Properties

Label 6008.2.a.b.1.29
Level 6008
Weight 2
Character 6008.1
Self dual yes
Analytic conductor 47.974
Analytic rank 1
Dimension 44
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(1\)
Dimension: \(44\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.29
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.663224 q^{3} -1.07871 q^{5} +2.50091 q^{7} -2.56013 q^{9} +O(q^{10})\) \(q+0.663224 q^{3} -1.07871 q^{5} +2.50091 q^{7} -2.56013 q^{9} +2.33005 q^{11} +3.30037 q^{13} -0.715424 q^{15} -4.49872 q^{17} -1.81768 q^{19} +1.65866 q^{21} +1.64341 q^{23} -3.83639 q^{25} -3.68762 q^{27} -7.87508 q^{29} -4.59701 q^{31} +1.54534 q^{33} -2.69775 q^{35} -5.73720 q^{37} +2.18889 q^{39} +10.3035 q^{41} +9.47732 q^{43} +2.76163 q^{45} +10.0950 q^{47} -0.745444 q^{49} -2.98366 q^{51} -11.8738 q^{53} -2.51344 q^{55} -1.20553 q^{57} -13.4477 q^{59} -6.38387 q^{61} -6.40267 q^{63} -3.56013 q^{65} +4.16459 q^{67} +1.08995 q^{69} -2.34141 q^{71} -13.9134 q^{73} -2.54439 q^{75} +5.82724 q^{77} -15.9669 q^{79} +5.23469 q^{81} +13.0428 q^{83} +4.85280 q^{85} -5.22295 q^{87} -13.1072 q^{89} +8.25394 q^{91} -3.04885 q^{93} +1.96075 q^{95} -12.3368 q^{97} -5.96523 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 0.663224 0.382913 0.191456 0.981501i \(-0.438679\pi\)
0.191456 + 0.981501i \(0.438679\pi\)
\(4\) 0 0
\(5\) −1.07871 −0.482412 −0.241206 0.970474i \(-0.577543\pi\)
−0.241206 + 0.970474i \(0.577543\pi\)
\(6\) 0 0
\(7\) 2.50091 0.945255 0.472628 0.881262i \(-0.343306\pi\)
0.472628 + 0.881262i \(0.343306\pi\)
\(8\) 0 0
\(9\) −2.56013 −0.853378
\(10\) 0 0
\(11\) 2.33005 0.702536 0.351268 0.936275i \(-0.385751\pi\)
0.351268 + 0.936275i \(0.385751\pi\)
\(12\) 0 0
\(13\) 3.30037 0.915358 0.457679 0.889117i \(-0.348681\pi\)
0.457679 + 0.889117i \(0.348681\pi\)
\(14\) 0 0
\(15\) −0.715424 −0.184722
\(16\) 0 0
\(17\) −4.49872 −1.09110 −0.545550 0.838078i \(-0.683679\pi\)
−0.545550 + 0.838078i \(0.683679\pi\)
\(18\) 0 0
\(19\) −1.81768 −0.417005 −0.208503 0.978022i \(-0.566859\pi\)
−0.208503 + 0.978022i \(0.566859\pi\)
\(20\) 0 0
\(21\) 1.65866 0.361950
\(22\) 0 0
\(23\) 1.64341 0.342676 0.171338 0.985212i \(-0.445191\pi\)
0.171338 + 0.985212i \(0.445191\pi\)
\(24\) 0 0
\(25\) −3.83639 −0.767279
\(26\) 0 0
\(27\) −3.68762 −0.709682
\(28\) 0 0
\(29\) −7.87508 −1.46237 −0.731183 0.682181i \(-0.761031\pi\)
−0.731183 + 0.682181i \(0.761031\pi\)
\(30\) 0 0
\(31\) −4.59701 −0.825648 −0.412824 0.910811i \(-0.635458\pi\)
−0.412824 + 0.910811i \(0.635458\pi\)
\(32\) 0 0
\(33\) 1.54534 0.269010
\(34\) 0 0
\(35\) −2.69775 −0.456003
\(36\) 0 0
\(37\) −5.73720 −0.943190 −0.471595 0.881815i \(-0.656322\pi\)
−0.471595 + 0.881815i \(0.656322\pi\)
\(38\) 0 0
\(39\) 2.18889 0.350502
\(40\) 0 0
\(41\) 10.3035 1.60913 0.804566 0.593863i \(-0.202398\pi\)
0.804566 + 0.593863i \(0.202398\pi\)
\(42\) 0 0
\(43\) 9.47732 1.44528 0.722639 0.691225i \(-0.242929\pi\)
0.722639 + 0.691225i \(0.242929\pi\)
\(44\) 0 0
\(45\) 2.76163 0.411680
\(46\) 0 0
\(47\) 10.0950 1.47251 0.736256 0.676704i \(-0.236592\pi\)
0.736256 + 0.676704i \(0.236592\pi\)
\(48\) 0 0
\(49\) −0.745444 −0.106492
\(50\) 0 0
\(51\) −2.98366 −0.417796
\(52\) 0 0
\(53\) −11.8738 −1.63099 −0.815496 0.578762i \(-0.803536\pi\)
−0.815496 + 0.578762i \(0.803536\pi\)
\(54\) 0 0
\(55\) −2.51344 −0.338912
\(56\) 0 0
\(57\) −1.20553 −0.159677
\(58\) 0 0
\(59\) −13.4477 −1.75075 −0.875373 0.483449i \(-0.839384\pi\)
−0.875373 + 0.483449i \(0.839384\pi\)
\(60\) 0 0
\(61\) −6.38387 −0.817371 −0.408685 0.912675i \(-0.634013\pi\)
−0.408685 + 0.912675i \(0.634013\pi\)
\(62\) 0 0
\(63\) −6.40267 −0.806660
\(64\) 0 0
\(65\) −3.56013 −0.441580
\(66\) 0 0
\(67\) 4.16459 0.508785 0.254393 0.967101i \(-0.418124\pi\)
0.254393 + 0.967101i \(0.418124\pi\)
\(68\) 0 0
\(69\) 1.08995 0.131215
\(70\) 0 0
\(71\) −2.34141 −0.277874 −0.138937 0.990301i \(-0.544369\pi\)
−0.138937 + 0.990301i \(0.544369\pi\)
\(72\) 0 0
\(73\) −13.9134 −1.62844 −0.814222 0.580554i \(-0.802836\pi\)
−0.814222 + 0.580554i \(0.802836\pi\)
\(74\) 0 0
\(75\) −2.54439 −0.293801
\(76\) 0 0
\(77\) 5.82724 0.664076
