Properties

Label 4012.2.a.f.1.2
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 3
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4012.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0359812909\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.321.1
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(0.239123\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+0.521753 q^{5}\) \(+1.00000 q^{7}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+0.521753 q^{5}\) \(+1.00000 q^{7}\) \(-2.00000 q^{9}\) \(-2.00000 q^{11}\) \(+0.478247 q^{13}\) \(-0.521753 q^{15}\) \(+1.00000 q^{17}\) \(-2.52175 q^{19}\) \(-1.00000 q^{21}\) \(+5.88564 q^{23}\) \(-4.72777 q^{25}\) \(+5.00000 q^{27}\) \(-1.47825 q^{29}\) \(+6.84213 q^{31}\) \(+2.00000 q^{33}\) \(+0.521753 q^{35}\) \(+7.32038 q^{37}\) \(-0.478247 q^{39}\) \(-2.52175 q^{41}\) \(+2.84213 q^{43}\) \(-1.04351 q^{45}\) \(-9.88564 q^{47}\) \(-6.00000 q^{49}\) \(-1.00000 q^{51}\) \(-5.72777 q^{53}\) \(-1.04351 q^{55}\) \(+2.52175 q^{57}\) \(-1.00000 q^{59}\) \(-2.47825 q^{61}\) \(-2.00000 q^{63}\) \(+0.249527 q^{65}\) \(-13.7713 q^{67}\) \(-5.88564 q^{69}\) \(-12.7278 q^{71}\) \(+2.00000 q^{73}\) \(+4.72777 q^{75}\) \(-2.00000 q^{77}\) \(-5.00000 q^{79}\) \(+1.00000 q^{81}\) \(+3.32038 q^{83}\) \(+0.521753 q^{85}\) \(+1.47825 q^{87}\) \(+8.84213 q^{89}\) \(+0.478247 q^{91}\) \(-6.84213 q^{93}\) \(-1.31573 q^{95}\) \(+7.20602 q^{97}\) \(+4.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 3q^{21} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut q^{35} \) \(\mathstrut +\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut -\mathstrut 7q^{41} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut -\mathstrut 18q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut +\mathstrut 7q^{57} \) \(\mathstrut -\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 34q^{65} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 6q^{73} \) \(\mathstrut -\mathstrut 20q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 3q^{81} \) \(\mathstrut -\mathstrut 6q^{83} \) \(\mathstrut +\mathstrut q^{85} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 2q^{91} \) \(\mathstrut -\mathstrut 4q^{93} \) \(\mathstrut -\mathstrut 37q^{95} \) \(\mathstrut -\mathstrut 12q^{97} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 0 0
\(5\) 0.521753 0.233335 0.116668 0.993171i \(-0.462779\pi\)
0.116668 + 0.993171i \(0.462779\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 0.478247 0.132642 0.0663209 0.997798i \(-0.478874\pi\)
0.0663209 + 0.997798i \(0.478874\pi\)
\(14\) 0 0
\(15\) −0.521753 −0.134716
\(16\) 0 0
\(17\) 1.00000 0.242536
\(18\) 0 0
\(19\) −2.52175 −0.578530 −0.289265 0.957249i \(-0.593411\pi\)
−0.289265 + 0.957249i \(0.593411\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) 5.88564 1.22724 0.613620 0.789601i \(-0.289713\pi\)
0.613620 + 0.789601i \(0.289713\pi\)
\(24\) 0 0
\(25\) −4.72777 −0.945555
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −1.47825 −0.274503 −0.137252 0.990536i \(-0.543827\pi\)
−0.137252 + 0.990536i \(0.543827\pi\)
\(30\) 0 0
\(31\) 6.84213 1.22888 0.614442 0.788962i \(-0.289381\pi\)
0.614442 + 0.788962i \(0.289381\pi\)
\(32\) 0 0
\(33\) 2.00000 0.348155
\(34\) 0 0
\(35\) 0.521753 0.0881924
\(36\) 0 0
\(37\) 7.32038 1.20346 0.601732 0.798698i \(-0.294478\pi\)
0.601732 + 0.798698i \(0.294478\pi\)
\(38\) 0 0
\(39\) −0.478247 −0.0765807
\(40\) 0 0
\(41\) −2.52175 −0.393832 −0.196916 0.980420i \(-0.563093\pi\)
−0.196916 + 0.980420i \(0.563093\pi\)
\(42\) 0 0
\(43\) 2.84213 0.433421 0.216711 0.976236i \(-0.430467\pi\)
0.216711 + 0.976236i \(0.430467\pi\)
\(44\) 0 0
\(45\) −1.04351 −0.155557
\(46\) 0 0
\(47\) −9.88564 −1.44197 −0.720984 0.692951i \(-0.756310\pi\)
−0.720984 + 0.692951i \(0.756310\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) −1.00000 −0.140028
\(52\) 0 0
\(53\) −5.72777 −0.786770 −0.393385 0.919374i \(-0.628696\pi\)
−0.393385 + 0.919374i \(0.628696\pi\)
\(54\) 0 0
\(55\) −1.04351 −0.140706
\(56\) 0 0
\(57\) 2.52175 0.334014
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) −2.47825 −0.317307 −0.158653 0.987334i \(-0.550715\pi\)
