Properties

Label 8001.2.a.u.1.1
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 18
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.55461\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.55461 q^{2} +4.52602 q^{4} +2.12871 q^{5} +1.00000 q^{7} -6.45298 q^{8} +O(q^{10})\) \(q-2.55461 q^{2} +4.52602 q^{4} +2.12871 q^{5} +1.00000 q^{7} -6.45298 q^{8} -5.43801 q^{10} +4.13995 q^{11} -4.75071 q^{13} -2.55461 q^{14} +7.43278 q^{16} +1.32611 q^{17} -5.03962 q^{19} +9.63456 q^{20} -10.5759 q^{22} -0.634865 q^{23} -0.468604 q^{25} +12.1362 q^{26} +4.52602 q^{28} +6.95445 q^{29} -3.31737 q^{31} -6.08189 q^{32} -3.38770 q^{34} +2.12871 q^{35} +7.32426 q^{37} +12.8742 q^{38} -13.7365 q^{40} -4.92704 q^{41} -0.118376 q^{43} +18.7375 q^{44} +1.62183 q^{46} -10.6971 q^{47} +1.00000 q^{49} +1.19710 q^{50} -21.5018 q^{52} -4.29353 q^{53} +8.81274 q^{55} -6.45298 q^{56} -17.7659 q^{58} +9.53007 q^{59} -9.70203 q^{61} +8.47457 q^{62} +0.671262 q^{64} -10.1129 q^{65} +2.95734 q^{67} +6.00202 q^{68} -5.43801 q^{70} -1.45245 q^{71} +7.08465 q^{73} -18.7106 q^{74} -22.8094 q^{76} +4.13995 q^{77} +5.36766 q^{79} +15.8222 q^{80} +12.5867 q^{82} +10.4852 q^{83} +2.82291 q^{85} +0.302403 q^{86} -26.7150 q^{88} +3.15112 q^{89} -4.75071 q^{91} -2.87341 q^{92} +27.3270 q^{94} -10.7279 q^{95} -16.7425 q^{97} -2.55461 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q + 6q^{2} + 22q^{4} + 10q^{5} + 18q^{7} + 21q^{8} + O(q^{10}) \) \( 18q + 6q^{2} + 22q^{4} + 10q^{5} + 18q^{7} + 21q^{8} - 4q^{10} + 9q^{11} - 25q^{13} + 6q^{14} + 34q^{16} + 17q^{17} - 5q^{19} + 21q^{20} + 5q^{22} + 14q^{23} + 28q^{25} + 8q^{26} + 22q^{28} + 17q^{29} + 5q^{31} + 53q^{32} - 19q^{34} + 10q^{35} - 15q^{37} + 22q^{38} - q^{40} + 17q^{41} + q^{43} + 33q^{44} + 10q^{46} + 31q^{47} + 18q^{49} + 35q^{50} - 70q^{52} + 35q^{53} + 4q^{55} + 21q^{56} + 3q^{58} + 46q^{59} - 5q^{61} + 10q^{62} + 63q^{64} + 12q^{65} + 6q^{67} + 56q^{68} - 4q^{70} + 22q^{71} - 16q^{73} - 18q^{74} + 32q^{76} + 9q^{77} + 46q^{79} + 30q^{80} - 12q^{82} + 46q^{83} + 4q^{85} - 18q^{86} + 30q^{88} + 42q^{89} - 25q^{91} + 48q^{92} + 3q^{94} + 2q^{95} - 35q^{97} + 6q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55461 −1.80638 −0.903190 0.429241i \(-0.858781\pi\)
−0.903190 + 0.429241i \(0.858781\pi\)
\(3\) 0 0
\(4\) 4.52602 2.26301
\(5\) 2.12871 0.951987 0.475993 0.879449i \(-0.342089\pi\)
0.475993 + 0.879449i \(0.342089\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −6.45298 −2.28147
\(9\) 0 0
\(10\) −5.43801 −1.71965
\(11\) 4.13995 1.24824 0.624121 0.781328i \(-0.285457\pi\)
0.624121 + 0.781328i \(0.285457\pi\)
\(12\) 0 0
\(13\) −4.75071 −1.31761 −0.658805 0.752313i \(-0.728938\pi\)
−0.658805 + 0.752313i \(0.728938\pi\)
\(14\) −2.55461 −0.682747
\(15\) 0 0
\(16\) 7.43278 1.85820
\(17\) 1.32611 0.321630 0.160815 0.986985i \(-0.448588\pi\)
0.160815 + 0.986985i \(0.448588\pi\)
\(18\) 0 0
\(19\) −5.03962 −1.15617 −0.578083 0.815978i \(-0.696199\pi\)
−0.578083 + 0.815978i \(0.696199\pi\)
\(20\) 9.63456 2.15435
\(21\) 0 0
\(22\) −10.5759 −2.25480
\(23\) −0.634865 −0.132378 −0.0661892 0.997807i \(-0.521084\pi\)
−0.0661892 + 0.997807i \(0.521084\pi\)
\(24\) 0 0
\(25\) −0.468604 −0.0937208
\(26\) 12.1362 2.38011
\(27\) 0 0
\(28\) 4.52602 0.855336
\(29\) 6.95445 1.29141 0.645705 0.763587i \(-0.276564\pi\)
0.645705 + 0.763587i \(0.276564\pi\)
\(30\) 0 0
\(31\) −3.31737 −0.595817 −0.297908 0.954594i \(-0.596289\pi\)
−0.297908 + 0.954594i \(0.596289\pi\)
\(32\) −6.08189 −1.07514
\(33\) 0 0
\(34\) −3.38770 −0.580986
\(35\) 2.12871 0.359817
\(36\) 0 0
\(37\) 7.32426 1.20410 0.602051 0.798458i \(-0.294350\pi\)
0.602051 + 0.798458i \(0.294350\pi\)
\(38\) 12.8742 2.08848
\(39\) 0 0
\(40\) −13.7365 −2.17193
\(41\) −4.92704 −0.769475 −0.384737 0.923026i \(-0.625708\pi\)
−0.384737 + 0.923026i \(0.625708\pi\)
\(42\) 0 0
\(43\) −0.118376 −0.0180521 −0.00902606 0.999959i \(-0.502873\pi\)
−0.00902606 + 0.999959i \(0.502873\pi\)
\(44\) 18.7375 2.82478
\(45\) 0 0
\(46\) 1.62183 0.239126
\(47\) −10.6971 −1.56034 −0.780169 0.625568i \(-0.784867\pi\)
−0.780169 + 0.625568i \(0.784867\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 1.19710 0.169295
\(51\) 0 0
\(52\) −21.5018 −2.98176
\(53\) −4.29353 −0.589762 −0.294881 0.955534i \(-0.595280\pi\)
−0.294881 + 0.955534i \(0.595280\pi\)
\(54\) 0 0
\(55\) 8.81274 1.18831
\(56\) −6.45298 −0.862315
\(57\) 0 0
\(58\) −17.7659 −2.33278
\(59\) 9.53007 1.24071 0.620355 0.784321i \(-0.286989\pi\)
