Properties

Label 4002.2.a.w.1.2
Level 4002
Weight 2
Character 4002.1
Self dual Yes
Analytic conductor 31.956
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9561308889\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{12})^+\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.73205\)
Character \(\chi\) = 4002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.00000 q^{5}\) \(+1.00000 q^{6}\) \(+3.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.00000 q^{5}\) \(+1.00000 q^{6}\) \(+3.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+3.00000 q^{10}\) \(+0.732051 q^{11}\) \(+1.00000 q^{12}\) \(+4.73205 q^{13}\) \(+3.00000 q^{14}\) \(+3.00000 q^{15}\) \(+1.00000 q^{16}\) \(+0.464102 q^{17}\) \(+1.00000 q^{18}\) \(-4.46410 q^{19}\) \(+3.00000 q^{20}\) \(+3.00000 q^{21}\) \(+0.732051 q^{22}\) \(+1.00000 q^{23}\) \(+1.00000 q^{24}\) \(+4.00000 q^{25}\) \(+4.73205 q^{26}\) \(+1.00000 q^{27}\) \(+3.00000 q^{28}\) \(-1.00000 q^{29}\) \(+3.00000 q^{30}\) \(-2.73205 q^{31}\) \(+1.00000 q^{32}\) \(+0.732051 q^{33}\) \(+0.464102 q^{34}\) \(+9.00000 q^{35}\) \(+1.00000 q^{36}\) \(+3.19615 q^{37}\) \(-4.46410 q^{38}\) \(+4.73205 q^{39}\) \(+3.00000 q^{40}\) \(-12.1244 q^{41}\) \(+3.00000 q^{42}\) \(-11.9282 q^{43}\) \(+0.732051 q^{44}\) \(+3.00000 q^{45}\) \(+1.00000 q^{46}\) \(-9.39230 q^{47}\) \(+1.00000 q^{48}\) \(+2.00000 q^{49}\) \(+4.00000 q^{50}\) \(+0.464102 q^{51}\) \(+4.73205 q^{52}\) \(+2.53590 q^{53}\) \(+1.00000 q^{54}\) \(+2.19615 q^{55}\) \(+3.00000 q^{56}\) \(-4.46410 q^{57}\) \(-1.00000 q^{58}\) \(+10.4641 q^{59}\) \(+3.00000 q^{60}\) \(-14.3923 q^{61}\) \(-2.73205 q^{62}\) \(+3.00000 q^{63}\) \(+1.00000 q^{64}\) \(+14.1962 q^{65}\) \(+0.732051 q^{66}\) \(-2.53590 q^{67}\) \(+0.464102 q^{68}\) \(+1.00000 q^{69}\) \(+9.00000 q^{70}\) \(-11.6603 q^{71}\) \(+1.00000 q^{72}\) \(+0.928203 q^{73}\) \(+3.19615 q^{74}\) \(+4.00000 q^{75}\) \(-4.46410 q^{76}\) \(+2.19615 q^{77}\) \(+4.73205 q^{78}\) \(+7.12436 q^{79}\) \(+3.00000 q^{80}\) \(+1.00000 q^{81}\) \(-12.1244 q^{82}\) \(-11.4641 q^{83}\) \(+3.00000 q^{84}\) \(+1.39230 q^{85}\) \(-11.9282 q^{86}\) \(-1.00000 q^{87}\) \(+0.732051 q^{88}\) \(+1.46410 q^{89}\) \(+3.00000 q^{90}\) \(+14.1962 q^{91}\) \(+1.00000 q^{92}\) \(-2.73205 q^{93}\) \(-9.39230 q^{94}\) \(-13.3923 q^{95}\) \(+1.00000 q^{96}\) \(+4.00000 q^{97}\) \(+2.00000 q^{98}\) \(+0.732051 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 6q^{21} \) \(\mathstrut -\mathstrut 2q^{22} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 8q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut +\mathstrut 6q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut +\mathstrut 2q^{32} \) \(\mathstrut -\mathstrut 2q^{33} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 4q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 2q^{48} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 12q^{53} \) \(\mathstrut +\mathstrut 2q^{54} \) \(\mathstrut -\mathstrut 6q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 2q^{58} \) \(\mathstrut +\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 2q^{62} \) \(\mathstrut +\mathstrut 6q^{63} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 18q^{65} \) \(\mathstrut -\mathstrut 2q^{66} \) \(\mathstrut -\mathstrut 12q^{67} \) \(\mathstrut -\mathstrut 6q^{68} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 6q^{71} \) \(\mathstrut +\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 12q^{73} \) \(\mathstrut -\mathstrut 4q^{74} \) \(\mathstrut +\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 2q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 18q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 2q^{87} \) \(\mathstrut -\mathstrut 2q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 18q^{91} \) \(\mathstrut +\mathstrut 2q^{92} \) \(\mathstrut -\mathstrut 2q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut -\mathstrut 6q^{95} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 1.00000 0.408248
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 3.00000 0.948683
\(11\) 0.732051 0.220722 0.110361 0.993892i \(-0.464799\pi\)
0.110361 + 0.993892i \(0.464799\pi\)
\(12\) 1.00000 0.288675
\(13\) 4.73205 1.31243 0.656217 0.754572i \(-0.272155\pi\)
0.656217 + 0.754572i \(0.272155\pi\)
\(14\) 3.00000 0.801784
\(15\) 3.00000 0.774597
\(16\) 1.00000 0.250000
\(17\) 0.464102 0.112561 0.0562806 0.998415i \(-0.482076\pi\)
0.0562806 + 0.998415i \(0.482076\pi\)
\(18\) 1.00000 0.235702
\(19\) −4.46410 −1.02414 −0.512068 0.858945i \(-0.671120\pi\)
−0.512068 + 0.858945i \(0.671120\pi\)
\(20\) 3.00000 0.670820
\(21\) 3.00000 0.654654
\(22\) 0.732051 0.156074
\(23\) 1.00000 0.208514
\(24\) 1.00000 0.204124
\(25\) 4.00000 0.800000
\(26\) 4.73205 0.928032
\(27\) 1.00000 0.192450
\(28\) 3.00000 0.566947
\(29\) −1.00000 −0.185695
\(30\) 3.00000 0.547723
\(31\) −2.73205 −0.490691 −0.245345 0.969436i \(-0.578901\pi\)
−0.245345 + 0.969436i \(0.578901\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.732051 0.127434
\(34\) 0.464102 0.0795928
\(35\) 9.00000 1.52128
\(36\) 1.00000 0.166667
\(37\) 3.19615 0.525444 0.262722 0.964872i \(-0.415380\pi\)
0.262722 + 0.964872i \(0.415380\pi\)
\(38\) −4.46410 −0.724173
