Properties

Label 4006.2.a.g.1.16
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 1.16
Character \(\chi\) = 4006.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.934245 q^{3} +1.00000 q^{4} -4.17073 q^{5} +0.934245 q^{6} +1.30479 q^{7} -1.00000 q^{8} -2.12719 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.934245 q^{3} +1.00000 q^{4} -4.17073 q^{5} +0.934245 q^{6} +1.30479 q^{7} -1.00000 q^{8} -2.12719 q^{9} +4.17073 q^{10} -6.29050 q^{11} -0.934245 q^{12} -3.79704 q^{13} -1.30479 q^{14} +3.89648 q^{15} +1.00000 q^{16} +3.77842 q^{17} +2.12719 q^{18} +8.63642 q^{19} -4.17073 q^{20} -1.21899 q^{21} +6.29050 q^{22} -0.896615 q^{23} +0.934245 q^{24} +12.3950 q^{25} +3.79704 q^{26} +4.79005 q^{27} +1.30479 q^{28} -5.01155 q^{29} -3.89648 q^{30} +4.64754 q^{31} -1.00000 q^{32} +5.87687 q^{33} -3.77842 q^{34} -5.44191 q^{35} -2.12719 q^{36} +0.395367 q^{37} -8.63642 q^{38} +3.54737 q^{39} +4.17073 q^{40} +11.0085 q^{41} +1.21899 q^{42} -5.38636 q^{43} -6.29050 q^{44} +8.87192 q^{45} +0.896615 q^{46} +6.22519 q^{47} -0.934245 q^{48} -5.29754 q^{49} -12.3950 q^{50} -3.52997 q^{51} -3.79704 q^{52} +5.28252 q^{53} -4.79005 q^{54} +26.2360 q^{55} -1.30479 q^{56} -8.06853 q^{57} +5.01155 q^{58} +8.08279 q^{59} +3.89648 q^{60} +7.71779 q^{61} -4.64754 q^{62} -2.77552 q^{63} +1.00000 q^{64} +15.8364 q^{65} -5.87687 q^{66} -5.28401 q^{67} +3.77842 q^{68} +0.837658 q^{69} +5.44191 q^{70} -13.2315 q^{71} +2.12719 q^{72} +5.22398 q^{73} -0.395367 q^{74} -11.5800 q^{75} +8.63642 q^{76} -8.20776 q^{77} -3.54737 q^{78} -7.87903 q^{79} -4.17073 q^{80} +1.90648 q^{81} -11.0085 q^{82} -4.95162 q^{83} -1.21899 q^{84} -15.7588 q^{85} +5.38636 q^{86} +4.68202 q^{87} +6.29050 q^{88} -15.5420 q^{89} -8.87192 q^{90} -4.95433 q^{91} -0.896615 q^{92} -4.34194 q^{93} -6.22519 q^{94} -36.0202 q^{95} +0.934245 q^{96} +4.55797 q^{97} +5.29754 q^{98} +13.3811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + O(q^{10}) \) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + 23q^{10} - 28q^{11} - q^{12} - 12q^{13} - 12q^{14} - 14q^{15} + 40q^{16} - 10q^{17} - 29q^{18} + 3q^{19} - 23q^{20} - 40q^{21} + 28q^{22} - 10q^{23} + q^{24} + 43q^{25} + 12q^{26} - 7q^{27} + 12q^{28} - 37q^{29} + 14q^{30} - 16q^{31} - 40q^{32} - 11q^{33} + 10q^{34} - 24q^{35} + 29q^{36} - 17q^{37} - 3q^{38} - 10q^{39} + 23q^{40} - 58q^{41} + 40q^{42} + 37q^{43} - 28q^{44} - 66q^{45} + 10q^{46} - 34q^{47} - q^{48} + 28q^{49} - 43q^{50} - 7q^{51} - 12q^{52} - 43q^{53} + 7q^{54} + 28q^{55} - 12q^{56} - 25q^{57} + 37q^{58} - 92q^{59} - 14q^{60} - 37q^{61} + 16q^{62} + 14q^{63} + 40q^{64} - 54q^{65} + 11q^{66} - 10q^{67} - 10q^{68} - 49q^{69} + 24q^{70} - 87q^{71} - 29q^{72} + 12q^{73} + 17q^{74} - 31q^{75} + 3q^{76} - 53q^{77} + 10q^{78} + 14q^{79} - 23q^{80} - 4q^{81} + 58q^{82} - 42q^{83} - 40q^{84} - 24q^{85} - 37q^{86} + 24q^{87} + 28q^{88} - 118q^{89} + 66q^{90} - 35q^{91} - 10q^{92} - 22q^{93} + 34q^{94} - 18q^{95} + q^{96} + 2q^{97} - 28q^{98} - 48q^{99} + O(q^{100}) \)

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
\(3\) −0.934245 −0.539387 −0.269693 0.962946i \(-0.586922\pi\)
−0.269693 + 0.962946i \(0.586922\pi\)
\(4\) 1.00000 0.500000
\(5\) −4.17073 −1.86521 −0.932604 0.360902i \(-0.882469\pi\)
−0.932604 + 0.360902i \(0.882469\pi\)
\(6\) 0.934245 0.381404
\(7\) 1.30479 0.493163 0.246581 0.969122i \(-0.420693\pi\)
0.246581 + 0.969122i \(0.420693\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.12719 −0.709062
\(10\) 4.17073 1.31890
\(11\) −6.29050 −1.89666 −0.948329 0.317288i \(-0.897228\pi\)
−0.948329 + 0.317288i \(0.897228\pi\)
\(12\) −0.934245 −0.269693
\(13\) −3.79704 −1.05311 −0.526555 0.850141i \(-0.676517\pi\)
−0.526555 + 0.850141i \(0.676517\pi\)
\(14\) −1.30479 −0.348719
\(15\) 3.89648 1.00607
\(16\) 1.00000 0.250000
\(17\) 3.77842 0.916402 0.458201 0.888849i \(-0.348494\pi\)
0.458201 + 0.888849i \(0.348494\pi\)
\(18\) 2.12719 0.501383
\(19\) 8.63642 1.98133 0.990665 0.136320i \(-0.0435277\pi\)
0.990665 + 0.136320i \(0.0435277\pi\)
\(20\) −4.17073 −0.932604
\(21\) −1.21899 −0.266005
\(22\) 6.29050 1.34114
\(23\) −0.896615 −0.186957 −0.0934786 0.995621i \(-0.529799\pi\)
−0.0934786 + 0.995621i \(0.529799\pi\)
\(24\) 0.934245 0.190702
\(25\) 12.3950 2.47900
\(26\) 3.79704 0.744661
\(27\) 4.79005 0.921845
\(28\) 1.30479 0.246581
\(29\) −5.01155 −0.930622 −0.465311 0.885147i \(-0.654058\pi\)
−0.465311 + 0.885147i \(0.654058\pi\)
\(30\) −3.89648 −0.711397
\(31\) 4.64754 0.834723 0.417362 0.908740i \(-0.362955\pi\)
0.417362 + 0.908740i \(0.362955\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.87687 1.02303
\(34\) −3.77842 −0.647994
\(35\) −5.44191 −0.919851
\(36\) −2.12719 −0.354531
\(37\) 0.395367 0.0649979 0.0324990 0.999472i \(-0.489653\pi\)
0.0324990 + 0.999472i \(0.489653\pi\)
\(38\) −8.63642 −1.40101
\(39\) 3.54737 0.568033
\(40\) 4.17073 0.659451
\(41\) 11.0085 1.71924 0.859618 0.510937i \(-0.170701\pi\)
0.859618 + 0.510937i \(0.170701\pi\)
\(42\) 1.21899 0.188094
\(43\) −5.38636 −0.821412 −0.410706 0.911768i \(-0.634718\pi\)
−0.410706 + 0.911768i \(0.634718\pi\)
\(44\) −6.29050 −0.948329
\(45\) 8.87192 1.32255
\(46\) 0.896615 0.132199
\(47\) 6.22519 0.908037 0.454018 0.890992i \(-0.349990\pi\)
