Properties

Label 6034.2.a.n.1.19
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.10114 q^{3} +1.00000 q^{4} +4.16694 q^{5} -2.10114 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.41477 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.10114 q^{3} +1.00000 q^{4} +4.16694 q^{5} -2.10114 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.41477 q^{9} -4.16694 q^{10} -3.72895 q^{11} +2.10114 q^{12} -3.37061 q^{13} +1.00000 q^{14} +8.75531 q^{15} +1.00000 q^{16} +1.77414 q^{17} -1.41477 q^{18} +0.724455 q^{19} +4.16694 q^{20} -2.10114 q^{21} +3.72895 q^{22} +1.41023 q^{23} -2.10114 q^{24} +12.3634 q^{25} +3.37061 q^{26} -3.33078 q^{27} -1.00000 q^{28} -0.0884609 q^{29} -8.75531 q^{30} +6.94489 q^{31} -1.00000 q^{32} -7.83502 q^{33} -1.77414 q^{34} -4.16694 q^{35} +1.41477 q^{36} +3.16503 q^{37} -0.724455 q^{38} -7.08212 q^{39} -4.16694 q^{40} +8.67761 q^{41} +2.10114 q^{42} +5.90642 q^{43} -3.72895 q^{44} +5.89526 q^{45} -1.41023 q^{46} +9.49335 q^{47} +2.10114 q^{48} +1.00000 q^{49} -12.3634 q^{50} +3.72771 q^{51} -3.37061 q^{52} -0.0494789 q^{53} +3.33078 q^{54} -15.5383 q^{55} +1.00000 q^{56} +1.52218 q^{57} +0.0884609 q^{58} +9.33056 q^{59} +8.75531 q^{60} +1.98664 q^{61} -6.94489 q^{62} -1.41477 q^{63} +1.00000 q^{64} -14.0452 q^{65} +7.83502 q^{66} +4.62317 q^{67} +1.77414 q^{68} +2.96309 q^{69} +4.16694 q^{70} +2.75923 q^{71} -1.41477 q^{72} -10.6270 q^{73} -3.16503 q^{74} +25.9772 q^{75} +0.724455 q^{76} +3.72895 q^{77} +7.08212 q^{78} -4.76465 q^{79} +4.16694 q^{80} -11.2427 q^{81} -8.67761 q^{82} -5.90454 q^{83} -2.10114 q^{84} +7.39275 q^{85} -5.90642 q^{86} -0.185868 q^{87} +3.72895 q^{88} -0.395919 q^{89} -5.89526 q^{90} +3.37061 q^{91} +1.41023 q^{92} +14.5921 q^{93} -9.49335 q^{94} +3.01876 q^{95} -2.10114 q^{96} +2.82779 q^{97} -1.00000 q^{98} -5.27560 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{2} + 7q^{3} + 24q^{4} + 8q^{5} - 7q^{6} - 24q^{7} - 24q^{8} + 19q^{9} + O(q^{10}) \) \( 24q - 24q^{2} + 7q^{3} + 24q^{4} + 8q^{5} - 7q^{6} - 24q^{7} - 24q^{8} + 19q^{9} - 8q^{10} + 15q^{11} + 7q^{12} - 7q^{13} + 24q^{14} + 13q^{15} + 24q^{16} - 5q^{17} - 19q^{18} + 6q^{19} + 8q^{20} - 7q^{21} - 15q^{22} + 3q^{23} - 7q^{24} + 12q^{25} + 7q^{26} + 22q^{27} - 24q^{28} + 5q^{29} - 13q^{30} + 13q^{31} - 24q^{32} - 8q^{33} + 5q^{34} - 8q^{35} + 19q^{36} + 2q^{37} - 6q^{38} + 7q^{39} - 8q^{40} + 25q^{41} + 7q^{42} - 15q^{43} + 15q^{44} + 41q^{45} - 3q^{46} + 35q^{47} + 7q^{48} + 24q^{49} - 12q^{50} + 31q^{51} - 7q^{52} + 2q^{53} - 22q^{54} + 14q^{55} + 24q^{56} - 13q^{57} - 5q^{58} + 35q^{59} + 13q^{60} - 7q^{61} - 13q^{62} - 19q^{63} + 24q^{64} - 4q^{65} + 8q^{66} + 10q^{67} - 5q^{68} + 6q^{69} + 8q^{70} + 58q^{71} - 19q^{72} + 9q^{73} - 2q^{74} + 7q^{75} + 6q^{76} - 15q^{77} - 7q^{78} + 31q^{79} + 8q^{80} + 16q^{81} - 25q^{82} - q^{83} - 7q^{84} - 4q^{85} + 15q^{86} + 30q^{87} - 15q^{88} + 45q^{89} - 41q^{90} + 7q^{91} + 3q^{92} + 25q^{93} - 35q^{94} - 10q^{95} - 7q^{96} - 9q^{97} - 24q^{98} + 64q^{99} + O(q^{100}) \)

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
\(3\) 2.10114 1.21309 0.606546 0.795049i \(-0.292555\pi\)
0.606546 + 0.795049i \(0.292555\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.16694 1.86351 0.931757 0.363084i \(-0.118276\pi\)
0.931757 + 0.363084i \(0.118276\pi\)
\(6\) −2.10114 −0.857785
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 1.41477 0.471590
\(10\) −4.16694 −1.31770
\(11\) −3.72895 −1.12432 −0.562160 0.827029i \(-0.690029\pi\)
−0.562160 + 0.827029i \(0.690029\pi\)
\(12\) 2.10114 0.606546
\(13\) −3.37061 −0.934840 −0.467420 0.884035i \(-0.654816\pi\)
−0.467420 + 0.884035i \(0.654816\pi\)
\(14\) 1.00000 0.267261
\(15\) 8.75531 2.26061
\(16\) 1.00000 0.250000
\(17\) 1.77414 0.430293 0.215146 0.976582i \(-0.430977\pi\)
0.215146 + 0.976582i \(0.430977\pi\)
\(18\) −1.41477 −0.333464
\(19\) 0.724455 0.166201 0.0831006 0.996541i \(-0.473518\pi\)
0.0831006 + 0.996541i \(0.473518\pi\)
\(20\) 4.16694 0.931757
\(21\) −2.10114 −0.458505
\(22\) 3.72895 0.795014
\(23\) 1.41023 0.294054 0.147027 0.989132i \(-0.453030\pi\)
0.147027 + 0.989132i \(0.453030\pi\)
\(24\) −2.10114 −0.428892
\(25\) 12.3634 2.47268
\(26\) 3.37061 0.661032
\(27\) −3.33078 −0.641010
\(28\) −1.00000 −0.188982
\(29\) −0.0884609 −0.0164268 −0.00821339 0.999966i \(-0.502614\pi\)
−0.00821339 + 0.999966i \(0.502614\pi\)
\(30\) −8.75531 −1.59849
\(31\) 6.94489 1.24734 0.623669 0.781688i \(-0.285641\pi\)
0.623669 + 0.781688i \(0.285641\pi\)
\(32\) −1.00000 −0.176777
\(33\) −7.83502 −1.36390
\(34\) −1.77414 −0.304263
\(35\) −4.16694 −0.704342
\(36\) 1.41477 0.235795
\(37\) 3.16503 0.520329 0.260164 0.965564i \(-0.416223\pi\)
0.260164 + 0.965564i \(0.416223\pi\)
\(38\) −0.724455 −0.117522
\(39\) −7.08212 −1.13405
\(40\) −4.16694 −0.658851
\(41\) 8.67761 1.35521 0.677607 0.735424i \(-0.263017\pi\)
0.677607 + 0.735424i \(0.263017\pi\)
\(42\) 2.10114 0.324212
\(43\) 5.90642 0.900720 0.450360 0.892847i \(-0.351296\pi\)
0.450360 + 0.892847i \(0.351296\pi\)
\(44\) −3.72895 −0.562160
\(45\) 5.89526 0.878814
\(46\) −1.41023 −0.207928
\(47\) 9.49335 1.38475 0.692374 0.721539i \(-0.256565\pi\)
0.692374 + 0.721539i \(0.256565\pi\)
\(48\) 2.10114 0.303273