\(78\) 0 0
\(79\) −15.9669 −1.79642 −0.898209 0.439568i \(-0.855132\pi\)
−0.898209 + 0.439568i \(0.855132\pi\)
\(80\) 0 0
\(81\) 5.23469 0.581632
\(82\) 0 0
\(83\) 13.0428 1.43163 0.715816 0.698289i \(-0.246055\pi\)
0.715816 + 0.698289i \(0.246055\pi\)
\(84\) 0 0
\(85\) 4.85280 0.526360
\(86\) 0 0
\(87\) −5.22295 −0.559959
\(88\) 0 0
\(89\) −13.1072 −1.38937 −0.694683 0.719316i \(-0.744455\pi\)
−0.694683 + 0.719316i \(0.744455\pi\)
\(90\) 0 0
\(91\) 8.25394 0.865248
\(92\) 0 0
\(93\) −3.04885 −0.316151
\(94\) 0 0
\(95\) 1.96075 0.201168
\(96\) 0 0
\(97\) −12.3368 −1.25261 −0.626307 0.779576i \(-0.715435\pi\)
−0.626307 + 0.779576i \(0.715435\pi\)
\(98\) 0 0
\(99\) −5.96523 −0.599529
\(100\) 0 0
\(101\) 4.20440 0.418354 0.209177 0.977878i \(-0.432922\pi\)
0.209177 + 0.977878i \(0.432922\pi\)
\(102\) 0 0
\(103\) 12.9174 1.27279 0.636393 0.771365i \(-0.280426\pi\)
0.636393 + 0.771365i \(0.280426\pi\)
\(104\) 0 0
\(105\) −1.78921 −0.174609
\(106\) 0 0
\(107\) 12.1232 1.17199 0.585995 0.810315i \(-0.300704\pi\)
0.585995 + 0.810315i \(0.300704\pi\)
\(108\) 0 0
\(109\) 5.76783 0.552458 0.276229 0.961092i \(-0.410915\pi\)
0.276229 + 0.961092i \(0.410915\pi\)
\(110\) 0 0
\(111\) −3.80505 −0.361160
\(112\) 0 0
\(113\) 17.4675 1.64320 0.821600 0.570064i \(-0.193082\pi\)
0.821600 + 0.570064i \(0.193082\pi\)
\(114\) 0 0
\(115\) −1.77276 −0.165311
\(116\) 0 0
\(117\) −8.44939 −0.781147
\(118\) 0 0
\(119\) −11.2509 −1.03137
\(120\) 0 0
\(121\) −5.57088 −0.506443
\(122\) 0 0
\(123\) 6.83351 0.616157
\(124\) 0 0
\(125\) 9.53187 0.852557
\(126\) 0 0
\(127\) 4.92480 0.437005 0.218503 0.975836i \(-0.429883\pi\)
0.218503 + 0.975836i \(0.429883\pi\)
\(128\) 0 0
\(129\) 6.28559 0.553415
\(130\) 0 0
\(131\) −0.308622 −0.0269645 −0.0134822 0.999909i \(-0.504292\pi\)
−0.0134822 + 0.999909i \(0.504292\pi\)
\(132\) 0 0
\(133\) −4.54587 −0.394177
\(134\) 0 0
\(135\) 3.97785 0.342359
\(136\) 0 0
\(137\) 1.71206 0.146271 0.0731354 0.997322i \(-0.476699\pi\)
0.0731354 + 0.997322i \(0.476699\pi\)
\(138\) 0 0
\(139\) −11.5652 −0.980949 −0.490474 0.871456i \(-0.663176\pi\)
−0.490474 + 0.871456i \(0.663176\pi\)
\(140\) 0 0
\(141\) 6.69527 0.563843
\(142\) 0 0
\(143\) 7.69002 0.643072
\(144\) 0 0
\(145\) 8.49490 0.705463
\(146\) 0 0
\(147\) −0.494397 −0.0407772
\(148\) 0 0
\(149\) −1.39289 −0.114110 −0.0570548 0.998371i \(-0.518171\pi\)
−0.0570548 + 0.998371i \(0.518171\pi\)
\(150\) 0 0
\(151\) −4.24994 −0.345855 −0.172928 0.984935i \(-0.555323\pi\)
−0.172928 + 0.984935i \(0.555323\pi\)
\(152\) 0 0
\(153\) 11.5173 0.931121
\(154\) 0 0
\(155\) 4.95883 0.398303
\(156\) 0 0
\(157\) 0.895739 0.0714877 0.0357439 0.999361i \(-0.488620\pi\)
0.0357439 + 0.999361i \(0.488620\pi\)
\(158\) 0 0
\(159\) −7.87499 −0.624528
\(160\) 0 0
\(161\) 4.11003 0.323916
\(162\) 0 0
\(163\) 6.20923 0.486345 0.243172 0.969983i \(-0.421812\pi\)
0.243172 + 0.969983i \(0.421812\pi\)
\(164\) 0 0
\(165\) −1.66697 −0.129774
\(166\) 0 0
\(167\) 12.2306 0.946430 0.473215 0.880947i \(-0.343093\pi\)
0.473215 + 0.880947i \(0.343093\pi\)
\(168\) 0 0
\(169\) −2.10755 −0.162119
\(170\) 0 0
\(171\) 4.65352 0.355863
\(172\) 0 0
\(173\) −23.9772 −1.82295 −0.911476 0.411354i \(-0.865056\pi\)
−0.911476 + 0.411354i \(0.865056\pi\)
\(174\) 0 0
\(175\) −9.59448 −0.725274
\(176\) 0 0
\(177\) −8.91886 −0.670383
\(178\) 0 0
\(179\) −14.3798 −1.07480 −0.537399 0.843328i \(-0.680593\pi\)
−0.537399 + 0.843328i \(0.680593\pi\)
\(180\) 0 0
\(181\) −19.3019 −1.43470 −0.717350 0.696713i \(-0.754645\pi\)
−0.717350 + 0.696713i \(0.754645\pi\)
\(182\) 0 0
\(183\) −4.23394 −0.312982
\(184\) 0 0
\(185\) 6.18876 0.455006
\(186\) 0 0
\(187\) −10.4822 −0.766537
\(188\) 0 0
\(189\) −9.22240 −0.670831
\(190\) 0 0
\(191\) −12.1365 −0.878163 −0.439082 0.898447i \(-0.644696\pi\)
−0.439082 + 0.898447i \(0.644696\pi\)
\(192\) 0 0
\(193\) −27.0151 −1.94459 −0.972294 0.233759i \(-0.924897\pi\)
−0.972294 + 0.233759i \(0.924897\pi\)
\(194\) 0 0
\(195\) −2.36117 −0.169087
\(196\) 0 0
\(197\) 17.5885 1.25313 0.626563 0.779371i \(-0.284461\pi\)
0.626563 + 0.779371i \(0.284461\pi\)
\(198\) 0 0
