Properties

Label 6008.2.a.b.1.14
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 1.14
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.75295 q^{3} +1.89627 q^{5} -3.72975 q^{7} +0.0728254 q^{9} +O(q^{10})\) \(q-1.75295 q^{3} +1.89627 q^{5} -3.72975 q^{7} +0.0728254 q^{9} +5.05766 q^{11} +3.05514 q^{13} -3.32407 q^{15} +0.674403 q^{17} -1.01821 q^{19} +6.53805 q^{21} -4.16593 q^{23} -1.40415 q^{25} +5.13118 q^{27} -6.08203 q^{29} +1.11741 q^{31} -8.86581 q^{33} -7.07262 q^{35} -8.11392 q^{37} -5.35549 q^{39} +9.59261 q^{41} -10.0470 q^{43} +0.138097 q^{45} -2.58604 q^{47} +6.91102 q^{49} -1.18219 q^{51} +8.96148 q^{53} +9.59070 q^{55} +1.78487 q^{57} -4.15484 q^{59} +7.74161 q^{61} -0.271620 q^{63} +5.79337 q^{65} -4.80625 q^{67} +7.30266 q^{69} -8.83390 q^{71} -0.804911 q^{73} +2.46140 q^{75} -18.8638 q^{77} +14.9038 q^{79} -9.21317 q^{81} +0.249592 q^{83} +1.27885 q^{85} +10.6615 q^{87} +12.3114 q^{89} -11.3949 q^{91} -1.95876 q^{93} -1.93081 q^{95} +6.87353 q^{97} +0.368326 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −1.75295 −1.01206 −0.506032 0.862514i \(-0.668888\pi\)
−0.506032 + 0.862514i \(0.668888\pi\)
\(4\) 0 0
\(5\) 1.89627 0.848039 0.424020 0.905653i \(-0.360619\pi\)
0.424020 + 0.905653i \(0.360619\pi\)
\(6\) 0 0
\(7\) −3.72975 −1.40971 −0.704856 0.709350i \(-0.748989\pi\)
−0.704856 + 0.709350i \(0.748989\pi\)
\(8\) 0 0
\(9\) 0.0728254 0.0242751
\(10\) 0 0
\(11\) 5.05766 1.52494 0.762471 0.647023i \(-0.223986\pi\)
0.762471 + 0.647023i \(0.223986\pi\)
\(12\) 0 0
\(13\) 3.05514 0.847342 0.423671 0.905816i \(-0.360741\pi\)
0.423671 + 0.905816i \(0.360741\pi\)
\(14\) 0 0
\(15\) −3.32407 −0.858271
\(16\) 0 0
\(17\) 0.674403 0.163567 0.0817834 0.996650i \(-0.473938\pi\)
0.0817834 + 0.996650i \(0.473938\pi\)
\(18\) 0 0
\(19\) −1.01821 −0.233594 −0.116797 0.993156i \(-0.537263\pi\)
−0.116797 + 0.993156i \(0.537263\pi\)
\(20\) 0 0
\(21\) 6.53805 1.42672
\(22\) 0 0
\(23\) −4.16593 −0.868657 −0.434329 0.900754i \(-0.643014\pi\)
−0.434329 + 0.900754i \(0.643014\pi\)
\(24\) 0 0
\(25\) −1.40415 −0.280829
\(26\) 0 0
\(27\) 5.13118 0.987497
\(28\) 0 0
\(29\) −6.08203 −1.12940 −0.564702 0.825295i \(-0.691009\pi\)
−0.564702 + 0.825295i \(0.691009\pi\)
\(30\) 0 0
\(31\) 1.11741 0.200693 0.100346 0.994953i \(-0.468005\pi\)
0.100346 + 0.994953i \(0.468005\pi\)
\(32\) 0 0
\(33\) −8.86581 −1.54334
\(34\) 0 0
\(35\) −7.07262 −1.19549
\(36\) 0 0
\(37\) −8.11392 −1.33392 −0.666960 0.745093i \(-0.732405\pi\)
−0.666960 + 0.745093i \(0.732405\pi\)
\(38\) 0 0
\(39\) −5.35549 −0.857565
\(40\) 0 0
\(41\) 9.59261 1.49811 0.749057 0.662505i \(-0.230507\pi\)
0.749057 + 0.662505i \(0.230507\pi\)
\(42\) 0 0
\(43\) −10.0470 −1.53216 −0.766080 0.642745i \(-0.777796\pi\)
−0.766080 + 0.642745i \(0.777796\pi\)
\(44\) 0 0
\(45\) 0.138097 0.0205863
\(46\) 0 0
\(47\) −2.58604 −0.377212 −0.188606 0.982053i \(-0.560397\pi\)
−0.188606 + 0.982053i \(0.560397\pi\)
\(48\) 0 0
\(49\) 6.91102 0.987289
\(50\) 0 0
\(51\) −1.18219 −0.165540
\(52\) 0 0
\(53\) 8.96148 1.23095 0.615477 0.788155i \(-0.288963\pi\)
0.615477 + 0.788155i \(0.288963\pi\)
\(54\) 0 0
\(55\) 9.59070 1.29321
\(56\) 0 0
\(57\) 1.78487 0.236412
\(58\) 0 0
\(59\) −4.15484 −0.540914 −0.270457 0.962732i \(-0.587175\pi\)
−0.270457 + 0.962732i \(0.587175\pi\)
\(60\) 0 0
\(61\) 7.74161 0.991212 0.495606 0.868548i \(-0.334946\pi\)
0.495606 + 0.868548i \(0.334946\pi\)
\(62\) 0 0
\(63\) −0.271620 −0.0342210
\(64\) 0 0
\(65\) 5.79337 0.718580
\(66\) 0 0
\(67\) −4.80625 −0.587176 −0.293588 0.955932i \(-0.594849\pi\)
−0.293588 + 0.955932i \(0.594849\pi\)
\(68\) 0 0
\(69\) 7.30266 0.879138
\(70\) 0 0
\(71\) −8.83390 −1.04839 −0.524196 0.851598i \(-0.675634\pi\)
−0.524196 + 0.851598i \(0.675634\pi\)
\(72\) 0 0
\(73\) −0.804911 −0.0942077 −0.0471038 0.998890i \(-0.514999\pi\)
−0.0471038 + 0.998890i \(0.514999\pi\)
\(74\) 0 0
\(75\) 2.46140 0.284218
\(76\) 0 0
\(77\) −18.8638 −2.14973
\(78\) 0 0
\(79\) 14.9038 1.67681 0.838403 0.545051i \(-0.183490\pi\)
0.838403 + 0.545051i \(0.183490\pi\)
\(80\) 0 0
\(81\) −9.21317 −1.02369
\(82\) 0 0
