Properties

Label 4003.2.a.c.1.3
Level 4003
Weight 2
Character 4003.1
Self dual yes
Analytic conductor 31.964
Analytic rank 0
Dimension 179
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(0\)
Dimension: \(179\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.71994 q^{2} -1.21777 q^{3} +5.39810 q^{4} +4.02685 q^{5} +3.31228 q^{6} -3.20136 q^{7} -9.24264 q^{8} -1.51703 q^{9} +O(q^{10})\) \(q-2.71994 q^{2} -1.21777 q^{3} +5.39810 q^{4} +4.02685 q^{5} +3.31228 q^{6} -3.20136 q^{7} -9.24264 q^{8} -1.51703 q^{9} -10.9528 q^{10} +0.459418 q^{11} -6.57366 q^{12} +1.82669 q^{13} +8.70752 q^{14} -4.90379 q^{15} +14.3433 q^{16} +6.01389 q^{17} +4.12623 q^{18} +1.50580 q^{19} +21.7373 q^{20} +3.89853 q^{21} -1.24959 q^{22} +9.07350 q^{23} +11.2554 q^{24} +11.2155 q^{25} -4.96850 q^{26} +5.50072 q^{27} -17.2812 q^{28} -8.29688 q^{29} +13.3380 q^{30} +8.55827 q^{31} -20.5276 q^{32} -0.559468 q^{33} -16.3574 q^{34} -12.8914 q^{35} -8.18905 q^{36} +3.64335 q^{37} -4.09570 q^{38} -2.22450 q^{39} -37.2187 q^{40} -3.50776 q^{41} -10.6038 q^{42} +5.04731 q^{43} +2.47998 q^{44} -6.10883 q^{45} -24.6794 q^{46} -3.06088 q^{47} -17.4669 q^{48} +3.24870 q^{49} -30.5055 q^{50} -7.32355 q^{51} +9.86067 q^{52} +8.50203 q^{53} -14.9616 q^{54} +1.85001 q^{55} +29.5890 q^{56} -1.83373 q^{57} +22.5670 q^{58} -7.92925 q^{59} -26.4711 q^{60} +0.108532 q^{61} -23.2780 q^{62} +4.85654 q^{63} +27.1474 q^{64} +7.35581 q^{65} +1.52172 q^{66} -14.4225 q^{67} +32.4635 q^{68} -11.0495 q^{69} +35.0638 q^{70} -7.04938 q^{71} +14.0213 q^{72} +10.0320 q^{73} -9.90970 q^{74} -13.6579 q^{75} +8.12847 q^{76} -1.47076 q^{77} +6.05052 q^{78} -4.30658 q^{79} +57.7581 q^{80} -2.14755 q^{81} +9.54093 q^{82} +9.06454 q^{83} +21.0447 q^{84} +24.2170 q^{85} -13.7284 q^{86} +10.1037 q^{87} -4.24623 q^{88} -3.72076 q^{89} +16.6157 q^{90} -5.84790 q^{91} +48.9796 q^{92} -10.4220 q^{93} +8.32543 q^{94} +6.06364 q^{95} +24.9980 q^{96} +5.86283 q^{97} -8.83628 q^{98} -0.696949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71994 −1.92329 −0.961646 0.274295i \(-0.911555\pi\)
−0.961646 + 0.274295i \(0.911555\pi\)
\(3\) −1.21777 −0.703082 −0.351541 0.936172i \(-0.614342\pi\)
−0.351541 + 0.936172i \(0.614342\pi\)
\(4\) 5.39810 2.69905
\(5\) 4.02685 1.80086 0.900430 0.435000i \(-0.143252\pi\)
0.900430 + 0.435000i \(0.143252\pi\)
\(6\) 3.31228 1.35223
\(7\) −3.20136 −1.21000 −0.605000 0.796226i \(-0.706827\pi\)
−0.605000 + 0.796226i \(0.706827\pi\)
\(8\) −9.24264 −3.26776
\(9\) −1.51703 −0.505675
\(10\) −10.9528 −3.46358
\(11\) 0.459418 0.138520 0.0692599 0.997599i \(-0.477936\pi\)
0.0692599 + 0.997599i \(0.477936\pi\)
\(12\) −6.57366 −1.89765
\(13\) 1.82669 0.506633 0.253317 0.967383i \(-0.418479\pi\)
0.253317 + 0.967383i \(0.418479\pi\)
\(14\) 8.70752 2.32718
\(15\) −4.90379 −1.26615
\(16\) 14.3433 3.58581
\(17\) 6.01389 1.45858 0.729291 0.684204i \(-0.239850\pi\)
0.729291 + 0.684204i \(0.239850\pi\)
\(18\) 4.12623 0.972561
\(19\) 1.50580 0.345455 0.172727 0.984970i \(-0.444742\pi\)
0.172727 + 0.984970i \(0.444742\pi\)
\(20\) 21.7373 4.86061
\(21\) 3.89853 0.850729
\(22\) −1.24959 −0.266414
\(23\) 9.07350 1.89196 0.945978 0.324231i \(-0.105106\pi\)
0.945978 + 0.324231i \(0.105106\pi\)
\(24\) 11.2554 2.29751
\(25\) 11.2155 2.24310
\(26\) −4.96850 −0.974404
\(27\) 5.50072 1.05861
\(28\) −17.2812 −3.26585
\(29\) −8.29688 −1.54069 −0.770346 0.637627i \(-0.779916\pi\)
−0.770346 + 0.637627i \(0.779916\pi\)
\(30\) 13.3380 2.43518
\(31\) 8.55827 1.53711 0.768555 0.639783i \(-0.220976\pi\)
0.768555 + 0.639783i \(0.220976\pi\)
\(32\) −20.5276 −3.62880
\(33\) −0.559468 −0.0973908
\(34\) −16.3574 −2.80528
\(35\) −12.8914 −2.17904
\(36\) −8.18905 −1.36484
\(37\) 3.64335 0.598963 0.299481 0.954102i \(-0.403186\pi\)
0.299481 + 0.954102i \(0.403186\pi\)
\(38\) −4.09570 −0.664410
\(39\) −2.22450 −0.356205
\(40\) −37.2187 −5.88479
\(41\) −3.50776 −0.547821 −0.273910 0.961755i \(-0.588317\pi\)
−0.273910 + 0.961755i \(0.588317\pi\)
\(42\) −10.6038 −1.63620
\(43\) 5.04731 0.769708 0.384854 0.922978i \(-0.374252\pi\)
0.384854 + 0.922978i \(0.374252\pi\)
\(44\) 2.47998 0.373872
\(45\) −6.10883 −0.910651
\(46\) −24.6794 −3.63878
\(47\) −3.06088 −0.446476 −0.223238 0.974764i \(-0.571663\pi\)
−0.223238 + 0.974764i \(0.571663\pi\)
\(48\) −17.4669 −2.52112
\(49\) 3.24870 0.464100
\(50\) −30.5055 −4.31413
\(51\) −7.32355 −1.02550
\(52\) 9.86067 1.36743
\(53\) 8.50203 1.16784 0.583922 0.811810i \(-0.301518\pi\)
0.583922 + 0.811810i \(0.301518\pi\)
\(54\) −14.9616 −2.03602
\(55\) 1.85001 0.249455
\(56\) 29.5890 3.95400
\(57\) −1.83373 −0.242883
\(58\) 22.5670 2.96320
\(59\) −7.92925 −1.03230 −0.516150 0.856498i \(-0.672635\pi\)
−0.516150 + 0.856498i \(0.672635\pi\)
\(60\) −26.4711 −3.41741
\(61\) 0.108532 0.0138961 0.00694803 0.999976i \(-0.497788\pi\)
0.00694803 + 0.999976i \(0.497788\pi\)
\(62\) −23.2780 −2.95631
\(63\) 4.85654 0.611867
\(64\) 27.1474 3.39342
\(65\) 7.35581 0.912376
\(66\) 1.52172 0.187311
\(67\) −14.4225 −1.76199 −0.880996 0.473125i \(-0.843126\pi\)
−0.880996 + 0.473125i \(0.843126\pi\)
