Properties

Label 4006.2.a.g.1.14
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 1.14
Character \(\chi\) = 4006.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.956879 q^{3} +1.00000 q^{4} -0.0953014 q^{5} +0.956879 q^{6} -4.20577 q^{7} -1.00000 q^{8} -2.08438 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.956879 q^{3} +1.00000 q^{4} -0.0953014 q^{5} +0.956879 q^{6} -4.20577 q^{7} -1.00000 q^{8} -2.08438 q^{9} +0.0953014 q^{10} -0.121483 q^{11} -0.956879 q^{12} -1.63495 q^{13} +4.20577 q^{14} +0.0911919 q^{15} +1.00000 q^{16} +3.22305 q^{17} +2.08438 q^{18} -1.33888 q^{19} -0.0953014 q^{20} +4.02442 q^{21} +0.121483 q^{22} +7.51615 q^{23} +0.956879 q^{24} -4.99092 q^{25} +1.63495 q^{26} +4.86514 q^{27} -4.20577 q^{28} +9.09309 q^{29} -0.0911919 q^{30} +1.34519 q^{31} -1.00000 q^{32} +0.116245 q^{33} -3.22305 q^{34} +0.400816 q^{35} -2.08438 q^{36} -0.847194 q^{37} +1.33888 q^{38} +1.56445 q^{39} +0.0953014 q^{40} -2.51290 q^{41} -4.02442 q^{42} +6.69337 q^{43} -0.121483 q^{44} +0.198645 q^{45} -7.51615 q^{46} +11.4944 q^{47} -0.956879 q^{48} +10.6885 q^{49} +4.99092 q^{50} -3.08407 q^{51} -1.63495 q^{52} +6.97986 q^{53} -4.86514 q^{54} +0.0115775 q^{55} +4.20577 q^{56} +1.28114 q^{57} -9.09309 q^{58} -3.92557 q^{59} +0.0911919 q^{60} -10.4678 q^{61} -1.34519 q^{62} +8.76644 q^{63} +1.00000 q^{64} +0.155813 q^{65} -0.116245 q^{66} -14.1662 q^{67} +3.22305 q^{68} -7.19205 q^{69} -0.400816 q^{70} +5.68177 q^{71} +2.08438 q^{72} +0.786531 q^{73} +0.847194 q^{74} +4.77571 q^{75} -1.33888 q^{76} +0.510931 q^{77} -1.56445 q^{78} -1.19208 q^{79} -0.0953014 q^{80} +1.59779 q^{81} +2.51290 q^{82} -11.7356 q^{83} +4.02442 q^{84} -0.307161 q^{85} -6.69337 q^{86} -8.70099 q^{87} +0.121483 q^{88} -5.77411 q^{89} -0.198645 q^{90} +6.87624 q^{91} +7.51615 q^{92} -1.28719 q^{93} -11.4944 q^{94} +0.127597 q^{95} +0.956879 q^{96} +4.53164 q^{97} -10.6885 q^{98} +0.253217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + O(q^{10}) \) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + 23q^{10} - 28q^{11} - q^{12} - 12q^{13} - 12q^{14} - 14q^{15} + 40q^{16} - 10q^{17} - 29q^{18} + 3q^{19} - 23q^{20} - 40q^{21} + 28q^{22} - 10q^{23} + q^{24} + 43q^{25} + 12q^{26} - 7q^{27} + 12q^{28} - 37q^{29} + 14q^{30} - 16q^{31} - 40q^{32} - 11q^{33} + 10q^{34} - 24q^{35} + 29q^{36} - 17q^{37} - 3q^{38} - 10q^{39} + 23q^{40} - 58q^{41} + 40q^{42} + 37q^{43} - 28q^{44} - 66q^{45} + 10q^{46} - 34q^{47} - q^{48} + 28q^{49} - 43q^{50} - 7q^{51} - 12q^{52} - 43q^{53} + 7q^{54} + 28q^{55} - 12q^{56} - 25q^{57} + 37q^{58} - 92q^{59} - 14q^{60} - 37q^{61} + 16q^{62} + 14q^{63} + 40q^{64} - 54q^{65} + 11q^{66} - 10q^{67} - 10q^{68} - 49q^{69} + 24q^{70} - 87q^{71} - 29q^{72} + 12q^{73} + 17q^{74} - 31q^{75} + 3q^{76} - 53q^{77} + 10q^{78} + 14q^{79} - 23q^{80} - 4q^{81} + 58q^{82} - 42q^{83} - 40q^{84} - 24q^{85} - 37q^{86} + 24q^{87} + 28q^{88} - 118q^{89} + 66q^{90} - 35q^{91} - 10q^{92} - 22q^{93} + 34q^{94} - 18q^{95} + q^{96} + 2q^{97} - 28q^{98} - 48q^{99} + O(q^{100}) \)

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
\(3\) −0.956879 −0.552454 −0.276227 0.961092i \(-0.589084\pi\)
−0.276227 + 0.961092i \(0.589084\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.0953014 −0.0426201 −0.0213100 0.999773i \(-0.506784\pi\)
−0.0213100 + 0.999773i \(0.506784\pi\)
\(6\) 0.956879 0.390644
\(7\) −4.20577 −1.58963 −0.794817 0.606850i \(-0.792433\pi\)
−0.794817 + 0.606850i \(0.792433\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.08438 −0.694794
\(10\) 0.0953014 0.0301369
\(11\) −0.121483 −0.0366286 −0.0183143 0.999832i \(-0.505830\pi\)
−0.0183143 + 0.999832i \(0.505830\pi\)
\(12\) −0.956879 −0.276227
\(13\) −1.63495 −0.453454 −0.226727 0.973958i \(-0.572802\pi\)
−0.226727 + 0.973958i \(0.572802\pi\)
\(14\) 4.20577 1.12404
\(15\) 0.0911919 0.0235457
\(16\) 1.00000 0.250000
\(17\) 3.22305 0.781703 0.390852 0.920454i \(-0.372181\pi\)
0.390852 + 0.920454i \(0.372181\pi\)
\(18\) 2.08438 0.491294
\(19\) −1.33888 −0.307159 −0.153580 0.988136i \(-0.549080\pi\)
−0.153580 + 0.988136i \(0.549080\pi\)
\(20\) −0.0953014 −0.0213100
\(21\) 4.02442 0.878200
\(22\) 0.121483 0.0259003
\(23\) 7.51615 1.56723 0.783613 0.621249i \(-0.213374\pi\)
0.783613 + 0.621249i \(0.213374\pi\)
\(24\) 0.956879 0.195322
\(25\) −4.99092 −0.998184
\(26\) 1.63495 0.320640
\(27\) 4.86514 0.936297
\(28\) −4.20577 −0.794817
\(29\) 9.09309 1.68854 0.844272 0.535914i \(-0.180033\pi\)
0.844272 + 0.535914i \(0.180033\pi\)
\(30\) −0.0911919 −0.0166493
\(31\) 1.34519 0.241604 0.120802 0.992677i \(-0.461453\pi\)
0.120802 + 0.992677i \(0.461453\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.116245 0.0202356
\(34\) −3.22305 −0.552748
\(35\) 0.400816 0.0677503
\(36\) −2.08438 −0.347397
\(37\) −0.847194 −0.139278 −0.0696389 0.997572i \(-0.522185\pi\)
−0.0696389 + 0.997572i \(0.522185\pi\)
\(38\) 1.33888 0.217194
\(39\) 1.56445 0.250513
\(40\) 0.0953014 0.0150685
\(41\) −2.51290 −0.392449 −0.196225 0.980559i \(-0.562868\pi\)
−0.196225 + 0.980559i \(0.562868\pi\)
\(42\) −4.02442 −0.620981
\(43\) 6.69337 1.02073 0.510365 0.859958i \(-0.329510\pi\)
0.510365 + 0.859958i \(0.329510\pi\)
\(44\) −0.121483 −0.0183143
\(45\) 0.198645 0.0296122
\(46\) −7.51615 −1.10820
\(47\) 11.4944 1.67664 0.838319 0.545181i \(-0.183539\pi\)
