Properties

Label 8007.2.a.f.1.38
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.38
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.79498 q^{2} -1.00000 q^{3} +1.22197 q^{4} +0.0102027 q^{5} -1.79498 q^{6} -0.754723 q^{7} -1.39655 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.79498 q^{2} -1.00000 q^{3} +1.22197 q^{4} +0.0102027 q^{5} -1.79498 q^{6} -0.754723 q^{7} -1.39655 q^{8} +1.00000 q^{9} +0.0183137 q^{10} +5.42760 q^{11} -1.22197 q^{12} -1.45815 q^{13} -1.35472 q^{14} -0.0102027 q^{15} -4.95073 q^{16} -1.00000 q^{17} +1.79498 q^{18} +3.28127 q^{19} +0.0124674 q^{20} +0.754723 q^{21} +9.74245 q^{22} -4.49344 q^{23} +1.39655 q^{24} -4.99990 q^{25} -2.61736 q^{26} -1.00000 q^{27} -0.922249 q^{28} -7.70081 q^{29} -0.0183137 q^{30} +1.34424 q^{31} -6.09338 q^{32} -5.42760 q^{33} -1.79498 q^{34} -0.00770024 q^{35} +1.22197 q^{36} +6.85692 q^{37} +5.88983 q^{38} +1.45815 q^{39} -0.0142487 q^{40} +10.8001 q^{41} +1.35472 q^{42} +4.83900 q^{43} +6.63236 q^{44} +0.0102027 q^{45} -8.06565 q^{46} -8.18535 q^{47} +4.95073 q^{48} -6.43039 q^{49} -8.97474 q^{50} +1.00000 q^{51} -1.78182 q^{52} +7.35778 q^{53} -1.79498 q^{54} +0.0553763 q^{55} +1.05401 q^{56} -3.28127 q^{57} -13.8228 q^{58} -1.35595 q^{59} -0.0124674 q^{60} -1.65482 q^{61} +2.41289 q^{62} -0.754723 q^{63} -1.03606 q^{64} -0.0148771 q^{65} -9.74245 q^{66} -13.7960 q^{67} -1.22197 q^{68} +4.49344 q^{69} -0.0138218 q^{70} -4.70130 q^{71} -1.39655 q^{72} -7.69655 q^{73} +12.3081 q^{74} +4.99990 q^{75} +4.00961 q^{76} -4.09633 q^{77} +2.61736 q^{78} +6.14149 q^{79} -0.0505110 q^{80} +1.00000 q^{81} +19.3860 q^{82} -9.19715 q^{83} +0.922249 q^{84} -0.0102027 q^{85} +8.68593 q^{86} +7.70081 q^{87} -7.57993 q^{88} +5.29491 q^{89} +0.0183137 q^{90} +1.10050 q^{91} -5.49084 q^{92} -1.34424 q^{93} -14.6926 q^{94} +0.0334779 q^{95} +6.09338 q^{96} -6.42846 q^{97} -11.5425 q^{98} +5.42760 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.79498 1.26925 0.634623 0.772822i \(-0.281155\pi\)
0.634623 + 0.772822i \(0.281155\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.22197 0.610985
\(5\) 0.0102027 0.00456280 0.00228140 0.999997i \(-0.499274\pi\)
0.00228140 + 0.999997i \(0.499274\pi\)
\(6\) −1.79498 −0.732799
\(7\) −0.754723 −0.285259 −0.142629 0.989776i \(-0.545556\pi\)
−0.142629 + 0.989776i \(0.545556\pi\)
\(8\) −1.39655 −0.493756
\(9\) 1.00000 0.333333
\(10\) 0.0183137 0.00579131
\(11\) 5.42760 1.63648 0.818241 0.574875i \(-0.194949\pi\)
0.818241 + 0.574875i \(0.194949\pi\)
\(12\) −1.22197 −0.352752
\(13\) −1.45815 −0.404418 −0.202209 0.979342i \(-0.564812\pi\)
−0.202209 + 0.979342i \(0.564812\pi\)
\(14\) −1.35472 −0.362063
\(15\) −0.0102027 −0.00263433
\(16\) −4.95073 −1.23768
\(17\) −1.00000 −0.242536
\(18\) 1.79498 0.423082
\(19\) 3.28127 0.752776 0.376388 0.926462i \(-0.377166\pi\)
0.376388 + 0.926462i \(0.377166\pi\)
\(20\) 0.0124674 0.00278780
\(21\) 0.754723 0.164694
\(22\) 9.74245 2.07710
\(23\) −4.49344 −0.936946 −0.468473 0.883478i \(-0.655196\pi\)
−0.468473 + 0.883478i \(0.655196\pi\)
\(24\) 1.39655 0.285070
\(25\) −4.99990 −0.999979
\(26\) −2.61736 −0.513306
\(27\) −1.00000 −0.192450
\(28\) −0.922249 −0.174289
\(29\) −7.70081 −1.43000 −0.715002 0.699122i \(-0.753574\pi\)
−0.715002 + 0.699122i \(0.753574\pi\)
\(30\) −0.0183137 −0.00334362
\(31\) 1.34424 0.241432 0.120716 0.992687i \(-0.461481\pi\)
0.120716 + 0.992687i \(0.461481\pi\)
\(32\) −6.09338 −1.07717
\(33\) −5.42760 −0.944824
\(34\) −1.79498 −0.307837
\(35\) −0.00770024 −0.00130158
\(36\) 1.22197 0.203662
\(37\) 6.85692 1.12727 0.563636 0.826023i \(-0.309402\pi\)
0.563636 + 0.826023i \(0.309402\pi\)
\(38\) 5.88983 0.955457
\(39\) 1.45815 0.233491
\(40\) −0.0142487 −0.00225291
\(41\) 10.8001 1.68669 0.843347 0.537369i \(-0.180582\pi\)
0.843347 + 0.537369i \(0.180582\pi\)
\(42\) 1.35472 0.209037
\(43\) 4.83900 0.737940 0.368970 0.929441i \(-0.379710\pi\)
0.368970 + 0.929441i \(0.379710\pi\)
\(44\) 6.63236 0.999865
\(45\) 0.0102027 0.00152093
\(46\) −8.06565 −1.18922
\(47\) −8.18535 −1.19396 −0.596978 0.802257i \(-0.703632\pi\)
−0.596978 + 0.802257i \(0.703632\pi\)
\(48\) 4.95073 0.714576
\(49\) −6.43039 −0.918628
\(50\) −8.97474 −1.26922
\(51\) 1.00000 0.140028
\(52\) −1.78182 −0.247093
\(53\) 7.35778 1.01067 0.505335 0.862923i \(-0.331369\pi\)
0.505335 + 0.862923i \(0.331369\pi\)
\(54\) −1.79498 −0.244266
\(55\) 0.0553763 0.00746694
\(56\) 1.05401 0.140848
\(57\) −3.28127 −0.434615
\(58\) −13.8228 −1.81503
\(59\) −1.35595 −0.176529 −0.0882645 0.996097i \(-0.528132\pi\)
−0.0882645 + 0.996097i \(0.528132\pi\)
\(60\) −0.0124674 −0.00160954
\(61\) −1.65482 −0.211878 −0.105939 0.994373i \(-0.533785\pi\)
−0.105939 + 0.994373i \(0.533785\pi\)
\(62\) 2.41289 0.306437
\(63\) −0.754723 −0.0950862
\(64\) −1.03606 −0.129507
\(65\) −0.0148771 −0.00184528
\(66\) −9.74245 −1.19921
\(67\) −13.7960 −1.68545 −0.842726 0.538343i \(-0.819051\pi\)
−0.842726 + 0.538343i \(0.819051\pi\)
\(68\) −1.22197 −0.148186
\(69\) 4.49344 0.540946
\(70\) −0.0138218 −0.00165202
\(71\) −4.70130 −0.557942 −0.278971 0.960300i \(-0.589993\pi\)
−0.278971 + 0.960300i \(0.589993\pi\)
\(72\) −1.39655 −0.164585
