Properties

Label 4005.2.a.l.1.1
Level 4005
Weight 2
Character 4005.1
Self dual Yes
Analytic conductor 31.980
Analytic rank 0
Dimension 4
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: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.725.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.477260\)
Character \(\chi\) = 4005.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.77222 q^{2} +1.14077 q^{4} +1.00000 q^{5} -3.19059 q^{7} +1.52274 q^{8} +O(q^{10})\) \(q-1.77222 q^{2} +1.14077 q^{4} +1.00000 q^{5} -3.19059 q^{7} +1.52274 q^{8} -1.77222 q^{10} +2.70504 q^{11} +2.03640 q^{13} +5.65443 q^{14} -4.98018 q^{16} -2.67180 q^{17} +1.45989 q^{19} +1.14077 q^{20} -4.79393 q^{22} +5.62632 q^{23} +1.00000 q^{25} -3.60895 q^{26} -3.63974 q^{28} -3.44007 q^{29} -8.62237 q^{31} +5.78051 q^{32} +4.73503 q^{34} -3.19059 q^{35} +9.46573 q^{37} -2.58725 q^{38} +1.52274 q^{40} +10.1119 q^{41} +2.51878 q^{43} +3.08584 q^{44} -9.97110 q^{46} -1.05810 q^{47} +3.17985 q^{49} -1.77222 q^{50} +2.32307 q^{52} +1.72802 q^{53} +2.70504 q^{55} -4.85844 q^{56} +6.09657 q^{58} +3.39934 q^{59} -14.9071 q^{61} +15.2808 q^{62} -0.283993 q^{64} +2.03640 q^{65} -2.16888 q^{67} -3.04793 q^{68} +5.65443 q^{70} -6.88221 q^{71} -8.79954 q^{73} -16.7754 q^{74} +1.66540 q^{76} -8.63066 q^{77} +5.97939 q^{79} -4.98018 q^{80} -17.9205 q^{82} +7.29685 q^{83} -2.67180 q^{85} -4.46385 q^{86} +4.11907 q^{88} +1.00000 q^{89} -6.49731 q^{91} +6.41837 q^{92} +1.87520 q^{94} +1.45989 q^{95} +15.6505 q^{97} -5.63541 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - q^{2} + 3q^{4} + 4q^{5} + 2q^{7} + 9q^{8} + O(q^{10}) \) \( 4q - q^{2} + 3q^{4} + 4q^{5} + 2q^{7} + 9q^{8} - q^{10} + 14q^{11} - 5q^{13} + 5q^{14} - 3q^{16} + 3q^{17} - q^{19} + 3q^{20} + 2q^{22} + 3q^{23} + 4q^{25} + 9q^{26} + 5q^{28} + 10q^{29} - 11q^{31} + 2q^{32} - 8q^{34} + 2q^{35} + 3q^{37} - 2q^{38} + 9q^{40} + 3q^{41} + 9q^{43} + 9q^{44} - 4q^{46} + 24q^{47} - q^{50} + 8q^{52} - 3q^{53} + 14q^{55} + 13q^{56} + 19q^{58} + 22q^{59} - 3q^{61} + 24q^{62} - 11q^{64} - 5q^{65} - 9q^{67} - 31q^{68} + 5q^{70} - 16q^{71} + 3q^{73} - 31q^{74} - 24q^{76} + 4q^{77} - 27q^{79} - 3q^{80} - 15q^{82} - 6q^{83} + 3q^{85} - 15q^{86} + 30q^{88} + 4q^{89} - 29q^{91} + 17q^{92} + 13q^{94} - q^{95} + 41q^{97} - 22q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.77222 −1.25315 −0.626575 0.779361i \(-0.715544\pi\)
−0.626575 + 0.779361i \(0.715544\pi\)
\(3\) 0 0
\(4\) 1.14077 0.570387
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −3.19059 −1.20593 −0.602964 0.797768i \(-0.706014\pi\)
−0.602964 + 0.797768i \(0.706014\pi\)
\(8\) 1.52274 0.538370
\(9\) 0 0
\(10\) −1.77222 −0.560426
\(11\) 2.70504 0.815599 0.407800 0.913071i \(-0.366296\pi\)
0.407800 + 0.913071i \(0.366296\pi\)
\(12\) 0 0
\(13\) 2.03640 0.564795 0.282398 0.959297i \(-0.408870\pi\)
0.282398 + 0.959297i \(0.408870\pi\)
\(14\) 5.65443 1.51121
\(15\) 0 0
\(16\) −4.98018 −1.24505
\(17\) −2.67180 −0.648008 −0.324004 0.946056i \(-0.605029\pi\)
−0.324004 + 0.946056i \(0.605029\pi\)
\(18\) 0 0
\(19\) 1.45989 0.334921 0.167461 0.985879i \(-0.446443\pi\)
0.167461 + 0.985879i \(0.446443\pi\)
\(20\) 1.14077 0.255085
\(21\) 0 0
\(22\) −4.79393 −1.02207
\(23\) 5.62632 1.17317 0.586585 0.809888i \(-0.300472\pi\)
0.586585 + 0.809888i \(0.300472\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −3.60895 −0.707774
\(27\) 0 0
\(28\) −3.63974 −0.687846
\(29\) −3.44007 −0.638805 −0.319403 0.947619i \(-0.603482\pi\)
−0.319403 + 0.947619i \(0.603482\pi\)
\(30\) 0 0
\(31\) −8.62237 −1.54862 −0.774312 0.632805i \(-0.781904\pi\)
−0.774312 + 0.632805i \(0.781904\pi\)
\(32\) 5.78051 1.02186
\(33\) 0 0
\(34\) 4.73503 0.812052
\(35\) −3.19059 −0.539308
\(36\) 0 0
\(37\) 9.46573 1.55616 0.778079 0.628167i \(-0.216195\pi\)
0.778079 + 0.628167i \(0.216195\pi\)
\(38\) −2.58725 −0.419707
\(39\) 0 0
\(40\) 1.52274 0.240766
\(41\) 10.1119 1.57921 0.789605 0.613616i \(-0.210286\pi\)
0.789605 + 0.613616i \(0.210286\pi\)
\(42\) 0 0
\(43\) 2.51878 0.384111 0.192055 0.981384i \(-0.438485\pi\)
0.192055 + 0.981384i \(0.438485\pi\)
\(44\) 3.08584 0.465207
\(45\) 0 0
\(46\) −9.97110 −1.47016
\(47\) −1.05810 −0.154340 −0.0771702 0.997018i \(-0.524588\pi\)
−0.0771702 + 0.997018i \(0.524588\pi\)
\(48\) 0 0
\(49\) 3.17985 0.454265
\(50\) −1.77222 −0.250630
\(51\) 0 0
\(52\) 2.32307 0.322152
\(53\) 1.72802 0.237362 0.118681 0.992932i \(-0.462133\pi\)
0.118681 + 0.992932i \(0.462133\pi\)
\(54\) 0 0
\(55\) 2.70504 0.364747
\(56\) −4.85844 −0.649236