0.620355 + 0.784321i \(0.286989\pi\)
\(60\) 0 0
\(61\) −9.70203 −1.24222 −0.621109 0.783724i \(-0.713318\pi\)
−0.621109 + 0.783724i \(0.713318\pi\)
\(62\) 8.47457 1.07627
\(63\) 0 0
\(64\) 0.671262 0.0839078
\(65\) −10.1129 −1.25435
\(66\) 0 0
\(67\) 2.95734 0.361297 0.180648 0.983548i \(-0.442180\pi\)
0.180648 + 0.983548i \(0.442180\pi\)
\(68\) 6.00202 0.727851
\(69\) 0 0
\(70\) −5.43801 −0.649967
\(71\) −1.45245 −0.172375 −0.0861873 0.996279i \(-0.527468\pi\)
−0.0861873 + 0.996279i \(0.527468\pi\)
\(72\) 0 0
\(73\) 7.08465 0.829195 0.414598 0.910005i \(-0.363922\pi\)
0.414598 + 0.910005i \(0.363922\pi\)
\(74\) −18.7106 −2.17506
\(75\) 0 0
\(76\) −22.8094 −2.61641
\(77\) 4.13995 0.471791
\(78\) 0 0
\(79\) 5.36766 0.603909 0.301954 0.953322i \(-0.402361\pi\)
0.301954 + 0.953322i \(0.402361\pi\)
\(80\) 15.8222 1.76898
\(81\) 0 0
\(82\) 12.5867 1.38996
\(83\) 10.4852 1.15090 0.575451 0.817836i \(-0.304826\pi\)
0.575451 + 0.817836i \(0.304826\pi\)
\(84\) 0 0
\(85\) 2.82291 0.306188
\(86\) 0.302403 0.0326090
\(87\) 0 0
\(88\) −26.7150 −2.84783
\(89\) 3.15112 0.334018 0.167009 0.985955i \(-0.446589\pi\)
0.167009 + 0.985955i \(0.446589\pi\)
\(90\) 0 0
\(91\) −4.75071 −0.498010
\(92\) −2.87341 −0.299574
\(93\) 0 0
\(94\) 27.3270 2.81856
\(95\) −10.7279 −1.10066
\(96\) 0 0
\(97\) −16.7425 −1.69994 −0.849970 0.526831i \(-0.823380\pi\)
−0.849970 + 0.526831i \(0.823380\pi\)
\(98\) −2.55461 −0.258054
\(99\) 0 0
\(100\) −2.12091 −0.212091
\(101\) 18.6303 1.85378 0.926891 0.375331i \(-0.122471\pi\)
0.926891 + 0.375331i \(0.122471\pi\)
\(102\) 0 0
\(103\) 7.48405 0.737426 0.368713 0.929543i \(-0.379799\pi\)
0.368713 + 0.929543i \(0.379799\pi\)
\(104\) 30.6562 3.00609
\(105\) 0 0
\(106\) 10.9683 1.06533
\(107\) 11.2137 1.08407 0.542035 0.840356i \(-0.317654\pi\)
0.542035 + 0.840356i \(0.317654\pi\)
\(108\) 0 0
\(109\) 3.85001 0.368765 0.184382 0.982855i \(-0.440972\pi\)
0.184382 + 0.982855i \(0.440972\pi\)
\(110\) −22.5131 −2.14654
\(111\) 0 0
\(112\) 7.43278 0.702332
\(113\) −4.76521 −0.448273 −0.224137 0.974558i \(-0.571956\pi\)
−0.224137 + 0.974558i \(0.571956\pi\)
\(114\) 0 0
\(115\) −1.35144 −0.126023
\(116\) 31.4759 2.92247
\(117\) 0 0
\(118\) −24.3456 −2.24119
\(119\) 1.32611 0.121565
\(120\) 0 0
\(121\) 6.13918 0.558107
\(122\) 24.7849 2.24392
\(123\) 0 0
\(124\) −15.0145 −1.34834
\(125\) −11.6411 −1.04121
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 10.4490 0.923567
\(129\) 0 0
\(130\) 25.8344 2.26583
\(131\) 11.0346 0.964098 0.482049 0.876144i \(-0.339893\pi\)
0.482049 + 0.876144i \(0.339893\pi\)
\(132\) 0 0
\(133\) −5.03962 −0.436990
\(134\) −7.55485 −0.652639
\(135\) 0 0
\(136\) −8.55738 −0.733790
\(137\) 10.6933 0.913589 0.456794 0.889572i \(-0.348997\pi\)
0.456794 + 0.889572i \(0.348997\pi\)
\(138\) 0 0
\(139\) −3.73393 −0.316708 −0.158354 0.987382i \(-0.550619\pi\)
−0.158354 + 0.987382i \(0.550619\pi\)
\(140\) 9.63456 0.814269
\(141\) 0 0
\(142\) 3.71045 0.311374
\(143\) −19.6677 −1.64470
\(144\) 0 0
\(145\) 14.8040 1.22940
\(146\) −18.0985 −1.49784
\(147\) 0 0
\(148\) 33.1497 2.72489
\(149\) 11.4885 0.941174 0.470587 0.882354i \(-0.344042\pi\)
0.470587 + 0.882354i \(0.344042\pi\)
\(150\) 0 0
\(151\) 12.9894 1.05707 0.528533 0.848913i \(-0.322742\pi\)
0.528533 + 0.848913i \(0.322742\pi\)
\(152\) 32.5205 2.63776
\(153\) 0 0
\(154\) −10.5759 −0.852234
\(155\) −7.06171 −0.567210
\(156\) 0 0
\(157\) 12.6471 1.00934 0.504672 0.863311i \(-0.331613\pi\)
0.504672 + 0.863311i \(0.331613\pi\)
\(158\) −13.7123 −1.09089
\(159\) 0 0
\(160\) −12.9466 −1.02352
\(161\) −0.634865 −0.0500344
\(162\) 0 0
\(163\) 6.11310 0.478815 0.239407 0.970919i \(-0.423047\pi\)
0.239407 + 0.970919i \(0.423047\pi\)
\(164\) −22.2999 −1.74133
\(165\) 0 0
\(166\) −26.7856 −2.07897
\(167\) −18.3586 −1.42063 −0.710314 0.703885i \(-0.751447\pi\)
−0.710314 + 0.703885i \(0.751447\pi\)
\(168\) 0 0
\(169\) 9.56928 0.736098
\(170\) −7.21143 −0.553091
\(171\) 0 0
\(172\) −0.535770 −0.0408521
\(173\) −18.7445 −1.42512 −0.712558 0.701613i \(-0.752464\pi\)
−0.712558 + 0.701613i \(0.752464\pi\)
\(174\) 0 0
\(175\) −0.468604 −0.0354231
\(176\) 30.7713 2.31948
\(177\) 0 0
\(178\) −8.04987 −0.603363
\(179\) −2.99701 −0.224007 −0.112004 0.993708i \(-0.535727\pi\)
−0.112004 + 0.993708i \(0.535727\pi\)
\(180\) 0 0
\(181\) 24.4052 1.81402 0.907012 0.421105i \(-0.138358\pi\)
0.907012 + 0.421105i \(0.138358\pi\)
\(182\) 12.1362 0.899595
\(183\) 0 0
\(184\) 4.09677 0.302018
\(185\) 15.5912 1.14629
