Properties

Label 6034.2.a.n.1.11
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+0.0287183 q^{3}\) \(+1.00000 q^{4}\) \(+1.06252 q^{5}\) \(-0.0287183 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.99918 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+0.0287183 q^{3}\) \(+1.00000 q^{4}\) \(+1.06252 q^{5}\) \(-0.0287183 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.99918 q^{9}\) \(-1.06252 q^{10}\) \(+2.45970 q^{11}\) \(+0.0287183 q^{12}\) \(-6.62293 q^{13}\) \(+1.00000 q^{14}\) \(+0.0305138 q^{15}\) \(+1.00000 q^{16}\) \(+4.12722 q^{17}\) \(+2.99918 q^{18}\) \(-6.10992 q^{19}\) \(+1.06252 q^{20}\) \(-0.0287183 q^{21}\) \(-2.45970 q^{22}\) \(-5.32796 q^{23}\) \(-0.0287183 q^{24}\) \(-3.87105 q^{25}\) \(+6.62293 q^{26}\) \(-0.172286 q^{27}\) \(-1.00000 q^{28}\) \(-4.61083 q^{29}\) \(-0.0305138 q^{30}\) \(+9.64040 q^{31}\) \(-1.00000 q^{32}\) \(+0.0706386 q^{33}\) \(-4.12722 q^{34}\) \(-1.06252 q^{35}\) \(-2.99918 q^{36}\) \(+5.32117 q^{37}\) \(+6.10992 q^{38}\) \(-0.190200 q^{39}\) \(-1.06252 q^{40}\) \(-8.80850 q^{41}\) \(+0.0287183 q^{42}\) \(+1.40953 q^{43}\) \(+2.45970 q^{44}\) \(-3.18669 q^{45}\) \(+5.32796 q^{46}\) \(-1.51431 q^{47}\) \(+0.0287183 q^{48}\) \(+1.00000 q^{49}\) \(+3.87105 q^{50}\) \(+0.118527 q^{51}\) \(-6.62293 q^{52}\) \(+6.97767 q^{53}\) \(+0.172286 q^{54}\) \(+2.61349 q^{55}\) \(+1.00000 q^{56}\) \(-0.175467 q^{57}\) \(+4.61083 q^{58}\) \(+1.91891 q^{59}\) \(+0.0305138 q^{60}\) \(+8.07712 q^{61}\) \(-9.64040 q^{62}\) \(+2.99918 q^{63}\) \(+1.00000 q^{64}\) \(-7.03700 q^{65}\) \(-0.0706386 q^{66}\) \(+4.82804 q^{67}\) \(+4.12722 q^{68}\) \(-0.153010 q^{69}\) \(+1.06252 q^{70}\) \(-3.67987 q^{71}\) \(+2.99918 q^{72}\) \(+2.42821 q^{73}\) \(-5.32117 q^{74}\) \(-0.111170 q^{75}\) \(-6.10992 q^{76}\) \(-2.45970 q^{77}\) \(+0.190200 q^{78}\) \(+1.75227 q^{79}\) \(+1.06252 q^{80}\) \(+8.99258 q^{81}\) \(+8.80850 q^{82}\) \(-10.6440 q^{83}\) \(-0.0287183 q^{84}\) \(+4.38526 q^{85}\) \(-1.40953 q^{86}\) \(-0.132415 q^{87}\) \(-2.45970 q^{88}\) \(+5.39821 q^{89}\) \(+3.18669 q^{90}\) \(+6.62293 q^{91}\) \(-5.32796 q^{92}\) \(+0.276856 q^{93}\) \(+1.51431 q^{94}\) \(-6.49191 q^{95}\) \(-0.0287183 q^{96}\) \(+15.1882 q^{97}\) \(-1.00000 q^{98}\) \(-7.37708 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.0287183 0.0165805 0.00829027 0.999966i \(-0.497361\pi\)
0.00829027 + 0.999966i \(0.497361\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.06252 0.475174 0.237587 0.971366i \(-0.423644\pi\)
0.237587 + 0.971366i \(0.423644\pi\)
\(6\) −0.0287183 −0.0117242
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −2.99918 −0.999725
\(10\) −1.06252 −0.335999
\(11\) 2.45970 0.741629 0.370814 0.928707i \(-0.379079\pi\)
0.370814 + 0.928707i \(0.379079\pi\)
\(12\) 0.0287183 0.00829027
\(13\) −6.62293 −1.83687 −0.918435 0.395571i \(-0.870547\pi\)
−0.918435 + 0.395571i \(0.870547\pi\)
\(14\) 1.00000 0.267261
\(15\) 0.0305138 0.00787864
\(16\) 1.00000 0.250000
\(17\) 4.12722 1.00100 0.500499 0.865737i \(-0.333150\pi\)
0.500499 + 0.865737i \(0.333150\pi\)
\(18\) 2.99918 0.706912
\(19\) −6.10992 −1.40171 −0.700855 0.713303i \(-0.747198\pi\)
−0.700855 + 0.713303i \(0.747198\pi\)
\(20\) 1.06252 0.237587
\(21\) −0.0287183 −0.00626686
\(22\) −2.45970 −0.524411
\(23\) −5.32796 −1.11096 −0.555478 0.831531i \(-0.687465\pi\)
−0.555478 + 0.831531i \(0.687465\pi\)
\(24\) −0.0287183 −0.00586211
\(25\) −3.87105 −0.774210
\(26\) 6.62293 1.29886
\(27\) −0.172286 −0.0331565
\(28\) −1.00000 −0.188982
\(29\) −4.61083 −0.856209 −0.428104 0.903729i \(-0.640818\pi\)
−0.428104 + 0.903729i \(0.640818\pi\)
\(30\) −0.0305138 −0.00557104
\(31\) 9.64040 1.73147 0.865733 0.500506i \(-0.166853\pi\)
0.865733 + 0.500506i \(0.166853\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.0706386 0.0122966
\(34\) −4.12722 −0.707813
\(35\) −1.06252 −0.179599
\(36\) −2.99918 −0.499863
\(37\) 5.32117 0.874795 0.437397 0.899268i \(-0.355900\pi\)
0.437397 + 0.899268i \(0.355900\pi\)
\(38\) 6.10992 0.991159
\(39\) −0.190200 −0.0304563
\(40\) −1.06252 −0.167999
\(41\) −8.80850 −1.37566 −0.687828 0.725873i \(-0.741436\pi\)
−0.687828 + 0.725873i \(0.741436\pi\)
\(42\) 0.0287183 0.00443134
\(43\) 1.40953 0.214951 0.107475 0.994208i \(-0.465723\pi\)
0.107475 + 0.994208i \(0.465723\pi\)
\(44\) 2.45970 0.370814
\(45\) −3.18669 −0.475043
\(46\) 5.32796 0.785565
\(47\) −1.51431 −0.220885 −0.110443 0.993883i \(-0.535227\pi\)
−0.110443 + 0.993883i \(0.535227\pi\)
\(48\) 0.0287183 0.00414514
\(49\) 1.00000 0.142857
\(50\) 3.87105 0.547449
\(51\) 0.118527 0.0165971
\(52\) −6.62293 −0.918435
\(53\) 6.97767 0.958457 0.479228 0.877690i \(-0.340917\pi\)
0.479228 + 0.877690i \(0.340917\pi\)
\(54\) 0.172286 0.0234452
\(55\) 2.61349 0.352403
\(56\) 1.00000 0.133631
\(57\) −0.175467 −0.0232411
\(58\) 4.61083 0.605431
\(59\) 1.91891 0.249821 0.124910 0.992168i \(-0.460136\pi\)
0.124910 + 0.992168i \(0.460136\pi\)
\(60\) 0.0305138 0.00393932
\(61\) 8.07712 1.03417 0.517084 0.855934i \(-0.327017\pi\)
0.517084 + 0.855934i \(0.327017\pi\)
\(62\) −9.64040 −1.22433
\(63\) 2.99918 0.377861
\(64\) 1.00000 0.125000
\(65\) −7.03700 −0.872833
\(66\) −0.0706386 −0.00869501
