Properties

Label 717.2.a.d.1.3
Level $717$
Weight $2$
Character 717.1
Self dual yes
Analytic conductor $5.725$
Analytic rank $1$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 717 = 3 \cdot 239 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 717.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.72527382493\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.1767625.1
Defining polynomial: \(x^{6} - 7 x^{4} - x^{3} + 11 x^{2} + x - 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.39213\) of defining polynomial
Character \(\chi\) \(=\) 717.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.899709 q^{2} -1.00000 q^{3} -1.19052 q^{4} +1.67380 q^{5} +0.899709 q^{6} -1.75765 q^{7} +2.87054 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.899709 q^{2} -1.00000 q^{3} -1.19052 q^{4} +1.67380 q^{5} +0.899709 q^{6} -1.75765 q^{7} +2.87054 q^{8} +1.00000 q^{9} -1.50593 q^{10} -5.08858 q^{11} +1.19052 q^{12} +6.43675 q^{13} +1.58137 q^{14} -1.67380 q^{15} -0.201602 q^{16} -2.24001 q^{17} -0.899709 q^{18} -3.96067 q^{19} -1.99270 q^{20} +1.75765 q^{21} +4.57824 q^{22} +7.71459 q^{23} -2.87054 q^{24} -2.19839 q^{25} -5.79120 q^{26} -1.00000 q^{27} +2.09253 q^{28} +0.101311 q^{29} +1.50593 q^{30} -4.63283 q^{31} -5.55970 q^{32} +5.08858 q^{33} +2.01536 q^{34} -2.94196 q^{35} -1.19052 q^{36} -7.78041 q^{37} +3.56345 q^{38} -6.43675 q^{39} +4.80472 q^{40} +1.42586 q^{41} -1.58137 q^{42} -3.65358 q^{43} +6.05808 q^{44} +1.67380 q^{45} -6.94088 q^{46} -7.73754 q^{47} +0.201602 q^{48} -3.91066 q^{49} +1.97791 q^{50} +2.24001 q^{51} -7.66311 q^{52} +1.61074 q^{53} +0.899709 q^{54} -8.51728 q^{55} -5.04542 q^{56} +3.96067 q^{57} -0.0911499 q^{58} -2.46261 q^{59} +1.99270 q^{60} -4.77088 q^{61} +4.16819 q^{62} -1.75765 q^{63} +5.40531 q^{64} +10.7738 q^{65} -4.57824 q^{66} -3.42357 q^{67} +2.66679 q^{68} -7.71459 q^{69} +2.64691 q^{70} -13.1223 q^{71} +2.87054 q^{72} -14.4582 q^{73} +7.00010 q^{74} +2.19839 q^{75} +4.71528 q^{76} +8.94396 q^{77} +5.79120 q^{78} -13.0644 q^{79} -0.337442 q^{80} +1.00000 q^{81} -1.28286 q^{82} -0.423954 q^{83} -2.09253 q^{84} -3.74933 q^{85} +3.28716 q^{86} -0.101311 q^{87} -14.6070 q^{88} +17.1426 q^{89} -1.50593 q^{90} -11.3136 q^{91} -9.18440 q^{92} +4.63283 q^{93} +6.96153 q^{94} -6.62938 q^{95} +5.55970 q^{96} +6.06424 q^{97} +3.51845 q^{98} -5.08858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 2q^{2} - 6q^{3} + 4q^{4} + 5q^{5} + 2q^{6} - 9q^{7} - 3q^{8} + 6q^{9} + O(q^{10}) \) \( 6q - 2q^{2} - 6q^{3} + 4q^{4} + 5q^{5} + 2q^{6} - 9q^{7} - 3q^{8} + 6q^{9} - 11q^{10} - 13q^{11} - 4q^{12} - q^{13} - 5q^{15} - 4q^{16} + 11q^{17} - 2q^{18} - 22q^{19} - q^{20} + 9q^{21} - 2q^{22} - 12q^{23} + 3q^{24} - q^{25} + 12q^{26} - 6q^{27} - 16q^{28} + 11q^{30} - 18q^{31} + 7q^{32} + 13q^{33} - 3q^{34} - 9q^{35} + 4q^{36} - 8q^{37} - 5q^{38} + q^{39} - 11q^{40} + 10q^{41} - 14q^{43} - 4q^{44} + 5q^{45} - 18q^{46} - 9q^{47} + 4q^{48} + 5q^{49} + 4q^{50} - 11q^{51} - 16q^{52} - 8q^{53} + 2q^{54} - 20q^{55} + 11q^{56} + 22q^{57} - 15q^{58} - 10q^{59} + q^{60} - 12q^{61} - 13q^{62} - 9q^{63} - 31q^{64} - 11q^{65} + 2q^{66} - 36q^{67} + 22q^{68} + 12q^{69} + q^{70} - 3q^{71} - 3q^{72} - 32q^{73} + 9q^{74} + q^{75} - 4q^{76} + 6q^{77} - 12q^{78} - q^{79} - 7q^{80} + 6q^{81} + 7q^{82} - 7q^{83} + 16q^{84} - 14q^{85} + 45q^{86} - 15q^{88} + 17q^{89} - 11q^{90} - 23q^{91} - 12q^{92} + 18q^{93} + 50q^{94} - 7q^{96} - 28q^{97} + 13q^{98} - 13q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.899709 −0.636190 −0.318095 0.948059i \(-0.603043\pi\)
−0.318095 + 0.948059i \(0.603043\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.19052 −0.595262
\(5\) 1.67380 0.748547 0.374273 0.927318i \(-0.377892\pi\)
0.374273 + 0.927318i \(0.377892\pi\)
\(6\) 0.899709 0.367304
\(7\) −1.75765 −0.664330 −0.332165 0.943221i \(-0.607779\pi\)
−0.332165 + 0.943221i \(0.607779\pi\)
\(8\) 2.87054 1.01489
\(9\) 1.00000 0.333333
\(10\) −1.50593 −0.476218
\(11\) −5.08858 −1.53427 −0.767133 0.641488i \(-0.778317\pi\)
−0.767133 + 0.641488i \(0.778317\pi\)
\(12\) 1.19052 0.343675
\(13\) 6.43675 1.78523 0.892617 0.450816i \(-0.148867\pi\)
0.892617 + 0.450816i \(0.148867\pi\)
\(14\) 1.58137 0.422640
\(15\) −1.67380 −0.432174
\(16\) −0.201602 −0.0504005
\(17\) −2.24001 −0.543283 −0.271641 0.962399i \(-0.587566\pi\)
−0.271641 + 0.962399i \(0.587566\pi\)
\(18\) −0.899709 −0.212063
\(19\) −3.96067 −0.908641 −0.454320 0.890838i \(-0.650118\pi\)
−0.454320 + 0.890838i \(0.650118\pi\)
\(20\) −1.99270 −0.445582
\(21\) 1.75765 0.383551
\(22\) 4.57824 0.976085
\(23\) 7.71459 1.60860 0.804301 0.594222i \(-0.202540\pi\)
0.804301 + 0.594222i \(0.202540\pi\)
\(24\) −2.87054 −0.585947
\(25\) −2.19839 −0.439678
\(26\) −5.79120 −1.13575
\(27\) −1.00000 −0.192450
\(28\) 2.09253 0.395451
\(29\) 0.101311 0.0188129 0.00940644 0.999956i \(-0.497006\pi\)
0.00940644 + 0.999956i \(0.497006\pi\)
\(30\) 1.50593 0.274945
\(31\) −4.63283 −0.832080 −0.416040 0.909346i \(-0.636582\pi\)
−0.416040 + 0.909346i \(0.636582\pi\)
\(32\) −5.55970 −0.982826
\(33\) 5.08858 0.885809
\(34\) 2.01536 0.345631
\(35\) −2.94196 −0.497282
\(36\) −1.19052 −0.198421
\(37\) −7.78041 −1.27909 −0.639546 0.768753i \(-0.720878\pi\)
−0.639546 + 0.768753i \(0.720878\pi\)
\(38\) 3.56345 0.578068
