Properties

Label 6008.2.a.b.1.10
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 1.10
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.12121 q^{3} -1.44700 q^{5} +4.49803 q^{7} +1.49952 q^{9} +O(q^{10})\) \(q-2.12121 q^{3} -1.44700 q^{5} +4.49803 q^{7} +1.49952 q^{9} +6.23238 q^{11} -4.90449 q^{13} +3.06938 q^{15} -4.00488 q^{17} +4.28340 q^{19} -9.54125 q^{21} -0.204761 q^{23} -2.90620 q^{25} +3.18283 q^{27} +2.81689 q^{29} -2.53881 q^{31} -13.2202 q^{33} -6.50863 q^{35} -4.71934 q^{37} +10.4034 q^{39} -5.20105 q^{41} -5.82940 q^{43} -2.16980 q^{45} -9.40255 q^{47} +13.2323 q^{49} +8.49517 q^{51} -6.67576 q^{53} -9.01823 q^{55} -9.08598 q^{57} -8.26497 q^{59} -3.12569 q^{61} +6.74487 q^{63} +7.09678 q^{65} +6.50847 q^{67} +0.434340 q^{69} +10.0115 q^{71} +3.29593 q^{73} +6.16465 q^{75} +28.0334 q^{77} +1.95811 q^{79} -11.2500 q^{81} +15.5377 q^{83} +5.79504 q^{85} -5.97520 q^{87} +0.548772 q^{89} -22.0605 q^{91} +5.38534 q^{93} -6.19806 q^{95} -18.6777 q^{97} +9.34556 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −2.12121 −1.22468 −0.612340 0.790595i \(-0.709771\pi\)
−0.612340 + 0.790595i \(0.709771\pi\)
\(4\) 0 0
\(5\) −1.44700 −0.647116 −0.323558 0.946208i \(-0.604879\pi\)
−0.323558 + 0.946208i \(0.604879\pi\)
\(6\) 0 0
\(7\) 4.49803 1.70009 0.850047 0.526706i \(-0.176573\pi\)
0.850047 + 0.526706i \(0.176573\pi\)
\(8\) 0 0
\(9\) 1.49952 0.499839
\(10\) 0 0
\(11\) 6.23238 1.87913 0.939567 0.342366i \(-0.111228\pi\)
0.939567 + 0.342366i \(0.111228\pi\)
\(12\) 0 0
\(13\) −4.90449 −1.36026 −0.680130 0.733091i \(-0.738077\pi\)
−0.680130 + 0.733091i \(0.738077\pi\)
\(14\) 0 0
\(15\) 3.06938 0.792510
\(16\) 0 0
\(17\) −4.00488 −0.971325 −0.485663 0.874146i \(-0.661422\pi\)
−0.485663 + 0.874146i \(0.661422\pi\)
\(18\) 0 0
\(19\) 4.28340 0.982679 0.491340 0.870968i \(-0.336507\pi\)
0.491340 + 0.870968i \(0.336507\pi\)
\(20\) 0 0
\(21\) −9.54125 −2.08207
\(22\) 0 0
\(23\) −0.204761 −0.0426956 −0.0213478 0.999772i \(-0.506796\pi\)
−0.0213478 + 0.999772i \(0.506796\pi\)
\(24\) 0 0
\(25\) −2.90620 −0.581240
\(26\) 0 0
\(27\) 3.18283 0.612537
\(28\) 0 0
\(29\) 2.81689 0.523083 0.261542 0.965192i \(-0.415769\pi\)
0.261542 + 0.965192i \(0.415769\pi\)
\(30\) 0 0
\(31\) −2.53881 −0.455984 −0.227992 0.973663i \(-0.573216\pi\)
−0.227992 + 0.973663i \(0.573216\pi\)
\(32\) 0 0
\(33\) −13.2202 −2.30134
\(34\) 0 0
\(35\) −6.50863 −1.10016
\(36\) 0 0
\(37\) −4.71934 −0.775854 −0.387927 0.921690i \(-0.626809\pi\)
−0.387927 + 0.921690i \(0.626809\pi\)
\(38\) 0 0
\(39\) 10.4034 1.66588
\(40\) 0 0
\(41\) −5.20105 −0.812267 −0.406133 0.913814i \(-0.633123\pi\)
−0.406133 + 0.913814i \(0.633123\pi\)
\(42\) 0 0
\(43\) −5.82940 −0.888975 −0.444488 0.895785i \(-0.646614\pi\)
−0.444488 + 0.895785i \(0.646614\pi\)
\(44\) 0 0
\(45\) −2.16980 −0.323454
\(46\) 0 0
\(47\) −9.40255 −1.37150 −0.685751 0.727836i \(-0.740526\pi\)
−0.685751 + 0.727836i \(0.740526\pi\)
\(48\) 0 0
\(49\) 13.2323 1.89032
\(50\) 0 0
\(51\) 8.49517 1.18956
\(52\) 0 0
\(53\) −6.67576 −0.916986 −0.458493 0.888698i \(-0.651611\pi\)
−0.458493 + 0.888698i \(0.651611\pi\)
\(54\) 0 0
\(55\) −9.01823 −1.21602
\(56\) 0 0
\(57\) −9.08598 −1.20347
\(58\) 0 0
\(59\) −8.26497 −1.07601 −0.538004 0.842942i \(-0.680821\pi\)
−0.538004 + 0.842942i \(0.680821\pi\)
\(60\) 0 0
\(61\) −3.12569 −0.400204 −0.200102 0.979775i \(-0.564127\pi\)
−0.200102 + 0.979775i \(0.564127\pi\)
\(62\) 0 0
\(63\) 6.74487 0.849774
\(64\) 0 0
\(65\) 7.09678 0.880247
\(66\) 0 0
\(67\) 6.50847 0.795136 0.397568 0.917573i \(-0.369854\pi\)
0.397568 + 0.917573i \(0.369854\pi\)
\(68\) 0 0
\(69\) 0.434340 0.0522884
\(70\) 0 0
\(71\) 10.0115 1.18814 0.594071 0.804413i \(-0.297520\pi\)
0.594071 + 0.804413i \(0.297520\pi\)
\(72\) 0 0
\(73\) 3.29593 0.385759 0.192880 0.981222i \(-0.438217\pi\)
0.192880 + 0.981222i \(0.438217\pi\)
\(74\) 0 0
\(75\) 6.16465 0.711833
\(76\) 0 0
\(77\) 28.0334 3.19470
\(78\) 0 0
\(79\) 1.95811 0.220305 0.110152 0.993915i \(-0.464866\pi\)
0.110152 + 0.993915i \(0.464866\pi\)
\(80\) 0 0
\(81\) −11.2500 −1.25000
\(82\) 0 0