\(49\) 1.00000 0.142857
\(50\) −12.3634 −1.74845
\(51\) 3.72771 0.521984
\(52\) −3.37061 −0.467420
\(53\) −0.0494789 −0.00679644 −0.00339822 0.999994i \(-0.501082\pi\)
−0.00339822 + 0.999994i \(0.501082\pi\)
\(54\) 3.33078 0.453262
\(55\) −15.5383 −2.09518
\(56\) 1.00000 0.133631
\(57\) 1.52218 0.201617
\(58\) 0.0884609 0.0116155
\(59\) 9.33056 1.21474 0.607368 0.794421i \(-0.292225\pi\)
0.607368 + 0.794421i \(0.292225\pi\)
\(60\) 8.75531 1.13031
\(61\) 1.98664 0.254364 0.127182 0.991879i \(-0.459407\pi\)
0.127182 + 0.991879i \(0.459407\pi\)
\(62\) −6.94489 −0.882001
\(63\) −1.41477 −0.178244
\(64\) 1.00000 0.125000
\(65\) −14.0452 −1.74209
\(66\) 7.83502 0.964424
\(67\) 4.62317 0.564810 0.282405 0.959295i \(-0.408868\pi\)
0.282405 + 0.959295i \(0.408868\pi\)
\(68\) 1.77414 0.215146
\(69\) 2.96309 0.356714
\(70\) 4.16694 0.498045
\(71\) 2.75923 0.327461 0.163730 0.986505i \(-0.447647\pi\)
0.163730 + 0.986505i \(0.447647\pi\)
\(72\) −1.41477 −0.166732
\(73\) −10.6270 −1.24379 −0.621897 0.783099i \(-0.713638\pi\)
−0.621897 + 0.783099i \(0.713638\pi\)
\(74\) −3.16503 −0.367928
\(75\) 25.9772 2.99959
\(76\) 0.724455 0.0831006
\(77\) 3.72895 0.424953
\(78\) 7.08212 0.801892
\(79\) −4.76465 −0.536066 −0.268033 0.963410i \(-0.586374\pi\)
−0.268033 + 0.963410i \(0.586374\pi\)
\(80\) 4.16694 0.465878
\(81\) −11.2427 −1.24919
\(82\) −8.67761 −0.958282
\(83\) −5.90454 −0.648107 −0.324054 0.946039i \(-0.605046\pi\)
−0.324054 + 0.946039i \(0.605046\pi\)
\(84\) −2.10114 −0.229253
\(85\) 7.39275 0.801856
\(86\) −5.90642 −0.636905
\(87\) −0.185868 −0.0199272
\(88\) 3.72895 0.397507
\(89\) −0.395919 −0.0419674 −0.0209837 0.999780i \(-0.506680\pi\)
−0.0209837 + 0.999780i \(0.506680\pi\)
\(90\) −5.89526 −0.621415
\(91\) 3.37061 0.353336
\(92\) 1.41023 0.147027
\(93\) 14.5921 1.51314
\(94\) −9.49335 −0.979164
\(95\) 3.01876 0.309718
\(96\) −2.10114 −0.214446
\(97\) 2.82779 0.287118 0.143559 0.989642i \(-0.454145\pi\)
0.143559 + 0.989642i \(0.454145\pi\)
\(98\) −1.00000 −0.101015
\(99\) −5.27560 −0.530218
\(100\) 12.3634 1.23634
\(101\) −4.25472 −0.423361 −0.211680 0.977339i \(-0.567894\pi\)
−0.211680 + 0.977339i \(0.567894\pi\)
\(102\) −3.72771 −0.369099
\(103\) −9.65549 −0.951384 −0.475692 0.879612i \(-0.657802\pi\)
−0.475692 + 0.879612i \(0.657802\pi\)
\(104\) 3.37061 0.330516
\(105\) −8.75531 −0.854431
\(106\) 0.0494789 0.00480581
\(107\) −2.00663 −0.193988 −0.0969941 0.995285i \(-0.530923\pi\)
−0.0969941 + 0.995285i \(0.530923\pi\)
\(108\) −3.33078 −0.320505
\(109\) −4.16416 −0.398854 −0.199427 0.979913i \(-0.563908\pi\)
−0.199427 + 0.979913i \(0.563908\pi\)
\(110\) 15.5383 1.48152
\(111\) 6.65017 0.631206
\(112\) −1.00000 −0.0944911
\(113\) −0.204182 −0.0192078 −0.00960391 0.999954i \(-0.503057\pi\)
−0.00960391 + 0.999954i \(0.503057\pi\)
\(114\) −1.52218 −0.142565
\(115\) 5.87636 0.547974
\(116\) −0.0884609 −0.00821339
\(117\) −4.76864 −0.440861
\(118\) −9.33056 −0.858948
\(119\) −1.77414 −0.162635
\(120\) −8.75531 −0.799247
\(121\) 2.90503 0.264094
\(122\) −1.98664 −0.179862
\(123\) 18.2328 1.64400
\(124\) 6.94489 0.623669
\(125\) 30.6829 2.74436
\(126\) 1.41477 0.126038
\(127\) 21.8542 1.93924 0.969621 0.244611i \(-0.0786604\pi\)
0.969621 + 0.244611i \(0.0786604\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 12.4102 1.09266
\(130\) 14.0452 1.23184
\(131\) 19.2128 1.67863 0.839317 0.543643i \(-0.182955\pi\)
0.839317 + 0.543643i \(0.182955\pi\)
\(132\) −7.83502 −0.681951
\(133\) −0.724455 −0.0628182
\(134\) −4.62317 −0.399381
\(135\) −13.8792 −1.19453
\(136\) −1.77414 −0.152132
\(137\) 10.4333 0.891379 0.445689 0.895188i \(-0.352959\pi\)
0.445689 + 0.895188i \(0.352959\pi\)
\(138\) −2.96309 −0.252235
\(139\) 19.5290 1.65643 0.828214 0.560412i \(-0.189357\pi\)
0.828214 + 0.560412i \(0.189357\pi\)
\(140\) −4.16694 −0.352171
\(141\) 19.9468 1.67982
\(142\) −2.75923 −0.231550
\(143\) 12.5688 1.05106
\(144\) 1.41477 0.117897
\(145\) −0.368612 −0.0306115
\(146\) 10.6270 0.879495
\(147\) 2.10114 0.173299
\(148\) 3.16503 0.260164
\(149\) −10.3545 −0.848271 −0.424136 0.905599i \(-0.639422\pi\)
−0.424136 + 0.905599i \(0.639422\pi\)
\(150\) −25.9772 −2.12103
\(151\) 6.14103 0.499750 0.249875 0.968278i \(-0.419611\pi\)
0.249875 + 0.968278i \(0.419611\pi\)
\(152\) −0.724455 −0.0587610
\(153\) 2.51000 0.202922
\(154\) −3.72895 −0.300487
\(155\) 28.9389 2.32443
\(156\) −7.08212 −0.567023
\(157\) 11.3661 0.907110 0.453555 0.891228i \(-0.350156\pi\)
0.453555 + 0.891228i \(0.350156\pi\)
\(158\) 4.76465 0.379056
\(159\) −0.103962 −0.00824470
\(160\) −4.16694 −0.329426
\(161\) −1.41023 −0.111142
\(162\) 11.2427 0.883313
\(163\) 4.48214 0.351068 0.175534 0.984473i \(-0.443835\pi\)
0.175534 + 0.984473i \(0.443835\pi\)
\(164\) 8.67761 0.677607
\(165\) −32.6481 −2.54165
\(166\) 5.90454 0.458281
\(167\) 2.78465 0.215483 0.107741 0.994179i \(-0.465638\pi\)
0.107741 + 0.994179i \(0.465638\pi\)
\(168\) 2.10114 0.162106
\(169\) −1.63896 −0.126074
\(170\) −7.39275 −0.566998
\(171\) 1.02494 0.0783788
\(172\) 5.90642 0.450360
\(173\) −7.26658 −0.552468 −0.276234 0.961090i \(-0.589086\pi\)
−0.276234 + 0.961090i \(0.589086\pi\)
\(174\) 0.185868 0.0140906
\(175\) −12.3634 −0.934586
\(176\) −3.72895 −0.281080