0.454018 + 0.890992i \(0.349990\pi\)
\(48\) −0.934245 −0.134847
\(49\) −5.29754 −0.756791
\(50\) −12.3950 −1.75292
\(51\) −3.52997 −0.494295
\(52\) −3.79704 −0.526555
\(53\) 5.28252 0.725610 0.362805 0.931865i \(-0.381819\pi\)
0.362805 + 0.931865i \(0.381819\pi\)
\(54\) −4.79005 −0.651843
\(55\) 26.2360 3.53766
\(56\) −1.30479 −0.174359
\(57\) −8.06853 −1.06870
\(58\) 5.01155 0.658049
\(59\) 8.08279 1.05229 0.526145 0.850395i \(-0.323637\pi\)
0.526145 + 0.850395i \(0.323637\pi\)
\(60\) 3.89648 0.503034
\(61\) 7.71779 0.988162 0.494081 0.869416i \(-0.335505\pi\)
0.494081 + 0.869416i \(0.335505\pi\)
\(62\) −4.64754 −0.590239
\(63\) −2.77552 −0.349683
\(64\) 1.00000 0.125000
\(65\) 15.8364 1.96427
\(66\) −5.87687 −0.723393
\(67\) −5.28401 −0.645544 −0.322772 0.946477i \(-0.604615\pi\)
−0.322772 + 0.946477i \(0.604615\pi\)
\(68\) 3.77842 0.458201
\(69\) 0.837658 0.100842
\(70\) 5.44191 0.650433
\(71\) −13.2315 −1.57029 −0.785145 0.619312i \(-0.787412\pi\)
−0.785145 + 0.619312i \(0.787412\pi\)
\(72\) 2.12719 0.250691
\(73\) 5.22398 0.611420 0.305710 0.952125i \(-0.401106\pi\)
0.305710 + 0.952125i \(0.401106\pi\)
\(74\) −0.395367 −0.0459605
\(75\) −11.5800 −1.33714
\(76\) 8.63642 0.990665
\(77\) −8.20776 −0.935361
\(78\) −3.54737 −0.401660
\(79\) −7.87903 −0.886460 −0.443230 0.896408i \(-0.646168\pi\)
−0.443230 + 0.896408i \(0.646168\pi\)
\(80\) −4.17073 −0.466302
\(81\) 1.90648 0.211831
\(82\) −11.0085 −1.21568
\(83\) −4.95162 −0.543511 −0.271755 0.962366i \(-0.587604\pi\)
−0.271755 + 0.962366i \(0.587604\pi\)
\(84\) −1.21899 −0.133003
\(85\) −15.7588 −1.70928
\(86\) 5.38636 0.580826
\(87\) 4.68202 0.501965
\(88\) 6.29050 0.670570
\(89\) −15.5420 −1.64745 −0.823725 0.566989i \(-0.808108\pi\)
−0.823725 + 0.566989i \(0.808108\pi\)
\(90\) −8.87192 −0.935183
\(91\) −4.95433 −0.519354
\(92\) −0.896615 −0.0934786
\(93\) −4.34194 −0.450239
\(94\) −6.22519 −0.642079
\(95\) −36.0202 −3.69559
\(96\) 0.934245 0.0953510
\(97\) 4.55797 0.462792 0.231396 0.972860i \(-0.425671\pi\)
0.231396 + 0.972860i \(0.425671\pi\)
\(98\) 5.29754 0.535132
\(99\) 13.3811 1.34485
\(100\) 12.3950 1.23950
\(101\) −8.68916 −0.864603 −0.432302 0.901729i \(-0.642298\pi\)
−0.432302 + 0.901729i \(0.642298\pi\)
\(102\) 3.52997 0.349519
\(103\) −2.54539 −0.250805 −0.125402 0.992106i \(-0.540022\pi\)
−0.125402 + 0.992106i \(0.540022\pi\)
\(104\) 3.79704 0.372331
\(105\) 5.08408 0.496155
\(106\) −5.28252 −0.513083
\(107\) −6.96570 −0.673400 −0.336700 0.941612i \(-0.609311\pi\)
−0.336700 + 0.941612i \(0.609311\pi\)
\(108\) 4.79005 0.460923
\(109\) −9.52787 −0.912605 −0.456302 0.889825i \(-0.650826\pi\)
−0.456302 + 0.889825i \(0.650826\pi\)
\(110\) −26.2360 −2.50151
\(111\) −0.369369 −0.0350590
\(112\) 1.30479 0.123291
\(113\) −2.68341 −0.252434 −0.126217 0.992003i \(-0.540284\pi\)
−0.126217 + 0.992003i \(0.540284\pi\)
\(114\) 8.06853 0.755687
\(115\) 3.73954 0.348714
\(116\) −5.01155 −0.465311
\(117\) 8.07702 0.746721
\(118\) −8.08279 −0.744081
\(119\) 4.93003 0.451935
\(120\) −3.89648 −0.355699
\(121\) 28.5705 2.59731
\(122\) −7.71779 −0.698736
\(123\) −10.2846 −0.927333
\(124\) 4.64754 0.417362
\(125\) −30.8426 −2.75864
\(126\) 2.77552 0.247263
\(127\) −13.4700 −1.19527 −0.597634 0.801769i \(-0.703892\pi\)
−0.597634 + 0.801769i \(0.703892\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 5.03218 0.443059
\(130\) −15.8364 −1.38895
\(131\) 18.2790 1.59705 0.798523 0.601964i \(-0.205615\pi\)
0.798523 + 0.601964i \(0.205615\pi\)
\(132\) 5.87687 0.511516
\(133\) 11.2687 0.977118
\(134\) 5.28401 0.456469
\(135\) −19.9780 −1.71943
\(136\) −3.77842 −0.323997
\(137\) 12.2643 1.04781 0.523904 0.851777i \(-0.324475\pi\)
0.523904 + 0.851777i \(0.324475\pi\)
\(138\) −0.837658 −0.0713062
\(139\) 14.0948 1.19551 0.597754 0.801680i \(-0.296060\pi\)
0.597754 + 0.801680i \(0.296060\pi\)
\(140\) −5.44191 −0.459925
\(141\) −5.81585 −0.489783
\(142\) 13.2315 1.11036
\(143\) 23.8853 1.99739
\(144\) −2.12719 −0.177266
\(145\) 20.9018 1.73580
\(146\) −5.22398 −0.432339
\(147\) 4.94919 0.408203
\(148\) 0.395367 0.0324990
\(149\) −1.23075 −0.100827 −0.0504136 0.998728i \(-0.516054\pi\)
−0.0504136 + 0.998728i \(0.516054\pi\)
\(150\) 11.5800 0.945500
\(151\) 6.00890 0.488997 0.244499 0.969650i \(-0.421377\pi\)
0.244499 + 0.969650i \(0.421377\pi\)
\(152\) −8.63642 −0.700506
\(153\) −8.03740 −0.649786
\(154\) 8.20776 0.661400
\(155\) −19.3837 −1.55693
\(156\) 3.54737 0.284017
\(157\) 22.5972 1.80345 0.901727 0.432305i \(-0.142300\pi\)
0.901727 + 0.432305i \(0.142300\pi\)
\(158\) 7.87903 0.626822
\(159\) −4.93516 −0.391384
\(160\) 4.17073 0.329725
\(161\) −1.16989 −0.0922003
\(162\) −1.90648 −0.149787
\(163\) −6.27626 −0.491595 −0.245797 0.969321i \(-0.579050\pi\)
−0.245797 + 0.969321i \(0.579050\pi\)
\(164\) 11.0085 0.859618
\(165\) −24.5109 −1.90817
\(166\) 4.95162 0.384320
\(167\) 8.07593 0.624934 0.312467 0.949929i \(-0.398845\pi\)
0.312467 + 0.949929i \(0.398845\pi\)
\(168\) 1.21899 0.0940470
\(169\) 1.41753 0.109041
\(170\) 15.7588 1.20864
\(171\) −18.3713 −1.40489
\(172\) −5.38636 −0.410706
\(173\) −12.9187 −0.982193 −0.491096 0.871105i \(-0.663404\pi\)
−0.491096 + 0.871105i \(0.663404\pi\)
\(174\) −4.68202 −0.354943
