\(283\) 7.51120 0.446495 0.223247 0.974762i \(-0.428334\pi\)
0.223247 + 0.974762i \(0.428334\pi\)
\(284\) 0 0
\(285\) 50.2558 2.97690
\(286\) 0 0
\(287\) 16.4939 0.973607
\(288\) 0 0
\(289\) 5.29630 0.311547
\(290\) 0 0
\(291\) 20.1069 1.17869
\(292\) 0 0
\(293\) −15.1600 −0.885659 −0.442830 0.896606i \(-0.646025\pi\)
−0.442830 + 0.896606i \(0.646025\pi\)
\(294\) 0 0
\(295\) 23.6029 1.37421
\(296\) 0 0
\(297\) 83.5522 4.84819
\(298\) 0 0
\(299\) −15.1940 −0.878691
\(300\) 0 0
\(301\) −4.19564 −0.241833
\(302\) 0 0
\(303\) −8.48845 −0.487649
\(304\) 0 0
\(305\) 40.6582 2.32808
\(306\) 0 0
\(307\) 14.7844 0.843789 0.421895 0.906645i \(-0.361365\pi\)
0.421895 + 0.906645i \(0.361365\pi\)
\(308\) 0 0
\(309\) −0.397851 −0.0226330
\(310\) 0 0
\(311\) 26.9521 1.52831 0.764156 0.645032i \(-0.223156\pi\)
0.764156 + 0.645032i \(0.223156\pi\)
\(312\) 0 0
\(313\) −25.9965 −1.46941 −0.734704 0.678388i \(-0.762679\pi\)
−0.734704 + 0.678388i \(0.762679\pi\)
\(314\) 0 0
\(315\) −50.5179 −2.84636
\(316\) 0 0
\(317\) 23.4660 1.31798 0.658991 0.752150i \(-0.270983\pi\)
0.658991 + 0.752150i \(0.270983\pi\)
\(318\) 0 0
\(319\) 19.5826 1.09642
\(320\) 0 0
\(321\) −54.0188 −3.01504
\(322\) 0 0
\(323\) −17.7355 −0.986829
\(324\) 0 0
\(325\) 38.5907 2.14063
\(326\) 0 0
\(327\) 25.8004 1.42677
\(328\) 0 0
\(329\) −11.0583 −0.609665
\(330\) 0 0
\(331\) 12.0296 0.661204 0.330602 0.943770i \(-0.392748\pi\)
0.330602 + 0.943770i \(0.392748\pi\)
\(332\) 0 0
\(333\) −0.784506 −0.0429907
\(334\) 0 0
\(335\) 56.8096 3.10384
\(336\) 0 0
\(337\) −8.67913 −0.472782 −0.236391 0.971658i \(-0.575965\pi\)
−0.236391 + 0.971658i \(0.575965\pi\)
\(338\) 0 0
\(339\) 26.0832 1.41664
\(340\) 0 0
\(341\) 31.8477 1.72465
\(342\) 0 0
\(343\) −18.3805 −0.992452
\(344\) 0 0
\(345\) −62.3123 −3.35478
\(346\) 0 0
\(347\) 11.8869 0.638125 0.319062 0.947734i \(-0.396632\pi\)
0.319062 + 0.947734i \(0.396632\pi\)
\(348\) 0 0
\(349\) −20.3590 −1.08979 −0.544896 0.838503i \(-0.683431\pi\)
−0.544896 + 0.838503i \(0.683431\pi\)
\(350\) 0 0
\(351\) −49.3585 −2.63456
\(352\) 0 0
\(353\) 32.0911 1.70804 0.854018 0.520243i \(-0.174159\pi\)
0.854018 + 0.520243i \(0.174159\pi\)
\(354\) 0 0
\(355\) 61.7451 3.27709
\(356\) 0 0
\(357\) 24.8300 1.31414
\(358\) 0 0
\(359\) −1.42583 −0.0752525 −0.0376262 0.999292i \(-0.511980\pi\)
−0.0376262 + 0.999292i \(0.511980\pi\)
\(360\) 0 0
\(361\) −4.89238 −0.257493
\(362\) 0 0
\(363\) −63.6038 −3.33833
\(364\) 0 0
\(365\) 64.1914 3.35993
\(366\) 0 0
\(367\) −20.1684 −1.05278 −0.526392 0.850242i \(-0.676455\pi\)
−0.526392 + 0.850242i \(0.676455\pi\)
\(368\) 0 0
\(369\) 78.1455 4.06809
\(370\) 0 0
\(371\) 6.08425 0.315878
\(372\) 0 0
\(373\) 27.9405 1.44671 0.723353 0.690478i \(-0.242600\pi\)