\(83\) 0.249592 0.0273962 0.0136981 0.999906i \(-0.495640\pi\)
0.0136981 + 0.999906i \(0.495640\pi\)
\(84\) 0 0
\(85\) 1.27885 0.138711
\(86\) 0 0
\(87\) 10.6615 1.14303
\(88\) 0 0
\(89\) 12.3114 1.30500 0.652502 0.757787i \(-0.273720\pi\)
0.652502 + 0.757787i \(0.273720\pi\)
\(90\) 0 0
\(91\) −11.3949 −1.19451
\(92\) 0 0
\(93\) −1.95876 −0.203114
\(94\) 0 0
\(95\) −1.93081 −0.198096
\(96\) 0 0
\(97\) 6.87353 0.697902 0.348951 0.937141i \(-0.386538\pi\)
0.348951 + 0.937141i \(0.386538\pi\)
\(98\) 0 0
\(99\) 0.368326 0.0370181
\(100\) 0 0
\(101\) 10.0233 0.997357 0.498679 0.866787i \(-0.333819\pi\)
0.498679 + 0.866787i \(0.333819\pi\)
\(102\) 0 0
\(103\) −4.61332 −0.454564 −0.227282 0.973829i \(-0.572984\pi\)
−0.227282 + 0.973829i \(0.572984\pi\)
\(104\) 0 0
\(105\) 12.3979 1.20991
\(106\) 0 0
\(107\) −3.80702 −0.368038 −0.184019 0.982923i \(-0.558911\pi\)
−0.184019 + 0.982923i \(0.558911\pi\)
\(108\) 0 0
\(109\) 19.4008 1.85826 0.929132 0.369748i \(-0.120556\pi\)
0.929132 + 0.369748i \(0.120556\pi\)
\(110\) 0 0
\(111\) 14.2233 1.35001
\(112\) 0 0
\(113\) 8.43393 0.793398 0.396699 0.917949i \(-0.370156\pi\)
0.396699 + 0.917949i \(0.370156\pi\)
\(114\) 0 0
\(115\) −7.89975 −0.736656
\(116\) 0 0
\(117\) 0.222491 0.0205693
\(118\) 0 0
\(119\) −2.51535 −0.230582
\(120\) 0 0
\(121\) 14.5799 1.32545
\(122\) 0 0
\(123\) −16.8153 −1.51619
\(124\) 0 0
\(125\) −12.1440 −1.08619
\(126\) 0 0
\(127\) 7.73505 0.686375 0.343188 0.939267i \(-0.388493\pi\)
0.343188 + 0.939267i \(0.388493\pi\)
\(128\) 0 0
\(129\) 17.6120 1.55065
\(130\) 0 0
\(131\) −19.7474 −1.72534 −0.862671 0.505766i \(-0.831210\pi\)
−0.862671 + 0.505766i \(0.831210\pi\)
\(132\) 0 0
\(133\) 3.79767 0.329300
\(134\) 0 0
\(135\) 9.73013 0.837436
\(136\) 0 0
\(137\) −20.4120 −1.74392 −0.871958 0.489581i \(-0.837150\pi\)
−0.871958 + 0.489581i \(0.837150\pi\)
\(138\) 0 0
\(139\) −17.7041 −1.50165 −0.750823 0.660504i \(-0.770343\pi\)
−0.750823 + 0.660504i \(0.770343\pi\)
\(140\) 0 0
\(141\) 4.53319 0.381763
\(142\) 0 0
\(143\) 15.4518 1.29215
\(144\) 0 0
\(145\) −11.5332 −0.957780
\(146\) 0 0
\(147\) −12.1147 −0.999201
\(148\) 0 0
\(149\) −17.3952 −1.42507 −0.712535 0.701637i \(-0.752453\pi\)
−0.712535 + 0.701637i \(0.752453\pi\)
\(150\) 0 0
\(151\) −21.2179 −1.72669 −0.863343 0.504618i \(-0.831633\pi\)
−0.863343 + 0.504618i \(0.831633\pi\)
\(152\) 0 0
\(153\) 0.0491136 0.00397060
\(154\) 0 0
\(155\) 2.11892 0.170196
\(156\) 0 0
\(157\) −20.3389 −1.62322 −0.811611 0.584198i \(-0.801409\pi\)
−0.811611 + 0.584198i \(0.801409\pi\)
\(158\) 0 0
\(159\) −15.7090 −1.24581
\(160\) 0 0
\(161\) 15.5379 1.22456
\(162\) 0 0
\(163\) −4.27200 −0.334609 −0.167305 0.985905i \(-0.553506\pi\)
−0.167305 + 0.985905i \(0.553506\pi\)
\(164\) 0 0
\(165\) −16.8120 −1.30881
\(166\) 0 0
\(167\) −4.05645 −0.313897 −0.156949 0.987607i \(-0.550166\pi\)
−0.156949 + 0.987607i \(0.550166\pi\)
\(168\) 0 0
\(169\) −3.66614 −0.282011
\(170\) 0 0
\(171\) −0.0741516 −0.00567051
\(172\) 0 0
\(173\) 3.26919 0.248552 0.124276 0.992248i \(-0.460339\pi\)
0.124276 + 0.992248i \(0.460339\pi\)
\(174\) 0 0
\(175\) 5.23712 0.395889
\(176\) 0 0
\(177\) 7.28322 0.547440
\(178\) 0 0
\(179\) −14.9313 −1.11602 −0.558010 0.829834i \(-0.688435\pi\)
−0.558010 + 0.829834i \(0.688435\pi\)
\(180\) 0 0
\(181\) 25.0446 1.86155 0.930776 0.365589i \(-0.119132\pi\)
0.930776 + 0.365589i \(0.119132\pi\)
\(182\) 0 0
\(183\) −13.5706 −1.00317
\(184\) 0 0
\(185\) −15.3862 −1.13122
\(186\) 0 0
\(187\) 3.41090 0.249430
\(188\) 0 0
\(189\) −19.1380 −1.39209
\(190\) 0 0
\(191\) −23.2734 −1.68401 −0.842003 0.539474i \(-0.818623\pi\)
−0.842003 + 0.539474i \(0.818623\pi\)
\(192\) 0 0
\(193\) −16.9863 −1.22270 −0.611351 0.791360i \(-0.709373\pi\)
−0.611351 + 0.791360i \(0.709373\pi\)
\(194\) 0 0
\(195\) −10.1555 −0.727249
\(196\) 0 0
\(197\) 1.57953 0.112537 0.0562684 0.998416i \(-0.482080\pi\)
0.0562684 + 0.998416i \(0.482080\pi\)
\(198\) 0 0
\(199\) 2.57289 0.182387 0.0911937 0.995833i \(-0.470932\pi\)
0.0911937 + 0.995833i \(0.470932\pi\)
\(200\) 0 0
\(201\) 8.42510 0.594261
\(202\) 0 0