\(67\) 4.82804 0.589838 0.294919 0.955522i \(-0.404707\pi\)
0.294919 + 0.955522i \(0.404707\pi\)
\(68\) 4.12722 0.500499
\(69\) −0.153010 −0.0184203
\(70\) 1.06252 0.126996
\(71\) −3.67987 −0.436720 −0.218360 0.975868i \(-0.570071\pi\)
−0.218360 + 0.975868i \(0.570071\pi\)
\(72\) 2.99918 0.353456
\(73\) 2.42821 0.284200 0.142100 0.989852i \(-0.454614\pi\)
0.142100 + 0.989852i \(0.454614\pi\)
\(74\) −5.32117 −0.618573
\(75\) −0.111170 −0.0128368
\(76\) −6.10992 −0.700855
\(77\) −2.45970 −0.280309
\(78\) 0.190200 0.0215359
\(79\) 1.75227 0.197146 0.0985728 0.995130i \(-0.468572\pi\)
0.0985728 + 0.995130i \(0.468572\pi\)
\(80\) 1.06252 0.118793
\(81\) 8.99258 0.999175
\(82\) 8.80850 0.972736
\(83\) −10.6440 −1.16833 −0.584166 0.811634i \(-0.698578\pi\)
−0.584166 + 0.811634i \(0.698578\pi\)
\(84\) −0.0287183 −0.00313343
\(85\) 4.38526 0.475648
\(86\) −1.40953 −0.151993
\(87\) −0.132415 −0.0141964
\(88\) −2.45970 −0.262205
\(89\) 5.39821 0.572209 0.286104 0.958198i \(-0.407640\pi\)
0.286104 + 0.958198i \(0.407640\pi\)
\(90\) 3.18669 0.335906
\(91\) 6.62293 0.694272
\(92\) −5.32796 −0.555478
\(93\) 0.276856 0.0287087
\(94\) 1.51431 0.156189
\(95\) −6.49191 −0.666056
\(96\) −0.0287183 −0.00293105
\(97\) 15.1882 1.54213 0.771067 0.636755i \(-0.219724\pi\)
0.771067 + 0.636755i \(0.219724\pi\)
\(98\) −1.00000 −0.101015
\(99\) −7.37708 −0.741425
\(100\) −3.87105 −0.387105
\(101\) 14.9170 1.48429 0.742146 0.670238i \(-0.233808\pi\)
0.742146 + 0.670238i \(0.233808\pi\)
\(102\) −0.118527 −0.0117359
\(103\) −12.6241 −1.24389 −0.621944 0.783062i \(-0.713657\pi\)
−0.621944 + 0.783062i \(0.713657\pi\)
\(104\) 6.62293 0.649432
\(105\) −0.0305138 −0.00297785
\(106\) −6.97767 −0.677731
\(107\) 11.2075 1.08347 0.541737 0.840548i \(-0.317767\pi\)
0.541737 + 0.840548i \(0.317767\pi\)
\(108\) −0.172286 −0.0165783
\(109\) 12.6375 1.21046 0.605228 0.796053i \(-0.293082\pi\)
0.605228 + 0.796053i \(0.293082\pi\)
\(110\) −2.61349 −0.249186
\(111\) 0.152815 0.0145046
\(112\) −1.00000 −0.0944911
\(113\) 2.54713 0.239614 0.119807 0.992797i \(-0.461772\pi\)
0.119807 + 0.992797i \(0.461772\pi\)
\(114\) 0.175467 0.0164340
\(115\) −5.66107 −0.527897
\(116\) −4.61083 −0.428104
\(117\) 19.8633 1.83637
\(118\) −1.91891 −0.176650
\(119\) −4.12722 −0.378342
\(120\) −0.0305138 −0.00278552
\(121\) −4.94986 −0.449987
\(122\) −8.07712 −0.731268
\(123\) −0.252966 −0.0228091
\(124\) 9.64040 0.865733
\(125\) −9.42568 −0.843058
\(126\) −2.99918 −0.267188
\(127\) −0.0642324 −0.00569970 −0.00284985 0.999996i \(-0.500907\pi\)
−0.00284985 + 0.999996i \(0.500907\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.0404793 0.00356400
\(130\) 7.03700 0.617186
\(131\) 8.57186 0.748927 0.374463 0.927242i \(-0.377827\pi\)
0.374463 + 0.927242i \(0.377827\pi\)
\(132\) 0.0706386 0.00614830
\(133\) 6.10992 0.529797
\(134\) −4.82804 −0.417079
\(135\) −0.183058 −0.0157551
\(136\) −4.12722 −0.353906
\(137\) −0.620788 −0.0530375 −0.0265188 0.999648i \(-0.508442\pi\)
−0.0265188 + 0.999648i \(0.508442\pi\)
\(138\) 0.153010 0.0130251
\(139\) 4.02932 0.341762 0.170881 0.985292i \(-0.445339\pi\)
0.170881 + 0.985292i \(0.445339\pi\)
\(140\) −1.06252 −0.0897994
\(141\) −0.0434885 −0.00366240
\(142\) 3.67987 0.308808
\(143\) −16.2904 −1.36228
\(144\) −2.99918 −0.249931
\(145\) −4.89910 −0.406848
\(146\) −2.42821 −0.200960
\(147\) 0.0287183 0.00236865
\(148\) 5.32117 0.437397
\(149\) 8.16563 0.668954 0.334477 0.942404i \(-0.391440\pi\)
0.334477 + 0.942404i \(0.391440\pi\)
\(150\) 0.111170 0.00907700
\(151\) −14.6403 −1.19141 −0.595707 0.803202i \(-0.703128\pi\)
−0.595707 + 0.803202i \(0.703128\pi\)
\(152\) 6.10992 0.495580
\(153\) −12.3783 −1.00072
\(154\) 2.45970 0.198209
\(155\) 10.2431 0.822747
\(156\) −0.190200 −0.0152282
\(157\) 18.8264 1.50251 0.751256 0.660011i \(-0.229449\pi\)
0.751256 + 0.660011i \(0.229449\pi\)
\(158\) −1.75227 −0.139403
\(159\) 0.200387 0.0158917
\(160\) −1.06252 −0.0839997
\(161\) 5.32796 0.419902
\(162\) −8.99258 −0.706524
\(163\) 11.0279 0.863775 0.431888 0.901927i \(-0.357848\pi\)
0.431888 + 0.901927i \(0.357848\pi\)
\(164\) −8.80850 −0.687828
\(165\) 0.0750550 0.00584303
\(166\) 10.6440 0.826136
\(167\) 3.39007 0.262331 0.131166 0.991360i \(-0.458128\pi\)
0.131166 + 0.991360i \(0.458128\pi\)
\(168\) 0.0287183 0.00221567
\(169\) 30.8632 2.37409
\(170\) −4.38526 −0.336334
\(171\) 18.3247 1.40133
\(172\) 1.40953 0.107475
\(173\) −7.32422 −0.556850 −0.278425 0.960458i \(-0.589812\pi\)
−0.278425 + 0.960458i \(0.589812\pi\)
\(174\) 0.132415 0.0100384
\(175\) 3.87105 0.292624
\(176\) 2.45970 0.185407
\(177\) 0.0551079 0.00414216
\(178\) −5.39821 −0.404613
\(179\) 6.91885 0.517139 0.258570 0.965993i \(-0.416749\pi\)
0.258570 + 0.965993i \(0.416749\pi\)
\(180\) −3.18669 −0.237522
\(181\) −20.2554 −1.50557 −0.752787 0.658264i \(-0.771291\pi\)
−0.752787 + 0.658264i \(0.771291\pi\)
\(182\) −6.62293 −0.490924
\(183\) 0.231961 0.0171471
\(184\) 5.32796 0.392782
\(185\) 5.65385 0.415680
\(186\) −0.276856 −0.0203001
\(187\) 10.1517 0.742369
\(188\) −1.51431 −0.110443
\(189\) 0.172286 0.0125320
\(190\) 6.49191 0.470973
\(191\) −0.799916 −0.0578799 −0.0289399 0.999581i \(-0.509213\pi\)
−0.0289399 + 0.999581i \(0.509213\pi\)