\(177\) 19.6048 1.47358
\(178\) 0.395919 0.0296754
\(179\) −15.0451 −1.12452 −0.562260 0.826960i \(-0.690068\pi\)
−0.562260 + 0.826960i \(0.690068\pi\)
\(180\) 5.89526 0.439407
\(181\) 7.54085 0.560507 0.280253 0.959926i \(-0.409581\pi\)
0.280253 + 0.959926i \(0.409581\pi\)
\(182\) −3.37061 −0.249847
\(183\) 4.17421 0.308566
\(184\) −1.41023 −0.103964
\(185\) 13.1885 0.969639
\(186\) −14.5921 −1.06995
\(187\) −6.61568 −0.483787
\(188\) 9.49335 0.692374
\(189\) 3.33078 0.242279
\(190\) −3.01876 −0.219004
\(191\) −11.0001 −0.795938 −0.397969 0.917399i \(-0.630285\pi\)
−0.397969 + 0.917399i \(0.630285\pi\)
\(192\) 2.10114 0.151636
\(193\) −12.4495 −0.896132 −0.448066 0.894001i \(-0.647887\pi\)
−0.448066 + 0.894001i \(0.647887\pi\)
\(194\) −2.82779 −0.203023
\(195\) −29.5108 −2.11331
\(196\) 1.00000 0.0714286
\(197\) −11.5949 −0.826105 −0.413052 0.910707i \(-0.635537\pi\)
−0.413052 + 0.910707i \(0.635537\pi\)
\(198\) 5.27560 0.374920
\(199\) 23.5489 1.66934 0.834670 0.550751i \(-0.185658\pi\)
0.834670 + 0.550751i \(0.185658\pi\)
\(200\) −12.3634 −0.874225
\(201\) 9.71391 0.685166
\(202\) 4.25472 0.299361
\(203\) 0.0884609 0.00620874
\(204\) 3.72771 0.260992
\(205\) 36.1591 2.52546
\(206\) 9.65549 0.672730
\(207\) 1.99516 0.138673
\(208\) −3.37061 −0.233710
\(209\) −2.70145 −0.186863
\(210\) 8.75531 0.604174
\(211\) 8.12493 0.559343 0.279672 0.960096i \(-0.409774\pi\)
0.279672 + 0.960096i \(0.409774\pi\)
\(212\) −0.0494789 −0.00339822
\(213\) 5.79752 0.397240
\(214\) 2.00663 0.137170
\(215\) 24.6117 1.67850
\(216\) 3.33078 0.226631
\(217\) −6.94489 −0.471450
\(218\) 4.16416 0.282033
\(219\) −22.3287 −1.50883
\(220\) −15.5383 −1.04759
\(221\) −5.97995 −0.402255
\(222\) −6.65017 −0.446330
\(223\) 0.299212 0.0200367 0.0100184 0.999950i \(-0.496811\pi\)
0.0100184 + 0.999950i \(0.496811\pi\)
\(224\) 1.00000 0.0668153
\(225\) 17.4914 1.16609
\(226\) 0.204182 0.0135820
\(227\) 2.38947 0.158595 0.0792973 0.996851i \(-0.474732\pi\)
0.0792973 + 0.996851i \(0.474732\pi\)
\(228\) 1.52218 0.100809
\(229\) 4.41118 0.291499 0.145749 0.989322i \(-0.453441\pi\)
0.145749 + 0.989322i \(0.453441\pi\)
\(230\) −5.87636 −0.387476
\(231\) 7.83502 0.515506
\(232\) 0.0884609 0.00580774
\(233\) −23.0826 −1.51219 −0.756094 0.654463i \(-0.772895\pi\)
−0.756094 + 0.654463i \(0.772895\pi\)
\(234\) 4.76864 0.311736
\(235\) 39.5582 2.58049
\(236\) 9.33056 0.607368
\(237\) −10.0112 −0.650296
\(238\) 1.77414 0.115001
\(239\) 6.62522 0.428550 0.214275 0.976773i \(-0.431261\pi\)
0.214275 + 0.976773i \(0.431261\pi\)
\(240\) 8.75531 0.565153
\(241\) −13.7325 −0.884585 −0.442292 0.896871i \(-0.645835\pi\)
−0.442292 + 0.896871i \(0.645835\pi\)
\(242\) −2.90503 −0.186743
\(243\) −13.6302 −0.874375
\(244\) 1.98664 0.127182
\(245\) 4.16694 0.266216
\(246\) −18.2328 −1.16248
\(247\) −2.44186 −0.155372
\(248\) −6.94489 −0.441001
\(249\) −12.4062 −0.786213
\(250\) −30.6829 −1.94056
\(251\) −21.9424 −1.38499 −0.692496 0.721422i \(-0.743489\pi\)
−0.692496 + 0.721422i \(0.743489\pi\)
\(252\) −1.41477 −0.0891221
\(253\) −5.25868 −0.330611
\(254\) −21.8542 −1.37125
\(255\) 15.5332 0.972725
\(256\) 1.00000 0.0625000
\(257\) −13.5009 −0.842160 −0.421080 0.907023i \(-0.638349\pi\)
−0.421080 + 0.907023i \(0.638349\pi\)
\(258\) −12.4102 −0.772624
\(259\) −3.16503 −0.196666
\(260\) −14.0452 −0.871044
\(261\) −0.125152 −0.00774670
\(262\) −19.2128 −1.18697
\(263\) −6.32792 −0.390196 −0.195098 0.980784i \(-0.562503\pi\)
−0.195098 + 0.980784i \(0.562503\pi\)
\(264\) 7.83502 0.482212
\(265\) −0.206176 −0.0126653
\(266\) 0.724455 0.0444192
\(267\) −0.831880 −0.0509102
\(268\) 4.62317 0.282405
\(269\) 27.9637 1.70498 0.852488 0.522747i \(-0.175093\pi\)
0.852488 + 0.522747i \(0.175093\pi\)
\(270\) 13.8792 0.844660
\(271\) −16.2051 −0.984387 −0.492194 0.870486i \(-0.663805\pi\)
−0.492194 + 0.870486i \(0.663805\pi\)
\(272\) 1.77414 0.107573
\(273\) 7.08212 0.428629
\(274\) −10.4333 −0.630300
\(275\) −46.1025 −2.78008
\(276\) 2.96309 0.178357
\(277\) 1.83271 0.110117 0.0550584 0.998483i \(-0.482466\pi\)
0.0550584 + 0.998483i \(0.482466\pi\)
\(278\) −19.5290 −1.17127
\(279\) 9.82541 0.588232
\(280\) 4.16694 0.249022
\(281\) 24.6518 1.47060 0.735300 0.677742i \(-0.237041\pi\)
0.735300 + 0.677742i \(0.237041\pi\)
\(282\) −19.9468 −1.18782
\(283\) −3.58234 −0.212948 −0.106474 0.994315i \(-0.533956\pi\)
−0.106474 + 0.994315i \(0.533956\pi\)
\(284\) 2.75923 0.163730
\(285\) 6.34282 0.375716
\(286\) −12.5688 −0.743211
\(287\) −8.67761 −0.512223
\(288\) −1.41477 −0.0833661
\(289\) −13.8524 −0.814848
\(290\) 0.368612 0.0216456
\(291\) 5.94156 0.348301
\(292\) −10.6270 −0.621897
\(293\) −25.6236 −1.49694 −0.748472 0.663166i \(-0.769212\pi\)
−0.748472 + 0.663166i \(0.769212\pi\)
\(294\) −2.10114 −0.122541
\(295\) 38.8799 2.26368
\(296\) −3.16503 −0.183964
\(297\) 12.4203 0.720700
\(298\) 10.3545 0.599818
\(299\) −4.75336 −0.274894
\(300\) 25.9772 1.49979
\(301\) −5.90642 −0.340440
\(302\) −6.14103 −0.353376
\(303\) −8.93975 −0.513575
\(304\) 0.724455 0.0415503
\(305\) 8.27823 0.474010
\(306\) −2.51000 −0.143487
\(307\) −26.0229 −1.48520 −0.742601 0.669734i \(-0.766408\pi\)
−0.742601 + 0.669734i \(0.766408\pi\)
\(308\) 3.72895 0.212476
