Properties

Label 6001.2.a.d.1.20
Level 6001
Weight 2
Character 6001.1
Self dual yes
Analytic conductor 47.918
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9182262530\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.98791 q^{2} +3.32266 q^{3} +1.95179 q^{4} +2.27659 q^{5} -6.60516 q^{6} +3.45158 q^{7} +0.0958417 q^{8} +8.04010 q^{9} +O(q^{10})\) \(q-1.98791 q^{2} +3.32266 q^{3} +1.95179 q^{4} +2.27659 q^{5} -6.60516 q^{6} +3.45158 q^{7} +0.0958417 q^{8} +8.04010 q^{9} -4.52565 q^{10} +6.11215 q^{11} +6.48514 q^{12} -0.519759 q^{13} -6.86143 q^{14} +7.56433 q^{15} -4.09410 q^{16} +1.00000 q^{17} -15.9830 q^{18} -2.29689 q^{19} +4.44341 q^{20} +11.4684 q^{21} -12.1504 q^{22} -3.58377 q^{23} +0.318450 q^{24} +0.182842 q^{25} +1.03323 q^{26} +16.7466 q^{27} +6.73675 q^{28} -8.65933 q^{29} -15.0372 q^{30} +5.26218 q^{31} +7.94702 q^{32} +20.3086 q^{33} -1.98791 q^{34} +7.85781 q^{35} +15.6926 q^{36} -0.510060 q^{37} +4.56602 q^{38} -1.72698 q^{39} +0.218192 q^{40} -7.51375 q^{41} -22.7982 q^{42} -9.58623 q^{43} +11.9296 q^{44} +18.3040 q^{45} +7.12422 q^{46} -8.88367 q^{47} -13.6033 q^{48} +4.91339 q^{49} -0.363474 q^{50} +3.32266 q^{51} -1.01446 q^{52} +2.49427 q^{53} -33.2906 q^{54} +13.9148 q^{55} +0.330805 q^{56} -7.63181 q^{57} +17.2140 q^{58} -12.5070 q^{59} +14.7640 q^{60} +8.80445 q^{61} -10.4607 q^{62} +27.7510 q^{63} -7.60976 q^{64} -1.18328 q^{65} -40.3717 q^{66} +14.5651 q^{67} +1.95179 q^{68} -11.9077 q^{69} -15.6206 q^{70} +13.0879 q^{71} +0.770577 q^{72} -1.80598 q^{73} +1.01395 q^{74} +0.607523 q^{75} -4.48305 q^{76} +21.0966 q^{77} +3.43309 q^{78} -7.14739 q^{79} -9.32057 q^{80} +31.5229 q^{81} +14.9367 q^{82} +8.73442 q^{83} +22.3839 q^{84} +2.27659 q^{85} +19.0566 q^{86} -28.7720 q^{87} +0.585799 q^{88} +3.08245 q^{89} -36.3867 q^{90} -1.79399 q^{91} -6.99477 q^{92} +17.4844 q^{93} +17.6599 q^{94} -5.22908 q^{95} +26.4053 q^{96} -10.9579 q^{97} -9.76738 q^{98} +49.1423 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.98791 −1.40566 −0.702832 0.711355i \(-0.748082\pi\)
−0.702832 + 0.711355i \(0.748082\pi\)
\(3\) 3.32266 1.91834 0.959171 0.282828i \(-0.0912727\pi\)
0.959171 + 0.282828i \(0.0912727\pi\)
\(4\) 1.95179 0.975894
\(5\) 2.27659 1.01812 0.509060 0.860731i \(-0.329993\pi\)
0.509060 + 0.860731i \(0.329993\pi\)
\(6\) −6.60516 −2.69654
\(7\) 3.45158 1.30457 0.652287 0.757972i \(-0.273810\pi\)
0.652287 + 0.757972i \(0.273810\pi\)
\(8\) 0.0958417 0.0338852
\(9\) 8.04010 2.68003
\(10\) −4.52565 −1.43114
\(11\) 6.11215 1.84288 0.921442 0.388517i \(-0.127012\pi\)
0.921442 + 0.388517i \(0.127012\pi\)
\(12\) 6.48514 1.87210
\(13\) −0.519759 −0.144155 −0.0720776 0.997399i \(-0.522963\pi\)
−0.0720776 + 0.997399i \(0.522963\pi\)
\(14\) −6.86143 −1.83379
\(15\) 7.56433 1.95310
\(16\) −4.09410 −1.02353
\(17\) 1.00000 0.242536
\(18\) −15.9830 −3.76723
\(19\) −2.29689 −0.526944 −0.263472 0.964667i \(-0.584868\pi\)
−0.263472 + 0.964667i \(0.584868\pi\)
\(20\) 4.44341 0.993577
\(21\) 11.4684 2.50262
\(22\) −12.1504 −2.59048
\(23\) −3.58377 −0.747269 −0.373634 0.927576i \(-0.621889\pi\)
−0.373634 + 0.927576i \(0.621889\pi\)
\(24\) 0.318450 0.0650033
\(25\) 0.182842 0.0365685
\(26\) 1.03323 0.202634
\(27\) 16.7466 3.22288
\(28\) 6.73675 1.27313
\(29\) −8.65933 −1.60800 −0.803998 0.594632i \(-0.797298\pi\)
−0.803998 + 0.594632i \(0.797298\pi\)
\(30\) −15.0372 −2.74541
\(31\) 5.26218 0.945115 0.472557 0.881300i \(-0.343331\pi\)
0.472557 + 0.881300i \(0.343331\pi\)
\(32\) 7.94702 1.40485
\(33\) 20.3086 3.53528
\(34\) −1.98791 −0.340924
\(35\) 7.85781 1.32821
\(36\) 15.6926 2.61543
\(37\) −0.510060 −0.0838534 −0.0419267 0.999121i \(-0.513350\pi\)
−0.0419267 + 0.999121i \(0.513350\pi\)
\(38\) 4.56602 0.740706
\(39\) −1.72698 −0.276539
\(40\) 0.218192 0.0344992
\(41\) −7.51375 −1.17345 −0.586726 0.809786i \(-0.699583\pi\)
−0.586726 + 0.809786i \(0.699583\pi\)
\(42\) −22.7982 −3.51784
\(43\) −9.58623 −1.46189 −0.730943 0.682438i \(-0.760920\pi\)
−0.730943 + 0.682438i \(0.760920\pi\)
\(44\) 11.9296 1.79846
\(45\) 18.3040 2.72859
\(46\) 7.12422 1.05041
\(47\) −8.88367 −1.29582 −0.647908 0.761718i \(-0.724356\pi\)
−0.647908 + 0.761718i \(0.724356\pi\)
\(48\) −13.6033 −1.96347
\(49\) 4.91339 0.701913
\(50\) −0.363474 −0.0514030
\(51\) 3.32266 0.465266
\(52\) −1.01446 −0.140680
\(53\) 2.49427 0.342615 0.171307 0.985218i \(-0.445201\pi\)
0.171307 + 0.985218i \(0.445201\pi\)
\(54\) −33.2906 −4.53028
\(55\) 13.9148 1.87628
\(56\) 0.330805 0.0442057
\(57\) −7.63181 −1.01086
\(58\) 17.2140 2.26030
\(59\) −12.5070 −1.62827 −0.814136 0.580674i \(-0.802789\pi\)
−0.814136 + 0.580674i \(0.802789\pi\)
\(60\) 14.7640 1.90602
\(61\) 8.80445 1.12729 0.563647 0.826016i \(-0.309398\pi\)
0.563647 + 0.826016i \(0.309398\pi\)
\(62\) −10.4607 −1.32851
\(63\) 27.7510 3.49630
\(64\) −7.60976 −0.951221
\(65\) −1.18328 −0.146767
\(66\) −40.3717 −4.96942
\(67\) 14.5651 1.77941 0.889704 0.456537i \(-0.150910\pi\)
0.889704 + 0.456537i \(0.150910\pi\)
\(68\) 1.95179 0.236689
\(69\) −11.9077 −1.43352
\(70\) −15.6206 −1.86702
