Properties

Label 4006.2.a.g.1.2
Level 4006
Weight 2
Character 4006.1
Self dual yes
Analytic conductor 31.988
Analytic rank 1
Dimension 40
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4006 = 2 \cdot 2003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4006.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9880710497\)
Analytic rank: \(1\)
Dimension: \(40\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 4006.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.11880 q^{3} +1.00000 q^{4} +1.57138 q^{5} +3.11880 q^{6} +2.57640 q^{7} -1.00000 q^{8} +6.72691 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.11880 q^{3} +1.00000 q^{4} +1.57138 q^{5} +3.11880 q^{6} +2.57640 q^{7} -1.00000 q^{8} +6.72691 q^{9} -1.57138 q^{10} -2.27747 q^{11} -3.11880 q^{12} +0.272260 q^{13} -2.57640 q^{14} -4.90081 q^{15} +1.00000 q^{16} +3.49514 q^{17} -6.72691 q^{18} +3.02570 q^{19} +1.57138 q^{20} -8.03526 q^{21} +2.27747 q^{22} +1.09989 q^{23} +3.11880 q^{24} -2.53078 q^{25} -0.272260 q^{26} -11.6235 q^{27} +2.57640 q^{28} -7.94298 q^{29} +4.90081 q^{30} +6.65335 q^{31} -1.00000 q^{32} +7.10296 q^{33} -3.49514 q^{34} +4.04849 q^{35} +6.72691 q^{36} -10.2457 q^{37} -3.02570 q^{38} -0.849126 q^{39} -1.57138 q^{40} -7.55369 q^{41} +8.03526 q^{42} -9.00970 q^{43} -2.27747 q^{44} +10.5705 q^{45} -1.09989 q^{46} +11.7619 q^{47} -3.11880 q^{48} -0.362182 q^{49} +2.53078 q^{50} -10.9006 q^{51} +0.272260 q^{52} -9.15701 q^{53} +11.6235 q^{54} -3.57875 q^{55} -2.57640 q^{56} -9.43656 q^{57} +7.94298 q^{58} -10.0195 q^{59} -4.90081 q^{60} -5.73379 q^{61} -6.65335 q^{62} +17.3312 q^{63} +1.00000 q^{64} +0.427824 q^{65} -7.10296 q^{66} -2.90990 q^{67} +3.49514 q^{68} -3.43035 q^{69} -4.04849 q^{70} -10.4554 q^{71} -6.72691 q^{72} +2.02729 q^{73} +10.2457 q^{74} +7.89299 q^{75} +3.02570 q^{76} -5.86765 q^{77} +0.849126 q^{78} +15.4765 q^{79} +1.57138 q^{80} +16.0706 q^{81} +7.55369 q^{82} +11.0624 q^{83} -8.03526 q^{84} +5.49217 q^{85} +9.00970 q^{86} +24.7726 q^{87} +2.27747 q^{88} -9.06665 q^{89} -10.5705 q^{90} +0.701451 q^{91} +1.09989 q^{92} -20.7505 q^{93} -11.7619 q^{94} +4.75452 q^{95} +3.11880 q^{96} -9.97049 q^{97} +0.362182 q^{98} -15.3203 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + O(q^{10}) \) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + 23q^{10} - 28q^{11} - q^{12} - 12q^{13} - 12q^{14} - 14q^{15} + 40q^{16} - 10q^{17} - 29q^{18} + 3q^{19} - 23q^{20} - 40q^{21} + 28q^{22} - 10q^{23} + q^{24} + 43q^{25} + 12q^{26} - 7q^{27} + 12q^{28} - 37q^{29} + 14q^{30} - 16q^{31} - 40q^{32} - 11q^{33} + 10q^{34} - 24q^{35} + 29q^{36} - 17q^{37} - 3q^{38} - 10q^{39} + 23q^{40} - 58q^{41} + 40q^{42} + 37q^{43} - 28q^{44} - 66q^{45} + 10q^{46} - 34q^{47} - q^{48} + 28q^{49} - 43q^{50} - 7q^{51} - 12q^{52} - 43q^{53} + 7q^{54} + 28q^{55} - 12q^{56} - 25q^{57} + 37q^{58} - 92q^{59} - 14q^{60} - 37q^{61} + 16q^{62} + 14q^{63} + 40q^{64} - 54q^{65} + 11q^{66} - 10q^{67} - 10q^{68} - 49q^{69} + 24q^{70} - 87q^{71} - 29q^{72} + 12q^{73} + 17q^{74} - 31q^{75} + 3q^{76} - 53q^{77} + 10q^{78} + 14q^{79} - 23q^{80} - 4q^{81} + 58q^{82} - 42q^{83} - 40q^{84} - 24q^{85} - 37q^{86} + 24q^{87} + 28q^{88} - 118q^{89} + 66q^{90} - 35q^{91} - 10q^{92} - 22q^{93} + 34q^{94} - 18q^{95} + q^{96} + 2q^{97} - 28q^{98} - 48q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −3.11880 −1.80064 −0.900320 0.435229i \(-0.856667\pi\)
−0.900320 + 0.435229i \(0.856667\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.57138 0.702741 0.351370 0.936237i \(-0.385716\pi\)
0.351370 + 0.936237i \(0.385716\pi\)
\(6\) 3.11880 1.27324
\(7\) 2.57640 0.973786 0.486893 0.873462i \(-0.338130\pi\)
0.486893 + 0.873462i \(0.338130\pi\)
\(8\) −1.00000 −0.353553
\(9\) 6.72691 2.24230
\(10\) −1.57138 −0.496913
\(11\) −2.27747 −0.686682 −0.343341 0.939211i \(-0.611559\pi\)
−0.343341 + 0.939211i \(0.611559\pi\)
\(12\) −3.11880 −0.900320
\(13\) 0.272260 0.0755115 0.0377557 0.999287i \(-0.487979\pi\)
0.0377557 + 0.999287i \(0.487979\pi\)
\(14\) −2.57640 −0.688571
\(15\) −4.90081 −1.26538
\(16\) 1.00000 0.250000
\(17\) 3.49514 0.847695 0.423847 0.905734i \(-0.360679\pi\)
0.423847 + 0.905734i \(0.360679\pi\)
\(18\) −6.72691 −1.58555
\(19\) 3.02570 0.694144 0.347072 0.937839i \(-0.387176\pi\)
0.347072 + 0.937839i \(0.387176\pi\)
\(20\) 1.57138 0.351370
\(21\) −8.03526 −1.75344
\(22\) 2.27747 0.485557
\(23\) 1.09989 0.229344 0.114672 0.993403i \(-0.463418\pi\)
0.114672 + 0.993403i \(0.463418\pi\)
\(24\) 3.11880 0.636622
\(25\) −2.53078 −0.506155
\(26\) −0.272260 −0.0533947
\(27\) −11.6235 −2.23694
\(28\) 2.57640 0.486893
\(29\) −7.94298 −1.47497 −0.737487 0.675362i \(-0.763988\pi\)
−0.737487 + 0.675362i \(0.763988\pi\)
\(30\) 4.90081 0.894761
\(31\) 6.65335 1.19498 0.597489 0.801877i \(-0.296165\pi\)
0.597489 + 0.801877i \(0.296165\pi\)
\(32\) −1.00000 −0.176777
\(33\) 7.10296 1.23647
\(34\) −3.49514 −0.599411
\(35\) 4.04849 0.684319
\(36\) 6.72691 1.12115
\(37\) −10.2457 −1.68437 −0.842187 0.539185i \(-0.818732\pi\)
−0.842187 + 0.539185i \(0.818732\pi\)
\(38\) −3.02570 −0.490834
\(39\) −0.849126 −0.135969
\(40\) −1.57138 −0.248456
\(41\) −7.55369 −1.17969 −0.589844 0.807517i \(-0.700811\pi\)
−0.589844 + 0.807517i \(0.700811\pi\)
\(42\) 8.03526 1.23987
