Properties

Label 6003.2.a.t.1.4
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.18238 q^{2} +2.76278 q^{4} +0.541552 q^{5} +0.936842 q^{7} -1.66467 q^{8} +O(q^{10})\) \(q-2.18238 q^{2} +2.76278 q^{4} +0.541552 q^{5} +0.936842 q^{7} -1.66467 q^{8} -1.18187 q^{10} -3.69864 q^{11} -4.89549 q^{13} -2.04454 q^{14} -1.89261 q^{16} +7.10752 q^{17} -1.09532 q^{19} +1.49619 q^{20} +8.07183 q^{22} +1.00000 q^{23} -4.70672 q^{25} +10.6838 q^{26} +2.58829 q^{28} +1.00000 q^{29} -5.91418 q^{31} +7.45974 q^{32} -15.5113 q^{34} +0.507349 q^{35} +10.3636 q^{37} +2.39040 q^{38} -0.901507 q^{40} -0.971796 q^{41} -1.94722 q^{43} -10.2185 q^{44} -2.18238 q^{46} +6.84150 q^{47} -6.12233 q^{49} +10.2718 q^{50} -13.5252 q^{52} +10.6007 q^{53} -2.00300 q^{55} -1.55953 q^{56} -2.18238 q^{58} -5.79346 q^{59} -3.13155 q^{61} +12.9070 q^{62} -12.4948 q^{64} -2.65117 q^{65} +12.7930 q^{67} +19.6365 q^{68} -1.10723 q^{70} +11.6056 q^{71} +9.09037 q^{73} -22.6173 q^{74} -3.02612 q^{76} -3.46504 q^{77} +12.3322 q^{79} -1.02495 q^{80} +2.12083 q^{82} +3.23404 q^{83} +3.84909 q^{85} +4.24957 q^{86} +6.15702 q^{88} -18.7802 q^{89} -4.58630 q^{91} +2.76278 q^{92} -14.9307 q^{94} -0.593172 q^{95} -13.0946 q^{97} +13.3612 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.18238 −1.54318 −0.771588 0.636123i \(-0.780537\pi\)
−0.771588 + 0.636123i \(0.780537\pi\)
\(3\) 0 0
\(4\) 2.76278 1.38139
\(5\) 0.541552 0.242190 0.121095 0.992641i \(-0.461360\pi\)
0.121095 + 0.992641i \(0.461360\pi\)
\(6\) 0 0
\(7\) 0.936842 0.354093 0.177046 0.984203i \(-0.443346\pi\)
0.177046 + 0.984203i \(0.443346\pi\)
\(8\) −1.66467 −0.588550
\(9\) 0 0
\(10\) −1.18187 −0.373741
\(11\) −3.69864 −1.11518 −0.557590 0.830116i \(-0.688274\pi\)
−0.557590 + 0.830116i \(0.688274\pi\)
\(12\) 0 0
\(13\) −4.89549 −1.35777 −0.678883 0.734247i \(-0.737536\pi\)
−0.678883 + 0.734247i \(0.737536\pi\)
\(14\) −2.04454 −0.546427
\(15\) 0 0
\(16\) −1.89261 −0.473153
\(17\) 7.10752 1.72383 0.861914 0.507055i \(-0.169266\pi\)
0.861914 + 0.507055i \(0.169266\pi\)
\(18\) 0 0
\(19\) −1.09532 −0.251283 −0.125642 0.992076i \(-0.540099\pi\)
−0.125642 + 0.992076i \(0.540099\pi\)
\(20\) 1.49619 0.334558
\(21\) 0 0
\(22\) 8.07183 1.72092
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.70672 −0.941344
\(26\) 10.6838 2.09527
\(27\) 0 0
\(28\) 2.58829 0.489140
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −5.91418 −1.06222 −0.531109 0.847303i \(-0.678225\pi\)
−0.531109 + 0.847303i \(0.678225\pi\)
\(32\) 7.45974 1.31871
\(33\) 0 0
\(34\) −15.5113 −2.66017
\(35\) 0.507349 0.0857576
\(36\) 0 0
\(37\) 10.3636 1.70377 0.851883 0.523732i \(-0.175461\pi\)
0.851883 + 0.523732i \(0.175461\pi\)
\(38\) 2.39040 0.387774
\(39\) 0 0
\(40\) −0.901507 −0.142541
\(41\) −0.971796 −0.151769 −0.0758845 0.997117i \(-0.524178\pi\)
−0.0758845 + 0.997117i \(0.524178\pi\)
\(42\) 0 0
\(43\) −1.94722 −0.296948 −0.148474 0.988916i \(-0.547436\pi\)
−0.148474 + 0.988916i \(0.547436\pi\)
\(44\) −10.2185 −1.54050
\(45\) 0 0
\(46\) −2.18238 −0.321774
\(47\) 6.84150 0.997935 0.498968 0.866621i \(-0.333713\pi\)
0.498968 + 0.866621i \(0.333713\pi\)
\(48\) 0 0
\(49\) −6.12233 −0.874618
\(50\) 10.2718 1.45266
\(51\) 0 0
\(52\) −13.5252 −1.87560
\(53\) 10.6007 1.45612 0.728061 0.685513i \(-0.240422\pi\)
0.728061 + 0.685513i \(0.240422\pi\)
\(54\) 0 0
\(55\) −2.00300 −0.270085
\(56\) −1.55953 −0.208401
\(57\) 0 0
\(58\) −2.18238 −0.286560
\(59\) −5.79346 −0.754244 −0.377122 0.926164i \(-0.623086\pi\)
−0.377122 + 0.926164i \(0.623086\pi\)
\(60\) 0 0
\(61\) −3.13155 −0.400954 −0.200477 0.979698i \(-0.564249\pi\)
−0.200477 + 0.979698i \(0.564249\pi\)
\(62\) 12.9070 1.63919
\(63\) 0 0
\(64\) −12.4948 −1.56184
\(65\) −2.65117 −0.328837
\(66\) 0 0
\(67\) 12.7930 1.56292 0.781459 0.623957i \(-0.214476\pi\)
0.781459 + 0.623957i \(0.214476\pi\)
\(68\) 19.6365 2.38128
\(69\) 0 0
\(70\) −1.10723 −0.132339
\(71\) 11.6056 1.37733 0.688666 0.725079i \(-0.258197\pi\)
0.688666 + 0.725079i \(0.258197\pi\)
\(72\) 0 0
\(73\) 9.09037 1.06395 0.531974 0.846761i \(-0.321451\pi\)
0.531974 + 0.846761i \(0.321451\pi\)
\(74\) −22.6173 −2.62921
\(75\) 0 0
\(76\) −3.02612 −0.347120
\(77\) −3.46504 −0.394877
\(78\) 0 0
\(79\) 12.3322 1.38748 0.693741 0.720224i \(-0.255961\pi\)
0.693741 + 0.720224i \(0.255961\pi\)
\(80\) −1.02495 −0.114593
\(81\) 0 0
\(82\) 2.12083 0.234206
