Properties

Label 6027.2.a.bk.1.14
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Root \(-2.69016\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.69016 q^{2} +1.00000 q^{3} +5.23695 q^{4} -3.40724 q^{5} +2.69016 q^{6} +8.70791 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.69016 q^{2} +1.00000 q^{3} +5.23695 q^{4} -3.40724 q^{5} +2.69016 q^{6} +8.70791 q^{8} +1.00000 q^{9} -9.16601 q^{10} -6.16208 q^{11} +5.23695 q^{12} -3.11534 q^{13} -3.40724 q^{15} +12.9518 q^{16} -2.71759 q^{17} +2.69016 q^{18} -7.15789 q^{19} -17.8435 q^{20} -16.5770 q^{22} +3.55326 q^{23} +8.70791 q^{24} +6.60927 q^{25} -8.38076 q^{26} +1.00000 q^{27} -1.79174 q^{29} -9.16601 q^{30} +6.90989 q^{31} +17.4265 q^{32} -6.16208 q^{33} -7.31075 q^{34} +5.23695 q^{36} -8.76601 q^{37} -19.2558 q^{38} -3.11534 q^{39} -29.6699 q^{40} -1.00000 q^{41} +3.02053 q^{43} -32.2705 q^{44} -3.40724 q^{45} +9.55884 q^{46} +4.99622 q^{47} +12.9518 q^{48} +17.7800 q^{50} -2.71759 q^{51} -16.3149 q^{52} -2.58012 q^{53} +2.69016 q^{54} +20.9957 q^{55} -7.15789 q^{57} -4.82007 q^{58} -9.63934 q^{59} -17.8435 q^{60} -4.52207 q^{61} +18.5887 q^{62} +20.9764 q^{64} +10.6147 q^{65} -16.5770 q^{66} -1.73848 q^{67} -14.2319 q^{68} +3.55326 q^{69} -14.2790 q^{71} +8.70791 q^{72} -0.984881 q^{73} -23.5820 q^{74} +6.60927 q^{75} -37.4855 q^{76} -8.38076 q^{78} -8.68549 q^{79} -44.1297 q^{80} +1.00000 q^{81} -2.69016 q^{82} -1.55919 q^{83} +9.25948 q^{85} +8.12570 q^{86} -1.79174 q^{87} -53.6589 q^{88} -4.47862 q^{89} -9.16601 q^{90} +18.6083 q^{92} +6.90989 q^{93} +13.4406 q^{94} +24.3886 q^{95} +17.4265 q^{96} +4.47579 q^{97} -6.16208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} - 3q^{10} - 16q^{11} + 14q^{12} - 21q^{13} - 10q^{15} + 22q^{16} - 12q^{17} - 2q^{18} - 2q^{19} - 40q^{20} + q^{22} - 7q^{23} - 6q^{24} + 22q^{25} - 2q^{26} + 14q^{27} - 16q^{29} - 3q^{30} - 8q^{31} - 19q^{32} - 16q^{33} - 33q^{34} + 14q^{36} + q^{37} - 32q^{38} - 21q^{39} + 13q^{40} - 14q^{41} + 14q^{43} - 36q^{44} - 10q^{45} - 12q^{46} - 12q^{47} + 22q^{48} - q^{50} - 12q^{51} - 60q^{52} - 20q^{53} - 2q^{54} + 11q^{55} - 2q^{57} + 21q^{58} - 25q^{59} - 40q^{60} - 26q^{61} + 33q^{62} + 42q^{64} - 8q^{65} + q^{66} - 22q^{67} - 15q^{68} - 7q^{69} - 36q^{71} - 6q^{72} - 31q^{73} - 65q^{74} + 22q^{75} + 2q^{76} - 2q^{78} + 12q^{79} - 112q^{80} + 14q^{81} + 2q^{82} - 20q^{83} + 40q^{85} - 9q^{86} - 16q^{87} - 54q^{88} - 39q^{89} - 3q^{90} + 63q^{92} - 8q^{93} - 14q^{94} - 55q^{95} - 19q^{96} - 18q^{97} - 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.69016 1.90223 0.951115 0.308838i \(-0.0999401\pi\)
0.951115 + 0.308838i \(0.0999401\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.23695 2.61848
\(5\) −3.40724 −1.52376 −0.761882 0.647716i \(-0.775724\pi\)
−0.761882 + 0.647716i \(0.775724\pi\)
\(6\) 2.69016 1.09825
\(7\) 0 0
\(8\) 8.70791 3.07871
\(9\) 1.00000 0.333333
\(10\) −9.16601 −2.89855
\(11\) −6.16208 −1.85794 −0.928968 0.370159i \(-0.879303\pi\)
−0.928968 + 0.370159i \(0.879303\pi\)
\(12\) 5.23695 1.51178
\(13\) −3.11534 −0.864041 −0.432020 0.901864i \(-0.642199\pi\)
−0.432020 + 0.901864i \(0.642199\pi\)
\(14\) 0 0
\(15\) −3.40724 −0.879745
\(16\) 12.9518 3.23794
\(17\) −2.71759 −0.659113 −0.329556 0.944136i \(-0.606899\pi\)
−0.329556 + 0.944136i \(0.606899\pi\)
\(18\) 2.69016 0.634076
\(19\) −7.15789 −1.64213 −0.821066 0.570833i \(-0.806620\pi\)
−0.821066 + 0.570833i \(0.806620\pi\)
\(20\) −17.8435 −3.98994
\(21\) 0 0
\(22\) −16.5770 −3.53422
\(23\) 3.55326 0.740906 0.370453 0.928851i \(-0.379202\pi\)
0.370453 + 0.928851i \(0.379202\pi\)
\(24\) 8.70791 1.77750
\(25\) 6.60927 1.32185
\(26\) −8.38076 −1.64360
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.79174 −0.332718 −0.166359 0.986065i \(-0.553201\pi\)
−0.166359 + 0.986065i \(0.553201\pi\)
\(30\) −9.16601 −1.67348
\(31\) 6.90989 1.24105 0.620527 0.784185i \(-0.286919\pi\)
0.620527 + 0.784185i \(0.286919\pi\)
\(32\) 17.4265 3.08059
\(33\) −6.16208 −1.07268
\(34\) −7.31075 −1.25378
\(35\) 0 0
\(36\) 5.23695 0.872825
\(37\) −8.76601 −1.44112 −0.720562 0.693391i \(-0.756116\pi\)
−0.720562 + 0.693391i \(0.756116\pi\)
\(38\) −19.2558 −3.12371
\(39\) −3.11534 −0.498854
\(40\) −29.6699 −4.69123
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 3.02053 0.460626 0.230313 0.973117i \(-0.426025\pi\)
0.230313 + 0.973117i \(0.426025\pi\)
\(44\) −32.2705 −4.86496
\(45\) −3.40724 −0.507921
\(46\) 9.55884 1.40937
\(47\) 4.99622 0.728773 0.364387 0.931248i \(-0.381279\pi\)
0.364387 + 0.931248i \(0.381279\pi\)
\(48\) 12.9518 1.86943
\(49\) 0 0
\(50\) 17.7800 2.51447
\(51\) −2.71759 −0.380539
\(52\) −16.3149 −2.26247
\(53\) −2.58012 −0.354406 −0.177203 0.984174i \(-0.556705\pi\)
−0.177203 + 0.984174i \(0.556705\pi\)
\(54\) 2.69016 0.366084
\(55\) 20.9957 2.83106
\(56\) 0 0
\(57\) −7.15789 −0.948085
\(58\) −4.82007 −0.632906
