Properties

Label 4034.2.a.d.1.17
Level 4034
Weight 2
Character 4034.1
Self dual yes
Analytic conductor 32.212
Analytic rank 0
Dimension 52
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(52\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.909483 q^{3} +1.00000 q^{4} +3.81385 q^{5} -0.909483 q^{6} +4.56339 q^{7} +1.00000 q^{8} -2.17284 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.909483 q^{3} +1.00000 q^{4} +3.81385 q^{5} -0.909483 q^{6} +4.56339 q^{7} +1.00000 q^{8} -2.17284 q^{9} +3.81385 q^{10} -3.92961 q^{11} -0.909483 q^{12} +5.78418 q^{13} +4.56339 q^{14} -3.46863 q^{15} +1.00000 q^{16} -2.17852 q^{17} -2.17284 q^{18} -5.55126 q^{19} +3.81385 q^{20} -4.15033 q^{21} -3.92961 q^{22} -7.56459 q^{23} -0.909483 q^{24} +9.54543 q^{25} +5.78418 q^{26} +4.70461 q^{27} +4.56339 q^{28} +6.68108 q^{29} -3.46863 q^{30} +5.62008 q^{31} +1.00000 q^{32} +3.57392 q^{33} -2.17852 q^{34} +17.4041 q^{35} -2.17284 q^{36} +0.397537 q^{37} -5.55126 q^{38} -5.26062 q^{39} +3.81385 q^{40} +8.48174 q^{41} -4.15033 q^{42} +5.40281 q^{43} -3.92961 q^{44} -8.28688 q^{45} -7.56459 q^{46} -1.01056 q^{47} -0.909483 q^{48} +13.8246 q^{49} +9.54543 q^{50} +1.98133 q^{51} +5.78418 q^{52} +3.74072 q^{53} +4.70461 q^{54} -14.9869 q^{55} +4.56339 q^{56} +5.04878 q^{57} +6.68108 q^{58} -7.17723 q^{59} -3.46863 q^{60} +11.6742 q^{61} +5.62008 q^{62} -9.91552 q^{63} +1.00000 q^{64} +22.0600 q^{65} +3.57392 q^{66} -5.51802 q^{67} -2.17852 q^{68} +6.87987 q^{69} +17.4041 q^{70} -5.97927 q^{71} -2.17284 q^{72} -4.89460 q^{73} +0.397537 q^{74} -8.68141 q^{75} -5.55126 q^{76} -17.9324 q^{77} -5.26062 q^{78} +4.24090 q^{79} +3.81385 q^{80} +2.23975 q^{81} +8.48174 q^{82} +5.78317 q^{83} -4.15033 q^{84} -8.30855 q^{85} +5.40281 q^{86} -6.07634 q^{87} -3.92961 q^{88} +10.4632 q^{89} -8.28688 q^{90} +26.3955 q^{91} -7.56459 q^{92} -5.11137 q^{93} -1.01056 q^{94} -21.1717 q^{95} -0.909483 q^{96} +3.37359 q^{97} +13.8246 q^{98} +8.53842 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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
\(3\) −0.909483 −0.525090 −0.262545 0.964920i \(-0.584562\pi\)
−0.262545 + 0.964920i \(0.584562\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.81385 1.70560 0.852802 0.522234i \(-0.174901\pi\)
0.852802 + 0.522234i \(0.174901\pi\)
\(6\) −0.909483 −0.371295
\(7\) 4.56339 1.72480 0.862400 0.506227i \(-0.168960\pi\)
0.862400 + 0.506227i \(0.168960\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.17284 −0.724280
\(10\) 3.81385 1.20604
\(11\) −3.92961 −1.18482 −0.592411 0.805636i \(-0.701824\pi\)
−0.592411 + 0.805636i \(0.701824\pi\)
\(12\) −0.909483 −0.262545
\(13\) 5.78418 1.60424 0.802122 0.597160i \(-0.203704\pi\)
0.802122 + 0.597160i \(0.203704\pi\)
\(14\) 4.56339 1.21962
\(15\) −3.46863 −0.895596
\(16\) 1.00000 0.250000
\(17\) −2.17852 −0.528369 −0.264185 0.964472i \(-0.585103\pi\)
−0.264185 + 0.964472i \(0.585103\pi\)
\(18\) −2.17284 −0.512143
\(19\) −5.55126 −1.27355 −0.636773 0.771051i \(-0.719731\pi\)
−0.636773 + 0.771051i \(0.719731\pi\)
\(20\) 3.81385 0.852802
\(21\) −4.15033 −0.905676
\(22\) −3.92961 −0.837796
\(23\) −7.56459 −1.57733 −0.788663 0.614826i \(-0.789226\pi\)
−0.788663 + 0.614826i \(0.789226\pi\)
\(24\) −0.909483 −0.185648
\(25\) 9.54543 1.90909
\(26\) 5.78418 1.13437
\(27\) 4.70461 0.905403
\(28\) 4.56339 0.862400
\(29\) 6.68108 1.24065 0.620323 0.784346i \(-0.287001\pi\)
0.620323 + 0.784346i \(0.287001\pi\)
\(30\) −3.46863 −0.633282
\(31\) 5.62008 1.00940 0.504699 0.863296i \(-0.331604\pi\)
0.504699 + 0.863296i \(0.331604\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.57392 0.622139
\(34\) −2.17852 −0.373614
\(35\) 17.4041 2.94183
\(36\) −2.17284 −0.362140
\(37\) 0.397537 0.0653546 0.0326773 0.999466i \(-0.489597\pi\)
0.0326773 + 0.999466i \(0.489597\pi\)
\(38\) −5.55126 −0.900534
\(39\) −5.26062 −0.842373
\(40\) 3.81385 0.603022
\(41\) 8.48174 1.32462 0.662312 0.749228i \(-0.269575\pi\)
0.662312 + 0.749228i \(0.269575\pi\)
\(42\) −4.15033 −0.640410
\(43\) 5.40281 0.823921 0.411961 0.911202i \(-0.364844\pi\)
0.411961 + 0.911202i \(0.364844\pi\)
\(44\) −3.92961 −0.592411
\(45\) −8.28688 −1.23533
\(46\) −7.56459 −1.11534
\(47\) −1.01056 −0.147405 −0.0737027 0.997280i \(-0.523482\pi\)
−0.0737027 + 0.997280i \(0.523482\pi\)
\(48\) −0.909483 −0.131273
\(49\) 13.8246 1.97494
\(50\) 9.54543 1.34993
\(51\) 1.98133 0.277442
\(52\) 5.78418 0.802122
\(53\) 3.74072 0.513828 0.256914 0.966434i \(-0.417294\pi\)
0.256914 + 0.966434i \(0.417294\pi\)
\(54\) 4.70461 0.640217
\(55\) −14.9869 −2.02084
\(56\) 4.56339 0.609809
\(57\) 5.04878 0.668727
\(58\) 6.68108 0.877269
\(59\) −7.17723 −0.934395 −0.467198 0.884153i \(-0.654736\pi\)
−0.467198 + 0.884153i \(0.654736\pi\)
\(60\) −3.46863 −0.447798
\(61\) 11.6742 1.49473 0.747366 0.664413i \(-0.231318\pi\)
0.747366 + 0.664413i \(0.231318\pi\)
\(62\) 5.62008 0.713752
\(63\) −9.91552 −1.24924
\(64\) 1.00000 0.125000
\(65\) 22.0600 2.73620
\(66\) 3.57392 0.439919
\(67\) −5.51802 −0.674133 −0.337066 0.941481i \(-0.609435\pi\)
−0.337066 + 0.941481i \(0.609435\pi\)
