Properties

Label 6008.2.a.b.1.22
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 1.22
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.447974 q^{3} +2.48474 q^{5} +3.20909 q^{7} -2.79932 q^{9} +O(q^{10})\) \(q-0.447974 q^{3} +2.48474 q^{5} +3.20909 q^{7} -2.79932 q^{9} -0.332333 q^{11} -4.86212 q^{13} -1.11310 q^{15} -4.61386 q^{17} -7.39401 q^{19} -1.43759 q^{21} +5.99857 q^{23} +1.17393 q^{25} +2.59794 q^{27} +8.23188 q^{29} +7.16322 q^{31} +0.148877 q^{33} +7.97375 q^{35} -5.58586 q^{37} +2.17810 q^{39} -3.18131 q^{41} +3.29032 q^{43} -6.95558 q^{45} -9.99363 q^{47} +3.29825 q^{49} +2.06689 q^{51} -2.53894 q^{53} -0.825761 q^{55} +3.31233 q^{57} -5.30087 q^{59} +8.55552 q^{61} -8.98326 q^{63} -12.0811 q^{65} -5.87268 q^{67} -2.68721 q^{69} -13.6528 q^{71} -2.82965 q^{73} -0.525891 q^{75} -1.06649 q^{77} -16.1660 q^{79} +7.23415 q^{81} +13.0448 q^{83} -11.4642 q^{85} -3.68767 q^{87} +6.60233 q^{89} -15.6030 q^{91} -3.20894 q^{93} -18.3722 q^{95} +12.8090 q^{97} +0.930306 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.447974 −0.258638 −0.129319 0.991603i \(-0.541279\pi\)
−0.129319 + 0.991603i \(0.541279\pi\)
\(4\) 0 0
\(5\) 2.48474 1.11121 0.555605 0.831447i \(-0.312487\pi\)
0.555605 + 0.831447i \(0.312487\pi\)
\(6\) 0 0
\(7\) 3.20909 1.21292 0.606461 0.795113i \(-0.292589\pi\)
0.606461 + 0.795113i \(0.292589\pi\)
\(8\) 0 0
\(9\) −2.79932 −0.933106
\(10\) 0 0
\(11\) −0.332333 −0.100202 −0.0501011 0.998744i \(-0.515954\pi\)
−0.0501011 + 0.998744i \(0.515954\pi\)
\(12\) 0 0
\(13\) −4.86212 −1.34851 −0.674254 0.738499i \(-0.735535\pi\)
−0.674254 + 0.738499i \(0.735535\pi\)
\(14\) 0 0
\(15\) −1.11310 −0.287401
\(16\) 0 0
\(17\) −4.61386 −1.11903 −0.559513 0.828822i \(-0.689012\pi\)
−0.559513 + 0.828822i \(0.689012\pi\)
\(18\) 0 0
\(19\) −7.39401 −1.69630 −0.848151 0.529754i \(-0.822284\pi\)
−0.848151 + 0.529754i \(0.822284\pi\)
\(20\) 0 0
\(21\) −1.43759 −0.313708
\(22\) 0 0
\(23\) 5.99857 1.25079 0.625395 0.780309i \(-0.284938\pi\)
0.625395 + 0.780309i \(0.284938\pi\)
\(24\) 0 0
\(25\) 1.17393 0.234786
\(26\) 0 0
\(27\) 2.59794 0.499975
\(28\) 0 0
\(29\) 8.23188 1.52862 0.764310 0.644848i \(-0.223080\pi\)
0.764310 + 0.644848i \(0.223080\pi\)
\(30\) 0 0
\(31\) 7.16322 1.28655 0.643276 0.765634i \(-0.277575\pi\)
0.643276 + 0.765634i \(0.277575\pi\)
\(32\) 0 0
\(33\) 0.148877 0.0259161
\(34\) 0 0
\(35\) 7.97375 1.34781
\(36\) 0 0
\(37\) −5.58586 −0.918309 −0.459155 0.888356i \(-0.651848\pi\)
−0.459155 + 0.888356i \(0.651848\pi\)
\(38\) 0 0
\(39\) 2.17810 0.348776
\(40\) 0 0
\(41\) −3.18131 −0.496837 −0.248418 0.968653i \(-0.579911\pi\)
−0.248418 + 0.968653i \(0.579911\pi\)
\(42\) 0 0
\(43\) 3.29032 0.501769 0.250884 0.968017i \(-0.419279\pi\)
0.250884 + 0.968017i \(0.419279\pi\)
\(44\) 0 0
\(45\) −6.95558 −1.03688
\(46\) 0 0
\(47\) −9.99363 −1.45772 −0.728861 0.684662i \(-0.759950\pi\)
−0.728861 + 0.684662i \(0.759950\pi\)
\(48\) 0 0
\(49\) 3.29825 0.471179
\(50\) 0 0
\(51\) 2.06689 0.289423
\(52\) 0 0
\(53\) −2.53894 −0.348750 −0.174375 0.984679i \(-0.555790\pi\)
−0.174375 + 0.984679i \(0.555790\pi\)
\(54\) 0 0
\(55\) −0.825761 −0.111346
\(56\) 0 0
\(57\) 3.31233 0.438728
\(58\) 0 0
\(59\) −5.30087 −0.690115 −0.345057 0.938582i \(-0.612141\pi\)
−0.345057 + 0.938582i \(0.612141\pi\)
\(60\) 0 0
\(61\) 8.55552 1.09542 0.547711 0.836668i \(-0.315499\pi\)
0.547711 + 0.836668i \(0.315499\pi\)
\(62\) 0 0
\(63\) −8.98326 −1.13178
\(64\) 0 0
\(65\) −12.0811 −1.49848
\(66\) 0 0
\(67\) −5.87268 −0.717462 −0.358731 0.933441i \(-0.616790\pi\)
−0.358731 + 0.933441i \(0.616790\pi\)
\(68\) 0 0
\(69\) −2.68721 −0.323502
\(70\) 0 0
\(71\) −13.6528 −1.62029 −0.810147 0.586226i \(-0.800613\pi\)
−0.810147 + 0.586226i \(0.800613\pi\)
\(72\) 0 0
\(73\) −2.82965 −0.331185 −0.165593 0.986194i \(-0.552954\pi\)
−0.165593 + 0.986194i \(0.552954\pi\)
\(74\) 0 0
\(75\) −0.525891 −0.0607246
\(76\) 0 0
\(77\) −1.06649 −0.121537
\(78\) 0 0
\(79\) −16.1660 −1.81881 −0.909407 0.415907i \(-0.863464\pi\)
−0.909407 + 0.415907i \(0.863464\pi\)
\(80\) 0 0
\(81\) 7.23415 0.803794