\(199\) 8.49827 0.602427 0.301213 0.953557i \(-0.402608\pi\)
0.301213 + 0.953557i \(0.402608\pi\)
\(200\) 0 0
\(201\) 2.76206 0.194820
\(202\) 0 0
\(203\) −19.6949 −1.38231
\(204\) 0 0
\(205\) −11.1144 −0.776265
\(206\) 0 0
\(207\) −4.20736 −0.292432
\(208\) 0 0
\(209\) −4.23529 −0.292961
\(210\) 0 0
\(211\) 9.46151 0.651357 0.325679 0.945480i \(-0.394407\pi\)
0.325679 + 0.945480i \(0.394407\pi\)
\(212\) 0 0
\(213\) −1.55288 −0.106402
\(214\) 0 0
\(215\) −10.2232 −0.697220
\(216\) 0 0
\(217\) −11.4967 −0.780448
\(218\) 0 0
\(219\) −9.22772 −0.623552
\(220\) 0 0
\(221\) −14.8475 −0.998748
\(222\) 0 0
\(223\) −20.7227 −1.38769 −0.693847 0.720122i \(-0.744086\pi\)
−0.693847 + 0.720122i \(0.744086\pi\)
\(224\) 0 0
\(225\) 9.82168 0.654779
\(226\) 0 0
\(227\) −10.3845 −0.689240 −0.344620 0.938742i \(-0.611992\pi\)
−0.344620 + 0.938742i \(0.611992\pi\)
\(228\) 0 0
\(229\) −0.506045 −0.0334404 −0.0167202 0.999860i \(-0.505322\pi\)
−0.0167202 + 0.999860i \(0.505322\pi\)
\(230\) 0 0
\(231\) 3.86477 0.254283
\(232\) 0 0
\(233\) 5.09021 0.333471 0.166735 0.986002i \(-0.446677\pi\)
0.166735 + 0.986002i \(0.446677\pi\)
\(234\) 0 0
\(235\) −10.8896 −0.710357
\(236\) 0 0
\(237\) −10.5896 −0.687872
\(238\) 0 0
\(239\) 0.711863 0.0460466 0.0230233 0.999735i \(-0.492671\pi\)
0.0230233 + 0.999735i \(0.492671\pi\)
\(240\) 0 0
\(241\) 27.3259 1.76021 0.880107 0.474776i \(-0.157471\pi\)
0.880107 + 0.474776i \(0.157471\pi\)
\(242\) 0 0
\(243\) 14.5346 0.932396
\(244\) 0 0
\(245\) 0.804115 0.0513731
\(246\) 0 0
\(247\) −5.99903 −0.381709
\(248\) 0 0
\(249\) 8.65030 0.548190
\(250\) 0 0
\(251\) −18.7231 −1.18179 −0.590896 0.806748i \(-0.701226\pi\)
−0.590896 + 0.806748i \(0.701226\pi\)
\(252\) 0 0
\(253\) 3.82923 0.240742
\(254\) 0 0
\(255\) 3.21849 0.201550
\(256\) 0 0
\(257\) 14.5018 0.904600 0.452300 0.891866i \(-0.350604\pi\)
0.452300 + 0.891866i \(0.350604\pi\)
\(258\) 0 0
\(259\) −14.3482 −0.891556
\(260\) 0 0
\(261\) 20.1613 1.24795
\(262\) 0 0
\(263\) −26.7006 −1.64643 −0.823213 0.567732i \(-0.807821\pi\)
−0.823213 + 0.567732i \(0.807821\pi\)
\(264\) 0 0
\(265\) 12.8083 0.786810
\(266\) 0 0
\(267\) −8.69304 −0.532006
\(268\) 0 0
\(269\) −10.1497 −0.618837 −0.309418 0.950926i \(-0.600134\pi\)
−0.309418 + 0.950926i \(0.600134\pi\)
\(270\) 0 0
\(271\) 1.47199 0.0894171 0.0447085 0.999000i \(-0.485764\pi\)
0.0447085 + 0.999000i \(0.485764\pi\)
\(272\) 0 0
\(273\) 5.47421 0.331314
\(274\) 0 0
\(275\) −8.93898 −0.539041
\(276\) 0 0
\(277\) −23.7554 −1.42732 −0.713661 0.700491i \(-0.752964\pi\)
−0.713661 + 0.700491i \(0.752964\pi\)
\(278\) 0 0
\(279\) 11.7690 0.704590
\(280\) 0 0
\(281\) 15.4337 0.920700 0.460350 0.887737i \(-0.347724\pi\)
0.460350 + 0.887737i \(0.347724\pi\)
\(282\) 0 0
\(283\) −7.12244 −0.423385 −0.211693 0.977336i \(-0.567898\pi\)
−0.211693 + 0.977336i \(0.567898\pi\)
\(284\) 0 0
\(285\) 1.30042 0.0770299
\(286\) 0 0
\(287\) 25.7681 1.52104
\(288\) 0 0
\(289\) 3.23850 0.190500
\(290\) 0 0
\(291\) −8.18208 −0.479642
\(292\) 0 0
\(293\) −5.92650 −0.346230 −0.173115 0.984902i \(-0.555383\pi\)
−0.173115 + 0.984902i \(0.555383\pi\)
\(294\) 0 0
\(295\) 14.5061 0.844581
\(296\) 0 0
\(297\) −8.59232 −0.498577
\(298\) 0 0
\(299\) 5.42388 0.313671
\(300\) 0 0
\(301\) 23.7019 1.36616
\(302\) 0 0
\(303\) 2.78846 0.160193
\(304\) 0 0
\(305\) 6.88632 0.394310
\(306\) 0 0
\(307\) −3.75785 −0.214472 −0.107236 0.994234i \(-0.534200\pi\)
−0.107236 + 0.994234i \(0.534200\pi\)
\(308\) 0 0
\(309\) 8.56711 0.487366
\(310\) 0 0
\(311\) 11.5667 0.655885 0.327943 0.944698i \(-0.393645\pi\)
0.327943 + 0.944698i \(0.393645\pi\)
\(312\) 0 0
\(313\) −18.0294 −1.01908 −0.509541 0.860446i \(-0.670185\pi\)
−0.509541 + 0.860446i \(0.670185\pi\)
\(314\) 0 0
\(315\) 6.90660 0.389143
\(316\) 0 0
\(317\) 7.77961 0.436946 0.218473 0.975843i \(-0.429892\pi\)
0.218473 + 0.975843i \(0.429892\pi\)
\(318\) 0 0
\(319\) −18.3493 −1.02736
\(320\) 0 0
\(321\) 8.04038 0.448770
\(322\) 0 0
\(323\) 8.17726 0.454995
\(324\) 0 0
\(325\) −12.6615 −0.702335
\(326\) 0 0
\(327\) 3.82537 0.211543
\(328\) 0 0
\(329\) 25.2468 1.39190
\(330\) 0 0
