Properties

Label 4016.2.a.m.1.11
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 1.11
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.259421 q^{3} -1.96371 q^{5} +4.76268 q^{7} -2.93270 q^{9} +O(q^{10})\) \(q-0.259421 q^{3} -1.96371 q^{5} +4.76268 q^{7} -2.93270 q^{9} -3.31268 q^{11} +0.493039 q^{13} +0.509426 q^{15} -3.02691 q^{17} -1.99518 q^{19} -1.23554 q^{21} -3.65140 q^{23} -1.14386 q^{25} +1.53906 q^{27} +5.29536 q^{29} +8.88848 q^{31} +0.859377 q^{33} -9.35250 q^{35} +6.88114 q^{37} -0.127904 q^{39} -3.94408 q^{41} -10.3912 q^{43} +5.75896 q^{45} +12.7776 q^{47} +15.6831 q^{49} +0.785243 q^{51} +5.75231 q^{53} +6.50513 q^{55} +0.517590 q^{57} +12.3248 q^{59} +8.92476 q^{61} -13.9675 q^{63} -0.968183 q^{65} -14.3282 q^{67} +0.947248 q^{69} -10.5818 q^{71} +8.88283 q^{73} +0.296741 q^{75} -15.7772 q^{77} -8.79170 q^{79} +8.39884 q^{81} -8.70243 q^{83} +5.94396 q^{85} -1.37372 q^{87} +10.7568 q^{89} +2.34819 q^{91} -2.30585 q^{93} +3.91794 q^{95} +13.1731 q^{97} +9.71510 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

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
\(3\) −0.259421 −0.149777 −0.0748883 0.997192i \(-0.523860\pi\)
−0.0748883 + 0.997192i \(0.523860\pi\)
\(4\) 0 0
\(5\) −1.96371 −0.878196 −0.439098 0.898439i \(-0.644702\pi\)
−0.439098 + 0.898439i \(0.644702\pi\)
\(6\) 0 0
\(7\) 4.76268 1.80012 0.900062 0.435762i \(-0.143521\pi\)
0.900062 + 0.435762i \(0.143521\pi\)
\(8\) 0 0
\(9\) −2.93270 −0.977567
\(10\) 0 0
\(11\) −3.31268 −0.998811 −0.499405 0.866368i \(-0.666448\pi\)
−0.499405 + 0.866368i \(0.666448\pi\)
\(12\) 0 0
\(13\) 0.493039 0.136744 0.0683722 0.997660i \(-0.478219\pi\)
0.0683722 + 0.997660i \(0.478219\pi\)
\(14\) 0 0
\(15\) 0.509426 0.131533
\(16\) 0 0
\(17\) −3.02691 −0.734134 −0.367067 0.930195i \(-0.619638\pi\)
−0.367067 + 0.930195i \(0.619638\pi\)
\(18\) 0 0
\(19\) −1.99518 −0.457725 −0.228863 0.973459i \(-0.573501\pi\)
−0.228863 + 0.973459i \(0.573501\pi\)
\(20\) 0 0
\(21\) −1.23554 −0.269616
\(22\) 0 0
\(23\) −3.65140 −0.761370 −0.380685 0.924705i \(-0.624312\pi\)
−0.380685 + 0.924705i \(0.624312\pi\)
\(24\) 0 0
\(25\) −1.14386 −0.228772
\(26\) 0 0
\(27\) 1.53906 0.296193
\(28\) 0 0
\(29\) 5.29536 0.983324 0.491662 0.870786i \(-0.336390\pi\)
0.491662 + 0.870786i \(0.336390\pi\)
\(30\) 0 0
\(31\) 8.88848 1.59642 0.798209 0.602380i \(-0.205781\pi\)
0.798209 + 0.602380i \(0.205781\pi\)
\(32\) 0 0
\(33\) 0.859377 0.149598
\(34\) 0 0
\(35\) −9.35250 −1.58086
\(36\) 0 0
\(37\) 6.88114 1.13125 0.565626 0.824662i \(-0.308635\pi\)
0.565626 + 0.824662i \(0.308635\pi\)
\(38\) 0 0
\(39\) −0.127904 −0.0204811
\(40\) 0 0
\(41\) −3.94408 −0.615961 −0.307981 0.951393i \(-0.599653\pi\)
−0.307981 + 0.951393i \(0.599653\pi\)
\(42\) 0 0
\(43\) −10.3912 −1.58465 −0.792323 0.610102i \(-0.791128\pi\)
−0.792323 + 0.610102i \(0.791128\pi\)
\(44\) 0 0
\(45\) 5.75896 0.858495
\(46\) 0 0
\(47\) 12.7776 1.86381 0.931905 0.362703i \(-0.118146\pi\)
0.931905 + 0.362703i \(0.118146\pi\)
\(48\) 0 0
\(49\) 15.6831 2.24045
\(50\) 0 0
\(51\) 0.785243 0.109956
\(52\) 0 0
\(53\) 5.75231 0.790140 0.395070 0.918651i \(-0.370720\pi\)
0.395070 + 0.918651i \(0.370720\pi\)
\(54\) 0 0
\(55\) 6.50513 0.877151
\(56\) 0 0
\(57\) 0.517590 0.0685565
\(58\) 0 0
\(59\) 12.3248 1.60456 0.802278 0.596950i \(-0.203621\pi\)
0.802278 + 0.596950i \(0.203621\pi\)
\(60\) 0 0
\(61\) 8.92476 1.14270 0.571349 0.820707i \(-0.306420\pi\)
0.571349 + 0.820707i \(0.306420\pi\)
\(62\) 0 0
\(63\) −13.9675 −1.75974
\(64\) 0 0
\(65\) −0.968183 −0.120088
\(66\) 0 0
\(67\) −14.3282 −1.75047 −0.875237 0.483695i \(-0.839294\pi\)
−0.875237 + 0.483695i \(0.839294\pi\)
\(68\) 0 0
\(69\) 0.947248 0.114035
\(70\) 0 0
\(71\) −10.5818 −1.25583 −0.627916 0.778281i \(-0.716092\pi\)
−0.627916 + 0.778281i \(0.716092\pi\)
\(72\) 0 0
\(73\) 8.88283 1.03966 0.519828 0.854271i \(-0.325996\pi\)
0.519828 + 0.854271i \(0.325996\pi\)
\(74\) 0 0
\(75\) 0.296741 0.0342647
\(76\) 0 0
\(77\) −15.7772 −1.79798
\(78\) 0 0
\(79\) −8.79170 −0.989143 −0.494572 0.869137i \(-0.664675\pi\)
−0.494572 + 0.869137i \(0.664675\pi\)
