Properties

Label 8047.2.a.b.1.3
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

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Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.74745 q^{2} -2.94528 q^{3} +5.54847 q^{4} +1.95253 q^{5} +8.09201 q^{6} +3.66595 q^{7} -9.74923 q^{8} +5.67469 q^{9} +O(q^{10})\) \(q-2.74745 q^{2} -2.94528 q^{3} +5.54847 q^{4} +1.95253 q^{5} +8.09201 q^{6} +3.66595 q^{7} -9.74923 q^{8} +5.67469 q^{9} -5.36448 q^{10} +2.28522 q^{11} -16.3418 q^{12} +1.00000 q^{13} -10.0720 q^{14} -5.75076 q^{15} +15.6885 q^{16} -5.27543 q^{17} -15.5909 q^{18} -6.83843 q^{19} +10.8336 q^{20} -10.7973 q^{21} -6.27851 q^{22} -5.42234 q^{23} +28.7142 q^{24} -1.18762 q^{25} -2.74745 q^{26} -7.87771 q^{27} +20.3404 q^{28} +3.26310 q^{29} +15.7999 q^{30} +4.92936 q^{31} -23.6050 q^{32} -6.73061 q^{33} +14.4940 q^{34} +7.15788 q^{35} +31.4858 q^{36} -0.423081 q^{37} +18.7882 q^{38} -2.94528 q^{39} -19.0357 q^{40} +1.80363 q^{41} +29.6649 q^{42} -7.67491 q^{43} +12.6794 q^{44} +11.0800 q^{45} +14.8976 q^{46} -1.57661 q^{47} -46.2072 q^{48} +6.43917 q^{49} +3.26293 q^{50} +15.5376 q^{51} +5.54847 q^{52} +8.57399 q^{53} +21.6436 q^{54} +4.46196 q^{55} -35.7402 q^{56} +20.1411 q^{57} -8.96521 q^{58} -0.00498498 q^{59} -31.9079 q^{60} -3.15109 q^{61} -13.5432 q^{62} +20.8031 q^{63} +33.4764 q^{64} +1.95253 q^{65} +18.4920 q^{66} +7.35369 q^{67} -29.2705 q^{68} +15.9703 q^{69} -19.6659 q^{70} +5.73892 q^{71} -55.3238 q^{72} -14.0956 q^{73} +1.16239 q^{74} +3.49788 q^{75} -37.9428 q^{76} +8.37748 q^{77} +8.09201 q^{78} +16.4326 q^{79} +30.6324 q^{80} +6.17802 q^{81} -4.95537 q^{82} -2.90991 q^{83} -59.9082 q^{84} -10.3004 q^{85} +21.0864 q^{86} -9.61076 q^{87} -22.2791 q^{88} -14.5759 q^{89} -30.4417 q^{90} +3.66595 q^{91} -30.0857 q^{92} -14.5184 q^{93} +4.33165 q^{94} -13.3523 q^{95} +69.5234 q^{96} -0.448125 q^{97} -17.6913 q^{98} +12.9679 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.74745 −1.94274 −0.971369 0.237575i \(-0.923648\pi\)
−0.971369 + 0.237575i \(0.923648\pi\)
\(3\) −2.94528 −1.70046 −0.850230 0.526412i \(-0.823537\pi\)
−0.850230 + 0.526412i \(0.823537\pi\)
\(4\) 5.54847 2.77423
\(5\) 1.95253 0.873199 0.436599 0.899656i \(-0.356183\pi\)
0.436599 + 0.899656i \(0.356183\pi\)
\(6\) 8.09201 3.30355
\(7\) 3.66595 1.38560 0.692799 0.721131i \(-0.256377\pi\)
0.692799 + 0.721131i \(0.256377\pi\)
\(8\) −9.74923 −3.44687
\(9\) 5.67469 1.89156
\(10\) −5.36448 −1.69640
\(11\) 2.28522 0.689019 0.344509 0.938783i \(-0.388045\pi\)
0.344509 + 0.938783i \(0.388045\pi\)
\(12\) −16.3418 −4.71747
\(13\) 1.00000 0.277350
\(14\) −10.0720 −2.69185
\(15\) −5.75076 −1.48484
\(16\) 15.6885 3.92214
\(17\) −5.27543 −1.27948 −0.639739 0.768592i \(-0.720958\pi\)
−0.639739 + 0.768592i \(0.720958\pi\)
\(18\) −15.5909 −3.67481
\(19\) −6.83843 −1.56884 −0.784422 0.620228i \(-0.787040\pi\)
−0.784422 + 0.620228i \(0.787040\pi\)
\(20\) 10.8336 2.42246
\(21\) −10.7973 −2.35615
\(22\) −6.27851 −1.33858
\(23\) −5.42234 −1.13064 −0.565318 0.824873i \(-0.691246\pi\)
−0.565318 + 0.824873i \(0.691246\pi\)
\(24\) 28.7142 5.86127
\(25\) −1.18762 −0.237524
\(26\) −2.74745 −0.538819
\(27\) −7.87771 −1.51607
\(28\) 20.3404 3.84397
\(29\) 3.26310 0.605943 0.302972 0.953000i \(-0.402021\pi\)
0.302972 + 0.953000i \(0.402021\pi\)
\(30\) 15.7999 2.88465
\(31\) 4.92936 0.885340 0.442670 0.896685i \(-0.354031\pi\)
0.442670 + 0.896685i \(0.354031\pi\)
\(32\) −23.6050 −4.17282
\(33\) −6.73061 −1.17165
\(34\) 14.4940 2.48569
\(35\) 7.15788 1.20990
\(36\) 31.4858 5.24764
\(37\) −0.423081 −0.0695541 −0.0347771 0.999395i \(-0.511072\pi\)
−0.0347771 + 0.999395i \(0.511072\pi\)
\(38\) 18.7882 3.04785
\(39\) −2.94528 −0.471623
\(40\) −19.0357 −3.00980
\(41\) 1.80363 0.281679 0.140840 0.990032i \(-0.455020\pi\)
0.140840 + 0.990032i \(0.455020\pi\)
\(42\) 29.6649 4.57739
\(43\) −7.67491 −1.17041 −0.585206 0.810884i \(-0.698986\pi\)
−0.585206 + 0.810884i \(0.698986\pi\)
\(44\) 12.6794 1.91150
\(45\) 11.0800 1.65171
\(46\) 14.8976 2.19653
\(47\) −1.57661 −0.229972 −0.114986 0.993367i \(-0.536682\pi\)
−0.114986 + 0.993367i \(0.536682\pi\)
\(48\) −46.2072 −6.66944
\(49\) 6.43917 0.919882
\(50\) 3.26293 0.461448
\(51\) 15.5376 2.17570
\(52\) 5.54847 0.769434
\(53\) 8.57399 1.17773 0.588864 0.808232i \(-0.299575\pi\)
0.588864 + 0.808232i \(0.299575\pi\)
\(54\) 21.6436 2.94532
\(55\) 4.46196 0.601650
\(56\) −35.7402 −4.77598
\(57\) 20.1411 2.66776
\(58\) −8.96521 −1.17719
\(59\) −0.00498498 −0.000648989 0 −0.000324494 1.00000i \(-0.500103\pi\)
−0.000324494 1.00000i \(0.500103\pi\)
\(60\) −31.9079 −4.11929
\(61\) −3.15109 −0.403456 −0.201728 0.979442i \(-0.564656\pi\)
−0.201728 + 0.979442i \(0.564656\pi\)
\(62\) −13.5432 −1.71998
\(63\) 20.8031 2.62095
\(64\) 33.4764 4.18455
\(65\) 1.95253 0.242182
\(66\) 18.4920 2.27621
\(67\) 7.35369 0.898396 0.449198 0.893432i \(-0.351710\pi\)
0.449198 + 0.893432i \(0.351710\pi\)
\(68\) −29.2705 −3.54957
\(69\) 15.9703 1.92260
\(70\) −19.6659 −2.35052
