Properties

Label 8027.2.a.f.1.12
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.54982 q^{2} -0.805163 q^{3} +4.50159 q^{4} -2.33665 q^{5} +2.05302 q^{6} +2.59075 q^{7} -6.37861 q^{8} -2.35171 q^{9} +O(q^{10})\) \(q-2.54982 q^{2} -0.805163 q^{3} +4.50159 q^{4} -2.33665 q^{5} +2.05302 q^{6} +2.59075 q^{7} -6.37861 q^{8} -2.35171 q^{9} +5.95805 q^{10} -5.57295 q^{11} -3.62451 q^{12} +4.69859 q^{13} -6.60596 q^{14} +1.88139 q^{15} +7.26113 q^{16} -5.12218 q^{17} +5.99645 q^{18} -1.42827 q^{19} -10.5186 q^{20} -2.08598 q^{21} +14.2100 q^{22} +1.00000 q^{23} +5.13582 q^{24} +0.459944 q^{25} -11.9806 q^{26} +4.30900 q^{27} +11.6625 q^{28} +6.55232 q^{29} -4.79720 q^{30} +3.56282 q^{31} -5.75737 q^{32} +4.48714 q^{33} +13.0607 q^{34} -6.05369 q^{35} -10.5864 q^{36} -5.48592 q^{37} +3.64183 q^{38} -3.78313 q^{39} +14.9046 q^{40} -0.275877 q^{41} +5.31887 q^{42} -3.49173 q^{43} -25.0871 q^{44} +5.49513 q^{45} -2.54982 q^{46} -2.00135 q^{47} -5.84639 q^{48} -0.287997 q^{49} -1.17278 q^{50} +4.12419 q^{51} +21.1511 q^{52} -1.80962 q^{53} -10.9872 q^{54} +13.0221 q^{55} -16.5254 q^{56} +1.14999 q^{57} -16.7072 q^{58} +2.39334 q^{59} +8.46923 q^{60} -4.11937 q^{61} -9.08457 q^{62} -6.09271 q^{63} +0.158006 q^{64} -10.9790 q^{65} -11.4414 q^{66} -2.86809 q^{67} -23.0580 q^{68} -0.805163 q^{69} +15.4358 q^{70} +13.9161 q^{71} +15.0006 q^{72} -12.0871 q^{73} +13.9881 q^{74} -0.370330 q^{75} -6.42947 q^{76} -14.4381 q^{77} +9.64631 q^{78} -4.26933 q^{79} -16.9667 q^{80} +3.58569 q^{81} +0.703437 q^{82} -8.54324 q^{83} -9.39022 q^{84} +11.9688 q^{85} +8.90328 q^{86} -5.27568 q^{87} +35.5477 q^{88} -15.6449 q^{89} -14.0116 q^{90} +12.1729 q^{91} +4.50159 q^{92} -2.86866 q^{93} +5.10310 q^{94} +3.33736 q^{95} +4.63562 q^{96} -12.7431 q^{97} +0.734341 q^{98} +13.1060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54982 −1.80300 −0.901498 0.432783i \(-0.857532\pi\)
−0.901498 + 0.432783i \(0.857532\pi\)
\(3\) −0.805163 −0.464861 −0.232431 0.972613i \(-0.574668\pi\)
−0.232431 + 0.972613i \(0.574668\pi\)
\(4\) 4.50159 2.25079
\(5\) −2.33665 −1.04498 −0.522491 0.852645i \(-0.674997\pi\)
−0.522491 + 0.852645i \(0.674997\pi\)
\(6\) 2.05302 0.838143
\(7\) 2.59075 0.979213 0.489606 0.871944i \(-0.337140\pi\)
0.489606 + 0.871944i \(0.337140\pi\)
\(8\) −6.37861 −2.25518
\(9\) −2.35171 −0.783904
\(10\) 5.95805 1.88410
\(11\) −5.57295 −1.68031 −0.840154 0.542348i \(-0.817536\pi\)
−0.840154 + 0.542348i \(0.817536\pi\)
\(12\) −3.62451 −1.04631
\(13\) 4.69859 1.30315 0.651577 0.758582i \(-0.274108\pi\)
0.651577 + 0.758582i \(0.274108\pi\)
\(14\) −6.60596 −1.76552
\(15\) 1.88139 0.485772
\(16\) 7.26113 1.81528
\(17\) −5.12218 −1.24231 −0.621156 0.783687i \(-0.713337\pi\)
−0.621156 + 0.783687i \(0.713337\pi\)
\(18\) 5.99645 1.41338
\(19\) −1.42827 −0.327667 −0.163834 0.986488i \(-0.552386\pi\)
−0.163834 + 0.986488i \(0.552386\pi\)
\(20\) −10.5186 −2.35204
\(21\) −2.08598 −0.455198
\(22\) 14.2100 3.02959
\(23\) 1.00000 0.208514
\(24\) 5.13582 1.04834
\(25\) 0.459944 0.0919889
\(26\) −11.9806 −2.34958
\(27\) 4.30900 0.829268
\(28\) 11.6625 2.20401
\(29\) 6.55232 1.21673 0.608367 0.793656i \(-0.291825\pi\)
0.608367 + 0.793656i \(0.291825\pi\)
\(30\) −4.79720 −0.875845
\(31\) 3.56282 0.639902 0.319951 0.947434i \(-0.396334\pi\)
0.319951 + 0.947434i \(0.396334\pi\)
\(32\) −5.75737 −1.01777
\(33\) 4.48714 0.781110
\(34\) 13.0607 2.23988
\(35\) −6.05369 −1.02326
\(36\) −10.5864 −1.76441
\(37\) −5.48592 −0.901879 −0.450940 0.892554i \(-0.648911\pi\)
−0.450940 + 0.892554i \(0.648911\pi\)
\(38\) 3.64183 0.590782
\(39\) −3.78313 −0.605786
\(40\) 14.9046 2.35662
\(41\) −0.275877 −0.0430848 −0.0215424 0.999768i \(-0.506858\pi\)
−0.0215424 + 0.999768i \(0.506858\pi\)
\(42\) 5.31887 0.820720
\(43\) −3.49173 −0.532483 −0.266242 0.963906i \(-0.585782\pi\)
−0.266242 + 0.963906i \(0.585782\pi\)
\(44\) −25.0871 −3.78203
\(45\) 5.49513 0.819166
\(46\) −2.54982 −0.375951
\(47\) −2.00135 −0.291928 −0.145964 0.989290i \(-0.546628\pi\)
−0.145964 + 0.989290i \(0.546628\pi\)
\(48\) −5.84639 −0.843854
\(49\) −0.287997 −0.0411424
\(50\) −1.17278 −0.165856
\(51\) 4.12419 0.577502
\(52\) 21.1511 2.93313
\(53\) −1.80962 −0.248571 −0.124285 0.992247i \(-0.539664\pi\)
−0.124285 + 0.992247i \(0.539664\pi\)
\(54\) −10.9872 −1.49517
\(55\) 13.0221 1.75589
\(56\) −16.5254 −2.20830
\(57\) 1.14999 0.152320
\(58\) −16.7072 −2.19377
\(59\) 2.39334 0.311587 0.155793 0.987790i \(-0.450207\pi\)
0.155793 + 0.987790i \(0.450207\pi\)
\(60\) 8.46923 1.09337
\(61\) −4.11937 −0.527431 −0.263715 0.964601i \(-0.584948\pi\)
−0.263715 + 0.964601i \(0.584948\pi\)
\(62\) −9.08457 −1.15374
\(63\) −6.09271 −0.767609
\(64\) 0.158006 0.0197507
\(65\) −10.9790 −1.36177
\(66\) −11.4414 −1.40834
\(67\) −2.86809 −0.350393 −0.175197 0.984533i \(-0.556056\pi\)
−0.175197 + 0.984533i \(0.556056\pi\)
\(68\) −23.0580 −2.79619
\(69\) −0.805163 −0.0969303
\(70\) 15.4358 1.84493
\(71\) 13.9161 1.65154 0.825771 0.564005i \(-0.190740\pi\)
0.825771 + 0.564005i \(0.190740\pi\)