\(68\) 32.4635 3.93678
\(69\) −11.0495 −1.33020
\(70\) 35.0638 4.19093
\(71\) −7.04938 −0.836607 −0.418304 0.908307i \(-0.637375\pi\)
−0.418304 + 0.908307i \(0.637375\pi\)
\(72\) 14.0213 1.65243
\(73\) 10.0320 1.17415 0.587076 0.809532i \(-0.300279\pi\)
0.587076 + 0.809532i \(0.300279\pi\)
\(74\) −9.90970 −1.15198
\(75\) −13.6579 −1.57708
\(76\) 8.12847 0.932399
\(77\) −1.47076 −0.167609
\(78\) 6.05052 0.685086
\(79\) −4.30658 −0.484528 −0.242264 0.970210i \(-0.577890\pi\)
−0.242264 + 0.970210i \(0.577890\pi\)
\(80\) 57.7581 6.45755
\(81\) −2.14755 −0.238617
\(82\) 9.54093 1.05362
\(83\) 9.06454 0.994963 0.497481 0.867475i \(-0.334258\pi\)
0.497481 + 0.867475i \(0.334258\pi\)
\(84\) 21.0447 2.29616
\(85\) 24.2170 2.62670
\(86\) −13.7284 −1.48037
\(87\) 10.1037 1.08323
\(88\) −4.24623 −0.452650
\(89\) −3.72076 −0.394400 −0.197200 0.980363i \(-0.563185\pi\)
−0.197200 + 0.980363i \(0.563185\pi\)
\(90\) 16.6157 1.75145
\(91\) −5.84790 −0.613026
\(92\) 48.9796 5.10648
\(93\) −10.4220 −1.08072
\(94\) 8.32543 0.858702
\(95\) 6.06364 0.622116
\(96\) 24.9980 2.55135
\(97\) 5.86283 0.595281 0.297640 0.954678i \(-0.403800\pi\)
0.297640 + 0.954678i \(0.403800\pi\)
\(98\) −8.83628 −0.892599
\(99\) −0.696949 −0.0700460
\(100\) 60.5423 6.05423
\(101\) 5.24825 0.522220 0.261110 0.965309i \(-0.415911\pi\)
0.261110 + 0.965309i \(0.415911\pi\)
\(102\) 19.9197 1.97234
\(103\) −19.0830 −1.88030 −0.940150 0.340761i \(-0.889315\pi\)
−0.940150 + 0.340761i \(0.889315\pi\)
\(104\) −16.8835 −1.65556
\(105\) 15.6988 1.53205
\(106\) −23.1250 −2.24610
\(107\) −16.1210 −1.55847 −0.779237 0.626729i \(-0.784393\pi\)
−0.779237 + 0.626729i \(0.784393\pi\)
\(108\) 29.6934 2.85725
\(109\) −3.82013 −0.365902 −0.182951 0.983122i \(-0.558565\pi\)
−0.182951 + 0.983122i \(0.558565\pi\)
\(110\) −5.03191 −0.479774
\(111\) −4.43678 −0.421120
\(112\) −45.9179 −4.33884
\(113\) 18.6882 1.75804 0.879021 0.476783i \(-0.158197\pi\)
0.879021 + 0.476783i \(0.158197\pi\)
\(114\) 4.98764 0.467135
\(115\) 36.5376 3.40715
\(116\) −44.7873 −4.15840
\(117\) −2.77114 −0.256192
\(118\) 21.5671 1.98541
\(119\) −19.2526 −1.76488
\(120\) 45.3239 4.13749
\(121\) −10.7889 −0.980812
\(122\) −0.295200 −0.0267262
\(123\) 4.27167 0.385163
\(124\) 46.1984 4.14874
\(125\) 25.0288 2.23865
\(126\) −13.2095 −1.17680
\(127\) −19.3664 −1.71849 −0.859245 0.511564i \(-0.829066\pi\)
−0.859245 + 0.511564i \(0.829066\pi\)
\(128\) −32.7842 −2.89774
\(129\) −6.14649 −0.541168
\(130\) −20.0074 −1.75476
\(131\) −3.93661 −0.343943 −0.171972 0.985102i \(-0.555014\pi\)
−0.171972 + 0.985102i \(0.555014\pi\)
\(132\) −3.02006 −0.262863
\(133\) −4.82061 −0.418000
\(134\) 39.2284 3.38882
\(135\) 22.1505 1.90642
\(136\) −55.5841 −4.76630
\(137\) 14.3996 1.23024 0.615121 0.788433i \(-0.289107\pi\)
0.615121 + 0.788433i \(0.289107\pi\)
\(138\) 30.0540 2.55836
\(139\) 0.951210 0.0806806 0.0403403 0.999186i \(-0.487156\pi\)
0.0403403 + 0.999186i \(0.487156\pi\)
\(140\) −69.5889 −5.88134
\(141\) 3.72746 0.313909
\(142\) 19.1739 1.60904
\(143\) 0.839216 0.0701788
\(144\) −21.7591 −1.81326
\(145\) −33.4102 −2.77457
\(146\) −27.2863 −2.25823
\(147\) −3.95618 −0.326300
\(148\) 19.6671 1.61663
\(149\) −3.58224 −0.293469 −0.146734 0.989176i \(-0.546876\pi\)
−0.146734 + 0.989176i \(0.546876\pi\)
\(150\) 37.1488 3.03319
\(151\) 15.2762 1.24316 0.621581 0.783350i \(-0.286490\pi\)
0.621581 + 0.783350i \(0.286490\pi\)
\(152\) −13.9176 −1.12886
\(153\) −9.12322 −0.737569
\(154\) 4.00039 0.322361
\(155\) 34.4628 2.76812
\(156\) −12.0081 −0.961415
\(157\) −0.271830 −0.0216944 −0.0108472 0.999941i \(-0.503453\pi\)
−0.0108472 + 0.999941i \(0.503453\pi\)
\(158\) 11.7137 0.931888
\(159\) −10.3535 −0.821090
\(160\) −82.6615 −6.53496
\(161\) −29.0475 −2.28927
\(162\) 5.84123 0.458930
\(163\) −5.05401 −0.395860 −0.197930 0.980216i \(-0.563422\pi\)
−0.197930 + 0.980216i \(0.563422\pi\)
\(164\) −18.9353 −1.47860
\(165\) −2.25289 −0.175387
\(166\) −24.6551 −1.91360
\(167\) 0.794472 0.0614781 0.0307390 0.999527i \(-0.490214\pi\)
0.0307390 + 0.999527i \(0.490214\pi\)
\(168\) −36.0327 −2.77998
\(169\) −9.66319 −0.743323
\(170\) −65.8689 −5.05191
\(171\) −2.28434 −0.174688
\(172\) 27.2459 2.07748
\(173\) 17.1358 1.30281 0.651406 0.758729i \(-0.274179\pi\)
0.651406 + 0.758729i \(0.274179\pi\)
\(174\) −27.4816 −2.08337
\(175\) −35.9048 −2.71415
\(176\) 6.58955 0.496706
\(177\) 9.65603 0.725792
\(178\) 10.1203 0.758546
\(179\) 16.8766 1.26142 0.630708 0.776020i \(-0.282765\pi\)
0.630708 + 0.776020i \(0.282765\pi\)
\(180\) −32.9761 −2.45789
\(181\) 20.6365 1.53390 0.766950 0.641707i \(-0.221774\pi\)
0.766950 + 0.641707i \(0.221774\pi\)
\(182\) 15.9060 1.17903
\(183\) −0.132167 −0.00977008
\(184\) −83.8631 −6.18247
\(185\) 14.6712 1.07865
\(186\) 28.3474 2.07853
\(187\) 2.76289 0.202042
\(188\) −16.5229 −1.20506
\(189\) −17.6098 −1.28092
\(190\) −16.4927 −1.19651
\(191\) 19.3645 1.40117 0.700584 0.713570i \(-0.252923\pi\)
0.700584 + 0.713570i \(0.252923\pi\)
\(192\) −33.0594 −2.38586
\(193\) −17.5334 −1.26208 −0.631042 0.775748i \(-0.717373\pi\)