−0.158653 + 0.987334i \(0.550715\pi\)
\(62\) 0 0
\(63\) −2.00000 −0.251976
\(64\) 0 0
\(65\) 0.249527 0.0309500
\(66\) 0 0
\(67\) −13.7713 −1.68243 −0.841215 0.540701i \(-0.818159\pi\)
−0.841215 + 0.540701i \(0.818159\pi\)
\(68\) 0 0
\(69\) −5.88564 −0.708548
\(70\) 0 0
\(71\) −12.7278 −1.51051 −0.755254 0.655432i \(-0.772487\pi\)
−0.755254 + 0.655432i \(0.772487\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 0 0
\(75\) 4.72777 0.545916
\(76\) 0 0
\(77\) −2.00000 −0.227921
\(78\) 0 0
\(79\) −5.00000 −0.562544 −0.281272 0.959628i \(-0.590756\pi\)
−0.281272 + 0.959628i \(0.590756\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.32038 0.364459 0.182230 0.983256i \(-0.441669\pi\)
0.182230 + 0.983256i \(0.441669\pi\)
\(84\) 0 0
\(85\) 0.521753 0.0565921
\(86\) 0 0
\(87\) 1.47825 0.158485
\(88\) 0 0
\(89\) 8.84213 0.937264 0.468632 0.883393i \(-0.344747\pi\)
0.468632 + 0.883393i \(0.344747\pi\)
\(90\) 0 0
\(91\) 0.478247 0.0501339
\(92\) 0 0
\(93\) −6.84213 −0.709496
\(94\) 0 0
\(95\) −1.31573 −0.134991
\(96\) 0 0
\(97\) 7.20602 0.731660 0.365830 0.930682i \(-0.380785\pi\)
0.365830 + 0.930682i \(0.380785\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −0.592606 −0.0589665 −0.0294833 0.999565i \(-0.509386\pi\)
−0.0294833 + 0.999565i \(0.509386\pi\)
\(102\) 0 0
\(103\) −19.2930 −1.90100 −0.950500 0.310726i \(-0.899428\pi\)
−0.950500 + 0.310726i \(0.899428\pi\)
\(104\) 0 0
\(105\) −0.521753 −0.0509179
\(106\) 0 0
\(107\) 2.04351 0.197553 0.0987766 0.995110i \(-0.468507\pi\)
0.0987766 + 0.995110i \(0.468507\pi\)
\(108\) 0 0
\(109\) 17.7713 1.70218 0.851090 0.525020i \(-0.175942\pi\)
0.851090 + 0.525020i \(0.175942\pi\)
\(110\) 0 0
\(111\) −7.32038 −0.694820
\(112\) 0 0
\(113\) 11.2930 1.06236 0.531180 0.847259i \(-0.321749\pi\)
0.531180 + 0.847259i \(0.321749\pi\)
\(114\) 0 0
\(115\) 3.07085 0.286359
\(116\) 0 0
\(117\) −0.956493 −0.0884278
\(118\) 0 0
\(119\) 1.00000 0.0916698
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 2.52175 0.227379
\(124\) 0 0
\(125\) −5.07550 −0.453966
\(126\) 0 0
\(127\) 7.56526 0.671308 0.335654 0.941985i \(-0.391043\pi\)
0.335654 + 0.941985i \(0.391043\pi\)
\(128\) 0 0
\(129\) −2.84213 −0.250236
\(130\) 0 0
\(131\) −21.6843 −1.89456 −0.947282 0.320402i \(-0.896182\pi\)
−0.947282 + 0.320402i \(0.896182\pi\)
\(132\) 0 0
\(133\) −2.52175 −0.218664
\(134\) 0 0
\(135\) 2.60877 0.224527
\(136\) 0 0
\(137\) 6.04351 0.516332 0.258166 0.966101i \(-0.416882\pi\)
0.258166 + 0.966101i \(0.416882\pi\)
\(138\) 0 0
\(139\) −12.7278 −1.07956 −0.539778 0.841808i \(-0.681492\pi\)
−0.539778 + 0.841808i \(0.681492\pi\)
\(140\) 0 0
\(141\) 9.88564 0.832521
\(142\) 0 0
\(143\) −0.956493 −0.0799860
\(144\) 0 0
\(145\) −0.771280 −0.0640513
\(146\) 0 0
\(147\) 6.00000 0.494872
\(148\) 0 0
\(149\) −5.52175 −0.452360 −0.226180 0.974086i \(-0.572624\pi\)
−0.226180 + 0.974086i \(0.572624\pi\)
\(150\) 0 0
\(151\) −16.3639 −1.33167 −0.665837 0.746097i \(-0.731925\pi\)
−0.665837 + 0.746097i \(0.731925\pi\)
\(152\) 0 0
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) 3.56991 0.286742
\(156\) 0 0
\(157\) 9.20602 0.734720 0.367360 0.930079i \(-0.380262\pi\)
0.367360 + 0.930079i \(0.380262\pi\)
\(158\) 0 0
\(159\) 5.72777 0.454242
\(160\) 0 0
\(161\) 5.88564 0.463853
\(162\) 0 0
\(163\) 14.8148 1.16038 0.580192 0.814480i \(-0.302978\pi\)
0.580192 + 0.814480i \(0.302978\pi\)
\(164\) 0 0
\(165\) 1.04351 0.0812369
\(166\) 0 0
\(167\) −14.7713 −1.14304 −0.571518 0.820590i \(-0.693645\pi\)
−0.571518 + 0.820590i \(0.693645\pi\)
\(168\) 0 0
\(169\) −12.7713 −0.982406
\(170\) 0 0
\(171\) 5.04351 0.385687
\(172\) 0 0
\(173\) −2.24953 −0.171028 −0.0855142 0.996337i \(-0.527253\pi\)
−0.0855142 + 0.996337i \(0.527253\pi\)
\(174\) 0 0
\(175\) −4.72777 −0.357386
\(176\) 0 0
\(177\) 1.00000 0.0751646
\(178\) 0 0
\(179\) −8.47825 −0.633694 −0.316847 0.948477i \(-0.602624\pi\)
−0.316847 + 0.948477i \(0.602624\pi\)
\(180\) 0 0
\(181\) −22.9338 −1.70466 −0.852328 0.523008i \(-0.824810\pi\)
−0.852328 + 0.523008i \(0.824810\pi\)
\(182\) 0 0
\(183\) 2.47825 0.183197
\(184\) 0 0
\(185\) 3.81943 0.280810
\(186\) 0 0
\(187\) −2.00000 −0.146254
\(188\) 0 0
\(189\) 5.00000 0.363696
