Properties

Label 6008.2.a.b.1.18
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 1.18
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.03287 q^{3} -2.90339 q^{5} -0.294834 q^{7} -1.93318 q^{9} +O(q^{10})\) \(q-1.03287 q^{3} -2.90339 q^{5} -0.294834 q^{7} -1.93318 q^{9} +3.78730 q^{11} -3.15992 q^{13} +2.99882 q^{15} -6.61105 q^{17} +1.57683 q^{19} +0.304526 q^{21} +5.53071 q^{23} +3.42966 q^{25} +5.09534 q^{27} +0.673445 q^{29} +6.77365 q^{31} -3.91179 q^{33} +0.856019 q^{35} +2.01059 q^{37} +3.26379 q^{39} +4.28870 q^{41} +0.897878 q^{43} +5.61277 q^{45} +6.08013 q^{47} -6.91307 q^{49} +6.82836 q^{51} +4.70499 q^{53} -10.9960 q^{55} -1.62866 q^{57} +6.44387 q^{59} -11.2916 q^{61} +0.569968 q^{63} +9.17448 q^{65} +0.579037 q^{67} -5.71250 q^{69} -14.0265 q^{71} +8.03585 q^{73} -3.54240 q^{75} -1.11663 q^{77} +13.2147 q^{79} +0.536712 q^{81} -9.03832 q^{83} +19.1945 q^{85} -0.695581 q^{87} -16.8649 q^{89} +0.931654 q^{91} -6.99631 q^{93} -4.57815 q^{95} +3.10244 q^{97} -7.32152 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −1.03287 −0.596328 −0.298164 0.954515i \(-0.596374\pi\)
−0.298164 + 0.954515i \(0.596374\pi\)
\(4\) 0 0
\(5\) −2.90339 −1.29843 −0.649217 0.760603i \(-0.724903\pi\)
−0.649217 + 0.760603i \(0.724903\pi\)
\(6\) 0 0
\(7\) −0.294834 −0.111437 −0.0557185 0.998447i \(-0.517745\pi\)
−0.0557185 + 0.998447i \(0.517745\pi\)
\(8\) 0 0
\(9\) −1.93318 −0.644393
\(10\) 0 0
\(11\) 3.78730 1.14191 0.570957 0.820980i \(-0.306572\pi\)
0.570957 + 0.820980i \(0.306572\pi\)
\(12\) 0 0
\(13\) −3.15992 −0.876405 −0.438202 0.898876i \(-0.644385\pi\)
−0.438202 + 0.898876i \(0.644385\pi\)
\(14\) 0 0
\(15\) 2.99882 0.774293
\(16\) 0 0
\(17\) −6.61105 −1.60342 −0.801708 0.597716i \(-0.796075\pi\)
−0.801708 + 0.597716i \(0.796075\pi\)
\(18\) 0 0
\(19\) 1.57683 0.361750 0.180875 0.983506i \(-0.442107\pi\)
0.180875 + 0.983506i \(0.442107\pi\)
\(20\) 0 0
\(21\) 0.304526 0.0664530
\(22\) 0 0
\(23\) 5.53071 1.15323 0.576616 0.817015i \(-0.304373\pi\)
0.576616 + 0.817015i \(0.304373\pi\)
\(24\) 0 0
\(25\) 3.42966 0.685932
\(26\) 0 0
\(27\) 5.09534 0.980598
\(28\) 0 0
\(29\) 0.673445 0.125056 0.0625278 0.998043i \(-0.480084\pi\)
0.0625278 + 0.998043i \(0.480084\pi\)
\(30\) 0 0
\(31\) 6.77365 1.21658 0.608292 0.793713i \(-0.291855\pi\)
0.608292 + 0.793713i \(0.291855\pi\)
\(32\) 0 0
\(33\) −3.91179 −0.680955
\(34\) 0 0
\(35\) 0.856019 0.144694
\(36\) 0 0
\(37\) 2.01059 0.330538 0.165269 0.986248i \(-0.447151\pi\)
0.165269 + 0.986248i \(0.447151\pi\)
\(38\) 0 0
\(39\) 3.26379 0.522625
\(40\) 0 0
\(41\) 4.28870 0.669783 0.334892 0.942257i \(-0.391300\pi\)
0.334892 + 0.942257i \(0.391300\pi\)
\(42\) 0 0
\(43\) 0.897878 0.136925 0.0684625 0.997654i \(-0.478191\pi\)
0.0684625 + 0.997654i \(0.478191\pi\)
\(44\) 0 0
\(45\) 5.61277 0.836702
\(46\) 0 0
\(47\) 6.08013 0.886878 0.443439 0.896304i \(-0.353758\pi\)
0.443439 + 0.896304i \(0.353758\pi\)
\(48\) 0 0
\(49\) −6.91307 −0.987582
\(50\) 0 0
\(51\) 6.82836 0.956162
\(52\) 0 0
\(53\) 4.70499 0.646280 0.323140 0.946351i \(-0.395262\pi\)
0.323140 + 0.946351i \(0.395262\pi\)
\(54\) 0 0
\(55\) −10.9960 −1.48270
\(56\) 0 0
\(57\) −1.62866 −0.215721
\(58\) 0 0
\(59\) 6.44387 0.838920 0.419460 0.907774i \(-0.362219\pi\)
0.419460 + 0.907774i \(0.362219\pi\)
\(60\) 0 0
\(61\) −11.2916 −1.44574 −0.722870 0.690984i \(-0.757178\pi\)
−0.722870 + 0.690984i \(0.757178\pi\)
\(62\) 0 0
\(63\) 0.569968 0.0718092
\(64\) 0 0
\(65\) 9.17448 1.13795
\(66\) 0 0
\(67\) 0.579037 0.0707406 0.0353703 0.999374i \(-0.488739\pi\)
0.0353703 + 0.999374i \(0.488739\pi\)
\(68\) 0 0
\(69\) −5.71250 −0.687705
\(70\) 0 0
\(71\) −14.0265 −1.66464 −0.832320 0.554296i \(-0.812988\pi\)
−0.832320 + 0.554296i \(0.812988\pi\)
\(72\) 0 0
\(73\) 8.03585 0.940526 0.470263 0.882526i \(-0.344159\pi\)
0.470263 + 0.882526i \(0.344159\pi\)
\(74\) 0 0
\(75\) −3.54240 −0.409041
\(76\) 0 0
\(77\) −1.11663 −0.127251
\(78\) 0 0
\(79\) 13.2147 1.48677 0.743385 0.668864i \(-0.233219\pi\)
0.743385 + 0.668864i \(0.233219\pi\)
\(80\) 0 0
\(81\) 0.536712 0.0596347
\(82\) 0 0