\(203\) 22.6844 1.59214
\(204\) 0 0
\(205\) 18.1902 1.27046
\(206\) 0 0
\(207\) −0.303386 −0.0210868
\(208\) 0 0
\(209\) −5.14976 −0.356216
\(210\) 0 0
\(211\) 11.8435 0.815341 0.407670 0.913129i \(-0.366341\pi\)
0.407670 + 0.913129i \(0.366341\pi\)
\(212\) 0 0
\(213\) 15.4854 1.06104
\(214\) 0 0
\(215\) −19.0520 −1.29933
\(216\) 0 0
\(217\) −4.16766 −0.282919
\(218\) 0 0
\(219\) 1.41097 0.0953443
\(220\) 0 0
\(221\) 2.06039 0.138597
\(222\) 0 0
\(223\) 18.8211 1.26035 0.630176 0.776453i \(-0.282983\pi\)
0.630176 + 0.776453i \(0.282983\pi\)
\(224\) 0 0
\(225\) −0.102258 −0.00681717
\(226\) 0 0
\(227\) 14.0465 0.932298 0.466149 0.884706i \(-0.345641\pi\)
0.466149 + 0.884706i \(0.345641\pi\)
\(228\) 0 0
\(229\) −11.6081 −0.767082 −0.383541 0.923524i \(-0.625296\pi\)
−0.383541 + 0.923524i \(0.625296\pi\)
\(230\) 0 0
\(231\) 33.0672 2.17566
\(232\) 0 0
\(233\) −28.1822 −1.84628 −0.923140 0.384465i \(-0.874386\pi\)
−0.923140 + 0.384465i \(0.874386\pi\)
\(234\) 0 0
\(235\) −4.90383 −0.319891
\(236\) 0 0
\(237\) −26.1255 −1.69704
\(238\) 0 0
\(239\) 21.2865 1.37691 0.688453 0.725280i \(-0.258290\pi\)
0.688453 + 0.725280i \(0.258290\pi\)
\(240\) 0 0
\(241\) 10.7858 0.694775 0.347387 0.937722i \(-0.387069\pi\)
0.347387 + 0.937722i \(0.387069\pi\)
\(242\) 0 0
\(243\) 0.756658 0.0485396
\(244\) 0 0
\(245\) 13.1052 0.837260
\(246\) 0 0
\(247\) −3.11077 −0.197934
\(248\) 0 0
\(249\) −0.437521 −0.0277268
\(250\) 0 0
\(251\) −12.9565 −0.817809 −0.408904 0.912577i \(-0.634089\pi\)
−0.408904 + 0.912577i \(0.634089\pi\)
\(252\) 0 0
\(253\) −21.0699 −1.32465
\(254\) 0 0
\(255\) −2.24176 −0.140385
\(256\) 0 0
\(257\) −6.37178 −0.397461 −0.198730 0.980054i \(-0.563682\pi\)
−0.198730 + 0.980054i \(0.563682\pi\)
\(258\) 0 0
\(259\) 30.2629 1.88044
\(260\) 0 0
\(261\) −0.442926 −0.0274164
\(262\) 0 0
\(263\) −18.6530 −1.15019 −0.575096 0.818086i \(-0.695035\pi\)
−0.575096 + 0.818086i \(0.695035\pi\)
\(264\) 0 0
\(265\) 16.9934 1.04390
\(266\) 0 0
\(267\) −21.5812 −1.32075
\(268\) 0 0
\(269\) −1.13990 −0.0695012 −0.0347506 0.999396i \(-0.511064\pi\)
−0.0347506 + 0.999396i \(0.511064\pi\)
\(270\) 0 0
\(271\) 18.3880 1.11699 0.558496 0.829507i \(-0.311379\pi\)
0.558496 + 0.829507i \(0.311379\pi\)
\(272\) 0 0
\(273\) 19.9746 1.20892
\(274\) 0 0
\(275\) −7.10169 −0.428248
\(276\) 0 0
\(277\) −20.4534 −1.22893 −0.614464 0.788945i \(-0.710628\pi\)
−0.614464 + 0.788945i \(0.710628\pi\)
\(278\) 0 0
\(279\) 0.0813759 0.00487185
\(280\) 0 0
\(281\) −8.10109 −0.483270 −0.241635 0.970367i \(-0.577684\pi\)
−0.241635 + 0.970367i \(0.577684\pi\)
\(282\) 0 0
\(283\) −21.0613 −1.25197 −0.625983 0.779837i \(-0.715302\pi\)
−0.625983 + 0.779837i \(0.715302\pi\)
\(284\) 0 0
\(285\) 3.38460 0.200486
\(286\) 0 0
\(287\) −35.7780 −2.11191
\(288\) 0 0
\(289\) −16.5452 −0.973246
\(290\) 0 0
\(291\) −12.0489 −0.706322
\(292\) 0 0
\(293\) −4.42170 −0.258319 −0.129159 0.991624i \(-0.541228\pi\)
−0.129159 + 0.991624i \(0.541228\pi\)
\(294\) 0 0
\(295\) −7.87872 −0.458717
\(296\) 0 0
\(297\) 25.9518 1.50587
\(298\) 0 0
\(299\) −12.7275 −0.736050
\(300\) 0 0
\(301\) 37.4730 2.15991
\(302\) 0 0
\(303\) −17.5703 −1.00939
\(304\) 0 0
\(305\) 14.6802 0.840586
\(306\) 0 0
\(307\) −20.7882 −1.18645 −0.593223 0.805038i \(-0.702145\pi\)
−0.593223 + 0.805038i \(0.702145\pi\)
\(308\) 0 0
\(309\) 8.08691 0.460048
\(310\) 0 0
\(311\) 14.8137 0.840006 0.420003 0.907523i \(-0.362029\pi\)
0.420003 + 0.907523i \(0.362029\pi\)
\(312\) 0 0
\(313\) −7.25930 −0.410320 −0.205160 0.978728i \(-0.565772\pi\)
−0.205160 + 0.978728i \(0.565772\pi\)
\(314\) 0 0
\(315\) −0.515067 −0.0290207
\(316\) 0 0
\(317\) 9.56337 0.537133 0.268566 0.963261i \(-0.413450\pi\)
0.268566 + 0.963261i \(0.413450\pi\)
\(318\) 0 0
\(319\) −30.7608 −1.72228
\(320\) 0 0
\(321\) 6.67351 0.372479
\(322\) 0 0
\(323\) −0.686684 −0.0382081
\(324\) 0 0
\(325\) −4.28986 −0.237959
\(326\) 0 0
\(327\) −34.0087 −1.88068
\(328\) 0 0
\(329\) 9.64527 0.531761
\(330\) 0 0
\(331\) 2.48873 0.136793 0.0683966 0.997658i \(-0.478212\pi\)
0.0683966 + 0.997658i \(0.478212\pi\)
\(332\) 0 0
\(333\) −0.590899 −0.0323811