\(83\) 3.23404 0.354982 0.177491 0.984122i \(-0.443202\pi\)
0.177491 + 0.984122i \(0.443202\pi\)
\(84\) 0 0
\(85\) 3.84909 0.417493
\(86\) 4.24957 0.458243
\(87\) 0 0
\(88\) 6.15702 0.656340
\(89\) −18.7802 −1.99070 −0.995350 0.0963207i \(-0.969293\pi\)
−0.995350 + 0.0963207i \(0.969293\pi\)
\(90\) 0 0
\(91\) −4.58630 −0.480775
\(92\) 2.76278 0.288040
\(93\) 0 0
\(94\) −14.9307 −1.53999
\(95\) −0.593172 −0.0608582
\(96\) 0 0
\(97\) −13.0946 −1.32956 −0.664778 0.747041i \(-0.731474\pi\)
−0.664778 + 0.747041i \(0.731474\pi\)
\(98\) 13.3612 1.34969
\(99\) 0 0
\(100\) −13.0036 −1.30036
\(101\) −10.0431 −0.999323 −0.499661 0.866221i \(-0.666542\pi\)
−0.499661 + 0.866221i \(0.666542\pi\)
\(102\) 0 0
\(103\) −20.0279 −1.97341 −0.986705 0.162522i \(-0.948037\pi\)
−0.986705 + 0.162522i \(0.948037\pi\)
\(104\) 8.14939 0.799114
\(105\) 0 0
\(106\) −23.1348 −2.24705
\(107\) −5.51804 −0.533449 −0.266724 0.963773i \(-0.585941\pi\)
−0.266724 + 0.963773i \(0.585941\pi\)
\(108\) 0 0
\(109\) −2.72927 −0.261416 −0.130708 0.991421i \(-0.541725\pi\)
−0.130708 + 0.991421i \(0.541725\pi\)
\(110\) 4.37132 0.416789
\(111\) 0 0
\(112\) −1.77308 −0.167540
\(113\) 10.7166 1.00814 0.504068 0.863664i \(-0.331836\pi\)
0.504068 + 0.863664i \(0.331836\pi\)
\(114\) 0 0
\(115\) 0.541552 0.0505000
\(116\) 2.76278 0.256518
\(117\) 0 0
\(118\) 12.6435 1.16393
\(119\) 6.65862 0.610395
\(120\) 0 0
\(121\) 2.67991 0.243628
\(122\) 6.83424 0.618743
\(123\) 0 0
\(124\) −16.3396 −1.46734
\(125\) −5.25670 −0.470173
\(126\) 0 0
\(127\) −13.5491 −1.20229 −0.601144 0.799141i \(-0.705288\pi\)
−0.601144 + 0.799141i \(0.705288\pi\)
\(128\) 12.3488 1.09149
\(129\) 0 0
\(130\) 5.78585 0.507452
\(131\) −5.07093 −0.443049 −0.221525 0.975155i \(-0.571103\pi\)
−0.221525 + 0.975155i \(0.571103\pi\)
\(132\) 0 0
\(133\) −1.02614 −0.0889776
\(134\) −27.9192 −2.41186
\(135\) 0 0
\(136\) −11.8317 −1.01456
\(137\) −14.4059 −1.23078 −0.615388 0.788224i \(-0.711001\pi\)
−0.615388 + 0.788224i \(0.711001\pi\)
\(138\) 0 0
\(139\) −11.2391 −0.953289 −0.476645 0.879096i \(-0.658147\pi\)
−0.476645 + 0.879096i \(0.658147\pi\)
\(140\) 1.40169 0.118465
\(141\) 0 0
\(142\) −25.3278 −2.12546
\(143\) 18.1066 1.51415
\(144\) 0 0
\(145\) 0.541552 0.0449735
\(146\) −19.8386 −1.64186
\(147\) 0 0
\(148\) 28.6323 2.35356
\(149\) −8.89024 −0.728317 −0.364159 0.931337i \(-0.618643\pi\)
−0.364159 + 0.931337i \(0.618643\pi\)
\(150\) 0 0
\(151\) 8.93585 0.727189 0.363594 0.931557i \(-0.381549\pi\)
0.363594 + 0.931557i \(0.381549\pi\)
\(152\) 1.82335 0.147893
\(153\) 0 0
\(154\) 7.56202 0.609365
\(155\) −3.20284 −0.257258
\(156\) 0 0
\(157\) −9.64721 −0.769931 −0.384966 0.922931i \(-0.625787\pi\)
−0.384966 + 0.922931i \(0.625787\pi\)
\(158\) −26.9136 −2.14113
\(159\) 0 0
\(160\) 4.03984 0.319377
\(161\) 0.936842 0.0738335
\(162\) 0 0
\(163\) 7.00313 0.548528 0.274264 0.961654i \(-0.411566\pi\)
0.274264 + 0.961654i \(0.411566\pi\)
\(164\) −2.68486 −0.209652
\(165\) 0 0
\(166\) −7.05790 −0.547799
\(167\) 3.28587 0.254268 0.127134 0.991886i \(-0.459422\pi\)
0.127134 + 0.991886i \(0.459422\pi\)
\(168\) 0 0
\(169\) 10.9659 0.843527
\(170\) −8.40018 −0.644265
\(171\) 0 0
\(172\) −5.37974 −0.410201
\(173\) 13.3537 1.01526 0.507630 0.861575i \(-0.330522\pi\)
0.507630 + 0.861575i \(0.330522\pi\)
\(174\) 0 0
\(175\) −4.40945 −0.333323
\(176\) 7.00008 0.527651
\(177\) 0 0
\(178\) 40.9856 3.07200
\(179\) −21.6038 −1.61474 −0.807371 0.590044i \(-0.799110\pi\)
−0.807371 + 0.590044i \(0.799110\pi\)
\(180\) 0 0
\(181\) 14.9136 1.10852 0.554258 0.832345i \(-0.313002\pi\)
0.554258 + 0.832345i \(0.313002\pi\)
\(182\) 10.0090 0.741920
\(183\) 0 0
\(184\) −1.66467 −0.122721
\(185\) 5.61243 0.412634
\(186\) 0 0
\(187\) −26.2881 −1.92238
\(188\) 18.9016 1.37854
\(189\) 0 0
\(190\) 1.29453 0.0939149
\(191\) 22.8259 1.65162 0.825811 0.563947i \(-0.190718\pi\)
0.825811 + 0.563947i \(0.190718\pi\)
\(192\) 0 0
\(193\) −22.4698 −1.61741 −0.808707 0.588212i \(-0.799832\pi\)
−0.808707 + 0.588212i \(0.799832\pi\)
\(194\) 28.5774 2.05174
\(195\) 0 0
\(196\) −16.9146 −1.20819
\(197\) −3.21964 −0.229390 −0.114695 0.993401i \(-0.536589\pi\)
−0.114695 + 0.993401i \(0.536589\pi\)
\(198\) 0 0
\(199\) 4.22747 0.299677 0.149839 0.988710i \(-0.452125\pi\)
0.149839 + 0.988710i \(0.452125\pi\)
\(200\) 7.83515 0.554029
\(201\) 0 0
\(202\) 21.9178 1.54213
\(203\) 0.936842 0.0657534
\(204\) 0 0
\(205\) −0.526278 −0.0367569