\(71\) 13.0879 1.55325 0.776626 0.629962i \(-0.216930\pi\)
0.776626 + 0.629962i \(0.216930\pi\)
\(72\) 0.770577 0.0908134
\(73\) −1.80598 −0.211374 −0.105687 0.994399i \(-0.533704\pi\)
−0.105687 + 0.994399i \(0.533704\pi\)
\(74\) 1.01395 0.117870
\(75\) 0.607523 0.0701508
\(76\) −4.48305 −0.514241
\(77\) 21.0966 2.40418
\(78\) 3.43309 0.388721
\(79\) −7.14739 −0.804144 −0.402072 0.915608i \(-0.631710\pi\)
−0.402072 + 0.915608i \(0.631710\pi\)
\(80\) −9.32057 −1.04207
\(81\) 31.5229 3.50254
\(82\) 14.9367 1.64948
\(83\) 8.73442 0.958727 0.479364 0.877616i \(-0.340867\pi\)
0.479364 + 0.877616i \(0.340867\pi\)
\(84\) 22.3839 2.44229
\(85\) 2.27659 0.246930
\(86\) 19.0566 2.05492
\(87\) −28.7720 −3.08469
\(88\) 0.585799 0.0624464
\(89\) 3.08245 0.326740 0.163370 0.986565i \(-0.447764\pi\)
0.163370 + 0.986565i \(0.447764\pi\)
\(90\) −36.3867 −3.83549
\(91\) −1.79399 −0.188061
\(92\) −6.99477 −0.729255
\(93\) 17.4844 1.81305
\(94\) 17.6599 1.82148
\(95\) −5.22908 −0.536492
\(96\) 26.4053 2.69498
\(97\) −10.9579 −1.11261 −0.556303 0.830979i \(-0.687781\pi\)
−0.556303 + 0.830979i \(0.687781\pi\)
\(98\) −9.76738 −0.986654
\(99\) 49.1423 4.93899
\(100\) 0.356869 0.0356869
\(101\) 1.58029 0.157245 0.0786226 0.996904i \(-0.474948\pi\)
0.0786226 + 0.996904i \(0.474948\pi\)
\(102\) −6.60516 −0.654008
\(103\) −9.32901 −0.919214 −0.459607 0.888122i \(-0.652010\pi\)
−0.459607 + 0.888122i \(0.652010\pi\)
\(104\) −0.0498146 −0.00488472
\(105\) 26.1089 2.54797
\(106\) −4.95839 −0.481602
\(107\) 17.5778 1.69931 0.849654 0.527340i \(-0.176811\pi\)
0.849654 + 0.527340i \(0.176811\pi\)
\(108\) 32.6857 3.14518
\(109\) −3.85129 −0.368886 −0.184443 0.982843i \(-0.559048\pi\)
−0.184443 + 0.982843i \(0.559048\pi\)
\(110\) −27.6615 −2.63742
\(111\) −1.69476 −0.160859
\(112\) −14.1311 −1.33526
\(113\) 2.91228 0.273964 0.136982 0.990574i \(-0.456260\pi\)
0.136982 + 0.990574i \(0.456260\pi\)
\(114\) 15.1714 1.42093
\(115\) −8.15877 −0.760809
\(116\) −16.9012 −1.56923
\(117\) −4.17891 −0.386341
\(118\) 24.8628 2.28881
\(119\) 3.45158 0.316406
\(120\) 0.724979 0.0661812
\(121\) 26.3584 2.39622
\(122\) −17.5025 −1.58460
\(123\) −24.9657 −2.25108
\(124\) 10.2707 0.922332
\(125\) −10.9667 −0.980889
\(126\) −55.1665 −4.91463
\(127\) 4.18509 0.371366 0.185683 0.982610i \(-0.440550\pi\)
0.185683 + 0.982610i \(0.440550\pi\)
\(128\) −0.766511 −0.0677507
\(129\) −31.8518 −2.80440
\(130\) 2.35225 0.206306
\(131\) −20.6711 −1.80604 −0.903022 0.429594i \(-0.858657\pi\)
−0.903022 + 0.429594i \(0.858657\pi\)
\(132\) 39.6381 3.45006
\(133\) −7.92791 −0.687437
\(134\) −28.9541 −2.50125
\(135\) 38.1250 3.28127
\(136\) 0.0958417 0.00821836
\(137\) −15.3648 −1.31270 −0.656352 0.754454i \(-0.727902\pi\)
−0.656352 + 0.754454i \(0.727902\pi\)
\(138\) 23.6714 2.01504
\(139\) 5.52109 0.468292 0.234146 0.972201i \(-0.424771\pi\)
0.234146 + 0.972201i \(0.424771\pi\)
\(140\) 15.3368 1.29619
\(141\) −29.5175 −2.48582
\(142\) −26.0176 −2.18335
\(143\) −3.17685 −0.265661
\(144\) −32.9170 −2.74308
\(145\) −19.7137 −1.63713
\(146\) 3.59013 0.297122
\(147\) 16.3255 1.34651
\(148\) −0.995529 −0.0818320
\(149\) −12.1874 −0.998431 −0.499216 0.866478i \(-0.666378\pi\)
−0.499216 + 0.866478i \(0.666378\pi\)
\(150\) −1.20770 −0.0986085
\(151\) −2.77927 −0.226173 −0.113087 0.993585i \(-0.536074\pi\)
−0.113087 + 0.993585i \(0.536074\pi\)
\(152\) −0.220138 −0.0178556
\(153\) 8.04010 0.650003
\(154\) −41.9381 −3.37947
\(155\) 11.9798 0.962240
\(156\) −3.37071 −0.269873
\(157\) 17.3186 1.38218 0.691089 0.722770i \(-0.257131\pi\)
0.691089 + 0.722770i \(0.257131\pi\)
\(158\) 14.2084 1.13036
\(159\) 8.28763 0.657252
\(160\) 18.0921 1.43030
\(161\) −12.3697 −0.974867
\(162\) −62.6647 −4.92340
\(163\) −4.76349 −0.373105 −0.186553 0.982445i \(-0.559732\pi\)
−0.186553 + 0.982445i \(0.559732\pi\)
\(164\) −14.6653 −1.14516
\(165\) 46.2343 3.59934
\(166\) −17.3632 −1.34765
\(167\) 14.1762 1.09699 0.548495 0.836154i \(-0.315201\pi\)
0.548495 + 0.836154i \(0.315201\pi\)
\(168\) 1.09915 0.0848016
\(169\) −12.7299 −0.979219
\(170\) −4.52565 −0.347101
\(171\) −18.4673 −1.41223
\(172\) −18.7103 −1.42665
\(173\) −3.29081 −0.250196 −0.125098 0.992144i \(-0.539924\pi\)
−0.125098 + 0.992144i \(0.539924\pi\)
\(174\) 57.1962 4.33604
\(175\) 0.631094 0.0477062
\(176\) −25.0238 −1.88624
\(177\) −41.5566 −3.12358
\(178\) −6.12764 −0.459286
\(179\) 18.8422 1.40834 0.704168 0.710034i \(-0.251320\pi\)
0.704168 + 0.710034i \(0.251320\pi\)
\(180\) 35.7255 2.66282
\(181\) 23.9360 1.77915 0.889574 0.456791i \(-0.151001\pi\)
0.889574 + 0.456791i \(0.151001\pi\)
\(182\) 3.56629 0.264351
\(183\) 29.2542 2.16254
\(184\) −0.343475 −0.0253213
\(185\) −1.16120 −0.0853728
\(186\) −34.7575 −2.54854
\(187\) 6.11215 0.446965
\(188\) −17.3390 −1.26458
\(189\) 57.8020 4.20448
\(190\) 10.3949 0.754128
\(191\) −5.68454 −0.411319 −0.205659 0.978624i \(-0.565934\pi\)
−0.205659 + 0.978624i \(0.565934\pi\)
\(192\) −25.2847 −1.82477
\(193\) −4.23541 −0.304872 −0.152436 0.988313i \(-0.548712\pi\)
−0.152436 + 0.988313i \(0.548712\pi\)
