Properties

Label 4005.2.a.p.1.2
Level 4005
Weight 2
Character 4005.1
Self dual Yes
Analytic conductor 31.980
Analytic rank 1
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4005.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9800860095\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.23321\)
Character \(\chi\) = 4005.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.23321 q^{2} +2.98721 q^{4} +1.00000 q^{5} +1.87039 q^{7} -2.20463 q^{8} +O(q^{10})\) \(q-2.23321 q^{2} +2.98721 q^{4} +1.00000 q^{5} +1.87039 q^{7} -2.20463 q^{8} -2.23321 q^{10} -2.02857 q^{11} +5.20418 q^{13} -4.17696 q^{14} -1.05101 q^{16} +1.73901 q^{17} -5.29579 q^{19} +2.98721 q^{20} +4.53022 q^{22} -3.33379 q^{23} +1.00000 q^{25} -11.6220 q^{26} +5.58724 q^{28} +3.53903 q^{29} -4.98395 q^{31} +6.75639 q^{32} -3.88356 q^{34} +1.87039 q^{35} -7.17561 q^{37} +11.8266 q^{38} -2.20463 q^{40} +1.08840 q^{41} -4.73941 q^{43} -6.05976 q^{44} +7.44504 q^{46} -7.45521 q^{47} -3.50165 q^{49} -2.23321 q^{50} +15.5460 q^{52} -12.1190 q^{53} -2.02857 q^{55} -4.12352 q^{56} -7.90338 q^{58} -3.66019 q^{59} +11.4032 q^{61} +11.1302 q^{62} -12.9864 q^{64} +5.20418 q^{65} -9.52615 q^{67} +5.19477 q^{68} -4.17696 q^{70} -2.81801 q^{71} +1.11516 q^{73} +16.0246 q^{74} -15.8196 q^{76} -3.79422 q^{77} -6.37686 q^{79} -1.05101 q^{80} -2.43062 q^{82} -11.6127 q^{83} +1.73901 q^{85} +10.5841 q^{86} +4.47226 q^{88} -1.00000 q^{89} +9.73384 q^{91} -9.95872 q^{92} +16.6490 q^{94} -5.29579 q^{95} +16.0880 q^{97} +7.81989 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} + O(q^{10}) \) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} - q^{10} - 14q^{11} - 7q^{13} - 15q^{14} + 9q^{16} - 17q^{17} + 17q^{19} + 7q^{20} + 2q^{22} + q^{23} + 8q^{25} - 3q^{26} - 29q^{28} - 10q^{29} + q^{31} - 2q^{32} - 16q^{34} - 6q^{35} - 11q^{37} + 30q^{38} - 3q^{40} - 15q^{41} - 5q^{43} - 7q^{44} - 12q^{46} - 12q^{47} + 4q^{49} - q^{50} - 14q^{52} + q^{53} - 14q^{55} - 3q^{56} - 37q^{58} - 26q^{59} + 13q^{61} - 22q^{62} - 15q^{64} - 7q^{65} - 25q^{67} - 23q^{68} - 15q^{70} - 28q^{71} - 17q^{73} + 5q^{74} + 8q^{76} - 7q^{79} + 9q^{80} + 5q^{82} - 44q^{83} - 17q^{85} + 13q^{86} - 66q^{88} - 8q^{89} + 27q^{91} - 15q^{92} - 27q^{94} + 17q^{95} + q^{97} + 34q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23321 −1.57911 −0.789557 0.613677i \(-0.789690\pi\)
−0.789557 + 0.613677i \(0.789690\pi\)
\(3\) 0 0
\(4\) 2.98721 1.49360
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.87039 0.706941 0.353470 0.935446i \(-0.385002\pi\)
0.353470 + 0.935446i \(0.385002\pi\)
\(8\) −2.20463 −0.779456
\(9\) 0 0
\(10\) −2.23321 −0.706202
\(11\) −2.02857 −0.611637 −0.305819 0.952090i \(-0.598930\pi\)
−0.305819 + 0.952090i \(0.598930\pi\)
\(12\) 0 0
\(13\) 5.20418 1.44338 0.721690 0.692216i \(-0.243366\pi\)
0.721690 + 0.692216i \(0.243366\pi\)
\(14\) −4.17696 −1.11634
\(15\) 0 0
\(16\) −1.05101 −0.262753
\(17\) 1.73901 0.421771 0.210886 0.977511i \(-0.432365\pi\)
0.210886 + 0.977511i \(0.432365\pi\)
\(18\) 0 0
\(19\) −5.29579 −1.21494 −0.607469 0.794343i \(-0.707815\pi\)
−0.607469 + 0.794343i \(0.707815\pi\)
\(20\) 2.98721 0.667960
\(21\) 0 0
\(22\) 4.53022 0.965845
\(23\) −3.33379 −0.695143 −0.347572 0.937653i \(-0.612994\pi\)
−0.347572 + 0.937653i \(0.612994\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −11.6220 −2.27926
\(27\) 0 0
\(28\) 5.58724 1.05589
\(29\) 3.53903 0.657182 0.328591 0.944472i \(-0.393426\pi\)
0.328591 + 0.944472i \(0.393426\pi\)
\(30\) 0 0
\(31\) −4.98395 −0.895144 −0.447572 0.894248i \(-0.647711\pi\)
−0.447572 + 0.894248i \(0.647711\pi\)
\(32\) 6.75639 1.19437
\(33\) 0 0
\(34\) −3.88356 −0.666025
\(35\) 1.87039 0.316153
\(36\) 0 0
\(37\) −7.17561 −1.17966 −0.589831 0.807526i \(-0.700806\pi\)
−0.589831 + 0.807526i \(0.700806\pi\)
\(38\) 11.8266 1.91853
\(39\) 0 0
\(40\) −2.20463 −0.348583
\(41\) 1.08840 0.169979 0.0849896 0.996382i \(-0.472914\pi\)
0.0849896 + 0.996382i \(0.472914\pi\)
\(42\) 0 0
\(43\) −4.73941 −0.722753 −0.361377 0.932420i \(-0.617693\pi\)
−0.361377 + 0.932420i \(0.617693\pi\)
\(44\) −6.05976 −0.913543
\(45\) 0 0
\(46\) 7.44504 1.09771
\(47\) −7.45521 −1.08745 −0.543727 0.839262i \(-0.682987\pi\)
−0.543727 + 0.839262i \(0.682987\pi\)
\(48\) 0 0
\(49\) −3.50165 −0.500235
\(50\) −2.23321 −0.315823
\(51\) 0 0
\(52\) 15.5460 2.15584
\(53\) −12.1190 −1.66468 −0.832340 0.554266i \(-0.812999\pi\)
−0.832340 + 0.554266i \(0.812999\pi\)
\(54\) 0 0
\(55\) −2.02857 −0.273533
\(56\) −4.12352 −0.551029
