Properties

Label 4006.2.a.g.1.6
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 1.6
Character \(\chi\) = 4006.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.30611 q^{3} +1.00000 q^{4} +3.88128 q^{5} +2.30611 q^{6} +0.245423 q^{7} -1.00000 q^{8} +2.31816 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.30611 q^{3} +1.00000 q^{4} +3.88128 q^{5} +2.30611 q^{6} +0.245423 q^{7} -1.00000 q^{8} +2.31816 q^{9} -3.88128 q^{10} -2.29954 q^{11} -2.30611 q^{12} -5.34839 q^{13} -0.245423 q^{14} -8.95067 q^{15} +1.00000 q^{16} -2.60721 q^{17} -2.31816 q^{18} +8.55592 q^{19} +3.88128 q^{20} -0.565974 q^{21} +2.29954 q^{22} +2.94694 q^{23} +2.30611 q^{24} +10.0643 q^{25} +5.34839 q^{26} +1.57240 q^{27} +0.245423 q^{28} -7.74114 q^{29} +8.95067 q^{30} -5.79274 q^{31} -1.00000 q^{32} +5.30300 q^{33} +2.60721 q^{34} +0.952555 q^{35} +2.31816 q^{36} +9.58016 q^{37} -8.55592 q^{38} +12.3340 q^{39} -3.88128 q^{40} -6.77464 q^{41} +0.565974 q^{42} +3.09940 q^{43} -2.29954 q^{44} +8.99742 q^{45} -2.94694 q^{46} -7.31928 q^{47} -2.30611 q^{48} -6.93977 q^{49} -10.0643 q^{50} +6.01252 q^{51} -5.34839 q^{52} +5.03416 q^{53} -1.57240 q^{54} -8.92516 q^{55} -0.245423 q^{56} -19.7309 q^{57} +7.74114 q^{58} -8.17961 q^{59} -8.95067 q^{60} -8.95515 q^{61} +5.79274 q^{62} +0.568930 q^{63} +1.00000 q^{64} -20.7586 q^{65} -5.30300 q^{66} -3.26763 q^{67} -2.60721 q^{68} -6.79598 q^{69} -0.952555 q^{70} +12.8152 q^{71} -2.31816 q^{72} +7.56389 q^{73} -9.58016 q^{74} -23.2094 q^{75} +8.55592 q^{76} -0.564361 q^{77} -12.3340 q^{78} +13.8552 q^{79} +3.88128 q^{80} -10.5806 q^{81} +6.77464 q^{82} -7.26049 q^{83} -0.565974 q^{84} -10.1193 q^{85} -3.09940 q^{86} +17.8519 q^{87} +2.29954 q^{88} -12.3995 q^{89} -8.99742 q^{90} -1.31262 q^{91} +2.94694 q^{92} +13.3587 q^{93} +7.31928 q^{94} +33.2079 q^{95} +2.30611 q^{96} -7.83860 q^{97} +6.93977 q^{98} -5.33070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + O(q^{10}) \) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + 23q^{10} - 28q^{11} - q^{12} - 12q^{13} - 12q^{14} - 14q^{15} + 40q^{16} - 10q^{17} - 29q^{18} + 3q^{19} - 23q^{20} - 40q^{21} + 28q^{22} - 10q^{23} + q^{24} + 43q^{25} + 12q^{26} - 7q^{27} + 12q^{28} - 37q^{29} + 14q^{30} - 16q^{31} - 40q^{32} - 11q^{33} + 10q^{34} - 24q^{35} + 29q^{36} - 17q^{37} - 3q^{38} - 10q^{39} + 23q^{40} - 58q^{41} + 40q^{42} + 37q^{43} - 28q^{44} - 66q^{45} + 10q^{46} - 34q^{47} - q^{48} + 28q^{49} - 43q^{50} - 7q^{51} - 12q^{52} - 43q^{53} + 7q^{54} + 28q^{55} - 12q^{56} - 25q^{57} + 37q^{58} - 92q^{59} - 14q^{60} - 37q^{61} + 16q^{62} + 14q^{63} + 40q^{64} - 54q^{65} + 11q^{66} - 10q^{67} - 10q^{68} - 49q^{69} + 24q^{70} - 87q^{71} - 29q^{72} + 12q^{73} + 17q^{74} - 31q^{75} + 3q^{76} - 53q^{77} + 10q^{78} + 14q^{79} - 23q^{80} - 4q^{81} + 58q^{82} - 42q^{83} - 40q^{84} - 24q^{85} - 37q^{86} + 24q^{87} + 28q^{88} - 118q^{89} + 66q^{90} - 35q^{91} - 10q^{92} - 22q^{93} + 34q^{94} - 18q^{95} + q^{96} + 2q^{97} - 28q^{98} - 48q^{99} + O(q^{100}) \)

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
\(3\) −2.30611 −1.33144 −0.665718 0.746204i \(-0.731874\pi\)
−0.665718 + 0.746204i \(0.731874\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.88128 1.73576 0.867880 0.496774i \(-0.165482\pi\)
0.867880 + 0.496774i \(0.165482\pi\)
\(6\) 2.30611 0.941467
\(7\) 0.245423 0.0927612 0.0463806 0.998924i \(-0.485231\pi\)
0.0463806 + 0.998924i \(0.485231\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.31816 0.772720
\(10\) −3.88128 −1.22737
\(11\) −2.29954 −0.693338 −0.346669 0.937988i \(-0.612687\pi\)
−0.346669 + 0.937988i \(0.612687\pi\)
\(12\) −2.30611 −0.665718
\(13\) −5.34839 −1.48338 −0.741689 0.670744i \(-0.765975\pi\)
−0.741689 + 0.670744i \(0.765975\pi\)
\(14\) −0.245423 −0.0655921
\(15\) −8.95067 −2.31105
\(16\) 1.00000 0.250000
\(17\) −2.60721 −0.632341 −0.316170 0.948702i \(-0.602397\pi\)
−0.316170 + 0.948702i \(0.602397\pi\)
\(18\) −2.31816 −0.546395
\(19\) 8.55592 1.96286 0.981431 0.191816i \(-0.0614377\pi\)
0.981431 + 0.191816i \(0.0614377\pi\)
\(20\) 3.88128 0.867880
\(21\) −0.565974 −0.123506
\(22\) 2.29954 0.490264
\(23\) 2.94694 0.614480 0.307240 0.951632i \(-0.400595\pi\)
0.307240 + 0.951632i \(0.400595\pi\)
\(24\) 2.30611 0.470733
\(25\) 10.0643 2.01286
\(26\) 5.34839 1.04891
\(27\) 1.57240 0.302609
\(28\) 0.245423 0.0463806
\(29\) −7.74114 −1.43749 −0.718747 0.695272i \(-0.755284\pi\)
−0.718747 + 0.695272i \(0.755284\pi\)
\(30\) 8.95067 1.63416
\(31\) −5.79274 −1.04041 −0.520204 0.854042i \(-0.674144\pi\)
−0.520204 + 0.854042i \(0.674144\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.30300 0.923135
\(34\) 2.60721 0.447132
\(35\) 0.952555 0.161011
\(36\) 2.31816 0.386360
\(37\) 9.58016 1.57497 0.787484 0.616335i \(-0.211383\pi\)
0.787484 + 0.616335i \(0.211383\pi\)
\(38\) −8.55592 −1.38795
\(39\) 12.3340 1.97502
\(40\) −3.88128 −0.613684
\(41\) −6.77464 −1.05802 −0.529010 0.848615i \(-0.677437\pi\)
−0.529010 + 0.848615i \(0.677437\pi\)
\(42\) 0.565974 0.0873316
\(43\) 3.09940 0.472654 0.236327 0.971674i \(-0.424056\pi\)
0.236327 + 0.971674i \(0.424056\pi\)
\(44\) −2.29954 −0.346669
\(45\) 8.99742 1.34126
\(46\) −2.94694 −0.434503
\(47\) −7.31928 −1.06763 −0.533814 0.845602i \(-0.679242\pi\)