0.723353 + 0.690478i \(0.242600\pi\)
\(374\) 0 0
\(375\) 91.3645 4.71804
\(376\) 0 0
\(377\) −11.5684 −0.595805
\(378\) 0 0
\(379\) 26.6630 1.36959 0.684793 0.728738i \(-0.259893\pi\)
0.684793 + 0.728738i \(0.259893\pi\)
\(380\) 0 0
\(381\) −12.6613 −0.648659
\(382\) 0 0
\(383\) −26.3023 −1.34398 −0.671992 0.740558i \(-0.734561\pi\)
−0.671992 + 0.740558i \(0.734561\pi\)
\(384\) 0 0
\(385\) 36.5255 1.86151
\(386\) 0 0
\(387\) −19.8782 −1.01047
\(388\) 0 0
\(389\) 28.0214 1.42074 0.710372 0.703827i \(-0.248527\pi\)
0.710372 + 0.703827i \(0.248527\pi\)
\(390\) 0 0
\(391\) 21.9903 1.11210
\(392\) 0 0
\(393\) −38.4594 −1.94002
\(394\) 0 0
\(395\) −26.0986 −1.31317
\(396\) 0 0
\(397\) −18.8475 −0.945930 −0.472965 0.881081i \(-0.656816\pi\)
−0.472965 + 0.881081i \(0.656816\pi\)
\(398\) 0 0
\(399\) −19.7509 −0.988782
\(400\) 0 0
\(401\) −0.486605 −0.0242999 −0.0121500 0.999926i \(-0.503868\pi\)
−0.0121500 + 0.999926i \(0.503868\pi\)
\(402\) 0 0
\(403\) −18.8140 −0.937193
\(404\) 0 0
\(405\) −108.421 −5.38750
\(406\) 0 0
\(407\) 0.567215 0.0281158
\(408\) 0 0
\(409\) −30.8030 −1.52311 −0.761555 0.648100i \(-0.775564\pi\)
−0.761555 + 0.648100i \(0.775564\pi\)
\(410\) 0 0
\(411\) −3.52685 −0.173967
\(412\) 0 0
\(413\) −9.27610 −0.456447
\(414\) 0 0
\(415\) 45.0916 2.21346
\(416\) 0 0
\(417\) 24.8978 1.21925
\(418\) 0 0
\(419\) 17.4763 0.853774 0.426887 0.904305i \(-0.359610\pi\)
0.426887 + 0.904305i \(0.359610\pi\)
\(420\) 0 0
\(421\) −15.4448 −0.752732 −0.376366 0.926471i \(-0.622826\pi\)
−0.376366 + 0.926471i \(0.622826\pi\)
\(422\) 0 0
\(423\) −52.3924 −2.54741
\(424\) 0 0
\(425\) −55.8524 −2.70924
\(426\) 0 0
\(427\) −15.9790 −0.773278
\(428\) 0 0
\(429\) 58.7690 2.83739
\(430\) 0 0
\(431\) −36.2976 −1.74839 −0.874196 0.485573i \(-0.838611\pi\)
−0.874196 + 0.485573i \(0.838611\pi\)
\(432\) 0 0
\(433\) −29.7835 −1.43130 −0.715651 0.698458i \(-0.753870\pi\)
−0.715651 + 0.698458i \(0.753870\pi\)
\(434\) 0 0
\(435\) −47.4435 −2.27474
\(436\) 0 0
\(437\) −17.4921 −0.836760
\(438\) 0 0
\(439\) 8.17330 0.390090 0.195045 0.980794i \(-0.437515\pi\)
0.195045 + 0.980794i \(0.437515\pi\)
\(440\) 0 0
\(441\) −33.6148 −1.60070
\(442\) 0 0
\(443\) 15.6197 0.742116 0.371058 0.928610i \(-0.378995\pi\)
0.371058 + 0.928610i \(0.378995\pi\)
\(444\) 0 0
\(445\) −6.43602 −0.305097
\(446\) 0 0
\(447\) −25.9731 −1.22849
\(448\) 0 0
\(449\) −9.19163 −0.433780 −0.216890 0.976196i \(-0.569591\pi\)
−0.216890 + 0.976196i \(0.569591\pi\)
\(450\) 0 0
\(451\) −56.5009 −2.66053
\(452\) 0 0
\(453\) −51.9381 −2.44027
\(454\) 0 0
\(455\) −21.5775 −1.01157
\(456\) 0 0
\(457\) 16.9137 0.791190 0.395595 0.918425i \(-0.370538\pi\)
0.395595 + 0.918425i \(0.370538\pi\)
\(458\) 0 0
\(459\) 71.4367 3.33438
\(460\) 0 0
