Properties

Label 4016.2.a.m.1.8
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 1.8
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.63778 q^{3} +2.87336 q^{5} +2.53418 q^{7} -0.317671 q^{9} +O(q^{10})\) \(q-1.63778 q^{3} +2.87336 q^{5} +2.53418 q^{7} -0.317671 q^{9} +3.58220 q^{11} +5.49911 q^{13} -4.70594 q^{15} +6.64173 q^{17} +3.16598 q^{19} -4.15044 q^{21} -2.23185 q^{23} +3.25622 q^{25} +5.43362 q^{27} +5.29424 q^{29} -6.91659 q^{31} -5.86686 q^{33} +7.28163 q^{35} +6.97947 q^{37} -9.00634 q^{39} +8.56040 q^{41} -7.68921 q^{43} -0.912784 q^{45} +2.74446 q^{47} -0.577911 q^{49} -10.8777 q^{51} -6.46446 q^{53} +10.2930 q^{55} -5.18518 q^{57} -2.83419 q^{59} -1.72071 q^{61} -0.805036 q^{63} +15.8009 q^{65} -6.56400 q^{67} +3.65528 q^{69} -8.23946 q^{71} +3.78141 q^{73} -5.33299 q^{75} +9.07795 q^{77} -1.99913 q^{79} -7.94607 q^{81} +3.83734 q^{83} +19.0841 q^{85} -8.67081 q^{87} -2.50063 q^{89} +13.9358 q^{91} +11.3279 q^{93} +9.09701 q^{95} -19.1894 q^{97} -1.13796 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

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
\(3\) −1.63778 −0.945574 −0.472787 0.881177i \(-0.656752\pi\)
−0.472787 + 0.881177i \(0.656752\pi\)
\(4\) 0 0
\(5\) 2.87336 1.28501 0.642504 0.766282i \(-0.277896\pi\)
0.642504 + 0.766282i \(0.277896\pi\)
\(6\) 0 0
\(7\) 2.53418 0.957832 0.478916 0.877861i \(-0.341030\pi\)
0.478916 + 0.877861i \(0.341030\pi\)
\(8\) 0 0
\(9\) −0.317671 −0.105890
\(10\) 0 0
\(11\) 3.58220 1.08007 0.540037 0.841641i \(-0.318410\pi\)
0.540037 + 0.841641i \(0.318410\pi\)
\(12\) 0 0
\(13\) 5.49911 1.52518 0.762589 0.646883i \(-0.223928\pi\)
0.762589 + 0.646883i \(0.223928\pi\)
\(14\) 0 0
\(15\) −4.70594 −1.21507
\(16\) 0 0
\(17\) 6.64173 1.61086 0.805428 0.592694i \(-0.201936\pi\)
0.805428 + 0.592694i \(0.201936\pi\)
\(18\) 0 0
\(19\) 3.16598 0.726325 0.363163 0.931726i \(-0.381697\pi\)
0.363163 + 0.931726i \(0.381697\pi\)
\(20\) 0 0
\(21\) −4.15044 −0.905700
\(22\) 0 0
\(23\) −2.23185 −0.465372 −0.232686 0.972552i \(-0.574751\pi\)
−0.232686 + 0.972552i \(0.574751\pi\)
\(24\) 0 0
\(25\) 3.25622 0.651245
\(26\) 0 0
\(27\) 5.43362 1.04570
\(28\) 0 0
\(29\) 5.29424 0.983116 0.491558 0.870845i \(-0.336428\pi\)
0.491558 + 0.870845i \(0.336428\pi\)
\(30\) 0 0
\(31\) −6.91659 −1.24226 −0.621128 0.783709i \(-0.713325\pi\)
−0.621128 + 0.783709i \(0.713325\pi\)
\(32\) 0 0
\(33\) −5.86686 −1.02129
\(34\) 0 0
\(35\) 7.28163 1.23082
\(36\) 0 0
\(37\) 6.97947 1.14742 0.573709 0.819059i \(-0.305504\pi\)
0.573709 + 0.819059i \(0.305504\pi\)
\(38\) 0 0
\(39\) −9.00634 −1.44217
\(40\) 0 0
\(41\) 8.56040 1.33691 0.668455 0.743753i \(-0.266956\pi\)
0.668455 + 0.743753i \(0.266956\pi\)
\(42\) 0 0
\(43\) −7.68921 −1.17259 −0.586297 0.810096i \(-0.699415\pi\)
−0.586297 + 0.810096i \(0.699415\pi\)
\(44\) 0 0
\(45\) −0.912784 −0.136070
\(46\) 0 0
\(47\) 2.74446 0.400321 0.200161 0.979763i \(-0.435854\pi\)
0.200161 + 0.979763i \(0.435854\pi\)
\(48\) 0 0
\(49\) −0.577911 −0.0825587
\(50\) 0 0
\(51\) −10.8777 −1.52318
\(52\) 0 0
\(53\) −6.46446 −0.887962 −0.443981 0.896036i \(-0.646434\pi\)
−0.443981 + 0.896036i \(0.646434\pi\)
\(54\) 0 0
\(55\) 10.2930 1.38790
\(56\) 0 0
\(57\) −5.18518 −0.686794
\(58\) 0 0
\(59\) −2.83419 −0.368980 −0.184490 0.982834i \(-0.559063\pi\)
−0.184490 + 0.982834i \(0.559063\pi\)
\(60\) 0 0
\(61\) −1.72071 −0.220315 −0.110157 0.993914i \(-0.535136\pi\)
−0.110157 + 0.993914i \(0.535136\pi\)
\(62\) 0 0
\(63\) −0.805036 −0.101425
\(64\) 0 0
\(65\) 15.8009 1.95987
\(66\) 0 0
\(67\) −6.56400 −0.801920 −0.400960 0.916095i \(-0.631323\pi\)
−0.400960 + 0.916095i \(0.631323\pi\)
\(68\) 0 0
\(69\) 3.65528 0.440043
\(70\) 0 0
\(71\) −8.23946 −0.977844 −0.488922 0.872327i \(-0.662610\pi\)
−0.488922 + 0.872327i \(0.662610\pi\)
\(72\) 0 0
\(73\) 3.78141 0.442581 0.221290 0.975208i \(-0.428973\pi\)
0.221290 + 0.975208i \(0.428973\pi\)
\(74\) 0 0
\(75\) −5.33299 −0.615800
\(76\) 0 0
\(77\) 9.07795 1.03453
\(78\) 0 0
\(79\) −1.99913 −0.224920 −0.112460 0.993656i \(-0.535873\pi\)
−0.112460 + 0.993656i \(0.535873\pi\)
\(80\) 0 0
