Properties

Label 2842.2.a.x.1.4
Level $2842$
Weight $2$
Character 2842.1
Self dual yes
Analytic conductor $22.693$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2842.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.6934842544\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.1019601.1
Defining polynomial: \( x^{5} - 10x^{3} - x^{2} + 24x + 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 406)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-2.48141\) of defining polynomial
Character \(\chi\) \(=\) 2842.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.714579 q^{3} +1.00000 q^{4} -0.233169 q^{5} +0.714579 q^{6} +1.00000 q^{8} -2.48938 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.714579 q^{3} +1.00000 q^{4} -0.233169 q^{5} +0.714579 q^{6} +1.00000 q^{8} -2.48938 q^{9} -0.233169 q^{10} +0.293388 q^{11} +0.714579 q^{12} -4.15740 q^{13} -0.166617 q^{15} +1.00000 q^{16} -0.609435 q^{17} -2.48938 q^{18} -6.67740 q^{19} -0.233169 q^{20} +0.293388 q^{22} -1.48774 q^{23} +0.714579 q^{24} -4.94563 q^{25} -4.15740 q^{26} -3.92259 q^{27} -1.00000 q^{29} -0.166617 q^{30} +1.35175 q^{31} +1.00000 q^{32} +0.209649 q^{33} -0.609435 q^{34} -2.48938 q^{36} +0.637171 q^{37} -6.67740 q^{38} -2.97079 q^{39} -0.233169 q^{40} -3.31605 q^{41} -3.29502 q^{43} +0.293388 q^{44} +0.580445 q^{45} -1.48774 q^{46} -2.18092 q^{47} +0.714579 q^{48} -4.94563 q^{50} -0.435489 q^{51} -4.15740 q^{52} +11.9922 q^{53} -3.92259 q^{54} -0.0684089 q^{55} -4.77153 q^{57} -1.00000 q^{58} -4.30113 q^{59} -0.166617 q^{60} -3.64803 q^{61} +1.35175 q^{62} +1.00000 q^{64} +0.969374 q^{65} +0.209649 q^{66} +4.95649 q^{67} -0.609435 q^{68} -1.06311 q^{69} +4.21106 q^{71} -2.48938 q^{72} -5.84298 q^{73} +0.637171 q^{74} -3.53404 q^{75} -6.67740 q^{76} -2.97079 q^{78} +2.10678 q^{79} -0.233169 q^{80} +4.66513 q^{81} -3.31605 q^{82} -6.73621 q^{83} +0.142101 q^{85} -3.29502 q^{86} -0.714579 q^{87} +0.293388 q^{88} +12.6247 q^{89} +0.580445 q^{90} -1.48774 q^{92} +0.965932 q^{93} -2.18092 q^{94} +1.55696 q^{95} +0.714579 q^{96} -5.70498 q^{97} -0.730354 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 7 q^{5} - 3 q^{6} + 5 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 7 q^{5} - 3 q^{6} + 5 q^{8} + 8 q^{9} - 7 q^{10} - 3 q^{12} - 10 q^{13} - 10 q^{15} + 5 q^{16} - 8 q^{17} + 8 q^{18} - 2 q^{19} - 7 q^{20} + q^{23} - 3 q^{24} + 12 q^{25} - 10 q^{26} - 15 q^{27} - 5 q^{29} - 10 q^{30} - 11 q^{31} + 5 q^{32} - 9 q^{33} - 8 q^{34} + 8 q^{36} - 8 q^{37} - 2 q^{38} + 18 q^{39} - 7 q^{40} - 23 q^{41} - 3 q^{43} - 4 q^{45} + q^{46} - 16 q^{47} - 3 q^{48} + 12 q^{50} + 7 q^{51} - 10 q^{52} + 7 q^{53} - 15 q^{54} - 6 q^{55} - 34 q^{57} - 5 q^{58} + 9 q^{59} - 10 q^{60} - 15 q^{61} - 11 q^{62} + 5 q^{64} + 5 q^{65} - 9 q^{66} - 4 q^{67} - 8 q^{68} - 14 q^{69} - 22 q^{71} + 8 q^{72} - 8 q^{74} + 34 q^{75} - 2 q^{76} + 18 q^{78} - 13 q^{79} - 7 q^{80} + 17 q^{81} - 23 q^{82} - 28 q^{83} - 7 q^{85} - 3 q^{86} + 3 q^{87} - 17 q^{89} - 4 q^{90} + q^{92} + 17 q^{93} - 16 q^{94} - 9 q^{95} - 3 q^{96} - 42 q^{97} - 42 q^{99}+O(q^{100}) \) 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
\(3\) 0.714579 0.412562 0.206281 0.978493i \(-0.433864\pi\)
0.206281 + 0.978493i \(0.433864\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.233169 −0.104276 −0.0521381 0.998640i \(-0.516604\pi\)
−0.0521381 + 0.998640i \(0.516604\pi\)
\(6\) 0.714579 0.291726
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −2.48938 −0.829792
\(10\) −0.233169 −0.0737344
\(11\) 0.293388 0.0884599 0.0442299 0.999021i \(-0.485917\pi\)
0.0442299 + 0.999021i \(0.485917\pi\)
\(12\) 0.714579 0.206281
\(13\) −4.15740 −1.15305 −0.576527 0.817078i \(-0.695592\pi\)
−0.576527 + 0.817078i \(0.695592\pi\)
\(14\) 0 0
\(15\) −0.166617 −0.0430204
\(16\) 1.00000 0.250000
\(17\) −0.609435 −0.147810 −0.0739048 0.997265i \(-0.523546\pi\)
−0.0739048 + 0.997265i \(0.523546\pi\)
\(18\) −2.48938 −0.586752
\(19\) −6.67740 −1.53190 −0.765950 0.642900i \(-0.777731\pi\)
−0.765950 + 0.642900i \(0.777731\pi\)
\(20\) −0.233169 −0.0521381
\(21\) 0 0
\(22\) 0.293388 0.0625506
\(23\) −1.48774 −0.310216 −0.155108 0.987898i \(-0.549572\pi\)
−0.155108 + 0.987898i \(0.549572\pi\)
\(24\) 0.714579 0.145863
\(25\) −4.94563 −0.989126
\(26\) −4.15740 −0.815333
\(27\) −3.92259 −0.754903
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) −0.166617 −0.0304200
\(31\) 1.35175 0.242781 0.121391 0.992605i \(-0.461265\pi\)
0.121391 + 0.992605i \(0.461265\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.209649 0.0364952
\(34\) −0.609435 −0.104517
\(35\) 0 0
\(36\) −2.48938 −0.414896
\(37\) 0.637171 0.104750 0.0523752 0.998627i \(-0.483321\pi\)
0.0523752 + 0.998627i \(0.483321\pi\)
\(38\) −6.67740 −1.08322
\(39\) −2.97079 −0.475707
\(40\) −0.233169 −0.0368672
\(41\) −3.31605 −0.517880 −0.258940 0.965893i \(-0.583373\pi\)
−0.258940 + 0.965893i \(0.583373\pi\)
\(42\) 0 0
\(43\) −3.29502 −0.502486 −0.251243 0.967924i \(-0.580839\pi\)
−0.251243 + 0.967924i \(0.580839\pi\)
\(44\) 0.293388 0.0442299
\(45\) 0.580445 0.0865276
