Properties

Label 4006.2.a.g.1.18
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 1.18
Character \(\chi\) = 4006.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.712075 q^{3} +1.00000 q^{4} -4.09209 q^{5} +0.712075 q^{6} +2.33011 q^{7} -1.00000 q^{8} -2.49295 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.712075 q^{3} +1.00000 q^{4} -4.09209 q^{5} +0.712075 q^{6} +2.33011 q^{7} -1.00000 q^{8} -2.49295 q^{9} +4.09209 q^{10} +4.23375 q^{11} -0.712075 q^{12} -0.870599 q^{13} -2.33011 q^{14} +2.91388 q^{15} +1.00000 q^{16} -6.84125 q^{17} +2.49295 q^{18} +1.01005 q^{19} -4.09209 q^{20} -1.65921 q^{21} -4.23375 q^{22} -2.53327 q^{23} +0.712075 q^{24} +11.7452 q^{25} +0.870599 q^{26} +3.91139 q^{27} +2.33011 q^{28} +0.501652 q^{29} -2.91388 q^{30} +5.40493 q^{31} -1.00000 q^{32} -3.01475 q^{33} +6.84125 q^{34} -9.53500 q^{35} -2.49295 q^{36} +7.79791 q^{37} -1.01005 q^{38} +0.619932 q^{39} +4.09209 q^{40} -6.82665 q^{41} +1.65921 q^{42} +0.979903 q^{43} +4.23375 q^{44} +10.2014 q^{45} +2.53327 q^{46} +0.948587 q^{47} -0.712075 q^{48} -1.57061 q^{49} -11.7452 q^{50} +4.87148 q^{51} -0.870599 q^{52} +12.3207 q^{53} -3.91139 q^{54} -17.3249 q^{55} -2.33011 q^{56} -0.719229 q^{57} -0.501652 q^{58} -8.74441 q^{59} +2.91388 q^{60} -3.12405 q^{61} -5.40493 q^{62} -5.80883 q^{63} +1.00000 q^{64} +3.56257 q^{65} +3.01475 q^{66} -2.12825 q^{67} -6.84125 q^{68} +1.80388 q^{69} +9.53500 q^{70} -0.135202 q^{71} +2.49295 q^{72} -5.71895 q^{73} -7.79791 q^{74} -8.36347 q^{75} +1.01005 q^{76} +9.86509 q^{77} -0.619932 q^{78} +15.1609 q^{79} -4.09209 q^{80} +4.69364 q^{81} +6.82665 q^{82} -6.20844 q^{83} -1.65921 q^{84} +27.9950 q^{85} -0.979903 q^{86} -0.357214 q^{87} -4.23375 q^{88} +3.24155 q^{89} -10.2014 q^{90} -2.02859 q^{91} -2.53327 q^{92} -3.84872 q^{93} -0.948587 q^{94} -4.13320 q^{95} +0.712075 q^{96} +18.9534 q^{97} +1.57061 q^{98} -10.5545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + O(q^{10}) \) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + 23q^{10} - 28q^{11} - q^{12} - 12q^{13} - 12q^{14} - 14q^{15} + 40q^{16} - 10q^{17} - 29q^{18} + 3q^{19} - 23q^{20} - 40q^{21} + 28q^{22} - 10q^{23} + q^{24} + 43q^{25} + 12q^{26} - 7q^{27} + 12q^{28} - 37q^{29} + 14q^{30} - 16q^{31} - 40q^{32} - 11q^{33} + 10q^{34} - 24q^{35} + 29q^{36} - 17q^{37} - 3q^{38} - 10q^{39} + 23q^{40} - 58q^{41} + 40q^{42} + 37q^{43} - 28q^{44} - 66q^{45} + 10q^{46} - 34q^{47} - q^{48} + 28q^{49} - 43q^{50} - 7q^{51} - 12q^{52} - 43q^{53} + 7q^{54} + 28q^{55} - 12q^{56} - 25q^{57} + 37q^{58} - 92q^{59} - 14q^{60} - 37q^{61} + 16q^{62} + 14q^{63} + 40q^{64} - 54q^{65} + 11q^{66} - 10q^{67} - 10q^{68} - 49q^{69} + 24q^{70} - 87q^{71} - 29q^{72} + 12q^{73} + 17q^{74} - 31q^{75} + 3q^{76} - 53q^{77} + 10q^{78} + 14q^{79} - 23q^{80} - 4q^{81} + 58q^{82} - 42q^{83} - 40q^{84} - 24q^{85} - 37q^{86} + 24q^{87} + 28q^{88} - 118q^{89} + 66q^{90} - 35q^{91} - 10q^{92} - 22q^{93} + 34q^{94} - 18q^{95} + q^{96} + 2q^{97} - 28q^{98} - 48q^{99} + O(q^{100}) \)

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
\(3\) −0.712075 −0.411117 −0.205558 0.978645i \(-0.565901\pi\)
−0.205558 + 0.978645i \(0.565901\pi\)
\(4\) 1.00000 0.500000
\(5\) −4.09209 −1.83004 −0.915019 0.403410i \(-0.867825\pi\)
−0.915019 + 0.403410i \(0.867825\pi\)
\(6\) 0.712075 0.290703
\(7\) 2.33011 0.880697 0.440348 0.897827i \(-0.354855\pi\)
0.440348 + 0.897827i \(0.354855\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.49295 −0.830983
\(10\) 4.09209 1.29403
\(11\) 4.23375 1.27652 0.638262 0.769819i \(-0.279654\pi\)
0.638262 + 0.769819i \(0.279654\pi\)
\(12\) −0.712075 −0.205558
\(13\) −0.870599 −0.241461 −0.120730 0.992685i \(-0.538524\pi\)
−0.120730 + 0.992685i \(0.538524\pi\)
\(14\) −2.33011 −0.622747
\(15\) 2.91388 0.752359
\(16\) 1.00000 0.250000
\(17\) −6.84125 −1.65925 −0.829623 0.558324i \(-0.811445\pi\)
−0.829623 + 0.558324i \(0.811445\pi\)
\(18\) 2.49295 0.587594
\(19\) 1.01005 0.231721 0.115860 0.993266i \(-0.463037\pi\)
0.115860 + 0.993266i \(0.463037\pi\)
\(20\) −4.09209 −0.915019
\(21\) −1.65921 −0.362069
\(22\) −4.23375 −0.902639
\(23\) −2.53327 −0.528223 −0.264111 0.964492i \(-0.585079\pi\)
−0.264111 + 0.964492i \(0.585079\pi\)
\(24\) 0.712075 0.145352
\(25\) 11.7452 2.34904
\(26\) 0.870599 0.170739
\(27\) 3.91139 0.752748
\(28\) 2.33011 0.440348
\(29\) 0.501652 0.0931545 0.0465772 0.998915i \(-0.485169\pi\)
0.0465772 + 0.998915i \(0.485169\pi\)
\(30\) −2.91388 −0.531998
\(31\) 5.40493 0.970754 0.485377 0.874305i \(-0.338682\pi\)
0.485377 + 0.874305i \(0.338682\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.01475 −0.524801
\(34\) 6.84125 1.17326
\(35\) −9.53500 −1.61171
\(36\) −2.49295 −0.415492
\(37\) 7.79791 1.28197 0.640984 0.767554i \(-0.278526\pi\)
0.640984 + 0.767554i \(0.278526\pi\)
\(38\) −1.01005 −0.163851
\(39\) 0.619932 0.0992686
\(40\) 4.09209 0.647016
\(41\) −6.82665 −1.06614 −0.533072 0.846070i \(-0.678962\pi\)
−0.533072 + 0.846070i \(0.678962\pi\)
\(42\) 1.65921 0.256022
\(43\) 0.979903 0.149434 0.0747169 0.997205i \(-0.476195\pi\)
0.0747169 + 0.997205i \(0.476195\pi\)
\(44\) 4.23375 0.638262
\(45\) 10.2014 1.52073
\(46\) 2.53327 0.373510
\(47\) 0.948587 0.138366 0.0691828 0.997604i \(-0.477961\pi\)
