Properties

Label 6040.2.a.p.1.17
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Root \(-2.06929\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.06929 q^{3}\) \(+1.00000 q^{5}\) \(-0.835530 q^{7}\) \(+1.28196 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.06929 q^{3}\) \(+1.00000 q^{5}\) \(-0.835530 q^{7}\) \(+1.28196 q^{9}\) \(-5.16889 q^{11}\) \(+4.52286 q^{13}\) \(+2.06929 q^{15}\) \(-5.30666 q^{17}\) \(-6.46213 q^{19}\) \(-1.72895 q^{21}\) \(-5.32449 q^{23}\) \(+1.00000 q^{25}\) \(-3.55513 q^{27}\) \(+7.21060 q^{29}\) \(+7.66896 q^{31}\) \(-10.6959 q^{33}\) \(-0.835530 q^{35}\) \(+7.65331 q^{37}\) \(+9.35910 q^{39}\) \(-3.14014 q^{41}\) \(+8.02225 q^{43}\) \(+1.28196 q^{45}\) \(-12.1777 q^{47}\) \(-6.30189 q^{49}\) \(-10.9810 q^{51}\) \(+11.3115 q^{53}\) \(-5.16889 q^{55}\) \(-13.3720 q^{57}\) \(-7.74516 q^{59}\) \(+10.1168 q^{61}\) \(-1.07111 q^{63}\) \(+4.52286 q^{65}\) \(-5.34910 q^{67}\) \(-11.0179 q^{69}\) \(-11.5813 q^{71}\) \(-8.45002 q^{73}\) \(+2.06929 q^{75}\) \(+4.31876 q^{77}\) \(-12.7154 q^{79}\) \(-11.2025 q^{81}\) \(-14.2329 q^{83}\) \(-5.30666 q^{85}\) \(+14.9208 q^{87}\) \(-16.3014 q^{89}\) \(-3.77898 q^{91}\) \(+15.8693 q^{93}\) \(-6.46213 q^{95}\) \(-12.9093 q^{97}\) \(-6.62628 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 2.06929 1.19470 0.597352 0.801979i \(-0.296219\pi\)
0.597352 + 0.801979i \(0.296219\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −0.835530 −0.315800 −0.157900 0.987455i \(-0.550472\pi\)
−0.157900 + 0.987455i \(0.550472\pi\)
\(8\) 0 0
\(9\) 1.28196 0.427318
\(10\) 0 0
\(11\) −5.16889 −1.55848 −0.779239 0.626727i \(-0.784394\pi\)
−0.779239 + 0.626727i \(0.784394\pi\)
\(12\) 0 0
\(13\) 4.52286 1.25441 0.627207 0.778852i \(-0.284198\pi\)
0.627207 + 0.778852i \(0.284198\pi\)
\(14\) 0 0
\(15\) 2.06929 0.534288
\(16\) 0 0
\(17\) −5.30666 −1.28705 −0.643527 0.765424i \(-0.722529\pi\)
−0.643527 + 0.765424i \(0.722529\pi\)
\(18\) 0 0
\(19\) −6.46213 −1.48251 −0.741257 0.671221i \(-0.765770\pi\)
−0.741257 + 0.671221i \(0.765770\pi\)
\(20\) 0 0
\(21\) −1.72895 −0.377288
\(22\) 0 0
\(23\) −5.32449 −1.11023 −0.555116 0.831773i \(-0.687326\pi\)
−0.555116 + 0.831773i \(0.687326\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −3.55513 −0.684185
\(28\) 0 0
\(29\) 7.21060 1.33898 0.669488 0.742823i \(-0.266514\pi\)
0.669488 + 0.742823i \(0.266514\pi\)
\(30\) 0 0
\(31\) 7.66896 1.37739 0.688693 0.725053i \(-0.258185\pi\)
0.688693 + 0.725053i \(0.258185\pi\)
\(32\) 0 0
\(33\) −10.6959 −1.86192
\(34\) 0 0
\(35\) −0.835530 −0.141230
\(36\) 0 0
\(37\) 7.65331 1.25820 0.629098 0.777326i \(-0.283424\pi\)
0.629098 + 0.777326i \(0.283424\pi\)
\(38\) 0 0
\(39\) 9.35910 1.49865
\(40\) 0 0
\(41\) −3.14014 −0.490408 −0.245204 0.969472i \(-0.578855\pi\)
−0.245204 + 0.969472i \(0.578855\pi\)
\(42\) 0 0
\(43\) 8.02225 1.22338 0.611691 0.791097i \(-0.290490\pi\)
0.611691 + 0.791097i \(0.290490\pi\)
\(44\) 0 0
\(45\) 1.28196 0.191103
\(46\) 0 0
\(47\) −12.1777 −1.77630 −0.888152 0.459551i \(-0.848010\pi\)
−0.888152 + 0.459551i \(0.848010\pi\)
\(48\) 0 0
\(49\) −6.30189 −0.900270
\(50\) 0 0
\(51\) −10.9810 −1.53765
\(52\) 0 0
\(53\) 11.3115 1.55375 0.776877 0.629653i \(-0.216803\pi\)
0.776877 + 0.629653i \(0.216803\pi\)
\(54\) 0 0
\(55\) −5.16889 −0.696973
\(56\) 0 0
\(57\) −13.3720 −1.77117
\(58\) 0 0
\(59\) −7.74516 −1.00833 −0.504167 0.863606i \(-0.668200\pi\)
−0.504167 + 0.863606i \(0.668200\pi\)
\(60\) 0 0
\(61\) 10.1168 1.29532 0.647661 0.761929i \(-0.275747\pi\)
0.647661 + 0.761929i \(0.275747\pi\)
\(62\) 0 0
\(63\) −1.07111 −0.134947
\(64\) 0 0
\(65\) 4.52286 0.560991
\(66\) 0 0
\(67\) −5.34910 −0.653497 −0.326748 0.945111i \(-0.605953\pi\)
−0.326748 + 0.945111i \(0.605953\pi\)
\(68\) 0 0
\(69\) −11.0179 −1.32640
\(70\) 0 0
\(71\) −11.5813 −1.37445 −0.687224 0.726446i \(-0.741171\pi\)
−0.687224 + 0.726446i \(0.741171\pi\)
\(72\) 0 0
\(73\) −8.45002 −0.989000 −0.494500 0.869178i \(-0.664649\pi\)
−0.494500 + 0.869178i \(0.664649\pi\)
\(74\) 0 0
\(75\) 2.06929 0.238941
\(76\) 0 0
\(77\) 4.31876 0.492168
\(78\) 0 0