\(175\) 16.1728 1.22255
\(176\) −6.29050 −0.474165
\(177\) −7.55130 −0.567591
\(178\) 15.5420 1.16492
\(179\) −23.2192 −1.73548 −0.867742 0.497014i \(-0.834430\pi\)
−0.867742 + 0.497014i \(0.834430\pi\)
\(180\) 8.87192 0.661274
\(181\) −5.10569 −0.379503 −0.189751 0.981832i \(-0.560768\pi\)
−0.189751 + 0.981832i \(0.560768\pi\)
\(182\) 4.95433 0.367239
\(183\) −7.21030 −0.533001
\(184\) 0.896615 0.0660993
\(185\) −1.64897 −0.121235
\(186\) 4.34194 0.318367
\(187\) −23.7682 −1.73810
\(188\) 6.22519 0.454018
\(189\) 6.24998 0.454619
\(190\) 36.0202 2.61318
\(191\) 20.2505 1.46527 0.732637 0.680619i \(-0.238289\pi\)
0.732637 + 0.680619i \(0.238289\pi\)
\(192\) −0.934245 −0.0674233
\(193\) 7.76495 0.558933 0.279467 0.960155i \(-0.409842\pi\)
0.279467 + 0.960155i \(0.409842\pi\)
\(194\) −4.55797 −0.327243
\(195\) −14.7951 −1.05950
\(196\) −5.29754 −0.378395
\(197\) 15.6146 1.11249 0.556246 0.831018i \(-0.312241\pi\)
0.556246 + 0.831018i \(0.312241\pi\)
\(198\) −13.3811 −0.950952
\(199\) −15.3893 −1.09092 −0.545461 0.838136i \(-0.683645\pi\)
−0.545461 + 0.838136i \(0.683645\pi\)
\(200\) −12.3950 −0.876459
\(201\) 4.93656 0.348198
\(202\) 8.68916 0.611367
\(203\) −6.53900 −0.458948
\(204\) −3.52997 −0.247147
\(205\) −45.9134 −3.20673
\(206\) 2.54539 0.177346
\(207\) 1.90727 0.132564
\(208\) −3.79704 −0.263278
\(209\) −54.3274 −3.75791
\(210\) −5.08408 −0.350835
\(211\) 27.6277 1.90197 0.950986 0.309235i \(-0.100073\pi\)
0.950986 + 0.309235i \(0.100073\pi\)
\(212\) 5.28252 0.362805
\(213\) 12.3615 0.846993
\(214\) 6.96570 0.476166
\(215\) 22.4651 1.53210
\(216\) −4.79005 −0.325921
\(217\) 6.06405 0.411654
\(218\) 9.52787 0.645309
\(219\) −4.88047 −0.329792
\(220\) 26.2360 1.76883
\(221\) −14.3468 −0.965072
\(222\) 0.369369 0.0247905
\(223\) −2.83303 −0.189714 −0.0948570 0.995491i \(-0.530239\pi\)
−0.0948570 + 0.995491i \(0.530239\pi\)
\(224\) −1.30479 −0.0871796
\(225\) −26.3665 −1.75777
\(226\) 2.68341 0.178498
\(227\) −16.4681 −1.09303 −0.546513 0.837451i \(-0.684045\pi\)
−0.546513 + 0.837451i \(0.684045\pi\)
\(228\) −8.06853 −0.534351
\(229\) 1.54283 0.101953 0.0509765 0.998700i \(-0.483767\pi\)
0.0509765 + 0.998700i \(0.483767\pi\)
\(230\) −3.73954 −0.246578
\(231\) 7.66806 0.504521
\(232\) 5.01155 0.329025
\(233\) 22.7015 1.48722 0.743612 0.668611i \(-0.233111\pi\)
0.743612 + 0.668611i \(0.233111\pi\)
\(234\) −8.07702 −0.528011
\(235\) −25.9636 −1.69368
\(236\) 8.08279 0.526145
\(237\) 7.36094 0.478145
\(238\) −4.93003 −0.319566
\(239\) 1.25406 0.0811183 0.0405592 0.999177i \(-0.487086\pi\)
0.0405592 + 0.999177i \(0.487086\pi\)
\(240\) 3.89648 0.251517
\(241\) 0.519454 0.0334610 0.0167305 0.999860i \(-0.494674\pi\)
0.0167305 + 0.999860i \(0.494674\pi\)
\(242\) −28.5705 −1.83658
\(243\) −16.1513 −1.03610
\(244\) 7.71779 0.494081
\(245\) 22.0946 1.41157
\(246\) 10.2846 0.655724
\(247\) −32.7928 −2.08656
\(248\) −4.64754 −0.295119
\(249\) 4.62603 0.293163
\(250\) 30.8426 1.95066
\(251\) 23.4513 1.48023 0.740117 0.672478i \(-0.234770\pi\)
0.740117 + 0.672478i \(0.234770\pi\)
\(252\) −2.77552 −0.174841
\(253\) 5.64016 0.354594
\(254\) 13.4700 0.845182
\(255\) 14.7226 0.921962
\(256\) 1.00000 0.0625000
\(257\) −0.960802 −0.0599332 −0.0299666 0.999551i \(-0.509540\pi\)
−0.0299666 + 0.999551i \(0.509540\pi\)
\(258\) −5.03218 −0.313290
\(259\) 0.515869 0.0320545
\(260\) 15.8364 0.982135
\(261\) 10.6605 0.659869
\(262\) −18.2790 −1.12928
\(263\) −18.8333 −1.16131 −0.580655 0.814150i \(-0.697203\pi\)
−0.580655 + 0.814150i \(0.697203\pi\)
\(264\) −5.87687 −0.361696
\(265\) −22.0320 −1.35341
\(266\) −11.2687 −0.690926
\(267\) 14.5200 0.888612
\(268\) −5.28401 −0.322772
\(269\) −13.2221 −0.806167 −0.403084 0.915163i \(-0.632062\pi\)
−0.403084 + 0.915163i \(0.632062\pi\)
\(270\) 19.9780 1.21582
\(271\) −4.48027 −0.272157 −0.136079 0.990698i \(-0.543450\pi\)
−0.136079 + 0.990698i \(0.543450\pi\)
\(272\) 3.77842 0.229100
\(273\) 4.62855 0.280133
\(274\) −12.2643 −0.740912
\(275\) −77.9708 −4.70182
\(276\) 0.837658 0.0504211
\(277\) −15.8791 −0.954082 −0.477041 0.878881i \(-0.658291\pi\)
−0.477041 + 0.878881i \(0.658291\pi\)
\(278\) −14.0948 −0.845352
\(279\) −9.88619 −0.591871
\(280\) 5.44191 0.325216
\(281\) −0.405076 −0.0241648 −0.0120824 0.999927i \(-0.503846\pi\)
−0.0120824 + 0.999927i \(0.503846\pi\)
\(282\) 5.81585 0.346329
\(283\) −6.16780 −0.366638 −0.183319 0.983053i \(-0.558684\pi\)
−0.183319 + 0.983053i \(0.558684\pi\)
\(284\) −13.2315 −0.785145
\(285\) 33.6517 1.99335
\(286\) −23.8853 −1.41237
\(287\) 14.3637 0.847863
\(288\) 2.12719 0.125346
\(289\) −2.72354 −0.160208
\(290\) −20.9018 −1.22740
\(291\) −4.25826 −0.249624
\(292\) 5.22398 0.305710
\(293\) 9.66195 0.564457 0.282229 0.959347i \(-0.408926\pi\)
0.282229 + 0.959347i \(0.408926\pi\)
\(294\) −4.94919 −0.288643
\(295\) −33.7111 −1.96274
\(296\) −0.395367 −0.0229802
\(297\) −30.1318 −1.74843
\(298\) 1.23075 0.0712956
\(299\) 3.40449 0.196887
\(300\) −11.5800 −0.668570
\(301\) −7.02804 −0.405090
\(302\) −6.00890 −0.345773
\(303\) 8.11780 0.466355
\(304\) 8.63642 0.495332
\(305\) −32.1888 −1.84313
\(306\) 8.03740 0.459468
\(307\) −20.2896 −1.15799 −0.578994 0.815331i \(-0.696555\pi\)
−0.578994 + 0.815331i \(0.696555\pi\)