\(192\) 0.0287183 0.00207257
\(193\) −9.00824 −0.648427 −0.324214 0.945984i \(-0.605100\pi\)
−0.324214 + 0.945984i \(0.605100\pi\)
\(194\) −15.1882 −1.09045
\(195\) −0.202091 −0.0144720
\(196\) 1.00000 0.0714286
\(197\) 5.93977 0.423191 0.211595 0.977357i \(-0.432134\pi\)
0.211595 + 0.977357i \(0.432134\pi\)
\(198\) 7.37708 0.524266
\(199\) 18.3723 1.30238 0.651188 0.758917i \(-0.274271\pi\)
0.651188 + 0.758917i \(0.274271\pi\)
\(200\) 3.87105 0.273724
\(201\) 0.138653 0.00977984
\(202\) −14.9170 −1.04955
\(203\) 4.61083 0.323617
\(204\) 0.118527 0.00829855
\(205\) −9.35922 −0.653676
\(206\) 12.6241 0.879561
\(207\) 15.9795 1.11065
\(208\) −6.62293 −0.459218
\(209\) −15.0286 −1.03955
\(210\) 0.0305138 0.00210566
\(211\) 0.477536 0.0328749 0.0164375 0.999865i \(-0.494768\pi\)
0.0164375 + 0.999865i \(0.494768\pi\)
\(212\) 6.97767 0.479228
\(213\) −0.105680 −0.00724106
\(214\) −11.2075 −0.766132
\(215\) 1.49765 0.102139
\(216\) 0.172286 0.0117226
\(217\) −9.64040 −0.654433
\(218\) −12.6375 −0.855921
\(219\) 0.0697341 0.00471220
\(220\) 2.61349 0.176201
\(221\) −27.3343 −1.83870
\(222\) −0.152815 −0.0102563
\(223\) 24.2316 1.62267 0.811333 0.584584i \(-0.198742\pi\)
0.811333 + 0.584584i \(0.198742\pi\)
\(224\) 1.00000 0.0668153
\(225\) 11.6100 0.773997
\(226\) −2.54713 −0.169433
\(227\) −6.21698 −0.412635 −0.206318 0.978485i \(-0.566148\pi\)
−0.206318 + 0.978485i \(0.566148\pi\)
\(228\) −0.175467 −0.0116206
\(229\) −27.1550 −1.79445 −0.897226 0.441571i \(-0.854421\pi\)
−0.897226 + 0.441571i \(0.854421\pi\)
\(230\) 5.66107 0.373280
\(231\) −0.0706386 −0.00464768
\(232\) 4.61083 0.302716
\(233\) −11.0857 −0.726251 −0.363125 0.931740i \(-0.618290\pi\)
−0.363125 + 0.931740i \(0.618290\pi\)
\(234\) −19.8633 −1.29851
\(235\) −1.60899 −0.104959
\(236\) 1.91891 0.124910
\(237\) 0.0503223 0.00326878
\(238\) 4.12722 0.267528
\(239\) −2.72895 −0.176521 −0.0882605 0.996097i \(-0.528131\pi\)
−0.0882605 + 0.996097i \(0.528131\pi\)
\(240\) 0.0305138 0.00196966
\(241\) 24.6476 1.58769 0.793846 0.608119i \(-0.208076\pi\)
0.793846 + 0.608119i \(0.208076\pi\)
\(242\) 4.94986 0.318189
\(243\) 0.775111 0.0497234
\(244\) 8.07712 0.517084
\(245\) 1.06252 0.0678820
\(246\) 0.252966 0.0161285
\(247\) 40.4656 2.57476
\(248\) −9.64040 −0.612166
\(249\) −0.305679 −0.0193716
\(250\) 9.42568 0.596132
\(251\) 10.8104 0.682348 0.341174 0.940000i \(-0.389175\pi\)
0.341174 + 0.940000i \(0.389175\pi\)
\(252\) 2.99918 0.188930
\(253\) −13.1052 −0.823917
\(254\) 0.0642324 0.00403030
\(255\) 0.125937 0.00788651
\(256\) 1.00000 0.0625000
\(257\) −7.07789 −0.441507 −0.220753 0.975330i \(-0.570852\pi\)
−0.220753 + 0.975330i \(0.570852\pi\)
\(258\) −0.0404793 −0.00252013
\(259\) −5.32117 −0.330641
\(260\) −7.03700 −0.436416
\(261\) 13.8287 0.855974
\(262\) −8.57186 −0.529571
\(263\) −18.3710 −1.13280 −0.566402 0.824129i \(-0.691665\pi\)
−0.566402 + 0.824129i \(0.691665\pi\)
\(264\) −0.0706386 −0.00434751
\(265\) 7.41392 0.455434
\(266\) −6.10992 −0.374623
\(267\) 0.155028 0.00948754
\(268\) 4.82804 0.294919
\(269\) −1.75253 −0.106854 −0.0534269 0.998572i \(-0.517014\pi\)
−0.0534269 + 0.998572i \(0.517014\pi\)
\(270\) 0.183058 0.0111406
\(271\) 16.5424 1.00488 0.502440 0.864612i \(-0.332436\pi\)
0.502440 + 0.864612i \(0.332436\pi\)
\(272\) 4.12722 0.250250
\(273\) 0.190200 0.0115114
\(274\) 0.620788 0.0375032
\(275\) −9.52163 −0.574176
\(276\) −0.153010 −0.00921013
\(277\) −13.9524 −0.838321 −0.419161 0.907912i \(-0.637676\pi\)
−0.419161 + 0.907912i \(0.637676\pi\)
\(278\) −4.02932 −0.241662
\(279\) −28.9132 −1.73099
\(280\) 1.06252 0.0634978
\(281\) 11.2306 0.669958 0.334979 0.942226i \(-0.391271\pi\)
0.334979 + 0.942226i \(0.391271\pi\)
\(282\) 0.0434885 0.00258971
\(283\) −17.0869 −1.01571 −0.507856 0.861442i \(-0.669562\pi\)
−0.507856 + 0.861442i \(0.669562\pi\)
\(284\) −3.67987 −0.218360
\(285\) −0.186437 −0.0110436
\(286\) 16.2904 0.963274
\(287\) 8.80850 0.519949
\(288\) 2.99918 0.176728
\(289\) 0.0339589 0.00199758
\(290\) 4.89910 0.287685
\(291\) 0.436181 0.0255694
\(292\) 2.42821 0.142100
\(293\) −0.694680 −0.0405836 −0.0202918 0.999794i \(-0.506460\pi\)
−0.0202918 + 0.999794i \(0.506460\pi\)
\(294\) −0.0287183 −0.00167489
\(295\) 2.03888 0.118708
\(296\) −5.32117 −0.309287
\(297\) −0.423773 −0.0245898
\(298\) −8.16563 −0.473022
\(299\) 35.2867 2.04068
\(300\) −0.111170 −0.00641841
\(301\) −1.40953 −0.0812438
\(302\) 14.6403 0.842457
\(303\) 0.428390 0.0246104
\(304\) −6.10992 −0.350428
\(305\) 8.58211 0.491410
\(306\) 12.3783 0.707618
\(307\) −17.4572 −0.996336 −0.498168 0.867081i \(-0.665994\pi\)
−0.498168 + 0.867081i \(0.665994\pi\)
\(308\) −2.45970 −0.140155
\(309\) −0.362543 −0.0206243
\(310\) −10.2431 −0.581770
\(311\) 24.5175 1.39026 0.695131 0.718883i \(-0.255346\pi\)
0.695131 + 0.718883i \(0.255346\pi\)
\(312\) 0.190200 0.0107679
\(313\) −17.3076 −0.978281 −0.489141 0.872205i \(-0.662690\pi\)
−0.489141 + 0.872205i \(0.662690\pi\)
\(314\) −18.8264 −1.06244
\(315\) 3.18669 0.179549
\(316\) 1.75227 0.0985728
\(317\) 6.80688 0.382313 0.191156 0.981560i \(-0.438776\pi\)
0.191156 + 0.981560i \(0.438776\pi\)
\(318\) −0.200387 −0.0112372
\(319\) −11.3413 −0.634989
\(320\) 1.06252 0.0593967
