Properties

Label 4029.2.a.l.1.19
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 32
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.437930 q^{2} -1.00000 q^{3} -1.80822 q^{4} -1.50297 q^{5} -0.437930 q^{6} -4.33772 q^{7} -1.66773 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.437930 q^{2} -1.00000 q^{3} -1.80822 q^{4} -1.50297 q^{5} -0.437930 q^{6} -4.33772 q^{7} -1.66773 q^{8} +1.00000 q^{9} -0.658196 q^{10} +3.26197 q^{11} +1.80822 q^{12} -1.64522 q^{13} -1.89962 q^{14} +1.50297 q^{15} +2.88608 q^{16} -1.00000 q^{17} +0.437930 q^{18} -5.97637 q^{19} +2.71770 q^{20} +4.33772 q^{21} +1.42851 q^{22} -5.62341 q^{23} +1.66773 q^{24} -2.74108 q^{25} -0.720490 q^{26} -1.00000 q^{27} +7.84354 q^{28} -9.77865 q^{29} +0.658196 q^{30} -9.36283 q^{31} +4.59937 q^{32} -3.26197 q^{33} -0.437930 q^{34} +6.51947 q^{35} -1.80822 q^{36} -4.38216 q^{37} -2.61723 q^{38} +1.64522 q^{39} +2.50655 q^{40} -1.29358 q^{41} +1.89962 q^{42} -3.12682 q^{43} -5.89834 q^{44} -1.50297 q^{45} -2.46266 q^{46} -3.57872 q^{47} -2.88608 q^{48} +11.8158 q^{49} -1.20040 q^{50} +1.00000 q^{51} +2.97491 q^{52} -1.24099 q^{53} -0.437930 q^{54} -4.90264 q^{55} +7.23416 q^{56} +5.97637 q^{57} -4.28236 q^{58} +12.9970 q^{59} -2.71770 q^{60} -4.49618 q^{61} -4.10027 q^{62} -4.33772 q^{63} -3.75797 q^{64} +2.47271 q^{65} -1.42851 q^{66} -8.36592 q^{67} +1.80822 q^{68} +5.62341 q^{69} +2.85507 q^{70} +2.73938 q^{71} -1.66773 q^{72} -15.4337 q^{73} -1.91908 q^{74} +2.74108 q^{75} +10.8066 q^{76} -14.1495 q^{77} +0.720490 q^{78} +1.00000 q^{79} -4.33770 q^{80} +1.00000 q^{81} -0.566495 q^{82} +2.32456 q^{83} -7.84354 q^{84} +1.50297 q^{85} -1.36933 q^{86} +9.77865 q^{87} -5.44009 q^{88} +1.70984 q^{89} -0.658196 q^{90} +7.13650 q^{91} +10.1683 q^{92} +9.36283 q^{93} -1.56723 q^{94} +8.98231 q^{95} -4.59937 q^{96} +1.17467 q^{97} +5.17450 q^{98} +3.26197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.437930 0.309663 0.154832 0.987941i \(-0.450516\pi\)
0.154832 + 0.987941i \(0.450516\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.80822 −0.904109
\(5\) −1.50297 −0.672149 −0.336074 0.941835i \(-0.609099\pi\)
−0.336074 + 0.941835i \(0.609099\pi\)
\(6\) −0.437930 −0.178784
\(7\) −4.33772 −1.63950 −0.819752 0.572718i \(-0.805889\pi\)
−0.819752 + 0.572718i \(0.805889\pi\)
\(8\) −1.66773 −0.589632
\(9\) 1.00000 0.333333
\(10\) −0.658196 −0.208140
\(11\) 3.26197 0.983520 0.491760 0.870731i \(-0.336354\pi\)
0.491760 + 0.870731i \(0.336354\pi\)
\(12\) 1.80822 0.521987
\(13\) −1.64522 −0.456301 −0.228151 0.973626i \(-0.573268\pi\)
−0.228151 + 0.973626i \(0.573268\pi\)
\(14\) −1.89962 −0.507694
\(15\) 1.50297 0.388065
\(16\) 2.88608 0.721521
\(17\) −1.00000 −0.242536
\(18\) 0.437930 0.103221
\(19\) −5.97637 −1.37107 −0.685537 0.728038i \(-0.740432\pi\)
−0.685537 + 0.728038i \(0.740432\pi\)
\(20\) 2.71770 0.607696
\(21\) 4.33772 0.946568
\(22\) 1.42851 0.304560
\(23\) −5.62341 −1.17256 −0.586281 0.810108i \(-0.699408\pi\)
−0.586281 + 0.810108i \(0.699408\pi\)
\(24\) 1.66773 0.340424
\(25\) −2.74108 −0.548216
\(26\) −0.720490 −0.141300
\(27\) −1.00000 −0.192450
\(28\) 7.84354 1.48229
\(29\) −9.77865 −1.81585 −0.907925 0.419133i \(-0.862334\pi\)
−0.907925 + 0.419133i \(0.862334\pi\)
\(30\) 0.658196 0.120170
\(31\) −9.36283 −1.68161 −0.840807 0.541335i \(-0.817919\pi\)
−0.840807 + 0.541335i \(0.817919\pi\)
\(32\) 4.59937 0.813061
\(33\) −3.26197 −0.567835
\(34\) −0.437930 −0.0751044
\(35\) 6.51947 1.10199
\(36\) −1.80822 −0.301370
\(37\) −4.38216 −0.720422 −0.360211 0.932871i \(-0.617295\pi\)
−0.360211 + 0.932871i \(0.617295\pi\)
\(38\) −2.61723 −0.424571
\(39\) 1.64522 0.263446
\(40\) 2.50655 0.396321
\(41\) −1.29358 −0.202022 −0.101011 0.994885i \(-0.532208\pi\)
−0.101011 + 0.994885i \(0.532208\pi\)
\(42\) 1.89962 0.293117
\(43\) −3.12682 −0.476836 −0.238418 0.971163i \(-0.576629\pi\)
−0.238418 + 0.971163i \(0.576629\pi\)
\(44\) −5.89834 −0.889209
\(45\) −1.50297 −0.224050
\(46\) −2.46266 −0.363099
\(47\) −3.57872 −0.522011 −0.261005 0.965337i \(-0.584054\pi\)
−0.261005 + 0.965337i \(0.584054\pi\)
\(48\) −2.88608 −0.416570
\(49\) 11.8158 1.68797
\(50\) −1.20040 −0.169762
\(51\) 1.00000 0.140028
\(52\) 2.97491 0.412546
\(53\) −1.24099 −0.170464 −0.0852319 0.996361i \(-0.527163\pi\)
−0.0852319 + 0.996361i \(0.527163\pi\)
\(54\) −0.437930 −0.0595947
\(55\) −4.90264 −0.661072
\(56\) 7.23416 0.966705
\(57\) 5.97637 0.791589
\(58\) −4.28236 −0.562302
\(59\) 12.9970 1.69206 0.846030 0.533136i \(-0.178987\pi\)
0.846030 + 0.533136i \(0.178987\pi\)
\(60\) −2.71770 −0.350853
\(61\) −4.49618 −0.575677 −0.287838 0.957679i \(-0.592937\pi\)
−0.287838 + 0.957679i \(0.592937\pi\)
\(62\) −4.10027 −0.520734
\(63\) −4.33772 −0.546501
\(64\) −3.75797 −0.469746
\(65\) 2.47271 0.306702
\(66\) −1.42851 −0.175838
\(67\) −8.36592 −1.02206 −0.511030 0.859563i \(-0.670736\pi\)
−0.511030 + 0.859563i \(0.670736\pi\)
\(68\) 1.80822 0.219279
\(69\) 5.62341 0.676978
\(70\) 2.85507 0.341246
\(71\) 2.73938 0.325105 0.162552 0.986700i \(-0.448027\pi\)
0.162552 + 0.986700i \(0.448027\pi\)
\(72\) −1.66773 −0.196544