\(334\) 0 0
\(335\) −9.11396 −0.497949
\(336\) 0 0
\(337\) −15.6733 −0.853778 −0.426889 0.904304i \(-0.640391\pi\)
−0.426889 + 0.904304i \(0.640391\pi\)
\(338\) 0 0
\(339\) −14.7842 −0.802970
\(340\) 0 0
\(341\) 5.65148 0.306045
\(342\) 0 0
\(343\) 0.331855 0.0179185
\(344\) 0 0
\(345\) 13.8478 0.745543
\(346\) 0 0
\(347\) −15.2317 −0.817680 −0.408840 0.912606i \(-0.634067\pi\)
−0.408840 + 0.912606i \(0.634067\pi\)
\(348\) 0 0
\(349\) −31.4164 −1.68168 −0.840839 0.541285i \(-0.817938\pi\)
−0.840839 + 0.541285i \(0.817938\pi\)
\(350\) 0 0
\(351\) 15.6765 0.836748
\(352\) 0 0
\(353\) 32.7629 1.74379 0.871895 0.489692i \(-0.162891\pi\)
0.871895 + 0.489692i \(0.162891\pi\)
\(354\) 0 0
\(355\) −16.7515 −0.889077
\(356\) 0 0
\(357\) 4.40928 0.233364
\(358\) 0 0
\(359\) −9.09599 −0.480068 −0.240034 0.970764i \(-0.577159\pi\)
−0.240034 + 0.970764i \(0.577159\pi\)
\(360\) 0 0
\(361\) −17.9632 −0.945434
\(362\) 0 0
\(363\) −25.5578 −1.34144
\(364\) 0 0
\(365\) −1.52633 −0.0798918
\(366\) 0 0
\(367\) 12.4768 0.651286 0.325643 0.945493i \(-0.394419\pi\)
0.325643 + 0.945493i \(0.394419\pi\)
\(368\) 0 0
\(369\) 0.698586 0.0363669
\(370\) 0 0
\(371\) −33.4241 −1.73529
\(372\) 0 0
\(373\) 13.0722 0.676853 0.338427 0.940993i \(-0.390105\pi\)
0.338427 + 0.940993i \(0.390105\pi\)
\(374\) 0 0
\(375\) 21.2878 1.09930
\(376\) 0 0
\(377\) −18.5814 −0.956992
\(378\) 0 0
\(379\) 6.50610 0.334196 0.167098 0.985940i \(-0.446560\pi\)
0.167098 + 0.985940i \(0.446560\pi\)
\(380\) 0 0
\(381\) −13.5591 −0.694656
\(382\) 0 0
\(383\) 22.3960 1.14438 0.572190 0.820121i \(-0.306094\pi\)
0.572190 + 0.820121i \(0.306094\pi\)
\(384\) 0 0
\(385\) −35.7709 −1.82305
\(386\) 0 0
\(387\) −0.731680 −0.0371934
\(388\) 0 0
\(389\) −16.4682 −0.834969 −0.417485 0.908684i \(-0.637088\pi\)
−0.417485 + 0.908684i \(0.637088\pi\)
\(390\) 0 0
\(391\) −2.80952 −0.142083
\(392\) 0 0
\(393\) 34.6162 1.74616
\(394\) 0 0
\(395\) 28.2616 1.42200
\(396\) 0 0
\(397\) −3.63052 −0.182210 −0.0911052 0.995841i \(-0.529040\pi\)
−0.0911052 + 0.995841i \(0.529040\pi\)
\(398\) 0 0
\(399\) −6.65712 −0.333273
\(400\) 0 0
\(401\) 24.0461 1.20081 0.600403 0.799698i \(-0.295007\pi\)
0.600403 + 0.799698i \(0.295007\pi\)
\(402\) 0 0
\(403\) 3.41384 0.170056
\(404\) 0 0
\(405\) −17.4707 −0.868126
\(406\) 0 0
\(407\) −41.0374 −2.03415
\(408\) 0 0
\(409\) −27.6023 −1.36485 −0.682423 0.730957i \(-0.739074\pi\)
−0.682423 + 0.730957i \(0.739074\pi\)
\(410\) 0 0
\(411\) 35.7812 1.76496
\(412\) 0 0
\(413\) 15.4965 0.762534
\(414\) 0 0
\(415\) 0.473294 0.0232331
\(416\) 0 0
\(417\) 31.0344 1.51976
\(418\) 0 0
\(419\) −21.0146 −1.02663 −0.513316 0.858200i \(-0.671583\pi\)
−0.513316 + 0.858200i \(0.671583\pi\)
\(420\) 0 0
\(421\) 20.1842 0.983718 0.491859 0.870675i \(-0.336318\pi\)
0.491859 + 0.870675i \(0.336318\pi\)
\(422\) 0 0
\(423\) −0.188329 −0.00915688
\(424\) 0 0
\(425\) −0.946961 −0.0459343
\(426\) 0 0
\(427\) −28.8743 −1.39732
\(428\) 0 0
\(429\) −27.0863 −1.30774
\(430\) 0 0
\(431\) −31.5905 −1.52166 −0.760830 0.648951i \(-0.775208\pi\)
−0.760830 + 0.648951i \(0.775208\pi\)
\(432\) 0 0
\(433\) 15.8618 0.762272 0.381136 0.924519i \(-0.375533\pi\)
0.381136 + 0.924519i \(0.375533\pi\)
\(434\) 0 0
\(435\) 20.2171 0.969335
\(436\) 0 0
\(437\) 4.24180 0.202913
\(438\) 0 0
\(439\) 30.7973 1.46988 0.734939 0.678134i \(-0.237211\pi\)
0.734939 + 0.678134i \(0.237211\pi\)
\(440\) 0 0
\(441\) 0.503298 0.0239666
\(442\) 0 0
\(443\) 1.70757 0.0811291 0.0405646 0.999177i \(-0.487084\pi\)
0.0405646 + 0.999177i \(0.487084\pi\)
\(444\) 0 0
\(445\) 23.3457 1.10669
\(446\) 0 0
\(447\) 30.4929 1.44226
\(448\) 0 0
\(449\) −34.9107 −1.64754 −0.823769 0.566926i \(-0.808133\pi\)
−0.823769 + 0.566926i \(0.808133\pi\)
\(450\) 0 0
\(451\) 48.5161 2.28454
\(452\) 0 0
\(453\) 37.1938 1.74752
\(454\) 0 0
\(455\) −21.6078 −1.01299
\(456\) 0 0
\(457\) −32.2219 −1.50728 −0.753638 0.657290i \(-0.771703\pi\)
−0.753638 + 0.657290i \(0.771703\pi\)
\(458\) 0 0
\(459\) 3.46048 0.161522
\(460\) 0 0
\(461\) −12.4947 −0.581936 −0.290968 0.956733i \(-0.593977\pi\)
