Properties

Label 8048.2.a.p.1.10
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-2.07227\)
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+3.07227 q^{3}\) \(+0.386144 q^{5}\) \(-0.194914 q^{7}\) \(+6.43884 q^{9}\) \(+O(q^{10})\) \(q\)\(+3.07227 q^{3}\) \(+0.386144 q^{5}\) \(-0.194914 q^{7}\) \(+6.43884 q^{9}\) \(-2.36326 q^{11}\) \(-1.22636 q^{13}\) \(+1.18634 q^{15}\) \(-5.04830 q^{17}\) \(-4.24460 q^{19}\) \(-0.598827 q^{21}\) \(-1.53457 q^{23}\) \(-4.85089 q^{25}\) \(+10.5650 q^{27}\) \(-7.31602 q^{29}\) \(-3.33893 q^{31}\) \(-7.26057 q^{33}\) \(-0.0752647 q^{35}\) \(-2.17138 q^{37}\) \(-3.76771 q^{39}\) \(-1.04840 q^{41}\) \(+1.53067 q^{43}\) \(+2.48632 q^{45}\) \(+1.08422 q^{47}\) \(-6.96201 q^{49}\) \(-15.5098 q^{51}\) \(+1.55308 q^{53}\) \(-0.912558 q^{55}\) \(-13.0406 q^{57}\) \(-14.8451 q^{59}\) \(-5.45056 q^{61}\) \(-1.25502 q^{63}\) \(-0.473551 q^{65}\) \(+11.3202 q^{67}\) \(-4.71461 q^{69}\) \(+11.4236 q^{71}\) \(-0.902229 q^{73}\) \(-14.9032 q^{75}\) \(+0.460631 q^{77}\) \(+12.7431 q^{79}\) \(+13.1421 q^{81}\) \(-6.10241 q^{83}\) \(-1.94937 q^{85}\) \(-22.4768 q^{87}\) \(+6.44432 q^{89}\) \(+0.239034 q^{91}\) \(-10.2581 q^{93}\) \(-1.63903 q^{95}\) \(-12.9886 q^{97}\) \(-15.2166 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(10q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut +\mathstrut 22q^{31} \) \(\mathstrut -\mathstrut 10q^{33} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 7q^{47} \) \(\mathstrut -\mathstrut 27q^{49} \) \(\mathstrut -\mathstrut 9q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut -\mathstrut 23q^{57} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 10q^{63} \) \(\mathstrut -\mathstrut 16q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut -\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 30q^{75} \) \(\mathstrut +\mathstrut 3q^{77} \) \(\mathstrut +\mathstrut 10q^{79} \) \(\mathstrut -\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 6q^{93} \) \(\mathstrut -\mathstrut 39q^{95} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 35q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 3.07227 1.77378 0.886888 0.461985i \(-0.152863\pi\)
0.886888 + 0.461985i \(0.152863\pi\)
\(4\) 0 0
\(5\) 0.386144 0.172689 0.0863445 0.996265i \(-0.472481\pi\)
0.0863445 + 0.996265i \(0.472481\pi\)
\(6\) 0 0
\(7\) −0.194914 −0.0736704 −0.0368352 0.999321i \(-0.511728\pi\)
−0.0368352 + 0.999321i \(0.511728\pi\)
\(8\) 0 0
\(9\) 6.43884 2.14628
\(10\) 0 0
\(11\) −2.36326 −0.712549 −0.356275 0.934381i \(-0.615953\pi\)
−0.356275 + 0.934381i \(0.615953\pi\)
\(12\) 0 0
\(13\) −1.22636 −0.340131 −0.170065 0.985433i \(-0.554398\pi\)
−0.170065 + 0.985433i \(0.554398\pi\)
\(14\) 0 0
\(15\) 1.18634 0.306311
\(16\) 0 0
\(17\) −5.04830 −1.22439 −0.612197 0.790705i \(-0.709714\pi\)
−0.612197 + 0.790705i \(0.709714\pi\)
\(18\) 0 0
\(19\) −4.24460 −0.973779 −0.486890 0.873464i \(-0.661869\pi\)
−0.486890 + 0.873464i \(0.661869\pi\)
\(20\) 0 0
\(21\) −0.598827 −0.130675
\(22\) 0 0
\(23\) −1.53457 −0.319980 −0.159990 0.987119i \(-0.551146\pi\)
−0.159990 + 0.987119i \(0.551146\pi\)
\(24\) 0 0
\(25\) −4.85089 −0.970179
\(26\) 0 0
\(27\) 10.5650 2.03324
\(28\) 0 0
\(29\) −7.31602 −1.35855 −0.679275 0.733883i \(-0.737706\pi\)
−0.679275 + 0.733883i \(0.737706\pi\)
\(30\) 0 0
\(31\) −3.33893 −0.599690 −0.299845 0.953988i \(-0.596935\pi\)
−0.299845 + 0.953988i \(0.596935\pi\)
\(32\) 0 0
\(33\) −7.26057 −1.26390
\(34\) 0 0
\(35\) −0.0752647 −0.0127221
\(36\) 0 0
\(37\) −2.17138 −0.356973 −0.178487 0.983942i \(-0.557120\pi\)
−0.178487 + 0.983942i \(0.557120\pi\)
\(38\) 0 0
\(39\) −3.76771 −0.603316
\(40\) 0 0
\(41\) −1.04840 −0.163733 −0.0818663 0.996643i \(-0.526088\pi\)
−0.0818663 + 0.996643i \(0.526088\pi\)
\(42\) 0 0
\(43\) 1.53067 0.233425 0.116712 0.993166i \(-0.462764\pi\)
0.116712 + 0.993166i \(0.462764\pi\)
\(44\) 0 0
\(45\) 2.48632 0.370639
\(46\) 0 0
\(47\) 1.08422 0.158150 0.0790748 0.996869i \(-0.474803\pi\)
0.0790748 + 0.996869i \(0.474803\pi\)
\(48\) 0 0
\(49\) −6.96201 −0.994573
\(50\) 0 0
\(51\) −15.5098 −2.17180
\(52\) 0 0
\(53\) 1.55308 0.213332 0.106666 0.994295i \(-0.465983\pi\)
0.106666 + 0.994295i \(0.465983\pi\)
\(54\) 0 0
