Properties

Label 1859.2.a.t.1.9
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.8441897358\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.603243 q^{2} -0.154529 q^{3} -1.63610 q^{4} +4.17643 q^{5} +0.0932187 q^{6} +2.73997 q^{7} +2.19345 q^{8} -2.97612 q^{9} +O(q^{10})\) \(q-0.603243 q^{2} -0.154529 q^{3} -1.63610 q^{4} +4.17643 q^{5} +0.0932187 q^{6} +2.73997 q^{7} +2.19345 q^{8} -2.97612 q^{9} -2.51940 q^{10} +1.00000 q^{11} +0.252825 q^{12} -1.65287 q^{14} -0.645380 q^{15} +1.94901 q^{16} -2.78947 q^{17} +1.79532 q^{18} +8.62913 q^{19} -6.83305 q^{20} -0.423406 q^{21} -0.603243 q^{22} -5.00464 q^{23} -0.338952 q^{24} +12.4426 q^{25} +0.923485 q^{27} -4.48287 q^{28} +5.70078 q^{29} +0.389321 q^{30} +6.49432 q^{31} -5.56263 q^{32} -0.154529 q^{33} +1.68273 q^{34} +11.4433 q^{35} +4.86923 q^{36} -3.15244 q^{37} -5.20546 q^{38} +9.16079 q^{40} +1.15203 q^{41} +0.255417 q^{42} -6.42524 q^{43} -1.63610 q^{44} -12.4296 q^{45} +3.01901 q^{46} -0.354093 q^{47} -0.301179 q^{48} +0.507462 q^{49} -7.50588 q^{50} +0.431055 q^{51} -11.4273 q^{53} -0.557086 q^{54} +4.17643 q^{55} +6.01000 q^{56} -1.33345 q^{57} -3.43895 q^{58} -3.55166 q^{59} +1.05591 q^{60} +9.99485 q^{61} -3.91765 q^{62} -8.15450 q^{63} -0.542409 q^{64} +0.0932187 q^{66} +8.44511 q^{67} +4.56385 q^{68} +0.773363 q^{69} -6.90310 q^{70} +5.99422 q^{71} -6.52797 q^{72} -4.94834 q^{73} +1.90169 q^{74} -1.92274 q^{75} -14.1181 q^{76} +2.73997 q^{77} -7.84360 q^{79} +8.13991 q^{80} +8.78566 q^{81} -0.694952 q^{82} +2.14414 q^{83} +0.692734 q^{84} -11.6500 q^{85} +3.87598 q^{86} -0.880937 q^{87} +2.19345 q^{88} +6.72386 q^{89} +7.49804 q^{90} +8.18808 q^{92} -1.00356 q^{93} +0.213604 q^{94} +36.0389 q^{95} +0.859589 q^{96} -10.5674 q^{97} -0.306123 q^{98} -2.97612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.603243 −0.426557 −0.213279 0.976991i \(-0.568414\pi\)
−0.213279 + 0.976991i \(0.568414\pi\)
\(3\) −0.154529 −0.0892175 −0.0446087 0.999005i \(-0.514204\pi\)
−0.0446087 + 0.999005i \(0.514204\pi\)
\(4\) −1.63610 −0.818049
\(5\) 4.17643 1.86776 0.933878 0.357592i \(-0.116402\pi\)
0.933878 + 0.357592i \(0.116402\pi\)
\(6\) 0.0932187 0.0380564
\(7\) 2.73997 1.03561 0.517807 0.855498i \(-0.326749\pi\)
0.517807 + 0.855498i \(0.326749\pi\)
\(8\) 2.19345 0.775502
\(9\) −2.97612 −0.992040
\(10\) −2.51940 −0.796705
\(11\) 1.00000 0.301511
\(12\) 0.252825 0.0729843
\(13\) 0 0
\(14\) −1.65287 −0.441748
\(15\) −0.645380 −0.166636
\(16\) 1.94901 0.487253
\(17\) −2.78947 −0.676546 −0.338273 0.941048i \(-0.609843\pi\)
−0.338273 + 0.941048i \(0.609843\pi\)
\(18\) 1.79532 0.423162
\(19\) 8.62913 1.97966 0.989829 0.142263i \(-0.0454379\pi\)
0.989829 + 0.142263i \(0.0454379\pi\)
\(20\) −6.83305 −1.52792
\(21\) −0.423406 −0.0923948
\(22\) −0.603243 −0.128612
\(23\) −5.00464 −1.04354 −0.521769 0.853087i \(-0.674728\pi\)
−0.521769 + 0.853087i \(0.674728\pi\)
\(24\) −0.338952 −0.0691883
\(25\) 12.4426 2.48851
\(26\) 0 0
\(27\) 0.923485 0.177725
\(28\) −4.48287 −0.847182
\(29\) 5.70078 1.05861 0.529304 0.848432i \(-0.322453\pi\)
0.529304 + 0.848432i \(0.322453\pi\)
\(30\) 0.389321 0.0710800
\(31\) 6.49432 1.16641 0.583207 0.812323i \(-0.301797\pi\)
0.583207 + 0.812323i \(0.301797\pi\)
\(32\) −5.56263 −0.983343
\(33\) −0.154529 −0.0269001
\(34\) 1.68273 0.288586
\(35\) 11.4433 1.93427
\(36\) 4.86923 0.811538
\(37\) −3.15244 −0.518258 −0.259129 0.965843i \(-0.583435\pi\)
−0.259129 + 0.965843i \(0.583435\pi\)
\(38\) −5.20546 −0.844437
\(39\) 0 0
\(40\) 9.16079 1.44845
\(41\) 1.15203 0.179916 0.0899582 0.995946i \(-0.471327\pi\)
0.0899582 + 0.995946i \(0.471327\pi\)
\(42\) 0.255417 0.0394117
\(43\) −6.42524 −0.979839 −0.489920 0.871768i \(-0.662974\pi\)
−0.489920 + 0.871768i \(0.662974\pi\)
\(44\) −1.63610 −0.246651
\(45\) −12.4296 −1.85289
\(46\) 3.01901 0.445129
\(47\) −0.354093 −0.0516498 −0.0258249 0.999666i \(-0.508221\pi\)
−0.0258249 + 0.999666i \(0.508221\pi\)
\(48\) −0.301179 −0.0434715
\(49\) 0.507462 0.0724945
\(50\) −7.50588 −1.06149
\(51\) 0.431055 0.0603598
\(52\) 0 0
\(53\) −11.4273 −1.56966 −0.784829 0.619712i \(-0.787249\pi\)
−0.784829 + 0.619712i \(0.787249\pi\)
\(54\) −0.557086 −0.0758098
\(55\) 4.17643 0.563149
\(56\) 6.01000 0.803120
\(57\) −1.33345 −0.176620
\(58\) −3.43895 −0.451557
\(59\) −3.55166 −0.462387 −0.231193 0.972908i \(-0.574263\pi\)
−0.231193 + 0.972908i \(0.574263\pi\)
\(60\) 1.05591 0.136317
\(61\) 9.99485 1.27971 0.639855 0.768496i \(-0.278995\pi\)
0.639855 + 0.768496i \(0.278995\pi\)
\(62\) −3.91765 −0.497543
\(63\) −8.15450 −1.02737
\(64\) −0.542409 −0.0678011
\(65\) 0 0
\(66\) 0.0932187 0.0114744
\(67\) 8.44511 1.03173 0.515867 0.856668i \(-0.327470\pi\)
0.515867 + 0.856668i \(0.327470\pi\)
\(68\) 4.56385 0.553448
\(69\) 0.773363 0.0931019
\(70\) −6.90310 −0.825078
\(71\) 5.99422 0.711383 0.355692 0.934603i \(-0.384245\pi\)
0.355692 + 0.934603i \(0.384245\pi\)
\(72\) −6.52797 −0.769329
\(73\) −4.94834 −0.579160 −0.289580 0.957154i \(-0.593516\pi\)