\(43\) −9.00970 −1.37397 −0.686983 0.726673i \(-0.741065\pi\)
−0.686983 + 0.726673i \(0.741065\pi\)
\(44\) −2.27747 −0.343341
\(45\) 10.5705 1.57576
\(46\) −1.09989 −0.162171
\(47\) 11.7619 1.71565 0.857823 0.513945i \(-0.171817\pi\)
0.857823 + 0.513945i \(0.171817\pi\)
\(48\) −3.11880 −0.450160
\(49\) −0.362182 −0.0517403
\(50\) 2.53078 0.357906
\(51\) −10.9006 −1.52639
\(52\) 0.272260 0.0377557
\(53\) −9.15701 −1.25781 −0.628906 0.777481i \(-0.716497\pi\)
−0.628906 + 0.777481i \(0.716497\pi\)
\(54\) 11.6235 1.58176
\(55\) −3.57875 −0.482559
\(56\) −2.57640 −0.344285
\(57\) −9.43656 −1.24990
\(58\) 7.94298 1.04296
\(59\) −10.0195 −1.30443 −0.652213 0.758036i \(-0.726159\pi\)
−0.652213 + 0.758036i \(0.726159\pi\)
\(60\) −4.90081 −0.632691
\(61\) −5.73379 −0.734137 −0.367068 0.930194i \(-0.619638\pi\)
−0.367068 + 0.930194i \(0.619638\pi\)
\(62\) −6.65335 −0.844976
\(63\) 17.3312 2.18352
\(64\) 1.00000 0.125000
\(65\) 0.427824 0.0530650
\(66\) −7.10296 −0.874314
\(67\) −2.90990 −0.355501 −0.177750 0.984076i \(-0.556882\pi\)
−0.177750 + 0.984076i \(0.556882\pi\)
\(68\) 3.49514 0.423847
\(69\) −3.43035 −0.412966
\(70\) −4.04849 −0.483887
\(71\) −10.4554 −1.24083 −0.620413 0.784275i \(-0.713035\pi\)
−0.620413 + 0.784275i \(0.713035\pi\)
\(72\) −6.72691 −0.792774
\(73\) 2.02729 0.237276 0.118638 0.992938i \(-0.462147\pi\)
0.118638 + 0.992938i \(0.462147\pi\)
\(74\) 10.2457 1.19103
\(75\) 7.89299 0.911404
\(76\) 3.02570 0.347072
\(77\) −5.86765 −0.668681
\(78\) 0.849126 0.0961446
\(79\) 15.4765 1.74124 0.870619 0.491957i \(-0.163718\pi\)
0.870619 + 0.491957i \(0.163718\pi\)
\(80\) 1.57138 0.175685
\(81\) 16.0706 1.78562
\(82\) 7.55369 0.834165
\(83\) 11.0624 1.21426 0.607128 0.794604i \(-0.292321\pi\)
0.607128 + 0.794604i \(0.292321\pi\)
\(84\) −8.03526 −0.876719
\(85\) 5.49217 0.595710
\(86\) 9.00970 0.971541
\(87\) 24.7726 2.65590
\(88\) 2.27747 0.242779
\(89\) −9.06665 −0.961062 −0.480531 0.876978i \(-0.659556\pi\)
−0.480531 + 0.876978i \(0.659556\pi\)
\(90\) −10.5705 −1.11423
\(91\) 0.701451 0.0735320
\(92\) 1.09989 0.114672
\(93\) −20.7505 −2.15172
\(94\) −11.7619 −1.21314
\(95\) 4.75452 0.487803
\(96\) 3.11880 0.318311
\(97\) −9.97049 −1.01235 −0.506175 0.862431i \(-0.668941\pi\)
−0.506175 + 0.862431i \(0.668941\pi\)
\(98\) 0.362182 0.0365859
\(99\) −15.3203 −1.53975
\(100\) −2.53078 −0.253078
\(101\) 1.94659 0.193693 0.0968463 0.995299i \(-0.469124\pi\)
0.0968463 + 0.995299i \(0.469124\pi\)
\(102\) 10.9006 1.07932
\(103\) 14.7599 1.45434 0.727168 0.686459i \(-0.240836\pi\)
0.727168 + 0.686459i \(0.240836\pi\)
\(104\) −0.272260 −0.0266973
\(105\) −12.6264 −1.23221
\(106\) 9.15701 0.889407
\(107\) −8.76868 −0.847701 −0.423850 0.905732i \(-0.639322\pi\)
−0.423850 + 0.905732i \(0.639322\pi\)
\(108\) −11.6235 −1.11847
\(109\) 16.3775 1.56868 0.784341 0.620331i \(-0.213002\pi\)
0.784341 + 0.620331i \(0.213002\pi\)
\(110\) 3.57875 0.341221
\(111\) 31.9541 3.03295
\(112\) 2.57640 0.243447
\(113\) 8.31720 0.782416 0.391208 0.920302i \(-0.372057\pi\)
0.391208 + 0.920302i \(0.372057\pi\)
\(114\) 9.43656 0.883815
\(115\) 1.72835 0.161169
\(116\) −7.94298 −0.737487
\(117\) 1.83147 0.169320
\(118\) 10.0195 0.922368
\(119\) 9.00485 0.825474
\(120\) 4.90081 0.447380
\(121\) −5.81315 −0.528468
\(122\) 5.73379 0.519113
\(123\) 23.5584 2.12419
\(124\) 6.65335 0.597489
\(125\) −11.8337 −1.05844
\(126\) −17.3312 −1.54398
\(127\) 10.5055 0.932211 0.466106 0.884729i \(-0.345657\pi\)
0.466106 + 0.884729i \(0.345657\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 28.0994 2.47402
\(130\) −0.427824 −0.0375226
\(131\) 9.40784 0.821967 0.410983 0.911643i \(-0.365185\pi\)
0.410983 + 0.911643i \(0.365185\pi\)
\(132\) 7.10296 0.618233
\(133\) 7.79541 0.675948
\(134\) 2.90990 0.251377
\(135\) −18.2649 −1.57199
\(136\) −3.49514 −0.299705
\(137\) 2.24860 0.192111 0.0960554 0.995376i \(-0.469377\pi\)
0.0960554 + 0.995376i \(0.469377\pi\)
\(138\) 3.43035 0.292011
\(139\) −10.9625 −0.929828 −0.464914 0.885356i \(-0.653915\pi\)
−0.464914 + 0.885356i \(0.653915\pi\)
\(140\) 4.04849 0.342160
\(141\) −36.6829 −3.08926
\(142\) 10.4554 0.877397
\(143\) −0.620064 −0.0518523
\(144\) 6.72691 0.560576
\(145\) −12.4814 −1.03652
\(146\) −2.02729 −0.167780
\(147\) 1.12957 0.0931656
\(148\) −10.2457 −0.842187
\(149\) −20.6707 −1.69341 −0.846703 0.532065i \(-0.821416\pi\)
−0.846703 + 0.532065i \(0.821416\pi\)
\(150\) −7.89299 −0.644460
\(151\) −11.1355 −0.906196 −0.453098 0.891461i \(-0.649681\pi\)
−0.453098 + 0.891461i \(0.649681\pi\)
\(152\) −3.02570 −0.245417
\(153\) 23.5115 1.90079
\(154\) 5.86765 0.472829
\(155\) 10.4549 0.839759
\(156\) −0.849126 −0.0679845
\(157\) 15.4422 1.23242 0.616211 0.787581i \(-0.288667\pi\)
0.616211 + 0.787581i \(0.288667\pi\)
\(158\) −15.4765 −1.23124
\(159\) 28.5589 2.26487
\(160\) −1.57138 −0.124228
\(161\) 2.83377 0.223332
\(162\) −16.0706 −1.26263
\(163\) −19.4247 −1.52146 −0.760728 0.649071i \(-0.775158\pi\)
−0.760728 + 0.649071i \(0.775158\pi\)
\(164\) −7.55369 −0.589844
\(165\) 11.1614 0.868915
\(166\) −11.0624 −0.858609
\(167\) −23.0061 −1.78026 −0.890132 0.455703i \(-0.849388\pi\)
−0.890132 + 0.455703i \(0.849388\pi\)
\(168\) 8.03526 0.619934
\(169\) −12.9259 −0.994298
\(170\) −5.49217 −0.421230