\(461\) 9.23677 0.430199 0.215100 0.976592i \(-0.430992\pi\)
0.215100 + 0.976592i \(0.430992\pi\)
\(462\) 0 0
\(463\) −5.60293 −0.260390 −0.130195 0.991488i \(-0.541560\pi\)
−0.130195 + 0.991488i \(0.541560\pi\)
\(464\) 0 0
\(465\) −77.1584 −3.57814
\(466\) 0 0
\(467\) 16.0004 0.740410 0.370205 0.928950i \(-0.379287\pi\)
0.370205 + 0.928950i \(0.379287\pi\)
\(468\) 0 0
\(469\) −22.3266 −1.03095
\(470\) 0 0
\(471\) −54.5019 −2.51132
\(472\) 0 0
\(473\) 14.3724 0.660843
\(474\) 0 0
\(475\) 44.4276 2.03848
\(476\) 0 0
\(477\) 28.8261 1.31986
\(478\) 0 0
\(479\) −3.99761 −0.182655 −0.0913276 0.995821i \(-0.529111\pi\)
−0.0913276 + 0.995821i \(0.529111\pi\)
\(480\) 0 0
\(481\) −0.335082 −0.0152784
\(482\) 0 0
\(483\) 24.4892 1.11430
\(484\) 0 0
\(485\) 25.2889 1.14831
\(486\) 0 0
\(487\) −24.6005 −1.11475 −0.557377 0.830260i \(-0.688192\pi\)
−0.557377 + 0.830260i \(0.688192\pi\)
\(488\) 0 0
\(489\) −23.9374 −1.08249
\(490\) 0 0
\(491\) 10.6307 0.479757 0.239879 0.970803i \(-0.422892\pi\)
0.239879 + 0.970803i \(0.422892\pi\)
\(492\) 0 0
\(493\) 16.7430 0.754068
\(494\) 0 0
\(495\) 173.052 7.77810
\(496\) 0 0
\(497\) −24.2663 −1.08849
\(498\) 0 0
\(499\) 10.4414 0.467422 0.233711 0.972306i \(-0.424913\pi\)
0.233711 + 0.972306i \(0.424913\pi\)
\(500\) 0 0
\(501\) −32.9424 −1.47176
\(502\) 0 0
\(503\) −13.2307 −0.589927 −0.294963 0.955509i \(-0.595307\pi\)
−0.294963 + 0.955509i \(0.595307\pi\)
\(504\) 0 0
\(505\) −10.6761 −0.475079
\(506\) 0 0
\(507\) 7.68371 0.341245
\(508\) 0 0
\(509\) 30.4125 1.34801 0.674006 0.738726i \(-0.264572\pi\)
0.674006 + 0.738726i \(0.264572\pi\)
\(510\) 0 0
\(511\) −25.2277 −1.11601
\(512\) 0 0
\(513\) −56.8240 −2.50884
\(514\) 0 0
\(515\) −0.500385 −0.0220496
\(516\) 0 0
\(517\) 37.8809 1.66600
\(518\) 0 0
\(519\) −5.53787 −0.243086
\(520\) 0 0
\(521\) 9.59122 0.420199 0.210099 0.977680i \(-0.432621\pi\)
0.210099 + 0.977680i \(0.432621\pi\)
\(522\) 0 0
\(523\) −41.7426 −1.82528 −0.912639 0.408767i \(-0.865959\pi\)
−0.912639 + 0.408767i \(0.865959\pi\)
\(524\) 0 0
\(525\) −62.1993 −2.71460
\(526\) 0 0
\(527\) 27.2296 1.18614
\(528\) 0 0
\(529\) −1.31152 −0.0570225
\(530\) 0 0
\(531\) −43.9486 −1.90721
\(532\) 0 0
\(533\) 33.3779 1.44576
\(534\) 0 0
\(535\) −67.9405 −2.93732
\(536\) 0 0
\(537\) 50.8484 2.19427
\(538\) 0 0
\(539\) 24.3042 1.04686
\(540\) 0 0
\(541\) 11.7164 0.503726 0.251863 0.967763i \(-0.418957\pi\)
0.251863 + 0.967763i \(0.418957\pi\)
\(542\) 0 0
\(543\) −5.42178 −0.232671
\(544\) 0 0
\(545\) 32.4497 1.38999
\(546\) 0 0
\(547\) −17.9143 −0.765959 −0.382979 0.923757i \(-0.625102\pi\)
−0.382979 + 0.923757i \(0.625102\pi\)
\(548\) 0 0
\(549\) −75.7058 −3.23104
\(550\) 0 0
\(551\) −13.3182 −0.567373
\(552\) 0 0
