Properties

Label 6037.2.a.b.1.13
Level $6037$
Weight $2$
Character 6037.1
Self dual yes
Analytic conductor $48.206$
Analytic rank $0$
Dimension $259$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6037 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6037.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2056877002\)
Analytic rank: \(0\)
Dimension: \(259\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.47379 q^{2} -1.46896 q^{3} +4.11964 q^{4} +2.18568 q^{5} +3.63389 q^{6} -2.37075 q^{7} -5.24354 q^{8} -0.842162 q^{9} +O(q^{10})\) \(q-2.47379 q^{2} -1.46896 q^{3} +4.11964 q^{4} +2.18568 q^{5} +3.63389 q^{6} -2.37075 q^{7} -5.24354 q^{8} -0.842162 q^{9} -5.40693 q^{10} -3.86510 q^{11} -6.05158 q^{12} -4.98021 q^{13} +5.86475 q^{14} -3.21068 q^{15} +4.73215 q^{16} -1.28037 q^{17} +2.08333 q^{18} +0.772103 q^{19} +9.00423 q^{20} +3.48254 q^{21} +9.56146 q^{22} +0.220061 q^{23} +7.70254 q^{24} -0.222783 q^{25} +12.3200 q^{26} +5.64398 q^{27} -9.76665 q^{28} -5.30558 q^{29} +7.94255 q^{30} -1.21044 q^{31} -1.21926 q^{32} +5.67768 q^{33} +3.16737 q^{34} -5.18172 q^{35} -3.46940 q^{36} +0.986815 q^{37} -1.91002 q^{38} +7.31572 q^{39} -11.4607 q^{40} -10.3919 q^{41} -8.61507 q^{42} -1.66810 q^{43} -15.9228 q^{44} -1.84070 q^{45} -0.544384 q^{46} -6.63286 q^{47} -6.95133 q^{48} -1.37952 q^{49} +0.551119 q^{50} +1.88081 q^{51} -20.5167 q^{52} +8.34931 q^{53} -13.9620 q^{54} -8.44790 q^{55} +12.4312 q^{56} -1.13419 q^{57} +13.1249 q^{58} -12.2752 q^{59} -13.2268 q^{60} +2.57632 q^{61} +2.99437 q^{62} +1.99656 q^{63} -6.44811 q^{64} -10.8852 q^{65} -14.0454 q^{66} -9.98001 q^{67} -5.27466 q^{68} -0.323260 q^{69} +12.8185 q^{70} -2.33144 q^{71} +4.41591 q^{72} -6.44092 q^{73} -2.44117 q^{74} +0.327259 q^{75} +3.18078 q^{76} +9.16321 q^{77} -18.0976 q^{78} -7.52346 q^{79} +10.3430 q^{80} -5.76428 q^{81} +25.7074 q^{82} +5.52765 q^{83} +14.3468 q^{84} -2.79848 q^{85} +4.12652 q^{86} +7.79367 q^{87} +20.2668 q^{88} -7.07792 q^{89} +4.55351 q^{90} +11.8069 q^{91} +0.906571 q^{92} +1.77808 q^{93} +16.4083 q^{94} +1.68757 q^{95} +1.79104 q^{96} -4.61343 q^{97} +3.41265 q^{98} +3.25504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.47379 −1.74923 −0.874617 0.484815i \(-0.838887\pi\)
−0.874617 + 0.484815i \(0.838887\pi\)
\(3\) −1.46896 −0.848103 −0.424052 0.905638i \(-0.639393\pi\)
−0.424052 + 0.905638i \(0.639393\pi\)
\(4\) 4.11964 2.05982
\(5\) 2.18568 0.977468 0.488734 0.872433i \(-0.337459\pi\)
0.488734 + 0.872433i \(0.337459\pi\)
\(6\) 3.63389 1.48353
\(7\) −2.37075 −0.896061 −0.448030 0.894018i \(-0.647874\pi\)
−0.448030 + 0.894018i \(0.647874\pi\)
\(8\) −5.24354 −1.85387
\(9\) −0.842162 −0.280721
\(10\) −5.40693 −1.70982
\(11\) −3.86510 −1.16537 −0.582686 0.812697i \(-0.697998\pi\)
−0.582686 + 0.812697i \(0.697998\pi\)
\(12\) −6.05158 −1.74694
\(13\) −4.98021 −1.38126 −0.690631 0.723207i \(-0.742667\pi\)
−0.690631 + 0.723207i \(0.742667\pi\)
\(14\) 5.86475 1.56742
\(15\) −3.21068 −0.828994
\(16\) 4.73215 1.18304
\(17\) −1.28037 −0.310535 −0.155268 0.987872i \(-0.549624\pi\)
−0.155268 + 0.987872i \(0.549624\pi\)
\(18\) 2.08333 0.491046
\(19\) 0.772103 0.177133 0.0885663 0.996070i \(-0.471771\pi\)
0.0885663 + 0.996070i \(0.471771\pi\)
\(20\) 9.00423 2.01341
\(21\) 3.48254 0.759952
\(22\) 9.56146 2.03851
\(23\) 0.220061 0.0458858 0.0229429 0.999737i \(-0.492696\pi\)
0.0229429 + 0.999737i \(0.492696\pi\)
\(24\) 7.70254 1.57228
\(25\) −0.222783 −0.0445566
\(26\) 12.3200 2.41615
\(27\) 5.64398 1.08618
\(28\) −9.76665 −1.84572
\(29\) −5.30558 −0.985221 −0.492610 0.870250i \(-0.663957\pi\)
−0.492610 + 0.870250i \(0.663957\pi\)
\(30\) 7.94255 1.45010
\(31\) −1.21044 −0.217401 −0.108700 0.994075i \(-0.534669\pi\)
−0.108700 + 0.994075i \(0.534669\pi\)
\(32\) −1.21926 −0.215536
\(33\) 5.67768 0.988356
\(34\) 3.16737 0.543199
\(35\) −5.18172 −0.875871
\(36\) −3.46940 −0.578234
\(37\) 0.986815 0.162231 0.0811157 0.996705i \(-0.474152\pi\)
0.0811157 + 0.996705i \(0.474152\pi\)
\(38\) −1.91002 −0.309846
\(39\) 7.31572 1.17145
\(40\) −11.4607 −1.81210
\(41\) −10.3919 −1.62294 −0.811472 0.584392i \(-0.801333\pi\)
−0.811472 + 0.584392i \(0.801333\pi\)
\(42\) −8.61507 −1.32933
\(43\) −1.66810 −0.254382 −0.127191 0.991878i \(-0.540596\pi\)
−0.127191 + 0.991878i \(0.540596\pi\)
\(44\) −15.9228 −2.40046
\(45\) −1.84070 −0.274395
\(46\) −0.544384 −0.0802650
\(47\) −6.63286 −0.967502 −0.483751 0.875206i \(-0.660726\pi\)
−0.483751 + 0.875206i \(0.660726\pi\)
\(48\) −6.95133 −1.00334
\(49\) −1.37952 −0.197075
\(50\) 0.551119 0.0779399
\(51\) 1.88081 0.263366
\(52\) −20.5167 −2.84515
\(53\) 8.34931 1.14687 0.573433 0.819252i \(-0.305611\pi\)
0.573433 + 0.819252i \(0.305611\pi\)
\(54\) −13.9620 −1.89999
\(55\) −8.44790 −1.13911
\(56\) 12.4312 1.66118
\(57\) −1.13419 −0.150227
\(58\) 13.1249 1.72338
\(59\) −12.2752 −1.59809 −0.799046 0.601270i \(-0.794662\pi\)
−0.799046 + 0.601270i \(0.794662\pi\)
\(60\) −13.2268 −1.70758
\(61\) 2.57632 0.329864 0.164932 0.986305i \(-0.447259\pi\)
0.164932 + 0.986305i \(0.447259\pi\)
\(62\) 2.99437 0.380285
\(63\) 1.99656 0.251543
\(64\) −6.44811 −0.806014
