Properties

Label 4016.2.a.m.1.20
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 1.20
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.74485 q^{3} +2.14962 q^{5} +3.54966 q^{7} +4.53421 q^{9} +O(q^{10})\) \(q+2.74485 q^{3} +2.14962 q^{5} +3.54966 q^{7} +4.53421 q^{9} -6.54587 q^{11} +5.92187 q^{13} +5.90040 q^{15} +3.02967 q^{17} +5.44528 q^{19} +9.74328 q^{21} +2.97810 q^{23} -0.379115 q^{25} +4.21117 q^{27} -7.08516 q^{29} +2.90565 q^{31} -17.9674 q^{33} +7.63043 q^{35} +5.80826 q^{37} +16.2547 q^{39} -8.06047 q^{41} -8.02892 q^{43} +9.74684 q^{45} -12.1568 q^{47} +5.60008 q^{49} +8.31599 q^{51} -4.41139 q^{53} -14.0712 q^{55} +14.9465 q^{57} -10.8456 q^{59} +3.39774 q^{61} +16.0949 q^{63} +12.7298 q^{65} -12.2601 q^{67} +8.17443 q^{69} +3.79662 q^{71} -5.43917 q^{73} -1.04061 q^{75} -23.2356 q^{77} +5.75747 q^{79} -2.04360 q^{81} +2.88983 q^{83} +6.51265 q^{85} -19.4477 q^{87} +17.2847 q^{89} +21.0206 q^{91} +7.97559 q^{93} +11.7053 q^{95} +10.2466 q^{97} -29.6803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

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
\(3\) 2.74485 1.58474 0.792370 0.610041i \(-0.208847\pi\)
0.792370 + 0.610041i \(0.208847\pi\)
\(4\) 0 0
\(5\) 2.14962 0.961341 0.480671 0.876901i \(-0.340393\pi\)
0.480671 + 0.876901i \(0.340393\pi\)
\(6\) 0 0
\(7\) 3.54966 1.34164 0.670822 0.741618i \(-0.265941\pi\)
0.670822 + 0.741618i \(0.265941\pi\)
\(8\) 0 0
\(9\) 4.53421 1.51140
\(10\) 0 0
\(11\) −6.54587 −1.97365 −0.986827 0.161780i \(-0.948276\pi\)
−0.986827 + 0.161780i \(0.948276\pi\)
\(12\) 0 0
\(13\) 5.92187 1.64243 0.821216 0.570617i \(-0.193296\pi\)
0.821216 + 0.570617i \(0.193296\pi\)
\(14\) 0 0
\(15\) 5.90040 1.52348
\(16\) 0 0
\(17\) 3.02967 0.734803 0.367402 0.930062i \(-0.380247\pi\)
0.367402 + 0.930062i \(0.380247\pi\)
\(18\) 0 0
\(19\) 5.44528 1.24923 0.624616 0.780932i \(-0.285255\pi\)
0.624616 + 0.780932i \(0.285255\pi\)
\(20\) 0 0
\(21\) 9.74328 2.12616
\(22\) 0 0
\(23\) 2.97810 0.620976 0.310488 0.950577i \(-0.399508\pi\)
0.310488 + 0.950577i \(0.399508\pi\)
\(24\) 0 0
\(25\) −0.379115 −0.0758230
\(26\) 0 0
\(27\) 4.21117 0.810439
\(28\) 0 0
\(29\) −7.08516 −1.31568 −0.657841 0.753157i \(-0.728530\pi\)
−0.657841 + 0.753157i \(0.728530\pi\)
\(30\) 0 0
\(31\) 2.90565 0.521871 0.260935 0.965356i \(-0.415969\pi\)
0.260935 + 0.965356i \(0.415969\pi\)
\(32\) 0 0
\(33\) −17.9674 −3.12773
\(34\) 0 0
\(35\) 7.63043 1.28978
\(36\) 0 0
\(37\) 5.80826 0.954872 0.477436 0.878666i \(-0.341566\pi\)
0.477436 + 0.878666i \(0.341566\pi\)
\(38\) 0 0
\(39\) 16.2547 2.60283
\(40\) 0 0
\(41\) −8.06047 −1.25883 −0.629417 0.777068i \(-0.716706\pi\)
−0.629417 + 0.777068i \(0.716706\pi\)
\(42\) 0 0
\(43\) −8.02892 −1.22440 −0.612200 0.790703i \(-0.709715\pi\)
−0.612200 + 0.790703i \(0.709715\pi\)
\(44\) 0 0
\(45\) 9.74684 1.45297
\(46\) 0 0
\(47\) −12.1568 −1.77325 −0.886623 0.462494i \(-0.846955\pi\)
−0.886623 + 0.462494i \(0.846955\pi\)
\(48\) 0 0
\(49\) 5.60008 0.800011
\(50\) 0 0
\(51\) 8.31599 1.16447
\(52\) 0 0
\(53\) −4.41139 −0.605952 −0.302976 0.952998i \(-0.597980\pi\)
−0.302976 + 0.952998i \(0.597980\pi\)
\(54\) 0 0
\(55\) −14.0712 −1.89735
\(56\) 0 0
\(57\) 14.9465 1.97971
\(58\) 0 0
\(59\) −10.8456 −1.41198 −0.705992 0.708220i \(-0.749498\pi\)
−0.705992 + 0.708220i \(0.749498\pi\)
\(60\) 0 0
\(61\) 3.39774 0.435036 0.217518 0.976056i \(-0.430204\pi\)
0.217518 + 0.976056i \(0.430204\pi\)
\(62\) 0 0
\(63\) 16.0949 2.02776
\(64\) 0 0
\(65\) 12.7298 1.57894
\(66\) 0 0
\(67\) −12.2601 −1.49780 −0.748902 0.662681i \(-0.769419\pi\)
−0.748902 + 0.662681i \(0.769419\pi\)
\(68\) 0 0
\(69\) 8.17443 0.984086
\(70\) 0 0
\(71\) 3.79662 0.450576 0.225288 0.974292i \(-0.427668\pi\)
0.225288 + 0.974292i \(0.427668\pi\)
\(72\) 0 0
\(73\) −5.43917 −0.636606 −0.318303 0.947989i \(-0.603113\pi\)
−0.318303 + 0.947989i \(0.603113\pi\)
\(74\) 0 0
\(75\) −1.04061 −0.120160
\(76\) 0 0
\(77\) −23.2356 −2.64794
\(78\) 0 0
\(79\) 5.75747 0.647766 0.323883 0.946097i \(-0.395012\pi\)
0.323883 + 0.946097i \(0.395012\pi\)
\(80\) 0 0
