Properties

Label 370.2.a.g.1.3
Level $370$
Weight $2$
Character 370.1
Self dual yes
Analytic conductor $2.954$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.892.1
Defining polynomial: \( x^{3} - x^{2} - 8x + 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.31955\) of defining polynomial
Character \(\chi\) \(=\) 370.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.93923 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.93923 q^{6} -1.31955 q^{7} +1.00000 q^{8} +5.63910 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.93923 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.93923 q^{6} -1.31955 q^{7} +1.00000 q^{8} +5.63910 q^{9} -1.00000 q^{10} -0.258786 q^{11} +2.93923 q^{12} -5.87847 q^{13} -1.31955 q^{14} -2.93923 q^{15} +1.00000 q^{16} +4.25879 q^{17} +5.63910 q^{18} +2.93923 q^{19} -1.00000 q^{20} -3.87847 q^{21} -0.258786 q^{22} -8.51757 q^{23} +2.93923 q^{24} +1.00000 q^{25} -5.87847 q^{26} +7.75694 q^{27} -1.31955 q^{28} -3.61968 q^{29} -2.93923 q^{30} +3.95865 q^{31} +1.00000 q^{32} -0.760632 q^{33} +4.25879 q^{34} +1.31955 q^{35} +5.63910 q^{36} -1.00000 q^{37} +2.93923 q^{38} -17.2782 q^{39} -1.00000 q^{40} -8.89789 q^{41} -3.87847 q^{42} -5.61968 q^{43} -0.258786 q^{44} -5.63910 q^{45} -8.51757 q^{46} +5.57834 q^{47} +2.93923 q^{48} -5.25879 q^{49} +1.00000 q^{50} +12.5176 q^{51} -5.87847 q^{52} +12.8979 q^{53} +7.75694 q^{54} +0.258786 q^{55} -1.31955 q^{56} +8.63910 q^{57} -3.61968 q^{58} +9.57834 q^{59} -2.93923 q^{60} +0.380316 q^{61} +3.95865 q^{62} -7.44108 q^{63} +1.00000 q^{64} +5.87847 q^{65} -0.760632 q^{66} +5.57834 q^{67} +4.25879 q^{68} -25.0351 q^{69} +1.31955 q^{70} +11.2394 q^{71} +5.63910 q^{72} +2.51757 q^{73} -1.00000 q^{74} +2.93923 q^{75} +2.93923 q^{76} +0.341481 q^{77} -17.2782 q^{78} -7.69987 q^{79} -1.00000 q^{80} +5.88216 q^{81} -8.89789 q^{82} -6.17860 q^{83} -3.87847 q^{84} -4.25879 q^{85} -5.61968 q^{86} -10.6391 q^{87} -0.258786 q^{88} +6.00000 q^{89} -5.63910 q^{90} +7.75694 q^{91} -8.51757 q^{92} +11.6354 q^{93} +5.57834 q^{94} -2.93923 q^{95} +2.93923 q^{96} -12.8979 q^{97} -5.25879 q^{98} -1.45932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - q^{7} + 3 q^{8} + 11 q^{9} - 3 q^{10} + 11 q^{11} - q^{14} + 3 q^{16} + q^{17} + 11 q^{18} - 3 q^{20} + 6 q^{21} + 11 q^{22} - 2 q^{23} + 3 q^{25} - 12 q^{27} - q^{28} - 5 q^{29} + 3 q^{31} + 3 q^{32} - 14 q^{33} + q^{34} + q^{35} + 11 q^{36} - 3 q^{37} - 40 q^{39} - 3 q^{40} - 9 q^{41} + 6 q^{42} - 11 q^{43} + 11 q^{44} - 11 q^{45} - 2 q^{46} + 2 q^{47} - 4 q^{49} + 3 q^{50} + 14 q^{51} + 21 q^{53} - 12 q^{54} - 11 q^{55} - q^{56} + 20 q^{57} - 5 q^{58} + 14 q^{59} + 7 q^{61} + 3 q^{62} - 37 q^{63} + 3 q^{64} - 14 q^{66} + 2 q^{67} + q^{68} - 28 q^{69} + q^{70} + 22 q^{71} + 11 q^{72} - 16 q^{73} - 3 q^{74} + 7 q^{77} - 40 q^{78} - 26 q^{79} - 3 q^{80} + 47 q^{81} - 9 q^{82} + 2 q^{83} + 6 q^{84} - q^{85} - 11 q^{86} - 26 q^{87} + 11 q^{88} + 18 q^{89} - 11 q^{90} - 12 q^{91} - 2 q^{92} - 18 q^{93} + 2 q^{94} - 21 q^{97} - 4 q^{98} + 19 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 2.93923 1.69697 0.848484 0.529221i \(-0.177516\pi\)
0.848484 + 0.529221i \(0.177516\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 2.93923 1.19994
\(7\) −1.31955 −0.498743 −0.249372 0.968408i \(-0.580224\pi\)
−0.249372 + 0.968408i \(0.580224\pi\)
\(8\) 1.00000 0.353553
\(9\) 5.63910 1.87970
\(10\) −1.00000 −0.316228
\(11\) −0.258786 −0.0780268 −0.0390134 0.999239i \(-0.512422\pi\)
−0.0390134 + 0.999239i \(0.512422\pi\)
\(12\) 2.93923 0.848484
\(13\) −5.87847 −1.63039 −0.815197 0.579184i \(-0.803371\pi\)
−0.815197 + 0.579184i \(0.803371\pi\)
\(14\) −1.31955 −0.352665
\(15\) −2.93923 −0.758907
\(16\) 1.00000 0.250000
\(17\) 4.25879 1.03291 0.516454 0.856315i \(-0.327252\pi\)
0.516454 + 0.856315i \(0.327252\pi\)
\(18\) 5.63910 1.32915
\(19\) 2.93923 0.674307 0.337153 0.941450i \(-0.390536\pi\)
0.337153 + 0.941450i \(0.390536\pi\)
\(20\) −1.00000 −0.223607
\(21\) −3.87847 −0.846351
\(22\) −0.258786 −0.0551733
\(23\) −8.51757 −1.77604 −0.888018 0.459808i \(-0.847918\pi\)
−0.888018 + 0.459808i \(0.847918\pi\)
\(24\) 2.93923 0.599969
\(25\) 1.00000 0.200000
\(26\) −5.87847 −1.15286
\(27\) 7.75694 1.49282
\(28\) −1.31955 −0.249372
\(29\) −3.61968 −0.672158 −0.336079 0.941834i \(-0.609101\pi\)
−0.336079 + 0.941834i \(0.609101\pi\)
\(30\) −2.93923 −0.536628
\(31\) 3.95865 0.710995 0.355497 0.934677i \(-0.384311\pi\)
0.355497 + 0.934677i \(0.384311\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.760632 −0.132409
\(34\) 4.25879 0.730376
\(35\) 1.31955 0.223045
\(36\) 5.63910 0.939850
\(37\) −1.00000 −0.164399
\(38\) 2.93923 0.476807
\(39\) −17.2782 −2.76673
\(40\) −1.00000 −0.158114
\(41\) −8.89789 −1.38962 −0.694808 0.719195i \(-0.744511\pi\)
−0.694808 + 0.719195i \(0.744511\pi\)
\(42\) −3.87847 −0.598461
\(43\) −5.61968 −0.856994 −0.428497 0.903543i \(-0.640957\pi\)
−0.428497 + 0.903543i \(0.640957\pi\)
\(44\) −0.258786 −0.0390134
\(45\) −5.63910 −0.840628
\(46\) −8.51757 −1.25585
\(47\) 5.57834 0.813684 0.406842 0.913499i \(-0.366630\pi\)
0.406842 + 0.913499i \(0.366630\pi\)
\(48\) 2.93923 0.424242
\(49\) −5.25879 −0.751255
\(50\) 1.00000 0.141421
\(51\) 12.5176 1.75281