0.0691828 + 0.997604i \(0.477961\pi\)
\(48\) −0.712075 −0.102779
\(49\) −1.57061 −0.224373
\(50\) −11.7452 −1.66102
\(51\) 4.87148 0.682144
\(52\) −0.870599 −0.120730
\(53\) 12.3207 1.69238 0.846192 0.532878i \(-0.178890\pi\)
0.846192 + 0.532878i \(0.178890\pi\)
\(54\) −3.91139 −0.532273
\(55\) −17.3249 −2.33609
\(56\) −2.33011 −0.311373
\(57\) −0.719229 −0.0952642
\(58\) −0.501652 −0.0658702
\(59\) −8.74441 −1.13842 −0.569212 0.822191i \(-0.692752\pi\)
−0.569212 + 0.822191i \(0.692752\pi\)
\(60\) 2.91388 0.376180
\(61\) −3.12405 −0.399994 −0.199997 0.979797i \(-0.564093\pi\)
−0.199997 + 0.979797i \(0.564093\pi\)
\(62\) −5.40493 −0.686427
\(63\) −5.80883 −0.731844
\(64\) 1.00000 0.125000
\(65\) 3.56257 0.441883
\(66\) 3.01475 0.371090
\(67\) −2.12825 −0.260007 −0.130003 0.991514i \(-0.541499\pi\)
−0.130003 + 0.991514i \(0.541499\pi\)
\(68\) −6.84125 −0.829623
\(69\) 1.80388 0.217161
\(70\) 9.53500 1.13965
\(71\) −0.135202 −0.0160455 −0.00802275 0.999968i \(-0.502554\pi\)
−0.00802275 + 0.999968i \(0.502554\pi\)
\(72\) 2.49295 0.293797
\(73\) −5.71895 −0.669352 −0.334676 0.942333i \(-0.608627\pi\)
−0.334676 + 0.942333i \(0.608627\pi\)
\(74\) −7.79791 −0.906488
\(75\) −8.36347 −0.965730
\(76\) 1.01005 0.115860
\(77\) 9.86509 1.12423
\(78\) −0.619932 −0.0701935
\(79\) 15.1609 1.70573 0.852867 0.522128i \(-0.174862\pi\)
0.852867 + 0.522128i \(0.174862\pi\)
\(80\) −4.09209 −0.457510
\(81\) 4.69364 0.521516
\(82\) 6.82665 0.753877
\(83\) −6.20844 −0.681465 −0.340732 0.940160i \(-0.610675\pi\)
−0.340732 + 0.940160i \(0.610675\pi\)
\(84\) −1.65921 −0.181035
\(85\) 27.9950 3.03648
\(86\) −0.979903 −0.105666
\(87\) −0.357214 −0.0382974
\(88\) −4.23375 −0.451320
\(89\) 3.24155 0.343603 0.171802 0.985132i \(-0.445041\pi\)
0.171802 + 0.985132i \(0.445041\pi\)
\(90\) −10.2014 −1.07532
\(91\) −2.02859 −0.212654
\(92\) −2.53327 −0.264111
\(93\) −3.84872 −0.399093
\(94\) −0.948587 −0.0978392
\(95\) −4.13320 −0.424058
\(96\) 0.712075 0.0726758
\(97\) 18.9534 1.92443 0.962213 0.272297i \(-0.0877834\pi\)
0.962213 + 0.272297i \(0.0877834\pi\)
\(98\) 1.57061 0.158656
\(99\) −10.5545 −1.06077
\(100\) 11.7452 1.17452
\(101\) 0.897568 0.0893114 0.0446557 0.999002i \(-0.485781\pi\)
0.0446557 + 0.999002i \(0.485781\pi\)
\(102\) −4.87148 −0.482349
\(103\) 1.99610 0.196681 0.0983406 0.995153i \(-0.468647\pi\)
0.0983406 + 0.995153i \(0.468647\pi\)
\(104\) 0.870599 0.0853693
\(105\) 6.78964 0.662601
\(106\) −12.3207 −1.19670
\(107\) 0.418296 0.0404382 0.0202191 0.999796i \(-0.493564\pi\)
0.0202191 + 0.999796i \(0.493564\pi\)
\(108\) 3.91139 0.376374
\(109\) −11.0518 −1.05857 −0.529285 0.848444i \(-0.677540\pi\)
−0.529285 + 0.848444i \(0.677540\pi\)
\(110\) 17.3249 1.65186
\(111\) −5.55269 −0.527038
\(112\) 2.33011 0.220174
\(113\) 8.73234 0.821469 0.410735 0.911755i \(-0.365272\pi\)
0.410735 + 0.911755i \(0.365272\pi\)
\(114\) 0.719229 0.0673620
\(115\) 10.3664 0.966668
\(116\) 0.501652 0.0465772
\(117\) 2.17036 0.200650
\(118\) 8.74441 0.804988
\(119\) −15.9408 −1.46129
\(120\) −2.91388 −0.265999
\(121\) 6.92467 0.629515
\(122\) 3.12405 0.282838
\(123\) 4.86109 0.438309
\(124\) 5.40493 0.485377
\(125\) −27.6020 −2.46880
\(126\) 5.80883 0.517492
\(127\) −2.79511 −0.248026 −0.124013 0.992281i \(-0.539576\pi\)
−0.124013 + 0.992281i \(0.539576\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.697765 −0.0614348
\(130\) −3.56257 −0.312458
\(131\) 7.27881 0.635953 0.317976 0.948099i \(-0.396997\pi\)
0.317976 + 0.948099i \(0.396997\pi\)
\(132\) −3.01475 −0.262400
\(133\) 2.35352 0.204076
\(134\) 2.12825 0.183853
\(135\) −16.0058 −1.37756
\(136\) 6.84125 0.586632
\(137\) 0.158074 0.0135052 0.00675259 0.999977i \(-0.497851\pi\)
0.00675259 + 0.999977i \(0.497851\pi\)
\(138\) −1.80388 −0.153556
\(139\) −16.6942 −1.41598 −0.707990 0.706223i \(-0.750398\pi\)
−0.707990 + 0.706223i \(0.750398\pi\)
\(140\) −9.53500 −0.805855
\(141\) −0.675465 −0.0568844
\(142\) 0.135202 0.0113459
\(143\) −3.68590 −0.308231
\(144\) −2.49295 −0.207746
\(145\) −2.05281 −0.170476
\(146\) 5.71895 0.473303
\(147\) 1.11839 0.0922435
\(148\) 7.79791 0.640984
\(149\) 11.6457 0.954055 0.477028 0.878888i \(-0.341714\pi\)
0.477028 + 0.878888i \(0.341714\pi\)
\(150\) 8.36347 0.682874
\(151\) −22.1165 −1.79981 −0.899907 0.436081i \(-0.856366\pi\)
−0.899907 + 0.436081i \(0.856366\pi\)
\(152\) −1.01005 −0.0819256
\(153\) 17.0549 1.37881
\(154\) −9.86509 −0.794952
\(155\) −22.1175 −1.77652
\(156\) 0.619932 0.0496343
\(157\) −12.3994 −0.989580 −0.494790 0.869013i \(-0.664755\pi\)
−0.494790 + 0.869013i \(0.664755\pi\)
\(158\) −15.1609 −1.20614
\(159\) −8.77329 −0.695767
\(160\) 4.09209 0.323508
\(161\) −5.90278 −0.465204
\(162\) −4.69364 −0.368767
\(163\) 2.20063 0.172367 0.0861833 0.996279i \(-0.472533\pi\)
0.0861833 + 0.996279i \(0.472533\pi\)
\(164\) −6.82665 −0.533072
\(165\) 12.3366 0.960405
\(166\) 6.20844 0.481868
\(167\) 12.5024 0.967467 0.483734 0.875215i \(-0.339280\pi\)
0.483734 + 0.875215i \(0.339280\pi\)
\(168\) 1.65921 0.128011
\(169\) −12.2421 −0.941697
\(170\) −27.9950 −2.14712
\(171\) −2.51800 −0.192556
\(172\) 0.979903 0.0747169
\(173\) 13.1085 0.996620 0.498310 0.866999i \(-0.333954\pi\)
0.498310 + 0.866999i \(0.333954\pi\)
\(174\) 0.357214 0.0270803
\(175\) 27.3676 2.06879
