Properties

Label 8034.2.a.bc.1.6
Level 8034
Weight 2
Character 8034.1
Self dual yes
Analytic conductor 64.152
Analytic rank 0
Dimension 15
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Defining polynomial: \(x^{15} - x^{14} - 48 x^{13} + 44 x^{12} + 872 x^{11} - 707 x^{10} - 7580 x^{9} + 5112 x^{8} + 33191 x^{7} - 16428 x^{6} - 71361 x^{5} + 21747 x^{4} + 65434 x^{3} - 11840 x^{2} - 17600 x + 2048\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.17201\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.17201 q^{5} -1.00000 q^{6} -4.40989 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.17201 q^{5} -1.00000 q^{6} -4.40989 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.17201 q^{10} +0.445599 q^{11} -1.00000 q^{12} -1.00000 q^{13} -4.40989 q^{14} +1.17201 q^{15} +1.00000 q^{16} +6.53411 q^{17} +1.00000 q^{18} -3.79076 q^{19} -1.17201 q^{20} +4.40989 q^{21} +0.445599 q^{22} -1.35290 q^{23} -1.00000 q^{24} -3.62640 q^{25} -1.00000 q^{26} -1.00000 q^{27} -4.40989 q^{28} -5.72200 q^{29} +1.17201 q^{30} -7.97242 q^{31} +1.00000 q^{32} -0.445599 q^{33} +6.53411 q^{34} +5.16841 q^{35} +1.00000 q^{36} +6.80648 q^{37} -3.79076 q^{38} +1.00000 q^{39} -1.17201 q^{40} +0.483328 q^{41} +4.40989 q^{42} -7.08156 q^{43} +0.445599 q^{44} -1.17201 q^{45} -1.35290 q^{46} +3.11266 q^{47} -1.00000 q^{48} +12.4471 q^{49} -3.62640 q^{50} -6.53411 q^{51} -1.00000 q^{52} -2.35869 q^{53} -1.00000 q^{54} -0.522245 q^{55} -4.40989 q^{56} +3.79076 q^{57} -5.72200 q^{58} +10.8330 q^{59} +1.17201 q^{60} -2.55140 q^{61} -7.97242 q^{62} -4.40989 q^{63} +1.00000 q^{64} +1.17201 q^{65} -0.445599 q^{66} -2.47808 q^{67} +6.53411 q^{68} +1.35290 q^{69} +5.16841 q^{70} +2.87156 q^{71} +1.00000 q^{72} +11.7695 q^{73} +6.80648 q^{74} +3.62640 q^{75} -3.79076 q^{76} -1.96504 q^{77} +1.00000 q^{78} -11.5317 q^{79} -1.17201 q^{80} +1.00000 q^{81} +0.483328 q^{82} -0.188229 q^{83} +4.40989 q^{84} -7.65802 q^{85} -7.08156 q^{86} +5.72200 q^{87} +0.445599 q^{88} +2.37544 q^{89} -1.17201 q^{90} +4.40989 q^{91} -1.35290 q^{92} +7.97242 q^{93} +3.11266 q^{94} +4.44279 q^{95} -1.00000 q^{96} -5.14559 q^{97} +12.4471 q^{98} +0.445599 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q + 15q^{2} - 15q^{3} + 15q^{4} - q^{5} - 15q^{6} + 5q^{7} + 15q^{8} + 15q^{9} + O(q^{10}) \) \( 15q + 15q^{2} - 15q^{3} + 15q^{4} - q^{5} - 15q^{6} + 5q^{7} + 15q^{8} + 15q^{9} - q^{10} + 3q^{11} - 15q^{12} - 15q^{13} + 5q^{14} + q^{15} + 15q^{16} - 2q^{17} + 15q^{18} + 8q^{19} - q^{20} - 5q^{21} + 3q^{22} + 3q^{23} - 15q^{24} + 22q^{25} - 15q^{26} - 15q^{27} + 5q^{28} + 26q^{29} + q^{30} + 15q^{32} - 3q^{33} - 2q^{34} - 8q^{35} + 15q^{36} + 25q^{37} + 8q^{38} + 15q^{39} - q^{40} - q^{41} - 5q^{42} + 10q^{43} + 3q^{44} - q^{45} + 3q^{46} - 3q^{47} - 15q^{48} + 32q^{49} + 22q^{50} + 2q^{51} - 15q^{52} + 13q^{53} - 15q^{54} - 2q^{55} + 5q^{56} - 8q^{57} + 26q^{58} + 28q^{59} + q^{60} + 22q^{61} + 5q^{63} + 15q^{64} + q^{65} - 3q^{66} + 29q^{67} - 2q^{68} - 3q^{69} - 8q^{70} + 18q^{71} + 15q^{72} + 23q^{73} + 25q^{74} - 22q^{75} + 8q^{76} + 17q^{77} + 15q^{78} + 27q^{79} - q^{80} + 15q^{81} - q^{82} + 7q^{83} - 5q^{84} + 43q^{85} + 10q^{86} - 26q^{87} + 3q^{88} + 35q^{89} - q^{90} - 5q^{91} + 3q^{92} - 3q^{94} + 6q^{95} - 15q^{96} + 19q^{97} + 32q^{98} + 3q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −1.17201 −0.524137 −0.262069 0.965049i \(-0.584405\pi\)
−0.262069 + 0.965049i \(0.584405\pi\)
\(6\) −1.00000 −0.408248
\(7\) −4.40989 −1.66678 −0.833390 0.552685i \(-0.813603\pi\)
−0.833390 + 0.552685i \(0.813603\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.17201 −0.370621
\(11\) 0.445599 0.134353 0.0671766 0.997741i \(-0.478601\pi\)
0.0671766 + 0.997741i \(0.478601\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350
\(14\) −4.40989 −1.17859
\(15\) 1.17201 0.302611
\(16\) 1.00000 0.250000
\(17\) 6.53411 1.58475 0.792377 0.610031i \(-0.208843\pi\)
0.792377 + 0.610031i \(0.208843\pi\)
\(18\) 1.00000 0.235702
\(19\) −3.79076 −0.869659 −0.434830 0.900513i \(-0.643191\pi\)
−0.434830 + 0.900513i \(0.643191\pi\)
\(20\) −1.17201 −0.262069
\(21\) 4.40989 0.962316
\(22\) 0.445599 0.0950021
\(23\) −1.35290 −0.282100 −0.141050 0.990002i \(-0.545048\pi\)
−0.141050 + 0.990002i \(0.545048\pi\)
\(24\) −1.00000 −0.204124
\(25\) −3.62640 −0.725280
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) −4.40989 −0.833390
\(29\) −5.72200 −1.06255 −0.531275 0.847200i \(-0.678287\pi\)
−0.531275 + 0.847200i \(0.678287\pi\)
\(30\) 1.17201 0.213978
\(31\) −7.97242 −1.43189 −0.715945 0.698157i \(-0.754004\pi\)
−0.715945 + 0.698157i \(0.754004\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.445599 −0.0775689
\(34\) 6.53411 1.12059
\(35\) 5.16841 0.873621
\(36\) 1.00000 0.166667
\(37\) 6.80648 1.11898 0.559489 0.828838i \(-0.310997\pi\)
0.559489 + 0.828838i \(0.310997\pi\)
\(38\) −3.79076 −0.614942
\(39\) 1.00000 0.160128
\(40\) −1.17201 −0.185310
\(41\) 0.483328 0.0754832 0.0377416 0.999288i \(-0.487984\pi\)
0.0377416 + 0.999288i \(0.487984\pi\)
\(42\) 4.40989 0.680460
\(43\) −7.08156 −1.07993 −0.539964 0.841688i \(-0.681562\pi\)
−0.539964 + 0.841688i \(0.681562\pi\)
\(44\) 0.445599 0.0671766
\(45\) −1.17201 −0.174712
\(46\) −1.35290 −0.199475