\(72\) 15.0006 1.76784
\(73\) −12.0871 −1.41469 −0.707344 0.706870i \(-0.750107\pi\)
−0.707344 + 0.706870i \(0.750107\pi\)
\(74\) 13.9881 1.62608
\(75\) −0.370330 −0.0427621
\(76\) −6.42947 −0.737511
\(77\) −14.4381 −1.64538
\(78\) 9.64631 1.09223
\(79\) −4.26933 −0.480337 −0.240169 0.970731i \(-0.577203\pi\)
−0.240169 + 0.970731i \(0.577203\pi\)
\(80\) −16.9667 −1.89694
\(81\) 3.58569 0.398410
\(82\) 0.703437 0.0776817
\(83\) −8.54324 −0.937743 −0.468871 0.883266i \(-0.655339\pi\)
−0.468871 + 0.883266i \(0.655339\pi\)
\(84\) −9.39022 −1.02456
\(85\) 11.9688 1.29819
\(86\) 8.90328 0.960065
\(87\) −5.27568 −0.565613
\(88\) 35.5477 3.78939
\(89\) −15.6449 −1.65836 −0.829180 0.558982i \(-0.811192\pi\)
−0.829180 + 0.558982i \(0.811192\pi\)
\(90\) −14.0116 −1.47695
\(91\) 12.1729 1.27607
\(92\) 4.50159 0.469323
\(93\) −2.86866 −0.297466
\(94\) 5.10310 0.526344
\(95\) 3.33736 0.342406
\(96\) 4.63562 0.473121
\(97\) −12.7431 −1.29387 −0.646935 0.762545i \(-0.723949\pi\)
−0.646935 + 0.762545i \(0.723949\pi\)
\(98\) 0.734341 0.0741796
\(99\) 13.1060 1.31720
\(100\) 2.07048 0.207048
\(101\) −9.85761 −0.980869 −0.490435 0.871478i \(-0.663162\pi\)
−0.490435 + 0.871478i \(0.663162\pi\)
\(102\) −10.5160 −1.04123
\(103\) −0.370649 −0.0365212 −0.0182606 0.999833i \(-0.505813\pi\)
−0.0182606 + 0.999833i \(0.505813\pi\)
\(104\) −29.9705 −2.93885
\(105\) 4.87421 0.475674
\(106\) 4.61422 0.448172
\(107\) 1.95601 0.189094 0.0945472 0.995520i \(-0.469860\pi\)
0.0945472 + 0.995520i \(0.469860\pi\)
\(108\) 19.3974 1.86651
\(109\) 19.7890 1.89544 0.947720 0.319103i \(-0.103382\pi\)
0.947720 + 0.319103i \(0.103382\pi\)
\(110\) −33.2039 −3.16587
\(111\) 4.41706 0.419249
\(112\) 18.8118 1.77755
\(113\) 6.81442 0.641046 0.320523 0.947241i \(-0.396141\pi\)
0.320523 + 0.947241i \(0.396141\pi\)
\(114\) −2.93227 −0.274632
\(115\) −2.33665 −0.217894
\(116\) 29.4958 2.73862
\(117\) −11.0497 −1.02155
\(118\) −6.10260 −0.561790
\(119\) −13.2703 −1.21649
\(120\) −12.0006 −1.09550
\(121\) 20.0578 1.82344
\(122\) 10.5036 0.950956
\(123\) 0.222126 0.0200284
\(124\) 16.0384 1.44029
\(125\) 10.6085 0.948856
\(126\) 15.5353 1.38400
\(127\) −3.21708 −0.285470 −0.142735 0.989761i \(-0.545590\pi\)
−0.142735 + 0.989761i \(0.545590\pi\)
\(128\) 11.1119 0.982158
\(129\) 2.81141 0.247531
\(130\) 27.9944 2.45527
\(131\) −12.3306 −1.07733 −0.538664 0.842521i \(-0.681071\pi\)
−0.538664 + 0.842521i \(0.681071\pi\)
\(132\) 20.1992 1.75812
\(133\) −3.70029 −0.320856
\(134\) 7.31313 0.631758
\(135\) −10.0686 −0.866570
\(136\) 32.6724 2.80163
\(137\) 1.88343 0.160912 0.0804560 0.996758i \(-0.474362\pi\)
0.0804560 + 0.996758i \(0.474362\pi\)
\(138\) 2.05302 0.174765
\(139\) −14.2618 −1.20967 −0.604835 0.796351i \(-0.706761\pi\)
−0.604835 + 0.796351i \(0.706761\pi\)
\(140\) −27.2512 −2.30315
\(141\) 1.61142 0.135706
\(142\) −35.4837 −2.97772
\(143\) −26.1850 −2.18970
\(144\) −17.0761 −1.42301
\(145\) −15.3105 −1.27147
\(146\) 30.8199 2.55068
\(147\) 0.231885 0.0191255
\(148\) −24.6953 −2.02995
\(149\) −4.74266 −0.388534 −0.194267 0.980949i \(-0.562233\pi\)
−0.194267 + 0.980949i \(0.562233\pi\)
\(150\) 0.944276 0.0770998
\(151\) 12.9508 1.05392 0.526959 0.849891i \(-0.323332\pi\)
0.526959 + 0.849891i \(0.323332\pi\)
\(152\) 9.11036 0.738948
\(153\) 12.0459 0.973853
\(154\) 36.8147 2.96661
\(155\) −8.32508 −0.668687
\(156\) −17.0301 −1.36350
\(157\) 13.1157 1.04674 0.523372 0.852104i \(-0.324674\pi\)
0.523372 + 0.852104i \(0.324674\pi\)
\(158\) 10.8860 0.866046
\(159\) 1.45704 0.115551
\(160\) 13.4530 1.06355
\(161\) 2.59075 0.204180
\(162\) −9.14286 −0.718331
\(163\) 6.99681 0.548032 0.274016 0.961725i \(-0.411648\pi\)
0.274016 + 0.961725i \(0.411648\pi\)
\(164\) −1.24189 −0.0969750
\(165\) −10.4849 −0.816247
\(166\) 21.7837 1.69075
\(167\) −22.2886 −1.72474 −0.862370 0.506278i \(-0.831021\pi\)
−0.862370 + 0.506278i \(0.831021\pi\)
\(168\) 13.3056 1.02655
\(169\) 9.07677 0.698213
\(170\) −30.5182 −2.34064
\(171\) 3.35887 0.256860
\(172\) −15.7183 −1.19851
\(173\) −19.5038 −1.48284 −0.741421 0.671040i \(-0.765848\pi\)
−0.741421 + 0.671040i \(0.765848\pi\)
\(174\) 13.4521 1.01980
\(175\) 1.19160 0.0900767
\(176\) −40.4659 −3.05023
\(177\) −1.92703 −0.144845
\(178\) 39.8918 2.99002
\(179\) 1.22468 0.0915369 0.0457684 0.998952i \(-0.485426\pi\)
0.0457684 + 0.998952i \(0.485426\pi\)
\(180\) 24.7368 1.84377
\(181\) −8.76576 −0.651553 −0.325777 0.945447i \(-0.605626\pi\)
−0.325777 + 0.945447i \(0.605626\pi\)
\(182\) −31.0387 −2.30074
\(183\) 3.31676 0.245182
\(184\) −6.37861 −0.470237
\(185\) 12.8187 0.942448
\(186\) 7.31456 0.536330
\(187\) 28.5457 2.08747
\(188\) −9.00927 −0.657069
\(189\) 11.1636 0.812030
\(190\) −8.50968 −0.617357
\(191\) −20.6322 −1.49290 −0.746448 0.665443i \(-0.768243\pi\)
−0.746448 + 0.665443i \(0.768243\pi\)
\(192\) −0.127220 −0.00918135
\(193\) −18.2631 −1.31461 −0.657304 0.753626i \(-0.728303\pi\)
−0.657304 + 0.753626i \(0.728303\pi\)
\(194\) 32.4927 2.33284
\(195\) 8.83987 0.633036
\(196\) −1.29644 −0.0926032