\(79\) −12.7154 −1.43060 −0.715299 0.698818i \(-0.753710\pi\)
−0.715299 + 0.698818i \(0.753710\pi\)
\(80\) 0 0
\(81\) −11.2025 −1.24472
\(82\) 0 0
\(83\) −14.2329 −1.56227 −0.781134 0.624364i \(-0.785358\pi\)
−0.781134 + 0.624364i \(0.785358\pi\)
\(84\) 0 0
\(85\) −5.30666 −0.575588
\(86\) 0 0
\(87\) 14.9208 1.59968
\(88\) 0 0
\(89\) −16.3014 −1.72795 −0.863974 0.503536i \(-0.832032\pi\)
−0.863974 + 0.503536i \(0.832032\pi\)
\(90\) 0 0
\(91\) −3.77898 −0.396145
\(92\) 0 0
\(93\) 15.8693 1.64557
\(94\) 0 0
\(95\) −6.46213 −0.663001
\(96\) 0 0
\(97\) −12.9093 −1.31074 −0.655372 0.755306i \(-0.727488\pi\)
−0.655372 + 0.755306i \(0.727488\pi\)
\(98\) 0 0
\(99\) −6.62628 −0.665967
\(100\) 0 0
\(101\) −15.2443 −1.51686 −0.758432 0.651752i \(-0.774034\pi\)
−0.758432 + 0.651752i \(0.774034\pi\)
\(102\) 0 0
\(103\) 7.56124 0.745031 0.372515 0.928026i \(-0.378495\pi\)
0.372515 + 0.928026i \(0.378495\pi\)
\(104\) 0 0
\(105\) −1.72895 −0.168728
\(106\) 0 0
\(107\) −10.6019 −1.02493 −0.512463 0.858709i \(-0.671267\pi\)
−0.512463 + 0.858709i \(0.671267\pi\)
\(108\) 0 0
\(109\) −2.61594 −0.250561 −0.125281 0.992121i \(-0.539983\pi\)
−0.125281 + 0.992121i \(0.539983\pi\)
\(110\) 0 0
\(111\) 15.8369 1.50317
\(112\) 0 0
\(113\) 12.3961 1.16613 0.583064 0.812426i \(-0.301854\pi\)
0.583064 + 0.812426i \(0.301854\pi\)
\(114\) 0 0
\(115\) −5.32449 −0.496511
\(116\) 0 0
\(117\) 5.79810 0.536035
\(118\) 0 0
\(119\) 4.43387 0.406452
\(120\) 0 0
\(121\) 15.7174 1.42886
\(122\) 0 0
\(123\) −6.49786 −0.585893
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −11.6039 −1.02968 −0.514838 0.857287i \(-0.672148\pi\)
−0.514838 + 0.857287i \(0.672148\pi\)
\(128\) 0 0
\(129\) 16.6003 1.46158
\(130\) 0 0
\(131\) 12.3615 1.08003 0.540013 0.841657i \(-0.318419\pi\)
0.540013 + 0.841657i \(0.318419\pi\)
\(132\) 0 0
\(133\) 5.39930 0.468179
\(134\) 0 0
\(135\) −3.55513 −0.305977
\(136\) 0 0
\(137\) 2.32336 0.198498 0.0992491 0.995063i \(-0.468356\pi\)
0.0992491 + 0.995063i \(0.468356\pi\)
\(138\) 0 0
\(139\) 19.0803 1.61837 0.809183 0.587557i \(-0.199910\pi\)
0.809183 + 0.587557i \(0.199910\pi\)
\(140\) 0 0
\(141\) −25.1992 −2.12216
\(142\) 0 0
\(143\) −23.3781 −1.95498
\(144\) 0 0
\(145\) 7.21060 0.598808
\(146\) 0 0
\(147\) −13.0404 −1.07556
\(148\) 0 0
\(149\) −14.4699 −1.18542 −0.592712 0.805415i \(-0.701943\pi\)
−0.592712 + 0.805415i \(0.701943\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) −6.80290 −0.549982
\(154\) 0 0
\(155\) 7.66896 0.615986
\(156\) 0 0
\(157\) −13.8769 −1.10750 −0.553749 0.832684i \(-0.686803\pi\)
−0.553749 + 0.832684i \(0.686803\pi\)
\(158\) 0 0
\(159\) 23.4067 1.85628
\(160\) 0 0
\(161\) 4.44877 0.350612
\(162\) 0 0
\(163\) 2.22611 0.174362 0.0871812 0.996192i \(-0.472214\pi\)
0.0871812 + 0.996192i \(0.472214\pi\)
\(164\) 0 0
\(165\) −10.6959 −0.832676
\(166\) 0 0
\(167\) −19.2210 −1.48736 −0.743682 0.668534i \(-0.766922\pi\)
−0.743682 + 0.668534i \(0.766922\pi\)
\(168\) 0 0
\(169\) 7.45624 0.573557
\(170\) 0 0
\(171\) −8.28416 −0.633506
\(172\) 0 0
\(173\) −13.9144 −1.05790 −0.528948 0.848654i \(-0.677413\pi\)
−0.528948 + 0.848654i \(0.677413\pi\)
\(174\) 0 0
\(175\) −0.835530 −0.0631601
\(176\) 0 0
\(177\) −16.0270 −1.20466
\(178\) 0 0
\(179\) 19.5790 1.46341 0.731703 0.681623i \(-0.238726\pi\)
0.731703 + 0.681623i \(0.238726\pi\)
\(180\) 0 0
\(181\) 17.2953 1.28555 0.642774 0.766056i \(-0.277783\pi\)
0.642774 + 0.766056i \(0.277783\pi\)
\(182\) 0 0
\(183\) 20.9345 1.54753
\(184\) 0 0
\(185\) 7.65331 0.562682
\(186\) 0 0
\(187\) 27.4295 2.00585
\(188\) 0 0
\(189\) 2.97042 0.216066
\(190\) 0 0
\(191\) 3.13159 0.226594 0.113297 0.993561i \(-0.463859\pi\)
0.113297 + 0.993561i \(0.463859\pi\)
\(192\) 0 0
\(193\) −3.32113 −0.239060 −0.119530 0.992831i \(-0.538139\pi\)
−0.119530 + 0.992831i \(0.538139\pi\)
\(194\) 0 0
\(195\) 9.35910 0.670219
\(196\) 0 0
\(197\) −1.47516 −0.105101 −0.0525503 0.998618i \(-0.516735\pi\)
−0.0525503 + 0.998618i \(0.516735\pi\)
\(198\) 0 0
\(199\) 14.5686 1.03274 0.516371 0.856365i \(-0.327282\pi\)
0.516371 + 0.856365i \(0.327282\pi\)