\(47\) 3.11266 0.454028 0.227014 0.973892i \(-0.427104\pi\)
0.227014 + 0.973892i \(0.427104\pi\)
\(48\) −1.00000 −0.144338
\(49\) 12.4471 1.77816
\(50\) −3.62640 −0.512851
\(51\) −6.53411 −0.914959
\(52\) −1.00000 −0.138675
\(53\) −2.35869 −0.323991 −0.161995 0.986792i \(-0.551793\pi\)
−0.161995 + 0.986792i \(0.551793\pi\)
\(54\) −1.00000 −0.136083
\(55\) −0.522245 −0.0704195
\(56\) −4.40989 −0.589296
\(57\) 3.79076 0.502098
\(58\) −5.72200 −0.751336
\(59\) 10.8330 1.41034 0.705168 0.709040i \(-0.250872\pi\)
0.705168 + 0.709040i \(0.250872\pi\)
\(60\) 1.17201 0.151305
\(61\) −2.55140 −0.326674 −0.163337 0.986570i \(-0.552226\pi\)
−0.163337 + 0.986570i \(0.552226\pi\)
\(62\) −7.97242 −1.01250
\(63\) −4.40989 −0.555594
\(64\) 1.00000 0.125000
\(65\) 1.17201 0.145369
\(66\) −0.445599 −0.0548495
\(67\) −2.47808 −0.302745 −0.151373 0.988477i \(-0.548369\pi\)
−0.151373 + 0.988477i \(0.548369\pi\)
\(68\) 6.53411 0.792377
\(69\) 1.35290 0.162870
\(70\) 5.16841 0.617744
\(71\) 2.87156 0.340791 0.170395 0.985376i \(-0.445495\pi\)
0.170395 + 0.985376i \(0.445495\pi\)
\(72\) 1.00000 0.117851
\(73\) 11.7695 1.37751 0.688757 0.724993i \(-0.258157\pi\)
0.688757 + 0.724993i \(0.258157\pi\)
\(74\) 6.80648 0.791237
\(75\) 3.62640 0.418741
\(76\) −3.79076 −0.434830
\(77\) −1.96504 −0.223937
\(78\) 1.00000 0.113228
\(79\) −11.5317 −1.29741 −0.648706 0.761039i \(-0.724690\pi\)
−0.648706 + 0.761039i \(0.724690\pi\)
\(80\) −1.17201 −0.131034
\(81\) 1.00000 0.111111
\(82\) 0.483328 0.0533747
\(83\) −0.188229 −0.0206608 −0.0103304 0.999947i \(-0.503288\pi\)
−0.0103304 + 0.999947i \(0.503288\pi\)
\(84\) 4.40989 0.481158
\(85\) −7.65802 −0.830629
\(86\) −7.08156 −0.763624
\(87\) 5.72200 0.613463
\(88\) 0.445599 0.0475011
\(89\) 2.37544 0.251796 0.125898 0.992043i \(-0.459819\pi\)
0.125898 + 0.992043i \(0.459819\pi\)
\(90\) −1.17201 −0.123540
\(91\) 4.40989 0.462282
\(92\) −1.35290 −0.141050
\(93\) 7.97242 0.826702
\(94\) 3.11266 0.321046
\(95\) 4.44279 0.455821
\(96\) −1.00000 −0.102062
\(97\) −5.14559 −0.522455 −0.261228 0.965277i \(-0.584127\pi\)
−0.261228 + 0.965277i \(0.584127\pi\)
\(98\) 12.4471 1.25735
\(99\) 0.445599 0.0447844
\(100\) −3.62640 −0.362640
\(101\) −7.45461 −0.741761 −0.370881 0.928681i \(-0.620944\pi\)
−0.370881 + 0.928681i \(0.620944\pi\)
\(102\) −6.53411 −0.646973
\(103\) −1.00000 −0.0985329
\(104\) −1.00000 −0.0980581
\(105\) −5.16841 −0.504386
\(106\) −2.35869 −0.229096
\(107\) 8.79608 0.850349 0.425175 0.905111i \(-0.360213\pi\)
0.425175 + 0.905111i \(0.360213\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 0.173361 0.0166049 0.00830246 0.999966i \(-0.497357\pi\)
0.00830246 + 0.999966i \(0.497357\pi\)
\(110\) −0.522245 −0.0497941
\(111\) −6.80648 −0.646042
\(112\) −4.40989 −0.416695
\(113\) 19.8490 1.86724 0.933619 0.358266i \(-0.116632\pi\)
0.933619 + 0.358266i \(0.116632\pi\)
\(114\) 3.79076 0.355037
\(115\) 1.58561 0.147859
\(116\) −5.72200 −0.531275
\(117\) −1.00000 −0.0924500
\(118\) 10.8330 0.997258
\(119\) −28.8147 −2.64144
\(120\) 1.17201 0.106989
\(121\) −10.8014 −0.981949
\(122\) −2.55140 −0.230993
\(123\) −0.483328 −0.0435802
\(124\) −7.97242 −0.715945
\(125\) 10.1102 0.904283
\(126\) −4.40989 −0.392864
\(127\) −0.472255 −0.0419059 −0.0209529 0.999780i \(-0.506670\pi\)
−0.0209529 + 0.999780i \(0.506670\pi\)
\(128\) 1.00000 0.0883883
\(129\) 7.08156 0.623496
\(130\) 1.17201 0.102792
\(131\) 8.07447 0.705469 0.352735 0.935723i \(-0.385252\pi\)
0.352735 + 0.935723i \(0.385252\pi\)
\(132\) −0.445599 −0.0387844
\(133\) 16.7168 1.44953
\(134\) −2.47808 −0.214073
\(135\) 1.17201 0.100870
\(136\) 6.53411 0.560295
\(137\) 10.2707 0.877485 0.438742 0.898613i \(-0.355424\pi\)
0.438742 + 0.898613i \(0.355424\pi\)
\(138\) 1.35290 0.115167
\(139\) 2.46420 0.209010 0.104505 0.994524i \(-0.466674\pi\)
0.104505 + 0.994524i \(0.466674\pi\)
\(140\) 5.16841 0.436811
\(141\) −3.11266 −0.262133
\(142\) 2.87156 0.240976
\(143\) −0.445599 −0.0372629
\(144\) 1.00000 0.0833333
\(145\) 6.70622 0.556922
\(146\) 11.7695 0.974049
\(147\) −12.4471 −1.02662
\(148\) 6.80648 0.559489
\(149\) 13.2726 1.08733 0.543665 0.839302i \(-0.317036\pi\)
0.543665 + 0.839302i \(0.317036\pi\)
\(150\) 3.62640 0.296094
\(151\) −10.0014 −0.813899 −0.406950 0.913451i \(-0.633408\pi\)
−0.406950 + 0.913451i \(0.633408\pi\)
\(152\) −3.79076 −0.307471
\(153\) 6.53411 0.528252
\(154\) −1.96504 −0.158348
\(155\) 9.34373 0.750506
\(156\) 1.00000 0.0800641
\(157\) −17.1361 −1.36761 −0.683805 0.729665i \(-0.739676\pi\)
−0.683805 + 0.729665i \(0.739676\pi\)
\(158\) −11.5317 −0.917409
\(159\) 2.35869 0.187056
\(160\) −1.17201 −0.0926552
\(161\) 5.96615 0.470199
\(162\) 1.00000 0.0785674
\(163\) 4.56114 0.357256 0.178628 0.983917i \(-0.442834\pi\)
0.178628 + 0.983917i \(0.442834\pi\)
\(164\) 0.483328 0.0377416
\(165\) 0.522245 0.0406567
\(166\) −0.188229 −0.0146094
\(167\) −14.7439 −1.14092 −0.570458 0.821327i \(-0.693234\pi\)
−0.570458 + 0.821327i \(0.693234\pi\)
\(168\) 4.40989 0.340230
\(169\) 1.00000 0.0769231
\(170\) −7.65802 −0.587343
\(171\) −3.79076 −0.289886
\(172\) −7.08156 −0.539964
\(173\) −2.88664 −0.219467 −0.109733 0.993961i \(-0.535000\pi\)
−0.109733 + 0.993961i \(0.535000\pi\)
\(174\) 5.72200 0.433784
\(175\) 15.9920 1.20888
\(176\) 0.445599 0.0335883
\(177\) −10.8330 −0.814258