\(197\) 11.1773 0.796351 0.398176 0.917309i \(-0.369643\pi\)
0.398176 + 0.917309i \(0.369643\pi\)
\(198\) −33.4179 −2.37491
\(199\) 20.1595 1.42907 0.714533 0.699602i \(-0.246639\pi\)
0.714533 + 0.699602i \(0.246639\pi\)
\(200\) −2.93380 −0.207451
\(201\) 2.30928 0.162884
\(202\) 25.1352 1.76850
\(203\) 16.9754 1.19144
\(204\) 18.5654 1.29984
\(205\) 0.644629 0.0450228
\(206\) 0.945090 0.0658475
\(207\) −2.35171 −0.163455
\(208\) 34.1171 2.36559
\(209\) 7.95967 0.550582
\(210\) −12.4284 −0.857638
\(211\) −6.81171 −0.468938 −0.234469 0.972124i \(-0.575335\pi\)
−0.234469 + 0.972124i \(0.575335\pi\)
\(212\) −8.14618 −0.559482
\(213\) −11.2048 −0.767738
\(214\) −4.98747 −0.340937
\(215\) 8.15895 0.556436
\(216\) −27.4854 −1.87015
\(217\) 9.23040 0.626600
\(218\) −50.4584 −3.41747
\(219\) 9.73209 0.657633
\(220\) 58.6199 3.95216
\(221\) −24.0670 −1.61892
\(222\) −11.2627 −0.755904
\(223\) 22.3364 1.49576 0.747878 0.663836i \(-0.231073\pi\)
0.747878 + 0.663836i \(0.231073\pi\)
\(224\) −14.9159 −0.996612
\(225\) −1.08166 −0.0721105
\(226\) −17.3755 −1.15580
\(227\) 4.61136 0.306066 0.153033 0.988221i \(-0.451096\pi\)
0.153033 + 0.988221i \(0.451096\pi\)
\(228\) 5.17678 0.342840
\(229\) 5.94990 0.393180 0.196590 0.980486i \(-0.437013\pi\)
0.196590 + 0.980486i \(0.437013\pi\)
\(230\) 5.95805 0.392862
\(231\) 11.6251 0.764873
\(232\) −41.7947 −2.74395
\(233\) 9.57400 0.627214 0.313607 0.949553i \(-0.398463\pi\)
0.313607 + 0.949553i \(0.398463\pi\)
\(234\) 28.1749 1.84185
\(235\) 4.67647 0.305059
\(236\) 10.7739 0.701318
\(237\) 3.43751 0.223290
\(238\) 33.8369 2.19332
\(239\) −6.18467 −0.400053 −0.200027 0.979790i \(-0.564103\pi\)
−0.200027 + 0.979790i \(0.564103\pi\)
\(240\) 13.6610 0.881813
\(241\) −18.4702 −1.18977 −0.594884 0.803811i \(-0.702802\pi\)
−0.594884 + 0.803811i \(0.702802\pi\)
\(242\) −51.1438 −3.28765
\(243\) −15.8141 −1.01447
\(244\) −18.5437 −1.18714
\(245\) 0.672949 0.0429931
\(246\) −0.566382 −0.0361112
\(247\) −6.71085 −0.427001
\(248\) −22.7259 −1.44309
\(249\) 6.87871 0.435920
\(250\) −27.0499 −1.71078
\(251\) −18.4607 −1.16523 −0.582615 0.812748i \(-0.697970\pi\)
−0.582615 + 0.812748i \(0.697970\pi\)
\(252\) −27.4269 −1.72773
\(253\) −5.57295 −0.350369
\(254\) 8.20299 0.514701
\(255\) −9.63680 −0.603480
\(256\) −28.6492 −1.79058
\(257\) 7.90883 0.493339 0.246670 0.969100i \(-0.420664\pi\)
0.246670 + 0.969100i \(0.420664\pi\)
\(258\) −7.16859 −0.446297
\(259\) −14.2127 −0.883132
\(260\) −49.4228 −3.06507
\(261\) −15.4092 −0.953803
\(262\) 31.4408 1.94242
\(263\) 21.0069 1.29534 0.647670 0.761921i \(-0.275743\pi\)
0.647670 + 0.761921i \(0.275743\pi\)
\(264\) −28.6217 −1.76154
\(265\) 4.22846 0.259752
\(266\) 9.43508 0.578502
\(267\) 12.5967 0.770907
\(268\) −12.9110 −0.788663
\(269\) −18.6069 −1.13448 −0.567240 0.823552i \(-0.691989\pi\)
−0.567240 + 0.823552i \(0.691989\pi\)
\(270\) 25.6732 1.56242
\(271\) 25.2772 1.53548 0.767741 0.640761i \(-0.221381\pi\)
0.767741 + 0.640761i \(0.221381\pi\)
\(272\) −37.1928 −2.25515
\(273\) −9.80117 −0.593194
\(274\) −4.80240 −0.290124
\(275\) −2.56325 −0.154570
\(276\) −3.62451 −0.218170
\(277\) 28.5315 1.71429 0.857145 0.515074i \(-0.172236\pi\)
0.857145 + 0.515074i \(0.172236\pi\)
\(278\) 36.3650 2.18103
\(279\) −8.37874 −0.501622
\(280\) 38.6141 2.30763
\(281\) −14.3823 −0.857977 −0.428988 0.903310i \(-0.641130\pi\)
−0.428988 + 0.903310i \(0.641130\pi\)
\(282\) −4.10882 −0.244677
\(283\) 24.3571 1.44788 0.723939 0.689864i \(-0.242330\pi\)
0.723939 + 0.689864i \(0.242330\pi\)
\(284\) 62.6448 3.71728
\(285\) −2.68712 −0.159171
\(286\) 66.7672 3.94802
\(287\) −0.714729 −0.0421891
\(288\) 13.5397 0.797833
\(289\) 9.23675 0.543338
\(290\) 39.0390 2.29245
\(291\) 10.2603 0.601470
\(292\) −54.4111 −3.18417
\(293\) 2.42978 0.141949 0.0709746 0.997478i \(-0.477389\pi\)
0.0709746 + 0.997478i \(0.477389\pi\)
\(294\) −0.591264 −0.0344832
\(295\) −5.59241 −0.325603
\(296\) 34.9925 2.03390
\(297\) −24.0139 −1.39343
\(298\) 12.0929 0.700525
\(299\) 4.69859 0.271727
\(300\) −1.66708 −0.0962486
\(301\) −9.04620 −0.521414
\(302\) −33.0221 −1.90021
\(303\) 7.93699 0.455968
\(304\) −10.3708 −0.594808
\(305\) 9.62553 0.551156
\(306\) −30.7149 −1.75585
\(307\) −7.78825 −0.444499 −0.222250 0.974990i \(-0.571340\pi\)
−0.222250 + 0.974990i \(0.571340\pi\)
\(308\) −64.9946 −3.70341
\(309\) 0.298433 0.0169773
\(310\) 21.2275 1.20564
\(311\) 16.0437 0.909756 0.454878 0.890554i \(-0.349683\pi\)
0.454878 + 0.890554i \(0.349683\pi\)
\(312\) 24.1311 1.36616
\(313\) −24.1866 −1.36711 −0.683555 0.729899i \(-0.739567\pi\)
−0.683555 + 0.729899i \(0.739567\pi\)
\(314\) −33.4426 −1.88728
\(315\) 14.2365 0.802138
\(316\) −19.2188 −1.08114
\(317\) −19.4406 −1.09189 −0.545946 0.837820i \(-0.683830\pi\)
−0.545946 + 0.837820i \(0.683830\pi\)
\(318\) −3.71520 −0.208338
\(319\) −36.5158 −2.04449
\(320\) −0.369205 −0.0206392
\(321\) −1.57491 −0.0879027
\(322\) −6.60596 −0.368136
\(323\) 7.31585 0.407065
\(324\) 16.1413 0.896738
\(325\) 2.16109 0.119876
\(326\) −17.8406 −0.988100