\(57\) 0 0
\(58\) −7.90338 −1.03777
\(59\) −3.66019 −0.476516 −0.238258 0.971202i \(-0.576576\pi\)
−0.238258 + 0.971202i \(0.576576\pi\)
\(60\) 0 0
\(61\) 11.4032 1.46003 0.730017 0.683429i \(-0.239512\pi\)
0.730017 + 0.683429i \(0.239512\pi\)
\(62\) 11.1302 1.41353
\(63\) 0 0
\(64\) −12.9864 −1.62330
\(65\) 5.20418 0.645499
\(66\) 0 0
\(67\) −9.52615 −1.16380 −0.581902 0.813259i \(-0.697691\pi\)
−0.581902 + 0.813259i \(0.697691\pi\)
\(68\) 5.19477 0.629959
\(69\) 0 0
\(70\) −4.17696 −0.499243
\(71\) −2.81801 −0.334436 −0.167218 0.985920i \(-0.553478\pi\)
−0.167218 + 0.985920i \(0.553478\pi\)
\(72\) 0 0
\(73\) 1.11516 0.130519 0.0652597 0.997868i \(-0.479212\pi\)
0.0652597 + 0.997868i \(0.479212\pi\)
\(74\) 16.0246 1.86282
\(75\) 0 0
\(76\) −15.8196 −1.81464
\(77\) −3.79422 −0.432391
\(78\) 0 0
\(79\) −6.37686 −0.717453 −0.358727 0.933443i \(-0.616789\pi\)
−0.358727 + 0.933443i \(0.616789\pi\)
\(80\) −1.05101 −0.117507
\(81\) 0 0
\(82\) −2.43062 −0.268417
\(83\) −11.6127 −1.27466 −0.637328 0.770593i \(-0.719960\pi\)
−0.637328 + 0.770593i \(0.719960\pi\)
\(84\) 0 0
\(85\) 1.73901 0.188622
\(86\) 10.5841 1.14131
\(87\) 0 0
\(88\) 4.47226 0.476744
\(89\) −1.00000 −0.106000
\(90\) 0 0
\(91\) 9.73384 1.02038
\(92\) −9.95872 −1.03827
\(93\) 0 0
\(94\) 16.6490 1.71721
\(95\) −5.29579 −0.543337
\(96\) 0 0
\(97\) 16.0880 1.63349 0.816745 0.576999i \(-0.195776\pi\)
0.816745 + 0.576999i \(0.195776\pi\)
\(98\) 7.81989 0.789928
\(99\) 0 0
\(100\) 2.98721 0.298721
\(101\) −4.93597 −0.491147 −0.245574 0.969378i \(-0.578976\pi\)
−0.245574 + 0.969378i \(0.578976\pi\)
\(102\) 0 0
\(103\) −17.7749 −1.75141 −0.875706 0.482844i \(-0.839604\pi\)
−0.875706 + 0.482844i \(0.839604\pi\)
\(104\) −11.4733 −1.12505
\(105\) 0 0
\(106\) 27.0643 2.62872
\(107\) −12.1644 −1.17597 −0.587987 0.808871i \(-0.700079\pi\)
−0.587987 + 0.808871i \(0.700079\pi\)
\(108\) 0 0
\(109\) 2.87280 0.275164 0.137582 0.990490i \(-0.456067\pi\)
0.137582 + 0.990490i \(0.456067\pi\)
\(110\) 4.53022 0.431939
\(111\) 0 0
\(112\) −1.96580 −0.185751
\(113\) 1.44516 0.135949 0.0679744 0.997687i \(-0.478346\pi\)
0.0679744 + 0.997687i \(0.478346\pi\)
\(114\) 0 0
\(115\) −3.33379 −0.310878
\(116\) 10.5718 0.981568
\(117\) 0 0
\(118\) 8.17395 0.752473
\(119\) 3.25262 0.298167
\(120\) 0 0
\(121\) −6.88490 −0.625900
\(122\) −25.4657 −2.30556
\(123\) 0 0
\(124\) −14.8881 −1.33699
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 12.5720 1.11559 0.557794 0.829979i \(-0.311648\pi\)
0.557794 + 0.829979i \(0.311648\pi\)
\(128\) 15.4885 1.36900
\(129\) 0 0
\(130\) −11.6220 −1.01932
\(131\) −0.192392 −0.0168093 −0.00840467 0.999965i \(-0.502675\pi\)
−0.00840467 + 0.999965i \(0.502675\pi\)
\(132\) 0 0
\(133\) −9.90520 −0.858889
\(134\) 21.2738 1.83778
\(135\) 0 0
\(136\) −3.83388 −0.328752
\(137\) −12.8576 −1.09850 −0.549249 0.835659i \(-0.685086\pi\)
−0.549249 + 0.835659i \(0.685086\pi\)
\(138\) 0 0
\(139\) 8.48167 0.719406 0.359703 0.933067i \(-0.382878\pi\)
0.359703 + 0.933067i \(0.382878\pi\)
\(140\) 5.58724 0.472208
\(141\) 0 0
\(142\) 6.29319 0.528113
\(143\) −10.5571 −0.882825
\(144\) 0 0
\(145\) 3.53903 0.293901
\(146\) −2.49038 −0.206105
\(147\) 0 0
\(148\) −21.4350 −1.76195
\(149\) 17.0248 1.39473 0.697363 0.716718i \(-0.254357\pi\)
0.697363 + 0.716718i \(0.254357\pi\)
\(150\) 0 0
\(151\) 14.8408 1.20772 0.603862 0.797089i \(-0.293628\pi\)
0.603862 + 0.797089i \(0.293628\pi\)
\(152\) 11.6753 0.946991
\(153\) 0 0
\(154\) 8.47327 0.682795
\(155\) −4.98395 −0.400320
\(156\) 0 0
\(157\) −9.36339 −0.747280 −0.373640 0.927574i \(-0.621890\pi\)
−0.373640 + 0.927574i \(0.621890\pi\)
\(158\) 14.2408 1.13294
\(159\) 0 0
\(160\) 6.75639 0.534140
\(161\) −6.23549 −0.491425
\(162\) 0 0
\(163\) −10.4206 −0.816203 −0.408101 0.912937i \(-0.633809\pi\)
−0.408101 + 0.912937i \(0.633809\pi\)
\(164\) 3.25127 0.253882
\(165\) 0 0
\(166\) 25.9335 2.01283
\(167\) 11.1930 0.866143 0.433072 0.901359i \(-0.357430\pi\)
0.433072 + 0.901359i \(0.357430\pi\)
\(168\) 0 0
\(169\) 14.0835 1.08335
\(170\) −3.88356 −0.297856
\(171\) 0 0
\(172\) −14.1576 −1.07951
\(173\) 9.43068 0.717001 0.358501 0.933530i \(-0.383288\pi\)
0.358501 + 0.933530i \(0.383288\pi\)
\(174\) 0 0
\(175\) 1.87039 0.141388
\(176\) 2.13205 0.160709
\(177\) 0 0
\(178\) 2.23321 0.167386
\(179\) −2.26640 −0.169399 −0.0846993 0.996407i \(-0.526993\pi\)
−0.0846993 + 0.996407i \(0.526993\pi\)
\(180\) 0 0
\(181\) −4.33424 −0.322161 −0.161081 0.986941i \(-0.551498\pi\)
−0.161081 + 0.986941i \(0.551498\pi\)
