Properties

Label 4012.2.a.g.1.9
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 12
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: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-0.864716\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.864716 q^{3}\) \(-1.40497 q^{5}\) \(-2.45790 q^{7}\) \(-2.25227 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.864716 q^{3}\) \(-1.40497 q^{5}\) \(-2.45790 q^{7}\) \(-2.25227 q^{9}\) \(+1.26992 q^{11}\) \(+3.79248 q^{13}\) \(-1.21490 q^{15}\) \(-1.00000 q^{17}\) \(+6.52341 q^{19}\) \(-2.12539 q^{21}\) \(+1.32346 q^{23}\) \(-3.02605 q^{25}\) \(-4.54172 q^{27}\) \(-7.10007 q^{29}\) \(+6.91840 q^{31}\) \(+1.09812 q^{33}\) \(+3.45329 q^{35}\) \(+6.38301 q^{37}\) \(+3.27942 q^{39}\) \(-7.21762 q^{41}\) \(+9.21157 q^{43}\) \(+3.16437 q^{45}\) \(-11.3544 q^{47}\) \(-0.958714 q^{49}\) \(-0.864716 q^{51}\) \(-12.1634 q^{53}\) \(-1.78421 q^{55}\) \(+5.64089 q^{57}\) \(+1.00000 q^{59}\) \(-2.31997 q^{61}\) \(+5.53585 q^{63}\) \(-5.32834 q^{65}\) \(-14.7359 q^{67}\) \(+1.14442 q^{69}\) \(-2.56458 q^{71}\) \(+4.85616 q^{73}\) \(-2.61667 q^{75}\) \(-3.12134 q^{77}\) \(+9.22521 q^{79}\) \(+2.82950 q^{81}\) \(-12.6201 q^{83}\) \(+1.40497 q^{85}\) \(-6.13954 q^{87}\) \(+10.0483 q^{89}\) \(-9.32155 q^{91}\) \(+5.98245 q^{93}\) \(-9.16521 q^{95}\) \(-6.67250 q^{97}\) \(-2.86020 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 15q^{19} \) \(\mathstrut +\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 33q^{33} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 30q^{45} \) \(\mathstrut -\mathstrut 60q^{47} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 41q^{57} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 23q^{63} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 62q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 13q^{87} \) \(\mathstrut -\mathstrut 29q^{89} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 31q^{93} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 3q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.864716 0.499244 0.249622 0.968343i \(-0.419694\pi\)
0.249622 + 0.968343i \(0.419694\pi\)
\(4\) 0 0
\(5\) −1.40497 −0.628323 −0.314162 0.949370i \(-0.601723\pi\)
−0.314162 + 0.949370i \(0.601723\pi\)
\(6\) 0 0
\(7\) −2.45790 −0.929000 −0.464500 0.885573i \(-0.653766\pi\)
−0.464500 + 0.885573i \(0.653766\pi\)
\(8\) 0 0
\(9\) −2.25227 −0.750755
\(10\) 0 0
\(11\) 1.26992 0.382896 0.191448 0.981503i \(-0.438682\pi\)
0.191448 + 0.981503i \(0.438682\pi\)
\(12\) 0 0
\(13\) 3.79248 1.05185 0.525923 0.850532i \(-0.323720\pi\)
0.525923 + 0.850532i \(0.323720\pi\)
\(14\) 0 0
\(15\) −1.21490 −0.313687
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 6.52341 1.49657 0.748286 0.663376i \(-0.230877\pi\)
0.748286 + 0.663376i \(0.230877\pi\)
\(20\) 0 0
\(21\) −2.12539 −0.463798
\(22\) 0 0
\(23\) 1.32346 0.275961 0.137981 0.990435i \(-0.455939\pi\)
0.137981 + 0.990435i \(0.455939\pi\)
\(24\) 0 0
\(25\) −3.02605 −0.605210
\(26\) 0 0
\(27\) −4.54172 −0.874054
\(28\) 0 0
\(29\) −7.10007 −1.31845 −0.659225 0.751946i \(-0.729115\pi\)
−0.659225 + 0.751946i \(0.729115\pi\)
\(30\) 0 0
\(31\) 6.91840 1.24258 0.621291 0.783580i \(-0.286609\pi\)
0.621291 + 0.783580i \(0.286609\pi\)
\(32\) 0 0
\(33\) 1.09812 0.191158
\(34\) 0 0
\(35\) 3.45329 0.583712
\(36\) 0 0
\(37\) 6.38301 1.04936 0.524681 0.851299i \(-0.324185\pi\)
0.524681 + 0.851299i \(0.324185\pi\)
\(38\) 0 0
\(39\) 3.27942 0.525127
\(40\) 0 0
\(41\) −7.21762 −1.12720 −0.563601 0.826047i \(-0.690585\pi\)
−0.563601 + 0.826047i \(0.690585\pi\)
\(42\) 0 0
\(43\) 9.21157 1.40475 0.702376 0.711807i \(-0.252123\pi\)
0.702376 + 0.711807i \(0.252123\pi\)
\(44\) 0 0
\(45\) 3.16437 0.471717
\(46\) 0 0
\(47\) −11.3544 −1.65621 −0.828103 0.560576i \(-0.810580\pi\)
−0.828103 + 0.560576i \(0.810580\pi\)
\(48\) 0 0
\(49\) −0.958714 −0.136959
\(50\) 0 0
\(51\) −0.864716 −0.121084
\(52\) 0 0
\(53\) −12.1634 −1.67077 −0.835385 0.549665i \(-0.814755\pi\)
−0.835385 + 0.549665i \(0.814755\pi\)
\(54\) 0 0
\(55\) −1.78421 −0.240582
\(56\) 0 0
\(57\) 5.64089 0.747155
\(58\) 0 0
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) −2.31997 −0.297042 −0.148521 0.988909i \(-0.547451\pi\)