\(176\) 4.23375 0.319131
\(177\) 6.22667 0.468025
\(178\) −3.24155 −0.242964
\(179\) −7.80940 −0.583702 −0.291851 0.956464i \(-0.594271\pi\)
−0.291851 + 0.956464i \(0.594271\pi\)
\(180\) 10.2014 0.760366
\(181\) −15.6233 −1.16127 −0.580636 0.814163i \(-0.697196\pi\)
−0.580636 + 0.814163i \(0.697196\pi\)
\(182\) 2.02859 0.150369
\(183\) 2.22456 0.164444
\(184\) 2.53327 0.186755
\(185\) −31.9097 −2.34605
\(186\) 3.84872 0.282202
\(187\) −28.9642 −2.11807
\(188\) 0.948587 0.0691828
\(189\) 9.11395 0.662943
\(190\) 4.13320 0.299854
\(191\) −25.5535 −1.84898 −0.924492 0.381202i \(-0.875510\pi\)
−0.924492 + 0.381202i \(0.875510\pi\)
\(192\) −0.712075 −0.0513896
\(193\) −14.3261 −1.03122 −0.515608 0.856825i \(-0.672434\pi\)
−0.515608 + 0.856825i \(0.672434\pi\)
\(194\) −18.9534 −1.36077
\(195\) −2.53682 −0.181665
\(196\) −1.57061 −0.112186
\(197\) 8.07366 0.575225 0.287612 0.957747i \(-0.407139\pi\)
0.287612 + 0.957747i \(0.407139\pi\)
\(198\) 10.5545 0.750078
\(199\) 9.45893 0.670526 0.335263 0.942125i \(-0.391175\pi\)
0.335263 + 0.942125i \(0.391175\pi\)
\(200\) −11.7452 −0.830512
\(201\) 1.51547 0.106893
\(202\) −0.897568 −0.0631527
\(203\) 1.16890 0.0820409
\(204\) 4.87148 0.341072
\(205\) 27.9353 1.95108
\(206\) −1.99610 −0.139075
\(207\) 6.31531 0.438944
\(208\) −0.870599 −0.0603652
\(209\) 4.27629 0.295797
\(210\) −6.78964 −0.468529
\(211\) −13.9975 −0.963625 −0.481812 0.876274i \(-0.660021\pi\)
−0.481812 + 0.876274i \(0.660021\pi\)
\(212\) 12.3207 0.846192
\(213\) 0.0962739 0.00659658
\(214\) −0.418296 −0.0285941
\(215\) −4.00985 −0.273470
\(216\) −3.91139 −0.266136
\(217\) 12.5941 0.854940
\(218\) 11.0518 0.748522
\(219\) 4.07232 0.275182
\(220\) −17.3249 −1.16804
\(221\) 5.95599 0.400643
\(222\) 5.55269 0.372672
\(223\) −7.35326 −0.492410 −0.246205 0.969218i \(-0.579184\pi\)
−0.246205 + 0.969218i \(0.579184\pi\)
\(224\) −2.33011 −0.155687
\(225\) −29.2802 −1.95201
\(226\) −8.73234 −0.580867
\(227\) −0.904122 −0.0600087 −0.0300043 0.999550i \(-0.509552\pi\)
−0.0300043 + 0.999550i \(0.509552\pi\)
\(228\) −0.719229 −0.0476321
\(229\) −10.6473 −0.703592 −0.351796 0.936077i \(-0.614429\pi\)
−0.351796 + 0.936077i \(0.614429\pi\)
\(230\) −10.3664 −0.683538
\(231\) −7.02468 −0.462190
\(232\) −0.501652 −0.0329351
\(233\) −20.9772 −1.37426 −0.687130 0.726535i \(-0.741130\pi\)
−0.687130 + 0.726535i \(0.741130\pi\)
\(234\) −2.17036 −0.141881
\(235\) −3.88170 −0.253214
\(236\) −8.74441 −0.569212
\(237\) −10.7957 −0.701256
\(238\) 15.9408 1.03329
\(239\) 12.1770 0.787663 0.393831 0.919183i \(-0.371149\pi\)
0.393831 + 0.919183i \(0.371149\pi\)
\(240\) 2.91388 0.188090
\(241\) −0.973327 −0.0626975 −0.0313488 0.999509i \(-0.509980\pi\)
−0.0313488 + 0.999509i \(0.509980\pi\)
\(242\) −6.92467 −0.445135
\(243\) −15.0764 −0.967152
\(244\) −3.12405 −0.199997
\(245\) 6.42708 0.410611
\(246\) −4.86109 −0.309932
\(247\) −0.879346 −0.0559515
\(248\) −5.40493 −0.343214
\(249\) 4.42087 0.280162
\(250\) 27.6020 1.74570
\(251\) −22.6555 −1.43000 −0.715000 0.699124i \(-0.753573\pi\)
−0.715000 + 0.699124i \(0.753573\pi\)
\(252\) −5.80883 −0.365922
\(253\) −10.7252 −0.674289
\(254\) 2.79511 0.175381
\(255\) −19.9345 −1.24835
\(256\) 1.00000 0.0625000
\(257\) 1.66655 0.103957 0.0519784 0.998648i \(-0.483447\pi\)
0.0519784 + 0.998648i \(0.483447\pi\)
\(258\) 0.697765 0.0434409
\(259\) 18.1699 1.12903
\(260\) 3.56257 0.220941
\(261\) −1.25059 −0.0774098
\(262\) −7.27881 −0.449687
\(263\) −21.7022 −1.33821 −0.669106 0.743167i \(-0.733323\pi\)
−0.669106 + 0.743167i \(0.733323\pi\)
\(264\) 3.01475 0.185545
\(265\) −50.4176 −3.09713
\(266\) −2.35352 −0.144303
\(267\) −2.30822 −0.141261
\(268\) −2.12825 −0.130003
\(269\) −21.5484 −1.31383 −0.656915 0.753965i \(-0.728139\pi\)
−0.656915 + 0.753965i \(0.728139\pi\)
\(270\) 16.0058 0.974080
\(271\) 4.49788 0.273227 0.136613 0.990624i \(-0.456378\pi\)
0.136613 + 0.990624i \(0.456378\pi\)
\(272\) −6.84125 −0.414812
\(273\) 1.44451 0.0874255
\(274\) −0.158074 −0.00954961
\(275\) 49.7263 2.99861
\(276\) 1.80388 0.108581
\(277\) −12.9141 −0.775935 −0.387968 0.921673i \(-0.626823\pi\)
−0.387968 + 0.921673i \(0.626823\pi\)
\(278\) 16.6942 1.00125
\(279\) −13.4742 −0.806681
\(280\) 9.53500 0.569825
\(281\) −3.82996 −0.228476 −0.114238 0.993453i \(-0.536443\pi\)
−0.114238 + 0.993453i \(0.536443\pi\)
\(282\) 0.675465 0.0402233
\(283\) −11.6200 −0.690735 −0.345367 0.938468i \(-0.612246\pi\)
−0.345367 + 0.938468i \(0.612246\pi\)
\(284\) −0.135202 −0.00802275
\(285\) 2.94315 0.174337
\(286\) 3.68590 0.217952
\(287\) −15.9068 −0.938949
\(288\) 2.49295 0.146898
\(289\) 29.8027 1.75310
\(290\) 2.05281 0.120545
\(291\) −13.4962 −0.791164
\(292\) −5.71895 −0.334676
\(293\) −18.8463 −1.10101 −0.550507 0.834831i \(-0.685565\pi\)
−0.550507 + 0.834831i \(0.685565\pi\)
\(294\) −1.11839 −0.0652260
\(295\) 35.7829 2.08336
\(296\) −7.79791 −0.453244
\(297\) 16.5599 0.960901
\(298\) −11.6457 −0.674619
\(299\) 2.20546 0.127545
\(300\) −8.36347 −0.482865
\(301\) 2.28328 0.131606
\(302\) 22.1165 1.27266
\(303\) −0.639136 −0.0367174
\(304\) 1.01005 0.0579302
\(305\) 12.7839 0.732004
\(306\) −17.0549 −0.974963
\(307\) 0.510129 0.0291146 0.0145573 0.999894i \(-0.495366\pi\)
0.0145573 + 0.999894i \(0.495366\pi\)