\(82\) 0 0
\(83\) 13.0448 1.43185 0.715927 0.698175i \(-0.246004\pi\)
0.715927 + 0.698175i \(0.246004\pi\)
\(84\) 0 0
\(85\) −11.4642 −1.24347
\(86\) 0 0
\(87\) −3.68767 −0.395359
\(88\) 0 0
\(89\) 6.60233 0.699845 0.349923 0.936779i \(-0.386208\pi\)
0.349923 + 0.936779i \(0.386208\pi\)
\(90\) 0 0
\(91\) −15.6030 −1.63564
\(92\) 0 0
\(93\) −3.20894 −0.332751
\(94\) 0 0
\(95\) −18.3722 −1.88495
\(96\) 0 0
\(97\) 12.8090 1.30055 0.650277 0.759697i \(-0.274653\pi\)
0.650277 + 0.759697i \(0.274653\pi\)
\(98\) 0 0
\(99\) 0.930306 0.0934993
\(100\) 0 0
\(101\) −15.8727 −1.57940 −0.789699 0.613495i \(-0.789763\pi\)
−0.789699 + 0.613495i \(0.789763\pi\)
\(102\) 0 0
\(103\) −6.96888 −0.686664 −0.343332 0.939214i \(-0.611556\pi\)
−0.343332 + 0.939214i \(0.611556\pi\)
\(104\) 0 0
\(105\) −3.57203 −0.348595
\(106\) 0 0
\(107\) −20.1653 −1.94945 −0.974725 0.223408i \(-0.928282\pi\)
−0.974725 + 0.223408i \(0.928282\pi\)
\(108\) 0 0
\(109\) 4.23463 0.405604 0.202802 0.979220i \(-0.434995\pi\)
0.202802 + 0.979220i \(0.434995\pi\)
\(110\) 0 0
\(111\) 2.50232 0.237510
\(112\) 0 0
\(113\) −13.7102 −1.28974 −0.644871 0.764291i \(-0.723089\pi\)
−0.644871 + 0.764291i \(0.723089\pi\)
\(114\) 0 0
\(115\) 14.9049 1.38989
\(116\) 0 0
\(117\) 13.6106 1.25830
\(118\) 0 0
\(119\) −14.8063 −1.35729
\(120\) 0 0
\(121\) −10.8896 −0.989960
\(122\) 0 0
\(123\) 1.42514 0.128501
\(124\) 0 0
\(125\) −9.50679 −0.850313
\(126\) 0 0
\(127\) 6.35585 0.563990 0.281995 0.959416i \(-0.409004\pi\)
0.281995 + 0.959416i \(0.409004\pi\)
\(128\) 0 0
\(129\) −1.47398 −0.129777
\(130\) 0 0
\(131\) −7.70378 −0.673082 −0.336541 0.941669i \(-0.609257\pi\)
−0.336541 + 0.941669i \(0.609257\pi\)
\(132\) 0 0
\(133\) −23.7280 −2.05748
\(134\) 0 0
\(135\) 6.45522 0.555577
\(136\) 0 0
\(137\) −7.49056 −0.639962 −0.319981 0.947424i \(-0.603677\pi\)
−0.319981 + 0.947424i \(0.603677\pi\)
\(138\) 0 0
\(139\) 6.23746 0.529054 0.264527 0.964378i \(-0.414784\pi\)
0.264527 + 0.964378i \(0.414784\pi\)
\(140\) 0 0
\(141\) 4.47689 0.377022
\(142\) 0 0
\(143\) 1.61584 0.135124
\(144\) 0 0
\(145\) 20.4541 1.69862
\(146\) 0 0
\(147\) −1.47753 −0.121865
\(148\) 0 0
\(149\) 5.46677 0.447855 0.223928 0.974606i \(-0.428112\pi\)
0.223928 + 0.974606i \(0.428112\pi\)
\(150\) 0 0
\(151\) 5.74213 0.467288 0.233644 0.972322i \(-0.424935\pi\)
0.233644 + 0.972322i \(0.424935\pi\)
\(152\) 0 0
\(153\) 12.9157 1.04417
\(154\) 0 0
\(155\) 17.7987 1.42963
\(156\) 0 0
\(157\) 5.05111 0.403122 0.201561 0.979476i \(-0.435399\pi\)
0.201561 + 0.979476i \(0.435399\pi\)
\(158\) 0 0
\(159\) 1.13738 0.0901999
\(160\) 0 0
\(161\) 19.2500 1.51711
\(162\) 0 0
\(163\) 2.48335 0.194511 0.0972554 0.995259i \(-0.468994\pi\)
0.0972554 + 0.995259i \(0.468994\pi\)
\(164\) 0 0
\(165\) 0.369920 0.0287982
\(166\) 0 0
\(167\) −13.6806 −1.05864 −0.529318 0.848423i \(-0.677552\pi\)
−0.529318 + 0.848423i \(0.677552\pi\)
\(168\) 0 0
\(169\) 10.6402 0.818476
\(170\) 0 0
\(171\) 20.6982 1.58283
\(172\) 0 0
\(173\) 2.89798 0.220330 0.110165 0.993913i \(-0.464862\pi\)
0.110165 + 0.993913i \(0.464862\pi\)
\(174\) 0 0
\(175\) 3.76725 0.284777
\(176\) 0 0
\(177\) 2.37465 0.178490
\(178\) 0 0
\(179\) −6.37568 −0.476541 −0.238271 0.971199i \(-0.576580\pi\)
−0.238271 + 0.971199i \(0.576580\pi\)
\(180\) 0 0
\(181\) 0.982308 0.0730144 0.0365072 0.999333i \(-0.488377\pi\)
0.0365072 + 0.999333i \(0.488377\pi\)
\(182\) 0 0
\(183\) −3.83265 −0.283318
\(184\) 0 0
\(185\) −13.8794 −1.02043
\(186\) 0 0
\(187\) 1.53334 0.112129
\(188\) 0 0
\(189\) 8.33704 0.606430
\(190\) 0 0
\(191\) −12.9651 −0.938121 −0.469060 0.883166i \(-0.655407\pi\)
−0.469060 + 0.883166i \(0.655407\pi\)
\(192\) 0 0
\(193\) −12.8917 −0.927965 −0.463983 0.885844i \(-0.653580\pi\)
−0.463983 + 0.885844i \(0.653580\pi\)
\(194\) 0 0
\(195\) 5.41202 0.387563
\(196\) 0 0
\(197\) 24.5782 1.75113 0.875564 0.483103i \(-0.160490\pi\)
0.875564 + 0.483103i \(0.160490\pi\)
\(198\) 0 0
\(199\) −22.1065 −1.56709 −0.783543 0.621338i \(-0.786590\pi\)
−0.783543 + 0.621338i \(0.786590\pi\)
\(200\) 0 0
\(201\) 2.63081 0.185563
\(202\) 0 0