\(80\) 0 0
\(81\) 8.39884 0.933204
\(82\) 0 0
\(83\) −8.70243 −0.955216 −0.477608 0.878573i \(-0.658496\pi\)
−0.477608 + 0.878573i \(0.658496\pi\)
\(84\) 0 0
\(85\) 5.94396 0.644713
\(86\) 0 0
\(87\) −1.37372 −0.147279
\(88\) 0 0
\(89\) 10.7568 1.14022 0.570108 0.821570i \(-0.306901\pi\)
0.570108 + 0.821570i \(0.306901\pi\)
\(90\) 0 0
\(91\) 2.34819 0.246157
\(92\) 0 0
\(93\) −2.30585 −0.239106
\(94\) 0 0
\(95\) 3.91794 0.401972
\(96\) 0 0
\(97\) 13.1731 1.33753 0.668764 0.743475i \(-0.266824\pi\)
0.668764 + 0.743475i \(0.266824\pi\)
\(98\) 0 0
\(99\) 9.71510 0.976404
\(100\) 0 0
\(101\) −9.38904 −0.934245 −0.467122 0.884193i \(-0.654709\pi\)
−0.467122 + 0.884193i \(0.654709\pi\)
\(102\) 0 0
\(103\) 9.79842 0.965467 0.482733 0.875767i \(-0.339644\pi\)
0.482733 + 0.875767i \(0.339644\pi\)
\(104\) 0 0
\(105\) 2.42623 0.236776
\(106\) 0 0
\(107\) −4.35926 −0.421425 −0.210713 0.977548i \(-0.567578\pi\)
−0.210713 + 0.977548i \(0.567578\pi\)
\(108\) 0 0
\(109\) −5.37187 −0.514532 −0.257266 0.966341i \(-0.582822\pi\)
−0.257266 + 0.966341i \(0.582822\pi\)
\(110\) 0 0
\(111\) −1.78511 −0.169435
\(112\) 0 0
\(113\) −0.594998 −0.0559727 −0.0279863 0.999608i \(-0.508909\pi\)
−0.0279863 + 0.999608i \(0.508909\pi\)
\(114\) 0 0
\(115\) 7.17028 0.668632
\(116\) 0 0
\(117\) −1.44594 −0.133677
\(118\) 0 0
\(119\) −14.4162 −1.32153
\(120\) 0 0
\(121\) −0.0261504 −0.00237731
\(122\) 0 0
\(123\) 1.02317 0.0922565
\(124\) 0 0
\(125\) 12.0647 1.07910
\(126\) 0 0
\(127\) 21.0814 1.87067 0.935337 0.353759i \(-0.115097\pi\)
0.935337 + 0.353759i \(0.115097\pi\)
\(128\) 0 0
\(129\) 2.69569 0.237343
\(130\) 0 0
\(131\) −6.41979 −0.560899 −0.280450 0.959869i \(-0.590484\pi\)
−0.280450 + 0.959869i \(0.590484\pi\)
\(132\) 0 0
\(133\) −9.50240 −0.823962
\(134\) 0 0
\(135\) −3.02227 −0.260116
\(136\) 0 0
\(137\) 10.2575 0.876354 0.438177 0.898889i \(-0.355624\pi\)
0.438177 + 0.898889i \(0.355624\pi\)
\(138\) 0 0
\(139\) 15.9338 1.35149 0.675743 0.737137i \(-0.263823\pi\)
0.675743 + 0.737137i \(0.263823\pi\)
\(140\) 0 0
\(141\) −3.31478 −0.279155
\(142\) 0 0
\(143\) −1.63328 −0.136582
\(144\) 0 0
\(145\) −10.3985 −0.863551
\(146\) 0 0
\(147\) −4.06852 −0.335566
\(148\) 0 0
\(149\) 10.0095 0.820008 0.410004 0.912084i \(-0.365527\pi\)
0.410004 + 0.912084i \(0.365527\pi\)
\(150\) 0 0
\(151\) 21.5890 1.75689 0.878443 0.477847i \(-0.158582\pi\)
0.878443 + 0.477847i \(0.158582\pi\)
\(152\) 0 0
\(153\) 8.87703 0.717665
\(154\) 0 0
\(155\) −17.4544 −1.40197
\(156\) 0 0
\(157\) −9.38585 −0.749072 −0.374536 0.927212i \(-0.622198\pi\)
−0.374536 + 0.927212i \(0.622198\pi\)
\(158\) 0 0
\(159\) −1.49227 −0.118344
\(160\) 0 0
\(161\) −17.3905 −1.37056
\(162\) 0 0
\(163\) −20.3983 −1.59772 −0.798860 0.601517i \(-0.794563\pi\)
−0.798860 + 0.601517i \(0.794563\pi\)
\(164\) 0 0
\(165\) −1.68756 −0.131377
\(166\) 0 0
\(167\) 8.88676 0.687678 0.343839 0.939029i \(-0.388272\pi\)
0.343839 + 0.939029i \(0.388272\pi\)
\(168\) 0 0
\(169\) −12.7569 −0.981301
\(170\) 0 0
\(171\) 5.85126 0.447457
\(172\) 0 0
\(173\) −9.23441 −0.702079 −0.351039 0.936361i \(-0.614172\pi\)
−0.351039 + 0.936361i \(0.614172\pi\)
\(174\) 0 0
\(175\) −5.44784 −0.411818
\(176\) 0 0
\(177\) −3.19731 −0.240325
\(178\) 0 0
\(179\) −0.666728 −0.0498336 −0.0249168 0.999690i \(-0.507932\pi\)
−0.0249168 + 0.999690i \(0.507932\pi\)
\(180\) 0 0
\(181\) −6.34647 −0.471729 −0.235865 0.971786i \(-0.575792\pi\)
−0.235865 + 0.971786i \(0.575792\pi\)
\(182\) 0 0
\(183\) −2.31527 −0.171149
\(184\) 0 0
\(185\) −13.5125 −0.993461
\(186\) 0 0
\(187\) 10.0272 0.733261
\(188\) 0 0
\(189\) 7.33007 0.533184
\(190\) 0 0
\(191\) 0.222688 0.0161131 0.00805656 0.999968i \(-0.497435\pi\)
0.00805656 + 0.999968i \(0.497435\pi\)
\(192\) 0 0
\(193\) 20.5186 1.47696 0.738480 0.674276i \(-0.235544\pi\)
0.738480 + 0.674276i \(0.235544\pi\)
\(194\) 0 0
\(195\) 0.251167 0.0179864
\(196\) 0 0
\(197\) 4.39141 0.312875 0.156437 0.987688i \(-0.449999\pi\)
0.156437 + 0.987688i \(0.449999\pi\)
\(198\) 0 0
\(199\) 23.7138 1.68103 0.840514 0.541790i \(-0.182253\pi\)
0.840514 + 0.541790i \(0.182253\pi\)
\(200\) 0 0