\(83\) 15.5377 1.70549 0.852743 0.522331i \(-0.174938\pi\)
0.852743 + 0.522331i \(0.174938\pi\)
\(84\) 0 0
\(85\) 5.79504 0.628561
\(86\) 0 0
\(87\) −5.97520 −0.640609
\(88\) 0 0
\(89\) 0.548772 0.0581697 0.0290848 0.999577i \(-0.490741\pi\)
0.0290848 + 0.999577i \(0.490741\pi\)
\(90\) 0 0
\(91\) −22.0605 −2.31257
\(92\) 0 0
\(93\) 5.38534 0.558434
\(94\) 0 0
\(95\) −6.19806 −0.635908
\(96\) 0 0
\(97\) −18.6777 −1.89643 −0.948217 0.317622i \(-0.897116\pi\)
−0.948217 + 0.317622i \(0.897116\pi\)
\(98\) 0 0
\(99\) 9.34556 0.939264
\(100\) 0 0
\(101\) 16.5083 1.64264 0.821318 0.570471i \(-0.193239\pi\)
0.821318 + 0.570471i \(0.193239\pi\)
\(102\) 0 0
\(103\) −4.24050 −0.417829 −0.208914 0.977934i \(-0.566993\pi\)
−0.208914 + 0.977934i \(0.566993\pi\)
\(104\) 0 0
\(105\) 13.8061 1.34734
\(106\) 0 0
\(107\) −7.24241 −0.700151 −0.350075 0.936722i \(-0.613844\pi\)
−0.350075 + 0.936722i \(0.613844\pi\)
\(108\) 0 0
\(109\) 1.67672 0.160601 0.0803003 0.996771i \(-0.474412\pi\)
0.0803003 + 0.996771i \(0.474412\pi\)
\(110\) 0 0
\(111\) 10.0107 0.950173
\(112\) 0 0
\(113\) −20.6027 −1.93814 −0.969068 0.246794i \(-0.920623\pi\)
−0.969068 + 0.246794i \(0.920623\pi\)
\(114\) 0 0
\(115\) 0.296288 0.0276290
\(116\) 0 0
\(117\) −7.35436 −0.679911
\(118\) 0 0
\(119\) −18.0140 −1.65134
\(120\) 0 0
\(121\) 27.8426 2.53114
\(122\) 0 0
\(123\) 11.0325 0.994766
\(124\) 0 0
\(125\) 11.4402 1.02325
\(126\) 0 0
\(127\) 8.73852 0.775418 0.387709 0.921782i \(-0.373266\pi\)
0.387709 + 0.921782i \(0.373266\pi\)
\(128\) 0 0
\(129\) 12.3654 1.08871
\(130\) 0 0
\(131\) 7.54410 0.659131 0.329566 0.944133i \(-0.393098\pi\)
0.329566 + 0.944133i \(0.393098\pi\)
\(132\) 0 0
\(133\) 19.2669 1.67065
\(134\) 0 0
\(135\) −4.60555 −0.396383
\(136\) 0 0
\(137\) −15.2211 −1.30043 −0.650213 0.759752i \(-0.725320\pi\)
−0.650213 + 0.759752i \(0.725320\pi\)
\(138\) 0 0
\(139\) −18.5988 −1.57753 −0.788765 0.614695i \(-0.789279\pi\)
−0.788765 + 0.614695i \(0.789279\pi\)
\(140\) 0 0
\(141\) 19.9447 1.67965
\(142\) 0 0
\(143\) −30.5666 −2.55611
\(144\) 0 0
\(145\) −4.07603 −0.338496
\(146\) 0 0
\(147\) −28.0683 −2.31504
\(148\) 0 0
\(149\) 12.0414 0.986472 0.493236 0.869896i \(-0.335814\pi\)
0.493236 + 0.869896i \(0.335814\pi\)
\(150\) 0 0
\(151\) −18.7370 −1.52479 −0.762396 0.647111i \(-0.775977\pi\)
−0.762396 + 0.647111i \(0.775977\pi\)
\(152\) 0 0
\(153\) −6.00538 −0.485506
\(154\) 0 0
\(155\) 3.67365 0.295075
\(156\) 0 0
\(157\) −9.51865 −0.759671 −0.379836 0.925054i \(-0.624019\pi\)
−0.379836 + 0.925054i \(0.624019\pi\)
\(158\) 0 0
\(159\) 14.1607 1.12301
\(160\) 0 0
\(161\) −0.921020 −0.0725865
\(162\) 0 0
\(163\) 15.8737 1.24333 0.621663 0.783285i \(-0.286457\pi\)
0.621663 + 0.783285i \(0.286457\pi\)
\(164\) 0 0
\(165\) 19.1295 1.48923
\(166\) 0 0
\(167\) 22.0856 1.70904 0.854519 0.519420i \(-0.173852\pi\)
0.854519 + 0.519420i \(0.173852\pi\)
\(168\) 0 0
\(169\) 11.0540 0.850308
\(170\) 0 0
\(171\) 6.42303 0.491182
\(172\) 0 0
\(173\) −21.5312 −1.63699 −0.818494 0.574515i \(-0.805191\pi\)
−0.818494 + 0.574515i \(0.805191\pi\)
\(174\) 0 0
\(175\) −13.0722 −0.988163
\(176\) 0 0
\(177\) 17.5317 1.31776
\(178\) 0 0
\(179\) 19.7410 1.47551 0.737757 0.675066i \(-0.235885\pi\)
0.737757 + 0.675066i \(0.235885\pi\)
\(180\) 0 0
\(181\) −0.932550 −0.0693159 −0.0346580 0.999399i \(-0.511034\pi\)
−0.0346580 + 0.999399i \(0.511034\pi\)
\(182\) 0 0
\(183\) 6.63024 0.490122
\(184\) 0 0
\(185\) 6.82887 0.502068
\(186\) 0 0
\(187\) −24.9599 −1.82525
\(188\) 0 0
\(189\) 14.3165 1.04137
\(190\) 0 0
\(191\) −18.0522 −1.30621 −0.653106 0.757267i \(-0.726534\pi\)
−0.653106 + 0.757267i \(0.726534\pi\)
\(192\) 0 0
\(193\) 14.0146 1.00879 0.504395 0.863473i \(-0.331715\pi\)
0.504395 + 0.863473i \(0.331715\pi\)
\(194\) 0 0
\(195\) −15.0537 −1.07802
\(196\) 0 0
\(197\) 5.90958 0.421040 0.210520 0.977590i \(-0.432484\pi\)
0.210520 + 0.977590i \(0.432484\pi\)
\(198\) 0 0
\(199\) 19.7131 1.39742 0.698712 0.715403i \(-0.253757\pi\)
0.698712 + 0.715403i \(0.253757\pi\)
\(200\) 0 0
\(201\) −13.8058 −0.973786
\(202\) 0 0