\(39\) −6.43675 −1.03071
\(40\) 4.80472 0.759692
\(41\) 1.42586 0.222682 0.111341 0.993782i \(-0.464485\pi\)
0.111341 + 0.993782i \(0.464485\pi\)
\(42\) −1.58137 −0.244011
\(43\) −3.65358 −0.557166 −0.278583 0.960412i \(-0.589865\pi\)
−0.278583 + 0.960412i \(0.589865\pi\)
\(44\) 6.05808 0.913291
\(45\) 1.67380 0.249516
\(46\) −6.94088 −1.02338
\(47\) −7.73754 −1.12864 −0.564318 0.825558i \(-0.690861\pi\)
−0.564318 + 0.825558i \(0.690861\pi\)
\(48\) 0.201602 0.0290987
\(49\) −3.91066 −0.558665
\(50\) 1.97791 0.279719
\(51\) 2.24001 0.313664
\(52\) −7.66311 −1.06268
\(53\) 1.61074 0.221252 0.110626 0.993862i \(-0.464715\pi\)
0.110626 + 0.993862i \(0.464715\pi\)
\(54\) 0.899709 0.122435
\(55\) −8.51728 −1.14847
\(56\) −5.04542 −0.674222
\(57\) 3.96067 0.524604
\(58\) −0.0911499 −0.0119686
\(59\) −2.46261 −0.320604 −0.160302 0.987068i \(-0.551247\pi\)
−0.160302 + 0.987068i \(0.551247\pi\)
\(60\) 1.99270 0.257257
\(61\) −4.77088 −0.610849 −0.305424 0.952216i \(-0.598798\pi\)
−0.305424 + 0.952216i \(0.598798\pi\)
\(62\) 4.16819 0.529361
\(63\) −1.75765 −0.221443
\(64\) 5.40531 0.675664
\(65\) 10.7738 1.33633
\(66\) −4.57824 −0.563543
\(67\) −3.42357 −0.418255 −0.209128 0.977888i \(-0.567062\pi\)
−0.209128 + 0.977888i \(0.567062\pi\)
\(68\) 2.66679 0.323396
\(69\) −7.71459 −0.928727
\(70\) 2.64691 0.316366
\(71\) −13.1223 −1.55733 −0.778665 0.627440i \(-0.784103\pi\)
−0.778665 + 0.627440i \(0.784103\pi\)
\(72\) 2.87054 0.338297
\(73\) −14.4582 −1.69220 −0.846100 0.533025i \(-0.821055\pi\)
−0.846100 + 0.533025i \(0.821055\pi\)
\(74\) 7.00010 0.813745
\(75\) 2.19839 0.253848
\(76\) 4.71528 0.540880
\(77\) 8.94396 1.01926
\(78\) 5.79120 0.655724
\(79\) −13.0644 −1.46986 −0.734930 0.678143i \(-0.762785\pi\)
−0.734930 + 0.678143i \(0.762785\pi\)
\(80\) −0.337442 −0.0377271
\(81\) 1.00000 0.111111
\(82\) −1.28286 −0.141668
\(83\) −0.423954 −0.0465350 −0.0232675 0.999729i \(-0.507407\pi\)
−0.0232675 + 0.999729i \(0.507407\pi\)
\(84\) −2.09253 −0.228314
\(85\) −3.74933 −0.406672
\(86\) 3.28716 0.354463
\(87\) −0.101311 −0.0108616
\(88\) −14.6070 −1.55711
\(89\) 17.1426 1.81711 0.908556 0.417763i \(-0.137186\pi\)
0.908556 + 0.417763i \(0.137186\pi\)
\(90\) −1.50593 −0.158739
\(91\) −11.3136 −1.18598
\(92\) −9.18440 −0.957540
\(93\) 4.63283 0.480402
\(94\) 6.96153 0.718027
\(95\) −6.62938 −0.680160
\(96\) 5.55970 0.567435
\(97\) 6.06424 0.615730 0.307865 0.951430i \(-0.400386\pi\)
0.307865 + 0.951430i \(0.400386\pi\)
\(98\) 3.51845 0.355417
\(99\) −5.08858 −0.511422
\(100\) 2.61724 0.261724
\(101\) 10.1166 1.00664 0.503320 0.864100i \(-0.332112\pi\)
0.503320 + 0.864100i \(0.332112\pi\)
\(102\) −2.01536 −0.199550
\(103\) 2.53914 0.250189 0.125094 0.992145i \(-0.460077\pi\)
0.125094 + 0.992145i \(0.460077\pi\)
\(104\) 18.4770 1.81182
\(105\) 2.94196 0.287106
\(106\) −1.44919 −0.140758
\(107\) 9.82497 0.949816 0.474908 0.880035i \(-0.342481\pi\)
0.474908 + 0.880035i \(0.342481\pi\)
\(108\) 1.19052 0.114558
\(109\) −15.1110 −1.44738 −0.723688 0.690127i \(-0.757555\pi\)
−0.723688 + 0.690127i \(0.757555\pi\)
\(110\) 7.66307 0.730645
\(111\) 7.78041 0.738484
\(112\) 0.354346 0.0334826
\(113\) 2.58916 0.243568 0.121784 0.992557i \(-0.461139\pi\)
0.121784 + 0.992557i \(0.461139\pi\)
\(114\) −3.56345 −0.333748
\(115\) 12.9127 1.20411
\(116\) −0.120613 −0.0111986
\(117\) 6.43675 0.595078
\(118\) 2.21563 0.203965
\(119\) 3.93716 0.360919
\(120\) −4.80472 −0.438609
\(121\) 14.8937 1.35397
\(122\) 4.29240 0.388616
\(123\) −1.42586 −0.128566
\(124\) 5.51549 0.495306
\(125\) −12.0487 −1.07767
\(126\) 1.58137 0.140880
\(127\) 7.24277 0.642692 0.321346 0.946962i \(-0.395865\pi\)
0.321346 + 0.946962i \(0.395865\pi\)
\(128\) 6.25619 0.552975
\(129\) 3.65358 0.321680
\(130\) −9.69332 −0.850160
\(131\) 2.14842 0.187709 0.0938543 0.995586i \(-0.470081\pi\)
0.0938543 + 0.995586i \(0.470081\pi\)
\(132\) −6.05808 −0.527289
\(133\) 6.96149 0.603637
\(134\) 3.08021 0.266090
\(135\) −1.67380 −0.144058
\(136\) −6.43005 −0.551372
\(137\) 6.53872 0.558640 0.279320 0.960198i \(-0.409891\pi\)
0.279320 + 0.960198i \(0.409891\pi\)
\(138\) 6.94088 0.590847
\(139\) 9.78192 0.829691 0.414846 0.909892i \(-0.363836\pi\)
0.414846 + 0.909892i \(0.363836\pi\)
\(140\) 3.50248 0.296013
\(141\) 7.73754 0.651618
\(142\) 11.8062 0.990758
\(143\) −32.7540 −2.73902
\(144\) −0.201602 −0.0168002
\(145\) 0.169574 0.0140823
\(146\) 13.0081 1.07656
\(147\) 3.91066 0.322546
\(148\) 9.26277 0.761395
\(149\) −12.0860 −0.990120 −0.495060 0.868859i \(-0.664854\pi\)
−0.495060 + 0.868859i \(0.664854\pi\)
\(150\) −1.97791 −0.161496
\(151\) 12.6923 1.03288 0.516442 0.856322i \(-0.327256\pi\)
0.516442 + 0.856322i \(0.327256\pi\)
\(152\) −11.3693 −0.922170
\(153\) −2.24001 −0.181094
\(154\) −8.04696 −0.648442
\(155\) −7.75443 −0.622851
\(156\) 7.66311 0.613540
\(157\) −20.3326 −1.62272 −0.811359 0.584548i \(-0.801272\pi\)
−0.811359 + 0.584548i \(0.801272\pi\)
\(158\) 11.7542 0.935110
\(159\) −1.61074 −0.127740
\(160\) −9.30583 −0.735691
\(161\) −13.5596 −1.06864
\(162\) −0.899709 −0.0706878
\(163\) −14.3750 −1.12593 −0.562967 0.826480i \(-0.690340\pi\)
−0.562967 + 0.826480i \(0.690340\pi\)
\(164\) −1.69752 −0.132554
\(165\) 8.51728 0.663069
\(166\) 0.381435 0.0296051
\(167\) −18.7294 −1.44933 −0.724663 0.689103i \(-0.758005\pi\)