\(81\) −2.04360 −0.227066
\(82\) 0 0
\(83\) 2.88983 0.317201 0.158600 0.987343i \(-0.449302\pi\)
0.158600 + 0.987343i \(0.449302\pi\)
\(84\) 0 0
\(85\) 6.51265 0.706396
\(86\) 0 0
\(87\) −19.4477 −2.08501
\(88\) 0 0
\(89\) 17.2847 1.83218 0.916090 0.400973i \(-0.131328\pi\)
0.916090 + 0.400973i \(0.131328\pi\)
\(90\) 0 0
\(91\) 21.0206 2.20356
\(92\) 0 0
\(93\) 7.97559 0.827030
\(94\) 0 0
\(95\) 11.7053 1.20094
\(96\) 0 0
\(97\) 10.2466 1.04039 0.520194 0.854048i \(-0.325859\pi\)
0.520194 + 0.854048i \(0.325859\pi\)
\(98\) 0 0
\(99\) −29.6803 −2.98298
\(100\) 0 0
\(101\) −15.2411 −1.51654 −0.758271 0.651939i \(-0.773956\pi\)
−0.758271 + 0.651939i \(0.773956\pi\)
\(102\) 0 0
\(103\) −4.10404 −0.404383 −0.202191 0.979346i \(-0.564806\pi\)
−0.202191 + 0.979346i \(0.564806\pi\)
\(104\) 0 0
\(105\) 20.9444 2.04396
\(106\) 0 0
\(107\) 4.91806 0.475447 0.237723 0.971333i \(-0.423599\pi\)
0.237723 + 0.971333i \(0.423599\pi\)
\(108\) 0 0
\(109\) 9.54452 0.914200 0.457100 0.889415i \(-0.348888\pi\)
0.457100 + 0.889415i \(0.348888\pi\)
\(110\) 0 0
\(111\) 15.9428 1.51322
\(112\) 0 0
\(113\) 7.77713 0.731611 0.365805 0.930691i \(-0.380794\pi\)
0.365805 + 0.930691i \(0.380794\pi\)
\(114\) 0 0
\(115\) 6.40179 0.596970
\(116\) 0 0
\(117\) 26.8510 2.48238
\(118\) 0 0
\(119\) 10.7543 0.985845
\(120\) 0 0
\(121\) 31.8484 2.89531
\(122\) 0 0
\(123\) −22.1248 −1.99492
\(124\) 0 0
\(125\) −11.5631 −1.03423
\(126\) 0 0
\(127\) −14.2833 −1.26744 −0.633720 0.773562i \(-0.718473\pi\)
−0.633720 + 0.773562i \(0.718473\pi\)
\(128\) 0 0
\(129\) −22.0382 −1.94036
\(130\) 0 0
\(131\) −7.04115 −0.615188 −0.307594 0.951518i \(-0.599524\pi\)
−0.307594 + 0.951518i \(0.599524\pi\)
\(132\) 0 0
\(133\) 19.3289 1.67603
\(134\) 0 0
\(135\) 9.05242 0.779109
\(136\) 0 0
\(137\) −0.449893 −0.0384370 −0.0192185 0.999815i \(-0.506118\pi\)
−0.0192185 + 0.999815i \(0.506118\pi\)
\(138\) 0 0
\(139\) 3.85143 0.326674 0.163337 0.986570i \(-0.447774\pi\)
0.163337 + 0.986570i \(0.447774\pi\)
\(140\) 0 0
\(141\) −33.3685 −2.81013
\(142\) 0 0
\(143\) −38.7638 −3.24159
\(144\) 0 0
\(145\) −15.2304 −1.26482
\(146\) 0 0
\(147\) 15.3714 1.26781
\(148\) 0 0
\(149\) 8.40916 0.688905 0.344453 0.938804i \(-0.388065\pi\)
0.344453 + 0.938804i \(0.388065\pi\)
\(150\) 0 0
\(151\) −3.60603 −0.293454 −0.146727 0.989177i \(-0.546874\pi\)
−0.146727 + 0.989177i \(0.546874\pi\)
\(152\) 0 0
\(153\) 13.7371 1.11058
\(154\) 0 0
\(155\) 6.24606 0.501696
\(156\) 0 0
\(157\) 22.2108 1.77261 0.886306 0.463100i \(-0.153263\pi\)
0.886306 + 0.463100i \(0.153263\pi\)
\(158\) 0 0
\(159\) −12.1086 −0.960276
\(160\) 0 0
\(161\) 10.5712 0.833129
\(162\) 0 0
\(163\) 12.1388 0.950781 0.475390 0.879775i \(-0.342307\pi\)
0.475390 + 0.879775i \(0.342307\pi\)
\(164\) 0 0
\(165\) −38.6232 −3.00681
\(166\) 0 0
\(167\) 1.16030 0.0897865 0.0448932 0.998992i \(-0.485705\pi\)
0.0448932 + 0.998992i \(0.485705\pi\)
\(168\) 0 0
\(169\) 22.0686 1.69758
\(170\) 0 0
\(171\) 24.6900 1.88809
\(172\) 0 0
\(173\) −24.8853 −1.89199 −0.945997 0.324175i \(-0.894913\pi\)
−0.945997 + 0.324175i \(0.894913\pi\)
\(174\) 0 0
\(175\) −1.34573 −0.101728
\(176\) 0 0
\(177\) −29.7697 −2.23763
\(178\) 0 0
\(179\) −18.2481 −1.36393 −0.681964 0.731386i \(-0.738874\pi\)
−0.681964 + 0.731386i \(0.738874\pi\)
\(180\) 0 0
\(181\) −13.0683 −0.971361 −0.485681 0.874136i \(-0.661428\pi\)
−0.485681 + 0.874136i \(0.661428\pi\)
\(182\) 0 0
\(183\) 9.32629 0.689419
\(184\) 0 0
\(185\) 12.4856 0.917958
\(186\) 0 0
\(187\) −19.8318 −1.45025
\(188\) 0 0
\(189\) 14.9482 1.08732
\(190\) 0 0
\(191\) 5.53780 0.400701 0.200351 0.979724i \(-0.435792\pi\)
0.200351 + 0.979724i \(0.435792\pi\)
\(192\) 0 0
\(193\) −10.2677 −0.739086 −0.369543 0.929214i \(-0.620486\pi\)
−0.369543 + 0.929214i \(0.620486\pi\)
\(194\) 0 0
\(195\) 34.9414 2.50221
\(196\) 0 0
\(197\) 25.7190 1.83240 0.916202 0.400716i \(-0.131239\pi\)
0.916202 + 0.400716i \(0.131239\pi\)
\(198\) 0 0
\(199\) −3.78676 −0.268436 −0.134218 0.990952i \(-0.542852\pi\)
−0.134218 + 0.990952i \(0.542852\pi\)
\(200\) 0 0
\(201\) −33.6520 −2.37363
\(202\) 0 0