\(59\) −9.63934 −1.25494 −0.627468 0.778643i \(-0.715909\pi\)
−0.627468 + 0.778643i \(0.715909\pi\)
\(60\) −17.8435 −2.30359
\(61\) −4.52207 −0.578991 −0.289496 0.957179i \(-0.593488\pi\)
−0.289496 + 0.957179i \(0.593488\pi\)
\(62\) 18.5887 2.36077
\(63\) 0 0
\(64\) 20.9764 2.62205
\(65\) 10.6147 1.31659
\(66\) −16.5770 −2.04048
\(67\) −1.73848 −0.212390 −0.106195 0.994345i \(-0.533867\pi\)
−0.106195 + 0.994345i \(0.533867\pi\)
\(68\) −14.2319 −1.72587
\(69\) 3.55326 0.427762
\(70\) 0 0
\(71\) −14.2790 −1.69460 −0.847301 0.531113i \(-0.821774\pi\)
−0.847301 + 0.531113i \(0.821774\pi\)
\(72\) 8.70791 1.02624
\(73\) −0.984881 −0.115272 −0.0576358 0.998338i \(-0.518356\pi\)
−0.0576358 + 0.998338i \(0.518356\pi\)
\(74\) −23.5820 −2.74135
\(75\) 6.60927 0.763173
\(76\) −37.4855 −4.29988
\(77\) 0 0
\(78\) −8.38076 −0.948935
\(79\) −8.68549 −0.977194 −0.488597 0.872510i \(-0.662491\pi\)
−0.488597 + 0.872510i \(0.662491\pi\)
\(80\) −44.1297 −4.93386
\(81\) 1.00000 0.111111
\(82\) −2.69016 −0.297078
\(83\) −1.55919 −0.171144 −0.0855719 0.996332i \(-0.527272\pi\)
−0.0855719 + 0.996332i \(0.527272\pi\)
\(84\) 0 0
\(85\) 9.25948 1.00433
\(86\) 8.12570 0.876217
\(87\) −1.79174 −0.192095
\(88\) −53.6589 −5.72005
\(89\) −4.47862 −0.474733 −0.237367 0.971420i \(-0.576284\pi\)
−0.237367 + 0.971420i \(0.576284\pi\)
\(90\) −9.16601 −0.966182
\(91\) 0 0
\(92\) 18.6083 1.94005
\(93\) 6.90989 0.716522
\(94\) 13.4406 1.38629
\(95\) 24.3886 2.50222
\(96\) 17.4265 1.77858
\(97\) 4.47579 0.454448 0.227224 0.973843i \(-0.427035\pi\)
0.227224 + 0.973843i \(0.427035\pi\)
\(98\) 0 0
\(99\) −6.16208 −0.619312
\(100\) 34.6124 3.46124
\(101\) −3.51262 −0.349519 −0.174760 0.984611i \(-0.555915\pi\)
−0.174760 + 0.984611i \(0.555915\pi\)
\(102\) −7.31075 −0.723872
\(103\) −11.5411 −1.13718 −0.568588 0.822622i \(-0.692510\pi\)
−0.568588 + 0.822622i \(0.692510\pi\)
\(104\) −27.1281 −2.66013
\(105\) 0 0
\(106\) −6.94093 −0.674162
\(107\) −5.39948 −0.521987 −0.260994 0.965341i \(-0.584050\pi\)
−0.260994 + 0.965341i \(0.584050\pi\)
\(108\) 5.23695 0.503926
\(109\) 18.6989 1.79103 0.895514 0.445032i \(-0.146808\pi\)
0.895514 + 0.445032i \(0.146808\pi\)
\(110\) 56.4817 5.38532
\(111\) −8.76601 −0.832033
\(112\) 0 0
\(113\) 9.53967 0.897417 0.448709 0.893678i \(-0.351884\pi\)
0.448709 + 0.893678i \(0.351884\pi\)
\(114\) −19.2558 −1.80348
\(115\) −12.1068 −1.12897
\(116\) −9.38326 −0.871214
\(117\) −3.11534 −0.288014
\(118\) −25.9314 −2.38717
\(119\) 0 0
\(120\) −29.6699 −2.70848
\(121\) 26.9712 2.45193
\(122\) −12.1651 −1.10137
\(123\) −1.00000 −0.0901670
\(124\) 36.1868 3.24967
\(125\) −5.48317 −0.490429
\(126\) 0 0
\(127\) 14.8639 1.31896 0.659478 0.751724i \(-0.270777\pi\)
0.659478 + 0.751724i \(0.270777\pi\)
\(128\) 21.5770 1.90715
\(129\) 3.02053 0.265943
\(130\) 28.5553 2.50446
\(131\) 6.15126 0.537438 0.268719 0.963219i \(-0.413400\pi\)
0.268719 + 0.963219i \(0.413400\pi\)
\(132\) −32.2705 −2.80879
\(133\) 0 0
\(134\) −4.67680 −0.404014
\(135\) −3.40724 −0.293248
\(136\) −23.6646 −2.02922
\(137\) 1.14084 0.0974688 0.0487344 0.998812i \(-0.484481\pi\)
0.0487344 + 0.998812i \(0.484481\pi\)
\(138\) 9.55884 0.813702
\(139\) 6.86085 0.581929 0.290965 0.956734i \(-0.406024\pi\)
0.290965 + 0.956734i \(0.406024\pi\)
\(140\) 0 0
\(141\) 4.99622 0.420758
\(142\) −38.4127 −3.22352
\(143\) 19.1970 1.60533
\(144\) 12.9518 1.07931
\(145\) 6.10489 0.506983
\(146\) −2.64948 −0.219273
\(147\) 0 0
\(148\) −45.9072 −3.77355
\(149\) −18.1936 −1.49048 −0.745241 0.666796i \(-0.767665\pi\)
−0.745241 + 0.666796i \(0.767665\pi\)
\(150\) 17.7800 1.45173
\(151\) −7.96692 −0.648338 −0.324169 0.945999i \(-0.605085\pi\)
−0.324169 + 0.945999i \(0.605085\pi\)
\(152\) −62.3303 −5.05565
\(153\) −2.71759 −0.219704
\(154\) 0 0
\(155\) −23.5436 −1.89107
\(156\) −16.3149 −1.30624
\(157\) 15.3395 1.22423 0.612113 0.790770i \(-0.290320\pi\)
0.612113 + 0.790770i \(0.290320\pi\)
\(158\) −23.3653 −1.85885
\(159\) −2.58012 −0.204617
\(160\) −59.3761 −4.69409
\(161\) 0 0
\(162\) 2.69016 0.211359
\(163\) 10.0612 0.788053 0.394027 0.919099i \(-0.371082\pi\)
0.394027 + 0.919099i \(0.371082\pi\)
\(164\) −5.23695 −0.408937
\(165\) 20.9957 1.63451
\(166\) −4.19448 −0.325555
\(167\) 25.0532 1.93868 0.969338 0.245732i \(-0.0790283\pi\)
0.969338 + 0.245732i \(0.0790283\pi\)
\(168\) 0 0
\(169\) −3.29464 −0.253434
\(170\) 24.9095 1.91047
\(171\) −7.15789 −0.547377
\(172\) 15.8184 1.20614
\(173\) 3.76556 0.286291 0.143145 0.989702i \(-0.454278\pi\)
0.143145 + 0.989702i \(0.454278\pi\)
\(174\) −4.82007 −0.365408
\(175\) 0 0
\(176\) −79.8098 −6.01589
\(177\) −9.63934 −0.724537
\(178\) −12.0482 −0.903052
\(179\) −17.0313 −1.27298 −0.636491 0.771284i \(-0.719615\pi\)
−0.636491 + 0.771284i \(0.719615\pi\)
\(180\) −17.8435 −1.32998
\(181\) −8.03112 −0.596948 −0.298474 0.954418i \(-0.596478\pi\)