−0.724663 + 0.689103i \(0.758005\pi\)
\(168\) 5.04542 0.389262
\(169\) 28.4318 2.18706
\(170\) 3.37331 0.258721
\(171\) −3.96067 −0.302880
\(172\) 4.34968 0.331660
\(173\) −11.7428 −0.892786 −0.446393 0.894837i \(-0.647292\pi\)
−0.446393 + 0.894837i \(0.647292\pi\)
\(174\) 0.0911499 0.00691006
\(175\) 3.86401 0.292091
\(176\) 1.02587 0.0773278
\(177\) 2.46261 0.185101
\(178\) −15.4233 −1.15603
\(179\) 24.5193 1.83266 0.916328 0.400429i \(-0.131139\pi\)
0.916328 + 0.400429i \(0.131139\pi\)
\(180\) −1.99270 −0.148527
\(181\) 2.13689 0.158833 0.0794167 0.996842i \(-0.474694\pi\)
0.0794167 + 0.996842i \(0.474694\pi\)
\(182\) 10.1789 0.754512
\(183\) 4.77088 0.352674
\(184\) 22.1450 1.63255
\(185\) −13.0229 −0.957460
\(186\) −4.16819 −0.305627
\(187\) 11.3985 0.833540
\(188\) 9.21173 0.671834
\(189\) 1.75765 0.127850
\(190\) 5.96451 0.432711
\(191\) 11.6936 0.846118 0.423059 0.906102i \(-0.360956\pi\)
0.423059 + 0.906102i \(0.360956\pi\)
\(192\) −5.40531 −0.390095
\(193\) 2.15548 0.155155 0.0775774 0.996986i \(-0.475282\pi\)
0.0775774 + 0.996986i \(0.475282\pi\)
\(194\) −5.45605 −0.391721
\(195\) −10.7738 −0.771531
\(196\) 4.65573 0.332552
\(197\) 6.46675 0.460737 0.230368 0.973104i \(-0.426007\pi\)
0.230368 + 0.973104i \(0.426007\pi\)
\(198\) 4.57824 0.325362
\(199\) 21.8975 1.55228 0.776138 0.630563i \(-0.217176\pi\)
0.776138 + 0.630563i \(0.217176\pi\)
\(200\) −6.31057 −0.446225
\(201\) 3.42357 0.241480
\(202\) −9.10200 −0.640415
\(203\) −0.178069 −0.0124980
\(204\) −2.66679 −0.186713
\(205\) 2.38661 0.166688
\(206\) −2.28449 −0.159168
\(207\) 7.71459 0.536201
\(208\) −1.29766 −0.0899767
\(209\) 20.1542 1.39410
\(210\) −2.64691 −0.182654
\(211\) 11.2465 0.774243 0.387122 0.922029i \(-0.373469\pi\)
0.387122 + 0.922029i \(0.373469\pi\)
\(212\) −1.91762 −0.131703
\(213\) 13.1223 0.899125
\(214\) −8.83961 −0.604263
\(215\) −6.11537 −0.417065
\(216\) −2.87054 −0.195316
\(217\) 8.14290 0.552776
\(218\) 13.5955 0.920806
\(219\) 14.4582 0.976992
\(220\) 10.1400 0.683641
\(221\) −14.4184 −0.969887
\(222\) −7.00010 −0.469816
\(223\) −19.8849 −1.33159 −0.665797 0.746133i \(-0.731908\pi\)
−0.665797 + 0.746133i \(0.731908\pi\)
\(224\) 9.77202 0.652921
\(225\) −2.19839 −0.146559
\(226\) −2.32949 −0.154955
\(227\) −6.20415 −0.411784 −0.205892 0.978575i \(-0.566010\pi\)
−0.205892 + 0.978575i \(0.566010\pi\)
\(228\) −4.71528 −0.312277
\(229\) −6.29386 −0.415910 −0.207955 0.978138i \(-0.566681\pi\)
−0.207955 + 0.978138i \(0.566681\pi\)
\(230\) −11.6177 −0.766045
\(231\) −8.94396 −0.588470
\(232\) 0.290816 0.0190930
\(233\) −1.37434 −0.0900362 −0.0450181 0.998986i \(-0.514335\pi\)
−0.0450181 + 0.998986i \(0.514335\pi\)
\(234\) −5.79120 −0.378583
\(235\) −12.9511 −0.844836
\(236\) 2.93179 0.190843
\(237\) 13.0644 0.848624
\(238\) −3.54230 −0.229613
\(239\) −1.00000 −0.0646846
\(240\) 0.337442 0.0217818
\(241\) −16.6512 −1.07260 −0.536299 0.844028i \(-0.680178\pi\)
−0.536299 + 0.844028i \(0.680178\pi\)
\(242\) −13.4000 −0.861383
\(243\) −1.00000 −0.0641500
\(244\) 5.67985 0.363615
\(245\) −6.54566 −0.418187
\(246\) 1.28286 0.0817921
\(247\) −25.4939 −1.62214
\(248\) −13.2987 −0.844470
\(249\) 0.423954 0.0268670
\(250\) 10.8403 0.685600
\(251\) 8.70369 0.549372 0.274686 0.961534i \(-0.411426\pi\)
0.274686 + 0.961534i \(0.411426\pi\)
\(252\) 2.09253 0.131817
\(253\) −39.2563 −2.46802
\(254\) −6.51638 −0.408874
\(255\) 3.74933 0.234792
\(256\) −16.4394 −1.02746
\(257\) −17.8087 −1.11087 −0.555437 0.831559i \(-0.687449\pi\)
−0.555437 + 0.831559i \(0.687449\pi\)
\(258\) −3.28716 −0.204650
\(259\) 13.6753 0.849739
\(260\) −12.8265 −0.795467
\(261\) 0.101311 0.00627096
\(262\) −1.93295 −0.119418
\(263\) 21.2660 1.31132 0.655658 0.755058i \(-0.272391\pi\)
0.655658 + 0.755058i \(0.272391\pi\)
\(264\) 14.6070 0.898998
\(265\) 2.69605 0.165617
\(266\) −6.26331 −0.384028
\(267\) −17.1426 −1.04911
\(268\) 4.07584 0.248971
\(269\) −17.1887 −1.04801 −0.524005 0.851715i \(-0.675563\pi\)
−0.524005 + 0.851715i \(0.675563\pi\)
\(270\) 1.50593 0.0916482
\(271\) 19.1030 1.16043 0.580213 0.814465i \(-0.302969\pi\)
0.580213 + 0.814465i \(0.302969\pi\)
\(272\) 0.451591 0.0273817
\(273\) 11.3136 0.684729
\(274\) −5.88294 −0.355401
\(275\) 11.1867 0.674583
\(276\) 9.18440 0.552836
\(277\) 19.3315 1.16152 0.580760 0.814075i \(-0.302755\pi\)
0.580760 + 0.814075i \(0.302755\pi\)
\(278\) −8.80087 −0.527841
\(279\) −4.63283 −0.277360
\(280\) −8.44502 −0.504687
\(281\) −4.05588 −0.241954 −0.120977 0.992655i \(-0.538603\pi\)
−0.120977 + 0.992655i \(0.538603\pi\)
\(282\) −6.96153 −0.414553
\(283\) −10.8007 −0.642035 −0.321018 0.947073i \(-0.604025\pi\)
−0.321018 + 0.947073i \(0.604025\pi\)
\(284\) 15.6224 0.927020
\(285\) 6.62938 0.392691
\(286\) 29.4690 1.74254
\(287\) −2.50617 −0.147934
\(288\) −5.55970 −0.327609
\(289\) −11.9823 −0.704844
\(290\) −0.152567 −0.00895903
\(291\) −6.06424 −0.355492
\(292\) 17.2128 1.00730
\(293\) 5.01609 0.293043 0.146522 0.989207i \(-0.453192\pi\)
0.146522 + 0.989207i \(0.453192\pi\)
\(294\) −3.51845 −0.205200
\(295\) −4.12191 −0.239987
\(296\) −22.3340 −1.29814
\(297\) 5.08858 0.295270
\(298\) 10.8738 0.629904
\(299\) 49.6569 2.87173
\(300\) −2.61724 −0.151106
\(301\) 6.42173 0.370142
\(302\) −11.4194 −0.657110
\(303\) −10.1166 −0.581184
\(304\) 0.798480 0.0457959