\(308\) 9.86509 0.562116
\(309\) −1.42137 −0.0808590
\(310\) 22.1175 1.25619
\(311\) −14.9458 −0.847498 −0.423749 0.905780i \(-0.639286\pi\)
−0.423749 + 0.905780i \(0.639286\pi\)
\(312\) −0.619932 −0.0350967
\(313\) 7.64337 0.432029 0.216014 0.976390i \(-0.430694\pi\)
0.216014 + 0.976390i \(0.430694\pi\)
\(314\) 12.3994 0.699739
\(315\) 23.7703 1.33930
\(316\) 15.1609 0.852867
\(317\) 29.8745 1.67792 0.838959 0.544194i \(-0.183164\pi\)
0.838959 + 0.544194i \(0.183164\pi\)
\(318\) 8.77329 0.491982
\(319\) 2.12387 0.118914
\(320\) −4.09209 −0.228755
\(321\) −0.297858 −0.0166248
\(322\) 5.90278 0.328949
\(323\) −6.90998 −0.384482
\(324\) 4.69364 0.260758
\(325\) −10.2254 −0.567201
\(326\) −2.20063 −0.121882
\(327\) 7.86970 0.435196
\(328\) 6.82665 0.376939
\(329\) 2.21031 0.121858
\(330\) −12.3366 −0.679109
\(331\) 18.3774 1.01011 0.505055 0.863087i \(-0.331472\pi\)
0.505055 + 0.863087i \(0.331472\pi\)
\(332\) −6.20844 −0.340732
\(333\) −19.4398 −1.06529
\(334\) −12.5024 −0.684103
\(335\) 8.70899 0.475823
\(336\) −1.65921 −0.0905173
\(337\) 8.21174 0.447322 0.223661 0.974667i \(-0.428199\pi\)
0.223661 + 0.974667i \(0.428199\pi\)
\(338\) 12.2421 0.665880
\(339\) −6.21808 −0.337720
\(340\) 27.9950 1.51824
\(341\) 22.8831 1.23919
\(342\) 2.51800 0.136158
\(343\) −19.9704 −1.07830
\(344\) −0.979903 −0.0528329
\(345\) −7.38163 −0.397413
\(346\) −13.1085 −0.704717
\(347\) 20.4850 1.09969 0.549847 0.835266i \(-0.314686\pi\)
0.549847 + 0.835266i \(0.314686\pi\)
\(348\) −0.357214 −0.0191487
\(349\) −32.6783 −1.74923 −0.874615 0.484819i \(-0.838886\pi\)
−0.874615 + 0.484819i \(0.838886\pi\)
\(350\) −27.3676 −1.46286
\(351\) −3.40525 −0.181759
\(352\) −4.23375 −0.225660
\(353\) 14.5838 0.776219 0.388110 0.921613i \(-0.373128\pi\)
0.388110 + 0.921613i \(0.373128\pi\)
\(354\) −6.22667 −0.330944
\(355\) 0.553258 0.0293639
\(356\) 3.24155 0.171802
\(357\) 11.3511 0.600762
\(358\) 7.80940 0.412740
\(359\) −13.0576 −0.689156 −0.344578 0.938758i \(-0.611978\pi\)
−0.344578 + 0.938758i \(0.611978\pi\)
\(360\) −10.2014 −0.537660
\(361\) −17.9798 −0.946306
\(362\) 15.6233 0.821144
\(363\) −4.93088 −0.258804
\(364\) −2.02859 −0.106327
\(365\) 23.4024 1.22494
\(366\) −2.22456 −0.116280
\(367\) −2.70482 −0.141190 −0.0705952 0.997505i \(-0.522490\pi\)
−0.0705952 + 0.997505i \(0.522490\pi\)
\(368\) −2.53327 −0.132056
\(369\) 17.0185 0.885947
\(370\) 31.9097 1.65891
\(371\) 28.7086 1.49048
\(372\) −3.84872 −0.199547
\(373\) −11.4842 −0.594630 −0.297315 0.954779i \(-0.596091\pi\)
−0.297315 + 0.954779i \(0.596091\pi\)
\(374\) 28.9642 1.49770
\(375\) 19.6547 1.01496
\(376\) −0.948587 −0.0489196
\(377\) −0.436738 −0.0224932
\(378\) −9.11395 −0.468771
\(379\) −4.40530 −0.226285 −0.113143 0.993579i \(-0.536092\pi\)
−0.113143 + 0.993579i \(0.536092\pi\)
\(380\) −4.13320 −0.212029
\(381\) 1.99033 0.101968
\(382\) 25.5535 1.30743
\(383\) −19.4014 −0.991366 −0.495683 0.868504i \(-0.665082\pi\)
−0.495683 + 0.868504i \(0.665082\pi\)
\(384\) 0.712075 0.0363379
\(385\) −40.3688 −2.05739
\(386\) 14.3261 0.729180
\(387\) −2.44285 −0.124177
\(388\) 18.9534 0.962213
\(389\) −21.2228 −1.07604 −0.538020 0.842932i \(-0.680828\pi\)
−0.538020 + 0.842932i \(0.680828\pi\)
\(390\) 2.53682 0.128457
\(391\) 17.3307 0.876452
\(392\) 1.57061 0.0793278
\(393\) −5.18306 −0.261451
\(394\) −8.07366 −0.406745
\(395\) −62.0398 −3.12156
\(396\) −10.5545 −0.530385
\(397\) −8.02549 −0.402788 −0.201394 0.979510i \(-0.564547\pi\)
−0.201394 + 0.979510i \(0.564547\pi\)
\(398\) −9.45893 −0.474134
\(399\) −1.67588 −0.0838989
\(400\) 11.7452 0.587260
\(401\) 19.9104 0.994280 0.497140 0.867670i \(-0.334384\pi\)
0.497140 + 0.867670i \(0.334384\pi\)
\(402\) −1.51547 −0.0755849
\(403\) −4.70553 −0.234399
\(404\) 0.897568 0.0446557
\(405\) −19.2068 −0.954394
\(406\) −1.16890 −0.0580116
\(407\) 33.0144 1.63646
\(408\) −4.87148 −0.241174
\(409\) 33.2530 1.64425 0.822127 0.569304i \(-0.192787\pi\)
0.822127 + 0.569304i \(0.192787\pi\)
\(410\) −27.9353 −1.37962
\(411\) −0.112561 −0.00555221
\(412\) 1.99610 0.0983406
\(413\) −20.3754 −1.00261
\(414\) −6.31531 −0.310380
\(415\) 25.4055 1.24711
\(416\) 0.870599 0.0426846
\(417\) 11.8875 0.582133
\(418\) −4.27629 −0.209160
\(419\) −33.4842 −1.63581 −0.817904 0.575355i \(-0.804864\pi\)
−0.817904 + 0.575355i \(0.804864\pi\)
\(420\) 6.78964 0.331300
\(421\) 26.8544 1.30880 0.654402 0.756147i \(-0.272920\pi\)
0.654402 + 0.756147i \(0.272920\pi\)
\(422\) 13.9975 0.681386
\(423\) −2.36478 −0.114979
\(424\) −12.3207 −0.598348
\(425\) −80.3519 −3.89764
\(426\) −0.0962739 −0.00466448
\(427\) −7.27937 −0.352273
\(428\) 0.418296 0.0202191
\(429\) 2.62464 0.126719
\(430\) 4.00985 0.193372
\(431\) 19.1591 0.922863 0.461431 0.887176i \(-0.347336\pi\)
0.461431 + 0.887176i \(0.347336\pi\)
\(432\) 3.91139 0.188187
\(433\) −36.0575 −1.73281 −0.866407 0.499338i \(-0.833577\pi\)
−0.866407 + 0.499338i \(0.833577\pi\)
\(434\) −12.5941 −0.604534
\(435\) 1.46175 0.0700856
\(436\) −11.0518 −0.529285
\(437\) −2.55872 −0.122400
\(438\) −4.07232 −0.194583
\(439\) −12.0904 −0.577042 −0.288521 0.957474i \(-0.593164\pi\)
−0.288521 + 0.957474i \(0.593164\pi\)
\(440\) 17.3249 0.825932
\(441\) 3.91545 0.186450
\(442\) −5.95599 −0.283297
\(443\) −10.2782 −0.488332 −0.244166 0.969733i \(-0.578514\pi\)
