Properties

Label 4034.2.a.d.1.6
Level 4034
Weight 2
Character 4034.1
Self dual yes
Analytic conductor 32.212
Analytic rank 0
Dimension 52
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(52\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.58772 q^{3} +1.00000 q^{4} -1.78395 q^{5} -2.58772 q^{6} -0.188589 q^{7} +1.00000 q^{8} +3.69628 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.58772 q^{3} +1.00000 q^{4} -1.78395 q^{5} -2.58772 q^{6} -0.188589 q^{7} +1.00000 q^{8} +3.69628 q^{9} -1.78395 q^{10} -4.86180 q^{11} -2.58772 q^{12} +5.13586 q^{13} -0.188589 q^{14} +4.61637 q^{15} +1.00000 q^{16} -4.65888 q^{17} +3.69628 q^{18} -2.98794 q^{19} -1.78395 q^{20} +0.488016 q^{21} -4.86180 q^{22} -1.55744 q^{23} -2.58772 q^{24} -1.81751 q^{25} +5.13586 q^{26} -1.80179 q^{27} -0.188589 q^{28} -4.32676 q^{29} +4.61637 q^{30} +0.532625 q^{31} +1.00000 q^{32} +12.5810 q^{33} -4.65888 q^{34} +0.336434 q^{35} +3.69628 q^{36} +9.81373 q^{37} -2.98794 q^{38} -13.2902 q^{39} -1.78395 q^{40} +9.33695 q^{41} +0.488016 q^{42} -0.538781 q^{43} -4.86180 q^{44} -6.59400 q^{45} -1.55744 q^{46} -9.10544 q^{47} -2.58772 q^{48} -6.96443 q^{49} -1.81751 q^{50} +12.0559 q^{51} +5.13586 q^{52} -4.35604 q^{53} -1.80179 q^{54} +8.67322 q^{55} -0.188589 q^{56} +7.73195 q^{57} -4.32676 q^{58} -9.08011 q^{59} +4.61637 q^{60} -3.15788 q^{61} +0.532625 q^{62} -0.697079 q^{63} +1.00000 q^{64} -9.16214 q^{65} +12.5810 q^{66} +6.33901 q^{67} -4.65888 q^{68} +4.03020 q^{69} +0.336434 q^{70} +3.02151 q^{71} +3.69628 q^{72} -0.972022 q^{73} +9.81373 q^{74} +4.70320 q^{75} -2.98794 q^{76} +0.916883 q^{77} -13.2902 q^{78} +7.94337 q^{79} -1.78395 q^{80} -6.42633 q^{81} +9.33695 q^{82} +3.66356 q^{83} +0.488016 q^{84} +8.31123 q^{85} -0.538781 q^{86} +11.1964 q^{87} -4.86180 q^{88} +1.04812 q^{89} -6.59400 q^{90} -0.968568 q^{91} -1.55744 q^{92} -1.37828 q^{93} -9.10544 q^{94} +5.33035 q^{95} -2.58772 q^{96} +9.63424 q^{97} -6.96443 q^{98} -17.9706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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
\(3\) −2.58772 −1.49402 −0.747010 0.664813i \(-0.768511\pi\)
−0.747010 + 0.664813i \(0.768511\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.78395 −0.797808 −0.398904 0.916993i \(-0.630609\pi\)
−0.398904 + 0.916993i \(0.630609\pi\)
\(6\) −2.58772 −1.05643
\(7\) −0.188589 −0.0712800 −0.0356400 0.999365i \(-0.511347\pi\)
−0.0356400 + 0.999365i \(0.511347\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.69628 1.23209
\(10\) −1.78395 −0.564136
\(11\) −4.86180 −1.46589 −0.732944 0.680289i \(-0.761854\pi\)
−0.732944 + 0.680289i \(0.761854\pi\)
\(12\) −2.58772 −0.747010
\(13\) 5.13586 1.42443 0.712216 0.701960i \(-0.247692\pi\)
0.712216 + 0.701960i \(0.247692\pi\)
\(14\) −0.188589 −0.0504026
\(15\) 4.61637 1.19194
\(16\) 1.00000 0.250000
\(17\) −4.65888 −1.12994 −0.564972 0.825110i \(-0.691113\pi\)
−0.564972 + 0.825110i \(0.691113\pi\)
\(18\) 3.69628 0.871223
\(19\) −2.98794 −0.685481 −0.342740 0.939430i \(-0.611355\pi\)
−0.342740 + 0.939430i \(0.611355\pi\)
\(20\) −1.78395 −0.398904
\(21\) 0.488016 0.106494
\(22\) −4.86180 −1.03654
\(23\) −1.55744 −0.324748 −0.162374 0.986729i \(-0.551915\pi\)
−0.162374 + 0.986729i \(0.551915\pi\)
\(24\) −2.58772 −0.528216
\(25\) −1.81751 −0.363502
\(26\) 5.13586 1.00723
\(27\) −1.80179 −0.346754
\(28\) −0.188589 −0.0356400
\(29\) −4.32676 −0.803459 −0.401730 0.915758i \(-0.631591\pi\)
−0.401730 + 0.915758i \(0.631591\pi\)
\(30\) 4.61637 0.842830
\(31\) 0.532625 0.0956623 0.0478312 0.998855i \(-0.484769\pi\)
0.0478312 + 0.998855i \(0.484769\pi\)
\(32\) 1.00000 0.176777
\(33\) 12.5810 2.19006
\(34\) −4.65888 −0.798992
\(35\) 0.336434 0.0568678
\(36\) 3.69628 0.616047
\(37\) 9.81373 1.61337 0.806684 0.590984i \(-0.201260\pi\)
0.806684 + 0.590984i \(0.201260\pi\)
\(38\) −2.98794 −0.484708
\(39\) −13.2902 −2.12813
\(40\) −1.78395 −0.282068
\(41\) 9.33695 1.45819 0.729093 0.684414i \(-0.239942\pi\)
0.729093 + 0.684414i \(0.239942\pi\)
\(42\) 0.488016 0.0753025
\(43\) −0.538781 −0.0821633 −0.0410817 0.999156i \(-0.513080\pi\)
−0.0410817 + 0.999156i \(0.513080\pi\)
\(44\) −4.86180 −0.732944
\(45\) −6.59400 −0.982976
\(46\) −1.55744 −0.229631
\(47\) −9.10544 −1.32817 −0.664083 0.747659i \(-0.731178\pi\)
−0.664083 + 0.747659i \(0.731178\pi\)
\(48\) −2.58772 −0.373505
\(49\) −6.96443 −0.994919
\(50\) −1.81751 −0.257035
\(51\) 12.0559 1.68816
\(52\) 5.13586 0.712216
\(53\) −4.35604 −0.598348 −0.299174 0.954199i \(-0.596711\pi\)
−0.299174 + 0.954199i \(0.596711\pi\)
\(54\) −1.80179 −0.245192
\(55\) 8.67322 1.16950
\(56\) −0.188589 −0.0252013
\(57\) 7.73195 1.02412
\(58\) −4.32676 −0.568132
\(59\) −9.08011 −1.18213 −0.591065 0.806624i \(-0.701292\pi\)
−0.591065 + 0.806624i \(0.701292\pi\)
\(60\) 4.61637 0.595971
\(61\) −3.15788 −0.404325 −0.202162 0.979352i \(-0.564797\pi\)
−0.202162 + 0.979352i \(0.564797\pi\)
\(62\) 0.532625 0.0676435
\(63\) −0.697079 −0.0878237
\(64\) 1.00000 0.125000
\(65\) −9.16214 −1.13642
\(66\) 12.5810 1.54861
\(67\) 6.33901 0.774433 0.387217 0.921989i \(-0.373437\pi\)
0.387217 + 0.921989i \(0.373437\pi\)