\(331\) 0.760125 0.0417803 0.0208901 0.999782i \(-0.493350\pi\)
0.0208901 + 0.999782i \(0.493350\pi\)
\(332\) 0 0
\(333\) 14.6880 0.804898
\(334\) 0 0
\(335\) −4.49237 −0.245444
\(336\) 0 0
\(337\) 1.93081 0.105178 0.0525889 0.998616i \(-0.483253\pi\)
0.0525889 + 0.998616i \(0.483253\pi\)
\(338\) 0 0
\(339\) 11.5848 0.629202
\(340\) 0 0
\(341\) −10.7113 −0.580047
\(342\) 0 0
\(343\) −19.3707 −1.04592
\(344\) 0 0
\(345\) −1.17574 −0.0632996
\(346\) 0 0
\(347\) −3.95219 −0.212165 −0.106082 0.994357i \(-0.533831\pi\)
−0.106082 + 0.994357i \(0.533831\pi\)
\(348\) 0 0
\(349\) −19.2682 −1.03140 −0.515702 0.856768i \(-0.672469\pi\)
−0.515702 + 0.856768i \(0.672469\pi\)
\(350\) 0 0
\(351\) −12.1705 −0.649613
\(352\) 0 0
\(353\) 36.0745 1.92005 0.960025 0.279914i \(-0.0903061\pi\)
0.960025 + 0.279914i \(0.0903061\pi\)
\(354\) 0 0
\(355\) 2.52569 0.134050
\(356\) 0 0
\(357\) −7.46187 −0.394924
\(358\) 0 0
\(359\) −12.0312 −0.634984 −0.317492 0.948261i \(-0.602841\pi\)
−0.317492 + 0.948261i \(0.602841\pi\)
\(360\) 0 0
\(361\) −15.6960 −0.826106
\(362\) 0 0
\(363\) −3.69474 −0.193924
\(364\) 0 0
\(365\) 15.0085 0.785581
\(366\) 0 0
\(367\) 7.08143 0.369648 0.184824 0.982772i \(-0.440829\pi\)
0.184824 + 0.982772i \(0.440829\pi\)
\(368\) 0 0
\(369\) −26.3783 −1.37320
\(370\) 0 0
\(371\) −29.6953 −1.54170
\(372\) 0 0
\(373\) −2.94072 −0.152265 −0.0761324 0.997098i \(-0.524257\pi\)
−0.0761324 + 0.997098i \(0.524257\pi\)
\(374\) 0 0
\(375\) 6.32177 0.326455
\(376\) 0 0
\(377\) −25.9907 −1.33859
\(378\) 0 0
\(379\) −7.12347 −0.365908 −0.182954 0.983121i \(-0.558566\pi\)
−0.182954 + 0.983121i \(0.558566\pi\)
\(380\) 0 0
\(381\) 3.26625 0.167335
\(382\) 0 0
\(383\) 20.2810 1.03631 0.518155 0.855287i \(-0.326619\pi\)
0.518155 + 0.855287i \(0.326619\pi\)
\(384\) 0 0
\(385\) −6.28588 −0.320358
\(386\) 0 0
\(387\) −24.2632 −1.23337
\(388\) 0 0
\(389\) 34.2986 1.73901 0.869504 0.493925i \(-0.164438\pi\)
0.869504 + 0.493925i \(0.164438\pi\)
\(390\) 0 0
\(391\) −7.39326 −0.373893
\(392\) 0 0
\(393\) −0.204686 −0.0103250
\(394\) 0 0
\(395\) 17.2236 0.866614
\(396\) 0 0
\(397\) 2.31254 0.116063 0.0580315 0.998315i \(-0.481518\pi\)
0.0580315 + 0.998315i \(0.481518\pi\)
\(398\) 0 0
\(399\) −3.01493 −0.150935
\(400\) 0 0
\(401\) −16.3015 −0.814056 −0.407028 0.913416i \(-0.633435\pi\)
−0.407028 + 0.913416i \(0.633435\pi\)
\(402\) 0 0
\(403\) −15.1719 −0.755764
\(404\) 0 0
\(405\) −5.64669 −0.280586
\(406\) 0 0
\(407\) −13.3680 −0.662625
\(408\) 0 0
\(409\) −17.4264 −0.861680 −0.430840 0.902428i \(-0.641783\pi\)
−0.430840 + 0.902428i \(0.641783\pi\)
\(410\) 0 0
\(411\) 1.13548 0.0560090
\(412\) 0 0
\(413\) −33.6316 −1.65490
\(414\) 0 0
\(415\) −14.0693 −0.690637
\(416\) 0 0
\(417\) −7.67033 −0.375618
\(418\) 0 0
\(419\) −32.0218 −1.56437 −0.782183 0.623049i \(-0.785894\pi\)
−0.782183 + 0.623049i \(0.785894\pi\)
\(420\) 0 0
\(421\) −5.63190 −0.274482 −0.137241 0.990538i \(-0.543824\pi\)
−0.137241 + 0.990538i \(0.543824\pi\)
\(422\) 0 0
\(423\) −25.8446 −1.25661
\(424\) 0 0
\(425\) 17.2589 0.837178
\(426\) 0 0
\(427\) −15.9655 −0.772624
\(428\) 0 0
\(429\) 5.10021 0.246240
\(430\) 0 0
\(431\) −0.666942 −0.0321255 −0.0160627 0.999871i \(-0.505113\pi\)
−0.0160627 + 0.999871i \(0.505113\pi\)
\(432\) 0 0
\(433\) 18.2033 0.874793 0.437397 0.899269i \(-0.355901\pi\)
0.437397 + 0.899269i \(0.355901\pi\)
\(434\) 0 0
\(435\) 5.63402 0.270131
\(436\) 0 0
\(437\) −2.98721 −0.142898
\(438\) 0 0
\(439\) −11.4257 −0.545320 −0.272660 0.962110i \(-0.587903\pi\)
−0.272660 + 0.962110i \(0.587903\pi\)
\(440\) 0 0
\(441\) 1.90844 0.0908780
\(442\) 0 0
\(443\) −31.3327 −1.48866 −0.744331 0.667811i \(-0.767231\pi\)
−0.744331 + 0.667811i \(0.767231\pi\)
\(444\) 0 0
\(445\) 14.1389 0.670247
\(446\) 0 0
\(447\) −0.923795 −0.0436940
\(448\) 0 0
\(449\) −15.1648 −0.715671 −0.357835 0.933785i \(-0.616485\pi\)
−0.357835 + 0.933785i \(0.616485\pi\)
\(450\) 0 0
\(451\) 24.0076 1.13047
\(452\) 0 0
\(453\) −2.81867 −0.132432
\(454\) 0 0
\(455\) −8.90357 −0.417406
\(456\) 0 0
\(457\) −12.6347 −0.591025 −0.295513 0.955339i \(-0.595490\pi\)
−0.295513 + 0.955339i \(0.595490\pi\)