\(171\) 20.3536 1.55648
\(172\) −9.00970 −0.686983
\(173\) 12.6019 0.958103 0.479051 0.877787i \(-0.340981\pi\)
0.479051 + 0.877787i \(0.340981\pi\)
\(174\) −24.7726 −1.87800
\(175\) −6.52029 −0.492887
\(176\) −2.27747 −0.171670
\(177\) 31.2488 2.34880
\(178\) 9.06665 0.679574
\(179\) −4.22919 −0.316105 −0.158052 0.987431i \(-0.550521\pi\)
−0.158052 + 0.987431i \(0.550521\pi\)
\(180\) 10.5705 0.787879
\(181\) 8.10763 0.602635 0.301318 0.953524i \(-0.402574\pi\)
0.301318 + 0.953524i \(0.402574\pi\)
\(182\) −0.701451 −0.0519950
\(183\) 17.8825 1.32192
\(184\) −1.09989 −0.0810853
\(185\) −16.0998 −1.18368
\(186\) 20.7505 1.52150
\(187\) −7.96005 −0.582096
\(188\) 11.7619 0.857823
\(189\) −29.9467 −2.17830
\(190\) −4.75452 −0.344929
\(191\) 3.58116 0.259124 0.129562 0.991571i \(-0.458643\pi\)
0.129562 + 0.991571i \(0.458643\pi\)
\(192\) −3.11880 −0.225080
\(193\) −4.77286 −0.343558 −0.171779 0.985135i \(-0.554952\pi\)
−0.171779 + 0.985135i \(0.554952\pi\)
\(194\) 9.97049 0.715840
\(195\) −1.33430 −0.0955509
\(196\) −0.362182 −0.0258701
\(197\) 3.42352 0.243915 0.121958 0.992535i \(-0.461083\pi\)
0.121958 + 0.992535i \(0.461083\pi\)
\(198\) 15.3203 1.08877
\(199\) 20.7544 1.47124 0.735619 0.677395i \(-0.236891\pi\)
0.735619 + 0.677395i \(0.236891\pi\)
\(200\) 2.53078 0.178953
\(201\) 9.07539 0.640129
\(202\) −1.94659 −0.136961
\(203\) −20.4643 −1.43631
\(204\) −10.9006 −0.763196
\(205\) −11.8697 −0.829015
\(206\) −14.7599 −1.02837
\(207\) 7.39889 0.514259
\(208\) 0.272260 0.0188779
\(209\) −6.89093 −0.476656
\(210\) 12.6264 0.871306
\(211\) 17.2684 1.18881 0.594403 0.804167i \(-0.297388\pi\)
0.594403 + 0.804167i \(0.297388\pi\)
\(212\) −9.15701 −0.628906
\(213\) 32.6083 2.23428
\(214\) 8.76868 0.599415
\(215\) −14.1576 −0.965542
\(216\) 11.6235 0.790878
\(217\) 17.1417 1.16365
\(218\) −16.3775 −1.10923
\(219\) −6.32270 −0.427249
\(220\) −3.57875 −0.241280
\(221\) 0.951587 0.0640107
\(222\) −31.9541 −2.14462
\(223\) 19.1328 1.28123 0.640613 0.767864i \(-0.278680\pi\)
0.640613 + 0.767864i \(0.278680\pi\)
\(224\) −2.57640 −0.172143
\(225\) −17.0243 −1.13495
\(226\) −8.31720 −0.553252
\(227\) −9.58723 −0.636327 −0.318163 0.948036i \(-0.603066\pi\)
−0.318163 + 0.948036i \(0.603066\pi\)
\(228\) −9.43656 −0.624952
\(229\) −15.4499 −1.02096 −0.510478 0.859891i \(-0.670532\pi\)
−0.510478 + 0.859891i \(0.670532\pi\)
\(230\) −1.72835 −0.113964
\(231\) 18.3000 1.20405
\(232\) 7.94298 0.521482
\(233\) 12.3262 0.807513 0.403757 0.914866i \(-0.367704\pi\)
0.403757 + 0.914866i \(0.367704\pi\)
\(234\) −1.83147 −0.119727
\(235\) 18.4823 1.20565
\(236\) −10.0195 −0.652213
\(237\) −48.2680 −3.13534
\(238\) −9.00485 −0.583698
\(239\) −25.2462 −1.63304 −0.816520 0.577317i \(-0.804100\pi\)
−0.816520 + 0.577317i \(0.804100\pi\)
\(240\) −4.90081 −0.316346
\(241\) −16.5545 −1.06637 −0.533184 0.845999i \(-0.679005\pi\)
−0.533184 + 0.845999i \(0.679005\pi\)
\(242\) 5.81315 0.373683
\(243\) −15.2505 −0.978320
\(244\) −5.73379 −0.367068
\(245\) −0.569124 −0.0363600
\(246\) −23.5584 −1.50203
\(247\) 0.823779 0.0524158
\(248\) −6.65335 −0.422488
\(249\) −34.5014 −2.18644
\(250\) 11.8337 0.748428
\(251\) 23.4094 1.47759 0.738793 0.673933i \(-0.235396\pi\)
0.738793 + 0.673933i \(0.235396\pi\)
\(252\) 17.3312 1.09176
\(253\) −2.50497 −0.157486
\(254\) −10.5055 −0.659173
\(255\) −17.1290 −1.07266
\(256\) 1.00000 0.0625000
\(257\) −9.81989 −0.612548 −0.306274 0.951943i \(-0.599082\pi\)
−0.306274 + 0.951943i \(0.599082\pi\)
\(258\) −28.0994 −1.74939
\(259\) −26.3969 −1.64022
\(260\) 0.427824 0.0265325
\(261\) −53.4317 −3.30734
\(262\) −9.40784 −0.581218
\(263\) −28.8537 −1.77919 −0.889596 0.456747i \(-0.849014\pi\)
−0.889596 + 0.456747i \(0.849014\pi\)
\(264\) −7.10296 −0.437157
\(265\) −14.3891 −0.883916
\(266\) −7.79541 −0.477967
\(267\) 28.2770 1.73053
\(268\) −2.90990 −0.177750
\(269\) −11.8656 −0.723461 −0.361731 0.932283i \(-0.617814\pi\)
−0.361731 + 0.932283i \(0.617814\pi\)
\(270\) 18.2649 1.11156
\(271\) −4.36320 −0.265046 −0.132523 0.991180i \(-0.542308\pi\)
−0.132523 + 0.991180i \(0.542308\pi\)
\(272\) 3.49514 0.211924
\(273\) −2.18768 −0.132405
\(274\) −2.24860 −0.135843
\(275\) 5.76376 0.347568
\(276\) −3.43035 −0.206483
\(277\) 18.1159 1.08848 0.544239 0.838930i \(-0.316819\pi\)
0.544239 + 0.838930i \(0.316819\pi\)
\(278\) 10.9625 0.657488
\(279\) 44.7565 2.67950
\(280\) −4.04849 −0.241943
\(281\) −28.0924 −1.67585 −0.837927 0.545782i \(-0.816233\pi\)
−0.837927 + 0.545782i \(0.816233\pi\)
\(282\) 36.6829 2.18444
\(283\) 13.8475 0.823148 0.411574 0.911376i \(-0.364979\pi\)
0.411574 + 0.911376i \(0.364979\pi\)
\(284\) −10.4554 −0.620413
\(285\) −14.8284 −0.878358
\(286\) 0.620064 0.0366651
\(287\) −19.4613 −1.14876
\(288\) −6.72691 −0.396387
\(289\) −4.78403 −0.281414
\(290\) 12.4814 0.732933
\(291\) 31.0960 1.82288
\(292\) 2.02729 0.118638
\(293\) −15.2879 −0.893129 −0.446564 0.894751i \(-0.647353\pi\)
−0.446564 + 0.894751i \(0.647353\pi\)
\(294\) −1.12957 −0.0658780
\(295\) −15.7444 −0.916673
\(296\) 10.2457 0.595516
\(297\) 26.4721 1.53607
\(298\) 20.6707 1.19742
\(299\) 0.299458 0.0173181
\(300\) 7.89299 0.455702
\(301\) −23.2126 −1.33795
\(302\) 11.1355 0.640777
\(303\) −6.07102 −0.348771
\(304\) 3.02570 0.173536