\(71\) 5.73892 0.681085 0.340542 0.940229i \(-0.389389\pi\)
0.340542 + 0.940229i \(0.389389\pi\)
\(72\) −55.3238 −6.51997
\(73\) −14.0956 −1.64976 −0.824882 0.565304i \(-0.808759\pi\)
−0.824882 + 0.565304i \(0.808759\pi\)
\(74\) 1.16239 0.135125
\(75\) 3.49788 0.403901
\(76\) −37.9428 −4.35234
\(77\) 8.37748 0.954703
\(78\) 8.09201 0.916239
\(79\) 16.4326 1.84881 0.924404 0.381415i \(-0.124563\pi\)
0.924404 + 0.381415i \(0.124563\pi\)
\(80\) 30.6324 3.42480
\(81\) 6.17802 0.686446
\(82\) −4.95537 −0.547229
\(83\) −2.90991 −0.319404 −0.159702 0.987165i \(-0.551053\pi\)
−0.159702 + 0.987165i \(0.551053\pi\)
\(84\) −59.9082 −6.53652
\(85\) −10.3004 −1.11724
\(86\) 21.0864 2.27381
\(87\) −9.61076 −1.03038
\(88\) −22.2791 −2.37496
\(89\) −14.5759 −1.54504 −0.772519 0.634992i \(-0.781004\pi\)
−0.772519 + 0.634992i \(0.781004\pi\)
\(90\) −30.4417 −3.20884
\(91\) 3.66595 0.384296
\(92\) −30.0857 −3.13665
\(93\) −14.5184 −1.50548
\(94\) 4.33165 0.446776
\(95\) −13.3523 −1.36991
\(96\) 69.5234 7.09570
\(97\) −0.448125 −0.0455002 −0.0227501 0.999741i \(-0.507242\pi\)
−0.0227501 + 0.999741i \(0.507242\pi\)
\(98\) −17.6913 −1.78709
\(99\) 12.9679 1.30332
\(100\) −6.58948 −0.658948
\(101\) 5.04151 0.501649 0.250825 0.968033i \(-0.419298\pi\)
0.250825 + 0.968033i \(0.419298\pi\)
\(102\) −42.6888 −4.22682
\(103\) 18.1746 1.79079 0.895397 0.445268i \(-0.146892\pi\)
0.895397 + 0.445268i \(0.146892\pi\)
\(104\) −9.74923 −0.955990
\(105\) −21.0820 −2.05739
\(106\) −23.5566 −2.28802
\(107\) −0.259001 −0.0250386 −0.0125193 0.999922i \(-0.503985\pi\)
−0.0125193 + 0.999922i \(0.503985\pi\)
\(108\) −43.7092 −4.20592
\(109\) 15.6963 1.50344 0.751718 0.659485i \(-0.229226\pi\)
0.751718 + 0.659485i \(0.229226\pi\)
\(110\) −12.2590 −1.16885
\(111\) 1.24609 0.118274
\(112\) 57.5134 5.43451
\(113\) −12.4639 −1.17250 −0.586251 0.810129i \(-0.699397\pi\)
−0.586251 + 0.810129i \(0.699397\pi\)
\(114\) −55.3366 −5.18275
\(115\) −10.5873 −0.987269
\(116\) 18.1052 1.68103
\(117\) 5.67469 0.524625
\(118\) 0.0136960 0.00126082
\(119\) −19.3394 −1.77284
\(120\) 56.0654 5.11805
\(121\) −5.77779 −0.525253
\(122\) 8.65746 0.783810
\(123\) −5.31219 −0.478984
\(124\) 27.3504 2.45614
\(125\) −12.0815 −1.08060
\(126\) −57.1554 −5.09181
\(127\) 20.1869 1.79129 0.895647 0.444765i \(-0.146713\pi\)
0.895647 + 0.444765i \(0.146713\pi\)
\(128\) −44.7647 −3.95668
\(129\) 22.6048 1.99024
\(130\) −5.36448 −0.470496
\(131\) −13.4179 −1.17233 −0.586163 0.810193i \(-0.699362\pi\)
−0.586163 + 0.810193i \(0.699362\pi\)
\(132\) −37.3445 −3.25043
\(133\) −25.0693 −2.17379
\(134\) −20.2039 −1.74535
\(135\) −15.3815 −1.32383
\(136\) 51.4313 4.41020
\(137\) −4.99604 −0.426840 −0.213420 0.976961i \(-0.568460\pi\)
−0.213420 + 0.976961i \(0.568460\pi\)
\(138\) −43.8776 −3.73511
\(139\) 3.68590 0.312634 0.156317 0.987707i \(-0.450038\pi\)
0.156317 + 0.987707i \(0.450038\pi\)
\(140\) 39.7152 3.35655
\(141\) 4.64356 0.391058
\(142\) −15.7674 −1.32317
\(143\) 2.28522 0.191099
\(144\) 89.0276 7.41897
\(145\) 6.37131 0.529109
\(146\) 38.7269 3.20506
\(147\) −18.9652 −1.56422
\(148\) −2.34745 −0.192959
\(149\) −9.50558 −0.778728 −0.389364 0.921084i \(-0.627305\pi\)
−0.389364 + 0.921084i \(0.627305\pi\)
\(150\) −9.61024 −0.784673
\(151\) 4.01953 0.327104 0.163552 0.986535i \(-0.447705\pi\)
0.163552 + 0.986535i \(0.447705\pi\)
\(152\) 66.6694 5.40760
\(153\) −29.9364 −2.42021
\(154\) −23.0167 −1.85474
\(155\) 9.62474 0.773078
\(156\) −16.3418 −1.30839
\(157\) 10.8566 0.866453 0.433226 0.901285i \(-0.357375\pi\)
0.433226 + 0.901285i \(0.357375\pi\)
\(158\) −45.1476 −3.59175
\(159\) −25.2528 −2.00268
\(160\) −46.0895 −3.64370
\(161\) −19.8780 −1.56661
\(162\) −16.9738 −1.33359
\(163\) 1.67072 0.130861 0.0654304 0.997857i \(-0.479158\pi\)
0.0654304 + 0.997857i \(0.479158\pi\)
\(164\) 10.0074 0.781443
\(165\) −13.1417 −1.02308
\(166\) 7.99481 0.620518
\(167\) −24.3283 −1.88258 −0.941292 0.337594i \(-0.890387\pi\)
−0.941292 + 0.337594i \(0.890387\pi\)
\(168\) 105.265 8.12136
\(169\) 1.00000 0.0769231
\(170\) 28.2999 2.17050
\(171\) −38.8060 −2.96757
\(172\) −42.5840 −3.24700
\(173\) −10.6576 −0.810279 −0.405140 0.914255i \(-0.632777\pi\)
−0.405140 + 0.914255i \(0.632777\pi\)
\(174\) 26.4051 2.00176
\(175\) −4.35376 −0.329113
\(176\) 35.8517 2.70243
\(177\) 0.0146822 0.00110358
\(178\) 40.0464 3.00160
\(179\) −18.7878 −1.40427 −0.702134 0.712045i \(-0.747769\pi\)
−0.702134 + 0.712045i \(0.747769\pi\)
\(180\) 61.4770 4.58223
\(181\) −17.9591 −1.33489 −0.667443 0.744661i \(-0.732611\pi\)
−0.667443 + 0.744661i \(0.732611\pi\)
\(182\) −10.0720 −0.746586
\(183\) 9.28086 0.686061
\(184\) 52.8636 3.89716
\(185\) −0.826079 −0.0607346
\(186\) 39.8885 2.92476
\(187\) −12.0555 −0.881585
\(188\) −8.74776 −0.637996
\(189\) −28.8793 −2.10066
\(190\) 36.6846 2.66138
\(191\) −4.22235 −0.305518 −0.152759 0.988263i \(-0.548816\pi\)
−0.152759 + 0.988263i \(0.548816\pi\)
\(192\) −98.5975 −7.11566
\(193\) 12.8962 0.928285 0.464143 0.885760i \(-0.346362\pi\)
0.464143 + 0.885760i \(0.346362\pi\)