\(39\) 4.73205 0.757735
\(40\) 3.00000 0.474342
\(41\) −12.1244 −1.89351 −0.946753 0.321960i \(-0.895658\pi\)
−0.946753 + 0.321960i \(0.895658\pi\)
\(42\) 3.00000 0.462910
\(43\) −11.9282 −1.81903 −0.909517 0.415667i \(-0.863548\pi\)
−0.909517 + 0.415667i \(0.863548\pi\)
\(44\) 0.732051 0.110361
\(45\) 3.00000 0.447214
\(46\) 1.00000 0.147442
\(47\) −9.39230 −1.37001 −0.685004 0.728539i \(-0.740200\pi\)
−0.685004 + 0.728539i \(0.740200\pi\)
\(48\) 1.00000 0.144338
\(49\) 2.00000 0.285714
\(50\) 4.00000 0.565685
\(51\) 0.464102 0.0649872
\(52\) 4.73205 0.656217
\(53\) 2.53590 0.348332 0.174166 0.984716i \(-0.444277\pi\)
0.174166 + 0.984716i \(0.444277\pi\)
\(54\) 1.00000 0.136083
\(55\) 2.19615 0.296129
\(56\) 3.00000 0.400892
\(57\) −4.46410 −0.591285
\(58\) −1.00000 −0.131306
\(59\) 10.4641 1.36231 0.681155 0.732139i \(-0.261478\pi\)
0.681155 + 0.732139i \(0.261478\pi\)
\(60\) 3.00000 0.387298
\(61\) −14.3923 −1.84275 −0.921373 0.388680i \(-0.872931\pi\)
−0.921373 + 0.388680i \(0.872931\pi\)
\(62\) −2.73205 −0.346971
\(63\) 3.00000 0.377964
\(64\) 1.00000 0.125000
\(65\) 14.1962 1.76082
\(66\) 0.732051 0.0901092
\(67\) −2.53590 −0.309809 −0.154905 0.987929i \(-0.549507\pi\)
−0.154905 + 0.987929i \(0.549507\pi\)
\(68\) 0.464102 0.0562806
\(69\) 1.00000 0.120386
\(70\) 9.00000 1.07571
\(71\) −11.6603 −1.38382 −0.691909 0.721985i \(-0.743230\pi\)
−0.691909 + 0.721985i \(0.743230\pi\)
\(72\) 1.00000 0.117851
\(73\) 0.928203 0.108638 0.0543190 0.998524i \(-0.482701\pi\)
0.0543190 + 0.998524i \(0.482701\pi\)
\(74\) 3.19615 0.371545
\(75\) 4.00000 0.461880
\(76\) −4.46410 −0.512068
\(77\) 2.19615 0.250275
\(78\) 4.73205 0.535799
\(79\) 7.12436 0.801553 0.400776 0.916176i \(-0.368740\pi\)
0.400776 + 0.916176i \(0.368740\pi\)
\(80\) 3.00000 0.335410
\(81\) 1.00000 0.111111
\(82\) −12.1244 −1.33891
\(83\) −11.4641 −1.25835 −0.629174 0.777264i \(-0.716607\pi\)
−0.629174 + 0.777264i \(0.716607\pi\)
\(84\) 3.00000 0.327327
\(85\) 1.39230 0.151017
\(86\) −11.9282 −1.28625
\(87\) −1.00000 −0.107211
\(88\) 0.732051 0.0780369
\(89\) 1.46410 0.155194 0.0775972 0.996985i \(-0.475275\pi\)
0.0775972 + 0.996985i \(0.475275\pi\)
\(90\) 3.00000 0.316228
\(91\) 14.1962 1.48816
\(92\) 1.00000 0.104257
\(93\) −2.73205 −0.283300
\(94\) −9.39230 −0.968742
\(95\) −13.3923 −1.37402
\(96\) 1.00000 0.102062
\(97\) 4.00000 0.406138 0.203069 0.979164i \(-0.434908\pi\)
0.203069 + 0.979164i \(0.434908\pi\)
\(98\) 2.00000 0.202031
\(99\) 0.732051 0.0735739
\(100\) 4.00000 0.400000
\(101\) 16.9282 1.68442 0.842210 0.539150i \(-0.181255\pi\)
0.842210 + 0.539150i \(0.181255\pi\)
\(102\) 0.464102 0.0459529
\(103\) −12.8564 −1.26678 −0.633390 0.773833i \(-0.718337\pi\)
−0.633390 + 0.773833i \(0.718337\pi\)
\(104\) 4.73205 0.464016
\(105\) 9.00000 0.878310
\(106\) 2.53590 0.246308
\(107\) 9.19615 0.889026 0.444513 0.895772i \(-0.353377\pi\)
0.444513 + 0.895772i \(0.353377\pi\)
\(108\) 1.00000 0.0962250
\(109\) −8.00000 −0.766261 −0.383131 0.923694i \(-0.625154\pi\)
−0.383131 + 0.923694i \(0.625154\pi\)
\(110\) 2.19615 0.209395
\(111\) 3.19615 0.303365
\(112\) 3.00000 0.283473
\(113\) 11.3923 1.07170 0.535849 0.844314i \(-0.319992\pi\)
0.535849 + 0.844314i \(0.319992\pi\)
\(114\) −4.46410 −0.418101
\(115\) 3.00000 0.279751
\(116\) −1.00000 −0.0928477
\(117\) 4.73205 0.437478
\(118\) 10.4641 0.963299
\(119\) 1.39230 0.127632
\(120\) 3.00000 0.273861
\(121\) −10.4641 −0.951282
\(122\) −14.3923 −1.30302
\(123\) −12.1244 −1.09322
\(124\) −2.73205 −0.245345
\(125\) −3.00000 −0.268328
\(126\) 3.00000 0.267261
\(127\) 11.4641 1.01727 0.508637 0.860981i \(-0.330149\pi\)
0.508637 + 0.860981i \(0.330149\pi\)
\(128\) 1.00000 0.0883883
\(129\) −11.9282 −1.05022
\(130\) 14.1962 1.24508
\(131\) −18.1962 −1.58981 −0.794903 0.606737i \(-0.792478\pi\)
−0.794903 + 0.606737i \(0.792478\pi\)
\(132\) 0.732051 0.0637168
\(133\) −13.3923 −1.16126
\(134\) −2.53590 −0.219068
\(135\) 3.00000 0.258199
\(136\) 0.464102 0.0397964
\(137\) −12.9282 −1.10453 −0.552265 0.833668i \(-0.686237\pi\)
−0.552265 + 0.833668i \(0.686237\pi\)
\(138\) 1.00000 0.0851257
\(139\) −19.8564 −1.68420 −0.842099 0.539323i \(-0.818680\pi\)
−0.842099 + 0.539323i \(0.818680\pi\)
\(140\) 9.00000 0.760639
\(141\) −9.39230 −0.790975
\(142\) −11.6603 −0.978507
\(143\) 3.46410 0.289683
\(144\) 1.00000 0.0833333
\(145\) −3.00000 −0.249136
\(146\) 0.928203 0.0768186
\(147\) 2.00000 0.164957
\(148\) 3.19615 0.262722
\(149\) 5.00000 0.409616 0.204808 0.978802i \(-0.434343\pi\)
0.204808 + 0.978802i \(0.434343\pi\)
\(150\) 4.00000 0.326599
\(151\) 14.1244 1.14942 0.574712 0.818356i \(-0.305114\pi\)
0.574712 + 0.818356i \(0.305114\pi\)
\(152\) −4.46410 −0.362086
\(153\) 0.464102 0.0375204
\(154\) 2.19615 0.176971
\(155\) −8.19615 −0.658331
\(156\) 4.73205 0.378867
\(157\) −0.267949 −0.0213847 −0.0106923 0.999943i \(-0.503404\pi\)
−0.0106923 + 0.999943i \(0.503404\pi\)
\(158\) 7.12436 0.566783
\(159\) 2.53590 0.201110
\(160\) 3.00000 0.237171
\(161\) 3.00000 0.236433
\(162\) 1.00000 0.0785674
\(163\) −20.2679 −1.58751 −0.793754 0.608239i \(-0.791876\pi\)
−0.793754 + 0.608239i \(0.791876\pi\)
\(164\) −12.1244 −0.946753
\(165\) 2.19615 0.170970
\(166\) −11.4641 −0.889787
\(167\) 19.8564 1.53653 0.768267 0.640129i \(-0.221119\pi\)