\(52\) −5.87847 −0.815197
\(53\) 12.8979 1.77166 0.885831 0.464009i \(-0.153589\pi\)
0.885831 + 0.464009i \(0.153589\pi\)
\(54\) 7.75694 1.05559
\(55\) 0.258786 0.0348947
\(56\) −1.31955 −0.176332
\(57\) 8.63910 1.14428
\(58\) −3.61968 −0.475288
\(59\) 9.57834 1.24699 0.623497 0.781826i \(-0.285712\pi\)
0.623497 + 0.781826i \(0.285712\pi\)
\(60\) −2.93923 −0.379454
\(61\) 0.380316 0.0486945 0.0243472 0.999704i \(-0.492249\pi\)
0.0243472 + 0.999704i \(0.492249\pi\)
\(62\) 3.95865 0.502749
\(63\) −7.44108 −0.937488
\(64\) 1.00000 0.125000
\(65\) 5.87847 0.729134
\(66\) −0.760632 −0.0936273
\(67\) 5.57834 0.681502 0.340751 0.940154i \(-0.389319\pi\)
0.340751 + 0.940154i \(0.389319\pi\)
\(68\) 4.25879 0.516454
\(69\) −25.0351 −3.01388
\(70\) 1.31955 0.157716
\(71\) 11.2394 1.33387 0.666934 0.745117i \(-0.267606\pi\)
0.666934 + 0.745117i \(0.267606\pi\)
\(72\) 5.63910 0.664574
\(73\) 2.51757 0.294659 0.147330 0.989087i \(-0.452932\pi\)
0.147330 + 0.989087i \(0.452932\pi\)
\(74\) −1.00000 −0.116248
\(75\) 2.93923 0.339394
\(76\) 2.93923 0.337153
\(77\) 0.341481 0.0389154
\(78\) −17.2782 −1.95637
\(79\) −7.69987 −0.866303 −0.433151 0.901321i \(-0.642598\pi\)
−0.433151 + 0.901321i \(0.642598\pi\)
\(80\) −1.00000 −0.111803
\(81\) 5.88216 0.653574
\(82\) −8.89789 −0.982607
\(83\) −6.17860 −0.678190 −0.339095 0.940752i \(-0.610121\pi\)
−0.339095 + 0.940752i \(0.610121\pi\)
\(84\) −3.87847 −0.423176
\(85\) −4.25879 −0.461930
\(86\) −5.61968 −0.605986
\(87\) −10.6391 −1.14063
\(88\) −0.258786 −0.0275866
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −5.63910 −0.594414
\(91\) 7.75694 0.813148
\(92\) −8.51757 −0.888018
\(93\) 11.6354 1.20654
\(94\) 5.57834 0.575361
\(95\) −2.93923 −0.301559
\(96\) 2.93923 0.299984
\(97\) −12.8979 −1.30958 −0.654791 0.755810i \(-0.727243\pi\)
−0.654791 + 0.755810i \(0.727243\pi\)
\(98\) −5.25879 −0.531218
\(99\) −1.45932 −0.146667
\(100\) 1.00000 0.100000
\(101\) 10.3960 1.03444 0.517222 0.855851i \(-0.326966\pi\)
0.517222 + 0.855851i \(0.326966\pi\)
\(102\) 12.5176 1.23942
\(103\) −13.8785 −1.36749 −0.683743 0.729723i \(-0.739649\pi\)
−0.683743 + 0.729723i \(0.739649\pi\)
\(104\) −5.87847 −0.576431
\(105\) 3.87847 0.378500
\(106\) 12.8979 1.25275
\(107\) −4.21744 −0.407715 −0.203858 0.979001i \(-0.565348\pi\)
−0.203858 + 0.979001i \(0.565348\pi\)
\(108\) 7.75694 0.746412
\(109\) 16.1373 1.54567 0.772834 0.634608i \(-0.218838\pi\)
0.772834 + 0.634608i \(0.218838\pi\)
\(110\) 0.258786 0.0246742
\(111\) −2.93923 −0.278980
\(112\) −1.31955 −0.124686
\(113\) 1.01942 0.0958987 0.0479494 0.998850i \(-0.484731\pi\)
0.0479494 + 0.998850i \(0.484731\pi\)
\(114\) 8.63910 0.809126
\(115\) 8.51757 0.794268
\(116\) −3.61968 −0.336079
\(117\) −33.1493 −3.06465
\(118\) 9.57834 0.881757
\(119\) −5.61968 −0.515156
\(120\) −2.93923 −0.268314
\(121\) −10.9330 −0.993912
\(122\) 0.380316 0.0344322
\(123\) −26.1530 −2.35813
\(124\) 3.95865 0.355497
\(125\) −1.00000 −0.0894427
\(126\) −7.44108 −0.662904
\(127\) 7.45681 0.661685 0.330842 0.943686i \(-0.392667\pi\)
0.330842 + 0.943686i \(0.392667\pi\)
\(128\) 1.00000 0.0883883
\(129\) −16.5176 −1.45429
\(130\) 5.87847 0.515576
\(131\) 2.42166 0.211582 0.105791 0.994388i \(-0.466263\pi\)
0.105791 + 0.994388i \(0.466263\pi\)
\(132\) −0.760632 −0.0662045
\(133\) −3.87847 −0.336306
\(134\) 5.57834 0.481895
\(135\) −7.75694 −0.667611
\(136\) 4.25879 0.365188
\(137\) 15.7958 1.34952 0.674762 0.738035i \(-0.264246\pi\)
0.674762 + 0.738035i \(0.264246\pi\)
\(138\) −25.0351 −2.13113
\(139\) −11.4155 −0.968247 −0.484123 0.875000i \(-0.660861\pi\)
−0.484123 + 0.875000i \(0.660861\pi\)
\(140\) 1.31955 0.111522
\(141\) 16.3960 1.38080
\(142\) 11.2394 0.943187
\(143\) 1.52126 0.127214
\(144\) 5.63910 0.469925
\(145\) 3.61968 0.300598
\(146\) 2.51757 0.208356
\(147\) −15.4568 −1.27486
\(148\) −1.00000 −0.0821995
\(149\) 18.3960 1.50706 0.753531 0.657412i \(-0.228349\pi\)
0.753531 + 0.657412i \(0.228349\pi\)
\(150\) 2.93923 0.239988
\(151\) 5.87847 0.478383 0.239192 0.970972i \(-0.423118\pi\)
0.239192 + 0.970972i \(0.423118\pi\)
\(152\) 2.93923 0.238403
\(153\) 24.0157 1.94156
\(154\) 0.341481 0.0275173
\(155\) −3.95865 −0.317967
\(156\) −17.2782 −1.38336
\(157\) 3.61968 0.288882 0.144441 0.989513i \(-0.453862\pi\)
0.144441 + 0.989513i \(0.453862\pi\)
\(158\) −7.69987 −0.612569
\(159\) 37.9099 3.00645
\(160\) −1.00000 −0.0790569
\(161\) 11.2394 0.885786
\(162\) 5.88216 0.462146
\(163\) −22.0546 −1.72745 −0.863723 0.503966i \(-0.831874\pi\)
−0.863723 + 0.503966i \(0.831874\pi\)
\(164\) −8.89789 −0.694808
\(165\) 0.760632 0.0592151
\(166\) −6.17860 −0.479553
\(167\) −0.600267 −0.0464500 −0.0232250 0.999730i \(-0.507393\pi\)
−0.0232250 + 0.999730i \(0.507393\pi\)
\(168\) −3.87847 −0.299230
\(169\) 21.5564 1.65819
\(170\) −4.25879 −0.326634
\(171\) 16.5746 1.26749
\(172\) −5.61968 −0.428497
\(173\) −22.6937 −1.72537 −0.862684 0.505744i \(-0.831218\pi\)
−0.862684 + 0.505744i \(0.831218\pi\)
\(174\) −10.6391 −0.806548
\(175\) −1.31955 −0.0997487
\(176\) −0.258786 −0.0195067
\(177\) 28.1530 2.11611
\(178\) 6.00000 0.449719
\(179\) −8.73501 −0.652885 −0.326443 0.945217i \(-0.605850\pi\)
−0.326443 + 0.945217i \(0.605850\pi\)
\(180\) −5.63910 −0.420314