\(73\) −15.4337 −1.80638 −0.903189 0.429242i \(-0.858781\pi\)
−0.903189 + 0.429242i \(0.858781\pi\)
\(74\) −1.91908 −0.223088
\(75\) 2.74108 0.316513
\(76\) 10.8066 1.23960
\(77\) −14.1495 −1.61248
\(78\) 0.720490 0.0815795
\(79\) 1.00000 0.112509
\(80\) −4.33770 −0.484970
\(81\) 1.00000 0.111111
\(82\) −0.566495 −0.0625589
\(83\) 2.32456 0.255153 0.127577 0.991829i \(-0.459280\pi\)
0.127577 + 0.991829i \(0.459280\pi\)
\(84\) −7.84354 −0.855801
\(85\) 1.50297 0.163020
\(86\) −1.36933 −0.147659
\(87\) 9.77865 1.04838
\(88\) −5.44009 −0.579915
\(89\) 1.70984 0.181242 0.0906211 0.995885i \(-0.471115\pi\)
0.0906211 + 0.995885i \(0.471115\pi\)
\(90\) −0.658196 −0.0693799
\(91\) 7.13650 0.748108
\(92\) 10.1683 1.06012
\(93\) 9.36283 0.970881
\(94\) −1.56723 −0.161647
\(95\) 8.98231 0.921565
\(96\) −4.59937 −0.469421
\(97\) 1.17467 0.119270 0.0596350 0.998220i \(-0.481006\pi\)
0.0596350 + 0.998220i \(0.481006\pi\)
\(98\) 5.17450 0.522704
\(99\) 3.26197 0.327840
\(100\) 4.95647 0.495647
\(101\) 9.86589 0.981693 0.490846 0.871246i \(-0.336688\pi\)
0.490846 + 0.871246i \(0.336688\pi\)
\(102\) 0.437930 0.0433615
\(103\) −1.75170 −0.172600 −0.0863000 0.996269i \(-0.527504\pi\)
−0.0863000 + 0.996269i \(0.527504\pi\)
\(104\) 2.74378 0.269050
\(105\) −6.51947 −0.636235
\(106\) −0.543469 −0.0527864
\(107\) 8.03891 0.777151 0.388576 0.921417i \(-0.372967\pi\)
0.388576 + 0.921417i \(0.372967\pi\)
\(108\) 1.80822 0.173996
\(109\) −6.17934 −0.591873 −0.295937 0.955208i \(-0.595632\pi\)
−0.295937 + 0.955208i \(0.595632\pi\)
\(110\) −2.14701 −0.204710
\(111\) 4.38216 0.415936
\(112\) −12.5190 −1.18294
\(113\) 4.11575 0.387177 0.193588 0.981083i \(-0.437987\pi\)
0.193588 + 0.981083i \(0.437987\pi\)
\(114\) 2.61723 0.245126
\(115\) 8.45181 0.788135
\(116\) 17.6819 1.64173
\(117\) −1.64522 −0.152100
\(118\) 5.69176 0.523969
\(119\) 4.33772 0.397638
\(120\) −2.50655 −0.228816
\(121\) −0.359578 −0.0326889
\(122\) −1.96901 −0.178266
\(123\) 1.29358 0.116638
\(124\) 16.9300 1.52036
\(125\) 11.6346 1.04063
\(126\) −1.89962 −0.169231
\(127\) 18.6911 1.65857 0.829285 0.558826i \(-0.188748\pi\)
0.829285 + 0.558826i \(0.188748\pi\)
\(128\) −10.8445 −0.958524
\(129\) 3.12682 0.275301
\(130\) 1.08288 0.0949745
\(131\) 0.435527 0.0380522 0.0190261 0.999819i \(-0.493943\pi\)
0.0190261 + 0.999819i \(0.493943\pi\)
\(132\) 5.89834 0.513385
\(133\) 25.9238 2.24788
\(134\) −3.66369 −0.316494
\(135\) 1.50297 0.129355
\(136\) 1.66773 0.143007
\(137\) −2.12012 −0.181134 −0.0905669 0.995890i \(-0.528868\pi\)
−0.0905669 + 0.995890i \(0.528868\pi\)
\(138\) 2.46266 0.209635
\(139\) −6.71447 −0.569514 −0.284757 0.958600i \(-0.591913\pi\)
−0.284757 + 0.958600i \(0.591913\pi\)
\(140\) −11.7886 −0.996320
\(141\) 3.57872 0.301383
\(142\) 1.19966 0.100673
\(143\) −5.36665 −0.448781
\(144\) 2.88608 0.240507
\(145\) 14.6970 1.22052
\(146\) −6.75888 −0.559369
\(147\) −11.8158 −0.974553
\(148\) 7.92389 0.651340
\(149\) −12.9832 −1.06363 −0.531814 0.846861i \(-0.678489\pi\)
−0.531814 + 0.846861i \(0.678489\pi\)
\(150\) 1.20040 0.0980123
\(151\) 16.6997 1.35901 0.679503 0.733673i \(-0.262195\pi\)
0.679503 + 0.733673i \(0.262195\pi\)
\(152\) 9.96699 0.808429
\(153\) −1.00000 −0.0808452
\(154\) −6.19649 −0.499327
\(155\) 14.0721 1.13030
\(156\) −2.97491 −0.238184
\(157\) 0.833868 0.0665499 0.0332749 0.999446i \(-0.489406\pi\)
0.0332749 + 0.999446i \(0.489406\pi\)
\(158\) 0.437930 0.0348398
\(159\) 1.24099 0.0984173
\(160\) −6.91271 −0.546498
\(161\) 24.3928 1.92242
\(162\) 0.437930 0.0344070
\(163\) −14.3333 −1.12267 −0.561336 0.827588i \(-0.689712\pi\)
−0.561336 + 0.827588i \(0.689712\pi\)
\(164\) 2.33906 0.182650
\(165\) 4.90264 0.381670
\(166\) 1.01799 0.0790116
\(167\) 6.31714 0.488835 0.244418 0.969670i \(-0.421403\pi\)
0.244418 + 0.969670i \(0.421403\pi\)
\(168\) −7.23416 −0.558127
\(169\) −10.2933 −0.791789
\(170\) 0.658196 0.0504813
\(171\) −5.97637 −0.457024
\(172\) 5.65398 0.431112
\(173\) 7.06072 0.536816 0.268408 0.963305i \(-0.413502\pi\)
0.268408 + 0.963305i \(0.413502\pi\)
\(174\) 4.28236 0.324645
\(175\) 11.8900 0.898803
\(176\) 9.41431 0.709630
\(177\) −12.9970 −0.976911
\(178\) 0.748788 0.0561241
\(179\) −8.51845 −0.636699 −0.318350 0.947973i \(-0.603129\pi\)
−0.318350 + 0.947973i \(0.603129\pi\)
\(180\) 2.71770 0.202565
\(181\) 14.1809 1.05406 0.527028 0.849848i \(-0.323306\pi\)
0.527028 + 0.849848i \(0.323306\pi\)
\(182\) 3.12529 0.231662
\(183\) 4.49618 0.332367
\(184\) 9.37834 0.691380
\(185\) 6.58625 0.484231
\(186\) 4.10027 0.300646
\(187\) −3.26197 −0.238539
\(188\) 6.47111 0.471954
\(189\) 4.33772 0.315523
\(190\) 3.93362 0.285375
\(191\) −8.16727 −0.590963 −0.295481 0.955348i \(-0.595480\pi\)
−0.295481 + 0.955348i \(0.595480\pi\)
\(192\) 3.75797 0.271208
\(193\) −11.3104 −0.814138 −0.407069 0.913397i \(-0.633449\pi\)
−0.407069 + 0.913397i \(0.633449\pi\)
\(194\) 0.514425 0.0369335
\(195\) −2.47271 −0.177075
\(196\) −21.3656 −1.52611
\(197\) −18.4207 −1.31242 −0.656210 0.754578i \(-0.727842\pi\)
−0.656210 + 0.754578i \(0.727842\pi\)
\(198\) 1.42851 0.101520