\(65\) −10.8852 −1.35014
\(66\) −14.0454 −1.72887
\(67\) −9.98001 −1.21925 −0.609626 0.792689i \(-0.708680\pi\)
−0.609626 + 0.792689i \(0.708680\pi\)
\(68\) −5.27466 −0.639647
\(69\) −0.323260 −0.0389159
\(70\) 12.8185 1.53210
\(71\) −2.33144 −0.276692 −0.138346 0.990384i \(-0.544179\pi\)
−0.138346 + 0.990384i \(0.544179\pi\)
\(72\) 4.41591 0.520420
\(73\) −6.44092 −0.753852 −0.376926 0.926243i \(-0.623019\pi\)
−0.376926 + 0.926243i \(0.623019\pi\)
\(74\) −2.44117 −0.283781
\(75\) 0.327259 0.0377886
\(76\) 3.18078 0.364861
\(77\) 9.16321 1.04424
\(78\) −18.0976 −2.04915
\(79\) −7.52346 −0.846456 −0.423228 0.906023i \(-0.639103\pi\)
−0.423228 + 0.906023i \(0.639103\pi\)
\(80\) 10.3430 1.15638
\(81\) −5.76428 −0.640475
\(82\) 25.7074 2.83891
\(83\) 5.52765 0.606738 0.303369 0.952873i \(-0.401889\pi\)
0.303369 + 0.952873i \(0.401889\pi\)
\(84\) 14.3468 1.56536
\(85\) −2.79848 −0.303538
\(86\) 4.12652 0.444974
\(87\) 7.79367 0.835569
\(88\) 20.2668 2.16045
\(89\) −7.07792 −0.750258 −0.375129 0.926973i \(-0.622402\pi\)
−0.375129 + 0.926973i \(0.622402\pi\)
\(90\) 4.55351 0.479982
\(91\) 11.8069 1.23770
\(92\) 0.906571 0.0945165
\(93\) 1.77808 0.184378
\(94\) 16.4083 1.69239
\(95\) 1.68757 0.173141
\(96\) 1.79104 0.182797
\(97\) −4.61343 −0.468423 −0.234211 0.972186i \(-0.575251\pi\)
−0.234211 + 0.972186i \(0.575251\pi\)
\(98\) 3.41265 0.344730
\(99\) 3.25504 0.327144
\(100\) −0.917786 −0.0917786
\(101\) −6.11949 −0.608912 −0.304456 0.952526i \(-0.598475\pi\)
−0.304456 + 0.952526i \(0.598475\pi\)
\(102\) −4.65273 −0.460689
\(103\) −7.91151 −0.779544 −0.389772 0.920911i \(-0.627446\pi\)
−0.389772 + 0.920911i \(0.627446\pi\)
\(104\) 26.1140 2.56068
\(105\) 7.61173 0.742829
\(106\) −20.6544 −2.00614
\(107\) 4.73276 0.457533 0.228767 0.973481i \(-0.426531\pi\)
0.228767 + 0.973481i \(0.426531\pi\)
\(108\) 23.2511 2.23734
\(109\) 9.14850 0.876267 0.438134 0.898910i \(-0.355640\pi\)
0.438134 + 0.898910i \(0.355640\pi\)
\(110\) 20.8983 1.99258
\(111\) −1.44959 −0.137589
\(112\) −11.2188 −1.06007
\(113\) −11.8129 −1.11127 −0.555634 0.831427i \(-0.687524\pi\)
−0.555634 + 0.831427i \(0.687524\pi\)
\(114\) 2.80574 0.262782
\(115\) 0.480983 0.0448519
\(116\) −21.8571 −2.02938
\(117\) 4.19414 0.387749
\(118\) 30.3662 2.79544
\(119\) 3.03544 0.278259
\(120\) 16.8353 1.53685
\(121\) 3.93903 0.358093
\(122\) −6.37328 −0.577010
\(123\) 15.2653 1.37642
\(124\) −4.98656 −0.447806
\(125\) −11.4154 −1.02102
\(126\) −4.93907 −0.440007
\(127\) 16.9039 1.49998 0.749988 0.661452i \(-0.230059\pi\)
0.749988 + 0.661452i \(0.230059\pi\)
\(128\) 18.3898 1.62544
\(129\) 2.45036 0.215742
\(130\) 26.9276 2.36171
\(131\) 10.2085 0.891920 0.445960 0.895053i \(-0.352862\pi\)
0.445960 + 0.895053i \(0.352862\pi\)
\(132\) 23.3900 2.03584
\(133\) −1.83047 −0.158722
\(134\) 24.6885 2.13276
\(135\) 12.3359 1.06171
\(136\) 6.71367 0.575693
\(137\) 10.7157 0.915507 0.457754 0.889079i \(-0.348654\pi\)
0.457754 + 0.889079i \(0.348654\pi\)
\(138\) 0.799677 0.0680731
\(139\) −13.5037 −1.14537 −0.572684 0.819776i \(-0.694098\pi\)
−0.572684 + 0.819776i \(0.694098\pi\)
\(140\) −21.3468 −1.80414
\(141\) 9.74339 0.820542
\(142\) 5.76750 0.483998
\(143\) 19.2490 1.60968
\(144\) −3.98524 −0.332103
\(145\) −11.5963 −0.963021
\(146\) 15.9335 1.31866
\(147\) 2.02646 0.167140
\(148\) 4.06532 0.334167
\(149\) −23.1488 −1.89642 −0.948211 0.317640i \(-0.897110\pi\)
−0.948211 + 0.317640i \(0.897110\pi\)
\(150\) −0.809570 −0.0661011
\(151\) 14.3587 1.16849 0.584247 0.811576i \(-0.301390\pi\)
0.584247 + 0.811576i \(0.301390\pi\)
\(152\) −4.04855 −0.328381
\(153\) 1.07828 0.0871737
\(154\) −22.6679 −1.82663
\(155\) −2.64563 −0.212502
\(156\) 30.1381 2.41298
\(157\) −1.71103 −0.136555 −0.0682776 0.997666i \(-0.521750\pi\)
−0.0682776 + 0.997666i \(0.521750\pi\)
\(158\) 18.6115 1.48065
\(159\) −12.2648 −0.972661
\(160\) −2.66491 −0.210680
\(161\) −0.521710 −0.0411165
\(162\) 14.2596 1.12034
\(163\) −14.7782 −1.15752 −0.578760 0.815498i \(-0.696463\pi\)
−0.578760 + 0.815498i \(0.696463\pi\)
\(164\) −42.8109 −3.34297
\(165\) 12.4096 0.966087
\(166\) −13.6742 −1.06133
\(167\) 11.8405 0.916248 0.458124 0.888888i \(-0.348522\pi\)
0.458124 + 0.888888i \(0.348522\pi\)
\(168\) −18.2608 −1.40885
\(169\) 11.8025 0.907885
\(170\) 6.92286 0.530959
\(171\) −0.650236 −0.0497248
\(172\) −6.87195 −0.523982
\(173\) 0.211551 0.0160839 0.00804197 0.999968i \(-0.497440\pi\)
0.00804197 + 0.999968i \(0.497440\pi\)
\(174\) −19.2799 −1.46161
\(175\) 0.528164 0.0399254
\(176\) −18.2902 −1.37868
\(177\) 18.0317 1.35535
\(178\) 17.5093 1.31238
\(179\) −0.884123 −0.0660825 −0.0330412 0.999454i \(-0.510519\pi\)
−0.0330412 + 0.999454i \(0.510519\pi\)
\(180\) −7.58302 −0.565205
\(181\) −23.9100 −1.77722 −0.888608 0.458668i \(-0.848327\pi\)
−0.888608 + 0.458668i \(0.848327\pi\)
\(182\) −29.2077 −2.16502
\(183\) −3.78451 −0.279759
\(184\) −1.15390 −0.0850665
\(185\) 2.15687 0.158576
\(186\) −4.39860 −0.322521
\(187\) 4.94876 0.361889
\(188\) −27.3250 −1.99288
\(189\) −13.3805 −0.973287
\(190\) −4.17470 −0.302865
\(191\) 12.2674 0.887638 0.443819 0.896116i \(-0.353623\pi\)