\(309\) −20.2875 −1.15412
\(310\) −28.9389 −1.64362
\(311\) −17.4574 −0.989918 −0.494959 0.868916i \(-0.664817\pi\)
−0.494959 + 0.868916i \(0.664817\pi\)
\(312\) 7.08212 0.400946
\(313\) 27.7186 1.56675 0.783375 0.621550i \(-0.213497\pi\)
0.783375 + 0.621550i \(0.213497\pi\)
\(314\) −11.3661 −0.641423
\(315\) −5.89526 −0.332160
\(316\) −4.76465 −0.268033
\(317\) −22.7307 −1.27668 −0.638341 0.769754i \(-0.720379\pi\)
−0.638341 + 0.769754i \(0.720379\pi\)
\(318\) 0.103962 0.00582989
\(319\) 0.329866 0.0184689
\(320\) 4.16694 0.232939
\(321\) −4.21620 −0.235325
\(322\) 1.41023 0.0785893
\(323\) 1.28529 0.0715152
\(324\) −11.2427 −0.624596
\(325\) −41.6723 −2.31156
\(326\) −4.48214 −0.248243
\(327\) −8.74946 −0.483847
\(328\) −8.67761 −0.479141
\(329\) −9.49335 −0.523385
\(330\) 32.6481 1.79722
\(331\) −12.7200 −0.699152 −0.349576 0.936908i \(-0.613674\pi\)
−0.349576 + 0.936908i \(0.613674\pi\)
\(332\) −5.90454 −0.324054
\(333\) 4.47779 0.245382
\(334\) −2.78465 −0.152369
\(335\) 19.2645 1.05253
\(336\) −2.10114 −0.114626
\(337\) −12.9452 −0.705171 −0.352586 0.935780i \(-0.614697\pi\)
−0.352586 + 0.935780i \(0.614697\pi\)
\(338\) 1.63896 0.0891475
\(339\) −0.429014 −0.0233008
\(340\) 7.39275 0.400928
\(341\) −25.8971 −1.40241
\(342\) −1.02494 −0.0554222
\(343\) −1.00000 −0.0539949
\(344\) −5.90642 −0.318453
\(345\) 12.3470 0.664742
\(346\) 7.26658 0.390654
\(347\) 22.5772 1.21201 0.606005 0.795461i \(-0.292771\pi\)
0.606005 + 0.795461i \(0.292771\pi\)
\(348\) −0.185868 −0.00996359
\(349\) −21.8222 −1.16812 −0.584058 0.811712i \(-0.698536\pi\)
−0.584058 + 0.811712i \(0.698536\pi\)
\(350\) 12.3634 0.660852
\(351\) 11.2268 0.599242
\(352\) 3.72895 0.198753
\(353\) 17.0465 0.907295 0.453647 0.891181i \(-0.350123\pi\)
0.453647 + 0.891181i \(0.350123\pi\)
\(354\) −19.6048 −1.04198
\(355\) 11.4976 0.610227
\(356\) −0.395919 −0.0209837
\(357\) −3.72771 −0.197292
\(358\) 15.0451 0.795156
\(359\) 6.03456 0.318492 0.159246 0.987239i \(-0.449094\pi\)
0.159246 + 0.987239i \(0.449094\pi\)
\(360\) −5.89526 −0.310708
\(361\) −18.4752 −0.972377
\(362\) −7.54085 −0.396338
\(363\) 6.10387 0.320370
\(364\) 3.37061 0.176668
\(365\) −44.2820 −2.31783
\(366\) −4.17421 −0.218189
\(367\) −14.3415 −0.748618 −0.374309 0.927304i \(-0.622120\pi\)
−0.374309 + 0.927304i \(0.622120\pi\)
\(368\) 1.41023 0.0735135
\(369\) 12.2768 0.639106
\(370\) −13.1885 −0.685638
\(371\) 0.0494789 0.00256881
\(372\) 14.5921 0.756568
\(373\) 8.07437 0.418075 0.209038 0.977908i \(-0.432967\pi\)
0.209038 + 0.977908i \(0.432967\pi\)
\(374\) 6.61568 0.342089
\(375\) 64.4689 3.32916
\(376\) −9.49335 −0.489582
\(377\) 0.298168 0.0153564
\(378\) −3.33078 −0.171317
\(379\) 3.16812 0.162735 0.0813677 0.996684i \(-0.474071\pi\)
0.0813677 + 0.996684i \(0.474071\pi\)
\(380\) 3.01876 0.154859
\(381\) 45.9185 2.35248
\(382\) 11.0001 0.562813
\(383\) −34.5340 −1.76460 −0.882301 0.470685i \(-0.844007\pi\)
−0.882301 + 0.470685i \(0.844007\pi\)
\(384\) −2.10114 −0.107223
\(385\) 15.5383 0.791905
\(386\) 12.4495 0.633661
\(387\) 8.35622 0.424771
\(388\) 2.82779 0.143559
\(389\) −6.41454 −0.325230 −0.162615 0.986690i \(-0.551993\pi\)
−0.162615 + 0.986690i \(0.551993\pi\)
\(390\) 29.5108 1.49434
\(391\) 2.50196 0.126529
\(392\) −1.00000 −0.0505076
\(393\) 40.3688 2.03633
\(394\) 11.5949 0.584144
\(395\) −19.8540 −0.998965
\(396\) −5.27560 −0.265109
\(397\) −11.3409 −0.569183 −0.284591 0.958649i \(-0.591858\pi\)
−0.284591 + 0.958649i \(0.591858\pi\)
\(398\) −23.5489 −1.18040
\(399\) −1.52218 −0.0762042
\(400\) 12.3634 0.618170
\(401\) 34.5847 1.72708 0.863539 0.504282i \(-0.168243\pi\)
0.863539 + 0.504282i \(0.168243\pi\)
\(402\) −9.71391 −0.484486
\(403\) −23.4085 −1.16606
\(404\) −4.25472 −0.211680
\(405\) −46.8478 −2.32789
\(406\) −0.0884609 −0.00439024
\(407\) −11.8022 −0.585015
\(408\) −3.72771 −0.184549
\(409\) −25.5737 −1.26454 −0.632268 0.774750i \(-0.717876\pi\)
−0.632268 + 0.774750i \(0.717876\pi\)
\(410\) −36.1591 −1.78577
\(411\) 21.9218 1.08132
\(412\) −9.65549 −0.475692
\(413\) −9.33056 −0.459127
\(414\) −1.99516 −0.0980566
\(415\) −24.6039 −1.20776
\(416\) 3.37061 0.165258
\(417\) 41.0331 2.00940
\(418\) 2.70145 0.132132
\(419\) −8.56975 −0.418659 −0.209330 0.977845i \(-0.567128\pi\)
−0.209330 + 0.977845i \(0.567128\pi\)
\(420\) −8.75531 −0.427215
\(421\) 7.18854 0.350348 0.175174 0.984537i \(-0.443951\pi\)
0.175174 + 0.984537i \(0.443951\pi\)
\(422\) −8.12493 −0.395515
\(423\) 13.4309 0.653033
\(424\) 0.0494789 0.00240291
\(425\) 21.9344 1.06398
\(426\) −5.79752 −0.280891
\(427\) −1.98664 −0.0961405
\(428\) −2.00663 −0.0969941
\(429\) 26.4088 1.27503
\(430\) −24.6117 −1.18688
\(431\) 1.00000 0.0481683
\(432\) −3.33078 −0.160252
\(433\) 0.351305 0.0168826 0.00844131 0.999964i \(-0.497313\pi\)
0.00844131 + 0.999964i \(0.497313\pi\)
\(434\) 6.94489 0.333365
\(435\) −0.774503 −0.0371346
\(436\) −4.16416 −0.199427
\(437\) 1.02165 0.0488722
\(438\) 22.3287 1.06691
\(439\) 25.3258 1.20874 0.604368 0.796706i \(-0.293426\pi\)
0.604368 + 0.796706i \(0.293426\pi\)
\(440\) 15.5383 0.740759
\(441\) 1.41477 0.0673700
\(442\) 5.97995 0.284437
\(443\) 39.5951 1.88122 0.940610 0.339490i \(-0.110254\pi\)
0.940610 + 0.339490i \(0.110254\pi\)
\(444\) 6.65017 0.315603