\(55\) −0.912558 −0.123049
\(56\) 0 0
\(57\) −13.0406 −1.72727
\(58\) 0 0
\(59\) −14.8451 −1.93267 −0.966334 0.257293i \(-0.917170\pi\)
−0.966334 + 0.257293i \(0.917170\pi\)
\(60\) 0 0
\(61\) −5.45056 −0.697873 −0.348936 0.937146i \(-0.613457\pi\)
−0.348936 + 0.937146i \(0.613457\pi\)
\(62\) 0 0
\(63\) −1.25502 −0.158117
\(64\) 0 0
\(65\) −0.473551 −0.0587368
\(66\) 0 0
\(67\) 11.3202 1.38298 0.691490 0.722386i \(-0.256955\pi\)
0.691490 + 0.722386i \(0.256955\pi\)
\(68\) 0 0
\(69\) −4.71461 −0.567572
\(70\) 0 0
\(71\) 11.4236 1.35573 0.677864 0.735187i \(-0.262906\pi\)
0.677864 + 0.735187i \(0.262906\pi\)
\(72\) 0 0
\(73\) −0.902229 −0.105598 −0.0527990 0.998605i \(-0.516814\pi\)
−0.0527990 + 0.998605i \(0.516814\pi\)
\(74\) 0 0
\(75\) −14.9032 −1.72088
\(76\) 0 0
\(77\) 0.460631 0.0524938
\(78\) 0 0
\(79\) 12.7431 1.43371 0.716853 0.697225i \(-0.245582\pi\)
0.716853 + 0.697225i \(0.245582\pi\)
\(80\) 0 0
\(81\) 13.1421 1.46024
\(82\) 0 0
\(83\) −6.10241 −0.669826 −0.334913 0.942249i \(-0.608707\pi\)
−0.334913 + 0.942249i \(0.608707\pi\)
\(84\) 0 0
\(85\) −1.94937 −0.211439
\(86\) 0 0
\(87\) −22.4768 −2.40976
\(88\) 0 0
\(89\) 6.44432 0.683097 0.341548 0.939864i \(-0.389049\pi\)
0.341548 + 0.939864i \(0.389049\pi\)
\(90\) 0 0
\(91\) 0.239034 0.0250576
\(92\) 0 0
\(93\) −10.2581 −1.06372
\(94\) 0 0
\(95\) −1.63903 −0.168161
\(96\) 0 0
\(97\) −12.9886 −1.31879 −0.659394 0.751797i \(-0.729187\pi\)
−0.659394 + 0.751797i \(0.729187\pi\)
\(98\) 0 0
\(99\) −15.2166 −1.52933
\(100\) 0 0
\(101\) 6.18139 0.615072 0.307536 0.951537i \(-0.400496\pi\)
0.307536 + 0.951537i \(0.400496\pi\)
\(102\) 0 0
\(103\) −7.78250 −0.766833 −0.383416 0.923576i \(-0.625253\pi\)
−0.383416 + 0.923576i \(0.625253\pi\)
\(104\) 0 0
\(105\) −0.231233 −0.0225661
\(106\) 0 0
\(107\) 8.18217 0.791000 0.395500 0.918466i \(-0.370571\pi\)
0.395500 + 0.918466i \(0.370571\pi\)
\(108\) 0 0
\(109\) −5.32486 −0.510029 −0.255015 0.966937i \(-0.582080\pi\)
−0.255015 + 0.966937i \(0.582080\pi\)
\(110\) 0 0
\(111\) −6.67107 −0.633190
\(112\) 0 0
\(113\) −3.60573 −0.339199 −0.169599 0.985513i \(-0.554247\pi\)
−0.169599 + 0.985513i \(0.554247\pi\)
\(114\) 0 0
\(115\) −0.592565 −0.0552570
\(116\) 0 0
\(117\) −7.89633 −0.730016
\(118\) 0 0
\(119\) 0.983983 0.0902016
\(120\) 0 0
\(121\) −5.41501 −0.492274
\(122\) 0 0
\(123\) −3.22097 −0.290425
\(124\) 0 0
\(125\) −3.80386 −0.340228
\(126\) 0 0
\(127\) 17.8352 1.58262 0.791308 0.611418i \(-0.209401\pi\)
0.791308 + 0.611418i \(0.209401\pi\)
\(128\) 0 0
\(129\) 4.70262 0.414043
\(130\) 0 0
\(131\) 12.1841 1.06453 0.532267 0.846577i \(-0.321340\pi\)
0.532267 + 0.846577i \(0.321340\pi\)
\(132\) 0 0
\(133\) 0.827331 0.0717387
\(134\) 0 0
\(135\) 4.07963 0.351118
\(136\) 0 0
\(137\) −13.9009 −1.18764 −0.593819 0.804599i \(-0.702380\pi\)
−0.593819 + 0.804599i \(0.702380\pi\)
\(138\) 0 0
\(139\) −4.99920 −0.424027 −0.212013 0.977267i \(-0.568002\pi\)
−0.212013 + 0.977267i \(0.568002\pi\)
\(140\) 0 0
\(141\) 3.33101 0.280522
\(142\) 0 0
\(143\) 2.89820 0.242360
\(144\) 0 0
\(145\) −2.82504 −0.234607
\(146\) 0 0
\(147\) −21.3892 −1.76415
\(148\) 0 0
\(149\) 17.4937 1.43314 0.716570 0.697515i \(-0.245711\pi\)
0.716570 + 0.697515i \(0.245711\pi\)
\(150\) 0 0
\(151\) −0.480306 −0.0390867 −0.0195434 0.999809i \(-0.506221\pi\)
−0.0195434 + 0.999809i \(0.506221\pi\)
\(152\) 0 0
\(153\) −32.5052 −2.62789
\(154\) 0 0
\(155\) −1.28931 −0.103560
\(156\) 0 0
\(157\) 0.117389 0.00936869 0.00468434 0.999989i \(-0.498509\pi\)
0.00468434 + 0.999989i \(0.498509\pi\)
\(158\) 0 0
\(159\) 4.77147 0.378402
\(160\) 0 0
\(161\) 0.299108 0.0235730
\(162\) 0 0
\(163\) 12.5273 0.981210 0.490605 0.871382i \(-0.336776\pi\)
0.490605 + 0.871382i \(0.336776\pi\)
\(164\) 0 0
\(165\) −2.80362 −0.218262
\(166\) 0 0
\(167\) 0.744061 0.0575772 0.0287886 0.999586i \(-0.490835\pi\)
0.0287886 + 0.999586i \(0.490835\pi\)
\(168\) 0 0
\(169\) −11.4960 −0.884311
\(170\) 0 0
\(171\) −27.3303 −2.09000
\(172\) 0 0
\(173\) 11.6073 0.882484 0.441242 0.897388i \(-0.354538\pi\)
0.441242 + 0.897388i \(0.354538\pi\)
\(174\) 0 0
\(175\) 0.945505 0.0714734
\(176\) 0 0
\(177\) −45.6081 −3.42812
\(178\) 0 0
\(179\) 21.1974 1.58437 0.792183 0.610284i \(-0.208945\pi\)