\(68\) −2.17852 −0.264185
\(69\) 6.87987 0.828239
\(70\) 17.4041 2.08019
\(71\) −5.97927 −0.709609 −0.354805 0.934941i \(-0.615453\pi\)
−0.354805 + 0.934941i \(0.615453\pi\)
\(72\) −2.17284 −0.256072
\(73\) −4.89460 −0.572870 −0.286435 0.958100i \(-0.592470\pi\)
−0.286435 + 0.958100i \(0.592470\pi\)
\(74\) 0.397537 0.0462127
\(75\) −8.68141 −1.00244
\(76\) −5.55126 −0.636773
\(77\) −17.9324 −2.04358
\(78\) −5.26062 −0.595648
\(79\) 4.24090 0.477139 0.238569 0.971125i \(-0.423322\pi\)
0.238569 + 0.971125i \(0.423322\pi\)
\(80\) 3.81385 0.426401
\(81\) 2.23975 0.248862
\(82\) 8.48174 0.936651
\(83\) 5.78317 0.634785 0.317393 0.948294i \(-0.397193\pi\)
0.317393 + 0.948294i \(0.397193\pi\)
\(84\) −4.15033 −0.452838
\(85\) −8.30855 −0.901189
\(86\) 5.40281 0.582600
\(87\) −6.07634 −0.651452
\(88\) −3.92961 −0.418898
\(89\) 10.4632 1.10910 0.554551 0.832150i \(-0.312890\pi\)
0.554551 + 0.832150i \(0.312890\pi\)
\(90\) −8.28688 −0.873514
\(91\) 26.3955 2.76700
\(92\) −7.56459 −0.788663
\(93\) −5.11137 −0.530025
\(94\) −1.01056 −0.104231
\(95\) −21.1717 −2.17217
\(96\) −0.909483 −0.0928238
\(97\) 3.37359 0.342536 0.171268 0.985225i \(-0.445214\pi\)
0.171268 + 0.985225i \(0.445214\pi\)
\(98\) 13.8246 1.39649
\(99\) 8.53842 0.858143
\(100\) 9.54543 0.954543
\(101\) −17.8025 −1.77141 −0.885705 0.464248i \(-0.846325\pi\)
−0.885705 + 0.464248i \(0.846325\pi\)
\(102\) 1.98133 0.196181
\(103\) 12.4501 1.22674 0.613370 0.789795i \(-0.289813\pi\)
0.613370 + 0.789795i \(0.289813\pi\)
\(104\) 5.78418 0.567186
\(105\) −15.8287 −1.54472
\(106\) 3.74072 0.363331
\(107\) 16.3542 1.58102 0.790511 0.612448i \(-0.209815\pi\)
0.790511 + 0.612448i \(0.209815\pi\)
\(108\) 4.70461 0.452701
\(109\) −15.9189 −1.52476 −0.762378 0.647132i \(-0.775968\pi\)
−0.762378 + 0.647132i \(0.775968\pi\)
\(110\) −14.9869 −1.42895
\(111\) −0.361553 −0.0343171
\(112\) 4.56339 0.431200
\(113\) −13.2343 −1.24498 −0.622488 0.782629i \(-0.713878\pi\)
−0.622488 + 0.782629i \(0.713878\pi\)
\(114\) 5.04878 0.472862
\(115\) −28.8502 −2.69029
\(116\) 6.68108 0.620323
\(117\) −12.5681 −1.16192
\(118\) −7.17723 −0.660717
\(119\) −9.94145 −0.911332
\(120\) −3.46863 −0.316641
\(121\) 4.44185 0.403805
\(122\) 11.6742 1.05693
\(123\) −7.71400 −0.695548
\(124\) 5.62008 0.504699
\(125\) 17.3356 1.55054
\(126\) −9.91552 −0.883345
\(127\) −11.0583 −0.981263 −0.490632 0.871367i \(-0.663234\pi\)
−0.490632 + 0.871367i \(0.663234\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.91377 −0.432633
\(130\) 22.0600 1.93479
\(131\) −2.89886 −0.253275 −0.126637 0.991949i \(-0.540418\pi\)
−0.126637 + 0.991949i \(0.540418\pi\)
\(132\) 3.57392 0.311069
\(133\) −25.3326 −2.19661
\(134\) −5.51802 −0.476684
\(135\) 17.9427 1.54426
\(136\) −2.17852 −0.186807
\(137\) −7.19573 −0.614772 −0.307386 0.951585i \(-0.599454\pi\)
−0.307386 + 0.951585i \(0.599454\pi\)
\(138\) 6.87987 0.585653
\(139\) −10.6266 −0.901341 −0.450670 0.892690i \(-0.648815\pi\)
−0.450670 + 0.892690i \(0.648815\pi\)
\(140\) 17.4041 1.47091
\(141\) 0.919088 0.0774012
\(142\) −5.97927 −0.501769
\(143\) −22.7296 −1.90074
\(144\) −2.17284 −0.181070
\(145\) 25.4806 2.11605
\(146\) −4.89460 −0.405080
\(147\) −12.5732 −1.03702
\(148\) 0.397537 0.0326773
\(149\) −5.00970 −0.410410 −0.205205 0.978719i \(-0.565786\pi\)
−0.205205 + 0.978719i \(0.565786\pi\)
\(150\) −8.68141 −0.708834
\(151\) −0.804620 −0.0654790 −0.0327395 0.999464i \(-0.510423\pi\)
−0.0327395 + 0.999464i \(0.510423\pi\)
\(152\) −5.55126 −0.450267
\(153\) 4.73358 0.382687
\(154\) −17.9324 −1.44503
\(155\) 21.4341 1.72163
\(156\) −5.26062 −0.421187
\(157\) 5.72338 0.456775 0.228388 0.973570i \(-0.426655\pi\)
0.228388 + 0.973570i \(0.426655\pi\)
\(158\) 4.24090 0.337388
\(159\) −3.40213 −0.269806
\(160\) 3.81385 0.301511
\(161\) −34.5202 −2.72057
\(162\) 2.23975 0.175972
\(163\) 15.0349 1.17762 0.588811 0.808271i \(-0.299596\pi\)
0.588811 + 0.808271i \(0.299596\pi\)
\(164\) 8.48174 0.662312
\(165\) 13.6304 1.06112
\(166\) 5.78317 0.448861
\(167\) −12.5980 −0.974866 −0.487433 0.873160i \(-0.662067\pi\)
−0.487433 + 0.873160i \(0.662067\pi\)
\(168\) −4.15033 −0.320205
\(169\) 20.4568 1.57360
\(170\) −8.30855 −0.637237
\(171\) 12.0620 0.922405
\(172\) 5.40281 0.411961
\(173\) −10.9464 −0.832242 −0.416121 0.909309i \(-0.636611\pi\)
−0.416121 + 0.909309i \(0.636611\pi\)
\(174\) −6.07634 −0.460646
\(175\) 43.5595 3.29279
\(176\) −3.92961 −0.296206
\(177\) 6.52757 0.490642
\(178\) 10.4632 0.784253
\(179\) −22.3155 −1.66794 −0.833970 0.551810i \(-0.813937\pi\)
−0.833970 + 0.551810i \(0.813937\pi\)
\(180\) −8.28688 −0.617667
\(181\) −22.5198 −1.67389 −0.836943 0.547290i \(-0.815660\pi\)
−0.836943 + 0.547290i \(0.815660\pi\)
\(182\) 26.3955 1.95656
\(183\) −10.6175 −0.784869
\(184\) −7.56459 −0.557669
\(185\) 1.51614 0.111469
\(186\) −5.11137 −0.374784
\(187\) 8.56075 0.626024
\(188\) −1.01056 −0.0737027
\(189\) 21.4690 1.56164
\(190\) −21.1717 −1.53595
\(191\) 14.1797 1.02601 0.513003 0.858387i \(-0.328533\pi\)
0.513003 + 0.858387i \(0.328533\pi\)
\(192\) −0.909483 −0.0656363