\(321\) 0.321862 0.0179646
\(322\) −5.32796 −0.296916
\(323\) −25.2170 −1.40311
\(324\) 8.99258 0.499588
\(325\) 25.6377 1.42212
\(326\) −11.0279 −0.610781
\(327\) 0.362929 0.0200700
\(328\) 8.80850 0.486368
\(329\) 1.51431 0.0834867
\(330\) −0.0750550 −0.00413164
\(331\) −18.7120 −1.02851 −0.514253 0.857639i \(-0.671931\pi\)
−0.514253 + 0.857639i \(0.671931\pi\)
\(332\) −10.6440 −0.584166
\(333\) −15.9591 −0.874554
\(334\) −3.39007 −0.185496
\(335\) 5.12989 0.280276
\(336\) −0.0287183 −0.00156671
\(337\) 16.0337 0.873411 0.436706 0.899604i \(-0.356145\pi\)
0.436706 + 0.899604i \(0.356145\pi\)
\(338\) −30.8632 −1.67874
\(339\) 0.0731495 0.00397293
\(340\) 4.38526 0.237824
\(341\) 23.7125 1.28410
\(342\) −18.3247 −0.990887
\(343\) −1.00000 −0.0539949
\(344\) −1.40953 −0.0759966
\(345\) −0.162577 −0.00875283
\(346\) 7.32422 0.393753
\(347\) 4.91272 0.263729 0.131864 0.991268i \(-0.457904\pi\)
0.131864 + 0.991268i \(0.457904\pi\)
\(348\) −0.132415 −0.00709820
\(349\) −30.3472 −1.62445 −0.812224 0.583346i \(-0.801743\pi\)
−0.812224 + 0.583346i \(0.801743\pi\)
\(350\) −3.87105 −0.206916
\(351\) 1.14104 0.0609043
\(352\) −2.45970 −0.131103
\(353\) 9.45289 0.503127 0.251563 0.967841i \(-0.419055\pi\)
0.251563 + 0.967841i \(0.419055\pi\)
\(354\) −0.0551079 −0.00292895
\(355\) −3.90994 −0.207518
\(356\) 5.39821 0.286104
\(357\) −0.118527 −0.00627311
\(358\) −6.91885 −0.365673
\(359\) 14.0749 0.742846 0.371423 0.928464i \(-0.378870\pi\)
0.371423 + 0.928464i \(0.378870\pi\)
\(360\) 3.18669 0.167953
\(361\) 18.3311 0.964794
\(362\) 20.2554 1.06460
\(363\) −0.142152 −0.00746103
\(364\) 6.62293 0.347136
\(365\) 2.58002 0.135045
\(366\) −0.231961 −0.0121248
\(367\) −6.31511 −0.329646 −0.164823 0.986323i \(-0.552705\pi\)
−0.164823 + 0.986323i \(0.552705\pi\)
\(368\) −5.32796 −0.277739
\(369\) 26.4182 1.37528
\(370\) −5.65385 −0.293930
\(371\) −6.97767 −0.362263
\(372\) 0.276856 0.0143543
\(373\) −15.2931 −0.791845 −0.395923 0.918284i \(-0.629575\pi\)
−0.395923 + 0.918284i \(0.629575\pi\)
\(374\) −10.1517 −0.524934
\(375\) −0.270690 −0.0139784
\(376\) 1.51431 0.0780947
\(377\) 30.5372 1.57275
\(378\) −0.172286 −0.00886146
\(379\) 21.2733 1.09274 0.546368 0.837545i \(-0.316010\pi\)
0.546368 + 0.837545i \(0.316010\pi\)
\(380\) −6.49191 −0.333028
\(381\) −0.00184465 −9.45041e−5 0
\(382\) 0.799916 0.0409273
\(383\) 9.50628 0.485748 0.242874 0.970058i \(-0.421910\pi\)
0.242874 + 0.970058i \(0.421910\pi\)
\(384\) −0.0287183 −0.00146553
\(385\) −2.61349 −0.133196
\(386\) 9.00824 0.458507
\(387\) −4.22742 −0.214892
\(388\) 15.1882 0.771067
\(389\) −25.4231 −1.28900 −0.644502 0.764603i \(-0.722935\pi\)
−0.644502 + 0.764603i \(0.722935\pi\)
\(390\) 0.202091 0.0102333
\(391\) −21.9897 −1.11207
\(392\) −1.00000 −0.0505076
\(393\) 0.246170 0.0124176
\(394\) −5.93977 −0.299241
\(395\) 1.86182 0.0936785
\(396\) −7.37708 −0.370712
\(397\) −28.0621 −1.40840 −0.704198 0.710003i \(-0.748693\pi\)
−0.704198 + 0.710003i \(0.748693\pi\)
\(398\) −18.3723 −0.920919
\(399\) 0.175467 0.00878432
\(400\) −3.87105 −0.193552
\(401\) −36.2410 −1.80979 −0.904894 0.425638i \(-0.860050\pi\)
−0.904894 + 0.425638i \(0.860050\pi\)
\(402\) −0.138653 −0.00691539
\(403\) −63.8477 −3.18048
\(404\) 14.9170 0.742146
\(405\) 9.55480 0.474782
\(406\) −4.61083 −0.228831
\(407\) 13.0885 0.648773
\(408\) −0.118527 −0.00586796
\(409\) 8.14209 0.402600 0.201300 0.979530i \(-0.435483\pi\)
0.201300 + 0.979530i \(0.435483\pi\)
\(410\) 9.35922 0.462219
\(411\) −0.0178280 −0.000879391 0
\(412\) −12.6241 −0.621944
\(413\) −1.91891 −0.0944233
\(414\) −15.9795 −0.785349
\(415\) −11.3095 −0.555161
\(416\) 6.62293 0.324716
\(417\) 0.115715 0.00566660
\(418\) 15.0286 0.735072
\(419\) 29.6280 1.44742 0.723712 0.690103i \(-0.242435\pi\)
0.723712 + 0.690103i \(0.242435\pi\)
\(420\) −0.0305138 −0.00148892
\(421\) 17.4957 0.852688 0.426344 0.904561i \(-0.359801\pi\)
0.426344 + 0.904561i \(0.359801\pi\)
\(422\) −0.477536 −0.0232461
\(423\) 4.54169 0.220824
\(424\) −6.97767 −0.338866
\(425\) −15.9767 −0.774983
\(426\) 0.105680 0.00512021
\(427\) −8.07712 −0.390879
\(428\) 11.2075 0.541737
\(429\) −0.467835 −0.0225873
\(430\) −1.49765 −0.0722232
\(431\) 1.00000 0.0481683
\(432\) −0.172286 −0.00828913
\(433\) 17.0741 0.820529 0.410264 0.911967i \(-0.365436\pi\)
0.410264 + 0.911967i \(0.365436\pi\)
\(434\) 9.64040 0.462754
\(435\) −0.140694 −0.00674576
\(436\) 12.6375 0.605228
\(437\) 32.5534 1.55724
\(438\) −0.0697341 −0.00333203
\(439\) −8.28965 −0.395643 −0.197822 0.980238i \(-0.563387\pi\)
−0.197822 + 0.980238i \(0.563387\pi\)
\(440\) −2.61349 −0.124593
\(441\) −2.99918 −0.142818
\(442\) 27.3343 1.30016
\(443\) −5.69101 −0.270388 −0.135194 0.990819i \(-0.543166\pi\)
−0.135194 + 0.990819i \(0.543166\pi\)
\(444\) 0.152815 0.00725229
\(445\) 5.73571 0.271899
\(446\) −24.2316 −1.14740
\(447\) 0.234503 0.0110916
\(448\) −1.00000 −0.0472456
\(449\) −16.2149 −0.765231 −0.382615 0.923908i \(-0.624977\pi\)
−0.382615 + 0.923908i \(0.624977\pi\)
\(450\) −11.6100 −0.547298
\(451\) −21.6663 −1.02023
\(452\) 2.54713 0.119807
\(453\) −0.420446 −0.0197543
\(454\) 6.21698 0.291777
\(455\) 7.03700 0.329900
\(456\) 0.175467 0.00821698