\(308\) −8.20776 −0.467680
\(309\) 2.37802 0.135281
\(310\) 19.3837 1.10092
\(311\) 14.9639 0.848527 0.424263 0.905539i \(-0.360533\pi\)
0.424263 + 0.905539i \(0.360533\pi\)
\(312\) −3.54737 −0.200830
\(313\) 33.8135 1.91125 0.955627 0.294578i \(-0.0951792\pi\)
0.955627 + 0.294578i \(0.0951792\pi\)
\(314\) −22.5972 −1.27524
\(315\) 11.5760 0.652231
\(316\) −7.87903 −0.443230
\(317\) −22.0889 −1.24064 −0.620319 0.784350i \(-0.712997\pi\)
−0.620319 + 0.784350i \(0.712997\pi\)
\(318\) 4.93516 0.276750
\(319\) 31.5252 1.76507
\(320\) −4.17073 −0.233151
\(321\) 6.50767 0.363223
\(322\) 1.16989 0.0651954
\(323\) 32.6320 1.81569
\(324\) 1.90648 0.105916
\(325\) −47.0644 −2.61066
\(326\) 6.27626 0.347610
\(327\) 8.90137 0.492247
\(328\) −11.0085 −0.607842
\(329\) 8.12253 0.447810
\(330\) 24.5109 1.34928
\(331\) −18.2309 −1.00206 −0.501031 0.865429i \(-0.667046\pi\)
−0.501031 + 0.865429i \(0.667046\pi\)
\(332\) −4.95162 −0.271755
\(333\) −0.841019 −0.0460876
\(334\) −8.07593 −0.441895
\(335\) 22.0382 1.20407
\(336\) −1.21899 −0.0665013
\(337\) −0.521940 −0.0284319 −0.0142159 0.999899i \(-0.504525\pi\)
−0.0142159 + 0.999899i \(0.504525\pi\)
\(338\) −1.41753 −0.0771037
\(339\) 2.50696 0.136159
\(340\) −15.7588 −0.854640
\(341\) −29.2354 −1.58319
\(342\) 18.3713 0.993404
\(343\) −16.0456 −0.866383
\(344\) 5.38636 0.290413
\(345\) −3.49365 −0.188092
\(346\) 12.9187 0.694515
\(347\) −16.6049 −0.891399 −0.445699 0.895183i \(-0.647045\pi\)
−0.445699 + 0.895183i \(0.647045\pi\)
\(348\) 4.68202 0.250983
\(349\) −2.71319 −0.145234 −0.0726169 0.997360i \(-0.523135\pi\)
−0.0726169 + 0.997360i \(0.523135\pi\)
\(350\) −16.1728 −0.864473
\(351\) −18.1880 −0.970805
\(352\) 6.29050 0.335285
\(353\) 13.9911 0.744674 0.372337 0.928098i \(-0.378557\pi\)
0.372337 + 0.928098i \(0.378557\pi\)
\(354\) 7.55130 0.401347
\(355\) 55.1850 2.92892
\(356\) −15.5420 −0.823725
\(357\) −4.60585 −0.243768
\(358\) 23.2192 1.22717
\(359\) 28.3376 1.49560 0.747801 0.663923i \(-0.231110\pi\)
0.747801 + 0.663923i \(0.231110\pi\)
\(360\) −8.87192 −0.467591
\(361\) 55.5877 2.92567
\(362\) 5.10569 0.268349
\(363\) −26.6918 −1.40096
\(364\) −4.95433 −0.259677
\(365\) −21.7878 −1.14043
\(366\) 7.21030 0.376889
\(367\) −29.5228 −1.54108 −0.770538 0.637395i \(-0.780012\pi\)
−0.770538 + 0.637395i \(0.780012\pi\)
\(368\) −0.896615 −0.0467393
\(369\) −23.4171 −1.21905
\(370\) 1.64897 0.0857258
\(371\) 6.89255 0.357843
\(372\) −4.34194 −0.225119
\(373\) −26.9628 −1.39608 −0.698040 0.716058i \(-0.745944\pi\)
−0.698040 + 0.716058i \(0.745944\pi\)
\(374\) 23.7682 1.22902
\(375\) 28.8145 1.48797
\(376\) −6.22519 −0.321039
\(377\) 19.0291 0.980048
\(378\) −6.24998 −0.321465
\(379\) −28.1649 −1.44674 −0.723368 0.690463i \(-0.757407\pi\)
−0.723368 + 0.690463i \(0.757407\pi\)
\(380\) −36.0202 −1.84780
\(381\) 12.5843 0.644711
\(382\) −20.2505 −1.03611
\(383\) 4.76207 0.243330 0.121665 0.992571i \(-0.461177\pi\)
0.121665 + 0.992571i \(0.461177\pi\)
\(384\) 0.934245 0.0476755
\(385\) 34.2324 1.74464
\(386\) −7.76495 −0.395226
\(387\) 11.4578 0.582432
\(388\) 4.55797 0.231396
\(389\) −23.8263 −1.20804 −0.604021 0.796969i \(-0.706436\pi\)
−0.604021 + 0.796969i \(0.706436\pi\)
\(390\) 14.7951 0.749180
\(391\) −3.38779 −0.171328
\(392\) 5.29754 0.267566
\(393\) −17.0771 −0.861426
\(394\) −15.6146 −0.786651
\(395\) 32.8613 1.65343
\(396\) 13.3811 0.672424
\(397\) 8.11106 0.407082 0.203541 0.979066i \(-0.434755\pi\)
0.203541 + 0.979066i \(0.434755\pi\)
\(398\) 15.3893 0.771398
\(399\) −10.5277 −0.527044
\(400\) 12.3950 0.619750
\(401\) −11.8831 −0.593416 −0.296708 0.954968i \(-0.595889\pi\)
−0.296708 + 0.954968i \(0.595889\pi\)
\(402\) −4.93656 −0.246213
\(403\) −17.6469 −0.879056
\(404\) −8.68916 −0.432302
\(405\) −7.95142 −0.395109
\(406\) 6.53900 0.324525
\(407\) −2.48706 −0.123279
\(408\) 3.52997 0.174760
\(409\) −21.0442 −1.04057 −0.520283 0.853994i \(-0.674174\pi\)
−0.520283 + 0.853994i \(0.674174\pi\)
\(410\) 45.9134 2.26750
\(411\) −11.4578 −0.565174
\(412\) −2.54539 −0.125402
\(413\) 10.5463 0.518950
\(414\) −1.90727 −0.0937371
\(415\) 20.6519 1.01376
\(416\) 3.79704 0.186165
\(417\) −13.1680 −0.644841
\(418\) 54.3274 2.65724
\(419\) −6.59641 −0.322256 −0.161128 0.986934i \(-0.551513\pi\)
−0.161128 + 0.986934i \(0.551513\pi\)
\(420\) 5.08408 0.248078
\(421\) 5.15248 0.251117 0.125558 0.992086i \(-0.459928\pi\)
0.125558 + 0.992086i \(0.459928\pi\)
\(422\) −27.6277 −1.34490
\(423\) −13.2421 −0.643854
\(424\) −5.28252 −0.256542
\(425\) 46.8335 2.27176
\(426\) −12.3615 −0.598915
\(427\) 10.0701 0.487324
\(428\) −6.96570 −0.336700
\(429\) −22.3147 −1.07737
\(430\) −22.4651 −1.08336
\(431\) 15.9709 0.769289 0.384645 0.923065i \(-0.374324\pi\)
0.384645 + 0.923065i \(0.374324\pi\)
\(432\) 4.79005 0.230461
\(433\) −10.3062 −0.495285 −0.247642 0.968852i \(-0.579656\pi\)
−0.247642 + 0.968852i \(0.579656\pi\)
\(434\) −6.06405 −0.291084
\(435\) −19.5274 −0.936269
\(436\) −9.52787 −0.456302
\(437\) −7.74354 −0.370424
\(438\) 4.88047 0.233198
\(439\) 17.0755 0.814967 0.407483 0.913213i \(-0.366406\pi\)
0.407483 + 0.913213i \(0.366406\pi\)
\(440\) −26.2360 −1.25075
\(441\) 11.2688 0.536612
\(442\) 14.3468 0.682409
\(443\) −2.09547 −0.0995586 −0.0497793 0.998760i \(-0.515852\pi\)