\(81\) −7.94607 −0.882897
\(82\) 0 0
\(83\) 3.83734 0.421202 0.210601 0.977572i \(-0.432458\pi\)
0.210601 + 0.977572i \(0.432458\pi\)
\(84\) 0 0
\(85\) 19.0841 2.06996
\(86\) 0 0
\(87\) −8.67081 −0.929608
\(88\) 0 0
\(89\) −2.50063 −0.265067 −0.132533 0.991179i \(-0.542311\pi\)
−0.132533 + 0.991179i \(0.542311\pi\)
\(90\) 0 0
\(91\) 13.9358 1.46086
\(92\) 0 0
\(93\) 11.3279 1.17465
\(94\) 0 0
\(95\) 9.09701 0.933334
\(96\) 0 0
\(97\) −19.1894 −1.94839 −0.974194 0.225712i \(-0.927529\pi\)
−0.974194 + 0.225712i \(0.927529\pi\)
\(98\) 0 0
\(99\) −1.13796 −0.114369
\(100\) 0 0
\(101\) −18.3520 −1.82609 −0.913047 0.407855i \(-0.866277\pi\)
−0.913047 + 0.407855i \(0.866277\pi\)
\(102\) 0 0
\(103\) 2.26082 0.222765 0.111382 0.993778i \(-0.464472\pi\)
0.111382 + 0.993778i \(0.464472\pi\)
\(104\) 0 0
\(105\) −11.9257 −1.16383
\(106\) 0 0
\(107\) 7.98752 0.772182 0.386091 0.922461i \(-0.373825\pi\)
0.386091 + 0.922461i \(0.373825\pi\)
\(108\) 0 0
\(109\) −10.4937 −1.00511 −0.502556 0.864545i \(-0.667607\pi\)
−0.502556 + 0.864545i \(0.667607\pi\)
\(110\) 0 0
\(111\) −11.4308 −1.08497
\(112\) 0 0
\(113\) −11.2368 −1.05707 −0.528535 0.848911i \(-0.677259\pi\)
−0.528535 + 0.848911i \(0.677259\pi\)
\(114\) 0 0
\(115\) −6.41291 −0.598006
\(116\) 0 0
\(117\) −1.74691 −0.161501
\(118\) 0 0
\(119\) 16.8314 1.54293
\(120\) 0 0
\(121\) 1.83216 0.166560
\(122\) 0 0
\(123\) −14.0201 −1.26415
\(124\) 0 0
\(125\) −5.01050 −0.448153
\(126\) 0 0
\(127\) 15.4562 1.37152 0.685758 0.727829i \(-0.259471\pi\)
0.685758 + 0.727829i \(0.259471\pi\)
\(128\) 0 0
\(129\) 12.5933 1.10877
\(130\) 0 0
\(131\) −4.77547 −0.417235 −0.208617 0.977997i \(-0.566896\pi\)
−0.208617 + 0.977997i \(0.566896\pi\)
\(132\) 0 0
\(133\) 8.02317 0.695697
\(134\) 0 0
\(135\) 15.6128 1.34373
\(136\) 0 0
\(137\) 0.915844 0.0782458 0.0391229 0.999234i \(-0.487544\pi\)
0.0391229 + 0.999234i \(0.487544\pi\)
\(138\) 0 0
\(139\) −10.3649 −0.879142 −0.439571 0.898208i \(-0.644869\pi\)
−0.439571 + 0.898208i \(0.644869\pi\)
\(140\) 0 0
\(141\) −4.49483 −0.378533
\(142\) 0 0
\(143\) 19.6989 1.64731
\(144\) 0 0
\(145\) 15.2123 1.26331
\(146\) 0 0
\(147\) 0.946492 0.0780654
\(148\) 0 0
\(149\) −3.02783 −0.248050 −0.124025 0.992279i \(-0.539580\pi\)
−0.124025 + 0.992279i \(0.539580\pi\)
\(150\) 0 0
\(151\) 13.3704 1.08807 0.544034 0.839063i \(-0.316896\pi\)
0.544034 + 0.839063i \(0.316896\pi\)
\(152\) 0 0
\(153\) −2.10988 −0.170574
\(154\) 0 0
\(155\) −19.8739 −1.59631
\(156\) 0 0
\(157\) 11.6842 0.932502 0.466251 0.884652i \(-0.345604\pi\)
0.466251 + 0.884652i \(0.345604\pi\)
\(158\) 0 0
\(159\) 10.5874 0.839633
\(160\) 0 0
\(161\) −5.65591 −0.445748
\(162\) 0 0
\(163\) −19.7450 −1.54655 −0.773273 0.634073i \(-0.781382\pi\)
−0.773273 + 0.634073i \(0.781382\pi\)
\(164\) 0 0
\(165\) −16.8576 −1.31237
\(166\) 0 0
\(167\) 12.2898 0.951012 0.475506 0.879712i \(-0.342265\pi\)
0.475506 + 0.879712i \(0.342265\pi\)
\(168\) 0 0
\(169\) 17.2402 1.32617
\(170\) 0 0
\(171\) −1.00574 −0.0769108
\(172\) 0 0
\(173\) 8.17998 0.621913 0.310956 0.950424i \(-0.399351\pi\)
0.310956 + 0.950424i \(0.399351\pi\)
\(174\) 0 0
\(175\) 8.25187 0.623783
\(176\) 0 0
\(177\) 4.64178 0.348898
\(178\) 0 0
\(179\) −12.4848 −0.933158 −0.466579 0.884480i \(-0.654514\pi\)
−0.466579 + 0.884480i \(0.654514\pi\)
\(180\) 0 0
\(181\) −14.3557 −1.06705 −0.533524 0.845785i \(-0.679132\pi\)
−0.533524 + 0.845785i \(0.679132\pi\)
\(182\) 0 0
\(183\) 2.81816 0.208324
\(184\) 0 0
\(185\) 20.0546 1.47444
\(186\) 0 0
\(187\) 23.7920 1.73984
\(188\) 0 0
\(189\) 13.7698 1.00161
\(190\) 0 0
\(191\) −15.3815 −1.11296 −0.556482 0.830860i \(-0.687849\pi\)
−0.556482 + 0.830860i \(0.687849\pi\)
\(192\) 0 0
\(193\) −19.8713 −1.43037 −0.715183 0.698938i \(-0.753656\pi\)
−0.715183 + 0.698938i \(0.753656\pi\)
\(194\) 0 0
\(195\) −25.8785 −1.85320
\(196\) 0 0
\(197\) −17.6912 −1.26045 −0.630225 0.776413i \(-0.717037\pi\)
−0.630225 + 0.776413i \(0.717037\pi\)
\(198\) 0 0
\(199\) 15.5377 1.10144 0.550720 0.834690i \(-0.314353\pi\)
0.550720 + 0.834690i \(0.314353\pi\)
\(200\) 0 0
\(201\) 10.7504 0.758275