\(203\) 12.6704 0.889291
\(204\) 0 0
\(205\) 7.52589 0.525631
\(206\) 0 0
\(207\) −0.307042 −0.0213409
\(208\) 0 0
\(209\) 26.6958 1.84659
\(210\) 0 0
\(211\) −20.1423 −1.38666 −0.693328 0.720622i \(-0.743856\pi\)
−0.693328 + 0.720622i \(0.743856\pi\)
\(212\) 0 0
\(213\) −21.2364 −1.45509
\(214\) 0 0
\(215\) 8.43512 0.575271
\(216\) 0 0
\(217\) −11.4196 −0.775215
\(218\) 0 0
\(219\) −6.99135 −0.472431
\(220\) 0 0
\(221\) 19.6419 1.32125
\(222\) 0 0
\(223\) −9.35548 −0.626489 −0.313245 0.949673i \(-0.601416\pi\)
−0.313245 + 0.949673i \(0.601416\pi\)
\(224\) 0 0
\(225\) −4.35790 −0.290527
\(226\) 0 0
\(227\) −16.2781 −1.08041 −0.540207 0.841532i \(-0.681654\pi\)
−0.540207 + 0.841532i \(0.681654\pi\)
\(228\) 0 0
\(229\) −17.4239 −1.15141 −0.575703 0.817659i \(-0.695272\pi\)
−0.575703 + 0.817659i \(0.695272\pi\)
\(230\) 0 0
\(231\) −59.4647 −3.91249
\(232\) 0 0
\(233\) 0.447459 0.0293140 0.0146570 0.999893i \(-0.495334\pi\)
0.0146570 + 0.999893i \(0.495334\pi\)
\(234\) 0 0
\(235\) 13.6055 0.887522
\(236\) 0 0
\(237\) −4.15356 −0.269802
\(238\) 0 0
\(239\) 17.7500 1.14815 0.574077 0.818801i \(-0.305361\pi\)
0.574077 + 0.818801i \(0.305361\pi\)
\(240\) 0 0
\(241\) −13.5592 −0.873424 −0.436712 0.899601i \(-0.643857\pi\)
−0.436712 + 0.899601i \(0.643857\pi\)
\(242\) 0 0
\(243\) 14.3151 0.918312
\(244\) 0 0
\(245\) −19.1470 −1.22326
\(246\) 0 0
\(247\) −21.0079 −1.33670
\(248\) 0 0
\(249\) −32.9587 −2.08867
\(250\) 0 0
\(251\) −23.7844 −1.50126 −0.750629 0.660724i \(-0.770249\pi\)
−0.750629 + 0.660724i \(0.770249\pi\)
\(252\) 0 0
\(253\) −1.27615 −0.0802307
\(254\) 0 0
\(255\) −12.2925 −0.769785
\(256\) 0 0
\(257\) −17.2316 −1.07488 −0.537439 0.843302i \(-0.680608\pi\)
−0.537439 + 0.843302i \(0.680608\pi\)
\(258\) 0 0
\(259\) −21.2277 −1.31903
\(260\) 0 0
\(261\) 4.22397 0.261457
\(262\) 0 0
\(263\) 11.3289 0.698572 0.349286 0.937016i \(-0.386424\pi\)
0.349286 + 0.937016i \(0.386424\pi\)
\(264\) 0 0
\(265\) 9.65980 0.593397
\(266\) 0 0
\(267\) −1.16406 −0.0712392
\(268\) 0 0
\(269\) 29.3592 1.79006 0.895031 0.446005i \(-0.147154\pi\)
0.895031 + 0.446005i \(0.147154\pi\)
\(270\) 0 0
\(271\) −10.2842 −0.624719 −0.312360 0.949964i \(-0.601119\pi\)
−0.312360 + 0.949964i \(0.601119\pi\)
\(272\) 0 0
\(273\) 46.7949 2.83216
\(274\) 0 0
\(275\) −18.1126 −1.09223
\(276\) 0 0
\(277\) −9.69167 −0.582316 −0.291158 0.956675i \(-0.594041\pi\)
−0.291158 + 0.956675i \(0.594041\pi\)
\(278\) 0 0
\(279\) −3.80699 −0.227918
\(280\) 0 0
\(281\) −29.0824 −1.73491 −0.867454 0.497517i \(-0.834245\pi\)
−0.867454 + 0.497517i \(0.834245\pi\)
\(282\) 0 0
\(283\) 4.01631 0.238745 0.119373 0.992850i \(-0.461912\pi\)
0.119373 + 0.992850i \(0.461912\pi\)
\(284\) 0 0
\(285\) 13.1474 0.778783
\(286\) 0 0
\(287\) −23.3944 −1.38093
\(288\) 0 0
\(289\) −0.960965 −0.0565274
\(290\) 0 0
\(291\) 39.6193 2.32252
\(292\) 0 0
\(293\) 3.60325 0.210504 0.105252 0.994446i \(-0.466435\pi\)
0.105252 + 0.994446i \(0.466435\pi\)
\(294\) 0 0
\(295\) 11.9594 0.696302
\(296\) 0 0
\(297\) 19.8366 1.15104
\(298\) 0 0
\(299\) 1.00425 0.0580771
\(300\) 0 0
\(301\) −26.2208 −1.51134
\(302\) 0 0
\(303\) −35.0175 −2.01170
\(304\) 0 0
\(305\) 4.52287 0.258979
\(306\) 0 0
\(307\) −13.3896 −0.764184 −0.382092 0.924124i \(-0.624796\pi\)
−0.382092 + 0.924124i \(0.624796\pi\)
\(308\) 0 0
\(309\) 8.99497 0.511706
\(310\) 0 0
\(311\) −4.82663 −0.273693 −0.136846 0.990592i \(-0.543697\pi\)
−0.136846 + 0.990592i \(0.543697\pi\)
\(312\) 0 0
\(313\) −12.5286 −0.708158 −0.354079 0.935216i \(-0.615206\pi\)
−0.354079 + 0.935216i \(0.615206\pi\)
\(314\) 0 0
\(315\) −9.75980 −0.549903
\(316\) 0 0
\(317\) 3.27657 0.184030 0.0920152 0.995758i \(-0.470669\pi\)
0.0920152 + 0.995758i \(0.470669\pi\)
\(318\) 0 0
\(319\) 17.5559 0.982943
\(320\) 0 0
\(321\) 15.3627 0.857460
\(322\) 0 0
\(323\) −17.1545 −0.954501
\(324\) 0 0
\(325\) 14.2534 0.790638
\(326\) 0 0
\(327\) −3.55667 −0.196684
\(328\) 0 0
\(329\) −42.2929 −2.33168
\(330\) 0 0
\(331\) 9.65832 0.530869 0.265435 0.964129i \(-0.414485\pi\)
0.265435 + 0.964129i \(0.414485\pi\)
\(332\) 0 0