\(206\) 43.7085 3.04532
\(207\) 0 0
\(208\) 9.26527 0.642431
\(209\) 4.05119 0.280226
\(210\) 0 0
\(211\) 15.8411 1.09054 0.545272 0.838259i \(-0.316426\pi\)
0.545272 + 0.838259i \(0.316426\pi\)
\(212\) 29.2875 2.01147
\(213\) 0 0
\(214\) 12.0424 0.823205
\(215\) −1.05452 −0.0719178
\(216\) 0 0
\(217\) −5.54065 −0.376124
\(218\) 5.95629 0.403411
\(219\) 0 0
\(220\) −5.53386 −0.373093
\(221\) −34.7948 −2.34055
\(222\) 0 0
\(223\) 5.13806 0.344070 0.172035 0.985091i \(-0.444966\pi\)
0.172035 + 0.985091i \(0.444966\pi\)
\(224\) 6.98859 0.466945
\(225\) 0 0
\(226\) −23.3878 −1.55573
\(227\) −23.1797 −1.53849 −0.769246 0.638953i \(-0.779368\pi\)
−0.769246 + 0.638953i \(0.779368\pi\)
\(228\) 0 0
\(229\) −27.6792 −1.82909 −0.914545 0.404484i \(-0.867451\pi\)
−0.914545 + 0.404484i \(0.867451\pi\)
\(230\) −1.18187 −0.0779304
\(231\) 0 0
\(232\) −1.66467 −0.109291
\(233\) −5.79047 −0.379347 −0.189673 0.981847i \(-0.560743\pi\)
−0.189673 + 0.981847i \(0.560743\pi\)
\(234\) 0 0
\(235\) 3.70503 0.241690
\(236\) −16.0060 −1.04190
\(237\) 0 0
\(238\) −14.5316 −0.941946
\(239\) 23.4674 1.51798 0.758991 0.651101i \(-0.225693\pi\)
0.758991 + 0.651101i \(0.225693\pi\)
\(240\) 0 0
\(241\) −3.03269 −0.195353 −0.0976765 0.995218i \(-0.531141\pi\)
−0.0976765 + 0.995218i \(0.531141\pi\)
\(242\) −5.84858 −0.375961
\(243\) 0 0
\(244\) −8.65179 −0.553874
\(245\) −3.31556 −0.211823
\(246\) 0 0
\(247\) 5.36213 0.341184
\(248\) 9.84518 0.625169
\(249\) 0 0
\(250\) 11.4721 0.725560
\(251\) 29.3351 1.85161 0.925807 0.377996i \(-0.123387\pi\)
0.925807 + 0.377996i \(0.123387\pi\)
\(252\) 0 0
\(253\) −3.69864 −0.232531
\(254\) 29.5693 1.85534
\(255\) 0 0
\(256\) −1.96029 −0.122518
\(257\) −18.4474 −1.15071 −0.575357 0.817902i \(-0.695137\pi\)
−0.575357 + 0.817902i \(0.695137\pi\)
\(258\) 0 0
\(259\) 9.70905 0.603291
\(260\) −7.32458 −0.454251
\(261\) 0 0
\(262\) 11.0667 0.683702
\(263\) −2.40266 −0.148155 −0.0740773 0.997253i \(-0.523601\pi\)
−0.0740773 + 0.997253i \(0.523601\pi\)
\(264\) 0 0
\(265\) 5.74085 0.352657
\(266\) 2.23943 0.137308
\(267\) 0 0
\(268\) 35.3443 2.15900
\(269\) 8.01329 0.488579 0.244290 0.969702i \(-0.421445\pi\)
0.244290 + 0.969702i \(0.421445\pi\)
\(270\) 0 0
\(271\) −22.2186 −1.34969 −0.674843 0.737961i \(-0.735789\pi\)
−0.674843 + 0.737961i \(0.735789\pi\)
\(272\) −13.4518 −0.815634
\(273\) 0 0
\(274\) 31.4391 1.89930
\(275\) 17.4084 1.04977
\(276\) 0 0
\(277\) 18.8850 1.13469 0.567344 0.823481i \(-0.307971\pi\)
0.567344 + 0.823481i \(0.307971\pi\)
\(278\) 24.5280 1.47109
\(279\) 0 0
\(280\) −0.844569 −0.0504727
\(281\) −22.4266 −1.33786 −0.668928 0.743327i \(-0.733247\pi\)
−0.668928 + 0.743327i \(0.733247\pi\)
\(282\) 0 0
\(283\) −16.9952 −1.01026 −0.505129 0.863044i \(-0.668555\pi\)
−0.505129 + 0.863044i \(0.668555\pi\)
\(284\) 32.0637 1.90263
\(285\) 0 0
\(286\) −39.5156 −2.33660
\(287\) −0.910419 −0.0537403
\(288\) 0 0
\(289\) 33.5169 1.97158
\(290\) −1.18187 −0.0694019
\(291\) 0 0
\(292\) 25.1147 1.46973
\(293\) −22.1283 −1.29275 −0.646374 0.763021i \(-0.723715\pi\)
−0.646374 + 0.763021i \(0.723715\pi\)
\(294\) 0 0
\(295\) −3.13746 −0.182670
\(296\) −17.2520 −1.00275
\(297\) 0 0
\(298\) 19.4019 1.12392
\(299\) −4.89549 −0.283114
\(300\) 0 0
\(301\) −1.82424 −0.105147
\(302\) −19.5014 −1.12218
\(303\) 0 0
\(304\) 2.07301 0.118895
\(305\) −1.69590 −0.0971069
\(306\) 0 0
\(307\) −9.55579 −0.545378 −0.272689 0.962102i \(-0.587913\pi\)
−0.272689 + 0.962102i \(0.587913\pi\)
\(308\) −9.57313 −0.545480
\(309\) 0 0
\(310\) 6.98981 0.396995
\(311\) 2.74915 0.155890 0.0779451 0.996958i \(-0.475164\pi\)
0.0779451 + 0.996958i \(0.475164\pi\)
\(312\) 0 0
\(313\) 13.1079 0.740905 0.370452 0.928851i \(-0.379203\pi\)
0.370452 + 0.928851i \(0.379203\pi\)
\(314\) 21.0539 1.18814
\(315\) 0 0
\(316\) 34.0712 1.91665
\(317\) 18.2291 1.02385 0.511923 0.859031i \(-0.328933\pi\)
0.511923 + 0.859031i \(0.328933\pi\)
\(318\) 0 0
\(319\) −3.69864 −0.207084
\(320\) −6.76656 −0.378262
\(321\) 0 0
\(322\) −2.04454 −0.113938
\(323\) −7.78500 −0.433169
\(324\) 0 0
\(325\) 23.0417 1.27812
\(326\) −15.2835 −0.846474
\(327\) 0 0
\(328\) 1.61772 0.0893237
\(329\) 6.40940 0.353362
\(330\) 0 0
\(331\) 15.7316 0.864686 0.432343 0.901709i \(-0.357687\pi\)
0.432343 + 0.901709i \(0.357687\pi\)
\(332\) 8.93493 0.490368
\(333\) 0 0
\(334\) −7.17102 −0.392381
\(335\) 6.92810 0.378522