−0.0497793 + 0.998760i \(0.515852\pi\)
\(444\) −0.369369 −0.0175295
\(445\) 64.8216 3.07284
\(446\) 2.83303 0.134148
\(447\) 1.14982 0.0543848
\(448\) 1.30479 0.0616453
\(449\) −32.2664 −1.52275 −0.761373 0.648314i \(-0.775474\pi\)
−0.761373 + 0.648314i \(0.775474\pi\)
\(450\) 26.3665 1.24293
\(451\) −69.2489 −3.26081
\(452\) −2.68341 −0.126217
\(453\) −5.61378 −0.263759
\(454\) 16.4681 0.772886
\(455\) 20.6632 0.968704
\(456\) 8.06853 0.377843
\(457\) −2.59763 −0.121512 −0.0607560 0.998153i \(-0.519351\pi\)
−0.0607560 + 0.998153i \(0.519351\pi\)
\(458\) −1.54283 −0.0720917
\(459\) 18.0988 0.844780
\(460\) 3.73954 0.174357
\(461\) −14.9302 −0.695368 −0.347684 0.937612i \(-0.613032\pi\)
−0.347684 + 0.937612i \(0.613032\pi\)
\(462\) −7.66806 −0.356750
\(463\) 13.4971 0.627265 0.313633 0.949544i \(-0.398454\pi\)
0.313633 + 0.949544i \(0.398454\pi\)
\(464\) −5.01155 −0.232656
\(465\) 18.1091 0.839789
\(466\) −22.7015 −1.05163
\(467\) −20.2483 −0.936982 −0.468491 0.883468i \(-0.655202\pi\)
−0.468491 + 0.883468i \(0.655202\pi\)
\(468\) 8.07702 0.373360
\(469\) −6.89450 −0.318358
\(470\) 25.9636 1.19761
\(471\) −21.1113 −0.972759
\(472\) −8.08279 −0.372041
\(473\) 33.8829 1.55794
\(474\) −7.36094 −0.338099
\(475\) 107.048 4.91172
\(476\) 4.93003 0.225967
\(477\) −11.2369 −0.514502
\(478\) −1.25406 −0.0573593
\(479\) −38.1793 −1.74446 −0.872229 0.489097i \(-0.837326\pi\)
−0.872229 + 0.489097i \(0.837326\pi\)
\(480\) −3.89648 −0.177849
\(481\) −1.50122 −0.0684500
\(482\) −0.519454 −0.0236605
\(483\) 1.09296 0.0497316
\(484\) 28.5705 1.29866
\(485\) −19.0101 −0.863203
\(486\) 16.1513 0.732636
\(487\) −24.2739 −1.09995 −0.549977 0.835180i \(-0.685363\pi\)
−0.549977 + 0.835180i \(0.685363\pi\)
\(488\) −7.71779 −0.349368
\(489\) 5.86356 0.265159
\(490\) −22.0946 −0.998132
\(491\) −11.5479 −0.521150 −0.260575 0.965454i \(-0.583912\pi\)
−0.260575 + 0.965454i \(0.583912\pi\)
\(492\) −10.2846 −0.463667
\(493\) −18.9358 −0.852824
\(494\) 32.7928 1.47542
\(495\) −55.8089 −2.50842
\(496\) 4.64754 0.208681
\(497\) −17.2643 −0.774408
\(498\) −4.62603 −0.207297
\(499\) −14.7381 −0.659770 −0.329885 0.944021i \(-0.607010\pi\)
−0.329885 + 0.944021i \(0.607010\pi\)
\(500\) −30.8426 −1.37932
\(501\) −7.54490 −0.337081
\(502\) −23.4513 −1.04668
\(503\) 31.8620 1.42066 0.710328 0.703871i \(-0.248547\pi\)
0.710328 + 0.703871i \(0.248547\pi\)
\(504\) 2.77552 0.123632
\(505\) 36.2401 1.61266
\(506\) −5.64016 −0.250736
\(507\) −1.32432 −0.0588153
\(508\) −13.4700 −0.597634
\(509\) 26.1479 1.15899 0.579493 0.814977i \(-0.303251\pi\)
0.579493 + 0.814977i \(0.303251\pi\)
\(510\) −14.7226 −0.651926
\(511\) 6.81617 0.301530
\(512\) −1.00000 −0.0441942
\(513\) 41.3688 1.82648
\(514\) 0.960802 0.0423792
\(515\) 10.6161 0.467803
\(516\) 5.03218 0.221529
\(517\) −39.1596 −1.72224
\(518\) −0.515869 −0.0226660
\(519\) 12.0693 0.529782
\(520\) −15.8364 −0.694474
\(521\) 4.61006 0.201970 0.100985 0.994888i \(-0.467801\pi\)
0.100985 + 0.994888i \(0.467801\pi\)
\(522\) −10.6605 −0.466598
\(523\) 25.0913 1.09716 0.548582 0.836097i \(-0.315168\pi\)
0.548582 + 0.836097i \(0.315168\pi\)
\(524\) 18.2790 0.798523
\(525\) −15.1094 −0.659427
\(526\) 18.8333 0.821169
\(527\) 17.5604 0.764942
\(528\) 5.87687 0.255758
\(529\) −22.1961 −0.965047
\(530\) 22.0320 0.957007
\(531\) −17.1936 −0.746139
\(532\) 11.2687 0.488559
\(533\) −41.7997 −1.81055
\(534\) −14.5200 −0.628344
\(535\) 29.0521 1.25603
\(536\) 5.28401 0.228234
\(537\) 21.6924 0.936097
\(538\) 13.2221 0.570046
\(539\) 33.3242 1.43537
\(540\) −19.9780 −0.859716
\(541\) −11.3338 −0.487278 −0.243639 0.969866i \(-0.578341\pi\)
−0.243639 + 0.969866i \(0.578341\pi\)
\(542\) 4.48027 0.192444
\(543\) 4.76996 0.204699
\(544\) −3.77842 −0.161998
\(545\) 39.7382 1.70220
\(546\) −4.62855 −0.198084
\(547\) 29.0927 1.24391 0.621957 0.783051i \(-0.286338\pi\)
0.621957 + 0.783051i \(0.286338\pi\)
\(548\) 12.2643 0.523904
\(549\) −16.4172 −0.700668
\(550\) 77.9708 3.32469
\(551\) −43.2819 −1.84387
\(552\) −0.837658 −0.0356531
\(553\) −10.2804 −0.437169
\(554\) 15.8791 0.674638
\(555\) 1.54054 0.0653923
\(556\) 14.0948 0.597754
\(557\) −24.3539 −1.03191 −0.515954 0.856616i \(-0.672563\pi\)
−0.515954 + 0.856616i \(0.672563\pi\)
\(558\) 9.88619 0.418516
\(559\) 20.4522 0.865037
\(560\) −5.44191 −0.229963
\(561\) 22.2053 0.937508
\(562\) 0.405076 0.0170871
\(563\) 34.9975 1.47497 0.737485 0.675363i \(-0.236013\pi\)
0.737485 + 0.675363i \(0.236013\pi\)
\(564\) −5.81585 −0.244891
\(565\) 11.1918 0.470841
\(566\) 6.16780 0.259252
\(567\) 2.48755 0.104467
\(568\) 13.2315 0.555181
\(569\) −10.6294 −0.445607 −0.222804 0.974863i \(-0.571521\pi\)
−0.222804 + 0.974863i \(0.571521\pi\)
\(570\) −33.6517 −1.40951
\(571\) 8.04737 0.336772 0.168386 0.985721i \(-0.446144\pi\)
0.168386 + 0.985721i \(0.446144\pi\)
\(572\) 23.8853 0.998695
\(573\) −18.9189 −0.790350
\(574\) −14.3637 −0.599530
\(575\) −11.1135 −0.463467
\(576\) −2.12719 −0.0886328
\(577\) 24.5992 1.02408 0.512039 0.858962i \(-0.328890\pi\)
0.512039 + 0.858962i \(0.328890\pi\)
\(578\) 2.72354 0.113284
\(579\) −7.25436 −0.301481
\(580\) 20.9018 0.867902
\(581\) −6.46080 −0.268039
\(582\) 4.25826 0.176511
\(583\) −33.2297 −1.37623
