Properties

Label 8007.2.a.f.1.32
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

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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 1.32
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.941352 q^{2} -1.00000 q^{3} -1.11386 q^{4} -2.91330 q^{5} -0.941352 q^{6} -1.76114 q^{7} -2.93124 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.941352 q^{2} -1.00000 q^{3} -1.11386 q^{4} -2.91330 q^{5} -0.941352 q^{6} -1.76114 q^{7} -2.93124 q^{8} +1.00000 q^{9} -2.74244 q^{10} -4.88957 q^{11} +1.11386 q^{12} -2.39917 q^{13} -1.65785 q^{14} +2.91330 q^{15} -0.531613 q^{16} -1.00000 q^{17} +0.941352 q^{18} +6.33142 q^{19} +3.24500 q^{20} +1.76114 q^{21} -4.60281 q^{22} +3.09254 q^{23} +2.93124 q^{24} +3.48733 q^{25} -2.25846 q^{26} -1.00000 q^{27} +1.96165 q^{28} +5.08146 q^{29} +2.74244 q^{30} +4.97869 q^{31} +5.36204 q^{32} +4.88957 q^{33} -0.941352 q^{34} +5.13072 q^{35} -1.11386 q^{36} +5.58869 q^{37} +5.96010 q^{38} +2.39917 q^{39} +8.53958 q^{40} +3.89049 q^{41} +1.65785 q^{42} +1.41729 q^{43} +5.44628 q^{44} -2.91330 q^{45} +2.91117 q^{46} -3.41885 q^{47} +0.531613 q^{48} -3.89840 q^{49} +3.28281 q^{50} +1.00000 q^{51} +2.67233 q^{52} -5.53042 q^{53} -0.941352 q^{54} +14.2448 q^{55} +5.16230 q^{56} -6.33142 q^{57} +4.78344 q^{58} +8.82698 q^{59} -3.24500 q^{60} -10.1434 q^{61} +4.68670 q^{62} -1.76114 q^{63} +6.11079 q^{64} +6.98951 q^{65} +4.60281 q^{66} -7.53148 q^{67} +1.11386 q^{68} -3.09254 q^{69} +4.82982 q^{70} +9.14600 q^{71} -2.93124 q^{72} -13.4556 q^{73} +5.26092 q^{74} -3.48733 q^{75} -7.05229 q^{76} +8.61120 q^{77} +2.25846 q^{78} +1.67678 q^{79} +1.54875 q^{80} +1.00000 q^{81} +3.66232 q^{82} +3.13668 q^{83} -1.96165 q^{84} +2.91330 q^{85} +1.33417 q^{86} -5.08146 q^{87} +14.3325 q^{88} +3.90643 q^{89} -2.74244 q^{90} +4.22526 q^{91} -3.44464 q^{92} -4.97869 q^{93} -3.21834 q^{94} -18.4454 q^{95} -5.36204 q^{96} +12.4025 q^{97} -3.66977 q^{98} -4.88957 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.941352 0.665637 0.332818 0.942991i \(-0.392000\pi\)
0.332818 + 0.942991i \(0.392000\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.11386 −0.556928
\(5\) −2.91330 −1.30287 −0.651434 0.758705i \(-0.725832\pi\)
−0.651434 + 0.758705i \(0.725832\pi\)
\(6\) −0.941352 −0.384305
\(7\) −1.76114 −0.665647 −0.332823 0.942989i \(-0.608001\pi\)
−0.332823 + 0.942989i \(0.608001\pi\)
\(8\) −2.93124 −1.03635
\(9\) 1.00000 0.333333
\(10\) −2.74244 −0.867237
\(11\) −4.88957 −1.47426 −0.737131 0.675750i \(-0.763820\pi\)
−0.737131 + 0.675750i \(0.763820\pi\)
\(12\) 1.11386 0.321543
\(13\) −2.39917 −0.665410 −0.332705 0.943031i \(-0.607961\pi\)
−0.332705 + 0.943031i \(0.607961\pi\)
\(14\) −1.65785 −0.443079
\(15\) 2.91330 0.752212
\(16\) −0.531613 −0.132903
\(17\) −1.00000 −0.242536
\(18\) 0.941352 0.221879
\(19\) 6.33142 1.45253 0.726264 0.687416i \(-0.241255\pi\)
0.726264 + 0.687416i \(0.241255\pi\)
\(20\) 3.24500 0.725604
\(21\) 1.76114 0.384311
\(22\) −4.60281 −0.981323
\(23\) 3.09254 0.644839 0.322420 0.946597i \(-0.395504\pi\)
0.322420 + 0.946597i \(0.395504\pi\)
\(24\) 2.93124 0.598336
\(25\) 3.48733 0.697467
\(26\) −2.25846 −0.442921
\(27\) −1.00000 −0.192450
\(28\) 1.96165 0.370717
\(29\) 5.08146 0.943603 0.471801 0.881705i \(-0.343604\pi\)
0.471801 + 0.881705i \(0.343604\pi\)
\(30\) 2.74244 0.500700
\(31\) 4.97869 0.894198 0.447099 0.894484i \(-0.352457\pi\)
0.447099 + 0.894484i \(0.352457\pi\)
\(32\) 5.36204 0.947883
\(33\) 4.88957 0.851166
\(34\) −0.941352 −0.161441
\(35\) 5.13072 0.867250
\(36\) −1.11386 −0.185643
\(37\) 5.58869 0.918774 0.459387 0.888236i \(-0.348069\pi\)
0.459387 + 0.888236i \(0.348069\pi\)
\(38\) 5.96010 0.966856
\(39\) 2.39917 0.384175
\(40\) 8.53958 1.35023
\(41\) 3.89049 0.607592 0.303796 0.952737i \(-0.401746\pi\)
0.303796 + 0.952737i \(0.401746\pi\)
\(42\) 1.65785 0.255812
\(43\) 1.41729 0.216135 0.108068 0.994144i \(-0.465534\pi\)
0.108068 + 0.994144i \(0.465534\pi\)
\(44\) 5.44628 0.821058
\(45\) −2.91330 −0.434290
\(46\) 2.91117 0.429228
\(47\) −3.41885 −0.498691 −0.249345 0.968415i \(-0.580215\pi\)
−0.249345 + 0.968415i \(0.580215\pi\)
\(48\) 0.531613 0.0767317
\(49\) −3.89840 −0.556914
\(50\) 3.28281 0.464259
\(51\) 1.00000 0.140028
\(52\) 2.67233 0.370586
\(53\) −5.53042 −0.759662 −0.379831 0.925056i \(-0.624018\pi\)
−0.379831 + 0.925056i \(0.624018\pi\)
\(54\) −0.941352 −0.128102
\(55\) 14.2448 1.92077
\(56\) 5.16230 0.689842
\(57\) −6.33142 −0.838617
\(58\) 4.78344 0.628097
\(59\) 8.82698 1.14917 0.574587 0.818443i \(-0.305163\pi\)
0.574587 + 0.818443i \(0.305163\pi\)
\(60\) −3.24500 −0.418928
\(61\) −10.1434 −1.29873 −0.649366 0.760476i \(-0.724966\pi\)
−0.649366 + 0.760476i \(0.724966\pi\)
\(62\) 4.68670 0.595211
\(63\) −1.76114 −0.221882
\(64\) 6.11079 0.763849
\(65\) 6.98951 0.866942
\(66\) 4.60281 0.566567
\(67\) −7.53148 −0.920117 −0.460058 0.887889i \(-0.652171\pi\)
−0.460058 + 0.887889i \(0.652171\pi\)
\(68\) 1.11386 0.135075
\(69\) −3.09254 −0.372298
\(70\) 4.82982 0.577273
\(71\) 9.14600 1.08543 0.542715 0.839917i \(-0.317396\pi\)