−0.298474 + 0.954418i \(0.596478\pi\)
\(182\) 0 0
\(183\) −4.52207 −0.334281
\(184\) 30.9415 2.28104
\(185\) 29.8679 2.19593
\(186\) 18.5887 1.36299
\(187\) 16.7460 1.22459
\(188\) 26.1650 1.90828
\(189\) 0 0
\(190\) 65.6093 4.75980
\(191\) 0.0253646 0.00183532 0.000917660 1.00000i \(-0.499708\pi\)
0.000917660 1.00000i \(0.499708\pi\)
\(192\) 20.9764 1.51384
\(193\) −6.47830 −0.466319 −0.233159 0.972439i \(-0.574906\pi\)
−0.233159 + 0.972439i \(0.574906\pi\)
\(194\) 12.0406 0.864464
\(195\) 10.6147 0.760135
\(196\) 0 0
\(197\) 5.96735 0.425156 0.212578 0.977144i \(-0.431814\pi\)
0.212578 + 0.977144i \(0.431814\pi\)
\(198\) −16.5770 −1.17807
\(199\) −0.700264 −0.0496404 −0.0248202 0.999692i \(-0.507901\pi\)
−0.0248202 + 0.999692i \(0.507901\pi\)
\(200\) 57.5530 4.06961
\(201\) −1.73848 −0.122623
\(202\) −9.44951 −0.664865
\(203\) 0 0
\(204\) −14.2319 −0.996432
\(205\) 3.40724 0.237972
\(206\) −31.0473 −2.16317
\(207\) 3.55326 0.246969
\(208\) −40.3492 −2.79771
\(209\) 44.1075 3.05098
\(210\) 0 0
\(211\) 5.72349 0.394021 0.197010 0.980401i \(-0.436877\pi\)
0.197010 + 0.980401i \(0.436877\pi\)
\(212\) −13.5120 −0.928005
\(213\) −14.2790 −0.978379
\(214\) −14.5255 −0.992940
\(215\) −10.2917 −0.701886
\(216\) 8.70791 0.592499
\(217\) 0 0
\(218\) 50.3030 3.40695
\(219\) −0.984881 −0.0665521
\(220\) 109.953 7.41305
\(221\) 8.46623 0.569500
\(222\) −23.5820 −1.58272
\(223\) 5.28384 0.353832 0.176916 0.984226i \(-0.443388\pi\)
0.176916 + 0.984226i \(0.443388\pi\)
\(224\) 0 0
\(225\) 6.60927 0.440618
\(226\) 25.6632 1.70709
\(227\) 11.5976 0.769758 0.384879 0.922967i \(-0.374243\pi\)
0.384879 + 0.922967i \(0.374243\pi\)
\(228\) −37.4855 −2.48254
\(229\) 13.2278 0.874119 0.437060 0.899433i \(-0.356020\pi\)
0.437060 + 0.899433i \(0.356020\pi\)
\(230\) −32.5692 −2.14755
\(231\) 0 0
\(232\) −15.6023 −1.02434
\(233\) 10.8820 0.712901 0.356451 0.934314i \(-0.383987\pi\)
0.356451 + 0.934314i \(0.383987\pi\)
\(234\) −8.38076 −0.547868
\(235\) −17.0233 −1.11048
\(236\) −50.4808 −3.28602
\(237\) −8.68549 −0.564183
\(238\) 0 0
\(239\) 19.8211 1.28212 0.641061 0.767490i \(-0.278494\pi\)
0.641061 + 0.767490i \(0.278494\pi\)
\(240\) −44.1297 −2.84856
\(241\) −10.6310 −0.684801 −0.342400 0.939554i \(-0.611240\pi\)
−0.342400 + 0.939554i \(0.611240\pi\)
\(242\) 72.5569 4.66413
\(243\) 1.00000 0.0641500
\(244\) −23.6818 −1.51607
\(245\) 0 0
\(246\) −2.69016 −0.171518
\(247\) 22.2993 1.41887
\(248\) 60.1707 3.82085
\(249\) −1.55919 −0.0988099
\(250\) −14.7506 −0.932909
\(251\) −7.22243 −0.455876 −0.227938 0.973676i \(-0.573198\pi\)
−0.227938 + 0.973676i \(0.573198\pi\)
\(252\) 0 0
\(253\) −21.8955 −1.37656
\(254\) 39.9862 2.50896
\(255\) 9.25948 0.579851
\(256\) 16.0927 1.00579
\(257\) −22.0393 −1.37477 −0.687387 0.726292i \(-0.741242\pi\)
−0.687387 + 0.726292i \(0.741242\pi\)
\(258\) 8.12570 0.505884
\(259\) 0 0
\(260\) 55.5887 3.44747
\(261\) −1.79174 −0.110906
\(262\) 16.5479 1.02233
\(263\) −9.27928 −0.572185 −0.286092 0.958202i \(-0.592356\pi\)
−0.286092 + 0.958202i \(0.592356\pi\)
\(264\) −53.6589 −3.30247
\(265\) 8.79108 0.540032
\(266\) 0 0
\(267\) −4.47862 −0.274087
\(268\) −9.10436 −0.556137
\(269\) 22.5924 1.37749 0.688743 0.725006i \(-0.258163\pi\)
0.688743 + 0.725006i \(0.258163\pi\)
\(270\) −9.16601 −0.557826
\(271\) −6.25846 −0.380175 −0.190087 0.981767i \(-0.560877\pi\)
−0.190087 + 0.981767i \(0.560877\pi\)
\(272\) −35.1976 −2.13417
\(273\) 0 0
\(274\) 3.06905 0.185408
\(275\) −40.7268 −2.45592
\(276\) 18.6083 1.12009
\(277\) 20.9071 1.25618 0.628092 0.778139i \(-0.283836\pi\)
0.628092 + 0.778139i \(0.283836\pi\)
\(278\) 18.4568 1.10696
\(279\) 6.90989 0.413684
\(280\) 0 0
\(281\) −4.42179 −0.263782 −0.131891 0.991264i \(-0.542105\pi\)
−0.131891 + 0.991264i \(0.542105\pi\)
\(282\) 13.4406 0.800377
\(283\) 20.2931 1.20630 0.603150 0.797628i \(-0.293912\pi\)
0.603150 + 0.797628i \(0.293912\pi\)
\(284\) −74.7783 −4.43728
\(285\) 24.3886 1.44466
\(286\) 51.6429 3.05371
\(287\) 0 0
\(288\) 17.4265 1.02686
\(289\) −9.61469 −0.565570
\(290\) 16.4231 0.964399
\(291\) 4.47579 0.262375
\(292\) −5.15777 −0.301836
\(293\) −17.7507 −1.03701 −0.518503 0.855076i \(-0.673510\pi\)
−0.518503 + 0.855076i \(0.673510\pi\)
\(294\) 0 0
\(295\) 32.8435 1.91222
\(296\) −76.3337 −4.43680
\(297\) −6.16208 −0.357560
\(298\) −48.9438 −2.83524
\(299\) −11.0696 −0.640173
\(300\) 34.6124 1.99835
\(301\) 0 0
\(302\) −21.4323 −1.23329
\(303\) −3.51262 −0.201795
\(304\) −92.7073 −5.31713
\(305\) 15.4078 0.882245
\(306\) −7.31075 −0.417928
\(307\) 0.0193606 0.00110497 0.000552483 1.00000i \(-0.499824\pi\)
0.000552483 1.00000i \(0.499824\pi\)
\(308\) 0 0
\(309\) −11.5411 −0.656549
\(310\) −63.3361 −3.59725
\(311\) −11.0698 −0.627713 −0.313857 0.949470i \(-0.601621\pi\)
−0.313857 + 0.949470i \(0.601621\pi\)
\(312\) −27.1281 −1.53583
\(313\) 2.12513 0.120119 0.0600596 0.998195i \(-0.480871\pi\)