\(202\) 0 0
\(203\) 13.4166 0.941659
\(204\) 0 0
\(205\) 24.5972 1.71794
\(206\) 0 0
\(207\) 0.708992 0.0492783
\(208\) 0 0
\(209\) 11.3412 0.784485
\(210\) 0 0
\(211\) −20.3588 −1.40156 −0.700780 0.713378i \(-0.747164\pi\)
−0.700780 + 0.713378i \(0.747164\pi\)
\(212\) 0 0
\(213\) 13.4944 0.924624
\(214\) 0 0
\(215\) −22.0939 −1.50679
\(216\) 0 0
\(217\) −17.5279 −1.18987
\(218\) 0 0
\(219\) −6.19313 −0.418493
\(220\) 0 0
\(221\) 36.5236 2.45684
\(222\) 0 0
\(223\) 1.77751 0.119031 0.0595156 0.998227i \(-0.481044\pi\)
0.0595156 + 0.998227i \(0.481044\pi\)
\(224\) 0 0
\(225\) −1.03441 −0.0689605
\(226\) 0 0
\(227\) 24.2202 1.60755 0.803777 0.594931i \(-0.202821\pi\)
0.803777 + 0.594931i \(0.202821\pi\)
\(228\) 0 0
\(229\) 24.9310 1.64749 0.823745 0.566960i \(-0.191881\pi\)
0.823745 + 0.566960i \(0.191881\pi\)
\(230\) 0 0
\(231\) −14.8677 −0.978223
\(232\) 0 0
\(233\) 3.63799 0.238333 0.119166 0.992874i \(-0.461978\pi\)
0.119166 + 0.992874i \(0.461978\pi\)
\(234\) 0 0
\(235\) 7.88584 0.514416
\(236\) 0 0
\(237\) 3.27414 0.212678
\(238\) 0 0
\(239\) 5.55109 0.359070 0.179535 0.983752i \(-0.442541\pi\)
0.179535 + 0.983752i \(0.442541\pi\)
\(240\) 0 0
\(241\) 22.6127 1.45661 0.728307 0.685251i \(-0.240308\pi\)
0.728307 + 0.685251i \(0.240308\pi\)
\(242\) 0 0
\(243\) −3.28693 −0.210857
\(244\) 0 0
\(245\) −1.66055 −0.106089
\(246\) 0 0
\(247\) 17.4101 1.10778
\(248\) 0 0
\(249\) −6.28472 −0.398278
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) −7.99492 −0.502636
\(254\) 0 0
\(255\) −31.2556 −1.95730
\(256\) 0 0
\(257\) −3.81945 −0.238250 −0.119125 0.992879i \(-0.538009\pi\)
−0.119125 + 0.992879i \(0.538009\pi\)
\(258\) 0 0
\(259\) 17.6873 1.09903
\(260\) 0 0
\(261\) −1.68182 −0.104102
\(262\) 0 0
\(263\) −14.7787 −0.911293 −0.455647 0.890161i \(-0.650592\pi\)
−0.455647 + 0.890161i \(0.650592\pi\)
\(264\) 0 0
\(265\) −18.5747 −1.14104
\(266\) 0 0
\(267\) 4.09549 0.250640
\(268\) 0 0
\(269\) −3.19011 −0.194505 −0.0972523 0.995260i \(-0.531005\pi\)
−0.0972523 + 0.995260i \(0.531005\pi\)
\(270\) 0 0
\(271\) 1.80281 0.109513 0.0547566 0.998500i \(-0.482562\pi\)
0.0547566 + 0.998500i \(0.482562\pi\)
\(272\) 0 0
\(273\) −22.8237 −1.38135
\(274\) 0 0
\(275\) 11.6644 0.703393
\(276\) 0 0
\(277\) −29.4958 −1.77223 −0.886117 0.463462i \(-0.846607\pi\)
−0.886117 + 0.463462i \(0.846607\pi\)
\(278\) 0 0
\(279\) 2.19720 0.131543
\(280\) 0 0
\(281\) −13.8365 −0.825417 −0.412709 0.910863i \(-0.635417\pi\)
−0.412709 + 0.910863i \(0.635417\pi\)
\(282\) 0 0
\(283\) 19.1061 1.13574 0.567870 0.823119i \(-0.307768\pi\)
0.567870 + 0.823119i \(0.307768\pi\)
\(284\) 0 0
\(285\) −14.8989 −0.882536
\(286\) 0 0
\(287\) 21.6936 1.28053
\(288\) 0 0
\(289\) 27.1125 1.59485
\(290\) 0 0
\(291\) 31.4280 1.84234
\(292\) 0 0
\(293\) 21.8992 1.27936 0.639682 0.768640i \(-0.279066\pi\)
0.639682 + 0.768640i \(0.279066\pi\)
\(294\) 0 0
\(295\) −8.14365 −0.474142
\(296\) 0 0
\(297\) 19.4643 1.12943
\(298\) 0 0
\(299\) −12.2732 −0.709775
\(300\) 0 0
\(301\) −19.4859 −1.12315
\(302\) 0 0
\(303\) 30.0566 1.72671
\(304\) 0 0
\(305\) −4.94424 −0.283106
\(306\) 0 0
\(307\) −17.5125 −0.999489 −0.499745 0.866173i \(-0.666573\pi\)
−0.499745 + 0.866173i \(0.666573\pi\)
\(308\) 0 0
\(309\) −3.70272 −0.210641
\(310\) 0 0
\(311\) −1.54200 −0.0874386 −0.0437193 0.999044i \(-0.513921\pi\)
−0.0437193 + 0.999044i \(0.513921\pi\)
\(312\) 0 0
\(313\) 22.7634 1.28667 0.643333 0.765587i \(-0.277551\pi\)
0.643333 + 0.765587i \(0.277551\pi\)
\(314\) 0 0
\(315\) −2.31316 −0.130332
\(316\) 0 0
\(317\) 6.17875 0.347033 0.173517 0.984831i \(-0.444487\pi\)
0.173517 + 0.984831i \(0.444487\pi\)
\(318\) 0 0
\(319\) 18.9650 1.06184
\(320\) 0 0
\(321\) −13.0818 −0.730155
\(322\) 0 0
\(323\) 21.0276 1.17001
\(324\) 0 0
\(325\) 17.9063 0.993264
\(326\) 0 0
\(327\) 17.1864 0.950408
\(328\) 0 0
\(329\) 6.95497 0.383440
\(330\) 0 0
\(331\) 15.0907 0.829460 0.414730 0.909944i \(-0.363876\pi\)
0.414730 + 0.909944i \(0.363876\pi\)
\(332\) 0 0
\(333\) −2.21717 −0.121500
\(334\) 0 0
\(335\) −18.8608 −1.03047
\(336\) 0 0