0.443819 + 0.896116i \(0.353623\pi\)
\(192\) 9.47200 0.683583
\(193\) 7.62392 0.548782 0.274391 0.961618i \(-0.411524\pi\)
0.274391 + 0.961618i \(0.411524\pi\)
\(194\) 11.4127 0.819381
\(195\) 15.9899 1.14506
\(196\) −5.68314 −0.405938
\(197\) −5.52933 −0.393949 −0.196974 0.980409i \(-0.563112\pi\)
−0.196974 + 0.980409i \(0.563112\pi\)
\(198\) −8.05230 −0.572252
\(199\) −0.226779 −0.0160759 −0.00803796 0.999968i \(-0.502559\pi\)
−0.00803796 + 0.999968i \(0.502559\pi\)
\(200\) 1.16817 0.0826023
\(201\) 14.6602 1.03405
\(202\) 15.1383 1.06513
\(203\) 12.5782 0.882818
\(204\) 7.74826 0.542486
\(205\) −22.7134 −1.58638
\(206\) 19.5714 1.36361
\(207\) −0.185327 −0.0128811
\(208\) −23.5671 −1.63408
\(209\) −2.98426 −0.206425
\(210\) −18.8298 −1.29938
\(211\) −19.3072 −1.32916 −0.664582 0.747215i \(-0.731391\pi\)
−0.664582 + 0.747215i \(0.731391\pi\)
\(212\) 34.3961 2.36234
\(213\) 3.42479 0.234663
\(214\) −11.7079 −0.800333
\(215\) −3.64593 −0.248651
\(216\) −29.5944 −2.01365
\(217\) 2.86965 0.194804
\(218\) −22.6315 −1.53280
\(219\) 9.46144 0.639345
\(220\) −34.8023 −2.34637
\(221\) 6.37651 0.428931
\(222\) 3.58598 0.240675
\(223\) −6.68365 −0.447570 −0.223785 0.974639i \(-0.571841\pi\)
−0.223785 + 0.974639i \(0.571841\pi\)
\(224\) 2.89056 0.193134
\(225\) 0.187619 0.0125080
\(226\) 29.2227 1.94387
\(227\) −3.12580 −0.207467 −0.103733 0.994605i \(-0.533079\pi\)
−0.103733 + 0.994605i \(0.533079\pi\)
\(228\) −4.67244 −0.309440
\(229\) −3.89333 −0.257279 −0.128639 0.991691i \(-0.541061\pi\)
−0.128639 + 0.991691i \(0.541061\pi\)
\(230\) −1.18985 −0.0784565
\(231\) −13.4604 −0.885628
\(232\) 27.8200 1.82647
\(233\) −2.28751 −0.149860 −0.0749298 0.997189i \(-0.523873\pi\)
−0.0749298 + 0.997189i \(0.523873\pi\)
\(234\) −10.3754 −0.678263
\(235\) −14.4973 −0.945702
\(236\) −50.5693 −3.29178
\(237\) 11.0517 0.717882
\(238\) −7.50905 −0.486739
\(239\) 23.0717 1.49239 0.746193 0.665729i \(-0.231879\pi\)
0.746193 + 0.665729i \(0.231879\pi\)
\(240\) −15.1934 −0.980730
\(241\) 8.31031 0.535314 0.267657 0.963514i \(-0.413751\pi\)
0.267657 + 0.963514i \(0.413751\pi\)
\(242\) −9.74433 −0.626389
\(243\) −8.46444 −0.542994
\(244\) 10.6135 0.679461
\(245\) −3.01520 −0.192634
\(246\) −37.7631 −2.40769
\(247\) −3.84523 −0.244666
\(248\) 6.34697 0.403033
\(249\) −8.11988 −0.514577
\(250\) 28.2392 1.78600
\(251\) −8.28701 −0.523071 −0.261536 0.965194i \(-0.584229\pi\)
−0.261536 + 0.965194i \(0.584229\pi\)
\(252\) 8.22510 0.518133
\(253\) −0.850557 −0.0534741
\(254\) −41.8166 −2.62381
\(255\) 4.11086 0.257432
\(256\) −32.5963 −2.03727
\(257\) −26.7133 −1.66633 −0.833164 0.553025i \(-0.813473\pi\)
−0.833164 + 0.553025i \(0.813473\pi\)
\(258\) −6.06169 −0.377384
\(259\) −2.33950 −0.145369
\(260\) −44.8430 −2.78104
\(261\) 4.46815 0.276572
\(262\) −25.2537 −1.56018
\(263\) 26.4639 1.63184 0.815918 0.578168i \(-0.196232\pi\)
0.815918 + 0.578168i \(0.196232\pi\)
\(264\) −29.7711 −1.83229
\(265\) 18.2490 1.12102
\(266\) 4.52819 0.277641
\(267\) 10.3972 0.636297
\(268\) −41.1140 −2.51144
\(269\) 1.35131 0.0823911 0.0411955 0.999151i \(-0.486883\pi\)
0.0411955 + 0.999151i \(0.486883\pi\)
\(270\) −30.5166 −1.85718
\(271\) −8.02043 −0.487207 −0.243603 0.969875i \(-0.578329\pi\)
−0.243603 + 0.969875i \(0.578329\pi\)
\(272\) −6.05890 −0.367375
\(273\) −17.3438 −1.04969
\(274\) −26.5085 −1.60144
\(275\) 0.861080 0.0519250
\(276\) −1.33171 −0.0801598
\(277\) 3.48765 0.209552 0.104776 0.994496i \(-0.466587\pi\)
0.104776 + 0.994496i \(0.466587\pi\)
\(278\) 33.4053 2.00352
\(279\) 1.01938 0.0610289
\(280\) 27.1706 1.62375
\(281\) 6.44566 0.384516 0.192258 0.981344i \(-0.438419\pi\)
0.192258 + 0.981344i \(0.438419\pi\)
\(282\) −24.1031 −1.43532
\(283\) −15.6708 −0.931530 −0.465765 0.884908i \(-0.654221\pi\)
−0.465765 + 0.884908i \(0.654221\pi\)
\(284\) −9.60471 −0.569935
\(285\) −2.47897 −0.146842
\(286\) −47.6181 −2.81572
\(287\) 24.6367 1.45426
\(288\) 1.02681 0.0605054
\(289\) −15.3607 −0.903568
\(290\) 28.6869 1.68455
\(291\) 6.77693 0.397271
\(292\) −26.5343 −1.55280
\(293\) −15.3790 −0.898448 −0.449224 0.893419i \(-0.648300\pi\)
−0.449224 + 0.893419i \(0.648300\pi\)
\(294\) −5.01304 −0.292366
\(295\) −26.8297 −1.56208
\(296\) −5.17441 −0.300756
\(297\) −21.8145 −1.26581
\(298\) 57.2653 3.31729
\(299\) −1.09595 −0.0633803
\(300\) 1.34819 0.0778377
\(301\) 3.95465 0.227942
\(302\) −35.5204 −2.04397
\(303\) 8.98928 0.516421
\(304\) 3.65370 0.209554
\(305\) 5.63103 0.322432
\(306\) −2.66744 −0.152487
\(307\) 26.7178 1.52487 0.762434 0.647066i \(-0.224004\pi\)
0.762434 + 0.647066i \(0.224004\pi\)
\(308\) 37.7491 2.15096
\(309\) 11.6217 0.661134
\(310\) 6.54474 0.371716
\(311\) −13.3488 −0.756941 −0.378470 0.925613i \(-0.623550\pi\)
−0.378470 + 0.925613i \(0.623550\pi\)
\(312\) −38.3603 −2.17172
\(313\) −11.1270 −0.628934 −0.314467 0.949268i \(-0.601826\pi\)
−0.314467 + 0.949268i \(0.601826\pi\)
\(314\) 4.23274 0.238867
\(315\) 4.36385 0.245875
\(316\) −30.9939 −1.74355
\(317\) 21.3453 1.19887 0.599436 0.800423i \(-0.295392\pi\)
0.599436 + 0.800423i \(0.295392\pi\)
\(318\) 30.3405 1.70141