\(57\) 0 0
\(58\) 6.09657 0.800519
\(59\) 3.39934 0.442556 0.221278 0.975211i \(-0.428977\pi\)
0.221278 + 0.975211i \(0.428977\pi\)
\(60\) 0 0
\(61\) −14.9071 −1.90866 −0.954328 0.298760i \(-0.903427\pi\)
−0.954328 + 0.298760i \(0.903427\pi\)
\(62\) 15.2808 1.94066
\(63\) 0 0
\(64\) −0.283993 −0.0354992
\(65\) 2.03640 0.252584
\(66\) 0 0
\(67\) −2.16888 −0.264971 −0.132486 0.991185i \(-0.542296\pi\)
−0.132486 + 0.991185i \(0.542296\pi\)
\(68\) −3.04793 −0.369615
\(69\) 0 0
\(70\) 5.65443 0.675834
\(71\) −6.88221 −0.816768 −0.408384 0.912810i \(-0.633908\pi\)
−0.408384 + 0.912810i \(0.633908\pi\)
\(72\) 0 0
\(73\) −8.79954 −1.02991 −0.514954 0.857218i \(-0.672191\pi\)
−0.514954 + 0.857218i \(0.672191\pi\)
\(74\) −16.7754 −1.95010
\(75\) 0 0
\(76\) 1.66540 0.191035
\(77\) −8.63066 −0.983555
\(78\) 0 0
\(79\) 5.97939 0.672734 0.336367 0.941731i \(-0.390802\pi\)
0.336367 + 0.941731i \(0.390802\pi\)
\(80\) −4.98018 −0.556801
\(81\) 0 0
\(82\) −17.9205 −1.97899
\(83\) 7.29685 0.800933 0.400467 0.916311i \(-0.368848\pi\)
0.400467 + 0.916311i \(0.368848\pi\)
\(84\) 0 0
\(85\) −2.67180 −0.289798
\(86\) −4.46385 −0.481349
\(87\) 0 0
\(88\) 4.11907 0.439094
\(89\) 1.00000 0.106000
\(90\) 0 0
\(91\) −6.49731 −0.681103
\(92\) 6.41837 0.669161
\(93\) 0 0
\(94\) 1.87520 0.193412
\(95\) 1.45989 0.149781
\(96\) 0 0
\(97\) 15.6505 1.58907 0.794533 0.607222i \(-0.207716\pi\)
0.794533 + 0.607222i \(0.207716\pi\)
\(98\) −5.63541 −0.569262
\(99\) 0 0
\(100\) 1.14077 0.114077
\(101\) −17.0561 −1.69715 −0.848575 0.529075i \(-0.822539\pi\)
−0.848575 + 0.529075i \(0.822539\pi\)
\(102\) 0 0
\(103\) 6.69162 0.659345 0.329673 0.944095i \(-0.393062\pi\)
0.329673 + 0.944095i \(0.393062\pi\)
\(104\) 3.10091 0.304069
\(105\) 0 0
\(106\) −3.06244 −0.297450
\(107\) 15.9256 1.53959 0.769794 0.638292i \(-0.220359\pi\)
0.769794 + 0.638292i \(0.220359\pi\)
\(108\) 0 0
\(109\) −1.65443 −0.158466 −0.0792330 0.996856i \(-0.525247\pi\)
−0.0792330 + 0.996856i \(0.525247\pi\)
\(110\) −4.79393 −0.457083
\(111\) 0 0
\(112\) 15.8897 1.50144
\(113\) 2.74388 0.258123 0.129061 0.991637i \(-0.458804\pi\)
0.129061 + 0.991637i \(0.458804\pi\)
\(114\) 0 0
\(115\) 5.62632 0.524657
\(116\) −3.92434 −0.364366
\(117\) 0 0
\(118\) −6.02438 −0.554590
\(119\) 8.52463 0.781451
\(120\) 0 0
\(121\) −3.68277 −0.334798
\(122\) 26.4187 2.39183
\(123\) 0 0
\(124\) −9.83617 −0.883314
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −0.0122478 −0.00108681 −0.000543407 1.00000i \(-0.500173\pi\)
−0.000543407 1.00000i \(0.500173\pi\)
\(128\) −11.0577 −0.977374
\(129\) 0 0
\(130\) −3.60895 −0.316526
\(131\) 18.4349 1.61067 0.805334 0.592821i \(-0.201986\pi\)
0.805334 + 0.592821i \(0.201986\pi\)
\(132\) 0 0
\(133\) −4.65790 −0.403891
\(134\) 3.84374 0.332049
\(135\) 0 0
\(136\) −4.06846 −0.348868
\(137\) −17.8348 −1.52373 −0.761864 0.647737i \(-0.775715\pi\)
−0.761864 + 0.647737i \(0.775715\pi\)
\(138\) 0 0
\(139\) −7.69547 −0.652721 −0.326361 0.945245i \(-0.605822\pi\)
−0.326361 + 0.945245i \(0.605822\pi\)
\(140\) −3.63974 −0.307614
\(141\) 0 0
\(142\) 12.1968 1.02353
\(143\) 5.50854 0.460647
\(144\) 0 0
\(145\) −3.44007 −0.285682
\(146\) 15.5947 1.29063
\(147\) 0 0
\(148\) 10.7983 0.887612
\(149\) 16.0825 1.31753 0.658764 0.752349i \(-0.271079\pi\)
0.658764 + 0.752349i \(0.271079\pi\)
\(150\) 0 0
\(151\) −3.01304 −0.245198 −0.122599 0.992456i \(-0.539123\pi\)
−0.122599 + 0.992456i \(0.539123\pi\)
\(152\) 2.22303 0.180312
\(153\) 0 0
\(154\) 15.2955 1.23254
\(155\) −8.62237 −0.692565
\(156\) 0 0
\(157\) −10.7128 −0.854972 −0.427486 0.904022i \(-0.640601\pi\)
−0.427486 + 0.904022i \(0.640601\pi\)
\(158\) −10.5968 −0.843037
\(159\) 0 0
\(160\) 5.78051 0.456990
\(161\) −17.9513 −1.41476
\(162\) 0 0
\(163\) −1.55250 −0.121601 −0.0608007 0.998150i \(-0.519365\pi\)
−0.0608007 + 0.998150i \(0.519365\pi\)
\(164\) 11.5354 0.900761
\(165\) 0 0
\(166\) −12.9316 −1.00369
\(167\) 12.8252 0.992444 0.496222 0.868196i \(-0.334720\pi\)
0.496222 + 0.868196i \(0.334720\pi\)
\(168\) 0 0
\(169\) −8.85308 −0.681006
\(170\) 4.73503 0.363161
\(171\) 0 0
\(172\) 2.87336 0.219092
\(173\) 14.9094 1.13354 0.566770 0.823876i \(-0.308193\pi\)
0.566770 + 0.823876i \(0.308193\pi\)
\(174\) 0 0
\(175\) −3.19059 −0.241186
\(176\) −13.4716 −1.01546
\(177\) 0 0
\(178\) −1.77222 −0.132834
\(179\) 20.1349 1.50495 0.752475 0.658621i \(-0.228860\pi\)
0.752475 + 0.658621i \(0.228860\pi\)
\(180\) 0 0
\(181\) −4.51916 −0.335907 −0.167953 0.985795i \(-0.553716\pi\)
−0.167953 + 0.985795i \(0.553716\pi\)