\(193\) 12.6187 0.908315 0.454157 0.890921i \(-0.349940\pi\)
0.454157 + 0.890921i \(0.349940\pi\)
\(194\) 3.37359 0.242209
\(195\) −20.0632 −1.43675
\(196\) 13.8246 0.987468
\(197\) 21.6427 1.54198 0.770990 0.636847i \(-0.219762\pi\)
0.770990 + 0.636847i \(0.219762\pi\)
\(198\) 8.53842 0.606799
\(199\) −11.1593 −0.791062 −0.395531 0.918453i \(-0.629439\pi\)
−0.395531 + 0.918453i \(0.629439\pi\)
\(200\) 9.54543 0.674964
\(201\) 5.01854 0.353981
\(202\) −17.8025 −1.25258
\(203\) 30.4884 2.13987
\(204\) 1.98133 0.138721
\(205\) 32.3480 2.25929
\(206\) 12.4501 0.867437
\(207\) 16.4366 1.14243
\(208\) 5.78418 0.401061
\(209\) 21.8143 1.50893
\(210\) −15.8287 −1.09229
\(211\) 7.76198 0.534357 0.267178 0.963647i \(-0.413909\pi\)
0.267178 + 0.963647i \(0.413909\pi\)
\(212\) 3.74072 0.256914
\(213\) 5.43805 0.372609
\(214\) 16.3542 1.11795
\(215\) 20.6055 1.40528
\(216\) 4.70461 0.320108
\(217\) 25.6467 1.74101
\(218\) −15.9189 −1.07817
\(219\) 4.45156 0.300808
\(220\) −14.9869 −1.01042
\(221\) −12.6010 −0.847633
\(222\) −0.361553 −0.0242658
\(223\) 22.9478 1.53670 0.768349 0.640031i \(-0.221079\pi\)
0.768349 + 0.640031i \(0.221079\pi\)
\(224\) 4.56339 0.304904
\(225\) −20.7407 −1.38271
\(226\) −13.2343 −0.880332
\(227\) −20.3165 −1.34846 −0.674228 0.738523i \(-0.735524\pi\)
−0.674228 + 0.738523i \(0.735524\pi\)
\(228\) 5.04878 0.334364
\(229\) 2.34851 0.155194 0.0775971 0.996985i \(-0.475275\pi\)
0.0775971 + 0.996985i \(0.475275\pi\)
\(230\) −28.8502 −1.90232
\(231\) 16.3092 1.07307
\(232\) 6.68108 0.438635
\(233\) 3.83142 0.251005 0.125502 0.992093i \(-0.459946\pi\)
0.125502 + 0.992093i \(0.459946\pi\)
\(234\) −12.5681 −0.821603
\(235\) −3.85412 −0.251415
\(236\) −7.17723 −0.467198
\(237\) −3.85703 −0.250541
\(238\) −9.94145 −0.644409
\(239\) −8.82897 −0.571099 −0.285549 0.958364i \(-0.592176\pi\)
−0.285549 + 0.958364i \(0.592176\pi\)
\(240\) −3.46863 −0.223899
\(241\) −19.6095 −1.26316 −0.631580 0.775311i \(-0.717593\pi\)
−0.631580 + 0.775311i \(0.717593\pi\)
\(242\) 4.44185 0.285533
\(243\) −16.1509 −1.03608
\(244\) 11.6742 0.747366
\(245\) 52.7247 3.36846
\(246\) −7.71400 −0.491826
\(247\) −32.1095 −2.04308
\(248\) 5.62008 0.356876
\(249\) −5.25969 −0.333320
\(250\) 17.3356 1.09640
\(251\) −17.3812 −1.09709 −0.548546 0.836121i \(-0.684818\pi\)
−0.548546 + 0.836121i \(0.684818\pi\)
\(252\) −9.91552 −0.624619
\(253\) 29.7259 1.86885
\(254\) −11.0583 −0.693858
\(255\) 7.55649 0.473206
\(256\) 1.00000 0.0625000
\(257\) −23.2040 −1.44742 −0.723711 0.690103i \(-0.757565\pi\)
−0.723711 + 0.690103i \(0.757565\pi\)
\(258\) −4.91377 −0.305918
\(259\) 1.81412 0.112724
\(260\) 22.0600 1.36810
\(261\) −14.5169 −0.898575
\(262\) −2.89886 −0.179092
\(263\) 8.37380 0.516350 0.258175 0.966098i \(-0.416879\pi\)
0.258175 + 0.966098i \(0.416879\pi\)
\(264\) 3.57392 0.219959
\(265\) 14.2665 0.876387
\(266\) −25.3326 −1.55324
\(267\) −9.51614 −0.582378
\(268\) −5.51802 −0.337066
\(269\) −10.3111 −0.628679 −0.314340 0.949311i \(-0.601783\pi\)
−0.314340 + 0.949311i \(0.601783\pi\)
\(270\) 17.9427 1.09196
\(271\) −6.42045 −0.390014 −0.195007 0.980802i \(-0.562473\pi\)
−0.195007 + 0.980802i \(0.562473\pi\)
\(272\) −2.17852 −0.132092
\(273\) −24.0063 −1.45293
\(274\) −7.19573 −0.434710
\(275\) −37.5098 −2.26193
\(276\) 6.87987 0.414119
\(277\) 24.9475 1.49895 0.749474 0.662034i \(-0.230306\pi\)
0.749474 + 0.662034i \(0.230306\pi\)
\(278\) −10.6266 −0.637344
\(279\) −12.2115 −0.731086
\(280\) 17.4041 1.04009
\(281\) −17.1583 −1.02358 −0.511789 0.859111i \(-0.671017\pi\)
−0.511789 + 0.859111i \(0.671017\pi\)
\(282\) 0.919088 0.0547309
\(283\) 15.7896 0.938597 0.469298 0.883040i \(-0.344507\pi\)
0.469298 + 0.883040i \(0.344507\pi\)
\(284\) −5.97927 −0.354805
\(285\) 19.2553 1.14058
\(286\) −22.7296 −1.34403
\(287\) 38.7055 2.28471
\(288\) −2.17284 −0.128036
\(289\) −12.2540 −0.720826
\(290\) 25.4806 1.49627
\(291\) −3.06822 −0.179862
\(292\) −4.89460 −0.286435
\(293\) −11.7153 −0.684415 −0.342208 0.939624i \(-0.611175\pi\)
−0.342208 + 0.939624i \(0.611175\pi\)
\(294\) −12.5732 −0.733284
\(295\) −27.3728 −1.59371
\(296\) 0.397537 0.0231063
\(297\) −18.4873 −1.07274
\(298\) −5.00970 −0.290204
\(299\) −43.7550 −2.53041
\(300\) −8.68141 −0.501221
\(301\) 24.6552 1.42110
\(302\) −0.804620 −0.0463007
\(303\) 16.1910 0.930151
\(304\) −5.55126 −0.318387
\(305\) 44.5237 2.54942
\(306\) 4.73358 0.270601
\(307\) −10.0457 −0.573336 −0.286668 0.958030i \(-0.592548\pi\)
−0.286668 + 0.958030i \(0.592548\pi\)
\(308\) −17.9324 −1.02179
\(309\) −11.3231 −0.644150
\(310\) 21.4341 1.21738
\(311\) 11.5924 0.657346 0.328673 0.944444i \(-0.393399\pi\)
0.328673 + 0.944444i \(0.393399\pi\)
\(312\) −5.26062 −0.297824
\(313\) 17.2100 0.972769 0.486384 0.873745i \(-0.338315\pi\)
0.486384 + 0.873745i \(0.338315\pi\)
\(314\) 5.72338 0.322989
\(315\) −37.8163 −2.13071
\(316\) 4.24090 0.238569
\(317\) 13.0661 0.733865 0.366933 0.930247i \(-0.380408\pi\)
0.366933 + 0.930247i \(0.380408\pi\)
\(318\) −3.40213 −0.190782
\(319\) −26.2541 −1.46995
\(320\) 3.81385 0.213201
\(321\) −14.8739 −0.830180
\(322\) −34.5202 −1.92373