\(203\) 26.4168 1.85410
\(204\) 0 0
\(205\) −7.90472 −0.552090
\(206\) 0 0
\(207\) −16.7919 −1.16712
\(208\) 0 0
\(209\) 2.45727 0.169973
\(210\) 0 0
\(211\) 18.9156 1.30221 0.651103 0.758989i \(-0.274307\pi\)
0.651103 + 0.758989i \(0.274307\pi\)
\(212\) 0 0
\(213\) 6.11612 0.419070
\(214\) 0 0
\(215\) 8.17559 0.557570
\(216\) 0 0
\(217\) 22.9874 1.56049
\(218\) 0 0
\(219\) 1.26761 0.0856571
\(220\) 0 0
\(221\) 22.4331 1.50902
\(222\) 0 0
\(223\) −9.30269 −0.622954 −0.311477 0.950254i \(-0.600824\pi\)
−0.311477 + 0.950254i \(0.600824\pi\)
\(224\) 0 0
\(225\) −3.28621 −0.219080
\(226\) 0 0
\(227\) −10.5996 −0.703521 −0.351760 0.936090i \(-0.614417\pi\)
−0.351760 + 0.936090i \(0.614417\pi\)
\(228\) 0 0
\(229\) 10.5095 0.694484 0.347242 0.937775i \(-0.387118\pi\)
0.347242 + 0.937775i \(0.387118\pi\)
\(230\) 0 0
\(231\) 0.477758 0.0314342
\(232\) 0 0
\(233\) 15.1138 0.990138 0.495069 0.868854i \(-0.335143\pi\)
0.495069 + 0.868854i \(0.335143\pi\)
\(234\) 0 0
\(235\) −24.8316 −1.61983
\(236\) 0 0
\(237\) 7.24194 0.470415
\(238\) 0 0
\(239\) 9.41488 0.608998 0.304499 0.952513i \(-0.401511\pi\)
0.304499 + 0.952513i \(0.401511\pi\)
\(240\) 0 0
\(241\) 25.2390 1.62578 0.812892 0.582414i \(-0.197892\pi\)
0.812892 + 0.582414i \(0.197892\pi\)
\(242\) 0 0
\(243\) −11.0345 −0.707866
\(244\) 0 0
\(245\) 8.19529 0.523578
\(246\) 0 0
\(247\) 35.9506 2.28748
\(248\) 0 0
\(249\) −5.84374 −0.370332
\(250\) 0 0
\(251\) 20.1843 1.27402 0.637012 0.770854i \(-0.280170\pi\)
0.637012 + 0.770854i \(0.280170\pi\)
\(252\) 0 0
\(253\) −1.99352 −0.125332
\(254\) 0 0
\(255\) 5.13568 0.321609
\(256\) 0 0
\(257\) −14.7762 −0.921711 −0.460856 0.887475i \(-0.652457\pi\)
−0.460856 + 0.887475i \(0.652457\pi\)
\(258\) 0 0
\(259\) −17.9255 −1.11384
\(260\) 0 0
\(261\) −23.0436 −1.42637
\(262\) 0 0
\(263\) −22.3298 −1.37692 −0.688458 0.725276i \(-0.741712\pi\)
−0.688458 + 0.725276i \(0.741712\pi\)
\(264\) 0 0
\(265\) −6.30859 −0.387534
\(266\) 0 0
\(267\) −2.95767 −0.181007
\(268\) 0 0
\(269\) 2.74236 0.167205 0.0836023 0.996499i \(-0.473357\pi\)
0.0836023 + 0.996499i \(0.473357\pi\)
\(270\) 0 0
\(271\) −21.3192 −1.29505 −0.647525 0.762044i \(-0.724196\pi\)
−0.647525 + 0.762044i \(0.724196\pi\)
\(272\) 0 0
\(273\) 6.98973 0.423037
\(274\) 0 0
\(275\) −0.390136 −0.0235261
\(276\) 0 0
\(277\) −0.644053 −0.0386974 −0.0193487 0.999813i \(-0.506159\pi\)
−0.0193487 + 0.999813i \(0.506159\pi\)
\(278\) 0 0
\(279\) −20.0521 −1.20049
\(280\) 0 0
\(281\) −7.38031 −0.440272 −0.220136 0.975469i \(-0.570650\pi\)
−0.220136 + 0.975469i \(0.570650\pi\)
\(282\) 0 0
\(283\) −7.22725 −0.429615 −0.214808 0.976656i \(-0.568912\pi\)
−0.214808 + 0.976656i \(0.568912\pi\)
\(284\) 0 0
\(285\) 8.23027 0.487519
\(286\) 0 0
\(287\) −10.2091 −0.602624
\(288\) 0 0
\(289\) 4.28771 0.252218
\(290\) 0 0
\(291\) −5.73809 −0.336373
\(292\) 0 0
\(293\) −32.9084 −1.92253 −0.961265 0.275626i \(-0.911115\pi\)
−0.961265 + 0.275626i \(0.911115\pi\)
\(294\) 0 0
\(295\) −13.1713 −0.766862
\(296\) 0 0
\(297\) −0.863383 −0.0500986
\(298\) 0 0
\(299\) −29.1658 −1.68670
\(300\) 0 0
\(301\) 10.5589 0.608606
\(302\) 0 0
\(303\) 7.11058 0.408492
\(304\) 0 0
\(305\) 21.2582 1.21724
\(306\) 0 0
\(307\) 0.389674 0.0222398 0.0111199 0.999938i \(-0.496460\pi\)
0.0111199 + 0.999938i \(0.496460\pi\)
\(308\) 0 0
\(309\) 3.12188 0.177598
\(310\) 0 0
\(311\) 0.0938662 0.00532267 0.00266133 0.999996i \(-0.499153\pi\)
0.00266133 + 0.999996i \(0.499153\pi\)
\(312\) 0 0
\(313\) 9.20154 0.520102 0.260051 0.965595i \(-0.416261\pi\)
0.260051 + 0.965595i \(0.416261\pi\)
\(314\) 0 0
\(315\) −22.3211 −1.25765
\(316\) 0 0
\(317\) 0.962046 0.0540339 0.0270170 0.999635i \(-0.491399\pi\)
0.0270170 + 0.999635i \(0.491399\pi\)
\(318\) 0 0
\(319\) −2.73572 −0.153171
\(320\) 0 0
\(321\) 9.03352 0.504202
\(322\) 0 0
\(323\) 34.1150 1.89821
\(324\) 0 0
\(325\) −5.70779 −0.316611
\(326\) 0 0
\(327\) −1.89700 −0.104905
\(328\) 0 0
\(329\) −32.0705 −1.76810
\(330\) 0 0
\(331\) −32.2189 −1.77091 −0.885455 0.464725i \(-0.846153\pi\)
−0.885455 + 0.464725i \(0.846153\pi\)
\(332\) 0 0