\(182\) 11.5147 0.853525
\(183\) 0 0
\(184\) 8.56743 0.631599
\(185\) 9.46573 0.695935
\(186\) 0 0
\(187\) −7.22733 −0.528515
\(188\) −1.20706 −0.0880338
\(189\) 0 0
\(190\) −2.58725 −0.187699
\(191\) −9.55425 −0.691321 −0.345661 0.938360i \(-0.612345\pi\)
−0.345661 + 0.938360i \(0.612345\pi\)
\(192\) 0 0
\(193\) 24.9743 1.79769 0.898844 0.438270i \(-0.144408\pi\)
0.898844 + 0.438270i \(0.144408\pi\)
\(194\) −27.7361 −1.99134
\(195\) 0 0
\(196\) 3.62749 0.259107
\(197\) −11.1011 −0.790923 −0.395462 0.918482i \(-0.629415\pi\)
−0.395462 + 0.918482i \(0.629415\pi\)
\(198\) 0 0
\(199\) −7.82995 −0.555050 −0.277525 0.960718i \(-0.589514\pi\)
−0.277525 + 0.960718i \(0.589514\pi\)
\(200\) 1.52274 0.107674
\(201\) 0 0
\(202\) 30.2273 2.12679
\(203\) 10.9758 0.770354
\(204\) 0 0
\(205\) 10.1119 0.706244
\(206\) −11.8590 −0.826259
\(207\) 0 0
\(208\) −10.1416 −0.703196
\(209\) 3.94905 0.273162
\(210\) 0 0
\(211\) 20.5375 1.41386 0.706929 0.707284i \(-0.250080\pi\)
0.706929 + 0.707284i \(0.250080\pi\)
\(212\) 1.97128 0.135388
\(213\) 0 0
\(214\) −28.2238 −1.92934
\(215\) 2.51878 0.171780
\(216\) 0 0
\(217\) 27.5104 1.86753
\(218\) 2.93202 0.198582
\(219\) 0 0
\(220\) 3.08584 0.208047
\(221\) −5.44086 −0.365992
\(222\) 0 0
\(223\) −4.16530 −0.278929 −0.139465 0.990227i \(-0.544538\pi\)
−0.139465 + 0.990227i \(0.544538\pi\)
\(224\) −18.4432 −1.23229
\(225\) 0 0
\(226\) −4.86277 −0.323467
\(227\) 7.69980 0.511054 0.255527 0.966802i \(-0.417751\pi\)
0.255527 + 0.966802i \(0.417751\pi\)
\(228\) 0 0
\(229\) 0.206071 0.0136176 0.00680879 0.999977i \(-0.497833\pi\)
0.00680879 + 0.999977i \(0.497833\pi\)
\(230\) −9.97110 −0.657475
\(231\) 0 0
\(232\) −5.23833 −0.343913
\(233\) −15.9391 −1.04421 −0.522104 0.852882i \(-0.674853\pi\)
−0.522104 + 0.852882i \(0.674853\pi\)
\(234\) 0 0
\(235\) −1.05810 −0.0690231
\(236\) 3.87788 0.252428
\(237\) 0 0
\(238\) −15.1075 −0.979276
\(239\) −16.9216 −1.09457 −0.547284 0.836947i \(-0.684338\pi\)
−0.547284 + 0.836947i \(0.684338\pi\)
\(240\) 0 0
\(241\) 3.84197 0.247483 0.123741 0.992315i \(-0.460511\pi\)
0.123741 + 0.992315i \(0.460511\pi\)
\(242\) 6.52670 0.419552
\(243\) 0 0
\(244\) −17.0056 −1.08867
\(245\) 3.17985 0.203153
\(246\) 0 0
\(247\) 2.97291 0.189162
\(248\) −13.1296 −0.833732
\(249\) 0 0
\(250\) −1.77222 −0.112085
\(251\) 1.25626 0.0792946 0.0396473 0.999214i \(-0.487377\pi\)
0.0396473 + 0.999214i \(0.487377\pi\)
\(252\) 0 0
\(253\) 15.2194 0.956837
\(254\) 0.0217058 0.00136194
\(255\) 0 0
\(256\) 20.1647 1.26030
\(257\) −6.84313 −0.426863 −0.213431 0.976958i \(-0.568464\pi\)
−0.213431 + 0.976958i \(0.568464\pi\)
\(258\) 0 0
\(259\) −30.2013 −1.87661
\(260\) 2.32307 0.144071
\(261\) 0 0
\(262\) −32.6708 −2.01841
\(263\) 4.38743 0.270541 0.135270 0.990809i \(-0.456810\pi\)
0.135270 + 0.990809i \(0.456810\pi\)
\(264\) 0 0
\(265\) 1.72802 0.106152
\(266\) 8.25484 0.506137
\(267\) 0 0
\(268\) −2.47420 −0.151136
\(269\) 25.5807 1.55968 0.779840 0.625978i \(-0.215300\pi\)
0.779840 + 0.625978i \(0.215300\pi\)
\(270\) 0 0
\(271\) 14.2568 0.866036 0.433018 0.901385i \(-0.357449\pi\)
0.433018 + 0.901385i \(0.357449\pi\)
\(272\) 13.3061 0.806799
\(273\) 0 0
\(274\) 31.6072 1.90946
\(275\) 2.70504 0.163120
\(276\) 0 0
\(277\) 9.43597 0.566952 0.283476 0.958979i \(-0.408512\pi\)
0.283476 + 0.958979i \(0.408512\pi\)
\(278\) 13.6381 0.817958
\(279\) 0 0
\(280\) −4.85844 −0.290347
\(281\) 20.3543 1.21423 0.607117 0.794612i \(-0.292326\pi\)
0.607117 + 0.794612i \(0.292326\pi\)
\(282\) 0 0
\(283\) 4.77106 0.283610 0.141805 0.989895i \(-0.454709\pi\)
0.141805 + 0.989895i \(0.454709\pi\)
\(284\) −7.85105 −0.465874
\(285\) 0 0
\(286\) −9.76235 −0.577260
\(287\) −32.2628 −1.90441
\(288\) 0 0
\(289\) −9.86146 −0.580086
\(290\) 6.09657 0.358003
\(291\) 0 0
\(292\) −10.0383 −0.587446
\(293\) −12.5065 −0.730636 −0.365318 0.930883i \(-0.619040\pi\)
−0.365318 + 0.930883i \(0.619040\pi\)
\(294\) 0 0
\(295\) 3.39934 0.197917
\(296\) 14.4139 0.837788
\(297\) 0 0
\(298\) −28.5018 −1.65106
\(299\) 11.4574 0.662601
\(300\) 0 0
\(301\) −8.03640 −0.463210
\(302\) 5.33977 0.307270
\(303\) 0 0
\(304\) −7.27051 −0.416992
\(305\) −14.9071 −0.853577
\(306\) 0 0
\(307\) 15.9679 0.911334 0.455667 0.890150i \(-0.349401\pi\)
0.455667 + 0.890150i \(0.349401\pi\)
\(308\) −9.84563 −0.561007
\(309\) 0 0
\(310\) 15.2808 0.867889
\(311\) 17.7230 1.00498 0.502490 0.864583i \(-0.332417\pi\)
0.502490 + 0.864583i \(0.332417\pi\)
\(312\) 0 0
\(313\) 19.8006 1.11920 0.559599 0.828763i \(-0.310955\pi\)