−0.148521 + 0.988909i \(0.547451\pi\)
\(62\) 0 0
\(63\) 5.53585 0.697452
\(64\) 0 0
\(65\) −5.32834 −0.660899
\(66\) 0 0
\(67\) −14.7359 −1.80027 −0.900137 0.435607i \(-0.856534\pi\)
−0.900137 + 0.435607i \(0.856534\pi\)
\(68\) 0 0
\(69\) 1.14442 0.137772
\(70\) 0 0
\(71\) −2.56458 −0.304359 −0.152180 0.988353i \(-0.548629\pi\)
−0.152180 + 0.988353i \(0.548629\pi\)
\(72\) 0 0
\(73\) 4.85616 0.568370 0.284185 0.958769i \(-0.408277\pi\)
0.284185 + 0.958769i \(0.408277\pi\)
\(74\) 0 0
\(75\) −2.61667 −0.302147
\(76\) 0 0
\(77\) −3.12134 −0.355710
\(78\) 0 0
\(79\) 9.22521 1.03792 0.518958 0.854799i \(-0.326320\pi\)
0.518958 + 0.854799i \(0.326320\pi\)
\(80\) 0 0
\(81\) 2.82950 0.314389
\(82\) 0 0
\(83\) −12.6201 −1.38524 −0.692619 0.721304i \(-0.743543\pi\)
−0.692619 + 0.721304i \(0.743543\pi\)
\(84\) 0 0
\(85\) 1.40497 0.152391
\(86\) 0 0
\(87\) −6.13954 −0.658228
\(88\) 0 0
\(89\) 10.0483 1.06512 0.532558 0.846393i \(-0.321231\pi\)
0.532558 + 0.846393i \(0.321231\pi\)
\(90\) 0 0
\(91\) −9.32155 −0.977164
\(92\) 0 0
\(93\) 5.98245 0.620351
\(94\) 0 0
\(95\) −9.16521 −0.940331
\(96\) 0 0
\(97\) −6.67250 −0.677490 −0.338745 0.940878i \(-0.610002\pi\)
−0.338745 + 0.940878i \(0.610002\pi\)
\(98\) 0 0
\(99\) −2.86020 −0.287461
\(100\) 0 0
\(101\) 13.4085 1.33420 0.667100 0.744969i \(-0.267536\pi\)
0.667100 + 0.744969i \(0.267536\pi\)
\(102\) 0 0
\(103\) 10.7335 1.05760 0.528800 0.848746i \(-0.322642\pi\)
0.528800 + 0.848746i \(0.322642\pi\)
\(104\) 0 0
\(105\) 2.98611 0.291415
\(106\) 0 0
\(107\) −15.7214 −1.51985 −0.759924 0.650012i \(-0.774764\pi\)
−0.759924 + 0.650012i \(0.774764\pi\)
\(108\) 0 0
\(109\) −10.8611 −1.04030 −0.520152 0.854074i \(-0.674125\pi\)
−0.520152 + 0.854074i \(0.674125\pi\)
\(110\) 0 0
\(111\) 5.51949 0.523887
\(112\) 0 0
\(113\) −12.1816 −1.14595 −0.572975 0.819573i \(-0.694211\pi\)
−0.572975 + 0.819573i \(0.694211\pi\)
\(114\) 0 0
\(115\) −1.85943 −0.173393
\(116\) 0 0
\(117\) −8.54168 −0.789678
\(118\) 0 0
\(119\) 2.45790 0.225316
\(120\) 0 0
\(121\) −9.38730 −0.853391
\(122\) 0 0
\(123\) −6.24119 −0.562749
\(124\) 0 0
\(125\) 11.2764 1.00859
\(126\) 0 0
\(127\) −17.4744 −1.55060 −0.775302 0.631591i \(-0.782402\pi\)
−0.775302 + 0.631591i \(0.782402\pi\)
\(128\) 0 0
\(129\) 7.96539 0.701314
\(130\) 0 0
\(131\) −7.99832 −0.698816 −0.349408 0.936971i \(-0.613617\pi\)
−0.349408 + 0.936971i \(0.613617\pi\)
\(132\) 0 0
\(133\) −16.0339 −1.39032
\(134\) 0 0
\(135\) 6.38099 0.549189
\(136\) 0 0
\(137\) 3.95226 0.337665 0.168832 0.985645i \(-0.446000\pi\)
0.168832 + 0.985645i \(0.446000\pi\)
\(138\) 0 0
\(139\) −10.9735 −0.930756 −0.465378 0.885112i \(-0.654082\pi\)
−0.465378 + 0.885112i \(0.654082\pi\)
\(140\) 0 0
\(141\) −9.81831 −0.826851
\(142\) 0 0
\(143\) 4.81615 0.402747
\(144\) 0 0
\(145\) 9.97541 0.828413
\(146\) 0 0
\(147\) −0.829015 −0.0683760
\(148\) 0 0
\(149\) −15.9686 −1.30820 −0.654100 0.756408i \(-0.726953\pi\)
−0.654100 + 0.756408i \(0.726953\pi\)
\(150\) 0 0
\(151\) −22.3823 −1.82145 −0.910724 0.413015i \(-0.864476\pi\)
−0.910724 + 0.413015i \(0.864476\pi\)
\(152\) 0 0
\(153\) 2.25227 0.182085
\(154\) 0 0
\(155\) −9.72017 −0.780743
\(156\) 0 0
\(157\) −19.8758 −1.58626 −0.793129 0.609054i \(-0.791549\pi\)
−0.793129 + 0.609054i \(0.791549\pi\)
\(158\) 0 0
\(159\) −10.5179 −0.834122
\(160\) 0 0
\(161\) −3.25295 −0.256368
\(162\) 0 0
\(163\) −2.77046 −0.216999 −0.108500 0.994096i \(-0.534605\pi\)
−0.108500 + 0.994096i \(0.534605\pi\)
\(164\) 0 0
\(165\) −1.54283 −0.120109
\(166\) 0 0
\(167\) 24.7982 1.91895 0.959473 0.281801i \(-0.0909319\pi\)
0.959473 + 0.281801i \(0.0909319\pi\)
\(168\) 0 0
\(169\) 1.38291 0.106378
\(170\) 0 0
\(171\) −14.6924 −1.12356
\(172\) 0 0
\(173\) −10.8989 −0.828630 −0.414315 0.910133i \(-0.635979\pi\)
−0.414315 + 0.910133i \(0.635979\pi\)
\(174\) 0 0
\(175\) 7.43773 0.562240
\(176\) 0 0
\(177\) 0.864716 0.0649960
\(178\) 0 0
\(179\) −1.69364 −0.126589 −0.0632943 0.997995i \(-0.520161\pi\)
−0.0632943 + 0.997995i \(0.520161\pi\)
\(180\) 0 0
\(181\) 1.29745 0.0964390 0.0482195 0.998837i \(-0.484645\pi\)
0.0482195 + 0.998837i \(0.484645\pi\)
\(182\) 0 0
\(183\) −2.00612 −0.148296