\(186\) 0 0
\(187\) 5.49005 0.401472
\(188\) −48.4154 −3.53106
\(189\) 0 0
\(190\) 27.4055 1.98820
\(191\) 15.5134 1.12251 0.561254 0.827643i \(-0.310319\pi\)
0.561254 + 0.827643i \(0.310319\pi\)
\(192\) 0 0
\(193\) 23.3101 1.67789 0.838947 0.544213i \(-0.183172\pi\)
0.838947 + 0.544213i \(0.183172\pi\)
\(194\) 42.7704 3.07074
\(195\) 0 0
\(196\) 4.52602 0.323287
\(197\) 22.0204 1.56889 0.784444 0.620200i \(-0.212949\pi\)
0.784444 + 0.620200i \(0.212949\pi\)
\(198\) 0 0
\(199\) −1.90444 −0.135002 −0.0675011 0.997719i \(-0.521503\pi\)
−0.0675011 + 0.997719i \(0.521503\pi\)
\(200\) 3.02389 0.213821
\(201\) 0 0
\(202\) −47.5930 −3.34863
\(203\) 6.95445 0.488107
\(204\) 0 0
\(205\) −10.4882 −0.732530
\(206\) −19.1188 −1.33207
\(207\) 0 0
\(208\) −35.3110 −2.44838
\(209\) −20.8637 −1.44318
\(210\) 0 0
\(211\) 14.5624 1.00252 0.501260 0.865297i \(-0.332870\pi\)
0.501260 + 0.865297i \(0.332870\pi\)
\(212\) −19.4326 −1.33464
\(213\) 0 0
\(214\) −28.6466 −1.95824
\(215\) −0.251987 −0.0171854
\(216\) 0 0
\(217\) −3.31737 −0.225198
\(218\) −9.83527 −0.666129
\(219\) 0 0
\(220\) 39.8866 2.68915
\(221\) −6.29999 −0.423783
\(222\) 0 0
\(223\) 2.83408 0.189784 0.0948919 0.995488i \(-0.469749\pi\)
0.0948919 + 0.995488i \(0.469749\pi\)
\(224\) −6.08189 −0.406363
\(225\) 0 0
\(226\) 12.1732 0.809751
\(227\) −1.45824 −0.0967865 −0.0483933 0.998828i \(-0.515410\pi\)
−0.0483933 + 0.998828i \(0.515410\pi\)
\(228\) 0 0
\(229\) 21.1581 1.39817 0.699084 0.715040i \(-0.253591\pi\)
0.699084 + 0.715040i \(0.253591\pi\)
\(230\) 3.45240 0.227645
\(231\) 0 0
\(232\) −44.8769 −2.94631
\(233\) 9.49469 0.622018 0.311009 0.950407i \(-0.399333\pi\)
0.311009 + 0.950407i \(0.399333\pi\)
\(234\) 0 0
\(235\) −22.7711 −1.48542
\(236\) 43.1332 2.80774
\(237\) 0 0
\(238\) −3.38770 −0.219592
\(239\) 25.7367 1.66477 0.832384 0.554199i \(-0.186975\pi\)
0.832384 + 0.554199i \(0.186975\pi\)
\(240\) 0 0
\(241\) 16.7397 1.07830 0.539149 0.842211i \(-0.318746\pi\)
0.539149 + 0.842211i \(0.318746\pi\)
\(242\) −15.6832 −1.00815
\(243\) 0 0
\(244\) −43.9115 −2.81115
\(245\) 2.12871 0.135998
\(246\) 0 0
\(247\) 23.9418 1.52338
\(248\) 21.4069 1.35934
\(249\) 0 0
\(250\) 29.7383 1.88082
\(251\) 5.36016 0.338330 0.169165 0.985588i \(-0.445893\pi\)
0.169165 + 0.985588i \(0.445893\pi\)
\(252\) 0 0
\(253\) −2.62831 −0.165240
\(254\) −2.55461 −0.160290
\(255\) 0 0
\(256\) −28.0355 −1.75222
\(257\) −13.1565 −0.820678 −0.410339 0.911933i \(-0.634590\pi\)
−0.410339 + 0.911933i \(0.634590\pi\)
\(258\) 0 0
\(259\) 7.32426 0.455108
\(260\) −45.7710 −2.83860
\(261\) 0 0
\(262\) −28.1891 −1.74153
\(263\) 15.6935 0.967702 0.483851 0.875150i \(-0.339238\pi\)
0.483851 + 0.875150i \(0.339238\pi\)
\(264\) 0 0
\(265\) −9.13968 −0.561446
\(266\) 12.8742 0.789370
\(267\) 0 0
\(268\) 13.3850 0.817618
\(269\) 28.0155 1.70813 0.854067 0.520163i \(-0.174129\pi\)
0.854067 + 0.520163i \(0.174129\pi\)
\(270\) 0 0
\(271\) −19.4489 −1.18143 −0.590717 0.806879i \(-0.701155\pi\)
−0.590717 + 0.806879i \(0.701155\pi\)
\(272\) 9.85672 0.597652
\(273\) 0 0
\(274\) −27.3171 −1.65029
\(275\) −1.94000 −0.116986
\(276\) 0 0
\(277\) −15.0931 −0.906858 −0.453429 0.891292i \(-0.649799\pi\)
−0.453429 + 0.891292i \(0.649799\pi\)
\(278\) 9.53872 0.572094
\(279\) 0 0
\(280\) −13.7365 −0.820913
\(281\) 15.7060 0.936943 0.468471 0.883479i \(-0.344805\pi\)
0.468471 + 0.883479i \(0.344805\pi\)
\(282\) 0 0
\(283\) 29.8370 1.77363 0.886813 0.462129i \(-0.152914\pi\)
0.886813 + 0.462129i \(0.152914\pi\)
\(284\) −6.57383 −0.390085
\(285\) 0 0
\(286\) 50.2433 2.97095
\(287\) −4.92704 −0.290834
\(288\) 0 0
\(289\) −15.2414 −0.896554
\(290\) −37.8184 −2.22077
\(291\) 0 0
\(292\) 32.0652 1.87648
\(293\) −17.2017 −1.00493 −0.502467 0.864596i \(-0.667574\pi\)
−0.502467 + 0.864596i \(0.667574\pi\)
\(294\) 0 0
\(295\) 20.2867 1.18114
\(296\) −47.2633 −2.74712
\(297\) 0 0
\(298\) −29.3486 −1.70012
\(299\) 3.01606 0.174423
\(300\) 0 0
\(301\) −0.118376 −0.00682306
\(302\) −33.1829 −1.90946
\(303\) 0 0
\(304\) −37.4584 −2.14838
\(305\) −20.6528 −1.18258
\(306\) 0 0
\(307\) −13.9522 −0.796294 −0.398147 0.917322i \(-0.630347\pi\)
−0.398147 + 0.917322i \(0.630347\pi\)
\(308\) 18.7375 1.06767
\(309\) 0 0
\(310\) 18.0399 1.02460
\(311\) −4.04310 −0.229263 −0.114632 0.993408i \(-0.536569\pi\)
−0.114632 + 0.993408i \(0.536569\pi\)
\(312\) 0 0
\(313\) 3.51810 0.198855 0.0994274 0.995045i \(-0.468299\pi\)
0.0994274 + 0.995045i \(0.468299\pi\)
\(314\) −32.3082 −1.82326