\(457\) −2.55941 −0.119724 −0.0598620 0.998207i \(-0.519066\pi\)
−0.0598620 + 0.998207i \(0.519066\pi\)
\(458\) 27.1550 1.26887
\(459\) −0.711064 −0.0331896
\(460\) −5.66107 −0.263949
\(461\) 6.26296 0.291695 0.145848 0.989307i \(-0.453409\pi\)
0.145848 + 0.989307i \(0.453409\pi\)
\(462\) 0.0706386 0.00328641
\(463\) 17.6757 0.821459 0.410729 0.911757i \(-0.365274\pi\)
0.410729 + 0.911757i \(0.365274\pi\)
\(464\) −4.61083 −0.214052
\(465\) 0.294166 0.0136416
\(466\) 11.0857 0.513537
\(467\) 27.1410 1.25594 0.627968 0.778239i \(-0.283887\pi\)
0.627968 + 0.778239i \(0.283887\pi\)
\(468\) 19.8633 0.918183
\(469\) −4.82804 −0.222938
\(470\) 1.60899 0.0742171
\(471\) 0.540663 0.0249125
\(472\) −1.91891 −0.0883249
\(473\) 3.46702 0.159414
\(474\) −0.0503223 −0.00231138
\(475\) 23.6518 1.08522
\(476\) −4.12722 −0.189171
\(477\) −20.9273 −0.958193
\(478\) 2.72895 0.124819
\(479\) −14.6389 −0.668866 −0.334433 0.942419i \(-0.608545\pi\)
−0.334433 + 0.942419i \(0.608545\pi\)
\(480\) −0.0305138 −0.00139276
\(481\) −35.2417 −1.60688
\(482\) −24.6476 −1.12267
\(483\) 0.153010 0.00696220
\(484\) −4.94986 −0.224994
\(485\) 16.1378 0.732781
\(486\) −0.775111 −0.0351598
\(487\) 21.3855 0.969068 0.484534 0.874773i \(-0.338989\pi\)
0.484534 + 0.874773i \(0.338989\pi\)
\(488\) −8.07712 −0.365634
\(489\) 0.316704 0.0143219
\(490\) −1.06252 −0.0479998
\(491\) −3.07368 −0.138713 −0.0693567 0.997592i \(-0.522095\pi\)
−0.0693567 + 0.997592i \(0.522095\pi\)
\(492\) −0.252966 −0.0114046
\(493\) −19.0299 −0.857064
\(494\) −40.4656 −1.82063
\(495\) −7.83831 −0.352306
\(496\) 9.64040 0.432867
\(497\) 3.67987 0.165065
\(498\) 0.305679 0.0136978
\(499\) 21.1264 0.945749 0.472875 0.881130i \(-0.343216\pi\)
0.472875 + 0.881130i \(0.343216\pi\)
\(500\) −9.42568 −0.421529
\(501\) 0.0973571 0.00434960
\(502\) −10.8104 −0.482493
\(503\) 29.7502 1.32650 0.663248 0.748400i \(-0.269177\pi\)
0.663248 + 0.748400i \(0.269177\pi\)
\(504\) −2.99918 −0.133594
\(505\) 15.8496 0.705297
\(506\) 13.1052 0.582597
\(507\) 0.886341 0.0393638
\(508\) −0.0642324 −0.00284985
\(509\) 42.3511 1.87718 0.938590 0.345033i \(-0.112132\pi\)
0.938590 + 0.345033i \(0.112132\pi\)
\(510\) −0.125937 −0.00557660
\(511\) −2.42821 −0.107418
\(512\) −1.00000 −0.0441942
\(513\) 1.05266 0.0464759
\(514\) 7.07789 0.312192
\(515\) −13.4134 −0.591063
\(516\) 0.0404793 0.00178200
\(517\) −3.72476 −0.163815
\(518\) 5.32117 0.233799
\(519\) −0.210339 −0.00923288
\(520\) 7.03700 0.308593
\(521\) 41.8406 1.83307 0.916534 0.399957i \(-0.130975\pi\)
0.916534 + 0.399957i \(0.130975\pi\)
\(522\) −13.8287 −0.605265
\(523\) 0.740439 0.0323772 0.0161886 0.999869i \(-0.494847\pi\)
0.0161886 + 0.999869i \(0.494847\pi\)
\(524\) 8.57186 0.374463
\(525\) 0.111170 0.00485186
\(526\) 18.3710 0.801013
\(527\) 39.7880 1.73319
\(528\) 0.0706386 0.00307415
\(529\) 5.38714 0.234224
\(530\) −7.41392 −0.322040
\(531\) −5.75514 −0.249752
\(532\) 6.10992 0.264898
\(533\) 58.3381 2.52690
\(534\) −0.155028 −0.00670870
\(535\) 11.9082 0.514838
\(536\) −4.82804 −0.208539
\(537\) 0.198698 0.00857445
\(538\) 1.75253 0.0755571
\(539\) 2.45970 0.105947
\(540\) −0.183058 −0.00787756
\(541\) 26.8779 1.15557 0.577786 0.816189i \(-0.303917\pi\)
0.577786 + 0.816189i \(0.303917\pi\)
\(542\) −16.5424 −0.710558
\(543\) −0.581702 −0.0249632
\(544\) −4.12722 −0.176953
\(545\) 13.4276 0.575177
\(546\) −0.190200 −0.00813979
\(547\) −14.5749 −0.623179 −0.311589 0.950217i \(-0.600861\pi\)
−0.311589 + 0.950217i \(0.600861\pi\)
\(548\) −0.620788 −0.0265188
\(549\) −24.2247 −1.03388
\(550\) 9.52163 0.406004
\(551\) 28.1718 1.20016
\(552\) 0.153010 0.00651254
\(553\) −1.75227 −0.0745141
\(554\) 13.9524 0.592783
\(555\) 0.162369 0.00689219
\(556\) 4.02932 0.170881
\(557\) −1.78967 −0.0758306 −0.0379153 0.999281i \(-0.512072\pi\)
−0.0379153 + 0.999281i \(0.512072\pi\)
\(558\) 28.9132 1.22399
\(559\) −9.33520 −0.394837
\(560\) −1.06252 −0.0448997
\(561\) 0.291541 0.0123089
\(562\) −11.2306 −0.473732
\(563\) 37.7035 1.58901 0.794506 0.607257i \(-0.207730\pi\)
0.794506 + 0.607257i \(0.207730\pi\)
\(564\) −0.0434885 −0.00183120
\(565\) 2.70638 0.113858
\(566\) 17.0869 0.718216
\(567\) −8.99258 −0.377653
\(568\) 3.67987 0.154404
\(569\) −1.95372 −0.0819042 −0.0409521 0.999161i \(-0.513039\pi\)
−0.0409521 + 0.999161i \(0.513039\pi\)
\(570\) 0.186437 0.00780899
\(571\) 8.13319 0.340364 0.170182 0.985413i \(-0.445565\pi\)
0.170182 + 0.985413i \(0.445565\pi\)
\(572\) −16.2904 −0.681138
\(573\) −0.0229723 −0.000959680 0
\(574\) −8.80850 −0.367660
\(575\) 20.6248 0.860113
\(576\) −2.99918 −0.124966
\(577\) −34.4562 −1.43443 −0.717215 0.696851i \(-0.754584\pi\)
−0.717215 + 0.696851i \(0.754584\pi\)
\(578\) −0.0339589 −0.00141250
\(579\) −0.258702 −0.0107513
\(580\) −4.89910 −0.203424
\(581\) 10.6440 0.441588
\(582\) −0.436181 −0.0180803
\(583\) 17.1630 0.710819
\(584\) −2.42821 −0.100480
\(585\) 21.1052 0.872593
\(586\) 0.694680 0.0286970
\(587\) −21.9544 −0.906155 −0.453078 0.891471i \(-0.649674\pi\)
−0.453078 + 0.891471i \(0.649674\pi\)
\(588\) 0.0287183 0.00118432
\(589\) −58.9020 −2.42702
\(590\) −2.03888 −0.0839394
\(591\) 0.170580 0.00701674
\(592\) 5.32117 0.218699