−0.533814 + 0.845602i \(0.679242\pi\)
\(48\) −2.30611 −0.332859
\(49\) −6.93977 −0.991395
\(50\) −10.0643 −1.42331
\(51\) 6.01252 0.841921
\(52\) −5.34839 −0.741689
\(53\) 5.03416 0.691495 0.345748 0.938328i \(-0.387625\pi\)
0.345748 + 0.938328i \(0.387625\pi\)
\(54\) −1.57240 −0.213977
\(55\) −8.92516 −1.20347
\(56\) −0.245423 −0.0327960
\(57\) −19.7309 −2.61342
\(58\) 7.74114 1.01646
\(59\) −8.17961 −1.06489 −0.532447 0.846463i \(-0.678727\pi\)
−0.532447 + 0.846463i \(0.678727\pi\)
\(60\) −8.95067 −1.15553
\(61\) −8.95515 −1.14659 −0.573295 0.819349i \(-0.694335\pi\)
−0.573295 + 0.819349i \(0.694335\pi\)
\(62\) 5.79274 0.735679
\(63\) 0.568930 0.0716784
\(64\) 1.00000 0.125000
\(65\) −20.7586 −2.57479
\(66\) −5.30300 −0.652755
\(67\) −3.26763 −0.399204 −0.199602 0.979877i \(-0.563965\pi\)
−0.199602 + 0.979877i \(0.563965\pi\)
\(68\) −2.60721 −0.316170
\(69\) −6.79598 −0.818140
\(70\) −0.952555 −0.113852
\(71\) 12.8152 1.52088 0.760440 0.649408i \(-0.224983\pi\)
0.760440 + 0.649408i \(0.224983\pi\)
\(72\) −2.31816 −0.273198
\(73\) 7.56389 0.885287 0.442643 0.896698i \(-0.354041\pi\)
0.442643 + 0.896698i \(0.354041\pi\)
\(74\) −9.58016 −1.11367
\(75\) −23.2094 −2.68000
\(76\) 8.55592 0.981431
\(77\) −0.564361 −0.0643149
\(78\) −12.3340 −1.39655
\(79\) 13.8552 1.55883 0.779417 0.626506i \(-0.215515\pi\)
0.779417 + 0.626506i \(0.215515\pi\)
\(80\) 3.88128 0.433940
\(81\) −10.5806 −1.17562
\(82\) 6.77464 0.748134
\(83\) −7.26049 −0.796942 −0.398471 0.917181i \(-0.630459\pi\)
−0.398471 + 0.917181i \(0.630459\pi\)
\(84\) −0.565974 −0.0617528
\(85\) −10.1193 −1.09759
\(86\) −3.09940 −0.334217
\(87\) 17.8519 1.91393
\(88\) 2.29954 0.245132
\(89\) −12.3995 −1.31434 −0.657172 0.753741i \(-0.728247\pi\)
−0.657172 + 0.753741i \(0.728247\pi\)
\(90\) −8.99742 −0.948411
\(91\) −1.31262 −0.137600
\(92\) 2.94694 0.307240
\(93\) 13.3587 1.38523
\(94\) 7.31928 0.754926
\(95\) 33.2079 3.40706
\(96\) 2.30611 0.235367
\(97\) −7.83860 −0.795889 −0.397944 0.917409i \(-0.630276\pi\)
−0.397944 + 0.917409i \(0.630276\pi\)
\(98\) 6.93977 0.701022
\(99\) −5.33070 −0.535756
\(100\) 10.0643 1.00643
\(101\) −2.14814 −0.213748 −0.106874 0.994273i \(-0.534084\pi\)
−0.106874 + 0.994273i \(0.534084\pi\)
\(102\) −6.01252 −0.595328
\(103\) −9.24718 −0.911152 −0.455576 0.890197i \(-0.650567\pi\)
−0.455576 + 0.890197i \(0.650567\pi\)
\(104\) 5.34839 0.524453
\(105\) −2.19670 −0.214376
\(106\) −5.03416 −0.488961
\(107\) 16.7483 1.61912 0.809558 0.587040i \(-0.199707\pi\)
0.809558 + 0.587040i \(0.199707\pi\)
\(108\) 1.57240 0.151305
\(109\) −13.1018 −1.25492 −0.627461 0.778648i \(-0.715906\pi\)
−0.627461 + 0.778648i \(0.715906\pi\)
\(110\) 8.92516 0.850981
\(111\) −22.0929 −2.09697
\(112\) 0.245423 0.0231903
\(113\) 0.805981 0.0758204 0.0379102 0.999281i \(-0.487930\pi\)
0.0379102 + 0.999281i \(0.487930\pi\)
\(114\) 19.7309 1.84797
\(115\) 11.4379 1.06659
\(116\) −7.74114 −0.718747
\(117\) −12.3984 −1.14623
\(118\) 8.17961 0.752994
\(119\) −0.639869 −0.0586567
\(120\) 8.95067 0.817080
\(121\) −5.71211 −0.519282
\(122\) 8.95515 0.810761
\(123\) 15.6231 1.40869
\(124\) −5.79274 −0.520204
\(125\) 19.6560 1.75809
\(126\) −0.568930 −0.0506843
\(127\) −12.8644 −1.14154 −0.570768 0.821112i \(-0.693354\pi\)
−0.570768 + 0.821112i \(0.693354\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −7.14756 −0.629308
\(130\) 20.7586 1.82065
\(131\) 1.17305 0.102489 0.0512447 0.998686i \(-0.483681\pi\)
0.0512447 + 0.998686i \(0.483681\pi\)
\(132\) 5.30300 0.461567
\(133\) 2.09982 0.182077
\(134\) 3.26763 0.282280
\(135\) 6.10293 0.525257
\(136\) 2.60721 0.223566
\(137\) 3.53163 0.301728 0.150864 0.988555i \(-0.451794\pi\)
0.150864 + 0.988555i \(0.451794\pi\)
\(138\) 6.79598 0.578512
\(139\) −1.28089 −0.108644 −0.0543218 0.998523i \(-0.517300\pi\)
−0.0543218 + 0.998523i \(0.517300\pi\)
\(140\) 0.952555 0.0805056
\(141\) 16.8791 1.42148
\(142\) −12.8152 −1.07542
\(143\) 12.2989 1.02848
\(144\) 2.31816 0.193180
\(145\) −30.0455 −2.49514
\(146\) −7.56389 −0.625992
\(147\) 16.0039 1.31998
\(148\) 9.58016 0.787484
\(149\) 11.0768 0.907446 0.453723 0.891143i \(-0.350096\pi\)
0.453723 + 0.891143i \(0.350096\pi\)
\(150\) 23.2094 1.89504
\(151\) −3.83532 −0.312114 −0.156057 0.987748i \(-0.549878\pi\)
−0.156057 + 0.987748i \(0.549878\pi\)
\(152\) −8.55592 −0.693976
\(153\) −6.04392 −0.488622
\(154\) 0.564361 0.0454775
\(155\) −22.4832 −1.80590
\(156\) 12.3340 0.987510
\(157\) 3.37953 0.269716 0.134858 0.990865i \(-0.456942\pi\)
0.134858 + 0.990865i \(0.456942\pi\)
\(158\) −13.8552 −1.10226
\(159\) −11.6094 −0.920681
\(160\) −3.88128 −0.306842
\(161\) 0.723247 0.0569999
\(162\) 10.5806 0.831292
\(163\) 21.8575 1.71201 0.856004 0.516969i \(-0.172940\pi\)
0.856004 + 0.516969i \(0.172940\pi\)
\(164\) −6.77464 −0.529010
\(165\) 20.5824 1.60234
\(166\) 7.26049 0.563523
\(167\) −0.223008 −0.0172569 −0.00862843 0.999963i \(-0.502747\pi\)
−0.00862843 + 0.999963i \(0.502747\pi\)
\(168\) 0.565974 0.0436658
\(169\) 15.6053 1.20041
\(170\) 10.1193 0.776114
\(171\) 19.8340 1.51674
\(172\) 3.09940 0.236327
\(173\) 3.38213 0.257139 0.128569 0.991701i \(-0.458961\pi\)
0.128569 + 0.991701i \(0.458961\pi\)
\(174\) −17.8519 −1.35335