\(184\) 0 0
\(185\) −8.96797 −0.659338
\(186\) 0 0
\(187\) −1.26992 −0.0928659
\(188\) 0 0
\(189\) 11.1631 0.811996
\(190\) 0 0
\(191\) −0.465653 −0.0336935 −0.0168467 0.999858i \(-0.505363\pi\)
−0.0168467 + 0.999858i \(0.505363\pi\)
\(192\) 0 0
\(193\) −13.1778 −0.948560 −0.474280 0.880374i \(-0.657292\pi\)
−0.474280 + 0.880374i \(0.657292\pi\)
\(194\) 0 0
\(195\) −4.60750 −0.329950
\(196\) 0 0
\(197\) 21.3903 1.52400 0.761998 0.647580i \(-0.224219\pi\)
0.761998 + 0.647580i \(0.224219\pi\)
\(198\) 0 0
\(199\) 9.46123 0.670689 0.335344 0.942096i \(-0.391147\pi\)
0.335344 + 0.942096i \(0.391147\pi\)
\(200\) 0 0
\(201\) −12.7423 −0.898776
\(202\) 0 0
\(203\) 17.4513 1.22484
\(204\) 0 0
\(205\) 10.1406 0.708248
\(206\) 0 0
\(207\) −2.98080 −0.207180
\(208\) 0 0
\(209\) 8.28421 0.573031
\(210\) 0 0
\(211\) −5.28272 −0.363678 −0.181839 0.983328i \(-0.558205\pi\)
−0.181839 + 0.983328i \(0.558205\pi\)
\(212\) 0 0
\(213\) −2.21763 −0.151949
\(214\) 0 0
\(215\) −12.9420 −0.882638
\(216\) 0 0
\(217\) −17.0048 −1.15436
\(218\) 0 0
\(219\) 4.19920 0.283756
\(220\) 0 0
\(221\) −3.79248 −0.255110
\(222\) 0 0
\(223\) 22.4443 1.50298 0.751492 0.659742i \(-0.229335\pi\)
0.751492 + 0.659742i \(0.229335\pi\)
\(224\) 0 0
\(225\) 6.81547 0.454365
\(226\) 0 0
\(227\) −1.16577 −0.0773751 −0.0386875 0.999251i \(-0.512318\pi\)
−0.0386875 + 0.999251i \(0.512318\pi\)
\(228\) 0 0
\(229\) −4.41708 −0.291889 −0.145944 0.989293i \(-0.546622\pi\)
−0.145944 + 0.989293i \(0.546622\pi\)
\(230\) 0 0
\(231\) −2.69908 −0.177586
\(232\) 0 0
\(233\) 22.7157 1.48815 0.744076 0.668095i \(-0.232890\pi\)
0.744076 + 0.668095i \(0.232890\pi\)
\(234\) 0 0
\(235\) 15.9526 1.04063
\(236\) 0 0
\(237\) 7.97718 0.518174
\(238\) 0 0
\(239\) −11.9563 −0.773388 −0.386694 0.922208i \(-0.626383\pi\)
−0.386694 + 0.922208i \(0.626383\pi\)
\(240\) 0 0
\(241\) 12.8737 0.829268 0.414634 0.909988i \(-0.363910\pi\)
0.414634 + 0.909988i \(0.363910\pi\)
\(242\) 0 0
\(243\) 16.0719 1.03101
\(244\) 0 0
\(245\) 1.34697 0.0860546
\(246\) 0 0
\(247\) 24.7399 1.57416
\(248\) 0 0
\(249\) −10.9128 −0.691572
\(250\) 0 0
\(251\) −13.6277 −0.860175 −0.430088 0.902787i \(-0.641517\pi\)
−0.430088 + 0.902787i \(0.641517\pi\)
\(252\) 0 0
\(253\) 1.68070 0.105664
\(254\) 0 0
\(255\) 1.21490 0.0760802
\(256\) 0 0
\(257\) −19.6606 −1.22640 −0.613199 0.789929i \(-0.710117\pi\)
−0.613199 + 0.789929i \(0.710117\pi\)
\(258\) 0 0
\(259\) −15.6888 −0.974856
\(260\) 0 0
\(261\) 15.9912 0.989833
\(262\) 0 0
\(263\) 5.48341 0.338121 0.169061 0.985606i \(-0.445927\pi\)
0.169061 + 0.985606i \(0.445927\pi\)
\(264\) 0 0
\(265\) 17.0892 1.04978
\(266\) 0 0
\(267\) 8.68892 0.531753
\(268\) 0 0
\(269\) 10.1449 0.618546 0.309273 0.950973i \(-0.399914\pi\)
0.309273 + 0.950973i \(0.399914\pi\)
\(270\) 0 0
\(271\) −3.54207 −0.215165 −0.107583 0.994196i \(-0.534311\pi\)
−0.107583 + 0.994196i \(0.534311\pi\)
\(272\) 0 0
\(273\) −8.06049 −0.487843
\(274\) 0 0
\(275\) −3.84285 −0.231732
\(276\) 0 0
\(277\) 19.2177 1.15468 0.577339 0.816504i \(-0.304091\pi\)
0.577339 + 0.816504i \(0.304091\pi\)
\(278\) 0 0
\(279\) −15.5821 −0.932875
\(280\) 0 0
\(281\) 9.71710 0.579674 0.289837 0.957076i \(-0.406399\pi\)
0.289837 + 0.957076i \(0.406399\pi\)
\(282\) 0 0
\(283\) 5.43775 0.323241 0.161620 0.986853i \(-0.448328\pi\)
0.161620 + 0.986853i \(0.448328\pi\)
\(284\) 0 0
\(285\) −7.92531 −0.469455
\(286\) 0 0
\(287\) 17.7402 1.04717
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −5.76982 −0.338233
\(292\) 0 0
\(293\) −12.9884 −0.758793 −0.379396 0.925234i \(-0.623868\pi\)
−0.379396 + 0.925234i \(0.623868\pi\)
\(294\) 0 0
\(295\) −1.40497 −0.0818007
\(296\) 0 0
\(297\) −5.76763 −0.334672
\(298\) 0 0
\(299\) 5.01922 0.290269
\(300\) 0 0
\(301\) −22.6411 −1.30501
\(302\) 0 0
\(303\) 11.5946 0.666091
\(304\) 0 0
\(305\) 3.25950 0.186638
\(306\) 0 0
\(307\) −13.8146 −0.788438 −0.394219 0.919016i \(-0.628985\pi\)
−0.394219 + 0.919016i \(0.628985\pi\)
\(308\) 0 0
\(309\) 9.28140 0.528000
\(310\) 0 0
\(311\) −18.0508 −1.02357 −0.511784 0.859114i \(-0.671015\pi\)
−0.511784 + 0.859114i \(0.671015\pi\)
\(312\) 0 0
\(313\) −23.8897 −1.35033 −0.675164 0.737668i \(-0.735927\pi\)