−0.631042 + 0.775748i \(0.717373\pi\)
\(194\) −15.9466 −1.14490
\(195\) −8.95772 −0.641476
\(196\) 17.5368 1.25263
\(197\) 18.8470 1.34279 0.671395 0.741099i \(-0.265695\pi\)
0.671395 + 0.741099i \(0.265695\pi\)
\(198\) 1.89566 0.134719
\(199\) 1.63812 0.116124 0.0580618 0.998313i \(-0.481508\pi\)
0.0580618 + 0.998313i \(0.481508\pi\)
\(200\) −103.661 −7.32992
\(201\) 17.5634 1.23882
\(202\) −14.2749 −1.00438
\(203\) 26.5613 1.86424
\(204\) −39.5333 −2.76788
\(205\) −14.1252 −0.986549
\(206\) 51.9046 3.61636
\(207\) −13.7647 −0.956715
\(208\) 26.2007 1.81669
\(209\) 0.691793 0.0478523
\(210\) −42.6998 −2.94657
\(211\) 8.40140 0.578376 0.289188 0.957272i \(-0.406615\pi\)
0.289188 + 0.957272i \(0.406615\pi\)
\(212\) 45.8948 3.15207
\(213\) 8.58455 0.588204
\(214\) 43.8482 2.99740
\(215\) 20.3247 1.38614
\(216\) −50.8411 −3.45930
\(217\) −27.3981 −1.85990
\(218\) 10.3905 0.703737
\(219\) −12.2167 −0.825525
\(220\) 9.98651 0.673291
\(221\) 10.9855 0.738966
\(222\) 12.0678 0.809937
\(223\) −4.66209 −0.312196 −0.156098 0.987742i \(-0.549892\pi\)
−0.156098 + 0.987742i \(0.549892\pi\)
\(224\) 65.7162 4.39085
\(225\) −17.0142 −1.13428
\(226\) −50.8310 −3.38123
\(227\) 12.7598 0.846898 0.423449 0.905920i \(-0.360819\pi\)
0.423449 + 0.905920i \(0.360819\pi\)
\(228\) −9.89864 −0.655553
\(229\) −3.53977 −0.233914 −0.116957 0.993137i \(-0.537314\pi\)
−0.116957 + 0.993137i \(0.537314\pi\)
\(230\) −99.3802 −6.55294
\(231\) 1.79106 0.117843
\(232\) 76.6850 5.03462
\(233\) −25.7783 −1.68880 −0.844398 0.535717i \(-0.820042\pi\)
−0.844398 + 0.535717i \(0.820042\pi\)
\(234\) 7.53735 0.492732
\(235\) −12.3257 −0.804040
\(236\) −42.8028 −2.78623
\(237\) 5.24444 0.340663
\(238\) 52.3660 3.39438
\(239\) 2.01486 0.130330 0.0651651 0.997874i \(-0.479243\pi\)
0.0651651 + 0.997874i \(0.479243\pi\)
\(240\) −70.3363 −4.54019
\(241\) 16.0437 1.03346 0.516732 0.856147i \(-0.327148\pi\)
0.516732 + 0.856147i \(0.327148\pi\)
\(242\) 29.3453 1.88639
\(243\) −13.8869 −0.890846
\(244\) 0.585865 0.0375061
\(245\) 13.0820 0.835779
\(246\) −11.6187 −0.740781
\(247\) 2.75064 0.175019
\(248\) −79.1010 −5.02292
\(249\) −11.0386 −0.699541
\(250\) −68.0770 −4.30557
\(251\) −1.18838 −0.0750098 −0.0375049 0.999296i \(-0.511941\pi\)
−0.0375049 + 0.999296i \(0.511941\pi\)
\(252\) 26.2161 1.65146
\(253\) 4.16853 0.262073
\(254\) 52.6755 3.30516
\(255\) −29.4908 −1.84679
\(256\) 34.8765 2.17978
\(257\) 28.4540 1.77491 0.887455 0.460895i \(-0.152472\pi\)
0.887455 + 0.460895i \(0.152472\pi\)
\(258\) 16.7181 1.04082
\(259\) −11.6637 −0.724745
\(260\) 39.7074 2.46255
\(261\) 12.5866 0.779089
\(262\) 10.7074 0.661503
\(263\) 17.0990 1.05437 0.527186 0.849750i \(-0.323247\pi\)
0.527186 + 0.849750i \(0.323247\pi\)
\(264\) 5.17096 0.318250
\(265\) 34.2364 2.10312
\(266\) 13.1118 0.803936
\(267\) 4.53105 0.277296
\(268\) −77.8542 −4.75570
\(269\) −0.103272 −0.00629660 −0.00314830 0.999995i \(-0.501002\pi\)
−0.00314830 + 0.999995i \(0.501002\pi\)
\(270\) −60.2483 −3.66659
\(271\) −24.5182 −1.48937 −0.744686 0.667415i \(-0.767401\pi\)
−0.744686 + 0.667415i \(0.767401\pi\)
\(272\) 86.2587 5.23020
\(273\) 7.12142 0.431008
\(274\) −39.1661 −2.36611
\(275\) 5.15260 0.310714
\(276\) −59.6461 −3.59028
\(277\) −13.3024 −0.799265 −0.399633 0.916675i \(-0.630862\pi\)
−0.399633 + 0.916675i \(0.630862\pi\)
\(278\) −2.58724 −0.155172
\(279\) −12.9831 −0.777279
\(280\) 119.150 7.12059
\(281\) 0.295352 0.0176192 0.00880962 0.999961i \(-0.497196\pi\)
0.00880962 + 0.999961i \(0.497196\pi\)
\(282\) −10.1385 −0.603738
\(283\) 25.2635 1.50176 0.750878 0.660441i \(-0.229630\pi\)
0.750878 + 0.660441i \(0.229630\pi\)
\(284\) −38.0532 −2.25804
\(285\) −7.38414 −0.437399
\(286\) −2.28262 −0.134974
\(287\) 11.2296 0.662863
\(288\) 31.1409 1.83499
\(289\) 19.1668 1.12746
\(290\) 90.8740 5.33631
\(291\) −7.13961 −0.418531
\(292\) 54.1534 3.16909
\(293\) −11.8178 −0.690404 −0.345202 0.938528i \(-0.612190\pi\)
−0.345202 + 0.938528i \(0.612190\pi\)
\(294\) 10.7606 0.627570
\(295\) −31.9299 −1.85903
\(296\) −33.6741 −1.95727
\(297\) 2.52713 0.146639
\(298\) 9.74350 0.564426
\(299\) 16.5745 0.958528
\(300\) −73.7269 −4.25662
\(301\) −16.1583 −0.931346
\(302\) −41.5505 −2.39096
\(303\) −6.39118 −0.367164
\(304\) 21.5981 1.23874
\(305\) 0.437041 0.0250249
\(306\) 24.8146 1.41856
\(307\) −20.3409 −1.16092 −0.580459 0.814289i \(-0.697127\pi\)
−0.580459 + 0.814289i \(0.697127\pi\)
\(308\) −7.93932 −0.452385
\(309\) 23.2387 1.32201
\(310\) −93.7370 −5.32390
\(311\) −13.8424 −0.784933 −0.392466 0.919766i \(-0.628378\pi\)
−0.392466 + 0.919766i \(0.628378\pi\)
\(312\) 20.5602 1.16399
\(313\) 31.0897 1.75729 0.878646 0.477474i \(-0.158448\pi\)
0.878646 + 0.477474i \(0.158448\pi\)
\(314\) 0.739362 0.0417246
\(315\) 19.5566 1.10189
\(316\) −23.2473 −1.30776
\(317\) 13.1335 0.737652 0.368826 0.929498i \(-0.379760\pi\)
0.368826 + 0.929498i \(0.379760\pi\)
\(318\) 28.1611 1.57919
\(319\) −3.81174 −0.213416
\(320\) 109.318 6.11108
\(321\) 19.6317 1.09574
\(322\) 79.0077 4.40292
\(323\) 9.05572 0.503874
\(324\) −11.5927 −0.644039