\(593\) 0.176565 0.00725064 0.00362532 0.999993i \(-0.498846\pi\)
0.00362532 + 0.999993i \(0.498846\pi\)
\(594\) 0.423773 0.0173876
\(595\) −4.38526 −0.179778
\(596\) 8.16563 0.334477
\(597\) 0.527621 0.0215941
\(598\) −35.2867 −1.44298
\(599\) 39.8238 1.62716 0.813578 0.581455i \(-0.197516\pi\)
0.813578 + 0.581455i \(0.197516\pi\)
\(600\) 0.111170 0.00453850
\(601\) 14.8626 0.606257 0.303129 0.952950i \(-0.401969\pi\)
0.303129 + 0.952950i \(0.401969\pi\)
\(602\) 1.40953 0.0574480
\(603\) −14.4801 −0.589676
\(604\) −14.6403 −0.595707
\(605\) −5.25933 −0.213822
\(606\) −0.428390 −0.0174022
\(607\) −42.2371 −1.71435 −0.857175 0.515025i \(-0.827783\pi\)
−0.857175 + 0.515025i \(0.827783\pi\)
\(608\) 6.10992 0.247790
\(609\) 0.132415 0.00536574
\(610\) −8.58211 −0.347479
\(611\) 10.0292 0.405738
\(612\) −12.3783 −0.500362
\(613\) 37.7803 1.52593 0.762966 0.646439i \(-0.223743\pi\)
0.762966 + 0.646439i \(0.223743\pi\)
\(614\) 17.4572 0.704516
\(615\) −0.268781 −0.0108383
\(616\) 2.45970 0.0991043
\(617\) 3.64644 0.146800 0.0734000 0.997303i \(-0.476615\pi\)
0.0734000 + 0.997303i \(0.476615\pi\)
\(618\) 0.362543 0.0145836
\(619\) 21.4603 0.862564 0.431282 0.902217i \(-0.358061\pi\)
0.431282 + 0.902217i \(0.358061\pi\)
\(620\) 10.2431 0.411374
\(621\) 0.917935 0.0368355
\(622\) −24.5175 −0.983063
\(623\) −5.39821 −0.216275
\(624\) −0.190200 −0.00761408
\(625\) 9.34026 0.373611
\(626\) 17.3076 0.691749
\(627\) −0.431596 −0.0172363
\(628\) 18.8264 0.751256
\(629\) 21.9616 0.875668
\(630\) −3.18669 −0.126961
\(631\) 23.2542 0.925735 0.462868 0.886427i \(-0.346821\pi\)
0.462868 + 0.886427i \(0.346821\pi\)
\(632\) −1.75227 −0.0697015
\(633\) 0.0137140 0.000545084 0
\(634\) −6.80688 −0.270336
\(635\) −0.0682482 −0.00270835
\(636\) 0.200387 0.00794587
\(637\) −6.62293 −0.262410
\(638\) 11.3413 0.449005
\(639\) 11.0366 0.436600
\(640\) −1.06252 −0.0419998
\(641\) 14.6227 0.577563 0.288782 0.957395i \(-0.406750\pi\)
0.288782 + 0.957395i \(0.406750\pi\)
\(642\) −0.321862 −0.0127029
\(643\) −5.01313 −0.197698 −0.0988492 0.995102i \(-0.531516\pi\)
−0.0988492 + 0.995102i \(0.531516\pi\)
\(644\) 5.32796 0.209951
\(645\) 0.0430101 0.00169352
\(646\) 25.2170 0.992149
\(647\) −3.50545 −0.137813 −0.0689067 0.997623i \(-0.521951\pi\)
−0.0689067 + 0.997623i \(0.521951\pi\)
\(648\) −8.99258 −0.353262
\(649\) 4.71995 0.185274
\(650\) −25.6377 −1.00559
\(651\) −0.276856 −0.0108509
\(652\) 11.0279 0.431888
\(653\) −8.69142 −0.340122 −0.170061 0.985434i \(-0.554396\pi\)
−0.170061 + 0.985434i \(0.554396\pi\)
\(654\) −0.362929 −0.0141916
\(655\) 9.10778 0.355870
\(656\) −8.80850 −0.343914
\(657\) −7.28262 −0.284122
\(658\) −1.51431 −0.0590340
\(659\) 3.30967 0.128926 0.0644632 0.997920i \(-0.479466\pi\)
0.0644632 + 0.997920i \(0.479466\pi\)
\(660\) 0.0750550 0.00292151
\(661\) 8.78312 0.341624 0.170812 0.985304i \(-0.445361\pi\)
0.170812 + 0.985304i \(0.445361\pi\)
\(662\) 18.7120 0.727263
\(663\) −0.784996 −0.0304867
\(664\) 10.6440 0.413068
\(665\) 6.49191 0.251746
\(666\) 15.9591 0.618403
\(667\) 24.5663 0.951211
\(668\) 3.39007 0.131166
\(669\) 0.695891 0.0269047
\(670\) −5.12989 −0.198185
\(671\) 19.8673 0.766969
\(672\) 0.0287183 0.00110783
\(673\) −18.9920 −0.732089 −0.366045 0.930597i \(-0.619288\pi\)
−0.366045 + 0.930597i \(0.619288\pi\)
\(674\) −16.0337 −0.617595
\(675\) 0.666929 0.0256701
\(676\) 30.8632 1.18705
\(677\) 30.3411 1.16610 0.583051 0.812436i \(-0.301859\pi\)
0.583051 + 0.812436i \(0.301859\pi\)
\(678\) −0.0731495 −0.00280929
\(679\) −15.1882 −0.582871
\(680\) −4.38526 −0.168167
\(681\) −0.178541 −0.00684172
\(682\) −23.7125 −0.907999
\(683\) −30.8857 −1.18181 −0.590904 0.806742i \(-0.701229\pi\)
−0.590904 + 0.806742i \(0.701229\pi\)
\(684\) 18.3247 0.700663
\(685\) −0.659601 −0.0252020
\(686\) 1.00000 0.0381802
\(687\) −0.779847 −0.0297530
\(688\) 1.40953 0.0537377
\(689\) −46.2126 −1.76056
\(690\) 0.162577 0.00618918
\(691\) 28.5409 1.08575 0.542873 0.839815i \(-0.317336\pi\)
0.542873 + 0.839815i \(0.317336\pi\)
\(692\) −7.32422 −0.278425
\(693\) 7.37708 0.280232
\(694\) −4.91272 −0.186484
\(695\) 4.28123 0.162396
\(696\) 0.132415 0.00501919
\(697\) −36.3546 −1.37703
\(698\) 30.3472 1.14866
\(699\) −0.318364 −0.0120416
\(700\) 3.87105 0.146312
\(701\) 49.8056 1.88113 0.940565 0.339613i \(-0.110296\pi\)
0.940565 + 0.339613i \(0.110296\pi\)
\(702\) −1.14104 −0.0430658
\(703\) −32.5119 −1.22621
\(704\) 2.45970 0.0927036
\(705\) −0.0462075 −0.00174028
\(706\) −9.45289 −0.355764
\(707\) −14.9170 −0.561010
\(708\) 0.0551079 0.00207108
\(709\) −18.4350 −0.692343 −0.346171 0.938171i \(-0.612518\pi\)
−0.346171 + 0.938171i \(0.612518\pi\)
\(710\) 3.90994 0.146738
\(711\) −5.25536 −0.197091
\(712\) −5.39821 −0.202306
\(713\) −51.3636 −1.92358
\(714\) 0.118527 0.00443576
\(715\) −17.3089 −0.647318
\(716\) 6.91885 0.258570
\(717\) −0.0783709 −0.00292682
\(718\) −14.0749 −0.525271
\(719\) 14.8122 0.552402 0.276201 0.961100i \(-0.410925\pi\)
0.276201 + 0.961100i \(0.410925\pi\)
\(720\) −3.18669 −0.118761
\(721\) 12.6241 0.470145
\(722\) −18.3311 −0.682212
\(723\) 0.707838 0.0263248
\(724\) −20.2554 −0.752787
\(725\) 17.8487 0.662885
\(726\) 0.142152 0.00527574
\(727\) −16.3511 −0.606428 −0.303214 0.952923i \(-0.598060\pi\)