0.559599 + 0.828763i \(0.310955\pi\)
\(314\) 18.9854 1.07141
\(315\) 0 0
\(316\) 6.82114 0.383719
\(317\) 1.15759 0.0650167 0.0325083 0.999471i \(-0.489650\pi\)
0.0325083 + 0.999471i \(0.489650\pi\)
\(318\) 0 0
\(319\) −9.30552 −0.521009
\(320\) −0.283993 −0.0158757
\(321\) 0 0
\(322\) 31.8137 1.77291
\(323\) −3.90054 −0.217032
\(324\) 0 0
\(325\) 2.03640 0.112959
\(326\) 2.75138 0.152385
\(327\) 0 0
\(328\) 15.3978 0.850199
\(329\) 3.37598 0.186124
\(330\) 0 0
\(331\) −1.88134 −0.103408 −0.0517040 0.998662i \(-0.516465\pi\)
−0.0517040 + 0.998662i \(0.516465\pi\)
\(332\) 8.32406 0.456842
\(333\) 0 0
\(334\) −22.7291 −1.24368
\(335\) −2.16888 −0.118499
\(336\) 0 0
\(337\) 1.86868 0.101794 0.0508969 0.998704i \(-0.483792\pi\)
0.0508969 + 0.998704i \(0.483792\pi\)
\(338\) 15.6896 0.853403
\(339\) 0 0
\(340\) −3.04793 −0.165297
\(341\) −23.3238 −1.26306
\(342\) 0 0
\(343\) 12.1885 0.658118
\(344\) 3.83545 0.206794
\(345\) 0 0
\(346\) −26.4228 −1.42050
\(347\) 9.65267 0.518182 0.259091 0.965853i \(-0.416577\pi\)
0.259091 + 0.965853i \(0.416577\pi\)
\(348\) 0 0
\(349\) 34.0970 1.82517 0.912585 0.408886i \(-0.134083\pi\)
0.912585 + 0.408886i \(0.134083\pi\)
\(350\) 5.65443 0.302242
\(351\) 0 0
\(352\) 15.6365 0.833428
\(353\) 36.9671 1.96756 0.983779 0.179382i \(-0.0574099\pi\)
0.983779 + 0.179382i \(0.0574099\pi\)
\(354\) 0 0
\(355\) −6.88221 −0.365270
\(356\) 1.14077 0.0604609
\(357\) 0 0
\(358\) −35.6835 −1.88593
\(359\) −1.00561 −0.0530742 −0.0265371 0.999648i \(-0.508448\pi\)
−0.0265371 + 0.999648i \(0.508448\pi\)
\(360\) 0 0
\(361\) −16.8687 −0.887828
\(362\) 8.00896 0.420942
\(363\) 0 0
\(364\) −7.41196 −0.388492
\(365\) −8.79954 −0.460589
\(366\) 0 0
\(367\) 4.09416 0.213713 0.106857 0.994274i \(-0.465921\pi\)
0.106857 + 0.994274i \(0.465921\pi\)
\(368\) −28.0201 −1.46065
\(369\) 0 0
\(370\) −16.7754 −0.872111
\(371\) −5.51340 −0.286242
\(372\) 0 0
\(373\) 6.86807 0.355615 0.177808 0.984065i \(-0.443099\pi\)
0.177808 + 0.984065i \(0.443099\pi\)
\(374\) 12.8084 0.662309
\(375\) 0 0
\(376\) −1.61122 −0.0830923
\(377\) −7.00536 −0.360794
\(378\) 0 0
\(379\) −1.27864 −0.0656791 −0.0328396 0.999461i \(-0.510455\pi\)
−0.0328396 + 0.999461i \(0.510455\pi\)
\(380\) 1.66540 0.0854333
\(381\) 0 0
\(382\) 16.9323 0.866330
\(383\) 19.8336 1.01345 0.506726 0.862107i \(-0.330856\pi\)
0.506726 + 0.862107i \(0.330856\pi\)
\(384\) 0 0
\(385\) −8.63066 −0.439859
\(386\) −44.2600 −2.25277
\(387\) 0 0
\(388\) 17.8537 0.906382
\(389\) −13.9074 −0.705132 −0.352566 0.935787i \(-0.614691\pi\)
−0.352566 + 0.935787i \(0.614691\pi\)
\(390\) 0 0
\(391\) −15.0324 −0.760223
\(392\) 4.84209 0.244562
\(393\) 0 0
\(394\) 19.6737 0.991146
\(395\) 5.97939 0.300856
\(396\) 0 0
\(397\) −2.27223 −0.114040 −0.0570201 0.998373i \(-0.518160\pi\)
−0.0570201 + 0.998373i \(0.518160\pi\)
\(398\) 13.8764 0.695562
\(399\) 0 0
\(400\) −4.98018 −0.249009
\(401\) 20.7709 1.03725 0.518624 0.855002i \(-0.326444\pi\)
0.518624 + 0.855002i \(0.326444\pi\)
\(402\) 0 0
\(403\) −17.5586 −0.874655
\(404\) −19.4572 −0.968032
\(405\) 0 0
\(406\) −19.4517 −0.965369
\(407\) 25.6052 1.26920
\(408\) 0 0
\(409\) 37.1089 1.83492 0.917458 0.397833i \(-0.130238\pi\)
0.917458 + 0.397833i \(0.130238\pi\)
\(410\) −17.9205 −0.885030
\(411\) 0 0
\(412\) 7.63363 0.376082
\(413\) −10.8459 −0.533691
\(414\) 0 0
\(415\) 7.29685 0.358188
\(416\) 11.7714 0.577142
\(417\) 0 0
\(418\) −6.99860 −0.342313
\(419\) −28.9496 −1.41428 −0.707139 0.707074i \(-0.750015\pi\)
−0.707139 + 0.707074i \(0.750015\pi\)
\(420\) 0 0
\(421\) 34.0480 1.65940 0.829699 0.558211i \(-0.188512\pi\)
0.829699 + 0.558211i \(0.188512\pi\)
\(422\) −36.3970 −1.77178
\(423\) 0 0
\(424\) 2.63133 0.127789
\(425\) −2.67180 −0.129602
\(426\) 0 0
\(427\) 47.5624 2.30170
\(428\) 18.1675 0.878161
\(429\) 0 0
\(430\) −4.46385 −0.215266
\(431\) −15.7133 −0.756881 −0.378441 0.925626i \(-0.623540\pi\)
−0.378441 + 0.925626i \(0.623540\pi\)
\(432\) 0 0
\(433\) −22.0260 −1.05850 −0.529251 0.848465i \(-0.677527\pi\)
−0.529251 + 0.848465i \(0.677527\pi\)
\(434\) −48.7546 −2.34030
\(435\) 0 0
\(436\) −1.88733 −0.0903869
\(437\) 8.21381 0.392920
\(438\) 0 0
\(439\) 32.5888 1.55538 0.777690 0.628648i \(-0.216391\pi\)
0.777690 + 0.628648i \(0.216391\pi\)
\(440\) 4.11907 0.196369
\(441\) 0 0
\(442\) 9.64242 0.458643
\(443\) −33.3935 −1.58657 −0.793287 0.608849i \(-0.791632\pi\)
−0.793287 + 0.608849i \(0.791632\pi\)
\(444\) 0 0
\(445\) 1.00000 0.0474045
\(446\) 7.38184 0.349540
\(447\) 0 0
\(448\) 0.906106 0.0428095