\(46\) −1.48774 −0.219356
\(47\) −2.18092 −0.318119 −0.159060 0.987269i \(-0.550846\pi\)
−0.159060 + 0.987269i \(0.550846\pi\)
\(48\) 0.714579 0.103141
\(49\) 0 0
\(50\) −4.94563 −0.699418
\(51\) −0.435489 −0.0609807
\(52\) −4.15740 −0.576527
\(53\) 11.9922 1.64725 0.823627 0.567132i \(-0.191947\pi\)
0.823627 + 0.567132i \(0.191947\pi\)
\(54\) −3.92259 −0.533797
\(55\) −0.0684089 −0.00922426
\(56\) 0 0
\(57\) −4.77153 −0.632004
\(58\) −1.00000 −0.131306
\(59\) −4.30113 −0.559960 −0.279980 0.960006i \(-0.590328\pi\)
−0.279980 + 0.960006i \(0.590328\pi\)
\(60\) −0.166617 −0.0215102
\(61\) −3.64803 −0.467082 −0.233541 0.972347i \(-0.575031\pi\)
−0.233541 + 0.972347i \(0.575031\pi\)
\(62\) 1.35175 0.171672
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.969374 0.120236
\(66\) 0.209649 0.0258060
\(67\) 4.95649 0.605531 0.302766 0.953065i \(-0.402090\pi\)
0.302766 + 0.953065i \(0.402090\pi\)
\(68\) −0.609435 −0.0739048
\(69\) −1.06311 −0.127983
\(70\) 0 0
\(71\) 4.21106 0.499761 0.249881 0.968277i \(-0.419609\pi\)
0.249881 + 0.968277i \(0.419609\pi\)
\(72\) −2.48938 −0.293376
\(73\) −5.84298 −0.683870 −0.341935 0.939724i \(-0.611082\pi\)
−0.341935 + 0.939724i \(0.611082\pi\)
\(74\) 0.637171 0.0740697
\(75\) −3.53404 −0.408076
\(76\) −6.67740 −0.765950
\(77\) 0 0
\(78\) −2.97079 −0.336375
\(79\) 2.10678 0.237031 0.118516 0.992952i \(-0.462186\pi\)
0.118516 + 0.992952i \(0.462186\pi\)
\(80\) −0.233169 −0.0260690
\(81\) 4.66513 0.518348
\(82\) −3.31605 −0.366196
\(83\) −6.73621 −0.739395 −0.369697 0.929152i \(-0.620539\pi\)
−0.369697 + 0.929152i \(0.620539\pi\)
\(84\) 0 0
\(85\) 0.142101 0.0154130
\(86\) −3.29502 −0.355312
\(87\) −0.714579 −0.0766109
\(88\) 0.293388 0.0312753
\(89\) 12.6247 1.33821 0.669106 0.743167i \(-0.266677\pi\)
0.669106 + 0.743167i \(0.266677\pi\)
\(90\) 0.580445 0.0611842
\(91\) 0 0
\(92\) −1.48774 −0.155108
\(93\) 0.965932 0.100162
\(94\) −2.18092 −0.224944
\(95\) 1.55696 0.159741
\(96\) 0.714579 0.0729314
\(97\) −5.70498 −0.579253 −0.289626 0.957140i \(-0.593531\pi\)
−0.289626 + 0.957140i \(0.593531\pi\)
\(98\) 0 0
\(99\) −0.730354 −0.0734033
\(100\) −4.94563 −0.494563
\(101\) −15.7339 −1.56558 −0.782789 0.622287i \(-0.786204\pi\)
−0.782789 + 0.622287i \(0.786204\pi\)
\(102\) −0.435489 −0.0431199
\(103\) 4.89549 0.482367 0.241184 0.970479i \(-0.422464\pi\)
0.241184 + 0.970479i \(0.422464\pi\)
\(104\) −4.15740 −0.407666
\(105\) 0 0
\(106\) 11.9922 1.16478
\(107\) 11.2315 1.08579 0.542894 0.839801i \(-0.317329\pi\)
0.542894 + 0.839801i \(0.317329\pi\)
\(108\) −3.92259 −0.377452
\(109\) 15.1865 1.45461 0.727304 0.686316i \(-0.240773\pi\)
0.727304 + 0.686316i \(0.240773\pi\)
\(110\) −0.0684089 −0.00652253
\(111\) 0.455309 0.0432160
\(112\) 0 0
\(113\) −10.2976 −0.968717 −0.484359 0.874870i \(-0.660947\pi\)
−0.484359 + 0.874870i \(0.660947\pi\)
\(114\) −4.77153 −0.446895
\(115\) 0.346895 0.0323481
\(116\) −1.00000 −0.0928477
\(117\) 10.3493 0.956796
\(118\) −4.30113 −0.395951
\(119\) 0 0
\(120\) −0.166617 −0.0152100
\(121\) −10.9139 −0.992175
\(122\) −3.64803 −0.330277
\(123\) −2.36958 −0.213658
\(124\) 1.35175 0.121391
\(125\) 2.31901 0.207419
\(126\) 0 0
\(127\) −15.3053 −1.35813 −0.679065 0.734078i \(-0.737615\pi\)
−0.679065 + 0.734078i \(0.737615\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.35455 −0.207307
\(130\) 0.969374 0.0850198
\(131\) −12.2176 −1.06745 −0.533726 0.845657i \(-0.679209\pi\)
−0.533726 + 0.845657i \(0.679209\pi\)
\(132\) 0.209649 0.0182476
\(133\) 0 0
\(134\) 4.95649 0.428175
\(135\) 0.914626 0.0787184
\(136\) −0.609435 −0.0522586
\(137\) 17.8291 1.52324 0.761622 0.648022i \(-0.224404\pi\)
0.761622 + 0.648022i \(0.224404\pi\)
\(138\) −1.06311 −0.0904978
\(139\) −7.99852 −0.678426 −0.339213 0.940710i \(-0.610161\pi\)
−0.339213 + 0.940710i \(0.610161\pi\)
\(140\) 0 0
\(141\) −1.55844 −0.131244
\(142\) 4.21106 0.353384
\(143\) −1.21973 −0.101999
\(144\) −2.48938 −0.207448
\(145\) 0.233169 0.0193636
\(146\) −5.84298 −0.483569
\(147\) 0 0
\(148\) 0.637171 0.0523752
\(149\) 7.81597 0.640309 0.320155 0.947365i \(-0.396265\pi\)
0.320155 + 0.947365i \(0.396265\pi\)
\(150\) −3.53404 −0.288553
\(151\) −16.2176 −1.31977 −0.659883 0.751368i \(-0.729394\pi\)
−0.659883 + 0.751368i \(0.729394\pi\)
\(152\) −6.67740 −0.541609
\(153\) 1.51711 0.122651
\(154\) 0 0
\(155\) −0.315186 −0.0253163
\(156\) −2.97079 −0.237853
\(157\) 23.6455 1.88711 0.943556 0.331212i \(-0.107457\pi\)
0.943556 + 0.331212i \(0.107457\pi\)
\(158\) 2.10678 0.167606
\(159\) 8.56937 0.679595
\(160\) −0.233169 −0.0184336
\(161\) 0 0
\(162\) 4.66513 0.366527
\(163\) −13.6125 −1.06621 −0.533106 0.846048i \(-0.678975\pi\)
−0.533106 + 0.846048i \(0.678975\pi\)
\(164\) −3.31605 −0.258940
\(165\) −0.0488836 −0.00380558
\(166\) −6.73621 −0.522831
\(167\) 3.59710 0.278352 0.139176 0.990268i \(-0.455555\pi\)
0.139176 + 0.990268i \(0.455555\pi\)
\(168\) 0 0
\(169\) 4.28394 0.329534
\(170\) 0.142101 0.0108987
\(171\) 16.6226 1.27116
\(172\) −3.29502 −0.251243
\(173\) −12.3956 −0.942423 −0.471212 0.882020i \(-0.656183\pi\)
