Properties

Label 1441.2.a.e.1.27
Level $1441$
Weight $2$
Character 1441.1
Self dual yes
Analytic conductor $11.506$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.5064429313\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.27
Character \(\chi\) \(=\) 1441.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.67178 q^{2} -1.26231 q^{3} +5.13839 q^{4} -0.362334 q^{5} -3.37261 q^{6} +0.0617708 q^{7} +8.38506 q^{8} -1.40657 q^{9} +O(q^{10})\) \(q+2.67178 q^{2} -1.26231 q^{3} +5.13839 q^{4} -0.362334 q^{5} -3.37261 q^{6} +0.0617708 q^{7} +8.38506 q^{8} -1.40657 q^{9} -0.968075 q^{10} +1.00000 q^{11} -6.48623 q^{12} +3.38570 q^{13} +0.165038 q^{14} +0.457377 q^{15} +12.1262 q^{16} +3.44123 q^{17} -3.75805 q^{18} +1.54031 q^{19} -1.86181 q^{20} -0.0779739 q^{21} +2.67178 q^{22} +6.24144 q^{23} -10.5845 q^{24} -4.86871 q^{25} +9.04584 q^{26} +5.56246 q^{27} +0.317402 q^{28} +2.65024 q^{29} +1.22201 q^{30} -3.16079 q^{31} +15.6285 q^{32} -1.26231 q^{33} +9.19419 q^{34} -0.0223817 q^{35} -7.22752 q^{36} +7.14203 q^{37} +4.11537 q^{38} -4.27381 q^{39} -3.03819 q^{40} -5.84051 q^{41} -0.208329 q^{42} +1.61375 q^{43} +5.13839 q^{44} +0.509650 q^{45} +16.6757 q^{46} -7.80153 q^{47} -15.3071 q^{48} -6.99618 q^{49} -13.0081 q^{50} -4.34390 q^{51} +17.3971 q^{52} +4.33413 q^{53} +14.8616 q^{54} -0.362334 q^{55} +0.517952 q^{56} -1.94435 q^{57} +7.08084 q^{58} -1.45377 q^{59} +2.35018 q^{60} -4.89476 q^{61} -8.44493 q^{62} -0.0868853 q^{63} +17.5033 q^{64} -1.22676 q^{65} -3.37261 q^{66} +6.96091 q^{67} +17.6824 q^{68} -7.87862 q^{69} -0.0597988 q^{70} -14.2913 q^{71} -11.7942 q^{72} +3.77596 q^{73} +19.0819 q^{74} +6.14582 q^{75} +7.91473 q^{76} +0.0617708 q^{77} -11.4187 q^{78} -4.66074 q^{79} -4.39375 q^{80} -2.80182 q^{81} -15.6045 q^{82} -9.72154 q^{83} -0.400660 q^{84} -1.24687 q^{85} +4.31159 q^{86} -3.34542 q^{87} +8.38506 q^{88} -1.46223 q^{89} +1.36167 q^{90} +0.209138 q^{91} +32.0709 q^{92} +3.98990 q^{93} -20.8439 q^{94} -0.558108 q^{95} -19.7279 q^{96} -9.53019 q^{97} -18.6922 q^{98} -1.40657 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + O(q^{10}) \) \( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.67178 1.88923 0.944615 0.328180i \(-0.106435\pi\)
0.944615 + 0.328180i \(0.106435\pi\)
\(3\) −1.26231 −0.728795 −0.364397 0.931244i \(-0.618725\pi\)
−0.364397 + 0.931244i \(0.618725\pi\)
\(4\) 5.13839 2.56919
\(5\) −0.362334 −0.162041 −0.0810203 0.996712i \(-0.525818\pi\)
−0.0810203 + 0.996712i \(0.525818\pi\)
\(6\) −3.37261 −1.37686
\(7\) 0.0617708 0.0233472 0.0116736 0.999932i \(-0.496284\pi\)
0.0116736 + 0.999932i \(0.496284\pi\)
\(8\) 8.38506 2.96457
\(9\) −1.40657 −0.468858
\(10\) −0.968075 −0.306132
\(11\) 1.00000 0.301511
\(12\) −6.48623 −1.87241
\(13\) 3.38570 0.939025 0.469513 0.882926i \(-0.344430\pi\)
0.469513 + 0.882926i \(0.344430\pi\)
\(14\) 0.165038 0.0441082
\(15\) 0.457377 0.118094
\(16\) 12.1262 3.03156
\(17\) 3.44123 0.834621 0.417310 0.908764i \(-0.362973\pi\)
0.417310 + 0.908764i \(0.362973\pi\)
\(18\) −3.75805 −0.885781
\(19\) 1.54031 0.353372 0.176686 0.984267i \(-0.443462\pi\)
0.176686 + 0.984267i \(0.443462\pi\)
\(20\) −1.86181 −0.416314
\(21\) −0.0779739 −0.0170153
\(22\) 2.67178 0.569625
\(23\) 6.24144 1.30143 0.650715 0.759322i \(-0.274469\pi\)
0.650715 + 0.759322i \(0.274469\pi\)
\(24\) −10.5845 −2.16056
\(25\) −4.86871 −0.973743
\(26\) 9.04584 1.77404
\(27\) 5.56246 1.07050
\(28\) 0.317402 0.0599834
\(29\) 2.65024 0.492137 0.246068 0.969252i \(-0.420861\pi\)
0.246068 + 0.969252i \(0.420861\pi\)
\(30\) 1.22201 0.223107
\(31\) −3.16079 −0.567695 −0.283848 0.958869i \(-0.591611\pi\)
−0.283848 + 0.958869i \(0.591611\pi\)
\(32\) 15.6285 2.76275
\(33\) −1.26231 −0.219740
\(34\) 9.19419 1.57679
\(35\) −0.0223817 −0.00378319
\(36\) −7.22752 −1.20459
\(37\) 7.14203 1.17414 0.587071 0.809535i \(-0.300281\pi\)
0.587071 + 0.809535i \(0.300281\pi\)
\(38\) 4.11537 0.667602
\(39\) −4.27381 −0.684357
\(40\) −3.03819 −0.480380
\(41\) −5.84051 −0.912135 −0.456067 0.889945i \(-0.650742\pi\)
−0.456067 + 0.889945i \(0.650742\pi\)
\(42\) −0.208329 −0.0321458
\(43\) 1.61375 0.246095 0.123048 0.992401i \(-0.460733\pi\)
0.123048 + 0.992401i \(0.460733\pi\)
\(44\) 5.13839 0.774641
\(45\) 0.509650 0.0759741
\(46\) 16.6757 2.45870
\(47\) −7.80153 −1.13797 −0.568985 0.822348i \(-0.692664\pi\)
−0.568985 + 0.822348i \(0.692664\pi\)
\(48\) −15.3071 −2.20938
\(49\) −6.99618 −0.999455
\(50\) −13.0081 −1.83962
\(51\) −4.34390 −0.608267
\(52\) 17.3971 2.41254
\(53\) 4.33413 0.595338 0.297669 0.954669i \(-0.403791\pi\)
0.297669 + 0.954669i \(0.403791\pi\)
\(54\) 14.8616 2.02241
\(55\) −0.362334 −0.0488571
\(56\) 0.517952 0.0692143
\(57\) −1.94435 −0.257536
\(58\) 7.08084 0.929760
\(59\) −1.45377 −0.189265 −0.0946323 0.995512i \(-0.530168\pi\)
−0.0946323 + 0.995512i \(0.530168\pi\)
\(60\) 2.35018 0.303407
\(61\) −4.89476 −0.626710 −0.313355 0.949636i \(-0.601453\pi\)
−0.313355 + 0.949636i \(0.601453\pi\)
\(62\) −8.44493 −1.07251
\(63\) −0.0868853 −0.0109465
\(64\) 17.5033 2.18791
\(65\) −1.22676 −0.152160
\(66\) −3.37261 −0.415139
\(67\) 6.96091 0.850410 0.425205 0.905097i \(-0.360202\pi\)