−0.675164 + 0.737668i \(0.735927\pi\)
\(314\) 0 0
\(315\) −7.77773 −0.438225
\(316\) 0 0
\(317\) 8.54912 0.480166 0.240083 0.970752i \(-0.422825\pi\)
0.240083 + 0.970752i \(0.422825\pi\)
\(318\) 0 0
\(319\) −9.01653 −0.504829
\(320\) 0 0
\(321\) −13.5946 −0.758775
\(322\) 0 0
\(323\) −6.52341 −0.362972
\(324\) 0 0
\(325\) −11.4762 −0.636587
\(326\) 0 0
\(327\) −9.39176 −0.519366
\(328\) 0 0
\(329\) 27.9080 1.53862
\(330\) 0 0
\(331\) 11.8675 0.652298 0.326149 0.945318i \(-0.394249\pi\)
0.326149 + 0.945318i \(0.394249\pi\)
\(332\) 0 0
\(333\) −14.3762 −0.787814
\(334\) 0 0
\(335\) 20.7035 1.13115
\(336\) 0 0
\(337\) −6.29403 −0.342858 −0.171429 0.985197i \(-0.554838\pi\)
−0.171429 + 0.985197i \(0.554838\pi\)
\(338\) 0 0
\(339\) −10.5336 −0.572109
\(340\) 0 0
\(341\) 8.78582 0.475779
\(342\) 0 0
\(343\) 19.5617 1.05623
\(344\) 0 0
\(345\) −1.60788 −0.0865654
\(346\) 0 0
\(347\) 3.19978 0.171773 0.0858866 0.996305i \(-0.472628\pi\)
0.0858866 + 0.996305i \(0.472628\pi\)
\(348\) 0 0
\(349\) 26.2383 1.40450 0.702252 0.711929i \(-0.252178\pi\)
0.702252 + 0.711929i \(0.252178\pi\)
\(350\) 0 0
\(351\) −17.2244 −0.919370
\(352\) 0 0
\(353\) 11.1625 0.594119 0.297059 0.954859i \(-0.403994\pi\)
0.297059 + 0.954859i \(0.403994\pi\)
\(354\) 0 0
\(355\) 3.60316 0.191236
\(356\) 0 0
\(357\) 2.12539 0.112487
\(358\) 0 0
\(359\) −31.3590 −1.65506 −0.827532 0.561418i \(-0.810256\pi\)
−0.827532 + 0.561418i \(0.810256\pi\)
\(360\) 0 0
\(361\) 23.5548 1.23973
\(362\) 0 0
\(363\) −8.11735 −0.426050
\(364\) 0 0
\(365\) −6.82278 −0.357120
\(366\) 0 0
\(367\) −8.85347 −0.462147 −0.231074 0.972936i \(-0.574224\pi\)
−0.231074 + 0.972936i \(0.574224\pi\)
\(368\) 0 0
\(369\) 16.2560 0.846253
\(370\) 0 0
\(371\) 29.8964 1.55215
\(372\) 0 0
\(373\) −31.6779 −1.64022 −0.820111 0.572205i \(-0.806088\pi\)
−0.820111 + 0.572205i \(0.806088\pi\)
\(374\) 0 0
\(375\) 9.75087 0.503533
\(376\) 0 0
\(377\) −26.9269 −1.38680
\(378\) 0 0
\(379\) 28.2687 1.45206 0.726032 0.687661i \(-0.241362\pi\)
0.726032 + 0.687661i \(0.241362\pi\)
\(380\) 0 0
\(381\) −15.1104 −0.774129
\(382\) 0 0
\(383\) 15.9554 0.815285 0.407643 0.913142i \(-0.366351\pi\)
0.407643 + 0.913142i \(0.366351\pi\)
\(384\) 0 0
\(385\) 4.38541 0.223501
\(386\) 0 0
\(387\) −20.7469 −1.05462
\(388\) 0 0
\(389\) 12.9543 0.656810 0.328405 0.944537i \(-0.393489\pi\)
0.328405 + 0.944537i \(0.393489\pi\)
\(390\) 0 0
\(391\) −1.32346 −0.0669305
\(392\) 0 0
\(393\) −6.91627 −0.348880
\(394\) 0 0
\(395\) −12.9612 −0.652147
\(396\) 0 0
\(397\) 9.98957 0.501362 0.250681 0.968070i \(-0.419345\pi\)
0.250681 + 0.968070i \(0.419345\pi\)
\(398\) 0 0
\(399\) −13.8648 −0.694107
\(400\) 0 0
\(401\) 8.07820 0.403406 0.201703 0.979447i \(-0.435352\pi\)
0.201703 + 0.979447i \(0.435352\pi\)
\(402\) 0 0
\(403\) 26.2379 1.30700
\(404\) 0 0
\(405\) −3.97538 −0.197538
\(406\) 0 0
\(407\) 8.10593 0.401796
\(408\) 0 0
\(409\) −5.07272 −0.250830 −0.125415 0.992104i \(-0.540026\pi\)
−0.125415 + 0.992104i \(0.540026\pi\)
\(410\) 0 0
\(411\) 3.41759 0.168577
\(412\) 0 0
\(413\) −2.45790 −0.120945
\(414\) 0 0
\(415\) 17.7309 0.870377
\(416\) 0 0
\(417\) −9.48892 −0.464674
\(418\) 0 0
\(419\) −2.11139 −0.103148 −0.0515742 0.998669i \(-0.516424\pi\)
−0.0515742 + 0.998669i \(0.516424\pi\)
\(420\) 0 0
\(421\) 17.8083 0.867922 0.433961 0.900932i \(-0.357116\pi\)
0.433961 + 0.900932i \(0.357116\pi\)
\(422\) 0 0
\(423\) 25.5731 1.24341
\(424\) 0 0
\(425\) 3.02605 0.146785
\(426\) 0 0
\(427\) 5.70226 0.275952
\(428\) 0 0
\(429\) 4.16461 0.201069
\(430\) 0 0
\(431\) −18.9057 −0.910656 −0.455328 0.890324i \(-0.650478\pi\)
−0.455328 + 0.890324i \(0.650478\pi\)
\(432\) 0 0
\(433\) 4.41653 0.212245 0.106122 0.994353i \(-0.466156\pi\)
0.106122 + 0.994353i \(0.466156\pi\)
\(434\) 0 0
\(435\) 8.62590 0.413580
\(436\) 0 0
\(437\) 8.63350 0.412996
\(438\) 0 0
\(439\) 24.8955 1.18820 0.594099 0.804392i \(-0.297509\pi\)
0.594099 + 0.804392i \(0.297509\pi\)
\(440\) 0 0
\(441\) 2.15928 0.102823
\(442\) 0 0
\(443\) −20.6050 −0.978975 −0.489487 0.872010i \(-0.662816\pi\)
−0.489487 + 0.872010i \(0.662816\pi\)
\(444\) 0 0
\(445\) −14.1176 −0.669238
\(446\) 0 0
\(447\) −13.8083 −0.653111
\(448\) 0 0