\(194\) 1.23120 0.0883951
\(195\) −5.75076 −0.411820
\(196\) 35.7275 2.55197
\(197\) 8.13195 0.579377 0.289689 0.957121i \(-0.406448\pi\)
0.289689 + 0.957121i \(0.406448\pi\)
\(198\) −35.6286 −2.53201
\(199\) −7.14405 −0.506429 −0.253214 0.967410i \(-0.581488\pi\)
−0.253214 + 0.967410i \(0.581488\pi\)
\(200\) 11.5784 0.818716
\(201\) −21.6587 −1.52769
\(202\) −13.8513 −0.974573
\(203\) 11.9624 0.839594
\(204\) 86.2100 6.03590
\(205\) 3.52164 0.245962
\(206\) −49.9337 −3.47905
\(207\) −30.7701 −2.13867
\(208\) 15.6885 1.08781
\(209\) −15.6273 −1.08096
\(210\) 57.9216 3.99697
\(211\) 15.7847 1.08666 0.543331 0.839519i \(-0.317163\pi\)
0.543331 + 0.839519i \(0.317163\pi\)
\(212\) 47.5725 3.26729
\(213\) −16.9027 −1.15816
\(214\) 0.711592 0.0486434
\(215\) −14.9855 −1.02200
\(216\) 76.8016 5.22568
\(217\) 18.0708 1.22673
\(218\) −43.1248 −2.92078
\(219\) 41.5155 2.80536
\(220\) 24.7570 1.66912
\(221\) −5.27543 −0.354864
\(222\) −3.42358 −0.229775
\(223\) −14.8024 −0.991240 −0.495620 0.868539i \(-0.665059\pi\)
−0.495620 + 0.868539i \(0.665059\pi\)
\(224\) −86.5347 −5.78185
\(225\) −6.73938 −0.449292
\(226\) 34.2438 2.27787
\(227\) −4.82453 −0.320215 −0.160108 0.987100i \(-0.551184\pi\)
−0.160108 + 0.987100i \(0.551184\pi\)
\(228\) 111.752 7.40098
\(229\) 20.5700 1.35930 0.679652 0.733535i \(-0.262131\pi\)
0.679652 + 0.733535i \(0.262131\pi\)
\(230\) 29.0880 1.91801
\(231\) −24.6741 −1.62343
\(232\) −31.8127 −2.08861
\(233\) 13.2007 0.864809 0.432405 0.901680i \(-0.357665\pi\)
0.432405 + 0.901680i \(0.357665\pi\)
\(234\) −15.5909 −1.01921
\(235\) −3.07838 −0.200811
\(236\) −0.0276590 −0.00180045
\(237\) −48.3985 −3.14382
\(238\) 53.1341 3.44417
\(239\) −0.793102 −0.0513015 −0.0256508 0.999671i \(-0.508166\pi\)
−0.0256508 + 0.999671i \(0.508166\pi\)
\(240\) −90.2210 −5.82374
\(241\) −9.18842 −0.591878 −0.295939 0.955207i \(-0.595633\pi\)
−0.295939 + 0.955207i \(0.595633\pi\)
\(242\) 15.8742 1.02043
\(243\) 5.43713 0.348792
\(244\) −17.4837 −1.11928
\(245\) 12.5727 0.803240
\(246\) 14.5950 0.930540
\(247\) −6.83843 −0.435119
\(248\) −48.0575 −3.05165
\(249\) 8.57050 0.543133
\(250\) 33.1934 2.09933
\(251\) −24.1779 −1.52610 −0.763048 0.646342i \(-0.776298\pi\)
−0.763048 + 0.646342i \(0.776298\pi\)
\(252\) 115.425 7.27111
\(253\) −12.3912 −0.779029
\(254\) −55.4623 −3.48002
\(255\) 30.3377 1.89982
\(256\) 56.0358 3.50224
\(257\) −3.74302 −0.233483 −0.116742 0.993162i \(-0.537245\pi\)
−0.116742 + 0.993162i \(0.537245\pi\)
\(258\) −62.1054 −3.86651
\(259\) −1.55099 −0.0963741
\(260\) 10.8336 0.671869
\(261\) 18.5171 1.14618
\(262\) 36.8649 2.27752
\(263\) 12.8466 0.792156 0.396078 0.918217i \(-0.370371\pi\)
0.396078 + 0.918217i \(0.370371\pi\)
\(264\) 65.6182 4.03852
\(265\) 16.7410 1.02839
\(266\) 68.8767 4.22310
\(267\) 42.9300 2.62727
\(268\) 40.8017 2.49236
\(269\) 7.59445 0.463042 0.231521 0.972830i \(-0.425630\pi\)
0.231521 + 0.972830i \(0.425630\pi\)
\(270\) 42.2598 2.57185
\(271\) 25.5517 1.55216 0.776079 0.630636i \(-0.217206\pi\)
0.776079 + 0.630636i \(0.217206\pi\)
\(272\) −82.7638 −5.01829
\(273\) −10.7973 −0.653479
\(274\) 13.7263 0.829239
\(275\) −2.71397 −0.163659
\(276\) 88.6108 5.33374
\(277\) −3.06330 −0.184056 −0.0920280 0.995756i \(-0.529335\pi\)
−0.0920280 + 0.995756i \(0.529335\pi\)
\(278\) −10.1268 −0.607366
\(279\) 27.9726 1.67468
\(280\) −69.7838 −4.17038
\(281\) 32.1505 1.91794 0.958968 0.283515i \(-0.0915004\pi\)
0.958968 + 0.283515i \(0.0915004\pi\)
\(282\) −12.7579 −0.759724
\(283\) 22.9498 1.36423 0.682113 0.731247i \(-0.261061\pi\)
0.682113 + 0.731247i \(0.261061\pi\)
\(284\) 31.8422 1.88949
\(285\) 39.3261 2.32948
\(286\) −6.27851 −0.371256
\(287\) 6.61200 0.390294
\(288\) −133.951 −7.89314
\(289\) 10.8301 0.637066
\(290\) −17.5048 −1.02792
\(291\) 1.31986 0.0773713
\(292\) −78.2090 −4.57683
\(293\) −11.9804 −0.699901 −0.349950 0.936768i \(-0.613802\pi\)
−0.349950 + 0.936768i \(0.613802\pi\)
\(294\) 52.1058 3.03887
\(295\) −0.00973332 −0.000566696 0
\(296\) 4.12471 0.239744
\(297\) −18.0023 −1.04460
\(298\) 26.1161 1.51286
\(299\) −5.42234 −0.313582
\(300\) 19.4079 1.12051
\(301\) −28.1358 −1.62172
\(302\) −11.0434 −0.635478
\(303\) −14.8487 −0.853034
\(304\) −107.285 −6.15322
\(305\) −6.15261 −0.352297
\(306\) 82.2487 4.70184
\(307\) −31.1310 −1.77674 −0.888371 0.459127i \(-0.848162\pi\)
−0.888371 + 0.459127i \(0.848162\pi\)
\(308\) 46.4822 2.64857
\(309\) −53.5293 −3.04517
\(310\) −26.4435 −1.50189
\(311\) −5.40376 −0.306419 −0.153210 0.988194i \(-0.548961\pi\)
−0.153210 + 0.988194i \(0.548961\pi\)
\(312\) 28.7142 1.62562
\(313\) −29.1137 −1.64561 −0.822803 0.568327i \(-0.807591\pi\)
−0.822803 + 0.568327i \(0.807591\pi\)
\(314\) −29.8280 −1.68329
\(315\) 40.6187 2.28861
\(316\) 91.1755 5.12903
\(317\) −13.7518 −0.772380 −0.386190 0.922419i \(-0.626209\pi\)
−0.386190 + 0.922419i \(0.626209\pi\)
\(318\) 69.3808 3.89068
\(319\) 7.45690 0.417506
\(320\) 65.3638 3.65395
\(321\) 0.762831 0.0425771
\(322\) 54.6138 3.04351
\(323\) 36.0756 2.00730
\(324\) 34.2785 1.90436