\(178\) 2.37544 0.178047
\(179\) 16.6474 1.24429 0.622144 0.782903i \(-0.286262\pi\)
0.622144 + 0.782903i \(0.286262\pi\)
\(180\) −1.17201 −0.0873562
\(181\) 7.52363 0.559227 0.279614 0.960113i \(-0.409794\pi\)
0.279614 + 0.960113i \(0.409794\pi\)
\(182\) 4.40989 0.326883
\(183\) 2.55140 0.188605
\(184\) −1.35290 −0.0997374
\(185\) −7.97723 −0.586498
\(186\) 7.97242 0.584566
\(187\) 2.91160 0.212917
\(188\) 3.11266 0.227014
\(189\) 4.40989 0.320772
\(190\) 4.44279 0.322314
\(191\) 6.41617 0.464258 0.232129 0.972685i \(-0.425431\pi\)
0.232129 + 0.972685i \(0.425431\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 18.5408 1.33460 0.667300 0.744789i \(-0.267450\pi\)
0.667300 + 0.744789i \(0.267450\pi\)
\(194\) −5.14559 −0.369432
\(195\) −1.17201 −0.0839291
\(196\) 12.4471 0.889079
\(197\) 3.43025 0.244396 0.122198 0.992506i \(-0.461006\pi\)
0.122198 + 0.992506i \(0.461006\pi\)
\(198\) 0.445599 0.0316674
\(199\) −20.4116 −1.44694 −0.723470 0.690356i \(-0.757454\pi\)
−0.723470 + 0.690356i \(0.757454\pi\)
\(200\) −3.62640 −0.256425
\(201\) 2.47808 0.174790
\(202\) −7.45461 −0.524504
\(203\) 25.2334 1.77104
\(204\) −6.53411 −0.457479
\(205\) −0.566464 −0.0395635
\(206\) −1.00000 −0.0696733
\(207\) −1.35290 −0.0940333
\(208\) −1.00000 −0.0693375
\(209\) −1.68916 −0.116842
\(210\) −5.16841 −0.356654
\(211\) 10.3909 0.715339 0.357669 0.933848i \(-0.383571\pi\)
0.357669 + 0.933848i \(0.383571\pi\)
\(212\) −2.35869 −0.161995
\(213\) −2.87156 −0.196756
\(214\) 8.79608 0.601288
\(215\) 8.29963 0.566030
\(216\) −1.00000 −0.0680414
\(217\) 35.1575 2.38665
\(218\) 0.173361 0.0117415
\(219\) −11.7695 −0.795308
\(220\) −0.522245 −0.0352098
\(221\) −6.53411 −0.439532
\(222\) −6.80648 −0.456821
\(223\) −3.71253 −0.248609 −0.124305 0.992244i \(-0.539670\pi\)
−0.124305 + 0.992244i \(0.539670\pi\)
\(224\) −4.40989 −0.294648
\(225\) −3.62640 −0.241760
\(226\) 19.8490 1.32034
\(227\) −11.8872 −0.788980 −0.394490 0.918900i \(-0.629079\pi\)
−0.394490 + 0.918900i \(0.629079\pi\)
\(228\) 3.79076 0.251049
\(229\) 14.5836 0.963713 0.481857 0.876250i \(-0.339963\pi\)
0.481857 + 0.876250i \(0.339963\pi\)
\(230\) 1.58561 0.104552
\(231\) 1.96504 0.129290
\(232\) −5.72200 −0.375668
\(233\) 4.17408 0.273453 0.136726 0.990609i \(-0.456342\pi\)
0.136726 + 0.990609i \(0.456342\pi\)
\(234\) −1.00000 −0.0653720
\(235\) −3.64805 −0.237973
\(236\) 10.8330 0.705168
\(237\) 11.5317 0.749061
\(238\) −28.8147 −1.86778
\(239\) −0.656747 −0.0424814 −0.0212407 0.999774i \(-0.506762\pi\)
−0.0212407 + 0.999774i \(0.506762\pi\)
\(240\) 1.17201 0.0756527
\(241\) 17.0766 1.10000 0.550000 0.835164i \(-0.314628\pi\)
0.550000 + 0.835164i \(0.314628\pi\)
\(242\) −10.8014 −0.694343
\(243\) −1.00000 −0.0641500
\(244\) −2.55140 −0.163337
\(245\) −14.5881 −0.931998
\(246\) −0.483328 −0.0308159
\(247\) 3.79076 0.241200
\(248\) −7.97242 −0.506249
\(249\) 0.188229 0.0119285
\(250\) 10.1102 0.639425
\(251\) 24.2454 1.53036 0.765178 0.643819i \(-0.222651\pi\)
0.765178 + 0.643819i \(0.222651\pi\)
\(252\) −4.40989 −0.277797
\(253\) −0.602853 −0.0379010
\(254\) −0.472255 −0.0296319
\(255\) 7.65802 0.479564
\(256\) 1.00000 0.0625000
\(257\) −12.8223 −0.799832 −0.399916 0.916552i \(-0.630961\pi\)
−0.399916 + 0.916552i \(0.630961\pi\)
\(258\) 7.08156 0.440878
\(259\) −30.0158 −1.86509
\(260\) 1.17201 0.0726847
\(261\) −5.72200 −0.354183
\(262\) 8.07447 0.498842
\(263\) 29.4695 1.81717 0.908584 0.417703i \(-0.137165\pi\)
0.908584 + 0.417703i \(0.137165\pi\)
\(264\) −0.445599 −0.0274247
\(265\) 2.76440 0.169816
\(266\) 16.7168 1.02497
\(267\) −2.37544 −0.145374
\(268\) −2.47808 −0.151373
\(269\) 22.9635 1.40011 0.700054 0.714090i \(-0.253159\pi\)
0.700054 + 0.714090i \(0.253159\pi\)
\(270\) 1.17201 0.0713260
\(271\) 3.57490 0.217159 0.108580 0.994088i \(-0.465370\pi\)
0.108580 + 0.994088i \(0.465370\pi\)
\(272\) 6.53411 0.396189
\(273\) −4.40989 −0.266898
\(274\) 10.2707 0.620475
\(275\) −1.61592 −0.0974438
\(276\) 1.35290 0.0814352
\(277\) 11.0480 0.663807 0.331904 0.943313i \(-0.392309\pi\)
0.331904 + 0.943313i \(0.392309\pi\)
\(278\) 2.46420 0.147793
\(279\) −7.97242 −0.477296
\(280\) 5.16841 0.308872
\(281\) 18.7003 1.11557 0.557783 0.829987i \(-0.311652\pi\)
0.557783 + 0.829987i \(0.311652\pi\)
\(282\) −3.11266 −0.185356
\(283\) 29.5791 1.75829 0.879147 0.476550i \(-0.158113\pi\)
0.879147 + 0.476550i \(0.158113\pi\)
\(284\) 2.87156 0.170395
\(285\) −4.44279 −0.263168
\(286\) −0.445599 −0.0263488
\(287\) −2.13142 −0.125814
\(288\) 1.00000 0.0589256
\(289\) 25.6946 1.51145
\(290\) 6.70622 0.393803
\(291\) 5.14559 0.301640
\(292\) 11.7695 0.688757
\(293\) 3.43588 0.200726 0.100363 0.994951i \(-0.468000\pi\)
0.100363 + 0.994951i \(0.468000\pi\)
\(294\) −12.4471 −0.725930
\(295\) −12.6963 −0.739209
\(296\) 6.80648 0.395619
\(297\) −0.445599 −0.0258563
\(298\) 13.2726 0.768859
\(299\) 1.35290 0.0782404
\(300\) 3.62640 0.209370
\(301\) 31.2289 1.80000
\(302\) −10.0014 −0.575514
\(303\) 7.45461 0.428256
\(304\) −3.79076 −0.217415
\(305\) 2.99026 0.171222
\(306\) 6.53411 0.373530
\(307\) 19.4875 1.11221 0.556106 0.831111i \(-0.312295\pi\)
0.556106 + 0.831111i \(0.312295\pi\)
\(308\) −1.96504 −0.111969
\(309\) 1.00000 0.0568880
\(310\) 9.34373 0.530688
\(311\) 33.4413 1.89628 0.948140 0.317853i \(-0.102962\pi\)