\(73\) −7.69655 −0.900813 −0.450406 0.892824i \(-0.648721\pi\)
−0.450406 + 0.892824i \(0.648721\pi\)
\(74\) 12.3081 1.43078
\(75\) 4.99990 0.577338
\(76\) 4.00961 0.459934
\(77\) −4.09633 −0.466821
\(78\) 2.61736 0.296357
\(79\) 6.14149 0.690971 0.345486 0.938424i \(-0.387714\pi\)
0.345486 + 0.938424i \(0.387714\pi\)
\(80\) −0.0505110 −0.00564730
\(81\) 1.00000 0.111111
\(82\) 19.3860 2.14083
\(83\) −9.19715 −1.00952 −0.504759 0.863260i \(-0.668419\pi\)
−0.504759 + 0.863260i \(0.668419\pi\)
\(84\) 0.922249 0.100626
\(85\) −0.0102027 −0.00110664
\(86\) 8.68593 0.936628
\(87\) 7.70081 0.825613
\(88\) −7.57993 −0.808023
\(89\) 5.29491 0.561260 0.280630 0.959816i \(-0.409457\pi\)
0.280630 + 0.959816i \(0.409457\pi\)
\(90\) 0.0183137 0.00193044
\(91\) 1.10050 0.115364
\(92\) −5.49084 −0.572460
\(93\) −1.34424 −0.139391
\(94\) −14.6926 −1.51542
\(95\) 0.0334779 0.00343476
\(96\) 6.09338 0.621903
\(97\) −6.42846 −0.652711 −0.326355 0.945247i \(-0.605821\pi\)
−0.326355 + 0.945247i \(0.605821\pi\)
\(98\) −11.5425 −1.16596
\(99\) 5.42760 0.545494
\(100\) −6.10972 −0.610972
\(101\) 12.4323 1.23706 0.618530 0.785761i \(-0.287728\pi\)
0.618530 + 0.785761i \(0.287728\pi\)
\(102\) 1.79498 0.177730
\(103\) −18.0303 −1.77658 −0.888288 0.459286i \(-0.848105\pi\)
−0.888288 + 0.459286i \(0.848105\pi\)
\(104\) 2.03639 0.199684
\(105\) 0.00770024 0.000751466 0
\(106\) 13.2071 1.28279
\(107\) 1.80692 0.174681 0.0873406 0.996179i \(-0.472163\pi\)
0.0873406 + 0.996179i \(0.472163\pi\)
\(108\) −1.22197 −0.117584
\(109\) −4.77864 −0.457711 −0.228855 0.973460i \(-0.573498\pi\)
−0.228855 + 0.973460i \(0.573498\pi\)
\(110\) 0.0993996 0.00947738
\(111\) −6.85692 −0.650830
\(112\) 3.73643 0.353060
\(113\) −10.7082 −1.00734 −0.503672 0.863895i \(-0.668018\pi\)
−0.503672 + 0.863895i \(0.668018\pi\)
\(114\) −5.88983 −0.551633
\(115\) −0.0458453 −0.00427510
\(116\) −9.41015 −0.873710
\(117\) −1.45815 −0.134806
\(118\) −2.43390 −0.224059
\(119\) 0.754723 0.0691854
\(120\) 0.0142487 0.00130072
\(121\) 18.4588 1.67807
\(122\) −2.97038 −0.268925
\(123\) −10.8001 −0.973813
\(124\) 1.64262 0.147511
\(125\) −0.102026 −0.00912550
\(126\) −1.35472 −0.120688
\(127\) −6.49180 −0.576054 −0.288027 0.957622i \(-0.592999\pi\)
−0.288027 + 0.957622i \(0.592999\pi\)
\(128\) 10.3270 0.912791
\(129\) −4.83900 −0.426050
\(130\) −0.0267042 −0.00234211
\(131\) −13.2086 −1.15404 −0.577022 0.816728i \(-0.695786\pi\)
−0.577022 + 0.816728i \(0.695786\pi\)
\(132\) −6.63236 −0.577273
\(133\) −2.47645 −0.214736
\(134\) −24.7636 −2.13925
\(135\) −0.0102027 −0.000878111 0
\(136\) 1.39655 0.119753
\(137\) −13.3146 −1.13754 −0.568771 0.822496i \(-0.692581\pi\)
−0.568771 + 0.822496i \(0.692581\pi\)
\(138\) 8.06565 0.686594
\(139\) −3.34993 −0.284138 −0.142069 0.989857i \(-0.545375\pi\)
−0.142069 + 0.989857i \(0.545375\pi\)
\(140\) −0.00940945 −0.000795244 0
\(141\) 8.18535 0.689331
\(142\) −8.43876 −0.708165
\(143\) −7.91426 −0.661823
\(144\) −4.95073 −0.412561
\(145\) −0.0785693 −0.00652482
\(146\) −13.8152 −1.14335
\(147\) 6.43039 0.530370
\(148\) 8.37895 0.688745
\(149\) 0.387473 0.0317430 0.0158715 0.999874i \(-0.494948\pi\)
0.0158715 + 0.999874i \(0.494948\pi\)
\(150\) 8.97474 0.732784
\(151\) 12.6614 1.03037 0.515186 0.857078i \(-0.327723\pi\)
0.515186 + 0.857078i \(0.327723\pi\)
\(152\) −4.58247 −0.371688
\(153\) −1.00000 −0.0808452
\(154\) −7.35286 −0.592510
\(155\) 0.0137149 0.00110161
\(156\) 1.78182 0.142659
\(157\) −1.00000 −0.0798087
\(158\) 11.0239 0.877012
\(159\) −7.35778 −0.583510
\(160\) −0.0621691 −0.00491490
\(161\) 3.39130 0.267272
\(162\) 1.79498 0.141027
\(163\) 6.97213 0.546100 0.273050 0.962000i \(-0.411968\pi\)
0.273050 + 0.962000i \(0.411968\pi\)
\(164\) 13.1974 1.03054
\(165\) −0.0553763 −0.00431104
\(166\) −16.5087 −1.28133
\(167\) 23.6493 1.83004 0.915018 0.403413i \(-0.132176\pi\)
0.915018 + 0.403413i \(0.132176\pi\)
\(168\) −1.05401 −0.0813187
\(169\) −10.8738 −0.836446
\(170\) −0.0183137 −0.00140460
\(171\) 3.28127 0.250925
\(172\) 5.91311 0.450870
\(173\) −19.7225 −1.49947 −0.749736 0.661737i \(-0.769820\pi\)
−0.749736 + 0.661737i \(0.769820\pi\)
\(174\) 13.8228 1.04791
\(175\) 3.77354 0.285253
\(176\) −26.8706 −2.02545
\(177\) 1.35595 0.101919
\(178\) 9.50428 0.712376
\(179\) 2.11966 0.158430 0.0792152 0.996858i \(-0.474759\pi\)
0.0792152 + 0.996858i \(0.474759\pi\)
\(180\) 0.0124674 0.000929267 0
\(181\) −4.47995 −0.332992 −0.166496 0.986042i \(-0.553245\pi\)
−0.166496 + 0.986042i \(0.553245\pi\)
\(182\) 1.97538 0.146425
\(183\) 1.65482 0.122328
\(184\) 6.27532 0.462623
\(185\) 0.0699593 0.00514351
\(186\) −2.41289 −0.176921
\(187\) −5.42760 −0.396905
\(188\) −10.0023 −0.729489
\(189\) 0.754723 0.0548980
\(190\) 0.0600924 0.00435956
\(191\) −3.34326 −0.241910 −0.120955 0.992658i \(-0.538596\pi\)
−0.120955 + 0.992658i \(0.538596\pi\)
\(192\) 1.03606 0.0747709
\(193\) −7.19308 −0.517769 −0.258884 0.965908i \(-0.583355\pi\)
−0.258884 + 0.965908i \(0.583355\pi\)
\(194\) −11.5390 −0.828450
\(195\) 0.0148771 0.00106537
\(196\) −7.85774 −0.561267
\(197\) −15.6419 −1.11444 −0.557221 0.830364i \(-0.688132\pi\)
−0.557221 + 0.830364i \(0.688132\pi\)
