Properties

Label 270.2.a.a.1.1
Level 270
Weight 2
Character 270.1
Self dual Yes
Analytic conductor 2.156
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 270.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(2.15596085457\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 270.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} +2.00000 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{10} +3.00000 q^{11} -1.00000 q^{13} -2.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} +8.00000 q^{19} -1.00000 q^{20} -3.00000 q^{22} -3.00000 q^{23} +1.00000 q^{25} +1.00000 q^{26} +2.00000 q^{28} +9.00000 q^{29} -7.00000 q^{31} -1.00000 q^{32} -3.00000 q^{34} -2.00000 q^{35} +2.00000 q^{37} -8.00000 q^{38} +1.00000 q^{40} +12.0000 q^{41} -7.00000 q^{43} +3.00000 q^{44} +3.00000 q^{46} +3.00000 q^{47} -3.00000 q^{49} -1.00000 q^{50} -1.00000 q^{52} -12.0000 q^{53} -3.00000 q^{55} -2.00000 q^{56} -9.00000 q^{58} -12.0000 q^{59} -10.0000 q^{61} +7.00000 q^{62} +1.00000 q^{64} +1.00000 q^{65} -4.00000 q^{67} +3.00000 q^{68} +2.00000 q^{70} +2.00000 q^{73} -2.00000 q^{74} +8.00000 q^{76} +6.00000 q^{77} -1.00000 q^{79} -1.00000 q^{80} -12.0000 q^{82} -18.0000 q^{83} -3.00000 q^{85} +7.00000 q^{86} -3.00000 q^{88} -2.00000 q^{91} -3.00000 q^{92} -3.00000 q^{94} -8.00000 q^{95} +14.0000 q^{97} +3.00000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.00000 0.316228
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) 8.00000 1.83533 0.917663 0.397360i \(-0.130073\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −3.00000 −0.639602
\(23\) −3.00000 −0.625543 −0.312772 0.949828i \(-0.601257\pi\)
−0.312772 + 0.949828i \(0.601257\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) 2.00000 0.377964
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) −2.00000 −0.338062
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −8.00000 −1.29777
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) 12.0000 1.87409 0.937043 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) 0 0
\(43\) −7.00000 −1.06749 −0.533745 0.845645i \(-0.679216\pi\)
−0.533745 + 0.845645i \(0.679216\pi\)
\(44\) 3.00000 0.452267
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) −1.00000 −0.138675
\(53\) −12.0000 −1.64833 −0.824163 0.566352i \(-0.808354\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) −2.00000 −0.267261
\(57\) 0 0
\(58\) −9.00000 −1.18176
\(59\) −12.0000 −1.56227 −0.781133 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 7.00000 0.889001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 3.00000 0.363803
\(69\) 0 0
\(70\) 2.00000 0.239046
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −2.00000 −0.232495
\(75\) 0 0
\(76\) 8.00000 0.917663
\(77\) 6.00000 0.683763
\(78\) 0 0
\(79\) −1.00000 −0.112509 −0.0562544 0.998416i \(-0.517916\pi\)
−0.0562544 + 0.998416i \(0.517916\pi\)
\(80\) −1.00000 −0.111803
\(81\) 0 0
\(82\) −12.0000 −1.32518
\(83\) −18.0000 −1.97576 −0.987878 0.155230i \(-0.950388\pi\)
−0.987878 + 0.155230i \(0.950388\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 7.00000 0.754829
\(87\) 0 0
\(88\) −3.00000 −0.319801
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) −2.00000 −0.209657
\(92\) −3.00000 −0.312772
\(93\) 0 0
\(94\) −3.00000 −0.309426
\(95\) −8.00000 −0.820783
\(96\) 0 0
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 3.00000 0.303046
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 3.00000 0.298511 0.149256 0.988799i \(-0.452312\pi\)
0.149256 + 0.988799i \(0.452312\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) 12.0000 1.16554
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 0 0
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 3.00000 0.286039