\(333\) −7.07673 −0.387802
\(334\) 0 0
\(335\) −9.41773 −0.514546
\(336\) 0 0
\(337\) 5.34955 0.291409 0.145704 0.989328i \(-0.453455\pi\)
0.145704 + 0.989328i \(0.453455\pi\)
\(338\) 0 0
\(339\) 43.7025 2.37359
\(340\) 0 0
\(341\) −15.8228 −0.856854
\(342\) 0 0
\(343\) 28.0328 1.51363
\(344\) 0 0
\(345\) −0.628488 −0.0338367
\(346\) 0 0
\(347\) −29.8999 −1.60511 −0.802557 0.596576i \(-0.796527\pi\)
−0.802557 + 0.596576i \(0.796527\pi\)
\(348\) 0 0
\(349\) −9.98747 −0.534617 −0.267309 0.963611i \(-0.586134\pi\)
−0.267309 + 0.963611i \(0.586134\pi\)
\(350\) 0 0
\(351\) −15.6102 −0.833209
\(352\) 0 0
\(353\) −35.0208 −1.86397 −0.931985 0.362497i \(-0.881924\pi\)
−0.931985 + 0.362497i \(0.881924\pi\)
\(354\) 0 0
\(355\) −14.4865 −0.768866
\(356\) 0 0
\(357\) 38.2115 2.02237
\(358\) 0 0
\(359\) −12.5783 −0.663855 −0.331927 0.943305i \(-0.607699\pi\)
−0.331927 + 0.943305i \(0.607699\pi\)
\(360\) 0 0
\(361\) −0.652483 −0.0343412
\(362\) 0 0
\(363\) −59.0598 −3.09984
\(364\) 0 0
\(365\) −4.76920 −0.249631
\(366\) 0 0
\(367\) −8.86760 −0.462885 −0.231442 0.972849i \(-0.574344\pi\)
−0.231442 + 0.972849i \(0.574344\pi\)
\(368\) 0 0
\(369\) −7.79906 −0.406003
\(370\) 0 0
\(371\) −30.0277 −1.55896
\(372\) 0 0
\(373\) −20.9957 −1.08712 −0.543559 0.839371i \(-0.682924\pi\)
−0.543559 + 0.839371i \(0.682924\pi\)
\(374\) 0 0
\(375\) −24.2671 −1.25315
\(376\) 0 0
\(377\) −13.8154 −0.711529
\(378\) 0 0
\(379\) 28.4112 1.45939 0.729694 0.683774i \(-0.239663\pi\)
0.729694 + 0.683774i \(0.239663\pi\)
\(380\) 0 0
\(381\) −18.5362 −0.949639
\(382\) 0 0
\(383\) −18.4370 −0.942087 −0.471043 0.882110i \(-0.656122\pi\)
−0.471043 + 0.882110i \(0.656122\pi\)
\(384\) 0 0
\(385\) −40.5643 −2.06735
\(386\) 0 0
\(387\) −8.74129 −0.444345
\(388\) 0 0
\(389\) 13.8738 0.703427 0.351714 0.936108i \(-0.385599\pi\)
0.351714 + 0.936108i \(0.385599\pi\)
\(390\) 0 0
\(391\) 0.820042 0.0414713
\(392\) 0 0
\(393\) −16.0026 −0.807224
\(394\) 0 0
\(395\) −2.83338 −0.142563
\(396\) 0 0
\(397\) −4.16206 −0.208888 −0.104444 0.994531i \(-0.533306\pi\)
−0.104444 + 0.994531i \(0.533306\pi\)
\(398\) 0 0
\(399\) −40.8690 −2.04601
\(400\) 0 0
\(401\) −2.44117 −0.121906 −0.0609532 0.998141i \(-0.519414\pi\)
−0.0609532 + 0.998141i \(0.519414\pi\)
\(402\) 0 0
\(403\) 12.4516 0.620256
\(404\) 0 0
\(405\) 16.2787 0.808896
\(406\) 0 0
\(407\) −29.4127 −1.45793
\(408\) 0 0
\(409\) −29.0807 −1.43795 −0.718974 0.695037i \(-0.755388\pi\)
−0.718974 + 0.695037i \(0.755388\pi\)
\(410\) 0 0
\(411\) 32.2871 1.59260
\(412\) 0 0
\(413\) −37.1761 −1.82931
\(414\) 0 0
\(415\) −22.4830 −1.10365
\(416\) 0 0
\(417\) 39.4519 1.93197
\(418\) 0 0
\(419\) 10.4102 0.508573 0.254286 0.967129i \(-0.418159\pi\)
0.254286 + 0.967129i \(0.418159\pi\)
\(420\) 0 0
\(421\) 14.9229 0.727297 0.363648 0.931536i \(-0.381531\pi\)
0.363648 + 0.931536i \(0.381531\pi\)
\(422\) 0 0
\(423\) −14.0993 −0.685531
\(424\) 0 0
\(425\) 11.6390 0.564573
\(426\) 0 0
\(427\) −14.0595 −0.680385
\(428\) 0 0
\(429\) 64.8381 3.13041
\(430\) 0 0
\(431\) −1.91003 −0.0920030 −0.0460015 0.998941i \(-0.514648\pi\)
−0.0460015 + 0.998941i \(0.514648\pi\)
\(432\) 0 0
\(433\) −16.2367 −0.780288 −0.390144 0.920754i \(-0.627575\pi\)
−0.390144 + 0.920754i \(0.627575\pi\)
\(434\) 0 0
\(435\) 8.64610 0.414549
\(436\) 0 0
\(437\) −0.877072 −0.0419561
\(438\) 0 0
\(439\) −12.9182 −0.616554 −0.308277 0.951297i \(-0.599752\pi\)
−0.308277 + 0.951297i \(0.599752\pi\)
\(440\) 0 0
\(441\) 19.8420 0.944856
\(442\) 0 0
\(443\) 38.9223 1.84926 0.924628 0.380872i \(-0.124376\pi\)
0.924628 + 0.380872i \(0.124376\pi\)
\(444\) 0 0
\(445\) −0.794071 −0.0376426
\(446\) 0 0
\(447\) −25.5423 −1.20811
\(448\) 0 0
\(449\) 3.99677 0.188619 0.0943096 0.995543i \(-0.469936\pi\)
0.0943096 + 0.995543i \(0.469936\pi\)
\(450\) 0 0
\(451\) −32.4149 −1.52636
\(452\) 0 0
\(453\) 39.7450 1.86738
\(454\) 0 0
\(455\) 31.9215 1.49650
\(456\) 0 0
\(457\) −8.08380 −0.378144 −0.189072 0.981963i \(-0.560548\pi\)
−0.189072 + 0.981963i \(0.560548\pi\)
\(458\) 0 0
\(459\) −12.7469 −0.594972
\(460\) 0 0