\(333\) 15.6366 0.856880
\(334\) 0 0
\(335\) −14.5921 −0.797250
\(336\) 0 0
\(337\) −28.5432 −1.55485 −0.777425 0.628976i \(-0.783474\pi\)
−0.777425 + 0.628976i \(0.783474\pi\)
\(338\) 0 0
\(339\) 6.14179 0.333576
\(340\) 0 0
\(341\) −2.38058 −0.128915
\(342\) 0 0
\(343\) −11.8792 −0.641419
\(344\) 0 0
\(345\) −6.67701 −0.359478
\(346\) 0 0
\(347\) −7.10425 −0.381376 −0.190688 0.981651i \(-0.561072\pi\)
−0.190688 + 0.981651i \(0.561072\pi\)
\(348\) 0 0
\(349\) −20.2532 −1.08413 −0.542065 0.840336i \(-0.682358\pi\)
−0.542065 + 0.840336i \(0.682358\pi\)
\(350\) 0 0
\(351\) −12.6315 −0.674220
\(352\) 0 0
\(353\) 17.3628 0.924130 0.462065 0.886846i \(-0.347109\pi\)
0.462065 + 0.886846i \(0.347109\pi\)
\(354\) 0 0
\(355\) −33.9238 −1.80049
\(356\) 0 0
\(357\) 6.63283 0.351047
\(358\) 0 0
\(359\) −2.05041 −0.108217 −0.0541083 0.998535i \(-0.517232\pi\)
−0.0541083 + 0.998535i \(0.517232\pi\)
\(360\) 0 0
\(361\) 35.6714 1.87744
\(362\) 0 0
\(363\) 4.87824 0.256041
\(364\) 0 0
\(365\) −7.03094 −0.368016
\(366\) 0 0
\(367\) −6.16599 −0.321862 −0.160931 0.986966i \(-0.551450\pi\)
−0.160931 + 0.986966i \(0.551450\pi\)
\(368\) 0 0
\(369\) 8.90550 0.463602
\(370\) 0 0
\(371\) −8.14767 −0.423006
\(372\) 0 0
\(373\) 3.30418 0.171084 0.0855419 0.996335i \(-0.472738\pi\)
0.0855419 + 0.996335i \(0.472738\pi\)
\(374\) 0 0
\(375\) 4.25879 0.219923
\(376\) 0 0
\(377\) −40.0244 −2.06136
\(378\) 0 0
\(379\) 9.91790 0.509448 0.254724 0.967014i \(-0.418015\pi\)
0.254724 + 0.967014i \(0.418015\pi\)
\(380\) 0 0
\(381\) −2.84726 −0.145869
\(382\) 0 0
\(383\) 26.6968 1.36414 0.682072 0.731285i \(-0.261079\pi\)
0.682072 + 0.731285i \(0.261079\pi\)
\(384\) 0 0
\(385\) −2.64994 −0.135053
\(386\) 0 0
\(387\) −9.21065 −0.468204
\(388\) 0 0
\(389\) 21.5226 1.09124 0.545620 0.838033i \(-0.316294\pi\)
0.545620 + 0.838033i \(0.316294\pi\)
\(390\) 0 0
\(391\) −27.6766 −1.39967
\(392\) 0 0
\(393\) 3.45109 0.174085
\(394\) 0 0
\(395\) −40.1682 −2.02108
\(396\) 0 0
\(397\) −26.5816 −1.33409 −0.667047 0.745016i \(-0.732442\pi\)
−0.667047 + 0.745016i \(0.732442\pi\)
\(398\) 0 0
\(399\) 10.6295 0.532143
\(400\) 0 0
\(401\) 31.5167 1.57387 0.786934 0.617037i \(-0.211667\pi\)
0.786934 + 0.617037i \(0.211667\pi\)
\(402\) 0 0
\(403\) −34.8284 −1.73493
\(404\) 0 0
\(405\) 17.9750 0.893183
\(406\) 0 0
\(407\) 1.85637 0.0920166
\(408\) 0 0
\(409\) −15.7098 −0.776797 −0.388399 0.921491i \(-0.626972\pi\)
−0.388399 + 0.921491i \(0.626972\pi\)
\(410\) 0 0
\(411\) 3.35558 0.165518
\(412\) 0 0
\(413\) −17.0110 −0.837055
\(414\) 0 0
\(415\) 32.4130 1.59109
\(416\) 0 0
\(417\) −2.79422 −0.136834
\(418\) 0 0
\(419\) −14.7265 −0.719436 −0.359718 0.933061i \(-0.617127\pi\)
−0.359718 + 0.933061i \(0.617127\pi\)
\(420\) 0 0
\(421\) 18.5655 0.904828 0.452414 0.891808i \(-0.350563\pi\)
0.452414 + 0.891808i \(0.350563\pi\)
\(422\) 0 0
\(423\) 27.9754 1.36021
\(424\) 0 0
\(425\) −5.41635 −0.262732
\(426\) 0 0
\(427\) 27.4554 1.32866
\(428\) 0 0
\(429\) −0.723856 −0.0349481
\(430\) 0 0
\(431\) 8.88531 0.427990 0.213995 0.976835i \(-0.431352\pi\)
0.213995 + 0.976835i \(0.431352\pi\)
\(432\) 0 0
\(433\) 24.3929 1.17225 0.586123 0.810222i \(-0.300653\pi\)
0.586123 + 0.810222i \(0.300653\pi\)
\(434\) 0 0
\(435\) −9.16289 −0.439327
\(436\) 0 0
\(437\) −44.3535 −2.12172
\(438\) 0 0
\(439\) 23.7205 1.13212 0.566058 0.824365i \(-0.308468\pi\)
0.566058 + 0.824365i \(0.308468\pi\)
\(440\) 0 0
\(441\) −9.23285 −0.439660
\(442\) 0 0
\(443\) 35.9712 1.70904 0.854521 0.519417i \(-0.173851\pi\)
0.854521 + 0.519417i \(0.173851\pi\)
\(444\) 0 0
\(445\) 16.4051 0.777675
\(446\) 0 0
\(447\) −2.44897 −0.115832
\(448\) 0 0
\(449\) 8.95175 0.422459 0.211230 0.977436i \(-0.432253\pi\)
0.211230 + 0.977436i \(0.432253\pi\)
\(450\) 0 0
\(451\) 1.05725 0.0497841
\(452\) 0 0
\(453\) −2.57233 −0.120858
\(454\) 0 0
\(455\) −38.7693 −1.81753
\(456\) 0 0
\(457\) −21.2645 −0.994713 −0.497357 0.867546i \(-0.665696\pi\)
−0.497357 + 0.867546i \(0.665696\pi\)
\(458\) 0 0
\(459\) −11.9866 −0.559485
\(460\) 0 0
\(461\) 2.06005 0.0959462 0.0479731 0.998849i \(-0.484724\pi\)