\(111\) 0 0
\(112\) 2.00000 0.188982
\(113\) 15.0000 1.41108 0.705541 0.708669i \(-0.250704\pi\)
0.705541 + 0.708669i \(0.250704\pi\)
\(114\) 0 0
\(115\) 3.00000 0.279751
\(116\) 9.00000 0.835629
\(117\) 0 0
\(118\) 12.0000 1.10469
\(119\) 6.00000 0.550019
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 10.0000 0.905357
\(123\) 0 0
\(124\) −7.00000 −0.628619
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −1.00000 −0.0877058
\(131\) −3.00000 −0.262111 −0.131056 0.991375i \(-0.541837\pi\)
−0.131056 + 0.991375i \(0.541837\pi\)
\(132\) 0 0
\(133\) 16.0000 1.38738
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) −3.00000 −0.257248
\(137\) 6.00000 0.512615 0.256307 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) −2.00000 −0.169031
\(141\) 0 0
\(142\) 0 0
\(143\) −3.00000 −0.250873
\(144\) 0 0
\(145\) −9.00000 −0.747409
\(146\) −2.00000 −0.165521
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) −15.0000 −1.22885 −0.614424 0.788976i \(-0.710612\pi\)
−0.614424 + 0.788976i \(0.710612\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788 −0.0406894 0.999172i \(-0.512955\pi\)
−0.0406894 + 0.999172i \(0.512955\pi\)
\(152\) −8.00000 −0.648886
\(153\) 0 0
\(154\) −6.00000 −0.483494
\(155\) 7.00000 0.562254
\(156\) 0 0
\(157\) 17.0000 1.35675 0.678374 0.734717i \(-0.262685\pi\)
0.678374 + 0.734717i \(0.262685\pi\)
\(158\) 1.00000 0.0795557
\(159\) 0 0
\(160\) 1.00000 0.0790569
\(161\) −6.00000 −0.472866
\(162\) 0 0
\(163\) −19.0000 −1.48819 −0.744097 0.668071i \(-0.767120\pi\)
−0.744097 + 0.668071i \(0.767120\pi\)
\(164\) 12.0000 0.937043
\(165\) 0 0
\(166\) 18.0000 1.39707
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 3.00000 0.230089
\(171\) 0 0
\(172\) −7.00000 −0.533745
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 0 0
\(175\) 2.00000 0.151186
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) 2.00000 0.148250
\(183\) 0 0
\(184\) 3.00000 0.221163
\(185\) −2.00000 −0.147043
\(186\) 0 0
\(187\) 9.00000 0.658145
\(188\) 3.00000 0.218797
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) −18.0000 −1.30243 −0.651217 0.758891i \(-0.725741\pi\)
−0.651217 + 0.758891i \(0.725741\pi\)
\(192\) 0 0
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) −14.0000 −1.00514
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) 5.00000 0.354441 0.177220 0.984171i \(-0.443289\pi\)
0.177220 + 0.984171i \(0.443289\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0 0
\(202\) −3.00000 −0.211079
\(203\) 18.0000 1.26335
\(204\) 0 0
\(205\) −12.0000 −0.838116
\(206\) −14.0000 −0.975426
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) 24.0000 1.66011
\(210\) 0 0
\(211\) −10.0000 −0.688428 −0.344214 0.938891i \(-0.611855\pi\)
−0.344214 + 0.938891i \(0.611855\pi\)
\(212\) −12.0000 −0.824163
\(213\) 0 0
\(214\) 6.00000 0.410152
\(215\) 7.00000 0.477396
\(216\) 0 0
\(217\) −14.0000 −0.950382
\(218\) 4.00000 0.270914
\(219\) 0 0
\(220\) −3.00000 −0.202260
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) −2.00000 −0.133631
\(225\) 0 0
\(226\) −15.0000 −0.997785
\(227\) −12.0000 −0.796468 −0.398234 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) 0 0
\(229\) −16.0000 −1.05731 −0.528655 0.848837i \(-0.677303\pi\)
−0.528655 + 0.848837i \(0.677303\pi\)
\(230\) −3.00000 −0.197814
\(231\) 0 0
\(232\) −9.00000 −0.590879
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) −3.00000 −0.195698
\(236\) −12.0000 −0.781133
\(237\) 0 0
\(238\) −6.00000 −0.388922
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) 0 0
\(241\) 5.00000 0.322078 0.161039 0.986948i \(-0.448515\pi\)
0.161039 + 0.986948i \(0.448515\pi\)
\(242\) 2.00000 0.128565