\(305\) −9.00994 −0.515908
\(306\) −23.5115 −1.34406
\(307\) −18.5486 −1.05862 −0.529312 0.848427i \(-0.677550\pi\)
−0.529312 + 0.848427i \(0.677550\pi\)
\(308\) −5.86765 −0.334341
\(309\) −46.0332 −2.61874
\(310\) −10.4549 −0.593799
\(311\) −15.5169 −0.879880 −0.439940 0.898027i \(-0.645000\pi\)
−0.439940 + 0.898027i \(0.645000\pi\)
\(312\) 0.849126 0.0480723
\(313\) −2.30508 −0.130291 −0.0651455 0.997876i \(-0.520751\pi\)
−0.0651455 + 0.997876i \(0.520751\pi\)
\(314\) −15.4422 −0.871454
\(315\) 27.2338 1.53445
\(316\) 15.4765 0.870619
\(317\) 11.3746 0.638864 0.319432 0.947609i \(-0.396508\pi\)
0.319432 + 0.947609i \(0.396508\pi\)
\(318\) −28.5589 −1.60150
\(319\) 18.0899 1.01284
\(320\) 1.57138 0.0878426
\(321\) 27.3478 1.52640
\(322\) −2.83377 −0.157920
\(323\) 10.5752 0.588422
\(324\) 16.0706 0.892811
\(325\) −0.689030 −0.0382205
\(326\) 19.4247 1.07583
\(327\) −51.0782 −2.82463
\(328\) 7.55369 0.417083
\(329\) 30.3032 1.67067
\(330\) −11.1614 −0.614416
\(331\) −14.3485 −0.788663 −0.394332 0.918968i \(-0.629024\pi\)
−0.394332 + 0.918968i \(0.629024\pi\)
\(332\) 11.0624 0.607128
\(333\) −68.9216 −3.77688
\(334\) 23.0061 1.25884
\(335\) −4.57254 −0.249825
\(336\) −8.03526 −0.438360
\(337\) −33.0436 −1.80000 −0.900000 0.435890i \(-0.856434\pi\)
−0.900000 + 0.435890i \(0.856434\pi\)
\(338\) 12.9259 0.703075
\(339\) −25.9397 −1.40885
\(340\) 5.49217 0.297855
\(341\) −15.1528 −0.820569
\(342\) −20.3536 −1.10060
\(343\) −18.9679 −1.02417
\(344\) 9.00970 0.485770
\(345\) −5.39037 −0.290208
\(346\) −12.6019 −0.677481
\(347\) 1.25935 0.0676054 0.0338027 0.999429i \(-0.489238\pi\)
0.0338027 + 0.999429i \(0.489238\pi\)
\(348\) 24.7726 1.32795
\(349\) −5.46754 −0.292671 −0.146335 0.989235i \(-0.546748\pi\)
−0.146335 + 0.989235i \(0.546748\pi\)
\(350\) 6.52029 0.348524
\(351\) −3.16462 −0.168915
\(352\) 2.27747 0.121389
\(353\) 28.6896 1.52699 0.763497 0.645811i \(-0.223481\pi\)
0.763497 + 0.645811i \(0.223481\pi\)
\(354\) −31.2488 −1.66085
\(355\) −16.4293 −0.871979
\(356\) −9.06665 −0.480531
\(357\) −28.0843 −1.48638
\(358\) 4.22919 0.223520
\(359\) 3.40290 0.179598 0.0897992 0.995960i \(-0.471377\pi\)
0.0897992 + 0.995960i \(0.471377\pi\)
\(360\) −10.5705 −0.557115
\(361\) −9.84512 −0.518164
\(362\) −8.10763 −0.426127
\(363\) 18.1301 0.951581
\(364\) 0.701451 0.0367660
\(365\) 3.18563 0.166744
\(366\) −17.8825 −0.934735
\(367\) −15.4357 −0.805735 −0.402868 0.915258i \(-0.631987\pi\)
−0.402868 + 0.915258i \(0.631987\pi\)
\(368\) 1.09989 0.0573360
\(369\) −50.8130 −2.64522
\(370\) 16.0998 0.836987
\(371\) −23.5921 −1.22484
\(372\) −20.7505 −1.07586
\(373\) 31.0288 1.60661 0.803304 0.595569i \(-0.203073\pi\)
0.803304 + 0.595569i \(0.203073\pi\)
\(374\) 7.96005 0.411604
\(375\) 36.9069 1.90586
\(376\) −11.7619 −0.606572
\(377\) −2.16256 −0.111377
\(378\) 29.9467 1.54029
\(379\) 0.478507 0.0245793 0.0122896 0.999924i \(-0.496088\pi\)
0.0122896 + 0.999924i \(0.496088\pi\)
\(380\) 4.75452 0.243902
\(381\) −32.7645 −1.67858
\(382\) −3.58116 −0.183228
\(383\) −23.3872 −1.19503 −0.597515 0.801858i \(-0.703845\pi\)
−0.597515 + 0.801858i \(0.703845\pi\)
\(384\) 3.11880 0.159156
\(385\) −9.22029 −0.469910
\(386\) 4.77286 0.242932
\(387\) −60.6074 −3.08085
\(388\) −9.97049 −0.506175
\(389\) 24.8239 1.25862 0.629310 0.777155i \(-0.283338\pi\)
0.629310 + 0.777155i \(0.283338\pi\)
\(390\) 1.33430 0.0675647
\(391\) 3.84428 0.194414
\(392\) 0.362182 0.0182929
\(393\) −29.3412 −1.48007
\(394\) −3.42352 −0.172474
\(395\) 24.3193 1.22364
\(396\) −15.3203 −0.769874
\(397\) 28.6504 1.43792 0.718960 0.695051i \(-0.244618\pi\)
0.718960 + 0.695051i \(0.244618\pi\)
\(398\) −20.7544 −1.04032
\(399\) −24.3123 −1.21714
\(400\) −2.53078 −0.126539
\(401\) 16.2022 0.809098 0.404549 0.914516i \(-0.367429\pi\)
0.404549 + 0.914516i \(0.367429\pi\)
\(402\) −9.07539 −0.452639
\(403\) 1.81144 0.0902345
\(404\) 1.94659 0.0968463
\(405\) 25.2529 1.25483
\(406\) 20.4643 1.01562
\(407\) 23.3341 1.15663
\(408\) 10.9006 0.539661
\(409\) −1.44491 −0.0714460 −0.0357230 0.999362i \(-0.511373\pi\)
−0.0357230 + 0.999362i \(0.511373\pi\)
\(410\) 11.8697 0.586202
\(411\) −7.01293 −0.345923
\(412\) 14.7599 0.727168
\(413\) −25.8142 −1.27023
\(414\) −7.39889 −0.363636
\(415\) 17.3832 0.853308
\(416\) −0.272260 −0.0133487
\(417\) 34.1899 1.67429
\(418\) 6.89093 0.337047
\(419\) −32.9567 −1.61004 −0.805021 0.593246i \(-0.797846\pi\)
−0.805021 + 0.593246i \(0.797846\pi\)
\(420\) −12.6264 −0.616106
\(421\) 35.1379 1.71252 0.856259 0.516546i \(-0.172783\pi\)
0.856259 + 0.516546i \(0.172783\pi\)
\(422\) −17.2684 −0.840613
\(423\) 79.1211 3.84700
\(424\) 9.15701 0.444704
\(425\) −8.84541 −0.429065
\(426\) −32.6083 −1.57988
\(427\) −14.7725 −0.714892
\(428\) −8.76868 −0.423850
\(429\) 1.93385 0.0933674
\(430\) 14.1576 0.682741
\(431\) 3.44601 0.165989 0.0829943 0.996550i \(-0.473552\pi\)
0.0829943 + 0.996550i \(0.473552\pi\)
\(432\) −11.6235 −0.559235
\(433\) 22.6597 1.08896 0.544479 0.838775i \(-0.316727\pi\)
0.544479 + 0.838775i \(0.316727\pi\)
\(434\) −17.1417 −0.822826
\(435\) 38.9270 1.86641
\(436\) 16.3775 0.784341
\(437\) 3.32796 0.159198
\(438\) 6.32270 0.302110
\(439\) −27.4365 −1.30947 −0.654736 0.755858i \(-0.727220\pi\)
−0.654736 + 0.755858i \(0.727220\pi\)