\(181\) 10.6391 0.790798 0.395399 0.918509i \(-0.370606\pi\)
0.395399 + 0.918509i \(0.370606\pi\)
\(182\) 7.75694 0.574983
\(183\) 1.11784 0.0826330
\(184\) −8.51757 −0.627924
\(185\) 1.00000 0.0735215
\(186\) 11.6354 0.853150
\(187\) −1.10211 −0.0805945
\(188\) 5.57834 0.406842
\(189\) −10.2357 −0.744536
\(190\) −2.93923 −0.213235
\(191\) 22.1116 1.59994 0.799971 0.600039i \(-0.204848\pi\)
0.799971 + 0.600039i \(0.204848\pi\)
\(192\) 2.93923 0.212121
\(193\) 7.03514 0.506401 0.253200 0.967414i \(-0.418517\pi\)
0.253200 + 0.967414i \(0.418517\pi\)
\(194\) −12.8979 −0.926014
\(195\) 17.2782 1.23732
\(196\) −5.25879 −0.375628
\(197\) 25.7569 1.83511 0.917553 0.397614i \(-0.130162\pi\)
0.917553 + 0.397614i \(0.130162\pi\)
\(198\) −1.45932 −0.103709
\(199\) −12.7350 −0.902761 −0.451380 0.892332i \(-0.649068\pi\)
−0.451380 + 0.892332i \(0.649068\pi\)
\(200\) 1.00000 0.0707107
\(201\) 16.3960 1.15649
\(202\) 10.3960 0.731463
\(203\) 4.77636 0.335235
\(204\) 12.5176 0.876405
\(205\) 8.89789 0.621455
\(206\) −13.8785 −0.966959
\(207\) −48.0315 −3.33842
\(208\) −5.87847 −0.407599
\(209\) −0.760632 −0.0526140
\(210\) 3.87847 0.267640
\(211\) −6.65483 −0.458137 −0.229069 0.973410i \(-0.573568\pi\)
−0.229069 + 0.973410i \(0.573568\pi\)
\(212\) 12.8979 0.885831
\(213\) 33.0351 2.26353
\(214\) −4.21744 −0.288298
\(215\) 5.61968 0.383259
\(216\) 7.75694 0.527793
\(217\) −5.22364 −0.354604
\(218\) 16.1373 1.09295
\(219\) 7.39973 0.500028
\(220\) 0.258786 0.0174473
\(221\) −25.0351 −1.68405
\(222\) −2.93923 −0.197269
\(223\) −16.5589 −1.10887 −0.554434 0.832228i \(-0.687065\pi\)
−0.554434 + 0.832228i \(0.687065\pi\)
\(224\) −1.31955 −0.0881662
\(225\) 5.63910 0.375940
\(226\) 1.01942 0.0678106
\(227\) −4.01573 −0.266533 −0.133267 0.991080i \(-0.542547\pi\)
−0.133267 + 0.991080i \(0.542547\pi\)
\(228\) 8.63910 0.572138
\(229\) 25.5139 1.68600 0.843002 0.537910i \(-0.180786\pi\)
0.843002 + 0.537910i \(0.180786\pi\)
\(230\) 8.51757 0.561632
\(231\) 1.00369 0.0660381
\(232\) −3.61968 −0.237644
\(233\) 7.96116 0.521553 0.260777 0.965399i \(-0.416021\pi\)
0.260777 + 0.965399i \(0.416021\pi\)
\(234\) −33.1493 −2.16704
\(235\) −5.57834 −0.363891
\(236\) 9.57834 0.623497
\(237\) −22.6317 −1.47009
\(238\) −5.61968 −0.364270
\(239\) 11.7983 0.763168 0.381584 0.924334i \(-0.375379\pi\)
0.381584 + 0.924334i \(0.375379\pi\)
\(240\) −2.93923 −0.189727
\(241\) 24.9963 1.61015 0.805077 0.593171i \(-0.202124\pi\)
0.805077 + 0.593171i \(0.202124\pi\)
\(242\) −10.9330 −0.702802
\(243\) −5.98176 −0.383730
\(244\) 0.380316 0.0243472
\(245\) 5.25879 0.335971
\(246\) −26.1530 −1.66745
\(247\) −17.2782 −1.09939
\(248\) 3.95865 0.251375
\(249\) −18.1604 −1.15087
\(250\) −1.00000 −0.0632456
\(251\) −8.81770 −0.556569 −0.278284 0.960499i \(-0.589766\pi\)
−0.278284 + 0.960499i \(0.589766\pi\)
\(252\) −7.44108 −0.468744
\(253\) 2.20423 0.138578
\(254\) 7.45681 0.467882
\(255\) −12.5176 −0.783881
\(256\) 1.00000 0.0625000
\(257\) 11.8396 0.738536 0.369268 0.929323i \(-0.379608\pi\)
0.369268 + 0.929323i \(0.379608\pi\)
\(258\) −16.5176 −1.02834
\(259\) 1.31955 0.0819929
\(260\) 5.87847 0.364567
\(261\) −20.4118 −1.26346
\(262\) 2.42166 0.149611
\(263\) −9.15919 −0.564780 −0.282390 0.959300i \(-0.591127\pi\)
−0.282390 + 0.959300i \(0.591127\pi\)
\(264\) −0.760632 −0.0468137
\(265\) −12.8979 −0.792311
\(266\) −3.87847 −0.237804
\(267\) 17.6354 1.07927
\(268\) 5.57834 0.340751
\(269\) 18.3960 1.12163 0.560813 0.827942i \(-0.310489\pi\)
0.560813 + 0.827942i \(0.310489\pi\)
\(270\) −7.75694 −0.472072
\(271\) −27.2394 −1.65467 −0.827337 0.561706i \(-0.810145\pi\)
−0.827337 + 0.561706i \(0.810145\pi\)
\(272\) 4.25879 0.258227
\(273\) 22.7995 1.37989
\(274\) 15.7958 0.954258
\(275\) −0.258786 −0.0156054
\(276\) −25.0351 −1.50694
\(277\) −21.8785 −1.31455 −0.657275 0.753651i \(-0.728291\pi\)
−0.657275 + 0.753651i \(0.728291\pi\)
\(278\) −11.4155 −0.684654
\(279\) 22.3232 1.33646
\(280\) 1.31955 0.0788582
\(281\) −20.9963 −1.25253 −0.626267 0.779608i \(-0.715418\pi\)
−0.626267 + 0.779608i \(0.715418\pi\)
\(282\) 16.3960 0.976370
\(283\) 18.9136 1.12430 0.562149 0.827036i \(-0.309975\pi\)
0.562149 + 0.827036i \(0.309975\pi\)
\(284\) 11.2394 0.666934
\(285\) −8.63910 −0.511736
\(286\) 1.52126 0.0899542
\(287\) 11.7412 0.693062
\(288\) 5.63910 0.332287
\(289\) 1.13726 0.0668974
\(290\) 3.61968 0.212555
\(291\) −37.9099 −2.22232
\(292\) 2.51757 0.147330
\(293\) −12.8979 −0.753503 −0.376751 0.926314i \(-0.622959\pi\)
−0.376751 + 0.926314i \(0.622959\pi\)
\(294\) −15.4568 −0.901459
\(295\) −9.57834 −0.557672
\(296\) −1.00000 −0.0581238
\(297\) −2.00738 −0.116480
\(298\) 18.3960 1.06565
\(299\) 50.0703 2.89564
\(300\) 2.93923 0.169697
\(301\) 7.41546 0.427420
\(302\) 5.87847 0.338268
\(303\) 30.5564 1.75542
\(304\) 2.93923 0.168577
\(305\) −0.380316 −0.0217768
\(306\) 24.0157 1.37289
\(307\) −3.78256 −0.215882 −0.107941 0.994157i \(-0.534426\pi\)
−0.107941 + 0.994157i \(0.534426\pi\)
\(308\) 0.341481 0.0194577
\(309\) −40.7921 −2.32058
\(310\) −3.95865 −0.224836
\(311\) −15.2807 −0.866490 −0.433245 0.901276i \(-0.642631\pi\)
−0.433245 + 0.901276i \(0.642631\pi\)
\(312\) −17.2782 −0.978186
\(313\) 19.0351 1.07593 0.537965 0.842967i \(-0.319193\pi\)