0.768267 + 0.640129i \(0.221119\pi\)
\(168\) 3.00000 0.231455
\(169\) 9.39230 0.722485
\(170\) 1.39230 0.106785
\(171\) −4.46410 −0.341378
\(172\) −11.9282 −0.909517
\(173\) 8.26795 0.628601 0.314300 0.949324i \(-0.398230\pi\)
0.314300 + 0.949324i \(0.398230\pi\)
\(174\) −1.00000 −0.0758098
\(175\) 12.0000 0.907115
\(176\) 0.732051 0.0551804
\(177\) 10.4641 0.786530
\(178\) 1.46410 0.109739
\(179\) 10.3923 0.776757 0.388379 0.921500i \(-0.373035\pi\)
0.388379 + 0.921500i \(0.373035\pi\)
\(180\) 3.00000 0.223607
\(181\) 19.1244 1.42150 0.710751 0.703444i \(-0.248355\pi\)
0.710751 + 0.703444i \(0.248355\pi\)
\(182\) 14.1962 1.05229
\(183\) −14.3923 −1.06391
\(184\) 1.00000 0.0737210
\(185\) 9.58846 0.704957
\(186\) −2.73205 −0.200324
\(187\) 0.339746 0.0248447
\(188\) −9.39230 −0.685004
\(189\) 3.00000 0.218218
\(190\) −13.3923 −0.971580
\(191\) −1.87564 −0.135717 −0.0678584 0.997695i \(-0.521617\pi\)
−0.0678584 + 0.997695i \(0.521617\pi\)
\(192\) 1.00000 0.0721688
\(193\) 9.46410 0.681241 0.340620 0.940201i \(-0.389363\pi\)
0.340620 + 0.940201i \(0.389363\pi\)
\(194\) 4.00000 0.287183
\(195\) 14.1962 1.01661
\(196\) 2.00000 0.142857
\(197\) 17.7321 1.26336 0.631678 0.775231i \(-0.282366\pi\)
0.631678 + 0.775231i \(0.282366\pi\)
\(198\) 0.732051 0.0520246
\(199\) 17.3205 1.22782 0.613909 0.789377i \(-0.289596\pi\)
0.613909 + 0.789377i \(0.289596\pi\)
\(200\) 4.00000 0.282843
\(201\) −2.53590 −0.178868
\(202\) 16.9282 1.19106
\(203\) −3.00000 −0.210559
\(204\) 0.464102 0.0324936
\(205\) −36.3731 −2.54041
\(206\) −12.8564 −0.895748
\(207\) 1.00000 0.0695048
\(208\) 4.73205 0.328109
\(209\) −3.26795 −0.226049
\(210\) 9.00000 0.621059
\(211\) 11.1962 0.770775 0.385387 0.922755i \(-0.374068\pi\)
0.385387 + 0.922755i \(0.374068\pi\)
\(212\) 2.53590 0.174166
\(213\) −11.6603 −0.798947
\(214\) 9.19615 0.628636
\(215\) −35.7846 −2.44049
\(216\) 1.00000 0.0680414
\(217\) −8.19615 −0.556391
\(218\) −8.00000 −0.541828
\(219\) 0.928203 0.0627222
\(220\) 2.19615 0.148065
\(221\) 2.19615 0.147729
\(222\) 3.19615 0.214512
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 3.00000 0.200446
\(225\) 4.00000 0.266667
\(226\) 11.3923 0.757805
\(227\) −25.5885 −1.69837 −0.849183 0.528099i \(-0.822905\pi\)
−0.849183 + 0.528099i \(0.822905\pi\)
\(228\) −4.46410 −0.295642
\(229\) 13.1962 0.872026 0.436013 0.899940i \(-0.356390\pi\)
0.436013 + 0.899940i \(0.356390\pi\)
\(230\) 3.00000 0.197814
\(231\) 2.19615 0.144496
\(232\) −1.00000 −0.0656532
\(233\) 23.3205 1.52778 0.763889 0.645348i \(-0.223288\pi\)
0.763889 + 0.645348i \(0.223288\pi\)
\(234\) 4.73205 0.309344
\(235\) −28.1769 −1.83806
\(236\) 10.4641 0.681155
\(237\) 7.12436 0.462777
\(238\) 1.39230 0.0902497
\(239\) −7.85641 −0.508189 −0.254094 0.967179i \(-0.581777\pi\)
−0.254094 + 0.967179i \(0.581777\pi\)
\(240\) 3.00000 0.193649
\(241\) 13.7321 0.884559 0.442280 0.896877i \(-0.354170\pi\)
0.442280 + 0.896877i \(0.354170\pi\)
\(242\) −10.4641 −0.672658
\(243\) 1.00000 0.0641500
\(244\) −14.3923 −0.921373
\(245\) 6.00000 0.383326
\(246\) −12.1244 −0.773021
\(247\) −21.1244 −1.34411
\(248\) −2.73205 −0.173485
\(249\) −11.4641 −0.726508
\(250\) −3.00000 −0.189737
\(251\) 1.46410 0.0924133 0.0462066 0.998932i \(-0.485287\pi\)
0.0462066 + 0.998932i \(0.485287\pi\)
\(252\) 3.00000 0.188982
\(253\) 0.732051 0.0460236
\(254\) 11.4641 0.719322
\(255\) 1.39230 0.0871895
\(256\) 1.00000 0.0625000
\(257\) −22.7321 −1.41799 −0.708993 0.705215i \(-0.750850\pi\)
−0.708993 + 0.705215i \(0.750850\pi\)
\(258\) −11.9282 −0.742617
\(259\) 9.58846 0.595798
\(260\) 14.1962 0.880408
\(261\) −1.00000 −0.0618984
\(262\) −18.1962 −1.12416
\(263\) 29.0526 1.79146 0.895729 0.444601i \(-0.146654\pi\)
0.895729 + 0.444601i \(0.146654\pi\)
\(264\) 0.732051 0.0450546
\(265\) 7.60770 0.467337
\(266\) −13.3923 −0.821135
\(267\) 1.46410 0.0896016
\(268\) −2.53590 −0.154905
\(269\) −11.6603 −0.710938 −0.355469 0.934688i \(-0.615679\pi\)
−0.355469 + 0.934688i \(0.615679\pi\)
\(270\) 3.00000 0.182574
\(271\) 24.7846 1.50556 0.752779 0.658273i \(-0.228713\pi\)
0.752779 + 0.658273i \(0.228713\pi\)
\(272\) 0.464102 0.0281403
\(273\) 14.1962 0.859190
\(274\) −12.9282 −0.781021
\(275\) 2.92820 0.176577
\(276\) 1.00000 0.0601929
\(277\) 19.1244 1.14907 0.574536 0.818480i \(-0.305183\pi\)
0.574536 + 0.818480i \(0.305183\pi\)
\(278\) −19.8564 −1.19091
\(279\) −2.73205 −0.163564
\(280\) 9.00000 0.537853
\(281\) 27.4641 1.63837 0.819185 0.573529i \(-0.194426\pi\)
0.819185 + 0.573529i \(0.194426\pi\)
\(282\) −9.39230 −0.559304
\(283\) 8.58846 0.510531 0.255265 0.966871i \(-0.417837\pi\)
0.255265 + 0.966871i \(0.417837\pi\)
\(284\) −11.6603 −0.691909
\(285\) −13.3923 −0.793292
\(286\) 3.46410 0.204837
\(287\) −36.3731 −2.14703
\(288\) 1.00000 0.0589256
\(289\) −16.7846 −0.987330
\(290\) −3.00000 −0.176166
\(291\) 4.00000 0.234484
\(292\) 0.928203 0.0543190
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 2.00000 0.116642
\(295\) 31.3923 1.82773
\(296\) 3.19615 0.185773
\(297\) 0.732051 0.0424779
\(298\) 5.00000 0.289642
\(299\) 4.73205 0.273662
\(300\) 4.00000 0.230940
\(301\) −35.7846 −2.06259
\(302\) 14.1244 0.812765
\(303\) 16.9282 0.972500
\(304\) −4.46410 −0.256034