\(198\) 9.74245 0.692366
\(199\) 17.7073 1.25524 0.627620 0.778520i \(-0.284029\pi\)
0.627620 + 0.778520i \(0.284029\pi\)
\(200\) 6.98262 0.493746
\(201\) 13.7960 0.973096
\(202\) 22.3158 1.57013
\(203\) 5.81198 0.407921
\(204\) 1.22197 0.0855549
\(205\) 0.110191 0.00769605
\(206\) −32.3641 −2.25491
\(207\) −4.49344 −0.312315
\(208\) 7.21891 0.500541
\(209\) 17.8094 1.23190
\(210\) 0.0138218 0.000953795 0
\(211\) 10.0885 0.694518 0.347259 0.937769i \(-0.387113\pi\)
0.347259 + 0.937769i \(0.387113\pi\)
\(212\) 8.99098 0.617503
\(213\) 4.70130 0.322128
\(214\) 3.24339 0.221713
\(215\) 0.0493710 0.00336707
\(216\) 1.39655 0.0950234
\(217\) −1.01453 −0.0688706
\(218\) −8.57758 −0.580947
\(219\) 7.69655 0.520085
\(220\) 0.0676681 0.00456219
\(221\) 1.45815 0.0980858
\(222\) −12.3081 −0.826064
\(223\) 0.869689 0.0582387 0.0291193 0.999576i \(-0.490730\pi\)
0.0291193 + 0.999576i \(0.490730\pi\)
\(224\) 4.59881 0.307271
\(225\) −4.99990 −0.333326
\(226\) −19.2211 −1.27857
\(227\) −26.6522 −1.76897 −0.884484 0.466570i \(-0.845490\pi\)
−0.884484 + 0.466570i \(0.845490\pi\)
\(228\) −4.00961 −0.265543
\(229\) −21.1980 −1.40080 −0.700402 0.713748i \(-0.746996\pi\)
−0.700402 + 0.713748i \(0.746996\pi\)
\(230\) −0.0822916 −0.00542615
\(231\) 4.09633 0.269519
\(232\) 10.7546 0.706073
\(233\) −4.80800 −0.314983 −0.157491 0.987520i \(-0.550341\pi\)
−0.157491 + 0.987520i \(0.550341\pi\)
\(234\) −2.61736 −0.171102
\(235\) −0.0835130 −0.00544778
\(236\) −1.65692 −0.107857
\(237\) −6.14149 −0.398932
\(238\) 1.35472 0.0878132
\(239\) −3.89140 −0.251714 −0.125857 0.992048i \(-0.540168\pi\)
−0.125857 + 0.992048i \(0.540168\pi\)
\(240\) 0.0505110 0.00326047
\(241\) 24.7305 1.59303 0.796516 0.604617i \(-0.206674\pi\)
0.796516 + 0.604617i \(0.206674\pi\)
\(242\) 33.1333 2.12989
\(243\) −1.00000 −0.0641500
\(244\) −2.02214 −0.129454
\(245\) −0.0656076 −0.00419151
\(246\) −19.3860 −1.23601
\(247\) −4.78459 −0.304436
\(248\) −1.87730 −0.119209
\(249\) 9.19715 0.582846
\(250\) −0.183135 −0.0115825
\(251\) −27.3307 −1.72510 −0.862550 0.505972i \(-0.831134\pi\)
−0.862550 + 0.505972i \(0.831134\pi\)
\(252\) −0.922249 −0.0580962
\(253\) −24.3886 −1.53330
\(254\) −11.6527 −0.731154
\(255\) 0.0102027 0.000638920 0
\(256\) 20.6090 1.28806
\(257\) −18.9062 −1.17934 −0.589668 0.807646i \(-0.700741\pi\)
−0.589668 + 0.807646i \(0.700741\pi\)
\(258\) −8.68593 −0.540762
\(259\) −5.17508 −0.321564
\(260\) −0.0181794 −0.00112744
\(261\) −7.70081 −0.476668
\(262\) −23.7093 −1.46477
\(263\) −10.0772 −0.621388 −0.310694 0.950510i \(-0.600562\pi\)
−0.310694 + 0.950510i \(0.600562\pi\)
\(264\) 7.57993 0.466512
\(265\) 0.0750695 0.00461148
\(266\) −4.44519 −0.272552
\(267\) −5.29491 −0.324043
\(268\) −16.8583 −1.02979
\(269\) −24.5672 −1.49789 −0.748943 0.662634i \(-0.769439\pi\)
−0.748943 + 0.662634i \(0.769439\pi\)
\(270\) −0.0183137 −0.00111454
\(271\) 6.25569 0.380006 0.190003 0.981784i \(-0.439150\pi\)
0.190003 + 0.981784i \(0.439150\pi\)
\(272\) 4.95073 0.300182
\(273\) −1.10050 −0.0666053
\(274\) −23.8995 −1.44382
\(275\) −27.1374 −1.63645
\(276\) 5.49084 0.330510
\(277\) −3.76858 −0.226432 −0.113216 0.993570i \(-0.536115\pi\)
−0.113216 + 0.993570i \(0.536115\pi\)
\(278\) −6.01308 −0.360641
\(279\) 1.34424 0.0804774
\(280\) 0.0107538 0.000642662 0
\(281\) 2.75449 0.164319 0.0821594 0.996619i \(-0.473818\pi\)
0.0821594 + 0.996619i \(0.473818\pi\)
\(282\) 14.6926 0.874931
\(283\) −27.6311 −1.64250 −0.821251 0.570568i \(-0.806723\pi\)
−0.821251 + 0.570568i \(0.806723\pi\)
\(284\) −5.74484 −0.340894
\(285\) −0.0334779 −0.00198306
\(286\) −14.2060 −0.840016
\(287\) −8.15110 −0.481144
\(288\) −6.09338 −0.359056
\(289\) 1.00000 0.0588235
\(290\) −0.141031 −0.00828160
\(291\) 6.42846 0.376843
\(292\) −9.40494 −0.550383
\(293\) 20.4974 1.19747 0.598736 0.800946i \(-0.295670\pi\)
0.598736 + 0.800946i \(0.295670\pi\)
\(294\) 11.5425 0.673170
\(295\) −0.0138343 −0.000805467 0
\(296\) −9.57606 −0.556597
\(297\) −5.42760 −0.314941
\(298\) 0.695508 0.0402897
\(299\) 6.55211 0.378918
\(300\) 6.10972 0.352745
\(301\) −3.65211 −0.210504
\(302\) 22.7271 1.30780
\(303\) −12.4323 −0.714217
\(304\) −16.2447 −0.931697
\(305\) −0.0168837 −0.000966757 0
\(306\) −1.79498 −0.102612
\(307\) −30.2160 −1.72452 −0.862260 0.506466i \(-0.830951\pi\)
−0.862260 + 0.506466i \(0.830951\pi\)
\(308\) −5.00559 −0.285220
\(309\) 18.0303 1.02571
\(310\) 0.0246180 0.00139821
\(311\) −7.09114 −0.402102 −0.201051 0.979581i \(-0.564436\pi\)
−0.201051 + 0.979581i \(0.564436\pi\)
\(312\) −2.03639 −0.115288
\(313\) 17.7291 1.00211 0.501053 0.865417i \(-0.332946\pi\)
0.501053 + 0.865417i \(0.332946\pi\)
\(314\) −1.79498 −0.101297
\(315\) −0.00770024 −0.000433859 0
\(316\) 7.50471 0.422173
\(317\) −1.60156 −0.0899525 −0.0449762 0.998988i \(-0.514321\pi\)
−0.0449762 + 0.998988i \(0.514321\pi\)
\(318\) −13.2071 −0.740618
\(319\) −41.7969 −2.34018
\(320\) −0.0105706 −0.000590914 0
\(321\) −1.80692 −0.100852
\(322\) 6.08733 0.339234
\(323\) −3.28127 −0.182575
\(324\) 1.22197 0.0678872
\(325\) 7.29060 0.404410
\(326\) 12.5149 0.693135
\(327\) 4.77864 0.264259
\(328\) −15.0829 −0.832816
\(329\) 6.17768 0.340586