\(68\) −4.65888 −0.564972
\(69\) 4.03020 0.485179
\(70\) 0.336434 0.0402116
\(71\) 3.02151 0.358588 0.179294 0.983796i \(-0.442619\pi\)
0.179294 + 0.983796i \(0.442619\pi\)
\(72\) 3.69628 0.435611
\(73\) −0.972022 −0.113767 −0.0568833 0.998381i \(-0.518116\pi\)
−0.0568833 + 0.998381i \(0.518116\pi\)
\(74\) 9.81373 1.14082
\(75\) 4.70320 0.543079
\(76\) −2.98794 −0.342740
\(77\) 0.916883 0.104488
\(78\) −13.2902 −1.50481
\(79\) 7.94337 0.893699 0.446850 0.894609i \(-0.352546\pi\)
0.446850 + 0.894609i \(0.352546\pi\)
\(80\) −1.78395 −0.199452
\(81\) −6.42633 −0.714037
\(82\) 9.33695 1.03109
\(83\) 3.66356 0.402127 0.201064 0.979578i \(-0.435560\pi\)
0.201064 + 0.979578i \(0.435560\pi\)
\(84\) 0.488016 0.0532469
\(85\) 8.31123 0.901479
\(86\) −0.538781 −0.0580982
\(87\) 11.1964 1.20038
\(88\) −4.86180 −0.518269
\(89\) 1.04812 0.111100 0.0555501 0.998456i \(-0.482309\pi\)
0.0555501 + 0.998456i \(0.482309\pi\)
\(90\) −6.59400 −0.695069
\(91\) −0.968568 −0.101534
\(92\) −1.55744 −0.162374
\(93\) −1.37828 −0.142921
\(94\) −9.10544 −0.939155
\(95\) 5.33035 0.546882
\(96\) −2.58772 −0.264108
\(97\) 9.63424 0.978209 0.489104 0.872225i \(-0.337324\pi\)
0.489104 + 0.872225i \(0.337324\pi\)
\(98\) −6.96443 −0.703514
\(99\) −17.9706 −1.80611
\(100\) −1.81751 −0.181751
\(101\) 13.1079 1.30429 0.652145 0.758094i \(-0.273869\pi\)
0.652145 + 0.758094i \(0.273869\pi\)
\(102\) 12.0559 1.19371
\(103\) 6.04571 0.595701 0.297851 0.954612i \(-0.403730\pi\)
0.297851 + 0.954612i \(0.403730\pi\)
\(104\) 5.13586 0.503613
\(105\) −0.870597 −0.0849616
\(106\) −4.35604 −0.423096
\(107\) −11.8997 −1.15039 −0.575194 0.818017i \(-0.695074\pi\)
−0.575194 + 0.818017i \(0.695074\pi\)
\(108\) −1.80179 −0.173377
\(109\) 11.9472 1.14433 0.572165 0.820138i \(-0.306104\pi\)
0.572165 + 0.820138i \(0.306104\pi\)
\(110\) 8.67322 0.826959
\(111\) −25.3952 −2.41040
\(112\) −0.188589 −0.0178200
\(113\) −1.70874 −0.160745 −0.0803726 0.996765i \(-0.525611\pi\)
−0.0803726 + 0.996765i \(0.525611\pi\)
\(114\) 7.73195 0.724163
\(115\) 2.77839 0.259086
\(116\) −4.32676 −0.401730
\(117\) 18.9836 1.75504
\(118\) −9.08011 −0.835892
\(119\) 0.878615 0.0805425
\(120\) 4.61637 0.421415
\(121\) 12.6371 1.14883
\(122\) −3.15788 −0.285901
\(123\) −24.1614 −2.17856
\(124\) 0.532625 0.0478312
\(125\) 12.1621 1.08781
\(126\) −0.697079 −0.0621008
\(127\) −17.9684 −1.59444 −0.797220 0.603689i \(-0.793697\pi\)
−0.797220 + 0.603689i \(0.793697\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.39421 0.122754
\(130\) −9.16214 −0.803573
\(131\) 12.7471 1.11372 0.556860 0.830607i \(-0.312006\pi\)
0.556860 + 0.830607i \(0.312006\pi\)
\(132\) 12.5810 1.09503
\(133\) 0.563493 0.0488611
\(134\) 6.33901 0.547607
\(135\) 3.21431 0.276643
\(136\) −4.65888 −0.399496
\(137\) 1.53024 0.130737 0.0653686 0.997861i \(-0.479178\pi\)
0.0653686 + 0.997861i \(0.479178\pi\)
\(138\) 4.03020 0.343074
\(139\) −13.2088 −1.12035 −0.560177 0.828373i \(-0.689267\pi\)
−0.560177 + 0.828373i \(0.689267\pi\)
\(140\) 0.336434 0.0284339
\(141\) 23.5623 1.98430
\(142\) 3.02151 0.253560
\(143\) −24.9695 −2.08806
\(144\) 3.69628 0.308024
\(145\) 7.71874 0.641007
\(146\) −0.972022 −0.0804451
\(147\) 18.0220 1.48643
\(148\) 9.81373 0.806684
\(149\) 4.94589 0.405183 0.202591 0.979263i \(-0.435064\pi\)
0.202591 + 0.979263i \(0.435064\pi\)
\(150\) 4.70320 0.384015
\(151\) 6.32400 0.514640 0.257320 0.966326i \(-0.417161\pi\)
0.257320 + 0.966326i \(0.417161\pi\)
\(152\) −2.98794 −0.242354
\(153\) −17.2206 −1.39220
\(154\) 0.916883 0.0738845
\(155\) −0.950179 −0.0763202
\(156\) −13.2902 −1.06406
\(157\) 8.30268 0.662626 0.331313 0.943521i \(-0.392508\pi\)
0.331313 + 0.943521i \(0.392508\pi\)
\(158\) 7.94337 0.631941
\(159\) 11.2722 0.893943
\(160\) −1.78395 −0.141034
\(161\) 0.293715 0.0231480
\(162\) −6.42633 −0.504900
\(163\) 21.5519 1.68808 0.844039 0.536282i \(-0.180171\pi\)
0.844039 + 0.536282i \(0.180171\pi\)
\(164\) 9.33695 0.729093
\(165\) −22.4439 −1.74725
\(166\) 3.66356 0.284347
\(167\) 19.9134 1.54094 0.770472 0.637474i \(-0.220021\pi\)
0.770472 + 0.637474i \(0.220021\pi\)
\(168\) 0.488016 0.0376512
\(169\) 13.3771 1.02901
\(170\) 8.31123 0.637442
\(171\) −11.0443 −0.844577
\(172\) −0.538781 −0.0410817
\(173\) 24.7307 1.88024 0.940119 0.340848i \(-0.110714\pi\)
0.940119 + 0.340848i \(0.110714\pi\)
\(174\) 11.1964 0.848800
\(175\) 0.342763 0.0259104
\(176\) −4.86180 −0.366472
\(177\) 23.4968 1.76613
\(178\) 1.04812 0.0785597
\(179\) 9.85095 0.736295 0.368147 0.929767i \(-0.379992\pi\)
0.368147 + 0.929767i \(0.379992\pi\)
\(180\) −6.59400 −0.491488
\(181\) 12.5456 0.932508 0.466254 0.884651i \(-0.345603\pi\)
0.466254 + 0.884651i \(0.345603\pi\)
\(182\) −0.968568 −0.0717951
\(183\) 8.17170 0.604069
\(184\) −1.55744 −0.114816
\(185\) −17.5072 −1.28716
\(186\) −1.37828 −0.101061
\(187\) 22.6505 1.65637
\(188\) −9.10544 −0.664083
\(189\) 0.339798 0.0247167
\(190\) 5.33035 0.386704
\(191\) −15.3966 −1.11406 −0.557030 0.830492i \(-0.688059\pi\)
−0.557030 + 0.830492i \(0.688059\pi\)
\(192\) −2.58772 −0.186752
\(193\) 16.3836 1.17932 0.589659 0.807652i \(-0.299262\pi\)
0.589659 + 0.807652i \(0.299262\pi\)