0.948140 + 0.317853i \(0.102962\pi\)
\(312\) 1.00000 0.0566139
\(313\) 13.3906 0.756881 0.378440 0.925626i \(-0.376460\pi\)
0.378440 + 0.925626i \(0.376460\pi\)
\(314\) −17.1361 −0.967046
\(315\) 5.16841 0.291207
\(316\) −11.5317 −0.648706
\(317\) 17.0064 0.955177 0.477589 0.878584i \(-0.341511\pi\)
0.477589 + 0.878584i \(0.341511\pi\)
\(318\) 2.35869 0.132269
\(319\) −2.54972 −0.142757
\(320\) −1.17201 −0.0655171
\(321\) −8.79608 −0.490949
\(322\) 5.96615 0.332481
\(323\) −24.7692 −1.37820
\(324\) 1.00000 0.0555556
\(325\) 3.62640 0.201157
\(326\) 4.56114 0.252618
\(327\) −0.173361 −0.00958686
\(328\) 0.483328 0.0266873
\(329\) −13.7265 −0.756765
\(330\) 0.522245 0.0287487
\(331\) −0.178182 −0.00979379 −0.00489689 0.999988i \(-0.501559\pi\)
−0.00489689 + 0.999988i \(0.501559\pi\)
\(332\) −0.188229 −0.0103304
\(333\) 6.80648 0.372993
\(334\) −14.7439 −0.806750
\(335\) 2.90432 0.158680
\(336\) 4.40989 0.240579
\(337\) 8.42074 0.458707 0.229353 0.973343i \(-0.426339\pi\)
0.229353 + 0.973343i \(0.426339\pi\)
\(338\) 1.00000 0.0543928
\(339\) −19.8490 −1.07805
\(340\) −7.65802 −0.415314
\(341\) −3.55251 −0.192379
\(342\) −3.79076 −0.204981
\(343\) −24.0211 −1.29702
\(344\) −7.08156 −0.381812
\(345\) −1.58561 −0.0853664
\(346\) −2.88664 −0.155186
\(347\) −32.1165 −1.72410 −0.862051 0.506822i \(-0.830820\pi\)
−0.862051 + 0.506822i \(0.830820\pi\)
\(348\) 5.72200 0.306732
\(349\) 11.1661 0.597707 0.298853 0.954299i \(-0.403396\pi\)
0.298853 + 0.954299i \(0.403396\pi\)
\(350\) 15.9920 0.854810
\(351\) 1.00000 0.0533761
\(352\) 0.445599 0.0237505
\(353\) −17.2853 −0.920003 −0.460001 0.887918i \(-0.652151\pi\)
−0.460001 + 0.887918i \(0.652151\pi\)
\(354\) −10.8330 −0.575767
\(355\) −3.36548 −0.178621
\(356\) 2.37544 0.125898
\(357\) 28.8147 1.52504
\(358\) 16.6474 0.879844
\(359\) −14.9764 −0.790426 −0.395213 0.918590i \(-0.629329\pi\)
−0.395213 + 0.918590i \(0.629329\pi\)
\(360\) −1.17201 −0.0617701
\(361\) −4.63016 −0.243692
\(362\) 7.52363 0.395433
\(363\) 10.8014 0.566929
\(364\) 4.40989 0.231141
\(365\) −13.7939 −0.722006
\(366\) 2.55140 0.133364
\(367\) −13.1108 −0.684376 −0.342188 0.939631i \(-0.611168\pi\)
−0.342188 + 0.939631i \(0.611168\pi\)
\(368\) −1.35290 −0.0705250
\(369\) 0.483328 0.0251611
\(370\) −7.97723 −0.414717
\(371\) 10.4015 0.540021
\(372\) 7.97242 0.413351
\(373\) 3.21477 0.166454 0.0832271 0.996531i \(-0.473477\pi\)
0.0832271 + 0.996531i \(0.473477\pi\)
\(374\) 2.91160 0.150555
\(375\) −10.1102 −0.522088
\(376\) 3.11266 0.160523
\(377\) 5.72200 0.294698
\(378\) 4.40989 0.226820
\(379\) 24.4364 1.25521 0.627607 0.778530i \(-0.284035\pi\)
0.627607 + 0.778530i \(0.284035\pi\)
\(380\) 4.44279 0.227910
\(381\) 0.472255 0.0241944
\(382\) 6.41617 0.328280
\(383\) 18.0568 0.922659 0.461330 0.887229i \(-0.347373\pi\)
0.461330 + 0.887229i \(0.347373\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 2.30304 0.117374
\(386\) 18.5408 0.943704
\(387\) −7.08156 −0.359976
\(388\) −5.14559 −0.261228
\(389\) −1.98143 −0.100462 −0.0502312 0.998738i \(-0.515996\pi\)
−0.0502312 + 0.998738i \(0.515996\pi\)
\(390\) −1.17201 −0.0593468
\(391\) −8.84002 −0.447059
\(392\) 12.4471 0.628674
\(393\) −8.07447 −0.407303
\(394\) 3.43025 0.172814
\(395\) 13.5152 0.680022
\(396\) 0.445599 0.0223922
\(397\) −22.7468 −1.14163 −0.570813 0.821080i \(-0.693372\pi\)
−0.570813 + 0.821080i \(0.693372\pi\)
\(398\) −20.4116 −1.02314
\(399\) −16.7168 −0.836887
\(400\) −3.62640 −0.181320
\(401\) −22.0727 −1.10226 −0.551130 0.834419i \(-0.685803\pi\)
−0.551130 + 0.834419i \(0.685803\pi\)
\(402\) 2.47808 0.123595
\(403\) 7.97242 0.397135
\(404\) −7.45461 −0.370881
\(405\) −1.17201 −0.0582374
\(406\) 25.2334 1.25231
\(407\) 3.03296 0.150338
\(408\) −6.53411 −0.323487
\(409\) 8.78100 0.434192 0.217096 0.976150i \(-0.430341\pi\)
0.217096 + 0.976150i \(0.430341\pi\)
\(410\) −0.566464 −0.0279756
\(411\) −10.2707 −0.506616
\(412\) −1.00000 −0.0492665
\(413\) −47.7723 −2.35072
\(414\) −1.35290 −0.0664916
\(415\) 0.220605 0.0108291
\(416\) −1.00000 −0.0490290
\(417\) −2.46420 −0.120672
\(418\) −1.68916 −0.0826195
\(419\) 12.0635 0.589343 0.294671 0.955599i \(-0.404790\pi\)
0.294671 + 0.955599i \(0.404790\pi\)
\(420\) −5.16841 −0.252193
\(421\) 1.57768 0.0768914 0.0384457 0.999261i \(-0.487759\pi\)
0.0384457 + 0.999261i \(0.487759\pi\)
\(422\) 10.3909 0.505821
\(423\) 3.11266 0.151343
\(424\) −2.35869 −0.114548
\(425\) −23.6953 −1.14939
\(426\) −2.87156 −0.139127
\(427\) 11.2514 0.544493
\(428\) 8.79608 0.425175
\(429\) 0.445599 0.0215137
\(430\) 8.29963 0.400243
\(431\) 25.2451 1.21601 0.608007 0.793931i \(-0.291969\pi\)
0.608007 + 0.793931i \(0.291969\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −17.2197 −0.827524 −0.413762 0.910385i \(-0.635785\pi\)
−0.413762 + 0.910385i \(0.635785\pi\)
\(434\) 35.1575 1.68761
\(435\) −6.70622 −0.321539
\(436\) 0.173361 0.00830246
\(437\) 5.12853 0.245331
\(438\) −11.7695 −0.562367
\(439\) −25.7156 −1.22734 −0.613670 0.789562i \(-0.710308\pi\)
−0.613670 + 0.789562i \(0.710308\pi\)
\(440\) −0.522245 −0.0248971
\(441\) 12.4471 0.592719
\(442\) −6.53411 −0.310796
\(443\) −21.4498 −1.01911 −0.509556 0.860438i \(-0.670190\pi\)
−0.509556 + 0.860438i \(0.670190\pi\)
\(444\) −6.80648 −0.323021