0.838319 + 0.545181i \(0.183539\pi\)
\(48\) −0.956879 −0.138114
\(49\) 10.6885 1.52693
\(50\) 4.99092 0.705822
\(51\) −3.08407 −0.431856
\(52\) −1.63495 −0.226727
\(53\) 6.97986 0.958757 0.479379 0.877608i \(-0.340862\pi\)
0.479379 + 0.877608i \(0.340862\pi\)
\(54\) −4.86514 −0.662062
\(55\) 0.0115775 0.00156111
\(56\) 4.20577 0.562020
\(57\) 1.28114 0.169692
\(58\) −9.09309 −1.19398
\(59\) −3.92557 −0.511066 −0.255533 0.966800i \(-0.582251\pi\)
−0.255533 + 0.966800i \(0.582251\pi\)
\(60\) 0.0911919 0.0117728
\(61\) −10.4678 −1.34026 −0.670130 0.742243i \(-0.733762\pi\)
−0.670130 + 0.742243i \(0.733762\pi\)
\(62\) −1.34519 −0.170840
\(63\) 8.76644 1.10447
\(64\) 1.00000 0.125000
\(65\) 0.155813 0.0193262
\(66\) −0.116245 −0.0143087
\(67\) −14.1662 −1.73068 −0.865339 0.501187i \(-0.832897\pi\)
−0.865339 + 0.501187i \(0.832897\pi\)
\(68\) 3.22305 0.390852
\(69\) −7.19205 −0.865821
\(70\) −0.400816 −0.0479067
\(71\) 5.68177 0.674302 0.337151 0.941451i \(-0.390537\pi\)
0.337151 + 0.941451i \(0.390537\pi\)
\(72\) 2.08438 0.245647
\(73\) 0.786531 0.0920565 0.0460283 0.998940i \(-0.485344\pi\)
0.0460283 + 0.998940i \(0.485344\pi\)
\(74\) 0.847194 0.0984843
\(75\) 4.77571 0.551451
\(76\) −1.33888 −0.153580
\(77\) 0.510931 0.0582260
\(78\) −1.56445 −0.177139
\(79\) −1.19208 −0.134119 −0.0670595 0.997749i \(-0.521362\pi\)
−0.0670595 + 0.997749i \(0.521362\pi\)
\(80\) −0.0953014 −0.0106550
\(81\) 1.59779 0.177533
\(82\) 2.51290 0.277504
\(83\) −11.7356 −1.28815 −0.644075 0.764963i \(-0.722757\pi\)
−0.644075 + 0.764963i \(0.722757\pi\)
\(84\) 4.02442 0.439100
\(85\) −0.307161 −0.0333163
\(86\) −6.69337 −0.721765
\(87\) −8.70099 −0.932844
\(88\) 0.121483 0.0129502
\(89\) −5.77411 −0.612055 −0.306027 0.952023i \(-0.599000\pi\)
−0.306027 + 0.952023i \(0.599000\pi\)
\(90\) −0.198645 −0.0209390
\(91\) 6.87624 0.720825
\(92\) 7.51615 0.783613
\(93\) −1.28719 −0.133475
\(94\) −11.4944 −1.18556
\(95\) 0.127597 0.0130912
\(96\) 0.956879 0.0976611
\(97\) 4.53164 0.460119 0.230059 0.973177i \(-0.426108\pi\)
0.230059 + 0.973177i \(0.426108\pi\)
\(98\) −10.6885 −1.07971
\(99\) 0.253217 0.0254493
\(100\) −4.99092 −0.499092
\(101\) −18.8485 −1.87549 −0.937746 0.347322i \(-0.887091\pi\)
−0.937746 + 0.347322i \(0.887091\pi\)
\(102\) 3.08407 0.305368
\(103\) −16.0310 −1.57958 −0.789792 0.613374i \(-0.789812\pi\)
−0.789792 + 0.613374i \(0.789812\pi\)
\(104\) 1.63495 0.160320
\(105\) −0.383533 −0.0374290
\(106\) −6.97986 −0.677944
\(107\) −7.85447 −0.759321 −0.379660 0.925126i \(-0.623959\pi\)
−0.379660 + 0.925126i \(0.623959\pi\)
\(108\) 4.86514 0.468148
\(109\) 12.9103 1.23659 0.618293 0.785947i \(-0.287824\pi\)
0.618293 + 0.785947i \(0.287824\pi\)
\(110\) −0.0115775 −0.00110387
\(111\) 0.810662 0.0769446
\(112\) −4.20577 −0.397408
\(113\) −5.40353 −0.508321 −0.254160 0.967162i \(-0.581799\pi\)
−0.254160 + 0.967162i \(0.581799\pi\)
\(114\) −1.28114 −0.119990
\(115\) −0.716300 −0.0667953
\(116\) 9.09309 0.844272
\(117\) 3.40786 0.315057
\(118\) 3.92557 0.361378
\(119\) −13.5554 −1.24262
\(120\) −0.0911919 −0.00832465
\(121\) −10.9852 −0.998658
\(122\) 10.4678 0.947708
\(123\) 2.40454 0.216810
\(124\) 1.34519 0.120802
\(125\) 0.952148 0.0851627
\(126\) −8.76644 −0.780977
\(127\) −11.4199 −1.01335 −0.506675 0.862137i \(-0.669126\pi\)
−0.506675 + 0.862137i \(0.669126\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −6.40475 −0.563907
\(130\) −0.155813 −0.0136657
\(131\) 2.73835 0.239251 0.119625 0.992819i \(-0.461831\pi\)
0.119625 + 0.992819i \(0.461831\pi\)
\(132\) 0.116245 0.0101178
\(133\) 5.63101 0.488271
\(134\) 14.1662 1.22377
\(135\) −0.463655 −0.0399050
\(136\) −3.22305 −0.276374
\(137\) −12.1095 −1.03458 −0.517292 0.855809i \(-0.673060\pi\)
−0.517292 + 0.855809i \(0.673060\pi\)
\(138\) 7.19205 0.612228
\(139\) 16.1577 1.37048 0.685241 0.728316i \(-0.259697\pi\)
0.685241 + 0.728316i \(0.259697\pi\)
\(140\) 0.400816 0.0338752
\(141\) −10.9988 −0.926266
\(142\) −5.68177 −0.476803
\(143\) 0.198619 0.0166094
\(144\) −2.08438 −0.173699
\(145\) −0.866584 −0.0719659
\(146\) −0.786531 −0.0650938
\(147\) −10.2276 −0.843562
\(148\) −0.847194 −0.0696389
\(149\) −4.96833 −0.407021 −0.203511 0.979073i \(-0.565235\pi\)
−0.203511 + 0.979073i \(0.565235\pi\)
\(150\) −4.77571 −0.389935
\(151\) 14.1500 1.15151 0.575754 0.817623i \(-0.304709\pi\)
0.575754 + 0.817623i \(0.304709\pi\)
\(152\) 1.33888 0.108597
\(153\) −6.71806 −0.543123
\(154\) −0.510931 −0.0411720
\(155\) −0.128199 −0.0102972
\(156\) 1.56445 0.125256
\(157\) −3.45379 −0.275642 −0.137821 0.990457i \(-0.544010\pi\)
−0.137821 + 0.990457i \(0.544010\pi\)
\(158\) 1.19208 0.0948365
\(159\) −6.67888 −0.529670
\(160\) 0.0953014 0.00753424
\(161\) −31.6113 −2.49132
\(162\) −1.59779 −0.125535
\(163\) 7.63173 0.597764 0.298882 0.954290i \(-0.403386\pi\)
0.298882 + 0.954290i \(0.403386\pi\)
\(164\) −2.51290 −0.196225
\(165\) −0.0110783 −0.000862444 0
\(166\) 11.7356 0.910859
\(167\) 13.2615 1.02621 0.513103 0.858327i \(-0.328496\pi\)
0.513103 + 0.858327i \(0.328496\pi\)
\(168\) −4.02442 −0.310491
\(169\) −10.3269 −0.794380
\(170\) 0.307161 0.0235582
\(171\) 2.79073 0.213412
\(172\) 6.69337 0.510365
\(173\) 23.1657 1.76126 0.880628 0.473809i \(-0.157121\pi\)
0.880628 + 0.473809i \(0.157121\pi\)
\(174\) 8.70099 0.659620
\(175\) 20.9907 1.58675