\(553\) 10.2570 0.436170
\(554\) 0 0
\(555\) −1.37421 −0.0583320
\(556\) 0 0
\(557\) −8.50127 −0.360210 −0.180105 0.983647i \(-0.557644\pi\)
−0.180105 + 0.983647i \(0.557644\pi\)
\(558\) 0 0
\(559\) −8.49050 −0.359110
\(560\) 0 0
\(561\) −85.0565 −3.59109
\(562\) 0 0
\(563\) 14.5512 0.613261 0.306631 0.951829i \(-0.400798\pi\)
0.306631 + 0.951829i \(0.400798\pi\)
\(564\) 0 0
\(565\) 32.8053 1.38013
\(566\) 0 0
\(567\) 42.6104 1.78947
\(568\) 0 0
\(569\) 25.2947 1.06041 0.530205 0.847870i \(-0.322115\pi\)
0.530205 + 0.847870i \(0.322115\pi\)
\(570\) 0 0
\(571\) 9.03101 0.377936 0.188968 0.981983i \(-0.439486\pi\)
0.188968 + 0.981983i \(0.439486\pi\)
\(572\) 0 0
\(573\) −38.3344 −1.60144
\(574\) 0 0
\(575\) −55.0859 −2.29724
\(576\) 0 0
\(577\) −4.75197 −0.197827 −0.0989135 0.995096i \(-0.531537\pi\)
−0.0989135 + 0.995096i \(0.531537\pi\)
\(578\) 0 0
\(579\) −54.9541 −2.28381
\(580\) 0 0
\(581\) −17.7213 −0.735205
\(582\) 0 0
\(583\) −20.8419 −0.863184
\(584\) 0 0
\(585\) −102.230 −4.22671
\(586\) 0 0
\(587\) 21.8558 0.902087 0.451044 0.892502i \(-0.351052\pi\)
0.451044 + 0.892502i \(0.351052\pi\)
\(588\) 0 0
\(589\) −21.6596 −0.892470
\(590\) 0 0
\(591\) 57.7615 2.37599
\(592\) 0 0
\(593\) −4.62303 −0.189845 −0.0949225 0.995485i \(-0.530260\pi\)
−0.0949225 + 0.995485i \(0.530260\pi\)
\(594\) 0 0
\(595\) 31.2291 1.28027
\(596\) 0 0
\(597\) −12.5733 −0.514590
\(598\) 0 0
\(599\) −31.1976 −1.27470 −0.637349 0.770575i \(-0.719969\pi\)
−0.637349 + 0.770575i \(0.719969\pi\)
\(600\) 0 0
\(601\) 25.2015 1.02799 0.513996 0.857792i \(-0.328165\pi\)
0.513996 + 0.857792i \(0.328165\pi\)
\(602\) 0 0
\(603\) −105.780 −4.30768
\(604\) 0 0
\(605\) −79.9956 −3.25228
\(606\) 0 0
\(607\) 25.2707 1.02570 0.512852 0.858477i \(-0.328589\pi\)
0.512852 + 0.858477i \(0.328589\pi\)
\(608\) 0 0
\(609\) 18.6456 0.755560
\(610\) 0 0
\(611\) −22.3781 −0.905323
\(612\) 0 0
\(613\) 10.4271 0.421148 0.210574 0.977578i \(-0.432467\pi\)
0.210574 + 0.977578i \(0.432467\pi\)
\(614\) 0 0
\(615\) 136.887 5.51981
\(616\) 0 0
\(617\) 1.66477 0.0670210 0.0335105 0.999438i \(-0.489331\pi\)
0.0335105 + 0.999438i \(0.489331\pi\)
\(618\) 0 0
\(619\) 46.7622 1.87953 0.939766 0.341818i \(-0.111043\pi\)
0.939766 + 0.341818i \(0.111043\pi\)
\(620\) 0 0
\(621\) 70.4562 2.82731
\(622\) 0 0
\(623\) 2.52941 0.101338
\(624\) 0 0
\(625\) 55.7688 2.23075
\(626\) 0 0
\(627\) 67.6578 2.70199
\(628\) 0 0
\(629\) 0.484966 0.0193368
\(630\) 0 0
\(631\) 12.8965 0.513403 0.256701 0.966491i \(-0.417364\pi\)
0.256701 + 0.966491i \(0.417364\pi\)
\(632\) 0 0
\(633\) −46.9944 −1.86786
\(634\) 0 0
\(635\) −15.9244 −0.631939
\(636\) 0 0
\(637\) −14.3577 −0.568874
\(638\) 0 0
\(639\) −114.970 −4.54812
\(640\) 0 0