\(190\) 0 0
\(191\) −13.7986 −0.998434 −0.499217 0.866477i \(-0.666379\pi\)
−0.499217 + 0.866477i \(0.666379\pi\)
\(192\) 0 0
\(193\) −0.434740 −0.0312932 −0.0156466 0.999878i \(-0.504981\pi\)
−0.0156466 + 0.999878i \(0.504981\pi\)
\(194\) 0 0
\(195\) −0.249527 −0.0178690
\(196\) 0 0
\(197\) −22.4991 −1.60299 −0.801496 0.598001i \(-0.795962\pi\)
−0.801496 + 0.598001i \(0.795962\pi\)
\(198\) 0 0
\(199\) 1.72777 0.122479 0.0612393 0.998123i \(-0.480495\pi\)
0.0612393 + 0.998123i \(0.480495\pi\)
\(200\) 0 0
\(201\) 13.7713 0.971351
\(202\) 0 0
\(203\) −1.47825 −0.103753
\(204\) 0 0
\(205\) −1.31573 −0.0918948
\(206\) 0 0
\(207\) −11.7713 −0.818161
\(208\) 0 0
\(209\) 5.04351 0.348867
\(210\) 0 0
\(211\) −6.92915 −0.477022 −0.238511 0.971140i \(-0.576659\pi\)
−0.238511 + 0.971140i \(0.576659\pi\)
\(212\) 0 0
\(213\) 12.7278 0.872093
\(214\) 0 0
\(215\) 1.48289 0.101132
\(216\) 0 0
\(217\) 6.84213 0.464474
\(218\) 0 0
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) 0.478247 0.0321703
\(222\) 0 0
\(223\) −25.6843 −1.71995 −0.859973 0.510340i \(-0.829520\pi\)
−0.859973 + 0.510340i \(0.829520\pi\)
\(224\) 0 0
\(225\) 9.45555 0.630370
\(226\) 0 0
\(227\) 23.4074 1.55360 0.776802 0.629745i \(-0.216841\pi\)
0.776802 + 0.629745i \(0.216841\pi\)
\(228\) 0 0
\(229\) 9.09166 0.600794 0.300397 0.953814i \(-0.402881\pi\)
0.300397 + 0.953814i \(0.402881\pi\)
\(230\) 0 0
\(231\) 2.00000 0.131590
\(232\) 0 0
\(233\) −12.2769 −0.804285 −0.402142 0.915577i \(-0.631734\pi\)
−0.402142 + 0.915577i \(0.631734\pi\)
\(234\) 0 0
\(235\) −5.15787 −0.336462
\(236\) 0 0
\(237\) 5.00000 0.324785
\(238\) 0 0
\(239\) −4.52175 −0.292488 −0.146244 0.989249i \(-0.546718\pi\)
−0.146244 + 0.989249i \(0.546718\pi\)
\(240\) 0 0
\(241\) −15.5653 −1.00265 −0.501323 0.865260i \(-0.667153\pi\)
−0.501323 + 0.865260i \(0.667153\pi\)
\(242\) 0 0
\(243\) −16.0000 −1.02640
\(244\) 0 0
\(245\) −3.13052 −0.200002
\(246\) 0 0
\(247\) −1.20602 −0.0767372
\(248\) 0 0
\(249\) −3.32038 −0.210421
\(250\) 0 0
\(251\) 13.1625 0.830810 0.415405 0.909636i \(-0.363640\pi\)
0.415405 + 0.909636i \(0.363640\pi\)
\(252\) 0 0
\(253\) −11.7713 −0.740054
\(254\) 0 0
\(255\) −0.521753 −0.0326735
\(256\) 0 0
\(257\) 18.6843 1.16549 0.582746 0.812654i \(-0.301978\pi\)
0.582746 + 0.812654i \(0.301978\pi\)
\(258\) 0 0
\(259\) 7.32038 0.454866
\(260\) 0 0
\(261\) 2.95649 0.183002
\(262\) 0 0
\(263\) −0.521753 −0.0321727 −0.0160863 0.999871i \(-0.505121\pi\)
−0.0160863 + 0.999871i \(0.505121\pi\)
\(264\) 0 0
\(265\) −2.98849 −0.183581
\(266\) 0 0
\(267\) −8.84213 −0.541130
\(268\) 0 0
\(269\) −10.1352 −0.617952 −0.308976 0.951070i \(-0.599986\pi\)
−0.308976 + 0.951070i \(0.599986\pi\)
\(270\) 0 0
\(271\) 13.0208 0.790958 0.395479 0.918475i \(-0.370579\pi\)
0.395479 + 0.918475i \(0.370579\pi\)
\(272\) 0 0
\(273\) −0.478247 −0.0289448
\(274\) 0 0
\(275\) 9.45555 0.570191
\(276\) 0 0
\(277\) 9.47825 0.569493 0.284746 0.958603i \(-0.408091\pi\)
0.284746 + 0.958603i \(0.408091\pi\)
\(278\) 0 0
\(279\) −13.6843 −0.819256
\(280\) 0 0
\(281\) −27.1833 −1.62162 −0.810810 0.585309i \(-0.800973\pi\)
−0.810810 + 0.585309i \(0.800973\pi\)
\(282\) 0 0
\(283\) 20.9773 1.24697 0.623486 0.781835i \(-0.285716\pi\)
0.623486 + 0.781835i \(0.285716\pi\)
\(284\) 0 0
\(285\) 1.31573 0.0779373
\(286\) 0 0
\(287\) −2.52175 −0.148854
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −7.20602 −0.422424
\(292\) 0 0
\(293\) −24.8583 −1.45224 −0.726119 0.687570i \(-0.758678\pi\)
−0.726119 + 0.687570i \(0.758678\pi\)
\(294\) 0 0
\(295\) −0.521753 −0.0303777
\(296\) 0 0
\(297\) −10.0000 −0.580259
\(298\) 0 0
\(299\) 2.81479 0.162783
\(300\) 0 0
\(301\) 2.84213 0.163818
\(302\) 0 0
\(303\) 0.592606 0.0340444
\(304\) 0 0
\(305\) −1.29303 −0.0740389
\(306\) 0 0
\(307\) 28.2060 1.60980 0.804901 0.593409i \(-0.202218\pi\)
0.804901 + 0.593409i \(0.202218\pi\)
\(308\) 0 0
\(309\) 19.2930 1.09754
\(310\) 0 0
\(311\) −15.0000 −0.850572 −0.425286 0.905059i \(-0.639826\pi\)
−0.425286 + 0.905059i \(0.639826\pi\)
\(312\) 0 0
\(313\) 10.4782 0.592266 0.296133 0.955147i \(-0.404303\pi\)
0.296133 + 0.955147i \(0.404303\pi\)
\(314\) 0 0
\(315\) −1.04351 −0.0587950