\(325\) −1.18762 −0.0658774
\(326\) −4.59021 −0.254228
\(327\) −46.2301 −2.55653
\(328\) −17.5840 −0.970912
\(329\) −5.77977 −0.318649
\(330\) 36.1062 1.98758
\(331\) −19.8673 −1.09200 −0.546002 0.837784i \(-0.683851\pi\)
−0.546002 + 0.837784i \(0.683851\pi\)
\(332\) −16.1455 −0.886100
\(333\) −2.40085 −0.131566
\(334\) 66.8408 3.65737
\(335\) 14.3583 0.784478
\(336\) −169.393 −9.24116
\(337\) −14.0276 −0.764134 −0.382067 0.924135i \(-0.624788\pi\)
−0.382067 + 0.924135i \(0.624788\pi\)
\(338\) −2.74745 −0.149441
\(339\) 36.7096 1.99379
\(340\) −57.1516 −3.09948
\(341\) 11.2647 0.610016
\(342\) 106.617 5.76521
\(343\) −2.05596 −0.111011
\(344\) 74.8244 4.03426
\(345\) 31.1825 1.67881
\(346\) 29.2811 1.57416
\(347\) 11.0188 0.591519 0.295760 0.955262i \(-0.404427\pi\)
0.295760 + 0.955262i \(0.404427\pi\)
\(348\) −53.3250 −2.85852
\(349\) −26.0618 −1.39505 −0.697527 0.716558i \(-0.745716\pi\)
−0.697527 + 0.716558i \(0.745716\pi\)
\(350\) 11.9617 0.639381
\(351\) −7.87771 −0.420481
\(352\) −53.9426 −2.87515
\(353\) −13.0911 −0.696766 −0.348383 0.937352i \(-0.613269\pi\)
−0.348383 + 0.937352i \(0.613269\pi\)
\(354\) −0.0403385 −0.00214397
\(355\) 11.2054 0.594722
\(356\) −80.8737 −4.28630
\(357\) 56.9601 3.01465
\(358\) 51.6186 2.72813
\(359\) 5.11130 0.269764 0.134882 0.990862i \(-0.456934\pi\)
0.134882 + 0.990862i \(0.456934\pi\)
\(360\) −108.021 −5.69323
\(361\) 27.7641 1.46127
\(362\) 49.3416 2.59333
\(363\) 17.0172 0.893172
\(364\) 20.3404 1.06613
\(365\) −27.5221 −1.44057
\(366\) −25.4987 −1.33284
\(367\) 17.1910 0.897362 0.448681 0.893692i \(-0.351894\pi\)
0.448681 + 0.893692i \(0.351894\pi\)
\(368\) −85.0686 −4.43451
\(369\) 10.2350 0.532814
\(370\) 2.26961 0.117991
\(371\) 31.4318 1.63186
\(372\) −80.5547 −4.17657
\(373\) −22.3103 −1.15518 −0.577592 0.816325i \(-0.696008\pi\)
−0.577592 + 0.816325i \(0.696008\pi\)
\(374\) 33.1218 1.71269
\(375\) 35.5835 1.83752
\(376\) 15.3707 0.792684
\(377\) 3.26310 0.168058
\(378\) 79.3443 4.08103
\(379\) −37.6487 −1.93389 −0.966943 0.254994i \(-0.917926\pi\)
−0.966943 + 0.254994i \(0.917926\pi\)
\(380\) −74.0845 −3.80046
\(381\) −59.4560 −3.04602
\(382\) 11.6007 0.593542
\(383\) −4.99819 −0.255395 −0.127698 0.991813i \(-0.540759\pi\)
−0.127698 + 0.991813i \(0.540759\pi\)
\(384\) 131.845 6.72817
\(385\) 16.3573 0.833645
\(386\) −35.4315 −1.80342
\(387\) −43.5527 −2.21391
\(388\) −2.48641 −0.126228
\(389\) 13.1940 0.668961 0.334480 0.942403i \(-0.391439\pi\)
0.334480 + 0.942403i \(0.391439\pi\)
\(390\) 15.7999 0.800059
\(391\) 28.6051 1.44662
\(392\) −62.7770 −3.17072
\(393\) 39.5194 1.99349
\(394\) −22.3421 −1.12558
\(395\) 32.0851 1.61438
\(396\) 71.9519 3.61572
\(397\) −38.9759 −1.95615 −0.978073 0.208262i \(-0.933219\pi\)
−0.978073 + 0.208262i \(0.933219\pi\)
\(398\) 19.6279 0.983858
\(399\) 73.8363 3.69644
\(400\) −18.6321 −0.931603
\(401\) 8.30201 0.414583 0.207291 0.978279i \(-0.433535\pi\)
0.207291 + 0.978279i \(0.433535\pi\)
\(402\) 59.5061 2.96790
\(403\) 4.92936 0.245549
\(404\) 27.9727 1.39169
\(405\) 12.0628 0.599404
\(406\) −32.8660 −1.63111
\(407\) −0.966832 −0.0479241
\(408\) −151.480 −7.49937
\(409\) 7.88315 0.389797 0.194898 0.980823i \(-0.437562\pi\)
0.194898 + 0.980823i \(0.437562\pi\)
\(410\) −9.67551 −0.477839
\(411\) 14.7147 0.725825
\(412\) 100.841 4.96808
\(413\) −0.0182747 −0.000899237 0
\(414\) 84.5392 4.15487
\(415\) −5.68168 −0.278903
\(416\) −23.6050 −1.15733
\(417\) −10.8560 −0.531621
\(418\) 42.9352 2.10003
\(419\) −5.54539 −0.270910 −0.135455 0.990783i \(-0.543250\pi\)
−0.135455 + 0.990783i \(0.543250\pi\)
\(420\) −116.973 −5.70768
\(421\) −8.09794 −0.394670 −0.197335 0.980336i \(-0.563229\pi\)
−0.197335 + 0.980336i \(0.563229\pi\)
\(422\) −43.3675 −2.11110
\(423\) −8.94676 −0.435007
\(424\) −83.5897 −4.05948
\(425\) 6.26521 0.303907
\(426\) 46.4394 2.25000
\(427\) −11.5517 −0.559028
\(428\) −1.43706 −0.0694628
\(429\) −6.73061 −0.324957
\(430\) 41.1719 1.98548
\(431\) −4.46152 −0.214904 −0.107452 0.994210i \(-0.534269\pi\)
−0.107452 + 0.994210i \(0.534269\pi\)
\(432\) −123.590 −5.94622
\(433\) −25.8081 −1.24026 −0.620128 0.784501i \(-0.712919\pi\)
−0.620128 + 0.784501i \(0.712919\pi\)
\(434\) −49.6485 −2.38321
\(435\) −18.7653 −0.899728
\(436\) 87.0906 4.17088
\(437\) 37.0803 1.77379
\(438\) −114.062 −5.45008
\(439\) 23.3538 1.11462 0.557309 0.830305i \(-0.311834\pi\)
0.557309 + 0.830305i \(0.311834\pi\)
\(440\) −43.5006 −2.07381
\(441\) 36.5403 1.74001
\(442\) 14.4940 0.689407
\(443\) −29.1327 −1.38413 −0.692067 0.721833i \(-0.743300\pi\)
−0.692067 + 0.721833i \(0.743300\pi\)
\(444\) 6.91391 0.328120
\(445\) −28.4598 −1.34912
\(446\) 40.6688 1.92572
\(447\) 27.9966 1.32420
\(448\) 122.723 5.79811
\(449\) −21.7596 −1.02690 −0.513449 0.858120i \(-0.671633\pi\)
−0.513449 + 0.858120i \(0.671633\pi\)
\(450\) 18.5161 0.872857
\(451\) 4.12168 0.194082
\(452\) −69.1554 −3.25280
\(453\) −11.8386 −0.556228
\(454\) 13.2551 0.622094
\(455\) 7.15788 0.335566
\(456\) −196.360 −9.19541