0.542715 + 0.839917i \(0.317396\pi\)
\(72\) −2.93124 −0.345449
\(73\) −13.4556 −1.57485 −0.787427 0.616408i \(-0.788587\pi\)
−0.787427 + 0.616408i \(0.788587\pi\)
\(74\) 5.26092 0.611570
\(75\) −3.48733 −0.402683
\(76\) −7.05229 −0.808953
\(77\) 8.61120 0.981338
\(78\) 2.25846 0.255721
\(79\) 1.67678 0.188653 0.0943264 0.995541i \(-0.469930\pi\)
0.0943264 + 0.995541i \(0.469930\pi\)
\(80\) 1.54875 0.173155
\(81\) 1.00000 0.111111
\(82\) 3.66232 0.404436
\(83\) 3.13668 0.344295 0.172148 0.985071i \(-0.444929\pi\)
0.172148 + 0.985071i \(0.444929\pi\)
\(84\) −1.96165 −0.214034
\(85\) 2.91330 0.315992
\(86\) 1.33417 0.143867
\(87\) −5.08146 −0.544789
\(88\) 14.3325 1.52785
\(89\) 3.90643 0.414081 0.207040 0.978332i \(-0.433617\pi\)
0.207040 + 0.978332i \(0.433617\pi\)
\(90\) −2.74244 −0.289079
\(91\) 4.22526 0.442928
\(92\) −3.44464 −0.359129
\(93\) −4.97869 −0.516266
\(94\) −3.21834 −0.331947
\(95\) −18.4454 −1.89245
\(96\) −5.36204 −0.547260
\(97\) 12.4025 1.25929 0.629644 0.776884i \(-0.283201\pi\)
0.629644 + 0.776884i \(0.283201\pi\)
\(98\) −3.66977 −0.370703
\(99\) −4.88957 −0.491421
\(100\) −3.88439 −0.388439
\(101\) 19.6558 1.95583 0.977914 0.209007i \(-0.0670230\pi\)
0.977914 + 0.209007i \(0.0670230\pi\)
\(102\) 0.941352 0.0932078
\(103\) −8.10501 −0.798611 −0.399305 0.916818i \(-0.630749\pi\)
−0.399305 + 0.916818i \(0.630749\pi\)
\(104\) 7.03253 0.689597
\(105\) −5.13072 −0.500707
\(106\) −5.20607 −0.505659
\(107\) −18.1965 −1.75912 −0.879560 0.475788i \(-0.842163\pi\)
−0.879560 + 0.475788i \(0.842163\pi\)
\(108\) 1.11386 0.107181
\(109\) −6.36457 −0.609615 −0.304808 0.952414i \(-0.598592\pi\)
−0.304808 + 0.952414i \(0.598592\pi\)
\(110\) 13.4094 1.27853
\(111\) −5.58869 −0.530455
\(112\) 0.936242 0.0884666
\(113\) 4.11886 0.387470 0.193735 0.981054i \(-0.437940\pi\)
0.193735 + 0.981054i \(0.437940\pi\)
\(114\) −5.96010 −0.558214
\(115\) −9.00951 −0.840141
\(116\) −5.66001 −0.525519
\(117\) −2.39917 −0.221803
\(118\) 8.30929 0.764933
\(119\) 1.76114 0.161443
\(120\) −8.53958 −0.779553
\(121\) 12.9079 1.17345
\(122\) −9.54854 −0.864484
\(123\) −3.89049 −0.350794
\(124\) −5.54554 −0.498004
\(125\) 4.40685 0.394161
\(126\) −1.65785 −0.147693
\(127\) −18.1323 −1.60899 −0.804493 0.593962i \(-0.797563\pi\)
−0.804493 + 0.593962i \(0.797563\pi\)
\(128\) −4.97167 −0.439437
\(129\) −1.41729 −0.124786
\(130\) 6.57959 0.577068
\(131\) −7.50153 −0.655412 −0.327706 0.944780i \(-0.606276\pi\)
−0.327706 + 0.944780i \(0.606276\pi\)
\(132\) −5.44628 −0.474038
\(133\) −11.1505 −0.966870
\(134\) −7.08977 −0.612463
\(135\) 2.91330 0.250737
\(136\) 2.93124 0.251351
\(137\) 9.16605 0.783109 0.391554 0.920155i \(-0.371937\pi\)
0.391554 + 0.920155i \(0.371937\pi\)
\(138\) −2.91117 −0.247815
\(139\) −14.3118 −1.21391 −0.606956 0.794735i \(-0.707610\pi\)
−0.606956 + 0.794735i \(0.707610\pi\)
\(140\) −5.71489 −0.482996
\(141\) 3.41885 0.287919
\(142\) 8.60961 0.722502
\(143\) 11.7309 0.980989
\(144\) −0.531613 −0.0443011
\(145\) −14.8038 −1.22939
\(146\) −12.6664 −1.04828
\(147\) 3.89840 0.321535
\(148\) −6.22499 −0.511691
\(149\) 3.10954 0.254743 0.127372 0.991855i \(-0.459346\pi\)
0.127372 + 0.991855i \(0.459346\pi\)
\(150\) −3.28281 −0.268040
\(151\) −5.37928 −0.437760 −0.218880 0.975752i \(-0.570240\pi\)
−0.218880 + 0.975752i \(0.570240\pi\)
\(152\) −18.5589 −1.50532
\(153\) −1.00000 −0.0808452
\(154\) 8.10618 0.653214
\(155\) −14.5044 −1.16502
\(156\) −2.67233 −0.213958
\(157\) −1.00000 −0.0798087
\(158\) 1.57844 0.125574
\(159\) 5.53042 0.438591
\(160\) −15.6212 −1.23497
\(161\) −5.44638 −0.429235
\(162\) 0.941352 0.0739596
\(163\) 9.43076 0.738674 0.369337 0.929296i \(-0.379585\pi\)
0.369337 + 0.929296i \(0.379585\pi\)
\(164\) −4.33344 −0.338385
\(165\) −14.2448 −1.10896
\(166\) 2.95272 0.229175
\(167\) −21.2647 −1.64551 −0.822757 0.568393i \(-0.807565\pi\)
−0.822757 + 0.568393i \(0.807565\pi\)
\(168\) −5.16230 −0.398280
\(169\) −7.24398 −0.557229
\(170\) 2.74244 0.210336
\(171\) 6.33142 0.484176
\(172\) −1.57866 −0.120372
\(173\) 15.0481 1.14409 0.572044 0.820223i \(-0.306151\pi\)
0.572044 + 0.820223i \(0.306151\pi\)
\(174\) −4.78344 −0.362632
\(175\) −6.14167 −0.464267
\(176\) 2.59936 0.195934
\(177\) −8.82698 −0.663476
\(178\) 3.67733 0.275627
\(179\) 23.4409 1.75205 0.876027 0.482263i \(-0.160185\pi\)
0.876027 + 0.482263i \(0.160185\pi\)
\(180\) 3.24500 0.241868
\(181\) 17.6018 1.30833 0.654165 0.756352i \(-0.273020\pi\)
0.654165 + 0.756352i \(0.273020\pi\)
\(182\) 3.97746 0.294829
\(183\) 10.1434 0.749824
\(184\) −9.06496 −0.668278
\(185\) −16.2815 −1.19704
\(186\) −4.68670 −0.343645
\(187\) 4.88957 0.357561
\(188\) 3.80811 0.277735
\(189\) 1.76114 0.128104
\(190\) −17.3636 −1.25969
\(191\) 12.0554 0.872295 0.436148 0.899875i \(-0.356343\pi\)
0.436148 + 0.899875i \(0.356343\pi\)
\(192\) −6.11079 −0.441008
\(193\) −6.84319 −0.492584 −0.246292 0.969196i \(-0.579212\pi\)
−0.246292 + 0.969196i \(0.579212\pi\)
\(194\) 11.6752 0.838228
\(195\) −6.98951 −0.500529
\(196\) 4.34226 0.310161
\(197\) −10.4592 −0.745184 −0.372592 0.927995i \(-0.621531\pi\)