0.425205 + 0.905097i \(0.360202\pi\)
\(68\) 17.6824 2.14430
\(69\) −7.87862 −0.948475
\(70\) −0.0597988 −0.00714732
\(71\) −14.2913 −1.69606 −0.848030 0.529949i \(-0.822211\pi\)
−0.848030 + 0.529949i \(0.822211\pi\)
\(72\) −11.7942 −1.38996
\(73\) 3.77596 0.441943 0.220971 0.975280i \(-0.429077\pi\)
0.220971 + 0.975280i \(0.429077\pi\)
\(74\) 19.0819 2.21823
\(75\) 6.14582 0.709659
\(76\) 7.91473 0.907882
\(77\) 0.0617708 0.00703944
\(78\) −11.4187 −1.29291
\(79\) −4.66074 −0.524374 −0.262187 0.965017i \(-0.584444\pi\)
−0.262187 + 0.965017i \(0.584444\pi\)
\(80\) −4.39375 −0.491236
\(81\) −2.80182 −0.311314
\(82\) −15.6045 −1.72323
\(83\) −9.72154 −1.06708 −0.533539 0.845776i \(-0.679138\pi\)
−0.533539 + 0.845776i \(0.679138\pi\)
\(84\) −0.400660 −0.0437156
\(85\) −1.24687 −0.135242
\(86\) 4.31159 0.464930
\(87\) −3.34542 −0.358667
\(88\) 8.38506 0.893851
\(89\) −1.46223 −0.154997 −0.0774983 0.996992i \(-0.524693\pi\)
−0.0774983 + 0.996992i \(0.524693\pi\)
\(90\) 1.36167 0.143533
\(91\) 0.209138 0.0219236
\(92\) 32.0709 3.34362
\(93\) 3.98990 0.413733
\(94\) −20.8439 −2.14989
\(95\) −0.558108 −0.0572607
\(96\) −19.7279 −2.01348
\(97\) −9.53019 −0.967644 −0.483822 0.875166i \(-0.660752\pi\)
−0.483822 + 0.875166i \(0.660752\pi\)
\(98\) −18.6922 −1.88820
\(99\) −1.40657 −0.141366
\(100\) −25.0173 −2.50173
\(101\) −1.26659 −0.126031 −0.0630153 0.998013i \(-0.520072\pi\)
−0.0630153 + 0.998013i \(0.520072\pi\)
\(102\) −11.6059 −1.14916
\(103\) 5.89359 0.580712 0.290356 0.956919i \(-0.406226\pi\)
0.290356 + 0.956919i \(0.406226\pi\)
\(104\) 28.3893 2.78380
\(105\) 0.0282526 0.00275717
\(106\) 11.5798 1.12473
\(107\) −0.264352 −0.0255559 −0.0127779 0.999918i \(-0.504067\pi\)
−0.0127779 + 0.999918i \(0.504067\pi\)
\(108\) 28.5821 2.75031
\(109\) −7.24105 −0.693566 −0.346783 0.937945i \(-0.612726\pi\)
−0.346783 + 0.937945i \(0.612726\pi\)
\(110\) −0.968075 −0.0923023
\(111\) −9.01545 −0.855709
\(112\) 0.749048 0.0707784
\(113\) 4.51580 0.424811 0.212405 0.977182i \(-0.431870\pi\)
0.212405 + 0.977182i \(0.431870\pi\)
\(114\) −5.19488 −0.486545
\(115\) −2.26148 −0.210884
\(116\) 13.6179 1.26439
\(117\) −4.76225 −0.440270
\(118\) −3.88414 −0.357564
\(119\) 0.212568 0.0194860
\(120\) 3.83514 0.350099
\(121\) 1.00000 0.0909091
\(122\) −13.0777 −1.18400
\(123\) 7.37253 0.664759
\(124\) −16.2414 −1.45852
\(125\) 3.57577 0.319827
\(126\) −0.232138 −0.0206805
\(127\) 15.5630 1.38099 0.690495 0.723337i \(-0.257393\pi\)
0.690495 + 0.723337i \(0.257393\pi\)
\(128\) 15.5079 1.37072
\(129\) −2.03706 −0.179353
\(130\) −3.27761 −0.287466
\(131\) −1.00000 −0.0873704
\(132\) −6.48623 −0.564554
\(133\) 0.0951465 0.00825025
\(134\) 18.5980 1.60662
\(135\) −2.01547 −0.173464
\(136\) 28.8549 2.47429
\(137\) 10.5481 0.901189 0.450594 0.892729i \(-0.351212\pi\)
0.450594 + 0.892729i \(0.351212\pi\)
\(138\) −21.0499 −1.79189
\(139\) −10.3031 −0.873897 −0.436949 0.899486i \(-0.643941\pi\)
−0.436949 + 0.899486i \(0.643941\pi\)
\(140\) −0.115006 −0.00971975
\(141\) 9.84795 0.829347
\(142\) −38.1830 −3.20425
\(143\) 3.38570 0.283127
\(144\) −17.0565 −1.42137
\(145\) −0.960271 −0.0797461
\(146\) 10.0885 0.834932
\(147\) 8.83135 0.728397
\(148\) 36.6985 3.01660
\(149\) −20.3503 −1.66716 −0.833580 0.552398i \(-0.813713\pi\)
−0.833580 + 0.552398i \(0.813713\pi\)
\(150\) 16.4203 1.34071
\(151\) 6.64718 0.540940 0.270470 0.962728i \(-0.412821\pi\)
0.270470 + 0.962728i \(0.412821\pi\)
\(152\) 12.9156 1.04760
\(153\) −4.84035 −0.391319
\(154\) 0.165038 0.0132991
\(155\) 1.14526 0.0919897
\(156\) −21.9605 −1.75824
\(157\) −20.1466 −1.60788 −0.803938 0.594713i \(-0.797266\pi\)
−0.803938 + 0.594713i \(0.797266\pi\)
\(158\) −12.4525 −0.990664
\(159\) −5.47101 −0.433879
\(160\) −5.66272 −0.447677
\(161\) 0.385539 0.0303847
\(162\) −7.48584 −0.588143
\(163\) 12.8598 1.00726 0.503630 0.863919i \(-0.331997\pi\)
0.503630 + 0.863919i \(0.331997\pi\)
\(164\) −30.0108 −2.34345
\(165\) 0.457377 0.0356068
\(166\) −25.9738 −2.01596
\(167\) −15.5537 −1.20358 −0.601792 0.798653i \(-0.705547\pi\)
−0.601792 + 0.798653i \(0.705547\pi\)
\(168\) −0.653816 −0.0504430
\(169\) −1.53701 −0.118231
\(170\) −3.33137 −0.255504
\(171\) −2.16657 −0.165682
\(172\) 8.29209 0.632266
\(173\) −12.1416 −0.923108 −0.461554 0.887112i \(-0.652708\pi\)
−0.461554 + 0.887112i \(0.652708\pi\)
\(174\) −8.93821 −0.677604
\(175\) −0.300745 −0.0227342
\(176\) 12.1262 0.914049
\(177\) 1.83511 0.137935
\(178\) −3.90676 −0.292824
\(179\) 23.2337 1.73657 0.868284 0.496067i \(-0.165223\pi\)
0.868284 + 0.496067i \(0.165223\pi\)
\(180\) 2.61878 0.195192
\(181\) 2.82673 0.210109 0.105054 0.994466i \(-0.466498\pi\)
0.105054 + 0.994466i \(0.466498\pi\)
\(182\) 0.558769 0.0414187
\(183\) 6.17871 0.456743
\(184\) 52.3348 3.85818
\(185\) −2.58780 −0.190259
\(186\) 10.6601 0.781638
\(187\) 3.44123 0.251648
\(188\) −40.0873 −2.92367
\(189\) 0.343598 0.0249931
\(190\) −1.49114 −0.108179
\(191\) −3.83470 −0.277469 −0.138735 0.990330i \(-0.544304\pi\)
−0.138735 + 0.990330i \(0.544304\pi\)
\(192\) −22.0945 −1.59454
\(193\) −14.3896 −1.03578 −0.517892 0.855446i \(-0.673283\pi\)