−0.244166 + 0.969733i \(0.578514\pi\)
\(444\) −5.55269 −0.263519
\(445\) −13.2647 −0.628807
\(446\) 7.35326 0.348187
\(447\) −8.29263 −0.392228
\(448\) 2.33011 0.110087
\(449\) 3.17411 0.149795 0.0748977 0.997191i \(-0.476137\pi\)
0.0748977 + 0.997191i \(0.476137\pi\)
\(450\) 29.2802 1.38028
\(451\) −28.9024 −1.36096
\(452\) 8.73234 0.410735
\(453\) 15.7486 0.739934
\(454\) 0.904122 0.0424325
\(455\) 8.30117 0.389165
\(456\) 0.719229 0.0336810
\(457\) 28.7951 1.34698 0.673489 0.739197i \(-0.264795\pi\)
0.673489 + 0.739197i \(0.264795\pi\)
\(458\) 10.6473 0.497515
\(459\) −26.7588 −1.24899
\(460\) 10.3664 0.483334
\(461\) −35.9244 −1.67317 −0.836583 0.547840i \(-0.815450\pi\)
−0.836583 + 0.547840i \(0.815450\pi\)
\(462\) 7.02468 0.326818
\(463\) −0.718497 −0.0333914 −0.0166957 0.999861i \(-0.505315\pi\)
−0.0166957 + 0.999861i \(0.505315\pi\)
\(464\) 0.501652 0.0232886
\(465\) 15.7493 0.730356
\(466\) 20.9772 0.971748
\(467\) 1.47721 0.0683572 0.0341786 0.999416i \(-0.489119\pi\)
0.0341786 + 0.999416i \(0.489119\pi\)
\(468\) 2.17036 0.100325
\(469\) −4.95904 −0.228987
\(470\) 3.88170 0.179050
\(471\) 8.82930 0.406833
\(472\) 8.74441 0.402494
\(473\) 4.14867 0.190756
\(474\) 10.7957 0.495863
\(475\) 11.8632 0.544321
\(476\) −15.9408 −0.730647
\(477\) −30.7150 −1.40634
\(478\) −12.1770 −0.556962
\(479\) 28.7909 1.31549 0.657745 0.753240i \(-0.271510\pi\)
0.657745 + 0.753240i \(0.271510\pi\)
\(480\) −2.91388 −0.133000
\(481\) −6.78885 −0.309545
\(482\) 0.973327 0.0443338
\(483\) 4.20322 0.191253
\(484\) 6.92467 0.314758
\(485\) −77.5590 −3.52177
\(486\) 15.0764 0.683879
\(487\) −35.3461 −1.60169 −0.800843 0.598875i \(-0.795615\pi\)
−0.800843 + 0.598875i \(0.795615\pi\)
\(488\) 3.12405 0.141419
\(489\) −1.56701 −0.0708628
\(490\) −6.42708 −0.290346
\(491\) −1.60442 −0.0724064 −0.0362032 0.999344i \(-0.511526\pi\)
−0.0362032 + 0.999344i \(0.511526\pi\)
\(492\) 4.86109 0.219155
\(493\) −3.43193 −0.154566
\(494\) 0.879346 0.0395637
\(495\) 43.1901 1.94125
\(496\) 5.40493 0.242689
\(497\) −0.315034 −0.0141312
\(498\) −4.42087 −0.198104
\(499\) −1.55989 −0.0698301 −0.0349151 0.999390i \(-0.511116\pi\)
−0.0349151 + 0.999390i \(0.511116\pi\)
\(500\) −27.6020 −1.23440
\(501\) −8.90267 −0.397742
\(502\) 22.6555 1.01116
\(503\) −8.95983 −0.399499 −0.199749 0.979847i \(-0.564013\pi\)
−0.199749 + 0.979847i \(0.564013\pi\)
\(504\) 5.80883 0.258746
\(505\) −3.67293 −0.163443
\(506\) 10.7252 0.476795
\(507\) 8.71726 0.387147
\(508\) −2.79511 −0.124013
\(509\) −9.01585 −0.399621 −0.199810 0.979835i \(-0.564033\pi\)
−0.199810 + 0.979835i \(0.564033\pi\)
\(510\) 19.9345 0.882716
\(511\) −13.3257 −0.589496
\(512\) −1.00000 −0.0441942
\(513\) 3.95069 0.174427
\(514\) −1.66655 −0.0735086
\(515\) −8.16821 −0.359934
\(516\) −0.697765 −0.0307174
\(517\) 4.01608 0.176627
\(518\) −18.1699 −0.798341
\(519\) −9.33423 −0.409727
\(520\) −3.56257 −0.156229
\(521\) −29.7055 −1.30142 −0.650710 0.759326i \(-0.725529\pi\)
−0.650710 + 0.759326i \(0.725529\pi\)
\(522\) 1.25059 0.0547370
\(523\) 25.0384 1.09485 0.547426 0.836854i \(-0.315608\pi\)
0.547426 + 0.836854i \(0.315608\pi\)
\(524\) 7.27881 0.317976
\(525\) −19.4878 −0.850515
\(526\) 21.7022 0.946259
\(527\) −36.9765 −1.61072
\(528\) −3.01475 −0.131200
\(529\) −16.5826 −0.720981
\(530\) 50.4176 2.19000
\(531\) 21.7994 0.946012
\(532\) 2.35352 0.102038
\(533\) 5.94328 0.257432
\(534\) 2.30822 0.0998866
\(535\) −1.71170 −0.0740034
\(536\) 2.12825 0.0919263
\(537\) 5.56088 0.239970
\(538\) 21.5484 0.929018
\(539\) −6.64958 −0.286418
\(540\) −16.0058 −0.688779
\(541\) −28.7667 −1.23678 −0.618388 0.785873i \(-0.712214\pi\)
−0.618388 + 0.785873i \(0.712214\pi\)
\(542\) −4.49788 −0.193200
\(543\) 11.1250 0.477419
\(544\) 6.84125 0.293316
\(545\) 45.2249 1.93722
\(546\) −1.44451 −0.0618192
\(547\) 27.9399 1.19462 0.597312 0.802009i \(-0.296235\pi\)
0.597312 + 0.802009i \(0.296235\pi\)
\(548\) 0.158074 0.00675259
\(549\) 7.78810 0.332388
\(550\) −49.7263 −2.12034
\(551\) 0.506692 0.0215858
\(552\) −1.80388 −0.0767781
\(553\) 35.3265 1.50223
\(554\) 12.9141 0.548669
\(555\) 22.7221 0.964501
\(556\) −16.6942 −0.707990
\(557\) 2.60449 0.110356 0.0551778 0.998477i \(-0.482427\pi\)
0.0551778 + 0.998477i \(0.482427\pi\)
\(558\) 13.4742 0.570409
\(559\) −0.853103 −0.0360824
\(560\) −9.53500 −0.402927
\(561\) 20.6247 0.870773
\(562\) 3.82996 0.161557
\(563\) 6.06500 0.255609 0.127805 0.991799i \(-0.459207\pi\)
0.127805 + 0.991799i \(0.459207\pi\)
\(564\) −0.675465 −0.0284422
\(565\) −35.7335 −1.50332
\(566\) 11.6200 0.488423
\(567\) 10.9367 0.459297
\(568\) 0.135202 0.00567294
\(569\) 25.3277 1.06179 0.530896 0.847437i \(-0.321855\pi\)
0.530896 + 0.847437i \(0.321855\pi\)
\(570\) −2.94315 −0.123275
\(571\) 46.1410 1.93094 0.965471 0.260511i \(-0.0838911\pi\)
0.965471 + 0.260511i \(0.0838911\pi\)
\(572\) −3.68590 −0.154115
\(573\) 18.1960 0.760148
\(574\) 15.9068 0.663937
\(575\) −29.7537 −1.24082
\(576\) −2.49295 −0.103873
\(577\) 31.7310 1.32098 0.660489 0.750836i \(-0.270349\pi\)
0.660489 + 0.750836i \(0.270349\pi\)
\(578\) −29.8027 −1.23963
\(579\) 10.2013 0.423950
\(580\) −2.05281 −0.0852381
\(581\) −14.4663 −0.600164
\(582\) 13.4962 0.559437
\(583\) 52.1630 2.16037