0.537965 + 0.842967i \(0.319193\pi\)
\(314\) 3.61968 0.204271
\(315\) 7.44108 0.419257
\(316\) −7.69987 −0.433151
\(317\) −24.1373 −1.35568 −0.677842 0.735208i \(-0.737085\pi\)
−0.677842 + 0.735208i \(0.737085\pi\)
\(318\) 37.9099 2.12588
\(319\) 0.936722 0.0524464
\(320\) −1.00000 −0.0559017
\(321\) −12.3960 −0.691880
\(322\) 11.2394 0.626345
\(323\) 12.5176 0.696496
\(324\) 5.88216 0.326787
\(325\) −5.87847 −0.326079
\(326\) −22.0546 −1.22149
\(327\) 47.4312 2.62295
\(328\) −8.89789 −0.491304
\(329\) −7.36090 −0.405819
\(330\) 0.760632 0.0418714
\(331\) 0.817705 0.0449451 0.0224726 0.999747i \(-0.492846\pi\)
0.0224726 + 0.999747i \(0.492846\pi\)
\(332\) −6.17860 −0.339095
\(333\) −5.63910 −0.309021
\(334\) −0.600267 −0.0328451
\(335\) −5.57834 −0.304777
\(336\) −3.87847 −0.211588
\(337\) −19.7958 −1.07834 −0.539172 0.842195i \(-0.681263\pi\)
−0.539172 + 0.842195i \(0.681263\pi\)
\(338\) 21.5564 1.17251
\(339\) 2.99631 0.162737
\(340\) −4.25879 −0.230965
\(341\) −1.02444 −0.0554767
\(342\) 16.5746 0.896254
\(343\) 16.1761 0.873427
\(344\) −5.61968 −0.302993
\(345\) 25.0351 1.34785
\(346\) −22.6937 −1.22002
\(347\) 15.7569 0.845877 0.422938 0.906158i \(-0.360999\pi\)
0.422938 + 0.906158i \(0.360999\pi\)
\(348\) −10.6391 −0.570316
\(349\) −0.160365 −0.00858416 −0.00429208 0.999991i \(-0.501366\pi\)
−0.00429208 + 0.999991i \(0.501366\pi\)
\(350\) −1.31955 −0.0705330
\(351\) −45.5989 −2.43389
\(352\) −0.258786 −0.0137933
\(353\) −30.2075 −1.60779 −0.803893 0.594775i \(-0.797241\pi\)
−0.803893 + 0.594775i \(0.797241\pi\)
\(354\) 28.1530 1.49631
\(355\) −11.2394 −0.596524
\(356\) 6.00000 0.317999
\(357\) −16.5176 −0.874203
\(358\) −8.73501 −0.461660
\(359\) −7.39973 −0.390543 −0.195271 0.980749i \(-0.562559\pi\)
−0.195271 + 0.980749i \(0.562559\pi\)
\(360\) −5.63910 −0.297207
\(361\) −10.3609 −0.545310
\(362\) 10.6391 0.559179
\(363\) −32.1347 −1.68664
\(364\) 7.75694 0.406574
\(365\) −2.51757 −0.131776
\(366\) 1.11784 0.0584303
\(367\) −13.9198 −0.726609 −0.363304 0.931671i \(-0.618351\pi\)
−0.363304 + 0.931671i \(0.618351\pi\)
\(368\) −8.51757 −0.444009
\(369\) −50.1761 −2.61206
\(370\) 1.00000 0.0519875
\(371\) −17.0194 −0.883604
\(372\) 11.6354 0.603268
\(373\) 20.2357 1.04776 0.523882 0.851791i \(-0.324483\pi\)
0.523882 + 0.851791i \(0.324483\pi\)
\(374\) −1.10211 −0.0569889
\(375\) −2.93923 −0.151781
\(376\) 5.57834 0.287681
\(377\) 21.2782 1.09588
\(378\) −10.2357 −0.526466
\(379\) −27.9488 −1.43563 −0.717816 0.696233i \(-0.754858\pi\)
−0.717816 + 0.696233i \(0.754858\pi\)
\(380\) −2.93923 −0.150780
\(381\) 21.9173 1.12286
\(382\) 22.1116 1.13133
\(383\) 11.7569 0.600752 0.300376 0.953821i \(-0.402888\pi\)
0.300376 + 0.953821i \(0.402888\pi\)
\(384\) 2.93923 0.149992
\(385\) −0.341481 −0.0174035
\(386\) 7.03514 0.358079
\(387\) −31.6900 −1.61089
\(388\) −12.8979 −0.654791
\(389\) −9.58085 −0.485768 −0.242884 0.970055i \(-0.578093\pi\)
−0.242884 + 0.970055i \(0.578093\pi\)
\(390\) 17.2782 0.874916
\(391\) −36.2745 −1.83448
\(392\) −5.25879 −0.265609
\(393\) 7.11784 0.359047
\(394\) 25.7569 1.29762
\(395\) 7.69987 0.387422
\(396\) −1.45932 −0.0733335
\(397\) −32.4787 −1.63006 −0.815031 0.579418i \(-0.803280\pi\)
−0.815031 + 0.579418i \(0.803280\pi\)
\(398\) −12.7350 −0.638348
\(399\) −11.3997 −0.570700
\(400\) 1.00000 0.0500000
\(401\) 7.27820 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(402\) 16.3960 0.817760
\(403\) −23.2708 −1.15920
\(404\) 10.3960 0.517222
\(405\) −5.88216 −0.292287
\(406\) 4.77636 0.237047
\(407\) 0.258786 0.0128275
\(408\) 12.5176 0.619712
\(409\) −32.9963 −1.63156 −0.815781 0.578361i \(-0.803693\pi\)
−0.815781 + 0.578361i \(0.803693\pi\)
\(410\) 8.89789 0.439435
\(411\) 46.4275 2.29010
\(412\) −13.8785 −0.683743
\(413\) −12.6391 −0.621930
\(414\) −48.0315 −2.36062
\(415\) 6.17860 0.303296
\(416\) −5.87847 −0.288216
\(417\) −33.5527 −1.64308
\(418\) −0.760632 −0.0372037
\(419\) 25.7131 1.25617 0.628083 0.778146i \(-0.283840\pi\)
0.628083 + 0.778146i \(0.283840\pi\)
\(420\) 3.87847 0.189250
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) −6.65483 −0.323952
\(423\) 31.4568 1.52948
\(424\) 12.8979 0.626377
\(425\) 4.25879 0.206581
\(426\) 33.0351 1.60056
\(427\) −0.501846 −0.0242860
\(428\) −4.21744 −0.203858
\(429\) 4.47135 0.215879
\(430\) 5.61968 0.271005
\(431\) 17.9198 0.863167 0.431584 0.902073i \(-0.357955\pi\)
0.431584 + 0.902073i \(0.357955\pi\)
\(432\) 7.75694 0.373206
\(433\) 4.96486 0.238596 0.119298 0.992859i \(-0.461936\pi\)
0.119298 + 0.992859i \(0.461936\pi\)
\(434\) −5.22364 −0.250743
\(435\) 10.6391 0.510106
\(436\) 16.1373 0.772834
\(437\) −25.0351 −1.19759
\(438\) 7.39973 0.353573
\(439\) −13.8371 −0.660410 −0.330205 0.943909i \(-0.607118\pi\)
−0.330205 + 0.943909i \(0.607118\pi\)
\(440\) 0.258786 0.0123371
\(441\) −29.6548 −1.41213
\(442\) −25.0351 −1.19080
\(443\) 14.3390 0.681265 0.340632 0.940197i \(-0.389359\pi\)
0.340632 + 0.940197i \(0.389359\pi\)
\(444\) −2.93923 −0.139490
\(445\) −6.00000 −0.284427
\(446\) −16.5589 −0.784088
\(447\) 54.0703 2.55744
\(448\) −1.31955 −0.0623429
\(449\) 12.4787 0.588908 0.294454 0.955666i \(-0.404862\pi\)
0.294454 + 0.955666i \(0.404862\pi\)
\(450\) 5.63910 0.265830