\(323\) 12.0935 0.672903
\(324\) 2.23975 0.124431
\(325\) 55.2125 3.06264
\(326\) 15.0349 0.832705
\(327\) 14.4780 0.800635
\(328\) 8.48174 0.468326
\(329\) −4.61158 −0.254245
\(330\) 13.6304 0.750327
\(331\) 10.6184 0.583642 0.291821 0.956473i \(-0.405739\pi\)
0.291821 + 0.956473i \(0.405739\pi\)
\(332\) 5.78317 0.317393
\(333\) −0.863784 −0.0473350
\(334\) −12.5980 −0.689335
\(335\) −21.0449 −1.14980
\(336\) −4.15033 −0.226419
\(337\) −2.17168 −0.118299 −0.0591495 0.998249i \(-0.518839\pi\)
−0.0591495 + 0.998249i \(0.518839\pi\)
\(338\) 20.4568 1.11270
\(339\) 12.0364 0.653725
\(340\) −8.30855 −0.450594
\(341\) −22.0848 −1.19596
\(342\) 12.0620 0.652238
\(343\) 31.1431 1.68157
\(344\) 5.40281 0.291300
\(345\) 26.2388 1.41265
\(346\) −10.9464 −0.588484
\(347\) −36.4191 −1.95508 −0.977541 0.210745i \(-0.932411\pi\)
−0.977541 + 0.210745i \(0.932411\pi\)
\(348\) −6.07634 −0.325726
\(349\) −21.3196 −1.14121 −0.570606 0.821224i \(-0.693292\pi\)
−0.570606 + 0.821224i \(0.693292\pi\)
\(350\) 43.5595 2.32835
\(351\) 27.2123 1.45249
\(352\) −3.92961 −0.209449
\(353\) 29.4288 1.56634 0.783168 0.621810i \(-0.213602\pi\)
0.783168 + 0.621810i \(0.213602\pi\)
\(354\) 6.52757 0.346936
\(355\) −22.8040 −1.21031
\(356\) 10.4632 0.554551
\(357\) 9.04159 0.478531
\(358\) −22.3155 −1.17941
\(359\) 19.7246 1.04103 0.520513 0.853853i \(-0.325741\pi\)
0.520513 + 0.853853i \(0.325741\pi\)
\(360\) −8.28688 −0.436757
\(361\) 11.8165 0.621921
\(362\) −22.5198 −1.18362
\(363\) −4.03979 −0.212034
\(364\) 26.3955 1.38350
\(365\) −18.6673 −0.977089
\(366\) −10.6175 −0.554986
\(367\) −10.5181 −0.549043 −0.274521 0.961581i \(-0.588519\pi\)
−0.274521 + 0.961581i \(0.588519\pi\)
\(368\) −7.56459 −0.394331
\(369\) −18.4295 −0.959399
\(370\) 1.51614 0.0788206
\(371\) 17.0704 0.886251
\(372\) −5.11137 −0.265012
\(373\) 13.9858 0.724157 0.362078 0.932148i \(-0.382067\pi\)
0.362078 + 0.932148i \(0.382067\pi\)
\(374\) 8.56075 0.442666
\(375\) −15.7664 −0.814173
\(376\) −1.01056 −0.0521157
\(377\) 38.6446 1.99030
\(378\) 21.4690 1.10425
\(379\) −0.336014 −0.0172599 −0.00862994 0.999963i \(-0.502747\pi\)
−0.00862994 + 0.999963i \(0.502747\pi\)
\(380\) −21.1717 −1.08608
\(381\) 10.0573 0.515252
\(382\) 14.1797 0.725496
\(383\) −31.9783 −1.63402 −0.817008 0.576626i \(-0.804369\pi\)
−0.817008 + 0.576626i \(0.804369\pi\)
\(384\) −0.909483 −0.0464119
\(385\) −68.3913 −3.48554
\(386\) 12.6187 0.642276
\(387\) −11.7394 −0.596750
\(388\) 3.37359 0.171268
\(389\) 2.40487 0.121932 0.0609658 0.998140i \(-0.480582\pi\)
0.0609658 + 0.998140i \(0.480582\pi\)
\(390\) −20.0632 −1.01594
\(391\) 16.4796 0.833410
\(392\) 13.8246 0.698245
\(393\) 2.63646 0.132992
\(394\) 21.6427 1.09034
\(395\) 16.1741 0.813809
\(396\) 8.53842 0.429072
\(397\) −27.0505 −1.35763 −0.678814 0.734311i \(-0.737506\pi\)
−0.678814 + 0.734311i \(0.737506\pi\)
\(398\) −11.1593 −0.559365
\(399\) 23.0396 1.15342
\(400\) 9.54543 0.477271
\(401\) −23.8839 −1.19270 −0.596352 0.802723i \(-0.703384\pi\)
−0.596352 + 0.802723i \(0.703384\pi\)
\(402\) 5.01854 0.250302
\(403\) 32.5076 1.61932
\(404\) −17.8025 −0.885705
\(405\) 8.54208 0.424459
\(406\) 30.4884 1.51311
\(407\) −1.56216 −0.0774336
\(408\) 1.98133 0.0980904
\(409\) −30.0686 −1.48680 −0.743398 0.668850i \(-0.766787\pi\)
−0.743398 + 0.668850i \(0.766787\pi\)
\(410\) 32.3480 1.59756
\(411\) 6.54439 0.322811
\(412\) 12.4501 0.613370
\(413\) −32.7525 −1.61165
\(414\) 16.4366 0.807817
\(415\) 22.0561 1.08269
\(416\) 5.78418 0.283593
\(417\) 9.66476 0.473285
\(418\) 21.8143 1.06697
\(419\) 24.9649 1.21962 0.609809 0.792549i \(-0.291246\pi\)
0.609809 + 0.792549i \(0.291246\pi\)
\(420\) −15.8287 −0.772362
\(421\) −38.4558 −1.87422 −0.937111 0.349031i \(-0.886511\pi\)
−0.937111 + 0.349031i \(0.886511\pi\)
\(422\) 7.76198 0.377847
\(423\) 2.19579 0.106763
\(424\) 3.74072 0.181666
\(425\) −20.7949 −1.00870
\(426\) 5.43805 0.263474
\(427\) 53.2741 2.57811
\(428\) 16.3542 0.790511
\(429\) 20.6722 0.998063
\(430\) 20.6055 0.993685
\(431\) 8.85993 0.426768 0.213384 0.976968i \(-0.431551\pi\)
0.213384 + 0.976968i \(0.431551\pi\)
\(432\) 4.70461 0.226351
\(433\) 25.2853 1.21513 0.607567 0.794269i \(-0.292146\pi\)
0.607567 + 0.794269i \(0.292146\pi\)
\(434\) 25.6467 1.23108
\(435\) −23.1742 −1.11112
\(436\) −15.9189 −0.762378
\(437\) 41.9930 2.00880
\(438\) 4.45156 0.212704
\(439\) 20.3042 0.969068 0.484534 0.874772i \(-0.338989\pi\)
0.484534 + 0.874772i \(0.338989\pi\)
\(440\) −14.9869 −0.714474
\(441\) −30.0385 −1.43041
\(442\) −12.6010 −0.599367
\(443\) −22.8603 −1.08613 −0.543063 0.839692i \(-0.682735\pi\)
−0.543063 + 0.839692i \(0.682735\pi\)
\(444\) −0.361553 −0.0171585
\(445\) 39.9052 1.89169
\(446\) 22.9478 1.08661
\(447\) 4.55624 0.215503
\(448\) 4.56339 0.215600
\(449\) 3.91945 0.184970 0.0924852 0.995714i \(-0.470519\pi\)
0.0924852 + 0.995714i \(0.470519\pi\)
\(450\) −20.7407 −0.977725
\(451\) −33.3299 −1.56945
\(452\) −13.2343 −0.622488
\(453\) 0.731788 0.0343824
\(454\) −20.3165 −0.953503
\(455\) 100.668 4.71941
\(456\) 5.04878 0.236431
\(457\) 27.2179 1.27320 0.636599 0.771195i \(-0.280341\pi\)