\(83\) −9.03832 −0.992084 −0.496042 0.868298i \(-0.665214\pi\)
−0.496042 + 0.868298i \(0.665214\pi\)
\(84\) 0 0
\(85\) 19.1945 2.08193
\(86\) 0 0
\(87\) −0.695581 −0.0745741
\(88\) 0 0
\(89\) −16.8649 −1.78768 −0.893838 0.448390i \(-0.851997\pi\)
−0.893838 + 0.448390i \(0.851997\pi\)
\(90\) 0 0
\(91\) 0.931654 0.0976639
\(92\) 0 0
\(93\) −6.99631 −0.725483
\(94\) 0 0
\(95\) −4.57815 −0.469708
\(96\) 0 0
\(97\) 3.10244 0.315005 0.157503 0.987519i \(-0.449656\pi\)
0.157503 + 0.987519i \(0.449656\pi\)
\(98\) 0 0
\(99\) −7.32152 −0.735841
\(100\) 0 0
\(101\) −7.78522 −0.774658 −0.387329 0.921942i \(-0.626602\pi\)
−0.387329 + 0.921942i \(0.626602\pi\)
\(102\) 0 0
\(103\) −1.68539 −0.166066 −0.0830330 0.996547i \(-0.526461\pi\)
−0.0830330 + 0.996547i \(0.526461\pi\)
\(104\) 0 0
\(105\) −0.884157 −0.0862849
\(106\) 0 0
\(107\) 4.87446 0.471232 0.235616 0.971846i \(-0.424289\pi\)
0.235616 + 0.971846i \(0.424289\pi\)
\(108\) 0 0
\(109\) −13.3360 −1.27736 −0.638679 0.769473i \(-0.720519\pi\)
−0.638679 + 0.769473i \(0.720519\pi\)
\(110\) 0 0
\(111\) −2.07668 −0.197109
\(112\) 0 0
\(113\) 15.0488 1.41568 0.707838 0.706375i \(-0.249671\pi\)
0.707838 + 0.706375i \(0.249671\pi\)
\(114\) 0 0
\(115\) −16.0578 −1.49740
\(116\) 0 0
\(117\) 6.10869 0.564749
\(118\) 0 0
\(119\) 1.94917 0.178680
\(120\) 0 0
\(121\) 3.34364 0.303967
\(122\) 0 0
\(123\) −4.42968 −0.399411
\(124\) 0 0
\(125\) 4.55930 0.407797
\(126\) 0 0
\(127\) 0.0329066 0.00291999 0.00146000 0.999999i \(-0.499535\pi\)
0.00146000 + 0.999999i \(0.499535\pi\)
\(128\) 0 0
\(129\) −0.927391 −0.0816523
\(130\) 0 0
\(131\) −11.2198 −0.980279 −0.490139 0.871644i \(-0.663054\pi\)
−0.490139 + 0.871644i \(0.663054\pi\)
\(132\) 0 0
\(133\) −0.464904 −0.0403123
\(134\) 0 0
\(135\) −14.7937 −1.27324
\(136\) 0 0
\(137\) 4.45518 0.380631 0.190316 0.981723i \(-0.439049\pi\)
0.190316 + 0.981723i \(0.439049\pi\)
\(138\) 0 0
\(139\) 11.5528 0.979895 0.489947 0.871752i \(-0.337016\pi\)
0.489947 + 0.871752i \(0.337016\pi\)
\(140\) 0 0
\(141\) −6.27999 −0.528871
\(142\) 0 0
\(143\) −11.9676 −1.00078
\(144\) 0 0
\(145\) −1.95527 −0.162376
\(146\) 0 0
\(147\) 7.14031 0.588923
\(148\) 0 0
\(149\) 13.2627 1.08652 0.543261 0.839564i \(-0.317189\pi\)
0.543261 + 0.839564i \(0.317189\pi\)
\(150\) 0 0
\(151\) 5.68002 0.462233 0.231117 0.972926i \(-0.425762\pi\)
0.231117 + 0.972926i \(0.425762\pi\)
\(152\) 0 0
\(153\) 12.7803 1.03323
\(154\) 0 0
\(155\) −19.6665 −1.57965
\(156\) 0 0
\(157\) −19.6391 −1.56737 −0.783687 0.621156i \(-0.786663\pi\)
−0.783687 + 0.621156i \(0.786663\pi\)
\(158\) 0 0
\(159\) −4.85965 −0.385395
\(160\) 0 0
\(161\) −1.63064 −0.128513
\(162\) 0 0
\(163\) 12.9564 1.01482 0.507412 0.861704i \(-0.330602\pi\)
0.507412 + 0.861704i \(0.330602\pi\)
\(164\) 0 0
\(165\) 11.3574 0.884176
\(166\) 0 0
\(167\) −15.4550 −1.19594 −0.597972 0.801517i \(-0.704027\pi\)
−0.597972 + 0.801517i \(0.704027\pi\)
\(168\) 0 0
\(169\) −3.01489 −0.231915
\(170\) 0 0
\(171\) −3.04829 −0.233109
\(172\) 0 0
\(173\) 15.1752 1.15375 0.576876 0.816832i \(-0.304272\pi\)
0.576876 + 0.816832i \(0.304272\pi\)
\(174\) 0 0
\(175\) −1.01118 −0.0764382
\(176\) 0 0
\(177\) −6.65568 −0.500272
\(178\) 0 0
\(179\) 9.20993 0.688383 0.344191 0.938900i \(-0.388153\pi\)
0.344191 + 0.938900i \(0.388153\pi\)
\(180\) 0 0
\(181\) 13.9465 1.03664 0.518319 0.855187i \(-0.326558\pi\)
0.518319 + 0.855187i \(0.326558\pi\)
\(182\) 0 0
\(183\) 11.6628 0.862136
\(184\) 0 0
\(185\) −5.83751 −0.429183
\(186\) 0 0
\(187\) −25.0380 −1.83096
\(188\) 0 0
\(189\) −1.50228 −0.109275
\(190\) 0 0
\(191\) 5.60336 0.405445 0.202722 0.979236i \(-0.435021\pi\)
0.202722 + 0.979236i \(0.435021\pi\)
\(192\) 0 0
\(193\) −22.7522 −1.63774 −0.818870 0.573979i \(-0.805399\pi\)
−0.818870 + 0.573979i \(0.805399\pi\)
\(194\) 0 0
\(195\) −9.47605 −0.678594
\(196\) 0 0
\(197\) 1.22689 0.0874123 0.0437062 0.999044i \(-0.486083\pi\)
0.0437062 + 0.999044i \(0.486083\pi\)
\(198\) 0 0
\(199\) −11.9389 −0.846328 −0.423164 0.906053i \(-0.639081\pi\)
−0.423164 + 0.906053i \(0.639081\pi\)
\(200\) 0 0
\(201\) −0.598070 −0.0421846
\(202\) 0 0