\(175\) 2.47002 0.186716
\(176\) −2.29954 −0.173334
\(177\) 18.8631 1.41784
\(178\) 12.3995 0.929381
\(179\) −17.8962 −1.33762 −0.668811 0.743433i \(-0.733196\pi\)
−0.668811 + 0.743433i \(0.733196\pi\)
\(180\) 8.99742 0.670628
\(181\) −20.8892 −1.55268 −0.776340 0.630314i \(-0.782926\pi\)
−0.776340 + 0.630314i \(0.782926\pi\)
\(182\) 1.31262 0.0972978
\(183\) 20.6516 1.52661
\(184\) −2.94694 −0.217251
\(185\) 37.1832 2.73377
\(186\) −13.3587 −0.979509
\(187\) 5.99538 0.438426
\(188\) −7.31928 −0.533814
\(189\) 0.385904 0.0280704
\(190\) −33.2079 −2.40915
\(191\) −19.5612 −1.41540 −0.707699 0.706514i \(-0.750267\pi\)
−0.707699 + 0.706514i \(0.750267\pi\)
\(192\) −2.30611 −0.166429
\(193\) −5.83600 −0.420085 −0.210042 0.977692i \(-0.567360\pi\)
−0.210042 + 0.977692i \(0.567360\pi\)
\(194\) 7.83860 0.562778
\(195\) 47.8717 3.42816
\(196\) −6.93977 −0.495698
\(197\) 5.29845 0.377499 0.188749 0.982025i \(-0.439557\pi\)
0.188749 + 0.982025i \(0.439557\pi\)
\(198\) 5.33070 0.378837
\(199\) 8.35379 0.592185 0.296092 0.955159i \(-0.404316\pi\)
0.296092 + 0.955159i \(0.404316\pi\)
\(200\) −10.0643 −0.711654
\(201\) 7.53552 0.531515
\(202\) 2.14814 0.151143
\(203\) −1.89985 −0.133344
\(204\) 6.01252 0.420960
\(205\) −26.2943 −1.83647
\(206\) 9.24718 0.644282
\(207\) 6.83148 0.474820
\(208\) −5.34839 −0.370844
\(209\) −19.6747 −1.36093
\(210\) 2.19670 0.151587
\(211\) 9.73855 0.670430 0.335215 0.942142i \(-0.391191\pi\)
0.335215 + 0.942142i \(0.391191\pi\)
\(212\) 5.03416 0.345748
\(213\) −29.5532 −2.02495
\(214\) −16.7483 −1.14489
\(215\) 12.0296 0.820414
\(216\) −1.57240 −0.106988
\(217\) −1.42167 −0.0965094
\(218\) 13.1018 0.887364
\(219\) −17.4432 −1.17870
\(220\) −8.92516 −0.601734
\(221\) 13.9444 0.938000
\(222\) 22.0929 1.48278
\(223\) −18.3042 −1.22574 −0.612871 0.790183i \(-0.709985\pi\)
−0.612871 + 0.790183i \(0.709985\pi\)
\(224\) −0.245423 −0.0163980
\(225\) 23.3307 1.55538
\(226\) −0.805981 −0.0536131
\(227\) −5.33077 −0.353816 −0.176908 0.984227i \(-0.556609\pi\)
−0.176908 + 0.984227i \(0.556609\pi\)
\(228\) −19.7309 −1.30671
\(229\) −17.6356 −1.16540 −0.582698 0.812689i \(-0.698003\pi\)
−0.582698 + 0.812689i \(0.698003\pi\)
\(230\) −11.4379 −0.754192
\(231\) 1.30148 0.0856311
\(232\) 7.74114 0.508231
\(233\) 20.1558 1.32045 0.660226 0.751067i \(-0.270461\pi\)
0.660226 + 0.751067i \(0.270461\pi\)
\(234\) 12.3984 0.810510
\(235\) −28.4082 −1.85314
\(236\) −8.17961 −0.532447
\(237\) −31.9517 −2.07549
\(238\) 0.639869 0.0414766
\(239\) −20.4747 −1.32440 −0.662198 0.749329i \(-0.730376\pi\)
−0.662198 + 0.749329i \(0.730376\pi\)
\(240\) −8.95067 −0.577763
\(241\) 12.6703 0.816167 0.408084 0.912945i \(-0.366197\pi\)
0.408084 + 0.912945i \(0.366197\pi\)
\(242\) 5.71211 0.367188
\(243\) 19.6829 1.26266
\(244\) −8.95515 −0.573295
\(245\) −26.9352 −1.72082
\(246\) −15.6231 −0.996092
\(247\) −45.7604 −2.91166
\(248\) 5.79274 0.367839
\(249\) 16.7435 1.06108
\(250\) −19.6560 −1.24315
\(251\) −13.6399 −0.860941 −0.430471 0.902605i \(-0.641652\pi\)
−0.430471 + 0.902605i \(0.641652\pi\)
\(252\) 0.568930 0.0358392
\(253\) −6.77661 −0.426042
\(254\) 12.8644 0.807187
\(255\) 23.3362 1.46137
\(256\) 1.00000 0.0625000
\(257\) −24.0699 −1.50144 −0.750720 0.660621i \(-0.770293\pi\)
−0.750720 + 0.660621i \(0.770293\pi\)
\(258\) 7.14756 0.444988
\(259\) 2.35119 0.146096
\(260\) −20.7586 −1.28739
\(261\) −17.9452 −1.11078
\(262\) −1.17305 −0.0724710
\(263\) 27.3360 1.68561 0.842804 0.538221i \(-0.180903\pi\)
0.842804 + 0.538221i \(0.180903\pi\)
\(264\) −5.30300 −0.326377
\(265\) 19.5390 1.20027
\(266\) −2.09982 −0.128748
\(267\) 28.5946 1.74996
\(268\) −3.26763 −0.199602
\(269\) −32.5010 −1.98162 −0.990809 0.135265i \(-0.956812\pi\)
−0.990809 + 0.135265i \(0.956812\pi\)
\(270\) −6.10293 −0.371413
\(271\) −3.73702 −0.227008 −0.113504 0.993538i \(-0.536207\pi\)
−0.113504 + 0.993538i \(0.536207\pi\)
\(272\) −2.60721 −0.158085
\(273\) 3.02705 0.183205
\(274\) −3.53163 −0.213354
\(275\) −23.1433 −1.39559
\(276\) −6.79598 −0.409070
\(277\) 10.3068 0.619275 0.309638 0.950855i \(-0.399792\pi\)
0.309638 + 0.950855i \(0.399792\pi\)
\(278\) 1.28089 0.0768226
\(279\) −13.4285 −0.803943
\(280\) −0.952555 −0.0569261
\(281\) −14.2098 −0.847687 −0.423843 0.905736i \(-0.639319\pi\)
−0.423843 + 0.905736i \(0.639319\pi\)
\(282\) −16.8791 −1.00514
\(283\) 21.5215 1.27932 0.639660 0.768658i \(-0.279075\pi\)
0.639660 + 0.768658i \(0.279075\pi\)
\(284\) 12.8152 0.760440
\(285\) −76.5811 −4.53628
\(286\) −12.2989 −0.727246
\(287\) −1.66265 −0.0981433
\(288\) −2.31816 −0.136599
\(289\) −10.2025 −0.600145
\(290\) 30.0455 1.76433
\(291\) 18.0767 1.05967
\(292\) 7.56389 0.442643
\(293\) −4.58164 −0.267662 −0.133831 0.991004i \(-0.542728\pi\)
−0.133831 + 0.991004i \(0.542728\pi\)
\(294\) −16.0039 −0.933366
\(295\) −31.7473 −1.84840
\(296\) −9.58016 −0.556835
\(297\) −3.61581 −0.209810
\(298\) −11.0768 −0.641661
\(299\) −15.7614 −0.911505
\(300\) −23.2094 −1.34000
\(301\) 0.760664 0.0438440
\(302\) 3.83532 0.220698
\(303\) 4.95385 0.284591
\(304\) 8.55592 0.490715
\(305\) −34.7574 −1.99020
\(306\) 6.04392 0.345508
\(307\) −29.3783 −1.67671 −0.838355 0.545125i \(-0.816482\pi\)
−0.838355 + 0.545125i \(0.816482\pi\)