\(440\) 3.57875 0.170610
\(441\) −2.43637 −0.116017
\(442\) −0.951587 −0.0452624
\(443\) 10.7107 0.508879 0.254439 0.967089i \(-0.418109\pi\)
0.254439 + 0.967089i \(0.418109\pi\)
\(444\) 31.9541 1.51648
\(445\) −14.2471 −0.675378
\(446\) −19.1328 −0.905964
\(447\) 64.4677 3.04922
\(448\) 2.57640 0.121723
\(449\) −23.3758 −1.10317 −0.551586 0.834118i \(-0.685977\pi\)
−0.551586 + 0.834118i \(0.685977\pi\)
\(450\) 17.0243 0.802534
\(451\) 17.2033 0.810070
\(452\) 8.31720 0.391208
\(453\) 34.7295 1.63173
\(454\) 9.58723 0.449951
\(455\) 1.10224 0.0516739
\(456\) 9.43656 0.441907
\(457\) 11.1400 0.521108 0.260554 0.965459i \(-0.416095\pi\)
0.260554 + 0.965459i \(0.416095\pi\)
\(458\) 15.4499 0.721925
\(459\) −40.6257 −1.89624
\(460\) 1.72835 0.0805847
\(461\) −22.5473 −1.05013 −0.525067 0.851061i \(-0.675960\pi\)
−0.525067 + 0.851061i \(0.675960\pi\)
\(462\) −18.3000 −0.851395
\(463\) 21.6006 1.00387 0.501933 0.864907i \(-0.332622\pi\)
0.501933 + 0.864907i \(0.332622\pi\)
\(464\) −7.94298 −0.368743
\(465\) −32.6068 −1.51210
\(466\) −12.3262 −0.570998
\(467\) 20.3649 0.942376 0.471188 0.882033i \(-0.343825\pi\)
0.471188 + 0.882033i \(0.343825\pi\)
\(468\) 1.83147 0.0846598
\(469\) −7.49705 −0.346182
\(470\) −18.4823 −0.852526
\(471\) −48.1611 −2.21915
\(472\) 10.0195 0.461184
\(473\) 20.5193 0.943477
\(474\) 48.2680 2.21702
\(475\) −7.65738 −0.351345
\(476\) 9.00485 0.412737
\(477\) −61.5984 −2.82040
\(478\) 25.2462 1.15473
\(479\) −2.02262 −0.0924158 −0.0462079 0.998932i \(-0.514714\pi\)
−0.0462079 + 0.998932i \(0.514714\pi\)
\(480\) 4.90081 0.223690
\(481\) −2.78949 −0.127190
\(482\) 16.5545 0.754037
\(483\) −8.83795 −0.402140
\(484\) −5.81315 −0.264234
\(485\) −15.6674 −0.711420
\(486\) 15.2505 0.691777
\(487\) −27.9143 −1.26492 −0.632458 0.774595i \(-0.717954\pi\)
−0.632458 + 0.774595i \(0.717954\pi\)
\(488\) 5.73379 0.259556
\(489\) 60.5816 2.73959
\(490\) 0.569124 0.0257104
\(491\) 13.4879 0.608700 0.304350 0.952560i \(-0.401561\pi\)
0.304350 + 0.952560i \(0.401561\pi\)
\(492\) 23.5584 1.06210
\(493\) −27.7618 −1.25033
\(494\) −0.823779 −0.0370636
\(495\) −24.0740 −1.08204
\(496\) 6.65335 0.298744
\(497\) −26.9372 −1.20830
\(498\) 34.5014 1.54605
\(499\) −37.4379 −1.67595 −0.837975 0.545709i \(-0.816260\pi\)
−0.837975 + 0.545709i \(0.816260\pi\)
\(500\) −11.8337 −0.529218
\(501\) 71.7514 3.20561
\(502\) −23.4094 −1.04481
\(503\) 14.2126 0.633708 0.316854 0.948474i \(-0.397373\pi\)
0.316854 + 0.948474i \(0.397373\pi\)
\(504\) −17.3312 −0.771992
\(505\) 3.05882 0.136116
\(506\) 2.50497 0.111360
\(507\) 40.3132 1.79037
\(508\) 10.5055 0.466106
\(509\) −10.3235 −0.457583 −0.228791 0.973475i \(-0.573477\pi\)
−0.228791 + 0.973475i \(0.573477\pi\)
\(510\) 17.1290 0.758484
\(511\) 5.22310 0.231056
\(512\) −1.00000 −0.0441942
\(513\) −35.1692 −1.55276
\(514\) 9.81989 0.433137
\(515\) 23.1934 1.02202
\(516\) 28.0994 1.23701
\(517\) −26.7873 −1.17810
\(518\) 26.3969 1.15981
\(519\) −39.3027 −1.72520
\(520\) −0.427824 −0.0187613
\(521\) −7.17528 −0.314355 −0.157177 0.987570i \(-0.550239\pi\)
−0.157177 + 0.987570i \(0.550239\pi\)
\(522\) 53.4317 2.33864
\(523\) −10.1334 −0.443104 −0.221552 0.975149i \(-0.571112\pi\)
−0.221552 + 0.975149i \(0.571112\pi\)
\(524\) 9.40784 0.410983
\(525\) 20.3355 0.887512
\(526\) 28.8537 1.25808
\(527\) 23.2544 1.01298
\(528\) 7.10296 0.309117
\(529\) −21.7902 −0.947401
\(530\) 14.3891 0.625023
\(531\) −67.4002 −2.92492
\(532\) 7.79541 0.337974
\(533\) −2.05657 −0.0890800
\(534\) −28.2770 −1.22367
\(535\) −13.7789 −0.595714
\(536\) 2.90990 0.125688
\(537\) 13.1900 0.569191
\(538\) 11.8656 0.511564
\(539\) 0.824857 0.0355291
\(540\) −18.2649 −0.785995
\(541\) 39.3072 1.68995 0.844974 0.534808i \(-0.179616\pi\)
0.844974 + 0.534808i \(0.179616\pi\)
\(542\) 4.36320 0.187416
\(543\) −25.2861 −1.08513
\(544\) −3.49514 −0.149853
\(545\) 25.7352 1.10238
\(546\) 2.18768 0.0936242
\(547\) −27.9640 −1.19565 −0.597827 0.801625i \(-0.703969\pi\)
−0.597827 + 0.801625i \(0.703969\pi\)
\(548\) 2.24860 0.0960554
\(549\) −38.5707 −1.64616
\(550\) −5.76376 −0.245767
\(551\) −24.0331 −1.02384
\(552\) 3.43035 0.146005
\(553\) 39.8735 1.69559
\(554\) −18.1159 −0.769670
\(555\) 50.2120 2.13138
\(556\) −10.9625 −0.464914
\(557\) 18.9856 0.804447 0.402224 0.915541i \(-0.368237\pi\)
0.402224 + 0.915541i \(0.368237\pi\)
\(558\) −44.7565 −1.89469
\(559\) −2.45298 −0.103750
\(560\) 4.04849 0.171080
\(561\) 24.8258 1.04815
\(562\) 28.0924 1.18501
\(563\) 39.5150 1.66536 0.832679 0.553756i \(-0.186806\pi\)
0.832679 + 0.553756i \(0.186806\pi\)
\(564\) −36.6829 −1.54463
\(565\) 13.0694 0.549836
\(566\) −13.8475 −0.582054
\(567\) 41.4042 1.73881
\(568\) 10.4554 0.438698
\(569\) −17.9652 −0.753141 −0.376571 0.926388i \(-0.622897\pi\)
−0.376571 + 0.926388i \(0.622897\pi\)
\(570\) 14.8284 0.621093
\(571\) 3.03513 0.127016 0.0635082 0.997981i \(-0.479771\pi\)
0.0635082 + 0.997981i \(0.479771\pi\)
\(572\) −0.620064 −0.0259262
\(573\) −11.1689 −0.466588
\(574\) 19.4613 0.812299
\(575\) −2.78359 −0.116084
\(576\) 6.72691 0.280288
\(577\) 2.82364 0.117550 0.0587749 0.998271i \(-0.481281\pi\)
0.0587749 + 0.998271i \(0.481281\pi\)
\(578\) 4.78403 0.198989
\(579\) 14.8856 0.618625
\(580\) −12.4814 −0.518262
\(581\) 28.5011 1.18243