\(305\) −7.98550 −0.457249
\(306\) 2.01536 0.115210
\(307\) −9.70591 −0.553945 −0.276973 0.960878i \(-0.589331\pi\)
−0.276973 + 0.960878i \(0.589331\pi\)
\(308\) −10.6480 −0.606727
\(309\) −2.53914 −0.144447
\(310\) 6.97673 0.396251
\(311\) −10.3411 −0.586389 −0.293195 0.956053i \(-0.594718\pi\)
−0.293195 + 0.956053i \(0.594718\pi\)
\(312\) −18.4770 −1.04605
\(313\) −23.8987 −1.35084 −0.675418 0.737435i \(-0.736037\pi\)
−0.675418 + 0.737435i \(0.736037\pi\)
\(314\) 18.2934 1.03236
\(315\) −2.94196 −0.165761
\(316\) 15.5535 0.874952
\(317\) −1.48619 −0.0834729 −0.0417365 0.999129i \(-0.513289\pi\)
−0.0417365 + 0.999129i \(0.513289\pi\)
\(318\) 1.44919 0.0812667
\(319\) −0.515527 −0.0288640
\(320\) 9.04742 0.505766
\(321\) −9.82497 −0.548377
\(322\) 12.1997 0.679860
\(323\) 8.87196 0.493649
\(324\) −1.19052 −0.0661403
\(325\) −14.1505 −0.784928
\(326\) 12.9333 0.716307
\(327\) 15.1110 0.835643
\(328\) 4.09299 0.225998
\(329\) 13.5999 0.749787
\(330\) −7.66307 −0.421838
\(331\) −17.6038 −0.967593 −0.483797 0.875180i \(-0.660743\pi\)
−0.483797 + 0.875180i \(0.660743\pi\)
\(332\) 0.504728 0.0277006
\(333\) −7.78041 −0.426364
\(334\) 16.8510 0.922047
\(335\) −5.73037 −0.313083
\(336\) −0.354346 −0.0193312
\(337\) 18.9294 1.03115 0.515576 0.856844i \(-0.327578\pi\)
0.515576 + 0.856844i \(0.327578\pi\)
\(338\) −25.5803 −1.39139
\(339\) −2.58916 −0.140624
\(340\) 4.46368 0.242077
\(341\) 23.5745 1.27663
\(342\) 3.56345 0.192689
\(343\) 19.1771 1.03547
\(344\) −10.4878 −0.565462
\(345\) −12.9127 −0.695195
\(346\) 10.5651 0.567982
\(347\) −1.63077 −0.0875444 −0.0437722 0.999042i \(-0.513938\pi\)
−0.0437722 + 0.999042i \(0.513938\pi\)
\(348\) 0.120613 0.00646552
\(349\) 8.00213 0.428344 0.214172 0.976796i \(-0.431295\pi\)
0.214172 + 0.976796i \(0.431295\pi\)
\(350\) −3.47648 −0.185826
\(351\) −6.43675 −0.343568
\(352\) 28.2910 1.50792
\(353\) 9.60124 0.511022 0.255511 0.966806i \(-0.417756\pi\)
0.255511 + 0.966806i \(0.417756\pi\)
\(354\) −2.21563 −0.117759
\(355\) −21.9641 −1.16573
\(356\) −20.4087 −1.08166
\(357\) −3.93716 −0.208377
\(358\) −22.0602 −1.16592
\(359\) −31.4338 −1.65901 −0.829506 0.558498i \(-0.811378\pi\)
−0.829506 + 0.558498i \(0.811378\pi\)
\(360\) 4.80472 0.253231
\(361\) −3.31307 −0.174372
\(362\) −1.92257 −0.101048
\(363\) −14.8937 −0.781716
\(364\) 13.4691 0.705972
\(365\) −24.2001 −1.26669
\(366\) −4.29240 −0.224367
\(367\) −9.76744 −0.509856 −0.254928 0.966960i \(-0.582052\pi\)
−0.254928 + 0.966960i \(0.582052\pi\)
\(368\) −1.55528 −0.0810744
\(369\) 1.42586 0.0742273
\(370\) 11.7168 0.609126
\(371\) −2.83111 −0.146984
\(372\) −5.51549 −0.285965
\(373\) 18.4876 0.957252 0.478626 0.878019i \(-0.341135\pi\)
0.478626 + 0.878019i \(0.341135\pi\)
\(374\) −10.2553 −0.530290
\(375\) 12.0487 0.622191
\(376\) −22.2109 −1.14544
\(377\) 0.652111 0.0335854
\(378\) −1.58137 −0.0813371
\(379\) −1.80626 −0.0927813 −0.0463907 0.998923i \(-0.514772\pi\)
−0.0463907 + 0.998923i \(0.514772\pi\)
\(380\) 7.89244 0.404874
\(381\) −7.24277 −0.371058
\(382\) −10.5208 −0.538292
\(383\) −25.2177 −1.28856 −0.644281 0.764789i \(-0.722843\pi\)
−0.644281 + 0.764789i \(0.722843\pi\)
\(384\) −6.25619 −0.319260
\(385\) 14.9704 0.762963
\(386\) −1.93930 −0.0987079
\(387\) −3.65358 −0.185722
\(388\) −7.21962 −0.366521
\(389\) 29.1698 1.47897 0.739485 0.673173i \(-0.235069\pi\)
0.739485 + 0.673173i \(0.235069\pi\)
\(390\) 9.69332 0.490840
\(391\) −17.2808 −0.873926
\(392\) −11.2257 −0.566984
\(393\) −2.14842 −0.108374
\(394\) −5.81819 −0.293116
\(395\) −21.8672 −1.10026
\(396\) 6.05808 0.304430
\(397\) 37.3463 1.87435 0.937177 0.348853i \(-0.113429\pi\)
0.937177 + 0.348853i \(0.113429\pi\)
\(398\) −19.7014 −0.987542
\(399\) −6.96149 −0.348510
\(400\) 0.443200 0.0221600
\(401\) 5.50916 0.275114 0.137557 0.990494i \(-0.456075\pi\)
0.137557 + 0.990494i \(0.456075\pi\)
\(402\) −3.08021 −0.153627
\(403\) −29.8204 −1.48546
\(404\) −12.0441 −0.599215
\(405\) 1.67380 0.0831718
\(406\) 0.160210 0.00795108
\(407\) 39.5913 1.96247
\(408\) 6.43005 0.318335
\(409\) −28.2723 −1.39797 −0.698987 0.715134i \(-0.746366\pi\)
−0.698987 + 0.715134i \(0.746366\pi\)
\(410\) −2.14725 −0.106045
\(411\) −6.53872 −0.322531
\(412\) −3.02291 −0.148928
\(413\) 4.32840 0.212987
\(414\) −6.94088 −0.341126
\(415\) −0.709615 −0.0348337
\(416\) −35.7864 −1.75457
\(417\) −9.78192 −0.479023
\(418\) −18.1329 −0.886910
\(419\) 12.0357 0.587983 0.293992 0.955808i \(-0.405016\pi\)
0.293992 + 0.955808i \(0.405016\pi\)
\(420\) −3.50248 −0.170903
\(421\) −29.9983 −1.46203 −0.731015 0.682362i \(-0.760953\pi\)
−0.731015 + 0.682362i \(0.760953\pi\)
\(422\) −10.1186 −0.492566
\(423\) −7.73754 −0.376212
\(424\) 4.62368 0.224546
\(425\) 4.92442 0.238869
\(426\) −11.8062 −0.572014
\(427\) 8.38555 0.405805
\(428\) −11.6969 −0.565390
\(429\) 32.7540 1.58138
\(430\) 5.50205 0.265332
\(431\) −17.8098 −0.857870 −0.428935 0.903335i \(-0.641111\pi\)
−0.428935 + 0.903335i \(0.641111\pi\)
\(432\) 0.201602 0.00969958
\(433\) 20.2488 0.973094 0.486547 0.873654i \(-0.338256\pi\)
0.486547 + 0.873654i \(0.338256\pi\)
\(434\) −7.32623 −0.351670
\(435\) −0.169574 −0.00813043
\(436\) 17.9901 0.861568
\(437\) −30.5550 −1.46164
\(438\) −13.0081 −0.621552
\(439\) −34.7608 −1.65904 −0.829521 0.558475i \(-0.811387\pi\)
