Properties

Label 6001.2.a.d.1.10
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 1.10
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.48199 q^{2} +1.43528 q^{3} +4.16025 q^{4} +0.277666 q^{5} -3.56234 q^{6} +3.77920 q^{7} -5.36171 q^{8} -0.939973 q^{9} +O(q^{10})\) \(q-2.48199 q^{2} +1.43528 q^{3} +4.16025 q^{4} +0.277666 q^{5} -3.56234 q^{6} +3.77920 q^{7} -5.36171 q^{8} -0.939973 q^{9} -0.689164 q^{10} +4.20622 q^{11} +5.97112 q^{12} +2.72188 q^{13} -9.37991 q^{14} +0.398529 q^{15} +4.98718 q^{16} +1.00000 q^{17} +2.33300 q^{18} -0.978299 q^{19} +1.15516 q^{20} +5.42421 q^{21} -10.4398 q^{22} -3.17903 q^{23} -7.69555 q^{24} -4.92290 q^{25} -6.75566 q^{26} -5.65496 q^{27} +15.7224 q^{28} +0.536296 q^{29} -0.989142 q^{30} -9.10459 q^{31} -1.65469 q^{32} +6.03709 q^{33} -2.48199 q^{34} +1.04936 q^{35} -3.91052 q^{36} -6.86711 q^{37} +2.42812 q^{38} +3.90665 q^{39} -1.48877 q^{40} +1.77455 q^{41} -13.4628 q^{42} +3.97589 q^{43} +17.4989 q^{44} -0.260999 q^{45} +7.89031 q^{46} +11.0202 q^{47} +7.15799 q^{48} +7.28234 q^{49} +12.2186 q^{50} +1.43528 q^{51} +11.3237 q^{52} +7.99396 q^{53} +14.0355 q^{54} +1.16792 q^{55} -20.2630 q^{56} -1.40413 q^{57} -1.33108 q^{58} -0.301193 q^{59} +1.65798 q^{60} +6.23491 q^{61} +22.5974 q^{62} -3.55235 q^{63} -5.86745 q^{64} +0.755773 q^{65} -14.9840 q^{66} +10.4834 q^{67} +4.16025 q^{68} -4.56280 q^{69} -2.60449 q^{70} -3.80575 q^{71} +5.03986 q^{72} -10.0591 q^{73} +17.0441 q^{74} -7.06574 q^{75} -4.06997 q^{76} +15.8961 q^{77} -9.69625 q^{78} +11.4349 q^{79} +1.38477 q^{80} -5.29653 q^{81} -4.40441 q^{82} +12.0659 q^{83} +22.5660 q^{84} +0.277666 q^{85} -9.86809 q^{86} +0.769734 q^{87} -22.5525 q^{88} +5.72993 q^{89} +0.647796 q^{90} +10.2865 q^{91} -13.2256 q^{92} -13.0676 q^{93} -27.3519 q^{94} -0.271641 q^{95} -2.37494 q^{96} +6.42228 q^{97} -18.0747 q^{98} -3.95373 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.48199 −1.75503 −0.877514 0.479551i \(-0.840800\pi\)
−0.877514 + 0.479551i \(0.840800\pi\)
\(3\) 1.43528 0.828659 0.414329 0.910127i \(-0.364016\pi\)
0.414329 + 0.910127i \(0.364016\pi\)
\(4\) 4.16025 2.08012
\(5\) 0.277666 0.124176 0.0620881 0.998071i \(-0.480224\pi\)
0.0620881 + 0.998071i \(0.480224\pi\)
\(6\) −3.56234 −1.45432
\(7\) 3.77920 1.42840 0.714201 0.699940i \(-0.246790\pi\)
0.714201 + 0.699940i \(0.246790\pi\)
\(8\) −5.36171 −1.89565
\(9\) −0.939973 −0.313324
\(10\) −0.689164 −0.217933
\(11\) 4.20622 1.26822 0.634111 0.773242i \(-0.281366\pi\)
0.634111 + 0.773242i \(0.281366\pi\)
\(12\) 5.97112 1.72371
\(13\) 2.72188 0.754913 0.377456 0.926027i \(-0.376799\pi\)
0.377456 + 0.926027i \(0.376799\pi\)
\(14\) −9.37991 −2.50689
\(15\) 0.398529 0.102900
\(16\) 4.98718 1.24679
\(17\) 1.00000 0.242536
\(18\) 2.33300 0.549893
\(19\) −0.978299 −0.224437 −0.112219 0.993684i \(-0.535796\pi\)
−0.112219 + 0.993684i \(0.535796\pi\)
\(20\) 1.15516 0.258302
\(21\) 5.42421 1.18366
\(22\) −10.4398 −2.22577
\(23\) −3.17903 −0.662874 −0.331437 0.943477i \(-0.607533\pi\)
−0.331437 + 0.943477i \(0.607533\pi\)
\(24\) −7.69555 −1.57085
\(25\) −4.92290 −0.984580
\(26\) −6.75566 −1.32489
\(27\) −5.65496 −1.08830
\(28\) 15.7224 2.97126
\(29\) 0.536296 0.0995876 0.0497938 0.998760i \(-0.484144\pi\)
0.0497938 + 0.998760i \(0.484144\pi\)
\(30\) −0.989142 −0.180592
\(31\) −9.10459 −1.63523 −0.817616 0.575764i \(-0.804705\pi\)
−0.817616 + 0.575764i \(0.804705\pi\)
\(32\) −1.65469 −0.292510
\(33\) 6.03709 1.05092
\(34\) −2.48199 −0.425657
\(35\) 1.04936 0.177374
\(36\) −3.91052 −0.651754
\(37\) −6.86711 −1.12895 −0.564473 0.825452i \(-0.690920\pi\)
−0.564473 + 0.825452i \(0.690920\pi\)
\(38\) 2.42812 0.393893
\(39\) 3.90665 0.625565
\(40\) −1.48877 −0.235395
\(41\) 1.77455 0.277139 0.138569 0.990353i \(-0.455750\pi\)
0.138569 + 0.990353i \(0.455750\pi\)
\(42\) −13.4628 −2.07735
\(43\) 3.97589 0.606317 0.303158 0.952940i \(-0.401959\pi\)
0.303158 + 0.952940i \(0.401959\pi\)
\(44\) 17.4989 2.63806
\(45\) −0.260999 −0.0389074
\(46\) 7.89031 1.16336
\(47\) 11.0202 1.60746 0.803728 0.594997i \(-0.202847\pi\)
0.803728 + 0.594997i \(0.202847\pi\)
\(48\) 7.15799 1.03317
\(49\) 7.28234 1.04033
\(50\) 12.2186 1.72797
\(51\) 1.43528 0.200979
\(52\) 11.3237 1.57031
\(53\) 7.99396 1.09805 0.549027 0.835804i \(-0.314998\pi\)
0.549027 + 0.835804i \(0.314998\pi\)
\(54\) 14.0355 1.90999
\(55\) 1.16792 0.157483
\(56\) −20.2630 −2.70775
\(57\) −1.40413 −0.185982
\(58\) −1.33108 −0.174779
\(59\) −0.301193 −0.0392120 −0.0196060 0.999808i \(-0.506241\pi\)
−0.0196060 + 0.999808i \(0.506241\pi\)
\(60\) 1.65798 0.214044
\(61\) 6.23491 0.798299 0.399149 0.916886i \(-0.369305\pi\)
0.399149 + 0.916886i \(0.369305\pi\)
\(62\) 22.5974 2.86988
\(63\) −3.55235 −0.447554
\(64\) −5.86745 −0.733431
\(65\) 0.755773 0.0937421
\(66\) −14.9840 −1.84440
\(67\) 10.4834 1.28075 0.640374 0.768064i \(-0.278780\pi\)
0.640374 + 0.768064i \(0.278780\pi\)
\(68\) 4.16025 0.504504
\(69\) −4.56280 −0.549297
\(70\) −2.60449 −0.311296
\(71\) −3.80575 −0.451659 −0.225829 0.974167i \(-0.572509\pi\)
−0.225829 + 0.974167i \(0.572509\pi\)