\(194\) 9.63424 0.691698
\(195\) 23.7090 1.69784
\(196\) −6.96443 −0.497460
\(197\) 18.7570 1.33638 0.668191 0.743990i \(-0.267069\pi\)
0.668191 + 0.743990i \(0.267069\pi\)
\(198\) −17.9706 −1.27711
\(199\) −2.48325 −0.176033 −0.0880163 0.996119i \(-0.528053\pi\)
−0.0880163 + 0.996119i \(0.528053\pi\)
\(200\) −1.81751 −0.128517
\(201\) −16.4036 −1.15702
\(202\) 13.1079 0.922272
\(203\) 0.815980 0.0572706
\(204\) 12.0559 0.844080
\(205\) −16.6567 −1.16335
\(206\) 6.04571 0.421224
\(207\) −5.75672 −0.400120
\(208\) 5.13586 0.356108
\(209\) 14.5268 1.00484
\(210\) −0.870597 −0.0600769
\(211\) 1.99921 0.137632 0.0688158 0.997629i \(-0.478078\pi\)
0.0688158 + 0.997629i \(0.478078\pi\)
\(212\) −4.35604 −0.299174
\(213\) −7.81883 −0.535737
\(214\) −11.8997 −0.813448
\(215\) 0.961160 0.0655506
\(216\) −1.80179 −0.122596
\(217\) −0.100447 −0.00681881
\(218\) 11.9472 0.809164
\(219\) 2.51532 0.169969
\(220\) 8.67322 0.584749
\(221\) −23.9274 −1.60953
\(222\) −25.3952 −1.70441
\(223\) 14.3800 0.962955 0.481478 0.876458i \(-0.340100\pi\)
0.481478 + 0.876458i \(0.340100\pi\)
\(224\) −0.188589 −0.0126006
\(225\) −6.71803 −0.447869
\(226\) −1.70874 −0.113664
\(227\) 21.3775 1.41888 0.709438 0.704768i \(-0.248949\pi\)
0.709438 + 0.704768i \(0.248949\pi\)
\(228\) 7.73195 0.512061
\(229\) 20.4269 1.34985 0.674924 0.737887i \(-0.264177\pi\)
0.674924 + 0.737887i \(0.264177\pi\)
\(230\) 2.77839 0.183202
\(231\) −2.37263 −0.156108
\(232\) −4.32676 −0.284066
\(233\) −21.3711 −1.40007 −0.700033 0.714110i \(-0.746831\pi\)
−0.700033 + 0.714110i \(0.746831\pi\)
\(234\) 18.9836 1.24100
\(235\) 16.2437 1.05962
\(236\) −9.08011 −0.591065
\(237\) −20.5552 −1.33520
\(238\) 0.878615 0.0569521
\(239\) 9.90077 0.640428 0.320214 0.947345i \(-0.396245\pi\)
0.320214 + 0.947345i \(0.396245\pi\)
\(240\) 4.61637 0.297985
\(241\) −15.2985 −0.985461 −0.492731 0.870182i \(-0.664001\pi\)
−0.492731 + 0.870182i \(0.664001\pi\)
\(242\) 12.6371 0.812342
\(243\) 22.0349 1.41354
\(244\) −3.15788 −0.202162
\(245\) 12.4242 0.793755
\(246\) −24.1614 −1.54047
\(247\) −15.3457 −0.976421
\(248\) 0.532625 0.0338217
\(249\) −9.48025 −0.600786
\(250\) 12.1621 0.769200
\(251\) 0.687735 0.0434095 0.0217047 0.999764i \(-0.493091\pi\)
0.0217047 + 0.999764i \(0.493091\pi\)
\(252\) −0.697079 −0.0439119
\(253\) 7.57194 0.476044
\(254\) −17.9684 −1.12744
\(255\) −21.5071 −1.34683
\(256\) 1.00000 0.0625000
\(257\) −10.9865 −0.685320 −0.342660 0.939460i \(-0.611328\pi\)
−0.342660 + 0.939460i \(0.611328\pi\)
\(258\) 1.39421 0.0867999
\(259\) −1.85076 −0.115001
\(260\) −9.16214 −0.568212
\(261\) −15.9929 −0.989938
\(262\) 12.7471 0.787518
\(263\) −23.6982 −1.46129 −0.730647 0.682755i \(-0.760782\pi\)
−0.730647 + 0.682755i \(0.760782\pi\)
\(264\) 12.5810 0.774305
\(265\) 7.77097 0.477367
\(266\) 0.563493 0.0345500
\(267\) −2.71223 −0.165986
\(268\) 6.33901 0.387217
\(269\) −19.9262 −1.21492 −0.607462 0.794349i \(-0.707812\pi\)
−0.607462 + 0.794349i \(0.707812\pi\)
\(270\) 3.21431 0.195616
\(271\) 17.5399 1.06548 0.532738 0.846280i \(-0.321163\pi\)
0.532738 + 0.846280i \(0.321163\pi\)
\(272\) −4.65888 −0.282486
\(273\) 2.50638 0.151693
\(274\) 1.53024 0.0924452
\(275\) 8.83636 0.532853
\(276\) 4.03020 0.242590
\(277\) −5.49191 −0.329977 −0.164988 0.986296i \(-0.552759\pi\)
−0.164988 + 0.986296i \(0.552759\pi\)
\(278\) −13.2088 −0.792209
\(279\) 1.96873 0.117865
\(280\) 0.336434 0.0201058
\(281\) −7.19172 −0.429022 −0.214511 0.976722i \(-0.568816\pi\)
−0.214511 + 0.976722i \(0.568816\pi\)
\(282\) 23.5623 1.40312
\(283\) −17.3016 −1.02848 −0.514238 0.857648i \(-0.671925\pi\)
−0.514238 + 0.857648i \(0.671925\pi\)
\(284\) 3.02151 0.179294
\(285\) −13.7934 −0.817053
\(286\) −24.9695 −1.47648
\(287\) −1.76085 −0.103940
\(288\) 3.69628 0.217806
\(289\) 4.70518 0.276775
\(290\) 7.71874 0.453260
\(291\) −24.9307 −1.46146
\(292\) −0.972022 −0.0568833
\(293\) 3.35447 0.195970 0.0979850 0.995188i \(-0.468760\pi\)
0.0979850 + 0.995188i \(0.468760\pi\)
\(294\) 18.0220 1.05106
\(295\) 16.1985 0.943113
\(296\) 9.81373 0.570411
\(297\) 8.75993 0.508303
\(298\) 4.94589 0.286508
\(299\) −7.99877 −0.462581
\(300\) 4.70320 0.271539
\(301\) 0.101608 0.00585660
\(302\) 6.32400 0.363905
\(303\) −33.9197 −1.94863
\(304\) −2.98794 −0.171370
\(305\) 5.63351 0.322574
\(306\) −17.2206 −0.984434
\(307\) 9.72930 0.555281 0.277640 0.960685i \(-0.410448\pi\)
0.277640 + 0.960685i \(0.410448\pi\)
\(308\) 0.916883 0.0522442
\(309\) −15.6446 −0.889989
\(310\) −0.950179 −0.0539665
\(311\) −20.2205 −1.14660 −0.573299 0.819346i \(-0.694337\pi\)
−0.573299 + 0.819346i \(0.694337\pi\)
\(312\) −13.2902 −0.752407
\(313\) 24.0688 1.36045 0.680225 0.733003i \(-0.261882\pi\)
0.680225 + 0.733003i \(0.261882\pi\)
\(314\) 8.30268 0.468547
\(315\) 1.24356 0.0700665
\(316\) 7.94337 0.446850
\(317\) −2.06845 −0.116176 −0.0580878 0.998311i \(-0.518500\pi\)
−0.0580878 + 0.998311i \(0.518500\pi\)
\(318\) 11.2722 0.632113
\(319\) 21.0358 1.17778
\(320\) −1.78395 −0.0997260
\(321\) 30.7931 1.71870
\(322\) 0.293715 0.0163681
\(323\) 13.9205 0.774555
\(324\) −6.42633 −0.357019
\(325\) −9.33448 −0.517784