\(203\) −0.198555 −0.0139358
\(204\) 0 0
\(205\) −12.4518 −0.869669
\(206\) 0 0
\(207\) −10.6918 −0.743134
\(208\) 0 0
\(209\) 5.97193 0.413087
\(210\) 0 0
\(211\) 15.0312 1.03479 0.517394 0.855747i \(-0.326902\pi\)
0.517394 + 0.855747i \(0.326902\pi\)
\(212\) 0 0
\(213\) 14.4876 0.992671
\(214\) 0 0
\(215\) −2.60689 −0.177788
\(216\) 0 0
\(217\) −1.99711 −0.135572
\(218\) 0 0
\(219\) −8.30000 −0.560862
\(220\) 0 0
\(221\) 20.8904 1.40524
\(222\) 0 0
\(223\) −17.4672 −1.16969 −0.584847 0.811144i \(-0.698845\pi\)
−0.584847 + 0.811144i \(0.698845\pi\)
\(224\) 0 0
\(225\) −6.63015 −0.442010
\(226\) 0 0
\(227\) 5.11642 0.339589 0.169794 0.985480i \(-0.445690\pi\)
0.169794 + 0.985480i \(0.445690\pi\)
\(228\) 0 0
\(229\) −5.04244 −0.333214 −0.166607 0.986023i \(-0.553281\pi\)
−0.166607 + 0.986023i \(0.553281\pi\)
\(230\) 0 0
\(231\) 1.15333 0.0758836
\(232\) 0 0
\(233\) −0.969065 −0.0634856 −0.0317428 0.999496i \(-0.510106\pi\)
−0.0317428 + 0.999496i \(0.510106\pi\)
\(234\) 0 0
\(235\) −17.6530 −1.15155
\(236\) 0 0
\(237\) −13.6491 −0.886603
\(238\) 0 0
\(239\) −20.6730 −1.33723 −0.668614 0.743610i \(-0.733112\pi\)
−0.668614 + 0.743610i \(0.733112\pi\)
\(240\) 0 0
\(241\) −5.90726 −0.380520 −0.190260 0.981734i \(-0.560933\pi\)
−0.190260 + 0.981734i \(0.560933\pi\)
\(242\) 0 0
\(243\) −15.8404 −1.01616
\(244\) 0 0
\(245\) 20.0713 1.28231
\(246\) 0 0
\(247\) −4.98266 −0.317039
\(248\) 0 0
\(249\) 9.33541 0.591608
\(250\) 0 0
\(251\) 10.4728 0.661040 0.330520 0.943799i \(-0.392776\pi\)
0.330520 + 0.943799i \(0.392776\pi\)
\(252\) 0 0
\(253\) 20.9464 1.31689
\(254\) 0 0
\(255\) −19.8254 −1.24151
\(256\) 0 0
\(257\) −23.1744 −1.44558 −0.722788 0.691070i \(-0.757140\pi\)
−0.722788 + 0.691070i \(0.757140\pi\)
\(258\) 0 0
\(259\) −0.592790 −0.0368342
\(260\) 0 0
\(261\) −1.30189 −0.0805849
\(262\) 0 0
\(263\) −21.2638 −1.31118 −0.655592 0.755115i \(-0.727581\pi\)
−0.655592 + 0.755115i \(0.727581\pi\)
\(264\) 0 0
\(265\) −13.6604 −0.839152
\(266\) 0 0
\(267\) 17.4193 1.06604
\(268\) 0 0
\(269\) 6.78938 0.413956 0.206978 0.978346i \(-0.433637\pi\)
0.206978 + 0.978346i \(0.433637\pi\)
\(270\) 0 0
\(271\) 30.9160 1.87801 0.939006 0.343900i \(-0.111748\pi\)
0.939006 + 0.343900i \(0.111748\pi\)
\(272\) 0 0
\(273\) −0.962278 −0.0582397
\(274\) 0 0
\(275\) 12.9892 0.783275
\(276\) 0 0
\(277\) −18.8902 −1.13501 −0.567503 0.823372i \(-0.692090\pi\)
−0.567503 + 0.823372i \(0.692090\pi\)
\(278\) 0 0
\(279\) −13.0947 −0.783958
\(280\) 0 0
\(281\) −28.8164 −1.71904 −0.859521 0.511100i \(-0.829238\pi\)
−0.859521 + 0.511100i \(0.829238\pi\)
\(282\) 0 0
\(283\) −29.8924 −1.77692 −0.888460 0.458954i \(-0.848224\pi\)
−0.888460 + 0.458954i \(0.848224\pi\)
\(284\) 0 0
\(285\) 4.72863 0.280100
\(286\) 0 0
\(287\) −1.26446 −0.0746386
\(288\) 0 0
\(289\) 26.7060 1.57094
\(290\) 0 0
\(291\) −3.20442 −0.187846
\(292\) 0 0
\(293\) 13.0526 0.762543 0.381272 0.924463i \(-0.375486\pi\)
0.381272 + 0.924463i \(0.375486\pi\)
\(294\) 0 0
\(295\) −18.7090 −1.08928
\(296\) 0 0
\(297\) 19.2976 1.11976
\(298\) 0 0
\(299\) −17.4766 −1.01070
\(300\) 0 0
\(301\) −0.264725 −0.0152585
\(302\) 0 0
\(303\) 8.04112 0.461950
\(304\) 0 0
\(305\) 32.7839 1.87720
\(306\) 0 0
\(307\) −33.9927 −1.94006 −0.970032 0.242978i \(-0.921876\pi\)
−0.970032 + 0.242978i \(0.921876\pi\)
\(308\) 0 0
\(309\) 1.74079 0.0990298
\(310\) 0 0
\(311\) 26.6297 1.51003 0.755016 0.655706i \(-0.227629\pi\)
0.755016 + 0.655706i \(0.227629\pi\)
\(312\) 0 0
\(313\) −33.0331 −1.86714 −0.933572 0.358391i \(-0.883326\pi\)
−0.933572 + 0.358391i \(0.883326\pi\)
\(314\) 0 0
\(315\) −1.65484 −0.0932395
\(316\) 0 0
\(317\) −16.4227 −0.922392 −0.461196 0.887298i \(-0.652580\pi\)
−0.461196 + 0.887298i \(0.652580\pi\)
\(318\) 0 0
\(319\) 2.55054 0.142803
\(320\) 0 0
\(321\) −5.03469 −0.281009
\(322\) 0 0
\(323\) −10.4245 −0.580035
\(324\) 0 0
\(325\) −10.8375 −0.601154
\(326\) 0 0
\(327\) 13.7744 0.761724
\(328\) 0 0
\(329\) −1.79263 −0.0988310
\(330\) 0 0
\(331\) −8.90351 −0.489381 −0.244691 0.969601i \(-0.578686\pi\)
−0.244691 + 0.969601i \(0.578686\pi\)
\(332\) 0 0