\(243\) 0 0
\(244\) −10.0000 −0.640184
\(245\) 3.00000 0.191663
\(246\) 0 0
\(247\) −8.00000 −0.509028
\(248\) 7.00000 0.444500
\(249\) 0 0
\(250\) 1.00000 0.0632456
\(251\) 15.0000 0.946792 0.473396 0.880850i \(-0.343028\pi\)
0.473396 + 0.880850i \(0.343028\pi\)
\(252\) 0 0
\(253\) −9.00000 −0.565825
\(254\) −2.00000 −0.125491
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 15.0000 0.935674 0.467837 0.883815i \(-0.345033\pi\)
0.467837 + 0.883815i \(0.345033\pi\)
\(258\) 0 0
\(259\) 4.00000 0.248548
\(260\) 1.00000 0.0620174
\(261\) 0 0
\(262\) 3.00000 0.185341
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 0 0
\(265\) 12.0000 0.737154
\(266\) −16.0000 −0.981023
\(267\) 0 0
\(268\) −4.00000 −0.244339
\(269\) −21.0000 −1.28039 −0.640196 0.768211i \(-0.721147\pi\)
−0.640196 + 0.768211i \(0.721147\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 3.00000 0.181902
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) 3.00000 0.180907
\(276\) 0 0
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) −14.0000 −0.839664
\(279\) 0 0
\(280\) 2.00000 0.119523
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) −16.0000 −0.951101 −0.475551 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 3.00000 0.177394
\(287\) 24.0000 1.41668
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 9.00000 0.528498
\(291\) 0 0
\(292\) 2.00000 0.117041
\(293\) 30.0000 1.75262 0.876309 0.481749i \(-0.159998\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(294\) 0 0
\(295\) 12.0000 0.698667
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 15.0000 0.868927
\(299\) 3.00000 0.173494
\(300\) 0 0
\(301\) −14.0000 −0.806947
\(302\) 1.00000 0.0575435
\(303\) 0 0
\(304\) 8.00000 0.458831
\(305\) 10.0000 0.572598
\(306\) 0 0
\(307\) 29.0000 1.65512 0.827559 0.561379i \(-0.189729\pi\)
0.827559 + 0.561379i \(0.189729\pi\)
\(308\) 6.00000 0.341882
\(309\) 0 0
\(310\) −7.00000 −0.397573
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 0 0
\(313\) −4.00000 −0.226093 −0.113047 0.993590i \(-0.536061\pi\)
−0.113047 + 0.993590i \(0.536061\pi\)
\(314\) −17.0000 −0.959366
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) −24.0000 −1.34797 −0.673987 0.738743i \(-0.735420\pi\)
−0.673987 + 0.738743i \(0.735420\pi\)
\(318\) 0 0
\(319\) 27.0000 1.51171
\(320\) −1.00000 −0.0559017
\(321\) 0 0
\(322\) 6.00000 0.334367
\(323\) 24.0000 1.33540
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 19.0000 1.05231
\(327\) 0 0
\(328\) −12.0000 −0.662589
\(329\) 6.00000 0.330791
\(330\) 0 0
\(331\) −10.0000 −0.549650 −0.274825 0.961494i \(-0.588620\pi\)
−0.274825 + 0.961494i \(0.588620\pi\)
\(332\) −18.0000 −0.987878
\(333\) 0 0
\(334\) 12.0000 0.656611
\(335\) 4.00000 0.218543
\(336\) 0 0
\(337\) −16.0000 −0.871576 −0.435788 0.900049i \(-0.643530\pi\)
−0.435788 + 0.900049i \(0.643530\pi\)
\(338\) 12.0000 0.652714
\(339\) 0 0
\(340\) −3.00000 −0.162698
\(341\) −21.0000 −1.13721
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 7.00000 0.377415
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) −2.00000 −0.106904
\(351\) 0 0
\(352\) −3.00000 −0.159901
\(353\) −3.00000 −0.159674 −0.0798369 0.996808i \(-0.525440\pi\)
−0.0798369 + 0.996808i \(0.525440\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) 45.0000 2.36842
\(362\) −8.00000 −0.420471
\(363\) 0 0
\(364\) −2.00000 −0.104828
\(365\) −2.00000 −0.104685
\(366\) 0 0
\(367\) −10.0000 −0.521996 −0.260998 0.965339i \(-0.584052\pi\)
−0.260998 + 0.965339i \(0.584052\pi\)
\(368\) −3.00000 −0.156386
\(369\) 0 0
\(370\) 2.00000 0.103975
\(371\) −24.0000 −1.24602
\(372\) 0 0
\(373\) 29.0000 1.50156 0.750782 0.660551i \(-0.229677\pi\)
0.750782 + 0.660551i \(0.229677\pi\)