0.0479731 + 0.998849i \(0.484724\pi\)
\(462\) 0 0
\(463\) 4.69056 0.217989 0.108994 0.994042i \(-0.465237\pi\)
0.108994 + 0.994042i \(0.465237\pi\)
\(464\) 0 0
\(465\) −7.97338 −0.369756
\(466\) 0 0
\(467\) 33.8156 1.56480 0.782401 0.622775i \(-0.213995\pi\)
0.782401 + 0.622775i \(0.213995\pi\)
\(468\) 0 0
\(469\) −18.8459 −0.870225
\(470\) 0 0
\(471\) −2.26276 −0.104263
\(472\) 0 0
\(473\) −1.09348 −0.0502783
\(474\) 0 0
\(475\) −8.68006 −0.398268
\(476\) 0 0
\(477\) 7.10729 0.325421
\(478\) 0 0
\(479\) 37.1794 1.69877 0.849385 0.527773i \(-0.176973\pi\)
0.849385 + 0.527773i \(0.176973\pi\)
\(480\) 0 0
\(481\) 27.1591 1.23835
\(482\) 0 0
\(483\) −8.62348 −0.392382
\(484\) 0 0
\(485\) 31.8270 1.44519
\(486\) 0 0
\(487\) 10.5261 0.476982 0.238491 0.971145i \(-0.423347\pi\)
0.238491 + 0.971145i \(0.423347\pi\)
\(488\) 0 0
\(489\) −1.11248 −0.0503079
\(490\) 0 0
\(491\) 39.4399 1.77990 0.889948 0.456062i \(-0.150740\pi\)
0.889948 + 0.456062i \(0.150740\pi\)
\(492\) 0 0
\(493\) −37.9807 −1.71057
\(494\) 0 0
\(495\) 2.31157 0.103897
\(496\) 0 0
\(497\) −43.8132 −1.96529
\(498\) 0 0
\(499\) 3.30276 0.147852 0.0739259 0.997264i \(-0.476447\pi\)
0.0739259 + 0.997264i \(0.476447\pi\)
\(500\) 0 0
\(501\) 6.12855 0.273804
\(502\) 0 0
\(503\) 19.7041 0.878564 0.439282 0.898349i \(-0.355233\pi\)
0.439282 + 0.898349i \(0.355233\pi\)
\(504\) 0 0
\(505\) −39.4396 −1.75504
\(506\) 0 0
\(507\) −4.76653 −0.211689
\(508\) 0 0
\(509\) −5.71119 −0.253144 −0.126572 0.991957i \(-0.540398\pi\)
−0.126572 + 0.991957i \(0.540398\pi\)
\(510\) 0 0
\(511\) −9.08059 −0.401702
\(512\) 0 0
\(513\) −19.2092 −0.848109
\(514\) 0 0
\(515\) −17.3159 −0.763028
\(516\) 0 0
\(517\) 3.32121 0.146067
\(518\) 0 0
\(519\) −1.29822 −0.0569856
\(520\) 0 0
\(521\) −33.3375 −1.46054 −0.730272 0.683157i \(-0.760607\pi\)
−0.730272 + 0.683157i \(0.760607\pi\)
\(522\) 0 0
\(523\) −21.2348 −0.928531 −0.464266 0.885696i \(-0.653682\pi\)
−0.464266 + 0.885696i \(0.653682\pi\)
\(524\) 0 0
\(525\) −1.68763 −0.0736542
\(526\) 0 0
\(527\) −33.0501 −1.43969
\(528\) 0 0
\(529\) 12.9829 0.564474
\(530\) 0 0
\(531\) 14.8388 0.643950
\(532\) 0 0
\(533\) 15.4679 0.669989
\(534\) 0 0
\(535\) −50.1054 −2.16625
\(536\) 0 0
\(537\) 2.85614 0.123252
\(538\) 0 0
\(539\) −1.09612 −0.0472131
\(540\) 0 0
\(541\) −20.4053 −0.877291 −0.438646 0.898660i \(-0.644542\pi\)
−0.438646 + 0.898660i \(0.644542\pi\)
\(542\) 0 0
\(543\) −0.440049 −0.0188843
\(544\) 0 0
\(545\) 10.5219 0.450711
\(546\) 0 0
\(547\) −10.7335 −0.458933 −0.229466 0.973317i \(-0.573698\pi\)
−0.229466 + 0.973317i \(0.573698\pi\)
\(548\) 0 0
\(549\) −23.9496 −1.02215
\(550\) 0 0
\(551\) −60.8666 −2.59300
\(552\) 0 0
\(553\) −51.8781 −2.20608
\(554\) 0 0
\(555\) 6.21761 0.263923
\(556\) 0 0
\(557\) 25.1020 1.06361 0.531804 0.846868i \(-0.321514\pi\)
0.531804 + 0.846868i \(0.321514\pi\)
\(558\) 0 0
\(559\) −15.9979 −0.676640
\(560\) 0 0
\(561\) −0.686896 −0.0290008
\(562\) 0 0
\(563\) −30.1743 −1.27169 −0.635847 0.771815i \(-0.719349\pi\)
−0.635847 + 0.771815i \(0.719349\pi\)
\(564\) 0 0
\(565\) −34.0662 −1.43317
\(566\) 0 0
\(567\) 23.2150 0.974939
\(568\) 0 0
\(569\) 38.8452 1.62848 0.814238 0.580531i \(-0.197155\pi\)
0.814238 + 0.580531i \(0.197155\pi\)
\(570\) 0 0
\(571\) 0.495491 0.0207357 0.0103678 0.999946i \(-0.496700\pi\)
0.0103678 + 0.999946i \(0.496700\pi\)
\(572\) 0 0
\(573\) 5.80802 0.242634
\(574\) 0 0
\(575\) 7.04191 0.293668
\(576\) 0 0
\(577\) 46.1553 1.92147 0.960735 0.277466i \(-0.0894946\pi\)
0.960735 + 0.277466i \(0.0894946\pi\)
\(578\) 0 0
\(579\) 5.77515 0.240007
\(580\) 0 0
\(581\) 41.8620 1.73673
\(582\) 0 0
\(583\) 0.843772 0.0349455
\(584\) 0 0
\(585\) 33.8188 1.39824
\(586\) 0 0
\(587\) 19.3829 0.800018 0.400009 0.916511i \(-0.369007\pi\)
0.400009 + 0.916511i \(0.369007\pi\)
\(588\) 0 0
\(589\) −52.9650 −2.18238
\(590\) 0 0
\(591\) −11.0104 −0.452908
\(592\) 0 0
\(593\) 11.7561 0.482764 0.241382 0.970430i \(-0.422399\pi\)
0.241382 + 0.970430i \(0.422399\pi\)
\(594\) 0 0
\(595\) −36.7898 −1.50823
\(596\) 0 0
\(597\) 9.90312 0.405308