\(194\) 21.7833 1.56395
\(195\) −3.93163 −0.281550
\(196\) 9.58989 0.684992
\(197\) 27.6564 1.97044 0.985219 0.171298i \(-0.0547961\pi\)
0.985219 + 0.171298i \(0.0547961\pi\)
\(198\) −97.6905 −6.94256
\(199\) −12.1198 −0.859152 −0.429576 0.903031i \(-0.641337\pi\)
−0.429576 + 0.903031i \(0.641337\pi\)
\(200\) 0.0175239 0.00123913
\(201\) 48.3949 3.41351
\(202\) −3.14148 −0.221034
\(203\) −29.8883 −2.09775
\(204\) 6.48514 0.454050
\(205\) −17.1057 −1.19471
\(206\) 18.5452 1.29211
\(207\) −28.8139 −2.00270
\(208\) 2.12795 0.147546
\(209\) −14.0390 −0.971096
\(210\) −51.9021 −3.58159
\(211\) −1.67037 −0.114993 −0.0574964 0.998346i \(-0.518312\pi\)
−0.0574964 + 0.998346i \(0.518312\pi\)
\(212\) 4.86829 0.334356
\(213\) 43.4868 2.97967
\(214\) −34.9431 −2.38866
\(215\) −21.8239 −1.48838
\(216\) 1.60502 0.109208
\(217\) 18.1628 1.23297
\(218\) 7.65602 0.518531
\(219\) −6.00068 −0.405488
\(220\) 27.1588 1.83105
\(221\) −0.519759 −0.0349628
\(222\) 3.36903 0.226114
\(223\) −16.6458 −1.11468 −0.557342 0.830283i \(-0.688179\pi\)
−0.557342 + 0.830283i \(0.688179\pi\)
\(224\) 27.4298 1.83273
\(225\) 1.47007 0.0980047
\(226\) −5.78935 −0.385102
\(227\) −20.0237 −1.32902 −0.664509 0.747281i \(-0.731359\pi\)
−0.664509 + 0.747281i \(0.731359\pi\)
\(228\) −14.8957 −0.986490
\(229\) 20.9662 1.38549 0.692743 0.721185i \(-0.256402\pi\)
0.692743 + 0.721185i \(0.256402\pi\)
\(230\) 16.2189 1.06944
\(231\) 70.0968 4.61203
\(232\) −0.829925 −0.0544872
\(233\) 4.78629 0.313560 0.156780 0.987634i \(-0.449889\pi\)
0.156780 + 0.987634i \(0.449889\pi\)
\(234\) 8.30731 0.543066
\(235\) −20.2244 −1.31930
\(236\) −24.4110 −1.58902
\(237\) −23.7484 −1.54262
\(238\) −6.86143 −0.444760
\(239\) 10.5393 0.681733 0.340866 0.940112i \(-0.389280\pi\)
0.340866 + 0.940112i \(0.389280\pi\)
\(240\) −30.9691 −1.99905
\(241\) −21.7438 −1.40064 −0.700321 0.713828i \(-0.746960\pi\)
−0.700321 + 0.713828i \(0.746960\pi\)
\(242\) −52.3981 −3.36828
\(243\) 54.5003 3.49619
\(244\) 17.1844 1.10012
\(245\) 11.1858 0.714631
\(246\) 49.6295 3.16426
\(247\) 1.19383 0.0759617
\(248\) 0.504336 0.0320254
\(249\) 29.0216 1.83917
\(250\) 21.8008 1.37880
\(251\) 6.16434 0.389090 0.194545 0.980894i \(-0.437677\pi\)
0.194545 + 0.980894i \(0.437677\pi\)
\(252\) 54.1641 3.41202
\(253\) −21.9046 −1.37713
\(254\) −8.31958 −0.522017
\(255\) 7.56433 0.473697
\(256\) 16.7433 1.04646
\(257\) −11.3099 −0.705495 −0.352748 0.935719i \(-0.614753\pi\)
−0.352748 + 0.935719i \(0.614753\pi\)
\(258\) 63.3186 3.94204
\(259\) −1.76051 −0.109393
\(260\) −2.30950 −0.143229
\(261\) −69.6218 −4.30948
\(262\) 41.0923 2.53869
\(263\) −9.99459 −0.616293 −0.308146 0.951339i \(-0.599709\pi\)
−0.308146 + 0.951339i \(0.599709\pi\)
\(264\) 1.94641 0.119794
\(265\) 5.67843 0.348823
\(266\) 15.7600 0.966306
\(267\) 10.2420 0.626798
\(268\) 28.4280 1.73651
\(269\) 9.84186 0.600069 0.300034 0.953928i \(-0.403002\pi\)
0.300034 + 0.953928i \(0.403002\pi\)
\(270\) −75.7890 −4.61237
\(271\) −22.4923 −1.36631 −0.683153 0.730275i \(-0.739392\pi\)
−0.683153 + 0.730275i \(0.739392\pi\)
\(272\) −4.09410 −0.248241
\(273\) −5.96082 −0.360765
\(274\) 30.5439 1.84522
\(275\) 1.11756 0.0673914
\(276\) −23.2413 −1.39896
\(277\) −25.0668 −1.50612 −0.753058 0.657954i \(-0.771422\pi\)
−0.753058 + 0.657954i \(0.771422\pi\)
\(278\) −10.9754 −0.658262
\(279\) 42.3084 2.53294
\(280\) 0.753106 0.0450067
\(281\) −19.3328 −1.15330 −0.576649 0.816992i \(-0.695640\pi\)
−0.576649 + 0.816992i \(0.695640\pi\)
\(282\) 58.6781 3.49423
\(283\) 8.00938 0.476108 0.238054 0.971252i \(-0.423490\pi\)
0.238054 + 0.971252i \(0.423490\pi\)
\(284\) 25.5449 1.51581
\(285\) −17.3745 −1.02917
\(286\) 6.31529 0.373431
\(287\) −25.9343 −1.53085
\(288\) 63.8948 3.76504
\(289\) 1.00000 0.0588235
\(290\) 39.1891 2.30126
\(291\) −36.4094 −2.13436
\(292\) −3.52490 −0.206279
\(293\) −8.26867 −0.483061 −0.241530 0.970393i \(-0.577649\pi\)
−0.241530 + 0.970393i \(0.577649\pi\)
\(294\) −32.4537 −1.89274
\(295\) −28.4732 −1.65778
\(296\) −0.0488851 −0.00284139
\(297\) 102.357 5.93938
\(298\) 24.2275 1.40346
\(299\) 1.86270 0.107723
\(300\) 1.18576 0.0684597
\(301\) −33.0876 −1.90714
\(302\) 5.52493 0.317924
\(303\) 5.25079 0.301650
\(304\) 9.40371 0.539340
\(305\) 20.0441 1.14772
\(306\) −15.9830 −0.913687
\(307\) −24.4083 −1.39306 −0.696529 0.717529i \(-0.745273\pi\)
−0.696529 + 0.717529i \(0.745273\pi\)
\(308\) 41.1760 2.34622
\(309\) −30.9972 −1.76337
\(310\) −23.8148 −1.35259
\(311\) 11.7842 0.668222 0.334111 0.942534i \(-0.391564\pi\)
0.334111 + 0.942534i \(0.391564\pi\)
\(312\) −0.165517 −0.00937057
\(313\) −1.55691 −0.0880020 −0.0440010 0.999031i \(-0.514010\pi\)
−0.0440010 + 0.999031i \(0.514010\pi\)
\(314\) −34.4279 −1.94288
\(315\) 63.1776 3.55965
\(316\) −13.9502 −0.784759
\(317\) 20.6816 1.16159 0.580797 0.814048i \(-0.302741\pi\)
0.580797 + 0.814048i \(0.302741\pi\)
\(318\) −16.4751 −0.923876
\(319\) −52.9271 −2.96335
\(320\) −17.3243 −0.968457
\(321\) 58.4051 3.25985
\(322\) 24.5898 1.37034
\(323\) −2.29689 −0.127803
\(324\) 61.5260 3.41811
\(325\) −0.0950339 −0.00527153