\(584\) −5.22398 −0.216170
\(585\) −33.6871 −1.39279
\(586\) −9.66195 −0.399132
\(587\) 45.1241 1.86247 0.931236 0.364416i \(-0.118731\pi\)
0.931236 + 0.364416i \(0.118731\pi\)
\(588\) 4.94919 0.204101
\(589\) 40.1381 1.65386
\(590\) 33.7111 1.38787
\(591\) −14.5878 −0.600063
\(592\) 0.395367 0.0162495
\(593\) −11.4214 −0.469022 −0.234511 0.972113i \(-0.575349\pi\)
−0.234511 + 0.972113i \(0.575349\pi\)
\(594\) 30.1318 1.23632
\(595\) −20.5618 −0.842953
\(596\) −1.23075 −0.0504136
\(597\) 14.3774 0.588429
\(598\) −3.40449 −0.139220
\(599\) −2.57802 −0.105335 −0.0526676 0.998612i \(-0.516772\pi\)
−0.0526676 + 0.998612i \(0.516772\pi\)
\(600\) 11.5800 0.472750
\(601\) −1.87053 −0.0763004 −0.0381502 0.999272i \(-0.512147\pi\)
−0.0381502 + 0.999272i \(0.512147\pi\)
\(602\) 7.02804 0.286442
\(603\) 11.2401 0.457731
\(604\) 6.00890 0.244499
\(605\) −119.160 −4.84453
\(606\) −8.11780 −0.329763
\(607\) 35.1472 1.42658 0.713290 0.700869i \(-0.247204\pi\)
0.713290 + 0.700869i \(0.247204\pi\)
\(608\) −8.63642 −0.350253
\(609\) 6.10903 0.247550
\(610\) 32.1888 1.30329
\(611\) −23.6373 −0.956263
\(612\) −8.03740 −0.324893
\(613\) 3.70585 0.149678 0.0748389 0.997196i \(-0.476156\pi\)
0.0748389 + 0.997196i \(0.476156\pi\)
\(614\) 20.2896 0.818822
\(615\) 42.8944 1.72967
\(616\) 8.20776 0.330700
\(617\) −19.9943 −0.804940 −0.402470 0.915433i \(-0.631848\pi\)
−0.402470 + 0.915433i \(0.631848\pi\)
\(618\) −2.37802 −0.0956580
\(619\) −30.3747 −1.22086 −0.610430 0.792070i \(-0.709003\pi\)
−0.610430 + 0.792070i \(0.709003\pi\)
\(620\) −19.3837 −0.778466
\(621\) −4.29483 −0.172346
\(622\) −14.9639 −0.599999
\(623\) −20.2790 −0.812461
\(624\) 3.54737 0.142008
\(625\) 66.6611 2.66644
\(626\) −33.8135 −1.35146
\(627\) 50.7551 2.02696
\(628\) 22.5972 0.901727
\(629\) 1.49386 0.0595642
\(630\) −11.5760 −0.461197
\(631\) 31.0024 1.23419 0.617093 0.786890i \(-0.288310\pi\)
0.617093 + 0.786890i \(0.288310\pi\)
\(632\) 7.87903 0.313411
\(633\) −25.8111 −1.02590
\(634\) 22.0889 0.877264
\(635\) 56.1797 2.22942
\(636\) −4.93516 −0.195692
\(637\) 20.1150 0.796984
\(638\) −31.5252 −1.24809
\(639\) 28.1459 1.11343
\(640\) 4.17073 0.164863
\(641\) 36.7042 1.44973 0.724864 0.688892i \(-0.241902\pi\)
0.724864 + 0.688892i \(0.241902\pi\)
\(642\) −6.50767 −0.256837
\(643\) 20.7356 0.817733 0.408867 0.912594i \(-0.365924\pi\)
0.408867 + 0.912594i \(0.365924\pi\)
\(644\) −1.16989 −0.0461001
\(645\) −20.9879 −0.826396
\(646\) −32.6320 −1.28389
\(647\) −5.71625 −0.224729 −0.112364 0.993667i \(-0.535842\pi\)
−0.112364 + 0.993667i \(0.535842\pi\)
\(648\) −1.90648 −0.0748937
\(649\) −50.8448 −1.99583
\(650\) 47.0644 1.84602
\(651\) −5.66530 −0.222041
\(652\) −6.27626 −0.245797
\(653\) 47.7908 1.87020 0.935099 0.354388i \(-0.115311\pi\)
0.935099 + 0.354388i \(0.115311\pi\)
\(654\) −8.90137 −0.348071
\(655\) −76.2370 −2.97882
\(656\) 11.0085 0.429809
\(657\) −11.1124 −0.433535
\(658\) −8.12253 −0.316649
\(659\) −2.76816 −0.107832 −0.0539161 0.998545i \(-0.517170\pi\)
−0.0539161 + 0.998545i \(0.517170\pi\)
\(660\) −24.5109 −0.954084
\(661\) −21.9511 −0.853799 −0.426900 0.904299i \(-0.640394\pi\)
−0.426900 + 0.904299i \(0.640394\pi\)
\(662\) 18.2309 0.708565
\(663\) 13.4034 0.520547
\(664\) 4.95162 0.192160
\(665\) −46.9986 −1.82253
\(666\) 0.841019 0.0325888
\(667\) 4.49343 0.173986
\(668\) 8.07593 0.312467
\(669\) 2.64675 0.102329
\(670\) −22.0382 −0.851409
\(671\) −48.5488 −1.87421
\(672\) 1.21899 0.0470235
\(673\) −41.9868 −1.61847 −0.809237 0.587483i \(-0.800119\pi\)
−0.809237 + 0.587483i \(0.800119\pi\)
\(674\) 0.521940 0.0201044
\(675\) 59.3726 2.28525
\(676\) 1.41753 0.0545206
\(677\) 9.83797 0.378104 0.189052 0.981967i \(-0.439459\pi\)
0.189052 + 0.981967i \(0.439459\pi\)
\(678\) −2.50696 −0.0962792
\(679\) 5.94717 0.228232
\(680\) 15.7588 0.604322
\(681\) 15.3852 0.589563
\(682\) 29.2354 1.11948
\(683\) 2.13712 0.0817747 0.0408874 0.999164i \(-0.486982\pi\)
0.0408874 + 0.999164i \(0.486982\pi\)
\(684\) −18.3713 −0.702443
\(685\) −51.1510 −1.95438
\(686\) 16.0456 0.612626
\(687\) −1.44138 −0.0549921
\(688\) −5.38636 −0.205353
\(689\) −20.0579 −0.764147
\(690\) 3.49365 0.133001
\(691\) −7.26539 −0.276388 −0.138194 0.990405i \(-0.544130\pi\)
−0.138194 + 0.990405i \(0.544130\pi\)
\(692\) −12.9187 −0.491096
\(693\) 17.4594 0.663229
\(694\) 16.6049 0.630314
\(695\) −58.7858 −2.22987
\(696\) −4.68202 −0.177471
\(697\) 41.5947 1.57551
\(698\) 2.71319 0.102696
\(699\) −21.2088 −0.802189
\(700\) 16.1728 0.611275
\(701\) 12.7895 0.483052 0.241526 0.970394i \(-0.422352\pi\)
0.241526 + 0.970394i \(0.422352\pi\)
\(702\) 18.1880 0.686462
\(703\) 3.41455 0.128782
\(704\) −6.29050 −0.237082
\(705\) 24.2563 0.913547
\(706\) −13.9911 −0.526564
\(707\) −11.3375 −0.426390
\(708\) −7.55130 −0.283795
\(709\) −29.2608 −1.09891 −0.549455 0.835523i \(-0.685165\pi\)
−0.549455 + 0.835523i \(0.685165\pi\)
\(710\) −55.1850 −2.07106
\(711\) 16.7602 0.628555
\(712\) 15.5420 0.582462
\(713\) −4.16706 −0.156058
\(714\) 4.60585 0.172370
\(715\) −99.6192 −3.72555
\(716\) −23.2192 −0.867742
\(717\) −1.17160 −0.0437541
\(718\) −28.3376 −1.05755
\(719\) 0.382835 0.0142773 0.00713867 0.999975i \(-0.497728\pi\)
0.00713867 + 0.999975i \(0.497728\pi\)