−0.517892 + 0.855446i \(0.673283\pi\)
\(194\) −25.4625 −1.82810
\(195\) 1.54854 0.110894
\(196\) −35.9491 −2.56779
\(197\) 5.58262 0.397745 0.198873 0.980025i \(-0.436272\pi\)
0.198873 + 0.980025i \(0.436272\pi\)
\(198\) −3.75805 −0.267073
\(199\) −11.1174 −0.788094 −0.394047 0.919090i \(-0.628925\pi\)
−0.394047 + 0.919090i \(0.628925\pi\)
\(200\) −40.8245 −2.88673
\(201\) −8.78682 −0.619775
\(202\) −3.38405 −0.238101
\(203\) 0.163707 0.0114900
\(204\) −22.3206 −1.56276
\(205\) 2.11622 0.147803
\(206\) 15.7463 1.09710
\(207\) −8.77905 −0.610186
\(208\) 41.0558 2.84671
\(209\) 1.54031 0.106546
\(210\) 0.0754846 0.00520893
\(211\) 8.83808 0.608438 0.304219 0.952602i \(-0.401604\pi\)
0.304219 + 0.952602i \(0.401604\pi\)
\(212\) 22.2704 1.52954
\(213\) 18.0400 1.23608
\(214\) −0.706290 −0.0482810
\(215\) −0.584717 −0.0398774
\(216\) 46.6416 3.17356
\(217\) −0.195245 −0.0132541
\(218\) −19.3465 −1.31031
\(219\) −4.76643 −0.322086
\(220\) −1.86181 −0.125523
\(221\) 11.6510 0.783730
\(222\) −24.0873 −1.61663
\(223\) −2.75777 −0.184674 −0.0923370 0.995728i \(-0.529434\pi\)
−0.0923370 + 0.995728i \(0.529434\pi\)
\(224\) 0.965383 0.0645024
\(225\) 6.84821 0.456547
\(226\) 12.0652 0.802565
\(227\) 20.2075 1.34122 0.670609 0.741811i \(-0.266033\pi\)
0.670609 + 0.741811i \(0.266033\pi\)
\(228\) −9.99084 −0.661659
\(229\) 16.9438 1.11968 0.559840 0.828601i \(-0.310863\pi\)
0.559840 + 0.828601i \(0.310863\pi\)
\(230\) −6.04218 −0.398409
\(231\) −0.0779739 −0.00513031
\(232\) 22.2224 1.45897
\(233\) −18.2780 −1.19743 −0.598717 0.800960i \(-0.704323\pi\)
−0.598717 + 0.800960i \(0.704323\pi\)
\(234\) −12.7237 −0.831771
\(235\) 2.82676 0.184397
\(236\) −7.47002 −0.486257
\(237\) 5.88330 0.382161
\(238\) 0.567933 0.0368136
\(239\) −3.51197 −0.227170 −0.113585 0.993528i \(-0.536234\pi\)
−0.113585 + 0.993528i \(0.536234\pi\)
\(240\) 5.54627 0.358010
\(241\) −12.8997 −0.830944 −0.415472 0.909606i \(-0.636384\pi\)
−0.415472 + 0.909606i \(0.636384\pi\)
\(242\) 2.67178 0.171748
\(243\) −13.1506 −0.843612
\(244\) −25.1512 −1.61014
\(245\) 2.53495 0.161952
\(246\) 19.6978 1.25588
\(247\) 5.21505 0.331826
\(248\) −26.5035 −1.68297
\(249\) 12.2716 0.777681
\(250\) 9.55365 0.604226
\(251\) 26.6418 1.68162 0.840808 0.541333i \(-0.182080\pi\)
0.840808 + 0.541333i \(0.182080\pi\)
\(252\) −0.446450 −0.0281237
\(253\) 6.24144 0.392396
\(254\) 41.5808 2.60901
\(255\) 1.57394 0.0985640
\(256\) 6.42704 0.401690
\(257\) 8.17989 0.510248 0.255124 0.966908i \(-0.417884\pi\)
0.255124 + 0.966908i \(0.417884\pi\)
\(258\) −5.44256 −0.338839
\(259\) 0.441169 0.0274129
\(260\) −6.30354 −0.390929
\(261\) −3.72776 −0.230742
\(262\) −2.67178 −0.165063
\(263\) 25.5379 1.57474 0.787368 0.616484i \(-0.211443\pi\)
0.787368 + 0.616484i \(0.211443\pi\)
\(264\) −10.5845 −0.651434
\(265\) −1.57040 −0.0964689
\(266\) 0.254210 0.0155866
\(267\) 1.84579 0.112961
\(268\) 35.7678 2.18487
\(269\) −29.3129 −1.78724 −0.893618 0.448827i \(-0.851842\pi\)
−0.893618 + 0.448827i \(0.851842\pi\)
\(270\) −5.38488 −0.327713
\(271\) 6.23258 0.378602 0.189301 0.981919i \(-0.439378\pi\)
0.189301 + 0.981919i \(0.439378\pi\)
\(272\) 41.7292 2.53020
\(273\) −0.263997 −0.0159778
\(274\) 28.1823 1.70255
\(275\) −4.86871 −0.293595
\(276\) −40.4834 −2.43682
\(277\) −7.20129 −0.432683 −0.216342 0.976318i \(-0.569413\pi\)
−0.216342 + 0.976318i \(0.569413\pi\)
\(278\) −27.5276 −1.65099
\(279\) 4.44589 0.266169
\(280\) −0.187672 −0.0112155
\(281\) 15.6597 0.934182 0.467091 0.884209i \(-0.345302\pi\)
0.467091 + 0.884209i \(0.345302\pi\)
\(282\) 26.3115 1.56683
\(283\) −13.0602 −0.776348 −0.388174 0.921586i \(-0.626894\pi\)
−0.388174 + 0.921586i \(0.626894\pi\)
\(284\) −73.4340 −4.35750
\(285\) 0.704505 0.0417313
\(286\) 9.04584 0.534892
\(287\) −0.360773 −0.0212958
\(288\) −21.9826 −1.29534
\(289\) −5.15794 −0.303408
\(290\) −2.56563 −0.150659
\(291\) 12.0300 0.705214
\(292\) 19.4023 1.13544
\(293\) −12.0268 −0.702612 −0.351306 0.936261i \(-0.614262\pi\)
−0.351306 + 0.936261i \(0.614262\pi\)
\(294\) 23.5954 1.37611
\(295\) 0.526749 0.0306685
\(296\) 59.8864 3.48082
\(297\) 5.56246 0.322767
\(298\) −54.3714 −3.14965
\(299\) 21.1317 1.22208
\(300\) 31.5796 1.82325
\(301\) 0.0996829 0.00574563
\(302\) 17.7598 1.02196
\(303\) 1.59883 0.0918505
\(304\) 18.6782 1.07127
\(305\) 1.77354 0.101553
\(306\) −12.9323 −0.739292
\(307\) −9.02517 −0.515093 −0.257547 0.966266i \(-0.582914\pi\)
−0.257547 + 0.966266i \(0.582914\pi\)
\(308\) 0.317402 0.0180857
\(309\) −7.43953 −0.423220
\(310\) 3.05989 0.173790
\(311\) 20.4716 1.16084 0.580418 0.814319i \(-0.302889\pi\)
0.580418 + 0.814319i \(0.302889\pi\)
\(312\) −35.8361 −2.02882
\(313\) −19.9927 −1.13005 −0.565026 0.825073i \(-0.691134\pi\)
−0.565026 + 0.825073i \(0.691134\pi\)
\(314\) −53.8273 −3.03765
\(315\) 0.0314815 0.00177378
\(316\) −23.9487 −1.34722
\(317\) 11.4354 0.642275 0.321138 0.947033i \(-0.395935\pi\)
0.321138 + 0.947033i \(0.395935\pi\)
\(318\) −14.6173 −0.819698
\(319\) 2.65024 0.148385
\(320\) −6.34202 −0.354530
\(321\) 0.333694 0.0186250
\(322\) 1.03007 0.0574037
\(323\) 5.30057 0.294932