\(203\) −25.1499 −1.76518
\(204\) 0 0
\(205\) −17.3270 −1.21017
\(206\) 0 0
\(207\) 13.5033 0.938544
\(208\) 0 0
\(209\) −35.6441 −2.46555
\(210\) 0 0
\(211\) 8.33696 0.573940 0.286970 0.957940i \(-0.407352\pi\)
0.286970 + 0.957940i \(0.407352\pi\)
\(212\) 0 0
\(213\) 10.4211 0.714045
\(214\) 0 0
\(215\) −17.2592 −1.17707
\(216\) 0 0
\(217\) 10.3141 0.700165
\(218\) 0 0
\(219\) −14.9297 −1.00886
\(220\) 0 0
\(221\) 17.9413 1.20686
\(222\) 0 0
\(223\) −9.94350 −0.665866 −0.332933 0.942950i \(-0.608038\pi\)
−0.332933 + 0.942950i \(0.608038\pi\)
\(224\) 0 0
\(225\) −1.71899 −0.114599
\(226\) 0 0
\(227\) 23.6972 1.57284 0.786418 0.617695i \(-0.211933\pi\)
0.786418 + 0.617695i \(0.211933\pi\)
\(228\) 0 0
\(229\) 4.54781 0.300528 0.150264 0.988646i \(-0.451988\pi\)
0.150264 + 0.988646i \(0.451988\pi\)
\(230\) 0 0
\(231\) −63.7783 −4.19630
\(232\) 0 0
\(233\) 10.0120 0.655909 0.327955 0.944694i \(-0.393641\pi\)
0.327955 + 0.944694i \(0.393641\pi\)
\(234\) 0 0
\(235\) −26.1325 −1.70469
\(236\) 0 0
\(237\) 15.8034 1.02654
\(238\) 0 0
\(239\) −25.3052 −1.63685 −0.818427 0.574610i \(-0.805154\pi\)
−0.818427 + 0.574610i \(0.805154\pi\)
\(240\) 0 0
\(241\) −16.7184 −1.07693 −0.538464 0.842649i \(-0.680995\pi\)
−0.538464 + 0.842649i \(0.680995\pi\)
\(242\) 0 0
\(243\) −18.2429 −1.17028
\(244\) 0 0
\(245\) 12.0381 0.769084
\(246\) 0 0
\(247\) 32.2463 2.05178
\(248\) 0 0
\(249\) 7.93216 0.502680
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) −19.4942 −1.22559
\(254\) 0 0
\(255\) 17.8763 1.11945
\(256\) 0 0
\(257\) 21.7416 1.35620 0.678101 0.734969i \(-0.262803\pi\)
0.678101 + 0.734969i \(0.262803\pi\)
\(258\) 0 0
\(259\) 20.6173 1.28110
\(260\) 0 0
\(261\) −32.1256 −1.98852
\(262\) 0 0
\(263\) 1.27198 0.0784339 0.0392169 0.999231i \(-0.487514\pi\)
0.0392169 + 0.999231i \(0.487514\pi\)
\(264\) 0 0
\(265\) −9.48284 −0.582526
\(266\) 0 0
\(267\) 47.4441 2.90353
\(268\) 0 0
\(269\) 6.77658 0.413175 0.206588 0.978428i \(-0.433764\pi\)
0.206588 + 0.978428i \(0.433764\pi\)
\(270\) 0 0
\(271\) −2.07518 −0.126058 −0.0630292 0.998012i \(-0.520076\pi\)
−0.0630292 + 0.998012i \(0.520076\pi\)
\(272\) 0 0
\(273\) 57.6985 3.49207
\(274\) 0 0
\(275\) 2.48164 0.149648
\(276\) 0 0
\(277\) 10.9588 0.658451 0.329226 0.944251i \(-0.393212\pi\)
0.329226 + 0.944251i \(0.393212\pi\)
\(278\) 0 0
\(279\) 13.1748 0.788757
\(280\) 0 0
\(281\) 2.68447 0.160142 0.0800711 0.996789i \(-0.474485\pi\)
0.0800711 + 0.996789i \(0.474485\pi\)
\(282\) 0 0
\(283\) −9.10824 −0.541428 −0.270714 0.962660i \(-0.587260\pi\)
−0.270714 + 0.962660i \(0.587260\pi\)
\(284\) 0 0
\(285\) 32.1293 1.90318
\(286\) 0 0
\(287\) −28.6119 −1.68891
\(288\) 0 0
\(289\) −7.82110 −0.460065
\(290\) 0 0
\(291\) 28.1255 1.64875
\(292\) 0 0
\(293\) −6.16669 −0.360262 −0.180131 0.983643i \(-0.557652\pi\)
−0.180131 + 0.983643i \(0.557652\pi\)
\(294\) 0 0
\(295\) −23.3141 −1.35740
\(296\) 0 0
\(297\) −27.5657 −1.59953
\(298\) 0 0
\(299\) 17.6359 1.01991
\(300\) 0 0
\(301\) −28.4999 −1.64271
\(302\) 0 0
\(303\) −41.8344 −2.40333
\(304\) 0 0
\(305\) 7.30387 0.418218
\(306\) 0 0
\(307\) 1.52823 0.0872205 0.0436102 0.999049i \(-0.486114\pi\)
0.0436102 + 0.999049i \(0.486114\pi\)
\(308\) 0 0
\(309\) −11.2650 −0.640842
\(310\) 0 0
\(311\) −1.12444 −0.0637610 −0.0318805 0.999492i \(-0.510150\pi\)
−0.0318805 + 0.999492i \(0.510150\pi\)
\(312\) 0 0
\(313\) 33.9524 1.91910 0.959550 0.281537i \(-0.0908441\pi\)
0.959550 + 0.281537i \(0.0908441\pi\)
\(314\) 0 0
\(315\) 34.5980 1.94937
\(316\) 0 0
\(317\) 11.9388 0.670551 0.335275 0.942120i \(-0.391171\pi\)
0.335275 + 0.942120i \(0.391171\pi\)
\(318\) 0 0
\(319\) 46.3785 2.59670
\(320\) 0 0
\(321\) 13.4993 0.753459
\(322\) 0 0
\(323\) 16.4974 0.917940
\(324\) 0 0
\(325\) −2.24507 −0.124534
\(326\) 0 0
\(327\) 26.1983 1.44877
\(328\) 0 0
\(329\) −43.1523 −2.37907
\(330\) 0 0
\(331\) 9.86021 0.541966 0.270983 0.962584i \(-0.412651\pi\)
0.270983 + 0.962584i \(0.412651\pi\)
\(332\) 0 0
\(333\) 26.3358 1.44320
\(334\) 0 0
\(335\) −26.3545 −1.43990
\(336\) 0 0
\(337\) 11.8956 0.647996 0.323998 0.946058i \(-0.394973\pi\)