\(461\) −30.7702 −1.43311 −0.716556 0.697529i \(-0.754283\pi\)
−0.716556 + 0.697529i \(0.754283\pi\)
\(462\) 0 0
\(463\) −8.32658 −0.386969 −0.193485 0.981103i \(-0.561979\pi\)
−0.193485 + 0.981103i \(0.561979\pi\)
\(464\) 0 0
\(465\) −7.79257 −0.361372
\(466\) 0 0
\(467\) 27.9628 1.29396 0.646982 0.762505i \(-0.276031\pi\)
0.646982 + 0.762505i \(0.276031\pi\)
\(468\) 0 0
\(469\) 29.2753 1.35181
\(470\) 0 0
\(471\) 20.1910 0.930354
\(472\) 0 0
\(473\) −36.3310 −1.67050
\(474\) 0 0
\(475\) −12.4484 −0.571173
\(476\) 0 0
\(477\) −10.0104 −0.458345
\(478\) 0 0
\(479\) −1.57546 −0.0719845 −0.0359923 0.999352i \(-0.511459\pi\)
−0.0359923 + 0.999352i \(0.511459\pi\)
\(480\) 0 0
\(481\) 23.1459 1.05536
\(482\) 0 0
\(483\) 1.95367 0.0888952
\(484\) 0 0
\(485\) 27.0266 1.22721
\(486\) 0 0
\(487\) −33.9377 −1.53786 −0.768932 0.639331i \(-0.779211\pi\)
−0.768932 + 0.639331i \(0.779211\pi\)
\(488\) 0 0
\(489\) −33.6714 −1.52267
\(490\) 0 0
\(491\) 15.5487 0.701704 0.350852 0.936431i \(-0.385892\pi\)
0.350852 + 0.936431i \(0.385892\pi\)
\(492\) 0 0
\(493\) −11.2813 −0.508084
\(494\) 0 0
\(495\) −13.5230 −0.607813
\(496\) 0 0
\(497\) 45.0318 2.01995
\(498\) 0 0
\(499\) −15.7538 −0.705237 −0.352618 0.935767i \(-0.614709\pi\)
−0.352618 + 0.935767i \(0.614709\pi\)
\(500\) 0 0
\(501\) −46.8482 −2.09302
\(502\) 0 0
\(503\) 37.7332 1.68244 0.841220 0.540693i \(-0.181838\pi\)
0.841220 + 0.540693i \(0.181838\pi\)
\(504\) 0 0
\(505\) −23.8874 −1.06298
\(506\) 0 0
\(507\) −23.4478 −1.04135
\(508\) 0 0
\(509\) 33.3709 1.47914 0.739570 0.673079i \(-0.235029\pi\)
0.739570 + 0.673079i \(0.235029\pi\)
\(510\) 0 0
\(511\) 14.8252 0.655827
\(512\) 0 0
\(513\) 13.6334 0.601927
\(514\) 0 0
\(515\) 6.13599 0.270384
\(516\) 0 0
\(517\) −58.6003 −2.57724
\(518\) 0 0
\(519\) 45.6722 2.00479
\(520\) 0 0
\(521\) −19.3107 −0.846017 −0.423009 0.906126i \(-0.639026\pi\)
−0.423009 + 0.906126i \(0.639026\pi\)
\(522\) 0 0
\(523\) 40.9844 1.79212 0.896061 0.443931i \(-0.146417\pi\)
0.896061 + 0.443931i \(0.146417\pi\)
\(524\) 0 0
\(525\) 27.7288 1.21018
\(526\) 0 0
\(527\) 10.1676 0.442908
\(528\) 0 0
\(529\) −22.9581 −0.998177
\(530\) 0 0
\(531\) −12.3935 −0.537831
\(532\) 0 0
\(533\) 25.5085 1.10489
\(534\) 0 0
\(535\) 10.4797 0.453079
\(536\) 0 0
\(537\) −41.8748 −1.80703
\(538\) 0 0
\(539\) 82.4684 3.55217
\(540\) 0 0
\(541\) −9.69332 −0.416748 −0.208374 0.978049i \(-0.566817\pi\)
−0.208374 + 0.978049i \(0.566817\pi\)
\(542\) 0 0
\(543\) 1.97813 0.0848898
\(544\) 0 0
\(545\) −2.42621 −0.103927
\(546\) 0 0
\(547\) 22.8915 0.978769 0.489384 0.872068i \(-0.337222\pi\)
0.489384 + 0.872068i \(0.337222\pi\)
\(548\) 0 0
\(549\) −4.68703 −0.200038
\(550\) 0 0
\(551\) 12.0659 0.514023
\(552\) 0 0
\(553\) 8.80763 0.374539
\(554\) 0 0
\(555\) −14.4854 −0.614873
\(556\) 0 0
\(557\) −31.3250 −1.32728 −0.663641 0.748051i \(-0.730990\pi\)
−0.663641 + 0.748051i \(0.730990\pi\)
\(558\) 0 0
\(559\) 28.5902 1.20924
\(560\) 0 0
\(561\) 52.9451 2.23535
\(562\) 0 0
\(563\) 15.2321 0.641955 0.320977 0.947087i \(-0.395989\pi\)
0.320977 + 0.947087i \(0.395989\pi\)
\(564\) 0 0
\(565\) 29.8120 1.25420
\(566\) 0 0
\(567\) −50.6028 −2.12512
\(568\) 0 0
\(569\) −17.4422 −0.731217 −0.365608 0.930769i \(-0.619139\pi\)
−0.365608 + 0.930769i \(0.619139\pi\)
\(570\) 0 0
\(571\) −23.1601 −0.969221 −0.484610 0.874730i \(-0.661039\pi\)
−0.484610 + 0.874730i \(0.661039\pi\)
\(572\) 0 0
\(573\) 38.2924 1.59969
\(574\) 0 0
\(575\) 0.595076 0.0248164
\(576\) 0 0
\(577\) 22.9808 0.956704 0.478352 0.878168i \(-0.341234\pi\)
0.478352 + 0.878168i \(0.341234\pi\)
\(578\) 0 0
\(579\) −29.7278 −1.23544
\(580\) 0 0
\(581\) 69.8890 2.89949
\(582\) 0 0
\(583\) −41.6059 −1.72314
\(584\) 0 0
\(585\) 10.6417 0.439982
\(586\) 0 0
\(587\) −44.1453 −1.82207 −0.911036 0.412327i \(-0.864716\pi\)
−0.911036 + 0.412327i \(0.864716\pi\)
\(588\) 0 0
\(589\) −10.8747 −0.448086
\(590\) 0 0
\(591\) −12.5354 −0.515639
\(592\) 0 0
\(593\) 16.7829 0.689192 0.344596 0.938751i \(-0.388016\pi\)
0.344596 + 0.938751i \(0.388016\pi\)
\(594\) 0 0
\(595\) 26.0663 1.06861
\(596\) 0 0
\(597\) −41.8155 −1.71140