\(451\) 2.30265 0.108427
\(452\) 1.01942 0.0479494
\(453\) 17.2782 0.811801
\(454\) −4.01573 −0.188467
\(455\) −7.75694 −0.363651
\(456\) 8.63910 0.404563
\(457\) 21.6585 1.01314 0.506571 0.862198i \(-0.330913\pi\)
0.506571 + 0.862198i \(0.330913\pi\)
\(458\) 25.5139 1.19219
\(459\) 33.0351 1.54195
\(460\) 8.51757 0.397134
\(461\) −29.4155 −1.37001 −0.685007 0.728536i \(-0.740201\pi\)
−0.685007 + 0.728536i \(0.740201\pi\)
\(462\) 1.00369 0.0466960
\(463\) −9.03514 −0.419899 −0.209949 0.977712i \(-0.567330\pi\)
−0.209949 + 0.977712i \(0.567330\pi\)
\(464\) −3.61968 −0.168040
\(465\) −11.6354 −0.539579
\(466\) 7.96116 0.368794
\(467\) 7.05825 0.326617 0.163308 0.986575i \(-0.447783\pi\)
0.163308 + 0.986575i \(0.447783\pi\)
\(468\) −33.1493 −1.53233
\(469\) −7.36090 −0.339895
\(470\) −5.57834 −0.257309
\(471\) 10.6391 0.490224
\(472\) 9.57834 0.440879
\(473\) 1.45429 0.0668685
\(474\) −22.6317 −1.03951
\(475\) 2.93923 0.134861
\(476\) −5.61968 −0.257578
\(477\) 72.7325 3.33019
\(478\) 11.7983 0.539641
\(479\) −29.3353 −1.34036 −0.670181 0.742197i \(-0.733784\pi\)
−0.670181 + 0.742197i \(0.733784\pi\)
\(480\) −2.93923 −0.134157
\(481\) 5.87847 0.268035
\(482\) 24.9963 1.13855
\(483\) 33.0351 1.50315
\(484\) −10.9330 −0.496956
\(485\) 12.8979 0.585663
\(486\) −5.98176 −0.271338
\(487\) −37.9099 −1.71786 −0.858931 0.512091i \(-0.828871\pi\)
−0.858931 + 0.512091i \(0.828871\pi\)
\(488\) 0.380316 0.0172161
\(489\) −64.8235 −2.93142
\(490\) 5.25879 0.237568
\(491\) −14.5564 −0.656921 −0.328461 0.944518i \(-0.606530\pi\)
−0.328461 + 0.944518i \(0.606530\pi\)
\(492\) −26.1530 −1.17907
\(493\) −15.4155 −0.694277
\(494\) −17.2782 −0.777383
\(495\) 1.45932 0.0655915
\(496\) 3.95865 0.177749
\(497\) −14.8309 −0.665258
\(498\) −18.1604 −0.813785
\(499\) 23.9744 1.07324 0.536620 0.843824i \(-0.319701\pi\)
0.536620 + 0.843824i \(0.319701\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −1.76432 −0.0788242
\(502\) −8.81770 −0.393553
\(503\) −43.7569 −1.95103 −0.975513 0.219943i \(-0.929413\pi\)
−0.975513 + 0.219943i \(0.929413\pi\)
\(504\) −7.44108 −0.331452
\(505\) −10.3960 −0.462618
\(506\) 2.20423 0.0979898
\(507\) 63.3593 2.81389
\(508\) 7.45681 0.330842
\(509\) 11.7958 0.522839 0.261419 0.965225i \(-0.415809\pi\)
0.261419 + 0.965225i \(0.415809\pi\)
\(510\) −12.5176 −0.554287
\(511\) −3.32206 −0.146959
\(512\) 1.00000 0.0441942
\(513\) 22.7995 1.00662
\(514\) 11.8396 0.522224
\(515\) 13.8785 0.611558
\(516\) −16.5176 −0.727146
\(517\) −1.44359 −0.0634892
\(518\) 1.31955 0.0579777
\(519\) −66.7020 −2.92789
\(520\) 5.87847 0.257788
\(521\) 14.9806 0.656311 0.328156 0.944624i \(-0.393573\pi\)
0.328156 + 0.944624i \(0.393573\pi\)
\(522\) −20.4118 −0.893399
\(523\) −27.5139 −1.20310 −0.601549 0.798836i \(-0.705450\pi\)
−0.601549 + 0.798836i \(0.705450\pi\)
\(524\) 2.42166 0.105791
\(525\) −3.87847 −0.169270
\(526\) −9.15919 −0.399359
\(527\) 16.8591 0.734392
\(528\) −0.760632 −0.0331023
\(529\) 49.5490 2.15431
\(530\) −12.8979 −0.560248
\(531\) 54.0132 2.34397
\(532\) −3.87847 −0.168153
\(533\) 52.3060 2.26562
\(534\) 17.6354 0.763159
\(535\) 4.21744 0.182336
\(536\) 5.57834 0.240947
\(537\) −25.6742 −1.10793
\(538\) 18.3960 0.793110
\(539\) 1.36090 0.0586180
\(540\) −7.75694 −0.333806
\(541\) −11.0351 −0.474438 −0.237219 0.971456i \(-0.576236\pi\)
−0.237219 + 0.971456i \(0.576236\pi\)
\(542\) −27.2394 −1.17003
\(543\) 31.2708 1.34196
\(544\) 4.25879 0.182594
\(545\) −16.1373 −0.691244
\(546\) 22.7995 0.975727
\(547\) −16.1761 −0.691640 −0.345820 0.938301i \(-0.612399\pi\)
−0.345820 + 0.938301i \(0.612399\pi\)
\(548\) 15.7958 0.674762
\(549\) 2.14464 0.0915310
\(550\) −0.258786 −0.0110347
\(551\) −10.6391 −0.453241
\(552\) −25.0351 −1.06557
\(553\) 10.1604 0.432063
\(554\) −21.8785 −0.929527
\(555\) 2.93923 0.124764
\(556\) −11.4155 −0.484123
\(557\) 11.1567 0.472723 0.236362 0.971665i \(-0.424045\pi\)
0.236362 + 0.971665i \(0.424045\pi\)
\(558\) 22.3232 0.945018
\(559\) 33.0351 1.39724
\(560\) 1.31955 0.0557612
\(561\) −3.23937 −0.136766
\(562\) −20.9963 −0.885676
\(563\) −41.7288 −1.75866 −0.879330 0.476213i \(-0.842009\pi\)
−0.879330 + 0.476213i \(0.842009\pi\)
\(564\) 16.3960 0.690398
\(565\) −1.01942 −0.0428872
\(566\) 18.9136 0.794998
\(567\) −7.76181 −0.325965
\(568\) 11.2394 0.471593
\(569\) −24.0703 −1.00908 −0.504539 0.863389i \(-0.668338\pi\)
−0.504539 + 0.863389i \(0.668338\pi\)
\(570\) −8.63910 −0.361852
\(571\) 37.6511 1.57565 0.787825 0.615899i \(-0.211207\pi\)
0.787825 + 0.615899i \(0.211207\pi\)
\(572\) 1.52126 0.0636072
\(573\) 64.9913 2.71505
\(574\) 11.7412 0.490069
\(575\) −8.51757 −0.355207
\(576\) 5.63910 0.234963
\(577\) 23.4312 0.975453 0.487726 0.872996i \(-0.337826\pi\)
0.487726 + 0.872996i \(0.337826\pi\)
\(578\) 1.13726 0.0473036
\(579\) 20.6779 0.859346
\(580\) 3.61968 0.150299
\(581\) 8.15298 0.338243
\(582\) −37.9099 −1.57142
\(583\) −3.33779 −0.138237
\(584\) 2.51757 0.104178
\(585\) 33.1493 1.37055
\(586\) −12.8979 −0.532807
\(587\) 6.30265 0.260138 0.130069 0.991505i \(-0.458480\pi\)
0.130069 + 0.991505i \(0.458480\pi\)
\(588\) −15.4568 −0.637428
\(589\) 11.6354 0.479429
\(590\) −9.57834 −0.394334
\(591\) 75.7057 3.11412
\(592\) −1.00000 −0.0410997