−0.372592 + 0.927995i \(0.621531\pi\)
\(198\) −4.60281 −0.327108
\(199\) −1.97722 −0.140161 −0.0700807 0.997541i \(-0.522326\pi\)
−0.0700807 + 0.997541i \(0.522326\pi\)
\(200\) −10.2222 −0.722819
\(201\) 7.53148 0.531230
\(202\) 18.5031 1.30187
\(203\) −8.94914 −0.628106
\(204\) −1.11386 −0.0779855
\(205\) −11.3342 −0.791613
\(206\) −7.62967 −0.531585
\(207\) 3.09254 0.214946
\(208\) 1.27543 0.0884351
\(209\) −30.9580 −2.14141
\(210\) −4.82982 −0.333289
\(211\) 22.2420 1.53120 0.765600 0.643317i \(-0.222442\pi\)
0.765600 + 0.643317i \(0.222442\pi\)
\(212\) 6.16009 0.423077
\(213\) −9.14600 −0.626674
\(214\) −17.1293 −1.17093
\(215\) −4.12900 −0.281596
\(216\) 2.93124 0.199445
\(217\) −8.76814 −0.595220
\(218\) −5.99130 −0.405782
\(219\) 13.4556 0.909242
\(220\) −15.8667 −1.06973
\(221\) 2.39917 0.161386
\(222\) −5.26092 −0.353090
\(223\) −14.8466 −0.994201 −0.497101 0.867693i \(-0.665602\pi\)
−0.497101 + 0.867693i \(0.665602\pi\)
\(224\) −9.44327 −0.630955
\(225\) 3.48733 0.232489
\(226\) 3.87730 0.257914
\(227\) 1.35159 0.0897083 0.0448541 0.998994i \(-0.485718\pi\)
0.0448541 + 0.998994i \(0.485718\pi\)
\(228\) 7.05229 0.467049
\(229\) 9.70817 0.641534 0.320767 0.947158i \(-0.396059\pi\)
0.320767 + 0.947158i \(0.396059\pi\)
\(230\) −8.48112 −0.559228
\(231\) −8.61120 −0.566576
\(232\) −14.8949 −0.977901
\(233\) 14.2832 0.935722 0.467861 0.883802i \(-0.345025\pi\)
0.467861 + 0.883802i \(0.345025\pi\)
\(234\) −2.25846 −0.147640
\(235\) 9.96015 0.649728
\(236\) −9.83198 −0.640007
\(237\) −1.67678 −0.108919
\(238\) 1.65785 0.107462
\(239\) −3.50372 −0.226637 −0.113318 0.993559i \(-0.536148\pi\)
−0.113318 + 0.993559i \(0.536148\pi\)
\(240\) −1.54875 −0.0999713
\(241\) −21.0468 −1.35574 −0.677871 0.735180i \(-0.737097\pi\)
−0.677871 + 0.735180i \(0.737097\pi\)
\(242\) 12.1509 0.781090
\(243\) −1.00000 −0.0641500
\(244\) 11.2983 0.723301
\(245\) 11.3572 0.725586
\(246\) −3.66232 −0.233501
\(247\) −15.1902 −0.966527
\(248\) −14.5937 −0.926701
\(249\) −3.13668 −0.198779
\(250\) 4.14840 0.262368
\(251\) 18.0563 1.13970 0.569851 0.821748i \(-0.307001\pi\)
0.569851 + 0.821748i \(0.307001\pi\)
\(252\) 1.96165 0.123572
\(253\) −15.1212 −0.950662
\(254\) −17.0689 −1.07100
\(255\) −2.91330 −0.182438
\(256\) −16.9017 −1.05635
\(257\) 29.4736 1.83851 0.919255 0.393663i \(-0.128792\pi\)
0.919255 + 0.393663i \(0.128792\pi\)
\(258\) −1.33417 −0.0830619
\(259\) −9.84243 −0.611579
\(260\) −7.78531 −0.482824
\(261\) 5.08146 0.314534
\(262\) −7.06158 −0.436266
\(263\) 30.4681 1.87874 0.939372 0.342901i \(-0.111409\pi\)
0.939372 + 0.342901i \(0.111409\pi\)
\(264\) −14.3325 −0.882104
\(265\) 16.1118 0.989740
\(266\) −10.4965 −0.643584
\(267\) −3.90643 −0.239070
\(268\) 8.38898 0.512439
\(269\) −15.1101 −0.921279 −0.460639 0.887587i \(-0.652380\pi\)
−0.460639 + 0.887587i \(0.652380\pi\)
\(270\) 2.74244 0.166900
\(271\) 23.2237 1.41074 0.705371 0.708838i \(-0.250780\pi\)
0.705371 + 0.708838i \(0.250780\pi\)
\(272\) 0.531613 0.0322338
\(273\) −4.22526 −0.255725
\(274\) 8.62848 0.521266
\(275\) −17.0516 −1.02825
\(276\) 3.44464 0.207343
\(277\) −2.13483 −0.128269 −0.0641347 0.997941i \(-0.520429\pi\)
−0.0641347 + 0.997941i \(0.520429\pi\)
\(278\) −13.4725 −0.808025
\(279\) 4.97869 0.298066
\(280\) −15.0394 −0.898773
\(281\) 17.4436 1.04060 0.520298 0.853985i \(-0.325821\pi\)
0.520298 + 0.853985i \(0.325821\pi\)
\(282\) 3.21834 0.191649
\(283\) −9.09374 −0.540567 −0.270283 0.962781i \(-0.587117\pi\)
−0.270283 + 0.962781i \(0.587117\pi\)
\(284\) −10.1873 −0.604507
\(285\) 18.4454 1.09261
\(286\) 11.0429 0.652982
\(287\) −6.85168 −0.404442
\(288\) 5.36204 0.315961
\(289\) 1.00000 0.0588235
\(290\) −13.9356 −0.818327
\(291\) −12.4025 −0.727050
\(292\) 14.9876 0.877080
\(293\) −0.0560033 −0.00327175 −0.00163587 0.999999i \(-0.500521\pi\)
−0.00163587 + 0.999999i \(0.500521\pi\)
\(294\) 3.66977 0.214025
\(295\) −25.7157 −1.49722
\(296\) −16.3818 −0.952170
\(297\) 4.88957 0.283722
\(298\) 2.92717 0.169566
\(299\) −7.41953 −0.429082
\(300\) 3.88439 0.224265
\(301\) −2.49604 −0.143870
\(302\) −5.06380 −0.291389
\(303\) −19.6558 −1.12920
\(304\) −3.36586 −0.193046
\(305\) 29.5509 1.69208
\(306\) −0.941352 −0.0538135
\(307\) −11.5596 −0.659741 −0.329871 0.944026i \(-0.607005\pi\)
−0.329871 + 0.944026i \(0.607005\pi\)
\(308\) −9.59164 −0.546534
\(309\) 8.10501 0.461078
\(310\) −13.6538 −0.775482
\(311\) −34.0306 −1.92970 −0.964849 0.262804i \(-0.915353\pi\)
−0.964849 + 0.262804i \(0.915353\pi\)
\(312\) −7.03253 −0.398139
\(313\) −28.8680 −1.63172 −0.815858 0.578253i \(-0.803735\pi\)
−0.815858 + 0.578253i \(0.803735\pi\)
\(314\) −0.941352 −0.0531236
\(315\) 5.13072 0.289083
\(316\) −1.86770 −0.105066
\(317\) 14.2126 0.798261 0.399130 0.916894i \(-0.369312\pi\)
0.399130 + 0.916894i \(0.369312\pi\)
\(318\) 5.20607 0.291942
\(319\) −24.8462 −1.39112
\(320\) −17.8026 −0.995195
\(321\) 18.1965 1.01563
\(322\) −5.12696 −0.285715
\(323\) −6.33142 −0.352290
\(324\) −1.11386 −0.0618809
\(325\) −8.36671 −0.464101
\(326\) 8.87766 0.491688
\(327\) 6.36457 0.351962
\(328\) −11.4039 −0.629677