\(199\) 14.4105 1.02153 0.510767 0.859719i \(-0.329362\pi\)
0.510767 + 0.859719i \(0.329362\pi\)
\(200\) 4.57139 0.323246
\(201\) 8.36592 0.590087
\(202\) 4.32057 0.303994
\(203\) 42.4170 2.97709
\(204\) −1.80822 −0.126601
\(205\) 1.94420 0.135789
\(206\) −0.767121 −0.0534479
\(207\) −5.62341 −0.390854
\(208\) −4.74824 −0.329231
\(209\) −19.4947 −1.34848
\(210\) −2.85507 −0.197019
\(211\) −4.16963 −0.287049 −0.143525 0.989647i \(-0.545844\pi\)
−0.143525 + 0.989647i \(0.545844\pi\)
\(212\) 2.24399 0.154118
\(213\) −2.73938 −0.187699
\(214\) 3.52048 0.240655
\(215\) 4.69952 0.320505
\(216\) 1.66773 0.113475
\(217\) 40.6134 2.75701
\(218\) −2.70612 −0.183281
\(219\) 15.4337 1.04291
\(220\) 8.86504 0.597681
\(221\) 1.64522 0.110669
\(222\) 1.91908 0.128800
\(223\) −12.0628 −0.807785 −0.403892 0.914806i \(-0.632343\pi\)
−0.403892 + 0.914806i \(0.632343\pi\)
\(224\) −19.9508 −1.33302
\(225\) −2.74108 −0.182739
\(226\) 1.80241 0.119894
\(227\) 25.4171 1.68699 0.843495 0.537138i \(-0.180494\pi\)
0.843495 + 0.537138i \(0.180494\pi\)
\(228\) −10.8066 −0.715683
\(229\) −11.6866 −0.772270 −0.386135 0.922442i \(-0.626190\pi\)
−0.386135 + 0.922442i \(0.626190\pi\)
\(230\) 3.70130 0.244057
\(231\) 14.1495 0.930969
\(232\) 16.3082 1.07068
\(233\) −1.16569 −0.0763670 −0.0381835 0.999271i \(-0.512157\pi\)
−0.0381835 + 0.999271i \(0.512157\pi\)
\(234\) −0.720490 −0.0470999
\(235\) 5.37872 0.350869
\(236\) −23.5013 −1.52981
\(237\) −1.00000 −0.0649570
\(238\) 1.89962 0.123134
\(239\) 11.1389 0.720517 0.360259 0.932853i \(-0.382688\pi\)
0.360259 + 0.932853i \(0.382688\pi\)
\(240\) 4.33770 0.279997
\(241\) 0.100901 0.00649959 0.00324980 0.999995i \(-0.498966\pi\)
0.00324980 + 0.999995i \(0.498966\pi\)
\(242\) −0.157470 −0.0101225
\(243\) −1.00000 −0.0641500
\(244\) 8.13007 0.520474
\(245\) −17.7588 −1.13457
\(246\) 0.566495 0.0361184
\(247\) 9.83243 0.625623
\(248\) 15.6147 0.991535
\(249\) −2.32456 −0.147313
\(250\) 5.09515 0.322245
\(251\) −12.5737 −0.793643 −0.396821 0.917896i \(-0.629887\pi\)
−0.396821 + 0.917896i \(0.629887\pi\)
\(252\) 7.84354 0.494097
\(253\) −18.3434 −1.15324
\(254\) 8.18541 0.513598
\(255\) −1.50297 −0.0941197
\(256\) 2.76682 0.172926
\(257\) −23.0907 −1.44036 −0.720179 0.693788i \(-0.755941\pi\)
−0.720179 + 0.693788i \(0.755941\pi\)
\(258\) 1.36933 0.0852507
\(259\) 19.0086 1.18114
\(260\) −4.47120 −0.277292
\(261\) −9.77865 −0.605283
\(262\) 0.190730 0.0117834
\(263\) −24.4508 −1.50770 −0.753851 0.657045i \(-0.771806\pi\)
−0.753851 + 0.657045i \(0.771806\pi\)
\(264\) 5.44009 0.334814
\(265\) 1.86518 0.114577
\(266\) 11.3528 0.696086
\(267\) −1.70984 −0.104640
\(268\) 15.1274 0.924054
\(269\) −23.7625 −1.44882 −0.724412 0.689368i \(-0.757888\pi\)
−0.724412 + 0.689368i \(0.757888\pi\)
\(270\) 0.658196 0.0400565
\(271\) −0.000261783 0 −1.59022e−5 0 −7.95110e−6 1.00000i \(-0.500003\pi\)
−7.95110e−6 1.00000i \(0.500003\pi\)
\(272\) −2.88608 −0.174995
\(273\) −7.13650 −0.431920
\(274\) −0.928463 −0.0560905
\(275\) −8.94131 −0.539181
\(276\) −10.1683 −0.612062
\(277\) −1.16032 −0.0697168 −0.0348584 0.999392i \(-0.511098\pi\)
−0.0348584 + 0.999392i \(0.511098\pi\)
\(278\) −2.94047 −0.176358
\(279\) −9.36283 −0.560538
\(280\) −10.8727 −0.649770
\(281\) 12.5464 0.748454 0.374227 0.927337i \(-0.377908\pi\)
0.374227 + 0.927337i \(0.377908\pi\)
\(282\) 1.56723 0.0933272
\(283\) −6.68518 −0.397393 −0.198696 0.980061i \(-0.563671\pi\)
−0.198696 + 0.980061i \(0.563671\pi\)
\(284\) −4.95339 −0.293930
\(285\) −8.98231 −0.532066
\(286\) −2.35021 −0.138971
\(287\) 5.61117 0.331217
\(288\) 4.59937 0.271020
\(289\) 1.00000 0.0588235
\(290\) 6.43626 0.377950
\(291\) −1.17467 −0.0688606
\(292\) 27.9075 1.63316
\(293\) −27.7696 −1.62231 −0.811157 0.584828i \(-0.801162\pi\)
−0.811157 + 0.584828i \(0.801162\pi\)
\(294\) −5.17450 −0.301783
\(295\) −19.5340 −1.13732
\(296\) 7.30826 0.424784
\(297\) −3.26197 −0.189278
\(298\) −5.68575 −0.329366
\(299\) 9.25173 0.535041
\(300\) −4.95647 −0.286162
\(301\) 13.5633 0.781775
\(302\) 7.31332 0.420834
\(303\) −9.86589 −0.566781
\(304\) −17.2483 −0.989258
\(305\) 6.75762 0.386940
\(306\) −0.437930 −0.0250348
\(307\) −22.2905 −1.27219 −0.636094 0.771611i \(-0.719451\pi\)
−0.636094 + 0.771611i \(0.719451\pi\)
\(308\) 25.5854 1.45786
\(309\) 1.75170 0.0996507
\(310\) 6.16258 0.350011
\(311\) 14.5941 0.827558 0.413779 0.910377i \(-0.364209\pi\)
0.413779 + 0.910377i \(0.364209\pi\)
\(312\) −2.74378 −0.155336
\(313\) 26.0956 1.47501 0.737505 0.675341i \(-0.236004\pi\)
0.737505 + 0.675341i \(0.236004\pi\)
\(314\) 0.365176 0.0206081
\(315\) 6.51947 0.367330
\(316\) −1.80822 −0.101720
\(317\) −24.8218 −1.39413 −0.697065 0.717008i \(-0.745511\pi\)
−0.697065 + 0.717008i \(0.745511\pi\)
\(318\) 0.543469 0.0304762
\(319\) −31.8976 −1.78592
\(320\) 5.64811 0.315739
\(321\) −8.03891 −0.448688
\(322\) 10.6823 0.595303
\(323\) 5.97637 0.332534
\(324\) −1.80822 −0.100457
\(325\) 4.50967 0.250152
\(326\) −6.27698 −0.347650
\(327\) 6.17934 0.341718
\(328\) 2.15734 0.119119
\(329\) 15.5235 0.855839
\(330\) 2.14701 0.118189
\(331\) 21.1658 1.16338 0.581688 0.813412i \(-0.302393\pi\)