\(593\) −34.0315 −1.39750 −0.698752 0.715364i \(-0.746261\pi\)
−0.698752 + 0.715364i \(0.746261\pi\)
\(594\) −2.00738 −0.0823640
\(595\) 5.61968 0.230385
\(596\) 18.3960 0.753531
\(597\) −37.4312 −1.53196
\(598\) 50.0703 2.04753
\(599\) 34.8359 1.42336 0.711679 0.702505i \(-0.247935\pi\)
0.711679 + 0.702505i \(0.247935\pi\)
\(600\) 2.93923 0.119994
\(601\) 15.2236 0.620985 0.310493 0.950576i \(-0.399506\pi\)
0.310493 + 0.950576i \(0.399506\pi\)
\(602\) 7.41546 0.302232
\(603\) 31.4568 1.28102
\(604\) 5.87847 0.239192
\(605\) 10.9330 0.444491
\(606\) 30.5564 1.24127
\(607\) −30.8309 −1.25139 −0.625694 0.780068i \(-0.715184\pi\)
−0.625694 + 0.780068i \(0.715184\pi\)
\(608\) 2.93923 0.119202
\(609\) 14.0388 0.568882
\(610\) −0.380316 −0.0153985
\(611\) −32.7921 −1.32663
\(612\) 24.0157 0.970778
\(613\) −11.2112 −0.452817 −0.226409 0.974032i \(-0.572698\pi\)
−0.226409 + 0.974032i \(0.572698\pi\)
\(614\) −3.78256 −0.152652
\(615\) 26.1530 1.05459
\(616\) 0.341481 0.0137587
\(617\) 26.5176 1.06756 0.533779 0.845624i \(-0.320772\pi\)
0.533779 + 0.845624i \(0.320772\pi\)
\(618\) −40.7921 −1.64090
\(619\) −3.41546 −0.137279 −0.0686394 0.997642i \(-0.521866\pi\)
−0.0686394 + 0.997642i \(0.521866\pi\)
\(620\) −3.95865 −0.158983
\(621\) −66.0703 −2.65131
\(622\) −15.2807 −0.612701
\(623\) −7.91730 −0.317200
\(624\) −17.2782 −0.691682
\(625\) 1.00000 0.0400000
\(626\) 19.0351 0.760797
\(627\) −2.23568 −0.0892843
\(628\) 3.61968 0.144441
\(629\) −4.25879 −0.169809
\(630\) 7.44108 0.296460
\(631\) 3.11533 0.124019 0.0620096 0.998076i \(-0.480249\pi\)
0.0620096 + 0.998076i \(0.480249\pi\)
\(632\) −7.69987 −0.306284
\(633\) −19.5601 −0.777444
\(634\) −24.1373 −0.958613
\(635\) −7.45681 −0.295914
\(636\) 37.9099 1.50323
\(637\) 30.9136 1.22484
\(638\) 0.936722 0.0370852
\(639\) 63.3799 2.50727
\(640\) −1.00000 −0.0395285
\(641\) −20.5018 −0.809774 −0.404887 0.914367i \(-0.632689\pi\)
−0.404887 + 0.914367i \(0.632689\pi\)
\(642\) −12.3960 −0.489233
\(643\) 5.70238 0.224880 0.112440 0.993659i \(-0.464133\pi\)
0.112440 + 0.993659i \(0.464133\pi\)
\(644\) 11.2394 0.442893
\(645\) 16.5176 0.650379
\(646\) 12.5176 0.492497
\(647\) −41.0351 −1.61326 −0.806629 0.591058i \(-0.798710\pi\)
−0.806629 + 0.591058i \(0.798710\pi\)
\(648\) 5.88216 0.231073
\(649\) −2.47874 −0.0972989
\(650\) −5.87847 −0.230573
\(651\) −15.3535 −0.601752
\(652\) −22.0546 −0.863723
\(653\) 14.9575 0.585331 0.292666 0.956215i \(-0.405458\pi\)
0.292666 + 0.956215i \(0.405458\pi\)
\(654\) 47.4312 1.85471
\(655\) −2.42166 −0.0946222
\(656\) −8.89789 −0.347404
\(657\) 14.1968 0.553872
\(658\) −7.36090 −0.286958
\(659\) −15.7569 −0.613803 −0.306902 0.951741i \(-0.599292\pi\)
−0.306902 + 0.951741i \(0.599292\pi\)
\(660\) 0.760632 0.0296076
\(661\) 11.6197 0.451953 0.225977 0.974133i \(-0.427443\pi\)
0.225977 + 0.974133i \(0.427443\pi\)
\(662\) 0.817705 0.0317810
\(663\) −73.5842 −2.85777
\(664\) −6.17860 −0.239776
\(665\) 3.87847 0.150401
\(666\) −5.63910 −0.218511
\(667\) 30.8309 1.19378
\(668\) −0.600267 −0.0232250
\(669\) −48.6706 −1.88171
\(670\) −5.57834 −0.215510
\(671\) −0.0984203 −0.00379947
\(672\) −3.87847 −0.149615
\(673\) 12.7218 0.490389 0.245195 0.969474i \(-0.421148\pi\)
0.245195 + 0.969474i \(0.421148\pi\)
\(674\) −19.7958 −0.762505
\(675\) 7.75694 0.298565
\(676\) 21.5564 0.829093
\(677\) −21.5139 −0.826846 −0.413423 0.910539i \(-0.635667\pi\)
−0.413423 + 0.910539i \(0.635667\pi\)
\(678\) 2.99631 0.115073
\(679\) 17.0194 0.653145
\(680\) −4.25879 −0.163317
\(681\) −11.8032 −0.452298
\(682\) −1.02444 −0.0392279
\(683\) 47.6900 1.82481 0.912403 0.409293i \(-0.134225\pi\)
0.912403 + 0.409293i \(0.134225\pi\)
\(684\) 16.5746 0.633747
\(685\) −15.7958 −0.603526
\(686\) 16.1761 0.617606
\(687\) 74.9913 2.86110
\(688\) −5.61968 −0.214248
\(689\) −75.8198 −2.88851
\(690\) 25.0351 0.953072
\(691\) 30.5721 1.16302 0.581509 0.813540i \(-0.302462\pi\)
0.581509 + 0.813540i \(0.302462\pi\)
\(692\) −22.6937 −0.862684
\(693\) 1.92565 0.0731492
\(694\) 15.7569 0.598125
\(695\) 11.4155 0.433013
\(696\) −10.6391 −0.403274
\(697\) −37.8942 −1.43534
\(698\) −0.160365 −0.00606992
\(699\) 23.3997 0.885059
\(700\) −1.31955 −0.0498743
\(701\) 32.0703 1.21128 0.605639 0.795740i \(-0.292918\pi\)
0.605639 + 0.795740i \(0.292918\pi\)
\(702\) −45.5989 −1.72102
\(703\) −2.93923 −0.110855
\(704\) −0.258786 −0.00975335
\(705\) −16.3960 −0.617511
\(706\) −30.2075 −1.13688
\(707\) −13.7181 −0.515922
\(708\) 28.1530 1.05805
\(709\) 10.6160 0.398692 0.199346 0.979929i \(-0.436118\pi\)
0.199346 + 0.979929i \(0.436118\pi\)
\(710\) −11.2394 −0.421806
\(711\) −43.4203 −1.62839
\(712\) 6.00000 0.224860
\(713\) −33.7181 −1.26275
\(714\) −16.5176 −0.618155
\(715\) −1.52126 −0.0568920
\(716\) −8.73501 −0.326443
\(717\) 34.6779 1.29507
\(718\) −7.39973 −0.276156
\(719\) −32.4663 −1.21079 −0.605395 0.795925i \(-0.706985\pi\)
−0.605395 + 0.795925i \(0.706985\pi\)
\(720\) −5.63910 −0.210157
\(721\) 18.3133 0.682025
\(722\) −10.3609 −0.385593
\(723\) 73.4700 2.73238
\(724\) 10.6391 0.395399
\(725\) −3.61968 −0.134432
\(726\) −32.1347 −1.19263
\(727\) 31.5139 1.16879 0.584393 0.811471i \(-0.301333\pi\)
0.584393 + 0.811471i \(0.301333\pi\)
\(728\) 7.75694 0.287491