−0.290968 + 0.956733i \(0.593977\pi\)
\(462\) 0 0
\(463\) 26.6131 1.23682 0.618408 0.785857i \(-0.287778\pi\)
0.618408 + 0.785857i \(0.287778\pi\)
\(464\) 0 0
\(465\) −3.71435 −0.172249
\(466\) 0 0
\(467\) 13.8570 0.641224 0.320612 0.947211i \(-0.396111\pi\)
0.320612 + 0.947211i \(0.396111\pi\)
\(468\) 0 0
\(469\) 17.9261 0.827750
\(470\) 0 0
\(471\) 35.6530 1.64281
\(472\) 0 0
\(473\) −50.8145 −2.33645
\(474\) 0 0
\(475\) 1.42972 0.0655999
\(476\) 0 0
\(477\) 0.652623 0.0298816
\(478\) 0 0
\(479\) −35.8675 −1.63883 −0.819413 0.573203i \(-0.805701\pi\)
−0.819413 + 0.573203i \(0.805701\pi\)
\(480\) 0 0
\(481\) −24.7891 −1.13029
\(482\) 0 0
\(483\) −27.2371 −1.23933
\(484\) 0 0
\(485\) 13.0341 0.591848
\(486\) 0 0
\(487\) −12.3128 −0.557948 −0.278974 0.960299i \(-0.589994\pi\)
−0.278974 + 0.960299i \(0.589994\pi\)
\(488\) 0 0
\(489\) 7.48860 0.338646
\(490\) 0 0
\(491\) 16.2634 0.733955 0.366978 0.930230i \(-0.380393\pi\)
0.366978 + 0.930230i \(0.380393\pi\)
\(492\) 0 0
\(493\) −4.10174 −0.184733
\(494\) 0 0
\(495\) 0.698447 0.0313928
\(496\) 0 0
\(497\) 32.9482 1.47793
\(498\) 0 0
\(499\) 28.6172 1.28108 0.640541 0.767924i \(-0.278710\pi\)
0.640541 + 0.767924i \(0.278710\pi\)
\(500\) 0 0
\(501\) 7.11074 0.317684
\(502\) 0 0
\(503\) −22.5407 −1.00504 −0.502521 0.864565i \(-0.667594\pi\)
−0.502521 + 0.864565i \(0.667594\pi\)
\(504\) 0 0
\(505\) 19.0069 0.845798
\(506\) 0 0
\(507\) 6.42656 0.285414
\(508\) 0 0
\(509\) −5.10159 −0.226124 −0.113062 0.993588i \(-0.536066\pi\)
−0.113062 + 0.993588i \(0.536066\pi\)
\(510\) 0 0
\(511\) 3.00211 0.132806
\(512\) 0 0
\(513\) −5.22463 −0.230673
\(514\) 0 0
\(515\) −8.74812 −0.385488
\(516\) 0 0
\(517\) −13.0793 −0.575227
\(518\) 0 0
\(519\) −5.73072 −0.251551
\(520\) 0 0
\(521\) −23.5200 −1.03043 −0.515215 0.857061i \(-0.672288\pi\)
−0.515215 + 0.857061i \(0.672288\pi\)
\(522\) 0 0
\(523\) 5.18959 0.226925 0.113462 0.993542i \(-0.463806\pi\)
0.113462 + 0.993542i \(0.463806\pi\)
\(524\) 0 0
\(525\) −9.18039 −0.400665
\(526\) 0 0
\(527\) 0.753585 0.0328267
\(528\) 0 0
\(529\) −5.64499 −0.245434
\(530\) 0 0
\(531\) −0.302578 −0.0131308
\(532\) 0 0
\(533\) 29.3067 1.26942
\(534\) 0 0
\(535\) −7.21915 −0.312111
\(536\) 0 0
\(537\) 26.1738 1.12948
\(538\) 0 0
\(539\) 34.9536 1.50556
\(540\) 0 0
\(541\) −23.1137 −0.993738 −0.496869 0.867826i \(-0.665517\pi\)
−0.496869 + 0.867826i \(0.665517\pi\)
\(542\) 0 0
\(543\) −43.9019 −1.88401
\(544\) 0 0
\(545\) 36.7893 1.57588
\(546\) 0 0
\(547\) −0.955705 −0.0408630 −0.0204315 0.999791i \(-0.506504\pi\)
−0.0204315 + 0.999791i \(0.506504\pi\)
\(548\) 0 0
\(549\) 0.563786 0.0240618
\(550\) 0 0
\(551\) 6.19279 0.263822
\(552\) 0 0
\(553\) −55.5873 −2.36381
\(554\) 0 0
\(555\) 26.9712 1.14486
\(556\) 0 0
\(557\) −44.1868 −1.87225 −0.936127 0.351663i \(-0.885616\pi\)
−0.936127 + 0.351663i \(0.885616\pi\)
\(558\) 0 0
\(559\) −30.6951 −1.29826
\(560\) 0 0
\(561\) −5.97913 −0.252439
\(562\) 0 0
\(563\) 23.5722 0.993450 0.496725 0.867908i \(-0.334536\pi\)
0.496725 + 0.867908i \(0.334536\pi\)
\(564\) 0 0
\(565\) 15.9930 0.672832
\(566\) 0 0
\(567\) 34.3628 1.44310
\(568\) 0 0
\(569\) −9.94642 −0.416976 −0.208488 0.978025i \(-0.566854\pi\)
−0.208488 + 0.978025i \(0.566854\pi\)
\(570\) 0 0
\(571\) 41.7250 1.74614 0.873069 0.487596i \(-0.162126\pi\)
0.873069 + 0.487596i \(0.162126\pi\)
\(572\) 0 0
\(573\) 40.7971 1.70432
\(574\) 0 0
\(575\) 5.84958 0.243945
\(576\) 0 0
\(577\) −3.15976 −0.131542 −0.0657712 0.997835i \(-0.520951\pi\)
−0.0657712 + 0.997835i \(0.520951\pi\)
\(578\) 0 0
\(579\) 29.7761 1.23745
\(580\) 0 0
\(581\) −0.930914 −0.0386208
\(582\) 0 0
\(583\) 45.3241 1.87713
\(584\) 0 0
\(585\) 0.421905 0.0174436
\(586\) 0 0
\(587\) −28.4982 −1.17625 −0.588124 0.808771i \(-0.700133\pi\)
−0.588124 + 0.808771i \(0.700133\pi\)
\(588\) 0 0
\(589\) −1.13776 −0.0468806
\(590\) 0 0
\(591\) −2.76883 −0.113894
\(592\) 0 0
\(593\) −36.1175 −1.48317 −0.741584 0.670860i \(-0.765925\pi\)
−0.741584 + 0.670860i \(0.765925\pi\)
\(594\) 0 0
\(595\) −4.76980 −0.195543
\(596\) 0 0
\(597\) −4.51014 −0.184588
\(598\) 0 0