\(325\) 20.4873 1.13643
\(326\) 13.7466 0.761355
\(327\) 4.65206 0.257259
\(328\) 32.4210 1.79015
\(329\) 9.79898 0.540235
\(330\) 6.12774 0.337321
\(331\) −23.1963 −1.27498 −0.637492 0.770457i \(-0.720028\pi\)
−0.637492 + 0.770457i \(0.720028\pi\)
\(332\) 48.9313 2.68545
\(333\) −5.52705 −0.302881
\(334\) −2.16092 −0.118240
\(335\) −58.0773 −3.17310
\(336\) 55.9177 3.05056
\(337\) 29.8241 1.62462 0.812312 0.583224i \(-0.198209\pi\)
0.812312 + 0.583224i \(0.198209\pi\)
\(338\) 26.2833 1.42963
\(339\) −22.7581 −1.23605
\(340\) 130.726 7.08960
\(341\) 3.93182 0.212920
\(342\) 6.21328 0.335976
\(343\) 12.0093 0.648439
\(344\) −46.6505 −2.51522
\(345\) −44.4945 −2.39551
\(346\) −46.6085 −2.50569
\(347\) 0.594697 0.0319250 0.0159625 0.999873i \(-0.494919\pi\)
0.0159625 + 0.999873i \(0.494919\pi\)
\(348\) 54.5409 2.92370
\(349\) 5.22964 0.279936 0.139968 0.990156i \(-0.455300\pi\)
0.139968 + 0.990156i \(0.455300\pi\)
\(350\) 97.6591 5.22010
\(351\) 10.0481 0.536329
\(352\) −9.43075 −0.502661
\(353\) −2.38060 −0.126706 −0.0633532 0.997991i \(-0.520179\pi\)
−0.0633532 + 0.997991i \(0.520179\pi\)
\(354\) −26.2639 −1.39591
\(355\) −28.3868 −1.50661
\(356\) −20.0850 −1.06450
\(357\) 23.4453 1.24086
\(358\) −45.9034 −2.42607
\(359\) −34.2529 −1.80780 −0.903899 0.427747i \(-0.859308\pi\)
−0.903899 + 0.427747i \(0.859308\pi\)
\(360\) 56.4617 2.97579
\(361\) −16.7326 −0.880661
\(362\) −56.1301 −2.95013
\(363\) 13.1385 0.689592
\(364\) −31.5675 −1.65459
\(365\) 40.3971 2.11448
\(366\) 0.359487 0.0187907
\(367\) −13.3305 −0.695845 −0.347923 0.937523i \(-0.613113\pi\)
−0.347923 + 0.937523i \(0.613113\pi\)
\(368\) 130.144 6.78420
\(369\) 5.32137 0.277019
\(370\) −39.9049 −2.07455
\(371\) −27.2180 −1.41309
\(372\) −56.2592 −2.91690
\(373\) 17.9688 0.930387 0.465194 0.885209i \(-0.345985\pi\)
0.465194 + 0.885209i \(0.345985\pi\)
\(374\) −7.51490 −0.388586
\(375\) −30.4795 −1.57395
\(376\) 28.2906 1.45898
\(377\) −15.1558 −0.780566
\(378\) 47.8976 2.46359
\(379\) 12.2948 0.631543 0.315772 0.948835i \(-0.397737\pi\)
0.315772 + 0.948835i \(0.397737\pi\)
\(380\) 32.7321 1.67912
\(381\) 23.5839 1.20824
\(382\) −52.6704 −2.69485
\(383\) 6.05097 0.309190 0.154595 0.987978i \(-0.450593\pi\)
0.154595 + 0.987978i \(0.450593\pi\)
\(384\) 39.9238 2.03735
\(385\) −5.92253 −0.301840
\(386\) 47.6900 2.42736
\(387\) −7.65690 −0.389222
\(388\) 31.6481 1.60669
\(389\) 14.6753 0.744068 0.372034 0.928219i \(-0.378660\pi\)
0.372034 + 0.928219i \(0.378660\pi\)
\(390\) 24.3645 1.23374
\(391\) 54.5670 2.75957
\(392\) −30.0265 −1.51657
\(393\) 4.79390 0.241820
\(394\) −51.2627 −2.58258
\(395\) −17.3419 −0.872567
\(396\) −3.76220 −0.189058
\(397\) 22.1773 1.11305 0.556523 0.830832i \(-0.312135\pi\)
0.556523 + 0.830832i \(0.312135\pi\)
\(398\) −4.45560 −0.223339
\(399\) 5.87042 0.293889
\(400\) 160.867 8.04334
\(401\) 29.2780 1.46208 0.731038 0.682337i \(-0.239036\pi\)
0.731038 + 0.682337i \(0.239036\pi\)
\(402\) −47.7714 −2.38262
\(403\) 15.6333 0.778752
\(404\) 28.3305 1.40950
\(405\) −8.64787 −0.429716
\(406\) −72.2452 −3.58547
\(407\) 1.67382 0.0829682
\(408\) 67.6889 3.35110
\(409\) −36.3638 −1.79807 −0.899037 0.437872i \(-0.855732\pi\)
−0.899037 + 0.437872i \(0.855732\pi\)
\(410\) 38.4198 1.89742
\(411\) −17.5355 −0.864961
\(412\) −103.012 −5.07502
\(413\) 25.3844 1.24908
\(414\) 37.4393 1.84004
\(415\) 36.5015 1.79179
\(416\) −37.4976 −1.83847
\(417\) −1.15836 −0.0567251
\(418\) −1.88164 −0.0920339
\(419\) 11.3644 0.555185 0.277593 0.960699i \(-0.410463\pi\)
0.277593 + 0.960699i \(0.410463\pi\)
\(420\) 84.7436 4.13506
\(421\) −2.66252 −0.129763 −0.0648816 0.997893i \(-0.520667\pi\)
−0.0648816 + 0.997893i \(0.520667\pi\)
\(422\) −22.8513 −1.11239
\(423\) 4.64344 0.225772
\(424\) −78.5811 −3.81624
\(425\) 67.4487 3.27174
\(426\) −23.3495 −1.13129
\(427\) −0.347449 −0.0168142
\(428\) −87.0226 −4.20640
\(429\) −1.02198 −0.0493414
\(430\) −55.2822 −2.66594
\(431\) 0.496165 0.0238994 0.0119497 0.999929i \(-0.496196\pi\)
0.0119497 + 0.999929i \(0.496196\pi\)
\(432\) 78.8982 3.79599
\(433\) −3.36511 −0.161717 −0.0808585 0.996726i \(-0.525766\pi\)
−0.0808585 + 0.996726i \(0.525766\pi\)
\(434\) 74.5213 3.57714
\(435\) 40.6861 1.95075
\(436\) −20.6214 −0.987588
\(437\) 13.6629 0.653585
\(438\) 33.2286 1.58772
\(439\) 17.1172 0.816960 0.408480 0.912767i \(-0.366059\pi\)
0.408480 + 0.912767i \(0.366059\pi\)
\(440\) −17.0989 −0.815160
\(441\) −4.92836 −0.234684
\(442\) −29.8800 −1.42125
\(443\) 33.7131 1.60176 0.800878 0.598828i \(-0.204366\pi\)
0.800878 + 0.598828i \(0.204366\pi\)
\(444\) −23.9501 −1.13662
\(445\) −14.9829 −0.710259
\(446\) 12.6806 0.600445
\(447\) 4.36236 0.206333
\(448\) −86.9086 −4.10604
\(449\) 18.2605 0.861767 0.430884 0.902407i \(-0.358202\pi\)
0.430884 + 0.902407i \(0.358202\pi\)
\(450\) 46.2777 2.18155
\(451\) −1.61153 −0.0758840
\(452\) 100.881 4.74504
\(453\) −18.6030 −0.874046
\(454\) −34.7060 −1.62883
\(455\) −23.5486 −1.10398
\(456\) 16.9485 0.793685
\(457\) −20.0636 −0.938538 −0.469269 0.883055i \(-0.655483\pi\)