\(330\) −0.0993996 −0.00547177
\(331\) 26.7555 1.47062 0.735308 0.677733i \(-0.237037\pi\)
0.735308 + 0.677733i \(0.237037\pi\)
\(332\) −11.2386 −0.616800
\(333\) 6.85692 0.375757
\(334\) 42.4501 2.32276
\(335\) −0.140757 −0.00769038
\(336\) −3.73643 −0.203839
\(337\) −24.0614 −1.31071 −0.655355 0.755321i \(-0.727481\pi\)
−0.655355 + 0.755321i \(0.727481\pi\)
\(338\) −19.5183 −1.06166
\(339\) 10.7082 0.581591
\(340\) −0.0124674 −0.000676141 0
\(341\) 7.29598 0.395100
\(342\) 5.88983 0.318486
\(343\) 10.1362 0.547305
\(344\) −6.75792 −0.364363
\(345\) 0.0458453 0.00246823
\(346\) −35.4015 −1.90320
\(347\) −9.78642 −0.525363 −0.262681 0.964883i \(-0.584607\pi\)
−0.262681 + 0.964883i \(0.584607\pi\)
\(348\) 9.41015 0.504437
\(349\) 26.7726 1.43311 0.716553 0.697533i \(-0.245719\pi\)
0.716553 + 0.697533i \(0.245719\pi\)
\(350\) 6.77344 0.362056
\(351\) 1.45815 0.0778303
\(352\) −33.0724 −1.76276
\(353\) 20.6307 1.09806 0.549031 0.835802i \(-0.314997\pi\)
0.549031 + 0.835802i \(0.314997\pi\)
\(354\) 2.43390 0.129360
\(355\) −0.0479661 −0.00254578
\(356\) 6.47022 0.342921
\(357\) −0.754723 −0.0399442
\(358\) 3.80475 0.201087
\(359\) −30.6491 −1.61760 −0.808798 0.588087i \(-0.799881\pi\)
−0.808798 + 0.588087i \(0.799881\pi\)
\(360\) −0.0142487 −0.000750970 0
\(361\) −8.23325 −0.433329
\(362\) −8.04145 −0.422649
\(363\) −18.4588 −0.968837
\(364\) 1.34478 0.0704855
\(365\) −0.0785258 −0.00411023
\(366\) 2.97038 0.155264
\(367\) −6.53411 −0.341078 −0.170539 0.985351i \(-0.554551\pi\)
−0.170539 + 0.985351i \(0.554551\pi\)
\(368\) 22.2458 1.15964
\(369\) 10.8001 0.562231
\(370\) 0.125576 0.00652838
\(371\) −5.55309 −0.288302
\(372\) −1.64262 −0.0851657
\(373\) −3.21571 −0.166503 −0.0832515 0.996529i \(-0.526530\pi\)
−0.0832515 + 0.996529i \(0.526530\pi\)
\(374\) −9.74245 −0.503770
\(375\) 0.102026 0.00526861
\(376\) 11.4313 0.589523
\(377\) 11.2289 0.578320
\(378\) 1.35472 0.0696791
\(379\) −17.6655 −0.907414 −0.453707 0.891151i \(-0.649899\pi\)
−0.453707 + 0.891151i \(0.649899\pi\)
\(380\) 0.0409090 0.00209859
\(381\) 6.49180 0.332585
\(382\) −6.00110 −0.307043
\(383\) 0.986883 0.0504274 0.0252137 0.999682i \(-0.491973\pi\)
0.0252137 + 0.999682i \(0.491973\pi\)
\(384\) −10.3270 −0.527000
\(385\) −0.0417938 −0.00213001
\(386\) −12.9115 −0.657176
\(387\) 4.83900 0.245980
\(388\) −7.85537 −0.398796
\(389\) 9.56794 0.485114 0.242557 0.970137i \(-0.422014\pi\)
0.242557 + 0.970137i \(0.422014\pi\)
\(390\) 0.0267042 0.00135222
\(391\) 4.49344 0.227243
\(392\) 8.98039 0.453578
\(393\) 13.2086 0.666288
\(394\) −28.0770 −1.41450
\(395\) 0.0626599 0.00315276
\(396\) 6.63236 0.333288
\(397\) 9.04054 0.453732 0.226866 0.973926i \(-0.427152\pi\)
0.226866 + 0.973926i \(0.427152\pi\)
\(398\) 31.7844 1.59321
\(399\) 2.47645 0.123978
\(400\) 24.7531 1.23766
\(401\) 25.1881 1.25783 0.628917 0.777472i \(-0.283499\pi\)
0.628917 + 0.777472i \(0.283499\pi\)
\(402\) 24.7636 1.23510
\(403\) −1.96010 −0.0976396
\(404\) 15.1919 0.755825
\(405\) 0.0102027 0.000506978 0
\(406\) 10.4324 0.517752
\(407\) 37.2166 1.84476
\(408\) −1.39655 −0.0691397
\(409\) 7.42521 0.367153 0.183576 0.983005i \(-0.441233\pi\)
0.183576 + 0.983005i \(0.441233\pi\)
\(410\) 0.197790 0.00976817
\(411\) 13.3146 0.656761
\(412\) −22.0325 −1.08546
\(413\) 1.02336 0.0503564
\(414\) −8.06565 −0.396405
\(415\) −0.0938360 −0.00460623
\(416\) 8.88506 0.435626
\(417\) 3.34993 0.164047
\(418\) 31.9676 1.56359
\(419\) −0.927350 −0.0453040 −0.0226520 0.999743i \(-0.507211\pi\)
−0.0226520 + 0.999743i \(0.507211\pi\)
\(420\) 0.00940945 0.000459134 0
\(421\) −21.6758 −1.05641 −0.528207 0.849115i \(-0.677136\pi\)
−0.528207 + 0.849115i \(0.677136\pi\)
\(422\) 18.1086 0.881513
\(423\) −8.18535 −0.397986
\(424\) −10.2755 −0.499024
\(425\) 4.99990 0.242531
\(426\) 8.43876 0.408859
\(427\) 1.24893 0.0604400
\(428\) 2.20800 0.106728
\(429\) 7.91426 0.382104
\(430\) 0.0886202 0.00427364
\(431\) 17.4969 0.842794 0.421397 0.906876i \(-0.361540\pi\)
0.421397 + 0.906876i \(0.361540\pi\)
\(432\) 4.95073 0.238192
\(433\) 9.74342 0.468239 0.234119 0.972208i \(-0.424779\pi\)
0.234119 + 0.972208i \(0.424779\pi\)
\(434\) −1.82106 −0.0874137
\(435\) 0.0785693 0.00376711
\(436\) −5.83935 −0.279654
\(437\) −14.7442 −0.705310
\(438\) 13.8152 0.660115
\(439\) −31.2586 −1.49189 −0.745946 0.666006i \(-0.768003\pi\)
−0.745946 + 0.666006i \(0.768003\pi\)
\(440\) −0.0773360 −0.00368685
\(441\) −6.43039 −0.306209
\(442\) 2.61736 0.124495
\(443\) −35.4375 −1.68369 −0.841843 0.539722i \(-0.818529\pi\)
−0.841843 + 0.539722i \(0.818529\pi\)
\(444\) −8.37895 −0.397647
\(445\) 0.0540226 0.00256091
\(446\) 1.56108 0.0739192
\(447\) −0.387473 −0.0183269
\(448\) 0.781935 0.0369430
\(449\) −28.9192 −1.36478 −0.682391 0.730988i \(-0.739060\pi\)
−0.682391 + 0.730988i \(0.739060\pi\)
\(450\) −8.97474 −0.423073
\(451\) 58.6187 2.76025
\(452\) −13.0851 −0.615472
\(453\) −12.6614 −0.594886
\(454\) −47.8403 −2.24526
\(455\) 0.0112281 0.000526382 0
\(456\) 4.58247 0.214594
\(457\) 25.3896 1.18767 0.593837 0.804585i \(-0.297612\pi\)
0.593837 + 0.804585i \(0.297612\pi\)
\(458\) −38.0501 −1.77797
\(459\) 1.00000 0.0466760
\(460\) −0.0560216 −0.00261202