\(329\) 6.02106 0.331952
\(330\) −13.4094 −0.738162
\(331\) 7.38597 0.405970 0.202985 0.979182i \(-0.434936\pi\)
0.202985 + 0.979182i \(0.434936\pi\)
\(332\) −3.49381 −0.191748
\(333\) 5.58869 0.306258
\(334\) −20.0176 −1.09531
\(335\) 21.9415 1.19879
\(336\) −0.936242 −0.0510762
\(337\) −9.42884 −0.513622 −0.256811 0.966462i \(-0.582672\pi\)
−0.256811 + 0.966462i \(0.582672\pi\)
\(338\) −6.81914 −0.370912
\(339\) −4.11886 −0.223706
\(340\) −3.24500 −0.175985
\(341\) −24.3437 −1.31828
\(342\) 5.96010 0.322285
\(343\) 19.1936 1.03635
\(344\) −4.15442 −0.223991
\(345\) 9.00951 0.485055
\(346\) 14.1656 0.761547
\(347\) −19.4280 −1.04295 −0.521474 0.853267i \(-0.674618\pi\)
−0.521474 + 0.853267i \(0.674618\pi\)
\(348\) 5.66001 0.303408
\(349\) 20.0175 1.07151 0.535757 0.844372i \(-0.320026\pi\)
0.535757 + 0.844372i \(0.320026\pi\)
\(350\) −5.78147 −0.309033
\(351\) 2.39917 0.128058
\(352\) −26.2181 −1.39743
\(353\) 2.03912 0.108532 0.0542658 0.998527i \(-0.482718\pi\)
0.0542658 + 0.998527i \(0.482718\pi\)
\(354\) −8.30929 −0.441634
\(355\) −26.6451 −1.41417
\(356\) −4.35120 −0.230613
\(357\) −1.76114 −0.0932092
\(358\) 22.0661 1.16623
\(359\) −11.6934 −0.617156 −0.308578 0.951199i \(-0.599853\pi\)
−0.308578 + 0.951199i \(0.599853\pi\)
\(360\) 8.53958 0.450075
\(361\) 21.0869 1.10984
\(362\) 16.5695 0.870873
\(363\) −12.9079 −0.677491
\(364\) −4.70634 −0.246679
\(365\) 39.2001 2.05183
\(366\) 9.54854 0.499110
\(367\) −5.17491 −0.270128 −0.135064 0.990837i \(-0.543124\pi\)
−0.135064 + 0.990837i \(0.543124\pi\)
\(368\) −1.64403 −0.0857012
\(369\) 3.89049 0.202531
\(370\) −15.3267 −0.796795
\(371\) 9.73982 0.505666
\(372\) 5.54554 0.287523
\(373\) 15.9628 0.826524 0.413262 0.910612i \(-0.364389\pi\)
0.413262 + 0.910612i \(0.364389\pi\)
\(374\) 4.60281 0.238006
\(375\) −4.40685 −0.227569
\(376\) 10.0215 0.516817
\(377\) −12.1913 −0.627883
\(378\) 1.65785 0.0852705
\(379\) 19.5606 1.00476 0.502381 0.864647i \(-0.332458\pi\)
0.502381 + 0.864647i \(0.332458\pi\)
\(380\) 20.5455 1.05396
\(381\) 18.1323 0.928948
\(382\) 11.3483 0.580632
\(383\) −16.4324 −0.839657 −0.419829 0.907603i \(-0.637910\pi\)
−0.419829 + 0.907603i \(0.637910\pi\)
\(384\) 4.97167 0.253709
\(385\) −25.0870 −1.27855
\(386\) −6.44186 −0.327882
\(387\) 1.41729 0.0720450
\(388\) −13.8147 −0.701333
\(389\) −5.65157 −0.286546 −0.143273 0.989683i \(-0.545763\pi\)
−0.143273 + 0.989683i \(0.545763\pi\)
\(390\) −6.57959 −0.333171
\(391\) −3.09254 −0.156396
\(392\) 11.4271 0.577157
\(393\) 7.50153 0.378402
\(394\) −9.84575 −0.496021
\(395\) −4.88498 −0.245790
\(396\) 5.44628 0.273686
\(397\) −17.9417 −0.900470 −0.450235 0.892910i \(-0.648660\pi\)
−0.450235 + 0.892910i \(0.648660\pi\)
\(398\) −1.86126 −0.0932965
\(399\) 11.1505 0.558223
\(400\) −1.85391 −0.0926956
\(401\) −7.57649 −0.378352 −0.189176 0.981943i \(-0.560582\pi\)
−0.189176 + 0.981943i \(0.560582\pi\)
\(402\) 7.08977 0.353606
\(403\) −11.9447 −0.595009
\(404\) −21.8938 −1.08926
\(405\) −2.91330 −0.144763
\(406\) −8.42429 −0.418090
\(407\) −27.3263 −1.35451
\(408\) −2.93124 −0.145118
\(409\) −7.71869 −0.381665 −0.190832 0.981623i \(-0.561119\pi\)
−0.190832 + 0.981623i \(0.561119\pi\)
\(410\) −10.6694 −0.526926
\(411\) −9.16605 −0.452128
\(412\) 9.02782 0.444769
\(413\) −15.5455 −0.764944
\(414\) 2.91117 0.143076
\(415\) −9.13809 −0.448571
\(416\) −12.8644 −0.630731
\(417\) 14.3118 0.700853
\(418\) −29.1423 −1.42540
\(419\) 29.0791 1.42061 0.710303 0.703896i \(-0.248558\pi\)
0.710303 + 0.703896i \(0.248558\pi\)
\(420\) 5.71489 0.278858
\(421\) −11.1478 −0.543308 −0.271654 0.962395i \(-0.587571\pi\)
−0.271654 + 0.962395i \(0.587571\pi\)
\(422\) 20.9375 1.01922
\(423\) −3.41885 −0.166230
\(424\) 16.2110 0.787274
\(425\) −3.48733 −0.169161
\(426\) −8.60961 −0.417137
\(427\) 17.8639 0.864497
\(428\) 20.2683 0.979703
\(429\) −11.7309 −0.566374
\(430\) −3.88685 −0.187440
\(431\) 32.1924 1.55065 0.775326 0.631561i \(-0.217585\pi\)
0.775326 + 0.631561i \(0.217585\pi\)
\(432\) 0.531613 0.0255772
\(433\) 22.1845 1.06612 0.533059 0.846078i \(-0.321042\pi\)
0.533059 + 0.846078i \(0.321042\pi\)
\(434\) −8.25391 −0.396200
\(435\) 14.8038 0.709789
\(436\) 7.08922 0.339512
\(437\) 19.5802 0.936647
\(438\) 12.6664 0.605225
\(439\) 32.0274 1.52859 0.764293 0.644869i \(-0.223088\pi\)
0.764293 + 0.644869i \(0.223088\pi\)
\(440\) −41.7549 −1.99059
\(441\) −3.89840 −0.185638
\(442\) 2.25846 0.107424
\(443\) 28.2636 1.34284 0.671422 0.741075i \(-0.265684\pi\)
0.671422 + 0.741075i \(0.265684\pi\)
\(444\) 6.22499 0.295425
\(445\) −11.3806 −0.539493
\(446\) −13.9759 −0.661777
\(447\) −3.10954 −0.147076
\(448\) −10.7619 −0.508453
\(449\) −37.2522 −1.75804 −0.879019 0.476786i \(-0.841802\pi\)
−0.879019 + 0.476786i \(0.841802\pi\)
\(450\) 3.28281 0.154753
\(451\) −19.0228 −0.895750
\(452\) −4.58782 −0.215793
\(453\) 5.37928 0.252741
\(454\) 1.27232 0.0597131
\(455\) −12.3095 −0.577077
\(456\) 18.5589 0.869100
\(457\) 20.3854 0.953589 0.476794 0.879015i \(-0.341799\pi\)
0.476794 + 0.879015i \(0.341799\pi\)
\(458\) 9.13881 0.427028
\(459\) 1.00000 0.0466760