\(200\) 0 0
\(201\) −11.0688 −0.780735
\(202\) 0 0
\(203\) −6.02467 −0.422849
\(204\) 0 0
\(205\) −3.14014 −0.219317
\(206\) 0 0
\(207\) −6.82576 −0.474423
\(208\) 0 0
\(209\) 33.4020 2.31047
\(210\) 0 0
\(211\) −8.78970 −0.605108 −0.302554 0.953132i \(-0.597839\pi\)
−0.302554 + 0.953132i \(0.597839\pi\)
\(212\) 0 0
\(213\) −23.9650 −1.64206
\(214\) 0 0
\(215\) 8.02225 0.547113
\(216\) 0 0
\(217\) −6.40764 −0.434979
\(218\) 0 0
\(219\) −17.4855 −1.18156
\(220\) 0 0
\(221\) −24.0013 −1.61450
\(222\) 0 0
\(223\) −4.60000 −0.308039 −0.154019 0.988068i \(-0.549222\pi\)
−0.154019 + 0.988068i \(0.549222\pi\)
\(224\) 0 0
\(225\) 1.28196 0.0854637
\(226\) 0 0
\(227\) 10.7763 0.715250 0.357625 0.933865i \(-0.383587\pi\)
0.357625 + 0.933865i \(0.383587\pi\)
\(228\) 0 0
\(229\) −8.39513 −0.554766 −0.277383 0.960759i \(-0.589467\pi\)
−0.277383 + 0.960759i \(0.589467\pi\)
\(230\) 0 0
\(231\) 8.93676 0.587996
\(232\) 0 0
\(233\) −14.1187 −0.924947 −0.462473 0.886633i \(-0.653038\pi\)
−0.462473 + 0.886633i \(0.653038\pi\)
\(234\) 0 0
\(235\) −12.1777 −0.794387
\(236\) 0 0
\(237\) −26.3119 −1.70914
\(238\) 0 0
\(239\) −13.4588 −0.870575 −0.435287 0.900292i \(-0.643353\pi\)
−0.435287 + 0.900292i \(0.643353\pi\)
\(240\) 0 0
\(241\) 9.39148 0.604958 0.302479 0.953156i \(-0.402186\pi\)
0.302479 + 0.953156i \(0.402186\pi\)
\(242\) 0 0
\(243\) −12.5157 −0.802884
\(244\) 0 0
\(245\) −6.30189 −0.402613
\(246\) 0 0
\(247\) −29.2273 −1.85969
\(248\) 0 0
\(249\) −29.4520 −1.86645
\(250\) 0 0
\(251\) 2.91069 0.183721 0.0918606 0.995772i \(-0.470719\pi\)
0.0918606 + 0.995772i \(0.470719\pi\)
\(252\) 0 0
\(253\) 27.5217 1.73027
\(254\) 0 0
\(255\) −10.9810 −0.687657
\(256\) 0 0
\(257\) −11.1799 −0.697386 −0.348693 0.937237i \(-0.613374\pi\)
−0.348693 + 0.937237i \(0.613374\pi\)
\(258\) 0 0
\(259\) −6.39456 −0.397339
\(260\) 0 0
\(261\) 9.24367 0.572169
\(262\) 0 0
\(263\) 15.2666 0.941378 0.470689 0.882299i \(-0.344005\pi\)
0.470689 + 0.882299i \(0.344005\pi\)
\(264\) 0 0
\(265\) 11.3115 0.694860
\(266\) 0 0
\(267\) −33.7324 −2.06439
\(268\) 0 0
\(269\) 16.2376 0.990023 0.495011 0.868887i \(-0.335164\pi\)
0.495011 + 0.868887i \(0.335164\pi\)
\(270\) 0 0
\(271\) 29.6327 1.80006 0.900030 0.435827i \(-0.143544\pi\)
0.900030 + 0.435827i \(0.143544\pi\)
\(272\) 0 0
\(273\) −7.81980 −0.473276
\(274\) 0 0
\(275\) −5.16889 −0.311696
\(276\) 0 0
\(277\) −3.52014 −0.211505 −0.105752 0.994392i \(-0.533725\pi\)
−0.105752 + 0.994392i \(0.533725\pi\)
\(278\) 0 0
\(279\) 9.83127 0.588582
\(280\) 0 0
\(281\) −9.54474 −0.569392 −0.284696 0.958618i \(-0.591893\pi\)
−0.284696 + 0.958618i \(0.591893\pi\)
\(282\) 0 0
\(283\) 10.1609 0.604002 0.302001 0.953308i \(-0.402345\pi\)
0.302001 + 0.953308i \(0.402345\pi\)
\(284\) 0 0
\(285\) −13.3720 −0.792090
\(286\) 0 0
\(287\) 2.62368 0.154871
\(288\) 0 0
\(289\) 11.1606 0.656506
\(290\) 0 0
\(291\) −26.7131 −1.56595
\(292\) 0 0
\(293\) 24.2837 1.41867 0.709334 0.704873i \(-0.248996\pi\)
0.709334 + 0.704873i \(0.248996\pi\)
\(294\) 0 0
\(295\) −7.74516 −0.450941
\(296\) 0 0
\(297\) 18.3761 1.06629
\(298\) 0 0
\(299\) −24.0819 −1.39269
\(300\) 0 0
\(301\) −6.70283 −0.386344
\(302\) 0 0
\(303\) −31.5449 −1.81220
\(304\) 0 0
\(305\) 10.1168 0.579285
\(306\) 0 0
\(307\) −3.63111 −0.207238 −0.103619 0.994617i \(-0.533042\pi\)
−0.103619 + 0.994617i \(0.533042\pi\)
\(308\) 0 0
\(309\) 15.6464 0.890092
\(310\) 0 0
\(311\) 16.5499 0.938458 0.469229 0.883077i \(-0.344532\pi\)
0.469229 + 0.883077i \(0.344532\pi\)
\(312\) 0 0
\(313\) 23.6185 1.33500 0.667499 0.744611i \(-0.267365\pi\)
0.667499 + 0.744611i \(0.267365\pi\)
\(314\) 0 0
\(315\) −1.07111 −0.0603503
\(316\) 0 0
\(317\) 23.4797 1.31875 0.659377 0.751813i \(-0.270820\pi\)
0.659377 + 0.751813i \(0.270820\pi\)
\(318\) 0 0
\(319\) −37.2708 −2.08676
\(320\) 0 0
\(321\) −21.9384 −1.22448
\(322\) 0 0
\(323\) 34.2923 1.90808
\(324\) 0 0
\(325\) 4.52286 0.250883
\(326\) 0 0
\(327\) −5.41313 −0.299347
\(328\) 0 0
\(329\) 10.1748 0.560957
\(330\) 0 0
\(331\) −11.4491 −0.629302 −0.314651 0.949207i \(-0.601887\pi\)
−0.314651 + 0.949207i \(0.601887\pi\)