\(176\) −0.121483 −0.00915714
\(177\) 3.75630 0.282341
\(178\) 5.77411 0.432788
\(179\) 0.199393 0.0149033 0.00745165 0.999972i \(-0.497628\pi\)
0.00745165 + 0.999972i \(0.497628\pi\)
\(180\) 0.198645 0.0148061
\(181\) −23.4780 −1.74511 −0.872554 0.488518i \(-0.837538\pi\)
−0.872554 + 0.488518i \(0.837538\pi\)
\(182\) −6.87624 −0.509701
\(183\) 10.0164 0.740433
\(184\) −7.51615 −0.554098
\(185\) 0.0807387 0.00593603
\(186\) 1.28719 0.0943812
\(187\) −0.391546 −0.0286327
\(188\) 11.4944 0.838319
\(189\) −20.4617 −1.48837
\(190\) −0.127597 −0.00925684
\(191\) 19.7628 1.42999 0.714994 0.699130i \(-0.246429\pi\)
0.714994 + 0.699130i \(0.246429\pi\)
\(192\) −0.956879 −0.0690568
\(193\) 9.71439 0.699257 0.349628 0.936888i \(-0.386308\pi\)
0.349628 + 0.936888i \(0.386308\pi\)
\(194\) −4.53164 −0.325353
\(195\) −0.149094 −0.0106769
\(196\) 10.6885 0.763467
\(197\) −1.91169 −0.136202 −0.0681011 0.997678i \(-0.521694\pi\)
−0.0681011 + 0.997678i \(0.521694\pi\)
\(198\) −0.253217 −0.0179954
\(199\) 10.3431 0.733205 0.366602 0.930378i \(-0.380521\pi\)
0.366602 + 0.930378i \(0.380521\pi\)
\(200\) 4.99092 0.352911
\(201\) 13.5554 0.956121
\(202\) 18.8485 1.32617
\(203\) −38.2435 −2.68417
\(204\) −3.08407 −0.215928
\(205\) 0.239483 0.0167262
\(206\) 16.0310 1.11693
\(207\) −15.6665 −1.08890
\(208\) −1.63495 −0.113363
\(209\) 0.162651 0.0112508
\(210\) 0.383533 0.0264663
\(211\) 26.4053 1.81782 0.908909 0.416995i \(-0.136917\pi\)
0.908909 + 0.416995i \(0.136917\pi\)
\(212\) 6.97986 0.479379
\(213\) −5.43676 −0.372521
\(214\) 7.85447 0.536921
\(215\) −0.637888 −0.0435036
\(216\) −4.86514 −0.331031
\(217\) −5.65758 −0.384062
\(218\) −12.9103 −0.874399
\(219\) −0.752615 −0.0508570
\(220\) 0.0115775 0.000780556 0
\(221\) −5.26952 −0.354466
\(222\) −0.810662 −0.0544081
\(223\) −2.87973 −0.192841 −0.0964204 0.995341i \(-0.530739\pi\)
−0.0964204 + 0.995341i \(0.530739\pi\)
\(224\) 4.20577 0.281010
\(225\) 10.4030 0.693532
\(226\) 5.40353 0.359437
\(227\) −17.7575 −1.17861 −0.589305 0.807911i \(-0.700598\pi\)
−0.589305 + 0.807911i \(0.700598\pi\)
\(228\) 1.28114 0.0848458
\(229\) −7.68778 −0.508023 −0.254011 0.967201i \(-0.581750\pi\)
−0.254011 + 0.967201i \(0.581750\pi\)
\(230\) 0.716300 0.0472314
\(231\) −0.488899 −0.0321672
\(232\) −9.09309 −0.596991
\(233\) −8.84240 −0.579285 −0.289643 0.957135i \(-0.593536\pi\)
−0.289643 + 0.957135i \(0.593536\pi\)
\(234\) −3.40786 −0.222779
\(235\) −1.09544 −0.0714584
\(236\) −3.92557 −0.255533
\(237\) 1.14067 0.0740947
\(238\) 13.5554 0.878666
\(239\) −20.4693 −1.32405 −0.662025 0.749481i \(-0.730303\pi\)
−0.662025 + 0.749481i \(0.730303\pi\)
\(240\) 0.0911919 0.00588641
\(241\) −30.2979 −1.95166 −0.975828 0.218538i \(-0.929871\pi\)
−0.975828 + 0.218538i \(0.929871\pi\)
\(242\) 10.9852 0.706158
\(243\) −16.1243 −1.03438
\(244\) −10.4678 −0.670130
\(245\) −1.01863 −0.0650781
\(246\) −2.40454 −0.153308
\(247\) 2.18900 0.139283
\(248\) −1.34519 −0.0854199
\(249\) 11.2296 0.711644
\(250\) −0.952148 −0.0602192
\(251\) 12.1789 0.768727 0.384363 0.923182i \(-0.374421\pi\)
0.384363 + 0.923182i \(0.374421\pi\)
\(252\) 8.76644 0.552234
\(253\) −0.913087 −0.0574053
\(254\) 11.4199 0.716547
\(255\) 0.293916 0.0184057
\(256\) 1.00000 0.0625000
\(257\) 12.0370 0.750845 0.375423 0.926854i \(-0.377498\pi\)
0.375423 + 0.926854i \(0.377498\pi\)
\(258\) 6.40475 0.398742
\(259\) 3.56311 0.221401
\(260\) 0.155813 0.00966312
\(261\) −18.9535 −1.17319
\(262\) −2.73835 −0.169176
\(263\) 0.138602 0.00854655 0.00427328 0.999991i \(-0.498640\pi\)
0.00427328 + 0.999991i \(0.498640\pi\)
\(264\) −0.116245 −0.00715437
\(265\) −0.665190 −0.0408623
\(266\) −5.63101 −0.345260
\(267\) 5.52513 0.338132
\(268\) −14.1662 −0.865339
\(269\) −19.3871 −1.18205 −0.591027 0.806652i \(-0.701277\pi\)
−0.591027 + 0.806652i \(0.701277\pi\)
\(270\) 0.463655 0.0282171
\(271\) −8.81160 −0.535267 −0.267633 0.963521i \(-0.586242\pi\)
−0.267633 + 0.963521i \(0.586242\pi\)
\(272\) 3.22305 0.195426
\(273\) −6.57973 −0.398223
\(274\) 12.1095 0.731561
\(275\) 0.606313 0.0365620
\(276\) −7.19205 −0.432911
\(277\) 25.6127 1.53892 0.769458 0.638698i \(-0.220527\pi\)
0.769458 + 0.638698i \(0.220527\pi\)
\(278\) −16.1577 −0.969077
\(279\) −2.80390 −0.167865
\(280\) −0.400816 −0.0239534
\(281\) −13.4325 −0.801316 −0.400658 0.916228i \(-0.631219\pi\)
−0.400658 + 0.916228i \(0.631219\pi\)
\(282\) 10.9988 0.654969
\(283\) 9.19969 0.546865 0.273432 0.961891i \(-0.411841\pi\)
0.273432 + 0.961891i \(0.411841\pi\)
\(284\) 5.68177 0.337151
\(285\) −0.122095 −0.00723227
\(286\) −0.198619 −0.0117446
\(287\) 10.5687 0.623850
\(288\) 2.08438 0.122823
\(289\) −6.61198 −0.388940
\(290\) 0.866584 0.0508876
\(291\) −4.33624 −0.254195
\(292\) 0.786531 0.0460283
\(293\) −6.94996 −0.406021 −0.203010 0.979177i \(-0.565073\pi\)
−0.203010 + 0.979177i \(0.565073\pi\)
\(294\) 10.2276 0.596488
\(295\) 0.374112 0.0217817
\(296\) 0.847194 0.0492421
\(297\) −0.591033 −0.0342952
\(298\) 4.96833 0.287808
\(299\) −12.2885 −0.710665
\(300\) 4.77571 0.275725
\(301\) −28.1508 −1.62259
\(302\) −14.1500 −0.814239
\(303\) 18.0357 1.03612
\(304\) −1.33888 −0.0767898
\(305\) 0.997593 0.0571220
\(306\) 6.71806 0.384046
\(307\) 26.4614 1.51023 0.755116 0.655591i \(-0.227581\pi\)
0.755116 + 0.655591i \(0.227581\pi\)
\(308\) 0.510931 0.0291130