0.0600596 + 0.998195i \(0.480871\pi\)
\(314\) 41.2657 2.32876
\(315\) 0 0
\(316\) −45.4855 −2.55876
\(317\) −20.5654 −1.15507 −0.577535 0.816366i \(-0.695985\pi\)
−0.577535 + 0.816366i \(0.695985\pi\)
\(318\) −6.94093 −0.389228
\(319\) 11.0409 0.618169
\(320\) −71.4717 −3.99539
\(321\) −5.39948 −0.301370
\(322\) 0 0
\(323\) 19.4522 1.08235
\(324\) 5.23695 0.290942
\(325\) −20.5901 −1.14214
\(326\) 27.0662 1.49906
\(327\) 18.6989 1.03405
\(328\) −8.70791 −0.480814
\(329\) 0 0
\(330\) 56.4817 3.10921
\(331\) −27.6456 −1.51954 −0.759769 0.650193i \(-0.774688\pi\)
−0.759769 + 0.650193i \(0.774688\pi\)
\(332\) −8.16542 −0.448136
\(333\) −8.76601 −0.480374
\(334\) 67.3971 3.68781
\(335\) 5.92343 0.323632
\(336\) 0 0
\(337\) −9.41963 −0.513120 −0.256560 0.966528i \(-0.582589\pi\)
−0.256560 + 0.966528i \(0.582589\pi\)
\(338\) −8.86311 −0.482089
\(339\) 9.53967 0.518124
\(340\) 48.4915 2.62982
\(341\) −42.5793 −2.30580
\(342\) −19.2558 −1.04124
\(343\) 0 0
\(344\) 26.3025 1.41814
\(345\) −12.1068 −0.651809
\(346\) 10.1300 0.544590
\(347\) −0.939304 −0.0504245 −0.0252123 0.999682i \(-0.508026\pi\)
−0.0252123 + 0.999682i \(0.508026\pi\)
\(348\) −9.38326 −0.502996
\(349\) −3.17758 −0.170092 −0.0850461 0.996377i \(-0.527104\pi\)
−0.0850461 + 0.996377i \(0.527104\pi\)
\(350\) 0 0
\(351\) −3.11534 −0.166285
\(352\) −107.383 −5.72355
\(353\) −19.4398 −1.03467 −0.517337 0.855782i \(-0.673077\pi\)
−0.517337 + 0.855782i \(0.673077\pi\)
\(354\) −25.9314 −1.37824
\(355\) 48.6519 2.58217
\(356\) −23.4543 −1.24308
\(357\) 0 0
\(358\) −45.8170 −2.42150
\(359\) −28.6801 −1.51368 −0.756839 0.653602i \(-0.773257\pi\)
−0.756839 + 0.653602i \(0.773257\pi\)
\(360\) −29.6699 −1.56374
\(361\) 32.2353 1.69660
\(362\) −21.6050 −1.13553
\(363\) 26.9712 1.41562
\(364\) 0 0
\(365\) 3.35572 0.175647
\(366\) −12.1651 −0.635879
\(367\) 35.6900 1.86301 0.931503 0.363735i \(-0.118499\pi\)
0.931503 + 0.363735i \(0.118499\pi\)
\(368\) 46.0210 2.39901
\(369\) −1.00000 −0.0520579
\(370\) 80.3493 4.17716
\(371\) 0 0
\(372\) 36.1868 1.87620
\(373\) 6.60288 0.341884 0.170942 0.985281i \(-0.445319\pi\)
0.170942 + 0.985281i \(0.445319\pi\)
\(374\) 45.0494 2.32945
\(375\) −5.48317 −0.283150
\(376\) 43.5066 2.24368
\(377\) 5.58189 0.287482
\(378\) 0 0
\(379\) 6.60966 0.339515 0.169758 0.985486i \(-0.445702\pi\)
0.169758 + 0.985486i \(0.445702\pi\)
\(380\) 127.722 6.55200
\(381\) 14.8639 0.761500
\(382\) 0.0682349 0.00349120
\(383\) −27.9782 −1.42962 −0.714809 0.699319i \(-0.753487\pi\)
−0.714809 + 0.699319i \(0.753487\pi\)
\(384\) 21.5770 1.10110
\(385\) 0 0
\(386\) −17.4277 −0.887045
\(387\) 3.02053 0.153542
\(388\) 23.4395 1.18996
\(389\) −23.9707 −1.21536 −0.607681 0.794181i \(-0.707900\pi\)
−0.607681 + 0.794181i \(0.707900\pi\)
\(390\) 28.5553 1.44595
\(391\) −9.65631 −0.488341
\(392\) 0 0
\(393\) 6.15126 0.310290
\(394\) 16.0531 0.808745
\(395\) 29.5935 1.48901
\(396\) −32.2705 −1.62165
\(397\) −6.27159 −0.314762 −0.157381 0.987538i \(-0.550305\pi\)
−0.157381 + 0.987538i \(0.550305\pi\)
\(398\) −1.88382 −0.0944274
\(399\) 0 0
\(400\) 85.6017 4.28009
\(401\) 2.29039 0.114376 0.0571882 0.998363i \(-0.481786\pi\)
0.0571882 + 0.998363i \(0.481786\pi\)
\(402\) −4.67680 −0.233258
\(403\) −21.5267 −1.07232
\(404\) −18.3954 −0.915207
\(405\) −3.40724 −0.169307
\(406\) 0 0
\(407\) 54.0168 2.67752
\(408\) −23.6646 −1.17157
\(409\) −6.54943 −0.323848 −0.161924 0.986803i \(-0.551770\pi\)
−0.161924 + 0.986803i \(0.551770\pi\)
\(410\) 9.16601 0.452677
\(411\) 1.14084 0.0562736
\(412\) −60.4401 −2.97767
\(413\) 0 0
\(414\) 9.55884 0.469791
\(415\) 5.31254 0.260783
\(416\) −54.2894 −2.66176
\(417\) 6.86085 0.335977
\(418\) 118.656 5.80366
\(419\) −29.0673 −1.42003 −0.710016 0.704185i \(-0.751312\pi\)
−0.710016 + 0.704185i \(0.751312\pi\)
\(420\) 0 0
\(421\) 30.5913 1.49093 0.745463 0.666547i \(-0.232228\pi\)
0.745463 + 0.666547i \(0.232228\pi\)
\(422\) 15.3971 0.749518
\(423\) 4.99622 0.242924
\(424\) −22.4674 −1.09112
\(425\) −17.9613 −0.871251
\(426\) −38.4127 −1.86110
\(427\) 0 0
\(428\) −28.2768 −1.36681
\(429\) 19.1970 0.926839
\(430\) −27.6862 −1.33515
\(431\) −2.61835 −0.126121 −0.0630607 0.998010i \(-0.520086\pi\)
−0.0630607 + 0.998010i \(0.520086\pi\)
\(432\) 12.9518 0.623142
\(433\) 32.7329 1.57304 0.786520 0.617564i \(-0.211880\pi\)
0.786520 + 0.617564i \(0.211880\pi\)
\(434\) 0 0
\(435\) 6.10489 0.292707
\(436\) 97.9252 4.68977
\(437\) −25.4338 −1.21667
\(438\) −2.64948 −0.126597
\(439\) −26.9874 −1.28804 −0.644019 0.765010i \(-0.722734\pi\)
−0.644019 + 0.765010i \(0.722734\pi\)
\(440\) 182.828 8.71601
\(441\) 0 0
\(442\) 22.7755 1.08332
\(443\) −35.2051 −1.67264 −0.836322 0.548239i \(-0.815299\pi\)
−0.836322 + 0.548239i \(0.815299\pi\)
\(444\) −45.9072 −2.17866
\(445\) 15.2597 0.723381
\(446\) 14.2144 0.673070
\(447\) −18.1936 −0.860530