\(326\) 9.46939 0.524461
\(327\) −12.7965 −0.707650
\(328\) −0.720131 −0.0397626
\(329\) −30.6627 −1.69049
\(330\) −91.9097 −5.05946
\(331\) 11.4097 0.627135 0.313567 0.949566i \(-0.398476\pi\)
0.313567 + 0.949566i \(0.398476\pi\)
\(332\) 17.0477 0.935616
\(333\) −4.10093 −0.224730
\(334\) −28.1811 −1.54200
\(335\) 33.1587 1.81165
\(336\) −46.9529 −2.56149
\(337\) 4.08606 0.222582 0.111291 0.993788i \(-0.464501\pi\)
0.111291 + 0.993788i \(0.464501\pi\)
\(338\) 25.3058 1.37645
\(339\) 9.67652 0.525557
\(340\) 4.44341 0.240978
\(341\) 32.1632 1.74174
\(342\) 36.7112 1.98512
\(343\) −7.20210 −0.388877
\(344\) −0.918761 −0.0495363
\(345\) −27.1089 −1.45949
\(346\) 6.54183 0.351691
\(347\) 10.3687 0.556622 0.278311 0.960491i \(-0.410225\pi\)
0.278311 + 0.960491i \(0.410225\pi\)
\(348\) −56.1569 −3.01033
\(349\) 24.9847 1.33740 0.668700 0.743532i \(-0.266851\pi\)
0.668700 + 0.743532i \(0.266851\pi\)
\(350\) −1.25456 −0.0670590
\(351\) −8.70417 −0.464594
\(352\) 48.5734 2.58897
\(353\) −1.00000 −0.0532246
\(354\) 82.6107 4.39071
\(355\) 29.7958 1.58140
\(356\) 6.01630 0.318863
\(357\) 11.4684 0.606974
\(358\) −37.4567 −1.97965
\(359\) −4.28903 −0.226366 −0.113183 0.993574i \(-0.536105\pi\)
−0.113183 + 0.993574i \(0.536105\pi\)
\(360\) 1.75428 0.0924589
\(361\) −13.7243 −0.722330
\(362\) −47.5826 −2.50089
\(363\) 87.5801 4.59676
\(364\) −3.50149 −0.183528
\(365\) −4.11148 −0.215205
\(366\) −58.1548 −3.03980
\(367\) 1.52370 0.0795362 0.0397681 0.999209i \(-0.487338\pi\)
0.0397681 + 0.999209i \(0.487338\pi\)
\(368\) 14.6723 0.764848
\(369\) −60.4113 −3.14489
\(370\) 2.30835 0.120006
\(371\) 8.60918 0.446966
\(372\) 34.1259 1.76935
\(373\) −9.41826 −0.487659 −0.243830 0.969818i \(-0.578404\pi\)
−0.243830 + 0.969818i \(0.578404\pi\)
\(374\) −12.1504 −0.628283
\(375\) −36.4386 −1.88168
\(376\) −0.851427 −0.0439090
\(377\) 4.50076 0.231801
\(378\) −114.905 −5.91009
\(379\) 8.75710 0.449822 0.224911 0.974379i \(-0.427791\pi\)
0.224911 + 0.974379i \(0.427791\pi\)
\(380\) −10.2060 −0.523559
\(381\) 13.9056 0.712407
\(382\) 11.3004 0.578176
\(383\) 9.52987 0.486953 0.243477 0.969907i \(-0.421712\pi\)
0.243477 + 0.969907i \(0.421712\pi\)
\(384\) −2.54686 −0.129969
\(385\) 48.0281 2.44774
\(386\) 8.41962 0.428547
\(387\) −77.0742 −3.91790
\(388\) −21.3875 −1.08579
\(389\) −11.8121 −0.598900 −0.299450 0.954112i \(-0.596803\pi\)
−0.299450 + 0.954112i \(0.596803\pi\)
\(390\) 7.81573 0.395765
\(391\) −3.58377 −0.181239
\(392\) 0.470908 0.0237844
\(393\) −68.6832 −3.46461
\(394\) −54.9785 −2.76978
\(395\) −16.2716 −0.818715
\(396\) 95.9153 4.81993
\(397\) −0.0218522 −0.00109673 −0.000548366 1.00000i \(-0.500175\pi\)
−0.000548366 1.00000i \(0.500175\pi\)
\(398\) 24.0931 1.20768
\(399\) −26.3418 −1.31874
\(400\) −0.748575 −0.0374287
\(401\) 17.7171 0.884752 0.442376 0.896830i \(-0.354136\pi\)
0.442376 + 0.896830i \(0.354136\pi\)
\(402\) −96.2047 −4.79826
\(403\) −2.73506 −0.136243
\(404\) 3.08440 0.153455
\(405\) 71.7645 3.56601
\(406\) 59.4153 2.94873
\(407\) −3.11757 −0.154532
\(408\) 0.318450 0.0157656
\(409\) 6.36231 0.314596 0.157298 0.987551i \(-0.449722\pi\)
0.157298 + 0.987551i \(0.449722\pi\)
\(410\) 34.0046 1.67937
\(411\) −51.0521 −2.51822
\(412\) −18.2082 −0.897055
\(413\) −43.1689 −2.12420
\(414\) 57.2794 2.81513
\(415\) 19.8847 0.976100
\(416\) −4.13054 −0.202516
\(417\) 18.3447 0.898345
\(418\) 27.9082 1.36504
\(419\) −16.0527 −0.784225 −0.392113 0.919917i \(-0.628256\pi\)
−0.392113 + 0.919917i \(0.628256\pi\)
\(420\) 50.9590 2.48654
\(421\) −26.1103 −1.27254 −0.636269 0.771468i \(-0.719523\pi\)
−0.636269 + 0.771468i \(0.719523\pi\)
\(422\) 3.32054 0.161641
\(423\) −71.4256 −3.47283
\(424\) 0.239056 0.0116096
\(425\) 0.182842 0.00886915
\(426\) −86.4479 −4.18841
\(427\) 30.3893 1.47064
\(428\) 34.3081 1.65834
\(429\) −10.5556 −0.509629
\(430\) 43.3839 2.09216
\(431\) −8.92201 −0.429758 −0.214879 0.976641i \(-0.568936\pi\)
−0.214879 + 0.976641i \(0.568936\pi\)
\(432\) −68.5621 −3.29869
\(433\) −9.96225 −0.478755 −0.239378 0.970927i \(-0.576943\pi\)
−0.239378 + 0.970927i \(0.576943\pi\)
\(434\) −36.1060 −1.73315
\(435\) −65.5020 −3.14058
\(436\) −7.51690 −0.359994
\(437\) 8.23155 0.393768
\(438\) 11.9288 0.569981
\(439\) −4.17571 −0.199296 −0.0996478 0.995023i \(-0.531772\pi\)
−0.0996478 + 0.995023i \(0.531772\pi\)
\(440\) 1.33362 0.0635779
\(441\) 39.5041 1.88115
\(442\) 1.03323 0.0491460
\(443\) 33.5286 1.59299 0.796496 0.604644i \(-0.206685\pi\)
0.796496 + 0.604644i \(0.206685\pi\)
\(444\) −3.30781 −0.156982
\(445\) 7.01747 0.332660
\(446\) 33.0903 1.56687
\(447\) −40.4947 −1.91533
\(448\) −26.2657 −1.24094
\(449\) 13.8952 0.655755 0.327878 0.944720i \(-0.393667\pi\)
0.327878 + 0.944720i \(0.393667\pi\)
\(450\) −2.92237 −0.137762
\(451\) −45.9252 −2.16253
\(452\) 5.68415 0.267360
\(453\) −9.23457 −0.433878
\(454\) 39.8052 1.86815
\(455\) −4.08417 −0.191469
\(456\) −0.731446 −0.0342531
\(457\) −30.2156 −1.41343 −0.706713 0.707500i \(-0.749823\pi\)
−0.706713 + 0.707500i \(0.749823\pi\)
\(458\) −41.6789 −1.94753