0.792183 + 0.610284i \(0.208945\pi\)
\(180\) 0 0
\(181\) 11.9508 0.888299 0.444150 0.895953i \(-0.353506\pi\)
0.444150 + 0.895953i \(0.353506\pi\)
\(182\) 0 0
\(183\) −16.7456 −1.23787
\(184\) 0 0
\(185\) −0.838467 −0.0616453
\(186\) 0 0
\(187\) 11.9304 0.872441
\(188\) 0 0
\(189\) −2.05927 −0.149790
\(190\) 0 0
\(191\) −24.2243 −1.75281 −0.876406 0.481574i \(-0.840065\pi\)
−0.876406 + 0.481574i \(0.840065\pi\)
\(192\) 0 0
\(193\) −5.78545 −0.416446 −0.208223 0.978081i \(-0.566768\pi\)
−0.208223 + 0.978081i \(0.566768\pi\)
\(194\) 0 0
\(195\) −1.45488 −0.104186
\(196\) 0 0
\(197\) 4.06793 0.289828 0.144914 0.989444i \(-0.453709\pi\)
0.144914 + 0.989444i \(0.453709\pi\)
\(198\) 0 0
\(199\) 11.4204 0.809571 0.404785 0.914412i \(-0.367346\pi\)
0.404785 + 0.914412i \(0.367346\pi\)
\(200\) 0 0
\(201\) 34.7786 2.45310
\(202\) 0 0
\(203\) 1.42599 0.100085
\(204\) 0 0
\(205\) −0.404834 −0.0282748
\(206\) 0 0
\(207\) −9.88084 −0.686766
\(208\) 0 0
\(209\) 10.0311 0.693866
\(210\) 0 0
\(211\) −18.0941 −1.24565 −0.622824 0.782362i \(-0.714015\pi\)
−0.622824 + 0.782362i \(0.714015\pi\)
\(212\) 0 0
\(213\) 35.0963 2.40476
\(214\) 0 0
\(215\) 0.591058 0.0403098
\(216\) 0 0
\(217\) 0.650804 0.0441794
\(218\) 0 0
\(219\) −2.77189 −0.187307
\(220\) 0 0
\(221\) 6.19103 0.416454
\(222\) 0 0
\(223\) 21.1665 1.41741 0.708706 0.705504i \(-0.249279\pi\)
0.708706 + 0.705504i \(0.249279\pi\)
\(224\) 0 0
\(225\) −31.2341 −2.08227
\(226\) 0 0
\(227\) 13.3828 0.888248 0.444124 0.895965i \(-0.353515\pi\)
0.444124 + 0.895965i \(0.353515\pi\)
\(228\) 0 0
\(229\) −12.5484 −0.829225 −0.414612 0.909998i \(-0.636083\pi\)
−0.414612 + 0.909998i \(0.636083\pi\)
\(230\) 0 0
\(231\) 1.41518 0.0931122
\(232\) 0 0
\(233\) 15.6538 1.02551 0.512757 0.858534i \(-0.328624\pi\)
0.512757 + 0.858534i \(0.328624\pi\)
\(234\) 0 0
\(235\) 0.418665 0.0273107
\(236\) 0 0
\(237\) 39.1501 2.54307
\(238\) 0 0
\(239\) −3.45659 −0.223588 −0.111794 0.993731i \(-0.535660\pi\)
−0.111794 + 0.993731i \(0.535660\pi\)
\(240\) 0 0
\(241\) 28.7843 1.85416 0.927080 0.374864i \(-0.122311\pi\)
0.927080 + 0.374864i \(0.122311\pi\)
\(242\) 0 0
\(243\) 8.68104 0.556889
\(244\) 0 0
\(245\) −2.68834 −0.171752
\(246\) 0 0
\(247\) 5.20541 0.331212
\(248\) 0 0
\(249\) −18.7482 −1.18812
\(250\) 0 0
\(251\) 1.82824 0.115397 0.0576986 0.998334i \(-0.481624\pi\)
0.0576986 + 0.998334i \(0.481624\pi\)
\(252\) 0 0
\(253\) 3.62658 0.228001
\(254\) 0 0
\(255\) −5.98900 −0.375046
\(256\) 0 0
\(257\) 3.65882 0.228231 0.114116 0.993467i \(-0.463597\pi\)
0.114116 + 0.993467i \(0.463597\pi\)
\(258\) 0 0
\(259\) 0.423232 0.0262983
\(260\) 0 0
\(261\) −47.1067 −2.91583
\(262\) 0 0
\(263\) 13.1581 0.811362 0.405681 0.914015i \(-0.367034\pi\)
0.405681 + 0.914015i \(0.367034\pi\)
\(264\) 0 0
\(265\) 0.599712 0.0368400
\(266\) 0 0
\(267\) 19.7987 1.21166
\(268\) 0 0
\(269\) −30.0225 −1.83050 −0.915251 0.402885i \(-0.868008\pi\)
−0.915251 + 0.402885i \(0.868008\pi\)
\(270\) 0 0
\(271\) 9.04876 0.549673 0.274837 0.961491i \(-0.411376\pi\)
0.274837 + 0.961491i \(0.411376\pi\)
\(272\) 0 0
\(273\) 0.734377 0.0444465
\(274\) 0 0
\(275\) 11.4639 0.691300
\(276\) 0 0
\(277\) 10.3482 0.621762 0.310881 0.950449i \(-0.399376\pi\)
0.310881 + 0.950449i \(0.399376\pi\)
\(278\) 0 0
\(279\) −21.4989 −1.28710
\(280\) 0 0
\(281\) −19.3686 −1.15543 −0.577716 0.816238i \(-0.696056\pi\)
−0.577716 + 0.816238i \(0.696056\pi\)
\(282\) 0 0
\(283\) −9.72949 −0.578358 −0.289179 0.957275i \(-0.593382\pi\)
−0.289179 + 0.957275i \(0.593382\pi\)
\(284\) 0 0
\(285\) −5.03554 −0.298280
\(286\) 0 0
\(287\) 0.204347 0.0120622
\(288\) 0 0
\(289\) 8.48538 0.499140
\(290\) 0 0
\(291\) −39.9044 −2.33924
\(292\) 0 0
\(293\) 26.2321 1.53249 0.766247 0.642546i \(-0.222122\pi\)
0.766247 + 0.642546i \(0.222122\pi\)
\(294\) 0 0
\(295\) −5.73235 −0.333750
\(296\) 0 0
\(297\) −24.9679 −1.44879
\(298\) 0 0
\(299\) 1.88193 0.108835
\(300\) 0 0
\(301\) −0.298348 −0.0171965
\(302\) 0 0
\(303\) 18.9909 1.09100
\(304\) 0 0
\(305\) −2.10470 −0.120515
\(306\) 0 0
\(307\) 13.7097 0.782455 0.391228 0.920294i \(-0.372050\pi\)
0.391228 + 0.920294i \(0.372050\pi\)
\(308\) 0 0
\(309\) −23.9099 −1.36019
\(310\) 0 0
\(311\) −30.9043 −1.75242 −0.876212 0.481926i \(-0.839937\pi\)