−0.471212 + 0.882020i \(0.656183\pi\)
\(174\) −0.714579 −0.0541721
\(175\) 0 0
\(176\) 0.293388 0.0221150
\(177\) −3.07350 −0.231018
\(178\) 12.6247 0.946259
\(179\) 9.58344 0.716300 0.358150 0.933664i \(-0.383408\pi\)
0.358150 + 0.933664i \(0.383408\pi\)
\(180\) 0.580445 0.0432638
\(181\) −0.148655 −0.0110495 −0.00552473 0.999985i \(-0.501759\pi\)
−0.00552473 + 0.999985i \(0.501759\pi\)
\(182\) 0 0
\(183\) −2.60680 −0.192700
\(184\) −1.48774 −0.109678
\(185\) −0.148568 −0.0109230
\(186\) 0.965932 0.0708256
\(187\) −0.178801 −0.0130752
\(188\) −2.18092 −0.159060
\(189\) 0 0
\(190\) 1.55696 0.112954
\(191\) 10.2831 0.744058 0.372029 0.928221i \(-0.378662\pi\)
0.372029 + 0.928221i \(0.378662\pi\)
\(192\) 0.714579 0.0515703
\(193\) 12.4681 0.897476 0.448738 0.893663i \(-0.351874\pi\)
0.448738 + 0.893663i \(0.351874\pi\)
\(194\) −5.70498 −0.409593
\(195\) 0.692694 0.0496049
\(196\) 0 0
\(197\) −19.0312 −1.35591 −0.677957 0.735101i \(-0.737135\pi\)
−0.677957 + 0.735101i \(0.737135\pi\)
\(198\) −0.730354 −0.0519040
\(199\) 10.6083 0.752005 0.376003 0.926619i \(-0.377298\pi\)
0.376003 + 0.926619i \(0.377298\pi\)
\(200\) −4.94563 −0.349709
\(201\) 3.54180 0.249819
\(202\) −15.7339 −1.10703
\(203\) 0 0
\(204\) −0.435489 −0.0304903
\(205\) 0.773198 0.0540025
\(206\) 4.89549 0.341085
\(207\) 3.70355 0.257415
\(208\) −4.15740 −0.288264
\(209\) −1.95907 −0.135512
\(210\) 0 0
\(211\) −8.69020 −0.598258 −0.299129 0.954213i \(-0.596696\pi\)
−0.299129 + 0.954213i \(0.596696\pi\)
\(212\) 11.9922 0.823627
\(213\) 3.00914 0.206183
\(214\) 11.2315 0.767767
\(215\) 0.768296 0.0523974
\(216\) −3.92259 −0.266899
\(217\) 0 0
\(218\) 15.1865 1.02856
\(219\) −4.17527 −0.282139
\(220\) −0.0684089 −0.00461213
\(221\) 2.53366 0.170433
\(222\) 0.455309 0.0305583
\(223\) −9.99383 −0.669236 −0.334618 0.942354i \(-0.608607\pi\)
−0.334618 + 0.942354i \(0.608607\pi\)
\(224\) 0 0
\(225\) 12.3115 0.820770
\(226\) −10.2976 −0.684986
\(227\) 25.3090 1.67982 0.839910 0.542726i \(-0.182608\pi\)
0.839910 + 0.542726i \(0.182608\pi\)
\(228\) −4.77153 −0.316002
\(229\) −18.4785 −1.22109 −0.610545 0.791981i \(-0.709050\pi\)
−0.610545 + 0.791981i \(0.709050\pi\)
\(230\) 0.346895 0.0228736
\(231\) 0 0
\(232\) −1.00000 −0.0656532
\(233\) −9.35908 −0.613134 −0.306567 0.951849i \(-0.599180\pi\)
−0.306567 + 0.951849i \(0.599180\pi\)
\(234\) 10.3493 0.676557
\(235\) 0.508521 0.0331723
\(236\) −4.30113 −0.279980
\(237\) 1.50546 0.0977901
\(238\) 0 0
\(239\) −17.5424 −1.13473 −0.567363 0.823468i \(-0.692036\pi\)
−0.567363 + 0.823468i \(0.692036\pi\)
\(240\) −0.166617 −0.0107551
\(241\) −3.04226 −0.195969 −0.0979845 0.995188i \(-0.531240\pi\)
−0.0979845 + 0.995188i \(0.531240\pi\)
\(242\) −10.9139 −0.701574
\(243\) 15.1014 0.968754
\(244\) −3.64803 −0.233541
\(245\) 0 0
\(246\) −2.36958 −0.151079
\(247\) 27.7606 1.76636
\(248\) 1.35175 0.0858362
\(249\) −4.81355 −0.305046
\(250\) 2.31901 0.146667
\(251\) 17.2275 1.08739 0.543694 0.839283i \(-0.317025\pi\)
0.543694 + 0.839283i \(0.317025\pi\)
\(252\) 0 0
\(253\) −0.436486 −0.0274416
\(254\) −15.3053 −0.960343
\(255\) 0.101542 0.00635883
\(256\) 1.00000 0.0625000
\(257\) −20.6454 −1.28783 −0.643913 0.765098i \(-0.722690\pi\)
−0.643913 + 0.765098i \(0.722690\pi\)
\(258\) −2.35455 −0.146588
\(259\) 0 0
\(260\) 0.969374 0.0601180
\(261\) 2.48938 0.154089
\(262\) −12.2176 −0.754803
\(263\) −16.5706 −1.02179 −0.510894 0.859644i \(-0.670686\pi\)
−0.510894 + 0.859644i \(0.670686\pi\)
\(264\) 0.209649 0.0129030
\(265\) −2.79620 −0.171769
\(266\) 0 0
\(267\) 9.02132 0.552096
\(268\) 4.95649 0.302766
\(269\) 2.62826 0.160248 0.0801239 0.996785i \(-0.474468\pi\)
0.0801239 + 0.996785i \(0.474468\pi\)
\(270\) 0.914626 0.0556623
\(271\) 12.6224 0.766756 0.383378 0.923592i \(-0.374761\pi\)
0.383378 + 0.923592i \(0.374761\pi\)
\(272\) −0.609435 −0.0369524
\(273\) 0 0
\(274\) 17.8291 1.07710
\(275\) −1.45099 −0.0874980
\(276\) −1.06311 −0.0639916
\(277\) 19.4595 1.16921 0.584605 0.811318i \(-0.301249\pi\)
0.584605 + 0.811318i \(0.301249\pi\)
\(278\) −7.99852 −0.479720
\(279\) −3.36502 −0.201458
\(280\) 0 0
\(281\) 15.9906 0.953917 0.476958 0.878926i \(-0.341739\pi\)
0.476958 + 0.878926i \(0.341739\pi\)
\(282\) −1.55844 −0.0928035
\(283\) −27.9827 −1.66340 −0.831699 0.555227i \(-0.812631\pi\)
−0.831699 + 0.555227i \(0.812631\pi\)
\(284\) 4.21106 0.249881
\(285\) 1.11257 0.0659030
\(286\) −1.21973 −0.0721242
\(287\) 0 0
\(288\) −2.48938 −0.146688
\(289\) −16.6286 −0.978152
\(290\) 0.233169 0.0136921
\(291\) −4.07666 −0.238978
\(292\) −5.84298 −0.341935
\(293\) −20.6845 −1.20840 −0.604202 0.796832i \(-0.706508\pi\)
−0.604202 + 0.796832i \(0.706508\pi\)
\(294\) 0 0
\(295\) 1.00289 0.0583905
\(296\) 0.637171 0.0370348
\(297\) −1.15084 −0.0667786
\(298\) 7.81597 0.452767
\(299\) 6.18513 0.357695
\(300\) −3.53404 −0.204038
\(301\) 0 0
\(302\) −16.2176 −0.933215
\(303\) −11.2431 −0.645899
\(304\) −6.67740 −0.382975
\(305\) 0.850606 0.0487055
\(306\) 1.51711 0.0867276
\(307\) 28.6540 1.63537 0.817686 0.575664i \(-0.195256\pi\)
0.817686 + 0.575664i \(0.195256\pi\)