\(461\) −29.6616 −1.38148 −0.690738 0.723105i \(-0.742714\pi\)
−0.690738 + 0.723105i \(0.742714\pi\)
\(462\) 7.35286 0.342086
\(463\) 20.3955 0.947858 0.473929 0.880563i \(-0.342835\pi\)
0.473929 + 0.880563i \(0.342835\pi\)
\(464\) 38.1246 1.76989
\(465\) −0.0137149 −0.000636013 0
\(466\) −8.63029 −0.399790
\(467\) 11.6712 0.540080 0.270040 0.962849i \(-0.412963\pi\)
0.270040 + 0.962849i \(0.412963\pi\)
\(468\) −1.78182 −0.0823644
\(469\) 10.4122 0.480790
\(470\) −0.149904 −0.00691458
\(471\) 1.00000 0.0460776
\(472\) 1.89365 0.0871623
\(473\) 26.2641 1.20763
\(474\) −11.0239 −0.506343
\(475\) −16.4060 −0.752760
\(476\) 0.922249 0.0422712
\(477\) 7.35778 0.336890
\(478\) −6.98500 −0.319487
\(479\) −5.64645 −0.257993 −0.128997 0.991645i \(-0.541176\pi\)
−0.128997 + 0.991645i \(0.541176\pi\)
\(480\) 0.0621691 0.00283762
\(481\) −9.99843 −0.455889
\(482\) 44.3909 2.02195
\(483\) −3.39130 −0.154310
\(484\) 22.5561 1.02528
\(485\) −0.0655878 −0.00297819
\(486\) −1.79498 −0.0814221
\(487\) −18.1145 −0.820847 −0.410423 0.911895i \(-0.634619\pi\)
−0.410423 + 0.911895i \(0.634619\pi\)
\(488\) 2.31104 0.104616
\(489\) −6.97213 −0.315291
\(490\) −0.117765 −0.00532006
\(491\) 21.6214 0.975762 0.487881 0.872910i \(-0.337770\pi\)
0.487881 + 0.872910i \(0.337770\pi\)
\(492\) −13.1974 −0.594985
\(493\) 7.70081 0.346827
\(494\) −8.58826 −0.386404
\(495\) 0.0553763 0.00248898
\(496\) −6.65496 −0.298816
\(497\) 3.54818 0.159158
\(498\) 16.5087 0.739774
\(499\) −1.21800 −0.0545253 −0.0272627 0.999628i \(-0.508679\pi\)
−0.0272627 + 0.999628i \(0.508679\pi\)
\(500\) −0.124673 −0.00557554
\(501\) −23.6493 −1.05657
\(502\) −49.0582 −2.18958
\(503\) 21.5253 0.959768 0.479884 0.877332i \(-0.340679\pi\)
0.479884 + 0.877332i \(0.340679\pi\)
\(504\) 1.05401 0.0469494
\(505\) 0.126843 0.00564446
\(506\) −43.7771 −1.94613
\(507\) 10.8738 0.482922
\(508\) −7.93278 −0.351960
\(509\) 13.8169 0.612424 0.306212 0.951963i \(-0.400938\pi\)
0.306212 + 0.951963i \(0.400938\pi\)
\(510\) 0.0183137 0.000810946 0
\(511\) 5.80876 0.256965
\(512\) 16.3387 0.722077
\(513\) −3.28127 −0.144872
\(514\) −33.9363 −1.49687
\(515\) −0.183958 −0.00810616
\(516\) −5.91311 −0.260310
\(517\) −44.4268 −1.95389
\(518\) −9.28919 −0.408144
\(519\) 19.7225 0.865721
\(520\) 0.0207767 0.000911118 0
\(521\) 18.1948 0.797129 0.398564 0.917140i \(-0.369509\pi\)
0.398564 + 0.917140i \(0.369509\pi\)
\(522\) −13.8228 −0.605009
\(523\) −37.7489 −1.65064 −0.825322 0.564662i \(-0.809006\pi\)
−0.825322 + 0.564662i \(0.809006\pi\)
\(524\) −16.1406 −0.705104
\(525\) −3.77354 −0.164691
\(526\) −18.0885 −0.788695
\(527\) −1.34424 −0.0585559
\(528\) 26.8706 1.16939
\(529\) −2.80902 −0.122131
\(530\) 0.134749 0.00585310
\(531\) −1.35595 −0.0588430
\(532\) −3.02615 −0.131200
\(533\) −15.7482 −0.682130
\(534\) −9.50428 −0.411291
\(535\) 0.0184355 0.000797036 0
\(536\) 19.2669 0.832202
\(537\) −2.11966 −0.0914699
\(538\) −44.0977 −1.90119
\(539\) −34.9016 −1.50332
\(540\) −0.0124674 −0.000536512 0
\(541\) 5.33593 0.229410 0.114705 0.993400i \(-0.463408\pi\)
0.114705 + 0.993400i \(0.463408\pi\)
\(542\) 11.2289 0.482321
\(543\) 4.47995 0.192253
\(544\) 6.09338 0.261251
\(545\) −0.0487552 −0.00208844
\(546\) −1.97538 −0.0845385
\(547\) −17.7687 −0.759734 −0.379867 0.925041i \(-0.624030\pi\)
−0.379867 + 0.925041i \(0.624030\pi\)
\(548\) −16.2700 −0.695021
\(549\) −1.65482 −0.0706260
\(550\) −48.7113 −2.07705
\(551\) −25.2685 −1.07647
\(552\) −6.27532 −0.267096
\(553\) −4.63512 −0.197105
\(554\) −6.76454 −0.287398
\(555\) −0.0699593 −0.00296961
\(556\) −4.09352 −0.173604
\(557\) 20.5319 0.869965 0.434982 0.900439i \(-0.356755\pi\)
0.434982 + 0.900439i \(0.356755\pi\)
\(558\) 2.41289 0.102146
\(559\) −7.05599 −0.298437
\(560\) 0.0381218 0.00161094
\(561\) 5.42760 0.229153
\(562\) 4.94426 0.208561
\(563\) 26.7027 1.12539 0.562693 0.826666i \(-0.309765\pi\)
0.562693 + 0.826666i \(0.309765\pi\)
\(564\) 10.0023 0.421171
\(565\) −0.109253 −0.00459631
\(566\) −49.5975 −2.08474
\(567\) −0.754723 −0.0316954
\(568\) 6.56562 0.275487
\(569\) 14.7963 0.620293 0.310146 0.950689i \(-0.399622\pi\)
0.310146 + 0.950689i \(0.399622\pi\)
\(570\) −0.0600924 −0.00251699
\(571\) −31.3423 −1.31163 −0.655817 0.754920i \(-0.727676\pi\)
−0.655817 + 0.754920i \(0.727676\pi\)
\(572\) −9.67098 −0.404364
\(573\) 3.34326 0.139667
\(574\) −14.6311 −0.610690
\(575\) 22.4667 0.936927
\(576\) −1.03606 −0.0431690
\(577\) 30.0055 1.24915 0.624573 0.780966i \(-0.285273\pi\)
0.624573 + 0.780966i \(0.285273\pi\)
\(578\) 1.79498 0.0746615
\(579\) 7.19308 0.298934
\(580\) −0.0960092 −0.00398657
\(581\) 6.94130 0.287974
\(582\) 11.5390 0.478306
\(583\) 39.9351 1.65394
\(584\) 10.7486 0.444782
\(585\) −0.0148771 −0.000615093 0
\(586\) 36.7926 1.51989
\(587\) 46.5471 1.92120 0.960602 0.277927i \(-0.0896475\pi\)
0.960602 + 0.277927i \(0.0896475\pi\)
\(588\) 7.85774 0.324048
\(589\) 4.41081 0.181744
\(590\) −0.0248324 −0.00102233
\(591\) 15.6419 0.643423
\(592\) −33.9468 −1.39520
\(593\) 0.0551661 0.00226540 0.00113270 0.999999i \(-0.499639\pi\)
0.00113270 + 0.999999i \(0.499639\pi\)
\(594\) −9.74245 −0.399738
\(595\) 0.00770024 0.000315679 0