\(305\) −43.1769 −2.47230
\(306\) 0.464102 0.0265309
\(307\) −9.07180 −0.517755 −0.258877 0.965910i \(-0.583353\pi\)
−0.258877 + 0.965910i \(0.583353\pi\)
\(308\) 2.19615 0.125137
\(309\) −12.8564 −0.731375
\(310\) −8.19615 −0.465510
\(311\) −6.32051 −0.358403 −0.179202 0.983812i \(-0.557351\pi\)
−0.179202 + 0.983812i \(0.557351\pi\)
\(312\) 4.73205 0.267900
\(313\) −20.1244 −1.13750 −0.568748 0.822512i \(-0.692572\pi\)
−0.568748 + 0.822512i \(0.692572\pi\)
\(314\) −0.267949 −0.0151212
\(315\) 9.00000 0.507093
\(316\) 7.12436 0.400776
\(317\) 10.3397 0.580738 0.290369 0.956915i \(-0.406222\pi\)
0.290369 + 0.956915i \(0.406222\pi\)
\(318\) 2.53590 0.142206
\(319\) −0.732051 −0.0409870
\(320\) 3.00000 0.167705
\(321\) 9.19615 0.513279
\(322\) 3.00000 0.167183
\(323\) −2.07180 −0.115278
\(324\) 1.00000 0.0555556
\(325\) 18.9282 1.04995
\(326\) −20.2679 −1.12254
\(327\) −8.00000 −0.442401
\(328\) −12.1244 −0.669456
\(329\) −28.1769 −1.55344
\(330\) 2.19615 0.120894
\(331\) 29.4449 1.61844 0.809218 0.587508i \(-0.199891\pi\)
0.809218 + 0.587508i \(0.199891\pi\)
\(332\) −11.4641 −0.629174
\(333\) 3.19615 0.175148
\(334\) 19.8564 1.08649
\(335\) −7.60770 −0.415653
\(336\) 3.00000 0.163663
\(337\) −20.9282 −1.14003 −0.570016 0.821634i \(-0.693063\pi\)
−0.570016 + 0.821634i \(0.693063\pi\)
\(338\) 9.39230 0.510874
\(339\) 11.3923 0.618745
\(340\) 1.39230 0.0755083
\(341\) −2.00000 −0.108306
\(342\) −4.46410 −0.241391
\(343\) −15.0000 −0.809924
\(344\) −11.9282 −0.643126
\(345\) 3.00000 0.161515
\(346\) 8.26795 0.444488
\(347\) 18.8564 1.01226 0.506132 0.862456i \(-0.331075\pi\)
0.506132 + 0.862456i \(0.331075\pi\)
\(348\) −1.00000 −0.0536056
\(349\) −6.39230 −0.342172 −0.171086 0.985256i \(-0.554728\pi\)
−0.171086 + 0.985256i \(0.554728\pi\)
\(350\) 12.0000 0.641427
\(351\) 4.73205 0.252578
\(352\) 0.732051 0.0390184
\(353\) −11.4641 −0.610173 −0.305086 0.952325i \(-0.598685\pi\)
−0.305086 + 0.952325i \(0.598685\pi\)
\(354\) 10.4641 0.556161
\(355\) −34.9808 −1.85659
\(356\) 1.46410 0.0775972
\(357\) 1.39230 0.0736886
\(358\) 10.3923 0.549250
\(359\) −4.26795 −0.225254 −0.112627 0.993637i \(-0.535926\pi\)
−0.112627 + 0.993637i \(0.535926\pi\)
\(360\) 3.00000 0.158114
\(361\) 0.928203 0.0488528
\(362\) 19.1244 1.00515
\(363\) −10.4641 −0.549223
\(364\) 14.1962 0.744081
\(365\) 2.78461 0.145753
\(366\) −14.3923 −0.752298
\(367\) 14.3397 0.748529 0.374264 0.927322i \(-0.377895\pi\)
0.374264 + 0.927322i \(0.377895\pi\)
\(368\) 1.00000 0.0521286
\(369\) −12.1244 −0.631169
\(370\) 9.58846 0.498480
\(371\) 7.60770 0.394972
\(372\) −2.73205 −0.141650
\(373\) 30.9282 1.60140 0.800701 0.599064i \(-0.204461\pi\)
0.800701 + 0.599064i \(0.204461\pi\)
\(374\) 0.339746 0.0175678
\(375\) −3.00000 −0.154919
\(376\) −9.39230 −0.484371
\(377\) −4.73205 −0.243713
\(378\) 3.00000 0.154303
\(379\) 3.85641 0.198090 0.0990451 0.995083i \(-0.468421\pi\)
0.0990451 + 0.995083i \(0.468421\pi\)
\(380\) −13.3923 −0.687011
\(381\) 11.4641 0.587324
\(382\) −1.87564 −0.0959663
\(383\) 9.80385 0.500953 0.250477 0.968123i \(-0.419413\pi\)
0.250477 + 0.968123i \(0.419413\pi\)
\(384\) 1.00000 0.0510310
\(385\) 6.58846 0.335779
\(386\) 9.46410 0.481710
\(387\) −11.9282 −0.606345
\(388\) 4.00000 0.203069
\(389\) 13.8564 0.702548 0.351274 0.936273i \(-0.385749\pi\)
0.351274 + 0.936273i \(0.385749\pi\)
\(390\) 14.1962 0.718850
\(391\) 0.464102 0.0234706
\(392\) 2.00000 0.101015
\(393\) −18.1962 −0.917874
\(394\) 17.7321 0.893328
\(395\) 21.3731 1.07540
\(396\) 0.732051 0.0367869
\(397\) 17.6603 0.886343 0.443171 0.896437i \(-0.353853\pi\)
0.443171 + 0.896437i \(0.353853\pi\)
\(398\) 17.3205 0.868199
\(399\) −13.3923 −0.670454
\(400\) 4.00000 0.200000
\(401\) 29.7128 1.48379 0.741894 0.670518i \(-0.233928\pi\)
0.741894 + 0.670518i \(0.233928\pi\)
\(402\) −2.53590 −0.126479
\(403\) −12.9282 −0.644000
\(404\) 16.9282 0.842210
\(405\) 3.00000 0.149071
\(406\) −3.00000 −0.148888
\(407\) 2.33975 0.115977
\(408\) 0.464102 0.0229765
\(409\) −5.12436 −0.253383 −0.126692 0.991942i \(-0.540436\pi\)
−0.126692 + 0.991942i \(0.540436\pi\)
\(410\) −36.3731 −1.79634
\(411\) −12.9282 −0.637701
\(412\) −12.8564 −0.633390
\(413\) 31.3923 1.54471
\(414\) 1.00000 0.0491473
\(415\) −34.3923 −1.68825
\(416\) 4.73205 0.232008
\(417\) −19.8564 −0.972372
\(418\) −3.26795 −0.159841
\(419\) 21.5885 1.05467 0.527333 0.849659i \(-0.323192\pi\)
0.527333 + 0.849659i \(0.323192\pi\)
\(420\) 9.00000 0.439155
\(421\) 9.60770 0.468250 0.234125 0.972206i \(-0.424777\pi\)
0.234125 + 0.972206i \(0.424777\pi\)
\(422\) 11.1962 0.545020
\(423\) −9.39230 −0.456669
\(424\) 2.53590 0.123154
\(425\) 1.85641 0.0900489
\(426\) −11.6603 −0.564941
\(427\) −43.1769 −2.08948
\(428\) 9.19615 0.444513
\(429\) 3.46410 0.167248
\(430\) −35.7846 −1.72569
\(431\) 19.8038 0.953918 0.476959 0.878926i \(-0.341739\pi\)
0.476959 + 0.878926i \(0.341739\pi\)
\(432\) 1.00000 0.0481125
\(433\) −33.5167 −1.61071 −0.805354 0.592794i \(-0.798025\pi\)
−0.805354 + 0.592794i \(0.798025\pi\)
\(434\) −8.19615 −0.393428
\(435\) −3.00000 −0.143839
\(436\) −8.00000 −0.383131
\(437\) −4.46410 −0.213547
\(438\) 0.928203 0.0443513
\(439\) 10.8038 0.515640 0.257820 0.966193i \(-0.416996\pi\)
0.257820 + 0.966193i \(0.416996\pi\)