\(326\) 21.5519 1.19365
\(327\) −30.9159 −1.70965
\(328\) 9.33695 0.515547
\(329\) 1.71719 0.0946716
\(330\) −22.4439 −1.23549
\(331\) −12.5101 −0.687618 −0.343809 0.939040i \(-0.611717\pi\)
−0.343809 + 0.939040i \(0.611717\pi\)
\(332\) 3.66356 0.201064
\(333\) 36.2743 1.98782
\(334\) 19.9134 1.08961
\(335\) −11.3085 −0.617849
\(336\) 0.488016 0.0266234
\(337\) −6.72045 −0.366086 −0.183043 0.983105i \(-0.558595\pi\)
−0.183043 + 0.983105i \(0.558595\pi\)
\(338\) 13.3771 0.727618
\(339\) 4.42175 0.240156
\(340\) 8.31123 0.450740
\(341\) −2.58952 −0.140230
\(342\) −11.0443 −0.597206
\(343\) 2.63354 0.142198
\(344\) −0.538781 −0.0290491
\(345\) −7.18970 −0.387080
\(346\) 24.7307 1.32953
\(347\) −17.9500 −0.963608 −0.481804 0.876279i \(-0.660018\pi\)
−0.481804 + 0.876279i \(0.660018\pi\)
\(348\) 11.1964 0.600192
\(349\) −17.5499 −0.939424 −0.469712 0.882820i \(-0.655642\pi\)
−0.469712 + 0.882820i \(0.655642\pi\)
\(350\) 0.342763 0.0183214
\(351\) −9.25374 −0.493928
\(352\) −4.86180 −0.259135
\(353\) −5.78118 −0.307701 −0.153851 0.988094i \(-0.549167\pi\)
−0.153851 + 0.988094i \(0.549167\pi\)
\(354\) 23.4968 1.24884
\(355\) −5.39024 −0.286084
\(356\) 1.04812 0.0555501
\(357\) −2.27361 −0.120332
\(358\) 9.85095 0.520639
\(359\) 11.2088 0.591578 0.295789 0.955253i \(-0.404418\pi\)
0.295789 + 0.955253i \(0.404418\pi\)
\(360\) −6.59400 −0.347534
\(361\) −10.0722 −0.530116
\(362\) 12.5456 0.659383
\(363\) −32.7012 −1.71637
\(364\) −0.968568 −0.0507668
\(365\) 1.73404 0.0907639
\(366\) 8.17170 0.427142
\(367\) 20.5509 1.07275 0.536373 0.843981i \(-0.319794\pi\)
0.536373 + 0.843981i \(0.319794\pi\)
\(368\) −1.55744 −0.0811869
\(369\) 34.5120 1.79662
\(370\) −17.5072 −0.910158
\(371\) 0.821502 0.0426502
\(372\) −1.37828 −0.0714607
\(373\) 28.2339 1.46189 0.730947 0.682434i \(-0.239079\pi\)
0.730947 + 0.682434i \(0.239079\pi\)
\(374\) 22.6505 1.17123
\(375\) −31.4721 −1.62521
\(376\) −9.10544 −0.469577
\(377\) −22.2217 −1.14447
\(378\) 0.339798 0.0174773
\(379\) −14.4738 −0.743469 −0.371735 0.928339i \(-0.621237\pi\)
−0.371735 + 0.928339i \(0.621237\pi\)
\(380\) 5.33035 0.273441
\(381\) 46.4972 2.38212
\(382\) −15.3966 −0.787760
\(383\) 37.0287 1.89208 0.946038 0.324056i \(-0.105047\pi\)
0.946038 + 0.324056i \(0.105047\pi\)
\(384\) −2.58772 −0.132054
\(385\) −1.63568 −0.0833618
\(386\) 16.3836 0.833903
\(387\) −1.99149 −0.101233
\(388\) 9.63424 0.489104
\(389\) 11.8961 0.603156 0.301578 0.953442i \(-0.402487\pi\)
0.301578 + 0.953442i \(0.402487\pi\)
\(390\) 23.7090 1.20055
\(391\) 7.25591 0.366947
\(392\) −6.96443 −0.351757
\(393\) −32.9859 −1.66392
\(394\) 18.7570 0.944964
\(395\) −14.1706 −0.713001
\(396\) −17.9706 −0.903056
\(397\) 25.1716 1.26333 0.631664 0.775243i \(-0.282372\pi\)
0.631664 + 0.775243i \(0.282372\pi\)
\(398\) −2.48325 −0.124474
\(399\) −1.45816 −0.0729994
\(400\) −1.81751 −0.0908755
\(401\) −9.88914 −0.493840 −0.246920 0.969036i \(-0.579418\pi\)
−0.246920 + 0.969036i \(0.579418\pi\)
\(402\) −16.4036 −0.818136
\(403\) 2.73549 0.136264
\(404\) 13.1079 0.652145
\(405\) 11.4643 0.569665
\(406\) 0.815980 0.0404964
\(407\) −47.7124 −2.36501
\(408\) 12.0559 0.596855
\(409\) 17.5995 0.870239 0.435120 0.900373i \(-0.356706\pi\)
0.435120 + 0.900373i \(0.356706\pi\)
\(410\) −16.6567 −0.822615
\(411\) −3.95983 −0.195324
\(412\) 6.04571 0.297851
\(413\) 1.71241 0.0842623
\(414\) −5.75672 −0.282928
\(415\) −6.53561 −0.320821
\(416\) 5.13586 0.251806
\(417\) 34.1806 1.67383
\(418\) 14.5268 0.710527
\(419\) −10.5762 −0.516683 −0.258342 0.966054i \(-0.583176\pi\)
−0.258342 + 0.966054i \(0.583176\pi\)
\(420\) −0.870597 −0.0424808
\(421\) −25.9219 −1.26335 −0.631677 0.775231i \(-0.717633\pi\)
−0.631677 + 0.775231i \(0.717633\pi\)
\(422\) 1.99921 0.0973202
\(423\) −33.6563 −1.63643
\(424\) −4.35604 −0.211548
\(425\) 8.46756 0.410737
\(426\) −7.81883 −0.378823
\(427\) 0.595542 0.0288203
\(428\) −11.8997 −0.575194
\(429\) 64.6141 3.11960
\(430\) 0.961160 0.0463513
\(431\) 16.8848 0.813311 0.406656 0.913582i \(-0.366695\pi\)
0.406656 + 0.913582i \(0.366695\pi\)
\(432\) −1.80179 −0.0866886
\(433\) −35.1768 −1.69049 −0.845244 0.534380i \(-0.820545\pi\)
−0.845244 + 0.534380i \(0.820545\pi\)
\(434\) −0.100447 −0.00482163
\(435\) −19.9739 −0.957676
\(436\) 11.9472 0.572165
\(437\) 4.65352 0.222608
\(438\) 2.51532 0.120187
\(439\) −12.5185 −0.597477 −0.298739 0.954335i \(-0.596566\pi\)
−0.298739 + 0.954335i \(0.596566\pi\)
\(440\) 8.67322 0.413480
\(441\) −25.7425 −1.22583
\(442\) −23.9274 −1.13811
\(443\) −40.9333 −1.94480 −0.972400 0.233318i \(-0.925042\pi\)
−0.972400 + 0.233318i \(0.925042\pi\)
\(444\) −25.3952 −1.20520
\(445\) −1.86979 −0.0886367
\(446\) 14.3800 0.680912
\(447\) −12.7986 −0.605351
\(448\) −0.188589 −0.00891000
\(449\) 1.33855 0.0631702 0.0315851 0.999501i \(-0.489944\pi\)
0.0315851 + 0.999501i \(0.489944\pi\)
\(450\) −6.71803 −0.316691
\(451\) −45.3944 −2.13754
\(452\) −1.70874 −0.0803726
\(453\) −16.3647 −0.768882
\(454\) 21.3775 1.00330
\(455\) 1.72788 0.0810043
\(456\) 7.73195 0.362082
\(457\) −20.2618 −0.947805 −0.473902 0.880577i \(-0.657155\pi\)
−0.473902 + 0.880577i \(0.657155\pi\)