\(333\) −3.88682 −0.212997
\(334\) 0 0
\(335\) −1.68117 −0.0918521
\(336\) 0 0
\(337\) −29.5849 −1.61159 −0.805797 0.592192i \(-0.798263\pi\)
−0.805797 + 0.592192i \(0.798263\pi\)
\(338\) 0 0
\(339\) −15.5435 −0.844207
\(340\) 0 0
\(341\) 25.6539 1.38923
\(342\) 0 0
\(343\) 4.10205 0.221490
\(344\) 0 0
\(345\) 16.5856 0.892939
\(346\) 0 0
\(347\) −9.96121 −0.534746 −0.267373 0.963593i \(-0.586156\pi\)
−0.267373 + 0.963593i \(0.586156\pi\)
\(348\) 0 0
\(349\) −14.4869 −0.775467 −0.387733 0.921772i \(-0.626742\pi\)
−0.387733 + 0.921772i \(0.626742\pi\)
\(350\) 0 0
\(351\) −16.1009 −0.859400
\(352\) 0 0
\(353\) −18.6779 −0.994124 −0.497062 0.867715i \(-0.665588\pi\)
−0.497062 + 0.867715i \(0.665588\pi\)
\(354\) 0 0
\(355\) 40.7244 2.16142
\(356\) 0 0
\(357\) −2.01324 −0.106552
\(358\) 0 0
\(359\) 3.70971 0.195791 0.0978956 0.995197i \(-0.468789\pi\)
0.0978956 + 0.995197i \(0.468789\pi\)
\(360\) 0 0
\(361\) −16.5136 −0.869137
\(362\) 0 0
\(363\) −3.45355 −0.181264
\(364\) 0 0
\(365\) −23.3312 −1.22121
\(366\) 0 0
\(367\) −12.3625 −0.645319 −0.322659 0.946515i \(-0.604577\pi\)
−0.322659 + 0.946515i \(0.604577\pi\)
\(368\) 0 0
\(369\) −8.29083 −0.431603
\(370\) 0 0
\(371\) −1.38719 −0.0720195
\(372\) 0 0
\(373\) −28.6593 −1.48392 −0.741962 0.670441i \(-0.766105\pi\)
−0.741962 + 0.670441i \(0.766105\pi\)
\(374\) 0 0
\(375\) −4.70917 −0.243181
\(376\) 0 0
\(377\) −2.12803 −0.109599
\(378\) 0 0
\(379\) −0.170698 −0.00876817 −0.00438409 0.999990i \(-0.501396\pi\)
−0.00438409 + 0.999990i \(0.501396\pi\)
\(380\) 0 0
\(381\) −0.0339883 −0.00174127
\(382\) 0 0
\(383\) −25.3702 −1.29636 −0.648178 0.761489i \(-0.724469\pi\)
−0.648178 + 0.761489i \(0.724469\pi\)
\(384\) 0 0
\(385\) 3.24200 0.165228
\(386\) 0 0
\(387\) −1.73576 −0.0882335
\(388\) 0 0
\(389\) −8.49042 −0.430481 −0.215241 0.976561i \(-0.569054\pi\)
−0.215241 + 0.976561i \(0.569054\pi\)
\(390\) 0 0
\(391\) −36.5638 −1.84911
\(392\) 0 0
\(393\) 11.5886 0.584568
\(394\) 0 0
\(395\) −38.3674 −1.93047
\(396\) 0 0
\(397\) 21.9563 1.10196 0.550978 0.834520i \(-0.314255\pi\)
0.550978 + 0.834520i \(0.314255\pi\)
\(398\) 0 0
\(399\) 0.480185 0.0240393
\(400\) 0 0
\(401\) 26.0246 1.29961 0.649804 0.760102i \(-0.274851\pi\)
0.649804 + 0.760102i \(0.274851\pi\)
\(402\) 0 0
\(403\) −21.4042 −1.06622
\(404\) 0 0
\(405\) −1.55828 −0.0774317
\(406\) 0 0
\(407\) 7.61470 0.377446
\(408\) 0 0
\(409\) −6.04512 −0.298912 −0.149456 0.988768i \(-0.547752\pi\)
−0.149456 + 0.988768i \(0.547752\pi\)
\(410\) 0 0
\(411\) −4.60162 −0.226981
\(412\) 0 0
\(413\) −1.89987 −0.0934867
\(414\) 0 0
\(415\) 26.2417 1.28816
\(416\) 0 0
\(417\) −11.9325 −0.584339
\(418\) 0 0
\(419\) 9.29453 0.454068 0.227034 0.973887i \(-0.427097\pi\)
0.227034 + 0.973887i \(0.427097\pi\)
\(420\) 0 0
\(421\) 38.2347 1.86345 0.931723 0.363171i \(-0.118306\pi\)
0.931723 + 0.363171i \(0.118306\pi\)
\(422\) 0 0
\(423\) −11.7540 −0.571498
\(424\) 0 0
\(425\) −22.6737 −1.09983
\(426\) 0 0
\(427\) 3.32915 0.161109
\(428\) 0 0
\(429\) 12.3610 0.596792
\(430\) 0 0
\(431\) 36.7139 1.76845 0.884223 0.467066i \(-0.154689\pi\)
0.884223 + 0.467066i \(0.154689\pi\)
\(432\) 0 0
\(433\) −27.9804 −1.34465 −0.672326 0.740255i \(-0.734705\pi\)
−0.672326 + 0.740255i \(0.734705\pi\)
\(434\) 0 0
\(435\) 2.01954 0.0968296
\(436\) 0 0
\(437\) 8.72098 0.417181
\(438\) 0 0
\(439\) −9.47577 −0.452254 −0.226127 0.974098i \(-0.572606\pi\)
−0.226127 + 0.974098i \(0.572606\pi\)
\(440\) 0 0
\(441\) 13.3642 0.636391
\(442\) 0 0
\(443\) 13.5105 0.641902 0.320951 0.947096i \(-0.395997\pi\)
0.320951 + 0.947096i \(0.395997\pi\)
\(444\) 0 0
\(445\) 48.9653 2.32118
\(446\) 0 0
\(447\) −13.6987 −0.647924
\(448\) 0 0
\(449\) −22.9747 −1.08424 −0.542121 0.840300i \(-0.682379\pi\)
−0.542121 + 0.840300i \(0.682379\pi\)
\(450\) 0 0
\(451\) 16.2426 0.764834
\(452\) 0 0
\(453\) −5.86672 −0.275643
\(454\) 0 0
\(455\) −2.70495 −0.126810
\(456\) 0 0
\(457\) −16.5105 −0.772329 −0.386164 0.922430i \(-0.626200\pi\)
−0.386164 + 0.922430i \(0.626200\pi\)
\(458\) 0 0
\(459\) −33.6855 −1.57231
\(460\) 0 0
\(461\) 38.4598 1.79125 0.895626 0.444808i \(-0.146728\pi\)