\(641\) 40.5589 1.60198 0.800990 0.598678i \(-0.204307\pi\)
0.800990 + 0.598678i \(0.204307\pi\)
\(642\) 0 0
\(643\) 4.90342 0.193372 0.0966861 0.995315i \(-0.469176\pi\)
0.0966861 + 0.995315i \(0.469176\pi\)
\(644\) 0 0
\(645\) −34.8205 −1.37106
\(646\) 0 0
\(647\) −31.2480 −1.22849 −0.614243 0.789117i \(-0.710538\pi\)
−0.614243 + 0.789117i \(0.710538\pi\)
\(648\) 0 0
\(649\) 31.7758 1.24731
\(650\) 0 0
\(651\) 30.3239 1.18849
\(652\) 0 0
\(653\) 12.9521 0.506853 0.253426 0.967355i \(-0.418442\pi\)
0.253426 + 0.967355i \(0.418442\pi\)
\(654\) 0 0
\(655\) −48.3711 −1.89001
\(656\) 0 0
\(657\) −119.525 −4.66310
\(658\) 0 0
\(659\) 28.5378 1.11167 0.555837 0.831291i \(-0.312398\pi\)
0.555837 + 0.831291i \(0.312398\pi\)
\(660\) 0 0
\(661\) 1.11255 0.0432734 0.0216367 0.999766i \(-0.493112\pi\)
0.0216367 + 0.999766i \(0.493112\pi\)
\(662\) 0 0
\(663\) 50.2471 1.95144
\(664\) 0 0
\(665\) −24.8411 −0.963295
\(666\) 0 0
\(667\) 16.5132 0.639395
\(668\) 0 0
\(669\) 53.9210 2.08471
\(670\) 0 0
\(671\) 54.7369 2.11310
\(672\) 0 0
\(673\) 38.1214 1.46947 0.734736 0.678353i \(-0.237306\pi\)
0.734736 + 0.678353i \(0.237306\pi\)
\(674\) 0 0
\(675\) −178.949 −6.88777
\(676\) 0 0
\(677\) −37.1434 −1.42754 −0.713768 0.700382i \(-0.753013\pi\)
−0.713768 + 0.700382i \(0.753013\pi\)
\(678\) 0 0
\(679\) −9.93872 −0.381413
\(680\) 0 0
\(681\) 16.9256 0.648592
\(682\) 0 0
\(683\) −6.33670 −0.242467 −0.121234 0.992624i \(-0.538685\pi\)
−0.121234 + 0.992624i \(0.538685\pi\)
\(684\) 0 0
\(685\) −4.43579 −0.169483
\(686\) 0 0
\(687\) 53.7427 2.05041
\(688\) 0 0
\(689\) 12.3124 0.469064
\(690\) 0 0
\(691\) 22.8522 0.869338 0.434669 0.900590i \(-0.356865\pi\)
0.434669 + 0.900590i \(0.356865\pi\)
\(692\) 0 0
\(693\) −68.0107 −2.58351
\(694\) 0 0
\(695\) 31.3145 1.18783
\(696\) 0 0
\(697\) −48.3080 −1.82980
\(698\) 0 0
\(699\) −54.8564 −2.07486
\(700\) 0 0
\(701\) 28.2026 1.06520 0.532599 0.846367i \(-0.321215\pi\)
0.532599 + 0.846367i \(0.321215\pi\)
\(702\) 0 0
\(703\) −0.385764 −0.0145494
\(704\) 0 0
\(705\) −91.7754 −3.45646
\(706\) 0 0
\(707\) 4.19578 0.157799
\(708\) 0 0
\(709\) 20.5816 0.772959 0.386480 0.922298i \(-0.373691\pi\)
0.386480 + 0.922298i \(0.373691\pi\)
\(710\) 0 0
\(711\) 48.5957 1.82248
\(712\) 0 0
\(713\) 26.8558 1.00576
\(714\) 0 0
\(715\) 73.9148 2.76426
\(716\) 0 0
\(717\) −35.5814 −1.32881
\(718\) 0 0
\(719\) 44.5493 1.66141 0.830704 0.556714i \(-0.187938\pi\)
0.830704 + 0.556714i \(0.187938\pi\)
\(720\) 0 0
\(721\) 0.196655 0.00732381
\(722\) 0 0
\(723\) 11.7007 0.435153
\(724\) 0 0
\(725\) −41.9414 −1.55766
\(726\) 0 0
\(727\) 20.2366 0.750535 0.375267 0.926917i \(-0.377551\pi\)
0.375267 + 0.926917i \(0.377551\pi\)
\(728\) 0 0
\(729\) 53.8461 1.99430
\(730\) 0 0
\(731\) 12.2883 0.454500