\(308\) −0.564361 −0.0321574
\(309\) 21.3251 1.21314
\(310\) 22.4832 1.27696
\(311\) 7.10079 0.402649 0.201324 0.979525i \(-0.435475\pi\)
0.201324 + 0.979525i \(0.435475\pi\)
\(312\) −12.3340 −0.698275
\(313\) 1.74949 0.0988872 0.0494436 0.998777i \(-0.484255\pi\)
0.0494436 + 0.998777i \(0.484255\pi\)
\(314\) −3.37953 −0.190718
\(315\) 2.20817 0.124417
\(316\) 13.8552 0.779417
\(317\) −24.5895 −1.38108 −0.690542 0.723292i \(-0.742628\pi\)
−0.690542 + 0.723292i \(0.742628\pi\)
\(318\) 11.6094 0.651020
\(319\) 17.8011 0.996669
\(320\) 3.88128 0.216970
\(321\) −38.6234 −2.15575
\(322\) −0.723247 −0.0403050
\(323\) −22.3070 −1.24120
\(324\) −10.5806 −0.587812
\(325\) −53.8279 −2.98583
\(326\) −21.8575 −1.21057
\(327\) 30.2142 1.67085
\(328\) 6.77464 0.374067
\(329\) −1.79632 −0.0990344
\(330\) −20.5824 −1.13303
\(331\) −1.60774 −0.0883692 −0.0441846 0.999023i \(-0.514069\pi\)
−0.0441846 + 0.999023i \(0.514069\pi\)
\(332\) −7.26049 −0.398471
\(333\) 22.2083 1.21701
\(334\) 0.223008 0.0122024
\(335\) −12.6826 −0.692923
\(336\) −0.565974 −0.0308764
\(337\) 20.8938 1.13816 0.569080 0.822282i \(-0.307299\pi\)
0.569080 + 0.822282i \(0.307299\pi\)
\(338\) −15.6053 −0.848816
\(339\) −1.85868 −0.100950
\(340\) −10.1193 −0.548796
\(341\) 13.3207 0.721354
\(342\) −19.8340 −1.07250
\(343\) −3.42114 −0.184724
\(344\) −3.09940 −0.167108
\(345\) −26.3771 −1.42009
\(346\) −3.38213 −0.181825
\(347\) −3.34010 −0.179306 −0.0896529 0.995973i \(-0.528576\pi\)
−0.0896529 + 0.995973i \(0.528576\pi\)
\(348\) 17.8519 0.956965
\(349\) 1.62440 0.0869522 0.0434761 0.999054i \(-0.486157\pi\)
0.0434761 + 0.999054i \(0.486157\pi\)
\(350\) −2.47002 −0.132028
\(351\) −8.40983 −0.448883
\(352\) 2.29954 0.122566
\(353\) −33.8642 −1.80241 −0.901206 0.433391i \(-0.857317\pi\)
−0.901206 + 0.433391i \(0.857317\pi\)
\(354\) −18.8631 −1.00256
\(355\) 49.7392 2.63988
\(356\) −12.3995 −0.657172
\(357\) 1.47561 0.0780976
\(358\) 17.8962 0.945842
\(359\) −12.7402 −0.672400 −0.336200 0.941791i \(-0.609142\pi\)
−0.336200 + 0.941791i \(0.609142\pi\)
\(360\) −8.99742 −0.474206
\(361\) 54.2037 2.85283
\(362\) 20.8892 1.09791
\(363\) 13.1728 0.691391
\(364\) −1.31262 −0.0687999
\(365\) 29.3576 1.53664
\(366\) −20.6516 −1.07948
\(367\) 27.2995 1.42502 0.712511 0.701661i \(-0.247558\pi\)
0.712511 + 0.701661i \(0.247558\pi\)
\(368\) 2.94694 0.153620
\(369\) −15.7047 −0.817553
\(370\) −37.1832 −1.93306
\(371\) 1.23550 0.0641440
\(372\) 13.3587 0.692617
\(373\) −12.3032 −0.637036 −0.318518 0.947917i \(-0.603185\pi\)
−0.318518 + 0.947917i \(0.603185\pi\)
\(374\) −5.99538 −0.310014
\(375\) −45.3290 −2.34078
\(376\) 7.31928 0.377463
\(377\) 41.4026 2.13234
\(378\) −0.385904 −0.0198488
\(379\) 28.5227 1.46511 0.732555 0.680708i \(-0.238328\pi\)
0.732555 + 0.680708i \(0.238328\pi\)
\(380\) 33.2079 1.70353
\(381\) 29.6669 1.51988
\(382\) 19.5612 1.00084
\(383\) 16.0293 0.819057 0.409528 0.912297i \(-0.365693\pi\)
0.409528 + 0.912297i \(0.365693\pi\)
\(384\) 2.30611 0.117683
\(385\) −2.19044 −0.111635
\(386\) 5.83600 0.297045
\(387\) 7.18490 0.365229
\(388\) −7.83860 −0.397944
\(389\) −24.6747 −1.25106 −0.625529 0.780201i \(-0.715117\pi\)
−0.625529 + 0.780201i \(0.715117\pi\)
\(390\) −47.8717 −2.42408
\(391\) −7.68329 −0.388560
\(392\) 6.93977 0.350511
\(393\) −2.70518 −0.136458
\(394\) −5.29845 −0.266932
\(395\) 53.7759 2.70576
\(396\) −5.33070 −0.267878
\(397\) −16.4833 −0.827275 −0.413638 0.910442i \(-0.635742\pi\)
−0.413638 + 0.910442i \(0.635742\pi\)
\(398\) −8.35379 −0.418738
\(399\) −4.84242 −0.242424
\(400\) 10.0643 0.503216
\(401\) 6.14759 0.306996 0.153498 0.988149i \(-0.450946\pi\)
0.153498 + 0.988149i \(0.450946\pi\)
\(402\) −7.53552 −0.375838
\(403\) 30.9819 1.54332
\(404\) −2.14814 −0.106874
\(405\) −41.0663 −2.04060
\(406\) 1.89985 0.0942882
\(407\) −22.0300 −1.09199
\(408\) −6.01252 −0.297664
\(409\) 5.18329 0.256297 0.128149 0.991755i \(-0.459097\pi\)
0.128149 + 0.991755i \(0.459097\pi\)
\(410\) 26.2943 1.29858
\(411\) −8.14435 −0.401731
\(412\) −9.24718 −0.455576
\(413\) −2.00746 −0.0987809
\(414\) −6.83148 −0.335749
\(415\) −28.1800 −1.38330
\(416\) 5.34839 0.262226
\(417\) 2.95387 0.144652
\(418\) 19.6747 0.962320
\(419\) −24.2792 −1.18611 −0.593057 0.805160i \(-0.702079\pi\)
−0.593057 + 0.805160i \(0.702079\pi\)
\(420\) −2.19670 −0.107188
\(421\) −39.2970 −1.91522 −0.957609 0.288071i \(-0.906986\pi\)
−0.957609 + 0.288071i \(0.906986\pi\)
\(422\) −9.73855 −0.474065
\(423\) −16.9673 −0.824976
\(424\) −5.03416 −0.244481
\(425\) −26.2398 −1.27281
\(426\) 29.5532 1.43186
\(427\) −2.19780 −0.106359
\(428\) 16.7483 0.809558
\(429\) −28.3625 −1.36936
\(430\) −12.0296 −0.580120
\(431\) 6.91347 0.333010 0.166505 0.986041i \(-0.446752\pi\)
0.166505 + 0.986041i \(0.446752\pi\)
\(432\) 1.57240 0.0756523
\(433\) 13.6592 0.656420 0.328210 0.944605i \(-0.393555\pi\)
0.328210 + 0.944605i \(0.393555\pi\)
\(434\) 1.42167 0.0682425
\(435\) 69.2883 3.32212
\(436\) −13.1018 −0.627461
\(437\) 25.2138 1.20614
\(438\) 17.4432 0.833468
\(439\) 25.1355 1.19965 0.599825 0.800131i \(-0.295237\pi\)
0.599825 + 0.800131i \(0.295237\pi\)
\(440\) 8.92516 0.425490
\(441\) −16.0875 −0.766071
\(442\) −13.9444 −0.663266