\(445\) −1.64977 −0.0782067
\(446\) −0.299212 −0.0141681
\(447\) −21.7561 −1.02903
\(448\) −1.00000 −0.0472456
\(449\) 10.7410 0.506897 0.253449 0.967349i \(-0.418435\pi\)
0.253449 + 0.967349i \(0.418435\pi\)
\(450\) −17.4914 −0.824551
\(451\) −32.3583 −1.52369
\(452\) −0.204182 −0.00960391
\(453\) 12.9031 0.606242
\(454\) −2.38947 −0.112143
\(455\) 14.0452 0.658447
\(456\) −1.52218 −0.0712825
\(457\) 7.78725 0.364272 0.182136 0.983273i \(-0.441699\pi\)
0.182136 + 0.983273i \(0.441699\pi\)
\(458\) −4.41118 −0.206121
\(459\) −5.90929 −0.275822
\(460\) 5.87636 0.273987
\(461\) −35.7287 −1.66405 −0.832026 0.554737i \(-0.812819\pi\)
−0.832026 + 0.554737i \(0.812819\pi\)
\(462\) −7.83502 −0.364518
\(463\) 28.2617 1.31343 0.656716 0.754138i \(-0.271945\pi\)
0.656716 + 0.754138i \(0.271945\pi\)
\(464\) −0.0884609 −0.00410670
\(465\) 60.8046 2.81975
\(466\) 23.0826 1.06928
\(467\) −8.99206 −0.416103 −0.208052 0.978118i \(-0.566712\pi\)
−0.208052 + 0.978118i \(0.566712\pi\)
\(468\) −4.76864 −0.220431
\(469\) −4.62317 −0.213478
\(470\) −39.5582 −1.82469
\(471\) 23.8816 1.10041
\(472\) −9.33056 −0.429474
\(473\) −22.0247 −1.01270
\(474\) 10.0112 0.459829
\(475\) 8.95673 0.410963
\(476\) −1.77414 −0.0813177
\(477\) −0.0700012 −0.00320513
\(478\) −6.62522 −0.303031
\(479\) −4.93539 −0.225504 −0.112752 0.993623i \(-0.535967\pi\)
−0.112752 + 0.993623i \(0.535967\pi\)
\(480\) −8.75531 −0.399623
\(481\) −10.6681 −0.486424
\(482\) 13.7325 0.625496
\(483\) −2.96309 −0.134825
\(484\) 2.90503 0.132047
\(485\) 11.7832 0.535049
\(486\) 13.6302 0.618276
\(487\) −14.9389 −0.676948 −0.338474 0.940976i \(-0.609911\pi\)
−0.338474 + 0.940976i \(0.609911\pi\)
\(488\) −1.98664 −0.0899312
\(489\) 9.41758 0.425878
\(490\) −4.16694 −0.188243
\(491\) −12.3283 −0.556370 −0.278185 0.960527i \(-0.589733\pi\)
−0.278185 + 0.960527i \(0.589733\pi\)
\(492\) 18.2328 0.822000
\(493\) −0.156942 −0.00706833
\(494\) 2.44186 0.109864
\(495\) −21.9831 −0.988067
\(496\) 6.94489 0.311835
\(497\) −2.75923 −0.123769
\(498\) 12.4062 0.555937
\(499\) 28.4866 1.27523 0.637617 0.770353i \(-0.279920\pi\)
0.637617 + 0.770353i \(0.279920\pi\)
\(500\) 30.6829 1.37218
\(501\) 5.85092 0.261400
\(502\) 21.9424 0.979337
\(503\) 27.8364 1.24116 0.620582 0.784141i \(-0.286896\pi\)
0.620582 + 0.784141i \(0.286896\pi\)
\(504\) 1.41477 0.0630188
\(505\) −17.7292 −0.788938
\(506\) 5.25868 0.233777
\(507\) −3.44367 −0.152939
\(508\) 21.8542 0.969621
\(509\) −29.4632 −1.30594 −0.652968 0.757386i \(-0.726476\pi\)
−0.652968 + 0.757386i \(0.726476\pi\)
\(510\) −15.5332 −0.687820
\(511\) 10.6270 0.470110
\(512\) −1.00000 −0.0441942
\(513\) −2.41300 −0.106537
\(514\) 13.5009 0.595497
\(515\) −40.2339 −1.77292
\(516\) 12.4102 0.546328
\(517\) −35.4002 −1.55690
\(518\) 3.16503 0.139064
\(519\) −15.2681 −0.670193
\(520\) 14.0452 0.615921
\(521\) −2.06603 −0.0905145 −0.0452573 0.998975i \(-0.514411\pi\)
−0.0452573 + 0.998975i \(0.514411\pi\)
\(522\) 0.125152 0.00547775
\(523\) 15.5160 0.678467 0.339234 0.940702i \(-0.389832\pi\)
0.339234 + 0.940702i \(0.389832\pi\)
\(524\) 19.2128 0.839317
\(525\) −25.9772 −1.13374
\(526\) 6.32792 0.275910
\(527\) 12.3212 0.536721
\(528\) −7.83502 −0.340975
\(529\) −21.0112 −0.913532
\(530\) 0.206176 0.00895569
\(531\) 13.2006 0.572857
\(532\) −0.724455 −0.0314091
\(533\) −29.2489 −1.26691
\(534\) 0.831880 0.0359990
\(535\) −8.36151 −0.361500
\(536\) −4.62317 −0.199691
\(537\) −31.6117 −1.36415
\(538\) −27.9637 −1.20560
\(539\) −3.72895 −0.160617
\(540\) −13.8792 −0.597265
\(541\) −25.7753 −1.10817 −0.554083 0.832461i \(-0.686931\pi\)
−0.554083 + 0.832461i \(0.686931\pi\)
\(542\) 16.2051 0.696067
\(543\) 15.8443 0.679946
\(544\) −1.77414 −0.0760658
\(545\) −17.3518 −0.743270
\(546\) −7.08212 −0.303087
\(547\) 14.5458 0.621935 0.310967 0.950421i \(-0.399347\pi\)
0.310967 + 0.950421i \(0.399347\pi\)
\(548\) 10.4333 0.445689
\(549\) 2.81064 0.119955
\(550\) 46.1025 1.96582
\(551\) −0.0640859 −0.00273015
\(552\) −2.96309 −0.126118
\(553\) 4.76465 0.202614
\(554\) −1.83271 −0.0778643
\(555\) 27.7109 1.17626
\(556\) 19.5290 0.828214
\(557\) 31.9790 1.35500 0.677498 0.735525i \(-0.263064\pi\)
0.677498 + 0.735525i \(0.263064\pi\)
\(558\) −9.82541 −0.415943
\(559\) −19.9083 −0.842030
\(560\) −4.16694 −0.176085
\(561\) −13.9004 −0.586877
\(562\) −24.6518 −1.03987
\(563\) −15.8799 −0.669259 −0.334629 0.942350i \(-0.608611\pi\)
−0.334629 + 0.942350i \(0.608611\pi\)
\(564\) 19.9468 0.839912
\(565\) −0.850814 −0.0357940
\(566\) 3.58234 0.150577
\(567\) 11.2427 0.472151
\(568\) −2.75923 −0.115775
\(569\) −9.83766 −0.412416 −0.206208 0.978508i \(-0.566112\pi\)
−0.206208 + 0.978508i \(0.566112\pi\)
\(570\) −6.34282 −0.265672
\(571\) −0.577642 −0.0241736 −0.0120868 0.999927i \(-0.503847\pi\)
−0.0120868 + 0.999927i \(0.503847\pi\)
\(572\) 12.5688 0.525530
\(573\) −23.1127 −0.965545
\(574\) 8.67761 0.362196
\(575\) 17.4353 0.727102
\(576\) 1.41477 0.0589487
\(577\) −20.8449 −0.867783 −0.433892 0.900965i \(-0.642860\pi\)
−0.433892 + 0.900965i \(0.642860\pi\)
\(578\) 13.8524 0.576185
\(579\) −26.1580 −1.08709
\(580\) −0.368612 −0.0153058
\(581\) 5.90454 0.244961
\(582\) −5.94156 −0.246286
\(583\) 0.184504 0.00764137