\(720\) 8.87192 0.330637
\(721\) −3.32119 −0.123688
\(722\) −55.5877 −2.06876
\(723\) −0.485297 −0.0180484
\(724\) −5.10569 −0.189751
\(725\) −62.1182 −2.30701
\(726\) 26.6918 0.990626
\(727\) −5.33183 −0.197747 −0.0988734 0.995100i \(-0.531524\pi\)
−0.0988734 + 0.995100i \(0.531524\pi\)
\(728\) 4.95433 0.183620
\(729\) 9.36979 0.347029
\(730\) 21.7878 0.806403
\(731\) −20.3519 −0.752743
\(732\) −7.21030 −0.266501
\(733\) −37.8541 −1.39817 −0.699087 0.715037i \(-0.746410\pi\)
−0.699087 + 0.715037i \(0.746410\pi\)
\(734\) 29.5228 1.08970
\(735\) −20.6418 −0.761383
\(736\) 0.896615 0.0330497
\(737\) 33.2391 1.22438
\(738\) 23.4171 0.861995
\(739\) 6.28613 0.231239 0.115620 0.993294i \(-0.463115\pi\)
0.115620 + 0.993294i \(0.463115\pi\)
\(740\) −1.64897 −0.0606173
\(741\) 30.6365 1.12546
\(742\) −6.89255 −0.253034
\(743\) −41.8927 −1.53689 −0.768447 0.639913i \(-0.778970\pi\)
−0.768447 + 0.639913i \(0.778970\pi\)
\(744\) 4.34194 0.159183
\(745\) 5.13314 0.188064
\(746\) 26.9628 0.987178
\(747\) 10.5330 0.385383
\(748\) −23.7682 −0.869050
\(749\) −9.08875 −0.332096
\(750\) −28.8145 −1.05216
\(751\) −4.92682 −0.179782 −0.0898911 0.995952i \(-0.528652\pi\)
−0.0898911 + 0.995952i \(0.528652\pi\)
\(752\) 6.22519 0.227009
\(753\) −21.9093 −0.798418
\(754\) −19.0291 −0.692998
\(755\) −25.0615 −0.912082
\(756\) 6.24998 0.227310
\(757\) 3.54979 0.129019 0.0645097 0.997917i \(-0.479452\pi\)
0.0645097 + 0.997917i \(0.479452\pi\)
\(758\) 28.1649 1.02300
\(759\) −5.26929 −0.191263
\(760\) 36.0202 1.30659
\(761\) 18.2164 0.660346 0.330173 0.943921i \(-0.392893\pi\)
0.330173 + 0.943921i \(0.392893\pi\)
\(762\) −12.5843 −0.455880
\(763\) −12.4318 −0.450062
\(764\) 20.2505 0.732637
\(765\) 33.5219 1.21199
\(766\) −4.76207 −0.172061
\(767\) −30.6907 −1.10818
\(768\) −0.934245 −0.0337117
\(769\) −13.3668 −0.482021 −0.241010 0.970523i \(-0.577479\pi\)
−0.241010 + 0.970523i \(0.577479\pi\)
\(770\) −34.2324 −1.23365
\(771\) 0.897624 0.0323272
\(772\) 7.76495 0.279467
\(773\) 37.1140 1.33490 0.667450 0.744655i \(-0.267386\pi\)
0.667450 + 0.744655i \(0.267386\pi\)
\(774\) −11.4578 −0.411842
\(775\) 57.6063 2.06928
\(776\) −4.55797 −0.163622
\(777\) −0.481948 −0.0172898
\(778\) 23.8263 0.854214
\(779\) 95.0739 3.40637
\(780\) −14.7951 −0.529750
\(781\) 83.2328 2.97830
\(782\) 3.38779 0.121147
\(783\) −24.0056 −0.857889
\(784\) −5.29754 −0.189198
\(785\) −94.2470 −3.36382
\(786\) 17.0771 0.609120
\(787\) 12.8219 0.457051 0.228525 0.973538i \(-0.426610\pi\)
0.228525 + 0.973538i \(0.426610\pi\)
\(788\) 15.6146 0.556246
\(789\) 17.5949 0.626394
\(790\) −32.8613 −1.16915
\(791\) −3.50127 −0.124491
\(792\) −13.3811 −0.475476
\(793\) −29.3048 −1.04064
\(794\) −8.11106 −0.287851
\(795\) 20.5832 0.730013
\(796\) −15.3893 −0.545461
\(797\) −42.5698 −1.50790 −0.753951 0.656931i \(-0.771854\pi\)
−0.753951 + 0.656931i \(0.771854\pi\)
\(798\) 10.5277 0.372676
\(799\) 23.5214 0.832126
\(800\) −12.3950 −0.438229
\(801\) 33.0608 1.16814
\(802\) 11.8831 0.419608
\(803\) −32.8615 −1.15966
\(804\) 4.93656 0.174099
\(805\) 4.87930 0.171973
\(806\) 17.6469 0.621586
\(807\) 12.3527 0.434836
\(808\) 8.68916 0.305683
\(809\) −4.66593 −0.164045 −0.0820227 0.996630i \(-0.526138\pi\)
−0.0820227 + 0.996630i \(0.526138\pi\)
\(810\) 7.95142 0.279385
\(811\) −22.3456 −0.784660 −0.392330 0.919824i \(-0.628331\pi\)
−0.392330 + 0.919824i \(0.628331\pi\)
\(812\) −6.53900 −0.229474
\(813\) 4.18567 0.146798
\(814\) 2.48706 0.0871713
\(815\) 26.1766 0.916926
\(816\) −3.52997 −0.123574
\(817\) −46.5188 −1.62749
\(818\) 21.0442 0.735792
\(819\) 10.5388 0.368255
\(820\) −45.9134 −1.60337
\(821\) 17.8228 0.622021 0.311011 0.950406i \(-0.399333\pi\)
0.311011 + 0.950406i \(0.399333\pi\)
\(822\) 11.4578 0.399638
\(823\) 5.48252 0.191109 0.0955543 0.995424i \(-0.469538\pi\)
0.0955543 + 0.995424i \(0.469538\pi\)
\(824\) 2.54539 0.0886729
\(825\) 72.8438 2.53610
\(826\) −10.5463 −0.366953
\(827\) 53.7308 1.86840 0.934202 0.356744i \(-0.116113\pi\)
0.934202 + 0.356744i \(0.116113\pi\)
\(828\) 1.90727 0.0662821
\(829\) −9.63718 −0.334713 −0.167357 0.985896i \(-0.553523\pi\)
−0.167357 + 0.985896i \(0.553523\pi\)
\(830\) −20.6519 −0.716837
\(831\) 14.8350 0.514619
\(832\) −3.79704 −0.131639
\(833\) −20.0163 −0.693524
\(834\) 13.1680 0.455971
\(835\) −33.6825 −1.16563
\(836\) −54.3274 −1.87895
\(837\) 22.2620 0.769486
\(838\) 6.59641 0.227869
\(839\) −15.0986 −0.521260 −0.260630 0.965439i \(-0.583930\pi\)
−0.260630 + 0.965439i \(0.583930\pi\)
\(840\) −5.08408 −0.175417
\(841\) −3.88433 −0.133942
\(842\) −5.15248 −0.177566
\(843\) 0.378440 0.0130342
\(844\) 27.6277 0.950986
\(845\) −5.91216 −0.203384
\(846\) 13.2421 0.455274
\(847\) 37.2783 1.28090
\(848\) 5.28252 0.181402
\(849\) 5.76224 0.197760
\(850\) −46.8335 −1.60638
\(851\) −0.354492 −0.0121518
\(852\) 12.3615 0.423497
\(853\) 0.329799 0.0112921 0.00564606 0.999984i \(-0.498203\pi\)
0.00564606 + 0.999984i \(0.498203\pi\)
\(854\) −10.0701 −0.344590
\(855\) 76.6216 2.62040
\(856\) 6.96570 0.238083
\(857\) −27.8084 −0.949918 −0.474959 0.880008i \(-0.657537\pi\)
−0.474959 + 0.880008i \(0.657537\pi\)
\(858\) 22.3147 0.761812
\(859\) 9.14814 0.312130 0.156065 0.987747i \(-0.450119\pi\)
0.156065 + 0.987747i \(0.450119\pi\)