\(460\) 10.0353 0.467898
\(461\) −25.0140 −1.16502 −0.582509 0.812824i \(-0.697929\pi\)
−0.582509 + 0.812824i \(0.697929\pi\)
\(462\) −8.10618 −0.377133
\(463\) −1.30736 −0.0607582 −0.0303791 0.999538i \(-0.509671\pi\)
−0.0303791 + 0.999538i \(0.509671\pi\)
\(464\) −2.70137 −0.125408
\(465\) 14.5044 0.672626
\(466\) 13.4455 0.622850
\(467\) 10.9088 0.504797 0.252399 0.967623i \(-0.418781\pi\)
0.252399 + 0.967623i \(0.418781\pi\)
\(468\) 2.67233 0.123529
\(469\) 13.2640 0.612473
\(470\) 9.37601 0.432483
\(471\) 1.00000 0.0460776
\(472\) −25.8739 −1.19094
\(473\) −6.92996 −0.318640
\(474\) −1.57844 −0.0725003
\(475\) 22.0798 1.01309
\(476\) −1.96165 −0.0899121
\(477\) −5.53042 −0.253221
\(478\) −3.29823 −0.150858
\(479\) −14.0791 −0.643291 −0.321645 0.946860i \(-0.604236\pi\)
−0.321645 + 0.946860i \(0.604236\pi\)
\(480\) 15.6212 0.713009
\(481\) −13.4082 −0.611362
\(482\) −19.8124 −0.902432
\(483\) 5.44638 0.247819
\(484\) −14.3776 −0.653527
\(485\) −36.1324 −1.64069
\(486\) −0.941352 −0.0427006
\(487\) −5.50370 −0.249397 −0.124698 0.992195i \(-0.539796\pi\)
−0.124698 + 0.992195i \(0.539796\pi\)
\(488\) 29.7328 1.34594
\(489\) −9.43076 −0.426474
\(490\) 10.6911 0.482977
\(491\) −0.659256 −0.0297518 −0.0148759 0.999889i \(-0.504735\pi\)
−0.0148759 + 0.999889i \(0.504735\pi\)
\(492\) 4.33344 0.195367
\(493\) −5.08146 −0.228857
\(494\) −14.2993 −0.643355
\(495\) 14.2448 0.640257
\(496\) −2.64673 −0.118842
\(497\) −16.1073 −0.722513
\(498\) −2.95272 −0.132314
\(499\) −19.3147 −0.864645 −0.432323 0.901719i \(-0.642306\pi\)
−0.432323 + 0.901719i \(0.642306\pi\)
\(500\) −4.90860 −0.219519
\(501\) 21.2647 0.950038
\(502\) 16.9973 0.758628
\(503\) −23.6373 −1.05393 −0.526967 0.849886i \(-0.676671\pi\)
−0.526967 + 0.849886i \(0.676671\pi\)
\(504\) 5.16230 0.229947
\(505\) −57.2634 −2.54819
\(506\) −14.2344 −0.632795
\(507\) 7.24398 0.321717
\(508\) 20.1968 0.896089
\(509\) 26.2537 1.16368 0.581838 0.813304i \(-0.302334\pi\)
0.581838 + 0.813304i \(0.302334\pi\)
\(510\) −2.74244 −0.121437
\(511\) 23.6971 1.04830
\(512\) −5.96709 −0.263711
\(513\) −6.33142 −0.279539
\(514\) 27.7450 1.22378
\(515\) 23.6124 1.04049
\(516\) 1.57866 0.0694966
\(517\) 16.7167 0.735201
\(518\) −9.26520 −0.407089
\(519\) −15.0481 −0.660540
\(520\) −20.4879 −0.898454
\(521\) −9.34762 −0.409527 −0.204763 0.978811i \(-0.565642\pi\)
−0.204763 + 0.978811i \(0.565642\pi\)
\(522\) 4.78344 0.209366
\(523\) 38.8854 1.70034 0.850170 0.526509i \(-0.176499\pi\)
0.850170 + 0.526509i \(0.176499\pi\)
\(524\) 8.35562 0.365017
\(525\) 6.14167 0.268044
\(526\) 28.6812 1.25056
\(527\) −4.97869 −0.216875
\(528\) −2.59936 −0.113123
\(529\) −13.4362 −0.584183
\(530\) 15.1669 0.658807
\(531\) 8.82698 0.383058
\(532\) 12.4200 0.538477
\(533\) −9.33394 −0.404298
\(534\) −3.67733 −0.159134
\(535\) 53.0118 2.29190
\(536\) 22.0765 0.953561
\(537\) −23.4409 −1.01155
\(538\) −14.2239 −0.613237
\(539\) 19.0615 0.821038
\(540\) −3.24500 −0.139643
\(541\) −34.1261 −1.46720 −0.733598 0.679584i \(-0.762160\pi\)
−0.733598 + 0.679584i \(0.762160\pi\)
\(542\) 21.8617 0.939042
\(543\) −17.6018 −0.755365
\(544\) −5.36204 −0.229895
\(545\) 18.5419 0.794249
\(546\) −3.97746 −0.170220
\(547\) 7.94965 0.339902 0.169951 0.985452i \(-0.445639\pi\)
0.169951 + 0.985452i \(0.445639\pi\)
\(548\) −10.2097 −0.436135
\(549\) −10.1434 −0.432911
\(550\) −16.0515 −0.684440
\(551\) 32.1729 1.37061
\(552\) 9.06496 0.385830
\(553\) −2.95304 −0.125576
\(554\) −2.00962 −0.0853808
\(555\) 16.2815 0.691113
\(556\) 15.9413 0.676062
\(557\) −41.5792 −1.76177 −0.880885 0.473331i \(-0.843051\pi\)
−0.880885 + 0.473331i \(0.843051\pi\)
\(558\) 4.68670 0.198404
\(559\) −3.40033 −0.143818
\(560\) −2.72756 −0.115260
\(561\) −4.88957 −0.206438
\(562\) 16.4205 0.692659
\(563\) 18.3520 0.773446 0.386723 0.922196i \(-0.373607\pi\)
0.386723 + 0.922196i \(0.373607\pi\)
\(564\) −3.80811 −0.160350
\(565\) −11.9995 −0.504822
\(566\) −8.56041 −0.359821
\(567\) −1.76114 −0.0739607
\(568\) −26.8091 −1.12488
\(569\) −29.8361 −1.25079 −0.625397 0.780307i \(-0.715063\pi\)
−0.625397 + 0.780307i \(0.715063\pi\)
\(570\) 17.3636 0.727280
\(571\) −12.2002 −0.510561 −0.255280 0.966867i \(-0.582168\pi\)
−0.255280 + 0.966867i \(0.582168\pi\)
\(572\) −13.0666 −0.546340
\(573\) −12.0554 −0.503620
\(574\) −6.44984 −0.269211
\(575\) 10.7847 0.449754
\(576\) 6.11079 0.254616
\(577\) −22.7635 −0.947658 −0.473829 0.880617i \(-0.657128\pi\)
−0.473829 + 0.880617i \(0.657128\pi\)
\(578\) 0.941352 0.0391551
\(579\) 6.84319 0.284393
\(580\) 16.4893 0.684682
\(581\) −5.52411 −0.229179
\(582\) −11.6752 −0.483951
\(583\) 27.0414 1.11994
\(584\) 39.4414 1.63210
\(585\) 6.98951 0.288981
\(586\) −0.0527188 −0.00217779
\(587\) −20.8736 −0.861545 −0.430773 0.902461i \(-0.641759\pi\)
−0.430773 + 0.902461i \(0.641759\pi\)
\(588\) −4.34226 −0.179072
\(589\) 31.5222 1.29885
\(590\) −24.2075 −0.996607
\(591\) 10.4592 0.430232
\(592\) −2.97102 −0.122108
\(593\) −12.8052 −0.525847 −0.262923 0.964817i \(-0.584687\pi\)
−0.262923 + 0.964817i \(0.584687\pi\)
\(594\) 4.60281 0.188856