\(201\) 3.71704 0.262180
\(202\) 0 0
\(203\) 25.2201 1.77010
\(204\) 0 0
\(205\) 7.74500 0.540935
\(206\) 0 0
\(207\) 10.7085 0.744290
\(208\) 0 0
\(209\) 6.60939 0.457181
\(210\) 0 0
\(211\) 10.7520 0.740195 0.370097 0.928993i \(-0.379324\pi\)
0.370097 + 0.928993i \(0.379324\pi\)
\(212\) 0 0
\(213\) 2.74515 0.188094
\(214\) 0 0
\(215\) 20.4053 1.39163
\(216\) 0 0
\(217\) 42.3330 2.87375
\(218\) 0 0
\(219\) −2.30439 −0.155716
\(220\) 0 0
\(221\) −1.49238 −0.100389
\(222\) 0 0
\(223\) 27.2728 1.82632 0.913160 0.407600i \(-0.133634\pi\)
0.913160 + 0.407600i \(0.133634\pi\)
\(224\) 0 0
\(225\) 3.35460 0.223640
\(226\) 0 0
\(227\) −24.5283 −1.62800 −0.814000 0.580865i \(-0.802715\pi\)
−0.814000 + 0.580865i \(0.802715\pi\)
\(228\) 0 0
\(229\) 6.80771 0.449866 0.224933 0.974374i \(-0.427784\pi\)
0.224933 + 0.974374i \(0.427784\pi\)
\(230\) 0 0
\(231\) 4.09294 0.269296
\(232\) 0 0
\(233\) 23.6993 1.55259 0.776296 0.630369i \(-0.217096\pi\)
0.776296 + 0.630369i \(0.217096\pi\)
\(234\) 0 0
\(235\) −25.0915 −1.63679
\(236\) 0 0
\(237\) 2.28075 0.148150
\(238\) 0 0
\(239\) −26.9335 −1.74218 −0.871092 0.491119i \(-0.836588\pi\)
−0.871092 + 0.491119i \(0.836588\pi\)
\(240\) 0 0
\(241\) 3.54758 0.228520 0.114260 0.993451i \(-0.463550\pi\)
0.114260 + 0.993451i \(0.463550\pi\)
\(242\) 0 0
\(243\) −6.79602 −0.435965
\(244\) 0 0
\(245\) −30.7970 −1.96755
\(246\) 0 0
\(247\) −0.983700 −0.0625914
\(248\) 0 0
\(249\) 2.25759 0.143069
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) 12.0959 0.760464
\(254\) 0 0
\(255\) −1.54199 −0.0965629
\(256\) 0 0
\(257\) 9.72022 0.606331 0.303165 0.952938i \(-0.401957\pi\)
0.303165 + 0.952938i \(0.401957\pi\)
\(258\) 0 0
\(259\) 32.7727 2.03639
\(260\) 0 0
\(261\) −15.5297 −0.961265
\(262\) 0 0
\(263\) −0.264944 −0.0163371 −0.00816857 0.999967i \(-0.502600\pi\)
−0.00816857 + 0.999967i \(0.502600\pi\)
\(264\) 0 0
\(265\) −11.2958 −0.693898
\(266\) 0 0
\(267\) −2.79053 −0.170777
\(268\) 0 0
\(269\) 1.29684 0.0790698 0.0395349 0.999218i \(-0.487412\pi\)
0.0395349 + 0.999218i \(0.487412\pi\)
\(270\) 0 0
\(271\) 4.32607 0.262790 0.131395 0.991330i \(-0.458054\pi\)
0.131395 + 0.991330i \(0.458054\pi\)
\(272\) 0 0
\(273\) −0.609168 −0.0368685
\(274\) 0 0
\(275\) 3.78924 0.228500
\(276\) 0 0
\(277\) 27.3368 1.64251 0.821253 0.570564i \(-0.193275\pi\)
0.821253 + 0.570564i \(0.193275\pi\)
\(278\) 0 0
\(279\) −26.0673 −1.56061
\(280\) 0 0
\(281\) 1.11608 0.0665799 0.0332899 0.999446i \(-0.489402\pi\)
0.0332899 + 0.999446i \(0.489402\pi\)
\(282\) 0 0
\(283\) 3.36117 0.199801 0.0999004 0.994997i \(-0.468148\pi\)
0.0999004 + 0.994997i \(0.468148\pi\)
\(284\) 0 0
\(285\) −1.01639 −0.0602060
\(286\) 0 0
\(287\) −18.7844 −1.10881
\(288\) 0 0
\(289\) −7.83781 −0.461048
\(290\) 0 0
\(291\) −3.41738 −0.200330
\(292\) 0 0
\(293\) 15.8718 0.927241 0.463621 0.886034i \(-0.346550\pi\)
0.463621 + 0.886034i \(0.346550\pi\)
\(294\) 0 0
\(295\) −24.2023 −1.40911
\(296\) 0 0
\(297\) −5.09843 −0.295841
\(298\) 0 0
\(299\) −1.80028 −0.104113
\(300\) 0 0
\(301\) −49.4900 −2.85256
\(302\) 0 0
\(303\) 2.43571 0.139928
\(304\) 0 0
\(305\) −17.5256 −1.00351
\(306\) 0 0
\(307\) −4.54729 −0.259528 −0.129764 0.991545i \(-0.541422\pi\)
−0.129764 + 0.991545i \(0.541422\pi\)
\(308\) 0 0
\(309\) −2.54191 −0.144604
\(310\) 0 0
\(311\) 1.05931 0.0600680 0.0300340 0.999549i \(-0.490438\pi\)
0.0300340 + 0.999549i \(0.490438\pi\)
\(312\) 0 0
\(313\) 24.7080 1.39658 0.698290 0.715815i \(-0.253945\pi\)
0.698290 + 0.715815i \(0.253945\pi\)
\(314\) 0 0
\(315\) 27.4281 1.54540
\(316\) 0 0
\(317\) 13.0254 0.731580 0.365790 0.930697i \(-0.380799\pi\)
0.365790 + 0.930697i \(0.380799\pi\)
\(318\) 0 0
\(319\) −17.5418 −0.982154
\(320\) 0 0
\(321\) 1.13088 0.0631196
\(322\) 0 0
\(323\) 6.03923 0.336032
\(324\) 0 0
\(325\) −0.563968 −0.0312833
\(326\) 0 0
\(327\) 1.39357 0.0770647
\(328\) 0 0
\(329\) 60.8558 3.35509
\(330\) 0 0
\(331\) −10.6130 −0.583345 −0.291673 0.956518i \(-0.594212\pi\)
−0.291673 + 0.956518i \(0.594212\pi\)
\(332\) 0 0
\(333\) −20.1803 −1.10587
\(334\) 0 0
\(335\) 28.1364 1.53726
\(336\) 0 0