\(324\) −14.3968 −0.799825
\(325\) −16.4840 −0.914369
\(326\) 34.3586 1.90295
\(327\) 9.14044 0.505468
\(328\) −48.9731 −2.70409
\(329\) −0.481907 −0.0265684
\(330\) 1.22201 0.0672694
\(331\) −11.3434 −0.623488 −0.311744 0.950166i \(-0.600913\pi\)
−0.311744 + 0.950166i \(0.600913\pi\)
\(332\) −49.9530 −2.74153
\(333\) −10.0458 −0.550506
\(334\) −41.5561 −2.27385
\(335\) −2.52217 −0.137801
\(336\) −0.945530 −0.0515829
\(337\) 19.1201 1.04154 0.520768 0.853698i \(-0.325646\pi\)
0.520768 + 0.853698i \(0.325646\pi\)
\(338\) −4.10654 −0.223366
\(339\) −5.70034 −0.309600
\(340\) −6.40692 −0.347464
\(341\) −3.16079 −0.171167
\(342\) −5.78858 −0.313011
\(343\) −0.864556 −0.0466816
\(344\) 13.5314 0.729565
\(345\) 2.85469 0.153691
\(346\) −32.4396 −1.74396
\(347\) −28.1563 −1.51151 −0.755756 0.654854i \(-0.772730\pi\)
−0.755756 + 0.654854i \(0.772730\pi\)
\(348\) −17.1901 −0.921484
\(349\) −3.42026 −0.183083 −0.0915413 0.995801i \(-0.529179\pi\)
−0.0915413 + 0.995801i \(0.529179\pi\)
\(350\) −0.803522 −0.0429501
\(351\) 18.8328 1.00522
\(352\) 15.6285 0.833000
\(353\) 14.7900 0.787193 0.393596 0.919283i \(-0.371231\pi\)
0.393596 + 0.919283i \(0.371231\pi\)
\(354\) 4.90299 0.260591
\(355\) 5.17820 0.274831
\(356\) −7.51352 −0.398216
\(357\) −0.268326 −0.0142013
\(358\) 62.0752 3.28078
\(359\) 36.3037 1.91604 0.958019 0.286706i \(-0.0925604\pi\)
0.958019 + 0.286706i \(0.0925604\pi\)
\(360\) 4.27344 0.225230
\(361\) −16.6274 −0.875128
\(362\) 7.55238 0.396944
\(363\) −1.26231 −0.0662541
\(364\) 1.07463 0.0563260
\(365\) −1.36816 −0.0716127
\(366\) 16.5081 0.862893
\(367\) −13.9395 −0.727637 −0.363819 0.931470i \(-0.618527\pi\)
−0.363819 + 0.931470i \(0.618527\pi\)
\(368\) 75.6851 3.94536
\(369\) 8.21512 0.427662
\(370\) −6.91402 −0.359443
\(371\) 0.267723 0.0138995
\(372\) 20.5017 1.06296
\(373\) −36.1906 −1.87388 −0.936939 0.349493i \(-0.886354\pi\)
−0.936939 + 0.349493i \(0.886354\pi\)
\(374\) 9.19419 0.475420
\(375\) −4.51373 −0.233088
\(376\) −65.4163 −3.37359
\(377\) 8.97292 0.462129
\(378\) 0.918017 0.0472177
\(379\) −26.4443 −1.35835 −0.679175 0.733976i \(-0.737662\pi\)
−0.679175 + 0.733976i \(0.737662\pi\)
\(380\) −2.86777 −0.147114
\(381\) −19.6453 −1.00646
\(382\) −10.2455 −0.524203
\(383\) −22.1632 −1.13249 −0.566244 0.824238i \(-0.691604\pi\)
−0.566244 + 0.824238i \(0.691604\pi\)
\(384\) −19.5757 −0.998970
\(385\) −0.0223817 −0.00114068
\(386\) −38.4457 −1.95684
\(387\) −2.26986 −0.115384
\(388\) −48.9698 −2.48606
\(389\) 7.43397 0.376917 0.188459 0.982081i \(-0.439651\pi\)
0.188459 + 0.982081i \(0.439651\pi\)
\(390\) 4.13736 0.209504
\(391\) 21.4782 1.08620
\(392\) −58.6634 −2.96295
\(393\) 1.26231 0.0636751
\(394\) 14.9155 0.751433
\(395\) 1.68874 0.0849699
\(396\) −7.22752 −0.363197
\(397\) 32.7419 1.64327 0.821634 0.570016i \(-0.193063\pi\)
0.821634 + 0.570016i \(0.193063\pi\)
\(398\) −29.7033 −1.48889
\(399\) −0.120104 −0.00601274
\(400\) −59.0392 −2.95196
\(401\) −10.0162 −0.500188 −0.250094 0.968222i \(-0.580461\pi\)
−0.250094 + 0.968222i \(0.580461\pi\)
\(402\) −23.4764 −1.17090
\(403\) −10.7015 −0.533080
\(404\) −6.50824 −0.323797
\(405\) 1.01520 0.0504455
\(406\) 0.437389 0.0217073
\(407\) 7.14203 0.354017
\(408\) −36.4238 −1.80325
\(409\) 18.2136 0.900605 0.450302 0.892876i \(-0.351316\pi\)
0.450302 + 0.892876i \(0.351316\pi\)
\(410\) 5.65405 0.279234
\(411\) −13.3150 −0.656782
\(412\) 30.2835 1.49196
\(413\) −0.0898005 −0.00441879
\(414\) −23.4556 −1.15278
\(415\) 3.52244 0.172910
\(416\) 52.9133 2.59429
\(417\) 13.0057 0.636892
\(418\) 4.11537 0.201290
\(419\) 17.2145 0.840981 0.420491 0.907297i \(-0.361858\pi\)
0.420491 + 0.907297i \(0.361858\pi\)
\(420\) 0.145173 0.00708370
\(421\) −14.0564 −0.685065 −0.342532 0.939506i \(-0.611285\pi\)
−0.342532 + 0.939506i \(0.611285\pi\)
\(422\) 23.6134 1.14948
\(423\) 10.9734 0.533547
\(424\) 36.3419 1.76492
\(425\) −16.7544 −0.812706
\(426\) 48.1988 2.33524
\(427\) −0.302354 −0.0146319
\(428\) −1.35834 −0.0656580
\(429\) −4.27381 −0.206341
\(430\) −1.56223 −0.0753376
\(431\) 2.13221 0.102705 0.0513525 0.998681i \(-0.483647\pi\)
0.0513525 + 0.998681i \(0.483647\pi\)
\(432\) 67.4517 3.24527
\(433\) 18.0792 0.868830 0.434415 0.900713i \(-0.356955\pi\)
0.434415 + 0.900713i \(0.356955\pi\)
\(434\) −0.521651 −0.0250400
\(435\) 1.21216 0.0581186
\(436\) −37.2073 −1.78191
\(437\) 9.61377 0.459889
\(438\) −12.7348 −0.608494
\(439\) −15.4440 −0.737103 −0.368552 0.929607i \(-0.620146\pi\)
−0.368552 + 0.929607i \(0.620146\pi\)
\(440\) −3.03819 −0.144840
\(441\) 9.84066 0.468603
\(442\) 31.1288 1.48065
\(443\) 5.61909 0.266971 0.133485 0.991051i \(-0.457383\pi\)
0.133485 + 0.991051i \(0.457383\pi\)
\(444\) −46.3249 −2.19848
\(445\) 0.529817 0.0251157
\(446\) −7.36814 −0.348892
\(447\) 25.6884 1.21502
\(448\) 1.08119 0.0510815
\(449\) 39.2975 1.85457 0.927283 0.374362i \(-0.122138\pi\)
0.927283 + 0.374362i \(0.122138\pi\)
\(450\) 18.2969 0.862523
\(451\) −5.84051 −0.275019
\(452\) 23.2039 1.09142
\(453\) −8.39080 −0.394234
\(454\) 53.9898 2.53387
\(455\) −0.0757777 −0.00355251
\(456\) −16.3035 −0.763482
\(457\) 36.8812 1.72523 0.862616 0.505860i \(-0.168825\pi\)