\(599\) −29.4776 −1.20442 −0.602211 0.798337i \(-0.705713\pi\)
−0.602211 + 0.798337i \(0.705713\pi\)
\(600\) 0 0
\(601\) 24.0688 0.981788 0.490894 0.871219i \(-0.336670\pi\)
0.490894 + 0.871219i \(0.336670\pi\)
\(602\) 0 0
\(603\) −0.350017 −0.0142538
\(604\) 0 0
\(605\) 27.6475 1.12403
\(606\) 0 0
\(607\) 4.16907 0.169217 0.0846087 0.996414i \(-0.473036\pi\)
0.0846087 + 0.996414i \(0.473036\pi\)
\(608\) 0 0
\(609\) −39.7646 −1.61134
\(610\) 0 0
\(611\) −7.90070 −0.319628
\(612\) 0 0
\(613\) −29.0558 −1.17355 −0.586777 0.809748i \(-0.699604\pi\)
−0.586777 + 0.809748i \(0.699604\pi\)
\(614\) 0 0
\(615\) −31.8865 −1.28579
\(616\) 0 0
\(617\) −6.36550 −0.256265 −0.128133 0.991757i \(-0.540898\pi\)
−0.128133 + 0.991757i \(0.540898\pi\)
\(618\) 0 0
\(619\) −16.9730 −0.682202 −0.341101 0.940027i \(-0.610800\pi\)
−0.341101 + 0.940027i \(0.610800\pi\)
\(620\) 0 0
\(621\) −21.3762 −0.857796
\(622\) 0 0
\(623\) −45.9183 −1.83968
\(624\) 0 0
\(625\) −16.0076 −0.640305
\(626\) 0 0
\(627\) 9.02726 0.360514
\(628\) 0 0
\(629\) −5.47205 −0.218185
\(630\) 0 0
\(631\) −11.5011 −0.457851 −0.228926 0.973444i \(-0.573521\pi\)
−0.228926 + 0.973444i \(0.573521\pi\)
\(632\) 0 0
\(633\) −20.7611 −0.825178
\(634\) 0 0
\(635\) 14.6678 0.582073
\(636\) 0 0
\(637\) 21.1141 0.836572
\(638\) 0 0
\(639\) −0.643332 −0.0254498
\(640\) 0 0
\(641\) −11.2156 −0.442989 −0.221495 0.975162i \(-0.571094\pi\)
−0.221495 + 0.975162i \(0.571094\pi\)
\(642\) 0 0
\(643\) 28.9503 1.14169 0.570844 0.821058i \(-0.306616\pi\)
0.570844 + 0.821058i \(0.306616\pi\)
\(644\) 0 0
\(645\) 33.3971 1.31501
\(646\) 0 0
\(647\) 23.5389 0.925410 0.462705 0.886512i \(-0.346879\pi\)
0.462705 + 0.886512i \(0.346879\pi\)
\(648\) 0 0
\(649\) −21.0138 −0.824863
\(650\) 0 0
\(651\) 7.30569 0.286333
\(652\) 0 0
\(653\) 29.7003 1.16226 0.581130 0.813810i \(-0.302611\pi\)
0.581130 + 0.813810i \(0.302611\pi\)
\(654\) 0 0
\(655\) −37.4465 −1.46316
\(656\) 0 0
\(657\) −0.0586179 −0.00228690
\(658\) 0 0
\(659\) −7.36190 −0.286779 −0.143389 0.989666i \(-0.545800\pi\)
−0.143389 + 0.989666i \(0.545800\pi\)
\(660\) 0 0
\(661\) 28.1623 1.09539 0.547694 0.836679i \(-0.315506\pi\)
0.547694 + 0.836679i \(0.315506\pi\)
\(662\) 0 0
\(663\) −3.61176 −0.140269
\(664\) 0 0
\(665\) 7.20142 0.279259
\(666\) 0 0
\(667\) 25.3373 0.981066
\(668\) 0 0
\(669\) −32.9923 −1.27556
\(670\) 0 0
\(671\) 39.1544 1.51154
\(672\) 0 0
\(673\) −35.0246 −1.35010 −0.675049 0.737773i \(-0.735878\pi\)
−0.675049 + 0.737773i \(0.735878\pi\)
\(674\) 0 0
\(675\) −7.20494 −0.277318
\(676\) 0 0
\(677\) 3.62092 0.139163 0.0695815 0.997576i \(-0.477834\pi\)
0.0695815 + 0.997576i \(0.477834\pi\)
\(678\) 0 0
\(679\) −25.6366 −0.983841
\(680\) 0 0
\(681\) −24.6228 −0.943546
\(682\) 0 0
\(683\) 35.2092 1.34724 0.673621 0.739077i \(-0.264738\pi\)
0.673621 + 0.739077i \(0.264738\pi\)
\(684\) 0 0
\(685\) −38.7067 −1.47891
\(686\) 0 0
\(687\) 20.3483 0.776337
\(688\) 0 0
\(689\) 27.3785 1.04304
\(690\) 0 0
\(691\) 2.61729 0.0995665 0.0497832 0.998760i \(-0.484147\pi\)
0.0497832 + 0.998760i \(0.484147\pi\)
\(692\) 0 0
\(693\) −1.37376 −0.0521849
\(694\) 0 0
\(695\) −33.5719 −1.27345
\(696\) 0 0
\(697\) 6.46928 0.245042
\(698\) 0 0
\(699\) 49.4020 1.86855
\(700\) 0 0
\(701\) −27.9810 −1.05683 −0.528413 0.848987i \(-0.677213\pi\)
−0.528413 + 0.848987i \(0.677213\pi\)
\(702\) 0 0
\(703\) 8.26168 0.311595
\(704\) 0 0
\(705\) 8.59617 0.323750
\(706\) 0 0
\(707\) −37.3844 −1.40599
\(708\) 0 0
\(709\) −21.7958 −0.818560 −0.409280 0.912409i \(-0.634220\pi\)
−0.409280 + 0.912409i \(0.634220\pi\)
\(710\) 0 0
\(711\) 1.08537 0.0407047
\(712\) 0 0
\(713\) −4.65506 −0.174333
\(714\) 0 0
\(715\) 29.3009 1.09579
\(716\) 0 0
\(717\) −37.3141 −1.39352
\(718\) 0 0
\(719\) 21.7011 0.809315 0.404657 0.914468i \(-0.367391\pi\)
0.404657 + 0.914468i \(0.367391\pi\)
\(720\) 0 0
\(721\) 17.2065 0.640804
\(722\) 0 0
\(723\) −18.9069 −0.703157
\(724\) 0 0
\(725\) 8.54007 0.317170
\(726\) 0 0
\(727\) 23.3049 0.864330 0.432165 0.901795i \(-0.357750\pi\)
0.432165 + 0.901795i \(0.357750\pi\)
\(728\) 0 0
\(729\) 26.3131 0.974561