\(445\) −2.78403 −0.131976
\(446\) −3.71253 −0.175793
\(447\) −13.2726 −0.627771
\(448\) −4.40989 −0.208348
\(449\) −9.64925 −0.455376 −0.227688 0.973734i \(-0.573117\pi\)
−0.227688 + 0.973734i \(0.573117\pi\)
\(450\) −3.62640 −0.170950
\(451\) 0.215371 0.0101414
\(452\) 19.8490 0.933619
\(453\) 10.0014 0.469905
\(454\) −11.8872 −0.557893
\(455\) −5.16841 −0.242299
\(456\) 3.79076 0.177518
\(457\) −21.4975 −1.00561 −0.502805 0.864400i \(-0.667699\pi\)
−0.502805 + 0.864400i \(0.667699\pi\)
\(458\) 14.5836 0.681448
\(459\) −6.53411 −0.304986
\(460\) 1.58561 0.0739295
\(461\) 2.06933 0.0963783 0.0481891 0.998838i \(-0.484655\pi\)
0.0481891 + 0.998838i \(0.484655\pi\)
\(462\) 1.96504 0.0914221
\(463\) −1.41092 −0.0655709 −0.0327855 0.999462i \(-0.510438\pi\)
−0.0327855 + 0.999462i \(0.510438\pi\)
\(464\) −5.72200 −0.265637
\(465\) −9.34373 −0.433305
\(466\) 4.17408 0.193360
\(467\) −28.7723 −1.33142 −0.665711 0.746210i \(-0.731872\pi\)
−0.665711 + 0.746210i \(0.731872\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 10.9280 0.504610
\(470\) −3.64805 −0.168272
\(471\) 17.1361 0.789590
\(472\) 10.8330 0.498629
\(473\) −3.15554 −0.145092
\(474\) 11.5317 0.529666
\(475\) 13.7468 0.630747
\(476\) −28.8147 −1.32072
\(477\) −2.35869 −0.107997
\(478\) −0.656747 −0.0300389
\(479\) 6.49308 0.296676 0.148338 0.988937i \(-0.452608\pi\)
0.148338 + 0.988937i \(0.452608\pi\)
\(480\) 1.17201 0.0534945
\(481\) −6.80648 −0.310349
\(482\) 17.0766 0.777818
\(483\) −5.96615 −0.271469
\(484\) −10.8014 −0.490975
\(485\) 6.03066 0.273838
\(486\) −1.00000 −0.0453609
\(487\) 31.9604 1.44826 0.724132 0.689661i \(-0.242241\pi\)
0.724132 + 0.689661i \(0.242241\pi\)
\(488\) −2.55140 −0.115497
\(489\) −4.56114 −0.206262
\(490\) −14.5881 −0.659022
\(491\) 14.3666 0.648357 0.324179 0.945996i \(-0.394912\pi\)
0.324179 + 0.945996i \(0.394912\pi\)
\(492\) −0.483328 −0.0217901
\(493\) −37.3882 −1.68388
\(494\) 3.79076 0.170554
\(495\) −0.522245 −0.0234732
\(496\) −7.97242 −0.357972
\(497\) −12.6632 −0.568024
\(498\) 0.188229 0.00843472
\(499\) 6.86384 0.307268 0.153634 0.988128i \(-0.450902\pi\)
0.153634 + 0.988128i \(0.450902\pi\)
\(500\) 10.1102 0.452142
\(501\) 14.7439 0.658709
\(502\) 24.2454 1.08212
\(503\) −9.95300 −0.443782 −0.221891 0.975071i \(-0.571223\pi\)
−0.221891 + 0.975071i \(0.571223\pi\)
\(504\) −4.40989 −0.196432
\(505\) 8.73685 0.388785
\(506\) −0.602853 −0.0268001
\(507\) −1.00000 −0.0444116
\(508\) −0.472255 −0.0209529
\(509\) −9.36790 −0.415225 −0.207612 0.978211i \(-0.566569\pi\)
−0.207612 + 0.978211i \(0.566569\pi\)
\(510\) 7.65802 0.339103
\(511\) −51.9021 −2.29601
\(512\) 1.00000 0.0441942
\(513\) 3.79076 0.167366
\(514\) −12.8223 −0.565567
\(515\) 1.17201 0.0516448
\(516\) 7.08156 0.311748
\(517\) 1.38700 0.0610001
\(518\) −30.0158 −1.31882
\(519\) 2.88664 0.126709
\(520\) 1.17201 0.0513959
\(521\) −13.4274 −0.588266 −0.294133 0.955765i \(-0.595031\pi\)
−0.294133 + 0.955765i \(0.595031\pi\)
\(522\) −5.72200 −0.250445
\(523\) −33.8560 −1.48042 −0.740210 0.672376i \(-0.765274\pi\)
−0.740210 + 0.672376i \(0.765274\pi\)
\(524\) 8.07447 0.352735
\(525\) −15.9920 −0.697949
\(526\) 29.4695 1.28493
\(527\) −52.0927 −2.26919
\(528\) −0.445599 −0.0193922
\(529\) −21.1697 −0.920420
\(530\) 2.76440 0.120078
\(531\) 10.8330 0.470112
\(532\) 16.7168 0.724766
\(533\) −0.483328 −0.0209353
\(534\) −2.37544 −0.102795
\(535\) −10.3091 −0.445700
\(536\) −2.47808 −0.107037
\(537\) −16.6474 −0.718390
\(538\) 22.9635 0.990026
\(539\) 5.54642 0.238901
\(540\) 1.17201 0.0504351
\(541\) 36.7350 1.57936 0.789680 0.613518i \(-0.210246\pi\)
0.789680 + 0.613518i \(0.210246\pi\)
\(542\) 3.57490 0.153555
\(543\) −7.52363 −0.322870
\(544\) 6.53411 0.280148
\(545\) −0.203180 −0.00870326
\(546\) −4.40989 −0.188726
\(547\) −27.3146 −1.16789 −0.583944 0.811794i \(-0.698491\pi\)
−0.583944 + 0.811794i \(0.698491\pi\)
\(548\) 10.2707 0.438742
\(549\) −2.55140 −0.108891
\(550\) −1.61592 −0.0689032
\(551\) 21.6907 0.924056
\(552\) 1.35290 0.0575834
\(553\) 50.8533 2.16250
\(554\) 11.0480 0.469383
\(555\) 7.97723 0.338615
\(556\) 2.46420 0.104505
\(557\) −1.15626 −0.0489925 −0.0244962 0.999700i \(-0.507798\pi\)
−0.0244962 + 0.999700i \(0.507798\pi\)
\(558\) −7.97242 −0.337500
\(559\) 7.08156 0.299518
\(560\) 5.16841 0.218405
\(561\) −2.91160 −0.122928
\(562\) 18.7003 0.788825
\(563\) −13.1468 −0.554073 −0.277036 0.960859i \(-0.589352\pi\)
−0.277036 + 0.960859i \(0.589352\pi\)
\(564\) −3.11266 −0.131067
\(565\) −23.2632 −0.978689
\(566\) 29.5791 1.24330
\(567\) −4.40989 −0.185198
\(568\) 2.87156 0.120488
\(569\) 25.2632 1.05909 0.529544 0.848283i \(-0.322363\pi\)
0.529544 + 0.848283i \(0.322363\pi\)
\(570\) −4.44279 −0.186088
\(571\) 37.0533 1.55063 0.775317 0.631572i \(-0.217590\pi\)
0.775317 + 0.631572i \(0.217590\pi\)
\(572\) −0.445599 −0.0186314
\(573\) −6.41617 −0.268039
\(574\) −2.13142 −0.0889639
\(575\) 4.90617 0.204601
\(576\) 1.00000 0.0416667
\(577\) 17.6715 0.735674 0.367837 0.929890i \(-0.380098\pi\)
0.367837 + 0.929890i \(0.380098\pi\)
\(578\) 25.6946 1.06875
\(579\) −18.5408 −0.770531
\(580\) 6.70622 0.278461
\(581\) 0.830067 0.0344370
\(582\) 5.14559 0.213291
\(583\) −1.05103 −0.0435292
\(584\) 11.7695 0.487024
\(585\) 1.17201 0.0484565
\(586\) 3.43588 0.141935