\(457\) 10.5026 0.491290 0.245645 0.969360i \(-0.421000\pi\)
0.245645 + 0.969360i \(0.421000\pi\)
\(458\) −56.5150 −2.64077
\(459\) 41.5583 1.93977
\(460\) −58.7432 −2.73892
\(461\) 12.3527 0.575322 0.287661 0.957732i \(-0.407122\pi\)
0.287661 + 0.957732i \(0.407122\pi\)
\(462\) 67.7907 3.15391
\(463\) 31.2732 1.45339 0.726694 0.686961i \(-0.241056\pi\)
0.726694 + 0.686961i \(0.241056\pi\)
\(464\) 51.1934 2.37659
\(465\) −28.3476 −1.31459
\(466\) −36.2683 −1.68010
\(467\) −18.9404 −0.876456 −0.438228 0.898864i \(-0.644394\pi\)
−0.438228 + 0.898864i \(0.644394\pi\)
\(468\) 31.4858 1.45543
\(469\) 26.9583 1.24482
\(470\) 8.45768 0.390124
\(471\) −31.9758 −1.47337
\(472\) 0.0485996 0.00223698
\(473\) −17.5388 −0.806436
\(474\) 132.972 6.10763
\(475\) 8.12147 0.372639
\(476\) −107.304 −4.91828
\(477\) 48.6547 2.22775
\(478\) 2.17901 0.0996654
\(479\) −1.41694 −0.0647415 −0.0323708 0.999476i \(-0.510306\pi\)
−0.0323708 + 0.999476i \(0.510306\pi\)
\(480\) 135.747 6.19596
\(481\) −0.423081 −0.0192908
\(482\) 25.2447 1.14986
\(483\) 58.5463 2.66395
\(484\) −32.0579 −1.45718
\(485\) −0.874979 −0.0397307
\(486\) −14.9382 −0.677612
\(487\) −15.3165 −0.694056 −0.347028 0.937855i \(-0.612809\pi\)
−0.347028 + 0.937855i \(0.612809\pi\)
\(488\) 30.7207 1.39066
\(489\) −4.92074 −0.222523
\(490\) −34.5428 −1.56048
\(491\) −6.60220 −0.297953 −0.148977 0.988841i \(-0.547598\pi\)
−0.148977 + 0.988841i \(0.547598\pi\)
\(492\) −29.4745 −1.32881
\(493\) −17.2143 −0.775291
\(494\) 18.7882 0.845322
\(495\) 25.3202 1.13806
\(496\) 77.3346 3.47242
\(497\) 21.0386 0.943709
\(498\) −23.5470 −1.05517
\(499\) 38.0051 1.70134 0.850672 0.525698i \(-0.176196\pi\)
0.850672 + 0.525698i \(0.176196\pi\)
\(500\) −67.0339 −2.99785
\(501\) 71.6538 3.20126
\(502\) 66.4275 2.96481
\(503\) 33.0104 1.47186 0.735930 0.677058i \(-0.236745\pi\)
0.735930 + 0.677058i \(0.236745\pi\)
\(504\) −202.814 −9.03406
\(505\) 9.84371 0.438039
\(506\) 34.0442 1.51345
\(507\) −2.94528 −0.130805
\(508\) 112.006 4.96947
\(509\) 43.4360 1.92527 0.962633 0.270809i \(-0.0872913\pi\)
0.962633 + 0.270809i \(0.0872913\pi\)
\(510\) −83.3512 −3.69085
\(511\) −51.6737 −2.28591
\(512\) −64.4260 −2.84725
\(513\) 53.8712 2.37847
\(514\) 10.2837 0.453597
\(515\) 35.4864 1.56372
\(516\) 125.422 5.52139
\(517\) −3.60289 −0.158455
\(518\) 4.26127 0.187230
\(519\) 31.3895 1.37785
\(520\) −19.0357 −0.834769
\(521\) −21.6497 −0.948489 −0.474244 0.880393i \(-0.657279\pi\)
−0.474244 + 0.880393i \(0.657279\pi\)
\(522\) −50.8747 −2.22673
\(523\) 33.9561 1.48480 0.742399 0.669958i \(-0.233688\pi\)
0.742399 + 0.669958i \(0.233688\pi\)
\(524\) −74.4486 −3.25230
\(525\) 12.8230 0.559644
\(526\) −35.2954 −1.53895
\(527\) −26.0045 −1.13277
\(528\) −105.593 −4.59536
\(529\) 6.40175 0.278337
\(530\) −45.9950 −1.99789
\(531\) −0.0282882 −0.00122760
\(532\) −139.096 −6.03059
\(533\) 1.80363 0.0781237
\(534\) −117.948 −5.10411
\(535\) −0.505708 −0.0218636
\(536\) −71.6928 −3.09666
\(537\) 55.3354 2.38790
\(538\) −20.8653 −0.899569
\(539\) 14.7149 0.633816
\(540\) −85.3436 −3.67260
\(541\) −21.9583 −0.944063 −0.472031 0.881582i \(-0.656479\pi\)
−0.472031 + 0.881582i \(0.656479\pi\)
\(542\) −70.2021 −3.01544
\(543\) 52.8945 2.26992
\(544\) 124.527 5.33903
\(545\) 30.6476 1.31280
\(546\) 29.6649 1.26954
\(547\) −31.5933 −1.35083 −0.675417 0.737436i \(-0.736036\pi\)
−0.675417 + 0.737436i \(0.736036\pi\)
\(548\) −27.7203 −1.18415
\(549\) −17.8815 −0.763162
\(550\) 7.45649 0.317946
\(551\) −22.3145 −0.950630
\(552\) −155.698 −6.62696
\(553\) 60.2409 2.56170
\(554\) 8.41626 0.357573
\(555\) 2.43304 0.103277
\(556\) 20.4511 0.867319
\(557\) 20.3956 0.864191 0.432095 0.901828i \(-0.357774\pi\)
0.432095 + 0.901828i \(0.357774\pi\)
\(558\) −76.8532 −3.25346
\(559\) −7.67491 −0.324614
\(560\) 112.297 4.74540
\(561\) 35.5068 1.49910
\(562\) −88.3317 −3.72605
\(563\) −8.69222 −0.366333 −0.183167 0.983082i \(-0.558635\pi\)
−0.183167 + 0.983082i \(0.558635\pi\)
\(564\) 25.7646 1.08489
\(565\) −24.3361 −1.02383
\(566\) −63.0534 −2.65033
\(567\) 22.6483 0.951139
\(568\) −55.9500 −2.34761
\(569\) 14.7472 0.618236 0.309118 0.951024i \(-0.399966\pi\)
0.309118 + 0.951024i \(0.399966\pi\)
\(570\) −108.047 −4.52557
\(571\) −6.55340 −0.274251 −0.137126 0.990554i \(-0.543786\pi\)
−0.137126 + 0.990554i \(0.543786\pi\)
\(572\) 12.6794 0.530154
\(573\) 12.4360 0.519521
\(574\) −18.1661 −0.758239
\(575\) 6.43969 0.268553
\(576\) 189.968 7.91534
\(577\) −38.9643 −1.62210 −0.811052 0.584974i \(-0.801105\pi\)
−0.811052 + 0.584974i \(0.801105\pi\)
\(578\) −29.7552 −1.23765
\(579\) −37.9828 −1.57851
\(580\) 35.3510 1.46787
\(581\) −10.6676 −0.442565
\(582\) −3.62623 −0.150312
\(583\) 19.5934 0.811476
\(584\) 137.421 5.68653
\(585\) 11.0800 0.458102
\(586\) 32.9154 1.35972
\(587\) 18.1136 0.747630 0.373815 0.927503i \(-0.378050\pi\)
0.373815 + 0.927503i \(0.378050\pi\)
\(588\) −105.228 −4.33952
\(589\) −33.7091 −1.38896
\(590\) 0.0267418 0.00110094
\(591\) −23.9509 −0.985208
\(592\) −6.63753 −0.272801
\(593\) −33.0794 −1.35841 −0.679205 0.733949i \(-0.737675\pi\)