0.862616 + 0.505860i \(0.168825\pi\)
\(458\) 45.2701 2.11533
\(459\) 19.1417 0.893458
\(460\) −11.6204 −0.541803
\(461\) 15.6920 0.730848 0.365424 0.930841i \(-0.380924\pi\)
0.365424 + 0.930841i \(0.380924\pi\)
\(462\) −0.208329 −0.00969234
\(463\) 18.5445 0.861835 0.430918 0.902391i \(-0.358190\pi\)
0.430918 + 0.902391i \(0.358190\pi\)
\(464\) 32.1374 1.49194
\(465\) −1.44568 −0.0670416
\(466\) −48.8348 −2.26223
\(467\) 34.4834 1.59570 0.797850 0.602856i \(-0.205971\pi\)
0.797850 + 0.602856i \(0.205971\pi\)
\(468\) −24.4703 −1.13114
\(469\) 0.429981 0.0198547
\(470\) 7.55247 0.348369
\(471\) 25.4313 1.17181
\(472\) −12.1899 −0.561087
\(473\) 1.61375 0.0742005
\(474\) 15.7188 0.721991
\(475\) −7.49935 −0.344094
\(476\) 1.09225 0.0500634
\(477\) −6.09627 −0.279129
\(478\) −9.38320 −0.429177
\(479\) 26.9256 1.23026 0.615131 0.788425i \(-0.289103\pi\)
0.615131 + 0.788425i \(0.289103\pi\)
\(480\) 7.14810 0.326265
\(481\) 24.1808 1.10255
\(482\) −34.4652 −1.56985
\(483\) −0.486669 −0.0221442
\(484\) 5.13839 0.233563
\(485\) 3.45311 0.156798
\(486\) −35.1355 −1.59378
\(487\) −1.22364 −0.0554485 −0.0277243 0.999616i \(-0.508826\pi\)
−0.0277243 + 0.999616i \(0.508826\pi\)
\(488\) −41.0429 −1.85792
\(489\) −16.2331 −0.734086
\(490\) 6.77283 0.305965
\(491\) 14.2588 0.643490 0.321745 0.946826i \(-0.395731\pi\)
0.321745 + 0.946826i \(0.395731\pi\)
\(492\) 37.8829 1.70789
\(493\) 9.12008 0.410748
\(494\) 13.9334 0.626895
\(495\) 0.509650 0.0229070
\(496\) −38.3285 −1.72100
\(497\) −0.882783 −0.0395982
\(498\) 32.7869 1.46922
\(499\) −36.6354 −1.64003 −0.820014 0.572344i \(-0.806034\pi\)
−0.820014 + 0.572344i \(0.806034\pi\)
\(500\) 18.3737 0.821696
\(501\) 19.6336 0.877166
\(502\) 71.1810 3.17696
\(503\) 13.1902 0.588124 0.294062 0.955786i \(-0.404993\pi\)
0.294062 + 0.955786i \(0.404993\pi\)
\(504\) −0.728539 −0.0324517
\(505\) 0.458929 0.0204221
\(506\) 16.6757 0.741326
\(507\) 1.94018 0.0861663
\(508\) 79.9686 3.54803
\(509\) −24.5919 −1.09002 −0.545009 0.838430i \(-0.683474\pi\)
−0.545009 + 0.838430i \(0.683474\pi\)
\(510\) 4.20522 0.186210
\(511\) 0.233244 0.0103181
\(512\) −13.8441 −0.611831
\(513\) 8.56794 0.378284
\(514\) 21.8548 0.963975
\(515\) −2.13545 −0.0940990
\(516\) −10.4672 −0.460792
\(517\) −7.80153 −0.343111
\(518\) 1.17871 0.0517893
\(519\) 15.3264 0.672756
\(520\) −10.2864 −0.451089
\(521\) −3.13351 −0.137282 −0.0686409 0.997641i \(-0.521866\pi\)
−0.0686409 + 0.997641i \(0.521866\pi\)
\(522\) −9.95973 −0.435926
\(523\) 4.59195 0.200792 0.100396 0.994948i \(-0.467989\pi\)
0.100396 + 0.994948i \(0.467989\pi\)
\(524\) −5.13839 −0.224471
\(525\) 0.379633 0.0165685
\(526\) 68.2316 2.97504
\(527\) −10.8770 −0.473810
\(528\) −15.3071 −0.666154
\(529\) 15.9555 0.693719
\(530\) −4.19576 −0.182252
\(531\) 2.04483 0.0887382
\(532\) 0.488899 0.0211965
\(533\) −19.7742 −0.856518
\(534\) 4.93154 0.213409
\(535\) 0.0957837 0.00414109
\(536\) 58.3677 2.52110
\(537\) −29.3281 −1.26560
\(538\) −78.3174 −3.37650
\(539\) −6.99618 −0.301347
\(540\) −10.3563 −0.445662
\(541\) 0.197899 0.00850833 0.00425417 0.999991i \(-0.498646\pi\)
0.00425417 + 0.999991i \(0.498646\pi\)
\(542\) 16.6521 0.715267
\(543\) −3.56820 −0.153126
\(544\) 53.7811 2.30585
\(545\) 2.62368 0.112386
\(546\) −0.705340 −0.0301858
\(547\) 28.9378 1.23729 0.618646 0.785670i \(-0.287682\pi\)
0.618646 + 0.785670i \(0.287682\pi\)
\(548\) 54.2004 2.31533
\(549\) 6.88485 0.293838
\(550\) −13.0081 −0.554668
\(551\) 4.08220 0.173907
\(552\) −66.0628 −2.81182
\(553\) −0.287898 −0.0122427
\(554\) −19.2402 −0.817439
\(555\) 3.26660 0.138660
\(556\) −52.9413 −2.24521
\(557\) 21.1726 0.897112 0.448556 0.893755i \(-0.351938\pi\)
0.448556 + 0.893755i \(0.351938\pi\)
\(558\) 11.8784 0.502854
\(559\) 5.46369 0.231090
\(560\) −0.271405 −0.0114690
\(561\) −4.34390 −0.183399
\(562\) 41.8393 1.76489
\(563\) −12.3698 −0.521323 −0.260662 0.965430i \(-0.583941\pi\)
−0.260662 + 0.965430i \(0.583941\pi\)
\(564\) 50.6026 2.13075
\(565\) −1.63623 −0.0688366
\(566\) −34.8939 −1.46670
\(567\) −0.173071 −0.00726830
\(568\) −119.833 −5.02808
\(569\) −14.2348 −0.596754 −0.298377 0.954448i \(-0.596445\pi\)
−0.298377 + 0.954448i \(0.596445\pi\)
\(570\) 1.88228 0.0788400
\(571\) 9.07399 0.379735 0.189867 0.981810i \(-0.439194\pi\)
0.189867 + 0.981810i \(0.439194\pi\)
\(572\) 17.3971 0.727407
\(573\) 4.84058 0.202218
\(574\) −0.963906 −0.0402326
\(575\) −30.3878 −1.26726
\(576\) −24.6196 −1.02582
\(577\) 25.6025 1.06585 0.532923 0.846164i \(-0.321094\pi\)
0.532923 + 0.846164i \(0.321094\pi\)
\(578\) −13.7809 −0.573208
\(579\) 18.1641 0.754874
\(580\) −4.93424 −0.204883
\(581\) −0.600508 −0.0249133
\(582\) 32.1416 1.33231
\(583\) 4.33413 0.179501
\(584\) 31.6617 1.31017
\(585\) 1.72552 0.0713416
\(586\) −32.1328 −1.32740
\(587\) 29.8738 1.23302 0.616512 0.787345i \(-0.288545\pi\)
0.616512 + 0.787345i \(0.288545\pi\)
\(588\) 45.3789 1.87139
\(589\) −4.86862 −0.200608
\(590\) 1.40736 0.0579400
\(591\) −7.04700 −0.289875
\(592\) 86.6059 3.55948
\(593\) −38.9969 −1.60141 −0.800705 0.599059i \(-0.795542\pi\)
−0.800705 + 0.599059i \(0.795542\pi\)