\(459\) 16.7466 0.781662
\(460\) −15.9242 −0.742469
\(461\) 23.3696 1.08843 0.544216 0.838945i \(-0.316827\pi\)
0.544216 + 0.838945i \(0.316827\pi\)
\(462\) −139.346 −6.48297
\(463\) −0.162094 −0.00753316 −0.00376658 0.999993i \(-0.501199\pi\)
−0.00376658 + 0.999993i \(0.501199\pi\)
\(464\) 35.4522 1.64582
\(465\) 39.8048 1.84591
\(466\) −9.51472 −0.440761
\(467\) 32.7777 1.51677 0.758386 0.651806i \(-0.225988\pi\)
0.758386 + 0.651806i \(0.225988\pi\)
\(468\) −8.15635 −0.377028
\(469\) 50.2725 2.32137
\(470\) 40.2044 1.85449
\(471\) 57.5440 2.65149
\(472\) −1.19869 −0.0551743
\(473\) −58.5925 −2.69409
\(474\) 47.2096 2.16841
\(475\) −0.419969 −0.0192695
\(476\) 6.73675 0.308778
\(477\) 20.0542 0.918219
\(478\) −20.9512 −0.958288
\(479\) 23.8671 1.09052 0.545258 0.838269i \(-0.316432\pi\)
0.545258 + 0.838269i \(0.316432\pi\)
\(480\) 60.1139 2.74381
\(481\) 0.265108 0.0120879
\(482\) 43.2248 1.96883
\(483\) −41.1003 −1.87013
\(484\) 51.4460 2.33845
\(485\) −24.9466 −1.13277
\(486\) −108.342 −4.91448
\(487\) −17.9179 −0.811939 −0.405969 0.913887i \(-0.633066\pi\)
−0.405969 + 0.913887i \(0.633066\pi\)
\(488\) 0.843834 0.0381986
\(489\) −15.8275 −0.715743
\(490\) −22.2363 −1.00453
\(491\) −30.9228 −1.39553 −0.697764 0.716327i \(-0.745822\pi\)
−0.697764 + 0.716327i \(0.745822\pi\)
\(492\) −48.7277 −2.19681
\(493\) −8.65933 −0.389996
\(494\) −2.37323 −0.106777
\(495\) 111.877 5.02848
\(496\) −21.5439 −0.967349
\(497\) 45.1740 2.02633
\(498\) −57.6922 −2.58525
\(499\) −25.2630 −1.13093 −0.565464 0.824773i \(-0.691303\pi\)
−0.565464 + 0.824773i \(0.691303\pi\)
\(500\) −21.4046 −0.957244
\(501\) 47.1028 2.10440
\(502\) −12.2542 −0.546930
\(503\) −15.6168 −0.696318 −0.348159 0.937436i \(-0.613193\pi\)
−0.348159 + 0.937436i \(0.613193\pi\)
\(504\) 2.65971 0.118473
\(505\) 3.59768 0.160094
\(506\) 43.5443 1.93578
\(507\) −42.2970 −1.87848
\(508\) 8.16840 0.362414
\(509\) −23.9056 −1.05960 −0.529799 0.848123i \(-0.677733\pi\)
−0.529799 + 0.848123i \(0.677733\pi\)
\(510\) −15.0372 −0.665859
\(511\) −6.23349 −0.275754
\(512\) −31.7511 −1.40321
\(513\) −38.4651 −1.69827
\(514\) 22.4832 0.991690
\(515\) −21.2383 −0.935870
\(516\) −62.1680 −2.73679
\(517\) −54.2984 −2.38804
\(518\) 3.49974 0.153770
\(519\) −10.9343 −0.479960
\(520\) −0.113407 −0.00497324
\(521\) 25.4275 1.11400 0.556999 0.830513i \(-0.311953\pi\)
0.556999 + 0.830513i \(0.311953\pi\)
\(522\) 138.402 6.05769
\(523\) −40.2729 −1.76101 −0.880506 0.474036i \(-0.842797\pi\)
−0.880506 + 0.474036i \(0.842797\pi\)
\(524\) −40.3456 −1.76251
\(525\) 2.09691 0.0915169
\(526\) 19.8684 0.866301
\(527\) 5.26218 0.229224
\(528\) −83.1456 −3.61845
\(529\) −10.1566 −0.441590
\(530\) −11.2882 −0.490328
\(531\) −100.557 −4.36382
\(532\) −15.4736 −0.670865
\(533\) 3.90534 0.169159
\(534\) −20.3601 −0.881068
\(535\) 40.0173 1.73010
\(536\) 1.39594 0.0602956
\(537\) 62.6065 2.70167
\(538\) −19.5647 −0.843495
\(539\) 30.0314 1.29354
\(540\) 74.4118 3.20218
\(541\) 0.601634 0.0258663 0.0129331 0.999916i \(-0.495883\pi\)
0.0129331 + 0.999916i \(0.495883\pi\)
\(542\) 44.7126 1.92057
\(543\) 79.5313 3.41301
\(544\) 7.94702 0.340726
\(545\) −8.76779 −0.375571
\(546\) 11.8496 0.507115
\(547\) 22.3693 0.956443 0.478221 0.878239i \(-0.341282\pi\)
0.478221 + 0.878239i \(0.341282\pi\)
\(548\) −29.9889 −1.28106
\(549\) 70.7887 3.02119
\(550\) −2.22161 −0.0947297
\(551\) 19.8896 0.847324
\(552\) −1.14125 −0.0485749
\(553\) −24.6698 −1.04906
\(554\) 49.8305 2.11709
\(555\) −3.85826 −0.163774
\(556\) 10.7760 0.457004
\(557\) 40.6274 1.72144 0.860720 0.509079i \(-0.170014\pi\)
0.860720 + 0.509079i \(0.170014\pi\)
\(558\) −84.1053 −3.56046
\(559\) 4.98253 0.210739
\(560\) −32.1707 −1.35946
\(561\) 20.3086 0.857431
\(562\) 38.4319 1.62115
\(563\) −45.0959 −1.90056 −0.950282 0.311389i \(-0.899206\pi\)
−0.950282 + 0.311389i \(0.899206\pi\)
\(564\) −57.6118 −2.42589
\(565\) 6.63005 0.278928
\(566\) −15.9219 −0.669249
\(567\) 108.804 4.56932
\(568\) 1.25437 0.0526322
\(569\) 35.5041 1.48841 0.744204 0.667952i \(-0.232829\pi\)
0.744204 + 0.667952i \(0.232829\pi\)
\(570\) 34.5389 1.44667
\(571\) −32.2936 −1.35145 −0.675723 0.737156i \(-0.736168\pi\)
−0.675723 + 0.737156i \(0.736168\pi\)
\(572\) −6.20053 −0.259257
\(573\) −18.8878 −0.789050
\(574\) 51.5551 2.15187
\(575\) −0.655266 −0.0273265
\(576\) −61.1833 −2.54930
\(577\) −11.0196 −0.458752 −0.229376 0.973338i \(-0.573668\pi\)
−0.229376 + 0.973338i \(0.573668\pi\)
\(578\) −1.98791 −0.0826862
\(579\) −14.0728 −0.584848
\(580\) −38.4770 −1.59767
\(581\) 30.1475 1.25073
\(582\) 72.3787 3.00019
\(583\) 15.2454 0.631399
\(584\) −0.173089 −0.00716246
\(585\) −9.51366 −0.393341
\(586\) 16.4374 0.679021
\(587\) 6.94379 0.286601 0.143301 0.989679i \(-0.454228\pi\)
0.143301 + 0.989679i \(0.454228\pi\)
\(588\) 31.8640 1.31405
\(589\) −12.0867 −0.498022
\(590\) 56.6023 2.33028
\(591\) 91.8930 3.77997
\(592\) 2.08824 0.0858260
\(593\) −16.3044 −0.669540 −0.334770 0.942300i \(-0.608659\pi\)
−0.334770 + 0.942300i \(0.608659\pi\)
\(594\) −203.477 −8.34878