\(582\) −31.0960 −1.28897
\(583\) 20.8548 0.863716
\(584\) −2.02729 −0.0838898
\(585\) 2.87793 0.118988
\(586\) 15.2879 0.631537
\(587\) −25.2865 −1.04369 −0.521843 0.853041i \(-0.674755\pi\)
−0.521843 + 0.853041i \(0.674755\pi\)
\(588\) 1.12957 0.0465828
\(589\) 20.1311 0.829486
\(590\) 15.7444 0.648186
\(591\) −10.6773 −0.439204
\(592\) −10.2457 −0.421094
\(593\) 0.413543 0.0169822 0.00849109 0.999964i \(-0.497297\pi\)
0.00849109 + 0.999964i \(0.497297\pi\)
\(594\) −26.4721 −1.08616
\(595\) 14.1500 0.580094
\(596\) −20.6707 −0.846703
\(597\) −64.7287 −2.64917
\(598\) −0.299458 −0.0122457
\(599\) 10.4742 0.427965 0.213982 0.976838i \(-0.431356\pi\)
0.213982 + 0.976838i \(0.431356\pi\)
\(600\) −7.89299 −0.322230
\(601\) 34.2647 1.39769 0.698844 0.715274i \(-0.253698\pi\)
0.698844 + 0.715274i \(0.253698\pi\)
\(602\) 23.2126 0.946073
\(603\) −19.5746 −0.797140
\(604\) −11.1355 −0.453098
\(605\) −9.13465 −0.371376
\(606\) 6.07102 0.246618
\(607\) 4.29781 0.174443 0.0872213 0.996189i \(-0.472201\pi\)
0.0872213 + 0.996189i \(0.472201\pi\)
\(608\) −3.02570 −0.122708
\(609\) 63.8239 2.58628
\(610\) 9.00994 0.364802
\(611\) 3.20229 0.129551
\(612\) 23.5115 0.950395
\(613\) −36.4900 −1.47382 −0.736908 0.675993i \(-0.763715\pi\)
−0.736908 + 0.675993i \(0.763715\pi\)
\(614\) 18.5486 0.748561
\(615\) 37.0192 1.49276
\(616\) 5.86765 0.236415
\(617\) −9.12631 −0.367411 −0.183706 0.982981i \(-0.558809\pi\)
−0.183706 + 0.982981i \(0.558809\pi\)
\(618\) 46.0332 1.85173
\(619\) 31.1512 1.25207 0.626035 0.779795i \(-0.284677\pi\)
0.626035 + 0.779795i \(0.284677\pi\)
\(620\) 10.4549 0.419880
\(621\) −12.7846 −0.513029
\(622\) 15.5169 0.622169
\(623\) −23.3593 −0.935869
\(624\) −0.849126 −0.0339922
\(625\) −5.94128 −0.237651
\(626\) 2.30508 0.0921297
\(627\) 21.4914 0.858286
\(628\) 15.4422 0.616211
\(629\) −35.8099 −1.42784
\(630\) −27.2338 −1.08502
\(631\) −27.4566 −1.09303 −0.546515 0.837449i \(-0.684046\pi\)
−0.546515 + 0.837449i \(0.684046\pi\)
\(632\) −15.4765 −0.615621
\(633\) −53.8567 −2.14061
\(634\) −11.3746 −0.451745
\(635\) 16.5081 0.655103
\(636\) 28.5589 1.13243
\(637\) −0.0986078 −0.00390698
\(638\) −18.0899 −0.716184
\(639\) −70.3325 −2.78231
\(640\) −1.57138 −0.0621141
\(641\) −9.93186 −0.392285 −0.196142 0.980575i \(-0.562841\pi\)
−0.196142 + 0.980575i \(0.562841\pi\)
\(642\) −27.3478 −1.07933
\(643\) 30.8635 1.21714 0.608569 0.793501i \(-0.291744\pi\)
0.608569 + 0.793501i \(0.291744\pi\)
\(644\) 2.83377 0.111666
\(645\) 44.1548 1.73859
\(646\) −10.5752 −0.416077
\(647\) −13.1275 −0.516096 −0.258048 0.966132i \(-0.583079\pi\)
−0.258048 + 0.966132i \(0.583079\pi\)
\(648\) −16.0706 −0.631313
\(649\) 22.8190 0.895725
\(650\) 0.689030 0.0270260
\(651\) −53.4614 −2.09532
\(652\) −19.4247 −0.760728
\(653\) −5.48671 −0.214711 −0.107356 0.994221i \(-0.534238\pi\)
−0.107356 + 0.994221i \(0.534238\pi\)
\(654\) 51.0782 1.99731
\(655\) 14.7833 0.577630
\(656\) −7.55369 −0.294922
\(657\) 13.6374 0.532045
\(658\) −30.3032 −1.18134
\(659\) −30.1775 −1.17555 −0.587774 0.809025i \(-0.699996\pi\)
−0.587774 + 0.809025i \(0.699996\pi\)
\(660\) 11.1614 0.434458
\(661\) −18.5785 −0.722620 −0.361310 0.932446i \(-0.617670\pi\)
−0.361310 + 0.932446i \(0.617670\pi\)
\(662\) 14.3485 0.557669
\(663\) −2.96781 −0.115260
\(664\) −11.0624 −0.429305
\(665\) 12.2495 0.475016
\(666\) 68.9216 2.67066
\(667\) −8.73644 −0.338276
\(668\) −23.0061 −0.890132
\(669\) −59.6713 −2.30703
\(670\) 4.57254 0.176653
\(671\) 13.0585 0.504118
\(672\) 8.03526 0.309967
\(673\) 40.9287 1.57768 0.788842 0.614596i \(-0.210681\pi\)
0.788842 + 0.614596i \(0.210681\pi\)
\(674\) 33.0436 1.27279
\(675\) 29.4165 1.13224
\(676\) −12.9259 −0.497149
\(677\) −34.2455 −1.31616 −0.658080 0.752948i \(-0.728631\pi\)
−0.658080 + 0.752948i \(0.728631\pi\)
\(678\) 25.9397 0.996207
\(679\) −25.6879 −0.985813
\(680\) −5.49217 −0.210615
\(681\) 29.9007 1.14580
\(682\) 15.1528 0.580230
\(683\) −23.3249 −0.892504 −0.446252 0.894907i \(-0.647241\pi\)
−0.446252 + 0.894907i \(0.647241\pi\)
\(684\) 20.3536 0.778241
\(685\) 3.53340 0.135004
\(686\) 18.9679 0.724198
\(687\) 48.1851 1.83837
\(688\) −9.00970 −0.343492
\(689\) −2.49309 −0.0949792
\(690\) 5.39037 0.205208
\(691\) −18.0107 −0.685161 −0.342581 0.939488i \(-0.611301\pi\)
−0.342581 + 0.939488i \(0.611301\pi\)
\(692\) 12.6019 0.479051
\(693\) −39.4712 −1.49939
\(694\) −1.25935 −0.0478042
\(695\) −17.2262 −0.653428
\(696\) −24.7726 −0.939001
\(697\) −26.4012 −1.00002
\(698\) 5.46754 0.206949
\(699\) −38.4428 −1.45404
\(700\) −6.52029 −0.246444
\(701\) −10.0324 −0.378918 −0.189459 0.981889i \(-0.560673\pi\)
−0.189459 + 0.981889i \(0.560673\pi\)
\(702\) 3.16462 0.119441
\(703\) −31.0003 −1.16920
\(704\) −2.27747 −0.0858352
\(705\) −57.6427 −2.17095
\(706\) −28.6896 −1.07975
\(707\) 5.01518 0.188615
\(708\) 31.2488 1.17440
\(709\) 41.6972 1.56597 0.782986 0.622039i \(-0.213696\pi\)
0.782986 + 0.622039i \(0.213696\pi\)
\(710\) 16.4293 0.616582
\(711\) 104.109 3.90439
\(712\) 9.06665 0.339787
\(713\) 7.31799 0.274061
\(714\) 28.0843 1.05103
\(715\) −0.974353 −0.0364387
\(716\) −4.22919 −0.158052
\(717\) 78.7378 2.94052
\(718\) −3.40290 −0.126995
\(719\) −18.8814 −0.704159 −0.352080 0.935970i \(-0.614525\pi\)