\(458\) 20.4269 0.954486
\(459\) 8.39432 0.391813
\(460\) 2.77839 0.129543
\(461\) −7.41470 −0.345337 −0.172669 0.984980i \(-0.555239\pi\)
−0.172669 + 0.984980i \(0.555239\pi\)
\(462\) −2.37263 −0.110385
\(463\) 2.77160 0.128807 0.0644035 0.997924i \(-0.479486\pi\)
0.0644035 + 0.997924i \(0.479486\pi\)
\(464\) −4.32676 −0.200865
\(465\) 2.45879 0.114024
\(466\) −21.3711 −0.989996
\(467\) −29.9082 −1.38398 −0.691992 0.721905i \(-0.743267\pi\)
−0.691992 + 0.721905i \(0.743267\pi\)
\(468\) 18.9836 0.877518
\(469\) −1.19547 −0.0552016
\(470\) 16.2437 0.749265
\(471\) −21.4850 −0.989976
\(472\) −9.08011 −0.417946
\(473\) 2.61944 0.120442
\(474\) −20.5552 −0.944132
\(475\) 5.43061 0.249174
\(476\) 0.878615 0.0402712
\(477\) −16.1012 −0.737221
\(478\) 9.90077 0.452851
\(479\) −8.86741 −0.405162 −0.202581 0.979265i \(-0.564933\pi\)
−0.202581 + 0.979265i \(0.564933\pi\)
\(480\) 4.61637 0.210707
\(481\) 50.4020 2.29813
\(482\) −15.2985 −0.696826
\(483\) −0.760053 −0.0345836
\(484\) 12.6371 0.574413
\(485\) −17.1870 −0.780423
\(486\) 22.0349 0.999524
\(487\) −17.1123 −0.775430 −0.387715 0.921779i \(-0.626736\pi\)
−0.387715 + 0.921779i \(0.626736\pi\)
\(488\) −3.15788 −0.142950
\(489\) −55.7703 −2.52202
\(490\) 12.4242 0.561269
\(491\) 19.7307 0.890433 0.445217 0.895423i \(-0.353127\pi\)
0.445217 + 0.895423i \(0.353127\pi\)
\(492\) −24.1614 −1.08928
\(493\) 20.1579 0.907865
\(494\) −15.3457 −0.690434
\(495\) 32.0587 1.44093
\(496\) 0.532625 0.0239156
\(497\) −0.569825 −0.0255601
\(498\) −9.48025 −0.424820
\(499\) −11.5043 −0.515003 −0.257502 0.966278i \(-0.582899\pi\)
−0.257502 + 0.966278i \(0.582899\pi\)
\(500\) 12.1621 0.543907
\(501\) −51.5302 −2.30220
\(502\) 0.687735 0.0306951
\(503\) 37.0855 1.65356 0.826781 0.562524i \(-0.190170\pi\)
0.826781 + 0.562524i \(0.190170\pi\)
\(504\) −0.697079 −0.0310504
\(505\) −23.3840 −1.04057
\(506\) 7.57194 0.336614
\(507\) −34.6161 −1.53736
\(508\) −17.9684 −0.797220
\(509\) 39.4830 1.75005 0.875026 0.484076i \(-0.160844\pi\)
0.875026 + 0.484076i \(0.160844\pi\)
\(510\) −21.5071 −0.952351
\(511\) 0.183313 0.00810928
\(512\) 1.00000 0.0441942
\(513\) 5.38364 0.237693
\(514\) −10.9865 −0.484594
\(515\) −10.7853 −0.475255
\(516\) 1.39421 0.0613768
\(517\) 44.2688 1.94694
\(518\) −1.85076 −0.0813179
\(519\) −63.9960 −2.80911
\(520\) −9.16214 −0.401786
\(521\) 22.3360 0.978560 0.489280 0.872127i \(-0.337260\pi\)
0.489280 + 0.872127i \(0.337260\pi\)
\(522\) −15.9929 −0.699992
\(523\) 7.71401 0.337310 0.168655 0.985675i \(-0.446058\pi\)
0.168655 + 0.985675i \(0.446058\pi\)
\(524\) 12.7471 0.556860
\(525\) −0.886973 −0.0387107
\(526\) −23.6982 −1.03329
\(527\) −2.48144 −0.108093
\(528\) 12.5810 0.547516
\(529\) −20.5744 −0.894539
\(530\) 7.77097 0.337549
\(531\) −33.5627 −1.45650
\(532\) 0.563493 0.0244305
\(533\) 47.9533 2.07709
\(534\) −2.71223 −0.117370
\(535\) 21.2285 0.917790
\(536\) 6.33901 0.273804
\(537\) −25.4915 −1.10004
\(538\) −19.9262 −0.859081
\(539\) 33.8597 1.45844
\(540\) 3.21431 0.138322
\(541\) 11.1053 0.477454 0.238727 0.971087i \(-0.423270\pi\)
0.238727 + 0.971087i \(0.423270\pi\)
\(542\) 17.5399 0.753405
\(543\) −32.4645 −1.39319
\(544\) −4.65888 −0.199748
\(545\) −21.3132 −0.912956
\(546\) 2.50638 0.107263
\(547\) −18.2371 −0.779761 −0.389880 0.920865i \(-0.627484\pi\)
−0.389880 + 0.920865i \(0.627484\pi\)
\(548\) 1.53024 0.0653686
\(549\) −11.6724 −0.498167
\(550\) 8.83636 0.376784
\(551\) 12.9281 0.550756
\(552\) 4.03020 0.171537
\(553\) −1.49803 −0.0637029
\(554\) −5.49191 −0.233329
\(555\) 45.3038 1.92304
\(556\) −13.2088 −0.560177
\(557\) 6.38777 0.270658 0.135329 0.990801i \(-0.456791\pi\)
0.135329 + 0.990801i \(0.456791\pi\)
\(558\) 1.96873 0.0833432
\(559\) −2.76710 −0.117036
\(560\) 0.336434 0.0142169
\(561\) −58.6132 −2.47465
\(562\) −7.19172 −0.303365
\(563\) −0.608978 −0.0256654 −0.0128327 0.999918i \(-0.504085\pi\)
−0.0128327 + 0.999918i \(0.504085\pi\)
\(564\) 23.5623 0.992152
\(565\) 3.04832 0.128244
\(566\) −17.3016 −0.727242
\(567\) 1.21194 0.0508966
\(568\) 3.02151 0.126780
\(569\) 34.4563 1.44448 0.722242 0.691641i \(-0.243112\pi\)
0.722242 + 0.691641i \(0.243112\pi\)
\(570\) −13.7934 −0.577744
\(571\) 44.0686 1.84422 0.922108 0.386933i \(-0.126466\pi\)
0.922108 + 0.386933i \(0.126466\pi\)
\(572\) −24.9695 −1.04403
\(573\) 39.8421 1.66443
\(574\) −1.76085 −0.0734964
\(575\) 2.83065 0.118046
\(576\) 3.69628 0.154012
\(577\) −15.4184 −0.641877 −0.320939 0.947100i \(-0.603998\pi\)
−0.320939 + 0.947100i \(0.603998\pi\)
\(578\) 4.70518 0.195710
\(579\) −42.3961 −1.76192
\(580\) 7.71874 0.320503
\(581\) −0.690907 −0.0286637
\(582\) −24.9307 −1.03341
\(583\) 21.1782 0.877110
\(584\) −0.972022 −0.0402225
\(585\) −33.8659 −1.40018
\(586\) 3.35447 0.138572
\(587\) −25.1760 −1.03912 −0.519562 0.854433i \(-0.673905\pi\)
−0.519562 + 0.854433i \(0.673905\pi\)
\(588\) 18.0220 0.743214
\(589\) −1.59145 −0.0655747
\(590\) 16.1985 0.666882
\(591\) −48.5378 −1.99658
\(592\) 9.81373 0.403342
\(593\) −27.7690 −1.14033 −0.570167 0.821529i \(-0.693122\pi\)
−0.570167 + 0.821529i \(0.693122\pi\)
\(594\) 8.75993 0.359424