\(595\) 7.85781 0.322139
\(596\) −23.7872 −0.974363
\(597\) −40.2701 −1.64815
\(598\) −3.70288 −0.151422
\(599\) −26.5861 −1.08628 −0.543140 0.839642i \(-0.682765\pi\)
−0.543140 + 0.839642i \(0.682765\pi\)
\(600\) 0.0582261 0.00237707
\(601\) 42.0482 1.71518 0.857591 0.514332i \(-0.171960\pi\)
0.857591 + 0.514332i \(0.171960\pi\)
\(602\) 65.7752 2.68080
\(603\) 117.105 4.76887
\(604\) −5.42454 −0.220721
\(605\) 60.0072 2.43964
\(606\) −10.4381 −0.424019
\(607\) −16.7122 −0.678327 −0.339163 0.940727i \(-0.610144\pi\)
−0.339163 + 0.940727i \(0.610144\pi\)
\(608\) −18.2535 −0.740276
\(609\) −99.3089 −4.02420
\(610\) −39.8459 −1.61331
\(611\) 4.61737 0.186799
\(612\) 15.6926 0.634334
\(613\) −28.5506 −1.15315 −0.576574 0.817045i \(-0.695611\pi\)
−0.576574 + 0.817045i \(0.695611\pi\)
\(614\) 48.5216 1.95817
\(615\) −56.8365 −2.29187
\(616\) 2.02193 0.0814660
\(617\) −8.76493 −0.352863 −0.176431 0.984313i \(-0.556455\pi\)
−0.176431 + 0.984313i \(0.556455\pi\)
\(618\) 61.6196 2.47870
\(619\) −26.3129 −1.05760 −0.528802 0.848745i \(-0.677358\pi\)
−0.528802 + 0.848745i \(0.677358\pi\)
\(620\) 23.3820 0.939044
\(621\) −60.0159 −2.40835
\(622\) −23.4260 −0.939297
\(623\) 10.6393 0.426256
\(624\) 7.07045 0.283045
\(625\) −25.8808 −1.03523
\(626\) 3.09501 0.123701
\(627\) −46.6468 −1.86289
\(628\) 33.8023 1.34886
\(629\) −0.510060 −0.0203374
\(630\) −125.591 −5.00368
\(631\) −32.6007 −1.29781 −0.648906 0.760869i \(-0.724773\pi\)
−0.648906 + 0.760869i \(0.724773\pi\)
\(632\) −0.685018 −0.0272486
\(633\) −5.55007 −0.220595
\(634\) −41.1132 −1.63281
\(635\) 9.52771 0.378096
\(636\) 16.1757 0.641408
\(637\) −2.55378 −0.101184
\(638\) 105.214 4.16548
\(639\) 105.228 4.16277
\(640\) −1.74503 −0.0689783
\(641\) −28.2601 −1.11621 −0.558104 0.829771i \(-0.688471\pi\)
−0.558104 + 0.829771i \(0.688471\pi\)
\(642\) −116.104 −4.58226
\(643\) 18.6631 0.736002 0.368001 0.929825i \(-0.380042\pi\)
0.368001 + 0.929825i \(0.380042\pi\)
\(644\) −24.1430 −0.951367
\(645\) −72.5134 −2.85521
\(646\) 4.56602 0.179648
\(647\) −11.0239 −0.433395 −0.216697 0.976239i \(-0.569528\pi\)
−0.216697 + 0.976239i \(0.569528\pi\)
\(648\) 3.02121 0.118684
\(649\) −76.4447 −3.00072
\(650\) 0.188919 0.00741001
\(651\) 60.3489 2.36526
\(652\) −9.29732 −0.364111
\(653\) 32.4444 1.26965 0.634823 0.772658i \(-0.281073\pi\)
0.634823 + 0.772658i \(0.281073\pi\)
\(654\) 25.4384 0.994719
\(655\) −47.0596 −1.83877
\(656\) 30.7621 1.20106
\(657\) −14.5203 −0.566490
\(658\) 60.9547 2.37626
\(659\) 41.5400 1.61817 0.809085 0.587692i \(-0.199963\pi\)
0.809085 + 0.587692i \(0.199963\pi\)
\(660\) 90.2396 3.51257
\(661\) 38.8679 1.51178 0.755892 0.654696i \(-0.227203\pi\)
0.755892 + 0.654696i \(0.227203\pi\)
\(662\) −22.6815 −0.881541
\(663\) −1.72698 −0.0670705
\(664\) 0.837122 0.0324866
\(665\) −18.0486 −0.699893
\(666\) 8.15229 0.315895
\(667\) 31.0331 1.20161
\(668\) 27.6690 1.07055
\(669\) −55.3084 −2.13835
\(670\) −65.9165 −2.54658
\(671\) 53.8142 2.07747
\(672\) 91.1399 3.51580
\(673\) −37.7162 −1.45385 −0.726926 0.686715i \(-0.759052\pi\)
−0.726926 + 0.686715i \(0.759052\pi\)
\(674\) −8.12272 −0.312876
\(675\) 3.06198 0.117856
\(676\) −24.8460 −0.955614
\(677\) 6.62891 0.254770 0.127385 0.991853i \(-0.459342\pi\)
0.127385 + 0.991853i \(0.459342\pi\)
\(678\) −19.2361 −0.738757
\(679\) −37.8220 −1.45148
\(680\) 0.218192 0.00836728
\(681\) −66.5319 −2.54951
\(682\) −63.9376 −2.44830
\(683\) −0.826382 −0.0316206 −0.0158103 0.999875i \(-0.505033\pi\)
−0.0158103 + 0.999875i \(0.505033\pi\)
\(684\) −36.0442 −1.37818
\(685\) −34.9793 −1.33649
\(686\) 14.3171 0.546630
\(687\) 69.6637 2.65783
\(688\) 39.2470 1.49628
\(689\) −1.29642 −0.0493897
\(690\) 53.8900 2.05156
\(691\) −15.2014 −0.578290 −0.289145 0.957285i \(-0.593371\pi\)
−0.289145 + 0.957285i \(0.593371\pi\)
\(692\) −6.42296 −0.244164
\(693\) 169.618 6.44327
\(694\) −20.6121 −0.782424
\(695\) 12.5692 0.476778
\(696\) −2.75756 −0.104525
\(697\) −7.51375 −0.284604
\(698\) −49.6673 −1.87994
\(699\) 15.9032 0.601516
\(700\) 1.23176 0.0465562
\(701\) −7.96957 −0.301006 −0.150503 0.988610i \(-0.548089\pi\)
−0.150503 + 0.988610i \(0.548089\pi\)
\(702\) 17.3031 0.653064
\(703\) 1.17155 0.0441860
\(704\) −46.5120 −1.75299
\(705\) −67.1990 −2.53086
\(706\) 1.98791 0.0748160
\(707\) 5.45451 0.205138
\(708\) −81.1096 −3.04828
\(709\) 27.8570 1.04619 0.523095 0.852274i \(-0.324777\pi\)
0.523095 + 0.852274i \(0.324777\pi\)
\(710\) −59.2314 −2.22291
\(711\) −57.4657 −2.15513
\(712\) 0.295428 0.0110716
\(713\) −18.8585 −0.706255
\(714\) −22.7982 −0.853202
\(715\) −7.23236 −0.270475
\(716\) 36.7761 1.37439
\(717\) 35.0187 1.30780
\(718\) 8.52621 0.318195
\(719\) 35.2649 1.31516 0.657579 0.753385i \(-0.271581\pi\)
0.657579 + 0.753385i \(0.271581\pi\)
\(720\) −74.9383 −2.79279
\(721\) −32.1998 −1.19918
\(722\) 27.2826 1.01535
\(723\) −72.2474 −2.68691
\(724\) 46.7180 1.73626
\(725\) −1.58329 −0.0588020
\(726\) −174.101 −6.46151
\(727\) 21.6712 0.803739 0.401870 0.915697i \(-0.368360\pi\)
0.401870 + 0.915697i \(0.368360\pi\)
\(728\) −0.171939 −0.00637248