0.636599 + 0.771195i \(0.280341\pi\)
\(458\) 2.34851 0.109739
\(459\) −10.2491 −0.478387
\(460\) −28.8502 −1.34515
\(461\) 24.7940 1.15477 0.577385 0.816472i \(-0.304073\pi\)
0.577385 + 0.816472i \(0.304073\pi\)
\(462\) 16.3092 0.758772
\(463\) −37.4416 −1.74006 −0.870030 0.492998i \(-0.835901\pi\)
−0.870030 + 0.492998i \(0.835901\pi\)
\(464\) 6.68108 0.310162
\(465\) −19.4940 −0.904012
\(466\) 3.83142 0.177487
\(467\) 9.78265 0.452687 0.226343 0.974048i \(-0.427323\pi\)
0.226343 + 0.974048i \(0.427323\pi\)
\(468\) −12.5681 −0.580961
\(469\) −25.1809 −1.16274
\(470\) −3.85412 −0.177777
\(471\) −5.20532 −0.239848
\(472\) −7.17723 −0.330359
\(473\) −21.2310 −0.976201
\(474\) −3.85703 −0.177159
\(475\) −52.9892 −2.43131
\(476\) −9.94145 −0.455666
\(477\) −8.12800 −0.372155
\(478\) −8.82897 −0.403828
\(479\) −36.4494 −1.66542 −0.832708 0.553712i \(-0.813211\pi\)
−0.832708 + 0.553712i \(0.813211\pi\)
\(480\) −3.46863 −0.158321
\(481\) 2.29942 0.104845
\(482\) −19.6095 −0.893189
\(483\) 31.3955 1.42855
\(484\) 4.44185 0.201902
\(485\) 12.8663 0.584230
\(486\) −16.1509 −0.732618
\(487\) −22.2659 −1.00897 −0.504483 0.863422i \(-0.668317\pi\)
−0.504483 + 0.863422i \(0.668317\pi\)
\(488\) 11.6742 0.528467
\(489\) −13.6740 −0.618358
\(490\) 52.7247 2.38186
\(491\) 9.30011 0.419708 0.209854 0.977733i \(-0.432701\pi\)
0.209854 + 0.977733i \(0.432701\pi\)
\(492\) −7.71400 −0.347774
\(493\) −14.5549 −0.655519
\(494\) −32.1095 −1.44468
\(495\) 32.5642 1.46365
\(496\) 5.62008 0.252349
\(497\) −27.2858 −1.22393
\(498\) −5.25969 −0.235693
\(499\) 15.8834 0.711041 0.355520 0.934669i \(-0.384304\pi\)
0.355520 + 0.934669i \(0.384304\pi\)
\(500\) 17.3356 0.775270
\(501\) 11.4577 0.511893
\(502\) −17.3812 −0.775761
\(503\) 2.21851 0.0989183 0.0494591 0.998776i \(-0.484250\pi\)
0.0494591 + 0.998776i \(0.484250\pi\)
\(504\) −9.91552 −0.441672
\(505\) −67.8958 −3.02133
\(506\) 29.7259 1.32148
\(507\) −18.6051 −0.826281
\(508\) −11.0583 −0.490632
\(509\) −29.3414 −1.30053 −0.650267 0.759706i \(-0.725343\pi\)
−0.650267 + 0.759706i \(0.725343\pi\)
\(510\) 7.55649 0.334607
\(511\) −22.3360 −0.988086
\(512\) 1.00000 0.0441942
\(513\) −26.1165 −1.15307
\(514\) −23.2040 −1.02348
\(515\) 47.4826 2.09233
\(516\) −4.91377 −0.216317
\(517\) 3.97111 0.174649
\(518\) 1.81412 0.0797077
\(519\) 9.95560 0.437002
\(520\) 22.0600 0.967394
\(521\) 8.04984 0.352670 0.176335 0.984330i \(-0.443576\pi\)
0.176335 + 0.984330i \(0.443576\pi\)
\(522\) −14.5169 −0.635389
\(523\) 1.02636 0.0448795 0.0224397 0.999748i \(-0.492857\pi\)
0.0224397 + 0.999748i \(0.492857\pi\)
\(524\) −2.89886 −0.126637
\(525\) −39.6167 −1.72901
\(526\) 8.37380 0.365115
\(527\) −12.2435 −0.533334
\(528\) 3.57392 0.155535
\(529\) 34.2230 1.48796
\(530\) 14.2665 0.619699
\(531\) 15.5950 0.676764
\(532\) −25.3326 −1.09831
\(533\) 49.0599 2.12502
\(534\) −9.51614 −0.411804
\(535\) 62.3725 2.69660
\(536\) −5.51802 −0.238342
\(537\) 20.2956 0.875819
\(538\) −10.3111 −0.444543
\(539\) −54.3251 −2.33995
\(540\) 17.9427 0.772129
\(541\) −10.1857 −0.437918 −0.218959 0.975734i \(-0.570266\pi\)
−0.218959 + 0.975734i \(0.570266\pi\)
\(542\) −6.42045 −0.275782
\(543\) 20.4814 0.878942
\(544\) −2.17852 −0.0934034
\(545\) −60.7123 −2.60063
\(546\) −24.0063 −1.02737
\(547\) 7.79684 0.333369 0.166684 0.986010i \(-0.446694\pi\)
0.166684 + 0.986010i \(0.446694\pi\)
\(548\) −7.19573 −0.307386
\(549\) −25.3662 −1.08260
\(550\) −37.5098 −1.59942
\(551\) −37.0885 −1.58002
\(552\) 6.87987 0.292827
\(553\) 19.3529 0.822969
\(554\) 24.9475 1.05992
\(555\) −1.37891 −0.0585314
\(556\) −10.6266 −0.450670
\(557\) 18.5775 0.787155 0.393578 0.919291i \(-0.371237\pi\)
0.393578 + 0.919291i \(0.371237\pi\)
\(558\) −12.2115 −0.516956
\(559\) 31.2509 1.32177
\(560\) 17.4041 0.735457
\(561\) −7.78586 −0.328719
\(562\) −17.1583 −0.723779
\(563\) 35.0113 1.47555 0.737775 0.675047i \(-0.235877\pi\)
0.737775 + 0.675047i \(0.235877\pi\)
\(564\) 0.919088 0.0387006
\(565\) −50.4735 −2.12344
\(566\) 15.7896 0.663688
\(567\) 10.2209 0.429237
\(568\) −5.97927 −0.250885
\(569\) 18.1945 0.762752 0.381376 0.924420i \(-0.375450\pi\)
0.381376 + 0.924420i \(0.375450\pi\)
\(570\) 19.2553 0.806515
\(571\) −39.9862 −1.67337 −0.836685 0.547684i \(-0.815510\pi\)
−0.836685 + 0.547684i \(0.815510\pi\)
\(572\) −22.7296 −0.950372
\(573\) −12.8962 −0.538746
\(574\) 38.7055 1.61554
\(575\) −72.2072 −3.01125
\(576\) −2.17284 −0.0905350
\(577\) −18.4247 −0.767029 −0.383515 0.923535i \(-0.625286\pi\)
−0.383515 + 0.923535i \(0.625286\pi\)
\(578\) −12.2540 −0.509701
\(579\) −11.4765 −0.476947
\(580\) 25.4806 1.05803
\(581\) 26.3909 1.09488
\(582\) −3.06822 −0.127182
\(583\) −14.6996 −0.608795
\(584\) −4.89460 −0.202540
\(585\) −47.9328 −1.98178
\(586\) −11.7153 −0.483955
\(587\) 2.39930 0.0990299 0.0495149 0.998773i \(-0.484232\pi\)
0.0495149 + 0.998773i \(0.484232\pi\)
\(588\) −12.5732 −0.518510
\(589\) −31.1986 −1.28551
\(590\) −27.3728 −1.12692
\(591\) −19.6837 −0.809679
\(592\) 0.397537 0.0163387
\(593\) 8.83218 0.362694 0.181347 0.983419i \(-0.441954\pi\)