0.323998 + 0.946058i \(0.394973\pi\)
\(338\) 0 0
\(339\) 21.3471 1.15941
\(340\) 0 0
\(341\) −19.0200 −1.02999
\(342\) 0 0
\(343\) −4.96924 −0.268314
\(344\) 0 0
\(345\) 17.5720 0.946042
\(346\) 0 0
\(347\) −11.6786 −0.626942 −0.313471 0.949598i \(-0.601492\pi\)
−0.313471 + 0.949598i \(0.601492\pi\)
\(348\) 0 0
\(349\) −24.0249 −1.28602 −0.643012 0.765856i \(-0.722315\pi\)
−0.643012 + 0.765856i \(0.722315\pi\)
\(350\) 0 0
\(351\) 24.9380 1.33109
\(352\) 0 0
\(353\) 1.37513 0.0731906 0.0365953 0.999330i \(-0.488349\pi\)
0.0365953 + 0.999330i \(0.488349\pi\)
\(354\) 0 0
\(355\) 8.16130 0.433157
\(356\) 0 0
\(357\) 29.5189 1.56231
\(358\) 0 0
\(359\) 32.1819 1.69850 0.849249 0.527993i \(-0.177055\pi\)
0.849249 + 0.527993i \(0.177055\pi\)
\(360\) 0 0
\(361\) 10.6511 0.560582
\(362\) 0 0
\(363\) 87.4191 4.58831
\(364\) 0 0
\(365\) −11.6922 −0.611996
\(366\) 0 0
\(367\) −8.98147 −0.468829 −0.234414 0.972137i \(-0.575317\pi\)
−0.234414 + 0.972137i \(0.575317\pi\)
\(368\) 0 0
\(369\) −36.5478 −1.90260
\(370\) 0 0
\(371\) −15.6589 −0.812972
\(372\) 0 0
\(373\) −26.9056 −1.39312 −0.696559 0.717499i \(-0.745287\pi\)
−0.696559 + 0.717499i \(0.745287\pi\)
\(374\) 0 0
\(375\) −31.7389 −1.63899
\(376\) 0 0
\(377\) −41.9574 −2.16092
\(378\) 0 0
\(379\) −10.2662 −0.527340 −0.263670 0.964613i \(-0.584933\pi\)
−0.263670 + 0.964613i \(0.584933\pi\)
\(380\) 0 0
\(381\) −39.2056 −2.00856
\(382\) 0 0
\(383\) 25.9393 1.32544 0.662718 0.748869i \(-0.269403\pi\)
0.662718 + 0.748869i \(0.269403\pi\)
\(384\) 0 0
\(385\) −49.9478 −2.54558
\(386\) 0 0
\(387\) −36.4048 −1.85056
\(388\) 0 0
\(389\) 16.6478 0.844079 0.422039 0.906577i \(-0.361314\pi\)
0.422039 + 0.906577i \(0.361314\pi\)
\(390\) 0 0
\(391\) 9.02265 0.456295
\(392\) 0 0
\(393\) −19.3269 −0.974914
\(394\) 0 0
\(395\) 12.3764 0.622724
\(396\) 0 0
\(397\) −22.9366 −1.15116 −0.575578 0.817747i \(-0.695223\pi\)
−0.575578 + 0.817747i \(0.695223\pi\)
\(398\) 0 0
\(399\) 53.0549 2.65607
\(400\) 0 0
\(401\) 14.4812 0.723154 0.361577 0.932342i \(-0.382238\pi\)
0.361577 + 0.932342i \(0.382238\pi\)
\(402\) 0 0
\(403\) 17.2069 0.857138
\(404\) 0 0
\(405\) −4.39296 −0.218288
\(406\) 0 0
\(407\) −38.0201 −1.88459
\(408\) 0 0
\(409\) −16.3102 −0.806486 −0.403243 0.915093i \(-0.632117\pi\)
−0.403243 + 0.915093i \(0.632117\pi\)
\(410\) 0 0
\(411\) −1.23489 −0.0609126
\(412\) 0 0
\(413\) −38.4984 −1.89438
\(414\) 0 0
\(415\) 6.21206 0.304938
\(416\) 0 0
\(417\) 10.5716 0.517693
\(418\) 0 0
\(419\) 2.69777 0.131795 0.0658973 0.997826i \(-0.479009\pi\)
0.0658973 + 0.997826i \(0.479009\pi\)
\(420\) 0 0
\(421\) 13.6445 0.664991 0.332495 0.943105i \(-0.392109\pi\)
0.332495 + 0.943105i \(0.392109\pi\)
\(422\) 0 0
\(423\) −55.1212 −2.68009
\(424\) 0 0
\(425\) −1.14859 −0.0557150
\(426\) 0 0
\(427\) 12.0608 0.583664
\(428\) 0 0
\(429\) −106.401 −5.13708
\(430\) 0 0
\(431\) 0.166970 0.00804268 0.00402134 0.999992i \(-0.498720\pi\)
0.00402134 + 0.999992i \(0.498720\pi\)
\(432\) 0 0
\(433\) 12.0726 0.580171 0.290085 0.957001i \(-0.406316\pi\)
0.290085 + 0.957001i \(0.406316\pi\)
\(434\) 0 0
\(435\) −41.8053 −2.00441
\(436\) 0 0
\(437\) 16.2166 0.775744
\(438\) 0 0
\(439\) −7.96878 −0.380329 −0.190165 0.981752i \(-0.560902\pi\)
−0.190165 + 0.981752i \(0.560902\pi\)
\(440\) 0 0
\(441\) 25.3919 1.20914
\(442\) 0 0
\(443\) −12.3635 −0.587407 −0.293704 0.955897i \(-0.594888\pi\)
−0.293704 + 0.955897i \(0.594888\pi\)
\(444\) 0 0
\(445\) 37.1557 1.76135
\(446\) 0 0
\(447\) 23.0819 1.09174
\(448\) 0 0
\(449\) 3.54161 0.167139 0.0835694 0.996502i \(-0.473368\pi\)
0.0835694 + 0.996502i \(0.473368\pi\)
\(450\) 0 0
\(451\) 52.7628 2.48450
\(452\) 0 0
\(453\) −9.89800 −0.465049
\(454\) 0 0
\(455\) 45.1865 2.11837
\(456\) 0 0
\(457\) −18.9259 −0.885314 −0.442657 0.896691i \(-0.645964\pi\)
−0.442657 + 0.896691i \(0.645964\pi\)
\(458\) 0 0
\(459\) 12.7584 0.595513
\(460\) 0 0
\(461\) 17.2051 0.801320 0.400660 0.916227i \(-0.368781\pi\)
0.400660 + 0.916227i \(0.368781\pi\)
\(462\) 0 0
\(463\) −16.2631 −0.755809 −0.377905 0.925844i \(-0.623355\pi\)