\(308\) 0 0
\(309\) 3.49822 0.199007
\(310\) −0.315186 −0.0179013
\(311\) −10.4647 −0.593399 −0.296699 0.954971i \(-0.595886\pi\)
−0.296699 + 0.954971i \(0.595886\pi\)
\(312\) −2.97079 −0.168188
\(313\) 31.4172 1.77580 0.887901 0.460034i \(-0.152163\pi\)
0.887901 + 0.460034i \(0.152163\pi\)
\(314\) 23.6455 1.33439
\(315\) 0 0
\(316\) 2.10678 0.118516
\(317\) 12.7478 0.715986 0.357993 0.933724i \(-0.383461\pi\)
0.357993 + 0.933724i \(0.383461\pi\)
\(318\) 8.56937 0.480546
\(319\) −0.293388 −0.0164266
\(320\) −0.233169 −0.0130345
\(321\) 8.02577 0.447955
\(322\) 0 0
\(323\) 4.06944 0.226430
\(324\) 4.66513 0.259174
\(325\) 20.5610 1.14052
\(326\) −13.6125 −0.753926
\(327\) 10.8520 0.600116
\(328\) −3.31605 −0.183098
\(329\) 0 0
\(330\) −0.0488836 −0.00269095
\(331\) −10.2619 −0.564046 −0.282023 0.959408i \(-0.591006\pi\)
−0.282023 + 0.959408i \(0.591006\pi\)
\(332\) −6.73621 −0.369697
\(333\) −1.58616 −0.0869210
\(334\) 3.59710 0.196825
\(335\) −1.15570 −0.0631425
\(336\) 0 0
\(337\) −26.9868 −1.47007 −0.735033 0.678031i \(-0.762833\pi\)
−0.735033 + 0.678031i \(0.762833\pi\)
\(338\) 4.28394 0.233016
\(339\) −7.35845 −0.399656
\(340\) 0.142101 0.00770652
\(341\) 0.396588 0.0214764
\(342\) 16.6226 0.898845
\(343\) 0 0
\(344\) −3.29502 −0.177656
\(345\) 0.247884 0.0133456
\(346\) −12.3956 −0.666394
\(347\) 0.0299869 0.00160978 0.000804890 1.00000i \(-0.499744\pi\)
0.000804890 1.00000i \(0.499744\pi\)
\(348\) −0.714579 −0.0383054
\(349\) −6.30027 −0.337246 −0.168623 0.985681i \(-0.553932\pi\)
−0.168623 + 0.985681i \(0.553932\pi\)
\(350\) 0 0
\(351\) 16.3078 0.870444
\(352\) 0.293388 0.0156376
\(353\) −27.6344 −1.47083 −0.735415 0.677617i \(-0.763013\pi\)
−0.735415 + 0.677617i \(0.763013\pi\)
\(354\) −3.07350 −0.163355
\(355\) −0.981888 −0.0521132
\(356\) 12.6247 0.669106
\(357\) 0 0
\(358\) 9.58344 0.506501
\(359\) −18.4797 −0.975322 −0.487661 0.873033i \(-0.662150\pi\)
−0.487661 + 0.873033i \(0.662150\pi\)
\(360\) 0.580445 0.0305921
\(361\) 25.5877 1.34672
\(362\) −0.148655 −0.00781314
\(363\) −7.79886 −0.409334
\(364\) 0 0
\(365\) 1.36240 0.0713113
\(366\) −2.60680 −0.136260
\(367\) 17.7335 0.925683 0.462841 0.886441i \(-0.346830\pi\)
0.462841 + 0.886441i \(0.346830\pi\)
\(368\) −1.48774 −0.0775539
\(369\) 8.25489 0.429732
\(370\) −0.148568 −0.00772370
\(371\) 0 0
\(372\) 0.965932 0.0500812
\(373\) 14.2392 0.737279 0.368639 0.929573i \(-0.379824\pi\)
0.368639 + 0.929573i \(0.379824\pi\)
\(374\) −0.178801 −0.00924558
\(375\) 1.65712 0.0855731
\(376\) −2.18092 −0.112472
\(377\) 4.15740 0.214117
\(378\) 0 0
\(379\) 33.9879 1.74584 0.872920 0.487863i \(-0.162224\pi\)
0.872920 + 0.487863i \(0.162224\pi\)
\(380\) 1.55696 0.0798704
\(381\) −10.9369 −0.560313
\(382\) 10.2831 0.526128
\(383\) 17.0812 0.872807 0.436404 0.899751i \(-0.356252\pi\)
0.436404 + 0.899751i \(0.356252\pi\)
\(384\) 0.714579 0.0364657
\(385\) 0 0
\(386\) 12.4681 0.634611
\(387\) 8.20256 0.416959
\(388\) −5.70498 −0.289626
\(389\) −11.3176 −0.573827 −0.286913 0.957957i \(-0.592629\pi\)
−0.286913 + 0.957957i \(0.592629\pi\)
\(390\) 0.692694 0.0350759
\(391\) 0.906682 0.0458529
\(392\) 0 0
\(393\) −8.73040 −0.440391
\(394\) −19.0312 −0.958776
\(395\) −0.491235 −0.0247167
\(396\) −0.730354 −0.0367017
\(397\) −10.2515 −0.514506 −0.257253 0.966344i \(-0.582817\pi\)
−0.257253 + 0.966344i \(0.582817\pi\)
\(398\) 10.6083 0.531748
\(399\) 0 0
\(400\) −4.94563 −0.247282
\(401\) −17.6102 −0.879410 −0.439705 0.898142i \(-0.644917\pi\)
−0.439705 + 0.898142i \(0.644917\pi\)
\(402\) 3.54180 0.176649
\(403\) −5.61976 −0.279940
\(404\) −15.7339 −0.782789
\(405\) −1.08776 −0.0540513
\(406\) 0 0
\(407\) 0.186939 0.00926620
\(408\) −0.435489 −0.0215599
\(409\) 38.8959 1.92328 0.961639 0.274317i \(-0.0884519\pi\)
0.961639 + 0.274317i \(0.0884519\pi\)
\(410\) 0.773198 0.0381855
\(411\) 12.7403 0.628433
\(412\) 4.89549 0.241184
\(413\) 0 0
\(414\) 3.70355 0.182020
\(415\) 1.57067 0.0771013
\(416\) −4.15740 −0.203833
\(417\) −5.71558 −0.279893
\(418\) −1.95907 −0.0958212
\(419\) 12.6437 0.617683 0.308842 0.951113i \(-0.400059\pi\)
0.308842 + 0.951113i \(0.400059\pi\)
\(420\) 0 0
\(421\) −10.7981 −0.526267 −0.263133 0.964759i \(-0.584756\pi\)
−0.263133 + 0.964759i \(0.584756\pi\)
\(422\) −8.69020 −0.423032
\(423\) 5.42912 0.263973
\(424\) 11.9922 0.582392
\(425\) 3.01404 0.146202
\(426\) 3.00914 0.145793
\(427\) 0 0
\(428\) 11.2315 0.542894
\(429\) −0.871594 −0.0420810
\(430\) 0.768296 0.0370505
\(431\) −36.1812 −1.74279 −0.871394 0.490583i \(-0.836784\pi\)
−0.871394 + 0.490583i \(0.836784\pi\)
\(432\) −3.92259 −0.188726
\(433\) −10.6350 −0.511084 −0.255542 0.966798i \(-0.582254\pi\)
−0.255542 + 0.966798i \(0.582254\pi\)
\(434\) 0 0
\(435\) 0.166617 0.00798869
\(436\) 15.1865 0.727304
\(437\) 9.93425 0.475219
\(438\) −4.17527 −0.199502
\(439\) 2.97507 0.141992 0.0709961 0.997477i \(-0.477382\pi\)
0.0709961 + 0.997477i \(0.477382\pi\)
\(440\) −0.0684089 −0.00326127
\(441\) 0 0
\(442\) 2.53366 0.120514
\(443\) −27.9429 −1.32761 −0.663804 0.747907i \(-0.731059\pi\)