\(596\) 0.473480 0.0193945
\(597\) −17.7073 −0.724713
\(598\) 11.7609 0.480940
\(599\) 30.5303 1.24743 0.623717 0.781650i \(-0.285622\pi\)
0.623717 + 0.781650i \(0.285622\pi\)
\(600\) −6.98262 −0.285064
\(601\) −32.1677 −1.31215 −0.656074 0.754696i \(-0.727784\pi\)
−0.656074 + 0.754696i \(0.727784\pi\)
\(602\) −6.55547 −0.267181
\(603\) −13.7960 −0.561817
\(604\) 15.4719 0.629542
\(605\) 0.188330 0.00765672
\(606\) −22.3158 −0.906517
\(607\) 25.7041 1.04330 0.521648 0.853161i \(-0.325317\pi\)
0.521648 + 0.853161i \(0.325317\pi\)
\(608\) −19.9940 −0.810865
\(609\) −5.81198 −0.235513
\(610\) −0.0303059 −0.00122705
\(611\) 11.9355 0.482858
\(612\) −1.22197 −0.0493952
\(613\) 28.4161 1.14772 0.573858 0.818955i \(-0.305446\pi\)
0.573858 + 0.818955i \(0.305446\pi\)
\(614\) −54.2373 −2.18884
\(615\) −0.110191 −0.00444331
\(616\) 5.72075 0.230496
\(617\) −10.6420 −0.428430 −0.214215 0.976786i \(-0.568719\pi\)
−0.214215 + 0.976786i \(0.568719\pi\)
\(618\) 32.3641 1.30187
\(619\) 18.2593 0.733904 0.366952 0.930240i \(-0.380401\pi\)
0.366952 + 0.930240i \(0.380401\pi\)
\(620\) 0.0167592 0.000673065 0
\(621\) 4.49344 0.180315
\(622\) −12.7285 −0.510366
\(623\) −3.99619 −0.160104
\(624\) −7.21891 −0.288988
\(625\) 24.9984 0.999938
\(626\) 31.8234 1.27192
\(627\) −17.8094 −0.711240
\(628\) −1.22197 −0.0487619
\(629\) −6.85692 −0.273403
\(630\) −0.0138218 −0.000550674 0
\(631\) 16.4950 0.656657 0.328328 0.944564i \(-0.393515\pi\)
0.328328 + 0.944564i \(0.393515\pi\)
\(632\) −8.57691 −0.341171
\(633\) −10.0885 −0.400980
\(634\) −2.87477 −0.114172
\(635\) −0.0662341 −0.00262842
\(636\) −8.99098 −0.356516
\(637\) 9.37648 0.371510
\(638\) −75.0248 −2.97026
\(639\) −4.70130 −0.185981
\(640\) 0.105364 0.00416488
\(641\) 0.997018 0.0393799 0.0196899 0.999806i \(-0.493732\pi\)
0.0196899 + 0.999806i \(0.493732\pi\)
\(642\) −3.24339 −0.128006
\(643\) 24.3649 0.960858 0.480429 0.877034i \(-0.340481\pi\)
0.480429 + 0.877034i \(0.340481\pi\)
\(644\) 4.14407 0.163299
\(645\) −0.0493710 −0.00194398
\(646\) −5.88983 −0.231732
\(647\) 47.6445 1.87310 0.936550 0.350535i \(-0.114000\pi\)
0.936550 + 0.350535i \(0.114000\pi\)
\(648\) −1.39655 −0.0548618
\(649\) −7.35953 −0.288887
\(650\) 13.0865 0.513295
\(651\) 1.01453 0.0397625
\(652\) 8.51973 0.333658
\(653\) 1.72060 0.0673322 0.0336661 0.999433i \(-0.489282\pi\)
0.0336661 + 0.999433i \(0.489282\pi\)
\(654\) 8.57758 0.335410
\(655\) −0.134764 −0.00526568
\(656\) −53.4684 −2.08759
\(657\) −7.69655 −0.300271
\(658\) 11.0888 0.432288
\(659\) −16.5903 −0.646265 −0.323133 0.946354i \(-0.604736\pi\)
−0.323133 + 0.946354i \(0.604736\pi\)
\(660\) −0.0676681 −0.00263398
\(661\) −43.8112 −1.70406 −0.852029 0.523495i \(-0.824628\pi\)
−0.852029 + 0.523495i \(0.824628\pi\)
\(662\) 48.0257 1.86657
\(663\) −1.45815 −0.0566299
\(664\) 12.8443 0.498456
\(665\) −0.0252666 −0.000979796 0
\(666\) 12.3081 0.476928
\(667\) 34.6031 1.33984
\(668\) 28.8987 1.11812
\(669\) −0.869689 −0.0336241
\(670\) −0.252657 −0.00976098
\(671\) −8.98170 −0.346735
\(672\) −4.59881 −0.177403
\(673\) −3.17627 −0.122436 −0.0612182 0.998124i \(-0.519499\pi\)
−0.0612182 + 0.998124i \(0.519499\pi\)
\(674\) −43.1899 −1.66361
\(675\) 4.99990 0.192446
\(676\) −13.2874 −0.511055
\(677\) 24.9742 0.959835 0.479918 0.877314i \(-0.340667\pi\)
0.479918 + 0.877314i \(0.340667\pi\)
\(678\) 19.2211 0.738182
\(679\) 4.85171 0.186191
\(680\) 0.0142487 0.000546411 0
\(681\) 26.6522 1.02131
\(682\) 13.0962 0.501478
\(683\) −23.2350 −0.889063 −0.444532 0.895763i \(-0.646630\pi\)
−0.444532 + 0.895763i \(0.646630\pi\)
\(684\) 4.00961 0.153311
\(685\) −0.135845 −0.00519038
\(686\) 18.1944 0.694665
\(687\) 21.1980 0.808755
\(688\) −23.9566 −0.913336
\(689\) −10.7288 −0.408733
\(690\) 0.0822916 0.00313279
\(691\) 20.1488 0.766498 0.383249 0.923645i \(-0.374805\pi\)
0.383249 + 0.923645i \(0.374805\pi\)
\(692\) −24.1003 −0.916154
\(693\) −4.09633 −0.155607
\(694\) −17.5665 −0.666814
\(695\) −0.0341785 −0.00129646
\(696\) −10.7546 −0.407652
\(697\) −10.8001 −0.409083
\(698\) 48.0564 1.81896
\(699\) 4.80800 0.181855
\(700\) 4.61115 0.174285
\(701\) 11.0618 0.417799 0.208899 0.977937i \(-0.433012\pi\)
0.208899 + 0.977937i \(0.433012\pi\)
\(702\) 2.61736 0.0987858
\(703\) 22.4994 0.848582
\(704\) −5.62329 −0.211936
\(705\) 0.0835130 0.00314528
\(706\) 37.0318 1.39371
\(707\) −9.38295 −0.352882
\(708\) 1.65692 0.0622710
\(709\) 14.7865 0.555318 0.277659 0.960680i \(-0.410441\pi\)
0.277659 + 0.960680i \(0.410441\pi\)
\(710\) −0.0860984 −0.00323121
\(711\) 6.14149 0.230324
\(712\) −7.39463 −0.277125
\(713\) −6.04025 −0.226209
\(714\) −1.35472 −0.0506990
\(715\) −0.0807470 −0.00301977
\(716\) 2.59015 0.0967986
\(717\) 3.89140 0.145327
\(718\) −55.0146 −2.05313
\(719\) −20.5960 −0.768102 −0.384051 0.923312i \(-0.625471\pi\)
−0.384051 + 0.923312i \(0.625471\pi\)
\(720\) −0.0505110 −0.00188243
\(721\) 13.6079 0.506784
\(722\) −14.7786 −0.550001
\(723\) −24.7305 −0.919738
\(724\) −5.47437 −0.203453
\(725\) 38.5032 1.42997
\(726\) −33.1333 −1.22969
\(727\) 32.3670 1.20043 0.600213 0.799840i \(-0.295082\pi\)
0.600213 + 0.799840i \(0.295082\pi\)
\(728\) −1.53691 −0.0569616