\(458\) 0 0
\(459\) 16.5896 0.774334
\(460\) 0 0
\(461\) 33.4631 1.55853 0.779265 0.626694i \(-0.215592\pi\)
0.779265 + 0.626694i \(0.215592\pi\)
\(462\) 0 0
\(463\) 5.07551 0.235879 0.117940 0.993021i \(-0.462371\pi\)
0.117940 + 0.993021i \(0.462371\pi\)
\(464\) 0 0
\(465\) 3.28881 0.152515
\(466\) 0 0
\(467\) 33.0914 1.53129 0.765644 0.643265i \(-0.222421\pi\)
0.765644 + 0.643265i \(0.222421\pi\)
\(468\) 0 0
\(469\) 10.4153 0.480932
\(470\) 0 0
\(471\) 0.594076 0.0273736
\(472\) 0 0
\(473\) 22.0826 1.01536
\(474\) 0 0
\(475\) 6.97335 0.319959
\(476\) 0 0
\(477\) 30.3985 1.39185
\(478\) 0 0
\(479\) −11.2745 −0.515147 −0.257573 0.966259i \(-0.582923\pi\)
−0.257573 + 0.966259i \(0.582923\pi\)
\(480\) 0 0
\(481\) −18.9349 −0.863357
\(482\) 0 0
\(483\) 2.72587 0.124032
\(484\) 0 0
\(485\) 13.3078 0.604277
\(486\) 0 0
\(487\) 10.3991 0.471226 0.235613 0.971847i \(-0.424290\pi\)
0.235613 + 0.971847i \(0.424290\pi\)
\(488\) 0 0
\(489\) 4.11811 0.186228
\(490\) 0 0
\(491\) −18.9188 −0.853794 −0.426897 0.904300i \(-0.640393\pi\)
−0.426897 + 0.904300i \(0.640393\pi\)
\(492\) 0 0
\(493\) 35.4278 1.59559
\(494\) 0 0
\(495\) 6.43474 0.289220
\(496\) 0 0
\(497\) −5.85566 −0.262662
\(498\) 0 0
\(499\) −7.07362 −0.316659 −0.158329 0.987386i \(-0.550611\pi\)
−0.158329 + 0.987386i \(0.550611\pi\)
\(500\) 0 0
\(501\) 8.11161 0.362400
\(502\) 0 0
\(503\) −8.88782 −0.396288 −0.198144 0.980173i \(-0.563491\pi\)
−0.198144 + 0.980173i \(0.563491\pi\)
\(504\) 0 0
\(505\) −4.53531 −0.201819
\(506\) 0 0
\(507\) −1.39778 −0.0620774
\(508\) 0 0
\(509\) 27.4046 1.21469 0.607344 0.794439i \(-0.292235\pi\)
0.607344 + 0.794439i \(0.292235\pi\)
\(510\) 0 0
\(511\) −34.7962 −1.53930
\(512\) 0 0
\(513\) 6.70292 0.295941
\(514\) 0 0
\(515\) −13.9340 −0.614007
\(516\) 0 0
\(517\) 23.5219 1.03449
\(518\) 0 0
\(519\) −15.9022 −0.698031
\(520\) 0 0
\(521\) 6.10425 0.267432 0.133716 0.991020i \(-0.457309\pi\)
0.133716 + 0.991020i \(0.457309\pi\)
\(522\) 0 0
\(523\) 12.5988 0.550908 0.275454 0.961314i \(-0.411172\pi\)
0.275454 + 0.961314i \(0.411172\pi\)
\(524\) 0 0
\(525\) −6.36329 −0.277717
\(526\) 0 0
\(527\) 20.6807 0.900865
\(528\) 0 0
\(529\) −20.2992 −0.882573
\(530\) 0 0
\(531\) 34.4280 1.49405
\(532\) 0 0
\(533\) 34.0053 1.47293
\(534\) 0 0
\(535\) −13.0773 −0.565382
\(536\) 0 0
\(537\) −9.53704 −0.411553
\(538\) 0 0
\(539\) −1.73692 −0.0748145
\(540\) 0 0
\(541\) 40.8577 1.75661 0.878305 0.478102i \(-0.158675\pi\)
0.878305 + 0.478102i \(0.158675\pi\)
\(542\) 0 0
\(543\) −12.8015 −0.549365
\(544\) 0 0
\(545\) −6.22180 −0.266512
\(546\) 0 0
\(547\) 18.3384 0.784094 0.392047 0.919945i \(-0.371767\pi\)
0.392047 + 0.919945i \(0.371767\pi\)
\(548\) 0 0
\(549\) 16.3436 0.697526
\(550\) 0 0
\(551\) 14.3144 0.609815
\(552\) 0 0
\(553\) −39.9318 −1.69807
\(554\) 0 0
\(555\) 4.10453 0.174228
\(556\) 0 0
\(557\) 14.3809 0.609338 0.304669 0.952458i \(-0.401454\pi\)
0.304669 + 0.952458i \(0.401454\pi\)
\(558\) 0 0
\(559\) 31.2787 1.32295
\(560\) 0 0
\(561\) −6.95207 −0.293517
\(562\) 0 0
\(563\) −23.8206 −1.00392 −0.501958 0.864892i \(-0.667387\pi\)
−0.501958 + 0.864892i \(0.667387\pi\)
\(564\) 0 0
\(565\) −18.8423 −0.792700
\(566\) 0 0
\(567\) 13.0915 0.549791
\(568\) 0 0
\(569\) −39.6960 −1.66414 −0.832072 0.554667i \(-0.812846\pi\)
−0.832072 + 0.554667i \(0.812846\pi\)
\(570\) 0 0
\(571\) 16.7390 0.700505 0.350253 0.936655i \(-0.386096\pi\)
0.350253 + 0.936655i \(0.386096\pi\)
\(572\) 0 0
\(573\) −8.04919 −0.336260
\(574\) 0 0
\(575\) −6.30478 −0.262928
\(576\) 0 0
\(577\) 9.71337 0.404373 0.202187 0.979347i \(-0.435195\pi\)
0.202187 + 0.979347i \(0.435195\pi\)
\(578\) 0 0
\(579\) −17.9171 −0.744608
\(580\) 0 0
\(581\) 32.6189 1.35326
\(582\) 0 0
\(583\) −27.6665 −1.14583
\(584\) 0 0
\(585\) 9.11441 0.376835
\(586\) 0 0
\(587\) 43.1562 1.78125 0.890623 0.454743i \(-0.150269\pi\)
0.890623 + 0.454743i \(0.150269\pi\)
\(588\) 0 0
\(589\) 8.35592 0.344300
\(590\) 0 0
\(591\) 11.6651 0.479838
\(592\) 0 0
\(593\) 25.8999 1.06358 0.531791 0.846875i \(-0.321519\pi\)
0.531791 + 0.846875i \(0.321519\pi\)
\(594\) 0 0