\(337\) 12.7597 0.695063 0.347532 0.937668i \(-0.387020\pi\)
0.347532 + 0.937668i \(0.387020\pi\)
\(338\) 0 0
\(339\) 18.4035 0.999538
\(340\) 0 0
\(341\) −24.7766 −1.34173
\(342\) 0 0
\(343\) −19.2038 −1.03691
\(344\) 0 0
\(345\) 10.5029 0.565459
\(346\) 0 0
\(347\) −8.65152 −0.464438 −0.232219 0.972664i \(-0.574599\pi\)
−0.232219 + 0.972664i \(0.574599\pi\)
\(348\) 0 0
\(349\) 21.4064 1.14586 0.572928 0.819606i \(-0.305807\pi\)
0.572928 + 0.819606i \(0.305807\pi\)
\(350\) 0 0
\(351\) 29.8801 1.59488
\(352\) 0 0
\(353\) −0.184444 −0.00981694 −0.00490847 0.999988i \(-0.501562\pi\)
−0.00490847 + 0.999988i \(0.501562\pi\)
\(354\) 0 0
\(355\) −23.6750 −1.25654
\(356\) 0 0
\(357\) −27.5661 −1.45895
\(358\) 0 0
\(359\) −26.8516 −1.41718 −0.708588 0.705623i \(-0.750667\pi\)
−0.708588 + 0.705623i \(0.750667\pi\)
\(360\) 0 0
\(361\) −8.97658 −0.472451
\(362\) 0 0
\(363\) −3.00068 −0.157495
\(364\) 0 0
\(365\) 10.8654 0.568720
\(366\) 0 0
\(367\) 33.8931 1.76920 0.884602 0.466347i \(-0.154430\pi\)
0.884602 + 0.466347i \(0.154430\pi\)
\(368\) 0 0
\(369\) −2.71939 −0.141566
\(370\) 0 0
\(371\) −16.3821 −0.850518
\(372\) 0 0
\(373\) −12.3751 −0.640757 −0.320378 0.947290i \(-0.603810\pi\)
−0.320378 + 0.947290i \(0.603810\pi\)
\(374\) 0 0
\(375\) 8.20611 0.423762
\(376\) 0 0
\(377\) 29.1136 1.49943
\(378\) 0 0
\(379\) 16.0864 0.826302 0.413151 0.910662i \(-0.364428\pi\)
0.413151 + 0.910662i \(0.364428\pi\)
\(380\) 0 0
\(381\) −25.3139 −1.29687
\(382\) 0 0
\(383\) 15.2145 0.777423 0.388712 0.921359i \(-0.372920\pi\)
0.388712 + 0.921359i \(0.372920\pi\)
\(384\) 0 0
\(385\) 26.0843 1.32938
\(386\) 0 0
\(387\) 2.44264 0.124166
\(388\) 0 0
\(389\) −14.1557 −0.717720 −0.358860 0.933391i \(-0.616835\pi\)
−0.358860 + 0.933391i \(0.616835\pi\)
\(390\) 0 0
\(391\) −14.8233 −0.749647
\(392\) 0 0
\(393\) 7.82118 0.394526
\(394\) 0 0
\(395\) −5.74424 −0.289024
\(396\) 0 0
\(397\) 0.221665 0.0111250 0.00556252 0.999985i \(-0.498229\pi\)
0.00556252 + 0.999985i \(0.498229\pi\)
\(398\) 0 0
\(399\) −13.1402 −0.657833
\(400\) 0 0
\(401\) 27.8688 1.39170 0.695850 0.718187i \(-0.255028\pi\)
0.695850 + 0.718187i \(0.255028\pi\)
\(402\) 0 0
\(403\) −38.0351 −1.89466
\(404\) 0 0
\(405\) −22.8320 −1.13453
\(406\) 0 0
\(407\) 25.0019 1.23930
\(408\) 0 0
\(409\) 0.197291 0.00975540 0.00487770 0.999988i \(-0.498447\pi\)
0.00487770 + 0.999988i \(0.498447\pi\)
\(410\) 0 0
\(411\) −1.49995 −0.0739872
\(412\) 0 0
\(413\) −7.18235 −0.353420
\(414\) 0 0
\(415\) 11.0261 0.541248
\(416\) 0 0
\(417\) 16.9755 0.831293
\(418\) 0 0
\(419\) 27.7060 1.35352 0.676762 0.736202i \(-0.263383\pi\)
0.676762 + 0.736202i \(0.263383\pi\)
\(420\) 0 0
\(421\) −21.6023 −1.05283 −0.526415 0.850227i \(-0.676464\pi\)
−0.526415 + 0.850227i \(0.676464\pi\)
\(422\) 0 0
\(423\) −0.871835 −0.0423901
\(424\) 0 0
\(425\) 21.6270 1.04906
\(426\) 0 0
\(427\) −4.36061 −0.211025
\(428\) 0 0
\(429\) −32.2625 −1.55765
\(430\) 0 0
\(431\) 10.9317 0.526563 0.263282 0.964719i \(-0.415195\pi\)
0.263282 + 0.964719i \(0.415195\pi\)
\(432\) 0 0
\(433\) 19.9311 0.957829 0.478914 0.877862i \(-0.341030\pi\)
0.478914 + 0.877862i \(0.341030\pi\)
\(434\) 0 0
\(435\) −24.9144 −1.19455
\(436\) 0 0
\(437\) −7.06597 −0.338011
\(438\) 0 0
\(439\) −8.46326 −0.403930 −0.201965 0.979393i \(-0.564733\pi\)
−0.201965 + 0.979393i \(0.564733\pi\)
\(440\) 0 0
\(441\) 0.183585 0.00874216
\(442\) 0 0
\(443\) 16.5587 0.786725 0.393363 0.919383i \(-0.371312\pi\)
0.393363 + 0.919383i \(0.371312\pi\)
\(444\) 0 0
\(445\) −7.18523 −0.340613
\(446\) 0 0
\(447\) 4.95893 0.234549
\(448\) 0 0
\(449\) 1.25857 0.0593956 0.0296978 0.999559i \(-0.490546\pi\)
0.0296978 + 0.999559i \(0.490546\pi\)
\(450\) 0 0
\(451\) 30.6651 1.44396
\(452\) 0 0
\(453\) −21.8978 −1.02885
\(454\) 0 0
\(455\) 40.0425 1.87722
\(456\) 0 0
\(457\) −32.9487 −1.54128 −0.770638 0.637273i \(-0.780062\pi\)
−0.770638 + 0.637273i \(0.780062\pi\)
\(458\) 0 0
\(459\) 36.0886 1.68447
\(460\) 0 0
\(461\) 26.2657 1.22332 0.611658 0.791122i \(-0.290503\pi\)
0.611658 + 0.791122i \(0.290503\pi\)
\(462\) 0 0
\(463\) 17.1906 0.798915 0.399458 0.916752i \(-0.369198\pi\)