\(182\) −21.7377 −1.61130
\(183\) 0 0
\(184\) 7.34979 0.541834
\(185\) −7.17561 −0.527561
\(186\) 0 0
\(187\) −3.52770 −0.257971
\(188\) −22.2702 −1.62422
\(189\) 0 0
\(190\) 11.8266 0.857991
\(191\) −12.6806 −0.917534 −0.458767 0.888557i \(-0.651709\pi\)
−0.458767 + 0.888557i \(0.651709\pi\)
\(192\) 0 0
\(193\) −20.3722 −1.46643 −0.733213 0.679999i \(-0.761980\pi\)
−0.733213 + 0.679999i \(0.761980\pi\)
\(194\) −35.9278 −2.57947
\(195\) 0 0
\(196\) −10.4601 −0.747153
\(197\) 19.8739 1.41595 0.707977 0.706236i \(-0.249608\pi\)
0.707977 + 0.706236i \(0.249608\pi\)
\(198\) 0 0
\(199\) 11.7504 0.832966 0.416483 0.909144i \(-0.363263\pi\)
0.416483 + 0.909144i \(0.363263\pi\)
\(200\) −2.20463 −0.155891
\(201\) 0 0
\(202\) 11.0230 0.775578
\(203\) 6.61937 0.464588
\(204\) 0 0
\(205\) 1.08840 0.0760170
\(206\) 39.6950 2.76568
\(207\) 0 0
\(208\) −5.46965 −0.379252
\(209\) 10.7429 0.743102
\(210\) 0 0
\(211\) 14.8159 1.01997 0.509983 0.860184i \(-0.329652\pi\)
0.509983 + 0.860184i \(0.329652\pi\)
\(212\) −36.2021 −2.48637
\(213\) 0 0
\(214\) 27.1655 1.85700
\(215\) −4.73941 −0.323225
\(216\) 0 0
\(217\) −9.32192 −0.632813
\(218\) −6.41555 −0.434516
\(219\) 0 0
\(220\) −6.05976 −0.408549
\(221\) 9.05011 0.608776
\(222\) 0 0
\(223\) 11.4234 0.764965 0.382482 0.923963i \(-0.375069\pi\)
0.382482 + 0.923963i \(0.375069\pi\)
\(224\) 12.6371 0.844351
\(225\) 0 0
\(226\) −3.22733 −0.214679
\(227\) −4.98795 −0.331062 −0.165531 0.986205i \(-0.552934\pi\)
−0.165531 + 0.986205i \(0.552934\pi\)
\(228\) 0 0
\(229\) 10.1895 0.673340 0.336670 0.941623i \(-0.390699\pi\)
0.336670 + 0.941623i \(0.390699\pi\)
\(230\) 7.44504 0.490911
\(231\) 0 0
\(232\) −7.80227 −0.512244
\(233\) 12.1002 0.792710 0.396355 0.918097i \(-0.370275\pi\)
0.396355 + 0.918097i \(0.370275\pi\)
\(234\) 0 0
\(235\) −7.45521 −0.486324
\(236\) −10.9337 −0.711725
\(237\) 0 0
\(238\) −7.26377 −0.470840
\(239\) −18.0630 −1.16840 −0.584200 0.811610i \(-0.698592\pi\)
−0.584200 + 0.811610i \(0.698592\pi\)
\(240\) 0 0
\(241\) 24.6768 1.58957 0.794785 0.606892i \(-0.207584\pi\)
0.794785 + 0.606892i \(0.207584\pi\)
\(242\) 15.3754 0.988368
\(243\) 0 0
\(244\) 34.0638 2.18071
\(245\) −3.50165 −0.223712
\(246\) 0 0
\(247\) −27.5603 −1.75362
\(248\) 10.9878 0.697725
\(249\) 0 0
\(250\) −2.23321 −0.141240
\(251\) 10.2474 0.646809 0.323404 0.946261i \(-0.395173\pi\)
0.323404 + 0.946261i \(0.395173\pi\)
\(252\) 0 0
\(253\) 6.76283 0.425176
\(254\) −28.0760 −1.76164
\(255\) 0 0
\(256\) −8.61620 −0.538512
\(257\) −1.31880 −0.0822644 −0.0411322 0.999154i \(-0.513096\pi\)
−0.0411322 + 0.999154i \(0.513096\pi\)
\(258\) 0 0
\(259\) −13.4212 −0.833952
\(260\) 15.5460 0.964119
\(261\) 0 0
\(262\) 0.429650 0.0265439
\(263\) 19.4751 1.20089 0.600444 0.799667i \(-0.294990\pi\)
0.600444 + 0.799667i \(0.294990\pi\)
\(264\) 0 0
\(265\) −12.1190 −0.744467
\(266\) 22.1203 1.35628
\(267\) 0 0
\(268\) −28.4566 −1.73826
\(269\) −24.0346 −1.46541 −0.732707 0.680544i \(-0.761743\pi\)
−0.732707 + 0.680544i \(0.761743\pi\)
\(270\) 0 0
\(271\) 10.4215 0.633061 0.316530 0.948582i \(-0.397482\pi\)
0.316530 + 0.948582i \(0.397482\pi\)
\(272\) −1.82772 −0.110822
\(273\) 0 0
\(274\) 28.7136 1.73465
\(275\) −2.02857 −0.122327
\(276\) 0 0
\(277\) −22.0943 −1.32752 −0.663760 0.747945i \(-0.731041\pi\)
−0.663760 + 0.747945i \(0.731041\pi\)
\(278\) −18.9413 −1.13602
\(279\) 0 0
\(280\) −4.12352 −0.246428
\(281\) 20.7756 1.23937 0.619685 0.784851i \(-0.287260\pi\)
0.619685 + 0.784851i \(0.287260\pi\)
\(282\) 0 0
\(283\) 30.0530 1.78646 0.893232 0.449597i \(-0.148432\pi\)
0.893232 + 0.449597i \(0.148432\pi\)
\(284\) −8.41798 −0.499515
\(285\) 0 0
\(286\) 23.5761 1.39408
\(287\) 2.03573 0.120165
\(288\) 0 0
\(289\) −13.9759 −0.822109
\(290\) −7.90338 −0.464103
\(291\) 0 0
\(292\) 3.33121 0.194944
\(293\) −21.0943 −1.23234 −0.616172 0.787612i \(-0.711317\pi\)
−0.616172 + 0.787612i \(0.711317\pi\)
\(294\) 0 0
\(295\) −3.66019 −0.213104
\(296\) 15.8196 0.919495
\(297\) 0 0
\(298\) −38.0199 −2.20243
\(299\) −17.3496 −1.00336
\(300\) 0 0
\(301\) −8.86454 −0.510944
\(302\) −33.1425 −1.90713
\(303\) 0 0
\(304\) 5.56594 0.319229
\(305\) 11.4032 0.652947
\(306\) 0 0
\(307\) −15.2829 −0.872242 −0.436121 0.899888i \(-0.643648\pi\)
−0.436121 + 0.899888i \(0.643648\pi\)
\(308\) −11.3341 −0.645821
\(309\) 0 0
\(310\) 11.1302 0.632152
\(311\) −4.45836 −0.252810 −0.126405 0.991979i \(-0.540344\pi\)
−0.126405 + 0.991979i \(0.540344\pi\)
\(312\) 0 0
\(313\) 8.03862 0.454369 0.227185 0.973852i \(-0.427048\pi\)