−0.469269 + 0.883055i \(0.655483\pi\)
\(458\) 9.62797 0.449885
\(459\) 33.0807 1.54407
\(460\) 197.233 9.19606
\(461\) 14.4955 0.675125 0.337562 0.941303i \(-0.390398\pi\)
0.337562 + 0.941303i \(0.390398\pi\)
\(462\) −4.87157 −0.226646
\(463\) −29.4419 −1.36828 −0.684140 0.729351i \(-0.739822\pi\)
−0.684140 + 0.729351i \(0.739822\pi\)
\(464\) −119.004 −5.52463
\(465\) −41.9680 −1.94622
\(466\) 70.1157 3.24805
\(467\) −41.3917 −1.91538 −0.957691 0.287800i \(-0.907076\pi\)
−0.957691 + 0.287800i \(0.907076\pi\)
\(468\) −14.9589 −0.691475
\(469\) 46.1717 2.13201
\(470\) 33.5252 1.54640
\(471\) 0.331027 0.0152529
\(472\) 73.2871 3.37331
\(473\) 2.31883 0.106620
\(474\) −14.2646 −0.655194
\(475\) 16.8883 0.774889
\(476\) −103.927 −4.76351
\(477\) −12.8978 −0.590549
\(478\) −5.48030 −0.250663
\(479\) 20.1633 0.921286 0.460643 0.887586i \(-0.347619\pi\)
0.460643 + 0.887586i \(0.347619\pi\)
\(480\) 100.663 4.59462
\(481\) 6.65528 0.303455
\(482\) −43.6379 −1.98765
\(483\) 35.3733 1.60954
\(484\) −58.2397 −2.64726
\(485\) 23.6087 1.07202
\(486\) 37.7716 1.71336
\(487\) −10.7142 −0.485509 −0.242754 0.970088i \(-0.578051\pi\)
−0.242754 + 0.970088i \(0.578051\pi\)
\(488\) −1.00312 −0.0454091
\(489\) 6.15464 0.278322
\(490\) −35.5823 −1.60745
\(491\) −1.10787 −0.0499975 −0.0249988 0.999687i \(-0.507958\pi\)
−0.0249988 + 0.999687i \(0.507958\pi\)
\(492\) 23.0589 1.03957
\(493\) −49.8965 −2.24722
\(494\) −7.48158 −0.336612
\(495\) −2.80651 −0.126143
\(496\) 122.753 5.51179
\(497\) 22.5676 1.01229
\(498\) 30.0243 1.34542
\(499\) −10.4445 −0.467562 −0.233781 0.972289i \(-0.575110\pi\)
−0.233781 + 0.972289i \(0.575110\pi\)
\(500\) 135.108 6.04222
\(501\) −0.967488 −0.0432242
\(502\) 3.23232 0.144266
\(503\) −1.51162 −0.0674000 −0.0337000 0.999432i \(-0.510729\pi\)
−0.0337000 + 0.999432i \(0.510729\pi\)
\(504\) −44.8873 −1.99944
\(505\) 21.1339 0.940446
\(506\) −11.3382 −0.504043
\(507\) 11.7676 0.522617
\(508\) −104.542 −4.63829
\(509\) 17.1997 0.762363 0.381181 0.924500i \(-0.375517\pi\)
0.381181 + 0.924500i \(0.375517\pi\)
\(510\) 80.2134 3.55191
\(511\) −32.1159 −1.42072
\(512\) −29.2936 −1.29461
\(513\) 8.28299 0.365703
\(514\) −77.3932 −3.41367
\(515\) −76.8441 −3.38616
\(516\) −33.1793 −1.46064
\(517\) −1.40622 −0.0618457
\(518\) 31.7245 1.39390
\(519\) −20.8676 −0.915985
\(520\) −67.9871 −2.98143
\(521\) 17.2772 0.756928 0.378464 0.925616i \(-0.376452\pi\)
0.378464 + 0.925616i \(0.376452\pi\)
\(522\) −34.2348 −1.49842
\(523\) 13.7550 0.601463 0.300732 0.953709i \(-0.402769\pi\)
0.300732 + 0.953709i \(0.402769\pi\)
\(524\) −21.2502 −0.928319
\(525\) 43.7240 1.90827
\(526\) −46.5084 −2.02786
\(527\) 51.4685 2.24200
\(528\) −8.02459 −0.349225
\(529\) 59.3284 2.57950
\(530\) −93.1210 −4.04492
\(531\) 12.0289 0.522009
\(532\) −26.0221 −1.12820
\(533\) −6.40761 −0.277544
\(534\) −12.3242 −0.533320
\(535\) −64.9167 −2.80659
\(536\) 133.302 5.75777
\(537\) −20.5519 −0.886879
\(538\) 0.280894 0.0121102
\(539\) 1.49251 0.0642870
\(540\) 119.571 5.14551
\(541\) 13.9719 0.600697 0.300348 0.953830i \(-0.402897\pi\)
0.300348 + 0.953830i \(0.402897\pi\)
\(542\) 66.6881 2.86450
\(543\) −25.1306 −1.07846
\(544\) −123.451 −5.29290
\(545\) −15.3831 −0.658939
\(546\) −19.3699 −0.828954
\(547\) 0.959405 0.0410212 0.0205106 0.999790i \(-0.493471\pi\)
0.0205106 + 0.999790i \(0.493471\pi\)
\(548\) 77.7305 3.32048
\(549\) −0.164645 −0.00702690
\(550\) −14.0148 −0.597593
\(551\) −12.4935 −0.532239
\(552\) 102.126 4.34678
\(553\) 13.7869 0.586279
\(554\) 36.1819 1.53722
\(555\) −17.8662 −0.758379
\(556\) 5.13472 0.217761
\(557\) −14.7282 −0.624052 −0.312026 0.950073i \(-0.601008\pi\)
−0.312026 + 0.950073i \(0.601008\pi\)
\(558\) 35.3134 1.49493
\(559\) 9.21989 0.389960
\(560\) −184.904 −7.81364
\(561\) −3.36457 −0.142052
\(562\) −0.803341 −0.0338869
\(563\) −25.3234 −1.06725 −0.533627 0.845720i \(-0.679171\pi\)
−0.533627 + 0.845720i \(0.679171\pi\)
\(564\) 20.1212 0.847256
\(565\) 75.2547 3.16599
\(566\) −68.7152 −2.88831
\(567\) 6.87509 0.288727
\(568\) 65.1548 2.73384
\(569\) −18.8440 −0.789980 −0.394990 0.918685i \(-0.629252\pi\)
−0.394990 + 0.918685i \(0.629252\pi\)
\(570\) 20.0844 0.841245
\(571\) 34.6258 1.44904 0.724522 0.689251i \(-0.242060\pi\)
0.724522 + 0.689251i \(0.242060\pi\)
\(572\) 4.53017 0.189416
\(573\) −23.5816 −0.985136
\(574\) −30.5439 −1.27488
\(575\) 101.764 4.24384
\(576\) −41.1833 −1.71597
\(577\) 42.9720 1.78895 0.894475 0.447119i \(-0.147550\pi\)
0.894475 + 0.447119i \(0.147550\pi\)
\(578\) −52.1327 −2.16843
\(579\) 21.3518 0.887350
\(580\) −180.352 −7.48870
\(581\) −29.0189 −1.20390
\(582\) 19.4193 0.804957
\(583\) 3.90599 0.161769
\(584\) −92.7217 −3.83685
\(585\) −11.1590 −0.461366
\(586\) 32.1438 1.32785
\(587\) −1.73862 −0.0717603 −0.0358802 0.999356i \(-0.511423\pi\)
−0.0358802 + 0.999356i \(0.511423\pi\)
\(588\) −21.3558 −0.880700
\(589\) 12.8871 0.531002
\(590\) 86.8474 3.57545
\(591\) −22.9513 −0.944092
\(592\) 52.2575 2.14777
\(593\) −28.6600 −1.17693 −0.588463 0.808524i \(-0.700267\pi\)
−0.588463 + 0.808524i \(0.700267\pi\)