\(374\) −9.00000 −0.465379
\(375\) 0 0
\(376\) −3.00000 −0.154713
\(377\) −9.00000 −0.463524
\(378\) 0 0
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) −8.00000 −0.410391
\(381\) 0 0
\(382\) 18.0000 0.920960
\(383\) −3.00000 −0.153293 −0.0766464 0.997058i \(-0.524421\pi\)
−0.0766464 + 0.997058i \(0.524421\pi\)
\(384\) 0 0
\(385\) −6.00000 −0.305788
\(386\) −14.0000 −0.712581
\(387\) 0 0
\(388\) 14.0000 0.710742
\(389\) −27.0000 −1.36895 −0.684477 0.729034i \(-0.739969\pi\)
−0.684477 + 0.729034i \(0.739969\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 3.00000 0.151523
\(393\) 0 0
\(394\) 12.0000 0.604551
\(395\) 1.00000 0.0503155
\(396\) 0 0
\(397\) 35.0000 1.75660 0.878300 0.478110i \(-0.158678\pi\)
0.878300 + 0.478110i \(0.158678\pi\)
\(398\) −5.00000 −0.250627
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 12.0000 0.599251 0.299626 0.954057i \(-0.403138\pi\)
0.299626 + 0.954057i \(0.403138\pi\)
\(402\) 0 0
\(403\) 7.00000 0.348695
\(404\) 3.00000 0.149256
\(405\) 0 0
\(406\) −18.0000 −0.893325
\(407\) 6.00000 0.297409
\(408\) 0 0
\(409\) −25.0000 −1.23617 −0.618085 0.786111i \(-0.712091\pi\)
−0.618085 + 0.786111i \(0.712091\pi\)
\(410\) 12.0000 0.592638
\(411\) 0 0
\(412\) 14.0000 0.689730
\(413\) −24.0000 −1.18096
\(414\) 0 0
\(415\) 18.0000 0.883585
\(416\) 1.00000 0.0490290
\(417\) 0 0
\(418\) −24.0000 −1.17388
\(419\) −3.00000 −0.146560 −0.0732798 0.997311i \(-0.523347\pi\)
−0.0732798 + 0.997311i \(0.523347\pi\)
\(420\) 0 0
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) 10.0000 0.486792
\(423\) 0 0
\(424\) 12.0000 0.582772
\(425\) 3.00000 0.145521
\(426\) 0 0
\(427\) −20.0000 −0.967868
\(428\) −6.00000 −0.290021
\(429\) 0 0
\(430\) −7.00000 −0.337570
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 14.0000 0.672022
\(435\) 0 0
\(436\) −4.00000 −0.191565
\(437\) −24.0000 −1.14808
\(438\) 0 0
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 3.00000 0.143019
\(441\) 0 0
\(442\) 3.00000 0.142695
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 4.00000 0.189405
\(447\) 0 0
\(448\) 2.00000 0.0944911
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) 36.0000 1.69517
\(452\) 15.0000 0.705541
\(453\) 0 0
\(454\) 12.0000 0.563188
\(455\) 2.00000 0.0937614
\(456\) 0 0
\(457\) −28.0000 −1.30978 −0.654892 0.755722i \(-0.727286\pi\)
−0.654892 + 0.755722i \(0.727286\pi\)
\(458\) 16.0000 0.747631
\(459\) 0 0
\(460\) 3.00000 0.139876
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 0 0
\(463\) −22.0000 −1.02243 −0.511213 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) 9.00000 0.417815
\(465\) 0 0
\(466\) −18.0000 −0.833834
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) −8.00000 −0.369406
\(470\) 3.00000 0.138380
\(471\) 0 0
\(472\) 12.0000 0.552345
\(473\) −21.0000 −0.965581
\(474\) 0 0
\(475\) 8.00000 0.367065
\(476\) 6.00000 0.275010
\(477\) 0 0
\(478\) 18.0000 0.823301
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −2.00000 −0.0911922
\(482\) −5.00000 −0.227744
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) −14.0000 −0.635707
\(486\) 0 0
\(487\) −4.00000 −0.181257 −0.0906287 0.995885i \(-0.528888\pi\)
−0.0906287 + 0.995885i \(0.528888\pi\)
\(488\) 10.0000 0.452679
\(489\) 0 0
\(490\) −3.00000 −0.135526
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 0 0
\(493\) 27.0000 1.21602
\(494\) 8.00000 0.359937
\(495\) 0 0
\(496\) −7.00000 −0.314309
\(497\) 0 0
\(498\) 0 0
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 0 0
\(502\) −15.0000 −0.669483
\(503\) 21.0000 0.936344 0.468172 0.883637i \(-0.344913\pi\)
0.468172 + 0.883637i \(0.344913\pi\)
\(504\) 0 0
\(505\) −3.00000 −0.133498
\(506\) 9.00000 0.400099
\(507\) 0 0