−0.679205 + 0.733949i \(0.737675\pi\)
\(594\) 49.4603 2.02938
\(595\) −37.7609 −1.54804
\(596\) −52.7414 −2.16037
\(597\) 21.0413 0.861161
\(598\) 14.8976 0.609208
\(599\) −34.0427 −1.39095 −0.695473 0.718552i \(-0.744805\pi\)
−0.695473 + 0.718552i \(0.744805\pi\)
\(600\) −34.1016 −1.39219
\(601\) −32.0597 −1.30774 −0.653871 0.756606i \(-0.726856\pi\)
−0.653871 + 0.756606i \(0.726856\pi\)
\(602\) 77.3017 3.15058
\(603\) 41.7299 1.69937
\(604\) 22.3022 0.907464
\(605\) −11.2813 −0.458651
\(606\) 40.7959 1.65722
\(607\) −15.5548 −0.631348 −0.315674 0.948868i \(-0.602231\pi\)
−0.315674 + 0.948868i \(0.602231\pi\)
\(608\) 161.421 6.54650
\(609\) −35.2325 −1.42769
\(610\) 16.9040 0.684421
\(611\) −1.57661 −0.0637828
\(612\) −166.101 −6.71424
\(613\) −23.7847 −0.960657 −0.480328 0.877089i \(-0.659483\pi\)
−0.480328 + 0.877089i \(0.659483\pi\)
\(614\) 85.5309 3.45174
\(615\) −10.3722 −0.418248
\(616\) −81.6740 −3.29074
\(617\) 18.0367 0.726131 0.363065 0.931764i \(-0.381730\pi\)
0.363065 + 0.931764i \(0.381730\pi\)
\(618\) 147.069 5.91598
\(619\) 1.00000 0.0401934
\(620\) 53.4025 2.14470
\(621\) 42.7156 1.71412
\(622\) 14.8465 0.595292
\(623\) −53.4343 −2.14080
\(624\) −46.2072 −1.84977
\(625\) −17.6514 −0.706058
\(626\) 79.9884 3.19698
\(627\) 46.0268 1.83813
\(628\) 60.2376 2.40374
\(629\) 2.23193 0.0889930
\(630\) −111.598 −4.44616
\(631\) −48.9443 −1.94844 −0.974222 0.225593i \(-0.927568\pi\)
−0.974222 + 0.225593i \(0.927568\pi\)
\(632\) −160.205 −6.37260
\(633\) −46.4903 −1.84782
\(634\) 37.7824 1.50053
\(635\) 39.4155 1.56416
\(636\) −140.114 −5.55590
\(637\) 6.43917 0.255129
\(638\) −20.4874 −0.811105
\(639\) 32.5666 1.28831
\(640\) −87.4045 −3.45497
\(641\) −21.5215 −0.850047 −0.425024 0.905182i \(-0.639734\pi\)
−0.425024 + 0.905182i \(0.639734\pi\)
\(642\) −2.09584 −0.0827161
\(643\) 32.7317 1.29081 0.645406 0.763839i \(-0.276688\pi\)
0.645406 + 0.763839i \(0.276688\pi\)
\(644\) −110.292 −4.34613
\(645\) 44.1365 1.73787
\(646\) −99.1159 −3.89966
\(647\) −40.2120 −1.58090 −0.790449 0.612528i \(-0.790153\pi\)
−0.790449 + 0.612528i \(0.790153\pi\)
\(648\) −60.2309 −2.36609
\(649\) −0.0113917 −0.000447165 0
\(650\) 3.26293 0.127983
\(651\) −53.2236 −2.08600
\(652\) 9.26992 0.363038
\(653\) −17.5689 −0.687524 −0.343762 0.939057i \(-0.611701\pi\)
−0.343762 + 0.939057i \(0.611701\pi\)
\(654\) 127.015 4.96667
\(655\) −26.1988 −1.02367
\(656\) 28.2963 1.10478
\(657\) −79.9881 −3.12063
\(658\) 15.8796 0.619052
\(659\) 28.9532 1.12786 0.563928 0.825824i \(-0.309290\pi\)
0.563928 + 0.825824i \(0.309290\pi\)
\(660\) −72.9164 −2.83827
\(661\) −8.96440 −0.348675 −0.174337 0.984686i \(-0.555778\pi\)
−0.174337 + 0.984686i \(0.555778\pi\)
\(662\) 54.5843 2.12148
\(663\) 15.5376 0.603431
\(664\) 28.3693 1.10094
\(665\) −48.9487 −1.89815
\(666\) 6.59622 0.255598
\(667\) −17.6937 −0.685101
\(668\) −134.985 −5.22273
\(669\) 43.5972 1.68556
\(670\) −39.4487 −1.52404
\(671\) −7.20093 −0.277989
\(672\) 254.869 9.83179
\(673\) −9.87647 −0.380710 −0.190355 0.981715i \(-0.560964\pi\)
−0.190355 + 0.981715i \(0.560964\pi\)
\(674\) 38.5402 1.48451
\(675\) 9.35574 0.360103
\(676\) 5.54847 0.213403
\(677\) 23.6149 0.907594 0.453797 0.891105i \(-0.350069\pi\)
0.453797 + 0.891105i \(0.350069\pi\)
\(678\) −100.858 −3.87342
\(679\) −1.64280 −0.0630450
\(680\) 100.421 3.85098
\(681\) 14.2096 0.544513
\(682\) −30.9491 −1.18510
\(683\) −8.81004 −0.337107 −0.168553 0.985693i \(-0.553910\pi\)
−0.168553 + 0.985693i \(0.553910\pi\)
\(684\) −215.314 −8.23272
\(685\) −9.75492 −0.372716
\(686\) 5.64864 0.215666
\(687\) −60.5845 −2.31144
\(688\) −120.408 −4.59052
\(689\) 8.57399 0.326643
\(690\) −85.6724 −3.26149
\(691\) 12.3878 0.471255 0.235628 0.971843i \(-0.424285\pi\)
0.235628 + 0.971843i \(0.424285\pi\)
\(692\) −59.1331 −2.24790
\(693\) 47.5396 1.80588
\(694\) −30.2735 −1.14917
\(695\) 7.19683 0.272991
\(696\) 93.6975 3.55159
\(697\) −9.51490 −0.360402
\(698\) 71.6033 2.71023
\(699\) −38.8799 −1.47057
\(700\) −24.1567 −0.913037
\(701\) 20.5655 0.776748 0.388374 0.921502i \(-0.373037\pi\)
0.388374 + 0.921502i \(0.373037\pi\)
\(702\) 21.6436 0.816885
\(703\) 2.89321 0.109120
\(704\) 76.5009 2.88323
\(705\) 9.06669 0.341471
\(706\) 35.9670 1.35364
\(707\) 18.4819 0.695084
\(708\) 0.0814635 0.00306158
\(709\) −33.9503 −1.27503 −0.637515 0.770438i \(-0.720037\pi\)
−0.637515 + 0.770438i \(0.720037\pi\)
\(710\) −30.7863 −1.15539
\(711\) 93.2497 3.49714
\(712\) 142.103 5.32555
\(713\) −26.7287 −1.00100
\(714\) −156.495 −5.85667
\(715\) 4.46196 0.166868
\(716\) −104.244 −3.89577
\(717\) 2.33591 0.0872362
\(718\) −14.0430 −0.524081
\(719\) −32.0988 −1.19708 −0.598541 0.801092i \(-0.704253\pi\)
−0.598541 + 0.801092i \(0.704253\pi\)
\(720\) 173.829 6.47823
\(721\) 66.6270 2.48132
\(722\) −76.2805 −2.83887
\(723\) 27.0625 1.00646
\(724\) −99.6452 −3.70329
\(725\) −3.87533 −0.143926
\(726\) −46.7539 −1.73520
\(727\) 15.9916 0.593096 0.296548 0.955018i \(-0.404165\pi\)
0.296548 + 0.955018i \(0.404165\pi\)