\(316\) 0 0
\(317\) 16.8148 0.944413 0.472206 0.881488i \(-0.343458\pi\)
0.472206 + 0.881488i \(0.343458\pi\)
\(318\) 0 0
\(319\) 2.95649 0.165532
\(320\) 0 0
\(321\) −2.04351 −0.114057
\(322\) 0 0
\(323\) −2.52175 −0.140314
\(324\) 0 0
\(325\) −2.26104 −0.125420
\(326\) 0 0
\(327\) −17.7713 −0.982754
\(328\) 0 0
\(329\) −9.88564 −0.545013
\(330\) 0 0
\(331\) −22.5218 −1.23791 −0.618954 0.785427i \(-0.712443\pi\)
−0.618954 + 0.785427i \(0.712443\pi\)
\(332\) 0 0
\(333\) −14.6408 −0.802309
\(334\) 0 0
\(335\) −7.18521 −0.392570
\(336\) 0 0
\(337\) −10.6408 −0.579639 −0.289820 0.957081i \(-0.593595\pi\)
−0.289820 + 0.957081i \(0.593595\pi\)
\(338\) 0 0
\(339\) −11.2930 −0.613353
\(340\) 0 0
\(341\) −13.6843 −0.741045
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) −3.07085 −0.165329
\(346\) 0 0
\(347\) −35.8194 −1.92289 −0.961444 0.275001i \(-0.911322\pi\)
−0.961444 + 0.275001i \(0.911322\pi\)
\(348\) 0 0
\(349\) −5.40739 −0.289451 −0.144726 0.989472i \(-0.546230\pi\)
−0.144726 + 0.989472i \(0.546230\pi\)
\(350\) 0 0
\(351\) 2.39123 0.127635
\(352\) 0 0
\(353\) 8.27687 0.440533 0.220267 0.975440i \(-0.429307\pi\)
0.220267 + 0.975440i \(0.429307\pi\)
\(354\) 0 0
\(355\) −6.64076 −0.352455
\(356\) 0 0
\(357\) −1.00000 −0.0529256
\(358\) 0 0
\(359\) −15.2495 −0.804839 −0.402420 0.915455i \(-0.631831\pi\)
−0.402420 + 0.915455i \(0.631831\pi\)
\(360\) 0 0
\(361\) −12.6408 −0.665303
\(362\) 0 0
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) 1.04351 0.0546196
\(366\) 0 0
\(367\) 15.8194 0.825768 0.412884 0.910784i \(-0.364522\pi\)
0.412884 + 0.910784i \(0.364522\pi\)
\(368\) 0 0
\(369\) 5.04351 0.262554
\(370\) 0 0
\(371\) −5.72777 −0.297371
\(372\) 0 0
\(373\) 6.72777 0.348351 0.174175 0.984715i \(-0.444274\pi\)
0.174175 + 0.984715i \(0.444274\pi\)
\(374\) 0 0
\(375\) 5.07550 0.262098
\(376\) 0 0
\(377\) −0.706966 −0.0364106
\(378\) 0 0
\(379\) −13.0870 −0.672235 −0.336117 0.941820i \(-0.609114\pi\)
−0.336117 + 0.941820i \(0.609114\pi\)
\(380\) 0 0
\(381\) −7.56526 −0.387580
\(382\) 0 0
\(383\) 16.4991 0.843062 0.421531 0.906814i \(-0.361493\pi\)
0.421531 + 0.906814i \(0.361493\pi\)
\(384\) 0 0
\(385\) −1.04351 −0.0531820
\(386\) 0 0
\(387\) −5.68427 −0.288948
\(388\) 0 0
\(389\) −15.6843 −0.795224 −0.397612 0.917554i \(-0.630161\pi\)
−0.397612 + 0.917554i \(0.630161\pi\)
\(390\) 0 0
\(391\) 5.88564 0.297650
\(392\) 0 0
\(393\) 21.6843 1.09383
\(394\) 0 0
\(395\) −2.60877 −0.131261
\(396\) 0 0
\(397\) 34.9773 1.75546 0.877730 0.479155i \(-0.159057\pi\)
0.877730 + 0.479155i \(0.159057\pi\)
\(398\) 0 0
\(399\) 2.52175 0.126246
\(400\) 0 0
\(401\) −20.2495 −1.01121 −0.505607 0.862764i \(-0.668731\pi\)
−0.505607 + 0.862764i \(0.668731\pi\)
\(402\) 0 0
\(403\) 3.27223 0.163001
\(404\) 0 0
\(405\) 0.521753 0.0259261
\(406\) 0 0
\(407\) −14.6408 −0.725716
\(408\) 0 0
\(409\) 24.2495 1.19906 0.599531 0.800352i \(-0.295354\pi\)
0.599531 + 0.800352i \(0.295354\pi\)
\(410\) 0 0
\(411\) −6.04351 −0.298104
\(412\) 0 0
\(413\) −1.00000 −0.0492068
\(414\) 0 0
\(415\) 1.73242 0.0850411
\(416\) 0 0
\(417\) 12.7278 0.623282
\(418\) 0 0
\(419\) −33.2060 −1.62222 −0.811110 0.584893i \(-0.801136\pi\)
−0.811110 + 0.584893i \(0.801136\pi\)
\(420\) 0 0
\(421\) 31.3412 1.52748 0.763738 0.645526i \(-0.223362\pi\)
0.763738 + 0.645526i \(0.223362\pi\)
\(422\) 0 0
\(423\) 19.7713 0.961313
\(424\) 0 0
\(425\) −4.72777 −0.229331
\(426\) 0 0
\(427\) −2.47825 −0.119931
\(428\) 0 0
\(429\) 0.956493 0.0461799
\(430\) 0 0
\(431\) 12.2287 0.589037 0.294518 0.955646i \(-0.404841\pi\)
0.294518 + 0.955646i \(0.404841\pi\)
\(432\) 0 0
\(433\) −26.6843 −1.28236 −0.641182 0.767389i \(-0.721556\pi\)
−0.641182 + 0.767389i \(0.721556\pi\)
\(434\) 0 0
\(435\) 0.771280 0.0369801
\(436\) 0 0
\(437\) −14.8421 −0.709996
\(438\) 0 0
\(439\) 4.72777 0.225644 0.112822 0.993615i \(-0.464011\pi\)
0.112822 + 0.993615i \(0.464011\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) 20.7551 0.986105 0.493053 0.869999i \(-0.335881\pi\)
0.493053 + 0.869999i \(0.335881\pi\)
\(444\) 0 0
\(445\) 4.61341 0.218697
\(446\) 0 0
\(447\) 5.52175 0.261170
\(448\) 0 0
\(449\) −13.9773 −0.659630 −0.329815 0.944046i \(-0.606986\pi\)