\(732\) 0 0
\(733\) −47.6432 −1.75974 −0.879871 0.475213i \(-0.842371\pi\)
−0.879871 + 0.475213i \(0.842371\pi\)
\(734\) 0 0
\(735\) −58.8827 −2.17192
\(736\) 0 0
\(737\) 76.4811 2.81722
\(738\) 0 0
\(739\) 21.0770 0.775328 0.387664 0.921801i \(-0.373282\pi\)
0.387664 + 0.921801i \(0.373282\pi\)
\(740\) 0 0
\(741\) −39.9689 −1.46829
\(742\) 0 0
\(743\) −40.9802 −1.50342 −0.751708 0.659496i \(-0.770770\pi\)
−0.751708 + 0.659496i \(0.770770\pi\)
\(744\) 0 0
\(745\) −32.6669 −1.19682
\(746\) 0 0
\(747\) −83.9606 −3.07196
\(748\) 0 0
\(749\) 26.7011 0.975638
\(750\) 0 0
\(751\) 21.2943 0.777040 0.388520 0.921440i \(-0.372986\pi\)
0.388520 + 0.921440i \(0.372986\pi\)
\(752\) 0 0
\(753\) −3.26165 −0.118861
\(754\) 0 0
\(755\) −65.3235 −2.37737
\(756\) 0 0
\(757\) −12.5443 −0.455929 −0.227964 0.973669i \(-0.573207\pi\)
−0.227964 + 0.973669i \(0.573207\pi\)
\(758\) 0 0
\(759\) −83.8891 −3.04498
\(760\) 0 0
\(761\) 15.3106 0.555008 0.277504 0.960725i \(-0.410493\pi\)
0.277504 + 0.960725i \(0.410493\pi\)
\(762\) 0 0
\(763\) −12.7530 −0.461688
\(764\) 0 0
\(765\) 147.958 5.34944
\(766\) 0 0
\(767\) −18.7716 −0.677802
\(768\) 0 0
\(769\) 29.6740 1.07007 0.535037 0.844829i \(-0.320298\pi\)
0.535037 + 0.844829i \(0.320298\pi\)
\(770\) 0 0
\(771\) 58.4101 2.10359
\(772\) 0 0
\(773\) −42.3396 −1.52285 −0.761425 0.648253i \(-0.775500\pi\)
−0.761425 + 0.648253i \(0.775500\pi\)
\(774\) 0 0
\(775\) −68.2103 −2.45019
\(776\) 0 0
\(777\) 0.540076 0.0193751
\(778\) 0 0
\(779\) 38.4264 1.37677
\(780\) 0 0
\(781\) 83.1255 2.97446
\(782\) 0 0
\(783\) 53.6441 1.91709
\(784\) 0 0
\(785\) −68.5481 −2.44659
\(786\) 0 0
\(787\) −10.6407 −0.379301 −0.189650 0.981852i \(-0.560735\pi\)
−0.189650 + 0.981852i \(0.560735\pi\)
\(788\) 0 0
\(789\) −17.5877 −0.626138
\(790\) 0 0
\(791\) −12.8927 −0.458413
\(792\) 0 0
\(793\) −32.3359 −1.14828
\(794\) 0 0
\(795\) 50.4945 1.79085
\(796\) 0 0
\(797\) 18.2419 0.646162 0.323081 0.946371i \(-0.395281\pi\)
0.323081 + 0.946371i \(0.395281\pi\)
\(798\) 0 0
\(799\) 32.3879 1.14580
\(800\) 0 0
\(801\) 11.9839 0.423430
\(802\) 0 0
\(803\) 86.4189 3.04966
\(804\) 0 0
\(805\) 30.8005 1.08558
\(806\) 0 0
\(807\) 67.8375 2.38799
\(808\) 0 0
\(809\) 39.8695 1.40174 0.700868 0.713291i \(-0.252796\pi\)
0.700868 + 0.713291i \(0.252796\pi\)
\(810\) 0 0
\(811\) 50.7282 1.78131 0.890654 0.454682i \(-0.150247\pi\)
0.890654 + 0.454682i \(0.150247\pi\)
\(812\) 0 0
\(813\) 77.8579 2.73059
\(814\) 0 0
\(815\) −30.1066 −1.05459
\(816\) 0 0
\(817\) −9.77469 −0.341973
\(818\) 0 0
\(819\) 40.1773 1.40391
\(820\) 0 0
\(821\) −7.53704 −0.263045 −0.131522 0.991313i \(-0.541986\pi\)
−0.131522 + 0.991313i \(0.541986\pi\)
\(822\) 0 0
\(823\) −23.9516 −0.834901 −0.417450 0.908700i \(-0.637076\pi\)