\(449\) 19.5452 0.922396 0.461198 0.887297i \(-0.347420\pi\)
0.461198 + 0.887297i \(0.347420\pi\)
\(450\) 0 0
\(451\) −9.16581 −0.431601
\(452\) 0 0
\(453\) −19.3544 −0.909347
\(454\) 0 0
\(455\) 13.0965 0.613975
\(456\) 0 0
\(457\) 3.66545 0.171462 0.0857312 0.996318i \(-0.472677\pi\)
0.0857312 + 0.996318i \(0.472677\pi\)
\(458\) 0 0
\(459\) 4.54172 0.211989
\(460\) 0 0
\(461\) −24.5705 −1.14436 −0.572181 0.820127i \(-0.693903\pi\)
−0.572181 + 0.820127i \(0.693903\pi\)
\(462\) 0 0
\(463\) 25.5385 1.18688 0.593439 0.804879i \(-0.297770\pi\)
0.593439 + 0.804879i \(0.297770\pi\)
\(464\) 0 0
\(465\) −8.40519 −0.389781
\(466\) 0 0
\(467\) −19.2767 −0.892020 −0.446010 0.895028i \(-0.647155\pi\)
−0.446010 + 0.895028i \(0.647155\pi\)
\(468\) 0 0
\(469\) 36.2194 1.67245
\(470\) 0 0
\(471\) −17.1869 −0.791930
\(472\) 0 0
\(473\) 11.6980 0.537873
\(474\) 0 0
\(475\) −19.7401 −0.905740
\(476\) 0 0
\(477\) 27.3952 1.25434
\(478\) 0 0
\(479\) 7.38871 0.337599 0.168799 0.985650i \(-0.446011\pi\)
0.168799 + 0.985650i \(0.446011\pi\)
\(480\) 0 0
\(481\) 24.2075 1.10377
\(482\) 0 0
\(483\) −2.81288 −0.127990
\(484\) 0 0
\(485\) 9.37469 0.425683
\(486\) 0 0
\(487\) −31.1498 −1.41153 −0.705767 0.708444i \(-0.749397\pi\)
−0.705767 + 0.708444i \(0.749397\pi\)
\(488\) 0 0
\(489\) −2.39566 −0.108336
\(490\) 0 0
\(491\) −12.5165 −0.564860 −0.282430 0.959288i \(-0.591140\pi\)
−0.282430 + 0.959288i \(0.591140\pi\)
\(492\) 0 0
\(493\) 7.10007 0.319771
\(494\) 0 0
\(495\) 4.01851 0.180618
\(496\) 0 0
\(497\) 6.30348 0.282750
\(498\) 0 0
\(499\) 0.205806 0.00921315 0.00460657 0.999989i \(-0.498534\pi\)
0.00460657 + 0.999989i \(0.498534\pi\)
\(500\) 0 0
\(501\) 21.4434 0.958022
\(502\) 0 0
\(503\) −10.5155 −0.468863 −0.234431 0.972133i \(-0.575323\pi\)
−0.234431 + 0.972133i \(0.575323\pi\)
\(504\) 0 0
\(505\) −18.8386 −0.838308
\(506\) 0 0
\(507\) 1.19583 0.0531086
\(508\) 0 0
\(509\) −13.6417 −0.604658 −0.302329 0.953204i \(-0.597764\pi\)
−0.302329 + 0.953204i \(0.597764\pi\)
\(510\) 0 0
\(511\) −11.9360 −0.528016
\(512\) 0 0
\(513\) −29.6275 −1.30808
\(514\) 0 0
\(515\) −15.0802 −0.664515
\(516\) 0 0
\(517\) −14.4192 −0.634154
\(518\) 0 0
\(519\) −9.42448 −0.413689
\(520\) 0 0
\(521\) 8.08894 0.354383 0.177191 0.984176i \(-0.443299\pi\)
0.177191 + 0.984176i \(0.443299\pi\)
\(522\) 0 0
\(523\) 9.32178 0.407613 0.203807 0.979011i \(-0.434669\pi\)
0.203807 + 0.979011i \(0.434669\pi\)
\(524\) 0 0
\(525\) 6.43153 0.280695
\(526\) 0 0
\(527\) −6.91840 −0.301370
\(528\) 0 0
\(529\) −21.2484 −0.923845
\(530\) 0 0
\(531\) −2.25227 −0.0977400
\(532\) 0 0
\(533\) −27.3727 −1.18564
\(534\) 0 0
\(535\) 22.0882 0.954956
\(536\) 0 0
\(537\) −1.46452 −0.0631986
\(538\) 0 0
\(539\) −1.21749 −0.0524411
\(540\) 0 0
\(541\) −0.687310 −0.0295498 −0.0147749 0.999891i \(-0.504703\pi\)
−0.0147749 + 0.999891i \(0.504703\pi\)
\(542\) 0 0
\(543\) 1.12193 0.0481466
\(544\) 0 0
\(545\) 15.2596 0.653647
\(546\) 0 0
\(547\) −26.5431 −1.13490 −0.567450 0.823408i \(-0.692070\pi\)
−0.567450 + 0.823408i \(0.692070\pi\)
\(548\) 0 0
\(549\) 5.22519 0.223006
\(550\) 0 0
\(551\) −46.3166 −1.97315
\(552\) 0 0
\(553\) −22.6747 −0.964225
\(554\) 0 0
\(555\) −7.75474 −0.329171
\(556\) 0 0
\(557\) 9.41792 0.399050 0.199525 0.979893i \(-0.436060\pi\)
0.199525 + 0.979893i \(0.436060\pi\)
\(558\) 0 0
\(559\) 34.9347 1.47758
\(560\) 0 0
\(561\) −1.09812 −0.0463627
\(562\) 0 0
\(563\) −25.8884 −1.09107 −0.545533 0.838090i \(-0.683673\pi\)
−0.545533 + 0.838090i \(0.683673\pi\)
\(564\) 0 0
\(565\) 17.1149 0.720027
\(566\) 0 0
\(567\) −6.95464 −0.292067
\(568\) 0 0
\(569\) −28.6163 −1.19966 −0.599830 0.800128i \(-0.704765\pi\)
−0.599830 + 0.800128i \(0.704765\pi\)
\(570\) 0 0
\(571\) −32.4796 −1.35923 −0.679614 0.733570i \(-0.737853\pi\)
−0.679614 + 0.733570i \(0.737853\pi\)
\(572\) 0 0
\(573\) −0.402658 −0.0168213
\(574\) 0 0
\(575\) −4.00487 −0.167015
\(576\) 0 0
\(577\) −16.5525 −0.689091 −0.344546 0.938770i \(-0.611967\pi\)
−0.344546 + 0.938770i \(0.611967\pi\)
\(578\) 0 0
\(579\) −11.3951 −0.473563
\(580\) 0 0
\(581\) 31.0190 1.28689
\(582\) 0 0
\(583\) −15.4466 −0.639731
\(584\) 0 0
\(585\) 12.0008 0.496173
\(586\) 0 0
\(587\) 21.7234 0.896622 0.448311 0.893878i \(-0.352026\pi\)