\(309\) 15.3398 0.872649
\(310\) 0.128199 0.00728121
\(311\) −5.51240 −0.312580 −0.156290 0.987711i \(-0.549953\pi\)
−0.156290 + 0.987711i \(0.549953\pi\)
\(312\) −1.56445 −0.0885696
\(313\) 6.03203 0.340950 0.170475 0.985362i \(-0.445470\pi\)
0.170475 + 0.985362i \(0.445470\pi\)
\(314\) 3.45379 0.194908
\(315\) −0.835454 −0.0470725
\(316\) −1.19208 −0.0670595
\(317\) 26.5260 1.48985 0.744923 0.667150i \(-0.232486\pi\)
0.744923 + 0.667150i \(0.232486\pi\)
\(318\) 6.67888 0.374533
\(319\) −1.10466 −0.0618490
\(320\) −0.0953014 −0.00532751
\(321\) 7.51578 0.419490
\(322\) 31.6113 1.76163
\(323\) −4.31526 −0.240107
\(324\) 1.59779 0.0887664
\(325\) 8.15991 0.452630
\(326\) −7.63173 −0.422683
\(327\) −12.3536 −0.683158
\(328\) 2.51290 0.138752
\(329\) −48.3430 −2.66524
\(330\) 0.0110783 0.000609840 0
\(331\) −31.7469 −1.74497 −0.872483 0.488645i \(-0.837491\pi\)
−0.872483 + 0.488645i \(0.837491\pi\)
\(332\) −11.7356 −0.644075
\(333\) 1.76588 0.0967694
\(334\) −13.2615 −0.725638
\(335\) 1.35006 0.0737616
\(336\) 4.02442 0.219550
\(337\) 31.0606 1.69198 0.845989 0.533200i \(-0.179011\pi\)
0.845989 + 0.533200i \(0.179011\pi\)
\(338\) 10.3269 0.561711
\(339\) 5.17052 0.280824
\(340\) −0.307161 −0.0166581
\(341\) −0.163419 −0.00884961
\(342\) −2.79073 −0.150905
\(343\) −15.5132 −0.837633
\(344\) −6.69337 −0.360882
\(345\) 0.685413 0.0369014
\(346\) −23.1657 −1.24540
\(347\) 6.01579 0.322945 0.161472 0.986877i \(-0.448376\pi\)
0.161472 + 0.986877i \(0.448376\pi\)
\(348\) −8.70099 −0.466422
\(349\) 18.7258 1.00237 0.501184 0.865341i \(-0.332898\pi\)
0.501184 + 0.865341i \(0.332898\pi\)
\(350\) −20.9907 −1.12200
\(351\) −7.95427 −0.424567
\(352\) 0.121483 0.00647508
\(353\) 17.2725 0.919324 0.459662 0.888094i \(-0.347971\pi\)
0.459662 + 0.888094i \(0.347971\pi\)
\(354\) −3.75630 −0.199645
\(355\) −0.541480 −0.0287388
\(356\) −5.77411 −0.306027
\(357\) 12.9709 0.686492
\(358\) −0.199393 −0.0105382
\(359\) 1.11572 0.0588852 0.0294426 0.999566i \(-0.490627\pi\)
0.0294426 + 0.999566i \(0.490627\pi\)
\(360\) −0.198645 −0.0104695
\(361\) −17.2074 −0.905653
\(362\) 23.4780 1.23398
\(363\) 10.5116 0.551713
\(364\) 6.87624 0.360413
\(365\) −0.0749575 −0.00392346
\(366\) −10.0164 −0.523565
\(367\) −9.30017 −0.485465 −0.242733 0.970093i \(-0.578044\pi\)
−0.242733 + 0.970093i \(0.578044\pi\)
\(368\) 7.51615 0.391807
\(369\) 5.23785 0.272671
\(370\) −0.0807387 −0.00419741
\(371\) −29.3557 −1.52407
\(372\) −1.28719 −0.0667376
\(373\) −34.6933 −1.79635 −0.898176 0.439635i \(-0.855108\pi\)
−0.898176 + 0.439635i \(0.855108\pi\)
\(374\) 0.391546 0.0202464
\(375\) −0.911091 −0.0470485
\(376\) −11.4944 −0.592781
\(377\) −14.8668 −0.765677
\(378\) 20.4617 1.05244
\(379\) 23.6958 1.21717 0.608587 0.793487i \(-0.291737\pi\)
0.608587 + 0.793487i \(0.291737\pi\)
\(380\) 0.127597 0.00654558
\(381\) 10.9274 0.559830
\(382\) −19.7628 −1.01115
\(383\) 1.12378 0.0574225 0.0287112 0.999588i \(-0.490860\pi\)
0.0287112 + 0.999588i \(0.490860\pi\)
\(384\) 0.956879 0.0488305
\(385\) −0.0486924 −0.00248160
\(386\) −9.71439 −0.494449
\(387\) −13.9515 −0.709197
\(388\) 4.53164 0.230059
\(389\) −28.5254 −1.44629 −0.723147 0.690694i \(-0.757305\pi\)
−0.723147 + 0.690694i \(0.757305\pi\)
\(390\) 0.149094 0.00754969
\(391\) 24.2249 1.22511
\(392\) −10.6885 −0.539853
\(393\) −2.62027 −0.132175
\(394\) 1.91169 0.0963095
\(395\) 0.113607 0.00571616
\(396\) 0.253217 0.0127247
\(397\) −14.8873 −0.747171 −0.373586 0.927596i \(-0.621872\pi\)
−0.373586 + 0.927596i \(0.621872\pi\)
\(398\) −10.3431 −0.518454
\(399\) −5.38820 −0.269747
\(400\) −4.99092 −0.249546
\(401\) 2.77313 0.138484 0.0692419 0.997600i \(-0.477942\pi\)
0.0692419 + 0.997600i \(0.477942\pi\)
\(402\) −13.5554 −0.676080
\(403\) −2.19933 −0.109556
\(404\) −18.8485 −0.937746
\(405\) −0.152272 −0.00756646
\(406\) 38.2435 1.89799
\(407\) 0.102920 0.00510155
\(408\) 3.08407 0.152684
\(409\) −37.2648 −1.84263 −0.921314 0.388820i \(-0.872883\pi\)
−0.921314 + 0.388820i \(0.872883\pi\)
\(410\) −0.239483 −0.0118272
\(411\) 11.5873 0.571560
\(412\) −16.0310 −0.789792
\(413\) 16.5101 0.812407
\(414\) 15.6665 0.769968
\(415\) 1.11842 0.0549010
\(416\) 1.63495 0.0801601
\(417\) −15.4610 −0.757129
\(418\) −0.162651 −0.00795552
\(419\) −29.5915 −1.44564 −0.722821 0.691036i \(-0.757155\pi\)
−0.722821 + 0.691036i \(0.757155\pi\)
\(420\) −0.383533 −0.0187145
\(421\) −24.0854 −1.17385 −0.586925 0.809641i \(-0.699662\pi\)
−0.586925 + 0.809641i \(0.699662\pi\)
\(422\) −26.4053 −1.28539
\(423\) −23.9588 −1.16492
\(424\) −6.97986 −0.338972
\(425\) −16.0860 −0.780283
\(426\) 5.43676 0.263412
\(427\) 44.0251 2.13052
\(428\) −7.85447 −0.379660
\(429\) −0.190055 −0.00917592
\(430\) 0.637888 0.0307617
\(431\) 34.2509 1.64981 0.824904 0.565274i \(-0.191229\pi\)
0.824904 + 0.565274i \(0.191229\pi\)
\(432\) 4.86514 0.234074
\(433\) −40.1135 −1.92773 −0.963865 0.266390i \(-0.914169\pi\)
−0.963865 + 0.266390i \(0.914169\pi\)
\(434\) 5.65758 0.271573
\(435\) 0.829217 0.0397579
\(436\) 12.9103 0.618293
\(437\) −10.0632 −0.481388
\(438\) 0.752615 0.0359613
\(439\) −30.1300 −1.43803 −0.719014 0.694995i \(-0.755406\pi\)
−0.719014 + 0.694995i \(0.755406\pi\)
\(440\) −0.0115775 −0.000551937 0
\(441\) −22.2790 −1.06090
\(442\) 5.26952 0.250646
\(443\) 11.0205 0.523599 0.261800 0.965122i \(-0.415684\pi\)