\(319\) 20.5066 1.14815
\(320\) −14.0935 −0.787853
\(321\) −6.95223 −0.388036
\(322\) 1.29060 0.0719224
\(323\) −0.988577 −0.0550059
\(324\) −23.7467 −1.31926
\(325\) 1.10951 0.0615444
\(326\) 36.5582 2.02477
\(327\) −13.4388 −0.743165
\(328\) 54.4904 3.00873
\(329\) 15.7249 0.866941
\(330\) −30.6988 −1.68991
\(331\) −14.9182 −0.819976 −0.409988 0.912091i \(-0.634467\pi\)
−0.409988 + 0.912091i \(0.634467\pi\)
\(332\) 22.7719 1.24977
\(333\) −0.831058 −0.0455417
\(334\) −29.2910 −1.60273
\(335\) −21.8132 −1.19178
\(336\) 16.4799 0.899052
\(337\) −5.66222 −0.308441 −0.154220 0.988036i \(-0.549287\pi\)
−0.154220 + 0.988036i \(0.549287\pi\)
\(338\) −29.1969 −1.58810
\(339\) 17.3527 0.942470
\(340\) −11.5287 −0.625234
\(341\) 4.67846 0.253353
\(342\) 1.60855 0.0869802
\(343\) 19.8658 1.07265
\(344\) 8.74673 0.471592
\(345\) −0.706544 −0.0380391
\(346\) −0.523334 −0.0281346
\(347\) 12.2096 0.655447 0.327723 0.944774i \(-0.393719\pi\)
0.327723 + 0.944774i \(0.393719\pi\)
\(348\) 32.1071 1.72112
\(349\) 26.9079 1.44035 0.720173 0.693795i \(-0.244063\pi\)
0.720173 + 0.693795i \(0.244063\pi\)
\(350\) −1.30657 −0.0698389
\(351\) −28.1082 −1.50030
\(352\) 4.71255 0.251180
\(353\) 25.7060 1.36819 0.684097 0.729391i \(-0.260196\pi\)
0.684097 + 0.729391i \(0.260196\pi\)
\(354\) −44.6067 −2.37082
\(355\) −5.09580 −0.270457
\(356\) −29.1585 −1.54540
\(357\) −4.45894 −0.235992
\(358\) 2.18714 0.115594
\(359\) 25.9311 1.36859 0.684296 0.729205i \(-0.260110\pi\)
0.684296 + 0.729205i \(0.260110\pi\)
\(360\) 9.65179 0.508694
\(361\) −18.4039 −0.968624
\(362\) 59.1483 3.10877
\(363\) −5.78626 −0.303700
\(364\) 48.6400 2.54943
\(365\) −14.0778 −0.736866
\(366\) 9.36209 0.489364
\(367\) −26.0945 −1.36212 −0.681060 0.732227i \(-0.738481\pi\)
−0.681060 + 0.732227i \(0.738481\pi\)
\(368\) 1.04136 0.0542846
\(369\) 8.75167 0.455594
\(370\) −5.33564 −0.277387
\(371\) −19.7942 −1.02766
\(372\) 7.32505 0.379786
\(373\) 14.6171 0.756845 0.378422 0.925633i \(-0.376467\pi\)
0.378422 + 0.925633i \(0.376467\pi\)
\(374\) −12.2422 −0.633029
\(375\) 16.7687 0.865931
\(376\) 34.7797 1.79363
\(377\) 26.4229 1.36085
\(378\) 33.1005 1.70251
\(379\) −10.7053 −0.549892 −0.274946 0.961460i \(-0.588660\pi\)
−0.274946 + 0.961460i \(0.588660\pi\)
\(380\) 6.95219 0.356640
\(381\) −24.8311 −1.27213
\(382\) −30.3470 −1.55269
\(383\) 36.2449 1.85203 0.926013 0.377492i \(-0.123214\pi\)
0.926013 + 0.377492i \(0.123214\pi\)
\(384\) −27.0138 −1.37854
\(385\) 20.0279 1.02072
\(386\) −18.8600 −0.959948
\(387\) 1.40481 0.0714104
\(388\) −19.0057 −0.964866
\(389\) −0.668258 −0.0338820 −0.0169410 0.999856i \(-0.505393\pi\)
−0.0169410 + 0.999856i \(0.505393\pi\)
\(390\) −39.5556 −2.00297
\(391\) −0.281759 −0.0142492
\(392\) 7.23359 0.365351
\(393\) −14.9959 −0.756441
\(394\) 13.6784 0.689108
\(395\) −16.4439 −0.827383
\(396\) 13.4096 0.673858
\(397\) 4.70934 0.236355 0.118178 0.992992i \(-0.462295\pi\)
0.118178 + 0.992992i \(0.462295\pi\)
\(398\) 0.561003 0.0281205
\(399\) 2.68888 0.134612
\(400\) −1.05424 −0.0527121
\(401\) −13.0622 −0.652296 −0.326148 0.945319i \(-0.605751\pi\)
−0.326148 + 0.945319i \(0.605751\pi\)
\(402\) −36.2663 −1.80880
\(403\) 6.02823 0.300287
\(404\) −25.2101 −1.25425
\(405\) −12.5989 −0.626044
\(406\) −31.1159 −1.54425
\(407\) −3.81414 −0.189060
\(408\) −9.86211 −0.488247
\(409\) −10.4640 −0.517412 −0.258706 0.965956i \(-0.583296\pi\)
−0.258706 + 0.965956i \(0.583296\pi\)
\(410\) 56.1883 2.77494
\(411\) −15.7410 −0.776445
\(412\) −32.5926 −1.60572
\(413\) 29.1014 1.43199
\(414\) 0.458460 0.0225321
\(415\) 12.0817 0.593067
\(416\) 6.07215 0.297712
\(417\) 19.8364 0.971391
\(418\) 7.38243 0.361086
\(419\) −11.3593 −0.554938 −0.277469 0.960735i \(-0.589496\pi\)
−0.277469 + 0.960735i \(0.589496\pi\)
\(420\) 31.3576 1.53009
\(421\) −20.0360 −0.976493 −0.488246 0.872706i \(-0.662363\pi\)
−0.488246 + 0.872706i \(0.662363\pi\)
\(422\) 47.7620 2.32502
\(423\) 5.58594 0.271598
\(424\) −43.7800 −2.12614
\(425\) 0.285245 0.0138364
\(426\) −8.47222 −0.410481
\(427\) −6.10783 −0.295579
\(428\) 19.4973 0.942436
\(429\) −28.2760 −1.36518
\(430\) 9.01927 0.434948
\(431\) −19.3623 −0.932650 −0.466325 0.884613i \(-0.654422\pi\)
−0.466325 + 0.884613i \(0.654422\pi\)
\(432\) 26.7081 1.28500
\(433\) −16.3994 −0.788107 −0.394053 0.919088i \(-0.628927\pi\)
−0.394053 + 0.919088i \(0.628927\pi\)
\(434\) −7.09891 −0.340758
\(435\) 17.0345 0.816742
\(436\) 37.6885 1.80495
\(437\) 0.169909 0.00812787
\(438\) −23.4056 −1.11836
\(439\) 9.56807 0.456659 0.228329 0.973584i \(-0.426674\pi\)
0.228329 + 0.973584i \(0.426674\pi\)
\(440\) 44.2969 2.11177
\(441\) 1.16178 0.0553229
\(442\) −15.7742 −0.750300
\(443\) 10.7900 0.512647 0.256323 0.966591i \(-0.417489\pi\)
0.256323 + 0.966591i \(0.417489\pi\)
\(444\) −5.97179 −0.283409
\(445\) −15.4701 −0.733354
\(446\) 16.5339 0.782905
\(447\) 34.0046 1.60836
\(448\) 15.2869 0.722238
\(449\) 21.8937 1.03323 0.516615 0.856218i \(-0.327192\pi\)
0.516615 + 0.856218i \(0.327192\pi\)
\(450\) −0.464131 −0.0218794
\(451\) 40.1658 1.89133
\(452\) −48.6650 −2.28901
\(453\) −21.0923 −0.991003