\(449\) 2.89521 0.136634 0.0683168 0.997664i \(-0.478237\pi\)
0.0683168 + 0.997664i \(0.478237\pi\)
\(450\) 0 0
\(451\) 27.3530 1.28800
\(452\) 3.13015 0.147230
\(453\) 0 0
\(454\) −13.6458 −0.640427
\(455\) −6.49731 −0.304599
\(456\) 0 0
\(457\) 18.5490 0.867686 0.433843 0.900988i \(-0.357157\pi\)
0.433843 + 0.900988i \(0.357157\pi\)
\(458\) −0.365204 −0.0170649
\(459\) 0 0
\(460\) 6.41837 0.299258
\(461\) −20.3168 −0.946248 −0.473124 0.880996i \(-0.656874\pi\)
−0.473124 + 0.880996i \(0.656874\pi\)
\(462\) 0 0
\(463\) 20.0650 0.932499 0.466250 0.884653i \(-0.345605\pi\)
0.466250 + 0.884653i \(0.345605\pi\)
\(464\) 17.1322 0.795342
\(465\) 0 0
\(466\) 28.2477 1.30855
\(467\) 35.1654 1.62726 0.813631 0.581382i \(-0.197488\pi\)
0.813631 + 0.581382i \(0.197488\pi\)
\(468\) 0 0
\(469\) 6.92001 0.319536
\(470\) 1.87520 0.0864964
\(471\) 0 0
\(472\) 5.17631 0.238259
\(473\) 6.81340 0.313281
\(474\) 0 0
\(475\) 1.45989 0.0669843
\(476\) 9.72467 0.445730
\(477\) 0 0
\(478\) 29.9888 1.37166
\(479\) 36.9126 1.68658 0.843290 0.537458i \(-0.180615\pi\)
0.843290 + 0.537458i \(0.180615\pi\)
\(480\) 0 0
\(481\) 19.2760 0.878910
\(482\) −6.80882 −0.310133
\(483\) 0 0
\(484\) −4.20121 −0.190964
\(485\) 15.6505 0.710652
\(486\) 0 0
\(487\) −13.4262 −0.608400 −0.304200 0.952608i \(-0.598389\pi\)
−0.304200 + 0.952608i \(0.598389\pi\)
\(488\) −22.6996 −1.02756
\(489\) 0 0
\(490\) −5.63541 −0.254582
\(491\) 29.1214 1.31423 0.657115 0.753791i \(-0.271777\pi\)
0.657115 + 0.753791i \(0.271777\pi\)
\(492\) 0 0
\(493\) 9.19120 0.413951
\(494\) −5.26867 −0.237049
\(495\) 0 0
\(496\) 42.9410 1.92811
\(497\) 21.9583 0.984964
\(498\) 0 0
\(499\) 6.11813 0.273885 0.136943 0.990579i \(-0.456272\pi\)
0.136943 + 0.990579i \(0.456272\pi\)
\(500\) 1.14077 0.0510170
\(501\) 0 0
\(502\) −2.22638 −0.0993681
\(503\) 16.6291 0.741456 0.370728 0.928742i \(-0.379108\pi\)
0.370728 + 0.928742i \(0.379108\pi\)
\(504\) 0 0
\(505\) −17.0561 −0.758989
\(506\) −26.9722 −1.19906
\(507\) 0 0
\(508\) −0.0139719 −0.000619905 0
\(509\) 6.47859 0.287159 0.143579 0.989639i \(-0.454139\pi\)
0.143579 + 0.989639i \(0.454139\pi\)
\(510\) 0 0
\(511\) 28.0757 1.24200
\(512\) −13.6210 −0.601967
\(513\) 0 0
\(514\) 12.1276 0.534924
\(515\) 6.69162 0.294868
\(516\) 0 0
\(517\) −2.86221 −0.125880
\(518\) 53.5234 2.35168
\(519\) 0 0
\(520\) 3.10091 0.135984
\(521\) −22.4933 −0.985449 −0.492724 0.870185i \(-0.663999\pi\)
−0.492724 + 0.870185i \(0.663999\pi\)
\(522\) 0 0
\(523\) 14.1820 0.620134 0.310067 0.950715i \(-0.399648\pi\)
0.310067 + 0.950715i \(0.399648\pi\)
\(524\) 21.0301 0.918705
\(525\) 0 0
\(526\) −7.77551 −0.339028
\(527\) 23.0373 1.00352
\(528\) 0 0
\(529\) 8.65553 0.376327
\(530\) −3.06244 −0.133024
\(531\) 0 0
\(532\) −5.31361 −0.230374
\(533\) 20.5918 0.891930
\(534\) 0 0
\(535\) 15.9256 0.688525
\(536\) −3.30264 −0.142652
\(537\) 0 0
\(538\) −45.3346 −1.95452
\(539\) 8.60162 0.370498
\(540\) 0 0
\(541\) −35.2225 −1.51433 −0.757166 0.653222i \(-0.773417\pi\)
−0.757166 + 0.653222i \(0.773417\pi\)
\(542\) −25.2661 −1.08527
\(543\) 0 0
\(544\) −15.4444 −0.662173
\(545\) −1.65443 −0.0708681
\(546\) 0 0
\(547\) −1.43480 −0.0613477 −0.0306739 0.999529i \(-0.509765\pi\)
−0.0306739 + 0.999529i \(0.509765\pi\)
\(548\) −20.3454 −0.869114
\(549\) 0 0
\(550\) −4.79393 −0.204414
\(551\) −5.02212 −0.213949
\(552\) 0 0
\(553\) −19.0778 −0.811270
\(554\) −16.7226 −0.710477
\(555\) 0 0
\(556\) −8.77879 −0.372304
\(557\) 0.533965 0.0226248 0.0113124 0.999936i \(-0.496399\pi\)
0.0113124 + 0.999936i \(0.496399\pi\)
\(558\) 0 0
\(559\) 5.12925 0.216944
\(560\) 15.8897 0.671463
\(561\) 0 0
\(562\) −36.0723 −1.52162
\(563\) 36.0788 1.52054 0.760270 0.649607i \(-0.225067\pi\)
0.760270 + 0.649607i \(0.225067\pi\)
\(564\) 0 0
\(565\) 2.74388 0.115436
\(566\) −8.45537 −0.355406
\(567\) 0 0
\(568\) −10.4798 −0.439723
\(569\) 39.9398 1.67436 0.837181 0.546925i \(-0.184202\pi\)
0.837181 + 0.546925i \(0.184202\pi\)
\(570\) 0 0
\(571\) −34.5619 −1.44637 −0.723184 0.690655i \(-0.757322\pi\)
−0.723184 + 0.690655i \(0.757322\pi\)
\(572\) 6.28399 0.262747
\(573\) 0 0
\(574\) 57.1769 2.38652
\(575\) 5.62632 0.234634
\(576\) 0 0
\(577\) 46.3225 1.92843 0.964215 0.265122i \(-0.0854121\pi\)
0.964215 + 0.265122i \(0.0854121\pi\)
\(578\) 17.4767 0.726935
\(579\) 0 0
\(580\) −3.92434 −0.162949
\(581\) −23.2812 −0.965869
\(582\) 0 0
\(583\) 4.67436 0.193592
\(584\) −13.3994 −0.554472
\(585\) 0 0
\(586\) 22.1642 0.915597
\(587\) −14.1115 −0.582445 −0.291223 0.956655i \(-0.594062\pi\)