\(587\) −32.9697 −1.36080 −0.680402 0.732839i \(-0.738195\pi\)
−0.680402 + 0.732839i \(0.738195\pi\)
\(588\) −12.4471 −0.513310
\(589\) 30.2215 1.24526
\(590\) −12.6963 −0.522700
\(591\) −3.43025 −0.141102
\(592\) 6.80648 0.279745
\(593\) −6.45229 −0.264964 −0.132482 0.991185i \(-0.542295\pi\)
−0.132482 + 0.991185i \(0.542295\pi\)
\(594\) −0.445599 −0.0182832
\(595\) 33.7710 1.38448
\(596\) 13.2726 0.543665
\(597\) 20.4116 0.835391
\(598\) 1.35290 0.0553243
\(599\) −41.9936 −1.71581 −0.857905 0.513808i \(-0.828234\pi\)
−0.857905 + 0.513808i \(0.828234\pi\)
\(600\) 3.62640 0.148047
\(601\) 4.32233 0.176311 0.0881557 0.996107i \(-0.471903\pi\)
0.0881557 + 0.996107i \(0.471903\pi\)
\(602\) 31.2289 1.27279
\(603\) −2.47808 −0.100915
\(604\) −10.0014 −0.406950
\(605\) 12.6594 0.514676
\(606\) 7.45461 0.302823
\(607\) 13.5384 0.549505 0.274753 0.961515i \(-0.411404\pi\)
0.274753 + 0.961515i \(0.411404\pi\)
\(608\) −3.79076 −0.153736
\(609\) −25.2334 −1.02251
\(610\) 2.99026 0.121072
\(611\) −3.11266 −0.125925
\(612\) 6.53411 0.264126
\(613\) 2.56880 0.103753 0.0518763 0.998654i \(-0.483480\pi\)
0.0518763 + 0.998654i \(0.483480\pi\)
\(614\) 19.4875 0.786452
\(615\) 0.566464 0.0228420
\(616\) −1.96504 −0.0791738
\(617\) −7.44553 −0.299746 −0.149873 0.988705i \(-0.547886\pi\)
−0.149873 + 0.988705i \(0.547886\pi\)
\(618\) 1.00000 0.0402259
\(619\) 17.2836 0.694688 0.347344 0.937738i \(-0.387084\pi\)
0.347344 + 0.937738i \(0.387084\pi\)
\(620\) 9.34373 0.375253
\(621\) 1.35290 0.0542901
\(622\) 33.4413 1.34087
\(623\) −10.4754 −0.419688
\(624\) 1.00000 0.0400320
\(625\) 6.28280 0.251312
\(626\) 13.3906 0.535196
\(627\) 1.68916 0.0674585
\(628\) −17.1361 −0.683805
\(629\) 44.4743 1.77331
\(630\) 5.16841 0.205915
\(631\) −11.1178 −0.442593 −0.221297 0.975207i \(-0.571029\pi\)
−0.221297 + 0.975207i \(0.571029\pi\)
\(632\) −11.5317 −0.458705
\(633\) −10.3909 −0.413001
\(634\) 17.0064 0.675412
\(635\) 0.553486 0.0219644
\(636\) 2.35869 0.0935281
\(637\) −12.4471 −0.493172
\(638\) −2.54972 −0.100944
\(639\) 2.87156 0.113597
\(640\) −1.17201 −0.0463276
\(641\) 3.74495 0.147917 0.0739584 0.997261i \(-0.476437\pi\)
0.0739584 + 0.997261i \(0.476437\pi\)
\(642\) −8.79608 −0.347154
\(643\) 29.7447 1.17302 0.586508 0.809944i \(-0.300502\pi\)
0.586508 + 0.809944i \(0.300502\pi\)
\(644\) 5.96615 0.235099
\(645\) −8.29963 −0.326797
\(646\) −24.7692 −0.974532
\(647\) 8.05132 0.316530 0.158265 0.987397i \(-0.449410\pi\)
0.158265 + 0.987397i \(0.449410\pi\)
\(648\) 1.00000 0.0392837
\(649\) 4.82718 0.189483
\(650\) 3.62640 0.142239
\(651\) −35.1575 −1.37793
\(652\) 4.56114 0.178628
\(653\) 3.25098 0.127221 0.0636103 0.997975i \(-0.479739\pi\)
0.0636103 + 0.997975i \(0.479739\pi\)
\(654\) −0.173361 −0.00677893
\(655\) −9.46332 −0.369763
\(656\) 0.483328 0.0188708
\(657\) 11.7695 0.459171
\(658\) −13.7265 −0.535113
\(659\) −1.71860 −0.0669471 −0.0334735 0.999440i \(-0.510657\pi\)
−0.0334735 + 0.999440i \(0.510657\pi\)
\(660\) 0.522245 0.0203284
\(661\) −26.0578 −1.01353 −0.506765 0.862084i \(-0.669159\pi\)
−0.506765 + 0.862084i \(0.669159\pi\)
\(662\) −0.178182 −0.00692525
\(663\) 6.53411 0.253764
\(664\) −0.188229 −0.00730469
\(665\) −19.5922 −0.759753
\(666\) 6.80648 0.263746
\(667\) 7.74132 0.299745
\(668\) −14.7439 −0.570458
\(669\) 3.71253 0.143535
\(670\) 2.90432 0.112204
\(671\) −1.13690 −0.0438897
\(672\) 4.40989 0.170115
\(673\) 22.1388 0.853390 0.426695 0.904396i \(-0.359678\pi\)
0.426695 + 0.904396i \(0.359678\pi\)
\(674\) 8.42074 0.324355
\(675\) 3.62640 0.139580
\(676\) 1.00000 0.0384615
\(677\) 17.4143 0.669287 0.334643 0.942345i \(-0.391384\pi\)
0.334643 + 0.942345i \(0.391384\pi\)
\(678\) −19.8490 −0.762297
\(679\) 22.6915 0.870818
\(680\) −7.65802 −0.293672
\(681\) 11.8872 0.455518
\(682\) −3.55251 −0.136033
\(683\) −29.1800 −1.11654 −0.558270 0.829659i \(-0.688535\pi\)
−0.558270 + 0.829659i \(0.688535\pi\)
\(684\) −3.79076 −0.144943
\(685\) −12.0373 −0.459922
\(686\) −24.0211 −0.917130
\(687\) −14.5836 −0.556400
\(688\) −7.08156 −0.269982
\(689\) 2.35869 0.0898589
\(690\) −1.58561 −0.0603632
\(691\) −20.3641 −0.774687 −0.387344 0.921935i \(-0.626607\pi\)
−0.387344 + 0.921935i \(0.626607\pi\)
\(692\) −2.88664 −0.109733
\(693\) −1.96504 −0.0746458
\(694\) −32.1165 −1.21912
\(695\) −2.88805 −0.109550
\(696\) 5.72200 0.216892
\(697\) 3.15812 0.119622
\(698\) 11.1661 0.422643
\(699\) −4.17408 −0.157878
\(700\) 15.9920 0.604442
\(701\) −32.9142 −1.24315 −0.621577 0.783353i \(-0.713508\pi\)
−0.621577 + 0.783353i \(0.713508\pi\)
\(702\) 1.00000 0.0377426
\(703\) −25.8017 −0.973130
\(704\) 0.445599 0.0167942
\(705\) 3.64805 0.137394
\(706\) −17.2853 −0.650540
\(707\) 32.8740 1.23635
\(708\) −10.8330 −0.407129
\(709\) 13.8759 0.521121 0.260561 0.965458i \(-0.416093\pi\)
0.260561 + 0.965458i \(0.416093\pi\)
\(710\) −3.36548 −0.126304
\(711\) −11.5317 −0.432471
\(712\) 2.37544 0.0890233
\(713\) 10.7859 0.403936
\(714\) 28.8147 1.07836
\(715\) 0.522245 0.0195309
\(716\) 16.6474 0.622144
\(717\) 0.656747 0.0245267
\(718\) −14.9764 −0.558915
\(719\) −11.5182 −0.429557 −0.214778 0.976663i \(-0.568903\pi\)
−0.214778 + 0.976663i \(0.568903\pi\)
\(720\) −1.17201 −0.0436781
\(721\) 4.40989 0.164233
\(722\) −4.63016 −0.172317
\(723\) −17.0766 −0.635086