0.895626 + 0.444808i \(0.146728\pi\)
\(462\) 0 0
\(463\) 15.0259 0.698315 0.349157 0.937064i \(-0.386468\pi\)
0.349157 + 0.937064i \(0.386468\pi\)
\(464\) 0 0
\(465\) 20.3130 0.941993
\(466\) 0 0
\(467\) −14.1325 −0.653972 −0.326986 0.945029i \(-0.606033\pi\)
−0.326986 + 0.945029i \(0.606033\pi\)
\(468\) 0 0
\(469\) −0.170720 −0.00788312
\(470\) 0 0
\(471\) 20.2847 0.934669
\(472\) 0 0
\(473\) 3.40053 0.156357
\(474\) 0 0
\(475\) 5.40799 0.248136
\(476\) 0 0
\(477\) −9.09558 −0.416458
\(478\) 0 0
\(479\) −0.892881 −0.0407968 −0.0203984 0.999792i \(-0.506493\pi\)
−0.0203984 + 0.999792i \(0.506493\pi\)
\(480\) 0 0
\(481\) −6.35330 −0.289685
\(482\) 0 0
\(483\) 1.68424 0.0766357
\(484\) 0 0
\(485\) −9.00759 −0.409013
\(486\) 0 0
\(487\) 8.98741 0.407258 0.203629 0.979048i \(-0.434726\pi\)
0.203629 + 0.979048i \(0.434726\pi\)
\(488\) 0 0
\(489\) −13.3823 −0.605168
\(490\) 0 0
\(491\) −36.7399 −1.65805 −0.829024 0.559212i \(-0.811104\pi\)
−0.829024 + 0.559212i \(0.811104\pi\)
\(492\) 0 0
\(493\) −4.45218 −0.200516
\(494\) 0 0
\(495\) 21.2572 0.955441
\(496\) 0 0
\(497\) 4.13550 0.185502
\(498\) 0 0
\(499\) 33.3965 1.49503 0.747515 0.664245i \(-0.231247\pi\)
0.747515 + 0.664245i \(0.231247\pi\)
\(500\) 0 0
\(501\) 15.9630 0.713175
\(502\) 0 0
\(503\) 17.5852 0.784085 0.392042 0.919947i \(-0.371769\pi\)
0.392042 + 0.919947i \(0.371769\pi\)
\(504\) 0 0
\(505\) 22.6035 1.00584
\(506\) 0 0
\(507\) 3.11399 0.138297
\(508\) 0 0
\(509\) 6.57152 0.291278 0.145639 0.989338i \(-0.453476\pi\)
0.145639 + 0.989338i \(0.453476\pi\)
\(510\) 0 0
\(511\) −2.36925 −0.104809
\(512\) 0 0
\(513\) 8.03448 0.354731
\(514\) 0 0
\(515\) 4.89333 0.215626
\(516\) 0 0
\(517\) 23.0273 1.01274
\(518\) 0 0
\(519\) −15.6741 −0.688015
\(520\) 0 0
\(521\) 19.2574 0.843683 0.421842 0.906670i \(-0.361384\pi\)
0.421842 + 0.906670i \(0.361384\pi\)
\(522\) 0 0
\(523\) 28.6560 1.25304 0.626519 0.779406i \(-0.284479\pi\)
0.626519 + 0.779406i \(0.284479\pi\)
\(524\) 0 0
\(525\) 1.04442 0.0455822
\(526\) 0 0
\(527\) −44.7810 −1.95069
\(528\) 0 0
\(529\) 7.58870 0.329944
\(530\) 0 0
\(531\) −12.4571 −0.540594
\(532\) 0 0
\(533\) −13.5520 −0.587001
\(534\) 0 0
\(535\) −14.1525 −0.611864
\(536\) 0 0
\(537\) −9.51267 −0.410502
\(538\) 0 0
\(539\) −26.1819 −1.12773
\(540\) 0 0
\(541\) −9.68729 −0.416489 −0.208245 0.978077i \(-0.566775\pi\)
−0.208245 + 0.978077i \(0.566775\pi\)
\(542\) 0 0
\(543\) −14.4050 −0.618176
\(544\) 0 0
\(545\) 38.7196 1.65857
\(546\) 0 0
\(547\) 15.6364 0.668565 0.334283 0.942473i \(-0.391506\pi\)
0.334283 + 0.942473i \(0.391506\pi\)
\(548\) 0 0
\(549\) 21.8287 0.931625
\(550\) 0 0
\(551\) 1.06191 0.0452388
\(552\) 0 0
\(553\) −3.89615 −0.165681
\(554\) 0 0
\(555\) 6.02940 0.255934
\(556\) 0 0
\(557\) 40.3448 1.70946 0.854731 0.519070i \(-0.173722\pi\)
0.854731 + 0.519070i \(0.173722\pi\)
\(558\) 0 0
\(559\) −2.83722 −0.120002
\(560\) 0 0
\(561\) 25.8611 1.09185
\(562\) 0 0
\(563\) 23.4714 0.989201 0.494601 0.869120i \(-0.335314\pi\)
0.494601 + 0.869120i \(0.335314\pi\)
\(564\) 0 0
\(565\) −43.6926 −1.83816
\(566\) 0 0
\(567\) −0.158241 −0.00664550
\(568\) 0 0
\(569\) −26.2503 −1.10047 −0.550235 0.835010i \(-0.685462\pi\)
−0.550235 + 0.835010i \(0.685462\pi\)
\(570\) 0 0
\(571\) 11.0641 0.463016 0.231508 0.972833i \(-0.425634\pi\)
0.231508 + 0.972833i \(0.425634\pi\)
\(572\) 0 0
\(573\) −5.78754 −0.241778
\(574\) 0 0
\(575\) 18.9684 0.791039
\(576\) 0 0
\(577\) −13.1312 −0.546659 −0.273330 0.961920i \(-0.588125\pi\)
−0.273330 + 0.961920i \(0.588125\pi\)
\(578\) 0 0
\(579\) 23.5001 0.976631
\(580\) 0 0
\(581\) 2.66481 0.110555
\(582\) 0 0
\(583\) 17.8192 0.737996
\(584\) 0 0
\(585\) −17.7359 −0.733289
\(586\) 0 0
\(587\) −30.1580 −1.24476 −0.622378 0.782717i \(-0.713833\pi\)
−0.622378 + 0.782717i \(0.713833\pi\)
\(588\) 0 0
\(589\) 10.6809 0.440099
\(590\) 0 0
\(591\) −1.26722 −0.0521264
\(592\) 0 0
\(593\) 15.5670 0.639261 0.319631 0.947542i \(-0.396441\pi\)
0.319631 + 0.947542i \(0.396441\pi\)
\(594\) 0 0
\(595\) −5.65919 −0.232004
\(596\) 0 0
\(597\) 12.3314 0.504689
\(598\) 0 0