\(337\) −21.4890 −1.17058 −0.585291 0.810823i \(-0.699020\pi\)
−0.585291 + 0.810823i \(0.699020\pi\)
\(338\) 0 0
\(339\) 0.154355 0.00838339
\(340\) 0 0
\(341\) −29.4447 −1.59452
\(342\) 0 0
\(343\) 41.3550 2.23296
\(344\) 0 0
\(345\) −1.86012 −0.100145
\(346\) 0 0
\(347\) 30.5178 1.63828 0.819140 0.573594i \(-0.194451\pi\)
0.819140 + 0.573594i \(0.194451\pi\)
\(348\) 0 0
\(349\) 22.4297 1.20063 0.600317 0.799762i \(-0.295041\pi\)
0.600317 + 0.799762i \(0.295041\pi\)
\(350\) 0 0
\(351\) 0.758819 0.0405027
\(352\) 0 0
\(353\) −12.2019 −0.649441 −0.324720 0.945810i \(-0.605270\pi\)
−0.324720 + 0.945810i \(0.605270\pi\)
\(354\) 0 0
\(355\) 20.7796 1.10287
\(356\) 0 0
\(357\) 3.73986 0.197934
\(358\) 0 0
\(359\) 2.54125 0.134122 0.0670611 0.997749i \(-0.478638\pi\)
0.0670611 + 0.997749i \(0.478638\pi\)
\(360\) 0 0
\(361\) −15.0193 −0.790488
\(362\) 0 0
\(363\) 0.00678395 0.000356065 0
\(364\) 0 0
\(365\) −17.4433 −0.913022
\(366\) 0 0
\(367\) −21.9765 −1.14716 −0.573582 0.819148i \(-0.694447\pi\)
−0.573582 + 0.819148i \(0.694447\pi\)
\(368\) 0 0
\(369\) 11.5668 0.602143
\(370\) 0 0
\(371\) 27.3964 1.42235
\(372\) 0 0
\(373\) −22.4020 −1.15993 −0.579965 0.814641i \(-0.696934\pi\)
−0.579965 + 0.814641i \(0.696934\pi\)
\(374\) 0 0
\(375\) −3.12984 −0.161624
\(376\) 0 0
\(377\) 2.61082 0.134464
\(378\) 0 0
\(379\) 27.5019 1.41268 0.706339 0.707873i \(-0.250345\pi\)
0.706339 + 0.707873i \(0.250345\pi\)
\(380\) 0 0
\(381\) −5.46895 −0.280183
\(382\) 0 0
\(383\) −22.7920 −1.16462 −0.582310 0.812967i \(-0.697851\pi\)
−0.582310 + 0.812967i \(0.697851\pi\)
\(384\) 0 0
\(385\) 30.9818 1.57898
\(386\) 0 0
\(387\) 30.4743 1.54910
\(388\) 0 0
\(389\) −12.4333 −0.630394 −0.315197 0.949026i \(-0.602071\pi\)
−0.315197 + 0.949026i \(0.602071\pi\)
\(390\) 0 0
\(391\) 11.0525 0.558947
\(392\) 0 0
\(393\) 1.66542 0.0840096
\(394\) 0 0
\(395\) 17.2643 0.868661
\(396\) 0 0
\(397\) 13.6525 0.685197 0.342599 0.939482i \(-0.388693\pi\)
0.342599 + 0.939482i \(0.388693\pi\)
\(398\) 0 0
\(399\) 2.46512 0.123410
\(400\) 0 0
\(401\) −23.6015 −1.17860 −0.589300 0.807914i \(-0.700597\pi\)
−0.589300 + 0.807914i \(0.700597\pi\)
\(402\) 0 0
\(403\) 4.38237 0.218301
\(404\) 0 0
\(405\) −16.4928 −0.819536
\(406\) 0 0
\(407\) −22.7950 −1.12991
\(408\) 0 0
\(409\) 16.0047 0.791381 0.395690 0.918384i \(-0.370505\pi\)
0.395690 + 0.918384i \(0.370505\pi\)
\(410\) 0 0
\(411\) −2.66100 −0.131257
\(412\) 0 0
\(413\) 58.6992 2.88840
\(414\) 0 0
\(415\) 17.0890 0.838866
\(416\) 0 0
\(417\) −4.13355 −0.202421
\(418\) 0 0
\(419\) −9.90724 −0.484000 −0.242000 0.970276i \(-0.577803\pi\)
−0.242000 + 0.970276i \(0.577803\pi\)
\(420\) 0 0
\(421\) 19.3614 0.943615 0.471808 0.881702i \(-0.343602\pi\)
0.471808 + 0.881702i \(0.343602\pi\)
\(422\) 0 0
\(423\) −37.4730 −1.82200
\(424\) 0 0
\(425\) 3.46236 0.167949
\(426\) 0 0
\(427\) 42.5058 2.05700
\(428\) 0 0
\(429\) 0.423706 0.0204567
\(430\) 0 0
\(431\) 5.24269 0.252531 0.126266 0.991996i \(-0.459701\pi\)
0.126266 + 0.991996i \(0.459701\pi\)
\(432\) 0 0
\(433\) −1.85655 −0.0892200 −0.0446100 0.999004i \(-0.514205\pi\)
−0.0446100 + 0.999004i \(0.514205\pi\)
\(434\) 0 0
\(435\) 2.69759 0.129340
\(436\) 0 0
\(437\) 7.28519 0.348498
\(438\) 0 0
\(439\) −35.5187 −1.69522 −0.847609 0.530622i \(-0.821958\pi\)
−0.847609 + 0.530622i \(0.821958\pi\)
\(440\) 0 0
\(441\) −45.9939 −2.19019
\(442\) 0 0
\(443\) 14.5959 0.693470 0.346735 0.937963i \(-0.387290\pi\)
0.346735 + 0.937963i \(0.387290\pi\)
\(444\) 0 0
\(445\) −21.1231 −1.00133
\(446\) 0 0
\(447\) −2.59666 −0.122818
\(448\) 0 0
\(449\) −25.6909 −1.21243 −0.606215 0.795301i \(-0.707313\pi\)
−0.606215 + 0.795301i \(0.707313\pi\)
\(450\) 0 0
\(451\) 13.0655 0.615229
\(452\) 0 0
\(453\) −5.60063 −0.263140
\(454\) 0 0
\(455\) −4.61115 −0.216174
\(456\) 0 0
\(457\) 18.7278 0.876049 0.438025 0.898963i \(-0.355678\pi\)
0.438025 + 0.898963i \(0.355678\pi\)
\(458\) 0 0
\(459\) −4.65861 −0.217445
\(460\) 0 0
\(461\) −9.56918 −0.445681 −0.222840 0.974855i \(-0.571533\pi\)
−0.222840 + 0.974855i \(0.571533\pi\)
\(462\) 0 0
\(463\) 13.0202 0.605101 0.302550 0.953133i \(-0.402162\pi\)