\(584\) 5.71895 0.236652
\(585\) −8.88131 −0.367197
\(586\) 18.8463 0.778534
\(587\) −7.93999 −0.327718 −0.163859 0.986484i \(-0.552394\pi\)
−0.163859 + 0.986484i \(0.552394\pi\)
\(588\) 1.11839 0.0461217
\(589\) 5.45923 0.224944
\(590\) −35.7829 −1.47316
\(591\) −5.74905 −0.236484
\(592\) 7.79791 0.320492
\(593\) 16.7180 0.686524 0.343262 0.939240i \(-0.388468\pi\)
0.343262 + 0.939240i \(0.388468\pi\)
\(594\) −16.5599 −0.679460
\(595\) 65.2313 2.67422
\(596\) 11.6457 0.477028
\(597\) −6.73547 −0.275664
\(598\) −2.20546 −0.0901880
\(599\) −24.2998 −0.992862 −0.496431 0.868076i \(-0.665356\pi\)
−0.496431 + 0.868076i \(0.665356\pi\)
\(600\) 8.36347 0.341437
\(601\) 20.9753 0.855602 0.427801 0.903873i \(-0.359288\pi\)
0.427801 + 0.903873i \(0.359288\pi\)
\(602\) −2.28328 −0.0930595
\(603\) 5.30561 0.216061
\(604\) −22.1165 −0.899907
\(605\) −28.3364 −1.15204
\(606\) 0.639136 0.0259631
\(607\) 19.3213 0.784229 0.392115 0.919916i \(-0.371744\pi\)
0.392115 + 0.919916i \(0.371744\pi\)
\(608\) −1.01005 −0.0409628
\(609\) −0.832346 −0.0337284
\(610\) −12.7839 −0.517605
\(611\) −0.825839 −0.0334099
\(612\) 17.0549 0.689403
\(613\) −17.4799 −0.706007 −0.353003 0.935622i \(-0.614840\pi\)
−0.353003 + 0.935622i \(0.614840\pi\)
\(614\) −0.510129 −0.0205871
\(615\) −19.8920 −0.802123
\(616\) −9.86509 −0.397476
\(617\) −9.31507 −0.375011 −0.187505 0.982264i \(-0.560040\pi\)
−0.187505 + 0.982264i \(0.560040\pi\)
\(618\) 1.42137 0.0571759
\(619\) 29.7035 1.19388 0.596942 0.802284i \(-0.296382\pi\)
0.596942 + 0.802284i \(0.296382\pi\)
\(620\) −22.1175 −0.888259
\(621\) −9.90860 −0.397618
\(622\) 14.9458 0.599272
\(623\) 7.55314 0.302610
\(624\) 0.619932 0.0248171
\(625\) 54.2238 2.16895
\(626\) −7.64337 −0.305490
\(627\) −3.04504 −0.121607
\(628\) −12.3994 −0.494790
\(629\) −53.3474 −2.12710
\(630\) −23.7703 −0.947030
\(631\) 38.6855 1.54004 0.770022 0.638017i \(-0.220245\pi\)
0.770022 + 0.638017i \(0.220245\pi\)
\(632\) −15.1609 −0.603068
\(633\) 9.96724 0.396162
\(634\) −29.8745 −1.18647
\(635\) 11.4378 0.453897
\(636\) −8.77329 −0.347884
\(637\) 1.36737 0.0541773
\(638\) −2.12387 −0.0840849
\(639\) 0.337051 0.0133335
\(640\) 4.09209 0.161754
\(641\) −32.8284 −1.29665 −0.648323 0.761366i \(-0.724529\pi\)
−0.648323 + 0.761366i \(0.724529\pi\)
\(642\) 0.297858 0.0117555
\(643\) 3.14040 0.123845 0.0619227 0.998081i \(-0.480277\pi\)
0.0619227 + 0.998081i \(0.480277\pi\)
\(644\) −5.90278 −0.232602
\(645\) 2.85532 0.112428
\(646\) 6.90998 0.271870
\(647\) −30.3503 −1.19319 −0.596597 0.802541i \(-0.703481\pi\)
−0.596597 + 0.802541i \(0.703481\pi\)
\(648\) −4.69364 −0.184384
\(649\) −37.0217 −1.45323
\(650\) 10.2254 0.401072
\(651\) −8.96791 −0.351480
\(652\) 2.20063 0.0861833
\(653\) −19.0354 −0.744912 −0.372456 0.928050i \(-0.621484\pi\)
−0.372456 + 0.928050i \(0.621484\pi\)
\(654\) −7.86970 −0.307730
\(655\) −29.7856 −1.16382
\(656\) −6.82665 −0.266536
\(657\) 14.2570 0.556220
\(658\) −2.21031 −0.0861667
\(659\) 12.5844 0.490218 0.245109 0.969495i \(-0.421176\pi\)
0.245109 + 0.969495i \(0.421176\pi\)
\(660\) 12.3366 0.480203
\(661\) −15.8137 −0.615081 −0.307541 0.951535i \(-0.599506\pi\)
−0.307541 + 0.951535i \(0.599506\pi\)
\(662\) −18.3774 −0.714256
\(663\) −4.24111 −0.164711
\(664\) 6.20844 0.240934
\(665\) −9.63080 −0.373466
\(666\) 19.4398 0.753276
\(667\) −1.27082 −0.0492063
\(668\) 12.5024 0.483734
\(669\) 5.23607 0.202438
\(670\) −8.70899 −0.336457
\(671\) −13.2265 −0.510602
\(672\) 1.65921 0.0640054
\(673\) 50.3738 1.94177 0.970883 0.239553i \(-0.0770010\pi\)
0.970883 + 0.239553i \(0.0770010\pi\)
\(674\) −8.21174 −0.316304
\(675\) 45.9401 1.76824
\(676\) −12.2421 −0.470848
\(677\) 20.9677 0.805855 0.402927 0.915232i \(-0.367993\pi\)
0.402927 + 0.915232i \(0.367993\pi\)
\(678\) 6.21808 0.238804
\(679\) 44.1634 1.69484
\(680\) −27.9950 −1.07356
\(681\) 0.643803 0.0246706
\(682\) −22.8831 −0.876241
\(683\) −35.5051 −1.35857 −0.679283 0.733876i \(-0.737709\pi\)
−0.679283 + 0.733876i \(0.737709\pi\)
\(684\) −2.51800 −0.0962780
\(685\) −0.646854 −0.0247150
\(686\) 19.9704 0.762474
\(687\) 7.58166 0.289258
\(688\) 0.979903 0.0373585
\(689\) −10.7264 −0.408644
\(690\) 7.38163 0.281014
\(691\) 16.6656 0.633989 0.316995 0.948427i \(-0.397326\pi\)
0.316995 + 0.948427i \(0.397326\pi\)
\(692\) 13.1085 0.498310
\(693\) −24.5932 −0.934217
\(694\) −20.4850 −0.777601
\(695\) 68.3140 2.59130
\(696\) 0.357214 0.0135402
\(697\) 46.7028 1.76899
\(698\) 32.6783 1.23689
\(699\) 14.9373 0.564981
\(700\) 27.3676 1.03440
\(701\) 16.9774 0.641226 0.320613 0.947210i \(-0.396111\pi\)
0.320613 + 0.947210i \(0.396111\pi\)
\(702\) 3.40525 0.128523
\(703\) 7.87625 0.297058
\(704\) 4.23375 0.159566
\(705\) 2.76406 0.104101
\(706\) −14.5838 −0.548870
\(707\) 2.09143 0.0786563
\(708\) 6.22667 0.234013
\(709\) −35.1698 −1.32083 −0.660415 0.750901i \(-0.729619\pi\)
−0.660415 + 0.750901i \(0.729619\pi\)
\(710\) −0.553258 −0.0207634
\(711\) −37.7953 −1.41744
\(712\) −3.24155 −0.121482
\(713\) −13.6921 −0.512775
\(714\) −11.3511 −0.424803
\(715\) 15.0830 0.564074
\(716\) −7.80940 −0.291851
\(717\) −8.67091 −0.323821
\(718\) 13.0576 0.487307
\(719\) −22.2923 −0.831362 −0.415681 0.909510i \(-0.636457\pi\)
−0.415681 + 0.909510i \(0.636457\pi\)
\(720\) 10.2014 0.380183