\(440\) 2.19615 0.104697
\(441\) 2.00000 0.0952381
\(442\) 2.19615 0.104460
\(443\) −37.1769 −1.76633 −0.883164 0.469064i \(-0.844591\pi\)
−0.883164 + 0.469064i \(0.844591\pi\)
\(444\) 3.19615 0.151683
\(445\) 4.39230 0.208215
\(446\) 8.00000 0.378811
\(447\) 5.00000 0.236492
\(448\) 3.00000 0.141737
\(449\) −8.66025 −0.408703 −0.204351 0.978898i \(-0.565508\pi\)
−0.204351 + 0.978898i \(0.565508\pi\)
\(450\) 4.00000 0.188562
\(451\) −8.87564 −0.417938
\(452\) 11.3923 0.535849
\(453\) 14.1244 0.663620
\(454\) −25.5885 −1.20093
\(455\) 42.5885 1.99658
\(456\) −4.46410 −0.209051
\(457\) −34.9090 −1.63297 −0.816486 0.577365i \(-0.804081\pi\)
−0.816486 + 0.577365i \(0.804081\pi\)
\(458\) 13.1962 0.616616
\(459\) 0.464102 0.0216624
\(460\) 3.00000 0.139876
\(461\) 30.0526 1.39969 0.699844 0.714296i \(-0.253253\pi\)
0.699844 + 0.714296i \(0.253253\pi\)
\(462\) 2.19615 0.102174
\(463\) 31.1769 1.44891 0.724457 0.689320i \(-0.242091\pi\)
0.724457 + 0.689320i \(0.242091\pi\)
\(464\) −1.00000 −0.0464238
\(465\) −8.19615 −0.380087
\(466\) 23.3205 1.08030
\(467\) 11.8038 0.546217 0.273108 0.961983i \(-0.411948\pi\)
0.273108 + 0.961983i \(0.411948\pi\)
\(468\) 4.73205 0.218739
\(469\) −7.60770 −0.351291
\(470\) −28.1769 −1.29970
\(471\) −0.267949 −0.0123464
\(472\) 10.4641 0.481649
\(473\) −8.73205 −0.401500
\(474\) 7.12436 0.327232
\(475\) −17.8564 −0.819308
\(476\) 1.39230 0.0638162
\(477\) 2.53590 0.116111
\(478\) −7.85641 −0.359344
\(479\) 25.8564 1.18141 0.590705 0.806888i \(-0.298850\pi\)
0.590705 + 0.806888i \(0.298850\pi\)
\(480\) 3.00000 0.136931
\(481\) 15.1244 0.689611
\(482\) 13.7321 0.625478
\(483\) 3.00000 0.136505
\(484\) −10.4641 −0.475641
\(485\) 12.0000 0.544892
\(486\) 1.00000 0.0453609
\(487\) −32.5167 −1.47347 −0.736735 0.676181i \(-0.763634\pi\)
−0.736735 + 0.676181i \(0.763634\pi\)
\(488\) −14.3923 −0.651509
\(489\) −20.2679 −0.916548
\(490\) 6.00000 0.271052
\(491\) −6.33975 −0.286109 −0.143054 0.989715i \(-0.545692\pi\)
−0.143054 + 0.989715i \(0.545692\pi\)
\(492\) −12.1244 −0.546608
\(493\) −0.464102 −0.0209021
\(494\) −21.1244 −0.950430
\(495\) 2.19615 0.0987097
\(496\) −2.73205 −0.122673
\(497\) −34.9808 −1.56910
\(498\) −11.4641 −0.513719
\(499\) 20.0526 0.897676 0.448838 0.893613i \(-0.351838\pi\)
0.448838 + 0.893613i \(0.351838\pi\)
\(500\) −3.00000 −0.134164
\(501\) 19.8564 0.887119
\(502\) 1.46410 0.0653461
\(503\) 8.66025 0.386142 0.193071 0.981185i \(-0.438155\pi\)
0.193071 + 0.981185i \(0.438155\pi\)
\(504\) 3.00000 0.133631
\(505\) 50.7846 2.25989
\(506\) 0.732051 0.0325436
\(507\) 9.39230 0.417127
\(508\) 11.4641 0.508637
\(509\) −10.1244 −0.448754 −0.224377 0.974502i \(-0.572035\pi\)
−0.224377 + 0.974502i \(0.572035\pi\)
\(510\) 1.39230 0.0616523
\(511\) 2.78461 0.123184
\(512\) 1.00000 0.0441942
\(513\) −4.46410 −0.197095
\(514\) −22.7321 −1.00267
\(515\) −38.5692 −1.69956
\(516\) −11.9282 −0.525110
\(517\) −6.87564 −0.302390
\(518\) 9.58846 0.421293
\(519\) 8.26795 0.362923
\(520\) 14.1962 0.622542
\(521\) 39.5167 1.73126 0.865628 0.500687i \(-0.166919\pi\)
0.865628 + 0.500687i \(0.166919\pi\)
\(522\) −1.00000 −0.0437688
\(523\) −44.2487 −1.93486 −0.967431 0.253137i \(-0.918538\pi\)
−0.967431 + 0.253137i \(0.918538\pi\)
\(524\) −18.1962 −0.794903
\(525\) 12.0000 0.523723
\(526\) 29.0526 1.26675
\(527\) −1.26795 −0.0552327
\(528\) 0.732051 0.0318584
\(529\) 1.00000 0.0434783
\(530\) 7.60770 0.330457
\(531\) 10.4641 0.454103
\(532\) −13.3923 −0.580630
\(533\) −57.3731 −2.48510
\(534\) 1.46410 0.0633579
\(535\) 27.5885 1.19275
\(536\) −2.53590 −0.109534
\(537\) 10.3923 0.448461
\(538\) −11.6603 −0.502709
\(539\) 1.46410 0.0630633
\(540\) 3.00000 0.129099
\(541\) −6.32051 −0.271740 −0.135870 0.990727i \(-0.543383\pi\)
−0.135870 + 0.990727i \(0.543383\pi\)
\(542\) 24.7846 1.06459
\(543\) 19.1244 0.820705
\(544\) 0.464102 0.0198982
\(545\) −24.0000 −1.02805
\(546\) 14.1962 0.607539
\(547\) −33.3205 −1.42468 −0.712341 0.701834i \(-0.752365\pi\)
−0.712341 + 0.701834i \(0.752365\pi\)
\(548\) −12.9282 −0.552265
\(549\) −14.3923 −0.614249
\(550\) 2.92820 0.124859
\(551\) 4.46410 0.190177
\(552\) 1.00000 0.0425628
\(553\) 21.3731 0.908875
\(554\) 19.1244 0.812516
\(555\) 9.58846 0.407007
\(556\) −19.8564 −0.842099
\(557\) 4.07180 0.172528 0.0862638 0.996272i \(-0.472507\pi\)
0.0862638 + 0.996272i \(0.472507\pi\)
\(558\) −2.73205 −0.115657
\(559\) −56.4449 −2.38736
\(560\) 9.00000 0.380319
\(561\) 0.339746 0.0143441
\(562\) 27.4641 1.15850
\(563\) 37.3205 1.57287 0.786436 0.617672i \(-0.211924\pi\)
0.786436 + 0.617672i \(0.211924\pi\)
\(564\) −9.39230 −0.395487
\(565\) 34.1769 1.43783
\(566\) 8.58846 0.361000
\(567\) 3.00000 0.125988
\(568\) −11.6603 −0.489253
\(569\) −10.6077 −0.444698 −0.222349 0.974967i \(-0.571372\pi\)
−0.222349 + 0.974967i \(0.571372\pi\)
\(570\) −13.3923 −0.560942
\(571\) −23.9090 −1.00056 −0.500280 0.865864i \(-0.666769\pi\)
−0.500280 + 0.865864i \(0.666769\pi\)
\(572\) 3.46410 0.144841
\(573\) −1.87564 −0.0783562
\(574\) −36.3731 −1.51818
\(575\) 4.00000 0.166812
\(576\) 1.00000 0.0416667
\(577\) 24.4449 1.01765 0.508826 0.860869i \(-0.330079\pi\)
0.508826 + 0.860869i \(0.330079\pi\)
\(578\) −16.7846 −0.698148
\(579\) 9.46410 0.393315