\(454\) 7.73258 0.362908
\(455\) 25.8061 1.20981
\(456\) 5.94716 0.278501
\(457\) 7.13656 0.333834 0.166917 0.985971i \(-0.446619\pi\)
0.166917 + 0.985971i \(0.446619\pi\)
\(458\) 9.63129 0.450041
\(459\) −7.22638 −0.337298
\(460\) 1.98148 0.0923869
\(461\) 22.6296 1.05396 0.526982 0.849877i \(-0.323324\pi\)
0.526982 + 0.849877i \(0.323324\pi\)
\(462\) 33.2981 1.54917
\(463\) 29.6123 1.37620 0.688100 0.725616i \(-0.258445\pi\)
0.688100 + 0.725616i \(0.258445\pi\)
\(464\) −25.1068 −1.16555
\(465\) 3.88632 0.180224
\(466\) 5.65881 0.262139
\(467\) −32.3594 −1.49741 −0.748706 0.662902i \(-0.769325\pi\)
−0.748706 + 0.662902i \(0.769325\pi\)
\(468\) 17.2784 0.798693
\(469\) 23.6602 1.09252
\(470\) 35.8634 1.65425
\(471\) 2.51344 0.115813
\(472\) 64.3654 2.96266
\(473\) 6.44736 0.296450
\(474\) −27.3395 −1.25574
\(475\) −0.172011 −0.00789242
\(476\) 12.5049 0.573162
\(477\) −7.03147 −0.321949
\(478\) −57.0746 −2.61053
\(479\) −25.8113 −1.17935 −0.589674 0.807641i \(-0.700744\pi\)
−0.589674 + 0.807641i \(0.700744\pi\)
\(480\) 3.91464 0.178678
\(481\) −4.91455 −0.224084
\(482\) −20.5580 −0.936390
\(483\) 0.766370 0.0348710
\(484\) 16.2274 0.737608
\(485\) −10.0835 −0.457868
\(486\) 20.9393 0.949824
\(487\) −10.9901 −0.498008 −0.249004 0.968502i \(-0.580103\pi\)
−0.249004 + 0.968502i \(0.580103\pi\)
\(488\) −13.5091 −0.611526
\(489\) 21.7086 0.981696
\(490\) 7.45898 0.336962
\(491\) 36.6058 1.65200 0.825999 0.563672i \(-0.190612\pi\)
0.825999 + 0.563672i \(0.190612\pi\)
\(492\) 62.8874 2.83518
\(493\) 6.79310 0.305946
\(494\) 9.51231 0.427979
\(495\) 7.11450 0.319773
\(496\) −5.72796 −0.257193
\(497\) 5.52728 0.247932
\(498\) 20.0869 0.900115
\(499\) −32.4769 −1.45386 −0.726932 0.686710i \(-0.759054\pi\)
−0.726932 + 0.686710i \(0.759054\pi\)
\(500\) −47.0271 −2.10312
\(501\) −17.3932 −0.777073
\(502\) 20.5003 0.914974
\(503\) 18.4884 0.824359 0.412179 0.911103i \(-0.364768\pi\)
0.412179 + 0.911103i \(0.364768\pi\)
\(504\) −10.4690 −0.466328
\(505\) −13.3753 −0.595192
\(506\) 2.10410 0.0935387
\(507\) −17.3374 −0.769980
\(508\) 69.6378 3.08968
\(509\) 15.2758 0.677090 0.338545 0.940950i \(-0.390065\pi\)
0.338545 + 0.940950i \(0.390065\pi\)
\(510\) −10.1694 −0.450308
\(511\) 15.2698 0.675498
\(512\) 43.8567 1.93821
\(513\) 4.35773 0.192398
\(514\) 66.0831 2.91480
\(515\) −17.2921 −0.761979
\(516\) 10.0946 0.444391
\(517\) 25.6367 1.12750
\(518\) 5.78742 0.254285
\(519\) −0.310760 −0.0136408
\(520\) 57.0769 2.50299
\(521\) 0.986700 0.0432281 0.0216141 0.999766i \(-0.493119\pi\)
0.0216141 + 0.999766i \(0.493119\pi\)
\(522\) −11.0533 −0.483789
\(523\) 7.40817 0.323937 0.161968 0.986796i \(-0.448216\pi\)
0.161968 + 0.986796i \(0.448216\pi\)
\(524\) 42.0553 1.83719
\(525\) −0.775851 −0.0338609
\(526\) −65.4662 −2.85446
\(527\) 1.54981 0.0675106
\(528\) 26.8676 1.16926
\(529\) −22.9516 −0.997894
\(530\) −45.1441 −1.96093
\(531\) 10.3377 0.448617
\(532\) −7.54086 −0.326938
\(533\) 51.7539 2.24171
\(534\) −25.7204 −1.11303
\(535\) 10.3443 0.447224
\(536\) 52.3306 2.26034
\(537\) 1.29874 0.0560448
\(538\) −3.34287 −0.144121
\(539\) 5.33200 0.229665
\(540\) 50.8197 2.18693
\(541\) 34.0028 1.46190 0.730948 0.682433i \(-0.239078\pi\)
0.730948 + 0.682433i \(0.239078\pi\)
\(542\) 19.8409 0.852238
\(543\) 35.1228 1.50726
\(544\) 1.56110 0.0669316
\(545\) 19.9957 0.856523
\(546\) 42.9049 1.83616
\(547\) −35.4902 −1.51745 −0.758726 0.651410i \(-0.774178\pi\)
−0.758726 + 0.651410i \(0.774178\pi\)
\(548\) 44.1450 1.88578
\(549\) −2.16968 −0.0925998
\(550\) −2.13013 −0.0908291
\(551\) −4.09645 −0.174515
\(552\) 1.69503 0.0721452
\(553\) 17.8363 0.758476
\(554\) −8.62771 −0.366556
\(555\) −3.16835 −0.134489
\(556\) −55.6303 −2.35925
\(557\) −24.7396 −1.04825 −0.524126 0.851641i \(-0.675608\pi\)
−0.524126 + 0.851641i \(0.675608\pi\)
\(558\) −2.52174 −0.106754
\(559\) 8.30747 0.351369
\(560\) −24.5207 −1.03619
\(561\) −7.26952 −0.306920
\(562\) −15.9452 −0.672608
\(563\) 27.5941 1.16295 0.581477 0.813563i \(-0.302475\pi\)
0.581477 + 0.813563i \(0.302475\pi\)
\(564\) 40.1393 1.69017
\(565\) −25.8194 −1.08623
\(566\) 38.7662 1.62946
\(567\) 13.6657 0.573905
\(568\) 12.2250 0.512951
\(569\) −26.5388 −1.11256 −0.556282 0.830993i \(-0.687773\pi\)
−0.556282 + 0.830993i \(0.687773\pi\)
\(570\) 6.13246 0.256861
\(571\) −19.5032 −0.816184 −0.408092 0.912941i \(-0.633806\pi\)
−0.408092 + 0.912941i \(0.633806\pi\)
\(572\) 79.2991 3.31566
\(573\) −18.0203 −0.752809
\(574\) −60.9459 −2.54383
\(575\) −0.0490258 −0.00204452
\(576\) 5.43035 0.226265
\(577\) −5.90538 −0.245844 −0.122922 0.992416i \(-0.539227\pi\)
−0.122922 + 0.992416i \(0.539227\pi\)
\(578\) 37.9990 1.58055
\(579\) −11.1992 −0.465424
\(580\) −47.7726 −1.98365
\(581\) −13.1047 −0.543674
\(582\) −16.7647 −0.694920
\(583\) −32.2710 −1.33653
\(584\) 33.7732 1.39755
\(585\) 9.16708 0.379012
\(586\) 38.0443 1.57160
\(587\) 23.1024 0.953540 0.476770 0.879028i \(-0.341808\pi\)
0.476770 + 0.879028i \(0.341808\pi\)
\(588\) 8.34829 0.344278
\(589\) −0.934581 −0.0385087
\(590\) 66.3710 2.73245
\(591\) 8.12236 0.334109
\(592\) 4.66976 0.191926