−0.329815 + 0.944046i \(0.606986\pi\)
\(450\) 0 0
\(451\) 5.04351 0.237489
\(452\) 0 0
\(453\) 16.3639 0.768842
\(454\) 0 0
\(455\) 0.249527 0.0116980
\(456\) 0 0
\(457\) 1.81014 0.0846748 0.0423374 0.999103i \(-0.486520\pi\)
0.0423374 + 0.999103i \(0.486520\pi\)
\(458\) 0 0
\(459\) 5.00000 0.233380
\(460\) 0 0
\(461\) 35.6843 1.66198 0.830991 0.556286i \(-0.187774\pi\)
0.830991 + 0.556286i \(0.187774\pi\)
\(462\) 0 0
\(463\) −10.0597 −0.467512 −0.233756 0.972295i \(-0.575102\pi\)
−0.233756 + 0.972295i \(0.575102\pi\)
\(464\) 0 0
\(465\) −3.56991 −0.165550
\(466\) 0 0
\(467\) 9.04351 0.418484 0.209242 0.977864i \(-0.432900\pi\)
0.209242 + 0.977864i \(0.432900\pi\)
\(468\) 0 0
\(469\) −13.7713 −0.635899
\(470\) 0 0
\(471\) −9.20602 −0.424191
\(472\) 0 0
\(473\) −5.68427 −0.261363
\(474\) 0 0
\(475\) 11.9223 0.547032
\(476\) 0 0
\(477\) 11.4555 0.524513
\(478\) 0 0
\(479\) −23.5973 −1.07819 −0.539093 0.842246i \(-0.681233\pi\)
−0.539093 + 0.842246i \(0.681233\pi\)
\(480\) 0 0
\(481\) 3.50095 0.159629
\(482\) 0 0
\(483\) −5.88564 −0.267806
\(484\) 0 0
\(485\) 3.75977 0.170722
\(486\) 0 0
\(487\) −36.2268 −1.64159 −0.820797 0.571220i \(-0.806470\pi\)
−0.820797 + 0.571220i \(0.806470\pi\)
\(488\) 0 0
\(489\) −14.8148 −0.669948
\(490\) 0 0
\(491\) −5.07550 −0.229054 −0.114527 0.993420i \(-0.536535\pi\)
−0.114527 + 0.993420i \(0.536535\pi\)
\(492\) 0 0
\(493\) −1.47825 −0.0665769
\(494\) 0 0
\(495\) 2.08701 0.0938043
\(496\) 0 0
\(497\) −12.7278 −0.570919
\(498\) 0 0
\(499\) 14.7713 0.661253 0.330627 0.943762i \(-0.392740\pi\)
0.330627 + 0.943762i \(0.392740\pi\)
\(500\) 0 0
\(501\) 14.7713 0.659932
\(502\) 0 0
\(503\) −43.0046 −1.91748 −0.958741 0.284280i \(-0.908245\pi\)
−0.958741 + 0.284280i \(0.908245\pi\)
\(504\) 0 0
\(505\) −0.309194 −0.0137590
\(506\) 0 0
\(507\) 12.7713 0.567192
\(508\) 0 0
\(509\) 5.60877 0.248604 0.124302 0.992244i \(-0.460331\pi\)
0.124302 + 0.992244i \(0.460331\pi\)
\(510\) 0 0
\(511\) 2.00000 0.0884748
\(512\) 0 0
\(513\) −12.6088 −0.556691
\(514\) 0 0
\(515\) −10.0662 −0.443570
\(516\) 0 0
\(517\) 19.7713 0.869540
\(518\) 0 0
\(519\) 2.24953 0.0987433
\(520\) 0 0
\(521\) 19.6843 0.862383 0.431192 0.902260i \(-0.358093\pi\)
0.431192 + 0.902260i \(0.358093\pi\)
\(522\) 0 0
\(523\) −40.0643 −1.75189 −0.875945 0.482411i \(-0.839761\pi\)
−0.875945 + 0.482411i \(0.839761\pi\)
\(524\) 0 0
\(525\) 4.72777 0.206337
\(526\) 0 0
\(527\) 6.84213 0.298048
\(528\) 0 0
\(529\) 11.6408 0.506120
\(530\) 0 0
\(531\) 2.00000 0.0867926
\(532\) 0 0
\(533\) −1.20602 −0.0522385
\(534\) 0 0
\(535\) 1.06621 0.0460961
\(536\) 0 0
\(537\) 8.47825 0.365863
\(538\) 0 0
\(539\) 12.0000 0.516877
\(540\) 0 0
\(541\) 41.0255 1.76382 0.881911 0.471416i \(-0.156257\pi\)
0.881911 + 0.471416i \(0.156257\pi\)
\(542\) 0 0
\(543\) 22.9338 0.984183
\(544\) 0 0
\(545\) 9.27223 0.397179
\(546\) 0 0
\(547\) 4.00000 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) 0 0
\(549\) 4.95649 0.211538
\(550\) 0 0
\(551\) 3.72777 0.158808
\(552\) 0 0
\(553\) −5.00000 −0.212622
\(554\) 0 0
\(555\) −3.81943 −0.162126
\(556\) 0 0
\(557\) 13.8695 0.587669 0.293834 0.955856i \(-0.405069\pi\)
0.293834 + 0.955856i \(0.405069\pi\)
\(558\) 0 0
\(559\) 1.35924 0.0574897
\(560\) 0 0
\(561\) 2.00000 0.0844401
\(562\) 0 0
\(563\) −13.6843 −0.576723 −0.288362 0.957522i \(-0.593110\pi\)
−0.288362 + 0.957522i \(0.593110\pi\)
\(564\) 0 0
\(565\) 5.89218 0.247886
\(566\) 0 0
\(567\) 1.00000 0.0419961
\(568\) 0 0
\(569\) 35.8194 1.50163 0.750814 0.660513i \(-0.229661\pi\)
0.750814 + 0.660513i \(0.229661\pi\)
\(570\) 0 0
\(571\) −34.3185 −1.43618 −0.718092 0.695948i \(-0.754984\pi\)
−0.718092 + 0.695948i \(0.754984\pi\)
\(572\) 0 0
\(573\) 13.7986 0.576446
\(574\) 0 0
\(575\) −27.8260 −1.16042
\(576\) 0 0
\(577\) 25.0000 1.04076 0.520382 0.853934i \(-0.325790\pi\)
0.520382 + 0.853934i \(0.325790\pi\)
\(578\) 0 0
\(579\) 0.434740 0.0180672
\(580\) 0 0
\(581\) 3.32038 0.137753
\(582\) 0 0
\(583\) 11.4555 0.474440
\(584\) 0 0
\(585\) −0.499054 −0.0206333
\(586\) 0 0
\(587\) 30.7004 1.26714 0.633571 0.773684i \(-0.281588\pi\)
0.633571 + 0.773684i \(0.281588\pi\)
\(588\) 0 0
\(589\) −17.2542 −0.710946