−0.289580 + 0.957154i \(0.593516\pi\)
\(74\) 1.90169 0.221067
\(75\) −1.92274 −0.222019
\(76\) −14.1181 −1.61946
\(77\) 2.73997 0.312249
\(78\) 0 0
\(79\) −7.84360 −0.882474 −0.441237 0.897391i \(-0.645460\pi\)
−0.441237 + 0.897391i \(0.645460\pi\)
\(80\) 8.13991 0.910070
\(81\) 8.78566 0.976184
\(82\) −0.694952 −0.0767447
\(83\) 2.14414 0.235350 0.117675 0.993052i \(-0.462456\pi\)
0.117675 + 0.993052i \(0.462456\pi\)
\(84\) 0.692734 0.0755835
\(85\) −11.6500 −1.26362
\(86\) 3.87598 0.417957
\(87\) −0.880937 −0.0944463
\(88\) 2.19345 0.233823
\(89\) 6.72386 0.712727 0.356364 0.934347i \(-0.384016\pi\)
0.356364 + 0.934347i \(0.384016\pi\)
\(90\) 7.49804 0.790363
\(91\) 0 0
\(92\) 8.18808 0.853666
\(93\) −1.00356 −0.104065
\(94\) 0.213604 0.0220316
\(95\) 36.0389 3.69752
\(96\) 0.859589 0.0877314
\(97\) −10.5674 −1.07296 −0.536481 0.843913i \(-0.680247\pi\)
−0.536481 + 0.843913i \(0.680247\pi\)
\(98\) −0.306123 −0.0309231
\(99\) −2.97612 −0.299111
\(100\) −20.3572 −2.03572
\(101\) 5.02737 0.500242 0.250121 0.968215i \(-0.419530\pi\)
0.250121 + 0.968215i \(0.419530\pi\)
\(102\) −0.260031 −0.0257469
\(103\) 1.17627 0.115902 0.0579509 0.998319i \(-0.481543\pi\)
0.0579509 + 0.998319i \(0.481543\pi\)
\(104\) 0 0
\(105\) −1.76833 −0.172571
\(106\) 6.89343 0.669549
\(107\) −5.53162 −0.534762 −0.267381 0.963591i \(-0.586158\pi\)
−0.267381 + 0.963591i \(0.586158\pi\)
\(108\) −1.51091 −0.145388
\(109\) 17.4224 1.66877 0.834384 0.551184i \(-0.185824\pi\)
0.834384 + 0.551184i \(0.185824\pi\)
\(110\) −2.51940 −0.240215
\(111\) 0.487144 0.0462377
\(112\) 5.34025 0.504606
\(113\) −2.29189 −0.215603 −0.107802 0.994172i \(-0.534381\pi\)
−0.107802 + 0.994172i \(0.534381\pi\)
\(114\) 0.804396 0.0753386
\(115\) −20.9015 −1.94908
\(116\) −9.32703 −0.865993
\(117\) 0 0
\(118\) 2.14251 0.197234
\(119\) −7.64308 −0.700640
\(120\) −1.41561 −0.129227
\(121\) 1.00000 0.0909091
\(122\) −6.02932 −0.545869
\(123\) −0.178022 −0.0160517
\(124\) −10.6253 −0.954185
\(125\) 31.0833 2.78017
\(126\) 4.91914 0.438232
\(127\) −3.76454 −0.334049 −0.167024 0.985953i \(-0.553416\pi\)
−0.167024 + 0.985953i \(0.553416\pi\)
\(128\) 11.4525 1.01226
\(129\) 0.992887 0.0874188
\(130\) 0 0
\(131\) −4.42684 −0.386775 −0.193387 0.981122i \(-0.561947\pi\)
−0.193387 + 0.981122i \(0.561947\pi\)
\(132\) 0.252825 0.0220056
\(133\) 23.6436 2.05016
\(134\) −5.09446 −0.440094
\(135\) 3.85687 0.331947
\(136\) −6.11857 −0.524663
\(137\) 11.9412 1.02020 0.510102 0.860114i \(-0.329608\pi\)
0.510102 + 0.860114i \(0.329608\pi\)
\(138\) −0.466526 −0.0397133
\(139\) 2.06266 0.174952 0.0874762 0.996167i \(-0.472120\pi\)
0.0874762 + 0.996167i \(0.472120\pi\)
\(140\) −18.7224 −1.58233
\(141\) 0.0547178 0.00460807
\(142\) −3.61597 −0.303446
\(143\) 0 0
\(144\) −5.80050 −0.483375
\(145\) 23.8089 1.97722
\(146\) 2.98505 0.247045
\(147\) −0.0784177 −0.00646778
\(148\) 5.15770 0.423960
\(149\) 19.5995 1.60566 0.802828 0.596211i \(-0.203328\pi\)
0.802828 + 0.596211i \(0.203328\pi\)
\(150\) 1.15988 0.0947037
\(151\) −5.91806 −0.481605 −0.240802 0.970574i \(-0.577411\pi\)
−0.240802 + 0.970574i \(0.577411\pi\)
\(152\) 18.9276 1.53523
\(153\) 8.30181 0.671161
\(154\) −1.65287 −0.133192
\(155\) 27.1231 2.17858
\(156\) 0 0
\(157\) 17.5345 1.39940 0.699702 0.714435i \(-0.253316\pi\)
0.699702 + 0.714435i \(0.253316\pi\)
\(158\) 4.73160 0.376426
\(159\) 1.76585 0.140041
\(160\) −23.2319 −1.83664
\(161\) −13.7126 −1.08070
\(162\) −5.29989 −0.416398
\(163\) 15.9728 1.25108 0.625542 0.780191i \(-0.284878\pi\)
0.625542 + 0.780191i \(0.284878\pi\)
\(164\) −1.88483 −0.147180
\(165\) −0.645380 −0.0502428
\(166\) −1.29344 −0.100390
\(167\) 23.3488 1.80678 0.903391 0.428818i \(-0.141070\pi\)
0.903391 + 0.428818i \(0.141070\pi\)
\(168\) −0.928720 −0.0716523
\(169\) 0 0
\(170\) 7.02780 0.539008
\(171\) −25.6813 −1.96390
\(172\) 10.5123 0.801556
\(173\) −12.7004 −0.965593 −0.482797 0.875733i \(-0.660379\pi\)
−0.482797 + 0.875733i \(0.660379\pi\)
\(174\) 0.531419 0.0402868
\(175\) 34.0923 2.57713
\(176\) 1.94901 0.146912
\(177\) 0.548835 0.0412530
\(178\) −4.05612 −0.304019
\(179\) −6.78692 −0.507278 −0.253639 0.967299i \(-0.581628\pi\)
−0.253639 + 0.967299i \(0.581628\pi\)
\(180\) 20.3360 1.51575
\(181\) −13.5531 −1.00739 −0.503696 0.863881i \(-0.668027\pi\)
−0.503696 + 0.863881i \(0.668027\pi\)
\(182\) 0 0
\(183\) −1.54450 −0.114172
\(184\) −10.9774 −0.809266
\(185\) −13.1659 −0.967979
\(186\) 0.605392 0.0443895
\(187\) −2.78947 −0.203986
\(188\) 0.579332 0.0422521
\(189\) 2.53033 0.184054
\(190\) −21.7402 −1.57720
\(191\) −5.48548 −0.396915 −0.198458 0.980109i \(-0.563593\pi\)
−0.198458 + 0.980109i \(0.563593\pi\)
\(192\) 0.0838180 0.00604904
\(193\) −5.20633 −0.374760 −0.187380 0.982287i \(-0.560000\pi\)
−0.187380 + 0.982287i \(0.560000\pi\)
\(194\) 6.37474 0.457679
\(195\) 0 0
\(196\) −0.830257 −0.0593041
\(197\) −18.8540 −1.34329 −0.671645 0.740873i \(-0.734412\pi\)
−0.671645 + 0.740873i \(0.734412\pi\)
\(198\) 1.79532 0.127588