\(598\) 0 0
\(599\) −23.6548 −0.966510 −0.483255 0.875480i \(-0.660546\pi\)
−0.483255 + 0.875480i \(0.660546\pi\)
\(600\) 0 0
\(601\) 5.55765 0.226701 0.113351 0.993555i \(-0.463842\pi\)
0.113351 + 0.993555i \(0.463842\pi\)
\(602\) 0 0
\(603\) 9.75956 0.397440
\(604\) 0 0
\(605\) −40.2881 −1.63794
\(606\) 0 0
\(607\) −31.9555 −1.29703 −0.648517 0.761200i \(-0.724610\pi\)
−0.648517 + 0.761200i \(0.724610\pi\)
\(608\) 0 0
\(609\) −26.8766 −1.08910
\(610\) 0 0
\(611\) 46.1147 1.86560
\(612\) 0 0
\(613\) 18.2622 0.737605 0.368803 0.929508i \(-0.379768\pi\)
0.368803 + 0.929508i \(0.379768\pi\)
\(614\) 0 0
\(615\) −15.9640 −0.643730
\(616\) 0 0
\(617\) −16.9416 −0.682045 −0.341022 0.940055i \(-0.610773\pi\)
−0.341022 + 0.940055i \(0.610773\pi\)
\(618\) 0 0
\(619\) 5.30458 0.213209 0.106605 0.994301i \(-0.466002\pi\)
0.106605 + 0.994301i \(0.466002\pi\)
\(620\) 0 0
\(621\) −0.651720 −0.0261526
\(622\) 0 0
\(623\) 2.46839 0.0988940
\(624\) 0 0
\(625\) −2.02299 −0.0809195
\(626\) 0 0
\(627\) −56.6273 −2.26148
\(628\) 0 0
\(629\) 18.9004 0.753607
\(630\) 0 0
\(631\) 6.29062 0.250425 0.125213 0.992130i \(-0.460039\pi\)
0.125213 + 0.992130i \(0.460039\pi\)
\(632\) 0 0
\(633\) 42.7261 1.69821
\(634\) 0 0
\(635\) −12.6446 −0.501786
\(636\) 0 0
\(637\) −64.8974 −2.57133
\(638\) 0 0
\(639\) 15.0124 0.593879
\(640\) 0 0
\(641\) 35.8546 1.41617 0.708085 0.706127i \(-0.249559\pi\)
0.708085 + 0.706127i \(0.249559\pi\)
\(642\) 0 0
\(643\) −25.9810 −1.02459 −0.512296 0.858809i \(-0.671205\pi\)
−0.512296 + 0.858809i \(0.671205\pi\)
\(644\) 0 0
\(645\) −17.8926 −0.704522
\(646\) 0 0
\(647\) 10.1906 0.400633 0.200317 0.979731i \(-0.435803\pi\)
0.200317 + 0.979731i \(0.435803\pi\)
\(648\) 0 0
\(649\) −51.5104 −2.02196
\(650\) 0 0
\(651\) 24.2234 0.949390
\(652\) 0 0
\(653\) 43.1161 1.68726 0.843631 0.536923i \(-0.180414\pi\)
0.843631 + 0.536923i \(0.180414\pi\)
\(654\) 0 0
\(655\) −10.9163 −0.426535
\(656\) 0 0
\(657\) 4.94230 0.192818
\(658\) 0 0
\(659\) −20.0234 −0.780003 −0.390001 0.920814i \(-0.627525\pi\)
−0.390001 + 0.920814i \(0.627525\pi\)
\(660\) 0 0
\(661\) −41.4419 −1.61190 −0.805952 0.591981i \(-0.798346\pi\)
−0.805952 + 0.591981i \(0.798346\pi\)
\(662\) 0 0
\(663\) −41.6645 −1.61811
\(664\) 0 0
\(665\) −27.8791 −1.08110
\(666\) 0 0
\(667\) −0.576788 −0.0223333
\(668\) 0 0
\(669\) 19.8449 0.767248
\(670\) 0 0
\(671\) −19.4805 −0.752037
\(672\) 0 0
\(673\) 19.7892 0.762818 0.381409 0.924406i \(-0.375439\pi\)
0.381409 + 0.924406i \(0.375439\pi\)
\(674\) 0 0
\(675\) −9.24996 −0.356031
\(676\) 0 0
\(677\) 30.8314 1.18495 0.592474 0.805590i \(-0.298151\pi\)
0.592474 + 0.805590i \(0.298151\pi\)
\(678\) 0 0
\(679\) −84.0129 −3.22412
\(680\) 0 0
\(681\) 34.5291 1.32316
\(682\) 0 0
\(683\) −6.55692 −0.250894 −0.125447 0.992100i \(-0.540036\pi\)
−0.125447 + 0.992100i \(0.540036\pi\)
\(684\) 0 0
\(685\) 22.0249 0.841527
\(686\) 0 0
\(687\) 36.9598 1.41010
\(688\) 0 0
\(689\) 32.7412 1.24734
\(690\) 0 0
\(691\) 21.9353 0.834458 0.417229 0.908801i \(-0.363001\pi\)
0.417229 + 0.908801i \(0.363001\pi\)
\(692\) 0 0
\(693\) 42.0366 1.59684
\(694\) 0 0
\(695\) 26.9124 1.02085
\(696\) 0 0
\(697\) 20.8295 0.788975
\(698\) 0 0
\(699\) −0.949152 −0.0359002
\(700\) 0 0
\(701\) 30.3752 1.14725 0.573627 0.819116i \(-0.305536\pi\)
0.573627 + 0.819116i \(0.305536\pi\)
\(702\) 0 0
\(703\) −20.2148 −0.762416
\(704\) 0 0
\(705\) −28.8600 −1.08693
\(706\) 0 0
\(707\) 74.2547 2.79264
\(708\) 0 0
\(709\) 9.87370 0.370815 0.185407 0.982662i \(-0.440640\pi\)
0.185407 + 0.982662i \(0.440640\pi\)
\(710\) 0 0
\(711\) 2.93622 0.110117
\(712\) 0 0
\(713\) 0.519849 0.0194685
\(714\) 0 0
\(715\) 44.2298 1.65410
\(716\) 0 0
\(717\) −37.6515 −1.40612
\(718\) 0 0
\(719\) 28.8966 1.07766 0.538831 0.842414i \(-0.318866\pi\)
0.538831 + 0.842414i \(0.318866\pi\)
\(720\) 0 0
\(721\) −19.0739 −0.710348
\(722\) 0 0
\(723\) 28.7618 1.06966
\(724\) 0 0
\(725\) −8.18645 −0.304037
\(726\) 0 0
\(727\) −32.4705 −1.20426 −0.602132 0.798397i \(-0.705682\pi\)
−0.602132 + 0.798397i \(0.705682\pi\)
\(728\) 0 0