\(584\) 10.6270 0.439747
\(585\) −19.8707 −0.821551
\(586\) 25.6236 1.05850
\(587\) 15.3372 0.633035 0.316518 0.948587i \(-0.397486\pi\)
0.316518 + 0.948587i \(0.397486\pi\)
\(588\) 2.10114 0.0866494
\(589\) 5.03125 0.207309
\(590\) −38.8799 −1.60066
\(591\) −24.3625 −1.00214
\(592\) 3.16503 0.130082
\(593\) −2.38692 −0.0980192 −0.0490096 0.998798i \(-0.515606\pi\)
−0.0490096 + 0.998798i \(0.515606\pi\)
\(594\) −12.4203 −0.509612
\(595\) −7.39275 −0.303073
\(596\) −10.3545 −0.424136
\(597\) 49.4795 2.02506
\(598\) 4.75336 0.194379
\(599\) 14.1797 0.579365 0.289682 0.957123i \(-0.406450\pi\)
0.289682 + 0.957123i \(0.406450\pi\)
\(600\) −25.9772 −1.06051
\(601\) 36.7754 1.50010 0.750049 0.661382i \(-0.230030\pi\)
0.750049 + 0.661382i \(0.230030\pi\)
\(602\) 5.90642 0.240728
\(603\) 6.54072 0.266359
\(604\) 6.14103 0.249875
\(605\) 12.1051 0.492142
\(606\) 8.93975 0.363152
\(607\) 8.74541 0.354965 0.177483 0.984124i \(-0.443205\pi\)
0.177483 + 0.984124i \(0.443205\pi\)
\(608\) −0.724455 −0.0293805
\(609\) 0.185868 0.00753177
\(610\) −8.27823 −0.335176
\(611\) −31.9984 −1.29452
\(612\) 2.51000 0.101461
\(613\) −37.4432 −1.51232 −0.756158 0.654389i \(-0.772926\pi\)
−0.756158 + 0.654389i \(0.772926\pi\)
\(614\) 26.0229 1.05020
\(615\) 75.9752 3.06361
\(616\) −3.72895 −0.150243
\(617\) −28.8062 −1.15970 −0.579848 0.814725i \(-0.696888\pi\)
−0.579848 + 0.814725i \(0.696888\pi\)
\(618\) 20.2875 0.816083
\(619\) 2.42681 0.0975419 0.0487709 0.998810i \(-0.484470\pi\)
0.0487709 + 0.998810i \(0.484470\pi\)
\(620\) 28.9389 1.16222
\(621\) −4.69718 −0.188492
\(622\) 17.4574 0.699977
\(623\) 0.395919 0.0158622
\(624\) −7.08212 −0.283512
\(625\) 66.0368 2.64147
\(626\) −27.7186 −1.10786
\(627\) −5.67611 −0.226682
\(628\) 11.3661 0.453555
\(629\) 5.61522 0.223894
\(630\) 5.89526 0.234873
\(631\) −43.8429 −1.74536 −0.872679 0.488293i \(-0.837620\pi\)
−0.872679 + 0.488293i \(0.837620\pi\)
\(632\) 4.76465 0.189528
\(633\) 17.0716 0.678534
\(634\) 22.7307 0.902750
\(635\) 91.0650 3.61380
\(636\) −0.103962 −0.00412235
\(637\) −3.37061 −0.133549
\(638\) −0.329866 −0.0130595
\(639\) 3.90368 0.154427
\(640\) −4.16694 −0.164713
\(641\) −18.2665 −0.721484 −0.360742 0.932666i \(-0.617477\pi\)
−0.360742 + 0.932666i \(0.617477\pi\)
\(642\) 4.21620 0.166400
\(643\) −15.3716 −0.606197 −0.303098 0.952959i \(-0.598021\pi\)
−0.303098 + 0.952959i \(0.598021\pi\)
\(644\) −1.41023 −0.0555710
\(645\) 51.7125 2.03618
\(646\) −1.28529 −0.0505689
\(647\) −4.70441 −0.184949 −0.0924747 0.995715i \(-0.529478\pi\)
−0.0924747 + 0.995715i \(0.529478\pi\)
\(648\) 11.2427 0.441656
\(649\) −34.7932 −1.36575
\(650\) 41.6723 1.63452
\(651\) −14.5921 −0.571911
\(652\) 4.48214 0.175534
\(653\) 4.11941 0.161205 0.0806024 0.996746i \(-0.474316\pi\)
0.0806024 + 0.996746i \(0.474316\pi\)
\(654\) 8.74946 0.342131
\(655\) 80.0588 3.12815
\(656\) 8.67761 0.338804
\(657\) −15.0347 −0.586560
\(658\) 9.49335 0.370089
\(659\) 40.4232 1.57466 0.787332 0.616529i \(-0.211462\pi\)
0.787332 + 0.616529i \(0.211462\pi\)
\(660\) −32.6481 −1.27082
\(661\) −9.16820 −0.356602 −0.178301 0.983976i \(-0.557060\pi\)
−0.178301 + 0.983976i \(0.557060\pi\)
\(662\) 12.7200 0.494375
\(663\) −12.5647 −0.487972
\(664\) 5.90454 0.229140
\(665\) −3.01876 −0.117062
\(666\) −4.47779 −0.173511
\(667\) −0.124751 −0.00483036
\(668\) 2.78465 0.107741
\(669\) 0.628685 0.0243063
\(670\) −19.2645 −0.744252
\(671\) −7.40809 −0.285986
\(672\) 2.10114 0.0810531
\(673\) 35.3917 1.36425 0.682126 0.731235i \(-0.261056\pi\)
0.682126 + 0.731235i \(0.261056\pi\)
\(674\) 12.9452 0.498631
\(675\) −41.1798 −1.58501
\(676\) −1.63896 −0.0630368
\(677\) −48.9462 −1.88116 −0.940578 0.339577i \(-0.889716\pi\)
−0.940578 + 0.339577i \(0.889716\pi\)
\(678\) 0.429014 0.0164762
\(679\) −2.82779 −0.108520
\(680\) −7.39275 −0.283499
\(681\) 5.02059 0.192390
\(682\) 25.8971 0.991651
\(683\) 24.5212 0.938276 0.469138 0.883125i \(-0.344565\pi\)
0.469138 + 0.883125i \(0.344565\pi\)
\(684\) 1.02494 0.0391894
\(685\) 43.4750 1.66110
\(686\) 1.00000 0.0381802
\(687\) 9.26848 0.353615
\(688\) 5.90642 0.225180
\(689\) 0.166774 0.00635359
\(690\) −12.3470 −0.470044
\(691\) −11.5290 −0.438582 −0.219291 0.975659i \(-0.570374\pi\)
−0.219291 + 0.975659i \(0.570374\pi\)
\(692\) −7.26658 −0.276234
\(693\) 5.27560 0.200403
\(694\) −22.5772 −0.857020
\(695\) 81.3762 3.08677
\(696\) 0.185868 0.00704532
\(697\) 15.3953 0.583139
\(698\) 21.8222 0.825983
\(699\) −48.4996 −1.83442
\(700\) −12.3634 −0.467293
\(701\) −29.3131 −1.10714 −0.553569 0.832803i \(-0.686735\pi\)
−0.553569 + 0.832803i \(0.686735\pi\)
\(702\) −11.2268 −0.423728
\(703\) 2.29292 0.0864793
\(704\) −3.72895 −0.140540
\(705\) 83.1172 3.13038
\(706\) −17.0465 −0.641554
\(707\) 4.25472 0.160015
\(708\) 19.6048 0.736792
\(709\) 10.5540 0.396363 0.198181 0.980165i \(-0.436496\pi\)
0.198181 + 0.980165i \(0.436496\pi\)
\(710\) −11.4976 −0.431496
\(711\) −6.74089 −0.252803
\(712\) 0.395919 0.0148377
\(713\) 9.79391 0.366785
\(714\) 3.72771 0.139506
\(715\) 52.3736 1.95866
\(716\) −15.0451 −0.562260
\(717\) 13.9205 0.519870
\(718\) −6.03456 −0.225208
\(719\) 45.7652 1.70676 0.853378 0.521293i \(-0.174550\pi\)
0.853378 + 0.521293i \(0.174550\pi\)
\(720\) 5.89526 0.219703