\(595\) −5.13072 −0.210339
\(596\) −3.46358 −0.141874
\(597\) 1.97722 0.0809222
\(598\) −6.98439 −0.285613
\(599\) −23.2934 −0.951742 −0.475871 0.879515i \(-0.657867\pi\)
−0.475871 + 0.879515i \(0.657867\pi\)
\(600\) 10.2222 0.417319
\(601\) −21.3993 −0.872895 −0.436448 0.899730i \(-0.643764\pi\)
−0.436448 + 0.899730i \(0.643764\pi\)
\(602\) −2.34966 −0.0957648
\(603\) −7.53148 −0.306706
\(604\) 5.99175 0.243801
\(605\) −37.6047 −1.52885
\(606\) −18.5031 −0.751635
\(607\) −36.6012 −1.48560 −0.742798 0.669515i \(-0.766502\pi\)
−0.742798 + 0.669515i \(0.766502\pi\)
\(608\) 33.9493 1.37683
\(609\) 8.94914 0.362637
\(610\) 27.8178 1.12631
\(611\) 8.20240 0.331834
\(612\) 1.11386 0.0450250
\(613\) −10.3878 −0.419559 −0.209780 0.977749i \(-0.567275\pi\)
−0.209780 + 0.977749i \(0.567275\pi\)
\(614\) −10.8817 −0.439148
\(615\) 11.3342 0.457038
\(616\) −25.2415 −1.01701
\(617\) −43.1873 −1.73865 −0.869327 0.494237i \(-0.835448\pi\)
−0.869327 + 0.494237i \(0.835448\pi\)
\(618\) 7.62967 0.306910
\(619\) −2.47567 −0.0995055 −0.0497528 0.998762i \(-0.515843\pi\)
−0.0497528 + 0.998762i \(0.515843\pi\)
\(620\) 16.1558 0.648834
\(621\) −3.09254 −0.124099
\(622\) −32.0348 −1.28448
\(623\) −6.87975 −0.275632
\(624\) −1.27543 −0.0510580
\(625\) −30.2752 −1.21101
\(626\) −27.1749 −1.08613
\(627\) 30.9580 1.23634
\(628\) 1.11386 0.0444477
\(629\) −5.58869 −0.222836
\(630\) 4.82982 0.192424
\(631\) −12.6402 −0.503199 −0.251600 0.967831i \(-0.580957\pi\)
−0.251600 + 0.967831i \(0.580957\pi\)
\(632\) −4.91505 −0.195510
\(633\) −22.2420 −0.884039
\(634\) 13.3791 0.531351
\(635\) 52.8250 2.09630
\(636\) −6.16009 −0.244264
\(637\) 9.35293 0.370577
\(638\) −23.3890 −0.925979
\(639\) 9.14600 0.361810
\(640\) 14.4840 0.572529
\(641\) −35.5654 −1.40475 −0.702375 0.711807i \(-0.747877\pi\)
−0.702375 + 0.711807i \(0.747877\pi\)
\(642\) 17.1293 0.676039
\(643\) 3.17037 0.125027 0.0625137 0.998044i \(-0.480088\pi\)
0.0625137 + 0.998044i \(0.480088\pi\)
\(644\) 6.06649 0.239053
\(645\) 4.12900 0.162579
\(646\) −5.96010 −0.234497
\(647\) 22.7973 0.896253 0.448127 0.893970i \(-0.352091\pi\)
0.448127 + 0.893970i \(0.352091\pi\)
\(648\) −2.93124 −0.115150
\(649\) −43.1602 −1.69418
\(650\) −7.87602 −0.308923
\(651\) 8.76814 0.343651
\(652\) −10.5045 −0.411388
\(653\) −27.3049 −1.06852 −0.534261 0.845319i \(-0.679410\pi\)
−0.534261 + 0.845319i \(0.679410\pi\)
\(654\) 5.99130 0.234279
\(655\) 21.8542 0.853915
\(656\) −2.06823 −0.0807509
\(657\) −13.4556 −0.524951
\(658\) 5.66794 0.220959
\(659\) −28.2346 −1.09987 −0.549933 0.835209i \(-0.685347\pi\)
−0.549933 + 0.835209i \(0.685347\pi\)
\(660\) 15.8667 0.617609
\(661\) 6.81184 0.264950 0.132475 0.991186i \(-0.457708\pi\)
0.132475 + 0.991186i \(0.457708\pi\)
\(662\) 6.95280 0.270228
\(663\) −2.39917 −0.0931760
\(664\) −9.19434 −0.356810
\(665\) 32.4848 1.25971
\(666\) 5.26092 0.203857
\(667\) 15.7146 0.608472
\(668\) 23.6858 0.916433
\(669\) 14.8466 0.574002
\(670\) 20.6547 0.797959
\(671\) 49.5970 1.91467
\(672\) 9.44327 0.364282
\(673\) −0.0174381 −0.000672190 0 −0.000336095 1.00000i \(-0.500107\pi\)
−0.000336095 1.00000i \(0.500107\pi\)
\(674\) −8.87586 −0.341885
\(675\) −3.48733 −0.134228
\(676\) 8.06875 0.310337
\(677\) 6.08369 0.233815 0.116908 0.993143i \(-0.462702\pi\)
0.116908 + 0.993143i \(0.462702\pi\)
\(678\) −3.87730 −0.148907
\(679\) −21.8426 −0.838241
\(680\) −8.53958 −0.327478
\(681\) −1.35159 −0.0517931
\(682\) −22.9160 −0.877497
\(683\) −39.1783 −1.49911 −0.749557 0.661940i \(-0.769734\pi\)
−0.749557 + 0.661940i \(0.769734\pi\)
\(684\) −7.05229 −0.269651
\(685\) −26.7035 −1.02029
\(686\) 18.0679 0.689836
\(687\) −9.70817 −0.370390
\(688\) −0.753451 −0.0287250
\(689\) 13.2684 0.505487
\(690\) 8.48112 0.322871
\(691\) −45.4727 −1.72986 −0.864931 0.501891i \(-0.832638\pi\)
−0.864931 + 0.501891i \(0.832638\pi\)
\(692\) −16.7615 −0.637175
\(693\) 8.61120 0.327113
\(694\) −18.2886 −0.694224
\(695\) 41.6947 1.58157
\(696\) 14.8949 0.564592
\(697\) −3.89049 −0.147363
\(698\) 18.8435 0.713238
\(699\) −14.2832 −0.540239
\(700\) 6.84093 0.258563
\(701\) 43.2405 1.63317 0.816585 0.577225i \(-0.195864\pi\)
0.816585 + 0.577225i \(0.195864\pi\)
\(702\) 2.25846 0.0852402
\(703\) 35.3843 1.33455
\(704\) −29.8792 −1.12611
\(705\) −9.96015 −0.375121
\(706\) 1.91953 0.0722426
\(707\) −34.6166 −1.30189
\(708\) 9.83198 0.369508
\(709\) −25.7634 −0.967566 −0.483783 0.875188i \(-0.660738\pi\)
−0.483783 + 0.875188i \(0.660738\pi\)
\(710\) −25.0824 −0.941325
\(711\) 1.67678 0.0628843
\(712\) −11.4507 −0.429132
\(713\) 15.3968 0.576614
\(714\) −1.65785 −0.0620434
\(715\) −34.1757 −1.27810
\(716\) −26.1098 −0.975768
\(717\) 3.50372 0.130849
\(718\) −11.0076 −0.410802
\(719\) −37.4482 −1.39658 −0.698291 0.715814i \(-0.746056\pi\)
−0.698291 + 0.715814i \(0.746056\pi\)
\(720\) 1.54875 0.0577185
\(721\) 14.2740 0.531593
\(722\) 19.8502 0.738748
\(723\) 21.0468 0.782739
\(724\) −19.6059 −0.728646
\(725\) 17.7207 0.658132
\(726\) −12.1509 −0.450963
\(727\) −25.1190 −0.931613 −0.465806 0.884887i \(-0.654236\pi\)
−0.465806 + 0.884887i \(0.654236\pi\)