−0.417450 + 0.908700i \(0.637076\pi\)
\(824\) 0 0
\(825\) 213.067 7.41805
\(826\) 0 0
\(827\) −34.1475 −1.18743 −0.593713 0.804677i \(-0.702339\pi\)
−0.593713 + 0.804677i \(0.702339\pi\)
\(828\) 0 0
\(829\) 53.3738 1.85375 0.926874 0.375373i \(-0.122485\pi\)
0.926874 + 0.375373i \(0.122485\pi\)
\(830\) 0 0
\(831\) 28.1346 0.975977
\(832\) 0 0
\(833\) 20.7800 0.719984
\(834\) 0 0
\(835\) −41.4322 −1.43382
\(836\) 0 0
\(837\) 87.2427 3.01555
\(838\) 0 0
\(839\) 0.308967 0.0106667 0.00533337 0.999986i \(-0.498302\pi\)
0.00533337 + 0.999986i \(0.498302\pi\)
\(840\) 0 0
\(841\) −16.4271 −0.566452
\(842\) 0 0
\(843\) −11.9524 −0.411662
\(844\) 0 0
\(845\) 9.66394 0.332450
\(846\) 0 0
\(847\) 31.4389 1.08025
\(848\) 0 0
\(849\) −24.4990 −0.840802
\(850\) 0 0
\(851\) 0.478310 0.0163962
\(852\) 0 0
\(853\) 39.2324 1.34329 0.671646 0.740872i \(-0.265588\pi\)
0.671646 + 0.740872i \(0.265588\pi\)
\(854\) 0 0
\(855\) −117.693 −4.02501
\(856\) 0 0
\(857\) −5.22022 −0.178319 −0.0891597 0.996017i \(-0.528418\pi\)
−0.0891597 + 0.996017i \(0.528418\pi\)
\(858\) 0 0
\(859\) −41.5588 −1.41797 −0.708983 0.705225i \(-0.750846\pi\)
−0.708983 + 0.705225i \(0.750846\pi\)
\(860\) 0 0
\(861\) −53.7975 −1.83342
\(862\) 0 0
\(863\) −14.0049 −0.476732 −0.238366 0.971175i \(-0.576612\pi\)
−0.238366 + 0.971175i \(0.576612\pi\)
\(864\) 0 0
\(865\) −6.96508 −0.236820
\(866\) 0 0
\(867\) −17.2747 −0.586680
\(868\) 0 0
\(869\) −35.1358 −1.19190
\(870\) 0 0
\(871\) −45.1812 −1.53091
\(872\) 0 0
\(873\) −47.0879 −1.59369
\(874\) 0 0
\(875\) −45.1608 −1.52671
\(876\) 0 0
\(877\) −3.62374 −0.122365 −0.0611825 0.998127i \(-0.519487\pi\)
−0.0611825 + 0.998127i \(0.519487\pi\)
\(878\) 0 0
\(879\) 49.4468 1.66780
\(880\) 0 0
\(881\) 1.57415 0.0530344 0.0265172 0.999648i \(-0.491558\pi\)
0.0265172 + 0.999648i \(0.491558\pi\)
\(882\) 0 0
\(883\) 32.9337 1.10831 0.554154 0.832414i \(-0.313042\pi\)
0.554154 + 0.832414i \(0.313042\pi\)
\(884\) 0 0
\(885\) −76.9843 −2.58780
\(886\) 0 0
\(887\) 7.15176 0.240132 0.120066 0.992766i \(-0.461689\pi\)
0.120066 + 0.992766i \(0.461689\pi\)
\(888\) 0 0
\(889\) 6.25839 0.209900
\(890\) 0 0
\(891\) −145.964 −4.88999
\(892\) 0 0
\(893\) −25.7629 −0.862121
\(894\) 0 0
\(895\) 63.9530 2.13771
\(896\) 0 0
\(897\) 49.5575 1.65468
\(898\) 0 0
\(899\) 20.4476 0.681965
\(900\) 0 0
\(901\) −17.8197 −0.593661
\(902\) 0 0
\(903\) 13.6847 0.455399
\(904\) 0 0
\(905\) −6.81907 −0.226674
\(906\) 0 0
\(907\) −11.8811 −0.394505 −0.197252 0.980353i \(-0.563202\pi\)
−0.197252 + 0.980353i \(0.563202\pi\)
\(908\) 0 0
\(909\) 19.8789 0.659341
\(910\) 0 0
\(911\) 32.0018 1.06027 0.530134 0.847914i \(-0.322142\pi\)
0.530134 + 0.847914i \(0.322142\pi\)
\(912\) 0 0
\(913\) 60.7054 2.00906