−0.876212 + 0.481926i \(0.839937\pi\)
\(312\) 0 0
\(313\) −28.2287 −1.59558 −0.797790 0.602935i \(-0.793998\pi\)
−0.797790 + 0.602935i \(0.793998\pi\)
\(314\) 0 0
\(315\) −0.484617 −0.0273051
\(316\) 0 0
\(317\) −7.55793 −0.424496 −0.212248 0.977216i \(-0.568078\pi\)
−0.212248 + 0.977216i \(0.568078\pi\)
\(318\) 0 0
\(319\) 17.2896 0.968034
\(320\) 0 0
\(321\) 25.1378 1.40306
\(322\) 0 0
\(323\) 21.4281 1.19229
\(324\) 0 0
\(325\) 5.94894 0.329988
\(326\) 0 0
\(327\) −16.3594 −0.904678
\(328\) 0 0
\(329\) −0.211329 −0.0116509
\(330\) 0 0
\(331\) −20.4225 −1.12252 −0.561260 0.827640i \(-0.689683\pi\)
−0.561260 + 0.827640i \(0.689683\pi\)
\(332\) 0 0
\(333\) −13.9812 −0.766164
\(334\) 0 0
\(335\) 4.37122 0.238825
\(336\) 0 0
\(337\) 16.7603 0.912994 0.456497 0.889725i \(-0.349104\pi\)
0.456497 + 0.889725i \(0.349104\pi\)
\(338\) 0 0
\(339\) −11.0778 −0.601662
\(340\) 0 0
\(341\) 7.89077 0.427309
\(342\) 0 0
\(343\) 2.72138 0.146941
\(344\) 0 0
\(345\) −1.82052 −0.0980135
\(346\) 0 0
\(347\) −14.1418 −0.759171 −0.379586 0.925157i \(-0.623933\pi\)
−0.379586 + 0.925157i \(0.623933\pi\)
\(348\) 0 0
\(349\) −22.1523 −1.18579 −0.592893 0.805282i \(-0.702014\pi\)
−0.592893 + 0.805282i \(0.702014\pi\)
\(350\) 0 0
\(351\) −12.9565 −0.691568
\(352\) 0 0
\(353\) 17.2209 0.916574 0.458287 0.888804i \(-0.348463\pi\)
0.458287 + 0.888804i \(0.348463\pi\)
\(354\) 0 0
\(355\) 4.41114 0.234119
\(356\) 0 0
\(357\) 3.02306 0.159997
\(358\) 0 0
\(359\) −21.9672 −1.15938 −0.579692 0.814836i \(-0.696827\pi\)
−0.579692 + 0.814836i \(0.696827\pi\)
\(360\) 0 0
\(361\) −0.983329 −0.0517541
\(362\) 0 0
\(363\) −16.6364 −0.873183
\(364\) 0 0
\(365\) −0.348390 −0.0182356
\(366\) 0 0
\(367\) 13.1841 0.688202 0.344101 0.938933i \(-0.388184\pi\)
0.344101 + 0.938933i \(0.388184\pi\)
\(368\) 0 0
\(369\) −6.75048 −0.351416
\(370\) 0 0
\(371\) −0.302716 −0.0157162
\(372\) 0 0
\(373\) −35.2516 −1.82526 −0.912630 0.408787i \(-0.865952\pi\)
−0.912630 + 0.408787i \(0.865952\pi\)
\(374\) 0 0
\(375\) −11.6865 −0.603488
\(376\) 0 0
\(377\) 8.97207 0.462085
\(378\) 0 0
\(379\) −23.6003 −1.21227 −0.606134 0.795363i \(-0.707280\pi\)
−0.606134 + 0.795363i \(0.707280\pi\)
\(380\) 0 0
\(381\) 54.7945 2.80721
\(382\) 0 0
\(383\) 13.1311 0.670970 0.335485 0.942046i \(-0.391100\pi\)
0.335485 + 0.942046i \(0.391100\pi\)
\(384\) 0 0
\(385\) 0.177870 0.00906509
\(386\) 0 0
\(387\) 9.85572 0.500994
\(388\) 0 0
\(389\) 29.2216 1.48159 0.740797 0.671729i \(-0.234448\pi\)
0.740797 + 0.671729i \(0.234448\pi\)
\(390\) 0 0
\(391\) 7.74697 0.391781
\(392\) 0 0
\(393\) 37.4330 1.88824
\(394\) 0 0
\(395\) 4.92065 0.247585
\(396\) 0 0
\(397\) 26.2129 1.31559 0.657795 0.753197i \(-0.271489\pi\)
0.657795 + 0.753197i \(0.271489\pi\)
\(398\) 0 0
\(399\) 2.54178 0.127248
\(400\) 0 0
\(401\) −24.3910 −1.21803 −0.609014 0.793160i \(-0.708435\pi\)
−0.609014 + 0.793160i \(0.708435\pi\)
\(402\) 0 0
\(403\) 4.09473 0.203973
\(404\) 0 0
\(405\) 5.07476 0.252167
\(406\) 0 0
\(407\) 5.13154 0.254361
\(408\) 0 0
\(409\) 13.2071 0.653051 0.326526 0.945188i \(-0.394122\pi\)
0.326526 + 0.945188i \(0.394122\pi\)
\(410\) 0 0
\(411\) −42.7074 −2.10660
\(412\) 0 0
\(413\) 2.89351 0.142380
\(414\) 0 0
\(415\) −2.35641 −0.115672
\(416\) 0 0
\(417\) −15.3589 −0.752129
\(418\) 0 0
\(419\) −15.8597 −0.774799 −0.387400 0.921912i \(-0.626627\pi\)
−0.387400 + 0.921912i \(0.626627\pi\)
\(420\) 0 0
\(421\) −4.53957 −0.221245 −0.110622 0.993863i \(-0.535284\pi\)
−0.110622 + 0.993863i \(0.535284\pi\)
\(422\) 0 0
\(423\) 6.98111 0.339433
\(424\) 0 0
\(425\) 24.4888 1.18788
\(426\) 0 0
\(427\) 1.06239 0.0514126
\(428\) 0 0
\(429\) 8.90406 0.429892
\(430\) 0 0
\(431\) 24.0460 1.15825 0.579126 0.815238i \(-0.303394\pi\)
0.579126 + 0.815238i \(0.303394\pi\)
\(432\) 0 0
\(433\) −20.8069 −0.999914 −0.499957 0.866050i \(-0.666651\pi\)
−0.499957 + 0.866050i \(0.666651\pi\)
\(434\) 0 0
\(435\) −8.67928 −0.416140
\(436\) 0 0
\(437\) 6.51364 0.311590
\(438\) 0 0
\(439\) 27.0822 1.29256 0.646282 0.763098i \(-0.276323\pi\)
0.646282 + 0.763098i \(0.276323\pi\)
\(440\) 0 0
\(441\) −44.8273 −2.13463
\(442\) 0 0
\(443\) −26.1108 −1.24056 −0.620282 0.784379i \(-0.712982\pi\)