0.399458 + 0.916752i \(0.369198\pi\)
\(464\) 0 0
\(465\) 32.5491 1.50943
\(466\) 0 0
\(467\) −0.188356 −0.00871607 −0.00435804 0.999991i \(-0.501387\pi\)
−0.00435804 + 0.999991i \(0.501387\pi\)
\(468\) 0 0
\(469\) −16.6344 −0.768105
\(470\) 0 0
\(471\) −19.1362 −0.881750
\(472\) 0 0
\(473\) −27.5443 −1.26649
\(474\) 0 0
\(475\) 10.3091 0.473016
\(476\) 0 0
\(477\) 2.05357 0.0940265
\(478\) 0 0
\(479\) 9.44361 0.431490 0.215745 0.976450i \(-0.430782\pi\)
0.215745 + 0.976450i \(0.430782\pi\)
\(480\) 0 0
\(481\) 38.3809 1.75002
\(482\) 0 0
\(483\) 9.26314 0.421488
\(484\) 0 0
\(485\) −55.1381 −2.50369
\(486\) 0 0
\(487\) −6.41931 −0.290887 −0.145443 0.989367i \(-0.546461\pi\)
−0.145443 + 0.989367i \(0.546461\pi\)
\(488\) 0 0
\(489\) 32.3380 1.46237
\(490\) 0 0
\(491\) 12.9623 0.584978 0.292489 0.956269i \(-0.405516\pi\)
0.292489 + 0.956269i \(0.405516\pi\)
\(492\) 0 0
\(493\) 35.1629 1.58366
\(494\) 0 0
\(495\) −3.26977 −0.146965
\(496\) 0 0
\(497\) −20.8803 −0.936610
\(498\) 0 0
\(499\) −27.8989 −1.24893 −0.624464 0.781054i \(-0.714682\pi\)
−0.624464 + 0.781054i \(0.714682\pi\)
\(500\) 0 0
\(501\) −20.1280 −0.899252
\(502\) 0 0
\(503\) 0.590849 0.0263446 0.0131723 0.999913i \(-0.495807\pi\)
0.0131723 + 0.999913i \(0.495807\pi\)
\(504\) 0 0
\(505\) −52.7320 −2.34654
\(506\) 0 0
\(507\) −28.2357 −1.25399
\(508\) 0 0
\(509\) 0.845673 0.0374838 0.0187419 0.999824i \(-0.494034\pi\)
0.0187419 + 0.999824i \(0.494034\pi\)
\(510\) 0 0
\(511\) 9.58279 0.423918
\(512\) 0 0
\(513\) 17.2027 0.759519
\(514\) 0 0
\(515\) 6.49615 0.286255
\(516\) 0 0
\(517\) 9.83122 0.432376
\(518\) 0 0
\(519\) −13.3970 −0.588064
\(520\) 0 0
\(521\) 1.78980 0.0784127 0.0392064 0.999231i \(-0.487517\pi\)
0.0392064 + 0.999231i \(0.487517\pi\)
\(522\) 0 0
\(523\) 10.8079 0.472598 0.236299 0.971680i \(-0.424065\pi\)
0.236299 + 0.971680i \(0.424065\pi\)
\(524\) 0 0
\(525\) −13.5148 −0.589833
\(526\) 0 0
\(527\) −45.9381 −2.00110
\(528\) 0 0
\(529\) −18.0189 −0.783429
\(530\) 0 0
\(531\) 0.900338 0.0390713
\(532\) 0 0
\(533\) 47.0746 2.03903
\(534\) 0 0
\(535\) 22.9511 0.992260
\(536\) 0 0
\(537\) 20.4474 0.882370
\(538\) 0 0
\(539\) −2.07019 −0.0891695
\(540\) 0 0
\(541\) −39.2633 −1.68806 −0.844031 0.536294i \(-0.819824\pi\)
−0.844031 + 0.536294i \(0.819824\pi\)
\(542\) 0 0
\(543\) 23.5114 1.00897
\(544\) 0 0
\(545\) −30.1522 −1.29158
\(546\) 0 0
\(547\) 11.3676 0.486042 0.243021 0.970021i \(-0.421862\pi\)
0.243021 + 0.970021i \(0.421862\pi\)
\(548\) 0 0
\(549\) 0.546621 0.0233292
\(550\) 0 0
\(551\) 16.7615 0.714062
\(552\) 0 0
\(553\) −5.06617 −0.215435
\(554\) 0 0
\(555\) −32.8450 −1.39419
\(556\) 0 0
\(557\) −20.2532 −0.858157 −0.429078 0.903267i \(-0.641162\pi\)
−0.429078 + 0.903267i \(0.641162\pi\)
\(558\) 0 0
\(559\) −42.2838 −1.78841
\(560\) 0 0
\(561\) −38.9661 −1.64515
\(562\) 0 0
\(563\) −33.0446 −1.39266 −0.696332 0.717720i \(-0.745186\pi\)
−0.696332 + 0.717720i \(0.745186\pi\)
\(564\) 0 0
\(565\) −32.2875 −1.35834
\(566\) 0 0
\(567\) −20.1368 −0.845667
\(568\) 0 0
\(569\) −5.96182 −0.249933 −0.124966 0.992161i \(-0.539882\pi\)
−0.124966 + 0.992161i \(0.539882\pi\)
\(570\) 0 0
\(571\) 25.3032 1.05891 0.529453 0.848339i \(-0.322397\pi\)
0.529453 + 0.848339i \(0.322397\pi\)
\(572\) 0 0
\(573\) 25.1915 1.05239
\(574\) 0 0
\(575\) −7.26739 −0.303071
\(576\) 0 0
\(577\) 28.2078 1.17431 0.587154 0.809475i \(-0.300248\pi\)
0.587154 + 0.809475i \(0.300248\pi\)
\(578\) 0 0
\(579\) 32.5448 1.35252
\(580\) 0 0
\(581\) 9.72451 0.403441
\(582\) 0 0
\(583\) −23.1570 −0.959064
\(584\) 0 0
\(585\) −5.01950 −0.207531
\(586\) 0 0
\(587\) −47.1038 −1.94418 −0.972091 0.234606i \(-0.924620\pi\)
−0.972091 + 0.234606i \(0.924620\pi\)
\(588\) 0 0
\(589\) −21.8978 −0.902283
\(590\) 0 0
\(591\) 28.9744 1.19185
\(592\) 0 0
\(593\) 20.0019 0.821378 0.410689 0.911775i \(-0.365288\pi\)
0.410689 + 0.911775i \(0.365288\pi\)
\(594\) 0 0
\(595\) 48.3626 1.98267
\(596\) 0 0
\(597\) −25.4474 −1.04149
\(598\) 0 0
\(599\) −42.2555 −1.72651 −0.863256 0.504767i \(-0.831578\pi\)
−0.863256 + 0.504767i \(0.831578\pi\)