\(595\) −1.56741 −0.0642575
\(596\) 4.94589 0.202591
\(597\) 6.42594 0.262996
\(598\) −7.99877 −0.327094
\(599\) 22.9439 0.937461 0.468731 0.883341i \(-0.344712\pi\)
0.468731 + 0.883341i \(0.344712\pi\)
\(600\) 4.70320 0.192007
\(601\) −5.69708 −0.232389 −0.116194 0.993227i \(-0.537070\pi\)
−0.116194 + 0.993227i \(0.537070\pi\)
\(602\) 0.101608 0.00414124
\(603\) 23.4308 0.954175
\(604\) 6.32400 0.257320
\(605\) −22.5440 −0.916543
\(606\) −33.9197 −1.37789
\(607\) −1.86678 −0.0757701 −0.0378851 0.999282i \(-0.512062\pi\)
−0.0378851 + 0.999282i \(0.512062\pi\)
\(608\) −2.98794 −0.121177
\(609\) −2.11153 −0.0855634
\(610\) 5.63351 0.228094
\(611\) −46.7643 −1.89188
\(612\) −17.2206 −0.696100
\(613\) −2.67093 −0.107878 −0.0539389 0.998544i \(-0.517178\pi\)
−0.0539389 + 0.998544i \(0.517178\pi\)
\(614\) 9.72930 0.392643
\(615\) 43.1028 1.73807
\(616\) 0.916883 0.0369423
\(617\) −17.1812 −0.691690 −0.345845 0.938292i \(-0.612408\pi\)
−0.345845 + 0.938292i \(0.612408\pi\)
\(618\) −15.6446 −0.629318
\(619\) 24.5804 0.987971 0.493985 0.869470i \(-0.335540\pi\)
0.493985 + 0.869470i \(0.335540\pi\)
\(620\) −0.950179 −0.0381601
\(621\) 2.80617 0.112608
\(622\) −20.2205 −0.810767
\(623\) −0.197664 −0.00791922
\(624\) −13.2902 −0.532032
\(625\) −12.6091 −0.504364
\(626\) 24.0688 0.961984
\(627\) −37.5912 −1.50125
\(628\) 8.30268 0.331313
\(629\) −45.7210 −1.82302
\(630\) 1.24356 0.0495445
\(631\) 25.8175 1.02778 0.513890 0.857856i \(-0.328204\pi\)
0.513890 + 0.857856i \(0.328204\pi\)
\(632\) 7.94337 0.315970
\(633\) −5.17340 −0.205624
\(634\) −2.06845 −0.0821486
\(635\) 32.0548 1.27206
\(636\) 11.2722 0.446972
\(637\) −35.7684 −1.41719
\(638\) 21.0358 0.832817
\(639\) 11.1684 0.441814
\(640\) −1.78395 −0.0705170
\(641\) −2.84770 −0.112477 −0.0562387 0.998417i \(-0.517911\pi\)
−0.0562387 + 0.998417i \(0.517911\pi\)
\(642\) 30.7931 1.21531
\(643\) −7.33837 −0.289397 −0.144699 0.989476i \(-0.546221\pi\)
−0.144699 + 0.989476i \(0.546221\pi\)
\(644\) 0.293715 0.0115740
\(645\) −2.48721 −0.0979339
\(646\) 13.9205 0.547693
\(647\) −24.3978 −0.959175 −0.479588 0.877494i \(-0.659214\pi\)
−0.479588 + 0.877494i \(0.659214\pi\)
\(648\) −6.42633 −0.252450
\(649\) 44.1457 1.73287
\(650\) −9.33448 −0.366128
\(651\) 0.259929 0.0101874
\(652\) 21.5519 0.844039
\(653\) 49.6987 1.94486 0.972430 0.233197i \(-0.0749187\pi\)
0.972430 + 0.233197i \(0.0749187\pi\)
\(654\) −30.9159 −1.20891
\(655\) −22.7402 −0.888534
\(656\) 9.33695 0.364547
\(657\) −3.59287 −0.140171
\(658\) 1.71719 0.0669430
\(659\) −2.60897 −0.101631 −0.0508155 0.998708i \(-0.516182\pi\)
−0.0508155 + 0.998708i \(0.516182\pi\)
\(660\) −22.4439 −0.873626
\(661\) −13.1593 −0.511837 −0.255919 0.966698i \(-0.582378\pi\)
−0.255919 + 0.966698i \(0.582378\pi\)
\(662\) −12.5101 −0.486219
\(663\) 61.9173 2.40467
\(664\) 3.66356 0.142174
\(665\) −1.00525 −0.0389818
\(666\) 36.2743 1.40560
\(667\) 6.73865 0.260922
\(668\) 19.9134 0.770472
\(669\) −37.2114 −1.43867
\(670\) −11.3085 −0.436885
\(671\) 15.3530 0.592695
\(672\) 0.488016 0.0188256
\(673\) −35.2053 −1.35706 −0.678532 0.734571i \(-0.737384\pi\)
−0.678532 + 0.734571i \(0.737384\pi\)
\(674\) −6.72045 −0.258862
\(675\) 3.27477 0.126046
\(676\) 13.3771 0.514503
\(677\) −13.0763 −0.502565 −0.251282 0.967914i \(-0.580852\pi\)
−0.251282 + 0.967914i \(0.580852\pi\)
\(678\) 4.42175 0.169816
\(679\) −1.81691 −0.0697267
\(680\) 8.31123 0.318721
\(681\) −55.3190 −2.11983
\(682\) −2.58952 −0.0991577
\(683\) −40.4784 −1.54886 −0.774432 0.632657i \(-0.781964\pi\)
−0.774432 + 0.632657i \(0.781964\pi\)
\(684\) −11.0443 −0.422289
\(685\) −2.72988 −0.104303
\(686\) 2.63354 0.100549
\(687\) −52.8591 −2.01670
\(688\) −0.538781 −0.0205408
\(689\) −22.3720 −0.852306
\(690\) −7.18970 −0.273707
\(691\) −8.91225 −0.339038 −0.169519 0.985527i \(-0.554221\pi\)
−0.169519 + 0.985527i \(0.554221\pi\)
\(692\) 24.7307 0.940119
\(693\) 3.38906 0.128740
\(694\) −17.9500 −0.681374
\(695\) 23.5638 0.893827
\(696\) 11.1964 0.424400
\(697\) −43.4997 −1.64767
\(698\) −17.5499 −0.664273
\(699\) 55.3023 2.09173
\(700\) 0.342763 0.0129552
\(701\) 50.3952 1.90340 0.951700 0.307028i \(-0.0993346\pi\)
0.951700 + 0.307028i \(0.0993346\pi\)
\(702\) −9.25374 −0.349260
\(703\) −29.3228 −1.10593
\(704\) −4.86180 −0.183236
\(705\) −42.0341 −1.58309
\(706\) −5.78118 −0.217578
\(707\) −2.47202 −0.0929698
\(708\) 23.4968 0.883063
\(709\) 41.7789 1.56904 0.784519 0.620105i \(-0.212910\pi\)
0.784519 + 0.620105i \(0.212910\pi\)
\(710\) −5.39024 −0.202292
\(711\) 29.3610 1.10112
\(712\) 1.04812 0.0392798
\(713\) −0.829529 −0.0310661
\(714\) −2.27361 −0.0850876
\(715\) 44.5445 1.66587
\(716\) 9.85095 0.368147
\(717\) −25.6204 −0.956812
\(718\) 11.2088 0.418309
\(719\) −16.3394 −0.609355 −0.304678 0.952456i \(-0.598549\pi\)
−0.304678 + 0.952456i \(0.598549\pi\)
\(720\) −6.59400 −0.245744
\(721\) −1.14016 −0.0424616
\(722\) −10.0722 −0.374849
\(723\) 39.5881 1.47230
\(724\) 12.5456 0.466254
\(725\) 7.86393 0.292059
\(726\) −32.7012 −1.21366
\(727\) −14.9533 −0.554586 −0.277293 0.960785i \(-0.589437\pi\)
−0.277293 + 0.960785i \(0.589437\pi\)
\(728\) −0.968568 −0.0358975