−0.352080 + 0.935970i \(0.614525\pi\)
\(720\) 10.5705 0.393940
\(721\) 38.0274 1.41621
\(722\) 9.84512 0.366398
\(723\) 51.6302 1.92015
\(724\) 8.10763 0.301318
\(725\) 20.1019 0.746566
\(726\) −18.1301 −0.672869
\(727\) 13.2857 0.492739 0.246369 0.969176i \(-0.420762\pi\)
0.246369 + 0.969176i \(0.420762\pi\)
\(728\) −0.701451 −0.0259975
\(729\) −0.648523 −0.0240194
\(730\) −3.18563 −0.117906
\(731\) −31.4901 −1.16470
\(732\) 17.8825 0.660958
\(733\) −3.01860 −0.111495 −0.0557473 0.998445i \(-0.517754\pi\)
−0.0557473 + 0.998445i \(0.517754\pi\)
\(734\) 15.4357 0.569741
\(735\) 1.77498 0.0654713
\(736\) −1.09989 −0.0405427
\(737\) 6.62719 0.244116
\(738\) 50.8130 1.87045
\(739\) −35.8354 −1.31822 −0.659112 0.752044i \(-0.729068\pi\)
−0.659112 + 0.752044i \(0.729068\pi\)
\(740\) −16.0998 −0.591839
\(741\) −2.56920 −0.0943820
\(742\) 23.5921 0.866093
\(743\) 40.7369 1.49449 0.747245 0.664548i \(-0.231376\pi\)
0.747245 + 0.664548i \(0.231376\pi\)
\(744\) 20.7505 0.760749
\(745\) −32.4814 −1.19003
\(746\) −31.0288 −1.13604
\(747\) 74.4158 2.72273
\(748\) −7.96005 −0.291048
\(749\) −22.5916 −0.825479
\(750\) −36.9069 −1.34765
\(751\) −36.7976 −1.34276 −0.671381 0.741112i \(-0.734299\pi\)
−0.671381 + 0.741112i \(0.734299\pi\)
\(752\) 11.7619 0.428911
\(753\) −73.0091 −2.66060
\(754\) 2.16256 0.0787557
\(755\) −17.4981 −0.636821
\(756\) −29.9467 −1.08915
\(757\) 14.3783 0.522587 0.261293 0.965259i \(-0.415851\pi\)
0.261293 + 0.965259i \(0.415851\pi\)
\(758\) −0.478507 −0.0173802
\(759\) 7.81251 0.283576
\(760\) −4.75452 −0.172464
\(761\) −2.38705 −0.0865306 −0.0432653 0.999064i \(-0.513776\pi\)
−0.0432653 + 0.999064i \(0.513776\pi\)
\(762\) 32.7645 1.18693
\(763\) 42.1950 1.52756
\(764\) 3.58116 0.129562
\(765\) 36.9453 1.33576
\(766\) 23.3872 0.845014
\(767\) −2.72791 −0.0984991
\(768\) −3.11880 −0.112540
\(769\) 49.9662 1.80183 0.900913 0.434000i \(-0.142898\pi\)
0.900913 + 0.434000i \(0.142898\pi\)
\(770\) 9.22029 0.332276
\(771\) 30.6263 1.10298
\(772\) −4.77286 −0.171779
\(773\) 50.3248 1.81006 0.905028 0.425352i \(-0.139850\pi\)
0.905028 + 0.425352i \(0.139850\pi\)
\(774\) 60.6074 2.17849
\(775\) −16.8381 −0.604844
\(776\) 9.97049 0.357920
\(777\) 82.3265 2.95345
\(778\) −24.8239 −0.889978
\(779\) −22.8552 −0.818873
\(780\) −1.33430 −0.0477755
\(781\) 23.8118 0.852053
\(782\) −3.84428 −0.137471
\(783\) 92.3251 3.29943
\(784\) −0.362182 −0.0129351
\(785\) 24.2655 0.866073
\(786\) 29.3412 1.04656
\(787\) −7.70296 −0.274581 −0.137290 0.990531i \(-0.543839\pi\)
−0.137290 + 0.990531i \(0.543839\pi\)
\(788\) 3.42352 0.121958
\(789\) 89.9888 3.20369
\(790\) −24.3193 −0.865244
\(791\) 21.4284 0.761906
\(792\) 15.3203 0.544383
\(793\) −1.56108 −0.0554357
\(794\) −28.6504 −1.01676
\(795\) 44.8767 1.59161
\(796\) 20.7544 0.735619
\(797\) 5.59061 0.198030 0.0990148 0.995086i \(-0.468431\pi\)
0.0990148 + 0.995086i \(0.468431\pi\)
\(798\) 24.3123 0.860647
\(799\) 41.1093 1.45434
\(800\) 2.53078 0.0894765
\(801\) −60.9905 −2.15499
\(802\) −16.2022 −0.572118
\(803\) −4.61708 −0.162933
\(804\) 9.07539 0.320064
\(805\) 4.45291 0.156944
\(806\) −1.81144 −0.0638054
\(807\) 37.0066 1.30269
\(808\) −1.94659 −0.0684807
\(809\) −19.8905 −0.699311 −0.349656 0.936878i \(-0.613701\pi\)
−0.349656 + 0.936878i \(0.613701\pi\)
\(810\) −25.2529 −0.887298
\(811\) 45.3870 1.59375 0.796877 0.604141i \(-0.206484\pi\)
0.796877 + 0.604141i \(0.206484\pi\)
\(812\) −20.4643 −0.718155
\(813\) 13.6080 0.477252
\(814\) −23.3341 −0.817860
\(815\) −30.5234 −1.06919
\(816\) −10.9006 −0.381598
\(817\) −27.2607 −0.953730
\(818\) 1.44491 0.0505199
\(819\) 4.71860 0.164881
\(820\) −11.8697 −0.414507
\(821\) −44.4262 −1.55048 −0.775242 0.631664i \(-0.782372\pi\)
−0.775242 + 0.631664i \(0.782372\pi\)
\(822\) 7.01293 0.244604
\(823\) −41.5587 −1.44864 −0.724322 0.689462i \(-0.757847\pi\)
−0.724322 + 0.689462i \(0.757847\pi\)
\(824\) −14.7599 −0.514186
\(825\) −17.9760 −0.625844
\(826\) 25.8142 0.898189
\(827\) −34.3142 −1.19322 −0.596611 0.802530i \(-0.703487\pi\)
−0.596611 + 0.802530i \(0.703487\pi\)
\(828\) 7.39889 0.257129
\(829\) 23.7097 0.823472 0.411736 0.911303i \(-0.364923\pi\)
0.411736 + 0.911303i \(0.364923\pi\)
\(830\) −17.3832 −0.603380
\(831\) −56.4998 −1.95996
\(832\) 0.272260 0.00943893
\(833\) −1.26587 −0.0438600
\(834\) −34.1899 −1.18390
\(835\) −36.1512 −1.25106
\(836\) −6.89093 −0.238328
\(837\) −77.3351 −2.67309
\(838\) 32.9567 1.13847
\(839\) −14.8177 −0.511564 −0.255782 0.966735i \(-0.582333\pi\)
−0.255782 + 0.966735i \(0.582333\pi\)
\(840\) 12.6264 0.435653
\(841\) 34.0909 1.17555
\(842\) −35.1379 −1.21093
\(843\) 87.6147 3.01761
\(844\) 17.2684 0.594403
\(845\) −20.3114 −0.698734
\(846\) −79.1211 −2.72024
\(847\) −14.9770 −0.514615
\(848\) −9.15701 −0.314453
\(849\) −43.1876 −1.48219
\(850\) 8.84541 0.303395
\(851\) −11.2691 −0.386301
\(852\) 32.6083 1.11714
\(853\) −44.7255 −1.53137 −0.765686 0.643215i \(-0.777600\pi\)
−0.765686 + 0.643215i \(0.777600\pi\)
\(854\) 14.7725 0.505505
\(855\) 31.9832 1.09380
\(856\) 8.76868 0.299707
\(857\) −45.9644 −1.57012 −0.785058 0.619422i \(-0.787367\pi\)
−0.785058 + 0.619422i \(0.787367\pi\)
\(858\) −1.93385 −0.0660207
\(859\) −20.9376 −0.714382 −0.357191 0.934031i \(-0.616265\pi\)
−0.357191 + 0.934031i \(0.616265\pi\)