\(327\) −15.9334 −0.881117
\(328\) 1.75971 0.0971638
\(329\) −5.18501 −0.285859
\(330\) 26.7346 1.47169
\(331\) −26.7069 −1.46794 −0.733972 0.679180i \(-0.762335\pi\)
−0.733972 + 0.679180i \(0.762335\pi\)
\(332\) −38.4582 −2.11067
\(333\) 12.9013 0.706987
\(334\) 56.8318 3.10970
\(335\) 6.70174 0.366155
\(336\) −15.1466 −0.826313
\(337\) 6.41473 0.349433 0.174716 0.984619i \(-0.444099\pi\)
0.174716 + 0.984619i \(0.444099\pi\)
\(338\) −23.1441 −1.25888
\(339\) −5.48672 −0.297998
\(340\) 53.8784 2.92197
\(341\) −19.8555 −1.07523
\(342\) −8.56453 −0.463117
\(343\) −18.8814 −1.01950
\(344\) 22.2723 1.20084
\(345\) 1.88139 0.101290
\(346\) 49.7311 2.67356
\(347\) 7.44496 0.399666 0.199833 0.979830i \(-0.435960\pi\)
0.199833 + 0.979830i \(0.435960\pi\)
\(348\) −23.7490 −1.27308
\(349\) −1.00000 −0.0535288
\(350\) −3.03837 −0.162408
\(351\) 20.2462 1.08066
\(352\) 32.0855 1.71017
\(353\) −6.46175 −0.343924 −0.171962 0.985104i \(-0.555011\pi\)
−0.171962 + 0.985104i \(0.555011\pi\)
\(354\) 4.91359 0.261154
\(355\) −32.5172 −1.72583
\(356\) −70.4271 −3.73263
\(357\) 10.6848 0.565498
\(358\) −3.12271 −0.165041
\(359\) 17.5803 0.927851 0.463925 0.885874i \(-0.346441\pi\)
0.463925 + 0.885874i \(0.346441\pi\)
\(360\) −35.0513 −1.84737
\(361\) −16.9601 −0.892634
\(362\) 22.3511 1.17475
\(363\) −16.1498 −0.847645
\(364\) 54.7974 2.87216
\(365\) 28.2433 1.47832
\(366\) −8.45715 −0.442062
\(367\) −27.9795 −1.46052 −0.730258 0.683172i \(-0.760600\pi\)
−0.730258 + 0.683172i \(0.760600\pi\)
\(368\) 7.26113 0.378513
\(369\) 0.648784 0.0337743
\(370\) −32.6854 −1.69923
\(371\) −4.68829 −0.243404
\(372\) −12.9135 −0.669534
\(373\) −14.3746 −0.744290 −0.372145 0.928175i \(-0.621378\pi\)
−0.372145 + 0.928175i \(0.621378\pi\)
\(374\) −72.7864 −3.76369
\(375\) −8.54160 −0.441086
\(376\) 12.7659 0.658348
\(377\) 30.7867 1.58559
\(378\) −28.4651 −1.46409
\(379\) −30.0028 −1.54114 −0.770569 0.637356i \(-0.780028\pi\)
−0.770569 + 0.637356i \(0.780028\pi\)
\(380\) 15.0234 0.770687
\(381\) 2.59028 0.132704
\(382\) 52.6085 2.69169
\(383\) −8.55415 −0.437097 −0.218548 0.975826i \(-0.570132\pi\)
−0.218548 + 0.975826i \(0.570132\pi\)
\(384\) −8.94685 −0.456567
\(385\) 33.7369 1.71939
\(386\) 46.5677 2.37023
\(387\) 8.21153 0.417416
\(388\) −57.3644 −2.91223
\(389\) 14.8713 0.754007 0.377003 0.926212i \(-0.376954\pi\)
0.377003 + 0.926212i \(0.376954\pi\)
\(390\) −22.5401 −1.14136
\(391\) −5.12218 −0.259040
\(392\) 1.83702 0.0927835
\(393\) 9.92813 0.500808
\(394\) −28.5002 −1.43582
\(395\) 9.97595 0.501944
\(396\) 58.9977 2.96475
\(397\) 7.50289 0.376559 0.188280 0.982115i \(-0.439709\pi\)
0.188280 + 0.982115i \(0.439709\pi\)
\(398\) −51.4030 −2.57660
\(399\) 2.97934 0.149153
\(400\) 3.33972 0.166986
\(401\) 38.8624 1.94070 0.970349 0.241710i \(-0.0777081\pi\)
0.970349 + 0.241710i \(0.0777081\pi\)
\(402\) −5.88826 −0.293680
\(403\) 16.7403 0.833892
\(404\) −44.3749 −2.20774
\(405\) −8.37850 −0.416331
\(406\) −43.2843 −2.14817
\(407\) 30.5728 1.51544
\(408\) −26.3066 −1.30237
\(409\) 20.0350 0.990666 0.495333 0.868703i \(-0.335046\pi\)
0.495333 + 0.868703i \(0.335046\pi\)
\(410\) −1.64369 −0.0811760
\(411\) −1.51647 −0.0748017
\(412\) −1.66851 −0.0822016
\(413\) 6.20056 0.305110
\(414\) 5.99645 0.294709
\(415\) 19.9626 0.979925
\(416\) −27.0515 −1.32631
\(417\) 11.4831 0.562329
\(418\) −20.2957 −0.992697
\(419\) 12.9460 0.632453 0.316226 0.948684i \(-0.397584\pi\)
0.316226 + 0.948684i \(0.397584\pi\)
\(420\) 21.9417 1.07064
\(421\) −29.2626 −1.42617 −0.713087 0.701076i \(-0.752704\pi\)
−0.713087 + 0.701076i \(0.752704\pi\)
\(422\) 17.3686 0.845492
\(423\) 4.70661 0.228843
\(424\) 11.5429 0.560572
\(425\) −2.35592 −0.114279
\(426\) 28.5702 1.38423
\(427\) −10.6723 −0.516467
\(428\) 8.80515 0.425613
\(429\) 21.0832 1.01791
\(430\) −20.8039 −1.00325
\(431\) −3.80195 −0.183133 −0.0915667 0.995799i \(-0.529187\pi\)
−0.0915667 + 0.995799i \(0.529187\pi\)
\(432\) 31.2882 1.50536
\(433\) 36.3491 1.74683 0.873414 0.486978i \(-0.161901\pi\)
0.873414 + 0.486978i \(0.161901\pi\)
\(434\) −23.5359 −1.12976
\(435\) 12.3274 0.591056
\(436\) 89.0819 4.26625
\(437\) −1.42827 −0.0683233
\(438\) −24.8151 −1.18571
\(439\) −32.7284 −1.56204 −0.781022 0.624504i \(-0.785301\pi\)
−0.781022 + 0.624504i \(0.785301\pi\)
\(440\) −83.0626 −3.95985
\(441\) 0.677286 0.0322517
\(442\) 61.3667 2.91891
\(443\) −22.5145 −1.06970 −0.534849 0.844947i \(-0.679632\pi\)
−0.534849 + 0.844947i \(0.679632\pi\)
\(444\) 19.8838 0.943643
\(445\) 36.5568 1.73296
\(446\) −56.9538 −2.69684
\(447\) 3.81862 0.180614
\(448\) 0.409354 0.0193402
\(449\) 4.32248 0.203991 0.101995 0.994785i \(-0.467477\pi\)
0.101995 + 0.994785i \(0.467477\pi\)
\(450\) 2.75803 0.130015
\(451\) 1.53745 0.0723957
\(452\) 30.6757 1.44286
\(453\) −10.4275 −0.489925
\(454\) −11.7581 −0.551837
\(455\) −28.4438 −1.33347
\(456\) −7.33532 −0.343508
\(457\) −8.44306 −0.394950 −0.197475 0.980308i \(-0.563274\pi\)
−0.197475 + 0.980308i \(0.563274\pi\)
\(458\) −15.1712 −0.708903
\(459\) −22.0715 −1.03021