−0.377905 + 0.925844i \(0.623355\pi\)
\(464\) 0 0
\(465\) 17.1445 0.795058
\(466\) 0 0
\(467\) 6.23047 0.288312 0.144156 0.989555i \(-0.453953\pi\)
0.144156 + 0.989555i \(0.453953\pi\)
\(468\) 0 0
\(469\) −43.5190 −2.00952
\(470\) 0 0
\(471\) 60.9652 2.80913
\(472\) 0 0
\(473\) 52.5563 2.41654
\(474\) 0 0
\(475\) −2.06439 −0.0947206
\(476\) 0 0
\(477\) −20.0022 −0.915837
\(478\) 0 0
\(479\) −31.2103 −1.42603 −0.713017 0.701147i \(-0.752672\pi\)
−0.713017 + 0.701147i \(0.752672\pi\)
\(480\) 0 0
\(481\) 34.3958 1.56831
\(482\) 0 0
\(483\) 29.0164 1.32029
\(484\) 0 0
\(485\) 22.0264 1.00017
\(486\) 0 0
\(487\) −14.6600 −0.664309 −0.332155 0.943225i \(-0.607776\pi\)
−0.332155 + 0.943225i \(0.607776\pi\)
\(488\) 0 0
\(489\) 33.3191 1.50674
\(490\) 0 0
\(491\) −36.8141 −1.66140 −0.830699 0.556722i \(-0.812059\pi\)
−0.830699 + 0.556722i \(0.812059\pi\)
\(492\) 0 0
\(493\) −21.4657 −0.966767
\(494\) 0 0
\(495\) −63.8015 −2.86767
\(496\) 0 0
\(497\) 13.4767 0.604512
\(498\) 0 0
\(499\) 8.75326 0.391850 0.195925 0.980619i \(-0.437229\pi\)
0.195925 + 0.980619i \(0.437229\pi\)
\(500\) 0 0
\(501\) 3.18484 0.142288
\(502\) 0 0
\(503\) 28.1327 1.25437 0.627187 0.778869i \(-0.284206\pi\)
0.627187 + 0.778869i \(0.284206\pi\)
\(504\) 0 0
\(505\) −32.7626 −1.45791
\(506\) 0 0
\(507\) 60.5750 2.69023
\(508\) 0 0
\(509\) −22.3215 −0.989385 −0.494692 0.869068i \(-0.664719\pi\)
−0.494692 + 0.869068i \(0.664719\pi\)
\(510\) 0 0
\(511\) −19.3072 −0.854100
\(512\) 0 0
\(513\) 22.9310 1.01243
\(514\) 0 0
\(515\) −8.82214 −0.388750
\(516\) 0 0
\(517\) 79.5765 3.49977
\(518\) 0 0
\(519\) −68.3064 −2.99832
\(520\) 0 0
\(521\) −29.1435 −1.27680 −0.638399 0.769705i \(-0.720403\pi\)
−0.638399 + 0.769705i \(0.720403\pi\)
\(522\) 0 0
\(523\) 23.0289 1.00698 0.503491 0.864000i \(-0.332049\pi\)
0.503491 + 0.864000i \(0.332049\pi\)
\(524\) 0 0
\(525\) −3.69383 −0.161212
\(526\) 0 0
\(527\) 8.80317 0.383472
\(528\) 0 0
\(529\) −14.1309 −0.614389
\(530\) 0 0
\(531\) −49.1764 −2.13407
\(532\) 0 0
\(533\) −47.7331 −2.06755
\(534\) 0 0
\(535\) 10.5720 0.457066
\(536\) 0 0
\(537\) −50.0883 −2.16147
\(538\) 0 0
\(539\) −36.6574 −1.57894
\(540\) 0 0
\(541\) −31.0582 −1.33530 −0.667649 0.744476i \(-0.732699\pi\)
−0.667649 + 0.744476i \(0.732699\pi\)
\(542\) 0 0
\(543\) −35.8706 −1.53936
\(544\) 0 0
\(545\) 20.5171 0.878858
\(546\) 0 0
\(547\) 0.154505 0.00660614 0.00330307 0.999995i \(-0.498949\pi\)
0.00330307 + 0.999995i \(0.498949\pi\)
\(548\) 0 0
\(549\) 15.4061 0.657515
\(550\) 0 0
\(551\) −38.5807 −1.64359
\(552\) 0 0
\(553\) 20.4371 0.869072
\(554\) 0 0
\(555\) 34.2710 1.45472
\(556\) 0 0
\(557\) 39.0419 1.65426 0.827129 0.562012i \(-0.189973\pi\)
0.827129 + 0.562012i \(0.189973\pi\)
\(558\) 0 0
\(559\) −47.5463 −2.01099
\(560\) 0 0
\(561\) −54.4354 −2.29826
\(562\) 0 0
\(563\) 31.9413 1.34616 0.673082 0.739567i \(-0.264970\pi\)
0.673082 + 0.739567i \(0.264970\pi\)
\(564\) 0 0
\(565\) 16.7179 0.703327
\(566\) 0 0
\(567\) −7.25407 −0.304642
\(568\) 0 0
\(569\) 0.966749 0.0405282 0.0202641 0.999795i \(-0.493549\pi\)
0.0202641 + 0.999795i \(0.493549\pi\)
\(570\) 0 0
\(571\) −3.10421 −0.129907 −0.0649535 0.997888i \(-0.520690\pi\)
−0.0649535 + 0.997888i \(0.520690\pi\)
\(572\) 0 0
\(573\) 15.2004 0.635007
\(574\) 0 0
\(575\) −1.12904 −0.0470843
\(576\) 0 0
\(577\) −43.6469 −1.81705 −0.908523 0.417835i \(-0.862789\pi\)
−0.908523 + 0.417835i \(0.862789\pi\)
\(578\) 0 0
\(579\) −28.1833 −1.17126
\(580\) 0 0
\(581\) 10.2579 0.425571
\(582\) 0 0
\(583\) 28.8764 1.19594
\(584\) 0 0
\(585\) 57.7196 2.38641
\(586\) 0 0
\(587\) 37.7925 1.55986 0.779931 0.625865i \(-0.215254\pi\)
0.779931 + 0.625865i \(0.215254\pi\)
\(588\) 0 0
\(589\) 15.8221 0.651938
\(590\) 0 0
\(591\) 70.5949 2.90389
\(592\) 0 0
\(593\) −16.4832 −0.676882 −0.338441 0.940988i \(-0.609900\pi\)
−0.338441 + 0.940988i \(0.609900\pi\)
\(594\) 0 0
\(595\) 23.1177 0.947733
\(596\) 0 0
\(597\) −10.3941 −0.425401
\(598\) 0 0
\(599\) 8.27806 0.338232 0.169116 0.985596i \(-0.445909\pi\)
0.169116 + 0.985596i \(0.445909\pi\)
\(600\) 0 0