0.302550 + 0.953133i \(0.402162\pi\)
\(464\) 0 0
\(465\) 4.52802 0.209982
\(466\) 0 0
\(467\) −38.6859 −1.79017 −0.895085 0.445896i \(-0.852885\pi\)
−0.895085 + 0.445896i \(0.852885\pi\)
\(468\) 0 0
\(469\) −68.2408 −3.15107
\(470\) 0 0
\(471\) 2.43488 0.112193
\(472\) 0 0
\(473\) 34.4228 1.58276
\(474\) 0 0
\(475\) 2.28220 0.104715
\(476\) 0 0
\(477\) −16.8698 −0.772415
\(478\) 0 0
\(479\) 0.216817 0.00990662 0.00495331 0.999988i \(-0.498423\pi\)
0.00495331 + 0.999988i \(0.498423\pi\)
\(480\) 0 0
\(481\) 3.39267 0.154692
\(482\) 0 0
\(483\) 4.51144 0.205278
\(484\) 0 0
\(485\) −25.8681 −1.17461
\(486\) 0 0
\(487\) 42.9856 1.94786 0.973932 0.226839i \(-0.0728391\pi\)
0.973932 + 0.226839i \(0.0728391\pi\)
\(488\) 0 0
\(489\) 5.29175 0.239301
\(490\) 0 0
\(491\) −20.8521 −0.941042 −0.470521 0.882389i \(-0.655934\pi\)
−0.470521 + 0.882389i \(0.655934\pi\)
\(492\) 0 0
\(493\) −16.0286 −0.721891
\(494\) 0 0
\(495\) −19.0776 −0.857474
\(496\) 0 0
\(497\) −50.3979 −2.26066
\(498\) 0 0
\(499\) −25.2821 −1.13178 −0.565891 0.824480i \(-0.691468\pi\)
−0.565891 + 0.824480i \(0.691468\pi\)
\(500\) 0 0
\(501\) −2.30541 −0.102998
\(502\) 0 0
\(503\) −38.0521 −1.69666 −0.848331 0.529467i \(-0.822392\pi\)
−0.848331 + 0.529467i \(0.822392\pi\)
\(504\) 0 0
\(505\) 18.4373 0.820450
\(506\) 0 0
\(507\) 3.30940 0.146976
\(508\) 0 0
\(509\) 19.4293 0.861189 0.430595 0.902545i \(-0.358304\pi\)
0.430595 + 0.902545i \(0.358304\pi\)
\(510\) 0 0
\(511\) 42.3061 1.87151
\(512\) 0 0
\(513\) −3.07071 −0.135575
\(514\) 0 0
\(515\) −19.2412 −0.847869
\(516\) 0 0
\(517\) −42.3282 −1.86159
\(518\) 0 0
\(519\) 2.39559 0.105155
\(520\) 0 0
\(521\) −5.72389 −0.250768 −0.125384 0.992108i \(-0.540016\pi\)
−0.125384 + 0.992108i \(0.540016\pi\)
\(522\) 0 0
\(523\) 5.17502 0.226288 0.113144 0.993579i \(-0.463908\pi\)
0.113144 + 0.993579i \(0.463908\pi\)
\(524\) 0 0
\(525\) 1.41328 0.0616807
\(526\) 0 0
\(527\) −26.9046 −1.17198
\(528\) 0 0
\(529\) −9.66727 −0.420316
\(530\) 0 0
\(531\) −36.1450 −1.56856
\(532\) 0 0
\(533\) −1.94458 −0.0842292
\(534\) 0 0
\(535\) 8.56029 0.370094
\(536\) 0 0
\(537\) 0.172963 0.00746391
\(538\) 0 0
\(539\) −51.9532 −2.23778
\(540\) 0 0
\(541\) 12.0026 0.516034 0.258017 0.966140i \(-0.416931\pi\)
0.258017 + 0.966140i \(0.416931\pi\)
\(542\) 0 0
\(543\) 1.64640 0.0706540
\(544\) 0 0
\(545\) 10.5488 0.451860
\(546\) 0 0
\(547\) −11.7088 −0.500632 −0.250316 0.968164i \(-0.580535\pi\)
−0.250316 + 0.968164i \(0.580535\pi\)
\(548\) 0 0
\(549\) −26.1737 −1.11706
\(550\) 0 0
\(551\) −10.5652 −0.450092
\(552\) 0 0
\(553\) −41.8720 −1.78058
\(554\) 0 0
\(555\) 3.50543 0.148797
\(556\) 0 0
\(557\) 34.8425 1.47633 0.738163 0.674623i \(-0.235694\pi\)
0.738163 + 0.674623i \(0.235694\pi\)
\(558\) 0 0
\(559\) −5.12327 −0.216691
\(560\) 0 0
\(561\) −2.60126 −0.109825
\(562\) 0 0
\(563\) 4.65603 0.196228 0.0981141 0.995175i \(-0.468719\pi\)
0.0981141 + 0.995175i \(0.468719\pi\)
\(564\) 0 0
\(565\) 1.16840 0.0491550
\(566\) 0 0
\(567\) 40.0010 1.67988
\(568\) 0 0
\(569\) 42.6440 1.78773 0.893865 0.448336i \(-0.147983\pi\)
0.893865 + 0.448336i \(0.147983\pi\)
\(570\) 0 0
\(571\) −11.6374 −0.487011 −0.243506 0.969899i \(-0.578297\pi\)
−0.243506 + 0.969899i \(0.578297\pi\)
\(572\) 0 0
\(573\) −0.0577698 −0.00241337
\(574\) 0 0
\(575\) 4.17669 0.174180
\(576\) 0 0
\(577\) −6.32219 −0.263196 −0.131598 0.991303i \(-0.542011\pi\)
−0.131598 + 0.991303i \(0.542011\pi\)
\(578\) 0 0
\(579\) −5.32294 −0.221214
\(580\) 0 0
\(581\) −41.4469 −1.71951
\(582\) 0 0
\(583\) −19.0556 −0.789201
\(584\) 0 0
\(585\) 2.83939 0.117394
\(586\) 0 0
\(587\) −11.5968 −0.478652 −0.239326 0.970939i \(-0.576927\pi\)
−0.239326 + 0.970939i \(0.576927\pi\)
\(588\) 0 0
\(589\) −17.7341 −0.730721
\(590\) 0 0
\(591\) −1.13922 −0.0468613
\(592\) 0 0
\(593\) 28.2933 1.16187 0.580934 0.813951i \(-0.302688\pi\)
0.580934 + 0.813951i \(0.302688\pi\)
\(594\) 0 0
\(595\) 28.3092 1.16056
\(596\) 0 0
\(597\) −6.15185 −0.251779
\(598\) 0 0
\(599\) −35.9025 −1.46694 −0.733468 0.679724i \(-0.762100\pi\)
−0.733468 + 0.679724i \(0.762100\pi\)
\(600\) 0 0