\(599\) 34.7367 1.41930 0.709652 0.704552i \(-0.248852\pi\)
0.709652 + 0.704552i \(0.248852\pi\)
\(600\) 0 0
\(601\) 5.81123 0.237045 0.118522 0.992951i \(-0.462184\pi\)
0.118522 + 0.992951i \(0.462184\pi\)
\(602\) 0 0
\(603\) −1.11938 −0.0455847
\(604\) 0 0
\(605\) −9.70788 −0.394681
\(606\) 0 0
\(607\) 7.58877 0.308019 0.154009 0.988069i \(-0.450781\pi\)
0.154009 + 0.988069i \(0.450781\pi\)
\(608\) 0 0
\(609\) 0.205081 0.00831032
\(610\) 0 0
\(611\) −19.2127 −0.777264
\(612\) 0 0
\(613\) −23.6306 −0.954432 −0.477216 0.878786i \(-0.658354\pi\)
−0.477216 + 0.878786i \(0.658354\pi\)
\(614\) 0 0
\(615\) 12.8611 0.518608
\(616\) 0 0
\(617\) −14.8838 −0.599198 −0.299599 0.954065i \(-0.596853\pi\)
−0.299599 + 0.954065i \(0.596853\pi\)
\(618\) 0 0
\(619\) 3.66844 0.147447 0.0737236 0.997279i \(-0.476512\pi\)
0.0737236 + 0.997279i \(0.476512\pi\)
\(620\) 0 0
\(621\) 28.1808 1.13086
\(622\) 0 0
\(623\) 4.97235 0.199213
\(624\) 0 0
\(625\) −30.3857 −1.21543
\(626\) 0 0
\(627\) −6.16823 −0.246335
\(628\) 0 0
\(629\) −13.2921 −0.529991
\(630\) 0 0
\(631\) −1.47434 −0.0586924 −0.0293462 0.999569i \(-0.509343\pi\)
−0.0293462 + 0.999569i \(0.509343\pi\)
\(632\) 0 0
\(633\) −15.5253 −0.617074
\(634\) 0 0
\(635\) −0.0955407 −0.00379142
\(636\) 0 0
\(637\) 21.8448 0.865521
\(638\) 0 0
\(639\) 27.1157 1.07268
\(640\) 0 0
\(641\) −39.2066 −1.54857 −0.774283 0.632839i \(-0.781889\pi\)
−0.774283 + 0.632839i \(0.781889\pi\)
\(642\) 0 0
\(643\) −1.62711 −0.0641669 −0.0320835 0.999485i \(-0.510214\pi\)
−0.0320835 + 0.999485i \(0.510214\pi\)
\(644\) 0 0
\(645\) 2.69258 0.106020
\(646\) 0 0
\(647\) −24.0334 −0.944849 −0.472424 0.881371i \(-0.656621\pi\)
−0.472424 + 0.881371i \(0.656621\pi\)
\(648\) 0 0
\(649\) 24.4049 0.957974
\(650\) 0 0
\(651\) 2.06275 0.0808457
\(652\) 0 0
\(653\) −2.99602 −0.117243 −0.0586216 0.998280i \(-0.518671\pi\)
−0.0586216 + 0.998280i \(0.518671\pi\)
\(654\) 0 0
\(655\) 32.5754 1.27283
\(656\) 0 0
\(657\) −15.5347 −0.606068
\(658\) 0 0
\(659\) 21.4521 0.835654 0.417827 0.908527i \(-0.362792\pi\)
0.417827 + 0.908527i \(0.362792\pi\)
\(660\) 0 0
\(661\) −2.81111 −0.109339 −0.0546697 0.998504i \(-0.517411\pi\)
−0.0546697 + 0.998504i \(0.517411\pi\)
\(662\) 0 0
\(663\) −21.5771 −0.837985
\(664\) 0 0
\(665\) 1.34980 0.0523428
\(666\) 0 0
\(667\) 3.72462 0.144218
\(668\) 0 0
\(669\) 18.0414 0.697521
\(670\) 0 0
\(671\) −42.7646 −1.65091
\(672\) 0 0
\(673\) 23.2536 0.896361 0.448181 0.893943i \(-0.352072\pi\)
0.448181 + 0.893943i \(0.352072\pi\)
\(674\) 0 0
\(675\) 17.4753 0.672624
\(676\) 0 0
\(677\) 36.9377 1.41963 0.709815 0.704389i \(-0.248779\pi\)
0.709815 + 0.704389i \(0.248779\pi\)
\(678\) 0 0
\(679\) −0.914706 −0.0351032
\(680\) 0 0
\(681\) −5.28460 −0.202506
\(682\) 0 0
\(683\) 25.6082 0.979870 0.489935 0.871759i \(-0.337021\pi\)
0.489935 + 0.871759i \(0.337021\pi\)
\(684\) 0 0
\(685\) −12.9351 −0.494225
\(686\) 0 0
\(687\) 5.20819 0.198705
\(688\) 0 0
\(689\) −14.8674 −0.566403
\(690\) 0 0
\(691\) −37.8360 −1.43935 −0.719675 0.694311i \(-0.755709\pi\)
−0.719675 + 0.694311i \(0.755709\pi\)
\(692\) 0 0
\(693\) 2.15864 0.0819999
\(694\) 0 0
\(695\) −33.5422 −1.27233
\(696\) 0 0
\(697\) −28.3529 −1.07394
\(698\) 0 0
\(699\) 1.00092 0.0378582
\(700\) 0 0
\(701\) 43.5010 1.64301 0.821504 0.570203i \(-0.193135\pi\)
0.821504 + 0.570203i \(0.193135\pi\)
\(702\) 0 0
\(703\) 3.17035 0.119572
\(704\) 0 0
\(705\) 18.2332 0.686704
\(706\) 0 0
\(707\) 2.29535 0.0863255
\(708\) 0 0
\(709\) −6.12453 −0.230012 −0.115006 0.993365i \(-0.536689\pi\)
−0.115006 + 0.993365i \(0.536689\pi\)
\(710\) 0 0
\(711\) −25.5464 −0.958064
\(712\) 0 0
\(713\) 37.4631 1.40300
\(714\) 0 0
\(715\) 34.7465 1.29945
\(716\) 0 0
\(717\) 21.3526 0.797426
\(718\) 0 0
\(719\) −41.4399 −1.54545 −0.772725 0.634741i \(-0.781107\pi\)
−0.772725 + 0.634741i \(0.781107\pi\)
\(720\) 0 0
\(721\) 0.496910 0.0185059
\(722\) 0 0
\(723\) 6.10144 0.226915
\(724\) 0 0
\(725\) 2.30969 0.0857796
\(726\) 0 0
\(727\) −40.3836 −1.49774 −0.748872 0.662715i \(-0.769404\pi\)
−0.748872 + 0.662715i \(0.769404\pi\)
\(728\) 0 0