−0.620282 + 0.784379i \(0.712982\pi\)
\(444\) 0 0
\(445\) 2.48844 0.117963
\(446\) 0 0
\(447\) 53.7454 2.54207
\(448\) 0 0
\(449\) 18.4224 0.869407 0.434703 0.900574i \(-0.356853\pi\)
0.434703 + 0.900574i \(0.356853\pi\)
\(450\) 0 0
\(451\) 2.47764 0.116668
\(452\) 0 0
\(453\) −1.47563 −0.0693311
\(454\) 0 0
\(455\) 0.0923016 0.00432716
\(456\) 0 0
\(457\) −3.55147 −0.166131 −0.0830654 0.996544i \(-0.526471\pi\)
−0.0830654 + 0.996544i \(0.526471\pi\)
\(458\) 0 0
\(459\) −53.3355 −2.48949
\(460\) 0 0
\(461\) −2.86665 −0.133513 −0.0667565 0.997769i \(-0.521265\pi\)
−0.0667565 + 0.997769i \(0.521265\pi\)
\(462\) 0 0
\(463\) −30.5287 −1.41879 −0.709395 0.704811i \(-0.751032\pi\)
−0.709395 + 0.704811i \(0.751032\pi\)
\(464\) 0 0
\(465\) −3.96111 −0.183692
\(466\) 0 0
\(467\) −18.7000 −0.865332 −0.432666 0.901554i \(-0.642427\pi\)
−0.432666 + 0.901554i \(0.642427\pi\)
\(468\) 0 0
\(469\) −2.20646 −0.101885
\(470\) 0 0
\(471\) 0.360652 0.0166179
\(472\) 0 0
\(473\) −3.61736 −0.166326
\(474\) 0 0
\(475\) 20.5901 0.944740
\(476\) 0 0
\(477\) 10.0000 0.457869
\(478\) 0 0
\(479\) −7.50976 −0.343130 −0.171565 0.985173i \(-0.554882\pi\)
−0.171565 + 0.985173i \(0.554882\pi\)
\(480\) 0 0
\(481\) 2.66289 0.121418
\(482\) 0 0
\(483\) 0.918941 0.0418133
\(484\) 0 0
\(485\) −5.01546 −0.227740
\(486\) 0 0
\(487\) −32.6786 −1.48081 −0.740404 0.672162i \(-0.765366\pi\)
−0.740404 + 0.672162i \(0.765366\pi\)
\(488\) 0 0
\(489\) 38.4871 1.74045
\(490\) 0 0
\(491\) −2.81716 −0.127137 −0.0635683 0.997977i \(-0.520248\pi\)
−0.0635683 + 0.997977i \(0.520248\pi\)
\(492\) 0 0
\(493\) 36.9335 1.66340
\(494\) 0 0
\(495\) −5.87582 −0.264098
\(496\) 0 0
\(497\) −2.22661 −0.0998770
\(498\) 0 0
\(499\) −29.0591 −1.30086 −0.650432 0.759564i \(-0.725412\pi\)
−0.650432 + 0.759564i \(0.725412\pi\)
\(500\) 0 0
\(501\) 2.28596 0.102129
\(502\) 0 0
\(503\) 1.00000 0.0445878
\(504\) 0 0
\(505\) 2.38691 0.106216
\(506\) 0 0
\(507\) −35.3189 −1.56857
\(508\) 0 0
\(509\) 7.58042 0.335996 0.167998 0.985787i \(-0.446270\pi\)
0.167998 + 0.985787i \(0.446270\pi\)
\(510\) 0 0
\(511\) 0.175857 0.00777944
\(512\) 0 0
\(513\) −44.8444 −1.97993
\(514\) 0 0
\(515\) −3.00517 −0.132423
\(516\) 0 0
\(517\) −2.56229 −0.112689
\(518\) 0 0
\(519\) 35.6607 1.56533
\(520\) 0 0
\(521\) −8.90148 −0.389981 −0.194990 0.980805i \(-0.562468\pi\)
−0.194990 + 0.980805i \(0.562468\pi\)
\(522\) 0 0
\(523\) −37.7311 −1.64986 −0.824932 0.565232i \(-0.808787\pi\)
−0.824932 + 0.565232i \(0.808787\pi\)
\(524\) 0 0
\(525\) 2.90484 0.126778
\(526\) 0 0
\(527\) 16.8560 0.734257
\(528\) 0 0
\(529\) −20.6451 −0.897613
\(530\) 0 0
\(531\) −95.5852 −4.14804
\(532\) 0 0
\(533\) 1.28572 0.0556905
\(534\) 0 0
\(535\) 3.15950 0.136597
\(536\) 0 0
\(537\) 65.1240 2.81031
\(538\) 0 0
\(539\) 16.4530 0.708682
\(540\) 0 0
\(541\) 11.6293 0.499981 0.249990 0.968248i \(-0.419573\pi\)
0.249990 + 0.968248i \(0.419573\pi\)
\(542\) 0 0
\(543\) 36.7162 1.57564
\(544\) 0 0
\(545\) −2.05616 −0.0880764
\(546\) 0 0
\(547\) 13.4958 0.577040 0.288520 0.957474i \(-0.406837\pi\)
0.288520 + 0.957474i \(0.406837\pi\)
\(548\) 0 0
\(549\) −35.0953 −1.49783
\(550\) 0 0
\(551\) 31.0536 1.32293
\(552\) 0 0
\(553\) −2.48379 −0.105622
\(554\) 0 0
\(555\) −2.57599 −0.109345
\(556\) 0 0
\(557\) −34.2002 −1.44911 −0.724554 0.689218i \(-0.757954\pi\)
−0.724554 + 0.689218i \(0.757954\pi\)
\(558\) 0 0
\(559\) −1.87715 −0.0793949
\(560\) 0 0
\(561\) 36.6536 1.54751
\(562\) 0 0
\(563\) −25.6005 −1.07893 −0.539467 0.842007i \(-0.681374\pi\)
−0.539467 + 0.842007i \(0.681374\pi\)
\(564\) 0 0
\(565\) −1.39233 −0.0585758
\(566\) 0 0
\(567\) −2.56158 −0.107576
\(568\) 0 0
\(569\) −17.2311 −0.722363 −0.361182 0.932495i \(-0.617627\pi\)
−0.361182 + 0.932495i \(0.617627\pi\)
\(570\) 0 0
\(571\) −2.79325 −0.116894 −0.0584470 0.998291i \(-0.518615\pi\)
−0.0584470 + 0.998291i \(0.518615\pi\)
\(572\) 0 0
\(573\) −74.4237 −3.10909
\(574\) 0 0
\(575\) 7.44403 0.310438
\(576\) 0 0
\(577\) −40.1143 −1.66998 −0.834991 0.550264i \(-0.814527\pi\)
−0.834991 + 0.550264i \(0.814527\pi\)
\(578\) 0 0
\(579\) −17.7745 −0.738682
\(580\) 0 0
\(581\) 1.18944 0.0493464
\(582\) 0 0
\(583\) −3.67032 −0.152009
\(584\) 0 0
\(585\) −3.04912 −0.126066
\(586\) 0 0