0.581688 + 0.813412i \(0.302393\pi\)
\(332\) −4.20330 −0.230686
\(333\) −4.38216 −0.240141
\(334\) 2.76647 0.151374
\(335\) 12.5737 0.686977
\(336\) 12.5190 0.682969
\(337\) 18.0523 0.983369 0.491684 0.870773i \(-0.336381\pi\)
0.491684 + 0.870773i \(0.336381\pi\)
\(338\) −4.50773 −0.245188
\(339\) −4.11575 −0.223537
\(340\) −2.71770 −0.147388
\(341\) −30.5412 −1.65390
\(342\) −2.61723 −0.141524
\(343\) −20.8897 −1.12794
\(344\) 5.21470 0.281158
\(345\) −8.45181 −0.455030
\(346\) 3.09210 0.166232
\(347\) −6.55557 −0.351922 −0.175961 0.984397i \(-0.556303\pi\)
−0.175961 + 0.984397i \(0.556303\pi\)
\(348\) −17.6819 −0.947850
\(349\) −0.809831 −0.0433493 −0.0216746 0.999765i \(-0.506900\pi\)
−0.0216746 + 0.999765i \(0.506900\pi\)
\(350\) 5.20701 0.278326
\(351\) 1.64522 0.0878152
\(352\) 15.0030 0.799662
\(353\) 16.7760 0.892894 0.446447 0.894810i \(-0.352689\pi\)
0.446447 + 0.894810i \(0.352689\pi\)
\(354\) −5.69176 −0.302513
\(355\) −4.11721 −0.218519
\(356\) −3.09175 −0.163863
\(357\) −4.33772 −0.229577
\(358\) −3.73049 −0.197162
\(359\) −0.886341 −0.0467793 −0.0233896 0.999726i \(-0.507446\pi\)
−0.0233896 + 0.999726i \(0.507446\pi\)
\(360\) 2.50655 0.132107
\(361\) 16.7170 0.879842
\(362\) 6.21023 0.326403
\(363\) 0.359578 0.0188729
\(364\) −12.9043 −0.676371
\(365\) 23.1964 1.21416
\(366\) 1.96901 0.102922
\(367\) −1.57783 −0.0823620 −0.0411810 0.999152i \(-0.513112\pi\)
−0.0411810 + 0.999152i \(0.513112\pi\)
\(368\) −16.2296 −0.846028
\(369\) −1.29358 −0.0673408
\(370\) 2.88432 0.149948
\(371\) 5.38309 0.279476
\(372\) −16.9300 −0.877782
\(373\) −25.0838 −1.29879 −0.649394 0.760452i \(-0.724978\pi\)
−0.649394 + 0.760452i \(0.724978\pi\)
\(374\) −1.42851 −0.0738666
\(375\) −11.6346 −0.600809
\(376\) 5.96835 0.307794
\(377\) 16.0880 0.828575
\(378\) 1.89962 0.0977058
\(379\) −33.7423 −1.73322 −0.866612 0.498983i \(-0.833707\pi\)
−0.866612 + 0.498983i \(0.833707\pi\)
\(380\) −16.2420 −0.833195
\(381\) −18.6911 −0.957576
\(382\) −3.57669 −0.183000
\(383\) −20.4661 −1.04577 −0.522885 0.852403i \(-0.675144\pi\)
−0.522885 + 0.852403i \(0.675144\pi\)
\(384\) 10.8445 0.553404
\(385\) 21.2663 1.08383
\(386\) −4.95315 −0.252109
\(387\) −3.12682 −0.158945
\(388\) −2.12407 −0.107833
\(389\) 13.8163 0.700514 0.350257 0.936654i \(-0.386094\pi\)
0.350257 + 0.936654i \(0.386094\pi\)
\(390\) −1.08288 −0.0548335
\(391\) 5.62341 0.284388
\(392\) −19.7056 −0.995285
\(393\) −0.435527 −0.0219694
\(394\) −8.06697 −0.406408
\(395\) −1.50297 −0.0756226
\(396\) −5.89834 −0.296403
\(397\) 25.9013 1.29995 0.649974 0.759956i \(-0.274780\pi\)
0.649974 + 0.759956i \(0.274780\pi\)
\(398\) 6.31079 0.316331
\(399\) −25.9238 −1.29781
\(400\) −7.91099 −0.395549
\(401\) −6.54455 −0.326819 −0.163410 0.986558i \(-0.552249\pi\)
−0.163410 + 0.986558i \(0.552249\pi\)
\(402\) 3.66369 0.182728
\(403\) 15.4039 0.767323
\(404\) −17.8397 −0.887557
\(405\) −1.50297 −0.0746832
\(406\) 18.5757 0.921896
\(407\) −14.2944 −0.708549
\(408\) −1.66773 −0.0825651
\(409\) 26.4569 1.30821 0.654104 0.756405i \(-0.273046\pi\)
0.654104 + 0.756405i \(0.273046\pi\)
\(410\) 0.851426 0.0420489
\(411\) 2.12012 0.104578
\(412\) 3.16745 0.156049
\(413\) −56.3772 −2.77414
\(414\) −2.46266 −0.121033
\(415\) −3.49374 −0.171501
\(416\) −7.56696 −0.371001
\(417\) 6.71447 0.328809
\(418\) −8.53732 −0.417574
\(419\) 15.6430 0.764212 0.382106 0.924118i \(-0.375199\pi\)
0.382106 + 0.924118i \(0.375199\pi\)
\(420\) 11.7886 0.575225
\(421\) −0.461461 −0.0224902 −0.0112451 0.999937i \(-0.503580\pi\)
−0.0112451 + 0.999937i \(0.503580\pi\)
\(422\) −1.82601 −0.0888886
\(423\) −3.57872 −0.174004
\(424\) 2.06965 0.100511
\(425\) 2.74108 0.132962
\(426\) −1.19966 −0.0581235
\(427\) 19.5032 0.943825
\(428\) −14.5361 −0.702629
\(429\) 5.36665 0.259104
\(430\) 2.05806 0.0992485
\(431\) −40.4790 −1.94981 −0.974903 0.222629i \(-0.928536\pi\)
−0.974903 + 0.222629i \(0.928536\pi\)
\(432\) −2.88608 −0.138857
\(433\) −26.2372 −1.26088 −0.630439 0.776238i \(-0.717125\pi\)
−0.630439 + 0.776238i \(0.717125\pi\)
\(434\) 17.7858 0.853746
\(435\) −14.6970 −0.704668
\(436\) 11.1736 0.535118
\(437\) 33.6075 1.60767
\(438\) 6.75888 0.322952
\(439\) 16.4759 0.786350 0.393175 0.919464i \(-0.371377\pi\)
0.393175 + 0.919464i \(0.371377\pi\)
\(440\) 8.17629 0.389789
\(441\) 11.8158 0.562658
\(442\) 0.720490 0.0342702
\(443\) 18.5159 0.879719 0.439859 0.898067i \(-0.355028\pi\)
0.439859 + 0.898067i \(0.355028\pi\)
\(444\) −7.92389 −0.376051
\(445\) −2.56983 −0.121822
\(446\) −5.28266 −0.250141
\(447\) 12.9832 0.614086
\(448\) 16.3010 0.770151
\(449\) −33.5917 −1.58529 −0.792646 0.609682i \(-0.791297\pi\)
−0.792646 + 0.609682i \(0.791297\pi\)
\(450\) −1.20040 −0.0565875
\(451\) −4.21960 −0.198693
\(452\) −7.44216 −0.350050
\(453\) −16.6997 −0.784622
\(454\) 11.1309 0.522399
\(455\) −10.7259 −0.502840
\(456\) −9.96699 −0.466747
\(457\) 27.8456 1.30256 0.651282 0.758836i \(-0.274232\pi\)
0.651282 + 0.758836i \(0.274232\pi\)
\(458\) −5.11790 −0.239144
\(459\) 1.00000 0.0466760
\(460\) −15.2827 −0.712560
\(461\) 2.59011 0.120633 0.0603166 0.998179i \(-0.480789\pi\)