\(72\) 5.03986 0.593953
\(73\) −10.0591 −1.17733 −0.588664 0.808378i \(-0.700346\pi\)
−0.588664 + 0.808378i \(0.700346\pi\)
\(74\) 17.0441 1.98133
\(75\) −7.06574 −0.815881
\(76\) −4.06997 −0.466857
\(77\) 15.8961 1.81153
\(78\) −9.69625 −1.09788
\(79\) 11.4349 1.28652 0.643261 0.765647i \(-0.277581\pi\)
0.643261 + 0.765647i \(0.277581\pi\)
\(80\) 1.38477 0.154822
\(81\) −5.29653 −0.588503
\(82\) −4.40441 −0.486386
\(83\) 12.0659 1.32440 0.662200 0.749327i \(-0.269623\pi\)
0.662200 + 0.749327i \(0.269623\pi\)
\(84\) 22.5660 2.46216
\(85\) 0.277666 0.0301171
\(86\) −9.86809 −1.06410
\(87\) 0.769734 0.0825241
\(88\) −22.5525 −2.40410
\(89\) 5.72993 0.607372 0.303686 0.952772i \(-0.401783\pi\)
0.303686 + 0.952772i \(0.401783\pi\)
\(90\) 0.647796 0.0682837
\(91\) 10.2865 1.07832
\(92\) −13.2256 −1.37886
\(93\) −13.0676 −1.35505
\(94\) −27.3519 −2.82113
\(95\) −0.271641 −0.0278697
\(96\) −2.37494 −0.242391
\(97\) 6.42228 0.652084 0.326042 0.945355i \(-0.394285\pi\)
0.326042 + 0.945355i \(0.394285\pi\)
\(98\) −18.0747 −1.82582
\(99\) −3.95373 −0.397365
\(100\) −20.4805 −2.04805
\(101\) 0.450826 0.0448588 0.0224294 0.999748i \(-0.492860\pi\)
0.0224294 + 0.999748i \(0.492860\pi\)
\(102\) −3.56234 −0.352724
\(103\) −5.08324 −0.500866 −0.250433 0.968134i \(-0.580573\pi\)
−0.250433 + 0.968134i \(0.580573\pi\)
\(104\) −14.5939 −1.43105
\(105\) 1.50612 0.146982
\(106\) −19.8409 −1.92712
\(107\) −4.14499 −0.400711 −0.200356 0.979723i \(-0.564210\pi\)
−0.200356 + 0.979723i \(0.564210\pi\)
\(108\) −23.5261 −2.26380
\(109\) 7.54018 0.722218 0.361109 0.932524i \(-0.382398\pi\)
0.361109 + 0.932524i \(0.382398\pi\)
\(110\) −2.89877 −0.276387
\(111\) −9.85622 −0.935511
\(112\) 18.8475 1.78092
\(113\) 14.6290 1.37618 0.688090 0.725625i \(-0.258449\pi\)
0.688090 + 0.725625i \(0.258449\pi\)
\(114\) 3.48503 0.326403
\(115\) −0.882711 −0.0823132
\(116\) 2.23112 0.207155
\(117\) −2.55849 −0.236533
\(118\) 0.747558 0.0688183
\(119\) 3.77920 0.346439
\(120\) −2.13679 −0.195062
\(121\) 6.69226 0.608387
\(122\) −15.4750 −1.40104
\(123\) 2.54698 0.229653
\(124\) −37.8774 −3.40149
\(125\) −2.75526 −0.246438
\(126\) 8.81687 0.785469
\(127\) 20.5742 1.82566 0.912831 0.408337i \(-0.133891\pi\)
0.912831 + 0.408337i \(0.133891\pi\)
\(128\) 17.8723 1.57970
\(129\) 5.70651 0.502430
\(130\) −1.87582 −0.164520
\(131\) 21.9445 1.91730 0.958651 0.284584i \(-0.0918554\pi\)
0.958651 + 0.284584i \(0.0918554\pi\)
\(132\) 25.1158 2.18605
\(133\) −3.69718 −0.320587
\(134\) −26.0196 −2.24775
\(135\) −1.57019 −0.135141
\(136\) −5.36171 −0.459763
\(137\) 8.31489 0.710389 0.355194 0.934792i \(-0.384415\pi\)
0.355194 + 0.934792i \(0.384415\pi\)
\(138\) 11.3248 0.964031
\(139\) 2.69931 0.228952 0.114476 0.993426i \(-0.463481\pi\)
0.114476 + 0.993426i \(0.463481\pi\)
\(140\) 4.36558 0.368959
\(141\) 15.8170 1.33203
\(142\) 9.44581 0.792674
\(143\) 11.4488 0.957397
\(144\) −4.68781 −0.390651
\(145\) 0.148911 0.0123664
\(146\) 24.9665 2.06624
\(147\) 10.4522 0.862083
\(148\) −28.5689 −2.34835
\(149\) 9.53406 0.781060 0.390530 0.920590i \(-0.372292\pi\)
0.390530 + 0.920590i \(0.372292\pi\)
\(150\) 17.5371 1.43189
\(151\) 10.5658 0.859836 0.429918 0.902868i \(-0.358542\pi\)
0.429918 + 0.902868i \(0.358542\pi\)
\(152\) 5.24535 0.425454
\(153\) −0.939973 −0.0759924
\(154\) −39.4539 −3.17929
\(155\) −2.52804 −0.203057
\(156\) 16.2526 1.30125
\(157\) −18.2513 −1.45661 −0.728306 0.685252i \(-0.759692\pi\)
−0.728306 + 0.685252i \(0.759692\pi\)
\(158\) −28.3812 −2.25788
\(159\) 11.4736 0.909913
\(160\) −0.459450 −0.0363227
\(161\) −12.0142 −0.946852
\(162\) 13.1459 1.03284
\(163\) −9.02054 −0.706543 −0.353272 0.935521i \(-0.614931\pi\)
−0.353272 + 0.935521i \(0.614931\pi\)
\(164\) 7.38258 0.576483
\(165\) 1.67630 0.130500
\(166\) −29.9473 −2.32436
\(167\) 8.77481 0.679016 0.339508 0.940603i \(-0.389740\pi\)
0.339508 + 0.940603i \(0.389740\pi\)
\(168\) −29.0830 −2.24380
\(169\) −5.59139 −0.430107
\(170\) −0.689164 −0.0528564
\(171\) 0.919575 0.0703216
\(172\) 16.5407 1.26121
\(173\) 21.7882 1.65653 0.828265 0.560337i \(-0.189328\pi\)
0.828265 + 0.560337i \(0.189328\pi\)
\(174\) −1.91047 −0.144832
\(175\) −18.6046 −1.40638
\(176\) 20.9771 1.58121
\(177\) −0.432297 −0.0324934
\(178\) −14.2216 −1.06595
\(179\) −20.7976 −1.55449 −0.777245 0.629199i \(-0.783383\pi\)
−0.777245 + 0.629199i \(0.783383\pi\)
\(180\) −1.08582 −0.0809323
\(181\) 0.360374 0.0267864 0.0133932 0.999910i \(-0.495737\pi\)
0.0133932 + 0.999910i \(0.495737\pi\)
\(182\) −25.5310 −1.89248
\(183\) 8.94884 0.661517
\(184\) 17.0450 1.25658
\(185\) −1.90676 −0.140188
\(186\) 32.4336 2.37815
\(187\) 4.20622 0.307589
\(188\) 45.8466 3.34371
\(189\) −21.3712 −1.55453
\(190\) 0.674208 0.0489122
\(191\) −4.50425 −0.325916 −0.162958 0.986633i \(-0.552104\pi\)
−0.162958 + 0.986633i \(0.552104\pi\)
\(192\) −8.42143 −0.607764
\(193\) −2.15128 −0.154853 −0.0774264 0.996998i \(-0.524670\pi\)
−0.0774264 + 0.996998i \(0.524670\pi\)
\(194\) −15.9400 −1.14443
\(195\) 1.08475 0.0776803
\(196\) 30.2964 2.16403