\(587\) 38.5445 1.59090 0.795451 0.606018i \(-0.207234\pi\)
0.795451 + 0.606018i \(0.207234\pi\)
\(588\) 0 0
\(589\) 14.1725 0.583966
\(590\) 0 0
\(591\) 12.4978 0.514090
\(592\) 0 0
\(593\) −25.0372 −1.02816 −0.514078 0.857744i \(-0.671866\pi\)
−0.514078 + 0.857744i \(0.671866\pi\)
\(594\) 0 0
\(595\) 0.379959 0.0155768
\(596\) 0 0
\(597\) 35.0865 1.43600
\(598\) 0 0
\(599\) 23.0220 0.940655 0.470328 0.882492i \(-0.344136\pi\)
0.470328 + 0.882492i \(0.344136\pi\)
\(600\) 0 0
\(601\) −33.9451 −1.38465 −0.692326 0.721585i \(-0.743414\pi\)
−0.692326 + 0.721585i \(0.743414\pi\)
\(602\) 0 0
\(603\) 72.8888 2.96826
\(604\) 0 0
\(605\) −2.09097 −0.0850102
\(606\) 0 0
\(607\) −24.3039 −0.986467 −0.493233 0.869897i \(-0.664185\pi\)
−0.493233 + 0.869897i \(0.664185\pi\)
\(608\) 0 0
\(609\) 4.38103 0.177528
\(610\) 0 0
\(611\) −1.32964 −0.0537916
\(612\) 0 0
\(613\) 34.5604 1.39588 0.697940 0.716156i \(-0.254100\pi\)
0.697940 + 0.716156i \(0.254100\pi\)
\(614\) 0 0
\(615\) −1.24376 −0.0501532
\(616\) 0 0
\(617\) 34.3607 1.38331 0.691655 0.722228i \(-0.256882\pi\)
0.691655 + 0.722228i \(0.256882\pi\)
\(618\) 0 0
\(619\) −1.08451 −0.0435902 −0.0217951 0.999762i \(-0.506938\pi\)
−0.0217951 + 0.999762i \(0.506938\pi\)
\(620\) 0 0
\(621\) −16.2128 −0.650597
\(622\) 0 0
\(623\) −1.25609 −0.0503240
\(624\) 0 0
\(625\) 22.7856 0.911425
\(626\) 0 0
\(627\) 30.8182 1.23076
\(628\) 0 0
\(629\) 10.9618 0.437076
\(630\) 0 0
\(631\) 6.03426 0.240220 0.120110 0.992761i \(-0.461675\pi\)
0.120110 + 0.992761i \(0.461675\pi\)
\(632\) 0 0
\(633\) −55.5899 −2.20950
\(634\) 0 0
\(635\) 6.88695 0.273300
\(636\) 0 0
\(637\) 8.53792 0.338285
\(638\) 0 0
\(639\) 73.5545 2.90977
\(640\) 0 0
\(641\) −22.0716 −0.871778 −0.435889 0.900001i \(-0.643566\pi\)
−0.435889 + 0.900001i \(0.643566\pi\)
\(642\) 0 0
\(643\) 40.6373 1.60258 0.801290 0.598277i \(-0.204148\pi\)
0.801290 + 0.598277i \(0.204148\pi\)
\(644\) 0 0
\(645\) 1.81589 0.0715006
\(646\) 0 0
\(647\) −22.9719 −0.903118 −0.451559 0.892241i \(-0.649132\pi\)
−0.451559 + 0.892241i \(0.649132\pi\)
\(648\) 0 0
\(649\) 35.0828 1.37712
\(650\) 0 0
\(651\) 1.99944 0.0783644
\(652\) 0 0
\(653\) −39.0459 −1.52798 −0.763992 0.645226i \(-0.776763\pi\)
−0.763992 + 0.645226i \(0.776763\pi\)
\(654\) 0 0
\(655\) 4.70483 0.183833
\(656\) 0 0
\(657\) −5.80931 −0.226643
\(658\) 0 0
\(659\) 26.6054 1.03640 0.518199 0.855260i \(-0.326603\pi\)
0.518199 + 0.855260i \(0.326603\pi\)
\(660\) 0 0
\(661\) −39.3661 −1.53116 −0.765582 0.643338i \(-0.777549\pi\)
−0.765582 + 0.643338i \(0.777549\pi\)
\(662\) 0 0
\(663\) 19.0205 0.738696
\(664\) 0 0
\(665\) 0.319469 0.0123885
\(666\) 0 0
\(667\) 11.2269 0.434709
\(668\) 0 0
\(669\) 65.0291 2.51417
\(670\) 0 0
\(671\) 12.8811 0.497269
\(672\) 0 0
\(673\) −13.4145 −0.517090 −0.258545 0.965999i \(-0.583243\pi\)
−0.258545 + 0.965999i \(0.583243\pi\)
\(674\) 0 0
\(675\) −51.2499 −1.97261
\(676\) 0 0
\(677\) −2.13435 −0.0820299 −0.0410149 0.999159i \(-0.513059\pi\)
−0.0410149 + 0.999159i \(0.513059\pi\)
\(678\) 0 0
\(679\) 2.53165 0.0971557
\(680\) 0 0
\(681\) 41.1156 1.57555
\(682\) 0 0
\(683\) −21.3544 −0.817105 −0.408552 0.912735i \(-0.633966\pi\)
−0.408552 + 0.912735i \(0.633966\pi\)
\(684\) 0 0
\(685\) −5.36777 −0.205092
\(686\) 0 0
\(687\) −38.5522 −1.47086
\(688\) 0 0
\(689\) −1.90463 −0.0725606
\(690\) 0 0
\(691\) −13.8167 −0.525614 −0.262807 0.964848i \(-0.584648\pi\)
−0.262807 + 0.964848i \(0.584648\pi\)
\(692\) 0 0
\(693\) 2.96593 0.112666
\(694\) 0 0
\(695\) −1.93041 −0.0732247
\(696\) 0 0
\(697\) 5.29265 0.200473
\(698\) 0 0
\(699\) 48.0927 1.81903
\(700\) 0 0
\(701\) 45.1209 1.70419 0.852097 0.523385i \(-0.175331\pi\)
0.852097 + 0.523385i \(0.175331\pi\)
\(702\) 0 0
\(703\) 9.21666 0.347613
\(704\) 0 0
\(705\) 1.28625 0.0484430
\(706\) 0 0
\(707\) −1.20484 −0.0453126
\(708\) 0 0
\(709\) −37.6350 −1.41341 −0.706706 0.707507i \(-0.749820\pi\)
−0.706706 + 0.707507i \(0.749820\pi\)
\(710\) 0 0
\(711\) 82.0505 3.07713
\(712\) 0 0
\(713\) 5.12383 0.191889
\(714\) 0 0
\(715\) 1.11912 0.0418529
\(716\) 0 0
\(717\) −10.6196 −0.396596
\(718\) 0 0
\(719\) 34.9860 1.30476 0.652380 0.757892i \(-0.273771\pi\)
0.652380 + 0.757892i \(0.273771\pi\)
\(720\) 0 0