\(448\) 0 0
\(449\) −5.93471 −0.280076 −0.140038 0.990146i \(-0.544723\pi\)
−0.140038 + 0.990146i \(0.544723\pi\)
\(450\) 17.7800 0.838156
\(451\) 6.16208 0.290161
\(452\) 49.9588 2.34987
\(453\) −7.96692 −0.374318
\(454\) 31.1993 1.46426
\(455\) 0 0
\(456\) −62.3303 −2.91888
\(457\) −32.5841 −1.52422 −0.762109 0.647448i \(-0.775836\pi\)
−0.762109 + 0.647448i \(0.775836\pi\)
\(458\) 35.5849 1.66277
\(459\) −2.71759 −0.126846
\(460\) −63.4028 −2.95617
\(461\) −33.2676 −1.54943 −0.774714 0.632311i \(-0.782106\pi\)
−0.774714 + 0.632311i \(0.782106\pi\)
\(462\) 0 0
\(463\) 8.98217 0.417437 0.208718 0.977976i \(-0.433071\pi\)
0.208718 + 0.977976i \(0.433071\pi\)
\(464\) −23.2062 −1.07732
\(465\) −23.5436 −1.09181
\(466\) 29.2742 1.35610
\(467\) −1.61981 −0.0749559 −0.0374780 0.999297i \(-0.511932\pi\)
−0.0374780 + 0.999297i \(0.511932\pi\)
\(468\) −16.3149 −0.754157
\(469\) 0 0
\(470\) −45.7954 −2.11238
\(471\) 15.3395 0.706808
\(472\) −83.9386 −3.86359
\(473\) −18.6127 −0.855815
\(474\) −23.3653 −1.07321
\(475\) −47.3084 −2.17066
\(476\) 0 0
\(477\) −2.58012 −0.118135
\(478\) 53.3220 2.43889
\(479\) 32.6374 1.49124 0.745620 0.666371i \(-0.232153\pi\)
0.745620 + 0.666371i \(0.232153\pi\)
\(480\) −59.3761 −2.71014
\(481\) 27.3091 1.24519
\(482\) −28.5990 −1.30265
\(483\) 0 0
\(484\) 141.247 6.42032
\(485\) −15.2501 −0.692471
\(486\) 2.69016 0.122028
\(487\) −35.6551 −1.61569 −0.807844 0.589396i \(-0.799366\pi\)
−0.807844 + 0.589396i \(0.799366\pi\)
\(488\) −39.3778 −1.78255
\(489\) 10.0612 0.454983
\(490\) 0 0
\(491\) −30.7265 −1.38667 −0.693335 0.720616i \(-0.743859\pi\)
−0.693335 + 0.720616i \(0.743859\pi\)
\(492\) −5.23695 −0.236100
\(493\) 4.86922 0.219299
\(494\) 59.9886 2.69901
\(495\) 20.9957 0.943685
\(496\) 89.4953 4.01846
\(497\) 0 0
\(498\) −4.19448 −0.187959
\(499\) −19.2668 −0.862501 −0.431251 0.902232i \(-0.641927\pi\)
−0.431251 + 0.902232i \(0.641927\pi\)
\(500\) −28.7151 −1.28418
\(501\) 25.0532 1.11929
\(502\) −19.4295 −0.867180
\(503\) −29.6789 −1.32332 −0.661659 0.749804i \(-0.730148\pi\)
−0.661659 + 0.749804i \(0.730148\pi\)
\(504\) 0 0
\(505\) 11.9683 0.532584
\(506\) −58.9023 −2.61853
\(507\) −3.29464 −0.146320
\(508\) 77.8414 3.45365
\(509\) −18.6264 −0.825599 −0.412799 0.910822i \(-0.635449\pi\)
−0.412799 + 0.910822i \(0.635449\pi\)
\(510\) 24.9095 1.10301
\(511\) 0 0
\(512\) 0.137808 0.00609032
\(513\) −7.15789 −0.316028
\(514\) −59.2892 −2.61513
\(515\) 39.3232 1.73279
\(516\) 15.8184 0.696365
\(517\) −30.7871 −1.35402
\(518\) 0 0
\(519\) 3.76556 0.165290
\(520\) 92.4320 4.05341
\(521\) 9.20530 0.403292 0.201646 0.979459i \(-0.435371\pi\)
0.201646 + 0.979459i \(0.435371\pi\)
\(522\) −4.82007 −0.210969
\(523\) 20.9820 0.917480 0.458740 0.888571i \(-0.348301\pi\)
0.458740 + 0.888571i \(0.348301\pi\)
\(524\) 32.2138 1.40727
\(525\) 0 0
\(526\) −24.9627 −1.08843
\(527\) −18.7783 −0.817994
\(528\) −79.8098 −3.47328
\(529\) −10.3743 −0.451058
\(530\) 23.6494 1.02726
\(531\) −9.63934 −0.418312
\(532\) 0 0
\(533\) 3.11534 0.134940
\(534\) −12.0482 −0.521377
\(535\) 18.3973 0.795385
\(536\) −15.1386 −0.653887
\(537\) −17.0313 −0.734957
\(538\) 60.7773 2.62029
\(539\) 0 0
\(540\) −17.8435 −0.767864
\(541\) 9.69119 0.416657 0.208328 0.978059i \(-0.433198\pi\)
0.208328 + 0.978059i \(0.433198\pi\)
\(542\) −16.8363 −0.723179
\(543\) −8.03112 −0.344648
\(544\) −47.3580 −2.03046
\(545\) −63.7116 −2.72910
\(546\) 0 0
\(547\) −13.5021 −0.577306 −0.288653 0.957434i \(-0.593207\pi\)
−0.288653 + 0.957434i \(0.593207\pi\)
\(548\) 5.97454 0.255220
\(549\) −4.52207 −0.192997
\(550\) −109.562 −4.67173
\(551\) 12.8251 0.546367
\(552\) 30.9415 1.31696
\(553\) 0 0
\(554\) 56.2433 2.38955
\(555\) 29.8679 1.26782
\(556\) 35.9299 1.52377
\(557\) −25.6589 −1.08720 −0.543602 0.839343i \(-0.682940\pi\)
−0.543602 + 0.839343i \(0.682940\pi\)
\(558\) 18.5887 0.786923
\(559\) −9.40998 −0.398000
\(560\) 0 0
\(561\) 16.7460 0.707017
\(562\) −11.8953 −0.501774
\(563\) 15.6493 0.659538 0.329769 0.944062i \(-0.393029\pi\)
0.329769 + 0.944062i \(0.393029\pi\)
\(564\) 26.1650 1.10174
\(565\) −32.5039 −1.36745
\(566\) 54.5917 2.29466
\(567\) 0 0
\(568\) −124.340 −5.21719
\(569\) 20.1795 0.845968 0.422984 0.906137i \(-0.360983\pi\)
0.422984 + 0.906137i \(0.360983\pi\)
\(570\) 65.6093 2.74807
\(571\) 36.3684 1.52197 0.760986 0.648769i \(-0.224716\pi\)
0.760986 + 0.648769i \(0.224716\pi\)
\(572\) 100.534 4.20353
\(573\) 0.0253646 0.00105962
\(574\) 0 0
\(575\) 23.4845 0.979370
\(576\) 20.9764 0.874018
\(577\) 11.6347 0.484358 0.242179 0.970232i \(-0.422138\pi\)
0.242179 + 0.970232i \(0.422138\pi\)
\(578\) −25.8650 −1.07584
\(579\) −6.47830 −0.269229
\(580\) 31.9710 1.32752
\(581\) 0 0
\(582\) 12.0406 0.499098
\(583\) 15.8989 0.658465
\(584\) −8.57626 −0.354888
\(585\) 10.6147 0.438864
\(586\) −47.7521 −1.97262
\(587\) 16.6760 0.688291 0.344146 0.938916i \(-0.388169\pi\)