0.448311 + 0.893878i \(0.352026\pi\)
\(588\) 0 0
\(589\) 45.1315 1.85961
\(590\) 0 0
\(591\) 18.4965 0.760846
\(592\) 0 0
\(593\) 21.4114 0.879260 0.439630 0.898179i \(-0.355109\pi\)
0.439630 + 0.898179i \(0.355109\pi\)
\(594\) 0 0
\(595\) −3.45329 −0.141571
\(596\) 0 0
\(597\) 8.18128 0.334837
\(598\) 0 0
\(599\) 26.7962 1.09486 0.547431 0.836851i \(-0.315606\pi\)
0.547431 + 0.836851i \(0.315606\pi\)
\(600\) 0 0
\(601\) 22.5975 0.921772 0.460886 0.887459i \(-0.347532\pi\)
0.460886 + 0.887459i \(0.347532\pi\)
\(602\) 0 0
\(603\) 33.1891 1.35157
\(604\) 0 0
\(605\) 13.1889 0.536205
\(606\) 0 0
\(607\) −29.8772 −1.21268 −0.606340 0.795206i \(-0.707363\pi\)
−0.606340 + 0.795206i \(0.707363\pi\)
\(608\) 0 0
\(609\) 15.0904 0.611494
\(610\) 0 0
\(611\) −43.0613 −1.74207
\(612\) 0 0
\(613\) 47.4094 1.91485 0.957423 0.288688i \(-0.0932190\pi\)
0.957423 + 0.288688i \(0.0932190\pi\)
\(614\) 0 0
\(615\) 8.76871 0.353588
\(616\) 0 0
\(617\) −30.4721 −1.22676 −0.613380 0.789788i \(-0.710190\pi\)
−0.613380 + 0.789788i \(0.710190\pi\)
\(618\) 0 0
\(619\) −12.9767 −0.521577 −0.260788 0.965396i \(-0.583982\pi\)
−0.260788 + 0.965396i \(0.583982\pi\)
\(620\) 0 0
\(621\) −6.01081 −0.241205
\(622\) 0 0
\(623\) −24.6977 −0.989493
\(624\) 0 0
\(625\) −0.712781 −0.0285112
\(626\) 0 0
\(627\) 7.16349 0.286082
\(628\) 0 0
\(629\) −6.38301 −0.254507
\(630\) 0 0
\(631\) −6.03775 −0.240359 −0.120179 0.992752i \(-0.538347\pi\)
−0.120179 + 0.992752i \(0.538347\pi\)
\(632\) 0 0
\(633\) −4.56805 −0.181564
\(634\) 0 0
\(635\) 24.5511 0.974280
\(636\) 0 0
\(637\) −3.63590 −0.144060
\(638\) 0 0
\(639\) 5.77611 0.228499
\(640\) 0 0
\(641\) 16.3185 0.644540 0.322270 0.946648i \(-0.395554\pi\)
0.322270 + 0.946648i \(0.395554\pi\)
\(642\) 0 0
\(643\) −10.4448 −0.411904 −0.205952 0.978562i \(-0.566029\pi\)
−0.205952 + 0.978562i \(0.566029\pi\)
\(644\) 0 0
\(645\) −11.1912 −0.440652
\(646\) 0 0
\(647\) 22.7049 0.892620 0.446310 0.894878i \(-0.352738\pi\)
0.446310 + 0.894878i \(0.352738\pi\)
\(648\) 0 0
\(649\) 1.26992 0.0498488
\(650\) 0 0
\(651\) −14.7043 −0.576306
\(652\) 0 0
\(653\) −11.2960 −0.442045 −0.221023 0.975269i \(-0.570939\pi\)
−0.221023 + 0.975269i \(0.570939\pi\)
\(654\) 0 0
\(655\) 11.2374 0.439083
\(656\) 0 0
\(657\) −10.9374 −0.426707
\(658\) 0 0
\(659\) −29.6163 −1.15369 −0.576843 0.816855i \(-0.695716\pi\)
−0.576843 + 0.816855i \(0.695716\pi\)
\(660\) 0 0
\(661\) 5.20393 0.202409 0.101205 0.994866i \(-0.467730\pi\)
0.101205 + 0.994866i \(0.467730\pi\)
\(662\) 0 0
\(663\) −3.27942 −0.127362
\(664\) 0 0
\(665\) 22.5272 0.873567
\(666\) 0 0
\(667\) −9.39669 −0.363841
\(668\) 0 0
\(669\) 19.4080 0.750356
\(670\) 0 0
\(671\) −2.94618 −0.113736
\(672\) 0 0
\(673\) −7.50186 −0.289175 −0.144588 0.989492i \(-0.546186\pi\)
−0.144588 + 0.989492i \(0.546186\pi\)
\(674\) 0 0
\(675\) 13.7435 0.528986
\(676\) 0 0
\(677\) 5.95163 0.228740 0.114370 0.993438i \(-0.463515\pi\)
0.114370 + 0.993438i \(0.463515\pi\)
\(678\) 0 0
\(679\) 16.4004 0.629388
\(680\) 0 0
\(681\) −1.00806 −0.0386290
\(682\) 0 0
\(683\) 21.0962 0.807222 0.403611 0.914931i \(-0.367755\pi\)
0.403611 + 0.914931i \(0.367755\pi\)
\(684\) 0 0
\(685\) −5.55283 −0.212163
\(686\) 0 0
\(687\) −3.81952 −0.145724
\(688\) 0 0
\(689\) −46.1294 −1.75739
\(690\) 0 0
\(691\) 23.8962 0.909053 0.454527 0.890733i \(-0.349808\pi\)
0.454527 + 0.890733i \(0.349808\pi\)
\(692\) 0 0
\(693\) 7.03010 0.267051
\(694\) 0 0
\(695\) 15.4174 0.584816
\(696\) 0 0
\(697\) 7.21762 0.273387
\(698\) 0 0
\(699\) 19.6426 0.742951
\(700\) 0 0
\(701\) −26.5315 −1.00208 −0.501041 0.865424i \(-0.667049\pi\)
−0.501041 + 0.865424i \(0.667049\pi\)
\(702\) 0 0
\(703\) 41.6390 1.57044
\(704\) 0 0
\(705\) 13.7945 0.519530
\(706\) 0 0
\(707\) −32.9569 −1.23947
\(708\) 0 0
\(709\) 27.9766 1.05068 0.525341 0.850892i \(-0.323938\pi\)
0.525341 + 0.850892i \(0.323938\pi\)
\(710\) 0 0
\(711\) −20.7776 −0.779222
\(712\) 0 0
\(713\) 9.15626 0.342905
\(714\) 0 0
\(715\) −6.76657 −0.253055
\(716\) 0 0
\(717\) −10.3388 −0.386110
\(718\) 0 0
\(719\) 7.10331 0.264909 0.132454 0.991189i \(-0.457714\pi\)
0.132454 + 0.991189i \(0.457714\pi\)
\(720\) 0 0