\(728\) −12.3852 −0.459028
\(729\) 1.00000 0.0370370
\(730\) 36.9011 1.36577
\(731\) −1.41729 −0.0524204
\(732\) −11.2983 −0.417598
\(733\) −50.4468 −1.86330 −0.931648 0.363362i \(-0.881629\pi\)
−0.931648 + 0.363362i \(0.881629\pi\)
\(734\) −4.87142 −0.179807
\(735\) −11.3572 −0.418918
\(736\) 16.5823 0.611232
\(737\) 36.8257 1.35649
\(738\) 3.66232 0.134812
\(739\) 37.1419 1.36629 0.683143 0.730284i \(-0.260612\pi\)
0.683143 + 0.730284i \(0.260612\pi\)
\(740\) 18.1353 0.666666
\(741\) 15.1902 0.558024
\(742\) 9.16860 0.336590
\(743\) −50.4784 −1.85187 −0.925937 0.377678i \(-0.876723\pi\)
−0.925937 + 0.377678i \(0.876723\pi\)
\(744\) 14.5937 0.535031
\(745\) −9.05902 −0.331897
\(746\) 15.0266 0.550165
\(747\) 3.13668 0.114765
\(748\) −5.44628 −0.199136
\(749\) 32.0465 1.17095
\(750\) −4.14840 −0.151478
\(751\) −12.7440 −0.465034 −0.232517 0.972592i \(-0.574696\pi\)
−0.232517 + 0.972592i \(0.574696\pi\)
\(752\) 1.81750 0.0662776
\(753\) −18.0563 −0.658007
\(754\) −11.4763 −0.417942
\(755\) 15.6715 0.570344
\(756\) −1.96165 −0.0713446
\(757\) 12.9725 0.471492 0.235746 0.971815i \(-0.424247\pi\)
0.235746 + 0.971815i \(0.424247\pi\)
\(758\) 18.4134 0.668806
\(759\) 15.1212 0.548865
\(760\) 54.0677 1.96124
\(761\) 40.4763 1.46726 0.733632 0.679547i \(-0.237824\pi\)
0.733632 + 0.679547i \(0.237824\pi\)
\(762\) 17.0689 0.618342
\(763\) 11.2089 0.405788
\(764\) −13.4279 −0.485806
\(765\) 2.91330 0.105331
\(766\) −15.4687 −0.558906
\(767\) −21.1774 −0.764672
\(768\) 16.9017 0.609886
\(769\) 33.9064 1.22269 0.611347 0.791362i \(-0.290628\pi\)
0.611347 + 0.791362i \(0.290628\pi\)
\(770\) −23.6157 −0.851052
\(771\) −29.4736 −1.06146
\(772\) 7.62233 0.274334
\(773\) 26.7256 0.961252 0.480626 0.876926i \(-0.340409\pi\)
0.480626 + 0.876926i \(0.340409\pi\)
\(774\) 1.33417 0.0479558
\(775\) 17.3623 0.623674
\(776\) −36.3548 −1.30506
\(777\) 9.84243 0.353095
\(778\) −5.32012 −0.190736
\(779\) 24.6323 0.882545
\(780\) 7.78531 0.278759
\(781\) −44.7200 −1.60021
\(782\) −2.91117 −0.104103
\(783\) −5.08146 −0.181596
\(784\) 2.07244 0.0740157
\(785\) 2.91330 0.103980
\(786\) 7.06158 0.251878
\(787\) −30.8969 −1.10136 −0.550678 0.834718i \(-0.685631\pi\)
−0.550678 + 0.834718i \(0.685631\pi\)
\(788\) 11.6500 0.415014
\(789\) −30.4681 −1.08469
\(790\) −4.59848 −0.163607
\(791\) −7.25387 −0.257918
\(792\) 14.3325 0.509283
\(793\) 24.3358 0.864190
\(794\) −16.8895 −0.599385
\(795\) −16.1118 −0.571426
\(796\) 2.20234 0.0780598
\(797\) −12.6648 −0.448611 −0.224305 0.974519i \(-0.572011\pi\)
−0.224305 + 0.974519i \(0.572011\pi\)
\(798\) 10.4965 0.371574
\(799\) 3.41885 0.120950
\(800\) 18.6992 0.661117
\(801\) 3.90643 0.138027
\(802\) −7.13214 −0.251845
\(803\) 65.7919 2.32175
\(804\) −8.38898 −0.295857
\(805\) 15.8670 0.559237
\(806\) −11.2442 −0.396059
\(807\) 15.1101 0.531901
\(808\) −57.6159 −2.02692
\(809\) −23.4934 −0.825985 −0.412992 0.910734i \(-0.635516\pi\)
−0.412992 + 0.910734i \(0.635516\pi\)
\(810\) −2.74244 −0.0963597
\(811\) 9.71434 0.341117 0.170558 0.985348i \(-0.445443\pi\)
0.170558 + 0.985348i \(0.445443\pi\)
\(812\) 9.96805 0.349810
\(813\) −23.2237 −0.814492
\(814\) −25.7237 −0.901614
\(815\) −27.4747 −0.962395
\(816\) −0.531613 −0.0186102
\(817\) 8.97348 0.313942
\(818\) −7.26601 −0.254050
\(819\) 4.22526 0.147643
\(820\) 12.6246 0.440871
\(821\) −3.14106 −0.109624 −0.0548118 0.998497i \(-0.517456\pi\)
−0.0548118 + 0.998497i \(0.517456\pi\)
\(822\) −8.62848 −0.300953
\(823\) −16.6914 −0.581824 −0.290912 0.956750i \(-0.593959\pi\)
−0.290912 + 0.956750i \(0.593959\pi\)
\(824\) 23.7577 0.827639
\(825\) 17.0516 0.593660
\(826\) −14.6338 −0.509175
\(827\) 25.9127 0.901072 0.450536 0.892758i \(-0.351233\pi\)
0.450536 + 0.892758i \(0.351233\pi\)
\(828\) −3.44464 −0.119710
\(829\) −8.25035 −0.286547 −0.143273 0.989683i \(-0.545763\pi\)
−0.143273 + 0.989683i \(0.545763\pi\)
\(830\) −8.60216 −0.298585
\(831\) 2.13483 0.0740563
\(832\) −14.6608 −0.508273
\(833\) 3.89840 0.135072
\(834\) 13.4725 0.466513
\(835\) 61.9506 2.14389
\(836\) 34.4827 1.19261
\(837\) −4.97869 −0.172089
\(838\) 27.3737 0.945607
\(839\) 31.8573 1.09984 0.549918 0.835218i \(-0.314659\pi\)
0.549918 + 0.835218i \(0.314659\pi\)
\(840\) 15.0394 0.518907
\(841\) −3.17879 −0.109613
\(842\) −10.4940 −0.361646
\(843\) −17.4436 −0.600788
\(844\) −24.7743 −0.852768
\(845\) 21.1039 0.725997
\(846\) −3.21834 −0.110649
\(847\) −22.7326 −0.781102
\(848\) 2.94004 0.100961
\(849\) 9.09374 0.312096
\(850\) −3.28281 −0.112599
\(851\) 17.2832 0.592462
\(852\) 10.1873 0.349012
\(853\) 50.7077 1.73620 0.868100 0.496389i \(-0.165341\pi\)
0.868100 + 0.496389i \(0.165341\pi\)
\(854\) 16.8163 0.575441
\(855\) −18.4454 −0.630818
\(856\) 53.3381 1.82306
\(857\) 33.2486 1.13575 0.567875 0.823115i \(-0.307766\pi\)
0.567875 + 0.823115i \(0.307766\pi\)
\(858\) −11.0429 −0.376999
\(859\) −0.777383 −0.0265240 −0.0132620 0.999912i \(-0.504222\pi\)
−0.0132620 + 0.999912i \(0.504222\pi\)
\(860\) 4.59911 0.156828
\(861\) 6.85168 0.233505
\(862\) 30.3044 1.03217
\(863\) 47.0297 1.60091 0.800456 0.599392i \(-0.204591\pi\)