\(729\) 14.7509 0.546330
\(730\) 0 0
\(731\) −5.93592 −0.219548
\(732\) 0 0
\(733\) −18.5995 −0.686987 −0.343494 0.939155i \(-0.611610\pi\)
−0.343494 + 0.939155i \(0.611610\pi\)
\(734\) 0 0
\(735\) −20.7311 −0.764678
\(736\) 0 0
\(737\) 2.19299 0.0807797
\(738\) 0 0
\(739\) −14.7396 −0.542206 −0.271103 0.962550i \(-0.587388\pi\)
−0.271103 + 0.962550i \(0.587388\pi\)
\(740\) 0 0
\(741\) 5.14644 0.189059
\(742\) 0 0
\(743\) −24.0762 −0.883269 −0.441635 0.897195i \(-0.645601\pi\)
−0.441635 + 0.897195i \(0.645601\pi\)
\(744\) 0 0
\(745\) −38.5068 −1.41078
\(746\) 0 0
\(747\) 17.4727 0.639292
\(748\) 0 0
\(749\) −1.43716 −0.0525127
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −10.8171 −0.394197
\(754\) 0 0
\(755\) −16.4913 −0.600179
\(756\) 0 0
\(757\) 9.92844 0.360855 0.180428 0.983588i \(-0.442252\pi\)
0.180428 + 0.983588i \(0.442252\pi\)
\(758\) 0 0
\(759\) −21.6350 −0.785299
\(760\) 0 0
\(761\) −0.917360 −0.0332543 −0.0166271 0.999862i \(-0.505293\pi\)
−0.0166271 + 0.999862i \(0.505293\pi\)
\(762\) 0 0
\(763\) 3.93191 0.142345
\(764\) 0 0
\(765\) −37.1063 −1.34158
\(766\) 0 0
\(767\) −20.3621 −0.735234
\(768\) 0 0
\(769\) 30.2720 1.09164 0.545818 0.837904i \(-0.316219\pi\)
0.545818 + 0.837904i \(0.316219\pi\)
\(770\) 0 0
\(771\) 23.9361 0.862038
\(772\) 0 0
\(773\) −30.0130 −1.07949 −0.539747 0.841827i \(-0.681480\pi\)
−0.539747 + 0.841827i \(0.681480\pi\)
\(774\) 0 0
\(775\) 23.2313 0.834494
\(776\) 0 0
\(777\) 0.612276 0.0219653
\(778\) 0 0
\(779\) 6.76256 0.242294
\(780\) 0 0
\(781\) −53.1226 −1.90087
\(782\) 0 0
\(783\) 3.43143 0.122629
\(784\) 0 0
\(785\) 57.0200 2.03513
\(786\) 0 0
\(787\) −23.0844 −0.822872 −0.411436 0.911439i \(-0.634973\pi\)
−0.411436 + 0.911439i \(0.634973\pi\)
\(788\) 0 0
\(789\) 21.9628 0.781896
\(790\) 0 0
\(791\) −4.43692 −0.157759
\(792\) 0 0
\(793\) 35.6806 1.26705
\(794\) 0 0
\(795\) 14.1094 0.500410
\(796\) 0 0
\(797\) −31.4740 −1.11487 −0.557433 0.830222i \(-0.688214\pi\)
−0.557433 + 0.830222i \(0.688214\pi\)
\(798\) 0 0
\(799\) −40.1961 −1.42204
\(800\) 0 0
\(801\) 32.6029 1.15197
\(802\) 0 0
\(803\) 30.4342 1.07400
\(804\) 0 0
\(805\) 4.73439 0.166865
\(806\) 0 0
\(807\) −7.01255 −0.246854
\(808\) 0 0
\(809\) −45.2043 −1.58930 −0.794650 0.607068i \(-0.792346\pi\)
−0.794650 + 0.607068i \(0.792346\pi\)
\(810\) 0 0
\(811\) 18.6776 0.655859 0.327930 0.944702i \(-0.393649\pi\)
0.327930 + 0.944702i \(0.393649\pi\)
\(812\) 0 0
\(813\) −31.9322 −1.11991
\(814\) 0 0
\(815\) −37.6175 −1.31768
\(816\) 0 0
\(817\) 1.41580 0.0495326
\(818\) 0 0
\(819\) −1.80105 −0.0629339
\(820\) 0 0
\(821\) 48.9989 1.71007 0.855036 0.518568i \(-0.173535\pi\)
0.855036 + 0.518568i \(0.173535\pi\)
\(822\) 0 0
\(823\) −2.49958 −0.0871297 −0.0435649 0.999051i \(-0.513872\pi\)
−0.0435649 + 0.999051i \(0.513872\pi\)
\(824\) 0 0
\(825\) −13.4161 −0.467089
\(826\) 0 0
\(827\) 46.8695 1.62981 0.814905 0.579594i \(-0.196789\pi\)
0.814905 + 0.579594i \(0.196789\pi\)
\(828\) 0 0
\(829\) 38.4392 1.33505 0.667525 0.744588i \(-0.267354\pi\)
0.667525 + 0.744588i \(0.267354\pi\)
\(830\) 0 0
\(831\) 19.5112 0.676835
\(832\) 0 0
\(833\) 45.7027 1.58350
\(834\) 0 0
\(835\) 44.8719 1.55286
\(836\) 0 0
\(837\) 34.5140 1.19298
\(838\) 0 0
\(839\) 34.0332 1.17496 0.587478 0.809240i \(-0.300121\pi\)
0.587478 + 0.809240i \(0.300121\pi\)
\(840\) 0 0
\(841\) −28.5465 −0.984361
\(842\) 0 0
\(843\) 29.7636 1.02511
\(844\) 0 0
\(845\) 8.75340 0.301126
\(846\) 0 0
\(847\) −0.985820 −0.0338732
\(848\) 0 0
\(849\) 30.8750 1.05963
\(850\) 0 0
\(851\) 11.1200 0.381187
\(852\) 0 0
\(853\) 35.8524 1.22756 0.613781 0.789477i \(-0.289648\pi\)
0.613781 + 0.789477i \(0.289648\pi\)
\(854\) 0 0
\(855\) 8.85038 0.302676
\(856\) 0 0
\(857\) −6.32951 −0.216212 −0.108106 0.994139i \(-0.534479\pi\)
−0.108106 + 0.994139i \(0.534479\pi\)
\(858\) 0 0
\(859\) −31.8565 −1.08693 −0.543464 0.839432i \(-0.682888\pi\)
−0.543464 + 0.839432i \(0.682888\pi\)
\(860\) 0 0
\(861\) 1.30602 0.0445091
\(862\) 0 0
\(863\) −24.0747 −0.819513 −0.409756 0.912195i \(-0.634386\pi\)
−0.409756 + 0.912195i \(0.634386\pi\)
\(864\) 0 0