\(590\) 0 0
\(591\) 22.4991 0.925487
\(592\) 0 0
\(593\) −35.2703 −1.44838 −0.724190 0.689601i \(-0.757786\pi\)
−0.724190 + 0.689601i \(0.757786\pi\)
\(594\) 0 0
\(595\) 0.521753 0.0213898
\(596\) 0 0
\(597\) −1.72777 −0.0707131
\(598\) 0 0
\(599\) −23.9773 −0.979686 −0.489843 0.871811i \(-0.662946\pi\)
−0.489843 + 0.871811i \(0.662946\pi\)
\(600\) 0 0
\(601\) 32.6731 1.33276 0.666381 0.745611i \(-0.267842\pi\)
0.666381 + 0.745611i \(0.267842\pi\)
\(602\) 0 0
\(603\) 27.5426 1.12162
\(604\) 0 0
\(605\) −3.65227 −0.148486
\(606\) 0 0
\(607\) 38.6296 1.56793 0.783963 0.620808i \(-0.213195\pi\)
0.783963 + 0.620808i \(0.213195\pi\)
\(608\) 0 0
\(609\) 1.47825 0.0599016
\(610\) 0 0
\(611\) −4.72777 −0.191265
\(612\) 0 0
\(613\) −9.24488 −0.373397 −0.186699 0.982417i \(-0.559779\pi\)
−0.186699 + 0.982417i \(0.559779\pi\)
\(614\) 0 0
\(615\) 1.31573 0.0530555
\(616\) 0 0
\(617\) 7.97730 0.321154 0.160577 0.987023i \(-0.448665\pi\)
0.160577 + 0.987023i \(0.448665\pi\)
\(618\) 0 0
\(619\) 23.8148 0.957197 0.478599 0.878034i \(-0.341145\pi\)
0.478599 + 0.878034i \(0.341145\pi\)
\(620\) 0 0
\(621\) 29.4282 1.18091
\(622\) 0 0
\(623\) 8.84213 0.354253
\(624\) 0 0
\(625\) 20.9907 0.839628
\(626\) 0 0
\(627\) −5.04351 −0.201418
\(628\) 0 0
\(629\) 7.32038 0.291883
\(630\) 0 0
\(631\) 25.2268 1.00426 0.502132 0.864791i \(-0.332549\pi\)
0.502132 + 0.864791i \(0.332549\pi\)
\(632\) 0 0
\(633\) 6.92915 0.275409
\(634\) 0 0
\(635\) 3.94720 0.156640
\(636\) 0 0
\(637\) −2.86948 −0.113693
\(638\) 0 0
\(639\) 25.4555 1.00701
\(640\) 0 0
\(641\) 40.4120 1.59618 0.798090 0.602539i \(-0.205844\pi\)
0.798090 + 0.602539i \(0.205844\pi\)
\(642\) 0 0
\(643\) −46.0528 −1.81615 −0.908073 0.418813i \(-0.862446\pi\)
−0.908073 + 0.418813i \(0.862446\pi\)
\(644\) 0 0
\(645\) −1.48289 −0.0583888
\(646\) 0 0
\(647\) −30.3800 −1.19436 −0.597181 0.802106i \(-0.703713\pi\)
−0.597181 + 0.802106i \(0.703713\pi\)
\(648\) 0 0
\(649\) 2.00000 0.0785069
\(650\) 0 0
\(651\) −6.84213 −0.268164
\(652\) 0 0
\(653\) −6.69578 −0.262026 −0.131013 0.991381i \(-0.541823\pi\)
−0.131013 + 0.991381i \(0.541823\pi\)
\(654\) 0 0
\(655\) −11.3138 −0.442068
\(656\) 0 0
\(657\) −4.00000 −0.156055
\(658\) 0 0
\(659\) 29.2657 1.14003 0.570015 0.821635i \(-0.306938\pi\)
0.570015 + 0.821635i \(0.306938\pi\)
\(660\) 0 0
\(661\) 10.5973 0.412185 0.206093 0.978532i \(-0.433925\pi\)
0.206093 + 0.978532i \(0.433925\pi\)
\(662\) 0 0
\(663\) −0.478247 −0.0185736
\(664\) 0 0
\(665\) −1.31573 −0.0510220
\(666\) 0 0
\(667\) −8.70043 −0.336882
\(668\) 0 0
\(669\) 25.6843 0.993011
\(670\) 0 0
\(671\) 4.95649 0.191343
\(672\) 0 0
\(673\) 40.1560 1.54790 0.773950 0.633247i \(-0.218278\pi\)
0.773950 + 0.633247i \(0.218278\pi\)
\(674\) 0 0
\(675\) −23.6389 −0.909860
\(676\) 0 0
\(677\) −38.4991 −1.47964 −0.739819 0.672805i \(-0.765089\pi\)
−0.739819 + 0.672805i \(0.765089\pi\)
\(678\) 0 0
\(679\) 7.20602 0.276542
\(680\) 0 0
\(681\) −23.4074 −0.896973
\(682\) 0 0
\(683\) 20.6616 0.790593 0.395296 0.918554i \(-0.370642\pi\)
0.395296 + 0.918554i \(0.370642\pi\)
\(684\) 0 0
\(685\) 3.15322 0.120478
\(686\) 0 0
\(687\) −9.09166 −0.346868
\(688\) 0 0
\(689\) −2.73929 −0.104359
\(690\) 0 0
\(691\) −25.2542 −0.960714 −0.480357 0.877073i \(-0.659493\pi\)
−0.480357 + 0.877073i \(0.659493\pi\)
\(692\) 0 0
\(693\) 4.00000 0.151947
\(694\) 0 0
\(695\) −6.64076 −0.251898
\(696\) 0 0
\(697\) −2.52175 −0.0955182
\(698\) 0 0
\(699\) 12.2769 0.464354
\(700\) 0 0
\(701\) 36.2977 1.37094 0.685472 0.728099i \(-0.259596\pi\)
0.685472 + 0.728099i \(0.259596\pi\)
\(702\) 0 0
\(703\) −18.4602 −0.696239
\(704\) 0 0
\(705\) 5.15787 0.194257
\(706\) 0 0
\(707\) −0.592606 −0.0222873
\(708\) 0 0
\(709\) 14.7505 0.553966 0.276983 0.960875i \(-0.410665\pi\)
0.276983 + 0.960875i \(0.410665\pi\)
\(710\) 0 0
\(711\) 10.0000 0.375029
\(712\) 0 0
\(713\) 40.2703 1.50814
\(714\) 0 0
\(715\) −0.499054 −0.0186635
\(716\) 0 0
\(717\) 4.52175 0.168868
\(718\) 0 0
\(719\) 4.73929 0.176746 0.0883728 0.996087i \(-0.471833\pi\)
0.0883728 + 0.996087i \(0.471833\pi\)
\(720\) 0 0
\(721\) −19.2930 −0.718510
\(722\) 0 0
\(723\) 15.5653 0.578878
\(724\) 0 0
\(725\) 6.98881 0.259558