\(914\) 0 0
\(915\) −132.613 −4.38405
\(916\) 0 0
\(917\) 19.0102 0.627772
\(918\) 0 0
\(919\) 46.9243 1.54789 0.773946 0.633252i \(-0.218280\pi\)
0.773946 + 0.633252i \(0.218280\pi\)
\(920\) 0 0
\(921\) −48.2215 −1.58895
\(922\) 0 0
\(923\) −49.1064 −1.61636
\(924\) 0 0
\(925\) −1.21484 −0.0399438
\(926\) 0 0
\(927\) 0.931718 0.0306016
\(928\) 0 0
\(929\) 37.1512 1.21889 0.609446 0.792827i \(-0.291392\pi\)
0.609446 + 0.792827i \(0.291392\pi\)
\(930\) 0 0
\(931\) −16.5294 −0.541728
\(932\) 0 0
\(933\) −87.9083 −2.87799
\(934\) 0 0
\(935\) −106.977 −3.49853
\(936\) 0 0
\(937\) −40.6438 −1.32778 −0.663888 0.747832i \(-0.731095\pi\)
−0.663888 + 0.747832i \(0.731095\pi\)
\(938\) 0 0
\(939\) 84.7915 2.76707
\(940\) 0 0
\(941\) −16.4220 −0.535341 −0.267670 0.963511i \(-0.586254\pi\)
−0.267670 + 0.963511i \(0.586254\pi\)
\(942\) 0 0
\(943\) −47.6450 −1.55153
\(944\) 0 0
\(945\) 100.057 3.25486
\(946\) 0 0
\(947\) −13.1461 −0.427192 −0.213596 0.976922i \(-0.568518\pi\)
−0.213596 + 0.976922i \(0.568518\pi\)
\(948\) 0 0
\(949\) −51.0520 −1.65722
\(950\) 0 0
\(951\) −76.5380 −2.48192
\(952\) 0 0
\(953\) −4.98372 −0.161439 −0.0807193 0.996737i \(-0.525722\pi\)
−0.0807193 + 0.996737i \(0.525722\pi\)
\(954\) 0 0
\(955\) −48.2138 −1.56016
\(956\) 0 0
\(957\) −63.8717 −2.06468
\(958\) 0 0
\(959\) 1.74330 0.0562941
\(960\) 0 0
\(961\) 2.25436 0.0727214
\(962\) 0 0
\(963\) 126.505 4.07658
\(964\) 0 0
\(965\) −69.1167 −2.22495
\(966\) 0 0
\(967\) −35.0081 −1.12578 −0.562892 0.826530i \(-0.690311\pi\)
−0.562892 + 0.826530i \(0.690311\pi\)
\(968\) 0 0
\(969\) 57.8471 1.85831
\(970\) 0 0
\(971\) 13.4959 0.433105 0.216552 0.976271i \(-0.430519\pi\)
0.216552 + 0.976271i \(0.430519\pi\)
\(972\) 0 0
\(973\) −12.3068 −0.394539
\(974\) 0 0
\(975\) −125.870 −4.03105
\(976\) 0 0
\(977\) −5.66777 −0.181328 −0.0906640 0.995882i \(-0.528899\pi\)
−0.0906640 + 0.995882i \(0.528899\pi\)
\(978\) 0 0
\(979\) −8.66462 −0.276922
\(980\) 0 0
\(981\) −60.4214 −1.92911
\(982\) 0 0
\(983\) 28.8757 0.920993 0.460497 0.887661i \(-0.347671\pi\)
0.460497 + 0.887661i \(0.347671\pi\)
\(984\) 0 0
\(985\) 72.6477 2.31475
\(986\) 0 0
\(987\) 36.0684 1.14807
\(988\) 0 0
\(989\) 12.1197 0.385383
\(990\) 0 0
\(991\) 15.4635 0.491214 0.245607 0.969370i \(-0.421013\pi\)
0.245607 + 0.969370i \(0.421013\pi\)
\(992\) 0 0
\(993\) −39.2363 −1.24513
\(994\) 0 0
\(995\) −15.8136 −0.501326
\(996\) 0 0
\(997\) −27.2654 −0.863503 −0.431751 0.901993i \(-0.642104\pi\)
−0.431751 + 0.901993i \(0.642104\pi\)
\(998\) 0 0
\(999\) 1.55382 0.0491605
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.1.2 23
4.3 odd 2 2008.2.a.d.1.22 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.22 23 4.3 odd 2
4016.2.a.m.1.2 23 1.1 even 1 trivial