\(865\) −44.0596 −1.49807
\(866\) 0 0
\(867\) −27.5839 −0.936798
\(868\) 0 0
\(869\) 50.0480 1.69776
\(870\) 0 0
\(871\) −1.82971 −0.0619974
\(872\) 0 0
\(873\) −5.99757 −0.202987
\(874\) 0 0
\(875\) −1.34424 −0.0454436
\(876\) 0 0
\(877\) −5.73142 −0.193536 −0.0967682 0.995307i \(-0.530851\pi\)
−0.0967682 + 0.995307i \(0.530851\pi\)
\(878\) 0 0
\(879\) −13.4817 −0.454726
\(880\) 0 0
\(881\) 19.6830 0.663136 0.331568 0.943431i \(-0.392422\pi\)
0.331568 + 0.943431i \(0.392422\pi\)
\(882\) 0 0
\(883\) −4.27683 −0.143927 −0.0719634 0.997407i \(-0.522926\pi\)
−0.0719634 + 0.997407i \(0.522926\pi\)
\(884\) 0 0
\(885\) 19.3240 0.649570
\(886\) 0 0
\(887\) 29.7672 0.999486 0.499743 0.866174i \(-0.333428\pi\)
0.499743 + 0.866174i \(0.333428\pi\)
\(888\) 0 0
\(889\) −0.00970201 −0.000325395 0
\(890\) 0 0
\(891\) 2.03269 0.0680976
\(892\) 0 0
\(893\) 9.58733 0.320828
\(894\) 0 0
\(895\) −26.7400 −0.893820
\(896\) 0 0
\(897\) 18.0511 0.602708
\(898\) 0 0
\(899\) 4.56168 0.152141
\(900\) 0 0
\(901\) −31.1049 −1.03626
\(902\) 0 0
\(903\) 0.273427 0.00909908
\(904\) 0 0
\(905\) −40.4922 −1.34601
\(906\) 0 0
\(907\) −39.2603 −1.30362 −0.651808 0.758384i \(-0.725989\pi\)
−0.651808 + 0.758384i \(0.725989\pi\)
\(908\) 0 0
\(909\) 15.0502 0.499184
\(910\) 0 0
\(911\) 26.6583 0.883227 0.441614 0.897205i \(-0.354406\pi\)
0.441614 + 0.897205i \(0.354406\pi\)
\(912\) 0 0
\(913\) −34.2308 −1.13287
\(914\) 0 0
\(915\) −33.8615 −1.11943
\(916\) 0 0
\(917\) 3.30798 0.109239
\(918\) 0 0
\(919\) −56.0219 −1.84799 −0.923995 0.382404i \(-0.875096\pi\)
−0.923995 + 0.382404i \(0.875096\pi\)
\(920\) 0 0
\(921\) 35.1100 1.15691
\(922\) 0 0
\(923\) 44.3226 1.45890
\(924\) 0 0
\(925\) 6.89563 0.226727
\(926\) 0 0
\(927\) 3.25815 0.107012
\(928\) 0 0
\(929\) −25.0444 −0.821681 −0.410840 0.911707i \(-0.634765\pi\)
−0.410840 + 0.911707i \(0.634765\pi\)
\(930\) 0 0
\(931\) −10.9007 −0.357257
\(932\) 0 0
\(933\) −27.5050 −0.900475
\(934\) 0 0
\(935\) 72.6951 2.37739
\(936\) 0 0
\(937\) −41.2844 −1.34870 −0.674351 0.738411i \(-0.735576\pi\)
−0.674351 + 0.738411i \(0.735576\pi\)
\(938\) 0 0
\(939\) 34.1190 1.11343
\(940\) 0 0
\(941\) −3.64571 −0.118847 −0.0594234 0.998233i \(-0.518926\pi\)
−0.0594234 + 0.998233i \(0.518926\pi\)
\(942\) 0 0
\(943\) 23.7196 0.772415
\(944\) 0 0
\(945\) 4.36170 0.141886
\(946\) 0 0
\(947\) 17.7881 0.578036 0.289018 0.957324i \(-0.406671\pi\)
0.289018 + 0.957324i \(0.406671\pi\)
\(948\) 0 0
\(949\) −25.3927 −0.824281
\(950\) 0 0
\(951\) 16.9626 0.550049
\(952\) 0 0
\(953\) 28.0504 0.908642 0.454321 0.890838i \(-0.349882\pi\)
0.454321 + 0.890838i \(0.349882\pi\)
\(954\) 0 0
\(955\) −16.2687 −0.526443
\(956\) 0 0
\(957\) −2.63437 −0.0851572
\(958\) 0 0
\(959\) −1.31354 −0.0424164
\(960\) 0 0
\(961\) 14.8824 0.480077
\(962\) 0 0
\(963\) −9.42321 −0.303659
\(964\) 0 0
\(965\) 66.0585 2.12650
\(966\) 0 0
\(967\) 40.4338 1.30026 0.650131 0.759822i \(-0.274714\pi\)
0.650131 + 0.759822i \(0.274714\pi\)
\(968\) 0 0
\(969\) 10.7672 0.345891
\(970\) 0 0
\(971\) −46.8956 −1.50495 −0.752475 0.658621i \(-0.771140\pi\)
−0.752475 + 0.658621i \(0.771140\pi\)
\(972\) 0 0
\(973\) −3.40616 −0.109196
\(974\) 0 0
\(975\) 11.1937 0.358485
\(976\) 0 0
\(977\) −40.3543 −1.29105 −0.645525 0.763739i \(-0.723361\pi\)
−0.645525 + 0.763739i \(0.723361\pi\)
\(978\) 0 0
\(979\) −63.8724 −2.04137
\(980\) 0 0
\(981\) 25.7809 0.823120
\(982\) 0 0
\(983\) 58.8995 1.87860 0.939301 0.343095i \(-0.111475\pi\)
0.939301 + 0.343095i \(0.111475\pi\)
\(984\) 0 0
\(985\) −3.56214 −0.113499
\(986\) 0 0
\(987\) 1.85156 0.0589357
\(988\) 0 0
\(989\) 4.96590 0.157906
\(990\) 0 0
\(991\) 2.93776 0.0933210 0.0466605 0.998911i \(-0.485142\pi\)
0.0466605 + 0.998911i \(0.485142\pi\)
\(992\) 0 0
\(993\) 9.19617 0.291832
\(994\) 0 0
\(995\) 34.6633 1.09890
\(996\) 0 0
\(997\) −3.53314 −0.111896 −0.0559478 0.998434i \(-0.517818\pi\)
−0.0559478 + 0.998434i \(0.517818\pi\)
\(998\) 0 0
\(999\) 10.2446 0.324125
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.1.18 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.18 44 1.1 even 1 trivial