\(199\) 18.8110 1.33347 0.666737 0.745293i \(-0.267690\pi\)
0.666737 + 0.745293i \(0.267690\pi\)
\(200\) 27.2921 1.92984
\(201\) −1.30502 −0.0920488
\(202\) −3.03273 −0.213382
\(203\) 15.6200 1.09631
\(204\) −0.705248 −0.0493772
\(205\) 4.81136 0.336040
\(206\) −0.709579 −0.0494387
\(207\) 14.8944 1.03523
\(208\) 0 0
\(209\) 8.62913 0.596889
\(210\) 1.06673 0.0736114
\(211\) −5.38555 −0.370757 −0.185378 0.982667i \(-0.559351\pi\)
−0.185378 + 0.982667i \(0.559351\pi\)
\(212\) 18.6962 1.28406
\(213\) −0.926282 −0.0634678
\(214\) 3.33691 0.228107
\(215\) −26.8345 −1.83010
\(216\) 2.02562 0.137826
\(217\) 17.7943 1.20795
\(218\) −10.5100 −0.711825
\(219\) 0.764664 0.0516712
\(220\) −6.83305 −0.460684
\(221\) 0 0
\(222\) −0.293866 −0.0197230
\(223\) −8.25185 −0.552585 −0.276292 0.961074i \(-0.589106\pi\)
−0.276292 + 0.961074i \(0.589106\pi\)
\(224\) −15.2415 −1.01836
\(225\) −37.0305 −2.46870
\(226\) 1.38257 0.0919671
\(227\) −15.4059 −1.02252 −0.511261 0.859425i \(-0.670822\pi\)
−0.511261 + 0.859425i \(0.670822\pi\)
\(228\) 2.18166 0.144484
\(229\) 0.144341 0.00953833 0.00476917 0.999989i \(-0.498482\pi\)
0.00476917 + 0.999989i \(0.498482\pi\)
\(230\) 12.6087 0.831392
\(231\) −0.423406 −0.0278581
\(232\) 12.5044 0.820952
\(233\) −23.1843 −1.51885 −0.759426 0.650593i \(-0.774520\pi\)
−0.759426 + 0.650593i \(0.774520\pi\)
\(234\) 0 0
\(235\) −1.47885 −0.0964693
\(236\) 5.81087 0.378255
\(237\) 1.21207 0.0787321
\(238\) 4.61064 0.298863
\(239\) −10.4269 −0.674461 −0.337231 0.941422i \(-0.609490\pi\)
−0.337231 + 0.941422i \(0.609490\pi\)
\(240\) −1.25785 −0.0811941
\(241\) 18.3629 1.18286 0.591431 0.806356i \(-0.298563\pi\)
0.591431 + 0.806356i \(0.298563\pi\)
\(242\) −0.603243 −0.0387779
\(243\) −4.12810 −0.264818
\(244\) −16.3526 −1.04687
\(245\) 2.11938 0.135402
\(246\) 0.107390 0.00684697
\(247\) 0 0
\(248\) 14.2450 0.904557
\(249\) −0.331333 −0.0209973
\(250\) −18.7508 −1.18590
\(251\) −0.622813 −0.0393116 −0.0196558 0.999807i \(-0.506257\pi\)
−0.0196558 + 0.999807i \(0.506257\pi\)
\(252\) 13.3416 0.840439
\(253\) −5.00464 −0.314639
\(254\) 2.27093 0.142491
\(255\) 1.80027 0.112737
\(256\) −5.82380 −0.363987
\(257\) 15.5574 0.970445 0.485222 0.874391i \(-0.338739\pi\)
0.485222 + 0.874391i \(0.338739\pi\)
\(258\) −0.598952 −0.0372891
\(259\) −8.63761 −0.536715
\(260\) 0 0
\(261\) −16.9662 −1.05018
\(262\) 2.67046 0.164982
\(263\) −5.12614 −0.316091 −0.158046 0.987432i \(-0.550519\pi\)
−0.158046 + 0.987432i \(0.550519\pi\)
\(264\) −0.338952 −0.0208611
\(265\) −47.7252 −2.93174
\(266\) −14.2628 −0.874510
\(267\) −1.03903 −0.0635877
\(268\) −13.8170 −0.844010
\(269\) 9.02443 0.550229 0.275115 0.961411i \(-0.411284\pi\)
0.275115 + 0.961411i \(0.411284\pi\)
\(270\) −2.32663 −0.141594
\(271\) 2.54851 0.154811 0.0774054 0.997000i \(-0.475336\pi\)
0.0774054 + 0.997000i \(0.475336\pi\)
\(272\) −5.43672 −0.329649
\(273\) 0 0
\(274\) −7.20343 −0.435175
\(275\) 12.4426 0.750314
\(276\) −1.26530 −0.0761619
\(277\) −9.42522 −0.566307 −0.283153 0.959075i \(-0.591381\pi\)
−0.283153 + 0.959075i \(0.591381\pi\)
\(278\) −1.24428 −0.0746272
\(279\) −19.3279 −1.15713
\(280\) 25.1003 1.50003
\(281\) 11.0792 0.660930 0.330465 0.943818i \(-0.392794\pi\)
0.330465 + 0.943818i \(0.392794\pi\)
\(282\) −0.0330081 −0.00196560
\(283\) −10.7080 −0.636522 −0.318261 0.948003i \(-0.603099\pi\)
−0.318261 + 0.948003i \(0.603099\pi\)
\(284\) −9.80713 −0.581946
\(285\) −5.56907 −0.329883
\(286\) 0 0
\(287\) 3.15653 0.186324
\(288\) 16.5551 0.975516
\(289\) −9.21885 −0.542285
\(290\) −14.3625 −0.843398
\(291\) 1.63298 0.0957269
\(292\) 8.09597 0.473781
\(293\) 2.86960 0.167644 0.0838219 0.996481i \(-0.473287\pi\)
0.0838219 + 0.996481i \(0.473287\pi\)
\(294\) 0.0473049 0.00275888
\(295\) −14.8333 −0.863626
\(296\) −6.91472 −0.401910
\(297\) 0.923485 0.0535860
\(298\) −11.8233 −0.684904
\(299\) 0 0
\(300\) 3.14579 0.181622
\(301\) −17.6050 −1.01473
\(302\) 3.57003 0.205432
\(303\) −0.776876 −0.0446303
\(304\) 16.8183 0.964594
\(305\) 41.7428 2.39018
\(306\) −5.00801 −0.286289
\(307\) −18.3260 −1.04592 −0.522959 0.852358i \(-0.675172\pi\)
−0.522959 + 0.852358i \(0.675172\pi\)
\(308\) −4.48287 −0.255435
\(309\) −0.181769 −0.0103405
\(310\) −16.3618 −0.929288
\(311\) −7.08340 −0.401663 −0.200831 0.979626i \(-0.564364\pi\)
−0.200831 + 0.979626i \(0.564364\pi\)
\(312\) 0 0
\(313\) −12.8140 −0.724290 −0.362145 0.932122i \(-0.617955\pi\)
−0.362145 + 0.932122i \(0.617955\pi\)
\(314\) −10.5776 −0.596926
\(315\) −34.0567 −1.91888
\(316\) 12.8329 0.721907
\(317\) −4.22486 −0.237292 −0.118646 0.992937i \(-0.537855\pi\)
−0.118646 + 0.992937i \(0.537855\pi\)
\(318\) −1.06524 −0.0597355
\(319\) 5.70078 0.319182
\(320\) −2.26533 −0.126636
\(321\) 0.854798 0.0477101
\(322\) 8.27202 0.460981
\(323\) −24.0707 −1.33933
\(324\) −14.3742 −0.798566
\(325\) 0 0
\(326\) −9.63546 −0.533659
\(327\) −2.69228 −0.148883
\(328\) 2.52692 0.139526
\(329\) −0.970207 −0.0534893
\(330\) 0.389321 0.0214314