\(332\) 0 0
\(333\) 9.81120 0.537650
\(334\) 0 0
\(335\) −5.34910 −0.292253
\(336\) 0 0
\(337\) −20.3593 −1.10904 −0.554521 0.832169i \(-0.687099\pi\)
−0.554521 + 0.832169i \(0.687099\pi\)
\(338\) 0 0
\(339\) 25.6512 1.39318
\(340\) 0 0
\(341\) −39.6400 −2.14663
\(342\) 0 0
\(343\) 11.1141 0.600106
\(344\) 0 0
\(345\) −11.0179 −0.593184
\(346\) 0 0
\(347\) 32.0321 1.71957 0.859787 0.510653i \(-0.170596\pi\)
0.859787 + 0.510653i \(0.170596\pi\)
\(348\) 0 0
\(349\) 5.48515 0.293614 0.146807 0.989165i \(-0.453100\pi\)
0.146807 + 0.989165i \(0.453100\pi\)
\(350\) 0 0
\(351\) −16.0793 −0.858252
\(352\) 0 0
\(353\) −9.04362 −0.481343 −0.240672 0.970607i \(-0.577368\pi\)
−0.240672 + 0.970607i \(0.577368\pi\)
\(354\) 0 0
\(355\) −11.5813 −0.614671
\(356\) 0 0
\(357\) 9.17495 0.485590
\(358\) 0 0
\(359\) 16.9220 0.893110 0.446555 0.894756i \(-0.352651\pi\)
0.446555 + 0.894756i \(0.352651\pi\)
\(360\) 0 0
\(361\) 22.7591 1.19785
\(362\) 0 0
\(363\) 32.5239 1.70706
\(364\) 0 0
\(365\) −8.45002 −0.442294
\(366\) 0 0
\(367\) −2.38029 −0.124250 −0.0621251 0.998068i \(-0.519788\pi\)
−0.0621251 + 0.998068i \(0.519788\pi\)
\(368\) 0 0
\(369\) −4.02552 −0.209560
\(370\) 0 0
\(371\) −9.45109 −0.490676
\(372\) 0 0
\(373\) −1.65463 −0.0856736 −0.0428368 0.999082i \(-0.513640\pi\)
−0.0428368 + 0.999082i \(0.513640\pi\)
\(374\) 0 0
\(375\) 2.06929 0.106858
\(376\) 0 0
\(377\) 32.6125 1.67963
\(378\) 0 0
\(379\) 15.2563 0.783665 0.391832 0.920037i \(-0.371841\pi\)
0.391832 + 0.920037i \(0.371841\pi\)
\(380\) 0 0
\(381\) −24.0117 −1.23016
\(382\) 0 0
\(383\) −22.0927 −1.12889 −0.564443 0.825472i \(-0.690909\pi\)
−0.564443 + 0.825472i \(0.690909\pi\)
\(384\) 0 0
\(385\) 4.31876 0.220104
\(386\) 0 0
\(387\) 10.2842 0.522773
\(388\) 0 0
\(389\) 20.8242 1.05583 0.527915 0.849297i \(-0.322974\pi\)
0.527915 + 0.849297i \(0.322974\pi\)
\(390\) 0 0
\(391\) 28.2552 1.42893
\(392\) 0 0
\(393\) 25.5794 1.29031
\(394\) 0 0
\(395\) −12.7154 −0.639783
\(396\) 0 0
\(397\) −1.91881 −0.0963023 −0.0481511 0.998840i \(-0.515333\pi\)
−0.0481511 + 0.998840i \(0.515333\pi\)
\(398\) 0 0
\(399\) 11.1727 0.559335
\(400\) 0 0
\(401\) −4.66802 −0.233110 −0.116555 0.993184i \(-0.537185\pi\)
−0.116555 + 0.993184i \(0.537185\pi\)
\(402\) 0 0
\(403\) 34.6856 1.72781
\(404\) 0 0
\(405\) −11.2025 −0.556655
\(406\) 0 0
\(407\) −39.5591 −1.96087
\(408\) 0 0
\(409\) −24.0822 −1.19079 −0.595393 0.803435i \(-0.703004\pi\)
−0.595393 + 0.803435i \(0.703004\pi\)
\(410\) 0 0
\(411\) 4.80771 0.237147
\(412\) 0 0
\(413\) 6.47131 0.318432
\(414\) 0 0
\(415\) −14.2329 −0.698667
\(416\) 0 0
\(417\) 39.4825 1.93347
\(418\) 0 0
\(419\) 18.5364 0.905564 0.452782 0.891621i \(-0.350432\pi\)
0.452782 + 0.891621i \(0.350432\pi\)
\(420\) 0 0
\(421\) 33.5023 1.63280 0.816400 0.577487i \(-0.195967\pi\)
0.816400 + 0.577487i \(0.195967\pi\)
\(422\) 0 0
\(423\) −15.6113 −0.759047
\(424\) 0 0
\(425\) −5.30666 −0.257411
\(426\) 0 0
\(427\) −8.45287 −0.409063
\(428\) 0 0
\(429\) −48.3761 −2.33562
\(430\) 0 0
\(431\) 32.0155 1.54213 0.771065 0.636756i \(-0.219724\pi\)
0.771065 + 0.636756i \(0.219724\pi\)
\(432\) 0 0
\(433\) −2.02308 −0.0972232 −0.0486116 0.998818i \(-0.515480\pi\)
−0.0486116 + 0.998818i \(0.515480\pi\)
\(434\) 0 0
\(435\) 14.9208 0.715399
\(436\) 0 0
\(437\) 34.4075 1.64594
\(438\) 0 0
\(439\) 0.818067 0.0390442 0.0195221 0.999809i \(-0.493786\pi\)
0.0195221 + 0.999809i \(0.493786\pi\)
\(440\) 0 0
\(441\) −8.07874 −0.384702
\(442\) 0 0
\(443\) 3.02456 0.143701 0.0718506 0.997415i \(-0.477110\pi\)
0.0718506 + 0.997415i \(0.477110\pi\)
\(444\) 0 0
\(445\) −16.3014 −0.772762
\(446\) 0 0
\(447\) −29.9425 −1.41623
\(448\) 0 0
\(449\) −29.8233 −1.40745 −0.703724 0.710474i \(-0.748481\pi\)
−0.703724 + 0.710474i \(0.748481\pi\)
\(450\) 0 0
\(451\) 16.2311 0.764290
\(452\) 0 0
\(453\) 2.06929 0.0972237
\(454\) 0 0
\(455\) −3.77898 −0.177161
\(456\) 0 0
\(457\) 16.7034 0.781350 0.390675 0.920529i \(-0.372242\pi\)
0.390675 + 0.920529i \(0.372242\pi\)
\(458\) 0 0
\(459\) 18.8659 0.880583
\(460\) 0 0
\(461\) 28.8849 1.34530 0.672652 0.739959i \(-0.265155\pi\)