\(197\) 4.53559 0.323148 0.161574 0.986861i \(-0.448343\pi\)
0.161574 + 0.986861i \(0.448343\pi\)
\(198\) 9.81310 0.697387
\(199\) −9.71419 −0.688621 −0.344310 0.938856i \(-0.611887\pi\)
−0.344310 + 0.938856i \(0.611887\pi\)
\(200\) 26.3952 1.86642
\(201\) 15.0466 1.06130
\(202\) −1.11894 −0.0787285
\(203\) 2.02677 0.142251
\(204\) 5.97112 0.418062
\(205\) 0.492734 0.0344140
\(206\) 12.6165 0.879035
\(207\) 2.98821 0.207695
\(208\) 13.5745 0.941221
\(209\) −4.11494 −0.284636
\(210\) −3.73817 −0.257958
\(211\) 15.7249 1.08254 0.541272 0.840847i \(-0.317943\pi\)
0.541272 + 0.840847i \(0.317943\pi\)
\(212\) 33.2569 2.28409
\(213\) −5.46231 −0.374271
\(214\) 10.2878 0.703260
\(215\) 1.10397 0.0752901
\(216\) 30.3203 2.06303
\(217\) −34.4080 −2.33577
\(218\) −18.7146 −1.26751
\(219\) −14.4376 −0.975603
\(220\) 4.85886 0.327584
\(221\) 2.72188 0.183093
\(222\) 24.4630 1.64185
\(223\) 0.194992 0.0130576 0.00652882 0.999979i \(-0.497922\pi\)
0.00652882 + 0.999979i \(0.497922\pi\)
\(224\) −6.25338 −0.417822
\(225\) 4.62740 0.308493
\(226\) −36.3089 −2.41523
\(227\) 3.56514 0.236627 0.118313 0.992976i \(-0.462251\pi\)
0.118313 + 0.992976i \(0.462251\pi\)
\(228\) −5.84154 −0.386865
\(229\) 9.58050 0.633097 0.316549 0.948576i \(-0.397476\pi\)
0.316549 + 0.948576i \(0.397476\pi\)
\(230\) 2.19087 0.144462
\(231\) 22.8154 1.50114
\(232\) −2.87546 −0.188783
\(233\) 17.2692 1.13134 0.565671 0.824631i \(-0.308617\pi\)
0.565671 + 0.824631i \(0.308617\pi\)
\(234\) 6.35014 0.415121
\(235\) 3.05993 0.199608
\(236\) −1.25304 −0.0815659
\(237\) 16.4122 1.06609
\(238\) −9.37991 −0.608010
\(239\) 3.04681 0.197081 0.0985407 0.995133i \(-0.468583\pi\)
0.0985407 + 0.995133i \(0.468583\pi\)
\(240\) 1.98753 0.128295
\(241\) 5.71679 0.368251 0.184125 0.982903i \(-0.441055\pi\)
0.184125 + 0.982903i \(0.441055\pi\)
\(242\) −16.6101 −1.06774
\(243\) 9.36289 0.600630
\(244\) 25.9388 1.66056
\(245\) 2.02206 0.129185
\(246\) −6.32156 −0.403048
\(247\) −2.66281 −0.169430
\(248\) 48.8161 3.09983
\(249\) 17.3179 1.09748
\(250\) 6.83850 0.432505
\(251\) 5.18002 0.326960 0.163480 0.986547i \(-0.447728\pi\)
0.163480 + 0.986547i \(0.447728\pi\)
\(252\) −14.7786 −0.930967
\(253\) −13.3717 −0.840672
\(254\) −51.0648 −3.20409
\(255\) 0.398529 0.0249568
\(256\) −32.6239 −2.03899
\(257\) 12.1992 0.760968 0.380484 0.924788i \(-0.375757\pi\)
0.380484 + 0.924788i \(0.375757\pi\)
\(258\) −14.1635 −0.881779
\(259\) −25.9522 −1.61259
\(260\) 3.14421 0.194995
\(261\) −0.504104 −0.0312032
\(262\) −54.4660 −3.36492
\(263\) −15.4227 −0.951005 −0.475502 0.879714i \(-0.657734\pi\)
−0.475502 + 0.879714i \(0.657734\pi\)
\(264\) −32.3691 −1.99218
\(265\) 2.21965 0.136352
\(266\) 9.17636 0.562639
\(267\) 8.22406 0.503304
\(268\) 43.6134 2.66411
\(269\) −11.3387 −0.691333 −0.345667 0.938357i \(-0.612347\pi\)
−0.345667 + 0.938357i \(0.612347\pi\)
\(270\) 3.89719 0.237176
\(271\) −8.83877 −0.536917 −0.268459 0.963291i \(-0.586514\pi\)
−0.268459 + 0.963291i \(0.586514\pi\)
\(272\) 4.98718 0.302392
\(273\) 14.7640 0.893559
\(274\) −20.6374 −1.24675
\(275\) −20.7068 −1.24867
\(276\) −18.9824 −1.14261
\(277\) 17.9184 1.07661 0.538306 0.842749i \(-0.319064\pi\)
0.538306 + 0.842749i \(0.319064\pi\)
\(278\) −6.69965 −0.401818
\(279\) 8.55807 0.512358
\(280\) −5.62634 −0.336238
\(281\) −0.602333 −0.0359321 −0.0179661 0.999839i \(-0.505719\pi\)
−0.0179661 + 0.999839i \(0.505719\pi\)
\(282\) −39.2576 −2.33775
\(283\) 24.1768 1.43716 0.718580 0.695445i \(-0.244793\pi\)
0.718580 + 0.695445i \(0.244793\pi\)
\(284\) −15.8329 −0.939507
\(285\) −0.389880 −0.0230945
\(286\) −28.4157 −1.68026
\(287\) 6.70639 0.395866
\(288\) 1.55536 0.0916505
\(289\) 1.00000 0.0588235
\(290\) −0.369595 −0.0217034
\(291\) 9.21777 0.540355
\(292\) −41.8483 −2.44899
\(293\) −5.78422 −0.337918 −0.168959 0.985623i \(-0.554040\pi\)
−0.168959 + 0.985623i \(0.554040\pi\)
\(294\) −25.9422 −1.51298
\(295\) −0.0836313 −0.00486920
\(296\) 36.8194 2.14009
\(297\) −23.7860 −1.38020
\(298\) −23.6634 −1.37078
\(299\) −8.65294 −0.500412
\(300\) −29.3952 −1.69713
\(301\) 15.0257 0.866065
\(302\) −26.2243 −1.50904
\(303\) 0.647061 0.0371727
\(304\) −4.87895 −0.279827
\(305\) 1.73123 0.0991297
\(306\) 2.33300 0.133369
\(307\) −23.9252 −1.36548 −0.682742 0.730659i \(-0.739213\pi\)
−0.682742 + 0.730659i \(0.739213\pi\)
\(308\) 66.1319 3.76821
\(309\) −7.29587 −0.415047
\(310\) 6.27455 0.356371
\(311\) 3.12328 0.177105 0.0885524 0.996072i \(-0.471776\pi\)
0.0885524 + 0.996072i \(0.471776\pi\)
\(312\) −20.9463 −1.18585
\(313\) −29.9803 −1.69459 −0.847295 0.531123i \(-0.821770\pi\)
−0.847295 + 0.531123i \(0.821770\pi\)
\(314\) 45.2994 2.55640
\(315\) −0.986367 −0.0555755
\(316\) 47.5719 2.67613
\(317\) −0.216064 −0.0121354 −0.00606770 0.999982i \(-0.501931\pi\)
−0.00606770 + 0.999982i \(0.501931\pi\)
\(318\) −28.4772 −1.59692
\(319\) 2.25578 0.126299
\(320\) −1.62919 −0.0910747
\(321\) −5.94922 −0.332053
\(322\) 29.8191 1.66175
\(323\) −0.978299 −0.0544340
\(324\) −22.0349 −1.22416
\(325\) −13.3995 −0.743272
\(326\) 22.3888 1.24000
\(327\) 10.8223 0.598472