\(331\) −6.06087 −0.333136 −0.166568 0.986030i \(-0.553268\pi\)
−0.166568 + 0.986030i \(0.553268\pi\)
\(332\) −3.50803 −0.192528
\(333\) 9.38204 0.514133
\(334\) −14.0850 −0.770696
\(335\) 35.2704 1.92703
\(336\) −0.825224 −0.0450197
\(337\) 19.9135 1.08476 0.542378 0.840135i \(-0.317524\pi\)
0.542378 + 0.840135i \(0.317524\pi\)
\(338\) 0 0
\(339\) 0.354165 0.0192356
\(340\) 19.0606 1.03371
\(341\) 6.49432 0.351687
\(342\) 15.4921 0.837716
\(343\) −17.7894 −0.960537
\(344\) −14.0934 −0.759867
\(345\) 3.22989 0.173892
\(346\) 7.66142 0.411881
\(347\) −22.7608 −1.22187 −0.610933 0.791682i \(-0.709205\pi\)
−0.610933 + 0.791682i \(0.709205\pi\)
\(348\) 1.44130 0.0772617
\(349\) −0.661068 −0.0353862 −0.0176931 0.999843i \(-0.505632\pi\)
−0.0176931 + 0.999843i \(0.505632\pi\)
\(350\) −20.5659 −1.09930
\(351\) 0 0
\(352\) −5.56263 −0.296489
\(353\) 8.10393 0.431329 0.215664 0.976468i \(-0.430808\pi\)
0.215664 + 0.976468i \(0.430808\pi\)
\(354\) −0.331081 −0.0175968
\(355\) 25.0344 1.32869
\(356\) −11.0009 −0.583046
\(357\) 1.18108 0.0625094
\(358\) 4.09416 0.216383
\(359\) −27.2296 −1.43712 −0.718562 0.695463i \(-0.755199\pi\)
−0.718562 + 0.695463i \(0.755199\pi\)
\(360\) −27.2636 −1.43692
\(361\) 55.4619 2.91904
\(362\) 8.17579 0.429710
\(363\) −0.154529 −0.00811068
\(364\) 0 0
\(365\) −20.6664 −1.08173
\(366\) 0.931707 0.0487011
\(367\) 25.4037 1.32606 0.663032 0.748591i \(-0.269269\pi\)
0.663032 + 0.748591i \(0.269269\pi\)
\(368\) −9.75410 −0.508468
\(369\) −3.42857 −0.178484
\(370\) 7.94226 0.412898
\(371\) −31.3105 −1.62556
\(372\) 1.64193 0.0851299
\(373\) 11.2123 0.580550 0.290275 0.956943i \(-0.406253\pi\)
0.290275 + 0.956943i \(0.406253\pi\)
\(374\) 1.68273 0.0870119
\(375\) −4.80328 −0.248040
\(376\) −0.776686 −0.0400545
\(377\) 0 0
\(378\) −1.52640 −0.0785096
\(379\) −14.8480 −0.762692 −0.381346 0.924432i \(-0.624539\pi\)
−0.381346 + 0.924432i \(0.624539\pi\)
\(380\) −58.9632 −3.02475
\(381\) 0.581731 0.0298030
\(382\) 3.30908 0.169307
\(383\) 18.2976 0.934963 0.467482 0.884003i \(-0.345161\pi\)
0.467482 + 0.884003i \(0.345161\pi\)
\(384\) −1.76974 −0.0903117
\(385\) 11.4433 0.583205
\(386\) 3.14068 0.159857
\(387\) 19.1223 0.972040
\(388\) 17.2894 0.877735
\(389\) −3.21120 −0.162814 −0.0814072 0.996681i \(-0.525941\pi\)
−0.0814072 + 0.996681i \(0.525941\pi\)
\(390\) 0 0
\(391\) 13.9603 0.706002
\(392\) 1.11309 0.0562197
\(393\) 0.684076 0.0345071
\(394\) 11.3735 0.572990
\(395\) −32.7583 −1.64825
\(396\) 4.86923 0.244688
\(397\) −3.70621 −0.186010 −0.0930048 0.995666i \(-0.529647\pi\)
−0.0930048 + 0.995666i \(0.529647\pi\)
\(398\) −11.3476 −0.568803
\(399\) −3.65363 −0.182910
\(400\) 24.2507 1.21253
\(401\) 30.6476 1.53047 0.765234 0.643752i \(-0.222623\pi\)
0.765234 + 0.643752i \(0.222623\pi\)
\(402\) 0.787242 0.0392641
\(403\) 0 0
\(404\) −8.22527 −0.409222
\(405\) 36.6927 1.82327
\(406\) −9.42265 −0.467638
\(407\) −3.15244 −0.156261
\(408\) 0.945498 0.0468091
\(409\) −6.59417 −0.326061 −0.163030 0.986621i \(-0.552127\pi\)
−0.163030 + 0.986621i \(0.552127\pi\)
\(410\) −2.90242 −0.143340
\(411\) −1.84526 −0.0910200
\(412\) −1.92450 −0.0948133
\(413\) −9.73146 −0.478854
\(414\) −8.98494 −0.441586
\(415\) 8.95486 0.439577
\(416\) 0 0
\(417\) −0.318741 −0.0156088
\(418\) −5.20546 −0.254607
\(419\) −11.5675 −0.565110 −0.282555 0.959251i \(-0.591182\pi\)
−0.282555 + 0.959251i \(0.591182\pi\)
\(420\) 2.89315 0.141171
\(421\) −23.5795 −1.14919 −0.574596 0.818437i \(-0.694841\pi\)
−0.574596 + 0.818437i \(0.694841\pi\)
\(422\) 3.24880 0.158149
\(423\) 1.05382 0.0512387
\(424\) −25.0652 −1.21727
\(425\) −34.7082 −1.68359
\(426\) 0.558773 0.0270726
\(427\) 27.3856 1.32528
\(428\) 9.05028 0.437462
\(429\) 0 0
\(430\) 16.1877 0.780642
\(431\) −18.9954 −0.914974 −0.457487 0.889216i \(-0.651250\pi\)
−0.457487 + 0.889216i \(0.651250\pi\)
\(432\) 1.79988 0.0865970
\(433\) −0.769340 −0.0369721 −0.0184860 0.999829i \(-0.505885\pi\)
−0.0184860 + 0.999829i \(0.505885\pi\)
\(434\) −10.7343 −0.515262
\(435\) −3.67917 −0.176403
\(436\) −28.5048 −1.36513
\(437\) −43.1857 −2.06585
\(438\) −0.461278 −0.0220407
\(439\) −27.8529 −1.32935 −0.664674 0.747134i \(-0.731429\pi\)
−0.664674 + 0.747134i \(0.731429\pi\)
\(440\) 9.16079 0.436723
\(441\) −1.51027 −0.0719175
\(442\) 0 0
\(443\) −23.1471 −1.09975 −0.549876 0.835246i \(-0.685325\pi\)
−0.549876 + 0.835246i \(0.685325\pi\)
\(444\) −0.797015 −0.0378247
\(445\) 28.0817 1.33120
\(446\) 4.97787 0.235709
\(447\) −3.02870 −0.143253
\(448\) −1.48619 −0.0702157
\(449\) 11.5156 0.543453 0.271727 0.962374i \(-0.412405\pi\)
0.271727 + 0.962374i \(0.412405\pi\)
\(450\) 22.3384 1.05304
\(451\) 1.15203 0.0542469
\(452\) 3.74976 0.176374
\(453\) 0.914513 0.0429675
\(454\) 9.29347 0.436164
\(455\) 0 0
\(456\) −2.92486 −0.136969
\(457\) 13.5305 0.632928 0.316464 0.948604i \(-0.397504\pi\)
0.316464 + 0.948604i \(0.397504\pi\)
\(458\) −0.0870728 −0.00406864
\(459\) −2.57604 −0.120239
\(460\) 34.1969 1.59444