0.0603166 + 0.998179i \(0.480789\pi\)
\(462\) 6.19649 0.288287
\(463\) −24.1873 −1.12408 −0.562040 0.827110i \(-0.689983\pi\)
−0.562040 + 0.827110i \(0.689983\pi\)
\(464\) −28.2220 −1.31017
\(465\) −14.0721 −0.652576
\(466\) −0.510491 −0.0236480
\(467\) 38.6618 1.78905 0.894526 0.447015i \(-0.147513\pi\)
0.894526 + 0.447015i \(0.147513\pi\)
\(468\) 2.97491 0.137515
\(469\) 36.2890 1.67567
\(470\) 2.35550 0.108651
\(471\) −0.833868 −0.0384226
\(472\) −21.6754 −0.997693
\(473\) −10.1996 −0.468978
\(474\) −0.437930 −0.0201148
\(475\) 16.3817 0.751644
\(476\) −7.84354 −0.359508
\(477\) −1.24099 −0.0568212
\(478\) 4.87807 0.223118
\(479\) −16.3504 −0.747069 −0.373535 0.927616i \(-0.621854\pi\)
−0.373535 + 0.927616i \(0.621854\pi\)
\(480\) 6.91271 0.315521
\(481\) 7.20960 0.328730
\(482\) 0.0441875 0.00201269
\(483\) −24.3928 −1.10991
\(484\) 0.650195 0.0295543
\(485\) −1.76550 −0.0801672
\(486\) −0.437930 −0.0198649
\(487\) 9.18913 0.416399 0.208200 0.978086i \(-0.433240\pi\)
0.208200 + 0.978086i \(0.433240\pi\)
\(488\) 7.49842 0.339438
\(489\) 14.3333 0.648174
\(490\) −7.77712 −0.351335
\(491\) 27.9077 1.25946 0.629729 0.776815i \(-0.283166\pi\)
0.629729 + 0.776815i \(0.283166\pi\)
\(492\) −2.33906 −0.105453
\(493\) 9.77865 0.440408
\(494\) 4.30592 0.193732
\(495\) −4.90264 −0.220357
\(496\) −27.0219 −1.21332
\(497\) −11.8827 −0.533010
\(498\) −1.01799 −0.0456174
\(499\) 9.56301 0.428099 0.214049 0.976823i \(-0.431335\pi\)
0.214049 + 0.976823i \(0.431335\pi\)
\(500\) −21.0379 −0.940844
\(501\) −6.31714 −0.282229
\(502\) −5.50638 −0.245762
\(503\) −21.6535 −0.965484 −0.482742 0.875763i \(-0.660359\pi\)
−0.482742 + 0.875763i \(0.660359\pi\)
\(504\) 7.23416 0.322235
\(505\) −14.8281 −0.659844
\(506\) −8.03311 −0.357115
\(507\) 10.2933 0.457140
\(508\) −33.7976 −1.49953
\(509\) 8.12136 0.359973 0.179987 0.983669i \(-0.442395\pi\)
0.179987 + 0.983669i \(0.442395\pi\)
\(510\) −0.658196 −0.0291454
\(511\) 66.9471 2.96157
\(512\) 22.9006 1.01207
\(513\) 5.97637 0.263863
\(514\) −10.1121 −0.446026
\(515\) 2.63275 0.116013
\(516\) −5.65398 −0.248902
\(517\) −11.6737 −0.513408
\(518\) 8.32442 0.365754
\(519\) −7.06072 −0.309931
\(520\) −4.12383 −0.180842
\(521\) 6.67701 0.292525 0.146263 0.989246i \(-0.453276\pi\)
0.146263 + 0.989246i \(0.453276\pi\)
\(522\) −4.28236 −0.187434
\(523\) 12.5513 0.548829 0.274414 0.961612i \(-0.411516\pi\)
0.274414 + 0.961612i \(0.411516\pi\)
\(524\) −0.787528 −0.0344033
\(525\) −11.8900 −0.518924
\(526\) −10.7078 −0.466880
\(527\) 9.36283 0.407851
\(528\) −9.41431 −0.409705
\(529\) 8.62269 0.374899
\(530\) 0.816818 0.0354803
\(531\) 12.9970 0.564020
\(532\) −46.8759 −2.03233
\(533\) 2.12821 0.0921831
\(534\) −0.748788 −0.0324032
\(535\) −12.0822 −0.522361
\(536\) 13.9521 0.602640
\(537\) 8.51845 0.367598
\(538\) −10.4063 −0.448647
\(539\) 38.5428 1.66016
\(540\) −2.71770 −0.116951
\(541\) −25.1800 −1.08257 −0.541286 0.840838i \(-0.682062\pi\)
−0.541286 + 0.840838i \(0.682062\pi\)
\(542\) −0.000114643 0 −4.92433e−6 0
\(543\) −14.1809 −0.608560
\(544\) −4.59937 −0.197196
\(545\) 9.28736 0.397827
\(546\) −3.12529 −0.133750
\(547\) 32.8011 1.40247 0.701236 0.712929i \(-0.252632\pi\)
0.701236 + 0.712929i \(0.252632\pi\)
\(548\) 3.83363 0.163765
\(549\) −4.49618 −0.191892
\(550\) −3.91567 −0.166965
\(551\) 58.4408 2.48966
\(552\) −9.37834 −0.399168
\(553\) −4.33772 −0.184459
\(554\) −0.508139 −0.0215887
\(555\) −6.58625 −0.279571
\(556\) 12.1412 0.514903
\(557\) −13.7616 −0.583097 −0.291548 0.956556i \(-0.594170\pi\)
−0.291548 + 0.956556i \(0.594170\pi\)
\(558\) −4.10027 −0.173578
\(559\) 5.14431 0.217581
\(560\) 18.8157 0.795110
\(561\) 3.26197 0.137720
\(562\) 5.49443 0.231769
\(563\) 21.1445 0.891136 0.445568 0.895248i \(-0.353002\pi\)
0.445568 + 0.895248i \(0.353002\pi\)
\(564\) −6.47111 −0.272483
\(565\) −6.18584 −0.260240
\(566\) −2.92764 −0.123058
\(567\) −4.33772 −0.182167
\(568\) −4.56855 −0.191692
\(569\) −16.6952 −0.699901 −0.349950 0.936768i \(-0.613802\pi\)
−0.349950 + 0.936768i \(0.613802\pi\)
\(570\) −3.93362 −0.164761
\(571\) 11.6810 0.488833 0.244417 0.969670i \(-0.421404\pi\)
0.244417 + 0.969670i \(0.421404\pi\)
\(572\) 9.70406 0.405747
\(573\) 8.16727 0.341193
\(574\) 2.45730 0.102566
\(575\) 15.4142 0.642817
\(576\) −3.75797 −0.156582
\(577\) −32.3742 −1.34776 −0.673878 0.738842i \(-0.735373\pi\)
−0.673878 + 0.738842i \(0.735373\pi\)
\(578\) 0.437930 0.0182155
\(579\) 11.3104 0.470043
\(580\) −26.5754 −1.10348
\(581\) −10.0833 −0.418325
\(582\) −0.514425 −0.0213236
\(583\) −4.04808 −0.167654
\(584\) 25.7393 1.06510
\(585\) 2.47271 0.102234
\(586\) −12.1611 −0.502371
\(587\) −3.67784 −0.151801 −0.0759003 0.997115i \(-0.524183\pi\)
−0.0759003 + 0.997115i \(0.524183\pi\)
\(588\) 21.3656 0.881101
\(589\) 55.9558 2.30562
\(590\) −8.55454 −0.352185
\(591\) 18.4207 0.757726
\(592\) −12.6473 −0.519800
\(593\) 34.5520 1.41888 0.709440 0.704766i \(-0.248948\pi\)
0.709440 + 0.704766i \(0.248948\pi\)
\(594\) −1.42851 −0.0586126
\(595\) −6.51947 −0.267272
\(596\) 23.4765 0.961635
\(597\) −14.4105 −0.589782