\(594\) −6.87365 −0.282029
\(595\) −77.5273 −3.17831
\(596\) −19.3373 −0.792086
\(597\) −1.99486 −0.0816444
\(598\) −45.0817 −1.84353
\(599\) −2.77020 −0.113187 −0.0565936 0.998397i \(-0.518024\pi\)
−0.0565936 + 0.998397i \(0.518024\pi\)
\(600\) 126.235 5.15354
\(601\) −21.7401 −0.886798 −0.443399 0.896324i \(-0.646228\pi\)
−0.443399 + 0.896324i \(0.646228\pi\)
\(602\) 43.9496 1.79125
\(603\) 21.8793 0.890995
\(604\) 82.4626 3.35536
\(605\) −43.4454 −1.76631
\(606\) 17.3837 0.706163
\(607\) −2.65821 −0.107893 −0.0539467 0.998544i \(-0.517180\pi\)
−0.0539467 + 0.998544i \(0.517180\pi\)
\(608\) −30.9105 −1.25359
\(609\) −32.3456 −1.31071
\(610\) −1.18873 −0.0481301
\(611\) −5.59129 −0.226199
\(612\) −49.2480 −1.99073
\(613\) −10.0197 −0.404693 −0.202346 0.979314i \(-0.564857\pi\)
−0.202346 + 0.979314i \(0.564857\pi\)
\(614\) 55.3262 2.23278
\(615\) 17.2013 0.693625
\(616\) 13.5937 0.547707
\(617\) 12.6179 0.507979 0.253989 0.967207i \(-0.418257\pi\)
0.253989 + 0.967207i \(0.418257\pi\)
\(618\) −63.2081 −2.54260
\(619\) −16.6475 −0.669118 −0.334559 0.942375i \(-0.608587\pi\)
−0.334559 + 0.942375i \(0.608587\pi\)
\(620\) 186.034 7.47129
\(621\) 49.9108 2.00285
\(622\) 37.6507 1.50965
\(623\) 11.9115 0.477224
\(624\) −31.9066 −1.27729
\(625\) 44.7098 1.78839
\(626\) −84.5622 −3.37978
\(627\) −0.842448 −0.0336441
\(628\) −1.46736 −0.0585542
\(629\) 21.9107 0.873636
\(630\) −53.1927 −2.11925
\(631\) 29.1968 1.16231 0.581153 0.813795i \(-0.302602\pi\)
0.581153 + 0.813795i \(0.302602\pi\)
\(632\) 39.8041 1.58332
\(633\) −10.2310 −0.406646
\(634\) −35.7224 −1.41872
\(635\) −77.9855 −3.09476
\(636\) −55.8895 −2.21616
\(637\) 5.93437 0.235128
\(638\) 10.3677 0.410462
\(639\) 10.6941 0.423052
\(640\) −132.017 −5.21843
\(641\) 11.2945 0.446105 0.223053 0.974806i \(-0.428398\pi\)
0.223053 + 0.974806i \(0.428398\pi\)
\(642\) −53.3972 −2.10742
\(643\) −26.8391 −1.05843 −0.529216 0.848487i \(-0.677514\pi\)
−0.529216 + 0.848487i \(0.677514\pi\)
\(644\) −156.801 −6.17884
\(645\) −24.7510 −0.974568
\(646\) −24.6311 −0.969096
\(647\) 1.17367 0.0461417 0.0230708 0.999734i \(-0.492656\pi\)
0.0230708 + 0.999734i \(0.492656\pi\)
\(648\) 19.8491 0.779745
\(649\) −3.64284 −0.142994
\(650\) −55.7242 −2.18568
\(651\) 33.3647 1.30767
\(652\) −27.2820 −1.06845
\(653\) −23.4210 −0.916533 −0.458267 0.888815i \(-0.651530\pi\)
−0.458267 + 0.888815i \(0.651530\pi\)
\(654\) −12.6533 −0.494785
\(655\) −15.8521 −0.619393
\(656\) −50.3128 −1.96438
\(657\) −15.2187 −0.593739
\(658\) −26.6527 −1.03903
\(659\) −23.6100 −0.919715 −0.459858 0.887993i \(-0.652100\pi\)
−0.459858 + 0.887993i \(0.652100\pi\)
\(660\) −12.1613 −0.473379
\(661\) −3.64224 −0.141667 −0.0708334 0.997488i \(-0.522566\pi\)
−0.0708334 + 0.997488i \(0.522566\pi\)
\(662\) 63.0927 2.45217
\(663\) −13.3779 −0.519554
\(664\) −83.7803 −3.25131
\(665\) −19.4119 −0.752760
\(666\) 15.0333 0.582528
\(667\) −75.2817 −2.91492
\(668\) 4.28864 0.165932
\(669\) 5.67737 0.219500
\(670\) 157.967 6.10279
\(671\) 0.0498614 0.00192488
\(672\) −80.0275 −3.08713
\(673\) −22.8464 −0.880662 −0.440331 0.897835i \(-0.645139\pi\)
−0.440331 + 0.897835i \(0.645139\pi\)
\(674\) −81.1199 −3.12462
\(675\) 61.6933 2.37457
\(676\) −52.1629 −2.00626
\(677\) 5.25133 0.201825 0.100913 0.994895i \(-0.467824\pi\)
0.100913 + 0.994895i \(0.467824\pi\)
\(678\) 61.9007 2.37728
\(679\) −18.7690 −0.720289
\(680\) −223.829 −8.58344
\(681\) −15.5386 −0.595439
\(682\) −10.6943 −0.409508
\(683\) 16.7060 0.639236 0.319618 0.947546i \(-0.396445\pi\)
0.319618 + 0.947546i \(0.396445\pi\)
\(684\) −12.3311 −0.471491
\(685\) 57.9850 2.21549
\(686\) −32.6645 −1.24714
\(687\) 4.31064 0.164461
\(688\) 72.3949 2.76003
\(689\) 15.5306 0.591668
\(690\) 121.023 4.60725
\(691\) 25.5190 0.970789 0.485395 0.874295i \(-0.338676\pi\)
0.485395 + 0.874295i \(0.338676\pi\)
\(692\) 92.5009 3.51635
\(693\) 2.23118 0.0847557
\(694\) −1.61754 −0.0614011
\(695\) 3.83038 0.145294
\(696\) −93.3850 −3.53975
\(697\) −21.0953 −0.799041
\(698\) −14.2243 −0.538399
\(699\) 31.3922 1.18736
\(700\) −193.818 −7.32562
\(701\) −4.63599 −0.175099 −0.0875494 0.996160i \(-0.527904\pi\)
−0.0875494 + 0.996160i \(0.527904\pi\)
\(702\) −27.3303 −1.03152
\(703\) 5.48616 0.206915
\(704\) 12.4720 0.470056
\(705\) 15.0099 0.565306
\(706\) 6.47509 0.243693
\(707\) −16.8015 −0.631886
\(708\) 52.1242 1.95895
\(709\) −45.9417 −1.72538 −0.862688 0.505737i \(-0.831221\pi\)
−0.862688 + 0.505737i \(0.831221\pi\)
\(710\) 77.2104 2.89765
\(711\) 6.53319 0.245014
\(712\) 34.3896 1.28881
\(713\) 77.6535 2.90814
\(714\) −63.7700 −2.38653
\(715\) 3.37939 0.126382
\(716\) 91.1015 3.40462
\(717\) −2.45364 −0.0916329
\(718\) 93.1659 3.47692
\(719\) −1.55512 −0.0579962 −0.0289981 0.999579i \(-0.509232\pi\)
−0.0289981 + 0.999579i \(0.509232\pi\)
\(720\) −87.6205 −3.26542
\(721\) 61.0914 2.27516
\(722\) 45.5116 1.69377
\(723\) −19.5376 −0.726610
\(724\) 111.398 4.14007
\(725\) −93.0535 −3.45592
\(726\) −35.7360 −1.32629
\(727\) 31.4168 1.16518 0.582591 0.812765i \(-0.302039\pi\)
0.582591 + 0.812765i \(0.302039\pi\)