\(601\) −4.84654 −0.197694 −0.0988472 0.995103i \(-0.531515\pi\)
−0.0988472 + 0.995103i \(0.531515\pi\)
\(602\) 0 0
\(603\) 42.0204 1.71120
\(604\) 0 0
\(605\) 0.0513517 0.00208774
\(606\) 0 0
\(607\) −30.4540 −1.23609 −0.618045 0.786143i \(-0.712075\pi\)
−0.618045 + 0.786143i \(0.712075\pi\)
\(608\) 0 0
\(609\) −6.54261 −0.265120
\(610\) 0 0
\(611\) 6.29987 0.254865
\(612\) 0 0
\(613\) 10.3728 0.418952 0.209476 0.977814i \(-0.432824\pi\)
0.209476 + 0.977814i \(0.432824\pi\)
\(614\) 0 0
\(615\) −2.00921 −0.0810193
\(616\) 0 0
\(617\) −9.15320 −0.368494 −0.184247 0.982880i \(-0.558985\pi\)
−0.184247 + 0.982880i \(0.558985\pi\)
\(618\) 0 0
\(619\) 32.8453 1.32016 0.660081 0.751194i \(-0.270522\pi\)
0.660081 + 0.751194i \(0.270522\pi\)
\(620\) 0 0
\(621\) −5.61974 −0.225512
\(622\) 0 0
\(623\) 51.2311 2.05253
\(624\) 0 0
\(625\) −17.9723 −0.718891
\(626\) 0 0
\(627\) −1.71461 −0.0684749
\(628\) 0 0
\(629\) −20.8286 −0.830490
\(630\) 0 0
\(631\) −38.1274 −1.51783 −0.758914 0.651191i \(-0.774270\pi\)
−0.758914 + 0.651191i \(0.774270\pi\)
\(632\) 0 0
\(633\) −2.78928 −0.110864
\(634\) 0 0
\(635\) −41.3977 −1.64282
\(636\) 0 0
\(637\) 7.73239 0.306368
\(638\) 0 0
\(639\) 31.0334 1.22766
\(640\) 0 0
\(641\) −5.22739 −0.206470 −0.103235 0.994657i \(-0.532919\pi\)
−0.103235 + 0.994657i \(0.532919\pi\)
\(642\) 0 0
\(643\) −11.5907 −0.457093 −0.228546 0.973533i \(-0.573397\pi\)
−0.228546 + 0.973533i \(0.573397\pi\)
\(644\) 0 0
\(645\) −5.29355 −0.208433
\(646\) 0 0
\(647\) −19.5074 −0.766915 −0.383457 0.923559i \(-0.625267\pi\)
−0.383457 + 0.923559i \(0.625267\pi\)
\(648\) 0 0
\(649\) −40.8282 −1.60265
\(650\) 0 0
\(651\) −10.9821 −0.430420
\(652\) 0 0
\(653\) 37.6926 1.47503 0.737513 0.675333i \(-0.236000\pi\)
0.737513 + 0.675333i \(0.236000\pi\)
\(654\) 0 0
\(655\) 12.6066 0.492580
\(656\) 0 0
\(657\) −26.0507 −1.01633
\(658\) 0 0
\(659\) 2.55314 0.0994562 0.0497281 0.998763i \(-0.484165\pi\)
0.0497281 + 0.998763i \(0.484165\pi\)
\(660\) 0 0
\(661\) 41.5397 1.61571 0.807853 0.589384i \(-0.200629\pi\)
0.807853 + 0.589384i \(0.200629\pi\)
\(662\) 0 0
\(663\) 0.387155 0.0150359
\(664\) 0 0
\(665\) 18.6599 0.723600
\(666\) 0 0
\(667\) −19.3355 −0.748673
\(668\) 0 0
\(669\) −7.07512 −0.273540
\(670\) 0 0
\(671\) −29.5649 −1.14134
\(672\) 0 0
\(673\) −42.7327 −1.64722 −0.823612 0.567154i \(-0.808044\pi\)
−0.823612 + 0.567154i \(0.808044\pi\)
\(674\) 0 0
\(675\) −1.76047 −0.0677607
\(676\) 0 0
\(677\) −23.9024 −0.918646 −0.459323 0.888269i \(-0.651908\pi\)
−0.459323 + 0.888269i \(0.651908\pi\)
\(678\) 0 0
\(679\) 62.7394 2.40772
\(680\) 0 0
\(681\) 6.36314 0.243836
\(682\) 0 0
\(683\) 41.1877 1.57600 0.788002 0.615672i \(-0.211115\pi\)
0.788002 + 0.615672i \(0.211115\pi\)
\(684\) 0 0
\(685\) −20.1426 −0.769611
\(686\) 0 0
\(687\) −1.76606 −0.0673794
\(688\) 0 0
\(689\) 2.83611 0.108047
\(690\) 0 0
\(691\) 6.38418 0.242866 0.121433 0.992600i \(-0.461251\pi\)
0.121433 + 0.992600i \(0.461251\pi\)
\(692\) 0 0
\(693\) 46.2699 1.75765
\(694\) 0 0
\(695\) −31.2893 −1.18687
\(696\) 0 0
\(697\) 11.9384 0.452198
\(698\) 0 0
\(699\) −6.14808 −0.232542
\(700\) 0 0
\(701\) −51.4514 −1.94329 −0.971647 0.236438i \(-0.924020\pi\)
−0.971647 + 0.236438i \(0.924020\pi\)
\(702\) 0 0
\(703\) −13.7291 −0.517803
\(704\) 0 0
\(705\) 6.50925 0.245153
\(706\) 0 0
\(707\) −44.7170 −1.68176
\(708\) 0 0
\(709\) 28.8547 1.08366 0.541830 0.840488i \(-0.317732\pi\)
0.541830 + 0.840488i \(0.317732\pi\)
\(710\) 0 0
\(711\) 25.7834 0.966954
\(712\) 0 0
\(713\) −32.4554 −1.21546
\(714\) 0 0
\(715\) 3.20728 0.119946
\(716\) 0 0
\(717\) 6.98711 0.260938
\(718\) 0 0
\(719\) 10.4747 0.390639 0.195319 0.980740i \(-0.437426\pi\)
0.195319 + 0.980740i \(0.437426\pi\)
\(720\) 0 0
\(721\) 46.6667 1.73796
\(722\) 0 0
\(723\) −0.920315 −0.0342269
\(724\) 0 0
\(725\) −6.05715 −0.224957
\(726\) 0 0
\(727\) −2.21072 −0.0819909 −0.0409955 0.999159i \(-0.513053\pi\)
−0.0409955 + 0.999159i \(0.513053\pi\)
\(728\) 0 0
\(729\) −23.4335 −0.867907
\(730\) 0 0
\(731\) 31.4533 1.16334
\(732\) 0 0
\(733\) 5.00026 0.184689 0.0923445 0.995727i \(-0.470564\pi\)