\(598\) 0 0
\(599\) 3.54616 0.144892 0.0724461 0.997372i \(-0.476919\pi\)
0.0724461 + 0.997372i \(0.476919\pi\)
\(600\) 0 0
\(601\) −11.2053 −0.457074 −0.228537 0.973535i \(-0.573394\pi\)
−0.228537 + 0.973535i \(0.573394\pi\)
\(602\) 0 0
\(603\) 16.4395 0.669468
\(604\) 0 0
\(605\) −27.0577 −1.10005
\(606\) 0 0
\(607\) −18.5933 −0.754681 −0.377340 0.926075i \(-0.623161\pi\)
−0.377340 + 0.926075i \(0.623161\pi\)
\(608\) 0 0
\(609\) −11.8341 −0.479540
\(610\) 0 0
\(611\) 48.5902 1.96575
\(612\) 0 0
\(613\) 42.8757 1.73173 0.865866 0.500276i \(-0.166768\pi\)
0.865866 + 0.500276i \(0.166768\pi\)
\(614\) 0 0
\(615\) 3.54111 0.142791
\(616\) 0 0
\(617\) −0.797878 −0.0321214 −0.0160607 0.999871i \(-0.505112\pi\)
−0.0160607 + 0.999871i \(0.505112\pi\)
\(618\) 0 0
\(619\) −18.2811 −0.734780 −0.367390 0.930067i \(-0.619749\pi\)
−0.367390 + 0.930067i \(0.619749\pi\)
\(620\) 0 0
\(621\) 15.5840 0.625363
\(622\) 0 0
\(623\) 21.1875 0.848857
\(624\) 0 0
\(625\) −29.4915 −1.17966
\(626\) 0 0
\(627\) −1.10080 −0.0439615
\(628\) 0 0
\(629\) 25.7724 1.02761
\(630\) 0 0
\(631\) −44.7225 −1.78037 −0.890187 0.455596i \(-0.849426\pi\)
−0.890187 + 0.455596i \(0.849426\pi\)
\(632\) 0 0
\(633\) −8.47372 −0.336800
\(634\) 0 0
\(635\) 15.7926 0.626711
\(636\) 0 0
\(637\) −16.0365 −0.635388
\(638\) 0 0
\(639\) 38.2187 1.51191
\(640\) 0 0
\(641\) −18.4267 −0.727812 −0.363906 0.931436i \(-0.618557\pi\)
−0.363906 + 0.931436i \(0.618557\pi\)
\(642\) 0 0
\(643\) 5.41011 0.213354 0.106677 0.994294i \(-0.465979\pi\)
0.106677 + 0.994294i \(0.465979\pi\)
\(644\) 0 0
\(645\) −3.66245 −0.144209
\(646\) 0 0
\(647\) 9.34078 0.367224 0.183612 0.982999i \(-0.441221\pi\)
0.183612 + 0.982999i \(0.441221\pi\)
\(648\) 0 0
\(649\) 1.76165 0.0691510
\(650\) 0 0
\(651\) −10.2978 −0.403601
\(652\) 0 0
\(653\) 7.12144 0.278683 0.139342 0.990244i \(-0.455501\pi\)
0.139342 + 0.990244i \(0.455501\pi\)
\(654\) 0 0
\(655\) −19.1419 −0.747935
\(656\) 0 0
\(657\) 7.92109 0.309031
\(658\) 0 0
\(659\) −28.3122 −1.10289 −0.551443 0.834213i \(-0.685922\pi\)
−0.551443 + 0.834213i \(0.685922\pi\)
\(660\) 0 0
\(661\) −12.6088 −0.490425 −0.245213 0.969469i \(-0.578858\pi\)
−0.245213 + 0.969469i \(0.578858\pi\)
\(662\) 0 0
\(663\) −10.0495 −0.390289
\(664\) 0 0
\(665\) −58.9580 −2.28629
\(666\) 0 0
\(667\) 49.3795 1.91198
\(668\) 0 0
\(669\) 4.16736 0.161120
\(670\) 0 0
\(671\) −2.84328 −0.109764
\(672\) 0 0
\(673\) 27.5804 1.06314 0.531572 0.847013i \(-0.321601\pi\)
0.531572 + 0.847013i \(0.321601\pi\)
\(674\) 0 0
\(675\) 3.04981 0.117387
\(676\) 0 0
\(677\) 14.4276 0.554496 0.277248 0.960798i \(-0.410578\pi\)
0.277248 + 0.960798i \(0.410578\pi\)
\(678\) 0 0
\(679\) 41.1052 1.57747
\(680\) 0 0
\(681\) 4.74835 0.181957
\(682\) 0 0
\(683\) 34.8825 1.33474 0.667371 0.744726i \(-0.267420\pi\)
0.667371 + 0.744726i \(0.267420\pi\)
\(684\) 0 0
\(685\) −18.6121 −0.711132
\(686\) 0 0
\(687\) −4.70796 −0.179620
\(688\) 0 0
\(689\) 12.3446 0.470292
\(690\) 0 0
\(691\) −38.6552 −1.47051 −0.735257 0.677789i \(-0.762938\pi\)
−0.735257 + 0.677789i \(0.762938\pi\)
\(692\) 0 0
\(693\) 2.98544 0.113407
\(694\) 0 0
\(695\) 15.4985 0.587890
\(696\) 0 0
\(697\) 14.6781 0.555973
\(698\) 0 0
\(699\) −6.77059 −0.256087
\(700\) 0 0
\(701\) 3.35833 0.126842 0.0634211 0.997987i \(-0.479799\pi\)
0.0634211 + 0.997987i \(0.479799\pi\)
\(702\) 0 0
\(703\) 41.3019 1.55773
\(704\) 0 0
\(705\) 11.1239 0.418950
\(706\) 0 0
\(707\) −50.9370 −1.91568
\(708\) 0 0
\(709\) −24.7796 −0.930618 −0.465309 0.885148i \(-0.654057\pi\)
−0.465309 + 0.885148i \(0.654057\pi\)
\(710\) 0 0
\(711\) 45.2537 1.69715
\(712\) 0 0
\(713\) 42.9691 1.60921
\(714\) 0 0
\(715\) 4.01495 0.150151
\(716\) 0 0
\(717\) −4.21762 −0.157510
\(718\) 0 0
\(719\) −50.8983 −1.89819 −0.949094 0.314993i \(-0.897998\pi\)
−0.949094 + 0.314993i \(0.897998\pi\)
\(720\) 0 0
\(721\) −22.3638 −0.832870
\(722\) 0 0
\(723\) −11.3064 −0.420490
\(724\) 0 0
\(725\) 9.66365 0.358899
\(726\) 0 0
\(727\) −36.4972 −1.35361 −0.676804 0.736163i \(-0.736636\pi\)
−0.676804 + 0.736163i \(0.736636\pi\)
\(728\) 0 0