\(328\) −9.51463 −0.525358
\(329\) 41.6474 2.29609
\(330\) −4.16055 −0.229031
\(331\) 4.90634 0.269677 0.134839 0.990868i \(-0.456948\pi\)
0.134839 + 0.990868i \(0.456948\pi\)
\(332\) 50.1970 2.75492
\(333\) 6.45490 0.353726
\(334\) −21.7790 −1.19169
\(335\) 2.91088 0.159038
\(336\) 27.0515 1.47578
\(337\) −8.78664 −0.478639 −0.239319 0.970941i \(-0.576924\pi\)
−0.239319 + 0.970941i \(0.576924\pi\)
\(338\) 13.8778 0.754850
\(339\) 20.9967 1.14038
\(340\) 1.15516 0.0626474
\(341\) −38.2959 −2.07384
\(342\) −2.28237 −0.123416
\(343\) 1.06703 0.0576143
\(344\) −21.3175 −1.14936
\(345\) −1.26694 −0.0682096
\(346\) −54.0781 −2.90726
\(347\) −20.1876 −1.08373 −0.541865 0.840466i \(-0.682282\pi\)
−0.541865 + 0.840466i \(0.682282\pi\)
\(348\) 3.20229 0.171661
\(349\) 2.76017 0.147749 0.0738743 0.997268i \(-0.476464\pi\)
0.0738743 + 0.997268i \(0.476464\pi\)
\(350\) 46.1764 2.46823
\(351\) −15.3921 −0.821570
\(352\) −6.95996 −0.370967
\(353\) −1.00000 −0.0532246
\(354\) 1.07295 0.0570269
\(355\) −1.05673 −0.0560853
\(356\) 23.8380 1.26341
\(357\) 5.42421 0.287079
\(358\) 51.6194 2.72817
\(359\) −21.4938 −1.13440 −0.567200 0.823580i \(-0.691973\pi\)
−0.567200 + 0.823580i \(0.691973\pi\)
\(360\) 1.39940 0.0737549
\(361\) −18.0429 −0.949628
\(362\) −0.894444 −0.0470109
\(363\) 9.60525 0.504145
\(364\) 42.7944 2.24304
\(365\) −2.79307 −0.146196
\(366\) −22.2109 −1.16098
\(367\) −6.79233 −0.354557 −0.177278 0.984161i \(-0.556729\pi\)
−0.177278 + 0.984161i \(0.556729\pi\)
\(368\) −15.8544 −0.826468
\(369\) −1.66803 −0.0868343
\(370\) 4.73256 0.246034
\(371\) 30.2108 1.56846
\(372\) −54.3646 −2.81867
\(373\) 7.58283 0.392624 0.196312 0.980541i \(-0.437103\pi\)
0.196312 + 0.980541i \(0.437103\pi\)
\(374\) −10.4398 −0.539827
\(375\) −3.95456 −0.204213
\(376\) −59.0869 −3.04717
\(377\) 1.45973 0.0751799
\(378\) 53.0431 2.72824
\(379\) −22.9866 −1.18074 −0.590372 0.807131i \(-0.701019\pi\)
−0.590372 + 0.807131i \(0.701019\pi\)
\(380\) −1.13009 −0.0579725
\(381\) 29.5297 1.51285
\(382\) 11.1795 0.571992
\(383\) −8.64576 −0.441778 −0.220889 0.975299i \(-0.570896\pi\)
−0.220889 + 0.975299i \(0.570896\pi\)
\(384\) 25.6517 1.30903
\(385\) 4.41382 0.224949
\(386\) 5.33946 0.271771
\(387\) −3.73723 −0.189974
\(388\) 26.7183 1.35642
\(389\) 23.6530 1.19926 0.599628 0.800279i \(-0.295315\pi\)
0.599628 + 0.800279i \(0.295315\pi\)
\(390\) −2.69232 −0.136331
\(391\) −3.17903 −0.160771
\(392\) −39.0458 −1.97211
\(393\) 31.4965 1.58879
\(394\) −11.2573 −0.567133
\(395\) 3.17508 0.159755
\(396\) −16.4485 −0.826569
\(397\) 10.2887 0.516374 0.258187 0.966095i \(-0.416875\pi\)
0.258187 + 0.966095i \(0.416875\pi\)
\(398\) 24.1105 1.20855
\(399\) −5.30649 −0.265657
\(400\) −24.5514 −1.22757
\(401\) −6.94438 −0.346786 −0.173393 0.984853i \(-0.555473\pi\)
−0.173393 + 0.984853i \(0.555473\pi\)
\(402\) −37.3453 −1.86262
\(403\) −24.7816 −1.23446
\(404\) 1.87555 0.0933120
\(405\) −1.47067 −0.0730781
\(406\) −5.03041 −0.249655
\(407\) −28.8845 −1.43175
\(408\) −7.69555 −0.380986
\(409\) −10.8554 −0.536767 −0.268383 0.963312i \(-0.586489\pi\)
−0.268383 + 0.963312i \(0.586489\pi\)
\(410\) −1.22296 −0.0603976
\(411\) 11.9342 0.588670
\(412\) −21.1475 −1.04186
\(413\) −1.13827 −0.0560106
\(414\) −7.41669 −0.364510
\(415\) 3.35028 0.164459
\(416\) −4.50385 −0.220819
\(417\) 3.87426 0.189723
\(418\) 10.2132 0.499544
\(419\) 5.20241 0.254154 0.127077 0.991893i \(-0.459440\pi\)
0.127077 + 0.991893i \(0.459440\pi\)
\(420\) 6.26583 0.305741
\(421\) −11.5056 −0.560750 −0.280375 0.959891i \(-0.590459\pi\)
−0.280375 + 0.959891i \(0.590459\pi\)
\(422\) −39.0289 −1.89990
\(423\) −10.3587 −0.503655
\(424\) −42.8613 −2.08153
\(425\) −4.92290 −0.238796
\(426\) 13.5574 0.656857
\(427\) 23.5630 1.14029
\(428\) −17.2442 −0.833530
\(429\) 16.4322 0.793355
\(430\) −2.74004 −0.132136
\(431\) −17.2942 −0.833033 −0.416517 0.909128i \(-0.636749\pi\)
−0.416517 + 0.909128i \(0.636749\pi\)
\(432\) −28.2023 −1.35688
\(433\) −0.921727 −0.0442954 −0.0221477 0.999755i \(-0.507050\pi\)
−0.0221477 + 0.999755i \(0.507050\pi\)
\(434\) 85.4002 4.09934
\(435\) 0.213729 0.0102475
\(436\) 31.3690 1.50230
\(437\) 3.11004 0.148774
\(438\) 35.8339 1.71221
\(439\) 29.2974 1.39829 0.699144 0.714981i \(-0.253565\pi\)
0.699144 + 0.714981i \(0.253565\pi\)
\(440\) −6.26207 −0.298532
\(441\) −6.84521 −0.325962
\(442\) −6.75566 −0.321334
\(443\) 1.35637 0.0644433 0.0322216 0.999481i \(-0.489742\pi\)
0.0322216 + 0.999481i \(0.489742\pi\)
\(444\) −41.0043 −1.94598
\(445\) 1.59101 0.0754211
\(446\) −0.483968 −0.0229165
\(447\) 13.6840 0.647233
\(448\) −22.1743 −1.04764
\(449\) −16.5590 −0.781468 −0.390734 0.920504i \(-0.627779\pi\)
−0.390734 + 0.920504i \(0.627779\pi\)
\(450\) −11.4851 −0.541414
\(451\) 7.46415 0.351473
\(452\) 60.8603 2.86263
\(453\) 15.1649 0.712511
\(454\) −8.84862 −0.415286
\(455\) 2.85622 0.133902
\(456\) 7.52854 0.352556
\(457\) −25.7376 −1.20395 −0.601976 0.798514i \(-0.705620\pi\)
−0.601976 + 0.798514i \(0.705620\pi\)
\(458\) −23.7787 −1.11110
\(459\) −5.65496 −0.263951