\(721\) −26.3818 −0.982510
\(722\) 0 0
\(723\) 11.1321 0.414007
\(724\) 0 0
\(725\) 21.4852 0.797939
\(726\) 0 0
\(727\) 17.9008 0.663903 0.331951 0.943296i \(-0.392293\pi\)
0.331951 + 0.943296i \(0.392293\pi\)
\(728\) 0 0
\(729\) 5.40910 0.200337
\(730\) 0 0
\(731\) −9.21157 −0.340702
\(732\) 0 0
\(733\) 47.3404 1.74856 0.874278 0.485425i \(-0.161335\pi\)
0.874278 + 0.485425i \(0.161335\pi\)
\(734\) 0 0
\(735\) 1.16474 0.0429622
\(736\) 0 0
\(737\) −18.7134 −0.689317
\(738\) 0 0
\(739\) −12.2291 −0.449855 −0.224928 0.974375i \(-0.572215\pi\)
−0.224928 + 0.974375i \(0.572215\pi\)
\(740\) 0 0
\(741\) 21.3930 0.785891
\(742\) 0 0
\(743\) −54.1701 −1.98731 −0.993654 0.112478i \(-0.964121\pi\)
−0.993654 + 0.112478i \(0.964121\pi\)
\(744\) 0 0
\(745\) 22.4355 0.821973
\(746\) 0 0
\(747\) 28.4239 1.03997
\(748\) 0 0
\(749\) 38.6418 1.41194
\(750\) 0 0
\(751\) 21.3321 0.778419 0.389209 0.921149i \(-0.372748\pi\)
0.389209 + 0.921149i \(0.372748\pi\)
\(752\) 0 0
\(753\) −11.7841 −0.429437
\(754\) 0 0
\(755\) 31.4466 1.14446
\(756\) 0 0
\(757\) −20.5162 −0.745676 −0.372838 0.927897i \(-0.621615\pi\)
−0.372838 + 0.927897i \(0.621615\pi\)
\(758\) 0 0
\(759\) 1.45333 0.0527524
\(760\) 0 0
\(761\) 35.0095 1.26909 0.634547 0.772884i \(-0.281187\pi\)
0.634547 + 0.772884i \(0.281187\pi\)
\(762\) 0 0
\(763\) 26.6955 0.966443
\(764\) 0 0
\(765\) −3.16437 −0.114408
\(766\) 0 0
\(767\) 3.79248 0.136939
\(768\) 0 0
\(769\) −47.7151 −1.72065 −0.860325 0.509745i \(-0.829740\pi\)
−0.860325 + 0.509745i \(0.829740\pi\)
\(770\) 0 0
\(771\) −17.0009 −0.612271
\(772\) 0 0
\(773\) 13.0274 0.468564 0.234282 0.972169i \(-0.424726\pi\)
0.234282 + 0.972169i \(0.424726\pi\)
\(774\) 0 0
\(775\) −20.9354 −0.752022
\(776\) 0 0
\(777\) −13.5664 −0.486691
\(778\) 0 0
\(779\) −47.0834 −1.68694
\(780\) 0 0
\(781\) −3.25681 −0.116538
\(782\) 0 0
\(783\) 32.2465 1.15240
\(784\) 0 0
\(785\) 27.9249 0.996683
\(786\) 0 0
\(787\) −50.7483 −1.80898 −0.904491 0.426493i \(-0.859749\pi\)
−0.904491 + 0.426493i \(0.859749\pi\)
\(788\) 0 0
\(789\) 4.74159 0.168805
\(790\) 0 0
\(791\) 29.9412 1.06459
\(792\) 0 0
\(793\) −8.79845 −0.312442
\(794\) 0 0
\(795\) 14.7773 0.524098
\(796\) 0 0
\(797\) 30.9689 1.09698 0.548488 0.836159i \(-0.315204\pi\)
0.548488 + 0.836159i \(0.315204\pi\)
\(798\) 0 0
\(799\) 11.3544 0.401689
\(800\) 0 0
\(801\) −22.6314 −0.799642
\(802\) 0 0
\(803\) 6.16694 0.217627
\(804\) 0 0
\(805\) 4.57031 0.161082
\(806\) 0 0
\(807\) 8.77247 0.308805
\(808\) 0 0
\(809\) 44.2100 1.55434 0.777171 0.629289i \(-0.216654\pi\)
0.777171 + 0.629289i \(0.216654\pi\)
\(810\) 0 0
\(811\) 43.4611 1.52612 0.763062 0.646325i \(-0.223695\pi\)
0.763062 + 0.646325i \(0.223695\pi\)
\(812\) 0 0
\(813\) −3.06288 −0.107420
\(814\) 0 0
\(815\) 3.89243 0.136346
\(816\) 0 0
\(817\) 60.0908 2.10231
\(818\) 0 0
\(819\) 20.9946 0.733611
\(820\) 0 0
\(821\) 10.9757 0.383053 0.191527 0.981487i \(-0.438656\pi\)
0.191527 + 0.981487i \(0.438656\pi\)
\(822\) 0 0
\(823\) −49.9430 −1.74090 −0.870452 0.492254i \(-0.836173\pi\)
−0.870452 + 0.492254i \(0.836173\pi\)
\(824\) 0 0
\(825\) −3.32297 −0.115691
\(826\) 0 0
\(827\) 3.81677 0.132722 0.0663610 0.997796i \(-0.478861\pi\)
0.0663610 + 0.997796i \(0.478861\pi\)
\(828\) 0 0
\(829\) 28.8265 1.00119 0.500594 0.865682i \(-0.333115\pi\)
0.500594 + 0.865682i \(0.333115\pi\)
\(830\) 0 0
\(831\) 16.6178 0.576466
\(832\) 0 0
\(833\) 0.958714 0.0332175
\(834\) 0 0
\(835\) −34.8409 −1.20572
\(836\) 0 0
\(837\) −31.4214 −1.08608
\(838\) 0 0
\(839\) 28.2710 0.976023 0.488011 0.872837i \(-0.337722\pi\)
0.488011 + 0.872837i \(0.337722\pi\)
\(840\) 0 0
\(841\) 21.4110 0.738309
\(842\) 0 0
\(843\) 8.40253 0.289399
\(844\) 0 0
\(845\) −1.94296 −0.0668398
\(846\) 0 0
\(847\) 23.0731 0.792800
\(848\) 0 0
\(849\) 4.70211 0.161376
\(850\) 0 0
\(851\) 8.44770 0.289583
\(852\) 0 0
\(853\) 55.3536 1.89527 0.947635 0.319354i \(-0.103466\pi\)
0.947635 + 0.319354i \(0.103466\pi\)
\(854\) 0 0
\(855\) 20.6425 0.705959
\(856\) 0 0
\(857\) 24.0285 0.820797 0.410399 0.911906i \(-0.365390\pi\)
0.410399 + 0.911906i \(0.365390\pi\)
\(858\) 0 0
\(859\) −43.9380 −1.49914 −0.749572 0.661923i \(-0.769741\pi\)
−0.749572 + 0.661923i \(0.769741\pi\)