−0.663804 + 0.747907i \(0.731059\pi\)
\(444\) 0.455309 0.0216080
\(445\) −2.94368 −0.139544
\(446\) −9.99383 −0.473221
\(447\) 5.58513 0.264167
\(448\) 0 0
\(449\) −0.604431 −0.0285248 −0.0142624 0.999898i \(-0.504540\pi\)
−0.0142624 + 0.999898i \(0.504540\pi\)
\(450\) 12.3115 0.580372
\(451\) −0.972889 −0.0458116
\(452\) −10.2976 −0.484359
\(453\) −11.5887 −0.544486
\(454\) 25.3090 1.18781
\(455\) 0 0
\(456\) −4.77153 −0.223447
\(457\) −7.10311 −0.332270 −0.166135 0.986103i \(-0.553129\pi\)
−0.166135 + 0.986103i \(0.553129\pi\)
\(458\) −18.4785 −0.863442
\(459\) 2.39057 0.111582
\(460\) 0.346895 0.0161741
\(461\) −3.81028 −0.177462 −0.0887312 0.996056i \(-0.528281\pi\)
−0.0887312 + 0.996056i \(0.528281\pi\)
\(462\) 0 0
\(463\) −3.42327 −0.159093 −0.0795464 0.996831i \(-0.525347\pi\)
−0.0795464 + 0.996831i \(0.525347\pi\)
\(464\) −1.00000 −0.0464238
\(465\) −0.225225 −0.0104446
\(466\) −9.35908 −0.433551
\(467\) −22.8701 −1.05830 −0.529151 0.848528i \(-0.677490\pi\)
−0.529151 + 0.848528i \(0.677490\pi\)
\(468\) 10.3493 0.478398
\(469\) 0 0
\(470\) 0.508521 0.0234563
\(471\) 16.8965 0.778552
\(472\) −4.30113 −0.197976
\(473\) −0.966721 −0.0444499
\(474\) 1.50546 0.0691481
\(475\) 33.0240 1.51524
\(476\) 0 0
\(477\) −29.8531 −1.36688
\(478\) −17.5424 −0.802372
\(479\) 4.57219 0.208909 0.104454 0.994530i \(-0.466690\pi\)
0.104454 + 0.994530i \(0.466690\pi\)
\(480\) −0.166617 −0.00760501
\(481\) −2.64897 −0.120783
\(482\) −3.04226 −0.138571
\(483\) 0 0
\(484\) −10.9139 −0.496087
\(485\) 1.33022 0.0604022
\(486\) 15.1014 0.685013
\(487\) 21.6569 0.981367 0.490683 0.871338i \(-0.336747\pi\)
0.490683 + 0.871338i \(0.336747\pi\)
\(488\) −3.64803 −0.165138
\(489\) −9.72719 −0.439879
\(490\) 0 0
\(491\) 32.0537 1.44656 0.723281 0.690554i \(-0.242633\pi\)
0.723281 + 0.690554i \(0.242633\pi\)
\(492\) −2.36958 −0.106829
\(493\) 0.609435 0.0274476
\(494\) 27.7606 1.24901
\(495\) 0.170296 0.00765422
\(496\) 1.35175 0.0606954
\(497\) 0 0
\(498\) −4.81355 −0.215700
\(499\) 24.6113 1.10175 0.550877 0.834587i \(-0.314293\pi\)
0.550877 + 0.834587i \(0.314293\pi\)
\(500\) 2.31901 0.103709
\(501\) 2.57041 0.114838
\(502\) 17.2275 0.768900
\(503\) 35.0600 1.56325 0.781623 0.623751i \(-0.214392\pi\)
0.781623 + 0.623751i \(0.214392\pi\)
\(504\) 0 0
\(505\) 3.66864 0.163253
\(506\) −0.436486 −0.0194042
\(507\) 3.06122 0.135953
\(508\) −15.3053 −0.679065
\(509\) 31.7592 1.40770 0.703851 0.710348i \(-0.251462\pi\)
0.703851 + 0.710348i \(0.251462\pi\)
\(510\) 0.101542 0.00449638
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 26.1927 1.15644
\(514\) −20.6454 −0.910631
\(515\) −1.14148 −0.0502994
\(516\) −2.35455 −0.103653
\(517\) −0.639855 −0.0281408
\(518\) 0 0
\(519\) −8.85766 −0.388808
\(520\) 0.969374 0.0425099
\(521\) 14.1681 0.620716 0.310358 0.950620i \(-0.399551\pi\)
0.310358 + 0.950620i \(0.399551\pi\)
\(522\) 2.48938 0.108957
\(523\) 19.7029 0.861547 0.430774 0.902460i \(-0.358241\pi\)
0.430774 + 0.902460i \(0.358241\pi\)
\(524\) −12.2176 −0.533726
\(525\) 0 0
\(526\) −16.5706 −0.722513
\(527\) −0.823804 −0.0358855
\(528\) 0.209649 0.00912380
\(529\) −20.7866 −0.903766
\(530\) −2.79620 −0.121459
\(531\) 10.7071 0.464650
\(532\) 0 0
\(533\) 13.7861 0.597143
\(534\) 9.02132 0.390391
\(535\) −2.61883 −0.113222
\(536\) 4.95649 0.214088
\(537\) 6.84812 0.295518
\(538\) 2.62826 0.113312
\(539\) 0 0
\(540\) 0.914626 0.0393592
\(541\) −13.2854 −0.571184 −0.285592 0.958351i \(-0.592190\pi\)
−0.285592 + 0.958351i \(0.592190\pi\)
\(542\) 12.6224 0.542178
\(543\) −0.106226 −0.00455859
\(544\) −0.609435 −0.0261293
\(545\) −3.54103 −0.151681
\(546\) 0 0
\(547\) −3.77149 −0.161257 −0.0806287 0.996744i \(-0.525693\pi\)
−0.0806287 + 0.996744i \(0.525693\pi\)
\(548\) 17.8291 0.761622
\(549\) 9.08132 0.387581
\(550\) −1.45099 −0.0618704
\(551\) 6.67740 0.284467
\(552\) −1.06311 −0.0452489
\(553\) 0 0
\(554\) 19.4595 0.826757
\(555\) −0.106164 −0.00450640
\(556\) −7.99852 −0.339213
\(557\) −41.3443 −1.75181 −0.875907 0.482480i \(-0.839736\pi\)
−0.875907 + 0.482480i \(0.839736\pi\)
\(558\) −3.36502 −0.142452
\(559\) 13.6987 0.579394
\(560\) 0 0
\(561\) −0.127767 −0.00539434
\(562\) 15.9906 0.674521
\(563\) 6.62591 0.279249 0.139624 0.990205i \(-0.455410\pi\)
0.139624 + 0.990205i \(0.455410\pi\)
\(564\) −1.55844 −0.0656220
\(565\) 2.40108 0.101014
\(566\) −27.9827 −1.17620
\(567\) 0 0
\(568\) 4.21106 0.176692
\(569\) −13.9549 −0.585022 −0.292511 0.956262i \(-0.594491\pi\)
−0.292511 + 0.956262i \(0.594491\pi\)
\(570\) 1.11257 0.0466005
\(571\) −2.11161 −0.0883682 −0.0441841 0.999023i \(-0.514069\pi\)
−0.0441841 + 0.999023i \(0.514069\pi\)
\(572\) −1.21973 −0.0509995
\(573\) 7.34807 0.306970
\(574\) 0 0
\(575\) 7.35782 0.306842
\(576\) −2.48938 −0.103724
\(577\) −2.79762 −0.116466 −0.0582331 0.998303i \(-0.518547\pi\)
−0.0582331 + 0.998303i \(0.518547\pi\)
\(578\) −16.6286 −0.691658
\(579\) 8.90946 0.370265
\(580\) 0.233169 0.00968180
\(581\) 0 0
\(582\) −4.07666 −0.168983
\(583\) 3.51837 0.145716
\(584\) −5.84298 −0.241784
\(585\) −2.41314 −0.0997710