\(460\) −3.67230 −0.171222
\(461\) −22.1859 −1.03330 −0.516650 0.856197i \(-0.672821\pi\)
−0.516650 + 0.856197i \(0.672821\pi\)
\(462\) −56.6274 −2.63455
\(463\) 11.8476 0.550604 0.275302 0.961358i \(-0.411222\pi\)
0.275302 + 0.961358i \(0.411222\pi\)
\(464\) 2.67460 0.124165
\(465\) −3.62844 −0.168265
\(466\) −42.8619 −1.98554
\(467\) 0.404557 0.0187206 0.00936032 0.999956i \(-0.497020\pi\)
0.00936032 + 0.999956i \(0.497020\pi\)
\(468\) −10.6440 −0.492017
\(469\) 39.6187 1.82942
\(470\) −7.59469 −0.350317
\(471\) −26.1957 −1.20703
\(472\) 1.61491 0.0743323
\(473\) 16.7234 0.768944
\(474\) −40.7349 −1.87102
\(475\) 4.81607 0.220976
\(476\) 15.7224 0.720635
\(477\) −7.51411 −0.344047
\(478\) −7.56213 −0.345884
\(479\) 1.71129 0.0781910 0.0390955 0.999235i \(-0.487552\pi\)
0.0390955 + 0.999235i \(0.487552\pi\)
\(480\) −0.659440 −0.0300992
\(481\) −18.6914 −0.852255
\(482\) −14.1890 −0.646290
\(483\) −17.2437 −0.784617
\(484\) 27.8415 1.26552
\(485\) 1.78325 0.0809733
\(486\) −23.2385 −1.05412
\(487\) −17.1105 −0.775352 −0.387676 0.921796i \(-0.626722\pi\)
−0.387676 + 0.921796i \(0.626722\pi\)
\(488\) −33.4298 −1.51329
\(489\) −12.9470 −0.585483
\(490\) −5.01873 −0.226723
\(491\) 27.1408 1.22485 0.612424 0.790530i \(-0.290195\pi\)
0.612424 + 0.790530i \(0.290195\pi\)
\(492\) 10.5961 0.477708
\(493\) 0.536296 0.0241535
\(494\) 6.60905 0.297355
\(495\) −1.09782 −0.0493433
\(496\) −45.4062 −2.03880
\(497\) −14.3827 −0.645151
\(498\) −42.9827 −1.92610
\(499\) −18.6038 −0.832820 −0.416410 0.909177i \(-0.636712\pi\)
−0.416410 + 0.909177i \(0.636712\pi\)
\(500\) −11.4626 −0.512621
\(501\) 12.5943 0.562672
\(502\) −12.8567 −0.573824
\(503\) −35.2784 −1.57298 −0.786492 0.617600i \(-0.788105\pi\)
−0.786492 + 0.617600i \(0.788105\pi\)
\(504\) 19.0466 0.848405
\(505\) 0.125179 0.00557040
\(506\) 33.1884 1.47540
\(507\) −8.02521 −0.356412
\(508\) 85.5937 3.79761
\(509\) 32.0007 1.41841 0.709203 0.705004i \(-0.249055\pi\)
0.709203 + 0.705004i \(0.249055\pi\)
\(510\) −0.989142 −0.0438000
\(511\) −38.0153 −1.68170
\(512\) 45.2274 1.99879
\(513\) 5.53224 0.244254
\(514\) −30.2783 −1.33552
\(515\) −1.41144 −0.0621957
\(516\) 23.7405 1.04512
\(517\) 46.3532 2.03861
\(518\) 64.4129 2.83014
\(519\) 31.2722 1.37270
\(520\) −4.05224 −0.177702
\(521\) −22.9815 −1.00684 −0.503419 0.864042i \(-0.667925\pi\)
−0.503419 + 0.864042i \(0.667925\pi\)
\(522\) 1.25118 0.0547626
\(523\) 15.3861 0.672789 0.336394 0.941721i \(-0.390793\pi\)
0.336394 + 0.941721i \(0.390793\pi\)
\(524\) 91.2947 3.98823
\(525\) −26.7028 −1.16541
\(526\) 38.2789 1.66904
\(527\) −9.10459 −0.396602
\(528\) 30.1081 1.31029
\(529\) −12.8937 −0.560598
\(530\) −5.50915 −0.239302
\(531\) 0.283114 0.0122861
\(532\) −15.3812 −0.666860
\(533\) 4.83011 0.209215
\(534\) −20.4120 −0.883313
\(535\) −1.15092 −0.0497588
\(536\) −56.2087 −2.42785
\(537\) −29.8504 −1.28814
\(538\) 28.1425 1.21331
\(539\) 30.6311 1.31938
\(540\) −6.53239 −0.281109
\(541\) −2.04470 −0.0879083 −0.0439542 0.999034i \(-0.513996\pi\)
−0.0439542 + 0.999034i \(0.513996\pi\)
\(542\) 21.9377 0.942305
\(543\) 0.517238 0.0221968
\(544\) −1.65469 −0.0709440
\(545\) 2.09365 0.0896823
\(546\) −36.6441 −1.56822
\(547\) 25.2900 1.08132 0.540661 0.841240i \(-0.318174\pi\)
0.540661 + 0.841240i \(0.318174\pi\)
\(548\) 34.5920 1.47770
\(549\) −5.86065 −0.250127
\(550\) 51.3939 2.19144
\(551\) −0.524657 −0.0223511
\(552\) 24.4644 1.04127
\(553\) 43.2146 1.83767
\(554\) −44.4732 −1.88948
\(555\) −2.73674 −0.116168
\(556\) 11.2298 0.476250
\(557\) 9.66350 0.409456 0.204728 0.978819i \(-0.434369\pi\)
0.204728 + 0.978819i \(0.434369\pi\)
\(558\) −21.2410 −0.899203
\(559\) 10.8219 0.457716
\(560\) 5.23333 0.221148
\(561\) 6.03709 0.254886
\(562\) 1.49498 0.0630619
\(563\) −25.0397 −1.05530 −0.527649 0.849462i \(-0.676926\pi\)
−0.527649 + 0.849462i \(0.676926\pi\)
\(564\) 65.8027 2.77079
\(565\) 4.06198 0.170889
\(566\) −60.0063 −2.52226
\(567\) −20.0166 −0.840620
\(568\) 20.4053 0.856187
\(569\) −31.1976 −1.30787 −0.653935 0.756551i \(-0.726883\pi\)
−0.653935 + 0.756551i \(0.726883\pi\)
\(570\) 0.967677 0.0405315
\(571\) 6.95777 0.291173 0.145587 0.989345i \(-0.453493\pi\)
0.145587 + 0.989345i \(0.453493\pi\)
\(572\) 47.6299 1.99150
\(573\) −6.46486 −0.270073
\(574\) −16.6452 −0.694755
\(575\) 15.6501 0.652653
\(576\) 5.51525 0.229802
\(577\) 43.7403 1.82093 0.910467 0.413581i \(-0.135722\pi\)
0.910467 + 0.413581i \(0.135722\pi\)
\(578\) −2.48199 −0.103237
\(579\) −3.08769 −0.128320
\(580\) 0.619508 0.0257237
\(581\) 45.5993 1.89178
\(582\) −22.8784 −0.948339
\(583\) 33.6243 1.39258
\(584\) 53.9339 2.23180
\(585\) −0.710407 −0.0293717
\(586\) 14.3563 0.593055
\(587\) −10.7018 −0.441709 −0.220855 0.975307i \(-0.570885\pi\)
−0.220855 + 0.975307i \(0.570885\pi\)
\(588\) 43.4837 1.79324
\(589\) 8.90700 0.367007
\(590\) 0.207572 0.00854559
\(591\) 6.50984 0.267779
\(592\) −34.2475 −1.40756
\(593\) −22.4523 −0.922007 −0.461003 0.887398i \(-0.652510\pi\)
−0.461003 + 0.887398i \(0.652510\pi\)
\(594\) 59.0365 2.42230
\(595\) 1.04936 0.0430194