\(601\) 24.0477 0.980928 0.490464 0.871461i \(-0.336827\pi\)
0.490464 + 0.871461i \(0.336827\pi\)
\(602\) 0 0
\(603\) −55.5896 −2.26378
\(604\) 0 0
\(605\) 68.4621 2.78338
\(606\) 0 0
\(607\) 12.1529 0.493271 0.246635 0.969108i \(-0.420675\pi\)
0.246635 + 0.969108i \(0.420675\pi\)
\(608\) 0 0
\(609\) −69.0328 −2.79735
\(610\) 0 0
\(611\) −71.9908 −2.91244
\(612\) 0 0
\(613\) −12.4177 −0.501547 −0.250774 0.968046i \(-0.580685\pi\)
−0.250774 + 0.968046i \(0.580685\pi\)
\(614\) 0 0
\(615\) −47.5600 −1.91780
\(616\) 0 0
\(617\) 44.3680 1.78619 0.893093 0.449871i \(-0.148530\pi\)
0.893093 + 0.449871i \(0.148530\pi\)
\(618\) 0 0
\(619\) −39.4107 −1.58405 −0.792025 0.610489i \(-0.790973\pi\)
−0.792025 + 0.610489i \(0.790973\pi\)
\(620\) 0 0
\(621\) 12.5413 0.503263
\(622\) 0 0
\(623\) 61.3550 2.45813
\(624\) 0 0
\(625\) −22.9607 −0.918428
\(626\) 0 0
\(627\) −97.8377 −3.90726
\(628\) 0 0
\(629\) 17.5971 0.701643
\(630\) 0 0
\(631\) 2.28040 0.0907815 0.0453907 0.998969i \(-0.485547\pi\)
0.0453907 + 0.998969i \(0.485547\pi\)
\(632\) 0 0
\(633\) 22.8837 0.909546
\(634\) 0 0
\(635\) −30.7038 −1.21844
\(636\) 0 0
\(637\) 33.1630 1.31396
\(638\) 0 0
\(639\) 17.2146 0.681001
\(640\) 0 0
\(641\) −17.2719 −0.682201 −0.341100 0.940027i \(-0.610800\pi\)
−0.341100 + 0.940027i \(0.610800\pi\)
\(642\) 0 0
\(643\) −26.1244 −1.03025 −0.515123 0.857116i \(-0.672254\pi\)
−0.515123 + 0.857116i \(0.672254\pi\)
\(644\) 0 0
\(645\) −47.3738 −1.86534
\(646\) 0 0
\(647\) −12.5710 −0.494216 −0.247108 0.968988i \(-0.579480\pi\)
−0.247108 + 0.968988i \(0.579480\pi\)
\(648\) 0 0
\(649\) 70.9942 2.78677
\(650\) 0 0
\(651\) 28.3106 1.10958
\(652\) 0 0
\(653\) 28.5660 1.11787 0.558936 0.829211i \(-0.311210\pi\)
0.558936 + 0.829211i \(0.311210\pi\)
\(654\) 0 0
\(655\) −15.1358 −0.591406
\(656\) 0 0
\(657\) −24.6623 −0.962168
\(658\) 0 0
\(659\) 0.868932 0.0338488 0.0169244 0.999857i \(-0.494613\pi\)
0.0169244 + 0.999857i \(0.494613\pi\)
\(660\) 0 0
\(661\) −24.5283 −0.954041 −0.477021 0.878892i \(-0.658283\pi\)
−0.477021 + 0.878892i \(0.658283\pi\)
\(662\) 0 0
\(663\) 49.2463 1.91257
\(664\) 0 0
\(665\) 41.5498 1.61123
\(666\) 0 0
\(667\) −21.1003 −0.817007
\(668\) 0 0
\(669\) −27.2934 −1.05522
\(670\) 0 0
\(671\) −22.2412 −0.858611
\(672\) 0 0
\(673\) 30.0673 1.15901 0.579504 0.814969i \(-0.303246\pi\)
0.579504 + 0.814969i \(0.303246\pi\)
\(674\) 0 0
\(675\) −1.59652 −0.0614500
\(676\) 0 0
\(677\) 34.7007 1.33366 0.666828 0.745212i \(-0.267652\pi\)
0.666828 + 0.745212i \(0.267652\pi\)
\(678\) 0 0
\(679\) 36.3721 1.39583
\(680\) 0 0
\(681\) 65.0452 2.49254
\(682\) 0 0
\(683\) 4.97088 0.190205 0.0951026 0.995467i \(-0.469682\pi\)
0.0951026 + 0.995467i \(0.469682\pi\)
\(684\) 0 0
\(685\) −0.967101 −0.0369510
\(686\) 0 0
\(687\) 12.4831 0.476258
\(688\) 0 0
\(689\) −26.1237 −0.995235
\(690\) 0 0
\(691\) 15.9682 0.607460 0.303730 0.952758i \(-0.401768\pi\)
0.303730 + 0.952758i \(0.401768\pi\)
\(692\) 0 0
\(693\) −105.355 −4.00211
\(694\) 0 0
\(695\) 8.27912 0.314045
\(696\) 0 0
\(697\) −24.4206 −0.924995
\(698\) 0 0
\(699\) 27.4815 1.03945
\(700\) 0 0
\(701\) −1.29023 −0.0487311 −0.0243656 0.999703i \(-0.507757\pi\)
−0.0243656 + 0.999703i \(0.507757\pi\)
\(702\) 0 0
\(703\) 31.6276 1.19286
\(704\) 0 0
\(705\) −71.7297 −2.70150
\(706\) 0 0
\(707\) −54.1006 −2.03466
\(708\) 0 0
\(709\) −35.7870 −1.34401 −0.672004 0.740547i \(-0.734566\pi\)
−0.672004 + 0.740547i \(0.734566\pi\)
\(710\) 0 0
\(711\) 26.1056 0.979035
\(712\) 0 0
\(713\) 8.65332 0.324069
\(714\) 0 0
\(715\) −83.3276 −3.11628
\(716\) 0 0
\(717\) −69.4589 −2.59399
\(718\) 0 0
\(719\) 15.0809 0.562424 0.281212 0.959646i \(-0.409264\pi\)
0.281212 + 0.959646i \(0.409264\pi\)
\(720\) 0 0
\(721\) −14.5679 −0.542538
\(722\) 0 0
\(723\) −45.8895 −1.70665
\(724\) 0 0
\(725\) 2.68609 0.0997590
\(726\) 0 0
\(727\) 4.95659 0.183830 0.0919150 0.995767i \(-0.470701\pi\)
0.0919150 + 0.995767i \(0.470701\pi\)
\(728\) 0 0
\(729\) −43.9431 −1.62752
\(730\) 0 0
\(731\) −24.3250 −0.899692
\(732\) 0 0
\(733\) 9.73805 0.359683 0.179842 0.983696i \(-0.442441\pi\)