0.181347 + 0.983419i \(0.441954\pi\)
\(594\) −18.4873 −0.758543
\(595\) −37.9152 −1.55437
\(596\) −5.00970 −0.205205
\(597\) 10.1492 0.415379
\(598\) −43.7550 −1.78927
\(599\) 19.5942 0.800597 0.400298 0.916385i \(-0.368907\pi\)
0.400298 + 0.916385i \(0.368907\pi\)
\(600\) −8.68141 −0.354417
\(601\) 6.11965 0.249626 0.124813 0.992180i \(-0.460167\pi\)
0.124813 + 0.992180i \(0.460167\pi\)
\(602\) 24.6552 1.00487
\(603\) 11.9898 0.488261
\(604\) −0.804620 −0.0327395
\(605\) 16.9405 0.688731
\(606\) 16.1910 0.657716
\(607\) −11.9210 −0.483859 −0.241930 0.970294i \(-0.577780\pi\)
−0.241930 + 0.970294i \(0.577780\pi\)
\(608\) −5.55126 −0.225133
\(609\) −27.7287 −1.12362
\(610\) 44.5237 1.80271
\(611\) −5.84527 −0.236474
\(612\) 4.73358 0.191344
\(613\) 38.5654 1.55764 0.778821 0.627246i \(-0.215818\pi\)
0.778821 + 0.627246i \(0.215818\pi\)
\(614\) −10.0457 −0.405410
\(615\) −29.4200 −1.18633
\(616\) −17.9324 −0.722515
\(617\) −43.9266 −1.76842 −0.884209 0.467091i \(-0.845302\pi\)
−0.884209 + 0.467091i \(0.845302\pi\)
\(618\) −11.3231 −0.455483
\(619\) 20.8759 0.839075 0.419537 0.907738i \(-0.362192\pi\)
0.419537 + 0.907738i \(0.362192\pi\)
\(620\) 21.4341 0.860816
\(621\) −35.5884 −1.42812
\(622\) 11.5924 0.464814
\(623\) 47.7479 1.91298
\(624\) −5.26062 −0.210593
\(625\) 18.3880 0.735521
\(626\) 17.2100 0.687851
\(627\) −19.8397 −0.792323
\(628\) 5.72338 0.228388
\(629\) −0.866043 −0.0345314
\(630\) −37.8163 −1.50664
\(631\) 15.6536 0.623159 0.311580 0.950220i \(-0.399142\pi\)
0.311580 + 0.950220i \(0.399142\pi\)
\(632\) 4.24090 0.168694
\(633\) −7.05939 −0.280586
\(634\) 13.0661 0.518921
\(635\) −42.1746 −1.67365
\(636\) −3.40213 −0.134903
\(637\) 79.9637 3.16828
\(638\) −26.2541 −1.03941
\(639\) 12.9920 0.513956
\(640\) 3.81385 0.150756
\(641\) −19.6541 −0.776291 −0.388146 0.921598i \(-0.626884\pi\)
−0.388146 + 0.921598i \(0.626884\pi\)
\(642\) −14.8739 −0.587026
\(643\) −33.3120 −1.31370 −0.656849 0.754022i \(-0.728111\pi\)
−0.656849 + 0.754022i \(0.728111\pi\)
\(644\) −34.5202 −1.36029
\(645\) −18.7404 −0.737901
\(646\) 12.0935 0.475814
\(647\) −31.6708 −1.24511 −0.622555 0.782576i \(-0.713905\pi\)
−0.622555 + 0.782576i \(0.713905\pi\)
\(648\) 2.23975 0.0879859
\(649\) 28.2037 1.10709
\(650\) 55.2125 2.16561
\(651\) −23.3252 −0.914187
\(652\) 15.0349 0.588811
\(653\) 12.2492 0.479349 0.239674 0.970853i \(-0.422959\pi\)
0.239674 + 0.970853i \(0.422959\pi\)
\(654\) 14.4780 0.566134
\(655\) −11.0558 −0.431986
\(656\) 8.48174 0.331156
\(657\) 10.6352 0.414918
\(658\) −4.61158 −0.179778
\(659\) 4.75684 0.185300 0.0926501 0.995699i \(-0.470466\pi\)
0.0926501 + 0.995699i \(0.470466\pi\)
\(660\) 13.6304 0.530561
\(661\) 2.45392 0.0954464 0.0477232 0.998861i \(-0.484803\pi\)
0.0477232 + 0.998861i \(0.484803\pi\)
\(662\) 10.6184 0.412697
\(663\) 11.4604 0.445084
\(664\) 5.78317 0.224430
\(665\) −96.6146 −3.74655
\(666\) −0.863784 −0.0334709
\(667\) −50.5397 −1.95690
\(668\) −12.5980 −0.487433
\(669\) −20.8706 −0.806905
\(670\) −21.0449 −0.813034
\(671\) −45.8752 −1.77099
\(672\) −4.15033 −0.160102
\(673\) 18.0457 0.695610 0.347805 0.937567i \(-0.386927\pi\)
0.347805 + 0.937567i \(0.386927\pi\)
\(674\) −2.17168 −0.0836500
\(675\) 44.9075 1.72849
\(676\) 20.4568 0.786799
\(677\) 26.6094 1.02268 0.511341 0.859378i \(-0.329149\pi\)
0.511341 + 0.859378i \(0.329149\pi\)
\(678\) 12.0364 0.462254
\(679\) 15.3950 0.590806
\(680\) −8.30855 −0.318618
\(681\) 18.4776 0.708062
\(682\) −22.0848 −0.845669
\(683\) −28.3101 −1.08326 −0.541628 0.840618i \(-0.682192\pi\)
−0.541628 + 0.840618i \(0.682192\pi\)
\(684\) 12.0620 0.461202
\(685\) −27.4434 −1.04856
\(686\) 31.1431 1.18905
\(687\) −2.13593 −0.0814910
\(688\) 5.40281 0.205980
\(689\) 21.6370 0.824305
\(690\) 26.2388 0.998892
\(691\) −17.2270 −0.655346 −0.327673 0.944791i \(-0.606264\pi\)
−0.327673 + 0.944791i \(0.606264\pi\)
\(692\) −10.9464 −0.416121
\(693\) 38.9642 1.48013
\(694\) −36.4191 −1.38245
\(695\) −40.5284 −1.53733
\(696\) −6.07634 −0.230323
\(697\) −18.4777 −0.699891
\(698\) −21.3196 −0.806959
\(699\) −3.48462 −0.131800
\(700\) 43.5595 1.64640
\(701\) 2.10923 0.0796645 0.0398322 0.999206i \(-0.487318\pi\)
0.0398322 + 0.999206i \(0.487318\pi\)
\(702\) 27.2123 1.02706
\(703\) −2.20683 −0.0832322
\(704\) −3.92961 −0.148103
\(705\) 3.50526 0.132016
\(706\) 29.4288 1.10757
\(707\) −81.2396 −3.05533
\(708\) 6.52757 0.245321
\(709\) −48.2100 −1.81057 −0.905283 0.424810i \(-0.860341\pi\)
−0.905283 + 0.424810i \(0.860341\pi\)
\(710\) −22.8040 −0.855820
\(711\) −9.21480 −0.345582
\(712\) 10.4632 0.392126
\(713\) −42.5136 −1.59215
\(714\) 9.04159 0.338373
\(715\) −86.6872 −3.24192
\(716\) −22.3155 −0.833970
\(717\) 8.02980 0.299878
\(718\) 19.7246 0.736117
\(719\) 40.8658 1.52404 0.762019 0.647554i \(-0.224208\pi\)
0.762019 + 0.647554i \(0.224208\pi\)
\(720\) −8.28688 −0.308834
\(721\) 56.8145 2.11588
\(722\) 11.8165 0.439765
\(723\) 17.8345 0.663273
\(724\) −22.5198 −0.836943
\(725\) 63.7738 2.36850
\(726\) −4.03979 −0.149931
\(727\) −34.1774 −1.26757 −0.633785 0.773509i \(-0.718500\pi\)
−0.633785 + 0.773509i \(0.718500\pi\)