\(860\) −14.1576 −0.482771
\(861\) 60.6959 2.06851
\(862\) −3.44601 −0.117372
\(863\) 27.1193 0.923152 0.461576 0.887101i \(-0.347284\pi\)
0.461576 + 0.887101i \(0.347284\pi\)
\(864\) 11.6235 0.395439
\(865\) 19.8023 0.673298
\(866\) −22.6597 −0.770010
\(867\) 14.9204 0.506724
\(868\) 17.1417 0.581826
\(869\) −35.2471 −1.19568
\(870\) −38.9270 −1.31975
\(871\) −0.792250 −0.0268444
\(872\) −16.3775 −0.554613
\(873\) −67.0706 −2.27000
\(874\) −3.32796 −0.112570
\(875\) −30.4883 −1.03069
\(876\) −6.32270 −0.213624
\(877\) 41.1367 1.38909 0.694544 0.719451i \(-0.255606\pi\)
0.694544 + 0.719451i \(0.255606\pi\)
\(878\) 27.4365 0.925936
\(879\) 47.6799 1.60820
\(880\) −3.57875 −0.120640
\(881\) 25.4253 0.856600 0.428300 0.903637i \(-0.359113\pi\)
0.428300 + 0.903637i \(0.359113\pi\)
\(882\) 2.43637 0.0820367
\(883\) −22.5281 −0.758131 −0.379066 0.925370i \(-0.623755\pi\)
−0.379066 + 0.925370i \(0.623755\pi\)
\(884\) 0.951587 0.0320053
\(885\) 49.1036 1.65060
\(886\) −10.7107 −0.359832
\(887\) −10.1145 −0.339612 −0.169806 0.985477i \(-0.554314\pi\)
−0.169806 + 0.985477i \(0.554314\pi\)
\(888\) −31.9541 −1.07231
\(889\) 27.0663 0.907774
\(890\) 14.2471 0.477564
\(891\) −36.6002 −1.22615
\(892\) 19.1328 0.640613
\(893\) 35.5879 1.19090
\(894\) −64.4677 −2.15612
\(895\) −6.64565 −0.222140
\(896\) −2.57640 −0.0860714
\(897\) −0.933949 −0.0311836
\(898\) 23.3758 0.780060
\(899\) −52.8474 −1.76256
\(900\) −17.0243 −0.567477
\(901\) −32.0050 −1.06624
\(902\) −17.2033 −0.572806
\(903\) 72.3953 2.40916
\(904\) −8.31720 −0.276626
\(905\) 12.7401 0.423496
\(906\) −34.7295 −1.15381
\(907\) −7.25000 −0.240732 −0.120366 0.992730i \(-0.538407\pi\)
−0.120366 + 0.992730i \(0.538407\pi\)
\(908\) −9.58723 −0.318163
\(909\) 13.0945 0.434318
\(910\) −1.10224 −0.0365390
\(911\) 23.8429 0.789950 0.394975 0.918692i \(-0.370753\pi\)
0.394975 + 0.918692i \(0.370753\pi\)
\(912\) −9.43656 −0.312476
\(913\) −25.1942 −0.833808
\(914\) −11.1400 −0.368479
\(915\) 28.1002 0.928964
\(916\) −15.4499 −0.510478
\(917\) 24.2383 0.800420
\(918\) 40.6257 1.34085
\(919\) 52.3672 1.72743 0.863717 0.503977i \(-0.168130\pi\)
0.863717 + 0.503977i \(0.168130\pi\)
\(920\) −1.72835 −0.0569820
\(921\) 57.8494 1.90620
\(922\) 22.5473 0.742557
\(923\) −2.84659 −0.0936966
\(924\) 18.3000 0.602027
\(925\) 25.9295 0.852555
\(926\) −21.6006 −0.709840
\(927\) 99.2885 3.26106
\(928\) 7.94298 0.260741
\(929\) −43.7670 −1.43595 −0.717974 0.696070i \(-0.754930\pi\)
−0.717974 + 0.696070i \(0.754930\pi\)
\(930\) 32.6068 1.06922
\(931\) −1.09585 −0.0359152
\(932\) 12.3262 0.403757
\(933\) 48.3940 1.58435
\(934\) −20.3649 −0.666360
\(935\) −12.5082 −0.409063
\(936\) −1.83147 −0.0598635
\(937\) 28.3684 0.926756 0.463378 0.886161i \(-0.346637\pi\)
0.463378 + 0.886161i \(0.346637\pi\)
\(938\) 7.49705 0.244787
\(939\) 7.18910 0.234607
\(940\) 18.4823 0.602827
\(941\) −22.7228 −0.740743 −0.370371 0.928884i \(-0.620770\pi\)
−0.370371 + 0.928884i \(0.620770\pi\)
\(942\) 48.1611 1.56917
\(943\) −8.30826 −0.270554
\(944\) −10.0195 −0.326106
\(945\) −47.0575 −1.53078
\(946\) −20.5193 −0.667139
\(947\) −35.7751 −1.16253 −0.581267 0.813713i \(-0.697443\pi\)
−0.581267 + 0.813713i \(0.697443\pi\)
\(948\) −48.2680 −1.56767
\(949\) 0.551950 0.0179171
\(950\) 7.65738 0.248438
\(951\) −35.4752 −1.15036
\(952\) −9.00485 −0.291849
\(953\) 37.2108 1.20538 0.602688 0.797977i \(-0.294097\pi\)
0.602688 + 0.797977i \(0.294097\pi\)
\(954\) 61.5984 1.99432
\(955\) 5.62735 0.182097
\(956\) −25.2462 −0.816520
\(957\) −56.4186 −1.82376
\(958\) 2.02262 0.0653479
\(959\) 5.79329 0.187075
\(960\) −4.90081 −0.158173
\(961\) 13.2671 0.427970
\(962\) 2.78949 0.0899366
\(963\) −58.9862 −1.90080
\(964\) −16.5545 −0.533184
\(965\) −7.49997 −0.241432
\(966\) 8.83795 0.284356
\(967\) 39.4358 1.26817 0.634085 0.773263i \(-0.281377\pi\)
0.634085 + 0.773263i \(0.281377\pi\)
\(968\) 5.81315 0.186842
\(969\) −32.9821 −1.05954
\(970\) 15.6674 0.503050
\(971\) 17.2603 0.553911 0.276955 0.960883i \(-0.410675\pi\)
0.276955 + 0.960883i \(0.410675\pi\)
\(972\) −15.2505 −0.489160
\(973\) −28.2438 −0.905454
\(974\) 27.9143 0.894431
\(975\) 2.14895 0.0688214
\(976\) −5.73379 −0.183534
\(977\) −5.50737 −0.176196 −0.0880982 0.996112i \(-0.528079\pi\)
−0.0880982 + 0.996112i \(0.528079\pi\)
\(978\) −60.5816 −1.93719
\(979\) 20.6490 0.659944
\(980\) −0.569124 −0.0181800
\(981\) 110.170 3.51746
\(982\) −13.4879 −0.430416
\(983\) 32.8004 1.04617 0.523086 0.852280i \(-0.324781\pi\)
0.523086 + 0.852280i \(0.324781\pi\)
\(984\) −23.5584 −0.751016
\(985\) 5.37963 0.171409
\(986\) 27.7618 0.884115
\(987\) −94.5098 −3.00828
\(988\) 0.823779 0.0262079
\(989\) −9.90972 −0.315111
\(990\) 24.0740 0.765121
\(991\) −4.37186 −0.138877 −0.0694383 0.997586i \(-0.522121\pi\)
−0.0694383 + 0.997586i \(0.522121\pi\)
\(992\) −6.65335 −0.211244
\(993\) 44.7500 1.42010
\(994\) 26.9372 0.854397
\(995\) 32.6129 1.03390
\(996\) −34.5014 −1.09322
\(997\) −34.1601 −1.08186 −0.540931 0.841067i \(-0.681928\pi\)
−0.540931 + 0.841067i \(0.681928\pi\)
\(998\) 37.4379 1.18508
\(999\) 119.090 3.76785
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 4006.2.a.g.1.2 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.2 40 1.1 even 1 trivial