\(729\) 1.00000 0.0370370
\(730\) −0.140953 −0.00521689
\(731\) −4.83900 −0.178977
\(732\) 2.02214 0.0747404
\(733\) −5.09237 −0.188091 −0.0940454 0.995568i \(-0.529980\pi\)
−0.0940454 + 0.995568i \(0.529980\pi\)
\(734\) −11.7286 −0.432911
\(735\) 0.0656076 0.00241997
\(736\) 27.3802 1.00925
\(737\) −74.8793 −2.75821
\(738\) 19.3860 0.713610
\(739\) 28.9003 1.06312 0.531558 0.847022i \(-0.321607\pi\)
0.531558 + 0.847022i \(0.321607\pi\)
\(740\) 0.0854882 0.00314261
\(741\) 4.78459 0.175766
\(742\) −9.96771 −0.365926
\(743\) 13.2250 0.485179 0.242589 0.970129i \(-0.422003\pi\)
0.242589 + 0.970129i \(0.422003\pi\)
\(744\) 1.87730 0.0688251
\(745\) 0.00395328 0.000144837 0
\(746\) −5.77214 −0.211333
\(747\) −9.19715 −0.336506
\(748\) −6.63236 −0.242503
\(749\) −1.36372 −0.0498293
\(750\) 0.183135 0.00668716
\(751\) 34.8688 1.27238 0.636190 0.771532i \(-0.280509\pi\)
0.636190 + 0.771532i \(0.280509\pi\)
\(752\) 40.5235 1.47774
\(753\) 27.3307 0.995987
\(754\) 20.1558 0.734030
\(755\) 0.129181 0.00470138
\(756\) 0.922249 0.0335419
\(757\) 28.5621 1.03811 0.519054 0.854742i \(-0.326285\pi\)
0.519054 + 0.854742i \(0.326285\pi\)
\(758\) −31.7092 −1.15173
\(759\) 24.3886 0.885249
\(760\) −0.0467537 −0.00169594
\(761\) 12.8611 0.466213 0.233107 0.972451i \(-0.425111\pi\)
0.233107 + 0.972451i \(0.425111\pi\)
\(762\) 11.6527 0.422132
\(763\) 3.60655 0.130566
\(764\) −4.08536 −0.147803
\(765\) −0.0102027 −0.000368880 0
\(766\) 1.77144 0.0640047
\(767\) 1.97717 0.0713916
\(768\) −20.6090 −0.743663
\(769\) −30.0907 −1.08510 −0.542549 0.840024i \(-0.682541\pi\)
−0.542549 + 0.840024i \(0.682541\pi\)
\(770\) −0.0750192 −0.00270350
\(771\) 18.9062 0.680890
\(772\) −8.78972 −0.316349
\(773\) 40.3903 1.45274 0.726370 0.687304i \(-0.241206\pi\)
0.726370 + 0.687304i \(0.241206\pi\)
\(774\) 8.68593 0.312209
\(775\) −6.72105 −0.241427
\(776\) 8.97768 0.322280
\(777\) 5.17508 0.185655
\(778\) 17.1743 0.615728
\(779\) 35.4381 1.26970
\(780\) 0.0181794 0.000650926 0
\(781\) −25.5168 −0.913062
\(782\) 8.06565 0.288427
\(783\) 7.70081 0.275204
\(784\) 31.8351 1.13697
\(785\) −0.0102027 −0.000364151 0
\(786\) 23.7093 0.845683
\(787\) −41.5019 −1.47938 −0.739692 0.672946i \(-0.765029\pi\)
−0.739692 + 0.672946i \(0.765029\pi\)
\(788\) −19.1140 −0.680906
\(789\) 10.0772 0.358759
\(790\) 0.112474 0.00400163
\(791\) 8.08175 0.287354
\(792\) −7.57993 −0.269341
\(793\) 2.41298 0.0856873
\(794\) 16.2276 0.575897
\(795\) −0.0750695 −0.00266244
\(796\) 21.6378 0.766932
\(797\) 26.1017 0.924568 0.462284 0.886732i \(-0.347030\pi\)
0.462284 + 0.886732i \(0.347030\pi\)
\(798\) 4.44519 0.157358
\(799\) 8.18535 0.289577
\(800\) 30.4662 1.07714
\(801\) 5.29491 0.187087
\(802\) 45.2123 1.59650
\(803\) −41.7738 −1.47416
\(804\) 16.8583 0.594547
\(805\) 0.0346005 0.00121951
\(806\) −3.51835 −0.123929
\(807\) 24.5672 0.864805
\(808\) −17.3624 −0.610806
\(809\) 21.2113 0.745750 0.372875 0.927881i \(-0.378372\pi\)
0.372875 + 0.927881i \(0.378372\pi\)
\(810\) 0.0183137 0.000643479 0
\(811\) 33.1130 1.16276 0.581378 0.813634i \(-0.302514\pi\)
0.581378 + 0.813634i \(0.302514\pi\)
\(812\) 7.10206 0.249233
\(813\) −6.25569 −0.219397
\(814\) 66.8033 2.34145
\(815\) 0.0711348 0.00249174
\(816\) −4.95073 −0.173310
\(817\) 15.8781 0.555504
\(818\) 13.3281 0.466007
\(819\) 1.10050 0.0384546
\(820\) 0.134650 0.00470217
\(821\) −48.7136 −1.70012 −0.850058 0.526689i \(-0.823433\pi\)
−0.850058 + 0.526689i \(0.823433\pi\)
\(822\) 23.8995 0.833591
\(823\) 50.5365 1.76159 0.880796 0.473496i \(-0.157008\pi\)
0.880796 + 0.473496i \(0.157008\pi\)
\(824\) 25.1803 0.877196
\(825\) 27.1374 0.944804
\(826\) 1.83692 0.0639147
\(827\) 21.4024 0.744235 0.372117 0.928186i \(-0.378632\pi\)
0.372117 + 0.928186i \(0.378632\pi\)
\(828\) −5.49084 −0.190820
\(829\) 31.7696 1.10340 0.551702 0.834041i \(-0.313978\pi\)
0.551702 + 0.834041i \(0.313978\pi\)
\(830\) −0.168434 −0.00584644
\(831\) 3.76858 0.130731
\(832\) 1.51073 0.0523750
\(833\) 6.43039 0.222800
\(834\) 6.01308 0.208216
\(835\) 0.241287 0.00835009
\(836\) 21.7626 0.752674
\(837\) −1.34424 −0.0464636
\(838\) −1.66458 −0.0575019
\(839\) 18.1262 0.625786 0.312893 0.949788i \(-0.398702\pi\)
0.312893 + 0.949788i \(0.398702\pi\)
\(840\) −0.0107538 −0.000371041 0
\(841\) 30.3025 1.04491
\(842\) −38.9078 −1.34085
\(843\) −2.75449 −0.0948695
\(844\) 12.3278 0.424340
\(845\) −0.110942 −0.00381653
\(846\) −14.6926 −0.505141
\(847\) −13.9313 −0.478685
\(848\) −36.4264 −1.25089
\(849\) 27.6311 0.948298
\(850\) 8.97474 0.307831
\(851\) −30.8112 −1.05619
\(852\) 5.74484 0.196815
\(853\) 30.2421 1.03547 0.517735 0.855541i \(-0.326775\pi\)
0.517735 + 0.855541i \(0.326775\pi\)
\(854\) 2.24181 0.0767132
\(855\) 0.0334779 0.00114492
\(856\) −2.52346 −0.0862500
\(857\) 5.11435 0.174703 0.0873514 0.996178i \(-0.472160\pi\)
0.0873514 + 0.996178i \(0.472160\pi\)
\(858\) 14.2060 0.484984
\(859\) −11.0389 −0.376641 −0.188321 0.982108i \(-0.560304\pi\)
−0.188321 + 0.982108i \(0.560304\pi\)
\(860\) 0.0603298 0.00205723
\(861\) 8.15110 0.277789
\(862\) 31.4066 1.06971
\(863\) −26.6681 −0.907793 −0.453897 0.891054i \(-0.649966\pi\)
−0.453897 + 0.891054i \(0.649966\pi\)