−0.829521 + 0.558475i \(0.811387\pi\)
\(440\) −24.4492 −1.16557
\(441\) −3.91066 −0.186222
\(442\) 12.9724 0.617032
\(443\) −25.7595 −1.22387 −0.611935 0.790908i \(-0.709608\pi\)
−0.611935 + 0.790908i \(0.709608\pi\)
\(444\) −9.26277 −0.439592
\(445\) 28.6933 1.36019
\(446\) 17.8907 0.847147
\(447\) 12.0860 0.571646
\(448\) −9.50066 −0.448864
\(449\) −30.2122 −1.42580 −0.712901 0.701265i \(-0.752619\pi\)
−0.712901 + 0.701265i \(0.752619\pi\)
\(450\) 1.97791 0.0932396
\(451\) −7.25561 −0.341653
\(452\) −3.08246 −0.144987
\(453\) −12.6923 −0.596336
\(454\) 5.58193 0.261973
\(455\) −18.9367 −0.887765
\(456\) 11.3693 0.532415
\(457\) 1.33578 0.0624850 0.0312425 0.999512i \(-0.490054\pi\)
0.0312425 + 0.999512i \(0.490054\pi\)
\(458\) 5.66264 0.264598
\(459\) 2.24001 0.104555
\(460\) −15.3729 −0.716764
\(461\) 16.6243 0.774272 0.387136 0.922023i \(-0.373464\pi\)
0.387136 + 0.922023i \(0.373464\pi\)
\(462\) 8.04696 0.374378
\(463\) 29.4246 1.36748 0.683739 0.729726i \(-0.260353\pi\)
0.683739 + 0.729726i \(0.260353\pi\)
\(464\) −0.0204244 −0.000948179 0
\(465\) 7.75443 0.359603
\(466\) 1.23651 0.0572801
\(467\) −2.53660 −0.117380 −0.0586899 0.998276i \(-0.518692\pi\)
−0.0586899 + 0.998276i \(0.518692\pi\)
\(468\) −7.66311 −0.354228
\(469\) 6.01744 0.277859
\(470\) 11.6522 0.537476
\(471\) 20.3326 0.936876
\(472\) −7.06901 −0.325378
\(473\) 18.5916 0.854841
\(474\) −11.7542 −0.539886
\(475\) 8.70710 0.399509
\(476\) −4.68729 −0.214842
\(477\) 1.61074 0.0737505
\(478\) 0.899709 0.0411517
\(479\) 38.6620 1.76651 0.883255 0.468893i \(-0.155347\pi\)
0.883255 + 0.468893i \(0.155347\pi\)
\(480\) 9.30583 0.424751
\(481\) −50.0806 −2.28348
\(482\) 14.9812 0.682376
\(483\) 13.5596 0.616981
\(484\) −17.7313 −0.805968
\(485\) 10.1503 0.460903
\(486\) 0.899709 0.0408116
\(487\) 9.29522 0.421207 0.210603 0.977572i \(-0.432457\pi\)
0.210603 + 0.977572i \(0.432457\pi\)
\(488\) −13.6950 −0.619944
\(489\) 14.3750 0.650058
\(490\) 5.88919 0.266046
\(491\) 11.3475 0.512105 0.256052 0.966663i \(-0.417578\pi\)
0.256052 + 0.966663i \(0.417578\pi\)
\(492\) 1.69752 0.0765302
\(493\) −0.226937 −0.0102207
\(494\) 22.9371 1.03199
\(495\) −8.51728 −0.382823
\(496\) 0.933987 0.0419372
\(497\) 23.0644 1.03458
\(498\) −0.381435 −0.0170925
\(499\) 24.8745 1.11353 0.556767 0.830669i \(-0.312042\pi\)
0.556767 + 0.830669i \(0.312042\pi\)
\(500\) 14.3442 0.641494
\(501\) 18.7294 0.836769
\(502\) −7.83078 −0.349505
\(503\) 13.2786 0.592064 0.296032 0.955178i \(-0.404337\pi\)
0.296032 + 0.955178i \(0.404337\pi\)
\(504\) −5.04542 −0.224741
\(505\) 16.9332 0.753517
\(506\) 35.3192 1.57013
\(507\) −28.4318 −1.26270
\(508\) −8.62270 −0.382570
\(509\) 33.4053 1.48067 0.740333 0.672241i \(-0.234668\pi\)
0.740333 + 0.672241i \(0.234668\pi\)
\(510\) −3.37331 −0.149373
\(511\) 25.4124 1.12418
\(512\) 2.27826 0.100686
\(513\) 3.96067 0.174868
\(514\) 16.0226 0.706727
\(515\) 4.25001 0.187278
\(516\) −4.34968 −0.191484
\(517\) 39.3731 1.73163
\(518\) −12.3037 −0.540596
\(519\) 11.7428 0.515451
\(520\) 30.9268 1.35623
\(521\) 33.4430 1.46516 0.732582 0.680678i \(-0.238315\pi\)
0.732582 + 0.680678i \(0.238315\pi\)
\(522\) −0.0911499 −0.00398952
\(523\) −25.7941 −1.12790 −0.563948 0.825810i \(-0.690718\pi\)
−0.563948 + 0.825810i \(0.690718\pi\)
\(524\) −2.55775 −0.111736
\(525\) −3.86401 −0.168639
\(526\) −19.1332 −0.834246
\(527\) 10.3776 0.452055
\(528\) −1.02587 −0.0446452
\(529\) 36.5148 1.58760
\(530\) −2.42566 −0.105364
\(531\) −2.46261 −0.106868
\(532\) −8.28782 −0.359323
\(533\) 9.17791 0.397540
\(534\) 15.4233 0.667433
\(535\) 16.4451 0.710982
\(536\) −9.82749 −0.424483
\(537\) −24.5193 −1.05808
\(538\) 15.4648 0.666734
\(539\) 19.8997 0.857141
\(540\) 1.99270 0.0857522
\(541\) 4.49430 0.193225 0.0966126 0.995322i \(-0.469199\pi\)
0.0966126 + 0.995322i \(0.469199\pi\)
\(542\) −17.1871 −0.738251
\(543\) −2.13689 −0.0917025
\(544\) 12.4538 0.533952
\(545\) −25.2929 −1.08343
\(546\) −10.1789 −0.435618
\(547\) −24.5160 −1.04823 −0.524114 0.851648i \(-0.675603\pi\)
−0.524114 + 0.851648i \(0.675603\pi\)
\(548\) −7.78450 −0.332537
\(549\) −4.77088 −0.203616
\(550\) −10.0648 −0.429163
\(551\) −0.401258 −0.0170942
\(552\) −22.1450 −0.942556
\(553\) 22.9627 0.976472
\(554\) −17.3928 −0.738947
\(555\) 13.0229 0.552790
\(556\) −11.6456 −0.493884
\(557\) 25.5502 1.08260 0.541299 0.840830i \(-0.317933\pi\)
0.541299 + 0.840830i \(0.317933\pi\)
\(558\) 4.16819 0.176454
\(559\) −23.5172 −0.994672
\(560\) 0.593105 0.0250633
\(561\) −11.3985 −0.481245
\(562\) 3.64911 0.153929
\(563\) −13.4776 −0.568011 −0.284006 0.958823i \(-0.591663\pi\)
−0.284006 + 0.958823i \(0.591663\pi\)
\(564\) −9.21173 −0.387884
\(565\) 4.33374 0.182322
\(566\) 9.71749 0.408456
\(567\) −1.75765 −0.0738145
\(568\) −37.6681 −1.58052
\(569\) −6.39428 −0.268062 −0.134031 0.990977i \(-0.542792\pi\)
−0.134031 + 0.990977i \(0.542792\pi\)
\(570\) −5.96451 −0.249826
\(571\) −17.9506 −0.751210 −0.375605 0.926780i \(-0.622565\pi\)
−0.375605 + 0.926780i \(0.622565\pi\)
\(572\) 38.9944 1.63044
\(573\) −11.6936 −0.488506
\(574\) 2.25482 0.0941144
\(575\) −16.9597 −0.707267
\(576\) 5.40531 0.225221
\(577\) −37.1291 −1.54571 −0.772853 0.634585i \(-0.781171\pi\)
−0.772853 + 0.634585i \(0.781171\pi\)
\(578\) 10.7806 0.448415
\(579\) −2.15548 −0.0895787