\(728\) 26.3955 0.978282
\(729\) 7.96967 0.295173
\(730\) −18.6673 −0.690906
\(731\) −11.7702 −0.435335
\(732\) −10.6175 −0.392434
\(733\) 14.8200 0.547389 0.273694 0.961817i \(-0.411754\pi\)
0.273694 + 0.961817i \(0.411754\pi\)
\(734\) −10.5181 −0.388232
\(735\) −47.9523 −1.76875
\(736\) −7.56459 −0.278834
\(737\) 21.6837 0.798728
\(738\) −18.4295 −0.678398
\(739\) −6.06416 −0.223074 −0.111537 0.993760i \(-0.535577\pi\)
−0.111537 + 0.993760i \(0.535577\pi\)
\(740\) 1.51614 0.0557346
\(741\) 29.2031 1.07280
\(742\) 17.0704 0.626674
\(743\) −13.9719 −0.512578 −0.256289 0.966600i \(-0.582500\pi\)
−0.256289 + 0.966600i \(0.582500\pi\)
\(744\) −5.11137 −0.187392
\(745\) −19.1062 −0.699998
\(746\) 13.9858 0.512056
\(747\) −12.5659 −0.459762
\(748\) 8.56075 0.313012
\(749\) 74.6307 2.72695
\(750\) −15.7664 −0.575707
\(751\) 5.72999 0.209090 0.104545 0.994520i \(-0.466661\pi\)
0.104545 + 0.994520i \(0.466661\pi\)
\(752\) −1.01056 −0.0368514
\(753\) 15.8079 0.576072
\(754\) 38.6446 1.40735
\(755\) −3.06870 −0.111681
\(756\) 21.4690 0.780820
\(757\) −2.04940 −0.0744867 −0.0372433 0.999306i \(-0.511858\pi\)
−0.0372433 + 0.999306i \(0.511858\pi\)
\(758\) −0.336014 −0.0122046
\(759\) −27.0352 −0.981316
\(760\) −21.1717 −0.767977
\(761\) 29.5508 1.07122 0.535608 0.844467i \(-0.320083\pi\)
0.535608 + 0.844467i \(0.320083\pi\)
\(762\) 10.0573 0.364338
\(763\) −72.6443 −2.62990
\(764\) 14.1797 0.513003
\(765\) 18.0532 0.652713
\(766\) −31.9783 −1.15542
\(767\) −41.5144 −1.49900
\(768\) −0.909483 −0.0328182
\(769\) −27.5950 −0.995101 −0.497550 0.867435i \(-0.665767\pi\)
−0.497550 + 0.867435i \(0.665767\pi\)
\(770\) −68.3913 −2.46465
\(771\) 21.1036 0.760028
\(772\) 12.6187 0.454157
\(773\) 37.3104 1.34196 0.670980 0.741475i \(-0.265874\pi\)
0.670980 + 0.741475i \(0.265874\pi\)
\(774\) −11.7394 −0.421966
\(775\) 53.6461 1.92702
\(776\) 3.37359 0.121105
\(777\) −1.64991 −0.0591901
\(778\) 2.40487 0.0862187
\(779\) −47.0843 −1.68697
\(780\) −20.0632 −0.718377
\(781\) 23.4962 0.840761
\(782\) 16.4796 0.589310
\(783\) 31.4319 1.12328
\(784\) 13.8246 0.493734
\(785\) 21.8281 0.779078
\(786\) 2.63646 0.0940396
\(787\) −45.2340 −1.61242 −0.806208 0.591632i \(-0.798484\pi\)
−0.806208 + 0.591632i \(0.798484\pi\)
\(788\) 21.6427 0.770990
\(789\) −7.61583 −0.271131
\(790\) 16.1741 0.575450
\(791\) −60.3932 −2.14734
\(792\) 8.53842 0.303399
\(793\) 67.5258 2.39791
\(794\) −27.0505 −0.959987
\(795\) −12.9752 −0.460182
\(796\) −11.1593 −0.395531
\(797\) −0.224719 −0.00795995 −0.00397997 0.999992i \(-0.501267\pi\)
−0.00397997 + 0.999992i \(0.501267\pi\)
\(798\) 23.0396 0.815592
\(799\) 2.20153 0.0778845
\(800\) 9.54543 0.337482
\(801\) −22.7349 −0.803300
\(802\) −23.8839 −0.843369
\(803\) 19.2339 0.678749
\(804\) 5.01854 0.176990
\(805\) −131.655 −4.64022
\(806\) 32.5076 1.14503
\(807\) 9.37778 0.330113
\(808\) −17.8025 −0.626288
\(809\) 36.8667 1.29616 0.648081 0.761571i \(-0.275572\pi\)
0.648081 + 0.761571i \(0.275572\pi\)
\(810\) 8.54208 0.300138
\(811\) 16.8995 0.593422 0.296711 0.954967i \(-0.404110\pi\)
0.296711 + 0.954967i \(0.404110\pi\)
\(812\) 30.4884 1.06993
\(813\) 5.83929 0.204793
\(814\) −1.56216 −0.0547538
\(815\) 57.3407 2.00856
\(816\) 1.98133 0.0693604
\(817\) −29.9924 −1.04930
\(818\) −30.0686 −1.05132
\(819\) −57.3532 −2.00408
\(820\) 32.3480 1.12964
\(821\) 54.0454 1.88620 0.943099 0.332511i \(-0.107896\pi\)
0.943099 + 0.332511i \(0.107896\pi\)
\(822\) 6.54439 0.228262
\(823\) 35.7657 1.24671 0.623356 0.781938i \(-0.285769\pi\)
0.623356 + 0.781938i \(0.285769\pi\)
\(824\) 12.4501 0.433718
\(825\) 34.1146 1.18772
\(826\) −32.7525 −1.13961
\(827\) 25.8396 0.898529 0.449265 0.893399i \(-0.351686\pi\)
0.449265 + 0.893399i \(0.351686\pi\)
\(828\) 16.4366 0.571213
\(829\) 4.81028 0.167068 0.0835340 0.996505i \(-0.473379\pi\)
0.0835340 + 0.996505i \(0.473379\pi\)
\(830\) 22.0561 0.765579
\(831\) −22.6893 −0.787083
\(832\) 5.78418 0.200530
\(833\) −30.1171 −1.04350
\(834\) 9.66476 0.334663
\(835\) −48.0470 −1.66274
\(836\) 21.8143 0.754463
\(837\) 26.4403 0.913911
\(838\) 24.9649 0.862400
\(839\) −47.9438 −1.65520 −0.827602 0.561316i \(-0.810295\pi\)
−0.827602 + 0.561316i \(0.810295\pi\)
\(840\) −15.8287 −0.546143
\(841\) 15.6369 0.539203
\(842\) −38.4558 −1.32528
\(843\) 15.6052 0.537471
\(844\) 7.76198 0.267178
\(845\) 78.0190 2.68394
\(846\) 2.19579 0.0754927
\(847\) 20.2699 0.696482
\(848\) 3.74072 0.128457
\(849\) −14.3604 −0.492848
\(850\) −20.7949 −0.713260
\(851\) −3.00720 −0.103086
\(852\) 5.43805 0.186304
\(853\) −7.81110 −0.267447 −0.133723 0.991019i \(-0.542693\pi\)
−0.133723 + 0.991019i \(0.542693\pi\)
\(854\) 53.2741 1.82300
\(855\) 46.0026 1.57326
\(856\) 16.3542 0.558976
\(857\) −47.2741 −1.61485 −0.807427 0.589968i \(-0.799140\pi\)
−0.807427 + 0.589968i \(0.799140\pi\)
\(858\) 20.6722 0.705737
\(859\) 9.76098 0.333040 0.166520 0.986038i \(-0.446747\pi\)
0.166520 + 0.986038i \(0.446747\pi\)
\(860\) 20.6055 0.702642
\(861\) −35.2020 −1.19968
\(862\) 8.85993 0.301770
\(863\) 15.4772 0.526849 0.263424 0.964680i \(-0.415148\pi\)