\(580\) −3.00000 −0.124568
\(581\) −34.3923 −1.42683
\(582\) 4.00000 0.165805
\(583\) 1.85641 0.0768845
\(584\) 0.928203 0.0384093
\(585\) 14.1962 0.586939
\(586\) 6.00000 0.247858
\(587\) 28.1769 1.16299 0.581493 0.813552i \(-0.302469\pi\)
0.581493 + 0.813552i \(0.302469\pi\)
\(588\) 2.00000 0.0824786
\(589\) 12.1962 0.502534
\(590\) 31.3923 1.29240
\(591\) 17.7321 0.729399
\(592\) 3.19615 0.131361
\(593\) 33.4641 1.37421 0.687103 0.726560i \(-0.258882\pi\)
0.687103 + 0.726560i \(0.258882\pi\)
\(594\) 0.732051 0.0300364
\(595\) 4.17691 0.171237
\(596\) 5.00000 0.204808
\(597\) 17.3205 0.708881
\(598\) 4.73205 0.193508
\(599\) −42.3923 −1.73210 −0.866051 0.499955i \(-0.833350\pi\)
−0.866051 + 0.499955i \(0.833350\pi\)
\(600\) 4.00000 0.163299
\(601\) 20.7846 0.847822 0.423911 0.905704i \(-0.360657\pi\)
0.423911 + 0.905704i \(0.360657\pi\)
\(602\) −35.7846 −1.45847
\(603\) −2.53590 −0.103270
\(604\) 14.1244 0.574712
\(605\) −31.3923 −1.27628
\(606\) 16.9282 0.687661
\(607\) 7.12436 0.289169 0.144584 0.989492i \(-0.453816\pi\)
0.144584 + 0.989492i \(0.453816\pi\)
\(608\) −4.46410 −0.181043
\(609\) −3.00000 −0.121566
\(610\) −43.1769 −1.74818
\(611\) −44.4449 −1.79805
\(612\) 0.464102 0.0187602
\(613\) −12.1436 −0.490475 −0.245238 0.969463i \(-0.578866\pi\)
−0.245238 + 0.969463i \(0.578866\pi\)
\(614\) −9.07180 −0.366108
\(615\) −36.3731 −1.46670
\(616\) 2.19615 0.0884855
\(617\) −21.1436 −0.851209 −0.425605 0.904909i \(-0.639939\pi\)
−0.425605 + 0.904909i \(0.639939\pi\)
\(618\) −12.8564 −0.517161
\(619\) −31.0000 −1.24600 −0.622998 0.782224i \(-0.714085\pi\)
−0.622998 + 0.782224i \(0.714085\pi\)
\(620\) −8.19615 −0.329165
\(621\) 1.00000 0.0401286
\(622\) −6.32051 −0.253429
\(623\) 4.39230 0.175974
\(624\) 4.73205 0.189434
\(625\) −29.0000 −1.16000
\(626\) −20.1244 −0.804331
\(627\) −3.26795 −0.130509
\(628\) −0.267949 −0.0106923
\(629\) 1.48334 0.0591446
\(630\) 9.00000 0.358569
\(631\) −17.0000 −0.676759 −0.338380 0.941010i \(-0.609879\pi\)
−0.338380 + 0.941010i \(0.609879\pi\)
\(632\) 7.12436 0.283392
\(633\) 11.1962 0.445007
\(634\) 10.3397 0.410644
\(635\) 34.3923 1.36482
\(636\) 2.53590 0.100555
\(637\) 9.46410 0.374981
\(638\) −0.732051 −0.0289822
\(639\) −11.6603 −0.461273
\(640\) 3.00000 0.118585
\(641\) 8.46410 0.334312 0.167156 0.985930i \(-0.446542\pi\)
0.167156 + 0.985930i \(0.446542\pi\)
\(642\) 9.19615 0.362943
\(643\) −29.9090 −1.17949 −0.589747 0.807588i \(-0.700773\pi\)
−0.589747 + 0.807588i \(0.700773\pi\)
\(644\) 3.00000 0.118217
\(645\) −35.7846 −1.40902
\(646\) −2.07180 −0.0815138
\(647\) −16.5885 −0.652160 −0.326080 0.945342i \(-0.605728\pi\)
−0.326080 + 0.945342i \(0.605728\pi\)
\(648\) 1.00000 0.0392837
\(649\) 7.66025 0.300691
\(650\) 18.9282 0.742425
\(651\) −8.19615 −0.321233
\(652\) −20.2679 −0.793754
\(653\) 17.6077 0.689042 0.344521 0.938779i \(-0.388041\pi\)
0.344521 + 0.938779i \(0.388041\pi\)
\(654\) −8.00000 −0.312825
\(655\) −54.5885 −2.13295
\(656\) −12.1244 −0.473377
\(657\) 0.928203 0.0362127
\(658\) −28.1769 −1.09845
\(659\) 32.0000 1.24654 0.623272 0.782006i \(-0.285803\pi\)
0.623272 + 0.782006i \(0.285803\pi\)
\(660\) 2.19615 0.0854851
\(661\) −16.0000 −0.622328 −0.311164 0.950356i \(-0.600719\pi\)
−0.311164 + 0.950356i \(0.600719\pi\)
\(662\) 29.4449 1.14441
\(663\) 2.19615 0.0852915
\(664\) −11.4641 −0.444893
\(665\) −40.1769 −1.55799
\(666\) 3.19615 0.123848
\(667\) −1.00000 −0.0387202
\(668\) 19.8564 0.768267
\(669\) 8.00000 0.309298
\(670\) −7.60770 −0.293911
\(671\) −10.5359 −0.406734
\(672\) 3.00000 0.115728
\(673\) 19.0000 0.732396 0.366198 0.930537i \(-0.380659\pi\)
0.366198 + 0.930537i \(0.380659\pi\)
\(674\) −20.9282 −0.806124
\(675\) 4.00000 0.153960
\(676\) 9.39230 0.361242
\(677\) 6.78461 0.260754 0.130377 0.991465i \(-0.458381\pi\)
0.130377 + 0.991465i \(0.458381\pi\)
\(678\) 11.3923 0.437519
\(679\) 12.0000 0.460518
\(680\) 1.39230 0.0533925
\(681\) −25.5885 −0.980552
\(682\) −2.00000 −0.0765840
\(683\) −21.5359 −0.824048 −0.412024 0.911173i \(-0.635178\pi\)
−0.412024 + 0.911173i \(0.635178\pi\)
\(684\) −4.46410 −0.170689
\(685\) −38.7846 −1.48188
\(686\) −15.0000 −0.572703
\(687\) 13.1962 0.503465
\(688\) −11.9282 −0.454758
\(689\) 12.0000 0.457164
\(690\) 3.00000 0.114208
\(691\) −39.5167 −1.50328 −0.751642 0.659571i \(-0.770738\pi\)
−0.751642 + 0.659571i \(0.770738\pi\)
\(692\) 8.26795 0.314300
\(693\) 2.19615 0.0834249
\(694\) 18.8564 0.715779
\(695\) −59.5692 −2.25959
\(696\) −1.00000 −0.0379049
\(697\) −5.62693 −0.213135
\(698\) −6.39230 −0.241952
\(699\) 23.3205 0.882063
\(700\) 12.0000 0.453557
\(701\) −23.7846 −0.898332 −0.449166 0.893448i \(-0.648279\pi\)
−0.449166 + 0.893448i \(0.648279\pi\)
\(702\) 4.73205 0.178600
\(703\) −14.2679 −0.538126
\(704\) 0.732051 0.0275902
\(705\) −28.1769 −1.06120
\(706\) −11.4641 −0.431457
\(707\) 50.7846 1.90995
\(708\) 10.4641 0.393265
\(709\) 4.33975 0.162983 0.0814913 0.996674i \(-0.474032\pi\)
0.0814913 + 0.996674i \(0.474032\pi\)
\(710\) −34.9808 −1.31280
\(711\) 7.12436 0.267184
\(712\) 1.46410 0.0548695
\(713\) −2.73205 −0.102316
\(714\) 1.39230 0.0521057
\(715\) 10.3923 0.388650
\(716\) 10.3923 0.388379
\(717\) −7.85641 −0.293403
\(718\) −4.26795 −0.159278
\(719\) 38.1962 1.42448 0.712238 0.701938i \(-0.247682\pi\)