0.344146 + 0.938916i \(0.388169\pi\)
\(588\) 0 0
\(589\) −49.4602 −2.03797
\(590\) 88.3543 3.63749
\(591\) 5.96735 0.245464
\(592\) −113.535 −4.66627
\(593\) 2.82243 0.115903 0.0579516 0.998319i \(-0.481543\pi\)
0.0579516 + 0.998319i \(0.481543\pi\)
\(594\) −16.5770 −0.680161
\(595\) 0 0
\(596\) −95.2792 −3.90279
\(597\) −0.700264 −0.0286599
\(598\) −29.7790 −1.21776
\(599\) 8.38636 0.342658 0.171329 0.985214i \(-0.445194\pi\)
0.171329 + 0.985214i \(0.445194\pi\)
\(600\) 57.5530 2.34959
\(601\) −27.8657 −1.13667 −0.568333 0.822799i \(-0.692411\pi\)
−0.568333 + 0.822799i \(0.692411\pi\)
\(602\) 0 0
\(603\) −1.73848 −0.0707966
\(604\) −41.7224 −1.69766
\(605\) −91.8974 −3.73616
\(606\) −9.44951 −0.383860
\(607\) −28.8976 −1.17292 −0.586459 0.809979i \(-0.699478\pi\)
−0.586459 + 0.809979i \(0.699478\pi\)
\(608\) −124.737 −5.05874
\(609\) 0 0
\(610\) 41.4493 1.67823
\(611\) −15.5649 −0.629690
\(612\) −14.2319 −0.575290
\(613\) 14.9001 0.601811 0.300905 0.953654i \(-0.402711\pi\)
0.300905 + 0.953654i \(0.402711\pi\)
\(614\) 0.0520830 0.00210190
\(615\) 3.40724 0.137393
\(616\) 0 0
\(617\) −31.5116 −1.26861 −0.634305 0.773083i \(-0.718714\pi\)
−0.634305 + 0.773083i \(0.718714\pi\)
\(618\) −31.0473 −1.24891
\(619\) 5.46701 0.219738 0.109869 0.993946i \(-0.464957\pi\)
0.109869 + 0.993946i \(0.464957\pi\)
\(620\) −123.297 −4.95172
\(621\) 3.55326 0.142587
\(622\) −29.7796 −1.19405
\(623\) 0 0
\(624\) −40.3492 −1.61526
\(625\) −14.3639 −0.574556
\(626\) 5.71692 0.228494
\(627\) 44.1075 1.76148
\(628\) 80.3323 3.20561
\(629\) 23.8224 0.949863
\(630\) 0 0
\(631\) 16.3281 0.650011 0.325005 0.945712i \(-0.394634\pi\)
0.325005 + 0.945712i \(0.394634\pi\)
\(632\) −75.6325 −3.00850
\(633\) 5.72349 0.227488
\(634\) −55.3243 −2.19721
\(635\) −50.6448 −2.00978
\(636\) −13.5120 −0.535784
\(637\) 0 0
\(638\) 29.7016 1.17590
\(639\) −14.2790 −0.564867
\(640\) −73.5179 −2.90605
\(641\) 18.7046 0.738787 0.369393 0.929273i \(-0.379566\pi\)
0.369393 + 0.929273i \(0.379566\pi\)
\(642\) −14.5255 −0.573274
\(643\) 10.5311 0.415307 0.207654 0.978202i \(-0.433417\pi\)
0.207654 + 0.978202i \(0.433417\pi\)
\(644\) 0 0
\(645\) −10.2917 −0.405234
\(646\) 52.3295 2.05888
\(647\) −11.2429 −0.442005 −0.221002 0.975273i \(-0.570933\pi\)
−0.221002 + 0.975273i \(0.570933\pi\)
\(648\) 8.70791 0.342079
\(649\) 59.3984 2.33159
\(650\) −55.3907 −2.17260
\(651\) 0 0
\(652\) 52.6900 2.06350
\(653\) 9.58250 0.374992 0.187496 0.982265i \(-0.439963\pi\)
0.187496 + 0.982265i \(0.439963\pi\)
\(654\) 50.3030 1.96700
\(655\) −20.9588 −0.818928
\(656\) −12.9518 −0.505681
\(657\) −0.984881 −0.0384239
\(658\) 0 0
\(659\) −7.57775 −0.295187 −0.147594 0.989048i \(-0.547153\pi\)
−0.147594 + 0.989048i \(0.547153\pi\)
\(660\) 109.953 4.27993
\(661\) −16.6975 −0.649457 −0.324729 0.945807i \(-0.605273\pi\)
−0.324729 + 0.945807i \(0.605273\pi\)
\(662\) −74.3709 −2.89051
\(663\) 8.46623 0.328801
\(664\) −13.5773 −0.526902
\(665\) 0 0
\(666\) −23.5820 −0.913782
\(667\) −6.36652 −0.246513
\(668\) 131.202 5.07638
\(669\) 5.28384 0.204285
\(670\) 15.9350 0.615622
\(671\) 27.8653 1.07573
\(672\) 0 0
\(673\) 30.0090 1.15676 0.578380 0.815767i \(-0.303685\pi\)
0.578380 + 0.815767i \(0.303685\pi\)
\(674\) −25.3403 −0.976072
\(675\) 6.60927 0.254391
\(676\) −17.2539 −0.663611
\(677\) 37.6766 1.44803 0.724014 0.689785i \(-0.242295\pi\)
0.724014 + 0.689785i \(0.242295\pi\)
\(678\) 25.6632 0.985591
\(679\) 0 0
\(680\) 80.6308 3.09205
\(681\) 11.5976 0.444420
\(682\) −114.545 −4.38616
\(683\) 21.5536 0.824727 0.412363 0.911019i \(-0.364703\pi\)
0.412363 + 0.911019i \(0.364703\pi\)
\(684\) −37.4855 −1.43329
\(685\) −3.88712 −0.148519
\(686\) 0 0
\(687\) 13.2278 0.504673
\(688\) 39.1212 1.49148
\(689\) 8.03795 0.306222
\(690\) −32.5692 −1.23989
\(691\) 31.7914 1.20940 0.604701 0.796453i \(-0.293293\pi\)
0.604701 + 0.796453i \(0.293293\pi\)
\(692\) 19.7201 0.749645
\(693\) 0 0
\(694\) −2.52688 −0.0959190
\(695\) −23.3765 −0.886723
\(696\) −15.6023 −0.591405
\(697\) 2.71759 0.102936
\(698\) −8.54820 −0.323554
\(699\) 10.8820 0.411594
\(700\) 0 0
\(701\) −27.0893 −1.02315 −0.511574 0.859239i \(-0.670937\pi\)
−0.511574 + 0.859239i \(0.670937\pi\)
\(702\) −8.38076 −0.316312
\(703\) 62.7461 2.36651
\(704\) −129.258 −4.87161
\(705\) −17.0233 −0.641135
\(706\) −52.2960 −1.96819
\(707\) 0 0
\(708\) −50.4808 −1.89718
\(709\) 32.4047 1.21699 0.608493 0.793560i \(-0.291775\pi\)
0.608493 + 0.793560i \(0.291775\pi\)
\(710\) 130.881 4.91188
\(711\) −8.68549 −0.325731
\(712\) −38.9995 −1.46157
\(713\) 24.5526 0.919504
\(714\) 0 0
\(715\) −65.4087 −2.44615
\(716\) −89.1923 −3.33327
\(717\) 19.8211 0.740234
\(718\) −77.1540 −2.87936
\(719\) 37.4880 1.39806 0.699032 0.715090i \(-0.253614\pi\)
0.699032 + 0.715090i \(0.253614\pi\)
\(720\) −44.1297 −1.64462
\(721\) 0 0
\(722\) 86.7182 3.22732