\(721\) 1.51691 0.0564929
\(722\) 0 0
\(723\) 88.4331 3.28886
\(724\) 0 0
\(725\) 35.4892 1.31804
\(726\) 0 0
\(727\) −0.0594046 −0.00220319 −0.00110160 0.999999i \(-0.500351\pi\)
−0.00110160 + 0.999999i \(0.500351\pi\)
\(728\) 0 0
\(729\) −12.7559 −0.472440
\(730\) 0 0
\(731\) −7.72727 −0.285804
\(732\) 0 0
\(733\) −23.6914 −0.875060 −0.437530 0.899204i \(-0.644147\pi\)
−0.437530 + 0.899204i \(0.644147\pi\)
\(734\) 0 0
\(735\) −8.25930 −0.304649
\(736\) 0 0
\(737\) −26.7525 −0.985441
\(738\) 0 0
\(739\) 13.2539 0.487551 0.243776 0.969832i \(-0.421614\pi\)
0.243776 + 0.969832i \(0.421614\pi\)
\(740\) 0 0
\(741\) 15.9924 0.587496
\(742\) 0 0
\(743\) 13.7983 0.506210 0.253105 0.967439i \(-0.418548\pi\)
0.253105 + 0.967439i \(0.418548\pi\)
\(744\) 0 0
\(745\) 6.75509 0.247487
\(746\) 0 0
\(747\) −39.2924 −1.43763
\(748\) 0 0
\(749\) −1.59481 −0.0582733
\(750\) 0 0
\(751\) −3.82043 −0.139410 −0.0697048 0.997568i \(-0.522206\pi\)
−0.0697048 + 0.997568i \(0.522206\pi\)
\(752\) 0 0
\(753\) 5.61683 0.204689
\(754\) 0 0
\(755\) −0.185467 −0.00674984
\(756\) 0 0
\(757\) 19.6215 0.713157 0.356578 0.934265i \(-0.383943\pi\)
0.356578 + 0.934265i \(0.383943\pi\)
\(758\) 0 0
\(759\) 11.1418 0.404423
\(760\) 0 0
\(761\) 47.5141 1.72238 0.861192 0.508280i \(-0.169719\pi\)
0.861192 + 0.508280i \(0.169719\pi\)
\(762\) 0 0
\(763\) 1.03789 0.0375741
\(764\) 0 0
\(765\) −12.5517 −0.453808
\(766\) 0 0
\(767\) 18.2054 0.657360
\(768\) 0 0
\(769\) −10.0139 −0.361111 −0.180556 0.983565i \(-0.557790\pi\)
−0.180556 + 0.983565i \(0.557790\pi\)
\(770\) 0 0
\(771\) 11.2409 0.404831
\(772\) 0 0
\(773\) −35.8956 −1.29108 −0.645538 0.763728i \(-0.723367\pi\)
−0.645538 + 0.763728i \(0.723367\pi\)
\(774\) 0 0
\(775\) 16.1968 0.581807
\(776\) 0 0
\(777\) 1.30028 0.0466474
\(778\) 0 0
\(779\) 4.45005 0.159439
\(780\) 0 0
\(781\) −26.9968 −0.966023
\(782\) 0 0
\(783\) −77.2940 −2.76226
\(784\) 0 0
\(785\) 0.0453292 0.00161787
\(786\) 0 0
\(787\) −1.89211 −0.0674464 −0.0337232 0.999431i \(-0.510736\pi\)
−0.0337232 + 0.999431i \(0.510736\pi\)
\(788\) 0 0
\(789\) 40.4252 1.43917
\(790\) 0 0
\(791\) 0.702806 0.0249889
\(792\) 0 0
\(793\) 6.68434 0.237368
\(794\) 0 0
\(795\) 1.84248 0.0653459
\(796\) 0 0
\(797\) 24.4028 0.864393 0.432197 0.901779i \(-0.357739\pi\)
0.432197 + 0.901779i \(0.357739\pi\)
\(798\) 0 0
\(799\) −5.47347 −0.193637
\(800\) 0 0
\(801\) 41.4940 1.46612
\(802\) 0 0
\(803\) 2.13220 0.0752437
\(804\) 0 0
\(805\) 0.115499 0.00407080
\(806\) 0 0
\(807\) −92.2371 −3.24690
\(808\) 0 0
\(809\) −32.9341 −1.15790 −0.578951 0.815363i \(-0.696538\pi\)
−0.578951 + 0.815363i \(0.696538\pi\)
\(810\) 0 0
\(811\) 42.8145 1.50342 0.751711 0.659493i \(-0.229229\pi\)
0.751711 + 0.659493i \(0.229229\pi\)
\(812\) 0 0
\(813\) 27.8002 0.974997
\(814\) 0 0
\(815\) 4.83732 0.169444
\(816\) 0 0
\(817\) −6.49708 −0.227304
\(818\) 0 0
\(819\) 1.53910 0.0537805
\(820\) 0 0
\(821\) −28.2632 −0.986393 −0.493196 0.869918i \(-0.664172\pi\)
−0.493196 + 0.869918i \(0.664172\pi\)
\(822\) 0 0
\(823\) −10.4127 −0.362962 −0.181481 0.983394i \(-0.558089\pi\)
−0.181481 + 0.983394i \(0.558089\pi\)
\(824\) 0 0
\(825\) 35.2202 1.22621
\(826\) 0 0
\(827\) 0.0841446 0.00292600 0.00146300 0.999999i \(-0.499534\pi\)
0.00146300 + 0.999999i \(0.499534\pi\)
\(828\) 0 0
\(829\) 46.3470 1.60970 0.804850 0.593479i \(-0.202246\pi\)
0.804850 + 0.593479i \(0.202246\pi\)
\(830\) 0 0
\(831\) 31.7924 1.10287
\(832\) 0 0
\(833\) 35.1463 1.21775
\(834\) 0 0
\(835\) 0.287315 0.00994294
\(836\) 0 0
\(837\) −35.2760 −1.21932
\(838\) 0 0
\(839\) 13.9611 0.481990 0.240995 0.970526i \(-0.422526\pi\)
0.240995 + 0.970526i \(0.422526\pi\)
\(840\) 0 0
\(841\) 24.5241 0.845660
\(842\) 0 0
\(843\) −59.5054 −2.04948
\(844\) 0 0
\(845\) −4.43913 −0.152711
\(846\) 0 0
\(847\) 1.05546 0.0362660
\(848\) 0 0
\(849\) −29.8916 −1.02588
\(850\) 0 0
\(851\) 3.33214 0.114224
\(852\) 0 0
\(853\) −54.5527 −1.86785 −0.933924 0.357472i \(-0.883639\pi\)
−0.933924 + 0.357472i \(0.883639\pi\)
\(854\) 0 0
\(855\) −10.5534 −0.360920
\(856\) 0 0
\(857\) 27.6798 0.945525 0.472762 0.881190i \(-0.343257\pi\)
0.472762 + 0.881190i \(0.343257\pi\)
\(858\) 0 0
\(859\) −27.1497 −0.926336 −0.463168 0.886270i \(-0.653287\pi\)