\(336\) 0 0
\(337\) −26.2825 −1.43170 −0.715849 0.698255i \(-0.753960\pi\)
−0.715849 + 0.698255i \(0.753960\pi\)
\(338\) −23.9317 −1.30171
\(339\) 0 0
\(340\) 10.6342 0.576720
\(341\) 21.8744 1.18457
\(342\) 0 0
\(343\) −12.2935 −0.663789
\(344\) 3.24148 0.174769
\(345\) 0 0
\(346\) −29.1428 −1.56673
\(347\) 8.60890 0.462150 0.231075 0.972936i \(-0.425776\pi\)
0.231075 + 0.972936i \(0.425776\pi\)
\(348\) 0 0
\(349\) 8.19419 0.438625 0.219312 0.975655i \(-0.429619\pi\)
0.219312 + 0.975655i \(0.429619\pi\)
\(350\) 9.62310 0.514376
\(351\) 0 0
\(352\) −27.5909 −1.47060
\(353\) 11.6822 0.621780 0.310890 0.950446i \(-0.399373\pi\)
0.310890 + 0.950446i \(0.399373\pi\)
\(354\) 0 0
\(355\) 6.28504 0.333575
\(356\) −51.8856 −2.74993
\(357\) 0 0
\(358\) 47.1476 2.49183
\(359\) 2.76963 0.146175 0.0730877 0.997326i \(-0.476715\pi\)
0.0730877 + 0.997326i \(0.476715\pi\)
\(360\) 0 0
\(361\) −17.8003 −0.936857
\(362\) −32.5471 −1.71064
\(363\) 0 0
\(364\) −12.6709 −0.664137
\(365\) 4.92291 0.257677
\(366\) 0 0
\(367\) −19.3751 −1.01137 −0.505687 0.862717i \(-0.668761\pi\)
−0.505687 + 0.862717i \(0.668761\pi\)
\(368\) −1.89261 −0.0986592
\(369\) 0 0
\(370\) −12.2485 −0.636767
\(371\) 9.93120 0.515602
\(372\) 0 0
\(373\) −7.92717 −0.410453 −0.205227 0.978714i \(-0.565793\pi\)
−0.205227 + 0.978714i \(0.565793\pi\)
\(374\) 57.3707 2.96657
\(375\) 0 0
\(376\) −11.3889 −0.587335
\(377\) −4.89549 −0.252131
\(378\) 0 0
\(379\) −22.6325 −1.16255 −0.581275 0.813707i \(-0.697446\pi\)
−0.581275 + 0.813707i \(0.697446\pi\)
\(380\) −1.63880 −0.0840689
\(381\) 0 0
\(382\) −49.8147 −2.54874
\(383\) 1.29715 0.0662813 0.0331406 0.999451i \(-0.489449\pi\)
0.0331406 + 0.999451i \(0.489449\pi\)
\(384\) 0 0
\(385\) −1.87650 −0.0956352
\(386\) 49.0377 2.49595
\(387\) 0 0
\(388\) −36.1775 −1.83663
\(389\) −12.9895 −0.658595 −0.329297 0.944226i \(-0.606812\pi\)
−0.329297 + 0.944226i \(0.606812\pi\)
\(390\) 0 0
\(391\) 7.10752 0.359443
\(392\) 10.1917 0.514757
\(393\) 0 0
\(394\) 7.02647 0.353988
\(395\) 6.67854 0.336034
\(396\) 0 0
\(397\) −24.3012 −1.21964 −0.609822 0.792538i \(-0.708759\pi\)
−0.609822 + 0.792538i \(0.708759\pi\)
\(398\) −9.22594 −0.462455
\(399\) 0 0
\(400\) 8.90800 0.445400
\(401\) 0.473592 0.0236500 0.0118250 0.999930i \(-0.496236\pi\)
0.0118250 + 0.999930i \(0.496236\pi\)
\(402\) 0 0
\(403\) 28.9528 1.44224
\(404\) −27.7468 −1.38045
\(405\) 0 0
\(406\) −2.04454 −0.101469
\(407\) −38.3312 −1.90001
\(408\) 0 0
\(409\) −15.4034 −0.761649 −0.380824 0.924647i \(-0.624360\pi\)
−0.380824 + 0.924647i \(0.624360\pi\)
\(410\) 1.14854 0.0567223
\(411\) 0 0
\(412\) −55.3327 −2.72605
\(413\) −5.42755 −0.267072
\(414\) 0 0
\(415\) 1.75140 0.0859729
\(416\) −36.5191 −1.79050
\(417\) 0 0
\(418\) −8.84122 −0.432438
\(419\) −7.23895 −0.353646 −0.176823 0.984243i \(-0.556582\pi\)
−0.176823 + 0.984243i \(0.556582\pi\)
\(420\) 0 0
\(421\) 18.7625 0.914430 0.457215 0.889356i \(-0.348847\pi\)
0.457215 + 0.889356i \(0.348847\pi\)
\(422\) −34.5712 −1.68290
\(423\) 0 0
\(424\) −17.6467 −0.857001
\(425\) −33.4531 −1.62271
\(426\) 0 0
\(427\) −2.93377 −0.141975
\(428\) −15.2451 −0.736900
\(429\) 0 0
\(430\) 2.30137 0.110982
\(431\) 35.3900 1.70468 0.852338 0.522991i \(-0.175184\pi\)
0.852338 + 0.522991i \(0.175184\pi\)
\(432\) 0 0
\(433\) −34.1692 −1.64207 −0.821034 0.570879i \(-0.806603\pi\)
−0.821034 + 0.570879i \(0.806603\pi\)
\(434\) 12.0918 0.580425
\(435\) 0 0
\(436\) −7.54036 −0.361118
\(437\) −1.09532 −0.0523962
\(438\) 0 0
\(439\) −23.9651 −1.14379 −0.571897 0.820326i \(-0.693792\pi\)
−0.571897 + 0.820326i \(0.693792\pi\)
\(440\) 3.33435 0.158959
\(441\) 0 0
\(442\) 75.9355 3.61188
\(443\) 25.7391 1.22290 0.611450 0.791283i \(-0.290586\pi\)
0.611450 + 0.791283i \(0.290586\pi\)
\(444\) 0 0
\(445\) −10.1705 −0.482127
\(446\) −11.2132 −0.530960
\(447\) 0 0
\(448\) −11.7056 −0.553038
\(449\) −18.3083 −0.864023 −0.432011 0.901868i \(-0.642196\pi\)
−0.432011 + 0.901868i \(0.642196\pi\)
\(450\) 0 0
\(451\) 3.59432 0.169250
\(452\) 29.6077 1.39263
\(453\) 0 0
\(454\) 50.5869 2.37416
\(455\) −2.48372 −0.116439
\(456\) 0 0
\(457\) 14.6410 0.684875 0.342437 0.939541i \(-0.388748\pi\)
0.342437 + 0.939541i \(0.388748\pi\)
\(458\) 60.4064 2.82261
\(459\) 0 0
\(460\) 1.49619 0.0697602
\(461\) −27.0760 −1.26106 −0.630528 0.776167i \(-0.717162\pi\)
−0.630528 + 0.776167i \(0.717162\pi\)
\(462\) 0 0