\(594\) 14.8616 0.609781
\(595\) −0.0770205 −0.00315753
\(596\) −104.568 −4.28326
\(597\) 14.0336 0.574359
\(598\) 56.4591 2.30878
\(599\) 29.4681 1.20403 0.602017 0.798483i \(-0.294364\pi\)
0.602017 + 0.798483i \(0.294364\pi\)
\(600\) 51.5331 2.10383
\(601\) 5.41893 0.221043 0.110521 0.993874i \(-0.464748\pi\)
0.110521 + 0.993874i \(0.464748\pi\)
\(602\) 0.266330 0.0108548
\(603\) −9.79104 −0.398722
\(604\) 34.1558 1.38978
\(605\) −0.362334 −0.0147310
\(606\) 4.27172 0.173527
\(607\) −5.67374 −0.230290 −0.115145 0.993349i \(-0.536733\pi\)
−0.115145 + 0.993349i \(0.536733\pi\)
\(608\) 24.0727 0.976278
\(609\) −0.206649 −0.00837386
\(610\) 4.73850 0.191856
\(611\) −26.4137 −1.06858
\(612\) −24.8716 −1.00537
\(613\) 6.79571 0.274476 0.137238 0.990538i \(-0.456177\pi\)
0.137238 + 0.990538i \(0.456177\pi\)
\(614\) −24.1132 −0.973130
\(615\) −2.67132 −0.107718
\(616\) 0.517952 0.0208689
\(617\) 9.85497 0.396746 0.198373 0.980127i \(-0.436434\pi\)
0.198373 + 0.980127i \(0.436434\pi\)
\(618\) −19.8768 −0.799560
\(619\) 8.89018 0.357327 0.178663 0.983910i \(-0.442823\pi\)
0.178663 + 0.983910i \(0.442823\pi\)
\(620\) 5.88480 0.236339
\(621\) 34.7177 1.39318
\(622\) 54.6954 2.19309
\(623\) −0.0903234 −0.00361873
\(624\) −51.8252 −2.07467
\(625\) 23.0479 0.921918
\(626\) −53.4159 −2.13493
\(627\) −1.94435 −0.0776500
\(628\) −103.521 −4.13094
\(629\) 24.5774 0.979964
\(630\) 0.0841115 0.00335108
\(631\) −15.4776 −0.616153 −0.308076 0.951362i \(-0.599685\pi\)
−0.308076 + 0.951362i \(0.599685\pi\)
\(632\) −39.0806 −1.55454
\(633\) −11.1564 −0.443427
\(634\) 30.5528 1.21341
\(635\) −5.63899 −0.223777
\(636\) −28.1122 −1.11472
\(637\) −23.6870 −0.938514
\(638\) 7.08084 0.280333
\(639\) 20.1017 0.795212
\(640\) −5.61903 −0.222112
\(641\) −28.2724 −1.11669 −0.558346 0.829608i \(-0.688564\pi\)
−0.558346 + 0.829608i \(0.688564\pi\)
\(642\) 0.891556 0.0351869
\(643\) 11.3126 0.446124 0.223062 0.974804i \(-0.428395\pi\)
0.223062 + 0.974804i \(0.428395\pi\)
\(644\) 1.98105 0.0780642
\(645\) 0.738094 0.0290624
\(646\) 14.1619 0.557194
\(647\) 36.6234 1.43981 0.719907 0.694070i \(-0.244184\pi\)
0.719907 + 0.694070i \(0.244184\pi\)
\(648\) −23.4935 −0.922910
\(649\) −1.45377 −0.0570654
\(650\) −44.0416 −1.72745
\(651\) 0.246460 0.00965951
\(652\) 66.0788 2.58785
\(653\) −16.0980 −0.629964 −0.314982 0.949098i \(-0.601998\pi\)
−0.314982 + 0.949098i \(0.601998\pi\)
\(654\) 24.4212 0.954945
\(655\) 0.362334 0.0141576
\(656\) −70.8234 −2.76519
\(657\) −5.31117 −0.207209
\(658\) −1.28755 −0.0501939
\(659\) −26.1107 −1.01713 −0.508565 0.861024i \(-0.669824\pi\)
−0.508565 + 0.861024i \(0.669824\pi\)
\(660\) 2.35018 0.0914807
\(661\) 10.4885 0.407954 0.203977 0.978976i \(-0.434613\pi\)
0.203977 + 0.978976i \(0.434613\pi\)
\(662\) −30.3070 −1.17791
\(663\) −14.7072 −0.571178
\(664\) −81.5157 −3.16342
\(665\) −0.0344748 −0.00133688
\(666\) −26.8401 −1.04003
\(667\) 16.5413 0.640481
\(668\) −79.9211 −3.09224
\(669\) 3.48116 0.134589
\(670\) −6.73868 −0.260338
\(671\) −4.89476 −0.188960
\(672\) −1.21861 −0.0470090
\(673\) 0.717453 0.0276558 0.0138279 0.999904i \(-0.495598\pi\)
0.0138279 + 0.999904i \(0.495598\pi\)
\(674\) 51.0845 1.96770
\(675\) −27.0820 −1.04239
\(676\) −7.89773 −0.303759
\(677\) −47.4107 −1.82214 −0.911070 0.412251i \(-0.864743\pi\)
−0.911070 + 0.412251i \(0.864743\pi\)
\(678\) −15.2300 −0.584905
\(679\) −0.588688 −0.0225918
\(680\) −10.4551 −0.400935
\(681\) −25.5081 −0.977472
\(682\) −8.44493 −0.323373
\(683\) 11.7603 0.449997 0.224999 0.974359i \(-0.427762\pi\)
0.224999 + 0.974359i \(0.427762\pi\)
\(684\) −11.1327 −0.425668
\(685\) −3.82195 −0.146029
\(686\) −2.30990 −0.0881924
\(687\) −21.3884 −0.816017
\(688\) 19.5688 0.746052
\(689\) 14.6741 0.559038
\(690\) 7.62710 0.290359
\(691\) −51.2945 −1.95134 −0.975668 0.219254i \(-0.929638\pi\)
−0.975668 + 0.219254i \(0.929638\pi\)
\(692\) −62.3882 −2.37164
\(693\) −0.0868853 −0.00330050
\(694\) −75.2274 −2.85559
\(695\) 3.73316 0.141607
\(696\) −28.0516 −1.06329
\(697\) −20.0985 −0.761287
\(698\) −9.13818 −0.345885
\(699\) 23.0726 0.872684
\(700\) −1.54534 −0.0584084
\(701\) 28.3838 1.07204 0.536021 0.844205i \(-0.319927\pi\)
0.536021 + 0.844205i \(0.319927\pi\)
\(702\) 50.3171 1.89910
\(703\) 11.0010 0.414909
\(704\) 17.5033 0.659679
\(705\) −3.56825 −0.134388
\(706\) 39.5156 1.48719
\(707\) −0.0782385 −0.00294246
\(708\) 9.42948 0.354382
\(709\) −2.57869 −0.0968448 −0.0484224 0.998827i \(-0.515419\pi\)
−0.0484224 + 0.998827i \(0.515419\pi\)
\(710\) 13.8350 0.519218
\(711\) 6.55568 0.245857
\(712\) −12.2609 −0.459498
\(713\) −19.7279 −0.738816
\(714\) −0.716907 −0.0268296
\(715\) −1.22676 −0.0458780
\(716\) 119.384 4.46158
\(717\) 4.43319 0.165561
\(718\) 96.9954 3.61984
\(719\) 5.68219 0.211910 0.105955 0.994371i \(-0.466210\pi\)
0.105955 + 0.994371i \(0.466210\pi\)
\(720\) 6.18013 0.230320
\(721\) 0.364052 0.0135580
\(722\) −44.4248 −1.65332
\(723\) 16.2834 0.605588
\(724\) 14.5248 0.539810
\(725\) −12.9032 −0.479215
\(726\) −3.37261 −0.125169
\(727\) 14.9429 0.554200 0.277100 0.960841i \(-0.410627\pi\)
0.277100 + 0.960841i \(0.410627\pi\)