−0.291223 + 0.956655i \(0.594062\pi\)
\(588\) 0 0
\(589\) −12.5877 −0.518667
\(590\) −6.02438 −0.248020
\(591\) 0 0
\(592\) −47.1411 −1.93749
\(593\) 46.5842 1.91298 0.956491 0.291760i \(-0.0942410\pi\)
0.956491 + 0.291760i \(0.0942410\pi\)
\(594\) 0 0
\(595\) 8.52463 0.349476
\(596\) 18.3465 0.751501
\(597\) 0 0
\(598\) −20.3051 −0.830339
\(599\) 4.68560 0.191448 0.0957241 0.995408i \(-0.469483\pi\)
0.0957241 + 0.995408i \(0.469483\pi\)
\(600\) 0 0
\(601\) −29.7661 −1.21419 −0.607093 0.794631i \(-0.707664\pi\)
−0.607093 + 0.794631i \(0.707664\pi\)
\(602\) 14.2423 0.580472
\(603\) 0 0
\(604\) −3.43720 −0.139857
\(605\) −3.68277 −0.149726
\(606\) 0 0
\(607\) 8.61468 0.349659 0.174829 0.984599i \(-0.444063\pi\)
0.174829 + 0.984599i \(0.444063\pi\)
\(608\) 8.43890 0.342243
\(609\) 0 0
\(610\) 26.4187 1.06966
\(611\) −2.15472 −0.0871708
\(612\) 0 0
\(613\) −16.8722 −0.681463 −0.340731 0.940161i \(-0.610675\pi\)
−0.340731 + 0.940161i \(0.610675\pi\)
\(614\) −28.2986 −1.14204
\(615\) 0 0
\(616\) −13.1422 −0.529516
\(617\) −0.826593 −0.0332774 −0.0166387 0.999862i \(-0.505297\pi\)
−0.0166387 + 0.999862i \(0.505297\pi\)
\(618\) 0 0
\(619\) −7.92336 −0.318467 −0.159233 0.987241i \(-0.550902\pi\)
−0.159233 + 0.987241i \(0.550902\pi\)
\(620\) −9.83617 −0.395030
\(621\) 0 0
\(622\) −31.4091 −1.25939
\(623\) −3.19059 −0.127828
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −35.0911 −1.40252
\(627\) 0 0
\(628\) −12.2209 −0.487665
\(629\) −25.2906 −1.00840
\(630\) 0 0
\(631\) 36.1596 1.43949 0.719745 0.694238i \(-0.244259\pi\)
0.719745 + 0.694238i \(0.244259\pi\)
\(632\) 9.10506 0.362180
\(633\) 0 0
\(634\) −2.05151 −0.0814757
\(635\) −0.0122478 −0.000486038 0
\(636\) 0 0
\(637\) 6.47545 0.256567
\(638\) 16.4915 0.652903
\(639\) 0 0
\(640\) −11.0577 −0.437095
\(641\) 17.4184 0.687984 0.343992 0.938973i \(-0.388221\pi\)
0.343992 + 0.938973i \(0.388221\pi\)
\(642\) 0 0
\(643\) −42.1096 −1.66064 −0.830321 0.557286i \(-0.811843\pi\)
−0.830321 + 0.557286i \(0.811843\pi\)
\(644\) −20.4784 −0.806960
\(645\) 0 0
\(646\) 6.91262 0.271973
\(647\) 21.0971 0.829413 0.414707 0.909955i \(-0.363884\pi\)
0.414707 + 0.909955i \(0.363884\pi\)
\(648\) 0 0
\(649\) 9.19533 0.360948
\(650\) −3.60895 −0.141555
\(651\) 0 0
\(652\) −1.77106 −0.0693599
\(653\) 28.2222 1.10442 0.552210 0.833705i \(-0.313785\pi\)
0.552210 + 0.833705i \(0.313785\pi\)
\(654\) 0 0
\(655\) 18.4349 0.720313
\(656\) −50.3590 −1.96619
\(657\) 0 0
\(658\) −5.98298 −0.233241
\(659\) −33.8928 −1.32028 −0.660138 0.751144i \(-0.729502\pi\)
−0.660138 + 0.751144i \(0.729502\pi\)
\(660\) 0 0
\(661\) −5.46911 −0.212724 −0.106362 0.994327i \(-0.533920\pi\)
−0.106362 + 0.994327i \(0.533920\pi\)
\(662\) 3.33416 0.129586
\(663\) 0 0
\(664\) 11.1112 0.431198
\(665\) −4.65790 −0.180626
\(666\) 0 0
\(667\) −19.3550 −0.749427
\(668\) 14.6307 0.566077
\(669\) 0 0
\(670\) 3.84374 0.148497
\(671\) −40.3242 −1.55670
\(672\) 0 0
\(673\) −40.9495 −1.57849 −0.789244 0.614080i \(-0.789527\pi\)
−0.789244 + 0.614080i \(0.789527\pi\)
\(674\) −3.31172 −0.127563
\(675\) 0 0
\(676\) −10.0994 −0.388437
\(677\) −12.1363 −0.466437 −0.233219 0.972424i \(-0.574926\pi\)
−0.233219 + 0.972424i \(0.574926\pi\)
\(678\) 0 0
\(679\) −49.9342 −1.91630
\(680\) −4.06846 −0.156018
\(681\) 0 0
\(682\) 41.3350 1.58280
\(683\) 12.9361 0.494986 0.247493 0.968890i \(-0.420393\pi\)
0.247493 + 0.968890i \(0.420393\pi\)
\(684\) 0 0
\(685\) −17.8348 −0.681432
\(686\) −21.6008 −0.824721
\(687\) 0 0
\(688\) −12.5440 −0.478236
\(689\) 3.51894 0.134061
\(690\) 0 0
\(691\) −6.09541 −0.231880 −0.115940 0.993256i \(-0.536988\pi\)
−0.115940 + 0.993256i \(0.536988\pi\)
\(692\) 17.0082 0.646556
\(693\) 0 0
\(694\) −17.1067 −0.649361
\(695\) −7.69547 −0.291906
\(696\) 0 0
\(697\) −27.0170 −1.02334
\(698\) −60.4275 −2.28721
\(699\) 0 0
\(700\) −3.63974 −0.137569
\(701\) −24.9250 −0.941403 −0.470701 0.882293i \(-0.655999\pi\)
−0.470701 + 0.882293i \(0.655999\pi\)
\(702\) 0 0
\(703\) 13.8189 0.521190
\(704\) −0.768213 −0.0289531
\(705\) 0 0
\(706\) −65.5139 −2.46565
\(707\) 54.4191 2.04664
\(708\) 0 0
\(709\) −48.1319 −1.80763 −0.903816 0.427921i \(-0.859246\pi\)
−0.903816 + 0.427921i \(0.859246\pi\)
\(710\) 12.1968 0.457738
\(711\) 0 0
\(712\) 1.52274 0.0570671
\(713\) −48.5122 −1.81680
\(714\) 0 0
\(715\) 5.50854 0.206008
\(716\) 22.9693 0.858404
\(717\) 0 0
\(718\) 1.78217 0.0665100
\(719\) −16.3018 −0.607954 −0.303977 0.952679i \(-0.598315\pi\)
−0.303977 + 0.952679i \(0.598315\pi\)
\(720\) 0 0
\(721\) −21.3502 −0.795123