0.672652 + 0.739959i \(0.265155\pi\)
\(462\) 0 0
\(463\) −36.2501 −1.68469 −0.842343 0.538942i \(-0.818824\pi\)
−0.842343 + 0.538942i \(0.818824\pi\)
\(464\) 0 0
\(465\) 15.8693 0.735921
\(466\) 0 0
\(467\) 31.4982 1.45756 0.728782 0.684746i \(-0.240087\pi\)
0.728782 + 0.684746i \(0.240087\pi\)
\(468\) 0 0
\(469\) 4.46933 0.206375
\(470\) 0 0
\(471\) −28.7153 −1.32313
\(472\) 0 0
\(473\) −41.4661 −1.90661
\(474\) 0 0
\(475\) −6.46213 −0.296503
\(476\) 0 0
\(477\) 14.5008 0.663947
\(478\) 0 0
\(479\) 31.6813 1.44756 0.723778 0.690033i \(-0.242404\pi\)
0.723778 + 0.690033i \(0.242404\pi\)
\(480\) 0 0
\(481\) 34.6148 1.57830
\(482\) 0 0
\(483\) 9.20578 0.418878
\(484\) 0 0
\(485\) −12.9093 −0.586183
\(486\) 0 0
\(487\) −4.69086 −0.212563 −0.106282 0.994336i \(-0.533894\pi\)
−0.106282 + 0.994336i \(0.533894\pi\)
\(488\) 0 0
\(489\) 4.60647 0.208312
\(490\) 0 0
\(491\) −14.9410 −0.674276 −0.337138 0.941455i \(-0.609459\pi\)
−0.337138 + 0.941455i \(0.609459\pi\)
\(492\) 0 0
\(493\) −38.2642 −1.72333
\(494\) 0 0
\(495\) −6.62628 −0.297829
\(496\) 0 0
\(497\) 9.67652 0.434051
\(498\) 0 0
\(499\) −24.6274 −1.10247 −0.551237 0.834349i \(-0.685844\pi\)
−0.551237 + 0.834349i \(0.685844\pi\)
\(500\) 0 0
\(501\) −39.7737 −1.77696
\(502\) 0 0
\(503\) 8.20454 0.365823 0.182911 0.983129i \(-0.441448\pi\)
0.182911 + 0.983129i \(0.441448\pi\)
\(504\) 0 0
\(505\) −15.2443 −0.678363
\(506\) 0 0
\(507\) 15.4291 0.685231
\(508\) 0 0
\(509\) −4.51038 −0.199919 −0.0999595 0.994992i \(-0.531871\pi\)
−0.0999595 + 0.994992i \(0.531871\pi\)
\(510\) 0 0
\(511\) 7.06024 0.312327
\(512\) 0 0
\(513\) 22.9737 1.01431
\(514\) 0 0
\(515\) 7.56124 0.333188
\(516\) 0 0
\(517\) 62.9453 2.76833
\(518\) 0 0
\(519\) −28.7930 −1.26387
\(520\) 0 0
\(521\) −30.8532 −1.35170 −0.675851 0.737038i \(-0.736224\pi\)
−0.675851 + 0.737038i \(0.736224\pi\)
\(522\) 0 0
\(523\) −21.0957 −0.922450 −0.461225 0.887283i \(-0.652590\pi\)
−0.461225 + 0.887283i \(0.652590\pi\)
\(524\) 0 0
\(525\) −1.72895 −0.0754576
\(526\) 0 0
\(527\) −40.6965 −1.77277
\(528\) 0 0
\(529\) 5.35017 0.232616
\(530\) 0 0
\(531\) −9.92895 −0.430880
\(532\) 0 0
\(533\) −14.2024 −0.615175
\(534\) 0 0
\(535\) −10.6019 −0.458361
\(536\) 0 0
\(537\) 40.5147 1.74834
\(538\) 0 0
\(539\) 32.5738 1.40305
\(540\) 0 0
\(541\) −29.8673 −1.28409 −0.642047 0.766666i \(-0.721914\pi\)
−0.642047 + 0.766666i \(0.721914\pi\)
\(542\) 0 0
\(543\) 35.7889 1.53585
\(544\) 0 0
\(545\) −2.61594 −0.112054
\(546\) 0 0
\(547\) −1.72185 −0.0736210 −0.0368105 0.999322i \(-0.511720\pi\)
−0.0368105 + 0.999322i \(0.511720\pi\)
\(548\) 0 0
\(549\) 12.9693 0.553515
\(550\) 0 0
\(551\) −46.5959 −1.98505
\(552\) 0 0
\(553\) 10.6241 0.451784
\(554\) 0 0
\(555\) 15.8369 0.672239
\(556\) 0 0
\(557\) 7.38990 0.313120 0.156560 0.987668i \(-0.449960\pi\)
0.156560 + 0.987668i \(0.449960\pi\)
\(558\) 0 0
\(559\) 36.2835 1.53463
\(560\) 0 0
\(561\) 56.7596 2.39639
\(562\) 0 0
\(563\) 1.76351 0.0743232 0.0371616 0.999309i \(-0.488168\pi\)
0.0371616 + 0.999309i \(0.488168\pi\)
\(564\) 0 0
\(565\) 12.3961 0.521509
\(566\) 0 0
\(567\) 9.35998 0.393082
\(568\) 0 0
\(569\) −23.7925 −0.997433 −0.498716 0.866765i \(-0.666195\pi\)
−0.498716 + 0.866765i \(0.666195\pi\)
\(570\) 0 0
\(571\) −24.6514 −1.03163 −0.515814 0.856700i \(-0.672511\pi\)
−0.515814 + 0.856700i \(0.672511\pi\)
\(572\) 0 0
\(573\) 6.48017 0.270713
\(574\) 0 0
\(575\) −5.32449 −0.222046
\(576\) 0 0
\(577\) −12.6431 −0.526340 −0.263170 0.964749i \(-0.584768\pi\)
−0.263170 + 0.964749i \(0.584768\pi\)
\(578\) 0 0
\(579\) −6.87237 −0.285606
\(580\) 0 0
\(581\) 11.8920 0.493365
\(582\) 0 0
\(583\) −58.4679 −2.42149
\(584\) 0 0
\(585\) 5.79810 0.239722
\(586\) 0 0
\(587\) 0.223982 0.00924472 0.00462236 0.999989i \(-0.498529\pi\)
0.00462236 + 0.999989i \(0.498529\pi\)
\(588\) 0 0
\(589\) −49.5578 −2.04199
\(590\) 0 0
\(591\) −3.05253 −0.125564
\(592\) 0 0
\(593\) −3.35704 −0.137857 −0.0689286 0.997622i \(-0.521958\pi\)
−0.0689286 + 0.997622i \(0.521958\pi\)
\(594\) 0 0
\(595\) 4.43387 0.181771
\(596\) 0 0