\(461\) −37.6661 −1.75428 −0.877142 0.480231i \(-0.840553\pi\)
−0.877142 + 0.480231i \(0.840553\pi\)
\(462\) 0.255417 0.0118831
\(463\) −31.7879 −1.47731 −0.738655 0.674084i \(-0.764539\pi\)
−0.738655 + 0.674084i \(0.764539\pi\)
\(464\) 11.1109 0.515810
\(465\) −4.19131 −0.194367
\(466\) 13.9858 0.647877
\(467\) −1.64872 −0.0762937 −0.0381469 0.999272i \(-0.512145\pi\)
−0.0381469 + 0.999272i \(0.512145\pi\)
\(468\) 0 0
\(469\) 23.1394 1.06848
\(470\) 0.892103 0.0411497
\(471\) −2.70959 −0.124851
\(472\) −7.79039 −0.358582
\(473\) −6.42524 −0.295433
\(474\) −0.731170 −0.0335838
\(475\) 107.368 4.92640
\(476\) 12.5048 0.573158
\(477\) 34.0090 1.55716
\(478\) 6.28996 0.287696
\(479\) −12.5405 −0.572988 −0.286494 0.958082i \(-0.592490\pi\)
−0.286494 + 0.958082i \(0.592490\pi\)
\(480\) 3.59001 0.163861
\(481\) 0 0
\(482\) −11.0773 −0.504558
\(483\) 2.11899 0.0964176
\(484\) −1.63610 −0.0743681
\(485\) −44.1342 −2.00403
\(486\) 2.49024 0.112960
\(487\) 31.0109 1.40524 0.702619 0.711566i \(-0.252014\pi\)
0.702619 + 0.711566i \(0.252014\pi\)
\(488\) 21.9232 0.992417
\(489\) −2.46826 −0.111619
\(490\) −1.27850 −0.0577567
\(491\) −0.580666 −0.0262051 −0.0131025 0.999914i \(-0.504171\pi\)
−0.0131025 + 0.999914i \(0.504171\pi\)
\(492\) 0.291261 0.0131311
\(493\) −15.9022 −0.716197
\(494\) 0 0
\(495\) −12.4296 −0.558667
\(496\) 12.6575 0.568339
\(497\) 16.4240 0.736718
\(498\) 0.199874 0.00895657
\(499\) 15.7550 0.705291 0.352645 0.935757i \(-0.385282\pi\)
0.352645 + 0.935757i \(0.385282\pi\)
\(500\) −50.8553 −2.27432
\(501\) −3.60807 −0.161197
\(502\) 0.375707 0.0167686
\(503\) −33.7223 −1.50360 −0.751801 0.659390i \(-0.770815\pi\)
−0.751801 + 0.659390i \(0.770815\pi\)
\(504\) −17.8865 −0.796727
\(505\) 20.9965 0.934330
\(506\) 3.01901 0.134211
\(507\) 0 0
\(508\) 6.15915 0.273268
\(509\) −40.4825 −1.79435 −0.897177 0.441671i \(-0.854386\pi\)
−0.897177 + 0.441671i \(0.854386\pi\)
\(510\) −1.08600 −0.0480889
\(511\) −13.5583 −0.599785
\(512\) −19.3918 −0.857003
\(513\) 7.96887 0.351834
\(514\) −9.38490 −0.413950
\(515\) 4.91263 0.216476
\(516\) −1.62446 −0.0715129
\(517\) −0.354093 −0.0155730
\(518\) 5.21057 0.228939
\(519\) 1.96258 0.0861478
\(520\) 0 0
\(521\) 28.6290 1.25426 0.627129 0.778915i \(-0.284230\pi\)
0.627129 + 0.778915i \(0.284230\pi\)
\(522\) 10.2347 0.447962
\(523\) 20.4531 0.894354 0.447177 0.894446i \(-0.352429\pi\)
0.447177 + 0.894446i \(0.352429\pi\)
\(524\) 7.24275 0.316401
\(525\) −5.26825 −0.229925
\(526\) 3.09231 0.134831
\(527\) −18.1157 −0.789134
\(528\) −0.301179 −0.0131072
\(529\) 2.04639 0.0889736
\(530\) 28.7899 1.25055
\(531\) 10.5702 0.458706
\(532\) −38.6832 −1.67713
\(533\) 0 0
\(534\) 0.626789 0.0271238
\(535\) −23.1024 −0.998805
\(536\) 18.5239 0.800112
\(537\) 1.04878 0.0452581
\(538\) −5.44392 −0.234704
\(539\) 0.507462 0.0218579
\(540\) −6.31022 −0.271549
\(541\) −14.2756 −0.613755 −0.306878 0.951749i \(-0.599284\pi\)
−0.306878 + 0.951749i \(0.599284\pi\)
\(542\) −1.53737 −0.0660356
\(543\) 2.09434 0.0898769
\(544\) 15.5168 0.665277
\(545\) 72.7636 3.11685
\(546\) 0 0
\(547\) 24.9378 1.06626 0.533131 0.846032i \(-0.321015\pi\)
0.533131 + 0.846032i \(0.321015\pi\)
\(548\) −19.5369 −0.834577
\(549\) −29.7459 −1.26952
\(550\) −7.50588 −0.320052
\(551\) 49.1927 2.09568
\(552\) 1.69633 0.0722007
\(553\) −21.4913 −0.913902
\(554\) 5.68570 0.241562
\(555\) 2.03452 0.0863607
\(556\) −3.37471 −0.143120
\(557\) 29.6736 1.25731 0.628655 0.777684i \(-0.283606\pi\)
0.628655 + 0.777684i \(0.283606\pi\)
\(558\) 11.6594 0.493582
\(559\) 0 0
\(560\) 22.3032 0.942480
\(561\) 0.431055 0.0181992
\(562\) −6.68345 −0.281924
\(563\) −31.5076 −1.32789 −0.663943 0.747783i \(-0.731118\pi\)
−0.663943 + 0.747783i \(0.731118\pi\)
\(564\) −0.0895237 −0.00376963
\(565\) −9.57193 −0.402694
\(566\) 6.45950 0.271513
\(567\) 24.0725 1.01095
\(568\) 13.1480 0.551679
\(569\) −18.4812 −0.774774 −0.387387 0.921917i \(-0.626622\pi\)
−0.387387 + 0.921917i \(0.626622\pi\)
\(570\) 3.35950 0.140714
\(571\) −15.2093 −0.636490 −0.318245 0.948009i \(-0.603093\pi\)
−0.318245 + 0.948009i \(0.603093\pi\)
\(572\) 0 0
\(573\) 0.847667 0.0354118
\(574\) −1.90415 −0.0794778
\(575\) −62.2705 −2.59686
\(576\) 1.61427 0.0672614
\(577\) 35.3665 1.47233 0.736164 0.676803i \(-0.236635\pi\)
0.736164 + 0.676803i \(0.236635\pi\)
\(578\) 5.56120 0.231316
\(579\) 0.804531 0.0334352
\(580\) −38.9537 −1.61746
\(581\) 5.87489 0.243732
\(582\) −0.985083 −0.0408330
\(583\) −11.4273 −0.473270
\(584\) −10.8539 −0.449139
\(585\) 0 0
\(586\) −1.73107 −0.0715097
\(587\) −14.0192 −0.578634 −0.289317 0.957233i \(-0.593428\pi\)
−0.289317 + 0.957233i \(0.593428\pi\)
\(588\) 0.128299 0.00529096
\(589\) 56.0403 2.30910
\(590\) 8.94806 0.368386
\(591\) 2.91349 0.119845
\(592\) −6.14414 −0.252523
\(593\) −1.04938 −0.0430927 −0.0215464 0.999768i \(-0.506859\pi\)
−0.0215464 + 0.999768i \(0.506859\pi\)
\(594\) −0.557086 −0.0228575
\(595\) −31.9208 −1.30862
\(596\) −32.0667 −1.31350
\(597\) −2.90685 −0.118969