\(722\) 29.8951 1.11258
\(723\) 0 0
\(724\) −5.15534 −0.191597
\(725\) −3.44007 −0.127761
\(726\) 0 0
\(727\) 44.8912 1.66492 0.832462 0.554083i \(-0.186931\pi\)
0.832462 + 0.554083i \(0.186931\pi\)
\(728\) −9.89371 −0.366685
\(729\) 0 0
\(730\) 15.5947 0.577188
\(731\) −6.72970 −0.248907
\(732\) 0 0
\(733\) 7.45088 0.275204 0.137602 0.990488i \(-0.456060\pi\)
0.137602 + 0.990488i \(0.456060\pi\)
\(734\) −7.25576 −0.267815
\(735\) 0 0
\(736\) 32.5230 1.19882
\(737\) −5.86691 −0.216110
\(738\) 0 0
\(739\) 11.2444 0.413633 0.206817 0.978380i \(-0.433690\pi\)
0.206817 + 0.978380i \(0.433690\pi\)
\(740\) 10.7983 0.396952
\(741\) 0 0
\(742\) 9.77098 0.358704
\(743\) −2.94251 −0.107950 −0.0539750 0.998542i \(-0.517189\pi\)
−0.0539750 + 0.998542i \(0.517189\pi\)
\(744\) 0 0
\(745\) 16.0825 0.589217
\(746\) −12.1718 −0.445640
\(747\) 0 0
\(748\) −8.24475 −0.301458
\(749\) −50.8121 −1.85663
\(750\) 0 0
\(751\) 13.0559 0.476416 0.238208 0.971214i \(-0.423440\pi\)
0.238208 + 0.971214i \(0.423440\pi\)
\(752\) 5.26956 0.192161
\(753\) 0 0
\(754\) 12.4151 0.452130
\(755\) −3.01304 −0.109656
\(756\) 0 0
\(757\) −16.1988 −0.588754 −0.294377 0.955689i \(-0.595112\pi\)
−0.294377 + 0.955689i \(0.595112\pi\)
\(758\) 2.26603 0.0823059
\(759\) 0 0
\(760\) 2.22303 0.0806378
\(761\) −23.7871 −0.862282 −0.431141 0.902285i \(-0.641889\pi\)
−0.431141 + 0.902285i \(0.641889\pi\)
\(762\) 0 0
\(763\) 5.27861 0.191099
\(764\) −10.8992 −0.394321
\(765\) 0 0
\(766\) −35.1496 −1.27001
\(767\) 6.92241 0.249954
\(768\) 0 0
\(769\) −20.9770 −0.756451 −0.378225 0.925714i \(-0.623466\pi\)
−0.378225 + 0.925714i \(0.623466\pi\)
\(770\) 15.2955 0.551210
\(771\) 0 0
\(772\) 28.4900 1.02538
\(773\) 16.6061 0.597280 0.298640 0.954366i \(-0.403467\pi\)
0.298640 + 0.954366i \(0.403467\pi\)
\(774\) 0 0
\(775\) −8.62237 −0.309725
\(776\) 23.8316 0.855505
\(777\) 0 0
\(778\) 24.6470 0.883637
\(779\) 14.7622 0.528911
\(780\) 0 0
\(781\) −18.6166 −0.666156
\(782\) 26.6408 0.952674
\(783\) 0 0
\(784\) −15.8362 −0.565580
\(785\) −10.7128 −0.382355
\(786\) 0 0
\(787\) −50.6611 −1.80587 −0.902937 0.429773i \(-0.858593\pi\)
−0.902937 + 0.429773i \(0.858593\pi\)
\(788\) −12.6639 −0.451132
\(789\) 0 0
\(790\) −10.5968 −0.377018
\(791\) −8.75460 −0.311278
\(792\) 0 0
\(793\) −30.3568 −1.07800
\(794\) 4.02691 0.142910
\(795\) 0 0
\(796\) −8.93220 −0.316594
\(797\) 47.4446 1.68057 0.840287 0.542142i \(-0.182386\pi\)
0.840287 + 0.542142i \(0.182386\pi\)
\(798\) 0 0
\(799\) 2.82705 0.100014
\(800\) 5.78051 0.204372
\(801\) 0 0
\(802\) −36.8106 −1.29983
\(803\) −23.8031 −0.839993
\(804\) 0 0
\(805\) −17.9513 −0.632700
\(806\) 31.1177 1.09607
\(807\) 0 0
\(808\) −25.9721 −0.913695
\(809\) −27.5792 −0.969631 −0.484816 0.874616i \(-0.661113\pi\)
−0.484816 + 0.874616i \(0.661113\pi\)
\(810\) 0 0
\(811\) 11.4096 0.400645 0.200322 0.979730i \(-0.435801\pi\)
0.200322 + 0.979730i \(0.435801\pi\)
\(812\) 12.5210 0.439400
\(813\) 0 0
\(814\) −45.3781 −1.59050
\(815\) −1.55250 −0.0543818
\(816\) 0 0
\(817\) 3.67714 0.128647
\(818\) −65.7652 −2.29943
\(819\) 0 0
\(820\) 11.5354 0.402832
\(821\) −28.7824 −1.00451 −0.502257 0.864719i \(-0.667497\pi\)
−0.502257 + 0.864719i \(0.667497\pi\)
\(822\) 0 0
\(823\) 52.5379 1.83136 0.915679 0.401911i \(-0.131654\pi\)
0.915679 + 0.401911i \(0.131654\pi\)
\(824\) 10.1896 0.354972
\(825\) 0 0
\(826\) 19.2213 0.668796
\(827\) −51.6561 −1.79626 −0.898129 0.439732i \(-0.855073\pi\)
−0.898129 + 0.439732i \(0.855073\pi\)
\(828\) 0 0
\(829\) −44.4506 −1.54383 −0.771917 0.635723i \(-0.780702\pi\)
−0.771917 + 0.635723i \(0.780702\pi\)
\(830\) −12.9316 −0.448864
\(831\) 0 0
\(832\) −0.578324 −0.0200498
\(833\) −8.49594 −0.294367
\(834\) 0 0
\(835\) 12.8252 0.443834
\(836\) 4.50498 0.155808
\(837\) 0 0
\(838\) 51.3051 1.77230
\(839\) 24.5071 0.846078 0.423039 0.906111i \(-0.360963\pi\)
0.423039 + 0.906111i \(0.360963\pi\)
\(840\) 0 0
\(841\) −17.1659 −0.591928
\(842\) −60.3406 −2.07948
\(843\) 0 0
\(844\) 23.4286 0.806447
\(845\) −8.85308 −0.304555
\(846\) 0 0
\(847\) 11.7502 0.403742
\(848\) −8.60586 −0.295526
\(849\) 0 0
\(850\) 4.73503 0.162410
\(851\) 53.2573 1.82564
\(852\) 0 0
\(853\) −7.76300 −0.265800 −0.132900 0.991129i \(-0.542429\pi\)
−0.132900 + 0.991129i \(0.542429\pi\)
\(854\) −84.2911 −2.88438
\(855\) 0 0
\(856\) 24.2506 0.828868
\(857\) 6.72226 0.229628 0.114814 0.993387i \(-0.463373\pi\)
0.114814 + 0.993387i \(0.463373\pi\)
\(858\) 0 0
\(859\) 6.13678 0.209384 0.104692 0.994505i \(-0.466614\pi\)
0.104692 + 0.994505i \(0.466614\pi\)