\(443\) 10.0652 0.478212 0.239106 0.970993i \(-0.423146\pi\)
0.239106 + 0.970993i \(0.423146\pi\)
\(444\) −22.0929 −1.04848
\(445\) −48.1259 −2.28139
\(446\) 18.3042 0.866730
\(447\) −25.5443 −1.20820
\(448\) 0.245423 0.0115952
\(449\) 6.76853 0.319426 0.159713 0.987163i \(-0.448943\pi\)
0.159713 + 0.987163i \(0.448943\pi\)
\(450\) −23.3307 −1.09982
\(451\) 15.5786 0.733566
\(452\) 0.805981 0.0379102
\(453\) 8.84469 0.415560
\(454\) 5.33077 0.250185
\(455\) −5.09464 −0.238840
\(456\) 19.7309 0.923985
\(457\) −32.9685 −1.54220 −0.771100 0.636714i \(-0.780293\pi\)
−0.771100 + 0.636714i \(0.780293\pi\)
\(458\) 17.6356 0.824059
\(459\) −4.09958 −0.191352
\(460\) 11.4379 0.533295
\(461\) 13.2362 0.616472 0.308236 0.951310i \(-0.400261\pi\)
0.308236 + 0.951310i \(0.400261\pi\)
\(462\) −1.30148 −0.0605503
\(463\) −33.6467 −1.56369 −0.781846 0.623471i \(-0.785722\pi\)
−0.781846 + 0.623471i \(0.785722\pi\)
\(464\) −7.74114 −0.359373
\(465\) 51.8489 2.40443
\(466\) −20.1558 −0.933700
\(467\) −26.2198 −1.21331 −0.606654 0.794966i \(-0.707489\pi\)
−0.606654 + 0.794966i \(0.707489\pi\)
\(468\) −12.3984 −0.573117
\(469\) −0.801952 −0.0370307
\(470\) 28.4082 1.31037
\(471\) −7.79359 −0.359110
\(472\) 8.17961 0.376497
\(473\) −7.12720 −0.327709
\(474\) 31.9517 1.46759
\(475\) 86.1094 3.95097
\(476\) −0.639869 −0.0293284
\(477\) 11.6700 0.534332
\(478\) 20.4747 0.936489
\(479\) 17.1251 0.782467 0.391234 0.920291i \(-0.372048\pi\)
0.391234 + 0.920291i \(0.372048\pi\)
\(480\) 8.95067 0.408540
\(481\) −51.2384 −2.33627
\(482\) −12.6703 −0.577117
\(483\) −1.66789 −0.0758917
\(484\) −5.71211 −0.259641
\(485\) −30.4238 −1.38147
\(486\) −19.6829 −0.892834
\(487\) −41.8693 −1.89728 −0.948640 0.316358i \(-0.897540\pi\)
−0.948640 + 0.316358i \(0.897540\pi\)
\(488\) 8.95515 0.405381
\(489\) −50.4058 −2.27943
\(490\) 26.9352 1.21681
\(491\) 9.28697 0.419115 0.209558 0.977796i \(-0.432798\pi\)
0.209558 + 0.977796i \(0.432798\pi\)
\(492\) 15.6231 0.704343
\(493\) 20.1828 0.908986
\(494\) 45.7604 2.05886
\(495\) −20.6899 −0.929944
\(496\) −5.79274 −0.260102
\(497\) 3.14514 0.141079
\(498\) −16.7435 −0.750295
\(499\) 15.5818 0.697539 0.348769 0.937209i \(-0.386600\pi\)
0.348769 + 0.937209i \(0.386600\pi\)
\(500\) 19.6560 0.879043
\(501\) 0.514281 0.0229764
\(502\) 13.6399 0.608778
\(503\) −17.0783 −0.761485 −0.380742 0.924681i \(-0.624332\pi\)
−0.380742 + 0.924681i \(0.624332\pi\)
\(504\) −0.568930 −0.0253421
\(505\) −8.33752 −0.371015
\(506\) 6.77661 0.301257
\(507\) −35.9876 −1.59826
\(508\) −12.8644 −0.570768
\(509\) −30.8133 −1.36577 −0.682887 0.730524i \(-0.739276\pi\)
−0.682887 + 0.730524i \(0.739276\pi\)
\(510\) −23.3362 −1.03335
\(511\) 1.85635 0.0821203
\(512\) −1.00000 −0.0441942
\(513\) 13.4533 0.593980
\(514\) 24.0699 1.06168
\(515\) −35.8909 −1.58154
\(516\) −7.14756 −0.314654
\(517\) 16.8310 0.740227
\(518\) −2.35119 −0.103305
\(519\) −7.79959 −0.342364
\(520\) 20.7586 0.910324
\(521\) 25.6533 1.12389 0.561945 0.827175i \(-0.310053\pi\)
0.561945 + 0.827175i \(0.310053\pi\)
\(522\) 17.9452 0.785440
\(523\) −10.6299 −0.464812 −0.232406 0.972619i \(-0.574660\pi\)
−0.232406 + 0.972619i \(0.574660\pi\)
\(524\) 1.17305 0.0512447
\(525\) −5.69614 −0.248600
\(526\) −27.3360 −1.19190
\(527\) 15.1029 0.657892
\(528\) 5.30300 0.230784
\(529\) −14.3155 −0.622415
\(530\) −19.5390 −0.848719
\(531\) −18.9616 −0.822864
\(532\) 2.09982 0.0910387
\(533\) 36.2334 1.56944
\(534\) −28.5946 −1.23741
\(535\) 65.0046 2.81040
\(536\) 3.26763 0.141140
\(537\) 41.2706 1.78096
\(538\) 32.5010 1.40122
\(539\) 15.9583 0.687372
\(540\) 6.10293 0.262628
\(541\) 29.3934 1.26372 0.631860 0.775082i \(-0.282292\pi\)
0.631860 + 0.775082i \(0.282292\pi\)
\(542\) 3.73702 0.160519
\(543\) 48.1728 2.06729
\(544\) 2.60721 0.111783
\(545\) −50.8516 −2.17824
\(546\) −3.02705 −0.129546
\(547\) −42.8685 −1.83292 −0.916462 0.400121i \(-0.868968\pi\)
−0.916462 + 0.400121i \(0.868968\pi\)
\(548\) 3.53163 0.150864
\(549\) −20.7595 −0.885992
\(550\) 23.1433 0.986834
\(551\) −66.2325 −2.82160
\(552\) 6.79598 0.289256
\(553\) 3.40039 0.144599
\(554\) −10.3068 −0.437894
\(555\) −85.7488 −3.63983
\(556\) −1.28089 −0.0543218
\(557\) 8.46717 0.358765 0.179383 0.983779i \(-0.442590\pi\)
0.179383 + 0.983779i \(0.442590\pi\)
\(558\) 13.4285 0.568473
\(559\) −16.5768 −0.701124
\(560\) 0.952555 0.0402528
\(561\) −13.8260 −0.583736
\(562\) 14.2098 0.599405
\(563\) −34.7945 −1.46641 −0.733206 0.680006i \(-0.761977\pi\)
−0.733206 + 0.680006i \(0.761977\pi\)
\(564\) 16.8791 0.710738
\(565\) 3.12824 0.131606
\(566\) −21.5215 −0.904616
\(567\) −2.59673 −0.109052
\(568\) −12.8152 −0.537712
\(569\) −32.1547 −1.34799 −0.673997 0.738734i \(-0.735424\pi\)
−0.673997 + 0.738734i \(0.735424\pi\)
\(570\) 76.5811 3.20763
\(571\) 10.2750 0.429997 0.214998 0.976614i \(-0.431025\pi\)
0.214998 + 0.976614i \(0.431025\pi\)
\(572\) 12.2989 0.514241
\(573\) 45.1103 1.88451
\(574\) 1.66265 0.0693978
\(575\) 29.6589 1.23686
\(576\) 2.31816 0.0965899
\(577\) 8.88109 0.369725 0.184862 0.982764i \(-0.440816\pi\)
0.184862 + 0.982764i \(0.440816\pi\)
\(578\) 10.2025 0.424367
\(579\) 13.4585 0.559316
\(580\) −30.0455 −1.24757
\(581\) −1.78189 −0.0739253
\(582\) −18.0767 −0.749303
\(583\) −11.5763 −0.479440