\(593\) −11.5850 −0.475737 −0.237869 0.971297i \(-0.576449\pi\)
−0.237869 + 0.971297i \(0.576449\pi\)
\(594\) 53.9646 2.21420
\(595\) 6.63452 0.271989
\(596\) −95.3647 −3.90629
\(597\) 0.333128 0.0136340
\(598\) 2.71115 0.110867
\(599\) 30.9145 1.26313 0.631566 0.775322i \(-0.282412\pi\)
0.631566 + 0.775322i \(0.282412\pi\)
\(600\) −1.71600 −0.0700553
\(601\) −39.7960 −1.62331 −0.811657 0.584135i \(-0.801434\pi\)
−0.811657 + 0.584135i \(0.801434\pi\)
\(602\) −9.78297 −0.398724
\(603\) 8.40479 0.342269
\(604\) 59.1526 2.40689
\(605\) 8.60947 0.350025
\(606\) −22.2376 −0.903340
\(607\) −10.3545 −0.420276 −0.210138 0.977672i \(-0.567391\pi\)
−0.210138 + 0.977672i \(0.567391\pi\)
\(608\) −0.941391 −0.0381785
\(609\) −18.4769 −0.748721
\(610\) −13.9300 −0.564009
\(611\) 33.0330 1.33637
\(612\) 4.44212 0.179562
\(613\) 17.7475 0.716813 0.358407 0.933566i \(-0.383320\pi\)
0.358407 + 0.933566i \(0.383320\pi\)
\(614\) −66.0943 −2.66735
\(615\) 33.3651 1.34541
\(616\) −48.0477 −1.93590
\(617\) −21.3758 −0.860556 −0.430278 0.902696i \(-0.641585\pi\)
−0.430278 + 0.902696i \(0.641585\pi\)
\(618\) −28.7496 −1.15648
\(619\) 25.2532 1.01501 0.507506 0.861648i \(-0.330568\pi\)
0.507506 + 0.861648i \(0.330568\pi\)
\(620\) −10.8990 −0.437716
\(621\) 1.24202 0.0498404
\(622\) 33.0221 1.32407
\(623\) 16.7800 0.672277
\(624\) 34.6191 1.38587
\(625\) −23.8365 −0.953458
\(626\) 27.5258 1.10015
\(627\) 4.38375 0.175070
\(628\) −7.04884 −0.281279
\(629\) −1.26349 −0.0503786
\(630\) −10.7952 −0.430093
\(631\) 5.99689 0.238732 0.119366 0.992850i \(-0.461914\pi\)
0.119366 + 0.992850i \(0.461914\pi\)
\(632\) 39.4496 1.56922
\(633\) 28.3615 1.12727
\(634\) −52.8038 −2.09711
\(635\) 36.9465 1.46618
\(636\) −50.5265 −2.00351
\(637\) 6.87032 0.272212
\(638\) −50.7290 −2.00838
\(639\) 1.96345 0.0776730
\(640\) 40.1943 1.58882
\(641\) 14.2203 0.561667 0.280833 0.959757i \(-0.409389\pi\)
0.280833 + 0.959757i \(0.409389\pi\)
\(642\) 17.1984 0.678765
\(643\) −8.46018 −0.333637 −0.166819 0.985988i \(-0.553349\pi\)
−0.166819 + 0.985988i \(0.553349\pi\)
\(644\) −2.14926 −0.0846926
\(645\) 5.35572 0.210881
\(646\) 2.44553 0.0962182
\(647\) −23.3606 −0.918399 −0.459199 0.888333i \(-0.651864\pi\)
−0.459199 + 0.888333i \(0.651864\pi\)
\(648\) 30.2252 1.18736
\(649\) 47.4448 1.86237
\(650\) −2.74469 −0.107655
\(651\) −4.21539 −0.165214
\(652\) −60.8809 −2.38428
\(653\) −40.3587 −1.57936 −0.789680 0.613519i \(-0.789753\pi\)
−0.789680 + 0.613519i \(0.789753\pi\)
\(654\) 33.2447 1.29997
\(655\) 22.3125 0.871823
\(656\) −49.1760 −1.92000
\(657\) 5.42430 0.211622
\(658\) −38.9001 −1.51648
\(659\) 30.7878 1.19932 0.599661 0.800254i \(-0.295302\pi\)
0.599661 + 0.800254i \(0.295302\pi\)
\(660\) 51.1231 1.98996
\(661\) −10.9732 −0.426809 −0.213405 0.976964i \(-0.568455\pi\)
−0.213405 + 0.976964i \(0.568455\pi\)
\(662\) 36.9044 1.43433
\(663\) −9.36683 −0.363778
\(664\) −28.9845 −1.12481
\(665\) −4.00082 −0.155145
\(666\) 2.05586 0.0796631
\(667\) −1.16755 −0.0452077
\(668\) 48.7787 1.88730
\(669\) 9.81800 0.379586
\(670\) 53.9612 2.08470
\(671\) −9.95776 −0.384415
\(672\) −4.24611 −0.163797
\(673\) 5.06520 0.195249 0.0976246 0.995223i \(-0.468876\pi\)
0.0976246 + 0.995223i \(0.468876\pi\)
\(674\) 14.0072 0.539535
\(675\) −1.25738 −0.0483967
\(676\) 48.6221 1.87008
\(677\) −3.06697 −0.117873 −0.0589365 0.998262i \(-0.518771\pi\)
−0.0589365 + 0.998262i \(0.518771\pi\)
\(678\) −42.9270 −1.64860
\(679\) 10.9373 0.419735
\(680\) 14.6740 0.562721
\(681\) 4.59167 0.175953
\(682\) −11.5735 −0.443173
\(683\) −1.58966 −0.0608267 −0.0304133 0.999537i \(-0.509682\pi\)
−0.0304133 + 0.999537i \(0.509682\pi\)
\(684\) −2.67874 −0.102424
\(685\) 23.4212 0.894879
\(686\) −49.1438 −1.87632
\(687\) 5.71914 0.218199
\(688\) −7.89368 −0.300944
\(689\) −41.5813 −1.58412
\(690\) 1.74784 0.0665392
\(691\) 24.3903 0.927851 0.463925 0.885874i \(-0.346441\pi\)
0.463925 + 0.885874i \(0.346441\pi\)
\(692\) 0.871515 0.0331300
\(693\) −7.71691 −0.293141
\(694\) −30.2040 −1.14653
\(695\) −29.5148 −1.11956
\(696\) −40.8664 −1.54904
\(697\) 13.3055 0.503981
\(698\) −66.5644 −2.51950
\(699\) 3.36025 0.127096
\(700\) 2.17584 0.0822392
\(701\) 28.0625 1.05991 0.529953 0.848027i \(-0.322210\pi\)
0.529953 + 0.848027i \(0.322210\pi\)
\(702\) 69.5338 2.62438
\(703\) 0.761923 0.0287365
\(704\) 24.9226 0.939306
\(705\) 21.2960 0.802053
\(706\) −63.5914 −2.39329
\(707\) 14.5078 0.545623
\(708\) 74.2842 2.79177
\(709\) 11.8122 0.443617 0.221808 0.975090i \(-0.428804\pi\)
0.221808 + 0.975090i \(0.428804\pi\)
\(710\) 12.6059 0.473093
\(711\) 6.33597 0.237618
\(712\) 37.1134 1.39088
\(713\) −0.266369 −0.00997561
\(714\) 11.0305 0.412805
\(715\) 42.0723 1.57342
\(716\) −3.64227 −0.136118
\(717\) −33.8914 −1.26570
\(718\) −64.1481 −2.39399
\(719\) 31.8279 1.18698 0.593490 0.804842i \(-0.297750\pi\)
0.593490 + 0.804842i \(0.297750\pi\)
\(720\) −8.71047 −0.324620
\(721\) 18.7562 0.698519
\(722\) 45.5273 1.69435
\(723\) −12.2075 −0.454002
\(724\) −98.5005 −3.66074
\(725\) 1.18199 0.0438981
\(726\) 14.3140 0.531243
\(727\) 40.9919 1.52030 0.760152 0.649745i \(-0.225124\pi\)