\(598\) 0 0
\(599\) −36.6575 −1.49778 −0.748892 0.662692i \(-0.769414\pi\)
−0.748892 + 0.662692i \(0.769414\pi\)
\(600\) −4.21743 −0.172176
\(601\) −33.4890 −1.36604 −0.683022 0.730398i \(-0.739335\pi\)
−0.683022 + 0.730398i \(0.739335\pi\)
\(602\) 10.6201 0.432842
\(603\) −25.1337 −1.02352
\(604\) 9.68252 0.393976
\(605\) 4.17643 0.169796
\(606\) 0.468645 0.0190374
\(607\) −28.9078 −1.17333 −0.586666 0.809829i \(-0.699560\pi\)
−0.586666 + 0.809829i \(0.699560\pi\)
\(608\) −48.0006 −1.94668
\(609\) −2.41374 −0.0978098
\(610\) −25.1810 −1.01955
\(611\) 0 0
\(612\) −13.5826 −0.549043
\(613\) −25.7244 −1.03900 −0.519498 0.854471i \(-0.673881\pi\)
−0.519498 + 0.854471i \(0.673881\pi\)
\(614\) 11.0550 0.446144
\(615\) −0.743496 −0.0299806
\(616\) 6.01000 0.242150
\(617\) 27.9072 1.12350 0.561751 0.827307i \(-0.310128\pi\)
0.561751 + 0.827307i \(0.310128\pi\)
\(618\) 0.109651 0.00441080
\(619\) 17.2993 0.695316 0.347658 0.937621i \(-0.386977\pi\)
0.347658 + 0.937621i \(0.386977\pi\)
\(620\) −44.3760 −1.78218
\(621\) −4.62171 −0.185463
\(622\) 4.27301 0.171332
\(623\) 18.4232 0.738110
\(624\) 0 0
\(625\) 67.6044 2.70418
\(626\) 7.72995 0.308951
\(627\) −1.33345 −0.0532530
\(628\) −28.6881 −1.14478
\(629\) 8.79364 0.350625
\(630\) 20.5444 0.818510
\(631\) 28.5282 1.13569 0.567845 0.823135i \(-0.307777\pi\)
0.567845 + 0.823135i \(0.307777\pi\)
\(632\) −17.2046 −0.684361
\(633\) 0.832225 0.0330780
\(634\) 2.54862 0.101219
\(635\) −15.7223 −0.623921
\(636\) −2.88910 −0.114560
\(637\) 0 0
\(638\) −3.43895 −0.136149
\(639\) −17.8395 −0.705721
\(640\) 47.8304 1.89066
\(641\) 3.46631 0.136911 0.0684555 0.997654i \(-0.478193\pi\)
0.0684555 + 0.997654i \(0.478193\pi\)
\(642\) −0.515651 −0.0203511
\(643\) −39.9565 −1.57573 −0.787866 0.615847i \(-0.788814\pi\)
−0.787866 + 0.615847i \(0.788814\pi\)
\(644\) 22.4351 0.884068
\(645\) 4.14672 0.163277
\(646\) 14.5205 0.571301
\(647\) −19.7561 −0.776694 −0.388347 0.921513i \(-0.626954\pi\)
−0.388347 + 0.921513i \(0.626954\pi\)
\(648\) 19.2709 0.757033
\(649\) −3.55166 −0.139415
\(650\) 0 0
\(651\) −2.74974 −0.107771
\(652\) −26.1330 −1.02345
\(653\) 23.2622 0.910319 0.455159 0.890410i \(-0.349582\pi\)
0.455159 + 0.890410i \(0.349582\pi\)
\(654\) 1.62410 0.0635072
\(655\) −18.4884 −0.722401
\(656\) 2.24532 0.0876649
\(657\) 14.7269 0.574550
\(658\) 0.585271 0.0228162
\(659\) −21.9368 −0.854538 −0.427269 0.904125i \(-0.640524\pi\)
−0.427269 + 0.904125i \(0.640524\pi\)
\(660\) 1.05591 0.0411011
\(661\) −25.6652 −0.998259 −0.499129 0.866527i \(-0.666347\pi\)
−0.499129 + 0.866527i \(0.666347\pi\)
\(662\) 3.65618 0.142101
\(663\) 0 0
\(664\) 4.70307 0.182514
\(665\) 98.7458 3.82920
\(666\) −5.65965 −0.219307
\(667\) −28.5303 −1.10470
\(668\) −38.2009 −1.47804
\(669\) 1.27515 0.0493002
\(670\) −21.2766 −0.821988
\(671\) 9.99485 0.385847
\(672\) 2.35525 0.0908558
\(673\) −2.40531 −0.0927179 −0.0463589 0.998925i \(-0.514762\pi\)
−0.0463589 + 0.998925i \(0.514762\pi\)
\(674\) −12.0127 −0.462710
\(675\) 11.4905 0.442270
\(676\) 0 0
\(677\) −32.8859 −1.26391 −0.631955 0.775005i \(-0.717747\pi\)
−0.631955 + 0.775005i \(0.717747\pi\)
\(678\) −0.213647 −0.00820508
\(679\) −28.9545 −1.11117
\(680\) −25.5538 −0.979942
\(681\) 2.38065 0.0912269
\(682\) −3.91765 −0.150015
\(683\) −15.4703 −0.591954 −0.295977 0.955195i \(-0.595645\pi\)
−0.295977 + 0.955195i \(0.595645\pi\)
\(684\) 42.0172 1.60657
\(685\) 49.8715 1.90549
\(686\) 10.7313 0.409724
\(687\) −0.0223049 −0.000850986 0
\(688\) −12.5229 −0.477430
\(689\) 0 0
\(690\) −1.94841 −0.0741747
\(691\) −18.4742 −0.702791 −0.351396 0.936227i \(-0.614293\pi\)
−0.351396 + 0.936227i \(0.614293\pi\)
\(692\) 20.7791 0.789902
\(693\) −8.15450 −0.309764
\(694\) 13.7303 0.521196
\(695\) 8.61455 0.326769
\(696\) −1.93229 −0.0732433
\(697\) −3.21355 −0.121722
\(698\) 0.398785 0.0150942
\(699\) 3.58265 0.135508
\(700\) −55.7783 −2.10822
\(701\) 42.1518 1.59205 0.796026 0.605262i \(-0.206932\pi\)
0.796026 + 0.605262i \(0.206932\pi\)
\(702\) 0 0
\(703\) −27.2028 −1.02597
\(704\) −0.542409 −0.0204428
\(705\) 0.228525 0.00860675
\(706\) −4.88864 −0.183986
\(707\) 13.7749 0.518057
\(708\) −0.897948 −0.0337470
\(709\) 38.6700 1.45228 0.726141 0.687546i \(-0.241312\pi\)
0.726141 + 0.687546i \(0.241312\pi\)
\(710\) −15.1018 −0.566762
\(711\) 23.3435 0.875450
\(712\) 14.7484 0.552721
\(713\) −32.5017 −1.21720
\(714\) −0.712478 −0.0266638
\(715\) 0 0
\(716\) 11.1041 0.414978
\(717\) 1.61126 0.0601737
\(718\) 16.4261 0.613015
\(719\) −12.4070 −0.462704 −0.231352 0.972870i \(-0.574315\pi\)
−0.231352 + 0.972870i \(0.574315\pi\)
\(720\) −24.2254 −0.902826
\(721\) 3.22296 0.120029
\(722\) −33.4570 −1.24514
\(723\) −2.83761 −0.105532
\(724\) 22.1741 0.824095
\(725\) 70.9322 2.63436
\(726\) 0.0932187 0.00345967
\(727\) −38.2088 −1.41708 −0.708542 0.705668i \(-0.750647\pi\)
−0.708542 + 0.705668i \(0.750647\pi\)
\(728\) 0 0
\(729\) −25.7191 −0.952558
\(730\) 12.4669 0.461419
\(731\) 17.9230 0.662907