0.179842 + 0.983696i \(0.442441\pi\)
\(734\) 0 0
\(735\) 33.0427 1.21880
\(736\) 0 0
\(737\) 80.2527 2.95615
\(738\) 0 0
\(739\) −4.94296 −0.181830 −0.0909149 0.995859i \(-0.528979\pi\)
−0.0909149 + 0.995859i \(0.528979\pi\)
\(740\) 0 0
\(741\) 88.5112 3.25154
\(742\) 0 0
\(743\) 29.6999 1.08958 0.544792 0.838571i \(-0.316609\pi\)
0.544792 + 0.838571i \(0.316609\pi\)
\(744\) 0 0
\(745\) 18.0765 0.662273
\(746\) 0 0
\(747\) 13.1031 0.479418
\(748\) 0 0
\(749\) 17.4574 0.637880
\(750\) 0 0
\(751\) 23.2689 0.849095 0.424548 0.905406i \(-0.360433\pi\)
0.424548 + 0.905406i \(0.360433\pi\)
\(752\) 0 0
\(753\) 2.74485 0.100028
\(754\) 0 0
\(755\) −7.75160 −0.282110
\(756\) 0 0
\(757\) −11.0623 −0.402065 −0.201032 0.979585i \(-0.564430\pi\)
−0.201032 + 0.979585i \(0.564430\pi\)
\(758\) 0 0
\(759\) −53.5087 −1.94224
\(760\) 0 0
\(761\) 51.7916 1.87744 0.938721 0.344678i \(-0.112012\pi\)
0.938721 + 0.344678i \(0.112012\pi\)
\(762\) 0 0
\(763\) 33.8798 1.22653
\(764\) 0 0
\(765\) 29.5297 1.06765
\(766\) 0 0
\(767\) −64.2266 −2.31909
\(768\) 0 0
\(769\) 1.44430 0.0520828 0.0260414 0.999661i \(-0.491710\pi\)
0.0260414 + 0.999661i \(0.491710\pi\)
\(770\) 0 0
\(771\) 59.6773 2.14923
\(772\) 0 0
\(773\) −9.47720 −0.340871 −0.170436 0.985369i \(-0.554517\pi\)
−0.170436 + 0.985369i \(0.554517\pi\)
\(774\) 0 0
\(775\) −1.10158 −0.0395698
\(776\) 0 0
\(777\) 56.5915 2.03021
\(778\) 0 0
\(779\) −43.8915 −1.57258
\(780\) 0 0
\(781\) −24.8522 −0.889280
\(782\) 0 0
\(783\) −29.8368 −1.06628
\(784\) 0 0
\(785\) 47.7448 1.70408
\(786\) 0 0
\(787\) 33.7921 1.20456 0.602280 0.798285i \(-0.294259\pi\)
0.602280 + 0.798285i \(0.294259\pi\)
\(788\) 0 0
\(789\) 3.49141 0.124297
\(790\) 0 0
\(791\) 27.6062 0.981562
\(792\) 0 0
\(793\) 20.1210 0.714518
\(794\) 0 0
\(795\) −26.0290 −0.923153
\(796\) 0 0
\(797\) −29.8090 −1.05589 −0.527944 0.849279i \(-0.677037\pi\)
−0.527944 + 0.849279i \(0.677037\pi\)
\(798\) 0 0
\(799\) −36.8310 −1.30299
\(800\) 0 0
\(801\) 78.3726 2.76916
\(802\) 0 0
\(803\) 35.6041 1.25644
\(804\) 0 0
\(805\) 22.7242 0.800922
\(806\) 0 0
\(807\) 18.6007 0.654776
\(808\) 0 0
\(809\) −14.7449 −0.518404 −0.259202 0.965823i \(-0.583460\pi\)
−0.259202 + 0.965823i \(0.583460\pi\)
\(810\) 0 0
\(811\) 16.1003 0.565359 0.282679 0.959214i \(-0.408777\pi\)
0.282679 + 0.959214i \(0.408777\pi\)
\(812\) 0 0
\(813\) −5.69606 −0.199770
\(814\) 0 0
\(815\) 26.0938 0.914025
\(816\) 0 0
\(817\) −43.7197 −1.52956
\(818\) 0 0
\(819\) 95.3119 3.33047
\(820\) 0 0
\(821\) −7.80936 −0.272549 −0.136274 0.990671i \(-0.543513\pi\)
−0.136274 + 0.990671i \(0.543513\pi\)
\(822\) 0 0
\(823\) 14.5503 0.507193 0.253597 0.967310i \(-0.418386\pi\)
0.253597 + 0.967310i \(0.418386\pi\)
\(824\) 0 0
\(825\) 6.81173 0.237154
\(826\) 0 0
\(827\) −30.9267 −1.07543 −0.537714 0.843127i \(-0.680712\pi\)
−0.537714 + 0.843127i \(0.680712\pi\)
\(828\) 0 0
\(829\) −22.6097 −0.785268 −0.392634 0.919695i \(-0.628436\pi\)
−0.392634 + 0.919695i \(0.628436\pi\)
\(830\) 0 0
\(831\) 30.0803 1.04347
\(832\) 0 0
\(833\) 16.9664 0.587851
\(834\) 0 0
\(835\) 2.49420 0.0863154
\(836\) 0 0
\(837\) 12.2362 0.422945
\(838\) 0 0
\(839\) 1.27665 0.0440747 0.0220374 0.999757i \(-0.492985\pi\)
0.0220374 + 0.999757i \(0.492985\pi\)
\(840\) 0 0
\(841\) 21.1995 0.731018
\(842\) 0 0
\(843\) 7.36847 0.253784
\(844\) 0 0
\(845\) 47.4392 1.63196
\(846\) 0 0
\(847\) 113.051 3.88448
\(848\) 0 0
\(849\) −25.0008 −0.858024
\(850\) 0 0
\(851\) 17.2976 0.592953
\(852\) 0 0
\(853\) −1.86031 −0.0636959 −0.0318480 0.999493i \(-0.510139\pi\)
−0.0318480 + 0.999493i \(0.510139\pi\)
\(854\) 0 0
\(855\) 53.0743 1.81510
\(856\) 0 0
\(857\) −6.76520 −0.231095 −0.115547 0.993302i \(-0.536862\pi\)
−0.115547 + 0.993302i \(0.536862\pi\)
\(858\) 0 0
\(859\) 29.5523 1.00831 0.504155 0.863613i \(-0.331804\pi\)
0.504155 + 0.863613i \(0.331804\pi\)
\(860\) 0 0
\(861\) −78.5354 −2.67648
\(862\) 0 0
\(863\) 56.5475 1.92490 0.962450 0.271458i \(-0.0875059\pi\)
0.962450 + 0.271458i \(0.0875059\pi\)
\(864\) 0 0
\(865\) −53.4940 −1.81885
\(866\) 0 0
\(867\) −21.4677 −0.729083