0.760152 + 0.649745i \(0.225124\pi\)
\(728\) −61.9098 −2.29453
\(729\) 29.7267 1.10099
\(730\) 34.8256 1.28895
\(731\) 2.13578 0.0789947
\(732\) −15.5908 −0.576253
\(733\) −41.8046 −1.54409 −0.772045 0.635568i \(-0.780766\pi\)
−0.772045 + 0.635568i \(0.780766\pi\)
\(734\) 64.5523 2.38267
\(735\) 4.42921 0.163374
\(736\) −0.268310 −0.00989005
\(737\) 38.5738 1.42088
\(738\) −21.6498 −0.796940
\(739\) 25.3594 0.932859 0.466430 0.884558i \(-0.345540\pi\)
0.466430 + 0.884558i \(0.345540\pi\)
\(740\) 8.88551 0.326638
\(741\) 5.64849 0.207502
\(742\) 48.9666 1.79762
\(743\) 1.09886 0.0403134 0.0201567 0.999797i \(-0.493583\pi\)
0.0201567 + 0.999797i \(0.493583\pi\)
\(744\) −9.32344 −0.341814
\(745\) −50.5960 −1.85369
\(746\) −36.1597 −1.32390
\(747\) −4.65517 −0.170324
\(748\) 20.3871 0.745427
\(749\) −11.2202 −0.409978
\(750\) −41.4822 −1.51472
\(751\) −33.7558 −1.23177 −0.615884 0.787837i \(-0.711201\pi\)
−0.615884 + 0.787837i \(0.711201\pi\)
\(752\) −31.3877 −1.14459
\(753\) 12.1733 0.443618
\(754\) −65.3647 −2.38044
\(755\) 31.3836 1.14216
\(756\) −55.1227 −2.00479
\(757\) 20.6483 0.750475 0.375237 0.926929i \(-0.377561\pi\)
0.375237 + 0.926929i \(0.377561\pi\)
\(758\) 26.4826 0.961890
\(759\) 1.24943 0.0453515
\(760\) −8.84886 −0.320982
\(761\) 8.45805 0.306604 0.153302 0.988179i \(-0.451009\pi\)
0.153302 + 0.988179i \(0.451009\pi\)
\(762\) 61.4269 2.22526
\(763\) −21.6888 −0.785189
\(764\) 50.5373 1.82837
\(765\) 2.35678 0.0852095
\(766\) −89.6622 −3.23963
\(767\) 61.1330 2.20738
\(768\) 47.8825 1.72781
\(769\) −43.3691 −1.56393 −0.781966 0.623321i \(-0.785783\pi\)
−0.781966 + 0.623321i \(0.785783\pi\)
\(770\) −49.5448 −1.78547
\(771\) 39.2407 1.41322
\(772\) 31.4078 1.13039
\(773\) −31.1542 −1.12054 −0.560269 0.828310i \(-0.689302\pi\)
−0.560269 + 0.828310i \(0.689302\pi\)
\(774\) −3.47520 −0.124913
\(775\) 0.269665 0.00968664
\(776\) 24.1907 0.868396
\(777\) 3.43662 0.123288
\(778\) 1.65313 0.0592676
\(779\) −8.02362 −0.287476
\(780\) 65.8725 2.35861
\(781\) 9.01127 0.322449
\(782\) 0.697013 0.0249251
\(783\) −29.9445 −1.07013
\(784\) −6.52811 −0.233147
\(785\) −3.73978 −0.133478
\(786\) 37.0966 1.32319
\(787\) 22.2358 0.792621 0.396311 0.918116i \(-0.370290\pi\)
0.396311 + 0.918116i \(0.370290\pi\)
\(788\) −22.7789 −0.811463
\(789\) −38.8744 −1.38397
\(790\) 40.6788 1.44729
\(791\) 28.0056 0.995764
\(792\) −17.0680 −0.606484
\(793\) −12.8306 −0.455629
\(794\) −11.6499 −0.413440
\(795\) −26.8070 −0.950745
\(796\) −0.934246 −0.0331135
\(797\) −10.9863 −0.389153 −0.194577 0.980887i \(-0.562333\pi\)
−0.194577 + 0.980887i \(0.562333\pi\)
\(798\) −6.65172 −0.235468
\(799\) 8.49251 0.300444
\(800\) 0.271630 0.00960356
\(801\) 5.96076 0.210613
\(802\) 32.3132 1.14102
\(803\) 24.8948 0.878519
\(804\) 60.3948 2.12996
\(805\) −1.14029 −0.0401901
\(806\) −14.9126 −0.525273
\(807\) −1.98502 −0.0698762
\(808\) 32.0878 1.12885
\(809\) 26.9226 0.946548 0.473274 0.880915i \(-0.343072\pi\)
0.473274 + 0.880915i \(0.343072\pi\)
\(810\) 31.1670 1.09510
\(811\) −6.56174 −0.230414 −0.115207 0.993342i \(-0.536753\pi\)
−0.115207 + 0.993342i \(0.536753\pi\)
\(812\) 51.8177 1.81845
\(813\) 11.7817 0.413202
\(814\) 9.43539 0.330710
\(815\) −32.3005 −1.13144
\(816\) 8.90027 0.311572
\(817\) −1.28794 −0.0450594
\(818\) 25.8858 0.905074
\(819\) −9.94329 −0.347447
\(820\) −93.5711 −3.26765
\(821\) −18.6500 −0.650891 −0.325445 0.945561i \(-0.605514\pi\)
−0.325445 + 0.945561i \(0.605514\pi\)
\(822\) 38.9399 1.35818
\(823\) 44.5775 1.55387 0.776936 0.629579i \(-0.216773\pi\)
0.776936 + 0.629579i \(0.216773\pi\)
\(824\) 41.4843 1.44518
\(825\) −1.26489 −0.0440378
\(826\) −71.9908 −2.50488
\(827\) 18.6174 0.647390 0.323695 0.946161i \(-0.395075\pi\)
0.323695 + 0.946161i \(0.395075\pi\)
\(828\) −0.763479 −0.0265327
\(829\) −15.8680 −0.551117 −0.275558 0.961284i \(-0.588863\pi\)
−0.275558 + 0.961284i \(0.588863\pi\)
\(830\) −29.8876 −1.03741
\(831\) −5.12321 −0.177722
\(832\) 32.1130 1.11332
\(833\) 1.76630 0.0611986
\(834\) −49.0710 −1.69919
\(835\) 25.8797 0.895603
\(836\) −12.2941 −0.425199
\(837\) −6.83167 −0.236137
\(838\) 28.1005 0.970717
\(839\) −9.41901 −0.325180 −0.162590 0.986694i \(-0.551985\pi\)
−0.162590 + 0.986694i \(0.551985\pi\)
\(840\) −39.9124 −1.37711
\(841\) −0.850872 −0.0293404
\(842\) 49.5647 1.70811
\(843\) −9.46840 −0.326109
\(844\) −79.5388 −2.73784
\(845\) 25.7966 0.887428
\(846\) −13.8185 −0.475088
\(847\) −9.33846 −0.320873
\(848\) 39.5102 1.35679
\(849\) 23.0197 0.790034
\(850\) −0.705636 −0.0242031
\(851\) 0.217159 0.00744412
\(852\) 14.1089 0.483363
\(853\) −54.3194 −1.85986 −0.929931 0.367734i \(-0.880134\pi\)
−0.929931 + 0.367734i \(0.880134\pi\)
\(854\) 15.1095 0.517036
\(855\) −1.42121 −0.0486044
\(856\) −24.8164 −0.848209
\(857\) 31.2793 1.06848 0.534240 0.845333i \(-0.320598\pi\)
0.534240 + 0.845333i \(0.320598\pi\)
\(858\) 69.9490 2.38802
\(859\) 3.11068 0.106135 0.0530674 0.998591i \(-0.483100\pi\)
0.0530674 + 0.998591i \(0.483100\pi\)
\(860\) −15.0199 −0.512175
\(861\) −36.1902 −1.23336
\(862\) 47.8983 1.63142
\(863\) 26.2309 0.892911 0.446456 0.894806i \(-0.352686\pi\)