\(598\) 4.05161 0.165683
\(599\) 30.9296 1.26375 0.631875 0.775071i \(-0.282286\pi\)
0.631875 + 0.775071i \(0.282286\pi\)
\(600\) −4.57139 −0.186626
\(601\) 26.2993 1.07277 0.536385 0.843973i \(-0.319789\pi\)
0.536385 + 0.843973i \(0.319789\pi\)
\(602\) 5.93977 0.242087
\(603\) −8.36592 −0.340687
\(604\) −30.1968 −1.22869
\(605\) 0.540435 0.0219718
\(606\) −4.32057 −0.175511
\(607\) −38.6827 −1.57008 −0.785042 0.619442i \(-0.787359\pi\)
−0.785042 + 0.619442i \(0.787359\pi\)
\(608\) −27.4875 −1.11477
\(609\) −42.4170 −1.71883
\(610\) 2.95937 0.119821
\(611\) 5.88778 0.238194
\(612\) 1.80822 0.0730929
\(613\) 37.1429 1.50019 0.750094 0.661332i \(-0.230008\pi\)
0.750094 + 0.661332i \(0.230008\pi\)
\(614\) −9.76170 −0.393950
\(615\) −1.94420 −0.0783979
\(616\) 23.5976 0.950773
\(617\) −12.1463 −0.488991 −0.244495 0.969650i \(-0.578622\pi\)
−0.244495 + 0.969650i \(0.578622\pi\)
\(618\) 0.767121 0.0308582
\(619\) −14.3051 −0.574970 −0.287485 0.957785i \(-0.592819\pi\)
−0.287485 + 0.957785i \(0.592819\pi\)
\(620\) −25.4453 −1.02191
\(621\) 5.62341 0.225659
\(622\) 6.39122 0.256264
\(623\) −7.41679 −0.297147
\(624\) 4.74824 0.190082
\(625\) −3.78108 −0.151243
\(626\) 11.4280 0.456757
\(627\) 19.4947 0.778544
\(628\) −1.50781 −0.0601683
\(629\) 4.38216 0.174728
\(630\) 2.85507 0.113749
\(631\) 14.3547 0.571452 0.285726 0.958311i \(-0.407765\pi\)
0.285726 + 0.958311i \(0.407765\pi\)
\(632\) −1.66773 −0.0663388
\(633\) 4.16963 0.165728
\(634\) −10.8702 −0.431711
\(635\) −28.0922 −1.11481
\(636\) −2.24399 −0.0889799
\(637\) −19.4396 −0.770225
\(638\) −13.9689 −0.553035
\(639\) 2.73938 0.108368
\(640\) 16.2989 0.644271
\(641\) −17.0613 −0.673882 −0.336941 0.941526i \(-0.609392\pi\)
−0.336941 + 0.941526i \(0.609392\pi\)
\(642\) −3.52048 −0.138942
\(643\) −30.4812 −1.20206 −0.601031 0.799226i \(-0.705243\pi\)
−0.601031 + 0.799226i \(0.705243\pi\)
\(644\) −44.1074 −1.73808
\(645\) −4.69952 −0.185044
\(646\) 2.61723 0.102974
\(647\) −17.8193 −0.700550 −0.350275 0.936647i \(-0.613912\pi\)
−0.350275 + 0.936647i \(0.613912\pi\)
\(648\) −1.66773 −0.0655147
\(649\) 42.3956 1.66417
\(650\) 1.97492 0.0774628
\(651\) −40.6134 −1.59176
\(652\) 25.9177 1.01502
\(653\) −27.5261 −1.07718 −0.538589 0.842569i \(-0.681042\pi\)
−0.538589 + 0.842569i \(0.681042\pi\)
\(654\) 2.70612 0.105818
\(655\) −0.654585 −0.0255767
\(656\) −3.73337 −0.145763
\(657\) −15.4337 −0.602126
\(658\) 6.79821 0.265022
\(659\) −13.3927 −0.521707 −0.260853 0.965378i \(-0.584004\pi\)
−0.260853 + 0.965378i \(0.584004\pi\)
\(660\) −8.86504 −0.345071
\(661\) −19.3318 −0.751919 −0.375960 0.926636i \(-0.622687\pi\)
−0.375960 + 0.926636i \(0.622687\pi\)
\(662\) 9.26912 0.360255
\(663\) −1.64522 −0.0638950
\(664\) −3.87674 −0.150447
\(665\) −38.9627 −1.51091
\(666\) −1.91908 −0.0743627
\(667\) 54.9893 2.12919
\(668\) −11.4228 −0.441960
\(669\) 12.0628 0.466375
\(670\) 5.50642 0.212731
\(671\) −14.6664 −0.566190
\(672\) 19.9508 0.769618
\(673\) −43.0773 −1.66051 −0.830254 0.557386i \(-0.811804\pi\)
−0.830254 + 0.557386i \(0.811804\pi\)
\(674\) 7.90562 0.304513
\(675\) 2.74108 0.105504
\(676\) 18.6124 0.715863
\(677\) −43.7804 −1.68262 −0.841309 0.540554i \(-0.818215\pi\)
−0.841309 + 0.540554i \(0.818215\pi\)
\(678\) −1.80241 −0.0692211
\(679\) −5.09541 −0.195544
\(680\) −2.50655 −0.0961219
\(681\) −25.4171 −0.973984
\(682\) −13.3749 −0.512152
\(683\) −28.2765 −1.08197 −0.540985 0.841032i \(-0.681949\pi\)
−0.540985 + 0.841032i \(0.681949\pi\)
\(684\) 10.8066 0.413200
\(685\) 3.18647 0.121749
\(686\) −9.14822 −0.349281
\(687\) 11.6866 0.445870
\(688\) −9.02428 −0.344047
\(689\) 2.04171 0.0777828
\(690\) −3.70130 −0.140906
\(691\) 18.9171 0.719642 0.359821 0.933021i \(-0.382838\pi\)
0.359821 + 0.933021i \(0.382838\pi\)
\(692\) −12.7673 −0.485340
\(693\) −14.1495 −0.537495
\(694\) −2.87088 −0.108977
\(695\) 10.0917 0.382798
\(696\) −16.3082 −0.618160
\(697\) 1.29358 0.0489976
\(698\) −0.354649 −0.0134237
\(699\) 1.16569 0.0440905
\(700\) −21.4998 −0.812615
\(701\) 10.8657 0.410391 0.205196 0.978721i \(-0.434217\pi\)
0.205196 + 0.978721i \(0.434217\pi\)
\(702\) 0.720490 0.0271932
\(703\) 26.1894 0.987751
\(704\) −12.2584 −0.462005
\(705\) −5.37872 −0.202574
\(706\) 7.34670 0.276497
\(707\) −42.7955 −1.60949
\(708\) 23.5013 0.883234
\(709\) 1.72491 0.0647802 0.0323901 0.999475i \(-0.489688\pi\)
0.0323901 + 0.999475i \(0.489688\pi\)
\(710\) −1.80305 −0.0676672
\(711\) 1.00000 0.0375029
\(712\) −2.85155 −0.106866
\(713\) 52.6510 1.97180
\(714\) −1.89962 −0.0710914
\(715\) 8.06591 0.301648
\(716\) 15.4032 0.575645
\(717\) −11.1389 −0.415991
\(718\) −0.388155 −0.0144858
\(719\) −22.6198 −0.843577 −0.421788 0.906694i \(-0.638597\pi\)
−0.421788 + 0.906694i \(0.638597\pi\)
\(720\) −4.33770 −0.161657
\(721\) 7.59838 0.282979
\(722\) 7.32087 0.272455
\(723\) −0.100901 −0.00375254
\(724\) −25.6421 −0.952982
\(725\) 26.8041 0.995478
\(726\) 0.157470 0.00584426
\(727\) 44.2704 1.64190 0.820950 0.571000i \(-0.193444\pi\)
0.820950 + 0.571000i \(0.193444\pi\)
\(728\) −11.9018 −0.441109
\(729\) 1.00000 0.0370370
\(730\) 10.1584 0.375979