\(600\) 0 0
\(601\) −24.0107 −0.979418 −0.489709 0.871886i \(-0.662897\pi\)
−0.489709 + 0.871886i \(0.662897\pi\)
\(602\) 0 0
\(603\) 2.08519 0.0849155
\(604\) 0 0
\(605\) 5.26446 0.214031
\(606\) 0 0
\(607\) 7.42764 0.301479 0.150739 0.988574i \(-0.451835\pi\)
0.150739 + 0.988574i \(0.451835\pi\)
\(608\) 0 0
\(609\) −21.9734 −0.890408
\(610\) 0 0
\(611\) 15.0921 0.610561
\(612\) 0 0
\(613\) −39.4174 −1.59205 −0.796027 0.605261i \(-0.793069\pi\)
−0.796027 + 0.605261i \(0.793069\pi\)
\(614\) 0 0
\(615\) −40.2848 −1.62444
\(616\) 0 0
\(617\) −11.5931 −0.466720 −0.233360 0.972390i \(-0.574972\pi\)
−0.233360 + 0.972390i \(0.574972\pi\)
\(618\) 0 0
\(619\) −35.3934 −1.42258 −0.711291 0.702897i \(-0.751889\pi\)
−0.711291 + 0.702897i \(0.751889\pi\)
\(620\) 0 0
\(621\) −12.1270 −0.486640
\(622\) 0 0
\(623\) −6.33707 −0.253889
\(624\) 0 0
\(625\) −30.6781 −1.22712
\(626\) 0 0
\(627\) −18.5744 −0.741789
\(628\) 0 0
\(629\) 46.3557 1.84832
\(630\) 0 0
\(631\) 30.4900 1.21379 0.606894 0.794783i \(-0.292415\pi\)
0.606894 + 0.794783i \(0.292415\pi\)
\(632\) 0 0
\(633\) 33.3433 1.32528
\(634\) 0 0
\(635\) 44.4113 1.76241
\(636\) 0 0
\(637\) −3.17799 −0.125917
\(638\) 0 0
\(639\) 2.61744 0.103544
\(640\) 0 0
\(641\) 46.2358 1.82620 0.913102 0.407732i \(-0.133680\pi\)
0.913102 + 0.407732i \(0.133680\pi\)
\(642\) 0 0
\(643\) 6.45425 0.254531 0.127265 0.991869i \(-0.459380\pi\)
0.127265 + 0.991869i \(0.459380\pi\)
\(644\) 0 0
\(645\) 36.1850 1.42478
\(646\) 0 0
\(647\) −32.7050 −1.28577 −0.642883 0.765964i \(-0.722262\pi\)
−0.642883 + 0.765964i \(0.722262\pi\)
\(648\) 0 0
\(649\) −10.1526 −0.398525
\(650\) 0 0
\(651\) 28.7069 1.12511
\(652\) 0 0
\(653\) −11.9520 −0.467719 −0.233860 0.972270i \(-0.575136\pi\)
−0.233860 + 0.972270i \(0.575136\pi\)
\(654\) 0 0
\(655\) −13.7217 −0.536150
\(656\) 0 0
\(657\) −1.20124 −0.0468650
\(658\) 0 0
\(659\) −2.87073 −0.111828 −0.0559139 0.998436i \(-0.517807\pi\)
−0.0559139 + 0.998436i \(0.517807\pi\)
\(660\) 0 0
\(661\) −42.7741 −1.66372 −0.831860 0.554985i \(-0.812724\pi\)
−0.831860 + 0.554985i \(0.812724\pi\)
\(662\) 0 0
\(663\) −59.8176 −2.32312
\(664\) 0 0
\(665\) 23.0535 0.893977
\(666\) 0 0
\(667\) −11.8159 −0.457514
\(668\) 0 0
\(669\) −2.91118 −0.112553
\(670\) 0 0
\(671\) −6.16395 −0.237956
\(672\) 0 0
\(673\) 6.73708 0.259695 0.129848 0.991534i \(-0.458551\pi\)
0.129848 + 0.991534i \(0.458551\pi\)
\(674\) 0 0
\(675\) 17.6931 0.681007
\(676\) 0 0
\(677\) −33.3391 −1.28133 −0.640663 0.767822i \(-0.721341\pi\)
−0.640663 + 0.767822i \(0.721341\pi\)
\(678\) 0 0
\(679\) −48.6295 −1.86623
\(680\) 0 0
\(681\) −39.6675 −1.52006
\(682\) 0 0
\(683\) −43.0975 −1.64908 −0.824539 0.565805i \(-0.808566\pi\)
−0.824539 + 0.565805i \(0.808566\pi\)
\(684\) 0 0
\(685\) 2.63155 0.100547
\(686\) 0 0
\(687\) −40.8316 −1.55782
\(688\) 0 0
\(689\) −35.5488 −1.35430
\(690\) 0 0
\(691\) 6.89619 0.262343 0.131172 0.991360i \(-0.458126\pi\)
0.131172 + 0.991360i \(0.458126\pi\)
\(692\) 0 0
\(693\) −2.88380 −0.109547
\(694\) 0 0
\(695\) −29.7822 −1.12970
\(696\) 0 0
\(697\) 56.8558 2.15357
\(698\) 0 0
\(699\) −5.95824 −0.225361
\(700\) 0 0
\(701\) −9.40633 −0.355272 −0.177636 0.984096i \(-0.556845\pi\)
−0.177636 + 0.984096i \(0.556845\pi\)
\(702\) 0 0
\(703\) 22.0969 0.833399
\(704\) 0 0
\(705\) −12.9153 −0.486418
\(706\) 0 0
\(707\) −46.5074 −1.74909
\(708\) 0 0
\(709\) 45.3168 1.70191 0.850954 0.525241i \(-0.176025\pi\)
0.850954 + 0.525241i \(0.176025\pi\)
\(710\) 0 0
\(711\) 0.635066 0.0238168
\(712\) 0 0
\(713\) 15.4368 0.578111
\(714\) 0 0
\(715\) 56.6021 2.11680
\(716\) 0 0
\(717\) −9.09148 −0.339528
\(718\) 0 0
\(719\) 33.9044 1.26442 0.632211 0.774796i \(-0.282148\pi\)
0.632211 + 0.774796i \(0.282148\pi\)
\(720\) 0 0
\(721\) 5.72932 0.213371
\(722\) 0 0
\(723\) −37.0347 −1.37734
\(724\) 0 0
\(725\) 17.2392 0.640249
\(726\) 0 0
\(727\) 11.4489 0.424615 0.212307 0.977203i \(-0.431902\pi\)
0.212307 + 0.977203i \(0.431902\pi\)
\(728\) 0 0
\(729\) 29.2215 1.08228
\(730\) 0 0
\(731\) −51.0696 −1.88888
\(732\) 0 0
\(733\) −19.3623 −0.715163 −0.357582 0.933882i \(-0.616399\pi\)