\(595\) 12.1364 0.497545
\(596\) 0 0
\(597\) 5.63626 0.230677
\(598\) 0 0
\(599\) −3.99357 −0.163173 −0.0815864 0.996666i \(-0.525999\pi\)
−0.0815864 + 0.996666i \(0.525999\pi\)
\(600\) 0 0
\(601\) −42.9892 −1.75357 −0.876784 0.480885i \(-0.840315\pi\)
−0.876784 + 0.480885i \(0.840315\pi\)
\(602\) 0 0
\(603\) −10.6619 −0.434186
\(604\) 0 0
\(605\) 6.00934 0.244314
\(606\) 0 0
\(607\) 9.71218 0.394205 0.197103 0.980383i \(-0.436847\pi\)
0.197103 + 0.980383i \(0.436847\pi\)
\(608\) 0 0
\(609\) −13.0621 −0.529304
\(610\) 0 0
\(611\) 33.3173 1.34788
\(612\) 0 0
\(613\) 19.9490 0.805731 0.402865 0.915259i \(-0.368014\pi\)
0.402865 + 0.915259i \(0.368014\pi\)
\(614\) 0 0
\(615\) −7.37135 −0.297242
\(616\) 0 0
\(617\) 26.5224 1.06775 0.533876 0.845563i \(-0.320735\pi\)
0.533876 + 0.845563i \(0.320735\pi\)
\(618\) 0 0
\(619\) −20.8690 −0.838798 −0.419399 0.907802i \(-0.637759\pi\)
−0.419399 + 0.907802i \(0.637759\pi\)
\(620\) 0 0
\(621\) −6.06028 −0.243191
\(622\) 0 0
\(623\) −32.7801 −1.31331
\(624\) 0 0
\(625\) 8.89988 0.355995
\(626\) 0 0
\(627\) −2.80895 −0.112179
\(628\) 0 0
\(629\) 25.8101 1.02912
\(630\) 0 0
\(631\) −11.5300 −0.459002 −0.229501 0.973308i \(-0.573709\pi\)
−0.229501 + 0.973308i \(0.573709\pi\)
\(632\) 0 0
\(633\) 6.27510 0.249413
\(634\) 0 0
\(635\) −5.31241 −0.210817
\(636\) 0 0
\(637\) −2.46024 −0.0974784
\(638\) 0 0
\(639\) 5.99432 0.237132
\(640\) 0 0
\(641\) −33.8084 −1.33535 −0.667676 0.744452i \(-0.732711\pi\)
−0.667676 + 0.744452i \(0.732711\pi\)
\(642\) 0 0
\(643\) −20.9985 −0.828098 −0.414049 0.910255i \(-0.635886\pi\)
−0.414049 + 0.910255i \(0.635886\pi\)
\(644\) 0 0
\(645\) −6.78031 −0.266974
\(646\) 0 0
\(647\) 38.1804 1.50103 0.750514 0.660855i \(-0.229806\pi\)
0.750514 + 0.660855i \(0.229806\pi\)
\(648\) 0 0
\(649\) −31.3339 −1.22996
\(650\) 0 0
\(651\) −7.62491 −0.298844
\(652\) 0 0
\(653\) 8.44328 0.330411 0.165206 0.986259i \(-0.447171\pi\)
0.165206 + 0.986259i \(0.447171\pi\)
\(654\) 0 0
\(655\) 0.332913 0.0130080
\(656\) 0 0
\(657\) 35.6202 1.38968
\(658\) 0 0
\(659\) −29.1024 −1.13367 −0.566834 0.823832i \(-0.691832\pi\)
−0.566834 + 0.823832i \(0.691832\pi\)
\(660\) 0 0
\(661\) 15.2277 0.592291 0.296145 0.955143i \(-0.404299\pi\)
0.296145 + 0.955143i \(0.404299\pi\)
\(662\) 0 0
\(663\) −9.84719 −0.382433
\(664\) 0 0
\(665\) 4.90365 0.190156
\(666\) 0 0
\(667\) −12.9420 −0.501117
\(668\) 0 0
\(669\) −13.7438 −0.531366
\(670\) 0 0
\(671\) −14.8747 −0.574232
\(672\) 0 0
\(673\) 12.9620 0.499649 0.249825 0.968291i \(-0.419627\pi\)
0.249825 + 0.968291i \(0.419627\pi\)
\(674\) 0 0
\(675\) 14.1471 0.544524
\(676\) 0 0
\(677\) −38.8478 −1.49304 −0.746521 0.665362i \(-0.768277\pi\)
−0.746521 + 0.665362i \(0.768277\pi\)
\(678\) 0 0
\(679\) −30.8533 −1.18404
\(680\) 0 0
\(681\) −6.88722 −0.263919
\(682\) 0 0
\(683\) 11.8915 0.455015 0.227507 0.973776i \(-0.426942\pi\)
0.227507 + 0.973776i \(0.426942\pi\)
\(684\) 0 0
\(685\) −1.84681 −0.0705628
\(686\) 0 0
\(687\) −0.335621 −0.0128047
\(688\) 0 0
\(689\) −39.1880 −1.49294
\(690\) 0 0
\(691\) −25.6778 −0.976829 −0.488415 0.872612i \(-0.662425\pi\)
−0.488415 + 0.872612i \(0.662425\pi\)
\(692\) 0 0
\(693\) −14.9185 −0.566708
\(694\) 0 0
\(695\) 12.4755 0.473221
\(696\) 0 0
\(697\) −46.3525 −1.75573
\(698\) 0 0
\(699\) 3.37595 0.127690
\(700\) 0 0
\(701\) −41.1163 −1.55294 −0.776470 0.630154i \(-0.782992\pi\)
−0.776470 + 0.630154i \(0.782992\pi\)
\(702\) 0 0
\(703\) 10.4284 0.393316
\(704\) 0 0
\(705\) −7.22223 −0.272005
\(706\) 0 0
\(707\) 10.5148 0.395451
\(708\) 0 0
\(709\) −9.65505 −0.362603 −0.181302 0.983428i \(-0.558031\pi\)
−0.181302 + 0.983428i \(0.558031\pi\)
\(710\) 0 0
\(711\) 40.8775 1.53302
\(712\) 0 0
\(713\) −7.55480 −0.282929
\(714\) 0 0
\(715\) −8.29528 −0.310226
\(716\) 0 0
\(717\) 0.472125 0.0176318
\(718\) 0 0
\(719\) 24.1834 0.901888 0.450944 0.892552i \(-0.351087\pi\)
0.450944 + 0.892552i \(0.351087\pi\)
\(720\) 0 0
\(721\) 32.3052 1.20311
\(722\) 0 0
\(723\) 18.1232 0.674008
\(724\) 0 0
\(725\) 30.2119 1.12204
\(726\) 0 0
\(727\) 19.4358 0.720832 0.360416 0.932792i \(-0.382635\pi\)