\(721\) 4.65112 0.173217
\(722\) 17.9798 0.669139
\(723\) 0.693082 0.0257760
\(724\) −15.6233 −0.580636
\(725\) 5.89201 0.218824
\(726\) 4.93088 0.183002
\(727\) −27.3474 −1.01426 −0.507129 0.861870i \(-0.669293\pi\)
−0.507129 + 0.861870i \(0.669293\pi\)
\(728\) 2.02859 0.0751845
\(729\) −3.34540 −0.123904
\(730\) −23.4024 −0.866163
\(731\) −6.70376 −0.247948
\(732\) 2.22456 0.0822221
\(733\) 20.8307 0.769398 0.384699 0.923042i \(-0.374305\pi\)
0.384699 + 0.923042i \(0.374305\pi\)
\(734\) 2.70482 0.0998368
\(735\) −4.57656 −0.168809
\(736\) 2.53327 0.0933775
\(737\) −9.01048 −0.331905
\(738\) −17.0185 −0.626459
\(739\) −44.5756 −1.63974 −0.819870 0.572550i \(-0.805954\pi\)
−0.819870 + 0.572550i \(0.805954\pi\)
\(740\) −31.9097 −1.17303
\(741\) 0.626160 0.0230026
\(742\) −28.7086 −1.05393
\(743\) −25.3011 −0.928208 −0.464104 0.885781i \(-0.653624\pi\)
−0.464104 + 0.885781i \(0.653624\pi\)
\(744\) 3.84872 0.141101
\(745\) −47.6554 −1.74596
\(746\) 11.4842 0.420467
\(747\) 15.4773 0.566286
\(748\) −28.9642 −1.05903
\(749\) 0.974673 0.0356138
\(750\) −19.6547 −0.717688
\(751\) 34.0226 1.24150 0.620751 0.784008i \(-0.286828\pi\)
0.620751 + 0.784008i \(0.286828\pi\)
\(752\) 0.948587 0.0345914
\(753\) 16.1324 0.587897
\(754\) 0.436738 0.0159051
\(755\) 90.5027 3.29373
\(756\) 9.11395 0.331471
\(757\) −30.7475 −1.11754 −0.558768 0.829324i \(-0.688726\pi\)
−0.558768 + 0.829324i \(0.688726\pi\)
\(758\) 4.40530 0.160008
\(759\) 7.63717 0.277212
\(760\) 4.13320 0.149927
\(761\) −1.63233 −0.0591720 −0.0295860 0.999562i \(-0.509419\pi\)
−0.0295860 + 0.999562i \(0.509419\pi\)
\(762\) −1.99033 −0.0721019
\(763\) −25.7518 −0.932279
\(764\) −25.5535 −0.924492
\(765\) −69.7901 −2.52327
\(766\) 19.4014 0.701002
\(767\) 7.61287 0.274885
\(768\) −0.712075 −0.0256948
\(769\) 35.8161 1.29156 0.645781 0.763523i \(-0.276532\pi\)
0.645781 + 0.763523i \(0.276532\pi\)
\(770\) 40.3688 1.45479
\(771\) −1.18671 −0.0427384
\(772\) −14.3261 −0.515608
\(773\) −38.5684 −1.38721 −0.693604 0.720357i \(-0.743978\pi\)
−0.693604 + 0.720357i \(0.743978\pi\)
\(774\) 2.44285 0.0878064
\(775\) 63.4820 2.28034
\(776\) −18.9534 −0.680387
\(777\) −12.9384 −0.464161
\(778\) 21.2228 0.760875
\(779\) −6.89524 −0.247047
\(780\) −2.53682 −0.0908327
\(781\) −0.572411 −0.0204825
\(782\) −17.3307 −0.619745
\(783\) 1.96216 0.0701218
\(784\) −1.57061 −0.0560932
\(785\) 50.7395 1.81097
\(786\) 5.18306 0.184874
\(787\) −5.94577 −0.211944 −0.105972 0.994369i \(-0.533795\pi\)
−0.105972 + 0.994369i \(0.533795\pi\)
\(788\) 8.07366 0.287612
\(789\) 15.4536 0.550161
\(790\) 62.0398 2.20728
\(791\) 20.3473 0.723465
\(792\) 10.5545 0.375039
\(793\) 2.71980 0.0965828
\(794\) 8.02549 0.284814
\(795\) 35.9011 1.27328
\(796\) 9.45893 0.335263
\(797\) 50.6289 1.79337 0.896684 0.442672i \(-0.145969\pi\)
0.896684 + 0.442672i \(0.145969\pi\)
\(798\) 1.67588 0.0593255
\(799\) −6.48952 −0.229583
\(800\) −11.7452 −0.415256
\(801\) −8.08101 −0.285528
\(802\) −19.9104 −0.703062
\(803\) −24.2126 −0.854444
\(804\) 1.51547 0.0534466
\(805\) 24.1547 0.851342
\(806\) 4.70553 0.165745
\(807\) 15.3441 0.540137
\(808\) −0.897568 −0.0315763
\(809\) −19.7695 −0.695058 −0.347529 0.937669i \(-0.612979\pi\)
−0.347529 + 0.937669i \(0.612979\pi\)
\(810\) 19.2068 0.674859
\(811\) 45.8141 1.60875 0.804376 0.594120i \(-0.202500\pi\)
0.804376 + 0.594120i \(0.202500\pi\)
\(812\) 1.16890 0.0410204
\(813\) −3.20283 −0.112328
\(814\) −33.0144 −1.15715
\(815\) −9.00518 −0.315438
\(816\) 4.87148 0.170536
\(817\) 0.989749 0.0346269
\(818\) −33.2530 −1.16266
\(819\) 5.05717 0.176712
\(820\) 27.9353 0.975542
\(821\) 7.56824 0.264133 0.132067 0.991241i \(-0.457839\pi\)
0.132067 + 0.991241i \(0.457839\pi\)
\(822\) 0.112561 0.00392600
\(823\) 41.6560 1.45204 0.726018 0.687676i \(-0.241369\pi\)
0.726018 + 0.687676i \(0.241369\pi\)
\(824\) −1.99610 −0.0695373
\(825\) −35.4089 −1.23278
\(826\) 20.3754 0.708950
\(827\) −54.2004 −1.88473 −0.942366 0.334582i \(-0.891405\pi\)
−0.942366 + 0.334582i \(0.891405\pi\)
\(828\) 6.31531 0.219472
\(829\) −8.66757 −0.301037 −0.150519 0.988607i \(-0.548094\pi\)
−0.150519 + 0.988607i \(0.548094\pi\)
\(830\) −25.4055 −0.881838
\(831\) 9.19583 0.319000
\(832\) −0.870599 −0.0301826
\(833\) 10.7449 0.372290
\(834\) −11.8875 −0.411630
\(835\) −51.1611 −1.77050
\(836\) 4.27629 0.147899
\(837\) 21.1408 0.730733
\(838\) 33.4842 1.15669
\(839\) 43.6592 1.50728 0.753642 0.657285i \(-0.228295\pi\)
0.753642 + 0.657285i \(0.228295\pi\)
\(840\) −6.78964 −0.234265
\(841\) −28.7483 −0.991322
\(842\) −26.8544 −0.925464
\(843\) 2.72722 0.0939303
\(844\) −13.9975 −0.481812
\(845\) 50.0956 1.72334
\(846\) 2.36478 0.0813027
\(847\) 16.1352 0.554412
\(848\) 12.3207 0.423096
\(849\) 8.27428 0.283973
\(850\) 80.3519 2.75605
\(851\) −19.7542 −0.677165
\(852\) 0.0962739 0.00329829
\(853\) −45.6881 −1.56433 −0.782166 0.623070i \(-0.785885\pi\)
−0.782166 + 0.623070i \(0.785885\pi\)
\(854\) 7.27937 0.249095
\(855\) 10.3039 0.352385
\(856\) −0.418296 −0.0142971
\(857\) 12.5219 0.427740 0.213870 0.976862i \(-0.431393\pi\)
0.213870 + 0.976862i \(0.431393\pi\)
\(858\) −2.62464 −0.0896037
\(859\) −49.8697 −1.70153 −0.850766 0.525544i \(-0.823862\pi\)
−0.850766 + 0.525544i \(0.823862\pi\)
\(860\) −4.00985 −0.136735