0.227185 + 0.973852i \(0.427048\pi\)
\(314\) 20.9104 1.18004
\(315\) 0 0
\(316\) −19.0490 −1.07159
\(317\) 34.1258 1.91670 0.958349 0.285600i \(-0.0921928\pi\)
0.958349 + 0.285600i \(0.0921928\pi\)
\(318\) 0 0
\(319\) −7.17918 −0.401957
\(320\) −12.9864 −0.725961
\(321\) 0 0
\(322\) 13.9251 0.776017
\(323\) −9.20943 −0.512426
\(324\) 0 0
\(325\) 5.20418 0.288676
\(326\) 23.2713 1.28888
\(327\) 0 0
\(328\) −2.39952 −0.132491
\(329\) −13.9441 −0.768765
\(330\) 0 0
\(331\) −4.76450 −0.261881 −0.130940 0.991390i \(-0.541800\pi\)
−0.130940 + 0.991390i \(0.541800\pi\)
\(332\) −34.6894 −1.90383
\(333\) 0 0
\(334\) −24.9964 −1.36774
\(335\) −9.52615 −0.520469
\(336\) 0 0
\(337\) −23.4733 −1.27867 −0.639335 0.768928i \(-0.720790\pi\)
−0.639335 + 0.768928i \(0.720790\pi\)
\(338\) −31.4513 −1.71073
\(339\) 0 0
\(340\) 5.19477 0.281726
\(341\) 10.1103 0.547503
\(342\) 0 0
\(343\) −19.6422 −1.06058
\(344\) 10.4487 0.563354
\(345\) 0 0
\(346\) −21.0606 −1.13223
\(347\) −25.5270 −1.37036 −0.685181 0.728373i \(-0.740277\pi\)
−0.685181 + 0.728373i \(0.740277\pi\)
\(348\) 0 0
\(349\) −1.62004 −0.0867185 −0.0433593 0.999060i \(-0.513806\pi\)
−0.0433593 + 0.999060i \(0.513806\pi\)
\(350\) −4.17696 −0.223268
\(351\) 0 0
\(352\) −13.7058 −0.730523
\(353\) −6.69225 −0.356192 −0.178096 0.984013i \(-0.556994\pi\)
−0.178096 + 0.984013i \(0.556994\pi\)
\(354\) 0 0
\(355\) −2.81801 −0.149564
\(356\) −2.98721 −0.158322
\(357\) 0 0
\(358\) 5.06133 0.267500
\(359\) −30.0892 −1.58805 −0.794025 0.607886i \(-0.792018\pi\)
−0.794025 + 0.607886i \(0.792018\pi\)
\(360\) 0 0
\(361\) 9.04544 0.476076
\(362\) 9.67924 0.508729
\(363\) 0 0
\(364\) 29.0770 1.52405
\(365\) 1.11516 0.0583700
\(366\) 0 0
\(367\) −2.37916 −0.124191 −0.0620955 0.998070i \(-0.519778\pi\)
−0.0620955 + 0.998070i \(0.519778\pi\)
\(368\) 3.50385 0.182651
\(369\) 0 0
\(370\) 16.0246 0.833080
\(371\) −22.6673 −1.17683
\(372\) 0 0
\(373\) −27.0739 −1.40183 −0.700917 0.713242i \(-0.747226\pi\)
−0.700917 + 0.713242i \(0.747226\pi\)
\(374\) 7.87808 0.407366
\(375\) 0 0
\(376\) 16.4360 0.847622
\(377\) 18.4178 0.948563
\(378\) 0 0
\(379\) −3.29019 −0.169006 −0.0845029 0.996423i \(-0.526930\pi\)
−0.0845029 + 0.996423i \(0.526930\pi\)
\(380\) −15.8196 −0.811530
\(381\) 0 0
\(382\) 28.3183 1.44889
\(383\) 10.8612 0.554981 0.277491 0.960728i \(-0.410497\pi\)
0.277491 + 0.960728i \(0.410497\pi\)
\(384\) 0 0
\(385\) −3.79422 −0.193371
\(386\) 45.4954 2.31566
\(387\) 0 0
\(388\) 48.0582 2.43979
\(389\) −14.3915 −0.729678 −0.364839 0.931071i \(-0.618876\pi\)
−0.364839 + 0.931071i \(0.618876\pi\)
\(390\) 0 0
\(391\) −5.79749 −0.293192
\(392\) 7.71985 0.389911
\(393\) 0 0
\(394\) −44.3824 −2.23595
\(395\) −6.37686 −0.320855
\(396\) 0 0
\(397\) 6.69988 0.336258 0.168129 0.985765i \(-0.446228\pi\)
0.168129 + 0.985765i \(0.446228\pi\)
\(398\) −26.2411 −1.31535
\(399\) 0 0
\(400\) −1.05101 −0.0525506
\(401\) 4.20979 0.210227 0.105113 0.994460i \(-0.466479\pi\)
0.105113 + 0.994460i \(0.466479\pi\)
\(402\) 0 0
\(403\) −25.9374 −1.29203
\(404\) −14.7448 −0.733579
\(405\) 0 0
\(406\) −14.7824 −0.733638
\(407\) 14.5562 0.721526
\(408\) 0 0
\(409\) −38.7813 −1.91761 −0.958805 0.284065i \(-0.908317\pi\)
−0.958805 + 0.284065i \(0.908317\pi\)
\(410\) −2.43062 −0.120040
\(411\) 0 0
\(412\) −53.0973 −2.61592
\(413\) −6.84597 −0.336868
\(414\) 0 0
\(415\) −11.6127 −0.570044
\(416\) 35.1615 1.72393
\(417\) 0 0
\(418\) −23.9911 −1.17344
\(419\) −12.4519 −0.608313 −0.304156 0.952622i \(-0.598375\pi\)
−0.304156 + 0.952622i \(0.598375\pi\)
\(420\) 0 0
\(421\) −39.4273 −1.92157 −0.960785 0.277294i \(-0.910562\pi\)
−0.960785 + 0.277294i \(0.910562\pi\)
\(422\) −33.0869 −1.61064
\(423\) 0 0
\(424\) 26.7181 1.29754
\(425\) 1.73901 0.0843543
\(426\) 0 0
\(427\) 21.3285 1.03216
\(428\) −36.3375 −1.75644
\(429\) 0 0
\(430\) 10.5841 0.510410
\(431\) 31.3424 1.50971 0.754855 0.655892i \(-0.227707\pi\)
0.754855 + 0.655892i \(0.227707\pi\)
\(432\) 0 0
\(433\) 33.1203 1.59166 0.795830 0.605520i \(-0.207035\pi\)
0.795830 + 0.605520i \(0.207035\pi\)
\(434\) 20.8178 0.999285
\(435\) 0 0
\(436\) 8.58164 0.410986
\(437\) 17.6551 0.844557
\(438\) 0 0
\(439\) −31.6765 −1.51184 −0.755918 0.654666i \(-0.772809\pi\)
−0.755918 + 0.654666i \(0.772809\pi\)
\(440\) 4.47226 0.213207
\(441\) 0 0
\(442\) −20.2107 −0.961327
\(443\) −16.2715 −0.773083 −0.386542 0.922272i \(-0.626330\pi\)
−0.386542 + 0.922272i \(0.626330\pi\)
\(444\) 0 0
\(445\) −1.00000 −0.0474045
\(446\) −25.5107 −1.20797
\(447\) 0 0