\(460\) −10.5186 −0.490435
\(461\) −24.3164 −1.13253 −0.566264 0.824224i \(-0.691612\pi\)
−0.566264 + 0.824224i \(0.691612\pi\)
\(462\) −29.6418 −1.37906
\(463\) −8.54814 −0.397266 −0.198633 0.980074i \(-0.563650\pi\)
−0.198633 + 0.980074i \(0.563650\pi\)
\(464\) 47.5772 2.20872
\(465\) 6.70305 0.310847
\(466\) −24.4120 −1.13086
\(467\) 11.1149 0.514337 0.257169 0.966367i \(-0.417210\pi\)
0.257169 + 0.966367i \(0.417210\pi\)
\(468\) −49.7414 −2.29930
\(469\) −7.43052 −0.343110
\(470\) −11.9242 −0.550021
\(471\) −10.5603 −0.486591
\(472\) −15.2662 −0.702684
\(473\) 19.4592 0.894736
\(474\) −8.76503 −0.402591
\(475\) −0.656924 −0.0301417
\(476\) −59.7375 −2.73806
\(477\) 4.25571 0.194856
\(478\) 15.7698 0.721295
\(479\) −4.38695 −0.200445 −0.100222 0.994965i \(-0.531955\pi\)
−0.100222 + 0.994965i \(0.531955\pi\)
\(480\) −10.8318 −0.494403
\(481\) −25.7761 −1.17529
\(482\) 47.0957 2.14515
\(483\) −2.08598 −0.0949153
\(484\) 90.2920 4.10418
\(485\) 29.7763 1.35207
\(486\) 40.3231 1.82909
\(487\) −2.45905 −0.111430 −0.0557152 0.998447i \(-0.517744\pi\)
−0.0557152 + 0.998447i \(0.517744\pi\)
\(488\) 26.2758 1.18945
\(489\) −5.63357 −0.254759
\(490\) −1.71590 −0.0775164
\(491\) 16.4487 0.742318 0.371159 0.928569i \(-0.378960\pi\)
0.371159 + 0.928569i \(0.378960\pi\)
\(492\) 0.999920 0.0450799
\(493\) −33.5622 −1.51156
\(494\) 17.1115 0.769881
\(495\) −30.6241 −1.37645
\(496\) 25.8701 1.16160
\(497\) 36.0533 1.61721
\(498\) −17.5395 −0.785963
\(499\) 30.6398 1.37163 0.685814 0.727777i \(-0.259446\pi\)
0.685814 + 0.727777i \(0.259446\pi\)
\(500\) 47.7553 2.13568
\(501\) 17.9459 0.801765
\(502\) 47.0715 2.10090
\(503\) −34.1722 −1.52366 −0.761832 0.647774i \(-0.775700\pi\)
−0.761832 + 0.647774i \(0.775700\pi\)
\(504\) 38.8630 1.73109
\(505\) 23.0338 1.02499
\(506\) 14.2100 0.631713
\(507\) −7.30828 −0.324572
\(508\) −14.4820 −0.642535
\(509\) 30.4163 1.34818 0.674088 0.738651i \(-0.264537\pi\)
0.674088 + 0.738651i \(0.264537\pi\)
\(510\) 24.5721 1.08807
\(511\) −31.3147 −1.38528
\(512\) 50.8268 2.24625
\(513\) −6.15441 −0.271724
\(514\) −20.1661 −0.889489
\(515\) 0.866079 0.0381640
\(516\) 12.6558 0.557141
\(517\) 11.1535 0.490528
\(518\) 36.2397 1.59228
\(519\) 15.7037 0.689316
\(520\) 70.0306 3.07104
\(521\) 8.14948 0.357035 0.178518 0.983937i \(-0.442870\pi\)
0.178518 + 0.983937i \(0.442870\pi\)
\(522\) 39.2906 1.71970
\(523\) 19.8083 0.866157 0.433079 0.901356i \(-0.357427\pi\)
0.433079 + 0.901356i \(0.357427\pi\)
\(524\) −55.5072 −2.42484
\(525\) −0.959435 −0.0418732
\(526\) −53.5638 −2.33549
\(527\) −18.2494 −0.794958
\(528\) 32.5817 1.41794
\(529\) 1.00000 0.0434783
\(530\) −10.7818 −0.468332
\(531\) −5.62846 −0.244254
\(532\) −16.6572 −0.722180
\(533\) −1.29623 −0.0561461
\(534\) −32.1194 −1.38994
\(535\) −4.57051 −0.197600
\(536\) 18.2944 0.790199
\(537\) −0.986067 −0.0425519
\(538\) 47.4442 2.04546
\(539\) 1.60499 0.0691320
\(540\) −45.3249 −1.95047
\(541\) 1.94251 0.0835150 0.0417575 0.999128i \(-0.486704\pi\)
0.0417575 + 0.999128i \(0.486704\pi\)
\(542\) −64.4524 −2.76847
\(543\) 7.05786 0.302882
\(544\) 29.4903 1.26439
\(545\) −46.2400 −1.98070
\(546\) 24.9912 1.06953
\(547\) 18.3804 0.785891 0.392945 0.919562i \(-0.371456\pi\)
0.392945 + 0.919562i \(0.371456\pi\)
\(548\) 8.47841 0.362180
\(549\) 9.68756 0.413455
\(550\) 6.53583 0.278689
\(551\) −9.35846 −0.398684
\(552\) 5.13582 0.218595
\(553\) −11.0608 −0.470352
\(554\) −72.7502 −3.09086
\(555\) −10.3211 −0.438108
\(556\) −64.2008 −2.72272
\(557\) 37.5538 1.59121 0.795604 0.605818i \(-0.207154\pi\)
0.795604 + 0.605818i \(0.207154\pi\)
\(558\) 21.3643 0.904422
\(559\) −16.4062 −0.693908
\(560\) −43.9566 −1.85751
\(561\) −22.9839 −0.970382
\(562\) 36.6723 1.54693
\(563\) 10.8382 0.456777 0.228389 0.973570i \(-0.426654\pi\)
0.228389 + 0.973570i \(0.426654\pi\)
\(564\) 7.25394 0.305446
\(565\) −15.9229 −0.669882
\(566\) −62.1062 −2.61052
\(567\) 9.28963 0.390128
\(568\) −88.7656 −3.72452
\(569\) −21.6790 −0.908829 −0.454415 0.890790i \(-0.650152\pi\)
−0.454415 + 0.890790i \(0.650152\pi\)
\(570\) 6.85168 0.286986
\(571\) 15.3382 0.641882 0.320941 0.947099i \(-0.396001\pi\)
0.320941 + 0.947099i \(0.396001\pi\)
\(572\) −117.874 −4.92857
\(573\) 16.6123 0.693990
\(574\) 1.82243 0.0760669
\(575\) 0.459944 0.0191810
\(576\) −0.371584 −0.0154827
\(577\) 9.59456 0.399427 0.199713 0.979854i \(-0.435999\pi\)
0.199713 + 0.979854i \(0.435999\pi\)
\(578\) −23.5521 −0.979637
\(579\) 14.7048 0.611110
\(580\) −68.9215 −2.86181
\(581\) −22.1334 −0.918250
\(582\) −26.1619 −1.08445
\(583\) 10.0849 0.417676
\(584\) 77.0988 3.19037
\(585\) 25.8194 1.06750
\(586\) −6.19550 −0.255934
\(587\) −9.87884 −0.407743 −0.203872 0.978998i \(-0.565353\pi\)
−0.203872 + 0.978998i \(0.565353\pi\)
\(588\) 1.04385 0.0430476
\(589\) −5.08867 −0.209675
\(590\) 14.2597 0.587061
\(591\) −8.99957 −0.370193
\(592\) −39.8340 −1.63717
\(593\) 30.5185 1.25324 0.626622 0.779323i \(-0.284437\pi\)
0.626622 + 0.779323i \(0.284437\pi\)
\(594\) 61.2311 2.51234