\(726\) 0 0
\(727\) 20.4991 0.760268 0.380134 0.924931i \(-0.375878\pi\)
0.380134 + 0.924931i \(0.375878\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 2.84213 0.105120
\(732\) 0 0
\(733\) −40.1833 −1.48420 −0.742102 0.670287i \(-0.766171\pi\)
−0.742102 + 0.670287i \(0.766171\pi\)
\(734\) 0 0
\(735\) 3.13052 0.115471
\(736\) 0 0
\(737\) 27.5426 1.01454
\(738\) 0 0
\(739\) 33.8791 1.24626 0.623131 0.782117i \(-0.285860\pi\)
0.623131 + 0.782117i \(0.285860\pi\)
\(740\) 0 0
\(741\) 1.20602 0.0443042
\(742\) 0 0
\(743\) 3.36853 0.123579 0.0617897 0.998089i \(-0.480319\pi\)
0.0617897 + 0.998089i \(0.480319\pi\)
\(744\) 0 0
\(745\) −2.88099 −0.105551
\(746\) 0 0
\(747\) −6.64076 −0.242973
\(748\) 0 0
\(749\) 2.04351 0.0746681
\(750\) 0 0
\(751\) −39.6843 −1.44810 −0.724050 0.689748i \(-0.757721\pi\)
−0.724050 + 0.689748i \(0.757721\pi\)
\(752\) 0 0
\(753\) −13.1625 −0.479669
\(754\) 0 0
\(755\) −8.53791 −0.310727
\(756\) 0 0
\(757\) −45.8148 −1.66517 −0.832583 0.553900i \(-0.813139\pi\)
−0.832583 + 0.553900i \(0.813139\pi\)
\(758\) 0 0
\(759\) 11.7713 0.427270
\(760\) 0 0
\(761\) 26.2268 0.950722 0.475361 0.879791i \(-0.342318\pi\)
0.475361 + 0.879791i \(0.342318\pi\)
\(762\) 0 0
\(763\) 17.7713 0.643364
\(764\) 0 0
\(765\) −1.04351 −0.0377281
\(766\) 0 0
\(767\) −0.478247 −0.0172685
\(768\) 0 0
\(769\) 9.52175 0.343363 0.171682 0.985152i \(-0.445080\pi\)
0.171682 + 0.985152i \(0.445080\pi\)
\(770\) 0 0
\(771\) −18.6843 −0.672897
\(772\) 0 0
\(773\) 25.5907 0.920434 0.460217 0.887806i \(-0.347772\pi\)
0.460217 + 0.887806i \(0.347772\pi\)
\(774\) 0 0
\(775\) −32.3481 −1.16198
\(776\) 0 0
\(777\) −7.32038 −0.262617
\(778\) 0 0
\(779\) 6.35924 0.227843
\(780\) 0 0
\(781\) 25.4555 0.910871
\(782\) 0 0
\(783\) −7.39123 −0.264141
\(784\) 0 0
\(785\) 4.80327 0.171436
\(786\) 0 0
\(787\) 4.49905 0.160374 0.0801870 0.996780i \(-0.474448\pi\)
0.0801870 + 0.996780i \(0.474448\pi\)
\(788\) 0 0
\(789\) 0.521753 0.0185749
\(790\) 0 0
\(791\) 11.2930 0.401534
\(792\) 0 0
\(793\) −1.18521 −0.0420881
\(794\) 0 0
\(795\) 2.98849 0.105991
\(796\) 0 0
\(797\) −10.0755 −0.356892 −0.178446 0.983950i \(-0.557107\pi\)
−0.178446 + 0.983950i \(0.557107\pi\)
\(798\) 0 0
\(799\) −9.88564 −0.349729
\(800\) 0 0
\(801\) −17.6843 −0.624843
\(802\) 0 0
\(803\) −4.00000 −0.141157
\(804\) 0 0
\(805\) 3.07085 0.108233
\(806\) 0 0
\(807\) 10.1352 0.356775
\(808\) 0 0
\(809\) 34.8629 1.22572 0.612858 0.790193i \(-0.290020\pi\)
0.612858 + 0.790193i \(0.290020\pi\)
\(810\) 0 0
\(811\) 26.6889 0.937174 0.468587 0.883417i \(-0.344763\pi\)
0.468587 + 0.883417i \(0.344763\pi\)
\(812\) 0 0
\(813\) −13.0208 −0.456660
\(814\) 0 0
\(815\) 7.72967 0.270758
\(816\) 0 0
\(817\) −7.16716 −0.250747
\(818\) 0 0
\(819\) −0.956493 −0.0334226
\(820\) 0 0
\(821\) −10.0482 −0.350683 −0.175341 0.984508i \(-0.556103\pi\)
−0.175341 + 0.984508i \(0.556103\pi\)
\(822\) 0 0
\(823\) 39.2060 1.36664 0.683318 0.730121i \(-0.260536\pi\)
0.683318 + 0.730121i \(0.260536\pi\)
\(824\) 0 0
\(825\) −9.45555 −0.329200
\(826\) 0 0
\(827\) −22.8148 −0.793348 −0.396674 0.917960i \(-0.629836\pi\)
−0.396674 + 0.917960i \(0.629836\pi\)
\(828\) 0 0
\(829\) −23.0963 −0.802168 −0.401084 0.916041i \(-0.631366\pi\)
−0.401084 + 0.916041i \(0.631366\pi\)
\(830\) 0 0
\(831\) −9.47825 −0.328797
\(832\) 0 0
\(833\) −6.00000 −0.207888
\(834\) 0 0
\(835\) −7.70697 −0.266711
\(836\) 0 0
\(837\) 34.2107 1.18249
\(838\) 0 0
\(839\) −13.5491 −0.467767 −0.233883 0.972265i \(-0.575143\pi\)
−0.233883 + 0.972265i \(0.575143\pi\)
\(840\) 0 0
\(841\) −26.8148 −0.924648
\(842\) 0 0
\(843\) 27.1833 0.936243
\(844\) 0 0
\(845\) −6.66346 −0.229230
\(846\) 0 0
\(847\) −7.00000 −0.240523
\(848\) 0 0
\(849\) −20.9773 −0.719939
\(850\) 0 0
\(851\) 43.0851 1.47694
\(852\) 0 0
\(853\) 24.0320 0.822840 0.411420 0.911446i \(-0.365033\pi\)
0.411420 + 0.911446i \(0.365033\pi\)
\(854\) 0 0
\(855\) 2.63147 0.0899943
\(856\) 0 0
\(857\) 33.5699 1.14673 0.573363 0.819301i \(-0.305638\pi\)
0.573363 + 0.819301i \(0.305638\pi\)
\(858\) 0 0
\(859\) 32.4717 1.10792 0.553960 0.832543i \(-0.313116\pi\)
0.553960 + 0.832543i \(0.313116\pi\)
\(860\) 0 0
\(861\) 2.52175 0.0859411