\(723\) −10.6310 −0.395370
\(724\) −42.0586 −1.56309
\(725\) −11.8421 −0.439805
\(726\) 72.5569 2.69284
\(727\) 45.2143 1.67690 0.838452 0.544975i \(-0.183461\pi\)
0.838452 + 0.544975i \(0.183461\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 9.02743 0.334120
\(731\) −8.20857 −0.303605
\(732\) −23.6818 −0.875306
\(733\) −31.6823 −1.17021 −0.585106 0.810957i \(-0.698947\pi\)
−0.585106 + 0.810957i \(0.698947\pi\)
\(734\) 96.0119 3.54386
\(735\) 0 0
\(736\) 61.9208 2.28243
\(737\) 10.7127 0.394607
\(738\) −2.69016 −0.0990261
\(739\) 11.4430 0.420937 0.210469 0.977601i \(-0.432501\pi\)
0.210469 + 0.977601i \(0.432501\pi\)
\(740\) 156.417 5.74999
\(741\) 22.2993 0.819184
\(742\) 0 0
\(743\) 6.82660 0.250444 0.125222 0.992129i \(-0.460036\pi\)
0.125222 + 0.992129i \(0.460036\pi\)
\(744\) 60.1707 2.20597
\(745\) 61.9901 2.27114
\(746\) 17.7628 0.650342
\(747\) −1.55919 −0.0570479
\(748\) 87.6981 3.20656
\(749\) 0 0
\(750\) −14.7506 −0.538615
\(751\) 29.9121 1.09151 0.545754 0.837945i \(-0.316243\pi\)
0.545754 + 0.837945i \(0.316243\pi\)
\(752\) 64.7099 2.35973
\(753\) −7.22243 −0.263200
\(754\) 15.0162 0.546856
\(755\) 27.1452 0.987914
\(756\) 0 0
\(757\) 38.1911 1.38808 0.694039 0.719938i \(-0.255830\pi\)
0.694039 + 0.719938i \(0.255830\pi\)
\(758\) 17.7810 0.645836
\(759\) −21.8955 −0.794755
\(760\) 212.374 7.70362
\(761\) −8.15452 −0.295601 −0.147801 0.989017i \(-0.547219\pi\)
−0.147801 + 0.989017i \(0.547219\pi\)
\(762\) 39.9862 1.44855
\(763\) 0 0
\(764\) 0.132833 0.00480574
\(765\) 9.25948 0.334777
\(766\) −75.2658 −2.71946
\(767\) 30.0298 1.08431
\(768\) 16.0927 0.580694
\(769\) 5.15883 0.186032 0.0930160 0.995665i \(-0.470349\pi\)
0.0930160 + 0.995665i \(0.470349\pi\)
\(770\) 0 0
\(771\) −22.0393 −0.793726
\(772\) −33.9266 −1.22104
\(773\) −2.29140 −0.0824158 −0.0412079 0.999151i \(-0.513121\pi\)
−0.0412079 + 0.999151i \(0.513121\pi\)
\(774\) 8.12570 0.292072
\(775\) 45.6693 1.64049
\(776\) 38.9748 1.39911
\(777\) 0 0
\(778\) −64.4850 −2.31190
\(779\) 7.15789 0.256458
\(780\) 55.5887 1.99040
\(781\) 87.9882 3.14846
\(782\) −25.9770 −0.928936
\(783\) −1.79174 −0.0640316
\(784\) 0 0
\(785\) −52.2654 −1.86543
\(786\) 16.5479 0.590242
\(787\) −5.23569 −0.186632 −0.0933161 0.995637i \(-0.529747\pi\)
−0.0933161 + 0.995637i \(0.529747\pi\)
\(788\) 31.2507 1.11326
\(789\) −9.27928 −0.330351
\(790\) 79.6112 2.83244
\(791\) 0 0
\(792\) −53.6589 −1.90668
\(793\) 14.0878 0.500272
\(794\) −16.8716 −0.598749
\(795\) 8.79108 0.311787
\(796\) −3.66725 −0.129982
\(797\) 36.8582 1.30558 0.652792 0.757537i \(-0.273598\pi\)
0.652792 + 0.757537i \(0.273598\pi\)
\(798\) 0 0
\(799\) −13.5777 −0.480344
\(800\) 115.176 4.07210
\(801\) −4.47862 −0.158244
\(802\) 6.16150 0.217570
\(803\) 6.06891 0.214167
\(804\) −9.10436 −0.321086
\(805\) 0 0
\(806\) −57.9102 −2.03980
\(807\) 22.5924 0.795292
\(808\) −30.5876 −1.07607
\(809\) 30.4494 1.07054 0.535272 0.844680i \(-0.320209\pi\)
0.535272 + 0.844680i \(0.320209\pi\)
\(810\) −9.16601 −0.322061
\(811\) −25.5091 −0.895747 −0.447874 0.894097i \(-0.647819\pi\)
−0.447874 + 0.894097i \(0.647819\pi\)
\(812\) 0 0
\(813\) −6.25846 −0.219494
\(814\) 145.314 5.09325
\(815\) −34.2809 −1.20081
\(816\) −35.1976 −1.23216
\(817\) −21.6206 −0.756409
\(818\) −17.6190 −0.616034
\(819\) 0 0
\(820\) 17.8435 0.623124
\(821\) 0.309981 0.0108184 0.00540921 0.999985i \(-0.498278\pi\)
0.00540921 + 0.999985i \(0.498278\pi\)
\(822\) 3.06905 0.107045
\(823\) −26.6484 −0.928904 −0.464452 0.885598i \(-0.653749\pi\)
−0.464452 + 0.885598i \(0.653749\pi\)
\(824\) −100.499 −3.50104
\(825\) −40.7268 −1.41793
\(826\) 0 0
\(827\) −29.5685 −1.02820 −0.514099 0.857731i \(-0.671874\pi\)
−0.514099 + 0.857731i \(0.671874\pi\)
\(828\) 18.6083 0.646682
\(829\) 15.7905 0.548427 0.274214 0.961669i \(-0.411582\pi\)
0.274214 + 0.961669i \(0.411582\pi\)
\(830\) 14.2916 0.496068
\(831\) 20.9071 0.725258
\(832\) −65.3488 −2.26556
\(833\) 0 0
\(834\) 18.4568 0.639105
\(835\) −85.3623 −2.95408
\(836\) 230.989 7.98891
\(837\) 6.90989 0.238841
\(838\) −78.1957 −2.70123
\(839\) −38.4714 −1.32818 −0.664091 0.747652i \(-0.731181\pi\)
−0.664091 + 0.747652i \(0.731181\pi\)
\(840\) 0 0
\(841\) −25.7897 −0.889299
\(842\) 82.2953 2.83608
\(843\) −4.42179 −0.152295
\(844\) 29.9736 1.03173
\(845\) 11.2256 0.386173
\(846\) 13.4406 0.462098
\(847\) 0 0
\(848\) −33.4171 −1.14755
\(849\) 20.2931 0.696458
\(850\) −48.3187 −1.65732
\(851\) −31.1479 −1.06774
\(852\) −74.7783 −2.56186
\(853\) −53.8643 −1.84428 −0.922140 0.386857i \(-0.873561\pi\)
−0.922140 + 0.386857i \(0.873561\pi\)
\(854\) 0 0
\(855\) 24.3886 0.834073
\(856\) −47.0182 −1.60705
\(857\) 13.5031 0.461257 0.230628 0.973042i \(-0.425922\pi\)
0.230628 + 0.973042i \(0.425922\pi\)
\(858\) 51.6429 1.76306
\(859\) −17.5376 −0.598376 −0.299188 0.954194i \(-0.596716\pi\)
−0.299188 + 0.954194i \(0.596716\pi\)