\(730\) 0 0
\(731\) −6.77576 −0.250611
\(732\) 0 0
\(733\) −21.0401 −0.777133 −0.388567 0.921421i \(-0.627030\pi\)
−0.388567 + 0.921421i \(0.627030\pi\)
\(734\) 0 0
\(735\) −22.9727 −0.847361
\(736\) 0 0
\(737\) −24.3083 −0.895409
\(738\) 0 0
\(739\) −21.1585 −0.778328 −0.389164 0.921168i \(-0.627236\pi\)
−0.389164 + 0.921168i \(0.627236\pi\)
\(740\) 0 0
\(741\) 5.45302 0.200322
\(742\) 0 0
\(743\) −7.87401 −0.288869 −0.144435 0.989514i \(-0.546136\pi\)
−0.144435 + 0.989514i \(0.546136\pi\)
\(744\) 0 0
\(745\) −32.9860 −1.20851
\(746\) 0 0
\(747\) 0.0181766 0.000665047 0
\(748\) 0 0
\(749\) 14.1992 0.518828
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 22.7121 0.827675
\(754\) 0 0
\(755\) −40.2349 −1.46430
\(756\) 0 0
\(757\) 46.6950 1.69716 0.848579 0.529069i \(-0.177459\pi\)
0.848579 + 0.529069i \(0.177459\pi\)
\(758\) 0 0
\(759\) 36.9344 1.34063
\(760\) 0 0
\(761\) −37.5950 −1.36282 −0.681408 0.731903i \(-0.738632\pi\)
−0.681408 + 0.731903i \(0.738632\pi\)
\(762\) 0 0
\(763\) −72.3603 −2.61962
\(764\) 0 0
\(765\) 0.0931329 0.00336723
\(766\) 0 0
\(767\) −12.6936 −0.458340
\(768\) 0 0
\(769\) 52.9079 1.90791 0.953954 0.299953i \(-0.0969709\pi\)
0.953954 + 0.299953i \(0.0969709\pi\)
\(770\) 0 0
\(771\) 11.1694 0.402256
\(772\) 0 0
\(773\) −0.392875 −0.0141307 −0.00706536 0.999975i \(-0.502249\pi\)
−0.00706536 + 0.999975i \(0.502249\pi\)
\(774\) 0 0
\(775\) −1.56901 −0.0563605
\(776\) 0 0
\(777\) −53.0492 −1.90313
\(778\) 0 0
\(779\) −9.76730 −0.349950
\(780\) 0 0
\(781\) −44.6788 −1.59873
\(782\) 0 0
\(783\) −31.2080 −1.11528
\(784\) 0 0
\(785\) −38.5681 −1.37656
\(786\) 0 0
\(787\) −22.8998 −0.816289 −0.408144 0.912917i \(-0.633824\pi\)
−0.408144 + 0.912917i \(0.633824\pi\)
\(788\) 0 0
\(789\) 32.6977 1.16407
\(790\) 0 0
\(791\) −31.4564 −1.11846
\(792\) 0 0
\(793\) 23.6517 0.839896
\(794\) 0 0
\(795\) −29.7886 −1.05649
\(796\) 0 0
\(797\) −24.1842 −0.856648 −0.428324 0.903625i \(-0.640896\pi\)
−0.428324 + 0.903625i \(0.640896\pi\)
\(798\) 0 0
\(799\) −1.74403 −0.0616994
\(800\) 0 0
\(801\) 0.896581 0.0316791
\(802\) 0 0
\(803\) −4.07096 −0.143661
\(804\) 0 0
\(805\) 29.4641 1.03847
\(806\) 0 0
\(807\) 1.99819 0.0703397
\(808\) 0 0
\(809\) 31.8383 1.11938 0.559688 0.828704i \(-0.310921\pi\)
0.559688 + 0.828704i \(0.310921\pi\)
\(810\) 0 0
\(811\) −17.1206 −0.601185 −0.300592 0.953753i \(-0.597184\pi\)
−0.300592 + 0.953753i \(0.597184\pi\)
\(812\) 0 0
\(813\) −32.2332 −1.13047
\(814\) 0 0
\(815\) −8.10089 −0.283762
\(816\) 0 0
\(817\) 10.2300 0.357903
\(818\) 0 0
\(819\) −0.829837 −0.0289969
\(820\) 0 0
\(821\) 36.7001 1.28084 0.640422 0.768023i \(-0.278760\pi\)
0.640422 + 0.768023i \(0.278760\pi\)
\(822\) 0 0
\(823\) 33.3886 1.16385 0.581927 0.813241i \(-0.302299\pi\)
0.581927 + 0.813241i \(0.302299\pi\)
\(824\) 0 0
\(825\) 12.4489 0.433415
\(826\) 0 0
\(827\) 1.09363 0.0380292 0.0190146 0.999819i \(-0.493947\pi\)
0.0190146 + 0.999819i \(0.493947\pi\)
\(828\) 0 0
\(829\) 47.3177 1.64341 0.821706 0.569912i \(-0.193023\pi\)
0.821706 + 0.569912i \(0.193023\pi\)
\(830\) 0 0
\(831\) 35.8538 1.24375
\(832\) 0 0
\(833\) 4.66081 0.161488
\(834\) 0 0
\(835\) −7.69213 −0.266197
\(836\) 0 0
\(837\) 5.73364 0.198184
\(838\) 0 0
\(839\) 36.1346 1.24751 0.623753 0.781622i \(-0.285607\pi\)
0.623753 + 0.781622i \(0.285607\pi\)
\(840\) 0 0
\(841\) 7.99111 0.275555
\(842\) 0 0
\(843\) 14.2008 0.489101
\(844\) 0 0
\(845\) −6.95201 −0.239156
\(846\) 0 0
\(847\) −54.3794 −1.86850
\(848\) 0 0
\(849\) 36.9194 1.26707
\(850\) 0 0
\(851\) 33.8021 1.15872
\(852\) 0 0
\(853\) −13.9612 −0.478023 −0.239012 0.971017i \(-0.576823\pi\)
−0.239012 + 0.971017i \(0.576823\pi\)
\(854\) 0 0
\(855\) −0.140612 −0.00480882
\(856\) 0 0
\(857\) −9.14438 −0.312366 −0.156183 0.987728i \(-0.549919\pi\)
−0.156183 + 0.987728i \(0.549919\pi\)
\(858\) 0 0
\(859\) −3.71451 −0.126737 −0.0633687 0.997990i \(-0.520184\pi\)
−0.0633687 + 0.997990i \(0.520184\pi\)
\(860\) 0 0
\(861\) 62.7170 2.13739
\(862\) 0 0
\(863\) −49.4067 −1.68182 −0.840912 0.541172i \(-0.817981\pi\)
−0.840912 + 0.541172i \(0.817981\pi\)
\(864\) 0 0