\(596\) 39.6641 1.62470
\(597\) −13.9426 −0.570632
\(598\) 21.4765 0.878238
\(599\) −34.9068 −1.42625 −0.713126 0.701036i \(-0.752721\pi\)
−0.713126 + 0.701036i \(0.752721\pi\)
\(600\) 37.8844 1.54662
\(601\) 16.6039 0.677287 0.338644 0.940915i \(-0.390032\pi\)
0.338644 + 0.940915i \(0.390032\pi\)
\(602\) −37.2935 −1.51997
\(603\) −9.85409 −0.401289
\(604\) 43.9566 1.78857
\(605\) 1.85821 0.0755471
\(606\) −1.60599 −0.0652391
\(607\) −22.9755 −0.932545 −0.466272 0.884641i \(-0.654403\pi\)
−0.466272 + 0.884641i \(0.654403\pi\)
\(608\) 1.61878 0.0656500
\(609\) 2.90898 0.117878
\(610\) −4.29688 −0.173975
\(611\) 29.9955 1.21349
\(612\) −3.91052 −0.158074
\(613\) −18.9947 −0.767187 −0.383594 0.923502i \(-0.625314\pi\)
−0.383594 + 0.923502i \(0.625314\pi\)
\(614\) 59.3821 2.39646
\(615\) 0.707210 0.0285175
\(616\) −85.2304 −3.43403
\(617\) 16.4094 0.660617 0.330309 0.943873i \(-0.392847\pi\)
0.330309 + 0.943873i \(0.392847\pi\)
\(618\) 18.1082 0.728420
\(619\) 31.2186 1.25478 0.627391 0.778704i \(-0.284123\pi\)
0.627391 + 0.778704i \(0.284123\pi\)
\(620\) −10.5173 −0.422384
\(621\) 17.9773 0.721405
\(622\) −7.75193 −0.310824
\(623\) 21.6546 0.867572
\(624\) 19.4832 0.779951
\(625\) 23.8495 0.953979
\(626\) 74.4108 2.97405
\(627\) −5.90608 −0.235866
\(628\) −75.9299 −3.02993
\(629\) −6.86711 −0.273809
\(630\) 2.44815 0.0975366
\(631\) −5.63100 −0.224166 −0.112083 0.993699i \(-0.535752\pi\)
−0.112083 + 0.993699i \(0.535752\pi\)
\(632\) −61.3104 −2.43880
\(633\) 22.5696 0.897060
\(634\) 0.536269 0.0212980
\(635\) 5.71275 0.226704
\(636\) 47.7329 1.89273
\(637\) 19.8216 0.785362
\(638\) −5.59880 −0.221659
\(639\) 3.57730 0.141516
\(640\) 4.96253 0.196161
\(641\) 28.7972 1.13742 0.568711 0.822538i \(-0.307442\pi\)
0.568711 + 0.822538i \(0.307442\pi\)
\(642\) 14.7659 0.582762
\(643\) −32.1411 −1.26752 −0.633760 0.773530i \(-0.718489\pi\)
−0.633760 + 0.773530i \(0.718489\pi\)
\(644\) −49.9821 −1.96957
\(645\) 1.58450 0.0623898
\(646\) 2.42812 0.0955332
\(647\) −46.0957 −1.81221 −0.906105 0.423053i \(-0.860958\pi\)
−0.906105 + 0.423053i \(0.860958\pi\)
\(648\) 28.3984 1.11560
\(649\) −1.26688 −0.0497296
\(650\) 33.2574 1.30446
\(651\) −49.3851 −1.93556
\(652\) −37.5277 −1.46970
\(653\) −3.99520 −0.156344 −0.0781722 0.996940i \(-0.524908\pi\)
−0.0781722 + 0.996940i \(0.524908\pi\)
\(654\) −26.8607 −1.05034
\(655\) 6.09326 0.238083
\(656\) 8.85001 0.345535
\(657\) 9.45528 0.368886
\(658\) −103.368 −4.02971
\(659\) 21.8916 0.852776 0.426388 0.904540i \(-0.359786\pi\)
0.426388 + 0.904540i \(0.359786\pi\)
\(660\) 6.97382 0.271456
\(661\) −43.9859 −1.71085 −0.855426 0.517925i \(-0.826705\pi\)
−0.855426 + 0.517925i \(0.826705\pi\)
\(662\) −12.1775 −0.473291
\(663\) 3.90665 0.151722
\(664\) −64.6936 −2.51060
\(665\) −1.02658 −0.0398092
\(666\) −16.0210 −0.620800
\(667\) −1.70490 −0.0660141
\(668\) 36.5054 1.41244
\(669\) 0.279868 0.0108203
\(670\) −7.22476 −0.279117
\(671\) 26.2254 1.01242
\(672\) −8.97535 −0.346232
\(673\) 49.5184 1.90879 0.954397 0.298540i \(-0.0964997\pi\)
0.954397 + 0.298540i \(0.0964997\pi\)
\(674\) 21.8083 0.840024
\(675\) 27.8388 1.07152
\(676\) −23.2616 −0.894676
\(677\) −15.6046 −0.599733 −0.299867 0.953981i \(-0.596942\pi\)
−0.299867 + 0.953981i \(0.596942\pi\)
\(678\) −52.1135 −2.00141
\(679\) 24.2711 0.931439
\(680\) −1.48877 −0.0570916
\(681\) 5.11697 0.196083
\(682\) 95.0498 3.63964
\(683\) 11.4695 0.438869 0.219435 0.975627i \(-0.429579\pi\)
0.219435 + 0.975627i \(0.429579\pi\)
\(684\) 3.82566 0.146278
\(685\) 2.30876 0.0882134
\(686\) −2.64835 −0.101115
\(687\) 13.7507 0.524622
\(688\) 19.8284 0.755953
\(689\) 21.7586 0.828935
\(690\) 3.14452 0.119710
\(691\) 12.3650 0.470387 0.235194 0.971949i \(-0.424428\pi\)
0.235194 + 0.971949i \(0.424428\pi\)
\(692\) 90.6445 3.44579
\(693\) −14.9419 −0.567597
\(694\) 50.1054 1.90198
\(695\) 0.749507 0.0284304
\(696\) −4.12709 −0.156437
\(697\) 1.77455 0.0672160
\(698\) −6.85071 −0.259303
\(699\) 24.7861 0.937497
\(700\) −77.3999 −2.92544
\(701\) 30.2062 1.14087 0.570435 0.821342i \(-0.306774\pi\)
0.570435 + 0.821342i \(0.306774\pi\)
\(702\) 38.2030 1.44188
\(703\) 6.71808 0.253377
\(704\) −24.6798 −0.930154
\(705\) 4.39185 0.165407
\(706\) 2.48199 0.0934107
\(707\) 1.70376 0.0640765
\(708\) −1.79846 −0.0675903
\(709\) −43.5355 −1.63501 −0.817505 0.575921i \(-0.804644\pi\)
−0.817505 + 0.575921i \(0.804644\pi\)
\(710\) 2.62278 0.0984313
\(711\) −10.7485 −0.403099
\(712\) −30.7222 −1.15136
\(713\) 28.9438 1.08395
\(714\) −13.4628 −0.503833
\(715\) 3.17895 0.118886
\(716\) −86.5234 −3.23353
\(717\) 4.37302 0.163313
\(718\) 53.3473 1.99090
\(719\) 28.2991 1.05538 0.527688 0.849438i \(-0.323059\pi\)
0.527688 + 0.849438i \(0.323059\pi\)
\(720\) −1.30165 −0.0485096
\(721\) −19.2106 −0.715439
\(722\) 44.7823 1.66662
\(723\) 8.20518 0.305154
\(724\) 1.49925 0.0557191
\(725\) −2.64013 −0.0980520
\(726\) −23.8401 −0.884789
\(727\) −5.72859 −0.212461 −0.106231 0.994342i \(-0.533878\pi\)
−0.106231 + 0.994342i \(0.533878\pi\)
\(728\) −55.1533 −2.04412
\(729\) 29.3279 1.08622