\(728\) 54.0500 2.00323
\(729\) 23.3538 0.864955
\(730\) −109.878 −4.06676
\(731\) 30.3540 1.12268
\(732\) −0.713451 −0.0263699
\(733\) −18.3588 −0.678097 −0.339048 0.940769i \(-0.610105\pi\)
−0.339048 + 0.940769i \(0.610105\pi\)
\(734\) 36.2582 1.33831
\(735\) −15.9309 −0.587621
\(736\) −186.257 −6.86553
\(737\) −6.62597 −0.244071
\(738\) −14.4738 −0.532789
\(739\) −5.76090 −0.211918 −0.105959 0.994370i \(-0.533791\pi\)
−0.105959 + 0.994370i \(0.533791\pi\)
\(740\) 79.1966 2.91132
\(741\) −3.34966 −0.123053
\(742\) 74.0315 2.71778
\(743\) −4.91138 −0.180181 −0.0900905 0.995934i \(-0.528716\pi\)
−0.0900905 + 0.995934i \(0.528716\pi\)
\(744\) 96.3271 3.53152
\(745\) −14.4251 −0.528496
\(746\) −48.8740 −1.78941
\(747\) −13.7511 −0.503128
\(748\) 14.9143 0.545322
\(749\) 51.6090 1.88575
\(750\) 82.9025 3.02717
\(751\) −23.3605 −0.852438 −0.426219 0.904620i \(-0.640155\pi\)
−0.426219 + 0.904620i \(0.640155\pi\)
\(752\) −43.9030 −1.60098
\(753\) 1.44718 0.0527380
\(754\) 41.2231 1.50126
\(755\) 61.5151 2.23876
\(756\) −95.0593 −3.45727
\(757\) −38.4371 −1.39702 −0.698510 0.715600i \(-0.746153\pi\)
−0.698510 + 0.715600i \(0.746153\pi\)
\(758\) −33.4413 −1.21464
\(759\) −5.07633 −0.184259
\(760\) −56.0440 −2.03293
\(761\) 11.0753 0.401479 0.200739 0.979645i \(-0.435666\pi\)
0.200739 + 0.979645i \(0.435666\pi\)
\(762\) −64.1469 −2.32380
\(763\) 12.2296 0.442742
\(764\) 104.532 3.78182
\(765\) −36.7378 −1.32826
\(766\) −16.4583 −0.594662
\(767\) −14.4843 −0.522998
\(768\) −42.4717 −1.53256
\(769\) −13.1433 −0.473960 −0.236980 0.971515i \(-0.576158\pi\)
−0.236980 + 0.971515i \(0.576158\pi\)
\(770\) 16.1090 0.580527
\(771\) −34.6505 −1.24791
\(772\) −94.6472 −3.40643
\(773\) 29.5537 1.06297 0.531487 0.847067i \(-0.321634\pi\)
0.531487 + 0.847067i \(0.321634\pi\)
\(774\) 20.8263 0.748588
\(775\) 95.9852 3.44789
\(776\) −54.1880 −1.94524
\(777\) 14.2037 0.509555
\(778\) −39.9160 −1.43106
\(779\) −5.28200 −0.189247
\(780\) −48.3546 −1.73137
\(781\) −3.23861 −0.115887
\(782\) −148.419 −5.30746
\(783\) −45.6388 −1.63100
\(784\) 46.5969 1.66418
\(785\) −1.09462 −0.0390685
\(786\) −13.0391 −0.465091
\(787\) 3.46853 0.123640 0.0618199 0.998087i \(-0.480310\pi\)
0.0618199 + 0.998087i \(0.480310\pi\)
\(788\) 101.738 3.62426
\(789\) −20.8228 −0.741310
\(790\) 47.1691 1.67820
\(791\) −59.8278 −2.12723
\(792\) 6.44165 0.228894
\(793\) 0.198254 0.00704021
\(794\) −60.3210 −2.14071
\(795\) −41.6921 −1.47867
\(796\) 8.84275 0.313423
\(797\) −18.0708 −0.640100 −0.320050 0.947401i \(-0.603700\pi\)
−0.320050 + 0.947401i \(0.603700\pi\)
\(798\) −15.9672 −0.565233
\(799\) −18.4078 −0.651221
\(800\) −230.227 −8.13976
\(801\) 5.64449 0.199438
\(802\) −79.6346 −2.81200
\(803\) 4.60886 0.162643
\(804\) 94.8088 3.34365
\(805\) −116.970 −4.12265
\(806\) −42.5218 −1.49777
\(807\) 0.125762 0.00442703
\(808\) −48.5076 −1.70649
\(809\) 20.4716 0.719743 0.359872 0.933002i \(-0.382820\pi\)
0.359872 + 0.933002i \(0.382820\pi\)
\(810\) 23.5217 0.826470
\(811\) 10.9773 0.385467 0.192733 0.981251i \(-0.438265\pi\)
0.192733 + 0.981251i \(0.438265\pi\)
\(812\) 143.380 5.03166
\(813\) 29.8576 1.04715
\(814\) −4.55270 −0.159572
\(815\) −20.3517 −0.712889
\(816\) −105.044 −3.67726
\(817\) 7.60025 0.265899
\(818\) 98.9075 3.45822
\(819\) 8.87141 0.309992
\(820\) −76.2494 −2.66274
\(821\) −0.274059 −0.00956472 −0.00478236 0.999989i \(-0.501522\pi\)
−0.00478236 + 0.999989i \(0.501522\pi\)
\(822\) 47.6955 1.66357
\(823\) 24.6248 0.858368 0.429184 0.903217i \(-0.358801\pi\)
0.429184 + 0.903217i \(0.358801\pi\)
\(824\) 176.377 6.14438
\(825\) −6.27470 −0.218457
\(826\) −69.0441 −2.40235
\(827\) 33.1968 1.15437 0.577183 0.816615i \(-0.304152\pi\)
0.577183 + 0.816615i \(0.304152\pi\)
\(828\) −74.3034 −2.58222
\(829\) 35.3098 1.22636 0.613181 0.789943i \(-0.289890\pi\)
0.613181 + 0.789943i \(0.289890\pi\)
\(830\) −99.2821 −3.44613
\(831\) 16.1994 0.561949
\(832\) 49.5900 1.71922
\(833\) 19.5373 0.676927
\(834\) 3.15067 0.109099
\(835\) 3.19922 0.110713
\(836\) 3.73437 0.129156
\(837\) 47.0766 1.62721
\(838\) −30.9104 −1.06778
\(839\) 45.9657 1.58691 0.793456 0.608627i \(-0.208280\pi\)
0.793456 + 0.608627i \(0.208280\pi\)
\(840\) −145.098 −5.00636
\(841\) 39.8382 1.37373
\(842\) 7.24190 0.249572
\(843\) −0.359672 −0.0123878
\(844\) 45.3516 1.56106
\(845\) −38.9122 −1.33862
\(846\) −12.6299 −0.434225
\(847\) 34.5393 1.18678
\(848\) 121.947 4.18767
\(849\) −30.7652 −1.05586
\(850\) −183.457 −6.29251
\(851\) 33.0579 1.13321
\(852\) 46.3402 1.58759
\(853\) 1.41203 0.0483468 0.0241734 0.999708i \(-0.492305\pi\)
0.0241734 + 0.999708i \(0.492305\pi\)
\(854\) 0.945042 0.0323387
\(855\) −9.19869 −0.314589
\(856\) 149.000 5.09273
\(857\) 30.4407 1.03984 0.519918 0.854216i \(-0.325963\pi\)
0.519918 + 0.854216i \(0.325963\pi\)
\(858\) 2.77972 0.0948980
\(859\) −24.4971 −0.835829 −0.417914 0.908486i \(-0.637239\pi\)
−0.417914 + 0.908486i \(0.637239\pi\)
\(860\) 109.715 3.74125
\(861\) −13.6751 −0.466047
\(862\) −1.34954 −0.0459655
\(863\) 29.1106 0.990937 0.495469 0.868626i \(-0.334996\pi\)