\(586\) −20.6845 −0.854470
\(587\) −6.93586 −0.286274 −0.143137 0.989703i \(-0.545719\pi\)
−0.143137 + 0.989703i \(0.545719\pi\)
\(588\) 0 0
\(589\) −9.02617 −0.371917
\(590\) 1.00289 0.0412883
\(591\) −13.5993 −0.559399
\(592\) 0.637171 0.0261876
\(593\) −3.39084 −0.139245 −0.0696225 0.997573i \(-0.522179\pi\)
−0.0696225 + 0.997573i \(0.522179\pi\)
\(594\) −1.15084 −0.0472196
\(595\) 0 0
\(596\) 7.81597 0.320155
\(597\) 7.58049 0.310249
\(598\) 6.18513 0.252929
\(599\) −30.7247 −1.25538 −0.627689 0.778464i \(-0.715999\pi\)
−0.627689 + 0.778464i \(0.715999\pi\)
\(600\) −3.53404 −0.144277
\(601\) −32.5720 −1.32864 −0.664320 0.747448i \(-0.731279\pi\)
−0.664320 + 0.747448i \(0.731279\pi\)
\(602\) 0 0
\(603\) −12.3386 −0.502465
\(604\) −16.2176 −0.659883
\(605\) 2.54478 0.103460
\(606\) −11.2431 −0.456719
\(607\) 1.92006 0.0779329 0.0389664 0.999241i \(-0.487593\pi\)
0.0389664 + 0.999241i \(0.487593\pi\)
\(608\) −6.67740 −0.270804
\(609\) 0 0
\(610\) 0.850606 0.0344400
\(611\) 9.06693 0.366809
\(612\) 1.51711 0.0613257
\(613\) −28.8055 −1.16344 −0.581722 0.813388i \(-0.697621\pi\)
−0.581722 + 0.813388i \(0.697621\pi\)
\(614\) 28.6540 1.15638
\(615\) 0.552511 0.0222794
\(616\) 0 0
\(617\) 41.9416 1.68850 0.844252 0.535946i \(-0.180045\pi\)
0.844252 + 0.535946i \(0.180045\pi\)
\(618\) 3.49822 0.140719
\(619\) 0.752705 0.0302538 0.0151269 0.999886i \(-0.495185\pi\)
0.0151269 + 0.999886i \(0.495185\pi\)
\(620\) −0.315186 −0.0126582
\(621\) 5.83581 0.234183
\(622\) −10.4647 −0.419596
\(623\) 0 0
\(624\) −2.97079 −0.118927
\(625\) 24.1874 0.967498
\(626\) 31.4172 1.25568
\(627\) −1.39991 −0.0559070
\(628\) 23.6455 0.943556
\(629\) −0.388314 −0.0154831
\(630\) 0 0
\(631\) −36.3961 −1.44891 −0.724453 0.689325i \(-0.757907\pi\)
−0.724453 + 0.689325i \(0.757907\pi\)
\(632\) 2.10678 0.0838032
\(633\) −6.20983 −0.246819
\(634\) 12.7478 0.506279
\(635\) 3.56873 0.141621
\(636\) 8.56937 0.339797
\(637\) 0 0
\(638\) −0.293388 −0.0116153
\(639\) −10.4829 −0.414698
\(640\) −0.233169 −0.00921680
\(641\) −20.4574 −0.808021 −0.404010 0.914754i \(-0.632384\pi\)
−0.404010 + 0.914754i \(0.632384\pi\)
\(642\) 8.02577 0.316752
\(643\) 36.0350 1.42108 0.710541 0.703656i \(-0.248450\pi\)
0.710541 + 0.703656i \(0.248450\pi\)
\(644\) 0 0
\(645\) 0.549008 0.0216172
\(646\) 4.06944 0.160110
\(647\) −42.7775 −1.68176 −0.840879 0.541223i \(-0.817961\pi\)
−0.840879 + 0.541223i \(0.817961\pi\)
\(648\) 4.66513 0.183264
\(649\) −1.26190 −0.0495340
\(650\) 20.5610 0.806467
\(651\) 0 0
\(652\) −13.6125 −0.533106
\(653\) 28.0322 1.09699 0.548493 0.836155i \(-0.315202\pi\)
0.548493 + 0.836155i \(0.315202\pi\)
\(654\) 10.8520 0.424346
\(655\) 2.84875 0.111310
\(656\) −3.31605 −0.129470
\(657\) 14.5454 0.567470
\(658\) 0 0
\(659\) 36.2772 1.41316 0.706579 0.707634i \(-0.250238\pi\)
0.706579 + 0.707634i \(0.250238\pi\)
\(660\) −0.0488836 −0.00190279
\(661\) 6.03049 0.234559 0.117279 0.993099i \(-0.462583\pi\)
0.117279 + 0.993099i \(0.462583\pi\)
\(662\) −10.2619 −0.398841
\(663\) 1.81050 0.0703141
\(664\) −6.73621 −0.261415
\(665\) 0 0
\(666\) −1.58616 −0.0614624
\(667\) 1.48774 0.0576056
\(668\) 3.59710 0.139176
\(669\) −7.14138 −0.276102
\(670\) −1.15570 −0.0446485
\(671\) −1.07029 −0.0413180
\(672\) 0 0
\(673\) 16.7412 0.645327 0.322663 0.946514i \(-0.395422\pi\)
0.322663 + 0.946514i \(0.395422\pi\)
\(674\) −26.9868 −1.03949
\(675\) 19.3997 0.746695
\(676\) 4.28394 0.164767
\(677\) −40.9926 −1.57547 −0.787737 0.616011i \(-0.788748\pi\)
−0.787737 + 0.616011i \(0.788748\pi\)
\(678\) −7.35845 −0.282600
\(679\) 0 0
\(680\) 0.142101 0.00544933
\(681\) 18.0853 0.693030
\(682\) 0.396588 0.0151861
\(683\) −34.1468 −1.30659 −0.653296 0.757102i \(-0.726614\pi\)
−0.653296 + 0.757102i \(0.726614\pi\)
\(684\) 16.6226 0.635580
\(685\) −4.15719 −0.158838
\(686\) 0 0
\(687\) −13.2043 −0.503776
\(688\) −3.29502 −0.125622
\(689\) −49.8563 −1.89937
\(690\) 0.247884 0.00943677
\(691\) 22.6343 0.861051 0.430525 0.902579i \(-0.358328\pi\)
0.430525 + 0.902579i \(0.358328\pi\)
\(692\) −12.3956 −0.471212
\(693\) 0 0
\(694\) 0.0299869 0.00113829
\(695\) 1.86500 0.0707437
\(696\) −0.714579 −0.0270860
\(697\) 2.02091 0.0765476
\(698\) −6.30027 −0.238469
\(699\) −6.68780 −0.252956
\(700\) 0 0
\(701\) −15.1951 −0.573911 −0.286955 0.957944i \(-0.592643\pi\)
−0.286955 + 0.957944i \(0.592643\pi\)
\(702\) 16.3078 0.615497
\(703\) −4.25465 −0.160467
\(704\) 0.293388 0.0110575
\(705\) 0.363378 0.0136856
\(706\) −27.6344 −1.04003
\(707\) 0 0
\(708\) −3.07350 −0.115509
\(709\) 8.01561 0.301033 0.150516 0.988608i \(-0.451906\pi\)
0.150516 + 0.988608i \(0.451906\pi\)
\(710\) −0.981888 −0.0368496
\(711\) −5.24457 −0.196687
\(712\) 12.6247 0.473129
\(713\) −2.01106 −0.0753146
\(714\) 0 0
\(715\) 0.284403 0.0106361
\(716\) 9.58344 0.358150
\(717\) −12.5354 −0.468145
\(718\) −18.4797 −0.689657
\(719\) −2.17601 −0.0811515 −0.0405757 0.999176i \(-0.512919\pi\)
−0.0405757 + 0.999176i \(0.512919\pi\)
\(720\) 0.580445 0.0216319
\(721\) 0 0
\(722\) 25.5877 0.952274
\(723\) −2.17393 −0.0808494
\(724\) −0.148655 −0.00552473