\(732\) 2.52695 0.0933987
\(733\) −7.45535 −0.275370 −0.137685 0.990476i \(-0.543966\pi\)
−0.137685 + 0.990476i \(0.543966\pi\)
\(734\) −15.3246 −0.565642
\(735\) −0.327506 −0.0120802
\(736\) 27.8389 1.02616
\(737\) 8.44511 0.311080
\(738\) 2.06826 0.0761338
\(739\) 13.1243 0.482784 0.241392 0.970428i \(-0.422396\pi\)
0.241392 + 0.970428i \(0.422396\pi\)
\(740\) 21.5408 0.791854
\(741\) 0 0
\(742\) 18.8878 0.693394
\(743\) 14.4180 0.528945 0.264473 0.964393i \(-0.414802\pi\)
0.264473 + 0.964393i \(0.414802\pi\)
\(744\) −2.20127 −0.0807023
\(745\) 81.8560 2.99897
\(746\) −6.76373 −0.247638
\(747\) −6.38122 −0.233477
\(748\) 4.56385 0.166871
\(749\) −15.1565 −0.553807
\(750\) 2.89754 0.105803
\(751\) 15.4568 0.564025 0.282012 0.959411i \(-0.408998\pi\)
0.282012 + 0.959411i \(0.408998\pi\)
\(752\) −0.690133 −0.0251665
\(753\) 0.0962428 0.00350728
\(754\) 0 0
\(755\) −24.7163 −0.899520
\(756\) −4.13986 −0.150565
\(757\) −37.8175 −1.37450 −0.687250 0.726421i \(-0.741182\pi\)
−0.687250 + 0.726421i \(0.741182\pi\)
\(758\) 8.95697 0.325332
\(759\) 0.773363 0.0280713
\(760\) 79.0496 2.86743
\(761\) −13.7020 −0.496697 −0.248349 0.968671i \(-0.579888\pi\)
−0.248349 + 0.968671i \(0.579888\pi\)
\(762\) −0.350925 −0.0127127
\(763\) 47.7371 1.72820
\(764\) 8.97478 0.324696
\(765\) 34.6719 1.25357
\(766\) −11.0379 −0.398815
\(767\) 0 0
\(768\) 0.899947 0.0324740
\(769\) 28.6385 1.03273 0.516365 0.856369i \(-0.327285\pi\)
0.516365 + 0.856369i \(0.327285\pi\)
\(770\) −6.90310 −0.248770
\(771\) −2.40407 −0.0865806
\(772\) 8.51807 0.306572
\(773\) 4.43381 0.159473 0.0797366 0.996816i \(-0.474592\pi\)
0.0797366 + 0.996816i \(0.474592\pi\)
\(774\) −11.5354 −0.414631
\(775\) 80.8060 2.90264
\(776\) −23.1792 −0.832084
\(777\) 1.33476 0.0478843
\(778\) 1.93713 0.0694496
\(779\) 9.94099 0.356173
\(780\) 0 0
\(781\) 5.99422 0.214490
\(782\) −8.42145 −0.301150
\(783\) 5.26458 0.188141
\(784\) 0.989049 0.0353232
\(785\) 73.2315 2.61374
\(786\) −0.412664 −0.0147192
\(787\) −55.4317 −1.97593 −0.987964 0.154686i \(-0.950563\pi\)
−0.987964 + 0.154686i \(0.950563\pi\)
\(788\) 30.8469 1.09888
\(789\) 0.792138 0.0282009
\(790\) 19.7612 0.703071
\(791\) −6.27973 −0.223282
\(792\) −6.52797 −0.231961
\(793\) 0 0
\(794\) 2.23575 0.0793437
\(795\) 7.37494 0.261562
\(796\) −30.7766 −1.09085
\(797\) −15.6093 −0.552910 −0.276455 0.961027i \(-0.589160\pi\)
−0.276455 + 0.961027i \(0.589160\pi\)
\(798\) 2.20402 0.0780216
\(799\) 0.987734 0.0349435
\(800\) −69.2133 −2.44706
\(801\) −20.0110 −0.707054
\(802\) −18.4880 −0.652832
\(803\) −4.94834 −0.174623
\(804\) 2.13514 0.0753004
\(805\) −57.2696 −2.01849
\(806\) 0 0
\(807\) −1.39454 −0.0490901
\(808\) 11.0273 0.387939
\(809\) 48.9142 1.71973 0.859867 0.510519i \(-0.170547\pi\)
0.859867 + 0.510519i \(0.170547\pi\)
\(810\) −22.1346 −0.777730
\(811\) −3.66769 −0.128790 −0.0643951 0.997924i \(-0.520512\pi\)
−0.0643951 + 0.997924i \(0.520512\pi\)
\(812\) −25.5558 −0.896834
\(813\) −0.393819 −0.0138118
\(814\) 1.90169 0.0666541
\(815\) 66.7091 2.33672
\(816\) 0.840131 0.0294105
\(817\) −55.4442 −1.93975
\(818\) 3.97789 0.139084
\(819\) 0 0
\(820\) −7.87186 −0.274897
\(821\) −54.7264 −1.90996 −0.954982 0.296665i \(-0.904125\pi\)
−0.954982 + 0.296665i \(0.904125\pi\)
\(822\) 1.11314 0.0388252
\(823\) 42.9535 1.49727 0.748633 0.662985i \(-0.230711\pi\)
0.748633 + 0.662985i \(0.230711\pi\)
\(824\) 2.58010 0.0898820
\(825\) −1.92274 −0.0669412
\(826\) 5.87044 0.204259
\(827\) 30.4806 1.05991 0.529957 0.848024i \(-0.322208\pi\)
0.529957 + 0.848024i \(0.322208\pi\)
\(828\) −24.3687 −0.846871
\(829\) 9.56411 0.332175 0.166088 0.986111i \(-0.446887\pi\)
0.166088 + 0.986111i \(0.446887\pi\)
\(830\) −5.40195 −0.187505
\(831\) 1.45647 0.0505245
\(832\) 0 0
\(833\) −1.41555 −0.0490459
\(834\) 0.192278 0.00665805
\(835\) 97.5145 3.37463
\(836\) −14.1181 −0.488285
\(837\) 5.99741 0.207301
\(838\) 6.97803 0.241052
\(839\) −13.6849 −0.472456 −0.236228 0.971698i \(-0.575911\pi\)
−0.236228 + 0.971698i \(0.575911\pi\)
\(840\) −3.87873 −0.133829
\(841\) 3.49886 0.120650
\(842\) 14.2241 0.490196
\(843\) −1.71206 −0.0589665
\(844\) 8.81129 0.303297
\(845\) 0 0
\(846\) −0.635712 −0.0218562
\(847\) 2.73997 0.0941466
\(848\) −22.2719 −0.764821
\(849\) 1.65469 0.0567889
\(850\) 20.9375 0.718149
\(851\) 15.7768 0.540822
\(852\) 1.51549 0.0519198
\(853\) −48.2728 −1.65283 −0.826415 0.563061i \(-0.809624\pi\)
−0.826415 + 0.563061i \(0.809624\pi\)
\(854\) −16.5202 −0.565309
\(855\) −107.256 −3.66809
\(856\) −12.1333 −0.414709
\(857\) −0.574419 −0.0196218 −0.00981090 0.999952i \(-0.503123\pi\)
−0.00981090 + 0.999952i \(0.503123\pi\)
\(858\) 0 0
\(859\) −56.0203 −1.91139 −0.955694 0.294361i \(-0.904893\pi\)
−0.955694 + 0.294361i \(0.904893\pi\)
\(860\) 43.9039 1.49711
\(861\) −0.487776 −0.0166233
\(862\) 11.4588 0.390289
\(863\) −24.3871 −0.830146 −0.415073 0.909788i \(-0.636244\pi\)
−0.415073 + 0.909788i \(0.636244\pi\)
\(864\) −5.13701 −0.174764
\(865\) −53.0423 −1.80349