\(860\) 2.87336 0.0979808
\(861\) 0 0
\(862\) 27.8474 0.948486
\(863\) 7.96255 0.271048 0.135524 0.990774i \(-0.456728\pi\)
0.135524 + 0.990774i \(0.456728\pi\)
\(864\) 0 0
\(865\) 14.9094 0.506934
\(866\) 39.0350 1.32646
\(867\) 0 0
\(868\) 31.3832 1.06521
\(869\) 16.1745 0.548682
\(870\) 0 0
\(871\) −4.41671 −0.149654
\(872\) −2.51927 −0.0853133
\(873\) 0 0
\(874\) −14.5567 −0.492388
\(875\) −3.19059 −0.107862
\(876\) 0 0
\(877\) 3.78873 0.127936 0.0639681 0.997952i \(-0.479624\pi\)
0.0639681 + 0.997952i \(0.479624\pi\)
\(878\) −57.7547 −1.94913
\(879\) 0 0
\(880\) −13.4716 −0.454127
\(881\) 35.4998 1.19602 0.598009 0.801490i \(-0.295959\pi\)
0.598009 + 0.801490i \(0.295959\pi\)
\(882\) 0 0
\(883\) −22.4461 −0.755371 −0.377685 0.925934i \(-0.623280\pi\)
−0.377685 + 0.925934i \(0.623280\pi\)
\(884\) −6.20679 −0.208757
\(885\) 0 0
\(886\) 59.1807 1.98822
\(887\) 25.8592 0.868267 0.434133 0.900849i \(-0.357055\pi\)
0.434133 + 0.900849i \(0.357055\pi\)
\(888\) 0 0
\(889\) 0.0390776 0.00131062
\(890\) −1.77222 −0.0594050
\(891\) 0 0
\(892\) −4.75167 −0.159098
\(893\) −1.54471 −0.0516919
\(894\) 0 0
\(895\) 20.1349 0.673034
\(896\) 35.2807 1.17864
\(897\) 0 0
\(898\) −5.13096 −0.171222
\(899\) 29.6616 0.989268
\(900\) 0 0
\(901\) −4.61694 −0.153812
\(902\) −48.4756 −1.61406
\(903\) 0 0
\(904\) 4.17822 0.138965
\(905\) −4.51916 −0.150222
\(906\) 0 0
\(907\) −45.8976 −1.52400 −0.762002 0.647575i \(-0.775783\pi\)
−0.762002 + 0.647575i \(0.775783\pi\)
\(908\) 8.78373 0.291498
\(909\) 0 0
\(910\) 11.5147 0.381708
\(911\) −50.0150 −1.65707 −0.828536 0.559936i \(-0.810826\pi\)
−0.828536 + 0.559936i \(0.810826\pi\)
\(912\) 0 0
\(913\) 19.7383 0.653241
\(914\) −32.8730 −1.08734
\(915\) 0 0
\(916\) 0.235081 0.00776729
\(917\) −58.8183 −1.94235
\(918\) 0 0
\(919\) −40.9072 −1.34940 −0.674702 0.738090i \(-0.735728\pi\)
−0.674702 + 0.738090i \(0.735728\pi\)
\(920\) 8.56743 0.282460
\(921\) 0 0
\(922\) 36.0059 1.18579
\(923\) −14.0149 −0.461307
\(924\) 0 0
\(925\) 9.46573 0.311231
\(926\) −35.5596 −1.16856
\(927\) 0 0
\(928\) −19.8854 −0.652769
\(929\) −22.6729 −0.743874 −0.371937 0.928258i \(-0.621306\pi\)
−0.371937 + 0.928258i \(0.621306\pi\)
\(930\) 0 0
\(931\) 4.64223 0.152143
\(932\) −18.1830 −0.595603
\(933\) 0 0
\(934\) −62.3210 −2.03920
\(935\) −7.22733 −0.236359
\(936\) 0 0
\(937\) −38.5330 −1.25882 −0.629409 0.777074i \(-0.716703\pi\)
−0.629409 + 0.777074i \(0.716703\pi\)
\(938\) −12.2638 −0.400427
\(939\) 0 0
\(940\) −1.20706 −0.0393699
\(941\) −4.39678 −0.143331 −0.0716655 0.997429i \(-0.522831\pi\)
−0.0716655 + 0.997429i \(0.522831\pi\)
\(942\) 0 0
\(943\) 56.8927 1.85268
\(944\) −16.9293 −0.551003
\(945\) 0 0
\(946\) −12.0749 −0.392588
\(947\) −5.70322 −0.185330 −0.0926649 0.995697i \(-0.529539\pi\)
−0.0926649 + 0.995697i \(0.529539\pi\)
\(948\) 0 0
\(949\) −17.9194 −0.581688
\(950\) −2.58725 −0.0839414
\(951\) 0 0
\(952\) 12.9808 0.420710
\(953\) 24.8332 0.804426 0.402213 0.915546i \(-0.368241\pi\)
0.402213 + 0.915546i \(0.368241\pi\)
\(954\) 0 0
\(955\) −9.55425 −0.309168
\(956\) −19.3037 −0.624327
\(957\) 0 0
\(958\) −65.4174 −2.11354
\(959\) 56.9034 1.83751
\(960\) 0 0
\(961\) 43.3452 1.39823
\(962\) −34.1614 −1.10141
\(963\) 0 0
\(964\) 4.38281 0.141161
\(965\) 24.9743 0.803950
\(966\) 0 0
\(967\) 43.4590 1.39755 0.698774 0.715343i \(-0.253730\pi\)
0.698774 + 0.715343i \(0.253730\pi\)
\(968\) −5.60791 −0.180245
\(969\) 0 0
\(970\) −27.7361 −0.890554
\(971\) 35.4713 1.13833 0.569165 0.822223i \(-0.307267\pi\)
0.569165 + 0.822223i \(0.307267\pi\)
\(972\) 0 0
\(973\) 24.5531 0.787135
\(974\) 23.7942 0.762417
\(975\) 0 0
\(976\) 74.2400 2.37636
\(977\) −7.14406 −0.228559 −0.114279 0.993449i \(-0.536456\pi\)
−0.114279 + 0.993449i \(0.536456\pi\)
\(978\) 0 0
\(979\) 2.70504 0.0864534
\(980\) 3.62749 0.115876
\(981\) 0 0
\(982\) −51.6096 −1.64693
\(983\) 14.0179 0.447100 0.223550 0.974692i \(-0.428235\pi\)
0.223550 + 0.974692i \(0.428235\pi\)
\(984\) 0 0
\(985\) −11.1011 −0.353712
\(986\) −16.2889 −0.518743
\(987\) 0 0
\(988\) 3.39142 0.107896
\(989\) 14.1715 0.450627
\(990\) 0 0
\(991\) −25.6111 −0.813565 −0.406782 0.913525i \(-0.633349\pi\)
−0.406782 + 0.913525i \(0.633349\pi\)
\(992\) −49.8417 −1.58248
\(993\) 0 0
\(994\) −38.9150 −1.23431
\(995\) −7.82995 −0.248226
\(996\) 0 0
\(997\) −27.3942 −0.867582 −0.433791 0.901013i \(-0.642824\pi\)
−0.433791 + 0.901013i \(0.642824\pi\)
\(998\) −10.8427 −0.343220
\(999\) 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 \(a_p\))