\(595\) 31.0081 1.27121
\(596\) −21.3495 −0.874510
\(597\) −16.2317 −0.664317
\(598\) −11.9806 −0.489922
\(599\) 8.29791 0.339043 0.169522 0.985526i \(-0.445778\pi\)
0.169522 + 0.985526i \(0.445778\pi\)
\(600\) 2.36219 0.0964361
\(601\) 42.5008 1.73364 0.866822 0.498618i \(-0.166159\pi\)
0.866822 + 0.498618i \(0.166159\pi\)
\(602\) 23.0662 0.940108
\(603\) 6.74493 0.274675
\(604\) 58.2990 2.37215
\(605\) −46.8681 −1.90546
\(606\) −20.2379 −0.822109
\(607\) −18.9333 −0.768479 −0.384240 0.923233i \(-0.625536\pi\)
−0.384240 + 0.923233i \(0.625536\pi\)
\(608\) 8.22306 0.333489
\(609\) −13.6680 −0.553855
\(610\) −24.5434 −0.993732
\(611\) −9.40355 −0.380427
\(612\) 54.2257 2.19194
\(613\) −43.7445 −1.76682 −0.883412 0.468596i \(-0.844760\pi\)
−0.883412 + 0.468596i \(0.844760\pi\)
\(614\) 19.8587 0.801430
\(615\) −0.519031 −0.0209294
\(616\) 92.0953 3.71062
\(617\) −14.3608 −0.578143 −0.289071 0.957308i \(-0.593347\pi\)
−0.289071 + 0.957308i \(0.593347\pi\)
\(618\) −0.760951 −0.0306100
\(619\) −15.7406 −0.632667 −0.316333 0.948648i \(-0.602452\pi\)
−0.316333 + 0.948648i \(0.602452\pi\)
\(620\) −37.4761 −1.50508
\(621\) 4.30900 0.172914
\(622\) −40.9086 −1.64029
\(623\) −40.5322 −1.62389
\(624\) −27.4698 −1.09967
\(625\) −27.0882 −1.08353
\(626\) 61.6716 2.46489
\(627\) −6.40883 −0.255944
\(628\) 59.0414 2.35601
\(629\) 28.0999 1.12042
\(630\) −36.3006 −1.44625
\(631\) 38.2252 1.52172 0.760861 0.648915i \(-0.224777\pi\)
0.760861 + 0.648915i \(0.224777\pi\)
\(632\) 27.2324 1.08325
\(633\) 5.48454 0.217991
\(634\) 49.5701 1.96868
\(635\) 7.51721 0.298311
\(636\) 6.55901 0.260082
\(637\) −1.35318 −0.0536150
\(638\) 93.1087 3.68621
\(639\) −32.7268 −1.29465
\(640\) −25.9645 −1.02634
\(641\) −24.8991 −0.983455 −0.491727 0.870749i \(-0.663634\pi\)
−0.491727 + 0.870749i \(0.663634\pi\)
\(642\) 4.01573 0.158488
\(643\) 21.4669 0.846570 0.423285 0.905997i \(-0.360877\pi\)
0.423285 + 0.905997i \(0.360877\pi\)
\(644\) 11.6625 0.459567
\(645\) −6.56928 −0.258665
\(646\) −18.6541 −0.733936
\(647\) 39.2075 1.54141 0.770703 0.637195i \(-0.219905\pi\)
0.770703 + 0.637195i \(0.219905\pi\)
\(648\) −22.8717 −0.898485
\(649\) −13.3380 −0.523562
\(650\) −5.51040 −0.216136
\(651\) −7.43198 −0.291282
\(652\) 31.4968 1.23351
\(653\) 49.2612 1.92774 0.963870 0.266375i \(-0.0858259\pi\)
0.963870 + 0.266375i \(0.0858259\pi\)
\(654\) 40.6272 1.58865
\(655\) 28.8123 1.12579
\(656\) −2.00318 −0.0782110
\(657\) 28.4254 1.10898
\(658\) 13.2209 0.515403
\(659\) 27.2408 1.06115 0.530576 0.847638i \(-0.321976\pi\)
0.530576 + 0.847638i \(0.321976\pi\)
\(660\) −47.1986 −1.83720
\(661\) −32.9619 −1.28207 −0.641034 0.767512i \(-0.721494\pi\)
−0.641034 + 0.767512i \(0.721494\pi\)
\(662\) 68.0978 2.64670
\(663\) 19.3779 0.752575
\(664\) 54.4940 2.11478
\(665\) 8.64629 0.335289
\(666\) −32.8960 −1.27469
\(667\) 6.55232 0.253707
\(668\) −100.334 −3.88204
\(669\) −17.9844 −0.695319
\(670\) −17.0882 −0.660176
\(671\) 22.9570 0.886246
\(672\) 12.0098 0.463286
\(673\) 14.2272 0.548419 0.274210 0.961670i \(-0.411584\pi\)
0.274210 + 0.961670i \(0.411584\pi\)
\(674\) −16.3564 −0.630026
\(675\) 1.98190 0.0762834
\(676\) 40.8599 1.57153
\(677\) −29.9477 −1.15098 −0.575492 0.817807i \(-0.695189\pi\)
−0.575492 + 0.817807i \(0.695189\pi\)
\(678\) 13.9901 0.537288
\(679\) −33.0143 −1.26697
\(680\) −76.3440 −2.92766
\(681\) −3.71289 −0.142278
\(682\) 50.6279 1.93864
\(683\) −10.6699 −0.408271 −0.204136 0.978943i \(-0.565438\pi\)
−0.204136 + 0.978943i \(0.565438\pi\)
\(684\) 15.1203 0.578138
\(685\) −4.40091 −0.168150
\(686\) 48.1442 1.83815
\(687\) −4.79064 −0.182774
\(688\) −25.3539 −0.966607
\(689\) −8.50268 −0.323926
\(690\) −4.79720 −0.182626
\(691\) −19.0115 −0.723232 −0.361616 0.932327i \(-0.617775\pi\)
−0.361616 + 0.932327i \(0.617775\pi\)
\(692\) −87.7979 −3.33757
\(693\) 33.9544 1.28982
\(694\) −18.9833 −0.720597
\(695\) 33.3249 1.26408
\(696\) 33.6515 1.27556
\(697\) 1.41309 0.0535247
\(698\) 2.54982 0.0965122
\(699\) −7.70864 −0.291567
\(700\) 5.36411 0.202744
\(701\) −20.3595 −0.768969 −0.384485 0.923131i \(-0.625621\pi\)
−0.384485 + 0.923131i \(0.625621\pi\)
\(702\) −51.6243 −1.94843
\(703\) 7.83536 0.295516
\(704\) −0.880559 −0.0331873
\(705\) −3.76532 −0.141810
\(706\) 16.4763 0.620094
\(707\) −25.5386 −0.960480
\(708\) −8.67471 −0.326016
\(709\) −36.2782 −1.36246 −0.681229 0.732071i \(-0.738554\pi\)
−0.681229 + 0.732071i \(0.738554\pi\)
\(710\) 82.9130 3.11167
\(711\) 10.0402 0.376538
\(712\) 99.7929 3.73990
\(713\) 3.56282 0.133429
\(714\) −27.2442 −1.01959
\(715\) 61.1853 2.28820
\(716\) 5.51301 0.206031
\(717\) 4.97967 0.185969
\(718\) −44.8265 −1.67291
\(719\) −26.0520 −0.971575 −0.485788 0.874077i \(-0.661467\pi\)
−0.485788 + 0.874077i \(0.661467\pi\)
\(720\) 39.9009 1.48702
\(721\) −0.960261 −0.0357620
\(722\) 43.2451 1.60942
\(723\) 14.8715 0.553077
\(724\) −39.4598 −1.46651
\(725\) 3.01370 0.111926
\(726\) 41.1791 1.52830
\(727\) −9.00115 −0.333834 −0.166917 0.985971i \(-0.553381\pi\)
−0.166917 + 0.985971i \(0.553381\pi\)