\(730\) 6.93236 0.256578
\(731\) 3.97589 0.147053
\(732\) 37.2294 1.37604
\(733\) 22.7946 0.841938 0.420969 0.907075i \(-0.361690\pi\)
0.420969 + 0.907075i \(0.361690\pi\)
\(734\) 16.8585 0.622257
\(735\) 2.90222 0.107050
\(736\) 5.26030 0.193897
\(737\) 44.0953 1.62427
\(738\) 4.14003 0.152397
\(739\) −33.8244 −1.24425 −0.622125 0.782918i \(-0.713731\pi\)
−0.622125 + 0.782918i \(0.713731\pi\)
\(740\) −7.93262 −0.291609
\(741\) −3.82187 −0.140400
\(742\) −74.9827 −2.75270
\(743\) −31.5709 −1.15823 −0.579113 0.815248i \(-0.696601\pi\)
−0.579113 + 0.815248i \(0.696601\pi\)
\(744\) 70.0648 2.56870
\(745\) 2.64729 0.0969891
\(746\) −18.8205 −0.689066
\(747\) −11.3416 −0.414967
\(748\) 17.4989 0.639823
\(749\) −15.6647 −0.572377
\(750\) 9.81516 0.358399
\(751\) −19.3264 −0.705230 −0.352615 0.935769i \(-0.614707\pi\)
−0.352615 + 0.935769i \(0.614707\pi\)
\(752\) 54.9595 2.00417
\(753\) 7.43477 0.270938
\(754\) −3.62303 −0.131943
\(755\) 2.93378 0.106771
\(756\) −88.9096 −3.23361
\(757\) 30.8417 1.12096 0.560480 0.828168i \(-0.310617\pi\)
0.560480 + 0.828168i \(0.310617\pi\)
\(758\) 57.0525 2.07224
\(759\) −19.1921 −0.696630
\(760\) 1.45646 0.0528313
\(761\) 46.7865 1.69601 0.848005 0.529989i \(-0.177804\pi\)
0.848005 + 0.529989i \(0.177804\pi\)
\(762\) −73.2922 −2.65510
\(763\) 28.4958 1.03162
\(764\) −18.7388 −0.677946
\(765\) −0.260999 −0.00943644
\(766\) 21.4587 0.775333
\(767\) −0.819811 −0.0296017
\(768\) −46.8244 −1.68963
\(769\) 51.8980 1.87149 0.935746 0.352676i \(-0.114728\pi\)
0.935746 + 0.352676i \(0.114728\pi\)
\(770\) −10.9550 −0.394792
\(771\) 17.5093 0.630583
\(772\) −8.94988 −0.322113
\(773\) −1.32053 −0.0474960 −0.0237480 0.999718i \(-0.507560\pi\)
−0.0237480 + 0.999718i \(0.507560\pi\)
\(774\) 9.27574 0.333410
\(775\) 44.8210 1.61002
\(776\) −34.4344 −1.23612
\(777\) −37.2486 −1.33629
\(778\) −58.7064 −2.10473
\(779\) −1.73604 −0.0622002
\(780\) 4.51281 0.161585
\(781\) −16.0078 −0.572804
\(782\) 7.89031 0.282157
\(783\) −3.03273 −0.108381
\(784\) 36.3183 1.29708
\(785\) −5.06777 −0.180876
\(786\) −78.1739 −2.78837
\(787\) −44.9079 −1.60079 −0.800397 0.599471i \(-0.795378\pi\)
−0.800397 + 0.599471i \(0.795378\pi\)
\(788\) 18.8692 0.672187
\(789\) −22.1359 −0.788059
\(790\) −7.88049 −0.280375
\(791\) 55.2859 1.96574
\(792\) 21.1988 0.753265
\(793\) 16.9707 0.602646
\(794\) −25.5364 −0.906252
\(795\) 3.18582 0.112989
\(796\) −40.4134 −1.43242
\(797\) 40.6535 1.44002 0.720011 0.693963i \(-0.244137\pi\)
0.720011 + 0.693963i \(0.244137\pi\)
\(798\) 13.1706 0.466235
\(799\) 11.0202 0.389865
\(800\) 8.14585 0.287999
\(801\) −5.38599 −0.190304
\(802\) 17.2358 0.608619
\(803\) −42.3107 −1.49311
\(804\) 62.5974 2.20764
\(805\) −3.33594 −0.117576
\(806\) 61.5074 2.16651
\(807\) −16.2742 −0.572880
\(808\) −2.41719 −0.0850366
\(809\) −9.72545 −0.341929 −0.170964 0.985277i \(-0.554688\pi\)
−0.170964 + 0.985277i \(0.554688\pi\)
\(810\) 3.65018 0.128254
\(811\) 16.6905 0.586081 0.293041 0.956100i \(-0.405333\pi\)
0.293041 + 0.956100i \(0.405333\pi\)
\(812\) 8.43186 0.295900
\(813\) −12.6861 −0.444921
\(814\) 71.6910 2.51277
\(815\) −2.50470 −0.0877358
\(816\) 7.15799 0.250580
\(817\) −3.88960 −0.136080
\(818\) 26.9430 0.942041
\(819\) −9.66905 −0.337864
\(820\) 2.04989 0.0715854
\(821\) 1.16610 0.0406972 0.0203486 0.999793i \(-0.493522\pi\)
0.0203486 + 0.999793i \(0.493522\pi\)
\(822\) −29.6205 −1.03313
\(823\) 26.1427 0.911276 0.455638 0.890165i \(-0.349411\pi\)
0.455638 + 0.890165i \(0.349411\pi\)
\(824\) 27.2548 0.949467
\(825\) −29.7200 −1.03472
\(826\) 2.82517 0.0983002
\(827\) −42.5667 −1.48019 −0.740094 0.672503i \(-0.765219\pi\)
−0.740094 + 0.672503i \(0.765219\pi\)
\(828\) 12.4317 0.432031
\(829\) −9.98421 −0.346766 −0.173383 0.984854i \(-0.555470\pi\)
−0.173383 + 0.984854i \(0.555470\pi\)
\(830\) −8.31535 −0.288630
\(831\) 25.7179 0.892144
\(832\) −15.9705 −0.553676
\(833\) 7.28234 0.252318
\(834\) −9.61586 −0.332970
\(835\) 2.43647 0.0843175
\(836\) −17.1192 −0.592078
\(837\) 51.4861 1.77962
\(838\) −12.9123 −0.446048
\(839\) −9.33042 −0.322122 −0.161061 0.986944i \(-0.551492\pi\)
−0.161061 + 0.986944i \(0.551492\pi\)
\(840\) −8.07537 −0.278627
\(841\) −28.7124 −0.990082
\(842\) 28.5568 0.984132
\(843\) −0.864515 −0.0297755
\(844\) 65.4194 2.25183
\(845\) −1.55254 −0.0534090
\(846\) 25.7100 0.883929
\(847\) 25.2914 0.869021
\(848\) 39.8673 1.36905
\(849\) 34.7004 1.19091
\(850\) 12.2186 0.419093
\(851\) 21.8308 0.748349
\(852\) −22.7246 −0.778531
\(853\) −13.9332 −0.477063 −0.238532 0.971135i \(-0.576666\pi\)
−0.238532 + 0.971135i \(0.576666\pi\)
\(854\) −58.4829 −2.00125
\(855\) 0.255335 0.00873227
\(856\) 22.2242 0.759608
\(857\) −23.3276 −0.796854 −0.398427 0.917200i \(-0.630444\pi\)
−0.398427 + 0.917200i \(0.630444\pi\)
\(858\) −40.7845 −1.39236
\(859\) −40.8289 −1.39306 −0.696532 0.717525i \(-0.745275\pi\)
−0.696532 + 0.717525i \(0.745275\pi\)
\(860\) 4.59279 0.156613
\(861\) 9.62554 0.328038
\(862\) 42.9240 1.46200
\(863\) −33.7882 −1.15016 −0.575082 0.818096i \(-0.695030\pi\)
−0.575082 + 0.818096i \(0.695030\pi\)