−0.357582 + 0.933882i \(0.616399\pi\)
\(734\) 0 0
\(735\) 2.71962 0.100315
\(736\) 0 0
\(737\) −23.5136 −0.866133
\(738\) 0 0
\(739\) 45.5699 1.67631 0.838157 0.545429i \(-0.183633\pi\)
0.838157 + 0.545429i \(0.183633\pi\)
\(740\) 0 0
\(741\) −28.5139 −1.04748
\(742\) 0 0
\(743\) −53.5695 −1.96527 −0.982637 0.185536i \(-0.940598\pi\)
−0.982637 + 0.185536i \(0.940598\pi\)
\(744\) 0 0
\(745\) −8.70007 −0.318746
\(746\) 0 0
\(747\) −1.21901 −0.0446012
\(748\) 0 0
\(749\) 20.2418 0.739621
\(750\) 0 0
\(751\) 22.0518 0.804683 0.402341 0.915490i \(-0.368197\pi\)
0.402341 + 0.915490i \(0.368197\pi\)
\(752\) 0 0
\(753\) −1.63778 −0.0596841
\(754\) 0 0
\(755\) 38.4181 1.39818
\(756\) 0 0
\(757\) −13.4488 −0.488804 −0.244402 0.969674i \(-0.578592\pi\)
−0.244402 + 0.969674i \(0.578592\pi\)
\(758\) 0 0
\(759\) 13.0939 0.475280
\(760\) 0 0
\(761\) −21.1601 −0.767052 −0.383526 0.923530i \(-0.625290\pi\)
−0.383526 + 0.923530i \(0.625290\pi\)
\(762\) 0 0
\(763\) −26.5929 −0.962728
\(764\) 0 0
\(765\) −6.06246 −0.219189
\(766\) 0 0
\(767\) −15.5855 −0.562760
\(768\) 0 0
\(769\) −42.7960 −1.54326 −0.771632 0.636069i \(-0.780559\pi\)
−0.771632 + 0.636069i \(0.780559\pi\)
\(770\) 0 0
\(771\) 6.25542 0.225283
\(772\) 0 0
\(773\) −25.2783 −0.909196 −0.454598 0.890697i \(-0.650217\pi\)
−0.454598 + 0.890697i \(0.650217\pi\)
\(774\) 0 0
\(775\) −22.5220 −0.809013
\(776\) 0 0
\(777\) −28.9679 −1.03922
\(778\) 0 0
\(779\) 27.1020 0.971032
\(780\) 0 0
\(781\) −29.5154 −1.05614
\(782\) 0 0
\(783\) 28.7669 1.02804
\(784\) 0 0
\(785\) 33.5730 1.19827
\(786\) 0 0
\(787\) 24.9621 0.889804 0.444902 0.895579i \(-0.353239\pi\)
0.444902 + 0.895579i \(0.353239\pi\)
\(788\) 0 0
\(789\) 24.2043 0.861695
\(790\) 0 0
\(791\) −28.4762 −1.01250
\(792\) 0 0
\(793\) −9.46240 −0.336020
\(794\) 0 0
\(795\) 30.4214 1.07894
\(796\) 0 0
\(797\) 12.7836 0.452819 0.226409 0.974032i \(-0.427301\pi\)
0.226409 + 0.974032i \(0.427301\pi\)
\(798\) 0 0
\(799\) 18.2280 0.644859
\(800\) 0 0
\(801\) 0.794378 0.0280680
\(802\) 0 0
\(803\) 13.5458 0.478020
\(804\) 0 0
\(805\) −16.2515 −0.572789
\(806\) 0 0
\(807\) 5.22471 0.183919
\(808\) 0 0
\(809\) −45.7716 −1.60924 −0.804621 0.593788i \(-0.797632\pi\)
−0.804621 + 0.593788i \(0.797632\pi\)
\(810\) 0 0
\(811\) −43.2043 −1.51711 −0.758554 0.651611i \(-0.774094\pi\)
−0.758554 + 0.651611i \(0.774094\pi\)
\(812\) 0 0
\(813\) −2.95262 −0.103553
\(814\) 0 0
\(815\) −56.7345 −1.98732
\(816\) 0 0
\(817\) −24.3439 −0.851685
\(818\) 0 0
\(819\) −4.42698 −0.154691
\(820\) 0 0
\(821\) 43.0066 1.50094 0.750470 0.660905i \(-0.229827\pi\)
0.750470 + 0.660905i \(0.229827\pi\)
\(822\) 0 0
\(823\) 19.6275 0.684172 0.342086 0.939669i \(-0.388867\pi\)
0.342086 + 0.939669i \(0.388867\pi\)
\(824\) 0 0
\(825\) −19.1038 −0.665110
\(826\) 0 0
\(827\) −37.3503 −1.29880 −0.649399 0.760448i \(-0.724980\pi\)
−0.649399 + 0.760448i \(0.724980\pi\)
\(828\) 0 0
\(829\) −54.5687 −1.89525 −0.947625 0.319385i \(-0.896524\pi\)
−0.947625 + 0.319385i \(0.896524\pi\)
\(830\) 0 0
\(831\) 48.3077 1.67578
\(832\) 0 0
\(833\) −3.83833 −0.132990
\(834\) 0 0
\(835\) 35.3130 1.22206
\(836\) 0 0
\(837\) −37.5821 −1.29903
\(838\) 0 0
\(839\) −23.4475 −0.809496 −0.404748 0.914428i \(-0.632641\pi\)
−0.404748 + 0.914428i \(0.632641\pi\)
\(840\) 0 0
\(841\) −0.971019 −0.0334834
\(842\) 0 0
\(843\) 22.6612 0.780493
\(844\) 0 0
\(845\) 49.5373 1.70414
\(846\) 0 0
\(847\) 4.64303 0.159536
\(848\) 0 0
\(849\) −31.2916 −1.07393
\(850\) 0 0
\(851\) −15.5771 −0.533976
\(852\) 0 0
\(853\) 16.9988 0.582028 0.291014 0.956719i \(-0.406007\pi\)
0.291014 + 0.956719i \(0.406007\pi\)
\(854\) 0 0
\(855\) −2.88985 −0.0988309
\(856\) 0 0
\(857\) 28.4443 0.971639 0.485820 0.874059i \(-0.338521\pi\)
0.485820 + 0.874059i \(0.338521\pi\)
\(858\) 0 0
\(859\) −30.6892 −1.04710 −0.523551 0.851994i \(-0.675393\pi\)
−0.523551 + 0.851994i \(0.675393\pi\)
\(860\) 0 0
\(861\) −35.5294 −1.21084
\(862\) 0 0
\(863\) 6.15386 0.209480 0.104740 0.994500i \(-0.466599\pi\)
0.104740 + 0.994500i \(0.466599\pi\)
\(864\) 0 0
\(865\) 23.5041 0.799163
\(866\) 0 0