\(584\) −7.56389 −0.312996
\(585\) −48.1217 −1.98959
\(586\) 4.58164 0.189266
\(587\) −4.48726 −0.185209 −0.0926044 0.995703i \(-0.529519\pi\)
−0.0926044 + 0.995703i \(0.529519\pi\)
\(588\) 16.0039 0.659989
\(589\) −49.5622 −2.04218
\(590\) 31.7473 1.30702
\(591\) −12.2188 −0.502615
\(592\) 9.58016 0.393742
\(593\) −21.6360 −0.888486 −0.444243 0.895906i \(-0.646527\pi\)
−0.444243 + 0.895906i \(0.646527\pi\)
\(594\) 3.61581 0.148358
\(595\) −2.48351 −0.101814
\(596\) 11.0768 0.453723
\(597\) −19.2648 −0.788456
\(598\) 15.7614 0.644531
\(599\) 24.4527 0.999110 0.499555 0.866282i \(-0.333497\pi\)
0.499555 + 0.866282i \(0.333497\pi\)
\(600\) 23.2094 0.947522
\(601\) 0.0653259 0.00266470 0.00133235 0.999999i \(-0.499576\pi\)
0.00133235 + 0.999999i \(0.499576\pi\)
\(602\) −0.760664 −0.0310024
\(603\) −7.57488 −0.308473
\(604\) −3.83532 −0.156057
\(605\) −22.1703 −0.901350
\(606\) −4.95385 −0.201236
\(607\) 34.2157 1.38877 0.694386 0.719602i \(-0.255676\pi\)
0.694386 + 0.719602i \(0.255676\pi\)
\(608\) −8.55592 −0.346988
\(609\) 4.38128 0.177538
\(610\) 34.7574 1.40729
\(611\) 39.1464 1.58369
\(612\) −6.04392 −0.244311
\(613\) −20.4991 −0.827952 −0.413976 0.910288i \(-0.635860\pi\)
−0.413976 + 0.910288i \(0.635860\pi\)
\(614\) 29.3783 1.18561
\(615\) 60.6375 2.44514
\(616\) 0.564361 0.0227387
\(617\) −4.26274 −0.171612 −0.0858058 0.996312i \(-0.527346\pi\)
−0.0858058 + 0.996312i \(0.527346\pi\)
\(618\) −21.3251 −0.857819
\(619\) −8.01079 −0.321981 −0.160990 0.986956i \(-0.551469\pi\)
−0.160990 + 0.986956i \(0.551469\pi\)
\(620\) −22.4832 −0.902948
\(621\) 4.63378 0.185947
\(622\) −7.10079 −0.284716
\(623\) −3.04312 −0.121920
\(624\) 12.3340 0.493755
\(625\) 25.9688 1.03875
\(626\) −1.74949 −0.0699238
\(627\) 45.3721 1.81199
\(628\) 3.37953 0.134858
\(629\) −24.9775 −0.995916
\(630\) −2.20817 −0.0879758
\(631\) 15.8989 0.632923 0.316462 0.948605i \(-0.397505\pi\)
0.316462 + 0.948605i \(0.397505\pi\)
\(632\) −13.8552 −0.551131
\(633\) −22.4582 −0.892634
\(634\) 24.5895 0.976575
\(635\) −49.9305 −1.98143
\(636\) −11.6094 −0.460341
\(637\) 37.1166 1.47061
\(638\) −17.8011 −0.704751
\(639\) 29.7076 1.17521
\(640\) −3.88128 −0.153421
\(641\) 3.74559 0.147942 0.0739710 0.997260i \(-0.476433\pi\)
0.0739710 + 0.997260i \(0.476433\pi\)
\(642\) 38.6234 1.52434
\(643\) 18.7864 0.740862 0.370431 0.928860i \(-0.379210\pi\)
0.370431 + 0.928860i \(0.379210\pi\)
\(644\) 0.723247 0.0284999
\(645\) −27.7417 −1.09233
\(646\) 22.3070 0.877659
\(647\) −11.8241 −0.464853 −0.232426 0.972614i \(-0.574666\pi\)
−0.232426 + 0.972614i \(0.574666\pi\)
\(648\) 10.5806 0.415646
\(649\) 18.8093 0.738332
\(650\) 53.8279 2.11130
\(651\) 3.27854 0.128496
\(652\) 21.8575 0.856004
\(653\) −18.5143 −0.724522 −0.362261 0.932077i \(-0.617995\pi\)
−0.362261 + 0.932077i \(0.617995\pi\)
\(654\) −30.2142 −1.18147
\(655\) 4.55292 0.177897
\(656\) −6.77464 −0.264505
\(657\) 17.5343 0.684078
\(658\) 1.79632 0.0700279
\(659\) 46.8917 1.82664 0.913321 0.407239i \(-0.133509\pi\)
0.913321 + 0.407239i \(0.133509\pi\)
\(660\) 20.5824 0.801170
\(661\) 8.68656 0.337868 0.168934 0.985627i \(-0.445968\pi\)
0.168934 + 0.985627i \(0.445968\pi\)
\(662\) 1.60774 0.0624864
\(663\) −32.1573 −1.24889
\(664\) 7.26049 0.281762
\(665\) 8.14998 0.316043
\(666\) −22.2083 −0.860555
\(667\) −22.8127 −0.883310
\(668\) −0.223008 −0.00862843
\(669\) 42.2116 1.63200
\(670\) 12.6826 0.489970
\(671\) 20.5927 0.794974
\(672\) 0.565974 0.0218329
\(673\) −12.5334 −0.483128 −0.241564 0.970385i \(-0.577660\pi\)
−0.241564 + 0.970385i \(0.577660\pi\)
\(674\) −20.8938 −0.804801
\(675\) 15.8252 0.609111
\(676\) 15.6053 0.600204
\(677\) 9.80719 0.376921 0.188460 0.982081i \(-0.439650\pi\)
0.188460 + 0.982081i \(0.439650\pi\)
\(678\) 1.85868 0.0713823
\(679\) −1.92377 −0.0738276
\(680\) 10.1193 0.388057
\(681\) 12.2934 0.471083
\(682\) −13.3207 −0.510074
\(683\) 12.9680 0.496205 0.248103 0.968734i \(-0.420193\pi\)
0.248103 + 0.968734i \(0.420193\pi\)
\(684\) 19.8340 0.758371
\(685\) 13.7072 0.523727
\(686\) 3.42114 0.130620
\(687\) 40.6698 1.55165
\(688\) 3.09940 0.118163
\(689\) −26.9247 −1.02575
\(690\) 26.3771 1.00416
\(691\) −38.8397 −1.47753 −0.738765 0.673963i \(-0.764591\pi\)
−0.738765 + 0.673963i \(0.764591\pi\)
\(692\) 3.38213 0.128569
\(693\) −1.30828 −0.0496974
\(694\) 3.34010 0.126788
\(695\) −4.97148 −0.188579
\(696\) −17.8519 −0.676676
\(697\) 17.6629 0.669030
\(698\) −1.62440 −0.0614845
\(699\) −46.4816 −1.75809
\(700\) 2.47002 0.0933578
\(701\) −28.6510 −1.08213 −0.541067 0.840980i \(-0.681979\pi\)
−0.541067 + 0.840980i \(0.681979\pi\)
\(702\) 8.40983 0.317409
\(703\) 81.9670 3.09144
\(704\) −2.29954 −0.0866672
\(705\) 65.5125 2.46734
\(706\) 33.8642 1.27450
\(707\) −0.527203 −0.0198275
\(708\) 18.8631 0.708919
\(709\) 34.3459 1.28989 0.644943 0.764230i \(-0.276881\pi\)
0.644943 + 0.764230i \(0.276881\pi\)
\(710\) −49.7392 −1.86668
\(711\) 32.1186 1.20454
\(712\) 12.3995 0.464691
\(713\) −17.0709 −0.639309
\(714\) −1.47561 −0.0552233
\(715\) 47.7353 1.78520
\(716\) −17.8962 −0.668811
\(717\) 47.2169 1.76335
\(718\) 12.7402 0.475458
\(719\) −22.7182 −0.847247 −0.423624 0.905838i \(-0.639242\pi\)
−0.423624 + 0.905838i \(0.639242\pi\)
\(720\) 8.99742 0.335314