\(729\) −35.2283 −1.30475
\(730\) −2.51757 −0.0931795
\(731\) −23.9330 −0.885195
\(732\) 1.11784 0.0413165
\(733\) −16.8202 −0.621269 −0.310634 0.950529i \(-0.600541\pi\)
−0.310634 + 0.950529i \(0.600541\pi\)
\(734\) −13.9198 −0.513790
\(735\) 15.4568 0.570133
\(736\) −8.51757 −0.313962
\(737\) −1.44359 −0.0531755
\(738\) −50.1761 −1.84701
\(739\) 9.69735 0.356723 0.178361 0.983965i \(-0.442920\pi\)
0.178361 + 0.983965i \(0.442920\pi\)
\(740\) 1.00000 0.0367607
\(741\) −50.7847 −1.86562
\(742\) −17.0194 −0.624802
\(743\) −39.1153 −1.43500 −0.717501 0.696557i \(-0.754714\pi\)
−0.717501 + 0.696557i \(0.754714\pi\)
\(744\) 11.6354 0.426575
\(745\) −18.3960 −0.673979
\(746\) 20.2357 0.740881
\(747\) −34.8418 −1.27479
\(748\) −1.10211 −0.0402972
\(749\) 5.56512 0.203345
\(750\) −2.93923 −0.107326
\(751\) −26.1530 −0.954336 −0.477168 0.878812i \(-0.658337\pi\)
−0.477168 + 0.878812i \(0.658337\pi\)
\(752\) 5.57834 0.203421
\(753\) −25.9173 −0.944479
\(754\) 21.2782 0.774906
\(755\) −5.87847 −0.213939
\(756\) −10.2357 −0.372268
\(757\) −33.5915 −1.22091 −0.610453 0.792053i \(-0.709013\pi\)
−0.610453 + 0.792053i \(0.709013\pi\)
\(758\) −27.9488 −1.01514
\(759\) 6.47874 0.235163
\(760\) −2.93923 −0.106617
\(761\) −51.3766 −1.86240 −0.931201 0.364507i \(-0.881237\pi\)
−0.931201 + 0.364507i \(0.881237\pi\)
\(762\) 21.9173 0.793980
\(763\) −21.2939 −0.770892
\(764\) 22.1116 0.799971
\(765\) −24.0157 −0.868290
\(766\) 11.7569 0.424795
\(767\) −56.3060 −2.03309
\(768\) 2.93923 0.106061
\(769\) 27.5527 0.993576 0.496788 0.867872i \(-0.334513\pi\)
0.496788 + 0.867872i \(0.334513\pi\)
\(770\) −0.341481 −0.0123061
\(771\) 34.7995 1.25327
\(772\) 7.03514 0.253200
\(773\) 13.4155 0.482521 0.241260 0.970460i \(-0.422439\pi\)
0.241260 + 0.970460i \(0.422439\pi\)
\(774\) −31.6900 −1.13907
\(775\) 3.95865 0.142199
\(776\) −12.8979 −0.463007
\(777\) 3.87847 0.139139
\(778\) −9.58085 −0.343490
\(779\) −26.1530 −0.937028
\(780\) 17.2782 0.618659
\(781\) −2.90859 −0.104077
\(782\) −36.2745 −1.29717
\(783\) −28.0777 −1.00341
\(784\) −5.25879 −0.187814
\(785\) −3.61968 −0.129192
\(786\) 7.11784 0.253885
\(787\) −25.4956 −0.908821 −0.454411 0.890792i \(-0.650150\pi\)
−0.454411 + 0.890792i \(0.650150\pi\)
\(788\) 25.7569 0.917553
\(789\) −26.9210 −0.958413
\(790\) 7.69987 0.273949
\(791\) −1.34517 −0.0478289
\(792\) −1.45932 −0.0518546
\(793\) −2.23568 −0.0793912
\(794\) −32.4787 −1.15263
\(795\) −37.9099 −1.34453
\(796\) −12.7350 −0.451380
\(797\) 48.4663 1.71677 0.858383 0.513010i \(-0.171470\pi\)
0.858383 + 0.513010i \(0.171470\pi\)
\(798\) −11.3997 −0.403546
\(799\) 23.7569 0.840460
\(800\) 1.00000 0.0353553
\(801\) 33.8346 1.19549
\(802\) 7.27820 0.257002
\(803\) −0.651511 −0.0229913
\(804\) 16.3960 0.578244
\(805\) −11.2394 −0.396136
\(806\) −23.2708 −0.819680
\(807\) 54.0703 1.90336
\(808\) 10.3960 0.365731
\(809\) −12.9649 −0.455820 −0.227910 0.973682i \(-0.573189\pi\)
−0.227910 + 0.973682i \(0.573189\pi\)
\(810\) −5.88216 −0.206678
\(811\) 0.0776702 0.00272737 0.00136368 0.999999i \(-0.499566\pi\)
0.00136368 + 0.999999i \(0.499566\pi\)
\(812\) 4.77636 0.167617
\(813\) −80.0629 −2.80793
\(814\) 0.258786 0.00907043
\(815\) 22.0546 0.772538
\(816\) 12.5176 0.438203
\(817\) −16.5176 −0.577877
\(818\) −32.9963 −1.15369
\(819\) 43.7422 1.52848
\(820\) 8.89789 0.310728
\(821\) 36.3448 1.26844 0.634221 0.773152i \(-0.281321\pi\)
0.634221 + 0.773152i \(0.281321\pi\)
\(822\) 46.4275 1.61934
\(823\) −23.0996 −0.805201 −0.402601 0.915376i \(-0.631894\pi\)
−0.402601 + 0.915376i \(0.631894\pi\)
\(824\) −13.8785 −0.483479
\(825\) −0.760632 −0.0264818
\(826\) −12.6391 −0.439771
\(827\) 15.2551 0.530472 0.265236 0.964184i \(-0.414550\pi\)
0.265236 + 0.964184i \(0.414550\pi\)
\(828\) −48.0315 −1.66921
\(829\) 28.1373 0.977247 0.488624 0.872495i \(-0.337499\pi\)
0.488624 + 0.872495i \(0.337499\pi\)
\(830\) 6.17860 0.214462
\(831\) −64.3060 −2.23075
\(832\) −5.87847 −0.203799
\(833\) −22.3960 −0.775977
\(834\) −33.5527 −1.16184
\(835\) 0.600267 0.0207731
\(836\) −0.760632 −0.0263070
\(837\) 30.7070 1.06139
\(838\) 25.7131 0.888244
\(839\) 4.24306 0.146487 0.0732434 0.997314i \(-0.476665\pi\)
0.0732434 + 0.997314i \(0.476665\pi\)
\(840\) 3.87847 0.133820
\(841\) −15.8979 −0.548203
\(842\) 22.0000 0.758170
\(843\) −61.7131 −2.12551
\(844\) −6.65483 −0.229069
\(845\) −21.5564 −0.741563
\(846\) 31.4568 1.08151
\(847\) 14.4267 0.495707
\(848\) 12.8979 0.442915
\(849\) 55.5915 1.90790
\(850\) 4.25879 0.146075
\(851\) 8.51757 0.291979
\(852\) 33.0351 1.13177
\(853\) 36.4787 1.24901 0.624504 0.781022i \(-0.285301\pi\)
0.624504 + 0.781022i \(0.285301\pi\)
\(854\) −0.501846 −0.0171728
\(855\) −16.5746 −0.566841
\(856\) −4.21744 −0.144149
\(857\) 23.7288 0.810561 0.405280 0.914192i \(-0.367174\pi\)
0.405280 + 0.914192i \(0.367174\pi\)
\(858\) 4.47135 0.152649
\(859\) 2.77887 0.0948138 0.0474069 0.998876i \(-0.484904\pi\)
0.0474069 + 0.998876i \(0.484904\pi\)
\(860\) 5.61968 0.191630
\(861\) 34.5102 1.17610
\(862\) 17.9198 0.610351
\(863\) 10.5151 0.357937 0.178968 0.983855i \(-0.442724\pi\)
0.178968 + 0.983855i \(0.442724\pi\)
\(864\) 7.75694 0.263896
\(865\) 22.6937 0.771608
\(866\) 4.96486 0.168713
\(867\) 3.34266 0.113523