\(508\) 2.00000 0.0887357
\(509\) 21.0000 0.930809 0.465404 0.885098i \(-0.345909\pi\)
0.465404 + 0.885098i \(0.345909\pi\)
\(510\) 0 0
\(511\) 4.00000 0.176950
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −15.0000 −0.661622
\(515\) −14.0000 −0.616914
\(516\) 0 0
\(517\) 9.00000 0.395820
\(518\) −4.00000 −0.175750
\(519\) 0 0
\(520\) −1.00000 −0.0438529
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) −25.0000 −1.09317 −0.546587 0.837402i \(-0.684073\pi\)
−0.546587 + 0.837402i \(0.684073\pi\)
\(524\) −3.00000 −0.131056
\(525\) 0 0
\(526\) −12.0000 −0.523225
\(527\) −21.0000 −0.914774
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) −12.0000 −0.521247
\(531\) 0 0
\(532\) 16.0000 0.693688
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) 6.00000 0.259403
\(536\) 4.00000 0.172774
\(537\) 0 0
\(538\) 21.0000 0.905374
\(539\) −9.00000 −0.387657
\(540\) 0 0
\(541\) −22.0000 −0.945854 −0.472927 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) 16.0000 0.687259
\(543\) 0 0
\(544\) −3.00000 −0.128624
\(545\) 4.00000 0.171341
\(546\) 0 0
\(547\) −19.0000 −0.812381 −0.406191 0.913788i \(-0.633143\pi\)
−0.406191 + 0.913788i \(0.633143\pi\)
\(548\) 6.00000 0.256307
\(549\) 0 0
\(550\) −3.00000 −0.127920
\(551\) 72.0000 3.06730
\(552\) 0 0
\(553\) −2.00000 −0.0850487
\(554\) 22.0000 0.934690
\(555\) 0 0
\(556\) 14.0000 0.593732
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 7.00000 0.296068
\(560\) −2.00000 −0.0845154
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) −18.0000 −0.758610 −0.379305 0.925272i \(-0.623837\pi\)
−0.379305 + 0.925272i \(0.623837\pi\)
\(564\) 0 0
\(565\) −15.0000 −0.631055
\(566\) 16.0000 0.672530
\(567\) 0 0
\(568\) 0 0
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) 26.0000 1.08807 0.544033 0.839064i \(-0.316897\pi\)
0.544033 + 0.839064i \(0.316897\pi\)
\(572\) −3.00000 −0.125436
\(573\) 0 0
\(574\) −24.0000 −1.00174
\(575\) −3.00000 −0.125109
\(576\) 0 0
\(577\) −16.0000 −0.666089 −0.333044 0.942911i \(-0.608076\pi\)
−0.333044 + 0.942911i \(0.608076\pi\)
\(578\) 8.00000 0.332756
\(579\) 0 0
\(580\) −9.00000 −0.373705
\(581\) −36.0000 −1.49353
\(582\) 0 0
\(583\) −36.0000 −1.49097
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) −30.0000 −1.23929
\(587\) 6.00000 0.247647 0.123823 0.992304i \(-0.460484\pi\)
0.123823 + 0.992304i \(0.460484\pi\)
\(588\) 0 0
\(589\) −56.0000 −2.30744
\(590\) −12.0000 −0.494032
\(591\) 0 0
\(592\) 2.00000 0.0821995
\(593\) −21.0000 −0.862367 −0.431183 0.902264i \(-0.641904\pi\)
−0.431183 + 0.902264i \(0.641904\pi\)
\(594\) 0 0
\(595\) −6.00000 −0.245976
\(596\) −15.0000 −0.614424
\(597\) 0 0
\(598\) −3.00000 −0.122679
\(599\) −6.00000 −0.245153 −0.122577 0.992459i \(-0.539116\pi\)
−0.122577 + 0.992459i \(0.539116\pi\)
\(600\) 0 0
\(601\) 29.0000 1.18293 0.591467 0.806329i \(-0.298549\pi\)
0.591467 + 0.806329i \(0.298549\pi\)
\(602\) 14.0000 0.570597
\(603\) 0 0
\(604\) −1.00000 −0.0406894
\(605\) 2.00000 0.0813116
\(606\) 0 0
\(607\) −22.0000 −0.892952 −0.446476 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) −8.00000 −0.324443
\(609\) 0 0
\(610\) −10.0000 −0.404888
\(611\) −3.00000 −0.121367
\(612\) 0 0
\(613\) −25.0000 −1.00974 −0.504870 0.863195i \(-0.668460\pi\)
−0.504870 + 0.863195i \(0.668460\pi\)
\(614\) −29.0000 −1.17034
\(615\) 0 0
\(616\) −6.00000 −0.241747
\(617\) 21.0000 0.845428 0.422714 0.906263i \(-0.361077\pi\)
0.422714 + 0.906263i \(0.361077\pi\)
\(618\) 0 0
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) 7.00000 0.281127
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 4.00000 0.159872
\(627\) 0 0
\(628\) 17.0000 0.678374
\(629\) 6.00000 0.239236