\(729\) −37.7411 −1.39782
\(730\) 1.73404 0.0641798
\(731\) 2.51012 0.0928400
\(732\) 8.17170 0.302035
\(733\) 4.31730 0.159463 0.0797315 0.996816i \(-0.474594\pi\)
0.0797315 + 0.996816i \(0.474594\pi\)
\(734\) 20.5509 0.758547
\(735\) −32.1504 −1.18589
\(736\) −1.55744 −0.0574078
\(737\) −30.8190 −1.13523
\(738\) 34.5120 1.27041
\(739\) −28.6425 −1.05363 −0.526816 0.849979i \(-0.676614\pi\)
−0.526816 + 0.849979i \(0.676614\pi\)
\(740\) −17.5072 −0.643579
\(741\) 39.7102 1.45879
\(742\) 0.821502 0.0301583
\(743\) 50.6615 1.85859 0.929295 0.369339i \(-0.120416\pi\)
0.929295 + 0.369339i \(0.120416\pi\)
\(744\) −1.37828 −0.0505303
\(745\) −8.82323 −0.323258
\(746\) 28.2339 1.03372
\(747\) 13.5415 0.495459
\(748\) 22.6505 0.828186
\(749\) 2.24416 0.0819997
\(750\) −31.4721 −1.14920
\(751\) −46.6551 −1.70247 −0.851235 0.524785i \(-0.824146\pi\)
−0.851235 + 0.524785i \(0.824146\pi\)
\(752\) −9.10544 −0.332041
\(753\) −1.77967 −0.0648546
\(754\) −22.2217 −0.809265
\(755\) −11.2817 −0.410584
\(756\) 0.339798 0.0123583
\(757\) −14.0526 −0.510751 −0.255376 0.966842i \(-0.582199\pi\)
−0.255376 + 0.966842i \(0.582199\pi\)
\(758\) −14.4738 −0.525712
\(759\) −19.5940 −0.711218
\(760\) 5.33035 0.193352
\(761\) 52.8641 1.91632 0.958161 0.286230i \(-0.0924020\pi\)
0.958161 + 0.286230i \(0.0924020\pi\)
\(762\) 46.4972 1.68442
\(763\) −2.25311 −0.0815679
\(764\) −15.3966 −0.557030
\(765\) 30.7207 1.11071
\(766\) 37.0287 1.33790
\(767\) −46.6342 −1.68386
\(768\) −2.58772 −0.0933762
\(769\) 48.6194 1.75326 0.876631 0.481163i \(-0.159786\pi\)
0.876631 + 0.481163i \(0.159786\pi\)
\(770\) −1.63568 −0.0589457
\(771\) 28.4300 1.02388
\(772\) 16.3836 0.589659
\(773\) 20.9686 0.754188 0.377094 0.926175i \(-0.376923\pi\)
0.377094 + 0.926175i \(0.376923\pi\)
\(774\) −1.99149 −0.0715825
\(775\) −0.968051 −0.0347734
\(776\) 9.63424 0.345849
\(777\) 4.78925 0.171814
\(778\) 11.8961 0.426496
\(779\) −27.8983 −0.999559
\(780\) 23.7090 0.848920
\(781\) −14.6900 −0.525649
\(782\) 7.25591 0.259471
\(783\) 7.79591 0.278603
\(784\) −6.96443 −0.248730
\(785\) −14.8116 −0.528648
\(786\) −32.9859 −1.17657
\(787\) 29.3425 1.04595 0.522974 0.852349i \(-0.324822\pi\)
0.522974 + 0.852349i \(0.324822\pi\)
\(788\) 18.7570 0.668191
\(789\) 61.3243 2.18320
\(790\) −14.1706 −0.504168
\(791\) 0.322251 0.0114579
\(792\) −17.9706 −0.638557
\(793\) −16.2184 −0.575933
\(794\) 25.1716 0.893307
\(795\) −20.1091 −0.713195
\(796\) −2.48325 −0.0880163
\(797\) −4.91715 −0.174175 −0.0870873 0.996201i \(-0.527756\pi\)
−0.0870873 + 0.996201i \(0.527756\pi\)
\(798\) −1.45816 −0.0516184
\(799\) 42.4212 1.50075
\(800\) −1.81751 −0.0642587
\(801\) 3.87414 0.136886
\(802\) −9.88914 −0.349198
\(803\) 4.72577 0.166769
\(804\) −16.4036 −0.578509
\(805\) −0.523975 −0.0184677
\(806\) 2.73549 0.0963535
\(807\) 51.5635 1.81512
\(808\) 13.1079 0.461136
\(809\) 51.7736 1.82026 0.910132 0.414319i \(-0.135980\pi\)
0.910132 + 0.414319i \(0.135980\pi\)
\(810\) 11.4643 0.402814
\(811\) −9.24815 −0.324746 −0.162373 0.986729i \(-0.551915\pi\)
−0.162373 + 0.986729i \(0.551915\pi\)
\(812\) 0.815980 0.0286353
\(813\) −45.3884 −1.59184
\(814\) −47.7124 −1.67232
\(815\) −38.4477 −1.34676
\(816\) 12.0559 0.422040
\(817\) 1.60985 0.0563214
\(818\) 17.5995 0.615352
\(819\) −3.58010 −0.125099
\(820\) −16.6567 −0.581677
\(821\) 17.2285 0.601277 0.300639 0.953738i \(-0.402800\pi\)
0.300639 + 0.953738i \(0.402800\pi\)
\(822\) −3.95983 −0.138115
\(823\) −23.0732 −0.804282 −0.402141 0.915578i \(-0.631734\pi\)
−0.402141 + 0.915578i \(0.631734\pi\)
\(824\) 6.04571 0.210612
\(825\) −22.8660 −0.796093
\(826\) 1.71241 0.0595824
\(827\) −5.07334 −0.176417 −0.0882087 0.996102i \(-0.528114\pi\)
−0.0882087 + 0.996102i \(0.528114\pi\)
\(828\) −5.75672 −0.200060
\(829\) 13.6574 0.474343 0.237171 0.971468i \(-0.423780\pi\)
0.237171 + 0.971468i \(0.423780\pi\)
\(830\) −6.53561 −0.226854
\(831\) 14.2115 0.492992
\(832\) 5.13586 0.178054
\(833\) 32.4465 1.12420
\(834\) 34.1806 1.18358
\(835\) −35.5246 −1.22938
\(836\) 14.5268 0.502419
\(837\) −0.959678 −0.0331713
\(838\) −10.5762 −0.365350
\(839\) 29.8396 1.03018 0.515089 0.857137i \(-0.327759\pi\)
0.515089 + 0.857137i \(0.327759\pi\)
\(840\) −0.870597 −0.0300385
\(841\) −10.2791 −0.354453
\(842\) −25.9219 −0.893327
\(843\) 18.6102 0.640968
\(844\) 1.99921 0.0688158
\(845\) −23.8641 −0.820950
\(846\) −33.6563 −1.15713
\(847\) −2.38322 −0.0818883
\(848\) −4.35604 −0.149587
\(849\) 44.7717 1.53656
\(850\) 8.46756 0.290435
\(851\) −15.2842 −0.523937
\(852\) −7.81883 −0.267869
\(853\) −3.57858 −0.122528 −0.0612640 0.998122i \(-0.519513\pi\)
−0.0612640 + 0.998122i \(0.519513\pi\)
\(854\) 0.595542 0.0203790
\(855\) 19.7025 0.673811
\(856\) −11.8997 −0.406724
\(857\) −33.0036 −1.12738 −0.563690 0.825986i \(-0.690619\pi\)
−0.563690 + 0.825986i \(0.690619\pi\)
\(858\) 64.6141 2.20589
\(859\) −10.3417 −0.352854 −0.176427 0.984314i \(-0.556454\pi\)
−0.176427 + 0.984314i \(0.556454\pi\)
\(860\) 0.961160 0.0327753
\(861\) 4.55658 0.155288
\(862\) 16.8848 0.575098
\(863\) −53.7026 −1.82806 −0.914029 0.405649i \(-0.867045\pi\)
−0.914029 + 0.405649i \(0.867045\pi\)