0.360416 + 0.932792i \(0.382635\pi\)
\(728\) 0 0
\(729\) −6.06435 −0.224605
\(730\) 0 0
\(731\) −42.6359 −1.57694
\(732\) 0 0
\(733\) 37.5471 1.38683 0.693416 0.720537i \(-0.256105\pi\)
0.693416 + 0.720537i \(0.256105\pi\)
\(734\) 0 0
\(735\) 0.533309 0.0196714
\(736\) 0 0
\(737\) 9.70369 0.357440
\(738\) 0 0
\(739\) 42.8033 1.57455 0.787273 0.616605i \(-0.211493\pi\)
0.787273 + 0.616605i \(0.211493\pi\)
\(740\) 0 0
\(741\) −3.97870 −0.146161
\(742\) 0 0
\(743\) −24.4878 −0.898369 −0.449184 0.893439i \(-0.648285\pi\)
−0.449184 + 0.893439i \(0.648285\pi\)
\(744\) 0 0
\(745\) 1.50251 0.0550478
\(746\) 0 0
\(747\) −33.3913 −1.22172
\(748\) 0 0
\(749\) 30.3190 1.10783
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −12.4176 −0.452523
\(754\) 0 0
\(755\) 4.58444 0.166845
\(756\) 0 0
\(757\) 9.33425 0.339259 0.169630 0.985508i \(-0.445743\pi\)
0.169630 + 0.985508i \(0.445743\pi\)
\(758\) 0 0
\(759\) 2.53964 0.0921831
\(760\) 0 0
\(761\) −17.6711 −0.640577 −0.320289 0.947320i \(-0.603780\pi\)
−0.320289 + 0.947320i \(0.603780\pi\)
\(762\) 0 0
\(763\) 14.4248 0.522214
\(764\) 0 0
\(765\) −12.4238 −0.449184
\(766\) 0 0
\(767\) −44.3825 −1.60256
\(768\) 0 0
\(769\) −23.1060 −0.833224 −0.416612 0.909084i \(-0.636783\pi\)
−0.416612 + 0.909084i \(0.636783\pi\)
\(770\) 0 0
\(771\) 9.61797 0.346383
\(772\) 0 0
\(773\) −3.82912 −0.137724 −0.0688619 0.997626i \(-0.521937\pi\)
−0.0688619 + 0.997626i \(0.521937\pi\)
\(774\) 0 0
\(775\) 17.6360 0.633502
\(776\) 0 0
\(777\) −9.51610 −0.341388
\(778\) 0 0
\(779\) −18.7285 −0.671017
\(780\) 0 0
\(781\) −5.45560 −0.195217
\(782\) 0 0
\(783\) 29.0403 1.03781
\(784\) 0 0
\(785\) −0.966239 −0.0344865
\(786\) 0 0
\(787\) −34.0734 −1.21458 −0.607292 0.794478i \(-0.707744\pi\)
−0.607292 + 0.794478i \(0.707744\pi\)
\(788\) 0 0
\(789\) −17.7085 −0.630438
\(790\) 0 0
\(791\) 43.6846 1.55324
\(792\) 0 0
\(793\) −21.0691 −0.748187
\(794\) 0 0
\(795\) 8.49480 0.301280
\(796\) 0 0
\(797\) 24.8759 0.881148 0.440574 0.897716i \(-0.354775\pi\)
0.440574 + 0.897716i \(0.354775\pi\)
\(798\) 0 0
\(799\) −45.4147 −1.60666
\(800\) 0 0
\(801\) 33.5563 1.18565
\(802\) 0 0
\(803\) −32.4190 −1.14404
\(804\) 0 0
\(805\) −4.43352 −0.156261
\(806\) 0 0
\(807\) −6.73151 −0.236960
\(808\) 0 0
\(809\) 16.0430 0.564042 0.282021 0.959408i \(-0.408995\pi\)
0.282021 + 0.959408i \(0.408995\pi\)
\(810\) 0 0
\(811\) 18.5400 0.651026 0.325513 0.945538i \(-0.394463\pi\)
0.325513 + 0.945538i \(0.394463\pi\)
\(812\) 0 0
\(813\) 0.976260 0.0342389
\(814\) 0 0
\(815\) −6.69794 −0.234619
\(816\) 0 0
\(817\) −17.2268 −0.602689
\(818\) 0 0
\(819\) −21.1312 −0.738383
\(820\) 0 0
\(821\) 36.8643 1.28657 0.643287 0.765625i \(-0.277570\pi\)
0.643287 + 0.765625i \(0.277570\pi\)
\(822\) 0 0
\(823\) 16.3958 0.571522 0.285761 0.958301i \(-0.407754\pi\)
0.285761 + 0.958301i \(0.407754\pi\)
\(824\) 0 0
\(825\) −5.92855 −0.206406
\(826\) 0 0
\(827\) 18.1533 0.631252 0.315626 0.948884i \(-0.397785\pi\)
0.315626 + 0.948884i \(0.397785\pi\)
\(828\) 0 0
\(829\) −32.2184 −1.11899 −0.559495 0.828834i \(-0.689005\pi\)
−0.559495 + 0.828834i \(0.689005\pi\)
\(830\) 0 0
\(831\) −15.7551 −0.546540
\(832\) 0 0
\(833\) 3.35355 0.116194
\(834\) 0 0
\(835\) −13.1932 −0.456569
\(836\) 0 0
\(837\) 16.9520 0.585948
\(838\) 0 0
\(839\) 40.7231 1.40592 0.702959 0.711230i \(-0.251862\pi\)
0.702959 + 0.711230i \(0.251862\pi\)
\(840\) 0 0
\(841\) 33.0169 1.13851
\(842\) 0 0
\(843\) 10.2360 0.352548
\(844\) 0 0
\(845\) 2.27342 0.0782082
\(846\) 0 0
\(847\) −13.9323 −0.478718
\(848\) 0 0
\(849\) −4.72378 −0.162120
\(850\) 0 0
\(851\) −9.42860 −0.323208
\(852\) 0 0
\(853\) 35.1478 1.20344 0.601719 0.798708i \(-0.294483\pi\)
0.601719 + 0.798708i \(0.294483\pi\)
\(854\) 0 0
\(855\) −5.01978 −0.171673
\(856\) 0 0
\(857\) −34.5643 −1.18069 −0.590347 0.807149i \(-0.701009\pi\)
−0.590347 + 0.807149i \(0.701009\pi\)
\(858\) 0 0
\(859\) 39.3824 1.34371 0.671855 0.740682i \(-0.265498\pi\)
0.671855 + 0.740682i \(0.265498\pi\)
\(860\) 0 0
\(861\) 17.0900 0.582426
\(862\) 0 0
\(863\) −25.8229 −0.879021 −0.439510 0.898237i \(-0.644848\pi\)
−0.439510 + 0.898237i \(0.644848\pi\)