\(597\) 30.1467 1.23382
\(598\) 0 0
\(599\) 37.1903 1.51956 0.759778 0.650182i \(-0.225307\pi\)
0.759778 + 0.650182i \(0.225307\pi\)
\(600\) 0 0
\(601\) 17.7225 0.722914 0.361457 0.932389i \(-0.382279\pi\)
0.361457 + 0.932389i \(0.382279\pi\)
\(602\) 0 0
\(603\) −6.85731 −0.279251
\(604\) 0 0
\(605\) 15.7174 0.639004
\(606\) 0 0
\(607\) 16.0325 0.650740 0.325370 0.945587i \(-0.394511\pi\)
0.325370 + 0.945587i \(0.394511\pi\)
\(608\) 0 0
\(609\) −12.4668 −0.505180
\(610\) 0 0
\(611\) −55.0781 −2.22822
\(612\) 0 0
\(613\) 25.0279 1.01087 0.505434 0.862865i \(-0.331332\pi\)
0.505434 + 0.862865i \(0.331332\pi\)
\(614\) 0 0
\(615\) −6.49786 −0.262019
\(616\) 0 0
\(617\) 29.6646 1.19425 0.597126 0.802147i \(-0.296309\pi\)
0.597126 + 0.802147i \(0.296309\pi\)
\(618\) 0 0
\(619\) 11.8356 0.475714 0.237857 0.971300i \(-0.423555\pi\)
0.237857 + 0.971300i \(0.423555\pi\)
\(620\) 0 0
\(621\) 18.9292 0.759604
\(622\) 0 0
\(623\) 13.6203 0.545687
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 69.1184 2.76032
\(628\) 0 0
\(629\) −40.6135 −1.61937
\(630\) 0 0
\(631\) −34.4927 −1.37313 −0.686566 0.727067i \(-0.740883\pi\)
−0.686566 + 0.727067i \(0.740883\pi\)
\(632\) 0 0
\(633\) −18.1884 −0.722925
\(634\) 0 0
\(635\) −11.6039 −0.460485
\(636\) 0 0
\(637\) −28.5026 −1.12931
\(638\) 0 0
\(639\) −14.8467 −0.587327
\(640\) 0 0
\(641\) −20.6030 −0.813770 −0.406885 0.913479i \(-0.633385\pi\)
−0.406885 + 0.913479i \(0.633385\pi\)
\(642\) 0 0
\(643\) 8.88259 0.350295 0.175148 0.984542i \(-0.443960\pi\)
0.175148 + 0.984542i \(0.443960\pi\)
\(644\) 0 0
\(645\) 16.6003 0.653638
\(646\) 0 0
\(647\) 19.4768 0.765713 0.382857 0.923808i \(-0.374940\pi\)
0.382857 + 0.923808i \(0.374940\pi\)
\(648\) 0 0
\(649\) 40.0339 1.57147
\(650\) 0 0
\(651\) −13.2593 −0.519672
\(652\) 0 0
\(653\) −41.9684 −1.64235 −0.821175 0.570676i \(-0.806681\pi\)
−0.821175 + 0.570676i \(0.806681\pi\)
\(654\) 0 0
\(655\) 12.3615 0.483002
\(656\) 0 0
\(657\) −10.8325 −0.422618
\(658\) 0 0
\(659\) −42.9151 −1.67174 −0.835868 0.548930i \(-0.815035\pi\)
−0.835868 + 0.548930i \(0.815035\pi\)
\(660\) 0 0
\(661\) 30.9219 1.20272 0.601362 0.798977i \(-0.294625\pi\)
0.601362 + 0.798977i \(0.294625\pi\)
\(662\) 0 0
\(663\) −49.6655 −1.92885
\(664\) 0 0
\(665\) 5.39930 0.209376
\(666\) 0 0
\(667\) −38.3928 −1.48657
\(668\) 0 0
\(669\) −9.51873 −0.368015
\(670\) 0 0
\(671\) −52.2925 −2.01873
\(672\) 0 0
\(673\) 23.4204 0.902789 0.451394 0.892325i \(-0.350927\pi\)
0.451394 + 0.892325i \(0.350927\pi\)
\(674\) 0 0
\(675\) −3.55513 −0.136837
\(676\) 0 0
\(677\) 26.3253 1.01176 0.505881 0.862603i \(-0.331167\pi\)
0.505881 + 0.862603i \(0.331167\pi\)
\(678\) 0 0
\(679\) 10.7861 0.413934
\(680\) 0 0
\(681\) 22.2993 0.854512
\(682\) 0 0
\(683\) 1.78192 0.0681833 0.0340917 0.999419i \(-0.489146\pi\)
0.0340917 + 0.999419i \(0.489146\pi\)
\(684\) 0 0
\(685\) 2.32336 0.0887711
\(686\) 0 0
\(687\) −17.3720 −0.662781
\(688\) 0 0
\(689\) 51.1603 1.94905
\(690\) 0 0
\(691\) −50.9347 −1.93765 −0.968824 0.247752i \(-0.920308\pi\)
−0.968824 + 0.247752i \(0.920308\pi\)
\(692\) 0 0
\(693\) 5.53646 0.210313
\(694\) 0 0
\(695\) 19.0803 0.723755
\(696\) 0 0
\(697\) 16.6637 0.631181
\(698\) 0 0
\(699\) −29.2157 −1.10504
\(700\) 0 0
\(701\) 12.2992 0.464533 0.232266 0.972652i \(-0.425386\pi\)
0.232266 + 0.972652i \(0.425386\pi\)
\(702\) 0 0
\(703\) −49.4567 −1.86529
\(704\) 0 0
\(705\) −25.1992 −0.949057
\(706\) 0 0
\(707\) 12.7371 0.479027
\(708\) 0 0
\(709\) 22.2798 0.836737 0.418368 0.908277i \(-0.362602\pi\)
0.418368 + 0.908277i \(0.362602\pi\)
\(710\) 0 0
\(711\) −16.3006 −0.611321
\(712\) 0 0
\(713\) −40.8333 −1.52922
\(714\) 0 0
\(715\) −23.3781 −0.874293
\(716\) 0 0
\(717\) −27.8501 −1.04008
\(718\) 0 0
\(719\) −46.9514 −1.75099 −0.875495 0.483227i \(-0.839465\pi\)
−0.875495 + 0.483227i \(0.839465\pi\)
\(720\) 0 0
\(721\) −6.31764 −0.235281
\(722\) 0 0
\(723\) 19.4337 0.722746
\(724\) 0 0
\(725\) 7.21060 0.267795
\(726\) 0 0
\(727\) −1.02745 −0.0381060 −0.0190530 0.999818i \(-0.506065\pi\)
−0.0190530 + 0.999818i \(0.506065\pi\)
\(728\) 0 0
\(729\) 7.70872 0.285508