\(448\) −24.2896 −1.14758
\(449\) 1.33672 0.0630839 0.0315420 0.999502i \(-0.489958\pi\)
0.0315420 + 0.999502i \(0.489958\pi\)
\(450\) 0 0
\(451\) −2.20789 −0.103966
\(452\) 4.31698 0.203054
\(453\) 0 0
\(454\) 11.1391 0.522785
\(455\) 9.73384 0.456330
\(456\) 0 0
\(457\) 10.8622 0.508114 0.254057 0.967189i \(-0.418235\pi\)
0.254057 + 0.967189i \(0.418235\pi\)
\(458\) −22.7552 −1.06328
\(459\) 0 0
\(460\) −9.95872 −0.464328
\(461\) 21.5031 1.00150 0.500750 0.865592i \(-0.333058\pi\)
0.500750 + 0.865592i \(0.333058\pi\)
\(462\) 0 0
\(463\) −27.7658 −1.29038 −0.645192 0.764020i \(-0.723223\pi\)
−0.645192 + 0.764020i \(0.723223\pi\)
\(464\) −3.71956 −0.172676
\(465\) 0 0
\(466\) −27.0222 −1.25178
\(467\) 7.57551 0.350553 0.175276 0.984519i \(-0.443918\pi\)
0.175276 + 0.984519i \(0.443918\pi\)
\(468\) 0 0
\(469\) −17.8176 −0.822740
\(470\) 16.6490 0.767962
\(471\) 0 0
\(472\) 8.06937 0.371423
\(473\) 9.61423 0.442063
\(474\) 0 0
\(475\) −5.29579 −0.242988
\(476\) 9.71625 0.445343
\(477\) 0 0
\(478\) 40.3385 1.84504
\(479\) 11.9206 0.544668 0.272334 0.962203i \(-0.412204\pi\)
0.272334 + 0.962203i \(0.412204\pi\)
\(480\) 0 0
\(481\) −37.3432 −1.70270
\(482\) −55.1083 −2.51011
\(483\) 0 0
\(484\) −20.5666 −0.934846
\(485\) 16.0880 0.730519
\(486\) 0 0
\(487\) −24.0047 −1.08776 −0.543879 0.839164i \(-0.683045\pi\)
−0.543879 + 0.839164i \(0.683045\pi\)
\(488\) −25.1399 −1.13803
\(489\) 0 0
\(490\) 7.81989 0.353267
\(491\) −7.03441 −0.317459 −0.158729 0.987322i \(-0.550740\pi\)
−0.158729 + 0.987322i \(0.550740\pi\)
\(492\) 0 0
\(493\) 6.15440 0.277180
\(494\) 61.5477 2.76916
\(495\) 0 0
\(496\) 5.23819 0.235202
\(497\) −5.27077 −0.236427
\(498\) 0 0
\(499\) 14.3771 0.643606 0.321803 0.946807i \(-0.395711\pi\)
0.321803 + 0.946807i \(0.395711\pi\)
\(500\) 2.98721 0.133592
\(501\) 0 0
\(502\) −22.8845 −1.02139
\(503\) 23.9794 1.06919 0.534595 0.845108i \(-0.320464\pi\)
0.534595 + 0.845108i \(0.320464\pi\)
\(504\) 0 0
\(505\) −4.93597 −0.219648
\(506\) −15.1028 −0.671401
\(507\) 0 0
\(508\) 37.5553 1.66625
\(509\) −5.59380 −0.247941 −0.123970 0.992286i \(-0.539563\pi\)
−0.123970 + 0.992286i \(0.539563\pi\)
\(510\) 0 0
\(511\) 2.08578 0.0922694
\(512\) −11.7352 −0.518629
\(513\) 0 0
\(514\) 2.94515 0.129905
\(515\) −17.7749 −0.783255
\(516\) 0 0
\(517\) 15.1234 0.665127
\(518\) 29.9722 1.31691
\(519\) 0 0
\(520\) −11.4733 −0.503138
\(521\) −9.47103 −0.414933 −0.207467 0.978242i \(-0.566522\pi\)
−0.207467 + 0.978242i \(0.566522\pi\)
\(522\) 0 0
\(523\) −1.98058 −0.0866048 −0.0433024 0.999062i \(-0.513788\pi\)
−0.0433024 + 0.999062i \(0.513788\pi\)
\(524\) −0.574714 −0.0251065
\(525\) 0 0
\(526\) −43.4920 −1.89634
\(527\) −8.66712 −0.377546
\(528\) 0 0
\(529\) −11.8858 −0.516776
\(530\) 27.0643 1.17560
\(531\) 0 0
\(532\) −29.5889 −1.28284
\(533\) 5.66422 0.245345
\(534\) 0 0
\(535\) −12.1644 −0.525911
\(536\) 21.0017 0.907134
\(537\) 0 0
\(538\) 53.6742 2.31406
\(539\) 7.10334 0.305962
\(540\) 0 0
\(541\) 1.70941 0.0734931 0.0367466 0.999325i \(-0.488301\pi\)
0.0367466 + 0.999325i \(0.488301\pi\)
\(542\) −23.2733 −0.999675
\(543\) 0 0
\(544\) 11.7494 0.503752
\(545\) 2.87280 0.123057
\(546\) 0 0
\(547\) 9.08547 0.388467 0.194233 0.980955i \(-0.437778\pi\)
0.194233 + 0.980955i \(0.437778\pi\)
\(548\) −38.4083 −1.64072
\(549\) 0 0
\(550\) 4.53022 0.193169
\(551\) −18.7420 −0.798435
\(552\) 0 0
\(553\) −11.9272 −0.507197
\(554\) 49.3412 2.09631
\(555\) 0 0
\(556\) 25.3365 1.07451
\(557\) −17.6171 −0.746462 −0.373231 0.927739i \(-0.621750\pi\)
−0.373231 + 0.927739i \(0.621750\pi\)
\(558\) 0 0
\(559\) −24.6647 −1.04321
\(560\) −1.96580 −0.0830702
\(561\) 0 0
\(562\) −46.3962 −1.95711
\(563\) 9.92488 0.418284 0.209142 0.977885i \(-0.432933\pi\)
0.209142 + 0.977885i \(0.432933\pi\)
\(564\) 0 0
\(565\) 1.44516 0.0607982
\(566\) −67.1144 −2.82103
\(567\) 0 0
\(568\) 6.21268 0.260678
\(569\) −15.0033 −0.628970 −0.314485 0.949262i \(-0.601832\pi\)
−0.314485 + 0.949262i \(0.601832\pi\)
\(570\) 0 0
\(571\) 23.1676 0.969532 0.484766 0.874644i \(-0.338905\pi\)
0.484766 + 0.874644i \(0.338905\pi\)
\(572\) −31.5361 −1.31859
\(573\) 0 0
\(574\) −4.54620 −0.189755
\(575\) −3.33379 −0.139029
\(576\) 0 0
\(577\) 14.4982 0.603566 0.301783 0.953377i \(-0.402418\pi\)
0.301783 + 0.953377i \(0.402418\pi\)
\(578\) 31.2109 1.29820
\(579\) 0 0
\(580\) 10.5718 0.438971
\(581\) −21.7202 −0.901106
\(582\) 0 0
\(583\) 24.5844 1.01818
\(584\) −2.45852 −0.101734
\(585\) 0 0
\(586\) 47.1080 1.94601