\(725\) 4.94563 0.183676
\(726\) −7.79886 −0.289443
\(727\) 53.7791 1.99456 0.997278 0.0737366i \(-0.0234924\pi\)
0.997278 + 0.0737366i \(0.0234924\pi\)
\(728\) 0 0
\(729\) −3.20426 −0.118676
\(730\) 1.36240 0.0504247
\(731\) 2.00810 0.0742724
\(732\) −2.60680 −0.0963502
\(733\) −26.7745 −0.988938 −0.494469 0.869195i \(-0.664637\pi\)
−0.494469 + 0.869195i \(0.664637\pi\)
\(734\) 17.7335 0.654556
\(735\) 0 0
\(736\) −1.48774 −0.0548389
\(737\) 1.45418 0.0535652
\(738\) 8.25489 0.303867
\(739\) 29.2936 1.07758 0.538791 0.842440i \(-0.318881\pi\)
0.538791 + 0.842440i \(0.318881\pi\)
\(740\) −0.148568 −0.00546148
\(741\) 19.8371 0.728735
\(742\) 0 0
\(743\) 6.53498 0.239745 0.119873 0.992789i \(-0.461751\pi\)
0.119873 + 0.992789i \(0.461751\pi\)
\(744\) 0.965932 0.0354128
\(745\) −1.82244 −0.0667690
\(746\) 14.2392 0.521335
\(747\) 16.7690 0.613544
\(748\) −0.178801 −0.00653761
\(749\) 0 0
\(750\) 1.65712 0.0605093
\(751\) 30.1997 1.10200 0.551002 0.834504i \(-0.314246\pi\)
0.551002 + 0.834504i \(0.314246\pi\)
\(752\) −2.18092 −0.0795298
\(753\) 12.3104 0.448616
\(754\) 4.15740 0.151403
\(755\) 3.78142 0.137620
\(756\) 0 0
\(757\) −26.5008 −0.963189 −0.481595 0.876394i \(-0.659942\pi\)
−0.481595 + 0.876394i \(0.659942\pi\)
\(758\) 33.9879 1.23450
\(759\) −0.311904 −0.0113214
\(760\) 1.55696 0.0564769
\(761\) −4.37410 −0.158561 −0.0792805 0.996852i \(-0.525262\pi\)
−0.0792805 + 0.996852i \(0.525262\pi\)
\(762\) −10.9369 −0.396201
\(763\) 0 0
\(764\) 10.2831 0.372029
\(765\) −0.353743 −0.0127896
\(766\) 17.0812 0.617168
\(767\) 17.8815 0.645664
\(768\) 0.714579 0.0257851
\(769\) −43.7523 −1.57775 −0.788874 0.614555i \(-0.789335\pi\)
−0.788874 + 0.614555i \(0.789335\pi\)
\(770\) 0 0
\(771\) −14.7528 −0.531309
\(772\) 12.4681 0.448738
\(773\) −14.3435 −0.515901 −0.257950 0.966158i \(-0.583047\pi\)
−0.257950 + 0.966158i \(0.583047\pi\)
\(774\) 8.20256 0.294835
\(775\) −6.68526 −0.240142
\(776\) −5.70498 −0.204797
\(777\) 0 0
\(778\) −11.3176 −0.405757
\(779\) 22.1426 0.793340
\(780\) 0.692694 0.0248024
\(781\) 1.23548 0.0442088
\(782\) 0.906682 0.0324229
\(783\) 3.92259 0.140182
\(784\) 0 0
\(785\) −5.51338 −0.196781
\(786\) −8.73040 −0.311403
\(787\) 31.6417 1.12791 0.563953 0.825807i \(-0.309280\pi\)
0.563953 + 0.825807i \(0.309280\pi\)
\(788\) −19.0312 −0.677957
\(789\) −11.8410 −0.421551
\(790\) −0.491235 −0.0174773
\(791\) 0 0
\(792\) −0.730354 −0.0259520
\(793\) 15.1663 0.538571
\(794\) −10.2515 −0.363811
\(795\) −1.99811 −0.0708656
\(796\) 10.6083 0.376003
\(797\) 12.6909 0.449536 0.224768 0.974412i \(-0.427838\pi\)
0.224768 + 0.974412i \(0.427838\pi\)
\(798\) 0 0
\(799\) 1.32913 0.0470211
\(800\) −4.94563 −0.174855
\(801\) −31.4276 −1.11044
\(802\) −17.6102 −0.621837
\(803\) −1.71426 −0.0604950
\(804\) 3.54180 0.124910
\(805\) 0 0
\(806\) −5.61976 −0.197948
\(807\) 1.87810 0.0661122
\(808\) −15.7339 −0.553516
\(809\) 10.5845 0.372132 0.186066 0.982537i \(-0.440426\pi\)
0.186066 + 0.982537i \(0.440426\pi\)
\(810\) −1.08776 −0.0382201
\(811\) 47.2614 1.65957 0.829786 0.558082i \(-0.188463\pi\)
0.829786 + 0.558082i \(0.188463\pi\)
\(812\) 0 0
\(813\) 9.01969 0.316334
\(814\) 0.186939 0.00655219
\(815\) 3.17400 0.111181
\(816\) −0.435489 −0.0152452
\(817\) 22.0022 0.769759
\(818\) 38.8959 1.35996
\(819\) 0 0
\(820\) 0.773198 0.0270012
\(821\) −0.820326 −0.0286296 −0.0143148 0.999898i \(-0.504557\pi\)
−0.0143148 + 0.999898i \(0.504557\pi\)
\(822\) 12.7403 0.444369
\(823\) 41.1702 1.43510 0.717551 0.696506i \(-0.245263\pi\)
0.717551 + 0.696506i \(0.245263\pi\)
\(824\) 4.89549 0.170543
\(825\) −1.03685 −0.0360984
\(826\) 0 0
\(827\) −24.2372 −0.842810 −0.421405 0.906872i \(-0.638463\pi\)
−0.421405 + 0.906872i \(0.638463\pi\)
\(828\) 3.70355 0.128707
\(829\) 29.7746 1.03411 0.517057 0.855951i \(-0.327028\pi\)
0.517057 + 0.855951i \(0.327028\pi\)
\(830\) 1.57067 0.0545188
\(831\) 13.9054 0.482372
\(832\) −4.15740 −0.144132
\(833\) 0 0
\(834\) −5.71558 −0.197914
\(835\) −0.838731 −0.0290255
\(836\) −1.95907 −0.0677559
\(837\) −5.30236 −0.183277
\(838\) 12.6437 0.436768
\(839\) −14.8726 −0.513459 −0.256730 0.966483i \(-0.582645\pi\)
−0.256730 + 0.966483i \(0.582645\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −10.7981 −0.372127
\(843\) 11.4265 0.393550
\(844\) −8.69020 −0.299129
\(845\) −0.998882 −0.0343626
\(846\) 5.42912 0.186657
\(847\) 0 0
\(848\) 11.9922 0.411814
\(849\) −19.9958 −0.686255
\(850\) 3.01404 0.103381
\(851\) −0.947946 −0.0324952
\(852\) 3.00914 0.103091
\(853\) −48.2468 −1.65194 −0.825970 0.563715i \(-0.809372\pi\)
−0.825970 + 0.563715i \(0.809372\pi\)
\(854\) 0 0
\(855\) −3.87586 −0.132552
\(856\) 11.2315 0.383884
\(857\) 22.2883 0.761355 0.380677 0.924708i \(-0.375691\pi\)
0.380677 + 0.924708i \(0.375691\pi\)
\(858\) −0.871594 −0.0297557
\(859\) −33.0107 −1.12631 −0.563155 0.826351i \(-0.690413\pi\)
−0.563155 + 0.826351i \(0.690413\pi\)
\(860\) 0.768296 0.0261987
\(861\) 0 0
\(862\) −36.1812 −1.23234
\(863\) 2.98200 0.101509 0.0507543 0.998711i \(-0.483837\pi\)
0.0507543 + 0.998711i \(0.483837\pi\)