\(721\) 9.65549 0.359589
\(722\) 18.4752 0.687574
\(723\) −28.8537 −1.07308
\(724\) 7.54085 0.280253
\(725\) −1.09368 −0.0406182
\(726\) −6.10387 −0.226536
\(727\) −19.4640 −0.721880 −0.360940 0.932589i \(-0.617544\pi\)
−0.360940 + 0.932589i \(0.617544\pi\)
\(728\) −3.37061 −0.124923
\(729\) 5.08940 0.188496
\(730\) 44.2820 1.63895
\(731\) 10.4788 0.387574
\(732\) 4.17421 0.154283
\(733\) −10.0824 −0.372401 −0.186201 0.982512i \(-0.559617\pi\)
−0.186201 + 0.982512i \(0.559617\pi\)
\(734\) 14.3415 0.529353
\(735\) 8.75531 0.322944
\(736\) −1.41023 −0.0519819
\(737\) −17.2396 −0.635027
\(738\) −12.2768 −0.451916
\(739\) −35.9632 −1.32293 −0.661464 0.749977i \(-0.730065\pi\)
−0.661464 + 0.749977i \(0.730065\pi\)
\(740\) 13.1885 0.484819
\(741\) −5.13067 −0.188480
\(742\) −0.0494789 −0.00181643
\(743\) 35.3905 1.29835 0.649176 0.760639i \(-0.275114\pi\)
0.649176 + 0.760639i \(0.275114\pi\)
\(744\) −14.5921 −0.534974
\(745\) −43.1465 −1.58076
\(746\) −8.07437 −0.295624
\(747\) −8.35356 −0.305641
\(748\) −6.61568 −0.241893
\(749\) 2.00663 0.0733207
\(750\) −64.4689 −2.35407
\(751\) 13.2709 0.484263 0.242131 0.970243i \(-0.422153\pi\)
0.242131 + 0.970243i \(0.422153\pi\)
\(752\) 9.49335 0.346187
\(753\) −46.1039 −1.68012
\(754\) −0.298168 −0.0108586
\(755\) 25.5893 0.931290
\(756\) 3.33078 0.121139
\(757\) −27.7626 −1.00905 −0.504525 0.863397i \(-0.668332\pi\)
−0.504525 + 0.863397i \(0.668332\pi\)
\(758\) −3.16812 −0.115071
\(759\) −11.0492 −0.401061
\(760\) −3.01876 −0.109502
\(761\) 11.7325 0.425302 0.212651 0.977128i \(-0.431790\pi\)
0.212651 + 0.977128i \(0.431790\pi\)
\(762\) −45.9185 −1.66345
\(763\) 4.16416 0.150753
\(764\) −11.0001 −0.397969
\(765\) 10.4590 0.378147
\(766\) 34.5340 1.24776
\(767\) −31.4497 −1.13558
\(768\) 2.10114 0.0758182
\(769\) −25.8694 −0.932875 −0.466438 0.884554i \(-0.654463\pi\)
−0.466438 + 0.884554i \(0.654463\pi\)
\(770\) −15.5383 −0.559961
\(771\) −28.3671 −1.02162
\(772\) −12.4495 −0.448066
\(773\) 1.57045 0.0564853 0.0282426 0.999601i \(-0.491009\pi\)
0.0282426 + 0.999601i \(0.491009\pi\)
\(774\) −8.35622 −0.300358
\(775\) 85.8624 3.08427
\(776\) −2.82779 −0.101512
\(777\) −6.65017 −0.238573
\(778\) 6.41454 0.229972
\(779\) 6.28653 0.225238
\(780\) −29.5108 −1.05666
\(781\) −10.2890 −0.368170
\(782\) −2.50196 −0.0894698
\(783\) 0.294644 0.0105297
\(784\) 1.00000 0.0357143
\(785\) 47.3617 1.69041
\(786\) −40.3688 −1.43991
\(787\) −38.5631 −1.37463 −0.687313 0.726361i \(-0.741210\pi\)
−0.687313 + 0.726361i \(0.741210\pi\)
\(788\) −11.5949 −0.413052
\(789\) −13.2958 −0.473343
\(790\) 19.8540 0.706375
\(791\) 0.204182 0.00725987
\(792\) 5.27560 0.187460
\(793\) −6.69621 −0.237790
\(794\) 11.3409 0.402473
\(795\) −0.433203 −0.0153641
\(796\) 23.5489 0.834670
\(797\) −37.4659 −1.32711 −0.663555 0.748127i \(-0.730953\pi\)
−0.663555 + 0.748127i \(0.730953\pi\)
\(798\) 1.52218 0.0538845
\(799\) 16.8426 0.595847
\(800\) −12.3634 −0.437112
\(801\) −0.560134 −0.0197914
\(802\) −34.5847 −1.22123
\(803\) 39.6274 1.39842
\(804\) 9.71391 0.342583
\(805\) −5.87636 −0.207115
\(806\) 23.4085 0.824531
\(807\) 58.7555 2.06829
\(808\) 4.25472 0.149681
\(809\) 52.6102 1.84968 0.924838 0.380361i \(-0.124200\pi\)
0.924838 + 0.380361i \(0.124200\pi\)
\(810\) 46.8478 1.64606
\(811\) −31.2247 −1.09645 −0.548224 0.836331i \(-0.684696\pi\)
−0.548224 + 0.836331i \(0.684696\pi\)
\(812\) 0.0884609 0.00310437
\(813\) −34.0490 −1.19415
\(814\) 11.8022 0.413668
\(815\) 18.6768 0.654220
\(816\) 3.72771 0.130496
\(817\) 4.27893 0.149701
\(818\) 25.5737 0.894162
\(819\) 4.76864 0.166630
\(820\) 36.1591 1.26273
\(821\) 5.07279 0.177041 0.0885207 0.996074i \(-0.471786\pi\)
0.0885207 + 0.996074i \(0.471786\pi\)
\(822\) −21.9218 −0.764611
\(823\) 8.66809 0.302151 0.151075 0.988522i \(-0.451726\pi\)
0.151075 + 0.988522i \(0.451726\pi\)
\(824\) 9.65549 0.336365
\(825\) −96.8675 −3.37249
\(826\) 9.33056 0.324652
\(827\) −8.35328 −0.290472 −0.145236 0.989397i \(-0.546394\pi\)
−0.145236 + 0.989397i \(0.546394\pi\)
\(828\) 1.99516 0.0693365
\(829\) −18.2454 −0.633688 −0.316844 0.948478i \(-0.602623\pi\)
−0.316844 + 0.948478i \(0.602623\pi\)
\(830\) 24.6039 0.854013
\(831\) 3.85077 0.133582
\(832\) −3.37061 −0.116855
\(833\) 1.77414 0.0614704
\(834\) −41.0331 −1.42086
\(835\) 11.6035 0.401554
\(836\) −2.70145 −0.0934317
\(837\) −23.1319 −0.799556
\(838\) 8.56975 0.296037
\(839\) 28.2759 0.976194 0.488097 0.872789i \(-0.337691\pi\)
0.488097 + 0.872789i \(0.337691\pi\)
\(840\) 8.75531 0.302087
\(841\) −28.9922 −0.999730
\(842\) −7.18854 −0.247733
\(843\) 51.7967 1.78397
\(844\) 8.12493 0.279672
\(845\) −6.82943 −0.234940
\(846\) −13.4309 −0.461764
\(847\) −2.90503 −0.0998181
\(848\) −0.0494789 −0.00169911
\(849\) −7.52699 −0.258326
\(850\) −21.9344 −0.752345
\(851\) 4.46344 0.153005
\(852\) 5.79752 0.198620
\(853\) −3.60131 −0.123306 −0.0616532 0.998098i \(-0.519637\pi\)
−0.0616532 + 0.998098i \(0.519637\pi\)
\(854\) 1.98664 0.0679816
\(855\) 4.27085 0.146060
\(856\) 2.00663 0.0685852
\(857\) −8.20880 −0.280407 −0.140204 0.990123i \(-0.544776\pi\)
−0.140204 + 0.990123i \(0.544776\pi\)
\(858\) −26.4088 −0.901583
\(859\) −6.14705 −0.209735 −0.104867 0.994486i \(-0.533442\pi\)