\(580\) −0.201882 −0.00838268
\(581\) 0.745165 0.0309146
\(582\) 5.45605 0.226160
\(583\) −8.19636 −0.339459
\(584\) −41.5027 −1.71740
\(585\) 10.7738 0.445444
\(586\) −4.51302 −0.186431
\(587\) −36.6232 −1.51160 −0.755800 0.654803i \(-0.772752\pi\)
−0.755800 + 0.654803i \(0.772752\pi\)
\(588\) −4.65573 −0.191999
\(589\) 18.3491 0.756062
\(590\) 3.70852 0.152677
\(591\) −6.46675 −0.266006
\(592\) 1.56855 0.0644669
\(593\) 38.1568 1.56691 0.783456 0.621447i \(-0.213455\pi\)
0.783456 + 0.621447i \(0.213455\pi\)
\(594\) −4.57824 −0.187848
\(595\) 6.59003 0.270165
\(596\) 14.3886 0.589381
\(597\) −21.8975 −0.896207
\(598\) −44.6767 −1.82697
\(599\) 48.4161 1.97823 0.989115 0.147148i \(-0.0470092\pi\)
0.989115 + 0.147148i \(0.0470092\pi\)
\(600\) 6.31057 0.257628
\(601\) 22.2469 0.907472 0.453736 0.891136i \(-0.350091\pi\)
0.453736 + 0.891136i \(0.350091\pi\)
\(602\) −5.77768 −0.235481
\(603\) −3.42357 −0.139418
\(604\) −15.1105 −0.614837
\(605\) 24.9291 1.01351
\(606\) 9.10200 0.369744
\(607\) 40.3888 1.63933 0.819665 0.572842i \(-0.194159\pi\)
0.819665 + 0.572842i \(0.194159\pi\)
\(608\) 22.0202 0.893035
\(609\) 0.178069 0.00721571
\(610\) 7.18463 0.290897
\(611\) −49.8046 −2.01488
\(612\) 2.66679 0.107799
\(613\) −16.3156 −0.658979 −0.329490 0.944159i \(-0.606877\pi\)
−0.329490 + 0.944159i \(0.606877\pi\)
\(614\) 8.73249 0.352415
\(615\) −2.38661 −0.0962373
\(616\) 25.6740 1.03444
\(617\) 5.46752 0.220114 0.110057 0.993925i \(-0.464897\pi\)
0.110057 + 0.993925i \(0.464897\pi\)
\(618\) 2.28449 0.0918955
\(619\) 43.6271 1.75352 0.876761 0.480926i \(-0.159700\pi\)
0.876761 + 0.480926i \(0.159700\pi\)
\(620\) 9.23184 0.370760
\(621\) −7.71459 −0.309576
\(622\) 9.30397 0.373055
\(623\) −30.1307 −1.20716
\(624\) 1.29766 0.0519481
\(625\) −9.17513 −0.367005
\(626\) 21.5019 0.859389
\(627\) −20.1542 −0.804882
\(628\) 24.2065 0.965943
\(629\) 17.4282 0.694908
\(630\) 2.64691 0.105455
\(631\) 25.7573 1.02538 0.512692 0.858573i \(-0.328648\pi\)
0.512692 + 0.858573i \(0.328648\pi\)
\(632\) −37.5019 −1.49175
\(633\) −11.2465 −0.447010
\(634\) 1.33714 0.0531046
\(635\) 12.1230 0.481085
\(636\) 1.91762 0.0760386
\(637\) −25.1719 −0.997349
\(638\) 0.463824 0.0183630
\(639\) −13.1223 −0.519110
\(640\) 10.4716 0.413927
\(641\) 2.85693 0.112842 0.0564210 0.998407i \(-0.482031\pi\)
0.0564210 + 0.998407i \(0.482031\pi\)
\(642\) 8.83961 0.348872
\(643\) 10.7053 0.422176 0.211088 0.977467i \(-0.432299\pi\)
0.211088 + 0.977467i \(0.432299\pi\)
\(644\) 16.1430 0.636123
\(645\) 6.11537 0.240792
\(646\) −7.98217 −0.314054
\(647\) 10.9862 0.431913 0.215956 0.976403i \(-0.430713\pi\)
0.215956 + 0.976403i \(0.430713\pi\)
\(648\) 2.87054 0.112766
\(649\) 12.5312 0.491892
\(650\) 12.7313 0.499363
\(651\) −8.14290 −0.319145
\(652\) 17.1137 0.670226
\(653\) −41.1768 −1.61137 −0.805687 0.592342i \(-0.798203\pi\)
−0.805687 + 0.592342i \(0.798203\pi\)
\(654\) −13.5955 −0.531628
\(655\) 3.59603 0.140509
\(656\) −0.287456 −0.0112233
\(657\) −14.4582 −0.564066
\(658\) −12.2359 −0.477007
\(659\) 1.39962 0.0545216 0.0272608 0.999628i \(-0.491322\pi\)
0.0272608 + 0.999628i \(0.491322\pi\)
\(660\) −10.1400 −0.394700
\(661\) 26.9112 1.04673 0.523363 0.852110i \(-0.324677\pi\)
0.523363 + 0.852110i \(0.324677\pi\)
\(662\) 15.8383 0.615573
\(663\) 14.4184 0.559964
\(664\) −1.21698 −0.0472280
\(665\) 11.6521 0.451851
\(666\) 7.00010 0.271248
\(667\) 0.781569 0.0302625
\(668\) 22.2978 0.862729
\(669\) 19.8849 0.768797
\(670\) 5.15566 0.199181
\(671\) 24.2770 0.937204
\(672\) −9.77202 −0.376964
\(673\) 35.4943 1.36821 0.684103 0.729386i \(-0.260194\pi\)
0.684103 + 0.729386i \(0.260194\pi\)
\(674\) −17.0310 −0.656009
\(675\) 2.19839 0.0846161
\(676\) −33.8487 −1.30187
\(677\) 7.66192 0.294471 0.147236 0.989101i \(-0.452962\pi\)
0.147236 + 0.989101i \(0.452962\pi\)
\(678\) 2.32949 0.0894635
\(679\) −10.6588 −0.409048
\(680\) −10.7626 −0.412728
\(681\) 6.20415 0.237744
\(682\) −21.2102 −0.812180
\(683\) −11.5533 −0.442074 −0.221037 0.975265i \(-0.570944\pi\)
−0.221037 + 0.975265i \(0.570944\pi\)
\(684\) 4.71528 0.180293
\(685\) 10.9445 0.418168
\(686\) −17.2538 −0.658755
\(687\) 6.29386 0.240126
\(688\) 0.736569 0.0280814
\(689\) 10.3679 0.394986
\(690\) 11.6177 0.442276
\(691\) 9.48943 0.360995 0.180498 0.983575i \(-0.442229\pi\)
0.180498 + 0.983575i \(0.442229\pi\)
\(692\) 13.9801 0.531442
\(693\) 8.94396 0.339753
\(694\) 1.46722 0.0556949
\(695\) 16.3730 0.621063
\(696\) −0.290816 −0.0110234
\(697\) −3.19395 −0.120979
\(698\) −7.19959 −0.272508
\(699\) 1.37434 0.0519824
\(700\) −4.60019 −0.173871
\(701\) −33.6461 −1.27079 −0.635397 0.772186i \(-0.719164\pi\)
−0.635397 + 0.772186i \(0.719164\pi\)
\(702\) 5.79120 0.218575
\(703\) 30.8157 1.16223
\(704\) −27.5054 −1.03665
\(705\) 12.9511 0.487766
\(706\) −8.63831 −0.325107
\(707\) −17.7815 −0.668742
\(708\) −2.93179 −0.110183
\(709\) −27.7519 −1.04224 −0.521122 0.853482i \(-0.674486\pi\)
−0.521122 + 0.853482i \(0.674486\pi\)
\(710\) 19.7613 0.741629
\(711\) −13.0644 −0.489953
\(712\) 49.2085 1.84417
\(713\) −35.7403 −1.33849
\(714\) 3.54230 0.132567
\(715\) −54.8236 −2.05029
\(716\) −29.1908 −1.09091
\(717\) 1.00000 0.0373457
\(718\) 28.2812 1.05545
\(719\) −28.9767 −1.08065 −0.540324 0.841457i \(-0.681698\pi\)
−0.540324 + 0.841457i \(0.681698\pi\)