0.712238 + 0.701938i \(0.247682\pi\)
\(720\) 3.00000 0.111803
\(721\) −38.5692 −1.43639
\(722\) 0.928203 0.0345441
\(723\) 13.7321 0.510700
\(724\) 19.1244 0.710751
\(725\) −4.00000 −0.148556
\(726\) −10.4641 −0.388359
\(727\) −20.2487 −0.750983 −0.375492 0.926826i \(-0.622526\pi\)
−0.375492 + 0.926826i \(0.622526\pi\)
\(728\) 14.1962 0.526144
\(729\) 1.00000 0.0370370
\(730\) 2.78461 0.103063
\(731\) −5.53590 −0.204753
\(732\) −14.3923 −0.531955
\(733\) −2.92820 −0.108156 −0.0540778 0.998537i \(-0.517222\pi\)
−0.0540778 + 0.998537i \(0.517222\pi\)
\(734\) 14.3397 0.529290
\(735\) 6.00000 0.221313
\(736\) 1.00000 0.0368605
\(737\) −1.85641 −0.0683816
\(738\) −12.1244 −0.446304
\(739\) −15.6077 −0.574138 −0.287069 0.957910i \(-0.592681\pi\)
−0.287069 + 0.957910i \(0.592681\pi\)
\(740\) 9.58846 0.352479
\(741\) −21.1244 −0.776023
\(742\) 7.60770 0.279287
\(743\) −47.4449 −1.74058 −0.870292 0.492537i \(-0.836070\pi\)
−0.870292 + 0.492537i \(0.836070\pi\)
\(744\) −2.73205 −0.100162
\(745\) 15.0000 0.549557
\(746\) 30.9282 1.13236
\(747\) −11.4641 −0.419450
\(748\) 0.339746 0.0124223
\(749\) 27.5885 1.00806
\(750\) −3.00000 −0.109545
\(751\) −29.3205 −1.06992 −0.534960 0.844877i \(-0.679673\pi\)
−0.534960 + 0.844877i \(0.679673\pi\)
\(752\) −9.39230 −0.342502
\(753\) 1.46410 0.0533548
\(754\) −4.73205 −0.172331
\(755\) 42.3731 1.54211
\(756\) 3.00000 0.109109
\(757\) −1.19615 −0.0434749 −0.0217374 0.999764i \(-0.506920\pi\)
−0.0217374 + 0.999764i \(0.506920\pi\)
\(758\) 3.85641 0.140071
\(759\) 0.732051 0.0265718
\(760\) −13.3923 −0.485790
\(761\) 11.8038 0.427889 0.213945 0.976846i \(-0.431369\pi\)
0.213945 + 0.976846i \(0.431369\pi\)
\(762\) 11.4641 0.415301
\(763\) −24.0000 −0.868858
\(764\) −1.87564 −0.0678584
\(765\) 1.39230 0.0503389
\(766\) 9.80385 0.354227
\(767\) 49.5167 1.78794
\(768\) 1.00000 0.0360844
\(769\) 7.94744 0.286592 0.143296 0.989680i \(-0.454230\pi\)
0.143296 + 0.989680i \(0.454230\pi\)
\(770\) 6.58846 0.237432
\(771\) −22.7321 −0.818675
\(772\) 9.46410 0.340620
\(773\) 24.9808 0.898496 0.449248 0.893407i \(-0.351692\pi\)
0.449248 + 0.893407i \(0.351692\pi\)
\(774\) −11.9282 −0.428750
\(775\) −10.9282 −0.392553
\(776\) 4.00000 0.143592
\(777\) 9.58846 0.343984
\(778\) 13.8564 0.496776
\(779\) 54.1244 1.93921
\(780\) 14.1962 0.508304
\(781\) −8.53590 −0.305438
\(782\) 0.464102 0.0165962
\(783\) −1.00000 −0.0357371
\(784\) 2.00000 0.0714286
\(785\) −0.803848 −0.0286906
\(786\) −18.1962 −0.649035
\(787\) −5.80385 −0.206885 −0.103442 0.994635i \(-0.532986\pi\)
−0.103442 + 0.994635i \(0.532986\pi\)
\(788\) 17.7321 0.631678
\(789\) 29.0526 1.03430
\(790\) 21.3731 0.760420
\(791\) 34.1769 1.21519
\(792\) 0.732051 0.0260123
\(793\) −68.1051 −2.41848
\(794\) 17.6603 0.626739
\(795\) 7.60770 0.269817
\(796\) 17.3205 0.613909
\(797\) −53.2295 −1.88548 −0.942742 0.333522i \(-0.891763\pi\)
−0.942742 + 0.333522i \(0.891763\pi\)
\(798\) −13.3923 −0.474082
\(799\) −4.35898 −0.154210
\(800\) 4.00000 0.141421
\(801\) 1.46410 0.0517315
\(802\) 29.7128 1.04920
\(803\) 0.679492 0.0239787
\(804\) −2.53590 −0.0894342
\(805\) 9.00000 0.317208
\(806\) −12.9282 −0.455377
\(807\) −11.6603 −0.410460
\(808\) 16.9282 0.595532
\(809\) 6.00000 0.210949 0.105474 0.994422i \(-0.466364\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(810\) 3.00000 0.105409
\(811\) −53.5692 −1.88107 −0.940535 0.339697i \(-0.889675\pi\)
−0.940535 + 0.339697i \(0.889675\pi\)
\(812\) −3.00000 −0.105279
\(813\) 24.7846 0.869234
\(814\) 2.33975 0.0820081
\(815\) −60.8038 −2.12987
\(816\) 0.464102 0.0162468
\(817\) 53.2487 1.86294
\(818\) −5.12436 −0.179169
\(819\) 14.1962 0.496054
\(820\) −36.3731 −1.27020
\(821\) 7.46410 0.260499 0.130249 0.991481i \(-0.458422\pi\)
0.130249 + 0.991481i \(0.458422\pi\)
\(822\) −12.9282 −0.450923
\(823\) 46.3013 1.61396 0.806980 0.590578i \(-0.201100\pi\)
0.806980 + 0.590578i \(0.201100\pi\)
\(824\) −12.8564 −0.447874
\(825\) 2.92820 0.101947
\(826\) 31.3923 1.09228
\(827\) −21.0718 −0.732738 −0.366369 0.930470i \(-0.619399\pi\)
−0.366369 + 0.930470i \(0.619399\pi\)
\(828\) 1.00000 0.0347524
\(829\) −14.6077 −0.507346 −0.253673 0.967290i \(-0.581639\pi\)
−0.253673 + 0.967290i \(0.581639\pi\)
\(830\) −34.3923 −1.19377
\(831\) 19.1244 0.663417
\(832\) 4.73205 0.164054
\(833\) 0.928203 0.0321603
\(834\) −19.8564 −0.687571
\(835\) 59.5692 2.06148
\(836\) −3.26795 −0.113024
\(837\) −2.73205 −0.0944335
\(838\) 21.5885 0.745761
\(839\) 20.2679 0.699727 0.349864 0.936801i \(-0.386228\pi\)
0.349864 + 0.936801i \(0.386228\pi\)
\(840\) 9.00000 0.310530
\(841\) 1.00000 0.0344828
\(842\) 9.60770 0.331103
\(843\) 27.4641 0.945914
\(844\) 11.1962 0.385387
\(845\) 28.1769 0.969315
\(846\) −9.39230 −0.322914
\(847\) −31.3923 −1.07865
\(848\) 2.53590 0.0870831
\(849\) 8.58846 0.294755
\(850\) 1.85641 0.0636742
\(851\) 3.19615 0.109563
\(852\) −11.6603 −0.399474
\(853\) 2.21539 0.0758535 0.0379268 0.999281i \(-0.487925\pi\)
0.0379268 + 0.999281i \(0.487925\pi\)
\(854\) −43.1769 −1.47748
\(855\) −13.3923 −0.458007
\(856\) 9.19615 0.314318
\(857\) 32.4449 1.10830 0.554148 0.832418i \(-0.313044\pi\)
0.554148 + 0.832418i \(0.313044\pi\)
\(858\) 3.46410 0.118262