\(315\) 0 0
\(316\) 24.2941 1.36665
\(317\) 11.1408 0.625731 0.312865 0.949797i \(-0.398711\pi\)
0.312865 + 0.949797i \(0.398711\pi\)
\(318\) 0 0
\(319\) 28.7911 1.61199
\(320\) 1.42892 0.0798791
\(321\) 0 0
\(322\) 1.62183 0.0903811
\(323\) −6.68311 −0.371858
\(324\) 0 0
\(325\) 2.22620 0.123487
\(326\) −15.6166 −0.864921
\(327\) 0 0
\(328\) 31.7941 1.75553
\(329\) −10.6971 −0.589753
\(330\) 0 0
\(331\) 24.8759 1.36730 0.683650 0.729810i \(-0.260391\pi\)
0.683650 + 0.729810i \(0.260391\pi\)
\(332\) 47.4563 2.60450
\(333\) 0 0
\(334\) 46.8989 2.56619
\(335\) 6.29532 0.343950
\(336\) 0 0
\(337\) −26.4887 −1.44293 −0.721465 0.692451i \(-0.756531\pi\)
−0.721465 + 0.692451i \(0.756531\pi\)
\(338\) −24.4457 −1.32967
\(339\) 0 0
\(340\) 12.7765 0.692905
\(341\) −13.7337 −0.743723
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0.763875 0.0411854
\(345\) 0 0
\(346\) 47.8848 2.57430
\(347\) −22.3607 −1.20039 −0.600193 0.799855i \(-0.704910\pi\)
−0.600193 + 0.799855i \(0.704910\pi\)
\(348\) 0 0
\(349\) 6.65405 0.356183 0.178092 0.984014i \(-0.443008\pi\)
0.178092 + 0.984014i \(0.443008\pi\)
\(350\) 1.19710 0.0639876
\(351\) 0 0
\(352\) −25.1787 −1.34203
\(353\) −5.95514 −0.316960 −0.158480 0.987362i \(-0.550659\pi\)
−0.158480 + 0.987362i \(0.550659\pi\)
\(354\) 0 0
\(355\) −3.09185 −0.164098
\(356\) 14.2620 0.755885
\(357\) 0 0
\(358\) 7.65618 0.404642
\(359\) 2.04929 0.108158 0.0540788 0.998537i \(-0.482778\pi\)
0.0540788 + 0.998537i \(0.482778\pi\)
\(360\) 0 0
\(361\) 6.39772 0.336722
\(362\) −62.3457 −3.27682
\(363\) 0 0
\(364\) −21.5018 −1.12700
\(365\) 15.0811 0.789383
\(366\) 0 0
\(367\) −17.1828 −0.896936 −0.448468 0.893799i \(-0.648030\pi\)
−0.448468 + 0.893799i \(0.648030\pi\)
\(368\) −4.71881 −0.245985
\(369\) 0 0
\(370\) −39.8294 −2.07063
\(371\) −4.29353 −0.222909
\(372\) 0 0
\(373\) 13.0837 0.677449 0.338725 0.940886i \(-0.390005\pi\)
0.338725 + 0.940886i \(0.390005\pi\)
\(374\) −14.0249 −0.725211
\(375\) 0 0
\(376\) 69.0284 3.55987
\(377\) −33.0386 −1.70157
\(378\) 0 0
\(379\) −20.7955 −1.06819 −0.534096 0.845424i \(-0.679348\pi\)
−0.534096 + 0.845424i \(0.679348\pi\)
\(380\) −48.5545 −2.49079
\(381\) 0 0
\(382\) −39.6306 −2.02768
\(383\) −6.61047 −0.337779 −0.168890 0.985635i \(-0.554018\pi\)
−0.168890 + 0.985635i \(0.554018\pi\)
\(384\) 0 0
\(385\) 8.81274 0.449139
\(386\) −59.5480 −3.03091
\(387\) 0 0
\(388\) −75.7767 −3.84698
\(389\) −7.82979 −0.396986 −0.198493 0.980102i \(-0.563605\pi\)
−0.198493 + 0.980102i \(0.563605\pi\)
\(390\) 0 0
\(391\) −0.841904 −0.0425769
\(392\) −6.45298 −0.325924
\(393\) 0 0
\(394\) −56.2534 −2.83401
\(395\) 11.4262 0.574913
\(396\) 0 0
\(397\) −23.8727 −1.19814 −0.599068 0.800698i \(-0.704462\pi\)
−0.599068 + 0.800698i \(0.704462\pi\)
\(398\) 4.86509 0.243865
\(399\) 0 0
\(400\) −3.48303 −0.174152
\(401\) −19.4992 −0.973741 −0.486871 0.873474i \(-0.661862\pi\)
−0.486871 + 0.873474i \(0.661862\pi\)
\(402\) 0 0
\(403\) 15.7599 0.785055
\(404\) 84.3209 4.19512
\(405\) 0 0
\(406\) −17.7659 −0.881706
\(407\) 30.3221 1.50301
\(408\) 0 0
\(409\) −26.3931 −1.30505 −0.652526 0.757766i \(-0.726291\pi\)
−0.652526 + 0.757766i \(0.726291\pi\)
\(410\) 26.7933 1.32323
\(411\) 0 0
\(412\) 33.8729 1.66880
\(413\) 9.53007 0.468944
\(414\) 0 0
\(415\) 22.3200 1.09564
\(416\) 28.8933 1.41661
\(417\) 0 0
\(418\) 53.2987 2.60692
\(419\) 21.2813 1.03966 0.519831 0.854269i \(-0.325995\pi\)
0.519831 + 0.854269i \(0.325995\pi\)
\(420\) 0 0
\(421\) 7.10895 0.346469 0.173235 0.984881i \(-0.444578\pi\)
0.173235 + 0.984881i \(0.444578\pi\)
\(422\) −37.2013 −1.81093
\(423\) 0 0
\(424\) 27.7061 1.34553
\(425\) −0.621422 −0.0301434
\(426\) 0 0
\(427\) −9.70203 −0.469514
\(428\) 50.7535 2.45326
\(429\) 0 0
\(430\) 0.643728 0.0310433
\(431\) −22.4856 −1.08309 −0.541546 0.840671i \(-0.682161\pi\)
−0.541546 + 0.840671i \(0.682161\pi\)
\(432\) 0 0
\(433\) −24.4030 −1.17273 −0.586367 0.810046i \(-0.699442\pi\)
−0.586367 + 0.810046i \(0.699442\pi\)
\(434\) 8.47457 0.406792
\(435\) 0 0
\(436\) 17.4252 0.834517
\(437\) 3.19947 0.153052
\(438\) 0 0
\(439\) −8.99162 −0.429147 −0.214573 0.976708i \(-0.568836\pi\)
−0.214573 + 0.976708i \(0.568836\pi\)
\(440\) −56.8684 −2.71109
\(441\) 0 0
\(442\) 16.0940 0.765513
\(443\) −3.16638 −0.150439 −0.0752196 0.997167i \(-0.523966\pi\)
−0.0752196 + 0.997167i \(0.523966\pi\)
\(444\) 0 0
\(445\) 6.70781 0.317981
\(446\) −7.23995 −0.342822
\(447\) 0 0
\(448\) 0.671262 0.0317142
\(449\) 3.58210 0.169050 0.0845248 0.996421i \(-0.473063\pi\)