\(463\) 33.9300 1.57686 0.788431 0.615123i \(-0.210894\pi\)
0.788431 + 0.615123i \(0.210894\pi\)
\(464\) −1.89261 −0.0878623
\(465\) 0 0
\(466\) 12.6370 0.585398
\(467\) −27.3244 −1.26442 −0.632210 0.774797i \(-0.717852\pi\)
−0.632210 + 0.774797i \(0.717852\pi\)
\(468\) 0 0
\(469\) 11.9850 0.553418
\(470\) −8.08578 −0.372969
\(471\) 0 0
\(472\) 9.64421 0.443911
\(473\) 7.20206 0.331151
\(474\) 0 0
\(475\) 5.15536 0.236544
\(476\) 18.3963 0.843193
\(477\) 0 0
\(478\) −51.2148 −2.34251
\(479\) −11.4058 −0.521146 −0.260573 0.965454i \(-0.583911\pi\)
−0.260573 + 0.965454i \(0.583911\pi\)
\(480\) 0 0
\(481\) −50.7350 −2.31331
\(482\) 6.61849 0.301464
\(483\) 0 0
\(484\) 7.40400 0.336545
\(485\) −7.09141 −0.322005
\(486\) 0 0
\(487\) 15.5110 0.702871 0.351435 0.936212i \(-0.385694\pi\)
0.351435 + 0.936212i \(0.385694\pi\)
\(488\) 5.21301 0.235982
\(489\) 0 0
\(490\) 7.23581 0.326881
\(491\) −1.80111 −0.0812829 −0.0406415 0.999174i \(-0.512940\pi\)
−0.0406415 + 0.999174i \(0.512940\pi\)
\(492\) 0 0
\(493\) 7.10752 0.320107
\(494\) −11.7022 −0.526507
\(495\) 0 0
\(496\) 11.1933 0.502592
\(497\) 10.8726 0.487703
\(498\) 0 0
\(499\) −41.5009 −1.85783 −0.928917 0.370289i \(-0.879259\pi\)
−0.928917 + 0.370289i \(0.879259\pi\)
\(500\) −14.5231 −0.649492
\(501\) 0 0
\(502\) −64.0203 −2.85737
\(503\) −29.8332 −1.33020 −0.665099 0.746755i \(-0.731611\pi\)
−0.665099 + 0.746755i \(0.731611\pi\)
\(504\) 0 0
\(505\) −5.43885 −0.242025
\(506\) 8.07183 0.358836
\(507\) 0 0
\(508\) −37.4332 −1.66083
\(509\) −25.3981 −1.12575 −0.562875 0.826542i \(-0.690305\pi\)
−0.562875 + 0.826542i \(0.690305\pi\)
\(510\) 0 0
\(511\) 8.51623 0.376736
\(512\) −20.4195 −0.902425
\(513\) 0 0
\(514\) 40.2591 1.77575
\(515\) −10.8462 −0.477939
\(516\) 0 0
\(517\) −25.3042 −1.11288
\(518\) −21.1888 −0.930984
\(519\) 0 0
\(520\) 4.41332 0.193537
\(521\) −25.0390 −1.09698 −0.548489 0.836158i \(-0.684797\pi\)
−0.548489 + 0.836158i \(0.684797\pi\)
\(522\) 0 0
\(523\) −20.3520 −0.889930 −0.444965 0.895548i \(-0.646784\pi\)
−0.444965 + 0.895548i \(0.646784\pi\)
\(524\) −14.0099 −0.612023
\(525\) 0 0
\(526\) 5.24352 0.228628
\(527\) −42.0352 −1.83108
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −12.5287 −0.544212
\(531\) 0 0
\(532\) −2.83500 −0.122913
\(533\) 4.75742 0.206067
\(534\) 0 0
\(535\) −2.98830 −0.129196
\(536\) −21.2962 −0.919856
\(537\) 0 0
\(538\) −17.4880 −0.753963
\(539\) 22.6443 0.975358
\(540\) 0 0
\(541\) 14.7556 0.634391 0.317196 0.948360i \(-0.397259\pi\)
0.317196 + 0.948360i \(0.397259\pi\)
\(542\) 48.4895 2.08280
\(543\) 0 0
\(544\) 53.0203 2.27323
\(545\) −1.47804 −0.0633123
\(546\) 0 0
\(547\) 31.0173 1.32620 0.663102 0.748529i \(-0.269240\pi\)
0.663102 + 0.748529i \(0.269240\pi\)
\(548\) −39.8002 −1.70018
\(549\) 0 0
\(550\) −37.9918 −1.61998
\(551\) −1.09532 −0.0466622
\(552\) 0 0
\(553\) 11.5533 0.491297
\(554\) −41.2142 −1.75102
\(555\) 0 0
\(556\) −31.0512 −1.31686
\(557\) −20.4619 −0.866997 −0.433498 0.901154i \(-0.642721\pi\)
−0.433498 + 0.901154i \(0.642721\pi\)
\(558\) 0 0
\(559\) 9.53261 0.403186
\(560\) −0.960214 −0.0405764
\(561\) 0 0
\(562\) 48.9433 2.06455
\(563\) 8.08437 0.340716 0.170358 0.985382i \(-0.445508\pi\)
0.170358 + 0.985382i \(0.445508\pi\)
\(564\) 0 0
\(565\) 5.80362 0.244160
\(566\) 37.0899 1.55901
\(567\) 0 0
\(568\) −19.3195 −0.810629
\(569\) 21.3865 0.896569 0.448284 0.893891i \(-0.352035\pi\)
0.448284 + 0.893891i \(0.352035\pi\)
\(570\) 0 0
\(571\) 17.9758 0.752262 0.376131 0.926567i \(-0.377254\pi\)
0.376131 + 0.926567i \(0.377254\pi\)
\(572\) 50.0247 2.09164
\(573\) 0 0
\(574\) 1.98688 0.0829307
\(575\) −4.70672 −0.196284
\(576\) 0 0
\(577\) 44.1313 1.83721 0.918604 0.395178i \(-0.129317\pi\)
0.918604 + 0.395178i \(0.129317\pi\)
\(578\) −73.1465 −3.04249
\(579\) 0 0
\(580\) 1.49619 0.0621259
\(581\) 3.02978 0.125696
\(582\) 0 0
\(583\) −39.2082 −1.62384
\(584\) −15.1325 −0.626187
\(585\) 0 0
\(586\) 48.2923 1.99494
\(587\) −19.9086 −0.821717 −0.410858 0.911699i \(-0.634771\pi\)
−0.410858 + 0.911699i \(0.634771\pi\)
\(588\) 0 0
\(589\) 6.47792 0.266918
\(590\) 6.84713 0.281892
\(591\) 0 0
\(592\) −19.6143 −0.806142
\(593\) −4.05650 −0.166581 −0.0832903 0.996525i \(-0.526543\pi\)
−0.0832903 + 0.996525i \(0.526543\pi\)
\(594\) 0 0
\(595\) 3.60599 0.147831
\(596\) −24.5618 −1.00609
\(597\) 0 0
\(598\) 10.6838 0.436894
\(599\) −41.4655 −1.69423 −0.847117 0.531407i \(-0.821664\pi\)