−0.104867 + 0.994486i \(0.533442\pi\)
\(860\) 24.6117 0.839252
\(861\) −18.2328 −0.621373
\(862\) −1.00000 −0.0340601
\(863\) 0.777033 0.0264505 0.0132253 0.999913i \(-0.495790\pi\)
0.0132253 + 0.999913i \(0.495790\pi\)
\(864\) 3.33078 0.113316
\(865\) −30.2794 −1.02953
\(866\) −0.351305 −0.0119378
\(867\) −29.1058 −0.988485
\(868\) −6.94489 −0.235725
\(869\) 17.7671 0.602709
\(870\) 0.774503 0.0262581
\(871\) −15.5829 −0.528008
\(872\) 4.16416 0.141016
\(873\) 4.00067 0.135402
\(874\) −1.02165 −0.0345578
\(875\) −30.6829 −1.03727
\(876\) −22.3287 −0.754417
\(877\) 42.9631 1.45076 0.725381 0.688348i \(-0.241664\pi\)
0.725381 + 0.688348i \(0.241664\pi\)
\(878\) −25.3258 −0.854705
\(879\) −53.8386 −1.81593
\(880\) −15.5383 −0.523796
\(881\) 15.6798 0.528264 0.264132 0.964486i \(-0.414914\pi\)
0.264132 + 0.964486i \(0.414914\pi\)
\(882\) −1.41477 −0.0476378
\(883\) −46.6948 −1.57140 −0.785702 0.618605i \(-0.787698\pi\)
−0.785702 + 0.618605i \(0.787698\pi\)
\(884\) −5.97995 −0.201128
\(885\) 81.6919 2.74604
\(886\) −39.5951 −1.33022
\(887\) −14.5601 −0.488882 −0.244441 0.969664i \(-0.578604\pi\)
−0.244441 + 0.969664i \(0.578604\pi\)
\(888\) −6.65017 −0.223165
\(889\) −21.8542 −0.732965
\(890\) 1.64977 0.0553005
\(891\) 41.9235 1.40449
\(892\) 0.299212 0.0100184
\(893\) 6.87750 0.230147
\(894\) 21.7561 0.727634
\(895\) −62.6919 −2.09556
\(896\) 1.00000 0.0334077
\(897\) −9.98744 −0.333471
\(898\) −10.7410 −0.358431
\(899\) −0.614351 −0.0204898
\(900\) 17.4914 0.583046
\(901\) −0.0877826 −0.00292446
\(902\) 32.3583 1.07741
\(903\) −12.4102 −0.412985
\(904\) 0.204182 0.00679099
\(905\) 31.4223 1.04451
\(906\) −12.9031 −0.428678
\(907\) −29.1050 −0.966417 −0.483209 0.875505i \(-0.660529\pi\)
−0.483209 + 0.875505i \(0.660529\pi\)
\(908\) 2.38947 0.0792973
\(909\) −6.01945 −0.199653
\(910\) −14.0452 −0.465592
\(911\) −21.3731 −0.708121 −0.354060 0.935223i \(-0.615199\pi\)
−0.354060 + 0.935223i \(0.615199\pi\)
\(912\) 1.52218 0.0504043
\(913\) 22.0177 0.728679
\(914\) −7.78725 −0.257579
\(915\) 17.3937 0.575018
\(916\) 4.41118 0.145749
\(917\) −19.2128 −0.634464
\(918\) 5.90929 0.195036
\(919\) 39.6249 1.30710 0.653552 0.756881i \(-0.273278\pi\)
0.653552 + 0.756881i \(0.273278\pi\)
\(920\) −5.87636 −0.193738
\(921\) −54.6775 −1.80169
\(922\) 35.7287 1.17666
\(923\) −9.30031 −0.306124
\(924\) 7.83502 0.257753
\(925\) 39.1306 1.28661
\(926\) −28.2617 −0.928736
\(927\) −13.6603 −0.448663
\(928\) 0.0884609 0.00290387
\(929\) 49.0030 1.60774 0.803868 0.594808i \(-0.202772\pi\)
0.803868 + 0.594808i \(0.202772\pi\)
\(930\) −60.8046 −1.99386
\(931\) 0.724455 0.0237430
\(932\) −23.0826 −0.756094
\(933\) −36.6803 −1.20086
\(934\) 8.99206 0.294229
\(935\) −27.5672 −0.901543
\(936\) 4.76864 0.155868
\(937\) −34.1545 −1.11578 −0.557890 0.829915i \(-0.688389\pi\)
−0.557890 + 0.829915i \(0.688389\pi\)
\(938\) 4.62317 0.150952
\(939\) 58.2406 1.90061
\(940\) 39.5582 1.29025
\(941\) 32.1044 1.04657 0.523286 0.852157i \(-0.324706\pi\)
0.523286 + 0.852157i \(0.324706\pi\)
\(942\) −23.8816 −0.778105
\(943\) 12.2375 0.398507
\(944\) 9.33056 0.303684
\(945\) 13.8792 0.451490
\(946\) 22.0247 0.716085
\(947\) 18.9027 0.614256 0.307128 0.951668i \(-0.400632\pi\)
0.307128 + 0.951668i \(0.400632\pi\)
\(948\) −10.0112 −0.325148
\(949\) 35.8195 1.16275
\(950\) −8.95673 −0.290595
\(951\) −47.7602 −1.54873
\(952\) 1.77414 0.0575003
\(953\) −10.6723 −0.345709 −0.172855 0.984947i \(-0.555299\pi\)
−0.172855 + 0.984947i \(0.555299\pi\)
\(954\) 0.0700012 0.00226637
\(955\) −45.8367 −1.48324
\(956\) 6.62522 0.214275
\(957\) 0.693093 0.0224045
\(958\) 4.93539 0.159455
\(959\) −10.4333 −0.336910
\(960\) 8.75531 0.282576
\(961\) 17.2314 0.555853
\(962\) 10.6681 0.343954
\(963\) −2.83892 −0.0914829
\(964\) −13.7325 −0.442292
\(965\) −51.8762 −1.66995
\(966\) 2.96309 0.0953359
\(967\) 8.52232 0.274059 0.137030 0.990567i \(-0.456244\pi\)
0.137030 + 0.990567i \(0.456244\pi\)
\(968\) −2.90503 −0.0933713
\(969\) 2.70056 0.0867545
\(970\) −11.7832 −0.378337
\(971\) −28.5639 −0.916660 −0.458330 0.888782i \(-0.651552\pi\)
−0.458330 + 0.888782i \(0.651552\pi\)
\(972\) −13.6302 −0.437187
\(973\) −19.5290 −0.626071
\(974\) 14.9389 0.478675
\(975\) −87.5591 −2.80414
\(976\) 1.98664 0.0635910
\(977\) 28.1693 0.901217 0.450608 0.892722i \(-0.351207\pi\)
0.450608 + 0.892722i \(0.351207\pi\)
\(978\) −9.41758 −0.301141
\(979\) 1.47636 0.0471847
\(980\) 4.16694 0.133108
\(981\) −5.89133 −0.188096
\(982\) 12.3283 0.393413
\(983\) 36.4579 1.16283 0.581413 0.813609i \(-0.302500\pi\)
0.581413 + 0.813609i \(0.302500\pi\)
\(984\) −18.2328 −0.581241
\(985\) −48.3154 −1.53946
\(986\) 0.156942 0.00499806
\(987\) −19.9468 −0.634914
\(988\) −2.44186 −0.0776858
\(989\) 8.32943 0.264861
\(990\) 21.9831 0.698669
\(991\) −23.0254 −0.731427 −0.365714 0.930727i \(-0.619175\pi\)
−0.365714 + 0.930727i \(0.619175\pi\)
\(992\) −6.94489 −0.220500
\(993\) −26.7263 −0.848135
\(994\) 2.75923 0.0875176
\(995\) 98.1270 3.11084
\(996\) −12.4062 −0.393106
\(997\) −11.5669 −0.366328 −0.183164 0.983082i \(-0.558634\pi\)
−0.183164 + 0.983082i \(0.558634\pi\)
\(998\) −28.4866 −0.901727
\(999\) −10.5420 −0.333536
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 \(a_p\))