0.0923445 + 0.995727i \(0.470564\pi\)
\(734\) 0 0
\(735\) 7.98938 0.294693
\(736\) 0 0
\(737\) 47.4649 1.74839
\(738\) 0 0
\(739\) 6.03692 0.222072 0.111036 0.993816i \(-0.464583\pi\)
0.111036 + 0.993816i \(0.464583\pi\)
\(740\) 0 0
\(741\) 0.255192 0.00937471
\(742\) 0 0
\(743\) 1.69036 0.0620134 0.0310067 0.999519i \(-0.490129\pi\)
0.0310067 + 0.999519i \(0.490129\pi\)
\(744\) 0 0
\(745\) −19.6557 −0.720128
\(746\) 0 0
\(747\) 25.5216 0.933787
\(748\) 0 0
\(749\) −20.7617 −0.758617
\(750\) 0 0
\(751\) 3.48556 0.127190 0.0635949 0.997976i \(-0.479743\pi\)
0.0635949 + 0.997976i \(0.479743\pi\)
\(752\) 0 0
\(753\) −0.259421 −0.00945381
\(754\) 0 0
\(755\) −42.3944 −1.54289
\(756\) 0 0
\(757\) 6.91788 0.251435 0.125717 0.992066i \(-0.459877\pi\)
0.125717 + 0.992066i \(0.459877\pi\)
\(758\) 0 0
\(759\) −3.13793 −0.113900
\(760\) 0 0
\(761\) 37.4085 1.35606 0.678028 0.735036i \(-0.262835\pi\)
0.678028 + 0.735036i \(0.262835\pi\)
\(762\) 0 0
\(763\) −25.5845 −0.926221
\(764\) 0 0
\(765\) −17.4319 −0.630250
\(766\) 0 0
\(767\) 6.07662 0.219414
\(768\) 0 0
\(769\) −27.3839 −0.987489 −0.493745 0.869607i \(-0.664372\pi\)
−0.493745 + 0.869607i \(0.664372\pi\)
\(770\) 0 0
\(771\) −2.52162 −0.0908141
\(772\) 0 0
\(773\) 20.8686 0.750590 0.375295 0.926905i \(-0.377541\pi\)
0.375295 + 0.926905i \(0.377541\pi\)
\(774\) 0 0
\(775\) −10.1672 −0.365216
\(776\) 0 0
\(777\) −8.50190 −0.305004
\(778\) 0 0
\(779\) 7.86913 0.281941
\(780\) 0 0
\(781\) 35.0542 1.25434
\(782\) 0 0
\(783\) 8.14990 0.291254
\(784\) 0 0
\(785\) 18.4310 0.657832
\(786\) 0 0
\(787\) −17.8159 −0.635069 −0.317535 0.948247i \(-0.602855\pi\)
−0.317535 + 0.948247i \(0.602855\pi\)
\(788\) 0 0
\(789\) 0.0687319 0.00244692
\(790\) 0 0
\(791\) −2.83378 −0.100758
\(792\) 0 0
\(793\) 4.40025 0.156258
\(794\) 0 0
\(795\) 2.93037 0.103930
\(796\) 0 0
\(797\) −22.7141 −0.804574 −0.402287 0.915514i \(-0.631785\pi\)
−0.402287 + 0.915514i \(0.631785\pi\)
\(798\) 0 0
\(799\) −38.6768 −1.36829
\(800\) 0 0
\(801\) −31.5464 −1.11464
\(802\) 0 0
\(803\) −29.4260 −1.03842
\(804\) 0 0
\(805\) 34.1497 1.20362
\(806\) 0 0
\(807\) −0.336427 −0.0118428
\(808\) 0 0
\(809\) 1.91286 0.0672527 0.0336264 0.999434i \(-0.489294\pi\)
0.0336264 + 0.999434i \(0.489294\pi\)
\(810\) 0 0
\(811\) 11.7428 0.412345 0.206172 0.978516i \(-0.433899\pi\)
0.206172 + 0.978516i \(0.433899\pi\)
\(812\) 0 0
\(813\) −1.12227 −0.0393598
\(814\) 0 0
\(815\) 40.0563 1.40311
\(816\) 0 0
\(817\) 20.7323 0.725332
\(818\) 0 0
\(819\) −6.88653 −0.240635
\(820\) 0 0
\(821\) 55.0109 1.91989 0.959947 0.280183i \(-0.0903950\pi\)
0.959947 + 0.280183i \(0.0903950\pi\)
\(822\) 0 0
\(823\) −16.2665 −0.567015 −0.283507 0.958970i \(-0.591498\pi\)
−0.283507 + 0.958970i \(0.591498\pi\)
\(824\) 0 0
\(825\) −0.983007 −0.0342239
\(826\) 0 0
\(827\) 51.4976 1.79075 0.895374 0.445315i \(-0.146908\pi\)
0.895374 + 0.445315i \(0.146908\pi\)
\(828\) 0 0
\(829\) −17.0310 −0.591512 −0.295756 0.955263i \(-0.595572\pi\)
−0.295756 + 0.955263i \(0.595572\pi\)
\(830\) 0 0
\(831\) −7.09172 −0.246009
\(832\) 0 0
\(833\) −47.4714 −1.64479
\(834\) 0 0
\(835\) −17.4510 −0.603916
\(836\) 0 0
\(837\) 13.6799 0.472848
\(838\) 0 0
\(839\) −0.140399 −0.00484713 −0.00242356 0.999997i \(-0.500771\pi\)
−0.00242356 + 0.999997i \(0.500771\pi\)
\(840\) 0 0
\(841\) −0.959168 −0.0330748
\(842\) 0 0
\(843\) −0.289535 −0.00997210
\(844\) 0 0
\(845\) 25.0508 0.861774
\(846\) 0 0
\(847\) −0.124546 −0.00427945
\(848\) 0 0
\(849\) −0.871957 −0.0299255
\(850\) 0 0
\(851\) −25.1258 −0.861301
\(852\) 0 0
\(853\) −37.4221 −1.28131 −0.640654 0.767829i \(-0.721337\pi\)
−0.640654 + 0.767829i \(0.721337\pi\)
\(854\) 0 0
\(855\) −11.4902 −0.392955
\(856\) 0 0
\(857\) 30.7419 1.05012 0.525062 0.851064i \(-0.324042\pi\)
0.525062 + 0.851064i \(0.324042\pi\)
\(858\) 0 0
\(859\) 17.2923 0.590004 0.295002 0.955497i \(-0.404680\pi\)
0.295002 + 0.955497i \(0.404680\pi\)
\(860\) 0 0
\(861\) 4.87305 0.166073
\(862\) 0 0
\(863\) −21.6653 −0.737497 −0.368748 0.929529i \(-0.620214\pi\)
−0.368748 + 0.929529i \(0.620214\pi\)
\(864\) 0 0
\(865\) 18.1337 0.616563
\(866\) 0 0