0.261800 + 0.965122i \(0.415684\pi\)
\(444\) 0.810662 0.0384723
\(445\) 0.550281 0.0260858
\(446\) 2.87973 0.136359
\(447\) 4.75409 0.224861
\(448\) −4.20577 −0.198704
\(449\) −6.50049 −0.306777 −0.153389 0.988166i \(-0.549019\pi\)
−0.153389 + 0.988166i \(0.549019\pi\)
\(450\) −10.4030 −0.490401
\(451\) 0.305275 0.0143749
\(452\) −5.40353 −0.254160
\(453\) −13.5398 −0.636156
\(454\) 17.7575 0.833403
\(455\) −0.655315 −0.0307216
\(456\) −1.28114 −0.0599950
\(457\) 8.73969 0.408826 0.204413 0.978885i \(-0.434472\pi\)
0.204413 + 0.978885i \(0.434472\pi\)
\(458\) 7.68778 0.359226
\(459\) 15.6806 0.731906
\(460\) −0.716300 −0.0333977
\(461\) −25.5346 −1.18927 −0.594633 0.803997i \(-0.702703\pi\)
−0.594633 + 0.803997i \(0.702703\pi\)
\(462\) 0.488899 0.0227457
\(463\) −14.6280 −0.679820 −0.339910 0.940458i \(-0.610397\pi\)
−0.339910 + 0.940458i \(0.610397\pi\)
\(464\) 9.09309 0.422136
\(465\) 0.122671 0.00568873
\(466\) 8.84240 0.409616
\(467\) 1.24904 0.0577987 0.0288993 0.999582i \(-0.490800\pi\)
0.0288993 + 0.999582i \(0.490800\pi\)
\(468\) 3.40786 0.157529
\(469\) 59.5799 2.75114
\(470\) 1.09544 0.0505287
\(471\) 3.30486 0.152280
\(472\) 3.92557 0.180689
\(473\) −0.813132 −0.0373879
\(474\) −1.14067 −0.0523928
\(475\) 6.68222 0.306601
\(476\) −13.5554 −0.621311
\(477\) −14.5487 −0.666139
\(478\) 20.4693 0.936245
\(479\) 11.4826 0.524655 0.262327 0.964979i \(-0.415510\pi\)
0.262327 + 0.964979i \(0.415510\pi\)
\(480\) −0.0911919 −0.00416232
\(481\) 1.38512 0.0631560
\(482\) 30.2979 1.38003
\(483\) 30.2482 1.37634
\(484\) −10.9852 −0.499329
\(485\) −0.431872 −0.0196103
\(486\) 16.1243 0.731414
\(487\) −21.9886 −0.996400 −0.498200 0.867062i \(-0.666005\pi\)
−0.498200 + 0.867062i \(0.666005\pi\)
\(488\) 10.4678 0.473854
\(489\) −7.30265 −0.330237
\(490\) 1.01863 0.0460171
\(491\) −23.7027 −1.06969 −0.534845 0.844950i \(-0.679630\pi\)
−0.534845 + 0.844950i \(0.679630\pi\)
\(492\) 2.40454 0.108405
\(493\) 29.3074 1.31994
\(494\) −2.18900 −0.0984876
\(495\) −0.0241320 −0.00108465
\(496\) 1.34519 0.0604010
\(497\) −23.8962 −1.07189
\(498\) −11.2296 −0.503208
\(499\) −14.8704 −0.665692 −0.332846 0.942981i \(-0.608009\pi\)
−0.332846 + 0.942981i \(0.608009\pi\)
\(500\) 0.952148 0.0425814
\(501\) −12.6897 −0.566933
\(502\) −12.1789 −0.543572
\(503\) −24.9490 −1.11242 −0.556210 0.831042i \(-0.687745\pi\)
−0.556210 + 0.831042i \(0.687745\pi\)
\(504\) −8.76644 −0.390488
\(505\) 1.79628 0.0799336
\(506\) 0.913087 0.0405917
\(507\) 9.88163 0.438859
\(508\) −11.4199 −0.506675
\(509\) −10.6418 −0.471689 −0.235845 0.971791i \(-0.575786\pi\)
−0.235845 + 0.971791i \(0.575786\pi\)
\(510\) −0.293916 −0.0130148
\(511\) −3.30797 −0.146336
\(512\) −1.00000 −0.0441942
\(513\) −6.51382 −0.287592
\(514\) −12.0370 −0.530928
\(515\) 1.52778 0.0673220
\(516\) −6.40475 −0.281953
\(517\) −1.39638 −0.0614128
\(518\) −3.56311 −0.156554
\(519\) −22.1668 −0.973013
\(520\) −0.155813 −0.00683286
\(521\) −28.6167 −1.25372 −0.626861 0.779131i \(-0.715661\pi\)
−0.626861 + 0.779131i \(0.715661\pi\)
\(522\) 18.9535 0.829571
\(523\) 32.4165 1.41747 0.708737 0.705473i \(-0.249265\pi\)
0.708737 + 0.705473i \(0.249265\pi\)
\(524\) 2.73835 0.119625
\(525\) −20.0855 −0.876605
\(526\) −0.138602 −0.00604333
\(527\) 4.33562 0.188863
\(528\) 0.116245 0.00505890
\(529\) 33.4926 1.45620
\(530\) 0.665190 0.0288940
\(531\) 8.18239 0.355085
\(532\) 5.63101 0.244135
\(533\) 4.10847 0.177958
\(534\) −5.52513 −0.239096
\(535\) 0.748542 0.0323623
\(536\) 14.1662 0.611887
\(537\) −0.190795 −0.00823340
\(538\) 19.3871 0.835838
\(539\) −1.29848 −0.0559294
\(540\) −0.463655 −0.0199525
\(541\) 41.3176 1.77638 0.888190 0.459476i \(-0.151963\pi\)
0.888190 + 0.459476i \(0.151963\pi\)
\(542\) 8.81160 0.378491
\(543\) 22.4656 0.964092
\(544\) −3.22305 −0.138187
\(545\) −1.23037 −0.0527034
\(546\) 6.57973 0.281586
\(547\) 1.57191 0.0672100 0.0336050 0.999435i \(-0.489301\pi\)
0.0336050 + 0.999435i \(0.489301\pi\)
\(548\) −12.1095 −0.517292
\(549\) 21.8188 0.931205
\(550\) −0.606313 −0.0258533
\(551\) −12.1745 −0.518652
\(552\) 7.19205 0.306114
\(553\) 5.01360 0.213200
\(554\) −25.6127 −1.08818
\(555\) −0.0772572 −0.00327939
\(556\) 16.1577 0.685241
\(557\) −11.5447 −0.489165 −0.244583 0.969628i \(-0.578651\pi\)
−0.244583 + 0.969628i \(0.578651\pi\)
\(558\) 2.80390 0.118699
\(559\) −10.9433 −0.462854
\(560\) 0.400816 0.0169376
\(561\) 0.374662 0.0158183
\(562\) 13.4325 0.566616
\(563\) 13.1451 0.553999 0.276999 0.960870i \(-0.410660\pi\)
0.276999 + 0.960870i \(0.410660\pi\)
\(564\) −10.9988 −0.463133
\(565\) 0.514964 0.0216647
\(566\) −9.19969 −0.386692
\(567\) −6.71997 −0.282212
\(568\) −5.68177 −0.238402
\(569\) −9.75665 −0.409020 −0.204510 0.978864i \(-0.565560\pi\)
−0.204510 + 0.978864i \(0.565560\pi\)
\(570\) 0.122095 0.00511399
\(571\) −15.2353 −0.637578 −0.318789 0.947826i \(-0.603276\pi\)
−0.318789 + 0.947826i \(0.603276\pi\)
\(572\) 0.198619 0.00830468
\(573\) −18.9107 −0.790004
\(574\) −10.5687 −0.441129
\(575\) −37.5125 −1.56438
\(576\) −2.08438 −0.0868493
\(577\) 37.1399 1.54616 0.773078 0.634311i \(-0.218716\pi\)
0.773078 + 0.634311i \(0.218716\pi\)
\(578\) 6.61198 0.275022
\(579\) −9.29549 −0.386308
\(580\) −0.866584 −0.0359830
\(581\) 49.3573 2.04769
\(582\) 4.33624 0.179743
\(583\) −0.847936 −0.0351179