\(864\) 6.09338 0.207301
\(865\) −0.201223 −0.00684179
\(866\) 17.4893 0.594310
\(867\) −1.00000 −0.0339618
\(868\) −1.23972 −0.0420789
\(869\) 33.3335 1.13076
\(870\) 0.141031 0.00478139
\(871\) 20.1167 0.681628
\(872\) 6.67362 0.225997
\(873\) −6.42846 −0.217570
\(874\) −26.4656 −0.895212
\(875\) 0.0770016 0.00260313
\(876\) 9.40494 0.317764
\(877\) −15.1534 −0.511695 −0.255847 0.966717i \(-0.582354\pi\)
−0.255847 + 0.966717i \(0.582354\pi\)
\(878\) −56.1088 −1.89358
\(879\) −20.4974 −0.691361
\(880\) −0.274153 −0.00924170
\(881\) 2.29125 0.0771941 0.0385971 0.999255i \(-0.487711\pi\)
0.0385971 + 0.999255i \(0.487711\pi\)
\(882\) −11.5425 −0.388655
\(883\) 51.7006 1.73986 0.869932 0.493171i \(-0.164162\pi\)
0.869932 + 0.493171i \(0.164162\pi\)
\(884\) 1.78182 0.0599289
\(885\) 0.0138343 0.000465036 0
\(886\) −63.6098 −2.13701
\(887\) 29.4024 0.987235 0.493618 0.869679i \(-0.335674\pi\)
0.493618 + 0.869679i \(0.335674\pi\)
\(888\) 9.57606 0.321352
\(889\) 4.89951 0.164324
\(890\) 0.0969696 0.00325043
\(891\) 5.42760 0.181831
\(892\) 1.06273 0.0355829
\(893\) −26.8584 −0.898781
\(894\) −0.695508 −0.0232613
\(895\) 0.0216263 0.000722886 0
\(896\) −7.79406 −0.260381
\(897\) −6.55211 −0.218769
\(898\) −51.9095 −1.73224
\(899\) −10.3517 −0.345249
\(900\) −6.10972 −0.203657
\(901\) −7.35778 −0.245123
\(902\) 105.220 3.50343
\(903\) 3.65211 0.121534
\(904\) 14.9546 0.497383
\(905\) −0.0457078 −0.00151938
\(906\) −22.7271 −0.755056
\(907\) −58.7345 −1.95025 −0.975123 0.221663i \(-0.928852\pi\)
−0.975123 + 0.221663i \(0.928852\pi\)
\(908\) −32.5682 −1.08081
\(909\) 12.4323 0.412353
\(910\) 0.0201543 0.000668108 0
\(911\) 9.31116 0.308492 0.154246 0.988032i \(-0.450705\pi\)
0.154246 + 0.988032i \(0.450705\pi\)
\(912\) 16.2447 0.537916
\(913\) −49.9184 −1.65206
\(914\) 45.5739 1.50745
\(915\) 0.0168837 0.000558157 0
\(916\) −25.9033 −0.855870
\(917\) 9.96888 0.329201
\(918\) 1.79498 0.0592433
\(919\) −48.0301 −1.58437 −0.792184 0.610283i \(-0.791056\pi\)
−0.792184 + 0.610283i \(0.791056\pi\)
\(920\) 0.0640254 0.00211086
\(921\) 30.2160 0.995652
\(922\) −53.2420 −1.75343
\(923\) 6.85520 0.225642
\(924\) 5.00559 0.164672
\(925\) −34.2839 −1.12725
\(926\) 36.6096 1.20307
\(927\) −18.0303 −0.592192
\(928\) 46.9239 1.54035
\(929\) −4.32220 −0.141807 −0.0709034 0.997483i \(-0.522588\pi\)
−0.0709034 + 0.997483i \(0.522588\pi\)
\(930\) −0.0246180 −0.000807256 0
\(931\) −21.0999 −0.691520
\(932\) −5.87523 −0.192450
\(933\) 7.09114 0.232154
\(934\) 20.9497 0.685494
\(935\) −0.0553763 −0.00181100
\(936\) 2.03639 0.0665613
\(937\) 39.3062 1.28408 0.642039 0.766672i \(-0.278089\pi\)
0.642039 + 0.766672i \(0.278089\pi\)
\(938\) 18.6897 0.610240
\(939\) −17.7291 −0.578566
\(940\) −0.102050 −0.00332851
\(941\) −14.9718 −0.488068 −0.244034 0.969767i \(-0.578471\pi\)
−0.244034 + 0.969767i \(0.578471\pi\)
\(942\) 1.79498 0.0584838
\(943\) −48.5296 −1.58034
\(944\) 6.71292 0.218487
\(945\) 0.00770024 0.000250489 0
\(946\) 47.1437 1.53277
\(947\) 19.1147 0.621143 0.310572 0.950550i \(-0.399480\pi\)
0.310572 + 0.950550i \(0.399480\pi\)
\(948\) −7.50471 −0.243742
\(949\) 11.2227 0.364305
\(950\) −29.4486 −0.955437
\(951\) 1.60156 0.0519341
\(952\) −1.05401 −0.0341607
\(953\) −14.7045 −0.476324 −0.238162 0.971225i \(-0.576545\pi\)
−0.238162 + 0.971225i \(0.576545\pi\)
\(954\) 13.2071 0.427596
\(955\) −0.0341104 −0.00110379
\(956\) −4.75517 −0.153793
\(957\) 41.7969 1.35110
\(958\) −10.1353 −0.327457
\(959\) 10.0488 0.324494
\(960\) 0.0105706 0.000341164 0
\(961\) −29.1930 −0.941711
\(962\) −17.9470 −0.578635
\(963\) 1.80692 0.0582271
\(964\) 30.2199 0.973318
\(965\) −0.0733890 −0.00236248
\(966\) −6.08733 −0.195857
\(967\) −33.0378 −1.06243 −0.531213 0.847238i \(-0.678264\pi\)
−0.531213 + 0.847238i \(0.678264\pi\)
\(968\) −25.7787 −0.828560
\(969\) 3.28127 0.105410
\(970\) −0.117729 −0.00378005
\(971\) 34.4952 1.10700 0.553502 0.832848i \(-0.313291\pi\)
0.553502 + 0.832848i \(0.313291\pi\)
\(972\) −1.22197 −0.0391947
\(973\) 2.52827 0.0810527
\(974\) −32.5153 −1.04186
\(975\) −7.29060 −0.233486
\(976\) 8.19257 0.262238
\(977\) 5.30164 0.169615 0.0848073 0.996397i \(-0.472973\pi\)
0.0848073 + 0.996397i \(0.472973\pi\)
\(978\) −12.5149 −0.400181
\(979\) 28.7387 0.918491
\(980\) −0.0801704 −0.00256095
\(981\) −4.77864 −0.152570
\(982\) 38.8102 1.23848
\(983\) 47.3162 1.50915 0.754577 0.656212i \(-0.227842\pi\)
0.754577 + 0.656212i \(0.227842\pi\)
\(984\) 15.0829 0.480826
\(985\) −0.159590 −0.00508497
\(986\) 13.8228 0.440209
\(987\) −6.17768 −0.196638
\(988\) −5.84662 −0.186006
\(989\) −21.7437 −0.691411
\(990\) 0.0993996 0.00315913
\(991\) −26.4526 −0.840293 −0.420147 0.907456i \(-0.638021\pi\)
−0.420147 + 0.907456i \(0.638021\pi\)
\(992\) −8.19094 −0.260063
\(993\) −26.7555 −0.849061
\(994\) 6.36893 0.202010
\(995\) 0.180663 0.00572741
\(996\) 11.2386 0.356110
\(997\) −56.5711 −1.79163 −0.895813 0.444432i \(-0.853406\pi\)
−0.895813 + 0.444432i \(0.853406\pi\)
\(998\) −2.18630 −0.0692060
\(999\) −6.85692 −0.216943
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 8007.2.a.f.1.38 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.38 48 1.1 even 1 trivial