\(721\) −2.26947 −0.0845196
\(722\) −54.2037 −2.01725
\(723\) −29.2192 −1.08667
\(724\) −20.8892 −0.776340
\(725\) −77.9092 −2.89348
\(726\) −13.1728 −0.488887
\(727\) 46.4425 1.72246 0.861229 0.508217i \(-0.169695\pi\)
0.861229 + 0.508217i \(0.169695\pi\)
\(728\) 1.31262 0.0486489
\(729\) −13.6491 −0.505523
\(730\) −29.3576 −1.08657
\(731\) −8.08078 −0.298878
\(732\) 20.6516 0.763305
\(733\) 19.4013 0.716604 0.358302 0.933606i \(-0.383356\pi\)
0.358302 + 0.933606i \(0.383356\pi\)
\(734\) −27.2995 −1.00764
\(735\) 62.1155 2.29117
\(736\) −2.94694 −0.108626
\(737\) 7.51405 0.276783
\(738\) 15.7047 0.578098
\(739\) −22.5901 −0.830989 −0.415495 0.909596i \(-0.636391\pi\)
−0.415495 + 0.909596i \(0.636391\pi\)
\(740\) 37.1832 1.36688
\(741\) 105.529 3.87669
\(742\) −1.23550 −0.0453566
\(743\) −17.9253 −0.657614 −0.328807 0.944397i \(-0.606647\pi\)
−0.328807 + 0.944397i \(0.606647\pi\)
\(744\) −13.3587 −0.489754
\(745\) 42.9921 1.57511
\(746\) 12.3032 0.450453
\(747\) −16.8310 −0.615813
\(748\) 5.99538 0.219213
\(749\) 4.11041 0.150191
\(750\) 45.3290 1.65518
\(751\) −7.23733 −0.264094 −0.132047 0.991243i \(-0.542155\pi\)
−0.132047 + 0.991243i \(0.542155\pi\)
\(752\) −7.31928 −0.266907
\(753\) 31.4551 1.14629
\(754\) −41.4026 −1.50780
\(755\) −14.8860 −0.541755
\(756\) 0.385904 0.0140352
\(757\) 14.5203 0.527749 0.263874 0.964557i \(-0.415000\pi\)
0.263874 + 0.964557i \(0.415000\pi\)
\(758\) −28.5227 −1.03599
\(759\) 15.6276 0.567247
\(760\) −33.2079 −1.20458
\(761\) 41.1224 1.49069 0.745343 0.666681i \(-0.232286\pi\)
0.745343 + 0.666681i \(0.232286\pi\)
\(762\) −29.6669 −1.07472
\(763\) −3.21548 −0.116408
\(764\) −19.5612 −0.707699
\(765\) −23.4581 −0.848131
\(766\) −16.0293 −0.579160
\(767\) 43.7477 1.57964
\(768\) −2.30611 −0.0832147
\(769\) −18.2255 −0.657227 −0.328614 0.944464i \(-0.606581\pi\)
−0.328614 + 0.944464i \(0.606581\pi\)
\(770\) 2.19044 0.0789380
\(771\) 55.5079 1.99907
\(772\) −5.83600 −0.210042
\(773\) 9.89491 0.355895 0.177948 0.984040i \(-0.443054\pi\)
0.177948 + 0.984040i \(0.443054\pi\)
\(774\) −7.18490 −0.258256
\(775\) −58.3000 −2.09420
\(776\) 7.83860 0.281389
\(777\) −5.42212 −0.194517
\(778\) 24.6747 0.884632
\(779\) −57.9632 −2.07675
\(780\) 47.8717 1.71408
\(781\) −29.4690 −1.05448
\(782\) 7.68329 0.274754
\(783\) −12.1722 −0.434999
\(784\) −6.93977 −0.247849
\(785\) 13.1169 0.468163
\(786\) 2.70518 0.0964905
\(787\) −26.8624 −0.957540 −0.478770 0.877940i \(-0.658917\pi\)
−0.478770 + 0.877940i \(0.658917\pi\)
\(788\) 5.29845 0.188749
\(789\) −63.0398 −2.24428
\(790\) −53.7759 −1.91326
\(791\) 0.197807 0.00703319
\(792\) 5.33070 0.189418
\(793\) 47.8957 1.70082
\(794\) 16.4833 0.584972
\(795\) −45.0591 −1.59808
\(796\) 8.35379 0.296092
\(797\) −34.4149 −1.21904 −0.609518 0.792772i \(-0.708637\pi\)
−0.609518 + 0.792772i \(0.708637\pi\)
\(798\) 4.84242 0.171420
\(799\) 19.0829 0.675104
\(800\) −10.0643 −0.355827
\(801\) −28.7440 −1.01562
\(802\) −6.14759 −0.217079
\(803\) −17.3935 −0.613803
\(804\) 7.53552 0.265757
\(805\) 2.80712 0.0989381
\(806\) −30.9819 −1.09129
\(807\) 74.9509 2.63840
\(808\) 2.14814 0.0755713
\(809\) 14.2937 0.502541 0.251270 0.967917i \(-0.419152\pi\)
0.251270 + 0.967917i \(0.419152\pi\)
\(810\) 41.0663 1.44292
\(811\) 36.8290 1.29324 0.646620 0.762812i \(-0.276182\pi\)
0.646620 + 0.762812i \(0.276182\pi\)
\(812\) −1.89985 −0.0666718
\(813\) 8.61800 0.302246
\(814\) 22.0300 0.772150
\(815\) 84.8349 2.97164
\(816\) 6.01252 0.210480
\(817\) 26.5182 0.927754
\(818\) −5.18329 −0.181230
\(819\) −3.04286 −0.106326
\(820\) −26.2943 −0.918235
\(821\) 24.3840 0.851008 0.425504 0.904957i \(-0.360097\pi\)
0.425504 + 0.904957i \(0.360097\pi\)
\(822\) 8.14435 0.284067
\(823\) −56.9478 −1.98507 −0.992537 0.121943i \(-0.961087\pi\)
−0.992537 + 0.121943i \(0.961087\pi\)
\(824\) 9.24718 0.322141
\(825\) 53.3711 1.85814
\(826\) 2.00746 0.0698486
\(827\) −23.0295 −0.800814 −0.400407 0.916337i \(-0.631131\pi\)
−0.400407 + 0.916337i \(0.631131\pi\)
\(828\) 6.83148 0.237410
\(829\) 11.1243 0.386364 0.193182 0.981163i \(-0.438119\pi\)
0.193182 + 0.981163i \(0.438119\pi\)
\(830\) 28.1800 0.978141
\(831\) −23.7686 −0.824525
\(832\) −5.34839 −0.185422
\(833\) 18.0934 0.626900
\(834\) −2.95387 −0.102284
\(835\) −0.865555 −0.0299538
\(836\) −19.6747 −0.680463
\(837\) −9.10852 −0.314837
\(838\) 24.2792 0.838710
\(839\) −27.2044 −0.939199 −0.469599 0.882880i \(-0.655602\pi\)
−0.469599 + 0.882880i \(0.655602\pi\)
\(840\) 2.19670 0.0757934
\(841\) 30.9252 1.06639
\(842\) 39.2970 1.35426
\(843\) 32.7695 1.12864
\(844\) 9.73855 0.335215
\(845\) 60.5685 2.08362
\(846\) 16.9673 0.583346
\(847\) −1.40188 −0.0481693
\(848\) 5.03416 0.172874
\(849\) −49.6310 −1.70333
\(850\) 26.2398 0.900016
\(851\) 28.2322 0.967786
\(852\) −29.5532 −1.01248
\(853\) −2.33799 −0.0800514 −0.0400257 0.999199i \(-0.512744\pi\)
−0.0400257 + 0.999199i \(0.512744\pi\)
\(854\) 2.19780 0.0752072
\(855\) 76.9811 2.63270
\(856\) −16.7483 −0.572444
\(857\) 24.7769 0.846363 0.423181 0.906045i \(-0.360913\pi\)
0.423181 + 0.906045i \(0.360913\pi\)
\(858\) 28.3625 0.968281
\(859\) −1.10000 −0.0375315 −0.0187657 0.999824i \(-0.505974\pi\)
−0.0187657 + 0.999824i \(0.505974\pi\)