\(584\) −0.786531 −0.0325469
\(585\) −0.324774 −0.0134278
\(586\) 6.94996 0.287100
\(587\) −9.51896 −0.392890 −0.196445 0.980515i \(-0.562940\pi\)
−0.196445 + 0.980515i \(0.562940\pi\)
\(588\) −10.2276 −0.421781
\(589\) −1.80105 −0.0742109
\(590\) −0.374112 −0.0154020
\(591\) 1.82926 0.0752455
\(592\) −0.847194 −0.0348194
\(593\) 39.9184 1.63925 0.819625 0.572900i \(-0.194182\pi\)
0.819625 + 0.572900i \(0.194182\pi\)
\(594\) 0.591033 0.0242504
\(595\) 1.29185 0.0529606
\(596\) −4.96833 −0.203511
\(597\) −9.89712 −0.405062
\(598\) 12.2885 0.502516
\(599\) −33.5087 −1.36913 −0.684564 0.728952i \(-0.740008\pi\)
−0.684564 + 0.728952i \(0.740008\pi\)
\(600\) −4.77571 −0.194967
\(601\) −6.98904 −0.285089 −0.142545 0.989788i \(-0.545528\pi\)
−0.142545 + 0.989788i \(0.545528\pi\)
\(602\) 28.1508 1.14734
\(603\) 29.5278 1.20246
\(604\) 14.1500 0.575754
\(605\) 1.04691 0.0425629
\(606\) −18.0357 −0.732650
\(607\) 34.3477 1.39413 0.697066 0.717007i \(-0.254489\pi\)
0.697066 + 0.717007i \(0.254489\pi\)
\(608\) 1.33888 0.0542986
\(609\) 36.5944 1.48288
\(610\) −0.997593 −0.0403914
\(611\) −18.7929 −0.760278
\(612\) −6.71806 −0.271561
\(613\) −38.4326 −1.55228 −0.776139 0.630561i \(-0.782825\pi\)
−0.776139 + 0.630561i \(0.782825\pi\)
\(614\) −26.4614 −1.06790
\(615\) −0.229156 −0.00924047
\(616\) −0.510931 −0.0205860
\(617\) −26.4663 −1.06549 −0.532747 0.846275i \(-0.678840\pi\)
−0.532747 + 0.846275i \(0.678840\pi\)
\(618\) −15.3398 −0.617056
\(619\) −0.365349 −0.0146846 −0.00734231 0.999973i \(-0.502337\pi\)
−0.00734231 + 0.999973i \(0.502337\pi\)
\(620\) −0.128199 −0.00514859
\(621\) 36.5671 1.46739
\(622\) 5.51240 0.221027
\(623\) 24.2846 0.972943
\(624\) 1.56445 0.0626282
\(625\) 24.8638 0.994554
\(626\) −6.03203 −0.241088
\(627\) −0.155637 −0.00621556
\(628\) −3.45379 −0.137821
\(629\) −2.73054 −0.108874
\(630\) 0.835454 0.0332853
\(631\) −15.5463 −0.618890 −0.309445 0.950917i \(-0.600143\pi\)
−0.309445 + 0.950917i \(0.600143\pi\)
\(632\) 1.19208 0.0474182
\(633\) −25.2667 −1.00426
\(634\) −26.5260 −1.05348
\(635\) 1.08833 0.0431891
\(636\) −6.67888 −0.264835
\(637\) −17.4752 −0.692394
\(638\) 1.10466 0.0437338
\(639\) −11.8430 −0.468501
\(640\) 0.0953014 0.00376712
\(641\) −23.9183 −0.944717 −0.472359 0.881406i \(-0.656597\pi\)
−0.472359 + 0.881406i \(0.656597\pi\)
\(642\) −7.51578 −0.296624
\(643\) −6.78173 −0.267445 −0.133723 0.991019i \(-0.542693\pi\)
−0.133723 + 0.991019i \(0.542693\pi\)
\(644\) −31.6113 −1.24566
\(645\) 0.610381 0.0240337
\(646\) 4.31526 0.169782
\(647\) 8.83427 0.347311 0.173655 0.984806i \(-0.444442\pi\)
0.173655 + 0.984806i \(0.444442\pi\)
\(648\) −1.59779 −0.0627673
\(649\) 0.476891 0.0187196
\(650\) −8.15991 −0.320058
\(651\) 5.41363 0.212177
\(652\) 7.63173 0.298882
\(653\) 16.4307 0.642984 0.321492 0.946912i \(-0.395816\pi\)
0.321492 + 0.946912i \(0.395816\pi\)
\(654\) 12.3536 0.483066
\(655\) −0.260969 −0.0101969
\(656\) −2.51290 −0.0981123
\(657\) −1.63943 −0.0639603
\(658\) 48.3430 1.88461
\(659\) 34.4579 1.34229 0.671145 0.741326i \(-0.265803\pi\)
0.671145 + 0.741326i \(0.265803\pi\)
\(660\) −0.0110783 −0.000431222 0
\(661\) −5.72848 −0.222812 −0.111406 0.993775i \(-0.535535\pi\)
−0.111406 + 0.993775i \(0.535535\pi\)
\(662\) 31.7469 1.23388
\(663\) 5.04230 0.195827
\(664\) 11.7356 0.455430
\(665\) −0.536643 −0.0208101
\(666\) −1.76588 −0.0684263
\(667\) 68.3451 2.64633
\(668\) 13.2615 0.513103
\(669\) 2.75555 0.106536
\(670\) −1.35006 −0.0521574
\(671\) 1.27166 0.0490918
\(672\) −4.02442 −0.155245
\(673\) 23.4230 0.902891 0.451445 0.892299i \(-0.350909\pi\)
0.451445 + 0.892299i \(0.350909\pi\)
\(674\) −31.0606 −1.19641
\(675\) −24.2815 −0.934596
\(676\) −10.3269 −0.397190
\(677\) 34.8354 1.33883 0.669416 0.742887i \(-0.266544\pi\)
0.669416 + 0.742887i \(0.266544\pi\)
\(678\) −5.17052 −0.198573
\(679\) −19.0591 −0.731420
\(680\) 0.307161 0.0117791
\(681\) 16.9918 0.651128
\(682\) 0.163419 0.00625762
\(683\) 4.47021 0.171048 0.0855239 0.996336i \(-0.472744\pi\)
0.0855239 + 0.996336i \(0.472744\pi\)
\(684\) 2.79073 0.106706
\(685\) 1.15405 0.0440940
\(686\) 15.5132 0.592296
\(687\) 7.35628 0.280660
\(688\) 6.69337 0.255182
\(689\) −11.4117 −0.434752
\(690\) −0.685413 −0.0260932
\(691\) 25.7956 0.981311 0.490656 0.871354i \(-0.336757\pi\)
0.490656 + 0.871354i \(0.336757\pi\)
\(692\) 23.1657 0.880628
\(693\) −1.06498 −0.0404551
\(694\) −6.01579 −0.228356
\(695\) −1.53986 −0.0584101
\(696\) 8.70099 0.329810
\(697\) −8.09919 −0.306779
\(698\) −18.7258 −0.708781
\(699\) 8.46111 0.320029
\(700\) 20.9907 0.793373
\(701\) −26.4901 −1.00052 −0.500259 0.865876i \(-0.666762\pi\)
−0.500259 + 0.865876i \(0.666762\pi\)
\(702\) 7.95427 0.300214
\(703\) 1.13429 0.0427805
\(704\) −0.121483 −0.00457857
\(705\) 1.04820 0.0394775
\(706\) −17.2725 −0.650060
\(707\) 79.2724 2.98134
\(708\) 3.75630 0.141170
\(709\) −34.3646 −1.29059 −0.645295 0.763933i \(-0.723266\pi\)
−0.645295 + 0.763933i \(0.723266\pi\)
\(710\) 0.541480 0.0203214
\(711\) 2.48474 0.0931851
\(712\) 5.77411 0.216394
\(713\) 10.1107 0.378648
\(714\) −12.9709 −0.485423
\(715\) −0.0189287 −0.000707893 0
\(716\) 0.199393 0.00745165
\(717\) 19.5867 0.731478
\(718\) −1.11572 −0.0416381
\(719\) 6.24457 0.232883 0.116442 0.993198i \(-0.462851\pi\)
0.116442 + 0.993198i \(0.462851\pi\)