\(728\) −35.7402 −1.32462
\(729\) −34.5479 −1.27955
\(730\) 75.6155 2.79866
\(731\) 40.4884 1.49752
\(732\) 51.4945 1.90329
\(733\) 27.8783 1.02971 0.514855 0.857277i \(-0.327846\pi\)
0.514855 + 0.857277i \(0.327846\pi\)
\(734\) −47.2313 −1.74334
\(735\) −37.0301 −1.36588
\(736\) 127.994 4.71793
\(737\) 16.8048 0.619012
\(738\) −28.1202 −1.03512
\(739\) −46.7004 −1.71790 −0.858952 0.512056i \(-0.828884\pi\)
−0.858952 + 0.512056i \(0.828884\pi\)
\(740\) −4.58347 −0.168492
\(741\) 20.1411 0.739902
\(742\) −86.3572 −3.17027
\(743\) −30.2815 −1.11092 −0.555461 0.831543i \(-0.687458\pi\)
−0.555461 + 0.831543i \(0.687458\pi\)
\(744\) 141.543 5.18921
\(745\) −18.5600 −0.679984
\(746\) 61.2964 2.24422
\(747\) −16.5128 −0.604172
\(748\) −66.8895 −2.44572
\(749\) −0.949484 −0.0346934
\(750\) −97.7638 −3.56983
\(751\) 5.32180 0.194195 0.0970976 0.995275i \(-0.469044\pi\)
0.0970976 + 0.995275i \(0.469044\pi\)
\(752\) −24.7347 −0.901982
\(753\) 71.2108 2.59506
\(754\) −8.96521 −0.326494
\(755\) 7.84825 0.285627
\(756\) −160.236 −5.82772
\(757\) −9.83335 −0.357399 −0.178700 0.983904i \(-0.557189\pi\)
−0.178700 + 0.983904i \(0.557189\pi\)
\(758\) 103.438 3.75703
\(759\) 36.4956 1.32471
\(760\) 130.174 4.72191
\(761\) 3.86812 0.140219 0.0701096 0.997539i \(-0.477665\pi\)
0.0701096 + 0.997539i \(0.477665\pi\)
\(762\) 163.352 5.91763
\(763\) 57.5419 2.08316
\(764\) −23.4275 −0.847579
\(765\) −58.4517 −2.11333
\(766\) 13.7323 0.496167
\(767\) −0.00498498 −0.000179997 0
\(768\) −165.041 −5.95541
\(769\) −33.4631 −1.20671 −0.603354 0.797473i \(-0.706170\pi\)
−0.603354 + 0.797473i \(0.706170\pi\)
\(770\) −44.9408 −1.61955
\(771\) 11.0242 0.397029
\(772\) 71.5539 2.57528
\(773\) −34.1128 −1.22695 −0.613476 0.789713i \(-0.710229\pi\)
−0.613476 + 0.789713i \(0.710229\pi\)
\(774\) 119.659 4.30105
\(775\) −5.85422 −0.210290
\(776\) 4.36887 0.156833
\(777\) 4.56811 0.163880
\(778\) −36.2497 −1.29962
\(779\) −12.3340 −0.441910
\(780\) −31.9079 −1.14249
\(781\) 13.1147 0.469280
\(782\) −78.5911 −2.81041
\(783\) −25.7058 −0.918650
\(784\) 101.021 3.60790
\(785\) 21.1979 0.756585
\(786\) −108.578 −3.87283
\(787\) 29.0325 1.03490 0.517448 0.855715i \(-0.326882\pi\)
0.517448 + 0.855715i \(0.326882\pi\)
\(788\) 45.1198 1.60733
\(789\) −37.8369 −1.34703
\(790\) −88.1521 −3.13631
\(791\) −45.6919 −1.62462
\(792\) −126.427 −4.49238
\(793\) −3.15109 −0.111899
\(794\) 107.084 3.80028
\(795\) −49.3069 −1.74874
\(796\) −39.6385 −1.40495
\(797\) −1.33539 −0.0473018 −0.0236509 0.999720i \(-0.507529\pi\)
−0.0236509 + 0.999720i \(0.507529\pi\)
\(798\) −202.861 −7.18121
\(799\) 8.31729 0.294244
\(800\) 28.0338 0.991145
\(801\) −82.7134 −2.92254
\(802\) −22.8093 −0.805426
\(803\) −32.2115 −1.13672
\(804\) −120.173 −4.23816
\(805\) −38.8124 −1.36796
\(806\) −13.5432 −0.477038
\(807\) −22.3678 −0.787384
\(808\) −49.1508 −1.72912
\(809\) −17.1935 −0.604492 −0.302246 0.953230i \(-0.597736\pi\)
−0.302246 + 0.953230i \(0.597736\pi\)
\(810\) −33.1418 −1.16448
\(811\) −27.8669 −0.978538 −0.489269 0.872133i \(-0.662736\pi\)
−0.489269 + 0.872133i \(0.662736\pi\)
\(812\) 66.3728 2.32923
\(813\) −75.2571 −2.63938
\(814\) 2.65632 0.0931040
\(815\) 3.26213 0.114267
\(816\) 243.763 8.53340
\(817\) 52.4843 1.83619
\(818\) −21.6586 −0.757273
\(819\) 20.8031 0.726919
\(820\) 19.5397 0.682355
\(821\) 3.27481 0.114292 0.0571459 0.998366i \(-0.481800\pi\)
0.0571459 + 0.998366i \(0.481800\pi\)
\(822\) −40.4280 −1.41009
\(823\) 15.9129 0.554688 0.277344 0.960771i \(-0.410546\pi\)
0.277344 + 0.960771i \(0.410546\pi\)
\(824\) −177.188 −6.17264
\(825\) 7.99341 0.278295
\(826\) 0.0502087 0.00174698
\(827\) 16.1047 0.560015 0.280007 0.959998i \(-0.409663\pi\)
0.280007 + 0.959998i \(0.409663\pi\)
\(828\) −170.727 −5.93316
\(829\) 11.2435 0.390504 0.195252 0.980753i \(-0.437447\pi\)
0.195252 + 0.980753i \(0.437447\pi\)
\(830\) 15.6101 0.541835
\(831\) 9.02229 0.312980
\(832\) 33.4764 1.16059
\(833\) −33.9694 −1.17697
\(834\) 29.8263 1.03280
\(835\) −47.5018 −1.64387
\(836\) −86.7075 −2.99884
\(837\) −38.8321 −1.34223
\(838\) 15.2357 0.526308
\(839\) 20.6361 0.712439 0.356219 0.934402i \(-0.384066\pi\)
0.356219 + 0.934402i \(0.384066\pi\)
\(840\) 205.533 7.09156
\(841\) −18.3522 −0.632833
\(842\) 22.2487 0.766740
\(843\) −94.6922 −3.26137
\(844\) 87.5807 3.01465
\(845\) 1.95253 0.0671691
\(846\) 24.5808 0.845104
\(847\) −21.1811 −0.727790
\(848\) 134.513 4.61921
\(849\) −67.5937 −2.31981
\(850\) −17.2133 −0.590413
\(851\) 2.29409 0.0786404
\(852\) −93.7843 −3.21300
\(853\) 3.44542 0.117969 0.0589845 0.998259i \(-0.481214\pi\)
0.0589845 + 0.998259i \(0.481214\pi\)
\(854\) 31.7378 1.08604
\(855\) −75.7699 −2.59127
\(856\) 2.52506 0.0863047
\(857\) −34.9011 −1.19220 −0.596100 0.802910i \(-0.703284\pi\)
−0.596100 + 0.802910i \(0.703284\pi\)
\(858\) 18.4920 0.631306
\(859\) 19.5148 0.665836 0.332918 0.942956i \(-0.391967\pi\)
0.332918 + 0.942956i \(0.391967\pi\)
\(860\) −83.1465 −2.83527
\(861\) −19.4742 −0.663679
\(862\) 12.2578 0.417502