−0.303214 + 0.952923i \(0.598060\pi\)
\(728\) −6.62293 −0.245462
\(729\) −26.9555 −0.998351
\(730\) −2.58002 −0.0954909
\(731\) 5.81743 0.215165
\(732\) 0.231961 0.00857354
\(733\) −23.8426 −0.880647 −0.440323 0.897839i \(-0.645136\pi\)
−0.440323 + 0.897839i \(0.645136\pi\)
\(734\) 6.31511 0.233095
\(735\) 0.0305138 0.00112552
\(736\) 5.32796 0.196391
\(737\) 11.8755 0.437441
\(738\) −26.4182 −0.972469
\(739\) 49.4464 1.81891 0.909457 0.415798i \(-0.136498\pi\)
0.909457 + 0.415798i \(0.136498\pi\)
\(740\) 5.65385 0.207840
\(741\) 1.16210 0.0426910
\(742\) 6.97767 0.256158
\(743\) −14.0586 −0.515759 −0.257880 0.966177i \(-0.583024\pi\)
−0.257880 + 0.966177i \(0.583024\pi\)
\(744\) −0.276856 −0.0101500
\(745\) 8.67615 0.317870
\(746\) 15.2931 0.559919
\(747\) 31.9233 1.16801
\(748\) 10.1517 0.371184
\(749\) −11.2075 −0.409515
\(750\) 0.270690 0.00988420
\(751\) 23.2895 0.849847 0.424924 0.905229i \(-0.360301\pi\)
0.424924 + 0.905229i \(0.360301\pi\)
\(752\) −1.51431 −0.0552213
\(753\) 0.310458 0.0113137
\(754\) −30.5372 −1.11210
\(755\) −15.5557 −0.566129
\(756\) 0.172286 0.00626600
\(757\) 24.6694 0.896625 0.448312 0.893877i \(-0.352025\pi\)
0.448312 + 0.893877i \(0.352025\pi\)
\(758\) −21.2733 −0.772682
\(759\) −0.376360 −0.0136610
\(760\) 6.49191 0.235487
\(761\) −34.3721 −1.24599 −0.622993 0.782227i \(-0.714084\pi\)
−0.622993 + 0.782227i \(0.714084\pi\)
\(762\) 0.00184465 6.68245e−5 0
\(763\) −12.6375 −0.457509
\(764\) −0.799916 −0.0289399
\(765\) −13.1522 −0.475517
\(766\) −9.50628 −0.343476
\(767\) −12.7088 −0.458888
\(768\) 0.0287183 0.00103628
\(769\) 39.3581 1.41929 0.709644 0.704560i \(-0.248856\pi\)
0.709644 + 0.704560i \(0.248856\pi\)
\(770\) 2.61349 0.0941835
\(771\) −0.203265 −0.00732042
\(772\) −9.00824 −0.324214
\(773\) −27.0496 −0.972905 −0.486453 0.873707i \(-0.661709\pi\)
−0.486453 + 0.873707i \(0.661709\pi\)
\(774\) 4.22742 0.151951
\(775\) −37.3184 −1.34052
\(776\) −15.1882 −0.545226
\(777\) −0.152815 −0.00548221
\(778\) 25.4231 0.911464
\(779\) 53.8192 1.92827
\(780\) −0.202091 −0.00723602
\(781\) −9.05140 −0.323884
\(782\) 21.9897 0.786349
\(783\) 0.794383 0.0283889
\(784\) 1.00000 0.0357143
\(785\) 20.0035 0.713954
\(786\) −0.246170 −0.00878058
\(787\) −7.38746 −0.263335 −0.131667 0.991294i \(-0.542033\pi\)
−0.131667 + 0.991294i \(0.542033\pi\)
\(788\) 5.93977 0.211595
\(789\) −0.527584 −0.0187825
\(790\) −1.86182 −0.0662407
\(791\) −2.54713 −0.0905656
\(792\) 7.37708 0.262133
\(793\) −53.4942 −1.89963
\(794\) 28.0621 0.995887
\(795\) 0.212916 0.00755134
\(796\) 18.3723 0.651188
\(797\) 23.7323 0.840640 0.420320 0.907376i \(-0.361918\pi\)
0.420320 + 0.907376i \(0.361918\pi\)
\(798\) −0.175467 −0.00621145
\(799\) −6.24990 −0.221106
\(800\) 3.87105 0.136862
\(801\) −16.1902 −0.572052
\(802\) 36.2410 1.27971
\(803\) 5.97267 0.210771
\(804\) 0.138653 0.00488992
\(805\) 5.66107 0.199526
\(806\) 63.8477 2.24894
\(807\) −0.0503299 −0.00177170
\(808\) −14.9170 −0.524777
\(809\) −33.3732 −1.17334 −0.586670 0.809826i \(-0.699561\pi\)
−0.586670 + 0.809826i \(0.699561\pi\)
\(810\) −9.55480 −0.335722
\(811\) −18.4021 −0.646184 −0.323092 0.946368i \(-0.604722\pi\)
−0.323092 + 0.946368i \(0.604722\pi\)
\(812\) 4.61083 0.161808
\(813\) 0.475071 0.0166615
\(814\) −13.0885 −0.458752
\(815\) 11.7174 0.410443
\(816\) 0.118527 0.00414927
\(817\) −8.61209 −0.301299
\(818\) −8.14209 −0.284682
\(819\) −19.8633 −0.694081
\(820\) −9.35922 −0.326838
\(821\) −49.6596 −1.73313 −0.866566 0.499062i \(-0.833678\pi\)
−0.866566 + 0.499062i \(0.833678\pi\)
\(822\) 0.0178280 0.000621823 0
\(823\) −0.566856 −0.0197594 −0.00987968 0.999951i \(-0.503145\pi\)
−0.00987968 + 0.999951i \(0.503145\pi\)
\(824\) 12.6241 0.439781
\(825\) −0.273446 −0.00952015
\(826\) 1.91891 0.0667673
\(827\) 36.7395 1.27756 0.638779 0.769391i \(-0.279440\pi\)
0.638779 + 0.769391i \(0.279440\pi\)
\(828\) 15.9795 0.555325
\(829\) −3.91283 −0.135898 −0.0679491 0.997689i \(-0.521646\pi\)
−0.0679491 + 0.997689i \(0.521646\pi\)
\(830\) 11.3095 0.392558
\(831\) −0.400691 −0.0138998
\(832\) −6.62293 −0.229609
\(833\) 4.12722 0.143000
\(834\) −0.115715 −0.00400689
\(835\) 3.60202 0.124653
\(836\) −15.0286 −0.519774
\(837\) −1.66091 −0.0574094
\(838\) −29.6280 −1.02348
\(839\) 45.6995 1.57772 0.788861 0.614571i \(-0.210671\pi\)
0.788861 + 0.614571i \(0.210671\pi\)
\(840\) 0.0305138 0.00105283
\(841\) −7.74028 −0.266906
\(842\) −17.4957 −0.602942
\(843\) 0.322523 0.0111083
\(844\) 0.477536 0.0164375
\(845\) 32.7928 1.12811
\(846\) −4.54169 −0.156146
\(847\) 4.94986 0.170079
\(848\) 6.97767 0.239614
\(849\) −0.490708 −0.0168410
\(850\) 15.9767 0.547996
\(851\) −28.3510 −0.971859
\(852\) −0.105680 −0.00362053
\(853\) 39.0590 1.33735 0.668677 0.743553i \(-0.266861\pi\)
0.668677 + 0.743553i \(0.266861\pi\)
\(854\) 8.07712 0.276393
\(855\) 19.4704 0.665873
\(856\) −11.2075 −0.383066
\(857\) −28.7515 −0.982131 −0.491066 0.871123i \(-0.663392\pi\)
−0.491066 + 0.871123i \(0.663392\pi\)
\(858\) 0.467835 0.0159716
\(859\) −28.1938 −0.961959 −0.480980 0.876732i \(-0.659719\pi\)
−0.480980 + 0.876732i \(0.659719\pi\)
\(860\) 1.49765 0.0510695
\(861\) 0.252966 0.00862104
\(862\) −1.00000 −0.0340601