\(730\) 0 0
\(731\) −42.5713 −1.57456
\(732\) 0 0
\(733\) 2.14311 0.0791576 0.0395788 0.999216i \(-0.487398\pi\)
0.0395788 + 0.999216i \(0.487398\pi\)
\(734\) 0 0
\(735\) −13.0404 −0.481004
\(736\) 0 0
\(737\) 27.6489 1.01846
\(738\) 0 0
\(739\) 27.3022 1.00433 0.502163 0.864773i \(-0.332538\pi\)
0.502163 + 0.864773i \(0.332538\pi\)
\(740\) 0 0
\(741\) −60.4797 −2.22178
\(742\) 0 0
\(743\) 13.7468 0.504322 0.252161 0.967685i \(-0.418859\pi\)
0.252161 + 0.967685i \(0.418859\pi\)
\(744\) 0 0
\(745\) −14.4699 −0.530137
\(746\) 0 0
\(747\) −18.2460 −0.667586
\(748\) 0 0
\(749\) 8.85822 0.323672
\(750\) 0 0
\(751\) −48.8584 −1.78287 −0.891433 0.453152i \(-0.850300\pi\)
−0.891433 + 0.453152i \(0.850300\pi\)
\(752\) 0 0
\(753\) 6.02306 0.219493
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) 5.67603 0.206299 0.103149 0.994666i \(-0.467108\pi\)
0.103149 + 0.994666i \(0.467108\pi\)
\(758\) 0 0
\(759\) 56.9503 2.06717
\(760\) 0 0
\(761\) 29.5687 1.07186 0.535932 0.844261i \(-0.319960\pi\)
0.535932 + 0.844261i \(0.319960\pi\)
\(762\) 0 0
\(763\) 2.18569 0.0791274
\(764\) 0 0
\(765\) −6.80290 −0.245959
\(766\) 0 0
\(767\) −35.0303 −1.26487
\(768\) 0 0
\(769\) −35.5967 −1.28365 −0.641824 0.766852i \(-0.721822\pi\)
−0.641824 + 0.766852i \(0.721822\pi\)
\(770\) 0 0
\(771\) −23.1345 −0.833170
\(772\) 0 0
\(773\) 41.2990 1.48542 0.742710 0.669613i \(-0.233540\pi\)
0.742710 + 0.669613i \(0.233540\pi\)
\(774\) 0 0
\(775\) 7.66896 0.275477
\(776\) 0 0
\(777\) −13.2322 −0.474702
\(778\) 0 0
\(779\) 20.2920 0.727037
\(780\) 0 0
\(781\) 59.8624 2.14205
\(782\) 0 0
\(783\) −25.6346 −0.916107
\(784\) 0 0
\(785\) −13.8769 −0.495288
\(786\) 0 0
\(787\) −2.71524 −0.0967879 −0.0483939 0.998828i \(-0.515410\pi\)
−0.0483939 + 0.998828i \(0.515410\pi\)
\(788\) 0 0
\(789\) 31.5910 1.12467
\(790\) 0 0
\(791\) −10.3573 −0.368264
\(792\) 0 0
\(793\) 45.7568 1.62487
\(794\) 0 0
\(795\) 23.4067 0.830152
\(796\) 0 0
\(797\) −6.18113 −0.218947 −0.109473 0.993990i \(-0.534916\pi\)
−0.109473 + 0.993990i \(0.534916\pi\)
\(798\) 0 0
\(799\) 64.6230 2.28620
\(800\) 0 0
\(801\) −20.8977 −0.738384
\(802\) 0 0
\(803\) 43.6772 1.54133
\(804\) 0 0
\(805\) 4.44877 0.156798
\(806\) 0 0
\(807\) 33.6002 1.18278
\(808\) 0 0
\(809\) 16.4970 0.580003 0.290002 0.957026i \(-0.406344\pi\)
0.290002 + 0.957026i \(0.406344\pi\)
\(810\) 0 0
\(811\) −2.38782 −0.0838478 −0.0419239 0.999121i \(-0.513349\pi\)
−0.0419239 + 0.999121i \(0.513349\pi\)
\(812\) 0 0
\(813\) 61.3187 2.15054
\(814\) 0 0
\(815\) 2.22611 0.0779773
\(816\) 0 0
\(817\) −51.8408 −1.81368
\(818\) 0 0
\(819\) −4.84448 −0.169280
\(820\) 0 0
\(821\) −15.8720 −0.553938 −0.276969 0.960879i \(-0.589330\pi\)
−0.276969 + 0.960879i \(0.589330\pi\)
\(822\) 0 0
\(823\) 27.6087 0.962378 0.481189 0.876617i \(-0.340205\pi\)
0.481189 + 0.876617i \(0.340205\pi\)
\(824\) 0 0
\(825\) −10.6959 −0.372384
\(826\) 0 0
\(827\) −7.41744 −0.257930 −0.128965 0.991649i \(-0.541165\pi\)
−0.128965 + 0.991649i \(0.541165\pi\)
\(828\) 0 0
\(829\) 2.22470 0.0772672 0.0386336 0.999253i \(-0.487699\pi\)
0.0386336 + 0.999253i \(0.487699\pi\)
\(830\) 0 0
\(831\) −7.28419 −0.252686
\(832\) 0 0
\(833\) 33.4420 1.15870
\(834\) 0 0
\(835\) −19.2210 −0.665169
\(836\) 0 0
\(837\) −27.2642 −0.942387
\(838\) 0 0
\(839\) −1.71578 −0.0592352 −0.0296176 0.999561i \(-0.509429\pi\)
−0.0296176 + 0.999561i \(0.509429\pi\)
\(840\) 0 0
\(841\) 22.9928 0.792856
\(842\) 0 0
\(843\) −19.7508 −0.680255
\(844\) 0 0
\(845\) 7.45624 0.256502
\(846\) 0 0
\(847\) −13.1324 −0.451233
\(848\) 0 0
\(849\) 21.0258 0.721604
\(850\) 0 0
\(851\) −40.7499 −1.39689
\(852\) 0 0
\(853\) −10.1804 −0.348571 −0.174285 0.984695i \(-0.555762\pi\)
−0.174285 + 0.984695i \(0.555762\pi\)
\(854\) 0 0
\(855\) −8.28416 −0.283312
\(856\) 0 0
\(857\) 7.11763 0.243134 0.121567 0.992583i \(-0.461208\pi\)
0.121567 + 0.992583i \(0.461208\pi\)
\(858\) 0 0
\(859\) 46.2733 1.57882 0.789412 0.613864i \(-0.210386\pi\)
0.789412 + 0.613864i \(0.210386\pi\)
\(860\) 0 0
\(861\) 5.42916 0.185025
\(862\) 0 0
\(863\) 11.4586 0.390054 0.195027 0.980798i \(-0.437521\pi\)