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 1.00000 0.0397779
\(633\) 0 0
\(634\) 24.0000 0.953162
\(635\) −2.00000 −0.0793676
\(636\) 0 0
\(637\) 3.00000 0.118864
\(638\) −27.0000 −1.06894
\(639\) 0 0
\(640\) 1.00000 0.0395285
\(641\) 42.0000 1.65890 0.829450 0.558581i \(-0.188654\pi\)
0.829450 + 0.558581i \(0.188654\pi\)
\(642\) 0 0
\(643\) 41.0000 1.61688 0.808441 0.588577i \(-0.200312\pi\)
0.808441 + 0.588577i \(0.200312\pi\)
\(644\) −6.00000 −0.236433
\(645\) 0 0
\(646\) −24.0000 −0.944267
\(647\) 12.0000 0.471769 0.235884 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) 0 0
\(649\) −36.0000 −1.41312
\(650\) 1.00000 0.0392232
\(651\) 0 0
\(652\) −19.0000 −0.744097
\(653\) −48.0000 −1.87839 −0.939193 0.343391i \(-0.888424\pi\)
−0.939193 + 0.343391i \(0.888424\pi\)
\(654\) 0 0
\(655\) 3.00000 0.117220
\(656\) 12.0000 0.468521
\(657\) 0 0
\(658\) −6.00000 −0.233904
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 10.0000 0.388661
\(663\) 0 0
\(664\) 18.0000 0.698535
\(665\) −16.0000 −0.620453
\(666\) 0 0
\(667\) −27.0000 −1.04544
\(668\) −12.0000 −0.464294
\(669\) 0 0
\(670\) −4.00000 −0.154533
\(671\) −30.0000 −1.15814
\(672\) 0 0
\(673\) 26.0000 1.00223 0.501113 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) 16.0000 0.616297
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) 36.0000 1.38359 0.691796 0.722093i \(-0.256820\pi\)
0.691796 + 0.722093i \(0.256820\pi\)
\(678\) 0 0
\(679\) 28.0000 1.07454
\(680\) 3.00000 0.115045
\(681\) 0 0
\(682\) 21.0000 0.804132
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) 0 0
\(685\) −6.00000 −0.229248
\(686\) 20.0000 0.763604
\(687\) 0 0
\(688\) −7.00000 −0.266872
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) −10.0000 −0.380418 −0.190209 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −14.0000 −0.531050
\(696\) 0 0
\(697\) 36.0000 1.36360
\(698\) −26.0000 −0.984115
\(699\) 0 0
\(700\) 2.00000 0.0755929
\(701\) 33.0000 1.24639 0.623196 0.782065i \(-0.285834\pi\)
0.623196 + 0.782065i \(0.285834\pi\)
\(702\) 0 0
\(703\) 16.0000 0.603451
\(704\) 3.00000 0.113067
\(705\) 0 0
\(706\) 3.00000 0.112906
\(707\) 6.00000 0.225653
\(708\) 0 0
\(709\) −4.00000 −0.150223 −0.0751116 0.997175i \(-0.523931\pi\)
−0.0751116 + 0.997175i \(0.523931\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 21.0000 0.786456
\(714\) 0 0
\(715\) 3.00000 0.112194
\(716\) 12.0000 0.448461
\(717\) 0 0
\(718\) −24.0000 −0.895672
\(719\) −18.0000 −0.671287 −0.335643 0.941989i \(-0.608954\pi\)
−0.335643 + 0.941989i \(0.608954\pi\)
\(720\) 0 0
\(721\) 28.0000 1.04277
\(722\) −45.0000 −1.67473
\(723\) 0 0
\(724\) 8.00000 0.297318
\(725\) 9.00000 0.334252
\(726\) 0 0
\(727\) 44.0000 1.63187 0.815935 0.578144i \(-0.196223\pi\)
0.815935 + 0.578144i \(0.196223\pi\)
\(728\) 2.00000 0.0741249
\(729\) 0 0
\(730\) 2.00000 0.0740233
\(731\) −21.0000 −0.776713
\(732\) 0 0
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) 10.0000 0.369107
\(735\) 0 0
\(736\) 3.00000 0.110581
\(737\) −12.0000 −0.442026
\(738\) 0 0
\(739\) −16.0000 −0.588570 −0.294285 0.955718i \(-0.595081\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) −2.00000 −0.0735215
\(741\) 0 0
\(742\) 24.0000 0.881068
\(743\) −33.0000 −1.21065 −0.605326 0.795977i \(-0.706957\pi\)
−0.605326 + 0.795977i \(0.706957\pi\)
\(744\) 0 0
\(745\) 15.0000 0.549557
\(746\) −29.0000 −1.06177
\(747\) 0 0
\(748\) 9.00000 0.329073
\(749\) −12.0000 −0.438470
\(750\) 0 0
\(751\) −13.0000 −0.474377 −0.237188 0.971464i \(-0.576226\pi\)
−0.237188 + 0.971464i \(0.576226\pi\)
\(752\) 3.00000 0.109399
\(753\) 0 0
\(754\) 9.00000 0.327761
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) −7.00000 −0.254419 −0.127210 0.991876i \(-0.540602\pi\)