−0.847117 + 0.531407i \(0.821664\pi\)
\(600\) 0 0
\(601\) 35.8970 1.46427 0.732134 0.681160i \(-0.238524\pi\)
0.732134 + 0.681160i \(0.238524\pi\)
\(602\) 3.98118 0.162261
\(603\) 0 0
\(604\) 24.6878 1.00453
\(605\) 1.45131 0.0590042
\(606\) 0 0
\(607\) −20.4894 −0.831640 −0.415820 0.909447i \(-0.636505\pi\)
−0.415820 + 0.909447i \(0.636505\pi\)
\(608\) −8.17079 −0.331369
\(609\) 0 0
\(610\) 3.70110 0.149853
\(611\) −33.4925 −1.35496
\(612\) 0 0
\(613\) 34.3964 1.38926 0.694629 0.719368i \(-0.255568\pi\)
0.694629 + 0.719368i \(0.255568\pi\)
\(614\) 20.8544 0.841614
\(615\) 0 0
\(616\) 5.76815 0.232405
\(617\) 25.0198 1.00726 0.503629 0.863920i \(-0.331998\pi\)
0.503629 + 0.863920i \(0.331998\pi\)
\(618\) 0 0
\(619\) −46.5200 −1.86980 −0.934899 0.354913i \(-0.884510\pi\)
−0.934899 + 0.354913i \(0.884510\pi\)
\(620\) −8.84874 −0.355374
\(621\) 0 0
\(622\) −5.99969 −0.240566
\(623\) −17.5941 −0.704893
\(624\) 0 0
\(625\) 20.6868 0.827473
\(626\) −28.6065 −1.14335
\(627\) 0 0
\(628\) −26.6531 −1.06357
\(629\) 73.6595 2.93700
\(630\) 0 0
\(631\) 3.86585 0.153897 0.0769485 0.997035i \(-0.475482\pi\)
0.0769485 + 0.997035i \(0.475482\pi\)
\(632\) −20.5291 −0.816603
\(633\) 0 0
\(634\) −39.7827 −1.57997
\(635\) −7.33754 −0.291182
\(636\) 0 0
\(637\) 29.9718 1.18753
\(638\) 8.07183 0.319567
\(639\) 0 0
\(640\) 6.68753 0.264348
\(641\) 2.36295 0.0933310 0.0466655 0.998911i \(-0.485141\pi\)
0.0466655 + 0.998911i \(0.485141\pi\)
\(642\) 0 0
\(643\) −0.885320 −0.0349136 −0.0174568 0.999848i \(-0.505557\pi\)
−0.0174568 + 0.999848i \(0.505557\pi\)
\(644\) 2.58829 0.101993
\(645\) 0 0
\(646\) 16.9898 0.668456
\(647\) 7.00425 0.275366 0.137683 0.990476i \(-0.456035\pi\)
0.137683 + 0.990476i \(0.456035\pi\)
\(648\) 0 0
\(649\) 21.4279 0.841118
\(650\) −50.2858 −1.97237
\(651\) 0 0
\(652\) 19.3481 0.757730
\(653\) −35.3399 −1.38296 −0.691480 0.722396i \(-0.743041\pi\)
−0.691480 + 0.722396i \(0.743041\pi\)
\(654\) 0 0
\(655\) −2.74617 −0.107302
\(656\) 1.83923 0.0718100
\(657\) 0 0
\(658\) −13.9877 −0.545299
\(659\) −14.6525 −0.570779 −0.285390 0.958412i \(-0.592123\pi\)
−0.285390 + 0.958412i \(0.592123\pi\)
\(660\) 0 0
\(661\) −1.85751 −0.0722486 −0.0361243 0.999347i \(-0.511501\pi\)
−0.0361243 + 0.999347i \(0.511501\pi\)
\(662\) −34.3323 −1.33436
\(663\) 0 0
\(664\) −5.38361 −0.208925
\(665\) −0.555709 −0.0215495
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 9.07813 0.351244
\(669\) 0 0
\(670\) −15.1197 −0.584126
\(671\) 11.5825 0.447136
\(672\) 0 0
\(673\) −1.59371 −0.0614330 −0.0307165 0.999528i \(-0.509779\pi\)
−0.0307165 + 0.999528i \(0.509779\pi\)
\(674\) 57.3583 2.20936
\(675\) 0 0
\(676\) 30.2962 1.16524
\(677\) −10.4718 −0.402466 −0.201233 0.979543i \(-0.564495\pi\)
−0.201233 + 0.979543i \(0.564495\pi\)
\(678\) 0 0
\(679\) −12.2676 −0.470786
\(680\) −6.40748 −0.245716
\(681\) 0 0
\(682\) −47.7383 −1.82799
\(683\) −14.6358 −0.560025 −0.280013 0.959996i \(-0.590339\pi\)
−0.280013 + 0.959996i \(0.590339\pi\)
\(684\) 0 0
\(685\) −7.80153 −0.298081
\(686\) 26.8292 1.02434
\(687\) 0 0
\(688\) 3.68533 0.140502
\(689\) −51.8958 −1.97707
\(690\) 0 0
\(691\) −6.81240 −0.259156 −0.129578 0.991569i \(-0.541362\pi\)
−0.129578 + 0.991569i \(0.541362\pi\)
\(692\) 36.8932 1.40247
\(693\) 0 0
\(694\) −18.7879 −0.713178
\(695\) −6.08657 −0.230877
\(696\) 0 0
\(697\) −6.90706 −0.261624
\(698\) −17.8828 −0.676875
\(699\) 0 0
\(700\) −12.1823 −0.460449
\(701\) −24.0612 −0.908781 −0.454390 0.890803i \(-0.650143\pi\)
−0.454390 + 0.890803i \(0.650143\pi\)
\(702\) 0 0
\(703\) −11.3515 −0.428128
\(704\) 46.2136 1.74174
\(705\) 0 0
\(706\) −25.4949 −0.959515
\(707\) −9.40876 −0.353853
\(708\) 0 0
\(709\) 7.05658 0.265016 0.132508 0.991182i \(-0.457697\pi\)
0.132508 + 0.991182i \(0.457697\pi\)
\(710\) −13.7163 −0.514765
\(711\) 0 0
\(712\) 31.2629 1.17163
\(713\) −5.91418 −0.221488
\(714\) 0 0
\(715\) 9.80570 0.366712
\(716\) −59.6864 −2.23059
\(717\) 0 0
\(718\) −6.04438 −0.225574
\(719\) −1.04045 −0.0388023 −0.0194011 0.999812i \(-0.506176\pi\)
−0.0194011 + 0.999812i \(0.506176\pi\)
\(720\) 0 0
\(721\) −18.7630 −0.698770
\(722\) 38.8470 1.44573
\(723\) 0 0
\(724\) 41.2029 1.53129
\(725\) −4.70672 −0.174803
\(726\) 0 0
\(727\) −33.9812 −1.26029 −0.630146 0.776477i \(-0.717005\pi\)
−0.630146 + 0.776477i \(0.717005\pi\)
\(728\) 7.63469 0.282960
\(729\) 0 0