\(587\) −14.6158 −0.603259 −0.301629 0.953425i \(-0.597531\pi\)
−0.301629 + 0.953425i \(0.597531\pi\)
\(588\) 0 0
\(589\) 26.3940 1.08754
\(590\) 8.17395 0.336516
\(591\) 0 0
\(592\) 7.54165 0.309960
\(593\) 42.3122 1.73755 0.868776 0.495205i \(-0.164907\pi\)
0.868776 + 0.495205i \(0.164907\pi\)
\(594\) 0 0
\(595\) 3.25262 0.133344
\(596\) 50.8566 2.08317
\(597\) 0 0
\(598\) 38.7453 1.58441
\(599\) 9.93515 0.405939 0.202970 0.979185i \(-0.434941\pi\)
0.202970 + 0.979185i \(0.434941\pi\)
\(600\) 0 0
\(601\) −37.0451 −1.51110 −0.755551 0.655090i \(-0.772631\pi\)
−0.755551 + 0.655090i \(0.772631\pi\)
\(602\) 19.7963 0.806839
\(603\) 0 0
\(604\) 44.3324 1.80386
\(605\) −6.88490 −0.279911
\(606\) 0 0
\(607\) −43.6916 −1.77339 −0.886693 0.462359i \(-0.847003\pi\)
−0.886693 + 0.462359i \(0.847003\pi\)
\(608\) −35.7805 −1.45109
\(609\) 0 0
\(610\) −25.4657 −1.03108
\(611\) −38.7982 −1.56961
\(612\) 0 0
\(613\) −33.8920 −1.36889 −0.684443 0.729066i \(-0.739955\pi\)
−0.684443 + 0.729066i \(0.739955\pi\)
\(614\) 34.1299 1.37737
\(615\) 0 0
\(616\) 8.36486 0.337030
\(617\) −28.5621 −1.14987 −0.574933 0.818201i \(-0.694972\pi\)
−0.574933 + 0.818201i \(0.694972\pi\)
\(618\) 0 0
\(619\) 15.7926 0.634759 0.317380 0.948299i \(-0.397197\pi\)
0.317380 + 0.948299i \(0.397197\pi\)
\(620\) −14.8881 −0.597920
\(621\) 0 0
\(622\) 9.95642 0.399216
\(623\) −1.87039 −0.0749356
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −17.9519 −0.717502
\(627\) 0 0
\(628\) −27.9704 −1.11614
\(629\) −12.4784 −0.497548
\(630\) 0 0
\(631\) 30.6532 1.22029 0.610143 0.792291i \(-0.291112\pi\)
0.610143 + 0.792291i \(0.291112\pi\)
\(632\) 14.0587 0.559223
\(633\) 0 0
\(634\) −76.2100 −3.02669
\(635\) 12.5720 0.498906
\(636\) 0 0
\(637\) −18.2232 −0.722029
\(638\) 16.0326 0.634736
\(639\) 0 0
\(640\) 15.4885 0.612236
\(641\) 36.2170 1.43049 0.715243 0.698876i \(-0.246316\pi\)
0.715243 + 0.698876i \(0.246316\pi\)
\(642\) 0 0
\(643\) 2.66217 0.104986 0.0524929 0.998621i \(-0.483283\pi\)
0.0524929 + 0.998621i \(0.483283\pi\)
\(644\) −18.6267 −0.733994
\(645\) 0 0
\(646\) 20.5665 0.809180
\(647\) −17.0540 −0.670463 −0.335232 0.942136i \(-0.608815\pi\)
−0.335232 + 0.942136i \(0.608815\pi\)
\(648\) 0 0
\(649\) 7.42495 0.291455
\(650\) −11.6220 −0.455852
\(651\) 0 0
\(652\) −31.1284 −1.21908
\(653\) −35.8249 −1.40194 −0.700969 0.713192i \(-0.747249\pi\)
−0.700969 + 0.713192i \(0.747249\pi\)
\(654\) 0 0
\(655\) −0.192392 −0.00751737
\(656\) −1.14392 −0.0446625
\(657\) 0 0
\(658\) 31.1401 1.21397
\(659\) 28.2716 1.10131 0.550653 0.834735i \(-0.314379\pi\)
0.550653 + 0.834735i \(0.314379\pi\)
\(660\) 0 0
\(661\) −9.72688 −0.378332 −0.189166 0.981945i \(-0.560578\pi\)
−0.189166 + 0.981945i \(0.560578\pi\)
\(662\) 10.6401 0.413540
\(663\) 0 0
\(664\) 25.6017 0.993538
\(665\) −9.90520 −0.384107
\(666\) 0 0
\(667\) −11.7984 −0.456836
\(668\) 33.4359 1.29367
\(669\) 0 0
\(670\) 21.2738 0.821880
\(671\) −23.1323 −0.893011
\(672\) 0 0
\(673\) −16.4032 −0.632298 −0.316149 0.948710i \(-0.602390\pi\)
−0.316149 + 0.948710i \(0.602390\pi\)
\(674\) 52.4206 2.01917
\(675\) 0 0
\(676\) 42.0703 1.61809
\(677\) −11.8450 −0.455242 −0.227621 0.973750i \(-0.573095\pi\)
−0.227621 + 0.973750i \(0.573095\pi\)
\(678\) 0 0
\(679\) 30.0908 1.15478
\(680\) −3.83388 −0.147022
\(681\) 0 0
\(682\) −22.5784 −0.864570
\(683\) 34.4819 1.31941 0.659706 0.751524i \(-0.270681\pi\)
0.659706 + 0.751524i \(0.270681\pi\)
\(684\) 0 0
\(685\) −12.8576 −0.491263
\(686\) 43.8650 1.67477
\(687\) 0 0
\(688\) 4.98118 0.189906
\(689\) −63.0697 −2.40276
\(690\) 0 0
\(691\) 46.7850 1.77979 0.889893 0.456169i \(-0.150779\pi\)
0.889893 + 0.456169i \(0.150779\pi\)
\(692\) 28.1714 1.07092
\(693\) 0 0
\(694\) 57.0070 2.16396
\(695\) 8.48167 0.321728
\(696\) 0 0
\(697\) 1.89273 0.0716924
\(698\) 3.61787 0.136939
\(699\) 0 0
\(700\) 5.58724 0.211178
\(701\) 31.5835 1.19289 0.596447 0.802653i \(-0.296579\pi\)
0.596447 + 0.802653i \(0.296579\pi\)
\(702\) 0 0
\(703\) 38.0005 1.43322
\(704\) 26.3438 0.992870
\(705\) 0 0
\(706\) 14.9452 0.562469
\(707\) −9.23218 −0.347212
\(708\) 0 0
\(709\) −26.1926 −0.983682 −0.491841 0.870685i \(-0.663676\pi\)
−0.491841 + 0.870685i \(0.663676\pi\)
\(710\) 6.29319 0.236179
\(711\) 0 0
\(712\) 2.20463 0.0826222
\(713\) 16.6154 0.622253
\(714\) 0 0
\(715\) −10.5571 −0.394811
\(716\) −6.77020 −0.253014
\(717\) 0 0
\(718\) 67.1954 2.50771
\(719\) −21.3275 −0.795382 −0.397691 0.917519i \(-0.630188\pi\)
−0.397691 + 0.917519i \(0.630188\pi\)
\(720\) 0 0
\(721\) −33.2460 −1.23814