\(864\) −1.80179 −0.0612981
\(865\) −44.1183 −1.50007
\(866\) −35.1768 −1.19536
\(867\) −12.1757 −0.413508
\(868\) −0.100447 −0.00340941
\(869\) −38.6191 −1.31006
\(870\) −19.9739 −0.677179
\(871\) 32.5563 1.10313
\(872\) 11.9472 0.404582
\(873\) 35.6109 1.20525
\(874\) 4.65352 0.157408
\(875\) −2.29364 −0.0775393
\(876\) 2.51532 0.0849847
\(877\) 17.2688 0.583126 0.291563 0.956552i \(-0.405825\pi\)
0.291563 + 0.956552i \(0.405825\pi\)
\(878\) −12.5185 −0.422480
\(879\) −8.68042 −0.292783
\(880\) 8.67322 0.292374
\(881\) 40.3331 1.35886 0.679429 0.733741i \(-0.262228\pi\)
0.679429 + 0.733741i \(0.262228\pi\)
\(882\) −25.7425 −0.866796
\(883\) 27.5690 0.927771 0.463885 0.885895i \(-0.346455\pi\)
0.463885 + 0.885895i \(0.346455\pi\)
\(884\) −23.9274 −0.804765
\(885\) −41.9172 −1.40903
\(886\) −40.9333 −1.37518
\(887\) 21.7101 0.728953 0.364476 0.931213i \(-0.381248\pi\)
0.364476 + 0.931213i \(0.381248\pi\)
\(888\) −25.3952 −0.852206
\(889\) 3.38865 0.113652
\(890\) −1.86979 −0.0626756
\(891\) 31.2435 1.04670
\(892\) 14.3800 0.481478
\(893\) 27.2065 0.910431
\(894\) −12.7986 −0.428048
\(895\) −17.5736 −0.587422
\(896\) −0.188589 −0.00630032
\(897\) 20.6986 0.691105
\(898\) 1.33855 0.0446681
\(899\) −2.30454 −0.0768608
\(900\) −6.71803 −0.223934
\(901\) 20.2943 0.676100
\(902\) −45.3944 −1.51147
\(903\) −0.262934 −0.00874988
\(904\) −1.70874 −0.0568320
\(905\) −22.3808 −0.743963
\(906\) −16.3647 −0.543682
\(907\) −4.57008 −0.151747 −0.0758735 0.997117i \(-0.524175\pi\)
−0.0758735 + 0.997117i \(0.524175\pi\)
\(908\) 21.3775 0.709438
\(909\) 48.4507 1.60701
\(910\) 1.72788 0.0572787
\(911\) 39.9399 1.32327 0.661634 0.749827i \(-0.269863\pi\)
0.661634 + 0.749827i \(0.269863\pi\)
\(912\) 7.73195 0.256030
\(913\) −17.8115 −0.589474
\(914\) −20.2618 −0.670199
\(915\) −14.5779 −0.481932
\(916\) 20.4269 0.674924
\(917\) −2.40396 −0.0793859
\(918\) 8.39432 0.277054
\(919\) −26.2921 −0.867298 −0.433649 0.901082i \(-0.642774\pi\)
−0.433649 + 0.901082i \(0.642774\pi\)
\(920\) 2.77839 0.0916009
\(921\) −25.1767 −0.829600
\(922\) −7.41470 −0.244190
\(923\) 15.5181 0.510784
\(924\) −2.37263 −0.0780539
\(925\) −17.8365 −0.586462
\(926\) 2.77160 0.0910803
\(927\) 22.3467 0.733960
\(928\) −4.32676 −0.142033
\(929\) −24.3855 −0.800062 −0.400031 0.916502i \(-0.631001\pi\)
−0.400031 + 0.916502i \(0.631001\pi\)
\(930\) 2.45879 0.0806270
\(931\) 20.8093 0.681998
\(932\) −21.3711 −0.700033
\(933\) 52.3249 1.71304
\(934\) −29.9082 −0.978625
\(935\) −40.4075 −1.32147
\(936\) 18.9836 0.620499
\(937\) −4.28486 −0.139980 −0.0699901 0.997548i \(-0.522297\pi\)
−0.0699901 + 0.997548i \(0.522297\pi\)
\(938\) −1.19547 −0.0390334
\(939\) −62.2833 −2.03254
\(940\) 16.2437 0.529811
\(941\) −29.8128 −0.971869 −0.485934 0.873995i \(-0.661521\pi\)
−0.485934 + 0.873995i \(0.661521\pi\)
\(942\) −21.4850 −0.700019
\(943\) −14.5417 −0.473543
\(944\) −9.08011 −0.295533
\(945\) −0.606183 −0.0197192
\(946\) 2.61944 0.0851655
\(947\) −20.4756 −0.665368 −0.332684 0.943038i \(-0.607954\pi\)
−0.332684 + 0.943038i \(0.607954\pi\)
\(948\) −20.5552 −0.667602
\(949\) −4.99217 −0.162053
\(950\) 5.43061 0.176192
\(951\) 5.35256 0.173569
\(952\) 0.878615 0.0284761
\(953\) −16.9026 −0.547530 −0.273765 0.961797i \(-0.588269\pi\)
−0.273765 + 0.961797i \(0.588269\pi\)
\(954\) −16.1012 −0.521294
\(955\) 27.4669 0.888807
\(956\) 9.90077 0.320214
\(957\) −54.4348 −1.75963
\(958\) −8.86741 −0.286493
\(959\) −0.288587 −0.00931895
\(960\) 4.61637 0.148993
\(961\) −30.7163 −0.990849
\(962\) 50.4020 1.62502
\(963\) −43.9847 −1.41739
\(964\) −15.2985 −0.492731
\(965\) −29.2276 −0.940869
\(966\) −0.760053 −0.0244543
\(967\) 1.78408 0.0573722 0.0286861 0.999588i \(-0.490868\pi\)
0.0286861 + 0.999588i \(0.490868\pi\)
\(968\) 12.6371 0.406171
\(969\) −36.0222 −1.15720
\(970\) −17.1870 −0.551842
\(971\) 34.0379 1.09233 0.546165 0.837678i \(-0.316087\pi\)
0.546165 + 0.837678i \(0.316087\pi\)
\(972\) 22.0349 0.706770
\(973\) 2.49103 0.0798588
\(974\) −17.1123 −0.548312
\(975\) 24.1550 0.773579
\(976\) −3.15788 −0.101081
\(977\) 6.94628 0.222231 0.111116 0.993807i \(-0.464558\pi\)
0.111116 + 0.993807i \(0.464558\pi\)
\(978\) −55.7703 −1.78334
\(979\) −5.09573 −0.162860
\(980\) 12.4242 0.396877
\(981\) 44.1601 1.40992
\(982\) 19.7307 0.629631
\(983\) −37.0341 −1.18120 −0.590602 0.806963i \(-0.701110\pi\)
−0.590602 + 0.806963i \(0.701110\pi\)
\(984\) −24.1614 −0.770237
\(985\) −33.4616 −1.06618
\(986\) 20.1579 0.641957
\(987\) −4.44360 −0.141441
\(988\) −15.3457 −0.488210
\(989\) 0.839116 0.0266823
\(990\) 32.0587 1.01889
\(991\) −5.32775 −0.169241 −0.0846207 0.996413i \(-0.526968\pi\)
−0.0846207 + 0.996413i \(0.526968\pi\)
\(992\) 0.532625 0.0169109
\(993\) 32.3726 1.02731
\(994\) −0.569825 −0.0180737
\(995\) 4.43000 0.140440
\(996\) −9.48025 −0.300393
\(997\) −24.1495 −0.764823 −0.382412 0.923992i \(-0.624906\pi\)
−0.382412 + 0.923992i \(0.624906\pi\)
\(998\) −11.5043 −0.364162
\(999\) −17.6823 −0.559442
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 4034.2.a.d.1.6 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.6 52 1.1 even 1 trivial