\(863\) −21.0744 −0.717380 −0.358690 0.933457i \(-0.616776\pi\)
−0.358690 + 0.933457i \(0.616776\pi\)
\(864\) 185.953 6.32626
\(865\) −20.8092 −0.707535
\(866\) 70.9063 2.40949
\(867\) −31.8978 −1.08330
\(868\) 100.265 3.40322
\(869\) 37.5520 1.27386
\(870\) 51.5567 1.74794
\(871\) 7.35369 0.249170
\(872\) −153.027 −5.18215
\(873\) −2.54297 −0.0860665
\(874\) −101.876 −3.44601
\(875\) −44.2902 −1.49728
\(876\) 230.347 7.78272
\(877\) 39.2382 1.32498 0.662491 0.749070i \(-0.269499\pi\)
0.662491 + 0.749070i \(0.269499\pi\)
\(878\) −64.1634 −2.16541
\(879\) 35.2856 1.19015
\(880\) 70.0016 2.35975
\(881\) 21.2169 0.714816 0.357408 0.933948i \(-0.383661\pi\)
0.357408 + 0.933948i \(0.383661\pi\)
\(882\) −100.393 −3.38039
\(883\) 12.5950 0.423855 0.211927 0.977285i \(-0.432026\pi\)
0.211927 + 0.977285i \(0.432026\pi\)
\(884\) −29.2705 −0.984474
\(885\) 0.0286674 0.000963643 0
\(886\) 80.0405 2.68901
\(887\) 50.0128 1.67927 0.839633 0.543154i \(-0.182770\pi\)
0.839633 + 0.543154i \(0.182770\pi\)
\(888\) −12.1484 −0.407675
\(889\) 74.0040 2.48201
\(890\) 78.1919 2.62100
\(891\) 14.1181 0.472974
\(892\) −82.1305 −2.74993
\(893\) 10.7815 0.360790
\(894\) −76.9193 −2.57257
\(895\) −36.6838 −1.22620
\(896\) −164.105 −5.48237
\(897\) 15.9703 0.533233
\(898\) 59.7833 1.99500
\(899\) 16.0850 0.536466
\(900\) −37.3932 −1.24644
\(901\) −45.2314 −1.50688
\(902\) −11.3241 −0.377051
\(903\) 82.8679 2.75767
\(904\) 121.513 4.04147
\(905\) −35.0656 −1.16562
\(906\) 32.5260 1.08061
\(907\) 13.3568 0.443505 0.221752 0.975103i \(-0.428822\pi\)
0.221752 + 0.975103i \(0.428822\pi\)
\(908\) −26.7687 −0.888352
\(909\) 28.6090 0.948900
\(910\) −19.6659 −0.651918
\(911\) −46.2227 −1.53143 −0.765714 0.643182i \(-0.777614\pi\)
−0.765714 + 0.643182i \(0.777614\pi\)
\(912\) 315.985 10.4633
\(913\) −6.64976 −0.220075
\(914\) −28.8553 −0.954448
\(915\) 18.1212 0.599067
\(916\) 114.132 3.77103
\(917\) −49.1892 −1.62437
\(918\) −114.179 −3.76847
\(919\) −38.8304 −1.28090 −0.640449 0.768001i \(-0.721252\pi\)
−0.640449 + 0.768001i \(0.721252\pi\)
\(920\) 103.218 3.40299
\(921\) 91.6897 3.02128
\(922\) −33.9383 −1.11770
\(923\) 5.73892 0.188899
\(924\) −136.903 −4.50378
\(925\) 0.502460 0.0165208
\(926\) −85.9214 −2.82355
\(927\) 103.135 3.38740
\(928\) −77.0256 −2.52849
\(929\) −6.97428 −0.228819 −0.114409 0.993434i \(-0.536498\pi\)
−0.114409 + 0.993434i \(0.536498\pi\)
\(930\) 77.8835 2.55390
\(931\) −44.0338 −1.44315
\(932\) 73.2439 2.39918
\(933\) 15.9156 0.521053
\(934\) 52.0377 1.70272
\(935\) −23.5387 −0.769798
\(936\) −55.3238 −1.80832
\(937\) −16.6437 −0.543726 −0.271863 0.962336i \(-0.587640\pi\)
−0.271863 + 0.962336i \(0.587640\pi\)
\(938\) −74.0664 −2.41835
\(939\) 85.7481 2.79829
\(940\) −17.0803 −0.557097
\(941\) −29.1680 −0.950850 −0.475425 0.879756i \(-0.657706\pi\)
−0.475425 + 0.879756i \(0.657706\pi\)
\(942\) 87.8519 2.86237
\(943\) −9.77987 −0.318476
\(944\) −0.0782070 −0.00254542
\(945\) −56.3877 −1.83429
\(946\) 48.1870 1.56669
\(947\) −48.3674 −1.57173 −0.785865 0.618398i \(-0.787782\pi\)
−0.785865 + 0.618398i \(0.787782\pi\)
\(948\) −268.538 −8.72170
\(949\) −14.0956 −0.457562
\(950\) −22.3133 −0.723939
\(951\) 40.5030 1.31340
\(952\) 188.545 6.11076
\(953\) −18.7614 −0.607742 −0.303871 0.952713i \(-0.598279\pi\)
−0.303871 + 0.952713i \(0.598279\pi\)
\(954\) −133.676 −4.32793
\(955\) −8.24426 −0.266778
\(956\) −4.40050 −0.142322
\(957\) −21.9627 −0.709952
\(958\) 3.89296 0.125776
\(959\) −18.3152 −0.591429
\(960\) −192.515 −6.21339
\(961\) −6.70137 −0.216173
\(962\) 1.16239 0.0374771
\(963\) −1.46975 −0.0473620
\(964\) −50.9816 −1.64201
\(965\) 25.1801 0.810577
\(966\) −160.853 −5.17536
\(967\) 6.12036 0.196818 0.0984088 0.995146i \(-0.468625\pi\)
0.0984088 + 0.995146i \(0.468625\pi\)
\(968\) 56.3290 1.81048
\(969\) −106.253 −3.41334
\(970\) 2.40396 0.0771864
\(971\) 7.84953 0.251903 0.125952 0.992036i \(-0.459802\pi\)
0.125952 + 0.992036i \(0.459802\pi\)
\(972\) 30.1677 0.967630
\(973\) 13.5123 0.433185
\(974\) 42.0812 1.34837
\(975\) 3.49788 0.112022
\(976\) −49.4361 −1.58241
\(977\) −41.4827 −1.32715 −0.663575 0.748110i \(-0.730962\pi\)
−0.663575 + 0.748110i \(0.730962\pi\)
\(978\) 13.5195 0.432305
\(979\) −33.3090 −1.06456
\(980\) 69.7591 2.22837
\(981\) 89.0718 2.84384
\(982\) 18.1392 0.578845
\(983\) −43.3280 −1.38195 −0.690974 0.722880i \(-0.742818\pi\)
−0.690974 + 0.722880i \(0.742818\pi\)
\(984\) 51.7897 1.65100
\(985\) 15.8779 0.505911
\(986\) 47.2953 1.50619
\(987\) 17.0230 0.541850
\(988\) −37.9428 −1.20712
\(989\) 41.6159 1.32331
\(990\) −69.5659 −2.21095
\(991\) −54.8689 −1.74297 −0.871484 0.490424i \(-0.836842\pi\)
−0.871484 + 0.490424i \(0.836842\pi\)
\(992\) −116.358 −3.69436
\(993\) 58.5147 1.85691
\(994\) −57.8024 −1.83338
\(995\) −13.9490 −0.442213
\(996\) 47.5531 1.50678
\(997\) −32.7353 −1.03674 −0.518369 0.855157i \(-0.673460\pi\)
−0.518369 + 0.855157i \(0.673460\pi\)
\(998\) −104.417 −3.30526
\(999\) 3.33291 0.105449
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 \(a_p\))