\(864\) −3.92259 −0.133449
\(865\) 2.89028 0.0982723
\(866\) −10.6350 −0.361391
\(867\) −11.8824 −0.403549
\(868\) 0 0
\(869\) 0.618104 0.0209677
\(870\) 0.166617 0.00564886
\(871\) −20.6061 −0.698211
\(872\) 15.1865 0.514281
\(873\) 14.2018 0.480659
\(874\) 9.93425 0.336031
\(875\) 0 0
\(876\) −4.17527 −0.141069
\(877\) −9.60117 −0.324208 −0.162104 0.986774i \(-0.551828\pi\)
−0.162104 + 0.986774i \(0.551828\pi\)
\(878\) 2.97507 0.100404
\(879\) −14.7807 −0.498541
\(880\) −0.0684089 −0.00230606
\(881\) −11.0461 −0.372153 −0.186076 0.982535i \(-0.559577\pi\)
−0.186076 + 0.982535i \(0.559577\pi\)
\(882\) 0 0
\(883\) −30.8011 −1.03654 −0.518269 0.855218i \(-0.673423\pi\)
−0.518269 + 0.855218i \(0.673423\pi\)
\(884\) 2.53366 0.0852163
\(885\) 0.716643 0.0240897
\(886\) −27.9429 −0.938760
\(887\) 39.0735 1.31196 0.655980 0.754778i \(-0.272256\pi\)
0.655980 + 0.754778i \(0.272256\pi\)
\(888\) 0.455309 0.0152792
\(889\) 0 0
\(890\) −2.94368 −0.0986723
\(891\) 1.36869 0.0458530
\(892\) −9.99383 −0.334618
\(893\) 14.5628 0.487327
\(894\) 5.58513 0.186795
\(895\) −2.23456 −0.0746930
\(896\) 0 0
\(897\) 4.41976 0.147572
\(898\) −0.604431 −0.0201701
\(899\) −1.35175 −0.0450834
\(900\) 12.3115 0.410385
\(901\) −7.30846 −0.243480
\(902\) −0.972889 −0.0323937
\(903\) 0 0
\(904\) −10.2976 −0.342493
\(905\) 0.0346617 0.00115219
\(906\) −11.5887 −0.385009
\(907\) −0.412413 −0.0136939 −0.00684697 0.999977i \(-0.502179\pi\)
−0.00684697 + 0.999977i \(0.502179\pi\)
\(908\) 25.3090 0.839910
\(909\) 39.1675 1.29911
\(910\) 0 0
\(911\) 31.6863 1.04981 0.524907 0.851160i \(-0.324100\pi\)
0.524907 + 0.851160i \(0.324100\pi\)
\(912\) −4.77153 −0.158001
\(913\) −1.97632 −0.0654068
\(914\) −7.10311 −0.234950
\(915\) 0.607825 0.0200941
\(916\) −18.4785 −0.610545
\(917\) 0 0
\(918\) 2.39057 0.0789004
\(919\) −55.1497 −1.81922 −0.909611 0.415462i \(-0.863620\pi\)
−0.909611 + 0.415462i \(0.863620\pi\)
\(920\) 0.346895 0.0114368
\(921\) 20.4756 0.674693
\(922\) −3.81028 −0.125485
\(923\) −17.5071 −0.576252
\(924\) 0 0
\(925\) −3.15122 −0.103611
\(926\) −3.42327 −0.112496
\(927\) −12.1867 −0.400265
\(928\) −1.00000 −0.0328266
\(929\) −39.6996 −1.30250 −0.651251 0.758863i \(-0.725755\pi\)
−0.651251 + 0.758863i \(0.725755\pi\)
\(930\) −0.225225 −0.00738542
\(931\) 0 0
\(932\) −9.35908 −0.306567
\(933\) −7.47785 −0.244814
\(934\) −22.8701 −0.748333
\(935\) 0.0416908 0.00136343
\(936\) 10.3493 0.338278
\(937\) −2.47672 −0.0809108 −0.0404554 0.999181i \(-0.512881\pi\)
−0.0404554 + 0.999181i \(0.512881\pi\)
\(938\) 0 0
\(939\) 22.4500 0.732629
\(940\) 0.508521 0.0165861
\(941\) −25.1780 −0.820780 −0.410390 0.911910i \(-0.634607\pi\)
−0.410390 + 0.911910i \(0.634607\pi\)
\(942\) 16.8965 0.550519
\(943\) 4.93342 0.160654
\(944\) −4.30113 −0.139990
\(945\) 0 0
\(946\) −0.966721 −0.0314308
\(947\) −38.1720 −1.24042 −0.620212 0.784434i \(-0.712953\pi\)
−0.620212 + 0.784434i \(0.712953\pi\)
\(948\) 1.50546 0.0488951
\(949\) 24.2916 0.788539
\(950\) 33.0240 1.07144
\(951\) 9.10929 0.295389
\(952\) 0 0
\(953\) 41.3605 1.33980 0.669900 0.742452i \(-0.266337\pi\)
0.669900 + 0.742452i \(0.266337\pi\)
\(954\) −29.8531 −0.966529
\(955\) −2.39769 −0.0775875
\(956\) −17.5424 −0.567363
\(957\) −0.209649 −0.00677699
\(958\) 4.57219 0.147721
\(959\) 0 0
\(960\) −0.166617 −0.00537755
\(961\) −29.1728 −0.941057
\(962\) −2.64897 −0.0854063
\(963\) −27.9594 −0.900978
\(964\) −3.04226 −0.0979845
\(965\) −2.90718 −0.0935853
\(966\) 0 0
\(967\) 7.05786 0.226965 0.113483 0.993540i \(-0.463799\pi\)
0.113483 + 0.993540i \(0.463799\pi\)
\(968\) −10.9139 −0.350787
\(969\) 2.90794 0.0934164
\(970\) 1.33022 0.0427108
\(971\) −35.4988 −1.13921 −0.569605 0.821919i \(-0.692904\pi\)
−0.569605 + 0.821919i \(0.692904\pi\)
\(972\) 15.1014 0.484377
\(973\) 0 0
\(974\) 21.6569 0.693931
\(975\) 14.6924 0.470534
\(976\) −3.64803 −0.116771
\(977\) 14.8701 0.475735 0.237868 0.971298i \(-0.423552\pi\)
0.237868 + 0.971298i \(0.423552\pi\)
\(978\) −9.72719 −0.311041
\(979\) 3.70393 0.118378
\(980\) 0 0
\(981\) −37.8050 −1.20702
\(982\) 32.0537 1.02287
\(983\) −36.7682 −1.17272 −0.586362 0.810049i \(-0.699440\pi\)
−0.586362 + 0.810049i \(0.699440\pi\)
\(984\) −2.36958 −0.0755393
\(985\) 4.43747 0.141390
\(986\) 0.609435 0.0194084
\(987\) 0 0
\(988\) 27.7606 0.883182
\(989\) 4.90214 0.155879
\(990\) 0.170296 0.00541235
\(991\) −26.9622 −0.856483 −0.428242 0.903664i \(-0.640867\pi\)
−0.428242 + 0.903664i \(0.640867\pi\)
\(992\) 1.35175 0.0429181
\(993\) −7.33295 −0.232704
\(994\) 0 0
\(995\) −2.47353 −0.0784162
\(996\) −4.81355 −0.152523
\(997\) −7.46930 −0.236555 −0.118278 0.992981i \(-0.537737\pi\)
−0.118278 + 0.992981i \(0.537737\pi\)
\(998\) 24.6113 0.779058
\(999\) −2.49936 −0.0790764
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 2842.2.a.x.1.4 5
7.3 odd 6 406.2.e.a.233.4 10
7.5 odd 6 406.2.e.a.291.4 yes 10
7.6 odd 2 2842.2.a.z.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
406.2.e.a.233.4 10 7.3 odd 6
406.2.e.a.291.4 yes 10 7.5 odd 6
2842.2.a.x.1.4 5 1.1 even 1 trivial
2842.2.a.z.1.2 5 7.6 odd 2