0.263424 + 0.964680i \(0.415148\pi\)
\(864\) 4.70461 0.160054
\(865\) −41.7480 −1.41948
\(866\) 25.2853 0.859229
\(867\) 11.1448 0.378499
\(868\) 25.6467 0.870504
\(869\) −16.6651 −0.565325
\(870\) −23.1742 −0.785679
\(871\) −31.9172 −1.08147
\(872\) −15.9189 −0.539083
\(873\) −7.33026 −0.248092
\(874\) 41.9930 1.42043
\(875\) 79.1089 2.67437
\(876\) 4.45156 0.150404
\(877\) 21.5246 0.726833 0.363416 0.931627i \(-0.381610\pi\)
0.363416 + 0.931627i \(0.381610\pi\)
\(878\) 20.3042 0.685234
\(879\) 10.6549 0.359380
\(880\) −14.9869 −0.505210
\(881\) 13.7560 0.463452 0.231726 0.972781i \(-0.425563\pi\)
0.231726 + 0.972781i \(0.425563\pi\)
\(882\) −30.0385 −1.01145
\(883\) −28.8034 −0.969313 −0.484657 0.874705i \(-0.661055\pi\)
−0.484657 + 0.874705i \(0.661055\pi\)
\(884\) −12.6010 −0.423817
\(885\) 24.8951 0.836841
\(886\) −22.8603 −0.768007
\(887\) 18.0592 0.606368 0.303184 0.952932i \(-0.401950\pi\)
0.303184 + 0.952932i \(0.401950\pi\)
\(888\) −0.361553 −0.0121329
\(889\) −50.4632 −1.69248
\(890\) 39.9052 1.33762
\(891\) −8.80137 −0.294857
\(892\) 22.9478 0.768349
\(893\) 5.60989 0.187728
\(894\) 4.55624 0.152383
\(895\) −85.1079 −2.84484
\(896\) 4.56339 0.152452
\(897\) 39.7944 1.32870
\(898\) 3.91945 0.130794
\(899\) 37.5483 1.25230
\(900\) −20.7407 −0.691356
\(901\) −8.14925 −0.271491
\(902\) −33.3299 −1.10977
\(903\) −22.4235 −0.746206
\(904\) −13.2343 −0.440166
\(905\) −85.8872 −2.85499
\(906\) 0.731788 0.0243120
\(907\) −12.0731 −0.400882 −0.200441 0.979706i \(-0.564238\pi\)
−0.200441 + 0.979706i \(0.564238\pi\)
\(908\) −20.3165 −0.674228
\(909\) 38.6819 1.28300
\(910\) 100.668 3.33712
\(911\) 24.8199 0.822318 0.411159 0.911564i \(-0.365124\pi\)
0.411159 + 0.911564i \(0.365124\pi\)
\(912\) 5.04878 0.167182
\(913\) −22.7256 −0.752108
\(914\) 27.2179 0.900287
\(915\) −40.4936 −1.33868
\(916\) 2.34851 0.0775971
\(917\) −13.2286 −0.436848
\(918\) −10.2491 −0.338271
\(919\) −11.5691 −0.381630 −0.190815 0.981626i \(-0.561113\pi\)
−0.190815 + 0.981626i \(0.561113\pi\)
\(920\) −28.8502 −0.951162
\(921\) 9.13635 0.301053
\(922\) 24.7940 0.816545
\(923\) −34.5852 −1.13839
\(924\) 16.3092 0.536533
\(925\) 3.79466 0.124768
\(926\) −37.4416 −1.23041
\(927\) −27.0520 −0.888504
\(928\) 6.68108 0.219317
\(929\) −38.6469 −1.26796 −0.633981 0.773348i \(-0.718580\pi\)
−0.633981 + 0.773348i \(0.718580\pi\)
\(930\) −19.4940 −0.639233
\(931\) −76.7437 −2.51517
\(932\) 3.83142 0.125502
\(933\) −10.5431 −0.345166
\(934\) 9.78265 0.320098
\(935\) 32.6494 1.06775
\(936\) −12.5681 −0.410801
\(937\) 32.3885 1.05809 0.529044 0.848595i \(-0.322551\pi\)
0.529044 + 0.848595i \(0.322551\pi\)
\(938\) −25.1809 −0.822185
\(939\) −15.6522 −0.510792
\(940\) −3.85412 −0.125708
\(941\) 18.1171 0.590600 0.295300 0.955405i \(-0.404580\pi\)
0.295300 + 0.955405i \(0.404580\pi\)
\(942\) −5.20532 −0.169598
\(943\) −64.1608 −2.08936
\(944\) −7.17723 −0.233599
\(945\) 81.8794 2.66354
\(946\) −21.2310 −0.690278
\(947\) 29.7221 0.965838 0.482919 0.875665i \(-0.339577\pi\)
0.482919 + 0.875665i \(0.339577\pi\)
\(948\) −3.85703 −0.125270
\(949\) −28.3113 −0.919023
\(950\) −52.9892 −1.71920
\(951\) −11.8834 −0.385346
\(952\) −9.94145 −0.322204
\(953\) −10.2263 −0.331262 −0.165631 0.986188i \(-0.552966\pi\)
−0.165631 + 0.986188i \(0.552966\pi\)
\(954\) −8.12800 −0.263154
\(955\) 54.0792 1.74996
\(956\) −8.82897 −0.285549
\(957\) 23.8776 0.771854
\(958\) −36.4494 −1.17763
\(959\) −32.8369 −1.06036
\(960\) −3.46863 −0.111950
\(961\) 0.585355 0.0188824
\(962\) 2.29942 0.0741364
\(963\) −35.5351 −1.14510
\(964\) −19.6095 −0.631580
\(965\) 48.1258 1.54923
\(966\) 31.3955 1.01013
\(967\) 24.6241 0.791859 0.395929 0.918281i \(-0.370423\pi\)
0.395929 + 0.918281i \(0.370423\pi\)
\(968\) 4.44185 0.142766
\(969\) −10.9989 −0.353335
\(970\) 12.8663 0.413113
\(971\) −7.14985 −0.229450 −0.114725 0.993397i \(-0.536599\pi\)
−0.114725 + 0.993397i \(0.536599\pi\)
\(972\) −16.1509 −0.518039
\(973\) −48.4936 −1.55463
\(974\) −22.2659 −0.713447
\(975\) −50.2148 −1.60816
\(976\) 11.6742 0.373683
\(977\) −34.0124 −1.08815 −0.544076 0.839036i \(-0.683120\pi\)
−0.544076 + 0.839036i \(0.683120\pi\)
\(978\) −13.6740 −0.437245
\(979\) −41.1165 −1.31409
\(980\) 52.7247 1.68423
\(981\) 34.5893 1.10435
\(982\) 9.30011 0.296779
\(983\) 19.8462 0.632996 0.316498 0.948593i \(-0.397493\pi\)
0.316498 + 0.948593i \(0.397493\pi\)
\(984\) −7.71400 −0.245913
\(985\) 82.5420 2.63001
\(986\) −14.5549 −0.463522
\(987\) 4.19416 0.133502
\(988\) −32.1095 −1.02154
\(989\) −40.8701 −1.29959
\(990\) 32.5642 1.03496
\(991\) 2.96887 0.0943094 0.0471547 0.998888i \(-0.484985\pi\)
0.0471547 + 0.998888i \(0.484985\pi\)
\(992\) 5.62008 0.178438
\(993\) −9.65729 −0.306465
\(994\) −27.2858 −0.865452
\(995\) −42.5599 −1.34924
\(996\) −5.25969 −0.166660
\(997\) −43.3553 −1.37308 −0.686538 0.727094i \(-0.740871\pi\)
−0.686538 + 0.727094i \(0.740871\pi\)
\(998\) 15.8834 0.502782
\(999\) 1.87026 0.0591723
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 4034.2.a.d.1.17 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.17 52 1.1 even 1 trivial