\(731\) 3.12682 0.115650
\(732\) −8.13007 −0.300496
\(733\) −1.87683 −0.0693224 −0.0346612 0.999399i \(-0.511035\pi\)
−0.0346612 + 0.999399i \(0.511035\pi\)
\(734\) −0.690978 −0.0255045
\(735\) 17.7588 0.655044
\(736\) −25.8641 −0.953364
\(737\) −27.2894 −1.00522
\(738\) −0.566495 −0.0208530
\(739\) 22.4601 0.826209 0.413105 0.910684i \(-0.364444\pi\)
0.413105 + 0.910684i \(0.364444\pi\)
\(740\) −11.9094 −0.437797
\(741\) −9.83243 −0.361203
\(742\) 2.35742 0.0865435
\(743\) 27.0418 0.992068 0.496034 0.868303i \(-0.334789\pi\)
0.496034 + 0.868303i \(0.334789\pi\)
\(744\) −15.6147 −0.572463
\(745\) 19.5134 0.714916
\(746\) −10.9849 −0.402187
\(747\) 2.32456 0.0850511
\(748\) 5.89834 0.215665
\(749\) −34.8706 −1.27414
\(750\) −5.09515 −0.186048
\(751\) −4.61891 −0.168546 −0.0842732 0.996443i \(-0.526857\pi\)
−0.0842732 + 0.996443i \(0.526857\pi\)
\(752\) −10.3285 −0.376642
\(753\) 12.5737 0.458210
\(754\) 7.04542 0.256579
\(755\) −25.0992 −0.913454
\(756\) −7.84354 −0.285267
\(757\) −38.6018 −1.40301 −0.701503 0.712666i \(-0.747487\pi\)
−0.701503 + 0.712666i \(0.747487\pi\)
\(758\) −14.7767 −0.536716
\(759\) 18.3434 0.665822
\(760\) −14.9801 −0.543385
\(761\) 45.3944 1.64554 0.822772 0.568371i \(-0.192426\pi\)
0.822772 + 0.568371i \(0.192426\pi\)
\(762\) −8.18541 −0.296526
\(763\) 26.8042 0.970379
\(764\) 14.7682 0.534295
\(765\) 1.50297 0.0543400
\(766\) −8.96273 −0.323837
\(767\) −21.3828 −0.772089
\(768\) −2.76682 −0.0998391
\(769\) −33.2058 −1.19743 −0.598717 0.800961i \(-0.704322\pi\)
−0.598717 + 0.800961i \(0.704322\pi\)
\(770\) 9.31314 0.335622
\(771\) 23.0907 0.831592
\(772\) 20.4516 0.736069
\(773\) −15.8934 −0.571646 −0.285823 0.958283i \(-0.592267\pi\)
−0.285823 + 0.958283i \(0.592267\pi\)
\(774\) −1.36933 −0.0492195
\(775\) 25.6643 0.921888
\(776\) −1.95904 −0.0703255
\(777\) −19.0086 −0.681929
\(778\) 6.05057 0.216923
\(779\) 7.73088 0.276988
\(780\) 4.47120 0.160095
\(781\) 8.93576 0.319747
\(782\) 2.46266 0.0880645
\(783\) 9.77865 0.349460
\(784\) 34.1015 1.21791
\(785\) −1.25328 −0.0447314
\(786\) −0.190730 −0.00680313
\(787\) −38.6133 −1.37642 −0.688208 0.725513i \(-0.741602\pi\)
−0.688208 + 0.725513i \(0.741602\pi\)
\(788\) 33.3086 1.18657
\(789\) 24.4508 0.870473
\(790\) −0.658196 −0.0234176
\(791\) −17.8530 −0.634778
\(792\) −5.44009 −0.193305
\(793\) 7.39720 0.262682
\(794\) 11.3429 0.402546
\(795\) −1.86518 −0.0661511
\(796\) −26.0573 −0.923577
\(797\) −7.87321 −0.278883 −0.139442 0.990230i \(-0.544531\pi\)
−0.139442 + 0.990230i \(0.544531\pi\)
\(798\) −11.3528 −0.401885
\(799\) 3.57872 0.126606
\(800\) −12.6072 −0.445733
\(801\) 1.70984 0.0604141
\(802\) −2.86606 −0.101204
\(803\) −50.3442 −1.77661
\(804\) −15.1274 −0.533503
\(805\) −36.6616 −1.29215
\(806\) 6.74583 0.237612
\(807\) 23.7625 0.836479
\(808\) −16.4537 −0.578838
\(809\) −38.2955 −1.34640 −0.673198 0.739462i \(-0.735080\pi\)
−0.673198 + 0.739462i \(0.735080\pi\)
\(810\) −0.658196 −0.0231266
\(811\) 19.9033 0.698900 0.349450 0.936955i \(-0.386368\pi\)
0.349450 + 0.936955i \(0.386368\pi\)
\(812\) −76.6992 −2.69162
\(813\) 0.000261783 0 9.18114e−6 0
\(814\) −6.25997 −0.219412
\(815\) 21.5425 0.754602
\(816\) 2.88608 0.101033
\(817\) 18.6870 0.653777
\(818\) 11.5863 0.405104
\(819\) 7.13650 0.249369
\(820\) −3.51555 −0.122768
\(821\) −5.55919 −0.194017 −0.0970086 0.995284i \(-0.530927\pi\)
−0.0970086 + 0.995284i \(0.530927\pi\)
\(822\) 0.928463 0.0323839
\(823\) −55.2647 −1.92641 −0.963203 0.268773i \(-0.913382\pi\)
−0.963203 + 0.268773i \(0.913382\pi\)
\(824\) 2.92137 0.101771
\(825\) 8.94131 0.311296
\(826\) −24.6892 −0.859049
\(827\) −23.6024 −0.820737 −0.410368 0.911920i \(-0.634600\pi\)
−0.410368 + 0.911920i \(0.634600\pi\)
\(828\) 10.1683 0.353374
\(829\) 50.5661 1.75623 0.878116 0.478448i \(-0.158800\pi\)
0.878116 + 0.478448i \(0.158800\pi\)
\(830\) −1.53001 −0.0531075
\(831\) 1.16032 0.0402510
\(832\) 6.18268 0.214346
\(833\) −11.8158 −0.409394
\(834\) 2.94047 0.101820
\(835\) −9.49448 −0.328570
\(836\) 35.2507 1.21917
\(837\) 9.36283 0.323627
\(838\) 6.85055 0.236648
\(839\) −8.51786 −0.294069 −0.147035 0.989131i \(-0.546973\pi\)
−0.147035 + 0.989131i \(0.546973\pi\)
\(840\) 10.8727 0.375145
\(841\) 66.6220 2.29731
\(842\) −0.202088 −0.00696440
\(843\) −12.5464 −0.432120
\(844\) 7.53960 0.259524
\(845\) 15.4705 0.532200
\(846\) −1.56723 −0.0538825
\(847\) 1.55975 0.0535936
\(848\) −3.58162 −0.122993
\(849\) 6.68518 0.229435
\(850\) 1.20040 0.0411734
\(851\) 24.6426 0.844739
\(852\) 4.95339 0.169700
\(853\) 3.31587 0.113533 0.0567667 0.998387i \(-0.481921\pi\)
0.0567667 + 0.998387i \(0.481921\pi\)
\(854\) 8.54102 0.292268
\(855\) 8.98231 0.307188
\(856\) −13.4068 −0.458234
\(857\) 13.5889 0.464189 0.232094 0.972693i \(-0.425442\pi\)
0.232094 + 0.972693i \(0.425442\pi\)
\(858\) 2.35021 0.0802350
\(859\) 17.4120 0.594089 0.297045 0.954864i \(-0.403999\pi\)
0.297045 + 0.954864i \(0.403999\pi\)
\(860\) −8.49776 −0.289771
\(861\) −5.61117 −0.191228
\(862\) −17.7270 −0.603783
\(863\) −45.2505 −1.54034 −0.770172 0.637836i \(-0.779830\pi\)
−0.770172 + 0.637836i \(0.779830\pi\)