−0.127210 + 0.991876i \(0.540602\pi\)
\(758\) −8.00000 −0.290573
\(759\) 0 0
\(760\) 8.00000 0.290191
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 0 0
\(763\) −8.00000 −0.289619
\(764\) −18.0000 −0.651217
\(765\) 0 0
\(766\) 3.00000 0.108394
\(767\) 12.0000 0.433295
\(768\) 0 0
\(769\) −1.00000 −0.0360609 −0.0180305 0.999837i \(-0.505740\pi\)
−0.0180305 + 0.999837i \(0.505740\pi\)
\(770\) 6.00000 0.216225
\(771\) 0 0
\(772\) 14.0000 0.503871
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) 0 0
\(775\) −7.00000 −0.251447
\(776\) −14.0000 −0.502571
\(777\) 0 0
\(778\) 27.0000 0.967997
\(779\) 96.0000 3.43956
\(780\) 0 0
\(781\) 0 0
\(782\) 9.00000 0.321839
\(783\) 0 0
\(784\) −3.00000 −0.107143
\(785\) −17.0000 −0.606756
\(786\) 0 0
\(787\) −31.0000 −1.10503 −0.552515 0.833503i \(-0.686332\pi\)
−0.552515 + 0.833503i \(0.686332\pi\)
\(788\) −12.0000 −0.427482
\(789\) 0 0
\(790\) −1.00000 −0.0355784
\(791\) 30.0000 1.06668
\(792\) 0 0
\(793\) 10.0000 0.355110
\(794\) −35.0000 −1.24210
\(795\) 0 0
\(796\) 5.00000 0.177220
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 9.00000 0.318397
\(800\) −1.00000 −0.0353553
\(801\) 0 0
\(802\) −12.0000 −0.423735
\(803\) 6.00000 0.211735
\(804\) 0 0
\(805\) 6.00000 0.211472
\(806\) −7.00000 −0.246564
\(807\) 0 0
\(808\) −3.00000 −0.105540
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 0 0
\(811\) −10.0000 −0.351147 −0.175574 0.984466i \(-0.556178\pi\)
−0.175574 + 0.984466i \(0.556178\pi\)
\(812\) 18.0000 0.631676
\(813\) 0 0
\(814\) −6.00000 −0.210300
\(815\) 19.0000 0.665541
\(816\) 0 0
\(817\) −56.0000 −1.95919
\(818\) 25.0000 0.874105
\(819\) 0 0
\(820\) −12.0000 −0.419058
\(821\) 30.0000 1.04701 0.523504 0.852023i \(-0.324625\pi\)
0.523504 + 0.852023i \(0.324625\pi\)
\(822\) 0 0
\(823\) 44.0000 1.53374 0.766872 0.641800i \(-0.221812\pi\)
0.766872 + 0.641800i \(0.221812\pi\)
\(824\) −14.0000 −0.487713
\(825\) 0 0
\(826\) 24.0000 0.835067
\(827\) 42.0000 1.46048 0.730242 0.683189i \(-0.239408\pi\)
0.730242 + 0.683189i \(0.239408\pi\)
\(828\) 0 0
\(829\) 20.0000 0.694629 0.347314 0.937749i \(-0.387094\pi\)
0.347314 + 0.937749i \(0.387094\pi\)
\(830\) −18.0000 −0.624789
\(831\) 0 0
\(832\) −1.00000 −0.0346688
\(833\) −9.00000 −0.311832
\(834\) 0 0
\(835\) 12.0000 0.415277
\(836\) 24.0000 0.830057
\(837\) 0 0
\(838\) 3.00000 0.103633
\(839\) 6.00000 0.207143 0.103572 0.994622i \(-0.466973\pi\)
0.103572 + 0.994622i \(0.466973\pi\)
\(840\) 0 0
\(841\) 52.0000 1.79310
\(842\) −8.00000 −0.275698
\(843\) 0 0
\(844\) −10.0000 −0.344214
\(845\) 12.0000 0.412813
\(846\) 0 0
\(847\) −4.00000 −0.137442
\(848\) −12.0000 −0.412082
\(849\) 0 0
\(850\) −3.00000 −0.102899
\(851\) −6.00000 −0.205677
\(852\) 0 0
\(853\) −1.00000 −0.0342393 −0.0171197 0.999853i \(-0.505450\pi\)
−0.0171197 + 0.999853i \(0.505450\pi\)
\(854\) 20.0000 0.684386
\(855\) 0 0
\(856\) 6.00000 0.205076
\(857\) 30.0000 1.02478 0.512390 0.858753i \(-0.328760\pi\)
0.512390 + 0.858753i \(0.328760\pi\)
\(858\) 0 0
\(859\) 50.0000 1.70598 0.852989 0.521929i \(-0.174787\pi\)
0.852989 + 0.521929i \(0.174787\pi\)
\(860\) 7.00000 0.238698
\(861\) 0 0
\(862\) 0 0
\(863\) −33.0000 −1.12333 −0.561667 0.827364i \(-0.689840\pi\)
−0.561667 + 0.827364i \(0.689840\pi\)
\(864\) 0 0
\(865\) 6.00000 0.204006
\(866\) −14.0000 −0.475739
\(867\) 0 0
\(868\) −14.0000 −0.475191
\(869\) −3.00000 −0.101768
\(870\) 0 0
\(871\) 4.00000 0.135535
\(872\) 4.00000 0.135457
\(873\) 0 0
\(874\) 24.0000 0.811812
\(875\) −2.00000 −0.0676123
\(876\) 0 0
\(877\) 53.0000 1.78968 0.894841 0.446384i \(-0.147289\pi\)
0.894841 + 0.446384i \(0.147289\pi\)
\(878\) −8.00000 −0.269987
\(879\) 0 0