\(729\) 3.38478 0.125362
\(730\) 0 0
\(731\) 23.3460 0.863484
\(732\) 0 0
\(733\) −24.9948 −0.923206 −0.461603 0.887087i \(-0.652725\pi\)
−0.461603 + 0.887087i \(0.652725\pi\)
\(734\) 0 0
\(735\) 40.6148 1.49810
\(736\) 0 0
\(737\) 40.5633 1.49417
\(738\) 0 0
\(739\) 22.9517 0.844292 0.422146 0.906528i \(-0.361277\pi\)
0.422146 + 0.906528i \(0.361277\pi\)
\(740\) 0 0
\(741\) 44.5621 1.63703
\(742\) 0 0
\(743\) −6.79612 −0.249326 −0.124663 0.992199i \(-0.539785\pi\)
−0.124663 + 0.992199i \(0.539785\pi\)
\(744\) 0 0
\(745\) −17.4239 −0.638362
\(746\) 0 0
\(747\) 23.2991 0.852468
\(748\) 0 0
\(749\) −32.5766 −1.19032
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 50.4516 1.83856
\(754\) 0 0
\(755\) 27.1123 0.986718
\(756\) 0 0
\(757\) 12.4167 0.451294 0.225647 0.974209i \(-0.427550\pi\)
0.225647 + 0.974209i \(0.427550\pi\)
\(758\) 0 0
\(759\) 2.70697 0.0982568
\(760\) 0 0
\(761\) 21.3936 0.775517 0.387759 0.921761i \(-0.373249\pi\)
0.387759 + 0.921761i \(0.373249\pi\)
\(762\) 0 0
\(763\) 7.54193 0.273036
\(764\) 0 0
\(765\) 8.68976 0.314179
\(766\) 0 0
\(767\) 40.5354 1.46365
\(768\) 0 0
\(769\) −47.9517 −1.72918 −0.864591 0.502476i \(-0.832422\pi\)
−0.864591 + 0.502476i \(0.832422\pi\)
\(770\) 0 0
\(771\) 36.5518 1.31638
\(772\) 0 0
\(773\) −39.7485 −1.42965 −0.714827 0.699301i \(-0.753495\pi\)
−0.714827 + 0.699301i \(0.753495\pi\)
\(774\) 0 0
\(775\) 7.37829 0.265036
\(776\) 0 0
\(777\) 45.0284 1.61538
\(778\) 0 0
\(779\) −22.2782 −0.798198
\(780\) 0 0
\(781\) 62.3952 2.23268
\(782\) 0 0
\(783\) 8.96569 0.320408
\(784\) 0 0
\(785\) 13.7735 0.491596
\(786\) 0 0
\(787\) 16.5231 0.588986 0.294493 0.955654i \(-0.404849\pi\)
0.294493 + 0.955654i \(0.404849\pi\)
\(788\) 0 0
\(789\) −24.0310 −0.855527
\(790\) 0 0
\(791\) −92.6714 −3.29501
\(792\) 0 0
\(793\) 15.3299 0.544382
\(794\) 0 0
\(795\) −20.4904 −0.726721
\(796\) 0 0
\(797\) −22.6335 −0.801720 −0.400860 0.916139i \(-0.631289\pi\)
−0.400860 + 0.916139i \(0.631289\pi\)
\(798\) 0 0
\(799\) 37.6560 1.33218
\(800\) 0 0
\(801\) 0.822893 0.0290755
\(802\) 0 0
\(803\) 20.5415 0.724893
\(804\) 0 0
\(805\) 1.33271 0.0469719
\(806\) 0 0
\(807\) −62.2769 −2.19225
\(808\) 0 0
\(809\) −20.2341 −0.711394 −0.355697 0.934601i \(-0.615756\pi\)
−0.355697 + 0.934601i \(0.615756\pi\)
\(810\) 0 0
\(811\) 7.92693 0.278352 0.139176 0.990268i \(-0.455555\pi\)
0.139176 + 0.990268i \(0.455555\pi\)
\(812\) 0 0
\(813\) 21.8149 0.765081
\(814\) 0 0
\(815\) −22.9692 −0.804576
\(816\) 0 0
\(817\) −24.9697 −0.873578
\(818\) 0 0
\(819\) −33.0801 −1.15591
\(820\) 0 0
\(821\) 1.52821 0.0533348 0.0266674 0.999644i \(-0.491510\pi\)
0.0266674 + 0.999644i \(0.491510\pi\)
\(822\) 0 0
\(823\) −3.59428 −0.125289 −0.0626444 0.998036i \(-0.519953\pi\)
−0.0626444 + 0.998036i \(0.519953\pi\)
\(824\) 0 0
\(825\) 38.4205 1.33763
\(826\) 0 0
\(827\) −56.8133 −1.97559 −0.987796 0.155751i \(-0.950220\pi\)
−0.987796 + 0.155751i \(0.950220\pi\)
\(828\) 0 0
\(829\) −54.1202 −1.87967 −0.939836 0.341626i \(-0.889022\pi\)
−0.939836 + 0.341626i \(0.889022\pi\)
\(830\) 0 0
\(831\) 20.5580 0.713150
\(832\) 0 0
\(833\) −52.9935 −1.83612
\(834\) 0 0
\(835\) −31.9578 −1.10595
\(836\) 0 0
\(837\) −8.08061 −0.279307
\(838\) 0 0
\(839\) 11.4490 0.395265 0.197632 0.980276i \(-0.436675\pi\)
0.197632 + 0.980276i \(0.436675\pi\)
\(840\) 0 0
\(841\) −21.0651 −0.726384
\(842\) 0 0
\(843\) 61.6897 2.12471
\(844\) 0 0
\(845\) −15.9951 −0.550248
\(846\) 0 0
\(847\) 125.237 4.30318
\(848\) 0 0
\(849\) −8.51943 −0.292386
\(850\) 0 0
\(851\) 0.966335 0.0331255
\(852\) 0 0
\(853\) −11.4782 −0.393005 −0.196502 0.980503i \(-0.562958\pi\)
−0.196502 + 0.980503i \(0.562958\pi\)
\(854\) 0 0
\(855\) −9.29410 −0.317852
\(856\) 0 0
\(857\) 39.3316 1.34354 0.671772 0.740758i \(-0.265534\pi\)
0.671772 + 0.740758i \(0.265534\pi\)
\(858\) 0 0
\(859\) −2.41706 −0.0824691 −0.0412346 0.999149i \(-0.513129\pi\)
−0.0412346 + 0.999149i \(0.513129\pi\)
\(860\) 0 0
\(861\) 49.6245 1.69120
\(862\) 0 0
\(863\) 38.5509 1.31229 0.656144 0.754636i \(-0.272186\pi\)
0.656144 + 0.754636i \(0.272186\pi\)