0.0845248 + 0.996421i \(0.473063\pi\)
\(450\) 0 0
\(451\) −20.3977 −0.960490
\(452\) −21.5674 −1.01445
\(453\) 0 0
\(454\) 3.72522 0.174833
\(455\) −10.1129 −0.474099
\(456\) 0 0
\(457\) −12.8800 −0.602500 −0.301250 0.953545i \(-0.597404\pi\)
−0.301250 + 0.953545i \(0.597404\pi\)
\(458\) −54.0507 −2.52562
\(459\) 0 0
\(460\) −6.11665 −0.285190
\(461\) 17.0189 0.792648 0.396324 0.918111i \(-0.370286\pi\)
0.396324 + 0.918111i \(0.370286\pi\)
\(462\) 0 0
\(463\) −26.4544 −1.22944 −0.614721 0.788745i \(-0.710731\pi\)
−0.614721 + 0.788745i \(0.710731\pi\)
\(464\) 51.6909 2.39969
\(465\) 0 0
\(466\) −24.2552 −1.12360
\(467\) −22.8012 −1.05511 −0.527557 0.849520i \(-0.676892\pi\)
−0.527557 + 0.849520i \(0.676892\pi\)
\(468\) 0 0
\(469\) 2.95734 0.136557
\(470\) 58.1712 2.68324
\(471\) 0 0
\(472\) −61.4973 −2.83064
\(473\) −0.490069 −0.0225334
\(474\) 0 0
\(475\) 2.36158 0.108357
\(476\) 6.00202 0.275102
\(477\) 0 0
\(478\) −65.7471 −3.00720
\(479\) 10.8867 0.497424 0.248712 0.968578i \(-0.419993\pi\)
0.248712 + 0.968578i \(0.419993\pi\)
\(480\) 0 0
\(481\) −34.7955 −1.58654
\(482\) −42.7633 −1.94781
\(483\) 0 0
\(484\) 27.7860 1.26300
\(485\) −35.6398 −1.61832
\(486\) 0 0
\(487\) −17.0508 −0.772645 −0.386323 0.922364i \(-0.626255\pi\)
−0.386323 + 0.922364i \(0.626255\pi\)
\(488\) 62.6070 2.83408
\(489\) 0 0
\(490\) −5.43801 −0.245664
\(491\) 27.2143 1.22817 0.614083 0.789241i \(-0.289526\pi\)
0.614083 + 0.789241i \(0.289526\pi\)
\(492\) 0 0
\(493\) 9.22240 0.415356
\(494\) −61.1618 −2.75180
\(495\) 0 0
\(496\) −24.6573 −1.10714
\(497\) −1.45245 −0.0651515
\(498\) 0 0
\(499\) 3.74789 0.167779 0.0838893 0.996475i \(-0.473266\pi\)
0.0838893 + 0.996475i \(0.473266\pi\)
\(500\) −52.6876 −2.35626
\(501\) 0 0
\(502\) −13.6931 −0.611152
\(503\) 3.01178 0.134289 0.0671443 0.997743i \(-0.478611\pi\)
0.0671443 + 0.997743i \(0.478611\pi\)
\(504\) 0 0
\(505\) 39.6584 1.76478
\(506\) 6.71429 0.298487
\(507\) 0 0
\(508\) 4.52602 0.200809
\(509\) −22.0551 −0.977576 −0.488788 0.872402i \(-0.662561\pi\)
−0.488788 + 0.872402i \(0.662561\pi\)
\(510\) 0 0
\(511\) 7.08465 0.313406
\(512\) 50.7218 2.24161
\(513\) 0 0
\(514\) 33.6096 1.48246
\(515\) 15.9314 0.702020
\(516\) 0 0
\(517\) −44.2856 −1.94768
\(518\) −18.7106 −0.822097
\(519\) 0 0
\(520\) 65.2582 2.86176
\(521\) −3.30328 −0.144719 −0.0723596 0.997379i \(-0.523053\pi\)
−0.0723596 + 0.997379i \(0.523053\pi\)
\(522\) 0 0
\(523\) 29.4263 1.28672 0.643362 0.765562i \(-0.277539\pi\)
0.643362 + 0.765562i \(0.277539\pi\)
\(524\) 49.9428 2.18176
\(525\) 0 0
\(526\) −40.0907 −1.74804
\(527\) −4.39921 −0.191633
\(528\) 0 0
\(529\) −22.5969 −0.982476
\(530\) 23.3483 1.01418
\(531\) 0 0
\(532\) −22.8094 −0.988912
\(533\) 23.4070 1.01387
\(534\) 0 0
\(535\) 23.8707 1.03202
\(536\) −19.0837 −0.824288
\(537\) 0 0
\(538\) −71.5686 −3.08554
\(539\) 4.13995 0.178320
\(540\) 0 0
\(541\) 27.5971 1.18649 0.593246 0.805021i \(-0.297846\pi\)
0.593246 + 0.805021i \(0.297846\pi\)
\(542\) 49.6842 2.13412
\(543\) 0 0
\(544\) −8.06528 −0.345796
\(545\) 8.19556 0.351059
\(546\) 0 0
\(547\) −1.48013 −0.0632860 −0.0316430 0.999499i \(-0.510074\pi\)
−0.0316430 + 0.999499i \(0.510074\pi\)
\(548\) 48.3980 2.06746
\(549\) 0 0
\(550\) 4.95593 0.211321
\(551\) −35.0478 −1.49308
\(552\) 0 0
\(553\) 5.36766 0.228256
\(554\) 38.5570 1.63813
\(555\) 0 0
\(556\) −16.8998 −0.716712
\(557\) 38.4105 1.62751 0.813753 0.581211i \(-0.197421\pi\)
0.813753 + 0.581211i \(0.197421\pi\)
\(558\) 0 0
\(559\) 0.562369 0.0237857
\(560\) 15.8222 0.668611
\(561\) 0 0
\(562\) −40.1227 −1.69247
\(563\) −43.0432 −1.81406 −0.907028 0.421070i \(-0.861655\pi\)
−0.907028 + 0.421070i \(0.861655\pi\)
\(564\) 0 0
\(565\) −10.1437 −0.426750
\(566\) −76.2218 −3.20384
\(567\) 0 0
\(568\) 9.37265 0.393268
\(569\) 1.66577 0.0698327 0.0349163 0.999390i \(-0.488884\pi\)
0.0349163 + 0.999390i \(0.488884\pi\)
\(570\) 0 0
\(571\) 33.4302 1.39901 0.699505 0.714627i \(-0.253404\pi\)
0.699505 + 0.714627i \(0.253404\pi\)
\(572\) −89.0164 −3.72196
\(573\) 0 0
\(574\) 12.5867 0.525357
\(575\) 0.297500 0.0124066
\(576\) 0 0
\(577\) −11.3687 −0.473286 −0.236643 0.971597i \(-0.576047\pi\)
−0.236643 + 0.971597i \(0.576047\pi\)
\(578\) 38.9358 1.61952
\(579\) 0 0
\(580\) 67.0031 2.78215
\(581\) 10.4852 0.435000
\(582\) 0 0
\(583\) −17.7750 −0.736165
\(584\) −45.7171 −1.89179
\(585\) 0 0
\(586\) 43.9436 1.81529
\(587\) 29.5488 1.21961 0.609805 0.792551i \(-0.291248\pi\)