\(728\) 1.75363 0.0649940
\(729\) 25.0056 0.926134
\(730\) −3.65541 −0.135293
\(731\) 5.55330 0.205396
\(732\) 31.7486 1.17346
\(733\) 4.57422 0.168953 0.0844763 0.996425i \(-0.473078\pi\)
0.0844763 + 0.996425i \(0.473078\pi\)
\(734\) −37.2433 −1.37468
\(735\) −3.19990 −0.118030
\(736\) 97.5440 3.59552
\(737\) 6.96091 0.256408
\(738\) 21.9490 0.807952
\(739\) 41.3271 1.52024 0.760120 0.649782i \(-0.225140\pi\)
0.760120 + 0.649782i \(0.225140\pi\)
\(740\) −13.2971 −0.488811
\(741\) −6.58300 −0.241833
\(742\) 0.715295 0.0262593
\(743\) −14.1869 −0.520466 −0.260233 0.965546i \(-0.583799\pi\)
−0.260233 + 0.965546i \(0.583799\pi\)
\(744\) 33.4556 1.22654
\(745\) 7.37360 0.270148
\(746\) −96.6932 −3.54019
\(747\) 13.6741 0.500308
\(748\) 17.6824 0.646531
\(749\) −0.0163293 −0.000596658 0
\(750\) −12.0597 −0.440357
\(751\) 7.69984 0.280971 0.140486 0.990083i \(-0.455134\pi\)
0.140486 + 0.990083i \(0.455134\pi\)
\(752\) −94.6032 −3.44982
\(753\) −33.6302 −1.22555
\(754\) 23.9736 0.873068
\(755\) −2.40850 −0.0876543
\(756\) 1.76554 0.0642120
\(757\) −21.2383 −0.771918 −0.385959 0.922516i \(-0.626129\pi\)
−0.385959 + 0.922516i \(0.626129\pi\)
\(758\) −70.6531 −2.56624
\(759\) −7.87862 −0.285976
\(760\) −4.67977 −0.169753
\(761\) −24.3557 −0.882893 −0.441447 0.897287i \(-0.645535\pi\)
−0.441447 + 0.897287i \(0.645535\pi\)
\(762\) −52.4878 −1.90143
\(763\) −0.447286 −0.0161928
\(764\) −19.7042 −0.712872
\(765\) 1.75382 0.0634096
\(766\) −59.2151 −2.13953
\(767\) −4.92203 −0.177724
\(768\) −8.11291 −0.292749
\(769\) −39.5851 −1.42747 −0.713737 0.700413i \(-0.752999\pi\)
−0.713737 + 0.700413i \(0.752999\pi\)
\(770\) −0.0597988 −0.00215500
\(771\) −10.3256 −0.371866
\(772\) −73.9392 −2.66113
\(773\) −38.8121 −1.39597 −0.697987 0.716110i \(-0.745921\pi\)
−0.697987 + 0.716110i \(0.745921\pi\)
\(774\) −6.06457 −0.217986
\(775\) 15.3890 0.552789
\(776\) −79.9112 −2.86865
\(777\) −0.556892 −0.0199784
\(778\) 19.8619 0.712083
\(779\) −8.99622 −0.322323
\(780\) 7.95702 0.284907
\(781\) −14.2913 −0.511381
\(782\) 57.3850 2.05208
\(783\) 14.7418 0.526830
\(784\) −84.8374 −3.02991
\(785\) 7.29981 0.260541
\(786\) 3.37261 0.120297
\(787\) 23.5647 0.839989 0.419995 0.907527i \(-0.362032\pi\)
0.419995 + 0.907527i \(0.362032\pi\)
\(788\) 28.6857 1.02188
\(789\) −32.2368 −1.14766
\(790\) 4.51194 0.160528
\(791\) 0.278945 0.00991813
\(792\) −11.7942 −0.419089
\(793\) −16.5722 −0.588497
\(794\) 87.4789 3.10451
\(795\) 1.98233 0.0703061
\(796\) −57.1257 −2.02477
\(797\) −0.201689 −0.00714420 −0.00357210 0.999994i \(-0.501137\pi\)
−0.00357210 + 0.999994i \(0.501137\pi\)
\(798\) −0.320892 −0.0113594
\(799\) −26.8469 −0.949774
\(800\) −76.0905 −2.69020
\(801\) 2.05674 0.0726714
\(802\) −26.7612 −0.944970
\(803\) 3.77596 0.133251
\(804\) −45.1501 −1.59232
\(805\) −0.139694 −0.00492356
\(806\) −28.5921 −1.00711
\(807\) 37.0019 1.30253
\(808\) −10.6205 −0.373626
\(809\) −22.7813 −0.800948 −0.400474 0.916308i \(-0.631155\pi\)
−0.400474 + 0.916308i \(0.631155\pi\)
\(810\) 2.71237 0.0953031
\(811\) 1.30949 0.0459825 0.0229912 0.999736i \(-0.492681\pi\)
0.0229912 + 0.999736i \(0.492681\pi\)
\(812\) 0.841192 0.0295200
\(813\) −7.86745 −0.275923
\(814\) 19.0819 0.668820
\(815\) −4.65955 −0.163217
\(816\) −52.6751 −1.84400
\(817\) 2.48569 0.0869632
\(818\) 48.6627 1.70145
\(819\) −0.294168 −0.0102791
\(820\) 10.8739 0.379734
\(821\) 14.0984 0.492039 0.246019 0.969265i \(-0.420877\pi\)
0.246019 + 0.969265i \(0.420877\pi\)
\(822\) −35.5748 −1.24081
\(823\) −5.57139 −0.194206 −0.0971032 0.995274i \(-0.530958\pi\)
−0.0971032 + 0.995274i \(0.530958\pi\)
\(824\) 49.4181 1.72156
\(825\) 6.14582 0.213970
\(826\) −0.239927 −0.00834812
\(827\) −28.5741 −0.993618 −0.496809 0.867860i \(-0.665495\pi\)
−0.496809 + 0.867860i \(0.665495\pi\)
\(828\) −45.1101 −1.56769
\(829\) 35.0682 1.21797 0.608984 0.793182i \(-0.291577\pi\)
0.608984 + 0.793182i \(0.291577\pi\)
\(830\) 9.41118 0.326667
\(831\) 9.09025 0.315337
\(832\) 59.2609 2.05450
\(833\) −24.0755 −0.834166
\(834\) 34.7483 1.20324
\(835\) 5.63565 0.195030
\(836\) 7.91473 0.273737
\(837\) −17.5818 −0.607716
\(838\) 45.9932 1.58881
\(839\) 27.3368 0.943771 0.471886 0.881660i \(-0.343574\pi\)
0.471886 + 0.881660i \(0.343574\pi\)
\(840\) 0.236900 0.00817382
\(841\) −21.9762 −0.757801
\(842\) −37.5554 −1.29425
\(843\) −19.7674 −0.680827
\(844\) 45.4134 1.56320
\(845\) 0.556910 0.0191583
\(846\) 29.3186 1.00799
\(847\) 0.0617708 0.00212247
\(848\) 52.5566 1.80480
\(849\) 16.4860 0.565798
\(850\) −44.7639 −1.53539
\(851\) 44.5765 1.52806
\(852\) 92.6964 3.17573
\(853\) −15.7514 −0.539316 −0.269658 0.962956i \(-0.586911\pi\)
−0.269658 + 0.962956i \(0.586911\pi\)
\(854\) −0.807821 −0.0276431
\(855\) 0.785020 0.0268471
\(856\) −2.21661 −0.0757622
\(857\) −35.0388 −1.19690 −0.598451 0.801159i \(-0.704217\pi\)
−0.598451 + 0.801159i \(0.704217\pi\)
\(858\) −11.4187 −0.389826
\(859\) −34.4884 −1.17673 −0.588365 0.808595i \(-0.700228\pi\)
−0.588365 + 0.808595i \(0.700228\pi\)
\(860\) −3.00450 −0.102453
\(861\) 0.455408 0.0155203
\(862\) 5.69680 0.194034
\(863\) 34.4711 1.17341 0.586705 0.809800i \(-0.300425\pi\)