\(720\) −0.337442 −0.0125757
\(721\) −4.46292 −0.166208
\(722\) 2.98080 0.110934
\(723\) 16.6512 0.619265
\(724\) −2.54402 −0.0945476
\(725\) −0.222720 −0.00827161
\(726\) 13.4000 0.497320
\(727\) −17.6229 −0.653599 −0.326799 0.945094i \(-0.605970\pi\)
−0.326799 + 0.945094i \(0.605970\pi\)
\(728\) −32.4761 −1.20364
\(729\) 1.00000 0.0370370
\(730\) 21.7730 0.805855
\(731\) 8.18407 0.302699
\(732\) −5.67985 −0.209933
\(733\) 10.2978 0.380359 0.190180 0.981749i \(-0.439093\pi\)
0.190180 + 0.981749i \(0.439093\pi\)
\(734\) 8.78785 0.324366
\(735\) 6.54566 0.241440
\(736\) −42.8908 −1.58098
\(737\) 17.4211 0.641714
\(738\) −1.28286 −0.0472227
\(739\) 13.2229 0.486411 0.243206 0.969975i \(-0.421801\pi\)
0.243206 + 0.969975i \(0.421801\pi\)
\(740\) 15.5040 0.569940
\(741\) 25.4939 0.936541
\(742\) 2.54718 0.0935098
\(743\) 7.80394 0.286299 0.143149 0.989701i \(-0.454277\pi\)
0.143149 + 0.989701i \(0.454277\pi\)
\(744\) 13.2987 0.487555
\(745\) −20.2295 −0.741151
\(746\) −16.6335 −0.608994
\(747\) −0.423954 −0.0155117
\(748\) −13.5702 −0.496175
\(749\) −17.2689 −0.630991
\(750\) −10.8403 −0.395832
\(751\) 50.3886 1.83871 0.919353 0.393435i \(-0.128713\pi\)
0.919353 + 0.393435i \(0.128713\pi\)
\(752\) 1.55990 0.0568838
\(753\) −8.70369 −0.317180
\(754\) −0.586710 −0.0213667
\(755\) 21.2444 0.773162
\(756\) −2.09253 −0.0761045
\(757\) −46.6796 −1.69660 −0.848299 0.529517i \(-0.822373\pi\)
−0.848299 + 0.529517i \(0.822373\pi\)
\(758\) 1.62511 0.0590265
\(759\) 39.2563 1.42491
\(760\) −19.0299 −0.690287
\(761\) 24.2370 0.878591 0.439296 0.898343i \(-0.355228\pi\)
0.439296 + 0.898343i \(0.355228\pi\)
\(762\) 6.51638 0.236064
\(763\) 26.5600 0.961536
\(764\) −13.9215 −0.503662
\(765\) −3.74933 −0.135557
\(766\) 22.6886 0.819771
\(767\) −15.8512 −0.572353
\(768\) 16.4394 0.593205
\(769\) 23.9656 0.864222 0.432111 0.901820i \(-0.357769\pi\)
0.432111 + 0.901820i \(0.357769\pi\)
\(770\) −13.4690 −0.485389
\(771\) 17.8087 0.641363
\(772\) −2.56615 −0.0923578
\(773\) 1.40235 0.0504391 0.0252195 0.999682i \(-0.491972\pi\)
0.0252195 + 0.999682i \(0.491972\pi\)
\(774\) 3.28716 0.118154
\(775\) 10.1848 0.365847
\(776\) 17.4076 0.624898
\(777\) −13.6753 −0.490597
\(778\) −26.2444 −0.940906
\(779\) −5.64737 −0.202338
\(780\) 12.8265 0.459263
\(781\) 66.7739 2.38936
\(782\) 15.5477 0.555983
\(783\) −0.101311 −0.00362054
\(784\) 0.788396 0.0281570
\(785\) −34.0327 −1.21468
\(786\) 1.93295 0.0689462
\(787\) −22.5141 −0.802540 −0.401270 0.915960i \(-0.631431\pi\)
−0.401270 + 0.915960i \(0.631431\pi\)
\(788\) −7.69882 −0.274259
\(789\) −21.2660 −0.757089
\(790\) 19.6741 0.699974
\(791\) −4.55085 −0.161809
\(792\) −14.6070 −0.519037
\(793\) −30.7090 −1.09051
\(794\) −33.6007 −1.19245
\(795\) −2.69605 −0.0956191
\(796\) −26.0696 −0.924011
\(797\) −35.7937 −1.26788 −0.633939 0.773383i \(-0.718563\pi\)
−0.633939 + 0.773383i \(0.718563\pi\)
\(798\) 6.26331 0.221719
\(799\) 17.3322 0.613168
\(800\) 12.2224 0.432127
\(801\) 17.1426 0.605704
\(802\) −4.95664 −0.175025
\(803\) 73.5715 2.59628
\(804\) −4.07584 −0.143744
\(805\) −22.6960 −0.799929
\(806\) 26.8296 0.945033
\(807\) 17.1887 0.605069
\(808\) 29.0402 1.02163
\(809\) −22.3480 −0.785712 −0.392856 0.919600i \(-0.628513\pi\)
−0.392856 + 0.919600i \(0.628513\pi\)
\(810\) −1.50593 −0.0529131
\(811\) 12.5070 0.439182 0.219591 0.975592i \(-0.429528\pi\)
0.219591 + 0.975592i \(0.429528\pi\)
\(812\) 0.211995 0.00743957
\(813\) −19.1030 −0.669972
\(814\) −35.6206 −1.24850
\(815\) −24.0608 −0.842813
\(816\) −0.451591 −0.0158088
\(817\) 14.4706 0.506264
\(818\) 25.4368 0.889377
\(819\) −11.3136 −0.395328
\(820\) −2.84131 −0.0992230
\(821\) −38.7711 −1.35312 −0.676560 0.736387i \(-0.736530\pi\)
−0.676560 + 0.736387i \(0.736530\pi\)
\(822\) 5.88294 0.205191
\(823\) 51.3284 1.78920 0.894598 0.446872i \(-0.147462\pi\)
0.894598 + 0.446872i \(0.147462\pi\)
\(824\) 7.28871 0.253914
\(825\) −11.1867 −0.389471
\(826\) −3.89430 −0.135500
\(827\) −15.0423 −0.523072 −0.261536 0.965194i \(-0.584229\pi\)
−0.261536 + 0.965194i \(0.584229\pi\)
\(828\) −9.18440 −0.319180
\(829\) −24.9052 −0.864992 −0.432496 0.901636i \(-0.642367\pi\)
−0.432496 + 0.901636i \(0.642367\pi\)
\(830\) 0.638447 0.0221608
\(831\) −19.3315 −0.670604
\(832\) 34.7927 1.20622
\(833\) 8.75992 0.303513
\(834\) 8.80087 0.304749
\(835\) −31.3493 −1.08489
\(836\) −23.9941 −0.829853
\(837\) 4.63283 0.160134
\(838\) −10.8286 −0.374069
\(839\) 14.5488 0.502279 0.251139 0.967951i \(-0.419195\pi\)
0.251139 + 0.967951i \(0.419195\pi\)
\(840\) 8.44502 0.291381
\(841\) −28.9897 −0.999646
\(842\) 26.9898 0.930129
\(843\) 4.05588 0.139692
\(844\) −13.3893 −0.460878
\(845\) 47.5892 1.63712
\(846\) 6.96153 0.239342
\(847\) −26.1779 −0.899484
\(848\) −0.324727 −0.0111512
\(849\) 10.8007 0.370679
\(850\) −4.43054 −0.151966
\(851\) −60.0226 −2.05755
\(852\) −15.6224 −0.535215
\(853\) −33.7550 −1.15575 −0.577875 0.816125i \(-0.696118\pi\)
−0.577875 + 0.816125i \(0.696118\pi\)
\(854\) −7.54455 −0.258169
\(855\) −6.62938 −0.226720
\(856\) 28.2030 0.963959
\(857\) 47.0497 1.60719 0.803593 0.595179i \(-0.202919\pi\)
0.803593 + 0.595179i \(0.202919\pi\)
\(858\) −29.4690 −1.00606
\(859\) −47.7888 −1.63053 −0.815267 0.579085i \(-0.803410\pi\)
−0.815267 + 0.579085i \(0.803410\pi\)
\(860\) 7.28050 0.248263