\(724\) 7.52363 0.279614
\(725\) 20.7503 0.770646
\(726\) 10.8014 0.400879
\(727\) 27.2771 1.01165 0.505827 0.862635i \(-0.331188\pi\)
0.505827 + 0.862635i \(0.331188\pi\)
\(728\) 4.40989 0.163441
\(729\) 1.00000 0.0370370
\(730\) −13.7939 −0.510535
\(731\) −46.2717 −1.71142
\(732\) 2.55140 0.0943025
\(733\) −23.4699 −0.866881 −0.433441 0.901182i \(-0.642701\pi\)
−0.433441 + 0.901182i \(0.642701\pi\)
\(734\) −13.1108 −0.483927
\(735\) 14.5881 0.538089
\(736\) −1.35290 −0.0498687
\(737\) −1.10423 −0.0406748
\(738\) 0.483328 0.0177916
\(739\) −6.93906 −0.255257 −0.127629 0.991822i \(-0.540737\pi\)
−0.127629 + 0.991822i \(0.540737\pi\)
\(740\) −7.97723 −0.293249
\(741\) −3.79076 −0.139257
\(742\) 10.4015 0.381853
\(743\) −13.7515 −0.504492 −0.252246 0.967663i \(-0.581169\pi\)
−0.252246 + 0.967663i \(0.581169\pi\)
\(744\) 7.97242 0.292283
\(745\) −15.5555 −0.569910
\(746\) 3.21477 0.117701
\(747\) −0.188229 −0.00688692
\(748\) 2.91160 0.106458
\(749\) −38.7897 −1.41735
\(750\) −10.1102 −0.369172
\(751\) 3.48376 0.127124 0.0635622 0.997978i \(-0.479754\pi\)
0.0635622 + 0.997978i \(0.479754\pi\)
\(752\) 3.11266 0.113507
\(753\) −24.2454 −0.883551
\(754\) 5.72200 0.208383
\(755\) 11.7217 0.426595
\(756\) 4.40989 0.160386
\(757\) −9.49162 −0.344979 −0.172489 0.985011i \(-0.555181\pi\)
−0.172489 + 0.985011i \(0.555181\pi\)
\(758\) 24.4364 0.887570
\(759\) 0.602853 0.0218822
\(760\) 4.44279 0.161157
\(761\) 2.52052 0.0913688 0.0456844 0.998956i \(-0.485453\pi\)
0.0456844 + 0.998956i \(0.485453\pi\)
\(762\) 0.472255 0.0171080
\(763\) −0.764500 −0.0276768
\(764\) 6.41617 0.232129
\(765\) −7.65802 −0.276876
\(766\) 18.0568 0.652419
\(767\) −10.8330 −0.391157
\(768\) −1.00000 −0.0360844
\(769\) −24.5967 −0.886981 −0.443490 0.896279i \(-0.646260\pi\)
−0.443490 + 0.896279i \(0.646260\pi\)
\(770\) 2.30304 0.0829959
\(771\) 12.8223 0.461783
\(772\) 18.5408 0.667300
\(773\) 22.5085 0.809573 0.404787 0.914411i \(-0.367346\pi\)
0.404787 + 0.914411i \(0.367346\pi\)
\(774\) −7.08156 −0.254541
\(775\) 28.9112 1.03852
\(776\) −5.14559 −0.184716
\(777\) 30.0158 1.07681
\(778\) −1.98143 −0.0710376
\(779\) −1.83218 −0.0656447
\(780\) −1.17201 −0.0419645
\(781\) 1.27956 0.0457864
\(782\) −8.84002 −0.316119
\(783\) 5.72200 0.204488
\(784\) 12.4471 0.444539
\(785\) 20.0836 0.716815
\(786\) −8.07447 −0.288007
\(787\) 12.1689 0.433774 0.216887 0.976197i \(-0.430410\pi\)
0.216887 + 0.976197i \(0.430410\pi\)
\(788\) 3.43025 0.122198
\(789\) −29.4695 −1.04914
\(790\) 13.5152 0.480848
\(791\) −87.5319 −3.11228
\(792\) 0.445599 0.0158337
\(793\) 2.55140 0.0906030
\(794\) −22.7468 −0.807252
\(795\) −2.76440 −0.0980430
\(796\) −20.4116 −0.723470
\(797\) −22.6668 −0.802899 −0.401449 0.915881i \(-0.631493\pi\)
−0.401449 + 0.915881i \(0.631493\pi\)
\(798\) −16.7168 −0.591769
\(799\) 20.3384 0.719523
\(800\) −3.62640 −0.128213
\(801\) 2.37544 0.0839320
\(802\) −22.0727 −0.779415
\(803\) 5.24447 0.185073
\(804\) 2.47808 0.0873950
\(805\) −6.99237 −0.246448
\(806\) 7.97242 0.280817
\(807\) −22.9635 −0.808353
\(808\) −7.45461 −0.262252
\(809\) −25.6679 −0.902434 −0.451217 0.892414i \(-0.649010\pi\)
−0.451217 + 0.892414i \(0.649010\pi\)
\(810\) −1.17201 −0.0411801
\(811\) 3.52014 0.123609 0.0618044 0.998088i \(-0.480315\pi\)
0.0618044 + 0.998088i \(0.480315\pi\)
\(812\) 25.2334 0.885518
\(813\) −3.57490 −0.125377
\(814\) 3.03296 0.106305
\(815\) −5.34569 −0.187251
\(816\) −6.53411 −0.228740
\(817\) 26.8445 0.939169
\(818\) 8.78100 0.307020
\(819\) 4.40989 0.154094
\(820\) −0.566464 −0.0197818
\(821\) 46.5064 1.62308 0.811542 0.584293i \(-0.198628\pi\)
0.811542 + 0.584293i \(0.198628\pi\)
\(822\) −10.2707 −0.358232
\(823\) 18.0385 0.628784 0.314392 0.949293i \(-0.398199\pi\)
0.314392 + 0.949293i \(0.398199\pi\)
\(824\) −1.00000 −0.0348367
\(825\) 1.61592 0.0562592
\(826\) −47.7723 −1.66221
\(827\) −1.68552 −0.0586113 −0.0293057 0.999570i \(-0.509330\pi\)
−0.0293057 + 0.999570i \(0.509330\pi\)
\(828\) −1.35290 −0.0470166
\(829\) 15.8168 0.549339 0.274669 0.961539i \(-0.411432\pi\)
0.274669 + 0.961539i \(0.411432\pi\)
\(830\) 0.220605 0.00765731
\(831\) −11.0480 −0.383249
\(832\) −1.00000 −0.0346688
\(833\) 81.3307 2.81794
\(834\) −2.46420 −0.0853281
\(835\) 17.2799 0.597997
\(836\) −1.68916 −0.0584208
\(837\) 7.97242 0.275567
\(838\) 12.0635 0.416728
\(839\) −43.8438 −1.51365 −0.756827 0.653615i \(-0.773252\pi\)
−0.756827 + 0.653615i \(0.773252\pi\)
\(840\) −5.16841 −0.178327
\(841\) 3.74133 0.129012
\(842\) 1.57768 0.0543704
\(843\) −18.7003 −0.644073
\(844\) 10.3909 0.357669
\(845\) −1.17201 −0.0403182
\(846\) 3.11266 0.107015
\(847\) 47.6331 1.63669
\(848\) −2.35869 −0.0809977
\(849\) −29.5791 −1.01515
\(850\) −23.6953 −0.812742
\(851\) −9.20851 −0.315664
\(852\) −2.87156 −0.0983779
\(853\) −6.88736 −0.235819 −0.117909 0.993024i \(-0.537619\pi\)
−0.117909 + 0.993024i \(0.537619\pi\)
\(854\) 11.2514 0.385015
\(855\) 4.44279 0.151940
\(856\) 8.79608 0.300644
\(857\) 19.8738 0.678877 0.339439 0.940628i \(-0.389763\pi\)
0.339439 + 0.940628i \(0.389763\pi\)
\(858\) 0.445599 0.0152125
\(859\) −22.5579 −0.769665 −0.384833 0.922986i \(-0.625741\pi\)
−0.384833 + 0.922986i \(0.625741\pi\)
\(860\) 8.29963 0.283015
\(861\) 2.13142 0.0726387
\(862\) 25.2451 0.859852