\(730\) −10.7437 −0.397640
\(731\) −13.8399 −0.511888
\(732\) 0 0
\(733\) 4.19306 0.154874 0.0774370 0.996997i \(-0.475326\pi\)
0.0774370 + 0.996997i \(0.475326\pi\)
\(734\) 42.2839 1.56073
\(735\) 0 0
\(736\) 7.45974 0.274970
\(737\) −47.3168 −1.74294
\(738\) 0 0
\(739\) 6.50021 0.239114 0.119557 0.992827i \(-0.461853\pi\)
0.119557 + 0.992827i \(0.461853\pi\)
\(740\) 15.5059 0.570009
\(741\) 0 0
\(742\) −21.6736 −0.795664
\(743\) 32.0119 1.17440 0.587201 0.809441i \(-0.300230\pi\)
0.587201 + 0.809441i \(0.300230\pi\)
\(744\) 0 0
\(745\) −4.81453 −0.176391
\(746\) 17.3001 0.633401
\(747\) 0 0
\(748\) −72.6283 −2.65555
\(749\) −5.16952 −0.188890
\(750\) 0 0
\(751\) −42.8138 −1.56230 −0.781150 0.624344i \(-0.785366\pi\)
−0.781150 + 0.624344i \(0.785366\pi\)
\(752\) −12.9483 −0.472176
\(753\) 0 0
\(754\) 10.6838 0.389082
\(755\) 4.83923 0.176118
\(756\) 0 0
\(757\) −21.0059 −0.763474 −0.381737 0.924271i \(-0.624674\pi\)
−0.381737 + 0.924271i \(0.624674\pi\)
\(758\) 49.3926 1.79402
\(759\) 0 0
\(760\) 0.987438 0.0358181
\(761\) 42.5421 1.54215 0.771075 0.636744i \(-0.219719\pi\)
0.771075 + 0.636744i \(0.219719\pi\)
\(762\) 0 0
\(763\) −2.55689 −0.0925656
\(764\) 63.0628 2.28153
\(765\) 0 0
\(766\) −2.83087 −0.102284
\(767\) 28.3618 1.02409
\(768\) 0 0
\(769\) −7.39163 −0.266549 −0.133274 0.991079i \(-0.542549\pi\)
−0.133274 + 0.991079i \(0.542549\pi\)
\(770\) 4.09523 0.147582
\(771\) 0 0
\(772\) −62.0792 −2.23428
\(773\) −44.3347 −1.59461 −0.797304 0.603578i \(-0.793741\pi\)
−0.797304 + 0.603578i \(0.793741\pi\)
\(774\) 0 0
\(775\) 27.8364 0.999914
\(776\) 21.7982 0.782511
\(777\) 0 0
\(778\) 28.3481 1.01633
\(779\) 1.06443 0.0381370
\(780\) 0 0
\(781\) −42.9249 −1.53597
\(782\) −15.5113 −0.554683
\(783\) 0 0
\(784\) 11.5872 0.413828
\(785\) −5.22447 −0.186469
\(786\) 0 0
\(787\) −6.28909 −0.224182 −0.112091 0.993698i \(-0.535755\pi\)
−0.112091 + 0.993698i \(0.535755\pi\)
\(788\) −8.89515 −0.316876
\(789\) 0 0
\(790\) −14.5751 −0.518559
\(791\) 10.0398 0.356974
\(792\) 0 0
\(793\) 15.3305 0.544402
\(794\) 53.0345 1.88212
\(795\) 0 0
\(796\) 11.6796 0.413971
\(797\) 14.1840 0.502422 0.251211 0.967932i \(-0.419171\pi\)
0.251211 + 0.967932i \(0.419171\pi\)
\(798\) 0 0
\(799\) 48.6261 1.72027
\(800\) −35.1109 −1.24136
\(801\) 0 0
\(802\) −1.03356 −0.0364961
\(803\) −33.6220 −1.18649
\(804\) 0 0
\(805\) 0.507349 0.0178817
\(806\) −63.1861 −2.22564
\(807\) 0 0
\(808\) 16.7184 0.588152
\(809\) −51.7618 −1.81985 −0.909923 0.414777i \(-0.863860\pi\)
−0.909923 + 0.414777i \(0.863860\pi\)
\(810\) 0 0
\(811\) −50.5755 −1.77595 −0.887973 0.459896i \(-0.847887\pi\)
−0.887973 + 0.459896i \(0.847887\pi\)
\(812\) 2.58829 0.0908310
\(813\) 0 0
\(814\) 83.6532 2.93204
\(815\) 3.79256 0.132848
\(816\) 0 0
\(817\) 2.13283 0.0746182
\(818\) 33.6160 1.17536
\(819\) 0 0
\(820\) −1.45399 −0.0507756
\(821\) −19.6402 −0.685447 −0.342724 0.939436i \(-0.611349\pi\)
−0.342724 + 0.939436i \(0.611349\pi\)
\(822\) 0 0
\(823\) 27.8234 0.969864 0.484932 0.874552i \(-0.338844\pi\)
0.484932 + 0.874552i \(0.338844\pi\)
\(824\) 33.3399 1.16145
\(825\) 0 0
\(826\) 11.8450 0.412139
\(827\) 39.4184 1.37071 0.685355 0.728209i \(-0.259647\pi\)
0.685355 + 0.728209i \(0.259647\pi\)
\(828\) 0 0
\(829\) −21.9728 −0.763147 −0.381573 0.924339i \(-0.624618\pi\)
−0.381573 + 0.924339i \(0.624618\pi\)
\(830\) −3.82222 −0.132671
\(831\) 0 0
\(832\) 61.1680 2.12062
\(833\) −43.5146 −1.50769
\(834\) 0 0
\(835\) 1.77947 0.0615811
\(836\) 11.1925 0.387102
\(837\) 0 0
\(838\) 15.7981 0.545737
\(839\) −27.8051 −0.959937 −0.479969 0.877286i \(-0.659352\pi\)
−0.479969 + 0.877286i \(0.659352\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −40.9470 −1.41113
\(843\) 0 0
\(844\) 43.7654 1.50647
\(845\) 5.93858 0.204293
\(846\) 0 0
\(847\) 2.51065 0.0862670
\(848\) −20.0631 −0.688968
\(849\) 0 0
\(850\) 73.0074 2.50413
\(851\) 10.3636 0.355260
\(852\) 0 0
\(853\) −40.5376 −1.38798 −0.693990 0.719984i \(-0.744149\pi\)
−0.693990 + 0.719984i \(0.744149\pi\)
\(854\) 6.40260 0.219092
\(855\) 0 0
\(856\) 9.18572 0.313961
\(857\) 44.5279 1.52104 0.760522 0.649312i \(-0.224943\pi\)
0.760522 + 0.649312i \(0.224943\pi\)
\(858\) 0 0
\(859\) 50.4132 1.72008 0.860038 0.510230i \(-0.170440\pi\)
0.860038 + 0.510230i \(0.170440\pi\)
\(860\) −2.91341 −0.0993465
\(861\) 0 0
\(862\) −77.2344 −2.63061
\(863\) 19.2717 0.656016 0.328008 0.944675i \(-0.393623\pi\)