0.609805 + 0.792551i \(0.291248\pi\)
\(588\) 0 0
\(589\) 16.7183 0.688864
\(590\) −51.8246 −2.13359
\(591\) 0 0
\(592\) 54.4397 2.23746
\(593\) 22.9545 0.942628 0.471314 0.881966i \(-0.343780\pi\)
0.471314 + 0.881966i \(0.343780\pi\)
\(594\) 0 0
\(595\) 2.82291 0.115728
\(596\) 51.9971 2.12988
\(597\) 0 0
\(598\) −7.70485 −0.315075
\(599\) −39.1632 −1.60016 −0.800082 0.599890i \(-0.795211\pi\)
−0.800082 + 0.599890i \(0.795211\pi\)
\(600\) 0 0
\(601\) −16.5220 −0.673947 −0.336973 0.941514i \(-0.609403\pi\)
−0.336973 + 0.941514i \(0.609403\pi\)
\(602\) 0.302403 0.0123250
\(603\) 0 0
\(604\) 58.7904 2.39215
\(605\) 13.0685 0.531311
\(606\) 0 0
\(607\) 5.46104 0.221657 0.110828 0.993840i \(-0.464650\pi\)
0.110828 + 0.993840i \(0.464650\pi\)
\(608\) 30.6504 1.24304
\(609\) 0 0
\(610\) 52.7597 2.13618
\(611\) 50.8191 2.05592
\(612\) 0 0
\(613\) −22.0546 −0.890779 −0.445389 0.895337i \(-0.646935\pi\)
−0.445389 + 0.895337i \(0.646935\pi\)
\(614\) 35.6424 1.43841
\(615\) 0 0
\(616\) −26.7150 −1.07638
\(617\) 42.7536 1.72119 0.860597 0.509287i \(-0.170091\pi\)
0.860597 + 0.509287i \(0.170091\pi\)
\(618\) 0 0
\(619\) 43.8372 1.76197 0.880983 0.473147i \(-0.156882\pi\)
0.880983 + 0.473147i \(0.156882\pi\)
\(620\) −31.9614 −1.28360
\(621\) 0 0
\(622\) 10.3285 0.414137
\(623\) 3.15112 0.126247
\(624\) 0 0
\(625\) −22.4374 −0.897496
\(626\) −8.98736 −0.359207
\(627\) 0 0
\(628\) 57.2408 2.28415
\(629\) 9.71281 0.387275
\(630\) 0 0
\(631\) −12.7391 −0.507135 −0.253568 0.967318i \(-0.581604\pi\)
−0.253568 + 0.967318i \(0.581604\pi\)
\(632\) −34.6374 −1.37780
\(633\) 0 0
\(634\) −28.4604 −1.13031
\(635\) 2.12871 0.0844752
\(636\) 0 0
\(637\) −4.75071 −0.188230
\(638\) −73.5499 −2.91187
\(639\) 0 0
\(640\) 22.2428 0.879223
\(641\) −6.94532 −0.274323 −0.137162 0.990549i \(-0.543798\pi\)
−0.137162 + 0.990549i \(0.543798\pi\)
\(642\) 0 0
\(643\) −38.9483 −1.53597 −0.767986 0.640467i \(-0.778741\pi\)
−0.767986 + 0.640467i \(0.778741\pi\)
\(644\) −2.87341 −0.113228
\(645\) 0 0
\(646\) 17.0727 0.671717
\(647\) 24.7855 0.974417 0.487209 0.873286i \(-0.338015\pi\)
0.487209 + 0.873286i \(0.338015\pi\)
\(648\) 0 0
\(649\) 39.4540 1.54871
\(650\) −5.68707 −0.223065
\(651\) 0 0
\(652\) 27.6680 1.08356
\(653\) 23.6675 0.926182 0.463091 0.886311i \(-0.346740\pi\)
0.463091 + 0.886311i \(0.346740\pi\)
\(654\) 0 0
\(655\) 23.4895 0.917809
\(656\) −36.6216 −1.42983
\(657\) 0 0
\(658\) 27.3270 1.06532
\(659\) −13.2866 −0.517572 −0.258786 0.965935i \(-0.583322\pi\)
−0.258786 + 0.965935i \(0.583322\pi\)
\(660\) 0 0
\(661\) −22.0055 −0.855915 −0.427958 0.903799i \(-0.640767\pi\)
−0.427958 + 0.903799i \(0.640767\pi\)
\(662\) −63.5480 −2.46986
\(663\) 0 0
\(664\) −67.6609 −2.62575
\(665\) −10.7279 −0.416009
\(666\) 0 0
\(667\) −4.41514 −0.170955
\(668\) −83.0912 −3.21489
\(669\) 0 0
\(670\) −16.0821 −0.621304
\(671\) −40.1659 −1.55059
\(672\) 0 0
\(673\) 24.1513 0.930964 0.465482 0.885057i \(-0.345881\pi\)
0.465482 + 0.885057i \(0.345881\pi\)
\(674\) 67.6681 2.60648
\(675\) 0 0
\(676\) 43.3107 1.66580
\(677\) 19.8265 0.761993 0.380996 0.924577i \(-0.375581\pi\)
0.380996 + 0.924577i \(0.375581\pi\)
\(678\) 0 0
\(679\) −16.7425 −0.642517
\(680\) −18.2162 −0.698558
\(681\) 0 0
\(682\) 35.0843 1.34345
\(683\) −11.5130 −0.440533 −0.220267 0.975440i \(-0.570693\pi\)
−0.220267 + 0.975440i \(0.570693\pi\)
\(684\) 0 0
\(685\) 22.7629 0.869725
\(686\) −2.55461 −0.0975353
\(687\) 0 0
\(688\) −0.879861 −0.0335444
\(689\) 20.3973 0.777077
\(690\) 0 0
\(691\) 8.79146 0.334443 0.167222 0.985919i \(-0.446520\pi\)
0.167222 + 0.985919i \(0.446520\pi\)
\(692\) −84.8378 −3.22505
\(693\) 0 0
\(694\) 57.1229 2.16835
\(695\) −7.94844 −0.301502
\(696\) 0 0
\(697\) −6.53382 −0.247486
\(698\) −16.9985 −0.643402
\(699\) 0 0
\(700\) −2.12091 −0.0801628
\(701\) 7.46770 0.282051 0.141026 0.990006i \(-0.454960\pi\)
0.141026 + 0.990006i \(0.454960\pi\)
\(702\) 0 0
\(703\) −36.9115 −1.39214
\(704\) 2.77899 0.104737
\(705\) 0 0
\(706\) 15.2130 0.572550
\(707\) 18.6303 0.700664
\(708\) 0 0
\(709\) 30.0859 1.12990 0.564950 0.825125i \(-0.308895\pi\)
0.564950 + 0.825125i \(0.308895\pi\)
\(710\) 7.89846 0.296424
\(711\) 0 0
\(712\) −20.3341 −0.762052
\(713\) 2.10608 0.0788733
\(714\) 0 0
\(715\) −41.8668 −1.56573
\(716\) −13.5645 −0.506930
\(717\) 0 0
\(718\) −5.23514 −0.195374
\(719\) 12.0466 0.449261 0.224631 0.974444i \(-0.427882\pi\)
0.224631 + 0.974444i \(0.427882\pi\)
\(720\) 0 0
\(721\) 7.48405 0.278721
\(722\) −16.3437 −0.608248