\(860\) 22.4651 0.766052
\(861\) −13.4192 −0.457326
\(862\) −15.9709 −0.543970
\(863\) −25.5236 −0.868834 −0.434417 0.900712i \(-0.643046\pi\)
−0.434417 + 0.900712i \(0.643046\pi\)
\(864\) −4.79005 −0.162961
\(865\) 53.8805 1.83199
\(866\) 10.3062 0.350219
\(867\) 2.54445 0.0864142
\(868\) 6.06405 0.205827
\(869\) 49.5631 1.68131
\(870\) 19.5274 0.662042
\(871\) 20.0636 0.679829
\(872\) 9.52787 0.322655
\(873\) −9.69565 −0.328148
\(874\) 7.74354 0.261929
\(875\) −40.2429 −1.36046
\(876\) −4.88047 −0.164896
\(877\) 44.8226 1.51355 0.756775 0.653675i \(-0.226774\pi\)
0.756775 + 0.653675i \(0.226774\pi\)
\(878\) −17.0755 −0.576269
\(879\) −9.02663 −0.304461
\(880\) 26.2360 0.884416
\(881\) −19.4925 −0.656718 −0.328359 0.944553i \(-0.606496\pi\)
−0.328359 + 0.944553i \(0.606496\pi\)
\(882\) −11.2688 −0.379442
\(883\) 40.1851 1.35234 0.676169 0.736747i \(-0.263639\pi\)
0.676169 + 0.736747i \(0.263639\pi\)
\(884\) −14.3468 −0.482536
\(885\) 31.4945 1.05867
\(886\) 2.09547 0.0703986
\(887\) 33.1379 1.11266 0.556330 0.830961i \(-0.312209\pi\)
0.556330 + 0.830961i \(0.312209\pi\)
\(888\) 0.369369 0.0123952
\(889\) −17.5754 −0.589461
\(890\) −64.8216 −2.17282
\(891\) −11.9927 −0.401772
\(892\) −2.83303 −0.0948570
\(893\) 53.7633 1.79912
\(894\) −1.14982 −0.0384559
\(895\) 96.8411 3.23704
\(896\) −1.30479 −0.0435898
\(897\) −3.18062 −0.106198
\(898\) 32.2664 1.07674
\(899\) −23.2914 −0.776812
\(900\) −26.3665 −0.878883
\(901\) 19.9596 0.664950
\(902\) 69.2489 2.30574
\(903\) 6.56591 0.218500
\(904\) 2.68341 0.0892488
\(905\) 21.2944 0.707851
\(906\) 5.61378 0.186505
\(907\) −14.9243 −0.495552 −0.247776 0.968817i \(-0.579700\pi\)
−0.247776 + 0.968817i \(0.579700\pi\)
\(908\) −16.4681 −0.546513
\(909\) 18.4835 0.613057
\(910\) −20.6632 −0.684977
\(911\) −40.1885 −1.33150 −0.665752 0.746173i \(-0.731889\pi\)
−0.665752 + 0.746173i \(0.731889\pi\)
\(912\) −8.06853 −0.267176
\(913\) 31.1482 1.03085
\(914\) 2.59763 0.0859219
\(915\) 30.0722 0.994158
\(916\) 1.54283 0.0509765
\(917\) 23.8502 0.787604
\(918\) −18.0988 −0.597350
\(919\) −30.4167 −1.00335 −0.501677 0.865055i \(-0.667283\pi\)
−0.501677 + 0.865055i \(0.667283\pi\)
\(920\) −3.73954 −0.123289
\(921\) 18.9555 0.624604
\(922\) 14.9302 0.491700
\(923\) 50.2406 1.65369
\(924\) 7.66806 0.252261
\(925\) 4.90057 0.161130
\(926\) −13.4971 −0.443543
\(927\) 5.41452 0.177836
\(928\) 5.01155 0.164512
\(929\) −36.2526 −1.18941 −0.594705 0.803944i \(-0.702731\pi\)
−0.594705 + 0.803944i \(0.702731\pi\)
\(930\) −18.1091 −0.593820
\(931\) −45.7517 −1.49945
\(932\) 22.7015 0.743612
\(933\) −13.9800 −0.457684
\(934\) 20.2483 0.662546
\(935\) 99.1307 3.24192
\(936\) −8.07702 −0.264006
\(937\) −23.4015 −0.764493 −0.382246 0.924060i \(-0.624849\pi\)
−0.382246 + 0.924060i \(0.624849\pi\)
\(938\) 6.89450 0.225113
\(939\) −31.5901 −1.03091
\(940\) −25.9636 −0.846839
\(941\) −18.2026 −0.593388 −0.296694 0.954973i \(-0.595884\pi\)
−0.296694 + 0.954973i \(0.595884\pi\)
\(942\) 21.1113 0.687845
\(943\) −9.87038 −0.321424
\(944\) 8.08279 0.263072
\(945\) −26.0670 −0.847960
\(946\) −33.8829 −1.10163
\(947\) −39.9245 −1.29737 −0.648686 0.761056i \(-0.724681\pi\)
−0.648686 + 0.761056i \(0.724681\pi\)
\(948\) 7.36094 0.239072
\(949\) −19.8357 −0.643893
\(950\) −107.048 −3.47311
\(951\) 20.6365 0.669184
\(952\) −4.93003 −0.159783
\(953\) 33.5945 1.08823 0.544117 0.839009i \(-0.316865\pi\)
0.544117 + 0.839009i \(0.316865\pi\)
\(954\) 11.2369 0.363808
\(955\) −84.4594 −2.73304
\(956\) 1.25406 0.0405592
\(957\) −29.4523 −0.952056
\(958\) 38.1793 1.23352
\(959\) 16.0023 0.516740
\(960\) 3.89648 0.125758
\(961\) −9.40034 −0.303237
\(962\) 1.50122 0.0484014
\(963\) 14.8173 0.477482
\(964\) 0.519454 0.0167305
\(965\) −32.3855 −1.04253
\(966\) −1.09296 −0.0351655
\(967\) 12.7735 0.410769 0.205385 0.978681i \(-0.434155\pi\)
0.205385 + 0.978681i \(0.434155\pi\)
\(968\) −28.5705 −0.918289
\(969\) −30.4863 −0.979361
\(970\) 19.0101 0.610377
\(971\) 8.13004 0.260905 0.130453 0.991455i \(-0.458357\pi\)
0.130453 + 0.991455i \(0.458357\pi\)
\(972\) −16.1513 −0.518052
\(973\) 18.3907 0.589580
\(974\) 24.2739 0.777785
\(975\) 43.9696 1.40816
\(976\) 7.71779 0.247040
\(977\) 49.8159 1.59375 0.796876 0.604143i \(-0.206485\pi\)
0.796876 + 0.604143i \(0.206485\pi\)
\(978\) −5.86356 −0.187496
\(979\) 97.7671 3.12465
\(980\) 22.0946 0.705786
\(981\) 20.2676 0.647094
\(982\) 11.5479 0.368509
\(983\) −19.4029 −0.618858 −0.309429 0.950923i \(-0.600138\pi\)
−0.309429 + 0.950923i \(0.600138\pi\)
\(984\) 10.2846 0.327862
\(985\) −65.1242 −2.07503
\(986\) 18.9358 0.603037
\(987\) −7.58843 −0.241542
\(988\) −32.7928 −1.04328
\(989\) 4.82949 0.153569
\(990\) 55.8089 1.77372
\(991\) 12.4473 0.395401 0.197701 0.980262i \(-0.436653\pi\)
0.197701 + 0.980262i \(0.436653\pi\)
\(992\) −4.64754 −0.147560
\(993\) 17.0321 0.540499
\(994\) 17.2643 0.547589
\(995\) 64.1848 2.03480
\(996\) 4.62603 0.146581
\(997\) −22.7094 −0.719213 −0.359607 0.933104i \(-0.617089\pi\)
−0.359607 + 0.933104i \(0.617089\pi\)
\(998\) 14.7381 0.466528
\(999\) 1.89383 0.0599180
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.1.16 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.16 40 1.1 even 1 trivial