\(864\) −4.59937 −0.156474
\(865\) −10.6121 −0.360821
\(866\) −11.4901 −0.390448
\(867\) −1.00000 −0.0339618
\(868\) −73.4378 −2.49264
\(869\) 3.26197 0.110655
\(870\) −6.43626 −0.218210
\(871\) 13.7638 0.466368
\(872\) 10.3055 0.348988
\(873\) 1.17467 0.0397567
\(874\) 14.7178 0.497835
\(875\) −50.4677 −1.70612
\(876\) −27.9075 −0.942907
\(877\) −6.01006 −0.202945 −0.101473 0.994838i \(-0.532355\pi\)
−0.101473 + 0.994838i \(0.532355\pi\)
\(878\) 7.21528 0.243504
\(879\) 27.7696 0.936644
\(880\) −14.1494 −0.476977
\(881\) 8.13198 0.273973 0.136987 0.990573i \(-0.456258\pi\)
0.136987 + 0.990573i \(0.456258\pi\)
\(882\) 5.17450 0.174235
\(883\) −56.5172 −1.90195 −0.950977 0.309261i \(-0.899918\pi\)
−0.950977 + 0.309261i \(0.899918\pi\)
\(884\) −2.97491 −0.100057
\(885\) 19.5340 0.656629
\(886\) 8.10868 0.272417
\(887\) −5.02720 −0.168797 −0.0843984 0.996432i \(-0.526897\pi\)
−0.0843984 + 0.996432i \(0.526897\pi\)
\(888\) −7.30826 −0.245249
\(889\) −81.0769 −2.71923
\(890\) −1.12541 −0.0377237
\(891\) 3.26197 0.109280
\(892\) 21.8122 0.730325
\(893\) 21.3878 0.715715
\(894\) 5.68575 0.190160
\(895\) 12.8030 0.427956
\(896\) 47.0403 1.57150
\(897\) −9.25173 −0.308906
\(898\) −14.7108 −0.490907
\(899\) 91.5559 3.05356
\(900\) 4.95647 0.165216
\(901\) 1.24099 0.0413435
\(902\) −1.84789 −0.0615280
\(903\) −13.5633 −0.451358
\(904\) −6.86396 −0.228292
\(905\) −21.3134 −0.708483
\(906\) −7.31332 −0.242969
\(907\) 4.36007 0.144774 0.0723869 0.997377i \(-0.476938\pi\)
0.0723869 + 0.997377i \(0.476938\pi\)
\(908\) −45.9596 −1.52522
\(909\) 9.86589 0.327231
\(910\) −4.69721 −0.155711
\(911\) −18.2410 −0.604350 −0.302175 0.953252i \(-0.597713\pi\)
−0.302175 + 0.953252i \(0.597713\pi\)
\(912\) 17.2483 0.571149
\(913\) 7.58263 0.250948
\(914\) 12.1944 0.403356
\(915\) −6.75762 −0.223400
\(916\) 21.1318 0.698216
\(917\) −1.88920 −0.0623868
\(918\) 0.437930 0.0144538
\(919\) −23.7165 −0.782334 −0.391167 0.920320i \(-0.627929\pi\)
−0.391167 + 0.920320i \(0.627929\pi\)
\(920\) −14.0954 −0.464710
\(921\) 22.2905 0.734498
\(922\) 1.13428 0.0373557
\(923\) −4.50688 −0.148346
\(924\) −25.5854 −0.841697
\(925\) 12.0118 0.394947
\(926\) −10.5923 −0.348086
\(927\) −1.75170 −0.0575333
\(928\) −44.9756 −1.47640
\(929\) −12.9490 −0.424844 −0.212422 0.977178i \(-0.568135\pi\)
−0.212422 + 0.977178i \(0.568135\pi\)
\(930\) −6.16258 −0.202079
\(931\) −70.6157 −2.31434
\(932\) 2.10782 0.0690440
\(933\) −14.5941 −0.477791
\(934\) 16.9311 0.554004
\(935\) 4.90264 0.160333
\(936\) 2.74378 0.0896834
\(937\) −23.0205 −0.752046 −0.376023 0.926610i \(-0.622709\pi\)
−0.376023 + 0.926610i \(0.622709\pi\)
\(938\) 15.8921 0.518894
\(939\) −26.0956 −0.851598
\(940\) −9.72589 −0.317223
\(941\) −24.7050 −0.805360 −0.402680 0.915341i \(-0.631921\pi\)
−0.402680 + 0.915341i \(0.631921\pi\)
\(942\) −0.365176 −0.0118981
\(943\) 7.27430 0.236884
\(944\) 37.5103 1.22086
\(945\) −6.51947 −0.212078
\(946\) −4.46671 −0.145225
\(947\) −8.35855 −0.271616 −0.135808 0.990735i \(-0.543363\pi\)
−0.135808 + 0.990735i \(0.543363\pi\)
\(948\) 1.80822 0.0587282
\(949\) 25.3918 0.824253
\(950\) 7.17404 0.232757
\(951\) 24.8218 0.804901
\(952\) −7.23416 −0.234460
\(953\) −43.8717 −1.42114 −0.710571 0.703625i \(-0.751563\pi\)
−0.710571 + 0.703625i \(0.751563\pi\)
\(954\) −0.543469 −0.0175955
\(955\) 12.2752 0.397215
\(956\) −20.1416 −0.651426
\(957\) 31.8976 1.03110
\(958\) −7.16033 −0.231340
\(959\) 9.19648 0.296970
\(960\) −5.64811 −0.182292
\(961\) 56.6627 1.82783
\(962\) 3.15730 0.101795
\(963\) 8.03891 0.259050
\(964\) −0.182451 −0.00587634
\(965\) 16.9992 0.547222
\(966\) −10.6823 −0.343698
\(967\) 51.6076 1.65959 0.829794 0.558070i \(-0.188458\pi\)
0.829794 + 0.558070i \(0.188458\pi\)
\(968\) 0.599680 0.0192744
\(969\) −5.97637 −0.191989
\(970\) −0.773165 −0.0248248
\(971\) 17.9100 0.574758 0.287379 0.957817i \(-0.407216\pi\)
0.287379 + 0.957817i \(0.407216\pi\)
\(972\) 1.80822 0.0579986
\(973\) 29.1255 0.933721
\(974\) 4.02420 0.128944
\(975\) −4.50967 −0.144425
\(976\) −12.9764 −0.415363
\(977\) −47.5348 −1.52077 −0.760386 0.649471i \(-0.774990\pi\)
−0.760386 + 0.649471i \(0.774990\pi\)
\(978\) 6.27698 0.200716
\(979\) 5.57743 0.178255
\(980\) 32.1118 1.02577
\(981\) −6.17934 −0.197291
\(982\) 12.2216 0.390008
\(983\) 40.5653 1.29383 0.646916 0.762561i \(-0.276058\pi\)
0.646916 + 0.762561i \(0.276058\pi\)
\(984\) −2.15734 −0.0687734
\(985\) 27.6858 0.882142
\(986\) 4.28236 0.136378
\(987\) −15.5235 −0.494119
\(988\) −17.7792 −0.565631
\(989\) 17.5834 0.559119
\(990\) −2.14701 −0.0682365
\(991\) −19.1569 −0.608540 −0.304270 0.952586i \(-0.598413\pi\)
−0.304270 + 0.952586i \(0.598413\pi\)
\(992\) −43.0631 −1.36726
\(993\) −21.1658 −0.671675
\(994\) −5.20377 −0.165054
\(995\) −21.6586 −0.686622
\(996\) 4.20330 0.133187
\(997\) −35.9163 −1.13748 −0.568740 0.822517i \(-0.692569\pi\)
−0.568740 + 0.822517i \(0.692569\pi\)
\(998\) 4.18793 0.132567
\(999\) 4.38216 0.138645
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 4029.2.a.l.1.19 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.19 32 1.1 even 1 trivial