\(723\) 0 0
\(724\) 110.458 4.10515
\(725\) −3.25888 −0.121032
\(726\) 0 0
\(727\) 12.0016 0.445115 0.222557 0.974920i \(-0.428560\pi\)
0.222557 + 0.974920i \(0.428560\pi\)
\(728\) 30.6562 1.13620
\(729\) 0 0
\(730\) −38.5264 −1.42593
\(731\) −0.156980 −0.00580610
\(732\) 0 0
\(733\) −2.59393 −0.0958090 −0.0479045 0.998852i \(-0.515254\pi\)
−0.0479045 + 0.998852i \(0.515254\pi\)
\(734\) 43.8954 1.62021
\(735\) 0 0
\(736\) 3.86118 0.142325
\(737\) 12.2432 0.450986
\(738\) 0 0
\(739\) −7.97887 −0.293508 −0.146754 0.989173i \(-0.546883\pi\)
−0.146754 + 0.989173i \(0.546883\pi\)
\(740\) 70.5661 2.59406
\(741\) 0 0
\(742\) 10.9683 0.402658
\(743\) 4.32447 0.158650 0.0793248 0.996849i \(-0.474724\pi\)
0.0793248 + 0.996849i \(0.474724\pi\)
\(744\) 0 0
\(745\) 24.4557 0.895986
\(746\) −33.4238 −1.22373
\(747\) 0 0
\(748\) 24.8480 0.908534
\(749\) 11.2137 0.409740
\(750\) 0 0
\(751\) 2.34648 0.0856244 0.0428122 0.999083i \(-0.486368\pi\)
0.0428122 + 0.999083i \(0.486368\pi\)
\(752\) −79.5095 −2.89941
\(753\) 0 0
\(754\) 84.4006 3.07369
\(755\) 27.6507 1.00631
\(756\) 0 0
\(757\) −26.4656 −0.961909 −0.480954 0.876746i \(-0.659710\pi\)
−0.480954 + 0.876746i \(0.659710\pi\)
\(758\) 53.1243 1.92956
\(759\) 0 0
\(760\) 69.2267 2.51111
\(761\) 40.6849 1.47483 0.737414 0.675441i \(-0.236047\pi\)
0.737414 + 0.675441i \(0.236047\pi\)
\(762\) 0 0
\(763\) 3.85001 0.139380
\(764\) 70.2138 2.54025
\(765\) 0 0
\(766\) 16.8871 0.610157
\(767\) −45.2746 −1.63477
\(768\) 0 0
\(769\) −9.94961 −0.358792 −0.179396 0.983777i \(-0.557414\pi\)
−0.179396 + 0.983777i \(0.557414\pi\)
\(770\) −22.5131 −0.811315
\(771\) 0 0
\(772\) 105.502 3.79709
\(773\) −31.8949 −1.14718 −0.573590 0.819142i \(-0.694450\pi\)
−0.573590 + 0.819142i \(0.694450\pi\)
\(774\) 0 0
\(775\) 1.55453 0.0558404
\(776\) 108.039 3.87837
\(777\) 0 0
\(778\) 20.0020 0.717108
\(779\) 24.8304 0.889641
\(780\) 0 0
\(781\) −6.01309 −0.215165
\(782\) 2.15073 0.0769100
\(783\) 0 0
\(784\) 7.43278 0.265457
\(785\) 26.9219 0.960883
\(786\) 0 0
\(787\) −38.6972 −1.37941 −0.689703 0.724093i \(-0.742259\pi\)
−0.689703 + 0.724093i \(0.742259\pi\)
\(788\) 99.6646 3.55040
\(789\) 0 0
\(790\) −29.1894 −1.03851
\(791\) −4.76521 −0.169431
\(792\) 0 0
\(793\) 46.0916 1.63676
\(794\) 60.9854 2.16429
\(795\) 0 0
\(796\) −8.61952 −0.305511
\(797\) 9.68211 0.342958 0.171479 0.985188i \(-0.445145\pi\)
0.171479 + 0.985188i \(0.445145\pi\)
\(798\) 0 0
\(799\) −14.1856 −0.501852
\(800\) 2.85000 0.100763
\(801\) 0 0
\(802\) 49.8127 1.75895
\(803\) 29.3301 1.03504
\(804\) 0 0
\(805\) −1.35144 −0.0476321
\(806\) −40.2603 −1.41811
\(807\) 0 0
\(808\) −120.221 −4.22935
\(809\) 25.8293 0.908111 0.454056 0.890973i \(-0.349977\pi\)
0.454056 + 0.890973i \(0.349977\pi\)
\(810\) 0 0
\(811\) 20.7060 0.727087 0.363544 0.931577i \(-0.381567\pi\)
0.363544 + 0.931577i \(0.381567\pi\)
\(812\) 31.4759 1.10459
\(813\) 0 0
\(814\) −77.4610 −2.71501
\(815\) 13.0130 0.455825
\(816\) 0 0
\(817\) 0.596568 0.0208713
\(818\) 67.4239 2.35742
\(819\) 0 0
\(820\) −47.4699 −1.65772
\(821\) 36.0955 1.25974 0.629871 0.776700i \(-0.283108\pi\)
0.629871 + 0.776700i \(0.283108\pi\)
\(822\) 0 0
\(823\) 45.5252 1.58691 0.793455 0.608629i \(-0.208280\pi\)
0.793455 + 0.608629i \(0.208280\pi\)
\(824\) −48.2944 −1.68242
\(825\) 0 0
\(826\) −24.3456 −0.847091
\(827\) −19.6678 −0.683916 −0.341958 0.939715i \(-0.611090\pi\)
−0.341958 + 0.939715i \(0.611090\pi\)
\(828\) 0 0
\(829\) −46.1390 −1.60247 −0.801237 0.598347i \(-0.795825\pi\)
−0.801237 + 0.598347i \(0.795825\pi\)
\(830\) −57.0187 −1.97915
\(831\) 0 0
\(832\) −3.18897 −0.110558
\(833\) 1.32611 0.0459471
\(834\) 0 0
\(835\) −39.0800 −1.35242
\(836\) −94.4296 −3.26592
\(837\) 0 0
\(838\) −54.3654 −1.87802
\(839\) 45.6364 1.57554 0.787772 0.615966i \(-0.211234\pi\)
0.787772 + 0.615966i \(0.211234\pi\)
\(840\) 0 0
\(841\) 19.3644 0.667737
\(842\) −18.1606 −0.625855
\(843\) 0 0
\(844\) 65.9098 2.26871
\(845\) 20.3702 0.700756
\(846\) 0 0
\(847\) 6.13918 0.210945
\(848\) −31.9129 −1.09589
\(849\) 0 0
\(850\) 1.58749 0.0544504
\(851\) −4.64992 −0.159397
\(852\) 0 0
\(853\) 14.5096 0.496799 0.248400 0.968658i \(-0.420095\pi\)
0.248400 + 0.968658i \(0.420095\pi\)
\(854\) 24.7849 0.848121
\(855\) 0 0
\(856\) −72.3618 −2.47328
\(857\) −3.03303 −0.103606 −0.0518031 0.998657i \(-0.516497\pi\)
−0.0518031 + 0.998657i \(0.516497\pi\)
\(858\) 0 0
\(859\) 54.2596 1.85131 0.925657 0.378365i \(-0.123513\pi\)
0.925657 + 0.378365i \(0.123513\pi\)