\(860\) 12.0296 0.410207
\(861\) 3.83427 0.130671
\(862\) −6.91347 −0.235474
\(863\) −20.1234 −0.685007 −0.342504 0.939517i \(-0.611275\pi\)
−0.342504 + 0.939517i \(0.611275\pi\)
\(864\) −1.57240 −0.0534942
\(865\) 13.1270 0.446332
\(866\) −13.6592 −0.464159
\(867\) 23.5281 0.799054
\(868\) −1.42167 −0.0482547
\(869\) −31.8607 −1.08080
\(870\) −69.2883 −2.34909
\(871\) 17.4766 0.592170
\(872\) 13.1018 0.443682
\(873\) −18.1711 −0.614999
\(874\) −25.2138 −0.852869
\(875\) 4.82404 0.163082
\(876\) −17.4432 −0.589351
\(877\) 34.3113 1.15861 0.579305 0.815111i \(-0.303324\pi\)
0.579305 + 0.815111i \(0.303324\pi\)
\(878\) −25.1355 −0.848281
\(879\) 10.5658 0.356375
\(880\) −8.92516 −0.300867
\(881\) −30.3058 −1.02103 −0.510515 0.859869i \(-0.670545\pi\)
−0.510515 + 0.859869i \(0.670545\pi\)
\(882\) 16.0875 0.541694
\(883\) −28.2442 −0.950492 −0.475246 0.879853i \(-0.657641\pi\)
−0.475246 + 0.879853i \(0.657641\pi\)
\(884\) 13.9444 0.469000
\(885\) 73.2129 2.46103
\(886\) −10.0652 −0.338147
\(887\) 24.7531 0.831129 0.415564 0.909564i \(-0.363584\pi\)
0.415564 + 0.909564i \(0.363584\pi\)
\(888\) 22.0929 0.741390
\(889\) −3.15723 −0.105890
\(890\) 48.1259 1.61318
\(891\) 24.3306 0.815105
\(892\) −18.3042 −0.612871
\(893\) −62.6232 −2.09560
\(894\) 25.5443 0.854330
\(895\) −69.4600 −2.32179
\(896\) −0.245423 −0.00819901
\(897\) 36.3476 1.21361
\(898\) −6.76853 −0.225869
\(899\) 44.8424 1.49558
\(900\) 23.3307 0.777689
\(901\) −13.1251 −0.437261
\(902\) −15.5786 −0.518710
\(903\) −1.75418 −0.0583754
\(904\) −0.805981 −0.0268065
\(905\) −81.0767 −2.69508
\(906\) −8.84469 −0.293845
\(907\) −37.3213 −1.23923 −0.619617 0.784904i \(-0.712712\pi\)
−0.619617 + 0.784904i \(0.712712\pi\)
\(908\) −5.33077 −0.176908
\(909\) −4.97973 −0.165167
\(910\) 5.09464 0.168886
\(911\) −44.6928 −1.48074 −0.740369 0.672201i \(-0.765349\pi\)
−0.740369 + 0.672201i \(0.765349\pi\)
\(912\) −19.7309 −0.653356
\(913\) 16.6958 0.552550
\(914\) 32.9685 1.09050
\(915\) 80.1546 2.64983
\(916\) −17.6356 −0.582698
\(917\) 0.287893 0.00950705
\(918\) 4.09958 0.135306
\(919\) 58.7669 1.93854 0.969271 0.245996i \(-0.0791151\pi\)
0.969271 + 0.245996i \(0.0791151\pi\)
\(920\) −11.4379 −0.377096
\(921\) 67.7497 2.23243
\(922\) −13.2362 −0.435912
\(923\) −68.5405 −2.25604
\(924\) 1.30148 0.0428156
\(925\) 96.4177 3.17019
\(926\) 33.6467 1.10570
\(927\) −21.4364 −0.704065
\(928\) 7.74114 0.254115
\(929\) −33.9373 −1.11345 −0.556723 0.830698i \(-0.687941\pi\)
−0.556723 + 0.830698i \(0.687941\pi\)
\(930\) −51.8489 −1.70019
\(931\) −59.3761 −1.94597
\(932\) 20.1558 0.660226
\(933\) −16.3752 −0.536101
\(934\) 26.2198 0.857939
\(935\) 23.2697 0.761002
\(936\) 12.3984 0.405255
\(937\) 16.3375 0.533722 0.266861 0.963735i \(-0.414013\pi\)
0.266861 + 0.963735i \(0.414013\pi\)
\(938\) 0.801952 0.0261846
\(939\) −4.03453 −0.131662
\(940\) −28.4082 −0.926572
\(941\) −28.7689 −0.937839 −0.468919 0.883241i \(-0.655356\pi\)
−0.468919 + 0.883241i \(0.655356\pi\)
\(942\) 7.79359 0.253929
\(943\) −19.9645 −0.650132
\(944\) −8.17961 −0.266224
\(945\) 1.49780 0.0487235
\(946\) 7.12720 0.231725
\(947\) 20.8200 0.676560 0.338280 0.941046i \(-0.390155\pi\)
0.338280 + 0.941046i \(0.390155\pi\)
\(948\) −31.9517 −1.03774
\(949\) −40.4547 −1.31321
\(950\) −86.1094 −2.79376
\(951\) 56.7062 1.83883
\(952\) 0.639869 0.0207383
\(953\) 44.5829 1.44418 0.722091 0.691798i \(-0.243181\pi\)
0.722091 + 0.691798i \(0.243181\pi\)
\(954\) −11.6700 −0.377830
\(955\) −75.9224 −2.45679
\(956\) −20.4747 −0.662198
\(957\) −41.0513 −1.32700
\(958\) −17.1251 −0.553288
\(959\) 0.866745 0.0279886
\(960\) −8.95067 −0.288881
\(961\) 2.55585 0.0824468
\(962\) 51.2384 1.65199
\(963\) 38.8251 1.25112
\(964\) 12.6703 0.408084
\(965\) −22.6511 −0.729166
\(966\) 1.66789 0.0536635
\(967\) 20.2883 0.652429 0.326214 0.945296i \(-0.394227\pi\)
0.326214 + 0.945296i \(0.394227\pi\)
\(968\) 5.71211 0.183594
\(969\) 51.4426 1.65257
\(970\) 30.4238 0.976848
\(971\) −16.8673 −0.541297 −0.270648 0.962678i \(-0.587238\pi\)
−0.270648 + 0.962678i \(0.587238\pi\)
\(972\) 19.6829 0.631329
\(973\) −0.314360 −0.0100779
\(974\) 41.8693 1.34158
\(975\) 124.133 3.97544
\(976\) −8.95515 −0.286647
\(977\) −17.5910 −0.562784 −0.281392 0.959593i \(-0.590796\pi\)
−0.281392 + 0.959593i \(0.590796\pi\)
\(978\) 50.4058 1.61180
\(979\) 28.5132 0.911285
\(980\) −26.9352 −0.860412
\(981\) −30.3720 −0.969703
\(982\) −9.28697 −0.296359
\(983\) −44.0687 −1.40557 −0.702786 0.711401i \(-0.748061\pi\)
−0.702786 + 0.711401i \(0.748061\pi\)
\(984\) −15.6231 −0.498046
\(985\) 20.5647 0.655247
\(986\) −20.1828 −0.642750
\(987\) 4.14252 0.131858
\(988\) −45.7604 −1.45583
\(989\) 9.13374 0.290436
\(990\) 20.6899 0.657569
\(991\) −24.4886 −0.777907 −0.388954 0.921257i \(-0.627163\pi\)
−0.388954 + 0.921257i \(0.627163\pi\)
\(992\) 5.79274 0.183920
\(993\) 3.70762 0.117658
\(994\) −3.14514 −0.0997577
\(995\) 32.4234 1.02789
\(996\) 16.7435 0.530538
\(997\) 16.0599 0.508622 0.254311 0.967122i \(-0.418151\pi\)
0.254311 + 0.967122i \(0.418151\pi\)
\(998\) −15.5818 −0.493234
\(999\) 15.0639 0.476600
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.1.6 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.6 40 1.1 even 1 trivial