\(859\) 5.58846 0.190676 0.0953379 0.995445i \(-0.469607\pi\)
0.0953379 + 0.995445i \(0.469607\pi\)
\(860\) −35.7846 −1.22025
\(861\) −36.3731 −1.23959
\(862\) 19.8038 0.674522
\(863\) 44.0526 1.49957 0.749783 0.661683i \(-0.230158\pi\)
0.749783 + 0.661683i \(0.230158\pi\)
\(864\) 1.00000 0.0340207
\(865\) 24.8038 0.843356
\(866\) −33.5167 −1.13894
\(867\) −16.7846 −0.570035
\(868\) −8.19615 −0.278196
\(869\) 5.21539 0.176920
\(870\) −3.00000 −0.101710
\(871\) −12.0000 −0.406604
\(872\) −8.00000 −0.270914
\(873\) 4.00000 0.135379
\(874\) −4.46410 −0.151000
\(875\) −9.00000 −0.304256
\(876\) 0.928203 0.0313611
\(877\) −13.1244 −0.443178 −0.221589 0.975140i \(-0.571124\pi\)
−0.221589 + 0.975140i \(0.571124\pi\)
\(878\) 10.8038 0.364612
\(879\) 6.00000 0.202375
\(880\) 2.19615 0.0740323
\(881\) 14.9282 0.502944 0.251472 0.967865i \(-0.419085\pi\)
0.251472 + 0.967865i \(0.419085\pi\)
\(882\) 2.00000 0.0673435
\(883\) −35.5167 −1.19523 −0.597615 0.801783i \(-0.703885\pi\)
−0.597615 + 0.801783i \(0.703885\pi\)
\(884\) 2.19615 0.0738646
\(885\) 31.3923 1.05524
\(886\) −37.1769 −1.24898
\(887\) −8.53590 −0.286607 −0.143304 0.989679i \(-0.545773\pi\)
−0.143304 + 0.989679i \(0.545773\pi\)
\(888\) 3.19615 0.107256
\(889\) 34.3923 1.15348
\(890\) 4.39230 0.147230
\(891\) 0.732051 0.0245246
\(892\) 8.00000 0.267860
\(893\) 41.9282 1.40307
\(894\) 5.00000 0.167225
\(895\) 31.1769 1.04213
\(896\) 3.00000 0.100223
\(897\) 4.73205 0.157999
\(898\) −8.66025 −0.288996
\(899\) 2.73205 0.0911190
\(900\) 4.00000 0.133333
\(901\) 1.17691 0.0392087
\(902\) −8.87564 −0.295527
\(903\) −35.7846 −1.19084
\(904\) 11.3923 0.378902
\(905\) 57.3731 1.90715
\(906\) 14.1244 0.469250
\(907\) −24.1436 −0.801675 −0.400837 0.916149i \(-0.631281\pi\)
−0.400837 + 0.916149i \(0.631281\pi\)
\(908\) −25.5885 −0.849183
\(909\) 16.9282 0.561473
\(910\) 42.5885 1.41179
\(911\) −16.0000 −0.530104 −0.265052 0.964234i \(-0.585389\pi\)
−0.265052 + 0.964234i \(0.585389\pi\)
\(912\) −4.46410 −0.147821
\(913\) −8.39230 −0.277745
\(914\) −34.9090 −1.15469
\(915\) −43.1769 −1.42738
\(916\) 13.1962 0.436013
\(917\) −54.5885 −1.80267
\(918\) 0.464102 0.0153176
\(919\) 32.6077 1.07563 0.537814 0.843063i \(-0.319250\pi\)
0.537814 + 0.843063i \(0.319250\pi\)
\(920\) 3.00000 0.0989071
\(921\) −9.07180 −0.298926
\(922\) 30.0526 0.989728
\(923\) −55.1769 −1.81617
\(924\) 2.19615 0.0722481
\(925\) 12.7846 0.420355
\(926\) 31.1769 1.02454
\(927\) −12.8564 −0.422260
\(928\) −1.00000 −0.0328266
\(929\) 42.0000 1.37798 0.688988 0.724773i \(-0.258055\pi\)
0.688988 + 0.724773i \(0.258055\pi\)
\(930\) −8.19615 −0.268762
\(931\) −8.92820 −0.292610
\(932\) 23.3205 0.763889
\(933\) −6.32051 −0.206924
\(934\) 11.8038 0.386234
\(935\) 1.01924 0.0333326
\(936\) 4.73205 0.154672
\(937\) −55.5885 −1.81600 −0.907998 0.418975i \(-0.862390\pi\)
−0.907998 + 0.418975i \(0.862390\pi\)
\(938\) −7.60770 −0.248400
\(939\) −20.1244 −0.656734
\(940\) −28.1769 −0.919030
\(941\) −37.1769 −1.21193 −0.605966 0.795490i \(-0.707213\pi\)
−0.605966 + 0.795490i \(0.707213\pi\)
\(942\) −0.267949 −0.00873026
\(943\) −12.1244 −0.394823
\(944\) 10.4641 0.340577
\(945\) 9.00000 0.292770
\(946\) −8.73205 −0.283903
\(947\) −28.0526 −0.911586 −0.455793 0.890086i \(-0.650644\pi\)
−0.455793 + 0.890086i \(0.650644\pi\)
\(948\) 7.12436 0.231388
\(949\) 4.39230 0.142580
\(950\) −17.8564 −0.579338
\(951\) 10.3397 0.335289
\(952\) 1.39230 0.0451249
\(953\) −38.5359 −1.24830 −0.624150 0.781304i \(-0.714555\pi\)
−0.624150 + 0.781304i \(0.714555\pi\)
\(954\) 2.53590 0.0821027
\(955\) −5.62693 −0.182083
\(956\) −7.85641 −0.254094
\(957\) −0.732051 −0.0236638
\(958\) 25.8564 0.835383
\(959\) −38.7846 −1.25242
\(960\) 3.00000 0.0968246
\(961\) −23.5359 −0.759223
\(962\) 15.1244 0.487629
\(963\) 9.19615 0.296342
\(964\) 13.7321 0.442280
\(965\) 28.3923 0.913981
\(966\) 3.00000 0.0965234
\(967\) −39.1244 −1.25815 −0.629077 0.777343i \(-0.716567\pi\)
−0.629077 + 0.777343i \(0.716567\pi\)
\(968\) −10.4641 −0.336329
\(969\) −2.07180 −0.0665557
\(970\) 12.0000 0.385297
\(971\) −9.41154 −0.302031 −0.151015 0.988531i \(-0.548254\pi\)
−0.151015 + 0.988531i \(0.548254\pi\)
\(972\) 1.00000 0.0320750
\(973\) −59.5692 −1.90970
\(974\) −32.5167 −1.04190
\(975\) 18.9282 0.606188
\(976\) −14.3923 −0.460686
\(977\) 18.9808 0.607248 0.303624 0.952792i \(-0.401803\pi\)
0.303624 + 0.952792i \(0.401803\pi\)
\(978\) −20.2679 −0.648098
\(979\) 1.07180 0.0342548
\(980\) 6.00000 0.191663
\(981\) −8.00000 −0.255420
\(982\) −6.33975 −0.202309
\(983\) −26.1051 −0.832624 −0.416312 0.909222i \(-0.636678\pi\)
−0.416312 + 0.909222i \(0.636678\pi\)
\(984\) −12.1244 −0.386510
\(985\) 53.1962 1.69497
\(986\) −0.464102 −0.0147800
\(987\) −28.1769 −0.896881
\(988\) −21.1244 −0.672055
\(989\) −11.9282 −0.379295
\(990\) 2.19615 0.0697983
\(991\) −13.4449 −0.427090 −0.213545 0.976933i \(-0.568501\pi\)
−0.213545 + 0.976933i \(0.568501\pi\)
\(992\) −2.73205 −0.0867427
\(993\) 29.4449 0.934405
\(994\) −34.9808 −1.10952
\(995\) 51.9615 1.64729
\(996\) −11.4641 −0.363254
\(997\) −53.4974 −1.69428 −0.847140 0.531369i \(-0.821678\pi\)
−0.847140 + 0.531369i \(0.821678\pi\)
\(998\) 20.0526 0.634753
\(999\) 3.19615 0.101122
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 \(a_p\))