\(868\) 0 0
\(869\) −37.6877 −1.27847
\(870\) 0 0
\(871\) −72.6025 −2.46004
\(872\) 0 0
\(873\) 46.4604 1.57245
\(874\) 0 0
\(875\) −41.0450 −1.38757
\(876\) 0 0
\(877\) 3.54396 0.119671 0.0598355 0.998208i \(-0.480942\pi\)
0.0598355 + 0.998208i \(0.480942\pi\)
\(878\) 0 0
\(879\) −16.9266 −0.570922
\(880\) 0 0
\(881\) −2.30576 −0.0776830 −0.0388415 0.999245i \(-0.512367\pi\)
−0.0388415 + 0.999245i \(0.512367\pi\)
\(882\) 0 0
\(883\) −37.0916 −1.24823 −0.624116 0.781332i \(-0.714541\pi\)
−0.624116 + 0.781332i \(0.714541\pi\)
\(884\) 0 0
\(885\) −63.9937 −2.15112
\(886\) 0 0
\(887\) 28.5188 0.957567 0.478784 0.877933i \(-0.341078\pi\)
0.478784 + 0.877933i \(0.341078\pi\)
\(888\) 0 0
\(889\) −50.7009 −1.70046
\(890\) 0 0
\(891\) 13.3771 0.448150
\(892\) 0 0
\(893\) −66.1969 −2.21520
\(894\) 0 0
\(895\) −39.2266 −1.31120
\(896\) 0 0
\(897\) 48.4079 1.61629
\(898\) 0 0
\(899\) −20.5870 −0.686616
\(900\) 0 0
\(901\) −13.3651 −0.445255
\(902\) 0 0
\(903\) −78.2281 −2.60327
\(904\) 0 0
\(905\) −28.0920 −0.933810
\(906\) 0 0
\(907\) −39.7450 −1.31971 −0.659855 0.751393i \(-0.729382\pi\)
−0.659855 + 0.751393i \(0.729382\pi\)
\(908\) 0 0
\(909\) −69.1061 −2.29210
\(910\) 0 0
\(911\) −36.7963 −1.21912 −0.609558 0.792742i \(-0.708653\pi\)
−0.609558 + 0.792742i \(0.708653\pi\)
\(912\) 0 0
\(913\) −18.9165 −0.626044
\(914\) 0 0
\(915\) 20.0480 0.662767
\(916\) 0 0
\(917\) −24.9937 −0.825365
\(918\) 0 0
\(919\) 7.53441 0.248537 0.124269 0.992249i \(-0.460342\pi\)
0.124269 + 0.992249i \(0.460342\pi\)
\(920\) 0 0
\(921\) 4.19475 0.138222
\(922\) 0 0
\(923\) 22.4831 0.740040
\(924\) 0 0
\(925\) −2.20200 −0.0724013
\(926\) 0 0
\(927\) −18.6086 −0.611185
\(928\) 0 0
\(929\) 12.5221 0.410838 0.205419 0.978674i \(-0.434144\pi\)
0.205419 + 0.978674i \(0.434144\pi\)
\(930\) 0 0
\(931\) 30.4940 0.999400
\(932\) 0 0
\(933\) −3.08641 −0.101045
\(934\) 0 0
\(935\) −42.6310 −1.39418
\(936\) 0 0
\(937\) 40.8994 1.33613 0.668063 0.744105i \(-0.267124\pi\)
0.668063 + 0.744105i \(0.267124\pi\)
\(938\) 0 0
\(939\) 93.1942 3.04128
\(940\) 0 0
\(941\) 9.09750 0.296570 0.148285 0.988945i \(-0.452625\pi\)
0.148285 + 0.988945i \(0.452625\pi\)
\(942\) 0 0
\(943\) −24.0048 −0.781705
\(944\) 0 0
\(945\) 32.1330 1.04529
\(946\) 0 0
\(947\) −22.4429 −0.729295 −0.364648 0.931146i \(-0.618811\pi\)
−0.364648 + 0.931146i \(0.618811\pi\)
\(948\) 0 0
\(949\) −32.2101 −1.04558
\(950\) 0 0
\(951\) 32.7703 1.06265
\(952\) 0 0
\(953\) 28.8722 0.935263 0.467631 0.883924i \(-0.345107\pi\)
0.467631 + 0.883924i \(0.345107\pi\)
\(954\) 0 0
\(955\) 11.9042 0.385210
\(956\) 0 0
\(957\) 127.302 4.11510
\(958\) 0 0
\(959\) −1.59697 −0.0515688
\(960\) 0 0
\(961\) −22.5572 −0.727651
\(962\) 0 0
\(963\) 22.2995 0.718591
\(964\) 0 0
\(965\) −22.0717 −0.710513
\(966\) 0 0
\(967\) −10.8350 −0.348430 −0.174215 0.984708i \(-0.555739\pi\)
−0.174215 + 0.984708i \(0.555739\pi\)
\(968\) 0 0
\(969\) 45.2829 1.45470
\(970\) 0 0
\(971\) 30.1539 0.967686 0.483843 0.875155i \(-0.339241\pi\)
0.483843 + 0.875155i \(0.339241\pi\)
\(972\) 0 0
\(973\) 13.6712 0.438280
\(974\) 0 0
\(975\) −6.16239 −0.197354
\(976\) 0 0
\(977\) −18.4510 −0.590301 −0.295150 0.955451i \(-0.595370\pi\)
−0.295150 + 0.955451i \(0.595370\pi\)
\(978\) 0 0
\(979\) −113.144 −3.61609
\(980\) 0 0
\(981\) 43.2768 1.38172
\(982\) 0 0
\(983\) 12.1888 0.388763 0.194382 0.980926i \(-0.437730\pi\)
0.194382 + 0.980926i \(0.437730\pi\)
\(984\) 0 0
\(985\) 55.2862 1.76157
\(986\) 0 0
\(987\) −118.447 −3.77020
\(988\) 0 0
\(989\) −23.9109 −0.760323
\(990\) 0 0
\(991\) 4.65661 0.147922 0.0739610 0.997261i \(-0.476436\pi\)
0.0739610 + 0.997261i \(0.476436\pi\)
\(992\) 0 0
\(993\) 27.0648 0.858876
\(994\) 0 0
\(995\) −8.14010 −0.258059
\(996\) 0 0
\(997\) −57.5641 −1.82307 −0.911536 0.411220i \(-0.865103\pi\)
−0.911536 + 0.411220i \(0.865103\pi\)
\(998\) 0 0
\(999\) 24.4595 0.773866
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.1.20 23
4.3 odd 2 2008.2.a.d.1.4 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.4 23 4.3 odd 2
4016.2.a.m.1.20 23 1.1 even 1 trivial