\(861\) 11.3268 0.386018
\(862\) −19.1591 −0.652562
\(863\) −18.7104 −0.636909 −0.318455 0.947938i \(-0.603164\pi\)
−0.318455 + 0.947938i \(0.603164\pi\)
\(864\) −3.91139 −0.133068
\(865\) −53.6411 −1.82385
\(866\) 36.0575 1.22529
\(867\) −21.2217 −0.720728
\(868\) 12.5941 0.427470
\(869\) 64.1875 2.17741
\(870\) −1.46175 −0.0495580
\(871\) 1.85285 0.0627815
\(872\) 11.0518 0.374261
\(873\) −47.2499 −1.59917
\(874\) 2.55872 0.0865500
\(875\) −64.3156 −2.17426
\(876\) 4.07232 0.137591
\(877\) 52.2040 1.76280 0.881402 0.472366i \(-0.156600\pi\)
0.881402 + 0.472366i \(0.156600\pi\)
\(878\) 12.0904 0.408031
\(879\) 13.4200 0.452645
\(880\) −17.3249 −0.584022
\(881\) −15.6956 −0.528799 −0.264400 0.964413i \(-0.585174\pi\)
−0.264400 + 0.964413i \(0.585174\pi\)
\(882\) −3.91545 −0.131840
\(883\) −15.0775 −0.507399 −0.253700 0.967283i \(-0.581647\pi\)
−0.253700 + 0.967283i \(0.581647\pi\)
\(884\) 5.95599 0.200321
\(885\) −25.4801 −0.856504
\(886\) 10.2782 0.345303
\(887\) 43.1336 1.44829 0.724143 0.689650i \(-0.242236\pi\)
0.724143 + 0.689650i \(0.242236\pi\)
\(888\) 5.55269 0.186336
\(889\) −6.51290 −0.218436
\(890\) 13.2647 0.444634
\(891\) 19.8717 0.665728
\(892\) −7.35326 −0.246205
\(893\) 0.958117 0.0320622
\(894\) 8.29263 0.277347
\(895\) 31.9568 1.06820
\(896\) −2.33011 −0.0778433
\(897\) −1.57045 −0.0524359
\(898\) −3.17411 −0.105921
\(899\) 2.71140 0.0904301
\(900\) −29.2802 −0.976007
\(901\) −84.2893 −2.80808
\(902\) 28.9024 0.962343
\(903\) −1.62587 −0.0541054
\(904\) −8.73234 −0.290433
\(905\) 63.9321 2.12517
\(906\) −15.7486 −0.523212
\(907\) 29.9261 0.993678 0.496839 0.867843i \(-0.334494\pi\)
0.496839 + 0.867843i \(0.334494\pi\)
\(908\) −0.904122 −0.0300043
\(909\) −2.23759 −0.0742163
\(910\) −8.30117 −0.275181
\(911\) −16.1721 −0.535806 −0.267903 0.963446i \(-0.586331\pi\)
−0.267903 + 0.963446i \(0.586331\pi\)
\(912\) −0.719229 −0.0238161
\(913\) −26.2850 −0.869907
\(914\) −28.7951 −0.952457
\(915\) −9.10310 −0.300939
\(916\) −10.6473 −0.351796
\(917\) 16.9604 0.560082
\(918\) 26.7588 0.883172
\(919\) 5.63291 0.185812 0.0929062 0.995675i \(-0.470384\pi\)
0.0929062 + 0.995675i \(0.470384\pi\)
\(920\) −10.3664 −0.341769
\(921\) −0.363250 −0.0119695
\(922\) 35.9244 1.18311
\(923\) 0.117707 0.00387436
\(924\) −7.02468 −0.231095
\(925\) 91.5880 3.01140
\(926\) 0.718497 0.0236113
\(927\) −4.97617 −0.163439
\(928\) −0.501652 −0.0164675
\(929\) −3.76229 −0.123437 −0.0617184 0.998094i \(-0.519658\pi\)
−0.0617184 + 0.998094i \(0.519658\pi\)
\(930\) −15.7493 −0.516440
\(931\) −1.58639 −0.0519918
\(932\) −20.9772 −0.687130
\(933\) 10.6425 0.348421
\(934\) −1.47721 −0.0483358
\(935\) 118.524 3.87615
\(936\) −2.17036 −0.0709404
\(937\) 15.2741 0.498983 0.249491 0.968377i \(-0.419737\pi\)
0.249491 + 0.968377i \(0.419737\pi\)
\(938\) 4.95904 0.161918
\(939\) −5.44265 −0.177614
\(940\) −3.88170 −0.126607
\(941\) 6.98732 0.227780 0.113890 0.993493i \(-0.463669\pi\)
0.113890 + 0.993493i \(0.463669\pi\)
\(942\) −8.82930 −0.287674
\(943\) 17.2937 0.563161
\(944\) −8.74441 −0.284606
\(945\) −37.2951 −1.21321
\(946\) −4.14867 −0.134885
\(947\) −45.3630 −1.47410 −0.737049 0.675839i \(-0.763781\pi\)
−0.737049 + 0.675839i \(0.763781\pi\)
\(948\) −10.7957 −0.350628
\(949\) 4.97891 0.161622
\(950\) −11.8632 −0.384893
\(951\) −21.2729 −0.689820
\(952\) 15.9408 0.516645
\(953\) 45.1998 1.46417 0.732083 0.681215i \(-0.238548\pi\)
0.732083 + 0.681215i \(0.238548\pi\)
\(954\) 30.7150 0.994434
\(955\) 104.567 3.38371
\(956\) 12.1770 0.393831
\(957\) −1.51236 −0.0488875
\(958\) −28.7909 −0.930192
\(959\) 0.368329 0.0118940
\(960\) 2.91388 0.0940449
\(961\) −1.78671 −0.0576358
\(962\) 6.78885 0.218881
\(963\) −1.04279 −0.0336034
\(964\) −0.973327 −0.0313488
\(965\) 58.6237 1.88716
\(966\) −4.20322 −0.135236
\(967\) −28.0220 −0.901126 −0.450563 0.892745i \(-0.648777\pi\)
−0.450563 + 0.892745i \(0.648777\pi\)
\(968\) −6.92467 −0.222567
\(969\) 4.92042 0.158067
\(970\) 77.5590 2.49027
\(971\) 36.0791 1.15783 0.578917 0.815386i \(-0.303475\pi\)
0.578917 + 0.815386i \(0.303475\pi\)
\(972\) −15.0764 −0.483576
\(973\) −38.8991 −1.24705
\(974\) 35.3461 1.13256
\(975\) 7.28123 0.233186
\(976\) −3.12405 −0.0999985
\(977\) 56.6369 1.81197 0.905987 0.423306i \(-0.139130\pi\)
0.905987 + 0.423306i \(0.139130\pi\)
\(978\) 1.56701 0.0501076
\(979\) 13.7239 0.438618
\(980\) 6.42708 0.205306
\(981\) 27.5515 0.879653
\(982\) 1.60442 0.0511990
\(983\) 28.1008 0.896275 0.448137 0.893965i \(-0.352088\pi\)
0.448137 + 0.893965i \(0.352088\pi\)
\(984\) −4.86109 −0.154966
\(985\) −33.0382 −1.05268
\(986\) 3.43193 0.109295
\(987\) −1.57390 −0.0500979
\(988\) −0.879346 −0.0279757
\(989\) −2.48236 −0.0789344
\(990\) −43.1901 −1.37267
\(991\) −37.2309 −1.18268 −0.591339 0.806423i \(-0.701401\pi\)
−0.591339 + 0.806423i \(0.701401\pi\)
\(992\) −5.40493 −0.171607
\(993\) −13.0861 −0.415273
\(994\) 0.315034 0.00999229
\(995\) −38.7068 −1.22709
\(996\) 4.42087 0.140081
\(997\) −10.8662 −0.344137 −0.172069 0.985085i \(-0.555045\pi\)
−0.172069 + 0.985085i \(0.555045\pi\)
\(998\) 1.55989 0.0493774
\(999\) 30.5007 0.964998
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.1.18 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.18 40 1.1 even 1 trivial