\(729\) −16.7592 −0.620713
\(730\) 0 0
\(731\) −15.1811 −0.561492
\(732\) 0 0
\(733\) 19.8000 0.731331 0.365666 0.930746i \(-0.380841\pi\)
0.365666 + 0.930746i \(0.380841\pi\)
\(734\) 0 0
\(735\) −3.67128 −0.135417
\(736\) 0 0
\(737\) 1.95168 0.0718912
\(738\) 0 0
\(739\) −23.2545 −0.855430 −0.427715 0.903914i \(-0.640681\pi\)
−0.427715 + 0.903914i \(0.640681\pi\)
\(740\) 0 0
\(741\) −16.1049 −0.591629
\(742\) 0 0
\(743\) 23.5523 0.864052 0.432026 0.901861i \(-0.357799\pi\)
0.432026 + 0.901861i \(0.357799\pi\)
\(744\) 0 0
\(745\) 13.5835 0.497661
\(746\) 0 0
\(747\) −36.5166 −1.33607
\(748\) 0 0
\(749\) −64.7121 −2.36453
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −9.04206 −0.329511
\(754\) 0 0
\(755\) 14.2677 0.519255
\(756\) 0 0
\(757\) −10.8167 −0.393139 −0.196570 0.980490i \(-0.562980\pi\)
−0.196570 + 0.980490i \(0.562980\pi\)
\(758\) 0 0
\(759\) 0.893047 0.0324156
\(760\) 0 0
\(761\) 8.49964 0.308112 0.154056 0.988062i \(-0.450766\pi\)
0.154056 + 0.988062i \(0.450766\pi\)
\(762\) 0 0
\(763\) 13.5893 0.491965
\(764\) 0 0
\(765\) 32.0921 1.16029
\(766\) 0 0
\(767\) 25.7735 0.930626
\(768\) 0 0
\(769\) 10.8173 0.390082 0.195041 0.980795i \(-0.437516\pi\)
0.195041 + 0.980795i \(0.437516\pi\)
\(770\) 0 0
\(771\) 6.61934 0.238390
\(772\) 0 0
\(773\) 14.9068 0.536159 0.268079 0.963397i \(-0.413611\pi\)
0.268079 + 0.963397i \(0.413611\pi\)
\(774\) 0 0
\(775\) 8.40913 0.302065
\(776\) 0 0
\(777\) 8.03017 0.288081
\(778\) 0 0
\(779\) 23.5226 0.842786
\(780\) 0 0
\(781\) 4.53729 0.162357
\(782\) 0 0
\(783\) 21.3860 0.764272
\(784\) 0 0
\(785\) 12.5507 0.447953
\(786\) 0 0
\(787\) −28.3524 −1.01066 −0.505328 0.862928i \(-0.668628\pi\)
−0.505328 + 0.862928i \(0.668628\pi\)
\(788\) 0 0
\(789\) 10.0032 0.356123
\(790\) 0 0
\(791\) −43.9971 −1.56436
\(792\) 0 0
\(793\) −41.5979 −1.47719
\(794\) 0 0
\(795\) 2.82609 0.100231
\(796\) 0 0
\(797\) 12.6015 0.446369 0.223185 0.974776i \(-0.428355\pi\)
0.223185 + 0.974776i \(0.428355\pi\)
\(798\) 0 0
\(799\) 46.1092 1.63123
\(800\) 0 0
\(801\) −18.4820 −0.653030
\(802\) 0 0
\(803\) 0.940386 0.0331855
\(804\) 0 0
\(805\) 47.8311 1.68583
\(806\) 0 0
\(807\) −1.22851 −0.0432455
\(808\) 0 0
\(809\) −14.5487 −0.511505 −0.255752 0.966742i \(-0.582323\pi\)
−0.255752 + 0.966742i \(0.582323\pi\)
\(810\) 0 0
\(811\) −9.97636 −0.350317 −0.175159 0.984540i \(-0.556044\pi\)
−0.175159 + 0.984540i \(0.556044\pi\)
\(812\) 0 0
\(813\) 9.55045 0.334949
\(814\) 0 0
\(815\) 6.17047 0.216142
\(816\) 0 0
\(817\) −24.3287 −0.851152
\(818\) 0 0
\(819\) 43.6777 1.52622
\(820\) 0 0
\(821\) −47.6090 −1.66157 −0.830784 0.556596i \(-0.812107\pi\)
−0.830784 + 0.556596i \(0.812107\pi\)
\(822\) 0 0
\(823\) 46.5601 1.62298 0.811491 0.584365i \(-0.198656\pi\)
0.811491 + 0.584365i \(0.198656\pi\)
\(824\) 0 0
\(825\) 0.174771 0.00608474
\(826\) 0 0
\(827\) 31.8537 1.10766 0.553831 0.832629i \(-0.313165\pi\)
0.553831 + 0.832629i \(0.313165\pi\)
\(828\) 0 0
\(829\) 35.9049 1.24703 0.623515 0.781811i \(-0.285704\pi\)
0.623515 + 0.781811i \(0.285704\pi\)
\(830\) 0 0
\(831\) 0.288519 0.0100086
\(832\) 0 0
\(833\) −15.2177 −0.527261
\(834\) 0 0
\(835\) −33.9927 −1.17637
\(836\) 0 0
\(837\) 18.6097 0.643244
\(838\) 0 0
\(839\) −49.7051 −1.71601 −0.858005 0.513641i \(-0.828296\pi\)
−0.858005 + 0.513641i \(0.828296\pi\)
\(840\) 0 0
\(841\) 38.7638 1.33668
\(842\) 0 0
\(843\) 3.30619 0.113871
\(844\) 0 0
\(845\) 26.4381 0.909498
\(846\) 0 0
\(847\) −34.9455 −1.20074
\(848\) 0 0
\(849\) 3.23762 0.111115
\(850\) 0 0
\(851\) −33.5072 −1.14861
\(852\) 0 0
\(853\) 21.6447 0.741100 0.370550 0.928812i \(-0.379169\pi\)
0.370550 + 0.928812i \(0.379169\pi\)
\(854\) 0 0
\(855\) 51.4296 1.75886
\(856\) 0 0
\(857\) 5.20395 0.177764 0.0888818 0.996042i \(-0.471671\pi\)
0.0888818 + 0.996042i \(0.471671\pi\)
\(858\) 0 0
\(859\) 48.2358 1.64578 0.822891 0.568199i \(-0.192360\pi\)
0.822891 + 0.568199i \(0.192360\pi\)
\(860\) 0 0
\(861\) 4.57341 0.155861
\(862\) 0 0
\(863\) 11.2075 0.381507 0.190754 0.981638i \(-0.438907\pi\)
0.190754 + 0.981638i \(0.438907\pi\)
\(864\) 0 0
\(865\) 7.20073 0.244832