0.495469 + 0.868626i \(0.334996\pi\)
\(864\) −112.917 −3.84150
\(865\) 69.0033 2.34618
\(866\) 9.15292 0.311029
\(867\) −23.3409 −0.792697
\(868\) −147.898 −5.01997
\(869\) −1.97852 −0.0671167
\(870\) −110.664 −3.75186
\(871\) −26.3455 −0.892684
\(872\) 35.3081 1.19568
\(873\) −8.89407 −0.301019
\(874\) −37.1623 −1.25703
\(875\) −80.1263 −2.70876
\(876\) −65.9467 −2.22813
\(877\) −41.8799 −1.41418 −0.707092 0.707122i \(-0.749993\pi\)
−0.707092 + 0.707122i \(0.749993\pi\)
\(878\) −46.5579 −1.57125
\(879\) 14.3914 0.485411
\(880\) 26.5351 0.894499
\(881\) −46.5679 −1.56891 −0.784456 0.620185i \(-0.787058\pi\)
−0.784456 + 0.620185i \(0.787058\pi\)
\(882\) 13.4049 0.451365
\(883\) 0.431972 0.0145370 0.00726851 0.999974i \(-0.497686\pi\)
0.00726851 + 0.999974i \(0.497686\pi\)
\(884\) 59.3009 1.99451
\(885\) 38.8834 1.30705
\(886\) −91.6977 −3.08064
\(887\) 41.8907 1.40655 0.703276 0.710917i \(-0.251720\pi\)
0.703276 + 0.710917i \(0.251720\pi\)
\(888\) 41.0075 1.37612
\(889\) 61.9988 2.07937
\(890\) 40.7528 1.36604
\(891\) −0.986626 −0.0330532
\(892\) −25.1664 −0.842633
\(893\) −4.60908 −0.154237
\(894\) −11.8654 −0.396838
\(895\) 67.9594 2.27163
\(896\) 104.954 3.50627
\(897\) −20.1840 −0.673924
\(898\) −49.6676 −1.65743
\(899\) −71.0069 −2.36821
\(900\) −91.8443 −3.06148
\(901\) 51.1302 1.70339
\(902\) 4.38327 0.145947
\(903\) 19.6771 0.654813
\(904\) −172.729 −5.74487
\(905\) 83.1000 2.76234
\(906\) 50.5992 1.68104
\(907\) −4.16495 −0.138295 −0.0691475 0.997606i \(-0.522028\pi\)
−0.0691475 + 0.997606i \(0.522028\pi\)
\(908\) 68.8787 2.28582
\(909\) −7.96173 −0.264074
\(910\) 64.0509 2.12327
\(911\) −36.5179 −1.20989 −0.604945 0.796267i \(-0.706805\pi\)
−0.604945 + 0.796267i \(0.706805\pi\)
\(912\) −26.3016 −0.870934
\(913\) 4.16442 0.137822
\(914\) 54.5720 1.80508
\(915\) −0.532217 −0.0175945
\(916\) −19.1080 −0.631346
\(917\) 12.6025 0.416171
\(918\) −89.9776 −2.96970
\(919\) 39.0154 1.28700 0.643499 0.765447i \(-0.277482\pi\)
0.643499 + 0.765447i \(0.277482\pi\)
\(920\) −337.704 −11.1338
\(921\) 24.7707 0.816221
\(922\) −39.4271 −1.29846
\(923\) −12.8770 −0.423853
\(924\) 9.66830 0.318064
\(925\) 40.8619 1.34353
\(926\) 80.0802 2.63160
\(927\) 28.9493 0.950821
\(928\) 170.315 5.59086
\(929\) −13.4461 −0.441153 −0.220577 0.975370i \(-0.570794\pi\)
−0.220577 + 0.975370i \(0.570794\pi\)
\(930\) 114.151 3.74314
\(931\) 4.89190 0.160325
\(932\) −139.154 −4.55814
\(933\) 16.8570 0.551872
\(934\) 112.583 3.68384
\(935\) 11.1257 0.363850
\(936\) 25.6126 0.837175
\(937\) 29.7410 0.971597 0.485799 0.874071i \(-0.338529\pi\)
0.485799 + 0.874071i \(0.338529\pi\)
\(938\) −125.584 −4.10047
\(939\) −37.8602 −1.23552
\(940\) −66.5353 −2.17014
\(941\) 26.8684 0.875884 0.437942 0.899003i \(-0.355708\pi\)
0.437942 + 0.899003i \(0.355708\pi\)
\(942\) −0.900376 −0.0293358
\(943\) −31.8277 −1.03645
\(944\) −113.731 −3.70164
\(945\) −70.9118 −2.30676
\(946\) −6.30708 −0.205061
\(947\) −15.9418 −0.518039 −0.259020 0.965872i \(-0.583399\pi\)
−0.259020 + 0.965872i \(0.583399\pi\)
\(948\) 28.3100 0.919466
\(949\) 18.3253 0.594864
\(950\) −45.9353 −1.49034
\(951\) −15.9937 −0.518630
\(952\) 177.945 5.76722
\(953\) 45.8542 1.48536 0.742681 0.669645i \(-0.233554\pi\)
0.742681 + 0.669645i \(0.233554\pi\)
\(954\) 35.0813 1.13580
\(955\) 77.9780 2.52331
\(956\) 10.8764 0.351768
\(957\) 4.64183 0.150049
\(958\) −54.8431 −1.77190
\(959\) −46.0983 −1.48859
\(960\) −133.125 −4.29660
\(961\) 42.2440 1.36271
\(962\) −18.1020 −0.583631
\(963\) 24.4559 0.788082
\(964\) 86.6053 2.78937
\(965\) −70.6045 −2.27284
\(966\) −96.2135 −3.09562
\(967\) 10.5685 0.339860 0.169930 0.985456i \(-0.445646\pi\)
0.169930 + 0.985456i \(0.445646\pi\)
\(968\) 99.7182 3.20506
\(969\) −11.0278 −0.354265
\(970\) −64.2144 −2.06180
\(971\) 9.29966 0.298440 0.149220 0.988804i \(-0.452324\pi\)
0.149220 + 0.988804i \(0.452324\pi\)
\(972\) −74.9629 −2.40444
\(973\) −3.04516 −0.0976235
\(974\) 29.1421 0.933774
\(975\) −24.9489 −0.799003
\(976\) 1.55670 0.0498287
\(977\) −55.5204 −1.77625 −0.888127 0.459598i \(-0.847994\pi\)
−0.888127 + 0.459598i \(0.847994\pi\)
\(978\) −16.7403 −0.535295
\(979\) −1.70939 −0.0546322
\(980\) 70.6179 2.25581
\(981\) 5.79524 0.185028
\(982\) 3.01335 0.0961598
\(983\) 26.9801 0.860531 0.430266 0.902702i \(-0.358420\pi\)
0.430266 + 0.902702i \(0.358420\pi\)
\(984\) −39.4814 −1.25862
\(985\) 75.8938 2.41818
\(986\) 135.716 4.32207
\(987\) −11.9329 −0.379830
\(988\) 14.8482 0.472385
\(989\) 45.7968 1.45625
\(990\) 7.63354 0.242610
\(991\) −6.09515 −0.193619 −0.0968094 0.995303i \(-0.530864\pi\)
−0.0968094 + 0.995303i \(0.530864\pi\)
\(992\) −175.681 −5.57787
\(993\) 28.2479 0.896419
\(994\) −61.3826 −1.94694
\(995\) 6.59647 0.209122
\(996\) −59.5873 −1.88809
\(997\) 0.267082 0.00845856 0.00422928 0.999991i \(-0.498654\pi\)
0.00422928 + 0.999991i \(0.498654\pi\)
\(998\) 28.4086 0.899258
\(999\) 20.0410 0.634070
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 4003.2.a.c.1.3 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.3 179 1.1 even 1 trivial