0.800456 + 0.599392i \(0.204591\pi\)
\(864\) −5.36204 −0.182420
\(865\) −43.8398 −1.49060
\(866\) 20.8834 0.709647
\(867\) −1.00000 −0.0339618
\(868\) 9.76645 0.331495
\(869\) −8.19876 −0.278124
\(870\) 13.9356 0.472462
\(871\) 18.0693 0.612255
\(872\) 18.6561 0.631774
\(873\) 12.4025 0.419763
\(874\) 18.4318 0.623466
\(875\) −7.76107 −0.262372
\(876\) −14.9876 −0.506382
\(877\) 25.5912 0.864153 0.432077 0.901837i \(-0.357781\pi\)
0.432077 + 0.901837i \(0.357781\pi\)
\(878\) 30.1491 1.01748
\(879\) 0.0560033 0.00188894
\(880\) −7.57272 −0.255276
\(881\) −21.2156 −0.714771 −0.357386 0.933957i \(-0.616332\pi\)
−0.357386 + 0.933957i \(0.616332\pi\)
\(882\) −3.66977 −0.123568
\(883\) −22.6184 −0.761170 −0.380585 0.924746i \(-0.624277\pi\)
−0.380585 + 0.924746i \(0.624277\pi\)
\(884\) −2.67233 −0.0898802
\(885\) 25.7157 0.864422
\(886\) 26.6060 0.893846
\(887\) 37.4665 1.25800 0.629002 0.777404i \(-0.283464\pi\)
0.629002 + 0.777404i \(0.283464\pi\)
\(888\) 16.3818 0.549736
\(889\) 31.9335 1.07102
\(890\) −10.7132 −0.359106
\(891\) −4.88957 −0.163807
\(892\) 16.5370 0.553698
\(893\) −21.6462 −0.724362
\(894\) −2.92717 −0.0978992
\(895\) −68.2904 −2.28270
\(896\) 8.75578 0.292510
\(897\) 7.41953 0.247731
\(898\) −35.0674 −1.17021
\(899\) 25.2990 0.843768
\(900\) −3.88439 −0.129480
\(901\) 5.53042 0.184245
\(902\) −17.9072 −0.596244
\(903\) 2.49604 0.0830631
\(904\) −12.0734 −0.401554
\(905\) −51.2793 −1.70458
\(906\) 5.06380 0.168233
\(907\) 21.8549 0.725678 0.362839 0.931852i \(-0.381807\pi\)
0.362839 + 0.931852i \(0.381807\pi\)
\(908\) −1.50548 −0.0499610
\(909\) 19.6558 0.651943
\(910\) −11.5876 −0.384124
\(911\) 41.5959 1.37813 0.689066 0.724698i \(-0.258021\pi\)
0.689066 + 0.724698i \(0.258021\pi\)
\(912\) 3.36586 0.111455
\(913\) −15.3370 −0.507581
\(914\) 19.1898 0.634743
\(915\) −29.5509 −0.976922
\(916\) −10.8135 −0.357288
\(917\) 13.2112 0.436273
\(918\) 0.941352 0.0310693
\(919\) 25.0396 0.825979 0.412989 0.910736i \(-0.364485\pi\)
0.412989 + 0.910736i \(0.364485\pi\)
\(920\) 26.4090 0.870678
\(921\) 11.5596 0.380902
\(922\) −23.5470 −0.775479
\(923\) −21.9428 −0.722256
\(924\) 9.59164 0.315542
\(925\) 19.4896 0.640815
\(926\) −1.23069 −0.0404429
\(927\) −8.10501 −0.266204
\(928\) 27.2470 0.894425
\(929\) 32.4361 1.06419 0.532097 0.846683i \(-0.321404\pi\)
0.532097 + 0.846683i \(0.321404\pi\)
\(930\) 13.6538 0.447725
\(931\) −24.6824 −0.808934
\(932\) −15.9094 −0.521130
\(933\) 34.0306 1.11411
\(934\) 10.2690 0.336011
\(935\) −14.2448 −0.465855
\(936\) 7.03253 0.229866
\(937\) 30.5064 0.996600 0.498300 0.867005i \(-0.333958\pi\)
0.498300 + 0.867005i \(0.333958\pi\)
\(938\) 12.4861 0.407684
\(939\) 28.8680 0.942071
\(940\) −11.0942 −0.361852
\(941\) −34.1634 −1.11369 −0.556847 0.830615i \(-0.687989\pi\)
−0.556847 + 0.830615i \(0.687989\pi\)
\(942\) 0.941352 0.0306709
\(943\) 12.0315 0.391799
\(944\) −4.69253 −0.152729
\(945\) −5.13072 −0.166902
\(946\) −6.52353 −0.212098
\(947\) −57.8640 −1.88033 −0.940163 0.340725i \(-0.889328\pi\)
−0.940163 + 0.340725i \(0.889328\pi\)
\(948\) 1.86770 0.0606599
\(949\) 32.2822 1.04792
\(950\) 20.7849 0.674350
\(951\) −14.2126 −0.460876
\(952\) −5.16230 −0.167311
\(953\) −40.0860 −1.29851 −0.649257 0.760569i \(-0.724920\pi\)
−0.649257 + 0.760569i \(0.724920\pi\)
\(954\) −5.20607 −0.168553
\(955\) −35.1209 −1.13649
\(956\) 3.90264 0.126220
\(957\) 24.8462 0.803162
\(958\) −13.2534 −0.428198
\(959\) −16.1427 −0.521274
\(960\) 17.8026 0.574576
\(961\) −6.21268 −0.200409
\(962\) −12.6218 −0.406945
\(963\) −18.1965 −0.586373
\(964\) 23.4431 0.755051
\(965\) 19.9363 0.641772
\(966\) 5.12696 0.164957
\(967\) 15.0131 0.482790 0.241395 0.970427i \(-0.422395\pi\)
0.241395 + 0.970427i \(0.422395\pi\)
\(968\) −37.8362 −1.21610
\(969\) 6.33142 0.203395
\(970\) −34.0133 −1.09210
\(971\) 10.4450 0.335194 0.167597 0.985856i \(-0.446399\pi\)
0.167597 + 0.985856i \(0.446399\pi\)
\(972\) 1.11386 0.0357269
\(973\) 25.2051 0.808037
\(974\) −5.18092 −0.166007
\(975\) 8.36671 0.267949
\(976\) 5.39237 0.172606
\(977\) −2.94413 −0.0941912 −0.0470956 0.998890i \(-0.514997\pi\)
−0.0470956 + 0.998890i \(0.514997\pi\)
\(978\) −8.87766 −0.283876
\(979\) −19.1008 −0.610464
\(980\) −12.6503 −0.404099
\(981\) −6.36457 −0.203205
\(982\) −0.620592 −0.0198039
\(983\) −56.1271 −1.79018 −0.895089 0.445888i \(-0.852888\pi\)
−0.895089 + 0.445888i \(0.852888\pi\)
\(984\) 11.4039 0.363544
\(985\) 30.4707 0.970877
\(986\) −4.78344 −0.152336
\(987\) −6.02106 −0.191652
\(988\) 16.9197 0.538286
\(989\) 4.38303 0.139372
\(990\) 13.4094 0.426178
\(991\) 2.77128 0.0880327 0.0440163 0.999031i \(-0.485985\pi\)
0.0440163 + 0.999031i \(0.485985\pi\)
\(992\) 26.6959 0.847595
\(993\) −7.38597 −0.234387
\(994\) −15.1627 −0.480931
\(995\) 5.76024 0.182612
\(996\) 3.49381 0.110705
\(997\) 62.8680 1.99105 0.995524 0.0945050i \(-0.0301268\pi\)
0.995524 + 0.0945050i \(0.0301268\pi\)
\(998\) −18.1819 −0.575540
\(999\) −5.58869 −0.176818
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.1.32 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.32 48 1.1 even 1 trivial