\(862\) 0 0
\(863\) 1.50095 0.0510928 0.0255464 0.999674i \(-0.491867\pi\)
0.0255464 + 0.999674i \(0.491867\pi\)
\(864\) 0 0
\(865\) −1.17370 −0.0399069
\(866\) 0 0
\(867\) −1.00000 −0.0339618
\(868\) 0 0
\(869\) 10.0000 0.339227
\(870\) 0 0
\(871\) −6.58607 −0.223160
\(872\) 0 0
\(873\) −14.4120 −0.487774
\(874\) 0 0
\(875\) −5.07550 −0.171583
\(876\) 0 0
\(877\) 1.61995 0.0547019 0.0273510 0.999626i \(-0.491293\pi\)
0.0273510 + 0.999626i \(0.491293\pi\)
\(878\) 0 0
\(879\) 24.8583 0.838449
\(880\) 0 0
\(881\) −31.2657 −1.05337 −0.526684 0.850061i \(-0.676565\pi\)
−0.526684 + 0.850061i \(0.676565\pi\)
\(882\) 0 0
\(883\) 13.6616 0.459748 0.229874 0.973220i \(-0.426169\pi\)
0.229874 + 0.973220i \(0.426169\pi\)
\(884\) 0 0
\(885\) 0.521753 0.0175386
\(886\) 0 0
\(887\) −6.90180 −0.231740 −0.115870 0.993264i \(-0.536966\pi\)
−0.115870 + 0.993264i \(0.536966\pi\)
\(888\) 0 0
\(889\) 7.56526 0.253731
\(890\) 0 0
\(891\) −2.00000 −0.0670025
\(892\) 0 0
\(893\) 24.9291 0.834222
\(894\) 0 0
\(895\) −4.42355 −0.147863
\(896\) 0 0
\(897\) −2.81479 −0.0939830
\(898\) 0 0
\(899\) −10.1144 −0.337333
\(900\) 0 0
\(901\) −5.72777 −0.190820
\(902\) 0 0
\(903\) −2.84213 −0.0945803
\(904\) 0 0
\(905\) −11.9658 −0.397756
\(906\) 0 0
\(907\) 24.9130 0.827222 0.413611 0.910454i \(-0.364267\pi\)
0.413611 + 0.910454i \(0.364267\pi\)
\(908\) 0 0
\(909\) 1.18521 0.0393110
\(910\) 0 0
\(911\) 41.4444 1.37311 0.686556 0.727076i \(-0.259121\pi\)
0.686556 + 0.727076i \(0.259121\pi\)
\(912\) 0 0
\(913\) −6.64076 −0.219777
\(914\) 0 0
\(915\) 1.29303 0.0427464
\(916\) 0 0
\(917\) −21.6843 −0.716078
\(918\) 0 0
\(919\) 0.180567 0.00595634 0.00297817 0.999996i \(-0.499052\pi\)
0.00297817 + 0.999996i \(0.499052\pi\)
\(920\) 0 0
\(921\) −28.2060 −0.929420
\(922\) 0 0
\(923\) −6.08701 −0.200356
\(924\) 0 0
\(925\) −34.6091 −1.13794
\(926\) 0 0
\(927\) 38.5861 1.26733
\(928\) 0 0
\(929\) −15.3592 −0.503920 −0.251960 0.967738i \(-0.581075\pi\)
−0.251960 + 0.967738i \(0.581075\pi\)
\(930\) 0 0
\(931\) 15.1305 0.495883
\(932\) 0 0
\(933\) 15.0000 0.491078
\(934\) 0 0
\(935\) −1.04351 −0.0341263
\(936\) 0 0
\(937\) 2.26104 0.0738650 0.0369325 0.999318i \(-0.488241\pi\)
0.0369325 + 0.999318i \(0.488241\pi\)
\(938\) 0 0
\(939\) −10.4782 −0.341945
\(940\) 0 0
\(941\) −25.5310 −0.832288 −0.416144 0.909299i \(-0.636619\pi\)
−0.416144 + 0.909299i \(0.636619\pi\)
\(942\) 0 0
\(943\) −14.8421 −0.483326
\(944\) 0 0
\(945\) 2.60877 0.0848632
\(946\) 0 0
\(947\) −10.1305 −0.329198 −0.164599 0.986361i \(-0.552633\pi\)
−0.164599 + 0.986361i \(0.552633\pi\)
\(948\) 0 0
\(949\) 0.956493 0.0310491
\(950\) 0 0
\(951\) −16.8148 −0.545257
\(952\) 0 0
\(953\) −55.2268 −1.78897 −0.894486 0.447096i \(-0.852458\pi\)
−0.894486 + 0.447096i \(0.852458\pi\)
\(954\) 0 0
\(955\) −7.19948 −0.232970
\(956\) 0 0
\(957\) −2.95649 −0.0955698
\(958\) 0 0
\(959\) 6.04351 0.195155
\(960\) 0 0
\(961\) 15.8148 0.510154
\(962\) 0 0
\(963\) −4.08701 −0.131702
\(964\) 0 0
\(965\) −0.226827 −0.00730182
\(966\) 0 0
\(967\) 33.1787 1.06695 0.533477 0.845815i \(-0.320885\pi\)
0.533477 + 0.845815i \(0.320885\pi\)
\(968\) 0 0
\(969\) 2.52175 0.0810104
\(970\) 0 0
\(971\) −5.97730 −0.191821 −0.0959103 0.995390i \(-0.530576\pi\)
−0.0959103 + 0.995390i \(0.530576\pi\)
\(972\) 0 0
\(973\) −12.7278 −0.408034
\(974\) 0 0
\(975\) 2.26104 0.0724113
\(976\) 0 0
\(977\) −44.7874 −1.43288 −0.716439 0.697650i \(-0.754229\pi\)
−0.716439 + 0.697650i \(0.754229\pi\)
\(978\) 0 0
\(979\) −17.6843 −0.565192
\(980\) 0 0
\(981\) −35.5426 −1.13479
\(982\) 0 0
\(983\) 18.9018 0.602874 0.301437 0.953486i \(-0.402534\pi\)
0.301437 + 0.953486i \(0.402534\pi\)
\(984\) 0 0
\(985\) −11.7390 −0.374034
\(986\) 0 0
\(987\) 9.88564 0.314663
\(988\) 0 0
\(989\) 16.7278 0.531912
\(990\) 0 0
\(991\) 26.4509 0.840241 0.420120 0.907468i \(-0.361988\pi\)
0.420120 + 0.907468i \(0.361988\pi\)
\(992\) 0 0
\(993\) 22.5218 0.714706
\(994\) 0 0
\(995\) 0.901472 0.0285786
\(996\) 0 0
\(997\) −3.21721 −0.101890 −0.0509450 0.998701i \(-0.516223\pi\)
−0.0509450 + 0.998701i \(0.516223\pi\)
\(998\) 0 0
\(999\) 36.6019 1.15803
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 \(a_p\))