\(722\) −20.2003 −0.751778
\(723\) 0 0
\(724\) −12.9473 −0.481181
\(725\) 3.53903 0.131436
\(726\) 0 0
\(727\) −13.9598 −0.517739 −0.258869 0.965912i \(-0.583350\pi\)
−0.258869 + 0.965912i \(0.583350\pi\)
\(728\) −21.4596 −0.795344
\(729\) 0 0
\(730\) −2.49038 −0.0921730
\(731\) −8.24187 −0.304837
\(732\) 0 0
\(733\) 46.7619 1.72719 0.863595 0.504186i \(-0.168207\pi\)
0.863595 + 0.504186i \(0.168207\pi\)
\(734\) 5.31315 0.196112
\(735\) 0 0
\(736\) −22.5244 −0.830261
\(737\) 19.3245 0.711826
\(738\) 0 0
\(739\) 41.6242 1.53117 0.765586 0.643334i \(-0.222449\pi\)
0.765586 + 0.643334i \(0.222449\pi\)
\(740\) −21.4350 −0.787967
\(741\) 0 0
\(742\) 50.6208 1.85835
\(743\) −24.3902 −0.894790 −0.447395 0.894336i \(-0.647648\pi\)
−0.447395 + 0.894336i \(0.647648\pi\)
\(744\) 0 0
\(745\) 17.0248 0.623740
\(746\) 60.4616 2.21366
\(747\) 0 0
\(748\) −10.5380 −0.385306
\(749\) −22.7521 −0.831344
\(750\) 0 0
\(751\) 44.6465 1.62917 0.814587 0.580041i \(-0.196963\pi\)
0.814587 + 0.580041i \(0.196963\pi\)
\(752\) 7.83551 0.285732
\(753\) 0 0
\(754\) −41.1306 −1.49789
\(755\) 14.8408 0.540110
\(756\) 0 0
\(757\) −5.48985 −0.199532 −0.0997659 0.995011i \(-0.531809\pi\)
−0.0997659 + 0.995011i \(0.531809\pi\)
\(758\) 7.34768 0.266880
\(759\) 0 0
\(760\) 11.6753 0.423507
\(761\) 13.9520 0.505761 0.252880 0.967498i \(-0.418622\pi\)
0.252880 + 0.967498i \(0.418622\pi\)
\(762\) 0 0
\(763\) 5.37325 0.194525
\(764\) −37.8795 −1.37043
\(765\) 0 0
\(766\) −24.2553 −0.876379
\(767\) −19.0483 −0.687793
\(768\) 0 0
\(769\) 12.3923 0.446876 0.223438 0.974718i \(-0.428272\pi\)
0.223438 + 0.974718i \(0.428272\pi\)
\(770\) 8.47327 0.305355
\(771\) 0 0
\(772\) −60.8561 −2.19026
\(773\) −49.2281 −1.77061 −0.885306 0.465008i \(-0.846051\pi\)
−0.885306 + 0.465008i \(0.846051\pi\)
\(774\) 0 0
\(775\) −4.98395 −0.179029
\(776\) −35.4682 −1.27323
\(777\) 0 0
\(778\) 32.1392 1.15225
\(779\) −5.76393 −0.206514
\(780\) 0 0
\(781\) 5.71653 0.204554
\(782\) 12.9470 0.462983
\(783\) 0 0
\(784\) 3.68027 0.131438
\(785\) −9.36339 −0.334194
\(786\) 0 0
\(787\) 14.2794 0.509006 0.254503 0.967072i \(-0.418088\pi\)
0.254503 + 0.967072i \(0.418088\pi\)
\(788\) 59.3673 2.11487
\(789\) 0 0
\(790\) 14.2408 0.506667
\(791\) 2.70300 0.0961077
\(792\) 0 0
\(793\) 59.3444 2.10738
\(794\) −14.9622 −0.530989
\(795\) 0 0
\(796\) 35.1010 1.24412
\(797\) −28.9742 −1.02632 −0.513160 0.858293i \(-0.671525\pi\)
−0.513160 + 0.858293i \(0.671525\pi\)
\(798\) 0 0
\(799\) −12.9647 −0.458657
\(800\) 6.75639 0.238875
\(801\) 0 0
\(802\) −9.40132 −0.331972
\(803\) −2.26218 −0.0798305
\(804\) 0 0
\(805\) −6.23549 −0.219772
\(806\) 57.9235 2.04027
\(807\) 0 0
\(808\) 10.8820 0.382828
\(809\) −42.1439 −1.48170 −0.740850 0.671671i \(-0.765577\pi\)
−0.740850 + 0.671671i \(0.765577\pi\)
\(810\) 0 0
\(811\) 36.3440 1.27621 0.638104 0.769950i \(-0.279719\pi\)
0.638104 + 0.769950i \(0.279719\pi\)
\(812\) 19.7734 0.693911
\(813\) 0 0
\(814\) −32.5071 −1.13937
\(815\) −10.4206 −0.365017
\(816\) 0 0
\(817\) 25.0989 0.878101
\(818\) 86.6065 3.02813
\(819\) 0 0
\(820\) 3.25127 0.113539
\(821\) −9.36717 −0.326917 −0.163458 0.986550i \(-0.552265\pi\)
−0.163458 + 0.986550i \(0.552265\pi\)
\(822\) 0 0
\(823\) −4.37609 −0.152541 −0.0762705 0.997087i \(-0.524301\pi\)
−0.0762705 + 0.997087i \(0.524301\pi\)
\(824\) 39.1871 1.36515
\(825\) 0 0
\(826\) 15.2885 0.531954
\(827\) −17.4196 −0.605739 −0.302869 0.953032i \(-0.597945\pi\)
−0.302869 + 0.953032i \(0.597945\pi\)
\(828\) 0 0
\(829\) −21.0368 −0.730640 −0.365320 0.930882i \(-0.619040\pi\)
−0.365320 + 0.930882i \(0.619040\pi\)
\(830\) 25.9335 0.900164
\(831\) 0 0
\(832\) −67.5835 −2.34304
\(833\) −6.08939 −0.210985
\(834\) 0 0
\(835\) 11.1930 0.387351
\(836\) 32.0912 1.10990
\(837\) 0 0
\(838\) 27.8075 0.960596
\(839\) −41.2797 −1.42513 −0.712567 0.701604i \(-0.752467\pi\)
−0.712567 + 0.701604i \(0.752467\pi\)
\(840\) 0 0
\(841\) −16.4753 −0.568112
\(842\) 88.0493 3.03438
\(843\) 0 0
\(844\) 44.2581 1.52343
\(845\) 14.0835 0.484487
\(846\) 0 0
\(847\) −12.8774 −0.442474
\(848\) 12.7373 0.437399
\(849\) 0 0
\(850\) −3.88356 −0.133205
\(851\) 23.9220 0.820035
\(852\) 0 0
\(853\) 1.62313 0.0555749 0.0277875 0.999614i \(-0.491154\pi\)
0.0277875 + 0.999614i \(0.491154\pi\)
\(854\) −47.6309 −1.62989
\(855\) 0 0
\(856\) 26.8180 0.916620
\(857\) −21.4347 −0.732196 −0.366098 0.930576i \(-0.619306\pi\)
−0.366098 + 0.930576i \(0.619306\pi\)
\(858\) 0 0
\(859\) 1.93092 0.0658822 0.0329411 0.999457i \(-0.489513\pi\)