0.328008 + 0.944675i \(0.393623\pi\)
\(864\) 0 0
\(865\) 7.23171 0.245886
\(866\) 74.5702 2.53400
\(867\) 0 0
\(868\) −15.3076 −0.519574
\(869\) −45.6124 −1.54729
\(870\) 0 0
\(871\) −62.6282 −2.12208
\(872\) 4.54333 0.153857
\(873\) 0 0
\(874\) 2.39040 0.0808565
\(875\) −4.92469 −0.166485
\(876\) 0 0
\(877\) −18.3077 −0.618208 −0.309104 0.951028i \(-0.600029\pi\)
−0.309104 + 0.951028i \(0.600029\pi\)
\(878\) 52.3010 1.76507
\(879\) 0 0
\(880\) 3.79091 0.127792
\(881\) 3.61086 0.121653 0.0608264 0.998148i \(-0.480626\pi\)
0.0608264 + 0.998148i \(0.480626\pi\)
\(882\) 0 0
\(883\) −10.7008 −0.360111 −0.180056 0.983656i \(-0.557628\pi\)
−0.180056 + 0.983656i \(0.557628\pi\)
\(884\) −96.1304 −3.23322
\(885\) 0 0
\(886\) −56.1724 −1.88715
\(887\) 55.8629 1.87569 0.937846 0.347053i \(-0.112818\pi\)
0.937846 + 0.347053i \(0.112818\pi\)
\(888\) 0 0
\(889\) −12.6934 −0.425721
\(890\) 22.1958 0.744006
\(891\) 0 0
\(892\) 14.1953 0.475295
\(893\) −7.49362 −0.250765
\(894\) 0 0
\(895\) −11.6996 −0.391074
\(896\) 11.5689 0.386489
\(897\) 0 0
\(898\) 39.9557 1.33334
\(899\) −5.91418 −0.197249
\(900\) 0 0
\(901\) 75.3449 2.51010
\(902\) −7.84417 −0.261182
\(903\) 0 0
\(904\) −17.8397 −0.593339
\(905\) 8.07648 0.268471
\(906\) 0 0
\(907\) −28.0825 −0.932465 −0.466233 0.884662i \(-0.654389\pi\)
−0.466233 + 0.884662i \(0.654389\pi\)
\(908\) −64.0404 −2.12526
\(909\) 0 0
\(910\) 5.42042 0.179685
\(911\) −19.0498 −0.631147 −0.315574 0.948901i \(-0.602197\pi\)
−0.315574 + 0.948901i \(0.602197\pi\)
\(912\) 0 0
\(913\) −11.9615 −0.395869
\(914\) −31.9521 −1.05688
\(915\) 0 0
\(916\) −76.4714 −2.52669
\(917\) −4.75066 −0.156881
\(918\) 0 0
\(919\) 34.7771 1.14719 0.573595 0.819139i \(-0.305549\pi\)
0.573595 + 0.819139i \(0.305549\pi\)
\(920\) −0.901507 −0.0297218
\(921\) 0 0
\(922\) 59.0901 1.94603
\(923\) −56.8152 −1.87009
\(924\) 0 0
\(925\) −48.7786 −1.60383
\(926\) −74.0482 −2.43337
\(927\) 0 0
\(928\) 7.45974 0.244878
\(929\) −19.4976 −0.639694 −0.319847 0.947469i \(-0.603632\pi\)
−0.319847 + 0.947469i \(0.603632\pi\)
\(930\) 0 0
\(931\) 6.70590 0.219777
\(932\) −15.9978 −0.524025
\(933\) 0 0
\(934\) 59.6321 1.95122
\(935\) −14.2364 −0.465580
\(936\) 0 0
\(937\) −32.4024 −1.05854 −0.529270 0.848454i \(-0.677534\pi\)
−0.529270 + 0.848454i \(0.677534\pi\)
\(938\) −26.1559 −0.854021
\(939\) 0 0
\(940\) 10.2362 0.333867
\(941\) 9.15194 0.298345 0.149172 0.988811i \(-0.452339\pi\)
0.149172 + 0.988811i \(0.452339\pi\)
\(942\) 0 0
\(943\) −0.971796 −0.0316460
\(944\) 10.9648 0.356873
\(945\) 0 0
\(946\) −15.7176 −0.511024
\(947\) −42.1843 −1.37081 −0.685403 0.728164i \(-0.740374\pi\)
−0.685403 + 0.728164i \(0.740374\pi\)
\(948\) 0 0
\(949\) −44.5018 −1.44459
\(950\) −11.2510 −0.365029
\(951\) 0 0
\(952\) −11.0844 −0.359248
\(953\) 29.2461 0.947376 0.473688 0.880693i \(-0.342923\pi\)
0.473688 + 0.880693i \(0.342923\pi\)
\(954\) 0 0
\(955\) 12.3614 0.400005
\(956\) 64.8353 2.09692
\(957\) 0 0
\(958\) 24.8918 0.804219
\(959\) −13.4960 −0.435809
\(960\) 0 0
\(961\) 3.97758 0.128309
\(962\) 110.723 3.56985
\(963\) 0 0
\(964\) −8.37866 −0.269859
\(965\) −12.1686 −0.391721
\(966\) 0 0
\(967\) 2.39429 0.0769952 0.0384976 0.999259i \(-0.487743\pi\)
0.0384976 + 0.999259i \(0.487743\pi\)
\(968\) −4.46117 −0.143388
\(969\) 0 0
\(970\) 15.4762 0.496909
\(971\) −16.9781 −0.544853 −0.272427 0.962177i \(-0.587826\pi\)
−0.272427 + 0.962177i \(0.587826\pi\)
\(972\) 0 0
\(973\) −10.5293 −0.337553
\(974\) −33.8509 −1.08465
\(975\) 0 0
\(976\) 5.92681 0.189713
\(977\) 46.4893 1.48733 0.743663 0.668555i \(-0.233087\pi\)
0.743663 + 0.668555i \(0.233087\pi\)
\(978\) 0 0
\(979\) 69.4613 2.21999
\(980\) −9.16016 −0.292611
\(981\) 0 0
\(982\) 3.93070 0.125434
\(983\) −49.4911 −1.57852 −0.789260 0.614059i \(-0.789536\pi\)
−0.789260 + 0.614059i \(0.789536\pi\)
\(984\) 0 0
\(985\) −1.74360 −0.0555558
\(986\) −15.5113 −0.493981
\(987\) 0 0
\(988\) 14.8144 0.471308
\(989\) −1.94722 −0.0619180
\(990\) 0 0
\(991\) 21.7522 0.690983 0.345491 0.938422i \(-0.387712\pi\)
0.345491 + 0.938422i \(0.387712\pi\)
\(992\) −44.1183 −1.40076
\(993\) 0 0
\(994\) −23.7282 −0.752612
\(995\) 2.28940 0.0725787
\(996\) 0 0
\(997\) −13.8349 −0.438157 −0.219079 0.975707i \(-0.570305\pi\)
−0.219079 + 0.975707i \(0.570305\pi\)
\(998\) 90.5706 2.86696
\(999\) 0 0
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 \(a_p\))