0.446456 + 0.894806i \(0.352686\pi\)
\(864\) −6.88145 −0.234112
\(865\) 0.462384 0.0157215
\(866\) 40.5688 1.37858
\(867\) 22.5642 0.766319
\(868\) 11.8219 0.401262
\(869\) 29.0790 0.986436
\(870\) −42.1398 −1.42867
\(871\) 49.7026 1.68411
\(872\) −47.9706 −1.62449
\(873\) 3.88525 0.131496
\(874\) −0.420320 −0.0142175
\(875\) 27.0630 0.914897
\(876\) 38.9777 1.31693
\(877\) −35.0992 −1.18522 −0.592608 0.805491i \(-0.701901\pi\)
−0.592608 + 0.805491i \(0.701901\pi\)
\(878\) −23.6694 −0.798803
\(879\) 22.5910 0.761977
\(880\) −39.9767 −1.34761
\(881\) −20.8340 −0.701914 −0.350957 0.936392i \(-0.614144\pi\)
−0.350957 + 0.936392i \(0.614144\pi\)
\(882\) −2.87400 −0.0967728
\(883\) 2.16972 0.0730168 0.0365084 0.999333i \(-0.488376\pi\)
0.0365084 + 0.999333i \(0.488376\pi\)
\(884\) 26.2689 0.883520
\(885\) 39.4116 1.32481
\(886\) −26.6921 −0.896740
\(887\) −15.2215 −0.511090 −0.255545 0.966797i \(-0.582255\pi\)
−0.255545 + 0.966797i \(0.582255\pi\)
\(888\) 7.60099 0.255072
\(889\) −40.0749 −1.34407
\(890\) 38.2698 1.28281
\(891\) 22.2795 0.746392
\(892\) −27.5342 −0.921914
\(893\) −5.12125 −0.171376
\(894\) −84.1203 −2.81340
\(895\) −1.93241 −0.0645935
\(896\) −43.5977 −1.45650
\(897\) 1.60990 0.0537531
\(898\) −54.1605 −1.80736
\(899\) 6.42206 0.214188
\(900\) 0.772924 0.0257641
\(901\) −10.6902 −0.356142
\(902\) −99.3618 −3.30839
\(903\) −5.80921 −0.193318
\(904\) 61.9417 2.06015
\(905\) −52.2597 −1.73717
\(906\) 52.1780 1.73350
\(907\) 16.7529 0.556271 0.278136 0.960542i \(-0.410284\pi\)
0.278136 + 0.960542i \(0.410284\pi\)
\(908\) −12.8772 −0.427344
\(909\) 5.15360 0.170934
\(910\) −63.8388 −2.11624
\(911\) −23.1253 −0.766175 −0.383088 0.923712i \(-0.625139\pi\)
−0.383088 + 0.923712i \(0.625139\pi\)
\(912\) −5.36714 −0.177724
\(913\) −21.3649 −0.707076
\(914\) −17.6543 −0.583954
\(915\) −8.27175 −0.273456
\(916\) −16.0391 −0.529948
\(917\) −24.2018 −0.799215
\(918\) 17.8765 0.590014
\(919\) −44.7453 −1.47601 −0.738006 0.674794i \(-0.764232\pi\)
−0.738006 + 0.674794i \(0.764232\pi\)
\(920\) −2.52206 −0.0831497
\(921\) −39.2474 −1.29325
\(922\) −55.9808 −1.84363
\(923\) 11.6111 0.382184
\(924\) −55.4519 −1.82423
\(925\) −0.219846 −0.00722848
\(926\) −73.2546 −2.40730
\(927\) 6.66277 0.218834
\(928\) 6.46886 0.212351
\(929\) 44.8013 1.46988 0.734941 0.678131i \(-0.237210\pi\)
0.734941 + 0.678131i \(0.237210\pi\)
\(930\) −9.61395 −0.315254
\(931\) −1.06513 −0.0349083
\(932\) −9.42370 −0.308684
\(933\) 19.6088 0.641964
\(934\) 80.0503 2.61932
\(935\) 10.8164 0.353735
\(936\) −21.9922 −0.718837
\(937\) 8.42958 0.275382 0.137691 0.990475i \(-0.456032\pi\)
0.137691 + 0.990475i \(0.456032\pi\)
\(938\) −58.5303 −1.91108
\(939\) 16.3451 0.533401
\(940\) −59.7238 −1.94798
\(941\) 19.8390 0.646734 0.323367 0.946274i \(-0.395185\pi\)
0.323367 + 0.946274i \(0.395185\pi\)
\(942\) −6.21771 −0.202584
\(943\) −2.28685 −0.0744701
\(944\) −58.0879 −1.89060
\(945\) −29.2455 −0.951356
\(946\) −15.9494 −0.518561
\(947\) 8.11400 0.263669 0.131835 0.991272i \(-0.457913\pi\)
0.131835 + 0.991272i \(0.457913\pi\)
\(948\) 45.5288 1.47871
\(949\) 32.0771 1.04127
\(950\) 0.425520 0.0138057
\(951\) −31.3553 −1.01677
\(952\) −15.9165 −0.515856
\(953\) 34.9071 1.13075 0.565376 0.824833i \(-0.308731\pi\)
0.565376 + 0.824833i \(0.308731\pi\)
\(954\) 17.3944 0.563164
\(955\) 26.8127 0.867638
\(956\) 95.0472 3.07405
\(957\) −30.1233 −0.973749
\(958\) 63.8517 2.06296
\(959\) −25.4044 −0.820350
\(960\) 20.7028 0.668180
\(961\) −29.5348 −0.952737
\(962\) 12.1576 0.391976
\(963\) −3.98575 −0.128439
\(964\) 34.2355 1.10265
\(965\) 16.6635 0.536416
\(966\) −1.89584 −0.0609976
\(967\) −21.3418 −0.686305 −0.343152 0.939280i \(-0.611495\pi\)
−0.343152 + 0.939280i \(0.611495\pi\)
\(968\) −20.6545 −0.663859
\(969\) 1.45218 0.0466507
\(970\) 24.9445 0.800919
\(971\) −5.56708 −0.178656 −0.0893281 0.996002i \(-0.528472\pi\)
−0.0893281 + 0.996002i \(0.528472\pi\)
\(972\) −34.8705 −1.11847
\(973\) 32.0139 1.02632
\(974\) 27.1871 0.871132
\(975\) −1.62982 −0.0521960
\(976\) 12.1915 0.390242
\(977\) 22.9010 0.732668 0.366334 0.930483i \(-0.380613\pi\)
0.366334 + 0.930483i \(0.380613\pi\)
\(978\) −53.7025 −1.71722
\(979\) 27.3569 0.874331
\(980\) −12.4215 −0.396792
\(981\) −7.70452 −0.245986
\(982\) −90.5552 −2.88973
\(983\) −14.2190 −0.453517 −0.226759 0.973951i \(-0.572813\pi\)
−0.226759 + 0.973951i \(0.572813\pi\)
\(984\) −80.0441 −2.55171
\(985\) −12.0854 −0.385072
\(986\) −16.8047 −0.535171
\(987\) −23.0992 −0.735255
\(988\) −15.8410 −0.503969
\(989\) −0.367082 −0.0116725
\(990\) −17.5998 −0.559358
\(991\) 12.0979 0.384301 0.192150 0.981365i \(-0.438454\pi\)
0.192150 + 0.981365i \(0.438454\pi\)
\(992\) 1.47583 0.0468577
\(993\) 21.9141 0.695424
\(994\) −13.6733 −0.433692
\(995\) −0.495667 −0.0157137
\(996\) −33.4510 −1.05993
\(997\) −33.2831 −1.05409 −0.527043 0.849839i \(-0.676699\pi\)
−0.527043 + 0.849839i \(0.676699\pi\)
\(998\) 80.3409 2.54315
\(999\) 5.56956 0.176213
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 6037.2.a.b.1.13 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.13 259 1.1 even 1 trivial