0.0329411 + 0.999457i \(0.489513\pi\)
\(860\) −14.1576 −0.482770
\(861\) 0 0
\(862\) −69.9940 −2.38400
\(863\) 35.4312 1.20609 0.603046 0.797707i \(-0.293954\pi\)
0.603046 + 0.797707i \(0.293954\pi\)
\(864\) 0 0
\(865\) 9.43068 0.320653
\(866\) −73.9644 −2.51341
\(867\) 0 0
\(868\) −27.8465 −0.945172
\(869\) 12.9359 0.438821
\(870\) 0 0
\(871\) −49.5758 −1.67981
\(872\) −6.33347 −0.214478
\(873\) 0 0
\(874\) −39.4274 −1.33365
\(875\) 1.87039 0.0632307
\(876\) 0 0
\(877\) 22.3502 0.754713 0.377356 0.926068i \(-0.376833\pi\)
0.377356 + 0.926068i \(0.376833\pi\)
\(878\) 70.7401 2.38736
\(879\) 0 0
\(880\) 2.13205 0.0718715
\(881\) 30.2395 1.01880 0.509398 0.860531i \(-0.329868\pi\)
0.509398 + 0.860531i \(0.329868\pi\)
\(882\) 0 0
\(883\) −36.2381 −1.21951 −0.609755 0.792590i \(-0.708732\pi\)
−0.609755 + 0.792590i \(0.708732\pi\)
\(884\) 27.0345 0.909270
\(885\) 0 0
\(886\) 36.3376 1.22079
\(887\) 53.5776 1.79896 0.899479 0.436963i \(-0.143946\pi\)
0.899479 + 0.436963i \(0.143946\pi\)
\(888\) 0 0
\(889\) 23.5146 0.788655
\(890\) 2.23321 0.0748572
\(891\) 0 0
\(892\) 34.1239 1.14255
\(893\) 39.4813 1.32119
\(894\) 0 0
\(895\) −2.26640 −0.0757574
\(896\) 28.9695 0.967803
\(897\) 0 0
\(898\) −2.98518 −0.0996168
\(899\) −17.6384 −0.588272
\(900\) 0 0
\(901\) −21.0751 −0.702114
\(902\) 4.93068 0.164174
\(903\) 0 0
\(904\) −3.18604 −0.105966
\(905\) −4.33424 −0.144075
\(906\) 0 0
\(907\) 50.5208 1.67751 0.838757 0.544506i \(-0.183283\pi\)
0.838757 + 0.544506i \(0.183283\pi\)
\(908\) −14.9000 −0.494475
\(909\) 0 0
\(910\) −21.7377 −0.720597
\(911\) 1.36013 0.0450630 0.0225315 0.999746i \(-0.492827\pi\)
0.0225315 + 0.999746i \(0.492827\pi\)
\(912\) 0 0
\(913\) 23.5571 0.779627
\(914\) −24.2576 −0.802371
\(915\) 0 0
\(916\) 30.4381 1.00570
\(917\) −0.359847 −0.0118832
\(918\) 0 0
\(919\) −32.2226 −1.06293 −0.531464 0.847081i \(-0.678358\pi\)
−0.531464 + 0.847081i \(0.678358\pi\)
\(920\) 7.34979 0.242315
\(921\) 0 0
\(922\) −48.0209 −1.58148
\(923\) −14.6654 −0.482719
\(924\) 0 0
\(925\) −7.17561 −0.235933
\(926\) 62.0067 2.03767
\(927\) 0 0
\(928\) 23.9111 0.784920
\(929\) 60.6939 1.99130 0.995652 0.0931538i \(-0.0296948\pi\)
0.995652 + 0.0931538i \(0.0296948\pi\)
\(930\) 0 0
\(931\) 18.5440 0.607755
\(932\) 36.1458 1.18399
\(933\) 0 0
\(934\) −16.9177 −0.553563
\(935\) −3.52770 −0.115368
\(936\) 0 0
\(937\) −40.5239 −1.32386 −0.661929 0.749566i \(-0.730262\pi\)
−0.661929 + 0.749566i \(0.730262\pi\)
\(938\) 39.7904 1.29920
\(939\) 0 0
\(940\) −22.2702 −0.726375
\(941\) −32.9515 −1.07419 −0.537093 0.843523i \(-0.680478\pi\)
−0.537093 + 0.843523i \(0.680478\pi\)
\(942\) 0 0
\(943\) −3.62849 −0.118160
\(944\) 3.84690 0.125206
\(945\) 0 0
\(946\) −21.4706 −0.698068
\(947\) −59.2296 −1.92470 −0.962352 0.271808i \(-0.912379\pi\)
−0.962352 + 0.271808i \(0.912379\pi\)
\(948\) 0 0
\(949\) 5.80348 0.188389
\(950\) 11.8266 0.383705
\(951\) 0 0
\(952\) −7.17084 −0.232408
\(953\) 25.0221 0.810545 0.405273 0.914196i \(-0.367177\pi\)
0.405273 + 0.914196i \(0.367177\pi\)
\(954\) 0 0
\(955\) −12.6806 −0.410334
\(956\) −53.9580 −1.74513
\(957\) 0 0
\(958\) −26.6213 −0.860094
\(959\) −24.0487 −0.776573
\(960\) 0 0
\(961\) −6.16025 −0.198718
\(962\) 83.3949 2.68876
\(963\) 0 0
\(964\) 73.7145 2.37419
\(965\) −20.3722 −0.655806
\(966\) 0 0
\(967\) −36.4358 −1.17170 −0.585848 0.810421i \(-0.699239\pi\)
−0.585848 + 0.810421i \(0.699239\pi\)
\(968\) 15.1787 0.487861
\(969\) 0 0
\(970\) −35.9278 −1.15357
\(971\) 57.6118 1.84885 0.924425 0.381363i \(-0.124545\pi\)
0.924425 + 0.381363i \(0.124545\pi\)
\(972\) 0 0
\(973\) 15.8640 0.508577
\(974\) 53.6075 1.71770
\(975\) 0 0
\(976\) −11.9849 −0.383628
\(977\) −25.0812 −0.802420 −0.401210 0.915986i \(-0.631410\pi\)
−0.401210 + 0.915986i \(0.631410\pi\)
\(978\) 0 0
\(979\) 2.02857 0.0648334
\(980\) −10.4601 −0.334137
\(981\) 0 0
\(982\) 15.7093 0.501304
\(983\) −5.65906 −0.180496 −0.0902479 0.995919i \(-0.528766\pi\)
−0.0902479 + 0.995919i \(0.528766\pi\)
\(984\) 0 0
\(985\) 19.8739 0.633234
\(986\) −13.7440 −0.437700
\(987\) 0 0
\(988\) −82.3282 −2.61921
\(989\) 15.8002 0.502417
\(990\) 0 0
\(991\) 29.1538 0.926100 0.463050 0.886332i \(-0.346755\pi\)
0.463050 + 0.886332i \(0.346755\pi\)
\(992\) −33.6735 −1.06914
\(993\) 0 0
\(994\) 11.7707 0.373345
\(995\) 11.7504 0.372514
\(996\) 0 0
\(997\) 8.91059 0.282201 0.141101 0.989995i \(-0.454936\pi\)
0.141101 + 0.989995i \(0.454936\pi\)
\(998\) −32.1070 −1.01633
\(999\) 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 \(a_p\))