\(720\) 0.198645 0.00740304
\(721\) 67.4229 2.51096
\(722\) 17.2074 0.640393
\(723\) 28.9914 1.07820
\(724\) −23.4780 −0.872554
\(725\) −45.3829 −1.68548
\(726\) −10.5116 −0.390120
\(727\) 36.3330 1.34752 0.673758 0.738952i \(-0.264679\pi\)
0.673758 + 0.738952i \(0.264679\pi\)
\(728\) −6.87624 −0.254850
\(729\) 10.6356 0.393913
\(730\) 0.0749575 0.00277430
\(731\) 21.5730 0.797908
\(732\) 10.0164 0.370217
\(733\) −30.4147 −1.12339 −0.561696 0.827344i \(-0.689851\pi\)
−0.561696 + 0.827344i \(0.689851\pi\)
\(734\) 9.30017 0.343276
\(735\) 0.974709 0.0359527
\(736\) −7.51615 −0.277049
\(737\) 1.72096 0.0633923
\(738\) −5.23785 −0.192808
\(739\) 3.06910 0.112899 0.0564493 0.998405i \(-0.482022\pi\)
0.0564493 + 0.998405i \(0.482022\pi\)
\(740\) 0.0807387 0.00296801
\(741\) −2.09461 −0.0769473
\(742\) 29.3557 1.07768
\(743\) −16.1309 −0.591787 −0.295893 0.955221i \(-0.595617\pi\)
−0.295893 + 0.955221i \(0.595617\pi\)
\(744\) 1.28719 0.0471906
\(745\) 0.473489 0.0173473
\(746\) 34.6933 1.27021
\(747\) 24.4615 0.894999
\(748\) −0.391546 −0.0143163
\(749\) 33.0341 1.20704
\(750\) 0.911091 0.0332683
\(751\) −34.5642 −1.26127 −0.630634 0.776081i \(-0.717205\pi\)
−0.630634 + 0.776081i \(0.717205\pi\)
\(752\) 11.4944 0.419159
\(753\) −11.6538 −0.424686
\(754\) 14.8668 0.541415
\(755\) −1.34851 −0.0490774
\(756\) −20.4617 −0.744184
\(757\) 30.4546 1.10689 0.553446 0.832885i \(-0.313312\pi\)
0.553446 + 0.832885i \(0.313312\pi\)
\(758\) −23.6958 −0.860672
\(759\) 0.873714 0.0317138
\(760\) −0.127597 −0.00462842
\(761\) −32.9139 −1.19313 −0.596564 0.802565i \(-0.703468\pi\)
−0.596564 + 0.802565i \(0.703468\pi\)
\(762\) −10.9274 −0.395859
\(763\) −54.2980 −1.96572
\(764\) 19.7628 0.714994
\(765\) 0.640240 0.0231479
\(766\) −1.12378 −0.0406038
\(767\) 6.41812 0.231745
\(768\) −0.956879 −0.0345284
\(769\) −31.4149 −1.13285 −0.566426 0.824113i \(-0.691674\pi\)
−0.566426 + 0.824113i \(0.691674\pi\)
\(770\) 0.0486924 0.00175475
\(771\) −11.5179 −0.414808
\(772\) 9.71439 0.349628
\(773\) −53.2187 −1.91414 −0.957072 0.289850i \(-0.906395\pi\)
−0.957072 + 0.289850i \(0.906395\pi\)
\(774\) 13.9515 0.501478
\(775\) −6.71375 −0.241165
\(776\) −4.53164 −0.162676
\(777\) −3.40946 −0.122314
\(778\) 28.5254 1.02268
\(779\) 3.36446 0.120544
\(780\) −0.149094 −0.00533843
\(781\) −0.690239 −0.0246987
\(782\) −24.2249 −0.866281
\(783\) 44.2392 1.58098
\(784\) 10.6885 0.381734
\(785\) 0.329151 0.0117479
\(786\) 2.62027 0.0934620
\(787\) −28.9785 −1.03297 −0.516486 0.856296i \(-0.672760\pi\)
−0.516486 + 0.856296i \(0.672760\pi\)
\(788\) −1.91169 −0.0681011
\(789\) −0.132625 −0.00472158
\(790\) −0.113607 −0.00404194
\(791\) 22.7260 0.808044
\(792\) −0.253217 −0.00899769
\(793\) 17.1143 0.607746
\(794\) 14.8873 0.528330
\(795\) 0.636507 0.0225746
\(796\) 10.3431 0.366602
\(797\) 4.76493 0.168782 0.0843912 0.996433i \(-0.473105\pi\)
0.0843912 + 0.996433i \(0.473105\pi\)
\(798\) 5.38820 0.190740
\(799\) 37.0471 1.31063
\(800\) 4.99092 0.176456
\(801\) 12.0355 0.425252
\(802\) −2.77313 −0.0979228
\(803\) −0.0955503 −0.00337190
\(804\) 13.5554 0.478060
\(805\) 3.01260 0.106180
\(806\) 2.19933 0.0774680
\(807\) 18.5511 0.653031
\(808\) 18.8485 0.663086
\(809\) 40.1670 1.41220 0.706098 0.708114i \(-0.250454\pi\)
0.706098 + 0.708114i \(0.250454\pi\)
\(810\) 0.152272 0.00535030
\(811\) −31.8495 −1.11839 −0.559193 0.829038i \(-0.688889\pi\)
−0.559193 + 0.829038i \(0.688889\pi\)
\(812\) −38.2435 −1.34208
\(813\) 8.43164 0.295711
\(814\) −0.102920 −0.00360734
\(815\) −0.727315 −0.0254767
\(816\) −3.08407 −0.107964
\(817\) −8.96160 −0.313527
\(818\) 37.2648 1.30293
\(819\) −14.3327 −0.500825
\(820\) 0.239483 0.00836311
\(821\) −23.3451 −0.814750 −0.407375 0.913261i \(-0.633556\pi\)
−0.407375 + 0.913261i \(0.633556\pi\)
\(822\) −11.5873 −0.404154
\(823\) −42.1552 −1.46944 −0.734718 0.678372i \(-0.762686\pi\)
−0.734718 + 0.678372i \(0.762686\pi\)
\(824\) 16.0310 0.558467
\(825\) −0.580168 −0.0201989
\(826\) −16.5101 −0.574459
\(827\) 37.8380 1.31576 0.657878 0.753125i \(-0.271454\pi\)
0.657878 + 0.753125i \(0.271454\pi\)
\(828\) −15.6665 −0.544450
\(829\) −21.8002 −0.757154 −0.378577 0.925570i \(-0.623586\pi\)
−0.378577 + 0.925570i \(0.623586\pi\)
\(830\) −1.11842 −0.0388209
\(831\) −24.5082 −0.850181
\(832\) −1.63495 −0.0566817
\(833\) 34.4497 1.19361
\(834\) 15.4610 0.535371
\(835\) −1.26384 −0.0437370
\(836\) 0.162651 0.00562540
\(837\) 6.54456 0.226213
\(838\) 29.5915 1.02222
\(839\) −2.66289 −0.0919330 −0.0459665 0.998943i \(-0.514637\pi\)
−0.0459665 + 0.998943i \(0.514637\pi\)
\(840\) 0.383533 0.0132331
\(841\) 53.6843 1.85118
\(842\) 24.0854 0.830037
\(843\) 12.8533 0.442691
\(844\) 26.4053 0.908909
\(845\) 0.984171 0.0338565
\(846\) 23.9588 0.823721
\(847\) 46.2015 1.58750
\(848\) 6.97986 0.239689
\(849\) −8.80299 −0.302118
\(850\) 16.0860 0.551744
\(851\) −6.36764 −0.218280
\(852\) −5.43676 −0.186260
\(853\) −53.5322 −1.83291 −0.916454 0.400139i \(-0.868962\pi\)
−0.916454 + 0.400139i \(0.868962\pi\)
\(854\) −44.0251 −1.50651
\(855\) −0.265960 −0.00909566
\(856\) 7.85447 0.268460
\(857\) 36.5661 1.24907 0.624537 0.780995i \(-0.285288\pi\)
0.624537 + 0.780995i \(0.285288\pi\)
\(858\) 0.190055 0.00648835
\(859\) 8.17959 0.279084 0.139542 0.990216i \(-0.455437\pi\)
0.139542 + 0.990216i \(0.455437\pi\)