\(864\) 9.35718 0.318338
\(865\) 6.04986 0.205702
\(866\) 2.28771 0.0777397
\(867\) 1.43528 0.0487446
\(868\) −143.146 −4.85869
\(869\) 48.0975 1.63160
\(870\) −0.530473 −0.0179847
\(871\) 28.5344 0.966852
\(872\) −40.4282 −1.36907
\(873\) −6.03678 −0.204314
\(874\) −7.71908 −0.261102
\(875\) −10.4127 −0.352012
\(876\) −60.0640 −2.02938
\(877\) 50.6075 1.70890 0.854448 0.519538i \(-0.173896\pi\)
0.854448 + 0.519538i \(0.173896\pi\)
\(878\) −72.7157 −2.45403
\(879\) −8.30197 −0.280018
\(880\) 5.82465 0.196349
\(881\) −1.32320 −0.0445796 −0.0222898 0.999752i \(-0.507096\pi\)
−0.0222898 + 0.999752i \(0.507096\pi\)
\(882\) 16.9897 0.572073
\(883\) −20.2995 −0.683134 −0.341567 0.939857i \(-0.610958\pi\)
−0.341567 + 0.939857i \(0.610958\pi\)
\(884\) 11.3237 0.380857
\(885\) −0.120034 −0.00403491
\(886\) −3.36650 −0.113100
\(887\) 1.96713 0.0660497 0.0330249 0.999455i \(-0.489486\pi\)
0.0330249 + 0.999455i \(0.489486\pi\)
\(888\) 52.8461 1.77340
\(889\) 77.7539 2.60778
\(890\) −3.94886 −0.132366
\(891\) −22.2783 −0.746353
\(892\) 0.811216 0.0271615
\(893\) −10.7810 −0.360773
\(894\) −33.9636 −1.13591
\(895\) −5.77481 −0.193030
\(896\) 67.5430 2.25645
\(897\) −12.4194 −0.414671
\(898\) 41.0992 1.37150
\(899\) −4.88275 −0.162849
\(900\) 19.2511 0.641704
\(901\) 7.99396 0.266317
\(902\) −18.5259 −0.616846
\(903\) 21.5660 0.717672
\(904\) −78.4364 −2.60875
\(905\) 0.100064 0.00332623
\(906\) −37.6391 −1.25048
\(907\) 16.8794 0.560472 0.280236 0.959931i \(-0.409587\pi\)
0.280236 + 0.959931i \(0.409587\pi\)
\(908\) 14.8319 0.492213
\(909\) −0.423764 −0.0140554
\(910\) −7.08909 −0.235001
\(911\) 49.7681 1.64889 0.824446 0.565941i \(-0.191487\pi\)
0.824446 + 0.565941i \(0.191487\pi\)
\(912\) −7.00265 −0.231881
\(913\) 50.7516 1.67963
\(914\) 63.8802 2.11297
\(915\) 2.48479 0.0821447
\(916\) 39.8573 1.31692
\(917\) 82.9327 2.73868
\(918\) 14.0355 0.463242
\(919\) −28.6267 −0.944308 −0.472154 0.881516i \(-0.656523\pi\)
−0.472154 + 0.881516i \(0.656523\pi\)
\(920\) 4.73284 0.156037
\(921\) −34.3394 −1.13152
\(922\) 55.0651 1.81347
\(923\) −10.3588 −0.340963
\(924\) 94.9177 3.12256
\(925\) 33.8061 1.11154
\(926\) −29.4055 −0.966326
\(927\) 4.77811 0.156934
\(928\) −0.887401 −0.0291303
\(929\) −22.7823 −0.747463 −0.373731 0.927537i \(-0.621922\pi\)
−0.373731 + 0.927537i \(0.621922\pi\)
\(930\) 9.00573 0.295310
\(931\) −7.12431 −0.233490
\(932\) 71.8441 2.35333
\(933\) 4.48277 0.146759
\(934\) −1.00410 −0.0328553
\(935\) 1.16792 0.0381952
\(936\) 13.7179 0.448383
\(937\) 16.7379 0.546804 0.273402 0.961900i \(-0.411851\pi\)
0.273402 + 0.961900i \(0.411851\pi\)
\(938\) −98.3331 −3.21069
\(939\) −43.0302 −1.40424
\(940\) 12.7301 0.415209
\(941\) −1.11472 −0.0363389 −0.0181695 0.999835i \(-0.505784\pi\)
−0.0181695 + 0.999835i \(0.505784\pi\)
\(942\) 65.0173 2.11838
\(943\) −5.64136 −0.183708
\(944\) −1.50211 −0.0488894
\(945\) −5.93407 −0.193035
\(946\) −41.5073 −1.34952
\(947\) −32.9839 −1.07183 −0.535916 0.844271i \(-0.680034\pi\)
−0.535916 + 0.844271i \(0.680034\pi\)
\(948\) 68.2789 2.21760
\(949\) −27.3796 −0.888779
\(950\) −11.9534 −0.387820
\(951\) −0.310113 −0.0100561
\(952\) −20.2630 −0.656726
\(953\) 4.22634 0.136904 0.0684522 0.997654i \(-0.478194\pi\)
0.0684522 + 0.997654i \(0.478194\pi\)
\(954\) 18.6499 0.603813
\(955\) −1.25068 −0.0404710
\(956\) 12.6755 0.409954
\(957\) 3.23767 0.104659
\(958\) −4.24741 −0.137227
\(959\) 31.4236 1.01472
\(960\) −2.33835 −0.0754698
\(961\) 51.8935 1.67398
\(962\) 46.3918 1.49573
\(963\) 3.89618 0.125553
\(964\) 23.7833 0.766007
\(965\) −0.597339 −0.0192290
\(966\) 42.7987 1.37703
\(967\) 14.6524 0.471190 0.235595 0.971851i \(-0.424296\pi\)
0.235595 + 0.971851i \(0.424296\pi\)
\(968\) −35.8819 −1.15329
\(969\) −1.40413 −0.0451072
\(970\) −4.42600 −0.142110
\(971\) 33.4018 1.07192 0.535958 0.844245i \(-0.319951\pi\)
0.535958 + 0.844245i \(0.319951\pi\)
\(972\) 38.9520 1.24938
\(973\) 10.2012 0.327036
\(974\) 42.4681 1.36076
\(975\) −19.2321 −0.615919
\(976\) 31.0946 0.995314
\(977\) −18.5838 −0.594547 −0.297274 0.954792i \(-0.596077\pi\)
−0.297274 + 0.954792i \(0.596077\pi\)
\(978\) 32.1342 1.02754
\(979\) 24.1013 0.770282
\(980\) 8.41228 0.268720
\(981\) −7.08757 −0.226289
\(982\) −67.3631 −2.14964
\(983\) −33.6536 −1.07338 −0.536691 0.843779i \(-0.680326\pi\)
−0.536691 + 0.843779i \(0.680326\pi\)
\(984\) −13.6562 −0.435342
\(985\) 1.25938 0.0401272
\(986\) −1.33108 −0.0423901
\(987\) 59.7756 1.90268
\(988\) −11.0779 −0.352436
\(989\) −12.6395 −0.401912
\(990\) 2.72477 0.0865988
\(991\) −8.79455 −0.279368 −0.139684 0.990196i \(-0.544609\pi\)
−0.139684 + 0.990196i \(0.544609\pi\)
\(992\) 15.0652 0.478321
\(993\) 7.04198 0.223470
\(994\) 35.6976 1.13226
\(995\) −2.69730 −0.0855103
\(996\) 72.0467 2.28289
\(997\) 3.58996 0.113695 0.0568476 0.998383i \(-0.481895\pi\)
0.0568476 + 0.998383i \(0.481895\pi\)
\(998\) 46.1743 1.46162
\(999\) 38.8332 1.22863
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.1.10 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.10 121 1.1 even 1 trivial