\(729\) 86.5175 3.20435
\(730\) 8.17325 0.302505
\(731\) −9.58623 −0.354560
\(732\) 57.0981 2.11041
\(733\) 39.4947 1.45877 0.729386 0.684103i \(-0.239806\pi\)
0.729386 + 0.684103i \(0.239806\pi\)
\(734\) −3.02897 −0.111801
\(735\) 37.1665 1.37091
\(736\) −28.4803 −1.04980
\(737\) 89.0240 3.27924
\(738\) 120.092 4.42066
\(739\) −20.2010 −0.743107 −0.371553 0.928412i \(-0.621175\pi\)
−0.371553 + 0.928412i \(0.621175\pi\)
\(740\) −2.26641 −0.0833148
\(741\) 3.96670 0.145720
\(742\) −17.1143 −0.628285
\(743\) 48.1858 1.76776 0.883882 0.467709i \(-0.154921\pi\)
0.883882 + 0.467709i \(0.154921\pi\)
\(744\) 1.67574 0.0614356
\(745\) −27.7457 −1.01652
\(746\) 18.7227 0.685485
\(747\) 70.2256 2.56942
\(748\) 11.9296 0.436190
\(749\) 60.6711 2.21687
\(750\) 72.4366 2.64501
\(751\) 41.5491 1.51615 0.758073 0.652169i \(-0.226141\pi\)
0.758073 + 0.652169i \(0.226141\pi\)
\(752\) 36.3706 1.32630
\(753\) 20.4820 0.746406
\(754\) −8.94712 −0.325835
\(755\) −6.32724 −0.230272
\(756\) 112.817 4.10313
\(757\) 52.2517 1.89912 0.949560 0.313586i \(-0.101530\pi\)
0.949560 + 0.313586i \(0.101530\pi\)
\(758\) −17.4083 −0.632299
\(759\) −72.7815 −2.64180
\(760\) −0.501164 −0.0181791
\(761\) 24.4842 0.887550 0.443775 0.896138i \(-0.353639\pi\)
0.443775 + 0.896138i \(0.353639\pi\)
\(762\) −27.6432 −1.00141
\(763\) −13.2930 −0.481240
\(764\) −11.0950 −0.401403
\(765\) 18.3040 0.661781
\(766\) −18.9445 −0.684493
\(767\) 6.50063 0.234724
\(768\) 55.6323 2.00746
\(769\) −13.5479 −0.488549 −0.244275 0.969706i \(-0.578550\pi\)
−0.244275 + 0.969706i \(0.578550\pi\)
\(770\) −95.4756 −3.44070
\(771\) −37.5792 −1.35338
\(772\) −8.26662 −0.297522
\(773\) 5.47779 0.197022 0.0985111 0.995136i \(-0.468592\pi\)
0.0985111 + 0.995136i \(0.468592\pi\)
\(774\) 153.217 5.50726
\(775\) 0.962148 0.0345614
\(776\) −1.05022 −0.0377009
\(777\) −5.84959 −0.209853
\(778\) 23.4815 0.841852
\(779\) 17.2583 0.618343
\(780\) −7.67371 −0.274763
\(781\) 79.9954 2.86246
\(782\) 7.12422 0.254762
\(783\) −145.014 −5.18237
\(784\) −20.1159 −0.718425
\(785\) 39.4273 1.40722
\(786\) 136.536 4.87008
\(787\) 15.5334 0.553707 0.276853 0.960912i \(-0.410708\pi\)
0.276853 + 0.960912i \(0.410708\pi\)
\(788\) 53.9795 1.92294
\(789\) −33.2087 −1.18226
\(790\) 32.3466 1.15084
\(791\) 10.0520 0.357406
\(792\) 4.70988 0.167358
\(793\) −4.57619 −0.162505
\(794\) 0.0434403 0.00154164
\(795\) 18.8675 0.669162
\(796\) −23.6553 −0.838441
\(797\) 26.1497 0.926271 0.463136 0.886287i \(-0.346724\pi\)
0.463136 + 0.886287i \(0.346724\pi\)
\(798\) 52.3651 1.85370
\(799\) −8.88367 −0.314282
\(800\) 1.45305 0.0513731
\(801\) 24.7832 0.875673
\(802\) −35.2201 −1.24367
\(803\) −11.0384 −0.389538
\(804\) 94.4566 3.33123
\(805\) −28.1606 −0.992532
\(806\) 5.43706 0.191512
\(807\) 32.7012 1.15114
\(808\) 0.151458 0.00532828
\(809\) −14.0108 −0.492593 −0.246297 0.969194i \(-0.579214\pi\)
−0.246297 + 0.969194i \(0.579214\pi\)
\(810\) −142.661 −5.01261
\(811\) 12.7423 0.447443 0.223722 0.974653i \(-0.428179\pi\)
0.223722 + 0.974653i \(0.428179\pi\)
\(812\) −58.3357 −2.04718
\(813\) −74.7342 −2.62104
\(814\) 6.19744 0.217220
\(815\) −10.8445 −0.379866
\(816\) −13.6033 −0.476211
\(817\) 22.0186 0.770332
\(818\) −12.6477 −0.442217
\(819\) −14.4238 −0.504010
\(820\) −33.3867 −1.16591
\(821\) −44.9893 −1.57014 −0.785070 0.619408i \(-0.787373\pi\)
−0.785070 + 0.619408i \(0.787373\pi\)
\(822\) 101.487 3.53977
\(823\) −35.8527 −1.24975 −0.624873 0.780726i \(-0.714849\pi\)
−0.624873 + 0.780726i \(0.714849\pi\)
\(824\) −0.894108 −0.0311477
\(825\) 3.71328 0.129280
\(826\) 85.8159 2.98592
\(827\) 47.6717 1.65771 0.828853 0.559466i \(-0.188994\pi\)
0.828853 + 0.559466i \(0.188994\pi\)
\(828\) −56.2386 −1.95443
\(829\) −14.4870 −0.503155 −0.251578 0.967837i \(-0.580949\pi\)
−0.251578 + 0.967837i \(0.580949\pi\)
\(830\) −39.5289 −1.37207
\(831\) −83.2884 −2.88924
\(832\) 3.95524 0.137123
\(833\) 4.91339 0.170239
\(834\) −36.4677 −1.26277
\(835\) 32.2734 1.11687
\(836\) −27.4011 −0.947686
\(837\) 88.1233 3.04599
\(838\) 31.9113 1.10236
\(839\) 24.6718 0.851764 0.425882 0.904779i \(-0.359964\pi\)
0.425882 + 0.904779i \(0.359964\pi\)
\(840\) 2.50232 0.0863382
\(841\) 45.9839 1.58565
\(842\) 51.9049 1.78876
\(843\) −64.2364 −2.21242
\(844\) −3.26020 −0.112221
\(845\) −28.9806 −0.996963
\(846\) 141.988 4.88164
\(847\) 90.9781 3.12604
\(848\) −10.2118 −0.350675
\(849\) 26.6125 0.913338
\(850\) −0.363474 −0.0124671
\(851\) 1.82794 0.0626610
\(852\) 84.8770 2.90784
\(853\) 20.1456 0.689773 0.344887 0.938644i \(-0.387917\pi\)
0.344887 + 0.938644i \(0.387917\pi\)
\(854\) −60.4111 −2.06723
\(855\) −42.0423 −1.43782
\(856\) 1.68469 0.0575814
\(857\) 21.2213 0.724907 0.362454 0.932002i \(-0.381939\pi\)
0.362454 + 0.932002i \(0.381939\pi\)
\(858\) 20.9836 0.716367
\(859\) 27.0128 0.921666 0.460833 0.887487i \(-0.347551\pi\)
0.460833 + 0.887487i \(0.347551\pi\)
\(860\) −42.5956 −1.45250
\(861\) −86.1710 −2.93670
\(862\) 17.7362 0.604096
\(863\) −32.6389 −1.11104 −0.555521 0.831502i \(-0.687481\pi\)
−0.555521 + 0.831502i \(0.687481\pi\)