\(860\) −0.637888 −0.0217518
\(861\) −10.1130 −0.344649
\(862\) −34.2509 −1.16659
\(863\) −8.52967 −0.290353 −0.145177 0.989406i \(-0.546375\pi\)
−0.145177 + 0.989406i \(0.546375\pi\)
\(864\) −4.86514 −0.165515
\(865\) −2.20772 −0.0750648
\(866\) 40.1135 1.36311
\(867\) 6.32686 0.214872
\(868\) −5.65758 −0.192031
\(869\) 0.144817 0.00491259
\(870\) −0.829217 −0.0281131
\(871\) 23.1611 0.784783
\(872\) −12.9103 −0.437199
\(873\) −9.44568 −0.319688
\(874\) 10.0632 0.340393
\(875\) −4.00452 −0.135378
\(876\) −0.752615 −0.0254285
\(877\) −20.2942 −0.685287 −0.342643 0.939466i \(-0.611322\pi\)
−0.342643 + 0.939466i \(0.611322\pi\)
\(878\) 30.1300 1.01684
\(879\) 6.65027 0.224308
\(880\) 0.0115775 0.000390278 0
\(881\) 10.6036 0.357243 0.178621 0.983918i \(-0.442836\pi\)
0.178621 + 0.983918i \(0.442836\pi\)
\(882\) 22.2790 0.750173
\(883\) 32.7047 1.10060 0.550301 0.834966i \(-0.314513\pi\)
0.550301 + 0.834966i \(0.314513\pi\)
\(884\) −5.26952 −0.177233
\(885\) −0.357980 −0.0120334
\(886\) −11.0205 −0.370241
\(887\) −12.5042 −0.419850 −0.209925 0.977717i \(-0.567322\pi\)
−0.209925 + 0.977717i \(0.567322\pi\)
\(888\) −0.810662 −0.0272040
\(889\) 48.0294 1.61086
\(890\) −0.550281 −0.0184455
\(891\) −0.194105 −0.00650277
\(892\) −2.87973 −0.0964204
\(893\) −15.3896 −0.514995
\(894\) −4.75409 −0.159001
\(895\) −0.0190024 −0.000635180 0
\(896\) 4.20577 0.140505
\(897\) 11.7587 0.392610
\(898\) 6.50049 0.216924
\(899\) 12.2320 0.407959
\(900\) 10.4030 0.346766
\(901\) 22.4964 0.749464
\(902\) −0.305275 −0.0101646
\(903\) 26.9369 0.896405
\(904\) 5.40353 0.179719
\(905\) 2.23749 0.0743766
\(906\) 13.5398 0.449830
\(907\) −26.3180 −0.873876 −0.436938 0.899492i \(-0.643937\pi\)
−0.436938 + 0.899492i \(0.643937\pi\)
\(908\) −17.7575 −0.589305
\(909\) 39.2874 1.30308
\(910\) 0.655315 0.0217235
\(911\) −9.48305 −0.314187 −0.157094 0.987584i \(-0.550212\pi\)
−0.157094 + 0.987584i \(0.550212\pi\)
\(912\) 1.28114 0.0424229
\(913\) 1.42568 0.0471831
\(914\) −8.73969 −0.289083
\(915\) −0.954576 −0.0315573
\(916\) −7.68778 −0.254011
\(917\) −11.5169 −0.380321
\(918\) −15.6806 −0.517536
\(919\) 33.0466 1.09011 0.545054 0.838401i \(-0.316509\pi\)
0.545054 + 0.838401i \(0.316509\pi\)
\(920\) 0.716300 0.0236157
\(921\) −25.3204 −0.834334
\(922\) 25.5346 0.840938
\(923\) −9.28941 −0.305765
\(924\) −0.488899 −0.0160836
\(925\) 4.22827 0.139025
\(926\) 14.6280 0.480705
\(927\) 33.4148 1.09749
\(928\) −9.09309 −0.298495
\(929\) 41.3770 1.35754 0.678768 0.734353i \(-0.262514\pi\)
0.678768 + 0.734353i \(0.262514\pi\)
\(930\) −0.122671 −0.00402254
\(931\) −14.3106 −0.469012
\(932\) −8.84240 −0.289643
\(933\) 5.27470 0.172686
\(934\) −1.24904 −0.0408698
\(935\) 0.0373149 0.00122033
\(936\) −3.40786 −0.111389
\(937\) 9.40734 0.307324 0.153662 0.988123i \(-0.450893\pi\)
0.153662 + 0.988123i \(0.450893\pi\)
\(938\) −59.5799 −1.94535
\(939\) −5.77192 −0.188360
\(940\) −1.09544 −0.0357292
\(941\) −30.9469 −1.00884 −0.504420 0.863459i \(-0.668293\pi\)
−0.504420 + 0.863459i \(0.668293\pi\)
\(942\) −3.30486 −0.107678
\(943\) −18.8874 −0.615057
\(944\) −3.92557 −0.127766
\(945\) 1.95003 0.0634344
\(946\) 0.813132 0.0264372
\(947\) −3.65377 −0.118732 −0.0593658 0.998236i \(-0.518908\pi\)
−0.0593658 + 0.998236i \(0.518908\pi\)
\(948\) 1.14067 0.0370473
\(949\) −1.28594 −0.0417434
\(950\) −6.68222 −0.216800
\(951\) −25.3821 −0.823072
\(952\) 13.5554 0.439333
\(953\) 28.6327 0.927504 0.463752 0.885965i \(-0.346503\pi\)
0.463752 + 0.885965i \(0.346503\pi\)
\(954\) 14.5487 0.471031
\(955\) −1.88343 −0.0609462
\(956\) −20.4693 −0.662025
\(957\) 1.05702 0.0341687
\(958\) −11.4826 −0.370987
\(959\) 50.9298 1.64461
\(960\) 0.0911919 0.00294321
\(961\) −29.1905 −0.941627
\(962\) −1.38512 −0.0446581
\(963\) 16.3717 0.527571
\(964\) −30.2979 −0.975828
\(965\) −0.925795 −0.0298024
\(966\) −30.2482 −0.973218
\(967\) 2.85719 0.0918811 0.0459406 0.998944i \(-0.485372\pi\)
0.0459406 + 0.998944i \(0.485372\pi\)
\(968\) 10.9852 0.353079
\(969\) 4.12918 0.132648
\(970\) 0.431872 0.0138666
\(971\) 37.8413 1.21439 0.607193 0.794555i \(-0.292296\pi\)
0.607193 + 0.794555i \(0.292296\pi\)
\(972\) −16.1243 −0.517188
\(973\) −67.9558 −2.17856
\(974\) 21.9886 0.704561
\(975\) −7.80804 −0.250058
\(976\) −10.4678 −0.335065
\(977\) −53.8163 −1.72174 −0.860868 0.508828i \(-0.830079\pi\)
−0.860868 + 0.508828i \(0.830079\pi\)
\(978\) 7.30265 0.233513
\(979\) 0.701458 0.0224187
\(980\) −1.01863 −0.0325390
\(981\) −26.9101 −0.859173
\(982\) 23.7027 0.756384
\(983\) 42.2353 1.34710 0.673548 0.739143i \(-0.264769\pi\)
0.673548 + 0.739143i \(0.264769\pi\)
\(984\) −2.40454 −0.0766540
\(985\) 0.182187 0.00580495
\(986\) −29.3074 −0.933339
\(987\) 46.2585 1.47242
\(988\) 2.18900 0.0696413
\(989\) 50.3084 1.59971
\(990\) 0.0241320 0.000766965 0
\(991\) 59.5820 1.89269 0.946343 0.323165i \(-0.104747\pi\)
0.946343 + 0.323165i \(0.104747\pi\)
\(992\) −1.34519 −0.0427100
\(993\) 30.3779 0.964014
\(994\) 23.8962 0.757942
\(995\) −0.985715 −0.0312493
\(996\) 11.2296 0.355822
\(997\) −29.0071 −0.918665 −0.459333 0.888264i \(-0.651911\pi\)
−0.459333 + 0.888264i \(0.651911\pi\)
\(998\) 14.8704 0.470715
\(999\) −4.12172 −0.130405
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.1.14 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.14 40 1.1 even 1 trivial