\(868\) −5.22364 −0.177302
\(869\) 1.99262 0.0675948
\(870\) 10.6391 0.360699
\(871\) −32.7921 −1.11112
\(872\) 16.1373 0.546476
\(873\) −72.7325 −2.46162
\(874\) −25.0351 −0.846826
\(875\) 1.31955 0.0446090
\(876\) 7.39973 0.250014
\(877\) 27.6197 0.932650 0.466325 0.884613i \(-0.345578\pi\)
0.466325 + 0.884613i \(0.345578\pi\)
\(878\) −13.8371 −0.466980
\(879\) −37.9099 −1.27867
\(880\) 0.258786 0.00872366
\(881\) 10.2200 0.344319 0.172159 0.985069i \(-0.444926\pi\)
0.172159 + 0.985069i \(0.444926\pi\)
\(882\) −29.6548 −0.998530
\(883\) 53.5684 1.80272 0.901361 0.433069i \(-0.142569\pi\)
0.901361 + 0.433069i \(0.142569\pi\)
\(884\) −25.0351 −0.842023
\(885\) −28.1530 −0.946352
\(886\) 14.3390 0.481727
\(887\) 36.5904 1.22858 0.614292 0.789079i \(-0.289442\pi\)
0.614292 + 0.789079i \(0.289442\pi\)
\(888\) −2.93923 −0.0986343
\(889\) −9.83963 −0.330011
\(890\) −6.00000 −0.201120
\(891\) −1.52222 −0.0509963
\(892\) −16.5589 −0.554434
\(893\) 16.3960 0.548673
\(894\) 54.0703 1.80838
\(895\) 8.73501 0.291979
\(896\) −1.31955 −0.0440831
\(897\) 147.168 4.91381
\(898\) 12.4787 0.416421
\(899\) −14.3291 −0.477901
\(900\) 5.63910 0.187970
\(901\) 54.9293 1.82996
\(902\) 2.30265 0.0766697
\(903\) 21.7958 0.725318
\(904\) 1.01942 0.0339053
\(905\) −10.6391 −0.353656
\(906\) 17.2782 0.574030
\(907\) 7.64279 0.253775 0.126887 0.991917i \(-0.459501\pi\)
0.126887 + 0.991917i \(0.459501\pi\)
\(908\) −4.01573 −0.133267
\(909\) 58.6243 1.94445
\(910\) −7.75694 −0.257140
\(911\) 22.0132 0.729330 0.364665 0.931139i \(-0.381183\pi\)
0.364665 + 0.931139i \(0.381183\pi\)
\(912\) 8.63910 0.286069
\(913\) 1.59893 0.0529170
\(914\) 21.6585 0.716400
\(915\) −1.11784 −0.0369546
\(916\) 25.5139 0.843002
\(917\) −3.19551 −0.105525
\(918\) 33.0351 1.09032
\(919\) 23.6999 0.781786 0.390893 0.920436i \(-0.372166\pi\)
0.390893 + 0.920436i \(0.372166\pi\)
\(920\) 8.51757 0.280816
\(921\) −11.1178 −0.366345
\(922\) −29.4155 −0.968747
\(923\) −66.0703 −2.17473
\(924\) 1.00369 0.0330191
\(925\) −1.00000 −0.0328798
\(926\) −9.03514 −0.296913
\(927\) −78.2621 −2.57046
\(928\) −3.61968 −0.118822
\(929\) 8.82022 0.289382 0.144691 0.989477i \(-0.453781\pi\)
0.144691 + 0.989477i \(0.453781\pi\)
\(930\) −11.6354 −0.381540
\(931\) −15.4568 −0.506576
\(932\) 7.96116 0.260777
\(933\) −44.9136 −1.47041
\(934\) 7.05825 0.230953
\(935\) 1.10211 0.0360429
\(936\) −33.1493 −1.08352
\(937\) 40.0703 1.30904 0.654520 0.756045i \(-0.272871\pi\)
0.654520 + 0.756045i \(0.272871\pi\)
\(938\) −7.36090 −0.240342
\(939\) 55.9488 1.82582
\(940\) −5.57834 −0.181945
\(941\) −31.4312 −1.02463 −0.512314 0.858798i \(-0.671211\pi\)
−0.512314 + 0.858798i \(0.671211\pi\)
\(942\) 10.6391 0.346641
\(943\) 75.7884 2.46801
\(944\) 9.57834 0.311748
\(945\) 10.2357 0.332967
\(946\) 1.45429 0.0472832
\(947\) −53.5370 −1.73972 −0.869859 0.493300i \(-0.835790\pi\)
−0.869859 + 0.493300i \(0.835790\pi\)
\(948\) −22.6317 −0.735044
\(949\) −14.7995 −0.480411
\(950\) 2.93923 0.0953614
\(951\) −70.9451 −2.30055
\(952\) −5.61968 −0.182135
\(953\) 5.23937 0.169720 0.0848599 0.996393i \(-0.472956\pi\)
0.0848599 + 0.996393i \(0.472956\pi\)
\(954\) 72.7325 2.35480
\(955\) −22.1116 −0.715516
\(956\) 11.7983 0.381584
\(957\) 2.75325 0.0889998
\(958\) −29.3353 −0.947780
\(959\) −20.8433 −0.673066
\(960\) −2.93923 −0.0948634
\(961\) −15.3291 −0.494486
\(962\) 5.87847 0.189529
\(963\) −23.7826 −0.766382
\(964\) 24.9963 0.805077
\(965\) −7.03514 −0.226469
\(966\) 33.0351 1.06289
\(967\) −46.5929 −1.49833 −0.749163 0.662386i \(-0.769544\pi\)
−0.749163 + 0.662386i \(0.769544\pi\)
\(968\) −10.9330 −0.351401
\(969\) 36.7921 1.18193
\(970\) 12.8979 0.414126
\(971\) 38.1373 1.22388 0.611941 0.790903i \(-0.290389\pi\)
0.611941 + 0.790903i \(0.290389\pi\)
\(972\) −5.98176 −0.191865
\(973\) 15.0633 0.482907
\(974\) −37.9099 −1.21471
\(975\) −17.2782 −0.553345
\(976\) 0.380316 0.0121736
\(977\) 40.8979 1.30844 0.654220 0.756305i \(-0.272997\pi\)
0.654220 + 0.756305i \(0.272997\pi\)
\(978\) −64.8235 −2.07283
\(979\) −1.55271 −0.0496250
\(980\) 5.25879 0.167986
\(981\) 90.9996 2.90539
\(982\) −14.5564 −0.464514
\(983\) 50.4638 1.60955 0.804773 0.593583i \(-0.202287\pi\)
0.804773 + 0.593583i \(0.202287\pi\)
\(984\) −26.1530 −0.833727
\(985\) −25.7569 −0.820684
\(986\) −15.4155 −0.490928
\(987\) −21.6354 −0.688663
\(988\) −17.2782 −0.549693
\(989\) 47.8661 1.52205
\(990\) 1.45932 0.0463802
\(991\) −15.9587 −0.506943 −0.253472 0.967343i \(-0.581572\pi\)
−0.253472 + 0.967343i \(0.581572\pi\)
\(992\) 3.95865 0.125687
\(993\) 2.40343 0.0762704
\(994\) −14.8309 −0.470408
\(995\) 12.7350 0.403727
\(996\) −18.1604 −0.575433
\(997\) −9.23937 −0.292614 −0.146307 0.989239i \(-0.546739\pi\)
−0.146307 + 0.989239i \(0.546739\pi\)
\(998\) 23.9744 0.758896
\(999\) −7.75694 −0.245419
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 370.2.a.g.1.3 3
3.2 odd 2 3330.2.a.bg.1.2 3
4.3 odd 2 2960.2.a.u.1.1 3
5.2 odd 4 1850.2.b.o.149.4 6
5.3 odd 4 1850.2.b.o.149.3 6
5.4 even 2 1850.2.a.z.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.a.g.1.3 3 1.1 even 1 trivial
1850.2.a.z.1.1 3 5.4 even 2
1850.2.b.o.149.3 6 5.3 odd 4
1850.2.b.o.149.4 6 5.2 odd 4
2960.2.a.u.1.1 3 4.3 odd 2
3330.2.a.bg.1.2 3 3.2 odd 2