\(728\) −77.6461 −2.87776
\(729\) 1.97584 0.0731794
\(730\) −72.0155 −2.66541
\(731\) 17.8853 0.661510
\(732\) 14.9307 0.551855
\(733\) 40.7487 1.50509 0.752545 0.658541i \(-0.228826\pi\)
0.752545 + 0.658541i \(0.228826\pi\)
\(734\) 71.3426 2.63330
\(735\) −0.541834 −0.0199858
\(736\) −5.75737 −0.212219
\(737\) 15.9837 0.588769
\(738\) −1.65428 −0.0608950
\(739\) −2.41253 −0.0887465 −0.0443732 0.999015i \(-0.514129\pi\)
−0.0443732 + 0.999015i \(0.514129\pi\)
\(740\) 57.7044 2.12126
\(741\) 5.40333 0.198496
\(742\) 11.9543 0.438856
\(743\) 32.1410 1.17914 0.589570 0.807718i \(-0.299297\pi\)
0.589570 + 0.807718i \(0.299297\pi\)
\(744\) 18.2980 0.670838
\(745\) 11.0819 0.406011
\(746\) 36.6528 1.34195
\(747\) 20.0913 0.735100
\(748\) 128.501 4.69846
\(749\) 5.06754 0.185164
\(750\) 21.7796 0.795277
\(751\) −8.05404 −0.293896 −0.146948 0.989144i \(-0.546945\pi\)
−0.146948 + 0.989144i \(0.546945\pi\)
\(752\) −14.5321 −0.529931
\(753\) 14.8639 0.541670
\(754\) −78.5005 −2.85882
\(755\) −30.2614 −1.10133
\(756\) 50.2538 1.82771
\(757\) −31.4687 −1.14375 −0.571875 0.820341i \(-0.693784\pi\)
−0.571875 + 0.820341i \(0.693784\pi\)
\(758\) 76.5017 2.77867
\(759\) 4.48714 0.162873
\(760\) −21.2877 −0.772187
\(761\) −37.4118 −1.35618 −0.678088 0.734981i \(-0.737191\pi\)
−0.678088 + 0.734981i \(0.737191\pi\)
\(762\) −6.60475 −0.239265
\(763\) 51.2684 1.85604
\(764\) −92.8779 −3.36020
\(765\) −28.1471 −1.01766
\(766\) 21.8116 0.788084
\(767\) 11.2453 0.406046
\(768\) 23.0673 0.832370
\(769\) 47.1971 1.70197 0.850985 0.525190i \(-0.176006\pi\)
0.850985 + 0.525190i \(0.176006\pi\)
\(770\) −86.0231 −3.10006
\(771\) −6.36790 −0.229334
\(772\) −82.2130 −2.95891
\(773\) 49.5916 1.78369 0.891843 0.452346i \(-0.149413\pi\)
0.891843 + 0.452346i \(0.149413\pi\)
\(774\) −20.9379 −0.752599
\(775\) 1.63870 0.0588639
\(776\) 81.2835 2.91791
\(777\) 11.4435 0.410534
\(778\) −37.9193 −1.35947
\(779\) 0.394026 0.0141175
\(780\) 39.7935 1.42483
\(781\) −77.5540 −2.77510
\(782\) 13.0607 0.467048
\(783\) 28.2339 1.00900
\(784\) −2.09118 −0.0746851
\(785\) −30.6468 −1.09383
\(786\) −25.3150 −0.902955
\(787\) 44.2238 1.57641 0.788205 0.615413i \(-0.211011\pi\)
0.788205 + 0.615413i \(0.211011\pi\)
\(788\) 50.3157 1.79242
\(789\) −16.9140 −0.602154
\(790\) −25.4369 −0.905004
\(791\) 17.6545 0.627721
\(792\) −83.5979 −2.97052
\(793\) −19.3552 −0.687324
\(794\) −19.1310 −0.678935
\(795\) −3.40460 −0.120749
\(796\) 90.7496 3.21653
\(797\) 47.6432 1.68761 0.843804 0.536651i \(-0.180311\pi\)
0.843804 + 0.536651i \(0.180311\pi\)
\(798\) −7.59678 −0.268923
\(799\) 10.2513 0.362665
\(800\) −2.64807 −0.0936234
\(801\) 36.7924 1.29999
\(802\) −99.0923 −3.49907
\(803\) 67.3608 2.37711
\(804\) 10.3954 0.366619
\(805\) −6.05369 −0.213365
\(806\) −42.6847 −1.50350
\(807\) 14.9816 0.527376
\(808\) 62.8778 2.21203
\(809\) 9.01054 0.316794 0.158397 0.987376i \(-0.449367\pi\)
0.158397 + 0.987376i \(0.449367\pi\)
\(810\) 21.3637 0.750644
\(811\) 3.10712 0.109106 0.0545529 0.998511i \(-0.482627\pi\)
0.0545529 + 0.998511i \(0.482627\pi\)
\(812\) 76.4165 2.68169
\(813\) −20.3523 −0.713786
\(814\) −77.9551 −2.73232
\(815\) −16.3491 −0.572684
\(816\) 29.9463 1.04833
\(817\) 4.98712 0.174477
\(818\) −51.0856 −1.78617
\(819\) −28.6271 −1.00031
\(820\) 2.90185 0.101337
\(821\) 38.8613 1.35627 0.678134 0.734938i \(-0.262789\pi\)
0.678134 + 0.734938i \(0.262789\pi\)
\(822\) 3.86672 0.134867
\(823\) 25.6819 0.895216 0.447608 0.894230i \(-0.352276\pi\)
0.447608 + 0.894230i \(0.352276\pi\)
\(824\) 2.36423 0.0823617
\(825\) 2.06383 0.0718535
\(826\) −15.8103 −0.550112
\(827\) 48.6896 1.69310 0.846552 0.532307i \(-0.178675\pi\)
0.846552 + 0.532307i \(0.178675\pi\)
\(828\) −10.5864 −0.367904
\(829\) 21.9659 0.762906 0.381453 0.924388i \(-0.375424\pi\)
0.381453 + 0.924388i \(0.375424\pi\)
\(830\) −50.9010 −1.76680
\(831\) −22.9725 −0.796907
\(832\) 0.742405 0.0257383
\(833\) 1.47517 0.0511117
\(834\) −29.2798 −1.01388
\(835\) 52.0806 1.80232
\(836\) 35.8312 1.23925
\(837\) 15.3522 0.530650
\(838\) −33.0100 −1.14031
\(839\) 36.1803 1.24908 0.624541 0.780992i \(-0.285286\pi\)
0.624541 + 0.780992i \(0.285286\pi\)
\(840\) −31.0907 −1.07273
\(841\) 13.9329 0.480443
\(842\) 74.6145 2.57139
\(843\) 11.5801 0.398840
\(844\) −30.6635 −1.05548
\(845\) −21.2092 −0.729620
\(846\) −12.0010 −0.412603
\(847\) 51.9648 1.78553
\(848\) −13.1399 −0.451226
\(849\) −19.6114 −0.673063
\(850\) 6.00717 0.206044
\(851\) −5.48592 −0.188055
\(852\) −50.4393 −1.72802
\(853\) −11.5104 −0.394108 −0.197054 0.980393i \(-0.563137\pi\)
−0.197054 + 0.980393i \(0.563137\pi\)
\(854\) 27.2124 0.931188
\(855\) −7.84852 −0.268414
\(856\) −12.4766 −0.426442
\(857\) −42.9683 −1.46777 −0.733885 0.679273i \(-0.762295\pi\)
−0.733885 + 0.679273i \(0.762295\pi\)
\(858\) −53.7585 −1.83528
\(859\) −22.5726 −0.770166 −0.385083 0.922882i \(-0.625827\pi\)
−0.385083 + 0.922882i \(0.625827\pi\)
\(860\) 36.7282 1.25242
\(861\) 0.575474 0.0196121
\(862\) 9.69429 0.330189