\(864\) 0 0
\(865\) 31.1556 1.05932
\(866\) 0 0
\(867\) 2.03841 0.0692279
\(868\) 0 0
\(869\) 12.2037 0.413982
\(870\) 0 0
\(871\) −31.9207 −1.08159
\(872\) 0 0
\(873\) −28.0076 −0.947912
\(874\) 0 0
\(875\) 51.4585 1.73962
\(876\) 0 0
\(877\) −30.2377 −1.02105 −0.510527 0.859862i \(-0.670550\pi\)
−0.510527 + 0.859862i \(0.670550\pi\)
\(878\) 0 0
\(879\) −7.64325 −0.257800
\(880\) 0 0
\(881\) 7.39401 0.249110 0.124555 0.992213i \(-0.460250\pi\)
0.124555 + 0.992213i \(0.460250\pi\)
\(882\) 0 0
\(883\) 36.7205 1.23574 0.617872 0.786278i \(-0.287995\pi\)
0.617872 + 0.786278i \(0.287995\pi\)
\(884\) 0 0
\(885\) −25.3683 −0.852747
\(886\) 0 0
\(887\) 41.8257 1.40437 0.702184 0.711995i \(-0.252208\pi\)
0.702184 + 0.711995i \(0.252208\pi\)
\(888\) 0 0
\(889\) 39.3061 1.31828
\(890\) 0 0
\(891\) −70.1143 −2.34892
\(892\) 0 0
\(893\) −40.2749 −1.34775
\(894\) 0 0
\(895\) −28.5652 −0.954830
\(896\) 0 0
\(897\) −2.13021 −0.0711258
\(898\) 0 0
\(899\) −7.15155 −0.238517
\(900\) 0 0
\(901\) 26.7356 0.890692
\(902\) 0 0
\(903\) 55.6197 1.85091
\(904\) 0 0
\(905\) 1.34940 0.0448555
\(906\) 0 0
\(907\) −3.58094 −0.118903 −0.0594517 0.998231i \(-0.518935\pi\)
−0.0594517 + 0.998231i \(0.518935\pi\)
\(908\) 0 0
\(909\) 24.7544 0.821053
\(910\) 0 0
\(911\) 24.6586 0.816977 0.408489 0.912763i \(-0.366056\pi\)
0.408489 + 0.912763i \(0.366056\pi\)
\(912\) 0 0
\(913\) 96.8369 3.20483
\(914\) 0 0
\(915\) −9.59394 −0.317166
\(916\) 0 0
\(917\) 33.9336 1.12059
\(918\) 0 0
\(919\) −12.9673 −0.427751 −0.213875 0.976861i \(-0.568609\pi\)
−0.213875 + 0.976861i \(0.568609\pi\)
\(920\) 0 0
\(921\) 28.4021 0.935881
\(922\) 0 0
\(923\) −49.1011 −1.61618
\(924\) 0 0
\(925\) 13.7153 0.450958
\(926\) 0 0
\(927\) −6.35870 −0.208847
\(928\) 0 0
\(929\) 7.52621 0.246927 0.123464 0.992349i \(-0.460600\pi\)
0.123464 + 0.992349i \(0.460600\pi\)
\(930\) 0 0
\(931\) 56.6790 1.85758
\(932\) 0 0
\(933\) 10.2383 0.335186
\(934\) 0 0
\(935\) 36.1169 1.18115
\(936\) 0 0
\(937\) 19.8176 0.647414 0.323707 0.946157i \(-0.395071\pi\)
0.323707 + 0.946157i \(0.395071\pi\)
\(938\) 0 0
\(939\) 26.5757 0.867266
\(940\) 0 0
\(941\) −6.08628 −0.198407 −0.0992036 0.995067i \(-0.531630\pi\)
−0.0992036 + 0.995067i \(0.531630\pi\)
\(942\) 0 0
\(943\) 1.06497 0.0346802
\(944\) 0 0
\(945\) −20.7159 −0.673888
\(946\) 0 0
\(947\) 49.8736 1.62068 0.810338 0.585963i \(-0.199284\pi\)
0.810338 + 0.585963i \(0.199284\pi\)
\(948\) 0 0
\(949\) −16.1648 −0.524733
\(950\) 0 0
\(951\) −6.95027 −0.225378
\(952\) 0 0
\(953\) 8.30962 0.269175 0.134588 0.990902i \(-0.457029\pi\)
0.134588 + 0.990902i \(0.457029\pi\)
\(954\) 0 0
\(955\) 26.1215 0.845271
\(956\) 0 0
\(957\) −37.2398 −1.20379
\(958\) 0 0
\(959\) −68.4649 −2.21085
\(960\) 0 0
\(961\) −24.5544 −0.792079
\(962\) 0 0
\(963\) −10.8601 −0.349963
\(964\) 0 0
\(965\) −20.2790 −0.652805
\(966\) 0 0
\(967\) 42.9990 1.38275 0.691377 0.722494i \(-0.257004\pi\)
0.691377 + 0.722494i \(0.257004\pi\)
\(968\) 0 0
\(969\) 36.3882 1.16896
\(970\) 0 0
\(971\) −30.8598 −0.990339 −0.495170 0.868796i \(-0.664894\pi\)
−0.495170 + 0.868796i \(0.664894\pi\)
\(972\) 0 0
\(973\) −83.6579 −2.68195
\(974\) 0 0
\(975\) −30.2345 −0.968278
\(976\) 0 0
\(977\) 17.5323 0.560909 0.280455 0.959867i \(-0.409515\pi\)
0.280455 + 0.959867i \(0.409515\pi\)
\(978\) 0 0
\(979\) 3.42016 0.109309
\(980\) 0 0
\(981\) 2.51427 0.0802744
\(982\) 0 0
\(983\) 43.6457 1.39208 0.696040 0.718003i \(-0.254944\pi\)
0.696040 + 0.718003i \(0.254944\pi\)
\(984\) 0 0
\(985\) −8.55114 −0.272462
\(986\) 0 0
\(987\) 89.7120 2.85556
\(988\) 0 0
\(989\) 1.19363 0.0379553
\(990\) 0 0
\(991\) 29.8081 0.946886 0.473443 0.880824i \(-0.343011\pi\)
0.473443 + 0.880824i \(0.343011\pi\)
\(992\) 0 0
\(993\) −20.4873 −0.650145
\(994\) 0 0
\(995\) −28.5248 −0.904296
\(996\) 0 0
\(997\) 15.9402 0.504833 0.252416 0.967619i \(-0.418775\pi\)
0.252416 + 0.967619i \(0.418775\pi\)
\(998\) 0 0
\(999\) −15.0209 −0.475239
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.1.10 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.10 44 1.1 even 1 trivial