0.195027 + 0.980798i \(0.437521\pi\)
\(864\) 0 0
\(865\) −13.9144 −0.473105
\(866\) 0 0
\(867\) 23.0945 0.784331
\(868\) 0 0
\(869\) 65.7247 2.22956
\(870\) 0 0
\(871\) −24.1932 −0.819756
\(872\) 0 0
\(873\) −16.5492 −0.560105
\(874\) 0 0
\(875\) −0.835530 −0.0282461
\(876\) 0 0
\(877\) −28.2457 −0.953791 −0.476896 0.878960i \(-0.658238\pi\)
−0.476896 + 0.878960i \(0.658238\pi\)
\(878\) 0 0
\(879\) 50.2499 1.69489
\(880\) 0 0
\(881\) −20.8395 −0.702100 −0.351050 0.936357i \(-0.614175\pi\)
−0.351050 + 0.936357i \(0.614175\pi\)
\(882\) 0 0
\(883\) −28.1261 −0.946520 −0.473260 0.880923i \(-0.656923\pi\)
−0.473260 + 0.880923i \(0.656923\pi\)
\(884\) 0 0
\(885\) −16.0270 −0.538741
\(886\) 0 0
\(887\) −10.6378 −0.357183 −0.178592 0.983923i \(-0.557154\pi\)
−0.178592 + 0.983923i \(0.557154\pi\)
\(888\) 0 0
\(889\) 9.69537 0.325172
\(890\) 0 0
\(891\) 57.9043 1.93987
\(892\) 0 0
\(893\) 78.6940 2.63339
\(894\) 0 0
\(895\) 19.5790 0.654455
\(896\) 0 0
\(897\) −49.8324 −1.66386
\(898\) 0 0
\(899\) 55.2978 1.84429
\(900\) 0 0
\(901\) −60.0262 −1.99976
\(902\) 0 0
\(903\) −13.8701 −0.461567
\(904\) 0 0
\(905\) 17.2953 0.574915
\(906\) 0 0
\(907\) −1.37638 −0.0457019 −0.0228509 0.999739i \(-0.507274\pi\)
−0.0228509 + 0.999739i \(0.507274\pi\)
\(908\) 0 0
\(909\) −19.5425 −0.648184
\(910\) 0 0
\(911\) −22.2833 −0.738278 −0.369139 0.929374i \(-0.620347\pi\)
−0.369139 + 0.929374i \(0.620347\pi\)
\(912\) 0 0
\(913\) 73.5684 2.43476
\(914\) 0 0
\(915\) 20.9345 0.692075
\(916\) 0 0
\(917\) −10.3284 −0.341073
\(918\) 0 0
\(919\) −29.6587 −0.978349 −0.489174 0.872186i \(-0.662702\pi\)
−0.489174 + 0.872186i \(0.662702\pi\)
\(920\) 0 0
\(921\) −7.51381 −0.247589
\(922\) 0 0
\(923\) −52.3806 −1.72413
\(924\) 0 0
\(925\) 7.65331 0.251639
\(926\) 0 0
\(927\) 9.69317 0.318365
\(928\) 0 0
\(929\) 13.5991 0.446171 0.223085 0.974799i \(-0.428387\pi\)
0.223085 + 0.974799i \(0.428387\pi\)
\(930\) 0 0
\(931\) 40.7236 1.33466
\(932\) 0 0
\(933\) 34.2465 1.12118
\(934\) 0 0
\(935\) 27.4295 0.897041
\(936\) 0 0
\(937\) 52.3218 1.70928 0.854640 0.519222i \(-0.173778\pi\)
0.854640 + 0.519222i \(0.173778\pi\)
\(938\) 0 0
\(939\) 48.8735 1.59493
\(940\) 0 0
\(941\) −18.7630 −0.611656 −0.305828 0.952087i \(-0.598933\pi\)
−0.305828 + 0.952087i \(0.598933\pi\)
\(942\) 0 0
\(943\) 16.7197 0.544467
\(944\) 0 0
\(945\) 2.97042 0.0966277
\(946\) 0 0
\(947\) 1.85285 0.0602095 0.0301047 0.999547i \(-0.490416\pi\)
0.0301047 + 0.999547i \(0.490416\pi\)
\(948\) 0 0
\(949\) −38.2182 −1.24062
\(950\) 0 0
\(951\) 48.5864 1.57552
\(952\) 0 0
\(953\) −15.4953 −0.501943 −0.250971 0.967995i \(-0.580750\pi\)
−0.250971 + 0.967995i \(0.580750\pi\)
\(954\) 0 0
\(955\) 3.13159 0.101336
\(956\) 0 0
\(957\) −77.1241 −2.49307
\(958\) 0 0
\(959\) −1.94124 −0.0626858
\(960\) 0 0
\(961\) 27.8130 0.897192
\(962\) 0 0
\(963\) −13.5912 −0.437970
\(964\) 0 0
\(965\) −3.32113 −0.106911
\(966\) 0 0
\(967\) −25.2727 −0.812714 −0.406357 0.913714i \(-0.633201\pi\)
−0.406357 + 0.913714i \(0.633201\pi\)
\(968\) 0 0
\(969\) 70.9607 2.27959
\(970\) 0 0
\(971\) −14.7912 −0.474673 −0.237336 0.971428i \(-0.576274\pi\)
−0.237336 + 0.971428i \(0.576274\pi\)
\(972\) 0 0
\(973\) −15.9421 −0.511081
\(974\) 0 0
\(975\) 9.35910 0.299731
\(976\) 0 0
\(977\) −19.6952 −0.630104 −0.315052 0.949074i \(-0.602022\pi\)
−0.315052 + 0.949074i \(0.602022\pi\)
\(978\) 0 0
\(979\) 84.2603 2.69297
\(980\) 0 0
\(981\) −3.35352 −0.107070
\(982\) 0 0
\(983\) 12.4893 0.398348 0.199174 0.979964i \(-0.436174\pi\)
0.199174 + 0.979964i \(0.436174\pi\)
\(984\) 0 0
\(985\) −1.47516 −0.0470024
\(986\) 0 0
\(987\) 21.0547 0.670178
\(988\) 0 0
\(989\) −42.7144 −1.35824
\(990\) 0 0
\(991\) 29.6774 0.942734 0.471367 0.881937i \(-0.343761\pi\)
0.471367 + 0.881937i \(0.343761\pi\)
\(992\) 0 0
\(993\) −23.6916 −0.751830
\(994\) 0 0
\(995\) 14.5686 0.461856
\(996\) 0 0
\(997\) 47.4881 1.50396 0.751981 0.659185i \(-0.229098\pi\)
0.751981 + 0.659185i \(0.229098\pi\)
\(998\) 0 0
\(999\) −27.2085 −0.860839
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 \(a_p\))