\(864\) 133.085 4.52765
\(865\) −7.49181 −0.254729
\(866\) 19.8041 0.672969
\(867\) 3.32266 0.112844
\(868\) 35.4500 1.20325
\(869\) −43.6859 −1.48194
\(870\) 130.212 4.41460
\(871\) −7.57034 −0.256511
\(872\) −0.369114 −0.0124998
\(873\) −88.1026 −2.98182
\(874\) −16.3636 −0.553507
\(875\) −37.8523 −1.27964
\(876\) −11.7120 −0.395713
\(877\) 52.2136 1.76313 0.881564 0.472065i \(-0.156491\pi\)
0.881564 + 0.472065i \(0.156491\pi\)
\(878\) 8.30093 0.280143
\(879\) −27.4740 −0.926675
\(880\) −56.9687 −1.92042
\(881\) −44.6500 −1.50430 −0.752149 0.658993i \(-0.770983\pi\)
−0.752149 + 0.658993i \(0.770983\pi\)
\(882\) −78.5307 −2.64427
\(883\) −24.6501 −0.829543 −0.414771 0.909926i \(-0.636138\pi\)
−0.414771 + 0.909926i \(0.636138\pi\)
\(884\) −1.01446 −0.0341200
\(885\) −94.6070 −3.18018
\(886\) −66.6518 −2.23921
\(887\) 5.04716 0.169467 0.0847335 0.996404i \(-0.472996\pi\)
0.0847335 + 0.996404i \(0.472996\pi\)
\(888\) −0.162429 −0.00545075
\(889\) 14.4452 0.484475
\(890\) −13.9501 −0.467609
\(891\) 192.673 6.45478
\(892\) −32.4891 −1.08781
\(893\) 20.4049 0.682822
\(894\) 80.4998 2.69231
\(895\) 42.8960 1.43385
\(896\) −2.64567 −0.0883857
\(897\) 6.18912 0.206649
\(898\) −27.6224 −0.921772
\(899\) −45.5669 −1.51974
\(900\) 2.86926 0.0956421
\(901\) 2.49427 0.0830963
\(902\) 91.2952 3.03980
\(903\) −109.939 −3.65854
\(904\) 0.279118 0.00928332
\(905\) 54.4923 1.81139
\(906\) 18.3575 0.609887
\(907\) 22.5584 0.749039 0.374519 0.927219i \(-0.377808\pi\)
0.374519 + 0.927219i \(0.377808\pi\)
\(908\) −39.0819 −1.29698
\(909\) 12.7057 0.421422
\(910\) 8.11896 0.269141
\(911\) 32.6449 1.08157 0.540786 0.841160i \(-0.318127\pi\)
0.540786 + 0.841160i \(0.318127\pi\)
\(912\) 31.2454 1.03464
\(913\) 53.3861 1.76682
\(914\) 60.0659 1.98680
\(915\) 66.5998 2.20172
\(916\) 40.9216 1.35209
\(917\) −71.3480 −2.35612
\(918\) −33.2906 −1.09876
\(919\) 6.72893 0.221967 0.110984 0.993822i \(-0.464600\pi\)
0.110984 + 0.993822i \(0.464600\pi\)
\(920\) −0.781951 −0.0257802
\(921\) −81.1007 −2.67236
\(922\) −46.4567 −1.52997
\(923\) −6.80257 −0.223909
\(924\) 136.814 4.50085
\(925\) −0.0932606 −0.00306639
\(926\) 0.322229 0.0105891
\(927\) −75.0061 −2.46352
\(928\) −68.8159 −2.25899
\(929\) 26.9571 0.884434 0.442217 0.896908i \(-0.354192\pi\)
0.442217 + 0.896908i \(0.354192\pi\)
\(930\) −79.1284 −2.59472
\(931\) −11.2855 −0.369868
\(932\) 9.34183 0.306002
\(933\) 39.1550 1.28188
\(934\) −65.1592 −2.13207
\(935\) 13.9148 0.455064
\(936\) −0.400514 −0.0130912
\(937\) 40.5490 1.32468 0.662339 0.749204i \(-0.269564\pi\)
0.662339 + 0.749204i \(0.269564\pi\)
\(938\) −99.9373 −3.26307
\(939\) −5.17310 −0.168818
\(940\) −39.4738 −1.28749
\(941\) −14.7308 −0.480209 −0.240104 0.970747i \(-0.577182\pi\)
−0.240104 + 0.970747i \(0.577182\pi\)
\(942\) −114.392 −3.72710
\(943\) 26.9276 0.876883
\(944\) 51.2049 1.66658
\(945\) 131.591 4.28066
\(946\) 116.477 3.78698
\(947\) −25.2505 −0.820530 −0.410265 0.911966i \(-0.634564\pi\)
−0.410265 + 0.911966i \(0.634564\pi\)
\(948\) −46.3518 −1.50544
\(949\) 0.938677 0.0304707
\(950\) 0.834861 0.0270865
\(951\) 68.7180 2.22833
\(952\) 0.330805 0.0107215
\(953\) −6.92681 −0.224381 −0.112191 0.993687i \(-0.535787\pi\)
−0.112191 + 0.993687i \(0.535787\pi\)
\(954\) −39.8660 −1.29071
\(955\) −12.9413 −0.418772
\(956\) 20.5705 0.665299
\(957\) −175.859 −5.68472
\(958\) −47.4456 −1.53290
\(959\) −53.0329 −1.71252
\(960\) −57.5628 −1.85783
\(961\) −3.30950 −0.106758
\(962\) −0.527012 −0.0169915
\(963\) 141.327 4.55420
\(964\) −42.4393 −1.36688
\(965\) −9.64228 −0.310396
\(966\) 81.7037 2.62877
\(967\) −7.51653 −0.241715 −0.120858 0.992670i \(-0.538564\pi\)
−0.120858 + 0.992670i \(0.538564\pi\)
\(968\) 2.52624 0.0811963
\(969\) −7.63181 −0.245169
\(970\) 49.5916 1.59229
\(971\) −36.5222 −1.17205 −0.586027 0.810291i \(-0.699309\pi\)
−0.586027 + 0.810291i \(0.699309\pi\)
\(972\) 106.373 3.41191
\(973\) 19.0565 0.610922
\(974\) 35.6192 1.14131
\(975\) −0.315766 −0.0101126
\(976\) −36.0463 −1.15381
\(977\) −29.2277 −0.935077 −0.467539 0.883973i \(-0.654859\pi\)
−0.467539 + 0.883973i \(0.654859\pi\)
\(978\) 31.4636 1.00610
\(979\) 18.8404 0.602143
\(980\) 21.8322 0.697404
\(981\) −30.9647 −0.988628
\(982\) 61.4719 1.96165
\(983\) −36.7686 −1.17274 −0.586369 0.810044i \(-0.699443\pi\)
−0.586369 + 0.810044i \(0.699443\pi\)
\(984\) −2.39275 −0.0762782
\(985\) 62.9622 2.00614
\(986\) 17.2140 0.548204
\(987\) −101.882 −3.24293
\(988\) 2.33011 0.0741305
\(989\) 34.3549 1.09242
\(990\) −222.401 −7.06836
\(991\) −8.57427 −0.272371 −0.136185 0.990683i \(-0.543484\pi\)
−0.136185 + 0.990683i \(0.543484\pi\)
\(992\) 41.8186 1.32774
\(993\) 37.9107 1.20306
\(994\) −89.8019 −2.84834
\(995\) −27.5918 −0.874720
\(996\) 56.6439 1.79483
\(997\) 47.3205 1.49866 0.749328 0.662199i \(-0.230377\pi\)
0.749328 + 0.662199i \(0.230377\pi\)
\(998\) 50.2206 1.58971
\(999\) −8.54175 −0.270249
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 6001.2.a.d.1.20 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.20 121 1.1 even 1 trivial