\(865\) 6.19928 0.210782
\(866\) 0 0
\(867\) 29.0028 0.984988
\(868\) 0 0
\(869\) 75.3782 2.55703
\(870\) 0 0
\(871\) −14.6837 −0.497539
\(872\) 0 0
\(873\) 0.500568 0.0169417
\(874\) 0 0
\(875\) 45.2941 1.53122
\(876\) 0 0
\(877\) −36.1953 −1.22223 −0.611115 0.791542i \(-0.709279\pi\)
−0.611115 + 0.791542i \(0.709279\pi\)
\(878\) 0 0
\(879\) 7.75101 0.261435
\(880\) 0 0
\(881\) −27.8304 −0.937631 −0.468815 0.883296i \(-0.655319\pi\)
−0.468815 + 0.883296i \(0.655319\pi\)
\(882\) 0 0
\(883\) 21.2567 0.715346 0.357673 0.933847i \(-0.383570\pi\)
0.357673 + 0.933847i \(0.383570\pi\)
\(884\) 0 0
\(885\) 13.8110 0.464251
\(886\) 0 0
\(887\) −36.6624 −1.23100 −0.615502 0.788136i \(-0.711047\pi\)
−0.615502 + 0.788136i \(0.711047\pi\)
\(888\) 0 0
\(889\) −28.8498 −0.967592
\(890\) 0 0
\(891\) −46.5971 −1.56106
\(892\) 0 0
\(893\) 2.63313 0.0881144
\(894\) 0 0
\(895\) −28.3139 −0.946429
\(896\) 0 0
\(897\) 22.3106 0.744930
\(898\) 0 0
\(899\) −6.79613 −0.226664
\(900\) 0 0
\(901\) 6.04365 0.201343
\(902\) 0 0
\(903\) −65.6882 −2.18596
\(904\) 0 0
\(905\) 47.4915 1.57867
\(906\) 0 0
\(907\) 10.8054 0.358786 0.179393 0.983777i \(-0.442587\pi\)
0.179393 + 0.983777i \(0.442587\pi\)
\(908\) 0 0
\(909\) 0.729952 0.0242110
\(910\) 0 0
\(911\) 22.3876 0.741733 0.370867 0.928686i \(-0.379061\pi\)
0.370867 + 0.928686i \(0.379061\pi\)
\(912\) 0 0
\(913\) 1.26235 0.0417776
\(914\) 0 0
\(915\) −25.7336 −0.850728
\(916\) 0 0
\(917\) 73.6530 2.43224
\(918\) 0 0
\(919\) 26.3710 0.869898 0.434949 0.900455i \(-0.356766\pi\)
0.434949 + 0.900455i \(0.356766\pi\)
\(920\) 0 0
\(921\) 36.4406 1.20076
\(922\) 0 0
\(923\) −26.9888 −0.888346
\(924\) 0 0
\(925\) 11.3931 0.374604
\(926\) 0 0
\(927\) −0.335967 −0.0110346
\(928\) 0 0
\(929\) −16.7360 −0.549091 −0.274545 0.961574i \(-0.588527\pi\)
−0.274545 + 0.961574i \(0.588527\pi\)
\(930\) 0 0
\(931\) −7.03688 −0.230624
\(932\) 0 0
\(933\) −25.9676 −0.850141
\(934\) 0 0
\(935\) 6.46800 0.211526
\(936\) 0 0
\(937\) 15.4001 0.503100 0.251550 0.967844i \(-0.419060\pi\)
0.251550 + 0.967844i \(0.419060\pi\)
\(938\) 0 0
\(939\) 12.7252 0.415271
\(940\) 0 0
\(941\) 55.1465 1.79773 0.898863 0.438230i \(-0.144395\pi\)
0.898863 + 0.438230i \(0.144395\pi\)
\(942\) 0 0
\(943\) −39.9622 −1.30135
\(944\) 0 0
\(945\) −36.2909 −1.18054
\(946\) 0 0
\(947\) 13.0896 0.425355 0.212678 0.977122i \(-0.431782\pi\)
0.212678 + 0.977122i \(0.431782\pi\)
\(948\) 0 0
\(949\) −2.45911 −0.0798261
\(950\) 0 0
\(951\) −16.7641 −0.543613
\(952\) 0 0
\(953\) −3.50919 −0.113674 −0.0568369 0.998383i \(-0.518101\pi\)
−0.0568369 + 0.998383i \(0.518101\pi\)
\(954\) 0 0
\(955\) −44.1328 −1.42810
\(956\) 0 0
\(957\) 53.9221 1.74305
\(958\) 0 0
\(959\) 76.1316 2.45842
\(960\) 0 0
\(961\) −29.7514 −0.959722
\(962\) 0 0
\(963\) −0.277248 −0.00893418
\(964\) 0 0
\(965\) −32.2107 −1.03690
\(966\) 0 0
\(967\) −24.0201 −0.772433 −0.386217 0.922408i \(-0.626218\pi\)
−0.386217 + 0.922408i \(0.626218\pi\)
\(968\) 0 0
\(969\) 1.20372 0.0386691
\(970\) 0 0
\(971\) −3.17730 −0.101964 −0.0509822 0.998700i \(-0.516235\pi\)
−0.0509822 + 0.998700i \(0.516235\pi\)
\(972\) 0 0
\(973\) 66.0320 2.11689
\(974\) 0 0
\(975\) 7.51990 0.240830
\(976\) 0 0
\(977\) 31.0978 0.994906 0.497453 0.867491i \(-0.334269\pi\)
0.497453 + 0.867491i \(0.334269\pi\)
\(978\) 0 0
\(979\) 62.2667 1.99005
\(980\) 0 0
\(981\) 1.41287 0.0451096
\(982\) 0 0
\(983\) −32.2134 −1.02745 −0.513724 0.857956i \(-0.671734\pi\)
−0.513724 + 0.857956i \(0.671734\pi\)
\(984\) 0 0
\(985\) 2.99522 0.0954355
\(986\) 0 0
\(987\) −16.9077 −0.538177
\(988\) 0 0
\(989\) 41.8554 1.33092
\(990\) 0 0
\(991\) −30.6297 −0.972984 −0.486492 0.873685i \(-0.661724\pi\)
−0.486492 + 0.873685i \(0.661724\pi\)
\(992\) 0 0
\(993\) −4.36262 −0.138444
\(994\) 0 0
\(995\) 4.87890 0.154672
\(996\) 0 0
\(997\) −52.9544 −1.67708 −0.838542 0.544837i \(-0.816592\pi\)
−0.838542 + 0.544837i \(0.816592\pi\)
\(998\) 0 0
\(999\) −41.6340 −1.31724
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.1.14 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.14 44 1.1 even 1 trivial