−0.463168 + 0.886270i \(0.653287\pi\)
\(860\) 0 0
\(861\) 0.627810 0.0213957
\(862\) 0 0
\(863\) −25.9641 −0.883827 −0.441913 0.897058i \(-0.645700\pi\)
−0.441913 + 0.897058i \(0.645700\pi\)
\(864\) 0 0
\(865\) 4.48208 0.152395
\(866\) 0 0
\(867\) 26.0694 0.885363
\(868\) 0 0
\(869\) −30.1151 −1.02159
\(870\) 0 0
\(871\) −13.8826 −0.470394
\(872\) 0 0
\(873\) −83.6313 −2.83049
\(874\) 0 0
\(875\) 0.741425 0.0250647
\(876\) 0 0
\(877\) 37.2176 1.25675 0.628374 0.777911i \(-0.283721\pi\)
0.628374 + 0.777911i \(0.283721\pi\)
\(878\) 0 0
\(879\) 80.5920 2.71830
\(880\) 0 0
\(881\) −6.44185 −0.217031 −0.108516 0.994095i \(-0.534610\pi\)
−0.108516 + 0.994095i \(0.534610\pi\)
\(882\) 0 0
\(883\) −45.9727 −1.54711 −0.773553 0.633732i \(-0.781522\pi\)
−0.773553 + 0.633732i \(0.781522\pi\)
\(884\) 0 0
\(885\) −17.6113 −0.591998
\(886\) 0 0
\(887\) 28.3187 0.950849 0.475425 0.879756i \(-0.342294\pi\)
0.475425 + 0.879756i \(0.342294\pi\)
\(888\) 0 0
\(889\) −3.47632 −0.116592
\(890\) 0 0
\(891\) −31.0582 −1.04049
\(892\) 0 0
\(893\) −4.60208 −0.154003
\(894\) 0 0
\(895\) 8.18524 0.273602
\(896\) 0 0
\(897\) 5.78181 0.193049
\(898\) 0 0
\(899\) 24.4277 0.814710
\(900\) 0 0
\(901\) −7.84041 −0.261202
\(902\) 0 0
\(903\) −0.916604 −0.0305027
\(904\) 0 0
\(905\) 4.61475 0.153399
\(906\) 0 0
\(907\) 12.5099 0.415384 0.207692 0.978194i \(-0.433405\pi\)
0.207692 + 0.978194i \(0.433405\pi\)
\(908\) 0 0
\(909\) 39.8010 1.32012
\(910\) 0 0
\(911\) −2.41940 −0.0801584 −0.0400792 0.999197i \(-0.512761\pi\)
−0.0400792 + 0.999197i \(0.512761\pi\)
\(912\) 0 0
\(913\) 14.4216 0.477284
\(914\) 0 0
\(915\) −6.46621 −0.213766
\(916\) 0 0
\(917\) −2.37485 −0.0784246
\(918\) 0 0
\(919\) −50.3462 −1.66077 −0.830384 0.557192i \(-0.811879\pi\)
−0.830384 + 0.557192i \(0.811879\pi\)
\(920\) 0 0
\(921\) 42.1200 1.38790
\(922\) 0 0
\(923\) −14.0094 −0.461125
\(924\) 0 0
\(925\) 10.5331 0.346328
\(926\) 0 0
\(927\) −50.1103 −1.64584
\(928\) 0 0
\(929\) −32.9858 −1.08223 −0.541115 0.840948i \(-0.681998\pi\)
−0.541115 + 0.840948i \(0.681998\pi\)
\(930\) 0 0
\(931\) 29.5510 0.968494
\(932\) 0 0
\(933\) −94.9464 −3.10841
\(934\) 0 0
\(935\) 4.60687 0.150661
\(936\) 0 0
\(937\) 47.9023 1.56490 0.782450 0.622714i \(-0.213970\pi\)
0.782450 + 0.622714i \(0.213970\pi\)
\(938\) 0 0
\(939\) −86.7262 −2.83020
\(940\) 0 0
\(941\) −4.42362 −0.144206 −0.0721030 0.997397i \(-0.522971\pi\)
−0.0721030 + 0.997397i \(0.522971\pi\)
\(942\) 0 0
\(943\) 1.60884 0.0523912
\(944\) 0 0
\(945\) −0.795175 −0.0258670
\(946\) 0 0
\(947\) −19.3253 −0.627987 −0.313994 0.949425i \(-0.601667\pi\)
−0.313994 + 0.949425i \(0.601667\pi\)
\(948\) 0 0
\(949\) 1.10646 0.0359171
\(950\) 0 0
\(951\) −23.2200 −0.752960
\(952\) 0 0
\(953\) 30.0968 0.974931 0.487465 0.873142i \(-0.337922\pi\)
0.487465 + 0.873142i \(0.337922\pi\)
\(954\) 0 0
\(955\) −9.35408 −0.302691
\(956\) 0 0
\(957\) 53.1184 1.71708
\(958\) 0 0
\(959\) 2.70948 0.0874937
\(960\) 0 0
\(961\) −19.8515 −0.640371
\(962\) 0 0
\(963\) 52.6836 1.69771
\(964\) 0 0
\(965\) −2.23402 −0.0719156
\(966\) 0 0
\(967\) 42.6607 1.37187 0.685937 0.727661i \(-0.259392\pi\)
0.685937 + 0.727661i \(0.259392\pi\)
\(968\) 0 0
\(969\) 65.8328 2.11485
\(970\) 0 0
\(971\) −33.0050 −1.05918 −0.529591 0.848253i \(-0.677655\pi\)
−0.529591 + 0.848253i \(0.677655\pi\)
\(972\) 0 0
\(973\) 0.974412 0.0312382
\(974\) 0 0
\(975\) 18.2767 0.585324
\(976\) 0 0
\(977\) −5.79949 −0.185542 −0.0927710 0.995687i \(-0.529572\pi\)
−0.0927710 + 0.995687i \(0.529572\pi\)
\(978\) 0 0
\(979\) −15.2296 −0.486740
\(980\) 0 0
\(981\) −34.2859 −1.09467
\(982\) 0 0
\(983\) 35.2304 1.12367 0.561837 0.827248i \(-0.310095\pi\)
0.561837 + 0.827248i \(0.310095\pi\)
\(984\) 0 0
\(985\) 1.57081 0.0500501
\(986\) 0 0
\(987\) −0.649260 −0.0206662
\(988\) 0 0
\(989\) −2.34891 −0.0746911
\(990\) 0 0
\(991\) −9.08023 −0.288443 −0.144221 0.989545i \(-0.546068\pi\)
−0.144221 + 0.989545i \(0.546068\pi\)
\(992\) 0 0
\(993\) −62.7433 −1.99110
\(994\) 0 0
\(995\) 4.40992 0.139804
\(996\) 0 0
\(997\) 59.6440 1.88894 0.944472 0.328591i \(-0.106574\pi\)
0.944472 + 0.328591i \(0.106574\pi\)
\(998\) 0 0
\(999\) −22.9407 −0.725813
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 \(a_p\))