\(880\) −3.00000 −0.101130
\(881\) −18.0000 −0.606435 −0.303218 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 0 0
\(883\) −28.0000 −0.942275 −0.471138 0.882060i \(-0.656156\pi\)
−0.471138 + 0.882060i \(0.656156\pi\)
\(884\) −3.00000 −0.100901
\(885\) 0 0
\(886\) 0 0
\(887\) 15.0000 0.503651 0.251825 0.967773i \(-0.418969\pi\)
0.251825 + 0.967773i \(0.418969\pi\)
\(888\) 0 0
\(889\) 4.00000 0.134156
\(890\) 0 0
\(891\) 0 0
\(892\) −4.00000 −0.133930
\(893\) 24.0000 0.803129
\(894\) 0 0
\(895\) −12.0000 −0.401116
\(896\) −2.00000 −0.0668153
\(897\) 0 0
\(898\) −6.00000 −0.200223
\(899\) −63.0000 −2.10117
\(900\) 0 0
\(901\) −36.0000 −1.19933
\(902\) −36.0000 −1.19867
\(903\) 0 0
\(904\) −15.0000 −0.498893
\(905\) −8.00000 −0.265929
\(906\) 0 0
\(907\) 53.0000 1.75984 0.879918 0.475125i \(-0.157597\pi\)
0.879918 + 0.475125i \(0.157597\pi\)
\(908\) −12.0000 −0.398234
\(909\) 0 0
\(910\) −2.00000 −0.0662994
\(911\) 24.0000 0.795155 0.397578 0.917568i \(-0.369851\pi\)
0.397578 + 0.917568i \(0.369851\pi\)
\(912\) 0 0
\(913\) −54.0000 −1.78714
\(914\) 28.0000 0.926158
\(915\) 0 0
\(916\) −16.0000 −0.528655
\(917\) −6.00000 −0.198137
\(918\) 0 0
\(919\) 11.0000 0.362857 0.181428 0.983404i \(-0.441928\pi\)
0.181428 + 0.983404i \(0.441928\pi\)
\(920\) −3.00000 −0.0989071
\(921\) 0 0
\(922\) 30.0000 0.987997
\(923\) 0 0
\(924\) 0 0
\(925\) 2.00000 0.0657596
\(926\) 22.0000 0.722965
\(927\) 0 0
\(928\) −9.00000 −0.295439
\(929\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) −24.0000 −0.786568
\(932\) 18.0000 0.589610
\(933\) 0 0
\(934\) 0 0
\(935\) −9.00000 −0.294331
\(936\) 0 0
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 8.00000 0.261209
\(939\) 0 0
\(940\) −3.00000 −0.0978492
\(941\) −3.00000 −0.0977972 −0.0488986 0.998804i \(-0.515571\pi\)
−0.0488986 + 0.998804i \(0.515571\pi\)
\(942\) 0 0
\(943\) −36.0000 −1.17232
\(944\) −12.0000 −0.390567
\(945\) 0 0
\(946\) 21.0000 0.682769
\(947\) −42.0000 −1.36482 −0.682408 0.730971i \(-0.739067\pi\)
−0.682408 + 0.730971i \(0.739067\pi\)
\(948\) 0 0
\(949\) −2.00000 −0.0649227
\(950\) −8.00000 −0.259554
\(951\) 0 0
\(952\) −6.00000 −0.194461
\(953\) 57.0000 1.84641 0.923206 0.384307i \(-0.125559\pi\)
0.923206 + 0.384307i \(0.125559\pi\)
\(954\) 0 0
\(955\) 18.0000 0.582466
\(956\) −18.0000 −0.582162
\(957\) 0 0
\(958\) 0 0
\(959\) 12.0000 0.387500
\(960\) 0 0
\(961\) 18.0000 0.580645
\(962\) 2.00000 0.0644826
\(963\) 0 0
\(964\) 5.00000 0.161039
\(965\) −14.0000 −0.450676
\(966\) 0 0
\(967\) −58.0000 −1.86515 −0.932577 0.360971i \(-0.882445\pi\)
−0.932577 + 0.360971i \(0.882445\pi\)
\(968\) 2.00000 0.0642824
\(969\) 0 0
\(970\) 14.0000 0.449513
\(971\) −33.0000 −1.05902 −0.529510 0.848304i \(-0.677624\pi\)
−0.529510 + 0.848304i \(0.677624\pi\)
\(972\) 0 0
\(973\) 28.0000 0.897639
\(974\) 4.00000 0.128168
\(975\) 0 0
\(976\) −10.0000 −0.320092
\(977\) −33.0000 −1.05576 −0.527882 0.849318i \(-0.677014\pi\)
−0.527882 + 0.849318i \(0.677014\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 3.00000 0.0958315
\(981\) 0 0
\(982\) −36.0000 −1.14881
\(983\) 45.0000 1.43528 0.717639 0.696416i \(-0.245223\pi\)
0.717639 + 0.696416i \(0.245223\pi\)
\(984\) 0 0
\(985\) 12.0000 0.382352
\(986\) −27.0000 −0.859855
\(987\) 0 0
\(988\) −8.00000 −0.254514
\(989\) 21.0000 0.667761
\(990\) 0 0
\(991\) −7.00000 −0.222362 −0.111181 0.993800i \(-0.535463\pi\)
−0.111181 + 0.993800i \(0.535463\pi\)
\(992\) 7.00000 0.222250
\(993\) 0 0
\(994\) 0 0
\(995\) −5.00000 −0.158511
\(996\) 0 0
\(997\) 17.0000 0.538395 0.269198 0.963085i \(-0.413241\pi\)
0.269198 + 0.963085i \(0.413241\pi\)
\(998\) 4.00000 0.126618
\(999\) 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 \(a_p\))