\(860\) 0 0
\(861\) 15.3402 0.522794
\(862\) 0 0
\(863\) −39.5113 −1.34498 −0.672490 0.740106i \(-0.734775\pi\)
−0.672490 + 0.740106i \(0.734775\pi\)
\(864\) 0 0
\(865\) 15.3127 0.520648
\(866\) 0 0
\(867\) 0.864716 0.0293673
\(868\) 0 0
\(869\) 11.7153 0.397414
\(870\) 0 0
\(871\) −55.8855 −1.89361
\(872\) 0 0
\(873\) 15.0282 0.508629
\(874\) 0 0
\(875\) −27.7163 −0.936981
\(876\) 0 0
\(877\) −56.9846 −1.92423 −0.962117 0.272638i \(-0.912104\pi\)
−0.962117 + 0.272638i \(0.912104\pi\)
\(878\) 0 0
\(879\) −11.2313 −0.378823
\(880\) 0 0
\(881\) 2.94417 0.0991915 0.0495958 0.998769i \(-0.484207\pi\)
0.0495958 + 0.998769i \(0.484207\pi\)
\(882\) 0 0
\(883\) −53.9659 −1.81610 −0.908049 0.418864i \(-0.862428\pi\)
−0.908049 + 0.418864i \(0.862428\pi\)
\(884\) 0 0
\(885\) −1.21490 −0.0408385
\(886\) 0 0
\(887\) 34.3259 1.15255 0.576276 0.817255i \(-0.304505\pi\)
0.576276 + 0.817255i \(0.304505\pi\)
\(888\) 0 0
\(889\) 42.9504 1.44051
\(890\) 0 0
\(891\) 3.59325 0.120378
\(892\) 0 0
\(893\) −74.0692 −2.47863
\(894\) 0 0
\(895\) 2.37952 0.0795385
\(896\) 0 0
\(897\) 4.34020 0.144915
\(898\) 0 0
\(899\) −49.1211 −1.63828
\(900\) 0 0
\(901\) 12.1634 0.405221
\(902\) 0 0
\(903\) −19.5782 −0.651520
\(904\) 0 0
\(905\) −1.82289 −0.0605949
\(906\) 0 0
\(907\) 49.9132 1.65734 0.828671 0.559736i \(-0.189097\pi\)
0.828671 + 0.559736i \(0.189097\pi\)
\(908\) 0 0
\(909\) −30.1996 −1.00166
\(910\) 0 0
\(911\) 13.2761 0.439857 0.219929 0.975516i \(-0.429418\pi\)
0.219929 + 0.975516i \(0.429418\pi\)
\(912\) 0 0
\(913\) −16.0266 −0.530402
\(914\) 0 0
\(915\) 2.81854 0.0931781
\(916\) 0 0
\(917\) 19.6591 0.649200
\(918\) 0 0
\(919\) −3.56725 −0.117673 −0.0588363 0.998268i \(-0.518739\pi\)
−0.0588363 + 0.998268i \(0.518739\pi\)
\(920\) 0 0
\(921\) −11.9457 −0.393623
\(922\) 0 0
\(923\) −9.72610 −0.320139
\(924\) 0 0
\(925\) −19.3153 −0.635084
\(926\) 0 0
\(927\) −24.1746 −0.793999
\(928\) 0 0
\(929\) −35.8713 −1.17690 −0.588450 0.808534i \(-0.700262\pi\)
−0.588450 + 0.808534i \(0.700262\pi\)
\(930\) 0 0
\(931\) −6.25408 −0.204969
\(932\) 0 0
\(933\) −15.6088 −0.511010
\(934\) 0 0
\(935\) 1.78421 0.0583498
\(936\) 0 0
\(937\) −2.19755 −0.0717907 −0.0358953 0.999356i \(-0.511428\pi\)
−0.0358953 + 0.999356i \(0.511428\pi\)
\(938\) 0 0
\(939\) −20.6578 −0.674143
\(940\) 0 0
\(941\) −24.1909 −0.788599 −0.394300 0.918982i \(-0.629013\pi\)
−0.394300 + 0.918982i \(0.629013\pi\)
\(942\) 0 0
\(943\) −9.55226 −0.311064
\(944\) 0 0
\(945\) −15.6839 −0.510196
\(946\) 0 0
\(947\) 12.3571 0.401552 0.200776 0.979637i \(-0.435654\pi\)
0.200776 + 0.979637i \(0.435654\pi\)
\(948\) 0 0
\(949\) 18.4169 0.597838
\(950\) 0 0
\(951\) 7.39256 0.239720
\(952\) 0 0
\(953\) 54.8634 1.77720 0.888600 0.458682i \(-0.151678\pi\)
0.888600 + 0.458682i \(0.151678\pi\)
\(954\) 0 0
\(955\) 0.654230 0.0211704
\(956\) 0 0
\(957\) −7.79674 −0.252033
\(958\) 0 0
\(959\) −9.71428 −0.313691
\(960\) 0 0
\(961\) 16.8642 0.544008
\(962\) 0 0
\(963\) 35.4088 1.14103
\(964\) 0 0
\(965\) 18.5145 0.596003
\(966\) 0 0
\(967\) 5.44333 0.175046 0.0875228 0.996163i \(-0.472105\pi\)
0.0875228 + 0.996163i \(0.472105\pi\)
\(968\) 0 0
\(969\) −5.64089 −0.181212
\(970\) 0 0
\(971\) −19.3852 −0.622102 −0.311051 0.950393i \(-0.600681\pi\)
−0.311051 + 0.950393i \(0.600681\pi\)
\(972\) 0 0
\(973\) 26.9717 0.864672
\(974\) 0 0
\(975\) −9.92368 −0.317812
\(976\) 0 0
\(977\) −30.0326 −0.960827 −0.480413 0.877042i \(-0.659513\pi\)
−0.480413 + 0.877042i \(0.659513\pi\)
\(978\) 0 0
\(979\) 12.7605 0.407829
\(980\) 0 0
\(981\) 24.4621 0.781014
\(982\) 0 0
\(983\) 23.9831 0.764943 0.382471 0.923967i \(-0.375073\pi\)
0.382471 + 0.923967i \(0.375073\pi\)
\(984\) 0 0
\(985\) −30.0528 −0.957562
\(986\) 0 0
\(987\) 24.1325 0.768144
\(988\) 0 0
\(989\) 12.1912 0.387657
\(990\) 0 0
\(991\) 44.0186 1.39830 0.699148 0.714977i \(-0.253563\pi\)
0.699148 + 0.714977i \(0.253563\pi\)
\(992\) 0 0
\(993\) 10.2620 0.325656
\(994\) 0 0
\(995\) −13.2928 −0.421409
\(996\) 0 0
\(997\) 57.1800 1.81091 0.905454 0.424445i \(-0.139531\pi\)
0.905454 + 0.424445i \(0.139531\pi\)
\(998\) 0 0
\(999\) −28.9899 −0.917198
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 \(a_p\))