\(866\) 0 0
\(867\) −1.92078 −0.0652333
\(868\) 0 0
\(869\) 5.37249 0.182249
\(870\) 0 0
\(871\) 28.5536 0.967503
\(872\) 0 0
\(873\) −35.8564 −1.21356
\(874\) 0 0
\(875\) −30.5081 −1.03136
\(876\) 0 0
\(877\) −26.0904 −0.881012 −0.440506 0.897750i \(-0.645201\pi\)
−0.440506 + 0.897750i \(0.645201\pi\)
\(878\) 0 0
\(879\) 14.7421 0.497239
\(880\) 0 0
\(881\) −9.32074 −0.314024 −0.157012 0.987597i \(-0.550186\pi\)
−0.157012 + 0.987597i \(0.550186\pi\)
\(882\) 0 0
\(883\) 29.1390 0.980605 0.490303 0.871552i \(-0.336886\pi\)
0.490303 + 0.871552i \(0.336886\pi\)
\(884\) 0 0
\(885\) 5.90039 0.198340
\(886\) 0 0
\(887\) −8.43141 −0.283099 −0.141550 0.989931i \(-0.545208\pi\)
−0.141550 + 0.989931i \(0.545208\pi\)
\(888\) 0 0
\(889\) 20.3965 0.684076
\(890\) 0 0
\(891\) −2.40415 −0.0805419
\(892\) 0 0
\(893\) 73.8931 2.47274
\(894\) 0 0
\(895\) −15.8419 −0.529537
\(896\) 0 0
\(897\) 13.0655 0.436245
\(898\) 0 0
\(899\) 58.9668 1.96665
\(900\) 0 0
\(901\) 11.7143 0.390260
\(902\) 0 0
\(903\) −4.73013 −0.157409
\(904\) 0 0
\(905\) 2.44078 0.0811343
\(906\) 0 0
\(907\) 21.4252 0.711411 0.355706 0.934598i \(-0.384241\pi\)
0.355706 + 0.934598i \(0.384241\pi\)
\(908\) 0 0
\(909\) 44.4329 1.47375
\(910\) 0 0
\(911\) −10.5613 −0.349913 −0.174956 0.984576i \(-0.555978\pi\)
−0.174956 + 0.984576i \(0.555978\pi\)
\(912\) 0 0
\(913\) −4.33522 −0.143475
\(914\) 0 0
\(915\) −9.52314 −0.314825
\(916\) 0 0
\(917\) −24.7221 −0.816396
\(918\) 0 0
\(919\) −29.1784 −0.962506 −0.481253 0.876582i \(-0.659818\pi\)
−0.481253 + 0.876582i \(0.659818\pi\)
\(920\) 0 0
\(921\) −0.174564 −0.00575207
\(922\) 0 0
\(923\) 66.3817 2.18498
\(924\) 0 0
\(925\) −6.55741 −0.215606
\(926\) 0 0
\(927\) 19.5081 0.640731
\(928\) 0 0
\(929\) −57.0488 −1.87171 −0.935855 0.352386i \(-0.885371\pi\)
−0.935855 + 0.352386i \(0.885371\pi\)
\(930\) 0 0
\(931\) −24.3873 −0.799262
\(932\) 0 0
\(933\) −0.0420496 −0.00137664
\(934\) 0 0
\(935\) 3.80995 0.124599
\(936\) 0 0
\(937\) 7.79456 0.254637 0.127319 0.991862i \(-0.459363\pi\)
0.127319 + 0.991862i \(0.459363\pi\)
\(938\) 0 0
\(939\) −4.12205 −0.134518
\(940\) 0 0
\(941\) 45.8670 1.49522 0.747611 0.664137i \(-0.231201\pi\)
0.747611 + 0.664137i \(0.231201\pi\)
\(942\) 0 0
\(943\) −19.0833 −0.621438
\(944\) 0 0
\(945\) 20.7154 0.673871
\(946\) 0 0
\(947\) −6.76210 −0.219739 −0.109869 0.993946i \(-0.535043\pi\)
−0.109869 + 0.993946i \(0.535043\pi\)
\(948\) 0 0
\(949\) 13.7581 0.446606
\(950\) 0 0
\(951\) −0.430972 −0.0139752
\(952\) 0 0
\(953\) 17.4991 0.566852 0.283426 0.958994i \(-0.408529\pi\)
0.283426 + 0.958994i \(0.408529\pi\)
\(954\) 0 0
\(955\) −32.2149 −1.04245
\(956\) 0 0
\(957\) 1.22553 0.0396159
\(958\) 0 0
\(959\) −24.0379 −0.776223
\(960\) 0 0
\(961\) 20.3118 0.655218
\(962\) 0 0
\(963\) 56.4490 1.81904
\(964\) 0 0
\(965\) −32.0325 −1.03116
\(966\) 0 0
\(967\) 15.2725 0.491129 0.245565 0.969380i \(-0.421027\pi\)
0.245565 + 0.969380i \(0.421027\pi\)
\(968\) 0 0
\(969\) −15.2826 −0.490948
\(970\) 0 0
\(971\) 47.8574 1.53582 0.767909 0.640560i \(-0.221298\pi\)
0.767909 + 0.640560i \(0.221298\pi\)
\(972\) 0 0
\(973\) 20.0166 0.641702
\(974\) 0 0
\(975\) 2.55694 0.0818877
\(976\) 0 0
\(977\) −46.7857 −1.49681 −0.748403 0.663244i \(-0.769179\pi\)
−0.748403 + 0.663244i \(0.769179\pi\)
\(978\) 0 0
\(979\) −2.19417 −0.0701260
\(980\) 0 0
\(981\) −11.8541 −0.378471
\(982\) 0 0
\(983\) −14.2822 −0.455530 −0.227765 0.973716i \(-0.573142\pi\)
−0.227765 + 0.973716i \(0.573142\pi\)
\(984\) 0 0
\(985\) 61.0705 1.94587
\(986\) 0 0
\(987\) 14.3667 0.457298
\(988\) 0 0
\(989\) 19.7372 0.627607
\(990\) 0 0
\(991\) −32.3109 −1.02639 −0.513195 0.858272i \(-0.671538\pi\)
−0.513195 + 0.858272i \(0.671538\pi\)
\(992\) 0 0
\(993\) 14.4332 0.458025
\(994\) 0 0
\(995\) −54.9288 −1.74136
\(996\) 0 0
\(997\) −56.2135 −1.78030 −0.890150 0.455669i \(-0.849400\pi\)
−0.890150 + 0.455669i \(0.849400\pi\)
\(998\) 0 0
\(999\) −14.5118 −0.459131
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.1.22 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.22 44 1.1 even 1 trivial