\(866\) 0.464099 0.0157707
\(867\) 1.42458 0.0483813
\(868\) −29.1132 −0.988166
\(869\) −7.84360 −0.266076
\(870\) 2.21943 0.0752458
\(871\) 0 0
\(872\) 38.2153 1.29413
\(873\) 31.4500 1.06442
\(874\) 26.0514 0.881203
\(875\) 85.1675 2.87919
\(876\) −1.25106 −0.0422696
\(877\) 11.9636 0.403982 0.201991 0.979387i \(-0.435259\pi\)
0.201991 + 0.979387i \(0.435259\pi\)
\(878\) 16.8021 0.567043
\(879\) −0.443437 −0.0149568
\(880\) 8.13991 0.274396
\(881\) −15.1233 −0.509516 −0.254758 0.967005i \(-0.581996\pi\)
−0.254758 + 0.967005i \(0.581996\pi\)
\(882\) 0.911058 0.0306769
\(883\) −24.3493 −0.819418 −0.409709 0.912216i \(-0.634370\pi\)
−0.409709 + 0.912216i \(0.634370\pi\)
\(884\) 0 0
\(885\) 2.29217 0.0770505
\(886\) 13.9633 0.469107
\(887\) −28.5969 −0.960190 −0.480095 0.877217i \(-0.659398\pi\)
−0.480095 + 0.877217i \(0.659398\pi\)
\(888\) 1.06853 0.0358574
\(889\) −10.3147 −0.345945
\(890\) −16.9401 −0.567833
\(891\) 8.78566 0.294331
\(892\) 13.5008 0.452041
\(893\) −3.05552 −0.102249
\(894\) 1.82704 0.0611054
\(895\) −28.3451 −0.947472
\(896\) 31.3795 1.04831
\(897\) 0 0
\(898\) −6.94669 −0.231814
\(899\) 37.0227 1.23478
\(900\) 60.5856 2.01952
\(901\) 31.8761 1.06195
\(902\) −0.694952 −0.0231394
\(903\) 2.72048 0.0905320
\(904\) −5.02716 −0.167201
\(905\) −56.6034 −1.88156
\(906\) −0.551673 −0.0183281
\(907\) 54.8751 1.82210 0.911049 0.412297i \(-0.135273\pi\)
0.911049 + 0.412297i \(0.135273\pi\)
\(908\) 25.2055 0.836473
\(909\) −14.9621 −0.496260
\(910\) 0 0
\(911\) 4.35325 0.144229 0.0721147 0.997396i \(-0.477025\pi\)
0.0721147 + 0.997396i \(0.477025\pi\)
\(912\) −2.59892 −0.0860587
\(913\) 2.14414 0.0709607
\(914\) −8.16215 −0.269980
\(915\) −6.45048 −0.213246
\(916\) −0.236156 −0.00780282
\(917\) −12.1294 −0.400549
\(918\) 1.55398 0.0512888
\(919\) −4.16367 −0.137347 −0.0686734 0.997639i \(-0.521877\pi\)
−0.0686734 + 0.997639i \(0.521877\pi\)
\(920\) −45.8464 −1.51151
\(921\) 2.83190 0.0933142
\(922\) 22.7218 0.748303
\(923\) 0 0
\(924\) 0.692734 0.0227893
\(925\) −39.2244 −1.28969
\(926\) 19.1758 0.630157
\(927\) −3.50074 −0.114979
\(928\) −31.7113 −1.04097
\(929\) −22.1678 −0.727303 −0.363652 0.931535i \(-0.618470\pi\)
−0.363652 + 0.931535i \(0.618470\pi\)
\(930\) 2.52838 0.0829087
\(931\) 4.37895 0.143514
\(932\) 37.9318 1.24250
\(933\) 1.09459 0.0358353
\(934\) 0.994579 0.0325436
\(935\) −11.6500 −0.380997
\(936\) 0 0
\(937\) 23.2278 0.758819 0.379409 0.925229i \(-0.376127\pi\)
0.379409 + 0.925229i \(0.376127\pi\)
\(938\) −13.9587 −0.455767
\(939\) 1.98014 0.0646193
\(940\) 2.41954 0.0789166
\(941\) 33.9577 1.10699 0.553495 0.832852i \(-0.313294\pi\)
0.553495 + 0.832852i \(0.313294\pi\)
\(942\) 1.63454 0.0532562
\(943\) −5.76548 −0.187750
\(944\) −6.92223 −0.225299
\(945\) 10.5677 0.343768
\(946\) 3.87598 0.126019
\(947\) −32.5647 −1.05821 −0.529106 0.848556i \(-0.677473\pi\)
−0.529106 + 0.848556i \(0.677473\pi\)
\(948\) −1.98306 −0.0644068
\(949\) 0 0
\(950\) −64.7692 −2.10139
\(951\) 0.652864 0.0211706
\(952\) −16.7647 −0.543348
\(953\) −40.2221 −1.30292 −0.651461 0.758682i \(-0.725843\pi\)
−0.651461 + 0.758682i \(0.725843\pi\)
\(954\) −20.5157 −0.664220
\(955\) −22.9097 −0.741341
\(956\) 17.0595 0.551742
\(957\) −0.880937 −0.0284766
\(958\) 7.56495 0.244412
\(959\) 32.7185 1.05654
\(960\) 0.350060 0.0112981
\(961\) 11.1762 0.360524
\(962\) 0 0
\(963\) 16.4628 0.530506
\(964\) −30.0436 −0.967639
\(965\) −21.7439 −0.699960
\(966\) −1.27827 −0.0411276
\(967\) −28.2981 −0.910006 −0.455003 0.890490i \(-0.650362\pi\)
−0.455003 + 0.890490i \(0.650362\pi\)
\(968\) 2.19345 0.0705002
\(969\) 3.71963 0.119492
\(970\) 26.6236 0.854833
\(971\) −32.0941 −1.02995 −0.514974 0.857206i \(-0.672198\pi\)
−0.514974 + 0.857206i \(0.672198\pi\)
\(972\) 6.75397 0.216634
\(973\) 5.65164 0.181183
\(974\) −18.7071 −0.599415
\(975\) 0 0
\(976\) 19.4801 0.623542
\(977\) 33.9087 1.08484 0.542418 0.840109i \(-0.317509\pi\)
0.542418 + 0.840109i \(0.317509\pi\)
\(978\) 1.48896 0.0476117
\(979\) 6.72386 0.214895
\(980\) −3.46751 −0.110766
\(981\) −51.8513 −1.65548
\(982\) 0.350283 0.0111780
\(983\) 37.3803 1.19225 0.596124 0.802893i \(-0.296707\pi\)
0.596124 + 0.802893i \(0.296707\pi\)
\(984\) −0.390482 −0.0124481
\(985\) −78.7423 −2.50894
\(986\) 9.59286 0.305499
\(987\) 0.149925 0.00477218
\(988\) 0 0
\(989\) 32.1560 1.02250
\(990\) 7.49804 0.238303
\(991\) 12.5110 0.397424 0.198712 0.980058i \(-0.436324\pi\)
0.198712 + 0.980058i \(0.436324\pi\)
\(992\) −36.1255 −1.14699
\(993\) 0.936582 0.0297215
\(994\) −9.90767 −0.314252
\(995\) 78.5627 2.49060
\(996\) 0.542093 0.0171769
\(997\) 60.2994 1.90970 0.954851 0.297086i \(-0.0960148\pi\)
0.954851 + 0.297086i \(0.0960148\pi\)
\(998\) −9.50410 −0.300847
\(999\) −2.91123 −0.0921073
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 1859.2.a.t.1.9 yes 21
13.12 even 2 1859.2.a.s.1.13 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.s.1.13 21 13.12 even 2
1859.2.a.t.1.9 yes 21 1.1 even 1 trivial