\(863\) −16.4555 −0.560152 −0.280076 0.959978i \(-0.590360\pi\)
−0.280076 + 0.959978i \(0.590360\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 3.38315 0.115031
\(866\) −17.2197 −0.585148
\(867\) −25.6946 −0.872635
\(868\) 35.1575 1.19332
\(869\) −5.13850 −0.174312
\(870\) −6.70622 −0.227362
\(871\) 2.47808 0.0839664
\(872\) 0.173361 0.00587073
\(873\) −5.14559 −0.174152
\(874\) 5.12853 0.173475
\(875\) −44.5848 −1.50724
\(876\) −11.7695 −0.397654
\(877\) −12.4616 −0.420800 −0.210400 0.977615i \(-0.567477\pi\)
−0.210400 + 0.977615i \(0.567477\pi\)
\(878\) −25.7156 −0.867861
\(879\) −3.43588 −0.115889
\(880\) −0.522245 −0.0176049
\(881\) −31.3557 −1.05640 −0.528199 0.849120i \(-0.677133\pi\)
−0.528199 + 0.849120i \(0.677133\pi\)
\(882\) 12.4471 0.419116
\(883\) −0.473730 −0.0159423 −0.00797114 0.999968i \(-0.502537\pi\)
−0.00797114 + 0.999968i \(0.502537\pi\)
\(884\) −6.53411 −0.219766
\(885\) 12.6963 0.426783
\(886\) −21.4498 −0.720621
\(887\) −32.5755 −1.09378 −0.546889 0.837205i \(-0.684188\pi\)
−0.546889 + 0.837205i \(0.684188\pi\)
\(888\) −6.80648 −0.228410
\(889\) 2.08259 0.0698479
\(890\) −2.78403 −0.0933208
\(891\) 0.445599 0.0149281
\(892\) −3.71253 −0.124305
\(893\) −11.7993 −0.394850
\(894\) −13.2726 −0.443901
\(895\) −19.5109 −0.652177
\(896\) −4.40989 −0.147324
\(897\) −1.35290 −0.0451721
\(898\) −9.64925 −0.322000
\(899\) 45.6182 1.52145
\(900\) −3.62640 −0.120880
\(901\) −15.4119 −0.513446
\(902\) 0.215371 0.00717106
\(903\) −31.2289 −1.03923
\(904\) 19.8490 0.660169
\(905\) −8.81774 −0.293112
\(906\) 10.0014 0.332273
\(907\) −48.6651 −1.61590 −0.807949 0.589252i \(-0.799422\pi\)
−0.807949 + 0.589252i \(0.799422\pi\)
\(908\) −11.8872 −0.394490
\(909\) −7.45461 −0.247254
\(910\) −5.16841 −0.171331
\(911\) 49.7482 1.64823 0.824116 0.566422i \(-0.191673\pi\)
0.824116 + 0.566422i \(0.191673\pi\)
\(912\) 3.79076 0.125525
\(913\) −0.0838745 −0.00277584
\(914\) −21.4975 −0.711074
\(915\) −2.99026 −0.0988549
\(916\) 14.5836 0.481857
\(917\) −35.6075 −1.17586
\(918\) −6.53411 −0.215658
\(919\) 44.6682 1.47347 0.736734 0.676183i \(-0.236367\pi\)
0.736734 + 0.676183i \(0.236367\pi\)
\(920\) 1.58561 0.0522760
\(921\) −19.4875 −0.642136
\(922\) 2.06933 0.0681497
\(923\) −2.87156 −0.0945184
\(924\) 1.96504 0.0646452
\(925\) −24.6830 −0.811573
\(926\) −1.41092 −0.0463656
\(927\) −1.00000 −0.0328443
\(928\) −5.72200 −0.187834
\(929\) −23.8368 −0.782061 −0.391030 0.920378i \(-0.627881\pi\)
−0.391030 + 0.920378i \(0.627881\pi\)
\(930\) −9.34373 −0.306393
\(931\) −47.1840 −1.54639
\(932\) 4.17408 0.136726
\(933\) −33.4413 −1.09482
\(934\) −28.7723 −0.941458
\(935\) −3.41241 −0.111598
\(936\) −1.00000 −0.0326860
\(937\) −11.4196 −0.373063 −0.186532 0.982449i \(-0.559725\pi\)
−0.186532 + 0.982449i \(0.559725\pi\)
\(938\) 10.9280 0.356813
\(939\) −13.3906 −0.436985
\(940\) −3.64805 −0.118986
\(941\) 21.3611 0.696352 0.348176 0.937429i \(-0.386801\pi\)
0.348176 + 0.937429i \(0.386801\pi\)
\(942\) 17.1361 0.558324
\(943\) −0.653896 −0.0212938
\(944\) 10.8330 0.352584
\(945\) −5.16841 −0.168129
\(946\) −3.15554 −0.102595
\(947\) 19.3464 0.628672 0.314336 0.949312i \(-0.398218\pi\)
0.314336 + 0.949312i \(0.398218\pi\)
\(948\) 11.5317 0.374531
\(949\) −11.7695 −0.382053
\(950\) 13.7468 0.446005
\(951\) −17.0064 −0.551472
\(952\) −28.8147 −0.933889
\(953\) −4.95543 −0.160522 −0.0802611 0.996774i \(-0.525575\pi\)
−0.0802611 + 0.996774i \(0.525575\pi\)
\(954\) −2.35869 −0.0763653
\(955\) −7.51979 −0.243335
\(956\) −0.656747 −0.0212407
\(957\) 2.54972 0.0824208
\(958\) 6.49308 0.209782
\(959\) −45.2926 −1.46257
\(960\) 1.17201 0.0378263
\(961\) 32.5595 1.05031
\(962\) −6.80648 −0.219450
\(963\) 8.79608 0.283450
\(964\) 17.0766 0.550000
\(965\) −21.7300 −0.699513
\(966\) −5.96615 −0.191958
\(967\) 56.4647 1.81578 0.907891 0.419206i \(-0.137692\pi\)
0.907891 + 0.419206i \(0.137692\pi\)
\(968\) −10.8014 −0.347171
\(969\) 24.7692 0.795702
\(970\) 6.03066 0.193633
\(971\) 23.9443 0.768408 0.384204 0.923248i \(-0.374476\pi\)
0.384204 + 0.923248i \(0.374476\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −10.8668 −0.348375
\(974\) 31.9604 1.02408
\(975\) −3.62640 −0.116138
\(976\) −2.55140 −0.0816684
\(977\) 15.0721 0.482198 0.241099 0.970500i \(-0.422492\pi\)
0.241099 + 0.970500i \(0.422492\pi\)
\(978\) −4.56114 −0.145849
\(979\) 1.05849 0.0338296
\(980\) −14.5881 −0.465999
\(981\) 0.173361 0.00553498
\(982\) 14.3666 0.458458
\(983\) 8.53695 0.272286 0.136143 0.990689i \(-0.456529\pi\)
0.136143 + 0.990689i \(0.456529\pi\)
\(984\) −0.483328 −0.0154079
\(985\) −4.02028 −0.128097
\(986\) −37.3882 −1.19068
\(987\) 13.7265 0.436918
\(988\) 3.79076 0.120600
\(989\) 9.58066 0.304647
\(990\) −0.522245 −0.0165980
\(991\) −40.2817 −1.27959 −0.639796 0.768545i \(-0.720981\pi\)
−0.639796 + 0.768545i \(0.720981\pi\)
\(992\) −7.97242 −0.253125
\(993\) 0.178182 0.00565444
\(994\) −12.6632 −0.401653
\(995\) 23.9225 0.758395
\(996\) 0.188229 0.00596425
\(997\) 27.8162 0.880949 0.440474 0.897765i \(-0.354810\pi\)
0.440474 + 0.897765i \(0.354810\pi\)
\(998\) 6.86384 0.217271
\(999\) −6.80648 −0.215347
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 8034.2.a.bc.1.6 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.bc.1.6 15 1.1 even 1 trivial