0.586705 + 0.809800i \(0.300425\pi\)
\(864\) 86.9327 2.95751
\(865\) 4.39931 0.149581
\(866\) 48.3035 1.64142
\(867\) 6.51091 0.221122
\(868\) −1.00324 −0.0340523
\(869\) −4.66074 −0.158105
\(870\) 3.23862 0.109799
\(871\) 23.5676 0.798557
\(872\) −60.7166 −2.05612
\(873\) 13.4049 0.453688
\(874\) 25.6858 0.868837
\(875\) 0.220878 0.00746705
\(876\) −24.4918 −0.827500
\(877\) −45.0624 −1.52165 −0.760824 0.648958i \(-0.775205\pi\)
−0.760824 + 0.648958i \(0.775205\pi\)
\(878\) −41.2630 −1.39256
\(879\) 15.1815 0.512060
\(880\) −4.39375 −0.148113
\(881\) −8.59302 −0.289506 −0.144753 0.989468i \(-0.546239\pi\)
−0.144753 + 0.989468i \(0.546239\pi\)
\(882\) 26.2920 0.885299
\(883\) −31.6322 −1.06451 −0.532255 0.846584i \(-0.678655\pi\)
−0.532255 + 0.846584i \(0.678655\pi\)
\(884\) 59.8673 2.01355
\(885\) −0.664921 −0.0223511
\(886\) 15.0129 0.504370
\(887\) 39.2355 1.31740 0.658699 0.752406i \(-0.271107\pi\)
0.658699 + 0.752406i \(0.271107\pi\)
\(888\) −75.5951 −2.53681
\(889\) 0.961338 0.0322423
\(890\) 1.41555 0.0474494
\(891\) −2.80182 −0.0938646
\(892\) −14.1705 −0.474463
\(893\) −12.0168 −0.402127
\(894\) 68.6335 2.29545
\(895\) −8.41836 −0.281395
\(896\) 0.957934 0.0320023
\(897\) −26.6747 −0.890642
\(898\) 104.994 3.50370
\(899\) −8.37686 −0.279384
\(900\) 35.1887 1.17296
\(901\) 14.9147 0.496882
\(902\) −15.6045 −0.519574
\(903\) −0.125831 −0.00418738
\(904\) 37.8653 1.25938
\(905\) −1.02422 −0.0340462
\(906\) −22.4183 −0.744799
\(907\) 34.5977 1.14880 0.574398 0.818576i \(-0.305236\pi\)
0.574398 + 0.818576i \(0.305236\pi\)
\(908\) 103.834 3.44585
\(909\) 1.78156 0.0590905
\(910\) −0.202461 −0.00671152
\(911\) 25.4890 0.844488 0.422244 0.906482i \(-0.361243\pi\)
0.422244 + 0.906482i \(0.361243\pi\)
\(912\) −23.5777 −0.780735
\(913\) −9.72154 −0.321736
\(914\) 98.5384 3.25936
\(915\) −2.23875 −0.0740109
\(916\) 87.0640 2.87667
\(917\) −0.0617708 −0.00203985
\(918\) 51.1423 1.68795
\(919\) −8.12354 −0.267971 −0.133985 0.990983i \(-0.542778\pi\)
−0.133985 + 0.990983i \(0.542778\pi\)
\(920\) −18.9627 −0.625181
\(921\) 11.3926 0.375397
\(922\) 41.9255 1.38074
\(923\) −48.3860 −1.59264
\(924\) −0.400660 −0.0131807
\(925\) −34.7725 −1.14331
\(926\) 49.5467 1.62821
\(927\) −8.28977 −0.272272
\(928\) 41.4191 1.35965
\(929\) 31.9219 1.04732 0.523662 0.851926i \(-0.324565\pi\)
0.523662 + 0.851926i \(0.324565\pi\)
\(930\) −3.86252 −0.126657
\(931\) −10.7763 −0.353180
\(932\) −93.9197 −3.07644
\(933\) −25.8414 −0.846011
\(934\) 92.1318 3.01464
\(935\) −1.24687 −0.0407771
\(936\) −39.9317 −1.30521
\(937\) −17.9348 −0.585903 −0.292952 0.956127i \(-0.594637\pi\)
−0.292952 + 0.956127i \(0.594637\pi\)
\(938\) 1.14881 0.0375101
\(939\) 25.2369 0.823576
\(940\) 14.5250 0.473753
\(941\) 17.1106 0.557788 0.278894 0.960322i \(-0.410032\pi\)
0.278894 + 0.960322i \(0.410032\pi\)
\(942\) 67.9467 2.21382
\(943\) −36.4532 −1.18708
\(944\) −17.6287 −0.573767
\(945\) −0.124497 −0.00404989
\(946\) 4.31159 0.140182
\(947\) 17.0969 0.555575 0.277788 0.960643i \(-0.410399\pi\)
0.277788 + 0.960643i \(0.410399\pi\)
\(948\) 30.2306 0.981846
\(949\) 12.7843 0.414996
\(950\) −20.0366 −0.650072
\(951\) −14.4350 −0.468087
\(952\) 1.78239 0.0577677
\(953\) 26.4772 0.857679 0.428840 0.903381i \(-0.358923\pi\)
0.428840 + 0.903381i \(0.358923\pi\)
\(954\) −16.2879 −0.527339
\(955\) 1.38944 0.0449613
\(956\) −18.0459 −0.583645
\(957\) −3.34542 −0.108142
\(958\) 71.9391 2.32425
\(959\) 0.651568 0.0210402
\(960\) 8.00560 0.258379
\(961\) −21.0094 −0.677722
\(962\) 64.6057 2.08297
\(963\) 0.371831 0.0119821
\(964\) −66.2837 −2.13486
\(965\) 5.21383 0.167839
\(966\) −1.30027 −0.0418355
\(967\) 42.4478 1.36503 0.682514 0.730872i \(-0.260887\pi\)
0.682514 + 0.730872i \(0.260887\pi\)
\(968\) 8.38506 0.269506
\(969\) −6.69097 −0.214945
\(970\) 9.22593 0.296227
\(971\) −43.2156 −1.38685 −0.693427 0.720527i \(-0.743900\pi\)
−0.693427 + 0.720527i \(0.743900\pi\)
\(972\) −67.5729 −2.16740
\(973\) −0.636431 −0.0204030
\(974\) −3.26930 −0.104755
\(975\) 20.8079 0.666387
\(976\) −59.3551 −1.89991
\(977\) 17.7521 0.567941 0.283971 0.958833i \(-0.408348\pi\)
0.283971 + 0.958833i \(0.408348\pi\)
\(978\) −43.3712 −1.38686
\(979\) −1.46223 −0.0467332
\(980\) 13.0256 0.416087
\(981\) 10.1851 0.325184
\(982\) 38.0963 1.21570
\(983\) 18.2539 0.582208 0.291104 0.956691i \(-0.405977\pi\)
0.291104 + 0.956691i \(0.405977\pi\)
\(984\) 61.8192 1.97072
\(985\) −2.02277 −0.0644509
\(986\) 24.3668 0.775997
\(987\) 0.608316 0.0193629
\(988\) 26.7969 0.852524
\(989\) 10.0721 0.320275
\(990\) 1.36167 0.0432767
\(991\) 23.9485 0.760748 0.380374 0.924833i \(-0.375795\pi\)
0.380374 + 0.924833i \(0.375795\pi\)
\(992\) −49.3983 −1.56840
\(993\) 14.3189 0.454395
\(994\) −2.35860 −0.0748102
\(995\) 4.02822 0.127703
\(996\) 63.0562 1.99801
\(997\) −41.6105 −1.31782 −0.658910 0.752222i \(-0.728982\pi\)
−0.658910 + 0.752222i \(0.728982\pi\)
\(998\) −97.8817 −3.09839
\(999\) 39.7273 1.25691
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 1441.2.a.e.1.27 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.2.a.e.1.27 28 1.1 even 1 trivial