\(863\) 29.8773 1.01704 0.508518 0.861051i \(-0.330193\pi\)
0.508518 + 0.861051i \(0.330193\pi\)
\(864\) 0.172286 0.00586130
\(865\) −7.78214 −0.264601
\(866\) −17.0741 −0.580201
\(867\) 0.000975242 0 3.31210e−5 0
\(868\) −9.64040 −0.327216
\(869\) 4.31006 0.146209
\(870\) 0.140694 0.00476997
\(871\) −31.9757 −1.08346
\(872\) −12.6375 −0.427961
\(873\) −45.5522 −1.54171
\(874\) −32.5534 −1.10113
\(875\) 9.42568 0.318646
\(876\) 0.0697341 0.00235610
\(877\) −11.0250 −0.372288 −0.186144 0.982522i \(-0.559599\pi\)
−0.186144 + 0.982522i \(0.559599\pi\)
\(878\) 8.28965 0.279762
\(879\) −0.0199501 −0.000672899 0
\(880\) 2.61349 0.0881006
\(881\) −33.9353 −1.14331 −0.571655 0.820494i \(-0.693698\pi\)
−0.571655 + 0.820494i \(0.693698\pi\)
\(882\) 2.99918 0.100987
\(883\) −0.568618 −0.0191355 −0.00956777 0.999954i \(-0.503046\pi\)
−0.00956777 + 0.999954i \(0.503046\pi\)
\(884\) −27.3343 −0.919352
\(885\) 0.0585533 0.00196825
\(886\) 5.69101 0.191193
\(887\) −7.57346 −0.254292 −0.127146 0.991884i \(-0.540582\pi\)
−0.127146 + 0.991884i \(0.540582\pi\)
\(888\) −0.152815 −0.00512814
\(889\) 0.0642324 0.00215428
\(890\) −5.73571 −0.192261
\(891\) 22.1191 0.741017
\(892\) 24.2316 0.811333
\(893\) 9.25232 0.309617
\(894\) −0.234503 −0.00784296
\(895\) 7.35143 0.245731
\(896\) 1.00000 0.0334077
\(897\) 1.01338 0.0338356
\(898\) 16.2149 0.541100
\(899\) −44.4502 −1.48250
\(900\) 11.6100 0.386998
\(901\) 28.7984 0.959414
\(902\) 21.6663 0.721409
\(903\) −0.0404793 −0.00134707
\(904\) −2.54713 −0.0847164
\(905\) −21.5218 −0.715409
\(906\) 0.420446 0.0139684
\(907\) −49.2313 −1.63470 −0.817350 0.576142i \(-0.804558\pi\)
−0.817350 + 0.576142i \(0.804558\pi\)
\(908\) −6.21698 −0.206318
\(909\) −44.7386 −1.48388
\(910\) −7.03700 −0.233274
\(911\) 39.0302 1.29313 0.646564 0.762860i \(-0.276205\pi\)
0.646564 + 0.762860i \(0.276205\pi\)
\(912\) −0.175467 −0.00581028
\(913\) −26.1811 −0.866469
\(914\) 2.55941 0.0846576
\(915\) 0.246464 0.00814785
\(916\) −27.1550 −0.897226
\(917\) −8.57186 −0.283068
\(918\) 0.711064 0.0234686
\(919\) 8.85403 0.292067 0.146034 0.989280i \(-0.453349\pi\)
0.146034 + 0.989280i \(0.453349\pi\)
\(920\) 5.66107 0.186640
\(921\) −0.501342 −0.0165198
\(922\) −6.26296 −0.206260
\(923\) 24.3715 0.802199
\(924\) −0.0706386 −0.00232384
\(925\) −20.5985 −0.677275
\(926\) −17.6757 −0.580859
\(927\) 37.8618 1.24355
\(928\) 4.61083 0.151358
\(929\) 28.2295 0.926180 0.463090 0.886311i \(-0.346741\pi\)
0.463090 + 0.886311i \(0.346741\pi\)
\(930\) −0.294166 −0.00964607
\(931\) −6.10992 −0.200244
\(932\) −11.0857 −0.363125
\(933\) 0.704103 0.0230513
\(934\) −27.1410 −0.888080
\(935\) 10.7864 0.352754
\(936\) −19.8633 −0.649253
\(937\) −24.1243 −0.788106 −0.394053 0.919088i \(-0.628927\pi\)
−0.394053 + 0.919088i \(0.628927\pi\)
\(938\) 4.82804 0.157641
\(939\) −0.497045 −0.0162204
\(940\) −1.60899 −0.0524794
\(941\) 6.05610 0.197423 0.0987116 0.995116i \(-0.468528\pi\)
0.0987116 + 0.995116i \(0.468528\pi\)
\(942\) −0.540663 −0.0176158
\(943\) 46.9313 1.52829
\(944\) 1.91891 0.0624551
\(945\) 0.183058 0.00595487
\(946\) −3.46702 −0.112723
\(947\) 28.2874 0.919217 0.459609 0.888122i \(-0.347990\pi\)
0.459609 + 0.888122i \(0.347990\pi\)
\(948\) 0.0503223 0.00163439
\(949\) −16.0819 −0.522039
\(950\) −23.6518 −0.767365
\(951\) 0.195482 0.00633895
\(952\) 4.12722 0.133764
\(953\) 16.6829 0.540413 0.270206 0.962802i \(-0.412908\pi\)
0.270206 + 0.962802i \(0.412908\pi\)
\(954\) 20.9273 0.677545
\(955\) −0.849927 −0.0275030
\(956\) −2.72895 −0.0882605
\(957\) −0.325702 −0.0105285
\(958\) 14.6389 0.472960
\(959\) 0.620788 0.0200463
\(960\) 0.0305138 0.000984830 0
\(961\) 61.9372 1.99798
\(962\) 35.2417 1.13624
\(963\) −33.6134 −1.08318
\(964\) 24.6476 0.793846
\(965\) −9.57145 −0.308116
\(966\) −0.153010 −0.00492302
\(967\) −24.1655 −0.777111 −0.388555 0.921425i \(-0.627026\pi\)
−0.388555 + 0.921425i \(0.627026\pi\)
\(968\) 4.94986 0.159094
\(969\) −0.724190 −0.0232643
\(970\) −16.1378 −0.518155
\(971\) 25.2372 0.809899 0.404949 0.914339i \(-0.367289\pi\)
0.404949 + 0.914339i \(0.367289\pi\)
\(972\) 0.775111 0.0248617
\(973\) −4.02932 −0.129174
\(974\) −21.3855 −0.685234
\(975\) 0.736272 0.0235796
\(976\) 8.07712 0.258542
\(977\) 4.98327 0.159429 0.0797145 0.996818i \(-0.474599\pi\)
0.0797145 + 0.996818i \(0.474599\pi\)
\(978\) −0.316704 −0.0101271
\(979\) 13.2780 0.424367
\(980\) 1.06252 0.0339410
\(981\) −37.9021 −1.21012
\(982\) 3.07368 0.0980852
\(983\) 10.3687 0.330711 0.165355 0.986234i \(-0.447123\pi\)
0.165355 + 0.986234i \(0.447123\pi\)
\(984\) 0.252966 0.00806425
\(985\) 6.31113 0.201089
\(986\) 19.0299 0.606036
\(987\) 0.0434885 0.00138426
\(988\) 40.4656 1.28738
\(989\) −7.50990 −0.238801
\(990\) 7.83831 0.249118
\(991\) 21.4849 0.682489 0.341245 0.939975i \(-0.389152\pi\)
0.341245 + 0.939975i \(0.389152\pi\)
\(992\) −9.64040 −0.306083
\(993\) −0.537378 −0.0170532
\(994\) −3.67987 −0.116718
\(995\) 19.5209 0.618855
\(996\) −0.305679 −0.00968580
\(997\) 8.32641 0.263700 0.131850 0.991270i \(-0.457908\pi\)
0.131850 + 0.991270i \(0.457908\pi\)
\(998\) −21.1264 −0.668746
\(999\) −0.916765 −0.0290052
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 \(a_p\))