\(863\) 6.42580 0.218737 0.109368 0.994001i \(-0.465117\pi\)
0.109368 + 0.994001i \(0.465117\pi\)
\(864\) −24.8085 −0.844003
\(865\) 45.5735 1.54955
\(866\) −92.6838 −3.14952
\(867\) −7.43709 −0.252577
\(868\) 41.5515 1.41035
\(869\) 23.7928 0.807115
\(870\) −31.4328 −1.06567
\(871\) −13.4760 −0.456617
\(872\) −126.226 −4.27456
\(873\) 29.9682 1.01427
\(874\) 3.64183 0.123187
\(875\) 27.4841 0.929132
\(876\) 43.8099 1.48020
\(877\) 48.7007 1.64451 0.822253 0.569123i \(-0.192717\pi\)
0.822253 + 0.569123i \(0.192717\pi\)
\(878\) 83.4517 2.81636
\(879\) −1.95637 −0.0659867
\(880\) 94.5548 3.18744
\(881\) −6.67843 −0.225002 −0.112501 0.993652i \(-0.535886\pi\)
−0.112501 + 0.993652i \(0.535886\pi\)
\(882\) −1.72696 −0.0581497
\(883\) 43.7705 1.47299 0.736497 0.676441i \(-0.236479\pi\)
0.736497 + 0.676441i \(0.236479\pi\)
\(884\) −108.340 −3.64387
\(885\) 4.50281 0.151360
\(886\) 57.4081 1.92866
\(887\) 40.1543 1.34825 0.674125 0.738617i \(-0.264521\pi\)
0.674125 + 0.738617i \(0.264521\pi\)
\(888\) −28.1747 −0.945480
\(889\) −8.33467 −0.279536
\(890\) −93.2132 −3.12451
\(891\) −19.9829 −0.669451
\(892\) 100.549 3.36664
\(893\) 2.85847 0.0956550
\(894\) −9.73679 −0.325647
\(895\) −2.86165 −0.0956544
\(896\) 28.7881 0.961742
\(897\) −3.78313 −0.126315
\(898\) −11.0216 −0.367794
\(899\) 23.3448 0.778591
\(900\) −4.86918 −0.162306
\(901\) 9.26922 0.308803
\(902\) −3.92022 −0.130529
\(903\) 7.28367 0.242385
\(904\) −43.4665 −1.44567
\(905\) 20.4825 0.680862
\(906\) 26.5882 0.883334
\(907\) −16.5618 −0.549926 −0.274963 0.961455i \(-0.588666\pi\)
−0.274963 + 0.961455i \(0.588666\pi\)
\(908\) 20.7584 0.688893
\(909\) 23.1823 0.768907
\(910\) 72.5267 2.40424
\(911\) −31.5857 −1.04648 −0.523240 0.852186i \(-0.675277\pi\)
−0.523240 + 0.852186i \(0.675277\pi\)
\(912\) 8.35021 0.276503
\(913\) 47.6111 1.57570
\(914\) 21.5283 0.712092
\(915\) −7.75012 −0.256211
\(916\) 26.7840 0.884969
\(917\) −31.9455 −1.05493
\(918\) 56.2784 1.85746
\(919\) −4.06181 −0.133987 −0.0669933 0.997753i \(-0.521341\pi\)
−0.0669933 + 0.997753i \(0.521341\pi\)
\(920\) 14.9046 0.491390
\(921\) 6.27082 0.206630
\(922\) 62.0025 2.04194
\(923\) 65.3863 2.15222
\(924\) 52.3313 1.72157
\(925\) −2.52322 −0.0829629
\(926\) 21.7962 0.716269
\(927\) 0.871661 0.0286291
\(928\) −37.7241 −1.23835
\(929\) 20.2801 0.665368 0.332684 0.943038i \(-0.392046\pi\)
0.332684 + 0.943038i \(0.392046\pi\)
\(930\) −17.0916 −0.560455
\(931\) 0.411337 0.0134810
\(932\) 43.0982 1.41173
\(933\) −12.9178 −0.422910
\(934\) −28.3411 −0.927348
\(935\) −66.7013 −2.18137
\(936\) 70.4819 2.30377
\(937\) −8.95649 −0.292596 −0.146298 0.989241i \(-0.546736\pi\)
−0.146298 + 0.989241i \(0.546736\pi\)
\(938\) 18.9465 0.618625
\(939\) 19.4742 0.635516
\(940\) 21.0515 0.686626
\(941\) −3.82069 −0.124551 −0.0622754 0.998059i \(-0.519836\pi\)
−0.0622754 + 0.998059i \(0.519836\pi\)
\(942\) 26.9268 0.877321
\(943\) −0.275877 −0.00898379
\(944\) 17.3784 0.565618
\(945\) −26.0854 −0.848557
\(946\) −49.6175 −1.61321
\(947\) 60.7367 1.97368 0.986839 0.161703i \(-0.0516987\pi\)
0.986839 + 0.161703i \(0.0516987\pi\)
\(948\) 15.4743 0.502580
\(949\) −56.7923 −1.84356
\(950\) 1.67504 0.0543454
\(951\) 15.6529 0.507579
\(952\) 84.6461 2.74340
\(953\) 12.5508 0.406562 0.203281 0.979120i \(-0.434840\pi\)
0.203281 + 0.979120i \(0.434840\pi\)
\(954\) −10.8513 −0.351324
\(955\) 48.2104 1.56005
\(956\) −27.8409 −0.900438
\(957\) 29.4011 0.950404
\(958\) 11.1859 0.361401
\(959\) 4.87949 0.157567
\(960\) 0.297270 0.00959435
\(961\) −18.3063 −0.590525
\(962\) 65.7244 2.11904
\(963\) −4.59997 −0.148232
\(964\) −83.1452 −2.67793
\(965\) 42.6745 1.37374
\(966\) 5.31887 0.171132
\(967\) −4.98598 −0.160338 −0.0801692 0.996781i \(-0.525546\pi\)
−0.0801692 + 0.996781i \(0.525546\pi\)
\(968\) −127.941 −4.11217
\(969\) −5.89045 −0.189229
\(970\) −75.9242 −2.43778
\(971\) 39.4529 1.26610 0.633051 0.774110i \(-0.281802\pi\)
0.633051 + 0.774110i \(0.281802\pi\)
\(972\) −71.1884 −2.28337
\(973\) −36.9488 −1.18452
\(974\) 6.27015 0.200909
\(975\) −1.74003 −0.0557256
\(976\) −29.9112 −0.957436
\(977\) 9.47862 0.303248 0.151624 0.988438i \(-0.451550\pi\)
0.151624 + 0.988438i \(0.451550\pi\)
\(978\) 14.3646 0.459329
\(979\) 87.1885 2.78656
\(980\) 3.02934 0.0967687
\(981\) −46.5380 −1.48584
\(982\) −41.9412 −1.33840
\(983\) −33.2045 −1.05906 −0.529530 0.848291i \(-0.677632\pi\)
−0.529530 + 0.848291i \(0.677632\pi\)
\(984\) −1.41685 −0.0451677
\(985\) −26.1175 −0.832174
\(986\) 85.5775 2.72534
\(987\) 4.17478 0.132885
\(988\) −30.2095 −0.961092
\(989\) −3.49173 −0.111030
\(990\) 78.0860 2.48174
\(991\) −11.4925 −0.365071 −0.182536 0.983199i \(-0.558430\pi\)
−0.182536 + 0.983199i \(0.558430\pi\)
\(992\) −20.5125 −0.651272
\(993\) 21.5034 0.682390
\(994\) −91.9295 −2.91583
\(995\) −47.1057 −1.49335
\(996\) 30.9651 0.981167
\(997\) 6.98474 0.221209 0.110604 0.993865i \(-0.464721\pi\)
0.110604 + 0.993865i \(0.464721\pi\)
\(998\) −78.1261 −2.47304
\(999\) −23.6388 −0.747899
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 \(a_p\))