\(860\) −1.14050 −0.0388906
\(861\) 0 0
\(862\) 57.4418 1.95648
\(863\) 48.8955 1.66442 0.832211 0.554460i \(-0.187075\pi\)
0.832211 + 0.554460i \(0.187075\pi\)
\(864\) 0 0
\(865\) −39.9015 −1.35669
\(866\) 62.3401 2.11840
\(867\) 0 0
\(868\) −15.0145 −0.509624
\(869\) 22.2218 0.753824
\(870\) 0 0
\(871\) −14.0495 −0.476049
\(872\) −24.8440 −0.841326
\(873\) 0 0
\(874\) −8.17340 −0.276469
\(875\) −11.6411 −0.393540
\(876\) 0 0
\(877\) −25.9003 −0.874590 −0.437295 0.899318i \(-0.644063\pi\)
−0.437295 + 0.899318i \(0.644063\pi\)
\(878\) 22.9701 0.775202
\(879\) 0 0
\(880\) 65.5032 2.20811
\(881\) 1.06900 0.0360156 0.0180078 0.999838i \(-0.494268\pi\)
0.0180078 + 0.999838i \(0.494268\pi\)
\(882\) 0 0
\(883\) −29.3081 −0.986295 −0.493147 0.869946i \(-0.664154\pi\)
−0.493147 + 0.869946i \(0.664154\pi\)
\(884\) −28.5139 −0.959025
\(885\) 0 0
\(886\) 8.08885 0.271750
\(887\) 40.0423 1.34449 0.672244 0.740330i \(-0.265331\pi\)
0.672244 + 0.740330i \(0.265331\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −17.1358 −0.574394
\(891\) 0 0
\(892\) 12.8271 0.429482
\(893\) 53.9095 1.80401
\(894\) 0 0
\(895\) −6.37976 −0.213252
\(896\) 10.4490 0.349075
\(897\) 0 0
\(898\) −9.15085 −0.305368
\(899\) −23.0705 −0.769443
\(900\) 0 0
\(901\) −5.69372 −0.189685
\(902\) 52.1081 1.73501
\(903\) 0 0
\(904\) 30.7498 1.02272
\(905\) 51.9515 1.72693
\(906\) 0 0
\(907\) 25.5478 0.848302 0.424151 0.905592i \(-0.360573\pi\)
0.424151 + 0.905592i \(0.360573\pi\)
\(908\) −6.60000 −0.219029
\(909\) 0 0
\(910\) 25.8344 0.856403
\(911\) −29.3845 −0.973553 −0.486777 0.873526i \(-0.661827\pi\)
−0.486777 + 0.873526i \(0.661827\pi\)
\(912\) 0 0
\(913\) 43.4083 1.43660
\(914\) 32.9033 1.08834
\(915\) 0 0
\(916\) 95.7619 3.16406
\(917\) 11.0346 0.364395
\(918\) 0 0
\(919\) −10.8678 −0.358494 −0.179247 0.983804i \(-0.557366\pi\)
−0.179247 + 0.983804i \(0.557366\pi\)
\(920\) 8.72082 0.287517
\(921\) 0 0
\(922\) −43.4766 −1.43182
\(923\) 6.90020 0.227123
\(924\) 0 0
\(925\) −3.43218 −0.112849
\(926\) 67.5807 2.22084
\(927\) 0 0
\(928\) −42.2962 −1.38844
\(929\) −4.66688 −0.153115 −0.0765577 0.997065i \(-0.524393\pi\)
−0.0765577 + 0.997065i \(0.524393\pi\)
\(930\) 0 0
\(931\) −5.03962 −0.165167
\(932\) 42.9731 1.40763
\(933\) 0 0
\(934\) 58.2481 1.90594
\(935\) 11.6867 0.382196
\(936\) 0 0
\(937\) −14.0249 −0.458175 −0.229088 0.973406i \(-0.573574\pi\)
−0.229088 + 0.973406i \(0.573574\pi\)
\(938\) −7.55485 −0.246674
\(939\) 0 0
\(940\) −103.062 −3.36152
\(941\) −46.2542 −1.50784 −0.753921 0.656965i \(-0.771840\pi\)
−0.753921 + 0.656965i \(0.771840\pi\)
\(942\) 0 0
\(943\) 3.12801 0.101862
\(944\) 70.8350 2.30548
\(945\) 0 0
\(946\) 1.25193 0.0407039
\(947\) −5.19190 −0.168714 −0.0843571 0.996436i \(-0.526884\pi\)
−0.0843571 + 0.996436i \(0.526884\pi\)
\(948\) 0 0
\(949\) −33.6571 −1.09256
\(950\) −6.03291 −0.195734
\(951\) 0 0
\(952\) −8.55738 −0.277346
\(953\) 31.0054 1.00436 0.502181 0.864762i \(-0.332531\pi\)
0.502181 + 0.864762i \(0.332531\pi\)
\(954\) 0 0
\(955\) 33.0235 1.06861
\(956\) 116.485 3.76738
\(957\) 0 0
\(958\) −27.8111 −0.898536
\(959\) 10.6933 0.345304
\(960\) 0 0
\(961\) −19.9951 −0.645002
\(962\) 88.8887 2.86589
\(963\) 0 0
\(964\) 75.7640 2.44020
\(965\) 49.6203 1.59733
\(966\) 0 0
\(967\) 6.06932 0.195176 0.0975881 0.995227i \(-0.468887\pi\)
0.0975881 + 0.995227i \(0.468887\pi\)
\(968\) −39.6159 −1.27330
\(969\) 0 0
\(970\) 91.0458 2.92330
\(971\) 8.98673 0.288398 0.144199 0.989549i \(-0.453939\pi\)
0.144199 + 0.989549i \(0.453939\pi\)
\(972\) 0 0
\(973\) −3.73393 −0.119704
\(974\) 43.5581 1.39569
\(975\) 0 0
\(976\) −72.1131 −2.30828
\(977\) −55.0884 −1.76243 −0.881217 0.472711i \(-0.843275\pi\)
−0.881217 + 0.472711i \(0.843275\pi\)
\(978\) 0 0
\(979\) 13.0455 0.416935
\(980\) 9.63456 0.307765
\(981\) 0 0
\(982\) −69.5219 −2.21853
\(983\) −59.7557 −1.90591 −0.952956 0.303109i \(-0.901975\pi\)
−0.952956 + 0.303109i \(0.901975\pi\)
\(984\) 0 0
\(985\) 46.8750 1.49356
\(986\) −23.5596 −0.750291
\(987\) 0 0
\(988\) 108.361 3.44742
\(989\) 0.0751526 0.00238971
\(990\) 0 0
\(991\) −0.373535 −0.0118657 −0.00593286 0.999982i \(-0.501888\pi\)
−0.00593286 + 0.999982i \(0.501888\pi\)
\(992\) 20.1759 0.640584
\(993\) 0 0
\(994\) 3.71045 0.117688
\(995\) −4.05399 −0.128520
\(996\) 0 0
\(997\) 38.3145 1.21343 0.606716 0.794919i \(-0.292487\pi\)
0.606716 + 0.794919i \(0.292487\pi\)
\(998\) −9.57439 −0.303072
\(999\) 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 \(a_p\))