\(864\) 0 0
\(865\) 25.8643 0.879414
\(866\) 0 0
\(867\) 2.14785 0.0729450
\(868\) 0 0
\(869\) −37.2037 −1.26205
\(870\) 0 0
\(871\) 13.7447 0.465721
\(872\) 0 0
\(873\) 31.5839 1.06895
\(874\) 0 0
\(875\) 23.8384 0.805884
\(876\) 0 0
\(877\) 20.0866 0.678278 0.339139 0.940736i \(-0.389864\pi\)
0.339139 + 0.940736i \(0.389864\pi\)
\(878\) 0 0
\(879\) −3.93060 −0.132576
\(880\) 0 0
\(881\) −37.8109 −1.27388 −0.636941 0.770913i \(-0.719800\pi\)
−0.636941 + 0.770913i \(0.719800\pi\)
\(882\) 0 0
\(883\) 19.6487 0.661231 0.330615 0.943766i \(-0.392744\pi\)
0.330615 + 0.943766i \(0.392744\pi\)
\(884\) 0 0
\(885\) 9.62083 0.323401
\(886\) 0 0
\(887\) 52.3896 1.75907 0.879536 0.475833i \(-0.157853\pi\)
0.879536 + 0.475833i \(0.157853\pi\)
\(888\) 0 0
\(889\) 12.3165 0.413082
\(890\) 0 0
\(891\) 12.1971 0.408617
\(892\) 0 0
\(893\) −18.3496 −0.614045
\(894\) 0 0
\(895\) 15.5116 0.518495
\(896\) 0 0
\(897\) 3.59725 0.120109
\(898\) 0 0
\(899\) 36.2019 1.20740
\(900\) 0 0
\(901\) 53.4169 1.77958
\(902\) 0 0
\(903\) 15.7197 0.523119
\(904\) 0 0
\(905\) 20.8211 0.692117
\(906\) 0 0
\(907\) −37.0499 −1.23022 −0.615111 0.788440i \(-0.710889\pi\)
−0.615111 + 0.788440i \(0.710889\pi\)
\(908\) 0 0
\(909\) −10.7638 −0.357014
\(910\) 0 0
\(911\) −6.35015 −0.210390 −0.105195 0.994452i \(-0.533547\pi\)
−0.105195 + 0.994452i \(0.533547\pi\)
\(912\) 0 0
\(913\) 30.3903 1.00577
\(914\) 0 0
\(915\) 4.56717 0.150986
\(916\) 0 0
\(917\) −0.771837 −0.0254883
\(918\) 0 0
\(919\) 19.5575 0.645143 0.322571 0.946545i \(-0.395453\pi\)
0.322571 + 0.946545i \(0.395453\pi\)
\(920\) 0 0
\(921\) −2.49230 −0.0821240
\(922\) 0 0
\(923\) −7.72752 −0.254354
\(924\) 0 0
\(925\) 22.0102 0.723690
\(926\) 0 0
\(927\) −33.0702 −1.08617
\(928\) 0 0
\(929\) −17.1791 −0.563629 −0.281815 0.959469i \(-0.590936\pi\)
−0.281815 + 0.959469i \(0.590936\pi\)
\(930\) 0 0
\(931\) 1.35498 0.0444078
\(932\) 0 0
\(933\) 7.67129 0.251147
\(934\) 0 0
\(935\) 11.3073 0.369787
\(936\) 0 0
\(937\) −60.0003 −1.96013 −0.980063 0.198689i \(-0.936332\pi\)
−0.980063 + 0.198689i \(0.936332\pi\)
\(938\) 0 0
\(939\) −11.9575 −0.390220
\(940\) 0 0
\(941\) −6.70401 −0.218544 −0.109272 0.994012i \(-0.534852\pi\)
−0.109272 + 0.994012i \(0.534852\pi\)
\(942\) 0 0
\(943\) 16.9329 0.551410
\(944\) 0 0
\(945\) 9.94826 0.323617
\(946\) 0 0
\(947\) −8.72414 −0.283496 −0.141748 0.989903i \(-0.545272\pi\)
−0.141748 + 0.989903i \(0.545272\pi\)
\(948\) 0 0
\(949\) −45.9195 −1.49061
\(950\) 0 0
\(951\) 5.15962 0.167312
\(952\) 0 0
\(953\) −7.65381 −0.247931 −0.123966 0.992287i \(-0.539561\pi\)
−0.123966 + 0.992287i \(0.539561\pi\)
\(954\) 0 0
\(955\) 13.0917 0.423637
\(956\) 0 0
\(957\) −12.1697 −0.393391
\(958\) 0 0
\(959\) 4.28170 0.138263
\(960\) 0 0
\(961\) −9.86746 −0.318305
\(962\) 0 0
\(963\) −31.0369 −1.00015
\(964\) 0 0
\(965\) 29.1413 0.938093
\(966\) 0 0
\(967\) 27.6620 0.889549 0.444774 0.895643i \(-0.353284\pi\)
0.444774 + 0.895643i \(0.353284\pi\)
\(968\) 0 0
\(969\) 5.42336 0.174223
\(970\) 0 0
\(971\) 25.3859 0.814672 0.407336 0.913278i \(-0.366458\pi\)
0.407336 + 0.913278i \(0.366458\pi\)
\(972\) 0 0
\(973\) −28.9236 −0.927247
\(974\) 0 0
\(975\) −8.39743 −0.268933
\(976\) 0 0
\(977\) 27.0512 0.865444 0.432722 0.901527i \(-0.357553\pi\)
0.432722 + 0.901527i \(0.357553\pi\)
\(978\) 0 0
\(979\) −30.5405 −0.976079
\(980\) 0 0
\(981\) −14.7664 −0.471456
\(982\) 0 0
\(983\) −55.0126 −1.75463 −0.877315 0.479915i \(-0.840667\pi\)
−0.877315 + 0.479915i \(0.840667\pi\)
\(984\) 0 0
\(985\) −18.9728 −0.604523
\(986\) 0 0
\(987\) 16.7443 0.532976
\(988\) 0 0
\(989\) 15.5752 0.495262
\(990\) 0 0
\(991\) −30.0813 −0.955564 −0.477782 0.878478i \(-0.658559\pi\)
−0.477782 + 0.878478i \(0.658559\pi\)
\(992\) 0 0
\(993\) 0.504133 0.0159982
\(994\) 0 0
\(995\) −9.16714 −0.290618
\(996\) 0 0
\(997\) 20.4955 0.649098 0.324549 0.945869i \(-0.394787\pi\)
0.324549 + 0.945869i \(0.394787\pi\)
\(998\) 0 0
\(999\) 21.1566 0.669365
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 6008.2.a.b.1.29 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.29 44 1.1 even 1 trivial