\(861\) 2.50617 0.0854100
\(862\) 16.0237 0.545768
\(863\) 30.8008 1.04847 0.524236 0.851573i \(-0.324351\pi\)
0.524236 + 0.851573i \(0.324351\pi\)
\(864\) 5.55970 0.189145
\(865\) −19.6551 −0.668292
\(866\) −18.2180 −0.619072
\(867\) 11.9823 0.406942
\(868\) −9.69432 −0.329047
\(869\) 66.4793 2.25516
\(870\) 0.152567 0.00517250
\(871\) −22.0366 −0.746683
\(872\) −43.3769 −1.46893
\(873\) 6.06424 0.205243
\(874\) 27.4906 0.929882
\(875\) 21.1774 0.715926
\(876\) −17.2128 −0.581566
\(877\) −43.0660 −1.45424 −0.727118 0.686512i \(-0.759141\pi\)
−0.727118 + 0.686512i \(0.759141\pi\)
\(878\) 31.2746 1.05547
\(879\) −5.01609 −0.169189
\(880\) 1.71710 0.0578834
\(881\) 30.2543 1.01929 0.509647 0.860384i \(-0.329776\pi\)
0.509647 + 0.860384i \(0.329776\pi\)
\(882\) 3.51845 0.118472
\(883\) 33.4773 1.12660 0.563300 0.826252i \(-0.309531\pi\)
0.563300 + 0.826252i \(0.309531\pi\)
\(884\) 17.1655 0.577337
\(885\) 4.12191 0.138557
\(886\) 23.1760 0.778613
\(887\) −34.7429 −1.16655 −0.583277 0.812274i \(-0.698230\pi\)
−0.583277 + 0.812274i \(0.698230\pi\)
\(888\) 22.3340 0.749480
\(889\) −12.7303 −0.426960
\(890\) −25.8156 −0.865341
\(891\) −5.08858 −0.170474
\(892\) 23.6735 0.792648
\(893\) 30.6458 1.02552
\(894\) −10.8738 −0.363676
\(895\) 41.0404 1.37183
\(896\) −10.9962 −0.367358
\(897\) −49.6569 −1.65800
\(898\) 27.1822 0.907081
\(899\) −0.469354 −0.0156538
\(900\) 2.61724 0.0872412
\(901\) −3.60807 −0.120202
\(902\) 6.52794 0.217356
\(903\) −6.42173 −0.213702
\(904\) 7.43230 0.247194
\(905\) 3.57672 0.118894
\(906\) 11.4194 0.379383
\(907\) −18.9277 −0.628484 −0.314242 0.949343i \(-0.601750\pi\)
−0.314242 + 0.949343i \(0.601750\pi\)
\(908\) 7.38620 0.245120
\(909\) 10.1166 0.335547
\(910\) 17.0375 0.564787
\(911\) −53.6024 −1.77593 −0.887964 0.459914i \(-0.847880\pi\)
−0.887964 + 0.459914i \(0.847880\pi\)
\(912\) −0.798480 −0.0264403
\(913\) 2.15733 0.0713971
\(914\) −1.20181 −0.0397524
\(915\) 7.98550 0.263993
\(916\) 7.49300 0.247576
\(917\) −3.77618 −0.124701
\(918\) −2.01536 −0.0665167
\(919\) −38.1249 −1.25762 −0.628812 0.777558i \(-0.716458\pi\)
−0.628812 + 0.777558i \(0.716458\pi\)
\(920\) 37.0664 1.22204
\(921\) 9.70591 0.319821
\(922\) −14.9571 −0.492584
\(923\) −84.4650 −2.78020
\(924\) 10.6480 0.350294
\(925\) 17.1044 0.562388
\(926\) −26.4736 −0.869976
\(927\) 2.53914 0.0833963
\(928\) −0.563256 −0.0184898
\(929\) 23.1631 0.759957 0.379978 0.924995i \(-0.375931\pi\)
0.379978 + 0.924995i \(0.375931\pi\)
\(930\) −6.97673 −0.228776
\(931\) 15.4888 0.507626
\(932\) 1.63619 0.0535952
\(933\) 10.3411 0.338552
\(934\) 2.28220 0.0746758
\(935\) 19.0788 0.623944
\(936\) 18.4770 0.603939
\(937\) 3.99000 0.130348 0.0651738 0.997874i \(-0.479240\pi\)
0.0651738 + 0.997874i \(0.479240\pi\)
\(938\) −5.41394 −0.176771
\(939\) 23.8987 0.779906
\(940\) 15.4186 0.502899
\(941\) 15.0860 0.491790 0.245895 0.969296i \(-0.420918\pi\)
0.245895 + 0.969296i \(0.420918\pi\)
\(942\) −18.2934 −0.596031
\(943\) 10.9999 0.358207
\(944\) 0.496466 0.0161586
\(945\) 2.94196 0.0957020
\(946\) −16.7270 −0.543841
\(947\) −55.4188 −1.80087 −0.900435 0.434991i \(-0.856752\pi\)
−0.900435 + 0.434991i \(0.856752\pi\)
\(948\) −15.5535 −0.505154
\(949\) −93.0636 −3.02097
\(950\) −7.83385 −0.254164
\(951\) 1.48619 0.0481931
\(952\) 11.3018 0.366293
\(953\) −46.8160 −1.51652 −0.758259 0.651953i \(-0.773950\pi\)
−0.758259 + 0.651953i \(0.773950\pi\)
\(954\) −1.44919 −0.0469193
\(955\) 19.5727 0.633359
\(956\) 1.19052 0.0385043
\(957\) 0.515527 0.0166646
\(958\) −34.7845 −1.12384
\(959\) −11.4928 −0.371122
\(960\) −9.04742 −0.292004
\(961\) −9.53693 −0.307643
\(962\) 45.0579 1.45273
\(963\) 9.82497 0.316605
\(964\) 19.8237 0.638477
\(965\) 3.60784 0.116141
\(966\) −12.1997 −0.392517
\(967\) −32.6031 −1.04844 −0.524222 0.851582i \(-0.675644\pi\)
−0.524222 + 0.851582i \(0.675644\pi\)
\(968\) 42.7530 1.37413
\(969\) −8.87196 −0.285008
\(970\) −9.13233 −0.293222
\(971\) −22.8194 −0.732310 −0.366155 0.930554i \(-0.619326\pi\)
−0.366155 + 0.930554i \(0.619326\pi\)
\(972\) 1.19052 0.0381861
\(973\) −17.1932 −0.551189
\(974\) −8.36299 −0.267967
\(975\) 14.1505 0.453178
\(976\) 0.961819 0.0307871
\(977\) −13.1827 −0.421751 −0.210875 0.977513i \(-0.567631\pi\)
−0.210875 + 0.977513i \(0.567631\pi\)
\(978\) −12.9333 −0.413560
\(979\) −87.2315 −2.78793
\(980\) 7.79277 0.248931
\(981\) −15.1110 −0.482459
\(982\) −10.2094 −0.325796
\(983\) −26.5649 −0.847290 −0.423645 0.905828i \(-0.639250\pi\)
−0.423645 + 0.905828i \(0.639250\pi\)
\(984\) −4.09299 −0.130480
\(985\) 10.8240 0.344883
\(986\) 0.204177 0.00650232
\(987\) −13.5999 −0.432890
\(988\) 30.3511 0.965597
\(989\) −28.1859 −0.896259
\(990\) 7.66307 0.243548
\(991\) 29.8250 0.947423 0.473711 0.880680i \(-0.342914\pi\)
0.473711 + 0.880680i \(0.342914\pi\)
\(992\) 25.7571 0.817790
\(993\) 17.6038 0.558640
\(994\) −20.7513 −0.658191
\(995\) 36.6521 1.16195
\(996\) −0.504728 −0.0159929
\(997\) 21.3442 0.675976 0.337988 0.941150i \(-0.390254\pi\)
0.337988 + 0.941150i \(0.390254\pi\)
\(998\) −22.3798 −0.708419
\(999\) 7.78041 0.246161
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 717.2.a.d.1.3 6
3.2 odd 2 2151.2.a.e.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
717.2.a.d.1.3 6 1.1 even 1 trivial
2151.2.a.e.1.4 6 3.2 odd 2