\(867\) −44.4044 −1.50805
\(868\) 0 0
\(869\) −7.16129 −0.242930
\(870\) 0 0
\(871\) −36.0962 −1.22307
\(872\) 0 0
\(873\) 6.09591 0.206315
\(874\) 0 0
\(875\) −12.6975 −0.429255
\(876\) 0 0
\(877\) 16.8524 0.569064 0.284532 0.958667i \(-0.408162\pi\)
0.284532 + 0.958667i \(0.408162\pi\)
\(878\) 0 0
\(879\) −35.8661 −1.20973
\(880\) 0 0
\(881\) 12.0892 0.407295 0.203648 0.979044i \(-0.434720\pi\)
0.203648 + 0.979044i \(0.434720\pi\)
\(882\) 0 0
\(883\) 31.8973 1.07343 0.536715 0.843764i \(-0.319665\pi\)
0.536715 + 0.843764i \(0.319665\pi\)
\(884\) 0 0
\(885\) 13.3375 0.448336
\(886\) 0 0
\(887\) −12.7775 −0.429026 −0.214513 0.976721i \(-0.568816\pi\)
−0.214513 + 0.976721i \(0.568816\pi\)
\(888\) 0 0
\(889\) 39.1689 1.31368
\(890\) 0 0
\(891\) −28.4644 −0.953594
\(892\) 0 0
\(893\) 8.68891 0.290763
\(894\) 0 0
\(895\) −35.8734 −1.19912
\(896\) 0 0
\(897\) 20.1008 0.671145
\(898\) 0 0
\(899\) −36.6181 −1.22128
\(900\) 0 0
\(901\) −42.9352 −1.43038
\(902\) 0 0
\(903\) 31.9136 1.06202
\(904\) 0 0
\(905\) −41.2490 −1.37116
\(906\) 0 0
\(907\) 5.24689 0.174220 0.0871101 0.996199i \(-0.472237\pi\)
0.0871101 + 0.996199i \(0.472237\pi\)
\(908\) 0 0
\(909\) 5.82990 0.193365
\(910\) 0 0
\(911\) −55.1166 −1.82609 −0.913047 0.407855i \(-0.866277\pi\)
−0.913047 + 0.407855i \(0.866277\pi\)
\(912\) 0 0
\(913\) 13.7461 0.454930
\(914\) 0 0
\(915\) 8.09759 0.267698
\(916\) 0 0
\(917\) −12.1019 −0.399641
\(918\) 0 0
\(919\) 41.9249 1.38297 0.691487 0.722389i \(-0.256956\pi\)
0.691487 + 0.722389i \(0.256956\pi\)
\(920\) 0 0
\(921\) 28.6816 0.945091
\(922\) 0 0
\(923\) −45.3097 −1.49139
\(924\) 0 0
\(925\) 22.7267 0.747250
\(926\) 0 0
\(927\) −0.718195 −0.0235886
\(928\) 0 0
\(929\) 7.71805 0.253221 0.126611 0.991953i \(-0.459590\pi\)
0.126611 + 0.991953i \(0.459590\pi\)
\(930\) 0 0
\(931\) −1.82965 −0.0599645
\(932\) 0 0
\(933\) 2.52545 0.0826796
\(934\) 0 0
\(935\) 68.3631 2.23571
\(936\) 0 0
\(937\) −36.3638 −1.18795 −0.593977 0.804482i \(-0.702443\pi\)
−0.593977 + 0.804482i \(0.702443\pi\)
\(938\) 0 0
\(939\) −37.2815 −1.21664
\(940\) 0 0
\(941\) −3.36459 −0.109682 −0.0548412 0.998495i \(-0.517465\pi\)
−0.0548412 + 0.998495i \(0.517465\pi\)
\(942\) 0 0
\(943\) −19.1055 −0.622160
\(944\) 0 0
\(945\) 39.5656 1.28707
\(946\) 0 0
\(947\) 23.6697 0.769161 0.384581 0.923091i \(-0.374346\pi\)
0.384581 + 0.923091i \(0.374346\pi\)
\(948\) 0 0
\(949\) 20.7944 0.675014
\(950\) 0 0
\(951\) −10.1194 −0.328145
\(952\) 0 0
\(953\) 5.20371 0.168565 0.0842823 0.996442i \(-0.473140\pi\)
0.0842823 + 0.996442i \(0.473140\pi\)
\(954\) 0 0
\(955\) −44.1965 −1.43017
\(956\) 0 0
\(957\) −31.0606 −1.00405
\(958\) 0 0
\(959\) 2.32092 0.0749463
\(960\) 0 0
\(961\) 16.8392 0.543202
\(962\) 0 0
\(963\) −2.53740 −0.0817666
\(964\) 0 0
\(965\) −57.0974 −1.83803
\(966\) 0 0
\(967\) 36.5099 1.17408 0.587040 0.809558i \(-0.300293\pi\)
0.587040 + 0.809558i \(0.300293\pi\)
\(968\) 0 0
\(969\) −34.4386 −1.10633
\(970\) 0 0
\(971\) 13.6329 0.437502 0.218751 0.975781i \(-0.429802\pi\)
0.218751 + 0.975781i \(0.429802\pi\)
\(972\) 0 0
\(973\) −26.2666 −0.842070
\(974\) 0 0
\(975\) −29.3267 −0.939205
\(976\) 0 0
\(977\) 23.1343 0.740132 0.370066 0.929005i \(-0.379335\pi\)
0.370066 + 0.929005i \(0.379335\pi\)
\(978\) 0 0
\(979\) −8.95777 −0.286292
\(980\) 0 0
\(981\) 3.33354 0.106432
\(982\) 0 0
\(983\) −55.7685 −1.77874 −0.889369 0.457190i \(-0.848856\pi\)
−0.889369 + 0.457190i \(0.848856\pi\)
\(984\) 0 0
\(985\) −50.8334 −1.61969
\(986\) 0 0
\(987\) −11.3907 −0.362571
\(988\) 0 0
\(989\) 17.1611 0.545692
\(990\) 0 0
\(991\) 31.6117 1.00418 0.502090 0.864816i \(-0.332565\pi\)
0.502090 + 0.864816i \(0.332565\pi\)
\(992\) 0 0
\(993\) −24.7153 −0.784316
\(994\) 0 0
\(995\) 44.6456 1.41536
\(996\) 0 0
\(997\) −5.90161 −0.186906 −0.0934530 0.995624i \(-0.529790\pi\)
−0.0934530 + 0.995624i \(0.529790\pi\)
\(998\) 0 0
\(999\) 37.9238 1.19986
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.1.8 23
4.3 odd 2 2008.2.a.d.1.16 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.16 23 4.3 odd 2
4016.2.a.m.1.8 23 1.1 even 1 trivial