\(867\) 2.03329 0.0690541
\(868\) 0 0
\(869\) 29.1241 0.987967
\(870\) 0 0
\(871\) −7.06438 −0.239367
\(872\) 0 0
\(873\) −38.6328 −1.30752
\(874\) 0 0
\(875\) 57.4605 1.94252
\(876\) 0 0
\(877\) −17.7954 −0.600909 −0.300455 0.953796i \(-0.597138\pi\)
−0.300455 + 0.953796i \(0.597138\pi\)
\(878\) 0 0
\(879\) −4.11747 −0.138879
\(880\) 0 0
\(881\) 14.2543 0.480238 0.240119 0.970743i \(-0.422813\pi\)
0.240119 + 0.970743i \(0.422813\pi\)
\(882\) 0 0
\(883\) −46.6843 −1.57105 −0.785526 0.618828i \(-0.787608\pi\)
−0.785526 + 0.618828i \(0.787608\pi\)
\(884\) 0 0
\(885\) 6.27858 0.211052
\(886\) 0 0
\(887\) 34.7724 1.16754 0.583772 0.811918i \(-0.301576\pi\)
0.583772 + 0.811918i \(0.301576\pi\)
\(888\) 0 0
\(889\) 100.404 3.36744
\(890\) 0 0
\(891\) −27.8227 −0.932094
\(892\) 0 0
\(893\) −25.4937 −0.853113
\(894\) 0 0
\(895\) 1.30926 0.0437637
\(896\) 0 0
\(897\) 0.467030 0.0155937
\(898\) 0 0
\(899\) 47.0677 1.56980
\(900\) 0 0
\(901\) −17.4117 −0.580069
\(902\) 0 0
\(903\) 12.8387 0.427246
\(904\) 0 0
\(905\) 12.4626 0.414271
\(906\) 0 0
\(907\) 11.2349 0.373050 0.186525 0.982450i \(-0.440278\pi\)
0.186525 + 0.982450i \(0.440278\pi\)
\(908\) 0 0
\(909\) 27.5353 0.913287
\(910\) 0 0
\(911\) −12.7604 −0.422771 −0.211385 0.977403i \(-0.567797\pi\)
−0.211385 + 0.977403i \(0.567797\pi\)
\(912\) 0 0
\(913\) 28.8284 0.954080
\(914\) 0 0
\(915\) 4.54650 0.150303
\(916\) 0 0
\(917\) −30.5754 −1.00969
\(918\) 0 0
\(919\) −3.03946 −0.100263 −0.0501313 0.998743i \(-0.515964\pi\)
−0.0501313 + 0.998743i \(0.515964\pi\)
\(920\) 0 0
\(921\) 1.17966 0.0388712
\(922\) 0 0
\(923\) −5.21726 −0.171728
\(924\) 0 0
\(925\) −7.87106 −0.258799
\(926\) 0 0
\(927\) −28.7358 −0.943808
\(928\) 0 0
\(929\) 24.2895 0.796911 0.398456 0.917188i \(-0.369546\pi\)
0.398456 + 0.917188i \(0.369546\pi\)
\(930\) 0 0
\(931\) −31.2906 −1.02551
\(932\) 0 0
\(933\) −0.274807 −0.00899678
\(934\) 0 0
\(935\) −19.6904 −0.643946
\(936\) 0 0
\(937\) −20.8628 −0.681556 −0.340778 0.940144i \(-0.610691\pi\)
−0.340778 + 0.940144i \(0.610691\pi\)
\(938\) 0 0
\(939\) −6.40977 −0.209175
\(940\) 0 0
\(941\) −47.9126 −1.56190 −0.780952 0.624590i \(-0.785266\pi\)
−0.780952 + 0.624590i \(0.785266\pi\)
\(942\) 0 0
\(943\) 14.4014 0.468974
\(944\) 0 0
\(945\) −14.3941 −0.468240
\(946\) 0 0
\(947\) 28.1670 0.915306 0.457653 0.889131i \(-0.348690\pi\)
0.457653 + 0.889131i \(0.348690\pi\)
\(948\) 0 0
\(949\) 4.37958 0.142167
\(950\) 0 0
\(951\) −3.37906 −0.109573
\(952\) 0 0
\(953\) 18.5877 0.602115 0.301057 0.953606i \(-0.402660\pi\)
0.301057 + 0.953606i \(0.402660\pi\)
\(954\) 0 0
\(955\) −0.437293 −0.0141505
\(956\) 0 0
\(957\) 4.55071 0.147104
\(958\) 0 0
\(959\) 48.8530 1.57755
\(960\) 0 0
\(961\) 48.0051 1.54855
\(962\) 0 0
\(963\) 12.7844 0.411971
\(964\) 0 0
\(965\) −40.2924 −1.29706
\(966\) 0 0
\(967\) −15.4754 −0.497654 −0.248827 0.968548i \(-0.580045\pi\)
−0.248827 + 0.968548i \(0.580045\pi\)
\(968\) 0 0
\(969\) −1.56670 −0.0503296
\(970\) 0 0
\(971\) −33.8048 −1.08485 −0.542424 0.840105i \(-0.682493\pi\)
−0.542424 + 0.840105i \(0.682493\pi\)
\(972\) 0 0
\(973\) 75.8876 2.43284
\(974\) 0 0
\(975\) 0.146305 0.00468550
\(976\) 0 0
\(977\) 12.0997 0.387104 0.193552 0.981090i \(-0.437999\pi\)
0.193552 + 0.981090i \(0.437999\pi\)
\(978\) 0 0
\(979\) −35.6337 −1.13886
\(980\) 0 0
\(981\) 15.7541 0.502989
\(982\) 0 0
\(983\) −18.4774 −0.589337 −0.294668 0.955600i \(-0.595209\pi\)
−0.294668 + 0.955600i \(0.595209\pi\)
\(984\) 0 0
\(985\) −8.62343 −0.274765
\(986\) 0 0
\(987\) −15.7872 −0.502513
\(988\) 0 0
\(989\) 37.9425 1.20650
\(990\) 0 0
\(991\) 20.7131 0.657974 0.328987 0.944334i \(-0.393293\pi\)
0.328987 + 0.944334i \(0.393293\pi\)
\(992\) 0 0
\(993\) 2.75324 0.0873714
\(994\) 0 0
\(995\) −46.5670 −1.47627
\(996\) 0 0
\(997\) 10.7767 0.341302 0.170651 0.985332i \(-0.445413\pi\)
0.170651 + 0.985332i \(0.445413\pi\)
\(998\) 0 0
\(999\) 10.5905 0.335069
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.1.11 23
4.3 odd 2 2008.2.a.d.1.13 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.13 23 4.3 odd 2
4016.2.a.m.1.11 23 1.1 even 1 trivial