\(860\) −53.8969 −1.83787
\(861\) 0 0
\(862\) −7.04377 −0.239912
\(863\) −12.3076 −0.418957 −0.209479 0.977813i \(-0.567177\pi\)
−0.209479 + 0.977813i \(0.567177\pi\)
\(864\) 17.4265 0.592860
\(865\) −12.8302 −0.436239
\(866\) 88.0566 2.99228
\(867\) −9.61469 −0.326532
\(868\) 0 0
\(869\) 53.5207 1.81556
\(870\) 16.4231 0.556796
\(871\) 5.41598 0.183513
\(872\) 162.828 5.51406
\(873\) 4.47579 0.151483
\(874\) −68.4211 −2.31438
\(875\) 0 0
\(876\) −5.15777 −0.174265
\(877\) 21.1044 0.712644 0.356322 0.934363i \(-0.384031\pi\)
0.356322 + 0.934363i \(0.384031\pi\)
\(878\) −72.6004 −2.45014
\(879\) −17.7507 −0.598715
\(880\) 271.931 9.16679
\(881\) 13.4813 0.454198 0.227099 0.973872i \(-0.427076\pi\)
0.227099 + 0.973872i \(0.427076\pi\)
\(882\) 0 0
\(883\) −27.9922 −0.942012 −0.471006 0.882130i \(-0.656109\pi\)
−0.471006 + 0.882130i \(0.656109\pi\)
\(884\) 44.3372 1.49122
\(885\) 32.8435 1.10402
\(886\) −94.7072 −3.18175
\(887\) −10.4872 −0.352124 −0.176062 0.984379i \(-0.556336\pi\)
−0.176062 + 0.984379i \(0.556336\pi\)
\(888\) −76.3337 −2.56159
\(889\) 0 0
\(890\) 41.0511 1.37604
\(891\) −6.16208 −0.206437
\(892\) 27.6712 0.926501
\(893\) −35.7624 −1.19674
\(894\) −48.9438 −1.63692
\(895\) 58.0298 1.93972
\(896\) 0 0
\(897\) −11.0696 −0.369604
\(898\) −15.9653 −0.532769
\(899\) −12.3807 −0.412921
\(900\) 34.6124 1.15375
\(901\) 7.01171 0.233594
\(902\) 16.5770 0.551953
\(903\) 0 0
\(904\) 83.0707 2.76289
\(905\) 27.3639 0.909608
\(906\) −21.4323 −0.712039
\(907\) −23.4770 −0.779541 −0.389770 0.920912i \(-0.627446\pi\)
−0.389770 + 0.920912i \(0.627446\pi\)
\(908\) 60.7359 2.01559
\(909\) −3.51262 −0.116506
\(910\) 0 0
\(911\) −9.86885 −0.326970 −0.163485 0.986546i \(-0.552273\pi\)
−0.163485 + 0.986546i \(0.552273\pi\)
\(912\) −92.7073 −3.06984
\(913\) 9.60788 0.317974
\(914\) −87.6563 −2.89941
\(915\) 15.4078 0.509365
\(916\) 69.2735 2.28886
\(917\) 0 0
\(918\) −7.31075 −0.241291
\(919\) −59.3869 −1.95899 −0.979497 0.201460i \(-0.935431\pi\)
−0.979497 + 0.201460i \(0.935431\pi\)
\(920\) −105.425 −3.47576
\(921\) 0.0193606 0.000637953 0
\(922\) −89.4952 −2.94737
\(923\) 44.4839 1.46421
\(924\) 0 0
\(925\) −57.9369 −1.90495
\(926\) 24.1635 0.794061
\(927\) −11.5411 −0.379059
\(928\) −31.2237 −1.02497
\(929\) 51.1638 1.67863 0.839314 0.543647i \(-0.182957\pi\)
0.839314 + 0.543647i \(0.182957\pi\)
\(930\) −63.3361 −2.07687
\(931\) 0 0
\(932\) 56.9883 1.86671
\(933\) −11.0698 −0.362410
\(934\) −4.35755 −0.142583
\(935\) −57.0577 −1.86599
\(936\) −27.1281 −0.886711
\(937\) 8.46933 0.276681 0.138341 0.990385i \(-0.455823\pi\)
0.138341 + 0.990385i \(0.455823\pi\)
\(938\) 0 0
\(939\) 2.12513 0.0693508
\(940\) −89.1502 −2.90776
\(941\) 37.4128 1.21962 0.609812 0.792546i \(-0.291245\pi\)
0.609812 + 0.792546i \(0.291245\pi\)
\(942\) 41.2657 1.34451
\(943\) −3.55326 −0.115710
\(944\) −124.846 −4.06341
\(945\) 0 0
\(946\) −50.0712 −1.62796
\(947\) −24.5064 −0.796351 −0.398176 0.917309i \(-0.630357\pi\)
−0.398176 + 0.917309i \(0.630357\pi\)
\(948\) −45.4855 −1.47730
\(949\) 3.06824 0.0995993
\(950\) −127.267 −4.12909
\(951\) −20.5654 −0.666880
\(952\) 0 0
\(953\) 38.4568 1.24574 0.622869 0.782326i \(-0.285967\pi\)
0.622869 + 0.782326i \(0.285967\pi\)
\(954\) −6.94093 −0.224721
\(955\) −0.0864233 −0.00279659
\(956\) 103.802 3.35721
\(957\) 11.0409 0.356900
\(958\) 87.7997 2.83668
\(959\) 0 0
\(960\) −71.4717 −2.30674
\(961\) 16.7466 0.540213
\(962\) 73.4659 2.36863
\(963\) −5.39948 −0.173996
\(964\) −55.6739 −1.79313
\(965\) 22.0731 0.710559
\(966\) 0 0
\(967\) 39.5442 1.27166 0.635828 0.771831i \(-0.280659\pi\)
0.635828 + 0.771831i \(0.280659\pi\)
\(968\) 234.863 7.54879
\(969\) 19.4522 0.624895
\(970\) −41.0251 −1.31724
\(971\) −19.2833 −0.618831 −0.309416 0.950927i \(-0.600133\pi\)
−0.309416 + 0.950927i \(0.600133\pi\)
\(972\) 5.23695 0.167975
\(973\) 0 0
\(974\) −95.9180 −3.07341
\(975\) −20.5901 −0.659412
\(976\) −58.5687 −1.87474
\(977\) 56.6543 1.81253 0.906266 0.422707i \(-0.138920\pi\)
0.906266 + 0.422707i \(0.138920\pi\)
\(978\) 27.0662 0.865481
\(979\) 27.5976 0.882024
\(980\) 0 0
\(981\) 18.6989 0.597010
\(982\) −82.6593 −2.63776
\(983\) −25.1899 −0.803434 −0.401717 0.915764i \(-0.631587\pi\)
−0.401717 + 0.915764i \(0.631587\pi\)
\(984\) −8.70791 −0.277598
\(985\) −20.3322 −0.647837
\(986\) 13.0990 0.417156
\(987\) 0 0
\(988\) 116.780 3.71527
\(989\) 10.7327 0.341281
\(990\) 56.4817 1.79511
\(991\) −31.5924 −1.00357 −0.501783 0.864994i \(-0.667322\pi\)
−0.501783 + 0.864994i \(0.667322\pi\)
\(992\) 120.415 3.82318
\(993\) −27.6456 −0.877305
\(994\) 0 0
\(995\) 2.38597 0.0756402
\(996\) −8.16542 −0.258731
\(997\) −49.0226 −1.55256 −0.776280 0.630388i \(-0.782896\pi\)
−0.776280 + 0.630388i \(0.782896\pi\)
\(998\) −51.8308 −1.64067
\(999\) −8.76601 −0.277344
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 \(a_p\))